LMFDB - Embedded newform 32.4.g.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,4,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.88806112018$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	32.13
Dual form			32.4.g.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82381 + 0.161516i) q^{2} +(-0.477813 + 1.15354i) q^{3} +(7.94783 - 0.912182i) q^{4} +(-16.3468 + 6.77105i) q^{5} +(1.16294 - 3.33456i) q^{6} +(-18.0222 + 18.0222i) q^{7} +(-22.2958 + 3.85953i) q^{8} +(17.9895 + 17.9895i) q^{9} +O(q^{10})$	\(q+(-2.82381 + 0.161516i) q^{2} +(-0.477813 + 1.15354i) q^{3} +(7.94783 - 0.912182i) q^{4} +(-16.3468 + 6.77105i) q^{5} +(1.16294 - 3.33456i) q^{6} +(-18.0222 + 18.0222i) q^{7} +(-22.2958 + 3.85953i) q^{8} +(17.9895 + 17.9895i) q^{9} +(45.0666 - 21.7604i) q^{10} +(-20.1053 - 48.5384i) q^{11} +(-2.74533 + 9.60400i) q^{12} +(37.8086 + 15.6609i) q^{13} +(47.9805 - 53.8022i) q^{14} -22.0920i q^{15} +(62.3358 - 14.4997i) q^{16} +53.0615i q^{17} +(-53.7046 - 47.8934i) q^{18} +(-32.4427 - 13.4382i) q^{19} +(-123.745 + 68.7264i) q^{20} +(-12.1781 - 29.4006i) q^{21} +(64.6132 + 133.816i) q^{22} +(32.1343 + 32.1343i) q^{23} +(6.20110 - 27.5633i) q^{24} +(132.981 - 132.981i) q^{25} +(-109.294 - 38.1166i) q^{26} +(-60.4929 + 25.0570i) q^{27} +(-126.798 + 159.677i) q^{28} +(-52.0634 + 125.692i) q^{29} +(3.56821 + 62.3836i) q^{30} -53.3354 q^{31} +(-173.683 + 51.0128i) q^{32} +65.5976 q^{33} +(-8.57029 - 149.836i) q^{34} +(172.576 - 416.634i) q^{35} +(159.387 + 126.568i) q^{36} +(-57.3789 + 23.7671i) q^{37} +(93.7826 + 32.7070i) q^{38} +(-36.1309 + 36.1309i) q^{39} +(338.332 - 214.057i) q^{40} +(240.383 + 240.383i) q^{41} +(39.1374 + 81.0549i) q^{42} +(56.3244 + 135.979i) q^{43} +(-204.069 - 367.435i) q^{44} +(-415.879 - 172.263i) q^{45} +(-95.9313 - 85.5509i) q^{46} +314.904i q^{47} +(-13.0588 + 78.8352i) q^{48} -306.601i q^{49} +(-354.035 + 396.993i) q^{50} +(-61.2086 - 25.3534i) q^{51} +(314.782 + 89.9813i) q^{52} +(-177.524 - 428.580i) q^{53} +(166.774 - 80.5268i) q^{54} +(657.312 + 657.312i) q^{55} +(332.263 - 471.378i) q^{56} +(31.0031 - 31.0031i) q^{57} +(126.716 - 363.340i) q^{58} +(-133.963 + 55.4894i) q^{59} +(-20.1519 - 175.583i) q^{60} +(-191.454 + 462.211i) q^{61} +(150.609 - 8.61453i) q^{62} -648.422 q^{63} +(482.208 - 172.103i) q^{64} -724.089 q^{65} +(-185.235 + 10.5951i) q^{66} +(-55.4766 + 133.932i) q^{67} +(48.4018 + 421.723i) q^{68} +(-52.4224 + 21.7141i) q^{69} +(-420.028 + 1204.37i) q^{70} +(191.132 - 191.132i) q^{71} +(-470.523 - 331.660i) q^{72} +(-175.452 - 175.452i) q^{73} +(158.188 - 76.3815i) q^{74} +(89.8593 + 216.940i) q^{75} +(-270.107 - 77.2109i) q^{76} +(1237.11 + 512.428i) q^{77} +(96.1911 - 107.863i) q^{78} -1222.08i q^{79} +(-920.811 + 659.103i) q^{80} +605.154i q^{81} +(-717.622 - 639.971i) q^{82} +(896.581 + 371.376i) q^{83} +(-123.608 - 222.562i) q^{84} +(-359.282 - 867.384i) q^{85} +(-181.012 - 374.882i) q^{86} +(-120.115 - 120.115i) q^{87} +(635.599 + 1004.61i) q^{88} +(883.293 - 883.293i) q^{89} +(1202.19 + 419.266i) q^{90} +(-963.639 + 399.152i) q^{91} +(284.710 + 226.085i) q^{92} +(25.4843 - 61.5246i) q^{93} +(-50.8622 - 889.231i) q^{94} +621.324 q^{95} +(24.1425 - 224.725i) q^{96} -682.976 q^{97} +(49.5210 + 865.783i) q^{98} +(511.499 - 1234.87i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 212 q^{14} - 304 q^{16} - 184 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 192 q^{22} + 324 q^{23} - 48 q^{24} - 4 q^{25} + 16 q^{26} - 268 q^{27} + 376 q^{28} - 4 q^{29} + 1188 q^{30} - 752 q^{31} + 616 q^{32} - 8 q^{33} + 528 q^{34} - 460 q^{35} + 1456 q^{36} - 4 q^{37} + 980 q^{38} + 596 q^{39} - 536 q^{40} - 4 q^{41} - 2264 q^{42} + 804 q^{43} - 2044 q^{44} + 104 q^{45} - 1444 q^{46} - 2448 q^{48} - 3564 q^{50} - 1384 q^{51} - 2524 q^{52} + 748 q^{53} - 1088 q^{54} - 292 q^{55} + 1192 q^{56} - 4 q^{57} + 3200 q^{58} + 1372 q^{59} + 5752 q^{60} - 1828 q^{61} + 3384 q^{62} + 2512 q^{63} + 4952 q^{64} - 8 q^{65} + 5996 q^{66} + 2036 q^{67} + 2768 q^{68} - 1060 q^{69} + 1400 q^{70} + 220 q^{71} - 1708 q^{72} - 4 q^{73} - 3476 q^{74} - 1712 q^{75} - 5124 q^{76} + 1900 q^{77} - 11916 q^{78} - 10312 q^{80} - 6404 q^{82} + 2436 q^{83} - 6560 q^{84} + 496 q^{85} - 928 q^{86} - 1292 q^{87} + 1248 q^{88} - 4 q^{89} + 7400 q^{90} - 3604 q^{91} + 10152 q^{92} - 112 q^{93} + 12840 q^{94} - 6088 q^{95} + 17792 q^{96} - 8 q^{97} + 11224 q^{98} - 5424 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 116 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 212 * q^14 - 304 * q^16 - 184 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 192 * q^22 + 324 * q^23 - 48 * q^24 - 4 * q^25 + 16 * q^26 - 268 * q^27 + 376 * q^28 - 4 * q^29 + 1188 * q^30 - 752 * q^31 + 616 * q^32 - 8 * q^33 + 528 * q^34 - 460 * q^35 + 1456 * q^36 - 4 * q^37 + 980 * q^38 + 596 * q^39 - 536 * q^40 - 4 * q^41 - 2264 * q^42 + 804 * q^43 - 2044 * q^44 + 104 * q^45 - 1444 * q^46 - 2448 * q^48 - 3564 * q^50 - 1384 * q^51 - 2524 * q^52 + 748 * q^53 - 1088 * q^54 - 292 * q^55 + 1192 * q^56 - 4 * q^57 + 3200 * q^58 + 1372 * q^59 + 5752 * q^60 - 1828 * q^61 + 3384 * q^62 + 2512 * q^63 + 4952 * q^64 - 8 * q^65 + 5996 * q^66 + 2036 * q^67 + 2768 * q^68 - 1060 * q^69 + 1400 * q^70 + 220 * q^71 - 1708 * q^72 - 4 * q^73 - 3476 * q^74 - 1712 * q^75 - 5124 * q^76 + 1900 * q^77 - 11916 * q^78 - 10312 * q^80 - 6404 * q^82 + 2436 * q^83 - 6560 * q^84 + 496 * q^85 - 928 * q^86 - 1292 * q^87 + 1248 * q^88 - 4 * q^89 + 7400 * q^90 - 3604 * q^91 + 10152 * q^92 - 112 * q^93 + 12840 * q^94 - 6088 * q^95 + 17792 * q^96 - 8 * q^97 + 11224 * q^98 - 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.82381	+	0.161516i	−0.998368	+	0.0571046i
$2$	−2.82381	+	0.161516i	−0.998368	+	0.0571046i
$3$	−0.477813	+	1.15354i	−0.0919551	+	0.221999i	−0.963165	−	0.268912i	$-0.913336\pi$
$3$	−0.477813	+	1.15354i	−0.0919551	+	0.221999i	0.871210	+	0.490911i	$0.163336\pi$
$4$	7.94783	−	0.912182i	0.993478	−	0.114023i
$5$	−16.3468	+	6.77105i	−1.46210	+	0.605621i	−0.965042	−	0.262096i	$-0.915586\pi$
$5$	−16.3468	+	6.77105i	−1.46210	+	0.605621i	−0.497057	+	0.867718i	$0.665586\pi$
$6$	1.16294	−	3.33456i	0.0791279	−	0.226888i
$7$	−18.0222	+	18.0222i	−0.973108	+	0.973108i	−0.999648	−	0.0265394i	$-0.991551\pi$
$7$	−18.0222	+	18.0222i	−0.973108	+	0.973108i	0.0265394	+	0.999648i	$0.491551\pi$
$8$	−22.2958	+	3.85953i	−0.985346	+	0.170569i
$9$	17.9895	+	17.9895i	0.666279	+	0.666279i
$10$	45.0666	−	21.7604i	1.42513	−	0.688126i
$11$	−20.1053	−	48.5384i	−0.551088	−	1.33044i	−0.916663	−	0.399662i	$-0.869128\pi$
$11$	−20.1053	−	48.5384i	−0.551088	−	1.33044i	0.365575	−	0.930782i	$-0.380872\pi$
$12$	−2.74533	+	9.60400i	−0.0660424	+	0.231036i
$13$	37.8086	+	15.6609i	0.806633	+	0.334118i	0.747610	−	0.664138i	$-0.231201\pi$
$13$	37.8086	+	15.6609i	0.806633	+	0.334118i	0.0590233	+	0.998257i	$0.481201\pi$
$14$	47.9805	−	53.8022i	0.915951	−	1.02709i
$15$		−	22.0920i		−	0.380275i
$16$	62.3358	−	14.4997i	0.973998	−	0.226558i
$17$			53.0615i			0.757018i	0.925598	+	0.378509i	$0.123563\pi$
$17$			53.0615i			0.757018i	−0.925598	+	0.378509i	$0.876437\pi$
$18$	−53.7046	−	47.8934i	−0.703239	−	0.627144i
$19$	−32.4427	−	13.4382i	−0.391730	−	0.162260i	0.178120	−	0.984009i	$-0.442999\pi$
$19$	−32.4427	−	13.4382i	−0.391730	−	0.162260i	−0.569850	+	0.821749i	$0.692999\pi$
$20$	−123.745	+	68.7264i	−1.38351	+	0.768384i
$21$	−12.1781	−	29.4006i	−0.126547	−	0.305512i
$22$	64.6132	+	133.816i	0.626163	+	1.29680i
$23$	32.1343	+	32.1343i	0.291324	+	0.291324i	0.837603	−	0.546279i	$-0.183956\pi$
$23$	32.1343	+	32.1343i	0.291324	+	0.291324i	−0.546279	+	0.837603i	$0.683956\pi$
$24$	6.20110	−	27.5633i	0.0527414	−	0.234431i
$25$	132.981	−	132.981i	1.06385	−	1.06385i
$26$	−109.294	−	38.1166i	−0.824397	−	0.287511i
$27$	−60.4929	+	25.0570i	−0.431180	+	0.178601i
$28$	−126.798	+	159.677i	−0.855805	+	1.07772i
$29$	−52.0634	+	125.692i	−0.333377	+	0.804842i	0.664943	+	0.746894i	$0.268456\pi$
$29$	−52.0634	+	125.692i	−0.333377	+	0.804842i	−0.998320	+	0.0579483i	$0.981544\pi$
$30$	3.56821	+	62.3836i	0.0217154	+	0.379654i
$31$	−53.3354			−0.309010			−0.154505	−	0.987992i	$-0.549378\pi$
$31$	−53.3354			−0.309010			−0.154505	+	0.987992i	$0.549378\pi$
$32$	−173.683	+	51.0128i	−0.959471	+	0.281808i
$33$	65.5976			0.346033
$34$	−8.57029	−	149.836i	−0.0432292	−	0.755782i
$35$	172.576	−	416.634i	0.833446	−	2.01212i
$36$	159.387	+	126.568i	0.737904	+	0.585963i
$37$	−57.3789	+	23.7671i	−0.254947	+	0.105602i	−0.506497	−	0.862242i	$-0.669060\pi$
$37$	−57.3789	+	23.7671i	−0.254947	+	0.105602i	0.251550	+	0.967844i	$0.419060\pi$
$38$	93.7826	+	32.7070i	0.400357	+	0.139626i
$39$	−36.1309	+	36.1309i	−0.148348	+	0.148348i
$40$	338.332	−	214.057i	1.33737	−	0.846135i
$41$	240.383	+	240.383i	0.915647	+	0.915647i	0.996709	−	0.0810624i	$-0.0258313\pi$
$41$	240.383	+	240.383i	0.915647	+	0.915647i	−0.0810624	+	0.996709i	$0.525831\pi$
$42$	39.1374	+	81.0549i	0.143787	+	0.297787i
$43$	56.3244	+	135.979i	0.199753	+	0.482247i	0.991736	−	0.128297i	$-0.0409510\pi$
$43$	56.3244	+	135.979i	0.199753	+	0.482247i	−0.791983	+	0.610544i	$0.790951\pi$
$44$	−204.069	−	367.435i	−0.699195	−	1.25893i
$45$	−415.879	−	172.263i	−1.37768	−	0.570653i
$46$	−95.9313	−	85.5509i	−0.307485	−	0.274213i
$47$			314.904i			0.977309i	0.872477	+	0.488655i	$0.162512\pi$
$47$			314.904i			0.977309i	−0.872477	+	0.488655i	$0.837488\pi$
$48$	−13.0588	+	78.8352i	−0.0392683	+	0.237060i
$49$		−	306.601i		−	0.893880i
$50$	−354.035	+	396.993i	−1.00136	+	1.12286i
$51$	−61.2086	−	25.3534i	−0.168057	−	0.0696116i
