LMFDB - Embedded newform 320.4.n.h.127.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,4,Mod(63,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("320.63"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	320.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$18.8806112018$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 22x^{5} + 532x^{4} - 636x^{3} + 450x^{2} + 2160x + 5184 $ x^8 - 2x^7 + 2x^6 + 22x^5 + 532x^4 - 636x^3 + 450x^2 + 2160*x + 5184
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.1
Root			$1.56751 - 1.56751i$ of defining polynomial
Character	$\chi$	$=$	320.127
Dual form			320.4.n.h.63.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.96543 - 4.96543i) q^{3} +(10.6555 - 3.38543i) q^{5} +(-1.30461 + 1.30461i) q^{7} +22.3109i q^{9} -26.4709i q^{11} +(44.6735 - 44.6735i) q^{13} +(-69.7190 - 36.0988i) q^{15} +(65.2528 + 65.2528i) q^{17} +91.3469 q^{19} +12.9559 q^{21} +(-108.379 - 108.379i) q^{23} +(102.078 - 72.1466i) q^{25} +(-23.2833 + 23.2833i) q^{27} -9.51196i q^{29} +87.4490i q^{31} +(-131.439 + 131.439i) q^{33} +(-9.48453 + 18.3178i) q^{35} +(-226.381 - 226.381i) q^{37} -443.646 q^{39} -285.699 q^{41} +(-276.545 - 276.545i) q^{43} +(75.5320 + 237.733i) q^{45} +(401.884 - 401.884i) q^{47} +339.596i q^{49} -648.016i q^{51} +(239.525 - 239.525i) q^{53} +(-89.6154 - 282.060i) q^{55} +(-453.576 - 453.576i) q^{57} -548.969 q^{59} -741.044 q^{61} +(-29.1070 - 29.1070i) q^{63} +(324.777 - 627.255i) q^{65} +(-160.692 + 160.692i) q^{67} +1076.30i q^{69} +67.8704i q^{71} +(372.290 - 372.290i) q^{73} +(-865.098 - 148.621i) q^{75} +(34.5341 + 34.5341i) q^{77} -3.62125 q^{79} +833.618 q^{81} +(804.332 + 804.332i) q^{83} +(916.207 + 474.390i) q^{85} +(-47.2309 + 47.2309i) q^{87} +652.940i q^{89} +116.563i q^{91} +(434.222 - 434.222i) q^{93} +(973.344 - 309.248i) q^{95} +(-260.189 - 260.189i) q^{97} +590.591 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 14 q^{5} - 10 q^{7} + 32 q^{13} - 22 q^{15} + 44 q^{17} + 80 q^{19} - 236 q^{21} - 230 q^{23} - 44 q^{25} + 80 q^{27} - 260 q^{33} - 866 q^{35} + 292 q^{37} - 1068 q^{39} + 932 q^{41} + 458 q^{43}+ \cdots + 1844 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 14 * q^5 - 10 * q^7 + 32 * q^13 - 22 * q^15 + 44 * q^17 + 80 * q^19 - 236 * q^21 - 230 * q^23 - 44 * q^25 + 80 * q^27 - 260 * q^33 - 866 * q^35 + 292 * q^37 - 1068 * q^39 + 932 * q^41 + 458 * q^43 + 110 * q^45 + 766 * q^47 + 892 * q^53 + 920 * q^55 - 1064 * q^57 + 16 * q^59 - 2564 * q^61 - 798 * q^63 - 888 * q^65 - 194 * q^67 - 1744 * q^73 - 4918 * q^75 + 1516 * q^77 - 3216 * q^79 + 4828 * q^81 + 3762 * q^83 + 920 * q^85 + 3904 * q^87 + 2420 * q^93 + 1544 * q^95 - 680 * q^97 + 1844 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−4.96543	−	4.96543i	−0.955597	−	0.955597i	0.0434584	−	0.999055i	$-0.486162\pi$
$3$	−4.96543	−	4.96543i	−0.955597	−	0.955597i	−0.999055	+	0.0434584i	$0.986162\pi$
$4$		0			0
$5$	10.6555	−	3.38543i	0.953053	−	0.302802i
$5$	10.6555	−	3.38543i	0.953053	−	0.302802i
$6$		0			0
$7$	−1.30461	+	1.30461i	−0.0704421	+	0.0704421i	−0.741450	−	0.671008i	$-0.765862\pi$
$7$	−1.30461	+	1.30461i	−0.0704421	+	0.0704421i	0.671008	+	0.741450i	$0.265862\pi$
$8$		0			0
$9$			22.3109i			0.826331i
$10$		0			0
$11$		−	26.4709i		−	0.725571i	−0.931873	−	0.362786i	$-0.881826\pi$
$11$		−	26.4709i		−	0.725571i	0.931873	−	0.362786i	$-0.118174\pi$
$12$		0			0
$13$	44.6735	−	44.6735i	0.953091	−	0.953091i	−0.0458567	−	0.998948i	$-0.514602\pi$
$13$	44.6735	−	44.6735i	0.953091	−	0.953091i	0.998948	+	0.0458567i	$0.0146018\pi$
$14$		0			0
$15$	−69.7190	−	36.0988i	−1.20009	−	0.621378i
$16$		0			0
$17$	65.2528	+	65.2528i	0.930948	+	0.930948i	0.997765	−	0.0668170i	$-0.0212844\pi$
$17$	65.2528	+	65.2528i	0.930948	+	0.930948i	−0.0668170	+	0.997765i	$0.521284\pi$
$18$		0			0
$19$	91.3469			1.10297			0.551485	−	0.834185i	$-0.314062\pi$
$19$	91.3469			1.10297			0.551485	+	0.834185i	$0.314062\pi$
$20$		0			0
$21$	12.9559			0.134629
$22$		0			0
$23$	−108.379	−	108.379i	−0.982549	−	0.982549i	0.0173010	−	0.999850i	$-0.494493\pi$
$23$	−108.379	−	108.379i	−0.982549	−	0.982549i	−0.999850	+	0.0173010i	$0.994493\pi$
$24$		0			0
$25$	102.078	−	72.1466i	0.816622	−	0.577173i
$26$		0			0
$27$	−23.2833	+	23.2833i	−0.165958	+	0.165958i
$28$		0			0
$29$		−	9.51196i		−	0.0609078i	−0.999536	−	0.0304539i	$-0.990305\pi$
$29$		−	9.51196i		−	0.0609078i	0.999536	−	0.0304539i	$-0.00969528\pi$
$30$		0			0
$31$			87.4490i			0.506655i	0.967381	+	0.253328i	$0.0815250\pi$
$31$			87.4490i			0.506655i	−0.967381	+	0.253328i	$0.918475\pi$
$32$		0			0
$33$	−131.439	+	131.439i	−0.693353	+	0.693353i
$34$		0			0
$35$	−9.48453	+	18.3178i	−0.0458051	+	0.0884651i
$36$		0			0
$37$	−226.381	−	226.381i	−1.00586	−	1.00586i	−0.999983	−	0.00587858i	$-0.998129\pi$
$37$	−226.381	−	226.381i	−1.00586	−	1.00586i	−0.00587858	−	0.999983i	$-0.501871\pi$
$38$		0			0
$39$	−443.646			−1.82154
$40$		0			0
$41$	−285.699			−1.08826			−0.544130	−	0.839001i	$-0.683140\pi$
$41$	−285.699			−1.08826			−0.544130	+	0.839001i	$0.683140\pi$
$42$		0			0
$43$	−276.545	−	276.545i	−0.980761	−	0.980761i	0.0190571	−	0.999818i	$-0.493934\pi$
$43$	−276.545	−	276.545i	−0.980761	−	0.980761i	−0.999818	+	0.0190571i	$0.993934\pi$
$44$		0			0
$45$	75.5320	+	237.733i	0.250215	+	0.787537i
$46$		0			0
$47$	401.884	−	401.884i	1.24725	−	1.24725i	0.290324	−	0.956928i	$-0.406237\pi$
$47$	401.884	−	401.884i	1.24725	−	1.24725i	0.956928	−	0.290324i	$-0.0937631\pi$
$48$		0			0
$49$			339.596i			0.990076i
$50$		0			0
$51$		−	648.016i		−	1.77922i
$52$		0			0
$53$	239.525	−	239.525i	0.620778	−	0.620778i	−0.324953	−	0.945730i	$-0.605348\pi$
$53$	239.525	−	239.525i	0.620778	−	0.620778i	0.945730	+	0.324953i	$0.105348\pi$
$54$		0			0
$55$	−89.6154	−	282.060i	−0.219704	−	0.691508i
$56$		0			0
$57$	−453.576	−	453.576i	−1.05399	−	1.05399i
$58$		0			0
$59$	−548.969			−1.21135			−0.605676	−	0.795712i	$-0.707097\pi$
$59$	−548.969			−1.21135			−0.605676	+	0.795712i	$0.707097\pi$
$60$		0			0
$61$	−741.044			−1.55543			−0.777713	−	0.628620i	$-0.783620\pi$
$61$	−741.044			−1.55543			−0.777713	+	0.628620i	$0.783620\pi$
$62$		0			0
$63$	−29.1070	−	29.1070i	−0.0582085	−	0.0582085i
$64$		0			0
$65$	324.777	−	627.255i	0.619749	−	1.19694i
$66$		0			0
$67$	−160.692	+	160.692i	−0.293010	+	0.293010i	−0.838268	−	0.545258i	$-0.816432\pi$
