LMFDB - Embedded newform 48.6.j.a.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(13,48)]

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([0, 3, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.j (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:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	48.13
Dual form			48.6.j.a.37.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76330 + 5.37502i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-25.7816 - 18.9555i) q^{4} +(47.6164 - 47.6164i) q^{5} +(-45.4279 + 22.9848i) q^{6} -212.678i q^{7} +(147.347 - 105.152i) q^{8} +81.0000i q^{9} +O(q^{10})$	\(q+(-1.76330 + 5.37502i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-25.7816 - 18.9555i) q^{4} +(47.6164 - 47.6164i) q^{5} +(-45.4279 + 22.9848i) q^{6} -212.678i q^{7} +(147.347 - 105.152i) q^{8} +81.0000i q^{9} +(171.977 + 339.901i) q^{10} +(62.9116 - 62.9116i) q^{11} +(-43.4410 - 284.705i) q^{12} +(-312.334 - 312.334i) q^{13} +(1143.15 + 375.014i) q^{14} +606.058 q^{15} +(305.379 + 977.404i) q^{16} -109.808 q^{17} +(-435.376 - 142.827i) q^{18} +(2149.92 + 2149.92i) q^{19} +(-2130.22 + 325.034i) q^{20} +(1353.47 - 1353.47i) q^{21} +(227.219 + 449.082i) q^{22} -4820.95i q^{23} +(1606.89 + 268.523i) q^{24} -1409.65i q^{25} +(2229.54 - 1128.06i) q^{26} +(-515.481 + 515.481i) q^{27} +(-4031.41 + 5483.17i) q^{28} +(-833.978 - 833.978i) q^{29} +(-1068.66 + 3257.57i) q^{30} -1512.55 q^{31} +(-5792.04 - 82.0337i) q^{32} +800.733 q^{33} +(193.624 - 590.219i) q^{34} +(-10126.9 - 10126.9i) q^{35} +(1535.39 - 2088.31i) q^{36} +(-4035.32 + 4035.32i) q^{37} +(-15346.8 + 7764.91i) q^{38} -3975.36i q^{39} +(2009.14 - 12023.1i) q^{40} +4212.68i q^{41} +(4888.36 + 9661.51i) q^{42} +(8423.34 - 8423.34i) q^{43} +(-2814.48 + 429.440i) q^{44} +(3856.93 + 3856.93i) q^{45} +(25912.7 + 8500.75i) q^{46} +22982.5 q^{47} +(-4276.74 + 8163.59i) q^{48} -28424.8 q^{49} +(7576.86 + 2485.62i) q^{50} +(-698.813 - 698.813i) q^{51} +(2132.02 + 13972.9i) q^{52} +(-5885.59 + 5885.59i) q^{53} +(-1861.77 - 3679.66i) q^{54} -5991.25i q^{55} +(-22363.5 - 31337.3i) q^{56} +27364.0i q^{57} +(5953.20 - 3012.10i) q^{58} +(16461.1 - 16461.1i) q^{59} +(-15625.1 - 11488.1i) q^{60} +(27924.4 + 27924.4i) q^{61} +(2667.07 - 8129.97i) q^{62} +17226.9 q^{63} +(10654.0 - 30987.6i) q^{64} -29744.5 q^{65} +(-1411.93 + 4303.95i) q^{66} +(-1653.60 - 1653.60i) q^{67} +(2831.02 + 2081.46i) q^{68} +(30680.3 - 30680.3i) q^{69} +(72289.3 - 36575.7i) q^{70} +48790.2i q^{71} +(8517.33 + 11935.1i) q^{72} +76908.0i q^{73} +(-14574.4 - 28805.4i) q^{74} +(8970.93 - 8970.93i) q^{75} +(-14675.6 - 96181.1i) q^{76} +(-13379.9 - 13379.9i) q^{77} +(21367.6 + 7009.74i) q^{78} -66434.8 q^{79} +(61081.6 + 31999.4i) q^{80} -6561.00 q^{81} +(-22643.2 - 7428.21i) q^{82} +(-46407.9 - 46407.9i) q^{83} +(-60550.4 + 9238.93i) q^{84} +(-5228.66 + 5228.66i) q^{85} +(30422.7 + 60128.4i) q^{86} -10614.8i q^{87} +(2654.51 - 15885.1i) q^{88} +33555.5i q^{89} +(-27532.0 + 13930.1i) q^{90} +(-66426.5 + 66426.5i) q^{91} +(-91383.4 + 124292. i) q^{92} +(-9625.80 - 9625.80i) q^{93} +(-40525.0 + 123531. i) q^{94} +204743. q^{95} +(-36338.2 - 37382.4i) q^{96} -50039.3 q^{97} +(50121.3 - 152784. i) q^{98} +(5095.84 + 5095.84i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) $ 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * 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 $

$2$	−1.76330	+	5.37502i	−0.311710	+	0.950177i
$2$	−1.76330	+	5.37502i	−0.311710	+	0.950177i
$3$	6.36396	+	6.36396i	0.408248	+	0.408248i
$3$	6.36396	+	6.36396i	0.408248	+	0.408248i
$4$	−25.7816	−	18.9555i	−0.805674	−	0.592359i
$5$	47.6164	−	47.6164i	0.851788	−	0.851788i	−0.138565	−	0.990353i	$-0.544249\pi$
$5$	47.6164	−	47.6164i	0.851788	−	0.851788i	0.990353	+	0.138565i	$0.0442490\pi$
$6$	−45.4279	+	22.9848i	−0.515163	+	0.260653i
$7$		−	212.678i		−	1.64050i	−0.572003	−	0.820251i	$-0.693834\pi$
$7$		−	212.678i		−	1.64050i	0.572003	−	0.820251i	$-0.306166\pi$
$8$	147.347	−	105.152i	0.813982	−	0.580890i
$9$			81.0000i			0.333333i
$10$	171.977	+	339.901i	0.543839	+	1.07486i
$11$	62.9116	−	62.9116i	0.156765	−	0.156765i	−0.624367	−	0.781131i	$-0.714643\pi$
$11$	62.9116	−	62.9116i	0.156765	−	0.156765i	0.781131	+	0.624367i	$0.214643\pi$
$12$	−43.4410	−	284.705i	−0.0870857	−	0.570745i
$13$	−312.334	−	312.334i	−0.512579	−	0.512579i	0.402737	−	0.915316i	$-0.368059\pi$
$13$	−312.334	−	312.334i	−0.512579	−	0.512579i	−0.915316	+	0.402737i	$0.868059\pi$
$14$	1143.15	+	375.014i	1.55877	+	0.511360i
$15$	606.058			0.695482
$16$	305.379	+	977.404i	0.298222	+	0.954496i
$17$	−109.808			−0.0921534			−0.0460767	−	0.998938i	$-0.514672\pi$
$17$	−109.808			−0.0921534			−0.0460767	+	0.998938i	$0.514672\pi$
$18$	−435.376	−	142.827i	−0.316726	−	0.103903i
$19$	2149.92	+	2149.92i	1.36628	+	1.36628i	0.865683	+	0.500593i	$0.166885\pi$
$19$	2149.92	+	2149.92i	1.36628	+	1.36628i	0.500593	+	0.865683i	$0.333115\pi$
$20$	−2130.22	+	325.034i	−1.19083	+	0.181700i
$21$	1353.47	−	1353.47i	0.669732	−	0.669732i
$22$	227.219	+	449.082i	0.100089	+	0.197820i
$23$		−	4820.95i		−	1.90026i	−0.311856	−	0.950129i	$-0.600951\pi$
$23$		−	4820.95i		−	1.90026i	0.311856	−	0.950129i	$-0.399049\pi$
$24$	1606.89	+	268.523i	0.569454	+	0.0951597i
$25$		−	1409.65i		−	0.451086i
$26$	2229.54	−	1128.06i	0.646817	−	0.327265i
$27$	−515.481	+	515.481i	−0.136083	+	0.136083i
$28$	−4031.41	+	5483.17i	−0.971766	+	1.32171i
$29$	−833.978	−	833.978i	−0.184145	−	0.184145i	0.609014	−	0.793159i	$-0.291565\pi$
$29$	−833.978	−	833.978i	−0.184145	−	0.184145i	−0.793159	+	0.609014i	$0.791565\pi$
$30$	−1068.66	+	3257.57i	−0.216788	+	0.660831i
$31$	−1512.55			−0.282687			−0.141343	−	0.989961i	$-0.545142\pi$
$31$	−1512.55			−0.282687			−0.141343	+	0.989961i	$0.545142\pi$
$32$	−5792.04	−	82.0337i	−0.999900	−	0.0141618i
$33$	800.733			0.127998
$34$	193.624	−	590.219i	0.0287251	−	0.0875621i
$35$	−10126.9	−	10126.9i	−1.39736	−	1.39736i
$36$	1535.39	−	2088.31i	0.197453	−	0.268558i
$37$	−4035.32	+	4035.32i	−0.484589	+	0.484589i	−0.906594	−	0.422005i	$-0.861327\pi$
$37$	−4035.32	+	4035.32i	−0.484589	+	0.484589i	0.422005	+	0.906594i	$0.361327\pi$
$38$	−15346.8	+	7764.91i	−1.72409	+	0.872323i
$39$		−	3975.36i		−	0.418519i
$40$	2009.14	−	12023.1i	0.198546	−	1.18814i
$41$			4212.68i			0.391381i	0.980666	+	0.195690i	$0.0626947\pi$
$41$			4212.68i			0.391381i	−0.980666	+	0.195690i	$0.937305\pi$
$42$	4888.36	+	9661.51i	0.427603	+	0.845127i
$43$	8423.34	−	8423.34i	0.694725	−	0.694725i	−0.268543	−	0.963268i	$-0.586542\pi$
$43$	8423.34	−	8423.34i	0.694725	−	0.694725i	0.963268	+	0.268543i	$0.0865420\pi$
$44$	−2814.48	+	429.440i	−0.219162	+	0.0334404i
$45$	3856.93	+	3856.93i	0.283929	+	0.283929i
$46$	25912.7	+	8500.75i	1.80558	+	0.592329i
$47$	22982.5			1.51758			0.758792	−	0.651333i	$-0.225790\pi$
$47$	22982.5			1.51758			0.758792	+	0.651333i	$0.225790\pi$
$48$	−4276.74	+	8163.59i	−0.267923	+	0.511420i
$49$	−28424.8			−1.69125
$50$	7576.86	+	2485.62i	0.428612	+	0.140608i
$51$	−698.813	−	698.813i	−0.0376215	−	0.0376215i
$52$	2132.02	+	13972.9i	0.109341	+	0.716603i
$53$	−5885.59	+	5885.59i	−0.287806	+	0.287806i	−0.836212	−	0.548406i	$-0.815235\pi$
$53$	−5885.59	+	5885.59i	−0.287806	+	0.287806i	0.548406	+	0.836212i	$0.315235\pi$
$54$	−1861.77	−	3679.66i	−0.0868845	−	0.171721i
$55$		−	5991.25i		−	0.267061i
$56$	−22363.5	−	31337.3i	−0.952951	−	1.33534i
$57$			27364.0i			1.11556i
$58$	5953.20	−	3012.10i	0.232370	−	0.117571i
$59$	16461.1	−	16461.1i	0.615643	−	0.615643i	−0.328767	−	0.944411i	$-0.606633\pi$
$59$	16461.1	−	16461.1i	0.615643	−	0.615643i	0.944411	+	0.328767i	$0.106633\pi$
$60$	−15625.1	−	11488.1i	−0.560332	−	0.411975i
$61$	27924.4	+	27924.4i	0.960857	+	0.960857i	0.999262	−	0.0384048i	$-0.0122276\pi$
$61$	27924.4	+	27924.4i	0.960857	+	0.960857i	−0.0384048	+	0.999262i	$0.512228\pi$
$62$	2667.07	−	8129.97i	0.0881161	−	0.268602i
$63$	17226.9			0.546834
$64$	10654.0	−	30987.6i	0.325134	−	0.945668i
$65$	−29744.5			−0.873218
$66$	−1411.93	+	4303.95i	−0.0398982	+	0.121621i
$67$	−1653.60	−	1653.60i	−0.0450033	−	0.0450033i	0.684247	−	0.729250i	$-0.260131\pi$
$67$	−1653.60	−	1653.60i	−0.0450033	−	0.0450033i	−0.729250	+	0.684247i	$0.760131\pi$
$68$	2831.02	+	2081.46i	0.0742456	+	0.0545879i
$69$	30680.3	−	30680.3i	0.775777	−	0.775777i
$70$	72289.3	−	36575.7i	1.76331	−	0.892170i
$71$			48790.2i			1.14865i	0.818628	+	0.574323i	$0.194735\pi$
$71$			48790.2i			1.14865i	−0.818628	+	0.574323i	$0.805265\pi$
$72$	8517.33	+	11935.1i	0.193630	+	0.271327i
$73$			76908.0i			1.68914i	0.535449	+	0.844568i	$0.320142\pi$
$73$			76908.0i			1.68914i	−0.535449	+	0.844568i	$0.679858\pi$
$74$	−14574.4	−	28805.4i	−0.309395	−	0.611497i
$75$	8970.93	−	8970.93i	0.184155	−	0.184155i
$76$	−14675.6	−	96181.1i	−0.291448	−	1.91010i
$77$	−13379.9	−	13379.9i	−0.257173	−	0.257173i
$78$	21367.6	+	7009.74i	0.397667	+	0.130456i
