LMFDB - Embedded newform 48.4.j.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, 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:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	48.37
Dual form			48.4.j.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92738 + 2.07008i) q^{2} +(2.12132 - 2.12132i) q^{3} +(-0.570442 - 7.97964i) q^{4} +(-7.29121 - 7.29121i) q^{5} +(0.302715 + 8.47988i) q^{6} -22.1610i q^{7} +(17.6179 + 14.1989i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(-1.92738 + 2.07008i) q^{2} +(2.12132 - 2.12132i) q^{3} +(-0.570442 - 7.97964i) q^{4} +(-7.29121 - 7.29121i) q^{5} +(0.302715 + 8.47988i) q^{6} -22.1610i q^{7} +(17.6179 + 14.1989i) q^{8} -9.00000i q^{9} +(29.1463 - 1.04047i) q^{10} +(8.24116 + 8.24116i) q^{11} +(-18.1375 - 15.7173i) q^{12} +(51.9094 - 51.9094i) q^{13} +(45.8751 + 42.7127i) q^{14} -30.9340 q^{15} +(-63.3492 + 9.10384i) q^{16} -58.7304 q^{17} +(18.6307 + 17.3464i) q^{18} +(-54.5389 + 54.5389i) q^{19} +(-54.0220 + 62.3404i) q^{20} +(-47.0107 - 47.0107i) q^{21} +(-32.9437 + 1.17603i) q^{22} +117.989i q^{23} +(67.4937 - 7.25284i) q^{24} -18.6766i q^{25} +(7.40755 + 207.506i) q^{26} +(-19.0919 - 19.0919i) q^{27} +(-176.837 + 12.6416i) q^{28} +(175.283 - 175.283i) q^{29} +(59.6214 - 64.0357i) q^{30} -6.58699 q^{31} +(103.252 - 148.684i) q^{32} +34.9643 q^{33} +(113.195 - 121.576i) q^{34} +(-161.581 + 161.581i) q^{35} +(-71.8167 + 5.13398i) q^{36} +(265.451 + 265.451i) q^{37} +(-7.78278 - 218.017i) q^{38} -220.233i q^{39} +(-24.9288 - 231.983i) q^{40} -98.7545i q^{41} +(187.923 - 6.70849i) q^{42} +(347.544 + 347.544i) q^{43} +(61.0604 - 70.4626i) q^{44} +(-65.6209 + 65.6209i) q^{45} +(-244.247 - 227.410i) q^{46} -141.880 q^{47} +(-115.072 + 153.696i) q^{48} -148.112 q^{49} +(38.6620 + 35.9968i) q^{50} +(-124.586 + 124.586i) q^{51} +(-443.830 - 384.607i) q^{52} +(-210.101 - 210.101i) q^{53} +(76.3189 - 2.72444i) q^{54} -120.176i q^{55} +(314.662 - 390.432i) q^{56} +231.389i q^{57} +(25.0132 + 700.687i) q^{58} +(427.318 + 427.318i) q^{59} +(17.6460 + 246.842i) q^{60} +(178.341 - 178.341i) q^{61} +(12.6956 - 13.6356i) q^{62} -199.449 q^{63} +(108.782 + 500.310i) q^{64} -756.965 q^{65} +(-67.3893 + 72.3788i) q^{66} +(480.715 - 480.715i) q^{67} +(33.5023 + 468.647i) q^{68} +(250.293 + 250.293i) q^{69} +(-23.0578 - 645.912i) q^{70} -884.186i q^{71} +(127.790 - 158.561i) q^{72} +794.543i q^{73} +(-1061.13 + 37.8802i) q^{74} +(-39.6190 - 39.6190i) q^{75} +(466.312 + 404.090i) q^{76} +(182.633 - 182.633i) q^{77} +(455.899 + 424.472i) q^{78} -421.166 q^{79} +(528.270 + 395.514i) q^{80} -81.0000 q^{81} +(204.429 + 190.337i) q^{82} +(-167.507 + 167.507i) q^{83} +(-348.311 + 401.945i) q^{84} +(428.215 + 428.215i) q^{85} +(-1389.29 + 49.5951i) q^{86} -743.664i q^{87} +(28.1767 + 262.208i) q^{88} -664.016i q^{89} +(-9.36419 - 262.316i) q^{90} +(-1150.37 - 1150.37i) q^{91} +(941.513 - 67.3062i) q^{92} +(-13.9731 + 13.9731i) q^{93} +(273.457 - 293.703i) q^{94} +795.309 q^{95} +(-96.3763 - 534.438i) q^{96} -1083.81 q^{97} +(285.467 - 306.603i) q^{98} +(74.1705 - 74.1705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) $ 24 * q - 20 * q^4 + 84 * q^8	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.92738	+	2.07008i	−0.681430	+	0.731883i
$2$	−1.92738	+	2.07008i	−0.681430	+	0.731883i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$	−0.570442	−	7.97964i	−0.0713053	−	0.997455i
$5$	−7.29121	−	7.29121i	−0.652145	−	0.652145i	0.301364	−	0.953509i	$-0.402558\pi$
$5$	−7.29121	−	7.29121i	−0.652145	−	0.652145i	−0.953509	+	0.301364i	$0.902558\pi$
$6$	0.302715	+	8.47988i	0.0205972	+	0.576983i
$7$		−	22.1610i		−	1.19658i	−0.801278	−	0.598292i	$-0.795846\pi$
$7$		−	22.1610i		−	1.19658i	0.801278	−	0.598292i	$-0.204154\pi$
$8$	17.6179	+	14.1989i	0.778610	+	0.627509i
$9$		−	9.00000i		−	0.333333i
$10$	29.1463	−	1.04047i	0.921686	−	0.0329024i
$11$	8.24116	+	8.24116i	0.225891	+	0.225891i	0.810974	−	0.585083i	$-0.198938\pi$
$11$	8.24116	+	8.24116i	0.225891	+	0.225891i	−0.585083	+	0.810974i	$0.698938\pi$
$12$	−18.1375	−	15.7173i	−0.436319	−	0.378099i
$13$	51.9094	−	51.9094i	1.10747	−	1.10747i	0.113986	−	0.993482i	$-0.463638\pi$
$13$	51.9094	−	51.9094i	1.10747	−	1.10747i	0.993482	−	0.113986i	$-0.0363618\pi$
$14$	45.8751	+	42.7127i	0.875759	+	0.815389i
$15$	−30.9340			−0.532475
$16$	−63.3492	+	9.10384i	−0.989831	+	0.142248i
$17$	−58.7304			−0.837894			−0.418947	−	0.908011i	$-0.637601\pi$
$17$	−58.7304			−0.837894			−0.418947	+	0.908011i	$0.637601\pi$
$18$	18.6307	+	17.3464i	0.243961	+	0.227143i
$19$	−54.5389	+	54.5389i	−0.658531	+	0.658531i	−0.955032	−	0.296501i	$-0.904180\pi$
$19$	−54.5389	+	54.5389i	−0.658531	+	0.658531i	0.296501	+	0.955032i	$0.404180\pi$
$20$	−54.0220	+	62.3404i	−0.603984	+	0.696987i
$21$	−47.0107	−	47.0107i	−0.488503	−	0.488503i
$22$	−32.9437	+	1.17603i	−0.319255	+	0.0113968i
$23$			117.989i			1.06967i	0.844955	+	0.534837i	$0.179627\pi$
$23$			117.989i			1.06967i	−0.844955	+	0.534837i	$0.820373\pi$
$24$	67.4937	−	7.25284i	0.574045	−	0.0616867i
$25$		−	18.6766i		−	0.149413i
$26$	7.40755	+	207.506i	0.0558746	+	1.56520i
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$	−176.837	+	12.6416i	−1.19354	+	0.0853227i
$29$	175.283	−	175.283i	1.12239	−	1.12239i	0.131007	−	0.991381i	$-0.458179\pi$
$29$	175.283	−	175.283i	1.12239	−	1.12239i	0.991381	−	0.131007i	$-0.0418212\pi$
$30$	59.6214	−	64.0357i	0.362844	−	0.389709i
$31$	−6.58699			−0.0381631			−0.0190816	−	0.999818i	$-0.506074\pi$
$31$	−6.58699			−0.0381631			−0.0190816	+	0.999818i	$0.506074\pi$
$32$	103.252	−	148.684i	0.570392	−	0.821372i
$33$	34.9643			0.184439
$34$	113.195	−	121.576i	0.570967	−	0.613241i
$35$	−161.581	+	161.581i	−0.780347	+	0.780347i
$36$	−71.8167	+	5.13398i	−0.332485	+	0.0237684i
$37$	265.451	+	265.451i	1.17946	+	1.17946i	0.979883	+	0.199574i	$0.0639557\pi$
$37$	265.451	+	265.451i	1.17946	+	1.17946i	0.199574	+	0.979883i	$0.436044\pi$
$38$	−7.78278	−	218.017i	−0.0332246	−	0.930711i
$39$		−	220.233i		−	0.904244i
$40$	−24.9288	−	231.983i	−0.0985397	−	0.916994i
$41$		−	98.7545i		−	0.376167i	−0.982153	−	0.188084i	$-0.939772\pi$
$41$		−	98.7545i		−	0.376167i	0.982153	−	0.188084i	$-0.0602276\pi$
$42$	187.923	−	6.70849i	0.690408	−	0.0246462i
$43$	347.544	+	347.544i	1.23256	+	1.23256i	0.962978	+	0.269580i	$0.0868850\pi$
$43$	347.544	+	347.544i	1.23256	+	1.23256i	0.269580	+	0.962978i	$0.413115\pi$
$44$	61.0604	−	70.4626i	0.209209	−	0.241424i
$45$	−65.6209	+	65.6209i	−0.217382	+	0.217382i
$46$	−244.247	−	227.410i	−0.782876	−	0.728908i
$47$	−141.880			−0.440327			−0.220164	−	0.975463i	$-0.570659\pi$
$47$	−141.880			−0.440327			−0.220164	+	0.975463i	$0.570659\pi$
$48$	−115.072	+	153.696i	−0.346025	+	0.462169i
$49$	−148.112			−0.431813
$50$	38.6620	+	35.9968i	0.109353	+	0.101814i
$51$	−124.586	+	124.586i	−0.342069	+	0.342069i
$52$	−443.830	−	384.607i	−1.18362	−	1.02568i
$53$	−210.101	−	210.101i	−0.544520	−	0.544520i	0.380331	−	0.924850i	$-0.375810\pi$
$53$	−210.101	−	210.101i	−0.544520	−	0.544520i	−0.924850	+	0.380331i	$0.875810\pi$
$54$	76.3189	−	2.72444i	0.192328	−	0.00686572i
$55$		−	120.176i		−	0.294628i
$56$	314.662	−	390.432i	0.750867	−	0.931672i
$57$			231.389i			0.537688i
$58$	25.0132	+	700.687i	0.0566274	+	1.58629i
$59$	427.318	+	427.318i	0.942917	+	0.942917i	0.998457	−	0.0555392i	$-0.0176878\pi$
$59$	427.318	+	427.318i	0.942917	+	0.942917i	−0.0555392	+	0.998457i	$0.517688\pi$
$60$	17.6460	+	246.842i	0.0379682	+	0.531119i
$61$	178.341	−	178.341i	0.374332	−	0.374332i	−0.494720	−	0.869052i	$-0.664730\pi$
$61$	178.341	−	178.341i	0.374332	−	0.374332i	0.869052	+	0.494720i	$0.164730\pi$
$62$	12.6956	−	13.6356i	0.0260055	−	0.0279310i
$63$	−199.449			−0.398861
$64$	108.782	+	500.310i	0.212466	+	0.977169i
$65$	−756.965			−1.44446
$66$	−67.3893	+	72.3788i	−0.125683	+	0.134988i
$67$	480.715	−	480.715i	0.876547	−	0.876547i	−0.116628	−	0.993176i	$-0.537209\pi$
$67$	480.715	−	480.715i	0.876547	−	0.876547i	0.993176	+	0.116628i	$0.0372086\pi$
$68$	33.5023	+	468.647i	0.0597463	+	0.835761i
$69$	250.293	+	250.293i	0.436693	+	0.436693i
$70$	−23.0578	−	645.912i	−0.0393705	−	1.10287i
$71$		−	884.186i		−	1.47794i	−0.673740	−	0.738969i	$-0.735313\pi$
$71$		−	884.186i		−	1.47794i	0.673740	−	0.738969i	$-0.264687\pi$
$72$	127.790	−	158.561i	0.209170	−	0.259537i
$73$			794.543i			1.27389i	0.770908	+	0.636947i	$0.219803\pi$
$73$			794.543i			1.27389i	−0.770908	+	0.636947i	$0.780197\pi$
$74$	−1061.13	+	37.8802i	−1.66694	+	0.0595066i
$75$	−39.6190	−	39.6190i	−0.0609975	−	0.0609975i
$76$	466.312	+	404.090i	0.703812	+	0.609898i