$67$	−160.692	+	160.692i	−0.293010	+	0.293010i	0.545258	+	0.838268i	$0.316432\pi$
$68$		0			0
$69$			1076.30i			1.87784i
$70$		0			0
$71$			67.8704i			0.113447i	0.998390	+	0.0567235i	$0.0180653\pi$
$71$			67.8704i			0.113447i	−0.998390	+	0.0567235i	$0.981935\pi$
$72$		0			0
$73$	372.290	−	372.290i	0.596894	−	0.596894i	−0.342591	−	0.939485i	$-0.611304\pi$
$73$	372.290	−	372.290i	0.596894	−	0.596894i	0.939485	+	0.342591i	$0.111304\pi$
$74$		0			0
$75$	−865.098	−	148.621i	−1.33191	−	0.228817i
$76$		0			0
$77$	34.5341	+	34.5341i	0.0511108	+	0.0511108i
$78$		0			0
$79$	−3.62125			−0.00515725			−0.00257863	−	0.999997i	$-0.500821\pi$
$79$	−3.62125			−0.00515725			−0.00257863	+	0.999997i	$0.500821\pi$
$80$		0			0
$81$	833.618			1.14351
$82$		0			0
$83$	804.332	+	804.332i	1.06370	+	1.06370i	0.997828	+	0.0658698i	$0.0209822\pi$
$83$	804.332	+	804.332i	1.06370	+	1.06370i	0.0658698	+	0.997828i	$0.479018\pi$
$84$		0			0
$85$	916.207	+	474.390i	1.16914	+	0.605350i
$86$		0			0
$87$	−47.2309	+	47.2309i	−0.0582033	+	0.0582033i
$88$		0			0
$89$			652.940i			0.777657i	0.921310	+	0.388829i	$0.127120\pi$
$89$			652.940i			0.777657i	−0.921310	+	0.388829i	$0.872880\pi$
$90$		0			0
$91$			116.563i			0.134276i
$92$		0			0
$93$	434.222	−	434.222i	0.484158	−	0.484158i
$94$		0			0
$95$	973.344	−	309.248i	1.05119	−	0.333981i
$96$		0			0
$97$	−260.189	−	260.189i	−0.272352	−	0.272352i	0.557694	−	0.830046i	$-0.311686\pi$
$97$	−260.189	−	260.189i	−0.272352	−	0.272352i	−0.830046	+	0.557694i	$0.811686\pi$
$98$		0			0
$99$	590.591			0.599562
$100$		0			0
$101$	−296.448			−0.292056			−0.146028	−	0.989280i	$-0.546649\pi$
$101$	−296.448			−0.292056			−0.146028	+	0.989280i	$0.546649\pi$
$102$		0			0
$103$	176.629	+	176.629i	0.168969	+	0.168969i	0.786526	−	0.617557i	$-0.211878\pi$
$103$	176.629	+	176.629i	0.168969	+	0.168969i	−0.617557	+	0.786526i	$0.711878\pi$
$104$		0			0
$105$	138.051	−	43.8611i	0.128308	−	0.0407658i
$106$		0			0
$107$	534.354	−	534.354i	0.482785	−	0.482785i	−0.423235	−	0.906020i	$-0.639106\pi$
$107$	534.354	−	534.354i	0.482785	−	0.482785i	0.906020	+	0.423235i	$0.139106\pi$
$108$		0			0
$109$		−	1479.12i		−	1.29976i	−0.760036	−	0.649881i	$-0.774819\pi$
$109$		−	1479.12i		−	1.29976i	0.760036	−	0.649881i	$-0.225181\pi$
$110$		0			0
$111$			2248.16i			1.92240i
$112$		0			0
$113$	−333.659	+	333.659i	−0.277769	+	0.277769i	−0.832218	−	0.554449i	$-0.812929\pi$
$113$	−333.659	+	333.659i	−0.277769	+	0.277769i	0.554449	+	0.832218i	$0.312929\pi$
$114$		0			0
$115$	−1521.74	−	787.921i	−1.23394	−	0.638904i
$116$		0			0
$117$	996.706	+	996.706i	0.787568	+	0.787568i
$118$		0			0
$119$	−170.258			−0.131156
$120$		0			0
$121$	630.290			0.473547
$122$		0			0
$123$	1418.62	+	1418.62i	1.03994	+	1.03994i
$124$		0			0
$125$	843.438	−	1114.33i	0.603515	−	0.797351i
$126$		0			0
$127$	413.402	−	413.402i	0.288846	−	0.288846i	−0.547778	−	0.836624i	$-0.684526\pi$
$127$	413.402	−	413.402i	0.288846	−	0.288846i	0.836624	+	0.547778i	$0.184526\pi$
$128$		0			0
$129$			2746.33i			1.87442i
$130$		0			0
$131$			1650.04i			1.10050i	0.835001	+	0.550248i	$0.185467\pi$
$131$			1650.04i			1.10050i	−0.835001	+	0.550248i	$0.814533\pi$
$132$		0			0
$133$	−119.172	+	119.172i	−0.0776955	+	0.0776955i
$134$		0			0
$135$	−169.270	+	326.918i	−0.107914	+	0.208419i
$136$		0			0
$137$	−1795.63	−	1795.63i	−1.11979	−	1.11979i	−0.991772	−	0.128014i	$-0.959140\pi$
$137$	−1795.63	−	1795.63i	−1.11979	−	1.11979i	−0.128014	−	0.991772i	$-0.540860\pi$
$138$		0			0
$139$	1864.83			1.13793			0.568967	−	0.822360i	$-0.307343\pi$
$139$	1864.83			1.13793			0.568967	+	0.822360i	$0.307343\pi$
$140$		0			0
$141$	−3991.05			−2.38374
$142$		0			0
$143$	−1182.55	−	1182.55i	−0.691536	−	0.691536i
$144$		0			0
$145$	−32.2021	−	101.354i	−0.0184430	−	0.0580484i
$146$		0			0
$147$	1686.24	−	1686.24i	0.946113	−	0.946113i
$148$		0			0
$149$		−	1216.54i		−	0.668881i	−0.942417	−	0.334440i	$-0.891453\pi$
$149$		−	1216.54i		−	0.668881i	0.942417	−	0.334440i	$-0.108547\pi$
$150$		0			0
$151$			1323.56i			0.713312i	0.934236	+	0.356656i	$0.116083\pi$
$151$			1323.56i			0.713312i	−0.934236	+	0.356656i	$0.883917\pi$
$152$		0			0
$153$	−1455.85	+	1455.85i	−0.769271	+	0.769271i
$154$		0			0
$155$	296.052	+	931.810i	0.153416	+	0.482869i
$156$		0			0
$157$	−1228.40	−	1228.40i	−0.624441	−	0.624441i	0.322223	−	0.946664i	$-0.395570\pi$
$157$	−1228.40	−	1228.40i	−0.624441	−	0.624441i	−0.946664	+	0.322223i	$0.895570\pi$
$158$		0			0
$159$	−2378.68			−1.18643
$160$		0			0
$161$	282.785			0.138426
$162$		0			0
$163$	2481.60	+	2481.60i	1.19248	+	1.19248i	0.976370	+	0.216107i	$0.0693361\pi$
$163$	2481.60	+	2481.60i	1.19248	+	1.19248i	0.216107	+	0.976370i	$0.430664\pi$
$164$		0			0
$165$	−955.569	+	1845.53i	−0.450854	+	0.870752i
$166$		0			0
$167$	1580.80	−	1580.80i	0.732491	−	0.732491i	−0.238622	−	0.971113i	$-0.576696\pi$
$167$	1580.80	−	1580.80i	0.732491	−	0.732491i	0.971113	+	0.238622i	$0.0766956\pi$
$168$		0			0
$169$		−	1794.44i		−	0.816766i
$170$		0			0
$171$			2038.03i			0.911417i
$172$		0			0
$173$	811.428	−	811.428i	0.356600	−	0.356600i	−0.505958	−	0.862558i	$-0.668861\pi$
$173$	811.428	−	811.428i	0.356600	−	0.356600i	0.862558	+	0.505958i	$0.168861\pi$
$174$		0			0
$175$	−39.0483	+	227.294i	−0.0168673	+	0.0981819i
$176$		0			0
$177$	2725.87	+	2725.87i	1.15756	+	1.15756i
$178$		0			0
$179$	−900.876			−0.376171			−0.188086	−	0.982153i	$-0.560228\pi$
$179$	−900.876			−0.376171			−0.188086	+	0.982153i	$0.560228\pi$
$180$		0			0
$181$	2458.41			1.00957			0.504784	−	0.863245i	$-0.331572\pi$
$181$	2458.41			1.00957			0.504784	+	0.863245i	$0.331572\pi$
$182$		0			0
$183$	3679.60	+	3679.60i	1.48636	+	1.48636i
$184$		0			0
$185$	−3178.60	−	1645.80i	−1.26322	−	0.654063i
$186$		0			0
$187$	1727.30	−	1727.30i	0.675469	−	0.675469i
$188$		0			0
$189$		−	60.7510i		−	0.0233809i
$190$		0			0
$191$			3574.58i			1.35418i	0.735902	+	0.677088i	$0.236758\pi$
$191$			3574.58i			1.35418i	−0.735902	+	0.677088i	$0.763242\pi$
$192$		0			0
$193$	536.362	−	536.362i	0.200042	−	0.200042i	−0.599976	−	0.800018i	$-0.704823\pi$
$193$	536.362	−	536.362i	0.200042	−	0.200042i	0.800018	+	0.599976i	$0.204823\pi$
$194$		0			0
$195$	−4727.25	+	1501.93i	−1.73603	+	0.551567i
$196$		0			0
$197$	2091.00	+	2091.00i	0.756232	+	0.756232i	0.975634	−	0.219403i	$-0.0704108\pi$
