LMFDB - Embedded newform 1045.6.a.b.1.29

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			1.29
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)

$f(q)$	$=$	$q+6.51695 q^{2} -24.1709 q^{3} +10.4706 q^{4} +25.0000 q^{5} -157.521 q^{6} +214.817 q^{7} -140.306 q^{8} +341.233 q^{9} +O(q^{10})$	\(q+6.51695 q^{2} -24.1709 q^{3} +10.4706 q^{4} +25.0000 q^{5} -157.521 q^{6} +214.817 q^{7} -140.306 q^{8} +341.233 q^{9} +162.924 q^{10} -121.000 q^{11} -253.084 q^{12} +302.196 q^{13} +1399.95 q^{14} -604.273 q^{15} -1249.43 q^{16} -661.004 q^{17} +2223.80 q^{18} +361.000 q^{19} +261.765 q^{20} -5192.32 q^{21} -788.551 q^{22} -4684.99 q^{23} +3391.32 q^{24} +625.000 q^{25} +1969.40 q^{26} -2374.37 q^{27} +2249.26 q^{28} +549.294 q^{29} -3938.01 q^{30} +5998.56 q^{31} -3652.65 q^{32} +2924.68 q^{33} -4307.73 q^{34} +5370.42 q^{35} +3572.91 q^{36} +8540.00 q^{37} +2352.62 q^{38} -7304.36 q^{39} -3507.65 q^{40} -12184.3 q^{41} -33838.1 q^{42} -20369.8 q^{43} -1266.94 q^{44} +8530.82 q^{45} -30531.9 q^{46} +21132.0 q^{47} +30199.8 q^{48} +29339.3 q^{49} +4073.09 q^{50} +15977.1 q^{51} +3164.18 q^{52} -23182.1 q^{53} -15473.7 q^{54} -3025.00 q^{55} -30140.1 q^{56} -8725.70 q^{57} +3579.72 q^{58} -17287.5 q^{59} -6327.10 q^{60} +40369.1 q^{61} +39092.3 q^{62} +73302.6 q^{63} +16177.5 q^{64} +7554.91 q^{65} +19060.0 q^{66} -38837.5 q^{67} -6921.12 q^{68} +113241. q^{69} +34998.8 q^{70} -8775.55 q^{71} -47877.0 q^{72} +55177.8 q^{73} +55654.7 q^{74} -15106.8 q^{75} +3779.89 q^{76} -25992.8 q^{77} -47602.1 q^{78} -38874.2 q^{79} -31235.6 q^{80} -25528.8 q^{81} -79404.6 q^{82} +108431. q^{83} -54366.7 q^{84} -16525.1 q^{85} -132749. q^{86} -13276.9 q^{87} +16977.0 q^{88} +101780. q^{89} +55594.9 q^{90} +64916.9 q^{91} -49054.7 q^{92} -144991. q^{93} +137716. q^{94} +9025.00 q^{95} +88287.9 q^{96} -54550.6 q^{97} +191203. q^{98} -41289.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.51695	1.15204	0.576022	−	0.817434i	$-0.304604\pi$
$2$	6.51695	1.15204	0.576022	+	0.817434i	$0.304604\pi$
$3$	−24.1709	−1.55056	−0.775282	−	0.631615i	$-0.782392\pi$
$3$	−24.1709	−1.55056	−0.775282	+	0.631615i	$0.782392\pi$
$4$	10.4706	0.327206
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−157.521	−1.78632
$7$	214.817	1.65700	0.828502	−	0.559987i	$-0.189194\pi$
$7$	214.817	1.65700	0.828502	+	0.559987i	$0.189194\pi$
$8$	−140.306	−0.775088
$9$	341.233	1.40425
$10$	162.924	0.515210
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−253.084	−0.507355
$13$	302.196	0.495942	0.247971	−	0.968767i	$-0.420236\pi$
$13$	302.196	0.495942	0.247971	+	0.968767i	$0.420236\pi$
$14$	1399.95	1.90894
$15$	−604.273	−0.693433
$16$	−1249.43	−1.22014
$17$	−661.004	−0.554731	−0.277365	−	0.960765i	$-0.589461\pi$
$17$	−661.004	−0.554731	−0.277365	+	0.960765i	$0.589461\pi$
$18$	2223.80	1.61776
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	261.765	0.146331
$21$	−5192.32	−2.56929
$22$	−788.551	−0.347354
$23$	−4684.99	−1.84667	−0.923335	−	0.383995i	$-0.874548\pi$
$23$	−4684.99	−1.84667	−0.923335	+	0.383995i	$0.874548\pi$
$24$	3391.32	1.20182
$25$	625.000	0.200000
$26$	1969.40	0.571347
$27$	−2374.37	−0.626816
$28$	2249.26	0.542182
$29$	549.294	0.121286	0.0606429	−	0.998160i	$-0.480685\pi$
$29$	549.294	0.121286	0.0606429	+	0.998160i	$0.480685\pi$
$30$	−3938.01	−0.798866
$31$	5998.56	1.12110	0.560548	−	0.828122i	$-0.310591\pi$
$31$	5998.56	1.12110	0.560548	+	0.828122i	$0.310591\pi$
$32$	−3652.65	−0.630570
$33$	2924.68	0.467513
$34$	−4307.73	−0.639074
$35$	5370.42	0.741034
$36$	3572.91	0.459480
$37$	8540.00	1.02554	0.512771	−	0.858525i	$-0.328619\pi$
$37$	8540.00	1.02554	0.512771	+	0.858525i	$0.328619\pi$
$38$	2352.62	0.264297
$39$	−7304.36	−0.768990
$40$	−3507.65	−0.346630
$41$	−12184.3	−1.13199	−0.565994	−	0.824410i	$-0.691507\pi$
$41$	−12184.3	−1.13199	−0.565994	+	0.824410i	$0.691507\pi$
$42$	−33838.1	−2.95994
$43$	−20369.8	−1.68003	−0.840014	−	0.542565i	$-0.817453\pi$
$43$	−20369.8	−1.68003	−0.840014	+	0.542565i	$0.817453\pi$
$44$	−1266.94	−0.0986565
$45$	8530.82	0.628000
$46$	−30531.9	−2.12745
$47$	21132.0	1.39539	0.697695	−	0.716394i	$-0.254209\pi$
$47$	21132.0	1.39539	0.697695	+	0.716394i	$0.254209\pi$
$48$	30199.8	1.89191
$49$	29339.3	1.74566
$50$	4073.09	0.230409
$51$	15977.1	0.860145
$52$	3164.18	0.162275
$53$	−23182.1	−1.13361	−0.566803	−	0.823853i	$-0.691820\pi$
$53$	−23182.1	−1.13361	−0.566803	+	0.823853i	$0.691820\pi$
$54$	−15473.7	−0.722119
$55$	−3025.00	−0.134840
$56$	−30140.1	−1.28432
$57$	−8725.70	−0.355724
$58$	3579.72	0.139727
$59$	−17287.5	−0.646551	−0.323275	−	0.946305i	$-0.604784\pi$
$59$	−17287.5	−0.646551	−0.323275	+	0.946305i	$0.604784\pi$
$60$	−6327.10	−0.226896
$61$	40369.1	1.38907	0.694536	−	0.719458i	$-0.255610\pi$
$61$	40369.1	1.38907	0.694536	+	0.719458i	$0.255610\pi$
$62$	39092.3	1.29155
$63$	73302.6	2.32685
$64$	16177.5	0.493697
$65$	7554.91	0.221792
$66$	19060.0	0.538595
$67$	−38837.5	−1.05697	−0.528487	−	0.848941i	$-0.677240\pi$
$67$	−38837.5	−1.05697	−0.528487	+	0.848941i	$0.677240\pi$
$68$	−6921.12	−0.181511
$69$	113241.	2.86338
$70$	34998.8	0.853704
$71$	−8775.55	−0.206599	−0.103300	−	0.994650i	$-0.532940\pi$
$71$	−8775.55	−0.206599	−0.103300	+	0.994650i	$0.532940\pi$
$72$	−47877.0	−1.08842
$73$	55177.8	1.21187	0.605937	−	0.795512i	$-0.292798\pi$
$73$	55177.8	1.21187	0.605937	+	0.795512i	$0.292798\pi$
$74$	55654.7	1.18147
$75$	−15106.8	−0.310113
$76$	3779.89	0.0750663
$77$	−25992.8	−0.499605
$78$	−47602.1	−0.885911
$79$	−38874.2	−0.700799	−0.350400	−	0.936600i	$-0.613954\pi$
$79$	−38874.2	−0.700799	−0.350400	+	0.936600i	$0.613954\pi$
$80$	−31235.6	−0.545664
$81$	−25528.8	−0.432332
$82$	−79404.6	−1.30410