$77$	182.633	−	182.633i	0.270298	−	0.270298i
$78$	455.899	+	424.472i	0.661801	+	0.616179i
$79$	−421.166			−0.599809			−0.299904	−	0.953969i	$-0.596955\pi$
$79$	−421.166			−0.599809			−0.299904	+	0.953969i	$0.596955\pi$
$80$	528.270	+	395.514i	0.738280	+	0.552748i
$81$	−81.0000			−0.111111
$82$	204.429	+	190.337i	0.275310	+	0.256332i
$83$	−167.507	+	167.507i	−0.221522	+	0.221522i	−0.809139	−	0.587617i	$-0.800066\pi$
$83$	−167.507	+	167.507i	−0.221522	+	0.221522i	0.587617	+	0.809139i	$0.300066\pi$
$84$	−348.311	+	401.945i	−0.452427	+	0.522093i
$85$	428.215	+	428.215i	0.546429	+	0.546429i
$86$	−1389.29	+	49.5951i	−1.74199	+	0.0621857i
$87$		−	743.664i		−	0.916427i
$88$	28.1767	+	262.208i	0.0341324	+	0.317630i
$89$		−	664.016i		−	0.790849i	−0.918498	−	0.395425i	$-0.870597\pi$
$89$		−	664.016i		−	0.790849i	0.918498	−	0.395425i	$-0.129403\pi$
$90$	−9.36419	−	262.316i	−0.0109675	−	0.307229i
$91$	−1150.37	−	1150.37i	−1.32518	−	1.32518i
$92$	941.513	−	67.3062i	1.06695	−	0.0762734i
$93$	−13.9731	+	13.9731i	−0.0155800	+	0.0155800i
$94$	273.457	−	293.703i	0.300052	−	0.322268i
$95$	795.309			0.858916
$96$	−96.3763	−	534.438i	−0.102462	−	0.568186i
$97$	−1083.81			−1.13447			−0.567236	−	0.823555i	$-0.691987\pi$
$97$	−1083.81			−1.13447			−0.567236	+	0.823555i	$0.691987\pi$
$98$	285.467	−	306.603i	0.294251	−	0.316037i
$99$	74.1705	−	74.1705i	0.0752971	−	0.0752971i
$100$	−149.032	+	10.6539i	−0.149032	+	0.0106539i
$101$	−600.838	−	600.838i	−0.591937	−	0.591937i	0.346217	−	0.938154i	$-0.387466\pi$
$101$	−600.838	−	600.838i	−0.591937	−	0.591937i	−0.938154	+	0.346217i	$0.887466\pi$
$102$	−17.7786	−	498.026i	−0.0172583	−	0.483451i
$103$		−	30.6830i		−	0.0293523i	−0.999892	−	0.0146762i	$-0.995328\pi$
$103$		−	30.6830i		−	0.0293523i	0.999892	−	0.0146762i	$-0.00467173\pi$
$104$	1651.59	−	177.479i	1.55723	−	0.167339i
$105$			685.529i			0.637150i
$106$	839.867	−	29.9816i	0.769577	−	0.0274724i
$107$	812.356	+	812.356i	0.733957	+	0.733957i	0.971401	−	0.237444i	$-0.0763097\pi$
$107$	812.356	+	812.356i	0.733957	+	0.733957i	−0.237444	+	0.971401i	$0.576310\pi$
$108$	−141.455	+	163.237i	−0.126033	+	0.145440i
$109$	−148.034	+	148.034i	−0.130083	+	0.130083i	−0.769151	−	0.639067i	$-0.779321\pi$
$109$	−148.034	+	148.034i	−0.130083	+	0.130083i	0.639067	+	0.769151i	$0.279321\pi$
$110$	248.774	+	231.624i	0.215633	+	0.200768i
$111$	1126.21			0.963022
$112$	201.751	+	1403.88i	0.170211	+	1.18442i
$113$	1801.39			1.49965			0.749826	−	0.661635i	$-0.230137\pi$
$113$	1801.39			1.49965			0.749826	+	0.661635i	$0.230137\pi$
$114$	−478.993	−	445.974i	−0.393525	−	0.366397i
$115$	860.286	−	860.286i	0.697583	−	0.697583i
$116$	−1498.69	−	1298.71i	−1.19956	−	1.03950i
$117$	−467.185	−	467.185i	−0.369156	−	0.369156i
$118$	−1708.19	+	60.9789i	−1.33264	+	0.0475726i
$119$			1301.53i			1.00261i
$120$	−544.992	−	439.228i	−0.414590	−	0.334132i
$121$		−	1195.17i		−	0.897946i
$122$	25.4495	+	712.910i	0.0188860	+	0.529048i
$123$	−209.490	−	209.490i	−0.153570	−	0.153570i
$124$	3.75749	+	52.5617i	0.00272123	+	0.0380660i
$125$	−1047.58	+	1047.58i	−0.749584	+	0.749584i
$126$	384.414	−	412.876i	0.271796	−	0.291920i
$127$	−876.738			−0.612582			−0.306291	−	0.951938i	$-0.599088\pi$
$127$	−876.738			−0.612582			−0.306291	+	0.951938i	$0.599088\pi$
$128$	−1245.35	−	739.098i	−0.859954	−	0.510372i
$129$	1474.51			1.00638
$130$	1458.96	−	1566.98i	0.984299	−	1.05718i
$131$	−1355.99	+	1355.99i	−0.904374	+	0.904374i	−0.995811	−	0.0914368i	$-0.970854\pi$
$131$	−1355.99	+	1355.99i	−0.904374	+	0.904374i	0.0914368	+	0.995811i	$0.470854\pi$
$132$	−19.9451	−	279.002i	−0.0131515	−	0.183970i
$133$	1208.64	+	1208.64i	0.787988	+	0.787988i
$134$	68.5987	+	1921.64i	0.0442241	+	1.23884i
$135$			278.406i			0.177492i
$136$	−1034.71	−	833.906i	−0.652392	−	0.525786i
$137$			1833.19i			1.14321i	0.820529	+	0.571605i	$0.193679\pi$
$137$			1833.19i			1.14321i	−0.820529	+	0.571605i	$0.806321\pi$
$138$	−1000.54	+	35.7172i	−0.617183	+	0.0220323i
$139$	−705.601	−	705.601i	−0.430563	−	0.430563i	0.458257	−	0.888820i	$-0.348474\pi$
$139$	−705.601	−	705.601i	−0.430563	−	0.430563i	−0.888820	+	0.458257i	$0.848474\pi$
$140$	1381.53	+	1197.18i	0.834003	+	0.722718i
$141$	−300.974	+	300.974i	−0.179763	+	0.179763i
$142$	1830.33	+	1704.16i	1.08168	+	1.00711i
$143$	855.588			0.500335
$144$	81.9346	+	570.143i	0.0474158	+	0.329944i
$145$	−2556.05			−1.46392
$146$	−1644.77	−	1531.38i	−0.932341	−	0.868070i
$147$	−314.193	+	314.193i	−0.176287	+	0.176287i
$148$	1966.78	−	2269.63i	1.09235	−	1.26056i
$149$	−714.815	−	714.815i	−0.393020	−	0.393020i	0.482743	−	0.875762i	$-0.339641\pi$
$149$	−714.815	−	714.815i	−0.393020	−	0.393020i	−0.875762	+	0.482743i	$0.839641\pi$
$150$	158.375	−	5.65369i	0.0862085	−	0.00307748i
$151$			3190.79i			1.71962i	0.510614	+	0.859810i	$0.329418\pi$
$151$			3190.79i			1.71962i	−0.510614	+	0.859810i	$0.670582\pi$
$152$	−1735.26	+	186.470i	−0.925973	+	0.0995046i
$153$			528.573i			0.279298i
$154$	26.0619	+	730.066i	0.0136372	+	0.382016i
$155$	48.0271	+	48.0271i	0.0248879	+	0.0248879i
$156$	−1757.38	+	125.630i	−0.901942	+	0.0644773i
$157$	471.880	−	471.880i	0.239874	−	0.239874i	−0.576924	−	0.816798i	$-0.695747\pi$
$157$	471.880	−	471.880i	0.239874	−	0.239874i	0.816798	+	0.576924i	$0.195747\pi$
$158$	811.746	−	871.847i	0.408728	−	0.438990i
$159$	−891.381			−0.444598
$160$	−1836.92	+	331.256i	−0.907633	+	0.163675i
$161$	2614.77			1.27995
$162$	156.117	−	167.676i	0.0757145	−	0.0813203i
$163$	275.466	−	275.466i	0.132369	−	0.132369i	−0.637818	−	0.770187i	$-0.720163\pi$
$163$	275.466	−	275.466i	0.132369	−	0.132369i	0.770187	+	0.637818i	$0.220163\pi$
$164$	−788.025	+	56.3337i	−0.375210	+	0.0268227i
$165$	−254.932	−	254.932i	−0.120281	−	0.120281i
$166$	−23.9035	−	669.602i	−0.0111763	−	0.313080i
$167$			1754.52i			0.812988i	0.913653	+	0.406494i	$0.133249\pi$
$167$			1754.52i			0.812988i	−0.913653	+	0.406494i	$0.866751\pi$
$168$	−160.731	−	1495.73i	−0.0738133	−	0.686893i
$169$		−	3192.18i		−	1.45297i
$170$	−1711.77	+	61.1069i	−0.772275	+	0.0275687i
$171$	490.850	+	490.850i	0.219510	+	0.219510i
$172$	2575.02	−	2971.53i	1.14153	−	1.31731i
$173$	972.532	−	972.532i	0.427400	−	0.427400i	−0.460342	−	0.887742i	$-0.652273\pi$
$173$	972.532	−	972.532i	0.427400	−	0.427400i	0.887742	+	0.460342i	$0.152273\pi$
$174$	1539.44	+	1433.32i	0.670717	+	0.624481i
$175$	−413.893			−0.178785
$176$	−597.097	−	447.045i	−0.255727	−	0.191462i
$177$	1812.96			0.769889
$178$	1374.57	+	1279.81i	0.578809	+	0.538909i
$179$	1944.54	−	1944.54i	0.811964	−	0.811964i	−0.172964	−	0.984928i	$-0.555335\pi$
$179$	1944.54	−	1944.54i	0.811964	−	0.811964i	0.984928	+	0.172964i	$0.0553345\pi$
$180$	561.064	+	486.198i	0.232329	+	0.201328i
$181$	−1388.85	−	1388.85i	−0.570345	−	0.570345i	0.361880	−	0.932225i	$-0.382135\pi$
$181$	−1388.85	−	1388.85i	−0.570345	−	0.570345i	−0.932225	+	0.361880i	$0.882135\pi$
$182$	4598.54	−	164.159i	1.87289	−	0.0668586i
$183$		−	756.637i		−	0.305641i
$184$	−1675.32	+	2078.73i	−0.671230	+	0.832858i
$185$		−	3870.92i		−	1.53835i
$186$	−1.99398	−	55.8568i	−0.000786053	−	0.0220195i
$187$	−484.006	−	484.006i	−0.189273	−	0.189273i
$188$	80.9345	+	1132.15i	0.0313976	+	0.439206i
$189$	−423.096	+	423.096i	−0.162834	+	0.162834i
$190$	−1532.86	+	1646.35i	−0.585292	+	0.628626i
$191$	−1754.58			−0.664695			−0.332347	−	0.943157i	$-0.607841\pi$
$191$	−1754.58			−0.664695			−0.332347	+	0.943157i	$0.607841\pi$
$192$	1292.08	+	830.556i	0.485666	+	0.312189i
$193$	4111.28			1.53335			0.766675	−	0.642036i	$-0.221910\pi$
$193$	4111.28			1.53335			0.766675	+	0.642036i	$0.221910\pi$
$194$	2088.90	−	2243.56i	0.773063	−	0.830300i
$195$	−1605.76	+	1605.76i	−0.589698	+	0.589698i
$196$	84.4893	+	1181.88i	0.0307906	+	0.430714i
$197$	−585.319	−	585.319i	−0.211686	−	0.211686i	0.593297	−	0.804984i	$-0.297826\pi$
$197$	−585.319	−	585.319i	−0.211686	−	0.211686i	−0.804984	+	0.593297i	$0.797826\pi$
$198$	10.5842	+	296.493i	0.00379893	+	0.106418i
$199$			2620.65i			0.933533i	0.884381	+	0.466766i	$0.154581\pi$
$199$			2620.65i			0.933533i	−0.884381	+	0.466766i	$0.845419\pi$
$200$	265.187	−	329.043i	0.0937577	−	0.116334i
$201$		−	2039.50i		−	0.715698i
$202$	2401.82	−	85.7405i	0.836593	−	0.0298647i
$203$	−3884.46	−	3884.46i	−1.34303	−	1.34303i
$204$	1065.22	+	923.081i	0.365589	+	0.316807i
$205$	−720.039	+	720.039i	−0.245316	+	0.245316i
$206$	63.5162	+	59.1377i	0.0214825	+	0.0200016i
$207$	1061.91			0.356558
$208$	−2815.84	+	3761.00i	−0.938672	+	1.25374i
$209$	−898.929			−0.297513
$210$	−1419.10	−	1321.27i	−0.466320	−	0.434174i
$211$	969.705	−	969.705i	0.316385	−	0.316385i	−0.530992	−	0.847377i	$-0.678181\pi$
