LMFDB - Embedded newform 48.6.j.a.13.6

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			13.6
Character	$\chi$	$=$	48.13
Dual form			48.6.j.a.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.74446 - 4.24017i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-3.95807 + 31.7543i) q^{4} +(-41.3210 + 41.3210i) q^{5} +(3.15468 - 50.8139i) q^{6} -215.468i q^{7} +(149.464 - 102.120i) q^{8} +81.0000i q^{9} +O(q^{10})$	\(q+(-3.74446 - 4.24017i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-3.95807 + 31.7543i) q^{4} +(-41.3210 + 41.3210i) q^{5} +(3.15468 - 50.8139i) q^{6} -215.468i q^{7} +(149.464 - 102.120i) q^{8} +81.0000i q^{9} +(329.933 + 20.4833i) q^{10} +(275.819 - 275.819i) q^{11} +(-227.272 + 176.894i) q^{12} +(-728.733 - 728.733i) q^{13} +(-913.622 + 806.812i) q^{14} -525.930 q^{15} +(-992.667 - 251.371i) q^{16} +1323.82 q^{17} +(343.454 - 303.301i) q^{18} +(-1676.04 - 1676.04i) q^{19} +(-1148.57 - 1475.67i) q^{20} +(1371.23 - 1371.23i) q^{21} +(-2202.31 - 136.726i) q^{22} +1361.94i q^{23} +(1601.07 + 301.299i) q^{24} -289.847i q^{25} +(-361.241 + 5818.66i) q^{26} +(-515.481 + 515.481i) q^{27} +(6842.04 + 852.838i) q^{28} +(-4950.18 - 4950.18i) q^{29} +(1969.32 + 2230.03i) q^{30} +6207.14 q^{31} +(2651.15 + 5150.33i) q^{32} +3510.60 q^{33} +(-4957.00 - 5613.24i) q^{34} +(8903.36 + 8903.36i) q^{35} +(-2572.10 - 320.603i) q^{36} +(4052.97 - 4052.97i) q^{37} +(-830.831 + 13382.5i) q^{38} -9275.25i q^{39} +(-1956.33 + 10395.7i) q^{40} -4429.64i q^{41} +(-10948.8 - 679.734i) q^{42} +(968.730 - 968.730i) q^{43} +(7666.72 + 9850.13i) q^{44} +(-3347.00 - 3347.00i) q^{45} +(5774.87 - 5099.74i) q^{46} -7741.43 q^{47} +(-4717.58 - 7917.01i) q^{48} -29619.6 q^{49} +(-1229.00 + 1085.32i) q^{50} +(8424.76 + 8424.76i) q^{51} +(26024.7 - 20256.0i) q^{52} +(-7480.21 + 7480.21i) q^{53} +(4115.92 + 255.529i) q^{54} +22794.2i q^{55} +(-22003.5 - 32204.8i) q^{56} -21332.5i q^{57} +(-2453.86 + 39525.3i) q^{58} +(-9193.55 + 9193.55i) q^{59} +(2081.67 - 16700.5i) q^{60} +(-18345.5 - 18345.5i) q^{61} +(-23242.4 - 26319.3i) q^{62} +17452.9 q^{63} +(11911.1 - 30526.5i) q^{64} +60223.9 q^{65} +(-13145.3 - 14885.5i) q^{66} +(20739.8 + 20739.8i) q^{67} +(-5239.78 + 42037.1i) q^{68} +(-8667.35 + 8667.35i) q^{69} +(4413.49 - 71090.0i) q^{70} +42287.5i q^{71} +(8271.69 + 12106.6i) q^{72} +28735.5i q^{73} +(-32361.4 - 2009.10i) q^{74} +(1844.58 - 1844.58i) q^{75} +(59855.3 - 46587.5i) q^{76} +(-59430.2 - 59430.2i) q^{77} +(-39328.6 + 34730.8i) q^{78} -25381.3 q^{79} +(51404.9 - 30631.1i) q^{80} -6561.00 q^{81} +(-18782.4 + 16586.6i) q^{82} +(18048.3 + 18048.3i) q^{83} +(38115.0 + 48969.9i) q^{84} +(-54701.7 + 54701.7i) q^{85} +(-7734.95 - 480.210i) q^{86} -63005.5i q^{87} +(13058.5 - 69391.6i) q^{88} -21155.1i q^{89} +(-1659.14 + 26724.5i) q^{90} +(-157019. + 157019. i) q^{91} +(-43247.5 - 5390.66i) q^{92} +(39502.0 + 39502.0i) q^{93} +(28987.5 + 32825.0i) q^{94} +138511. q^{95} +(-15904.7 + 49648.3i) q^{96} +85767.2 q^{97} +(110909. + 125592. i) q^{98} +(22341.3 + 22341.3i) 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 $

$2$	−3.74446	−	4.24017i	−0.661933	−	0.749563i
$2$	−3.74446	−	4.24017i	−0.661933	−	0.749563i
$3$	6.36396	+	6.36396i	0.408248	+	0.408248i
$3$	6.36396	+	6.36396i	0.408248	+	0.408248i
$4$	−3.95807	+	31.7543i	−0.123690	+	0.992321i
$5$	−41.3210	+	41.3210i	−0.739172	+	0.739172i	−0.972418	−	0.233246i	$-0.925065\pi$
$5$	−41.3210	+	41.3210i	−0.739172	+	0.739172i	0.233246	+	0.972418i	$0.425065\pi$
$6$	3.15468	−	50.8139i	0.0357749	−	0.576241i
$7$		−	215.468i		−	1.66203i	−0.556252	−	0.831014i	$-0.687761\pi$
$7$		−	215.468i		−	1.66203i	0.556252	−	0.831014i	$-0.312239\pi$
$8$	149.464	−	102.120i	0.825681	−	0.564137i
$9$			81.0000i			0.333333i
$10$	329.933	+	20.4833i	1.04334	+	0.0647738i
$11$	275.819	−	275.819i	0.687293	−	0.687293i	−0.274340	−	0.961633i	$-0.588459\pi$
$11$	275.819	−	275.819i	0.687293	−	0.687293i	0.961633	+	0.274340i	$0.0884592\pi$
$12$	−227.272	+	176.894i	−0.455609	+	0.354617i
$13$	−728.733	−	728.733i	−1.19594	−	1.19594i	−0.975371	−	0.220570i	$-0.929208\pi$
$13$	−728.733	−	728.733i	−1.19594	−	1.19594i	−0.220570	−	0.975371i	$-0.570792\pi$
$14$	−913.622	+	806.812i	−1.24579	+	1.10015i
$15$	−525.930			−0.603532
$16$	−992.667	−	251.371i	−0.969402	−	0.245480i
$17$	1323.82			1.11098			0.555492	−	0.831522i	$-0.312530\pi$
$17$	1323.82			1.11098			0.555492	+	0.831522i	$0.312530\pi$
$18$	343.454	−	303.301i	0.249854	−	0.220644i
$19$	−1676.04	−	1676.04i	−1.06512	−	1.06512i	−0.997726	−	0.0673977i	$-0.978530\pi$
$19$	−1676.04	−	1676.04i	−1.06512	−	1.06512i	−0.0673977	−	0.997726i	$-0.521470\pi$
$20$	−1148.57	−	1475.67i	−0.642068	−	0.824924i
$21$	1371.23	−	1371.23i	0.678520	−	0.678520i
$22$	−2202.31	−	136.726i	−0.970112	−	0.0602276i
$23$			1361.94i			0.536833i	0.963303	+	0.268417i	$0.0865004\pi$
$23$			1361.94i			0.536833i	−0.963303	+	0.268417i	$0.913500\pi$
$24$	1601.07	+	301.299i	0.567391	+	0.106775i
$25$		−	289.847i		−	0.0927511i
$26$	−361.241	+	5818.66i	−0.104800	+	1.68807i
$27$	−515.481	+	515.481i	−0.136083	+	0.136083i
$28$	6842.04	+	852.838i	1.64926	+	0.205575i
$29$	−4950.18	−	4950.18i	−1.09301	−	1.09301i	−0.995205	−	0.0978095i	$-0.968816\pi$
$29$	−4950.18	−	4950.18i	−1.09301	−	1.09301i	−0.0978095	−	0.995205i	$-0.531184\pi$
$30$	1969.32	+	2230.03i	0.399497	+	0.452385i
$31$	6207.14			1.16008			0.580039	−	0.814589i	$-0.303037\pi$
$31$	6207.14			1.16008			0.580039	+	0.814589i	$0.303037\pi$
$32$	2651.15	+	5150.33i	0.457677	+	0.889119i
$33$	3510.60			0.561173
$34$	−4957.00	−	5613.24i	−0.735397	−	0.832753i
$35$	8903.36	+	8903.36i	1.22852	+	1.22852i
$36$	−2572.10	−	320.603i	−0.330774	−	0.0412299i
$37$	4052.97	−	4052.97i	0.486709	−	0.486709i	−0.420557	−	0.907266i	$-0.638165\pi$
$37$	4052.97	−	4052.97i	0.486709	−	0.486709i	0.907266	+	0.420557i	$0.138165\pi$
$38$	−830.831	+	13382.5i	−0.0933369	+	1.50342i
$39$		−	9275.25i		−	0.976482i
$40$	−1956.33	+	10395.7i	−0.193326	+	1.02731i
$41$		−	4429.64i		−	0.411537i	−0.978601	−	0.205768i	$-0.934031\pi$
$41$		−	4429.64i		−	0.411537i	0.978601	−	0.205768i	$-0.0659693\pi$
$42$	−10948.8	−	679.734i	−0.957728	−	0.0594588i
$43$	968.730	−	968.730i	0.0798972	−	0.0798972i	−0.666029	−	0.745926i	$-0.732007\pi$
$43$	968.730	−	968.730i	0.0798972	−	0.0798972i	0.745926	+	0.666029i	$0.232007\pi$
$44$	7666.72	+	9850.13i	0.597005	+	0.767027i
$45$	−3347.00	−	3347.00i	−0.246391	−	0.246391i
$46$	5774.87	−	5099.74i	0.402390	−	0.355348i
$47$	−7741.43			−0.511183			−0.255592	−	0.966785i	$-0.582270\pi$
$47$	−7741.43			−0.511183			−0.255592	+	0.966785i	$0.582270\pi$
$48$	−4717.58	−	7917.01i	−0.295540	−	0.495973i
$49$	−29619.6			−1.76234
$50$	−1229.00	+	1085.32i	−0.0695228	+	0.0613950i
$51$	8424.76	+	8424.76i	0.453557	+	0.453557i
$52$	26024.7	−	20256.0i	1.33468	−	1.03883i
$53$	−7480.21	+	7480.21i	−0.365784	+	0.365784i	−0.865937	−	0.500153i	$-0.833277\pi$
$53$	−7480.21	+	7480.21i	−0.365784	+	0.365784i	0.500153	+	0.865937i	$0.333277\pi$
$54$	4115.92	+	255.529i	0.192080	+	0.0119250i
$55$			22794.2i			1.01606i
$56$	−22003.5	−	32204.8i	−0.937611	−	1.37231i
$57$		−	21332.5i		−	0.869670i
$58$	−2453.86	+	39525.3i	−0.0957810	+	1.54279i
$59$	−9193.55	+	9193.55i	−0.343837	+	0.343837i	−0.857808	−	0.513970i	$-0.828174\pi$
$59$	−9193.55	+	9193.55i	−0.343837	+	0.343837i	0.513970	+	0.857808i	$0.328174\pi$
$60$	2081.67	−	16700.5i	0.0746506	−	0.598897i
$61$	−18345.5	−	18345.5i	−0.631254	−	0.631254i	0.317129	−	0.948382i	$-0.397281\pi$
$61$	−18345.5	−	18345.5i	−0.631254	−	0.631254i	−0.948382	+	0.317129i	$0.897281\pi$
$62$	−23242.4	−	26319.3i	−0.767894	−	0.869552i
$63$	17452.9			0.554009
$64$	11911.1	−	30526.5i	0.363499	−	0.931594i
$65$	60223.9			1.76801
$66$	−13145.3	−	14885.5i	−0.371459	−	0.420634i
$67$	20739.8	+	20739.8i	0.564440	+	0.564440i	0.930565	−	0.366126i	$-0.119316\pi$
$67$	20739.8	+	20739.8i	0.564440	+	0.564440i	−0.366126	+	0.930565i	$0.619316\pi$
$68$	−5239.78	+	42037.1i	−0.137417	+	1.10245i
$69$	−8667.35	+	8667.35i	−0.219161	+	0.219161i
$70$	4413.49	−	71090.0i	0.107656	−	1.73406i
$71$			42287.5i			0.995557i	0.867304	+	0.497779i	$0.165851\pi$
$71$			42287.5i			0.995557i	−0.867304	+	0.497779i	$0.834149\pi$
$72$	8271.69	+	12106.6i	0.188046	+	0.275227i
$73$			28735.5i			0.631120i	0.948906	+	0.315560i	$0.102192\pi$
$73$			28735.5i			0.631120i	−0.948906	+	0.315560i	$0.897808\pi$
$74$	−32361.4	−	2009.10i	−0.686987	−	0.0426503i
$75$	1844.58	−	1844.58i	0.0378655	−	0.0378655i
$76$	59855.3	−	46587.5i	1.18869	−	0.925200i
$77$	−59430.2	−	59430.2i	−1.14230	−	1.14230i
$78$	−39328.6	+	34730.8i	−0.731935	+	0.646366i
$79$	−25381.3			−0.457557			−0.228779	−	0.973478i	$-0.573473\pi$
$79$	−25381.3			−0.457557			−0.228779	+	0.973478i	$0.573473\pi$
$80$	51404.9	−	30631.1i	0.898007	−	0.535103i
$81$	−6561.00			−0.111111
$82$	−18782.4	+	16586.6i	−0.308473	+	0.272410i