$83$	108431.	1.72766	0.863832	−	0.503779i	$-0.168057\pi$
$83$	108431.	1.72766	0.863832	+	0.503779i	$0.168057\pi$
$84$	−54366.7	−0.840688
$85$	−16525.1	−0.248083
$86$	−132749.	−1.93547
$87$	−13276.9	−0.188061
$88$	16977.0	0.233698
$89$	101780.	1.36203	0.681013	−	0.732271i	$-0.261540\pi$
$89$	101780.	1.36203	0.681013	+	0.732271i	$0.261540\pi$
$90$	55594.9	0.723484
$91$	64916.9	0.821777
$92$	−49054.7	−0.604243
$93$	−144991.	−1.73833
$94$	137716.	1.60755
$95$	9025.00	0.102598
$96$	88287.9	0.977740
$97$	−54550.6	−0.588668	−0.294334	−	0.955703i	$-0.595098\pi$
$97$	−54550.6	−0.588668	−0.294334	+	0.955703i	$0.595098\pi$
$98$	191203.	2.01108
$99$	−41289.2	−0.423397
$100$	6544.13	0.0654413
$101$	−127596.	−1.24461	−0.622303	−	0.782776i	$-0.713803\pi$
$101$	−127596.	−1.24461	−0.622303	+	0.782776i	$0.713803\pi$
$102$	104122.	0.990926
$103$	109108.	1.01336	0.506680	−	0.862134i	$-0.330873\pi$
$103$	109108.	1.01336	0.506680	+	0.862134i	$0.330873\pi$
$104$	−42399.9	−0.384399
$105$	−129808.	−1.14902
$106$	−151076.	−1.30597
$107$	−164189.	−1.38639	−0.693195	−	0.720750i	$-0.743798\pi$
$107$	−164189.	−1.38639	−0.693195	+	0.720750i	$0.743798\pi$
$108$	−24861.1	−0.205098
$109$	153900.	1.24071	0.620357	−	0.784320i	$-0.286988\pi$
$109$	153900.	1.24071	0.620357	+	0.784320i	$0.286988\pi$
$110$	−19713.8	−0.155342
$111$	−206420.	−1.59017
$112$	−268398.	−2.02178
$113$	1438.98	0.0106013	0.00530063	−	0.999986i	$-0.498313\pi$
$113$	1438.98	0.0106013	0.00530063	+	0.999986i	$0.498313\pi$
$114$	−56864.9	−0.409810
$115$	−117125.	−0.825856
$116$	5751.44	0.0396855
$117$	103119.	0.696427
$118$	−112662.	−0.744855
$119$	−141995.	−0.919190
$120$	84783.0	0.537472
$121$	14641.0	0.0909091
$122$	263083.	1.60027
$123$	294506.	1.75522
$124$	62808.5	0.366830
$125$	15625.0	0.0894427
$126$	477709.	2.68063
$127$	−119172.	−0.655641	−0.327821	−	0.944740i	$-0.606314\pi$
$127$	−119172.	−0.655641	−0.327821	+	0.944740i	$0.606314\pi$
$128$	222313.	1.19933
$129$	492358.	2.60499
$130$	49234.9	0.255514
$131$	−182751.	−0.930424	−0.465212	−	0.885199i	$-0.654022\pi$
$131$	−182751.	−0.930424	−0.465212	+	0.885199i	$0.654022\pi$
$132$	30623.2	0.152973
$133$	77548.9	0.380143
$134$	−253102.	−1.21768
$135$	−59359.4	−0.280320
$136$	92742.8	0.429965
$137$	−431980.	−1.96636	−0.983178	−	0.182652i	$-0.941532\pi$
$137$	−431980.	−1.96636	−0.983178	+	0.182652i	$0.941532\pi$
$138$	737983.	3.29874
$139$	−288819.	−1.26791	−0.633956	−	0.773369i	$-0.718570\pi$
$139$	−288819.	−1.26791	−0.633956	+	0.773369i	$0.718570\pi$
$140$	56231.6	0.242471
$141$	−510780.	−2.16364
$142$	−57189.8	−0.238011
$143$	−36565.8	−0.149532
$144$	−426345.	−1.71338
$145$	13732.4	0.0542407
$146$	359591.	1.39613
$147$	−709157.	−2.70676
$148$	89419.0	0.335564
$149$	−282709.	−1.04322	−0.521608	−	0.853185i	$-0.674668\pi$
$149$	−282709.	−1.04322	−0.521608	+	0.853185i	$0.674668\pi$
$150$	−98450.3	−0.357264
$151$	−286861.	−1.02383	−0.511916	−	0.859035i	$-0.671064\pi$
$151$	−286861.	−1.02383	−0.511916	+	0.859035i	$0.671064\pi$
$152$	−50650.4	−0.177817
$153$	−225556.	−0.778980
$154$	−169394.	−0.575567
$155$	149964.	0.501369
$156$	−76481.1	−0.251619
$157$	−283234.	−0.917057	−0.458529	−	0.888680i	$-0.651623\pi$
$157$	−283234.	−0.917057	−0.458529	+	0.888680i	$0.651623\pi$
$158$	−253341.	−0.807352
$159$	560332.	1.75773
$160$	−91316.3	−0.282000
$161$	−1.00642e6	−3.05994
$162$	−166370.	−0.498066
$163$	−160492.	−0.473135	−0.236567	−	0.971615i	$-0.576022\pi$
$163$	−160492.	−0.473135	−0.236567	+	0.971615i	$0.576022\pi$
$164$	−127577.	−0.370394
$165$	73117.0	0.209078
$166$	706641.	1.99035
$167$	101485.	0.281586	0.140793	−	0.990039i	$-0.455035\pi$
$167$	101485.	0.281586	0.140793	+	0.990039i	$0.455035\pi$
$168$	728513.	1.99143
$169$	−279970.	−0.754042
$170$	−107693.	−0.285803
$171$	123185.	0.322157
$172$	−213285.	−0.549716
$173$	−702616.	−1.78485	−0.892427	−	0.451192i	$-0.850999\pi$
$173$	−702616.	−1.78485	−0.892427	+	0.451192i	$0.850999\pi$
$174$	−86525.1	−0.216655
$175$	134261.	0.331401
$176$	151181.	0.367887
$177$	417855.	1.00252
$178$	663292.	1.56911
$179$	−63227.7	−0.147494	−0.0737471	−	0.997277i	$-0.523496\pi$
$179$	−63227.7	−0.147494	−0.0737471	+	0.997277i	$0.523496\pi$
$180$	89322.9	0.205486
$181$	−66153.6	−0.150092	−0.0750459	−	0.997180i	$-0.523910\pi$
$181$	−66153.6	−0.150092	−0.0750459	+	0.997180i	$0.523910\pi$
$182$	423060.	0.946724
$183$	−975758.	−2.15385
$184$	657332.	1.43133
$185$	213500.	0.458636
$186$	−944896.	−2.00263
$187$	79981.5	0.167258
$188$	221265.	0.456581
$189$	−510056.	−1.03864
$190$	58815.5	0.118197
$191$	112015.	0.222175	0.111087	−	0.993811i	$-0.464567\pi$
$191$	112015.	0.222175	0.111087	+	0.993811i	$0.464567\pi$
$192$	−391024.	−0.765510
$193$	−426460.	−0.824110	−0.412055	−	0.911159i	$-0.635189\pi$
$193$	−426460.	−0.824110	−0.412055	+	0.911159i	$0.635189\pi$
$194$	−355504.	−0.678172
$195$	−182609.	−0.343903
$196$	307200.	0.571191
$197$	621028.	1.14011	0.570053	−	0.821608i	$-0.306923\pi$
$197$	621028.	1.14011	0.570053	+	0.821608i	$0.306923\pi$
$198$	−269079.	−0.487773
$199$	122686.	0.219615	0.109807	−	0.993953i	$-0.464977\pi$
$199$	122686.	0.219615	0.109807	+	0.993953i	$0.464977\pi$
$200$	−87691.2	−0.155018
$201$	938737.	1.63891
$202$	−831534.	−1.43384
$203$	117998.	0.200971
$204$	167290.	0.281445
$205$	−304608.	−0.506240
$206$	711052.	1.16744
$207$	−1.59867e6	−2.59319
$208$	−377572.	−0.605120
$209$	−43681.0	−0.0691714
$210$	−845952.	−1.32372
$211$	24776.3	0.0383117	0.0191558	−	0.999817i	$-0.493902\pi$
$211$	24776.3	0.0383117	0.0191558	+	0.999817i	$0.493902\pi$
$212$	−242730.	−0.370923
$213$	212113.	0.320345
$214$	−1.07001e6	−1.59718
$215$	−509246.	−0.751331
$216$	333139.	0.485837
$217$	1.28859e6	1.85766
$218$	1.00296e6	1.42936