$211$	969.705	−	969.705i	0.316385	−	0.316385i	0.847377	+	0.530992i	$0.178181\pi$
$212$	−1556.68	+	1796.38i	−0.504306	+	0.581961i
$213$	−1875.64	−	1875.64i	−0.603365	−	0.603365i
$214$	−3247.35	+	115.924i	−1.03731	+	0.0370300i
$215$		−	5068.04i		−	1.60761i
$216$	−65.2756	−	607.443i	−0.0205622	−	0.191348i
$217$			145.974i			0.0456654i
$218$	−21.1247	−	591.760i	−0.00656304	−	0.183849i
$219$	1685.48	+	1685.48i	0.520065	+	0.520065i
$220$	−958.961	+	68.5535i	−0.293878	+	0.0210085i
$221$	−3048.66	+	3048.66i	−0.927941	+	0.927941i
$222$	−2170.64	+	2331.35i	−0.656233	+	0.704820i
$223$	63.3747			0.0190309			0.00951544	−	0.999955i	$-0.496971\pi$
$223$	63.3747			0.0190309			0.00951544	+	0.999955i	$0.496971\pi$
$224$	−3295.00	−	2288.17i	−0.982841	−	0.682522i
$225$	−168.089			−0.0498042
$226$	−3471.96	+	3729.02i	−1.02191	+	1.09757i
$227$	−1802.55	+	1802.55i	−0.527047	+	0.527047i	−0.919691	−	0.392644i	$-0.871561\pi$
$227$	−1802.55	+	1802.55i	−0.527047	+	0.527047i	0.392644	+	0.919691i	$0.371561\pi$
$228$	1846.40	−	131.994i	0.536320	−	0.0383400i
$229$	2895.47	+	2895.47i	0.835538	+	0.835538i	0.988268	−	0.152730i	$-0.0488066\pi$
$229$	2895.47	+	2895.47i	0.835538	+	0.835538i	−0.152730	+	0.988268i	$0.548807\pi$
$230$	122.764	+	3438.95i	0.0351948	+	0.985903i
$231$		−	774.845i		−	0.220697i
$232$	5576.96	−	599.297i	1.57821	−	0.169594i
$233$			4262.01i			1.19834i	0.800621	+	0.599171i	$0.204503\pi$
$233$			4262.01i			1.19834i	−0.800621	+	0.599171i	$0.795497\pi$
$234$	1867.55	−	66.6679i	0.521733	−	0.0186249i
$235$	1034.48	+	1034.48i	0.287157	+	0.287157i
$236$	3166.09	−	3653.61i	0.873282	−	1.00775i
$237$	−893.428	+	893.428i	−0.244871	+	0.244871i
$238$	−2694.26	−	2508.53i	−0.733794	−	0.683209i
$239$	3308.14			0.895337			0.447669	−	0.894200i	$-0.352254\pi$
$239$	3308.14			0.895337			0.447669	+	0.894200i	$0.352254\pi$
$240$	1959.64	−	281.618i	0.527060	−	0.0757432i
$241$	−3200.02			−0.855316			−0.427658	−	0.903941i	$-0.640661\pi$
$241$	−3200.02			−0.855316			−0.427658	+	0.903941i	$0.640661\pi$
$242$	2474.09	+	2303.54i	0.657192	+	0.611888i
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$	−1524.83	−	1321.36i	−0.400071	−	0.346687i
$245$	1079.91	+	1079.91i	0.281605	+	0.281605i
$246$	837.426	−	29.8945i	0.217042	−	0.00774798i
$247$			5662.17i			1.45860i
$248$	−116.049	−	93.5280i	−0.0297142	−	0.0239477i
$249$			710.673i			0.180872i
$250$	−149.491	−	4187.64i	−0.0378184	−	1.05940i
$251$	−1945.31	−	1945.31i	−0.489190	−	0.489190i	0.418860	−	0.908051i	$-0.362430\pi$
$251$	−1945.31	−	1945.31i	−0.489190	−	0.489190i	−0.908051	+	0.418860i	$0.862430\pi$
$252$	113.774	+	1591.53i	0.0284409	+	0.397846i
$253$	−972.370	+	972.370i	−0.241630	+	0.241630i
$254$	1689.80	−	1814.92i	0.417432	−	0.448339i
$255$	1816.76			0.446157
$256$	3930.24	−	1153.44i	0.959531	−	0.281602i
$257$	−82.9830			−0.0201414			−0.0100707	−	0.999949i	$-0.503206\pi$
$257$	−82.9830			−0.0201414			−0.0100707	+	0.999949i	$0.503206\pi$
$258$	−2841.93	+	3052.34i	−0.685778	+	0.736552i
$259$	5882.67	−	5882.67i	1.41132	−	1.41132i
$260$	431.805	+	6040.30i	0.102998	+	1.44078i
$261$	−1577.55	−	1577.55i	−0.374130	−	0.374130i
$262$	−193.501	−	5420.49i	−0.0456280	−	1.27816i
$263$		−	2139.57i		−	0.501641i	−0.968034	−	0.250821i	$-0.919300\pi$
$263$		−	2139.57i		−	0.501641i	0.968034	−	0.250821i	$-0.0807004\pi$
$264$	615.998	+	496.455i	0.143606	+	0.115737i
$265$			3063.77i			0.710212i
$266$	−4831.48	+	172.475i	−1.11367	+	0.0397560i
$267$	−1408.59	−	1408.59i	−0.322863	−	0.322863i
$268$	−4110.15	−	3561.71i	−0.936818	−	0.811814i
$269$	2564.40	−	2564.40i	0.581243	−	0.581243i	−0.354002	−	0.935245i	$-0.615179\pi$
$269$	2564.40	−	2564.40i	0.581243	−	0.581243i	0.935245	+	0.354002i	$0.115179\pi$
$270$	−576.322	−	536.593i	−0.129903	−	0.120948i
$271$	1373.88			0.307960			0.153980	−	0.988074i	$-0.450791\pi$
$271$	1373.88			0.307960			0.153980	+	0.988074i	$0.450791\pi$
$272$	3720.52	−	534.672i	0.829374	−	0.119188i
$273$	−4880.59			−1.08200
$274$	−3794.84	−	3533.24i	−0.836696	−	0.779018i
$275$	153.917	−	153.917i	0.0337510	−	0.0337510i
$276$	1854.47	−	2140.03i	0.404443	−	0.466719i
$277$	1763.08	+	1763.08i	0.382431	+	0.382431i	0.871977	−	0.489546i	$-0.162838\pi$
$277$	1763.08	+	1763.08i	0.382431	+	0.382431i	−0.489546	+	0.871977i	$0.662838\pi$
$278$	2820.61	−	100.690i	0.608521	−	0.0217230i
$279$			59.2829i			0.0127210i
$280$	−5140.99	+	552.448i	−1.09726	+	0.117911i
$281$			8170.89i			1.73464i	0.497748	+	0.867321i	$0.334160\pi$
$281$			8170.89i			1.73464i	−0.497748	+	0.867321i	$0.665840\pi$
$282$	−42.9493	−	1203.13i	−0.00906949	−	0.254061i
$283$	1217.94	+	1217.94i	0.255827	+	0.255827i	0.823354	−	0.567528i	$-0.192100\pi$
$283$	1217.94	+	1217.94i	0.255827	+	0.255827i	−0.567528	+	0.823354i	$0.692100\pi$
$284$	−7055.48	+	504.377i	−1.47418	+	0.105385i
$285$	1687.11	−	1687.11i	0.350651	−	0.350651i
$286$	−1649.04	+	1771.13i	−0.340943	+	0.366186i
$287$	−2188.50			−0.450116
$288$	−1338.16	−	929.269i	−0.273791	−	0.190131i
$289$	−1463.75			−0.297933
$290$	4926.47	−	5291.23i	0.997561	−	1.07142i
$291$	−2299.10	+	2299.10i	−0.463146	+	0.463146i
$292$	6340.16	−	453.241i	1.27065	−	0.0908353i
$293$	2994.08	+	2994.08i	0.596984	+	0.596984i	0.939509	−	0.342525i	$-0.111282\pi$
$293$	2994.08	+	2994.08i	0.596984	+	0.596984i	−0.342525	+	0.939509i	$0.611282\pi$
$294$	−44.8357	−	1255.97i	−0.00889413	−	0.249149i
$295$		−	6231.33i		−	1.22984i
$296$	907.583	+	8445.81i	0.178217	+	1.65846i
$297$		−	314.679i		−	0.0614798i
$298$	2857.44	−	102.005i	0.555460	−	0.0198288i
$299$	6124.76	+	6124.76i	1.18463	+	1.18463i
$300$	−293.545	+	338.746i	−0.0564928	+	0.0651916i
$301$	7701.94	−	7701.94i	1.47486	−	1.47486i
$302$	−6605.18	−	6149.85i	−1.25856	−	1.17180i
$303$	−2549.14			−0.483315
$304$	2958.48	−	3951.51i	0.558160	−	0.745509i
$305$	−2600.64			−0.488238
$306$	−1094.19	−	1018.76i	−0.204414	−	0.190322i
$307$	−5382.02	+	5382.02i	−1.00055	+	1.00055i	−0.000548529		1.00000i	$0.500175\pi$
$307$	−5382.02	+	5382.02i	−1.00055	+	1.00055i	−1.00000		0.000548529i	$0.999825\pi$
$308$	−1561.52	−	1353.16i	−0.288884	−	0.250336i
$309$	−65.0885	−	65.0885i	−0.0119830	−	0.0119830i
$310$	−191.986	+	6.85353i	−0.0351744	+	0.00125566i
$311$		−	7805.69i		−	1.42322i	−0.702577	−	0.711608i	$-0.747967\pi$
$311$		−	7805.69i		−	1.42322i	0.702577	−	0.711608i	$-0.252033\pi$
$312$	3127.07	−	3880.05i	0.567421	−	0.704053i
$313$		−	1549.25i		−	0.279772i	−0.990168	−	0.139886i	$-0.955326\pi$
$313$		−	1549.25i		−	0.279772i	0.990168	−	0.139886i	$-0.0446736\pi$
$314$	67.3380	+	1886.32i	0.0121022	+	0.339017i
$315$	1454.23	+	1454.23i	0.260116	+	0.260116i
$316$	240.251	+	3360.75i	0.0427695	+	0.598282i
$317$	−6112.35	+	6112.35i	−1.08298	+	1.08298i	−0.0867460	+	0.996230i	$0.527647\pi$
$317$	−6112.35	+	6112.35i	−1.08298	+	1.08298i	−0.996230	+	0.0867460i	$0.972353\pi$
$318$	1718.03	−	1845.23i	0.302963	−	0.325394i
$319$	2889.07			0.507076
$320$	2854.71	−	4441.02i	0.498698	−	0.775814i
$321$	3446.53			0.599273
$322$	−5039.64	+	5412.78i	−0.872200	+	0.936777i
$323$	3203.09	−	3203.09i	0.551779	−	0.551779i
$324$	46.2058	+	646.351i	0.00792281	+	0.110828i
$325$	−969.491	−	969.491i	−0.165470	−	0.165470i
$326$	39.3094	+	1101.16i	0.00667836	+	0.187079i
$327$			628.056i			0.106213i
$328$	1402.21	−	1739.85i	0.236048	−	0.292887i
$329$			3144.22i			0.526888i
$330$	1019.08	−	36.3791i	0.169995	−	0.00606850i
$331$	3539.08	+	3539.08i	0.587690	+	0.587690i	0.937005	−	0.349316i	$-0.113586\pi$
$331$	3539.08	+	3539.08i	0.587690	+	0.587690i	−0.349316	+	0.937005i	$0.613586\pi$
$332$	1432.20	+	1241.09i	0.236753	+	0.205162i
$333$	2389.06	−	2389.06i	0.393152	−	0.393152i
$334$	−3632.00	−	3381.62i	−0.595012	−	0.553995i
$335$	−7009.98			−1.14327
$336$	3406.07	+	2550.11i	0.553024	+	0.414047i
$337$	−7315.83			−1.18255			−0.591274	−	0.806471i	$-0.701375\pi$
$337$	−7315.83			−1.18255			−0.591274	+	0.806471i	$0.701375\pi$
$338$	6608.05	+	6152.52i	1.06340	+	0.990098i
$339$	3821.33	−	3821.33i	0.612231	−	0.612231i
$340$	3172.73	−	3661.27i	0.506075	−	0.584001i
$341$	−54.2844	−	54.2844i	−0.00862072	−	0.00862072i
$342$	−1962.15	+	70.0450i	−0.310237	+	0.0110749i
$343$		−	4318.92i		−	0.679883i
$344$	1188.26	+	11057.8i	0.186241	+	1.73312i
$345$		−	3649.88i		−	0.569574i
$346$	138.782	+	3887.65i	0.0215634	+	0.604050i
$347$	−1214.48	−	1214.48i	−0.187886	−	0.187886i	0.606895	−	0.794782i	$-0.292415\pi$
$347$	−1214.48	−	1214.48i	−0.187886	−	0.187886i	−0.794782	+	0.606895i	$0.792415\pi$
$348$	−5934.17	+	424.217i	−0.914094	+	0.0653460i
$349$	−3823.99	+	3823.99i	−0.586514	+	0.586514i	−0.936686	−	0.350171i	$-0.886123\pi$
