LMFDB - Embedded newform 48.6.j.a.13.10

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			13.10
Character	$\chi$	$=$	48.13
Dual form			48.6.j.a.37.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0662295 - 5.65647i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-31.9912 - 0.749250i) q^{4} +(-23.0892 + 23.0892i) q^{5} +(36.4190 - 35.5761i) q^{6} +103.844i q^{7} +(-6.35687 + 180.908i) q^{8} +81.0000i q^{9} +O(q^{10})$	\(q+(0.0662295 - 5.65647i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-31.9912 - 0.749250i) q^{4} +(-23.0892 + 23.0892i) q^{5} +(36.4190 - 35.5761i) q^{6} +103.844i q^{7} +(-6.35687 + 180.908i) q^{8} +81.0000i q^{9} +(129.074 + 132.132i) q^{10} +(-300.574 + 300.574i) q^{11} +(-198.823 - 208.359i) q^{12} +(142.725 + 142.725i) q^{13} +(587.392 + 6.87756i) q^{14} -293.877 q^{15} +(1022.88 + 47.9389i) q^{16} -12.5897 q^{17} +(458.174 + 5.36459i) q^{18} +(844.592 + 844.592i) q^{19} +(755.950 - 721.351i) q^{20} +(-660.861 + 660.861i) q^{21} +(1680.28 + 1720.09i) q^{22} -335.743i q^{23} +(-1191.74 + 1110.83i) q^{24} +2058.78i q^{25} +(816.773 - 797.868i) q^{26} +(-515.481 + 515.481i) q^{27} +(77.8053 - 3322.11i) q^{28} +(-5867.56 - 5867.56i) q^{29} +(-19.4633 + 1662.30i) q^{30} -2544.50 q^{31} +(338.909 - 5782.70i) q^{32} -3825.68 q^{33} +(-0.833812 + 71.2133i) q^{34} +(-2397.68 - 2397.68i) q^{35} +(60.6893 - 2591.29i) q^{36} +(-10199.6 + 10199.6i) q^{37} +(4833.34 - 4721.47i) q^{38} +1816.60i q^{39} +(-4030.23 - 4323.78i) q^{40} -384.749i q^{41} +(3694.37 + 3781.91i) q^{42} +(7526.05 - 7526.05i) q^{43} +(9840.92 - 9390.51i) q^{44} +(-1870.22 - 1870.22i) q^{45} +(-1899.12 - 22.2361i) q^{46} +15332.9 q^{47} +(6204.47 + 6814.63i) q^{48} +6023.37 q^{49} +(11645.4 + 136.352i) q^{50} +(-80.1205 - 80.1205i) q^{51} +(-4459.02 - 4672.89i) q^{52} +(-16207.2 + 16207.2i) q^{53} +(2881.66 + 2949.94i) q^{54} -13880.0i q^{55} +(-18786.2 - 660.125i) q^{56} +10749.9i q^{57} +(-33578.3 + 32801.1i) q^{58} +(27348.9 - 27348.9i) q^{59} +(9401.48 + 220.187i) q^{60} +(11205.3 + 11205.3i) q^{61} +(-168.521 + 14392.9i) q^{62} -8411.38 q^{63} +(-32687.2 - 2300.01i) q^{64} -6590.81 q^{65} +(-253.373 + 21639.8i) q^{66} +(49741.8 + 49741.8i) q^{67} +(402.761 + 9.43285i) q^{68} +(2136.65 - 2136.65i) q^{69} +(-13721.2 + 13403.6i) q^{70} -34891.3i q^{71} +(-14653.5 - 514.907i) q^{72} -9349.15i q^{73} +(57017.9 + 58368.9i) q^{74} +(-13102.0 + 13102.0i) q^{75} +(-26386.7 - 27652.4i) q^{76} +(-31212.8 - 31212.8i) q^{77} +(10275.5 + 120.312i) q^{78} +68675.6 q^{79} +(-24724.2 + 22510.5i) q^{80} -6561.00 q^{81} +(-2176.32 - 25.4817i) q^{82} +(43762.8 + 43762.8i) q^{83} +(21636.9 - 20646.6i) q^{84} +(290.686 - 290.686i) q^{85} +(-42072.4 - 43069.3i) q^{86} -74681.9i q^{87} +(-52465.4 - 56286.8i) q^{88} -66964.6i q^{89} +(-10702.7 + 10455.0i) q^{90} +(-14821.2 + 14821.2i) q^{91} +(-251.555 + 10740.8i) q^{92} +(-16193.1 - 16193.1i) q^{93} +(1015.49 - 86730.0i) q^{94} -39001.8 q^{95} +(38957.7 - 34644.0i) q^{96} +163694. q^{97} +(398.925 - 34071.0i) q^{98} +(-24346.5 - 24346.5i) 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 $

$2$	0.0662295	−	5.65647i	0.0117078	−	0.999931i
$2$	0.0662295	−	5.65647i	0.0117078	−	0.999931i
$3$	6.36396	+	6.36396i	0.408248	+	0.408248i
$3$	6.36396	+	6.36396i	0.408248	+	0.408248i
$4$	−31.9912	−	0.749250i	−0.999726	−	0.0234141i
$5$	−23.0892	+	23.0892i	−0.413031	+	0.413031i	−0.882793	−	0.469762i	$-0.844340\pi$
$5$	−23.0892	+	23.0892i	−0.413031	+	0.413031i	0.469762	+	0.882793i	$0.344340\pi$
$6$	36.4190	−	35.5761i	0.413000	−	0.403441i
$7$			103.844i			0.801009i	0.916295	+	0.400504i	$0.131165\pi$
$7$			103.844i			0.801009i	−0.916295	+	0.400504i	$0.868835\pi$
$8$	−6.35687	+	180.908i	−0.0351171	+	0.999383i
$9$			81.0000i			0.333333i
$10$	129.074	+	132.132i	0.408167	+	0.417839i
$11$	−300.574	+	300.574i	−0.748978	+	0.748978i	−0.974287	−	0.225309i	$-0.927661\pi$
$11$	−300.574	+	300.574i	−0.748978	+	0.748978i	0.225309	+	0.974287i	$0.427661\pi$
$12$	−198.823	−	208.359i	−0.398578	−	0.417695i
$13$	142.725	+	142.725i	0.234230	+	0.234230i	0.814456	−	0.580226i	$-0.197036\pi$
$13$	142.725	+	142.725i	0.234230	+	0.234230i	−0.580226	+	0.814456i	$0.697036\pi$
$14$	587.392	+	6.87756i	0.800954	+	0.00937808i
$15$	−293.877			−0.337239
$16$	1022.88	+	47.9389i	0.998904	+	0.0468153i
$17$	−12.5897			−0.0105656			−0.00528280	−	0.999986i	$-0.501682\pi$
$17$	−12.5897			−0.0105656			−0.00528280	+	0.999986i	$0.501682\pi$
$18$	458.174	+	5.36459i	0.333310	+	0.00390261i
$19$	844.592	+	844.592i	0.536739	+	0.536739i	0.922570	−	0.385831i	$-0.126085\pi$
$19$	844.592	+	844.592i	0.536739	+	0.536739i	−0.385831	+	0.922570i	$0.626085\pi$
$20$	755.950	−	721.351i	0.422589	−	0.403247i
$21$	−660.861	+	660.861i	−0.327011	+	0.327011i
$22$	1680.28	+	1720.09i	0.740158	+	0.757696i
$23$		−	335.743i		−	0.132339i	−0.997808	−	0.0661694i	$-0.978922\pi$
$23$		−	335.743i		−	0.132339i	0.997808	−	0.0661694i	$-0.0210778\pi$
$24$	−1191.74	+	1110.83i	−0.422333	+	0.393660i
$25$			2058.78i			0.658810i
$26$	816.773	−	797.868i	0.236956	−	0.231471i
$27$	−515.481	+	515.481i	−0.136083	+	0.136083i
$28$	77.8053	−	3322.11i	0.0187549	−	0.800789i
$29$	−5867.56	−	5867.56i	−1.29558	−	1.29558i	−0.931285	−	0.364290i	$-0.881312\pi$
$29$	−5867.56	−	5867.56i	−1.29558	−	1.29558i	−0.364290	−	0.931285i	$-0.618688\pi$
$30$	−19.4633	+	1662.30i	−0.00394834	+	0.337216i
$31$	−2544.50			−0.475552			−0.237776	−	0.971320i	$-0.576418\pi$
$31$	−2544.50			−0.475552			−0.237776	+	0.971320i	$0.576418\pi$
$32$	338.909	−	5782.70i	0.0585071	−	0.998287i
$33$	−3825.68			−0.611538
$34$	−0.833812	+	71.2133i	−0.000123700	+	0.0105649i
$35$	−2397.68	−	2397.68i	−0.330842	−	0.330842i
$36$	60.6893	−	2591.29i	0.00780469	−	0.333242i
$37$	−10199.6	+	10199.6i	−1.22483	+	1.22483i	−0.258939	+	0.965894i	$0.583373\pi$
$37$	−10199.6	+	10199.6i	−1.22483	+	1.22483i	−0.965894	+	0.258939i	$0.916627\pi$
$38$	4833.34	−	4721.47i	0.542986	−	0.530418i
$39$			1816.60i			0.191248i
$40$	−4030.23	−	4323.78i	−0.398272	−	0.427281i
$41$		−	384.749i		−	0.0357452i	−0.999840	−	0.0178726i	$-0.994311\pi$
$41$		−	384.749i		−	0.0357452i	0.999840	−	0.0178726i	$-0.00568933\pi$
$42$	3694.37	+	3781.91i	0.323160	+	0.330817i
$43$	7526.05	−	7526.05i	0.620720	−	0.620720i	−0.324995	−	0.945716i	$-0.605363\pi$
$43$	7526.05	−	7526.05i	0.620720	−	0.620720i	0.945716	+	0.324995i	$0.105363\pi$
$44$	9840.92	−	9390.51i	0.766309	−	0.731236i
$45$	−1870.22	−	1870.22i	−0.137677	−	0.137677i
$46$	−1899.12	−	22.2361i	−0.132330	−	0.00154940i
$47$	15332.9			1.01246			0.506232	−	0.862397i	$-0.331038\pi$
$47$	15332.9			1.01246			0.506232	+	0.862397i	$0.331038\pi$
$48$	6204.47	+	6814.63i	0.388688	+	0.426913i
$49$	6023.37			0.358385
$50$	11645.4	+	136.352i	0.658765	+	0.00771325i
$51$	−80.1205	−	80.1205i	−0.00431338	−	0.00431338i
$52$	−4459.02	−	4672.89i	−0.228681	−	0.239650i
$53$	−16207.2	+	16207.2i	−0.792537	+	0.792537i	−0.981906	−	0.189369i	$-0.939356\pi$
$53$	−16207.2	+	16207.2i	−0.792537	+	0.792537i	0.189369	+	0.981906i	$0.439356\pi$
$54$	2881.66	+	2949.94i	0.134480	+	0.137667i
$55$		−	13880.0i		−	0.618703i
$56$	−18786.2	−	660.125i	−0.800515	−	0.0281291i
$57$			10749.9i			0.438245i
$58$	−33578.3	+	32801.1i	−1.31066	+	1.28032i
$59$	27348.9	−	27348.9i	1.02284	−	1.02284i	0.0231112	−	0.999733i	$-0.492643\pi$
$59$	27348.9	−	27348.9i	1.02284	−	1.02284i	0.999733	−	0.0231112i	$-0.00735718\pi$
$60$	9401.48	+	220.187i	0.337146	+	0.00789613i
$61$	11205.3	+	11205.3i	0.385566	+	0.385566i	0.873103	−	0.487536i	$-0.162104\pi$
$61$	11205.3	+	11205.3i	0.385566	+	0.385566i	−0.487536	+	0.873103i	$0.662104\pi$
$62$	−168.521	+	14392.9i	−0.00556769	+	0.475520i
$63$	−8411.38			−0.267003
$64$	−32687.2	−	2300.01i	−0.997534	−	0.0701909i
$65$	−6590.81			−0.193489
$66$	−253.373	+	21639.8i	−0.00715979	+	0.611496i
$67$	49741.8	+	49741.8i	1.35374	+	1.35374i	0.881438	+	0.472299i	$0.156576\pi$
$67$	49741.8	+	49741.8i	1.35374	+	1.35374i	0.472299	+	0.881438i	$0.343424\pi$
$68$	402.761	+	9.43285i	0.0105627	+	0.000247384i
$69$	2136.65	−	2136.65i	0.0540271	−	0.0540271i
$70$	−13721.2	+	13403.6i	−0.334693	+	0.326946i
$71$		−	34891.3i		−	0.821431i	−0.911764	−	0.410715i	$-0.865279\pi$
$71$		−	34891.3i		−	0.821431i	0.911764	−	0.410715i	$-0.134721\pi$
$72$	−14653.5	−	514.907i	−0.333128	−	0.0117057i
$73$		−	9349.15i		−	0.205336i	−0.994716	−	0.102668i	$-0.967262\pi$
$73$		−	9349.15i		−	0.205336i	0.994716	−	0.102668i	$-0.0327379\pi$
$74$	57017.9	+	58368.9i	1.21041	+	1.23909i
$75$	−13102.0	+	13102.0i	−0.268958	+	0.268958i
$76$	−26386.7	−	27652.4i	−0.524024	−	0.549159i
$77$	−31212.8	−	31212.8i	−0.599938	−	0.599938i
$78$	10275.5	+	120.312i	0.191235	+	0.00223910i
$79$	68675.6			1.23804			0.619020	−	0.785375i	$-0.287530\pi$
$79$	68675.6			1.23804			0.619020	+	0.785375i	$0.287530\pi$
$80$	−24724.2	+	22510.5i	−0.431915	+	0.393242i
$81$	−6561.00			−0.111111
$82$	−2176.32	−	25.4817i	−0.0357428	−	0.000418499i
