LMFDB - Embedded newform 959.6.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [959,6,Mod(1,959)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(959, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("959.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 959 = 7 \cdot 137 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	959.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:	$153.808083201$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	959.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.84789 q^{2} -9.48815 q^{3} +64.9809 q^{4} -43.0135 q^{5} +93.4383 q^{6} +49.0000 q^{7} -324.793 q^{8} -152.975 q^{9} +O(q^{10})$	\(q-9.84789 q^{2} -9.48815 q^{3} +64.9809 q^{4} -43.0135 q^{5} +93.4383 q^{6} +49.0000 q^{7} -324.793 q^{8} -152.975 q^{9} +423.592 q^{10} -560.609 q^{11} -616.549 q^{12} -1158.92 q^{13} -482.547 q^{14} +408.119 q^{15} +1119.13 q^{16} -231.070 q^{17} +1506.48 q^{18} +585.435 q^{19} -2795.06 q^{20} -464.919 q^{21} +5520.82 q^{22} -52.8169 q^{23} +3081.68 q^{24} -1274.84 q^{25} +11412.9 q^{26} +3757.07 q^{27} +3184.07 q^{28} +4208.69 q^{29} -4019.11 q^{30} -106.880 q^{31} -627.722 q^{32} +5319.14 q^{33} +2275.55 q^{34} -2107.66 q^{35} -9940.46 q^{36} +4436.42 q^{37} -5765.30 q^{38} +10996.0 q^{39} +13970.5 q^{40} -8691.59 q^{41} +4578.48 q^{42} -14394.6 q^{43} -36428.9 q^{44} +6579.99 q^{45} +520.135 q^{46} +1942.75 q^{47} -10618.5 q^{48} +2401.00 q^{49} +12554.5 q^{50} +2192.43 q^{51} -75307.6 q^{52} +28471.4 q^{53} -36999.2 q^{54} +24113.7 q^{55} -15914.8 q^{56} -5554.70 q^{57} -41446.7 q^{58} +28955.8 q^{59} +26519.9 q^{60} -18132.2 q^{61} +1052.54 q^{62} -7495.77 q^{63} -29630.5 q^{64} +49849.1 q^{65} -52382.3 q^{66} -2057.61 q^{67} -15015.2 q^{68} +501.135 q^{69} +20756.0 q^{70} +5054.33 q^{71} +49685.1 q^{72} -17540.1 q^{73} -43689.4 q^{74} +12095.9 q^{75} +38042.1 q^{76} -27469.8 q^{77} -108287. q^{78} +17026.8 q^{79} -48137.7 q^{80} +1525.26 q^{81} +85593.8 q^{82} -187.406 q^{83} -30210.9 q^{84} +9939.13 q^{85} +141756. q^{86} -39932.7 q^{87} +182082. q^{88} +37575.2 q^{89} -64799.0 q^{90} -56787.0 q^{91} -3432.09 q^{92} +1014.10 q^{93} -19132.0 q^{94} -25181.6 q^{95} +5955.92 q^{96} +20199.1 q^{97} -23644.8 q^{98} +85759.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9}+O(q^{10}) $ 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9} - 1322 q^{10} - 1446 q^{11} - 1466 q^{12} - 1746 q^{13} - 980 q^{14} - 4313 q^{15} + 9208 q^{16} - 3681 q^{17} - 10234 q^{18} - 2860 q^{19} - 7308 q^{20} - 2401 q^{21} - 13879 q^{22} - 13685 q^{23} - 13424 q^{24} + 18155 q^{25} - 9144 q^{26} - 6865 q^{27} + 47824 q^{28} - 19489 q^{29} + 2307 q^{30} - 33560 q^{31} - 27274 q^{32} - 40132 q^{33} - 35811 q^{34} - 8281 q^{35} - 27689 q^{36} - 70663 q^{37} - 37203 q^{38} - 51201 q^{39} - 86817 q^{40} - 67917 q^{41} - 13377 q^{42} - 104475 q^{43} - 45827 q^{44} - 93598 q^{45} - 137776 q^{46} - 43192 q^{47} - 135425 q^{48} + 177674 q^{49} - 73802 q^{50} - 110795 q^{51} - 107131 q^{52} - 99015 q^{53} - 