$219$	−1.33370e6	−1.87909
$220$	−31673.6	−0.0441205
$221$	−199753.	−0.275114
$222$	−1.34523e6	−1.83195
$223$	−167715.	−0.225845	−0.112922	−	0.993604i	$-0.536021\pi$
$223$	−167715.	−0.225845	−0.112922	+	0.993604i	$0.536021\pi$
$224$	−784652.	−1.04486
$225$	213270.	0.280850
$226$	9377.73	0.0122131
$227$	−956890.	−1.23253	−0.616265	−	0.787539i	$-0.711355\pi$
$227$	−956890.	−1.23253	−0.616265	+	0.787539i	$0.711355\pi$
$228$	−91363.4	−0.116395
$229$	−830618.	−1.04668	−0.523338	−	0.852125i	$-0.675314\pi$
$229$	−830618.	−1.04668	−0.523338	+	0.852125i	$0.675314\pi$
$230$	−763296.	−0.951423
$231$	628271.	0.774670
$232$	−77069.2	−0.0940072
$233$	−763451.	−0.921280	−0.460640	−	0.887587i	$-0.652380\pi$
$233$	−763451.	−0.921280	−0.460640	+	0.887587i	$0.652380\pi$
$234$	672023.	0.802314
$235$	528300.	0.624038
$236$	−181011.	−0.211556
$237$	939625.	1.08663
$238$	−925373.	−1.05895
$239$	1.38761e6	1.57135	0.785674	−	0.618640i	$-0.212316\pi$
$239$	1.38761e6	1.57135	0.785674	+	0.618640i	$0.212316\pi$
$240$	754994.	0.846088
$241$	−524726.	−0.581956	−0.290978	−	0.956730i	$-0.593981\pi$
$241$	−524726.	−0.581956	−0.290978	+	0.956730i	$0.593981\pi$
$242$	95414.6	0.104731
$243$	1.19403e6	1.29717
$244$	422689.	0.454513
$245$	733482.	0.780683
$246$	1.91928e6	2.02209
$247$	109093.	0.113777
$248$	−841633.	−0.868947
$249$	−2.62088e6	−2.67886
$250$	101827.	0.103042
$251$	−691490.	−0.692790	−0.346395	−	0.938089i	$-0.612594\pi$
$251$	−691490.	−0.692790	−0.346395	+	0.938089i	$0.612594\pi$
$252$	767522.	0.761359
$253$	566884.	0.556792
$254$	−776640.	−0.755328
$255$	399427.	0.384669
$256$	931121.	0.887986
$257$	1.64736e6	1.55581	0.777905	−	0.628382i	$-0.216283\pi$
$257$	1.64736e6	1.55581	0.777905	+	0.628382i	$0.216283\pi$
$258$	3.20867e6	3.00107
$259$	1.83454e6	1.69933
$260$	79104.5	0.0725718
$261$	187437.	0.170316
$262$	−1.19098e6	−1.07189
$263$	−249203.	−0.222159	−0.111079	−	0.993812i	$-0.535431\pi$
$263$	−249203.	−0.222159	−0.111079	+	0.993812i	$0.535431\pi$
$264$	−410350.	−0.362364
$265$	−579552.	−0.506964
$266$	505382.	0.437941
$267$	−2.46010e6	−2.11191
$268$	−406652.	−0.345849
$269$	−1.81321e6	−1.52780	−0.763900	−	0.645335i	$-0.776718\pi$
$269$	−1.81321e6	−1.52780	−0.763900	+	0.645335i	$0.776718\pi$
$270$	−386842.	−0.322942
$271$	70842.1	0.0585960	0.0292980	−	0.999571i	$-0.490673\pi$
$271$	70842.1	0.0585960	0.0292980	+	0.999571i	$0.490673\pi$
$272$	825876.	0.676850
$273$	−1.56910e6	−1.27422
$274$	−2.81519e6	−2.26533
$275$	−75625.0	−0.0603023
$276$	1.18570e6	0.936917
$277$	−774832.	−0.606747	−0.303374	−	0.952872i	$-0.598113\pi$
$277$	−774832.	−0.606747	−0.303374	+	0.952872i	$0.598113\pi$
$278$	−1.88222e6	−1.46069
$279$	2.04690e6	1.57430
$280$	−753502.	−0.574367
$281$	−1.00745e6	−0.761127	−0.380564	−	0.924755i	$-0.624270\pi$
$281$	−1.00745e6	−0.761127	−0.380564	+	0.924755i	$0.624270\pi$
$282$	−3.32872e6	−2.49261
$283$	1.92188e6	1.42646	0.713232	−	0.700928i	$-0.247230\pi$
$283$	1.92188e6	1.42646	0.713232	+	0.700928i	$0.247230\pi$
$284$	−91885.3	−0.0676006
$285$	−218142.	−0.159085
$286$	−238297.	−0.172268
$287$	−2.61740e6	−1.87571
$288$	−1.24640e6	−0.885478
$289$	−982930.	−0.692274
$290$	89493.0	0.0624877
$291$	1.31854e6	0.912768
$292$	577746.	0.396533
$293$	2.59359e6	1.76495	0.882476	−	0.470357i	$-0.155875\pi$
$293$	2.59359e6	1.76495	0.882476	+	0.470357i	$0.155875\pi$
$294$	−4.62154e6	−3.11830
$295$	−432188.	−0.289146
$296$	−1.19821e6	−0.794886
$297$	287299.	0.188992
$298$	−1.84240e6	−1.20183
$299$	−1.41579e6	−0.915841
$300$	−158178.	−0.101471
$301$	−4.37579e6	−2.78381
$302$	−1.86946e6	−1.17950
$303$	3.08410e6	1.92984
$304$	−451043.	−0.279920
$305$	1.00923e6	0.621212
$306$	−1.46994e6	−0.897420
$307$	1.01662e6	0.615617	0.307809	−	0.951448i	$-0.400404\pi$
$307$	1.01662e6	0.615617	0.307809	+	0.951448i	$0.400404\pi$
$308$	−272161.	−0.163474
$309$	−2.63724e6	−1.57128
$310$	977307.	0.577599
$311$	−771876.	−0.452529	−0.226265	−	0.974066i	$-0.572651\pi$
$311$	−771876.	−0.452529	−0.226265	+	0.974066i	$0.572651\pi$
$312$	1.02485e6	0.596035
$313$	681850.	0.393394	0.196697	−	0.980464i	$-0.436978\pi$
$313$	681850.	0.393394	0.196697	+	0.980464i	$0.436978\pi$
$314$	−1.84582e6	−1.05649
$315$	1.83256e6	1.04060
$316$	−407036.	−0.229306
$317$	−1.20058e6	−0.671031	−0.335516	−	0.942035i	$-0.608911\pi$
$317$	−1.20058e6	−0.671031	−0.335516	+	0.942035i	$0.608911\pi$
$318$	3.65165e6	2.02498
$319$	−66464.6	−0.0365690
$320$	404437.	0.220788
$321$	3.96861e6	2.14969
$322$	−6.55876e6	−3.52519
$323$	−238623.	−0.127264
$324$	−267302.	−0.141462
$325$	188873.	0.0991884
$326$	−1.04592e6	−0.545072
$327$	−3.71990e6	−1.92381
$328$	1.70953e6	0.877390
$329$	4.53951e6	2.31217
$330$	476500.	0.240867
$331$	1.40682e6	0.705781	0.352890	−	0.935665i	$-0.385199\pi$
$331$	1.40682e6	0.705781	0.352890	+	0.935665i	$0.385199\pi$
$332$	1.13534e6	0.565303
$333$	2.91413e6	1.44012
$334$	661373.	0.324400
$335$	−970937.	−0.472693
$336$	6.48742e6	3.13490
$337$	1.42011e6	0.681157	0.340578	−	0.940216i	$-0.389377\pi$
$337$	1.42011e6	0.681157	0.340578	+	0.940216i	$0.389377\pi$
$338$	−1.82455e6	−0.868689
$339$	−34781.4	−0.0164379
$340$	−173028.	−0.0811744
$341$	−725825.	−0.338023
$342$	802790.	0.371139
$343$	2.69215e6	1.23556
$344$	2.85801e6	1.30217
$345$	2.83101e6	1.28054
$346$	−4.57891e6	−2.05623
$347$	−479562.	−0.213807	−0.106903	−	0.994269i	$-0.534094\pi$
$347$	−479562.	−0.213807	−0.106903	+	0.994269i	$0.534094\pi$
$348$	−139018.	−0.0615349
$349$	31808.8	0.0139792	0.00698961	−	0.999976i	$-0.497775\pi$
$349$	31808.8	0.0139792	0.00698961	+	0.999976i	$0.497775\pi$
$350$	874969.	0.381788
$351$	−717527.	−0.310864
$352$	441971.	0.190124
$353$	−3.62249e6	−1.54729	−0.773643	−	0.633622i	$-0.781567\pi$
