LMFDB - Embedded newform 48.5.l.a.19.6

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			19.6
Character	$\chi$	$=$	48.19
Dual form			48.5.l.a.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62589 - 3.65465i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-10.7130 + 11.8841i) q^{4} +(-2.10268 + 2.10268i) q^{5} +(19.4020 + 7.45415i) q^{6} +84.8276 q^{7} +(60.8504 + 19.8299i) q^{8} -27.0000i q^{9} +O(q^{10})$	\(q+(-1.62589 - 3.65465i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-10.7130 + 11.8841i) q^{4} +(-2.10268 + 2.10268i) q^{5} +(19.4020 + 7.45415i) q^{6} +84.8276 q^{7} +(60.8504 + 19.8299i) q^{8} -27.0000i q^{9} +(11.1033 + 4.26583i) q^{10} +(-57.8744 - 57.8744i) q^{11} +(-4.30314 - 83.0270i) q^{12} +(192.435 + 192.435i) q^{13} +(-137.920 - 310.015i) q^{14} -15.4515i q^{15} +(-26.4649 - 254.628i) q^{16} +507.642 q^{17} +(-98.6756 + 43.8990i) q^{18} +(-126.683 + 126.683i) q^{19} +(-2.46259 - 47.5144i) q^{20} +(-311.677 + 311.677i) q^{21} +(-117.413 + 305.608i) q^{22} -173.371 q^{23} +(-296.438 + 150.719i) q^{24} +616.157i q^{25} +(390.406 - 1016.16i) q^{26} +(99.2043 + 99.2043i) q^{27} +(-908.755 + 1008.10i) q^{28} +(-64.7538 - 64.7538i) q^{29} +(-56.4697 + 25.1224i) q^{30} +366.621i q^{31} +(-887.549 + 510.718i) q^{32} +425.288 q^{33} +(-825.370 - 1855.25i) q^{34} +(-178.365 + 178.365i) q^{35} +(320.871 + 289.250i) q^{36} +(801.887 - 801.887i) q^{37} +(668.953 + 257.009i) q^{38} -1414.11 q^{39} +(-169.645 + 86.2531i) q^{40} -461.370i q^{41} +(1645.82 + 632.317i) q^{42} +(-1147.51 - 1147.51i) q^{43} +(1307.79 - 67.7806i) q^{44} +(56.7723 + 56.7723i) q^{45} +(281.882 + 633.611i) q^{46} -4098.44i q^{47} +(1032.80 + 838.326i) q^{48} +4794.73 q^{49} +(2251.84 - 1001.80i) q^{50} +(-1865.20 + 1865.20i) q^{51} +(-4348.48 + 225.374i) q^{52} +(-2542.44 + 2542.44i) q^{53} +(201.262 - 523.853i) q^{54} +243.383 q^{55} +(5161.80 + 1682.12i) q^{56} -930.924i q^{57} +(-131.370 + 341.935i) q^{58} +(959.072 + 959.072i) q^{59} +(183.627 + 165.531i) q^{60} +(-162.570 - 162.570i) q^{61} +(1339.87 - 596.086i) q^{62} -2290.35i q^{63} +(3309.55 + 2413.31i) q^{64} -809.260 q^{65} +(-691.472 - 1554.28i) q^{66} +(-771.580 + 771.580i) q^{67} +(-5438.35 + 6032.88i) q^{68} +(637.006 - 637.006i) q^{69} +(941.865 + 361.860i) q^{70} -2063.45 q^{71} +(535.406 - 1642.96i) q^{72} +463.678i q^{73} +(-4234.40 - 1626.84i) q^{74} +(-2263.91 - 2263.91i) q^{75} +(-148.366 - 2862.66i) q^{76} +(-4909.35 - 4909.35i) q^{77} +(2299.18 + 5168.07i) q^{78} -8437.39i q^{79} +(591.049 + 479.754i) q^{80} -729.000 q^{81} +(-1686.15 + 750.138i) q^{82} +(-3103.77 + 3103.77i) q^{83} +(-365.025 - 7042.98i) q^{84} +(-1067.41 + 1067.41i) q^{85} +(-2328.03 + 6059.49i) q^{86} +475.841 q^{87} +(-2374.04 - 4669.33i) q^{88} +7668.88i q^{89} +(115.177 - 299.789i) q^{90} +(16323.8 + 16323.8i) q^{91} +(1857.32 - 2060.36i) q^{92} +(-1347.05 - 1347.05i) q^{93} +(-14978.4 + 6663.61i) q^{94} -532.746i q^{95} +(1384.57 - 5137.56i) q^{96} +16387.4 q^{97} +(-7795.70 - 17523.1i) q^{98} +(-1562.61 + 1562.61i) 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 $

$2$	−1.62589	−	3.65465i	−0.406473	−	0.913663i
$2$	−1.62589	−	3.65465i	−0.406473	−	0.913663i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$4$	−10.7130	+	11.8841i	−0.669560	+	0.742758i
$5$	−2.10268	+	2.10268i	−0.0841071	+	0.0841071i	−0.747909	−	0.663802i	$-0.768942\pi$
$5$	−2.10268	+	2.10268i	−0.0841071	+	0.0841071i	0.663802	+	0.747909i	$0.268942\pi$
$6$	19.4020	+	7.45415i	0.538943	+	0.207060i
$7$	84.8276			1.73118			0.865588	−	0.500757i	$-0.166945\pi$
$7$	84.8276			1.73118			0.865588	+	0.500757i	$0.166945\pi$
$8$	60.8504	+	19.8299i	0.950788	+	0.309841i
$9$		−	27.0000i		−	0.333333i
$10$	11.1033	+	4.26583i	0.111033	+	0.0426583i
$11$	−57.8744	−	57.8744i	−0.478301	−	0.478301i	0.426287	−	0.904588i	$-0.359821\pi$
$11$	−57.8744	−	57.8744i	−0.478301	−	0.478301i	−0.904588	+	0.426287i	$0.859821\pi$
$12$	−4.30314	−	83.0270i	−0.0298829	−	0.576576i
$13$	192.435	+	192.435i	1.13867	+	1.13867i	0.988689	+	0.149983i	$0.0479219\pi$
$13$	192.435	+	192.435i	1.13867	+	1.13867i	0.149983	+	0.988689i	$0.452078\pi$
$14$	−137.920	−	310.015i	−0.703676	−	1.58171i
$15$		−	15.4515i		−	0.0686732i
$16$	−26.4649	−	254.628i	−0.103379	−	0.994642i
$17$	507.642			1.75655			0.878273	−	0.478159i	$-0.158696\pi$
$17$	507.642			1.75655			0.878273	+	0.478159i	$0.158696\pi$
$18$	−98.6756	+	43.8990i	−0.304554	+	0.135491i
$19$	−126.683	+	126.683i	−0.350922	+	0.350922i	−0.860452	−	0.509531i	$-0.829819\pi$
$19$	−126.683	+	126.683i	−0.350922	+	0.350922i	0.509531	+	0.860452i	$0.329819\pi$
$20$	−2.46259	−	47.5144i	−0.00615646	−	0.118786i
$21$	−311.677	+	311.677i	−0.706750	+	0.706750i
$22$	−117.413	+	305.608i	−0.242590	+	0.631422i
$23$	−173.371			−0.327734			−0.163867	−	0.986482i	$-0.552397\pi$
$23$	−173.371			−0.327734			−0.163867	+	0.986482i	$0.552397\pi$
$24$	−296.438	+	150.719i	−0.514650	+	0.261665i
$25$			616.157i			0.985852i
$26$	390.406	−	1016.16i	0.577523	−	1.50320i
$27$	99.2043	+	99.2043i	0.136083	+	0.136083i
$28$	−908.755	+	1008.10i	−1.15913	+	1.28584i
$29$	−64.7538	−	64.7538i	−0.0769961	−	0.0769961i	0.667560	−	0.744556i	$-0.267339\pi$
$29$	−64.7538	−	64.7538i	−0.0769961	−	0.0769961i	−0.744556	+	0.667560i	$0.767339\pi$
$30$	−56.4697	+	25.1224i	−0.0627441	+	0.0279138i
$31$			366.621i			0.381500i	0.981639	+	0.190750i	$0.0610920\pi$
$31$			366.621i			0.381500i	−0.981639	+	0.190750i	$0.938908\pi$
$32$	−887.549	+	510.718i	−0.866747	+	0.498748i
$33$	425.288			0.390531
$34$	−825.370	−	1855.25i	−0.713988	−	1.60489i
$35$	−178.365	+	178.365i	−0.145604	+	0.145604i
$36$	320.871	+	289.250i	0.247586	+	0.223187i
$37$	801.887	−	801.887i	0.585747	−	0.585747i	−0.350730	−	0.936477i	$-0.614066\pi$
$37$	801.887	−	801.887i	0.585747	−	0.585747i	0.936477	+	0.350730i	$0.114066\pi$
$38$	668.953	+	257.009i	0.463264	+	0.177984i
$39$	−1414.11			−0.929721
$40$	−169.645	+	86.2531i	−0.106028	+	0.0539082i
$41$		−	461.370i		−	0.274462i	−0.990539	−	0.137231i	$-0.956180\pi$
$41$		−	461.370i		−	0.274462i	0.990539	−	0.137231i	$-0.0438202\pi$
$42$	1645.82	+	632.317i	0.933005	+	0.358457i
$43$	−1147.51	−	1147.51i	−0.620613	−	0.620613i	0.325075	−	0.945688i	$-0.394610\pi$
$43$	−1147.51	−	1147.51i	−0.620613	−	0.620613i	−0.945688	+	0.325075i	$0.894610\pi$
$44$	1307.79	−	67.7806i	0.675513	−	0.0350106i
$45$	56.7723	+	56.7723i	0.0280357	+	0.0280357i
$46$	281.882	+	633.611i	0.133215	+	0.299438i
$47$		−	4098.44i		−	1.85534i	−0.373406	−	0.927668i	$-0.621810\pi$
$47$		−	4098.44i		−	1.85534i	0.373406	−	0.927668i	$-0.378190\pi$
$48$	1032.80	+	838.326i	0.448265	+	0.363857i
$49$	4794.73			1.99697
$50$	2251.84	−	1001.80i	0.900736	−	0.400722i
$51$	−1865.20	+	1865.20i	−0.717107	+	0.717107i
$52$	−4348.48	+	225.374i	−1.60817	+	0.0833483i
$53$	−2542.44	+	2542.44i	−0.905106	+	0.905106i	−0.995872	−	0.0907664i	$-0.971068\pi$
$53$	−2542.44	+	2542.44i	−0.905106	+	0.905106i	0.0907664	+	0.995872i	$0.471068\pi$
$54$	201.262	−	523.853i	0.0690199	−	0.179648i
$55$	243.383			0.0804571
$56$	5161.80	+	1682.12i	1.64598	+	0.536390i
$57$		−	930.924i		−	0.286526i
$58$	−131.370	+	341.935i	−0.0390517	+	0.101645i
$59$	959.072	+	959.072i	0.275516	+	0.275516i	0.831316	−	0.555800i	$-0.187588\pi$
$59$	959.072	+	959.072i	0.275516	+	0.275516i	−0.555800	+	0.831316i	$0.687588\pi$
$60$	183.627	+	165.531i	0.0510075	+	0.0459808i
$61$	−162.570	−	162.570i	−0.0436898	−	0.0436898i	0.684924	−	0.728614i	$-0.259835\pi$
$61$	−162.570	−	162.570i	−0.0436898	−	0.0436898i	−0.728614	+	0.684924i	$0.759835\pi$
$62$	1339.87	−	596.086i	0.348562	−	0.155069i
$63$		−	2290.35i		−	0.577059i
$64$	3309.55	+	2413.31i	0.807997	+	0.589187i
$65$	−809.260			−0.191541
$66$	−691.472	−	1554.28i	−0.158740	−	0.356814i
$67$	−771.580	+	771.580i	−0.171882	+	0.171882i	−0.787806	−	0.615924i	$-0.788783\pi$
$67$	−771.580	+	771.580i	−0.171882	+	0.171882i	0.615924	+	0.787806i	$0.288783\pi$
$68$	−5438.35	+	6032.88i	−1.17611	+	1.30469i
$69$	637.006	−	637.006i	0.133797	−	0.133797i
$70$	941.865	+	361.860i	0.192217	+	0.0738491i
$71$	−2063.45			−0.409334			−0.204667	−	0.978832i	$-0.565611\pi$
$71$	−2063.45			−0.409334			−0.204667	+	0.978832i	$0.565611\pi$
$72$	535.406	−	1642.96i	0.103280	−	0.316929i
$73$			463.678i			0.0870103i	0.999053	+	0.0435052i	$0.0138525\pi$
$73$			463.678i			0.0870103i	−0.999053	+	0.0435052i	$0.986148\pi$
$74$	−4234.40	−	1626.84i	−0.773265	−	0.297085i
$75$	−2263.91	−	2263.91i	−0.402472	−	0.402472i
$76$	−148.366	−	2862.66i	−0.0256867	−	0.495613i
$77$	−4909.35	−	4909.35i	−0.828023	−	0.828023i
$78$	2299.18	+	5168.07i	0.377906	+	0.849452i
