LMFDB - Embedded newform 130.4.n.a.9.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,4,Mod(9,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.9"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	130.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.67024830075$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	130.9
Dual form			130.4.n.a.29.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 - 1.00000i) q^{2} +(-2.39309 - 1.38165i) q^{3} +(2.00000 + 3.46410i) q^{4} +(-10.8544 - 2.68005i) q^{5} +(2.76331 + 4.78619i) q^{6} +(29.2023 - 16.8600i) q^{7} -8.00000i q^{8} +(-9.68207 - 16.7698i) q^{9} +(16.1203 + 15.4964i) q^{10} +(-21.7724 + 37.7109i) q^{11} -11.0532i q^{12} +(-46.7468 + 3.42620i) q^{13} -67.4399 q^{14} +(22.2726 + 21.4106i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-52.6299 + 30.3859i) q^{17} +38.7283i q^{18} +(54.4507 + 94.3113i) q^{19} +(-12.4248 - 42.9607i) q^{20} -93.1786 q^{21} +(75.4219 - 43.5448i) q^{22} +(-49.0940 - 28.3445i) q^{23} +(-11.0532 + 19.1448i) q^{24} +(110.635 + 58.1805i) q^{25} +(84.3940 + 40.8124i) q^{26} +128.118i q^{27} +(116.809 + 67.4399i) q^{28} +(-70.6859 + 122.432i) q^{29} +(-17.1667 - 59.3569i) q^{30} -263.182 q^{31} +(27.7128 - 16.0000i) q^{32} +(104.207 - 60.1639i) q^{33} +121.544 q^{34} +(-362.158 + 104.741i) q^{35} +(38.7283 - 67.0793i) q^{36} +(-220.211 - 127.139i) q^{37} -217.803i q^{38} +(116.603 + 56.3886i) q^{39} +(-21.4404 + 86.8350i) q^{40} +(-69.1898 + 119.840i) q^{41} +(161.390 + 93.1786i) q^{42} +(247.329 - 142.795i) q^{43} -174.179 q^{44} +(60.1487 + 207.974i) q^{45} +(56.6889 + 98.1881i) q^{46} +40.5106i q^{47} +(38.2895 - 22.1065i) q^{48} +(397.017 - 687.654i) q^{49} +(-133.444 - 211.406i) q^{50} +167.931 q^{51} +(-105.362 - 155.083i) q^{52} -20.5468i q^{53} +(128.118 - 221.907i) q^{54} +(337.393 - 350.977i) q^{55} +(-134.880 - 233.619i) q^{56} -300.928i q^{57} +(244.863 - 141.372i) q^{58} +(-107.238 - 185.742i) q^{59} +(-29.6232 + 119.976i) q^{60} +(184.800 + 320.082i) q^{61} +(455.844 + 263.182i) q^{62} +(-565.478 - 326.479i) q^{63} -64.0000 q^{64} +(516.589 + 88.0946i) q^{65} -240.655 q^{66} +(-738.510 - 426.379i) q^{67} +(-210.520 - 121.544i) q^{68} +(78.3244 + 135.662i) q^{69} +(732.017 + 180.742i) q^{70} +(-5.93007 - 10.2712i) q^{71} +(-134.159 + 77.4565i) q^{72} +435.900i q^{73} +(254.278 + 440.423i) q^{74} +(-184.374 - 292.090i) q^{75} +(-217.803 + 377.245i) q^{76} +1468.33i q^{77} +(-145.574 - 214.271i) q^{78} -173.279 q^{79} +(123.971 - 128.962i) q^{80} +(-84.4007 + 146.186i) q^{81} +(239.680 - 138.380i) q^{82} -191.080i q^{83} +(-186.357 - 322.780i) q^{84} +(652.701 - 188.769i) q^{85} -571.182 q^{86} +(338.316 - 195.327i) q^{87} +(301.687 + 174.179i) q^{88} +(761.478 - 1318.92i) q^{89} +(103.794 - 420.371i) q^{90} +(-1307.35 + 888.202i) q^{91} -226.756i q^{92} +(629.819 + 363.626i) q^{93} +(40.5106 - 70.1664i) q^{94} +(-338.268 - 1169.62i) q^{95} -88.4258 q^{96} +(56.3476 - 32.5323i) q^{97} +(-1375.31 + 794.035i) q^{98} +843.208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) $ 44 * q + 88 * q^4 - 12 * q^5 + 266 * q^9 + 28 * q^10 + 2 * q^11 - 216 * q^14 - 64 * q^15 - 352 * q^16 + 14 * q^19 - 24 * q^20 - 32 * q^21 + 504 * q^25 + 336 * q^26 + 308 * q^29 + 104 * q^30 + 792 * q^31 - 352 * q^34 + 106 * q^35 - 1064 * q^36 + 120 * q^39 + 224 * q^40 + 140 * q^41 + 16 * q^44 - 522 * q^45 - 320 * q^46 + 536 * q^49 - 96 * q^50 - 256 * q^51 + 552 * q^54 + 1188 * q^55 - 432 * q^56 - 500 * q^59 - 512 * q^60 - 2352 * q^61 - 2816 * q^64 - 2924 * q^65 + 496 * q^66 + 376 * q^69 - 1008 * q^70 - 1268 * q^71 + 436 * q^74 + 3560 * q^75 - 56 * q^76 - 264 * q^79 + 96 * q^80 - 6326 * q^81 - 64 * q^84 + 606 * q^85 + 336 * q^86 + 4730 * q^89 + 3560 * q^90 + 5866 * q^91 + 1732 * q^94 + 2224 * q^95 + 2916 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	−2.39309	−	1.38165i	−0.460551	−	0.265899i	0.251725	−	0.967799i	$-0.419002\pi$
$3$	−2.39309	−	1.38165i	−0.460551	−	0.265899i	−0.712276	+	0.701900i	$0.752336\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$	−10.8544	−	2.68005i	−0.970844	−	0.239711i
$5$	−10.8544	−	2.68005i	−0.970844	−	0.239711i
$6$	2.76331	+	4.78619i	0.188019	+	0.325659i
$7$	29.2023	−	16.8600i	1.57678	−	0.910353i	0.581472	−	0.813566i	$-0.302477\pi$
$7$	29.2023	−	16.8600i	1.57678	−	0.910353i	0.995305	−	0.0967869i	$-0.0308565\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−9.68207	−	16.7698i	−0.358595	−	0.621105i
$10$	16.1203	+	15.4964i	0.509768	+	0.490038i
$11$	−21.7724	+	37.7109i	−0.596785	+	1.03366i	0.396508	+	0.918031i	$0.370222\pi$
$11$	−21.7724	+	37.7109i	−0.596785	+	1.03366i	−0.993292	+	0.115630i	$0.963111\pi$
$12$		−	11.0532i		−	0.265899i
$13$	−46.7468	+	3.42620i	−0.997325	+	0.0730967i
$13$	−46.7468	+	3.42620i	−0.997325	+	0.0730967i
$14$	−67.4399			−1.28743
$15$	22.2726	+	21.4106i	0.383384	+	0.368546i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−52.6299	+	30.3859i	−0.750861	+	0.433510i	−0.826005	−	0.563663i	$-0.809392\pi$
$17$	−52.6299	+	30.3859i	−0.750861	+	0.433510i	0.0751440	+	0.997173i	$0.476058\pi$
$18$			38.7283i			0.507130i
$19$	54.4507	+	94.3113i	0.657465	+	1.13876i	0.981270	+	0.192639i	$0.0617047\pi$
$19$	54.4507	+	94.3113i	0.657465	+	1.13876i	−0.323804	+	0.946124i	$0.604962\pi$
$20$	−12.4248	−	42.9607i	−0.138913	−	0.480316i
$21$	−93.1786			−0.968249
$22$	75.4219	−	43.5448i	0.730909	−	0.421990i
$23$	−49.0940	−	28.3445i	−0.445079	−	0.256966i	0.260671	−	0.965428i	$-0.416056\pi$
$23$	−49.0940	−	28.3445i	−0.445079	−	0.256966i	−0.705750	+	0.708461i	$0.749390\pi$
$24$	−11.0532	+	19.1448i	−0.0940096	+	0.162829i
$25$	110.635	+	58.1805i	0.885077	+	0.465444i
$26$	84.3940	+	40.8124i	0.636578	+	0.307845i
$27$			128.118i			0.913199i
$28$	116.809	+	67.4399i	0.788389	+	0.455176i
$29$	−70.6859	+	122.432i	−0.452622	+	0.783965i	−0.998548	−	0.0538687i	$-0.982845\pi$
$29$	−70.6859	+	122.432i	−0.452622	+	0.783965i	0.545926	+	0.837834i	$0.316178\pi$
$30$	−17.1667	−	59.3569i	−0.104473	−	0.361234i
$31$	−263.182			−1.52480			−0.762401	−	0.647105i	$-0.775980\pi$
$31$	−263.182			−1.52480			−0.762401	+	0.647105i	$0.775980\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	104.207	−	60.1639i	0.549700	−	0.317369i
$34$	121.544			0.613075
$35$	−362.158	+	104.741i	−1.74903	+	0.505840i
$36$	38.7283	−	67.0793i	0.179298	−	0.310552i
$37$	−220.211	−	127.139i	−0.978447	−	0.564907i	−0.0766462	−	0.997058i	$-0.524421\pi$
$37$	−220.211	−	127.139i	−0.978447	−	0.564907i	−0.901801	+	0.432152i	$0.857755\pi$
$38$		−	217.803i		−	0.929796i
$39$	116.603	+	56.3886i	0.478755	+	0.231523i
$40$	−21.4404	+	86.8350i	−0.0847507	+	0.343245i
$41$	−69.1898	+	119.840i	−0.263552	+	0.456485i	−0.967183	−	0.254080i	$-0.918227\pi$
$41$	−69.1898	+	119.840i	−0.263552	+	0.456485i	0.703631	+	0.710565i	$0.251561\pi$
$42$	161.390	+	93.1786i	0.592929	+	0.342328i
$43$	247.329	−	142.795i	0.877146	−	0.506421i	0.00742997	−	0.999972i	$-0.497635\pi$
$43$	247.329	−	142.795i	0.877146	−	0.506421i	0.869716	+	0.493552i	$0.164302\pi$
$44$	−174.179			−0.596785
$45$	60.1487	+	207.974i	0.199254	+	0.688955i
$46$	56.6889	+	98.1881i	0.181703	+	0.314718i
$47$			40.5106i			0.125725i	0.998022	+	0.0628625i	$0.0200230\pi$
$47$			40.5106i			0.125725i	−0.998022	+	0.0628625i	$0.979977\pi$
$48$	38.2895	−	22.1065i	0.115138	−	0.0664748i
$49$	397.017	−	687.654i	1.15749	−	2.00482i
$50$	−133.444	−	211.406i	−0.377437	−	0.597947i
$51$	167.931			0.461080
$52$	−105.362	−	155.083i	−0.280983	−	0.413580i
$53$		−	20.5468i		−	0.0532512i	−0.999645	−	0.0266256i	$-0.991524\pi$
$53$		−	20.5468i		−	0.0532512i	0.999645	−	0.0266256i	$-0.00847620\pi$
$54$	128.118	−	221.907i	0.322865	−	0.559218i
$55$	337.393	−	350.977i	0.827165	−	0.860468i
$56$	−134.880	−	233.619i	−0.321858	−	0.557475i
$57$		−	300.928i		−	0.699278i
$58$	244.863	−	141.372i	0.554347	−	0.320052i
$59$	−107.238	−	185.742i	−0.236631	−	0.409857i	0.723115	−	0.690728i	$-0.242710\pi$
$59$	−107.238	−	185.742i	−0.236631	−	0.409857i	−0.959745	+	0.280871i	$0.909377\pi$
$60$	−29.6232	+	119.976i	−0.0637390	+	0.258147i
$61$	184.800	+	320.082i	0.387888	+	0.671841i	0.992165	−	0.124933i	$-0.0398715\pi$
$61$	184.800	+	320.082i	0.387888	+	0.671841i	−0.604277	+	0.796774i	$0.706538\pi$
$62$	455.844	+	263.182i	0.933747	+	0.539099i
$63$	−565.478	−	326.479i	−1.13085	−	0.652896i
$64$	−64.0000			−0.125000
$65$	516.589	+	88.0946i	0.985769	+	0.168104i
$66$	−240.655			−0.448828
$67$	−738.510	−	426.379i	−1.34662	−	0.777470i	−0.358849	−	0.933396i	$-0.616831\pi$
$67$	−738.510	−	426.379i	−1.34662	−	0.777470i	−0.987769	+	0.155925i	$0.950164\pi$
$68$	−210.520	−	121.544i	−0.375430	−	0.216755i
$69$	78.3244	+	135.662i	0.136654	+	0.236692i
$70$	732.017	+	180.742i	1.24990	+	0.308612i