$353$	−3.62249e6	−1.54729	−0.773643	+	0.633622i	$0.781567\pi$
$354$	2.72314e6	1.15495
$355$	−219389.	−0.0923939
$356$	1.06569e6	0.445664
$357$	3.43215e6	1.42526
$358$	−412052.	−0.169920
$359$	−2.79419e6	−1.14425	−0.572123	−	0.820168i	$-0.693880\pi$
$359$	−2.79419e6	−1.14425	−0.572123	+	0.820168i	$0.693880\pi$
$360$	−1.19692e6	−0.486755
$361$	130321.	0.0526316
$362$	−431119.	−0.172912
$363$	−353886.	−0.140960
$364$	679719.	0.268891
$365$	1.37945e6	0.541967
$366$	−6.35897e6	−2.48133
$367$	−1.61569e6	−0.626170	−0.313085	−	0.949725i	$-0.601362\pi$
$367$	−1.61569e6	−0.626170	−0.313085	+	0.949725i	$0.601362\pi$
$368$	5.85355e6	2.25320
$369$	−4.15769e6	−1.58959
$370$	1.39137e6	0.528370
$371$	−4.97990e6	−1.87839
$372$	−1.51814e6	−0.568793
$373$	827056.	0.307796	0.153898	−	0.988087i	$-0.450817\pi$
$373$	827056.	0.307796	0.153898	+	0.988087i	$0.450817\pi$
$374$	521236.	0.192688
$375$	−377670.	−0.138687
$376$	−2.96494e6	−1.08155
$377$	165995.	0.0601507
$378$	−3.32401e6	−1.19655
$379$	−4.84208e6	−1.73155	−0.865773	−	0.500437i	$-0.833173\pi$
$379$	−4.84208e6	−1.73155	−0.865773	+	0.500437i	$0.833173\pi$
$380$	94497.2	0.0335707
$381$	2.88051e6	1.01661
$382$	729999.	0.255955
$383$	−3.62773e6	−1.26368	−0.631841	−	0.775098i	$-0.717701\pi$
$383$	−3.62773e6	−1.26368	−0.631841	+	0.775098i	$0.717701\pi$
$384$	−5.37350e6	−1.85964
$385$	−649821.	−0.223430
$386$	−2.77922e6	−0.949411
$387$	−6.95086e6	−2.35918
$388$	−571178.	−0.192616
$389$	−762213.	−0.255389	−0.127695	−	0.991814i	$-0.540758\pi$
$389$	−762213.	−0.255389	−0.127695	+	0.991814i	$0.540758\pi$
$390$	−1.19005e6	−0.396191
$391$	3.09680e6	1.02440
$392$	−4.11648e6	−1.35304
$393$	4.41725e6	1.44268
$394$	4.04720e6	1.31345
$395$	−971855.	−0.313407
$396$	−432323.	−0.138538
$397$	4.50344e6	1.43406	0.717032	−	0.697040i	$-0.245500\pi$
$397$	4.50344e6	1.43406	0.717032	+	0.697040i	$0.245500\pi$
$398$	799537.	0.253006
$399$	−1.87443e6	−0.589436
$400$	−780891.	−0.244028
$401$	−3.65360e6	−1.13465	−0.567323	−	0.823495i	$-0.692021\pi$
$401$	−3.65360e6	−1.13465	−0.567323	+	0.823495i	$0.692021\pi$
$402$	6.11770e6	1.88809
$403$	1.81274e6	0.555998
$404$	−1.33600e6	−0.407243
$405$	−638219.	−0.193345
$406$	768985.	0.231528
$407$	−1.03334e6	−0.309213
$408$	−2.24168e6	−0.666688
$409$	2.62096e6	0.774732	0.387366	−	0.921926i	$-0.373385\pi$
$409$	2.62096e6	0.774732	0.387366	+	0.921926i	$0.373385\pi$
$410$	−1.98511e6	−0.583211
$411$	1.04413e7	3.04896
$412$	1.14243e6	0.331578
$413$	−3.71365e6	−1.07134
$414$	−1.04185e7	−2.98747
$415$	2.71078e6	0.772635
$416$	−1.10382e6	−0.312726
$417$	6.98103e6	1.96598
$418$	−284667.	−0.0796886
$419$	2.23537e6	0.622035	0.311018	−	0.950404i	$-0.399330\pi$
$419$	2.23537e6	0.622035	0.311018	+	0.950404i	$0.399330\pi$
$420$	−1.35917e6	−0.375967
$421$	2.85745e6	0.785730	0.392865	−	0.919596i	$-0.371484\pi$
$421$	2.85745e6	0.785730	0.392865	+	0.919596i	$0.371484\pi$
$422$	161466.	0.0441367
$423$	7.21093e6	1.95948
$424$	3.25258e6	0.878645
$425$	−413128.	−0.110946
$426$	1.38233e6	0.369052
$427$	8.67197e6	2.30170
$428$	−1.71916e6	−0.453636
$429$	883828.	0.231859
$430$	−3.31873e6	−0.865567
$431$	−3.10728e6	−0.805725	−0.402862	−	0.915261i	$-0.631985\pi$
$431$	−3.10728e6	−0.805725	−0.402862	+	0.915261i	$0.631985\pi$
$432$	2.96660e6	0.764804
$433$	−1.57614e6	−0.403993	−0.201997	−	0.979386i	$-0.564743\pi$
$433$	−1.57614e6	−0.403993	−0.201997	+	0.979386i	$0.564743\pi$
$434$	8.39768e6	2.14010
$435$	−331923.	−0.0841036
$436$	1.61142e6	0.405970
$437$	−1.69128e6	−0.423655
$438$	−8.69164e6	−2.16479
$439$	6.46363e6	1.60072	0.800360	−	0.599519i	$-0.204642\pi$
$439$	6.46363e6	1.60072	0.800360	+	0.599519i	$0.204642\pi$
$440$	424425.	0.104513
$441$	1.00115e7	2.45134
$442$	−1.30178e6	−0.316944
$443$	−887681.	−0.214905	−0.107453	−	0.994210i	$-0.534269\pi$
$443$	−887681.	−0.214905	−0.107453	+	0.994210i	$0.534269\pi$
$444$	−2.16134e6	−0.520314
$445$	2.54449e6	0.609117
$446$	−1.09299e6	−0.260183
$447$	6.83334e6	1.61757
$448$	3.47520e6	0.818058
$449$	−1.66511e6	−0.389786	−0.194893	−	0.980825i	$-0.562436\pi$
$449$	−1.66511e6	−0.389786	−0.194893	+	0.980825i	$0.562436\pi$
$450$	1.38987e6	0.323552
$451$	1.47430e6	0.341307
$452$	15067.0	0.00346880
$453$	6.93369e6	1.58752
$454$	−6.23600e6	−1.41993
$455$	1.62292e6	0.367510
$456$	1.22427e6	0.275717
$457$	5.09752e6	1.14174	0.570872	−	0.821039i	$-0.306605\pi$
$457$	5.09752e6	1.14174	0.570872	+	0.821039i	$0.306605\pi$
$458$	−5.41309e6	−1.20582
$459$	1.56947e6	0.347714
$460$	−1.22637e6	−0.270225
$461$	4.85665e6	1.06435	0.532175	−	0.846634i	$-0.321375\pi$
$461$	4.85665e6	1.06435	0.532175	+	0.846634i	$0.321375\pi$
$462$	4.09441e6	0.892454
$463$	−6.29508e6	−1.36474	−0.682368	−	0.731009i	$-0.739050\pi$
$463$	−6.29508e6	−1.36474	−0.682368	+	0.731009i	$0.739050\pi$
$464$	−686302.	−0.147986
$465$	−3.62476e6	−0.777405
$466$	−4.97537e6	−1.06136
$467$	−6.21123e6	−1.31791	−0.658954	−	0.752183i	$-0.729001\pi$
$467$	−6.21123e6	−1.31791	−0.658954	+	0.752183i	$0.729001\pi$
$468$	1.07972e6	0.227875
$469$	−8.34295e6	−1.75141
$470$	3.44290e6	0.718919
$471$	6.84603e6	1.42196
$472$	2.42554e6	0.501134
$473$	2.46475e6	0.506548
$474$	6.12348e6	1.25185
$475$	225625.	0.0458831
$476$	−1.48677e6	−0.300765
$477$	−7.91048e6	−1.59187
$478$	9.04298e6	1.81026
$479$	240850.	0.0479633	0.0239816	−	0.999712i	$-0.492366\pi$
$479$	240850.	0.0479633	0.0239816	+	0.999712i	$0.492366\pi$
$480$	2.20720e6	0.437259
$481$	2.58076e6	0.508609
$482$	−3.41961e6	−0.670439
$483$	2.43260e7	4.74463
$484$	153300.	0.0297460
$485$	−1.36377e6	−0.263260
$486$	7.78141e6	1.49440
$487$	7.20253e6	1.37614	0.688070	−	0.725644i	$-0.258458\pi$
$487$	7.20253e6	1.37614	0.688070	+	0.725644i	$0.258458\pi$
$488$	−5.66403e6	−1.07665
$489$	3.87924e6	0.733626
