LMFDB - Embedded newform 48.5.l.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,5,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.96175822802$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	48.19
Dual form			48.5.l.a.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.827018 - 3.91357i) q^{2} +(3.67423 - 3.67423i) q^{3} +(-14.6321 + 6.47318i) q^{4} +(-25.9147 + 25.9147i) q^{5} +(-17.4180 - 11.3407i) q^{6} -48.6273 q^{7} +(37.4343 + 51.9103i) q^{8} -27.0000i q^{9} +O(q^{10})$	\(q+(-0.827018 - 3.91357i) q^{2} +(3.67423 - 3.67423i) q^{3} +(-14.6321 + 6.47318i) q^{4} +(-25.9147 + 25.9147i) q^{5} +(-17.4180 - 11.3407i) q^{6} -48.6273 q^{7} +(37.4343 + 51.9103i) q^{8} -27.0000i q^{9} +(122.851 + 79.9872i) q^{10} +(-111.386 - 111.386i) q^{11} +(-29.9777 + 77.5457i) q^{12} +(151.271 + 151.271i) q^{13} +(40.2156 + 190.306i) q^{14} +190.434i q^{15} +(172.196 - 189.432i) q^{16} -518.259 q^{17} +(-105.666 + 22.3295i) q^{18} +(63.3585 - 63.3585i) q^{19} +(211.436 - 546.937i) q^{20} +(-178.668 + 178.668i) q^{21} +(-343.800 + 528.037i) q^{22} +286.324 q^{23} +(328.273 + 53.1882i) q^{24} -718.145i q^{25} +(466.908 - 717.116i) q^{26} +(-99.2043 - 99.2043i) q^{27} +(711.519 - 314.773i) q^{28} +(-1041.14 - 1041.14i) q^{29} +(745.275 - 157.492i) q^{30} +221.852i q^{31} +(-883.766 - 517.236i) q^{32} -818.520 q^{33} +(428.609 + 2028.24i) q^{34} +(1260.16 - 1260.16i) q^{35} +(174.776 + 395.066i) q^{36} +(-252.595 + 252.595i) q^{37} +(-300.357 - 195.559i) q^{38} +1111.61 q^{39} +(-2315.34 - 375.142i) q^{40} +2059.53i q^{41} +(846.992 + 551.469i) q^{42} +(220.483 + 220.483i) q^{43} +(2350.84 + 908.791i) q^{44} +(699.697 + 699.697i) q^{45} +(-236.795 - 1120.55i) q^{46} +1409.73i q^{47} +(-63.3314 - 1328.71i) q^{48} -36.3871 q^{49} +(-2810.51 + 593.919i) q^{50} +(-1904.21 + 1904.21i) q^{51} +(-3192.62 - 1234.21i) q^{52} +(757.451 - 757.451i) q^{53} +(-306.200 + 470.287i) q^{54} +5773.10 q^{55} +(-1820.33 - 2524.26i) q^{56} -465.588i q^{57} +(-3213.53 + 4935.61i) q^{58} +(849.016 + 849.016i) q^{59} +(-1232.71 - 2786.44i) q^{60} +(587.739 + 587.739i) q^{61} +(868.232 - 183.475i) q^{62} +1312.94i q^{63} +(-1293.35 + 3886.45i) q^{64} -7840.31 q^{65} +(676.930 + 3203.34i) q^{66} +(5160.59 - 5160.59i) q^{67} +(7583.21 - 3354.79i) q^{68} +(1052.02 - 1052.02i) q^{69} +(-5973.91 - 3889.56i) q^{70} -2903.36 q^{71} +(1401.58 - 1010.73i) q^{72} -1452.74i q^{73} +(1197.45 + 779.648i) q^{74} +(-2638.63 - 2638.63i) q^{75} +(-516.936 + 1337.20i) q^{76} +(5416.42 + 5416.42i) q^{77} +(-919.324 - 4350.38i) q^{78} +7274.97i q^{79} +(446.682 + 9371.49i) q^{80} -729.000 q^{81} +(8060.13 - 1703.27i) q^{82} +(5533.91 - 5533.91i) q^{83} +(1457.73 - 3770.84i) q^{84} +(13430.5 - 13430.5i) q^{85} +(680.532 - 1045.22i) q^{86} -7650.77 q^{87} +(1612.43 - 9951.77i) q^{88} +8996.63i q^{89} +(2159.65 - 3316.98i) q^{90} +(-7355.92 - 7355.92i) q^{91} +(-4189.51 + 1853.43i) q^{92} +(815.135 + 815.135i) q^{93} +(5517.07 - 1165.87i) q^{94} +3283.84i q^{95} +(-5147.61 + 1346.72i) q^{96} -4814.94 q^{97} +(30.0927 + 142.403i) q^{98} +(-3007.43 + 3007.43i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) $ 32 * q + 12 * q^4 + 180 * q^8	$ 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.827018	−	3.91357i	−0.206754	−	0.978393i
$2$	−0.827018	−	3.91357i	−0.206754	−	0.978393i
$3$	3.67423	−	3.67423i	0.408248	−	0.408248i
$3$	3.67423	−	3.67423i	0.408248	−	0.408248i
$4$	−14.6321	+	6.47318i	−0.914505	+	0.404574i
$5$	−25.9147	+	25.9147i	−1.03659	+	1.03659i	−0.0372841	+	0.999305i	$0.511871\pi$
$5$	−25.9147	+	25.9147i	−1.03659	+	1.03659i	−0.999305	+	0.0372841i	$0.988129\pi$
$6$	−17.4180	−	11.3407i	−0.483834	−	0.315020i
$7$	−48.6273			−0.992394			−0.496197	−	0.868210i	$-0.665271\pi$
$7$	−48.6273			−0.992394			−0.496197	+	0.868210i	$0.665271\pi$
$8$	37.4343	+	51.9103i	0.584910	+	0.811098i
$9$		−	27.0000i		−	0.333333i
$10$	122.851	+	79.9872i	1.22851	+	0.799872i
$11$	−111.386	−	111.386i	−0.920549	−	0.920549i	0.0765188	−	0.997068i	$-0.475619\pi$
$11$	−111.386	−	111.386i	−0.920549	−	0.920549i	−0.997068	+	0.0765188i	$0.975619\pi$
$12$	−29.9777	+	77.5457i	−0.208179	+	0.538512i
$13$	151.271	+	151.271i	0.895097	+	0.895097i	0.994997	−	0.0999001i	$-0.0318523\pi$
$13$	151.271	+	151.271i	0.895097	+	0.895097i	−0.0999001	+	0.994997i	$0.531852\pi$
$14$	40.2156	+	190.306i	0.205182	+	0.970951i
$15$			190.434i			0.846371i
$16$	172.196	−	189.432i	0.672640	−	0.739970i
$17$	−518.259			−1.79328			−0.896642	−	0.442756i	$-0.854001\pi$
$17$	−518.259			−1.79328			−0.896642	+	0.442756i	$0.854001\pi$
$18$	−105.666	+	22.3295i	−0.326131	+	0.0689181i
$19$	63.3585	−	63.3585i	0.175508	−	0.175508i	−0.613886	−	0.789395i	$-0.710395\pi$
$19$	63.3585	−	63.3585i	0.175508	−	0.175508i	0.789395	+	0.613886i	$0.210395\pi$
$20$	211.436	−	546.937i	0.528589	−	1.36734i
$21$	−178.668	+	178.668i	−0.405143	+	0.405143i
$22$	−343.800	+	528.037i	−0.710331	+	1.09099i
$23$	286.324			0.541255			0.270627	−	0.962684i	$-0.412769\pi$
$23$	286.324			0.541255			0.270627	+	0.962684i	$0.412769\pi$
$24$	328.273	+	53.1882i	0.569918	+	0.0923407i
$25$		−	718.145i		−	1.14903i
$26$	466.908	−	717.116i	0.690692	−	1.06082i
$27$	−99.2043	−	99.2043i	−0.136083	−	0.136083i
$28$	711.519	−	314.773i	0.907549	−	0.401497i
$29$	−1041.14	−	1041.14i	−1.23798	−	1.23798i	−0.960827	−	0.277150i	$-0.910610\pi$
$29$	−1041.14	−	1041.14i	−1.23798	−	1.23798i	−0.277150	−	0.960827i	$-0.589390\pi$
$30$	745.275	−	157.492i	0.828084	−	0.174991i
$31$			221.852i			0.230855i	0.993316	+	0.115427i	$0.0368238\pi$
$31$			221.852i			0.230855i	−0.993316	+	0.115427i	$0.963176\pi$
$32$	−883.766	−	517.236i	−0.863053	−	0.505114i
$33$	−818.520			−0.751625
$34$	428.609	+	2028.24i	0.370769	+	1.75454i
$35$	1260.16	−	1260.16i	1.02870	−	1.02870i
$36$	174.776	+	395.066i	0.134858	+	0.304835i
$37$	−252.595	+	252.595i	−0.184511	+	0.184511i	−0.793318	−	0.608807i	$-0.791648\pi$
$37$	−252.595	+	252.595i	−0.184511	+	0.184511i	0.608807	+	0.793318i	$0.291648\pi$
$38$	−300.357	−	195.559i	−0.208003	−	0.135429i
$39$	1111.61			0.730844
$40$	−2315.34	−	375.142i	−1.44709	−	0.234464i
$41$			2059.53i			1.22518i	0.790399	+	0.612592i	$0.209873\pi$
$41$			2059.53i			1.22518i	−0.790399	+	0.612592i	$0.790127\pi$
$42$	846.992	+	551.469i	0.480154	+	0.312624i
$43$	220.483	+	220.483i	0.119244	+	0.119244i	0.764211	−	0.644966i	$-0.223129\pi$
$43$	220.483	+	220.483i	0.119244	+	0.119244i	−0.644966	+	0.764211i	$0.723129\pi$
$44$	2350.84	+	908.791i	1.21428	+	0.469417i
$45$	699.697	+	699.697i	0.345530	+	0.345530i
$46$	−236.795	−	1120.55i	−0.111907	−	0.529560i
$47$			1409.73i			0.638174i	0.947725	+	0.319087i	$0.103376\pi$
$47$			1409.73i			0.638174i	−0.947725	+	0.319087i	$0.896624\pi$
$48$	−63.3314	−	1328.71i	−0.0274876	−	0.576696i
$49$	−36.3871			−0.0151550
$50$	−2810.51	+	593.919i	−1.12421	+	0.237568i
$51$	−1904.21	+	1904.21i	−0.732105	+	0.732105i
$52$	−3192.62	−	1234.21i	−1.18070	−	0.456438i
$53$	757.451	−	757.451i	0.269651	−	0.269651i	−0.559308	−	0.828960i	$-0.688933\pi$
$53$	757.451	−	757.451i	0.269651	−	0.269651i	0.828960	+	0.559308i	$0.188933\pi$
$54$	−306.200	+	470.287i	−0.105007	+	0.161278i
$55$	5773.10			1.90846
$56$	−1820.33	−	2524.26i	−0.580461	−	0.804928i
$57$		−	465.588i		−	0.143302i
$58$	−3213.53	+	4935.61i	−0.955270	+	1.46718i
$59$	849.016	+	849.016i	0.243900	+	0.243900i	0.818461	−	0.574561i	$-0.194827\pi$
$59$	849.016	+	849.016i	0.243900	+	0.243900i	−0.574561	+	0.818461i	$0.694827\pi$
$60$	−1232.71	−	2786.44i	−0.342420	−	0.774011i
$61$	587.739	+	587.739i	0.157952	+	0.157952i	0.781658	−	0.623707i	$-0.214374\pi$
$61$	587.739	+	587.739i	0.157952	+	0.157952i	−0.623707	+	0.781658i	$0.714374\pi$
$62$	868.232	−	183.475i	0.225867	−	0.0477303i
$63$			1312.94i			0.330798i
$64$	−1293.35	+	3886.45i	−0.315760	+	0.948839i
$65$	−7840.31			−1.85570
$66$	676.930	+	3203.34i	0.155402	+	0.735385i
$67$	5160.59	−	5160.59i	1.14961	−	1.14961i	0.162978	−	0.986630i	$-0.447890\pi$
$67$	5160.59	−	5160.59i	1.14961	−	1.14961i	0.986630	−	0.162978i	$-0.0521099\pi$
$68$	7583.21	−	3354.79i	1.63997	−	0.725516i
$69$	1052.02	−	1052.02i	0.220966	−	0.220966i
$70$	−5973.91	−	3889.56i	−1.21917	−	0.793788i
$71$	−2903.36			−0.575949			−0.287974	−	0.957638i	$-0.592982\pi$
$71$	−2903.36			−0.575949			−0.287974	+	0.957638i	$0.592982\pi$
$72$	1401.58	−	1010.73i	0.270366	−	0.194970i
$73$		−	1452.74i		−	0.272610i	−0.990667	−	0.136305i	$-0.956477\pi$
$73$		−	1452.74i		−	0.272610i	0.990667	−	0.136305i	$-0.0435227\pi$
$74$	1197.45	+	779.648i	0.218672	+	0.142376i
$75$	−2638.63	−	2638.63i	−0.469091	−	0.469091i
$76$	−516.936	+	1337.20i	−0.0894972	+	0.231509i
