LMFDB - Embedded newform 25.4.e.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.e (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	25.4
Dual form			25.4.e.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.331937 + 0.107853i) q^{2} +(3.76234 - 5.17842i) q^{3} +(-6.37359 - 4.63068i) q^{4} +(10.0178 + 4.96433i) q^{5} +(1.80737 - 1.31313i) q^{6} +14.4107i q^{7} +(-3.25738 - 4.48340i) q^{8} +(-4.31736 - 13.2875i) q^{9} +O(q^{10})$	\(q+(0.331937 + 0.107853i) q^{2} +(3.76234 - 5.17842i) q^{3} +(-6.37359 - 4.63068i) q^{4} +(10.0178 + 4.96433i) q^{5} +(1.80737 - 1.31313i) q^{6} +14.4107i q^{7} +(-3.25738 - 4.48340i) q^{8} +(-4.31736 - 13.2875i) q^{9} +(2.78985 + 2.72829i) q^{10} +(-4.11778 + 12.6732i) q^{11} +(-47.9592 + 15.5829i) q^{12} +(-51.6163 + 16.7712i) q^{13} +(-1.55424 + 4.78345i) q^{14} +(63.3976 - 33.1987i) q^{15} +(18.8782 + 58.1013i) q^{16} +(-4.55371 - 6.26764i) q^{17} -4.87624i q^{18} +(123.269 - 89.5605i) q^{19} +(-40.8608 - 78.0296i) q^{20} +(74.6248 + 54.2181i) q^{21} +(-2.73369 + 3.76260i) q^{22} +(-137.982 - 44.8332i) q^{23} -35.4723 q^{24} +(75.7109 + 99.4629i) q^{25} -18.9422 q^{26} +(79.3136 + 25.7706i) q^{27} +(66.7315 - 91.8480i) q^{28} +(-133.102 - 96.7042i) q^{29} +(24.6246 - 4.18224i) q^{30} +(25.0210 - 18.1788i) q^{31} +65.6563i q^{32} +(50.1348 + 69.0046i) q^{33} +(-0.835560 - 2.57159i) q^{34} +(-71.5396 + 144.363i) q^{35} +(-34.0130 + 104.681i) q^{36} +(-297.170 + 96.5563i) q^{37} +(50.5770 - 16.4335i) q^{38} +(-107.350 + 330.390i) q^{39} +(-10.3746 - 61.0843i) q^{40} +(-142.202 - 437.652i) q^{41} +(18.9232 + 26.0455i) q^{42} +43.4059i q^{43} +(84.9307 - 61.7058i) q^{44} +(22.7131 - 154.543i) q^{45} +(-40.9661 - 29.7636i) q^{46} +(200.696 - 276.234i) q^{47} +(371.899 + 120.837i) q^{48} +135.331 q^{49} +(14.4039 + 41.1810i) q^{50} -49.5891 q^{51} +(406.643 + 132.126i) q^{52} +(-140.527 + 193.419i) q^{53} +(23.5477 + 17.1084i) q^{54} +(-104.165 + 106.515i) q^{55} +(64.6091 - 46.9412i) q^{56} -975.298i q^{57} +(-33.7516 - 46.4551i) q^{58} +(182.656 + 562.158i) q^{59} +(-557.803 - 81.9798i) q^{60} +(-32.7748 + 100.870i) q^{61} +(10.2660 - 3.33563i) q^{62} +(191.482 - 62.2163i) q^{63} +(143.945 - 443.016i) q^{64} +(-600.337 - 88.2310i) q^{65} +(9.19925 + 28.3124i) q^{66} +(304.832 + 419.565i) q^{67} +61.0341i q^{68} +(-751.303 + 545.853i) q^{69} +(-39.3166 + 40.2037i) q^{70} +(352.384 + 256.022i) q^{71} +(-45.5098 + 62.6389i) q^{72} +(172.721 + 56.1205i) q^{73} -109.055 q^{74} +(799.911 - 17.8493i) q^{75} -1200.39 q^{76} +(-182.630 - 59.3402i) q^{77} +(-71.2670 + 98.0905i) q^{78} +(377.609 + 274.349i) q^{79} +(-99.3162 + 675.762i) q^{80} +(737.037 - 535.489i) q^{81} -160.610i q^{82} +(-226.113 - 311.218i) q^{83} +(-224.561 - 691.128i) q^{84} +(-14.5033 - 85.3938i) q^{85} +(-4.68145 + 14.4080i) q^{86} +(-1001.55 + 325.423i) q^{87} +(70.2324 - 22.8199i) q^{88} +(156.078 - 480.360i) q^{89} +(24.2073 - 48.8490i) q^{90} +(-241.685 - 743.829i) q^{91} +(671.835 + 924.701i) q^{92} -197.964i q^{93} +(96.4111 - 70.0467i) q^{94} +(1679.49 - 285.245i) q^{95} +(339.996 + 247.022i) q^{96} +(-519.989 + 715.703i) q^{97} +(44.9213 + 14.5958i) q^{98} +186.173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) $ 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.331937	+	0.107853i	0.117357	+	0.0381317i	0.367107	−	0.930179i	$-0.380348\pi$
$2$	0.331937	+	0.107853i	0.117357	+	0.0381317i	−0.249750	+	0.968310i	$0.580348\pi$
$3$	3.76234	−	5.17842i	0.724063	−	0.996588i	−0.275316	−	0.961354i	$-0.588782\pi$
$3$	3.76234	−	5.17842i	0.724063	−	0.996588i	0.999379	−	0.0352338i	$-0.0112176\pi$
$4$	−6.37359	−	4.63068i	−0.796698	−	0.578835i
$5$	10.0178	+	4.96433i	0.896015	+	0.444023i
$5$	10.0178	+	4.96433i	0.896015	+	0.444023i
$6$	1.80737	−	1.31313i	0.122976	−	0.0893471i
$7$			14.4107i			0.778106i	0.921215	+	0.389053i	$0.127198\pi$
$7$			14.4107i			0.778106i	−0.921215	+	0.389053i	$0.872802\pi$
$8$	−3.25738	−	4.48340i	−0.143957	−	0.198140i
$9$	−4.31736	−	13.2875i	−0.159902	−	0.492129i
$10$	2.78985	+	2.72829i	0.0882227	+	0.0862760i
$11$	−4.11778	+	12.6732i	−0.112869	+	0.347375i	−0.991497	−	0.130133i	$-0.958460\pi$
$11$	−4.11778	+	12.6732i	−0.112869	+	0.347375i	0.878628	+	0.477507i	$0.158460\pi$
$12$	−47.9592	+	15.5829i	−1.15372	+	0.374866i
$13$	−51.6163	+	16.7712i	−1.10121	+	0.357806i	−0.802570	−	0.596558i	$-0.796535\pi$
$13$	−51.6163	+	16.7712i	−1.10121	+	0.357806i	−0.298645	+	0.954364i	$0.596535\pi$
$14$	−1.55424	+	4.78345i	−0.0296705	+	0.0913165i
$15$	63.3976	−	33.1987i	1.09128	−	0.571457i
$16$	18.8782	+	58.1013i	0.294973	+	0.907832i
$17$	−4.55371	−	6.26764i	−0.0649668	−	0.0894192i	0.775297	−	0.631597i	$-0.217600\pi$
$17$	−4.55371	−	6.26764i	−0.0649668	−	0.0894192i	−0.840264	+	0.542177i	$0.817600\pi$
$18$		−	4.87624i		−	0.0638523i
$19$	123.269	−	89.5605i	1.48842	−	1.08140i	0.513697	−	0.857972i	$-0.328275\pi$
$19$	123.269	−	89.5605i	1.48842	−	1.08140i	0.974721	−	0.223427i	$-0.0717245\pi$
$20$	−40.8608	−	78.0296i	−0.456838	−	0.872398i
$21$	74.6248	+	54.2181i	0.775451	+	0.563398i
$22$	−2.73369	+	3.76260i	−0.0264920	+	0.0364631i
$23$	−137.982	−	44.8332i	−1.25093	−	0.406451i	−0.392674	−	0.919678i	$-0.628450\pi$
$23$	−137.982	−	44.8332i	−1.25093	−	0.406451i	−0.858253	+	0.513226i	$0.828450\pi$
$24$	−35.4723			−0.301698
$25$	75.7109	+	99.4629i	0.605687	+	0.795703i
$26$	−18.9422			−0.142879
$27$	79.3136	+	25.7706i	0.565330	+	0.183687i
$28$	66.7315	−	91.8480i	0.450395	−	0.619916i
$29$	−133.102	−	96.7042i	−0.852290	−	0.619225i	0.0734864	−	0.997296i	$-0.476587\pi$
$29$	−133.102	−	96.7042i	−0.852290	−	0.619225i	−0.925777	+	0.378071i	$0.876587\pi$
$30$	24.6246	−	4.18224i	0.149860	−	0.0254523i
$31$	25.0210	−	18.1788i	0.144965	−	0.105323i	−0.512939	−	0.858425i	$-0.671443\pi$
$31$	25.0210	−	18.1788i	0.144965	−	0.105323i	0.657904	+	0.753102i	$0.271443\pi$
$32$			65.6563i			0.362703i
$33$	50.1348	+	69.0046i	0.264465	+	0.364005i
$34$	−0.835560	−	2.57159i	−0.00421463	−	0.0129713i
$35$	−71.5396	+	144.363i	−0.345497	+	0.697195i
$36$	−34.0130	+	104.681i	−0.157468	+	0.484635i
$37$	−297.170	+	96.5563i	−1.32039	+	0.429020i	−0.882628	−	0.470071i	$-0.844228\pi$
$37$	−297.170	+	96.5563i	−1.32039	+	0.429020i	−0.437761	+	0.899092i	$0.644228\pi$
$38$	50.5770	−	16.4335i	0.215912	−	0.0701542i
$39$	−107.350	+	330.390i	−0.440764	+	1.35653i
$40$	−10.3746	−	61.0843i	−0.0410091	−	0.241457i
$41$	−142.202	−	437.652i	−0.541663	−	1.66707i	−0.728795	−	0.684732i	$-0.759919\pi$
$41$	−142.202	−	437.652i	−0.541663	−	1.66707i	0.187133	−	0.982335i	$-0.440081\pi$
$42$	18.9232	+	26.0455i	0.0695216	+	0.0956882i
$43$			43.4059i			0.153938i	0.997033	+	0.0769690i	$0.0245243\pi$
$43$			43.4059i			0.153938i	−0.997033	+	0.0769690i	$0.975476\pi$
$44$	84.9307	−	61.7058i	0.290995	−	0.211420i
$45$	22.7131	−	154.543i	0.0752416	−	0.511955i
$46$	−40.9661	−	29.7636i	−0.131307	−	0.0954001i
$47$	200.696	−	276.234i	0.622862	−	0.857296i	−0.374695	−	0.927148i	$-0.622253\pi$
$47$	200.696	−	276.234i	0.622862	−	0.857296i	0.997557	+	0.0698517i	$0.0222526\pi$
$48$	371.899	+	120.837i	1.11831	+	0.363362i
$49$	135.331			0.394551
$50$	14.4039	+	41.1810i	0.0407403	+	0.116478i
$51$	−49.5891			−0.136154
$52$	406.643	+	132.126i	1.08445	+	0.352358i
$53$	−140.527	+	193.419i	−0.364205	+	0.501285i	−0.951314	−	0.308223i	$-0.900266\pi$
$53$	−140.527	+	193.419i	−0.364205	+	0.501285i	0.587110	+	0.809507i	$0.300266\pi$
$54$	23.5477	+	17.1084i	0.0593414	+	0.0431140i
$55$	−104.165	+	106.515i	−0.255375	+	0.261137i
$56$	64.6091	−	46.9412i	0.154174	−	0.112014i
$57$		−	975.298i		−	2.26634i
$58$	−33.7516	−	46.4551i	−0.0764104	−	0.105170i
$59$	182.656	+	562.158i	0.403048	+	1.24045i	0.922514	+	0.385963i	$0.126131\pi$
$59$	182.656	+	562.158i	0.403048	+	1.24045i	−0.519467	+	0.854491i	$0.673869\pi$
$60$	−557.803	−	81.9798i	−1.20020	−	0.176392i
$61$	−32.7748	+	100.870i	−0.0687932	+	0.211724i	−0.979543	−	0.201235i	$-0.935505\pi$
$61$	−32.7748	+	100.870i	−0.0687932	+	0.211724i	0.910750	+	0.412959i	$0.135505\pi$
$62$	10.2660	−	3.33563i	0.0210288	−	0.00683267i
$63$	191.482	−	62.2163i	0.382928	−	0.124421i
$64$	143.945	−	443.016i	0.281142	−	0.865266i
$65$	−600.337	−	88.2310i	−1.14558	−	0.168365i
$66$	9.19925	+	28.3124i	0.0171568	+	0.0528032i
$67$	304.832	+	419.565i	0.555838	+	0.765045i	0.990790	−	0.135409i	$-0.0432348\pi$
$67$	304.832	+	419.565i	0.555838	+	0.765045i	−0.434952	+	0.900454i	$0.643235\pi$
$68$			61.0341i			0.108845i
$69$	−751.303	+	545.853i	−1.31081	+	0.952363i
$70$	−39.3166	+	40.2037i	−0.0671319	+	0.0686466i
$71$	352.384	+	256.022i	0.589019	+	0.427947i	0.841964	−	0.539533i	$-0.181399\pi$
$71$	352.384	+	256.022i	0.589019	+	0.427947i	−0.252946	+	0.967481i	$0.581399\pi$
$72$	−45.5098	+	62.6389i	−0.0744914	+	0.102529i
$73$	172.721	+	56.1205i	0.276925	+	0.0899783i	0.444187	−	0.895934i	$-0.353493\pi$
$73$	172.721	+	56.1205i	0.276925	+	0.0899783i	−0.167262	+	0.985912i	$0.553493\pi$
$74$	−109.055			−0.171317
$75$	799.911	−	17.8493i	1.23154	−	0.0274808i
$76$	−1200.39			−1.81177
