LMFDB - Embedded newform 1045.6.a.b.1.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

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:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.36
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.5279 q^{2} +5.80405 q^{3} +78.8357 q^{4} +25.0000 q^{5} +61.1042 q^{6} -179.552 q^{7} +493.079 q^{8} -209.313 q^{9} +O(q^{10})$	\(q+10.5279 q^{2} +5.80405 q^{3} +78.8357 q^{4} +25.0000 q^{5} +61.1042 q^{6} -179.552 q^{7} +493.079 q^{8} -209.313 q^{9} +263.196 q^{10} -121.000 q^{11} +457.567 q^{12} -195.158 q^{13} -1890.30 q^{14} +145.101 q^{15} +2668.32 q^{16} -1280.08 q^{17} -2203.62 q^{18} +361.000 q^{19} +1970.89 q^{20} -1042.13 q^{21} -1273.87 q^{22} +3484.39 q^{23} +2861.86 q^{24} +625.000 q^{25} -2054.60 q^{26} -2625.25 q^{27} -14155.1 q^{28} -4999.20 q^{29} +1527.61 q^{30} -4050.09 q^{31} +12313.2 q^{32} -702.290 q^{33} -13476.5 q^{34} -4488.80 q^{35} -16501.3 q^{36} -5943.92 q^{37} +3800.55 q^{38} -1132.71 q^{39} +12327.0 q^{40} -2944.98 q^{41} -10971.4 q^{42} +17880.9 q^{43} -9539.12 q^{44} -5232.82 q^{45} +36683.1 q^{46} +2223.76 q^{47} +15487.1 q^{48} +15431.9 q^{49} +6579.91 q^{50} -7429.66 q^{51} -15385.4 q^{52} -35502.8 q^{53} -27638.2 q^{54} -3025.00 q^{55} -88533.3 q^{56} +2095.26 q^{57} -52630.9 q^{58} -53250.5 q^{59} +11439.2 q^{60} -13158.7 q^{61} -42638.8 q^{62} +37582.6 q^{63} +44245.0 q^{64} -4878.95 q^{65} -7393.61 q^{66} +64692.8 q^{67} -100916. q^{68} +20223.6 q^{69} -47257.4 q^{70} -13078.9 q^{71} -103208. q^{72} -71642.3 q^{73} -62576.8 q^{74} +3627.53 q^{75} +28459.7 q^{76} +21725.8 q^{77} -11925.0 q^{78} -43172.0 q^{79} +66708.1 q^{80} +35626.0 q^{81} -31004.3 q^{82} -35799.1 q^{83} -82157.0 q^{84} -32002.0 q^{85} +188248. q^{86} -29015.6 q^{87} -59662.6 q^{88} -116730. q^{89} -55090.4 q^{90} +35041.0 q^{91} +274694. q^{92} -23507.0 q^{93} +23411.4 q^{94} +9025.00 q^{95} +71466.4 q^{96} +72141.6 q^{97} +162465. q^{98} +25326.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) $ 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	10.5279	1.86108	0.930540	−	0.366191i	$-0.119338\pi$
$2$	10.5279	1.86108	0.930540	+	0.366191i	$0.119338\pi$
$3$	5.80405	0.372330	0.186165	−	0.982518i	$-0.440394\pi$
$3$	5.80405	0.372330	0.186165	+	0.982518i	$0.440394\pi$
$4$	78.8357	2.46362
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	61.1042	0.692936
$7$	−179.552	−1.38498	−0.692492	−	0.721425i	$-0.743487\pi$
$7$	−179.552	−1.38498	−0.692492	+	0.721425i	$0.743487\pi$
$8$	493.079	2.72390
$9$	−209.313	−0.861370
$10$	263.196	0.832300
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	457.567	0.917278
$13$	−195.158	−0.320279	−0.160139	−	0.987094i	$-0.551194\pi$
$13$	−195.158	−0.320279	−0.160139	+	0.987094i	$0.551194\pi$
$14$	−1890.30	−2.57757
$15$	145.101	0.166511
$16$	2668.32	2.60578
$17$	−1280.08	−1.07427	−0.537137	−	0.843495i	$-0.680494\pi$
$17$	−1280.08	−1.07427	−0.537137	+	0.843495i	$0.680494\pi$
$18$	−2203.62	−1.60308
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	1970.89	1.10176
$21$	−1042.13	−0.515672
$22$	−1273.87	−0.561136
$23$	3484.39	1.37343	0.686716	−	0.726926i	$-0.259052\pi$
$23$	3484.39	1.37343	0.686716	+	0.726926i	$0.259052\pi$
$24$	2861.86	1.01419
$25$	625.000	0.200000
$26$	−2054.60	−0.596064
$27$	−2625.25	−0.693044
$28$	−14155.1	−3.41207
$29$	−4999.20	−1.10384	−0.551920	−	0.833897i	$-0.686104\pi$
$29$	−4999.20	−1.10384	−0.551920	+	0.833897i	$0.686104\pi$
$30$	1527.61	0.309890
$31$	−4050.09	−0.756939	−0.378469	−	0.925614i	$-0.623549\pi$
$31$	−4050.09	−0.756939	−0.378469	+	0.925614i	$0.623549\pi$
$32$	12313.2	2.12567
$33$	−702.290	−0.112262
$34$	−13476.5	−1.99931
$35$	−4488.80	−0.619384
$36$	−16501.3	−2.12208
$37$	−5943.92	−0.713788	−0.356894	−	0.934145i	$-0.616164\pi$
$37$	−5943.92	−0.713788	−0.356894	+	0.934145i	$0.616164\pi$
$38$	3800.55	0.426961
$39$	−1132.71	−0.119250
$40$	12327.0	1.21817
$41$	−2944.98	−0.273604	−0.136802	−	0.990598i	$-0.543682\pi$
$41$	−2944.98	−0.273604	−0.136802	+	0.990598i	$0.543682\pi$
$42$	−10971.4	−0.959706
$43$	17880.9	1.47475	0.737375	−	0.675483i	$-0.236065\pi$
$43$	17880.9	1.47475	0.737375	+	0.675483i	$0.236065\pi$
$44$	−9539.12	−0.742808
$45$	−5232.82	−0.385216
$46$	36683.1	2.55606
$47$	2223.76	0.146840	0.0734198	−	0.997301i	$-0.476609\pi$
$47$	2223.76	0.146840	0.0734198	+	0.997301i	$0.476609\pi$
$48$	15487.1	0.970212
$49$	15431.9	0.918183
$50$	6579.91	0.372216
$51$	−7429.66	−0.399985
$52$	−15385.4	−0.789044
$53$	−35502.8	−1.73609	−0.868046	−	0.496484i	$-0.834624\pi$
$53$	−35502.8	−1.73609	−0.868046	+	0.496484i	$0.834624\pi$
$54$	−27638.2	−1.28981
$55$	−3025.00	−0.134840
$56$	−88533.3	−3.77257
$57$	2095.26	0.0854184
$58$	−52630.9	−2.05433
$59$	−53250.5	−1.99156	−0.995780	−	0.0917699i	$-0.970748\pi$
$59$	−53250.5	−1.99156	−0.995780	+	0.0917699i	$0.970748\pi$
$60$	11439.2	0.410219
$61$	−13158.7	−0.452780	−0.226390	−	0.974037i	$-0.572692\pi$
$61$	−13158.7	−0.452780	−0.226390	+	0.974037i	$0.572692\pi$
$62$	−42638.8	−1.40872
$63$	37582.6	1.19298
$64$	44245.0	1.35025
$65$	−4878.95	−0.143233
$66$	−7393.61	−0.208928
$67$	64692.8	1.76063	0.880317	−	0.474386i	$-0.157330\pi$
$67$	64692.8	1.76063	0.880317	+	0.474386i	$0.157330\pi$
$68$	−100916.	−2.64660
$69$	20223.6	0.511370
$70$	−47257.4	−1.15272
$71$	−13078.9	−0.307910	−0.153955	−	0.988078i	$-0.549201\pi$
$71$	−13078.9	−0.307910	−0.153955	+	0.988078i	$0.549201\pi$
$72$	−103208.	−2.34629
$73$	−71642.3	−1.57348	−0.786742	−	0.617282i	$-0.788234\pi$
$73$	−71642.3	−1.57348	−0.786742	+	0.617282i	$0.788234\pi$
$74$	−62576.8	−1.32842
$75$	3627.53	0.0744660
$76$	28459.7	0.565192
$77$	21725.8	0.417589
$78$	−11925.0	−0.221933
$79$	−43172.0	−0.778277	−0.389139	−	0.921179i	$-0.627227\pi$
