LMFDB - Embedded newform 320.4.n.h.63.3

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			63.3
Root			$-3.22067 - 3.22067i$ of defining polynomial
Character	$\chi$	$=$	320.63
Dual form			320.4.n.h.127.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.64336 - 3.64336i) q^{3} +(-0.725933 + 11.1567i) q^{5} +(9.23932 + 9.23932i) q^{7} +0.451865i q^{9} -29.0521i q^{11} +(22.1709 + 22.1709i) q^{13} +(38.0032 + 43.2929i) q^{15} +(-68.5560 + 68.5560i) q^{17} +46.3417 q^{19} +67.3243 q^{21} +(-82.3020 + 82.3020i) q^{23} +(-123.946 - 16.1981i) q^{25} +(100.017 + 100.017i) q^{27} +110.111i q^{29} +250.150i q^{31} +(-105.847 - 105.847i) q^{33} +(-109.788 + 96.3737i) q^{35} +(190.450 - 190.450i) q^{37} +161.553 q^{39} +386.818 q^{41} +(215.698 - 215.698i) q^{43} +(-5.04135 - 0.328024i) q^{45} +(258.459 + 258.459i) q^{47} -172.270i q^{49} +499.548i q^{51} +(-313.780 - 313.780i) q^{53} +(324.127 + 21.0899i) q^{55} +(168.840 - 168.840i) q^{57} +195.564 q^{59} -423.865 q^{61} +(-4.17493 + 4.17493i) q^{63} +(-263.449 + 231.260i) q^{65} +(598.492 + 598.492i) q^{67} +599.711i q^{69} -993.953i q^{71} +(22.8188 + 22.8188i) q^{73} +(-510.595 + 392.564i) q^{75} +(268.421 - 268.421i) q^{77} -612.099 q^{79} +716.595 q^{81} +(-176.546 + 176.546i) q^{83} +(-715.095 - 814.629i) q^{85} +(401.174 + 401.174i) q^{87} +1256.16i q^{89} +409.688i q^{91} +(911.388 + 911.388i) q^{93} +(-33.6410 + 517.023i) q^{95} +(269.898 - 269.898i) q^{97} +13.1276 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	3.64336	−	3.64336i	0.701165	−	0.701165i	−0.263496	−	0.964661i	$-0.584875\pi$
$3$	3.64336	−	3.64336i	0.701165	−	0.701165i	0.964661	+	0.263496i	$0.0848755\pi$
$4$		0			0
$5$	−0.725933	+	11.1567i	−0.0649294	+	0.997890i
$5$	−0.725933	+	11.1567i	−0.0649294	+	0.997890i
$6$		0			0
$7$	9.23932	+	9.23932i	0.498876	+	0.498876i	0.911088	−	0.412212i	$-0.135244\pi$
$7$	9.23932	+	9.23932i	0.498876	+	0.498876i	−0.412212	+	0.911088i	$0.635244\pi$
$8$		0			0
$9$			0.451865i			0.0167358i
$10$		0			0
$11$		−	29.0521i		−	0.796321i	−0.917316	−	0.398161i	$-0.869649\pi$
$11$		−	29.0521i		−	0.796321i	0.917316	−	0.398161i	$-0.130351\pi$
$12$		0			0
$13$	22.1709	+	22.1709i	0.473007	+	0.473007i	0.902886	−	0.429879i	$-0.141444\pi$
$13$	22.1709	+	22.1709i	0.473007	+	0.473007i	−0.429879	+	0.902886i	$0.641444\pi$
$14$		0			0
$15$	38.0032	+	43.2929i	0.654159	+	0.745211i
$16$		0			0
$17$	−68.5560	+	68.5560i	−0.978075	+	0.978075i	−0.999765	−	0.0216896i	$-0.993095\pi$
$17$	−68.5560	+	68.5560i	−0.978075	+	0.978075i	0.0216896	+	0.999765i	$0.493095\pi$
$18$		0			0
$19$	46.3417			0.559554			0.279777	−	0.960065i	$-0.409739\pi$
$19$	46.3417			0.559554			0.279777	+	0.960065i	$0.409739\pi$
$20$		0			0
$21$	67.3243			0.699589
$22$		0			0
$23$	−82.3020	+	82.3020i	−0.746137	+	0.746137i	−0.973751	−	0.227614i	$-0.926907\pi$
$23$	−82.3020	+	82.3020i	−0.746137	+	0.746137i	0.227614	+	0.973751i	$0.426907\pi$
$24$		0			0
$25$	−123.946	−	16.1981i	−0.991568	−	0.129585i
$26$		0			0
$27$	100.017	+	100.017i	0.712899	+	0.712899i
$28$		0			0
$29$			110.111i			0.705072i	0.935798	+	0.352536i	$0.114681\pi$
$29$			110.111i			0.705072i	−0.935798	+	0.352536i	$0.885319\pi$
$30$		0			0
$31$			250.150i			1.44930i	0.689116	+	0.724651i	$0.257999\pi$
$31$			250.150i			1.44930i	−0.689116	+	0.724651i	$0.742001\pi$
$32$		0			0
$33$	−105.847	−	105.847i	−0.558352	−	0.558352i
$34$		0			0
$35$	−109.788	+	96.3737i	−0.530215	+	0.465432i
$36$		0			0
$37$	190.450	−	190.450i	0.846212	−	0.846212i	−0.143446	−	0.989658i	$-0.545818\pi$
$37$	190.450	−	190.450i	0.846212	−	0.846212i	0.989658	+	0.143446i	$0.0458183\pi$
$38$		0			0
$39$	161.553			0.663312
$40$		0			0
$41$	386.818			1.47344			0.736718	−	0.676200i	$-0.236375\pi$
$41$	386.818			1.47344			0.736718	+	0.676200i	$0.236375\pi$
$42$		0			0
$43$	215.698	−	215.698i	0.764969	−	0.764969i	−0.212247	−	0.977216i	$-0.568078\pi$
$43$	215.698	−	215.698i	0.764969	−	0.764969i	0.977216	+	0.212247i	$0.0680781\pi$
$44$		0			0
$45$	−5.04135	−	0.328024i	−0.0167004	−	0.00108664i
$46$		0			0
$47$	258.459	+	258.459i	0.802130	+	0.802130i	0.983428	−	0.181298i	$-0.0580300\pi$
$47$	258.459	+	258.459i	0.802130	+	0.802130i	−0.181298	+	0.983428i	$0.558030\pi$
$48$		0			0
$49$		−	172.270i		−	0.502245i
$50$		0			0
$51$			499.548i			1.37158i
$52$		0			0
$53$	−313.780	−	313.780i	−0.813225	−	0.813225i	0.171891	−	0.985116i	$-0.445012\pi$
$53$	−313.780	−	313.780i	−0.813225	−	0.813225i	−0.985116	+	0.171891i	$0.945012\pi$
$54$		0			0
$55$	324.127	+	21.0899i	0.794641	+	0.0517046i
$56$		0			0
$57$	168.840	−	168.840i	0.392340	−	0.392340i
$58$		0			0
$59$	195.564			0.431531			0.215765	−	0.976445i	$-0.430775\pi$
$59$	195.564			0.431531			0.215765	+	0.976445i	$0.430775\pi$
$60$		0			0
$61$	−423.865			−0.889677			−0.444838	−	0.895611i	$-0.646739\pi$
$61$	−423.865			−0.889677			−0.444838	+	0.895611i	$0.646739\pi$
$62$		0			0
$63$	−4.17493	+	4.17493i	−0.00834907	+	0.00834907i
$64$		0			0
$65$	−263.449	+	231.260i	−0.502721	+	0.441297i
$66$		0			0
$67$	598.492	+	598.492i	1.09130	+	1.09130i	0.995389	+	0.0959153i	$0.0305778\pi$
$67$	598.492	+	598.492i	1.09130	+	1.09130i	0.0959153	+	0.995389i	$0.469422\pi$
$68$		0			0
$69$			599.711i			1.04633i
$70$		0			0
$71$		−	993.953i		−	1.66141i	−0.556709	−	0.830707i	$-0.687936\pi$
$71$		−	993.953i		−	1.66141i	0.556709	−	0.830707i	$-0.312064\pi$
$72$		0			0
$73$	22.8188	+	22.8188i	0.0365854	+	0.0365854i	0.725163	−	0.688577i	$-0.241764\pi$
$73$	22.8188	+	22.8188i	0.0365854	+	0.0365854i	−0.688577	+	0.725163i	$0.741764\pi$
$74$		0			0
$75$	−510.595	+	392.564i	−0.786113	+	0.604393i
$76$		0			0
$77$	268.421	−	268.421i	0.397266	−	0.397266i
$78$		0			0
$79$	−612.099			−0.871728			−0.435864	−	0.900013i	$-0.643557\pi$
$79$	−612.099			−0.871728			−0.435864	+	0.900013i	$0.643557\pi$
$80$		0			0
$81$	716.595			0.982984
$82$		0			0
$83$	−176.546	+	176.546i	−0.233476	+	0.233476i	−0.814142	−	0.580666i	$-0.802792\pi$
$83$	−176.546	+	176.546i	−0.233476	+	0.233476i	0.580666	+	0.814142i	$0.302792\pi$
$84$		0			0
$85$	−715.095	−	814.629i	−0.912505	−	1.03952i
$86$		0			0
$87$	401.174	+	401.174i	0.494372	+	0.494372i