$349$	−3823.99	+	3823.99i	−0.586514	+	0.586514i	0.350171	+	0.936686i	$0.386123\pi$
$350$	797.727	−	856.790i	0.121829	−	0.130850i
$351$	−1982.10			−0.301415
$352$	2076.25	−	374.414i	0.314388	−	0.0566942i
$353$	4475.44			0.674797			0.337399	−	0.941362i	$-0.390453\pi$
$353$	4475.44			0.674797			0.337399	+	0.941362i	$0.390453\pi$
$354$	−3494.25	+	3752.96i	−0.524626	+	0.563468i
$355$	−6446.78	+	6446.78i	−0.963830	+	0.963830i
$356$	−5298.61	+	378.783i	−0.788836	+	0.0563917i
$357$	2760.95	+	2760.95i	0.409314	+	0.409314i
$358$	277.488	+	7773.20i	0.0409656	+	1.14756i
$359$			1340.95i			0.197138i	0.995130	+	0.0985688i	$0.0314264\pi$
$359$			1340.95i			0.197138i	−0.995130	+	0.0985688i	$0.968574\pi$
$360$	−2087.85	+	224.359i	−0.305665	+	0.0328466i
$361$			910.008i			0.132674i
$362$	5551.87	−	198.191i	0.806077	−	0.0287754i
$363$	−2535.33	−	2535.33i	−0.366585	−	0.366585i
$364$	−8523.29	+	9835.73i	−1.22731	+	1.41630i
$365$	5793.18	−	5793.18i	0.830764	−	0.830764i
$366$	1566.30	+	1458.32i	0.223693	+	0.208273i
$367$	−5859.22			−0.833376			−0.416688	−	0.909050i	$-0.636809\pi$
$367$	−5859.22			−0.833376			−0.416688	+	0.909050i	$0.636809\pi$
$368$	−1074.16	−	7474.54i	−0.152158	−	1.05880i
$369$	−888.790			−0.125389
$370$	8013.10	+	7460.72i	1.12590	+	1.04828i
$371$	−4656.05	+	4656.05i	−0.651563	+	0.651563i
$372$	119.471	+	103.529i	0.0166513	+	0.0144294i
$373$	−4717.98	−	4717.98i	−0.654927	−	0.654927i	0.299248	−	0.954175i	$-0.403264\pi$
$373$	−4717.98	−	4717.98i	−0.654927	−	0.654927i	−0.954175	+	0.299248i	$0.903264\pi$
$374$	1934.79	−	69.0684i	0.267502	−	0.00954931i
$375$			4444.49i			0.612033i
$376$	−2499.64	−	2014.54i	−0.342843	−	0.276309i
$377$		−	18197.7i		−	2.48602i
$378$	−60.3764	−	1691.31i	−0.00821541	−	0.230136i
$379$	252.484	+	252.484i	0.0342197	+	0.0342197i	0.724010	−	0.689790i	$-0.242297\pi$
$379$	252.484	+	252.484i	0.0342197	+	0.0342197i	−0.689790	+	0.724010i	$0.742297\pi$
$380$	−453.678	−	6346.28i	−0.0612452	−	0.856730i
$381$	−1859.84	+	1859.84i	−0.250086	+	0.250086i
$382$	3381.73	−	3632.11i	0.452943	−	0.486479i
$383$	2526.32			0.337047			0.168524	−	0.985698i	$-0.446100\pi$
$383$	2526.32			0.337047			0.168524	+	0.985698i	$0.446100\pi$
$384$	−4209.64	+	1073.91i	−0.559433	+	0.142716i
$385$	−2663.23			−0.352547
$386$	−7923.98	+	8510.67i	−1.04487	+	1.12223i
$387$	3127.90	−	3127.90i	0.410853	−	0.410853i
$388$	618.248	+	8648.37i	0.0808938	+	1.13158i
$389$	1772.59	+	1772.59i	0.231038	+	0.231038i	0.813126	−	0.582088i	$-0.197764\pi$
$389$	1772.59	+	1772.59i	0.231038	+	0.231038i	−0.582088	+	0.813126i	$0.697764\pi$
$390$	−229.145	−	6418.97i	−0.0297518	−	0.833429i
$391$		−	6929.56i		−	0.896274i
$392$	−2609.42	−	2103.03i	−0.336214	−	0.270967i
$393$			5752.96i			0.738418i
$394$	2339.78	−	83.5258i	0.299179	−	0.0106801i
$395$	3070.81	+	3070.81i	0.391163	+	0.391163i
$396$	−634.163	−	549.543i	−0.0804745	−	0.0697363i
$397$	4182.28	−	4182.28i	0.528722	−	0.528722i	−0.391469	−	0.920191i	$-0.628033\pi$
$397$	4182.28	−	4182.28i	0.528722	−	0.528722i	0.920191	+	0.391469i	$0.128033\pi$
$398$	−5424.95	−	5050.98i	−0.683237	−	0.636138i
$399$	5127.82			0.643389
$400$	170.029	+	1183.15i	0.0212536	+	0.147893i
$401$	−5929.46			−0.738411			−0.369206	−	0.929348i	$-0.620370\pi$
$401$	−5929.46			−0.738411			−0.369206	+	0.929348i	$0.620370\pi$
$402$	4221.92	+	3930.88i	0.523807	+	0.487698i
$403$	−341.927	+	341.927i	−0.0422645	+	0.0422645i
$404$	−4451.73	+	5137.21i	−0.548222	+	0.632639i
$405$	590.588	+	590.588i	0.0724606	+	0.0724606i
$406$	15527.9	−	554.318i	1.89813	−	0.0677594i
$407$			4375.25i			0.532858i
$408$	−3963.93	+	425.962i	−0.480989	+	0.0516869i
$409$		−	9651.64i		−	1.16685i	−0.812166	−	0.583427i	$-0.801712\pi$
$409$		−	9651.64i		−	1.16685i	0.812166	−	0.583427i	$-0.198288\pi$
$410$	−102.751	−	2878.32i	−0.0123768	−	0.346708i
$411$	3888.78	+	3888.78i	0.466713	+	0.466713i
$412$	−244.839	+	17.5029i	−0.0292776	+	0.00209297i
$413$	9469.82	−	9469.82i	1.12828	−	1.12828i
$414$	−2046.69	+	2198.23i	−0.242969	+	0.260959i
$415$	2442.66			0.288929
$416$	−2358.36	−	13077.9i	−0.277952	−	1.54133i
$417$	−2993.61			−0.351553
$418$	1732.57	−	1860.85i	0.202734	−	0.217745i
$419$	39.7232	−	39.7232i	0.00463152	−	0.00463152i	−0.704787	−	0.709419i	$-0.748958\pi$
$419$	39.7232	−	39.7232i	0.00463152	−	0.00463152i	0.709419	+	0.704787i	$0.248958\pi$
$420$	5470.27	−	391.055i	0.635529	−	0.0454322i
$421$	1741.60	+	1741.60i	0.201616	+	0.201616i	0.800692	−	0.599076i	$-0.204465\pi$
$421$	1741.60	+	1741.60i	0.201616	+	0.201616i	−0.599076	+	0.800692i	$0.704465\pi$
$422$	138.378	+	3876.35i	0.0159624	+	0.447151i
$423$			1276.92i			0.146776i
$424$	−718.338	−	6684.73i	−0.0822774	−	0.765659i
$425$			1096.88i			0.125192i
$426$	7497.79	−	267.657i	0.852744	−	0.0304413i
$427$	−3952.23	−	3952.23i	−0.447919	−	0.447919i
$428$	6018.90	−	6945.71i	0.679754	−	0.784424i
$429$	1814.98	−	1814.98i	0.204261	−	0.204261i
$430$	10491.2	+	9768.01i	1.17659	+	1.09548i
$431$	115.905			0.0129535			0.00647673	−	0.999979i	$-0.497938\pi$
$431$	115.905			0.0129535			0.00647673	+	0.999979i	$0.497938\pi$
$432$	1383.26	+	1035.65i	0.154056	+	0.115342i
$433$	10706.1			1.18823			0.594115	−	0.804380i	$-0.297502\pi$
$433$	10706.1			1.18823			0.594115	+	0.804380i	$0.297502\pi$
$434$	−302.178	−	281.348i	−0.0334217	−	0.0311178i
$435$	−5422.21	+	5422.21i	−0.597643	+	0.597643i
$436$	1265.70	+	1096.81i	0.139028	+	0.120477i
$437$	−6435.02	−	6435.02i	−0.704414	−	0.704414i
$438$	−6737.63	+	240.520i	−0.735015	+	0.0262386i
$439$			1275.83i			0.138706i	0.997592	+	0.0693531i	$0.0220935\pi$
$439$			1275.83i			0.138706i	−0.997592	+	0.0693531i	$0.977906\pi$
$440$	1706.37	−	2117.25i	0.184882	−	0.229400i
$441$			1333.01i			0.143938i
$442$	−435.048	−	12186.9i	−0.0468170	−	1.31147i
$443$	1291.45	+	1291.45i	0.138507	+	0.138507i	0.772961	−	0.634454i	$-0.218775\pi$
$443$	1291.45	+	1291.45i	0.138507	+	0.138507i	−0.634454	+	0.772961i	$0.718775\pi$
$444$	−642.440	−	8986.77i	−0.0686686	−	0.960571i
$445$	−4841.48	+	4841.48i	−0.515749	+	0.515749i
$446$	−122.147	+	131.191i	−0.0129682	+	0.0139284i
$447$	−3032.70			−0.320899
$448$	11087.4	−	2410.73i	1.16926	−	0.254233i
$449$	2137.82			0.224699			0.112350	−	0.993669i	$-0.464162\pi$
$449$	2137.82			0.224699			0.112350	+	0.993669i	$0.464162\pi$
$450$	323.971	−	347.958i	0.0339381	−	0.0364509i
$451$	813.852	−	813.852i	0.0849729	−	0.0849729i
$452$	−1027.59	−	14374.5i	−0.106933	−	1.49584i
$453$	6768.69	+	6768.69i	0.702032	+	0.702032i
$454$	−257.227	−	7205.62i	−0.0265909	−	0.744882i
$455$			16775.1i			1.72842i
$456$	−3285.47	+	4076.60i	−0.337404	+	0.418649i
$457$			15629.9i			1.59986i	0.600092	+	0.799931i	$0.295131\pi$
$457$			15629.9i			1.59986i	−0.600092	+	0.799931i	$0.704869\pi$
$458$	−11574.5	+	413.188i	−1.18088	+	0.0421550i
$459$	1121.27	+	1121.27i	0.114023	+	0.114023i
$460$	−7355.51	−	6374.02i	−0.745549	−	0.646066i
$461$	−2333.25	+	2333.25i	−0.235727	+	0.235727i	−0.815078	−	0.579351i	$-0.803306\pi$
$461$	−2333.25	+	2333.25i	−0.235727	+	0.235727i	0.579351	+	0.815078i	$0.303306\pi$
$462$	1603.99	+	1493.42i	0.161525	+	0.150390i
$463$	−16917.7			−1.69812			−0.849061	−	0.528294i	$-0.822832\pi$
$463$	−16917.7			−1.69812			−0.849061	+	0.528294i	$0.822832\pi$
$464$	−9508.30	+	12699.8i	−0.951318	+	1.27063i
$465$	203.762			0.0203209
$466$	−8822.70	−	8214.50i	−0.877046	−	0.816587i
$467$	3249.62	−	3249.62i	0.322001	−	0.322001i	−0.527533	−	0.849534i	$-0.676883\pi$
$467$	3249.62	−	3249.62i	0.322001	−	0.322001i	0.849534	+	0.527533i	$0.176883\pi$
$468$	−3461.46	+	3994.47i	−0.341894	+	0.394539i
$469$	−10653.1	−	10653.1i	−1.04886	−	1.04886i
$470$	−4135.28	+	147.622i	−0.405843	+	0.0144878i
$471$		−	2002.02i		−	0.195856i
$472$	1461.01	+	13595.9i	0.142476	+	1.32585i
$473$			5728.34i			0.556848i
$474$	−127.493	−	3571.44i	−0.0123544	−	0.346079i
$475$	1018.60	+	1018.60i	0.0983929	+	0.0983929i
$476$	10385.7	−	742.445i	1.00006	−	0.0714914i
$477$	−1890.91	+	1890.91i	−0.181507	+	0.181507i
$478$	−6376.02	+	6848.10i	−0.610110	+	0.655282i
$479$	9780.09			0.932910			0.466455	−	0.884545i	$-0.345531\pi$
$479$	9780.09			0.932910			0.466455	+	0.884545i	$0.345531\pi$
$480$	−3194.00	+	4599.40i	−0.303719	+	0.437360i
$481$	27558.8			2.61242
$482$	6167.64	−	6624.28i	0.582838	−	0.625991i
$483$	5546.76	−	5546.76i	0.522539	−	0.522539i
$484$	−9536.99	+	681.773i	−0.895661	+	0.0640283i
$485$	7902.25	+	7902.25i	0.739840	+	0.739840i
$486$	−24.5199	−	686.870i	−0.00228857	−	0.0641092i
$487$		−	2710.17i		−	0.252176i	−0.992019	−	0.126088i	$-0.959758\pi$
$487$		−	2710.17i		−	0.252176i	0.992019	−	0.126088i	$-0.0402421\pi$
$488$	5674.25	−	609.752i	0.526355	−	0.0565618i
$489$		−	1168.70i		−	0.108079i