$77$	−182.630	−	59.3402i	−0.270294	−	0.0878240i
$78$	−71.2670	+	98.0905i	−0.103454	+	0.142392i
$79$	377.609	+	274.349i	0.537777	+	0.390718i	0.823259	−	0.567667i	$-0.192154\pi$
$79$	377.609	+	274.349i	0.537777	+	0.390718i	−0.285482	+	0.958384i	$0.592154\pi$
$80$	−99.3162	+	675.762i	−0.138799	+	0.944406i
$81$	737.037	−	535.489i	1.01102	−	0.734552i
$82$		−	160.610i		−	0.216297i
$83$	−226.113	−	311.218i	−0.299026	−	0.411574i	0.632894	−	0.774239i	$-0.281867\pi$
$83$	−226.113	−	311.218i	−0.299026	−	0.411574i	−0.931920	+	0.362665i	$0.881867\pi$
$84$	−224.561	−	691.128i	−0.291686	−	0.897717i
$85$	−14.5033	−	85.3938i	−0.0185071	−	0.108968i
$86$	−4.68145	+	14.4080i	−0.00586992	+	0.0180658i
$87$	−1001.55	+	325.423i	−1.23422	+	0.401024i
$88$	70.2324	−	22.8199i	0.0850772	−	0.0276433i
$89$	156.078	−	480.360i	0.185891	−	0.572113i	−0.814072	−	0.580764i	$-0.802754\pi$
$89$	156.078	−	480.360i	0.185891	−	0.572113i	0.999963	+	0.00865124i	$0.00275381\pi$
$90$	24.2073	−	48.8490i	0.0283519	−	0.0572126i
$91$	−241.685	−	743.829i	−0.278411	−	0.856862i
$92$	671.835	+	924.701i	0.761344	+	1.04790i
$93$		−	197.964i		−	0.220730i
$94$	96.4111	−	70.0467i	0.105788	−	0.0768592i
$95$	1679.49	−	285.245i	1.81381	−	0.308058i
$96$	339.996	+	247.022i	0.361466	+	0.262620i
$97$	−519.989	+	715.703i	−0.544298	+	0.749162i	−0.989225	−	0.146405i	$-0.953230\pi$
$97$	−519.989	+	715.703i	−0.544298	+	0.749162i	0.444927	+	0.895567i	$0.353230\pi$
$98$	44.9213	+	14.5958i	0.0463034	+	0.0150449i
$99$	186.173			0.189001
$100$	−21.9688	−	984.528i	−0.0219688	−	0.984528i
$101$	844.424			0.831914			0.415957	−	0.909384i	$-0.363447\pi$
$101$	844.424			0.831914			0.415957	+	0.909384i	$0.363447\pi$
$102$	−16.4604	−	5.34832i	−0.0159787	−	0.00519179i
$103$	7.59349	−	10.4515i	0.00726416	−	0.00999826i	−0.805369	−	0.592773i	$-0.798033\pi$
$103$	7.59349	−	10.4515i	0.00726416	−	0.00999826i	0.812634	+	0.582775i	$0.198033\pi$
$104$	243.326	+	176.787i	0.229424	+	0.166686i
$105$	478.417	+	913.606i	0.444654	+	0.849132i
$106$	−67.5068	+	49.0465i	−0.0618570	+	0.0449417i
$107$		−	1425.87i		−	1.28827i	−0.764914	−	0.644133i	$-0.777219\pi$
$107$		−	1425.87i		−	1.28827i	0.764914	−	0.644133i	$-0.222781\pi$
$108$	−386.177	−	531.527i	−0.344073	−	0.473576i
$109$	−348.518	−	1072.63i	−0.306256	−	0.942560i	−0.979205	−	0.202871i	$-0.934973\pi$
$109$	−348.518	−	1072.63i	−0.306256	−	0.942560i	0.672949	−	0.739689i	$-0.265027\pi$
$110$	−46.0642	+	24.1219i	−0.0399277	+	0.0209084i
$111$	−618.045	+	1902.15i	−0.528489	+	1.62652i
$112$	−837.282	+	272.049i	−0.706390	+	0.229520i
$113$	−888.926	+	288.830i	−0.740028	+	0.240450i	−0.654685	−	0.755902i	$-0.727199\pi$
$113$	−888.926	+	288.830i	−0.740028	+	0.240450i	−0.0853432	+	0.996352i	$0.527199\pi$
$114$	105.189	−	323.737i	0.0864195	−	0.265972i
$115$	−1159.71	−	1134.12i	−0.940377	−	0.919627i
$116$	400.530	+	1232.71i	0.320589	+	0.986671i
$117$	445.693	+	613.443i	0.352173	+	0.484725i
$118$			206.301i			0.160945i
$119$	90.3212	−	65.6222i	0.0695776	−	0.0505511i
$120$	−355.353	−	176.096i	−0.270326	−	0.133961i
$121$	933.147	+	677.971i	0.701087	+	0.509370i
$122$	−21.7583	+	29.9478i	−0.0161468	+	0.0222241i
$123$	−2801.36	−	910.216i	−2.05358	−	0.667247i
$124$	−243.654			−0.176458
$125$	264.687	+	1372.25i	0.189394	+	0.981901i
$126$	70.2702			0.0496839
$127$	726.264	+	235.977i	0.507445	+	0.164879i	0.551540	−	0.834149i	$-0.314040\pi$
$127$	726.264	+	235.977i	0.507445	+	0.164879i	−0.0440952	+	0.999027i	$0.514040\pi$
$128$	404.296	−	556.465i	0.279180	−	0.384258i
$129$	224.774	+	163.308i	0.153413	+	0.111461i
$130$	−189.758	−	94.0352i	−0.128022	−	0.0634418i
$131$	−342.410	+	248.775i	−0.228370	+	0.165921i	−0.696086	−	0.717958i	$-0.745077\pi$
$131$	−342.410	+	248.775i	−0.228370	+	0.165921i	0.467716	+	0.883879i	$0.345077\pi$
$132$		−	671.965i		−	0.443084i
$133$	1290.63	+	1776.40i	0.841443	+	1.15815i
$134$	55.9336	+	172.146i	0.0360592	+	0.110979i
$135$	666.611	+	651.902i	0.424983	+	0.415606i
$136$	−13.2672	+	40.8322i	−0.00836508	+	0.0257451i
$137$	−767.243	+	249.292i	−0.478467	+	0.155463i	−0.538314	−	0.842744i	$-0.680939\pi$
$137$	−767.243	+	249.292i	−0.478467	+	0.155463i	0.0598471	+	0.998208i	$0.480939\pi$
$138$	−308.257	+	100.159i	−0.190149	+	0.0617832i
$139$	114.572	−	352.615i	0.0699125	−	0.215168i	−0.909996	−	0.414618i	$-0.863915\pi$
$139$	114.572	−	352.615i	0.0699125	−	0.215168i	0.979908	+	0.199449i	$0.0639153\pi$
$140$	1124.46	−	588.834i	0.678818	−	0.355468i
$141$	−675.371	−	2078.58i	−0.403379	−	1.24147i
$142$	89.3566	+	122.989i	0.0528073	+	0.0726830i
$143$		−	723.205i		−	0.422919i
$144$	690.515	−	501.689i	0.399604	−	0.290329i
$145$	−853.311	−	1629.52i	−0.488715	−	0.933272i
$146$	51.2798	+	37.2570i	0.0290681	+	0.0211192i
$147$	509.161	−	700.800i	0.285680	−	0.393204i
$148$	2341.16	+	760.688i	1.30028	+	0.422488i
$149$	−846.167			−0.465240			−0.232620	−	0.972568i	$-0.574730\pi$
$149$	−846.167			−0.465240			−0.232620	+	0.972568i	$0.574730\pi$
$150$	267.445	+	80.3478i	0.145579	+	0.0437358i
$151$	−1999.47			−1.07758			−0.538790	−	0.842440i	$-0.681118\pi$
$151$	−1999.47			−1.07758			−0.538790	+	0.842440i	$0.681118\pi$
$152$	−803.071	−	260.934i	−0.428537	−	0.139240i
$153$	−63.6211	+	87.5669i	−0.0336174	+	0.0462704i
$154$	−54.2218	−	39.3944i	−0.0283722	−	0.0206136i
$155$	340.900	−	57.8985i	0.176656	−	0.0300033i
$156$	2214.14	−	1608.66i	1.13636	−	0.825617i
$157$			1251.06i			0.635958i	0.948098	+	0.317979i	$0.103004\pi$
$157$			1251.06i			0.635958i	−0.948098	+	0.317979i	$0.896996\pi$
$158$	95.7531	+	131.793i	0.0482133	+	0.0663599i
$159$	472.893	+	1455.41i	0.235867	+	0.725924i
$160$	−325.940	+	657.729i	−0.161049	+	0.324988i
$161$	646.079	−	1988.43i	0.316262	−	0.973355i
$162$	302.404	−	98.2569i	0.146661	−	0.0476530i
$163$	2446.08	−	794.780i	1.17541	−	0.381914i	0.344750	−	0.938694i	$-0.387964\pi$
$163$	2446.08	−	794.780i	1.17541	−	0.381914i	0.830660	+	0.556780i	$0.187964\pi$
$164$	−1120.29	+	3447.90i	−0.533415	+	1.64168i
$165$	159.677	+	940.157i	0.0753382	+	0.443583i
$166$	−41.4896	−	127.692i	−0.0193989	−	0.0597036i
$167$	−736.487	−	1013.69i	−0.341264	−	0.469710i	0.603546	−	0.797328i	$-0.293754\pi$
$167$	−736.487	−	1013.69i	−0.341264	−	0.469710i	−0.944810	+	0.327619i	$0.893754\pi$
$168$		−	511.182i		−	0.234753i
$169$	605.561	−	439.966i	0.275631	−	0.200258i
$170$	4.39578	−	29.9096i	0.00198318	−	0.0134939i
$171$	−1722.23	−	1251.27i	−0.770189	−	0.559575i
$172$	200.999	−	276.651i	0.0891048	−	0.122642i
$173$	504.022	+	163.767i	0.221503	+	0.0719708i	0.417666	−	0.908601i	$-0.362848\pi$
$173$	504.022	+	163.767i	0.221503	+	0.0719708i	−0.196163	+	0.980571i	$0.562848\pi$
$174$	−367.549			−0.160137
$175$	−1433.33	+	1091.05i	−0.619141	+	0.471289i
$176$	−814.067			−0.348651
$177$	3598.31	+	1169.16i	1.52805	+	0.496494i
$178$	103.616	−	142.616i	0.0436313	−	0.0600534i
$179$	−2318.33	−	1684.37i	−0.968047	−	0.703327i	−0.0130415	−	0.999915i	$-0.504151\pi$
$179$	−2318.33	−	1684.37i	−0.968047	−	0.703327i	−0.955006	+	0.296587i	$0.904151\pi$
$180$	−860.406	+	879.819i	−0.356283	+	0.364321i
$181$	−1753.58	+	1274.05i	−0.720127	+	0.523203i	−0.886425	−	0.462873i	$-0.846819\pi$
$181$	−1753.58	+	1274.05i	−0.720127	+	0.523203i	0.166298	+	0.986076i	$0.446819\pi$
$182$		−	272.970i		−	0.111175i
$183$	399.040	+	549.231i	0.161191	+	0.221860i
$184$	248.456	+	764.670i	0.0995459	+	0.306371i
$185$	−3456.31	−	507.971i	−1.37358	−	0.201874i
$186$	21.3510	−	65.7116i	0.00841683	−	0.0259043i
$187$	98.1824	−	31.9014i	0.0383947	−	0.0124752i
$188$	−2558.31	+	831.244i	−0.992467	+	0.322472i
$189$	−371.373	+	1142.97i	−0.142928	+	0.439887i
$190$	588.249	+	86.4545i	0.224611	+	0.0330109i
$191$	539.915	+	1661.69i	0.204539	+	0.629505i	0.999732	+	0.0231494i	$0.00736936\pi$
$191$	539.915	+	1661.69i	0.204539	+	0.629505i	−0.795193	+	0.606356i	$0.792631\pi$
$192$	−1752.56	−	2412.19i	−0.658749	−	0.906691i
$193$			3575.55i			1.33354i	0.745262	+	0.666772i	$0.232324\pi$
$193$			3575.55i			1.33354i	−0.745262	+	0.666772i	$0.767676\pi$
$194$	−249.794	+	181.486i	−0.0924442	+	0.0671646i
$195$	−2715.57	+	2776.84i	−0.997262	+	1.01976i
$196$	−862.543	−	626.674i	−0.314338	−	0.228380i
$197$	2452.92	−	3376.15i	0.887122	−	1.22102i	−0.0872745	−	0.996184i	$-0.527816\pi$
$197$	2452.92	−	3376.15i	0.887122	−	1.22102i	0.974397	−	0.224835i	$-0.0721843\pi$
$198$	61.7977	+	20.0793i	0.0221807	+	0.00720694i
$199$	3701.39			1.31852			0.659259	−	0.751916i	$-0.270870\pi$
$199$	3701.39			1.31852			0.659259	+	0.751916i	$0.270870\pi$
$200$	199.313	−	663.431i	0.0704677	−	0.234558i
$201$	3319.56			1.16490
$202$	280.295	+	91.0735i	0.0976313	+	0.0317223i
$203$	1393.58	−	1918.10i	0.481823	−	0.663172i
$204$	316.060	+	229.631i	0.108474	+	0.0788108i
$205$	748.106	−	5090.22i	0.254878	−	1.73423i
$206$	3.64779	−	2.65027i	0.00123375	−	0.000896375i
$207$			2027.00i			0.680610i
$208$	−1948.85	−	2682.36i	−0.649656	−	0.894175i
$209$	627.424	+	1931.01i	0.207655	+	0.639095i
$210$	60.2692	+	354.858i	0.0198046	+	0.116607i
$211$	−354.061	+	1089.69i	−0.115519	+	0.355531i	−0.992055	−	0.125805i	$-0.959849\pi$