$52$	314.782	+	89.9813i	0.839469	+	0.239965i
$53$	−177.524	−	428.580i	−0.460089	−	1.11075i	−0.968360	−	0.249557i	$-0.919715\pi$
$53$	−177.524	−	428.580i	−0.460089	−	1.11075i	0.508271	−	0.861197i	$-0.330285\pi$
$54$	166.774	−	80.5268i	0.420278	−	0.202932i
$55$	657.312	+	657.312i	1.61149	+	1.61149i
$56$	332.263	−	471.378i	0.792866	−	1.12483i
$57$	31.0031	−	31.0031i	0.0720431	−	0.0720431i
$58$	126.716	−	363.340i	0.286872	−	0.822566i
$59$	−133.963	+	55.4894i	−0.295602	+	0.122442i	−0.525556	−	0.850759i	$-0.676143\pi$
$59$	−133.963	+	55.4894i	−0.295602	+	0.122442i	0.229954	+	0.973202i	$0.426143\pi$
$60$	−20.1519	−	175.583i	−0.0433600	−	0.377795i
$61$	−191.454	+	462.211i	−0.401855	+	0.970164i	0.585360	+	0.810773i	$0.300953\pi$
$61$	−191.454	+	462.211i	−0.401855	+	0.970164i	−0.987216	+	0.159391i	$0.949047\pi$
$62$	150.609	−	8.61453i	0.308506	−	0.0176459i
$63$	−648.422			−1.29672
$64$	482.208	−	172.103i	0.941813	−	0.336139i
$65$	−724.089			−1.38173
$66$	−185.235	+	10.5951i	−0.345468	+	0.0197601i
$67$	−55.4766	+	133.932i	−0.101157	+	0.244216i	−0.966353	−	0.257218i	$-0.917194\pi$
$67$	−55.4766	+	133.932i	−0.101157	+	0.244216i	0.865196	+	0.501434i	$0.167194\pi$
$68$	48.4018	+	421.723i	0.0863173	+	0.752081i
$69$	−52.4224	+	21.7141i	−0.0914625	+	0.0378850i
$70$	−420.028	+	1204.37i	−0.717185	+	2.05643i
$71$	191.132	−	191.132i	0.319482	−	0.319482i	−0.529086	−	0.848568i	$-0.677465\pi$
$71$	191.132	−	191.132i	0.319482	−	0.319482i	0.848568	+	0.529086i	$0.177465\pi$
$72$	−470.523	−	331.660i	−0.770161	−	0.542869i
$73$	−175.452	−	175.452i	−0.281302	−	0.281302i	0.552326	−	0.833628i	$-0.313740\pi$
$73$	−175.452	−	175.452i	−0.281302	−	0.281302i	−0.833628	+	0.552326i	$0.813740\pi$
$74$	158.188	−	76.3815i	0.248500	−	0.119989i
$75$	89.8593	+	216.940i	0.138347	+	0.334000i
$76$	−270.107	−	77.2109i	−0.407676	−	0.116535i
$77$	1237.11	+	512.428i	1.83093	+	0.758398i
$78$	96.1911	−	107.863i	0.139635	−	0.156577i
$79$		−	1222.08i		−	1.74043i	−0.492668	−	0.870217i	$-0.663978\pi$
$79$		−	1222.08i		−	1.74043i	0.492668	−	0.870217i	$-0.336022\pi$
$80$	−920.811	+	659.103i	−1.28687	+	0.921124i
$81$			605.154i			0.830116i
$82$	−717.622	−	639.971i	−0.966440	−	0.861865i
$83$	896.581	+	371.376i	1.18569	+	0.491131i	0.886351	−	0.463015i	$-0.153232\pi$
$83$	896.581	+	371.376i	1.18569	+	0.491131i	0.299344	+	0.954145i	$0.403232\pi$
$84$	−123.608	−	222.562i	−0.160557	−	0.289090i
$85$	−359.282	−	867.384i	−0.458466	−	1.10684i
$86$	−181.012	−	374.882i	−0.226966	−	0.470053i
$87$	−120.115	−	120.115i	−0.148019	−	0.148019i
$88$	635.599	+	1004.61i	0.769944	+	1.21695i
$89$	883.293	−	883.293i	1.05201	−	1.05201i	0.0534390	−	0.998571i	$-0.482982\pi$
$89$	883.293	−	883.293i	1.05201	−	1.05201i	0.998571	−	0.0534390i	$-0.0170183\pi$
$90$	1202.19	+	419.266i	1.40802	+	0.491050i
$91$	−963.639	+	399.152i	−1.11007	+	0.459808i
$92$	284.710	+	226.085i	0.322642	+	0.256207i
$93$	25.4843	−	61.5246i	0.0284151	−	0.0686001i
$94$	−50.8622	−	889.231i	−0.0558088	−	0.975715i
$95$	621.324			0.671016
$96$	24.1425	−	224.725i	0.0256670	−	0.238915i
$97$	−682.976			−0.714904			−0.357452	−	0.933932i	$-0.616354\pi$
$97$	−682.976			−0.714904			−0.357452	+	0.933932i	$0.616354\pi$
$98$	49.5210	+	865.783i	0.0510446	+	0.892421i
$99$	511.499	−	1234.87i	0.519268	−	1.25362i
$100$	935.609	−	1178.21i	0.935609	−	1.17821i
$101$	919.967	−	381.063i	0.906338	−	0.375417i	0.119684	−	0.992812i	$-0.461812\pi$
$101$	919.967	−	381.063i	0.906338	−	0.375417i	0.786654	+	0.617395i	$0.211812\pi$
$102$	176.937	+	61.7072i	0.171758	+	0.0599012i
$103$	−188.265	+	188.265i	−0.180100	+	0.180100i	−0.791400	−	0.611299i	$-0.790647\pi$
$103$	−188.265	+	188.265i	−0.180100	+	0.180100i	0.611299	+	0.791400i	$0.290647\pi$
$104$	−903.419	−	203.248i	−0.851803	−	0.191636i
$105$	398.146	+	398.146i	0.370049	+	0.370049i
$106$	570.516	+	1181.56i	0.522768	+	1.08267i
$107$	−48.3932	−	116.832i	−0.0437229	−	0.105556i	0.900509	−	0.434837i	$-0.143194\pi$
$107$	−48.3932	−	116.832i	−0.0437229	−	0.105556i	−0.944232	+	0.329280i	$0.893194\pi$
$108$	−457.931	+	254.329i	−0.408004	+	0.226600i
$109$	394.289	+	163.320i	0.346477	+	0.143516i	0.549134	−	0.835734i	$-0.314958\pi$
$109$	394.289	+	163.320i	0.346477	+	0.143516i	−0.202657	+	0.979250i	$0.564958\pi$
$110$	−1962.29	−	1749.96i	−1.70088	−	1.51684i
$111$		−	77.5452i		−	0.0663087i
$112$	−862.113	+	1384.75i	−0.727339	+	1.16827i
$113$			914.060i			0.760952i	0.924791	+	0.380476i	$0.124240\pi$
$113$			914.060i			0.760952i	−0.924791	+	0.380476i	$0.875760\pi$
$114$	−82.5394	+	92.5543i	−0.0678116	+	0.0760395i
$115$	−742.874	−	307.709i	−0.602377	−	0.249513i
$116$	−299.136	+	1046.47i	−0.239432	+	0.837606i
$117$	398.428	+	961.891i	0.314827	+	0.760059i
$118$	369.324	−	178.329i	0.288128	−	0.139123i
$119$	−956.286	−	956.286i	−0.736660	−	0.736660i
$120$	85.2647	+	492.559i	0.0648630	+	0.374702i
$121$	−1010.60	+	1010.60i	−0.759276	+	0.759276i
$122$	465.976	−	1336.12i	0.345799	−	0.991529i
$123$	−392.150	+	162.434i	−0.287471	+	0.119074i
$124$	−423.901	+	48.6516i	−0.306995	+	0.0352342i
$125$	−427.009	+	1030.89i	−0.305543	+	0.737645i
$126$	1831.02	−	104.731i	1.29461	−	0.0740488i
$127$	−2159.36			−1.50876			−0.754379	−	0.656439i	$-0.772062\pi$
$127$	−2159.36			−1.50876			−0.754379	+	0.656439i	$0.772062\pi$
$128$	−1333.87	+	563.871i	−0.921081	+	0.389372i
$129$	−183.770			−0.125427
$130$	2044.69	−	116.952i	1.37947	−	0.0789029i
$131$	−896.246	+	2163.73i	−0.597751	+	1.44310i	0.278116	+	0.960547i	$0.410290\pi$
$131$	−896.246	+	2163.73i	−0.597751	+	1.44310i	−0.875867	+	0.482552i	$0.839710\pi$
$132$	521.359	−	59.8370i	0.343776	−	0.0394556i
$133$	826.876	−	342.503i	0.539092	−	0.223299i
$134$	135.023	−	387.160i	0.0870466	−	0.249594i
$135$	819.201	−	819.201i	0.522264	−	0.522264i
$136$	−204.793	−	1183.05i	−0.129124	−	0.745924i
$137$	−118.307	−	118.307i	−0.0737786	−	0.0737786i	0.669255	−	0.743033i	$-0.266614\pi$
$137$	−118.307	−	118.307i	−0.0737786	−	0.0737786i	−0.743033	+	0.669255i	$0.766614\pi$
$138$	144.524	−	69.7835i	0.0891499	−	0.0430461i
$139$	924.203	+	2231.22i	0.563956	+	1.36151i	0.906579	+	0.422037i	$0.138685\pi$
$139$	924.203	+	2231.22i	0.563956	+	1.36151i	−0.342623	+	0.939473i	$0.611315\pi$
$140$	991.554	−	3468.76i	0.598583	−	2.09403i
$141$	−363.255	−	150.465i	−0.216962	−	0.0898686i
$142$	−508.851	+	570.593i	−0.300717	+	0.337205i
$143$		−	2150.04i		−	1.25731i
$144$	1382.24	+	860.549i	0.799905	+	0.498003i
$145$		−	2407.18i		−	1.37866i
$146$	523.780	+	467.104i	0.296907	+	0.264779i
$147$	353.677	+	146.498i	0.198441	+	0.0821968i
$148$	−434.358	+	241.237i	−0.241243	+	0.133983i
$149$	366.708	+	885.311i	0.201623	+	0.486762i	0.992058	−	0.125785i	$-0.0401450\pi$
$149$	366.708	+	885.311i	0.201623	+	0.486762i	−0.790434	+	0.612547i	$0.790145\pi$
$150$	−288.785	−	598.083i	−0.157195	−	0.325555i
$151$	1212.74	+	1212.74i	0.653584	+	0.653584i	0.953854	−	0.300270i	$-0.0970768\pi$
$151$	1212.74	+	1212.74i	0.653584	+	0.653584i	−0.300270	+	0.953854i	$0.597077\pi$
$152$	775.202	+	174.402i	0.413666	+	0.0930651i
$153$	−954.551	+	954.551i	−0.504385	+	0.504385i
$154$	−3576.14	−	1247.19i	−1.87125	−	0.652606i
$155$	871.861	−	361.137i	0.451804	−	0.187143i
$156$	−254.204	+	320.120i	−0.130465	+	0.164296i
$157$	896.752	−	2164.95i	0.455851	−	1.10052i	−0.514211	−	0.857664i	$-0.671915\pi$
$157$	896.752	−	2164.95i	0.455851	−	1.10052i	0.970062	−	0.242858i	$-0.0780848\pi$
$158$	197.385	+	3450.91i	0.0993868	+	1.73759i
$159$	579.208			0.288894
$160$	2493.74	−	2009.91i	1.23217	−	0.993108i
$161$	−1158.26			−0.566980
$162$	−97.7422	−	1708.84i	−0.0474034	−	0.828761i
$163$	363.960	−	878.678i	0.174893	−	0.422229i	−0.811989	−	0.583673i	$-0.801615\pi$
$163$	363.960	−	878.678i	0.174893	−	0.422229i	0.986882	+	0.161444i	$0.0516150\pi$
$164$	2129.79	+	1691.25i	1.01408	+	0.805270i
$165$	−1072.31	+	444.165i	−0.505934	+	0.209565i
$166$	−2591.76	−	903.884i	−1.21181	−	0.422621i
$167$	800.950	−	800.950i	0.371134	−	0.371134i	−0.496756	−	0.867890i	$-0.665476\pi$
$167$	800.950	−	800.950i	0.371134	−	0.371134i	0.867890	+	0.496756i	$0.165476\pi$
$168$	384.994	+	608.509i	0.176803	+	0.279450i
$169$	−369.282	−	369.282i	−0.168085	−	0.168085i
$170$	1154.64	+	2391.30i	0.520923	+	1.07885i
$171$	−341.882	−	825.376i	−0.152891	−	0.369112i
$172$	571.694	+	1029.36i	0.253438	+	0.456326i
$173$	217.486	+	90.0857i	0.0955790	+	0.0395901i	0.429961	−	0.902848i	$-0.358527\pi$
$173$	217.486	+	90.0857i	0.0955790	+	0.0395901i	−0.334382	+	0.942438i	$0.608527\pi$
$174$	358.581	+	319.780i	0.156230	+	0.139325i
$175$			4793.23i			2.07048i
$176$	−1957.07	−	2734.16i	−0.838181	−	1.17100i
$177$		−	181.046i		−	0.0768826i
$178$	−2351.59	+	2636.92i	−0.990219	+	1.11037i
$179$	−1959.23	−	811.539i	−0.818099	−	0.338868i	−0.0659185	−	0.997825i	$-0.520998\pi$
$179$	−1959.23	−	811.539i	−0.818099	−	0.338868i	−0.752180	+	0.658957i	$0.770998\pi$
$180$	−3462.47	−	989.756i	−1.43376	−	0.409845i
$181$	−468.260	−	1130.48i	−0.192295	−	0.464242i	0.798097	−	0.602529i	$-0.205840\pi$
$181$	−468.260	−	1130.48i	−0.192295	−	0.464242i	−0.990392	+	0.138287i	$0.955840\pi$
$182$	2656.67	−	1282.77i	1.08201	−	0.522448i
$183$	−441.700	−	441.700i	−0.178423	−	0.178423i
$184$	−840.484	−	592.437i	−0.336746	−	0.237364i
$185$	777.031	−	777.031i	0.308803	−	0.308803i
$186$	−62.0257	+	177.850i	−0.0244513	+	0.0701108i
$187$	2575.52	−	1066.82i	1.00717	−	0.417183i
$188$	287.250	+	2502.81i	0.111436	+	0.970935i
$189$	638.634	−	1541.80i	0.245787	−	0.593383i
$190$	−1754.50	+	100.354i	−0.669921	+	0.0383181i
$191$	5115.66			1.93799			0.968996	−	0.247078i	$-0.0794705\pi$