$83$	43762.8	+	43762.8i	0.697284	+	0.697284i	0.963824	−	0.266540i	$-0.0858805\pi$
$83$	43762.8	+	43762.8i	0.697284	+	0.697284i	−0.266540	+	0.963824i	$0.585880\pi$
$84$	21636.9	−	20646.6i	0.334578	−	0.319264i
$85$	290.686	−	290.686i	0.00436392	−	0.00436392i
$86$	−42072.4	−	43069.3i	−0.613410	−	0.627945i
$87$		−	74681.9i		−	1.05783i
$88$	−52465.4	−	56286.8i	−0.722214	−	0.774818i
$89$		−	66964.6i		−	0.896128i	−0.894001	−	0.448064i	$-0.852114\pi$
$89$		−	66964.6i		−	0.896128i	0.894001	−	0.448064i	$-0.147886\pi$
$90$	−10702.7	+	10455.0i	−0.139280	+	0.136056i
$91$	−14821.2	+	14821.2i	−0.187620	+	0.187620i
$92$	−251.555	+	10740.8i	−0.00309859	+	0.132302i
$93$	−16193.1	−	16193.1i	−0.194143	−	0.194143i
$94$	1015.49	−	86730.0i	0.0118538	−	1.01239i
$95$	−39001.8			−0.443380
$96$	38957.7	−	34644.0i	0.431434	−	0.383664i
$97$	163694.			1.76646			0.883228	−	0.468945i	$-0.155366\pi$
$97$	163694.			1.76646			0.883228	+	0.468945i	$0.155366\pi$
$98$	398.925	−	34071.0i	0.00419591	−	0.358360i
$99$	−24346.5	−	24346.5i	−0.249659	−	0.249659i
$100$	1542.54	−	65863.0i	0.0154254	−	0.658630i
$101$	−128583.	+	128583.i	−1.25424	+	1.25424i	−0.300441	+	0.953800i	$0.597134\pi$
$101$	−128583.	+	128583.i	−1.25424	+	1.25424i	−0.953800	+	0.300441i	$0.902866\pi$
$102$	−458.505	+	447.893i	−0.00436359	+	0.00426259i
$103$		−	117936.i		−	1.09536i	−0.836689	−	0.547678i	$-0.815512\pi$
$103$		−	117936.i		−	1.09536i	0.836689	−	0.547678i	$-0.184488\pi$
$104$	−26727.4	+	24912.8i	−0.242311	+	0.225860i
$105$		−	30517.4i		−	0.270131i
$106$	90602.3	+	92749.1i	0.783204	+	0.801761i
$107$	−121281.	+	121281.i	−1.02408	+	1.02408i	−0.0243785	+	0.999703i	$0.507761\pi$
$107$	−121281.	+	121281.i	−1.02408	+	1.02408i	−0.999703	+	0.0243785i	$0.992239\pi$
$108$	16877.1	−	16104.6i	0.139232	−	0.132859i
$109$	37897.6	+	37897.6i	0.305524	+	0.305524i	0.843170	−	0.537647i	$-0.180687\pi$
$109$	37897.6	+	37897.6i	0.305524	+	0.305524i	−0.537647	+	0.843170i	$0.680687\pi$
$110$	−78511.6	−	919.265i	−0.618660	−	0.00724367i
$111$	−129819.			−1.00007
$112$	−4978.18	+	106220.i	−0.0374995	+	0.800131i
$113$	−8112.53			−0.0597668			−0.0298834	−	0.999553i	$-0.509514\pi$
$113$	−8112.53			−0.0597668			−0.0298834	+	0.999553i	$0.509514\pi$
$114$	60806.5	+	711.961i	0.438215	+	0.00513091i
$115$	7752.02	+	7752.02i	0.0546601	+	0.0546601i
$116$	183314.	+	192107.i	1.26489	+	1.32556i
$117$	−11560.7	+	11560.7i	−0.0780766	+	0.0780766i
$118$	−152887.	−	156509.i	−1.01080	−	1.03475i
$119$		−	1307.37i		−	0.00846313i
$120$	1868.14	−	53164.6i	0.0118428	−	0.337031i
$121$		−	19637.9i		−	0.121936i
$122$	64124.6	−	62640.3i	0.390054	−	0.381026i
$123$	2448.53	−	2448.53i	0.0145929	−	0.0145929i
$124$	81401.7	+	1906.47i	0.475422	+	0.0111346i
$125$	−119689.	−	119689.i	−0.685141	−	0.685141i
$126$	−557.082	+	47578.7i	−0.00312603	+	0.266985i
$127$	−165770.			−0.912004			−0.456002	−	0.889979i	$-0.650719\pi$
$127$	−165770.			−0.912004			−0.456002	+	0.889979i	$0.650719\pi$
$128$	−15174.8	+	184742.i	−0.0818650	+	0.996643i
$129$	95791.0			0.506816
$130$	−436.506	+	37280.7i	−0.00226533	+	0.193475i
$131$	220959.	+	220959.i	1.12495	+	1.12495i	0.990986	+	0.133962i	$0.0427701\pi$
$131$	220959.	+	220959.i	1.12495	+	1.12495i	0.133962	+	0.990986i	$0.457230\pi$
$132$	122388.	+	2866.39i	0.611370	+	0.0143186i
$133$	−87706.0	+	87706.0i	−0.429933	+	0.429933i
$134$	284657.	−	278068.i	1.36949	−	1.33780i
$135$		−	23804.0i		−	0.112413i
$136$	80.0313	−	2277.58i	0.000371033	−	0.0105591i
$137$			45545.2i			0.207320i	0.994613	+	0.103660i	$0.0330554\pi$
$137$			45545.2i			0.207320i	−0.994613	+	0.103660i	$0.966945\pi$
$138$	−11944.4	−	12227.4i	−0.0533908	−	0.0546559i
$139$	−195187.	+	195187.i	−0.856869	+	0.856869i	−0.990968	−	0.134099i	$-0.957186\pi$
$139$	−195187.	+	195187.i	−0.856869	+	0.856869i	0.134099	+	0.990968i	$0.457186\pi$
$140$	74908.1	+	78501.0i	0.323005	+	0.338497i
$141$	97578.0	+	97578.0i	0.413337	+	0.413337i
$142$	−197361.	−	2310.83i	−0.821374	−	0.00961718i
$143$	−85798.8			−0.350866
$144$	−3883.05	+	82853.1i	−0.0156051	+	0.332968i
$145$	270954.			1.07023
$146$	−52883.2	−	619.190i	−0.205322	−	0.00240404i
$147$	38332.5	+	38332.5i	0.146310	+	0.146310i
$148$	333938.	−	318654.i	1.25318	−	1.19582i
$149$	55197.9	−	55197.9i	0.203684	−	0.203684i	−0.597892	−	0.801576i	$-0.703995\pi$
$149$	55197.9	−	55197.9i	0.203684	−	0.203684i	0.801576	+	0.597892i	$0.203995\pi$
$150$	73243.3	+	74978.8i	0.265791	+	0.272089i
$151$			132971.i			0.474586i	0.971438	+	0.237293i	$0.0762602\pi$
$151$			132971.i			0.474586i	−0.971438	+	0.237293i	$0.923740\pi$
$152$	−158162.	+	147424.i	−0.555257	+	0.517559i
$153$		−	1019.77i		−	0.00352186i
$154$	−178622.	+	174487.i	−0.606921	+	0.592873i
$155$	58750.3	−	58750.3i	0.196418	−	0.196418i
$156$	1361.08	−	58115.1i	0.00447789	−	0.191195i
$157$	86355.7	+	86355.7i	0.279603	+	0.279603i	0.832951	−	0.553347i	$-0.186650\pi$
$157$	86355.7	+	86355.7i	0.279603	+	0.279603i	−0.553347	+	0.832951i	$0.686650\pi$
$158$	4548.35	−	388461.i	0.0144948	−	1.23795i
$159$	−206285.			−0.647104
$160$	125692.	+	141343.i	0.388158	+	0.436489i
$161$	34865.0			0.106005
$162$	−434.532	+	37112.1i	−0.00130087	+	0.111103i
$163$	−332603.	−	332603.i	−0.980523	−	0.980523i	0.0192913	−	0.999814i	$-0.493859\pi$
$163$	−332603.	−	332603.i	−0.980523	−	0.980523i	−0.999814	+	0.0192913i	$0.993859\pi$
$164$	−288.273	+	12308.6i	−0.000836941	+	0.0357354i
$165$	88331.6	−	88331.6i	0.252584	−	0.252584i
$166$	250441.	−	244644.i	0.705400	−	0.689072i
$167$		−	238403.i		−	0.661486i	−0.943721	−	0.330743i	$-0.892701\pi$
$167$		−	238403.i		−	0.661486i	0.943721	−	0.330743i	$-0.107299\pi$
$168$	−115354.	−	123756.i	−0.315325	−	0.338293i
$169$		−	330552.i		−	0.890273i
$170$	−1625.00	−	1663.51i	−0.00431253	−	0.00441471i
$171$	−68412.0	+	68412.0i	−0.178913	+	0.178913i
$172$	−246406.	+	235129.i	−0.635084	+	0.606017i
$173$	−244592.	−	244592.i	−0.621336	−	0.621336i	0.324537	−	0.945873i	$-0.394791\pi$
$173$	−244592.	−	244592.i	−0.621336	−	0.621336i	−0.945873	+	0.324537i	$0.894791\pi$
$174$	−422436.	−	4946.15i	−1.05776	−	0.0123849i
$175$	−213793.			−0.527713
$176$	−321859.	+	293041.i	−0.783220	+	0.713093i
$177$	348094.			0.835149
$178$	−378783.	−	4435.03i	−0.896067	−	0.0104917i
$179$	315506.	+	315506.i	0.735996	+	0.735996i	0.971800	−	0.235805i	$-0.0757725\pi$
$179$	315506.	+	315506.i	0.735996	+	0.735996i	−0.235805	+	0.971800i	$0.575773\pi$
$180$	58429.4	+	61231.9i	0.134416	+	0.140863i
$181$	−82856.2	+	82856.2i	−0.187987	+	0.187987i	−0.794825	−	0.606838i	$-0.792438\pi$
$181$	−82856.2	+	82856.2i	−0.187987	+	0.187987i	0.606838	+	0.794825i	$0.292438\pi$
$182$	82854.0	+	84817.2i	0.185411	+	0.189804i
$183$			142620.i			0.314814i
$184$	60738.5	+	2134.27i	0.132257	+	0.00464735i
$185$		−	470998.i		−	1.01179i
$186$	−92668.2	+	90523.3i	−0.196403	+	0.191857i
$187$	3784.14	−	3784.14i	0.00791340	−	0.00791340i
$188$	−490518.	−	11488.2i	−1.01219	−	0.0237059i
$189$	−53529.7	−	53529.7i	−0.109004	−	0.109004i
$190$	−2583.07	+	220613.i	−0.00519102	+	0.443350i
$191$	461019.			0.914398			0.457199	−	0.889364i	$-0.348853\pi$
$191$	461019.			0.914398			0.457199	+	0.889364i	$0.348853\pi$
$192$	−193383.	−	222657.i	−0.378586	−	0.435897i
$193$	594457.			1.14875			0.574377	−	0.818591i	$-0.305244\pi$
$193$	594457.			1.14875			0.574377	+	0.818591i	$0.305244\pi$
$194$	10841.4	−	925928.i	0.0206814	−	1.76633i
$195$	−41943.6	−	41943.6i	−0.0789914	−	0.0789914i
$196$	−192695.	−	4513.01i	−0.358286	−	0.00839124i
$197$	329343.	−	329343.i	0.604620	−	0.604620i	−0.336915	−	0.941535i	$-0.609384\pi$
$197$	329343.	−	329343.i	0.604620	−	0.604620i	0.941535	+	0.336915i	$0.109384\pi$
$198$	−139327.	+	136102.i	−0.252565	+	0.246719i
$199$		−	157176.i		−	0.281354i	−0.990056	−	0.140677i	$-0.955072\pi$
$199$		−	157176.i		−	0.281354i	0.990056	−	0.140677i	$-0.0449279\pi$
$200$	−372450.	−	13087.4i	−0.658404	−	0.0231355i
$201$			633110.i			1.10532i
$202$	718811.	+	735843.i	1.23947	+	1.26884i
$203$	609313.	−	609313.i	1.03777	−	1.03777i
$204$	2503.12	+	2623.18i	0.00421121	+	0.00441320i
$205$	8883.53	+	8883.53i	0.0147639	+	0.0147639i
$206$	−667104.	−	7810.88i	−1.09528	−	0.0128242i
$207$	27195.2			0.0441129
$208$	139148.	+	152832.i	0.223008	+	0.244939i
$209$	−507724.			−0.804011
$210$	−172621.	−	2021.16i	−0.270113	−	0.00316265i
$211$	−270220.	−	270220.i	−0.417841	−	0.417841i	0.466618	−	0.884459i	$-0.345472\pi$
$211$	−270220.	−	270220.i	−0.417841	−	0.417841i	−0.884459	+	0.466618i	$0.845472\pi$
$212$	530633.	−	506346.i	0.810876	−	0.773763i
$213$	222047.	−	222047.i	0.335348	−	0.335348i
$214$	677991.	+	694056.i	1.01202	+	1.03600i
$215$			347540.i			0.512754i
$216$	−89977.6	−	96531.3i	−0.131220	−	0.140778i
$217$		−	264232.i		−	0.380922i
$218$	216876.	−	211856.i	0.309080	−	0.301926i
$219$	59497.6	−	59497.6i	0.0838281	−	0.0838281i
$220$	−10399.6	+	444038.i	−0.0144864	+	0.618533i
$221$	−1796.87	−	1796.87i	−0.00247478	−	0.00247478i