$71$	−5.93007	−	10.2712i	−0.00991226	−	0.0171685i	0.861027	−	0.508560i	$-0.169822\pi$
$71$	−5.93007	−	10.2712i	−0.00991226	−	0.0171685i	−0.870939	+	0.491391i	$0.836489\pi$
$72$	−134.159	+	77.4565i	−0.219594	+	0.126783i
$73$			435.900i			0.698880i	0.936959	+	0.349440i	$0.113628\pi$
$73$			435.900i			0.698880i	−0.936959	+	0.349440i	$0.886372\pi$
$74$	254.278	+	440.423i	0.399449	+	0.691867i
$75$	−184.374	−	292.090i	−0.283862	−	0.449702i
$76$	−217.803	+	377.245i	−0.328733	+	0.569382i
$77$			1468.33i			2.17314i
$78$	−145.574	−	214.271i	−0.211321	−	0.311044i
$79$	−173.279			−0.246777			−0.123388	−	0.992358i	$-0.539376\pi$
$79$	−173.279			−0.246777			−0.123388	+	0.992358i	$0.539376\pi$
$80$	123.971	−	128.962i	0.173255	−	0.180230i
$81$	−84.4007	+	146.186i	−0.115776	+	0.200530i
$82$	239.680	−	138.380i	0.322784	−	0.186359i
$83$		−	191.080i		−	0.252696i	−0.991986	−	0.126348i	$-0.959674\pi$
$83$		−	191.080i		−	0.252696i	0.991986	−	0.126348i	$-0.0403256\pi$
$84$	−186.357	−	322.780i	−0.242062	−	0.419264i
$85$	652.701	−	188.769i	0.832886	−	0.240881i
$86$	−571.182			−0.716187
$87$	338.316	−	195.327i	0.416912	−	0.240704i
$88$	301.687	+	174.179i	0.365454	+	0.210995i
$89$	761.478	−	1318.92i	0.906927	−	1.57084i	0.0886164	−	0.996066i	$-0.471755\pi$
$89$	761.478	−	1318.92i	0.906927	−	1.57084i	0.818310	−	0.574777i	$-0.194911\pi$
$90$	103.794	−	420.371i	0.121565	−	0.492344i
$91$	−1307.35	+	888.202i	−1.50602	+	1.02317i
$92$		−	226.756i		−	0.256966i
$93$	629.819	+	363.626i	0.702249	+	0.405444i
$94$	40.5106	−	70.1664i	0.0444505	−	0.0769906i
$95$	−338.268	−	1169.62i	−0.365322	−	1.26316i
$96$	−88.4258			−0.0940096
$97$	56.3476	−	32.5323i	0.0589817	−	0.0340531i	−0.470219	−	0.882550i	$-0.655825\pi$
$97$	56.3476	−	32.5323i	0.0589817	−	0.0340531i	0.529201	+	0.848497i	$0.322492\pi$
$98$	−1375.31	+	794.035i	−1.41762	+	0.818466i
$99$	843.208			0.856016
$100$	19.7260	+	499.611i	0.0197260	+	0.499611i
$101$	−719.502	+	1246.21i	−0.708843	+	1.22775i	0.256443	+	0.966559i	$0.417449\pi$
$101$	−719.502	+	1246.21i	−0.708843	+	1.22775i	−0.965287	+	0.261193i	$0.915884\pi$
$102$	−290.865	−	167.931i	−0.282353	−	0.163016i
$103$		−	840.853i		−	0.804386i	−0.915555	−	0.402193i	$-0.868248\pi$
$103$		−	840.853i		−	0.804386i	0.915555	−	0.402193i	$-0.131752\pi$
$104$	27.4096	+	373.974i	0.0258436	+	0.352608i
$105$	1011.39	+	249.723i	0.940019	+	0.232100i
$106$	−20.5468	+	35.5880i	−0.0188271	+	0.0326096i
$107$	181.790	+	104.957i	0.164246	+	0.0948275i	0.579870	−	0.814709i	$-0.303103\pi$
$107$	181.790	+	104.957i	0.164246	+	0.0948275i	−0.415624	+	0.909537i	$0.636437\pi$
$108$	−443.815	+	256.237i	−0.395427	+	0.228300i
$109$	−719.002			−0.631816			−0.315908	−	0.948790i	$-0.602309\pi$
$109$	−719.002			−0.631816			−0.315908	+	0.948790i	$0.602309\pi$
$110$	−935.359	+	270.517i	−0.810754	+	0.234480i
$111$	351.325	+	608.512i	0.300417	+	0.520337i
$112$			539.519i			0.455176i
$113$	−168.423	+	97.2391i	−0.140212	+	0.0809512i	−0.568465	−	0.822708i	$-0.692462\pi$
$113$	−168.423	+	97.2391i	−0.140212	+	0.0809512i	0.428253	+	0.903659i	$0.359129\pi$
$114$	−300.928	+	521.222i	−0.247232	+	0.428219i
$115$	456.920	+	439.236i	0.370505	+	0.356165i
$116$	−565.487			−0.452622
$117$	510.062	+	750.763i	0.403036	+	0.593231i
$118$			428.953i			0.334647i
$119$	−1024.61	+	1774.68i	−0.789294	+	1.36710i
$120$	171.285	−	178.181i	0.130301	−	0.135547i
$121$	−282.576	−	489.436i	−0.212304	−	0.367721i
$122$		−	739.198i		−	0.548556i
$123$	331.155	−	191.193i	0.242758	−	0.140157i
$124$	−526.364	−	911.689i	−0.381200	−	0.660259i
$125$	−1044.94	−	928.020i	−0.747700	−	0.664037i
$126$	652.958	+	1130.96i	0.461667	+	0.799631i
$127$	−231.666	−	133.752i	−0.161866	−	0.0934536i	0.416879	−	0.908962i	$-0.363124\pi$
$127$	−231.666	−	133.752i	−0.161866	−	0.0934536i	−0.578745	+	0.815509i	$0.696457\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	−789.175			−0.538628
$130$	−806.664	−	669.173i	−0.544224	−	0.451465i
$131$	−1521.34			−1.01466			−0.507329	−	0.861752i	$-0.669367\pi$
$131$	−1521.34			−1.01466			−0.507329	+	0.861752i	$0.669367\pi$
$132$	416.828	+	240.655i	0.274850	+	0.158685i
$133$	3180.17	+	1836.07i	2.07335	+	1.19705i
$134$	852.758	+	1477.02i	0.549754	+	0.952203i
$135$	343.364	−	1390.64i	0.218904	−	0.886574i
$136$	243.087	+	421.039i	0.153269	+	0.265469i
$137$	−473.403	+	273.320i	−0.295223	+	0.170447i	−0.640295	−	0.768129i	$-0.721188\pi$
$137$	−473.403	+	273.320i	−0.295223	+	0.170447i	0.345072	+	0.938576i	$0.387855\pi$
$138$		−	313.298i		−	0.193259i
$139$	1293.65	+	2240.66i	0.789393	+	1.36727i	0.926339	+	0.376690i	$0.122938\pi$
$139$	1293.65	+	2240.66i	0.789393	+	1.36727i	−0.136947	+	0.990578i	$0.543729\pi$
$140$	−1087.15	−	1045.07i	−0.656292	−	0.630891i
$141$	55.9716	−	96.9457i	0.0334302	−	0.0579028i
$142$			23.7203i			0.0140180i
$143$	888.585	−	1837.46i	0.519631	−	1.07452i
$144$	309.826			0.179298
$145$	1095.37	−	1139.48i	0.627351	−	0.652609i
$146$	435.900	−	755.001i	0.247091	−	0.427975i
$147$	−1900.20	+	1097.08i	−1.06616	+	0.615549i
$148$		−	1017.11i		−	0.564907i
$149$	−1663.88	−	2881.92i	−0.914833	−	1.58454i	−0.807146	−	0.590352i	$-0.798989\pi$
$149$	−1663.88	−	2881.92i	−0.914833	−	1.58454i	−0.107687	−	0.994185i	$-0.534344\pi$
$150$	27.2545	+	690.289i	0.0148354	+	0.375746i
$151$	−929.590			−0.500987			−0.250493	−	0.968118i	$-0.580593\pi$
$151$	−929.590			−0.500987			−0.250493	+	0.968118i	$0.580593\pi$
$152$	754.491	−	435.605i	0.402614	−	0.232449i
$153$	1019.13	+	588.397i	0.538510	+	0.310909i
$154$	1468.33	−	2543.22i	0.768320	−	1.33077i
$155$	2856.67	+	705.341i	1.48035	+	0.365512i
$156$	37.8706	+	516.703i	0.0194364	+	0.265188i
$157$		−	3587.36i		−	1.82358i	−0.410652	−	0.911792i	$-0.634699\pi$
$157$		−	3587.36i		−	1.82358i	0.410652	−	0.911792i	$-0.365301\pi$
$158$	300.128	+	173.279i	0.151119	+	0.0872488i
$159$	−28.3885	+	49.1703i	−0.0141595	+	0.0245249i
$160$	−343.686	+	99.3981i	−0.169817	+	0.0491132i
$161$	−1911.55			−0.935721
$162$	292.373	−	168.801i	0.141796	−	0.0818660i
$163$	−3099.14	+	1789.29i	−1.48922	+	0.859804i	−0.999924	−	0.0123125i	$-0.996081\pi$
$163$	−3099.14	+	1789.29i	−1.48922	+	0.859804i	−0.489299	+	0.872116i	$0.662747\pi$
$164$	−553.518			−0.263552
$165$	−1292.34	+	373.761i	−0.609750	+	0.176347i
$166$	−191.080	+	330.961i	−0.0893415	+	0.154744i
$167$	−2349.43	−	1356.45i	−1.08865	−	0.628532i	−0.155433	−	0.987846i	$-0.549677\pi$
$167$	−2349.43	−	1356.45i	−1.08865	−	0.628532i	−0.933217	+	0.359314i	$0.883011\pi$
$168$			745.428i			0.342328i
$169$	2173.52	−	320.328i	0.989314	−	0.145802i
$170$	−1319.28	−	325.743i	−0.595201	−	0.146961i
$171$	1054.39	−	1826.26i	0.471528	−	0.816710i
$172$	989.315	+	571.182i	0.438573	+	0.253210i
$173$	−2161.34	+	1247.85i	−0.949849	+	0.548395i	−0.893034	−	0.449989i	$-0.851428\pi$
$173$	−2161.34	+	1247.85i	−0.949849	+	0.548395i	−0.0568148	+	0.998385i	$0.518094\pi$
$174$	−781.308			−0.340407
$175$	4211.71	−	166.290i	1.81929	−	0.0718304i
$176$	−348.359	−	603.375i	−0.149196	−	0.258415i
$177$			592.664i			0.251680i
$178$	−2637.84	+	1522.96i	−1.11075	+	0.641294i
$179$	2099.07	−	3635.70i	0.876492	−	1.51813i	0.0213263	−	0.999773i	$-0.493211\pi$
$179$	2099.07	−	3635.70i	0.876492	−	1.51813i	0.855165	−	0.518355i	$-0.173456\pi$
$180$	−600.147	+	624.310i	−0.248513	+	0.258518i
$181$	4029.33			1.65469			0.827343	−	0.561697i	$-0.189851\pi$
$181$	4029.33			1.65469			0.827343	+	0.561697i	$0.189851\pi$
$182$	3152.60	−	231.063i	1.28399	−	0.0941071i
$183$		−	1021.32i		−	0.412556i
$184$	−226.756	+	392.752i	−0.0908514	+	0.157359i
$185$	2049.52	+	1970.19i	0.814505	+	0.782981i
$186$	−727.252	−	1259.64i	−0.286692	−	0.496565i
$187$		−	2646.30i		−	1.03485i
$188$	−140.333	+	81.0212i	−0.0544406	+	0.0314313i
$189$	2160.07	+	3741.35i	0.831334	+	1.43991i
$190$	−583.723	+	2364.11i	−0.222883	+	0.902688i
$191$	−1837.69	−	3182.97i	−0.696181	−	1.20582i	−0.969781	−	0.243977i	$-0.921548\pi$
$191$	−1837.69	−	3182.97i	−0.696181	−	1.20582i	0.273600	−	0.961843i	$-0.411785\pi$
$192$	153.158	+	88.4258i	0.0575689	+	0.0332374i
$193$	−784.470	−	452.914i	−0.292577	−	0.168919i	0.346526	−	0.938040i	$-0.387361\pi$
$193$	−784.470	−	452.914i	−0.292577	−	0.168919i	−0.639103	+	0.769121i	$0.720694\pi$
$194$	−130.129			−0.0481584
$195$	−1114.53	−	924.566i	−0.409298	−	0.339536i
$196$	3176.14			1.15749
$197$	2051.06	+	1184.18i	0.741788	+	0.428272i	0.822719	−	0.568448i	$-0.192456\pi$
$197$	2051.06	+	1184.18i	0.741788	+	0.428272i	−0.0809310	+	0.996720i	$0.525789\pi$
$198$	−1460.48	−	843.208i	−0.524201	−	0.302647i
$199$	977.928	+	1693.82i	0.348359	+	0.603376i	0.985958	−	0.166993i	$-0.0534057\pi$
$199$	977.928	+	1693.82i	0.348359	+	0.603376i	−0.637599	+	0.770368i	$0.720072\pi$
$200$	465.444	−	885.077i	0.164559	−	0.312922i
$201$	1178.22	+	2040.73i	0.413458	+	0.716130i