$191$	5115.66			1.93799			0.968996	+	0.247078i	$0.0794705\pi$
$192$	−31.8771	+	638.480i	−0.0119819	+	0.239991i
$193$	4101.82			1.52982			0.764910	−	0.644137i	$-0.222783\pi$
$193$	4101.82			1.52982			0.764910	+	0.644137i	$0.222783\pi$
$194$	1928.60	−	110.312i	0.713737	−	0.0408243i
$195$	345.979	−	835.267i	0.127057	−	0.306742i
$196$	−279.676	−	2436.81i	−0.101923	−	0.888050i
$197$	−2365.10	+	979.657i	−0.855363	+	0.354303i	−0.766892	−	0.641776i	$-0.778198\pi$
$197$	−2365.10	+	979.657i	−0.855363	+	0.354303i	−0.0884706	+	0.996079i	$0.528198\pi$
$198$	−1244.93	+	3569.65i	−0.446833	+	1.28123i
$199$	−3419.40	+	3419.40i	−1.21807	+	1.21807i	−0.249757	+	0.968309i	$0.580351\pi$
$199$	−3419.40	+	3419.40i	−1.21807	+	1.21807i	−0.968309	+	0.249757i	$0.919649\pi$
$200$	−2451.68	+	3478.17i	−0.866800	+	1.22972i
$201$	−127.989	−	127.989i	−0.0449138	−	0.0449138i
$202$	−2536.27	+	1224.64i	−0.883421	+	0.426561i
$203$	−1326.95	−	3203.55i	−0.458787	−	1.10761i
$204$	−509.603	−	145.671i	−0.174899	−	0.0499953i
$205$	−5557.13	−	2301.84i	−1.89330	−	0.784231i
$206$	501.218	−	562.034i	0.169522	−	0.190091i
$207$			1156.16i			0.388206i
$208$	2583.91	+	428.017i	0.861356	+	0.142681i
$209$			1844.90i			0.610594i
$210$	−1188.60	−	1059.98i	−0.390576	−	0.348313i
$211$	4175.73	+	1729.64i	1.36241	+	0.564330i	0.939720	−	0.341944i	$-0.111085\pi$
$211$	4175.73	+	1729.64i	1.36241	+	0.564330i	0.422692	+	0.906273i	$0.361085\pi$
$212$	−1801.87	−	3244.34i	−0.583740	−	1.05105i
$213$	129.154	+	311.805i	0.0415468	+	0.100303i
$214$	155.524	+	322.094i	0.0496793	+	0.102887i
$215$	−1841.44	−	1841.44i	−0.584118	−	0.584118i
$216$	1252.03	−	792.141i	0.394398	−	0.249529i
$217$	961.222	−	961.222i	0.300701	−	0.300701i
$218$	−1139.78	−	397.500i	−0.354107	−	0.123496i
$219$	286.224	−	118.558i	0.0883160	−	0.0365817i
$220$	5823.79	+	4624.61i	1.78473	+	1.41723i
$221$	−830.988	+	2006.18i	−0.252934	+	0.610636i
$222$	12.5248	+	218.973i	0.00378653	+	0.0662005i
$223$	717.256			0.215386			0.107693	−	0.994184i	$-0.465654\pi$
$223$	717.256			0.215386			0.107693	+	0.994184i	$0.465654\pi$
$224$	2210.79	−	4049.51i	0.659439	−	1.20790i
$225$	4784.54			1.41764
$226$	−147.635	−	2581.13i	−0.0434538	−	0.759710i
$227$	−2316.16	+	5591.71i	−0.677221	+	1.63496i	0.0918358	+	0.995774i	$0.470727\pi$
$227$	−2316.16	+	5591.71i	−0.677221	+	1.63496i	−0.769056	+	0.639181i	$0.779273\pi$
$228$	218.127	−	274.687i	0.0633587	−	0.0797878i
$229$	−197.065	+	81.6271i	−0.0568665	+	0.0235549i	−0.410935	−	0.911664i	$-0.634798\pi$
$229$	−197.065	+	81.6271i	−0.0568665	+	0.0235549i	0.354069	+	0.935219i	$0.384798\pi$
$230$	2147.44	+	748.925i	0.615643	+	0.214707i
$231$	−1182.21	+	1182.21i	−0.336727	+	0.336727i
$232$	675.683	−	3003.35i	0.191210	−	0.849912i
$233$	−4600.59	−	4600.59i	−1.29354	−	1.29354i	−0.932583	−	0.360955i	$-0.882451\pi$
$233$	−4600.59	−	4600.59i	−1.29354	−	1.29354i	−0.360955	−	0.932583i	$-0.617549\pi$
$234$	−1280.45	−	2651.85i	−0.357716	−	0.740840i
$235$	−2132.23	−	5147.67i	−0.591879	−	1.42892i
$236$	−1014.10	+	563.219i	−0.279713	+	0.155349i
$237$	1409.72	+	583.924i	0.386375	+	0.160042i
$238$	2854.83	+	2545.92i	0.777525	+	0.693392i
$239$			1366.19i			0.369755i	0.982762	+	0.184878i	$0.0591889\pi$
$239$			1366.19i			0.369755i	−0.982762	+	0.184878i	$0.940811\pi$
$240$	−320.328	−	1377.12i	−0.0861544	−	0.370387i
$241$			1568.87i			0.419336i	0.977773	+	0.209668i	$0.0672382\pi$
$241$			1568.87i			0.419336i	−0.977773	+	0.209668i	$0.932762\pi$
$242$	2690.51	−	3016.96i	0.714679	−	0.801395i
$243$	−2331.38	−	965.689i	−0.615465	−	0.254934i
$244$	−1100.02	+	3848.21i	−0.288614	+	1.00966i
$245$	2076.01	+	5011.93i	0.541353	+	1.30694i
$246$	1081.12	−	522.021i	0.280202	−	0.135296i
$247$	−1016.16	−	1016.16i	−0.261768	−	0.261768i
$248$	1189.16	−	205.850i	0.304482	−	0.0527076i
$249$	−856.796	+	856.796i	−0.218061	+	0.218061i
$250$	1039.29	−	2980.01i	0.262921	−	0.753889i
$251$	1774.13	−	734.870i	0.446144	−	0.184799i	−0.148289	−	0.988944i	$-0.547377\pi$
$251$	1774.13	−	734.870i	0.446144	−	0.184799i	0.594433	+	0.804145i	$0.297377\pi$
$252$	−5153.55	+	591.479i	−1.28827	+	0.147856i
$253$	913.678	−	2205.81i	0.227045	−	0.548136i
$254$	6097.63	−	348.771i	1.50630	−	0.0861570i
$255$	1172.23			0.287875
$256$	3675.52	−	1807.71i	0.897343	−	0.441334i
$257$	805.660			0.195547			0.0977737	−	0.995209i	$-0.468828\pi$
$257$	805.660			0.195547			0.0977737	+	0.995209i	$0.468828\pi$
$258$	518.932	−	29.6818i	0.125222	−	0.00716244i
$259$	605.759	−	1462.43i	0.145328	−	0.350854i
$260$	−5754.94	+	660.502i	−1.37272	+	0.157548i
$261$	−3197.74	+	1324.55i	−0.758371	+	0.314128i
$262$	2181.35	−	6254.73i	0.514368	−	1.47488i
$263$	2159.44	−	2159.44i	0.506300	−	0.506300i	−0.407089	−	0.913389i	$-0.633456\pi$
$263$	2159.44	−	2159.44i	0.506300	−	0.506300i	0.913389	+	0.407089i	$0.133456\pi$
$264$	−1462.55	+	253.176i	−0.340962	+	0.0590224i
$265$	5803.87	+	5803.87i	1.34539	+	1.34539i
$266$	−2279.62	+	1100.72i	−0.525461	+	0.253720i
$267$	596.867	+	1440.96i	0.136808	+	0.330283i
$268$	−318.748	+	1115.08i	−0.0726516	+	0.254157i
$269$	2403.35	+	995.499i	0.544738	+	0.225638i	0.638045	−	0.769999i	$-0.279744\pi$
$269$	2403.35	+	995.499i	0.544738	+	0.225638i	−0.0933062	+	0.995637i	$0.529744\pi$
$270$	−2180.96	+	2445.58i	−0.491588	+	0.551235i
$271$			363.916i			0.0815731i	0.999168	+	0.0407866i	$0.0129864\pi$
$271$			363.916i			0.0815731i	−0.999168	+	0.0407866i	$0.987014\pi$
$272$	769.377	+	3307.63i	0.171509	+	0.737333i
$273$		−	1302.32i		−	0.288717i
$274$	353.186	+	314.969i	0.0778713	+	0.0694451i
$275$	−9128.32	−	3781.08i	−2.00167	−	0.829118i
$276$	−396.837	+	220.398i	−0.0865463	+	0.0480667i
$277$	236.874	+	571.865i	0.0513805	+	0.124043i	0.947486	−	0.319798i	$-0.103615\pi$
$277$	236.874	+	571.865i	0.0513805	+	0.124043i	−0.896105	+	0.443842i	$0.853615\pi$
$278$	−2970.15	−	6151.28i	−0.640784	−	1.32708i
$279$	−959.479	−	959.479i	−0.205887	−	0.205887i
$280$	−2239.70	+	9955.27i	−0.478028	+	2.12479i
$281$	−5905.54	+	5905.54i	−1.25372	+	1.25372i	−0.299680	+	0.954040i	$0.596880\pi$
$281$	−5905.54	+	5905.54i	−1.25372	+	1.25372i	−0.954040	+	0.299680i	$0.903120\pi$
$282$	1050.07	+	366.214i	0.221740	+	0.0773324i
$283$	−2127.03	+	881.046i	−0.446781	+	0.185063i	−0.594719	−	0.803934i	$-0.702736\pi$
$283$	−2127.03	+	881.046i	−0.446781	+	0.185063i	0.147938	+	0.988997i	$0.452736\pi$
$284$	1344.74	−	1693.43i	0.280970	−	0.353827i
$285$	−296.877	+	716.723i	−0.0617033	+	0.148965i
$286$	347.266	+	6071.30i	0.0717981	+	1.25526i
$287$	−8664.47			−1.78205
$288$	−4042.17	−	2206.78i	−0.827038	−	0.451512i
$289$	2097.48			0.426924
$290$	388.799	+	6797.43i	0.0787278	+	1.37641i
$291$	326.334	−	787.841i	0.0657391	−	0.158708i
$292$	−1554.50	−	1234.41i	−0.311542	−	0.247393i
$293$	1783.51	−	738.755i	0.355610	−	0.147299i	−0.197724	−	0.980258i	$-0.563355\pi$
$293$	1783.51	−	738.755i	0.355610	−	0.147299i	0.553335	+	0.832959i	$0.313355\pi$
$294$	−1022.38	−	356.557i	−0.202811	−	0.0707308i
$295$	1814.14	−	1814.14i	0.358046	−	0.358046i
$296$	1187.58	−	751.363i	0.233198	−	0.147541i
$297$	2432.45	+	2432.45i	0.475237	+	0.475237i
$298$	−1178.51	−	2440.72i	−0.229091	−	0.474454i
$299$	711.703	+	1718.20i	0.137655	+	0.332329i
$300$	912.074	+	1642.23i	0.175529	+	0.316047i
$301$	−3465.74	−	1435.56i	−0.663660	−	0.274897i
$302$	−3620.42	−	3228.67i	−0.689840	−	0.615195i
$303$			1243.30i			0.235728i
$304$	−2217.19	−	367.272i	−0.418305	−	0.0692910i
$305$		−	8852.00i		−	1.66185i
$306$	2541.30	−	2849.65i	0.474759	−	0.532365i
$307$	6622.54	+	2743.14i	1.23117	+	0.509966i	0.900943	−	0.433937i	$-0.142876\pi$
$307$	6622.54	+	2743.14i	1.23117	+	0.509966i	0.330223	+	0.943903i	$0.392876\pi$
$308$	10299.8	+	2944.22i	1.90547	+	0.544683i
$309$	−127.216	−	307.128i	−0.0234210	−	0.0565433i
$310$	−2403.64	+	1160.60i	−0.440380	+	0.212638i
$311$	777.649	+	777.649i	0.141789	+	0.141789i	0.774438	−	0.632649i	$-0.218033\pi$
$311$	777.649	+	777.649i	0.141789	+	0.141789i	−0.632649	+	0.774438i	$0.718033\pi$
$312$	666.120	−	945.017i	0.120871	−	0.171478i
$313$	3478.96	−	3478.96i	0.628251	−	0.628251i	−0.319377	−	0.947628i	$-0.603474\pi$
$313$	3478.96	−	3478.96i	0.628251	−	0.628251i	0.947628	+	0.319377i	$0.103474\pi$
$314$	−2182.58	+	6258.25i	−0.392262	+	1.12476i
$315$	10599.6	−	4390.50i	1.89594	−	0.785323i
$316$	−1114.76	−	9712.85i	−0.198449	−	1.72908i
$317$	2639.41	−	6372.11i	0.467648	−	1.12900i	−0.497540	−	0.867441i	$-0.665763\pi$
$317$	2639.41	−	6372.11i	0.467648	−	1.12900i	0.965187	−	0.261560i	$-0.0842369\pi$
$318$	−1635.57	+	93.5514i	−0.288423	+	0.0164972i
$319$	7147.64			1.25452
$320$	−6717.22	+	6078.38i	−1.17345	+	1.06185i
$321$	157.893			0.0274540
$322$	3270.71	−	187.078i	0.566055	−	0.0323772i
$323$	713.052	−	1721.46i	0.122834	−	0.296547i
$324$	552.011	+	4809.66i	0.0946521	+	0.824702i
$325$	7110.44	−	2945.24i	1.21359	−	0.502685i
$326$	−885.835	+	2540.01i	−0.150496	+	0.431528i
$327$	−376.792	+	376.792i	−0.0637207	+	0.0637207i
$328$	−6287.30	−	4431.77i	−1.05841	−	0.746048i
$329$	−5675.28	−	5675.28i	−0.951028	−	0.951028i
$330$	2956.26	−	1427.43i	0.493142	−	0.238114i
$331$	1414.82	+	3415.68i	0.234941	+	0.567198i	0.996746	−	0.0806085i	$-0.0256864\pi$
$331$	1414.82	+	3415.68i	0.234941	+	0.567198i	−0.761805	+	0.647807i	$0.775686\pi$
$332$	7464.64	+	2133.79i	1.23396	+	0.352731i
$333$	−1459.78	−	604.660i	−0.240226	−	0.0995050i
$334$	−2132.36	+	2391.10i	−0.349335	+	0.391722i
$335$		−	2565.00i		−	0.418331i
$336$	−1185.44	−	1656.13i	−0.192473	−	0.268897i
$337$			5963.90i			0.964018i	0.876166	+	0.482009i	$0.160093\pi$
$337$			5963.90i			0.964018i	−0.876166	+	0.482009i	$0.839907\pi$
$338$	1102.43	+	983.139i	0.177409	+	0.158212i