$77$	5416.42	+	5416.42i	0.913547	+	0.913547i
$78$	−919.324	−	4350.38i	−0.151105	−	0.715053i
$79$			7274.97i			1.16567i	0.812589	+	0.582837i	$0.198057\pi$
$79$			7274.97i			1.16567i	−0.812589	+	0.582837i	$0.801943\pi$
$80$	446.682	+	9371.49i	0.0697941	+	1.46430i
$81$	−729.000			−0.111111
$82$	8060.13	−	1703.27i	1.19871	−	0.253312i
$83$	5533.91	−	5533.91i	0.803297	−	0.803297i	−0.180312	−	0.983609i	$-0.557711\pi$
$83$	5533.91	−	5533.91i	0.803297	−	0.803297i	0.983609	+	0.180312i	$0.0577108\pi$
$84$	1457.73	−	3770.84i	0.206595	−	0.534416i
$85$	13430.5	−	13430.5i	1.85890	−	1.85890i
$86$	680.532	−	1045.22i	0.0920136	−	0.141322i
$87$	−7650.77			−1.01080
$88$	1612.43	−	9951.77i	0.208217	−	1.28509i
$89$			8996.63i			1.13579i	0.823099	+	0.567897i	$0.192243\pi$
$89$			8996.63i			1.13579i	−0.823099	+	0.567897i	$0.807757\pi$
$90$	2159.65	−	3316.98i	0.266624	−	0.409503i
$91$	−7355.92	−	7355.92i	−0.888289	−	0.888289i
$92$	−4189.51	+	1853.43i	−0.494980	+	0.218978i
$93$	815.135	+	815.135i	0.0942461	+	0.0942461i
$94$	5517.07	−	1165.87i	0.624385	−	0.131945i
$95$			3283.84i			0.363860i
$96$	−5147.61	+	1346.72i	−0.558552	+	0.146128i
$97$	−4814.94			−0.511738			−0.255869	−	0.966711i	$-0.582362\pi$
$97$	−4814.94			−0.511738			−0.255869	+	0.966711i	$0.582362\pi$
$98$	30.0927	+	142.403i	0.00313336	+	0.0148275i
$99$	−3007.43	+	3007.43i	−0.306850	+	0.306850i
$100$	4648.69	+	10508.0i	0.464869	+	1.05080i
$101$	−5215.97	+	5215.97i	−0.511320	+	0.511320i	−0.914931	−	0.403611i	$-0.867755\pi$
$101$	−5215.97	+	5215.97i	−0.511320	+	0.511320i	0.403611	+	0.914931i	$0.367755\pi$
$102$	9027.06	+	5877.43i	0.867652	+	0.564921i
$103$	−19410.6			−1.82964			−0.914819	−	0.403863i	$-0.867667\pi$
$103$	−19410.6			−1.82964			−0.914819	+	0.403863i	$0.867667\pi$
$104$	−2189.81	+	13515.3i	−0.202460	+	1.24956i
$105$		−	9260.27i		−	0.839933i
$106$	−3590.76	−	2337.91i	−0.319577	−	0.208073i
$107$	−9743.17	−	9743.17i	−0.851006	−	0.851006i	0.139251	−	0.990257i	$-0.455530\pi$
$107$	−9743.17	−	9743.17i	−0.851006	−	0.851006i	−0.990257	+	0.139251i	$0.955530\pi$
$108$	2093.73	+	809.398i	0.179504	+	0.0693928i
$109$	421.003	+	421.003i	0.0354349	+	0.0354349i	0.724602	−	0.689167i	$-0.242024\pi$
$109$	421.003	+	421.003i	0.0354349	+	0.0354349i	−0.689167	+	0.724602i	$0.742024\pi$
$110$	−4774.45	−	22593.4i	−0.394583	−	1.86723i
$111$			1856.19i			0.150652i
$112$	−8373.41	+	9211.58i	−0.667523	+	0.734342i
$113$	−8132.34			−0.636882			−0.318441	−	0.947943i	$-0.603159\pi$
$113$	−8132.34			−0.636882			−0.318441	+	0.947943i	$0.603159\pi$
$114$	−1822.11	+	385.049i	−0.140206	+	0.0296283i
$115$	−7420.00	+	7420.00i	−0.561058	+	0.561058i
$116$	21973.5	+	8494.54i	1.63299	+	0.631283i
$117$	4084.33	−	4084.33i	0.298366	−	0.298366i
$118$	2620.53	−	4024.83i	0.188203	−	0.289057i
$119$	25201.5			1.77964
$120$	−9885.46	+	7128.74i	−0.686490	+	0.495051i
$121$			10172.9i			0.694822i
$122$	1814.09	−	2786.23i	0.121882	−	0.187196i
$123$	7567.21	+	7567.21i	0.500179	+	0.500179i
$124$	−1436.09	−	3246.15i	−0.0933979	−	0.211118i
$125$	2413.84	+	2413.84i	0.154485	+	0.154485i
$126$	5138.27	−	1085.82i	0.323650	−	0.0683939i
$127$			19774.1i			1.22600i	0.790083	+	0.612999i	$0.210037\pi$
$127$			19774.1i			1.22600i	−0.790083	+	0.612999i	$0.789963\pi$
$128$	16279.5	+	1847.47i	0.993622	+	0.112760i
$129$	1620.21			0.0973626
$130$	6484.08	+	30683.6i	0.383673	+	1.81560i
$131$	−13031.7	+	13031.7i	−0.759378	+	0.759378i	−0.976209	−	0.216831i	$-0.930428\pi$
$131$	−13031.7	+	13031.7i	−0.759378	+	0.759378i	0.216831	+	0.976209i	$0.430428\pi$
$132$	11976.7	−	5298.43i	0.687365	−	0.304088i
$133$	−3080.95	+	3080.95i	−0.174173	+	0.174173i
$134$	−24464.2	−	15928.4i	−1.36245	−	0.887081i
$135$	5141.70			0.282124
$136$	−19400.6	−	26903.0i	−1.04891	−	1.45453i
$137$		−	21181.9i		−	1.12856i	−0.825585	−	0.564278i	$-0.809155\pi$
$137$		−	21181.9i		−	1.12856i	0.825585	−	0.564278i	$-0.190845\pi$
$138$	−4987.20	−	3247.12i	−0.261878	−	0.170506i
$139$	−12063.4	−	12063.4i	−0.624367	−	0.624367i	0.322278	−	0.946645i	$-0.395551\pi$
$139$	−12063.4	−	12063.4i	−0.624367	−	0.624367i	−0.946645	+	0.322278i	$0.895551\pi$
$140$	−10281.5	+	26596.1i	−0.524568	+	1.35694i
$141$	5179.67	+	5179.67i	0.260534	+	0.260534i
$142$	2401.13	+	11362.5i	0.119080	+	0.563504i
$143$		−	33699.2i		−	1.64796i
$144$	−5114.67	−	4649.29i	−0.246657	−	0.224213i
$145$	53961.6			2.56655
$146$	−5685.39	+	1201.44i	−0.266719	+	0.0563633i
$147$	−133.695	+	133.695i	−0.00618699	+	0.00618699i
$148$	2060.90	−	5331.09i	0.0940877	−	0.243384i
$149$	−3075.82	+	3075.82i	−0.138544	+	0.138544i	−0.772978	−	0.634433i	$-0.781233\pi$
$149$	−3075.82	+	3075.82i	−0.138544	+	0.138544i	0.634433	+	0.772978i	$0.281233\pi$
$150$	−8144.29	+	12508.7i	−0.361968	+	0.555941i
$151$	−18744.4			−0.822086			−0.411043	−	0.911616i	$-0.634835\pi$
$151$	−18744.4			−0.822086			−0.411043	+	0.911616i	$0.634835\pi$
$152$	5660.74	+	917.178i	0.245011	+	0.0396978i
$153$			13993.0i			0.597761i
$154$	16718.1	−	25677.0i	0.704928	−	1.08269i
$155$	−5749.22	−	5749.22i	−0.239302	−	0.239302i
$156$	−16265.2	+	7195.68i	−0.668361	+	0.295681i
$157$	−18079.1	−	18079.1i	−0.733464	−	0.733464i	0.237840	−	0.971304i	$-0.423560\pi$
$157$	−18079.1	−	18079.1i	−0.733464	−	0.733464i	−0.971304	+	0.237840i	$0.923560\pi$
$158$	28471.1	−	6016.53i	1.14049	−	0.241008i
$159$		−	5566.10i		−	0.220169i
$160$	36306.6	−	9498.51i	1.41823	−	0.371036i
$161$	−13923.1			−0.537138
$162$	602.896	+	2852.99i	0.0229727	+	0.108710i
$163$	19149.2	−	19149.2i	0.720735	−	0.720735i	−0.248020	−	0.968755i	$-0.579780\pi$
$163$	19149.2	−	19149.2i	0.720735	−	0.720735i	0.968755	+	0.248020i	$0.0797799\pi$
$164$	−13331.7	−	30135.3i	−0.495678	−	1.12044i
$165$	21211.7	−	21211.7i	0.779126	−	0.779126i
$166$	−26234.0	−	17080.7i	−0.952026	−	0.619855i
$167$	27043.1			0.969668			0.484834	−	0.874606i	$-0.338880\pi$
$167$	27043.1			0.969668			0.484834	+	0.874606i	$0.338880\pi$
$168$	−15963.0	−	2586.40i	−0.565583	−	0.0916383i
$169$			17205.1i			0.602399i
$170$	−63668.7	−	41454.1i	−2.20307	−	1.43440i
$171$	−1710.68	−	1710.68i	−0.0585028	−	0.0585028i
$172$	−4653.35	−	1798.90i	−0.157293	−	0.0608064i
$173$	35090.6	+	35090.6i	1.17246	+	1.17246i	0.981621	+	0.190842i	$0.0611220\pi$
$173$	35090.6	+	35090.6i	1.17246	+	1.17246i	0.190842	+	0.981621i	$0.438878\pi$
$174$	6327.32	+	29941.8i	0.208988	+	0.988963i
$175$			34921.5i			1.14029i
$176$	−40280.5	+	1919.93i	−1.30038	+	0.0619811i
$177$	6238.97			0.199143
$178$	35209.0	−	7440.37i	1.11125	−	0.234831i
$179$	33781.6	−	33781.6i	1.05432	−	1.05432i	0.0558879	−	0.998437i	$-0.482201\pi$
$179$	33781.6	−	33781.6i	1.05432	−	1.05432i	0.998437	−	0.0558879i	$-0.0177989\pi$
$180$	−14767.3	−	5708.76i	−0.455781	−	0.176196i
$181$	−28790.8	+	28790.8i	−0.878814	+	0.878814i	−0.993412	−	0.114598i	$-0.963442\pi$
$181$	−28790.8	+	28790.8i	−0.878814	+	0.878814i	0.114598	+	0.993412i	$0.463442\pi$
$182$	−22704.4	+	34871.4i	−0.685438	+	1.05275i
$183$	4318.98			0.128967
$184$	10718.3	+	14863.1i	0.316585	+	0.439010i
$185$		−	13091.9i		−	0.382523i
$186$	2515.96	−	3864.22i	0.0727239	−	0.111696i
$187$	57727.1	+	57727.1i	1.65081	+	1.65081i
$188$	−9125.42	−	20627.2i	−0.258189	−	0.583614i
$189$	4824.04	+	4824.04i	0.135048	+	0.135048i
$190$	12851.5	−	2715.79i	0.355998	−	0.0752296i
$191$		−	28576.1i		−	0.783315i	−0.920111	−	0.391658i	$-0.871902\pi$
$191$		−	28576.1i		−	0.783315i	0.920111	−	0.391658i	$-0.128098\pi$
$192$	9527.63	+	19031.8i	0.258454	+	0.516270i
$193$	−43301.7			−1.16249			−0.581247	−	0.813727i	$-0.697435\pi$
$193$	−43301.7			−1.16249			−0.581247	+	0.813727i	$0.697435\pi$
$194$	3982.04	+	18843.6i	0.105804	+	0.500681i
$195$	−28807.2	+	28807.2i	−0.757585	+	0.757585i
$196$	532.419	−	235.540i	0.0138593	−	0.00613131i
$197$	−19588.6	+	19588.6i	−0.504745	+	0.504745i	−0.912909	−	0.408164i	$-0.866169\pi$
$197$	−19588.6	+	19588.6i	−0.504745	+	0.504745i	0.408164	+	0.912909i	$0.366169\pi$
$198$	14257.0	+	9282.61i	0.363662	+	0.236777i
$199$	−25125.4			−0.634465			−0.317232	−	0.948348i	$-0.602754\pi$
$199$	−25125.4			−0.634465			−0.317232	+	0.948348i	$0.602754\pi$
$200$	37279.1	−	26883.2i	0.931978	−	0.672081i
$201$		−	37922.4i		−	0.938651i
$202$	24726.8	+	16099.4i	0.605989	+	0.394554i
$203$	50627.7	+	50627.7i	1.22856	+	1.22856i
$204$	15536.2	−	40188.8i	0.373323	−	0.965705i
$205$	−53372.3	−	53372.3i	−1.27001	−	1.27001i
$206$	16052.9	+	75964.9i	0.378286	+	1.79011i
$207$		−	7730.74i		−	0.180418i
$208$	54704.0	−	2607.41i	1.26442	−	0.0602674i
$209$	−14114.6			−0.323128
$210$	−36240.7	+	7658.40i	−0.821785	+	0.173660i
$211$	2854.29	−	2854.29i	0.0641111	−	0.0641111i	−0.674324	−	0.738435i	$-0.735565\pi$