$197$	2091.00	+	2091.00i	0.756232	+	0.756232i	−0.219403	+	0.975634i	$0.570411\pi$
$198$		0			0
$199$	2672.91			0.952148			0.476074	−	0.879405i	$-0.342059\pi$
$199$	2672.91			0.952148			0.476074	+	0.879405i	$0.342059\pi$
$200$		0			0
$201$	1595.81			0.559999
$202$		0			0
$203$	12.4094	+	12.4094i	0.00429047	+	0.00429047i
$204$		0			0
$205$	−3044.25	+	967.212i	−1.03717	+	0.329527i
$206$		0			0
$207$	2418.04	−	2418.04i	0.811910	−	0.811910i
$208$		0			0
$209$		−	2418.04i		−	0.800283i
$210$		0			0
$211$		−	5375.95i		−	1.75401i	−0.480482	−	0.877004i	$-0.659538\pi$
$211$		−	5375.95i		−	1.75401i	0.480482	−	0.877004i	$-0.340462\pi$
$212$		0			0
$213$	337.005	−	337.005i	0.108410	−	0.108410i
$214$		0			0
$215$	−3882.94	−	2010.49i	−1.23169	−	0.637742i
$216$		0			0
$217$	−114.087	−	114.087i	−0.0356899	−	0.0356899i
$218$		0			0
$219$	−3697.16			−1.14078
$220$		0			0
$221$	5830.13			1.77456
$222$		0			0
$223$	850.012	+	850.012i	0.255251	+	0.255251i	0.823119	−	0.567868i	$-0.192232\pi$
$223$	850.012	+	850.012i	0.255251	+	0.255251i	−0.567868	+	0.823119i	$0.692232\pi$
$224$		0			0
$225$	1609.66	+	2277.45i	0.476936	+	0.674800i
$226$		0			0
$227$	−4013.01	+	4013.01i	−1.17336	+	1.17336i	−0.191956	+	0.981403i	$0.561483\pi$
$227$	−4013.01	+	4013.01i	−1.17336	+	1.17336i	−0.981403	+	0.191956i	$0.938517\pi$
$228$		0			0
$229$		−	230.627i		−	0.0665513i	−0.999446	−	0.0332757i	$-0.989406\pi$
$229$		−	230.627i		−	0.0665513i	0.999446	−	0.0332757i	$-0.0105939\pi$
$230$		0			0
$231$		−	342.953i		−	0.0976826i
$232$		0			0
$233$	−209.000	+	209.000i	−0.0587641	+	0.0587641i	−0.735878	−	0.677114i	$-0.763230\pi$
$233$	−209.000	+	209.000i	−0.0587641	+	0.0587641i	0.677114	+	0.735878i	$0.263230\pi$
$234$		0			0
$235$	2921.71	−	5642.81i	0.811028	−	1.56637i
$236$		0			0
$237$	17.9811	+	17.9811i	0.00492825	+	0.00492825i
$238$		0			0
$239$	−4890.31			−1.32355			−0.661774	−	0.749704i	$-0.730196\pi$
$239$	−4890.31			−1.32355			−0.661774	+	0.749704i	$0.730196\pi$
$240$		0			0
$241$	2416.64			0.645931			0.322966	−	0.946411i	$-0.395320\pi$
$241$	2416.64			0.645931			0.322966	+	0.946411i	$0.395320\pi$
$242$		0			0
$243$	−3510.62	−	3510.62i	−0.926775	−	0.926775i
$244$		0			0
$245$	1149.68	+	3618.55i	0.299797	+	0.943595i
$246$		0			0
$247$	4080.78	−	4080.78i	1.05123	−	1.05123i
$248$		0			0
$249$		−	7987.71i		−	2.03293i
$250$		0			0
$251$			5842.78i			1.46929i	0.678449	+	0.734647i	$0.262652\pi$
$251$			5842.78i			1.46929i	−0.678449	+	0.734647i	$0.737348\pi$
$252$		0			0
$253$	−2868.90	+	2868.90i	−0.712909	+	0.712909i
$254$		0			0
$255$	−2193.81	−	6904.91i	−0.538752	−	1.69569i
$256$		0			0
$257$	3125.99	+	3125.99i	0.758731	+	0.758731i	0.976091	−	0.217360i	$-0.0697446\pi$
$257$	3125.99	+	3125.99i	0.758731	+	0.758731i	−0.217360	+	0.976091i	$0.569745\pi$
$258$		0			0
$259$	590.677			0.141710
$260$		0			0
$261$	212.221			0.0503300
$262$		0			0
$263$	−423.507	−	423.507i	−0.0992950	−	0.0992950i	0.655714	−	0.755009i	$-0.272368\pi$
$263$	−423.507	−	423.507i	−0.0992950	−	0.0992950i	−0.755009	+	0.655714i	$0.772368\pi$
$264$		0			0
$265$	1741.35	−	3363.14i	0.403662	−	0.779607i
$266$		0			0
$267$	3242.13	−	3242.13i	0.743127	−	0.743127i
$268$		0			0
$269$		−	461.980i		−	0.104712i	−0.998628	−	0.0523558i	$-0.983327\pi$
$269$		−	461.980i		−	0.104712i	0.998628	−	0.0523558i	$-0.0166730\pi$
$270$		0			0
$271$			358.950i			0.0804599i	0.999190	+	0.0402299i	$0.0128090\pi$
$271$			358.950i			0.0804599i	−0.999190	+	0.0402299i	$0.987191\pi$
$272$		0			0
$273$	578.783	−	578.783i	0.128313	−	0.128313i
$274$		0			0
$275$	−1909.79	−	2702.09i	−0.418780	−	0.592517i
$276$		0			0
$277$	−127.536	−	127.536i	−0.0276638	−	0.0276638i	0.693140	−	0.720803i	$-0.256227\pi$
$277$	−127.536	−	127.536i	−0.0276638	−	0.0276638i	−0.720803	+	0.693140i	$0.756227\pi$
$278$		0			0
$279$	−1951.07			−0.418665
$280$		0			0
$281$	−5906.63			−1.25395			−0.626975	−	0.779040i	$-0.715707\pi$
$281$	−5906.63			−1.25395			−0.626975	+	0.779040i	$0.715707\pi$
$282$		0			0
$283$	−2686.79	−	2686.79i	−0.564357	−	0.564357i	0.366185	−	0.930542i	$-0.380664\pi$
$283$	−2686.79	−	2686.79i	−0.564357	−	0.564357i	−0.930542	+	0.366185i	$0.880664\pi$
$284$		0			0
$285$	−6368.62	−	3297.52i	−1.32366	−	0.685361i
$286$		0			0
$287$	372.724	−	372.724i	0.0766593	−	0.0766593i
$288$		0			0
$289$			3602.85i			0.733329i
$290$		0			0
$291$			2583.90i			0.520518i
$292$		0			0
$293$	−2591.70	+	2591.70i	−0.516753	+	0.516753i	−0.916587	−	0.399835i	$-0.869068\pi$
$293$	−2591.70	+	2591.70i	−0.516753	+	0.516753i	0.399835	+	0.916587i	$0.369068\pi$
$294$		0			0
$295$	−5849.52	+	1858.50i	−1.15448	+	0.366800i
$296$		0			0
$297$	616.329	+	616.329i	0.120414	+	0.120414i
$298$		0			0
$299$	−9683.35			−1.87292
$300$		0			0
$301$	721.565			0.138174
$302$		0			0
$303$	1471.99	+	1471.99i	0.279088	+	0.279088i
$304$		0			0
$305$	−7896.16	+	2508.75i	−1.48240	+	0.470986i
$306$		0			0
$307$	6493.85	−	6493.85i	1.20724	−	1.20724i	0.235327	−	0.971916i	$-0.424384\pi$
$307$	6493.85	−	6493.85i	1.20724	−	1.20724i	0.971916	−	0.235327i	$-0.0756161\pi$
$308$		0			0
$309$		−	1754.08i		−	0.322933i
$310$		0			0
$311$		−	6172.43i		−	1.12542i	−0.826653	−	0.562711i	$-0.809758\pi$
$311$		−	6172.43i		−	1.12542i	0.826653	−	0.562711i	$-0.190242\pi$
$312$		0			0
$313$	−3860.56	+	3860.56i	−0.697162	+	0.697162i	−0.963797	−	0.266636i	$-0.914088\pi$
$313$	−3860.56	+	3860.56i	−0.697162	+	0.697162i	0.266636	+	0.963797i	$0.414088\pi$
$314$		0			0
$315$	−408.688	−	211.609i	−0.0731014	−	0.0378502i
$316$		0			0
$317$	−2685.37	−	2685.37i	−0.475791	−	0.475791i	0.427992	−	0.903783i	$-0.359221\pi$
$317$	−2685.37	−	2685.37i	−0.475791	−	0.475791i	−0.903783	+	0.427992i	$0.859221\pi$
$318$		0			0
$319$	−251.790			−0.0441929
$320$		0			0
$321$	−5306.59			−0.922695
$322$		0			0
$323$	5960.64	+	5960.64i	1.02681	+	1.02681i
$324$		0			0
$325$	1337.13	−	7783.20i	0.228217	−	1.32841i
$326$		0			0
$327$	−7344.47	+	7344.47i	−1.24205	+	1.24205i
$328$		0			0
$329$			1048.60i			0.175718i
$330$		0			0
$331$			2464.95i			0.409323i	0.978833	+	0.204661i	$0.0656093\pi$
$331$			2464.95i			0.409323i	−0.978833	+	0.204661i	$0.934391\pi$
$332$		0			0
$333$	5050.78	−	5050.78i	0.831174	−	0.831174i
$334$		0			0
$335$	−1168.24	+	2256.26i	−0.190530	+	0.367978i
$336$		0			0
$337$	1119.47	+	1119.47i	0.180954	+	0.180954i	0.791771	−	0.610817i	$-0.209159\pi$