$211$	−354.061	+	1089.69i	−0.115519	+	0.355531i	0.876536	+	0.481337i	$0.159849\pi$
$212$	1791.32	−	582.035i	0.580322	−	0.188558i
$213$	2651.58	−	861.551i	0.852974	−	0.277148i
$214$	153.784	−	473.300i	0.0491238	−	0.151187i
$215$	−215.481	+	434.830i	−0.0683521	+	0.137931i
$216$	−142.815	−	439.539i	−0.0449876	−	0.138458i
$217$	261.970	+	360.571i	0.0819524	+	0.112798i
$218$		−	393.633i		−	0.122294i
$219$	940.453	−	683.279i	0.290182	−	0.210830i
$220$	1157.14	−	196.529i	0.354612	−	0.0602273i
$221$	340.161	+	247.141i	0.103537	+	0.0752241i
$222$	−410.304	+	564.735i	−0.124044	+	0.170732i
$223$	1738.99	+	565.033i	0.522204	+	0.169674i	0.558246	−	0.829676i	$-0.311475\pi$
$223$	1738.99	+	565.033i	0.522204	+	0.169674i	−0.0360411	+	0.999350i	$0.511475\pi$
$224$	−946.156			−0.282222
$225$	994.739	−	1435.42i	0.294738	−	0.425311i
$226$	−326.219			−0.0960165
$227$	−5903.36	−	1918.12i	−1.72608	−	0.560837i	−0.733204	−	0.680009i	$-0.761976\pi$
$227$	−5903.36	−	1918.12i	−1.72608	−	0.560837i	−0.992874	+	0.119172i	$0.961976\pi$
$228$	−4516.29	+	6216.15i	−1.31184	+	1.80559i
$229$	−1223.21	−	888.716i	−0.352979	−	0.256454i	0.397139	−	0.917759i	$-0.370003\pi$
$229$	−1223.21	−	888.716i	−0.352979	−	0.256454i	−0.750118	+	0.661304i	$0.770003\pi$
$230$	−262.632	−	501.534i	−0.0752932	−	0.143783i
$231$	−994.407	+	722.479i	−0.283235	+	0.205782i
$232$			911.752i			0.258015i
$233$	−463.529	−	637.993i	−0.130330	−	0.179383i	0.738865	−	0.673854i	$-0.235362\pi$
$233$	−463.529	−	637.993i	−0.130330	−	0.179383i	−0.869195	+	0.494470i	$0.835362\pi$
$234$	81.7802	+	251.694i	0.0228468	+	0.0703151i
$235$	3381.84	−	1770.93i	0.938754	−	0.491585i
$236$	1439.00	−	4428.79i	0.396911	−	1.22157i
$237$	2841.39	−	923.224i	0.778769	−	0.253037i
$238$	37.0585	−	12.0410i	0.0100930	−	0.00327943i
$239$	1368.90	−	4213.05i	0.370490	−	1.14025i	−0.575982	−	0.817463i	$-0.695380\pi$
$239$	1368.90	−	4213.05i	0.370490	−	1.14025i	0.946471	−	0.322788i	$-0.104620\pi$
$240$	3125.72	+	3056.75i	0.840685	+	0.822135i
$241$	818.517	+	2519.14i	0.218777	+	0.673327i	0.998864	+	0.0476557i	$0.0151750\pi$
$241$	818.517	+	2519.14i	0.218777	+	0.673327i	−0.780086	+	0.625672i	$0.784825\pi$
$242$	236.625	+	325.686i	0.0628546	+	0.0865120i
$243$		−	3579.71i		−	0.945014i
$244$	675.992	−	491.137i	0.177361	−	0.128860i
$245$	1355.71	+	671.827i	0.353523	+	0.175190i
$246$	−831.704	−	604.268i	−0.215559	−	0.156613i
$247$	−4860.68	+	6690.15i	−1.25214	+	1.72342i
$248$	−163.006	−	52.9638i	−0.0417374	−	0.0135613i
$249$	−2462.34			−0.626683
$250$	−60.1417	+	484.047i	−0.0152148	+	0.122455i
$251$	846.211			0.212798			0.106399	−	0.994324i	$-0.466068\pi$
$251$	846.211			0.212798			0.106399	+	0.994324i	$0.466068\pi$
$252$	−1508.53	−	490.152i	−0.377098	−	0.122526i
$253$	1136.36	−	1564.07i	0.282382	−	0.388665i
$254$	215.623	+	156.659i	0.0532653	+	0.0386995i
$255$	−496.771	−	246.177i	−0.121996	−	0.0604556i
$256$	−2820.60	+	2049.29i	−0.688623	+	0.500314i
$257$			7920.18i			1.92236i	0.275919	+	0.961181i	$0.411018\pi$
$257$			7920.18i			1.92236i	−0.275919	+	0.961181i	$0.588982\pi$
$258$	56.9976	+	78.4504i	0.0137539	+	0.0189307i
$259$	−1391.45	−	4282.43i	−0.333823	−	1.02740i
$260$	3417.73	+	3342.32i	0.815226	+	0.797238i
$261$	−710.306	+	2186.10i	−0.168455	+	0.518452i
$262$	−140.489	+	45.6478i	−0.0331277	+	0.0107639i
$263$	−1913.99	+	621.892i	−0.448751	+	0.145808i	−0.524670	−	0.851306i	$-0.675811\pi$
$263$	−1913.99	+	621.892i	−0.448751	+	0.145808i	0.0759185	+	0.997114i	$0.475811\pi$
$264$	146.067	−	449.549i	0.0340524	−	0.104802i
$265$	−2367.96	+	1240.00i	−0.548915	+	0.287443i
$266$	236.818	+	728.851i	0.0545874	+	0.168003i
$267$	−1900.29	−	2615.52i	−0.435564	−	0.599503i
$268$		−	4085.71i		−	0.931248i
$269$	−5274.38	+	3832.06i	−1.19548	+	0.868568i	−0.993833	−	0.110890i	$-0.964630\pi$
$269$	−5274.38	+	3832.06i	−1.19548	+	0.868568i	−0.201649	+	0.979458i	$0.564630\pi$
$270$	150.963	+	288.286i	0.0340272	+	0.0649798i
$271$	1123.76	+	816.462i	0.251896	+	0.183013i	0.706567	−	0.707647i	$-0.250243\pi$
$271$	1123.76	+	816.462i	0.251896	+	0.183013i	−0.454671	+	0.890660i	$0.650243\pi$
$272$	278.192	−	382.898i	0.0620142	−	0.0853552i
$273$	−4761.16	−	1546.99i	−1.05553	−	0.342961i
$274$	−281.563			−0.0620798
$275$	−1572.28	+	549.935i	−0.344770	+	0.120590i
$276$	7316.17			1.59559
$277$	−342.976	−	111.440i	−0.0743950	−	0.0241724i	0.271583	−	0.962415i	$-0.412453\pi$
$277$	−342.976	−	111.440i	−0.0743950	−	0.0241724i	−0.345978	+	0.938243i	$0.612453\pi$
$278$	76.0611	−	104.689i	0.0164095	−	0.0225857i
$279$	−349.575	−	253.981i	−0.0750126	−	0.0544998i
$280$	880.270	−	149.505i	0.187879	−	0.0319094i
$281$	−2251.77	+	1636.00i	−0.478039	+	0.347316i	−0.800566	−	0.599244i	$-0.795468\pi$
$281$	−2251.77	+	1636.00i	−0.478039	+	0.347316i	0.322527	+	0.946560i	$0.395468\pi$
$282$		−	762.797i		−	0.161078i
$283$	−654.684	−	901.095i	−0.137516	−	0.189274i	0.734705	−	0.678387i	$-0.237321\pi$
$283$	−654.684	−	901.095i	−0.137516	−	0.189274i	−0.872221	+	0.489113i	$0.837321\pi$
$284$	−1060.39	−	3263.56i	−0.221559	−	0.681889i
$285$	4841.70	−	9770.30i	1.00631	−	2.03068i
$286$	77.9997	−	240.058i	0.0161266	−	0.0496327i
$287$	6306.88	−	2049.23i	1.29715	−	0.421471i
$288$	872.407	−	283.462i	0.178497	−	0.0579971i
$289$	1499.65	−	4615.46i	0.305242	−	0.939438i
$290$	−107.497	−	632.930i	−0.0217670	−	0.128162i
$291$	1749.84	+	5385.44i	0.352499	+	1.08488i
$292$	−840.978	−	1157.51i	−0.168543	−	0.231979i
$293$			5872.53i			1.17091i	0.810705	+	0.585455i	$0.199084\pi$
$293$			5872.53i			1.17091i	−0.810705	+	0.585455i	$0.800916\pi$
$294$	244.593	−	177.707i	0.0485202	−	0.0352520i
$295$	−960.932	+	6538.33i	−0.189653	+	1.29043i
$296$	1400.90	+	1017.81i	0.275086	+	0.199862i
$297$	−653.193	+	899.042i	−0.127616	+	0.175649i
$298$	−280.874	−	91.2615i	−0.0545993	−	0.0177404i
$299$	7874.05			1.52297
$300$	−5180.96	−	3590.37i	−0.997075	−	0.690967i
$301$	−625.511			−0.119780
$302$	−663.698	−	215.649i	−0.126462	−	0.0410900i
$303$	3177.01	−	4372.78i	0.602359	−	0.829076i
$304$	7530.69	+	5471.36i	1.42077	+	1.03225i
$305$	−829.084	+	847.791i	−0.155650	+	0.159162i
$306$	−30.5625	+	22.2050i	−0.00570962	+	0.00414828i
$307$		−	1766.52i		−	0.328405i	−0.986427	−	0.164203i	$-0.947495\pi$
$307$		−	1766.52i		−	0.328405i	0.986427	−	0.164203i	$-0.0525051\pi$
$308$	889.225	+	1223.91i	0.164508	+	0.226425i
$309$	−25.5532	−	78.6446i	−0.00470443	−	0.0144787i
$310$	119.402	+	17.5484i	0.0218760	+	0.00321510i
$311$	1249.86	−	3846.68i	0.227888	−	0.701367i	−0.770098	−	0.637926i	$-0.779793\pi$
$311$	1249.86	−	3846.68i	0.227888	−	0.701367i	0.997986	−	0.0634410i	$-0.0202075\pi$
$312$	1830.95	−	594.912i	0.332235	−	0.107950i
$313$	−6248.49	+	2030.26i	−1.12839	+	0.366636i	−0.812963	−	0.582315i	$-0.802147\pi$
$313$	−6248.49	+	2030.26i	−1.12839	+	0.366636i	−0.315425	+	0.948950i	$0.602147\pi$
$314$	−134.930	+	415.273i	−0.0242502	+	0.0746344i
$315$	2227.08	+	327.313i	0.398356	+	0.0585460i
$316$	−1136.30	−	3497.18i	−0.202285	−	0.622568i
$317$	249.804	+	343.825i	0.0442598	+	0.0609184i	0.830573	−	0.556909i	$-0.188013\pi$
$317$	249.804	+	343.825i	0.0442598	+	0.0609184i	−0.786313	+	0.617828i	$0.788013\pi$
$318$			534.108i			0.0941865i
$319$	1773.64	−	1288.62i	0.311300	−	0.226173i
$320$	3641.28	−	3723.44i	0.636106	−	0.650458i
$321$	−7383.77	−	5364.62i	−1.28387	−	0.932786i
$322$	428.915	−	590.351i	0.0742314	−	0.102171i
$323$	−1122.67	−	364.776i	−0.193396	−	0.0628380i
$324$	−7177.25			−1.23067
$325$	−5576.02	−	3864.15i	−0.951699	−	0.659521i
$326$	897.664			0.152506
$327$	−6865.76	−	2230.82i	−1.16109	−	0.377262i
$328$	−1498.96	+	2063.15i	−0.252337	+	0.347312i
$329$	3980.74	+	2892.18i	0.667068	+	0.484653i
$330$	−48.3961	+	329.294i	−0.00807309	+	0.0549305i
$331$	1313.25	−	954.134i	0.218075	−	0.158441i	−0.473385	−	0.880856i	$-0.656968\pi$
$331$	1313.25	−	954.134i	0.218075	−	0.158441i	0.691460	+	0.722415i	$0.256968\pi$
$332$			3030.63i			0.500987i
$333$	2565.98	+	3531.77i	0.422267	+	0.581200i
$334$	−135.138	−	415.912i	−0.0221390	−	0.0681369i
$335$	970.871	+	5716.38i	0.158341	+	0.932297i
$336$	−1741.36	+	5359.34i	−0.282734	+	0.870167i
$337$	7853.66	−	2551.81i	1.26948	−	0.412480i	0.404619	−	0.914485i	$-0.367404\pi$
$337$	7853.66	−	2551.81i	1.26948	−	0.412480i	0.864865	+	0.502005i	$0.167404\pi$
$338$	248.460	−	80.7294i	0.0399835	−	0.0129914i
$339$	−1848.76	+	5689.91i	−0.296198	+	0.911604i
$340$	−302.993	+	611.425i	−0.0483298	+	0.0975269i
$341$	127.353	+	391.953i	0.0202245	+	0.0622447i
$342$	−436.718	−	601.091i	−0.0690498	−	0.0950389i
$343$			6893.10i			1.08511i
$344$	194.606	−	141.390i	0.0305013	−	0.0221605i
$345$	−10236.2	+	1738.51i	−1.59738	+	0.271300i
$346$	149.641	+	108.720i	0.0232507	+	0.0168926i
$347$	138.529	−	190.669i	0.0214312	−	0.0294976i	−0.798167	−	0.602436i	$-0.794197\pi$
$347$	138.529	−	190.669i	0.0214312	−	0.0294976i	0.819598	+	0.572939i	$0.194197\pi$
$348$	7890.40	+	2563.75i	1.21543	+	0.394917i
$349$	−9364.65			−1.43633			−0.718164	−	0.695874i	$-0.755017\pi$
$349$	−9364.65			−1.43633			−0.718164	+	0.695874i	$0.755017\pi$