$79$		−	8437.39i		−	1.35193i	−0.736934	−	0.675965i	$-0.763727\pi$
$79$		−	8437.39i		−	1.35193i	0.736934	−	0.675965i	$-0.236273\pi$
$80$	591.049	+	479.754i	0.0923514	+	0.0749616i
$81$	−729.000			−0.111111
$82$	−1686.15	+	750.138i	−0.250766	+	0.111561i
$83$	−3103.77	+	3103.77i	−0.450540	+	0.450540i	−0.895534	−	0.444993i	$-0.853206\pi$
$83$	−3103.77	+	3103.77i	−0.450540	+	0.450540i	0.444993	+	0.895534i	$0.353206\pi$
$84$	−365.025	−	7042.98i	−0.0517326	−	0.998155i
$85$	−1067.41	+	1067.41i	−0.147738	+	0.147738i
$86$	−2328.03	+	6059.49i	−0.314769	+	0.819293i
$87$	475.841			0.0628671
$88$	−2374.04	−	4669.33i	−0.306566	−	0.602961i
$89$			7668.88i			0.968171i	0.875021	+	0.484085i	$0.160848\pi$
$89$			7668.88i			0.968171i	−0.875021	+	0.484085i	$0.839152\pi$
$90$	115.177	−	299.789i	0.0142194	−	0.0370109i
$91$	16323.8	+	16323.8i	1.97124	+	1.97124i
$92$	1857.32	−	2060.36i	0.219437	−	0.243427i
$93$	−1347.05	−	1347.05i	−0.155747	−	0.155747i
$94$	−14978.4	+	6663.61i	−1.69515	+	0.754143i
$95$		−	532.746i		−	0.0590300i
$96$	1384.57	−	5137.56i	0.150235	−	0.557461i
$97$	16387.4			1.74167			0.870835	−	0.491575i	$-0.163579\pi$
$97$	16387.4			1.74167			0.870835	+	0.491575i	$0.163579\pi$
$98$	−7795.70	−	17523.1i	−0.811714	−	1.82456i
$99$	−1562.61	+	1562.61i	−0.159434	+	0.159434i
$100$	−7322.49	−	6600.87i	−0.732249	−	0.660087i
$101$	−7819.54	+	7819.54i	−0.766546	+	0.766546i	−0.977497	−	0.210951i	$-0.932344\pi$
$101$	−7819.54	+	7819.54i	−0.766546	+	0.766546i	0.210951	+	0.977497i	$0.432344\pi$
$102$	9849.24	+	3784.04i	0.946679	+	0.363710i
$103$	−5373.34			−0.506489			−0.253244	−	0.967402i	$-0.581498\pi$
$103$	−5373.34			−0.506489			−0.253244	+	0.967402i	$0.581498\pi$
$104$	7893.82	+	15525.8i	0.729828	+	1.43544i
$105$		−	1310.71i		−	0.118885i
$106$	13425.5	+	5158.01i	1.19486	+	0.459061i
$107$	9702.27	+	9702.27i	0.847434	+	0.847434i	0.989812	−	0.142378i	$-0.0454749\pi$
$107$	9702.27	+	9702.27i	0.847434	+	0.847434i	−0.142378	+	0.989812i	$0.545475\pi$
$108$	−2241.73	+	116.185i	−0.192192	+	0.00996097i
$109$	−10200.4	−	10200.4i	−0.858550	−	0.858550i	0.132618	−	0.991167i	$-0.457662\pi$
$109$	−10200.4	−	10200.4i	−0.858550	−	0.858550i	−0.991167	+	0.132618i	$0.957662\pi$
$110$	−395.713	−	889.479i	−0.0327036	−	0.0735106i
$111$			5892.64i			0.478260i
$112$	−2244.96	−	21599.5i	−0.178967	−	1.72190i
$113$	−13057.9			−1.02262			−0.511311	−	0.859395i	$-0.670840\pi$
$113$	−13057.9			−1.02262			−0.511311	+	0.859395i	$0.670840\pi$
$114$	−3402.20	+	1513.58i	−0.261788	+	0.116465i
$115$	364.543	−	364.543i	0.0275647	−	0.0275647i
$116$	1463.25	−	75.8374i	0.108743	−	0.00563595i
$117$	5195.76	−	5195.76i	0.379557	−	0.379557i
$118$	1945.73	−	5064.42i	0.139739	−	0.363719i
$119$	43062.1			3.04089
$120$	306.400	−	940.229i	0.0212778	−	0.0652936i
$121$		−	7942.10i		−	0.542456i
$122$	−329.815	+	858.457i	−0.0221591	+	0.0576765i
$123$	1695.18	+	1695.18i	0.112049	+	0.112049i
$124$	−4356.98	−	3927.60i	−0.283362	−	0.255437i
$125$	−2609.75	−	2609.75i	−0.167024	−	0.167024i
$126$	−8370.42	+	3723.85i	−0.527237	+	0.234559i
$127$			12757.2i			0.790948i	0.918477	+	0.395474i	$0.129420\pi$
$127$			12757.2i			0.790948i	−0.918477	+	0.395474i	$0.870580\pi$
$128$	3438.84	−	16019.0i	0.209890	−	0.977725i
$129$	8432.47			0.506728
$130$	1315.77	+	2957.56i	0.0778561	+	0.175004i
$131$	6898.48	−	6898.48i	0.401986	−	0.401986i	−0.476946	−	0.878932i	$-0.658256\pi$
$131$	6898.48	−	6898.48i	0.401986	−	0.401986i	0.878932	+	0.476946i	$0.158256\pi$
$132$	−4556.10	+	5054.18i	−0.261484	+	0.290070i
$133$	−10746.2	+	10746.2i	−0.607507	+	0.607507i
$134$	4074.36	+	1565.35i	0.226908	+	0.0871771i
$135$	−417.190			−0.0228911
$136$	30890.2	+	10066.5i	1.67010	+	0.544251i
$137$		−	19730.1i		−	1.05121i	−0.850730	−	0.525603i	$-0.823840\pi$
$137$		−	19730.1i		−	1.05121i	0.850730	−	0.525603i	$-0.176160\pi$
$138$	−3363.74	−	1292.33i	−0.176630	−	0.0678604i
$139$	−22880.9	−	22880.9i	−1.18425	−	1.18425i	−0.978632	−	0.205619i	$-0.934079\pi$
$139$	−22880.9	−	22880.9i	−1.18425	−	1.18425i	−0.205619	−	0.978632i	$-0.565921\pi$
$140$	−208.895	−	4030.53i	−0.0106579	−	0.205639i
$141$	15058.6	+	15058.6i	0.757438	+	0.757438i
$142$	3354.95	+	7541.21i	0.166383	+	0.373994i
$143$		−	22274.2i		−	1.08926i
$144$	−6874.97	+	714.553i	−0.331547	+	0.0344596i
$145$	272.313			0.0129518
$146$	1694.58	−	753.890i	0.0794981	−	0.0353673i
$147$	−17616.9	+	17616.9i	−0.815260	+	0.815260i
$148$	939.143	+	18120.3i	0.0428754	+	0.827261i
$149$	−14167.4	+	14167.4i	−0.638141	+	0.638141i	−0.950097	−	0.311955i	$-0.899016\pi$
$149$	−14167.4	+	14167.4i	−0.638141	+	0.638141i	0.311955	+	0.950097i	$0.399016\pi$
$150$	−4592.93	+	11954.7i	−0.204130	+	0.531318i
$151$	−30206.8			−1.32480			−0.662402	−	0.749149i	$-0.730463\pi$
$151$	−30206.8			−1.32480			−0.662402	+	0.749149i	$0.730463\pi$
$152$	−10220.8	+	5196.60i	−0.442382	+	0.224922i
$153$		−	13706.3i		−	0.585516i
$154$	−9959.90	+	25924.0i	−0.419965	+	1.09310i
$155$	−770.887	−	770.887i	−0.0320869	−	0.0320869i
$156$	15149.3	−	16805.4i	0.622504	−	0.690558i
$157$	−17987.6	−	17987.6i	−0.729749	−	0.729749i	0.240820	−	0.970570i	$-0.422584\pi$
$157$	−17987.6	−	17987.6i	−0.729749	−	0.729749i	−0.970570	+	0.240820i	$0.922584\pi$
$158$	−30835.7	+	13718.3i	−1.23521	+	0.549522i
$159$		−	18683.1i		−	0.739016i
$160$	792.354	−	2940.11i	0.0309513	−	0.114848i
$161$	−14706.7			−0.567364
$162$	1185.27	+	2664.24i	0.0451636	+	0.101518i
$163$	3229.11	−	3229.11i	0.121537	−	0.121537i	−0.643722	−	0.765259i	$-0.722611\pi$
$163$	3229.11	−	3229.11i	0.121537	−	0.121537i	0.765259	+	0.643722i	$0.222611\pi$
$164$	5482.98	+	4942.64i	0.203859	+	0.183769i
$165$	−894.245	+	894.245i	−0.0328465	+	0.0328465i
$166$	16389.6	+	6296.82i	0.594774	+	0.228510i
$167$	−16592.4			−0.594946			−0.297473	−	0.954730i	$-0.596144\pi$
$167$	−16592.4			−0.594946			−0.297473	+	0.954730i	$0.596144\pi$
$168$	−25146.2	+	12785.2i	−0.890950	+	0.452989i
$169$			45501.8i			1.59315i
$170$	5636.49	+	2165.52i	0.195034	+	0.0749313i
$171$	3420.43	+	3420.43i	0.116974	+	0.116974i
$172$	25930.5	−	1343.93i	0.876503	−	0.0454275i
$173$	4707.05	+	4707.05i	0.157274	+	0.157274i	0.781358	−	0.624084i	$-0.214528\pi$
$173$	4707.05	+	4707.05i	0.157274	+	0.157274i	−0.624084	+	0.781358i	$0.714528\pi$
$174$	−773.665	−	1739.03i	−0.0255538	−	0.0574393i
$175$			52267.2i			1.70668i
$176$	−13204.8	+	16268.1i	−0.426292	+	0.525185i
$177$	−7047.71			−0.224958
$178$	28027.1	−	12468.8i	0.884582	−	0.393535i
$179$	26175.4	−	26175.4i	0.816934	−	0.816934i	−0.168729	−	0.985663i	$-0.553966\pi$
$179$	26175.4	−	26175.4i	0.816934	−	0.816934i	0.985663	+	0.168729i	$0.0539662\pi$
$180$	−1282.89	+	66.4898i	−0.0395953	+	0.00205215i
$181$	40133.6	−	40133.6i	1.22504	−	1.22504i	0.259223	−	0.965817i	$-0.416533\pi$
$181$	40133.6	−	40133.6i	1.22504	−	1.22504i	0.965817	−	0.259223i	$-0.0834665\pi$
$182$	33117.2	−	86198.8i	0.999794	−	2.60230i
$183$	1194.64			0.0356726
$184$	−10549.7	−	3437.92i	−0.311605	−	0.101545i
$185$			3372.22i			0.0985310i
$186$	−2732.85	+	7113.17i	−0.0789932	+	0.205607i
$187$	−29379.5	−	29379.5i	−0.840158	−	0.840158i
$188$	48706.3	+	43906.4i	1.37807	+	1.24226i
$189$	8415.27	+	8415.27i	0.235583	+	0.235583i
$190$	−1947.00	+	866.186i	−0.0539335	+	0.0239941i
$191$		−	10298.6i		−	0.282299i	−0.989988	−	0.141150i	$-0.954920\pi$
$191$		−	10298.6i		−	0.282299i	0.989988	−	0.141150i	$-0.0450798\pi$
$192$	−21027.1	+	3293.01i	−0.570398	+	0.0893285i
$193$	−21315.6			−0.572245			−0.286122	−	0.958193i	$-0.592366\pi$
$193$	−21315.6			−0.572245			−0.286122	+	0.958193i	$0.592366\pi$
$194$	−26644.1	−	59890.2i	−0.707941	−	1.59130i
$195$	2973.41	−	2973.41i	0.0781962	−	0.0781962i
$196$	−51365.7	+	56981.1i	−1.33709	+	1.48327i
$197$	35224.5	−	35224.5i	0.907638	−	0.907638i	−0.0884429	−	0.996081i	$-0.528189\pi$
$197$	35224.5	−	35224.5i	0.907638	−	0.907638i	0.996081	+	0.0884429i	$0.0281891\pi$
$198$	8251.43	+	3170.16i	0.210474	+	0.0808632i
$199$	−31089.7			−0.785074			−0.392537	−	0.919736i	$-0.628402\pi$
$199$	−31089.7			−0.785074			−0.392537	+	0.919736i	$0.628402\pi$
$200$	−12218.3	+	37493.5i	−0.305458	+	0.937336i
$201$		−	5669.93i		−	0.140341i
$202$	41291.4	+	15864.0i	1.01194	+	0.388785i
$203$	−5492.91	−	5492.91i	−0.133294	−	0.133294i
$204$	−2184.45	−	42148.0i	−0.0524907	−	1.01278i
$205$	970.113	+	970.113i	0.0230842	+	0.0230842i
$206$	8736.46	+	19637.7i	0.205874	+	0.462760i
$207$			4681.02i			0.109245i
$208$	43906.7	−	54092.3i	1.01486	−	1.25028i
$209$	14663.4			0.335692
$210$	−4790.19	+	2131.07i	−0.108621	+	0.0483236i
$211$	37821.8	−	37821.8i	0.849528	−	0.849528i	−0.140546	−	0.990074i	$-0.544886\pi$
$211$	37821.8	−	37821.8i	0.849528	−	0.849528i	0.990074	+	0.140546i	$0.0448858\pi$