$490$	−4316.91	+	154.105i	−0.397996	+	0.0142077i
$491$	−1884.20	−	1884.20i	−0.173183	−	0.173183i	0.615193	−	0.788376i	$-0.289078\pi$
$491$	−1884.20	−	1884.20i	−0.173183	−	0.173183i	−0.788376	+	0.615193i	$0.789078\pi$
$492$	−1552.15	+	1791.16i	−0.142228	+	0.164129i
$493$	−10294.4	+	10294.4i	−0.940443	+	0.940443i
$494$	−11721.1	−	10913.1i	−1.06753	−	0.993937i
$495$	−1081.58			−0.0982093
$496$	417.280	−	59.9669i	0.0377751	−	0.00542861i
$497$	−19594.5			−1.76848
$498$	−1471.15	−	1369.73i	−0.132377	−	0.123251i
$499$	−11085.6	+	11085.6i	−0.994509	+	0.994509i	−0.999985	−	0.00547579i	$-0.998257\pi$
$499$	−11085.6	+	11085.6i	−0.994509	+	0.994509i	0.00547579	+	0.999985i	$0.498257\pi$
$500$	8956.86	+	7761.69i	0.801125	+	0.694227i
$501$	3721.90	+	3721.90i	0.331901	+	0.331901i
$502$	7776.28	−	277.598i	0.691379	−	0.0246809i
$503$			9544.26i			0.846039i	0.906121	+	0.423020i	$0.139030\pi$
$503$			9544.26i			0.846039i	−0.906121	+	0.423020i	$0.860970\pi$
$504$	−3513.88	−	2831.96i	−0.310557	−	0.250289i
$505$			8761.67i			0.772058i
$506$	−138.759	−	3887.01i	−0.0121909	−	0.341499i
$507$	−6771.63	−	6771.63i	−0.593173	−	0.593173i
$508$	500.129	+	6996.05i	0.0436803	+	0.611023i
$509$	1874.95	−	1874.95i	0.163272	−	0.163272i	−0.620742	−	0.784015i	$-0.713169\pi$
$509$	1874.95	−	1874.95i	0.163272	−	0.163272i	0.784015	+	0.620742i	$0.213169\pi$
$510$	−3501.59	+	3760.84i	−0.304025	+	0.326535i
$511$	17607.9			1.52432
$512$	−5187.34	+	10359.0i	−0.447754	+	0.894157i
$513$	2082.50			0.179229
$514$	159.939	−	171.781i	0.0137250	−	0.0147411i
$515$	−223.716	+	223.716i	−0.0191420	+	0.0191420i
$516$	−841.120	−	11766.0i	−0.0717602	−	1.00382i
$517$	−1169.26	−	1169.26i	−0.0994660	−	0.0994660i
$518$	839.466	+	23515.7i	0.0712046	+	1.99464i
$519$		−	4126.10i		−	0.348971i
$520$	−13336.1	−	10748.1i	−1.12467	−	0.906411i
$521$		−	12549.3i		−	1.05527i	−0.849471	−	0.527635i	$-0.823079\pi$
$521$		−	12549.3i		−	1.05527i	0.849471	−	0.527635i	$-0.176921\pi$
$522$	6306.18	−	225.118i	0.528762	−	0.0188758i
$523$	−5583.16	−	5583.16i	−0.466797	−	0.466797i	0.434078	−	0.900875i	$-0.357074\pi$
$523$	−5583.16	−	5583.16i	−0.466797	−	0.466797i	−0.900875	+	0.434078i	$0.857074\pi$
$524$	11593.8	+	10046.8i	0.966559	+	0.837585i
$525$	−877.999	+	877.999i	−0.0729886	+	0.0729886i
$526$	4429.08	+	4123.76i	0.367143	+	0.341833i
$527$	386.856			0.0319767
$528$	−2214.96	+	318.309i	−0.182564	+	0.0262361i
$529$	−1754.51			−0.144202
$530$	−6342.25	−	5905.05i	−0.519792	−	0.483960i
$531$	3845.87	−	3845.87i	0.314306	−	0.314306i
$532$	8955.05	−	10334.0i	0.729794	−	0.842170i
$533$	−5126.29	−	5126.29i	−0.416593	−	0.416593i
$534$	5630.78	−	201.008i	0.456306	−	0.0162893i
$535$		−	11846.1i		−	0.957293i
$536$	15294.8	−	1643.57i	1.23253	−	0.132447i
$537$		−	8249.97i		−	0.662966i
$538$	365.944	+	10251.1i	0.0293252	+	0.821479i
$539$	−1220.61	−	1220.61i	−0.0975428	−	0.0975428i
$540$	2221.58	−	158.814i	0.177040	−	0.0126561i
$541$	−7722.24	+	7722.24i	−0.613688	+	0.613688i	−0.943905	−	0.330217i	$-0.892878\pi$
$541$	−7722.24	+	7722.24i	−0.613688	+	0.613688i	0.330217	+	0.943905i	$0.392878\pi$
$542$	−2647.98	+	2844.04i	−0.209853	+	0.225391i
$543$	−5892.40			−0.465685
$544$	−6064.03	+	8732.28i	−0.477929	+	0.688223i
$545$	2158.70			0.169667
$546$	9406.74	−	10103.2i	0.737310	−	0.791900i
$547$	7464.17	−	7464.17i	0.583446	−	0.583446i	−0.352403	−	0.935848i	$-0.614635\pi$
$547$	7464.17	−	7464.17i	0.583446	−	0.583446i	0.935848	+	0.352403i	$0.114635\pi$
$548$	14628.2	−	1045.73i	1.14030	−	0.0815169i
$549$	−1605.07	−	1605.07i	−0.124777	−	0.124777i
$550$	21.9641	+	615.275i	0.00170283	+	0.0477008i
$551$			19119.5i			1.47826i
$552$	855.759	+	7963.54i	0.0659846	+	0.614041i
$553$			9333.48i			0.717722i
$554$	−7047.84	+	251.594i	−0.540495	+	0.0192946i
$555$	−8211.46	−	8211.46i	−0.628031	−	0.628031i
$556$	−5227.93	+	6032.94i	−0.398766	+	0.460169i
$557$	−10501.3	+	10501.3i	−0.798841	+	0.798841i	−0.982913	−	0.184072i	$-0.941072\pi$
$557$	−10501.3	+	10501.3i	−0.798841	+	0.798841i	0.184072	+	0.982913i	$0.441072\pi$
$558$	−122.720	−	114.260i	−0.00931032	−	0.00866851i
$559$	36081.6			2.73004
$560$	8765.01	−	11707.0i	0.661409	−	0.883414i
$561$	−2053.47			−0.154541
$562$	−16914.4	−	15748.4i	−1.26956	−	1.18204i
$563$	16986.4	−	16986.4i	1.27157	−	1.27157i	0.326300	−	0.945266i	$-0.394198\pi$
$563$	16986.4	−	16986.4i	1.27157	−	1.27157i	0.945266	−	0.326300i	$-0.105802\pi$
$564$	2573.35	+	2229.97i	0.192123	+	0.166487i
$565$	−13134.3	−	13134.3i	−0.977991	−	0.977991i
$566$	−4868.65	+	173.801i	−0.361563	+	0.0129071i
$567$			1795.04i			0.132954i
$568$	12554.5	−	15577.5i	0.927419	−	1.15074i
$569$		−	10274.2i		−	0.756971i	−0.925607	−	0.378486i	$-0.876445\pi$
$569$		−	10274.2i		−	0.756971i	0.925607	−	0.378486i	$-0.123555\pi$
$570$	240.752	+	6744.13i	0.0176912	+	0.495580i
$571$	−5116.90	−	5116.90i	−0.375019	−	0.375019i	0.494283	−	0.869301i	$-0.335431\pi$
$571$	−5116.90	−	5116.90i	−0.375019	−	0.375019i	−0.869301	+	0.494283i	$0.835431\pi$
$572$	−488.063	−	6827.28i	−0.0356765	−	0.499061i
$573$	−3722.02	+	3722.02i	−0.271361	+	0.271361i
$574$	4218.07	−	4530.37i	0.306723	−	0.329432i
$575$	2203.64			0.159823
$576$	4502.79	−	979.042i	0.325723	−	0.0708219i
$577$	4648.41			0.335383			0.167691	−	0.985840i	$-0.446369\pi$
$577$	4648.41			0.335383			0.167691	+	0.985840i	$0.446369\pi$
$578$	2821.19	−	3030.07i	0.203021	−	0.218052i
$579$	8721.34	−	8721.34i	0.625987	−	0.625987i
$580$	1458.08	+	20396.4i	0.104385	+	1.46020i
$581$	3712.13	+	3712.13i	0.265069	+	0.265069i
$582$	−328.084	−	9190.54i	−0.0233669	−	0.654570i
$583$		−	3462.95i		−	0.246004i
$584$	−11281.6	+	13998.2i	−0.799379	+	0.991866i
$585$			6812.68i			0.481487i
$586$	−11968.7	+	427.260i	−0.843725	+	0.0301194i
$587$	−16839.3	−	16839.3i	−1.18404	−	1.18404i	−0.978688	−	0.205351i	$-0.934166\pi$
$587$	−16839.3	−	16839.3i	−1.18404	−	1.18404i	−0.205351	−	0.978688i	$-0.565834\pi$
$588$	2686.37	+	2327.92i	0.188408	+	0.163268i
$589$	359.247	−	359.247i	0.0251316	−	0.0251316i
$590$	12899.3	+	12010.1i	0.900098	+	0.838049i
$591$	−2483.30			−0.172841
$592$	−19232.7	−	14399.5i	−1.33524	−	0.999688i
$593$	15004.6			1.03906			0.519530	−	0.854452i	$-0.326107\pi$
$593$	15004.6			1.03906			0.519530	+	0.854452i	$0.326107\pi$
$594$	651.409	+	606.504i	0.0449960	+	0.0418942i
$595$	9489.70	−	9489.70i	0.653848	−	0.653848i
$596$	−5296.20	+	6111.72i	−0.363995	+	0.420044i
$597$	5559.24	+	5559.24i	0.381113	+	0.381113i
$598$	−24483.5	+	874.012i	−1.67425	+	0.0597676i
$599$		−	7740.90i		−	0.528021i	−0.964520	−	0.264011i	$-0.914955\pi$
$599$		−	7740.90i		−	0.528021i	0.964520	−	0.264011i	$-0.0850454\pi$
$600$	−135.458	−	1260.55i	−0.00921677	−	0.0857696i
$601$		−	19210.1i		−	1.30382i	−0.758295	−	0.651912i	$-0.773967\pi$
$601$		−	19210.1i		−	1.30382i	0.758295	−	0.651912i	$-0.226033\pi$
$602$	1099.08	+	30788.2i	0.0744104	+	2.08444i
$603$	−4326.43	−	4326.43i	−0.292182	−	0.292182i
$604$	25461.3	−	1820.16i	1.71524	−	0.122618i
$605$	−8714.21	+	8714.21i	−0.585592	+	0.585592i
$606$	4913.15	−	5276.92i	0.329345	−	0.353730i
$607$	−25349.2			−1.69505			−0.847524	−	0.530758i	$-0.821907\pi$
$607$	−25349.2			−1.69505			−0.847524	+	0.530758i	$0.821907\pi$
$608$	2477.82	+	13740.3i	0.165278	+	0.916520i
$609$	−16480.4			−1.09658
$610$	5012.42	−	5383.54i	0.332700	−	0.357333i
$611$	−7364.93	+	7364.93i	−0.487648	+	0.487648i
$612$	4217.82	−	301.520i	0.278587	−	0.0199154i
$613$	12517.8	+	12517.8i	0.824780	+	0.824780i	0.986789	−	0.162010i	$-0.0517975\pi$
$613$	12517.8	+	12517.8i	0.824780	+	0.824780i	−0.162010	+	0.986789i	$0.551798\pi$
$614$	−768.022	−	21514.4i	−0.0504802	−	1.41409i
$615$			3054.87i			0.200300i
$616$	5810.79	−	624.425i	0.380071	−	0.0408422i
$617$			12650.0i			0.825399i	0.910867	+	0.412700i	$0.135414\pi$
$617$			12650.0i			0.825399i	−0.910867	+	0.412700i	$0.864586\pi$
$618$	260.188	−	9.28822i	0.0169358	−	0.000604575i
$619$	5166.55	+	5166.55i	0.335479	+	0.335479i	0.854663	−	0.519184i	$-0.173764\pi$
$619$	5166.55	+	5166.55i	0.335479	+	0.335479i	−0.519184	+	0.854663i	$0.673764\pi$
$620$	355.842	−	410.635i	0.0230499	−	0.0265992i
$621$	2252.64	−	2252.64i	0.145564	−	0.145564i
$622$	16158.4	+	15044.5i	1.04163	+	0.969823i
$623$	−14715.3			−0.946318
$624$	2004.97	+	13951.6i	0.128626	+	0.895049i
$625$	12941.6			0.828263
$626$	3207.06	+	2985.98i	0.204760	+	0.190645i
$627$	−1906.92	+	1906.92i	−0.121459	+	0.121459i
$628$	−4034.62	−	3496.25i	−0.256367	−	0.222159i
$629$	−15590.0	−	15590.0i	−0.988260	−	0.988260i
$630$	−5813.21	+	207.520i	−0.367625	+	0.0131235i
$631$		−	12728.9i		−	0.803056i	−0.915847	−	0.401528i	$-0.868479\pi$
$631$		−	12728.9i		−	0.803056i	0.915847	−	0.401528i	$-0.131521\pi$