$202$	2492.43	−	1439.00i	0.868152	−	0.501228i
$203$			4767.05i			1.64818i
$204$	335.862	+	581.731i	0.115270	+	0.199653i
$205$	1072.19	−	1115.36i	0.365292	−	0.380000i
$206$	−840.853	+	1456.40i	−0.284393	+	0.492584i
$207$			1097.73i			0.368588i
$208$	326.499	−	675.152i	0.108840	−	0.225064i
$209$	−4742.09			−1.56946
$210$	−1502.06	−	1443.93i	−0.493582	−	0.474479i
$211$	−650.683	+	1127.02i	−0.212298	+	0.367711i	−0.952433	−	0.304747i	$-0.901428\pi$
$211$	−650.683	+	1127.02i	−0.212298	+	0.367711i	0.740135	+	0.672458i	$0.234761\pi$
$212$	71.1761	−	41.0935i	0.0230585	−	0.0133128i
$213$			32.7732i			0.0105426i
$214$	−209.913	−	363.581i	−0.0670532	−	0.116140i
$215$	−3067.30	+	887.100i	−0.972967	+	0.281394i
$216$	1024.95			0.322865
$217$	−7685.52	+	4437.24i	−2.40427	+	1.38811i
$218$	1245.35	+	719.002i	0.386906	+	0.223381i
$219$	602.263	−	1043.15i	0.185832	−	0.321870i
$220$	1890.61	+	466.810i	0.579385	+	0.143056i
$221$	2356.17	−	1600.76i	0.717164	−	0.487235i
$222$		−	1405.30i		−	0.424853i
$223$	−4311.08	−	2489.00i	−1.29458	−	0.747425i	−0.315117	−	0.949053i	$-0.602044\pi$
$223$	−4311.08	−	2489.00i	−1.29458	−	0.747425i	−0.979462	+	0.201628i	$0.935377\pi$
$224$	539.519	−	934.475i	0.160929	−	0.278738i
$225$	−95.4941	−	2418.63i	−0.0282945	−	0.716632i
$226$	388.957			0.114482
$227$	1325.20	−	765.104i	0.387474	−	0.223708i	−0.293591	−	0.955931i	$-0.594850\pi$
$227$	1325.20	−	765.104i	0.387474	−	0.223708i	0.681065	+	0.732223i	$0.261517\pi$
$228$	1042.44	−	601.856i	0.302796	−	0.174820i
$229$	641.587			0.185141			0.0925704	−	0.995706i	$-0.470492\pi$
$229$	641.587			0.185141			0.0925704	+	0.995706i	$0.470492\pi$
$230$	−352.173	−	1217.70i	−0.100964	−	0.349099i
$231$	2028.72	−	3513.85i	0.577836	−	1.00084i
$232$	979.453	+	565.487i	0.277173	+	0.160026i
$233$		−	3312.61i		−	0.931401i	−0.884942	−	0.465701i	$-0.845802\pi$
$233$		−	3312.61i		−	0.931401i	0.884942	−	0.465701i	$-0.154198\pi$
$234$	−132.691	−	1810.42i	−0.0370695	−	0.505773i
$235$	108.571	−	439.717i	0.0301377	−	0.122059i
$236$	428.953	−	742.968i	0.118315	−	0.204928i
$237$	414.672	+	239.411i	0.113653	+	0.0656178i
$238$	3549.36	−	2049.22i	0.966683	−	0.558115i
$239$	−4058.34			−1.09838			−0.549189	−	0.835698i	$-0.685063\pi$
$239$	−4058.34			−1.09838			−0.549189	+	0.835698i	$0.685063\pi$
$240$	−474.855	+	137.334i	−0.127716	+	0.0369369i
$241$	729.605	+	1263.71i	0.195012	+	0.337771i	0.946905	−	0.321515i	$-0.104192\pi$
$241$	729.605	+	1263.71i	0.195012	+	0.337771i	−0.751892	+	0.659286i	$0.770859\pi$
$242$			1130.30i			0.300243i
$243$	3399.71	−	1962.82i	0.897495	−	0.518169i
$244$	−739.198	+	1280.33i	−0.193944	+	0.335921i
$245$	−6152.32	+	6400.03i	−1.60432	+	1.66891i
$246$	−764.770			−0.198211
$247$	−2868.52	−	4222.19i	−0.738946	−	1.08766i
$248$			2105.45i			0.539099i
$249$	−264.007	+	457.273i	−0.0671917	+	0.116379i
$250$	881.874	+	2652.32i	0.223098	+	0.670990i
$251$	2559.91	+	4433.89i	0.643745	+	1.11500i	0.984590	+	0.174879i	$0.0559535\pi$
$251$	2559.91	+	4433.89i	0.643745	+	1.11500i	−0.340845	+	0.940120i	$0.610713\pi$
$252$		−	2611.83i		−	0.652896i
$253$	2137.79	−	1234.25i	0.531233	−	0.306707i
$254$	267.505	+	463.332i	0.0660816	+	0.114457i
$255$	−1822.79	−	450.064i	−0.447637	−	0.110526i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	4448.83	+	2568.53i	1.07981	+	0.623427i	0.930844	−	0.365416i	$-0.119073\pi$
$257$	4448.83	+	2568.53i	1.07981	+	0.623427i	0.148962	+	0.988843i	$0.452407\pi$
$258$	1366.89	+	789.175i	0.329841	+	0.190434i
$259$	−8574.25			−2.05706
$260$	728.010	+	1965.71i	0.173651	+	0.468877i
$261$	2737.54			0.649233
$262$	2635.04	+	1521.34i	0.621349	+	0.358736i
$263$	2235.35	+	1290.58i	0.524096	+	0.302587i	0.738609	−	0.674134i	$-0.235483\pi$
$263$	2235.35	+	1290.58i	0.524096	+	0.302587i	−0.214513	+	0.976721i	$0.568816\pi$
$264$	−481.311	−	833.655i	−0.112207	−	0.194348i
$265$	−55.0664	+	223.022i	−0.0127649	+	0.0516986i
$266$	−3672.15	−	6360.35i	−0.846443	−	1.46608i
$267$	−3644.57	+	2104.20i	−0.835372	+	0.482302i
$268$		−	3411.03i		−	0.777470i
$269$	−98.9162	−	171.328i	−0.0224202	−	0.0388329i	0.854598	−	0.519291i	$-0.173804\pi$
$269$	−98.9162	−	171.328i	−0.0224202	−	0.0388329i	−0.877018	+	0.480458i	$0.840470\pi$
$270$	−1985.37	+	2065.30i	−0.447502	+	0.465519i
$271$	−960.080	+	1662.91i	−0.215205	+	0.372747i	−0.953336	−	0.301911i	$-0.902375\pi$
$271$	−960.080	+	1662.91i	−0.215205	+	0.372747i	0.738131	+	0.674658i	$0.235709\pi$
$272$		−	972.349i		−	0.216755i
$273$	4355.80	−	319.248i	0.965659	−	0.0707758i
$274$	1093.28			0.241049
$275$	−4602.83	+	2905.40i	−1.00931	+	0.637100i
$276$	−313.298	+	542.648i	−0.0683272	+	0.118346i
$277$	−2081.80	+	1201.93i	−0.451564	+	0.260710i	−0.708490	−	0.705720i	$-0.750623\pi$
$277$	−2081.80	+	1201.93i	−0.451564	+	0.260710i	0.256927	+	0.966431i	$0.417290\pi$
$278$		−	5174.58i		−	1.11637i
$279$	2548.14	+	4413.52i	0.546786	+	0.947062i
$280$	837.925	+	2897.27i	0.178841	+	0.618375i
$281$	−2169.92			−0.460663			−0.230332	−	0.973112i	$-0.573981\pi$
$281$	−2169.92			−0.460663			−0.230332	+	0.973112i	$0.573981\pi$
$282$	−193.891	+	111.943i	−0.0409435	+	0.0236387i
$283$	−1797.08	−	1037.54i	−0.377474	−	0.217935i	0.299244	−	0.954176i	$-0.403265\pi$
$283$	−1797.08	−	1037.54i	−0.377474	−	0.217935i	−0.676719	+	0.736242i	$0.736599\pi$
$284$	23.7203	−	41.0847i	0.00495613	−	0.00858426i
$285$	−806.502	+	3266.38i	−0.167625	+	0.678890i
$286$	−3376.54	+	2293.99i	−0.698107	+	0.474289i
$287$			4666.15i			0.959701i
$288$	−536.635	−	309.826i	−0.109797	−	0.0633913i
$289$	−609.893	+	1056.37i	−0.124139	+	0.215014i
$290$	−3036.72	+	878.256i	−0.614905	+	0.177838i
$291$	−179.793			−0.0362188
$292$	−1510.00	+	871.800i	−0.302624	+	0.174720i
$293$	2961.47	−	1709.81i	0.590482	−	0.340915i	−0.174806	−	0.984603i	$-0.555930\pi$
$293$	2961.47	−	1709.81i	0.590482	−	0.340915i	0.765288	+	0.643688i	$0.222597\pi$
$294$	4388.32			0.870518
$295$	666.205	+	2303.52i	0.131485	+	0.454630i
$296$	−1017.11	+	1761.69i	−0.199725	+	0.345933i
$297$	−4831.46	−	2789.45i	−0.943939	−	0.544983i
$298$			6655.51i			1.29377i
$299$	2392.10	+	1156.81i	0.462672	+	0.223745i
$300$	643.083	−	1222.87i	0.123761	−	0.235341i
$301$	4815.05	−	8339.92i	0.922043	−	1.59703i
$302$	1610.10	+	929.590i	0.306790	+	0.177126i
$303$	3443.67	−	1988.21i	0.652917	−	0.376962i
$304$	−1742.42			−0.328733
$305$	−1148.05	−	3969.56i	−0.215531	−	0.745234i
$306$	−1176.79	−	2038.27i	−0.219846	−	0.380784i
$307$			7196.25i			1.33782i	0.743342	+	0.668912i	$0.233240\pi$
$307$			7196.25i			1.33782i	−0.743342	+	0.668912i	$0.766760\pi$
$308$	−5086.44	+	2936.66i	−0.940997	+	0.543285i
$309$	−1161.77	+	2012.24i	−0.213886	+	0.370461i
$310$	−4242.56	−	4078.36i	−0.777295	−	0.747211i
$311$	3812.83			0.695195			0.347598	−	0.937644i	$-0.386997\pi$
$311$	3812.83			0.695195			0.347598	+	0.937644i	$0.386997\pi$
$312$	451.109	−	932.826i	0.0818558	−	0.169266i
$313$			2472.47i			0.446494i	0.974762	+	0.223247i	$0.0716656\pi$
$313$			2472.47i			0.446494i	−0.974762	+	0.223247i	$0.928334\pi$
$314$	−3587.36	+	6213.49i	−0.644734	+	1.11671i
$315$	5262.92	+	5059.23i	0.941372	+	0.904938i
$316$	−346.557	−	600.255i	−0.0616942	−	0.106858i
$317$		−	4401.69i		−	0.779885i	−0.920839	−	0.389942i	$-0.872495\pi$
$317$		−	4401.69i		−	0.779885i	0.920839	−	0.389942i	$-0.127505\pi$
$318$	98.3407	−	56.7770i	0.0173417	−	0.0100123i
$319$	−3078.01	−	5331.26i	−0.540236	−	0.935716i
$320$	694.680	+	171.523i	0.121356	+	0.0299639i
$321$	−290.028	−	502.342i	−0.0504292	−	0.0873459i
$322$	3310.90	+	1911.55i	0.573010	+	0.330827i
$323$	−5731.47	−	3309.07i	−0.987330	−	0.570035i
$324$	−675.205			−0.115776
$325$	−5371.15	−	2340.70i	−0.916732	−	0.399503i
$326$	7157.16			1.21595
$327$	1720.64	+	993.412i	0.290983	+	0.167999i
$328$	958.722	+	553.518i	0.161392	+	0.0931797i
$329$	683.008	+	1183.00i	0.114454	+	0.198240i
$330$	2612.16	+	644.969i	0.435742	+	0.107589i
$331$	−701.131	−	1214.39i	−0.116428	−	0.201659i	0.801922	−	0.597429i	$-0.203811\pi$
$331$	−701.131	−	1214.39i	−0.116428	−	0.201659i	−0.918350	+	0.395770i	$0.870478\pi$
$332$	661.921	−	382.160i	0.109421	−	0.0631740i
$333$			4923.88i			0.810291i
$334$	2712.89	+	4698.86i	0.444439	+	0.769792i
$335$	6873.35	+	6607.32i	1.12099	+	1.07760i
$336$	745.428	−	1291.12i	0.121031	−	0.209632i
$337$			2468.50i			0.399014i	0.979896	+	0.199507i	$0.0639341\pi$
$337$			2468.50i			0.399014i	−0.979896	+	0.199507i	$0.936066\pi$
$338$	−4084.98	−	1618.70i	−0.657377	−	0.260490i
$339$	537.403			0.0860995
$340$	1959.32	+	1883.48i	0.312526	+	0.300430i
$341$	5730.10	−	9924.83i	0.909978	−	1.57613i
$342$	−3652.52	+	2108.78i	−0.577501	+	0.333420i
$343$		−	15208.9i		−	2.39417i
$344$	−1142.36	−	1978.63i	−0.179047	−	0.310118i
$345$	−486.581	−	1682.44i	−0.0759324	−	0.262549i
$346$	4991.41			0.775548