$79$	−66434.8			−1.19764			−0.598822	−	0.800882i	$-0.704364\pi$
$79$	−66434.8			−1.19764			−0.598822	+	0.800882i	$0.704364\pi$
$80$	61081.6	+	31999.4i	1.06705	+	0.559007i
$81$	−6561.00			−0.111111
$82$	−22643.2	−	7428.21i	−0.371881	−	0.121997i
$83$	−46407.9	−	46407.9i	−0.739429	−	0.739429i	0.233039	−	0.972468i	$-0.425133\pi$
$83$	−46407.9	−	46407.9i	−0.739429	−	0.739429i	−0.972468	+	0.233039i	$0.925133\pi$
$84$	−60550.4	+	9238.93i	−0.936308	+	0.142864i
$85$	−5228.66	+	5228.66i	−0.0784952	+	0.0784952i
$86$	30422.7	+	60128.4i	0.443560	+	0.876665i
$87$		−	10614.8i		−	0.150354i
$88$	2654.51	−	15885.1i	0.0365407	−	0.218667i
$89$			33555.5i			0.449044i	0.974469	+	0.224522i	$0.0720820\pi$
$89$			33555.5i			0.449044i	−0.974469	+	0.224522i	$0.927918\pi$
$90$	−27532.0	+	13930.1i	−0.358287	+	0.181280i
$91$	−66426.5	+	66426.5i	−0.840887	+	0.840887i
$92$	−91383.4	+	124292.i	−1.12563	+	1.53099i
$93$	−9625.80	−	9625.80i	−0.115406	−	0.115406i
$94$	−40525.0	+	123531.i	−0.473045	+	1.44197i
$95$	204743.			2.32756
$96$	−36338.2	−	37382.4i	−0.402426	−	0.413989i
$97$	−50039.3			−0.539985			−0.269992	−	0.962862i	$-0.587021\pi$
$97$	−50039.3			−0.539985			−0.269992	+	0.962862i	$0.587021\pi$
$98$	50121.3	−	152784.i	0.527178	−	1.60699i
$99$	5095.84	+	5095.84i	0.0522550	+	0.0522550i
$100$	−26720.5	+	36342.9i	−0.267205	+	0.363429i
$101$	−28876.5	+	28876.5i	−0.281670	+	0.281670i	−0.833775	−	0.552105i	$-0.813825\pi$
$101$	−28876.5	+	28876.5i	−0.281670	+	0.281670i	0.552105	+	0.833775i	$0.313825\pi$
$102$	4988.35	−	2523.92i	0.0474740	−	0.0240201i
$103$			136331.i			1.26619i	0.774072	+	0.633097i	$0.218217\pi$
$103$			136331.i			1.26619i	−0.774072	+	0.633097i	$0.781783\pi$
$104$	−78864.0	−	13178.7i	−0.714982	−	0.119478i
$105$		−	128895.i		−	1.14094i
$106$	−21257.1	−	42013.2i	−0.183755	−	0.363179i
$107$	103242.	−	103242.i	0.871763	−	0.871763i	−0.120901	−	0.992665i	$-0.538578\pi$
$107$	103242.	−	103242.i	0.871763	−	0.871763i	0.992665	+	0.120901i	$0.0385784\pi$
$108$	23061.1	−	3518.72i	0.190248	−	0.0290286i
$109$	−136270.	−	136270.i	−1.09859	−	1.09859i	−0.994576	−	0.104011i	$-0.966832\pi$
$109$	−136270.	−	136270.i	−1.09859	−	1.09859i	−0.104011	−	0.994576i	$-0.533168\pi$
$110$	32203.0	+	10564.3i	0.253755	+	0.0832455i
$111$	−51361.2			−0.395665
$112$	207872.	−	64947.4i	1.56585	−	0.489234i
$113$	59761.4			0.440276			0.220138	−	0.975469i	$-0.429349\pi$
$113$	59761.4			0.440276			0.220138	+	0.975469i	$0.429349\pi$
$114$	−147082.	−	48250.9i	−1.05998	−	0.347731i
$115$	−229556.	−	229556.i	−1.61862	−	1.61862i
$116$	5692.82	+	37309.7i	0.0392810	+	0.257441i
$117$	25299.1	−	25299.1i	0.170860	−	0.170860i
$118$	59452.9	+	117505.i	0.393069	+	0.776872i
$119$			23353.7i			0.151178i
$120$	89300.5	−	63728.4i	0.566110	−	0.403998i
$121$			153135.i			0.950850i
$122$	−199333.	+	100855.i	−1.21249	+	0.613477i
$123$	−26809.4	+	26809.4i	−0.159780	+	0.159780i
$124$	38995.9	+	28671.1i	0.227753	+	0.167452i
$125$	81679.0	+	81679.0i	0.467558	+	0.467558i
$126$	−30376.1	+	92594.8i	−0.170453	+	0.519589i
$127$	111557.			0.613747			0.306873	−	0.951750i	$-0.400717\pi$
$127$	111557.			0.613747			0.306873	+	0.951750i	$0.400717\pi$
$128$	147773.	+	111906.i	0.797205	+	0.603709i
$129$	107212.			0.567241
$130$	52448.3	−	159877.i	0.272190	−	0.829712i
$131$	50385.1	+	50385.1i	0.256521	+	0.256521i	0.823638	−	0.567116i	$-0.191941\pi$
$131$	50385.1	+	50385.1i	0.256521	+	0.256521i	−0.567116	+	0.823638i	$0.691941\pi$
$132$	−20644.2	−	15178.3i	−0.103125	−	0.0758207i
$133$	457240.	−	457240.i	2.24138	−	2.24138i
$134$	11803.9	−	5972.35i	0.0567890	−	0.0287331i
$135$			49090.7i			0.231827i
$136$	−16179.8	+	11546.6i	−0.0750113	+	0.0535310i
$137$		−	82044.4i		−	0.373463i	−0.982411	−	0.186731i	$-0.940211\pi$
$137$		−	82044.4i		−	0.373463i	0.982411	−	0.186731i	$-0.0597894\pi$
$138$	110809.	+	219006.i	0.495309	+	0.978943i
$139$	−44101.5	+	44101.5i	−0.193605	+	0.193605i	−0.797252	−	0.603647i	$-0.793714\pi$
$139$	−44101.5	+	44101.5i	−0.193605	+	0.193605i	0.603647	+	0.797252i	$0.293714\pi$
$140$	69127.5	+	453050.i	0.298079	+	1.95356i
$141$	146260.	+	146260.i	0.619551	+	0.619551i
$142$	−262248.	−	86031.5i	−1.09142	−	0.358044i
$143$	−39298.8			−0.160709
$144$	−79169.8	+	24735.7i	−0.318165	+	0.0994074i
$145$	−79422.1			−0.313705
$146$	−413382.	−	135612.i	−1.60498	−	0.526520i
$147$	−180894.	−	180894.i	−0.690449	−	0.690449i
$148$	180528.	−	27545.5i	0.677472	−	0.103370i
$149$	314027.	−	314027.i	1.15878	−	1.15878i	0.174041	−	0.984738i	$-0.444317\pi$
$149$	314027.	−	314027.i	1.15878	−	1.15878i	0.984738	−	0.174041i	$-0.0556826\pi$
$150$	32400.5	+	64037.3i	0.117577	+	0.232383i
$151$			232485.i			0.829758i	0.909877	+	0.414879i	$0.136176\pi$
$151$			232485.i			0.829758i	−0.909877	+	0.414879i	$0.863824\pi$
$152$	542852.	+	90714.4i	1.90578	+	0.318469i
$153$		−	8894.44i		−	0.0307178i
$154$	95509.8	−	48324.4i	0.324523	−	0.164197i
$155$	−72022.1	+	72022.1i	−0.240789	+	0.240789i
$156$	−75354.9	+	102491.i	−0.247914	+	0.337190i
$157$	97621.3	+	97621.3i	0.316079	+	0.316079i	0.847259	−	0.531180i	$-0.178251\pi$
$157$	97621.3	+	97621.3i	0.316079	+	0.316079i	−0.531180	+	0.847259i	$0.678251\pi$
$158$	117144.	−	357088.i	0.373317	−	1.13798i
$159$	−74911.3			−0.234993
$160$	−279702.	+	271890.i	−0.863766	+	0.839640i
$161$	−1.02531e6			−3.11738
$162$	11569.0	−	35265.5i	0.0346344	−	0.105575i
$163$	219834.	+	219834.i	0.648076	+	0.648076i	0.952528	−	0.304452i	$-0.0984733\pi$
$163$	219834.	+	219834.i	0.648076	+	0.648076i	−0.304452	+	0.952528i	$0.598473\pi$
$164$	79853.5	−	108610.i	0.231838	−	0.315325i
$165$	38128.1	−	38128.1i	0.109027	−	0.109027i
$166$	331274.	−	167612.i	0.933076	−	0.472102i
$167$			158209.i			0.438976i	0.975615	+	0.219488i	$0.0704387\pi$
$167$			158209.i			0.438976i	−0.975615	+	0.219488i	$0.929561\pi$
$168$	57108.8	−	341750.i	0.156110	−	0.934191i
$169$		−	176188.i		−	0.474525i
$170$	−18884.5	−	37323.8i	−0.0501167	−	0.0990521i
$171$	−174144.	+	174144.i	−0.455425	+	0.455425i
$172$	−376835.	+	57498.5i	−0.971249	+	0.148196i
$173$	−312339.	−	312339.i	−0.793433	−	0.793433i	0.188617	−	0.982051i	$-0.439599\pi$
$173$	−312339.	−	312339.i	−0.793433	−	0.793433i	−0.982051	+	0.188617i	$0.939599\pi$
$174$	57054.8	+	18717.0i	0.142863	+	0.0468667i
$175$	−299800.			−0.740008
$176$	80701.9	+	42278.1i	0.196382	+	0.102881i
$177$	209516.			0.502671
$178$	−180361.	−	59168.3i	−0.426671	−	0.139971i
$179$	71034.6	+	71034.6i	0.165706	+	0.165706i	0.785089	−	0.619383i	$-0.212617\pi$
$179$	71034.6	+	71034.6i	0.165706	+	0.165706i	−0.619383	+	0.785089i	$0.712617\pi$
$180$	−26327.8	−	172548.i	−0.0605665	−	0.396943i
$181$	−152267.	+	152267.i	−0.345469	+	0.345469i	−0.858419	−	0.512949i	$-0.828553\pi$
$181$	−152267.	+	152267.i	−0.345469	+	0.345469i	0.512949	+	0.858419i	$0.328553\pi$
$182$	−239914.	−	474173.i	−0.536880	−	1.06110i
$183$			355419.i			0.784537i
$184$	−506933.	−	710350.i	−1.10384	−	1.54678i
$185$			384295.i			0.825535i
$186$	68712.0	−	34765.7i	0.145630	−	0.0736832i
$187$	−6908.19	+	6908.19i	−0.0144464	+	0.0144464i
$188$	−592525.	−	435644.i	−1.22268	−	0.898954i
$189$	109631.	+	109631.i	0.223244	+	0.223244i
$190$	−361022.	+	1.10050e6i	−0.725521	+	2.21159i
$191$	487625.			0.967169			0.483584	−	0.875298i	$-0.339335\pi$
$191$	487625.			0.967169			0.483584	+	0.875298i	$0.339335\pi$
$192$	265006.	−	129402.i	0.518803	−	0.253332i
$193$	592062.			1.14413			0.572063	−	0.820210i	$-0.306143\pi$
$193$	592062.			1.14413			0.572063	+	0.820210i	$0.306143\pi$
$194$	88234.0	−	268962.i	0.168318	−	0.513081i
$195$	−189293.	−	189293.i	−0.356490	−	0.356490i
$196$	732837.	+	538806.i	1.36260	+	1.00183i
$197$	−580683.	+	580683.i	−1.06604	+	1.06604i	−0.0683813	+	0.997659i	$0.521783\pi$
$197$	−580683.	+	580683.i	−1.06604	+	1.06604i	−0.997659	+	0.0683813i	$0.978217\pi$
$198$	−36375.7	+	18404.7i	−0.0659398	+	0.0333631i
$199$		−	51767.7i		−	0.0926673i	−0.998926	−	0.0463337i	$-0.985246\pi$
$199$		−	51767.7i		−	0.0926673i	0.998926	−	0.0463337i	$-0.0147537\pi$
$200$	−148227.	−	207706.i	−0.262031	−	0.367176i
$201$		−	21046.9i		−	0.0367450i
$202$	−104294.	−	206129.i	−0.179837	−	0.355436i
$203$	−177369.	+	177369.i	−0.302090	+	0.302090i
$204$	4770.17	+	31262.9i	0.00802524	+	0.0525961i
$205$	200593.	+	200593.i	0.333373	+	0.333373i
$206$	−732779.	−	240391.i	−1.20311	−	0.394685i
$207$	390497.			0.633420
$208$	209896.	−	400657.i	0.336393	−	0.642118i
$209$	270510.			0.428368
$210$	692813.	+	227280.i	1.08410	+	0.355642i
$211$	211598.	+	211598.i	0.327194	+	0.327194i	0.851519	−	0.524324i	$-0.175682\pi$
$211$	211598.	+	211598.i	0.327194	+	0.327194i	−0.524324	+	0.851519i	$0.675682\pi$
$212$	263304.	−	40175.6i	0.402363	−	0.0613935i
$213$	−310499.	+	310499.i	−0.468933	+	0.468933i
$214$	372883.	+	736976.i	0.556593	+	1.10007i
$215$		−	802178.i		−	1.18352i
$216$	−21750.3	+	130158.i	−0.0317199	+	0.189818i
$217$			321685.i			0.463748i
$218$	972739.	−	492170.i	1.38629	−	0.701413i