$632$	−7420.07	−	5980.10i	−0.467017	−	0.376385i
$633$		−	4114.11i		−	0.258327i
$634$	−872.240	−	24433.8i	−0.0546389	−	1.53059i
$635$	6392.48	+	6392.48i	0.399493	+	0.399493i
$636$	508.482	+	7112.90i	0.0317022	+	0.443467i
$637$	−7688.40	+	7688.40i	−0.478219	+	0.478219i
$638$	−5568.33	+	5980.61i	−0.345537	+	0.371120i
$639$	−7957.67			−0.492646
$640$	3691.16	+	14469.0i	0.227978	+	0.893652i
$641$	8725.04			0.537626			0.268813	−	0.963192i	$-0.413369\pi$
$641$	8725.04			0.537626			0.268813	+	0.963192i	$0.413369\pi$
$642$	−6642.77	+	7134.59i	−0.408363	+	0.438598i
$643$	−11974.6	+	11974.6i	−0.734418	+	0.734418i	−0.971492	−	0.237073i	$-0.923812\pi$
$643$	−11974.6	+	11974.6i	−0.734418	+	0.734418i	0.237073	+	0.971492i	$0.423812\pi$
$644$	−1491.57	−	20864.9i	−0.0912675	−	1.27670i
$645$	−10750.9	−	10750.9i	−0.656306	−	0.656306i
$646$	457.086	+	12804.2i	0.0278387	+	0.779837i
$647$		−	16791.7i		−	1.02033i	−0.860078	−	0.510163i	$-0.829585\pi$
$647$		−	16791.7i		−	1.02033i	0.860078	−	0.510163i	$-0.170415\pi$
$648$	−1427.05	−	1150.11i	−0.0865122	−	0.0697232i
$649$			7043.20i			0.425994i
$650$	3875.49	−	138.348i	0.233861	−	0.00834837i
$651$	309.659	+	309.659i	0.0186428	+	0.0186428i
$652$	−2355.26	−	2040.98i	−0.141471	−	0.122594i
$653$	12379.7	−	12379.7i	0.741894	−	0.741894i	−0.231049	−	0.972942i	$-0.574216\pi$
$653$	12379.7	−	12379.7i	0.741894	−	0.741894i	0.972942	+	0.231049i	$0.0742156\pi$
$654$	−1300.12	−	1210.50i	−0.0777353	−	0.0723766i
$655$	19773.5			1.17957
$656$	899.045	+	6256.02i	0.0535089	+	0.372342i
$657$	7150.89			0.424631
$658$	−6508.77	−	6060.09i	−0.385621	−	0.359038i
$659$	−2164.94	+	2164.94i	−0.127973	+	0.127973i	−0.768192	−	0.640219i	$-0.778843\pi$
$659$	−2164.94	+	2164.94i	−0.127973	+	0.127973i	0.640219	+	0.768192i	$0.278843\pi$
$660$	−1888.84	+	2179.69i	−0.111398	+	0.128552i
$661$	16951.5	+	16951.5i	0.997481	+	0.997481i	0.999997	−	0.00251552i	$-0.000800717\pi$
$661$	16951.5	+	16951.5i	0.997481	+	0.997481i	−0.00251552	+	0.999997i	$0.500801\pi$
$662$	−14147.3	+	505.031i	−0.830589	+	0.0296504i
$663$			12934.4i			0.757661i
$664$	−5329.55	+	572.711i	−0.311486	+	0.0334721i
$665$		−	17624.9i		−	1.02777i
$666$	340.922	+	9550.16i	0.0198355	+	0.555647i
$667$	20681.6	+	20681.6i	1.20059	+	1.20059i
$668$	14000.4	−	1000.85i	0.810918	−	0.0579703i
$669$	134.438	−	134.438i	0.00776932	−	0.00776932i
$670$	13510.9	−	14511.2i	0.779061	−	0.836742i
$671$	2939.48			0.169117
$672$	−11843.7	+	2135.80i	−0.679882	+	0.122604i
$673$	−3167.92			−0.181448			−0.0907238	−	0.995876i	$-0.528918\pi$
$673$	−3167.92			−0.181448			−0.0907238	+	0.995876i	$0.528918\pi$
$674$	14100.3	−	15144.3i	0.805824	−	0.865486i
$675$	−356.571	+	356.571i	−0.0203325	+	0.0203325i
$676$	−25472.4	+	1820.95i	−1.44927	+	0.103604i
$677$	8613.73	+	8613.73i	0.488999	+	0.488999i	0.907990	−	0.418991i	$-0.137616\pi$
$677$	8613.73	+	8613.73i	0.488999	+	0.488999i	−0.418991	+	0.907990i	$0.637616\pi$
$678$	545.309	+	15275.6i	0.0308886	+	0.865274i
$679$			24018.3i			1.35749i
$680$	1464.08	+	13624.4i	0.0825659	+	0.768344i
$681$			7647.58i			0.430332i
$682$	216.999	−	7.74646i	0.0121838	−	0.000434937i
$683$	23079.8	+	23079.8i	1.29301	+	1.29301i	0.932916	+	0.360093i	$0.117255\pi$
$683$	23079.8	+	23079.8i	1.29301	+	1.29301i	0.360093	+	0.932916i	$0.382745\pi$
$684$	3636.81	−	4196.81i	0.203299	−	0.234604i
$685$	13366.1	−	13366.1i	0.745539	−	0.745539i
$686$	8940.51	+	8324.19i	0.497595	+	0.463293i
$687$	12284.4			0.682214
$688$	−25180.6	−	18852.7i	−1.39535	−	1.04470i
$689$	−21812.4			−1.20608
$690$	7555.54	+	7034.70i	0.416862	+	0.388125i
$691$	−10996.2	+	10996.2i	−0.605375	+	0.605375i	−0.941734	−	0.336359i	$-0.890804\pi$
$691$	−10996.2	+	10996.2i	−0.605375	+	0.605375i	0.336359	+	0.941734i	$0.390804\pi$
$692$	−8315.22	−	7205.68i	−0.456788	−	0.395836i
$693$	−1643.69	−	1643.69i	−0.0900993	−	0.0900993i
$694$	4854.82	−	173.308i	0.265542	−	0.00947934i
$695$			10289.4i			0.561580i
$696$	10559.2	−	13101.8i	0.575066	−	0.713539i
$697$			5799.89i			0.315188i
$698$	−545.689	−	15286.2i	−0.0295912	−	0.828929i
$699$	9041.10	+	9041.10i	0.489221	+	0.489221i
$700$	236.102	+	3302.71i	0.0127483	+	0.178330i
$701$	−15045.8	+	15045.8i	−0.810659	+	0.810659i	−0.984733	−	0.174074i	$-0.944307\pi$
$701$	−15045.8	+	15045.8i	−0.810659	+	0.810659i	0.174074	+	0.984733i	$0.444307\pi$
$702$	3820.25	−	4103.09i	0.205393	−	0.220600i
$703$	−28954.8			−1.55342
$704$	−3226.65	+	5019.63i	−0.172740	+	0.268728i
$705$	4388.92			0.234463
$706$	−8625.85	+	9264.50i	−0.459827	+	0.493873i
$707$	−13315.2	+	13315.2i	−0.708302	+	0.708302i
$708$	−1034.19	−	14466.7i	−0.0548971	−	0.767929i
$709$	−13939.7	−	13939.7i	−0.738388	−	0.738388i	0.233878	−	0.972266i	$-0.424859\pi$
$709$	−13939.7	−	13939.7i	−0.738388	−	0.738388i	−0.972266	+	0.233878i	$0.924859\pi$
$710$	−919.965	−	25770.7i	−0.0486277	−	1.36219i
$711$			3790.50i			0.199936i
$712$	9428.30	−	11698.6i	0.496265	−	0.615763i
$713$		−	777.195i		−	0.0408221i
$714$	−11036.8	+	393.992i	−0.578489	+	0.0206509i
$715$	−6238.27	−	6238.27i	−0.326291	−	0.326291i
$716$	−16625.9	−	14407.5i	−0.867794	−	0.752000i
$717$	7017.62	−	7017.62i	0.365520	−	0.365520i
$718$	−2775.86	−	2584.51i	−0.144282	−	0.134336i
$719$	−32099.6			−1.66497			−0.832484	−	0.554050i	$-0.813082\pi$
$719$	−32099.6			−1.66497			−0.832484	+	0.554050i	$0.813082\pi$
$720$	3559.63	−	4754.43i	0.184249	−	0.246093i
$721$	−679.968			−0.0351225
$722$	−1883.79	−	1753.93i	−0.0971015	−	0.0904078i
$723$	−6788.26	+	6788.26i	−0.349181	+	0.349181i
$724$	−10290.3	+	11874.8i	−0.528225	+	0.609562i
$725$	−3273.69	−	3273.69i	−0.167699	−	0.167699i
$726$	10134.9	−	361.795i	0.518100	−	0.0184952i
$727$			1706.65i			0.0870646i	0.999052	+	0.0435323i	$0.0138611\pi$
$727$			1706.65i			0.0870646i	−0.999052	+	0.0435323i	$0.986139\pi$
$728$	−3933.13	−	36601.0i	−0.200236	−	1.86336i
$729$			729.000i			0.0370370i
$730$	826.695	+	23158.0i	0.0419142	+	1.17413i
$731$	−20411.4	−	20411.4i	−1.03275	−	1.03275i
$732$	−6037.69	+	431.618i	−0.304863	+	0.0217938i
$733$	19995.6	−	19995.6i	1.00758	−	1.00758i	0.00760565	−	0.999971i	$-0.497579\pi$
$733$	19995.6	−	19995.6i	1.00758	−	1.00758i	0.999971	−	0.00760565i	$-0.00242098\pi$
$734$	11292.9	−	12129.0i	0.567887	−	0.609933i
$735$	4581.69			0.229930
$736$	17543.2	+	12182.7i	0.878601	+	0.610134i
$737$	7923.30			0.396009
$738$	1713.03	−	1839.86i	0.0854439	−	0.0917701i
$739$	−3123.50	+	3123.50i	−0.155480	+	0.155480i	−0.780560	−	0.625080i	$-0.785066\pi$
$739$	−3123.50	+	3123.50i	−0.155480	+	0.155480i	0.625080	+	0.780560i	$0.285066\pi$
$740$	−30888.5	+	2208.13i	−1.53444	+	0.109693i
$741$	12011.3	+	12011.3i	0.595473	+	0.595473i
$742$	−664.425	−	18612.3i	−0.0328730	−	0.920863i
$743$		−	7764.79i		−	0.383395i	−0.981454	−	0.191698i	$-0.938601\pi$
$743$		−	7764.79i		−	0.383395i	0.981454	−	0.191698i	$-0.0613993\pi$
$744$	−444.580	+	47.7743i	−0.0219074	+	0.00235416i
$745$			10423.7i			0.512612i
$746$	18859.9	−	673.262i	0.925617	−	0.0330427i
$747$	1507.56	+	1507.56i	0.0738406	+	0.0738406i
$748$	−3586.10	+	4138.29i	−0.175295	+	0.202287i
$749$	18002.7	−	18002.7i	0.878241	−	0.878241i
$750$	−9200.43	−	8566.20i	−0.447936	−	0.417058i
$751$	7697.83			0.374032			0.187016	−	0.982357i	$-0.440118\pi$
$751$	7697.83			0.374032			0.187016	+	0.982357i	$0.440118\pi$
$752$	8988.00	−	1291.66i	0.435849	−	0.0626354i
$753$	−8253.25			−0.399422
$754$	37670.7	+	35073.8i	1.81948	+	1.69405i
$755$	23264.7	−	23264.7i	1.12144	−	1.12144i
$756$	3617.50	+	3134.80i	0.174031	+	0.150809i
$757$	3022.39	+	3022.39i	0.145113	+	0.145113i	0.775931	−	0.630818i	$-0.217280\pi$
$757$	3022.39	+	3022.39i	0.145113	+	0.145113i	−0.630818	+	0.775931i	$0.717280\pi$
$758$	−1009.29	+	36.0299i	−0.0483631	+	0.00172647i
$759$			4125.42i			0.197290i
$760$	14011.7	+	11292.5i	0.668760	+	0.538977i
$761$			26737.7i			1.27364i	0.771012	+	0.636820i	$0.219751\pi$
$761$			26737.7i			1.27364i	−0.771012	+	0.636820i	$0.780249\pi$
$762$	−265.402	−	7434.64i	−0.0126175	−	0.353449i
$763$	3280.59	+	3280.59i	0.155656	+	0.155656i
$764$	1000.88	+	14000.9i	0.0473963	+	0.663003i
$765$	3853.94	−	3853.94i	0.182143	−	0.182143i
$766$	−4869.17	+	5229.68i	−0.229674	+	0.246679i
$767$	44363.7			2.08850
$768$	5890.48	−	10784.1i	0.276763	−	0.506691i
$769$	−14158.4			−0.663934			−0.331967	−	0.943291i	$-0.607712\pi$
$769$	−14158.4			−0.663934			−0.331967	+	0.943291i	$0.607712\pi$
$770$	5133.04	−	5513.09i	0.240236	−	0.258023i
$771$	−176.033	+	176.033i	−0.00822269	+	0.00822269i
$772$	−2345.25	−	32806.5i	−0.109336	−	1.52945i
$773$	15285.5	+	15285.5i	0.711231	+	0.711231i	0.966793	−	0.255562i	$-0.0822605\pi$