$347$	893.246	−	515.716i	0.138190	−	0.0797841i	−0.429311	−	0.903157i	$-0.641244\pi$
$347$	893.246	−	515.716i	0.138190	−	0.0797841i	0.567501	+	0.823373i	$0.307910\pi$
$348$	1353.26	+	781.308i	0.208456	+	0.120352i
$349$	−2397.36	+	4152.34i	−0.367701	+	0.636876i	−0.989206	−	0.146534i	$-0.953188\pi$
$349$	−2397.36	+	4152.34i	−0.367701	+	0.636876i	0.621505	+	0.783410i	$0.286522\pi$
$350$	−7461.19	−	3923.69i	−1.13948	−	0.599229i
$351$	−438.959	−	5989.12i	−0.0667518	−	0.910757i
$352$			1393.43i			0.210995i
$353$	4861.98	+	2807.07i	0.733080	+	0.423244i	0.819548	−	0.573011i	$-0.194225\pi$
$353$	4861.98	+	2807.07i	0.733080	+	0.423244i	−0.0864680	+	0.996255i	$0.527558\pi$
$354$	592.664	−	1026.52i	0.0889823	−	0.154122i
$355$	36.8399	+	127.380i	0.00550777	+	0.0190440i
$356$	6091.82			0.906927
$357$	4903.98	−	2831.32i	0.727020	−	0.419745i
$358$	−7271.40	+	4198.14i	−1.07348	+	0.619773i
$359$	5501.53			0.808801			0.404400	−	0.914582i	$-0.367480\pi$
$359$	5501.53			0.808801			0.404400	+	0.914582i	$0.367480\pi$
$360$	1663.80	−	481.190i	0.243583	−	0.0704470i
$361$	−2500.25	+	4330.57i	−0.364521	+	0.631370i
$362$	−6979.01	−	4029.33i	−1.01328	−	0.585020i
$363$			1561.69i			0.225806i
$364$	−5691.52	−	2752.39i	−0.819552	−	0.396330i
$365$	1168.23	−	4731.42i	0.167529	−	0.678504i
$366$	−1021.32	+	1768.97i	−0.145861	+	0.252638i
$367$	1656.52	+	956.394i	0.235613	+	0.136031i	0.613159	−	0.789960i	$-0.289899\pi$
$367$	1656.52	+	956.394i	0.235613	+	0.136031i	−0.377546	+	0.925991i	$0.623232\pi$
$368$	785.505	−	453.511i	0.111270	−	0.0642416i
$369$	2679.60			0.378034
$370$	−1579.67	−	5461.99i	−0.221955	−	0.767447i
$371$	−346.418	−	600.013i	−0.0484774	−	0.0839653i
$372$			2909.01i			0.405444i
$373$	−9116.57	+	5263.45i	−1.26552	+	0.730647i	−0.974137	−	0.225960i	$-0.927448\pi$
$373$	−9116.57	+	5263.45i	−1.26552	+	0.730647i	−0.291381	+	0.956607i	$0.594115\pi$
$374$	−2646.30	+	4583.52i	−0.365874	+	0.633712i
$375$	1218.44	+	3664.59i	0.167787	+	0.504636i
$376$	324.085			0.0444505
$377$	2884.86	−	5965.47i	0.394106	−	0.814953i
$378$		−	8640.29i		−	1.17568i
$379$	2466.68	−	4272.42i	0.334314	−	0.579048i	−0.649039	−	0.760755i	$-0.724829\pi$
$379$	2466.68	−	4272.42i	0.334314	−	0.579048i	0.983353	+	0.181707i	$0.0581622\pi$
$380$	3375.15	−	3511.04i	0.455635	−	0.473980i
$381$	369.599	+	640.164i	0.0496985	+	0.0860803i
$382$			7350.76i			0.984548i
$383$	−7999.28	+	4618.38i	−1.06722	+	0.616158i	−0.927420	−	0.374023i	$-0.877978\pi$
$383$	−7999.28	+	4618.38i	−1.06722	+	0.616158i	−0.139797	+	0.990180i	$0.544645\pi$
$384$	−176.852	−	306.316i	−0.0235024	−	0.0407074i
$385$	3935.20	−	15937.8i	0.520925	−	2.10978i
$386$	905.828	+	1568.94i	0.119444	+	0.206883i
$387$	−4789.31	−	2765.11i	−0.629081	−	0.363200i
$388$	225.390	+	130.129i	0.0294909	+	0.0170266i
$389$	11305.3			1.47353			0.736766	−	0.676148i	$-0.236352\pi$
$389$	11305.3			1.47353			0.736766	+	0.676148i	$0.236352\pi$
$390$	1005.86	+	2715.93i	0.130599	+	0.352631i
$391$	3445.09			0.445590
$392$	−5501.23	−	3176.14i	−0.708812	−	0.409233i
$393$	3640.71	+	2101.97i	0.467302	+	0.269797i
$394$	−2368.36	−	4102.13i	−0.302834	−	0.524523i
$395$	1880.83	+	464.396i	0.239582	+	0.0591552i
$396$	1686.42	+	2920.96i	0.214004	+	0.370666i
$397$	453.201	−	261.656i	0.0572934	−	0.0330784i	−0.471080	−	0.882091i	$-0.656136\pi$
$397$	453.201	−	261.656i	0.0572934	−	0.0330784i	0.528373	+	0.849012i	$0.322802\pi$
$398$		−	3911.71i		−	0.492654i
$399$	−5073.64	−	8787.80i	−0.636590	−	1.10261i
$400$	−1691.25	+	1067.55i	−0.211406	+	0.133444i
$401$	1542.73	−	2672.08i	0.192120	−	0.332762i	−0.753833	−	0.657067i	$-0.771797\pi$
$401$	1542.73	−	2672.08i	0.192120	−	0.332762i	0.945953	+	0.324305i	$0.105130\pi$
$402$		−	4712.87i		−	0.584717i
$403$	12302.9	−	901.714i	1.52072	−	0.111458i
$404$	−5756.02			−0.708843
$405$	1307.90	−	1360.56i	0.160470	−	0.166930i
$406$	4767.05	−	8256.78i	0.582721	−	1.00930i
$407$	9589.07	−	5536.25i	1.16784	−	0.674255i
$408$		−	1343.45i		−	0.163016i
$409$	5656.03	+	9796.53i	0.683796	+	1.18437i	0.973813	+	0.227348i	$0.0730056\pi$
$409$	5656.03	+	9796.53i	0.683796	+	1.18437i	−0.290017	+	0.957021i	$0.593661\pi$
$410$	−2972.44	+	859.667i	−0.358045	+	0.103551i
$411$	1510.53			0.181287
$412$	2912.80	−	1681.71i	0.348309	−	0.201096i
$413$	−6263.21	−	3616.07i	−0.746229	−	0.430835i
$414$	1097.73	−	1901.33i	0.130315	−	0.225713i
$415$	−512.105	+	2074.05i	−0.0605741	+	0.245329i
$416$	−1240.67	+	842.898i	−0.146223	+	0.0993425i
$417$		−	7149.48i		−	0.839596i
$418$	8213.54	+	4742.09i	0.961095	+	0.554888i
$419$	4874.39	−	8442.69i	0.568328	−	0.984374i	−0.428403	−	0.903588i	$-0.640924\pi$
$419$	4874.39	−	8442.69i	0.568328	−	0.984374i	0.996731	−	0.0807859i	$-0.0257430\pi$
$420$	1157.72	+	4003.02i	0.134502	+	0.465065i
$421$	−12233.7			−1.41623			−0.708115	−	0.706097i	$-0.750454\pi$
$421$	−12233.7			−1.41623			−0.708115	+	0.706097i	$0.750454\pi$
$422$	2254.03	−	1301.37i	0.260011	−	0.150117i
$423$	679.356	−	392.226i	0.0780885	−	0.0450844i
$424$	−164.374			−0.0188271
$425$	−7590.56	+	299.696i	−0.866344	+	0.0342056i
$426$	32.7732	−	56.7649i	0.00372739	−	0.00645603i
$427$	10793.2	+	6231.43i	1.22323	+	0.706230i
$428$			839.653i			0.0948275i
$429$	−4665.20	+	3169.50i	−0.525030	+	0.356701i
$430$	6199.81	+	1530.80i	0.695306	+	0.171678i
$431$	−4313.78	+	7471.68i	−0.482105	+	0.835031i	−0.999789	−	0.0205412i	$-0.993461\pi$
$431$	−4313.78	+	7471.68i	−0.482105	+	0.835031i	0.517684	+	0.855572i	$0.326794\pi$
$432$	−1775.26	−	1024.95i	−0.197713	−	0.114150i
$433$	1744.21	−	1007.02i	0.193583	−	0.111765i	−0.400076	−	0.916482i	$-0.631016\pi$
$433$	1744.21	−	1007.02i	0.193583	−	0.111765i	0.593659	+	0.804717i	$0.297683\pi$
$434$	17749.0			1.96308
$435$	−4195.69	+	1213.45i	−0.462456	+	0.133748i
$436$	−1438.00	−	2490.70i	−0.157954	−	0.273584i
$437$		−	6173.50i		−	0.675786i
$438$	−2086.30	+	1204.53i	−0.227596	+	0.131403i
$439$	4881.30	−	8454.65i	0.530687	−	0.919177i	−0.468672	−	0.883372i	$-0.655267\pi$
$439$	4881.30	−	8454.65i	0.530687	−	0.919177i	0.999359	−	0.0358045i	$-0.0113994\pi$
$440$	−2807.82	−	2699.14i	−0.304221	−	0.292447i
$441$	−15375.8			−1.66027
$442$	−5681.77	+	416.433i	−0.611435	+	0.0448138i
$443$			11454.5i			1.22849i	0.789116	+	0.614244i	$0.210539\pi$
$443$			11454.5i			1.22849i	−0.789116	+	0.614244i	$0.789461\pi$
$444$	−1405.30	+	2434.05i	−0.150208	+	0.260168i
$445$	−11800.1	+	12275.2i	−1.25703	+	1.30764i
$446$	4978.00	+	8622.15i	0.528510	+	0.915405i
$447$			9195.60i			0.973014i
$448$	−1868.95	+	1079.04i	−0.197097	+	0.113794i
$449$	162.684	+	281.777i	0.0170992	+	0.0296166i	0.874448	−	0.485119i	$-0.161224\pi$
$449$	162.684	+	281.777i	0.0170992	+	0.0296166i	−0.857349	+	0.514735i	$0.827890\pi$
$450$	−2253.23	+	4284.69i	−0.236041	+	0.448849i
$451$	−3012.86	−	5218.42i	−0.314567	−	0.544847i
$452$	−673.693	−	388.957i	−0.0701058	−	0.0404756i
$453$	2224.60	+	1284.37i	0.230730	+	0.133212i
$454$	−3060.42			−0.316371
$455$	16570.9	−	6137.11i	1.70737	−	0.632335i
$456$	−2407.42			−0.247232
$457$	−10184.3	−	5879.89i	−1.04245	−	0.601860i	−0.121925	−	0.992539i	$-0.538907\pi$
$457$	−10184.3	−	5879.89i	−1.04245	−	0.601860i	−0.920527	+	0.390680i	$0.872240\pi$
$458$	−1111.26	−	641.587i	−0.113375	−	0.0654572i
$459$	−3892.99	−	6742.86i	−0.395881	−	0.685686i
$460$	−607.717	+	2461.29i	−0.0615977	+	0.249474i
$461$	5942.14	+	10292.1i	0.600332	+	1.03981i	0.992771	+	0.120028i	$0.0382984\pi$
$461$	5942.14	+	10292.1i	0.600332	+	1.03981i	−0.392438	+	0.919778i	$0.628368\pi$
$462$	−7027.70	+	4057.44i	−0.707702	+	0.408592i
$463$			5902.02i			0.592420i	0.955123	+	0.296210i	$0.0957228\pi$
$463$			5902.02i			0.592420i	−0.955123	+	0.296210i	$0.904277\pi$
$464$	−1130.97	−	1958.91i	−0.113156	−	0.195991i
$465$	−5861.75	−	5634.88i	−0.584585	−	0.561960i
$466$	−3312.61	+	5737.61i	−0.329300	+	0.570364i
$467$			12675.0i			1.25596i	0.778231	+	0.627978i	$0.216117\pi$
$467$			12675.0i			1.25596i	−0.778231	+	0.627978i	$0.783883\pi$
$468$	−1580.59	+	3268.43i	−0.156118	+	0.322828i
$469$	−28755.0			−2.83109
$470$	−627.767	+	653.042i	−0.0616100	+	0.0640906i
$471$	−4956.49	+	8584.90i	−0.484890	+	0.839854i
$472$	−1485.94	+	857.905i	−0.144906	+	0.0836616i
$473$			12436.0i			1.20890i
$474$	−478.822	−	829.344i	−0.0463988	−	0.0803651i
$475$	537.046	+	13602.1i	0.0518766	+	1.31391i
$476$	−8196.89			−0.789294
$477$	−344.566	+	198.935i	−0.0330746	+	0.0190956i
$478$	7029.26	+	4058.34i	0.672617	+	0.388335i
$479$	−6527.38	+	11305.8i	−0.622638	+	1.07844i	0.366355	+	0.930475i	$0.380606\pi$
$479$	−6527.38	+	11305.8i	−0.622638	+	1.07844i	−0.988993	+	0.147965i	$0.952728\pi$
$480$	959.806	+	236.986i	0.0912687	+	0.0225352i
$481$	10729.8	+	5188.86i	1.01712	+	0.491874i
$482$		−	2918.42i		−	0.275789i
$483$	4574.51	+	2641.10i	0.430947	+	0.248808i
$484$	1130.30	−	1957.75i	0.106152	−	0.183860i