$219$	−489440.	+	489440.i	−0.689587	+	0.689587i
$220$	−113567.	+	154464.i	−0.158196	+	0.215164i
$221$	34296.8	+	34296.8i	0.0472359	+	0.0472359i
$222$	90565.0	−	276067.i	0.123333	−	0.375952i
$223$	−766351.			−1.03197			−0.515983	−	0.856599i	$-0.672573\pi$
$223$	−766351.			−1.03197			−0.515983	+	0.856599i	$0.672573\pi$
$224$	−17446.7	+	1.23184e6i	−0.0232324	+	1.64034i
$225$	114181.			0.150362
$226$	−105377.	+	321218.i	−0.137238	+	0.418340i
$227$	18473.1	+	18473.1i	0.0237944	+	0.0237944i	0.718904	−	0.695109i	$-0.244644\pi$
$227$	18473.1	+	18473.1i	0.0237944	+	0.0237944i	−0.695109	+	0.718904i	$0.744644\pi$
$228$	518698.	−	705488.i	0.660811	−	0.898778i
$229$	325425.	−	325425.i	0.410075	−	0.410075i	−0.471690	−	0.881764i	$-0.656356\pi$
$229$	325425.	−	325425.i	0.410075	−	0.410075i	0.881764	+	0.471690i	$0.156356\pi$
$230$	1.63864e6	−	829093.i	2.04251	−	1.03344i
$231$		−	170298.i		−	0.209981i
$232$	−210579.	−	35189.1i	−0.256859	−	0.0429228i
$233$		−	176408.i		−	0.212877i	−0.994319	−	0.106439i	$-0.966055\pi$
$233$		−	176408.i		−	0.212877i	0.994319	−	0.106439i	$-0.0339448\pi$
$234$	91373.1	+	180593.i	0.109088	+	0.215606i
$235$	1.09434e6	−	1.09434e6i	1.29266	−	1.29266i
$236$	−736422.	+	112365.i	−0.860690	+	0.131326i
$237$	−422789.	−	422789.i	−0.488936	−	0.488936i
$238$	−125527.	−	41179.5i	−0.143646	−	0.0471236i
$239$	500332.			0.566583			0.283291	−	0.959034i	$-0.408574\pi$
$239$	500332.			0.566583			0.283291	+	0.959034i	$0.408574\pi$
$240$	185078.	+	592364.i	0.207408	+	0.663835i
$241$	1.21327e6			1.34560			0.672799	−	0.739826i	$-0.265092\pi$
$241$	1.21327e6			1.34560			0.672799	+	0.739826i	$0.265092\pi$
$242$	−823104.	−	270023.i	−0.903476	−	0.296389i
$243$	−41753.9	−	41753.9i	−0.0453609	−	0.0453609i
$244$	−190615.	−	1.24925e6i	−0.204966	−	1.34331i
$245$	−1.35349e6	+	1.35349e6i	−1.44059	+	1.44059i
$246$	−96827.9	−	191374.i	−0.102015	−	0.201625i
$247$		−	1.34299e6i		−	1.40065i
$248$	−222869.	+	159048.i	−0.230102	+	0.164210i
$249$		−	590676.i		−	0.603741i
$250$	−583050.	+	295002.i	−0.590006	+	0.298521i
$251$	1.12399e6	−	1.12399e6i	1.12610	−	1.12610i	0.135300	−	0.990805i	$-0.456800\pi$
$251$	1.12399e6	−	1.12399e6i	1.12610	−	1.12610i	0.990805	−	0.135300i	$-0.0431999\pi$
$252$	−444137.	−	326544.i	−0.440570	−	0.323922i
$253$	−303293.	−	303293.i	−0.297894	−	0.297894i
$254$	−196709.	+	599623.i	−0.191311	+	0.583168i
$255$	−66550.0			−0.0640911
$256$	−862063.	+	596958.i	−0.822127	+	0.569304i
$257$	−585052.			−0.552537			−0.276269	−	0.961080i	$-0.589098\pi$
$257$	−585052.			−0.552537			−0.276269	+	0.961080i	$0.589098\pi$
$258$	−189046.	+	576264.i	−0.176814	+	0.538979i
$259$	858223.	+	858223.i	0.794970	+	0.794970i
$260$	766859.	+	563820.i	0.703529	+	0.517258i
$261$	67552.2	−	67552.2i	0.0613816	−	0.0613816i
$262$	−359664.	+	181977.i	−0.323701	+	0.163781i
$263$		−	699917.i		−	0.623961i	−0.950089	−	0.311980i	$-0.899008\pi$
$263$		−	699917.i		−	0.623961i	0.950089	−	0.311980i	$-0.100992\pi$
$264$	117985.	−	84198.9i	0.104188	−	0.0743527i
$265$			560501.i			0.490300i
$266$	1.65142e6	+	3.26392e6i	1.43105	+	2.82837i
$267$	−213546.	+	213546.i	−0.183321	+	0.183321i
$268$	11287.6	+	73977.3i	0.00959989	+	0.0629161i
$269$	345337.	+	345337.i	0.290979	+	0.290979i	0.837467	−	0.546488i	$-0.184035\pi$
$269$	345337.	+	345337.i	0.290979	+	0.290979i	−0.546488	+	0.837467i	$0.684035\pi$
$270$	−263863.	−	86561.4i	−0.220277	−	0.0722628i
$271$	−1.90982e6			−1.57968			−0.789840	−	0.613313i	$-0.789836\pi$
$271$	−1.90982e6			−1.57968			−0.789840	+	0.613313i	$0.789836\pi$
$272$	−33533.1	−	107327.i	−0.0274822	−	0.0879601i
$273$	−845471.			−0.686582
$274$	440990.	+	144669.i	0.354856	+	0.116412i
$275$	−88683.0	−	88683.0i	−0.0707145	−	0.0707145i
$276$	−1.37255e6	+	209427.i	−1.08456	+	0.165485i
$277$	369110.	−	369110.i	0.289039	−	0.289039i	−0.547661	−	0.836700i	$-0.684482\pi$
$277$	369110.	−	369110.i	0.289039	−	0.289039i	0.836700	+	0.547661i	$0.184482\pi$
$278$	−159282.	−	314810.i	−0.123610	−	0.244307i
$279$		−	122516.i		−	0.0942289i
$280$	−2.55704e6	−	427299.i	−1.94914	−	0.325715i
$281$		−	663400.i		−	0.501198i	−0.968091	−	0.250599i	$-0.919372\pi$
$281$		−	663400.i		−	0.501198i	0.968091	−	0.250599i	$-0.0806276\pi$
$282$	−1.04405e6	+	528249.i	−0.781803	+	0.395563i
$283$	1.26388e6	−	1.26388e6i	0.938079	−	0.938079i	−0.0601126	−	0.998192i	$-0.519146\pi$
$283$	1.26388e6	−	1.26388e6i	0.938079	−	0.938079i	0.998192	+	0.0601126i	$0.0191460\pi$
$284$	924841.	−	1.25789e6i	0.680411	−	0.925435i
$285$	1.30298e6	+	1.30298e6i	0.950220	+	0.950220i
$286$	69295.5	−	211232.i	0.0500945	−	0.152702i
$287$	895944.			0.642061
$288$	6644.73	−	469155.i	0.00472059	−	0.333300i
$289$	−1.40780e6			−0.991508
$290$	140045.	−	426895.i	0.0977848	−	0.298075i
$291$	−318448.	−	318448.i	−0.220448	−	0.220448i
$292$	1.45783e6	−	1.98281e6i	1.00057	−	1.36089i
$293$	−863629.	+	863629.i	−0.587703	+	0.587703i	−0.937009	−	0.349305i	$-0.886418\pi$
$293$	−863629.	+	863629.i	−0.587703	+	0.587703i	0.349305	+	0.937009i	$0.386418\pi$
$294$	1.29128e6	−	653340.i	0.871269	−	0.440830i
$295$		−	1.56764e6i		−	1.04880i
$296$	−170267.	+	1.01891e6i	−0.112954	+	0.675940i
$297$			64859.4i			0.0426660i
$298$	1.13418e6	+	2.24162e6i	0.739844	+	1.46225i
$299$	−1.50575e6	+	1.50575e6i	−0.974033	+	0.974033i
$300$	−401333.	+	61236.4i	−0.257455	+	0.0392832i
$301$	−1.79146e6	−	1.79146e6i	−1.13970	−	1.13970i
$302$	−1.24961e6	−	409939.i	−0.788418	−	0.258644i
$303$	−367537.			−0.229982
$304$	−1.44480e6	+	2.75788e6i	−0.896652	+	1.71156i
$305$	2.65932e6			1.63689
$306$	47807.8	+	15683.5i	0.0291874	+	0.00957503i
$307$	899239.	+	899239.i	0.544539	+	0.544539i	0.924856	−	0.380317i	$-0.124185\pi$
$307$	899239.	+	899239.i	0.544539	+	0.544539i	−0.380317	+	0.924856i	$0.624185\pi$
$308$	91332.4	+	598577.i	0.0548590	+	0.359537i
$309$	−867603.	+	867603.i	−0.516922	+	0.516922i
$310$	−260124.	−	514116.i	−0.153736	−	0.303849i
$311$			3.22742e6i			1.89215i	0.323953	+	0.946073i	$0.394988\pi$
$311$			3.22742e6i			1.89215i	−0.323953	+	0.946073i	$0.605012\pi$
$312$	−418018.	−	585756.i	−0.243113	−	0.340667i
$313$			545249.i			0.314582i	0.987552	+	0.157291i	$0.0502761\pi$
$313$			545249.i			0.314582i	−0.987552	+	0.157291i	$0.949724\pi$
$314$	−696851.	+	352581.i	−0.398856	+	0.201806i
$315$	820283.	−	820283.i	0.465787	−	0.465787i
$316$	1.71279e6	+	1.25930e6i	0.964912	+	0.709435i
$317$	−49252.9	−	49252.9i	−0.0275286	−	0.0275286i	0.693209	−	0.720737i	$-0.256196\pi$
$317$	−49252.9	−	49252.9i	−0.0275286	−	0.0275286i	−0.720737	+	0.693209i	$0.756196\pi$
$318$	132091.	−	402649.i	0.0732495	−	0.223285i
$319$	−104934.			−0.0577349
$320$	−968215.	−	1.98283e6i	−0.528563	−	1.08245i
$321$	1.31406e6			0.711792
$322$	1.80792e6	−	5.51105e6i	0.971717	−	2.96206i
$323$	−236078.	−	236078.i	−0.125907	−	0.125907i
$324$	169153.	+	124367.i	0.0895194	+	0.0658176i
$325$	−440280.	+	440280.i	−0.231218	+	0.231218i
$326$	−1.56924e6	+	793979.i	−0.817798	+	0.413776i
$327$		−	1.73444e6i		−	0.896993i
$328$	442973.	+	620724.i	0.227349	+	0.318577i
$329$		−	4.88787e6i		−	2.48960i
$330$	137708.	+	272170.i	0.0696103	+	0.137580i
$331$	−2.33799e6	+	2.33799e6i	−1.17293	+	1.17293i	−0.191423	+	0.981508i	$0.561310\pi$
$331$	−2.33799e6	+	2.33799e6i	−1.17293	+	1.17293i	−0.981508	+	0.191423i	$0.938690\pi$
$332$	316785.	+	2.07615e6i	0.157732	+	1.03375i
$333$	−326861.	−	326861.i	−0.161530	−	0.161530i
$334$	−850378.	−	278970.i	−0.417105	−	0.136833i
$335$	−157477.			−0.0766665
$336$	1.73621e6	+	909567.i	0.838986	+	0.439528i
$337$	−743068.			−0.356413			−0.178207	−	0.983993i	$-0.557030\pi$
$337$	−743068.			−0.356413			−0.178207	+	0.983993i	$0.557030\pi$
$338$	947012.	+	310671.i	0.450883	+	0.147914i
$339$	380319.	+	380319.i	0.179742	+	0.179742i
$340$	233915.	−	35691.3i	0.109739	−	0.0167442i
$341$	−95156.8	+	95156.8i	−0.0443153	+	0.0443153i
$342$	−628958.	−	1.24309e6i	−0.290774	−	0.574695i
$343$			2.47085e6i			1.13399i
$344$	355417.	−	2.12688e6i	0.161935	−	0.969053i
$345$		−	2.92177e6i		−	1.32160i
$346$	2.22957e6	−	1.12808e6i	1.00122	−	0.506582i
$347$	78130.3	−	78130.3i	0.0348334	−	0.0348334i	−0.689476	−	0.724309i	$-0.742159\pi$
$347$	78130.3	−	78130.3i	0.0348334	−	0.0348334i	0.724309	+	0.689476i	$0.242159\pi$
$348$	−201209.	+	273667.i	−0.0890633	+	0.121136i
$349$	−154874.	−	154874.i	−0.0680637	−	0.0680637i	0.672256	−	0.740319i	$-0.265326\pi$
$349$	−154874.	−	154874.i	−0.0680637	−	0.0680637i	−0.740319	+	0.672256i	$0.765326\pi$
$350$	528636.	−	1.61143e6i	0.230668	−	0.703139i
$351$	322004.			0.139506
$352$	−369547.	+	359225.i	−0.158969	+	0.154529i
$353$	4.00016e6			1.70860			0.854301	−	0.519779i	$-0.173986\pi$
$353$	4.00016e6			1.70860			0.854301	+	0.519779i	$0.173986\pi$
$354$	−369438.	+	1.12615e6i	−0.156687	+	0.477626i
$355$	2.32321e6	+	2.32321e6i	0.978404	+	0.978404i
$356$	636061.	−	865114.i	0.265995	−	0.361783i
$357$	−148622.	+	148622.i	−0.0617181	+	0.0617181i
$358$	−507067.	+	256557.i	−0.209102	+	0.105798i