$83$	18048.3	+	18048.3i	0.287568	+	0.287568i	0.836118	−	0.548550i	$-0.184820\pi$
$83$	18048.3	+	18048.3i	0.287568	+	0.287568i	−0.548550	+	0.836118i	$0.684820\pi$
$84$	38115.0	+	48969.9i	0.589384	+	0.757235i
$85$	−54701.7	+	54701.7i	−0.821209	+	0.821209i
$86$	−7734.95	−	480.210i	−0.112775	−	0.00700140i
$87$		−	63005.5i		−	0.892443i
$88$	13058.5	−	69391.6i	0.179758	−	0.955213i
$89$		−	21155.1i		−	0.283100i	−0.989931	−	0.141550i	$-0.954791\pi$
$89$		−	21155.1i		−	0.283100i	0.989931	−	0.141550i	$-0.0452086\pi$
$90$	−1659.14	+	26724.5i	−0.0215913	+	0.347780i
$91$	−157019.	+	157019.i	−1.98769	+	1.98769i
$92$	−43247.5	−	5390.66i	−0.532711	−	0.0664007i
$93$	39502.0	+	39502.0i	0.473600	+	0.473600i
$94$	28987.5	+	32825.0i	0.338369	+	0.383164i
$95$	138511.			1.57462
$96$	−15904.7	+	49648.3i	−0.176136	+	0.549827i
$97$	85767.2			0.925533			0.462766	−	0.886480i	$-0.346857\pi$
$97$	85767.2			0.925533			0.462766	+	0.886480i	$0.346857\pi$
$98$	110909.	+	125592.i	1.16655	+	1.32098i
$99$	22341.3	+	22341.3i	0.229098	+	0.229098i
$100$	9203.89	+	1147.23i	0.0920389	+	0.0114723i
$101$	60061.4	−	60061.4i	0.585858	−	0.585858i	−0.350649	−	0.936507i	$-0.614039\pi$
$101$	60061.4	−	60061.4i	0.585858	−	0.585858i	0.936507	+	0.350649i	$0.114039\pi$
$102$	4176.25	−	67268.6i	0.0397453	−	0.640195i
$103$		−	173174.i		−	1.60838i	−0.594369	−	0.804192i	$-0.702598\pi$
$103$		−	173174.i		−	1.60838i	0.594369	−	0.804192i	$-0.297402\pi$
$104$	−183337.	−	34501.6i	−1.66214	−	0.312792i
$105$			113321.i			1.00309i
$106$	59726.7	+	3708.02i	0.516302	+	0.0320537i
$107$	−45960.2	+	45960.2i	−0.388081	+	0.388081i	−0.874003	−	0.485921i	$-0.838484\pi$
$107$	−45960.2	+	45960.2i	−0.388081	+	0.388081i	0.485921	+	0.874003i	$0.338484\pi$
$108$	−14328.4	−	18409.0i	−0.118206	−	0.151870i
$109$	−13500.7	−	13500.7i	−0.108841	−	0.108841i	0.650589	−	0.759430i	$-0.274522\pi$
$109$	−13500.7	−	13500.7i	−0.108841	−	0.108841i	−0.759430	+	0.650589i	$0.774522\pi$
$110$	96651.3	−	85352.0i	0.761598	−	0.672561i
$111$	51585.9			0.397396
$112$	−54162.5	+	213888.i	−0.407994	+	1.61117i
$113$	53534.7			0.394402			0.197201	−	0.980363i	$-0.436815\pi$
$113$	53534.7			0.394402			0.197201	+	0.980363i	$0.436815\pi$
$114$	−90453.4	+	79878.6i	−0.651873	+	0.575663i
$115$	−56276.8	−	56276.8i	−0.396812	−	0.396812i
$116$	176782.	−	137596.i	1.21982	−	0.949427i
$117$	59027.3	−	59027.3i	0.398647	−	0.398647i
$118$	73407.1	+	4557.34i	0.485325	+	0.0301305i
$119$		−	285242.i		−	1.84649i
$120$	−78607.8	+	53707.8i	−0.498325	+	0.340474i
$121$			8899.00i			0.0552558i
$122$	−9094.04	+	146482.i	−0.0553168	+	0.891012i
$123$	28190.0	−	28190.0i	0.168009	−	0.168009i
$124$	−24568.3	+	197103.i	−0.143490	+	1.15117i
$125$	−117151.	−	117151.i	−0.670613	−	0.670613i
$126$	−65351.8	−	74003.4i	−0.366717	−	0.415265i
$127$	90137.2			0.495901			0.247950	−	0.968773i	$-0.420243\pi$
$127$	90137.2			0.495901			0.247950	+	0.968773i	$0.420243\pi$
$128$	−174038.	+	63799.9i	−0.938901	+	0.344187i
$129$	12329.9			0.0652358
$130$	−225506.	−	255360.i	−1.17031	−	1.32524i
$131$	51539.8	+	51539.8i	0.262401	+	0.262401i	0.826029	−	0.563628i	$-0.190595\pi$
$131$	51539.8	+	51539.8i	0.262401	+	0.262401i	−0.563628	+	0.826029i	$0.690595\pi$
$132$	−13895.2	+	111477.i	−0.0694112	+	0.556863i
$133$	−361133.	+	361133.i	−1.77027	+	1.77027i
$134$	10280.9	−	165600.i	0.0494619	−	0.796704i
$135$		−	42600.4i		−	0.201177i
$136$	197864.	−	135188.i	0.917319	−	0.626747i
$137$		−	178438.i		−	0.812244i	−0.913819	−	0.406122i	$-0.866881\pi$
$137$		−	178438.i		−	0.812244i	0.913819	−	0.406122i	$-0.133119\pi$
$138$	69205.6	+	4296.50i	0.309345	+	0.0192051i
$139$	190012.	−	190012.i	0.834151	−	0.834151i	−0.153931	−	0.988082i	$-0.549193\pi$
$139$	190012.	−	190012.i	0.834151	−	0.834151i	0.988082	+	0.153931i	$0.0491933\pi$
$140$	−317960.	+	247480.i	−1.37105	+	1.06713i
$141$	−49266.2	−	49266.2i	−0.208690	−	0.208690i
$142$	179306.	−	158344.i	0.746233	−	0.658992i
$143$	−401996.			−1.64392
$144$	20361.1	−	80406.1i	0.0818265	−	0.323134i
$145$	409093.			1.61585
$146$	121843.	−	107599.i	0.473064	−	0.417759i
$147$	−188498.	−	188498.i	−0.719470	−	0.719470i
$148$	112657.	+	144741.i	0.422770	+	0.543172i
$149$	240510.	−	240510.i	0.887498	−	0.887498i	−0.106784	−	0.994282i	$-0.534055\pi$
$149$	240510.	−	240510.i	0.887498	−	0.887498i	0.994282	+	0.106784i	$0.0340554\pi$
$150$	−14728.3	−	914.377i	−0.0534470	−	0.00331816i
$151$		−	219888.i		−	0.784800i	−0.919795	−	0.392400i	$-0.871645\pi$
$151$		−	219888.i		−	0.784800i	0.919795	−	0.392400i	$-0.128355\pi$
$152$	−421665.	−	79351.4i	−1.48033	−	0.278577i
$153$			107230.i			0.370328i
$154$	−29460.2	+	474528.i	−0.100100	+	1.61235i
$155$	−256485.	+	256485.i	−0.857498	+	0.857498i
$156$	294529.	+	36712.1i	0.968984	+	0.120781i
$157$	−194371.	−	194371.i	−0.629335	−	0.629335i	0.318566	−	0.947901i	$-0.396799\pi$
$157$	−194371.	−	194371.i	−0.629335	−	0.629335i	−0.947901	+	0.318566i	$0.896799\pi$
$158$	95039.0	+	107621.i	0.302872	+	0.342968i
$159$	−95207.6			−0.298661
$160$	−322364.	−	103269.i	−0.995514	−	0.318910i
$161$	293455.			0.892231
$162$	24567.4	+	27819.7i	0.0735481	+	0.0832848i
$163$	−9481.82	−	9481.82i	−0.0279526	−	0.0279526i	0.692992	−	0.720945i	$-0.256292\pi$
$163$	−9481.82	−	9481.82i	−0.0279526	−	0.0279526i	−0.720945	+	0.692992i	$0.756292\pi$
$164$	140660.	+	17532.8i	0.408376	+	0.0509028i
$165$	−145061.	+	145061.i	−0.414803	+	0.414803i
$166$	8946.72	−	144109.i	0.0251996	−	0.405901i
$167$			348139.i			0.965965i	0.875630	+	0.482982i	$0.160446\pi$
$167$			348139.i			0.965965i	−0.875630	+	0.482982i	$0.839554\pi$
$168$	64920.4	−	344980.i	0.177463	−	0.943019i
$169$			690810.i			1.86055i
$170$	436773.	+	27116.2i	1.15913	+	0.0719626i
$171$	135759.	−	135759.i	0.355041	−	0.355041i
$172$	26927.0	+	34595.6i	0.0694012	+	0.0891661i
$173$	443545.	+	443545.i	1.12674	+	1.12674i	0.990704	+	0.136033i	$0.0434353\pi$
$173$	443545.	+	443545.i	1.12674	+	1.12674i	0.136033	+	0.990704i	$0.456565\pi$
$174$	−267154.	+	235921.i	−0.668942	+	0.590737i
$175$	−62452.9			−0.154155
$176$	−343129.	+	204463.i	−0.834980	+	0.497547i
$177$	−117015.			−0.280742
$178$	−89701.2	+	79214.4i	−0.212201	+	0.187393i
$179$	184365.	+	184365.i	0.430078	+	0.430078i	0.888655	−	0.458577i	$-0.151641\pi$
$179$	184365.	+	184365.i	0.430078	+	0.430078i	−0.458577	+	0.888655i	$0.651641\pi$
$180$	119529.	−	93033.9i	0.274975	−	0.214023i
$181$	120438.	−	120438.i	0.273253	−	0.273253i	−0.557155	−	0.830408i	$-0.688107\pi$
$181$	120438.	−	120438.i	0.273253	−	0.273253i	0.830408	+	0.557155i	$0.188107\pi$
$182$	1.25374e6	+	77835.9i	2.80561	+	0.174181i
$183$		−	233500.i		−	0.515416i
$184$	139081.	+	203562.i	0.302847	+	0.443253i
$185$			334945.i			0.719523i
$186$	19581.6	−	315409.i	0.0415016	−	0.668484i
$187$	365136.	−	365136.i	0.763572	−	0.763572i
$188$	30641.1	−	245824.i	0.0632281	−	0.507258i
$189$	111070.	+	111070.i	0.226173	+	0.226173i
$190$	−518649.	−	587311.i	−1.04229	−	1.18028i
$191$	222074.			0.440468			0.220234	−	0.975447i	$-0.429318\pi$
$191$	222074.			0.440468			0.220234	+	0.975447i	$0.429318\pi$
$192$	270071.	−	118467.i	0.528720	−	0.231924i
$193$	80078.7			0.154748			0.0773738	−	0.997002i	$-0.475347\pi$
$193$	80078.7			0.154748			0.0773738	+	0.997002i	$0.475347\pi$
$194$	−321152.	−	363667.i	−0.612641	−	0.693745i
$195$	383263.	+	383263.i	0.721788	+	0.721788i
$196$	117236.	−	940548.i	0.217982	−	1.74880i
$197$	−274374.	+	274374.i	−0.503707	+	0.503707i	−0.912588	−	0.408881i	$-0.865919\pi$
$197$	−274374.	+	274374.i	−0.503707	+	0.503707i	0.408881	+	0.912588i	$0.365919\pi$
$198$	11074.8	−	178387.i	0.0200759	−	0.323371i
$199$			232874.i			0.416859i	0.978037	+	0.208429i	$0.0668351\pi$
$199$			232874.i			0.416859i	−0.978037	+	0.208429i	$0.933165\pi$
$200$	−29599.1	−	43321.8i	−0.0523243	−	0.0765829i
$201$			263974.i			0.460863i
$202$	−479568.	−	29773.1i	−0.826936	−	0.0513388i
$203$	−1.06661e6	+	1.06661e6i	−1.81662	+	1.81662i
$204$	−300868.	+	234176.i	−0.506175	+	0.393974i
$205$	183037.	+	183037.i	0.304196	+	0.304196i
$206$	−734287.	+	648443.i	−1.20559	+	1.06464i
$207$	−110317.			−0.178944
$208$	540207.	+	906571.i	0.865768	+	1.45293i
$209$	−924566.			−1.46411
$210$	480501.	−	424327.i	0.751876	−	0.663976i
$211$	−741790.	−	741790.i	−1.14703	−	1.14703i	−0.987134	−	0.159897i	$-0.948884\pi$
$211$	−741790.	−	741790.i	−1.14703	−	1.14703i	−0.159897	−	0.987134i	$-0.551116\pi$
$212$	−207922.	−	267136.i	−0.317731	−	0.408218i
$213$	−269116.	+	269116.i	−0.406435	+	0.406435i
$214$	366975.	+	22783.0i	0.547775	+	0.0340076i
$215$			80057.7i			0.118116i
$216$	−24405.2	+	129687.i	−0.0355917	+	0.189130i
$217$		−	1.33744e6i		−	1.92808i
$218$	−6692.46	+	107798.i	−0.00953772	+	0.153628i
$219$	−182872.	+	182872.i	−0.257654	+	0.257654i
$220$	−723813.	−	90221.0i	−1.00825	−	0.125676i
$221$	−964714.	−	964714.i	−1.32867	−	1.32867i
$222$	−193161.	−	218733.i	−0.263049	−	0.297873i
$223$	988226.			1.33074			0.665372	−	0.746512i	$-0.268273\pi$