$490$	4.78007e6	0.899381
$491$	−5.07826e6	−0.950630	−0.475315	−	0.879816i	$-0.657666\pi$
$491$	−5.07826e6	−0.950630	−0.475315	+	0.879816i	$0.657666\pi$
$492$	3.08366e6	0.574319
$493$	−363086.	−0.0672809
$494$	710953.	0.131076
$495$	−1.03223e6	−0.189349
$496$	−7.49475e6	−1.36790
$497$	−1.88514e6	−0.342335
$498$	−1.70802e7	−3.08616
$499$	7.92876e6	1.42546	0.712728	−	0.701440i	$-0.247459\pi$
$499$	7.92876e6	1.42546	0.712728	+	0.701440i	$0.247459\pi$
$500$	163603.	0.0292662
$501$	−2.45299e6	−0.436617
$502$	−4.50641e6	−0.798125
$503$	−1.02023e7	−1.79795	−0.898976	−	0.437997i	$-0.855688\pi$
$503$	−1.02023e7	−1.79795	−0.898976	+	0.437997i	$0.855688\pi$
$504$	−1.02848e7	−1.80351
$505$	−3.18989e6	−0.556605
$506$	3.69435e6	0.641449
$507$	6.76714e6	1.16919
$508$	−1.24781e6	−0.214530
$509$	6.91870e6	1.18367	0.591834	−	0.806060i	$-0.298404\pi$
$509$	6.91870e6	1.18367	0.591834	+	0.806060i	$0.298404\pi$
$510$	2.60304e6	0.443155
$511$	1.18531e7	2.00808
$512$	−1.04594e6	−0.176332
$513$	−857149.	−0.143801
$514$	1.07358e7	1.79236
$515$	2.72770e6	0.453188
$516$	5.15528e6	0.852370
$517$	−2.55697e6	−0.420726
$518$	1.19556e7	1.95770
$519$	1.69829e7	2.76753
$520$	−1.06000e6	−0.171908
$521$	9.74762e6	1.57327	0.786637	−	0.617416i	$-0.211820\pi$
$521$	9.74762e6	1.57327	0.786637	+	0.617416i	$0.211820\pi$
$522$	1.22152e6	0.196211
$523$	2.17132e6	0.347111	0.173556	−	0.984824i	$-0.444474\pi$
$523$	2.17132e6	0.347111	0.173556	+	0.984824i	$0.444474\pi$
$524$	−1.91351e6	−0.304441
$525$	−3.24520e6	−0.513858
$526$	−1.62404e6	−0.255937
$527$	−3.96507e6	−0.621906
$528$	−3.65417e6	−0.570432
$529$	1.55128e7	2.41019
$530$	−3.77691e6	−0.584046
$531$	−5.89907e6	−0.907919
$532$	811984.	0.124385
$533$	−3.68206e6	−0.561400
$534$	−1.60324e7	−2.43301
$535$	−4.10473e6	−0.620013
$536$	5.44913e6	0.819248
$537$	1.52827e6	0.228699
$538$	−1.18166e7	−1.76009
$539$	−3.55005e6	−0.526336
$540$	−621529.	−0.0917227
$541$	−335601.	−0.0492980	−0.0246490	−	0.999696i	$-0.507847\pi$
$541$	−335601.	−0.0492980	−0.0246490	+	0.999696i	$0.507847\pi$
$542$	461674.	0.0675052
$543$	1.59899e6	0.232727
$544$	2.41442e6	0.349797
$545$	3.84749e6	0.554864
$546$	−1.02257e7	−1.46796
$547$	4.09434e6	0.585081	0.292540	−	0.956253i	$-0.405499\pi$
$547$	4.09434e6	0.585081	0.292540	+	0.956253i	$0.405499\pi$
$548$	−4.52309e6	−0.643404
$549$	1.37753e7	1.95060
$550$	−492844.	−0.0694709
$551$	198295.	0.0278249
$552$	−1.58883e7	−2.21937
$553$	−8.35083e6	−1.16123
$554$	−5.04954e6	−0.699000
$555$	−5.16049e6	−0.711145
$556$	−3.02411e6	−0.414869
$557$	−9.76827e6	−1.33407	−0.667037	−	0.745025i	$-0.732438\pi$
$557$	−9.76827e6	−1.33407	−0.667037	+	0.745025i	$0.732438\pi$
$558$	1.33396e7	1.81366
$559$	−6.15569e6	−0.833197
$560$	−6.70994e6	−0.904167
$561$	−1.93323e6	−0.259344
$562$	−6.56549e6	−0.876852
$563$	−9.23766e6	−1.22826	−0.614131	−	0.789204i	$-0.710493\pi$
$563$	−9.23766e6	−1.22826	−0.614131	+	0.789204i	$0.710493\pi$
$564$	−5.34817e6	−0.707958
$565$	35974.4	0.00474103
$566$	1.25248e7	1.64335
$567$	−5.48401e6	−0.716375
$568$	1.23126e6	0.160133
$569$	4.46257e6	0.577836	0.288918	−	0.957354i	$-0.406705\pi$
$569$	4.46257e6	0.577836	0.288918	+	0.957354i	$0.406705\pi$
$570$	−1.42162e6	−0.183272
$571$	−6.60686e6	−0.848017	−0.424009	−	0.905658i	$-0.639377\pi$
$571$	−6.60686e6	−0.848017	−0.424009	+	0.905658i	$0.639377\pi$
$572$	−382866.	−0.0489279
$573$	−2.70752e6	−0.344496
$574$	−1.70574e7	−2.16090
$575$	−2.92812e6	−0.369334
$576$	5.52028e6	0.693275
$577$	−1.30945e7	−1.63738	−0.818690	−	0.574236i	$-0.805299\pi$
$577$	−1.30945e7	−1.63738	−0.818690	+	0.574236i	$0.805299\pi$
$578$	−6.40570e6	−0.797530
$579$	1.03079e7	1.27784
$580$	143786.	0.0177479
$581$	2.32929e7	2.86275
$582$	8.59284e6	1.05155
$583$	2.80503e6	0.341795
$584$	−7.74178e6	−0.939309
$585$	2.57798e6	0.311451
$586$	1.69023e7	2.03330
$587$	−6.85978e6	−0.821703	−0.410851	−	0.911702i	$-0.634769\pi$
$587$	−6.85978e6	−0.821703	−0.410851	+	0.911702i	$0.634769\pi$
$588$	−7.42531e6	−0.885668
$589$	2.16548e6	0.257197
$590$	−2.81655e6	−0.333109
$591$	−1.50108e7	−1.76781
$592$	−1.06701e7	−1.25131
$593$	−175684.	−0.0205161	−0.0102580	−	0.999947i	$-0.503265\pi$
$593$	−175684.	−0.0205161	−0.0102580	+	0.999947i	$0.503265\pi$
$594$	1.87231e6	0.217727
$595$	−3.54987e6	−0.411074
$596$	−2.96014e6	−0.341347
$597$	−2.96543e6	−0.340527
$598$	−9.22662e6	−1.05509
$599$	1.35935e6	0.154797	0.0773987	−	0.997000i	$-0.475339\pi$
$599$	1.35935e6	0.154797	0.0773987	+	0.997000i	$0.475339\pi$
$600$	2.11958e6	0.240365
$601$	993650.	0.112214	0.0561070	−	0.998425i	$-0.482131\pi$
$601$	993650.	0.112214	0.0561070	+	0.998425i	$0.482131\pi$
$602$	−2.85168e7	−3.20708
$603$	−1.32526e7	−1.48426
$604$	−3.00361e6	−0.335005
$605$	366025.	0.0406558
$606$	2.00989e7	2.22326
$607$	−9.94585e6	−1.09565	−0.547823	−	0.836594i	$-0.684543\pi$
$607$	−9.94585e6	−1.09565	−0.547823	+	0.836594i	$0.684543\pi$
$608$	−1.31861e6	−0.144663
$609$	−2.85211e6	−0.311618
$610$	6.57709e6	0.715664
$611$	6.38601e6	0.692033
$612$	−2.36171e6	−0.254887
$613$	−1.96658e6	−0.211378	−0.105689	−	0.994399i	$-0.533705\pi$
$613$	−1.96658e6	−0.211378	−0.105689	+	0.994399i	$0.533705\pi$
$614$	6.62523e6	0.709219
$615$	7.36265e6	0.784958
$616$	3.64695e6	0.387238
$617$	1.08627e7	1.14875	0.574373	−	0.818594i	$-0.305246\pi$
$617$	1.08627e7	1.14875	0.574373	+	0.818594i	$0.305246\pi$
$618$	−1.71868e7	−1.81018
$619$	−1.58165e7	−1.65914	−0.829569	−	0.558404i	$-0.811414\pi$
$619$	−1.58165e7	−1.65914	−0.829569	+	0.558404i	$0.811414\pi$
$620$	1.57021e6	0.164051
$621$	1.11239e7	1.15752
$622$	−5.03028e6	−0.521334
$623$	2.18640e7	2.25688
$624$	9.12626e6	0.938277
$625$	390625.	0.0400000
$626$	4.44358e6	0.453208
$627$	1.05581e6	0.107255