$212$	−2977.62	−	57451.8i	−0.0662518	−	1.27830i
$213$	7581.61	−	7581.61i	0.167110	−	0.167110i
$214$	19683.6	−	51233.3i	0.429810	−	1.11873i
$215$	4825.70			0.104396
$216$	4069.42	+	8003.84i	0.0872218	+	0.171550i
$217$			31099.6i			0.660444i
$218$	−20694.2	+	53863.8i	−0.435448	+	1.13340i
$219$	−1703.66	−	1703.66i	−0.0355218	−	0.0355218i
$220$	−2607.35	+	2892.39i	−0.0538708	+	0.0597601i
$221$	97688.3	+	97688.3i	2.00013	+	2.00013i
$222$	21535.6	−	9580.79i	0.436969	−	0.194400i
$223$		−	2858.47i		−	0.0574809i	−0.999587	−	0.0287404i	$-0.990850\pi$
$223$		−	2858.47i		−	0.0574809i	0.999587	−	0.0287404i	$-0.00914963\pi$
$224$	−75288.7	+	43323.0i	−1.50049	+	0.863421i
$225$	16636.3			0.328617
$226$	21230.7	+	47722.0i	0.415668	+	0.934333i
$227$	−70688.1	+	70688.1i	−1.37181	+	1.37181i	−0.514053	+	0.857758i	$0.671857\pi$
$227$	−70688.1	+	70688.1i	−1.37181	+	1.37181i	−0.857758	+	0.514053i	$0.828143\pi$
$228$	11063.2	+	9972.95i	0.212820	+	0.191847i
$229$	−394.626	+	394.626i	−0.00752514	+	0.00752514i	−0.710859	−	0.703334i	$-0.751694\pi$
$229$	−394.626	+	394.626i	−0.00752514	+	0.00752514i	0.703334	+	0.710859i	$0.251694\pi$
$230$	−1924.99	−	739.572i	−0.0363892	−	0.0139806i
$231$	36076.2			0.676078
$232$	−2656.24	−	5224.35i	−0.0493504	−	0.0970636i
$233$		−	21767.8i		−	0.400961i	−0.979698	−	0.200481i	$-0.935750\pi$
$233$		−	21767.8i		−	0.400961i	0.979698	−	0.200481i	$-0.0642504\pi$
$234$	−27436.4	−	10541.0i	−0.501067	−	0.192508i
$235$	8617.69	+	8617.69i	0.156047	+	0.156047i
$236$	−21672.2	+	1123.23i	−0.389116	+	0.0201672i
$237$	31001.0	+	31001.0i	0.551923	+	0.551923i
$238$	−70014.2	−	157377.i	−1.23604	−	2.77835i
$239$			81943.0i			1.43455i	0.696789	+	0.717276i	$0.254611\pi$
$239$			81943.0i			1.43455i	−0.696789	+	0.717276i	$0.745389\pi$
$240$	−3934.38	+	408.922i	−0.0683052	+	0.00709934i
$241$	11957.8			0.205882			0.102941	−	0.994687i	$-0.467175\pi$
$241$	11957.8			0.205882			0.102941	+	0.994687i	$0.467175\pi$
$242$	−29025.6	+	12913.0i	−0.495622	+	0.220494i
$243$	2678.52	−	2678.52i	0.0453609	−	0.0453609i
$244$	3673.61	−	190.396i	0.0617039	−	0.00319800i
$245$	−10081.8	+	10081.8i	−0.167959	+	0.167959i
$246$	3439.12	−	8951.48i	0.0568300	−	0.147919i
$247$	−48756.5			−0.799169
$248$	−7270.05	+	22309.1i	−0.118205	+	0.362726i
$249$		−	22808.0i		−	0.367865i
$250$	−5294.57	+	13780.9i	−0.0847131	+	0.220495i
$251$	−33809.8	−	33809.8i	−0.536655	−	0.536655i	0.385890	−	0.922545i	$-0.373894\pi$
$251$	−33809.8	−	33809.8i	−0.536655	−	0.536655i	−0.922545	+	0.385890i	$0.873894\pi$
$252$	27218.8	+	24536.4i	0.428615	+	0.386375i
$253$	10033.7	+	10033.7i	0.156755	+	0.156755i
$254$	46623.1	−	20741.8i	0.722660	−	0.321499i
$255$		−	7843.81i		−	0.120628i
$256$	−64135.2	+	13477.4i	−0.978626	+	0.205650i
$257$	−119487.			−1.80907			−0.904536	−	0.426396i	$-0.859783\pi$
$257$	−119487.			−1.80907			−0.904536	+	0.426396i	$0.859783\pi$
$258$	−13710.3	−	30817.7i	−0.205971	−	0.462979i
$259$	68022.2	−	68022.2i	1.01403	−	1.01403i
$260$	8669.57	−	9617.34i	0.128248	−	0.142268i
$261$	−1748.35	+	1748.35i	−0.0256654	+	0.0256654i
$262$	−36427.7	−	13995.4i	−0.530676	−	0.203884i
$263$	34094.4			0.492915			0.246457	−	0.969154i	$-0.420733\pi$
$263$	34094.4			0.492915			0.246457	+	0.969154i	$0.420733\pi$
$264$	25879.0	+	8433.41i	0.371312	+	0.121003i
$265$		−	10691.9i		−	0.152252i
$266$	56745.7	+	21801.5i	0.801991	+	0.308122i
$267$	−28177.3	−	28177.3i	−0.395254	−	0.395254i
$268$	−903.648	−	17435.5i	−0.0125814	−	0.242753i
$269$	−46201.7	−	46201.7i	−0.638489	−	0.638489i	0.311694	−	0.950183i	$-0.399104\pi$
$269$	−46201.7	−	46201.7i	−0.638489	−	0.638489i	−0.950183	+	0.311694i	$0.899104\pi$
$270$	678.304	+	1524.68i	0.00930459	+	0.0209147i
$271$			90603.1i			1.23369i	0.787086	+	0.616843i	$0.211589\pi$
$271$			90603.1i			1.23369i	−0.787086	+	0.616843i	$0.788411\pi$
$272$	−13434.7	−	129260.i	−0.181589	−	1.74714i
$273$	−119955.			−1.60951
$274$	−72106.6	+	32079.0i	−0.960449	+	0.427287i
$275$	35659.8	−	35659.8i	0.471534	−	0.471534i
$276$	746.040	+	14394.5i	0.00979363	+	0.188963i
$277$	259.186	−	259.186i	0.00337794	−	0.00337794i	−0.705416	−	0.708794i	$-0.749240\pi$
$277$	259.186	−	259.186i	0.00337794	−	0.00337794i	0.708794	+	0.705416i	$0.249240\pi$
$278$	−46419.9	+	120824.i	−0.600641	+	1.56337i
$279$	9898.78			0.127167
$280$	−14390.6	+	7316.65i	−0.183553	+	0.0933246i
$281$			114309.i			1.44766i	0.689979	+	0.723829i	$0.257620\pi$
$281$			114309.i			1.44766i	−0.689979	+	0.723829i	$0.742380\pi$
$282$	30550.3	−	79517.7i	0.384165	−	0.999920i
$283$	33739.3	+	33739.3i	0.421273	+	0.421273i	0.885642	−	0.464369i	$-0.153719\pi$
$283$	33739.3	+	33739.3i	0.421273	+	0.421273i	−0.464369	+	0.885642i	$0.653719\pi$
$284$	22105.7	−	24522.3i	0.274074	−	0.304036i
$285$	1957.43	+	1957.43i	0.0240989	+	0.0240989i
$286$	−81404.4	+	36215.4i	−0.995213	+	0.442753i
$287$		−	39136.9i		−	0.475142i
$288$	13789.4	+	23963.8i	0.166249	+	0.288916i
$289$	174179.			2.08546
$290$	−442.750	−	995.208i	−0.00526457	−	0.0118336i
$291$	−60211.1	+	60211.1i	−0.711034	+	0.711034i
$292$	−5510.41	−	4967.37i	−0.0646276	−	0.0582586i
$293$	53831.9	−	53831.9i	0.627054	−	0.627054i	−0.320272	−	0.947326i	$-0.603774\pi$
$293$	53831.9	−	53831.9i	0.627054	−	0.627054i	0.947326	+	0.320272i	$0.103774\pi$
$294$	93027.0	+	35740.6i	1.07625	+	0.413492i
$295$	−4033.24			−0.0463458
$296$	64696.5	−	32893.9i	0.738410	−	0.375433i
$297$		−	11482.8i		−	0.130177i
$298$	74811.4	+	28742.2i	0.842433	+	0.323659i
$299$	−33362.7	−	33362.7i	−0.373181	−	0.373181i
$300$	51157.7	−	2651.41i	0.568419	−	0.0294601i
$301$	−97340.8	−	97340.8i	−1.07439	−	1.07439i
$302$	49113.0	+	110396.i	0.538496	+	1.21042i
$303$		−	57461.6i		−	0.625882i
$304$	35609.7	+	28904.4i	0.385319	+	0.312763i
$305$	683.664			0.00734925
$306$	−50091.9	+	22285.0i	−0.534964	+	0.237996i
$307$	99665.1	−	99665.1i	1.05747	−	1.05747i	0.0592206	−	0.998245i	$-0.481138\pi$
$307$	99665.1	−	99665.1i	1.05747	−	1.05747i	0.998245	−	0.0592206i	$-0.0188615\pi$
$308$	110937.	−	5749.66i	1.16943	−	0.0606096i
$309$	19742.9	−	19742.9i	0.206773	−	0.206773i
$310$	−1563.95	+	4070.70i	−0.0162741	+	0.0423590i
$311$	−81209.1			−0.839622			−0.419811	−	0.907612i	$-0.637904\pi$
$311$	−81209.1			−0.839622			−0.419811	+	0.907612i	$0.637904\pi$
$312$	−86049.0	−	28041.5i	−0.883968	−	0.288066i
$313$			16053.4i			0.163862i	0.996638	+	0.0819310i	$0.0261087\pi$
$313$			16053.4i			0.163862i	−0.996638	+	0.0819310i	$0.973891\pi$
$314$	−36492.5	+	94984.2i	−0.370122	+	0.963368i
$315$	4815.86	+	4815.86i	0.0485347	+	0.0485347i
$316$	100271.	+	90389.5i	1.00416	+	0.905198i
$317$	5778.79	+	5778.79i	0.0575067	+	0.0575067i	0.735275	−	0.677769i	$-0.237053\pi$
$317$	5778.79	+	5778.79i	0.0575067	+	0.0575067i	−0.677769	+	0.735275i	$0.737053\pi$
$318$	−68280.1	+	30376.6i	−0.675211	+	0.300390i
$319$			7495.17i			0.0736547i
$320$	−12033.3	+	1884.51i	−0.117513	+	0.0184034i
$321$	−71296.9			−0.691927
$322$	23911.4	+	53747.7i	0.230618	+	0.518380i
$323$	−64309.4	+	64309.4i	−0.616410	+	0.616410i
$324$	7809.75	−	8663.53i	0.0743956	−	0.0825287i
$325$	−118571.	+	118571.i	−1.12256	+	1.12256i
$326$	−17051.5	−	6551.10i	−0.160445	−	0.0616423i
$327$	74957.5			0.701003
$328$	9148.91	−	28074.6i	0.0850396	−	0.260955i
$329$		−	347661.i		−	3.21191i
$330$	4722.10	+	1814.21i	0.0433618	+	0.0166594i
$331$	79971.6	+	79971.6i	0.729928	+	0.729928i	0.970605	−	0.240677i	$-0.0773695\pi$
$331$	79971.6	+	79971.6i	0.729928	+	0.729928i	−0.240677	+	0.970605i	$0.577370\pi$
$332$	−3635.03	−	70136.2i	−0.0329786	−	0.636306i
$333$	−21651.0	−	21651.0i	−0.195249	−	0.195249i
$334$	26977.5	+	60639.6i	0.241829	+	0.543580i
$335$		−	3244.77i		−	0.0289131i
$336$	87610.2	+	71113.2i	0.776026	+	0.629900i
$337$	−129995.			−1.14464			−0.572319	−	0.820031i	$-0.693956\pi$
$337$	−129995.			−1.14464			−0.572319	+	0.820031i	$0.693956\pi$
$338$	166293.	−	73981.0i	1.45560	−	0.647570i
$339$	47977.7	−	47977.7i	0.417484	−	0.417484i
$340$	−1250.11	−	24120.3i	−0.0108141	−	0.208653i
$341$	21218.0	−	21218.0i	0.182472	−	0.182472i
$342$	6939.24	−	18061.7i	0.0593280	−	0.154421i
$343$	203054.			1.72593
$344$	−47071.7	−	92581.7i	−0.397780	−	0.782363i
$345$			2678.84i			0.0225065i
$346$	9549.48	−	24855.8i	0.0797678	−	0.207623i
$347$	22976.9	+	22976.9i	0.190824	+	0.190824i	0.796052	−	0.605228i	$-0.206918\pi$
$347$	22976.9	+	22976.9i	0.190824	+	0.190824i	−0.605228	+	0.796052i	$0.706918\pi$
$348$	−5097.67	+	5654.96i	−0.0420933	+	0.0466950i
$349$	−87638.2	−	87638.2i	−0.719520	−	0.719520i	0.248987	−	0.968507i	$-0.419902\pi$
$349$	−87638.2	−	87638.2i	−0.719520	−	0.719520i	−0.968507	+	0.248987i	$0.919902\pi$