$223$	988226.			1.33074			0.665372	+	0.746512i	$0.268273\pi$
$224$	1.10973e6	−	571238.i	1.47774	−	0.760671i
$225$	23477.6			0.0309170
$226$	−200458.	−	226996.i	−0.261068	−	0.295629i
$227$	856256.	+	856256.i	1.10291	+	1.10291i	0.994058	+	0.108849i	$0.0347165\pi$
$227$	856256.	+	856256.i	1.10291	+	1.10291i	0.108849	+	0.994058i	$0.465284\pi$
$228$	677398.	+	84435.4i	0.862992	+	0.107569i
$229$	429500.	−	429500.i	0.541220	−	0.541220i	−0.382666	−	0.923887i	$-0.624994\pi$
$229$	429500.	−	429500.i	0.541220	−	0.541220i	0.923887	+	0.382666i	$0.124994\pi$
$230$	−27897.0	+	449349.i	−0.0347727	+	0.560099i
$231$		−	756423.i		−	0.932684i
$232$	−1.24539e6	−	234364.i	−1.51909	−	0.285872i
$233$		−	871615.i		−	1.05180i	−0.850545	−	0.525902i	$-0.823728\pi$
$233$		−	871615.i		−	1.05180i	0.850545	−	0.525902i	$-0.176272\pi$
$234$	−471311.	−	29260.5i	−0.562689	−	0.0349335i
$235$	319884.	−	319884.i	0.377853	−	0.377853i
$236$	−255546.	−	328323.i	−0.298668	−	0.383726i
$237$	−161525.	−	161525.i	−0.186797	−	0.186797i
$238$	−1.20947e6	+	1.06808e6i	−1.38406	+	1.22225i
$239$	−287437.			−0.325498			−0.162749	−	0.986668i	$-0.552036\pi$
$239$	−287437.			−0.325498			−0.162749	+	0.986668i	$0.552036\pi$
$240$	522074.	+	132204.i	0.585065	+	0.148155i
$241$	202648.			0.224750			0.112375	−	0.993666i	$-0.464154\pi$
$241$	202648.			0.224750			0.112375	+	0.993666i	$0.464154\pi$
$242$	37733.3	−	33321.9i	0.0414177	−	0.0365756i
$243$	−41753.9	−	41753.9i	−0.0453609	−	0.0453609i
$244$	655159.	−	509934.i	0.704486	−	0.548327i
$245$	1.22391e6	−	1.22391e6i	1.30267	−	1.30267i
$246$	−225087.	−	13974.1i	−0.237144	−	0.0147227i
$247$			2.44277e6i			2.54765i
$248$	927746.	−	633871.i	0.957855	−	0.654443i
$249$			229717.i			0.234798i
$250$	−58073.2	+	935409.i	−0.0587659	+	0.946568i
$251$	1.22484e6	−	1.22484e6i	1.22714	−	1.22714i	0.262103	−	0.965040i	$-0.415584\pi$
$251$	1.22484e6	−	1.22484e6i	1.22714	−	1.22714i	0.965040	−	0.262103i	$-0.0844162\pi$
$252$	−69079.9	+	554205.i	−0.0685252	+	0.549755i
$253$	375649.	+	375649.i	0.368962	+	0.368962i
$254$	−337515.	−	382197.i	−0.328253	−	0.371709i
$255$	−696239.			−0.670514
$256$	922201.	+	499056.i	0.879480	+	0.475937i
$257$	−1.27697e6			−1.20600			−0.602999	−	0.797742i	$-0.706028\pi$
$257$	−1.27697e6			−1.20600			−0.602999	+	0.797742i	$0.706028\pi$
$258$	−46168.9	−	52280.9i	−0.0431817	−	0.0488983i
$259$	−873286.	−	873286.i	−0.808923	−	0.808923i
$260$	−238370.	+	1.91237e6i	−0.218685	+	1.75444i
$261$	400965.	−	400965.i	0.364338	−	0.364338i
$262$	25548.9	−	411526.i	0.0229942	−	0.370377i
$263$			830076.i			0.739995i	0.929033	+	0.369997i	$0.120641\pi$
$263$			830076.i			0.739995i	−0.929033	+	0.369997i	$0.879359\pi$
$264$	524709.	−	358501.i	0.463350	−	0.316578i
$265$		−	618180.i		−	0.540754i
$266$	2.88351e6	+	179018.i	2.49872	+	0.155129i
$267$	134630.	−	134630.i	0.115575	−	0.115575i
$268$	−740666.	+	576488.i	−0.629920	+	0.490290i
$269$	413354.	+	413354.i	0.348290	+	0.348290i	0.859472	−	0.511182i	$-0.170792\pi$
$269$	413354.	+	413354.i	0.348290	+	0.348290i	−0.511182	+	0.859472i	$0.670792\pi$
$270$	−180633.	+	159515.i	−0.150795	+	0.133166i
$271$	1.38141e6			1.14261			0.571306	−	0.820737i	$-0.306437\pi$
$271$	1.38141e6			1.14261			0.571306	+	0.820737i	$0.306437\pi$
$272$	−1.31412e6	−	332771.i	−1.07699	−	0.272724i
$273$	−1.99852e6			−1.62294
$274$	−756609.	+	668155.i	−0.608828	+	0.537651i
$275$	−79945.3	−	79945.3i	−0.0637472	−	0.0637472i
$276$	−240919.	−	309531.i	−0.190370	−	0.244586i
$277$	−1.52814e6	+	1.52814e6i	−1.19664	+	1.19664i	−0.221470	+	0.975167i	$0.571085\pi$
$277$	−1.52814e6	+	1.52814e6i	−1.19664	+	1.19664i	−0.975167	+	0.221470i	$0.928915\pi$
$278$	−1.51718e6	−	94191.1i	−1.17740	−	0.0730967i
$279$			502778.i			0.386693i
$280$	2.23994e6	+	421526.i	1.70743	+	0.321314i
$281$		−	1.52469e6i		−	1.15190i	−0.817484	−	0.575952i	$-0.804632\pi$
$281$		−	1.52469e6i		−	1.15190i	0.817484	−	0.575952i	$-0.195368\pi$
$282$	−24421.8	+	393372.i	−0.0182875	+	0.294565i
$283$	1.07644e6	−	1.07644e6i	0.798961	−	0.798961i	−0.183970	−	0.982932i	$-0.558895\pi$
$283$	1.07644e6	−	1.07644e6i	0.798961	−	0.798961i	0.982932	+	0.183970i	$0.0588951\pi$
$284$	−1.34281e6	−	167377.i	−0.987912	−	0.123140i
$285$	881480.	+	881480.i	0.642836	+	0.642836i
$286$	1.50526e6	+	1.70453e6i	1.08817	+	1.23223i
$287$	−954446.			−0.683985
$288$	−417176.	+	214743.i	−0.296373	+	0.152559i
$289$	332653.			0.234286
$290$	−1.53183e6	−	1.73462e6i	−1.06959	−	1.21118i
$291$	545819.	+	545819.i	0.377847	+	0.377847i
$292$	−912475.	−	113737.i	−0.626273	−	0.0780630i
$293$	7459.55	−	7459.55i	0.00507626	−	0.00507626i	−0.704564	−	0.709640i	$-0.748857\pi$
$293$	7459.55	−	7459.55i	0.00507626	−	0.00507626i	0.709640	+	0.704564i	$0.248857\pi$
$294$	−93440.4	+	1.50508e6i	−0.0630473	+	1.01553i
$295$		−	759773.i		−	0.508310i
$296$	191886.	−	1.01966e6i	0.127296	−	0.676436i
$297$			284359.i			0.187058i
$298$	−1.92038e6	−	119223.i	−1.25270	−	0.0777716i
$299$	992492.	−	992492.i	0.642021	−	0.642021i
$300$	51272.2	+	65874.1i	0.0328912	+	0.0422583i
$301$	−208730.	−	208730.i	−0.132791	−	0.132791i
$302$	−932362.	+	823361.i	−0.588257	+	0.519485i
$303$	764457.			0.478351
$304$	1.24244e6	+	2.08506e6i	0.771067	+	1.29400i
$305$	1.51610e6			0.933210
$306$	454672.	−	401517.i	0.277584	−	0.245132i
$307$	1.07157e6	+	1.07157e6i	0.648896	+	0.648896i	0.952726	−	0.303830i	$-0.0982655\pi$
$307$	1.07157e6	+	1.07157e6i	0.648896	+	0.648896i	−0.303830	+	0.952726i	$0.598266\pi$
$308$	2.12239e6	−	1.65193e6i	1.27482	−	0.992238i
$309$	1.10207e6	−	1.10207e6i	0.656620	−	0.656620i
$310$	2.04794e6	+	127142.i	1.21035	+	0.0751426i
$311$			862274.i			0.505527i	0.967528	+	0.252763i	$0.0813394\pi$
$311$			862274.i			0.505527i	−0.967528	+	0.252763i	$0.918661\pi$
$312$	−947186.	−	1.38632e6i	−0.550869	−	0.806263i
$313$		−	1.42271e6i		−	0.820834i	−0.911898	−	0.410417i	$-0.865383\pi$
$313$		−	1.42271e6i		−	0.820834i	0.911898	−	0.410417i	$-0.134617\pi$
$314$	−96351.7	+	1.55198e6i	−0.0551487	+	0.888304i
$315$	−721172.	+	721172.i	−0.409508	+	0.409508i
$316$	100461.	−	805963.i	0.0565951	−	0.454044i
$317$	2.06598e6	+	2.06598e6i	1.15472	+	1.15472i	0.985594	+	0.169131i	$0.0540962\pi$
$317$	2.06598e6	+	2.06598e6i	1.15472	+	1.15472i	0.169131	+	0.985594i	$0.445904\pi$
$318$	356501.	+	403696.i	0.197694	+	0.223865i
$319$	−2.73071e6			−1.50244
$320$	769204.	+	1.75356e6i	0.419920	+	0.957297i
$321$	−584978.			−0.316867
$322$	−1.09883e6	−	1.24430e6i	−0.590597	−	0.668784i
$323$	−2.21878e6	−	2.21878e6i	−1.18334	−	1.18334i
$324$	25968.9	−	208340.i	0.0137433	−	0.110258i
$325$	−211221.	+	211221.i	−0.110925	+	0.110925i
$326$	−4700.24	+	75708.8i	−0.00244949	+	0.0394550i
$327$		−	171836.i		−	0.0888680i
$328$	−452353.	−	662072.i	−0.232163	−	0.339798i
$329$			1.66803e6i			0.849601i
$330$	1.15826e6	+	71908.5i	0.585493	+	0.0363493i
$331$	−1.35290e6	+	1.35290e6i	−0.678728	+	0.678728i	−0.959712	−	0.280984i	$-0.909339\pi$
$331$	−1.35290e6	+	1.35290e6i	−0.678728	+	0.678728i	0.280984	+	0.959712i	$0.409339\pi$
$332$	−644545.	+	501673.i	−0.320928	+	0.249790i
$333$	328290.	+	328290.i	0.162236	+	0.162236i
$334$	1.47617e6	−	1.30359e6i	0.724051	−	0.639404i
$335$	−1.71398e6			−0.834436
$336$	−1.70586e6	+	1.01649e6i	−0.824321	+	0.491196i
$337$	−1.26314e6			−0.605864			−0.302932	−	0.953012i	$-0.597966\pi$
$337$	−1.26314e6			−0.605864			−0.302932	+	0.953012i	$0.597966\pi$
$338$	2.92915e6	−	2.58671e6i	1.39460	−	1.23156i
$339$	340693.	+	340693.i	0.161014	+	0.161014i
$340$	−1.52050e6	−	1.95353e6i	−0.713328	−	0.916478i
$341$	1.71205e6	−	1.71205e6i	0.797314	−	0.797314i
$342$	−1.08399e6	−	67297.3i	−0.501139	−	0.0311123i
$343$			2.76070e6i			1.26702i
$344$	45864.1	−	243717.i	0.0208967	−	0.111043i
$345$		−	716287.i		−	0.323996i
$346$	219870.	−	3.54154e6i	0.0987361	−	1.59039i
$347$	164634.	−	164634.i	0.0734000	−	0.0734000i	−0.669454	−	0.742854i	$-0.733472\pi$
$347$	164634.	−	164634.i	0.0734000	−	0.0734000i	0.742854	+	0.669454i	$0.233472\pi$
$348$	2.00069e6	+	249380.i	0.885590	+	0.110386i
$349$	−79038.5	−	79038.5i	−0.0347356	−	0.0347356i	0.689526	−	0.724261i	$-0.257819\pi$
$349$	−79038.5	−	79038.5i	−0.0347356	−	0.0347356i	−0.724261	+	0.689526i	$0.757819\pi$
$350$	233852.	+	264811.i	0.102040	+	0.115549i
$351$	751295.			0.325494
$352$	2.15179e6	+	689321.i	0.925643	+	0.296527i
$353$	−4.02288e6			−1.71831			−0.859153	−	0.511719i	$-0.829009\pi$
$353$	−4.02288e6			−1.71831			−0.859153	+	0.511719i	$0.829009\pi$
$354$	438157.	+	496162.i	0.185832	+	0.210434i
$355$	−1.74736e6	−	1.74736e6i	−0.735888	−	0.735888i
$356$	671765.	+	83733.3i	0.280926	+	0.0350165i
$357$	1.81527e6	−	1.81527e6i	0.753825	−	0.753825i
$358$	91392.0	−	1.47209e6i	0.0376878	−	0.607053i
$359$		−	2.50448e6i		−	1.02561i	−0.858506	−	0.512804i	$-0.828607\pi$
$359$		−	2.50448e6i		−	1.02561i	0.858506	−	0.512804i	$-0.171393\pi$
$360$	−842051.	−	158462.i	−0.342438	−	0.0644422i