$211$	2854.29	−	2854.29i	0.0641111	−	0.0641111i	0.738435	+	0.674324i	$0.235565\pi$
$212$	−6179.96	+	15986.2i	−0.137504	+	0.355692i
$213$	−10667.6	+	10667.6i	−0.235130	+	0.235130i
$214$	−30072.8	+	46188.4i	−0.656669	+	1.00857i
$215$	−11427.5			−0.247215
$216$	1436.08	−	8863.36i	0.0307802	−	0.189973i
$217$		−	10788.0i		−	0.229099i
$218$	1299.45	−	1995.80i	0.0273430	−	0.0419956i
$219$	−5337.70	−	5337.70i	−0.111292	−	0.111292i
$220$	−84472.5	+	37370.3i	−1.74530	+	0.772114i
$221$	−78397.8	−	78397.8i	−1.60516	−	1.60516i
$222$	7264.32	−	1535.10i	0.147397	−	0.0311480i
$223$		−	52706.1i		−	1.05987i	−0.848039	−	0.529933i	$-0.822217\pi$
$223$		−	52706.1i		−	1.05987i	0.848039	−	0.529933i	$-0.177783\pi$
$224$	42975.1	+	25151.8i	0.856488	+	0.501272i
$225$	−19389.9			−0.383011
$226$	6725.59	+	31826.5i	0.131678	+	0.623121i
$227$	−39733.5	+	39733.5i	−0.771089	+	0.771089i	−0.978297	−	0.207208i	$-0.933562\pi$
$227$	−39733.5	+	39733.5i	−0.771089	+	0.771089i	0.207208	+	0.978297i	$0.433562\pi$
$228$	3013.84	+	6812.52i	0.0579762	+	0.131050i
$229$	−38954.9	+	38954.9i	−0.742834	+	0.742834i	−0.973122	−	0.230289i	$-0.926033\pi$
$229$	−38954.9	+	38954.9i	−0.742834	+	0.742834i	0.230289	+	0.973122i	$0.426033\pi$
$230$	35175.2	+	22902.2i	0.664937	+	0.432934i
$231$	39802.4			0.745908
$232$	15071.5	−	93020.0i	0.280015	−	1.72823i
$233$			73939.5i			1.36196i	0.732302	+	0.680981i	$0.238446\pi$
$233$			73939.5i			1.36196i	−0.732302	+	0.680981i	$0.761554\pi$
$234$	−19362.1	−	12606.5i	−0.353607	−	0.230231i
$235$	−36532.7	−	36532.7i	−0.661524	−	0.661524i
$236$	−17918.7	−	6927.03i	−0.321723	−	0.124372i
$237$	26730.0	+	26730.0i	0.475884	+	0.475884i
$238$	−20842.1	−	98628.0i	−0.367949	−	1.74119i
$239$		−	3780.14i		−	0.0661778i	−0.999452	−	0.0330889i	$-0.989466\pi$
$239$		−	3780.14i		−	0.0661778i	0.999452	−	0.0330889i	$-0.0105344\pi$
$240$	36074.3	+	32791.8i	0.626289	+	0.569303i
$241$	68400.0			1.17767			0.588833	−	0.808255i	$-0.299588\pi$
$241$	68400.0			1.17767			0.588833	+	0.808255i	$0.299588\pi$
$242$	39812.3	−	8413.16i	0.679809	−	0.143658i
$243$	−2678.52	+	2678.52i	−0.0453609	+	0.0453609i
$244$	−12404.4	−	4795.30i	−0.208351	−	0.0805445i
$245$	942.961	−	942.961i	0.0157095	−	0.0157095i
$246$	23356.6	−	35873.0i	0.385958	−	0.592786i
$247$	19168.7			0.314194
$248$	−11516.4	+	8304.85i	−0.187246	+	0.135029i
$249$		−	40665.8i		−	0.655889i
$250$	7450.43	−	11443.0i	0.119207	−	0.183088i
$251$	16017.1	+	16017.1i	0.254235	+	0.254235i	0.822705	−	0.568469i	$-0.192464\pi$
$251$	16017.1	+	16017.1i	0.254235	+	0.254235i	−0.568469	+	0.822705i	$0.692464\pi$
$252$	−8498.88	−	19211.0i	−0.133832	−	0.302516i
$253$	−31892.6	−	31892.6i	−0.498252	−	0.498252i
$254$	77387.5	−	16353.6i	1.19951	−	0.253481i
$255$		−	98693.9i		−	1.51778i
$256$	−6233.24	−	65238.9i	−0.0951118	−	0.995467i
$257$	77771.7			1.17749			0.588743	−	0.808321i	$-0.299623\pi$
$257$	77771.7			1.17749			0.588743	+	0.808321i	$0.299623\pi$
$258$	−1339.94	−	6340.81i	−0.0201302	−	0.0952589i
$259$	12283.0	−	12283.0i	0.183107	−	0.183107i
$260$	114720.	−	50751.8i	1.69704	−	0.750766i
$261$	−28110.7	+	28110.7i	−0.412659	+	0.412659i
$262$	61777.9	+	40223.0i	0.899975	+	0.585966i
$263$	−40295.1			−0.582560			−0.291280	−	0.956638i	$-0.594081\pi$
$263$	−40295.1			−0.582560			−0.291280	+	0.956638i	$0.594081\pi$
$264$	−30640.7	−	42489.6i	−0.439633	−	0.609642i
$265$			39258.2i			0.559035i
$266$	14605.5	+	9509.52i	0.206421	+	0.134399i
$267$	33055.7	+	33055.7i	0.463686	+	0.463686i
$268$	−42104.7	+	108916.i	−0.586221	+	1.51642i
$269$	23698.7	+	23698.7i	0.327507	+	0.327507i	0.851638	−	0.524131i	$-0.175610\pi$
$269$	23698.7	+	23698.7i	0.327507	+	0.327507i	−0.524131	+	0.851638i	$0.675610\pi$
$270$	−4252.28	−	20122.4i	−0.0583303	−	0.276028i
$271$		−	3089.97i		−	0.0420742i	−0.999779	−	0.0210371i	$-0.993303\pi$
$271$		−	3089.97i		−	0.0420742i	0.999779	−	0.0210371i	$-0.00669681\pi$
$272$	−89242.0	+	98175.1i	−1.20623	+	1.32698i
$273$	−54054.8			−0.725285
$274$	−82896.7	+	17517.8i	−1.10417	+	0.233334i
$275$	−79991.7	+	79991.7i	−1.05774	+	1.05774i
$276$	−8583.33	+	22203.2i	−0.112678	+	0.291472i
$277$	7680.44	−	7680.44i	0.100098	−	0.100098i	−0.655284	−	0.755382i	$-0.727451\pi$
$277$	7680.44	−	7680.44i	0.100098	−	0.100098i	0.755382	+	0.655284i	$0.227451\pi$
$278$	−37234.3	+	57187.6i	−0.481786	+	0.739967i
$279$	5989.99			0.0769516
$280$	112589.	+	18242.1i	1.43608	+	0.232680i
$281$		−	73434.0i		−	0.930004i	−0.885310	−	0.465002i	$-0.846054\pi$
$281$		−	73434.0i		−	0.930004i	0.885310	−	0.465002i	$-0.153946\pi$
$282$	15987.3	−	24554.7i	0.201038	−	0.308771i
$283$	−23931.7	−	23931.7i	−0.298813	−	0.298813i	0.541736	−	0.840549i	$-0.317767\pi$
$283$	−23931.7	−	23931.7i	−0.298813	−	0.298813i	−0.840549	+	0.541736i	$0.817767\pi$
$284$	42482.2	−	18794.0i	0.526708	−	0.233014i
$285$	12065.6	+	12065.6i	0.148545	+	0.148545i
$286$	−131884.	+	27869.8i	−1.61235	+	0.340724i
$287$		−	100150.i		−	1.21586i
$288$	−13965.4	+	23861.7i	−0.168371	+	0.287684i
$289$	185072.			2.21587
$290$	−44627.2	−	211183.i	−0.530644	−	2.51109i
$291$	−17691.2	+	17691.2i	−0.208916	+	0.208916i
$292$	9403.84	+	21256.6i	0.110291	+	0.249303i
$293$	47626.2	−	47626.2i	0.554767	−	0.554767i	−0.373046	−	0.927813i	$-0.621687\pi$
$293$	47626.2	−	47626.2i	0.554767	−	0.554767i	0.927813	+	0.373046i	$0.121687\pi$
$294$	633.791	+	412.656i	0.00733249	+	0.00477412i
$295$	−44004.0			−0.505648
$296$	−22568.0	−	3656.57i	−0.257578	−	0.0417340i
$297$			22100.0i			0.250542i
$298$	14581.2	+	9493.68i	0.164195	+	0.106906i
$299$	43312.6	+	43312.6i	0.484476	+	0.484476i
$300$	55689.1	+	21528.4i	0.618768	+	0.239204i
$301$	−10721.5	−	10721.5i	−0.118337	−	0.118337i
$302$	15501.9	+	73357.5i	0.169970	+	0.804323i
$303$			38329.4i			0.417491i
$304$	−1092.09	−	22912.2i	−0.0118171	−	0.247925i
$305$	−30462.2			−0.327462
$306$	54762.6	−	11572.5i	0.584845	−	0.123590i
$307$	125287.	−	125287.i	1.32932	−	1.32932i	0.423351	−	0.905966i	$-0.360854\pi$
$307$	125287.	−	125287.i	1.32932	−	1.32932i	0.905966	−	0.423351i	$-0.139146\pi$
$308$	−114315.	−	44192.0i	−1.20504	−	0.465846i
$309$	−71319.2	+	71319.2i	−0.746947	+	0.746947i
$310$	−17745.3	+	27254.7i	−0.184654	+	0.283608i
$311$	−59742.4			−0.617678			−0.308839	−	0.951114i	$-0.599940\pi$
$311$	−59742.4			−0.617678			−0.308839	+	0.951114i	$0.599940\pi$
$312$	41612.4	+	57704.2i	0.427478	+	0.592786i
$313$			16531.1i			0.168738i	0.996435	+	0.0843691i	$0.0268875\pi$
$313$			16531.1i			0.168738i	−0.996435	+	0.0843691i	$0.973113\pi$
$314$	−55802.3	+	85705.8i	−0.565969	+	0.869263i
$315$	−34024.4	−	34024.4i	−0.342901	−	0.342901i
$316$	−47092.2	−	106448.i	−0.471602	−	1.06602i
$317$	109926.	+	109926.i	1.09391	+	1.09391i	0.995107	+	0.0988015i	$0.0315009\pi$
$317$	109926.	+	109926.i	1.09391	+	1.09391i	0.0988015	+	0.995107i	$0.468499\pi$
$318$	−21783.3	+	4603.27i	−0.215412	+	0.0455210i
$319$			231937.i			2.27924i
$320$	−67199.3	−	134233.i	−0.656243	−	1.31087i
$321$	−71597.4			−0.694843
$322$	11514.7	+	54489.2i	0.111056	+	0.525532i
$323$	−32836.1	+	32836.1i	−0.314736	+	0.314736i
$324$	10666.8	−	4718.95i	0.101612	−	0.0449527i
$325$	108635.	−	108635.i	1.02850	−	1.02850i
$326$	−90778.5	−	59105.1i	−0.854177	−	0.556147i
$327$	3093.72			0.0289325
$328$	−106911.	+	77097.1i	−0.993744	+	0.716623i
$329$		−	68551.2i		−	0.633320i
$330$	−100556.	−	65471.1i	−0.923380	−	0.601204i
$331$	−54132.0	−	54132.0i	−0.494081	−	0.494081i	0.415508	−	0.909589i	$-0.363604\pi$
$331$	−54132.0	−	54132.0i	−0.494081	−	0.494081i	−0.909589	+	0.415508i	$0.863604\pi$
$332$	−45150.6	+	116795.i	−0.409626	+	1.05961i
$333$	6820.07	+	6820.07i	0.0615035	+	0.0615035i
$334$	−22365.1	−	105835.i	−0.200483	−	0.948716i
$335$			267470.i			2.38334i
$336$	3079.63	+	64611.4i	0.0272785	+	0.572309i
$337$	41800.1			0.368059			0.184030	−	0.982921i	$-0.441086\pi$
$337$	41800.1			0.368059			0.184030	+	0.982921i	$0.441086\pi$
$338$	67333.4	−	14228.9i	0.589383	−	0.124549i
$339$	−29880.1	+	29880.1i	−0.260006	+	0.260006i
$340$	−109578.	+	283455.i	−0.947910	+	2.45203i
$341$	24711.3	−	24711.3i	0.212513	−	0.212513i
$342$	−5280.10	+	8109.63i	−0.0451430	+	0.0693344i
$343$	118524.			1.00743
$344$	−3191.71	+	19698.9i	−0.0269716	+	0.166466i
$345$			54525.6i			0.458102i
$346$	108309.	−	166350.i	0.904718	−	1.38954i
$347$	−133899.	−	133899.i	−1.11203	−	1.11203i	−0.992875	−	0.119160i	$-0.961980\pi$
$347$	−133899.	−	133899.i	−1.11203	−	1.11203i	−0.119160	−	0.992875i	$-0.538020\pi$
$348$	111947.	−	49524.9i	0.924385	−	0.408945i
$349$	71369.7	+	71369.7i	0.585953	+	0.585953i	0.936533	−	0.350580i	$-0.114015\pi$
$349$	71369.7	+	71369.7i	0.585953	+	0.585953i	−0.350580	+	0.936533i	$0.614015\pi$