$628$	−2.96563e6	−0.300067
$629$	−5.64498e6	−0.568900
$630$	1.19427e7	1.19881
$631$	−8.12151e6	−0.812014	−0.406007	−	0.913870i	$-0.633079\pi$
$631$	−8.12151e6	−0.812014	−0.406007	+	0.913870i	$0.633079\pi$
$632$	5.45428e6	0.543181
$633$	−598867.	−0.0594047
$634$	−7.82411e6	−0.773058
$635$	−2.97931e6	−0.293212
$636$	5.86701e6	0.575141
$637$	8.86623e6	0.865746
$638$	−433146.	−0.0421292
$639$	−2.99451e6	−0.290117
$640$	5.55782e6	0.536357
$641$	−1.40848e7	−1.35395	−0.676977	−	0.736004i	$-0.736711\pi$
$641$	−1.40848e7	−1.35395	−0.676977	+	0.736004i	$0.736711\pi$
$642$	2.58632e7	2.47654
$643$	−1.31330e7	−1.25267	−0.626337	−	0.779552i	$-0.715447\pi$
$643$	−1.31330e7	−1.25267	−0.626337	+	0.779552i	$0.715447\pi$
$644$	−1.05378e7	−1.00123
$645$	1.23089e7	1.16499
$646$	−1.55509e6	−0.146614
$647$	−1.43612e7	−1.34875	−0.674373	−	0.738391i	$-0.735586\pi$
$647$	−1.43612e7	−1.34875	−0.674373	+	0.738391i	$0.735586\pi$
$648$	3.58184e6	0.335095
$649$	2.09179e6	0.194942
$650$	1.23087e6	0.114269
$651$	−3.11464e7	−2.88042
$652$	−1.68045e6	−0.154813
$653$	−486043.	−0.0446058	−0.0223029	−	0.999751i	$-0.507100\pi$
$653$	−486043.	−0.0446058	−0.0223029	+	0.999751i	$0.507100\pi$
$654$	−2.42424e7	−2.21631
$655$	−4.56877e6	−0.416098
$656$	1.52234e7	1.38119
$657$	1.88285e7	1.70177
$658$	2.95837e7	2.66372
$659$	2.07163e6	0.185823	0.0929115	−	0.995674i	$-0.470383\pi$
$659$	2.07163e6	0.185823	0.0929115	+	0.995674i	$0.470383\pi$
$660$	765579.	0.0684117
$661$	−913570.	−0.0813277	−0.0406638	−	0.999173i	$-0.512947\pi$
$661$	−913570.	−0.0813277	−0.0406638	+	0.999173i	$0.512947\pi$
$662$	9.16820e6	0.813091
$663$	4.82821e6	0.426582
$664$	−1.52136e7	−1.33909
$665$	1.93872e6	0.170005
$666$	1.89912e7	1.65908
$667$	−2.57344e6	−0.223975
$668$	1.06261e6	0.0921368
$669$	4.05383e6	0.350187
$670$	−6.32755e6	−0.544563
$671$	−4.88466e6	−0.418821
$672$	1.89657e7	1.62012
$673$	−1.41933e7	−1.20794	−0.603971	−	0.797006i	$-0.706416\pi$
$673$	−1.41933e7	−1.20794	−0.603971	+	0.797006i	$0.706416\pi$
$674$	9.25478e6	0.784723
$675$	−1.48398e6	−0.125363
$676$	−2.93146e6	−0.246727
$677$	9.87716e6	0.828248	0.414124	−	0.910221i	$-0.364088\pi$
$677$	9.87716e6	0.828248	0.414124	+	0.910221i	$0.364088\pi$
$678$	−226668.	−0.0189372
$679$	−1.17184e7	−0.975425
$680$	2.31857e6	0.192286
$681$	2.31289e7	1.91112
$682$	−4.73016e6	−0.389417
$683$	−1.75672e7	−1.44096	−0.720478	−	0.693478i	$-0.756078\pi$
$683$	−1.75672e7	−1.44096	−0.720478	+	0.693478i	$0.756078\pi$
$684$	1.28982e6	0.105412
$685$	−1.07995e7	−0.879381
$686$	1.75446e7	1.42342
$687$	2.00768e7	1.62294
$688$	2.54506e7	2.04987
$689$	−7.00554e6	−0.562203
$690$	1.84496e7	1.47524
$691$	5.34842e6	0.426118	0.213059	−	0.977039i	$-0.431657\pi$
$691$	5.34842e6	0.426118	0.213059	+	0.977039i	$0.431657\pi$
$692$	−7.35681e6	−0.584016
$693$	−8.86961e6	−0.701571
$694$	−3.12528e6	−0.246315
$695$	−7.22048e6	−0.567028
$696$	1.86283e6	0.145764
$697$	8.05389e6	0.627948
$698$	207296.	0.0161047
$699$	1.84533e7	1.42850
$700$	1.40579e6	0.108436
$701$	1.79442e7	1.37921	0.689604	−	0.724186i	$-0.257784\pi$
$701$	1.79442e7	1.37921	0.689604	+	0.724186i	$0.257784\pi$
$702$	−4.67609e6	−0.358129
$703$	3.08294e6	0.235276
$704$	−1.95747e6	−0.148855
$705$	−1.27695e7	−0.967611
$706$	−2.36076e7	−1.78254
$707$	−2.74097e7	−2.06232
$708$	4.37520e6	0.328031
$709$	−2.11168e7	−1.57766	−0.788828	−	0.614614i	$-0.789312\pi$
$709$	−2.11168e7	−1.57766	−0.788828	+	0.614614i	$0.789312\pi$
$710$	−1.42975e6	−0.106442
$711$	−1.32652e7	−0.984098
$712$	−1.42803e7	−1.05569
$713$	−2.81032e7	−2.07029
$714$	2.23671e7	1.64197
$715$	−914144.	−0.0668728
$716$	−662032.	−0.0482610
$717$	−3.35398e7	−2.43648
$718$	−1.82096e7	−1.31822
$719$	7.67525e6	0.553695	0.276847	−	0.960914i	$-0.410710\pi$
$719$	7.67525e6	0.553695	0.276847	+	0.960914i	$0.410710\pi$
$720$	−1.06586e7	−0.766249
$721$	2.34383e7	1.67914
$722$	849295.	0.0606339
$723$	1.26831e7	0.902360
$724$	−692668.	−0.0491110
$725$	343309.	0.0242572
$726$	−2.30626e6	−0.162393
$727$	−8.94159e6	−0.627449	−0.313725	−	0.949514i	$-0.601577\pi$
$727$	−8.94159e6	−0.627449	−0.313725	+	0.949514i	$0.601577\pi$
$728$	−9.10822e6	−0.636950
$729$	−2.26572e7	−1.57902
$730$	8.98978e6	0.624370
$731$	1.34646e7	0.931963
$732$	−1.02168e7	−0.704752
$733$	1.77878e7	1.22282	0.611410	−	0.791314i	$-0.290603\pi$
$733$	1.77878e7	1.22282	0.611410	+	0.791314i	$0.290603\pi$
$734$	−1.05293e7	−0.721375
$735$	−1.77289e7	−1.21050
$736$	1.71127e7	1.16446
$737$	4.69934e6	0.318690
$738$	−2.70954e7	−1.83128
$739$	−9.61277e6	−0.647497	−0.323748	−	0.946143i	$-0.604943\pi$
$739$	−9.61277e6	−0.647497	−0.323748	+	0.946143i	$0.604943\pi$
$740$	2.23547e6	0.150069
$741$	−2.63687e6	−0.176418
$742$	−3.24537e7	−2.16399
$743$	2.35655e6	0.156605	0.0783024	−	0.996930i	$-0.475050\pi$
$743$	2.35655e6	0.156605	0.0783024	+	0.996930i	$0.475050\pi$
$744$	2.03430e7	1.34736
$745$	−7.06773e6	−0.466541
$746$	5.38988e6	0.354595
$747$	3.70003e7	2.42607
$748$	837455.	0.0547278
$749$	−3.52706e7	−2.29725
$750$	−2.46126e6	−0.159773
$751$	9.32113e6	0.603071	0.301536	−	0.953455i	$-0.402501\pi$
$751$	9.32113e6	0.603071	0.301536	+	0.953455i	$0.402501\pi$
$752$	−2.64029e7	−1.70258
$753$	1.67139e7	1.07422
$754$	1.08178e6	0.0692963
$755$	−7.17152e6	−0.457872
$756$	−5.34059e6	−0.339848
$757$	1.00722e7	0.638828	0.319414	−	0.947615i	$-0.396514\pi$
$757$	1.00722e7	0.638828	0.319414	+	0.947615i	$0.396514\pi$
$758$	−3.15556e7	−1.99482
$759$	−1.37021e7	−0.863342
$760$	−1.26626e6	−0.0795224
$761$	3.45986e6	0.216570	0.108285	−	0.994120i	$-0.465464\pi$
$761$	3.45986e6	0.216570	0.108285	+	0.994120i	$0.465464\pi$
$762$	1.87721e7	1.17118
$763$	3.30603e7	2.05587
$764$	1.17287e6	0.0726970
$765$	−5.63891e6	−0.348371
$766$	−2.36417e7	−1.45582