$361$			3.14211e6i			1.26898i
$362$	−961649.	−	59702.2i	−0.385696	−	0.0239452i
$363$	−56632.9	+	56632.9i	−0.0225581	+	0.0225581i
$364$	−4.36453e6	−	5.60751e6i	−1.72657	−	2.21828i
$365$	−1.18738e6	−	1.18738e6i	−0.466506	−	0.466506i
$366$	−990078.	+	874329.i	−0.386337	+	0.341171i
$367$	451720.			0.175067			0.0875335	−	0.996162i	$-0.472102\pi$
$367$	451720.			0.175067			0.0875335	+	0.996162i	$0.472102\pi$
$368$	342353.	−	1.35196e6i	0.131782	−	0.520407i
$369$	358801.			0.137179
$370$	1.42022e6	−	1.25419e6i	0.539328	−	0.476276i
$371$	1.61175e6	+	1.61175e6i	0.607942	+	0.607942i
$372$	−1.41071e6	+	1.09801e6i	−0.528542	+	0.411384i
$373$	−3.69996e6	+	3.69996e6i	−1.37697	+	1.37697i	−0.527278	+	0.849693i	$0.676787\pi$
$373$	−3.69996e6	+	3.69996e6i	−1.37697	+	1.37697i	−0.849693	+	0.527278i	$0.823213\pi$
$374$	−2.91547e6	−	181002.i	−1.07778	−	0.0669119i
$375$		−	1.49109e6i		−	0.547553i
$376$	−1.15707e6	+	790552.i	−0.422075	+	0.288377i
$377$			7.21472e6i			2.61436i
$378$	55058.5	−	886851.i	0.0198196	−	0.319243i
$379$	1.98682e6	−	1.98682e6i	0.710495	−	0.710495i	−0.256144	−	0.966639i	$-0.582452\pi$
$379$	1.98682e6	−	1.98682e6i	0.710495	−	0.710495i	0.966639	+	0.256144i	$0.0824520\pi$
$380$	−548236.	+	4.39832e6i	−0.194764	+	1.56253i
$381$	573630.	+	573630.i	0.202451	+	0.202451i
$382$	−831546.	−	941631.i	−0.291560	−	0.330158i
$383$	4.46316e6			1.55470			0.777348	−	0.629071i	$-0.216565\pi$
$383$	4.46316e6			1.55470			0.777348	+	0.629071i	$0.216565\pi$
$384$	−1.51359e6	−	701553.i	−0.523819	−	0.242791i
$385$	4.91143e6			1.68871
$386$	−299851.	−	339547.i	−0.102432	−	0.115993i
$387$	78467.1	+	78467.1i	0.0266324	+	0.0266324i
$388$	−339472.	+	2.72347e6i	−0.114479	+	0.918426i
$389$	−3.05786e6	+	3.05786e6i	−1.02457	+	1.02457i	−0.0248841	+	0.999690i	$0.507922\pi$
$389$	−3.05786e6	+	3.05786e6i	−1.02457	+	1.02457i	−0.999690	+	0.0248841i	$0.992078\pi$
$390$	189987.	−	3.06021e6i	0.0632504	−	1.01880i
$391$			1.80297e6i			0.596413i
$392$	−4.42707e6	+	3.02474e6i	−1.45513	+	0.994198i
$393$			655995.i			0.214249i
$394$	2.19078e6	+	136010.i	0.710980	+	0.0441399i
$395$	1.04878e6	−	1.04878e6i	0.338214	−	0.338214i
$396$	−797861.	+	621004.i	−0.255676	+	0.199002i
$397$	−1.38060e6	−	1.38060e6i	−0.439636	−	0.439636i	0.452254	−	0.891889i	$-0.350620\pi$
$397$	−1.38060e6	−	1.38060e6i	−0.439636	−	0.439636i	−0.891889	+	0.452254i	$0.850620\pi$
$398$	987426.	−	871988.i	0.312462	−	0.275932i
$399$	−4.59648e6			−1.44542
$400$	−72859.2	+	287722.i	−0.0227685	+	0.0899131i
$401$	3.32538e6			1.03271			0.516357	−	0.856374i	$-0.327288\pi$
$401$	3.32538e6			1.03271			0.516357	+	0.856374i	$0.327288\pi$
$402$	1.11930e6	−	988441.i	0.345446	−	0.305060i
$403$	−4.52334e6	−	4.52334e6i	−1.38739	−	1.38739i
$404$	1.66948e6	+	2.14493e6i	0.508894	+	0.653824i
$405$	271107.	−	271107.i	0.0821302	−	0.0821302i
$406$	8.51646e6	+	528729.i	2.56415	+	0.159191i
$407$		−	2.23577e6i		−	0.669023i
$408$	2.11954e6	+	398867.i	0.630362	+	0.118625i
$409$		−	2.71674e6i		−	0.803046i	−0.915849	−	0.401523i	$-0.868481\pi$
$409$		−	2.71674e6i		−	0.803046i	0.915849	−	0.401523i	$-0.131519\pi$
$410$	90733.4	−	1.46148e6i	0.0266568	−	0.429372i
$411$	1.13557e6	−	1.13557e6i	0.331597	−	0.331597i
$412$	5.49902e6	+	685435.i	1.59603	+	0.198940i
$413$	1.98092e6	+	1.98092e6i	0.571467	+	0.571467i
$414$	413079.	+	467764.i	0.118449	+	0.134130i
$415$	−1.49154e6			−0.425124
$416$	1.82123e6	−	5.68519e6i	0.515980	−	1.61069i
$417$	2.41846e6			0.681081
$418$	3.46200e6	+	3.92032e6i	0.969139	+	1.09744i
$419$	2.71477e6	+	2.71477e6i	0.755437	+	0.755437i	0.975488	−	0.220052i	$-0.0706226\pi$
$419$	2.71477e6	+	2.71477e6i	0.755437	+	0.755437i	−0.220052	+	0.975488i	$0.570623\pi$
$420$	−3.59843e6	−	448533.i	−0.995383	−	0.124071i
$421$	−935357.	+	935357.i	−0.257201	+	0.257201i	−0.823915	−	0.566714i	$-0.808214\pi$
$421$	−935357.	+	935357.i	−0.257201	+	0.257201i	0.566714	+	0.823915i	$0.308214\pi$
$422$	−367714.	+	5.92292e6i	−0.100514	+	1.61903i
$423$		−	627056.i		−	0.170394i
$424$	−354148.	+	1.88190e6i	−0.0956687	+	0.508373i
$425$		−	383707.i		−	0.103045i
$426$	2.14879e6	+	133404.i	0.573681	+	0.0356159i
$427$	−3.95286e6	+	3.95286e6i	−1.04916	+	1.04916i
$428$	−1.27752e6	−	1.64135e6i	−0.337099	−	0.433103i
$429$	−2.55829e6	−	2.55829e6i	−0.671130	−	0.671130i
$430$	339458.	−	299773.i	0.0885351	−	0.0781846i
$431$	−1.39740e6			−0.362349			−0.181175	−	0.983451i	$-0.557990\pi$
$431$	−1.39740e6			−0.362349			−0.181175	+	0.983451i	$0.557990\pi$
$432$	641278.	−	382124.i	0.165324	−	0.0985133i
$433$	6.72588e6			1.72397			0.861984	−	0.506935i	$-0.169222\pi$
$433$	6.72588e6			1.72397			0.861984	+	0.506935i	$0.169222\pi$
$434$	−5.67098e6	+	5.00799e6i	−1.44522	+	1.27626i
$435$	2.60345e6	+	2.60345e6i	0.659669	+	0.659669i
$436$	482143.	−	375269.i	0.121467	−	0.0945424i
$437$	2.28267e6	−	2.28267e6i	0.571794	−	0.571794i
$438$	1.46016e6	+	90651.5i	0.363677	+	0.0225782i
$439$			5.37352e6i			1.33075i	0.746508	+	0.665377i	$0.231729\pi$
$439$			5.37352e6i			1.33075i	−0.746508	+	0.665377i	$0.768271\pi$
$440$	2.32774e6	+	3.40692e6i	0.573195	+	0.838939i
$441$		−	2.39918e6i		−	0.587445i
$442$	−478219.	+	7.70288e6i	−0.116432	+	1.87542i
$443$	−154396.	+	154396.i	−0.0373789	+	0.0373789i	−0.725549	−	0.688170i	$-0.758414\pi$
$443$	−154396.	+	154396.i	−0.0373789	+	0.0373789i	0.688170	+	0.725549i	$0.258414\pi$
$444$	−204180.	+	1.63807e6i	−0.0491537	+	0.394344i
$445$	874150.	+	874150.i	0.209260	+	0.209260i
$446$	−3.70037e6	−	4.19025e6i	−0.880863	−	0.997476i
$447$	3.06119e6			0.724639
$448$	−6.57749e6	−	2.56647e6i	−1.54834	−	0.604146i
$449$	−7.96158e6			−1.86373			−0.931866	−	0.362802i	$-0.881820\pi$
$449$	−7.96158e6			−1.86373			−0.931866	+	0.362802i	$0.881820\pi$
$450$	−87911.0	−	99549.1i	−0.0204650	−	0.0231743i
$451$	−1.22178e6	−	1.22178e6i	−0.282846	−	0.282846i
$452$	−211894.	+	1.69996e6i	−0.0487834	+	0.391373i
$453$	1.39936e6	−	1.39936e6i	0.320393	−	0.320393i
$454$	424455.	−	6.83688e6i	0.0966479	−	1.55675i
$455$		−	1.29763e7i		−	2.93849i
$456$	−2.17847e6	−	3.18845e6i	−0.490613	−	0.718070i
$457$		−	7.11476e6i		−	1.59356i	−0.604266	−	0.796782i	$-0.706534\pi$
$457$		−	7.11476e6i		−	1.59356i	0.604266	−	0.796782i	$-0.293466\pi$
$458$	−3.42939e6	−	212908.i	−0.763930	−	0.0474272i
$459$	−682406.	+	682406.i	−0.151186	+	0.151186i
$460$	2.00978e6	−	1.56428e6i	0.442847	−	0.344683i
$461$	4.45613e6	+	4.45613e6i	0.976576	+	0.976576i	0.999732	−	0.0231560i	$-0.00737145\pi$
$461$	4.45613e6	+	4.45613e6i	0.976576	+	0.976576i	−0.0231560	+	0.999732i	$0.507371\pi$
$462$	−3.20736e6	+	2.83239e6i	−0.699106	+	0.617374i
$463$	4.98566e6			1.08086			0.540431	−	0.841388i	$-0.318261\pi$
$463$	4.98566e6			1.08086			0.540431	+	0.841388i	$0.318261\pi$
$464$	3.66955e6	+	6.15821e6i	0.791258	+	1.32788i
$465$	−3.26452e6			−0.700144
$466$	−3.69579e6	+	3.26372e6i	−0.788393	+	0.696224i
$467$	−3.12361e6	−	3.12361e6i	−0.662772	−	0.662772i	0.293261	−	0.956032i	$-0.405260\pi$
$467$	−3.12361e6	−	3.12361e6i	−0.662772	−	0.662772i	−0.956032	+	0.293261i	$0.905260\pi$
$468$	1.64074e6	+	2.10800e6i	0.346277	+	0.444894i
$469$	4.46877e6	−	4.46877e6i	0.938114	−	0.938114i
$470$	−2.55415e6	−	158570.i	−0.533337	−	0.0331113i
$471$		−	2.47394e6i		−	0.513850i
$472$	−435265.	+	2.31295e6i	−0.0899288	+	0.477872i
$473$		−	534388.i		−	0.109826i
$474$	−80069.9	+	1.28972e6i	−0.0163690	+	0.263663i
$475$	−485795.	+	485795.i	−0.0987914	+	0.0987914i
$476$	9.05765e6	+	1.12901e6i	1.83231	+	0.228391i
$477$	−605897.	−	605897.i	−0.121928	−	0.121928i
$478$	1.07630e6	+	1.21878e6i	0.215458	+	0.243981i
$479$	−3.64390e6			−0.725650			−0.362825	−	0.931857i	$-0.618188\pi$
$479$	−3.64390e6			−0.725650			−0.362825	+	0.931857i	$0.618188\pi$
$480$	−1.39432e6	−	2.70871e6i	−0.276222	−	0.536611i
$481$	−5.90706e6			−1.16415
$482$	−758807.	−	859262.i	−0.148769	−	0.168464i
$483$	1.86754e6	+	1.86754e6i	0.364252	+	0.364252i
$484$	−282581.	−	35222.8i	−0.0548315	−	0.00683457i
$485$	−3.54398e6	+	3.54398e6i	−0.684128	+	0.684128i
$486$	−20697.9	+	333390.i	−0.00397498	+	0.0640268i
$487$		−	42648.8i		−	0.00814863i	−0.999992	−	0.00407432i	$-0.998703\pi$
$487$		−	42648.8i		−	0.00814863i	0.999992	−	0.00407432i	$-0.00129690\pi$
$488$	−4.61542e6	−	868559.i	−0.877328	−	0.165101i
$489$		−	120684.i		−	0.0228232i
$490$	−9.77246e6	−	606705.i	−1.83871	−	0.114153i
$491$	−3.00648e6	+	3.00648e6i	−0.562800	+	0.562800i	−0.930102	−	0.367302i	$-0.880282\pi$
$491$	−3.00648e6	+	3.00648e6i	−0.562800	+	0.562800i	0.367302	+	0.930102i	$0.380282\pi$
$492$	783576.	+	1.00673e6i	0.145938	+	0.187500i
$493$	−6.55317e6	−	6.55317e6i	−1.21432	−	1.21432i
$494$	1.03578e7	−	9.14685e6i	1.90963	−	1.68637i
$495$	−1.84633e6			−0.338685
$496$	−6.16162e6	−	1.56030e6i	−1.12458	−	0.284775i
$497$	9.11162e6			1.65464
$498$	974038.	−	860165.i	0.175996	−	0.155421i
$499$	2.94633e6	+	2.94633e6i	0.529700	+	0.529700i	0.920483	−	0.390783i	$-0.127796\pi$