$79$	−43172.0	−0.778277	−0.389139	+	0.921179i	$0.627227\pi$
$80$	66708.1	1.16534
$81$	35626.0	0.603329
$82$	−31004.3	−0.509199
$83$	−35799.1	−0.570396	−0.285198	−	0.958469i	$-0.592059\pi$
$83$	−35799.1	−0.570396	−0.285198	+	0.958469i	$0.592059\pi$
$84$	−82157.0	−1.27042
$85$	−32002.0	−0.480430
$86$	188248.	2.74463
$87$	−29015.6	−0.410993
$88$	−59662.6	−0.821288
$89$	−116730.	−1.56210	−0.781048	−	0.624471i	$-0.785315\pi$
$89$	−116730.	−1.56210	−0.781048	+	0.624471i	$0.785315\pi$
$90$	−55090.4	−0.716918
$91$	35041.0	0.443581
$92$	274694.	3.38361
$93$	−23507.0	−0.281831
$94$	23411.4	0.273280
$95$	9025.00	0.102598
$96$	71466.4	0.791450
$97$	72141.6	0.778496	0.389248	−	0.921133i	$-0.372735\pi$
$97$	72141.6	0.778496	0.389248	+	0.921133i	$0.372735\pi$
$98$	162465.	1.70881
$99$	25326.9	0.259713
$100$	49272.3	0.492723
$101$	−20974.2	−0.204589	−0.102294	−	0.994754i	$-0.532618\pi$
$101$	−20974.2	−0.204589	−0.102294	+	0.994754i	$0.532618\pi$
$102$	−78218.4	−0.744404
$103$	−59775.5	−0.555176	−0.277588	−	0.960700i	$-0.589535\pi$
$103$	−59775.5	−0.555176	−0.277588	+	0.960700i	$0.589535\pi$
$104$	−96228.4	−0.872409
$105$	−26053.2	−0.230615
$106$	−373768.	−3.23100
$107$	−25258.9	−0.213283	−0.106641	−	0.994298i	$-0.534010\pi$
$107$	−25258.9	−0.213283	−0.106641	+	0.994298i	$0.534010\pi$
$108$	−206963.	−1.70739
$109$	157385.	1.26881	0.634404	−	0.773002i	$-0.281246\pi$
$109$	157385.	1.26881	0.634404	+	0.773002i	$0.281246\pi$
$110$	−31846.8	−0.250948
$111$	−34498.9	−0.265765
$112$	−479103.	−3.60897
$113$	−112289.	−0.827262	−0.413631	−	0.910445i	$-0.635740\pi$
$113$	−112289.	−0.827262	−0.413631	+	0.910445i	$0.635740\pi$
$114$	22058.6	0.158970
$115$	87109.7	0.614217
$116$	−394116.	−2.71943
$117$	40849.1	0.275879
$118$	−560613.	−3.70645
$119$	229841.	1.48785
$120$	71546.5	0.453560
$121$	14641.0	0.0909091
$122$	−138533.	−0.842660
$123$	−17092.8	−0.101871
$124$	−319292.	−1.86481
$125$	15625.0	0.0894427
$126$	395664.	2.22024
$127$	196309.	1.08002	0.540010	−	0.841659i	$-0.318420\pi$
$127$	196309.	1.08002	0.540010	+	0.841659i	$0.318420\pi$
$128$	71783.3	0.387256
$129$	103782.	0.549094
$130$	−51364.9	−0.266568
$131$	273874.	1.39435	0.697177	−	0.716899i	$-0.254439\pi$
$131$	273874.	1.39435	0.697177	+	0.716899i	$0.254439\pi$
$132$	−55365.6	−0.276570
$133$	−64818.3	−0.317737
$134$	681076.	3.27668
$135$	−65631.2	−0.309939
$136$	−631182.	−2.92622
$137$	422976.	1.92537	0.962685	−	0.270624i	$-0.0872300\pi$
$137$	422976.	1.92537	0.962685	+	0.270624i	$0.0872300\pi$
$138$	212911.	0.951700
$139$	−101100.	−0.443828	−0.221914	−	0.975066i	$-0.571230\pi$
$139$	−101100.	−0.443828	−0.221914	+	0.975066i	$0.571230\pi$
$140$	−353878.	−1.52592
$141$	12906.8	0.0546728
$142$	−137692.	−0.573045
$143$	23614.1	0.0965677
$144$	−558515.	−2.24455
$145$	−124980.	−0.493652
$146$	−754240.	−2.92838
$147$	89567.6	0.341867
$148$	−468593.	−1.75850
$149$	−520625.	−1.92114	−0.960570	−	0.278037i	$-0.910316\pi$
$149$	−520625.	−1.92114	−0.960570	+	0.278037i	$0.910316\pi$
$150$	38190.1	0.138587
$151$	380718.	1.35882	0.679409	−	0.733760i	$-0.262236\pi$
$151$	380718.	1.35882	0.679409	+	0.733760i	$0.262236\pi$
$152$	178002.	0.624906
$153$	267938.	0.925348
$154$	228726.	0.777165
$155$	−101252.	−0.338513
$156$	−89297.8	−0.293785
$157$	145218.	0.470187	0.235093	−	0.971973i	$-0.424460\pi$
$157$	145218.	0.470187	0.235093	+	0.971973i	$0.424460\pi$
$158$	−454508.	−1.44844
$159$	−206060.	−0.646399
$160$	307830.	0.950628
$161$	−625629.	−1.90218
$162$	375065.	1.12284
$163$	500549.	1.47563	0.737815	−	0.675003i	$-0.235858\pi$
$163$	500549.	1.47563	0.737815	+	0.675003i	$0.235858\pi$
$164$	−232170.	−0.674056
$165$	−17557.3	−0.0502050
$166$	−376887.	−1.06155
$167$	618299.	1.71557	0.857783	−	0.514013i	$-0.171842\pi$
$167$	618299.	1.71557	0.857783	+	0.514013i	$0.171842\pi$
$168$	−513852.	−1.40464
$169$	−333206.	−0.897421
$170$	−336913.	−0.894119
$171$	−75562.0	−0.197612
$172$	1.40965e6	3.63322
$173$	−225507.	−0.572854	−0.286427	−	0.958102i	$-0.592468\pi$
$173$	−225507.	−0.572854	−0.286427	+	0.958102i	$0.592468\pi$
$174$	−305472.	−0.764890
$175$	−112220.	−0.276997
$176$	−322867.	−0.785674
$177$	−309069.	−0.741518
$178$	−1.22892e6	−2.90718
$179$	−430948.	−1.00529	−0.502646	−	0.864492i	$-0.667640\pi$
$179$	−430948.	−1.00529	−0.502646	+	0.864492i	$0.667640\pi$
$180$	−412533.	−0.949025
$181$	177113.	0.401841	0.200920	−	0.979608i	$-0.435607\pi$
$181$	177113.	0.401841	0.200920	+	0.979608i	$0.435607\pi$
$182$	368907.	0.825540
$183$	−76373.7	−0.168584
$184$	1.71808e6	3.74110
$185$	−148598.	−0.319216
$186$	−247478.	−0.524510
$187$	154890.	0.323906
$188$	175312.	0.361756
$189$	471369.	0.959856
$190$	95013.9	0.190943
$191$	−320114.	−0.634923	−0.317461	−	0.948271i	$-0.602830\pi$
$191$	−320114.	−0.634923	−0.317461	+	0.948271i	$0.602830\pi$
$192$	256801.	0.502739
$193$	614662.	1.18780	0.593899	−	0.804539i	$-0.297588\pi$
$193$	614662.	1.18780	0.593899	+	0.804539i	$0.297588\pi$
$194$	759496.	1.44884
$195$	−28317.7	−0.0533300
$196$	1.21658e6	2.26205
$197$	490150.	0.899836	0.449918	−	0.893070i	$-0.351453\pi$
$197$	490150.	0.899836	0.449918	+	0.893070i	$0.351453\pi$
$198$	266638.	0.483346
$199$	130672.	0.233910	0.116955	−	0.993137i	$-0.462687\pi$
$199$	130672.	0.233910	0.116955	+	0.993137i	$0.462687\pi$
$200$	308175.	0.544781
$201$	375481.	0.655537
$202$	−220813.	−0.380756
$203$	897617.	1.52880
$204$	−585723.	−0.985409
$205$	−73624.5	−0.122360
$206$	−629308.	−1.03323
$207$	−729328.	−1.18303
$208$	−520745.	−0.834578
$209$	−43681.0	−0.0691714
$210$	−274285.	−0.429193
$211$	904919.	1.39928	0.699638	−	0.714497i	$-0.253344\pi$
$211$	904919.	1.39928	0.699638	+	0.714497i	$0.253344\pi$
$212$	−2.79889e6	−4.27706