$485$	−698.805	+	202.103i	−0.0654250	+	0.0189217i
$486$	−7851.29			−0.732802
$487$	14179.9	−	8186.80i	1.31941	−	0.761764i	0.335780	−	0.941940i	$-0.391000\pi$
$487$	14179.9	−	8186.80i	1.31941	−	0.761764i	0.983634	+	0.180176i	$0.0576668\pi$
$488$	2560.66	−	1478.40i	0.237532	−	0.137139i
$489$	9888.71			0.914485
$490$	17056.2	−	4932.85i	1.57249	−	0.454782i
$491$	3448.42	−	5972.85i	0.316956	−	0.548983i	−0.662896	−	0.748712i	$-0.730673\pi$
$491$	3448.42	−	5972.85i	0.316956	−	0.548983i	0.979851	+	0.199729i	$0.0640060\pi$
$492$	1324.62	+	764.770i	0.121379	+	0.0700783i
$493$		−	8591.43i		−	0.784865i
$494$	746.236	+	10181.6i	0.0679650	+	0.927309i
$495$	−9152.49	−	2259.84i	−0.831058	−	0.205197i
$496$	2105.45	−	3646.75i	0.190600	−	0.330129i
$497$	−346.344	−	199.962i	−0.0312588	−	0.0180473i
$498$	914.546	−	528.013i	0.0822927	−	0.0475117i
$499$	−1666.76			−0.149528			−0.0747640	−	0.997201i	$-0.523820\pi$
$499$	−1666.76			−0.149528			−0.0747640	+	0.997201i	$0.523820\pi$
$500$	1124.87	−	5475.83i	0.100611	−	0.489773i
$501$	3748.28	+	6492.20i	0.334253	+	0.578943i
$502$		−	10239.6i		−	0.910393i
$503$	2701.72	−	1559.84i	0.239491	−	0.138270i	−0.375452	−	0.926842i	$-0.622513\pi$
$503$	2701.72	−	1559.84i	0.239491	−	0.138270i	0.614943	+	0.788572i	$0.289179\pi$
$504$	−2611.83	+	4523.82i	−0.230834	+	0.399816i
$505$	11149.7	−	11598.6i	0.982482	−	1.02204i
$506$	−4937.02			−0.433750
$507$	−5644.02	−	2236.48i	−0.494398	−	0.195908i
$508$		−	1070.02i		−	0.0934536i
$509$	984.980	−	1706.04i	0.0857730	−	0.148563i	−0.819947	−	0.572439i	$-0.805997\pi$
$509$	984.980	−	1706.04i	0.0857730	−	0.148563i	0.905720	+	0.423876i	$0.139331\pi$
$510$	2707.10	+	2602.32i	0.235044	+	0.225947i
$511$	7349.26	+	12729.3i	0.636227	+	1.10198i
$512$			512.000i			0.0441942i
$513$	−12083.0	+	6976.13i	−1.03992	+	0.600397i
$514$	−5137.07	−	8897.66i	−0.440829	−	0.763539i
$515$	−2253.53	+	9126.93i	−0.192820	+	0.780933i
$516$	−1578.35	−	2733.78i	−0.134657	−	0.233233i
$517$	−1527.69	−	882.014i	−0.129957	−	0.0750308i
$518$	14851.0	+	8574.25i	1.25969	+	0.727280i
$519$	6896.39			0.583272
$520$	704.756	−	4132.71i	0.0594339	−	0.348522i
$521$	−11585.1			−0.974188			−0.487094	−	0.873350i	$-0.661943\pi$
$521$	−11585.1			−0.974188			−0.487094	+	0.873350i	$0.661943\pi$
$522$	−4741.57	−	2737.54i	−0.397572	−	0.229538i
$523$	−16787.0	−	9691.95i	−1.40352	−	0.810324i	−0.408770	−	0.912637i	$-0.634042\pi$
$523$	−16787.0	−	9691.95i	−1.40352	−	0.810324i	−0.994752	+	0.102313i	$0.967376\pi$
$524$	−3042.68	−	5270.08i	−0.253665	−	0.439360i
$525$	−10308.8	−	5421.18i	−0.856975	−	0.450666i
$526$	−2581.15	−	4470.69i	−0.213961	−	0.370592i
$527$	13851.2	−	7997.02i	1.14491	−	0.661016i
$528$			1925.24i			0.158685i
$529$	−4476.68	−	7753.84i	−0.367936	−	0.637285i
$530$	318.400	−	331.219i	0.0260951	−	0.0271457i
$531$	−2076.57	+	3596.73i	−0.169709	+	0.293945i
$532$			14688.6i			1.19705i
$533$	2823.80	−	5839.20i	0.229479	−	0.474529i
$534$	8416.78			0.682078
$535$	−1691.93	−	1626.45i	−0.136726	−	0.131434i
$536$	−3411.03	+	5908.08i	−0.274877	+	0.476101i
$537$	−10046.6	+	5800.38i	−0.807338	+	0.466117i
$538$			395.665i			0.0317069i
$539$	17288.1	+	29943.8i	1.38154	+	2.39289i
$540$	5504.06	−	1591.84i	0.438624	−	0.126855i
$541$	837.798			0.0665799			0.0332900	−	0.999446i	$-0.489402\pi$
$541$	837.798			0.0665799			0.0332900	+	0.999446i	$0.489402\pi$
$542$	3325.81	−	1920.16i	0.263572	−	0.152173i
$543$	−9642.58	−	5567.14i	−0.762067	−	0.439980i
$544$	−972.349	+	1684.16i	−0.0766344	+	0.132735i
$545$	7804.31	+	1926.96i	0.613395	+	0.151453i
$546$	−7863.71	−	3802.84i	−0.616366	−	0.298071i
$547$		−	1246.74i		−	0.0974526i	−0.998812	−	0.0487263i	$-0.984484\pi$
$547$		−	1246.74i		−	0.0974526i	0.998812	−	0.0487263i	$-0.0155162\pi$
$548$	−1893.61	−	1093.28i	−0.147612	−	0.0852236i
$549$	3578.48	−	6198.11i	0.278189	−	0.481838i
$550$	10877.7	−	429.482i	0.843324	−	0.0332967i
$551$	−15395.6			−1.19033
$552$	1085.30	−	626.596i	0.0836834	−	0.0483146i
$553$	−5060.14	+	2921.47i	−0.389112	+	0.224654i
$554$	4807.71			0.368700
$555$	−2182.56	−	7546.58i	−0.166927	−	0.577179i
$556$	−5174.58	+	8962.64i	−0.394696	+	0.683634i
$557$	2356.75	+	1360.67i	0.179280	+	0.103507i	0.586954	−	0.809620i	$-0.300327\pi$
$557$	2356.75	+	1360.67i	0.179280	+	0.103507i	−0.407675	+	0.913127i	$0.633660\pi$
$558$		−	10192.6i		−	0.773273i
$559$	−11072.6	+	7522.62i	−0.837782	+	0.569182i
$560$	1445.94	−	5856.14i	0.109111	−	0.441905i
$561$	−3656.27	+	6332.84i	−0.275165	+	0.476600i
$562$	3758.41	+	2169.92i	0.282098	+	0.162869i
$563$	−17479.4	+	10091.8i	−1.30847	+	0.755447i	−0.981841	−	0.189704i	$-0.939247\pi$
$563$	−17479.4	+	10091.8i	−1.30847	+	0.755447i	−0.326632	+	0.945152i	$0.605914\pi$
$564$	447.773			0.0334302
$565$	2088.73	−	604.087i	0.155529	−	0.0449807i
$566$	2075.09	+	3594.16i	0.154103	+	0.266915i
$567$			5691.97i			0.421588i
$568$	−82.1695	+	47.4406i	−0.00606999	+	0.00350451i
$569$	3471.17	−	6012.25i	0.255745	−	0.442964i	−0.709352	−	0.704854i	$-0.751012\pi$
$569$	3471.17	−	6012.25i	0.255745	−	0.442964i	0.965098	+	0.261890i	$0.0843458\pi$
$570$	4663.29	−	4851.04i	0.342673	−	0.356469i
$571$	3020.33			0.221361			0.110680	−	0.993856i	$-0.464697\pi$
$571$	3020.33			0.221361			0.110680	+	0.993856i	$0.464697\pi$
$572$	8142.32	−	596.773i	0.595188	−	0.0436230i
$573$			10156.2i			0.740456i
$574$	4666.15	−	8082.01i	0.339306	−	0.587694i
$575$	−3782.41	−	5992.20i	−0.274326	−	0.434595i
$576$	619.652	+	1073.27i	0.0448244	+	0.0776381i
$577$		−	12261.2i		−	0.884647i	−0.896856	−	0.442323i	$-0.854154\pi$
$577$		−	12261.2i		−	0.884647i	0.896856	−	0.442323i	$-0.145846\pi$
$578$	2112.73	−	1219.79i	0.152038	−	0.0877793i
$579$	1251.54	+	2167.73i	0.0898311	+	0.155592i
$580$	6138.01	+	1515.54i	0.439426	+	0.108499i
$581$	−3221.61	−	5579.99i	−0.230043	−	0.398445i
$582$	311.411	+	179.793i	0.0221794	+	0.0128053i
$583$	774.837	+	447.353i	0.0550437	+	0.0317795i
$584$	3487.20			0.247091
$585$	−3524.32	−	9516.05i	−0.249082	−	0.672547i
$586$	−6839.23			−0.482126
$587$	8461.09	+	4885.01i	0.594934	+	0.343485i	0.767046	−	0.641592i	$-0.221726\pi$
$587$	8461.09	+	4885.01i	0.594934	+	0.343485i	−0.172112	+	0.985077i	$0.555059\pi$
$588$	−7600.80	−	4388.32i	−0.533081	−	0.307775i
$589$	−14330.4	−	24821.0i	−1.00250	−	1.73639i
$590$	1149.62	−	4656.01i	0.0802185	−	0.324890i
$591$	−3272.26	−	5667.72i	−0.227754	−	0.394482i
$592$	3523.38	−	2034.23i	0.244612	−	0.141227i
$593$		−	13558.3i		−	0.938909i	−0.882957	−	0.469454i	$-0.844451\pi$
$593$		−	13558.3i		−	0.938909i	0.882957	−	0.469454i	$-0.155549\pi$
$594$	5578.89	+	9662.92i	0.385361	+	0.667466i
$595$	15877.7	−	16517.0i	1.09399	−	1.13804i
$596$	6655.51	−	11527.7i	0.457416	−	0.792268i
$597$		−	5404.63i		−	0.370514i
$598$	−2986.44	−	4395.75i	−0.204222	−	0.300595i
$599$	16763.0			1.14344			0.571718	−	0.820450i	$-0.306277\pi$
$599$	16763.0			1.14344			0.571718	+	0.820450i	$0.306277\pi$
$600$	−2336.72	+	1474.99i	−0.158994	+	0.100360i
$601$	−11855.3	+	20534.0i	−0.804640	+	1.39368i	0.111893	+	0.993720i	$0.464308\pi$
$601$	−11855.3	+	20534.0i	−0.804640	+	1.39368i	−0.916534	+	0.399957i	$0.869025\pi$
$602$	−16679.8	+	9630.11i	−1.12927	+	0.651983i
$603$			16512.9i			1.11519i
$604$	−1859.18	−	3220.19i	−0.125247	−	0.216934i
$605$	1755.47	+	6069.84i	0.117967	+	0.407891i
$606$	−7952.82			−0.533105
$607$	7258.06	−	4190.44i	0.485330	−	0.280206i	−0.237305	−	0.971435i	$-0.576264\pi$
$607$	7258.06	−	4190.44i	0.485330	−	0.280206i	0.722635	+	0.691230i	$0.242931\pi$
$608$	3017.96	+	1742.42i	0.201307	+	0.116225i
$609$	6586.41	−	11408.0i	0.438251	−	0.759073i
$610$	−1981.09	+	8023.53i	−0.131495	+	0.532563i
$611$	−138.797	−	1893.74i	−0.00919008	−	0.125389i
$612$			4707.17i			0.310909i
$613$	21962.1	+	12679.8i	1.44705	+	0.835455i	0.998305	−	0.0582047i	$-0.0185376\pi$
$613$	21962.1	+	12679.8i	1.44705	+	0.835455i	0.448746	+	0.893660i	$0.351871\pi$
$614$	7196.25	−	12464.3i	0.472992	−	0.819246i
$615$	−4106.89	+	1187.76i	−0.269278	+	0.0778783i
$616$	11746.6			0.768320
$617$	1527.82	−	882.089i	0.0996886	−	0.0575552i	−0.449327	−	0.893367i	$-0.648336\pi$
$617$	1527.82	−	882.089i	0.0996886	−	0.0575552i	0.549015	+	0.835812i	$0.315003\pi$
$618$	4024.48	−	2323.54i	0.261955	−	0.151240i
$619$	−17363.0			−1.12743			−0.563714	−	0.825970i	$-0.690628\pi$
$619$	−17363.0			−1.12743			−0.563714	+	0.825970i	$0.690628\pi$
$620$	3269.97	+	11306.5i	0.211815	+	0.732386i
$621$	3631.45	−	6289.85i	0.234662	−	0.406446i
$622$	−6604.02	−	3812.83i	−0.425719	−	0.245789i
$623$		−	51354.0i		−	3.30249i
$624$	−1714.17	+	1164.59i	−0.109971	+	0.0747132i
$625$	8855.05	+	12873.6i	0.566723	+	0.823908i
$626$	2472.47	−	4282.45i	0.157859	−	0.273420i
$627$	11348.3	+	6551.93i	0.722817	+	0.417319i
$628$	12427.0	−	7174.72i	0.789635	−	0.455896i
$629$	15453.0			0.979570