$222$	−8597.86	+	734317.i	−0.0117087	+	1.00000i
$223$	751759.			1.01232			0.506158	−	0.862441i	$-0.331065\pi$
$223$	751759.			1.01232			0.506158	+	0.862441i	$0.331065\pi$
$224$	600500.	+	35193.8i	0.799637	+	0.0468647i
$225$	−166761.			−0.219603
$226$	−537.289	+	45888.3i	−0.000699741	+	0.0597627i
$227$	526061.	+	526061.i	0.677597	+	0.677597i	0.959456	−	0.281859i	$-0.0909511\pi$
$227$	526061.	+	526061.i	0.677597	+	0.677597i	−0.281859	+	0.959456i	$0.590951\pi$
$228$	8054.37	−	343903.i	0.0102611	−	0.438125i
$229$	−1.00436e6	+	1.00436e6i	−1.26561	+	1.26561i	−0.317271	+	0.948335i	$0.602767\pi$
$229$	−1.00436e6	+	1.00436e6i	−1.26561	+	1.26561i	−0.948335	+	0.317271i	$0.897233\pi$
$230$	44362.4	−	43335.6i	0.0552963	−	0.0540164i
$231$		−	397275.i		−	0.489847i
$232$	1.09879e6	−	1.02419e6i	1.34027	−	1.24928i
$233$			1.22740e6i			1.48114i	0.671982	+	0.740568i	$0.265443\pi$
$233$			1.22740e6i			1.48114i	−0.671982	+	0.740568i	$0.734557\pi$
$234$	64627.3	+	66158.6i	0.0771572	+	0.0789854i
$235$	−354024.	+	354024.i	−0.418179	+	0.418179i
$236$	−895415.	+	854433.i	−1.04651	+	0.998615i
$237$	437049.	+	437049.i	0.505427	+	0.505427i
$238$	−7395.10	−	86.5865i	−0.00846255	−	9.90850e-5i
$239$	648833.			0.734748			0.367374	−	0.930073i	$-0.380257\pi$
$239$	648833.			0.734748			0.367374	+	0.930073i	$0.380257\pi$
$240$	−300600.	−	14088.1i	−0.336869	−	0.0157879i
$241$	−1.66642e6			−1.84817			−0.924084	−	0.382189i	$-0.875170\pi$
$241$	−1.66642e6			−1.84817			−0.924084	+	0.382189i	$0.875170\pi$
$242$	−111081.	−	1300.61i	−0.121928	−	0.00142761i
$243$	−41753.9	−	41753.9i	−0.0453609	−	0.0453609i
$244$	−350076.	−	366867.i	−0.376433	−	0.394488i
$245$	−139075.	+	139075.i	−0.148024	+	0.148024i
$246$	−13687.8	−	14012.2i	−0.0144211	−	0.0147628i
$247$			241089.i			0.251441i
$248$	16175.1	−	460320.i	0.0167000	−	0.475259i
$249$			557009.i			0.569330i
$250$	−684945.	+	669091.i	−0.693115	+	0.677072i
$251$	−28378.0	+	28378.0i	−0.0284313	+	0.0284313i	−0.721180	−	0.692748i	$-0.756400\pi$
$251$	−28378.0	+	28378.0i	−0.0284313	+	0.0284313i	0.692748	+	0.721180i	$0.256400\pi$
$252$	269091.	+	6302.23i	0.266930	+	0.00625163i
$253$	100915.	+	100915.i	0.0991188	+	0.0991188i
$254$	−10978.9	+	937672.i	−0.0106776	+	0.911941i
$255$	3699.83			0.00356313
$256$	1.04398e6	+	98071.2i	0.995617	+	0.0935280i
$257$	−1.88178e6			−1.77720			−0.888602	−	0.458680i	$-0.848323\pi$
$257$	−1.88178e6			−1.77720			−0.888602	+	0.458680i	$0.848323\pi$
$258$	6344.19	−	541838.i	0.00593372	−	0.506781i
$259$	−1.05916e6	−	1.05916e6i	−0.981102	−	0.981102i
$260$	210848.	+	4938.16i	0.193435	+	0.00453035i
$261$	475273.	−	475273.i	0.431859	−	0.431859i
$262$	1.26448e6	−	1.23521e6i	1.13804	−	1.11170i
$263$			311596.i			0.277781i	0.990308	+	0.138891i	$0.0443536\pi$
$263$			311596.i			0.277781i	−0.990308	+	0.138891i	$0.955646\pi$
$264$	24319.3	−	692094.i	0.0214754	−	0.611161i
$265$		−	748423.i		−	0.654685i
$266$	490298.	+	501915.i	0.424870	+	0.434937i
$267$	426160.	−	426160.i	0.365843	−	0.365843i
$268$	−1.55403e6	−	1.62857e6i	−1.32167	−	1.38506i
$269$	−10376.1	−	10376.1i	−0.00874282	−	0.00874282i	0.702722	−	0.711465i	$-0.251968\pi$
$269$	−10376.1	−	10376.1i	−0.00874282	−	0.00874282i	−0.711465	+	0.702722i	$0.751968\pi$
$270$	−134647.	−	1576.53i	−0.112405	−	0.00131611i
$271$	74716.4			0.0618006			0.0309003	−	0.999522i	$-0.490163\pi$
$271$	74716.4			0.0618006			0.0309003	+	0.999522i	$0.490163\pi$
$272$	−12877.7	−	603.537i	−0.0105540	−	0.000494631i
$273$	−188643.			−0.153191
$274$	257625.	+	3016.44i	0.207306	+	0.00242727i
$275$	−618816.	−	618816.i	−0.493434	−	0.493434i
$276$	−69955.1	+	66753.3i	−0.0552773	+	0.0527473i
$277$	679443.	−	679443.i	0.532051	−	0.532051i	−0.389131	−	0.921182i	$-0.627225\pi$
$277$	679443.	−	679443.i	0.532051	−	0.532051i	0.921182	+	0.389131i	$0.127225\pi$
$278$	1.09114e6	+	1.11700e6i	0.846778	+	0.866842i
$279$		−	206105.i		−	0.158517i
$280$	449000.	−	418516.i	0.342256	−	0.319019i
$281$			596905.i			0.450961i	0.974248	+	0.225481i	$0.0723952\pi$
$281$			596905.i			0.450961i	−0.974248	+	0.225481i	$0.927605\pi$
$282$	558409.	−	545484.i	0.418148	−	0.408469i
$283$	583682.	−	583682.i	0.433222	−	0.433222i	−0.456501	−	0.889723i	$-0.650898\pi$
$283$	583682.	−	583682.i	0.433222	−	0.433222i	0.889723	+	0.456501i	$0.150898\pi$
$284$	−26142.3	+	1.11621e6i	−0.0192330	+	0.821205i
$285$	−248206.	−	248206.i	−0.181009	−	0.181009i
$286$	−5682.42	+	485318.i	−0.00410788	+	0.350842i
$287$	39954.0			0.0286322
$288$	468398.	+	27451.7i	0.332762	+	0.0195024i
$289$	−1.41970e6			−0.999888
$290$	17945.2	−	1.53264e6i	0.0125300	−	1.07015i
$291$	1.04174e6	+	1.04174e6i	0.721152	+	0.721152i
$292$	−7004.86	+	299091.i	−0.00480775	+	0.205280i
$293$	469452.	−	469452.i	0.319464	−	0.319464i	−0.529097	−	0.848561i	$-0.677469\pi$
$293$	469452.	−	469452.i	0.319464	−	0.319464i	0.848561	+	0.529097i	$0.177469\pi$
$294$	219365.	−	214288.i	0.148013	−	0.144587i
$295$			1.26292e6i			0.844933i
$296$	−1.78034e6	−	1.91001e6i	−1.18106	−	1.26709i
$297$		−	309880.i		−	0.203846i
$298$	−308569.	−	315881.i	−0.201285	−	0.206055i
$299$	47919.0	−	47919.0i	0.0309977	−	0.0309977i
$300$	428966.	−	409333.i	0.275182	−	0.262587i
$301$	781537.	+	781537.i	0.497203	+	0.497203i
$302$	752147.	+	8806.62i	0.474554	+	0.00555638i
$303$	−1.63660e6			−1.02408
$304$	823425.	+	904403.i	0.511023	+	0.561278i
$305$	−517442.			−0.318502
$306$	−5768.28	−	67.5387i	−0.00352162	−	4.12334e-5i
$307$	−2.12215e6	−	2.12215e6i	−1.28508	−	1.28508i	−0.937739	−	0.347340i	$-0.887085\pi$
$307$	−2.12215e6	−	2.12215e6i	−1.28508	−	1.28508i	−0.347340	−	0.937739i	$-0.612915\pi$
$308$	975151.	+	1.02192e6i	0.585727	+	0.613821i
$309$	750543.	−	750543.i	0.447177	−	0.447177i
$310$	−328428.	−	336210.i	−0.194105	−	0.198704i
$311$			1.54065e6i			0.903239i	0.892211	+	0.451619i	$0.149154\pi$
$311$			1.54065e6i			0.903239i	−0.892211	+	0.451619i	$0.850846\pi$
$312$	−328636.	−	11547.9i	−0.191130	−	0.00671607i
$313$		−	403396.i		−	0.232740i	−0.993206	−	0.116370i	$-0.962874\pi$
$313$		−	403396.i		−	0.232740i	0.993206	−	0.116370i	$-0.0371258\pi$
$314$	494188.	−	482749.i	0.282857	−	0.276310i
$315$	194212.	−	194212.i	0.110281	−	0.110281i
$316$	−2.19702e6	−	51455.2i	−1.23770	−	0.0289875i
$317$	−318048.	−	318048.i	−0.177765	−	0.177765i	0.612616	−	0.790381i	$-0.290117\pi$
$317$	−318048.	−	318048.i	−0.177765	−	0.177765i	−0.790381	+	0.612616i	$0.790117\pi$
$318$	−13662.1	+	1.16684e6i	−0.00757618	+	0.647059i
$319$	3.52727e6			1.94072
$320$	807825.	−	701614.i	0.441004	−	0.383022i
$321$	−1.54366e6			−0.836159
$322$	2309.09	−	197212.i	0.00124108	−	0.105997i
$323$	−10633.2	−	10633.2i	−0.00567096	−	0.00567096i
$324$	209894.	+	4915.83i	0.111081	+	0.00260156i
$325$	−293840.	+	293840.i	−0.154313	+	0.154313i
$326$	−1.90339e6	+	1.85933e6i	−0.991935	+	0.968976i
$327$			482357.i			0.249459i
$328$	69604.0	+	2445.80i	0.0357232	+	0.00125527i
$329$			1.59223e6i			0.810993i
$330$	−493795.	−	505495.i	−0.249610	−	0.255524i
$331$	−601358.	+	601358.i	−0.301691	+	0.301691i	−0.841675	−	0.539984i	$-0.818430\pi$
$331$	−601358.	+	601358.i	−0.301691	+	0.301691i	0.539984	+	0.841675i	$0.318430\pi$
$332$	−1.36724e6	−	1.43281e6i	−0.680766	−	0.713419i
$333$	−826164.	−	826164.i	−0.408278	−	0.408278i
$334$	−1.34852e6	−	15789.3i	−0.661441	−	0.00774457i
$335$	−2.29699e6			−1.11827
$336$	−707660.	+	644299.i	−0.341961	+	0.311343i
$337$	4.01029e6			1.92354			0.961768	−	0.273864i	$-0.0883018\pi$
$337$	4.01029e6			1.92354			0.961768	+	0.273864i	$0.0883018\pi$
$338$	−1.86976e6	−	21892.3i	−0.890212	−	0.0104232i
$339$	−51627.8	−	51627.8i	−0.0243997	−	0.0243997i
$340$	−9517.20	+	9081.60i	−0.00446490	+	0.00426055i
$341$	764810.	−	764810.i	0.356178	−	0.356178i
$342$	382439.	+	391501.i	0.176806	+	0.180995i
$343$			2.37080e6i			1.08808i
$344$	1.31368e6	+	1.40936e6i	0.598540	+	0.642135i
$345$			98667.1i			0.0446297i
$346$	−1.39972e6	+	1.36732e6i	−0.628567	+	0.614018i
$347$	1.11013e6	−	1.11013e6i	0.494935	−	0.494935i	−0.414922	−	0.909857i	$-0.636191\pi$
$347$	1.11013e6	−	1.11013e6i	0.494935	−	0.494935i	0.909857	+	0.414922i	$0.136191\pi$
$348$	−55955.4	+	2.38917e6i	−0.0247682	+	1.05754i
$349$	2.05577e6	+	2.05577e6i	0.903463	+	0.903463i	0.995734	−	0.0922712i	$-0.0294127\pi$
$349$	2.05577e6	+	2.05577e6i	0.903463	+	0.903463i	−0.0922712	+	0.995734i	$0.529413\pi$
$350$	−14159.4	+	1.20931e6i	−0.00617838	+	0.527677i
$351$	−147144.			−0.0637493
$352$	1.63626e6	+	1.83999e6i	0.703874	+	0.791516i
$353$	3.37189e6			1.44025			0.720123	−	0.693847i	$-0.244085\pi$
$353$	3.37189e6			1.44025			0.720123	+	0.693847i	$0.244085\pi$
$354$	23054.1	−	1.96898e6i	0.00977779	−	0.835091i
$355$	805610.	+	805610.i	0.339277	+	0.339277i
$356$	−50173.2	+	2.14228e6i	−0.0209820	+	0.895883i
$357$	8320.05	−	8320.05i	0.00345506	−	0.00345506i
$358$	1.80555e6	−	1.76375e6i	0.744562	−	0.727329i
$359$			138176.i			0.0565844i	0.999600	+	0.0282922i	$0.00900689\pi$