$350$	136668.	−	28880.7i	1.11565	−	0.235760i
$351$		−	30013.6i		−	0.243615i
$352$	40826.4	+	156053.i	0.329501	+	1.25946i
$353$	2442.26			0.0195994			0.00979969	−	0.999952i	$-0.496881\pi$
$353$	2442.26			0.0195994			0.00979969	+	0.999952i	$0.496881\pi$
$354$	−5159.73	−	24416.6i	−0.0411738	−	0.194841i
$355$	75239.7	−	75239.7i	0.597022	−	0.597022i
$356$	−58236.8	−	131639.i	−0.459513	−	1.03869i
$357$	92596.3	−	92596.3i	0.726536	−	0.726536i
$358$	−160145.	−	104269.i	−1.24953	−	0.813558i
$359$	−47386.8			−0.367679			−0.183839	−	0.982956i	$-0.558853\pi$
$359$	−47386.8			−0.367679			−0.183839	+	0.982956i	$0.558853\pi$
$360$	−10128.8	+	62514.1i	−0.0781545	+	0.482362i
$361$			122292.i			0.938394i
$362$	136486.	+	88864.5i	1.04152	+	0.678127i
$363$	37377.6	+	37377.6i	0.283660	+	0.283660i
$364$	155249.	+	60016.2i	1.17172	+	0.452966i
$365$	37647.3	+	37647.3i	0.282584	+	0.282584i
$366$	−3571.87	−	16902.6i	−0.0266645	−	0.126180i
$367$		−	256767.i		−	1.90637i	−0.302386	−	0.953186i	$-0.597783\pi$
$367$		−	256767.i		−	1.90637i	0.302386	−	0.953186i	$-0.402217\pi$
$368$	49303.7	−	54239.0i	0.364069	−	0.400512i
$369$	55607.4			0.408395
$370$	−51235.9	+	10827.2i	−0.374258	+	0.0790884i
$371$	−36832.8	+	36832.8i	−0.267600	+	0.267600i
$372$	−17203.6	−	6650.60i	−0.124318	−	0.0480590i
$373$	−140699.	+	140699.i	−1.01129	+	1.01129i	−0.0113524	+	0.999936i	$0.503614\pi$
$373$	−140699.	+	140699.i	−1.01129	+	1.01129i	−0.999936	+	0.0113524i	$0.996386\pi$
$374$	178178.	−	273660.i	1.27383	−	1.95645i
$375$	17738.0			0.126137
$376$	−73179.3	+	52772.1i	−0.517622	+	0.373275i
$377$		−	314989.i		−	2.21622i
$378$	14889.7	−	22868.8i	0.104208	−	0.160051i
$379$	105273.	+	105273.i	0.732888	+	0.732888i	0.971191	−	0.238303i	$-0.0765911\pi$
$379$	105273.	+	105273.i	0.732888	+	0.732888i	−0.238303	+	0.971191i	$0.576591\pi$
$380$	−21256.9	−	48049.4i	−0.147208	−	0.332752i
$381$	72654.8	+	72654.8i	0.500512	+	0.500512i
$382$	−111835.	+	23633.0i	−0.766390	+	0.161954i
$383$		−	129358.i		−	0.881854i	−0.897543	−	0.440927i	$-0.854650\pi$
$383$		−	129358.i		−	0.881854i	0.897543	−	0.440927i	$-0.145350\pi$
$384$	66602.8	−	53026.7i	0.451679	−	0.359610i
$385$	−280730.			−1.89395
$386$	35811.3	+	169464.i	0.240351	+	1.13738i
$387$	5953.04	−	5953.04i	0.0397481	−	0.0397481i
$388$	70452.6	−	31168.0i	0.467987	−	0.207036i
$389$	110435.	−	110435.i	0.729805	−	0.729805i	−0.240776	−	0.970581i	$-0.577402\pi$
$389$	110435.	−	110435.i	0.729805	−	0.729805i	0.970581	+	0.240776i	$0.0774020\pi$
$390$	136563.	+	88914.8i	0.897849	+	0.584581i
$391$	−148390.			−0.970623
$392$	−1362.12	−	1888.86i	−0.00886430	−	0.0122922i
$393$			95763.0i			0.620030i
$394$	92861.7	+	60461.4i	0.598197	+	0.389481i
$395$	−188529.	−	188529.i	−1.20832	−	1.20832i
$396$	24537.4	−	63472.7i	0.156472	−	0.404759i
$397$	−105244.	−	105244.i	−0.667756	−	0.667756i	0.289440	−	0.957196i	$-0.406531\pi$
$397$	−105244.	−	105244.i	−0.667756	−	0.667756i	−0.957196	+	0.289440i	$0.906531\pi$
$398$	20779.2	+	98330.2i	0.131178	+	0.620756i
$399$			22640.3i			0.142212i
$400$	−136040.	−	123662.i	−0.850250	−	0.772885i
$401$	−25637.1			−0.159434			−0.0797170	−	0.996818i	$-0.525402\pi$
$401$	−25637.1			−0.159434			−0.0797170	+	0.996818i	$0.525402\pi$
$402$	−148412.	+	31362.5i	−0.918369	+	0.194070i
$403$	−33559.8	+	33559.8i	−0.206638	+	0.206638i
$404$	42556.6	−	110084.i	0.260738	−	0.674471i
$405$	18891.8	−	18891.8i	0.115177	−	0.115177i
$406$	156265.	−	240005.i	0.948004	−	1.45602i
$407$	56271.3			0.339702
$408$	−170130.	−	27565.3i	−1.02202	−	0.165593i
$409$		−	26950.6i		−	0.161110i	−0.996750	−	0.0805549i	$-0.974331\pi$
$409$		−	26950.6i		−	0.161110i	0.996750	−	0.0805549i	$-0.0256692\pi$
$410$	−164736.	+	253016.i	−0.979990	+	1.50515i
$411$	−77827.1	−	77827.1i	−0.460731	−	0.460731i
$412$	284018.	−	125649.i	1.67321	−	0.740224i
$413$	−41285.3	−	41285.3i	−0.242045	−	0.242045i
$414$	−30254.8	+	6393.46i	−0.176520	+	0.0373023i
$415$			286820.i			1.66538i
$416$	−55445.5	−	211932.i	−0.320390	−	1.22464i
$417$	−88647.5			−0.509794
$418$	11673.0	+	55238.3i	0.0668082	+	0.316146i
$419$	−119464.	+	119464.i	−0.680469	+	0.680469i	−0.960106	−	0.279637i	$-0.909786\pi$
$419$	−119464.	+	119464.i	−0.680469	+	0.680469i	0.279637	+	0.960106i	$0.409786\pi$
$420$	59943.4	+	135497.i	0.339815	+	0.768123i
$421$	152293.	−	152293.i	0.859243	−	0.859243i	−0.132006	−	0.991249i	$-0.542142\pi$
$421$	152293.	−	152293.i	0.859243	−	0.859243i	0.991249	+	0.132006i	$0.0421419\pi$
$422$	−13531.0	−	8809.92i	−0.0759811	−	0.0494706i
$423$	38062.6			0.212725
$424$	67674.1	+	10964.9i	0.376436	+	0.0609918i
$425$			372185.i			2.06054i
$426$	50570.8	+	32926.2i	0.278664	+	0.181435i
$427$	−28580.1	−	28580.1i	−0.156750	−	0.156750i
$428$	205632.	+	79493.5i	1.12254	+	0.433954i
$429$	−123819.	−	123819.i	−0.672778	−	0.672778i
$430$	9450.75	+	44722.4i	0.0511127	+	0.241873i
$431$			66806.9i			0.359639i	0.983700	+	0.179819i	$0.0575513\pi$
$431$			66806.9i			0.359639i	−0.983700	+	0.179819i	$0.942449\pi$
$432$	−35875.1	+	1709.95i	−0.192232	+	0.00916252i
$433$	−79759.0			−0.425406			−0.212703	−	0.977117i	$-0.568227\pi$
$433$	−79759.0			−0.425406			−0.212703	+	0.977117i	$0.568227\pi$
$434$	−42219.8	+	8921.90i	−0.224149	+	0.0473672i
$435$	198268.	−	198268.i	1.04779	−	1.04779i
$436$	−8885.37	−	3434.92i	−0.0467415	−	0.0180694i
$437$	18141.0	−	18141.0i	0.0949947	−	0.0949947i
$438$	−16475.1	+	25303.8i	−0.0858776	+	0.131898i
$439$	−104452.			−0.541984			−0.270992	−	0.962582i	$-0.587352\pi$
$439$	−104452.			−0.541984			−0.270992	+	0.962582i	$0.587352\pi$
$440$	216112.	+	299683.i	1.11628	+	1.54795i
$441$			982.451i			0.00505166i
$442$	−241979.	+	371652.i	−1.23861	+	1.90236i
$443$	162038.	+	162038.i	0.825676	+	0.825676i	0.986915	−	0.161239i	$-0.0515490\pi$
$443$	162038.	+	162038.i	0.825676	+	0.825676i	−0.161239	+	0.986915i	$0.551549\pi$
$444$	−12015.4	−	27159.9i	−0.0609500	−	0.137772i
$445$	−233145.	−	233145.i	−1.17735	−	1.17735i
$446$	−206269.	+	43588.9i	−1.03697	+	0.219132i
$447$			22602.6i			0.113121i
$448$	62892.2	−	188987.i	0.313358	−	0.941622i
$449$	−304806.			−1.51193			−0.755963	−	0.654615i	$-0.772831\pi$
$449$	−304806.			−1.51193			−0.755963	+	0.654615i	$0.772831\pi$
$450$	16035.8	+	75883.9i	0.0791892	+	0.374735i
$451$	229404.	−	229404.i	1.12784	−	1.12784i
$452$	118993.	−	52642.2i	0.582432	−	0.257666i
$453$	−68871.3	+	68871.3i	−0.335615	+	0.335615i
$454$	188360.	+	122639.i	0.913854	+	0.595002i
$455$	381253.			1.84158
$456$	24168.8	−	17428.9i	0.116232	−	0.0838188i
$457$			200942.i			0.962138i	0.876683	+	0.481069i	$0.159751\pi$
$457$			200942.i			0.962138i	−0.876683	+	0.481069i	$0.840249\pi$
$458$	184669.	+	120237.i	0.880368	+	0.573199i
$459$	51413.6	+	51413.6i	0.244035	+	0.244035i
$460$	60539.0	−	156601.i	0.286101	−	0.740081i
$461$	128467.	+	128467.i	0.604493	+	0.604493i	0.941502	−	0.337009i	$-0.109415\pi$
$461$	128467.	+	128467.i	0.604493	+	0.604493i	−0.337009	+	0.941502i	$0.609415\pi$
$462$	−32917.3	−	155770.i	−0.154220	−	0.729791i
$463$		−	26357.2i		−	0.122952i	−0.998109	−	0.0614761i	$-0.980419\pi$
$463$		−	26357.2i		−	0.122952i	0.998109	−	0.0614761i	$-0.0195808\pi$
$464$	−376505.	+	17945.7i	−1.74878	+	0.0833536i
$465$	−42248.0			−0.195389
$466$	289368.	−	61149.3i	1.33253	−	0.281591i
$467$	17864.7	−	17864.7i	0.0819148	−	0.0819148i	−0.664962	−	0.746877i	$-0.731552\pi$
$467$	17864.7	−	17864.7i	0.0819148	−	0.0819148i	0.746877	+	0.664962i	$0.231552\pi$
$468$	−33323.6	+	86200.9i	−0.152146	+	0.393568i
$469$	−250945.	+	250945.i	−1.14086	+	1.14086i
$470$	−112760.	+	173186.i	−0.510458	+	0.784004i
$471$	−132854.			−0.598871
$472$	−12290.4	+	75854.9i	−0.0551671	+	0.340486i
$473$		−	49117.6i		−	0.219541i
$474$	82503.4	−	126716.i	0.367211	−	0.563993i
$475$	−45500.6	−	45500.6i	−0.201665	−	0.201665i
$476$	−368751.	+	163134.i	−1.62749	+	0.719998i
$477$	−20451.2	−	20451.2i	−0.0898838	−	0.0898838i
$478$	−14793.9	+	3126.24i	−0.0647479	+	0.0136825i
$479$			274857.i			1.19794i	0.800770	+	0.598972i	$0.204424\pi$
$479$			274857.i			1.19794i	−0.800770	+	0.598972i	$0.795576\pi$
$480$	98499.2	−	168299.i	0.427514	−	0.730463i
$481$	−76420.8			−0.330310
$482$	−56568.0	−	267688.i	−0.243487	−	1.15222i
$483$	−51156.9	+	51156.9i	−0.219286	+	0.219286i
$484$	−65851.0	−	148851.i	−0.281107	−	0.635419i
$485$	124778.	−	124778.i	0.530462	−	0.530462i
$486$	12697.7	+	8267.39i	0.0537594	+	0.0350022i
$487$	26509.7			0.111776			0.0558878	−	0.998437i	$-0.482201\pi$
$487$	26509.7			0.111776			0.0558878	+	0.998437i	$0.482201\pi$
$488$	−8508.11	+	52511.2i	−0.0357267	+	0.220502i
$489$		−	140717.i		−	0.588478i
$490$	−4470.19	−	2910.50i	−0.0186180	−	0.0121220i