$337$	1119.47	+	1119.47i	0.180954	+	0.180954i	−0.610817	+	0.791771i	$0.709159\pi$
$338$		0			0
$339$	3313.51			0.530871
$340$		0			0
$341$	2314.86			0.367614
$342$		0			0
$343$	−890.519	−	890.519i	−0.140185	−	0.140185i
$344$		0			0
$345$	3643.73	+	11468.5i	0.568614	+	1.78968i
$346$		0			0
$347$	3015.84	−	3015.84i	0.466566	−	0.466566i	−0.434234	−	0.900800i	$-0.642981\pi$
$347$	3015.84	−	3015.84i	0.466566	−	0.466566i	0.900800	+	0.434234i	$0.142981\pi$
$348$		0			0
$349$		−	1787.59i		−	0.274177i	−0.990559	−	0.137088i	$-0.956226\pi$
$349$		−	1787.59i		−	0.274177i	0.990559	−	0.137088i	$-0.0437745\pi$
$350$		0			0
$351$			2080.29i			0.316346i
$352$		0			0
$353$	3120.12	−	3120.12i	0.470445	−	0.470445i	−0.431613	−	0.902059i	$-0.642056\pi$
$353$	3120.12	−	3120.12i	0.470445	−	0.470445i	0.902059	+	0.431613i	$0.142056\pi$
$354$		0			0
$355$	229.770	+	723.190i	0.0343520	+	0.108121i
$356$		0			0
$357$	845.405	+	845.405i	0.125332	+	0.125332i
$358$		0			0
$359$	1883.69			0.276928			0.138464	−	0.990367i	$-0.455783\pi$
$359$	1883.69			0.276928			0.138464	+	0.990367i	$0.455783\pi$
$360$		0			0
$361$	1485.26			0.216542
$362$		0			0
$363$	−3129.66	−	3129.66i	−0.452520	−	0.452520i
$364$		0			0
$365$	2706.56	−	5227.28i	0.388131	−	0.749613i
$366$		0			0
$367$	8159.12	−	8159.12i	1.16050	−	1.16050i	0.176130	−	0.984367i	$-0.443642\pi$
$367$	8159.12	−	8159.12i	1.16050	−	1.16050i	0.984367	−	0.176130i	$-0.0563580\pi$
$368$		0			0
$369$		−	6374.20i		−	0.899262i
$370$		0			0
$371$			624.970i			0.0874578i
$372$		0			0
$373$	−9453.68	+	9453.68i	−1.31231	+	1.31231i	−0.392607	+	0.919706i	$0.628427\pi$
$373$	−9453.68	+	9453.68i	−1.31231	+	1.31231i	−0.919706	+	0.392607i	$0.871573\pi$
$374$		0			0
$375$	−9721.17	+	1345.11i	−1.33866	+	0.185229i
$376$		0			0
$377$	−424.932	−	424.932i	−0.0580507	−	0.0580507i
$378$		0			0
$379$	−1188.31			−0.161054			−0.0805270	−	0.996752i	$-0.525660\pi$
$379$	−1188.31			−0.161054			−0.0805270	+	0.996752i	$0.525660\pi$
$380$		0			0
$381$	−4105.43			−0.552041
$382$		0			0
$383$	−1777.70	−	1777.70i	−0.237170	−	0.237170i	0.578507	−	0.815677i	$-0.303635\pi$
$383$	−1777.70	−	1777.70i	−0.237170	−	0.237170i	−0.815677	+	0.578507i	$0.803635\pi$
$384$		0			0
$385$	484.890	+	251.064i	0.0641877	+	0.0332349i
$386$		0			0
$387$	6169.98	−	6169.98i	0.810433	−	0.810433i
$388$		0			0
$389$			6744.45i			0.879068i	0.898226	+	0.439534i	$0.144856\pi$
$389$			6744.45i			0.879068i	−0.898226	+	0.439534i	$0.855144\pi$
$390$		0			0
$391$		−	14144.1i		−	1.82941i
$392$		0			0
$393$	8193.17	−	8193.17i	1.05163	−	1.05163i
$394$		0			0
$395$	−38.5861	+	12.2595i	−0.00491514	+	0.00156163i
$396$		0			0
$397$	3970.53	+	3970.53i	0.501953	+	0.501953i	0.912044	−	0.410091i	$-0.134503\pi$
$397$	3970.53	+	3970.53i	0.501953	+	0.501953i	−0.410091	+	0.912044i	$0.634503\pi$
$398$		0			0
$399$	1183.48			0.148491
$400$		0			0
$401$	6700.66			0.834451			0.417225	−	0.908803i	$-0.363003\pi$
$401$	6700.66			0.834451			0.417225	+	0.908803i	$0.363003\pi$
$402$		0			0
$403$	3906.65	+	3906.65i	0.482889	+	0.482889i
$404$		0			0
$405$	8882.58	−	2822.15i	1.08982	−	0.346257i
$406$		0			0
$407$	−5992.52	+	5992.52i	−0.729824	+	0.729824i
$408$		0			0
$409$			12814.0i			1.54917i	0.632470	+	0.774585i	$0.282041\pi$
$409$			12814.0i			1.54917i	−0.632470	+	0.774585i	$0.717959\pi$
$410$		0			0
$411$			17832.1i			2.14013i
$412$		0			0
$413$	716.189	−	716.189i	0.0853302	−	0.0853302i
$414$		0			0
$415$	11293.5	+	5847.52i	1.33585	+	0.691671i
$416$		0			0
$417$	−9259.69	−	9259.69i	−1.08741	−	1.08741i
$418$		0			0
$419$	−1981.16			−0.230993			−0.115496	−	0.993308i	$-0.536846\pi$
$419$	−1981.16			−0.230993			−0.115496	+	0.993308i	$0.536846\pi$
$420$		0			0
$421$	9522.14			1.10233			0.551165	−	0.834396i	$-0.314184\pi$
$421$	9522.14			1.10233			0.551165	+	0.834396i	$0.314184\pi$
$422$		0			0
$423$	8966.41	+	8966.41i	1.03064	+	1.03064i
$424$		0			0
$425$	11368.6	+	1953.09i	1.29755	+	0.222915i
$426$		0			0
$427$	966.771	−	966.771i	0.109567	−	0.109567i
$428$		0			0
$429$			11743.7i			1.32166i
$430$		0			0
$431$			7709.75i			0.861638i	0.902438	+	0.430819i	$0.141775\pi$
$431$			7709.75i			0.861638i	−0.902438	+	0.430819i	$0.858225\pi$
$432$		0			0
$433$	10058.6	−	10058.6i	1.11637	−	1.11637i	0.124099	−	0.992270i	$-0.460396\pi$
$433$	10058.6	−	10058.6i	1.11637	−	1.11637i	0.992270	−	0.124099i	$-0.0396039\pi$
$434$		0			0
$435$	−343.370	+	663.164i	−0.0378468	+	0.0730949i
$436$		0			0
$437$	−9900.11	−	9900.11i	−1.08372	−	1.08372i
$438$		0			0
$439$	11958.3			1.30009			0.650046	−	0.759895i	$-0.274750\pi$
$439$	11958.3			1.30009			0.650046	+	0.759895i	$0.274750\pi$
$440$		0			0
$441$	−7576.70			−0.818130
$442$		0			0
$443$	−1505.18	−	1505.18i	−0.161430	−	0.161430i	0.621770	−	0.783200i	$-0.286414\pi$
$443$	−1505.18	−	1505.18i	−0.161430	−	0.161430i	−0.783200	+	0.621770i	$0.786414\pi$
$444$		0			0
$445$	2210.48	+	6957.38i	0.235476	+	0.741149i
$446$		0			0
$447$	−6040.66	+	6040.66i	−0.639180	+	0.639180i
$448$		0			0
$449$			10336.7i			1.08646i	0.839585	+	0.543228i	$0.182798\pi$
$449$			10336.7i			1.08646i	−0.839585	+	0.543228i	$0.817202\pi$
$450$		0			0
$451$			7562.71i			0.789610i
$452$		0			0
$453$	6572.06	−	6572.06i	0.681638	−	0.681638i
$454$		0			0
$455$	394.614	+	1242.03i	0.0406589	+	0.127972i
$456$		0			0
$457$	−2064.01	−	2064.01i	−0.211270	−	0.211270i	0.593537	−	0.804807i	$-0.297731\pi$
$457$	−2064.01	−	2064.01i	−0.211270	−	0.211270i	−0.804807	+	0.593537i	$0.797731\pi$
$458$		0			0
$459$	−3038.59			−0.308997
$460$		0			0
$461$	−894.060			−0.0903265			−0.0451632	−	0.998980i	$-0.514381\pi$
$461$	−894.060			−0.0903265			−0.0451632	+	0.998980i	$0.514381\pi$
$462$		0			0
$463$	4604.34	+	4604.34i	0.462164	+	0.462164i	0.899364	−	0.437201i	$-0.144030\pi$
$463$	4604.34	+	4604.34i	0.462164	+	0.462164i	−0.437201	+	0.899364i	$0.644030\pi$
$464$		0			0
$465$	3156.81	−	6096.86i	0.314824	−	0.608032i
$466$		0			0
$467$	−10159.8	+	10159.8i	−1.00672	+	1.00672i	−0.00674491	+	0.999977i	$0.502147\pi$
$467$	−10159.8	+	10159.8i	−1.00672	+	1.00672i	−0.999977	+	0.00674491i	$0.997853\pi$
$468$		0			0
$469$		−	419.280i		−	0.0412805i
$470$		0			0
$471$			12199.1i			1.19343i
$472$		0			0
$473$	−7320.40	+	7320.40i	−0.711612	+	0.711612i
$474$		0			0
$475$	9324.49	−	6590.37i	0.900709	−	0.636604i
$476$		0			0
$477$	5344.01	+	5344.01i	0.512968	+	0.512968i
$478$		0			0