46226 q^{54} - 71678 q^{55} - 36603 q^{56} - 146490 q^{57} - 143069 q^{58} - 12512 q^{59} - 177875 q^{60} - 125581 q^{61} - 75283 q^{62} + 209475 q^{63} - 8449 q^{64} - 95447 q^{65} + 213311 q^{66} - 282713 q^{67} + 191684 q^{68} - 171171 q^{69} - 64778 q^{70} - 189029 q^{71} + 20181 q^{72} - 96401 q^{73} - 96089 q^{74} - 21522 q^{75} - 276776 q^{76} - 70854 q^{77} + 106155 q^{78} - 454125 q^{79} + 253095 q^{80} + 12226 q^{81} + 107086 q^{82} - 168146 q^{83} - 71834 q^{84} - 329524 q^{85} + 191853 q^{86} + 61244 q^{87} - 505209 q^{88} - 325374 q^{89} - 277645 q^{90} - 85554 q^{91} - 189827 q^{92} - 347054 q^{93} - 125581 q^{94} - 343566 q^{95} + 289017 q^{96} - 844266 q^{97} - 48020 q^{98} - 490575 q^{99}+O(q^{100}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9 - 1322 * q^10 - 1446 * q^11 - 1466 * q^12 - 1746 * q^13 - 980 * q^14 - 4313 * q^15 + 9208 * q^16 - 3681 * q^17 - 10234 * q^18 - 2860 * q^19 - 7308 * q^20 - 2401 * q^21 - 13879 * q^22 - 13685 * q^23 - 13424 * q^24 + 18155 * q^25 - 9144 * q^26 - 6865 * q^27 + 47824 * q^28 - 19489 * q^29 + 2307 * q^30 - 33560 * q^31 - 27274 * q^32 - 40132 * q^33 - 35811 * q^34 - 8281 * q^35 - 27689 * q^36 - 70663 * q^37 - 37203 * q^38 - 51201 * q^39 - 86817 * q^40 - 67917 * q^41 - 13377 * q^42 - 104475 * q^43 - 45827 * q^44 - 93598 * q^45 - 137776 * q^46 - 43192 * q^47 - 135425 * q^48 + 177674 * q^49 - 73802 * q^50 - 110795 * q^51 - 107131 * q^52 - 99015 * q^53 - 46226 * q^54 - 71678 * q^55 - 36603 * q^56 - 146490 * q^57 - 143069 * q^58 - 12512 * q^59 - 177875 * q^60 - 125581 * q^61 - 75283 * q^62 + 209475 * q^63 - 8449 * q^64 - 95447 * q^65 + 213311 * q^66 - 282713 * q^67 + 191684 * q^68 - 171171 * q^69 - 64778 * q^70 - 189029 * q^71 + 20181 * q^72 - 96401 * q^73 - 96089 * q^74 - 21522 * q^75 - 276776 * q^76 - 70854 * q^77 + 106155 * q^78 - 454125 * q^79 + 253095 * q^80 + 12226 * q^81 + 107086 * q^82 - 168146 * q^83 - 71834 * q^84 - 329524 * q^85 + 191853 * q^86 + 61244 * q^87 - 505209 * q^88 - 325374 * q^89 - 277645 * q^90 - 85554 * q^91 - 189827 * q^92 - 347054 * q^93 - 125581 * q^94 - 343566 * q^95 + 289017 * q^96 - 844266 * q^97 - 48020 * q^98 - 490575 * 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 $

$2$	−9.84789	−1.74088	−0.870439	−	0.492277i	$-0.836165\pi$
$2$	−9.84789	−1.74088	−0.870439	+	0.492277i	$0.836165\pi$
$3$	−9.48815	−0.608665	−0.304333	−	0.952566i	$-0.598433\pi$
$3$	−9.48815	−0.608665	−0.304333	+	0.952566i	$0.598433\pi$
$4$	64.9809	2.03065
$5$	−43.0135	−0.769449	−0.384724	−	0.923032i	$-0.625703\pi$
$5$	−43.0135	−0.769449	−0.384724	+	0.923032i	$0.625703\pi$
$6$	93.4383	1.05961
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−324.793	−1.79424
$9$	−152.975	−0.629527
$10$	423.592	1.33952
$11$	−560.609	−1.39694	−0.698471	−	0.715638i	$-0.746136\pi$
$11$	−560.609	−1.39694	−0.698471	+	0.715638i	$0.746136\pi$
$12$	−616.549	−1.23599
$13$	−1158.92	−1.90193	−0.950965	−	0.309299i	$-0.899905\pi$
$13$	−1158.92	−1.90193	−0.950965	+	0.309299i	$0.899905\pi$
$14$	−482.547	−0.657990