$359$		−	4.22809e6i		−	1.73144i	−0.500528	−	0.865720i	$-0.666861\pi$
$359$		−	4.22809e6i		−	1.73144i	0.500528	−	0.865720i	$-0.333139\pi$
$360$	973870.	+	162740.i	0.396045	+	0.0661819i
$361$			6.76822e6i			2.73342i
$362$	−549946.	−	1.08693e6i	−0.220571	−	0.435943i
$363$	−974547.	+	974547.i	−0.388183	+	0.388183i
$364$	2.97173e6	−	453434.i	1.17559	−	0.179374i
$365$	3.66208e6	+	3.66208e6i	1.43879	+	1.43879i
$366$	−1.91038e6	−	626709.i	−0.745449	−	0.244548i
$367$	−2.02450e6			−0.784609			−0.392305	−	0.919835i	$-0.628322\pi$
$367$	−2.02450e6			−0.784609			−0.392305	+	0.919835i	$0.628322\pi$
$368$	4.71201e6	−	1.47222e6i	1.81379	−	0.566699i
$369$	−341227.			−0.130460
$370$	−2.06559e6	−	677625.i	−0.784404	−	0.257327i
$371$	1.25173e6	+	1.25173e6i	0.472147	+	0.472147i
$372$	65706.7	+	430630.i	0.0246180	+	0.161342i
$373$	2.10708e6	−	2.10708e6i	0.784169	−	0.784169i	−0.196363	−	0.980531i	$-0.562913\pi$
$373$	2.10708e6	−	2.10708e6i	0.784169	−	0.784169i	0.980531	+	0.196363i	$0.0629130\pi$
$374$	−24950.4	−	49312.8i	−0.00922357	−	0.0182297i
$375$			1.03960e6i			0.381760i
$376$	3.38639e6	−	2.41666e6i	1.23529	−	0.881549i
$377$			520960.i			0.188778i
$378$	−782582.	+	395957.i	−0.281709	+	0.142534i
$379$	−1.43790e6	+	1.43790e6i	−0.514197	+	0.514197i	−0.915810	−	0.401612i	$-0.868450\pi$
$379$	−1.43790e6	+	1.43790e6i	−0.514197	+	0.514197i	0.401612	+	0.915810i	$0.368450\pi$
$380$	−5.27860e6	−	3.88100e6i	−1.87525	−	1.37875i
$381$	709947.	+	709947.i	0.250561	+	0.250561i
$382$	−859826.	+	2.62099e6i	−0.301476	+	0.918982i
$383$	−4.15338e6			−1.44679			−0.723394	−	0.690435i	$-0.757419\pi$
$383$	−4.15338e6			−1.44679			−0.723394	+	0.690435i	$0.757419\pi$
$384$	228257.	+	1.65259e6i	0.0789942	+	0.571921i
$385$	−1.27420e6			−0.438114
$386$	−1.04398e6	+	3.18234e6i	−0.356635	+	1.08712i
$387$	682290.	+	682290.i	0.231575	+	0.231575i
$388$	1.29009e6	+	948518.i	0.435052	+	0.319865i
$389$	−432999.	+	432999.i	−0.145082	+	0.145082i	−0.775917	−	0.630835i	$-0.782712\pi$
$389$	−432999.	+	432999.i	−0.145082	+	0.145082i	0.630835	+	0.775917i	$0.282712\pi$
$390$	1.35123e6	−	683672.i	0.449850	−	0.227607i
$391$			529378.i			0.175115i
$392$	−4.18830e6	+	2.98893e6i	−1.37665	+	0.982429i
$393$			641297.i			0.209449i
$394$	−2.09727e6	−	4.14510e6i	−0.680633	−	1.34522i
$395$	−3.16339e6	+	3.16339e6i	−1.02014	+	1.02014i
$396$	−34784.7	−	227973.i	−0.0111468	−	0.0730542i
$397$	−2.64553e6	−	2.64553e6i	−0.842434	−	0.842434i	0.146741	−	0.989175i	$-0.453122\pi$
$397$	−2.64553e6	−	2.64553e6i	−0.842434	−	0.842434i	−0.989175	+	0.146741i	$0.953122\pi$
$398$	278252.	+	91281.8i	0.0880504	+	0.0288853i
$399$	5.81972e6			1.83008
$400$	1.37779e6	−	430477.i	0.430560	−	0.134524i
$401$	−3.04857e6			−0.946751			−0.473375	−	0.880861i	$-0.656965\pi$
$401$	−3.04857e6			−0.946751			−0.473375	+	0.880861i	$0.656965\pi$
$402$	113128.	+	37111.9i	0.0349143	+	0.0114538i
$403$	472421.	+	472421.i	0.144899	+	0.144899i
$404$	1.29185e6	−	197113.i	0.393784	−	0.0600845i
$405$	−312411.	+	312411.i	−0.0946431	+	0.0946431i
$406$	−640606.	−	1.26611e6i	−0.192875	−	0.381204i
$407$			507736.i			0.151933i
$408$	−176450.	−	29485.9i	−0.0524771	−	0.00876929i
$409$		−	3.00149e6i		−	0.887214i	−0.896222	−	0.443607i	$-0.853699\pi$
$409$		−	3.00149e6i		−	0.887214i	0.896222	−	0.443607i	$-0.146301\pi$
$410$	−1.43189e6	+	724485.i	−0.420680	+	0.212848i
$411$	522127.	−	522127.i	0.152466	−	0.152466i
$412$	2.58421e6	−	3.51482e6i	0.750041	−	1.02014i
$413$	−3.50091e6	−	3.50091e6i	−1.00996	−	1.00996i
$414$	−688561.	+	2.09893e6i	−0.197443	+	0.601861i
$415$	−4.41955e6			−1.25967
$416$	1.78343e6	+	1.83467e6i	0.505269	+	0.519787i
$417$	−561320.			−0.158078
$418$	−476989.	+	1.45399e6i	−0.133526	+	0.407026i
$419$	−4.69428e6	−	4.69428e6i	−1.30627	−	1.30627i	−0.924084	−	0.382189i	$-0.875170\pi$
$419$	−4.69428e6	−	4.69428e6i	−1.30627	−	1.30627i	−0.382189	−	0.924084i	$-0.624830\pi$
$420$	−2.44327e6	+	3.32312e6i	−0.675846	+	0.919226i
$421$	−426113.	+	426113.i	−0.117171	+	0.117171i	−0.763261	−	0.646090i	$-0.776403\pi$
$421$	−426113.	+	426113.i	−0.117171	+	0.117171i	0.646090	+	0.763261i	$0.276403\pi$
$422$	−1.51045e6	+	764233.i	−0.412882	+	0.208903i
$423$			1.86158e6i			0.505861i
$424$	−248338.	+	1.48610e6i	−0.0670855	+	0.401453i
$425$			154790.i			0.0415692i
$426$	−1.12143e6	−	2.21644e6i	−0.299399	−	0.591741i
$427$	5.93889e6	−	5.93889e6i	1.57629	−	1.57629i
$428$	−4.61876e6	+	704742.i	−1.21875	+	0.185961i
$429$	−250096.	−	250096.i	−0.0656091	−	0.0656091i
$430$	4.31172e6	+	1.41448e6i	1.12455	+	0.368914i
$431$	2.40450e6			0.623492			0.311746	−	0.950165i	$-0.399086\pi$
$431$	2.40450e6			0.623492			0.311746	+	0.950165i	$0.399086\pi$
$432$	−661251.	−	346416.i	−0.170473	−	0.0893076i
$433$	378152.			0.0969274			0.0484637	−	0.998825i	$-0.484567\pi$
$433$	378152.			0.0969274			0.0484637	+	0.998825i	$0.484567\pi$
$434$	−1.72906e6	−	567227.i	−0.440643	−	0.144555i
$435$	−505439.	−	505439.i	−0.128070	−	0.128070i
$436$	930193.	+	6.09633e6i	0.234346	+	1.53586i
$437$	1.03647e7	−	1.03647e7i	2.59628	−	2.59628i
$438$	−1.76772e6	−	3.49377e6i	−0.440279	−	0.870180i
$439$		−	1.08378e6i		−	0.268399i	−0.990954	−	0.134199i	$-0.957154\pi$
$439$		−	1.08378e6i		−	0.268399i	0.990954	−	0.134199i	$-0.0428462\pi$
$440$	−629993.	−	882789.i	−0.155133	−	0.217383i
$441$		−	2.30241e6i		−	0.563750i
$442$	−244821.	+	123870.i	−0.0596064	+	0.0301586i
$443$	−2.25647e6	+	2.25647e6i	−0.546285	+	0.546285i	−0.925364	−	0.379079i	$-0.876241\pi$
$443$	−2.25647e6	+	2.25647e6i	−0.546285	+	0.546285i	0.379079	+	0.925364i	$0.376241\pi$
$444$	1.32417e6	+	973577.i	0.318777	+	0.234376i
$445$	1.59779e6	+	1.59779e6i	0.382490	+	0.382490i
$446$	1.35130e6	−	4.11915e6i	0.321674	−	0.980551i
$447$	3.99691e6			0.946140
$448$	−6.59038e6	−	2.26587e6i	−1.55137	−	0.533384i
$449$	−4.01329e6			−0.939475			−0.469737	−	0.882806i	$-0.655651\pi$
$449$	−4.01329e6			−0.939475			−0.469737	+	0.882806i	$0.655651\pi$
$450$	−201335.	+	613726.i	−0.0468693	+	0.142871i
$451$	265027.	+	265027.i	0.0613547	+	0.0613547i
$452$	−1.54074e6	−	1.13281e6i	−0.354719	−	0.260801i
$453$	−1.47952e6	+	1.47952e6i	−0.338747	+	0.338747i
$454$	−131867.	+	66719.6i	−0.0300259	+	0.0151920i
$455$			6.32598e6i			1.43252i
$456$	2.87739e6	+	4.03199e6i	0.648017	+	0.908046i
$457$			666098.i			0.149193i	0.997214	+	0.0745964i	$0.0237668\pi$
$457$			666098.i			0.149193i	−0.997214	+	0.0745964i	$0.976233\pi$
$458$	1.17535e6	+	2.32299e6i	0.261819	+	0.517468i
$459$	56603.9	−	56603.9i	0.0125405	−	0.0125405i
$460$	1.56697e6	+	1.02697e7i	0.345276	+	2.26288i
$461$	2.03803e6	+	2.03803e6i	0.446641	+	0.446641i	0.894236	−	0.447595i	$-0.147720\pi$
$461$	2.03803e6	+	2.03803e6i	0.446641	+	0.446641i	−0.447595	+	0.894236i	$0.647720\pi$
$462$	915355.	+	300286.i	0.199519	+	0.0654531i
$463$	−3.85991e6			−0.836807			−0.418403	−	0.908261i	$-0.637410\pi$
$463$	−3.85991e6			−0.836807			−0.418403	+	0.908261i	$0.637410\pi$
$464$	560454.	−	1.06981e6i	0.120850	−	0.230682i
$465$	−916692.			−0.196603
$466$	948198.	+	311060.i	0.202271	+	0.0663559i
$467$	−4.27595e6	−	4.27595e6i	−0.907279	−	0.907279i	0.0887729	−	0.996052i	$-0.471705\pi$
$467$	−4.27595e6	−	4.27595e6i	−0.907279	−	0.907279i	−0.996052	+	0.0887729i	$0.971705\pi$
$468$	−1.13181e6	+	172694.i	−0.238868	+	0.0364470i
$469$	−351684.	+	351684.i	−0.0738280	+	0.0738280i
$470$	3.95247e6	+	7.81177e6i	0.825322	+	1.63119i
$471$			1.24252e6i			0.258077i
$472$	694565.	−	4.15641e6i	0.143502	−	0.858744i
$473$		−	1.05985e6i		−	0.217817i
$474$	3.01800e6	−	1.52699e6i	0.616983	−	0.312170i
$475$	3.03062e6	−	3.03062e6i	0.616308	−	0.616308i
$476$	442681.	−	602095.i	0.0895516	−	0.121800i
$477$	−476733.	−	476733.i	−0.0959354	−	0.0959354i
$478$	−882233.	+	2.68929e6i	−0.176609	+	0.538354i
$479$	4.03106e6			0.802749			0.401375	−	0.915914i	$-0.368533\pi$
$479$	4.03106e6			0.802749			0.401375	+	0.915914i	$0.368533\pi$
$480$	−3.51031e6	−	49717.1i	−0.695412	−	0.00984925i
$481$	2.52074e6			0.496781
$482$	−2.13935e6	+	6.52135e6i	−0.419436	+	1.27856i
$483$	−6.52502e6	−	6.52502e6i	−1.27266	−	1.27266i
$484$	2.90275e6	−	3.94807e6i	0.563244	−	0.766075i
$485$	−2.38269e6	+	2.38269e6i	−0.459953	+	0.459953i
$486$	298053.	−	150804.i	0.0572404	−	0.0289615i
$487$			8.05846e6i			1.53968i	0.638238	+	0.769839i	$0.279663\pi$
$487$			8.05846e6i			1.53968i	−0.638238	+	0.769839i	$0.720337\pi$
$488$	7.05087e6	+	1.17825e6i	1.34027	+	0.223969i
$489$			2.79803e6i			0.529152i
$490$	−4.88842e6	−	9.66162e6i	−0.919768	−	1.81786i
$491$	3.41092e6	−	3.41092e6i	0.638509	−	0.638509i	−0.311678	−	0.950188i	$-0.600891\pi$
$491$	3.41092e6	−	3.41092e6i	0.638509	−	0.638509i	0.950188	+	0.311678i	$0.100891\pi$
$492$	1.19937e6	−	183003.i	0.223378	−	0.0340836i
$493$	91577.4	+	91577.4i	0.0169696	+	0.0169696i
$494$	7.21857e6	+	2.36808e6i	1.33087	+	0.436596i
$495$	485291.			0.0890203
$496$	−461901.	−	1.47837e6i	−0.0843034	−	0.269823i
$497$	1.03766e7			1.88436
$498$	3.17489e6	+	1.04154e6i	0.573661	+	0.188192i