$630$	−4056.42	−	14025.8i	−0.256527	−	0.886984i
$631$	−7568.61	−	13109.2i	−0.477498	−	0.827052i	0.522169	−	0.852842i	$-0.325123\pi$
$631$	−7568.61	−	13109.2i	−0.477498	−	0.827052i	−0.999667	+	0.0257905i	$0.991790\pi$
$632$			1386.23i			0.0872488i
$633$	3114.29	−	1798.04i	0.195548	−	0.112900i
$634$	−4401.69	+	7623.95i	−0.275731	+	0.477580i
$635$	2156.12	+	2072.67i	0.134745	+	0.129530i
$636$	−227.108			−0.0141595
$637$	−16203.2	+	33505.9i	−1.00784	+	2.08407i
$638$			12312.0i			0.764009i
$639$	−114.831	+	198.893i	−0.00710897	+	0.0123131i
$640$	−1031.70	−	991.767i	−0.0637209	−	0.0612547i
$641$	8195.38	+	14194.8i	0.504989	+	0.874667i	0.999983	+	0.00577055i	$0.00183683\pi$
$641$	8195.38	+	14194.8i	0.504989	+	0.874667i	−0.494994	+	0.868896i	$0.664830\pi$
$642$			1160.11i			0.0713176i
$643$	−8759.81	+	5057.48i	−0.537252	+	0.310183i	−0.743965	−	0.668219i	$-0.767057\pi$
$643$	−8759.81	+	5057.48i	−0.537252	+	0.310183i	0.206712	+	0.978402i	$0.433724\pi$
$644$	−3823.09	−	6621.79i	−0.233930	−	0.405179i
$645$	8566.00	+	2115.03i	0.522924	+	0.129115i
$646$	6618.13	+	11462.9i	0.403076	+	0.698148i
$647$	−14280.7	−	8244.95i	−0.867745	−	0.500993i	−0.00114709	−	0.999999i	$-0.500365\pi$
$647$	−14280.7	−	8244.95i	−0.867745	−	0.500993i	−0.866598	+	0.499006i	$0.833698\pi$
$648$	1169.49	+	675.205i	0.0708980	+	0.0409330i
$649$	9339.34			0.564871
$650$	6962.41	+	9425.36i	0.420136	+	0.568758i
$651$	24522.9			1.47639
$652$	−12396.6	−	7157.16i	−0.744612	−	0.429902i
$653$	−18337.0	−	10586.9i	−1.09890	−	0.634451i	−0.162969	−	0.986631i	$-0.552107\pi$
$653$	−18337.0	−	10586.9i	−1.09890	−	0.634451i	−0.935932	+	0.352181i	$0.885440\pi$
$654$	−1986.82	−	3441.28i	−0.118793	−	0.205756i
$655$	16513.2	+	4077.28i	0.985076	+	0.243225i
$656$	−1107.04	−	1917.44i	−0.0658880	−	0.114121i
$657$	7309.97	−	4220.41i	0.434078	−	0.250615i
$658$		−	2732.03i		−	0.161863i
$659$	9186.60	+	15911.7i	0.543033	+	0.940562i	0.998728	+	0.0504253i	$0.0160577\pi$
$659$	9186.60	+	15911.7i	0.543033	+	0.940562i	−0.455694	+	0.890136i	$0.650609\pi$
$660$	−3879.43	−	3729.28i	−0.228798	−	0.219943i
$661$	2051.05	−	3552.52i	0.120691	−	0.209042i	−0.799350	−	0.600866i	$-0.794822\pi$
$661$	2051.05	−	3552.52i	0.120691	−	0.209042i	0.920040	+	0.391824i	$0.128156\pi$
$662$			2804.52i			0.164654i
$663$	−7850.24	+	575.366i	−0.459846	+	0.0337034i
$664$	−1528.64			−0.0893415
$665$	−29598.0	−	28452.5i	−1.72596	−	1.65916i
$666$	4923.88	−	8528.41i	0.286481	−	0.496200i
$667$	6940.52	−	4007.11i	0.402905	−	0.232618i
$668$		−	10851.6i		−	0.628532i
$669$	6877.88	+	11912.8i	0.397480	+	0.688455i
$670$	−5297.66	−	18317.6i	−0.305472	−	1.05622i
$671$	−16094.1			−0.925942
$672$	−2582.24	+	1490.86i	−0.148232	+	0.0855819i
$673$	28995.2	+	16740.4i	1.66075	+	0.958833i	0.972359	+	0.233490i	$0.0750145\pi$
$673$	28995.2	+	16740.4i	1.66075	+	0.958833i	0.688388	+	0.725343i	$0.258319\pi$
$674$	2468.50	−	4275.57i	0.141073	−	0.244345i
$675$	−7453.99	+	14174.3i	−0.425044	+	0.808252i
$676$	5456.69	+	6888.65i	0.310463	+	0.391935i
$677$			538.301i			0.0305592i	0.999883	+	0.0152796i	$0.00486384\pi$
$677$			538.301i			0.0305592i	−0.999883	+	0.0152796i	$0.995136\pi$
$678$	−930.810	−	537.403i	−0.0527250	−	0.0304408i
$679$	1096.99	−	1900.04i	0.0620007	−	0.107388i
$680$	−1510.15	−	5221.60i	−0.0851642	−	0.294470i
$681$	−4228.44			−0.237935
$682$	−19849.7	+	11460.2i	−1.11449	+	0.643452i
$683$	3227.85	−	1863.60i	0.180835	−	0.104405i	−0.406850	−	0.913495i	$-0.633373\pi$
$683$	3227.85	−	1863.60i	0.180835	−	0.104405i	0.587685	+	0.809090i	$0.300039\pi$
$684$	8435.12			0.471528
$685$	5871.01	−	1697.97i	0.327474	−	0.0947094i
$686$	−15208.9	+	26342.5i	−0.846468	+	1.46613i
$687$	−1535.38	−	886.451i	−0.0852668	−	0.0492288i
$688$			4569.45i			0.253210i
$689$	70.3973	+	960.495i	0.00389249	+	0.0531088i
$690$	−839.654	+	3400.65i	−0.0463262	+	0.187624i
$691$	−895.301	+	1550.71i	−0.0492892	+	0.0853715i	−0.889617	−	0.456707i	$-0.849029\pi$
$691$	−895.301	+	1550.71i	−0.0492892	+	0.0853715i	0.840328	+	0.542078i	$0.182362\pi$
$692$	−8645.37	−	4991.41i	−0.474924	−	0.274198i
$693$	24623.6	−	14216.5i	1.34975	−	0.779277i
$694$	−2062.86			−0.112832
$695$	−8036.62	−	27788.0i	−0.438628	−	1.51663i
$696$	−1562.62	−	2706.53i	−0.0851017	−	0.147400i
$697$		−	8409.58i		−	0.457009i
$698$	8304.69	−	4794.71i	0.450340	−	0.260004i
$699$	−4576.88	+	7927.39i	−0.247659	+	0.428958i
$700$	8999.47	+	14257.2i	0.485926	+	0.769817i
$701$	−5111.70			−0.275416			−0.137708	−	0.990473i	$-0.543973\pi$
$701$	−5111.70			−0.275416			−0.137708	+	0.990473i	$0.543973\pi$
$702$	−5228.82	+	10812.4i	−0.281124	+	0.581323i
$703$		−	27691.3i		−	1.48563i
$704$	1393.43	−	2413.50i	0.0745981	−	0.129208i
$705$	−867.356	+	902.277i	−0.0463355	+	0.0482010i
$706$	−5614.13	−	9723.96i	−0.299279	−	0.518366i
$707$			48523.2i			2.58119i
$708$	−2053.05	+	1185.33i	−0.108981	+	0.0629200i
$709$	−6410.08	−	11102.6i	−0.339542	−	0.588105i	0.644804	−	0.764348i	$-0.276939\pi$
$709$	−6410.08	−	11102.6i	−0.339542	−	0.588105i	−0.984347	+	0.176243i	$0.943606\pi$
$710$	63.5716	−	257.469i	0.00336028	−	0.0136093i
$711$	1677.70	+	2905.85i	0.0884930	+	0.153274i
$712$	−10551.3	−	6091.82i	−0.555377	−	0.320647i
$713$	12920.7	+	7459.75i	0.678657	+	0.391823i
$714$	−11325.3			−0.593610
$715$	−14569.5	+	17563.0i	−0.762055	+	0.918629i
$716$	16792.6			0.876492
$717$	9712.00	+	5607.22i	0.505859	+	0.292058i
$718$	−9528.93	−	5501.53i	−0.495287	−	0.285954i
$719$	−11404.4	−	19753.1i	−0.591535	−	1.02457i	−0.994026	−	0.109144i	$-0.965189\pi$
$719$	−11404.4	−	19753.1i	−0.591535	−	1.02457i	0.402491	−	0.915424i	$-0.368144\pi$
$720$	−3362.97	−	830.350i	−0.174070	−	0.0429796i
$721$	−14176.8	−	24554.9i	−0.732275	−	1.26834i
$722$	8661.13	−	5000.51i	0.446446	−	0.257756i
$723$		−	4032.24i		−	0.207415i
$724$	8058.67	+	13958.0i	0.413671	+	0.716500i
$725$	−14943.5	+	9432.63i	−0.765498	+	0.483199i
$726$	1561.69	−	2704.93i	0.0798343	−	0.138277i
$727$		−	19876.3i		−	1.01399i	−0.861948	−	0.506996i	$-0.830756\pi$
$727$		−	19876.3i		−	1.01399i	0.861948	−	0.506996i	$-0.169244\pi$
$728$	7105.62	+	10458.8i	0.361747	+	0.532457i
$729$	−6290.13			−0.319572
$730$	−6754.86	+	7026.82i	−0.342478	+	0.356266i
$731$	−8677.93	+	15030.6i	−0.439077	+	0.760503i
$732$	3537.94	−	2042.63i	0.178642	−	0.103139i
$733$			21102.7i			1.06337i	0.846943	+	0.531683i	$0.178440\pi$
$733$			21102.7i			1.06337i	−0.846943	+	0.531683i	$0.821560\pi$
$734$	−1912.79	−	3313.05i	−0.0961885	−	0.166603i
$735$	23565.7	−	6815.49i	1.18263	−	0.342031i
$736$	−1814.05			−0.0908514
$737$	32158.3	−	18566.6i	1.60728	−	0.927964i
$738$	−4641.20	−	2679.60i	−0.231497	−	0.133655i
$739$	4520.45	−	7829.65i	0.225017	−	0.389740i	−0.731308	−	0.682048i	$-0.761090\pi$
$739$	4520.45	−	7829.65i	0.225017	−	0.389740i	0.956324	+	0.292307i	$0.0944230\pi$
$740$	−2725.92	+	11040.1i	−0.135414	+	0.548436i
$741$	1031.04	+	14067.4i	0.0511149	+	0.697408i
$742$			1385.67i			0.0685574i
$743$	18120.5	+	10461.9i	0.894719	+	0.516567i	0.875483	−	0.483248i	$-0.160543\pi$
$743$	18120.5	+	10461.9i	0.894719	+	0.516567i	0.0192362	+	0.999815i	$0.493877\pi$
$744$	2909.01	−	5038.55i	0.143346	−	0.248283i
$745$	10336.6	+	35740.7i	0.508329	+	1.75763i
$746$	21053.8			1.03329
$747$	−3204.38	+	1850.05i	−0.156951	+	0.0906156i
$748$	9167.05	−	5292.60i	0.448102	−	0.258712i
$749$	7078.27			0.345306
$750$	1554.18	−	7565.69i	0.0756675	−	0.368347i
$751$	10266.7	−	17782.5i	0.498852	−	0.864036i	−0.501147	−	0.865362i	$-0.667089\pi$
$751$	10266.7	−	17782.5i	0.498852	−	0.864036i	0.999999	+	0.00132549i	$0.000421917\pi$
$752$	−561.331	−	324.085i	−0.0272203	−	0.0157156i
$753$		−	14147.6i		−	0.684685i
$754$	−10962.2	+	7447.63i	−0.529469	+	0.359717i
$755$	10090.1	+	2491.35i	0.486380	+	0.120092i
$756$	−8640.29	+	14965.4i	−0.415667	+	0.719956i
$757$	−33377.8	−	19270.7i	−1.60256	−	0.925237i	−0.990974	−	0.134057i	$-0.957200\pi$
$757$	−33377.8	−	19270.7i	−1.60256	−	0.925237i	−0.611583	−	0.791180i	$-0.709467\pi$
$758$	−8544.83	+	4933.36i	−0.409449	+	0.236395i
$759$	−6821.25			−0.326213
$760$	−9356.97	+	2706.15i	−0.446596	+	0.129161i
$761$	6532.26	+	11314.2i	0.311162	+	0.538948i	0.978614	−	0.205704i	$-0.0659485\pi$
$761$	6532.26	+	11314.2i	0.311162	+	0.538948i	−0.667452	+	0.744653i	$0.732615\pi$
$762$		−	1478.40i		−	0.0702843i
$763$	−20996.5	+	12122.4i	−0.996233	+	0.575175i
$764$	7350.76	−	12731.9i	0.348090	−	0.602910i
$765$	−9485.11	−	9118.01i	−0.448281	−	0.430931i
$766$	18473.5			0.871379
$767$	5649.43	+	8315.42i	0.265957	+	0.391463i
$768$			707.407i			0.0332374i
$769$	−15275.6	+	26458.1i	−0.716322	+	1.24071i	0.246126	+	0.969238i	$0.420842\pi$
$769$	−15275.6	+	26458.1i	−0.716322	+	1.24071i	−0.962448	+	0.271468i	$0.912491\pi$
$770$	−22753.8	+	23669.9i	−1.06492	+	1.10780i
$771$	−7097.64	−	12293.5i	−0.331537	−	0.574240i