$359$			138176.i			0.0565844i	−0.999600	+	0.0282922i	$0.990993\pi$
$360$	350226.	−	326449.i	0.142427	−	0.132757i
$361$		−	1.04943e6i		−	0.423823i
$362$	463186.	+	474161.i	0.185774	+	0.190175i
$363$	124975.	−	124975.i	0.0497803	−	0.0497803i
$364$	485253.	−	463043.i	0.191962	−	0.183176i
$365$	215864.	+	215864.i	0.0848102	+	0.0848102i
$366$	806727.	+	9445.67i	0.314792	+	0.00368579i
$367$	4.32486e6			1.67613			0.838063	−	0.545573i	$-0.183688\pi$
$367$	4.32486e6			1.67613			0.838063	+	0.545573i	$0.183688\pi$
$368$	16095.1	−	343424.i	0.00619548	−	0.132194i
$369$	31164.7			0.0119151
$370$	−2.66418e6	−	31194.0i	−1.01172	−	0.0118459i
$371$	−1.68303e6	−	1.68303e6i	−0.634829	−	0.634829i
$372$	505904.	+	530170.i	0.189544	+	0.198636i
$373$	357560.	−	357560.i	0.133069	−	0.133069i	−0.637435	−	0.770504i	$-0.720005\pi$
$373$	357560.	−	357560.i	0.133069	−	0.133069i	0.770504	+	0.637435i	$0.220005\pi$
$374$	−21154.2	−	21655.5i	−0.00782021	−	0.00800550i
$375$		−	1.52339e6i		−	0.559415i
$376$	−97469.3	+	2.77384e6i	−0.0355548	+	1.01184i
$377$		−	1.67490e6i		−	0.606925i
$378$	−306334.	+	299244.i	−0.110272	+	0.107720i
$379$	−424399.	+	424399.i	−0.151767	+	0.151767i	−0.778907	−	0.627140i	$-0.784225\pi$
$379$	−424399.	+	424399.i	−0.151767	+	0.151767i	0.627140	+	0.778907i	$0.284225\pi$
$380$	1.24772e6	+	29222.1i	0.443258	+	0.0103813i
$381$	−1.05495e6	−	1.05495e6i	−0.372324	−	0.372324i
$382$	30533.1	−	2.60774e6i	0.0107056	−	0.914336i
$383$	−3.56067e6			−1.24032			−0.620161	−	0.784475i	$-0.712933\pi$
$383$	−3.56067e6			−1.24032			−0.620161	+	0.784475i	$0.712933\pi$
$384$	−1.27226e6	+	1.07912e6i	−0.440299	+	0.373457i
$385$	1.44136e6			0.495586
$386$	39370.6	−	3.36253e6i	0.0134494	−	1.14868i
$387$	609610.	+	609610.i	0.206907	+	0.206907i
$388$	−5.23676e6	−	122648.i	−1.76597	−	0.0413599i
$389$	3.78459e6	−	3.78459e6i	1.26808	−	1.26808i	0.320994	−	0.947081i	$-0.395983\pi$
$389$	3.78459e6	−	3.78459e6i	1.26808	−	1.26808i	0.947081	−	0.320994i	$-0.104017\pi$
$390$	−240031.	+	234475.i	−0.0799108	+	0.0780611i
$391$			4226.91i			0.00139824i
$392$	−38289.8	+	1.08967e6i	−0.0125854	+	0.358164i
$393$			2.81234e6i			0.918517i
$394$	−1.84110e6	−	1.88473e6i	−0.597500	−	0.611657i
$395$	−1.58566e6	+	1.58566e6i	−0.511349	+	0.511349i
$396$	760632.	+	797115.i	0.243745	+	0.255436i
$397$	−2.12168e6	−	2.12168e6i	−0.675620	−	0.675620i	0.283386	−	0.959006i	$-0.408542\pi$
$397$	−2.12168e6	−	2.12168e6i	−0.675620	−	0.675620i	−0.959006	+	0.283386i	$0.908542\pi$
$398$	−889060.	−	10409.7i	−0.281335	−	0.00329405i
$399$	−1.11632e6			−0.351039
$400$	−98695.7	+	2.10588e6i	−0.0308424	+	0.658088i
$401$	351937.			0.109296			0.0546479	−	0.998506i	$-0.482596\pi$
$401$	351937.			0.109296			0.0546479	+	0.998506i	$0.482596\pi$
$402$	3.58116e6	+	41930.6i	1.10525	+	0.0129409i
$403$	−363164.	−	363164.i	−0.111389	−	0.111389i
$404$	4.20988e6	−	4.01720e6i	1.28326	−	1.22453i
$405$	151488.	−	151488.i	0.0458924	−	0.0458924i
$406$	−3.40620e6	−	3.48691e6i	−1.02555	−	1.04985i
$407$		−	6.13143e6i		−	1.83475i
$408$	15003.7	−	13985.1i	0.00446220	−	0.00415925i
$409$		−	1.80354e6i		−	0.533111i	−0.963820	−	0.266556i	$-0.914114\pi$
$409$		−	1.80354e6i		−	0.533111i	0.963820	−	0.266556i	$-0.0858856\pi$
$410$	50837.7	−	49661.0i	0.0149357	−	0.0145900i
$411$	−289848.	+	289848.i	−0.0846380	+	0.0846380i
$412$	−88363.9	+	3.77293e6i	−0.0256467	+	1.09506i
$413$	2.84002e6	+	2.84002e6i	0.819307	+	0.819307i
$414$	1801.12	−	153829.i	0.000516467	−	0.0441099i
$415$	−2.02089e6			−0.576000
$416$	873707.	−	776966.i	0.247533	−	0.220125i
$417$	−2.48433e6			−0.699630
$418$	−33626.3	+	2.87192e6i	−0.00941323	+	0.803956i
$419$	474167.	+	474167.i	0.131946	+	0.131946i	0.769995	−	0.638049i	$-0.220258\pi$
$419$	474167.	+	474167.i	0.131946	+	0.131946i	−0.638049	+	0.769995i	$0.720258\pi$
$420$	−22865.2	+	976290.i	−0.00632487	+	0.270057i
$421$	−3.60394e6	+	3.60394e6i	−0.990997	+	0.990997i	−0.999960	−	0.00896319i	$-0.997147\pi$
$421$	−3.60394e6	+	3.60394e6i	−0.990997	+	0.990997i	0.00896319	+	0.999960i	$0.497147\pi$
$422$	−1.54639e6	+	1.51059e6i	−0.422704	+	0.412920i
$423$			1.24196e6i			0.337488i
$424$	−2.82899e6	−	3.03504e6i	−0.764216	−	0.819880i
$425$		−	25919.5i		−	0.00696072i
$426$	−1.24129e6	−	1.27071e6i	−0.331398	−	0.339251i
$427$	−1.16361e6	+	1.16361e6i	−0.308842	+	0.308842i
$428$	3.97081e6	−	3.78907e6i	1.04778	−	0.999823i
$429$	−546021.	−	546021.i	−0.143240	−	0.143240i
$430$	1.96585e6	+	23017.4i	0.512719	+	0.00600324i
$431$	−7.04065e6			−1.82566			−0.912829	−	0.408342i	$-0.866107\pi$
$431$	−7.04065e6			−1.82566			−0.912829	+	0.408342i	$0.866107\pi$
$432$	−551985.	+	502562.i	−0.142304	+	0.129563i
$433$	856990.			0.219663			0.109831	−	0.993950i	$-0.464969\pi$
$433$	856990.			0.219663			0.109831	+	0.993950i	$0.464969\pi$
$434$	−1.49462e6	−	17499.9i	−0.380896	−	0.00445977i
$435$	1.72434e6	+	1.72434e6i	0.436918	+	0.436918i
$436$	−1.18399e6	−	1.24078e6i	−0.298287	−	0.312594i
$437$	283566.	−	283566.i	0.0710314	−	0.0710314i
$438$	−332606.	−	340487.i	−0.0828409	−	0.0848038i
$439$			3.56385e6i			0.882588i	0.897363	+	0.441294i	$0.145480\pi$
$439$			3.56385e6i			0.882588i	−0.897363	+	0.441294i	$0.854520\pi$
$440$	2.51099e6	+	88233.3i	0.618321	+	0.0217270i
$441$			487893.i			0.119462i
$442$	−10282.9	+	10044.9i	−0.00250358	+	0.00244563i
$443$	−985213.	+	985213.i	−0.238518	+	0.238518i	−0.816236	−	0.577718i	$-0.803943\pi$
$443$	−985213.	+	985213.i	−0.238518	+	0.238518i	0.577718	+	0.816236i	$0.303943\pi$
$444$	4.15307e6	+	97267.0i	0.999797	+	0.0234158i
$445$	1.54616e6	+	1.54616e6i	0.370129	+	0.370129i
$446$	49788.6	−	4.25230e6i	0.0118520	−	1.01225i
$447$	702555.			0.166307
$448$	238843.	−	3.39438e6i	0.0562235	−	0.799033i
$449$	217414.			0.0508945			0.0254472	−	0.999676i	$-0.491899\pi$
$449$	217414.			0.0508945			0.0254472	+	0.999676i	$0.491899\pi$
$450$	−11044.5	+	943280.i	−0.00257108	+	0.219588i
$451$	115645.	+	115645.i	0.0267724	+	0.0267724i
$452$	259530.	+	6078.32i	0.0597504	+	0.00139939i
$453$	−846224.	+	846224.i	−0.193749	+	0.193749i
$454$	3.01049e6	−	2.94080e6i	0.685483	−	0.669617i
$455$		−	684417.i		−	0.154986i
$456$	−1.94474e6	−	68335.8i	−0.437975	−	0.0153899i
$457$		−	6.51310e6i		−	1.45880i	−0.684085	−	0.729402i	$-0.739798\pi$
$457$		−	6.51310e6i		−	1.45880i	0.684085	−	0.729402i	$-0.260202\pi$
$458$	5.61458e6	+	5.74762e6i	1.25070	+	1.28034i
$459$	6489.76	−	6489.76i	0.00143779	−	0.00143779i
$460$	−242188.	−	253805.i	−0.0533653	−	0.0559249i
$461$	−3.46313e6	−	3.46313e6i	−0.758955	−	0.758955i	0.217177	−	0.976132i	$-0.430315\pi$
$461$	−3.46313e6	−	3.46313e6i	−0.758955	−	0.758955i	−0.976132	+	0.217177i	$0.930315\pi$
$462$	−2.24717e6	−	26311.3i	−0.489814	−	0.00573506i
$463$	2.79216e6			0.605324			0.302662	−	0.953098i	$-0.402125\pi$
$463$	2.79216e6			0.605324			0.302662	+	0.953098i	$0.402125\pi$
$464$	−5.72051e6	−	6.28308e6i	−1.23350	−	1.35481i
$465$	747770.			0.160375
$466$	6.94272e6	+	81289.8i	1.48103	+	0.0173409i
$467$	1.23547e6	+	1.23547e6i	0.262143	+	0.262143i	0.825924	−	0.563781i	$-0.190654\pi$
$467$	1.23547e6	+	1.23547e6i	0.262143	+	0.262143i	−0.563781	+	0.825924i	$0.690654\pi$
$468$	378504.	−	361180.i	0.0798833	−	0.0762271i
$469$	−5.16540e6	+	5.16540e6i	−1.08436	+	1.08436i
$470$	1.97908e6	+	2.02597e6i	0.413255	+	0.423047i
$471$			1.09913e6i			0.228295i
$472$	4.77377e6	+	5.12148e6i	0.986294	+	1.05813i
$473$			4.52426e6i			0.929812i
$474$	2.50110e6	−	2.44320e6i	0.511310	−	0.499475i
$475$	−1.73883e6	+	1.73883e6i	−0.353609	+	0.353609i
$476$	−979.548	+	41824.4i	−0.000198156	+	0.00846081i
$477$	−1.31279e6	−	1.31279e6i	−0.264179	−	0.264179i
$478$	42971.9	−	3.67010e6i	0.00860231	−	0.734697i
$479$	3.02754e6			0.602908			0.301454	−	0.953481i	$-0.402528\pi$
$479$	3.02754e6			0.602908			0.301454	+	0.953481i	$0.402528\pi$
$480$	−99597.6	+	1.69940e6i	−0.0197309	+	0.336661i
$481$	−2.91147e6			−0.573785
$482$	−110366.	+	9.42604e6i	−0.0216381	+	1.84804i
$483$	221879.	+	221879.i	0.0432762	+	0.0432762i
$484$	−14713.7	+	628242.i	−0.00285502	+	0.121903i
$485$	−3.77955e6	+	3.77955e6i	−0.729601	+	0.729601i
$486$	−238945.	+	233414.i	−0.0458889	+	0.0448267i
$487$		−	4.95409e6i		−	0.946546i	−0.880916	−	0.473273i	$-0.843072\pi$
$487$		−	4.95409e6i		−	0.946546i	0.880916	−	0.473273i	$-0.156928\pi$
$488$	−2.09836e6	+	1.95590e6i	−0.398868	+	0.371789i
$489$		−	4.23335e6i		−	0.800593i
$490$	777459.	+	795881.i	0.146281	+	0.149747i
$491$	−2.09507e6	+	2.09507e6i	−0.392188	+	0.392188i	−0.875467	−	0.483278i	$-0.839446\pi$
$491$	−2.09507e6	+	2.09507e6i	−0.392188	+	0.392188i	0.483278	+	0.875467i	$0.339446\pi$
$492$	−80166.0	+	76496.8i	−0.0149306	+	0.0142472i
$493$	73871.0	+	73871.0i	0.0136885	+	0.0136885i
$494$	1.36371e6	+	15967.2i	0.251423	+	0.00294383i
$495$	1.12428e6			0.206234
$496$	−2.60271e6	−	121980.i	−0.475031	−	0.0222631i
$497$	3.62326e6			0.657973
$498$	3.15070e6	+	36890.5i	0.569291	+	0.00666562i
$499$	4.46864e6	+	4.46864e6i	0.803385	+	0.803385i	0.983623	−	0.180238i	$-0.0576867\pi$