$88$		0			0
$89$			1256.16i			1.49610i	0.663643	+	0.748049i	$0.269009\pi$
$89$			1256.16i			1.49610i	−0.663643	+	0.748049i	$0.730991\pi$
$90$		0			0
$91$			409.688i			0.471944i
$92$		0			0
$93$	911.388	+	911.388i	1.01620	+	1.01620i
$94$		0			0
$95$	−33.6410	+	517.023i	−0.0363315	+	0.558373i
$96$		0			0
$97$	269.898	−	269.898i	0.282516	−	0.282516i	−0.551596	−	0.834111i	$-0.685981\pi$
$97$	269.898	−	269.898i	0.282516	−	0.282516i	0.834111	+	0.551596i	$0.185981\pi$
$98$		0			0
$99$	13.1276			0.0133270
$100$		0			0
$101$	−794.410			−0.782641			−0.391320	−	0.920255i	$-0.627982\pi$
$101$	−794.410			−0.782641			−0.391320	+	0.920255i	$0.627982\pi$
$102$		0			0
$103$	−13.6891	+	13.6891i	−0.0130954	+	0.0130954i	−0.713624	−	0.700529i	$-0.752948\pi$
$103$	−13.6891	+	13.6891i	−0.0130954	+	0.0130954i	0.700529	+	0.713624i	$0.252948\pi$
$104$		0			0
$105$	−48.8729	+	751.121i	−0.0454239	+	0.698113i
$106$		0			0
$107$	−1132.24	−	1132.24i	−1.02297	−	1.02297i	−0.999730	−	0.0232410i	$-0.992601\pi$
$107$	−1132.24	−	1132.24i	−1.02297	−	1.02297i	−0.0232410	−	0.999730i	$-0.507399\pi$
$108$		0			0
$109$			1611.09i			1.41573i	0.706347	+	0.707866i	$0.250342\pi$
$109$			1611.09i			1.41573i	−0.706347	+	0.707866i	$0.749658\pi$
$110$		0			0
$111$		−	1387.76i		−	1.18667i
$112$		0			0
$113$	−1283.90	−	1283.90i	−1.06884	−	1.06884i	−0.997448	−	0.0713924i	$-0.977256\pi$
$113$	−1283.90	−	1283.90i	−1.06884	−	1.06884i	−0.0713924	−	0.997448i	$-0.522744\pi$
$114$		0			0
$115$	−858.477	−	977.968i	−0.696116	−	0.793009i
$116$		0			0
$117$	−10.0182	+	10.0182i	−0.00791613	+	0.00791613i
$118$		0			0
$119$	−1266.82			−0.975877
$120$		0			0
$121$	486.977			0.365873
$122$		0			0
$123$	1409.32	−	1409.32i	1.03312	−	1.03312i
$124$		0			0
$125$	270.695	−	1371.08i	0.193693	−	0.981062i
$126$		0			0
$127$	634.636	+	634.636i	0.443424	+	0.443424i	0.893161	−	0.449737i	$-0.148482\pi$
$127$	634.636	+	634.636i	0.443424	+	0.443424i	−0.449737	+	0.893161i	$0.648482\pi$
$128$		0			0
$129$		−	1571.73i		−	1.07274i
$130$		0			0
$131$		−	1439.02i		−	0.959751i	−0.877336	−	0.479876i	$-0.840682\pi$
$131$		−	1439.02i		−	0.959751i	0.877336	−	0.479876i	$-0.159318\pi$
$132$		0			0
$133$	428.166	+	428.166i	0.279148	+	0.279148i
$134$		0			0
$135$	−1188.47	+	1043.26i	−0.757683	+	0.665107i
$136$		0			0
$137$	−778.649	+	778.649i	−0.485580	+	0.485580i	−0.906908	−	0.421328i	$-0.861564\pi$
$137$	−778.649	+	778.649i	−0.485580	+	0.485580i	0.421328	+	0.906908i	$0.361564\pi$
$138$		0			0
$139$	955.284			0.582922			0.291461	−	0.956583i	$-0.405859\pi$
$139$	955.284			0.582922			0.291461	+	0.956583i	$0.405859\pi$
$140$		0			0
$141$	1883.32			1.12485
$142$		0			0
$143$	644.110	−	644.110i	0.376666	−	0.376666i
$144$		0			0
$145$	−1228.48	−	79.9331i	−0.703584	−	0.0457799i
$146$		0			0
$147$	−627.641	−	627.641i	−0.352156	−	0.352156i
$148$		0			0
$149$		−	2213.52i		−	1.21704i	−0.793540	−	0.608518i	$-0.791764\pi$
$149$		−	2213.52i		−	1.21704i	0.793540	−	0.608518i	$-0.208236\pi$
$150$		0			0
$151$		−	3105.29i		−	1.67354i	−0.547553	−	0.836771i	$-0.684440\pi$
$151$		−	3105.29i		−	1.67354i	0.547553	−	0.836771i	$-0.315560\pi$
$152$		0			0
$153$	−30.9781	−	30.9781i	−0.0163688	−	0.0163688i
$154$		0			0
$155$	−2790.87	−	181.592i	−1.44624	−	0.0941023i
$156$		0			0
$157$	457.388	−	457.388i	0.232507	−	0.232507i	−0.581232	−	0.813738i	$-0.697429\pi$
$157$	457.388	−	457.388i	0.232507	−	0.232507i	0.813738	+	0.581232i	$0.197429\pi$
$158$		0			0
$159$	−2286.42			−1.14041
$160$		0			0
$161$	−1520.83			−0.744460
$162$		0			0
$163$	2156.05	−	2156.05i	1.03604	−	1.03604i	0.0367187	−	0.999326i	$-0.488309\pi$
$163$	2156.05	−	2156.05i	1.03604	−	1.03604i	0.999326	−	0.0367187i	$-0.0116906\pi$
$164$		0			0
$165$	1257.75	−	1104.07i	0.593428	−	0.520921i
$166$		0			0
$167$	1534.62	+	1534.62i	0.711094	+	0.711094i	0.966764	−	0.255670i	$-0.0822961\pi$
$167$	1534.62	+	1534.62i	0.711094	+	0.711094i	−0.255670	+	0.966764i	$0.582296\pi$
$168$		0			0
$169$		−	1213.90i		−	0.552528i
$170$		0			0
$171$			20.9402i			0.00936456i
$172$		0			0
$173$	1185.22	+	1185.22i	0.520872	+	0.520872i	0.917835	−	0.396963i	$-0.129936\pi$
$173$	1185.22	+	1185.22i	0.520872	+	0.520872i	−0.396963	+	0.917835i	$0.629936\pi$
$174$		0			0
$175$	−995.518	−	1294.84i	−0.430023	−	0.559317i
$176$		0			0
$177$	712.512	−	712.512i	0.302574	−	0.302574i
$178$		0			0
$179$	−4187.67			−1.74861			−0.874304	−	0.485379i	$-0.838682\pi$
$179$	−4187.67			−1.74861			−0.874304	+	0.485379i	$0.838682\pi$
$180$		0			0
$181$	−2925.93			−1.20156			−0.600781	−	0.799414i	$-0.705143\pi$
$181$	−2925.93			−1.20156			−0.600781	+	0.799414i	$0.705143\pi$
$182$		0			0
$183$	−1544.29	+	1544.29i	−0.623810	+	0.623810i
$184$		0			0
$185$	1986.55	+	2263.06i	0.789483	+	0.899371i
$186$		0			0
$187$	1991.70	+	1991.70i	0.778862	+	0.778862i
$188$		0			0
$189$			1848.18i			0.711297i
$190$		0			0
$191$		−	758.994i		−	0.287534i	−0.989612	−	0.143767i	$-0.954078\pi$
$191$		−	758.994i		−	0.287534i	0.989612	−	0.143767i	$-0.0459215\pi$
$192$		0			0
$193$	−586.196	−	586.196i	−0.218629	−	0.218629i	0.589292	−	0.807920i	$-0.299407\pi$
$193$	−586.196	−	586.196i	−0.218629	−	0.218629i	−0.807920	+	0.589292i	$0.799407\pi$
$194$		0			0
$195$	−117.277	+	1802.41i	−0.0430684	+	0.661912i
$196$		0			0
$197$	−30.2257	+	30.2257i	−0.0109314	+	0.0109314i	−0.712551	−	0.701620i	$-0.752460\pi$
$197$	−30.2257	+	30.2257i	−0.0109314	+	0.0109314i	0.701620	+	0.712551i	$0.252460\pi$
$198$		0			0
$199$	−1491.16			−0.531184			−0.265592	−	0.964085i	$-0.585567\pi$
$199$	−1491.16			−0.531184			−0.265592	+	0.964085i	$0.585567\pi$
$200$		0			0
$201$	4361.04			1.53037
$202$		0			0
$203$	−1017.35	+	1017.35i	−0.351744	+	0.351744i
$204$		0			0
$205$	−280.804	+	4315.63i	−0.0956693	+	1.47033i
$206$		0			0
$207$	−37.1894	−	37.1894i	−0.0124872	−	0.0124872i
$208$		0			0
$209$		−	1346.32i		−	0.445585i
$210$		0			0
$211$		−	3689.79i		−	1.20387i	−0.798547	−	0.601933i	$-0.794398\pi$
$211$		−	3689.79i		−	1.20387i	0.798547	−	0.601933i	$-0.205602\pi$
$212$		0			0
$213$	−3621.33	−	3621.33i	−1.16493	−	1.16493i
$214$		0			0
$215$	2249.91	+	2563.07i	0.713686	+	0.813024i
$216$		0			0