$772$		−	3623.31i		−	0.168919i
$773$	−872.369	+	503.662i	−0.0405911	+	0.0234353i	−0.520158	−	0.854070i	$-0.674127\pi$
$773$	−872.369	+	503.662i	−0.0405911	+	0.0234353i	0.479567	+	0.877505i	$0.340794\pi$
$774$	5530.22	+	9578.62i	0.256821	+	0.444827i
$775$	−29117.0	−	15312.1i	−1.34957	−	0.709710i
$776$	−260.258	−	450.781i	−0.0120396	−	0.0208532i
$777$	20519.0	+	11846.6i	0.947381	+	0.546970i
$778$	−19581.4	−	11305.3i	−0.902350	−	0.520972i
$779$	−15069.7			−0.693105
$780$	973.729	−	5709.98i	0.0446988	−	0.262115i
$781$	516.448			0.0236619
$782$	−5967.07	−	3445.09i	−0.272867	−	0.157540i
$783$	−15685.7	−	9056.16i	−0.715916	−	0.413334i
$784$	6352.28	+	11002.5i	0.289371	+	0.501206i
$785$	−9614.32	+	38938.6i	−0.437133	+	1.77042i
$786$	−4203.94	−	7281.43i	−0.190775	−	0.330433i
$787$	4171.27	−	2408.29i	0.188933	−	0.109080i	−0.402550	−	0.915398i	$-0.631876\pi$
$787$	4171.27	−	2408.29i	0.188933	−	0.109080i	0.591483	+	0.806318i	$0.298543\pi$
$788$			9473.46i			0.428272i
$789$	−3566.26	−	6176.94i	−0.160915	−	0.278714i
$790$	−2793.30	−	2685.19i	−0.125799	−	0.120930i
$791$	−3278.90	+	5679.22i	−0.147388	+	0.255284i
$792$		−	6745.66i		−	0.302647i
$793$	−9735.45	−	14329.7i	−0.435960	−	0.641691i
$794$	−1046.62			−0.0467799
$795$	439.918	−	457.630i	0.0196255	−	0.0204157i
$796$	−3911.71	+	6775.28i	−0.174180	+	0.301688i
$797$	33694.0	−	19453.2i	1.49749	−	0.864578i	0.497497	−	0.867466i	$-0.334253\pi$
$797$	33694.0	−	19453.2i	1.49749	−	0.864578i	0.999996	+	0.00288793i	$0.000919258\pi$
$798$			20294.5i			0.900275i
$799$	−1230.95	−	2132.07i	−0.0545030	−	0.0944020i
$800$	3996.89	−	157.808i	0.176639	−	0.00697418i
$801$	−29490.7			−1.30088
$802$	−5344.16	+	3085.45i	−0.235298	+	0.135849i
$803$	−16438.2	−	9490.60i	−0.722405	−	0.417081i
$804$	−4712.87	+	8162.92i	−0.206729	+	0.358065i
$805$	20748.6	+	5123.05i	0.908439	+	0.224303i
$806$	−22211.0	−	10741.1i	−0.970655	−	0.469403i
$807$			546.671i			0.0238460i
$808$	9969.72	+	5756.02i	0.434076	+	0.250614i
$809$	−8961.69	+	15522.1i	−0.389464	+	0.674571i	−0.992377	−	0.123236i	$-0.960673\pi$
$809$	−8961.69	+	15522.1i	−0.389464	+	0.674571i	0.602914	+	0.797806i	$0.294006\pi$
$810$	−3625.92	+	1048.66i	−0.157286	+	0.0454890i
$811$	−4690.92			−0.203108			−0.101554	−	0.994830i	$-0.532381\pi$
$811$	−4690.92			−0.203108			−0.101554	+	0.994830i	$0.532381\pi$
$812$	−16513.6	+	9534.10i	−0.713685	+	0.412046i
$813$	4595.12	−	2652.99i	0.198226	−	0.114446i
$814$	−22145.0			−0.953541
$815$	38434.6	−	11115.8i	1.65191	−	0.477752i
$816$	−1343.45	+	2326.92i	−0.0576350	+	0.0998267i
$817$	26934.4	+	15550.6i	1.15339	+	0.665908i
$818$		−	22624.1i		−	0.967034i
$819$	27552.8	+	13324.4i	1.17555	+	0.568488i
$820$	6008.09	+	1483.46i	0.255868	+	0.0631763i
$821$	21896.9	−	37926.5i	0.930824	−	1.61223i	0.148907	−	0.988851i	$-0.452424\pi$
$821$	21896.9	−	37926.5i	0.930824	−	1.61223i	0.781916	−	0.623383i	$-0.214242\pi$
$822$	−2616.32	−	1510.53i	−0.111015	−	0.0640947i
$823$	8765.74	−	5060.90i	0.371269	−	0.214352i	−0.302744	−	0.953072i	$-0.597903\pi$
$823$	8765.74	−	5060.90i	0.371269	−	0.214352i	0.674013	+	0.738720i	$0.264569\pi$
$824$	−6726.83			−0.284393
$825$	15029.3	−	593.395i	0.634244	−	0.0250417i
$826$	7232.13	+	12526.4i	0.304647	+	0.527663i
$827$		−	27444.0i		−	1.15396i	−0.816759	−	0.576978i	$-0.804232\pi$
$827$		−	27444.0i		−	1.15396i	0.816759	−	0.576978i	$-0.195768\pi$
$828$	−3802.65	+	2195.46i	−0.159603	+	0.0921469i
$829$	7410.73	−	12835.8i	0.310477	−	0.537761i	−0.667989	−	0.744171i	$-0.732845\pi$
$829$	7410.73	−	12835.8i	0.310477	−	0.537761i	0.978466	+	0.206410i	$0.0661780\pi$
$830$	2961.05	−	3080.26i	0.123831	−	0.128816i
$831$	6642.59			0.277291
$832$	2991.79	−	219.277i	0.124666	−	0.00913708i
$833$			48254.9i			2.00712i
$834$	−7149.48	+	12383.3i	−0.296842	+	0.514145i
$835$	21866.3	+	21020.0i	0.906243	+	0.871169i
$836$	−9484.18	−	16427.1i	−0.392365	−	0.679596i
$837$		−	33718.4i		−	1.39245i
$838$	−16885.4	+	9748.78i	−0.696057	+	0.401869i
$839$	5110.86	+	8852.26i	0.210306	+	0.364260i	0.951810	−	0.306688i	$-0.0992208\pi$
$839$	5110.86	+	8852.26i	0.210306	+	0.364260i	−0.741505	+	0.670948i	$0.765887\pi$
$840$	1997.79	−	8091.16i	0.0820598	−	0.332347i
$841$	2201.50	+	3813.11i	0.0902660	+	0.156345i
$842$	21189.4	+	12233.7i	0.867261	+	0.500713i
$843$	5192.82	+	2998.07i	0.212159	+	0.122490i
$844$	−5205.46			−0.212298
$845$	−24450.7	−	2348.20i	−0.995420	−	0.0955982i
$846$	−1568.91			−0.0637590
$847$	−16503.8	−	9528.45i	−0.669511	−	0.386543i
$848$	284.704	+	164.374i	0.0115292	+	0.00665640i
$849$	2867.05	+	4965.88i	0.115898	+	0.200740i
$850$	13446.9	+	7071.47i	0.542619	+	0.285352i
$851$	7207.38	+	12483.6i	0.290324	+	0.502856i
$852$	−113.530	+	65.5464i	−0.00456510	+	0.00263566i
$853$			42629.9i			1.71116i	0.517669	+	0.855581i	$0.326800\pi$
$853$			42629.9i			1.71116i	−0.517669	+	0.855581i	$0.673200\pi$
$854$	−12462.9	−	21586.3i	−0.499380	−	0.864951i
$855$	−16339.2	+	16997.1i	−0.653554	+	0.679868i
$856$	839.653	−	1454.32i	0.0335266	−	0.0580698i
$857$			28197.3i			1.12392i	0.827163	+	0.561962i	$0.189953\pi$
$857$			28197.3i			1.12392i	−0.827163	+	0.561962i	$0.810047\pi$
$858$	11249.9	−	824.534i	0.447627	−	0.0328078i
$859$	−42849.4			−1.70198			−0.850990	−	0.525181i	$-0.823998\pi$
$859$	−42849.4			−1.70198			−0.850990	+	0.525181i	$0.823998\pi$
$860$	−9207.60	−	8851.23i	−0.365089	−	0.350959i
$861$	6447.00	−	11166.5i	0.255184	−	0.441991i
$862$	14943.4	−	8627.56i	0.590456	−	0.340900i
$863$		−	18595.5i		−	0.733484i	−0.930323	−	0.366742i	$-0.880473\pi$
$863$		−	18595.5i		−	0.733484i	0.930323	−	0.366742i	$-0.119527\pi$
$864$	2049.89	+	3550.52i	0.0807162	+	0.139805i
$865$	26804.3	−	7752.13i	1.05361	−	0.304717i
$866$	−4028.09			−0.158060
$867$	2919.06	−	1685.32i	0.114344	−	0.0660168i
$868$	−30742.1	−	17749.0i	−1.20214	−	0.694054i
$869$	3772.70	−	6534.50i	0.147273	−	0.255084i
$870$	8480.60	+	2093.95i	0.330482	+	0.0815993i
$871$	35983.8	+	17401.6i	1.39985	+	0.676957i
$872$			5752.02i			0.223381i
$873$	−1091.12	−	629.959i	−0.0423011	−	0.0244226i
$874$	−6173.50	+	10692.8i	−0.238927	+	0.413833i
$875$	−46161.1	−	9482.64i	−1.78346	−	0.366368i
$876$	4818.10			0.185832
$877$	−20133.0	+	11623.8i	−0.775190	+	0.447556i	−0.834723	−	0.550670i	$-0.814372\pi$
$877$	−20133.0	+	11623.8i	−0.775190	+	0.447556i	0.0595330	+	0.998226i	$0.481039\pi$
$878$	−16909.3	+	9762.59i	−0.649956	+	0.375252i
$879$	−9449.45			−0.362596
$880$	2164.14	+	7482.87i	0.0829012	+	0.286645i
$881$	8995.93	−	15581.4i	0.344019	−	0.595858i	−0.641156	−	0.767410i	$-0.721545\pi$
$881$	8995.93	−	15581.4i	0.344019	−	0.595858i	0.985175	+	0.171552i	$0.0548782\pi$
$882$	26631.7	+	15375.8i	1.01671	+	0.586995i
$883$		−	14934.0i		−	0.569162i	−0.958652	−	0.284581i	$-0.908146\pi$
$883$		−	14934.0i		−	0.569162i	0.958652	−	0.284581i	$-0.0918544\pi$
$884$	10257.6	+	4960.49i	0.390270	+	0.188732i
$885$	1588.37	−	6432.99i	0.0603305	−	0.244342i
$886$	11454.5	−	19839.8i	0.434336	−	0.752292i
$887$	7591.45	+	4382.93i	0.287369	+	0.165912i	0.636755	−	0.771067i	$-0.280276\pi$
$887$	7591.45	+	4382.93i	0.287369	+	0.165912i	−0.349386	+	0.936979i	$0.613610\pi$
$888$	4868.10	−	2810.60i	0.183967	−	0.106213i
$889$	−9020.24			−0.340303
$890$	32713.6	−	9461.18i	1.23209	−	0.356336i
$891$	−3675.21	−	6365.66i	−0.138187	−	0.239346i
$892$		−	19912.0i		−	0.747425i
$893$	−3820.61	+	2205.83i	−0.143171	+	0.0826599i
$894$	9195.60	−	15927.3i	0.344012	−	0.595847i
$895$	−32528.0	+	33837.6i	−1.21485	+	1.26376i
$896$	4316.15			0.160929
$897$	−4126.22	−	6073.40i	−0.153590	−	0.226070i
$898$		−	650.735i		−	0.0241819i
$899$	18603.3	−	32221.8i	0.690159	−	1.19539i
$900$	8187.40	−	5168.07i	0.303237	−	0.191410i
$901$	624.332	+	1081.37i	0.0230849	+	0.0399843i
$902$			12051.4i			0.444865i
$903$	−23045.7	+	13305.5i	−0.849296	+	0.490341i
$904$	777.913	+	1347.39i	0.0286206	+	0.0495723i
$905$	−43735.9	−	10798.8i	−1.60644	−	0.396647i
$906$	−2568.74	−	4449.19i	−0.0941951	−	0.163151i
$907$	−36700.2	−	21188.8i	−1.34356	−	0.775705i	−0.356232	−	0.934398i	$-0.615939\pi$
$907$	−36700.2	−	21188.8i	−1.34356	−	0.775705i	−0.987328	+	0.158693i	$0.949272\pi$
$908$	5300.80	+	3060.42i	0.193737	+	0.111854i
$909$	27865.1			1.01675
$910$	−34838.7	−	5941.09i	−1.26911	−	0.216423i
$911$	2238.33			0.0814043			0.0407022	−	0.999171i	$-0.487041\pi$
$911$	2238.33			0.0814043			0.0407022	+	0.999171i	$0.487041\pi$
$912$	4169.78	+	2407.42i	0.151398	+	0.0874098i
$913$	7205.81	+	4160.28i	0.261202	+	0.150805i
$914$	11759.8	+	20368.6i	0.425579	+	0.737124i
$915$	−2737.18	+	11085.7i	−0.0988944	+	0.400528i
$916$	1283.17	+	2222.52i	0.0462852	+	0.0801684i
$917$	−44426.7	+	25649.8i	−1.59989	+	0.923698i
$918$			15572.0i			0.559860i
$919$	−10604.9	−	18368.1i	−0.380655	−	0.659314i	0.610501	−	0.792015i	$-0.290968\pi$