$491$	130474.	+	130474.i	0.541204	+	0.541204i	0.923882	−	0.382678i	$-0.124998\pi$
$491$	130474.	+	130474.i	0.541204	+	0.541204i	−0.382678	+	0.923882i	$0.624998\pi$
$492$	−159708.	−	61740.1i	−0.659776	−	0.255057i
$493$	539579.	+	539579.i	2.22004	+	2.22004i
$494$	−15852.8	−	75017.9i	−0.0649610	−	0.307405i
$495$		−	155874.i		−	0.636154i
$496$	42025.9	+	38201.9i	0.170826	+	0.155282i
$497$	141182.			0.571568
$498$	−159149.	+	33631.3i	−0.641718	+	0.135608i
$499$	−247971.	+	247971.i	−0.995863	+	0.995863i	−0.999991	−	0.00412869i	$-0.998686\pi$
$499$	−247971.	+	247971.i	−0.995863	+	0.995863i	0.00412869	+	0.999991i	$0.498686\pi$
$500$	−50944.7	−	19694.2i	−0.203779	−	0.0787770i
$501$	99362.5	−	99362.5i	0.395865	−	0.395865i
$502$	49437.6	−	75930.4i	0.196178	−	0.301307i
$503$	−81953.2			−0.323914			−0.161957	−	0.986798i	$-0.551781\pi$
$503$	−81953.2			−0.323914			−0.161957	+	0.986798i	$0.551781\pi$
$504$	−68154.9	+	49148.8i	−0.268309	+	0.193487i
$505$		−	270341.i		−	1.06006i
$506$	−98438.2	+	151190.i	−0.384470	+	0.590501i
$507$	63215.6	+	63215.6i	0.245928	+	0.245928i
$508$	−128002.	−	289337.i	−0.496007	−	1.12118i
$509$	−120184.	−	120184.i	−0.463886	−	0.463886i	0.436041	−	0.899927i	$-0.356380\pi$
$509$	−120184.	−	120184.i	−0.463886	−	0.463886i	−0.899927	+	0.436041i	$0.856380\pi$
$510$	−386246.	+	81621.6i	−1.48499	+	0.313809i
$511$			70642.7i			0.270536i
$512$	−250162.	+	78348.0i	−0.954293	+	0.298874i
$513$	−12570.9			−0.0477673
$514$	−64318.6	−	304365.i	−0.243450	−	1.15204i
$515$	503021.	−	503021.i	1.89658	−	1.89658i
$516$	−23707.1	+	10487.9i	−0.0890386	+	0.0393904i
$517$	157025.	−	157025.i	0.587471	−	0.587471i
$518$	−58228.7	−	37912.2i	−0.217009	−	0.141293i
$519$	257863.			0.957312
$520$	−293496.	−	406993.i	−1.08542	−	1.50515i
$521$		−	38303.1i		−	0.141110i	−0.997508	−	0.0705551i	$-0.977523\pi$
$521$		−	38303.1i		−	0.141110i	0.997508	−	0.0705551i	$-0.0224771\pi$
$522$	133261.	+	86765.3i	0.489061	+	0.318423i
$523$	−308610.	−	308610.i	−1.12825	−	1.12825i	−0.990461	−	0.137790i	$-0.956000\pi$
$523$	−308610.	−	308610.i	−1.12825	−	1.12825i	−0.137790	−	0.990461i	$-0.544000\pi$
$524$	106324.	−	275037.i	0.387231	−	1.00168i
$525$	128310.	+	128310.i	0.465522	+	0.465522i
$526$	33324.8	+	157698.i	0.120447	+	0.569973i
$527$		−	114977.i		−	0.413988i
$528$	−140946.	+	155054.i	−0.505573	+	0.556180i
$529$	−197860.			−0.707043
$530$	153640.	−	32467.3i	0.546956	−	0.115583i
$531$	22923.4	−	22923.4i	0.0813000	−	0.0813000i
$532$	25137.2	−	65024.3i	0.0888164	−	0.229748i
$533$	−311549.	+	311549.i	−1.09666	+	1.09666i
$534$	102028.	−	156704.i	0.357798	−	0.549536i
$535$	504983.			1.76429
$536$	461070.	+	74704.7i	1.60486	+	0.260027i
$537$		−	248243.i		−	0.860853i
$538$	73147.3	−	112346.i	0.252717	−	0.388144i
$539$	4053.03	+	4053.03i	0.0139509	+	0.0139509i
$540$	−75233.9	+	33283.2i	−0.258004	+	0.114140i
$541$	−75816.7	−	75816.7i	−0.259042	−	0.259042i	0.565622	−	0.824664i	$-0.308636\pi$
$541$	−75816.7	−	75816.7i	−0.259042	−	0.259042i	−0.824664	+	0.565622i	$0.808636\pi$
$542$	−12092.8	+	2555.46i	−0.0411651	+	0.00869902i
$543$			211569.i			0.717549i
$544$	458020.	+	268063.i	1.54770	+	0.905813i
$545$	−21820.3			−0.0734629
$546$	44704.2	+	211547.i	0.149956	+	0.709614i
$547$	−284459.	+	284459.i	−0.950702	+	0.950702i	−0.998841	−	0.0481389i	$-0.984671\pi$
$547$	−284459.	+	284459.i	−0.950702	+	0.950702i	0.0481389	+	0.998841i	$0.484671\pi$
$548$	137114.	+	309935.i	0.456584	+	1.03207i
$549$	15868.9	−	15868.9i	0.0526506	−	0.0526506i
$550$	379208.	+	246899.i	1.25358	+	0.816194i
$551$	−131930.			−0.434550
$552$	93992.3	+	15229.1i	0.308471	+	0.0499798i
$553$		−	353762.i		−	1.15681i
$554$	−36409.8	−	23706.1i	−0.118631	−	0.0772397i
$555$	−48102.6	−	48102.6i	−0.156164	−	0.156164i
$556$	254601.	+	98424.0i	0.823590	+	0.318384i
$557$	−176263.	−	176263.i	−0.568133	−	0.568133i	0.363472	−	0.931605i	$-0.381591\pi$
$557$	−176263.	−	176263.i	−0.568133	−	0.568133i	−0.931605	+	0.363472i	$0.881591\pi$
$558$	−4953.83	−	23442.3i	−0.0159101	−	0.0752889i
$559$			66705.5i			0.213471i
$560$	−21720.9	−	455710.i	−0.0692632	−	1.45316i
$561$	424205.			1.34788
$562$	−287389.	+	60731.2i	−0.909909	+	0.192282i
$563$	374796.	−	374796.i	1.18244	−	1.18244i	0.203328	−	0.979111i	$-0.434824\pi$
$563$	374796.	−	374796.i	1.18244	−	1.18244i	0.979111	−	0.203328i	$-0.0651758\pi$
$564$	−109318.	−	42260.4i	−0.343664	−	0.132854i
$565$	210747.	−	210747.i	0.660185	−	0.660185i
$566$	−73866.4	+	113450.i	−0.230576	+	0.354138i
$567$	35449.3			0.110266
$568$	−108685.	−	150714.i	−0.336878	−	0.467151i
$569$			301015.i			0.929745i	0.885378	+	0.464873i	$0.153900\pi$
$569$			301015.i			0.929745i	−0.885378	+	0.464873i	$0.846100\pi$
$570$	37241.1	−	57198.0i	0.114623	−	0.176048i
$571$	307433.	+	307433.i	0.942929	+	0.942929i	0.998457	−	0.0555283i	$-0.0176843\pi$
$571$	307433.	+	307433.i	0.942929	+	0.942929i	−0.0555283	+	0.998457i	$0.517684\pi$
$572$	218141.	+	493089.i	0.666723	+	1.50707i
$573$	−104995.	−	104995.i	−0.319787	−	0.319787i
$574$	−391942.	+	82825.4i	−1.18959	+	0.251385i
$575$		−	205622.i		−	0.621919i
$576$	104934.	+	34920.5i	0.316280	+	0.105253i
$577$	40887.2			0.122810			0.0614052	−	0.998113i	$-0.480442\pi$
$577$	40887.2			0.122810			0.0614052	+	0.998113i	$0.480442\pi$
$578$	−153057.	−	724291.i	−0.458140	−	2.16799i
$579$	−159101.	+	159101.i	−0.474586	+	0.474586i
$580$	−789571.	+	349303.i	−2.34712	+	1.03836i
$581$	−269099.	+	269099.i	−0.797187	+	0.797187i
$582$	83866.8	+	54604.9i	0.247596	+	0.161208i
$583$	−168740.			−0.496455
$584$	75412.0	−	54382.2i	0.221113	−	0.159452i
$585$			211689.i			0.618565i
$586$	−225776.	−	147001.i	−0.657481	−	0.428080i
$587$	186131.	+	186131.i	0.540184	+	0.540184i	0.923583	−	0.383399i	$-0.125247\pi$
$587$	186131.	+	186131.i	0.540184	+	0.540184i	−0.383399	+	0.923583i	$0.625247\pi$
$588$	1090.80	−	2821.66i	0.00315494	−	0.00816113i
$589$	14056.2	+	14056.2i	0.0405170	+	0.0405170i
$590$	36392.1	+	172213.i	0.104545	+	0.494722i
$591$			143947.i			0.412123i
$592$	4353.88	+	91345.5i	0.0124232	+	0.260642i
$593$	639660.			1.81903			0.909515	−	0.415671i	$-0.136453\pi$
$593$	639660.			1.81903			0.909515	+	0.415671i	$0.136453\pi$
$594$	86490.1	−	18277.1i	0.245128	−	0.0518006i
$595$	−653091.	+	653091.i	−1.84476	+	1.84476i
$596$	25095.3	−	64916.0i	0.0706480	−	0.182751i
$597$	−92316.8	+	92316.8i	−0.259019	+	0.259019i
$598$	133687.	−	205327.i	0.373840	−	0.574175i
$599$	−511540.			−1.42569			−0.712847	−	0.701320i	$-0.752595\pi$
$599$	−511540.			−1.42569			−0.712847	+	0.701320i	$0.752595\pi$
$600$	38196.9	−	235748.i	0.106102	−	0.654854i
$601$			297145.i			0.822658i	0.911487	+	0.411329i	$0.134935\pi$
$601$			297145.i			0.822658i	−0.911487	+	0.411329i	$0.865065\pi$
$602$	−33092.4	+	50826.2i	−0.0913137	+	0.140247i
$603$	−139336.	−	139336.i	−0.383202	−	0.383202i
$604$	274269.	−	121336.i	0.751802	−	0.332595i
$605$	−263628.	−	263628.i	−0.720245	−	0.720245i
$606$	150005.	−	31699.1i	0.408470	−	0.0863180i
$607$		−	687348.i		−	1.86552i	−0.360502	−	0.932759i	$-0.617395\pi$
$607$		−	687348.i		−	1.86552i	0.360502	−	0.932759i	$-0.382605\pi$
$608$	−88765.4	+	23222.8i	−0.240125	+	0.0628213i
$609$	372036.			1.00311
$610$	25192.7	+	119216.i	0.0677042	+	0.320387i
$611$	−213251.	+	213251.i	−0.571228	+	0.571228i
$612$	−90579.3	−	204747.i	−0.241839	−	0.546656i
$613$	−256488.	+	256488.i	−0.682567	+	0.682567i	−0.960578	−	0.278011i	$-0.910325\pi$
$613$	−256488.	+	256488.i	−0.682567	+	0.682567i	0.278011	+	0.960578i	$0.410325\pi$
$614$	−593933.	−	386704.i	−1.57544	−	1.02575i
$615$	−392204.			−1.03696
$616$	−78408.2	+	483928.i	−0.206633	+	1.27532i
$617$			348664.i			0.915877i	0.888984	+	0.457938i	$0.151412\pi$
$617$			348664.i			0.915877i	−0.888984	+	0.457938i	$0.848588\pi$
$618$	338095.	+	220131.i	0.885242	+	0.576373i
$619$	233789.	+	233789.i	0.610158	+	0.610158i	0.942987	−	0.332829i	$-0.108003\pi$
$619$	233789.	+	233789.i	0.610158	+	0.610158i	−0.332829	+	0.942987i	$0.608003\pi$
$620$	121339.	+	46907.3i	0.315658	+	0.122027i
$621$	−28404.5	−	28404.5i	−0.0736554	−	0.0736554i
$622$	49408.0	+	233806.i	0.127708	+	0.604331i
$623$		−	437482.i		−	1.12716i
$624$	191415.	−	210576.i	0.491595	−	0.540803i
$625$	323733.			0.828757
$626$	64695.7	−	13671.5i	0.165092	−	0.0348874i
$627$	−51860.2	+	51860.2i	−0.131917	+	0.131917i
$628$	381565.	+	147506.i	0.967497	+	0.374016i
$629$	130910.	−	130910.i	0.330880	−	0.330880i
$630$	−105018.	+	161296.i	−0.264596	+	0.406389i
$631$	−142317.			−0.357436			−0.178718	−	0.983900i	$-0.557195\pi$
$631$	−142317.			−0.357436			−0.178718	+	0.983900i	$0.557195\pi$
$632$	−377646.	+	272333.i	−0.945476	+	0.681815i