$499$	−6.17565e6	−	6.17565e6i	−1.11028	−	1.11028i	−0.993113	−	0.117164i	$-0.962620\pi$
$499$	−6.17565e6	−	6.17565e6i	−1.11028	−	1.11028i	−0.117164	−	0.993113i	$-0.537380\pi$
$500$	−557549.	−	3.65408e6i	−0.0997374	−	0.653662i
$501$	−1.00684e6	+	1.00684e6i	−0.179211	+	0.179211i
$502$	4.05954e6	+	8.02340e6i	0.718982	+	1.42102i
$503$		−	186001.i		−	0.0327790i	−0.999866	−	0.0163895i	$-0.994783\pi$
$503$		−	186001.i		−	0.0327790i	0.999866	−	0.0163895i	$-0.00521717\pi$
$504$	2.53832e6	−	1.81145e6i	0.445113	−	0.317650i
$505$			2.74999e6i			0.479846i
$506$	2.16500e6	−	1.09541e6i	0.375908	−	0.190196i
$507$	1.12125e6	−	1.12125e6i	0.193724	−	0.193724i
$508$	−2.87613e6	−	2.11462e6i	−0.494480	−	0.363558i
$509$	2.36413e6	+	2.36413e6i	0.404462	+	0.404462i	0.879802	−	0.475340i	$-0.157675\pi$
$509$	2.36413e6	+	2.36413e6i	0.404462	+	0.404462i	−0.475340	+	0.879802i	$0.657675\pi$
$510$	117347.	−	357707.i	0.0199778	−	0.0608979i
$511$	1.63566e7			2.77103
$512$	−1.68859e6	−	5.68621e6i	−0.284675	−	0.958624i
$513$	−2.21649e6			−0.371853
$514$	1.03162e6	−	3.14466e6i	0.172231	−	0.525009i
$515$	6.49157e6	+	6.49157e6i	1.07853	+	1.07853i
$516$	−2.76408e6	−	2.03225e6i	−0.457011	−	0.336010i
$517$	1.44587e6	−	1.44587e6i	0.237904	−	0.237904i
$518$	−6.12626e6	+	3.09966e6i	−1.00316	+	0.507563i
$519$		−	3.97542e6i		−	0.647836i
$520$	−4.38274e6	+	3.12770e6i	−0.710784	+	0.507243i
$521$			5.38194e6i			0.868649i	0.900756	+	0.434325i	$0.143013\pi$
$521$			5.38194e6i			0.868649i	−0.900756	+	0.434325i	$0.856987\pi$
$522$	243980.	+	482209.i	0.0391902	+	0.0774567i
$523$	4.38747e6	−	4.38747e6i	0.701390	−	0.701390i	−0.263319	−	0.964709i	$-0.584817\pi$
$523$	4.38747e6	−	4.38747e6i	0.701390	−	0.701390i	0.964709	+	0.263319i	$0.0848171\pi$
$524$	−343933.	−	2.25408e6i	−0.0547200	−	0.358625i
$525$	−1.90792e6	−	1.90792e6i	−0.302107	−	0.302107i
$526$	3.76206e6	+	1.23416e6i	0.592873	+	0.194494i
$527$	166090.			0.0260505
$528$	244528.	+	782640.i	0.0381718	+	0.122174i
$529$	−1.68052e7			−2.61098
$530$	−3.01270e6	−	988329.i	−0.465872	−	0.152831i
$531$	1.33335e6	+	1.33335e6i	0.205214	+	0.205214i
$532$	−2.04556e7	+	3.12117e6i	−3.13352	+	0.478121i
$533$	1.31576e6	−	1.31576e6i	0.200614	−	0.200614i
$534$	−771268.	−	1.52436e6i	−0.117045	−	0.231331i
$535$		−	9.83206e6i		−	1.48512i
$536$	−417533.	−	69772.6i	−0.0627738	−	0.0104899i
$537$			904123.i			0.135298i
$538$	−2.46512e6	+	1.24726e6i	−0.367183	+	0.185781i
$539$	−1.78825e6	+	1.78825e6i	−0.265128	+	0.265128i
$540$	930538.	−	1.26564e6i	0.137325	−	0.186777i
$541$	−2.86766e6	−	2.86766e6i	−0.421244	−	0.421244i	0.464388	−	0.885632i	$-0.346274\pi$
$541$	−2.86766e6	−	2.86766e6i	−0.421244	−	0.421244i	−0.885632	+	0.464388i	$0.846274\pi$
$542$	3.36758e6	−	1.02653e7i	0.492401	−	1.50098i
$543$	−1.93804e6			−0.282075
$544$	636012.	+	9007.95i	0.0921442	+	0.00130505i
$545$	−1.29774e7			−1.87153
$546$	1.49082e6	−	4.54442e6i	0.214014	−	0.652374i
$547$	4.80244e6	+	4.80244e6i	0.686268	+	0.686268i	0.961405	−	0.275137i	$-0.0887231\pi$
$547$	4.80244e6	+	4.80244e6i	0.686268	+	0.686268i	−0.275137	+	0.961405i	$0.588723\pi$
$548$	−1.55519e6	+	2.11523e6i	−0.221224	+	0.300890i
$549$	−2.26187e6	+	2.26187e6i	−0.320286	+	0.320286i
$550$	633047.	−	320298.i	0.0892337	−	0.0451489i
$551$		−	3.58597e6i		−	0.503185i
$552$	1.29453e6	−	7.74674e6i	0.180828	−	1.08211i
$553$			1.41292e7i			1.96474i
$554$	1.33312e6	+	2.63482e6i	0.184542	+	0.364734i
$555$	−2.44564e6	+	2.44564e6i	−0.337023	+	0.337023i
$556$	1.97297e6	−	301041.i	0.270666	−	0.0412989i
$557$	180917.	+	180917.i	0.0247082	+	0.0247082i	0.719353	−	0.694645i	$-0.244438\pi$
$557$	180917.	+	180917.i	0.0247082	+	0.0247082i	−0.694645	+	0.719353i	$0.744438\pi$
$558$	658528.	+	216033.i	0.0895341	+	0.0293720i
$559$	−5.26179e6			−0.712203
$560$	6.80556e6	−	1.29907e7i	0.917052	−	1.75050i
$561$	−87926.9			−0.0117955
$562$	3.56578e6	+	1.16977e6i	0.476227	+	0.156228i
$563$	−6.06459e6	−	6.06459e6i	−0.806363	−	0.806363i	0.177718	−	0.984081i	$-0.443128\pi$
$563$	−6.06459e6	−	6.06459e6i	−0.806363	−	0.806363i	−0.984081	+	0.177718i	$0.943128\pi$
$564$	−998383.	−	6.54323e6i	−0.132160	−	0.866153i
$565$	2.84562e6	−	2.84562e6i	0.375022	−	0.375022i
$566$	4.56478e6	+	9.02196e6i	0.598933	+	1.18375i
$567$			1.39538e6i			0.182278i
$568$	5.13040e6	+	7.18906e6i	0.667237	+	0.934978i
$569$			1.11550e7i			1.44441i	0.691680	+	0.722204i	$0.256871\pi$
$569$			1.11550e7i			1.44441i	−0.691680	+	0.722204i	$0.743129\pi$
$570$	−9.30105e6	+	4.70599e6i	−1.19907	+	0.606685i
$571$	−5.07906e6	+	5.07906e6i	−0.651918	+	0.651918i	−0.953455	−	0.301537i	$-0.902500\pi$
$571$	−5.07906e6	+	5.07906e6i	−0.651918	+	0.651918i	0.301537	+	0.953455i	$0.402500\pi$
$572$	1.01319e6	+	744929.i	0.129479	+	0.0951973i
$573$	3.10322e6	+	3.10322e6i	0.394845	+	0.394845i
$574$	−1.57981e6	+	4.81571e6i	−0.200136	+	0.610072i
$575$	−6.79582e6			−0.857181
$576$	2.51000e6	+	862975.i	0.315223	+	0.108378i
$577$	5.78551e6			0.723439			0.361719	−	0.932287i	$-0.382190\pi$
$577$	5.78551e6			0.723439			0.361719	+	0.932287i	$0.382190\pi$
$578$	2.48237e6	−	7.56694e6i	0.309062	−	0.942108i
$579$	3.76786e6	+	3.76786e6i	0.467088	+	0.467088i
$580$	2.04763e6	+	1.50548e6i	0.252744	+	0.185826i
$581$	−9.86992e6	+	9.86992e6i	−1.21304	+	1.21304i
$582$	2.27318e6	−	1.15014e6i	0.278180	−	0.140749i
$583$			740543.i			0.0902358i
$584$	8.08705e6	+	1.13321e7i	0.981201	+	1.37493i
$585$		−	2.40930e6i		−	0.291073i
$586$	−3.11919e6	−	6.16485e6i	−0.375230	−	0.741615i
$587$	−4.38500e6	+	4.38500e6i	−0.525260	+	0.525260i	−0.919155	−	0.393896i	$-0.871127\pi$
$587$	−4.38500e6	+	4.38500e6i	−0.525260	+	0.525260i	0.393896	+	0.919155i	$0.371127\pi$
$588$	1.23480e6	+	8.09268e6i	0.147284	+	0.965271i
$589$	−3.25186e6	−	3.25186e6i	−0.386228	−	0.386228i
$590$	8.42608e6	+	2.76421e6i	0.996542	+	0.326920i
$591$	−7.39089e6			−0.870419
$592$	−5.17644e6	−	2.71184e6i	−0.607054	−	0.318023i
$593$	5.35681e6			0.625561			0.312780	−	0.949825i	$-0.398740\pi$
$593$	5.35681e6			0.625561			0.312780	+	0.949825i	$0.398740\pi$
$594$	−348620.	−	114366.i	−0.0405403	−	0.0132994i
$595$	1.11202e6	+	1.11202e6i	0.128772	+	0.128772i
$596$	−1.40486e7	+	2.14358e6i	−1.62001	+	0.247186i
$597$	329448.	−	329448.i	0.0378313	−	0.0378313i
$598$	−5.43833e6	−	1.07485e7i	−0.621889	−	1.22912i
$599$			1.38862e6i			0.158131i	0.996869	+	0.0790655i	$0.0251936\pi$
$599$			1.38862e6i			0.158131i	−0.996869	+	0.0790655i	$0.974806\pi$
$600$	378522.	−	2.26515e6i	0.0429252	−	0.256873i
$601$		−	1.13088e7i		−	1.27711i	−0.769576	−	0.638556i	$-0.779532\pi$
$601$		−	1.13088e7i		−	1.27711i	0.769576	−	0.638556i	$-0.220468\pi$
$602$	1.27880e7	−	6.47024e6i	1.43817	−	0.727661i
$603$	133942.	−	133942.i	0.0150011	−	0.0150011i
$604$	4.40686e6	−	5.99382e6i	0.491515	−	0.668515i
$605$	7.29175e6	+	7.29175e6i	0.809922	+	0.809922i
$606$	648077.	−	1.97552e6i	0.0716877	−	0.218524i
$607$	9.49313e6			1.04577			0.522887	−	0.852402i	$-0.324855\pi$
$607$	9.49313e6			1.04577			0.522887	+	0.852402i	$0.324855\pi$
$608$	−1.22761e7	−	1.26288e7i	−1.34679	−	1.38549i
$609$	−2.25753e6			−0.246656
$610$	−4.68916e6	+	1.42939e7i	−0.510236	+	1.55534i
$611$	−7.17822e6	−	7.17822e6i	−0.777882	−	0.777882i
$612$	−168598.	+	229313.i	−0.0181960	+	0.0247485i
$613$	5.96732e6	−	5.96732e6i	0.641399	−	0.641399i	−0.309501	−	0.950899i	$-0.600162\pi$
$613$	5.96732e6	−	5.96732e6i	0.641399	−	0.641399i	0.950899	+	0.309501i	$0.100162\pi$
$614$	−6.41905e6	+	3.24780e6i	−0.687147	+	0.347671i
$615$			2.55313e6i			0.272198i
$616$	−3.37841e6	−	564555.i	−0.358724	−	0.0599452i
$617$			3.35492e6i			0.354788i	0.984140	+	0.177394i	$0.0567667\pi$
$617$			3.35492e6i			0.354788i	−0.984140	+	0.177394i	$0.943233\pi$
$618$	−3.13354e6	−	6.19322e6i	−0.330038	−	0.652297i
$619$	215042.	−	215042.i	0.0225578	−	0.0225578i	−0.695738	−	0.718296i	$-0.744922\pi$
$619$	215042.	−	215042.i	0.0225578	−	0.0225578i	0.718296	+	0.695738i	$0.244922\pi$
$620$	3.22206e6	−	491630.i	0.336631	−	0.0513640i
$621$	2.48511e6	+	2.48511e6i	0.258592	+	0.258592i
$622$	−1.73474e7	−	5.69090e6i	−1.79787	−	0.589800i
$623$	7.13651e6			0.736657
$624$	3.88554e6	−	1.21399e6i	0.399475	−	0.124812i
$625$	1.21837e7			1.24761
$626$	−2.93072e6	−	961435.i	−0.298909	−	0.0980582i
$627$	1.72151e6	+	1.72151e6i	0.174881	+	0.174881i
$628$	−666372.	−	4.36729e6i	−0.0674245	−	0.441889i
$629$	443110.	−	443110.i	0.0446565	−	0.0446565i
$630$	2.96263e6	+	5.85543e6i	0.297390	+	0.587770i
$631$		−	4.52626e6i		−	0.452549i	−0.974064	−	0.226275i	$-0.927345\pi$
$631$		−	4.52626e6i		−	0.452549i	0.974064	−	0.226275i	$-0.0726547\pi$
$632$	−9.78894e6	+	6.98577e6i	−0.974862	+	0.695699i
$633$			2.69320e6i			0.267153i
$634$	351582.	−	177888.i	0.0347379	−	0.0175761i
$635$	5.31196e6	−	5.31196e6i	0.522782	−	0.522782i
$636$	1.93133e6	+	1.41998e6i	0.189328	+	0.139200i
$637$	8.87804e6	+	8.87804e6i	0.866899	+	0.866899i
$638$	185029.	−	564020.i	0.0179965	−	0.0548584i
$639$	−3.95200e6			−0.382882