$217$	−2311.22	+	2311.22i	−0.723023	+	0.723023i
$218$		0			0
$219$	166.274			0.0513049
$220$		0			0
$221$	−3039.89			−0.925273
$222$		0			0
$223$	4144.87	−	4144.87i	1.24467	−	1.24467i	0.286626	−	0.958042i	$-0.407466\pi$
$223$	4144.87	−	4144.87i	1.24467	−	1.24467i	0.958042	−	0.286626i	$-0.0925338\pi$
$224$		0			0
$225$	7.31936	−	56.0069i	0.00216870	−	0.0165946i
$226$		0			0
$227$	4522.77	+	4522.77i	1.32241	+	1.32241i	0.911822	+	0.410587i	$0.134676\pi$
$227$	4522.77	+	4522.77i	1.32241	+	1.32241i	0.410587	+	0.911822i	$0.365324\pi$
$228$		0			0
$229$		−	1301.65i		−	0.375615i	−0.982206	−	0.187807i	$-0.939862\pi$
$229$		−	1301.65i		−	0.375615i	0.982206	−	0.187807i	$-0.0601380\pi$
$230$		0			0
$231$		−	1955.91i		−	0.557098i
$232$		0			0
$233$	3272.46	+	3272.46i	0.920112	+	0.920112i	0.997037	−	0.0769247i	$-0.0245101\pi$
$233$	3272.46	+	3272.46i	0.920112	+	0.920112i	−0.0769247	+	0.997037i	$0.524510\pi$
$234$		0			0
$235$	−3071.18	+	2695.94i	−0.852519	+	0.748355i
$236$		0			0
$237$	−2230.10	+	2230.10i	−0.611225	+	0.611225i
$238$		0			0
$239$	4329.93			1.17188			0.585941	−	0.810354i	$-0.300725\pi$
$239$	4329.93			1.17188			0.585941	+	0.810354i	$0.300725\pi$
$240$		0			0
$241$	−1311.41			−0.350520			−0.175260	−	0.984522i	$-0.556077\pi$
$241$	−1311.41			−0.350520			−0.175260	+	0.984522i	$0.556077\pi$
$242$		0			0
$243$	−89.6445	+	89.6445i	−0.0236654	+	0.0236654i
$244$		0			0
$245$	1921.97	+	125.056i	0.501185	+	0.0326104i
$246$		0			0
$247$	1027.44	+	1027.44i	0.264673	+	0.264673i
$248$		0			0
$249$			1286.44i			0.327410i
$250$		0			0
$251$			2488.09i			0.625684i	0.949805	+	0.312842i	$0.101281\pi$
$251$			2488.09i			0.625684i	−0.949805	+	0.312842i	$0.898719\pi$
$252$		0			0
$253$	2391.04	+	2391.04i	0.594165	+	0.594165i
$254$		0			0
$255$	−5573.34	−	362.639i	−1.36869	−	0.0890561i
$256$		0			0
$257$	−2636.48	+	2636.48i	−0.639919	+	0.639919i	−0.950535	−	0.310616i	$-0.899465\pi$
$257$	−2636.48	+	2636.48i	−0.639919	+	0.639919i	0.310616	+	0.950535i	$0.399465\pi$
$258$		0			0
$259$	3519.27			0.844311
$260$		0			0
$261$	−49.7553			−0.0117999
$262$		0			0
$263$	1573.96	−	1573.96i	0.369028	−	0.369028i	−0.498095	−	0.867123i	$-0.665967\pi$
$263$	1573.96	−	1573.96i	0.369028	−	0.369028i	0.867123	+	0.498095i	$0.165967\pi$
$264$		0			0
$265$	3728.54	−	3272.98i	0.864312	−	0.758707i
$266$		0			0
$267$	4576.65	+	4576.65i	1.04901	+	1.04901i
$268$		0			0
$269$		−	5976.42i		−	1.35461i	−0.735704	−	0.677303i	$-0.763149\pi$
$269$		−	5976.42i		−	1.35461i	0.735704	−	0.677303i	$-0.236851\pi$
$270$		0			0
$271$			3883.45i			0.870491i	0.900312	+	0.435246i	$0.143338\pi$
$271$			3883.45i			0.870491i	−0.900312	+	0.435246i	$0.856662\pi$
$272$		0			0
$273$	1492.64	+	1492.64i	0.330911	+	0.330911i
$274$		0			0
$275$	−470.588	+	3600.89i	−0.103191	+	0.789607i
$276$		0			0
$277$	136.325	−	136.325i	0.0295702	−	0.0295702i	−0.692167	−	0.721737i	$-0.743344\pi$
$277$	136.325	−	136.325i	0.0295702	−	0.0295702i	0.721737	+	0.692167i	$0.243344\pi$
$278$		0			0
$279$	−113.034			−0.0242552
$280$		0			0
$281$	−3612.73			−0.766966			−0.383483	−	0.923548i	$-0.625275\pi$
$281$	−3612.73			−0.766966			−0.383483	+	0.923548i	$0.625275\pi$
$282$		0			0
$283$	3438.03	−	3438.03i	0.722155	−	0.722155i	−0.246889	−	0.969044i	$-0.579408\pi$
$283$	3438.03	−	3438.03i	0.722155	−	0.722155i	0.969044	+	0.246889i	$0.0794082\pi$
$284$		0			0
$285$	1761.14	+	2006.27i	0.366037	+	0.416986i
$286$		0			0
$287$	3573.94	+	3573.94i	0.735062	+	0.735062i
$288$		0			0
$289$		−	4486.86i		−	0.913262i
$290$		0			0
$291$		−	1966.67i		−	0.396180i
$292$		0			0
$293$	−1073.27	−	1073.27i	−0.213996	−	0.213996i	0.591966	−	0.805963i	$-0.298352\pi$
$293$	−1073.27	−	1073.27i	−0.213996	−	0.213996i	−0.805963	+	0.591966i	$0.798352\pi$
$294$		0			0
$295$	−141.967	+	2181.86i	−0.0280190	+	0.430620i
$296$		0			0
$297$	2905.70	−	2905.70i	0.567697	−	0.567697i
$298$		0			0
$299$	−3649.41			−0.705856
$300$		0			0
$301$	3985.81			0.763250
$302$		0			0
$303$	−2894.32	+	2894.32i	−0.548760	+	0.548760i
$304$		0			0
$305$	307.697	−	4728.95i	0.0577662	−	0.887800i
$306$		0			0
$307$	2493.39	+	2493.39i	0.463536	+	0.463536i	0.899812	−	0.436277i	$-0.143703\pi$
$307$	2493.39	+	2493.39i	0.463536	+	0.463536i	−0.436277	+	0.899812i	$0.643703\pi$
$308$		0			0
$309$			99.7488i			0.0183641i
$310$		0			0
$311$			4994.84i			0.910712i	0.890309	+	0.455356i	$0.150488\pi$
$311$			4994.84i			0.910712i	−0.890309	+	0.455356i	$0.849512\pi$
$312$		0			0
$313$	−781.883	−	781.883i	−0.141197	−	0.141197i	0.632975	−	0.774172i	$-0.281834\pi$
$313$	−781.883	−	781.883i	−0.141197	−	0.141197i	−0.774172	+	0.632975i	$0.781834\pi$
$314$		0			0
$315$	−43.5479	−	49.6093i	−0.00778936	−	0.00887356i
$316$		0			0
$317$	1141.41	−	1141.41i	0.202234	−	0.202234i	−0.598723	−	0.800956i	$-0.704325\pi$
$317$	1141.41	−	1141.41i	0.202234	−	0.202234i	0.800956	+	0.598723i	$0.204325\pi$
$318$		0			0
$319$	3198.95			0.561464
$320$		0			0
$321$	−8250.32			−1.43454
$322$		0			0
$323$	−3177.01	+	3177.01i	−0.547286	+	0.547286i
$324$		0			0
$325$	−2388.87	−	3107.12i	−0.407724	−	0.530314i
$326$		0			0
$327$	5869.79	+	5869.79i	0.992661	+	0.992661i
$328$		0			0
$329$			4775.97i			0.800327i
$330$		0			0
$331$		−	9143.85i		−	1.51840i	−0.650856	−	0.759202i	$-0.725590\pi$
$331$		−	9143.85i		−	1.51840i	0.650856	−	0.759202i	$-0.274410\pi$
$332$		0			0
$333$	86.0579	+	86.0579i	0.0141620	+	0.0141620i
$334$		0			0
$335$	−7111.69	+	6242.76i	−1.15986	+	1.01814i
$336$		0			0
$337$	4458.95	−	4458.95i	0.720755	−	0.720755i	−0.248004	−	0.968759i	$-0.579775\pi$
$337$	4458.95	−	4458.95i	0.720755	−	0.720755i	0.968759	+	0.248004i	$0.0797746\pi$
$338$		0			0
$339$	−9355.41			−1.49887
$340$		0			0
$341$	7267.39			1.15411
$342$		0			0
$343$	4760.74	−	4760.74i	0.749434	−	0.749434i
$344$		0			0
$345$	−6690.83	−	435.350i	−1.04412	−	0.0679376i
$346$		0			0
$347$	−1453.17	−	1453.17i	−0.224813	−	0.224813i	0.585709	−	0.810522i	$-0.300816\pi$
$347$	−1453.17	−	1453.17i	−0.224813	−	0.224813i	−0.810522	+	0.585709i	$0.800816\pi$
$348$		0			0
$349$		−	458.850i		−	0.0703772i	−0.999381	−	0.0351886i	$-0.988797\pi$
$349$		−	458.850i		−	0.0703772i	0.999381	−	0.0351886i	$-0.0112032\pi$