$479$	18384.7			1.75369			0.876844	−	0.480775i	$-0.159645\pi$
$479$	18384.7			1.75369			0.876844	+	0.480775i	$0.159645\pi$
$480$		0			0
$481$	−20226.5			−1.91736
$482$		0			0
$483$	−1404.15	−	1404.15i	−0.132279	−	0.132279i
$484$		0			0
$485$	−3653.28	−	1891.58i	−0.342035	−	0.177097i
$486$		0			0
$487$	8981.67	−	8981.67i	0.835726	−	0.835726i	−0.152567	−	0.988293i	$-0.548754\pi$
$487$	8981.67	−	8981.67i	0.835726	−	0.835726i	0.988293	+	0.152567i	$0.0487541\pi$
$488$		0			0
$489$		−	24644.4i		−	2.27905i
$490$		0			0
$491$		−	5020.03i		−	0.461407i	−0.973024	−	0.230704i	$-0.925897\pi$
$491$		−	5020.03i		−	0.461407i	0.973024	−	0.230704i	$-0.0741028\pi$
$492$		0			0
$493$	620.681	−	620.681i	0.0567020	−	0.0567020i
$494$		0			0
$495$	6293.02	−	1999.40i	0.571414	−	0.181548i
$496$		0			0
$497$	−88.5441	−	88.5441i	−0.00799144	−	0.00799144i
$498$		0			0
$499$	7828.81			0.702336			0.351168	−	0.936312i	$-0.385785\pi$
$499$	7828.81			0.702336			0.351168	+	0.936312i	$0.385785\pi$
$500$		0			0
$501$	−15698.7			−1.39993
$502$		0			0
$503$	9107.48	+	9107.48i	0.807321	+	0.807321i	0.984228	−	0.176907i	$-0.0566090\pi$
$503$	9107.48	+	9107.48i	0.807321	+	0.807321i	−0.176907	+	0.984228i	$0.556609\pi$
$504$		0			0
$505$	−3158.79	+	1003.60i	−0.278345	+	0.0884352i
$506$		0			0
$507$	−8910.14	+	8910.14i	−0.780499	+	0.780499i
$508$		0			0
$509$			21319.1i			1.85649i	0.371975	+	0.928243i	$0.378681\pi$
$509$			21319.1i			1.85649i	−0.371975	+	0.928243i	$0.621319\pi$
$510$		0			0
$511$			971.384i			0.0840930i
$512$		0			0
$513$	−2126.85	+	2126.85i	−0.183047	+	0.183047i
$514$		0			0
$515$	2480.03	+	1284.10i	0.212201	+	0.109872i
$516$		0			0
$517$	−10638.2	−	10638.2i	−0.904970	−	0.904970i
$518$		0			0
$519$	−8058.18			−0.681531
$520$		0			0
$521$	12182.6			1.02444			0.512218	−	0.858856i	$-0.328824\pi$
$521$	12182.6			1.02444			0.512218	+	0.858856i	$0.328824\pi$
$522$		0			0
$523$	−873.920	−	873.920i	−0.0730666	−	0.0730666i	0.669629	−	0.742696i	$-0.266453\pi$
$523$	−873.920	−	873.920i	−0.0730666	−	0.0730666i	−0.742696	+	0.669629i	$0.766453\pi$
$524$		0			0
$525$	1322.50	−	934.721i	0.109941	−	0.0777040i
$526$		0			0
$527$	−5706.29	+	5706.29i	−0.471670	+	0.471670i
$528$		0			0
$529$			11325.1i			0.930806i
$530$		0			0
$531$		−	12248.0i		−	1.00098i
$532$		0			0
$533$	−12763.1	+	12763.1i	−1.03721	+	1.03721i
$534$		0			0
$535$	3884.77	−	7502.81i	0.313932	−	0.606308i
$536$		0			0
$537$	4473.23	+	4473.23i	0.359468	+	0.359468i
$538$		0			0
$539$	8989.42			0.718370
$540$		0			0
$541$	−3081.17			−0.244861			−0.122430	−	0.992477i	$-0.539069\pi$
$541$	−3081.17			−0.244861			−0.122430	+	0.992477i	$0.539069\pi$
$542$		0			0
$543$	−12207.0	−	12207.0i	−0.964741	−	0.964741i
$544$		0			0
$545$	−5007.46	−	15760.7i	−0.393571	−	1.23874i
$546$		0			0
$547$	−6184.51	+	6184.51i	−0.483419	+	0.483419i	−0.906222	−	0.422802i	$-0.861046\pi$
$547$	−6184.51	+	6184.51i	−0.483419	+	0.483419i	0.422802	+	0.906222i	$0.361046\pi$
$548$		0			0
$549$		−	16533.4i		−	1.28530i
$550$		0			0
$551$		−	868.888i		−	0.0671794i
$552$		0			0
$553$	4.72431	−	4.72431i	0.000363288	−	0.000363288i
$554$		0			0
$555$	7610.99	+	23955.2i	0.582105	+	1.83215i
$556$		0			0
$557$	2117.68	+	2117.68i	0.161093	+	0.161093i	0.783051	−	0.621958i	$-0.213662\pi$
$557$	2117.68	+	2117.68i	0.161093	+	0.161093i	−0.621958	+	0.783051i	$0.713662\pi$
$558$		0			0
$559$	−24708.5			−1.86951
$560$		0			0
$561$	−17153.6			−1.29095
$562$		0			0
$563$	5986.35	+	5986.35i	0.448125	+	0.448125i	0.894731	−	0.446606i	$-0.147367\pi$
$563$	5986.35	+	5986.35i	0.448125	+	0.448125i	−0.446606	+	0.894731i	$0.647367\pi$
$564$		0			0
$565$	−2425.71	+	4684.86i	−0.180620	+	0.348838i
$566$		0			0
$567$	−1087.54	+	1087.54i	−0.0805512	+	0.0805512i
$568$		0			0
$569$			11232.8i			0.827596i	0.910369	+	0.413798i	$0.135798\pi$
$569$			11232.8i			0.827596i	−0.910369	+	0.413798i	$0.864202\pi$
$570$		0			0
$571$		−	18982.2i		−	1.39121i	−0.718423	−	0.695606i	$-0.755136\pi$
$571$		−	18982.2i		−	1.39121i	0.718423	−	0.695606i	$-0.244864\pi$
$572$		0			0
$573$	17749.3	−	17749.3i	1.29405	−	1.29405i
$574$		0			0
$575$	−18882.3	−	3243.91i	−1.36947	−	0.235270i
$576$		0			0
$577$	2310.66	+	2310.66i	0.166714	+	0.166714i	0.785533	−	0.618819i	$-0.212389\pi$
$577$	2310.66	+	2310.66i	0.166714	+	0.166714i	−0.618819	+	0.785533i	$0.712389\pi$
$578$		0			0
$579$	−5326.53			−0.382320
$580$		0			0
$581$	−2098.67			−0.149858
$582$		0			0
$583$	−6340.43	−	6340.43i	−0.450418	−	0.450418i
$584$		0			0
$585$	13994.6	+	7246.09i	0.989072	+	0.512118i
$586$		0			0
$587$	3134.61	−	3134.61i	0.220407	−	0.220407i	−0.588263	−	0.808670i	$-0.700188\pi$
$587$	3134.61	−	3134.61i	0.220407	−	0.220407i	0.808670	+	0.588263i	$0.200188\pi$
$588$		0			0
$589$			7988.20i			0.558825i
$590$		0			0
$591$		−	20765.4i		−	1.44531i
$592$		0			0
$593$	−2217.40	+	2217.40i	−0.153554	+	0.153554i	−0.779703	−	0.626149i	$-0.784630\pi$
$593$	−2217.40	+	2217.40i	−0.153554	+	0.153554i	0.626149	+	0.779703i	$0.284630\pi$
$594$		0			0
$595$	−1814.18	+	576.398i	−0.124999	+	0.0397143i
$596$		0			0
$597$	−13272.1	−	13272.1i	−0.909870	−	0.909870i
$598$		0			0
$599$	−3238.95			−0.220935			−0.110467	−	0.993880i	$-0.535235\pi$
$599$	−3238.95			−0.220935			−0.110467	+	0.993880i	$0.535235\pi$
$600$		0			0
$601$	9080.07			0.616279			0.308140	−	0.951341i	$-0.400294\pi$
$601$	9080.07			0.616279			0.308140	+	0.951341i	$0.400294\pi$
$602$		0			0
$603$	−3585.19	−	3585.19i	−0.242123	−	0.242123i
$604$		0			0
$605$	6716.04	−	2133.80i	0.451315	−	0.143391i
$606$		0			0
$607$	1926.10	−	1926.10i	0.128794	−	0.128794i	−0.639771	−	0.768565i	$-0.720971\pi$
$607$	1926.10	−	1926.10i	0.128794	−	0.128794i	0.768565	+	0.639771i	$0.220971\pi$
$608$		0			0
$609$		−	123.236i		−	0.00819993i
$610$		0			0
$611$		−	35907.1i		−	2.37749i
$612$		0			0
$613$	12046.5	−	12046.5i	0.793726	−	0.793726i	−0.188372	−	0.982098i	$-0.560321\pi$
$613$	12046.5	−	12046.5i	0.793726	−	0.793726i	0.982098	+	0.188372i	$0.0603210\pi$
$614$		0			0
$615$	19918.6	+	10313.4i	1.30601	+	0.676221i
$616$		0			0
$617$	5140.77	+	5140.77i	0.335429	+	0.335429i	0.854644	−	0.519215i	$-0.173776\pi$
$617$	5140.77	+	5140.77i	0.335429	+	0.335429i	−0.519215	+	0.854644i	$0.673776\pi$
$618$		0			0
$619$	26915.2			1.74768			0.873841	−	0.486212i	$-0.161622\pi$
$619$	26915.2			1.74768			0.873841	+	0.486212i	$0.161622\pi$
$620$		0			0