$15$	408.119	0.468337
$16$	1119.13	1.09290
$17$	−231.070	−0.193920	−0.0969598	−	0.995288i	$-0.530912\pi$
$17$	−231.070	−0.193920	−0.0969598	+	0.995288i	$0.530912\pi$
$18$	1506.48	1.09593
$19$	585.435	0.372045	0.186022	−	0.982546i	$-0.440440\pi$
$19$	585.435	0.372045	0.186022	+	0.982546i	$0.440440\pi$
$20$	−2795.06	−1.56248
$21$	−464.919	−0.230054
$22$	5520.82	2.43190
$23$	−52.8169	−0.0208187	−0.0104093	−	0.999946i	$-0.503313\pi$
$23$	−52.8169	−0.0208187	−0.0104093	+	0.999946i	$0.503313\pi$
$24$	3081.68	1.09209
$25$	−1274.84	−0.407949
$26$	11412.9	3.31103
$27$	3757.07	0.991836
$28$	3184.07	0.767515
$29$	4208.69	0.929292	0.464646	−	0.885497i	$-0.346182\pi$
$29$	4208.69	0.929292	0.464646	+	0.885497i	$0.346182\pi$
$30$	−4019.11	−0.815317
$31$	−106.880	−0.0199753	−0.00998765	−	0.999950i	$-0.503179\pi$
$31$	−106.880	−0.0199753	−0.00998765	+	0.999950i	$0.503179\pi$
$32$	−627.722	−0.108366
$33$	5319.14	0.850270
$34$	2275.55	0.337590
$35$	−2107.66	−0.290824
$36$	−9940.46	−1.27835
$37$	4436.42	0.532756	0.266378	−	0.963869i	$-0.414173\pi$
$37$	4436.42	0.532756	0.266378	+	0.963869i	$0.414173\pi$
$38$	−5765.30	−0.647684
$39$	10996.0	1.15764
$40$	13970.5	1.38058
$41$	−8691.59	−0.807494	−0.403747	−	0.914871i	$-0.632292\pi$
$41$	−8691.59	−0.807494	−0.403747	+	0.914871i	$0.632292\pi$
$42$	4578.48	0.400496
$43$	−14394.6	−1.18721	−0.593604	−	0.804757i	$-0.702296\pi$
$43$	−14394.6	−1.18721	−0.593604	+	0.804757i	$0.702296\pi$
$44$	−36428.9	−2.83671
$45$	6579.99	0.484388
$46$	520.135	0.0362428
$47$	1942.75	0.128284	0.0641420	−	0.997941i	$-0.479569\pi$
$47$	1942.75	0.128284	0.0641420	+	0.997941i	$0.479569\pi$
$48$	−10618.5	−0.665211
$49$	2401.00	0.142857
$50$	12554.5	0.710189
$51$	2192.43	0.118032
$52$	−75307.6	−3.86216
$53$	28471.4	1.39226	0.696128	−	0.717918i	$-0.254905\pi$
$53$	28471.4	1.39226	0.696128	+	0.717918i	$0.254905\pi$
$54$	−36999.2	−1.72667
$55$	24113.7	1.07488
$56$	−15914.8	−0.678160
$57$	−5554.70	−0.226451
$58$	−41446.7	−1.61778
$59$	28955.8	1.08294	0.541471	−	0.840720i	$-0.317868\pi$
$59$	28955.8	1.08294	0.541471	+	0.840720i	$0.317868\pi$
$60$	26519.9	0.951030
$61$	−18132.2	−0.623916	−0.311958	−	0.950096i	$-0.600985\pi$
$61$	−18132.2	−0.623916	−0.311958	+	0.950096i	$0.600985\pi$
$62$	1052.54	0.0347745
$63$	−7495.77	−0.237939
$64$	−29630.5	−0.904250
$65$	49849.1	1.46344
$66$	−52382.3	−1.48022
$67$	−2057.61	−0.0559986	−0.0279993	−	0.999608i	$-0.508914\pi$
$67$	−2057.61	−0.0559986	−0.0279993	+	0.999608i	$0.508914\pi$
$68$	−15015.2	−0.393784
$69$	501.135	0.0126716
$70$	20756.0	0.506289
$71$	5054.33	0.118992	0.0594959	−	0.998229i	$-0.481051\pi$
$71$	5054.33	0.118992	0.0594959	+	0.998229i	$0.481051\pi$
$72$	49685.1	1.12952
$73$	−17540.1	−0.385233	−0.192617	−	0.981274i	$-0.561697\pi$
$73$	−17540.1	−0.385233	−0.192617	+	0.981274i	$0.561697\pi$
$74$	−43689.4	−0.927464
$75$	12095.9	0.248304
$76$	38042.1	0.755494
$77$	−27469.8	−0.527994
$78$	−108287.	−2.01531
$79$	17026.8	0.306949	0.153475	−	0.988153i	$-0.450954\pi$
$79$	17026.8	0.306949	0.153475	+	0.988153i	$0.450954\pi$