$350$		0			0
$351$			4434.93i			0.674413i
$352$		0			0
$353$	2666.42	+	2666.42i	0.402037	+	0.402037i	0.878950	−	0.476913i	$-0.158244\pi$
$353$	2666.42	+	2666.42i	0.402037	+	0.402037i	−0.476913	+	0.878950i	$0.658244\pi$
$354$		0			0
$355$	11089.3	+	721.543i	1.65791	+	0.107875i
$356$		0			0
$357$	−4615.49	+	4615.49i	−0.684251	+	0.684251i
$358$		0			0
$359$	−6721.44			−0.988145			−0.494073	−	0.869421i	$-0.664492\pi$
$359$	−6721.44			−0.988145			−0.494073	+	0.869421i	$0.664492\pi$
$360$		0			0
$361$	−4711.44			−0.686899
$362$		0			0
$363$	1774.23	−	1774.23i	0.256537	−	0.256537i
$364$		0			0
$365$	−271.148	+	238.019i	−0.0388837	+	0.0341328i
$366$		0			0
$367$	929.164	+	929.164i	0.132158	+	0.132158i	0.770091	−	0.637933i	$-0.220211\pi$
$367$	929.164	+	929.164i	0.132158	+	0.132158i	−0.637933	+	0.770091i	$0.720211\pi$
$368$		0			0
$369$			174.790i			0.0246590i
$370$		0			0
$371$		−	5798.22i		−	0.811398i
$372$		0			0
$373$	−89.0374	−	89.0374i	−0.0123597	−	0.0123597i	0.700900	−	0.713260i	$-0.252782\pi$
$373$	−89.0374	−	89.0374i	−0.0123597	−	0.0123597i	−0.713260	+	0.700900i	$0.752782\pi$
$374$		0			0
$375$	−4009.09	−	5981.56i	−0.552075	−	0.823697i
$376$		0			0
$377$	−2441.26	+	2441.26i	−0.333504	+	0.333504i
$378$		0			0
$379$	8951.06			1.21315			0.606576	−	0.795025i	$-0.292542\pi$
$379$	8951.06			1.21315			0.606576	+	0.795025i	$0.292542\pi$
$380$		0			0
$381$	4624.41			0.621826
$382$		0			0
$383$	3792.48	−	3792.48i	0.505970	−	0.505970i	−0.407317	−	0.913287i	$-0.633536\pi$
$383$	3792.48	−	3792.48i	0.505970	−	0.505970i	0.913287	+	0.407317i	$0.133536\pi$
$384$		0			0
$385$	2799.85	+	3189.57i	0.370633	+	0.422222i
$386$		0			0
$387$	97.4666	+	97.4666i	0.0128023	+	0.0128023i
$388$		0			0
$389$			3116.97i			0.406264i	0.979151	+	0.203132i	$0.0651120\pi$
$389$			3116.97i			0.406264i	−0.979151	+	0.203132i	$0.934888\pi$
$390$		0			0
$391$		−	11284.6i		−	1.45956i
$392$		0			0
$393$	−5242.85	−	5242.85i	−0.672944	−	0.672944i
$394$		0			0
$395$	444.342	−	6829.03i	0.0566008	−	0.869888i
$396$		0			0
$397$	2645.06	−	2645.06i	0.334388	−	0.334388i	−0.519862	−	0.854250i	$-0.674017\pi$
$397$	2645.06	−	2645.06i	0.334388	−	0.334388i	0.854250	+	0.519862i	$0.174017\pi$
$398$		0			0
$399$	3119.93			0.391458
$400$		0			0
$401$	248.852			0.0309902			0.0154951	−	0.999880i	$-0.495068\pi$
$401$	248.852			0.0309902			0.0154951	+	0.999880i	$0.495068\pi$
$402$		0			0
$403$	−5546.05	+	5546.05i	−0.685530	+	0.685530i
$404$		0			0
$405$	−520.200	+	7994.87i	−0.0638246	+	0.980910i
$406$		0			0
$407$	−5532.98	−	5532.98i	−0.673857	−	0.673857i
$408$		0			0
$409$			16002.4i			1.93464i	0.253565	+	0.967318i	$0.418397\pi$
$409$			16002.4i			1.93464i	−0.253565	+	0.967318i	$0.581603\pi$
$410$		0			0
$411$			5673.79i			0.680943i
$412$		0			0
$413$	1806.88	+	1806.88i	0.215281	+	0.215281i
$414$		0			0
$415$	−1841.52	−	2097.84i	−0.217824	−	0.248142i
$416$		0			0
$417$	3480.44	−	3480.44i	0.408724	−	0.408724i
$418$		0			0
$419$	−6214.46			−0.724573			−0.362286	−	0.932067i	$-0.618004\pi$
$419$	−6214.46			−0.724573			−0.362286	+	0.932067i	$0.618004\pi$
$420$		0			0
$421$	6181.66			0.715619			0.357810	−	0.933795i	$-0.383524\pi$
$421$	6181.66			0.715619			0.357810	+	0.933795i	$0.383524\pi$
$422$		0			0
$423$	−116.789	+	116.789i	−0.0134242	+	0.0134242i
$424$		0			0
$425$	9607.73	−	7386.77i	1.09657	−	0.843085i
$426$		0			0
$427$	−3916.22	−	3916.22i	−0.443839	−	0.443839i
$428$		0			0
$429$		−	4693.45i		−	0.528209i
$430$		0			0
$431$			1261.72i			0.141009i	0.997511	+	0.0705043i	$0.0224608\pi$
$431$			1261.72i			0.141009i	−0.997511	+	0.0705043i	$0.977539\pi$
$432$		0			0
$433$	6691.55	+	6691.55i	0.742668	+	0.742668i	0.973091	−	0.230423i	$-0.0740109\pi$
$433$	6691.55	+	6691.55i	0.742668	+	0.742668i	−0.230423	+	0.973091i	$0.574011\pi$
$434$		0			0
$435$	−4767.02	+	4184.57i	−0.525428	+	0.461229i
$436$		0			0
$437$	−3814.02	+	3814.02i	−0.417504	+	0.417504i
$438$		0			0
$439$	686.081			0.0745897			0.0372948	−	0.999304i	$-0.488126\pi$
$439$	686.081			0.0745897			0.0372948	+	0.999304i	$0.488126\pi$
$440$		0			0
$441$	77.8428			0.00840544
$442$		0			0
$443$	933.427	−	933.427i	0.100109	−	0.100109i	−0.655278	−	0.755388i	$-0.727449\pi$
$443$	933.427	−	933.427i	0.100109	−	0.100109i	0.755388	+	0.655278i	$0.227449\pi$
$444$		0			0
$445$	−14014.7	−	911.888i	−1.49294	−	0.0971408i
$446$		0			0
$447$	−8064.64	−	8064.64i	−0.853343	−	0.853343i
$448$		0			0
$449$			10101.6i			1.06175i	0.847450	+	0.530875i	$0.178137\pi$
$449$			10101.6i			1.06175i	−0.847450	+	0.530875i	$0.821863\pi$
$450$		0			0
$451$		−	11237.9i		−	1.17333i
$452$		0			0
$453$	−11313.7	−	11313.7i	−1.17343	−	1.17343i
$454$		0			0
$455$	−4570.78	−	297.406i	−0.470948	−	0.0306431i
$456$		0			0
$457$	6537.04	−	6537.04i	0.669124	−	0.669124i	−0.288389	−	0.957513i	$-0.593120\pi$
$457$	6537.04	−	6537.04i	0.669124	−	0.669124i	0.957513	+	0.288389i	$0.0931197\pi$
$458$		0			0
$459$	−13713.5			−1.39454
$460$		0			0
$461$	−12652.2			−1.27825			−0.639124	−	0.769103i	$-0.720703\pi$
$461$	−12652.2			−1.27825			−0.639124	+	0.769103i	$0.720703\pi$
$462$		0			0
$463$	9841.39	−	9841.39i	0.987836	−	0.987836i	−0.0120905	−	0.999927i	$-0.503849\pi$
$463$	9841.39	−	9841.39i	0.987836	−	0.987836i	0.999927	+	0.0120905i	$0.00384862\pi$
$464$		0			0
$465$	−10829.7	+	9506.52i	−1.08004	+	0.948074i
$466$		0			0
$467$	−1406.79	−	1406.79i	−0.139397	−	0.139397i	0.633965	−	0.773362i	$-0.281426\pi$
$467$	−1406.79	−	1406.79i	−0.139397	−	0.139397i	−0.773362	+	0.633965i	$0.781426\pi$
$468$		0			0
$469$			11059.3i			1.08885i
$470$		0			0
$471$		−	3332.86i		−	0.326051i
$472$		0			0
$473$	−6266.48	−	6266.48i	−0.609161	−	0.609161i
$474$		0			0
$475$	−5743.88	−	750.648i	−0.554836	−	0.0725097i
$476$		0			0
$477$	141.786	−	141.786i	0.0136099	−	0.0136099i
$478$		0			0
$479$	−7266.01			−0.693095			−0.346548	−	0.938032i	$-0.612646\pi$
$479$	−7266.01			−0.693095			−0.346548	+	0.938032i	$0.612646\pi$
$480$		0			0
$481$	8444.90			0.800529
$482$		0			0
$483$	−5540.93	+	5540.93i	−0.521989	+	0.521989i
$484$		0			0
$485$	2815.26	+	3207.11i	0.263576	+	0.300263i
$486$		0			0