$350$	−593.449	+	207.570i	−0.0906319	+	0.0317003i
$351$	−4526.08			−0.688274
$352$	−832.078	−	270.358i	−0.125994	−	0.0409379i
$353$	4977.30	−	6850.66i	0.750467	−	1.03293i	−0.247481	−	0.968893i	$-0.579603\pi$
$353$	4977.30	−	6850.66i	0.750467	−	1.03293i	0.997948	−	0.0640361i	$-0.0203973\pi$
$354$	1068.31	+	776.175i	0.160396	+	0.116535i
$355$	2259.12	+	4314.12i	0.337751	+	0.644985i
$356$	−3219.17	+	2338.87i	−0.479258	+	0.348201i
$357$		−	714.615i		−	0.105942i
$358$	−587.877	−	809.143i	−0.0867884	−	0.119454i
$359$	1368.75	+	4212.58i	0.201225	+	0.619308i	0.999847	+	0.0174751i	$0.00556280\pi$
$359$	1368.75	+	4212.58i	0.201225	+	0.619308i	−0.798622	+	0.601833i	$0.794437\pi$
$360$	−766.866	+	401.575i	−0.112270	+	0.0587913i
$361$	5054.72	−	15556.8i	0.736947	−	2.26809i
$362$	−719.490	+	233.776i	−0.104463	+	0.0339420i
$363$	7021.64	−	2281.47i	1.01526	−	0.329879i
$364$	−1904.04	+	5860.02i	−0.274172	+	0.843815i
$365$	1451.68	+	1419.65i	0.208176	+	0.203583i
$366$	73.2199	+	225.348i	0.0104570	+	0.0321834i
$367$	−710.411	−	977.796i	−0.101044	−	0.139075i	0.755501	−	0.655147i	$-0.227394\pi$
$367$	−710.411	−	977.796i	−0.101044	−	0.139075i	−0.856545	+	0.516072i	$0.827394\pi$
$368$		−	8863.33i		−	1.25552i
$369$	−5201.35	+	3779.00i	−0.733798	+	0.533136i
$370$	−1092.49	−	541.387i	−0.153502	−	0.0760686i
$371$	−2787.30	−	2025.09i	−0.390053	−	0.283390i
$372$	−916.709	+	1261.74i	−0.127766	+	0.175855i
$373$	−2738.77	−	889.880i	−0.380183	−	0.123529i	0.112690	−	0.993630i	$-0.464053\pi$
$373$	−2738.77	−	889.880i	−0.380183	−	0.123529i	−0.492873	+	0.870101i	$0.664053\pi$
$374$	36.0310			0.00498160
$375$	8101.92	+	3792.21i	1.11568	+	0.522211i
$376$	−1892.21			−0.259530
$377$	8492.07	+	2759.24i	1.16012	+	0.376945i
$378$	−246.544	+	339.339i	−0.0335473	+	0.0461739i
$379$	−6256.41	−	4545.55i	−0.847943	−	0.616066i	0.0766353	−	0.997059i	$-0.475582\pi$
$379$	−6256.41	−	4545.55i	−0.847943	−	0.616066i	−0.924578	+	0.380993i	$0.875582\pi$
$380$	−12025.3	−	5959.15i	−1.62338	−	0.804468i
$381$	3954.44	−	2873.07i	0.531738	−	0.386330i
$382$			609.807i			0.0816765i
$383$	4660.69	+	6414.89i	0.621802	+	0.855836i	0.997483	−	0.0709126i	$-0.0225911\pi$
$383$	4660.69	+	6414.89i	0.621802	+	0.855836i	−0.375681	+	0.926749i	$0.622591\pi$
$384$	−1360.51	−	4187.23i	−0.180803	−	0.556455i
$385$	−1534.96	−	1501.09i	−0.203192	−	0.198709i
$386$	−385.633	+	1186.86i	−0.0508503	+	0.156501i
$387$	576.755	−	187.399i	0.0757573	−	0.0246151i
$388$	6628.39	−	2153.69i	0.867282	−	0.281797i
$389$	1365.45	−	4202.43i	0.177972	−	0.547742i	−0.821784	−	0.569798i	$-0.807021\pi$
$389$	1365.45	−	4202.43i	0.177972	−	0.547742i	0.999757	+	0.0220561i	$0.00702126\pi$
$390$	−1200.89	+	628.855i	−0.155921	+	0.0816495i
$391$	347.333	+	1068.98i	0.0449243	+	0.138263i
$392$	−440.824	−	606.743i	−0.0567985	−	0.0781764i
$393$			2709.12i			0.347728i
$394$	1178.34	−	856.115i	0.150670	−	0.109468i
$395$	2420.84	+	4622.94i	0.308368	+	0.588874i
$396$	−1186.59	−	862.109i	−0.150577	−	0.109400i
$397$	7545.73	−	10385.8i	0.953928	−	1.31297i	0.00416722	−	0.999991i	$-0.498674\pi$
$397$	7545.73	−	10385.8i	0.953928	−	1.31297i	0.949761	−	0.312978i	$-0.101326\pi$
$398$	1228.63	+	399.206i	0.154738	+	0.0502773i
$399$	14054.8			1.76345
$400$	−4349.63	+	6276.58i	−0.543704	+	0.784573i
$401$	−57.5652			−0.00716875			−0.00358438	−	0.999994i	$-0.501141\pi$
$401$	−57.5652			−0.00716875			−0.00358438	+	0.999994i	$0.501141\pi$
$402$	1101.89	+	358.024i	0.136709	+	0.0444195i
$403$	−986.611	+	1357.95i	−0.121952	+	0.167852i
$404$	−5382.01	−	3910.26i	−0.662785	−	0.481541i
$405$	10041.8	−	1705.50i	1.23205	−	0.209252i
$406$	669.452	−	486.385i	0.0818334	−	0.0594554i
$407$		−	4163.70i		−	0.507093i
$408$	161.531	+	222.328i	0.0196004	+	0.0269776i
$409$	4069.60	+	12525.0i	0.492002	+	1.51423i	0.821577	+	0.570098i	$0.193095\pi$
$409$	4069.60	+	12525.0i	0.492002	+	1.51423i	−0.329574	+	0.944130i	$0.606905\pi$
$410$	797.319	−	1608.95i	0.0960409	−	0.193806i
$411$	−1595.69	+	4911.03i	−0.191508	+	0.589400i
$412$	−96.7955	+	31.4508i	−0.0115747	+	0.00376084i
$413$	−8101.11	+	2632.21i	−0.965204	+	0.313614i
$414$	−218.618	+	672.836i	−0.0259528	+	0.0798746i
$415$	−720.158	−	4240.21i	−0.0851835	−	0.501551i
$416$	−1101.13	−	3388.94i	−0.129778	−	0.399414i
$417$	−1394.93	−	1919.96i	−0.163813	−	0.225470i
$418$			708.643i			0.0829208i
$419$	4786.40	−	3477.52i	0.558069	−	0.405461i	−0.272683	−	0.962104i	$-0.587911\pi$
$419$	4786.40	−	3477.52i	0.558069	−	0.405461i	0.830752	+	0.556643i	$0.187911\pi$
$420$	1181.39	−	8038.34i	0.137252	−	0.933883i
$421$	5978.40	+	4343.56i	0.692089	+	0.502832i	0.877346	−	0.479858i	$-0.159312\pi$
$421$	5978.40	+	4343.56i	0.692089	+	0.502832i	−0.185257	+	0.982690i	$0.559312\pi$
$422$	−235.052	+	323.521i	−0.0271141	+	0.0373193i
$423$	−4536.94	−	1474.14i	−0.521497	−	0.169445i
$424$	1324.92			0.151755
$425$	278.632	−	927.453i	0.0318015	−	0.105854i
$426$	973.078			0.110671
$427$	−1453.62	−	472.309i	−0.164744	−	0.0535284i
$428$	−6602.76	+	9087.93i	−0.745693	+	1.02636i
$429$	−3745.06	−	2720.95i	−0.421476	−	0.306220i
$430$	−118.424	+	121.096i	−0.0132812	+	0.0135808i
$431$	−2095.14	+	1522.21i	−0.234152	+	0.170121i	−0.698674	−	0.715440i	$-0.746226\pi$
$431$	−2095.14	+	1522.21i	−0.234152	+	0.170121i	0.464522	+	0.885562i	$0.346226\pi$
$432$			5094.73i			0.567408i
$433$	−7170.94	−	9869.95i	−0.795874	−	1.09543i	−0.993352	−	0.115119i	$-0.963275\pi$
$433$	−7170.94	−	9869.95i	−0.795874	−	1.09543i	0.197478	−	0.980307i	$-0.436725\pi$
$434$	48.0689	+	147.941i	0.00531655	+	0.0163626i
$435$	−11648.8	−	1712.01i	−1.28395	−	0.188701i
$436$	−2745.69	+	8450.35i	−0.301593	+	0.928208i
$437$	−21024.3	+	6831.21i	−2.30144	+	0.747783i
$438$	385.864	−	125.375i	0.0420943	−	0.0136773i
$439$	−3919.79	+	12063.9i	−0.426154	+	1.31157i	0.475731	+	0.879591i	$0.342184\pi$
$439$	−3919.79	+	12063.9i	−0.426154	+	1.31157i	−0.901885	+	0.431976i	$0.857816\pi$
$440$	816.856	+	120.053i	0.0885047	+	0.0130075i
$441$	−584.273	−	1798.21i	−0.0630896	−	0.194170i
$442$	86.2571	+	118.723i	0.00928242	+	0.0127762i
$443$		−	3498.02i		−	0.375161i	−0.982249	−	0.187580i	$-0.939936\pi$
$443$		−	3498.02i		−	0.375161i	0.982249	−	0.187580i	$-0.0600645\pi$
$444$	12747.4	−	9261.53i	1.36253	−	0.989939i
$445$	3948.22	−	4037.30i	0.420592	−	0.430082i
$446$	516.295	+	375.111i	0.0548146	+	0.0398251i
$447$	−3183.57	+	4381.81i	−0.336863	+	0.463652i
$448$	6384.19	+	2074.35i	0.673269	+	0.218758i
$449$	1964.32			0.206464			0.103232	−	0.994657i	$-0.467082\pi$
$449$	1964.32			0.206464			0.103232	+	0.994657i	$0.467082\pi$
$450$	485.005	−	369.185i	0.0508075	−	0.0386745i
$451$	6132.02			0.640234
$452$	7003.13	+	2275.45i	0.728760	+	0.236788i
$453$	−7522.70	+	10354.1i	−0.780236	+	1.07390i
$454$	−1752.67	−	1273.39i	−0.181182	−	0.131637i
$455$	1271.47	−	8651.30i	0.131006	−	0.891382i
$456$	−4372.65	+	3176.92i	−0.449053	+	0.326256i
$457$			962.448i			0.0985151i	0.998786	+	0.0492575i	$0.0156855\pi$
$457$			962.448i			0.0985151i	−0.998786	+	0.0492575i	$0.984314\pi$
$458$	−310.179	−	426.925i	−0.0316457	−	0.0435565i
$459$	−199.650	−	614.461i	−0.0203026	−	0.0624849i
$460$	2139.76	+	12598.6i	0.216884	+	1.27699i
$461$	−2883.59	+	8874.77i	−0.291328	+	0.896615i	0.693103	+	0.720839i	$0.256243\pi$
$461$	−2883.59	+	8874.77i	−0.291328	+	0.896615i	−0.984430	+	0.175776i	$0.943757\pi$
$462$	−408.002	+	132.568i	−0.0410865	+	0.0133498i
$463$	−3131.92	+	1017.62i	−0.314368	+	0.102144i	−0.461951	−	0.886905i	$-0.652851\pi$
$463$	−3131.92	+	1017.62i	−0.314368	+	0.102144i	0.147583	+	0.989050i	$0.452851\pi$
$464$	3105.91	−	9559.00i	0.310750	−	0.956391i
$465$	982.759	−	1983.16i	0.0980094	−	0.197778i
$466$	−85.0531	−	261.766i	−0.00845495	−	0.0260217i
$467$	−3927.34	−	5405.51i	−0.389155	−	0.535626i	0.568826	−	0.822458i	$-0.307398\pi$
$467$	−3927.34	−	5405.51i	−0.389155	−	0.535626i	−0.957981	+	0.286832i	$0.907398\pi$
$468$		−	5973.69i		−	0.590030i
$469$	−6046.23	+	4392.85i	−0.595286	+	0.432501i
$470$	1313.56	−	223.095i	0.128915	−	0.0218949i
$471$	6478.51	+	4706.92i	0.633788	+	0.460474i
$472$	1925.40	−	2650.08i	0.187762	−	0.258432i
$473$	−550.093	−	178.736i	−0.0534742	−	0.0173748i
$474$	1042.73			0.101043
$475$	18240.8	+	5480.03i	1.76199	+	0.529349i
$476$	−879.546			−0.0846931
$477$	3176.75	+	1032.19i	0.304934	+	0.0990790i
$478$	908.780	−	1250.83i	0.0869594	−	0.119689i
$479$	−8181.60	−	5944.28i	−0.780432	−	0.567017i	0.124677	−	0.992197i	$-0.460211\pi$
$479$	−8181.60	−	5944.28i	−0.780432	−	0.567017i	−0.905109	+	0.425180i	$0.860211\pi$
$480$	2179.70	+	4162.46i	0.207269	+	0.395811i
$481$	13719.4	−	9967.76i	1.30053	−	0.944887i
$482$			924.474i			0.0873623i
$483$	−7866.15	−	10826.8i	−0.741039	−	1.01995i
$484$	−2808.03	−	8642.21i	−0.263714	−	0.811628i
$485$	−8762.11	+	4588.35i	−0.820344	+	0.429579i
$486$	386.082	−	1188.24i	0.0360350	−	0.110904i
$487$	−7115.74	+	2312.04i	−0.662104	+	0.215131i	−0.620744	−	0.784014i	$-0.713169\pi$
$487$	−7115.74	+	2312.04i	−0.662104	+	0.215131i	−0.0413606	+	0.999144i	$0.513169\pi$