$767$	−5.22423e6	−0.320652
$768$	−2.25060e7	−1.37688
$769$	−8.41555e6	−0.513176	−0.256588	−	0.966521i	$-0.582598\pi$
$769$	−8.41555e6	−0.513176	−0.256588	+	0.966521i	$0.582598\pi$
$770$	−4.23485e6	−0.257402
$771$	−3.98182e7	−2.41238
$772$	−4.46530e6	−0.269654
$773$	1.12145e7	0.675044	0.337522	−	0.941318i	$-0.390411\pi$
$773$	1.12145e7	0.675044	0.337522	+	0.941318i	$0.390411\pi$
$774$	−4.52984e7	−2.71788
$775$	3.74910e6	0.224219
$776$	7.65378e6	0.456270
$777$	−4.43424e7	−2.63492
$778$	−4.96730e6	−0.294220
$779$	−4.39854e6	−0.259696
$780$	−1.91203e6	−0.112527
$781$	1.06184e6	0.0622920
$782$	2.01817e7	1.18016
$783$	−1.30423e6	−0.0760238
$784$	−3.66573e7	−2.12995
$785$	−7.08085e6	−0.410121
$786$	2.87870e7	1.66203
$787$	−1.29732e7	−0.746638	−0.373319	−	0.927703i	$-0.621780\pi$
$787$	−1.29732e7	−0.746638	−0.373319	+	0.927703i	$0.621780\pi$
$788$	6.50254e6	0.373050
$789$	6.02345e6	0.344471
$790$	−6.33353e6	−0.361059
$791$	309116.	0.0175663
$792$	5.79311e6	0.328170
$793$	1.21994e7	0.688899
$794$	2.93487e7	1.65211
$795$	1.40083e7	0.786081
$796$	1.28460e6	0.0718594
$797$	1.21651e7	0.678372	0.339186	−	0.940719i	$-0.389848\pi$
$797$	1.21651e7	0.678372	0.339186	+	0.940719i	$0.389848\pi$
$798$	−1.22155e7	−0.679056
$799$	−1.39683e7	−0.774066
$800$	−2.28291e6	−0.126114
$801$	3.47305e7	1.91263
$802$	−2.38103e7	−1.30716
$803$	−6.67652e6	−0.365394
$804$	9.82915e6	0.536261
$805$	−2.51604e7	−1.36845
$806$	1.18135e7	0.640535
$807$	4.38268e7	2.36895
$808$	1.79024e7	0.964680
$809$	2.10851e7	1.13267	0.566336	−	0.824175i	$-0.308361\pi$
$809$	2.10851e7	1.13267	0.566336	+	0.824175i	$0.308361\pi$
$810$	−4.15924e6	−0.222742
$811$	−1.69233e7	−0.903512	−0.451756	−	0.892142i	$-0.649202\pi$
$811$	−1.69233e7	−0.903512	−0.451756	+	0.892142i	$0.649202\pi$
$812$	1.23551e6	0.0657590
$813$	−1.71232e6	−0.0908569
$814$	−6.73422e6	−0.356227
$815$	−4.01230e6	−0.211592
$816$	−1.99622e7	−1.04950
$817$	−7.35351e6	−0.385425
$818$	1.70806e7	0.892526
$819$	2.21518e7	1.15398
$820$	−3.18943e6	−0.165645
$821$	5.42915e6	0.281108	0.140554	−	0.990073i	$-0.455112\pi$
$821$	5.42915e6	0.281108	0.140554	+	0.990073i	$0.455112\pi$
$822$	6.80457e7	3.51254
$823$	−1.67321e7	−0.861096	−0.430548	−	0.902568i	$-0.641680\pi$
$823$	−1.67321e7	−0.861096	−0.430548	+	0.902568i	$0.641680\pi$
$824$	−1.53085e7	−0.785443
$825$	1.82792e6	0.0935026
$826$	−2.42017e7	−1.23423
$827$	1.29643e7	0.659152	0.329576	−	0.944129i	$-0.393094\pi$
$827$	1.29643e7	0.659152	0.329576	+	0.944129i	$0.393094\pi$
$828$	−1.67391e7	−0.848508
$829$	2.90748e7	1.46937	0.734684	−	0.678409i	$-0.237330\pi$
$829$	2.90748e7	1.46937	0.734684	+	0.678409i	$0.237330\pi$
$830$	1.76660e7	0.890110
$831$	1.87284e7	0.940801
$832$	4.88878e6	0.244845
$833$	−1.93934e7	−0.968371
$834$	4.54950e7	2.26490
$835$	2.53713e6	0.125929
$836$	−457367.	−0.0226333
$837$	−1.42428e7	−0.702720
$838$	1.45678e7	0.716612
$839$	1.35562e7	0.664865	0.332432	−	0.943127i	$-0.392131\pi$
$839$	1.35562e7	0.664865	0.332432	+	0.943127i	$0.392131\pi$
$840$	1.82128e7	0.890593
$841$	−2.02094e7	−0.985290
$842$	1.86218e7	0.905196
$843$	2.43510e7	1.18018
$844$	259423.	0.0125358
$845$	−6.99926e6	−0.337218
$846$	4.69932e7	2.25741
$847$	3.14513e6	0.150637
$848$	2.89643e7	1.38316
$849$	−4.64537e7	−2.21183
$850$	−2.69233e6	−0.127815
$851$	−4.00098e7	−1.89384
$852$	2.22095e6	0.104819
$853$	1.70734e7	0.803430	0.401715	−	0.915765i	$-0.368414\pi$
$853$	1.70734e7	0.803430	0.401715	+	0.915765i	$0.368414\pi$
$854$	5.65148e7	2.65166
$855$	3.07963e6	0.144073
$856$	2.30367e7	1.07457
$857$	1.96675e7	0.914739	0.457370	−	0.889277i	$-0.348792\pi$
$857$	1.96675e7	0.914739	0.457370	+	0.889277i	$0.348792\pi$
$858$	5.75986e6	0.267112
$859$	1.82811e7	0.845318	0.422659	−	0.906289i	$-0.361097\pi$
$859$	1.82811e7	0.845318	0.422659	+	0.906289i	$0.361097\pi$
$860$	−5.33212e6	−0.245841
$861$	6.32649e7	2.90840
$862$	−2.02500e7	−0.928231
$863$	−3.16040e7	−1.44449	−0.722245	−	0.691637i	$-0.756890\pi$
$863$	−3.16040e7	−1.44449	−0.722245	+	0.691637i	$0.756890\pi$
$864$	8.67277e6	0.395251
$865$	−1.75654e7	−0.798211
$866$	−1.02716e7	−0.465418
$867$	2.37583e7	1.07342
$868$	1.34923e7	0.607838
$869$	4.70378e6	0.211299
$870$	−2.16313e6	−0.0968911
$871$	−1.17366e7	−0.524198
$872$	−2.15930e7	−0.961662
$873$	−1.86145e7	−0.826637
$874$	−1.10220e7	−0.488070
$875$	3.35651e6	0.148207
$876$	−1.39646e7	−0.614850
$877$	9.74759e6	0.427955	0.213977	−	0.976839i	$-0.431358\pi$
$877$	9.74759e6	0.427955	0.213977	+	0.976839i	$0.431358\pi$
$878$	4.21232e7	1.84410
$879$	−6.26895e7	−2.73667
$880$	3.77951e6	0.164524
$881$	−1.49518e7	−0.649012	−0.324506	−	0.945884i	$-0.605198\pi$
$881$	−1.49518e7	−0.649012	−0.324506	+	0.945884i	$0.605198\pi$
$882$	6.52446e7	2.82406
$883$	2.37609e7	1.02556	0.512779	−	0.858521i	$-0.328616\pi$
$883$	2.37609e7	1.02556	0.512779	+	0.858521i	$0.328616\pi$
$884$	−2.09154e6	−0.0900191
$885$	1.04464e7	0.448340
$886$	−5.78497e6	−0.247581
$887$	1.97782e7	0.844067	0.422033	−	0.906580i	$-0.361316\pi$
$887$	1.97782e7	0.844067	0.422033	+	0.906580i	$0.361316\pi$
$888$	2.89619e7	1.23252
$889$	−2.56002e7	−1.08640
$890$	1.65823e7	0.701729
$891$	3.08898e6	0.130353
$892$	−1.75608e6	−0.0738979
$893$	7.62865e6	0.320125
$894$	4.45325e7	1.86352
$895$	−1.58069e6	−0.0659614
$896$	4.77565e7	1.98730
$897$	3.42209e7	1.42007
$898$	−1.08514e7	−0.449051
$899$	3.29497e6	0.135973
$900$	2.23307e6	0.0918959
$901$	1.53234e7	0.628846
$902$	9.60795e6	0.393201
$903$	1.05767e8	4.31648
$904$	−201897.	−0.00821691
$905$	−1.65384e6	−0.0671231
$906$	4.51865e7	1.82889
$907$	−2.45075e7	−0.989192	−0.494596	−	0.869123i	$-0.664684\pi$
$907$	−2.45075e7	−0.989192	−0.494596	+	0.869123i	$0.664684\pi$
$908$	−1.00192e7	−0.403292
$909$	−4.35398e7	−1.74774