$213$	−75910.4	−0.114644
$214$	−265922.	−0.396936
$215$	447023.	0.659529
$216$	−1.29446e6	−1.88779
$217$	727202.	1.04835
$218$	1.65692e6	2.36135
$219$	−415816.	−0.585856
$220$	−238478.	−0.332194
$221$	249818.	0.344067
$222$	−363199.	−0.494609
$223$	404551.	0.544767	0.272383	−	0.962189i	$-0.412188\pi$
$223$	404551.	0.544767	0.272383	+	0.962189i	$0.412188\pi$
$224$	−2.21086e6	−2.94402
$225$	−130821.	−0.172274
$226$	−1.18217e6	−1.53960
$227$	−924471.	−1.19077	−0.595386	−	0.803440i	$-0.703001\pi$
$227$	−924471.	−1.19077	−0.595386	+	0.803440i	$0.703001\pi$
$228$	165182.	0.210438
$229$	1.18166e6	1.48904	0.744518	−	0.667603i	$-0.232680\pi$
$229$	1.18166e6	1.48904	0.744518	+	0.667603i	$0.232680\pi$
$230$	917078.	1.14311
$231$	126098.	0.155481
$232$	−2.46500e6	−3.00675
$233$	92540.8	0.111672	0.0558359	−	0.998440i	$-0.482218\pi$
$233$	92540.8	0.111672	0.0558359	+	0.998440i	$0.482218\pi$
$234$	430054.	0.513432
$235$	55594.0	0.0656687
$236$	−4.19804e6	−4.90644
$237$	−250573.	−0.289776
$238$	2.41973e6	2.76901
$239$	1.24252e6	1.40705	0.703523	−	0.710672i	$-0.251609\pi$
$239$	1.24252e6	1.40705	0.703523	+	0.710672i	$0.251609\pi$
$240$	387177.	0.433892
$241$	316315.	0.350815	0.175407	−	0.984496i	$-0.443876\pi$
$241$	316315.	0.350815	0.175407	+	0.984496i	$0.443876\pi$
$242$	154138.	0.169189
$243$	844710.	0.917682
$244$	−1.03737e6	−1.11548
$245$	385798.	0.410624
$246$	−179951.	−0.189590
$247$	−70452.1	−0.0734770
$248$	−1.99702e6	−2.06183
$249$	−207780.	−0.212376
$250$	164498.	0.166460
$251$	−396871.	−0.397617	−0.198808	−	0.980038i	$-0.563707\pi$
$251$	−396871.	−0.397617	−0.198808	+	0.980038i	$0.563707\pi$
$252$	2.96285e6	2.93906
$253$	−421611.	−0.414105
$254$	2.06672e6	2.01000
$255$	−185742.	−0.178879
$256$	−660117.	−0.629537
$257$	214685.	0.202753	0.101377	−	0.994848i	$-0.467675\pi$
$257$	214685.	0.202753	0.101377	+	0.994848i	$0.467675\pi$
$258$	1.09260e6	1.02191
$259$	1.06724e6	0.988585
$260$	−384636.	−0.352871
$261$	1.04640e6	0.950814
$262$	2.88331e6	2.59500
$263$	−1.48979e6	−1.32812	−0.664059	−	0.747680i	$-0.731168\pi$
$263$	−1.48979e6	−1.32812	−0.664059	+	0.747680i	$0.731168\pi$
$264$	−346285.	−0.305790
$265$	−887569.	−0.776404
$266$	−682397.	−0.591334
$267$	−677508.	−0.581616
$268$	5.10010e6	4.33752
$269$	−1.82483e6	−1.53759	−0.768795	−	0.639495i	$-0.779143\pi$
$269$	−1.82483e6	−1.53759	−0.768795	+	0.639495i	$0.779143\pi$
$270$	−690956.	−0.576821
$271$	2.17882e6	1.80218	0.901088	−	0.433636i	$-0.142770\pi$
$271$	2.17882e6	1.80218	0.901088	+	0.433636i	$0.142770\pi$
$272$	−3.41567e6	−2.79933
$273$	203380.	0.165159
$274$	4.45303e6	3.58327
$275$	−75625.0	−0.0603023
$276$	1.59434e6	1.25982
$277$	−2.16416e6	−1.69469	−0.847346	−	0.531041i	$-0.821801\pi$
$277$	−2.16416e6	−1.69469	−0.847346	+	0.531041i	$0.821801\pi$
$278$	−1.06437e6	−0.825999
$279$	847737.	0.652005
$280$	−2.21333e6	−1.68714
$281$	−940365.	−0.710445	−0.355223	−	0.934782i	$-0.615595\pi$
$281$	−940365.	−0.710445	−0.355223	+	0.934782i	$0.615595\pi$
$282$	135881.	0.101750
$283$	−332377.	−0.246698	−0.123349	−	0.992363i	$-0.539363\pi$
$283$	−332377.	−0.246698	−0.123349	+	0.992363i	$0.539363\pi$
$284$	−1.03108e6	−0.758572
$285$	52381.6	0.0382003
$286$	248606.	0.179720
$287$	528777.	0.378938
$288$	−2.57731e6	−1.83099
$289$	218752.	0.154066
$290$	−1.31577e6	−0.918725
$291$	418714.	0.289858
$292$	−5.64797e6	−3.87646
$293$	1.55665e6	1.05931	0.529653	−	0.848214i	$-0.322322\pi$
$293$	1.55665e6	1.05931	0.529653	+	0.848214i	$0.322322\pi$
$294$	942954.	0.636242
$295$	−1.33126e6	−0.890653
$296$	−2.93083e6	−1.94429
$297$	317655.	0.208961
$298$	−5.48106e6	−3.57539
$299$	−680007.	−0.439881
$300$	285979.	0.183456
$301$	−3.21055e6	−2.04251
$302$	4.00815e6	2.52887
$303$	−121735.	−0.0761747
$304$	963265.	0.597808
$305$	−328967.	−0.202490
$306$	2.82081e6	1.72215
$307$	−1.44301e6	−0.873825	−0.436913	−	0.899504i	$-0.643928\pi$
$307$	−1.44301e6	−0.873825	−0.436913	+	0.899504i	$0.643928\pi$
$308$	1.71277e6	1.02878
$309$	−346940.	−0.206709
$310$	−1.06597e6	−0.630000
$311$	1.24266e6	0.728536	0.364268	−	0.931294i	$-0.381319\pi$
$311$	1.24266e6	0.728536	0.364268	+	0.931294i	$0.381319\pi$
$312$	−558515.	−0.324824
$313$	−2.36260e6	−1.36311	−0.681554	−	0.731768i	$-0.738695\pi$
$313$	−2.36260e6	−1.36311	−0.681554	+	0.731768i	$0.738695\pi$
$314$	1.52883e6	0.875055
$315$	939564.	0.533519
$316$	−3.40349e6	−1.91738
$317$	−289086.	−0.161577	−0.0807883	−	0.996731i	$-0.525744\pi$
$317$	−289086.	−0.161577	−0.0807883	+	0.996731i	$0.525744\pi$
$318$	−2.16937e6	−1.20300
$319$	604904.	0.332820
$320$	1.10613e6	0.603851
$321$	−146604.	−0.0794116
$322$	−6.58653e6	−3.54011
$323$	−462109.	−0.246456
$324$	2.80860e6	1.48637
$325$	−121974.	−0.0640558
$326$	5.26971e6	2.74627
$327$	913468.	0.472415
$328$	−1.45211e6	−0.745272
$329$	−399281.	−0.203371
$330$	−184840.	−0.0934355
$331$	−518096.	−0.259920	−0.129960	−	0.991519i	$-0.541485\pi$
$331$	−518096.	−0.259920	−0.129960	+	0.991519i	$0.541485\pi$
$332$	−2.82224e6	−1.40524
$333$	1.24414e6	0.614835
$334$	6.50936e6	3.19280
$335$	1.61732e6	0.787379
$336$	−2.78074e6	−1.34373
$337$	1.89904e6	0.910878	0.455439	−	0.890267i	$-0.349482\pi$
$337$	1.89904e6	0.910878	0.455439	+	0.890267i	$0.349482\pi$
$338$	−3.50795e6	−1.67017
$339$	−651734.	−0.308015
$340$	−2.52290e6	−1.18360
$341$	490061.	0.228226
$342$	−795505.	−0.367771
$343$	246901.	0.113315
$344$	8.81671e6	4.01708
$345$	505589.	0.228692
$346$	−2.37410e6	−1.06613
$347$	−3.69858e6	−1.64897	−0.824483	−	0.565887i	$-0.808534\pi$
$347$	−3.69858e6	−1.64897	−0.824483	+	0.565887i	$0.808534\pi$
$348$	−2.28747e6	−1.01253
$349$	−408920.	−0.179711	−0.0898555	−	0.995955i	$-0.528641\pi$
$349$	−408920.	−0.179711	−0.0898555	+	0.995955i	$0.528641\pi$