$488$	559.003	−	181.631i	0.0518543	−	0.0168485i
$489$	5087.29	−	15657.1i	0.470461	−	1.44793i
$490$	377.552	+	369.221i	0.0348083	+	0.0340403i
$491$	−29.0870	−	89.5205i	−0.00267348	−	0.00822811i	0.949711	−	0.313128i	$-0.101377\pi$
$491$	−29.0870	−	89.5205i	−0.00267348	−	0.00822811i	−0.952384	+	0.304900i	$0.901377\pi$
$492$	13639.8	+	18773.5i	1.24985	+	1.72028i
$493$			1274.60i			0.116440i
$494$	−2334.99	+	1696.47i	−0.212664	+	0.154510i
$495$	1865.04	+	924.225i	0.169348	+	0.0839209i
$496$	1528.56	+	1110.57i	0.138376	+	0.100536i
$497$	−3689.47	+	5078.11i	−0.332988	+	0.458319i
$498$	−817.340	−	265.570i	−0.0735459	−	0.0238965i
$499$	−13104.6			−1.17564			−0.587818	−	0.808993i	$-0.700013\pi$
$499$	−13104.6			−1.17564			−0.587818	+	0.808993i	$0.700013\pi$
$500$	4667.44	−	9971.82i	0.417469	−	0.891907i
$501$	−8020.22			−0.715203
$502$	280.889	+	91.2662i	0.0249734	+	0.00811437i
$503$	12833.5	−	17663.8i	1.13761	−	1.56578i	0.364865	−	0.931061i	$-0.381115\pi$
$503$	12833.5	−	17663.8i	1.13761	−	1.56578i	0.772742	−	0.634721i	$-0.218885\pi$
$504$	−902.672	−	655.829i	−0.0797781	−	0.0579622i
$505$	8459.24	+	4192.00i	0.745408	+	0.369389i
$506$	545.890	−	396.612i	0.0479600	−	0.0348450i
$507$		−	4791.16i		−	0.419690i
$508$	−3536.17	−	4867.12i	−0.308843	−	0.425085i
$509$	1428.76	+	4397.28i	0.124418	+	0.382920i	0.993795	−	0.111231i	$-0.0354793\pi$
$509$	1428.76	+	4397.28i	0.124418	+	0.382920i	−0.869376	+	0.494150i	$0.835479\pi$
$510$	−138.346	−	135.293i	−0.0120119	−	0.0117468i
$511$	−808.738	+	2489.04i	−0.0700126	+	0.215477i
$512$	−6390.60	+	2076.43i	−0.551616	+	0.179231i
$513$	12085.0	−	3926.64i	1.04009	−	0.337945i
$514$	−854.213	+	2629.00i	−0.0733030	+	0.225603i
$515$	127.955	−	67.0044i	0.0109483	−	0.00573314i
$516$	−676.390	−	2081.71i	−0.0577062	−	0.177601i
$517$	2674.36	+	3680.94i	0.227501	+	0.313129i
$518$		−	1571.57i		−	0.133303i
$519$	2744.35	−	1993.89i	0.232108	−	0.168636i
$520$	1559.95	+	2978.95i	0.131555	+	0.251223i
$521$	6354.86	+	4617.08i	0.534379	+	0.388249i	0.821993	−	0.569497i	$-0.192862\pi$
$521$	6354.86	+	4617.08i	0.534379	+	0.388249i	−0.287614	+	0.957746i	$0.592862\pi$
$522$	−471.553	+	649.037i	−0.0395389	+	0.0544207i
$523$	−17720.6	−	5757.77i	−1.48158	−	0.481395i	−0.546997	−	0.837135i	$-0.684229\pi$
$523$	−17720.6	−	5757.77i	−1.48158	−	0.481395i	−0.934585	+	0.355740i	$0.884229\pi$
$524$	3334.38			0.277983
$525$	257.221	+	11527.3i	0.0213830	+	0.958272i
$526$	−702.396			−0.0582242
$527$	−227.876	−	74.0415i	−0.0188358	−	0.00612011i
$528$	−3062.80	+	4215.58i	−0.252446	+	0.347462i
$529$	7185.84	+	5220.82i	0.590601	+	0.429096i
$530$	−919.750	+	156.210i	−0.0753799	+	0.0128025i
$531$	6681.07	−	4854.08i	0.546014	−	0.396703i
$532$		−	17298.6i		−	1.40975i
$533$	14679.9	+	20205.1i	1.19297	+	1.64199i
$534$	−348.684	−	1073.14i	−0.0282566	−	0.0869649i
$535$	7078.50	−	14284.1i	0.572019	−	1.15431i
$536$	888.124	−	2733.37i	0.0715693	−	0.220268i
$537$	−17444.7	+	5668.14i	−1.40185	+	0.455490i
$538$	−2164.06	+	703.145i	−0.173419	+	0.0563471i
$539$	−557.263	+	1715.08i	−0.0445325	+	0.137057i
$540$	−1229.95	−	7241.82i	−0.0980161	−	0.577108i
$541$	2428.79	+	7475.05i	0.193016	+	0.594044i	0.999994	+	0.00346150i	$0.00110183\pi$
$541$	2428.79	+	7475.05i	0.193016	+	0.594044i	−0.806978	+	0.590582i	$0.798898\pi$
$542$	284.961	+	392.215i	0.0225832	+	0.0310832i
$543$			13874.2i			1.09650i
$544$	411.510	−	298.980i	0.0324326	−	0.0235637i
$545$	1833.51	−	12475.5i	0.144108	−	0.980533i
$546$	−1413.56	−	1027.01i	−0.110796	−	0.0804980i
$547$	−377.183	+	519.147i	−0.0294829	+	0.0405798i	−0.823504	−	0.567310i	$-0.807984\pi$
$547$	−377.183	+	519.147i	−0.0294829	+	0.0405798i	0.794021	+	0.607890i	$0.207984\pi$
$548$	6044.49	+	1963.97i	0.471182	+	0.153096i
$549$	1481.82			0.115195
$550$	−581.209	+	12.9691i	−0.0450597	+	0.00100547i
$551$	−25068.3			−1.93819
$552$	4894.56	+	1590.34i	0.377403	+	0.122626i
$553$	−3953.57	+	5441.62i	−0.304020	+	0.418447i
$554$	−101.827	−	73.9818i	−0.00780907	−	0.00567362i
$555$	−15634.3	+	15987.1i	−1.19575	+	1.22273i
$556$	−2363.08	+	1716.88i	−0.180246	+	0.130957i
$557$		−	19007.4i		−	1.44590i	−0.690898	−	0.722952i	$-0.742785\pi$
$557$		−	19007.4i		−	1.44590i	0.690898	−	0.722952i	$-0.257215\pi$
$558$	−88.6443	−	122.008i	−0.00672511	−	0.00925632i
$559$	−727.967	−	2240.45i	−0.0550800	−	0.169519i
$560$	−9738.23	−	1431.22i	−0.734849	−	0.108000i
$561$	204.197	−	628.454i	0.0153676	−	0.0472965i
$562$	−923.892	+	300.191i	−0.0693452	+	0.0225316i
$563$	−17960.1	+	5835.60i	−1.34446	+	0.436841i	−0.890824	−	0.454348i	$-0.849872\pi$
$563$	−17960.1	+	5835.60i	−1.34446	+	0.436841i	−0.453633	+	0.891188i	$0.649872\pi$
$564$	−5320.70	+	16375.4i	−0.397237	+	1.22257i
$565$	−10338.9	−	1519.50i	−0.769842	−	0.113143i
$566$	−120.128	−	369.716i	−0.00892113	−	0.0274564i
$567$	7716.78	+	10621.2i	0.571560	+	0.786685i
$568$		−	2413.84i		−	0.178314i
$569$	−7384.29	+	5365.00i	−0.544052	+	0.395277i	−0.825588	−	0.564274i	$-0.809156\pi$
$569$	−7384.29	+	5365.00i	−0.544052	+	0.395277i	0.281536	+	0.959551i	$0.409156\pi$
$570$	2660.89	−	2720.93i	0.195531	−	0.199943i
$571$	1845.78	+	1341.04i	0.135277	+	0.0982848i	0.653366	−	0.757042i	$-0.273356\pi$
$571$	1845.78	+	1341.04i	0.135277	+	0.0982848i	−0.518089	+	0.855327i	$0.673356\pi$
$572$	−3348.93	+	4609.41i	−0.244801	+	0.336939i
$573$	10636.3	+	3455.93i	0.775456	+	0.251961i
$574$	2314.50			0.168302
$575$	−5987.53	−	17118.5i	−0.434256	−	1.24155i
$576$	−6508.03			−0.470778
$577$	−88.0747	−	28.6172i	−0.00635459	−	0.00206473i	0.305838	−	0.952084i	$-0.401063\pi$
$577$	−88.0747	−	28.6172i	−0.00635459	−	0.00206473i	−0.312193	+	0.950019i	$0.601063\pi$
$578$	995.580	−	1370.30i	0.0716448	−	0.0986106i
$579$	18515.7	+	13452.5i	1.32899	+	0.965570i
$580$	−2107.14	+	14337.3i	−0.150852	+	1.02642i
$581$	4484.88	−	3258.46i	0.320248	−	0.232674i
$582$			1976.35i			0.140760i
$583$	−1872.58	−	2577.38i	−0.133026	−	0.183095i
$584$	−311.008	−	957.185i	−0.0220370	−	0.0678229i
$585$	1419.51	+	8357.89i	0.100324	+	0.590694i
$586$	−633.369	+	1949.31i	−0.0446488	+	0.137415i
$587$	24328.8	−	7904.91i	1.71066	−	0.555827i	0.720217	−	0.693749i	$-0.244042\pi$
$587$	24328.8	−	7904.91i	1.71066	−	0.555827i	0.990443	+	0.137922i	$0.0440422\pi$
$588$	−6490.37	+	2108.85i	−0.455201	+	0.147904i
$589$	1456.22	−	4481.78i	0.101872	−	0.313529i
$590$	−1024.15	+	2066.67i	−0.0714634	+	0.144209i
$591$	−8254.41	−	25404.5i	−0.574520	−	1.76819i
$592$	−11220.1	−	15443.1i	−0.778957	−	1.07214i
$593$		−	1106.43i		−	0.0766200i	−0.999266	−	0.0383100i	$-0.987803\pi$
$593$		−	1106.43i		−	0.0766200i	0.999266	−	0.0383100i	$-0.0121974\pi$
$594$	−313.783	+	227.977i	−0.0216745	+	0.0157475i
$595$	1230.59	−	209.003i	0.0847885	−	0.0144005i
$596$	5393.12	+	3918.33i	0.370656	+	0.269297i
$597$	13925.9	−	19167.4i	0.954690	−	1.31402i
$598$	2613.69	+	849.239i	0.178732	+	0.0580735i
$599$	9360.91			0.638525			0.319262	−	0.947666i	$-0.396565\pi$
$599$	9360.91			0.638525			0.319262	+	0.947666i	$0.396565\pi$
$600$	−2685.64	−	3528.18i	−0.182735	−	0.240062i
$601$	18680.3			1.26786			0.633930	−	0.773391i	$-0.281441\pi$
$601$	18680.3			1.26786			0.633930	+	0.773391i	$0.281441\pi$
$602$	−207.630	−	67.4631i	−0.0140571	−	0.00456743i
$603$	4258.89	−	5861.86i	0.287621	−	0.395876i
$604$	12743.8	+	9258.91i	0.858506	+	0.623741i
$605$	5982.37	+	11424.2i	0.402013	+	0.767702i
$606$	1526.19	−	1108.84i	0.102305	−	0.0743292i
$607$		−	17776.3i		−	1.18867i	−0.804219	−	0.594333i	$-0.797416\pi$
$607$		−	17776.3i		−	1.18867i	0.804219	−	0.594333i	$-0.202584\pi$
$608$	5880.21	+	8093.42i	0.392227	+	0.539854i
$609$	−4689.59	−	14433.1i	−0.312039	−	0.960357i
$610$	−366.640	+	191.994i	−0.0243358	+	0.0127436i
$611$	−5726.42	+	17624.1i	−0.379159	+	1.16693i
$612$	810.989	−	263.506i	0.0535658	−	0.0174046i
$613$	19323.4	−	6278.56i	1.27319	−	0.413685i	0.407013	−	0.913422i	$-0.366570\pi$
$613$	19323.4	−	6278.56i	1.27319	−	0.413685i	0.866177	+	0.499738i	$0.166570\pi$
$614$	190.524	−	586.372i	0.0125227	−	0.0385408i
$615$	−23544.7	−	23025.2i	−1.54376	−	1.50970i
$616$	328.851	+	1012.10i	0.0215094	+	0.0661991i
$617$	15876.6	+	21852.2i	1.03593	+	1.42583i	0.900403	+	0.435057i	$0.143272\pi$
$617$	15876.6	+	21852.2i	1.03593	+	1.42583i	0.135524	+	0.990774i	$0.456728\pi$
$618$		−	28.8610i		−	0.00187858i
$619$	−12550.5	+	9118.48i	−0.814940	+	0.592088i	−0.915258	−	0.402867i	$-0.868014\pi$
$619$	−12550.5	+	9118.48i	−0.814940	+	0.592088i	0.100319	+	0.994955i	$0.468014\pi$
$620$	−2440.86	−	1209.58i	−0.158109	−	0.0783513i
$621$	−9788.52	−	7111.77i	−0.632528	−	0.459558i
$622$	829.750	−	1142.05i	0.0534887	−	0.0736208i
$623$	6922.34	+	2249.20i	0.445165	+	0.144643i
$624$	−21222.7			−1.36152
$625$	−4160.73	+	15060.8i	−0.266287	+	0.963894i
$626$	−2293.07			−0.146405
$627$	12360.2	+	4016.06i	0.787269	+	0.255799i
$628$	5793.26	−	7973.74i	0.368115	−	0.506667i
$629$	1958.40	+	1422.86i	0.124144	+	0.0901960i
$630$	703.950	+	348.844i	0.0445175	+	0.0220608i
$631$	−6359.95	+	4620.78i	−0.401245	+	0.291522i	−0.770048	−	0.637986i	$-0.779768\pi$