$499$	2.94633e6	+	2.94633e6i	0.529700	+	0.529700i	−0.390783	+	0.920483i	$0.627796\pi$
$500$	4.18375e6	−	3.25636e6i	0.748411	−	0.582516i
$501$	−2.21554e6	+	2.21554e6i	−0.394353	+	0.394353i
$502$	−9.77990e6	−	607167.i	−1.73211	−	0.107535i
$503$		−	8.76170e6i		−	1.54407i	−0.635577	−	0.772037i	$-0.719238\pi$
$503$		−	8.76170e6i		−	1.54407i	0.635577	−	0.772037i	$-0.280762\pi$
$504$	2.60859e6	−	1.78229e6i	0.457435	−	0.312537i
$505$			4.96359e6i			0.866100i
$506$	186214.	−	2.99942e6i	0.0323322	−	0.520788i
$507$	−4.39629e6	+	4.39629e6i	−0.759567	+	0.759567i
$508$	−356769.	+	2.86224e6i	−0.0613377	+	0.492093i
$509$	−6.36511e6	−	6.36511e6i	−1.08896	−	1.08896i	−0.995636	−	0.0933229i	$-0.970251\pi$
$509$	−6.36511e6	−	6.36511e6i	−1.08896	−	1.08896i	−0.0933229	−	0.995636i	$-0.529749\pi$
$510$	2.60704e6	+	2.95217e6i	0.443835	+	0.502593i
$511$	6.19159e6			1.04894
$512$	−1.33706e6	−	5.77898e6i	−0.225412	−	0.974264i
$513$	1.72793e6			0.289890
$514$	4.78154e6	+	5.41455e6i	0.798289	+	0.903971i
$515$	7.15572e6	+	7.15572e6i	1.18887	+	1.18887i
$516$	−48802.6	+	391527.i	−0.00806899	+	0.0647348i
$517$	−2.13523e6	+	2.13523e6i	−0.351333	+	0.351333i
$518$	−432897.	+	6.97286e6i	−0.0708860	+	1.14179i
$519$			5.64541e6i			0.919977i
$520$	9.00132e6	−	6.15004e6i	1.45982	−	0.997401i
$521$		−	8.11480e6i		−	1.30973i	−0.755744	−	0.654867i	$-0.772724\pi$
$521$		−	8.11480e6i		−	1.30973i	0.755744	−	0.654867i	$-0.227276\pi$
$522$	−3.20155e6	−	198763.i	−0.514262	−	0.0319270i
$523$	2.84468e6	−	2.84468e6i	0.454757	−	0.454757i	−0.442173	−	0.896930i	$-0.645792\pi$
$523$	2.84468e6	−	2.84468e6i	0.454757	−	0.454757i	0.896930	+	0.442173i	$0.145792\pi$
$524$	−1.84061e6	+	1.43261e6i	−0.292842	+	0.227929i
$525$	−397448.	−	397448.i	−0.0629335	−	0.0629335i
$526$	3.51966e6	−	3.10819e6i	0.554673	−	0.489827i
$527$	8.21716e6			1.28883
$528$	−3.48486e6	−	882463.i	−0.544002	−	0.137756i
$529$	4.58145e6			0.711810
$530$	−2.62119e6	+	2.31475e6i	−0.405329	+	0.357943i
$531$	−744677.	−	744677.i	−0.114612	−	0.114612i
$532$	−1.00381e7	−	1.28969e7i	−1.53771	−	1.97563i
$533$	−3.22802e6	+	3.22802e6i	−0.492174	+	0.492174i
$534$	−1.07497e6	−	66737.7i	−0.163134	−	0.0101279i
$535$		−	3.79824e6i		−	0.573718i
$536$	5.21780e6	+	981918.i	0.784468	+	0.147626i
$537$			2.34659e6i			0.351157i
$538$	204904.	−	3.30048e6i	0.0305207	−	0.491611i
$539$	−8.16963e6	+	8.16963e6i	−1.21124	+	1.21124i
$540$	1.35274e6	+	168615.i	0.199632	+	0.0248835i
$541$	−839774.	−	839774.i	−0.123359	−	0.123359i	0.642732	−	0.766091i	$-0.277801\pi$
$541$	−839774.	−	839774.i	−0.123359	−	0.123359i	−0.766091	+	0.642732i	$0.777801\pi$
$542$	−5.17263e6	−	5.85741e6i	−0.756333	−	0.856460i
$543$	1.53292e6			0.223111
$544$	3.50965e6	+	6.81813e6i	0.508471	+	0.987797i
$545$	1.11573e6			0.160904
$546$	7.48338e6	+	8.47407e6i	1.07428	+	1.21650i
$547$	1.40410e6	+	1.40410e6i	0.200646	+	0.200646i	0.800277	−	0.599631i	$-0.204686\pi$
$547$	1.40410e6	+	1.40410e6i	0.200646	+	0.200646i	−0.599631	+	0.800277i	$0.704686\pi$
$548$	5.66618e6	+	706271.i	0.806007	+	0.100466i
$549$	1.48598e6	−	1.48598e6i	0.210418	−	0.210418i
$550$	−39629.8	+	638334.i	−0.00558618	+	0.0899790i
$551$			1.65934e7i			2.32839i
$552$	−410353.	+	2.18057e6i	−0.0573204	+	0.304594i
$553$			5.46885e6i			0.760473i
$554$	1.22016e7	+	757513.i	1.68905	+	0.104861i
$555$	−2.13158e6	+	2.13158e6i	−0.293744	+	0.293744i
$556$	5.28162e6	+	6.78578e6i	0.724569	+	0.930921i
$557$	−5.91838e6	−	5.91838e6i	−0.808286	−	0.808286i	0.176088	−	0.984374i	$-0.443656\pi$
$557$	−5.91838e6	−	5.91838e6i	−0.808286	−	0.808286i	−0.984374	+	0.176088i	$0.943656\pi$
$558$	2.13186e6	−	1.88263e6i	0.289851	−	0.255965i
$559$	−1.41189e6			−0.191105
$560$	−6.60003e6	−	1.10761e7i	−0.889356	−	1.49251i
$561$	4.64742e6			0.623454
$562$	−6.46495e6	+	5.70914e6i	−0.863424	+	0.762483i
$563$	−4.66096e6	−	4.66096e6i	−0.619733	−	0.619733i	0.325730	−	0.945463i	$-0.394390\pi$
$563$	−4.66096e6	−	4.66096e6i	−0.619733	−	0.619733i	−0.945463	+	0.325730i	$0.894390\pi$
$564$	1.75941e6	−	1.36941e6i	0.232900	−	0.181274i
$565$	−2.21211e6	+	2.21211e6i	−0.291531	+	0.291531i
$566$	−8.59501e6	−	533605.i	−1.12773	−	0.0700131i
$567$			1.41369e6i			0.184670i
$568$	4.31839e6	+	6.32047e6i	0.561630	+	0.822013i
$569$			9.42705e6i			1.22066i	0.792147	+	0.610330i	$0.208963\pi$
$569$			9.42705e6i			1.22066i	−0.792147	+	0.610330i	$0.791037\pi$
$570$	436959.	−	7.03829e6i	0.0563318	−	0.907360i
$571$	370250.	−	370250.i	0.0475232	−	0.0475232i	−0.682946	−	0.730469i	$-0.739302\pi$
$571$	370250.	−	370250.i	0.0475232	−	0.0475232i	0.730469	+	0.682946i	$0.239302\pi$
$572$	1.59113e6	−	1.27651e7i	0.203336	−	1.63130i
$573$	1.41327e6	+	1.41327e6i	0.179820	+	0.179820i
$574$	3.57388e6	+	4.04701e6i	0.452752	+	0.512690i
$575$	394755.			0.0497919
$576$	2.47265e6	+	964803.i	0.310531	+	0.121166i
$577$	7.28531e6			0.910979			0.455489	−	0.890241i	$-0.349464\pi$
$577$	7.28531e6			0.910979			0.455489	+	0.890241i	$0.349464\pi$
$578$	−1.24560e6	−	1.41050e6i	−0.155082	−	0.175612i
$579$	509618.	+	509618.i	0.0631754	+	0.0631754i
$580$	−1.61922e6	+	1.29904e7i	−0.199864	+	1.60344i
$581$	3.88883e6	−	3.88883e6i	0.477945	−	0.477945i
$582$	270568.	−	4.35816e6i	0.0331108	−	0.533330i
$583$			4.12637e6i			0.502801i
$584$	2.93446e6	+	4.29493e6i	0.356038	+	0.521104i
$585$			4.87814e6i			0.589338i
$586$	−59561.7	−	3697.78i	−0.00716512	−	0.000444833i
$587$	1.07294e7	−	1.07294e7i	1.28523	−	1.28523i	0.347581	−	0.937650i	$-0.387003\pi$
$587$	1.07294e7	−	1.07294e7i	1.28523	−	1.28523i	0.937650	−	0.347581i	$-0.112997\pi$
$588$	6.73170e6	−	5.23952e6i	0.802936	−	0.624954i
$589$	−1.04034e7	−	1.04034e7i	−1.23563	−	1.23563i
$590$	−3.22157e6	+	2.84494e6i	−0.381011	+	0.336467i
$591$	−3.49222e6			−0.411275
$592$	−5.04205e6	+	3.00445e6i	−0.591293	+	0.352339i
$593$	−8.69923e6			−1.01588			−0.507942	−	0.861391i	$-0.669594\pi$
$593$	−8.69923e6			−1.01588			−0.507942	+	0.861391i	$0.669594\pi$
$594$	1.20573e6	−	1.06477e6i	0.140211	−	0.123820i
$595$	1.17865e7	+	1.17865e7i	1.36487	+	1.36487i
$596$	6.68526e6	+	8.58917e6i	0.770909	+	0.990457i
$597$	−1.48200e6	+	1.48200e6i	−0.170182	+	0.170182i
$598$	−7.92468e6	−	491989.i	−0.906210	−	0.0562604i
$599$			2.40337e6i			0.273686i	0.990593	+	0.136843i	$0.0436956\pi$
$599$			2.40337e6i			0.273686i	−0.990593	+	0.136843i	$0.956304\pi$
$600$	87330.8	−	464066.i	0.00990351	−	0.0526261i
$601$		−	1.39197e7i		−	1.57197i	−0.618247	−	0.785984i	$-0.712157\pi$
$601$		−	1.39197e7i		−	1.57197i	0.618247	−	0.785984i	$-0.287843\pi$
$602$	−103470.	+	1.66664e6i	−0.0116365	+	0.187434i
$603$	−1.67992e6	+	1.67992e6i	−0.188147	+	0.188147i
$604$	6.98238e6	+	870331.i	0.778774	+	0.0970716i
$605$	−367715.	−	367715.i	−0.0408435	−	0.0408435i
$606$	−2.86248e6	−	3.24143e6i	−0.316636	−	0.358554i
$607$	1.86255e6			0.205181			0.102590	−	0.994724i	$-0.467287\pi$
$607$	1.86255e6			0.205181			0.102590	+	0.994724i	$0.467287\pi$
$608$	4.18872e6	−	1.30756e7i	0.459539	−	1.43450i
$609$	−1.35757e7			−1.48326
$610$	−5.67699e6	−	6.42854e6i	−0.617723	−	0.699500i
$611$	5.64143e6	+	5.64143e6i	0.611345	+	0.611345i
$612$	−3.40500e6	−	424422.i	−0.367484	−	0.0458057i
$613$	−4.58926e6	+	4.58926e6i	−0.493278	+	0.493278i	−0.909337	−	0.416060i	$-0.863411\pi$
$613$	−4.58926e6	+	4.58926e6i	−0.493278	+	0.493278i	0.416060	+	0.909337i	$0.363411\pi$
$614$	531190.	−	8.55610e6i	0.0568629	−	0.915914i
$615$			2.32968e6i			0.248375i
$616$	−1.49517e7	−	2.81370e6i	−1.58759	−	0.298762i
$617$			1.75932e7i			1.86051i	0.366915	+	0.930255i	$0.380414\pi$
$617$			1.75932e7i			1.86051i	−0.366915	+	0.930255i	$0.619586\pi$
$618$	−8.79964e6	−	546310.i	−0.926817	−	0.0575397i
$619$	−9.03302e6	+	9.03302e6i	−0.947559	+	0.947559i	−0.998692	−	0.0511331i	$-0.983717\pi$
$619$	−9.03302e6	+	9.03302e6i	−0.947559	+	0.947559i	0.0511331	+	0.998692i	$0.483717\pi$
$620$	−7.12931e6	−	9.15968e6i	−0.744849	−	0.956976i
$621$	−702055.	−	702055.i	−0.0730537	−	0.0730537i
$622$	3.65619e6	−	3.22875e6i	0.378924	−	0.334625i
$623$	−4.55825e6			−0.470520
$624$	−2.33153e6	+	9.20724e6i	−0.239706	+	0.946603i
$625$	1.05874e7			1.08415
$626$	−6.03253e6	+	5.32727e6i	−0.615267	+	0.543337i
$627$	−5.88390e6	−	5.88390e6i	−0.597718	−	0.597718i
$628$	6.94143e6	−	5.40277e6i	0.702344	−	0.546660i
$629$	5.36542e6	−	5.36542e6i	0.540726	−	0.540726i
$630$	5.75829e6	+	357493.i	0.578019	+	0.0358853i
$631$		−	1.68988e7i		−	1.68959i	−0.535087	−	0.844797i	$-0.679721\pi$
$631$		−	1.68988e7i		−	1.68959i	0.535087	−	0.844797i	$-0.320279\pi$
$632$	−3.79359e6	+	2.59193e6i	−0.377796	+	0.258125i
$633$		−	9.44145e6i		−	0.936547i
$634$	1.02413e6	−	1.64961e7i	0.101189	−	1.62989i
$635$	−3.72456e6	+	3.72456e6i	−0.366556	+	0.366556i
$636$	376838.	−	3.02325e6i	0.0369413	−	0.296368i
$637$	2.15847e7	+	2.15847e7i	2.10765	+	2.10765i
$638$	1.02250e7	+	1.15787e7i	0.994517	+	1.12618i
$639$	−3.42529e6			−0.331852
$640$	4.55516e6	−	9.82771e6i	0.439596	−	0.948423i
$641$	−776431.			−0.0746376			−0.0373188	−	0.999303i	$-0.511882\pi$