$487$	−1881.59	−	1881.59i	−0.175078	−	0.175078i	0.614128	−	0.789206i	$-0.289508\pi$
$487$	−1881.59	−	1881.59i	−0.175078	−	0.175078i	−0.789206	+	0.614128i	$0.789508\pi$
$488$		0			0
$489$		−	15710.6i		−	1.45288i
$490$		0			0
$491$			7998.87i			0.735201i	0.929984	+	0.367601i	$0.119821\pi$
$491$			7998.87i			0.735201i	−0.929984	+	0.367601i	$0.880179\pi$
$492$		0			0
$493$	−7548.77	−	7548.77i	−0.689613	−	0.689613i
$494$		0			0
$495$	−9.52977	+	146.462i	−0.000865316	+	0.0132989i
$496$		0			0
$497$	9183.45	−	9183.45i	0.828841	−	0.828841i
$498$		0			0
$499$	16852.3			1.51185			0.755926	−	0.654658i	$-0.227187\pi$
$499$	16852.3			1.51185			0.755926	+	0.654658i	$0.227187\pi$
$500$		0			0
$501$	11182.4			0.997188
$502$		0			0
$503$	−5639.57	+	5639.57i	−0.499912	+	0.499912i	−0.911411	−	0.411498i	$-0.865006\pi$
$503$	−5639.57	+	5639.57i	−0.499912	+	0.499912i	0.411498	+	0.911411i	$0.365006\pi$
$504$		0			0
$505$	576.688	−	8863.03i	0.0508164	−	0.780989i
$506$		0			0
$507$	−4422.69	−	4422.69i	−0.387413	−	0.387413i
$508$		0			0
$509$		−	6988.53i		−	0.608568i	−0.952581	−	0.304284i	$-0.901583\pi$
$509$		−	6988.53i		−	0.608568i	0.952581	−	0.304284i	$-0.0984172\pi$
$510$		0			0
$511$			421.660i			0.0365032i
$512$		0			0
$513$	4634.96	+	4634.96i	0.398906	+	0.398906i
$514$		0			0
$515$	−142.789	−	162.664i	−0.0122175	−	0.0139181i
$516$		0			0
$517$	7508.77	−	7508.77i	0.638753	−	0.638753i
$518$		0			0
$519$	8636.38			0.730434
$520$		0			0
$521$	17064.2			1.43493			0.717465	−	0.696595i	$-0.245302\pi$
$521$	17064.2			1.43493			0.717465	+	0.696595i	$0.245302\pi$
$522$		0			0
$523$	−488.933	+	488.933i	−0.0408787	+	0.0408787i	−0.727251	−	0.686372i	$-0.759202\pi$
$523$	−488.933	+	488.933i	−0.0408787	+	0.0408787i	0.686372	+	0.727251i	$0.259202\pi$
$524$		0			0
$525$	−8344.58	−	1090.53i	−0.693691	−	0.0906561i
$526$		0			0
$527$	−17149.3	−	17149.3i	−1.41753	−	1.41753i
$528$		0			0
$529$		−	1380.24i		−	0.113441i
$530$		0			0
$531$			88.3688i			0.00722199i
$532$		0			0
$533$	8576.10	+	8576.10i	0.696946	+	0.696946i
$534$		0			0
$535$	13454.1	−	11810.2i	1.08723	−	0.954391i
$536$		0			0
$537$	−15257.2	+	15257.2i	−1.22606	+	1.22606i
$538$		0			0
$539$	−5004.80			−0.399948
$540$		0			0
$541$	3084.77			0.245147			0.122573	−	0.992459i	$-0.460885\pi$
$541$	3084.77			0.245147			0.122573	+	0.992459i	$0.460885\pi$
$542$		0			0
$543$	−10660.2	+	10660.2i	−0.842492	+	0.842492i
$544$		0			0
$545$	−17974.6	−	1169.54i	−1.41274	−	0.0919226i
$546$		0			0
$547$	−3748.46	−	3748.46i	−0.293003	−	0.293003i	0.545262	−	0.838265i	$-0.316430\pi$
$547$	−3748.46	−	3748.46i	−0.293003	−	0.293003i	−0.838265	+	0.545262i	$0.816430\pi$
$548$		0			0
$549$		−	191.530i		−	0.0148894i
$550$		0			0
$551$			5102.73i			0.394526i
$552$		0			0
$553$	−5655.38	−	5655.38i	−0.434884	−	0.434884i
$554$		0			0
$555$	15482.9	+	1007.42i	1.18416	+	0.0770497i
$556$		0			0
$557$	10556.2	−	10556.2i	0.803017	−	0.803017i	−0.180549	−	0.983566i	$-0.557788\pi$
$557$	10556.2	−	10556.2i	0.803017	−	0.803017i	0.983566	+	0.180549i	$0.0577875\pi$
$558$		0			0
$559$	9564.44			0.723672
$560$		0			0
$561$	14512.9			1.09222
$562$		0			0
$563$	10411.3	−	10411.3i	0.779371	−	0.779371i	−0.200353	−	0.979724i	$-0.564209\pi$
$563$	10411.3	−	10411.3i	0.779371	−	0.779371i	0.979724	+	0.200353i	$0.0642089\pi$
$564$		0			0
$565$	15256.2	−	13392.1i	1.13598	−	0.997186i
$566$		0			0
$567$	6620.86	+	6620.86i	0.490388	+	0.490388i
$568$		0			0
$569$		−	7846.12i		−	0.578078i	−0.957317	−	0.289039i	$-0.906664\pi$
$569$		−	7846.12i		−	0.578078i	0.957317	−	0.289039i	$-0.0933357\pi$
$570$		0			0
$571$		−	1800.64i		−	0.131970i	−0.997821	−	0.0659848i	$-0.978981\pi$
$571$		−	1800.64i		−	0.131970i	0.997821	−	0.0659848i	$-0.0210189\pi$
$572$		0			0
$573$	−2765.29	−	2765.29i	−0.201608	−	0.201608i
$574$		0			0
$575$	11534.1	−	8867.87i	0.836534	−	0.643158i
$576$		0			0
$577$	−15299.1	+	15299.1i	−1.10383	+	1.10383i	−0.109887	+	0.993944i	$0.535049\pi$
$577$	−15299.1	+	15299.1i	−1.10383	+	1.10383i	−0.993944	+	0.109887i	$0.964951\pi$
$578$		0			0
$579$	−4271.45			−0.306589
$580$		0			0
$581$	−3262.34			−0.232951
$582$		0			0
$583$	−9115.95	+	9115.95i	−0.647589	+	0.647589i
$584$		0			0
$585$	−104.499	−	119.044i	−0.00738544	−	0.00841342i
$586$		0			0
$587$	5400.19	+	5400.19i	0.379710	+	0.379710i	0.870997	−	0.491287i	$-0.163474\pi$
$587$	5400.19	+	5400.19i	0.379710	+	0.379710i	−0.491287	+	0.870997i	$0.663474\pi$
$588$		0			0
$589$			11592.4i			0.810963i
$590$		0			0
$591$			220.246i			0.0153295i
$592$		0			0
$593$	5379.58	+	5379.58i	0.372535	+	0.372535i	0.868400	−	0.495865i	$-0.165149\pi$
$593$	5379.58	+	5379.58i	0.372535	+	0.372535i	−0.495865	+	0.868400i	$0.665149\pi$
$594$		0			0
$595$	919.628	−	14133.6i	0.0633631	−	0.973818i
$596$		0			0
$597$	−5432.84	+	5432.84i	−0.372448	+	0.372448i
$598$		0			0
$599$	−10474.4			−0.714476			−0.357238	−	0.934013i	$-0.616281\pi$
$599$	−10474.4			−0.714476			−0.357238	+	0.934013i	$0.616281\pi$
$600$		0			0
$601$	−29203.8			−1.98211			−0.991055	−	0.133455i	$-0.957393\pi$
$601$	−29203.8			−1.98211			−0.991055	+	0.133455i	$0.957393\pi$
$602$		0			0
$603$	−270.438	+	270.438i	−0.0182638	+	0.0182638i
$604$		0			0
$605$	−353.512	+	5433.08i	−0.0237559	+	0.365101i
$606$		0			0
$607$	16886.0	+	16886.0i	1.12913	+	1.12913i	0.990319	+	0.138813i	$0.0443288\pi$
$607$	16886.0	+	16886.0i	1.12913	+	1.12913i	0.138813	+	0.990319i	$0.455671\pi$
$608$		0			0
$609$			7413.15i			0.493261i
$610$		0			0
$611$			11460.5i			0.758826i
$612$		0			0
$613$	7827.59	+	7827.59i	0.515748	+	0.515748i	0.916282	−	0.400534i	$-0.131175\pi$
$613$	7827.59	+	7827.59i	0.515748	+	0.515748i	−0.400534	+	0.916282i	$0.631175\pi$
$614$		0			0
$615$	14700.3	+	16746.5i	0.963861	+	1.09802i
$616$		0			0
$617$	11193.8	−	11193.8i	0.730383	−	0.730383i	−0.240312	−	0.970696i	$-0.577250\pi$
$617$	11193.8	−	11193.8i	0.730383	−	0.730383i	0.970696	+	0.240312i	$0.0772498\pi$
$618$		0			0
$619$	13112.7			0.851445			0.425723	−	0.904854i	$-0.360020\pi$
$619$	13112.7			0.851445			0.425723	+	0.904854i	$0.360020\pi$
$620$		0			0
$621$	−16463.2			−1.06384
$622$		0			0
$623$	−11606.1	+	11606.1i	−0.746368	+	0.746368i