$631$	−6359.95	+	4620.78i	−0.401245	+	0.291522i	0.368803	+	0.929508i	$0.379768\pi$
$632$		−	2586.63i		−	0.162802i
$633$	4310.76	+	5933.25i	0.270675	+	0.372552i
$634$	45.8365	+	141.070i	0.00287129	+	0.00883693i
$635$	6104.06	+	5969.37i	0.381468	+	0.373051i
$636$	3725.54	−	11466.0i	0.232275	−	0.714870i
$637$	−6985.28	+	2269.66i	−0.434485	+	0.141173i
$638$	727.718	−	236.450i	0.0451577	−	0.0146726i
$639$	1880.52	−	5787.64i	0.116420	−	0.358303i
$640$	6812.61	−	3567.48i	0.420769	−	0.220339i
$641$	−6688.01	−	20583.6i	−0.412107	−	1.26833i	−0.914813	−	0.403877i	$-0.867662\pi$
$641$	−6688.01	−	20583.6i	−0.412107	−	1.26833i	0.502706	−	0.864457i	$-0.332338\pi$
$642$	−1872.36	−	2577.08i	−0.115103	−	0.158425i
$643$		−	6467.47i		−	0.396660i	−0.980135	−	0.198330i	$-0.936448\pi$
$643$		−	6467.47i		−	0.396660i	0.980135	−	0.198330i	$-0.0635517\pi$
$644$	−13325.6	+	9681.63i	−0.815377	+	0.592406i
$645$	1441.02	+	2751.83i	0.0879690	+	0.167990i
$646$	−333.312	−	242.165i	−0.0203003	−	0.0147490i
$647$	−8289.63	+	11409.7i	−0.503708	+	0.693294i	−0.982842	−	0.184447i	$-0.940951\pi$
$647$	−8289.63	+	11409.7i	−0.503708	+	0.693294i	0.479135	+	0.877741i	$0.340951\pi$
$648$	−4801.62	−	1560.14i	−0.291089	−	0.0945805i
$649$	−7876.50			−0.476394
$650$	−1434.13	−	1884.04i	−0.0865402	−	0.113690i
$651$	2852.81			0.171752
$652$	−19270.7	−	6261.42i	−1.15751	−	0.376099i
$653$	12671.0	−	17440.2i	0.759351	−	1.04516i	−0.237917	−	0.971285i	$-0.576465\pi$
$653$	12671.0	−	17440.2i	0.759351	−	1.04516i	0.997268	−	0.0738712i	$-0.0235354\pi$
$654$	−2038.40	−	1480.98i	−0.121877	−	0.0885489i
$655$	−4665.18	+	792.335i	−0.278296	+	0.0472658i
$656$	22743.6	−	16524.2i	1.35364	−	0.983478i
$657$		−	2537.32i		−	0.150670i
$658$	1009.42	+	1389.35i	0.0598047	+	0.0823141i
$659$	5532.10	+	17026.0i	0.327010	+	1.00643i	0.970525	+	0.241001i	$0.0774756\pi$
$659$	5532.10	+	17026.0i	0.327010	+	1.00643i	−0.643514	+	0.765434i	$0.722524\pi$
$660$	3335.86	−	6731.59i	0.196740	−	0.397010i
$661$	304.887	−	938.346i	0.0179406	−	0.0552155i	−0.941685	−	0.336495i	$-0.890759\pi$
$661$	304.887	−	938.346i	0.0179406	−	0.0552155i	0.959626	+	0.281279i	$0.0907586\pi$
$662$	538.823	−	175.074i	0.0316344	−	0.0102786i
$663$	2559.61	−	831.666i	0.149935	−	0.0487168i
$664$	−658.779	+	2027.51i	−0.0385024	+	0.118498i
$665$	4110.59	+	24202.7i	0.239702	+	1.41134i
$666$	470.832	+	1449.07i	0.0273939	+	0.0843099i
$667$	14030.2	+	19310.9i	0.814469	+	1.12102i
$668$			9871.26i			0.571752i
$669$	9468.67	−	6879.39i	0.547205	−	0.397567i
$670$	−294.260	+	2002.19i	−0.0169675	+	0.115450i
$671$	−1143.40	−	830.725i	−0.0657828	−	0.0477940i
$672$	−3559.76	+	4899.59i	−0.204346	+	0.281259i
$673$	−13248.1	−	4304.55i	−0.758804	−	0.246550i	−0.0960385	−	0.995378i	$-0.530617\pi$
$673$	−13248.1	−	4304.55i	−0.758804	−	0.246550i	−0.662765	+	0.748827i	$0.730617\pi$
$674$	2882.14			0.164712
$675$	3441.69	+	9839.87i	0.196253	+	0.561092i
$676$	−5896.94			−0.335511
$677$	−1021.54	−	331.919i	−0.0579927	−	0.0188430i	0.279877	−	0.960036i	$-0.409706\pi$
$677$	−1021.54	−	331.919i	−0.0579927	−	0.0188430i	−0.337870	+	0.941193i	$0.609706\pi$
$678$	−1227.35	+	1689.30i	−0.0695220	+	0.0956889i
$679$	−10313.8	−	7493.42i	−0.582927	−	0.423521i
$680$	−335.612	+	343.184i	−0.0189267	+	0.0193537i
$681$	−32143.3	+	23353.5i	−1.80871	+	1.31411i
$682$			143.839i			0.00807607i
$683$	9457.15	+	13016.6i	0.529821	+	0.729236i	0.987103	−	0.160086i	$-0.0511771\pi$
$683$	9457.15	+	13016.6i	0.529821	+	0.729236i	−0.457282	+	0.889322i	$0.651177\pi$
$684$	5182.54	+	15950.2i	0.289706	+	0.891625i
$685$	−8923.63	−	1311.50i	−0.497743	−	0.0731529i
$686$	−743.440	+	2288.07i	−0.0413771	+	0.127346i
$687$	−9204.30	+	2990.66i	−0.511158	+	0.166085i
$688$	−2521.94	+	819.427i	−0.139750	+	0.0454075i
$689$	4009.62	−	12340.4i	0.221705	−	0.682337i
$690$	−3585.26	−	526.923i	−0.197810	−	0.0290719i
$691$	−4143.29	−	12751.7i	−0.228101	−	0.702024i	−0.997962	−	0.0638117i	$-0.979674\pi$
$691$	−4143.29	−	12751.7i	−0.228101	−	0.702024i	0.769861	−	0.638212i	$-0.220326\pi$
$692$	−2454.07	−	3377.74i	−0.134812	−	0.185553i
$693$			2682.89i			0.147063i
$694$	66.5472	−	48.3494i	0.00363991	−	0.00264455i
$695$	2898.25	−	2963.64i	0.158182	−	0.161752i
$696$	4721.44	+	3430.32i	0.257134	+	0.186819i
$697$	−2095.50	+	2884.21i	−0.113878	+	0.156739i
$698$	−3108.47	−	1010.00i	−0.168564	−	0.0547697i
$699$	−5047.75			−0.273138
$700$	14187.8	−	316.587i	0.766067	−	0.0170941i
$701$	4448.20			0.239667			0.119833	−	0.992794i	$-0.461764\pi$
$701$	4448.20			0.239667			0.119833	+	0.992794i	$0.461764\pi$
$702$	−1502.37	−	488.150i	−0.0807741	−	0.0262451i
$703$	−27984.3	+	38517.1i	−1.50135	+	2.06643i
$704$	5021.72	+	3648.49i	0.268840	+	0.195323i
$705$	3553.04	−	24175.4i	0.189809	−	1.29149i
$706$	2391.01	−	1737.17i	0.127460	−	0.0926053i
$707$			12168.8i			0.647318i
$708$	−17520.1	−	24114.4i	−0.930008	−	1.28005i
$709$	−8615.17	−	26514.8i	−0.456346	−	1.40449i	−0.869548	−	0.493849i	$-0.835589\pi$
$709$	−8615.17	−	26514.8i	−0.456346	−	1.40449i	0.413201	−	0.910640i	$-0.364411\pi$
$710$	284.596	+	1675.67i	0.0150432	+	0.0885728i
$711$	2015.13	−	6201.94i	0.106292	−	0.327132i
$712$	−2662.05	+	864.954i	−0.140119	+	0.0455274i
$713$	−4267.47	+	1386.59i	−0.224149	+	0.0728304i
$714$	77.0732	−	237.207i	0.00403977	−	0.0124331i
$715$	3590.23	−	7244.89i	0.187786	−	0.378942i
$716$	6976.33	+	21470.9i	0.364131	+	1.12068i
$717$	−16666.7	−	22939.7i	−0.868101	−	1.19484i
$718$			1545.94i			0.0803535i
$719$	14644.7	−	10640.0i	0.759602	−	0.551883i	−0.139186	−	0.990266i	$-0.544449\pi$
$719$	14644.7	−	10640.0i	0.759602	−	0.551883i	0.898788	+	0.438383i	$0.144449\pi$
$720$	9407.96	−	1597.85i	0.486964	−	0.0827060i
$721$	150.614	+	109.428i	0.00777971	+	0.00565229i
$722$	3355.70	−	4618.72i	0.172972	−	0.238076i
$723$	16124.7	+	5239.23i	0.829439	+	0.269501i
$724$	17076.4			0.876572
$725$	−458.784	−	20560.3i	−0.0235018	−	1.05323i
$726$	2576.80			0.131727
$727$	10105.4	+	3283.45i	0.515528	+	0.167505i	0.555215	−	0.831707i	$-0.312636\pi$
$727$	10105.4	+	3283.45i	0.515528	+	0.167505i	−0.0396867	+	0.999212i	$0.512636\pi$
$728$	−2547.62	+	3506.50i	−0.129699	+	0.178516i
$729$	1362.76	+	990.105i	0.0692355	+	0.0503025i
$730$	328.753	+	627.801i	0.0166681	+	0.0318301i
$731$	272.052	−	197.658i	0.0137650	−	0.0100009i
$732$		−	5348.40i		−	0.270058i
$733$	−11783.2	−	16218.1i	−0.593753	−	0.817230i	0.401366	−	0.915918i	$-0.368536\pi$
$733$	−11783.2	−	16218.1i	−0.593753	−	0.817230i	−0.995118	+	0.0986876i	$0.968536\pi$
$734$	−130.353	−	401.186i	−0.00655508	−	0.0201745i
$735$	8579.66	−	4492.80i	0.430565	−	0.225469i
$736$	2943.59	−	9059.42i	0.147421	−	0.453716i
$737$	−6572.47	+	2135.53i	−0.328494	+	0.106734i
$738$	−2134.10	+	693.410i	−0.106446	+	0.0345864i
$739$	−3665.12	+	11280.1i	−0.182441	+	0.561495i	−0.999895	−	0.0144989i	$-0.995385\pi$
$739$	−3665.12	+	11280.1i	−0.182441	+	0.561495i	0.817454	+	0.575994i	$0.195385\pi$
$740$	19676.8	+	19242.7i	0.977480	+	0.955912i
$741$	16356.9	+	50341.3i	0.810911	+	2.49573i
$742$	−706.796	−	972.822i	−0.0349694	−	0.0481313i
$743$		−	32431.0i		−	1.60132i	−0.599120	−	0.800659i	$-0.704483\pi$
$743$		−	32431.0i		−	1.60132i	0.599120	−	0.800659i	$-0.295517\pi$
$744$	−887.553	+	644.845i	−0.0437356	+	0.0317757i
$745$	−8476.70	−	4200.65i	−0.416862	−	0.206577i
$746$	−813.122	−	590.768i	−0.0399069	−	0.0289940i
$747$	−3159.09	+	4348.12i	−0.154732	+	0.212971i
$748$	−773.499	−	251.325i	−0.0378101	−	0.0122852i
$749$	20547.9			1.00241
$750$	2280.33	+	2132.59i	0.111021	+	0.103828i
$751$	5600.17			0.272108			0.136054	−	0.990701i	$-0.456558\pi$
$751$	5600.17			0.272108			0.136054	+	0.990701i	$0.456558\pi$
$752$	19838.4	+	6445.87i	0.962009	+	0.312576i
$753$	3183.74	−	4382.04i	0.154079	−	0.212072i
$754$	2521.24	+	1831.79i	0.121775	+	0.0884745i
$755$	−20030.2	−	9926.03i	−0.965529	−	0.478471i
$756$	7659.69	−	5565.09i	0.368493	−	0.267725i
$757$			39175.8i			1.88093i	0.339885	+	0.940467i	$0.389612\pi$
$757$			39175.8i			1.88093i	−0.339885	+	0.940467i	$0.610388\pi$
$758$	−1586.48	−	2183.61i	−0.0760207	−	0.104633i
$759$	−3824.02	−	11769.1i	−0.182877	−	0.562836i
$760$	−6749.61	−	6600.68i	−0.322150	−	0.315042i
$761$	−5708.14	+	17567.9i	−0.271905	+	0.836839i	0.718116	+	0.695923i	$0.245005\pi$
$761$	−5708.14	+	17567.9i	−0.271905	+	0.836839i	−0.990022	+	0.140916i	$0.954995\pi$
$762$	1622.49	−	527.180i	0.0771349	−	0.0250626i
$763$	15457.3	−	5022.39i	0.733412	−	0.238300i
$764$	4253.55	−	13091.1i	0.201424	−	0.619920i
$765$	−1072.05	+	561.388i	−0.0506668	+	0.0265321i
$766$	855.190	+	2632.01i	0.0403385	+	0.124149i
$767$	−18856.1	−	25953.2i	−0.887684	−	1.22179i
$768$			22316.4i			1.04853i
$769$	19555.5	−	14207.9i	0.917023	−	0.666256i	−0.0257584	−	0.999668i	$-0.508200\pi$
$769$	19555.5	−	14207.9i	0.917023	−	0.666256i	0.942781	+	0.333412i	$0.108200\pi$
$770$	−347.614	−	663.818i	−0.0162690	−	0.0310680i
$771$	41014.0	+	29798.4i	1.91580	+	1.39191i
$772$	16557.2	−	22789.1i	0.771902	−	1.06243i
$773$	−24270.0	−	7885.79i	−1.12928	−	0.366924i	−0.315975	−	0.948768i	$-0.602331\pi$