$641$	−776431.			−0.0746376			−0.0373188	+	0.999303i	$0.511882\pi$
$642$	2.19043e6	+	2.48041e6i	0.209745	+	0.237512i
$643$	−4.12660e6	−	4.12660e6i	−0.393609	−	0.393609i	0.482362	−	0.875972i	$-0.339779\pi$
$643$	−4.12660e6	−	4.12660e6i	−0.393609	−	0.393609i	−0.875972	+	0.482362i	$0.839779\pi$
$644$	−1.16152e6	+	9.31846e6i	−0.110360	+	0.885380i
$645$	−509484.	+	509484.i	−0.0482205	+	0.0482205i
$646$	−1.09987e6	+	1.77161e7i	−0.103696	+	1.67027i
$647$			5.42337e6i			0.509341i	0.967028	+	0.254671i	$0.0819670\pi$
$647$			5.42337e6i			0.509341i	−0.967028	+	0.254671i	$0.918033\pi$
$648$	−980635.	+	670007.i	−0.0917424	+	0.0626819i
$649$			5.07151e6i			0.472634i
$650$	1.68652e6	+	104705.i	0.156570	+	0.00972036i
$651$	8.51142e6	−	8.51142e6i	0.787136	−	0.787136i
$652$	338618.	−	263558.i	0.0311954	−	0.0242805i
$653$	−1.25536e6	−	1.25536e6i	−0.115208	−	0.115208i	0.647152	−	0.762361i	$-0.275960\pi$
$653$	−1.25536e6	−	1.25536e6i	−0.115208	−	0.115208i	−0.762361	+	0.647152i	$0.775960\pi$
$654$	−728615.	+	643434.i	−0.0666122	+	0.0588247i
$655$	−4.25935e6			−0.387918
$656$	−1.11348e6	+	4.39716e6i	−0.101024	+	0.398944i
$657$	−2.32758e6			−0.210373
$658$	7.07274e6	−	6.24588e6i	0.636829	−	0.562379i
$659$	−9.38952e6	−	9.38952e6i	−0.842228	−	0.842228i	0.146920	−	0.989148i	$-0.453064\pi$
$659$	−9.38952e6	−	9.38952e6i	−0.842228	−	0.842228i	−0.989148	+	0.146920i	$0.953064\pi$
$660$	−4.03216e6	−	5.18048e6i	−0.360311	−	0.462925i
$661$	9.78639e6	−	9.78639e6i	0.871202	−	0.871202i	−0.121402	−	0.992603i	$-0.538739\pi$
$661$	9.78639e6	−	9.78639e6i	0.871202	−	0.871202i	0.992603	+	0.121402i	$0.0387389\pi$
$662$	1.08024e7	+	670647.i	0.958022	+	0.0594770i
$663$		−	1.22788e7i		−	1.08486i
$664$	4.54065e6	+	854488.i	0.399667	+	0.0752117i
$665$		−	2.98448e7i		−	2.61706i
$666$	162737.	−	2.62128e6i	0.0142168	−	0.228996i
$667$	6.74186e6	−	6.74186e6i	0.586766	−	0.586766i
$668$	−1.10549e7	−	1.37796e6i	−0.958547	−	0.119480i
$669$	6.28903e6	+	6.28903e6i	0.543274	+	0.543274i
$670$	6.41792e6	+	7.26755e6i	0.552341	+	0.625462i
$671$	−1.01200e7			−0.867713
$672$	1.06976e7	+	3.42695e6i	0.913827	+	0.292742i
$673$	−9.15217e6			−0.778908			−0.389454	−	0.921046i	$-0.627336\pi$
$673$	−9.15217e6			−0.778908			−0.389454	+	0.921046i	$0.627336\pi$
$674$	4.72976e6	+	5.35591e6i	0.401042	+	0.454134i
$675$	149411.	+	149411.i	0.0126218	+	0.0126218i
$676$	−2.19362e7	−	2.73427e6i	−1.84626	−	0.230131i
$677$	−5.53216e6	+	5.53216e6i	−0.463898	+	0.463898i	−0.899931	−	0.436033i	$-0.856383\pi$
$677$	−5.53216e6	+	5.53216e6i	−0.463898	+	0.463898i	0.436033	+	0.899931i	$0.356383\pi$
$678$	168885.	−	2.72030e6i	0.0141097	−	0.227271i
$679$		−	1.84801e7i		−	1.53826i
$680$	−2.58983e6	+	1.37621e7i	−0.214783	+	1.14133i
$681$			1.08984e7i			0.900520i
$682$	−1.36700e7	−	848680.i	−1.12541	−	0.0698687i
$683$	5.05391e6	−	5.05391e6i	0.414549	−	0.414549i	−0.468771	−	0.883320i	$-0.655303\pi$
$683$	5.05391e6	−	5.05391e6i	0.414549	−	0.414549i	0.883320	+	0.468771i	$0.155303\pi$
$684$	3.77359e6	+	4.84828e6i	0.308400	+	0.396230i
$685$	7.37325e6	+	7.37325e6i	0.600388	+	0.600388i
$686$	1.17058e7	−	1.03373e7i	0.949713	−	0.838683i
$687$	5.46664e6			0.441905
$688$	−1.20514e6	+	718116.i	−0.0970656	+	0.0578393i
$689$	1.09022e7			0.874912
$690$	−3.03718e6	+	2.68211e6i	−0.242855	+	0.214463i
$691$	−6.80745e6	−	6.80745e6i	−0.542362	−	0.542362i	0.381859	−	0.924221i	$-0.375284\pi$
$691$	−6.80745e6	−	6.80745e6i	−0.542362	−	0.542362i	−0.924221	+	0.381859i	$0.875284\pi$
$692$	−1.58400e7	+	1.23289e7i	−1.25745	+	0.978719i
$693$	4.81385e6	−	4.81385e6i	0.380767	−	0.380767i
$694$	−1.31454e6	−	81610.9i	−0.103604	−	0.00643205i
$695$			1.57030e7i			1.23316i
$696$	−6.43410e6	−	9.41707e6i	−0.503460	−	0.736873i
$697$		−	5.86406e6i		−	0.457211i
$698$	−39180.2	+	631093.i	−0.00304389	+	0.0490292i
$699$	5.54692e6	−	5.54692e6i	0.429397	−	0.429397i
$700$	247193.	−	1.98315e6i	0.0190674	−	0.152971i
$701$	5.30646e6	+	5.30646e6i	0.407859	+	0.407859i	0.880991	−	0.473132i	$-0.156877\pi$
$701$	5.30646e6	+	5.30646e6i	0.407859	+	0.407859i	−0.473132	+	0.880991i	$0.656877\pi$
$702$	−2.81319e6	−	3.18562e6i	−0.215455	−	0.243978i
$703$	−1.35859e7			−1.03681
$704$	−5.13446e6	−	1.17051e7i	−0.390448	−	0.890109i
$705$	4.07145e6			0.308515
$706$	1.50635e7	+	1.70577e7i	1.13740	+	1.28798i
$707$	−1.29413e7	−	1.29413e7i	−0.973712	−	0.973712i
$708$	463152.	−	3.71572e6i	0.0347249	−	0.278586i
$709$	2.21939e6	−	2.21939e6i	0.165813	−	0.165813i	−0.619323	−	0.785136i	$-0.712593\pi$
$709$	2.21939e6	−	2.21939e6i	0.165813	−	0.165813i	0.785136	+	0.619323i	$0.212593\pi$
$710$	−866186.	+	1.39520e7i	−0.0644860	+	1.03870i
$711$		−	2.05588e6i		−	0.152519i
$712$	−2.16035e6	−	3.16193e6i	−0.159707	−	0.233751i
$713$			8.45377e6i			0.622768i
$714$	−1.44942e7	−	899849.i	−1.06402	−	0.0660578i
$715$	1.66109e7	−	1.66109e7i	1.21514	−	1.21514i
$716$	−6.58412e6	+	5.12466e6i	−0.479971	+	0.373579i
$717$	−1.82924e6	−	1.82924e6i	−0.132884	−	0.132884i
$718$	−1.06194e7	+	9.37791e6i	−0.768757	+	0.678883i
$719$	−5.43581e6			−0.392141			−0.196070	−	0.980590i	$-0.562818\pi$
$719$	−5.43581e6			−0.392141			−0.196070	+	0.980590i	$0.562818\pi$
$720$	2.48112e6	+	4.16380e6i	0.178368	+	0.299336i
$721$	−3.73135e7			−2.67318
$722$	1.33231e7	−	1.17655e7i	0.951179	−	0.839978i
$723$	1.28964e6	+	1.28964e6i	0.0917538	+	0.0917538i
$724$	3.34771e6	+	4.30111e6i	0.237357	+	0.304954i
$725$	−1.43480e6	+	1.43480e6i	−0.101378	+	0.101378i
$726$	452192.	+	28073.5i	0.0318406	+	0.00197677i
$727$			1.58718e7i			1.11375i	0.830595	+	0.556877i	$0.188000\pi$
$727$			1.58718e7i			1.11375i	−0.830595	+	0.556877i	$0.812000\pi$
$728$	−7.43399e6	+	3.95034e7i	−0.519869	+	2.76252i
$729$		−	531441.i		−	0.0370370i
$730$	−588597.	+	9.48078e6i	−0.0408800	+	0.658472i
$731$	1.28243e6	−	1.28243e6i	0.0887645	−	0.0887645i
$732$	7.41461e6	+	924207.i	0.511459	+	0.0637517i
$733$	−5.38587e6	−	5.38587e6i	−0.370251	−	0.370251i	0.497318	−	0.867568i	$-0.334318\pi$
$733$	−5.38587e6	−	5.38587e6i	−0.370251	−	0.370251i	−0.867568	+	0.497318i	$0.834318\pi$
$734$	−1.69145e6	−	1.91537e6i	−0.115883	−	0.131224i
$735$	1.55778e7			1.06362
$736$	−7.01445e6	+	3.61071e6i	−0.477308	+	0.245696i
$737$	1.14408e7			0.775871
$738$	−1.34351e6	−	1.52137e6i	−0.0908032	−	0.102824i
$739$	−1.30357e7	−	1.30357e7i	−0.878055	−	0.878055i	0.115278	−	0.993333i	$-0.463224\pi$
$739$	−1.30357e7	−	1.30357e7i	−0.878055	−	0.878055i	−0.993333	+	0.115278i	$0.963224\pi$
$740$	−1.06359e7	−	1.32574e6i	−0.713998	−	0.0889975i
$741$	−1.55457e7	+	1.55457e7i	−1.04007	+	1.04007i
$742$	798961.	−	1.28692e7i	0.0532741	−	0.858108i
$743$			1.35820e7i			0.902594i	0.892374	+	0.451297i	$0.149039\pi$
$743$			1.35820e7i			0.902594i	−0.892374	+	0.451297i	$0.850961\pi$
$744$	9.93807e6	+	1.87021e6i	0.658218	+	0.123867i
$745$			1.98762e7i			1.31203i
$746$	2.95428e7	+	1.83411e6i	1.94359	+	0.120664i
$747$	−1.46191e6	+	1.46191e6i	−0.0958559	+	0.0958559i
$748$	1.01494e7	+	1.30398e7i	0.663263	+	0.852155i
$749$	9.90297e6	+	9.90297e6i	0.645001	+	0.645001i
$750$	−6.32248e6	+	5.58333e6i	−0.410426	+	0.362444i
$751$	1.81815e6			0.117633			0.0588165	−	0.998269i	$-0.481267\pi$
$751$	1.81815e6			0.117633			0.0588165	+	0.998269i	$0.481267\pi$
$752$	7.68467e6	+	1.94597e6i	0.495542	+	0.125485i
$753$	1.55897e7			1.00196
$754$	3.05916e7	−	2.70152e7i	1.95963	−	1.73053i
$755$	9.08599e6	+	9.08599e6i	0.580102	+	0.580102i
$756$	−3.96656e6	+	3.08732e6i	−0.252412	+	0.196461i
$757$	1.81070e7	−	1.81070e7i	1.14843	−	1.14843i	0.161574	−	0.986861i	$-0.448343\pi$
$757$	1.81070e7	−	1.81070e7i	1.14843	−	1.14843i	0.986861	−	0.161574i	$-0.0516571\pi$
$758$	−1.58640e7	−	984890.i	−1.00286	−	0.0622608i
$759$			4.78124e6i			0.301256i
$760$	2.07025e7	−	1.41447e7i	1.30013	−	0.888301i
$761$		−	1.40032e7i		−	0.876526i	−0.898847	−	0.438263i	$-0.855594\pi$
$761$		−	1.40032e7i		−	0.876526i	0.898847	−	0.438263i	$-0.144406\pi$
$762$	284354.	−	4.58022e6i	0.0177408	−	0.285758i
$763$	−2.90898e6	+	2.90898e6i	−0.180896	+	0.180896i
$764$	−878983.	+	7.05180e6i	−0.0544813	+	0.437085i
$765$	−4.43084e6	−	4.43084e6i	−0.273736	−	0.273736i
$766$	−1.67121e7	−	1.89245e7i	−1.02910	−	1.16534i
$767$	1.33993e7			0.822419
$768$	2.69288e6	+	9.04482e6i	0.164746	+	0.553346i
$769$	−2.17431e7			−1.32589			−0.662943	−	0.748670i	$-0.730693\pi$
$769$	−2.17431e7			−1.32589			−0.662943	+	0.748670i	$0.730693\pi$
$770$	−1.83906e7	−	2.08253e7i	−1.11781	−	1.26580i
$771$	−8.12656e6	−	8.12656e6i	−0.492346	−	0.492346i
$772$	−316957.	+	2.54284e6i	−0.0191407	+	0.153559i
$773$	1.33820e6	−	1.33820e6i	0.0805510	−	0.0805510i	−0.665683	−	0.746234i	$-0.731860\pi$
$773$	1.33820e6	−	1.33820e6i	0.0805510	−	0.0805510i	0.746234	+	0.665683i	$0.231860\pi$
$774$	38897.0	−	626531.i	0.00233380	−	0.0375915i
$775$		−	1.79912e6i		−	0.107599i
$776$	1.28191e7	−	8.75852e6i	0.764195	−	0.522127i
$777$		−	1.11151e7i		−	0.660483i
$778$	2.44159e7	+	1.51581e6i	1.44618	+	0.0897836i