$499$	4.46864e6	+	4.46864e6i	0.803385	+	0.803385i	−0.180238	+	0.983623i	$0.557687\pi$
$500$	3.73933e6	+	3.91868e6i	0.668911	+	0.700995i
$501$	1.51719e6	−	1.51719e6i	0.270051	−	0.270051i
$502$	158640.	+	162398.i	0.0280965	+	0.0287622i
$503$		−	2.57540e6i		−	0.453863i	−0.973911	−	0.226931i	$-0.927131\pi$
$503$		−	2.57540e6i		−	0.453863i	0.973911	−	0.226931i	$-0.0728693\pi$
$504$	53470.1	−	1.52168e6i	0.00937637	−	0.266838i
$505$		−	5.93776e6i		−	1.03608i
$506$	577508.	−	564141.i	0.100273	−	0.0979516i
$507$	2.10362e6	−	2.10362e6i	0.363452	−	0.363452i
$508$	5.30318e6	+	124203.i	0.911754	+	0.0213537i
$509$	5.15738e6	+	5.15738e6i	0.882338	+	0.882338i	0.993772	−	0.111434i	$-0.0355443\pi$
$509$	5.15738e6	+	5.15738e6i	0.882338	+	0.882338i	−0.111434	+	0.993772i	$0.535544\pi$
$510$	245.038	−	20928.0i	4.17165e−5	−	0.00356288i
$511$	970856.			0.164476
$512$	623879.	−	5.89874e6i	0.105178	−	0.994453i
$513$	−870742.			−0.146082
$514$	−124630.	+	1.06443e7i	−0.0208072	+	1.77708i
$515$	2.72305e6	+	2.72305e6i	0.452416	+	0.452416i
$516$	−3.06447e6	−	71771.4i	−0.506677	−	0.0118666i
$517$	−4.60866e6	+	4.60866e6i	−0.758313	+	0.758313i
$518$	−6.06128e6	+	5.92098e6i	−0.992521	+	0.969548i
$519$		−	3.11314e6i		−	0.507318i
$520$	41896.9	−	1.19233e6i	0.00679476	−	0.193369i
$521$			9.39254e6i			1.51596i	0.652275	+	0.757982i	$0.273815\pi$
$521$			9.39254e6i			1.51596i	−0.652275	+	0.757982i	$0.726185\pi$
$522$	−2.65689e6	−	2.71984e6i	−0.426773	−	0.436885i
$523$	1.61286e6	−	1.61286e6i	0.257835	−	0.257835i	−0.566338	−	0.824173i	$-0.691640\pi$
$523$	1.61286e6	−	1.61286e6i	0.257835	−	0.257835i	0.824173	+	0.566338i	$0.191640\pi$
$524$	−6.90318e6	−	7.23429e6i	−1.09830	−	1.15098i
$525$	−1.36057e6	−	1.36057e6i	−0.215438	−	0.215438i
$526$	1.76253e6	+	20636.9i	0.277762	+	0.00325222i
$527$	32034.5			0.00502449
$528$	−3.91320e6	−	183399.i	−0.610867	−	0.0286293i
$529$	6.32362e6			0.982486
$530$	−4.23343e6	−	49567.7i	−0.654640	−	0.00766495i
$531$	2.21526e6	+	2.21526e6i	0.340948	+	0.340948i
$532$	2.87154e6	−	2.74011e6i	0.439881	−	0.419748i
$533$	54913.4	−	54913.4i	0.00837259	−	0.00837259i
$534$	−2.38234e6	−	2.43878e6i	−0.361535	−	0.370101i
$535$		−	5.60056e6i		−	0.845955i
$536$	−9.31487e6	+	8.68247e6i	−1.40044	+	1.30536i
$537$			4.01574e6i			0.600938i
$538$	−59379.0	+	58004.6i	−0.00884458	+	0.00863986i
$539$	−1.81047e6	+	1.81047e6i	−0.268422	+	0.268422i
$540$	−17835.2	+	761520.i	−0.00263204	+	0.112382i
$541$	−5.89032e6	−	5.89032e6i	−0.865258	−	0.865258i	0.126685	−	0.991943i	$-0.459566\pi$
$541$	−5.89032e6	−	5.89032e6i	−0.865258	−	0.865258i	−0.991943	+	0.126685i	$0.959566\pi$
$542$	4948.44	−	422631.i	0.000723552	−	0.0617964i
$543$	−1.05459e6			−0.153491
$544$	−4266.77	+	72802.5i	−0.000618162	+	0.0105475i
$545$	−1.75005e6			−0.252382
$546$	−12493.7	+	1.06705e6i	−0.00179354	+	0.153181i
$547$	−3.40367e6	−	3.40367e6i	−0.486384	−	0.486384i	0.420779	−	0.907163i	$-0.361757\pi$
$547$	−3.40367e6	−	3.40367e6i	−0.486384	−	0.486384i	−0.907163	+	0.420779i	$0.861757\pi$
$548$	34124.7	−	1.45705e6i	0.00485420	−	0.207263i
$549$	−907630.	+	907630.i	−0.128522	+	0.128522i
$550$	−3.54129e6	+	3.45933e6i	−0.499178	+	0.487624i
$551$		−	9.91140e6i		−	1.39077i
$552$	372955.	+	400120.i	0.0520965	+	0.0558910i
$553$			7.13156e6i			0.991681i
$554$	−3.79825e6	−	3.88824e6i	−0.525785	−	0.538244i
$555$	2.99741e6	−	2.99741e6i	0.413061	−	0.413061i
$556$	6.39052e6	−	6.09803e6i	0.876697	−	0.836571i
$557$	−4.48503e6	−	4.48503e6i	−0.612530	−	0.612530i	0.331075	−	0.943604i	$-0.392589\pi$
$557$	−4.48503e6	−	4.48503e6i	−0.612530	−	0.612530i	−0.943604	+	0.331075i	$0.892589\pi$
$558$	−1.16582e6	−	13650.2i	−0.158507	−	0.00185590i
$559$	2.14831e6			0.290782
$560$	−2.33759e6	−	2.56747e6i	−0.314991	−	0.345967i
$561$	48164.2			0.00646126
$562$	3.37637e6	+	39532.7i	0.450930	+	0.00527978i
$563$	4.39116e6	+	4.39116e6i	0.583860	+	0.583860i	0.935962	−	0.352102i	$-0.114533\pi$
$563$	4.39116e6	+	4.39116e6i	0.583860	+	0.583860i	−0.352102	+	0.935962i	$0.614533\pi$
$564$	−3.04853e6	−	3.19475e6i	−0.403545	−	0.422901i
$565$	187311.	−	187311.i	0.0246856	−	0.0246856i
$566$	−3.26292e6	−	3.34023e6i	−0.428120	−	0.438264i
$567$		−	681322.i		−	0.0890010i
$568$	6.31210e6	+	221799.i	0.820924	+	0.0288463i
$569$		−	1.06762e7i		−	1.38241i	−0.722659	−	0.691205i	$-0.757080\pi$
$569$		−	1.06762e7i		−	1.38241i	0.722659	−	0.691205i	$-0.242920\pi$
$570$	−1.42041e6	+	1.38753e6i	−0.183116	+	0.178877i
$571$	6.14616e6	−	6.14616e6i	0.788885	−	0.788885i	−0.192426	−	0.981311i	$-0.561636\pi$
$571$	6.14616e6	−	6.14616e6i	0.788885	−	0.788885i	0.981311	+	0.192426i	$0.0616356\pi$
$572$	2.74481e6	+	64284.8i	0.350770	+	0.00821520i
$573$	2.93391e6	+	2.93391e6i	0.373302	+	0.373302i
$574$	2646.13	−	225998.i	0.000335222	−	0.0286303i
$575$	691221.			0.0871861
$576$	186301.	−	2.64766e6i	0.0233970	−	0.332511i
$577$	−7.11939e6			−0.890232			−0.445116	−	0.895473i	$-0.646838\pi$
$577$	−7.11939e6			−0.890232			−0.445116	+	0.895473i	$0.646838\pi$
$578$	−94026.0	+	8.03048e6i	−0.0117065	+	0.999820i
$579$	3.78310e6	+	3.78310e6i	0.468977	+	0.468977i
$580$	−8.66816e6	−	203012.i	−1.06993	−	0.0250584i
$581$	−4.54451e6	+	4.54451e6i	−0.558531	+	0.558531i
$582$	5.96156e6	−	5.82358e6i	0.729546	−	0.712660i
$583$		−	9.74294e6i		−	1.18719i
$584$	1.69133e6	+	59431.4i	0.205209	+	0.00721080i
$585$		−	533855.i		−	0.0644962i
$586$	−2.62435e6	−	2.68653e6i	−0.315702	−	0.323182i
$587$	8.67388e6	−	8.67388e6i	1.03901	−	1.03901i	0.0397990	−	0.999208i	$-0.487328\pi$
$587$	8.67388e6	−	8.67388e6i	1.03901	−	1.03901i	0.999208	−	0.0397990i	$-0.0126718\pi$
$588$	−1.19758e6	−	1.25502e6i	−0.142844	−	0.149696i
$589$	−2.14906e6	−	2.14906e6i	−0.255247	−	0.255247i
$590$	7.14369e6	+	83642.9i	0.844875	+	0.00989234i
$591$	4.19185e6			0.493670
$592$	−1.09218e7	+	9.94393e6i	−1.28083	+	1.16615i
$593$	8.91375e6			1.04094			0.520468	−	0.853881i	$-0.325758\pi$
$593$	8.91375e6			1.04094			0.520468	+	0.853881i	$0.325758\pi$
$594$	−1.75282e6	−	20523.2i	−0.203832	−	0.00238660i
$595$	30186.1	+	30186.1i	0.00349554	+	0.00349554i
$596$	−1.80721e6	+	1.72449e6i	−0.208397	+	0.198859i
$597$	1.00026e6	−	1.00026e6i	0.114862	−	0.114862i
$598$	−267878.	−	274226.i	−0.0306327	−	0.0313585i
$599$			1.07941e7i			1.22919i	0.788844	+	0.614593i	$0.210680\pi$
$599$			1.07941e7i			1.22919i	−0.788844	+	0.614593i	$0.789320\pi$
$600$	−2.28697e6	−	2.45354e6i	−0.259347	−	0.278237i
$601$		−	3.75927e6i		−	0.424538i	−0.977211	−	0.212269i	$-0.931915\pi$
$601$		−	3.75927e6i		−	0.424538i	0.977211	−	0.212269i	$-0.0680854\pi$
$602$	4.47250e6	−	4.36898e6i	0.502990	−	0.491347i
$603$	−4.02909e6	+	4.02909e6i	−0.451246	+	0.451246i
$604$	99628.8	−	4.25391e6i	0.0111120	−	0.474456i
$605$	453424.	+	453424.i	0.0503635	+	0.0503635i
$606$	−108391.	+	9.25736e6i	−0.0119898	+	1.02401i
$607$	−2.50835e6			−0.276322			−0.138161	−	0.990410i	$-0.544119\pi$
$607$	−2.50835e6			−0.276322			−0.138161	+	0.990410i	$0.544119\pi$
$608$	5.17026e6	−	4.59778e6i	0.567222	−	0.504416i
$609$	7.75529e6			0.847334
$610$	−34269.9	+	2.92689e6i	−0.00372897	+	0.318480i
$611$	2.18839e6	+	2.18839e6i	0.237149	+	0.237149i
$612$	−764.061	+	32623.6i	−8.24612e−5	+	0.00352090i
$613$	3.13622e6	−	3.13622e6i	0.337097	−	0.337097i	−0.518176	−	0.855274i	$-0.673389\pi$
$613$	3.13622e6	−	3.13622e6i	0.337097	−	0.337097i	0.855274	+	0.518176i	$0.173389\pi$
$614$	−1.21444e7	+	1.18633e7i	−1.30004	+	1.26995i
$615$			113069.i			0.0120547i
$616$	5.84506e6	−	5.44823e6i	0.620636	−	0.578500i
$617$		−	5.40297e6i		−	0.571372i	−0.958323	−	0.285686i	$-0.907778\pi$
$617$		−	5.40297e6i		−	0.571372i	0.958323	−	0.285686i	$-0.0922215\pi$
$618$	−4.19571e6	−	4.29513e6i	−0.441911	−	0.452382i
$619$	−8.94221e6	+	8.94221e6i	−0.938033	+	0.938033i	−0.998189	−	0.0601557i	$-0.980840\pi$
$619$	−8.94221e6	+	8.94221e6i	−0.938033	+	0.938033i	0.0601557	+	0.998189i	$0.480840\pi$
$620$	−1.92351e6	+	1.83548e6i	−0.200963	+	0.191765i
$621$	173069.	+	173069.i	0.0180090	+	0.0180090i
$622$	8.71463e6	+	102036.i	0.903177	+	0.0105750i
$623$	6.95389e6			0.717807
$624$	−87085.5	+	1.85815e6i	−0.00895333	+	0.191038i
$625$	−906654.			−0.0928413
$626$	−2.28180e6	−	26716.8i	−0.232724	−	0.00272488i
$627$	−3.23114e6	−	3.23114e6i	−0.328236	−	0.328236i
$628$	−2.69792e6	−	2.82733e6i	−0.272980	−	0.286073i
$629$	128409.	−	128409.i	0.0129411	−	0.0129411i
$630$	−1.08569e6	−	1.11141e6i	−0.108982	−	0.111564i
$631$			9.54226e6i			0.954065i	0.878886	+	0.477032i	$0.158288\pi$
$631$			9.54226e6i			0.954065i	−0.878886	+	0.477032i	$0.841712\pi$
$632$	−436562.	+	1.24239e7i	−0.0434764	+	1.23728i
$633$		−	3.43934e6i		−	0.341166i
$634$	−1.82009e6	+	1.77797e6i	−0.179834	+	0.175671i
$635$	3.82749e6	−	3.82749e6i	0.376686	−	0.376686i
$636$	6.59929e6	+	154559.i	0.646926	+	0.0151513i
$637$	859687.	+	859687.i	0.0839444	+	0.0839444i
$638$	233609.	−	1.99519e7i	0.0227216	−	1.94058i
$639$	2.82619e6			0.273810
$640$	−3.91515e6	−	4.61590e6i	−0.377832	−	0.445458i