$339$	−1054.41	−	436.750i	−0.168931	−	0.0699734i
$340$	−3646.72	−	6566.08i	−0.581680	−	1.04734i
$341$	1072.32	+	2588.82i	0.170292	+	0.411121i
$342$	1098.72	+	2275.49i	0.173720	+	0.359779i
$343$	−655.996	−	655.996i	−0.103267	−	0.103267i
$344$	−1780.62	−	2814.38i	−0.279082	−	0.441108i
$345$	709.909	−	709.909i	0.110783	−	0.110783i
$346$	−628.690	−	219.257i	−0.0976838	−	0.0340675i
$347$	−11609.9	+	4808.98i	−1.79612	+	0.743975i	−0.808214	+	0.588889i	$0.799566\pi$
$347$	−11609.9	+	4808.98i	−1.79612	+	0.743975i	−0.987901	+	0.155086i	$0.950434\pi$
$348$	−1064.22	−	845.083i	−0.163931	−	0.130176i
$349$	−3007.79	+	7261.44i	−0.461327	+	1.11374i	0.506525	+	0.862225i	$0.330930\pi$
$349$	−3007.79	+	7261.44i	−0.461327	+	1.11374i	−0.967853	+	0.251518i	$0.919070\pi$
$350$	−774.185	−	13535.2i	−0.118234	−	2.06710i
$351$	−2679.57			−0.407478
$352$	5968.02	+	7404.66i	0.903683	+	1.12122i
$353$	−4646.74			−0.700627			−0.350313	−	0.936633i	$-0.613925\pi$
$353$	−4646.74			−0.700627			−0.350313	+	0.936633i	$0.613925\pi$
$354$	29.2418	+	511.239i	0.00439035	+	0.0767572i
$355$	−1830.23	+	4418.57i	−0.273630	+	0.660600i
$356$	6214.54	−	7825.98i	0.925196	−	1.16510i
$357$	1560.04	−	646.190i	0.231278	−	0.0957983i
$358$	5663.57	+	1975.19i	0.836115	+	0.291597i
$359$	1380.53	−	1380.53i	0.202957	−	0.202957i	−0.598309	−	0.801266i	$-0.704160\pi$
$359$	1380.53	−	1380.53i	0.202957	−	0.202957i	0.801266	+	0.598309i	$0.204160\pi$
$360$	9937.21	+	2235.64i	1.45483	+	0.327302i
$361$	−3978.10	−	3978.10i	−0.579983	−	0.579983i
$362$	1504.87	+	3116.63i	0.218492	+	0.452504i
$363$	−682.890	−	1648.64i	−0.0987394	−	0.238378i
$364$	−7294.73	+	4051.41i	−1.05041	+	0.583383i
$365$	4056.06	+	1680.07i	0.581654	+	0.240929i
$366$	1318.62	+	1175.94i	0.188321	+	0.167943i
$367$		−	8418.93i		−	1.19745i	−0.800954	−	0.598725i	$-0.795674\pi$
$367$		−	8418.93i		−	1.19745i	0.800954	−	0.598725i	$-0.204326\pi$
$368$	2469.06	+	1537.18i	0.349751	+	0.217747i
$369$			8648.75i			1.22015i
$370$	−2068.69	+	2319.69i	−0.290665	+	0.325933i
$371$	10923.3	+	4524.59i	1.52860	+	0.633167i
$372$	146.423	−	512.233i	0.0204078	−	0.0713926i
$373$	−2147.40	−	5184.27i	−0.298091	−	0.719655i	−0.999973	−	0.00736187i	$-0.997657\pi$
$373$	−2147.40	−	5184.27i	−0.298091	−	0.719655i	0.701882	−	0.712293i	$-0.252343\pi$
$374$	−7100.48	+	3428.47i	−0.981703	+	0.474017i
$375$	−985.145	−	985.145i	−0.135660	−	0.135660i
$376$	−1215.38	−	7021.06i	−0.166699	−	0.962988i
$377$	−3936.89	+	3936.89i	−0.537825	+	0.537825i
$378$	−1554.36	+	4456.90i	−0.211501	+	0.606450i
$379$	−7606.92	+	3150.89i	−1.03098	+	0.427046i	−0.833066	−	0.553173i	$-0.813417\pi$
$379$	−7606.92	+	3150.89i	−1.03098	+	0.427046i	−0.197914	+	0.980219i	$0.563417\pi$
$380$	4938.18	−	566.761i	0.666640	−	0.0765111i
$381$	1031.77	−	2490.91i	0.138738	−	0.334943i
$382$	−14445.7	+	826.262i	−1.93483	+	0.110668i
$383$	12379.9			1.65166			0.825828	−	0.563922i	$-0.190708\pi$
$383$	12379.9			1.65166			0.825828	+	0.563922i	$0.190708\pi$
$384$	−13.1099	−	1808.10i	−0.00174221	−	0.240284i
$385$	−23692.5			−3.13631
$386$	−11582.8	+	662.510i	−1.52732	+	0.0873598i
$387$	−1432.95	+	3459.45i	−0.188220	+	0.454402i
$388$	−5428.17	+	622.998i	−0.710242	+	0.0815153i
$389$	−2056.29	+	851.744i	−0.268016	+	0.111016i	−0.512644	−	0.858601i	$-0.671334\pi$
$389$	−2056.29	+	851.744i	−0.268016	+	0.111016i	0.244629	+	0.969617i	$0.421334\pi$
$390$	−842.071	+	2414.52i	−0.109333	+	0.313497i
$391$	−1705.09	+	1705.09i	−0.220538	+	0.220538i
$392$	1183.34	+	6835.92i	0.152468	+	0.880781i
$393$	−2067.72	−	2067.72i	−0.265401	−	0.265401i
$394$	6520.37	−	3148.37i	0.833735	−	0.402570i
$395$	8274.74	+	19977.0i	1.05404	+	2.54469i
$396$	2938.88	−	10281.1i	0.372940	−	1.30466i
$397$	10550.8	+	4370.29i	1.33383	+	0.552490i	0.931745	−	0.363114i	$-0.118286\pi$
$397$	10550.8	+	4370.29i	1.33383	+	0.552490i	0.402083	+	0.915603i	$0.368286\pi$
$398$	9103.46	−	10208.0i	1.14652	−	1.28563i
$399$			1117.49i			0.140212i
$400$	6361.31	−	10217.7i	0.795163	−	1.27721i
$401$		−	3711.66i		−	0.462224i	−0.972927	−	0.231112i	$-0.925764\pi$
$401$		−	3711.66i		−	0.462224i	0.972927	−	0.231112i	$-0.0742363\pi$
$402$	382.090	+	340.745i	0.0474052	+	0.0422757i
$403$	−2016.54	−	835.278i	−0.249258	−	0.103246i
$404$	6964.14	−	3867.80i	0.857621	−	0.476312i
$405$	−4097.53	−	9892.32i	−0.502736	−	1.21371i
$406$	4264.49	+	8831.89i	0.521288	+	1.07960i
$407$	2307.24	+	2307.24i	0.280996	+	0.280996i
$408$	1462.55	+	329.039i	0.177468	+	0.0399262i
$409$	6598.84	−	6598.84i	0.797780	−	0.797780i	−0.184965	−	0.982745i	$-0.559217\pi$
$409$	6598.84	−	6598.84i	0.797780	−	0.797780i	0.982745	+	0.184965i	$0.0592173\pi$
$410$	16064.1	+	5602.39i	1.93500	+	0.674835i
$411$	193.001	−	79.9436i	0.0231631	−	0.00959447i
$412$	−1324.57	+	1668.03i	−0.158390	+	0.199461i
$413$	1414.27	−	3414.36i	0.168503	−	0.406803i
$414$	−186.739	−	3264.78i	−0.0221684	−	0.387573i
$415$	−17170.8			−2.03104
$416$	−7365.61	−	791.297i	−0.868098	−	0.0932609i
$417$	−3015.41			−0.354113
$418$	−297.981	−	5209.64i	−0.0348677	−	0.609598i
$419$	866.138	−	2091.04i	0.100987	−	0.243804i	−0.865308	−	0.501240i	$-0.832877\pi$
$419$	866.138	−	2091.04i	0.100987	−	0.243804i	0.966296	+	0.257435i	$0.0828774\pi$
$420$	3527.58	+	2801.22i	0.409829	+	0.325441i
$421$	−5360.95	+	2220.58i	−0.620610	+	0.257065i	−0.670757	−	0.741677i	$-0.734031\pi$
$421$	−5360.95	+	2220.58i	−0.620610	+	0.257065i	0.0501475	+	0.998742i	$0.484031\pi$
$422$	−12070.8	−	4209.74i	−1.39241	−	0.485609i
$423$	−5664.98	+	5664.98i	−0.651161	+	0.651161i
$424$	5612.15	+	8870.38i	0.642807	+	1.01600i
$425$	7056.18	+	7056.18i	0.805353	+	0.805353i
$426$	−415.067	−	859.617i	−0.0472068	−	0.0977667i
$427$	−4879.64	−	11780.5i	−0.553026	−	1.33512i
$428$	−491.192	−	884.413i	−0.0554736	−	0.0998826i
$429$	2480.16	+	1027.31i	0.279122	+	0.115616i
$430$	5497.31	+	4902.47i	0.616521	+	0.549809i
$431$		−	3632.29i		−	0.405943i	−0.979185	−	0.202971i	$-0.934940\pi$
$431$		−	3632.29i		−	0.405943i	0.979185	−	0.202971i	$-0.0650599\pi$
$432$	−3407.56	+	2439.08i	−0.379505	+	0.271644i
$433$		−	4662.59i		−	0.517482i	−0.965947	−	0.258741i	$-0.916692\pi$
$433$		−	4662.59i		−	0.517482i	0.965947	−	0.258741i	$-0.0833076\pi$
$434$	−2559.06	+	2869.56i	−0.283039	+	0.317381i
$435$	2776.79	+	1150.18i	0.306061	+	0.126775i
$436$	3282.72	+	938.374i	0.360582	+	0.103073i
$437$	−610.696	−	1474.35i	−0.0668502	−	0.161391i
$438$	−789.093	+	381.014i	−0.0860829	+	0.0415652i
$439$	8537.50	+	8537.50i	0.928184	+	0.928184i	0.997589	−	0.0694048i	$-0.0221100\pi$
$439$	8537.50	+	8537.50i	0.928184	+	0.928184i	−0.0694048	+	0.997589i	$0.522110\pi$
$440$	−17192.2	−	12118.4i	−1.86275	−	1.31301i
$441$	5515.60	−	5515.60i	0.595573	−	0.595573i
$442$	2022.52	−	5799.30i	0.217651	−	0.624083i
$443$	4536.01	−	1878.88i	0.486484	−	0.201508i	−0.125940	−	0.992038i	$-0.540195\pi$
$443$	4536.01	−	1878.88i	0.486484	−	0.201508i	0.612424	+	0.790530i	$0.290195\pi$
$444$	−70.7353	−	616.316i	−0.00756070	−	0.0658762i
$445$	−8458.16	+	20419.8i	−0.901023	+	2.17526i
$446$	−2025.40	+	115.848i	−0.215034	+	0.0122995i
$447$	−1196.46			−0.126601
$448$	−5588.78	+	11792.1i	−0.589386	+	1.24358i
$449$	17669.7			1.85720			0.928602	−	0.371077i	$-0.121011\pi$
$449$	17669.7			1.85720			0.928602	+	0.371077i	$0.121011\pi$
$450$	−13510.6	+	772.780i	−1.41533	+	0.0809538i
$451$	6834.84	−	16500.8i	0.713615	−	1.72282i
$452$	833.790	+	7264.79i	0.0867658	+	0.755989i
$453$	−1978.41	+	819.482i	−0.205196	+	0.0849948i
$454$	5637.25	−	16164.0i	0.582752	−	1.67096i
$455$	13049.7	−	13049.7i	1.34457	−	1.34457i
$456$	−571.582	+	810.897i	−0.0586991	+	0.0832757i
$457$	10783.5	+	10783.5i	1.10378	+	1.10378i	0.993950	+	0.109833i	$0.0350317\pi$
$457$	10783.5	+	10783.5i	1.10378	+	1.10378i	0.109833	+	0.993950i	$0.464968\pi$
$458$	543.291	−	262.329i	0.0554287	−	0.0267638i
$459$	−1329.56	−	3209.84i	−0.135204	−	0.326411i
$460$	−6184.92	−	1767.98i	−0.626899	−	0.179201i
$461$	−96.4913	−	39.9680i	−0.00974847	−	0.00403795i	0.377804	−	0.925886i	$-0.376679\pi$
$461$	−96.4913	−	39.9680i	−0.00974847	−	0.00403795i	−0.387552	+	0.921848i	$0.626679\pi$
$462$	3147.41	−	3529.30i	0.316949	−	0.355407i
$463$		−	16514.0i		−	1.65761i	−0.559539	−	0.828804i	$-0.689022\pi$
$463$		−	16514.0i		−	1.65761i	0.559539	−	0.828804i	$-0.310978\pi$
$464$	−1422.91	+	8590.03i	−0.142364	+	0.859444i
$465$			1178.28i			0.117509i
$466$	13734.3	+	12248.1i	1.36529	+	1.21756i
$467$	−4949.67	−	2050.22i	−0.490457	−	0.203154i	0.123728	−	0.992316i	$-0.460515\pi$
$467$	−4949.67	−	2050.22i	−0.490457	−	0.203154i	−0.614185	+	0.789162i	$0.710515\pi$
$468$	4044.06	+	7281.50i	0.399437	+	0.719204i
$469$	−1413.95	−	3413.57i	−0.139211	−	0.336086i
$470$	6852.46	+	14191.7i	0.672512	+	1.39279i
$471$	2068.88	+	2068.88i	0.202397	+	0.202397i
$472$	2772.66	−	1754.22i	0.270385	−	0.171069i
$473$	5467.80	−	5467.80i	0.531521	−	0.531521i
$474$	−4075.09	−	1421.20i	−0.394884	−	0.137717i
$475$	−6101.30	+	2527.24i	−0.589362	+	0.244122i
$476$	−8472.70	−	6728.09i	−0.815852	−	0.647860i
$477$	4516.38	−	10903.5i	0.433524	−	1.04662i
$478$	−220.662	−	3857.87i	−0.0211147	−	0.369152i
$479$	−19166.1			−1.82823			−0.914114	−	0.405456i	$-0.867113\pi$
$479$	−19166.1			−1.82823			−0.914114	+	0.405456i	$0.867113\pi$
$480$	1126.97	+	3836.99i	0.107165	+	0.364863i
$481$	−2541.63			−0.240932
$482$	−253.398	−	4430.20i	−0.0239460	−	0.418651i
$483$	553.432	−	1336.10i	0.0521367	−	0.125869i
$484$	−7110.20	+	8953.89i	−0.667750	+	0.840899i
$485$	11164.4	−	4624.46i	1.04526	−	0.432961i
$486$	6739.35	+	2350.37i	0.629019	+	0.219372i
$487$	−3738.42	+	3738.42i	−0.347852	+	0.347852i	−0.859309	−	0.511457i	$-0.829106\pi$