$621$	5046.84			0.326124
$622$		0			0
$623$	−851.830	−	851.830i	−0.0547798	−	0.0547798i
$624$		0			0
$625$	5214.73	−	14729.1i	0.333743	−	0.942664i
$626$		0			0
$627$	−12006.6	+	12006.6i	−0.764748	+	0.764748i
$628$		0			0
$629$		−	29544.0i		−	1.87281i
$630$		0			0
$631$		−	3852.28i		−	0.243038i	−0.992589	−	0.121519i	$-0.961224\pi$
$631$		−	3852.28i		−	0.243038i	0.992589	−	0.121519i	$-0.0387765\pi$
$632$		0			0
$633$	−26693.9	+	26693.9i	−1.67613	+	1.67613i
$634$		0			0
$635$	3005.45	−	5804.53i	0.187823	−	0.362749i
$636$		0			0
$637$	15170.9	+	15170.9i	0.943633	+	0.943633i
$638$		0			0
$639$	−1514.25			−0.0937447
$640$		0			0
$641$	14531.1			0.895387			0.447694	−	0.894187i	$-0.352246\pi$
$641$	14531.1			0.895387			0.447694	+	0.894187i	$0.352246\pi$
$642$		0			0
$643$	−17683.7	−	17683.7i	−1.08457	−	1.08457i	−0.996077	−	0.0884910i	$-0.971796\pi$
$643$	−17683.7	−	17683.7i	−1.08457	−	1.08457i	−0.0884910	−	0.996077i	$-0.528204\pi$
$644$		0			0
$645$	9297.50	+	29263.4i	0.567579	+	1.78643i
$646$		0			0
$647$	−8971.25	+	8971.25i	−0.545126	+	0.545126i	−0.925027	−	0.379901i	$-0.875958\pi$
$647$	−8971.25	+	8971.25i	−0.545126	+	0.545126i	0.379901	+	0.925027i	$0.375958\pi$
$648$		0			0
$649$			14531.7i			0.878921i
$650$		0			0
$651$			1132.98i			0.0682102i
$652$		0			0
$653$	1316.94	−	1316.94i	0.0789214	−	0.0789214i	−0.666544	−	0.745466i	$-0.732227\pi$
$653$	1316.94	−	1316.94i	0.0789214	−	0.0789214i	0.745466	+	0.666544i	$0.232227\pi$
$654$		0			0
$655$	5586.11	+	17582.0i	0.333232	+	1.04883i
$656$		0			0
$657$	8306.14	+	8306.14i	0.493232	+	0.493232i
$658$		0			0
$659$	−13761.4			−0.813459			−0.406729	−	0.913549i	$-0.633331\pi$
$659$	−13761.4			−0.813459			−0.406729	+	0.913549i	$0.633331\pi$
$660$		0			0
$661$	24292.9			1.42948			0.714738	−	0.699392i	$-0.246546\pi$
$661$	24292.9			1.42948			0.714738	+	0.699392i	$0.246546\pi$
$662$		0			0
$663$	−28949.1	−	28949.1i	−1.69576	−	1.69576i
$664$		0			0
$665$	−866.383	+	1673.28i	−0.0505216	+	0.0975743i
$666$		0			0
$667$	−1030.90	+	1030.90i	−0.0598449	+	0.0598449i
$668$		0			0
$669$		−	8441.34i		−	0.487834i
$670$		0			0
$671$			19616.1i			1.12857i
$672$		0			0
$673$	2363.45	−	2363.45i	0.135370	−	0.135370i	−0.636175	−	0.771545i	$-0.719484\pi$
$673$	2363.45	−	2363.45i	0.135370	−	0.135370i	0.771545	+	0.636175i	$0.219484\pi$
$674$		0			0
$675$	−696.894	+	4056.51i	−0.0397385	+	0.231311i
$676$		0			0
$677$	9.52502	+	9.52502i	0.000540733	+	0.000540733i	0.707377	−	0.706836i	$-0.249878\pi$
$677$	9.52502	+	9.52502i	0.000540733	+	0.000540733i	−0.706836	+	0.707377i	$0.749878\pi$
$678$		0			0
$679$	678.888			0.0383701
$680$		0			0
$681$	39852.6			2.24252
$682$		0			0
$683$	2412.55	+	2412.55i	0.135159	+	0.135159i	0.771449	−	0.636291i	$-0.219532\pi$
$683$	2412.55	+	2412.55i	0.135159	+	0.135159i	−0.636291	+	0.771449i	$0.719532\pi$
$684$		0			0
$685$	−25212.2	−	13054.3i	−1.40629	−	0.728143i
$686$		0			0
$687$	−1145.16	+	1145.16i	−0.0635962	+	0.0635962i
$688$		0			0
$689$		−	21400.8i		−	1.18332i
$690$		0			0
$691$			24706.7i			1.36018i	0.733128	+	0.680091i	$0.238060\pi$
$691$			24706.7i			1.36018i	−0.733128	+	0.680091i	$0.761940\pi$
$692$		0			0
$693$	−770.488	+	770.488i	−0.0422344	+	0.0422344i
$694$		0			0
$695$	19870.6	−	6313.26i	1.08451	−	0.344569i
$696$		0			0
$697$	−18642.6	−	18642.6i	−1.01311	−	1.01311i
$698$		0			0
$699$	2075.55			0.112310
$700$		0			0
$701$	−12435.9			−0.670039			−0.335019	−	0.942211i	$-0.608743\pi$
$701$	−12435.9			−0.670039			−0.335019	+	0.942211i	$0.608743\pi$
$702$		0			0
$703$	−20679.2	−	20679.2i	−1.10943	−	1.10943i
$704$		0			0
$705$	−42526.5	+	13511.4i	−2.27183	+	0.721801i
$706$		0			0
$707$	386.748	−	386.748i	0.0205731	−	0.0205731i
$708$		0			0
$709$		−	14894.0i		−	0.788939i	−0.918909	−	0.394469i	$-0.870928\pi$
$709$		−	14894.0i		−	0.788939i	0.918909	−	0.394469i	$-0.129072\pi$
$710$		0			0
$711$		−	80.7935i		−	0.00426160i
$712$		0			0
$713$	9477.66	−	9477.66i	0.497814	−	0.497814i
$714$		0			0
$715$	−16604.0	−	8597.16i	−0.868469	−	0.449672i
$716$		0			0
$717$	24282.5	+	24282.5i	1.26478	+	1.26478i
$718$		0			0
$719$	−19874.4			−1.03086			−0.515432	−	0.856930i	$-0.672369\pi$
$719$	−19874.4			−1.03086			−0.515432	+	0.856930i	$0.672369\pi$
$720$		0			0
$721$	−460.864			−0.0238051
$722$		0			0
$723$	−11999.6	−	11999.6i	−0.617250	−	0.617250i
$724$		0			0
$725$	−686.256	−	970.959i	−0.0351543	−	0.0497386i
$726$		0			0
$727$	965.676	−	965.676i	0.0492640	−	0.0492640i	−0.682046	−	0.731310i	$-0.738909\pi$
$727$	965.676	−	965.676i	0.0492640	−	0.0492640i	0.731310	+	0.682046i	$0.238909\pi$
$728$		0			0
$729$			12355.8i			0.627738i
$730$		0			0
$731$		−	36090.7i		−	1.82608i
$732$		0			0
$733$	−8560.56	+	8560.56i	−0.431366	+	0.431366i	−0.889093	−	0.457727i	$-0.848664\pi$
$733$	−8560.56	+	8560.56i	−0.431366	+	0.431366i	0.457727	+	0.889093i	$0.348664\pi$
$734$		0			0
$735$	12259.0	−	23676.3i	0.615212	−	1.18818i
$736$		0			0
$737$	4253.67	+	4253.67i	0.212600	+	0.212600i
$738$		0			0
$739$	27397.3			1.36377			0.681886	−	0.731458i	$-0.261160\pi$
$739$	27397.3			1.36377			0.681886	+	0.731458i	$0.261160\pi$
$740$		0			0
$741$	−40525.6			−2.00911
$742$		0			0
$743$	−9432.24	−	9432.24i	−0.465727	−	0.465727i	0.434800	−	0.900527i	$-0.356819\pi$
$743$	−9432.24	−	9432.24i	−0.465727	−	0.465727i	−0.900527	+	0.434800i	$0.856819\pi$
$744$		0			0
$745$	−4118.53	−	12962.8i	−0.202538	−	0.637479i
$746$		0			0
$747$	−17945.4	+	17945.4i	−0.878966	+	0.878966i
$748$		0			0
$749$			1394.24i			0.0680168i
$750$		0			0
$751$		−	30518.7i		−	1.48288i	−0.671019	−	0.741440i	$-0.734143\pi$
$751$		−	30518.7i		−	1.48288i	0.671019	−	0.741440i	$-0.265857\pi$
$752$		0			0
$753$	29011.9	−	29011.9i	1.40405	−	1.40405i
$754$		0			0
$755$	4480.83	+	14103.2i	0.215992	+	0.679824i
$756$		0			0
$757$	16325.1	+	16325.1i	0.783814	+	0.783814i	0.980472	−	0.196658i	$-0.0630090\pi$
$757$	16325.1	+	16325.1i	0.783814	+	0.783814i	−0.196658	+	0.980472i	$0.563009\pi$
$758$		0			0
$759$	28490.6			1.36251
$760$		0			0
$761$	15012.5			0.715114			0.357557	−	0.933891i	$-0.383610\pi$
$761$	15012.5			0.715114			0.357557	+	0.933891i	$0.383610\pi$
$762$		0			0
$763$	1929.67	+	1929.67i	0.0915580	+	0.0915580i
$764$		0			0
$765$	−10584.1	+	20441.4i	−0.500220	+	0.966093i
$766$		0			0
$767$	−24524.4	+	24524.4i	−1.15453	+	1.15453i
$768$		0			0
$769$		−	15829.7i		−	0.742306i	−0.928572	−	0.371153i	$-0.878963\pi$