$641$	396928.			0.0381563			0.0190782	−	0.999818i	$-0.493927\pi$
$641$	396928.			0.0381563			0.0190782	+	0.999818i	$0.493927\pi$
$642$	−102236.	+	8.73166e6i	−0.00978961	+	0.836102i
$643$	−1.20318e7	−	1.20318e7i	−1.14763	−	1.14763i	−0.987017	−	0.160618i	$-0.948651\pi$
$643$	−1.20318e7	−	1.20318e7i	−1.14763	−	1.14763i	−0.160618	−	0.987017i	$-0.551349\pi$
$644$	−1.11537e6	−	26122.6i	−0.105975	−	0.00248200i
$645$	−2.21173e6	+	2.21173e6i	−0.209331	+	0.209331i
$646$	−60850.5	+	59442.0i	−0.00573697	+	0.00560418i
$647$			1.80155e7i			1.69194i	0.533228	+	0.845972i	$0.320979\pi$
$647$			1.80155e7i			1.69194i	−0.533228	+	0.845972i	$0.679021\pi$
$648$	41707.5	−	1.18694e6i	0.00390190	−	0.111043i
$649$			1.64407e7i			1.53218i
$650$	1.64264e6	+	1.68156e6i	0.152496	+	0.156109i
$651$	1.68156e6	−	1.68156e6i	0.155511	−	0.155511i
$652$	1.03912e7	+	1.08896e7i	0.957296	+	1.00321i
$653$	−831997.	−	831997.i	−0.0763553	−	0.0763553i	0.667898	−	0.744253i	$-0.267194\pi$
$653$	−831997.	−	831997.i	−0.0763553	−	0.0763553i	−0.744253	+	0.667898i	$0.767194\pi$
$654$	2.72844e6	+	31946.3i	0.249442	+	0.00292063i
$655$	−1.02035e7			−0.929278
$656$	18444.4	−	393551.i	0.00167342	−	0.0357060i
$657$	757281.			0.0684453
$658$	9.00641e6	+	105453.i	0.810937	+	0.00949497i
$659$	−4.43620e6	−	4.43620e6i	−0.397922	−	0.397922i	0.479578	−	0.877499i	$-0.340790\pi$
$659$	−4.43620e6	−	4.43620e6i	−0.397922	−	0.397922i	−0.877499	+	0.479578i	$0.840790\pi$
$660$	−2.89202e6	+	2.75965e6i	−0.258429	+	0.246601i
$661$	7.43698e6	−	7.43698e6i	0.662054	−	0.662054i	−0.293810	−	0.955864i	$-0.594923\pi$
$661$	7.43698e6	−	7.43698e6i	0.662054	−	0.662054i	0.955864	+	0.293810i	$0.0949234\pi$
$662$	3.36173e6	+	3.44139e6i	0.298139	+	0.305203i
$663$		−	22870.4i		−	0.00202065i
$664$	−8.19522e6	+	7.63883e6i	−0.721340	+	0.672367i
$665$		−	4.05012e6i		−	0.355151i
$666$	−4.72788e6	+	4.61845e6i	−0.413030	+	0.403469i
$667$	−1.96999e6	+	1.96999e6i	−0.171455	+	0.171455i
$668$	−178624.	+	7.62681e6i	−0.0154881	+	0.661305i
$669$	4.78416e6	+	4.78416e6i	0.413277	+	0.413277i
$670$	−152129.	+	1.29929e7i	−0.0130925	+	1.11820i
$671$	−6.73604e6			−0.577561
$672$	3.59759e6	+	4.04553e6i	0.307318	+	0.345583i
$673$	−7.12043e6			−0.605994			−0.302997	−	0.952991i	$-0.597987\pi$
$673$	−7.12043e6			−0.605994			−0.302997	+	0.952991i	$0.597987\pi$
$674$	265599.	−	2.26840e7i	0.0225205	−	1.92341i
$675$	−1.06126e6	−	1.06126e6i	−0.0896527	−	0.0896527i
$676$	−247666.	+	1.05748e7i	−0.0208449	+	0.890029i
$677$	−924981.	+	924981.i	−0.0775642	+	0.0775642i	−0.744825	−	0.667260i	$-0.767467\pi$
$677$	−924981.	+	924981.i	−0.0775642	+	0.0775642i	0.667260	+	0.744825i	$0.267467\pi$
$678$	−295450.	+	288612.i	−0.0246837	+	0.0241124i
$679$			1.69987e7i			1.41495i
$680$	50739.5	+	54435.2i	0.00420798	+	0.00451448i
$681$			6.69566e6i			0.553255i
$682$	−4.27547e6	−	4.37677e6i	−0.351984	−	0.360324i
$683$	−6.77530e6	+	6.77530e6i	−0.555746	+	0.555746i	−0.928094	−	0.372347i	$-0.878553\pi$
$683$	−6.77530e6	+	6.77530e6i	−0.555746	+	0.555746i	0.372347	+	0.928094i	$0.378553\pi$
$684$	2.23984e6	−	2.13733e6i	0.183053	−	0.174675i
$685$	−1.05160e6	−	1.05160e6i	−0.0856296	−	0.0856296i
$686$	1.34104e7	+	157017.i	1.08800	+	0.0127390i
$687$	−1.27834e7			−1.03336
$688$	8.05902e6	−	7.33743e6i	0.649099	−	0.590981i
$689$	−4.62636e6			−0.371272
$690$	558107.	+	6534.67i	0.0446267	+	0.000522518i
$691$	9.49920e6	+	9.49920e6i	0.756818	+	0.756818i	0.975742	−	0.218924i	$-0.0702545\pi$
$691$	9.49920e6	+	9.49920e6i	0.756818	+	0.756818i	−0.218924	+	0.975742i	$0.570255\pi$
$692$	7.64152e6	+	8.00804e6i	0.606617	+	0.635713i
$693$	2.52824e6	−	2.52824e6i	0.199979	−	0.199979i
$694$	−6.20587e6	−	6.35291e6i	−0.489107	−	0.500696i
$695$		−	9.01341e6i		−	0.707827i
$696$	1.35105e7	+	474743.i	1.05718	+	0.0371480i
$697$			4843.88i			0.000377669i
$698$	1.17645e7	−	1.14922e7i	0.913978	−	0.892823i
$699$	−7.81110e6	+	7.81110e6i	−0.604671	+	0.604671i
$700$	6.83949e6	+	160184.i	0.527568	+	0.0123559i
$701$	5.30069e6	+	5.30069e6i	0.407415	+	0.407415i	0.880836	−	0.473421i	$-0.156981\pi$
$701$	5.30069e6	+	5.30069e6i	0.407415	+	0.407415i	−0.473421	+	0.880836i	$0.656981\pi$
$702$	−9745.29	+	832316.i	−0.000746367	+	0.0637449i
$703$	−1.72289e7			−1.31483
$704$	1.05162e7	−	9.13358e6i	0.799702	−	0.694559i
$705$	−4.50598e6			−0.341442
$706$	223319.	−	1.90730e7i	0.0168622	−	1.44015i
$707$	−1.33526e7	−	1.33526e7i	−1.00466	−	1.00466i
$708$	−1.11360e7	−	260810.i	−0.834920	−	0.0195542i
$709$	8.86141e6	−	8.86141e6i	0.662044	−	0.662044i	−0.293817	−	0.955862i	$-0.594926\pi$
$709$	8.86141e6	−	8.86141e6i	0.662044	−	0.662044i	0.955862	+	0.293817i	$0.0949257\pi$
$710$	4.61026e6	−	4.50355e6i	0.343225	−	0.335281i
$711$			5.56272e6i			0.412680i
$712$	1.21144e7	+	425686.i	0.895576	+	0.0314694i
$713$			854298.i			0.0629340i
$714$	−46511.1	−	47613.1i	−0.00341437	−	0.00349527i
$715$	1.98102e6	−	1.98102e6i	0.144919	−	0.144919i
$716$	−9.85704e6	−	1.03298e7i	−0.718561	−	0.753027i
$717$	4.12915e6	+	4.12915e6i	0.299960	+	0.299960i
$718$	781589.	+	9151.34i	0.0565806	+	0.000662482i
$719$	1.88949e7			1.36309			0.681543	−	0.731778i	$-0.261309\pi$
$719$	1.88949e7			1.36309			0.681543	+	0.731778i	$0.261309\pi$
$720$	−1.82335e6	−	2.00266e6i	−0.131081	−	0.143972i
$721$	1.22470e7			0.877390
$722$	−5.93605e6	−	69503.1i	−0.423794	−	0.00496205i
$723$	−1.06050e7	−	1.06050e7i	−0.754512	−	0.754512i
$724$	2.71275e6	−	2.58859e6i	0.192337	−	0.183534i
$725$	1.20800e7	−	1.20800e7i	0.853539	−	0.853539i
$726$	−698641.	−	715195.i	−0.0491940	−	0.0503597i
$727$		−	5.59788e6i		−	0.392814i	−0.980522	−	0.196407i	$-0.937073\pi$
$727$		−	5.59788e6i		−	0.392814i	0.980522	−	0.196407i	$-0.0629275\pi$
$728$	−2.58705e6	−	2.77548e6i	−0.180916	−	0.194093i
$729$		−	531441.i		−	0.0370370i
$730$	1.23532e6	−	1.20673e6i	0.0857973	−	0.0838114i
$731$	−94750.9	+	94750.9i	−0.00655828	+	0.00655828i
$732$	106858.	−	4.56260e6i	0.00737107	−	0.314727i
$733$	1.16484e7	+	1.16484e7i	0.800770	+	0.800770i	0.983216	−	0.182446i	$-0.0584013\pi$
$733$	1.16484e7	+	1.16484e7i	0.800770	+	0.800770i	−0.182446	+	0.983216i	$0.558401\pi$
$734$	286433.	−	2.44634e7i	0.0196238	−	1.67601i
$735$	−1.77013e6			−0.120861
$736$	−1.94150e6	−	113786.i	−0.132112	−	0.00774276i
$737$	−2.99021e7			−2.02784
$738$	2064.02	−	176282.i	0.000139500	−	0.0119143i
$739$	1.12735e7	+	1.12735e7i	0.759357	+	0.759357i	0.976205	−	0.216849i	$-0.0695778\pi$
$739$	1.12735e7	+	1.12735e7i	0.759357	+	0.759357i	−0.216849	+	0.976205i	$0.569578\pi$
$740$	−352895.	+	1.50678e7i	−0.0236901	+	1.01151i
$741$	−1.53428e6	+	1.53428e6i	−0.102650	+	0.102650i
$742$	−9.63146e6	+	9.40853e6i	−0.642218	+	0.627353i
$743$			6.99502e6i			0.464854i	0.972614	+	0.232427i	$0.0746667\pi$
$743$			6.99502e6i			0.464854i	−0.972614	+	0.232427i	$0.925333\pi$
$744$	3.03239e6	−	2.82652e6i	0.200841	−	0.187206i
$745$			2.54895e6i			0.168256i
$746$	−1.99885e6	−	2.04621e6i	−0.131502	−	0.134618i
$747$	−3.54478e6	+	3.54478e6i	−0.232428	+	0.232428i
$748$	−123894.	+	118224.i	−0.00809651	+	0.00772594i
$749$	−1.25944e7	−	1.25944e7i	−0.820298	−	0.820298i
$750$	−8.61703e6	−	100894.i	−0.559377	−	0.00654954i
$751$	262316.			0.0169717			0.00848583	−	0.999964i	$-0.497299\pi$
$751$	262316.			0.0169717			0.00848583	+	0.999964i	$0.497299\pi$
$752$	1.56837e7	+	735042.i	1.01135	+	0.0473988i
$753$	−361193.			−0.0232141
$754$	−9.47401e6	−	110928.i	−0.606884	−	0.00710578i
$755$	−3.07019e6	−	3.07019e6i	−0.196019	−	0.196019i
$756$	1.67237e6	+	1.75259e6i	0.106421	+	0.111526i
$757$	1.92975e7	−	1.92975e7i	1.22394	−	1.22394i	0.257725	−	0.966218i	$-0.417027\pi$
$757$	1.92975e7	−	1.92975e7i	1.22394	−	1.22394i	0.966218	−	0.257725i	$-0.0829729\pi$
$758$	2.37249e6	+	2.42871e6i	0.149979	+	0.153533i
$759$			1.28444e6i			0.0809302i
$760$	247930.	−	7.05573e6i	0.0155702	−	0.443106i
$761$		−	9.30497e6i		−	0.582443i	−0.956656	−	0.291222i	$-0.905938\pi$
$761$		−	9.30497e6i		−	0.582443i	0.956656	−	0.291222i	$-0.0940617\pi$
$762$	−6.03718e6	+	5.89744e6i	−0.376657	+	0.367939i
$763$	−3.93544e6	+	3.93544e6i	−0.244727	+	0.244727i
$764$	−1.47486e7	−	345419.i	−0.914148	−	0.0214098i
$765$	23545.6	+	23545.6i	0.00145464	+	0.00145464i
$766$	−235821.	+	2.01408e7i	−0.0145215	+	1.24024i
$767$	7.80675e6			0.479161
$768$	6.01973e6	+	7.26797e6i	0.368276	+	0.444641i
$769$	−1.41518e7			−0.862970			−0.431485	−	0.902120i	$-0.642010\pi$
$769$	−1.41518e7			−0.862970			−0.431485	+	0.902120i	$0.642010\pi$
$770$	95460.3	−	8.15298e6i	0.00580225	−	0.495552i
$771$	−1.19756e7	−	1.19756e7i	−0.725540	−	0.725540i
$772$	−1.90174e7	−	445397.i	−1.14844	−	0.0268970i
$773$	−1.25781e7	+	1.25781e7i	−0.757122	+	0.757122i	−0.975798	−	0.218675i	$-0.929826\pi$
$773$	−1.25781e7	+	1.25781e7i	−0.757122	+	0.757122i	0.218675	+	0.975798i	$0.429826\pi$
$774$	3.48861e6	−	3.40786e6i	0.209315	−	0.204470i
$775$		−	5.23857e6i		−	0.313299i
$776$	−1.04058e6	+	2.96134e7i	−0.0620328	+	1.76537i