$350$	191018.	−	84980.7i	1.55933	−	0.693720i
$351$			38180.9i			0.309907i
$352$	80923.9	+	21808.9i	0.653118	+	0.176014i
$353$	144112.			1.15651			0.578257	−	0.815854i	$-0.303733\pi$
$353$	144112.			1.15651			0.578257	+	0.815854i	$0.303733\pi$
$354$	11458.8	+	25756.9i	0.0914393	+	0.205536i
$355$	4338.78	−	4338.78i	0.0344279	−	0.0344279i
$356$	−91137.9	−	82156.4i	−0.719116	−	0.648248i
$357$	−158220.	+	158220.i	−1.24144	+	1.24144i
$358$	−138220.	−	53103.6i	−1.07846	−	0.414341i
$359$	30554.2			0.237073			0.118536	−	0.992950i	$-0.462180\pi$
$359$	30554.2			0.237073			0.118536	+	0.992950i	$0.462180\pi$
$360$	2328.83	+	4580.41i	0.0179694	+	0.0353426i
$361$			98224.0i			0.753708i
$362$	−211927.	−	81421.4i	−1.61722	−	0.621329i
$363$	29181.1	+	29181.1i	0.221457	+	0.221457i
$364$	−368871.	+	19117.9i	−2.78402	+	0.144291i
$365$	−974.966	−	974.966i	−0.00731819	−	0.00731819i
$366$	−1942.35	−	4365.99i	−0.0144999	−	0.0325927i
$367$		−	27735.4i		−	0.205922i	−0.994685	−	0.102961i	$-0.967168\pi$
$367$		−	27735.4i		−	0.205922i	0.994685	−	0.102961i	$-0.0328316\pi$
$368$	4588.25	+	44145.2i	0.0338807	+	0.325978i
$369$	−12457.0			−0.0914873
$370$	12324.3	−	5482.86i	0.0900241	−	0.0400501i
$371$	−215669.	+	215669.i	−1.56690	+	1.56690i
$372$	30439.5	−	1577.62i	0.219964	−	0.0114003i
$373$	91259.4	−	91259.4i	0.655934	−	0.655934i	−0.298481	−	0.954415i	$-0.596480\pi$
$373$	91259.4	−	91259.4i	0.655934	−	0.655934i	0.954415	+	0.298481i	$0.0964801\pi$
$374$	−59604.0	+	155140.i	−0.426120	+	1.10912i
$375$	19177.7			0.136375
$376$	81271.4	−	249392.i	0.574860	−	1.76403i
$377$		−	24921.8i		−	0.175347i
$378$	17072.6	−	44437.2i	0.119486	−	0.311002i
$379$	−725.899	−	725.899i	−0.00505356	−	0.00505356i	0.704575	−	0.709629i	$-0.251137\pi$
$379$	−725.899	−	725.899i	−0.00505356	−	0.00505356i	−0.709629	+	0.704575i	$0.751137\pi$
$380$	6331.22	+	5707.28i	0.0438450	+	0.0395241i
$381$	−46872.9	−	46872.9i	−0.322903	−	0.322903i
$382$	−37637.6	+	16744.3i	−0.257926	+	0.114747i
$383$		−	81078.9i		−	0.552727i	−0.961053	−	0.276363i	$-0.910871\pi$
$383$		−	81078.9i		−	0.552727i	0.961053	−	0.276363i	$-0.0891293\pi$
$384$	46222.6	+	71492.8i	0.313467	+	0.484842i
$385$	20645.6			0.139285
$386$	34656.8	+	77900.9i	0.232602	+	0.522839i
$387$	−30982.9	+	30982.9i	−0.206871	+	0.206871i
$388$	−175557.	+	194750.i	−1.16615	+	1.29364i
$389$	−77667.7	+	77667.7i	−0.513265	+	0.513265i	−0.915525	−	0.402260i	$-0.868225\pi$
$389$	−77667.7	+	77667.7i	−0.513265	+	0.513265i	0.402260	+	0.915525i	$0.368225\pi$
$390$	−15701.2	−	6032.34i	−0.103230	−	0.0396604i
$391$	−88010.4			−0.575679
$392$	291761.	+	95078.7i	1.89870	+	0.618744i
$393$			50693.3i			0.328220i
$394$	−186005.	−	71462.2i	−1.19821	−	0.460345i
$395$	17741.1	+	17741.1i	0.113707	+	0.113707i
$396$	−1830.08	−	35310.4i	−0.0116702	−	0.225171i
$397$	21877.8	+	21877.8i	0.138811	+	0.138811i	0.773098	−	0.634287i	$-0.218706\pi$
$397$	21877.8	+	21877.8i	0.138811	+	0.138811i	−0.634287	+	0.773098i	$0.718706\pi$
$398$	50548.5	+	113622.i	0.319111	+	0.717293i
$399$		−	78968.0i		−	0.496027i
$400$	156891.	−	16306.6i	0.980570	−	0.101916i
$401$	175824.			1.09343			0.546714	−	0.837319i	$-0.315879\pi$
$401$	175824.			1.09343			0.546714	+	0.837319i	$0.315879\pi$
$402$	−20721.6	+	9218.69i	−0.128225	+	0.0570449i
$403$	−70551.0	+	70551.0i	−0.434403	+	0.434403i
$404$	−9157.98	−	176699.i	−0.0561095	−	1.08261i
$405$	1532.85	−	1532.85i	0.00934524	−	0.00934524i
$406$	−11143.8	+	29005.5i	−0.0676054	+	0.175966i
$407$	−92817.6			−0.560327
$408$	−150485.	+	76511.4i	−0.904007	+	0.459627i
$409$			174646.i			1.04402i	0.852938	+	0.522012i	$0.174819\pi$
$409$			174646.i			1.04402i	−0.852938	+	0.522012i	$0.825181\pi$
$410$	1968.13	−	5122.72i	0.0117081	−	0.0304743i
$411$	72493.0	+	72493.0i	0.429153	+	0.429153i
$412$	57564.4	−	63857.5i	0.339125	−	0.376199i
$413$	81355.8	+	81355.8i	0.476967	+	0.476967i
$414$	17107.5	−	7610.82i	0.0998127	−	0.0444049i
$415$		−	13052.5i		−	0.0757873i
$416$	−269076.	−	72515.7i	−1.55485	−	0.419030i
$417$	168140.			0.966937
$418$	−23841.0	−	53589.5i	−0.136450	−	0.306710i
$419$	167807.	−	167807.i	0.955831	−	0.955831i	−0.0432336	−	0.999065i	$-0.513766\pi$
$419$	167807.	−	167807.i	0.955831	−	0.955831i	0.999065	+	0.0432336i	$0.0137660\pi$
$420$	15576.7	+	14041.6i	0.0883030	+	0.0796009i
$421$	18489.0	−	18489.0i	0.104316	−	0.104316i	−0.653023	−	0.757338i	$-0.726499\pi$
$421$	18489.0	−	18489.0i	0.104316	−	0.104316i	0.757338	+	0.653023i	$0.226499\pi$
$422$	−199720.	−	76731.5i	−1.12149	−	0.430872i
$423$	−110658.			−0.618445
$424$	−205125.	+	104292.i	−1.14100	+	0.580125i
$425$			312787.i			1.73169i
$426$	−40035.0	−	15381.3i	−0.220608	−	0.0847566i
$427$	−13790.4	−	13790.4i	−0.0756348	−	0.0756348i
$428$	−219243.	+	11363.0i	−1.19685	+	0.0620304i
$429$	81840.6	+	81840.6i	0.444687	+	0.444687i
$430$	−7846.06	−	17636.3i	−0.0424341	−	0.0953827i
$431$		−	206513.i		−	1.11171i	−0.831278	−	0.555857i	$-0.812390\pi$
$431$		−	206513.i		−	1.11171i	0.831278	−	0.555857i	$-0.187610\pi$
$432$	22634.8	−	27885.7i	0.121286	−	0.149422i
$433$	29880.3			0.159371			0.0796855	−	0.996820i	$-0.474608\pi$
$433$	29880.3			0.159371			0.0796855	+	0.996820i	$0.474608\pi$
$434$	113658.	−	50564.6i	0.603423	−	0.268452i
$435$	−1000.54	+	1000.54i	−0.00528757	+	0.00528757i
$436$	230500.	−	11946.4i	1.21255	−	0.0628440i
$437$	21963.1	−	21963.1i	0.115009	−	0.115009i
$438$	−3456.32	+	8996.26i	−0.0180163	+	0.0468936i
$439$	−82988.1			−0.430612			−0.215306	−	0.976547i	$-0.569075\pi$
$439$	−82988.1			−0.430612			−0.215306	+	0.976547i	$0.569075\pi$
$440$	14809.9	+	4826.24i	0.0764976	+	0.0249289i
$441$		−	129458.i		−	0.665657i
$442$	198186.	−	515847.i	1.01445	−	2.64044i
$443$	213195.	+	213195.i	1.08635	+	1.08635i	0.995901	+	0.0904459i	$0.0288292\pi$
$443$	213195.	+	213195.i	1.08635	+	1.08635i	0.0904459	+	0.995901i	$0.471171\pi$
$444$	−70028.9	−	63127.7i	−0.355232	−	0.320224i
$445$	−16125.2	−	16125.2i	−0.0814300	−	0.0814300i
$446$	−10446.7	+	4647.55i	−0.0525182	+	0.0233644i
$447$		−	104109.i		−	0.521040i
$448$	280742.	+	204715.i	1.39878	+	1.01999i
$449$	174583.			0.865984			0.432992	−	0.901398i	$-0.357458\pi$
$449$	174583.			0.865984			0.432992	+	0.901398i	$0.357458\pi$
$450$	−27048.7	−	60799.7i	−0.133574	−	0.300245i
$451$	−26701.5	+	26701.5i	−0.131275	+	0.131275i
$452$	139888.	−	155181.i	0.684707	−	0.759561i
$453$	110987.	−	110987.i	0.540849	−	0.540849i
$454$	373271.	+	143409.i	1.81098	+	0.695770i
$455$	−68647.6			−0.331591
$456$	18460.1	−	56647.1i	0.0887777	−	0.272426i
$457$		−	129994.i		−	0.622429i	−0.950340	−	0.311214i	$-0.899264\pi$
$457$		−	129994.i		−	0.622429i	0.950340	−	0.311214i	$-0.100736\pi$
$458$	2083.84	+	800.602i	0.00993421	+	0.00381668i
$459$	50360.3	+	50360.3i	0.239036	+	0.239036i
$460$	426.941	+	8237.62i	0.00201768	+	0.0389302i
$461$	−160419.	−	160419.i	−0.754840	−	0.754840i	0.220538	−	0.975378i	$-0.429219\pi$
$461$	−160419.	−	160419.i	−0.754840	−	0.754840i	−0.975378	+	0.220538i	$0.929219\pi$
$462$	−58656.0	−	131846.i	−0.274807	−	0.617708i
$463$		−	237870.i		−	1.10963i	−0.831974	−	0.554815i	$-0.812789\pi$
$463$		−	237870.i		−	1.10963i	0.831974	−	0.554815i	$-0.187211\pi$
$464$	−14774.4	+	18201.8i	−0.0686238	+	0.0845434i
$465$	5664.84			0.0261988
$466$	−79553.7	+	35392.0i	−0.366343	+	0.162980i
$467$	−154822.	+	154822.i	−0.709902	+	0.709902i	−0.966514	−	0.256612i	$-0.917394\pi$
$467$	−154822.	+	154822.i	−0.709902	+	0.709902i	0.256612	+	0.966514i	$0.417394\pi$
$468$	6085.10	+	117409.i	0.0277828	+	0.536055i
$469$	−65451.3	+	65451.3i	−0.297559	+	0.297559i
$470$	17483.2	−	45506.1i	0.0791455	−	0.206003i
$471$	132181.			0.595838
$472$	39341.7	+	77378.2i	0.176591	+	0.347324i
$473$			132823.i			0.593680i
$474$	62893.6	−	163702.i	0.279930	−	0.728613i
$475$	−78056.5	−	78056.5i	−0.345957	−	0.345957i
$476$	−461322.	+	511755.i	−2.03606	+	2.25865i
$477$	68645.9	+	68645.9i	0.301702	+	0.301702i
$478$	299473.	−	133230.i	1.31070	−	0.583106i
$479$			75781.5i			0.330288i	0.986270	+	0.165144i	$0.0528088\pi$
$479$			75781.5i			0.330288i	−0.986270	+	0.165144i	$0.947191\pi$
$480$	7891.34	+	13713.9i	0.0342506	+	0.0595223i
$481$	308623.			1.33395
$482$	−19442.1	−	43701.8i	−0.0836855	−	0.188107i
$483$	54035.7	−	54035.7i	0.231626	−	0.231626i
$484$	94384.9	+	85083.4i	0.402914	+	0.363207i
$485$	−34457.4	+	34457.4i	−0.146487	+	0.146487i
$486$	−14144.0	−	5434.07i	−0.0598826	−	0.0230066i
$487$	−198624.			−0.837481			−0.418740	−	0.908106i	$-0.637528\pi$
$487$	−198624.			−0.837481			−0.418740	+	0.908106i	$0.637528\pi$
$488$	−6668.71	−	13116.2i	−0.0280029	−	0.0550767i
$489$			23729.0i			0.0992345i
$490$	53237.2	+	20453.5i	0.221729	+	0.0851874i