$640$	1.23650e7	−	1.70786e6i	1.19328	−	0.164817i
$641$	−7.29319e6			−0.701088			−0.350544	−	0.936546i	$-0.614003\pi$
$641$	−7.29319e6			−0.701088			−0.350544	+	0.936546i	$0.614003\pi$
$642$	−2.31708e6	+	7.06310e6i	−0.221872	+	0.676328i
$643$	−1.39212e6	−	1.39212e6i	−0.132785	−	0.132785i	0.637590	−	0.770376i	$-0.279931\pi$
$643$	−1.39212e6	−	1.39212e6i	−0.132785	−	0.132785i	−0.770376	+	0.637590i	$0.779931\pi$
$644$	2.64341e7	+	1.94352e7i	2.51159	+	1.84661i
$645$	5.10503e6	−	5.10503e6i	0.483169	−	0.483169i
$646$	1.68520e6	−	852649.i	0.158880	−	0.0803876i
$647$			7.66813e6i			0.720160i	0.932921	+	0.360080i	$0.117251\pi$
$647$			7.66813e6i			0.720160i	−0.932921	+	0.360080i	$0.882749\pi$
$648$	−966741.	+	689904.i	−0.0904425	+	0.0645433i
$649$		−	2.07119e6i		−	0.193023i
$650$	−1.59017e6	−	3.14286e6i	−0.147625	−	0.291770i
$651$	−2.04719e6	+	2.04719e6i	−0.189324	+	0.189324i
$652$	−1.50061e6	−	9.83472e6i	−0.138245	−	0.906031i
$653$	−9.46513e6	−	9.46513e6i	−0.868648	−	0.868648i	0.123675	−	0.992323i	$-0.460532\pi$
$653$	−9.46513e6	−	9.46513e6i	−0.868648	−	0.868648i	−0.992323	+	0.123675i	$0.960532\pi$
$654$	9.32262e6	+	3.05832e6i	0.852302	+	0.279601i
$655$	4.79831e6			0.437004
$656$	−4.11750e6	+	1.28647e6i	−0.373571	+	0.116718i
$657$	−6.22955e6			−0.563045
$658$	2.62724e7	+	8.61875e6i	2.36556	+	0.776032i
$659$	1.04859e7	+	1.04859e7i	0.940574	+	0.940574i	0.998331	−	0.0577566i	$-0.0183947\pi$
$659$	1.04859e7	+	1.04859e7i	0.940574	+	0.940574i	−0.0577566	+	0.998331i	$0.518395\pi$
$660$	−1.70574e6	+	260266.i	−0.152424	+	0.0232572i
$661$	5.64271e6	−	5.64271e6i	0.502324	−	0.502324i	−0.409835	−	0.912160i	$-0.634414\pi$
$661$	5.64271e6	−	5.64271e6i	0.502324	−	0.502324i	0.912160	+	0.409835i	$0.134414\pi$
$662$	−8.44416e6	−	1.66893e7i	−0.748878	−	1.48011i
$663$			436526.i			0.0385680i
$664$	−1.17179e7	−	1.95815e6i	−1.03141	−	0.172356i
$665$		−	4.35443e7i		−	3.81836i
$666$	2.33323e6	−	1.18053e6i	0.203832	−	0.103132i
$667$	−4.02056e6	+	4.02056e6i	−0.349923	+	0.349923i
$668$	2.99893e6	−	4.07889e6i	0.260031	−	0.353672i
$669$	−4.87703e6	−	4.87703e6i	−0.421298	−	0.421298i
$670$	277679.	−	846442.i	0.0238977	−	0.0728468i
$671$	3.51353e6			0.301257
$672$	−7.95040e6	+	7.72834e6i	−0.679150	+	0.660181i
$673$	−6.60164e6			−0.561842			−0.280921	−	0.959731i	$-0.590640\pi$
$673$	−6.60164e6			−0.561842			−0.280921	+	0.959731i	$0.590640\pi$
$674$	1.31025e6	−	3.99400e6i	0.111097	−	0.338656i
$675$	726645.	+	726645.i	0.0613851	+	0.0613851i
$676$	−3.33973e6	+	4.54240e6i	−0.281089	+	0.382313i
$677$	−5.65299e6	+	5.65299e6i	−0.474031	+	0.474031i	−0.903216	−	0.429186i	$-0.858801\pi$
$677$	−5.65299e6	+	5.65299e6i	−0.474031	+	0.474031i	0.429186	+	0.903216i	$0.358801\pi$
$678$	−2.71484e6	+	1.37361e6i	−0.226814	+	0.114759i
$679$			1.06422e7i			0.885847i
$680$	−220620.	+	1.32023e6i	−0.0182967	+	0.109491i
$681$			235124.i			0.0194281i
$682$	−343680.	−	679259.i	−0.0282939	−	0.0559209i
$683$	1.06582e7	−	1.06582e7i	0.874246	−	0.874246i	−0.118686	−	0.992932i	$-0.537868\pi$
$683$	1.06582e7	−	1.06582e7i	0.874246	−	0.874246i	0.992932	+	0.118686i	$0.0378682\pi$
$684$	7.79067e6	−	1.18872e6i	0.636700	−	0.0971493i
$685$	−3.90666e6	−	3.90666e6i	−0.318111	−	0.318111i
$686$	−1.32809e7	−	4.35684e6i	−1.07750	−	0.353477i
$687$	4.14199e6			0.334824
$688$	1.08053e7	+	5.66069e6i	0.870295	+	0.455930i
$689$	3.67654e6			0.295047
$690$	1.57046e7	+	5.15195e6i	1.25575	+	0.411954i
$691$	−8.29852e6	−	8.29852e6i	−0.661158	−	0.661158i	0.294495	−	0.955653i	$-0.404849\pi$
$691$	−8.29852e6	−	8.29852e6i	−0.661158	−	0.661158i	−0.955653	+	0.294495i	$0.904849\pi$
$692$	2.13205e6	+	1.39731e7i	0.169252	+	1.10925i
$693$	1.08377e6	−	1.08377e6i	0.0857244	−	0.0857244i
$694$	282185.	+	557719.i	0.0222400	+	0.0439558i
$695$			4.19991e6i			0.329821i
$696$	−1.11617e6	−	1.56406e6i	−0.0873389	−	0.122385i
$697$		−	462586.i		−	0.0360671i
$698$	1.10554e6	−	559362.i	0.0858887	−	0.0434565i
$699$	1.12266e6	−	1.12266e6i	0.0869068	−	0.0869068i
$700$	7.72932e6	+	5.68286e6i	0.596206	+	0.438350i
$701$	−7.11003e6	−	7.11003e6i	−0.546483	−	0.546483i	0.378939	−	0.925422i	$-0.376289\pi$
$701$	−7.11003e6	−	7.11003e6i	−0.546483	−	0.546483i	−0.925422	+	0.378939i	$0.876289\pi$
$702$	−567789.	+	1.73078e6i	−0.0434855	+	0.132556i
$703$	−1.73512e7			−1.32416
$704$	−1.27922e6	−	2.61974e6i	−0.0972778	−	0.199217i
$705$	1.39287e7			1.05545
$706$	−7.05347e6	+	2.15009e7i	−0.532587	+	1.62347i
$707$	6.14138e6	+	6.14138e6i	0.462080	+	0.462080i
$708$	−5.40165e6	−	3.97147e6i	−0.404989	−	0.297761i
$709$	−6.44066e6	+	6.44066e6i	−0.481188	+	0.481188i	−0.905511	−	0.424323i	$-0.860512\pi$
$709$	−6.44066e6	+	6.44066e6i	−0.481188	+	0.481188i	0.424323	+	0.905511i	$0.360512\pi$
$710$	−1.65838e7	+	8.39079e6i	−1.23464	+	0.624679i
$711$		−	5.38122e6i		−	0.399215i
$712$	3.52844e6	+	4.94429e6i	0.260845	+	0.365514i
$713$			7.29192e6i			0.537178i
$714$	−536781.	−	1.06091e6i	−0.0394050	−	0.0778813i
$715$	−1.87127e6	+	1.87127e6i	−0.136890	+	0.136890i
$716$	−484889.	−	3.17788e6i	−0.0353476	−	0.231662i
$717$	3.18409e6	+	3.18409e6i	0.231307	+	0.231307i
$718$	2.27260e7	+	7.45536e6i	1.64518	+	0.539707i
$719$	−6.10329e6			−0.440293			−0.220147	−	0.975467i	$-0.570654\pi$
$719$	−6.10329e6			−0.440293			−0.220147	+	0.975467i	$0.570654\pi$
$720$	−2.59195e6	+	4.94761e6i	−0.186336	+	0.355684i
$721$	2.89945e7			2.07719
$722$	−3.63793e7	−	1.19344e7i	−2.59723	−	0.852033i
$723$	7.72121e6	+	7.72121e6i	0.549338	+	0.549338i
$724$	6.81198e6	−	1.03939e6i	0.482978	−	0.0736940i
$725$	−1.17561e6	+	1.17561e6i	−0.0830653	+	0.0830653i
$726$	−3.51979e6	−	6.95662e6i	−0.247842	−	0.489843i
$727$		−	1.04167e7i		−	0.730960i	−0.930819	−	0.365480i	$-0.880905\pi$
$727$		−	1.04167e7i		−	0.730960i	0.930819	−	0.365480i	$-0.119095\pi$
$728$	−2.80282e6	+	1.67726e7i	−0.196005	+	1.17293i
$729$		−	531441.i		−	0.0370370i
$730$	−2.61411e7	+	1.32264e7i	−1.81558	+	0.918618i
$731$	−924949.	+	924949.i	−0.0640213	+	0.0640213i
$732$	6.73714e6	−	9.16327e6i	0.464727	−	0.632081i
$733$	1.55330e7	+	1.55330e7i	1.06781	+	1.06781i	0.997527	+	0.0702869i	$0.0223915\pi$
$733$	1.55330e7	+	1.55330e7i	1.06781	+	1.06781i	0.0702869	+	0.997527i	$0.477609\pi$
$734$	3.56980e6	−	1.08817e7i	0.244570	−	0.745518i
$735$	−1.72271e7			−1.17623
$736$	−395480.	+	2.79231e7i	−0.0269110	+	1.90007i
$737$	−208061.			−0.0141099
$738$	601685.	−	1.83410e6i	0.0406657	−	0.123960i
$739$	−1.41388e6	−	1.41388e6i	−0.0952362	−	0.0952362i	0.657884	−	0.753120i	$-0.271452\pi$
$739$	−1.41388e6	−	1.41388e6i	−0.0952362	−	0.0952362i	−0.753120	+	0.657884i	$0.771452\pi$
$740$	7.28449e6	−	9.90773e6i	0.489013	−	0.665112i
$741$	8.54672e6	−	8.54672e6i	0.571813	−	0.571813i
$742$	−8.93526e6	+	4.52091e6i	−0.595796	+	0.301451i
$743$		−	2.22949e7i		−	1.48161i	−0.671720	−	0.740805i	$-0.734444\pi$
$743$		−	2.22949e7i		−	1.48161i	0.671720	−	0.740805i	$-0.265556\pi$
$744$	−2.43050e6	−	406154.i	−0.160977	−	0.0269004i
$745$		−	2.99056e7i		−	1.97407i
$746$	7.61019e6	+	1.50410e7i	0.500666	+	0.989532i
$747$	3.75904e6	−	3.75904e6i	0.246476	−	0.246476i
$748$	309052.	−	47156.0i	0.0201966	−	0.00308164i
$749$	−2.19574e7	−	2.19574e7i	−1.43013	−	1.43013i
$750$	−5.58789e6	−	1.83313e6i	−0.362739	−	0.118998i
$751$	−1.95084e7			−1.26218			−0.631090	−	0.775710i	$-0.717392\pi$
$751$	−1.95084e7			−1.26218			−0.631090	+	0.775710i	$0.717392\pi$
$752$	7.01839e6	+	2.24632e7i	0.452577	+	1.44853i
$753$	1.43061e7			0.919461
$754$	−2.80017e6	−	918606.i	−0.179372	−	0.0588438i
$755$	1.10701e7	+	1.10701e7i	0.706778	+	0.706778i
$756$	−748354.	−	4.90458e6i	−0.0476214	−	0.312103i
$757$	−8.40634e6	+	8.40634e6i	−0.533172	+	0.533172i	−0.921515	−	0.388343i	$-0.873048\pi$
$757$	−8.40634e6	+	8.40634e6i	−0.533172	+	0.533172i	0.388343	+	0.921515i	$0.373048\pi$
$758$	−5.19328e6	−	1.02642e7i	−0.328298	−	0.648859i
$759$		−	3.86029e6i		−	0.243229i
$760$	3.01682e7	−	2.15292e7i	1.89459	−	1.35205i
$761$			1.53906e7i			0.963370i	0.876344	+	0.481685i	$0.159975\pi$
$761$			1.53906e7i			0.963370i	−0.876344	+	0.481685i	$0.840025\pi$
$762$	−5.06782e6	+	2.56413e6i	−0.316180	+	0.159975i
$763$	−2.89816e7	+	2.89816e7i	−1.80224	+	1.80224i
$764$	−1.25717e7	−	9.24316e6i	−0.779223	−	0.572911i
$765$	−423521.	−	423521.i	−0.0261651	−	0.0261651i
$766$	7.32364e6	−	2.23245e7i	0.450978	−	1.37471i
$767$	−1.02827e7			−0.631132
$768$	−9.28515e6	−	1.68711e6i	−0.568049	−	0.103215i
$769$	−1.94141e7			−1.18387			−0.591933	−	0.805987i	$-0.701635\pi$
$769$	−1.94141e7			−1.18387			−0.591933	+	0.805987i	$0.701635\pi$
$770$	2.24680e6	−	6.84887e6i	0.136564	−	0.416286i
$771$	−3.72325e6	−	3.72325e6i	−0.225572	−	0.225572i
$772$	−1.52643e7	−	1.12228e7i	−0.921793	−	0.677733i
$773$	1.07542e7	−	1.07542e7i	0.647338	−	0.647338i	−0.305011	−	0.952349i	$-0.598660\pi$
$773$	1.07542e7	−	1.07542e7i	0.647338	−	0.647338i	0.952349	+	0.305011i	$0.0986601\pi$
$774$	−4.87040e6	+	2.46424e6i	−0.292222	+	0.147853i
$775$			2.13216e6i			0.127516i
$776$	−7.37311e6	+	5.26174e6i	−0.439538	+	0.313672i