$487$	−3738.42	+	3738.42i	−0.347852	+	0.347852i	0.511457	+	0.859309i	$0.329106\pi$
$488$	2484.71	−	11044.3i	0.230487	−	1.02449i
$489$	839.687	+	839.687i	0.0776523	+	0.0776523i
$490$	−6671.77	−	13817.4i	−0.615101	−	1.27389i
$491$	−1743.88	−	4210.09i	−0.160285	−	0.386963i	0.823250	−	0.567679i	$-0.192158\pi$
$491$	−1743.88	−	4210.09i	−0.160285	−	0.386963i	−0.983535	+	0.180716i	$0.942158\pi$
$492$	−2968.57	+	1648.71i	−0.272019	+	0.151076i
$493$	−6669.41	−	2762.56i	−0.609280	−	0.252372i
$494$	3033.57	+	2705.32i	0.276289	+	0.246393i
$495$			23649.5i			2.14740i
$496$	−3324.71	+	773.349i	−0.300975	+	0.0700089i
$497$			6889.26i			0.621782i
$498$	2281.04	−	2557.82i	0.205253	−	0.230158i
$499$	−6509.03	−	2696.13i	−0.583936	−	0.241874i	0.0711034	−	0.997469i	$-0.477348\pi$
$499$	−6509.03	−	2696.13i	−0.583936	−	0.241874i	−0.655039	+	0.755595i	$0.727348\pi$
$500$	−2453.43	+	8582.85i	−0.219442	+	0.767673i
$501$	541.225	+	1306.63i	0.0482638	+	0.116519i
$502$	−4891.12	+	2361.68i	−0.434863	+	0.209974i
$503$	3534.14	+	3534.14i	0.313280	+	0.313280i	0.846179	−	0.532899i	$-0.178897\pi$
$503$	3534.14	+	3534.14i	0.313280	+	0.313280i	−0.532899	+	0.846179i	$0.678897\pi$
$504$	14457.1	−	2502.61i	1.27772	−	0.221181i
$505$	−12458.3	+	12458.3i	−1.09780	+	1.09780i
$506$	−2223.78	+	6376.38i	−0.195374	+	0.560207i
$507$	602.430	−	249.535i	0.0527710	−	0.0218584i
$508$	−17162.2	+	1969.73i	−1.49892	+	0.172033i
$509$	−4345.28	+	10490.4i	−0.378391	+	0.913518i	0.613876	+	0.789402i	$0.289609\pi$
$509$	−4345.28	+	10490.4i	−0.378391	+	0.913518i	−0.992268	+	0.124115i	$0.960391\pi$
$510$	−3310.16	+	189.335i	−0.287405	+	0.0164390i
$511$	6324.05			0.547475
$512$	−10087.0	+	5698.28i	−0.870676	+	0.491857i
$513$	2299.28			0.197886
$514$	−2275.03	+	130.127i	−0.195228	+	0.0111666i
$515$	1802.78	−	4352.28i	0.154252	−	0.372397i
$516$	−1460.57	+	167.632i	−0.124609	+	0.0143015i
$517$	15285.0	−	6331.24i	1.30026	−	0.538583i
$518$	−1474.34	+	4227.47i	−0.125056	+	0.358580i
$519$	−207.835	+	207.835i	−0.0175779	+	0.0175779i
$520$	16144.2	−	2794.65i	1.36148	−	0.235680i
$521$	−8864.19	−	8864.19i	−0.745388	−	0.745388i	0.228221	−	0.973609i	$-0.426709\pi$
$521$	−8864.19	−	8864.19i	−0.745388	−	0.745388i	−0.973609	+	0.228221i	$0.926709\pi$
$522$	8815.87	−	4256.75i	0.739196	−	0.356922i
$523$	1505.26	+	3634.02i	0.125852	+	0.303833i	0.974230	−	0.225558i	$-0.0724206\pi$
$523$	1505.26	+	3634.02i	0.125852	+	0.303833i	−0.848378	+	0.529391i	$0.822421\pi$
$524$	−5149.49	+	18014.5i	−0.429307	+	1.50184i
$525$	−5529.20	−	2290.27i	−0.459645	−	0.190391i
$526$	−5749.07	+	6446.64i	−0.476562	+	0.534386i
$527$		−	2830.06i		−	0.233926i
$528$	4089.08	−	951.148i	0.337035	−	0.0783966i
$529$		−	10101.8i		−	0.830260i
$530$	−17326.5	−	15451.6i	−1.42003	−	1.26637i
$531$	−3408.16	−	1411.71i	−0.278534	−	0.115373i
$532$	6259.44	−	3476.42i	0.510115	−	0.283312i
$533$	5323.95	+	12853.2i	0.432657	+	1.04453i
$534$	−1918.18	−	3972.61i	−0.155445	−	0.321932i
$535$	1582.15	+	1582.15i	0.127854	+	0.127854i
$536$	719.981	−	3200.25i	0.0580195	−	0.257891i
$537$	1872.29	−	1872.29i	0.150457	−	0.150457i
$538$	−6947.39	−	2422.92i	−0.556734	−	0.194163i
$539$	−14881.9	+	6164.29i	−1.18926	+	0.492606i
$540$	5763.61	−	7258.13i	0.459308	−	0.578408i
$541$	−4671.40	+	11277.8i	−0.371237	+	0.896245i	0.622305	+	0.782775i	$0.286196\pi$
$541$	−4671.40	+	11277.8i	−0.371237	+	0.896245i	−0.993541	+	0.113470i	$0.963804\pi$
$542$	−58.7783	−	1027.63i	−0.00465820	−	0.0814400i
$543$	1527.80			0.120744
$544$	−2706.81	−	9215.87i	−0.213334	−	0.726336i
$545$	−7551.19			−0.593500
$546$	210.345	+	3677.50i	0.0164871	+	0.288246i
$547$	6749.10	−	16293.8i	0.527552	−	1.27362i	−0.405571	−	0.914064i	$-0.632927\pi$
$547$	6749.10	−	16293.8i	0.527552	−	1.27362i	0.933122	−	0.359559i	$-0.117073\pi$
$548$	−1048.20	−	832.367i	−0.0817098	−	0.0648849i
$549$	−11759.1	+	4870.79i	−0.914148	+	0.378652i
$550$	26387.4	+	9202.67i	2.04575	+	0.713461i
$551$	3378.15	−	3378.15i	0.261187	−	0.261187i
$552$	1084.99	−	686.459i	0.0836602	−	0.0529305i
$553$	22024.5	+	22024.5i	1.69363	+	1.69363i
$554$	−761.254	−	1576.58i	−0.0583801	−	0.120907i
$555$	525.063	+	1267.61i	0.0401580	+	0.0969499i
$556$	9380.69	+	16890.3i	0.715521	+	1.28833i
$557$	−2590.39	−	1072.98i	−0.197053	−	0.0816220i	0.281975	−	0.959422i	$-0.409011\pi$
$557$	−2590.39	−	1072.98i	−0.197053	−	0.0816220i	−0.479028	+	0.877800i	$0.659011\pi$
$558$	2864.36	+	2554.42i	0.217308	+	0.193794i
$559$			6023.28i			0.455738i
$560$	4716.56	−	28473.6i	0.355913	−	2.14862i
$561$			3480.71i			0.261953i
$562$	15722.3	−	17630.0i	1.18008	−	1.32327i
$563$	−7377.58	−	3055.89i	−0.552270	−	0.228758i	0.0890556	−	0.996027i	$-0.471615\pi$
$563$	−7377.58	−	3055.89i	−0.552270	−	0.228758i	−0.641325	+	0.767269i	$0.721615\pi$
$564$	−3024.34	−	864.517i	−0.225794	−	0.0645438i
$565$	−6189.15	−	14941.9i	−0.460849	−	1.11259i
$566$	5864.04	−	2831.46i	0.435484	−	0.210274i
$567$	−10906.2	−	10906.2i	−0.807792	−	0.807792i
$568$	−3523.77	+	4999.14i	−0.260307	+	0.369294i
$569$	16799.5	−	16799.5i	1.23773	−	1.23773i	0.276810	−	0.960925i	$-0.410723\pi$
$569$	16799.5	−	16799.5i	1.23773	−	1.23773i	0.960925	−	0.276810i	$-0.0892773\pi$
$570$	722.561	−	2071.84i	0.0530961	−	0.152245i
$571$	8801.25	−	3645.60i	0.645045	−	0.267186i	−0.0360851	−	0.999349i	$-0.511489\pi$
$571$	8801.25	−	3645.60i	0.645045	−	0.267186i	0.681130	+	0.732162i	$0.261489\pi$
$572$	−1961.23	−	17088.1i	−0.143362	−	1.24911i
$573$	−2444.33	+	5901.13i	−0.178208	+	0.430232i
$574$	24466.8	−	1399.45i	1.77914	−	0.101763i
$575$	8546.51			0.619851
$576$	11770.7	+	5578.64i	0.851472	+	0.403548i
$577$	11551.9			0.833472			0.416736	−	0.909028i	$-0.363174\pi$
$577$	11551.9			0.833472			0.416736	+	0.909028i	$0.363174\pi$
$578$	−5922.88	+	338.777i	−0.426227	+	0.0243793i
$579$	−1959.90	+	4731.62i	−0.140675	+	0.339619i
$580$	−2195.79	−	19131.9i	−0.157199	−	1.36967i
$581$	−22851.4	+	9465.36i	−1.63173	+	0.675886i
$582$	−794.258	+	2277.42i	−0.0565688	+	0.162203i
$583$	−17233.4	+	17233.4i	−1.22425	+	1.22425i
$584$	4589.00	+	3234.68i	0.325161	+	0.229198i
$585$	−13026.0	−	13026.0i	−0.920615	−	0.920615i
$586$	−4916.98	+	2374.17i	−0.346619	+	0.167365i
$587$	2507.65	+	6054.00i	0.176323	+	0.425682i	0.987190	−	0.159549i	$-0.0510040\pi$
$587$	2507.65	+	6054.00i	0.176323	+	0.425682i	−0.810867	+	0.585231i	$0.801004\pi$
$588$	2944.59	+	841.720i	0.206519	+	0.0590340i
$589$	1730.35	+	716.733i	0.121049	+	0.0501400i
$590$	−4829.79	+	5415.81i	−0.337016	+	0.377908i
$591$		−	3196.34i		−	0.222470i
$592$	−3232.15	+	2313.52i	−0.224393	+	0.160617i
$593$			7192.49i			0.498078i	0.968493	+	0.249039i	$0.0801147\pi$
$593$			7192.49i			0.498078i	−0.968493	+	0.249039i	$0.919885\pi$
$594$	−7261.67	−	6475.91i	−0.501599	−	0.447323i
$595$	22107.2	+	9157.12i	1.52321	+	0.630933i
$596$	3722.10	+	6701.79i	0.255810	+	0.460598i
$597$	−2310.59	−	5578.26i	−0.158402	−	0.382417i
$598$	−2287.23	−	4736.93i	−0.156408	−	0.323926i
$599$	8885.88	+	8885.88i	0.606122	+	0.606122i	0.941930	−	0.335808i	$-0.109009\pi$
$599$	8885.88	+	8885.88i	0.606122	+	0.606122i	−0.335808	+	0.941930i	$0.609009\pi$
$600$	−2840.77	−	4490.03i	−0.193290	−	0.305508i
$601$	1468.96	−	1468.96i	0.0997009	−	0.0997009i	−0.655497	−	0.755198i	$-0.727541\pi$
$601$	1468.96	−	1468.96i	0.0997009	−	0.0997009i	0.755198	+	0.655497i	$0.227541\pi$
$602$	10018.5	+	3493.97i	0.678275	+	0.236550i
$603$	−3407.38	+	1411.38i	−0.230115	+	0.0953167i
$604$	10744.9	+	8532.39i	0.723845	+	0.574798i
$605$	9677.19	−	23362.8i	0.650303	−	1.56997i
$606$	−200.812	−	3510.84i	−0.0134611	−	0.235343i
$607$	−1305.90			−0.0873225			−0.0436613	−	0.999046i	$-0.513902\pi$
$607$	−1305.90			−0.0873225			−0.0436613	+	0.999046i	$0.513902\pi$
$608$	6320.26	+	678.994i	0.421580	+	0.0452908i
$609$	4329.46			0.288076
$610$	1429.74	+	24996.4i	0.0948992	+	1.65914i
$611$	−4931.67	+	11906.1i	−0.326537	+	0.788330i
$612$	−6715.88	+	8457.33i	−0.443584	+	0.558607i
$613$	−15396.4	+	6377.39i	−1.01444	+	0.420196i	−0.827074	−	0.562093i	$-0.809996\pi$
$613$	−15396.4	+	6377.39i	−1.01444	+	0.420196i	−0.187370	+	0.982289i	$0.559996\pi$
$614$	−19143.9	−	6676.48i	−1.25828	−	0.438828i
$615$	5310.53	−	5310.53i	0.348197	−	0.348197i
$616$	−29560.2	−	6650.34i	−1.93346	−	0.434984i
$617$	−14943.6	−	14943.6i	−0.975049	−	0.975049i	0.0246473	−	0.999696i	$-0.492154\pi$
$617$	−14943.6	−	14943.6i	−0.975049	−	0.975049i	−0.999696	+	0.0246473i	$0.992154\pi$
$618$	408.841	+	846.723i	0.0266117	+	0.0551136i
$619$	−9902.61	−	23907.0i	−0.643004	−	1.55235i	−0.822608	−	0.568609i	$-0.807482\pi$
$619$	−9902.61	−	23907.0i	−0.643004	−	1.55235i	0.179604	−	0.983739i	$-0.442518\pi$
$620$	6599.98	−	3665.55i	0.427519	−	0.237439i
$621$	−2749.08	−	1138.71i	−0.177644	−	0.0735826i
$622$	−2321.54	−	2070.33i	−0.149655	−	0.133461i
$623$			31837.8i			2.04744i
$624$	−1728.36	+	2776.14i	−0.110881	+	0.178100i
$625$			3764.96i			0.240957i
$626$	−9262.02	+	10385.8i	−0.591350	+	0.663102i
$627$	−2128.17	−	881.515i	−0.135551	−	0.0561472i
$628$	5152.40	−	18024.6i	0.327393	−	1.14532i
$629$	−1261.12	−	3044.61i	−0.0799429	−	0.192999i
$630$	−29222.2	+	14110.0i	−1.84800	+	0.892308i
$631$	11209.4	+	11209.4i	0.707191	+	0.707191i	0.965944	−	0.258753i	$-0.0833115\pi$
$631$	11209.4	+	11209.4i	0.707191	+	0.707191i	−0.258753	+	0.965944i	$0.583312\pi$
$632$	4716.65	+	27247.2i	0.296864	+	1.71493i
$633$	−3990.43	+	3990.43i	−0.250561	+	0.250561i
$634$	−6424.01	+	18419.9i	−0.402413	+	1.15386i
$635$	35298.5	−	14621.1i	2.20595	−	0.913736i
$636$	4603.44	−	528.343i	0.287010	−	0.0329405i
$637$	4801.63	−	11592.2i	0.298662	−	0.721033i