$624$		0			0
$625$	15100.2	+	4015.38i	0.966416	+	0.256984i
$626$		0			0
$627$	−4905.14	−	4905.14i	−0.312428	−	0.312428i
$628$		0			0
$629$			26113.0i			1.65532i
$630$		0			0
$631$			26227.5i			1.65468i	0.561704	+	0.827338i	$0.310146\pi$
$631$			26227.5i			1.65468i	−0.561704	+	0.827338i	$0.689854\pi$
$632$		0			0
$633$	−13443.2	−	13443.2i	−0.844108	−	0.844108i
$634$		0			0
$635$	−7541.17	+	6619.77i	−0.471279	+	0.413697i
$636$		0			0
$637$	3819.37	−	3819.37i	0.237565	−	0.237565i
$638$		0			0
$639$	449.133			0.0278050
$640$		0			0
$641$	−15346.9			−0.945659			−0.472829	−	0.881154i	$-0.656767\pi$
$641$	−15346.9			−0.945659			−0.472829	+	0.881154i	$0.656767\pi$
$642$		0			0
$643$	2266.75	−	2266.75i	0.139023	−	0.139023i	−0.634170	−	0.773193i	$-0.718658\pi$
$643$	2266.75	−	2266.75i	0.139023	−	0.139023i	0.773193	+	0.634170i	$0.218658\pi$
$644$		0			0
$645$	17535.4	+	1140.97i	1.07048	+	0.0696523i
$646$		0			0
$647$	−9000.05	−	9000.05i	−0.546876	−	0.546876i	0.378660	−	0.925536i	$-0.376385\pi$
$647$	−9000.05	−	9000.05i	−0.546876	−	0.546876i	−0.925536	+	0.378660i	$0.876385\pi$
$648$		0			0
$649$		−	5681.55i		−	0.343637i
$650$		0			0
$651$			16841.2i			1.01392i
$652$		0			0
$653$	17384.8	+	17384.8i	1.04184	+	1.04184i	0.999086	+	0.0427498i	$0.0136118\pi$
$653$	17384.8	+	17384.8i	1.04184	+	1.04184i	0.0427498	+	0.999086i	$0.486388\pi$
$654$		0			0
$655$	16054.7	+	1044.63i	0.957726	+	0.0623161i
$656$		0			0
$657$	−10.3110	+	10.3110i	−0.000612285	+	0.000612285i
$658$		0			0
$659$	21162.3			1.25093			0.625467	−	0.780251i	$-0.284909\pi$
$659$	21162.3			1.25093			0.625467	+	0.780251i	$0.284909\pi$
$660$		0			0
$661$	−9011.75			−0.530282			−0.265141	−	0.964210i	$-0.585418\pi$
$661$	−9011.75			−0.530282			−0.265141	+	0.964210i	$0.585418\pi$
$662$		0			0
$663$	−11075.4	+	11075.4i	−0.648769	+	0.648769i
$664$		0			0
$665$	−5087.76	+	4466.12i	−0.296684	+	0.260434i
$666$		0			0
$667$	−9062.35	−	9062.35i	−0.526080	−	0.526080i
$668$		0			0
$669$		−	30202.5i		−	1.74544i
$670$		0			0
$671$			12314.1i			0.708468i
$672$		0			0
$673$	13638.8	+	13638.8i	0.781182	+	0.781182i	0.980030	−	0.198848i	$-0.0637201\pi$
$673$	13638.8	+	13638.8i	0.781182	+	0.781182i	−0.198848	+	0.980030i	$0.563720\pi$
$674$		0			0
$675$	−10776.6	−	14016.8i	−0.614508	−	0.799269i
$676$		0			0
$677$	−14189.7	+	14189.7i	−0.805543	+	0.805543i	−0.983956	−	0.178412i	$-0.942904\pi$
$677$	−14189.7	+	14189.7i	−0.805543	+	0.805543i	0.178412	+	0.983956i	$0.442904\pi$
$678$		0			0
$679$	4987.35			0.281881
$680$		0			0
$681$	32956.1			1.85445
$682$		0			0
$683$	−5657.98	+	5657.98i	−0.316979	+	0.316979i	−0.847606	−	0.530627i	$-0.821957\pi$
$683$	−5657.98	+	5657.98i	−0.316979	+	0.316979i	0.530627	+	0.847606i	$0.321957\pi$
$684$		0			0
$685$	−8121.94	−	9252.43i	−0.453027	−	0.516084i
$686$		0			0
$687$	−4742.39	−	4742.39i	−0.263368	−	0.263368i
$688$		0			0
$689$		−	13913.5i		−	0.769323i
$690$		0			0
$691$			34070.0i			1.87567i	0.347086	+	0.937833i	$0.387171\pi$
$691$			34070.0i			1.87567i	−0.347086	+	0.937833i	$0.612829\pi$
$692$		0			0
$693$	121.290	+	121.290i	0.00664854	+	0.00664854i
$694$		0			0
$695$	−693.472	+	10657.9i	−0.0378488	+	0.581692i
$696$		0			0
$697$	−26518.7	+	26518.7i	−1.44113	+	1.44113i
$698$		0			0
$699$	23845.5			1.29030
$700$		0			0
$701$	−17802.0			−0.959160			−0.479580	−	0.877498i	$-0.659211\pi$
$701$	−17802.0			−0.959160			−0.479580	+	0.877498i	$0.659211\pi$
$702$		0			0
$703$	8825.81	−	8825.81i	0.473502	−	0.473502i
$704$		0			0
$705$	−1367.16	+	21011.7i	−0.0730358	+	1.12248i
$706$		0			0
$707$	−7339.80	−	7339.80i	−0.390441	−	0.390441i
$708$		0			0
$709$			19283.7i			1.02146i	0.859742	+	0.510729i	$0.170624\pi$
$709$			19283.7i			1.02146i	−0.859742	+	0.510729i	$0.829376\pi$
$710$		0			0
$711$		−	276.586i		−	0.0145890i
$712$		0			0
$713$	−20587.9	−	20587.9i	−1.08138	−	1.08138i
$714$		0			0
$715$	6718.59	+	7653.75i	0.351414	+	0.400327i
$716$		0			0
$717$	15775.5	−	15775.5i	0.821682	−	0.821682i
$718$		0			0
$719$	9212.84			0.477859			0.238930	−	0.971037i	$-0.423203\pi$
$719$	9212.84			0.477859			0.238930	+	0.971037i	$0.423203\pi$
$720$		0			0
$721$	−252.957			−0.0130660
$722$		0			0
$723$	−4777.94	+	4777.94i	−0.245772	+	0.245772i
$724$		0			0
$725$	1783.59	−	13647.8i	0.0913666	−	0.699127i
$726$		0			0
$727$	4245.50	+	4245.50i	0.216585	+	0.216585i	0.807057	−	0.590473i	$-0.201059\pi$
$727$	4245.50	+	4245.50i	0.216585	+	0.216585i	−0.590473	+	0.807057i	$0.701059\pi$
$728$		0			0
$729$			20001.3i			1.01617i
$730$		0			0
$731$			29574.8i			1.49640i
$732$		0			0
$733$	7930.54	+	7930.54i	0.399620	+	0.399620i	0.878099	−	0.478479i	$-0.158812\pi$
$733$	7930.54	+	7930.54i	0.399620	+	0.399620i	−0.478479	+	0.878099i	$0.658812\pi$
$734$		0			0
$735$	7458.06	−	6546.81i	0.374278	−	0.328548i
$736$		0			0
$737$	17387.4	−	17387.4i	0.869029	−	0.869029i
$738$		0			0
$739$	−411.087			−0.0204629			−0.0102314	−	0.999948i	$-0.503257\pi$
$739$	−411.087			−0.0204629			−0.0102314	+	0.999948i	$0.503257\pi$
$740$		0			0
$741$	7486.64			0.371159
$742$		0			0
$743$	1624.05	−	1624.05i	0.0801894	−	0.0801894i	−0.665874	−	0.746064i	$-0.731941\pi$
$743$	1624.05	−	1624.05i	0.0801894	−	0.0801894i	0.746064	+	0.665874i	$0.231941\pi$
$744$		0			0
$745$	24695.7	+	1606.86i	1.21447	+	0.0790214i
$746$		0			0
$747$	−79.7752	−	79.7752i	−0.00390739	−	0.00390739i
$748$		0			0
$749$		−	20922.3i		−	1.02067i
$750$		0			0
$751$		−	29981.1i		−	1.45676i	−0.685175	−	0.728378i	$-0.740274\pi$
$751$		−	29981.1i		−	1.45676i	0.685175	−	0.728378i	$-0.259726\pi$
$752$		0			0
$753$	9065.00	+	9065.00i	0.438708	+	0.438708i
$754$		0			0
$755$	34644.9	+	2254.23i	1.67001	+	0.108662i
$756$		0			0
$757$	5299.37	−	5299.37i	0.254437	−	0.254437i	−0.568350	−	0.822787i	$-0.692418\pi$
$757$	5299.37	−	5299.37i	0.254437	−	0.254437i	0.822787	+	0.568350i	$0.192418\pi$
$758$		0			0
$759$	17422.9			0.833215
$760$		0			0
$761$	−3511.34			−0.167261			−0.0836307	−	0.996497i	$-0.526652\pi$
$761$	−3511.34			−0.167261			−0.0836307	+	0.996497i	$0.526652\pi$
$762$		0			0
$763$	−14885.4	+	14885.4i	−0.706275	+	0.706275i
$764$		0			0
$765$	368.103	−	323.127i	0.0173971	−	0.0152715i