$777$		−	1.34810e7i		−	0.801066i
$778$	−2.11568e7	−	2.16581e7i	−1.25314	−	1.28283i
$779$	324956.	−	324956.i	0.0191858	−	0.0191858i
$780$	1.31040e6	+	1.37325e6i	0.0771202	+	0.0808192i
$781$	1.04874e7	+	1.04874e7i	0.615233	+	0.615233i
$782$	23909.4	+	279.946i	0.00139814	+	1.63703e-5i
$783$	6.04923e6			0.352611
$784$	6.16117e6	+	288754.i	0.357992	+	0.0167779i
$785$	−3.98776e6			−0.230970
$786$	1.59079e7	+	186260.i	0.918454	+	0.0107538i
$787$	−7.97391e6	−	7.97391e6i	−0.458918	−	0.458918i	0.439382	−	0.898300i	$-0.355197\pi$
$787$	−7.97391e6	−	7.97391e6i	−0.458918	−	0.458918i	−0.898300	+	0.439382i	$0.855197\pi$
$788$	−1.07828e7	+	1.02893e7i	−0.618611	+	0.590297i
$789$	−1.98299e6	+	1.98299e6i	−0.113404	+	0.113404i
$790$	8.86422e6	+	9.07425e6i	0.505327	+	0.517301i
$791$		−	842440.i		−	0.0478738i
$792$	4.55923e6	−	4.24969e6i	0.258273	−	0.240738i
$793$			3.19856e6i			0.180622i
$794$	−1.21417e7	+	1.18607e7i	−0.683484	+	0.667664i
$795$	4.76293e6	−	4.76293e6i	0.267274	−	0.267274i
$796$	−117764.	+	5.02825e6i	−0.00658765	+	0.281277i
$797$	−8.08395e6	−	8.08395e6i	−0.450794	−	0.450794i	0.444824	−	0.895618i	$-0.353266\pi$
$797$	−8.08395e6	−	8.08395e6i	−0.450794	−	0.450794i	−0.895618	+	0.444824i	$0.853266\pi$
$798$	−73933.1	+	6.31440e6i	−0.00410990	+	0.351014i
$799$	−193037.			−0.0106973
$800$	1.19053e7	+	697741.i	0.657682	+	0.0385451i
$801$	5.42413e6			0.298709
$802$	23308.6	−	1.99072e6i	0.00127962	−	0.109288i
$803$	2.81011e6	+	2.81011e6i	0.153792	+	0.153792i
$804$	474358.	−	2.02540e7i	0.0258801	−	1.10502i
$805$	−805002.	+	805002.i	−0.0437832	+	0.0437832i
$806$	−2.07828e6	+	2.03017e6i	−0.112685	+	0.110077i
$807$		−	132066.i		−	0.00713848i
$808$	−2.24443e7	−	2.40791e7i	−1.20942	−	1.29751i
$809$			1.73466e7i			0.931843i	0.884826	+	0.465922i	$0.154277\pi$
$809$			1.73466e7i			0.931843i	−0.884826	+	0.465922i	$0.845723\pi$
$810$	−846853.	−	866919.i	−0.0453519	−	0.0464265i
$811$	1.94718e7	−	1.94718e7i	1.03957	−	1.03957i	0.0403843	−	0.999184i	$-0.487142\pi$
$811$	1.94718e7	−	1.94718e7i	1.03957	−	1.03957i	0.999184	−	0.0403843i	$-0.0128582\pi$
$812$	−1.99492e7	+	1.90361e7i	−1.06178	+	1.01318i
$813$	475493.	+	475493.i	0.0252300	+	0.0252300i
$814$	−3.46822e7	−	406082.i	−1.83462	−	0.0214809i
$815$	1.53591e7			0.809973
$816$	−78112.5	−	85794.3i	−0.00410672	−	0.00451059i
$817$	1.27129e7			0.666329
$818$	−1.02017e7	−	119448.i	−0.533075	−	0.00624158i
$819$	−1.20052e6	−	1.20052e6i	−0.0625401	−	0.0625401i
$820$	−277539.	−	290851.i	−0.0144142	−	0.0151055i
$821$	2.15267e7	−	2.15267e7i	1.11460	−	1.11460i	0.122079	−	0.992520i	$-0.461044\pi$
$821$	2.15267e7	−	2.15267e7i	1.11460	−	1.11460i	0.992520	−	0.122079i	$-0.0389563\pi$
$822$	1.62032e6	+	1.65871e6i	0.0836413	+	0.0856231i
$823$		−	1.29648e7i		−	0.667217i	−0.942712	−	0.333608i	$-0.891734\pi$
$823$		−	1.29648e7i		−	0.667217i	0.942712	−	0.333608i	$-0.108266\pi$
$824$	2.13356e7	+	749707.i	1.09468	+	0.0384657i
$825$		−	7.87624e6i		−	0.402888i
$826$	1.62526e7	−	1.58764e7i	0.828843	−	0.809659i
$827$	−1.08230e7	+	1.08230e7i	−0.550278	+	0.550278i	−0.926521	−	0.376243i	$-0.877216\pi$
$827$	−1.08230e7	+	1.08230e7i	−0.550278	+	0.550278i	0.376243	+	0.926521i	$0.377216\pi$
$828$	−870007.	−	20376.0i	−0.0441008	−	0.00103286i
$829$	1.53126e7	+	1.53126e7i	0.773858	+	0.773858i	0.978779	−	0.204920i	$-0.0656936\pi$
$829$	1.53126e7	+	1.53126e7i	0.773858	+	0.773858i	−0.204920	+	0.978779i	$0.565694\pi$
$830$	−133843.	+	1.14311e7i	−0.00674372	+	0.575961i
$831$	8.64789e6			0.434418
$832$	−4.33701e6	−	4.99355e6i	−0.217211	−	0.250093i
$833$	−75832.6			−0.00378655
$834$	−164536.	+	1.40525e7i	−0.00819116	+	0.699583i
$835$	5.50453e6	+	5.50453e6i	0.273214	+	0.273214i
$836$	1.62427e7	+	380413.i	0.803791	+	0.0188252i
$837$	1.31164e6	−	1.31164e6i	0.0647145	−	0.0647145i
$838$	2.71351e6	−	2.65071e6i	0.133482	−	0.130392i
$839$			2.91392e7i			1.42913i	0.699568	+	0.714566i	$0.253376\pi$
$839$			2.91392e7i			1.42913i	−0.699568	+	0.714566i	$0.746624\pi$
$840$	5.52084e6	+	193995.i	0.269965	+	0.00948622i
$841$			4.83455e7i			2.35703i
$842$	2.01469e7	+	2.06242e7i	0.979326	+	1.00253i
$843$	−3.79868e6	+	3.79868e6i	−0.184104	+	0.184104i
$844$	8.44220e6	+	8.84713e6i	0.407943	+	0.427510i
$845$	7.63217e6	+	7.63217e6i	0.367710	+	0.367710i
$846$	7.02513e6	+	82254.7i	0.337465	+	0.00395126i
$847$	2.03929e6			0.0976720
$848$	−1.73550e7	+	1.58011e7i	−0.828771	+	0.754565i
$849$	7.42906e6			0.353724
$850$	−146613.	−	1716.64i	−0.00696024	−	8.14950e-5i
$851$	3.42443e6	+	3.42443e6i	0.162093	+	0.162093i
$852$	−7.26991e6	+	6.93718e6i	−0.343108	+	0.327404i
$853$	1.61542e7	−	1.61542e7i	0.760176	−	0.760176i	−0.216178	−	0.976354i	$-0.569359\pi$
$853$	1.61542e7	−	1.61542e7i	0.760176	−	0.760176i	0.976354	+	0.216178i	$0.0693593\pi$
$854$	6.50484e6	+	6.65897e6i	0.305205	+	0.312437i
$855$		−	3.15915e6i		−	0.147793i
$856$	−2.11698e7	−	2.27117e7i	−0.987487	−	1.05941i
$857$		−	2.59798e7i		−	1.20832i	−0.796861	−	0.604162i	$-0.793508\pi$
$857$		−	2.59798e7i		−	1.20832i	0.796861	−	0.604162i	$-0.206492\pi$
$858$	−3.12471e6	+	3.05238e6i	−0.144908	+	0.141554i
$859$	1.58731e7	−	1.58731e7i	0.733972	−	0.733972i	−0.237432	−	0.971404i	$-0.576306\pi$
$859$	1.58731e7	−	1.58731e7i	0.733972	−	0.733972i	0.971404	+	0.237432i	$0.0763057\pi$
$860$	260395.	−	1.11182e7i	0.0120057	−	0.512613i
$861$	254265.	+	254265.i	0.0116891	+	0.0116891i
$862$	−466299.	+	3.98252e7i	−0.0213745	+	1.82553i
$863$	1.61890e7			0.739936			0.369968	−	0.929044i	$-0.379369\pi$
$863$	1.61890e7			0.739936			0.369968	+	0.929044i	$0.379369\pi$
$864$	2.80617e6	+	3.15557e6i	0.127888	+	0.143811i
$865$	1.12948e7			0.513262
$866$	56758.1	−	4.84754e6i	0.00257177	−	0.219648i
$867$	−9.03491e6	−	9.03491e6i	−0.408203	−	0.408203i
$868$	−197976.	+	8.45310e6i	−0.00891893	+	0.380817i
$869$	−2.06421e7	+	2.06421e7i	−0.927264	+	0.927264i
$870$	9.86788e6	−	9.63948e6i	0.442004	−	0.431773i
$871$			1.41988e7i			0.634171i
$872$	−7.09687e6	+	6.61505e6i	−0.316064	+	0.294606i
$873$			1.32592e7i			0.588818i
$874$	−1.58520e6	−	1.62276e6i	−0.0701949	−	0.0718581i
$875$	1.24290e7	−	1.24290e7i	0.548804	−	0.548804i
$876$	−1.94798e6	+	1.85882e6i	−0.0857678	+	0.0818423i
$877$	−2.53400e7	−	2.53400e7i	−1.11252	−	1.11252i	−0.992809	−	0.119711i	$-0.961803\pi$
$877$	−2.53400e7	−	2.53400e7i	−1.11252	−	1.11252i	−0.119711	−	0.992809i	$-0.538197\pi$
$878$	2.01588e7	+	236032.i	0.882527	+	0.0103332i
$879$	5.97515e6			0.260841
$880$	665391.	−	1.41975e7i	0.0289648	−	0.618024i
$881$	−1.55125e7			−0.673353			−0.336676	−	0.941620i	$-0.609303\pi$
$881$	−1.55125e7			−0.673353			−0.336676	+	0.941620i	$0.609303\pi$
$882$	2.75975e6	+	32312.9i	0.119453	+	0.00139864i
$883$	8.32386e6	+	8.32386e6i	0.359272	+	0.359272i	0.863544	−	0.504273i	$-0.168239\pi$
$883$	8.32386e6	+	8.32386e6i	0.359272	+	0.359272i	−0.504273	+	0.863544i	$0.668239\pi$
$884$	56137.8	+	58830.4i	0.00241615	+	0.00253204i
$885$	−8.03720e6	+	8.03720e6i	−0.344943	+	0.344943i
$886$	5.50757e6	+	5.63807e6i	0.235709	+	0.241294i
$887$		−	414474.i		−	0.0176884i	−0.999961	−	0.00884420i	$-0.997185\pi$
$887$		−	414474.i		−	0.0176884i	0.999961	−	0.00884420i	$-0.00281523\pi$
$888$	825244.	−	2.34853e7i	0.0351196	−	0.999455i
$889$		−	1.72143e7i		−	0.730523i
$890$	8.84818e6	−	8.64338e6i	0.374437	−	0.365770i
$891$	1.97206e6	−	1.97206e6i	0.0832198	−	0.0832198i
$892$	−2.40497e7	−	563256.i	−1.01204	−	0.0237025i
$893$	1.29500e7	+	1.29500e7i	0.543429	+	0.543429i
$894$	46529.9	−	3.97398e6i	0.00194710	−	0.166296i
$895$	−1.45695e7			−0.607979
$896$	−1.91844e7	−	1.57582e6i	−0.798320	−	0.0655746i
$897$	609909.			0.0253095
$898$	14399.2	−	1.22979e6i	0.000595864	−	0.0508910i
$899$	1.49300e7	+	1.49300e7i	0.616114	+	0.616114i
$900$	5.33490e6	+	124946.i	0.219543	+	0.00514181i
$901$	204045.	−	204045.i	0.00837362	−	0.00837362i
$902$	661803.	−	646485.i	0.0270840	−	0.0264571i
$903$			9.94734e6i			0.405964i
$904$	51570.3	−	1.46762e6i	0.00209884	−	0.0597300i
$905$		−	3.82616e6i		−	0.155289i
$906$	4.73059e6	+	4.84268e6i	0.191467	+	0.196004i
$907$	8.58660e6	−	8.58660e6i	0.346580	−	0.346580i	−0.512254	−	0.858834i	$-0.671189\pi$
$907$	8.58660e6	−	8.58660e6i	0.346580	−	0.346580i	0.858834	+	0.512254i	$0.171189\pi$
$908$	−1.64352e7	−	1.72235e7i	−0.661546	−	0.693276i
$909$	−1.04152e7	−	1.04152e7i	−0.418080	−	0.418080i
$910$	−3.87138e6	−	45328.7i	−0.154975	−	0.00181455i
$911$	−7.55265e6			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$911$	−7.55265e6			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$912$	−515338.	+	1.09958e7i	−0.0205166	+	0.437765i
$913$	−2.63079e7			−1.04450
$914$	−3.68411e7	−	431359.i	−1.45870	−	0.0170794i
$915$	−3.29298e6	−	3.29298e6i	−0.130028	−	0.130028i
$916$	3.28831e7	−	3.13780e7i	1.29489	−	1.23563i
$917$	−2.29453e7	+	2.29453e7i	−0.901094	+	0.901094i
$918$	−36279.3	−	37138.9i	−0.00142086	−	0.00145453i
$919$			5.70263e6i			0.222734i	0.993779	+	0.111367i	$0.0355229\pi$
$919$			5.70263e6i			0.222734i	−0.993779	+	0.111367i	$0.964477\pi$