$773$	−24270.0	−	7885.79i	−1.12928	−	0.366924i	−0.813300	+	0.581844i	$0.802331\pi$
$774$	211.658			0.00982930
$775$	3702.48	+	1112.33i	0.171609	+	0.0515560i
$776$	4902.59			0.226795
$777$	−27411.3	−	8906.48i	−1.26561	−	0.411220i
$778$	906.488	−	1247.67i	0.0417727	−	0.0574952i
$779$	−56725.4	−	41213.4i	−2.60898	−	1.89554i
$780$	30166.6	−	5123.50i	1.38479	−	0.235193i
$781$	−4695.67	+	3411.60i	−0.215140	+	0.156308i
$782$			392.295i			0.0179392i
$783$	−8064.68	−	11100.1i	−0.368082	−	0.506621i
$784$	2554.81	+	7862.90i	0.116382	+	0.358186i
$785$	−6210.67	+	12532.8i	−0.282380	+	0.569828i
$786$	−292.186	+	899.256i	−0.0132595	+	0.0408084i
$787$	32863.2	−	10677.9i	1.48850	−	0.483642i	0.551859	−	0.833938i	$-0.313919\pi$
$787$	32863.2	−	10677.9i	1.48850	−	0.483642i	0.936639	+	0.350295i	$0.113919\pi$
$788$	−31267.8	+	10159.5i	−1.41354	+	0.459286i
$789$	−3980.66	+	12251.2i	−0.179614	+	0.552794i
$790$	304.968	+	1795.62i	0.0137345	+	0.0808673i
$791$	−4162.25	−	12810.1i	−0.187095	−	0.575820i
$792$	−606.437	−	834.689i	−0.0272081	−	0.0374487i
$793$		−	5756.23i		−	0.257768i
$794$	3624.84	−	2633.60i	0.162016	−	0.117712i
$795$	−2487.83	+	16927.6i	−0.110987	+	0.755169i
$796$	−23591.2	−	17140.0i	−1.05046	−	0.763204i
$797$	−13621.5	+	18748.4i	−0.605394	+	0.833254i	−0.996189	−	0.0872241i	$-0.972200\pi$
$797$	−13621.5	+	18748.4i	−0.605394	+	0.833254i	0.390794	+	0.920478i	$0.372200\pi$
$798$	4665.29	+	1515.85i	0.206954	+	0.0672435i
$799$	−2645.25			−0.117124
$800$	−6530.37	+	4970.90i	−0.288604	+	0.219685i
$801$	−7056.62			−0.311278
$802$	−19.1080	−	6.20857i	−0.000841306	−	0.000273357i
$803$	−1422.46	+	1957.84i	−0.0625123	+	0.0860409i
$804$	−21157.5	−	15371.8i	−0.928070	−	0.674283i
$805$	16343.5	−	16712.2i	0.715568	−	0.731713i
$806$	−473.952	+	344.346i	−0.0207125	+	0.0150485i
$807$			41730.5i			1.82030i
$808$	−2750.61	−	3785.89i	−0.119760	−	0.164836i
$809$	11248.1	+	34618.2i	0.488829	+	1.50446i	0.826357	+	0.563146i	$0.190409\pi$
$809$	11248.1	+	34618.2i	0.488829	+	1.50446i	−0.337528	+	0.941315i	$0.609591\pi$
$810$	3517.19	+	516.918i	0.152570	+	0.0224230i
$811$	−2501.30	+	7698.20i	−0.108301	+	0.333318i	−0.990491	−	0.137577i	$-0.956069\pi$
$811$	−2501.30	+	7698.20i	−0.108301	+	0.333318i	0.882190	+	0.470894i	$0.156069\pi$
$812$	−17764.2	+	5771.93i	−0.767735	+	0.249452i
$813$	8455.97	−	2747.51i	0.364777	−	0.118523i
$814$	449.066	−	1382.08i	0.0193363	−	0.0595111i
$815$	28449.8	+	4181.24i	1.22276	+	0.179709i
$816$	−936.155	−	2881.19i	−0.0401617	−	0.123605i
$817$	3887.45	+	5350.62i	0.166468	+	0.229124i
$818$			4596.41i			0.196467i
$819$	−8840.16	+	6422.76i	−0.377168	+	0.274028i
$820$	−28339.3	+	28978.7i	−1.20689	+	1.23412i
$821$	−34868.3	−	25333.3i	−1.48223	−	1.07690i	−0.976830	−	0.214019i	$-0.931345\pi$
$821$	−34868.3	−	25333.3i	−1.48223	−	1.07690i	−0.505401	−	0.862885i	$-0.668655\pi$
$822$	−1059.34	+	1458.05i	−0.0449497	+	0.0618679i
$823$	37217.8	+	12092.8i	1.57635	+	0.512186i	0.961112	−	0.276159i	$-0.0890617\pi$
$823$	37217.8	+	12092.8i	1.57635	+	0.512186i	0.615234	+	0.788345i	$0.289062\pi$
$824$	−71.5933			−0.00302679
$825$	−3067.65	+	10211.0i	−0.129457	+	0.430909i
$826$	−2972.95			−0.125233
$827$	−1415.40	−	459.891i	−0.0595142	−	0.0193374i	0.279109	−	0.960260i	$-0.409961\pi$
$827$	−1415.40	−	459.891i	−0.0595142	−	0.0193374i	−0.338623	+	0.940922i	$0.609961\pi$
$828$	9386.39	−	12919.3i	0.393961	−	0.542241i
$829$	12040.5	+	8747.91i	0.504442	+	0.366499i	0.810711	−	0.585446i	$-0.199081\pi$
$829$	12040.5	+	8747.91i	0.504442	+	0.366499i	−0.306269	+	0.951945i	$0.599081\pi$
$830$	218.272	−	1485.15i	0.00912809	−	0.0621089i
$831$	−1867.47	+	1356.80i	−0.0779567	+	0.0566388i
$832$			25281.0i			1.05344i
$833$	−616.257	−	848.205i	−0.0256327	−	0.0352804i
$834$	−255.956	−	787.752i	−0.0106271	−	0.0327070i
$835$	−2345.67	−	13811.0i	−0.0972158	−	0.572396i
$836$	4942.96	−	15212.9i	0.204493	−	0.629364i
$837$	2452.98	−	797.023i	0.101299	−	0.0329141i
$838$	1963.84	−	638.091i	0.0809545	−	0.0263037i
$839$	−257.164	+	791.470i	−0.0105820	+	0.0325680i	−0.956208	−	0.292688i	$-0.905450\pi$
$839$	−257.164	+	791.470i	−0.0105820	+	0.0325680i	0.945626	+	0.325256i	$0.105450\pi$
$840$	2537.68	−	5120.90i	0.104236	−	0.210343i
$841$	827.806	+	2547.72i	0.0339418	+	0.104462i
$842$	1515.99	+	2086.58i	0.0620479	+	0.0854016i
$843$			17815.8i			0.727887i
$844$	7302.63	−	5305.67i	0.297828	−	0.216385i
$845$	8250.50	−	1401.27i	0.335889	−	0.0570474i
$846$	−1346.99	−	978.643i	−0.0547403	−	0.0397712i
$847$	−9770.06	+	13447.3i	−0.396344	+	0.545520i
$848$	−13890.8	−	4513.38i	−0.562513	−	0.182772i
$849$	−7129.39			−0.288198
$850$	192.517	−	277.805i	0.00776855	−	0.0112101i
$851$	45333.1			1.82609
$852$	−20889.7	−	6787.46i	−0.839985	−	0.272928i
$853$	−3079.16	+	4238.10i	−0.123597	+	0.170117i	−0.866332	−	0.499469i	$-0.833528\pi$
$853$	−3079.16	+	4238.10i	−0.123597	+	0.170117i	0.742734	+	0.669586i	$0.233528\pi$
$854$	−431.569	−	313.553i	−0.0172927	−	0.0125639i
$855$	−11041.2	−	21084.7i	−0.441637	−	0.843369i
$856$	−6392.76	+	4644.61i	−0.255257	+	0.185455i
$857$		−	30677.2i		−	1.22277i	−0.791334	−	0.611384i	$-0.790613\pi$
$857$		−	30677.2i		−	1.22277i	0.791334	−	0.611384i	$-0.209387\pi$
$858$	−949.662	−	1307.10i	−0.0377866	−	0.0520088i
$859$	2120.20	+	6525.31i	0.0842145	+	0.259186i	0.984293	−	0.176542i	$-0.0564911\pi$
$859$	2120.20	+	6525.31i	0.0842145	+	0.259186i	−0.900079	+	0.435728i	$0.856491\pi$
$860$	3386.95	−	1773.60i	0.134295	−	0.0703247i
$861$	13116.9	−	40369.6i	0.519189	−	1.59790i
$862$	−859.630	+	279.311i	−0.0339665	+	0.0110364i
$863$	5782.73	−	1878.92i	0.228095	−	0.0741127i	−0.192739	−	0.981250i	$-0.561737\pi$
$863$	5782.73	−	1878.92i	0.228095	−	0.0741127i	0.420835	+	0.907137i	$0.361737\pi$
$864$	−1692.00	+	5207.44i	−0.0666239	+	0.205047i
$865$	4236.17	+	4142.70i	0.166514	+	0.162839i
$866$	−1315.80	−	4049.61i	−0.0516312	−	0.158904i
$867$	−18258.6	−	25130.8i	−0.715218	−	0.984413i
$868$		−	3511.23i		−	0.137303i
$869$	−5031.80	+	3655.82i	−0.196424	+	0.142710i
$870$	−3682.02	−	1824.64i	−0.143485	−	0.0711045i
$871$	−22770.9	−	16544.0i	−0.885834	−	0.643596i
$872$	−3673.76	+	5056.50i	−0.142671	+	0.196370i
$873$	11754.9	+	3819.39i	0.455718	+	0.148072i
$874$	−7715.51			−0.298605
$875$	−19775.1	+	3814.33i	−0.764023	+	0.147369i
$876$	−9158.10			−0.353223
$877$	15815.0	+	5138.62i	0.608935	+	0.197855i	0.597221	−	0.802077i	$-0.296271\pi$
$877$	15815.0	+	5138.62i	0.608935	+	0.197855i	0.0117134	+	0.999931i	$0.496271\pi$
$878$	−2602.25	+	3581.69i	−0.100025	+	0.137672i
$879$	30410.4	+	22094.5i	1.16691	+	0.847813i
$880$	−8155.13	−	4041.30i	−0.312397	−	0.154809i
$881$	−19560.7	+	14211.7i	−0.748033	+	0.543478i	−0.895217	−	0.445631i	$-0.852979\pi$
$881$	−19560.7	+	14211.7i	−0.748033	+	0.543478i	0.147184	+	0.989109i	$0.452979\pi$
$882$		−	659.906i		−	0.0251930i
$883$	22818.3	+	31406.8i	0.869647	+	1.19697i	0.979182	+	0.202984i	$0.0650639\pi$
$883$	22818.3	+	31406.8i	0.869647	+	1.19697i	−0.109535	+	0.993983i	$0.534936\pi$
$884$	−1023.61	−	3150.35i	−0.0389455	−	0.119862i
$885$	30242.9	+	29575.5i	1.14870	+	1.12336i
$886$	377.272	−	1161.12i	0.0143055	−	0.0440279i
$887$	36451.0	−	11843.7i	1.37983	−	0.448333i	0.477214	−	0.878787i	$-0.341647\pi$
$887$	36451.0	−	11843.7i	1.37983	−	0.448333i	0.902612	+	0.430455i	$0.141647\pi$
$888$	10541.3	−	3425.08i	0.398359	−	0.129435i
$889$	−3400.61	+	10466.0i	−0.128293	+	0.394846i
$890$	1745.99	−	914.303i	0.0657594	−	0.0344354i
$891$	3751.41	+	11545.7i	0.141052	+	0.434113i
$892$	−8467.13	−	11654.0i	−0.317826	−	0.437450i
$893$		−	52025.7i		−	1.94958i
$894$	−1529.34	+	1111.13i	−0.0572132	+	0.0415679i
$895$	−14862.7	−	28382.6i	−0.555091	−	1.06003i
$896$	8019.07	+	5826.20i	0.298994	+	0.217232i
$897$	29624.9	−	40775.2i	1.10273	−	1.51777i
$898$	652.032	+	211.858i	0.0242300	+	0.00787282i
$899$	−5088.31			−0.188770
$900$	−12987.0	+	4542.48i	−0.481002	+	0.168240i
$901$	1852.20			0.0684857
$902$	2035.44	+	661.355i	0.0751361	+	0.0244132i
$903$	−2353.39	+	3239.16i	−0.0867284	+	0.119371i
$904$	4190.51	+	3044.59i	0.154175	+	0.112015i
$905$	−23891.8	+	4057.79i	−0.877558	+	0.149045i
$906$	−3613.78	+	2625.56i	−0.132516	+	0.0962787i
$907$			19258.6i			0.705040i	0.935804	+	0.352520i	$0.114675\pi$
$907$			19258.6i			0.705040i	−0.935804	+	0.352520i	$0.885325\pi$
$908$	28743.4	+	39561.8i	1.05053	+	1.44593i
$909$	−3645.69	−	11220.3i	−0.133025	−	0.409409i
$910$	1355.12	−	2734.55i	0.0493644	−	0.0996148i
$911$	5226.97	−	16087.0i	0.190096	−	0.585054i	−0.809903	−	0.586564i	$-0.800480\pi$
$911$	5226.97	−	16087.0i	0.190096	−	0.585054i	0.999999	+	0.00150920i	$0.000480392\pi$
$912$	56666.1	−	18411.9i	2.05746	−	0.668508i
$913$	4875.23	−	1584.06i	0.176721	−	0.0574202i
$914$	−103.803	+	319.472i	−0.00375655	+	0.0115615i
$915$	1270.92	+	7483.03i	0.0459184	+	0.270362i
$916$	3680.89	+	11328.6i	0.132773	+	0.408633i
$917$	−3585.03	−	4934.37i	−0.129104	−	0.177696i
$918$		−	225.495i		−	0.00810724i
$919$	21257.2	−	15444.3i	0.763014	−	0.554362i	−0.136819	−	0.990596i	$-0.543688\pi$