$777$			1.09234e7i			0.649090i
$778$	−1.56387e6	−	3.09088e6i	−0.0926301	−	0.183077i
$779$	−9.05694e6	+	9.05694e6i	−0.534734	+	0.534734i
$780$	1.29213e6	+	8.46839e6i	0.0760448	+	0.498384i
$781$	3.06947e6	+	3.06947e6i	0.180067	+	0.180067i
$782$	−2.84542e6	−	933450.i	−0.166391	−	0.0545851i
$783$	859800.			0.0501179
$784$	−8.68035e6	−	2.77825e7i	−0.504368	−	1.61429i
$785$	9.29675e6			0.538465
$786$	−3.44698e6	−	1.13080e6i	−0.199014	−	0.0652872i
$787$	1.38920e7	+	1.38920e7i	0.799517	+	0.799517i	0.983019	−	0.183502i	$-0.0587434\pi$
$787$	1.38920e7	+	1.38920e7i	0.799517	+	0.799517i	−0.183502	+	0.983019i	$0.558743\pi$
$788$	2.59781e7	−	3.96380e6i	1.49036	−	0.227403i
$789$	4.45424e6	−	4.45424e6i	0.254731	−	0.254731i
$790$	−1.14253e7	−	2.25812e7i	−0.651326	−	1.28730i
$791$		−	1.27099e7i		−	0.722273i
$792$	1.28669e6	+	215015.i	0.0728890	+	0.0121802i
$793$		−	1.74435e7i		−	0.985031i
$794$	1.88846e7	−	9.55490e6i	1.06306	−	0.537867i
$795$	−3.56701e6	+	3.56701e6i	−0.200164	+	0.200164i
$796$	−981283.	+	1.33465e6i	−0.0548923	+	0.0746597i
$797$	1.02529e7	+	1.02529e7i	0.571744	+	0.571744i	0.932616	−	0.360872i	$-0.117521\pi$
$797$	1.02529e7	+	1.02529e7i	0.571744	+	0.571744i	−0.360872	+	0.932616i	$0.617521\pi$
$798$	−1.02619e7	+	3.12811e7i	−0.570453	+	1.73890i
$799$	−2.52366e6			−0.139851
$800$	−115638.	+	8.16472e6i	−0.00638818	+	0.451041i
$801$	−2.71800e6			−0.149681
$802$	5.37553e6	−	1.63861e7i	0.295111	−	0.899581i
$803$	4.83840e6	+	4.83840e6i	0.264797	+	0.264797i
$804$	−398955.	+	542623.i	−0.0217662	+	0.0296045i
$805$	−4.88215e7	+	4.88215e7i	−2.65535	+	2.65535i
$806$	−3.37228e6	+	1.70625e6i	−0.182846	+	0.0925135i
$807$			4.39542e6i			0.237584i
$808$	−1.21842e6	+	7.29127e6i	−0.0656552	+	0.392893i
$809$			2.12557e7i			1.14184i	0.821006	+	0.570920i	$0.193413\pi$
$809$			2.12557e7i			1.14184i	−0.821006	+	0.570920i	$0.806587\pi$
$810$	−1.12834e6	−	2.23009e6i	−0.0604266	−	0.119429i
$811$	6.43979e6	−	6.43979e6i	0.343811	−	0.343811i	−0.513987	−	0.857798i	$-0.671832\pi$
$811$	6.43979e6	−	6.43979e6i	0.343811	−	0.343811i	0.857798	+	0.513987i	$0.171832\pi$
$812$	7.93495e6	−	1.21074e6i	0.422332	−	0.0644405i
$813$	−1.21540e7	−	1.21540e7i	−0.644901	−	0.644901i
$814$	−2.72909e6	−	895289.i	−0.144363	−	0.0473590i
$815$	2.09354e7			1.10405
$816$	469620.	−	896427.i	0.0246900	−	0.0471291i
$817$	3.62190e7			1.89837
$818$	1.61330e7	+	5.29251e6i	0.843010	+	0.276553i
$819$	−5.38055e6	−	5.38055e6i	−0.280296	−	0.280296i
$820$	−1.36927e6	−	8.97394e6i	−0.0711137	−	0.466067i
$821$	−1.31405e7	+	1.31405e7i	−0.680381	+	0.680381i	−0.960086	−	0.279705i	$-0.909763\pi$
$821$	−1.31405e7	+	1.31405e7i	−0.680381	+	0.680381i	0.279705	+	0.960086i	$0.409763\pi$
$822$	1.88578e6	+	3.72711e6i	0.0973444	+	0.192394i
$823$			1.05317e7i			0.541999i	0.962579	+	0.270999i	$0.0873542\pi$
$823$			1.05317e7i			0.541999i	−0.962579	+	0.270999i	$0.912646\pi$
$824$	1.43355e7	+	2.00878e7i	0.735519	+	1.03066i
$825$		−	1.12875e6i		−	0.0577382i
$826$	2.49906e7	−	1.26443e7i	1.27446	−	0.644830i
$827$	1.72982e7	−	1.72982e7i	0.879505	−	0.879505i	−0.113978	−	0.993483i	$-0.536359\pi$
$827$	1.72982e7	−	1.72982e7i	0.879505	−	0.879505i	0.993483	+	0.113978i	$0.0363594\pi$
$828$	−1.00676e7	−	7.40205e6i	−0.510330	−	0.375212i
$829$	−2.53791e6	−	2.53791e6i	−0.128260	−	0.128260i	0.640063	−	0.768323i	$-0.278908\pi$
$829$	−2.53791e6	−	2.53791e6i	−0.128260	−	0.128260i	−0.768323	+	0.640063i	$0.778908\pi$
$830$	7.79298e6	−	2.37552e7i	0.392652	−	1.19691i
$831$	4.69800e6			0.235999
$832$	−1.30061e7	+	6.35089e6i	−0.651387	+	0.318072i
$833$	3.12127e6			0.155854
$834$	989773.	−	3.01710e6i	0.0492743	−	0.150202i
$835$	7.53336e6	+	7.53336e6i	0.373915	+	0.373915i
$836$	−6.97417e6	−	5.12764e6i	−0.345125	−	0.253748i
$837$	779690.	−	779690.i	0.0384688	−	0.0384688i
$838$	3.35092e7	−	1.69544e7i	1.64837	−	0.834013i
$839$			9.41570e6i			0.461794i	0.972978	+	0.230897i	$0.0741660\pi$
$839$			9.41570e6i			0.461794i	−0.972978	+	0.230897i	$0.925834\pi$
$840$	−1.35536e7	−	1.89922e7i	−0.662760	−	0.928705i
$841$		−	1.91201e7i		−	0.932181i
$842$	−1.53900e6	−	3.04172e6i	−0.0748098	−	0.147856i
$843$	4.22185e6	−	4.22185e6i	0.204613	−	0.204613i
$844$	−1.44439e6	−	9.46627e6i	−0.0697956	−	0.457428i
$845$	−8.38943e6	−	8.38943e6i	−0.404195	−	0.404195i
$846$	−1.00060e7	−	3.28252e6i	−0.480658	−	0.157682i
$847$	3.25685e7			1.55987
$848$	−7.54994e6	−	3.95526e6i	−0.360540	−	0.188880i
$849$	1.60866e7			0.765938
$850$	−832000.	−	272941.i	−0.0394981	−	0.0129575i
$851$	1.94541e7	+	1.94541e7i	0.920845	+	0.920845i
$852$	1.38908e7	−	2.11949e6i	0.655584	−	0.100031i
$853$	−4.52864e6	+	4.52864e6i	−0.213106	+	0.213106i	−0.805585	−	0.592480i	$-0.798149\pi$
$853$	−4.52864e6	+	4.52864e6i	−0.213106	+	0.213106i	0.592480	+	0.805585i	$0.298149\pi$
$854$	2.14496e7	+	4.23937e7i	1.00641	+	1.98910i
$855$			1.65842e7i			0.775852i
$856$	4.35624e6	−	2.60686e7i	0.203202	−	1.21600i
$857$			2.27344e7i			1.05738i	0.848815	+	0.528690i	$0.177317\pi$
$857$			2.27344e7i			1.05738i	−0.848815	+	0.528690i	$0.822683\pi$
$858$	1.78527e6	−	903278.i	0.0827913	−	0.0418893i
$859$	3.66186e6	−	3.66186e6i	0.169324	−	0.169324i	−0.617358	−	0.786682i	$-0.711797\pi$
$859$	3.66186e6	−	3.66186e6i	0.169324	−	0.169324i	0.786682	+	0.617358i	$0.211797\pi$
$860$	−1.52057e7	+	2.06814e7i	−0.701067	+	0.953530i
$861$	5.70175e6	+	5.70175e6i	0.262120	+	0.262120i
$862$	−4.23984e6	+	1.29242e7i	−0.194349	+	0.592428i
$863$	−1.91352e7			−0.874595			−0.437297	−	0.899317i	$-0.644064\pi$
$863$	−1.91352e7			−0.874595			−0.437297	+	0.899317i	$0.644064\pi$
$864$	3.02797e6	−	2.94340e6i	0.137996	−	0.134142i
$865$	−2.97449e7			−1.35167
$866$	−666793.	+	2.03257e6i	−0.0302132	+	0.0920982i
$867$	−8.95918e6	−	8.95918e6i	−0.404781	−	0.404781i
$868$	6.09770e6	−	8.29356e6i	0.274705	−	0.373630i
$869$	−4.17952e6	+	4.17952e6i	−0.187749	+	0.187749i
$870$	3.60798e6	−	1.82550e6i	0.161609	−	0.0817683i
$871$			1.03295e6i			0.0461355i
$872$	−3.44081e7	−	5.74982e6i	−1.53239	−	0.256073i
$873$		−	4.05318e6i		−	0.179995i
$874$	3.74342e7	+	7.39861e7i	1.65764	+	3.27621i
$875$	1.73713e7	−	1.73713e7i	0.767030	−	0.767030i
$876$	2.18961e7	−	3.34096e6i	0.964065	−	0.147100i
$877$	−2.05191e6	−	2.05191e6i	−0.0900862	−	0.0900862i	0.660628	−	0.750714i	$-0.270290\pi$
$877$	−2.05191e6	−	2.05191e6i	−0.0900862	−	0.0900862i	−0.750714	+	0.660628i	$0.770290\pi$
$878$	5.82534e6	+	1.91103e6i	0.255026	+	0.0836624i
$879$	−1.09922e7			−0.479858
$880$	5.85587e6	−	1.82960e6i	0.254909	−	0.0796435i
$881$	−2.16856e7			−0.941310			−0.470655	−	0.882317i	$-0.655982\pi$
$881$	−2.16856e7			−0.941310			−0.470655	+	0.882317i	$0.655982\pi$
$882$	1.23755e7	+	4.05983e6i	0.535662	+	0.175726i
$883$	−1.82709e7	−	1.82709e7i	−0.788603	−	0.788603i	0.192662	−	0.981265i	$-0.438288\pi$
$883$	−1.82709e7	−	1.82709e7i	−0.788603	−	0.788603i	−0.981265	+	0.192662i	$0.938288\pi$
$884$	−234113.	−	1.53434e6i	−0.0100762	−	0.0660374i
$885$	9.97639e6	−	9.97639e6i	0.428169	−	0.428169i
$886$	−8.14972e6	−	1.61074e7i	−0.348786	−	0.689350i
$887$		−	2.66029e7i		−	1.13532i	−0.823262	−	0.567661i	$-0.807848\pi$
$887$		−	2.66029e7i		−	1.13532i	0.823262	−	0.567661i	$-0.192152\pi$
$888$	−7.56790e6	+	5.40075e6i	−0.322065	+	0.229838i
$889$		−	2.37258e7i		−	1.00685i
$890$	−1.14055e7	+	5.77078e6i	−0.482659	+	0.244208i
$891$	−412763.	+	412763.i	−0.0174183	+	0.0174183i
$892$	1.97577e7	+	1.45266e7i	0.831429	+	0.611294i
$893$	4.94106e7	+	4.94106e7i	2.07344	+	2.07344i
$894$	−7.04773e6	+	2.14834e7i	−0.294921	+	0.899000i
$895$	6.76482e6			0.282292
$896$	2.37999e7	−	3.14280e7i	0.990386	−	1.30782i
$897$	−1.91650e7			−0.795295
$898$	7.07662e6	−	2.15715e7i	0.292843	−	0.892668i
$899$	1.26143e6	+	1.26143e6i	0.0520553	+	0.0520553i
$900$	−2.94377e6	−	2.16436e6i	−0.121143	−	0.0890683i
$901$	646284.	−	646284.i	0.0265223	−	0.0265223i
$902$	−1.89184e6	+	957202.i	−0.0774227	+	0.0391730i
$903$		−	2.28015e7i		−	0.930560i
$904$	8.80564e6	−	6.28405e6i	0.358377	−	0.255752i
$905$			1.45008e7i			0.588534i
$906$	−5.34362e6	−	1.05613e7i	−0.216279	−	0.427461i
$907$	−2.50879e7	+	2.50879e7i	−1.01262	+	1.01262i	−0.0126984	+	0.999919i	$0.504042\pi$
$907$	−2.50879e7	+	2.50879e7i	−1.01262	+	1.01262i	−0.999919	+	0.0126984i	$0.995958\pi$
$908$	−126099.	−	826432.i	−0.00507572	−	0.0332654i
$909$	−2.33899e6	−	2.33899e6i	−0.0938900	−	0.0938900i
$910$	−3.40023e7	−	1.11546e7i	−1.36114	−	0.446529i
$911$	7.99187e6			0.319045			0.159523	−	0.987194i	$-0.449004\pi$
$911$	7.99187e6			0.319045			0.159523	+	0.987194i	$0.449004\pi$
$912$	−2.67457e7	+	8.35641e6i	−1.06480	+	0.332685i
$913$	−5.83918e6			−0.231833
$914$	−3.58029e6	−	1.17453e6i	−0.141760	−	0.0465048i
$915$	1.69238e7	+	1.69238e7i	0.668259	+	0.668259i
$916$	−1.45586e7	+	2.22139e6i	−0.573298	+	0.0874753i
$917$	1.07158e7	−	1.07158e7i	0.420824	−	0.420824i
$918$	204437.	+	404056.i	0.00800670	+	0.0158247i
$919$			1.38178e7i			0.539695i	0.962903	+	0.269848i	$0.0869733\pi$