$350$	−1.18144e6	−0.515513
$351$	512339.	0.221967
$352$	−1.48990e6	−0.640913
$353$	−2.30387e6	−0.984059	−0.492030	−	0.870578i	$-0.663745\pi$
$353$	−2.30387e6	−0.984059	−0.492030	+	0.870578i	$0.663745\pi$
$354$	−3.25383e6	−1.38002
$355$	−326972.	−0.137702
$356$	−9.20250e6	−3.84840
$357$	1.33401e6	0.553973
$358$	−4.53696e6	−1.87093
$359$	−3.38529e6	−1.38631	−0.693154	−	0.720790i	$-0.743779\pi$
$359$	−3.38529e6	−1.38631	−0.693154	+	0.720790i	$0.743779\pi$
$360$	−2.58020e6	−1.04929
$361$	130321.	0.0526316
$362$	1.86462e6	0.747857
$363$	84977.1	0.0338482
$364$	2.76248e6	1.09281
$365$	−1.79106e6	−0.703683
$366$	−804051.	−0.313748
$367$	−2.54581e6	−0.986645	−0.493323	−	0.869846i	$-0.664218\pi$
$367$	−2.54581e6	−0.986645	−0.493323	+	0.869846i	$0.664218\pi$
$368$	9.29748e6	3.57887
$369$	616423.	0.235675
$370$	−1.56442e6	−0.594085
$371$	6.37459e6	2.40446
$372$	−1.85319e6	−0.694324
$373$	−2.93007e6	−1.09045	−0.545225	−	0.838290i	$-0.683556\pi$
$373$	−2.93007e6	−1.09045	−0.545225	+	0.838290i	$0.683556\pi$
$374$	1.63066e6	0.602815
$375$	90688.3	0.0333022
$376$	1.09649e6	0.399977
$377$	975635.	0.353536
$378$	4.96250e6	1.78637
$379$	3.18959e6	1.14061	0.570304	−	0.821434i	$-0.306825\pi$
$379$	3.18959e6	1.14061	0.570304	+	0.821434i	$0.306825\pi$
$380$	711492.	0.252762
$381$	1.13939e6	0.402124
$382$	−3.37011e6	−1.18164
$383$	4.43059e6	1.54335	0.771675	−	0.636017i	$-0.219419\pi$
$383$	4.43059e6	1.54335	0.771675	+	0.636017i	$0.219419\pi$
$384$	416634.	0.144187
$385$	543145.	0.186751
$386$	6.47107e6	2.21059
$387$	−3.74271e6	−1.27031
$388$	5.68733e6	1.91792
$389$	−815706.	−0.273313	−0.136656	−	0.990619i	$-0.543636\pi$
$389$	−815706.	−0.273313	−0.136656	+	0.990619i	$0.543636\pi$
$390$	−298125.	−0.0992513
$391$	−4.46030e6	−1.47544
$392$	7.60915e6	2.50104
$393$	1.58958e6	0.519160
$394$	5.16022e6	1.67467
$395$	−1.07930e6	−0.348056
$396$	1.99666e6	0.639833
$397$	−3.18492e6	−1.01420	−0.507098	−	0.861888i	$-0.669282\pi$
$397$	−3.18492e6	−1.01420	−0.507098	+	0.861888i	$0.669282\pi$
$398$	1.37569e6	0.435325
$399$	−376209.	−0.118303
$400$	1.66770e6	0.521157
$401$	−1.04967e6	−0.325981	−0.162991	−	0.986628i	$-0.552114\pi$
$401$	−1.04967e6	−0.325981	−0.162991	+	0.986628i	$0.552114\pi$
$402$	3.95300e6	1.22001
$403$	790409.	0.242432
$404$	−1.65352e6	−0.504029
$405$	890649.	0.269817
$406$	9.44998e6	2.84522
$407$	719215.	0.215215
$408$	−3.66341e6	−1.08952
$409$	4.69991e6	1.38925	0.694627	−	0.719370i	$-0.255569\pi$
$409$	4.69991e6	1.38925	0.694627	+	0.719370i	$0.255569\pi$
$410$	−775108.	−0.227721
$411$	2.45498e6	0.716874
$412$	−4.71245e6	−1.36774
$413$	9.56123e6	2.75828
$414$	−7.67825e6	−2.20172
$415$	−894976.	−0.255089
$416$	−2.40302e6	−0.680807
$417$	−586790.	−0.165251
$418$	−459867.	−0.128734
$419$	−4.49380e6	−1.25049	−0.625243	−	0.780430i	$-0.715000\pi$
$419$	−4.49380e6	−1.25049	−0.625243	+	0.780430i	$0.715000\pi$
$420$	−2.05392e6	−0.568148
$421$	−593096.	−0.163087	−0.0815436	−	0.996670i	$-0.525985\pi$
$421$	−593096.	−0.163087	−0.0815436	+	0.996670i	$0.525985\pi$
$422$	9.52686e6	2.60417
$423$	−465462.	−0.126483
$424$	−1.75057e7	−4.72895
$425$	−800051.	−0.214855
$426$	−799174.	−0.213362
$427$	2.36267e6	0.627094
$428$	−1.99130e6	−0.525446
$429$	137058.	0.0359551
$430$	4.70619e6	1.22743
$431$	6.85356e6	1.77715	0.888573	−	0.458735i	$-0.151697\pi$
$431$	6.85356e6	1.77715	0.888573	+	0.458735i	$0.151697\pi$
$432$	−7.00501e6	−1.80592
$433$	−3.12154e6	−0.800108	−0.400054	−	0.916492i	$-0.631009\pi$
$433$	−3.12154e6	−0.800108	−0.400054	+	0.916492i	$0.631009\pi$
$434$	7.65588e6	1.95106
$435$	−725391.	−0.183801
$436$	1.24075e7	3.12585
$437$	1.25786e6	0.315087
$438$	−4.37765e6	−1.09032
$439$	657870.	0.162922	0.0814608	−	0.996677i	$-0.474041\pi$
$439$	657870.	0.162922	0.0814608	+	0.996677i	$0.474041\pi$
$440$	−1.49156e6	−0.367291
$441$	−3.23010e6	−0.790896
$442$	2.63005e6	0.640337
$443$	−8.10988e6	−1.96338	−0.981691	−	0.190479i	$-0.938996\pi$
$443$	−8.10988e6	−1.96338	−0.981691	+	0.190479i	$0.938996\pi$
$444$	−2.71974e6	−0.654742
$445$	−2.91825e6	−0.698591
$446$	4.25905e6	1.01385
$447$	−3.02173e6	−0.715299
$448$	−7.94428e6	−1.87008
$449$	−1.89479e6	−0.443553	−0.221776	−	0.975098i	$-0.571185\pi$
$449$	−1.89479e6	−0.443553	−0.221776	+	0.975098i	$0.571185\pi$
$450$	−1.37726e6	−0.320616
$451$	356343.	0.0824948
$452$	−8.85242e6	−2.03805
$453$	2.20971e6	0.505929
$454$	−9.73269e6	−2.21612
$455$	876026.	0.198376
$456$	1.03313e6	0.232672
$457$	1.05703e6	0.236754	0.118377	−	0.992969i	$-0.462231\pi$
$457$	1.05703e6	0.236754	0.118377	+	0.992969i	$0.462231\pi$
$458$	1.24404e7	2.77121
$459$	3.36053e6	0.744520
$460$	6.86735e6	1.51319
$461$	−2.15422e6	−0.472103	−0.236052	−	0.971741i	$-0.575853\pi$
$461$	−2.15422e6	−0.472103	−0.236052	+	0.971741i	$0.575853\pi$
$462$	1.32754e6	0.289362
$463$	−1.38797e6	−0.300903	−0.150452	−	0.988617i	$-0.548073\pi$
$463$	−1.38797e6	−0.300903	−0.150452	+	0.988617i	$0.548073\pi$
$464$	−1.33395e7	−2.87637
$465$	−587674.	−0.126039
$466$	974256.	0.207830
$467$	2.72032e6	0.577202	0.288601	−	0.957450i	$-0.406810\pi$
$467$	2.72032e6	0.577202	0.288601	+	0.957450i	$0.406810\pi$
$468$	3.22037e6	0.679659
$469$	−1.16157e7	−2.43845
$470$	585286.	0.122215
$471$	842851.	0.175065
$472$	−2.62567e7	−5.42482
$473$	−2.16359e6	−0.444654
$474$	−2.63799e6	−0.539296
$475$	225625.	0.0458831
$476$	1.81197e7	3.66550
$477$	7.43119e6	1.49542
$478$	1.30811e7	2.61862
$479$	3.21725e6	0.640687	0.320344	−	0.947301i	$-0.396202\pi$
$479$	3.21725e6	0.640687	0.320344	+	0.947301i	$0.396202\pi$
$480$	1.78666e6	0.353947
$481$	1.16001e6	0.228611
$482$	3.33012e6	0.652894
$483$	−3.63118e6	−0.708240
$484$	1.15423e6	0.223965
$485$	1.80354e6	0.348154
$486$	8.89299e6	1.70788