$633$		−	20974.7i		−	0.0523465i
$634$	339292.	−	521113.i	0.844102	−	1.29644i
$635$	−512441.	−	512441.i	−1.27086	−	1.27086i
$636$	36030.4	+	81443.7i	0.0890748	+	0.201346i
$637$	−5504.33	−	5504.33i	−0.0135652	−	0.0135652i
$638$	907704.	−	191816.i	2.22999	−	0.471242i
$639$			78390.6i			0.191983i
$640$	−469755.	+	374002.i	−1.14686	+	0.913091i
$641$	−40213.5			−0.0978714			−0.0489357	−	0.998802i	$-0.515583\pi$
$641$	−40213.5			−0.0978714			−0.0489357	+	0.998802i	$0.515583\pi$
$642$	59212.3	+	280201.i	0.143662	+	0.679830i
$643$	65562.2	−	65562.2i	0.158574	−	0.158574i	−0.623361	−	0.781935i	$-0.714233\pi$
$643$	65562.2	−	65562.2i	0.158574	−	0.158574i	0.781935	+	0.623361i	$0.214233\pi$
$644$	203725.	−	90127.1i	0.491215	−	0.217312i
$645$	−41987.3	+	41987.3i	−0.100925	+	0.100925i
$646$	155663.	+	101350.i	0.373009	+	0.242863i
$647$	−267536.			−0.639106			−0.319553	−	0.947568i	$-0.603533\pi$
$647$	−267536.			−0.639106			−0.319553	+	0.947568i	$0.603533\pi$
$648$	−27289.6	−	37842.6i	−0.0649900	−	0.0901220i
$649$		−	189138.i		−	0.449044i
$650$	−514993.	−	335307.i	−1.21892	−	0.793627i
$651$	−39637.8	−	39637.8i	−0.0935292	−	0.0935292i
$652$	−156236.	+	404149.i	−0.367525	+	0.950706i
$653$	147054.	+	147054.i	0.344866	+	0.344866i	0.858193	−	0.513327i	$-0.171587\pi$
$653$	147054.	+	147054.i	0.344866	+	0.344866i	−0.513327	+	0.858193i	$0.671587\pi$
$654$	−2558.56	−	12107.5i	−0.00598192	−	0.0283074i
$655$		−	675425.i		−	1.57433i
$656$	390142.	+	354643.i	0.906600	+	0.824107i
$657$	−39223.9			−0.0908699
$658$	−268280.	+	56693.1i	−0.619636	+	0.130942i
$659$	−528043.	+	528043.i	−1.21590	+	1.21590i	−0.246847	+	0.969054i	$0.579395\pi$
$659$	−528043.	+	528043.i	−1.21590	+	1.21590i	−0.969054	+	0.246847i	$0.920605\pi$
$660$	−173064.	+	447679.i	−0.397301	+	1.02773i
$661$	−48471.2	+	48471.2i	−0.110938	+	0.110938i	−0.760397	−	0.649459i	$-0.774996\pi$
$661$	−48471.2	+	48471.2i	−0.110938	+	0.110938i	0.649459	+	0.760397i	$0.274996\pi$
$662$	−167081.	+	256618.i	−0.381252	+	0.585559i
$663$	−576104.			−1.31061
$664$	494425.	+	80109.0i	1.12141	+	0.181696i
$665$		−	159684.i		−	0.361092i
$666$	21050.5	−	32331.1i	0.0474585	−	0.0728908i
$667$	−298103.	−	298103.i	−0.670060	−	0.670060i
$668$	−395696.	+	175055.i	−0.886766	+	0.392302i
$669$	−193655.	−	193655.i	−0.432689	−	0.432689i
$670$	1.04676e6	−	221203.i	2.33184	−	0.492766i
$671$		−	130932.i		−	0.290805i
$672$	250314.	−	65487.1i	0.554303	−	0.145016i
$673$	−124450.			−0.274767			−0.137383	−	0.990518i	$-0.543869\pi$
$673$	−124450.			−0.274767			−0.137383	+	0.990518i	$0.543869\pi$
$674$	−34569.4	−	163588.i	−0.0760979	−	0.360107i
$675$	−71243.1	+	71243.1i	−0.156364	+	0.156364i
$676$	−111372.	−	251747.i	−0.243715	−	0.550897i
$677$	88125.2	−	88125.2i	0.192275	−	0.192275i	−0.604403	−	0.796678i	$-0.706588\pi$
$677$	88125.2	−	88125.2i	0.192275	−	0.192275i	0.796678	+	0.604403i	$0.206588\pi$
$678$	141649.	+	92226.7i	0.308145	+	0.200631i
$679$	234138.			0.507845
$680$	1.19995e6	+	194421.i	2.59504	+	0.420460i
$681$			291980.i			0.629592i
$682$	−117146.	−	76272.6i	−0.251860	−	0.163983i
$683$	363797.	+	363797.i	0.779861	+	0.779861i	0.979807	−	0.199946i	$-0.0640766\pi$
$683$	363797.	+	363797.i	0.779861	+	0.779861i	−0.199946	+	0.979807i	$0.564077\pi$
$684$	36104.4	+	13957.3i	0.0771698	+	0.0298324i
$685$	548922.	+	548922.i	1.16985	+	1.16985i
$686$	−98021.0	−	463850.i	−0.208291	−	0.985666i
$687$			286259.i			0.606521i
$688$	79732.8	−	3800.38i	0.168446	−	0.00802879i
$689$	229161.			0.482729
$690$	213390.	−	45093.7i	0.448204	−	0.0947147i
$691$	169608.	−	169608.i	0.355215	−	0.355215i	−0.506831	−	0.862046i	$-0.669183\pi$
$691$	169608.	−	169608.i	0.355215	−	0.355215i	0.862046	+	0.506831i	$0.169183\pi$
$692$	−740598.	−	286301.i	−1.54657	−	0.597876i
$693$	146243.	−	146243.i	0.304516	−	0.304516i
$694$	−413287.	+	634760.i	−0.858089	+	1.31793i
$695$	625239.			1.29442
$696$	−286401.	−	397154.i	−0.591229	−	0.819861i
$697$		−	1.06737e6i		−	2.19710i
$698$	220286.	−	338334.i	0.452144	−	0.694441i
$699$	271671.	+	271671.i	0.556018	+	0.556018i
$700$	−226053.	−	510974.i	−0.461333	−	1.04280i
$701$	−604083.	−	604083.i	−1.22931	−	1.22931i	−0.964226	−	0.265082i	$-0.914601\pi$
$701$	−604083.	−	604083.i	−1.22931	−	1.22931i	−0.265082	−	0.964226i	$-0.585399\pi$
$702$	−117460.	+	24821.7i	−0.238351	+	0.0503684i
$703$			32008.1i			0.0647663i
$704$	576959.	−	288836.i	1.16413	−	0.582781i
$705$	−268459.			−0.540132
$706$	−2019.79	−	9557.95i	−0.00405226	−	0.0191759i
$707$	253639.	−	253639.i	0.507430	−	0.507430i
$708$	−91289.1	+	40386.0i	−0.182118	+	0.0805683i
$709$	351933.	−	351933.i	0.700112	−	0.700112i	−0.264322	−	0.964434i	$-0.585148\pi$
$709$	351933.	−	351933.i	0.700112	−	0.700112i	0.964434	+	0.264322i	$0.0851483\pi$
$710$	−356680.	−	232231.i	−0.707559	−	0.460685i
$711$	196424.			0.388558
$712$	−467017.	+	336782.i	−0.921241	+	0.664338i
$713$			63521.4i			0.124951i
$714$	−438961.	−	285804.i	−0.861053	−	0.560624i
$715$	873305.	+	873305.i	1.70826	+	1.70826i
$716$	−275621.	+	712970.i	−0.537633	+	1.39074i
$717$	−13889.1	−	13889.1i	−0.0270170	−	0.0270170i
$718$	39189.7	+	185452.i	0.0760192	+	0.359734i
$719$			144595.i			0.279703i	0.990173	+	0.139851i	$0.0446625\pi$
$719$			144595.i			0.279703i	−0.990173	+	0.139851i	$0.955338\pi$
$720$	253030.	−	12060.4i	0.488099	−	0.0232647i
$721$	943887.			1.81572
$722$	478600.	−	101138.i	0.918118	−	0.194017i
$723$	251318.	−	251318.i	0.480780	−	0.480780i
$724$	234901.	−	607638.i	0.448135	−	1.15923i
$725$	−747689.	+	747689.i	−1.42248	+	1.42248i
$726$	115368.	−	177192.i	0.218883	−	0.336179i
$727$	−259307.			−0.490621			−0.245310	−	0.969445i	$-0.578890\pi$
$727$	−259307.			−0.490621			−0.245310	+	0.969445i	$0.578890\pi$
$728$	106484.	−	657211.i	0.200920	−	1.24006i
$729$			19683.0i			0.0370370i
$730$	116200.	−	178470.i	0.218053	−	0.334904i
$731$	−114267.	−	114267.i	−0.213839	−	0.213839i
$732$	−63195.7	+	27957.5i	−0.117941	+	0.0521767i
$733$	−92594.8	−	92594.8i	−0.172337	−	0.172337i	0.615668	−	0.788005i	$-0.288886\pi$
$733$	−92594.8	−	92594.8i	−0.172337	−	0.172337i	−0.788005	+	0.615668i	$0.788886\pi$
$734$	−1.00488e6	+	212351.i	−1.86518	+	0.394151i
$735$		−	6929.32i		−	0.0128267i
$736$	−253043.	−	148097.i	−0.467131	−	0.273395i
$737$	−1.14964e6			−2.11654
$738$	−45988.3	−	217624.i	−0.0844374	−	0.399570i
$739$	−134779.	+	134779.i	−0.246793	+	0.246793i	−0.819653	−	0.572860i	$-0.805834\pi$
$739$	−134779.	+	134779.i	−0.246793	+	0.246793i	0.572860	+	0.819653i	$0.305834\pi$
$740$	84746.0	+	191561.i	0.154759	+	0.349820i
$741$	70430.2	−	70430.2i	0.128269	−	0.128269i
$742$	174609.	+	113686.i	0.317146	+	0.206491i
$743$	152758.			0.276711			0.138355	−	0.990383i	$-0.455818\pi$
$743$	152758.			0.276711			0.138355	+	0.990383i	$0.455818\pi$
$744$	−11799.9	+	72827.8i	−0.0213173	+	0.131568i
$745$		−	159418.i		−	0.287227i
$746$	666998.	+	434277.i	1.19853	+	0.780349i
$747$	−149416.	−	149416.i	−0.267766	−	0.267766i
$748$	−1.21835e6	−	470989.i	−2.17754	−	0.841798i
$749$	473784.	+	473784.i	0.844533	+	0.844533i
$750$	−14669.6	−	69418.9i	−0.0260794	−	0.123411i
$751$			161735.i			0.286764i	0.989667	+	0.143382i	$0.0457977\pi$
$751$			161735.i			0.286764i	−0.989667	+	0.143382i	$0.954202\pi$
$752$	267048.	+	242749.i	0.472230	+	0.429261i
$753$	117701.			0.207582
$754$	−1.23273e6	+	260501.i	−2.16833	+	0.458213i
$755$	485756.	−	485756.i	0.852165	−	0.852165i
$756$	−101813.	−	39358.8i	−0.178139	−	0.0688650i
$757$	162117.	−	162117.i	0.282903	−	0.282903i	−0.551362	−	0.834266i	$-0.685892\pi$
$757$	162117.	−	162117.i	0.282903	−	0.282903i	0.834266	+	0.551362i	$0.185892\pi$
$758$	324930.	−	499055.i	0.565524	−	0.868580i
$759$	−234362.			−0.406821
$760$	−170465.	+	122928.i	−0.295126	+	0.212825i
$761$			430340.i			0.743092i	0.928415	+	0.371546i	$0.121172\pi$
$761$			430340.i			0.743092i	−0.928415	+	0.371546i	$0.878828\pi$
$762$	224253.	−	344427.i	0.386214	−	0.593180i
$763$	−20472.2	−	20472.2i	−0.0351654	−	0.0351654i
$764$	184979.	+	418128.i	0.316909	+	0.716346i
$765$	−362625.	−	362625.i	−0.619633	−	0.619633i
$766$	−506253.	+	106982.i	−0.862800	+	0.182327i
$767$			256864.i			0.436628i
$768$	−262605.	−	216801.i	−0.445227	−	0.367568i
$769$	−795637.			−1.34543			−0.672717	−	0.739900i	$-0.734873\pi$
$769$	−795637.			−1.34543			−0.672717	+	0.739900i	$0.734873\pi$
$770$	232169.	+	1.09866e6i	0.391582	+	1.85302i
$771$	285752.	−	285752.i	0.480706	−	0.480706i
$772$	633595.	−	280300.i	1.06311	−	0.470315i
$773$	4647.04	−	4647.04i	0.00777710	−	0.00777710i	−0.703208	−	0.710985i	$-0.748250\pi$
$773$	4647.04	−	4647.04i	0.00777710	−	0.00777710i	0.710985	+	0.703208i	$0.248250\pi$