$919$	21257.2	−	15444.3i	0.763014	−	0.554362i	0.899833	+	0.436234i	$0.143688\pi$
$920$	−1307.10	+	8893.69i	−0.0468410	+	0.318714i
$921$	−9147.77	−	6646.24i	−0.327285	−	0.237786i
$922$	−1914.34	+	2634.86i	−0.0683789	+	0.0941155i
$923$	−22482.6	−	7305.03i	−0.801758	−	0.260507i
$924$	9683.51			0.344766
$925$	−32102.7	−	22247.0i	−1.14112	−	0.790785i
$926$	−1149.35			−0.0407884
$927$	−171.658	−	55.7752i	−0.00608199	−	0.00197616i
$928$	6349.25	−	8738.99i	0.224595	−	0.309129i
$929$	24697.2	+	17943.6i	0.872218	+	0.633703i	0.931181	−	0.364557i	$-0.118780\pi$
$929$	24697.2	+	17943.6i	0.872218	+	0.633703i	−0.0589635	+	0.998260i	$0.518780\pi$
$930$	540.103	−	552.289i	0.0190437	−	0.0194734i
$931$	16682.2	−	12120.3i	0.587256	−	0.426667i
$932$			6212.76i			0.218354i
$933$	−15217.3	−	20944.8i	−0.533968	−	0.734945i
$934$	−720.627	−	2217.86i	−0.0252459	−	0.0776988i
$935$	1141.94	+	167.829i	0.0399415	+	0.00587017i
$936$	1298.52	−	3996.44i	0.0453456	−	0.139559i
$937$	−2487.97	+	808.391i	−0.0867433	+	0.0281846i	−0.352067	−	0.935975i	$-0.614521\pi$
$937$	−2487.97	+	808.391i	−0.0867433	+	0.0281846i	0.265324	+	0.964159i	$0.414521\pi$
$938$	−2480.75	+	806.044i	−0.0863532	+	0.0280579i
$939$	−12995.4	+	39995.9i	−0.451640	+	1.39001i
$940$	−29755.1	−	4373.08i	−1.03245	−	0.151738i
$941$	504.114	+	1551.50i	0.0174640	+	0.0537487i	0.959409	−	0.282019i	$-0.0910042\pi$
$941$	504.114	+	1551.50i	0.0174640	+	0.0537487i	−0.941945	+	0.335768i	$0.891004\pi$
$942$	1642.80	+	2261.12i	0.0568210	+	0.0782075i
$943$			66763.6i			2.30554i
$944$	−29213.9	+	21225.1i	−1.00724	+	0.731800i
$945$	−9394.39	+	9606.35i	−0.323386	+	0.330682i
$946$	−163.319	−	118.658i	−0.00561306	−	0.00407813i
$947$	23363.2	−	32156.7i	0.801691	−	1.10343i	−0.190861	−	0.981617i	$-0.561128\pi$
$947$	23363.2	−	32156.7i	0.801691	−	1.10343i	0.992553	−	0.121816i	$-0.0388719\pi$
$948$	−22385.0	−	7273.33i	−0.766910	−	0.249184i
$949$	−9856.44			−0.337148
$950$	5463.75	+	3786.34i	0.186597	+	0.129311i
$951$	2720.32			0.0927575
$952$	−588.422	−	191.190i	−0.0200324	−	0.00650892i
$953$	4325.72	−	5953.84i	0.147034	−	0.202376i	−0.729147	−	0.684357i	$-0.760083\pi$
$953$	4325.72	−	5953.84i	0.147034	−	0.202376i	0.876181	+	0.481982i	$0.160083\pi$
$954$	943.156	+	685.243i	0.0320082	+	0.0232553i
$955$	−2840.43	+	19326.7i	−0.0962451	+	0.654866i
$956$	−28234.1	+	20513.3i	−0.955186	+	0.693983i
$957$		−	14032.9i		−	0.474001i
$958$	−2074.67	−	2855.53i	−0.0699681	−	0.0963029i
$959$	−3592.49	−	11056.5i	−0.120967	−	0.372298i
$960$	−5581.79	−	32865.0i	−0.187658	−	1.10491i
$961$	−8910.34	+	27423.2i	−0.299095	+	0.920520i
$962$	5629.04	−	1828.99i	0.188656	−	0.0612982i
$963$	−18946.3	+	6156.01i	−0.633992	+	0.205997i
$964$	6448.43	−	19846.2i	0.215446	−	0.663075i
$965$	−17750.2	+	35819.0i	−0.592124	+	1.19488i
$966$	−1443.36	−	4442.21i	−0.0480739	−	0.147956i
$967$	−3885.83	−	5348.38i	−0.129224	−	0.177862i	0.739502	−	0.673154i	$-0.235061\pi$
$967$	−3885.83	−	5348.38i	−0.129224	−	0.177862i	−0.868726	+	0.495292i	$0.835061\pi$
$968$		−	6392.08i		−	0.212241i
$969$	−6112.82	+	4441.22i	−0.202654	+	0.147237i
$970$	−3403.33	+	578.023i	−0.112654	+	0.0191332i
$971$	−10328.2	−	7503.88i	−0.341347	−	0.248003i	0.403883	−	0.914811i	$-0.367660\pi$
$971$	−10328.2	−	7503.88i	−0.341347	−	0.248003i	−0.745230	+	0.666808i	$0.767660\pi$
$972$	−16576.5	+	22815.6i	−0.547007	+	0.752891i
$973$	5081.44	+	1651.06i	0.167424	+	0.0543993i
$974$	−2611.34			−0.0859062
$975$	−40989.1	+	14336.7i	−1.34636	+	0.470916i
$976$	−6479.44			−0.212502
$977$	−47535.7	−	15445.3i	−1.55660	−	0.505771i	−0.600706	−	0.799470i	$-0.705114\pi$
$977$	−47535.7	−	15445.3i	−1.55660	−	0.505771i	−0.955898	+	0.293698i	$0.905114\pi$
$978$	3377.32	−	4648.48i	0.110424	−	0.151986i
$979$	5445.02	+	3956.04i	0.177756	+	0.129148i
$980$	−5529.73	−	10559.8i	−0.180246	−	0.344205i
$981$	−12747.8	+	9261.84i	−0.414890	+	0.301435i
$982$		−	32.8523i		−	0.00106757i
$983$	23700.0	+	32620.3i	0.768986	+	1.05842i	0.996413	+	0.0846232i	$0.0269687\pi$
$983$	23700.0	+	32620.3i	0.768986	+	1.05842i	−0.227427	+	0.973795i	$0.573031\pi$
$984$	5044.22	+	15524.5i	0.163419	+	0.502951i
$985$	41333.0	−	21644.4i	1.33704	−	0.700149i
$986$	−137.469	+	423.086i	−0.00444006	+	0.0136651i
$987$	29953.8	−	9732.58i	0.965998	−	0.313872i
$988$	61959.9	−	20132.0i	1.99515	−	0.648263i
$989$	1946.03	−	5989.25i	0.0625683	−	0.192565i
$990$	519.394	+	507.934i	0.0166742	+	0.0163063i
$991$	−2670.45	−	8218.80i	−0.0856001	−	0.263450i	0.899090	−	0.437764i	$-0.144229\pi$
$991$	−2670.45	−	8218.80i	−0.0856001	−	0.263450i	−0.984690	+	0.174314i	$0.944229\pi$
$992$	1193.55	+	1642.79i	0.0382010	+	0.0525791i
$993$		−	10390.4i		−	0.332052i
$994$	−1772.36	+	1287.69i	−0.0565551	+	0.0410897i
$995$	37079.7	+	18374.9i	1.18141	+	0.585452i
$996$	15693.9	+	11402.3i	0.499278	+	0.362746i
$997$	−18630.9	+	25643.2i	−0.591822	+	0.814573i	−0.994929	−	0.100580i	$-0.967930\pi$
$997$	−18630.9	+	25643.2i	−0.591822	+	0.814573i	0.403107	+	0.915153i	$0.367930\pi$
$998$	−4349.90	−	1413.37i	−0.137970	−	0.0448290i
$999$	−26057.9			−0.825261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.e.a.4.4	✓	24
3.2	odd	2		225.4.m.a.154.3		24
5.2	odd	4		125.4.d.b.101.6		48
5.3	odd	4		125.4.d.b.101.7		48
5.4	even	2		125.4.e.a.24.3		24
25.6	even	5		125.4.e.a.99.3		24
25.8	odd	20		125.4.d.b.26.7		48
25.12	odd	20		625.4.a.g.1.12		24
25.13	odd	20		625.4.a.g.1.13		24
25.17	odd	20		125.4.d.b.26.6		48
25.19	even	10	inner	25.4.e.a.19.4	yes	24
75.44	odd	10		225.4.m.a.19.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.e.a.4.4	✓	24	1.1	even	1	trivial
25.4.e.a.19.4	yes	24	25.19	even	10	inner
125.4.d.b.26.6		48	25.17	odd	20
125.4.d.b.26.7		48	25.8	odd	20
125.4.d.b.101.6		48	5.2	odd	4
125.4.d.b.101.7		48	5.3	odd	4
125.4.e.a.24.3		24	5.4	even	2
125.4.e.a.99.3		24	25.6	even	5
225.4.m.a.19.3		24	75.44	odd	10
225.4.m.a.154.3		24	3.2	odd	2
625.4.a.g.1.12		24	25.12	odd	20
625.4.a.g.1.13		24	25.13	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.331937 + 0.107853i) q^{2} +(3.76234 - 5.17842i) q^{3} +(-6.37359 - 4.63068i) q^{4} +(10.0178 + 4.96433i) q^{5} +(1.80737 - 1.31313i) q^{6} +14.4107i q^{7} +(-3.25738 - 4.48340i) q^{8} +(-4.31736 - 13.2875i) q^{9} +O(q^{10})\)	\(q+(0.331937 + 0.107853i) q^{2} +(3.76234 - 5.17842i) q^{3} +(-6.37359 - 4.63068i) q^{4} +(10.0178 + 4.96433i) q^{5} +(1.80737 - 1.31313i) q^{6} +14.4107i q^{7} +(-3.25738 - 4.48340i) q^{8} +(-4.31736 - 13.2875i) q^{9} +(2.78985 + 2.72829i) q^{10} +(-4.11778 + 12.6732i) q^{11} +(-47.9592 + 15.5829i) q^{12} +(-51.6163 + 16.7712i) q^{13} +(-1.55424 + 4.78345i) q^{14} +(63.3976 - 33.1987i) q^{15} +(18.8782 + 58.1013i) q^{16} +(-4.55371 - 6.26764i) q^{17} -4.87624i q^{18} +(123.269 - 89.5605i) q^{19} +(-40.8608 - 78.0296i) q^{20} +(74.6248 + 54.2181i) q^{21} +(-2.73369 + 3.76260i) q^{22} +(-137.982 - 44.8332i) q^{23} -35.4723 q^{24} +(75.7109 + 99.4629i) q^{25} -18.9422 q^{26} +(79.3136 + 25.7706i) q^{27} +(66.7315 - 91.8480i) q^{28} +(-133.102 - 96.7042i) q^{29} +(24.6246 - 4.18224i) q^{30} +(25.0210 - 18.1788i) q^{31} +65.6563i q^{32} +(50.1348 + 69.0046i) q^{33} +(-0.835560 - 2.57159i) q^{34} +(-71.5396 + 144.363i) q^{35} +(-34.0130 + 104.681i) q^{36} +(-297.170 + 96.5563i) q^{37} +(50.5770 - 16.4335i) q^{38} +(-107.350 + 330.390i) q^{39} +(-10.3746 - 61.0843i) q^{40} +(-142.202 - 437.652i) q^{41} +(18.9232 + 26.0455i) q^{42} +43.4059i q^{43} +(84.9307 - 61.7058i) q^{44} +(22.7131 - 154.543i) q^{45} +(-40.9661 - 29.7636i) q^{46} +(200.696 - 276.234i) q^{47} +(371.899 + 120.837i) q^{48} +135.331 q^{49} +(14.4039 + 41.1810i) q^{50} -49.5891 q^{51} +(406.643 + 132.126i) q^{52} +(-140.527 + 193.419i) q^{53} +(23.5477 + 17.1084i) q^{54} +(-104.165 + 106.515i) q^{55} +(64.6091 - 46.9412i) q^{56} -975.298i q^{57} +(-33.7516 - 46.4551i) q^{58} +(182.656 + 562.158i) q^{59} +(-557.803 - 81.9798i) q^{60} +(-32.7748 + 100.870i) q^{61} +(10.2660 - 3.33563i) q^{62} +(191.482 - 62.2163i) q^{63} +(143.945 - 443.016i) q^{64} +(-600.337 - 88.2310i) q^{65} +(9.19925 + 28.3124i) q^{66} +(304.832 + 419.565i) q^{67} +61.0341i q^{68} +(-751.303 + 545.853i) q^{69} +(-39.3166 + 40.2037i) q^{70} +(352.384 + 256.022i) q^{71} +(-45.5098 + 62.6389i) q^{72} +(172.721 + 56.1205i) q^{73} -109.055 q^{74} +(799.911 - 17.8493i) q^{75} -1200.39 q^{76} +(-182.630 - 59.3402i) q^{77} +(-71.2670 + 98.0905i) q^{78} +(377.609 + 274.349i) q^{79} +(-99.3162 + 675.762i) q^{80} +(737.037 - 535.489i) q^{81} -160.610i q^{82} +(-226.113 - 311.218i) q^{83} +(-224.561 - 691.128i) q^{84} +(-14.5033 - 85.3938i) q^{85} +(-4.68145 + 14.4080i) q^{86} +(-1001.55 + 325.423i) q^{87} +(70.2324 - 22.8199i) q^{88} +(156.078 - 480.360i) q^{89} +(24.2073 - 48.8490i) q^{90} +(-241.685 - 743.829i) q^{91} +(671.835 + 924.701i) q^{92} -197.964i q^{93} +(96.4111 - 70.0467i) q^{94} +(1679.49 - 285.245i) q^{95} +(339.996 + 247.022i) q^{96} +(-519.989 + 715.703i) q^{97} +(44.9213 + 14.5958i) q^{98} +186.173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

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