$769$		−	15829.7i		−	0.742306i	0.928572	−	0.371153i	$-0.121037\pi$
$770$		0			0
$771$		−	31043.8i		−	1.45008i
$772$		0			0
$773$	−23486.9	+	23486.9i	−1.09284	+	1.09284i	−0.0976135	+	0.995224i	$0.531121\pi$
$773$	−23486.9	+	23486.9i	−1.09284	+	1.09284i	−0.995224	+	0.0976135i	$0.968879\pi$
$774$		0			0
$775$	6309.15	+	8926.60i	0.292428	+	0.413746i
$776$		0			0
$777$	−2932.96	−	2932.96i	−0.135418	−	0.135418i
$778$		0			0
$779$	−26097.7			−1.20032
$780$		0			0
$781$	1796.59			0.0823138
$782$		0			0
$783$	221.469	+	221.469i	0.0101081	+	0.0101081i
$784$		0			0
$785$	−17247.9	−	8930.53i	−0.784207	−	0.406043i
$786$		0			0
$787$	−9415.74	+	9415.74i	−0.426474	+	0.426474i	−0.887425	−	0.460952i	$-0.847508\pi$
$787$	−9415.74	+	9415.74i	−0.426474	+	0.426474i	0.460952	+	0.887425i	$0.347508\pi$
$788$		0			0
$789$			4205.79i			0.189772i
$790$		0			0
$791$		−	870.586i		−	0.0391333i
$792$		0			0
$793$	−33105.0	+	33105.0i	−1.48246	+	1.48246i
$794$		0			0
$795$	−25346.0	+	8052.86i	−1.13073	+	0.359252i
$796$		0			0
$797$	−7971.30	−	7971.30i	−0.354276	−	0.354276i	0.507422	−	0.861698i	$-0.330599\pi$
$797$	−7971.30	−	7971.30i	−0.354276	−	0.354276i	−0.861698	+	0.507422i	$0.830599\pi$
$798$		0			0
$799$	52448.1			2.32225
$800$		0			0
$801$	−14567.7			−0.642602
$802$		0			0
$803$	−9854.86	−	9854.86i	−0.433089	−	0.433089i
$804$		0			0
$805$	3013.20	−	957.347i	0.131927	−	0.0419156i
$806$		0			0
$807$	−2293.93	+	2293.93i	−0.100062	+	0.100062i
$808$		0			0
$809$		−	42121.9i		−	1.83056i	−0.402814	−	0.915282i	$-0.631968\pi$
$809$		−	42121.9i		−	1.83056i	0.402814	−	0.915282i	$-0.368032\pi$
$810$		0			0
$811$		−	11544.1i		−	0.499838i	−0.968267	−	0.249919i	$-0.919596\pi$
$811$		−	11544.1i		−	0.499838i	0.968267	−	0.249919i	$-0.0804040\pi$
$812$		0			0
$813$	1782.34	−	1782.34i	0.0768872	−	0.0768872i
$814$		0			0
$815$	34843.8	+	18041.3i	1.49758	+	0.775410i
$816$		0			0
$817$	−25261.5	−	25261.5i	−1.08175	−	1.08175i
$818$		0			0
$819$	−2600.62			−0.110956
$820$		0			0
$821$	−1537.35			−0.0653518			−0.0326759	−	0.999466i	$-0.510403\pi$
$821$	−1537.35			−0.0653518			−0.0326759	+	0.999466i	$0.510403\pi$
$822$		0			0
$823$	1127.89	+	1127.89i	0.0477714	+	0.0477714i	0.730589	−	0.682818i	$-0.239246\pi$
$823$	1127.89	+	1127.89i	0.0477714	+	0.0477714i	−0.682818	+	0.730589i	$0.739246\pi$
$824$		0			0
$825$	−3934.13	+	22899.9i	−0.166023	+	0.966393i
$826$		0			0
$827$	−2821.68	+	2821.68i	−0.118645	+	0.118645i	−0.763937	−	0.645291i	$-0.776736\pi$
$827$	−2821.68	+	2821.68i	−0.118645	+	0.118645i	0.645291	+	0.763937i	$0.276736\pi$
$828$		0			0
$829$		−	21939.1i		−	0.919151i	−0.888139	−	0.459575i	$-0.848002\pi$
$829$		−	21939.1i		−	0.919151i	0.888139	−	0.459575i	$-0.151998\pi$
$830$		0			0
$831$			1266.54i			0.0528709i
$832$		0			0
$833$	−22159.6	+	22159.6i	−0.921709	+	0.921709i
$834$		0			0
$835$	11492.5	−	22195.8i	0.476303	−	0.919903i
$836$		0			0
$837$	−2036.10	−	2036.10i	−0.0840835	−	0.0840835i
$838$		0			0
$839$	−31924.7			−1.31366			−0.656831	−	0.754038i	$-0.728104\pi$
$839$	−31924.7			−1.31366			−0.656831	+	0.754038i	$0.728104\pi$
$840$		0			0
$841$	24298.5			0.996290
$842$		0			0
$843$	29328.9	+	29328.9i	1.19827	+	1.19827i
$844$		0			0
$845$	−6074.93	−	19120.5i	−0.247318	−	0.778422i
$846$		0			0
$847$	−822.281	+	822.281i	−0.0333576	+	0.0333576i
$848$		0			0
$849$			26682.1i			1.07860i
$850$		0			0
$851$			49070.1i			1.97662i
$852$		0			0
$853$	−1821.97	+	1821.97i	−0.0731337	+	0.0731337i	−0.742728	−	0.669594i	$-0.766468\pi$
$853$	−1821.97	+	1821.97i	−0.0731337	+	0.0731337i	0.669594	+	0.742728i	$0.266468\pi$
$854$		0			0
$855$	6899.62	+	21716.2i	0.275979	+	0.868629i
$856$		0			0
$857$	−4529.29	−	4529.29i	−0.180534	−	0.180534i	0.611054	−	0.791589i	$-0.290746\pi$
$857$	−4529.29	−	4529.29i	−0.180534	−	0.180534i	−0.791589	+	0.611054i	$0.790746\pi$
$858$		0			0
$859$	8593.70			0.341342			0.170671	−	0.985328i	$-0.445406\pi$
$859$	8593.70			0.341342			0.170671	+	0.985328i	$0.445406\pi$
$860$		0			0
$861$	−3701.47			−0.146511
$862$		0			0
$863$	30314.5	+	30314.5i	1.19573	+	1.19573i	0.975432	+	0.220301i	$0.0707039\pi$
$863$	30314.5	+	30314.5i	1.19573	+	1.19573i	0.220301	+	0.975432i	$0.429296\pi$
$864$		0			0
$865$	5899.11	−	11393.2i	0.231880	−	0.447838i
$866$		0			0
$867$	17889.7	−	17889.7i	0.700767	−	0.700767i
$868$		0			0
$869$			95.8579i			0.00374195i
$870$		0			0
$871$			14357.3i			0.558530i
$872$		0			0
$873$	5805.05	−	5805.05i	0.225053	−	0.225053i
$874$		0			0
$875$	353.410	+	2554.12i	0.0136542	+	0.0986800i
$876$		0			0
$877$	17952.6	+	17952.6i	0.691239	+	0.691239i	0.962504	−	0.271266i	$-0.0874422\pi$
$877$	17952.6	+	17952.6i	0.691239	+	0.691239i	−0.271266	+	0.962504i	$0.587442\pi$
$878$		0			0
$879$	25737.8			0.987615
$880$		0			0
$881$	21855.6			0.835792			0.417896	−	0.908495i	$-0.362768\pi$
$881$	21855.6			0.835792			0.417896	+	0.908495i	$0.362768\pi$
$882$		0			0
$883$	12704.5	+	12704.5i	0.484192	+	0.484192i	0.906468	−	0.422275i	$-0.138768\pi$
$883$	12704.5	+	12704.5i	0.484192	+	0.484192i	−0.422275	+	0.906468i	$0.638768\pi$
$884$		0			0
$885$	38273.6	+	19817.1i	1.45373	+	0.752707i
$886$		0			0
$887$	−19861.9	+	19861.9i	−0.751858	+	0.751858i	−0.974826	−	0.222968i	$-0.928426\pi$
$887$	−19861.9	+	19861.9i	−0.751858	+	0.751858i	0.222968	+	0.974826i	$0.428426\pi$
$888$		0			0
$889$			1078.65i			0.0406939i
$890$		0			0
$891$		−	22066.6i		−	0.829697i
$892$		0			0
$893$	36710.9	−	36710.9i	1.37568	−	1.37568i
$894$		0			0
$895$	−9599.25	+	3049.85i	−0.358511	+	0.113905i
$896$		0			0
$897$	48082.0	+	48082.0i	1.78975	+	1.78975i
$898$		0			0
$899$	831.811			0.0308592
$900$		0			0
$901$	31259.3			1.15582
$902$		0			0
$903$	−3582.88	−	3582.88i	−0.132038	−	0.132038i
$904$		0			0
$905$	26195.5	−	8322.76i	0.962173	−	0.305699i
$906$		0			0
$907$	−34271.6	+	34271.6i	−1.25465	+	1.25465i	−0.301039	+	0.953612i	$0.597333\pi$
$907$	−34271.6	+	34271.6i	−1.25465	+	1.25465i	−0.953612	+	0.301039i	$0.902667\pi$
$908$		0			0
$909$		−	6614.03i		−	0.241335i
$910$		0			0
$911$		−	28286.7i		−	1.02874i	−0.857569	−	0.514370i	$-0.828026\pi$
$911$		−	28286.7i		−	1.02874i	0.857569	−	0.514370i	$-0.171974\pi$
$912$		0			0
$913$	21291.4	−	21291.4i	0.771789	−	0.771789i
$914$		0			0
$915$	51664.8	+	26750.8i	1.86665	+	0.966507i
$916$		0			0
$917$	−2152.66	−	2152.66i	−0.0775213	−	0.0775213i
$918$		0			0