$766$		0			0
$767$	4335.83	+	4335.83i	0.204117	+	0.204117i
$768$		0			0
$769$		−	37995.1i		−	1.78171i	−0.454286	−	0.890856i	$-0.650105\pi$
$769$		−	37995.1i		−	1.78171i	0.454286	−	0.890856i	$-0.349895\pi$
$770$		0			0
$771$			19211.3i			0.897378i
$772$		0			0
$773$	−8421.79	−	8421.79i	−0.391864	−	0.391864i	0.483487	−	0.875351i	$-0.339370\pi$
$773$	−8421.79	−	8421.79i	−0.391864	−	0.391864i	−0.875351	+	0.483487i	$0.839370\pi$
$774$		0			0
$775$	4051.96	−	31005.2i	0.187807	−	1.43708i
$776$		0			0
$777$	12821.9	−	12821.9i	0.592001	−	0.592001i
$778$		0			0
$779$	17925.8			0.824467
$780$		0			0
$781$	−28876.4			−1.32302
$782$		0			0
$783$	−11013.0	+	11013.0i	−0.502645	+	0.502645i
$784$		0			0
$785$	4770.93	+	5434.99i	0.216919	+	0.247112i
$786$		0			0
$787$	−9436.26	−	9436.26i	−0.427403	−	0.427403i	0.460340	−	0.887743i	$-0.347728\pi$
$787$	−9436.26	−	9436.26i	−0.427403	−	0.427403i	−0.887743	+	0.460340i	$0.847728\pi$
$788$		0			0
$789$		−	11469.0i		−	0.517499i
$790$		0			0
$791$		−	23724.7i		−	1.06644i
$792$		0			0
$793$	−9397.45	−	9397.45i	−0.420824	−	0.420824i
$794$		0			0
$795$	1659.79	−	25509.1i	0.0740461	−	1.13800i
$796$		0			0
$797$	−18825.0	+	18825.0i	−0.836658	+	0.836658i	−0.988417	−	0.151760i	$-0.951506\pi$
$797$	−18825.0	+	18825.0i	−0.836658	+	0.836658i	0.151760	+	0.988417i	$0.451506\pi$
$798$		0			0
$799$	−35437.8			−1.56909
$800$		0			0
$801$	−567.616			−0.0250383
$802$		0			0
$803$	662.933	−	662.933i	0.0291338	−	0.0291338i
$804$		0			0
$805$	1104.02	−	16967.5i	0.0483374	−	0.742889i
$806$		0			0
$807$	−21774.3	−	21774.3i	−0.949802	−	0.949802i
$808$		0			0
$809$		−	8845.58i		−	0.384418i	−0.981354	−	0.192209i	$-0.938435\pi$
$809$		−	8845.58i		−	0.384418i	0.981354	−	0.192209i	$-0.0615651\pi$
$810$		0			0
$811$		−	26366.4i		−	1.14161i	−0.821084	−	0.570807i	$-0.806631\pi$
$811$		−	26366.4i		−	1.14161i	0.821084	−	0.570807i	$-0.193369\pi$
$812$		0			0
$813$	14148.8	+	14148.8i	0.610358	+	0.610358i
$814$		0			0
$815$	22489.4	+	25619.7i	0.966588	+	1.10113i
$816$		0			0
$817$	9995.84	−	9995.84i	0.428042	−	0.428042i
$818$		0			0
$819$	−185.124			−0.00789834
$820$		0			0
$821$	−23708.8			−1.00785			−0.503925	−	0.863748i	$-0.668111\pi$
$821$	−23708.8			−1.00785			−0.503925	+	0.863748i	$0.668111\pi$
$822$		0			0
$823$	5488.36	−	5488.36i	0.232457	−	0.232457i	−0.581260	−	0.813718i	$-0.697440\pi$
$823$	5488.36	−	5488.36i	0.232457	−	0.232457i	0.813718	+	0.581260i	$0.197440\pi$
$824$		0			0
$825$	11404.8	+	14833.9i	0.481291	+	0.625998i
$826$		0			0
$827$	−17844.4	−	17844.4i	−0.750317	−	0.750317i	0.224221	−	0.974538i	$-0.428016\pi$
$827$	−17844.4	−	17844.4i	−0.750317	−	0.750317i	−0.974538	+	0.224221i	$0.928016\pi$
$828$		0			0
$829$		−	21290.2i		−	0.891965i	−0.895042	−	0.445983i	$-0.852854\pi$
$829$		−	21290.2i		−	0.891965i	0.895042	−	0.445983i	$-0.147146\pi$
$830$		0			0
$831$		−	993.360i		−	0.0414672i
$832$		0			0
$833$	11810.1	+	11810.1i	0.491233	+	0.491233i
$834$		0			0
$835$	−18235.4	+	16007.4i	−0.755765	+	0.663423i
$836$		0			0
$837$	−25019.3	+	25019.3i	−1.03321	+	1.03321i
$838$		0			0
$839$	18663.5			0.767982			0.383991	−	0.923337i	$-0.374549\pi$
$839$	18663.5			0.767982			0.383991	+	0.923337i	$0.374549\pi$
$840$		0			0
$841$	12264.6			0.502873
$842$		0			0
$843$	−13162.5	+	13162.5i	−0.537769	+	0.537769i
$844$		0			0
$845$	13543.2	+	881.213i	0.551362	+	0.0358753i
$846$		0			0
$847$	4499.33	+	4499.33i	0.182525	+	0.182525i
$848$		0			0
$849$		−	25052.0i		−	1.01270i
$850$		0			0
$851$			31348.9i			1.26278i
$852$		0			0
$853$	−29213.1	−	29213.1i	−1.17261	−	1.17261i	−0.981585	−	0.191028i	$-0.938818\pi$
$853$	−29213.1	−	29213.1i	−1.17261	−	1.17261i	−0.191028	−	0.981585i	$-0.561182\pi$
$854$		0			0
$855$	−233.625	−	15.2012i	−0.00934480	−	0.000608035i
$856$		0			0
$857$	−20195.6	+	20195.6i	−0.804982	+	0.804982i	−0.983870	−	0.178887i	$-0.942750\pi$
$857$	−20195.6	+	20195.6i	−0.804982	+	0.804982i	0.178887	+	0.983870i	$0.442750\pi$
$858$		0			0
$859$	−18130.9			−0.720163			−0.360081	−	0.932921i	$-0.617251\pi$
$859$	−18130.9			−0.720163			−0.360081	+	0.932921i	$0.617251\pi$
$860$		0			0
$861$	26042.3			1.03080
$862$		0			0
$863$	−20555.9	+	20555.9i	−0.810813	+	0.810813i	−0.984756	−	0.173943i	$-0.944349\pi$
$863$	−20555.9	+	20555.9i	−0.810813	+	0.810813i	0.173943	+	0.984756i	$0.444349\pi$
$864$		0			0
$865$	−14083.6	+	12362.8i	−0.553593	+	0.485953i
$866$		0			0
$867$	−16347.2	−	16347.2i	−0.640347	−	0.640347i
$868$		0			0
$869$			17782.7i			0.694175i
$870$		0			0
$871$			26538.2i			1.03239i
$872$		0			0
$873$	121.958	+	121.958i	0.00472811	+	0.00472811i
$874$		0			0
$875$	15168.8	−	10166.8i	0.586058	−	0.392800i
$876$		0			0
$877$	−7869.09	+	7869.09i	−0.302988	+	0.302988i	−0.842182	−	0.539194i	$-0.818729\pi$
$877$	−7869.09	+	7869.09i	−0.302988	+	0.302988i	0.539194	+	0.842182i	$0.318729\pi$
$878$		0			0
$879$	−7820.60			−0.300094
$880$		0			0
$881$	−8171.00			−0.312472			−0.156236	−	0.987720i	$-0.549936\pi$
$881$	−8171.00			−0.312472			−0.156236	+	0.987720i	$0.549936\pi$
$882$		0			0
$883$	8770.49	−	8770.49i	0.334259	−	0.334259i	−0.519943	−	0.854201i	$-0.674047\pi$
$883$	8770.49	−	8770.49i	0.334259	−	0.334259i	0.854201	+	0.519943i	$0.174047\pi$
$884$		0			0
$885$	7432.08	+	8466.55i	0.282290	+	0.321582i
$886$		0			0
$887$	−17832.7	−	17832.7i	−0.675045	−	0.675045i	0.283830	−	0.958875i	$-0.408395\pi$
$887$	−17832.7	−	17832.7i	−0.675045	−	0.675045i	−0.958875	+	0.283830i	$0.908395\pi$
$888$		0			0
$889$			11727.2i			0.442427i
$890$		0			0
$891$		−	20818.6i		−	0.782771i
$892$		0			0
$893$	11977.4	+	11977.4i	0.448835	+	0.448835i
$894$		0			0
$895$	3039.96	−	46720.7i	0.113536	−	1.74492i
$896$		0			0
$897$	−13296.1	+	13296.1i	−0.494922	+	0.494922i
$898$		0			0
$899$	−27544.3			−1.02186
$900$		0			0
$901$	43023.0			1.59079
$902$		0			0
$903$	14521.7	−	14521.7i	0.535164	−	0.535164i
$904$		0			0
$905$	2124.03	−	32643.8i	0.0780166	−	1.19903i
$906$		0			0
$907$	−14576.9	−	14576.9i	−0.533647	−	0.533647i	0.388009	−	0.921656i	$-0.373163\pi$
$907$	−14576.9	−	14576.9i	−0.533647	−	0.533647i	−0.921656	+	0.388009i	$0.873163\pi$
$908$		0			0
$909$		−	358.966i		−	0.0130981i