$774$	−28220.9	−	18374.4i	−0.0471074	−	0.0306712i
$775$	159322.			0.265260
$776$	−180244.	−	249945.i	−0.299321	−	0.415069i
$777$		−	90261.3i		−	0.149506i
$778$	−523526.	−	340863.i	−0.864926	−	0.563145i
$779$	130489.	+	130489.i	0.215030	+	0.215030i
$780$	235035.	−	607983.i	0.386316	−	0.999314i
$781$	323395.	+	323395.i	0.530189	+	0.530189i
$782$	122721.	+	580734.i	0.200681	+	0.949651i
$783$			206571.i			0.336935i
$784$	−6265.70	+	6892.89i	−0.0101938	+	0.0112142i
$785$	937032.			1.52060
$786$	374775.	−	79197.7i	0.606633	−	0.128194i
$787$	123993.	−	123993.i	0.200192	−	0.200192i	−0.599890	−	0.800082i	$-0.704789\pi$
$787$	123993.	−	123993.i	0.200192	−	0.200192i	0.800082	+	0.599890i	$0.204789\pi$
$788$	159822.	−	413424.i	0.257385	−	0.665799i
$789$	−148054.	+	148054.i	−0.237829	+	0.237829i
$790$	−581905.	+	893738.i	−0.932390	+	1.43204i
$791$	395454.			0.632037
$792$	−268698.	−	43535.6i	−0.428365	−	0.0694056i
$793$			177816.i			0.282764i
$794$	−324843.	+	498920.i	−0.515266	+	0.791389i
$795$	144244.	+	144244.i	0.228225	+	0.228225i
$796$	367638.	−	162642.i	0.580221	−	0.256688i
$797$	391326.	+	391326.i	0.616058	+	0.616058i	0.944518	−	0.328460i	$-0.106530\pi$
$797$	391326.	+	391326.i	0.616058	+	0.616058i	−0.328460	+	0.944518i	$0.606530\pi$
$798$	88604.4	−	18723.9i	0.139139	−	0.0294029i
$799$		−	730604.i		−	1.14443i
$800$	−371451.	+	634672.i	−0.580392	+	0.991676i
$801$	242909.			0.378598
$802$	21202.4	+	100333.i	0.0329637	+	0.155989i
$803$	−161815.	+	161815.i	−0.250951	+	0.250951i
$804$	245479.	+	554884.i	0.379754	+	0.858401i
$805$	360814.	−	360814.i	0.556791	−	0.556791i
$806$	159093.	+	103584.i	0.244896	+	0.159450i
$807$	174149.			0.267408
$808$	−466019.	−	75506.4i	−0.713806	−	0.115654i
$809$		−	35996.3i		−	0.0549998i	−0.999622	−	0.0274999i	$-0.991245\pi$
$809$		−	35996.3i		−	0.0549998i	0.999622	−	0.0274999i	$-0.00875459\pi$
$810$	−89558.4	−	58310.7i	−0.136501	−	0.0888746i
$811$	−405524.	−	405524.i	−0.616560	−	0.616560i	0.328087	−	0.944647i	$-0.393596\pi$
$811$	−405524.	−	405524.i	−0.616560	−	0.616560i	−0.944647	+	0.328087i	$0.893596\pi$
$812$	−1.06851e6	−	413066.i	−1.62057	−	0.626481i
$813$	−11353.3	−	11353.3i	−0.0171767	−	0.0171767i
$814$	−46537.4	−	220222.i	−0.0702349	−	0.332362i
$815$			992493.i			1.49421i
$816$	32822.1	+	688614.i	0.0492930	+	1.03418i
$817$	27938.9			0.0418568
$818$	−105473.	+	22288.6i	−0.157629	+	0.0333102i
$819$	−198610.	+	198610.i	−0.296096	+	0.296096i
$820$	1.12644e6	+	435459.i	1.67525	+	0.647619i
$821$	−528286.	+	528286.i	−0.783759	+	0.783759i	−0.980463	−	0.196704i	$-0.936976\pi$
$821$	−528286.	+	528286.i	−0.783759	+	0.783759i	0.196704	+	0.980463i	$0.436976\pi$
$822$	−240218.	+	368946.i	−0.355518	+	0.546034i
$823$	52224.5			0.0771036			0.0385518	−	0.999257i	$-0.487726\pi$
$823$	52224.5			0.0771036			0.0385518	+	0.999257i	$0.487726\pi$
$824$	−726623.	−	1.00761e6i	−1.07017	−	1.48402i
$825$			587816.i			0.863642i
$826$	−127429.	+	195717.i	−0.186771	+	0.286859i
$827$	126358.	+	126358.i	0.184752	+	0.184752i	0.793423	−	0.608671i	$-0.208297\pi$
$827$	126358.	+	126358.i	0.184752	+	0.184752i	−0.608671	+	0.793423i	$0.708297\pi$
$828$	50042.5	+	113117.i	0.0729925	+	0.164993i
$829$	−204246.	−	204246.i	−0.297197	−	0.297197i	0.542718	−	0.839915i	$-0.317395\pi$
$829$	−204246.	−	204246.i	−0.297197	−	0.297197i	−0.839915	+	0.542718i	$0.817395\pi$
$830$	1.12249e6	−	237205.i	1.62939	−	0.344324i
$831$		−	56439.5i		−	0.0817299i
$832$	−783555.	+	392261.i	−1.13194	+	0.566668i
$833$	18857.9			0.0271772
$834$	73313.1	+	346928.i	0.105402	+	0.498778i
$835$	−700813.	+	700813.i	−1.00515	+	1.00515i
$836$	206525.	−	91366.2i	0.295502	−	0.130729i
$837$	22008.6	−	22008.6i	0.0314154	−	0.0314154i
$838$	566329.	+	368731.i	0.806456	+	0.525076i
$839$	379858.			0.539632			0.269816	−	0.962912i	$-0.413037\pi$
$839$	379858.			0.539632			0.269816	+	0.962912i	$0.413037\pi$
$840$	480703.	−	346651.i	0.681268	−	0.491286i
$841$			1.46066e6i			2.06517i
$842$	−721959.	−	470061.i	−1.01833	−	0.663025i
$843$	−269814.	−	269814.i	−0.379673	−	0.379673i
$844$	−23287.9	+	60240.6i	−0.0326923	+	0.0845676i
$845$	−445866.	−	445866.i	−0.624440	−	0.624440i
$846$	−31478.5	−	148961.i	−0.0439818	−	0.208128i
$847$		−	494680.i		−	0.689537i
$848$	−13055.9	−	273916.i	−0.0181558	−	0.380912i
$849$	−175861.			−0.243980
$850$	1.45657e6	−	307804.i	2.01602	−	0.426026i
$851$	−72323.9	+	72323.9i	−0.0998672	+	0.0998672i
$852$	87036.0	−	225143.i	0.119900	−	0.310155i
$853$	−539713.	+	539713.i	−0.741762	+	0.741762i	−0.972917	−	0.231155i	$-0.925750\pi$
$853$	−539713.	+	539713.i	−0.741762	+	0.741762i	0.231155	+	0.972917i	$0.425750\pi$
$854$	−88214.1	+	135487.i	−0.120955	+	0.185772i
$855$	88663.6			0.121287
$856$	141042.	−	870499.i	0.192487	−	1.18801i
$857$		−	772314.i		−	1.05156i	−0.850622	−	0.525778i	$-0.823774\pi$
$857$		−	772314.i		−	1.05156i	0.850622	−	0.525778i	$-0.176226\pi$
$858$	−382173.	+	586974.i	−0.519141	+	0.797341i
$859$	16249.6	+	16249.6i	0.0220220	+	0.0220220i	0.718032	−	0.696010i	$-0.245043\pi$
$859$	16249.6	+	16249.6i	0.0220220	+	0.0220220i	−0.696010	+	0.718032i	$0.745043\pi$
$860$	167208.	−	73972.4i	0.226079	−	0.100017i
$861$	−367973.	−	367973.i	−0.496375	−	0.496375i
$862$	261453.	−	55250.4i	0.351868	−	0.0743569i
$863$		−	561548.i		−	0.753989i	−0.926215	−	0.376995i	$-0.876958\pi$
$863$		−	561548.i		−	0.753989i	0.926215	−	0.376995i	$-0.123042\pi$
$864$	36361.3	+	138986.i	0.0487093	+	0.186184i
$865$	−1.81873e6			−2.43072
$866$	65962.1	+	312142.i	0.0879546	+	0.416214i
$867$	679996.	−	679996.i	0.904624	−	0.904624i
$868$	69833.0	+	157851.i	0.0926875	+	0.209512i
$869$	810334.	−	810334.i	1.07306	−	1.07306i
$870$	−939905.	−	611964.i	−1.24178	−	0.808513i
$871$	1.56130e6			2.05802
$872$	−6094.44	+	37614.3i	−0.00801495	+	0.0494675i
$873$			130003.i			0.170579i
$874$	−85999.2	−	55993.3i	−0.112583	−	0.0733016i
$875$	−117378.	−	117378.i	−0.153310	−	0.153310i
$876$	112654.	+	43549.7i	0.146804	+	0.0567515i
$877$	−438835.	−	438835.i	−0.570561	−	0.570561i	0.361724	−	0.932285i	$-0.382188\pi$
$877$	−438835.	−	438835.i	−0.570561	−	0.570561i	−0.932285	+	0.361724i	$0.882188\pi$
$878$	86383.4	+	408779.i	0.112058	+	0.530274i
$879$		−	349980.i		−	0.452965i
$880$	994103.	−	1.09361e6i	1.28371	−	1.41221i
$881$	−199429.			−0.256943			−0.128472	−	0.991713i	$-0.541007\pi$
$881$	−199429.			−0.256943			−0.128472	+	0.991713i	$0.541007\pi$
$882$	3844.89	−	812.504i	0.00494250	−	0.00104445i
$883$	600221.	−	600221.i	0.769822	−	0.769822i	−0.208253	−	0.978075i	$-0.566778\pi$
$883$	600221.	−	600221.i	0.769822	−	0.769822i	0.978075	+	0.208253i	$0.0667778\pi$
$884$	1.65461e6	+	639640.i	2.11734	+	0.818523i
$885$	−161681.	+	161681.i	−0.206430	+	0.206430i
$886$	500139.	−	768156.i	0.637124	−	0.978548i
$887$	261273.			0.332083			0.166042	−	0.986119i	$-0.446901\pi$
$887$	261273.			0.332083			0.166042	+	0.986119i	$0.446901\pi$
$888$	−96355.2	+	69485.0i	−0.122194	+	0.0881181i
$889$		−	961562.i		−	1.21667i
$890$	−719615.	+	1.10525e6i	−0.908490	+	1.39534i
$891$	81200.7	+	81200.7i	0.102283	+	0.102283i
$892$	341176.	+	771200.i	0.428795	+	0.969254i
$893$	89318.2	+	89318.2i	0.112005	+	0.112005i
$894$	88456.7	−	18692.7i	0.110677	−	0.0233882i
$895$			1.75088e6i			2.18580i
$896$	−791628.	−	89837.3i	−0.986064	−	0.111903i
$897$	318281.			0.395573
$898$	252080.	+	1.19288e6i	0.312597	+	1.47926i
$899$	230978.	−	230978.i	0.285793	−	0.285793i
$900$	283715.	−	125515.i	0.350265	−	0.154956i
$901$	−392556.	+	392556.i	−0.483562	+	0.483562i
$902$	−1.08751e6	−	708069.i	−1.33666	−	0.870287i
$903$	−78786.5			−0.0966221
$904$	−304428.	−	422152.i	−0.372519	−	0.516574i
$905$		−	1.49221e6i		−	1.82194i
$906$	326490.	+	212575.i	0.397754	+	0.258974i
$907$	−1.05786e6	−	1.05786e6i	−1.28592	−	1.28592i	−0.937242	−	0.348679i	$-0.886630\pi$
$907$	−1.05786e6	−	1.05786e6i	−1.28592	−	1.28592i	−0.348679	−	0.937242i	$-0.613370\pi$
$908$	324181.	−	838585.i	0.393202	−	1.01713i
$909$	140831.	+	140831.i	0.170440	+	0.170440i
$910$	−315303.	−	1.49206e6i	−0.380755	−	1.80179i
$911$			353334.i			0.425744i	0.977080	+	0.212872i	$0.0682817\pi$
$911$			353334.i			0.425744i	−0.977080	+	0.212872i	$0.931718\pi$
$912$	−88197.4	−	80172.3i	−0.106039	−	0.0963906i
$913$	−1.23281e6			−1.47895
$914$	786399.	−	166182.i	0.941349	−	0.198926i
$915$	−111925.	+	111925.i	−0.133686	+	0.133686i
$916$	317829.	−	822155.i	0.378794	−	0.979857i
$917$	633696.	−	633696.i	0.753602	−	0.753602i
$918$	158691.	−	243731.i	0.188307	−	0.289217i
$919$	−497513.			−0.589079			−0.294540	−	0.955639i	$-0.595166\pi$
$919$	−497513.			−0.589079			−0.294540	+	0.955639i	$0.595166\pi$
$920$	−662936.	−	107412.i	−0.783242	−	0.126904i