$919$	−50078.4			−1.79754			−0.898768	−	0.438425i	$-0.855537\pi$
$919$	−50078.4			−1.79754			−0.898768	+	0.438425i	$0.855537\pi$
$920$		0			0
$921$	−64489.5			−2.30728
$922$		0			0
$923$	3032.00	+	3032.00i	0.108125	+	0.108125i
$924$		0			0
$925$	−39441.1	−	6775.85i	−1.40196	−	0.240852i
$926$		0			0
$927$	−3940.77	+	3940.77i	−0.139624	+	0.139624i
$928$		0			0
$929$			33711.0i			1.19055i	0.803522	+	0.595275i	$0.202957\pi$
$929$			33711.0i			1.19055i	−0.803522	+	0.595275i	$0.797043\pi$
$930$		0			0
$931$			31021.0i			1.09202i
$932$		0			0
$933$	−30648.8	+	30648.8i	−1.07545	+	1.07545i
$934$		0			0
$935$	12557.5	−	24252.8i	0.439225	−	0.848292i
$936$		0			0
$937$	258.796	+	258.796i	0.00902294	+	0.00902294i	0.711604	−	0.702581i	$-0.247969\pi$
$937$	258.796	+	258.796i	0.00902294	+	0.00902294i	−0.702581	+	0.711604i	$0.747969\pi$
$938$		0			0
$939$	38338.6			1.33241
$940$		0			0
$941$	−11887.5			−0.411817			−0.205909	−	0.978571i	$-0.566015\pi$
$941$	−11887.5			−0.411817			−0.205909	+	0.978571i	$0.566015\pi$
$942$		0			0
$943$	30963.8	+	30963.8i	1.06927	+	1.06927i
$944$		0			0
$945$	−205.668	−	647.330i	−0.00707977	−	0.0222832i
$946$		0			0
$947$	15621.4	−	15621.4i	0.536037	−	0.536037i	−0.386326	−	0.922362i	$-0.626256\pi$
$947$	15621.4	−	15621.4i	0.536037	−	0.536037i	0.922362	+	0.386326i	$0.126256\pi$
$948$		0			0
$949$		−	33263.0i		−	1.13779i
$950$		0			0
$951$			26668.1i			0.909328i
$952$		0			0
$953$	−1813.00	+	1813.00i	−0.0616251	+	0.0616251i	−0.737248	−	0.675623i	$-0.763875\pi$
$953$	−1813.00	+	1813.00i	−0.0616251	+	0.0616251i	0.675623	+	0.737248i	$0.263875\pi$
$954$		0			0
$955$	12101.5	+	38088.8i	0.410047	+	1.29060i
$956$		0			0
$957$	1250.25	+	1250.25i	0.0422306	+	0.0422306i
$958$		0			0
$959$	4685.17			0.157760
$960$		0			0
$961$	22143.7			0.743301
$962$		0			0
$963$	11921.9	+	11921.9i	0.398940	+	0.398940i
$964$		0			0
$965$	3899.37	−	7531.00i	0.130078	−	0.251224i
$966$		0			0
$967$	27754.8	−	27754.8i	0.922993	−	0.922993i	−0.0742472	−	0.997240i	$-0.523655\pi$
$967$	27754.8	−	27754.8i	0.922993	−	0.922993i	0.997240	+	0.0742472i	$0.0236554\pi$
$968$		0			0
$969$		−	59194.2i		−	1.96243i
$970$		0			0
$971$		−	9248.74i		−	0.305671i	−0.988252	−	0.152835i	$-0.951160\pi$
$971$		−	9248.74i		−	0.305671i	0.988252	−	0.152835i	$-0.0488404\pi$
$972$		0			0
$973$	−2432.87	+	2432.87i	−0.0801586	+	0.0801586i
$974$		0			0
$975$	−45286.3	+	32007.5i	−1.48751	+	1.05134i
$976$		0			0
$977$	20409.9	+	20409.9i	0.668344	+	0.668344i	0.957332	−	0.288989i	$-0.0933190\pi$
$977$	20409.9	+	20409.9i	0.668344	+	0.668344i	−0.288989	+	0.957332i	$0.593319\pi$
$978$		0			0
$979$	17283.9			0.564246
$980$		0			0
$981$	33000.6			1.07403
$982$		0			0
$983$	−21268.7	−	21268.7i	−0.690098	−	0.690098i	0.272155	−	0.962253i	$-0.412263\pi$
$983$	−21268.7	−	21268.7i	−0.690098	−	0.690098i	−0.962253	+	0.272155i	$0.912263\pi$
$984$		0			0
$985$	29359.5	+	15201.6i	0.949718	+	0.491741i
$986$		0			0
$987$	5206.76	−	5206.76i	0.167916	−	0.167916i
$988$		0			0
$989$			59943.5i			1.92729i
$990$		0			0
$991$		−	885.856i		−	0.0283957i	−0.999899	−	0.0141979i	$-0.995481\pi$
$991$		−	885.856i		−	0.0283957i	0.999899	−	0.0141979i	$-0.00451947\pi$
$992$		0			0
$993$	12239.5	−	12239.5i	0.391148	−	0.391148i
$994$		0			0
$995$	28481.1	−	9048.94i	0.907448	−	0.288312i
$996$		0			0
$997$	−27624.7	−	27624.7i	−0.877515	−	0.877515i	0.115762	−	0.993277i	$-0.463069\pi$
$997$	−27624.7	−	27624.7i	−0.877515	−	0.877515i	−0.993277	+	0.115762i	$0.963069\pi$
$998$		0			0
$999$	10541.8			0.333861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.4.n.h.127.1		8
4.3	odd	2		320.4.n.g.127.4		8
5.3	odd	4		320.4.n.g.63.4		8
8.3	odd	2		160.4.n.e.127.1	yes	8
8.5	even	2		160.4.n.d.127.4	yes	8
20.3	even	4	inner	320.4.n.h.63.1		8
40.3	even	4		160.4.n.d.63.4	✓	8
40.13	odd	4		160.4.n.e.63.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.n.d.63.4	✓	8	40.3	even	4
160.4.n.d.127.4	yes	8	8.5	even	2
160.4.n.e.63.1	yes	8	40.13	odd	4
160.4.n.e.127.1	yes	8	8.3	odd	2
320.4.n.g.63.4		8	5.3	odd	4
320.4.n.g.127.4		8	4.3	odd	2
320.4.n.h.63.1		8	20.3	even	4	inner
320.4.n.h.127.1		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	320.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.96543 - 4.96543i) q^{3} +(10.6555 - 3.38543i) q^{5} +(-1.30461 + 1.30461i) q^{7} +22.3109i q^{9} -26.4709i q^{11} +(44.6735 - 44.6735i) q^{13} +(-69.7190 - 36.0988i) q^{15} +(65.2528 + 65.2528i) q^{17} +91.3469 q^{19} +12.9559 q^{21} +(-108.379 - 108.379i) q^{23} +(102.078 - 72.1466i) q^{25} +(-23.2833 + 23.2833i) q^{27} -9.51196i q^{29} +87.4490i q^{31} +(-131.439 + 131.439i) q^{33} +(-9.48453 + 18.3178i) q^{35} +(-226.381 - 226.381i) q^{37} -443.646 q^{39} -285.699 q^{41} +(-276.545 - 276.545i) q^{43} +(75.5320 + 237.733i) q^{45} +(401.884 - 401.884i) q^{47} +339.596i q^{49} -648.016i q^{51} +(239.525 - 239.525i) q^{53} +(-89.6154 - 282.060i) q^{55} +(-453.576 - 453.576i) q^{57} -548.969 q^{59} -741.044 q^{61} +(-29.1070 - 29.1070i) q^{63} +(324.777 - 627.255i) q^{65} +(-160.692 + 160.692i) q^{67} +1076.30i q^{69} +67.8704i q^{71} +(372.290 - 372.290i) q^{73} +(-865.098 - 148.621i) q^{75} +(34.5341 + 34.5341i) q^{77} -3.62125 q^{79} +833.618 q^{81} +(804.332 + 804.332i) q^{83} +(916.207 + 474.390i) q^{85} +(-47.2309 + 47.2309i) q^{87} +652.940i q^{89} +116.563i q^{91} +(434.222 - 434.222i) q^{93} +(973.344 - 309.248i) q^{95} +(-260.189 - 260.189i) q^{97} +590.591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 14 q^{5} - 10 q^{7} + 32 q^{13} - 22 q^{15} + 44 q^{17} + 80 q^{19} - 236 q^{21} - 230 q^{23} - 44 q^{25} + 80 q^{27} - 260 q^{33} - 866 q^{35} + 292 q^{37} - 1068 q^{39} + 932 q^{41} + 458 q^{43}+ \cdots + 1844 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 14 * q^5 - 10 * q^7 + 32 * q^13 - 22 * q^15 + 44 * q^17 + 80 * q^19 - 236 * q^21 - 230 * q^23 - 44 * q^25 + 80 * q^27 - 260 * q^33 - 866 * q^35 + 292 * q^37 - 1068 * q^39 + 932 * q^41 + 458 * q^43 + 110 * q^45 + 766 * q^47 + 892 * q^53 + 920 * q^55 - 1064 * q^57 + 16 * q^59 - 2564 * q^61 - 798 * q^63 - 888 * q^65 - 194 * q^67 - 1744 * q^73 - 4918 * q^75 + 1516 * q^77 - 3216 * q^79 + 4828 * q^81 + 3762 * q^83 + 920 * q^85 + 3904 * q^87 + 2420 * q^93 + 1544 * q^95 - 680 * q^97 + 1844 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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