$779$	−7.42424e6	+	7.42424e6i	−0.438337	+	0.438337i
$780$	−1.36872e7	+	1.06532e7i	−0.805523	+	0.626968i
$781$	1.16637e7	+	1.16637e7i	0.684240	+	0.684240i
$782$	7.64491e6	−	6.75116e6i	0.447049	−	0.394786i
$783$	5.10345e6			0.297481
$784$	2.94024e7	+	7.44550e6i	1.70841	+	0.432617i
$785$	1.60632e7			0.930374
$786$	2.78153e6	−	2.45635e6i	0.160593	−	0.141819i
$787$	1.96781e7	+	1.96781e7i	1.13252	+	1.13252i	0.989757	+	0.142763i	$0.0455986\pi$
$787$	1.96781e7	+	1.96781e7i	1.13252	+	1.13252i	0.142763	+	0.989757i	$0.454401\pi$
$788$	−7.62657e6	−	9.79855e6i	−0.437536	−	0.562142i
$789$	−5.28257e6	+	5.28257e6i	−0.302102	+	0.302102i
$790$	−8.37410e6	−	519891.i	−0.477387	−	0.0296377i
$791$		−	1.15350e7i		−	0.655507i
$792$	5.62072e6	+	1.05774e6i	0.318404	+	0.0599193i
$793$			2.67379e7i			1.50988i
$794$	−684381.	+	1.10236e7i	−0.0385254	+	0.620544i
$795$	3.93407e6	−	3.93407e6i	0.220762	−	0.220762i
$796$	−7.39475e6	−	921732.i	−0.413658	−	0.0515611i
$797$	1.13108e7	+	1.13108e7i	0.630737	+	0.630737i	0.948253	−	0.317516i	$-0.102849\pi$
$797$	1.13108e7	+	1.13108e7i	0.630737	+	0.630737i	−0.317516	+	0.948253i	$0.602849\pi$
$798$	1.72113e7	+	1.94898e7i	0.956768	+	1.08343i
$799$	−1.02483e7			−0.567917
$800$	1.49281e6	−	768427.i	0.0824668	−	0.0424500i
$801$	1.71356e6			0.0943667
$802$	−1.24517e7	−	1.41002e7i	−0.683587	−	0.774084i
$803$	7.92580e6	+	7.92580e6i	0.433764	+	0.433764i
$804$	−8.38232e6	−	1.04483e6i	−0.457324	−	0.0570039i
$805$	−1.21259e7	+	1.21259e7i	−0.659513	+	0.659513i
$806$	−2.24227e6	+	3.61172e7i	−0.121577	+	1.95829i
$807$			5.26114e6i			0.284378i
$808$	2.84359e6	−	1.51105e7i	0.153228	−	0.814236i
$809$		−	2.05855e7i		−	1.10584i	−0.833236	−	0.552918i	$-0.813514\pi$
$809$		−	2.05855e7i		−	1.10584i	0.833236	−	0.552918i	$-0.186486\pi$
$810$	−2.16469e6	−	134391.i	−0.115927	−	0.00719708i
$811$	−1.28711e7	+	1.28711e7i	−0.687168	+	0.687168i	−0.961605	−	0.274437i	$-0.911509\pi$
$811$	−1.28711e7	+	1.28711e7i	−0.687168	+	0.687168i	0.274437	+	0.961605i	$0.411509\pi$
$812$	−2.96476e7	−	3.80910e7i	−1.57797	−	2.02737i
$813$	8.79123e6	+	8.79123e6i	0.466470	+	0.466470i
$814$	−9.48004e6	+	8.37175e6i	−0.501475	+	0.442848i
$815$	783596.			0.0413236
$816$	−6.24525e6	−	1.04807e7i	−0.328340	−	0.551018i
$817$	−3.24726e6			−0.170201
$818$	−1.15195e7	+	1.01727e7i	−0.601934	+	0.531563i
$819$	−1.27185e7	−	1.27185e7i	−0.662562	−	0.662562i
$820$	−6.53668e6	+	5.08773e6i	−0.339486	+	0.264235i
$821$	1.88643e7	−	1.88643e7i	0.976748	−	0.976748i	−0.0229877	−	0.999736i	$-0.507318\pi$
$821$	1.88643e7	−	1.88643e7i	0.976748	−	0.976748i	0.999736	+	0.0229877i	$0.00731787\pi$
$822$	−9.06714e6	−	562917.i	−0.468048	−	0.0290579i
$823$			2.11691e7i			1.08944i	0.838619	+	0.544719i	$0.183364\pi$
$823$			2.11691e7i			1.08944i	−0.838619	+	0.544719i	$0.816636\pi$
$824$	−1.76845e7	−	2.58833e7i	−0.907349	−	1.32801i
$825$		−	1.01754e6i		−	0.0520494i
$826$	981963.	−	1.58169e7i	0.0500778	−	0.806624i
$827$	9.32727e6	−	9.32727e6i	0.474232	−	0.474232i	−0.429049	−	0.903281i	$-0.641151\pi$
$827$	9.32727e6	−	9.32727e6i	0.474232	−	0.474232i	0.903281	+	0.429049i	$0.141151\pi$
$828$	436644.	−	3.50305e6i	0.0221336	−	0.177570i
$829$	4.74783e6	+	4.74783e6i	0.239944	+	0.239944i	0.816827	−	0.576883i	$-0.195731\pi$
$829$	4.74783e6	+	4.74783e6i	0.239944	+	0.239944i	−0.576883	+	0.816827i	$0.695731\pi$
$830$	5.58502e6	+	6.32440e6i	0.281404	+	0.318657i
$831$	−1.94500e7			−0.977050
$832$	−3.09257e7	+	1.35656e7i	−1.54886	+	0.679408i
$833$	−3.92111e7			−1.95793
$834$	−9.05583e6	−	1.02547e7i	−0.450830	−	0.510513i
$835$	−1.43854e7	−	1.43854e7i	−0.714014	−	0.714014i
$836$	3.65949e6	−	2.93589e7i	0.181095	−	1.45286i
$837$	−3.19966e6	+	3.19966e6i	−0.157867	+	0.157867i
$838$	1.34574e6	−	2.16764e7i	0.0661990	−	1.06630i
$839$			1.14886e7i			0.563460i	0.959494	+	0.281730i	$0.0909083\pi$
$839$			1.14886e7i			0.563460i	−0.959494	+	0.281730i	$0.909092\pi$
$840$	1.15723e7	+	1.69375e7i	0.565878	+	0.828229i
$841$			2.84974e7i			1.38936i
$842$	7.46847e6	+	463667.i	0.363038	+	0.0225385i
$843$	9.70308e6	−	9.70308e6i	0.470263	−	0.470263i
$844$	2.64911e7	−	2.06190e7i	1.28010	−	0.996347i
$845$	−2.85449e7	−	2.85449e7i	−1.37527	−	1.37527i
$846$	−2.65882e6	+	2.34799e6i	−0.127721	+	0.112790i
$847$	1.91745e6			0.0918366
$848$	9.30567e6	−	5.54505e6i	0.444384	−	0.264799i
$849$	1.37009e7			0.652349
$850$	−1.62698e6	+	1.43677e6i	−0.0772388	+	0.0682089i
$851$	5.51991e6	+	5.51991e6i	0.261281	+	0.261281i
$852$	−7.48040e6	−	9.61076e6i	−0.353042	−	0.453585i
$853$	4.62622e6	−	4.62622e6i	0.217698	−	0.217698i	−0.589830	−	0.807528i	$-0.700805\pi$
$853$	4.62622e6	−	4.62622e6i	0.217698	−	0.217698i	0.807528	+	0.589830i	$0.200805\pi$
$854$	3.15621e7	+	1.95948e6i	1.48089	+	0.0919381i
$855$			1.12194e7i			0.524873i
$856$	−2.17597e6	+	1.15629e7i	−0.101501	+	0.539362i
$857$		−	3.34246e7i		−	1.55458i	−0.629140	−	0.777292i	$-0.716593\pi$
$857$		−	3.34246e7i		−	1.55458i	0.629140	−	0.777292i	$-0.283407\pi$
$858$	−1.26817e6	+	2.04270e7i	−0.0588112	+	0.947297i
$859$	−8.57932e6	+	8.57932e6i	−0.396707	+	0.396707i	−0.877070	−	0.480363i	$-0.840505\pi$
$859$	−8.57932e6	+	8.57932e6i	−0.396707	+	0.396707i	0.480363	+	0.877070i	$0.340505\pi$
$860$	−2.54217e6	−	316874.i	−0.117209	−	0.0146097i
$861$	−6.07406e6	−	6.07406e6i	−0.279236	−	0.279236i
$862$	5.23250e6	+	5.92521e6i	0.239851	+	0.271604i
$863$	1.58687e6			0.0725295			0.0362647	−	0.999342i	$-0.488454\pi$
$863$	1.58687e6			0.0725295			0.0362647	+	0.999342i	$0.488454\pi$
$864$	−4.02151e6	−	1.28828e6i	−0.183276	−	0.0587118i
$865$	−3.66555e7			−1.66571
$866$	−2.51848e7	−	2.85189e7i	−1.14115	−	1.29222i
$867$	2.11699e6	+	2.11699e6i	0.0956469	+	0.0956469i
$868$	4.24695e7	+	5.29368e6i	1.91328	+	0.238484i
$869$	−7.00063e6	+	7.00063e6i	−0.314476	+	0.314476i
$870$	1.29056e6	−	2.07876e7i	0.0578069	−	0.931120i
$871$		−	3.02275e7i		−	1.35007i
$872$	−3.39657e6	−	639187.i	−0.151269	−	0.0284667i
$873$			6.94714e6i			0.308511i
$874$	−1.82263e7	−	1.13154e6i	−0.807085	−	0.0501064i
$875$	−2.52424e7	+	2.52424e7i	−1.11458	+	1.11458i
$876$	−5.08314e6	−	6.53078e6i	−0.223806	−	0.287544i
$877$	8.18596e6	+	8.18596e6i	0.359394	+	0.359394i	0.863589	−	0.504196i	$-0.168211\pi$
$877$	8.18596e6	+	8.18596e6i	0.359394	+	0.359394i	−0.504196	+	0.863589i	$0.668211\pi$
$878$	2.27846e7	−	2.01209e7i	0.997484	−	0.880870i
$879$	94944.6			0.00414475
$880$	5.72980e6	−	2.26271e7i	0.249421	−	0.984967i
$881$	−2.12594e7			−0.922809			−0.461404	−	0.887190i	$-0.652654\pi$
$881$	−2.12594e7			−0.922809			−0.461404	+	0.887190i	$0.652654\pi$
$882$	−1.01729e7	+	8.98365e6i	−0.440327	+	0.388849i
$883$	1.53991e7	+	1.53991e7i	0.664649	+	0.664649i	0.956472	−	0.291823i	$-0.0942618\pi$
$883$	1.53991e7	+	1.53991e7i	0.664649	+	0.664649i	−0.291823	+	0.956472i	$0.594262\pi$
$884$	3.44522e7	−	2.68154e7i	1.48281	−	1.15413i
$885$	4.83517e6	−	4.83517e6i	0.207517	−	0.207517i
$886$	1.23279e6	+	76535.7i	0.0527601	+	0.00327552i
$887$			8.02330e6i			0.342408i	0.985236	+	0.171204i	$0.0547658\pi$
$887$			8.02330e6i			0.342408i	−0.985236	+	0.171204i	$0.945234\pi$
$888$	7.71025e6	−	5.26793e6i	0.328122	−	0.224186i
$889$		−	1.94217e7i		−	0.824201i
$890$	433326.	−	6.97976e6i	0.0183375	−	0.295369i
$891$	−1.80965e6	+	1.80965e6i	−0.0763659	+	0.0763659i
$892$	−3.91147e6	+	3.13804e7i	−0.164599	+	1.32052i
$893$	1.29749e7	+	1.29749e7i	0.544474	+	0.544474i
$894$	−1.14625e7	−	1.29800e7i	−0.479662	−	0.543163i
$895$	−1.52363e7			−0.635803
$896$	1.37468e7	+	3.74997e7i	0.572049	+	1.56048i
$897$	1.26324e7			0.524208
$898$	2.98118e7	+	3.37585e7i	1.23367	+	1.39699i
$899$	−3.07265e7	−	3.07265e7i	−1.26798	−	1.26798i
$900$	−92926.0	+	745515.i	−0.00382412	+	0.0306796i
$901$	−9.90249e6	+	9.90249e6i	−0.406380	+	0.406380i
$902$	−605648.	+	9.75543e6i	−0.0247859	+	0.399236i
$903$		−	2.65671e6i		−	0.108424i
$904$	8.00152e6	−	5.46694e6i	0.325650	−	0.222497i
$905$			9.95320e6i			0.403963i
$906$	−1.11734e7	−	693677.i	−0.452234	−	0.0280761i
$907$	2.11154e7	−	2.11154e7i	0.852276	−	0.852276i	−0.138137	−	0.990413i	$-0.544111\pi$
$907$	2.11154e7	−	2.11154e7i	0.852276	−	0.852276i	0.990413	+	0.138137i	$0.0441113\pi$
$908$	−3.05789e7	+	2.38007e7i	−1.23086	+	0.958020i
$909$	4.86498e6	+	4.86498e6i	0.195286	+	0.195286i
$910$	−5.50219e7	+	4.85894e7i	−2.20258	+	1.94508i
$911$	2.62189e7			1.04669			0.523345	−	0.852121i	$-0.324684\pi$
$911$	2.62189e7			1.04669			0.523345	+	0.852121i	$0.324684\pi$
$912$	−5.36237e6	+	2.11761e7i	−0.213486	+	0.843060i
$913$	9.95610e6			0.395287
$914$	−3.01678e7	+	2.66409e7i	−1.19448	+	1.05483i
$915$	9.64843e6	+	9.64843e6i	0.380982	+	0.380982i
$916$	1.19385e7	+	1.53384e7i	0.470121	+	0.604008i
$917$	1.11052e7	−	1.11052e7i	0.436117	−	0.436117i
$918$	5.44876e6	+	338276.i	0.213398	+	0.0132484i
$919$			1.40968e7i			0.550593i	0.961359	+	0.275297i	$0.0887760\pi$
$919$			1.40968e7i			0.550593i	−0.961359	+	0.275297i	$0.911224\pi$