$920$	−1.45168e6	+	1.35312e6i	−0.0565458	+	0.0527068i
$921$		−	2.70105e7i		−	1.04926i
$922$	−1.98184e7	+	1.93597e7i	−0.767789	+	0.750017i
$923$	4.97986e6	−	4.97986e6i	0.192404	−	0.192404i
$924$	−297658.	+	1.27093e7i	−0.0114693	+	0.489713i
$925$	−2.09987e7	−	2.09987e7i	−0.806932	−	0.806932i
$926$	184923.	−	1.57938e7i	0.00708703	−	0.605282i
$927$	9.55285e6			0.365118
$928$	−3.59189e7	+	3.19418e7i	−1.36916	+	1.21756i
$929$	−2.19940e7			−0.836115			−0.418057	−	0.908421i	$-0.637289\pi$
$929$	−2.19940e7			−0.836115			−0.418057	+	0.908421i	$0.637289\pi$
$930$	49524.5	−	4.22974e6i	0.00187764	−	0.160364i
$931$	5.08729e6	+	5.08729e6i	0.192359	+	0.192359i
$932$	919626.	−	3.92659e7i	0.0346794	−	1.48073i
$933$	−9.80463e6	+	9.80463e6i	−0.368746	+	0.368746i
$934$	7.07020e6	−	6.90655e6i	0.265195	−	0.259056i
$935$			174745.i			0.00653696i
$936$	−2.01794e6	−	2.16492e6i	−0.0752866	−	0.0807703i
$937$			1.91571e7i			0.712820i	0.934330	+	0.356410i	$0.115999\pi$
$937$			1.91571e7i			0.712820i	−0.934330	+	0.356410i	$0.884001\pi$
$938$	2.88758e7	+	2.95600e7i	1.07159	+	1.09698i
$939$	2.56720e6	−	2.56720e6i	0.0950157	−	0.0950157i
$940$	1.15909e7	−	1.10604e7i	0.427856	−	0.408273i
$941$	−5.98327e6	−	5.98327e6i	−0.220274	−	0.220274i	0.588340	−	0.808614i	$-0.299782\pi$
$941$	−5.98327e6	−	5.98327e6i	−0.220274	−	0.220274i	−0.808614	+	0.588340i	$0.799782\pi$
$942$	6.21719e6	+	72794.8i	0.228279	+	0.00267284i
$943$	−129177.			−0.00473048
$944$	2.92856e7	−	2.66635e7i	1.06961	−	0.973838i
$945$	2.47191e6			0.0900437
$946$	2.55913e7	+	299640.i	0.929748	+	0.0108861i
$947$	−2.53510e7	−	2.53510e7i	−0.918588	−	0.918588i	0.0783388	−	0.996927i	$-0.475038\pi$
$947$	−2.53510e7	−	2.53510e7i	−0.918588	−	0.918588i	−0.996927	+	0.0783388i	$0.975038\pi$
$948$	−1.36543e7	−	1.43092e7i	−0.493455	−	0.517123i
$949$	1.33436e6	−	1.33436e6i	0.0480958	−	0.0480958i
$950$	9.72048e6	+	9.95080e6i	0.349445	+	0.357725i
$951$		−	4.04810e6i		−	0.145144i
$952$	236513.	+	8310.79i	0.00845791	+	0.000297201i
$953$			1.03948e7i			0.370751i	0.982668	+	0.185376i	$0.0593502\pi$
$953$			1.03948e7i			0.370751i	−0.982668	+	0.185376i	$0.940650\pi$
$954$	−7.51268e6	+	7.33879e6i	−0.267254	+	0.261068i
$955$	−1.06445e7	+	1.06445e7i	−0.377675	+	0.377675i
$956$	−2.07570e7	−	486138.i	−0.734546	−	0.0172034i
$957$	2.24474e7	+	2.24474e7i	0.792294	+	0.792294i
$958$	200513.	−	1.71252e7i	0.00705875	−	0.602867i
$959$	−4.72961e6			−0.166065
$960$	9.60601e6	+	675921.i	0.336407	+	0.0236711i
$961$	−2.21547e7			−0.773850
$962$	−192825.	+	1.64686e7i	−0.00671778	+	0.573745i
$963$	−9.82379e6	−	9.82379e6i	−0.341360	−	0.341360i
$964$	5.33108e7	+	1.24856e6i	1.84766	+	0.0432732i
$965$	−1.37255e7	+	1.37255e7i	−0.474472	+	0.474472i
$966$	1.26975e6	−	1.24036e6i	0.0437799	−	0.0427665i
$967$		−	5.12508e7i		−	1.76252i	−0.472631	−	0.881261i	$-0.656695\pi$
$967$		−	5.12508e7i		−	1.76252i	0.472631	−	0.881261i	$-0.343305\pi$
$968$	3.55266e6	+	124836.i	0.121861	+	0.00428205i
$969$		−	135338.i		−	0.00463032i
$970$	2.11286e7	+	2.16292e7i	0.721009	+	0.738093i
$971$	8.57705e6	−	8.57705e6i	0.291938	−	0.291938i	−0.545908	−	0.837845i	$-0.683815\pi$
$971$	8.57705e6	−	8.57705e6i	0.291938	−	0.291938i	0.837845	+	0.545908i	$0.183815\pi$
$972$	1.30448e6	+	1.36704e6i	0.0442864	+	0.0464106i
$973$	−2.02691e7	−	2.02691e7i	−0.686360	−	0.686360i
$974$	−2.80227e7	−	328107.i	−0.946482	−	0.0110820i
$975$	−3.73997e6			−0.125996
$976$	1.09245e7	+	1.19988e7i	0.367093	+	0.403194i
$977$	4.48051e7			1.50173			0.750864	−	0.660457i	$-0.229637\pi$
$977$	4.48051e7			1.50173			0.750864	+	0.660457i	$0.229637\pi$
$978$	−2.39458e7	−	280373.i	−0.800539	−	0.00937322i
$979$	2.01278e7	+	2.01278e7i	0.671180	+	0.671180i
$980$	4.55337e6	−	4.34496e6i	0.151449	−	0.144518i
$981$	−3.06970e6	+	3.06970e6i	−0.101841	+	0.101841i
$982$	1.17119e7	+	1.19894e7i	0.387570	+	0.396753i
$983$		−	3.31593e7i		−	1.09451i	−0.836964	−	0.547257i	$-0.815672\pi$
$983$		−	3.31593e7i		−	1.09451i	0.836964	−	0.547257i	$-0.184328\pi$
$984$	427392.	+	458522.i	0.0140715	+	0.0150964i
$985$			1.52085e7i			0.499454i
$986$	422741.	−	412956.i	0.0138479	−	0.0135273i
$987$	−1.01329e7	+	1.01329e7i	−0.331086	+	0.331086i
$988$	180636.	−	7.71274e6i	0.00588725	−	0.251372i
$989$	−2.52682e6	−	2.52682e6i	−0.0821454	−	0.0821454i
$990$	74460.4	−	6.35944e6i	0.00241456	−	0.206220i
$991$	−946499.			−0.0306151			−0.0153076	−	0.999883i	$-0.504873\pi$
$991$	−946499.			−0.0306151			−0.0153076	+	0.999883i	$0.504873\pi$
$992$	−862355.	+	1.47141e7i	−0.0278232	+	0.474738i
$993$	−7.65404e6			−0.246330
$994$	239967.	−	2.04948e7i	0.00770345	−	0.657928i
$995$	3.62906e6	+	3.62906e6i	0.116208	+	0.116208i
$996$	417339.	−	1.78194e7i	0.0133303	−	0.569174i
$997$	−2.07587e7	+	2.07587e7i	−0.661396	+	0.661396i	−0.955709	−	0.294313i	$-0.904909\pi$
$997$	−2.07587e7	+	2.07587e7i	−0.661396	+	0.661396i	0.294313	+	0.955709i	$0.404909\pi$
$998$	2.55727e7	−	2.49807e7i	0.812736	−	0.793924i
$999$		−	1.05153e7i		−	0.333357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.j.a.13.10	✓	40
3.2	odd	2		144.6.k.c.109.11		40
4.3	odd	2		192.6.j.a.145.6		40
8.3	odd	2		384.6.j.b.289.15		40
8.5	even	2		384.6.j.a.289.6		40
12.11	even	2		576.6.k.c.145.13		40
16.3	odd	4		384.6.j.b.97.15		40
16.5	even	4	inner	48.6.j.a.37.10	yes	40
16.11	odd	4		192.6.j.a.49.6		40
16.13	even	4		384.6.j.a.97.6		40
48.5	odd	4		144.6.k.c.37.11		40
48.11	even	4		576.6.k.c.433.13		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.j.a.13.10	✓	40	1.1	even	1	trivial
48.6.j.a.37.10	yes	40	16.5	even	4	inner
144.6.k.c.37.11		40	48.5	odd	4
144.6.k.c.109.11		40	3.2	odd	2
192.6.j.a.49.6		40	16.11	odd	4
192.6.j.a.145.6		40	4.3	odd	2
384.6.j.a.97.6		40	16.13	even	4
384.6.j.a.289.6		40	8.5	even	2
384.6.j.b.97.15		40	16.3	odd	4
384.6.j.b.289.15		40	8.3	odd	2
576.6.k.c.145.13		40	12.11	even	2
576.6.k.c.433.13		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)

\(f(q)\)	\(=\)	\(q+(0.0662295 - 5.65647i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-31.9912 - 0.749250i) q^{4} +(-23.0892 + 23.0892i) q^{5} +(36.4190 - 35.5761i) q^{6} +103.844i q^{7} +(-6.35687 + 180.908i) q^{8} +81.0000i q^{9} +O(q^{10})\)	\(q+(0.0662295 - 5.65647i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-31.9912 - 0.749250i) q^{4} +(-23.0892 + 23.0892i) q^{5} +(36.4190 - 35.5761i) q^{6} +103.844i q^{7} +(-6.35687 + 180.908i) q^{8} +81.0000i q^{9} +(129.074 + 132.132i) q^{10} +(-300.574 + 300.574i) q^{11} +(-198.823 - 208.359i) q^{12} +(142.725 + 142.725i) q^{13} +(587.392 + 6.87756i) q^{14} -293.877 q^{15} +(1022.88 + 47.9389i) q^{16} -12.5897 q^{17} +(458.174 + 5.36459i) q^{18} +(844.592 + 844.592i) q^{19} +(755.950 - 721.351i) q^{20} +(-660.861 + 660.861i) q^{21} +(1680.28 + 1720.09i) q^{22} -335.743i q^{23} +(-1191.74 + 1110.83i) q^{24} +2058.78i q^{25} +(816.773 - 797.868i) q^{26} +(-515.481 + 515.481i) q^{27} +(77.8053 - 3322.11i) q^{28} +(-5867.56 - 5867.56i) q^{29} +(-19.4633 + 1662.30i) q^{30} -2544.50 q^{31} +(338.909 - 5782.70i) q^{32} -3825.68 q^{33} +(-0.833812 + 71.2133i) q^{34} +(-2397.68 - 2397.68i) q^{35} +(60.6893 - 2591.29i) q^{36} +(-10199.6 + 10199.6i) q^{37} +(4833.34 - 4721.47i) q^{38} +1816.60i q^{39} +(-4030.23 - 4323.78i) q^{40} -384.749i q^{41} +(3694.37 + 3781.91i) q^{42} +(7526.05 - 7526.05i) q^{43} +(9840.92 - 9390.51i) q^{44} +(-1870.22 - 1870.22i) q^{45} +(-1899.12 - 22.2361i) q^{46} +15332.9 q^{47} +(6204.47 + 6814.63i) q^{48} +6023.37 q^{49} +(11645.4 + 136.352i) q^{50} +(-80.1205 - 80.1205i) q^{51} +(-4459.02 - 4672.89i) q^{52} +(-16207.2 + 16207.2i) q^{53} +(2881.66 + 2949.94i) q^{54} -13880.0i q^{55} +(-18786.2 - 660.125i) q^{56} +10749.9i q^{57} +(-33578.3 + 32801.1i) q^{58} +(27348.9 - 27348.9i) q^{59} +(9401.48 + 220.187i) q^{60} +(11205.3 + 11205.3i) q^{61} +(-168.521 + 14392.9i) q^{62} -8411.38 q^{63} +(-32687.2 - 2300.01i) q^{64} -6590.81 q^{65} +(-253.373 + 21639.8i) q^{66} +(49741.8 + 49741.8i) q^{67} +(402.761 + 9.43285i) q^{68} +(2136.65 - 2136.65i) q^{69} +(-13721.2 + 13403.6i) q^{70} -34891.3i q^{71} +(-14653.5 - 514.907i) q^{72} -9349.15i q^{73} +(57017.9 + 58368.9i) q^{74} +(-13102.0 + 13102.0i) q^{75} +(-26386.7 - 27652.4i) q^{76} +(-31212.8 - 31212.8i) q^{77} +(10275.5 + 120.312i) q^{78} +68675.6 q^{79} +(-24724.2 + 22510.5i) q^{80} -6561.00 q^{81} +(-2176.32 - 25.4817i) q^{82} +(43762.8 + 43762.8i) q^{83} +(21636.9 - 20646.6i) q^{84} +(290.686 - 290.686i) q^{85} +(-42072.4 - 43069.3i) q^{86} -74681.9i q^{87} +(-52465.4 - 56286.8i) q^{88} -66964.6i q^{89} +(-10702.7 + 10455.0i) q^{90} +(-14821.2 + 14821.2i) q^{91} +(-251.555 + 10740.8i) q^{92} +(-16193.1 - 16193.1i) q^{93} +(1015.49 - 86730.0i) q^{94} -39001.8 q^{95} +(38957.7 - 34644.0i) q^{96} +163694. q^{97} +(398.925 - 34071.0i) q^{98} +(-24346.5 - 24346.5i) 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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