$638$	−20183.6	+	1154.46i	−1.25247	+	0.0716387i
$639$	6876.77			0.425729
$640$	17986.4	−	18249.1i	1.11090	−	1.12713i
$641$	−8922.84			−0.549814			−0.274907	−	0.961471i	$-0.588647\pi$
$641$	−8922.84			−0.549814			−0.274907	+	0.961471i	$0.588647\pi$
$642$	−445.860	+	25.5023i	−0.0274092	+	0.00156775i
$643$	−7149.00	+	17259.2i	−0.438459	+	1.05853i	0.538022	+	0.842930i	$0.319172\pi$
$643$	−7149.00	+	17259.2i	−0.438459	+	1.05853i	−0.976481	+	0.215603i	$0.930828\pi$
$644$	−9205.66	+	1056.55i	−0.563282	+	0.0646487i
$645$	3004.05	−	1244.32i	0.183386	−	0.0759611i
$646$	−1735.48	+	4976.24i	−0.105699	+	0.303077i
$647$	−15074.6	+	15074.6i	−0.915985	+	0.915985i	−0.996734	−	0.0807492i	$-0.974269\pi$
$647$	−15074.6	+	15074.6i	−0.915985	+	0.915985i	0.0807492	+	0.996734i	$0.474269\pi$
$648$	−2335.61	−	13492.4i	−0.141592	−	0.817951i
$649$	5386.73	+	5386.73i	0.325805	+	0.325805i
$650$	−19602.8	+	9465.26i	−1.18290	+	0.571166i
$651$	649.526	+	1568.09i	0.0391043	+	0.0944062i
$652$	2091.18	−	7315.58i	0.125609	−	0.439417i
$653$	717.534	+	297.212i	0.0430004	+	0.0178114i	0.404080	−	0.914724i	$-0.367592\pi$
$653$	717.534	+	297.212i	0.0430004	+	0.0178114i	−0.361080	+	0.932535i	$0.617592\pi$
$654$	1003.13	−	1124.85i	0.0599780	−	0.0672555i
$655$		−	41438.5i		−	2.47197i
$656$	18470.0	+	11499.0i	1.09928	+	0.684390i
$657$		−	6312.58i		−	0.374851i
$658$	16942.6	+	15109.3i	1.00378	+	0.895168i
$659$	6945.56	+	2876.95i	0.410562	+	0.170061i	0.578398	−	0.815754i	$-0.303678\pi$
$659$	6945.56	+	2876.95i	0.410562	+	0.170061i	−0.167836	+	0.985815i	$0.553678\pi$
$660$	−8117.37	+	4508.29i	−0.478739	+	0.265886i
$661$	−797.182	−	1924.57i	−0.0469089	−	0.113248i	0.898688	−	0.438588i	$-0.144521\pi$
$661$	−797.182	−	1924.57i	−0.0469089	−	0.113248i	−0.945597	+	0.325340i	$0.894521\pi$
$662$	−4546.87	−	9416.72i	−0.266948	−	0.552857i
$663$	−1917.16	−	1917.16i	−0.112302	−	0.112302i
$664$	−21423.4	−	4819.75i	−1.25209	−	0.281691i
$665$	−11197.6	+	11197.6i	−0.652971	+	0.652971i
$666$	4219.80	+	1471.67i	0.245517	+	0.0856246i
$667$	−5712.04	+	2366.01i	−0.331591	+	0.137349i
$668$	5635.20	−	7096.42i	0.326396	−	0.411031i
$669$	−342.714	+	827.385i	−0.0198058	+	0.0478155i
$670$	414.289	+	7243.07i	0.0238886	+	0.417648i
$671$	26284.2			1.51221
$672$	3614.94	+	4485.14i	0.207514	+	0.257467i
$673$	6013.47			0.344431			0.172216	−	0.985059i	$-0.444907\pi$
$673$	6013.47			0.344431			0.172216	+	0.985059i	$0.444907\pi$
$674$	−963.265	−	16840.9i	−0.0550498	−	0.962445i
$675$	−4712.31	+	11376.5i	−0.268707	+	0.648716i
$676$	−3271.84	−	2598.14i	−0.186154	−	0.147823i
$677$	19577.8	−	8109.41i	1.11143	−	0.460369i	0.250000	−	0.968246i	$-0.419569\pi$
$677$	19577.8	−	8109.41i	1.11143	−	0.460369i	0.861430	+	0.507877i	$0.169569\pi$
$678$	3047.99	+	1062.99i	0.172651	+	0.0602125i
$679$	12308.7	−	12308.7i	0.695679	−	0.695679i
$680$	11358.2	+	17952.4i	0.640539	+	1.01242i
$681$	−5343.58	−	5343.58i	−0.300685	−	0.300685i
$682$	−3446.17	−	7137.13i	−0.193491	−	0.400726i
$683$	−5715.60	−	13798.7i	−0.320207	−	0.773048i	−0.999241	−	0.0389416i	$-0.987601\pi$
$683$	−5715.60	−	13798.7i	−0.320207	−	0.773048i	0.679035	−	0.734106i	$-0.262399\pi$
$684$	−3470.11	−	6248.09i	−0.193981	−	0.349271i
$685$	2735.00	+	1132.88i	0.152553	+	0.0631897i
$686$	1958.36	+	1746.45i	0.108995	+	0.0972011i
$687$		−	266.325i		−	0.0147903i
$688$	5482.69	+	7659.69i	0.303816	+	0.424452i
$689$		−	18984.2i		−	1.04970i
$690$	−1889.99	+	2119.31i	−0.104276	+	0.116929i
$691$	−8261.06	−	3421.84i	−0.454798	−	0.188384i	0.143511	−	0.989649i	$-0.454161\pi$
$691$	−8261.06	−	3421.84i	−0.454798	−	0.188384i	−0.598310	+	0.801265i	$0.704161\pi$
$692$	1810.72	+	517.598i	0.0994698	+	0.0284337i
$693$	13036.7	+	31473.4i	0.714608	+	1.72522i
$694$	32007.4	−	15454.8i	1.75070	−	0.845328i
$695$	−30215.5	−	30215.5i	−1.64912	−	1.64912i
$696$	3141.64	+	2214.47i	0.171097	+	0.120602i
$697$	−12755.1	+	12755.1i	−0.693161	+	0.693161i
$698$	7320.59	−	20990.8i	0.396975	−	1.13827i
$699$	7505.19	−	3108.75i	0.406112	−	0.168217i
$700$	4372.30	+	38095.8i	0.236082	+	2.05698i
$701$	8530.14	−	20593.6i	0.459599	−	1.10957i	−0.508961	−	0.860790i	$-0.669970\pi$
$701$	8530.14	−	20593.6i	0.459599	−	1.10957i	0.968560	−	0.248780i	$-0.0800298\pi$
$702$	7566.60	−	432.794i	0.406813	−	0.0232689i
$703$	2180.92			0.117005
$704$	−18048.5	−	19945.4i	−0.966235	−	1.06779i
$705$	6956.86			0.371646
$706$	13121.5	−	750.524i	0.699483	−	0.0400090i
$707$	−9712.25	+	23447.4i	−0.516643	+	1.24729i
$708$	−165.147	−	1438.92i	−0.00876637	−	0.0763812i
$709$	11948.6	−	4949.27i	0.632919	−	0.262163i	−0.0430740	−	0.999072i	$-0.513715\pi$
$709$	11948.6	−	4949.27i	0.632919	−	0.262163i	0.675993	+	0.736908i	$0.263715\pi$
$710$	4454.55	−	12772.8i	0.235460	−	0.675148i
$711$	21984.6	−	21984.6i	1.15962	−	1.15962i
$712$	−16284.7	+	23102.9i	−0.857154	+	1.21603i
$713$	−1713.89	−	1713.89i	−0.0900222	−	0.0900222i
$714$	−4300.89	+	2076.69i	−0.225430	+	0.108849i
$715$	14558.0	+	35146.2i	0.761453	+	1.83831i
$716$	−16311.9	−	4662.80i	−0.851402	−	0.243376i
$717$	−1575.96	−	652.783i	−0.0820854	−	0.0340009i
$718$	−3675.37	+	4121.33i	−0.191036	+	0.214215i
$719$			3624.32i			0.187989i	0.995573	+	0.0939947i	$0.0299637\pi$
$719$			3624.32i			0.187989i	−0.995573	+	0.0939947i	$0.970036\pi$
$720$	−28421.9	−	4708.01i	−1.47114	−	0.243690i
$721$		−	6785.92i		−	0.350514i
$722$	11875.9	+	10590.9i	0.612156	+	0.545917i
$723$	−1809.76	−	749.626i	−0.0930921	−	0.0385600i
$724$	−4752.85	−	8557.71i	−0.243976	−	0.439288i
$725$	9791.24	+	23638.1i	0.501569	+	1.21089i
$726$	2194.63	+	4545.16i	0.112191	+	0.232351i
$727$	−24377.4	−	24377.4i	−1.24361	−	1.24361i	−0.958491	−	0.285123i	$-0.907966\pi$
$727$	−24377.4	−	24377.4i	−1.24361	−	1.24361i	−0.285123	−	0.958491i	$-0.592034\pi$
$728$	19944.6	−	12618.6i	1.01538	−	0.642414i
$729$	−9325.61	+	9325.61i	−0.473790	+	0.473790i
$730$	−11724.9	−	4089.09i	−0.594463	−	0.207321i
$731$	−7215.26	+	2988.66i	−0.365070	+	0.151217i
$732$	−3913.47	−	3107.65i	−0.197604	−	0.156915i
$733$	−2874.93	+	6940.70i	−0.144868	+	0.349742i	−0.979613	−	0.200895i	$-0.935615\pi$
$733$	−2874.93	+	6940.70i	−0.144868	+	0.349742i	0.834745	+	0.550637i	$0.185615\pi$
$734$	1359.79	+	23773.5i	0.0683799	+	1.19550i
$735$	−6773.41			−0.339920
$736$	−7220.43	−	3941.91i	−0.361615	−	0.197420i
$737$	7616.24			0.380662
$738$	−1396.91	−	24422.5i	−0.0696763	−	1.21816i
$739$	9423.24	−	22749.7i	0.469066	−	1.13242i	−0.495506	−	0.868604i	$-0.665017\pi$
$739$	9423.24	−	22749.7i	0.469066	−	1.13242i	0.964572	−	0.263820i	$-0.0849825\pi$
$740$	5466.91	−	6884.50i	0.271578	−	0.341999i
$741$	1657.72	−	686.650i	0.0821833	−	0.0340414i
$742$	−31576.2	−	11012.3i	−1.56226	−	0.544844i
$743$	−4515.42	+	4515.42i	−0.222954	+	0.222954i	−0.809741	−	0.586787i	$-0.800393\pi$
$743$	−4515.42	+	4515.42i	−0.222954	+	0.222954i	0.586787	+	0.809741i	$0.300393\pi$
$744$	−330.738	+	1470.10i	−0.0162976	+	0.0724415i
$745$	−11989.0	−	11989.0i	−0.589587	−	0.589587i
$746$	6901.18	+	14292.6i	0.338700	+	0.701458i
$747$	9448.20	+	22810.0i	0.462773	+	1.11723i
$748$	19496.7	−	10828.2i	0.953033	−	0.529303i
$749$	2977.72	+	1233.41i	0.145265	+	0.0601707i
$750$	2940.98	+	2622.75i	0.143186	+	0.127692i
$751$			25582.2i			1.24302i	0.783406	+	0.621510i	$0.213481\pi$
$751$			25582.2i			1.24302i	−0.783406	+	0.621510i	$0.786519\pi$
$752$	4566.03	+	19629.8i	0.221418	+	0.951897i
$753$			2397.67i			0.116037i
$754$	10481.2	−	11752.9i	0.506235	−	0.567660i
$755$	−28035.9	−	11612.8i	−1.35143	−	0.559780i
$756$	3669.35	−	12836.5i	0.176525	−	0.617538i
$757$	7681.53	+	18544.9i	0.368811	+	0.890389i	0.993946	+	0.109872i	$0.0350440\pi$
$757$	7681.53	+	18544.9i	0.368811	+	0.890389i	−0.625135	+	0.780517i	$0.714956\pi$
$758$	20971.6	−	10126.2i	1.00491	−	0.485223i
$759$	2107.93	+	2107.93i	0.100808	+	0.100808i
$760$	−13852.9	+	2398.02i	−0.661183	+	0.114454i
$761$	−9053.82	+	9053.82i	−0.431276	+	0.431276i	−0.889062	−	0.457786i	$-0.848642\pi$
$761$	−9053.82	+	9053.82i	−0.431276	+	0.431276i	0.457786	+	0.889062i	$0.348642\pi$
$762$	−2511.20	+	7200.51i	−0.119385	+	0.342319i
$763$	−10049.3	+	4162.58i	−0.476816	+	0.197504i
$764$	40658.4	−	4666.42i	1.92535	−	0.220975i
$765$	9140.51	−	22067.1i	0.431995	−	1.04293i
$766$	−34958.6	+	1999.56i	−1.64896	+	0.0943171i
$767$	−5933.98			−0.279353
$768$	329.056	+	5103.61i	0.0154607	+	0.239792i
$769$	−22171.5			−1.03969			−0.519847	−	0.854259i	$-0.674011\pi$
$769$	−22171.5			−1.03969			−0.519847	+	0.854259i	$0.674011\pi$
$770$	66903.0	−	3826.71i	3.13119	−	0.179098i
$771$	−384.954	+	929.362i	−0.0179816	+	0.0434113i
$772$	32600.5	−	3741.61i	1.51984	−	0.174434i
$773$	4511.27	−	1868.63i	0.209908	−	0.0869469i	−0.275252	−	0.961372i	$-0.588761\pi$
$773$	4511.27	−	1868.63i	0.209908	−	0.0869469i	0.485160	+	0.874425i	$0.338761\pi$
$774$	3487.63	−	10000.3i	0.161964	−	0.464409i
$775$	−7092.61	+	7092.61i	−0.328741	+	0.328741i
$776$	15227.5	−	2635.97i	0.704428	−	0.121940i
$777$	1397.54	+	1397.54i	0.0645255	+	0.0645255i
$778$	5669.01	−	2737.29i	0.261239	−	0.126139i
$779$	−4568.36	−	11029.0i	−0.210114	−	0.507259i
$780$	1987.87	−	6954.16i	0.0912525	−	0.319229i
$781$	−13120.0	−	5434.50i	−0.601116	−	0.248991i
$782$	4539.46	−	5090.26i	0.207584	−	0.232772i
$783$		−	8908.03i		−	0.406574i
$784$	−4445.63	−	19112.2i	−0.202516	−	0.870637i
$785$			41461.9i			1.88514i
$786$	6172.81	+	5504.87i	0.280123	+	0.249812i
$787$	23455.4	+	9715.54i	1.06238	+	0.440053i	0.844296	−	0.535877i	$-0.180019\pi$
$787$	23455.4	+	9715.54i	1.06238	+	0.440053i	0.218086	+	0.975930i	$0.430019\pi$
$788$	−17903.8	+	9943.55i	−0.809386	+	0.449523i
$789$	1459.20	+	3522.81i	0.0658413	+	0.158955i