$919$			1.38178e7i			0.539695i	−0.962903	+	0.269848i	$0.913027\pi$
$920$	−5.79627e7	−	9.68596e6i	−2.25776	−	0.377288i
$921$			1.14454e7i			0.444614i
$922$	−1.45481e7	+	7.36079e6i	−0.563610	+	0.285166i
$923$	1.52388e7	−	1.52388e7i	0.588772	−	0.588772i
$924$	−3.22808e6	+	4.39056e6i	−0.124384	+	0.169176i
$925$	5.68837e6	+	5.68837e6i	0.218592	+	0.218592i
$926$	6.80617e6	−	2.07471e7i	0.260841	−	0.795115i
$927$	−1.10428e7			−0.422065
$928$	4.76202e6	+	4.89885e6i	0.181519	+	0.186734i
$929$	−2.41882e7			−0.919526			−0.459763	−	0.888042i	$-0.652066\pi$
$929$	−2.41882e7			−0.919526			−0.459763	+	0.888042i	$0.652066\pi$
$930$	1.61640e6	−	4.92724e6i	0.0612832	−	0.186808i
$931$	−6.11111e7	−	6.11111e7i	−2.31071	−	2.31071i
$932$	−3.34391e6	+	4.54809e6i	−0.126100	+	0.171510i
$933$	−2.05392e7	+	2.05392e7i	−0.772465	+	0.772465i
$934$	3.05231e7	−	1.54435e7i	1.14488	−	0.579269i
$935$			657886.i			0.0246106i
$936$	1.06748e6	−	6.38798e6i	0.0398262	−	0.238327i
$937$			3.49441e7i			1.30024i	0.759831	+	0.650121i	$0.225282\pi$
$937$			3.49441e7i			1.30024i	−0.759831	+	0.650121i	$0.774718\pi$
$938$	−1.27019e6	−	2.51043e6i	−0.0471368	−	0.0931626i
$939$	−3.46994e6	+	3.46994e6i	−0.128428	+	0.128428i
$940$	−4.89578e7	+	7.47010e6i	−1.80718	+	0.275744i
$941$	−2.05724e7	−	2.05724e7i	−0.757376	−	0.757376i	0.218468	−	0.975844i	$-0.429894\pi$
$941$	−2.05724e7	−	2.05724e7i	−0.757376	−	0.757376i	−0.975844	+	0.218468i	$0.929894\pi$
$942$	−6.67854e6	−	2.19092e6i	−0.245219	−	0.0804452i
$943$	2.03091e7			0.743724
$944$	2.11161e7	+	1.10623e7i	0.771228	+	0.404031i
$945$	1.04405e7			0.380313
$946$	5.69671e6	+	1.86883e6i	0.206965	+	0.0678956i
$947$	1.36807e7	+	1.36807e7i	0.495717	+	0.495717i	0.910102	−	0.414385i	$-0.136003\pi$
$947$	1.36807e7	+	1.36807e7i	0.495717	+	0.495717i	−0.414385	+	0.910102i	$0.636003\pi$
$948$	2.88600e6	+	1.89143e7i	0.104298	+	0.683549i
$949$	2.40210e7	−	2.40210e7i	0.865816	−	0.865816i
$950$	1.09458e7	+	2.16335e7i	0.393493	+	0.777712i
$951$		−	626887.i		−	0.0224770i
$952$	2.45569e6	+	3.44109e6i	0.0878177	+	0.123056i
$953$		−	2.91781e7i		−	1.04070i	−0.853954	−	0.520348i	$-0.825802\pi$
$953$		−	2.91781e7i		−	1.04070i	0.853954	−	0.520348i	$-0.174198\pi$
$954$	3.40307e6	−	1.72182e6i	0.121060	−	0.0612517i
$955$	2.32189e7	−	2.32189e7i	0.823823	−	0.823823i
$956$	−1.28993e7	−	9.48403e6i	−0.456481	−	0.335620i
$957$	−667794.	−	667794.i	−0.0235702	−	0.0235702i
$958$	−7.10794e6	+	2.16670e7i	−0.250225	+	0.762754i
$959$	−1.74490e7			−0.612667
$960$	6.45695e6	−	1.87803e7i	0.226125	−	0.657695i
$961$	−2.63413e7			−0.920088
$962$	−4.44480e6	+	1.35490e7i	−0.154851	+	0.472030i
$963$	8.36263e6	+	8.36263e6i	0.290588	+	0.290588i
$964$	−3.12800e7	−	2.29981e7i	−1.08411	−	0.797076i
$965$	2.81919e7	−	2.81919e7i	0.974553	−	0.974553i
$966$	4.65776e7	−	2.35665e7i	1.60596	−	0.812556i
$967$		−	4.91685e7i		−	1.69091i	−0.534046	−	0.845456i	$-0.679329\pi$
$967$		−	4.91685e7i		−	1.69091i	0.534046	−	0.845456i	$-0.320671\pi$
$968$	1.61025e7	+	2.25640e7i	0.552339	+	0.773975i
$969$		−	3.00479e6i		−	0.102803i
$970$	−8.60561e6	−	1.70084e7i	−0.293665	−	0.580408i
$971$	−3.06265e7	+	3.06265e7i	−1.04244	+	1.04244i	−0.0433762	+	0.999059i	$0.513811\pi$
$971$	−3.06265e7	+	3.06265e7i	−1.04244	+	1.04244i	−0.999059	+	0.0433762i	$0.986189\pi$
$972$	285016.	+	1.86795e6i	0.00967619	+	0.0634161i
$973$	9.37940e6	+	9.37940e6i	0.317609	+	0.317609i
$974$	−4.33144e7	−	1.42095e7i	−1.46297	−	0.479932i
$975$	−5.60385e6			−0.188788
$976$	−1.87659e7	+	3.58209e7i	−0.630586	+	1.20368i
$977$	−5.92051e6			−0.198437			−0.0992184	−	0.995066i	$-0.531634\pi$
$977$	−5.92051e6			−0.198437			−0.0992184	+	0.995066i	$0.531634\pi$
$978$	−1.50395e7	−	4.93375e6i	−0.502788	−	0.164942i
$979$	2.11103e6	+	2.11103e6i	0.0703943	+	0.0703943i
$980$	6.05511e7	−	9.23904e6i	2.01399	−	0.307299i
$981$	1.10379e7	−	1.10379e7i	0.366196	−	0.366196i
$982$	1.23193e7	+	2.43482e7i	0.407668	+	0.805727i
$983$			1.23884e7i			0.408913i	0.978876	+	0.204457i	$0.0655428\pi$
$983$			1.23884e7i			0.408913i	−0.978876	+	0.204457i	$0.934457\pi$
$984$	−1.13120e6	+	6.76933e6i	−0.0372437	+	0.222873i
$985$			5.53001e7i			1.81608i
$986$	−653708.	+	330752.i	−0.0214137	+	0.0108345i
$987$	3.11062e7	−	3.11062e7i	1.01638	−	1.01638i
$988$	−2.54570e7	+	3.46243e7i	−0.829687	+	1.12847i
$989$	−4.06085e7	−	4.06085e7i	−1.32016	−	1.32016i
$990$	−855711.	+	2.60845e6i	−0.0277485	+	0.0845851i
$991$	4.86282e7			1.57291			0.786455	−	0.617648i	$-0.211914\pi$
$991$	4.86282e7			1.57291			0.786455	+	0.617648i	$0.211914\pi$
$992$	8.76074e6	+	124080.i	0.282658	+	0.00400334i
$993$	−2.97577e7			−0.957694
$994$	−1.82970e7	+	5.57743e7i	−0.587372	+	1.79047i
$995$	−2.46499e6	−	2.46499e6i	−0.0789329	−	0.0789329i
$996$	−1.11965e7	+	1.52286e7i	−0.357631	+	0.486419i
$997$	6.59465e6	−	6.59465e6i	0.210113	−	0.210113i	−0.594202	−	0.804316i	$-0.702532\pi$
$997$	6.59465e6	−	6.59465e6i	0.210113	−	0.210113i	0.804316	+	0.594202i	$0.202532\pi$
$998$	4.40837e7	−	2.23047e7i	1.40104	−	0.708876i
$999$		−	4.16026e6i		−	0.131888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.j.a.13.9	✓	40
3.2	odd	2		144.6.k.c.109.12		40
4.3	odd	2		192.6.j.a.145.9		40
8.3	odd	2		384.6.j.b.289.12		40
8.5	even	2		384.6.j.a.289.9		40
12.11	even	2		576.6.k.c.145.3		40
16.3	odd	4		384.6.j.b.97.12		40
16.5	even	4	inner	48.6.j.a.37.9	yes	40
16.11	odd	4		192.6.j.a.49.9		40
16.13	even	4		384.6.j.a.97.9		40
48.5	odd	4		144.6.k.c.37.12		40
48.11	even	4		576.6.k.c.433.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.j.a.13.9	✓	40	1.1	even	1	trivial
48.6.j.a.37.9	yes	40	16.5	even	4	inner
144.6.k.c.37.12		40	48.5	odd	4
144.6.k.c.109.12		40	3.2	odd	2
192.6.j.a.49.9		40	16.11	odd	4
192.6.j.a.145.9		40	4.3	odd	2
384.6.j.a.97.9		40	16.13	even	4
384.6.j.a.289.9		40	8.5	even	2
384.6.j.b.97.12		40	16.3	odd	4
384.6.j.b.289.12		40	8.3	odd	2
576.6.k.c.145.3		40	12.11	even	2
576.6.k.c.433.3		40	48.11	even	4

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76330 + 5.37502i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-25.7816 - 18.9555i) q^{4} +(47.6164 - 47.6164i) q^{5} +(-45.4279 + 22.9848i) q^{6} -212.678i q^{7} +(147.347 - 105.152i) q^{8} +81.0000i q^{9} +O(q^{10})\)	\(q+(-1.76330 + 5.37502i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-25.7816 - 18.9555i) q^{4} +(47.6164 - 47.6164i) q^{5} +(-45.4279 + 22.9848i) q^{6} -212.678i q^{7} +(147.347 - 105.152i) q^{8} +81.0000i q^{9} +(171.977 + 339.901i) q^{10} +(62.9116 - 62.9116i) q^{11} +(-43.4410 - 284.705i) q^{12} +(-312.334 - 312.334i) q^{13} +(1143.15 + 375.014i) q^{14} +606.058 q^{15} +(305.379 + 977.404i) q^{16} -109.808 q^{17} +(-435.376 - 142.827i) q^{18} +(2149.92 + 2149.92i) q^{19} +(-2130.22 + 325.034i) q^{20} +(1353.47 - 1353.47i) q^{21} +(227.219 + 449.082i) q^{22} -4820.95i q^{23} +(1606.89 + 268.523i) q^{24} -1409.65i q^{25} +(2229.54 - 1128.06i) q^{26} +(-515.481 + 515.481i) q^{27} +(-4031.41 + 5483.17i) q^{28} +(-833.978 - 833.978i) q^{29} +(-1068.66 + 3257.57i) q^{30} -1512.55 q^{31} +(-5792.04 - 82.0337i) q^{32} +800.733 q^{33} +(193.624 - 590.219i) q^{34} +(-10126.9 - 10126.9i) q^{35} +(1535.39 - 2088.31i) q^{36} +(-4035.32 + 4035.32i) q^{37} +(-15346.8 + 7764.91i) q^{38} -3975.36i q^{39} +(2009.14 - 12023.1i) q^{40} +4212.68i q^{41} +(4888.36 + 9661.51i) q^{42} +(8423.34 - 8423.34i) q^{43} +(-2814.48 + 429.440i) q^{44} +(3856.93 + 3856.93i) q^{45} +(25912.7 + 8500.75i) q^{46} +22982.5 q^{47} +(-4276.74 + 8163.59i) q^{48} -28424.8 q^{49} +(7576.86 + 2485.62i) q^{50} +(-698.813 - 698.813i) q^{51} +(2132.02 + 13972.9i) q^{52} +(-5885.59 + 5885.59i) q^{53} +(-1861.77 - 3679.66i) q^{54} -5991.25i q^{55} +(-22363.5 - 31337.3i) q^{56} +27364.0i q^{57} +(5953.20 - 3012.10i) q^{58} +(16461.1 - 16461.1i) q^{59} +(-15625.1 - 11488.1i) q^{60} +(27924.4 + 27924.4i) q^{61} +(2667.07 - 8129.97i) q^{62} +17226.9 q^{63} +(10654.0 - 30987.6i) q^{64} -29744.5 q^{65} +(-1411.93 + 4303.95i) q^{66} +(-1653.60 - 1653.60i) q^{67} +(2831.02 + 2081.46i) q^{68} +(30680.3 - 30680.3i) q^{69} +(72289.3 - 36575.7i) q^{70} +48790.2i q^{71} +(8517.33 + 11935.1i) q^{72} +76908.0i q^{73} +(-14574.4 - 28805.4i) q^{74} +(8970.93 - 8970.93i) q^{75} +(-14675.6 - 96181.1i) q^{76} +(-13379.9 - 13379.9i) q^{77} +(21367.6 + 7009.74i) q^{78} -66434.8 q^{79} +(61081.6 + 31999.4i) q^{80} -6561.00 q^{81} +(-22643.2 - 7428.21i) q^{82} +(-46407.9 - 46407.9i) q^{83} +(-60550.4 + 9238.93i) q^{84} +(-5228.66 + 5228.66i) q^{85} +(30422.7 + 60128.4i) q^{86} -10614.8i q^{87} +(2654.51 - 15885.1i) q^{88} +33555.5i q^{89} +(-27532.0 + 13930.1i) q^{90} +(-66426.5 + 66426.5i) q^{91} +(-91383.4 + 124292. i) q^{92} +(-9625.80 - 9625.80i) q^{93} +(-40525.0 + 123531. i) q^{94} +204743. q^{95} +(-36338.2 - 37382.4i) q^{96} -50039.3 q^{97} +(50121.3 - 152784. i) q^{98} +(5095.84 + 5095.84i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) \) 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more