$910$		0			0
$911$		−	12206.6i		−	0.443931i	−0.975055	−	0.221966i	$-0.928753\pi$
$911$		−	12206.6i		−	0.443931i	0.975055	−	0.221966i	$-0.0712472\pi$
$912$		0			0
$913$	5129.04	+	5129.04i	0.185922	+	0.185922i
$914$		0			0
$915$	−16108.2	−	18350.3i	−0.581990	−	0.662997i
$916$		0			0
$917$	13295.5	−	13295.5i	0.478797	−	0.478797i
$918$		0			0
$919$	−23873.7			−0.856933			−0.428466	−	0.903558i	$-0.640946\pi$
$919$	−23873.7			−0.856933			−0.428466	+	0.903558i	$0.640946\pi$
$920$		0			0
$921$	18168.6			0.650030
$922$		0			0
$923$	22036.8	−	22036.8i	0.785861	−	0.785861i
$924$		0			0
$925$	−26690.5	+	20520.6i	−0.948734	+	0.729421i
$926$		0			0
$927$	−6.18564	−	6.18564i	−0.000219162	−	0.000219162i
$928$		0			0
$929$			35418.8i			1.25087i	0.780278	+	0.625433i	$0.215078\pi$
$929$			35418.8i			1.25087i	−0.780278	+	0.625433i	$0.784922\pi$
$930$		0			0
$931$		−	7983.29i		−	0.281033i
$932$		0			0
$933$	18198.0	+	18198.0i	0.638559	+	0.638559i
$934$		0			0
$935$	−23666.7	+	20775.0i	−0.827789	+	0.726647i
$936$		0			0
$937$	−12118.3	+	12118.3i	−0.422504	+	0.422504i	−0.886065	−	0.463561i	$-0.846572\pi$
$937$	−12118.3	+	12118.3i	−0.422504	+	0.422504i	0.463561	+	0.886065i	$0.346572\pi$
$938$		0			0
$939$	−5697.36			−0.198005
$940$		0			0
$941$	18810.5			0.651652			0.325826	−	0.945430i	$-0.394358\pi$
$941$	18810.5			0.651652			0.325826	+	0.945430i	$0.394358\pi$
$942$		0			0
$943$	−31835.9	+	31835.9i	−1.09938	+	1.09938i
$944$		0			0
$945$	−20619.7	−	1341.65i	−0.709796	−	0.0461841i
$946$		0			0
$947$	10061.3	+	10061.3i	0.345248	+	0.345248i	0.858336	−	0.513088i	$-0.171499\pi$
$947$	10061.3	+	10061.3i	0.345248	+	0.345248i	−0.513088	+	0.858336i	$0.671499\pi$
$948$		0			0
$949$			1011.83i			0.0346104i
$950$		0			0
$951$		−	8317.16i		−	0.283599i
$952$		0			0
$953$	−4617.23	−	4617.23i	−0.156943	−	0.156943i	0.624267	−	0.781211i	$-0.285398\pi$
$953$	−4617.23	−	4617.23i	−0.156943	−	0.156943i	−0.781211	+	0.624267i	$0.785398\pi$
$954$		0			0
$955$	8467.91	+	550.979i	0.286927	+	0.0186694i
$956$		0			0
$957$	11654.9	−	11654.9i	0.393679	−	0.393679i
$958$		0			0
$959$	−14388.4			−0.484489
$960$		0			0
$961$	−32784.3			−1.10048
$962$		0			0
$963$	511.621	−	511.621i	0.0171202	−	0.0171202i
$964$		0			0
$965$	6965.58	−	6114.50i	0.232363	−	0.203972i
$966$		0			0
$967$	−19358.2	−	19358.2i	−0.643761	−	0.643761i	0.307717	−	0.951478i	$-0.400435\pi$
$967$	−19358.2	−	19358.2i	−0.643761	−	0.643761i	−0.951478	+	0.307717i	$0.900435\pi$
$968$		0			0
$969$			23149.9i			0.767475i
$970$		0			0
$971$		−	48233.1i		−	1.59410i	−0.603912	−	0.797051i	$-0.706392\pi$
$971$		−	48233.1i		−	1.59410i	0.603912	−	0.797051i	$-0.293608\pi$
$972$		0			0
$973$	8826.18	+	8826.18i	0.290806	+	0.290806i
$974$		0			0
$975$	−20023.8	−	2616.85i	−0.657719	−	0.0859551i
$976$		0			0
$977$	−7570.57	+	7570.57i	−0.247906	+	0.247906i	−0.820111	−	0.572205i	$-0.806088\pi$
$977$	−7570.57	+	7570.57i	−0.247906	+	0.247906i	0.572205	+	0.820111i	$0.306088\pi$
$978$		0			0
$979$	36494.1			1.19137
$980$		0			0
$981$	−727.997			−0.0236933
$982$		0			0
$983$	35285.1	−	35285.1i	1.14488	−	1.14488i	0.157340	−	0.987545i	$-0.449708\pi$
$983$	35285.1	−	35285.1i	1.14488	−	1.14488i	0.987545	−	0.157340i	$-0.0502918\pi$
$984$		0			0
$985$	−315.279	−	359.163i	−0.0101986	−	0.0116181i
$986$		0			0
$987$	17400.6	+	17400.6i	0.561161	+	0.561161i
$988$		0			0
$989$			35504.8i			1.14154i
$990$		0			0
$991$			51953.1i			1.66533i	0.553774	+	0.832667i	$0.313187\pi$
$991$			51953.1i			1.66533i	−0.553774	+	0.832667i	$0.686813\pi$
$992$		0			0
$993$	−33314.3	−	33314.3i	−1.06465	−	1.06465i
$994$		0			0
$995$	1082.48	−	16636.5i	0.0344895	−	0.530063i
$996$		0			0
$997$	20466.1	−	20466.1i	0.650119	−	0.650119i	−0.302903	−	0.953021i	$-0.597956\pi$
$997$	20466.1	−	20466.1i	0.650119	−	0.650119i	0.953021	+	0.302903i	$0.0979557\pi$
$998$		0			0
$999$	38096.6			1.20653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.4.n.h.63.3		8
4.3	odd	2		320.4.n.g.63.2		8
5.2	odd	4		320.4.n.g.127.2		8
8.3	odd	2		160.4.n.e.63.3	yes	8
8.5	even	2		160.4.n.d.63.2	✓	8
20.7	even	4	inner	320.4.n.h.127.3		8
40.27	even	4		160.4.n.d.127.2	yes	8
40.37	odd	4		160.4.n.e.127.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.n.d.63.2	✓	8	8.5	even	2
160.4.n.d.127.2	yes	8	40.27	even	4
160.4.n.e.63.3	yes	8	8.3	odd	2
160.4.n.e.127.3	yes	8	40.37	odd	4
320.4.n.g.63.2		8	4.3	odd	2
320.4.n.g.127.2		8	5.2	odd	4
320.4.n.h.63.3		8	1.1	even	1	trivial
320.4.n.h.127.3		8	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.64336 - 3.64336i) q^{3} +(-0.725933 + 11.1567i) q^{5} +(9.23932 + 9.23932i) q^{7} +0.451865i q^{9} -29.0521i q^{11} +(22.1709 + 22.1709i) q^{13} +(38.0032 + 43.2929i) q^{15} +(-68.5560 + 68.5560i) q^{17} +46.3417 q^{19} +67.3243 q^{21} +(-82.3020 + 82.3020i) q^{23} +(-123.946 - 16.1981i) q^{25} +(100.017 + 100.017i) q^{27} +110.111i q^{29} +250.150i q^{31} +(-105.847 - 105.847i) q^{33} +(-109.788 + 96.3737i) q^{35} +(190.450 - 190.450i) q^{37} +161.553 q^{39} +386.818 q^{41} +(215.698 - 215.698i) q^{43} +(-5.04135 - 0.328024i) q^{45} +(258.459 + 258.459i) q^{47} -172.270i q^{49} +499.548i q^{51} +(-313.780 - 313.780i) q^{53} +(324.127 + 21.0899i) q^{55} +(168.840 - 168.840i) q^{57} +195.564 q^{59} -423.865 q^{61} +(-4.17493 + 4.17493i) q^{63} +(-263.449 + 231.260i) q^{65} +(598.492 + 598.492i) q^{67} +599.711i q^{69} -993.953i q^{71} +(22.8188 + 22.8188i) q^{73} +(-510.595 + 392.564i) q^{75} +(268.421 - 268.421i) q^{77} -612.099 q^{79} +716.595 q^{81} +(-176.546 + 176.546i) q^{83} +(-715.095 - 814.629i) q^{85} +(401.174 + 401.174i) q^{87} +1256.16i q^{89} +409.688i q^{91} +(911.388 + 911.388i) q^{93} +(-33.6410 + 517.023i) q^{95} +(269.898 - 269.898i) q^{97} +13.1276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 14 q^{5} - 10 q^{7} + 32 q^{13} - 22 q^{15} + 44 q^{17} + 80 q^{19} - 236 q^{21} - 230 q^{23} - 44 q^{25} + 80 q^{27} - 260 q^{33} - 866 q^{35} + 292 q^{37} - 1068 q^{39} + 932 q^{41} + 458 q^{43}+ \cdots + 1844 q^{99}+O(q^{100}) \) 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

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