$790$	−26592.9	−	55074.8i	−1.19764	−	2.48035i
$791$	−16473.4	−	16473.4i	−0.740489	−	0.740489i
$792$	−6638.28	+	29506.5i	−0.297830	+	1.32382i
$793$	−14477.2	+	14477.2i	−0.648300	+	0.648300i
$794$	−30499.4	−	10636.7i	−1.36320	−	0.475420i
$795$	−9468.17	+	3921.84i	−0.422392	+	0.174960i
$796$	−24057.7	+	30295.9i	−1.07123	+	1.34901i
$797$	−11912.1	+	28758.4i	−0.529421	+	1.27814i	0.402482	+	0.915428i	$0.368148\pi$
$797$	−11912.1	+	28758.4i	−0.529421	+	1.27814i	−0.931903	+	0.362708i	$0.881852\pi$
$798$	−180.492	−	3155.58i	−0.00800672	−	0.139983i
$799$	−16709.3			−0.739841
$800$	−16312.8	+	29880.3i	−0.720931	+	1.32053i
$801$	31780.1			1.40186
$802$	599.494	+	10481.0i	0.0263951	+	0.461469i
$803$	−4988.64	+	12043.6i	−0.219234	+	0.529279i
$804$	−1133.99	−	900.487i	−0.0497420	−	0.0394996i
$805$	18933.8	−	7842.65i	0.828981	−	0.343375i
$806$	5829.24	+	2032.96i	0.254747	+	0.0888438i
$807$	−2296.70	+	2296.70i	−0.100183	+	0.100183i
$808$	−19040.7	+	12046.8i	−0.829022	+	0.524509i
$809$	2278.00	+	2278.00i	0.0989992	+	0.0989992i	0.754872	−	0.655873i	$-0.227699\pi$
$809$	2278.00	+	2278.00i	0.0989992	+	0.0989992i	−0.655873	+	0.754872i	$0.727699\pi$
$810$	13168.4	+	27272.2i	0.571224	+	1.18302i
$811$	−11666.4	−	28165.2i	−0.505134	−	1.21950i	−0.946655	−	0.322250i	$-0.895561\pi$
$811$	−11666.4	−	28165.2i	−0.505134	−	1.21950i	0.441521	−	0.897251i	$-0.354439\pi$
$812$	−13468.6	−	24250.8i	−0.582088	−	1.04807i
$813$	−419.792	−	173.884i	−0.0181092	−	0.00750106i
$814$	−6887.86	−	6142.55i	−0.296584	−	0.264492i
$815$			16827.9i			0.723260i
$816$	−4183.11	−	692.920i	−0.179459	−	0.0297268i
$817$		−	5168.43i		−	0.221323i
$818$	−17568.1	+	19699.7i	−0.750921	+	0.842035i
$819$	−24516.0	−	10154.8i	−1.04598	−	0.433259i
$820$	−46266.8	−	13225.5i	−1.97037	−	0.563237i
$821$	−12455.2	−	30069.5i	−0.529463	−	1.27824i	−0.931876	−	0.362778i	$-0.881828\pi$
$821$	−12455.2	−	30069.5i	−0.529463	−	1.27824i	0.402413	−	0.915458i	$-0.368172\pi$
$822$	−532.086	+	256.918i	−0.0225774	+	0.0109015i
$823$	18709.3	+	18709.3i	0.792424	+	0.792424i	0.981888	−	0.189464i	$-0.0606751\pi$
$823$	18709.3	+	18709.3i	0.792424	+	0.792424i	−0.189464	+	0.981888i	$0.560675\pi$
$824$	3470.92	−	4924.15i	0.146742	−	0.208181i
$825$	8723.26	−	8723.26i	0.368127	−	0.368127i
$826$	−3442.17	+	9869.92i	−0.144998	+	0.415761i
$827$	31391.1	−	13002.6i	1.31992	−	0.546730i	0.392160	−	0.919897i	$-0.371728\pi$
$827$	31391.1	−	13002.6i	1.31992	−	0.546730i	0.927764	+	0.373167i	$0.121728\pi$
$828$	1054.63	+	9188.96i	0.0442644	+	0.385675i
$829$	3317.38	−	8008.87i	0.138984	−	0.335536i	−0.839027	−	0.544089i	$-0.816875\pi$
$829$	3317.38	−	8008.87i	0.138984	−	0.335536i	0.978011	+	0.208553i	$0.0668753\pi$
$830$	48487.1	−	2773.36i	2.02773	−	0.115982i
$831$	−772.852			−0.0322622
$832$	20926.9	+	1044.81i	0.872007	+	0.0435363i
$833$	16268.7			0.676683
$834$	8514.94	−	487.037i	0.353535	−	0.0202215i
$835$	−7669.66	+	18516.2i	−0.317868	+	0.767401i
$836$	1682.88	+	14662.9i	0.0696216	+	0.606612i
$837$	3226.41	−	1336.42i	0.133239	−	0.0551895i
$838$	−2108.07	+	6044.60i	−0.0869000	+	0.249173i
$839$	13722.1	−	13722.1i	0.564649	−	0.564649i	−0.365976	−	0.930624i	$-0.619265\pi$
$839$	13722.1	−	13722.1i	0.564649	−	0.564649i	0.930624	+	0.365976i	$0.119265\pi$
$840$	−10413.7	−	7340.34i	−0.427745	−	0.301507i
$841$	4157.72	+	4157.72i	0.170475	+	0.170475i
$842$	14779.7	−	7136.38i	0.604918	−	0.292085i
$843$	−3990.55	−	9634.04i	−0.163039	−	0.393611i
$844$	34765.7	+	9937.88i	1.41787	+	0.405303i
$845$	8537.00	+	3536.14i	0.347552	+	0.143961i
$846$	15081.9	−	16911.8i	0.612914	−	0.687282i
$847$		−	36426.4i		−	1.47772i
$848$	−17280.4	−	24141.8i	−0.699776	−	0.977635i
$849$		−	2874.60i		−	0.116202i
$850$	−21065.0	−	18785.6i	−0.850029	−	0.758050i
$851$	−2607.57	−	1080.09i	−0.105037	−	0.0435077i
$852$	1310.91	+	2360.36i	0.0527127	+	0.0949114i
$853$	8865.17	+	21402.4i	0.355847	+	0.859092i	0.995875	+	0.0907394i	$0.0289230\pi$
$853$	8865.17	+	21402.4i	0.355847	+	0.859092i	−0.640027	+	0.768352i	$0.721077\pi$
$854$	15681.9	+	32477.7i	0.628366	+	1.30136i
$855$	11177.3	+	11177.3i	0.447084	+	0.447084i
$856$	1529.88	+	2418.08i	0.0610868	+	0.0965518i
$857$	−7933.81	+	7933.81i	−0.316236	+	0.316236i	−0.847319	−	0.531084i	$-0.821785\pi$
$857$	−7933.81	+	7933.81i	−0.316236	+	0.316236i	0.531084	+	0.847319i	$0.321785\pi$
$858$	−7169.43	−	2500.36i	−0.285268	−	0.0994881i
$859$	−3978.15	+	1647.80i	−0.158012	+	0.0654509i	−0.460288	−	0.887770i	$-0.652254\pi$
$859$	−3978.15	+	1647.80i	−0.158012	+	0.0654509i	0.302275	+	0.953221i	$0.402254\pi$
$860$	−16315.2	−	12955.7i	−0.646912	−	0.513706i
$861$	4139.99	−	9994.83i	0.163868	−	0.395613i
$862$	586.674	+	10256.9i	0.0231812	+	0.405280i
$863$	11315.5			0.446331			0.223166	−	0.974781i	$-0.428361\pi$
$863$	11315.5			0.446331			0.223166	+	0.974781i	$0.428361\pi$
$864$	9228.35	−	7437.88i	0.363374	−	0.292872i
$865$	−4165.17			−0.163723
$866$	753.083	+	13166.3i	0.0295506	+	0.516638i
$867$	−1002.20	+	2419.53i	−0.0392578	+	0.0947768i
$868$	6762.82	−	8516.44i	0.264453	−	0.333026i
$869$	−59317.7	+	24570.2i	−2.31555	+	0.959133i
$870$	−8026.89	−	2799.40i	−0.312801	−	0.109090i
$871$	−4194.99	+	4194.99i	−0.163194	+	0.163194i
$872$	−9421.34	−	2119.58i	−0.365879	−	0.0823142i
$873$	−12286.4	−	12286.4i	−0.476325	−	0.476325i
$874$	1962.62	+	4064.65i	0.0759573	+	0.157310i
$875$	−10883.3	−	26274.6i	−0.420483	−	1.01513i
$876$	2166.71	−	1203.36i	0.0835689	−	0.0464131i
$877$	7769.43	+	3218.20i	0.299151	+	0.123912i	0.527210	−	0.849735i	$-0.323238\pi$
$877$	7769.43	+	3218.20i	0.299151	+	0.123912i	−0.228060	+	0.973647i	$0.573238\pi$
$878$	−25487.2	−	22729.4i	−0.979673	−	0.873666i
$879$			2410.34i			0.0924901i
$880$	50505.0	+	31443.3i	1.93468	+	1.20449i
$881$		−	15431.2i		−	0.590115i	−0.955479	−	0.295058i	$-0.904661\pi$
$881$		−	15431.2i		−	0.590115i	0.955479	−	0.295058i	$-0.0953389\pi$
$882$	−14684.2	+	16465.9i	−0.560591	+	0.628611i
$883$	39311.6	+	16283.4i	1.49824	+	0.620589i	0.973090	−	0.230424i	$-0.0740112\pi$
$883$	39311.6	+	16283.4i	1.49824	+	0.620589i	0.525145	+	0.851013i	$0.324011\pi$
$884$	−4774.54	+	16702.8i	−0.181658	+	0.635493i
$885$	1225.87	+	2959.51i	0.0465618	+	0.112410i
$886$	−12505.4	+	6038.23i	−0.474183	+	0.228960i
$887$	−24315.7	−	24315.7i	−0.920451	−	0.920451i	0.0766105	−	0.997061i	$-0.475590\pi$
$887$	−24315.7	−	24315.7i	−0.920451	−	0.920451i	−0.997061	+	0.0766105i	$0.975590\pi$
$888$	299.288	+	1728.93i	0.0113102	+	0.0653370i
$889$	38916.5	−	38916.5i	1.46818	−	1.46818i
$890$	20586.1	−	59027.8i	0.775336	−	2.22317i
$891$	29373.2	−	12166.8i	1.10442	−	0.457467i
$892$	5700.63	−	654.268i	0.213981	−	0.0245589i
$893$	4231.75	−	10216.4i	0.158578	−	0.382841i
$894$	3378.58	−	193.248i	0.126394	−	0.00722950i
$895$	37522.0			1.40137
$896$	13877.0	−	34201.4i	0.517410	−	1.27521i
$897$	−2322.08			−0.0864348
$898$	−49895.9	+	2853.94i	−1.85417	+	0.106055i
$899$	2776.82	−	6703.84i	0.103017	−	0.248705i
$900$	38026.7	−	4364.37i	1.40840	−	0.161643i
$901$	22741.1	−	9419.66i	0.840860	−	0.348296i
$902$	−16635.2	+	47699.0i	−0.614069	+	1.76076i
$903$	3311.95	−	3311.95i	0.122054	−	0.122054i
$904$	−3527.85	−	20379.7i	−0.129795	−	0.749801i
$905$	15309.1	+	15309.1i	0.562310	+	0.562310i
$906$	5454.28	−	2633.61i	0.200007	−	0.0965737i
$907$	10871.5	+	26246.1i	0.397996	+	0.960848i	0.988141	+	0.153550i	$0.0490707\pi$
$907$	10871.5	+	26246.1i	0.397996	+	0.960848i	−0.590145	+	0.807297i	$0.700929\pi$
$908$	−13307.8	+	46554.7i	−0.486382	+	1.70151i
$909$	23404.9	+	9694.63i	0.854007	+	0.353741i
$910$	−34742.2	+	38957.6i	−1.26559	+	1.41916i
$911$		−	2752.62i		−	0.100108i	−0.998747	−	0.0500540i	$-0.984061\pi$
$911$		−	2752.62i		−	0.100108i	0.998747	−	0.0500540i	$-0.0159394\pi$
$912$	1483.07	−	2382.14i	0.0538479	−	0.0864918i
$913$		−	50985.3i		−	1.84816i
$914$	−32192.2	−	28708.8i	−1.16501	−	1.03895i
$915$	10211.1	+	4229.60i	0.368929	+	0.152815i
$916$	−1491.78	+	828.517i	−0.0538099	+	0.0298854i
$917$	−22842.9	−	55147.6i	−0.822615	−	1.98597i
$918$	4272.87	+	8849.25i	0.153623	+	0.318158i
$919$	27290.8	+	27290.8i	0.979586	+	0.979586i	0.999796	−	0.0202098i	$-0.00643343\pi$
$919$	27290.8	+	27290.8i	0.979586	+	0.979586i	−0.0202098	+	0.999796i	$0.506433\pi$
$920$	17750.6	+	3993.47i	0.636109	+	0.143110i
$921$	−6328.66	+	6328.66i	−0.226424	+	0.226424i
$922$	278.929	+	97.2772i	0.00996315	+	0.00347468i
$923$	10219.8	−	4233.16i	0.364450	−	0.150960i
$924$	−8317.64	+	10474.4i	−0.296137	+	0.372926i
$925$	−4469.74	+	10790.9i	−0.158880	+	0.383570i
$926$	2667.28	+	46632.5i	0.0946570	+	1.65490i
$927$	−6773.61			−0.239994
$928$	2630.61	−	24486.4i	0.0930539	−	0.866171i
$929$	−19815.1			−0.699798			−0.349899	−	0.936787i	$-0.613784\pi$
$929$	−19815.1			−0.699798			−0.349899	+	0.936787i	$0.613784\pi$
$930$	−190.312	−	3327.25i	−0.00671029	−	0.117317i
$931$	−4120.17	+	9946.96i	−0.145041	+	0.350159i
$932$	−40761.2	−	32368.1i	−1.43259	−	1.13761i
$933$	−1268.62	+	525.480i	−0.0445153	+	0.0184388i
$934$	14308.1	+	4989.99i	0.501258	+	0.174815i
$935$	−34878.0	+	34878.0i	−1.21993	+	1.21993i
$936$	−12595.7	−	19908.4i	−0.439855	−	0.695221i
$937$	−19332.2	−	19332.2i	−0.674018	−	0.674018i	0.284622	−	0.958640i	$-0.408132\pi$
$937$	−19332.2	−	19332.2i	−0.674018	−	0.674018i	−0.958640	+	0.284622i	$0.908132\pi$
$938$	4544.07	+	9410.91i	0.158176	+	0.327588i
$939$	2350.83	+	5675.42i	0.0817003	+	0.197242i
$940$	−21642.2	−	38967.8i	−0.750949	−	1.35212i
$941$	−4000.39	−	1657.02i	−0.138586	−	0.0574041i	0.312313	−	0.949979i	$-0.398896\pi$
$941$	−4000.39	−	1657.02i	−0.138586	−	0.0574041i	−0.450898	+	0.892575i	$0.648896\pi$
$942$	−6176.29	−	5507.97i	−0.213625	−	0.190509i