$491$	−160150.	−	160150.i	−0.664301	−	0.664301i	0.292090	−	0.956391i	$-0.405649\pi$
$491$	−160150.	−	160150.i	−0.664301	−	0.664301i	−0.956391	+	0.292090i	$0.905649\pi$
$492$	−38306.2	+	1985.34i	−0.158248	+	0.00820172i
$493$	−32871.7	−	32871.7i	−0.135247	−	0.135247i
$494$	79272.7	+	178188.i	0.324840	+	0.730171i
$495$		−	6571.33i		−	0.0268190i
$496$	93352.2	−	9702.62i	0.379456	−	0.0394390i
$497$	−175038.			−0.708630
$498$	−83355.2	+	37083.3i	−0.336104	+	0.149527i
$499$	−169851.	+	169851.i	−0.682131	+	0.682131i	−0.960480	−	0.278349i	$-0.910213\pi$
$499$	−169851.	+	169851.i	−0.682131	+	0.682131i	0.278349	+	0.960480i	$0.410213\pi$
$500$	58972.9	−	3056.46i	0.235891	−	0.0122258i
$501$	60964.5	−	60964.5i	0.242886	−	0.242886i
$502$	−68592.0	+	178534.i	−0.272186	+	0.708457i
$503$	115453.			0.456320			0.228160	−	0.973624i	$-0.426729\pi$
$503$	115453.			0.456320			0.228160	+	0.973624i	$0.426729\pi$
$504$	45417.2	−	139369.i	0.178797	−	0.548661i
$505$		−	32883.9i		−	0.128944i
$506$	20356.1	−	52983.6i	0.0795048	−	0.206938i
$507$	−167184.	−	167184.i	−0.650399	−	0.650399i
$508$	−151608.	−	136667.i	−0.587483	−	0.529587i
$509$	174996.	+	174996.i	0.675449	+	0.675449i	0.958967	−	0.283518i	$-0.0915016\pi$
$509$	174996.	+	174996.i	0.675449	+	0.675449i	−0.283518	+	0.958967i	$0.591502\pi$
$510$	−28666.4	+	12753.2i	−0.110213	+	0.0490318i
$511$			39332.7i			0.150630i
$512$	153532.	+	212479.i	0.585679	+	0.810543i
$513$	−25134.9			−0.0955087
$514$	194273.	+	436685.i	0.735339	+	1.65288i
$515$	11298.4	−	11298.4i	0.0425993	−	0.0425993i
$516$	−90336.7	+	100212.i	−0.339285	+	0.376376i
$517$	−237195.	+	237195.i	−0.887409	+	0.887409i
$518$	−359194.	−	138001.i	−1.33866	−	0.514307i
$519$	−34589.6			−0.128414
$520$	−49243.8	−	16047.5i	−0.182115	−	0.0593473i
$521$		−	408830.i		−	1.50615i	−0.657936	−	0.753074i	$-0.728570\pi$
$521$		−	408830.i		−	1.50615i	0.657936	−	0.753074i	$-0.271430\pi$
$522$	9232.24	+	3546.99i	0.0338818	+	0.0130172i
$523$	−186677.	−	186677.i	−0.682477	−	0.682477i	0.278080	−	0.960558i	$-0.410302\pi$
$523$	−186677.	−	186677.i	−0.682477	−	0.682477i	−0.960558	+	0.278080i	$0.910302\pi$
$524$	8079.27	+	155886.i	0.0294245	+	0.567732i
$525$	−192042.	−	192042.i	−0.696751	−	0.696751i
$526$	−55433.8	−	124603.i	−0.200356	−	0.450358i
$527$			186112.i			0.670122i
$528$	−11255.2	−	108291.i	−0.0403726	−	0.388439i
$529$	−249783.			−0.892591
$530$	−39075.1	+	17383.8i	−0.139107	+	0.0618861i
$531$	25894.9	−	25894.9i	0.0918387	−	0.0918387i
$532$	−12585.6	−	242833.i	−0.0444682	−	0.857993i
$533$	88784.0	−	88784.0i	0.312522	−	0.312522i
$534$	−57164.9	+	148791.i	−0.200469	+	0.521789i
$535$	−40801.5			−0.142550
$536$	−62251.3	+	31650.7i	−0.216680	+	0.110167i
$537$			192349.i			0.667024i
$538$	−93732.2	+	243970.i	−0.323835	+	0.842892i
$539$	−277492.	−	277492.i	−0.955153	−	0.955153i
$540$	4469.34	−	4957.93i	0.0153269	−	0.0170025i
$541$	133417.	+	133417.i	0.455844	+	0.455844i	0.897288	−	0.441445i	$-0.145534\pi$
$541$	133417.	+	133417.i	0.455844	+	0.455844i	−0.441445	+	0.897288i	$0.645534\pi$
$542$	331123.	−	147311.i	1.12717	−	0.501460i
$543$			294920.i			1.00024i
$544$	−450557.	+	259262.i	−1.52248	+	0.876074i
$545$	42896.4			0.144420
$546$	195034.	+	438395.i	0.654222	+	1.47055i
$547$	−95416.9	+	95416.9i	−0.318897	+	0.318897i	−0.848343	−	0.529446i	$-0.822400\pi$
$547$	−95416.9	+	95416.9i	−0.318897	+	0.318897i	0.529446	+	0.848343i	$0.322400\pi$
$548$	234475.	+	211368.i	0.780792	+	0.703846i
$549$	−4389.39	+	4389.39i	−0.0145633	+	0.0145633i
$550$	−188303.	−	72345.2i	−0.622489	−	0.239158i
$551$	16406.4			0.0540392
$552$	51393.8	−	26130.4i	0.168668	−	0.0857565i
$553$		−	715724.i		−	2.34043i
$554$	−1368.64	−	525.827i	−0.00445934	−	0.00171326i
$555$	−12390.3	−	12390.3i	−0.0402251	−	0.0402251i
$556$	517042.	−	26797.4i	1.67254	−	0.0866847i
$557$	−175167.	−	175167.i	−0.564600	−	0.564600i	0.366011	−	0.930611i	$-0.380723\pi$
$557$	−175167.	−	175167.i	−0.564600	−	0.564600i	−0.930611	+	0.366011i	$0.880723\pi$
$558$	−16094.3	−	36176.6i	−0.0516898	−	0.116187i
$559$		−	441644.i		−	1.41335i
$560$	50137.3	+	40696.4i	0.159876	+	0.129772i
$561$	215894.			0.685986
$562$	417758.	−	185853.i	1.32267	−	0.588433i
$563$	163587.	−	163587.i	0.516097	−	0.516097i	−0.400291	−	0.916388i	$-0.631091\pi$
$563$	163587.	−	163587.i	0.516097	−	0.516097i	0.916388	+	0.400291i	$0.131091\pi$
$564$	−340281.	+	17636.1i	−1.06974	+	0.0554428i
$565$	27456.5	−	27456.5i	0.0860099	−	0.0860099i
$566$	68449.1	−	178162.i	0.213666	−	0.556137i
$567$	−61839.3			−0.192353
$568$	−125562.	−	40918.0i	−0.389190	−	0.126829i
$569$			361331.i			1.11604i	0.829826	+	0.558022i	$0.188439\pi$
$569$			361331.i			1.11604i	−0.829826	+	0.558022i	$0.811561\pi$
$570$	3971.16	−	10336.3i	0.0122227	−	0.0318138i
$571$	263234.	+	263234.i	0.807364	+	0.807364i	0.984234	−	0.176871i	$-0.0565974\pi$
$571$	263234.	+	263234.i	0.807364	+	0.807364i	−0.176871	+	0.984234i	$0.556597\pi$
$572$	264709.	+	238623.i	0.809053	+	0.729322i
$573$	37839.3	+	37839.3i	0.115248	+	0.115248i
$574$	−143032.	+	63632.4i	−0.434119	+	0.193132i
$575$		−	106824.i		−	0.323097i
$576$	65159.4	−	89358.0i	0.196396	−	0.269332i
$577$	−328682.			−0.987243			−0.493622	−	0.869677i	$-0.664327\pi$
$577$	−328682.			−0.987243			−0.493622	+	0.869677i	$0.664327\pi$
$578$	−283197.	−	636565.i	−0.847681	−	1.90540i
$579$	78318.3	−	78318.3i	0.233618	−	0.233618i
$580$	−2917.27	+	3236.20i	−0.00867204	+	0.00962009i
$581$	−263286.	+	263286.i	−0.779965	+	0.779965i
$582$	317947.	+	122154.i	0.938661	+	0.360630i
$583$	294285.			0.865826
$584$	−9194.67	+	28215.0i	−0.0269594	+	0.0827284i
$585$			21850.0i			0.0638469i
$586$	−284262.	−	109212.i	−0.827796	−	0.318036i
$587$	349626.	+	349626.i	1.01468	+	1.01468i	0.999891	+	0.0147866i	$0.00470690\pi$
$587$	349626.	+	349626.i	1.01468	+	1.01468i	0.0147866	+	0.999891i	$0.495293\pi$
$588$	−20632.4	−	398092.i	−0.0596753	−	1.15141i
$589$	−46444.6	−	46444.6i	−0.133877	−	0.133877i
$590$	6557.60	+	14740.1i	0.0188383	+	0.0423444i
$591$			258846.i			0.741084i
$592$	−225405.	−	182961.i	−0.643162	−	0.522055i
$593$	−414406.			−1.17846			−0.589232	−	0.807964i	$-0.700570\pi$
$593$	−414406.			−1.17846			−0.589232	+	0.807964i	$0.700570\pi$
$594$	−41965.6	+	18669.8i	−0.118938	+	0.0529134i
$595$	−90545.6	+	90545.6i	−0.255761	+	0.255761i
$596$	−16592.3	−	320141.i	−0.0467106	−	0.901258i
$597$	114231.	−	114231.i	0.320505	−	0.320505i
$598$	−67685.0	+	176173.i	−0.189274	+	0.492649i
$599$	369814.			1.03069			0.515347	−	0.856982i	$-0.327663\pi$
$599$	369814.			1.03069			0.515347	+	0.856982i	$0.327663\pi$
$600$	−92866.8	−	182653.i	−0.257963	−	0.507369i
$601$			318196.i			0.880940i	0.897767	+	0.440470i	$0.145188\pi$
$601$			318196.i			0.880940i	−0.897767	+	0.440470i	$0.854812\pi$
$602$	−197481.	+	514012.i	−0.544920	+	1.41834i
$603$	20832.7	+	20832.7i	0.0572941	+	0.0572941i
$604$	323605.	−	358982.i	0.887036	−	0.984008i
$605$	16699.7	+	16699.7i	0.0456244	+	0.0456244i
$606$	−210002.	+	93426.3i	−0.571845	+	0.254404i
$607$			568888.i			1.54401i	0.635618	+	0.772003i	$0.280745\pi$
$607$			568888.i			1.54401i	−0.635618	+	0.772003i	$0.719255\pi$
$608$	47738.0	−	177136.i	0.129139	−	0.479182i
$609$	40364.5			0.108834
$610$	−1111.56	−	2498.55i	−0.00298727	−	0.00671474i
$611$	788685.	−	788685.i	2.11262	−	2.11262i
$612$	162888.	+	146835.i	0.434896	+	0.392038i
$613$	290102.	−	290102.i	0.772023	−	0.772023i	−0.206437	−	0.978460i	$-0.566187\pi$
$613$	290102.	−	290102.i	0.772023	−	0.772023i	0.978460	+	0.206437i	$0.0661868\pi$
$614$	−526286.	−	202197.i	−1.39600	−	0.536336i
$615$	−7128.85			−0.0188482
$616$	−201384.	−	396088.i	−0.530719	−	1.04383i
$617$			222944.i			0.585633i	0.956169	+	0.292817i	$0.0945925\pi$
$617$			222944.i			0.585633i	−0.956169	+	0.292817i	$0.905407\pi$
$618$	−104253.	−	40053.7i	−0.272969	−	0.104873i
$619$	−52984.5	−	52984.5i	−0.138283	−	0.138283i	0.634577	−	0.772860i	$-0.281174\pi$
$619$	−52984.5	−	52984.5i	−0.138283	−	0.138283i	−0.772860	+	0.634577i	$0.781174\pi$
$620$	17419.8	−	902.837i	0.0453169	−	0.00234869i
$621$	−17199.2	−	17199.2i	−0.0445989	−	0.0445989i
$622$	132037.	+	296791.i	0.341283	+	0.767132i
$623$			650533.i			1.67607i
$624$	37424.2	+	360072.i	0.0961134	+	0.924740i
$625$	−374123.			−0.957756
$626$	58669.6	−	26101.1i	0.149715	−	0.0666054i
$627$	−53876.7	+	53876.7i	−0.137046	+	0.137046i
$628$	406467.	−	21066.5i	1.03064	−	0.0534161i
$629$	407072.	−	407072.i	1.02889	−	1.02889i
$630$	9770.23	−	25430.4i	0.0246164	−	0.0640724i
$631$	−178806.			−0.449079			−0.224540	−	0.974465i	$-0.572088\pi$
$631$	−178806.			−0.449079			−0.224540	+	0.974465i	$0.572088\pi$