$919$	−10604.9	−	18368.1i	−0.380655	−	0.659314i	−0.991156	+	0.132702i	$0.957635\pi$
$920$	3513.89	−	3655.36i	0.125923	−	0.130993i
$921$	9942.73	−	17221.3i	0.355726	−	0.616136i
$922$		−	23768.6i		−	0.848998i
$923$	312.403	+	459.827i	0.0111407	+	0.0163980i
$924$	16229.8			0.577836
$925$	−16966.0	−	26878.0i	−0.603069	−	0.955399i
$926$	5902.02	−	10222.6i	0.209452	−	0.362781i
$927$	−14101.0	+	8141.20i	−0.499608	+	0.288449i
$928$			4523.90i			0.160026i
$929$	−1170.37	−	2027.13i	−0.0413331	−	0.0715911i	0.844619	−	0.535368i	$-0.179827\pi$
$929$	−1170.37	−	2027.13i	−0.0413331	−	0.0715911i	−0.885952	+	0.463777i	$0.846494\pi$
$930$	4517.97	+	15621.6i	0.159301	+	0.550811i
$931$	86471.5			3.04403
$932$	11475.2	−	6625.22i	0.403308	−	0.232850i
$933$	−9124.46	−	5268.01i	−0.320173	−	0.184852i
$934$	12675.0	−	21953.8i	0.444047	−	0.769113i
$935$	−7092.22	+	28723.9i	−0.248065	+	1.00468i
$936$	6006.10	−	4080.50i	0.209739	−	0.142495i
$937$			16668.9i			0.581163i	0.956850	+	0.290582i	$0.0938488\pi$
$937$			16668.9i			0.581163i	−0.956850	+	0.290582i	$0.906151\pi$
$938$	49805.1	+	28755.0i	1.73368	+	1.00094i
$939$	3416.10	−	5916.86i	0.118722	−	0.205633i
$940$	1740.37	−	503.335i	0.0603877	−	0.0174649i
$941$	5537.89			0.191849			0.0959246	−	0.995389i	$-0.469419\pi$
$941$	5537.89			0.191849			0.0959246	+	0.995389i	$0.469419\pi$
$942$	17169.8	−	9912.98i	0.593866	−	0.342869i
$943$	6793.61	−	3922.29i	0.234603	−	0.135448i
$944$	3431.62			0.118315
$945$	−13419.2	−	46399.1i	−0.461933	−	1.59721i
$946$	12436.0	−	21539.8i	0.427409	−	0.740295i
$947$	−29623.1	−	17102.9i	−1.01650	−	0.586874i	−0.103409	−	0.994639i	$-0.532975\pi$
$947$	−29623.1	−	17102.9i	−1.01650	−	0.586874i	−0.913087	+	0.407764i	$0.866308\pi$
$948$			1915.29i			0.0656178i
$949$	−1493.48	−	20376.9i	−0.0510858	−	0.697010i
$950$	12671.9	−	24096.5i	0.432769	−	0.822942i
$951$	−6081.61	+	10533.7i	−0.207371	+	0.359177i
$952$	14197.4	+	8196.89i	0.483342	+	0.279057i
$953$	6175.09	−	3565.19i	0.209896	−	0.121183i	−0.391367	−	0.920235i	$-0.627998\pi$
$953$	6175.09	−	3565.19i	0.209896	−	0.121183i	0.601263	+	0.799051i	$0.294664\pi$
$954$	795.740			0.0270053
$955$	11416.4	+	39474.2i	0.386834	+	1.33755i
$956$	−8116.69	−	14058.5i	−0.274595	−	0.475612i
$957$			17011.0i			0.574594i
$958$	22611.5	−	13054.8i	0.762573	−	0.440271i
$959$	−9216.32	+	15963.1i	−0.310334	+	0.537515i
$960$	−1425.45	−	1370.28i	−0.0479231	−	0.0460683i
$961$	39473.7			1.32502
$962$	−13395.7	−	19717.1i	−0.448954	−	0.660817i
$963$		−	4064.79i		−	0.136019i
$964$	−2918.42	+	5054.85i	−0.0975062	+	0.168886i
$965$	7301.09	+	7018.51i	0.243555	+	0.234128i
$966$	−5282.19	−	9149.03i	−0.175933	−	0.304726i
$967$			19109.2i			0.635483i	0.948177	+	0.317741i	$0.102924\pi$
$967$			19109.2i			0.635483i	−0.948177	+	0.317741i	$0.897076\pi$
$968$	−3915.49	+	2260.61i	−0.130009	+	0.0750607i
$969$	9143.97	+	15837.8i	0.303144	+	0.525061i
$970$	1412.47	+	348.753i	0.0467543	+	0.0115441i
$971$	−508.113	−	880.078i	−0.0167931	−	0.0290866i	0.857507	−	0.514473i	$-0.172012\pi$
$971$	−508.113	−	880.078i	−0.0167931	−	0.0290866i	−0.874300	+	0.485386i	$0.838679\pi$
$972$	13598.8	+	7851.29i	0.448748	+	0.259085i
$973$	75554.9	+	43621.7i	2.48939	+	1.43725i
$974$	−32747.2			−1.07730
$975$	9619.64	+	13022.6i	0.315974	+	0.427750i
$976$	−5913.59			−0.193944
$977$	−30085.9	−	17370.1i	−0.985192	−	0.568801i	−0.0813583	−	0.996685i	$-0.525926\pi$
$977$	−30085.9	−	17370.1i	−0.985192	−	0.568801i	−0.903834	+	0.427884i	$0.859259\pi$
$978$	−17127.8	−	9888.71i	−0.560005	−	0.323319i
$979$	33158.4	+	57432.1i	1.08248	+	1.87491i
$980$	−34475.0	−	8512.22i	−1.12374	−	0.277462i
$981$	6961.43	+	12057.5i	0.226566	+	0.392424i
$982$	−11945.7	+	6896.85i	−0.388190	+	0.224121i
$983$		−	59475.8i		−	1.92979i	−0.262638	−	0.964895i	$-0.584592\pi$
$983$		−	59475.8i		−	1.92979i	0.262638	−	0.964895i	$-0.415408\pi$
$984$	−1529.54	−	2649.24i	−0.0495528	−	0.0858280i
$985$	−19089.3	−	18350.5i	−0.617499	−	0.593600i
$986$	−8591.43	+	14880.8i	−0.277492	+	0.480630i
$987$		−	3774.72i		−	0.121733i
$988$	8889.06	−	18381.2i	0.286233	−	0.591888i
$989$	−16189.8			−0.520533
$990$	13592.7	+	13066.6i	0.436369	+	0.419480i
$991$	−3159.99	+	5473.26i	−0.101292	+	0.175443i	−0.912217	−	0.409707i	$-0.865631\pi$
$991$	−3159.99	+	5473.26i	−0.101292	+	0.175443i	0.810925	+	0.585150i	$0.198964\pi$
$992$	−7293.51	+	4210.91i	−0.233437	+	0.134775i
$993$			3874.88i			0.123832i
$994$	399.923	+	692.688i	0.0127614	+	0.0221033i
$995$	−6075.26	−	21006.2i	−0.193567	−	0.669289i
$996$	−2112.05			−0.0671917
$997$	49701.4	−	28695.1i	1.57880	−	0.911519i	0.583769	−	0.811919i	$-0.301577\pi$
$997$	49701.4	−	28695.1i	1.57880	−	0.911519i	0.995028	−	0.0995995i	$-0.0317562\pi$
$998$	2886.91	+	1666.76i	0.0915668	+	0.0528661i
$999$	16288.9	−	28213.1i	0.515873	−	0.893517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.n.a.9.5	✓	44
5.4	even	2	inner	130.4.n.a.9.18	yes	44
13.3	even	3	inner	130.4.n.a.29.18	yes	44
65.29	even	6	inner	130.4.n.a.29.5	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.n.a.9.5	✓	44	1.1	even	1	trivial
130.4.n.a.9.18	yes	44	5.4	even	2	inner
130.4.n.a.29.5	yes	44	65.29	even	6	inner
130.4.n.a.29.18	yes	44	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	130.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(-2.39309 - 1.38165i) q^{3} +(2.00000 + 3.46410i) q^{4} +(-10.8544 - 2.68005i) q^{5} +(2.76331 + 4.78619i) q^{6} +(29.2023 - 16.8600i) q^{7} -8.00000i q^{8} +(-9.68207 - 16.7698i) q^{9} +(16.1203 + 15.4964i) q^{10} +(-21.7724 + 37.7109i) q^{11} -11.0532i q^{12} +(-46.7468 + 3.42620i) q^{13} -67.4399 q^{14} +(22.2726 + 21.4106i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-52.6299 + 30.3859i) q^{17} +38.7283i q^{18} +(54.4507 + 94.3113i) q^{19} +(-12.4248 - 42.9607i) q^{20} -93.1786 q^{21} +(75.4219 - 43.5448i) q^{22} +(-49.0940 - 28.3445i) q^{23} +(-11.0532 + 19.1448i) q^{24} +(110.635 + 58.1805i) q^{25} +(84.3940 + 40.8124i) q^{26} +128.118i q^{27} +(116.809 + 67.4399i) q^{28} +(-70.6859 + 122.432i) q^{29} +(-17.1667 - 59.3569i) q^{30} -263.182 q^{31} +(27.7128 - 16.0000i) q^{32} +(104.207 - 60.1639i) q^{33} +121.544 q^{34} +(-362.158 + 104.741i) q^{35} +(38.7283 - 67.0793i) q^{36} +(-220.211 - 127.139i) q^{37} -217.803i q^{38} +(116.603 + 56.3886i) q^{39} +(-21.4404 + 86.8350i) q^{40} +(-69.1898 + 119.840i) q^{41} +(161.390 + 93.1786i) q^{42} +(247.329 - 142.795i) q^{43} -174.179 q^{44} +(60.1487 + 207.974i) q^{45} +(56.6889 + 98.1881i) q^{46} +40.5106i q^{47} +(38.2895 - 22.1065i) q^{48} +(397.017 - 687.654i) q^{49} +(-133.444 - 211.406i) q^{50} +167.931 q^{51} +(-105.362 - 155.083i) q^{52} -20.5468i q^{53} +(128.118 - 221.907i) q^{54} +(337.393 - 350.977i) q^{55} +(-134.880 - 233.619i) q^{56} -300.928i q^{57} +(244.863 - 141.372i) q^{58} +(-107.238 - 185.742i) q^{59} +(-29.6232 + 119.976i) q^{60} +(184.800 + 320.082i) q^{61} +(455.844 + 263.182i) q^{62} +(-565.478 - 326.479i) q^{63} -64.0000 q^{64} +(516.589 + 88.0946i) q^{65} -240.655 q^{66} +(-738.510 - 426.379i) q^{67} +(-210.520 - 121.544i) q^{68} +(78.3244 + 135.662i) q^{69} +(732.017 + 180.742i) q^{70} +(-5.93007 - 10.2712i) q^{71} +(-134.159 + 77.4565i) q^{72} +435.900i q^{73} +(254.278 + 440.423i) q^{74} +(-184.374 - 292.090i) q^{75} +(-217.803 + 377.245i) q^{76} +1468.33i q^{77} +(-145.574 - 214.271i) q^{78} -173.279 q^{79} +(123.971 - 128.962i) q^{80} +(-84.4007 + 146.186i) q^{81} +(239.680 - 138.380i) q^{82} -191.080i q^{83} +(-186.357 - 322.780i) q^{84} +(652.701 - 188.769i) q^{85} -571.182 q^{86} +(338.316 - 195.327i) q^{87} +(301.687 + 174.179i) q^{88} +(761.478 - 1318.92i) q^{89} +(103.794 - 420.371i) q^{90} +(-1307.35 + 888.202i) q^{91} -226.756i q^{92} +(629.819 + 363.626i) q^{93} +(40.5106 - 70.1664i) q^{94} +(-338.268 - 1169.62i) q^{95} -88.4258 q^{96} +(56.3476 - 32.5323i) q^{97} +(-1375.31 + 794.035i) q^{98} +843.208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) \) 44 * q + 88 * q^4 - 12 * q^5 + 266 * q^9 + 28 * q^10 + 2 * q^11 - 216 * q^14 - 64 * q^15 - 352 * q^16 + 14 * q^19 - 24 * q^20 - 32 * q^21 + 504 * q^25 + 336 * q^26 + 308 * q^29 + 104 * q^30 + 792 * q^31 - 352 * q^34 + 106 * q^35 - 1064 * q^36 + 120 * q^39 + 224 * q^40 + 140 * q^41 + 16 * q^44 - 522 * q^45 - 320 * q^46 + 536 * q^49 - 96 * q^50 - 256 * q^51 + 552 * q^54 + 1188 * q^55 - 432 * q^56 - 500 * q^59 - 512 * q^60 - 2352 * q^61 - 2816 * q^64 - 2924 * q^65 + 496 * q^66 + 376 * q^69 - 1008 * q^70 - 1268 * q^71 + 436 * q^74 + 3560 * q^75 - 56 * q^76 - 264 * q^79 + 96 * q^80 - 6326 * q^81 - 64 * q^84 + 606 * q^85 + 336 * q^86 + 4730 * q^89 + 3560 * q^90 + 5866 * q^91 + 1732 * q^94 + 2224 * q^95 + 2916 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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