$943$			15449.1i			0.533500i
$944$	−7546.13	+	5401.41i	−0.260175	+	0.186230i
$945$			29527.7i			1.01644i
$946$	−14556.9	+	16323.2i	−0.500301	+	0.561006i
$947$	35953.4	+	14892.4i	1.23372	+	0.511022i	0.901745	−	0.432268i	$-0.142287\pi$
$947$	35953.4	+	14892.4i	1.23372	+	0.511022i	0.331970	+	0.943290i	$0.392287\pi$
$948$	11736.8	+	3355.00i	0.402104	+	0.114942i
$949$	−3885.86	−	9381.31i	−0.132919	−	0.320896i
$950$	16820.7	−	8121.92i	0.574460	−	0.277379i
$951$	6089.35	+	6089.35i	0.207635	+	0.207635i
$952$	25012.0	+	17630.4i	0.851516	+	0.600214i
$953$	1350.98	−	1350.98i	0.0459208	−	0.0459208i	−0.683773	−	0.729694i	$-0.739662\pi$
$953$	1350.98	−	1350.98i	0.0459208	−	0.0459208i	0.729694	+	0.683773i	$0.239662\pi$
$954$	−10992.3	+	31518.9i	−0.373050	+	1.06967i
$955$	−83624.5	+	34638.4i	−2.83354	+	1.17369i
$956$	1246.22	+	10858.2i	0.0421605	+	0.367344i
$957$	−3415.23	+	8245.10i	−0.115359	+	0.278502i
$958$	54121.5	−	3095.64i	1.82525	−	0.104400i
$959$	4264.31			0.143589
$960$	−3802.09	−	10652.9i	−0.127825	−	0.358148i
$961$	−26946.3			−0.904513
$962$	7177.09	−	410.515i	0.240539	−	0.0137583i
$963$	1231.17	−	2972.32i	0.0411984	−	0.0994616i
$964$	1431.10	+	12469.1i	0.0478138	+	0.416601i
$965$	−67051.5	+	27773.6i	−2.23675	+	0.926492i
$966$	−1346.99	+	3862.29i	−0.0448639	+	0.128641i
$967$	−2303.21	+	2303.21i	−0.0765939	+	0.0765939i	−0.744366	−	0.667772i	$-0.767248\pi$
$967$	−2303.21	+	2303.21i	−0.0765939	+	0.0765939i	0.667772	+	0.744366i	$0.267248\pi$
$968$	18631.7	−	26432.5i	0.618641	−	0.877659i
$969$	1645.07	+	1645.07i	0.0545379	+	0.0545379i
$970$	−30779.4	+	14861.9i	−1.01883	+	0.491944i
$971$	3262.48	+	7876.32i	0.107825	+	0.260312i	0.968578	−	0.248711i	$-0.0800069\pi$
$971$	3262.48	+	7876.32i	0.107825	+	0.260312i	−0.860753	+	0.509023i	$0.830007\pi$
$972$	−19410.3	−	5548.48i	−0.640520	−	0.183094i
$973$	−56867.8	−	23555.4i	−1.87369	−	0.776107i
$974$	9952.77	−	11160.4i	0.327420	−	0.367148i
$975$			9609.46i			0.315640i
$976$	−5232.51	+	31588.3i	−0.171607	+	1.03598i
$977$			43245.0i			1.41610i	0.706162	+	0.708050i	$0.250425\pi$
$977$			43245.0i			1.41610i	−0.706162	+	0.708050i	$0.749575\pi$
$978$	−2506.74	−	2235.49i	−0.0819598	−	0.0730912i
$979$	−60632.5	−	25114.8i	−1.97939	−	0.819890i
$980$	21071.6	+	37940.2i	0.686843	+	1.23669i
$981$	4155.03	+	10031.1i	0.135229	+	0.326472i
$982$	5604.37	+	11606.8i	0.182121	+	0.377178i
$983$	14901.6	+	14901.6i	0.483506	+	0.483506i	0.906249	−	0.422743i	$-0.138933\pi$
$983$	14901.6	+	14901.6i	0.483506	+	0.483506i	−0.422743	+	0.906249i	$0.638933\pi$
$984$	8116.39	−	5135.11i	0.262948	−	0.166363i
$985$	32028.4	−	32028.4i	1.03605	−	1.03605i
$986$	19279.4	+	6723.73i	0.622697	+	0.217168i
$987$	9258.39	−	3834.95i	0.298579	−	0.123676i
$988$	−9003.20	−	7149.35i	−0.289909	−	0.230214i
$989$	−2559.65	+	6179.54i	−0.0822973	+	0.198683i
$990$	−3819.77	−	66781.7i	−0.122627	−	2.14390i
$991$	−18330.8			−0.587586			−0.293793	−	0.955869i	$-0.594918\pi$
$991$	−18330.8			−0.587586			−0.293793	+	0.955869i	$0.594918\pi$
$992$	9263.44	−	2720.79i	0.296486	−	0.0870817i
$993$	−4616.15			−0.147522
$994$	−1112.73	−	19454.0i	−0.0355066	−	0.620767i
$995$	32743.2	−	79049.1i	1.04325	−	2.51862i
$996$	−6028.11	+	7591.22i	−0.191775	+	0.241503i
$997$	39601.9	−	16403.7i	1.25798	−	0.521072i	0.348690	−	0.937238i	$-0.386626\pi$
$997$	39601.9	−	16403.7i	1.25798	−	0.521072i	0.909289	+	0.416166i	$0.136626\pi$
$998$	18815.7	+	6562.04i	0.596795	+	0.208134i
$999$	2875.49	−	2875.49i	0.0910674	−	0.0910674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.4.g.a.13.1	yes	44
4.3	odd	2		128.4.g.a.17.6		44
8.3	odd	2		256.4.g.a.33.6		44
8.5	even	2		256.4.g.b.33.6		44
32.5	even	8	inner	32.4.g.a.5.1	✓	44
32.11	odd	8		256.4.g.a.225.6		44
32.21	even	8		256.4.g.b.225.6		44
32.27	odd	8		128.4.g.a.113.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.1	✓	44	32.5	even	8	inner
32.4.g.a.13.1	yes	44	1.1	even	1	trivial
128.4.g.a.17.6		44	4.3	odd	2
128.4.g.a.113.6		44	32.27	odd	8
256.4.g.a.33.6		44	8.3	odd	2
256.4.g.a.225.6		44	32.11	odd	8
256.4.g.b.33.6		44	8.5	even	2
256.4.g.b.225.6		44	32.21	even	8

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82381 + 0.161516i) q^{2} +(-0.477813 + 1.15354i) q^{3} +(7.94783 - 0.912182i) q^{4} +(-16.3468 + 6.77105i) q^{5} +(1.16294 - 3.33456i) q^{6} +(-18.0222 + 18.0222i) q^{7} +(-22.2958 + 3.85953i) q^{8} +(17.9895 + 17.9895i) q^{9} +O(q^{10})\)	\(q+(-2.82381 + 0.161516i) q^{2} +(-0.477813 + 1.15354i) q^{3} +(7.94783 - 0.912182i) q^{4} +(-16.3468 + 6.77105i) q^{5} +(1.16294 - 3.33456i) q^{6} +(-18.0222 + 18.0222i) q^{7} +(-22.2958 + 3.85953i) q^{8} +(17.9895 + 17.9895i) q^{9} +(45.0666 - 21.7604i) q^{10} +(-20.1053 - 48.5384i) q^{11} +(-2.74533 + 9.60400i) q^{12} +(37.8086 + 15.6609i) q^{13} +(47.9805 - 53.8022i) q^{14} -22.0920i q^{15} +(62.3358 - 14.4997i) q^{16} +53.0615i q^{17} +(-53.7046 - 47.8934i) q^{18} +(-32.4427 - 13.4382i) q^{19} +(-123.745 + 68.7264i) q^{20} +(-12.1781 - 29.4006i) q^{21} +(64.6132 + 133.816i) q^{22} +(32.1343 + 32.1343i) q^{23} +(6.20110 - 27.5633i) q^{24} +(132.981 - 132.981i) q^{25} +(-109.294 - 38.1166i) q^{26} +(-60.4929 + 25.0570i) q^{27} +(-126.798 + 159.677i) q^{28} +(-52.0634 + 125.692i) q^{29} +(3.56821 + 62.3836i) q^{30} -53.3354 q^{31} +(-173.683 + 51.0128i) q^{32} +65.5976 q^{33} +(-8.57029 - 149.836i) q^{34} +(172.576 - 416.634i) q^{35} +(159.387 + 126.568i) q^{36} +(-57.3789 + 23.7671i) q^{37} +(93.7826 + 32.7070i) q^{38} +(-36.1309 + 36.1309i) q^{39} +(338.332 - 214.057i) q^{40} +(240.383 + 240.383i) q^{41} +(39.1374 + 81.0549i) q^{42} +(56.3244 + 135.979i) q^{43} +(-204.069 - 367.435i) q^{44} +(-415.879 - 172.263i) q^{45} +(-95.9313 - 85.5509i) q^{46} +314.904i q^{47} +(-13.0588 + 78.8352i) q^{48} -306.601i q^{49} +(-354.035 + 396.993i) q^{50} +(-61.2086 - 25.3534i) q^{51} +(314.782 + 89.9813i) q^{52} +(-177.524 - 428.580i) q^{53} +(166.774 - 80.5268i) q^{54} +(657.312 + 657.312i) q^{55} +(332.263 - 471.378i) q^{56} +(31.0031 - 31.0031i) q^{57} +(126.716 - 363.340i) q^{58} +(-133.963 + 55.4894i) q^{59} +(-20.1519 - 175.583i) q^{60} +(-191.454 + 462.211i) q^{61} +(150.609 - 8.61453i) q^{62} -648.422 q^{63} +(482.208 - 172.103i) q^{64} -724.089 q^{65} +(-185.235 + 10.5951i) q^{66} +(-55.4766 + 133.932i) q^{67} +(48.4018 + 421.723i) q^{68} +(-52.4224 + 21.7141i) q^{69} +(-420.028 + 1204.37i) q^{70} +(191.132 - 191.132i) q^{71} +(-470.523 - 331.660i) q^{72} +(-175.452 - 175.452i) q^{73} +(158.188 - 76.3815i) q^{74} +(89.8593 + 216.940i) q^{75} +(-270.107 - 77.2109i) q^{76} +(1237.11 + 512.428i) q^{77} +(96.1911 - 107.863i) q^{78} -1222.08i q^{79} +(-920.811 + 659.103i) q^{80} +605.154i q^{81} +(-717.622 - 639.971i) q^{82} +(896.581 + 371.376i) q^{83} +(-123.608 - 222.562i) q^{84} +(-359.282 - 867.384i) q^{85} +(-181.012 - 374.882i) q^{86} +(-120.115 - 120.115i) q^{87} +(635.599 + 1004.61i) q^{88} +(883.293 - 883.293i) q^{89} +(1202.19 + 419.266i) q^{90} +(-963.639 + 399.152i) q^{91} +(284.710 + 226.085i) q^{92} +(25.4843 - 61.5246i) q^{93} +(-50.8622 - 889.231i) q^{94} +621.324 q^{95} +(24.1425 - 224.725i) q^{96} -682.976 q^{97} +(49.5210 + 865.783i) q^{98} +(511.499 - 1234.87i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 212 q^{14} - 304 q^{16} - 184 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 192 q^{22} + 324 q^{23} - 48 q^{24} - 4 q^{25} + 16 q^{26} - 268 q^{27} + 376 q^{28} - 4 q^{29} + 1188 q^{30} - 752 q^{31} + 616 q^{32} - 8 q^{33} + 528 q^{34} - 460 q^{35} + 1456 q^{36} - 4 q^{37} + 980 q^{38} + 596 q^{39} - 536 q^{40} - 4 q^{41} - 2264 q^{42} + 804 q^{43} - 2044 q^{44} + 104 q^{45} - 1444 q^{46} - 2448 q^{48} - 3564 q^{50} - 1384 q^{51} - 2524 q^{52} + 748 q^{53} - 1088 q^{54} - 292 q^{55} + 1192 q^{56} - 4 q^{57} + 3200 q^{58} + 1372 q^{59} + 5752 q^{60} - 1828 q^{61} + 3384 q^{62} + 2512 q^{63} + 4952 q^{64} - 8 q^{65} + 5996 q^{66} + 2036 q^{67} + 2768 q^{68} - 1060 q^{69} + 1400 q^{70} + 220 q^{71} - 1708 q^{72} - 4 q^{73} - 3476 q^{74} - 1712 q^{75} - 5124 q^{76} + 1900 q^{77} - 11916 q^{78} - 10312 q^{80} - 6404 q^{82} + 2436 q^{83} - 6560 q^{84} + 496 q^{85} - 928 q^{86} - 1292 q^{87} + 1248 q^{88} - 4 q^{89} + 7400 q^{90} - 3604 q^{91} + 10152 q^{92} - 112 q^{93} + 12840 q^{94} - 6088 q^{95} + 17792 q^{96} - 8 q^{97} + 11224 q^{98} - 5424 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 116 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 212 * q^14 - 304 * q^16 - 184 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 192 * q^22 + 324 * q^23 - 48 * q^24 - 4 * q^25 + 16 * q^26 - 268 * q^27 + 376 * q^28 - 4 * q^29 + 1188 * q^30 - 752 * q^31 + 616 * q^32 - 8 * q^33 + 528 * q^34 - 460 * q^35 + 1456 * q^36 - 4 * q^37 + 980 * q^38 + 596 * q^39 - 536 * q^40 - 4 * q^41 - 2264 * q^42 + 804 * q^43 - 2044 * q^44 + 104 * q^45 - 1444 * q^46 - 2448 * q^48 - 3564 * q^50 - 1384 * q^51 - 2524 * q^52 + 748 * q^53 - 1088 * q^54 - 292 * q^55 + 1192 * q^56 - 4 * q^57 + 3200 * q^58 + 1372 * q^59 + 5752 * q^60 - 1828 * q^61 + 3384 * q^62 + 2512 * q^63 + 4952 * q^64 - 8 * q^65 + 5996 * q^66 + 2036 * q^67 + 2768 * q^68 - 1060 * q^69 + 1400 * q^70 + 220 * q^71 - 1708 * q^72 - 4 * q^73 - 3476 * q^74 - 1712 * q^75 - 5124 * q^76 + 1900 * q^77 - 11916 * q^78 - 10312 * q^80 - 6404 * q^82 + 2436 * q^83 - 6560 * q^84 + 496 * q^85 - 928 * q^86 - 1292 * q^87 + 1248 * q^88 - 4 * q^89 + 7400 * q^90 - 3604 * q^91 + 10152 * q^92 - 112 * q^93 + 12840 * q^94 - 6088 * q^95 + 17792 * q^96 - 8 * q^97 + 11224 * q^98 - 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more