$632$	167312.	−	513419.i	0.418884	−	1.28540i
$633$			277933.i			0.693637i
$634$	11723.8	−	30515.1i	0.0291668	−	0.0759166i
$635$	−26824.3	−	26824.3i	−0.0665243	−	0.0665243i
$636$	222032.	+	200151.i	0.548910	+	0.494815i
$637$	922675.	+	922675.i	2.27389	+	2.27389i
$638$	27392.3	−	12186.3i	0.0672956	−	0.0299386i
$639$			55713.3i			0.136445i
$640$	26452.1	+	40913.7i	0.0645804	+	0.0998869i
$641$	−20182.3			−0.0491196			−0.0245598	−	0.999698i	$-0.507818\pi$
$641$	−20182.3			−0.0491196			−0.0245598	+	0.999698i	$0.507818\pi$
$642$	115921.	+	260565.i	0.281249	+	0.632188i
$643$	−220638.	+	220638.i	−0.533652	+	0.533652i	−0.921657	−	0.388005i	$-0.873164\pi$
$643$	−220638.	+	220638.i	−0.533652	+	0.533652i	0.388005	+	0.921657i	$0.373164\pi$
$644$	157552.	−	174776.i	0.379885	−	0.421414i
$645$	−17730.8	+	17730.8i	−0.0426195	+	0.0426195i
$646$	339589.	+	130469.i	0.813745	+	0.312637i
$647$	−29047.0			−0.0693893			−0.0346946	−	0.999398i	$-0.511046\pi$
$647$	−29047.0			−0.0693893			−0.0346946	+	0.999398i	$0.511046\pi$
$648$	−44360.0	−	14456.0i	−0.105643	−	0.0344268i
$649$		−	111011.i		−	0.263559i
$650$	626117.	+	240551.i	1.48193	+	0.569352i
$651$	−114267.	−	114267.i	−0.269625	−	0.269625i
$652$	3781.83	+	72968.6i	0.00889624	+	0.171649i
$653$	−438317.	−	438317.i	−1.02793	−	1.02793i	−0.999599	−	0.0283280i	$-0.990982\pi$
$653$	−438317.	−	438317.i	−1.02793	−	1.02793i	−0.0283280	−	0.999599i	$-0.509018\pi$
$654$	−121873.	−	273944.i	−0.284938	−	0.640480i
$655$			29010.6i			0.0676198i
$656$	−117478.	+	12210.1i	−0.272991	+	0.0283735i
$657$	12519.3			0.0290034
$658$	−1.27058e6	+	565258.i	−2.93461	+	1.30555i
$659$	453511.	−	453511.i	1.04428	−	1.04428i	0.0453069	−	0.998973i	$-0.485573\pi$
$659$	453511.	−	453511.i	1.04428	−	1.04428i	0.998973	−	0.0453069i	$-0.0144266\pi$
$660$	−1047.31	−	20207.3i	−0.00240429	−	0.0463896i
$661$	387740.	−	387740.i	0.887436	−	0.887436i	−0.106840	−	0.994276i	$-0.534073\pi$
$661$	387740.	−	387740.i	0.887436	−	0.887436i	0.994276	+	0.106840i	$0.0340732\pi$
$662$	162243.	−	422294.i	0.370212	−	0.963604i
$663$	−717860.			−1.63310
$664$	−250413.	+	127319.i	−0.567965	+	0.288772i
$665$		−	45191.6i		−	0.102191i
$666$	−43924.6	+	114329.i	−0.0990284	+	0.257755i
$667$	11226.4	+	11226.4i	0.0252342	+	0.0252342i
$668$	177754.	−	197187.i	0.398352	−	0.441901i
$669$	10502.7	+	10502.7i	0.0234665	+	0.0234665i
$670$	−11858.5	+	5275.64i	−0.0264168	+	0.0117524i
$671$			18817.3i			0.0417938i
$672$	117449.	−	435807.i	0.260083	−	0.965063i
$673$	82244.9			0.181585			0.0907923	−	0.995870i	$-0.471060\pi$
$673$	82244.9			0.181585			0.0907923	+	0.995870i	$0.471060\pi$
$674$	211358.	+	475088.i	0.465264	+	1.04581i
$675$	−61125.5	+	61125.5i	−0.134157	+	0.134157i
$676$	−540749.	−	487459.i	−1.18332	−	1.06671i
$677$	−576584.	+	576584.i	−1.25801	+	1.25801i	−0.305972	+	0.952041i	$0.598981\pi$
$677$	−576584.	+	576584.i	−1.25801	+	1.25801i	−0.952041	+	0.305972i	$0.901019\pi$
$678$	−253348.	−	97335.3i	−0.551136	−	0.211744i
$679$	1.39010e6			3.01514
$680$	−86118.8	+	43785.7i	−0.186243	+	0.0946922i
$681$		−	519449.i		−	1.12008i
$682$	−112043.	−	43046.3i	−0.240888	−	0.0925480i
$683$	342109.	+	342109.i	0.733371	+	0.733371i	0.971286	−	0.237915i	$-0.0764641\pi$
$683$	342109.	+	342109.i	0.733371	+	0.733371i	−0.237915	+	0.971286i	$0.576464\pi$
$684$	−77291.8	+	4005.89i	−0.165204	+	0.00856224i
$685$	41486.0	+	41486.0i	0.0884140	+	0.0884140i
$686$	−330144.	−	742092.i	−0.701544	−	1.57692i
$687$		−	2899.90i		−	0.00614425i
$688$	−261821.	+	322558.i	−0.553130	+	0.681446i
$689$	−978512.			−2.06124
$690$	9790.21	−	4355.49i	0.0205634	−	0.00914828i
$691$	213096.	−	213096.i	0.446293	−	0.446293i	−0.447827	−	0.894120i	$-0.647802\pi$
$691$	213096.	−	213096.i	0.446293	−	0.446293i	0.894120	+	0.447827i	$0.147802\pi$
$692$	−106366.	+	5512.74i	−0.222121	+	0.0115121i
$693$	−132552.	+	132552.i	−0.276008	+	0.276008i
$694$	46614.6	−	121330.i	0.0967840	−	0.251913i
$695$	96222.4			0.199208
$696$	28955.1	+	9435.86i	0.0597733	+	0.0194788i
$697$		−	234211.i		−	0.482105i
$698$	−177797.	+	462777.i	−0.364933	+	0.949864i
$699$	79980.0	+	79980.0i	0.163692	+	0.163692i
$700$	−621150.	−	559936.i	−1.26765	−	1.14273i
$701$	−293532.	−	293532.i	−0.597337	−	0.597337i	0.342266	−	0.939603i	$-0.388806\pi$
$701$	−293532.	−	293532.i	−0.597337	−	0.597337i	−0.939603	+	0.342266i	$0.888806\pi$
$702$	139538.	−	62077.9i	0.283151	−	0.125969i
$703$			203170.i			0.411102i
$704$	−51869.5	−	331208.i	−0.104657	−	0.668275i
$705$	−63326.8			−0.127412
$706$	−234311.	−	526680.i	−0.470092	−	1.05666i
$707$	−663313.	+	663313.i	−1.32703	+	1.32703i
$708$	75501.8	−	83755.9i	0.150623	−	0.167089i
$709$	−13231.5	+	13231.5i	−0.0263218	+	0.0263218i	−0.720145	−	0.693823i	$-0.755925\pi$
$709$	−13231.5	+	13231.5i	−0.0263218	+	0.0263218i	0.693823	+	0.720145i	$0.255925\pi$
$710$	−22911.1	−	8802.35i	−0.0454495	−	0.0174615i
$711$	−227810.			−0.450643
$712$	−152073.	+	466655.i	−0.299979	+	0.920525i
$713$		−	63561.5i		−	0.125030i
$714$	835488.	+	320991.i	1.63887	+	0.629646i
$715$	46835.4	+	46835.4i	0.0916142	+	0.0916142i
$716$	30655.7	+	591487.i	0.0597978	+	1.15377i
$717$	−301078.	−	301078.i	−0.585653	−	0.585653i
$718$	−49677.8	−	111665.i	−0.0963636	−	0.216605i
$719$		−	477459.i		−	0.923587i	−0.886987	−	0.461794i	$-0.847206\pi$
$719$		−	477459.i		−	0.923587i	0.886987	−	0.461794i	$-0.152794\pi$
$720$	12953.4	−	15958.3i	0.0249872	−	0.0307838i
$721$	−455808.			−0.876821
$722$	358975.	−	159701.i	0.688635	−	0.306362i
$723$	−43935.9	+	43935.9i	−0.0840511	+	0.0840511i
$724$	47003.1	+	906901.i	0.0896704	+	1.73015i
$725$	39898.5	−	39898.5i	0.0759068	−	0.0759068i
$726$	59201.6	−	154092.i	0.112321	−	0.292353i
$727$	−212060.			−0.401227			−0.200614	−	0.979670i	$-0.564294\pi$
$727$	−212060.			−0.401227			−0.200614	+	0.979670i	$0.564294\pi$
$728$	669614.	+	1.31701e6i	1.26346	+	2.48500i
$729$			19683.0i			0.0370370i
$730$	−1977.97	+	5148.35i	−0.00371171	+	0.00966100i
$731$	−582526.	−	582526.i	−1.09014	−	1.09014i
$732$	−12798.1	+	14197.2i	−0.0238849	+	0.0264961i
$733$	84332.9	+	84332.9i	0.156960	+	0.156960i	0.781218	−	0.624258i	$-0.214599\pi$
$733$	84332.9	+	84332.9i	0.156960	+	0.156960i	−0.624258	+	0.781218i	$0.714599\pi$
$734$	−101363.	+	45094.7i	−0.188143	+	0.0837015i
$735$		−	74085.5i		−	0.137138i
$736$	153875.	−	88543.7i	0.284062	−	0.163456i
$737$	89309.5			0.164423
$738$	20253.7	+	45526.0i	0.0371871	+	0.0835885i
$739$	−190782.	+	190782.i	−0.349340	+	0.349340i	−0.859864	−	0.510524i	$-0.829452\pi$
$739$	−190782.	+	190782.i	−0.349340	+	0.349340i	0.510524	+	0.859864i	$0.329452\pi$
$740$	−40075.9	−	36126.5i	−0.0731846	−	0.0659724i
$741$	179143.	−	179143.i	0.326259	−	0.326259i
$742$	1.13885e6	+	437542.i	2.06852	+	0.794715i
$743$	−131122.			−0.237518			−0.118759	−	0.992923i	$-0.537892\pi$
$743$	−131122.			−0.237518			−0.118759	+	0.992923i	$0.537892\pi$
$744$	−55256.9	−	108681.i	−0.0998253	−	0.196339i
$745$		−	59578.9i		−	0.107344i
$746$	−481899.	−	185144.i	−0.865922	−	0.332683i
$747$	83801.9	+	83801.9i	0.150180	+	0.150180i
$748$	663891.	−	34408.3i	1.18657	−	0.0614978i
$749$	823021.	+	823021.i	1.46706	+	1.46706i
$750$	−31180.8	−	70087.8i	−0.0554326	−	0.124601i
$751$			704733.i			1.24952i	0.780815	+	0.624762i	$0.214804\pi$
$751$			704733.i			1.24952i	−0.780815	+	0.624762i	$0.785196\pi$
$752$	−1.04358e6	+	108465.i	−1.84539	+	0.191802i
$753$	248450.			0.438177
$754$	−91080.7	+	40520.2i	−0.160208	+	0.0712736i
$755$	63515.3	−	63515.3i	0.111425	−	0.111425i
$756$	−190161.	+	9855.68i	−0.332718	+	0.0172442i
$757$	411751.	−	411751.i	0.718526	−	0.718526i	−0.249777	−	0.968303i	$-0.580357\pi$
$757$	411751.	−	411751.i	0.718526	−	0.718526i	0.968303	+	0.249777i	$0.0803574\pi$
$758$	−1472.67	+	3833.14i	−0.00256312	+	0.00667139i
$759$	−73732.7			−0.127990
$760$	10564.3	−	32417.8i	0.0182899	−	0.0561250i
$761$			82790.4i			0.142959i	0.997442	+	0.0714793i	$0.0227720\pi$
$761$			82790.4i			0.142959i	−0.997442	+	0.0714793i	$0.977228\pi$
$762$	−95094.0	+	247515.i	−0.163773	+	0.426276i
$763$	−865278.	−	865278.i	−1.48630	−	1.48630i
$764$	122389.	+	110328.i	0.209680	+	0.189016i
$765$	28820.0	+	28820.0i	0.0492460	+	0.0492460i
$766$	−296315.	+	131825.i	−0.505006	+	0.224668i
$767$			369119.i			0.627445i
$768$	186129.	−	285167.i	0.315566	−	0.483478i
$769$	107378.			0.181578			0.0907888	−	0.995870i	$-0.471061\pi$
$769$	107378.			0.181578			0.0907888	+	0.995870i	$0.471061\pi$
$770$	−33567.4	−	75452.4i	−0.0566157	−	0.127260i
$771$	439025.	−	439025.i	0.738551	−	0.738551i
$772$	228353.	−	253317.i	0.383152	−	0.425040i
$773$	136137.	−	136137.i	0.227833	−	0.227833i	−0.583954	−	0.811787i	$-0.698495\pi$