$487$	516886.	0.0987581	0.0493790	−	0.998780i	$-0.484276\pi$
$487$	516886.	0.0987581	0.0493790	+	0.998780i	$0.484276\pi$
$488$	−6.48827e6	−1.23333
$489$	2.90521e6	0.549422
$490$	4.06162e6	0.764204
$491$	−719674.	−0.134720	−0.0673600	−	0.997729i	$-0.521458\pi$
$491$	−719674.	−0.134720	−0.0673600	+	0.997729i	$0.521458\pi$
$492$	−1.34752e6	−0.250971
$493$	6.39939e6	1.18583
$494$	−741709.	−0.136747
$495$	633172.	0.116147
$496$	−1.08070e7	−1.97242
$497$	2.34834e6	0.426451
$498$	−2.18747e6	−0.395248
$499$	−3.52951e6	−0.634546	−0.317273	−	0.948334i	$-0.602767\pi$
$499$	−3.52951e6	−0.634546	−0.317273	+	0.948334i	$0.602767\pi$
$500$	1.23181e6	0.220352
$501$	3.58864e6	0.638757
$502$	−4.17820e6	−0.739996
$503$	1.66228e6	0.292944	0.146472	−	0.989215i	$-0.453208\pi$
$503$	1.66228e6	0.292944	0.146472	+	0.989215i	$0.453208\pi$
$504$	1.85312e7	3.24958
$505$	−524355.	−0.0914950
$506$	−4.43866e6	−0.770682
$507$	−1.93395e6	−0.334137
$508$	1.54762e7	2.66075
$509$	−7.32047e6	−1.25240	−0.626202	−	0.779661i	$-0.715391\pi$
$509$	−7.32047e6	−1.25240	−0.626202	+	0.779661i	$0.715391\pi$
$510$	−1.95546e6	−0.332907
$511$	1.28635e7	2.17925
$512$	−9.24668e6	−1.55887
$513$	−947715.	−0.158995
$514$	2.26017e6	0.377340
$515$	−1.49439e6	−0.248282
$516$	8.18171e6	1.35276
$517$	−269075.	−0.0442738
$518$	1.12358e7	1.83983
$519$	−1.30885e6	−0.213291
$520$	−2.40571e6	−0.390153
$521$	5.28049e6	0.852275	0.426138	−	0.904658i	$-0.359874\pi$
$521$	5.28049e6	0.852275	0.426138	+	0.904658i	$0.359874\pi$
$522$	1.10163e7	1.76954
$523$	−938869.	−0.150090	−0.0750448	−	0.997180i	$-0.523910\pi$
$523$	−938869.	−0.150090	−0.0750448	+	0.997180i	$0.523910\pi$
$524$	2.15911e7	3.43515
$525$	−651331.	−0.103134
$526$	−1.56843e7	−2.47173
$527$	5.18445e6	0.813160
$528$	−1.87394e6	−0.292530
$529$	5.70462e6	0.886314
$530$	−9.34420e6	−1.44495
$531$	1.11460e7	1.71547
$532$	−5.10999e6	−0.782783
$533$	574737.	0.0876297
$534$	−7.13270e6	−1.08243
$535$	−631473.	−0.0953829
$536$	3.18987e7	4.79580
$537$	−2.50125e6	−0.374301
$538$	−1.92115e7	−2.86158
$539$	−1.86726e6	−0.276843
$540$	−5.17408e6	−0.763570
$541$	6.00046e6	0.881438	0.440719	−	0.897645i	$-0.354724\pi$
$541$	6.00046e6	0.881438	0.440719	+	0.897645i	$0.354724\pi$
$542$	2.29383e7	3.35399
$543$	1.02797e6	0.149617
$544$	−1.57619e7	−2.28355
$545$	3.93461e6	0.567428
$546$	2.14115e6	0.307374
$547$	−9.40752e6	−1.34433	−0.672166	−	0.740400i	$-0.734636\pi$
$547$	−9.40752e6	−1.34433	−0.672166	+	0.740400i	$0.734636\pi$
$548$	3.33456e7	4.74337
$549$	2.75428e6	0.390012
$550$	−796169.	−0.112227
$551$	−1.80471e6	−0.253238
$552$	9.97183e6	1.39292
$553$	7.75162e6	1.07790
$554$	−2.27840e7	−3.15396
$555$	−862471.	−0.118854
$556$	−7.97030e6	−1.09342
$557$	3.11873e6	0.425932	0.212966	−	0.977060i	$-0.431688\pi$
$557$	3.11873e6	0.425932	0.212966	+	0.977060i	$0.431688\pi$
$558$	8.92485e6	1.21343
$559$	−3.48961e6	−0.472332
$560$	−1.19776e7	−1.61398
$561$	898989.	0.120600
$562$	−9.90002e6	−1.32219
$563$	−6.55490e6	−0.871555	−0.435778	−	0.900054i	$-0.643527\pi$
$563$	−6.55490e6	−0.871555	−0.435778	+	0.900054i	$0.643527\pi$
$564$	1.01752e6	0.134693
$565$	−2.80724e6	−0.369963
$566$	−3.49922e6	−0.459124
$567$	−6.39671e6	−0.835601
$568$	−6.44892e6	−0.838718
$569$	−6.18682e6	−0.801100	−0.400550	−	0.916275i	$-0.631181\pi$
$569$	−6.18682e6	−0.801100	−0.400550	+	0.916275i	$0.631181\pi$
$570$	551466.	0.0710937
$571$	8.83796e6	1.13439	0.567194	−	0.823584i	$-0.308029\pi$
$571$	8.83796e6	1.13439	0.567194	+	0.823584i	$0.308029\pi$
$572$	1.86164e6	0.237906
$573$	−1.85796e6	−0.236401
$574$	5.56689e6	0.705233
$575$	2.17774e6	0.274686
$576$	−9.26106e6	−1.16307
$577$	1.51256e7	1.89136	0.945679	−	0.325102i	$-0.105399\pi$
$577$	1.51256e7	1.89136	0.945679	+	0.325102i	$0.105399\pi$
$578$	2.30299e6	0.286729
$579$	3.56753e6	0.442253
$580$	−9.85289e6	−1.21617
$581$	6.42779e6	0.789990
$582$	4.40816e6	0.539448
$583$	4.29584e6	0.523451
$584$	−3.53253e7	−4.28602
$585$	1.02123e6	0.123377
$586$	1.63882e7	1.97145
$587$	−1.42473e7	−1.70663	−0.853313	−	0.521399i	$-0.825410\pi$
$587$	−1.42473e7	−1.70663	−0.853313	+	0.521399i	$0.825410\pi$
$588$	7.06112e6	0.842230
$589$	−1.46208e6	−0.173654
$590$	−1.40153e7	−1.65758
$591$	2.84485e6	0.335036
$592$	−1.58603e7	−1.85998
$593$	−3.23836e6	−0.378171	−0.189085	−	0.981961i	$-0.560552\pi$
$593$	−3.23836e6	−0.378171	−0.189085	+	0.981961i	$0.560552\pi$
$594$	3.34423e6	0.388892
$595$	5.74603e6	0.665389
$596$	−4.10438e7	−4.73295
$597$	758426.	0.0870918
$598$	−7.15901e6	−0.818654
$599$	9.86134e6	1.12297	0.561486	−	0.827486i	$-0.310230\pi$
$599$	9.86134e6	1.12297	0.561486	+	0.827486i	$0.310230\pi$
$600$	1.78866e6	0.202838
$601$	−5.32678e6	−0.601560	−0.300780	−	0.953694i	$-0.597247\pi$
$601$	−5.32678e6	−0.601560	−0.300780	+	0.953694i	$0.597247\pi$
$602$	−3.38002e7	−3.80127
$603$	−1.35410e7	−1.51656
$604$	3.00142e7	3.34761
$605$	366025.	0.0406558
$606$	−1.28161e6	−0.141767
$607$	−1.19252e7	−1.31369	−0.656847	−	0.754024i	$-0.728110\pi$
$607$	−1.19252e7	−1.31369	−0.656847	+	0.754024i	$0.728110\pi$
$608$	4.44506e6	0.487662
$609$	5.20981e6	0.569219
$610$	−3.46332e6	−0.376849
$611$	−433985.	−0.0470296
$612$	2.11230e7	2.27970
$613$	−5.24144e6	−0.563378	−0.281689	−	0.959506i	$-0.590895\pi$
$613$	−5.24144e6	−0.563378	−0.281689	+	0.959506i	$0.590895\pi$
$614$	−1.51918e7	−1.62626
$615$	−427321.	−0.0455582
$616$	1.07125e7	1.13747
$617$	5.59173e6	0.591334	0.295667	−	0.955291i	$-0.404458\pi$
$617$	5.59173e6	0.591334	0.295667	+	0.955291i	$0.404458\pi$
$618$	−3.65254e6	−0.384701
$619$	8.51658e6	0.893385	0.446693	−	0.894687i	$-0.352602\pi$
$619$	8.51658e6	0.893385	0.446693	+	0.894687i	$0.352602\pi$
$620$	−7.98230e6	−0.833967
$621$	−9.14739e6	−0.951849
$622$	1.30825e7	1.35586
$623$	2.09591e7	2.16348