$921$		−	920666.i		−	1.08538i
$922$	396522.	−	609011.i	0.466450	−	0.716413i
$923$	−439195.	−	439195.i	−0.515530	−	0.515530i
$924$	−582392.	+	257648.i	−0.682137	+	0.301775i
$925$	181400.	+	181400.i	0.212009	+	0.212009i
$926$	−103151.	+	21797.8i	−0.120296	+	0.0254209i
$927$			524087.i			0.609880i
$928$	381608.	+	1.45864e6i	0.443120	+	1.69376i
$929$	72094.5			0.0835354			0.0417677	−	0.999127i	$-0.486701\pi$
$929$	72094.5			0.0835354			0.0417677	+	0.999127i	$0.486701\pi$
$930$	34939.8	+	165340.i	0.0403975	+	0.191167i
$931$	−2305.43	+	2305.43i	−0.00265982	+	0.00265982i
$932$	−478624.	−	1.08189e6i	−0.551014	−	1.24552i
$933$	−219508.	+	219508.i	−0.252166	+	0.252166i
$934$	−84689.3	−	55140.4i	−0.0970811	−	0.0632086i
$935$	−2.99196e6			−3.42242
$936$	364912.	+	59124.8i	0.416521	+	0.0674866i
$937$			915849.i			1.04314i	0.853207	+	0.521572i	$0.174654\pi$
$937$			915849.i			1.04314i	−0.853207	+	0.521572i	$0.825346\pi$
$938$	1.18963e6	+	774556.i	1.35209	+	0.880334i
$939$	60739.2	+	60739.2i	0.0688871	+	0.0688871i
$940$	771032.	+	298066.i	0.872603	+	0.337332i
$941$	−102598.	−	102598.i	−0.115867	−	0.115867i	0.646796	−	0.762663i	$-0.276108\pi$
$941$	−102598.	−	102598.i	−0.115867	−	0.115867i	−0.762663	+	0.646796i	$0.776108\pi$
$942$	109873.	+	519934.i	0.123819	+	0.585931i
$943$			589693.i			0.663136i
$944$	307028.	−	14634.2i	0.344535	−	0.0164219i
$945$	−250027.			−0.279978
$946$	−192225.	+	40621.1i	−0.214797	+	0.0453910i
$947$	−693598.	+	693598.i	−0.773406	+	0.773406i	−0.978700	−	0.205294i	$-0.934185\pi$
$947$	−693598.	+	693598.i	−0.773406	+	0.773406i	0.205294	+	0.978700i	$0.434185\pi$
$948$	−564143.	−	218087.i	−0.627729	−	0.242668i
$949$	219758.	−	219758.i	0.244012	−	0.244012i
$950$	−140440.	+	215700.i	−0.155612	+	0.239002i
$951$	807786.			0.893173
$952$	943401.	+	1.30822e6i	1.04093	+	1.44347i
$953$			1.02647e6i			1.13022i	0.825017	+	0.565108i	$0.191166\pi$
$953$			1.02647e6i			1.13022i	−0.825017	+	0.565108i	$0.808834\pi$
$954$	−63123.6	+	96950.6i	−0.0693578	+	0.106526i
$955$	740542.	+	740542.i	0.811976	+	0.811976i
$956$	24469.6	+	55311.3i	0.0267738	+	0.0605199i
$957$	852193.	+	852193.i	0.930495	+	0.930495i
$958$	1.07567e6	−	227312.i	1.17206	−	0.247680i
$959$			1.03002e6i			1.11997i
$960$	−740109.	−	246298.i	−0.803070	−	0.267250i
$961$	874303.			0.946706
$962$	63201.4	+	299078.i	0.0682930	+	0.323173i
$963$	−263066.	+	263066.i	−0.283669	+	0.283669i
$964$	−1.00083e6	+	442766.i	−1.07698	+	0.476453i
$965$	1.12215e6	−	1.12215e6i	1.20503	−	1.20503i
$966$	242514.	+	157899.i	0.259886	+	0.169209i
$967$	1.46061e6			1.56200			0.780998	−	0.624533i	$-0.214711\pi$
$967$	1.46061e6			1.56200			0.780998	+	0.624533i	$0.214711\pi$
$968$	−528078.	+	380815.i	−0.563569	+	0.406409i
$969$			241295.i			0.256981i
$970$	−591520.	−	385134.i	−0.628675	−	0.409325i
$971$	−668817.	−	668817.i	−0.709364	−	0.709364i	0.257037	−	0.966401i	$-0.417254\pi$
$971$	−668817.	−	668817.i	−0.709364	−	0.709364i	−0.966401	+	0.257037i	$0.917254\pi$
$972$	21853.7	−	56530.8i	0.0231309	−	0.0598347i
$973$	586610.	+	586610.i	0.619618	+	0.619618i
$974$	−21924.0	−	103748.i	−0.0231101	−	0.109360i
$975$		−	798300.i		−	0.839764i
$976$	212543.	−	10130.6i	0.223124	−	0.0106350i
$977$	−835449.			−0.875247			−0.437624	−	0.899158i	$-0.644180\pi$
$977$	−835449.			−0.875247			−0.437624	+	0.899158i	$0.644180\pi$
$978$	−550707.	+	116376.i	−0.575762	+	0.121670i
$979$	1.00210e6	−	1.00210e6i	1.04556	−	1.04556i
$980$	−7693.52	+	19901.4i	−0.00801075	+	0.0207220i
$981$	11367.1	−	11367.1i	0.0118116	−	0.0118116i
$982$	402715.	−	618524.i	0.417614	−	0.641406i
$983$	−35476.5			−0.0367142			−0.0183571	−	0.999831i	$-0.505844\pi$
$983$	−35476.5			−0.0367142			−0.0183571	+	0.999831i	$0.505844\pi$
$984$	−109543.	+	676089.i	−0.113134	+	0.698254i
$985$		−	1.01527e6i		−	1.04643i
$986$	1.66544e6	−	2.55792e6i	1.71307	−	2.63108i
$987$	−251873.	−	251873.i	−0.258552	−	0.258552i
$988$	−280478.	+	124082.i	−0.287332	+	0.127115i
$989$	63129.5	+	63129.5i	0.0645416	+	0.0645416i
$990$	−610023.	+	128910.i	−0.622409	+	0.131528i
$991$		−	461202.i		−	0.469617i	−0.972042	−	0.234809i	$-0.924554\pi$
$991$		−	461202.i		−	0.469617i	0.972042	−	0.234809i	$-0.0754464\pi$
$992$	114750.	−	196065.i	0.116608	−	0.199240i
$993$	−397787.			−0.403415
$994$	−116760.	−	552527.i	−0.118174	−	0.559218i
$995$	651119.	−	651119.i	0.657679	−	0.657679i
$996$	263237.	+	595025.i	0.265356	+	0.599814i
$997$	−406068.	+	406068.i	−0.408515	+	0.408515i	−0.881221	−	0.472705i	$-0.843278\pi$
$997$	−406068.	+	406068.i	−0.408515	+	0.408515i	0.472705	+	0.881221i	$0.343278\pi$
$998$	1.17553e6	+	765375.i	1.18024	+	0.768446i
$999$	50117.0			0.0502174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.l.a.19.8	✓	32
3.2	odd	2		144.5.m.c.19.9		32
4.3	odd	2		192.5.l.a.175.6		32
8.3	odd	2		384.5.l.a.223.11		32
8.5	even	2		384.5.l.b.223.6		32
12.11	even	2		576.5.m.b.559.15		32
16.3	odd	4		384.5.l.b.31.6		32
16.5	even	4		192.5.l.a.79.6		32
16.11	odd	4	inner	48.5.l.a.43.8	yes	32
16.13	even	4		384.5.l.a.31.11		32
48.5	odd	4		576.5.m.b.271.15		32
48.11	even	4		144.5.m.c.91.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.8	✓	32	1.1	even	1	trivial
48.5.l.a.43.8	yes	32	16.11	odd	4	inner
144.5.m.c.19.9		32	3.2	odd	2
144.5.m.c.91.9		32	48.11	even	4
192.5.l.a.79.6		32	16.5	even	4
192.5.l.a.175.6		32	4.3	odd	2
384.5.l.a.31.11		32	16.13	even	4
384.5.l.a.223.11		32	8.3	odd	2
384.5.l.b.31.6		32	16.3	odd	4
384.5.l.b.223.6		32	8.5	even	2
576.5.m.b.271.15		32	48.5	odd	4
576.5.m.b.559.15		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.827018 - 3.91357i) q^{2} +(3.67423 - 3.67423i) q^{3} +(-14.6321 + 6.47318i) q^{4} +(-25.9147 + 25.9147i) q^{5} +(-17.4180 - 11.3407i) q^{6} -48.6273 q^{7} +(37.4343 + 51.9103i) q^{8} -27.0000i q^{9} +O(q^{10})\)	\(q+(-0.827018 - 3.91357i) q^{2} +(3.67423 - 3.67423i) q^{3} +(-14.6321 + 6.47318i) q^{4} +(-25.9147 + 25.9147i) q^{5} +(-17.4180 - 11.3407i) q^{6} -48.6273 q^{7} +(37.4343 + 51.9103i) q^{8} -27.0000i q^{9} +(122.851 + 79.9872i) q^{10} +(-111.386 - 111.386i) q^{11} +(-29.9777 + 77.5457i) q^{12} +(151.271 + 151.271i) q^{13} +(40.2156 + 190.306i) q^{14} +190.434i q^{15} +(172.196 - 189.432i) q^{16} -518.259 q^{17} +(-105.666 + 22.3295i) q^{18} +(63.3585 - 63.3585i) q^{19} +(211.436 - 546.937i) q^{20} +(-178.668 + 178.668i) q^{21} +(-343.800 + 528.037i) q^{22} +286.324 q^{23} +(328.273 + 53.1882i) q^{24} -718.145i q^{25} +(466.908 - 717.116i) q^{26} +(-99.2043 - 99.2043i) q^{27} +(711.519 - 314.773i) q^{28} +(-1041.14 - 1041.14i) q^{29} +(745.275 - 157.492i) q^{30} +221.852i q^{31} +(-883.766 - 517.236i) q^{32} -818.520 q^{33} +(428.609 + 2028.24i) q^{34} +(1260.16 - 1260.16i) q^{35} +(174.776 + 395.066i) q^{36} +(-252.595 + 252.595i) q^{37} +(-300.357 - 195.559i) q^{38} +1111.61 q^{39} +(-2315.34 - 375.142i) q^{40} +2059.53i q^{41} +(846.992 + 551.469i) q^{42} +(220.483 + 220.483i) q^{43} +(2350.84 + 908.791i) q^{44} +(699.697 + 699.697i) q^{45} +(-236.795 - 1120.55i) q^{46} +1409.73i q^{47} +(-63.3314 - 1328.71i) q^{48} -36.3871 q^{49} +(-2810.51 + 593.919i) q^{50} +(-1904.21 + 1904.21i) q^{51} +(-3192.62 - 1234.21i) q^{52} +(757.451 - 757.451i) q^{53} +(-306.200 + 470.287i) q^{54} +5773.10 q^{55} +(-1820.33 - 2524.26i) q^{56} -465.588i q^{57} +(-3213.53 + 4935.61i) q^{58} +(849.016 + 849.016i) q^{59} +(-1232.71 - 2786.44i) q^{60} +(587.739 + 587.739i) q^{61} +(868.232 - 183.475i) q^{62} +1312.94i q^{63} +(-1293.35 + 3886.45i) q^{64} -7840.31 q^{65} +(676.930 + 3203.34i) q^{66} +(5160.59 - 5160.59i) q^{67} +(7583.21 - 3354.79i) q^{68} +(1052.02 - 1052.02i) q^{69} +(-5973.91 - 3889.56i) q^{70} -2903.36 q^{71} +(1401.58 - 1010.73i) q^{72} -1452.74i q^{73} +(1197.45 + 779.648i) q^{74} +(-2638.63 - 2638.63i) q^{75} +(-516.936 + 1337.20i) q^{76} +(5416.42 + 5416.42i) q^{77} +(-919.324 - 4350.38i) q^{78} +7274.97i q^{79} +(446.682 + 9371.49i) q^{80} -729.000 q^{81} +(8060.13 - 1703.27i) q^{82} +(5533.91 - 5533.91i) q^{83} +(1457.73 - 3770.84i) q^{84} +(13430.5 - 13430.5i) q^{85} +(680.532 - 1045.22i) q^{86} -7650.77 q^{87} +(1612.43 - 9951.77i) q^{88} +8996.63i q^{89} +(2159.65 - 3316.98i) q^{90} +(-7355.92 - 7355.92i) q^{91} +(-4189.51 + 1853.43i) q^{92} +(815.135 + 815.135i) q^{93} +(5517.07 - 1165.87i) q^{94} +3283.84i q^{95} +(-5147.61 + 1346.72i) q^{96} -4814.94 q^{97} +(30.0927 + 142.403i) q^{98} +(-3007.43 + 3007.43i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) \) 32 * q + 12 * q^4 + 180 * q^8	\( 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Introduction

L-functions

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