$773$	136137.	−	136137.i	0.227833	−	0.227833i	0.811787	+	0.583954i	$0.198495\pi$
$774$	163606.	+	62856.8i	0.273098	+	0.104923i
$775$	−225897.			−0.376103
$776$	997179.	+	324959.i	1.65596	+	0.539642i
$777$			499859.i			0.827953i
$778$	410128.	+	157569.i	0.677579	+	0.260323i
$779$	58447.6	+	58447.6i	0.0963145	+	0.0963145i
$780$	3482.36	+	67190.4i	0.00572379	+	0.110438i
$781$	119421.	+	119421.i	0.195785	+	0.195785i
$782$	143095.	+	321647.i	0.233998	+	0.525977i
$783$		−	12847.7i		−	0.0209557i
$784$	−126892.	−	1.22087e6i	−0.206444	−	1.98627i
$785$	75644.2			0.122754
$786$	185266.	−	82421.8i	0.299883	−	0.133413i
$787$	−39500.6	+	39500.6i	−0.0637756	+	0.0637756i	−0.738275	−	0.674500i	$-0.764359\pi$
$787$	−39500.6	+	39500.6i	−0.0637756	+	0.0637756i	0.674500	+	0.738275i	$0.264359\pi$
$788$	41253.8	+	795972.i	0.0664372	+	1.28187i
$789$	−125271.	+	125271.i	−0.201232	+	0.201232i
$790$	35992.5	−	93682.8i	0.0576711	−	0.150109i
$791$	−1.10767e6			−1.77034
$792$	−126072.	+	64099.2i	−0.200987	+	0.102189i
$793$		−	62568.4i		−	0.0994967i
$794$	44384.9	−	115527.i	0.0704035	−	0.183249i
$795$	39284.5	+	39284.5i	0.0621565	+	0.0621565i
$796$	333063.	−	369474.i	0.525654	−	0.583120i
$797$	−504452.	−	504452.i	−0.794151	−	0.794151i	0.188015	−	0.982166i	$-0.439794\pi$
$797$	−504452.	−	504452.i	−0.794151	−	0.794151i	−0.982166	+	0.188015i	$0.939794\pi$
$798$	−288601.	+	128393.i	−0.453202	+	0.201622i
$799$		−	2.08054e6i		−	3.25898i
$800$	−314683.	−	546870.i	−0.491692	−	0.854484i
$801$	207060.			0.322724
$802$	−285871.	−	642577.i	−0.444448	−	0.999024i
$803$	26835.1	−	26835.1i	0.0416171	−	0.0416171i
$804$	67382.2	+	60741.8i	0.104240	+	0.0939670i
$805$	30923.4	−	30923.4i	0.0477194	−	0.0477194i
$806$	372547.	+	143131.i	0.573471	+	0.220325i
$807$	339512.			0.521324
$808$	−630883.	+	320762.i	−0.966331	+	0.491315i
$809$			647248.i			0.988948i	0.869192	+	0.494474i	$0.164639\pi$
$809$			647248.i			0.988948i	−0.869192	+	0.494474i	$0.835361\pi$
$810$	−8094.29	−	3109.79i	−0.0123370	−	0.00473981i
$811$	149216.	+	149216.i	0.226868	+	0.226868i	0.811383	−	0.584515i	$-0.198715\pi$
$811$	149216.	+	149216.i	0.226868	+	0.226868i	−0.584515	+	0.811383i	$0.698715\pi$
$812$	124124.	−	6433.11i	0.188253	−	0.00975683i
$813$	−332897.	−	332897.i	−0.503650	−	0.503650i
$814$	150911.	+	339216.i	0.227757	+	0.511950i
$815$			13579.6i			0.0204442i
$816$	524294.	+	425569.i	0.787398	+	0.639131i
$817$	290740.			0.435573
$818$	638269.	−	283954.i	0.953887	−	0.424367i
$819$	440744.	−	440744.i	0.657080	−	0.657080i
$820$	−21921.7	+	1136.16i	−0.0326022	+	0.00168971i
$821$	172848.	−	172848.i	0.256435	−	0.256435i	−0.567168	−	0.823602i	$-0.691961\pi$
$821$	172848.	−	172848.i	0.256435	−	0.256435i	0.823602	+	0.567168i	$0.191961\pi$
$822$	147071.	−	382802.i	0.217662	−	0.566541i
$823$	21410.9			0.0316107			0.0158054	−	0.999875i	$-0.494969\pi$
$823$	21410.9			0.0316107			0.0158054	+	0.999875i	$0.494969\pi$
$824$	−326970.	−	106553.i	−0.481564	−	0.156931i
$825$			262045.i			0.385006i
$826$	165051.	−	429603.i	0.241913	−	0.629661i
$827$	−1742.56	−	1742.56i	−0.00254786	−	0.00254786i	0.705832	−	0.708380i	$-0.250573\pi$
$827$	−1742.56	−	1742.56i	−0.00254786	−	0.00254786i	−0.708380	+	0.705832i	$0.750573\pi$
$828$	−55629.8	−	50147.6i	−0.0811422	−	0.0731458i
$829$	193828.	+	193828.i	0.282037	+	0.282037i	0.833921	−	0.551884i	$-0.186091\pi$
$829$	193828.	+	193828.i	0.282037	+	0.282037i	−0.551884	+	0.833921i	$0.686091\pi$
$830$	−47702.2	+	21221.9i	−0.0692441	+	0.0308055i
$831$			1904.62i			0.00275808i
$832$	172469.	+	1.10128e6i	0.249152	+	1.59093i
$833$	2.43400e6			3.50777
$834$	−273377.	−	614492.i	−0.393033	−	0.883455i
$835$	34888.6	−	34888.6i	0.0500392	−	0.0500392i
$836$	−157088.	+	174261.i	−0.224766	+	0.249338i
$837$	−36370.4	+	36370.4i	−0.0519156	+	0.0519156i
$838$	−886110.	−	340440.i	−1.26183	−	0.484788i
$839$	−742266.			−1.05447			−0.527237	−	0.849718i	$-0.676772\pi$
$839$	−742266.			−1.05447			−0.527237	+	0.849718i	$0.676772\pi$
$840$	25991.2	−	79757.4i	0.0368356	−	0.113035i
$841$		−	698895.i		−	0.988143i
$842$	−97631.9	−	37509.8i	−0.137711	−	0.0529078i
$843$	−419996.	−	419996.i	−0.591004	−	0.591004i
$844$	44295.7	+	854663.i	0.0621837	+	1.19980i
$845$	−95675.7	−	95675.7i	−0.133995	−	0.133995i
$846$	179917.	+	404416.i	0.251381	+	0.565051i
$847$		−	673709.i		−	0.939087i
$848$	714664.	+	580092.i	0.993825	+	0.806688i
$849$	−247932.			−0.343968
$850$	1.14313e6	−	508558.i	1.58219	−	0.703887i
$851$	−139024.	+	139024.i	−0.191969	+	0.191969i
$852$	8879.33	+	171322.i	0.0122321	+	0.236012i
$853$	−575553.	+	575553.i	−0.791020	+	0.791020i	−0.981660	−	0.190640i	$-0.938944\pi$
$853$	−575553.	+	575553.i	−0.791020	+	0.791020i	0.190640	+	0.981660i	$0.438944\pi$
$854$	−27977.5	+	72820.9i	−0.0383612	+	0.0998482i
$855$	−14384.1			−0.0196767
$856$	397993.	+	782782.i	0.543160	+	1.06830i
$857$		−	541248.i		−	0.736944i	−0.929639	−	0.368472i	$-0.879881\pi$
$857$		−	541248.i		−	0.736944i	0.929639	−	0.368472i	$-0.120119\pi$
$858$	166035.	−	432163.i	0.225541	−	0.587047i
$859$	971934.	+	971934.i	1.31720	+	1.31720i	0.915986	+	0.401210i	$0.131410\pi$
$859$	971934.	+	971934.i	1.31720	+	1.31720i	0.401210	+	0.915986i	$0.368590\pi$
$860$	−51697.6	+	57349.2i	−0.0698993	+	0.0775409i
$861$	143798.	+	143798.i	0.193976	+	0.193976i
$862$	−754733.	+	335767.i	−1.01573	+	0.451881i
$863$			373292.i			0.501219i	0.968088	+	0.250610i	$0.0806310\pi$
$863$			373292.i			0.501219i	−0.968088	+	0.250610i	$0.919369\pi$
$864$	−138714.	−	37383.3i	−0.185820	−	0.0500783i
$865$	−19794.8			−0.0264557
$866$	−48582.1	−	109202.i	−0.0647799	−	0.145611i
$867$	−639976.	+	639976.i	−0.851384	+	0.851384i
$868$	−369592.	−	333169.i	−0.490550	−	0.442207i
$869$	−488309.	+	488309.i	−0.646630	+	0.646630i
$870$	5283.40	+	2029.86i	0.00698031	+	0.00268180i
$871$	−296959.			−0.391435
$872$	−418428.	−	822974.i	−0.550285	−	1.08231i
$873$		−	442459.i		−	0.580557i
$874$	−115977.	−	44557.9i	−0.151827	−	0.0583313i
$875$	−221379.	−	221379.i	−0.289148	−	0.289148i
$876$	38497.8	−	1995.27i	0.0501681	−	0.00260012i
$877$	−109748.	−	109748.i	−0.142691	−	0.142691i	0.632153	−	0.774844i	$-0.282172\pi$
$877$	−109748.	−	109748.i	−0.142691	−	0.142691i	−0.774844	+	0.632153i	$0.782172\pi$
$878$	134929.	+	303292.i	0.175032	+	0.393435i
$879$			395582.i			0.511987i
$880$	−6441.11	−	61972.1i	−0.00831754	−	0.0800260i
$881$	−309685.			−0.398996			−0.199498	−	0.979898i	$-0.563931\pi$
$881$	−309685.			−0.398996			−0.199498	+	0.979898i	$0.563931\pi$
$882$	−473122.	+	210484.i	−0.608186	+	0.270571i
$883$	−931347.	+	931347.i	−1.19451	+	1.19451i	−0.218724	+	0.975787i	$0.570189\pi$
$883$	−931347.	+	931347.i	−1.19451	+	1.19451i	−0.975787	+	0.218724i	$0.929811\pi$
$884$	−2.20747e6	+	114409.i	−2.82482	+	0.146405i
$885$	14819.1	−	14819.1i	0.0189206	−	0.0189206i
$886$	432521.	−	1.12578e6i	0.550985	−	1.43413i
$887$	1.22870e6			1.56170			0.780849	−	0.624720i	$-0.214787\pi$
$887$	1.22870e6			1.56170			0.780849	+	0.624720i	$0.214787\pi$
$888$	−116850.	+	358570.i	−0.148185	+	0.454724i
$889$			1.08216e6i			1.36927i
$890$	−32714.2	+	85149.7i	−0.0413005	+	0.107499i
$891$	42190.5	+	42190.5i	0.0531446	+	0.0531446i
$892$	33970.4	+	30622.6i	0.0426944	+	0.0384869i
$893$	519201.	+	519201.i	0.651077	+	0.651077i
$894$	−380480.	+	169269.i	−0.476055	+	0.211789i
$895$			110077.i			0.137420i
$896$	291709.	−	1.35886e6i	0.363357	−	1.69261i
$897$	245165.			0.304701
$898$	−283853.	−	638041.i	−0.351999	−	0.791217i
$899$	23740.1	−	23740.1i	0.0293740	−	0.0293740i
$900$	−178224.	+	197707.i	−0.220029	+	0.244083i
$901$	−1.29065e6	+	1.29065e6i	−1.58986	+	1.58986i
$902$	140999.	+	54171.1i	0.173301	+	0.0665816i
$903$	715306.			0.877236
$904$	−794577.	−	258936.i	−0.972298	−	0.316851i
$905$			168776.i			0.206069i
$906$	−586072.	−	225166.i	−0.713994	−	0.274313i
$907$	−33259.1	−	33259.1i	−0.0404292	−	0.0404292i	0.686603	−	0.727032i	$-0.259101\pi$
$907$	−33259.1	−	33259.1i	−0.0404292	−	0.0404292i	−0.727032	+	0.686603i	$0.759101\pi$
$908$	−82787.5	−	1.59734e6i	−0.100414	−	1.93743i
$909$	211127.	+	211127.i	0.255515	+	0.255515i
$910$	111613.	+	250883.i	0.134783	+	0.302962i
$911$			224558.i			0.270577i	0.990806	+	0.135289i	$0.0431962\pi$
$911$			224558.i			0.270577i	−0.990806	+	0.135289i	$0.956804\pi$
$912$	−237040.	+	24636.8i	−0.284991	+	0.0296207i
$913$	359258.			0.430988
$914$	−475081.	+	211355.i	−0.568690	+	0.253000i
$915$	−2511.94	+	2511.94i	−0.00300032	+	0.00300032i
$916$	−462.173	−	8917.40i	−0.000550825	−	0.0106279i
$917$	585182.	−	585182.i	0.695909	−	0.695909i
$918$	102169.	−	265930.i	0.121237	−	0.315560i
$919$	596247.			0.705984			0.352992	−	0.935626i	$-0.385164\pi$