$920$	−1.41583e7	−	2.66440e6i	−0.551497	−	0.103784i
$921$			1.36389e7i			0.529821i
$922$	2.20895e6	−	3.55806e7i	0.0855775	−	1.37843i
$923$	3.08163e7	−	3.08163e7i	1.19063	−	1.19063i
$924$	2.40197e7	+	2.99397e6i	0.925522	+	0.115363i
$925$	−1.17474e6	−	1.17474e6i	−0.0451428	−	0.0451428i
$926$	−1.86686e7	−	2.11400e7i	−0.715458	−	0.810174i
$927$	1.40271e7			0.536128
$928$	1.23714e7	−	3.86187e7i	0.471573	−	1.47207i
$929$	3.81148e7			1.44895			0.724476	−	0.689300i	$-0.242082\pi$
$929$	3.81148e7			1.44895			0.724476	+	0.689300i	$0.242082\pi$
$930$	1.22239e7	+	1.38421e7i	0.463448	+	0.524802i
$931$	4.96435e7	+	4.96435e7i	1.87711	+	1.87711i
$932$	2.76775e7	+	3.44991e6i	1.04373	+	0.130097i
$933$	−5.48748e6	+	5.48748e6i	−0.206380	+	0.206380i
$934$	−1.54841e6	+	2.49408e7i	−0.0580788	+	0.935500i
$935$			3.01755e7i			1.12882i
$936$	2.79463e6	−	1.48503e7i	0.104264	−	0.554047i
$937$		−	4.25158e7i		−	1.58198i	−0.611829	−	0.790990i	$-0.709566\pi$
$937$		−	4.25158e7i		−	1.58198i	0.611829	−	0.790990i	$-0.290434\pi$
$938$	−3.56814e7	−	2.21522e6i	−1.32414	−	0.0822071i
$939$	9.05406e6	−	9.05406e6i	0.335104	−	0.335104i
$940$	8.89155e6	+	1.14238e7i	0.328215	+	0.421687i
$941$	−2.11968e7	−	2.11968e7i	−0.780361	−	0.780361i	0.199531	−	0.979892i	$-0.436058\pi$
$941$	−2.11968e7	−	2.11968e7i	−0.780361	−	0.780361i	−0.979892	+	0.199531i	$0.936058\pi$
$942$	−1.04899e7	+	9.26355e6i	−0.385163	+	0.340134i
$943$	6.03291e6			0.220926
$944$	1.14371e7	−	6.81514e6i	0.417722	−	0.248912i
$945$	−9.17902e6			−0.334362
$946$	−2.26589e6	+	2.00099e6i	−0.0823212	+	0.0726972i
$947$	3.03148e7	+	3.03148e7i	1.09845	+	1.09845i	0.994592	+	0.103855i	$0.0331178\pi$
$947$	3.03148e7	+	3.03148e7i	1.09845	+	1.09845i	0.103855	+	0.994592i	$0.466882\pi$
$948$	5.76845e6	−	4.48979e6i	0.208467	−	0.162258i
$949$	2.09405e7	−	2.09405e7i	0.754782	−	0.754782i
$950$	3.87889e6	+	240814.i	0.139444	+	0.00865711i
$951$			2.62957e7i			0.942829i
$952$	−2.91288e7	−	4.26335e7i	−1.04167	−	1.52461i
$953$		−	4.47936e6i		−	0.159766i	−0.996804	−	0.0798829i	$-0.974545\pi$
$953$		−	4.47936e6i		−	0.159766i	0.996804	−	0.0798829i	$-0.0254546\pi$
$954$	−300350.	+	4.83786e6i	−0.0106846	+	0.172101i
$955$	−9.17631e6	+	9.17631e6i	−0.325582	+	0.325582i
$956$	1.13770e6	−	9.12735e6i	0.0402607	−	0.322998i
$957$	−1.73781e7	−	1.73781e7i	−0.613370	−	0.613370i
$958$	1.36444e7	+	1.54507e7i	0.480332	+	0.543920i
$959$	−3.84478e7			−1.34997
$960$	−6.26443e6	+	1.60548e7i	−0.219383	+	0.562247i
$961$	9.89942e6			0.345781
$962$	2.21187e7	+	2.50469e7i	0.770589	+	0.872604i
$963$	−3.72278e6	−	3.72278e6i	−0.129360	−	0.129360i
$964$	−802095.	+	6.43494e6i	−0.0277992	+	0.223024i
$965$	−3.30893e6	+	3.30893e6i	−0.114385	+	0.114385i
$966$	925759.	−	1.49116e7i	0.0319194	−	0.514140i
$967$		−	4.28745e6i		−	0.147446i	−0.997279	−	0.0737230i	$-0.976512\pi$
$967$		−	4.28745e6i		−	0.147446i	0.997279	−	0.0737230i	$-0.0234881\pi$
$968$	908763.	+	1.33008e6i	0.0311718	+	0.0456237i
$969$		−	2.82405e7i		−	0.966190i
$970$	2.82974e7	+	1.75679e6i	0.965644	+	0.0599502i
$971$	−8.84243e6	+	8.84243e6i	−0.300970	+	0.300970i	−0.841393	−	0.540423i	$-0.818264\pi$
$971$	−8.84243e6	+	8.84243e6i	−0.300970	+	0.300970i	0.540423	+	0.841393i	$0.318264\pi$
$972$	1.49113e6	−	1.16060e6i	0.0506233	−	0.0394019i
$973$	−4.09416e7	−	4.09416e7i	−1.38638	−	1.38638i
$974$	−180838.	+	159697.i	−0.00610791	+	0.00539385i
$975$	−2.68841e6			−0.0905698
$976$	1.35994e7	+	2.28225e7i	0.456979	+	0.766898i
$977$	3.82588e7			1.28231			0.641157	−	0.767410i	$-0.278455\pi$
$977$	3.82588e7			1.28231			0.641157	+	0.767410i	$0.278455\pi$
$978$	−511720.	+	451895.i	−0.0171074	+	0.0151074i
$979$	−5.83498e6	−	5.83498e6i	−0.194573	−	0.194573i
$980$	3.40200e7	+	4.37087e7i	1.13154	+	1.45379i
$981$	1.09356e6	−	1.09356e6i	0.0362802	−	0.0362802i
$982$	2.40056e7	+	1.49034e6i	0.794390	+	0.0493182i
$983$		−	2.34714e7i		−	0.774739i	−0.921924	−	0.387370i	$-0.873384\pi$
$983$		−	2.34714e7i		−	0.774739i	0.921924	−	0.387370i	$-0.126616\pi$
$984$	1.33465e6	−	7.09216e6i	0.0439419	−	0.233502i
$985$		−	2.26748e7i		−	0.744652i
$986$	−3.24848e6	+	5.23246e7i	−0.106411	+	1.71401i
$987$	−1.06153e7	+	1.06153e7i	−0.346848	+	0.346848i
$988$	−7.75683e7	−	9.66864e6i	−2.52809	−	0.315118i
$989$	1.31935e6	+	1.31935e6i	0.0428915	+	0.0428915i
$990$	6.91351e6	+	7.82875e6i	0.224187	+	0.253866i
$991$	−4.23100e7			−1.36854			−0.684272	−	0.729227i	$-0.739880\pi$
$991$	−4.23100e7			−1.36854			−0.684272	+	0.729227i	$0.739880\pi$
$992$	1.64560e7	+	3.19688e7i	0.530941	+	1.03145i
$993$	−1.72196e7			−0.554179
$994$	−3.41181e7	−	3.86348e7i	−1.09526	−	1.24026i
$995$	−9.62259e6	−	9.62259e6i	−0.308130	−	0.308130i
$996$	−7.29449e6	−	909234.i	−0.232995	−	0.0290421i
$997$	−1.03281e6	+	1.03281e6i	−0.0329066	+	0.0329066i	−0.723369	−	0.690462i	$-0.757407\pi$
$997$	−1.03281e6	+	1.03281e6i	−0.0329066	+	0.0329066i	0.690462	+	0.723369i	$0.257407\pi$
$998$	1.46053e6	−	2.35254e7i	0.0464177	−	0.747670i
$999$			4.17846e6i			0.132465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.j.a.13.6	✓	40
3.2	odd	2		144.6.k.c.109.15		40
4.3	odd	2		192.6.j.a.145.2		40
8.3	odd	2		384.6.j.b.289.19		40
8.5	even	2		384.6.j.a.289.2		40
12.11	even	2		576.6.k.c.145.16		40
16.3	odd	4		384.6.j.b.97.19		40
16.5	even	4	inner	48.6.j.a.37.6	yes	40
16.11	odd	4		192.6.j.a.49.2		40
16.13	even	4		384.6.j.a.97.2		40
48.5	odd	4		144.6.k.c.37.15		40
48.11	even	4		576.6.k.c.433.16		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.j.a.13.6	✓	40	1.1	even	1	trivial
48.6.j.a.37.6	yes	40	16.5	even	4	inner
144.6.k.c.37.15		40	48.5	odd	4
144.6.k.c.109.15		40	3.2	odd	2
192.6.j.a.49.2		40	16.11	odd	4
192.6.j.a.145.2		40	4.3	odd	2
384.6.j.a.97.2		40	16.13	even	4
384.6.j.a.289.2		40	8.5	even	2
384.6.j.b.97.19		40	16.3	odd	4
384.6.j.b.289.19		40	8.3	odd	2
576.6.k.c.145.16		40	12.11	even	2
576.6.k.c.433.16		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)

\(f(q)\)	\(=\)	\(q+(-3.74446 - 4.24017i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-3.95807 + 31.7543i) q^{4} +(-41.3210 + 41.3210i) q^{5} +(3.15468 - 50.8139i) q^{6} -215.468i q^{7} +(149.464 - 102.120i) q^{8} +81.0000i q^{9} +O(q^{10})\)	\(q+(-3.74446 - 4.24017i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-3.95807 + 31.7543i) q^{4} +(-41.3210 + 41.3210i) q^{5} +(3.15468 - 50.8139i) q^{6} -215.468i q^{7} +(149.464 - 102.120i) q^{8} +81.0000i q^{9} +(329.933 + 20.4833i) q^{10} +(275.819 - 275.819i) q^{11} +(-227.272 + 176.894i) q^{12} +(-728.733 - 728.733i) q^{13} +(-913.622 + 806.812i) q^{14} -525.930 q^{15} +(-992.667 - 251.371i) q^{16} +1323.82 q^{17} +(343.454 - 303.301i) q^{18} +(-1676.04 - 1676.04i) q^{19} +(-1148.57 - 1475.67i) q^{20} +(1371.23 - 1371.23i) q^{21} +(-2202.31 - 136.726i) q^{22} +1361.94i q^{23} +(1601.07 + 301.299i) q^{24} -289.847i q^{25} +(-361.241 + 5818.66i) q^{26} +(-515.481 + 515.481i) q^{27} +(6842.04 + 852.838i) q^{28} +(-4950.18 - 4950.18i) q^{29} +(1969.32 + 2230.03i) q^{30} +6207.14 q^{31} +(2651.15 + 5150.33i) q^{32} +3510.60 q^{33} +(-4957.00 - 5613.24i) q^{34} +(8903.36 + 8903.36i) q^{35} +(-2572.10 - 320.603i) q^{36} +(4052.97 - 4052.97i) q^{37} +(-830.831 + 13382.5i) q^{38} -9275.25i q^{39} +(-1956.33 + 10395.7i) q^{40} -4429.64i q^{41} +(-10948.8 - 679.734i) q^{42} +(968.730 - 968.730i) q^{43} +(7666.72 + 9850.13i) q^{44} +(-3347.00 - 3347.00i) q^{45} +(5774.87 - 5099.74i) q^{46} -7741.43 q^{47} +(-4717.58 - 7917.01i) q^{48} -29619.6 q^{49} +(-1229.00 + 1085.32i) q^{50} +(8424.76 + 8424.76i) q^{51} +(26024.7 - 20256.0i) q^{52} +(-7480.21 + 7480.21i) q^{53} +(4115.92 + 255.529i) q^{54} +22794.2i q^{55} +(-22003.5 - 32204.8i) q^{56} -21332.5i q^{57} +(-2453.86 + 39525.3i) q^{58} +(-9193.55 + 9193.55i) q^{59} +(2081.67 - 16700.5i) q^{60} +(-18345.5 - 18345.5i) q^{61} +(-23242.4 - 26319.3i) q^{62} +17452.9 q^{63} +(11911.1 - 30526.5i) q^{64} +60223.9 q^{65} +(-13145.3 - 14885.5i) q^{66} +(20739.8 + 20739.8i) q^{67} +(-5239.78 + 42037.1i) q^{68} +(-8667.35 + 8667.35i) q^{69} +(4413.49 - 71090.0i) q^{70} +42287.5i q^{71} +(8271.69 + 12106.6i) q^{72} +28735.5i q^{73} +(-32361.4 - 2009.10i) q^{74} +(1844.58 - 1844.58i) q^{75} +(59855.3 - 46587.5i) q^{76} +(-59430.2 - 59430.2i) q^{77} +(-39328.6 + 34730.8i) q^{78} -25381.3 q^{79} +(51404.9 - 30631.1i) q^{80} -6561.00 q^{81} +(-18782.4 + 16586.6i) q^{82} +(18048.3 + 18048.3i) q^{83} +(38115.0 + 48969.9i) q^{84} +(-54701.7 + 54701.7i) q^{85} +(-7734.95 - 480.210i) q^{86} -63005.5i q^{87} +(13058.5 - 69391.6i) q^{88} -21155.1i q^{89} +(-1659.14 + 26724.5i) q^{90} +(-157019. + 157019. i) q^{91} +(-43247.5 - 5390.66i) q^{92} +(39502.0 + 39502.0i) q^{93} +(28987.5 + 32825.0i) q^{94} +138511. q^{95} +(-15904.7 + 49648.3i) q^{96} +85767.2 q^{97} +(110909. + 125592. i) q^{98} +(22341.3 + 22341.3i) 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

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