$624$	−3.02243e6	−0.310739
$625$	390625.	0.0400000
$626$	−2.48731e7	−2.53685
$627$	−253527.	−0.0257546
$628$	1.14483e7	1.15836
$629$	7.60871e6	0.766804
$630$	9.89159e6	0.992921
$631$	−5.69250e6	−0.569153	−0.284577	−	0.958653i	$-0.591853\pi$
$631$	−5.69250e6	−0.569153	−0.284577	+	0.958653i	$0.591853\pi$
$632$	−2.12872e7	−2.11995
$633$	5.25220e6	0.520993
$634$	−3.04345e6	−0.300707
$635$	4.90774e6	0.483000
$636$	−1.62449e7	−1.59248
$637$	−3.01166e6	−0.294075
$638$	6.36834e6	0.619404
$639$	2.73758e6	0.265225
$640$	1.79458e6	0.173186
$641$	3.93903e6	0.378655	0.189328	−	0.981914i	$-0.439369\pi$
$641$	3.93903e6	0.378655	0.189328	+	0.981914i	$0.439369\pi$
$642$	−1.54343e6	−0.147791
$643$	−1.92354e7	−1.83473	−0.917366	−	0.398044i	$-0.869689\pi$
$643$	−1.92354e7	−1.83473	−0.917366	+	0.398044i	$0.869689\pi$
$644$	−4.93219e7	−4.68624
$645$	2.59454e6	0.245562
$646$	−4.86502e6	−0.458673
$647$	−7.19000e6	−0.675256	−0.337628	−	0.941280i	$-0.609625\pi$
$647$	−7.19000e6	−0.675256	−0.337628	+	0.941280i	$0.609625\pi$
$648$	1.75664e7	1.64341
$649$	6.44331e6	0.600478
$650$	−1.28412e6	−0.119213
$651$	4.22072e6	0.390332
$652$	3.94611e7	3.63539
$653$	−782147.	−0.0717803	−0.0358902	−	0.999356i	$-0.511427\pi$
$653$	−782147.	−0.0717803	−0.0358902	+	0.999356i	$0.511427\pi$
$654$	9.61686e6	0.879203
$655$	6.84686e6	0.623574
$656$	−7.85816e6	−0.712954
$657$	1.49957e7	1.35535
$658$	−4.20357e6	−0.378489
$659$	−1.62884e7	−1.46105	−0.730525	−	0.682886i	$-0.760724\pi$
$659$	−1.62884e7	−1.46105	−0.730525	+	0.682886i	$0.760724\pi$
$660$	−1.38414e6	−0.123686
$661$	−1.78570e7	−1.58966	−0.794831	−	0.606830i	$-0.792441\pi$
$661$	−1.78570e7	−1.58966	−0.794831	+	0.606830i	$0.792441\pi$
$662$	−5.45444e6	−0.483732
$663$	1.44996e6	0.128107
$664$	−1.76518e7	−1.55370
$665$	−1.62046e6	−0.142096
$666$	1.30981e7	1.14426
$667$	−1.74192e7	−1.51605
$668$	4.87440e7	4.22649
$669$	2.34803e6	0.202833
$670$	1.70269e7	1.46538
$671$	1.59220e6	0.136518
$672$	−1.28319e7	−1.09615
$673$	1.48287e7	1.26202	0.631010	−	0.775774i	$-0.282641\pi$
$673$	1.48287e7	1.26202	0.631010	+	0.775774i	$0.282641\pi$
$674$	1.99928e7	1.69522
$675$	−1.64078e6	−0.138609
$676$	−2.62685e7	−2.21090
$677$	4.02904e6	0.337855	0.168927	−	0.985629i	$-0.445970\pi$
$677$	4.02904e6	0.337855	0.168927	+	0.985629i	$0.445970\pi$
$678$	−6.86136e6	−0.573239
$679$	−1.29532e7	−1.07821
$680$	−1.57795e7	−1.30865
$681$	−5.36568e6	−0.443360
$682$	5.15929e6	0.424746
$683$	2.34362e7	1.92237	0.961183	−	0.275911i	$-0.0889795\pi$
$683$	2.34362e7	1.92237	0.961183	+	0.275911i	$0.0889795\pi$
$684$	−5.95698e6	−0.486840
$685$	1.05744e7	0.861052
$686$	2.59934e6	0.210888
$687$	6.85844e6	0.554413
$688$	4.77121e7	3.84288
$689$	6.92865e6	0.556033
$690$	5.32277e6	0.425613
$691$	−8.91006e6	−0.709881	−0.354941	−	0.934889i	$-0.615499\pi$
$691$	−8.91006e6	−0.709881	−0.354941	+	0.934889i	$0.615499\pi$
$692$	−1.77780e7	−1.41129
$693$	−4.54749e6	−0.359698
$694$	−3.89381e7	−3.06885
$695$	−2.52750e6	−0.198486
$696$	−1.43070e7	−1.11950
$697$	3.76982e6	0.293926
$698$	−4.30505e6	−0.334457
$699$	537112.	0.0415788
$700$	−8.84694e6	−0.682414
$701$	−4.47339e6	−0.343829	−0.171914	−	0.985112i	$-0.554995\pi$
$701$	−4.47339e6	−0.343829	−0.171914	+	0.985112i	$0.554995\pi$
$702$	5.39383e6	0.413099
$703$	−2.14576e6	−0.163754
$704$	−5.35365e6	−0.407116
$705$	322671.	0.0244504
$706$	−2.42548e7	−1.83141
$707$	3.76596e6	0.283353
$708$	−2.43656e7	−1.82682
$709$	−3.53807e6	−0.264333	−0.132166	−	0.991228i	$-0.542193\pi$
$709$	−3.53807e6	−0.264333	−0.132166	+	0.991228i	$0.542193\pi$
$710$	−3.44231e6	−0.256274
$711$	9.03646e6	0.670385
$712$	−5.75572e7	−4.25500
$713$	−1.41121e7	−1.03960
$714$	1.40443e7	1.03099
$715$	590353.	0.0431864
$716$	−3.39741e7	−2.47665
$717$	7.21165e6	0.523886
$718$	−3.56398e7	−2.58003
$719$	−1.32837e7	−0.958287	−0.479143	−	0.877737i	$-0.659053\pi$
$719$	−1.32837e7	−0.958287	−0.479143	+	0.877737i	$0.659053\pi$
$720$	−1.39629e7	−1.00379
$721$	1.07328e7	0.768910
$722$	1.37200e6	0.0979515
$723$	1.83591e6	0.130619
$724$	1.39628e7	0.989980
$725$	−3.12450e6	−0.220768
$726$	894627.	0.0629942
$727$	1.89408e7	1.32912	0.664558	−	0.747236i	$-0.268620\pi$
$727$	1.89408e7	1.32912	0.664558	+	0.747236i	$0.268620\pi$
$728$	1.72780e7	1.20827
$729$	−3.75437e6	−0.261648
$730$	−1.88560e7	−1.30961
$731$	−2.28890e7	−1.58429
$732$	−6.02097e6	−0.415326
$733$	2.53568e7	1.74315	0.871575	−	0.490262i	$-0.163099\pi$
$733$	2.53568e7	1.74315	0.871575	+	0.490262i	$0.163099\pi$
$734$	−2.68019e7	−1.83623
$735$	2.23919e6	0.152888
$736$	4.29039e7	2.91946
$737$	−7.82783e6	−0.530851
$738$	6.48961e6	0.438609
$739$	1.90016e7	1.27991	0.639953	−	0.768414i	$-0.278954\pi$
$739$	1.90016e7	1.27991	0.639953	+	0.768414i	$0.278954\pi$
$740$	−1.17148e7	−0.786424
$741$	−408908.	−0.0273577
$742$	6.71108e7	4.47489
$743$	−1.93151e7	−1.28358	−0.641792	−	0.766879i	$-0.721809\pi$
$743$	−1.93151e7	−1.28358	−0.641792	+	0.766879i	$0.721809\pi$
$744$	−1.15908e7	−0.767681
$745$	−1.30156e7	−0.859160
$746$	−3.08473e7	−2.02941
$747$	7.49321e6	0.491322
$748$	1.22108e7	0.797980
$749$	4.53529e6	0.295393
$750$	954753.	0.0619781
$751$	−1.89416e7	−1.22551	−0.612756	−	0.790273i	$-0.709939\pi$
$751$	−1.89416e7	−1.22551	−0.612756	+	0.790273i	$0.709939\pi$
$752$	5.93371e6	0.382633
$753$	−2.30346e6	−0.148045
$754$	1.02713e7	0.657959
$755$	9.51796e6	0.607682
$756$	3.71607e7	2.36472
$757$	−1.94423e7	−1.23313	−0.616563	−	0.787306i	$-0.711475\pi$
$757$	−1.94423e7	−1.23313	−0.616563	+	0.787306i	$0.711475\pi$
$758$	3.35795e7	2.12276
$759$	−2.44705e6	−0.154184
$760$	4.45004e6	0.279467
$761$	4.26596e6	0.267027	0.133513	−	0.991047i	$-0.457374\pi$
$761$	4.26596e6	0.267027	0.133513	+	0.991047i	$0.457374\pi$
$762$	1.19953e7	0.748385