$919$	596247.			0.705984			0.352992	+	0.935626i	$0.385164\pi$
$920$	29411.5	−	14953.8i	0.0347489	−	0.0176675i
$921$			732386.i			0.863417i
$922$	−325453.	+	847101.i	−0.382848	+	0.996491i
$923$	−397082.	−	397082.i	−0.466097	−	0.466097i
$924$	−386483.	+	428734.i	−0.452675	+	0.502162i
$925$	494089.	+	494089.i	0.577460	+	0.577460i
$926$	−869333.	+	386751.i	−1.01383	+	0.451034i
$927$			145080.i			0.168830i
$928$	90543.0	+	24401.2i	0.105138	+	0.0283345i
$929$	−153462.			−0.177816			−0.0889079	−	0.996040i	$-0.528338\pi$
$929$	−153462.			−0.177816			−0.0889079	+	0.996040i	$0.528338\pi$
$930$	−9210.41	−	20703.0i	−0.0106491	−	0.0239369i
$931$	−607409.	+	607409.i	−0.700780	+	0.700780i
$932$	258691.	+	233197.i	0.297817	+	0.268468i
$933$	298381.	−	298381.i	0.342774	−	0.342774i
$934$	817543.	+	314097.i	0.937167	+	0.360055i
$935$	123551.			0.141327
$936$	419195.	−	213133.i	0.478481	−	0.243276i
$937$		−	1.23354e6i		−	1.40499i	−0.711689	−	0.702494i	$-0.752070\pi$
$937$		−	1.23354e6i		−	1.40499i	0.711689	−	0.702494i	$-0.247930\pi$
$938$	345618.	+	132785.i	0.392818	+	0.150919i
$939$	−58984.0	−	58984.0i	−0.0668964	−	0.0668964i
$940$	−194735.	+	10092.7i	−0.220388	+	0.0114223i
$941$	−537413.	−	537413.i	−0.606917	−	0.606917i	0.335222	−	0.942139i	$-0.391189\pi$
$941$	−537413.	−	537413.i	−0.606917	−	0.606917i	−0.942139	+	0.335222i	$0.891189\pi$
$942$	−214912.	−	483077.i	−0.242192	−	0.544395i
$943$			79988.2i			0.0899503i
$944$	218825.	−	269589.i	0.245558	−	0.302523i
$945$	−35389.2			−0.0396285
$946$	485423.	−	215956.i	0.542423	−	0.241314i
$947$	−621957.	+	621957.i	−0.693522	+	0.693522i	−0.963005	−	0.269483i	$-0.913147\pi$
$947$	−621957.	+	621957.i	−0.693522	+	0.693522i	0.269483	+	0.963005i	$0.413147\pi$
$948$	−700532.	+	36307.3i	−0.779491	+	0.0403996i
$949$	−89228.1	+	89228.1i	−0.0990762	+	0.0990762i
$950$	−158358.	+	412181.i	−0.175466	+	0.456710i
$951$	−42465.3			−0.0469540
$952$	2.62035e6	+	853914.i	2.89124	+	0.942194i
$953$			609536.i			0.671140i	0.942015	+	0.335570i	$0.108929\pi$
$953$			609536.i			0.671140i	−0.942015	+	0.335570i	$0.891071\pi$
$954$	139266.	−	362488.i	0.153020	−	0.398287i
$955$	21654.5	+	21654.5i	0.0237434	+	0.0237434i
$956$	−973821.	−	877852.i	−1.06552	−	0.960519i
$957$	−27539.0	−	27539.0i	−0.0300694	−	0.0300694i
$958$	276955.	−	123212.i	0.301772	−	0.134253i
$959$		−	1.67366e6i		−	1.81982i
$960$	37289.2	−	51137.5i	0.0404614	−	0.0554877i
$961$	789110.			0.854458
$962$	−501787.	−	1.12791e6i	−0.542213	−	1.21878i
$963$	261961.	−	261961.i	0.282478	−	0.282478i
$964$	−128104.	+	142109.i	−0.137850	+	0.152921i
$965$	44819.7	−	44819.7i	0.0481299	−	0.0481299i
$966$	−285338.	−	109626.i	−0.305777	−	0.117478i
$967$	−1.17833e6			−1.26013			−0.630063	−	0.776544i	$-0.716971\pi$
$967$	−1.17833e6			−1.26013			−0.630063	+	0.776544i	$0.716971\pi$
$968$	157491.	−	483280.i	0.168075	−	0.515761i
$969$		−	472576.i		−	0.503297i
$970$	181954.	+	69905.8i	0.193383	+	0.0742967i
$971$	1.17466e6	+	1.17466e6i	1.24588	+	1.24588i	0.957525	+	0.288351i	$0.0931070\pi$
$971$	1.17466e6	+	1.17466e6i	1.24588	+	1.24588i	0.288351	+	0.957525i	$0.406893\pi$
$972$	3136.99	+	60526.7i	0.00332032	+	0.0640640i
$973$	−1.94093e6	−	1.94093e6i	−2.05015	−	2.05015i
$974$	322942.	+	725903.i	0.340413	+	0.765175i
$975$		−	871312.i		−	0.916568i
$976$	−37092.5	+	45697.3i	−0.0389391	+	0.0479723i
$977$	1.03389e6			1.08314			0.541568	−	0.840657i	$-0.317831\pi$
$977$	1.03389e6			1.08314			0.541568	+	0.840657i	$0.317831\pi$
$978$	86721.4	−	38580.8i	0.0906669	−	0.0403361i
$979$	443832.	−	443832.i	0.463077	−	0.463077i
$980$	−11807.4	−	227819.i	−0.0122943	−	0.237212i
$981$	−275412.	+	275412.i	−0.286183	+	0.286183i
$982$	−324907.	+	845681.i	−0.336927	+	0.876968i
$983$	782606.			0.809909			0.404954	−	0.914337i	$-0.367287\pi$
$983$	782606.			0.809909			0.404954	+	0.914337i	$0.367287\pi$
$984$	69537.4	+	136768.i	0.0718172	+	0.141252i
$985$			148132.i			0.152678i
$986$	−66688.9	+	173581.i	−0.0685961	+	0.178545i
$987$	1.27739e6	+	1.27739e6i	1.31126	+	1.31126i
$988$	522326.	−	579428.i	0.535091	−	0.593589i
$989$	198946.	+	198946.i	0.203396	+	0.203396i
$990$	−24015.9	+	10684.3i	−0.0245035	+	0.0109012i
$991$			831804.i			0.846981i	0.905900	+	0.423491i	$0.139195\pi$
$991$			831804.i			0.846981i	−0.905900	+	0.423491i	$0.860805\pi$
$992$	−187240.	−	325395.i	−0.190272	−	0.330664i
$993$	−587669.			−0.595984
$994$	284592.	+	639703.i	0.288039	+	0.647449i
$995$	65371.7	−	65371.7i	0.0660303	−	0.0660303i
$996$	271053.	+	244341.i	0.273234	+	0.246308i
$997$	−481944.	+	481944.i	−0.484849	+	0.484849i	−0.906676	−	0.421827i	$-0.861389\pi$
$997$	−481944.	+	481944.i	−0.484849	+	0.484849i	0.421827	+	0.906676i	$0.361389\pi$
$998$	896907.	+	344588.i	0.900505	+	0.345970i
$999$	159101.			0.159420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.l.a.19.6	✓	32
3.2	odd	2		144.5.m.c.19.11		32
4.3	odd	2		192.5.l.a.175.11		32
8.3	odd	2		384.5.l.a.223.6		32
8.5	even	2		384.5.l.b.223.11		32
12.11	even	2		576.5.m.b.559.9		32
16.3	odd	4		384.5.l.b.31.11		32
16.5	even	4		192.5.l.a.79.11		32
16.11	odd	4	inner	48.5.l.a.43.6	yes	32
16.13	even	4		384.5.l.a.31.6		32
48.5	odd	4		576.5.m.b.271.9		32
48.11	even	4		144.5.m.c.91.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.6	✓	32	1.1	even	1	trivial
48.5.l.a.43.6	yes	32	16.11	odd	4	inner
144.5.m.c.19.11		32	3.2	odd	2
144.5.m.c.91.11		32	48.11	even	4
192.5.l.a.79.11		32	16.5	even	4
192.5.l.a.175.11		32	4.3	odd	2
384.5.l.a.31.6		32	16.13	even	4
384.5.l.a.223.6		32	8.3	odd	2
384.5.l.b.31.11		32	16.3	odd	4
384.5.l.b.223.11		32	8.5	even	2
576.5.m.b.271.9		32	48.5	odd	4
576.5.m.b.559.9		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)

\(f(q)\)	\(=\)	\(q+(-1.62589 - 3.65465i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-10.7130 + 11.8841i) q^{4} +(-2.10268 + 2.10268i) q^{5} +(19.4020 + 7.45415i) q^{6} +84.8276 q^{7} +(60.8504 + 19.8299i) q^{8} -27.0000i q^{9} +O(q^{10})\)	\(q+(-1.62589 - 3.65465i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-10.7130 + 11.8841i) q^{4} +(-2.10268 + 2.10268i) q^{5} +(19.4020 + 7.45415i) q^{6} +84.8276 q^{7} +(60.8504 + 19.8299i) q^{8} -27.0000i q^{9} +(11.1033 + 4.26583i) q^{10} +(-57.8744 - 57.8744i) q^{11} +(-4.30314 - 83.0270i) q^{12} +(192.435 + 192.435i) q^{13} +(-137.920 - 310.015i) q^{14} -15.4515i q^{15} +(-26.4649 - 254.628i) q^{16} +507.642 q^{17} +(-98.6756 + 43.8990i) q^{18} +(-126.683 + 126.683i) q^{19} +(-2.46259 - 47.5144i) q^{20} +(-311.677 + 311.677i) q^{21} +(-117.413 + 305.608i) q^{22} -173.371 q^{23} +(-296.438 + 150.719i) q^{24} +616.157i q^{25} +(390.406 - 1016.16i) q^{26} +(99.2043 + 99.2043i) q^{27} +(-908.755 + 1008.10i) q^{28} +(-64.7538 - 64.7538i) q^{29} +(-56.4697 + 25.1224i) q^{30} +366.621i q^{31} +(-887.549 + 510.718i) q^{32} +425.288 q^{33} +(-825.370 - 1855.25i) q^{34} +(-178.365 + 178.365i) q^{35} +(320.871 + 289.250i) q^{36} +(801.887 - 801.887i) q^{37} +(668.953 + 257.009i) q^{38} -1414.11 q^{39} +(-169.645 + 86.2531i) q^{40} -461.370i q^{41} +(1645.82 + 632.317i) q^{42} +(-1147.51 - 1147.51i) q^{43} +(1307.79 - 67.7806i) q^{44} +(56.7723 + 56.7723i) q^{45} +(281.882 + 633.611i) q^{46} -4098.44i q^{47} +(1032.80 + 838.326i) q^{48} +4794.73 q^{49} +(2251.84 - 1001.80i) q^{50} +(-1865.20 + 1865.20i) q^{51} +(-4348.48 + 225.374i) q^{52} +(-2542.44 + 2542.44i) q^{53} +(201.262 - 523.853i) q^{54} +243.383 q^{55} +(5161.80 + 1682.12i) q^{56} -930.924i q^{57} +(-131.370 + 341.935i) q^{58} +(959.072 + 959.072i) q^{59} +(183.627 + 165.531i) q^{60} +(-162.570 - 162.570i) q^{61} +(1339.87 - 596.086i) q^{62} -2290.35i q^{63} +(3309.55 + 2413.31i) q^{64} -809.260 q^{65} +(-691.472 - 1554.28i) q^{66} +(-771.580 + 771.580i) q^{67} +(-5438.35 + 6032.88i) q^{68} +(637.006 - 637.006i) q^{69} +(941.865 + 361.860i) q^{70} -2063.45 q^{71} +(535.406 - 1642.96i) q^{72} +463.678i q^{73} +(-4234.40 - 1626.84i) q^{74} +(-2263.91 - 2263.91i) q^{75} +(-148.366 - 2862.66i) q^{76} +(-4909.35 - 4909.35i) q^{77} +(2299.18 + 5168.07i) q^{78} -8437.39i q^{79} +(591.049 + 479.754i) q^{80} -729.000 q^{81} +(-1686.15 + 750.138i) q^{82} +(-3103.77 + 3103.77i) q^{83} +(-365.025 - 7042.98i) q^{84} +(-1067.41 + 1067.41i) q^{85} +(-2328.03 + 6059.49i) q^{86} +475.841 q^{87} +(-2374.04 - 4669.33i) q^{88} +7668.88i q^{89} +(115.177 - 299.789i) q^{90} +(16323.8 + 16323.8i) q^{91} +(1857.32 - 2060.36i) q^{92} +(-1347.05 - 1347.05i) q^{93} +(-14978.4 + 6663.61i) q^{94} -532.746i q^{95} +(1384.57 - 5137.56i) q^{96} +16387.4 q^{97} +(-7795.70 - 17523.1i) q^{98} +(-1562.61 + 1562.61i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more