$773$	15285.5	+	15285.5i	0.711231	+	0.711231i	−0.255562	+	0.966793i	$0.582260\pi$
$774$	446.355	+	12503.6i	0.0207286	+	0.580664i
$775$			123.022i			0.00570206i
$776$	−19094.4	−	15388.8i	−0.883310	−	0.711891i
$777$		−	24958.1i		−	1.15234i
$778$	−7085.85	+	252.951i	−0.326529	+	0.0116565i
$779$	5385.96	+	5385.96i	0.247718	+	0.247718i
$780$	13729.4	+	11897.4i	0.630246	+	0.546149i
$781$	7286.72	−	7286.72i	0.333853	−	0.333853i
$782$	14344.7	+	13355.9i	0.655967	+	0.610748i
$783$	−6692.97			−0.305476
$784$	9382.77	−	1348.39i	0.427422	−	0.0614244i
$785$	−6881.16			−0.312865
$786$	−11909.1	−	11088.1i	−0.540436	−	0.503181i
$787$	−11317.7	+	11317.7i	−0.512622	+	0.512622i	−0.915329	−	0.402707i	$-0.868069\pi$
$787$	−11317.7	+	11317.7i	−0.512622	+	0.512622i	0.402707	+	0.915329i	$0.368069\pi$
$788$	−4336.74	+	5004.52i	−0.196053	+	0.226242i
$789$	−4538.72	−	4538.72i	−0.204794	−	0.204794i
$790$	−12275.4	+	438.209i	−0.552835	+	0.0197352i
$791$		−	39920.7i		−	1.79446i
$792$	2359.87	−	253.590i	0.105877	−	0.0113775i
$793$		−	18515.2i		−	0.829121i
$794$	596.817	+	16718.5i	0.0266754	+	0.747250i
$795$	6499.25	+	6499.25i	0.289943	+	0.289943i
$796$	20911.8	−	1494.93i	0.931157	−	0.0665658i
$797$	24453.7	−	24453.7i	1.08682	−	1.08682i	0.0909639	−	0.995854i	$-0.471005\pi$
$797$	24453.7	−	24453.7i	1.08682	−	1.08682i	0.995854	−	0.0909639i	$-0.0289948\pi$
$798$	−9883.25	+	10615.0i	−0.438425	+	0.470886i
$799$	8332.68			0.368948
$800$	−2776.91	−	1928.40i	−0.122723	−	0.0852238i
$801$	−5976.15			−0.263616
$802$	11428.3	−	12274.4i	0.503176	−	0.540431i
$803$	−6547.96	+	6547.96i	−0.287761	+	0.287761i
$804$	−16274.5	+	1163.42i	−0.713876	+	0.0510330i
$805$	−19064.8	−	19064.8i	−0.834717	−	0.834717i
$806$	−48.7934	−	1366.84i	−0.00213235	−	0.0597329i
$807$		−	10879.8i		−	0.474583i
$808$	−2054.28	−	19116.8i	−0.0894422	−	0.832334i
$809$			4516.01i			0.196260i	0.995174	+	0.0981301i	$0.0312861\pi$
$809$			4516.01i			0.196260i	−0.995174	+	0.0981301i	$0.968714\pi$
$810$	−2360.85	+	84.2777i	−0.102410	+	0.00365582i
$811$	−14460.0	−	14460.0i	−0.626092	−	0.626092i	0.320990	−	0.947082i	$-0.395984\pi$
$811$	−14460.0	−	14460.0i	−0.626092	−	0.626092i	−0.947082	+	0.320990i	$0.895984\pi$
$812$	−28780.7	+	33212.4i	−1.24385	+	1.43538i
$813$	2914.44	−	2914.44i	0.125724	−	0.125724i
$814$	−9057.11	−	8432.75i	−0.389990	−	0.363106i
$815$	−4016.96			−0.172648
$816$	6758.20	−	9026.63i	0.289932	−	0.387249i
$817$	−37909.4			−1.62336
$818$	19979.6	+	18602.3i	0.854000	+	0.795129i
$819$	−10353.3	+	10353.3i	−0.441726	+	0.441726i
$820$	6156.39	+	5334.91i	0.262184	+	0.227199i
$821$	20286.7	+	20286.7i	0.862377	+	0.862377i	0.991614	−	0.129237i	$-0.0412527\pi$
$821$	20286.7	+	20286.7i	0.862377	+	0.862377i	−0.129237	+	0.991614i	$0.541253\pi$
$822$	−15545.2	+	554.934i	−0.659612	+	0.0235469i
$823$			27490.2i			1.16434i	0.813068	+	0.582168i	$0.197796\pi$
$823$			27490.2i			1.16434i	−0.813068	+	0.582168i	$0.802204\pi$
$824$	435.665	−	540.571i	0.0184188	−	0.0228540i
$825$		−	653.013i		−	0.0275576i
$826$	1351.36	+	37855.2i	0.0569246	+	1.59461i
$827$	−4576.46	−	4576.46i	−0.192429	−	0.192429i	0.604316	−	0.796745i	$-0.293447\pi$
$827$	−4576.46	−	4576.46i	−0.192429	−	0.192429i	−0.796745	+	0.604316i	$0.793447\pi$
$828$	−605.755	−	8473.62i	−0.0254245	−	0.355650i
$829$	−14697.8	+	14697.8i	−0.615772	+	0.615772i	−0.944444	−	0.328672i	$-0.893399\pi$
$829$	−14697.8	+	14697.8i	−0.615772	+	0.615772i	0.328672	+	0.944444i	$0.393399\pi$
$830$	−4707.92	+	5056.49i	−0.196885	+	0.211462i
$831$	7480.13			0.312254
$832$	31617.6	+	20324.0i	1.31748	+	0.846884i
$833$	8698.66			0.361814
$834$	5769.81	−	6197.01i	0.239559	−	0.257296i
$835$	12792.6	−	12792.6i	0.530186	−	0.530186i
$836$	512.787	+	7173.12i	0.0212142	+	0.296756i
$837$	125.758	+	125.758i	0.00519335	+	0.00519335i
$838$	5.66856	+	158.792i	0.000233672	+	0.00654579i
$839$		−	9206.59i		−	0.378840i	−0.981896	−	0.189420i	$-0.939339\pi$
$839$		−	9206.59i		−	0.378840i	0.981896	−	0.189420i	$-0.0606608\pi$
$840$	−9733.76	+	12077.6i	−0.399817	+	0.496091i
$841$		−	37059.4i		−	1.51951i
$842$	−6961.97	+	248.529i	−0.284947	+	0.0101721i
$843$	17333.1	+	17333.1i	0.708165	+	0.708165i
$844$	−8291.05	−	7184.73i	−0.338139	−	0.293020i
$845$	−23274.8	+	23274.8i	−0.947548	+	0.947548i
$846$	−2643.33	−	2461.11i	−0.107423	−	0.100017i
$847$	−26486.1			−1.07447
$848$	15222.4	+	11397.0i	0.616439	+	0.461526i
$849$	5167.27			0.208881
$850$	−2270.63	−	2114.10i	−0.0916259	−	0.0853096i
$851$	−31320.4	+	31320.4i	−1.26163	+	1.26163i
$852$	−13897.0	+	16036.9i	−0.558806	+	0.644853i
$853$	−17252.0	−	17252.0i	−0.692494	−	0.692494i	0.270286	−	0.962780i	$-0.412882\pi$
$853$	−17252.0	−	17252.0i	−0.692494	−	0.692494i	−0.962780	+	0.270286i	$0.912882\pi$
$854$	15798.8	−	563.988i	0.633051	−	0.0225987i
$855$		−	7157.79i		−	0.286305i
$856$	2777.46	+	25846.6i	0.110902	+	1.03203i
$857$			22957.2i			0.915057i	0.889195	+	0.457529i	$0.151265\pi$
$857$			22957.2i			0.915057i	−0.889195	+	0.457529i	$0.848735\pi$
$858$	259.000	+	7255.28i	0.0103055	+	0.288684i
$859$	6376.26	+	6376.26i	0.253266	+	0.253266i	0.822308	−	0.569043i	$-0.192686\pi$
$859$	6376.26	+	6376.26i	0.253266	+	0.253266i	−0.569043	+	0.822308i	$0.692686\pi$
$860$	−40441.1	+	2891.02i	−1.60352	+	0.114631i
$861$	−4642.51	+	4642.51i	−0.183759	+	0.183759i
$862$	−223.392	+	239.932i	−0.00882688	+	0.00948042i
$863$	−35795.9			−1.41194			−0.705971	−	0.708241i	$-0.749489\pi$
$863$	−35795.9			−1.41194			−0.705971	+	0.708241i	$0.749489\pi$
$864$	−4809.94	+	867.386i	−0.189395	+	0.0341540i
$865$	−14181.9			−0.557454
$866$	−20634.7	+	22162.5i	−0.809696	+	0.869645i
$867$	−3105.07	+	3105.07i	−0.121631	+	0.121631i
$868$	1164.82	−	83.2700i	0.0455492	−	0.00325618i
$869$	−3470.90	−	3470.90i	−0.135492	−	0.135492i
$870$	−773.756	−	21675.0i	−0.0301526	−	0.844657i
$871$		−	49907.3i		−	1.94150i
$872$	−4709.98	+	506.132i	−0.182913	+	0.0196557i
$873$			9754.25i			0.378157i
$874$	25723.7	−	918.286i	0.995557	−	0.0355395i
$875$	23215.4	+	23215.4i	0.896940	+	0.896940i
$876$	12488.1	−	14411.0i	0.481658	−	0.555824i
$877$	9797.22	−	9797.22i	0.377228	−	0.377228i	−0.492873	−	0.870101i	$-0.664053\pi$
$877$	9797.22	−	9797.22i	0.377228	−	0.377228i	0.870101	+	0.492873i	$0.164053\pi$
$878$	−2641.07	−	2459.00i	−0.101517	−	0.0945186i
$879$	12702.8			0.487435
$880$	1094.06	+	7613.06i	0.0419101	+	0.291632i
$881$	−3227.81			−0.123437			−0.0617183	−	0.998094i	$-0.519658\pi$
$881$	−3227.81			−0.123437			−0.0617183	+	0.998094i	$0.519658\pi$
$882$	−2759.43	−	2569.21i	−0.105346	−	0.0980835i
$883$	33226.7	−	33226.7i	1.26633	−	1.26633i	0.318354	−	0.947972i	$-0.396870\pi$
$883$	33226.7	−	33226.7i	1.26633	−	1.26633i	0.947972	−	0.318354i	$-0.103130\pi$
$884$	26066.3	+	22588.1i	0.991746	+	0.859412i
$885$	−13218.7	−	13218.7i	−0.502079	−	0.502079i
$886$	−5162.50	+	184.291i	−0.195753	+	0.00698801i
$887$		−	3411.07i		−	0.129123i	−0.997914	−	0.0645617i	$-0.979435\pi$
$887$		−	3411.07i		−	0.129123i	0.997914	−	0.0645617i	$-0.0205649\pi$
$888$	19841.5	+	15991.0i	0.749818	+	0.604305i
$889$			19429.4i			0.733006i
$890$	−690.886	−	19353.6i	−0.0260208	−	0.728915i
$891$	−667.534	−	667.534i	−0.0250990	−	0.0250990i
$892$	−36.1516	−	505.707i	−0.00135700	−	0.0189824i
$893$	7738.00	−	7738.00i	0.289969	−	0.289969i
$894$	5845.16	−	6277.93i	0.218670	−	0.234861i
$895$	−28356.0			−1.05904
$896$	−16379.2	+	27598.2i	−0.610703	+	1.02901i
$897$	25985.2			0.967246
$898$	−4120.39	+	4425.46i	−0.153117	+	0.164454i
$899$	−1154.59	+	1154.59i	−0.0428339	+	0.0428339i
$900$	95.8852	+	1341.29i	0.00355130	+	0.0496774i
$901$	12339.3	+	12339.3i	0.456250	+	0.456250i
$902$	116.138	+	3253.33i	0.00428710	+	0.120093i
$903$		−	32676.6i		−	1.20422i
$904$	31736.8	+	25577.8i	1.16764	+	0.941045i
$905$			20252.8i			0.743896i
$906$	−27057.5	+	965.901i	−0.992191	+	0.0354193i
$907$	11317.0	+	11317.0i	0.414305	+	0.414305i	0.883235	−	0.468930i	$-0.155360\pi$
$907$	11317.0	+	11317.0i	0.414305	+	0.414305i	−0.468930	+	0.883235i	$0.655360\pi$
$908$	15412.0	+	13355.5i	0.563286	+	0.488124i
$909$	−5407.54	+	5407.54i	−0.197312	+	0.197312i
$910$	−34725.8	−	32332.0i	−1.26500	−	1.17780i
$911$	5574.60			0.202738			0.101369	−	0.994849i	$-0.467678\pi$
$911$	5574.60			0.202738			0.101369	+	0.994849i	$0.467678\pi$
$912$	−2106.53	−	14658.3i	−0.0764849	−	0.532221i
$913$	−2760.91			−0.100080
$914$	−32355.2	−	30124.7i	−1.17091	−	1.09019i
$915$	−5516.80	+	5516.80i	−0.199322	+	0.199322i
$916$	21453.1	−	24756.5i	0.773833	−	0.892989i
$917$	30050.1	+	30050.1i	1.08216	+	1.08216i
$918$	−4482.24	+	160.007i	−0.161150	+	0.00575275i
$919$			10717.9i			0.384713i	0.981325	+	0.192356i	$0.0616130\pi$