$763$	−2.82587e7	−1.75728
$764$	−2.52364e7	−1.56421
$765$	6.69844e6	0.413828
$766$	4.66446e7	2.87230
$767$	1.03923e7	0.637855
$768$	−3.83135e6	−0.234395
$769$	−7.43366e6	−0.453301	−0.226651	−	0.973976i	$-0.572778\pi$
$769$	−7.43366e6	−0.453301	−0.226651	+	0.973976i	$0.572778\pi$
$770$	5.71815e6	0.347559
$771$	1.24604e6	0.0754912
$772$	4.84573e7	2.92628
$773$	2.24088e6	0.134887	0.0674434	−	0.997723i	$-0.478516\pi$
$773$	2.24088e6	0.134887	0.0674434	+	0.997723i	$0.478516\pi$
$774$	−3.94027e7	−2.36414
$775$	−2.53131e6	−0.151388
$776$	3.55715e7	2.12055
$777$	6.19434e6	0.368080
$778$	−8.58764e6	−0.508657
$779$	−1.06314e6	−0.0627691
$780$	−2.23245e6	−0.131385
$781$	1.58254e6	0.0928384
$782$	−4.69574e7	−2.74592
$783$	1.31242e7	0.765009
$784$	4.11773e7	2.39259
$785$	3.63044e6	0.210274
$786$	1.67349e7	0.966198
$787$	−1.21725e7	−0.700558	−0.350279	−	0.936645i	$-0.613913\pi$
$787$	−1.21725e7	−0.700558	−0.350279	+	0.936645i	$0.613913\pi$
$788$	3.86413e7	2.21685
$789$	−8.64684e6	−0.494498
$790$	−1.13627e7	−0.647760
$791$	2.01618e7	1.14575
$792$	1.24882e7	0.707433
$793$	2.56802e6	0.145016
$794$	−3.35304e7	−1.88750
$795$	−5.15150e6	−0.289079
$796$	1.03016e7	0.576264
$797$	114930.	0.00640896	0.00320448	−	0.999995i	$-0.498980\pi$
$797$	114930.	0.00640896	0.00320448	+	0.999995i	$0.498980\pi$
$798$	−3.96067e6	−0.220172
$799$	−2.84659e6	−0.157746
$800$	7.69574e6	0.425134
$801$	2.44331e7	1.34554
$802$	−1.10508e7	−0.606677
$803$	8.66872e6	0.474423
$804$	2.96013e7	1.61499
$805$	−1.56407e7	−0.850682
$806$	8.32131e6	0.451184
$807$	−1.05914e7	−0.572491
$808$	−1.03419e7	−0.557281
$809$	1.60795e7	0.863776	0.431888	−	0.901927i	$-0.357848\pi$
$809$	1.60795e7	0.863776	0.431888	+	0.901927i	$0.357848\pi$
$810$	9.37662e6	0.502151
$811$	3.03196e6	0.161872	0.0809359	−	0.996719i	$-0.474209\pi$
$811$	3.03196e6	0.161872	0.0809359	+	0.996719i	$0.474209\pi$
$812$	7.07642e7	3.76638
$813$	1.26460e7	0.671005
$814$	7.57179e6	0.400532
$815$	1.25137e7	0.659922
$816$	−1.98247e7	−1.04227
$817$	6.45501e6	0.338331
$818$	4.94800e7	2.58551
$819$	−7.33454e6	−0.382088
$820$	−5.80424e6	−0.301447
$821$	8.84855e6	0.458157	0.229079	−	0.973408i	$-0.426429\pi$
$821$	8.84855e6	0.458157	0.229079	+	0.973408i	$0.426429\pi$
$822$	2.58456e7	1.33416
$823$	−317628.	−0.0163463	−0.00817314	−	0.999967i	$-0.502602\pi$
$823$	−317628.	−0.0163463	−0.00817314	+	0.999967i	$0.502602\pi$
$824$	−2.94741e7	−1.51225
$825$	−438932.	−0.0224524
$826$	1.00659e8	5.13338
$827$	2.42019e7	1.23051	0.615255	−	0.788328i	$-0.289053\pi$
$827$	2.42019e7	1.23051	0.615255	+	0.788328i	$0.289053\pi$
$828$	−5.74971e7	−2.91454
$829$	2.18918e7	1.10635	0.553177	−	0.833064i	$-0.313415\pi$
$829$	2.18918e7	1.10635	0.553177	+	0.833064i	$0.313415\pi$
$830$	−9.42218e6	−0.474740
$831$	−1.25609e7	−0.630985
$832$	−8.63478e6	−0.432457
$833$	−1.97541e7	−0.986381
$834$	−6.17764e6	−0.307544
$835$	1.54575e7	0.767224
$836$	−3.44362e6	−0.170412
$837$	1.06325e7	0.524592
$838$	−4.73101e7	−2.32725
$839$	−3.37808e7	−1.65678	−0.828391	−	0.560151i	$-0.810743\pi$
$839$	−3.37808e7	−1.65678	−0.828391	+	0.560151i	$0.810743\pi$
$840$	−1.28463e7	−0.628174
$841$	4.48088e6	0.218461
$842$	−6.24403e6	−0.303518
$843$	−5.45793e6	−0.264520
$844$	7.13399e7	3.44728
$845$	−8.33016e6	−0.401339
$846$	−4.90031e6	−0.235395
$847$	−2.62882e6	−0.125908
$848$	−9.47329e7	−4.52388
$849$	−1.92913e6	−0.0918530
$850$	−8.42282e6	−0.399862
$851$	−2.07109e7	−0.980338
$852$	−5.98445e6	−0.282439
$853$	1.56338e7	0.735687	0.367844	−	0.929888i	$-0.380096\pi$
$853$	1.56338e7	0.735687	0.367844	+	0.929888i	$0.380096\pi$
$854$	2.48738e7	1.16707
$855$	−1.88905e6	−0.0883747
$856$	−1.24547e7	−0.580961
$857$	−1.88336e7	−0.875953	−0.437976	−	0.898986i	$-0.644305\pi$
$857$	−1.88336e7	−0.875953	−0.437976	+	0.898986i	$0.644305\pi$
$858$	1.44292e6	0.0669152
$859$	−2.23839e7	−1.03503	−0.517515	−	0.855674i	$-0.673143\pi$
$859$	−2.23839e7	−1.03503	−0.517515	+	0.855674i	$0.673143\pi$
$860$	3.52414e7	1.62482
$861$	3.06905e6	0.141090
$862$	7.21533e7	3.30741
$863$	1.64579e6	0.0752224	0.0376112	−	0.999292i	$-0.488025\pi$
$863$	1.64579e6	0.0752224	0.0376112	+	0.999292i	$0.488025\pi$
$864$	−3.23252e7	−1.47318
$865$	−5.63766e6	−0.256188
$866$	−3.28631e7	−1.48906
$867$	1.26965e6	0.0573634
$868$	5.73295e7	2.58273
$869$	5.22381e6	0.234659
$870$	−7.63681e6	−0.342069
$871$	−1.26253e7	−0.563894
$872$	7.76031e7	3.45611
$873$	−1.51002e7	−0.670573
$874$	1.32426e7	0.586401
$875$	−2.80550e6	−0.123877
$876$	−3.27811e7	−1.44332
$877$	8.02711e6	0.352420	0.176210	−	0.984353i	$-0.443616\pi$
$877$	8.02711e6	0.352420	0.176210	+	0.984353i	$0.443616\pi$
$878$	6.92596e6	0.303210
$879$	9.03487e6	0.394412
$880$	−8.07168e6	−0.351364
$881$	2.81181e7	1.22052	0.610262	−	0.792199i	$-0.291064\pi$
$881$	2.81181e7	1.22052	0.610262	+	0.792199i	$0.291064\pi$
$882$	−3.40060e7	−1.47192
$883$	−2.63734e7	−1.13832	−0.569161	−	0.822226i	$-0.692732\pi$
$883$	−2.63734e7	−1.13832	−0.569161	+	0.822226i	$0.692732\pi$
$884$	1.96946e7	0.847650
$885$	−7.72672e6	−0.331617
$886$	−8.53796e7	−3.65401
$887$	−2.62816e7	−1.12161	−0.560805	−	0.827948i	$-0.689508\pi$
$887$	−2.62816e7	−1.12161	−0.560805	+	0.827948i	$0.689508\pi$
$888$	−1.70107e7	−0.723917
$889$	−3.52477e7	−1.49581
$890$	−3.07229e7	−1.30013
$891$	−4.31074e6	−0.181910
$892$	3.18930e7	1.34210
$893$	802778.	0.0336873
$894$	−3.18124e7	−1.33123
$895$	−1.07737e7	−0.449581
$896$	−1.28888e7	−0.536344
$897$	−3.94680e6	−0.163781
$898$	−1.99481e7	−0.825486
$899$	2.02472e7	0.835539
$900$	−1.03133e7	−0.424417
$901$	4.54464e7	1.86504
$902$	3.75152e6	0.153529
$903$	−1.86342e7	−0.760487
$904$	−5.53676e7	−2.25338
$905$	4.42782e6	0.179709
$906$	2.32635e7	0.941574
$907$	7.31800e6	0.295375	0.147688	−	0.989034i	$-0.452817\pi$