$910$	1.05765e7	0.423388
$911$	4.91507e7	1.96216	0.981078	−	0.193613i	$-0.0620207\pi$
$911$	4.91507e7	1.96216	0.981078	+	0.193613i	$0.0620207\pi$
$912$	1.09021e7	0.434034
$913$	−1.31202e7	−0.520911
$914$	3.32203e7	1.31534
$915$	−2.43940e7	−0.963229
$916$	−8.69707e6	−0.342479
$917$	−3.92579e7	−1.54172
$918$	1.02282e7	0.400582
$919$	1.70007e7	0.664015	0.332008	−	0.943277i	$-0.392274\pi$
$919$	1.70007e7	0.664015	0.332008	+	0.943277i	$0.392274\pi$
$920$	1.64333e7	0.640111
$921$	−2.45725e7	−0.954554
$922$	3.16505e7	1.22618
$923$	−2.65194e6	−0.102461
$924$	6.57837e6	0.253477
$925$	5.33750e6	0.205108
$926$	−4.10247e7	−1.57224
$927$	3.72312e7	1.42301
$928$	−2.00638e6	−0.0764792
$929$	4.99083e7	1.89729	0.948645	−	0.316342i	$-0.102455\pi$
$929$	4.99083e7	1.89729	0.948645	+	0.316342i	$0.102455\pi$
$930$	−2.36224e7	−0.895605
$931$	1.05915e7	0.400482
$932$	−7.99380e6	−0.301449
$933$	1.86570e7	0.701676
$934$	−4.04782e7	−1.51829
$935$	1.99954e6	0.0747999
$936$	−1.44682e7	−0.539792
$937$	1.95261e6	0.0726553	0.0363276	−	0.999340i	$-0.488434\pi$
$937$	1.95261e6	0.0726553	0.0363276	+	0.999340i	$0.488434\pi$
$938$	−5.43706e7	−2.01770
$939$	−1.64809e7	−0.609983
$940$	5.53162e6	0.204189
$941$	1.55971e7	0.574210	0.287105	−	0.957899i	$-0.407307\pi$
$941$	1.55971e7	0.574210	0.287105	+	0.957899i	$0.407307\pi$
$942$	4.46152e7	1.63816
$943$	5.70834e7	2.09041
$944$	2.15995e7	0.788884
$945$	−1.27514e7	−0.464492
$946$	1.60627e7	0.583565
$947$	1.07298e7	0.388790	0.194395	−	0.980923i	$-0.437726\pi$
$947$	1.07298e7	0.388790	0.194395	+	0.980923i	$0.437726\pi$
$948$	9.83844e6	0.355554
$949$	1.66745e7	0.601019
$950$	1.47039e6	0.0528594
$951$	2.90191e7	1.04048
$952$	1.99227e7	0.712453
$953$	−1.52624e7	−0.544366	−0.272183	−	0.962245i	$-0.587746\pi$
$953$	−1.52624e7	−0.544366	−0.272183	+	0.962245i	$0.587746\pi$
$954$	−5.15522e7	−1.83390
$955$	2.80039e6	0.0993596
$956$	1.45291e7	0.514156
$957$	1.60651e6	0.0567027
$958$	1.56961e6	0.0552558
$959$	−9.27965e7	−3.25826
$960$	−9.77561e6	−0.342346
$961$	7.35351e6	0.256854
$962$	1.68187e7	0.585941
$963$	−5.60268e7	−1.94684
$964$	−5.49420e6	−0.190420
$965$	−1.06615e7	−0.368553
$966$	1.58531e8	5.46603
$967$	2.15155e7	0.739922	0.369961	−	0.929047i	$-0.379371\pi$
$967$	2.15155e7	0.739922	0.369961	+	0.929047i	$0.379371\pi$
$968$	−2.05422e6	−0.0704626
$969$	5.76772e6	0.197331
$970$	−8.88759e6	−0.303288
$971$	2.89403e7	0.985043	0.492521	−	0.870300i	$-0.336075\pi$
$971$	2.89403e7	0.985043	0.492521	+	0.870300i	$0.336075\pi$
$972$	1.25022e7	0.424444
$973$	−6.20433e7	−2.10094
$974$	4.69385e7	1.58537
$975$	−4.56523e6	−0.153798
$976$	−5.04382e7	−1.69487
$977$	−2.15739e7	−0.723090	−0.361545	−	0.932355i	$-0.617751\pi$
$977$	−2.15739e7	−0.723090	−0.361545	+	0.932355i	$0.617751\pi$
$978$	2.52808e7	0.845170
$979$	−1.23153e7	−0.410666
$980$	7.68001e6	0.255444
$981$	5.25156e7	1.74227
$982$	−3.30948e7	−1.09517
$983$	72084.2	0.00237934	0.00118967	−	0.999999i	$-0.499621\pi$
$983$	72084.2	0.00237934	0.00118967	+	0.999999i	$0.499621\pi$
$984$	−4.13209e7	−1.36045
$985$	1.55257e7	0.509871
$986$	−2.36621e6	−0.0775106
$987$	−1.09724e8	−3.58516
$988$	1.14227e6	0.0372285
$989$	9.54326e7	3.10246
$990$	−6.72698e6	−0.218139
$991$	5.25857e7	1.70092	0.850459	−	0.526042i	$-0.176324\pi$
$991$	5.25857e7	1.70092	0.850459	+	0.526042i	$0.176324\pi$
$992$	−2.19106e7	−0.706929
$993$	−3.40042e7	−1.09436
$994$	−1.22853e7	−0.394386
$995$	3.06715e6	0.0982148
$996$	−2.74422e7	−0.876539
$997$	−3.94216e7	−1.25602	−0.628010	−	0.778205i	$-0.716130\pi$
$997$	−3.94216e7	−1.25602	−0.628010	+	0.778205i	$0.716130\pi$
$998$	5.16713e7	1.64219
$999$	−2.02772e7	−0.642826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.b.1.29	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.29	✓	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)

\(f(q)\)	\(=\)	\(q+6.51695 q^{2} -24.1709 q^{3} +10.4706 q^{4} +25.0000 q^{5} -157.521 q^{6} +214.817 q^{7} -140.306 q^{8} +341.233 q^{9} +O(q^{10})\)	\(q+6.51695 q^{2} -24.1709 q^{3} +10.4706 q^{4} +25.0000 q^{5} -157.521 q^{6} +214.817 q^{7} -140.306 q^{8} +341.233 q^{9} +162.924 q^{10} -121.000 q^{11} -253.084 q^{12} +302.196 q^{13} +1399.95 q^{14} -604.273 q^{15} -1249.43 q^{16} -661.004 q^{17} +2223.80 q^{18} +361.000 q^{19} +261.765 q^{20} -5192.32 q^{21} -788.551 q^{22} -4684.99 q^{23} +3391.32 q^{24} +625.000 q^{25} +1969.40 q^{26} -2374.37 q^{27} +2249.26 q^{28} +549.294 q^{29} -3938.01 q^{30} +5998.56 q^{31} -3652.65 q^{32} +2924.68 q^{33} -4307.73 q^{34} +5370.42 q^{35} +3572.91 q^{36} +8540.00 q^{37} +2352.62 q^{38} -7304.36 q^{39} -3507.65 q^{40} -12184.3 q^{41} -33838.1 q^{42} -20369.8 q^{43} -1266.94 q^{44} +8530.82 q^{45} -30531.9 q^{46} +21132.0 q^{47} +30199.8 q^{48} +29339.3 q^{49} +4073.09 q^{50} +15977.1 q^{51} +3164.18 q^{52} -23182.1 q^{53} -15473.7 q^{54} -3025.00 q^{55} -30140.1 q^{56} -8725.70 q^{57} +3579.72 q^{58} -17287.5 q^{59} -6327.10 q^{60} +40369.1 q^{61} +39092.3 q^{62} +73302.6 q^{63} +16177.5 q^{64} +7554.91 q^{65} +19060.0 q^{66} -38837.5 q^{67} -6921.12 q^{68} +113241. q^{69} +34998.8 q^{70} -8775.55 q^{71} -47877.0 q^{72} +55177.8 q^{73} +55654.7 q^{74} -15106.8 q^{75} +3779.89 q^{76} -25992.8 q^{77} -47602.1 q^{78} -38874.2 q^{79} -31235.6 q^{80} -25528.8 q^{81} -79404.6 q^{82} +108431. q^{83} -54366.7 q^{84} -16525.1 q^{85} -132749. q^{86} -13276.9 q^{87} +16977.0 q^{88} +101780. q^{89} +55594.9 q^{90} +64916.9 q^{91} -49054.7 q^{92} -144991. q^{93} +137716. q^{94} +9025.00 q^{95} +88287.9 q^{96} -54550.6 q^{97} +191203. q^{98} -41289.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 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

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