$919$			10717.9i			0.384713i	−0.981325	+	0.192356i	$0.938387\pi$
$920$	27371.6	−	2941.33i	0.980884	−	0.105405i
$921$			22834.0i			0.816944i
$922$	−332.958	−	9327.05i	−0.0118930	−	0.333156i
$923$	−45897.6	−	45897.6i	−1.63677	−	1.63677i
$924$	−6182.98	+	442.004i	−0.220136	+	0.0157369i
$925$	4957.72	−	4957.72i	0.176226	−	0.176226i
$926$	32606.7	−	35020.9i	1.15715	−	1.24283i
$927$	−276.147			−0.00978410
$928$	−7963.50	−	44160.2i	−0.281697	−	1.56210i
$929$	−5276.25			−0.186338			−0.0931692	−	0.995650i	$-0.529700\pi$
$929$	−5276.25			−0.186338			−0.0931692	+	0.995650i	$0.529700\pi$
$930$	−392.725	+	421.802i	−0.0138473	+	0.0148725i
$931$	8077.87	−	8077.87i	0.284362	−	0.284362i
$932$	34009.3	−	2431.23i	1.19529	−	0.0854481i
$933$	−16558.4	−	16558.4i	−0.581025	−	0.581025i
$934$	463.726	+	12990.2i	0.0162458	+	0.455089i
$935$			7057.98i			0.246867i
$936$	−1597.31	−	14864.3i	−0.0557798	−	0.519077i
$937$		−	34230.9i		−	1.19346i	−0.802441	−	0.596731i	$-0.796466\pi$
$937$		−	34230.9i		−	1.19346i	0.802441	−	0.596731i	$-0.203534\pi$
$938$	42585.4	−	1520.22i	1.48237	−	0.0529178i
$939$	−3286.45	−	3286.45i	−0.114216	−	0.114216i
$940$	7664.65	−	8844.88i	0.265951	−	0.306902i
$941$	2969.85	−	2969.85i	0.102884	−	0.102884i	−0.653791	−	0.756675i	$-0.726822\pi$
$941$	2969.85	−	2969.85i	0.102884	−	0.102884i	0.756675	+	0.653791i	$0.226822\pi$
$942$	4144.34	+	3858.64i	0.143344	+	0.133462i
$943$	11652.0			0.402376
$944$	−30960.5	−	23180.0i	−1.06746	−	0.799201i
$945$	6169.76			0.212383
$946$	−11858.1	−	11040.7i	−0.407548	−	0.379453i
$947$	37250.4	−	37250.4i	1.27822	−	1.27822i	0.336557	−	0.941663i	$-0.390737\pi$
$947$	37250.4	−	37250.4i	1.27822	−	1.27822i	0.941663	−	0.336557i	$-0.109263\pi$
$948$	7638.88	+	6619.58i	0.261708	+	0.226787i
$949$	41244.3	+	41244.3i	1.41080	+	1.41080i
$950$	−4071.81	+	145.356i	−0.139060	+	0.00496417i
$951$			25932.5i			0.884247i
$952$	−18480.2	+	22930.2i	−0.629147	+	0.780642i
$953$			39434.0i			1.34039i	0.742185	+	0.670195i	$0.233790\pi$
$953$			39434.0i			1.34039i	−0.742185	+	0.670195i	$0.766210\pi$
$954$	−269.835	−	7558.81i	−0.00915747	−	0.256526i
$955$	12793.0	+	12793.0i	0.433478	+	0.433478i
$956$	−1887.10	−	26397.7i	−0.0638423	−	0.893058i
$957$	6128.65	−	6128.65i	0.207013	−	0.207013i
$958$	−18849.9	+	20245.5i	−0.635713	+	0.682781i
$959$	40625.3			1.36795
$960$	−3365.07	−	15476.6i	−0.113133	−	0.520317i
$961$	−29747.6			−0.998544
$962$	−53116.2	+	57048.9i	−1.78018	+	1.91199i
$963$	7311.20	−	7311.20i	0.244652	−	0.244652i
$964$	1825.42	+	25535.0i	0.0609885	+	0.853139i
$965$	−29976.2	−	29976.2i	−0.999967	−	0.999967i
$966$	791.531	+	22172.9i	0.0263634	+	0.738512i
$967$		−	2688.08i		−	0.0893927i	−0.999001	−	0.0446964i	$-0.985768\pi$
$967$		−	2688.08i		−	0.0893927i	0.999001	−	0.0446964i	$-0.0142320\pi$
$968$	16970.1	−	21056.4i	0.563469	−	0.699150i
$969$		−	13589.6i		−	0.450526i
$970$	−31588.9	+	1127.66i	−1.04563	+	0.0373268i
$971$	33370.7	+	33370.7i	1.10290	+	1.10290i	0.994059	+	0.108840i	$0.0347137\pi$
$971$	33370.7	+	33370.7i	1.10290	+	1.10290i	0.108840	+	0.994059i	$0.465286\pi$
$972$	1469.13	+	1273.10i	0.0484799	+	0.0420110i
$973$	−15636.9	+	15636.9i	−0.515205	+	0.515205i
$974$	5610.26	+	5223.52i	0.184563	+	0.171840i
$975$	−4113.20			−0.135105
$976$	−9674.18	+	12921.4i	−0.317277	+	0.423773i
$977$	8643.45			0.283039			0.141519	−	0.989936i	$-0.454801\pi$
$977$	8643.45			0.283039			0.141519	+	0.989936i	$0.454801\pi$
$978$	2419.31	+	2252.53i	0.0791012	+	0.0736483i
$979$	5472.27	−	5472.27i	0.178646	−	0.178646i
$980$	8001.30	−	9233.36i	0.260808	−	0.300968i
$981$	1332.31	+	1332.31i	0.0433612	+	0.0433612i
$982$	7532.02	−	268.879i	0.244762	−	0.00873753i
$983$		−	50643.1i		−	1.64320i	−0.570067	−	0.821598i	$-0.693083\pi$
$983$		−	50643.1i		−	1.64320i	0.570067	−	0.821598i	$-0.306917\pi$
$984$	−716.250	−	6665.30i	−0.0232045	−	0.215937i
$985$			8535.36i			0.276101i
$986$	−1469.03	−	41151.6i	−0.0474478	−	1.32914i
$987$	6669.89	+	6669.89i	0.215101	+	0.215101i
$988$	45182.1	−	3229.94i	1.45489	−	0.104006i
$989$	−41006.6	+	41006.6i	−1.31844	+	1.31844i
$990$	2084.62	−	2238.96i	0.0669228	−	0.0718777i
$991$	−11424.2			−0.366198			−0.183099	−	0.983094i	$-0.558613\pi$
$991$	−11424.2			−0.366198			−0.183099	+	0.983094i	$0.558613\pi$
$992$	−680.120	+	979.381i	−0.0217680	+	0.0313462i
$993$	15015.0			0.479846
$994$	37765.9	−	40562.1i	1.20509	−	1.29432i
$995$	19107.7	−	19107.7i	0.608799	−	0.608799i
$996$	5670.91	−	405.398i	0.180411	−	0.0128971i
$997$	35877.3	+	35877.3i	1.13967	+	1.13967i	0.988510	+	0.151155i	$0.0482993\pi$
$997$	35877.3	+	35877.3i	1.13967	+	1.13967i	0.151155	+	0.988510i	$0.451701\pi$
$998$	−1581.93	−	44314.2i	−0.0501755	−	1.40555i
$999$		−	10135.9i		−	0.321007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.37.3	yes	24
3.2	odd	2		144.4.k.b.37.10		24
4.3	odd	2		192.4.j.a.49.2		24
8.3	odd	2		384.4.j.a.97.8		24
8.5	even	2		384.4.j.b.97.5		24
12.11	even	2		576.4.k.b.433.9		24
16.3	odd	4		192.4.j.a.145.2		24
16.5	even	4		384.4.j.b.289.5		24
16.11	odd	4		384.4.j.a.289.8		24
16.13	even	4	inner	48.4.j.a.13.3	✓	24
48.29	odd	4		144.4.k.b.109.10		24
48.35	even	4		576.4.k.b.145.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.3	✓	24	16.13	even	4	inner
48.4.j.a.37.3	yes	24	1.1	even	1	trivial
144.4.k.b.37.10		24	3.2	odd	2
144.4.k.b.109.10		24	48.29	odd	4
192.4.j.a.49.2		24	4.3	odd	2
192.4.j.a.145.2		24	16.3	odd	4
384.4.j.a.97.8		24	8.3	odd	2
384.4.j.a.289.8		24	16.11	odd	4
384.4.j.b.97.5		24	8.5	even	2
384.4.j.b.289.5		24	16.5	even	4
576.4.k.b.145.9		24	48.35	even	4
576.4.k.b.433.9		24	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92738 + 2.07008i) q^{2} +(2.12132 - 2.12132i) q^{3} +(-0.570442 - 7.97964i) q^{4} +(-7.29121 - 7.29121i) q^{5} +(0.302715 + 8.47988i) q^{6} -22.1610i q^{7} +(17.6179 + 14.1989i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(-1.92738 + 2.07008i) q^{2} +(2.12132 - 2.12132i) q^{3} +(-0.570442 - 7.97964i) q^{4} +(-7.29121 - 7.29121i) q^{5} +(0.302715 + 8.47988i) q^{6} -22.1610i q^{7} +(17.6179 + 14.1989i) q^{8} -9.00000i q^{9} +(29.1463 - 1.04047i) q^{10} +(8.24116 + 8.24116i) q^{11} +(-18.1375 - 15.7173i) q^{12} +(51.9094 - 51.9094i) q^{13} +(45.8751 + 42.7127i) q^{14} -30.9340 q^{15} +(-63.3492 + 9.10384i) q^{16} -58.7304 q^{17} +(18.6307 + 17.3464i) q^{18} +(-54.5389 + 54.5389i) q^{19} +(-54.0220 + 62.3404i) q^{20} +(-47.0107 - 47.0107i) q^{21} +(-32.9437 + 1.17603i) q^{22} +117.989i q^{23} +(67.4937 - 7.25284i) q^{24} -18.6766i q^{25} +(7.40755 + 207.506i) q^{26} +(-19.0919 - 19.0919i) q^{27} +(-176.837 + 12.6416i) q^{28} +(175.283 - 175.283i) q^{29} +(59.6214 - 64.0357i) q^{30} -6.58699 q^{31} +(103.252 - 148.684i) q^{32} +34.9643 q^{33} +(113.195 - 121.576i) q^{34} +(-161.581 + 161.581i) q^{35} +(-71.8167 + 5.13398i) q^{36} +(265.451 + 265.451i) q^{37} +(-7.78278 - 218.017i) q^{38} -220.233i q^{39} +(-24.9288 - 231.983i) q^{40} -98.7545i q^{41} +(187.923 - 6.70849i) q^{42} +(347.544 + 347.544i) q^{43} +(61.0604 - 70.4626i) q^{44} +(-65.6209 + 65.6209i) q^{45} +(-244.247 - 227.410i) q^{46} -141.880 q^{47} +(-115.072 + 153.696i) q^{48} -148.112 q^{49} +(38.6620 + 35.9968i) q^{50} +(-124.586 + 124.586i) q^{51} +(-443.830 - 384.607i) q^{52} +(-210.101 - 210.101i) q^{53} +(76.3189 - 2.72444i) q^{54} -120.176i q^{55} +(314.662 - 390.432i) q^{56} +231.389i q^{57} +(25.0132 + 700.687i) q^{58} +(427.318 + 427.318i) q^{59} +(17.6460 + 246.842i) q^{60} +(178.341 - 178.341i) q^{61} +(12.6956 - 13.6356i) q^{62} -199.449 q^{63} +(108.782 + 500.310i) q^{64} -756.965 q^{65} +(-67.3893 + 72.3788i) q^{66} +(480.715 - 480.715i) q^{67} +(33.5023 + 468.647i) q^{68} +(250.293 + 250.293i) q^{69} +(-23.0578 - 645.912i) q^{70} -884.186i q^{71} +(127.790 - 158.561i) q^{72} +794.543i q^{73} +(-1061.13 + 37.8802i) q^{74} +(-39.6190 - 39.6190i) q^{75} +(466.312 + 404.090i) q^{76} +(182.633 - 182.633i) q^{77} +(455.899 + 424.472i) q^{78} -421.166 q^{79} +(528.270 + 395.514i) q^{80} -81.0000 q^{81} +(204.429 + 190.337i) q^{82} +(-167.507 + 167.507i) q^{83} +(-348.311 + 401.945i) q^{84} +(428.215 + 428.215i) q^{85} +(-1389.29 + 49.5951i) q^{86} -743.664i q^{87} +(28.1767 + 262.208i) q^{88} -664.016i q^{89} +(-9.36419 - 262.316i) q^{90} +(-1150.37 - 1150.37i) q^{91} +(941.513 - 67.3062i) q^{92} +(-13.9731 + 13.9731i) q^{93} +(273.457 - 293.703i) q^{94} +795.309 q^{95} +(-96.3763 - 534.438i) q^{96} -1083.81 q^{97} +(285.467 - 306.603i) q^{98} +(74.1705 - 74.1705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) \) 24 * q - 20 * q^4 + 84 * q^8	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

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