$907$	7.31800e6	0.295375	0.147688	+	0.989034i	$0.452817\pi$
$908$	−7.28813e7	−2.93360
$909$	4.39017e6	0.176227
$910$	9.22267e6	0.369193
$911$	−2.40364e7	−0.959562	−0.479781	−	0.877388i	$-0.659284\pi$
$911$	−2.40364e7	−0.959562	−0.479781	+	0.877388i	$0.659284\pi$
$912$	5.59084e6	0.222582
$913$	4.33169e6	0.171981
$914$	1.11283e7	0.440618
$915$	−1.90934e6	−0.0753930
$916$	9.31572e7	3.66841
$917$	−4.91747e7	−1.93116
$918$	3.53792e7	1.38561
$919$	−1.61198e7	−0.629610	−0.314805	−	0.949156i	$-0.601939\pi$
$919$	−1.61198e7	−0.629610	−0.314805	+	0.949156i	$0.601939\pi$
$920$	4.29520e7	1.67307
$921$	−8.37533e6	−0.325352
$922$	−2.26793e7	−0.878621
$923$	2.55245e6	0.0986171
$924$	9.94099e6	0.383045
$925$	−3.71495e6	−0.142758
$926$	−1.46123e7	−0.560005
$927$	1.25118e7	0.478212
$928$	−6.15561e7	−2.34640
$929$	−3.97837e6	−0.151240	−0.0756198	−	0.997137i	$-0.524094\pi$
$929$	−3.97837e6	−0.151240	−0.0756198	+	0.997137i	$0.524094\pi$
$930$	−6.18694e6	−0.234568
$931$	5.57092e6	0.210646
$932$	7.29552e6	0.275116
$933$	7.21246e6	0.271256
$934$	2.86391e7	1.07422
$935$	3.87225e6	0.144855
$936$	2.01419e7	0.751467
$937$	1.00458e7	0.373798	0.186899	−	0.982379i	$-0.440156\pi$
$937$	1.00458e7	0.373798	0.186899	+	0.982379i	$0.440156\pi$
$938$	−1.22289e8	−4.53815
$939$	−1.37127e7	−0.507526
$940$	4.38279e6	0.161782
$941$	−2.60081e7	−0.957491	−0.478745	−	0.877954i	$-0.658908\pi$
$941$	−2.60081e7	−0.957491	−0.478745	+	0.877954i	$0.658908\pi$
$942$	8.87341e6	0.325809
$943$	−1.02615e7	−0.375777
$944$	−1.42090e8	−5.18958
$945$	1.17842e7	0.429261
$946$	−2.27780e7	−0.827536
$947$	4.26355e7	1.54489	0.772443	−	0.635084i	$-0.219034\pi$
$947$	4.26355e7	1.54489	0.772443	+	0.635084i	$0.219034\pi$
$948$	−1.97541e7	−0.713897
$949$	1.39816e7	0.503954
$950$	2.37535e6	0.0853922
$951$	−1.67787e6	−0.0601599
$952$	1.13330e8	4.05277
$953$	1.84269e7	0.657235	0.328617	−	0.944463i	$-0.393417\pi$
$953$	1.84269e7	0.657235	0.328617	+	0.944463i	$0.393417\pi$
$954$	7.82345e7	2.78309
$955$	−8.00285e6	−0.283946
$956$	9.79549e7	3.46642
$957$	3.51089e6	0.123919
$958$	3.38707e7	1.19237
$959$	−7.59462e7	−2.66661
$960$	6.42001e6	0.224832
$961$	−1.22259e7	−0.427044
$962$	1.22124e7	0.425463
$963$	5.28702e6	0.183715
$964$	2.49369e7	0.864272
$965$	1.53665e7	0.531200
$966$	−3.82286e7	−1.31809
$967$	2.88916e7	0.993586	0.496793	−	0.867869i	$-0.334511\pi$
$967$	2.88916e7	0.993586	0.496793	+	0.867869i	$0.334511\pi$
$968$	7.21917e6	0.247628
$969$	−2.68211e6	−0.0917628
$970$	1.89874e7	0.647942
$971$	6.54714e6	0.222845	0.111423	−	0.993773i	$-0.464459\pi$
$971$	6.54714e6	0.222845	0.111423	+	0.993773i	$0.464459\pi$
$972$	6.65933e7	2.26082
$973$	1.81527e7	0.614695
$974$	5.44170e6	0.183797
$975$	−707943.	−0.0238499
$976$	−3.51116e7	−1.17985
$977$	−2.18433e7	−0.732120	−0.366060	−	0.930591i	$-0.619293\pi$
$977$	−2.18433e7	−0.732120	−0.366060	+	0.930591i	$0.619293\pi$
$978$	3.05857e7	1.02252
$979$	1.41243e7	0.470990
$980$	3.04146e7	1.01162
$981$	−3.29426e7	−1.09291
$982$	−7.57663e6	−0.250725
$983$	3.22091e6	0.106315	0.0531576	−	0.998586i	$-0.483071\pi$
$983$	3.22091e6	0.106315	0.0531576	+	0.998586i	$0.483071\pi$
$984$	−8.42812e6	−0.277487
$985$	1.22537e7	0.402419
$986$	6.73718e7	2.20692
$987$	−2.31745e6	−0.0757211
$988$	−5.55414e6	−0.181019
$989$	6.23041e7	2.02547
$990$	6.66594e6	0.216159
$991$	1.89957e7	0.614429	0.307214	−	0.951640i	$-0.400603\pi$
$991$	1.89957e7	0.614429	0.307214	+	0.951640i	$0.400603\pi$
$992$	−4.98695e7	−1.60900
$993$	−3.00706e6	−0.0967762
$994$	2.47229e7	0.793659
$995$	3.26679e6	0.104608
$996$	−1.63805e7	−0.523212
$997$	−2.68185e7	−0.854470	−0.427235	−	0.904141i	$-0.640512\pi$
$997$	−2.68185e7	−0.854470	−0.427235	+	0.904141i	$0.640512\pi$
$998$	−3.71582e7	−1.18094
$999$	1.56043e7	0.494686

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.b.1.36	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.36	✓	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+10.5279 q^{2} +5.80405 q^{3} +78.8357 q^{4} +25.0000 q^{5} +61.1042 q^{6} -179.552 q^{7} +493.079 q^{8} -209.313 q^{9} +O(q^{10})\)	\(q+10.5279 q^{2} +5.80405 q^{3} +78.8357 q^{4} +25.0000 q^{5} +61.1042 q^{6} -179.552 q^{7} +493.079 q^{8} -209.313 q^{9} +263.196 q^{10} -121.000 q^{11} +457.567 q^{12} -195.158 q^{13} -1890.30 q^{14} +145.101 q^{15} +2668.32 q^{16} -1280.08 q^{17} -2203.62 q^{18} +361.000 q^{19} +1970.89 q^{20} -1042.13 q^{21} -1273.87 q^{22} +3484.39 q^{23} +2861.86 q^{24} +625.000 q^{25} -2054.60 q^{26} -2625.25 q^{27} -14155.1 q^{28} -4999.20 q^{29} +1527.61 q^{30} -4050.09 q^{31} +12313.2 q^{32} -702.290 q^{33} -13476.5 q^{34} -4488.80 q^{35} -16501.3 q^{36} -5943.92 q^{37} +3800.55 q^{38} -1132.71 q^{39} +12327.0 q^{40} -2944.98 q^{41} -10971.4 q^{42} +17880.9 q^{43} -9539.12 q^{44} -5232.82 q^{45} +36683.1 q^{46} +2223.76 q^{47} +15487.1 q^{48} +15431.9 q^{49} +6579.91 q^{50} -7429.66 q^{51} -15385.4 q^{52} -35502.8 q^{53} -27638.2 q^{54} -3025.00 q^{55} -88533.3 q^{56} +2095.26 q^{57} -52630.9 q^{58} -53250.5 q^{59} +11439.2 q^{60} -13158.7 q^{61} -42638.8 q^{62} +37582.6 q^{63} +44245.0 q^{64} -4878.95 q^{65} -7393.61 q^{66} +64692.8 q^{67} -100916. q^{68} +20223.6 q^{69} -47257.4 q^{70} -13078.9 q^{71} -103208. q^{72} -71642.3 q^{73} -62576.8 q^{74} +3627.53 q^{75} +28459.7 q^{76} +21725.8 q^{77} -11925.0 q^{78} -43172.0 q^{79} +66708.1 q^{80} +35626.0 q^{81} -31004.3 q^{82} -35799.1 q^{83} -82157.0 q^{84} -32002.0 q^{85} +188248. q^{86} -29015.6 q^{87} -59662.6 q^{88} -116730. q^{89} -55090.4 q^{90} +35041.0 q^{91} +274694. q^{92} -23507.0 q^{93} +23411.4 q^{94} +9025.00 q^{95} +71466.4 q^{96} +72141.6 q^{97} +162465. q^{98} +25326.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more