$80$	−48137.7	−0.840932
$81$	1525.26	0.0258303
$82$	85593.8	1.40575
$83$	−187.406	−0.00298599	−0.00149300	−	0.999999i	$-0.500475\pi$
$83$	−187.406	−0.00298599	−0.00149300	+	0.999999i	$0.500475\pi$
$84$	−30210.9	−0.467160
$85$	9939.13	0.149211
$86$	141756.	2.06679
$87$	−39932.7	−0.565628
$88$	182082.	2.50645
$89$	37575.2	0.502836	0.251418	−	0.967879i	$-0.419103\pi$
$89$	37575.2	0.502836	0.251418	+	0.967879i	$0.419103\pi$
$90$	−64799.0	−0.843261
$91$	−56787.0	−0.718862
$92$	−3432.09	−0.0422755
$93$	1014.10	0.0121583
$94$	−19132.0	−0.223327
$95$	−25181.6	−0.286269
$96$	5955.92	0.0659585
$97$	20199.1	0.217973	0.108987	−	0.994043i	$-0.465239\pi$
$97$	20199.1	0.217973	0.108987	+	0.994043i	$0.465239\pi$
$98$	−23644.8	−0.248697
$99$	85759.1	0.879412
$100$	−82840.3	−0.828403
$101$	−21251.1	−0.207290	−0.103645	−	0.994614i	$-0.533051\pi$
$101$	−21251.1	−0.207290	−0.103645	+	0.994614i	$0.533051\pi$
$102$	−21590.8	−0.205479
$103$	23812.1	0.221159	0.110580	−	0.993867i	$-0.464729\pi$
$103$	23812.1	0.221159	0.110580	+	0.993867i	$0.464729\pi$
$104$	376408.	3.41252
$105$	19997.8	0.177015
$106$	−280383.	−2.42375
$107$	54363.6	0.459038	0.229519	−	0.973304i	$-0.426285\pi$
$107$	54363.6	0.459038	0.229519	+	0.973304i	$0.426285\pi$
$108$	244138.	2.01408
$109$	−35349.8	−0.284984	−0.142492	−	0.989796i	$-0.545512\pi$
$109$	−35349.8	−0.284984	−0.142492	+	0.989796i	$0.545512\pi$
$110$	−237470.	−1.87123
$111$	−42093.5	−0.324270
$112$	54837.4	0.413078
$113$	−105933.	−0.780432	−0.390216	−	0.920723i	$-0.627600\pi$
$113$	−105933.	−0.780432	−0.390216	+	0.920723i	$0.627600\pi$
$114$	54702.1	0.394223
$115$	2271.84	0.0160189
$116$	273485.	1.88707
$117$	177285.	1.19732
$118$	−285153.	−1.88527
$119$	−11322.4	−0.0732947
$120$	−132554.	−0.840309
$121$	153231.	0.951447
$122$	178564.	1.08616
$123$	82467.1	0.491494
$124$	−6945.18	−0.0405629
$125$	189252.	1.08334
$126$	73817.5	0.414222
$127$	73441.1	0.404045	0.202022	−	0.979381i	$-0.435249\pi$
$127$	73441.1	0.404045	0.202022	+	0.979381i	$0.435249\pi$
$128$	311885.	1.68255
$129$	136578.	0.722613
$130$	−490909.	−2.54766
$131$	206882.	1.05328	0.526642	−	0.850087i	$-0.323451\pi$
$131$	206882.	1.05328	0.526642	+	0.850087i	$0.323451\pi$
$132$	345643.	1.72660
$133$	28686.3	0.140620
$134$	20263.2	0.0974867
$135$	−161605.	−0.763167
$136$	75049.9	0.347939
$137$	18769.0	0.0854358
$137$	18769.0	0.0854358
$138$	−4935.12	−0.0220597
$139$	204012.	0.895609	0.447805	−	0.894131i	$-0.352206\pi$
$139$	204012.	0.895609	0.447805	+	0.894131i	$0.352206\pi$
$140$	−136958.	−0.590563
$141$	−18433.1	−0.0780820
$142$	−49774.4	−0.207150
$143$	649700.	2.65688
$144$	−171199.	−0.688011
$145$	−181031.	−0.715042
$146$	172733.	0.670644
$147$	−22781.1	−0.0869522
$148$	288283.	1.08184
$149$	143050.	0.527865	0.263932	−	0.964541i	$-0.414980\pi$
$149$	143050.	0.527865	0.263932	+	0.964541i	$0.414980\pi$
$150$	−119119.	−0.432267
$151$	−322175.	−1.14987	−0.574936	−	0.818198i	$-0.694973\pi$
$151$	−322175.	−1.14987	−0.574936	+	0.818198i	$0.694973\pi$
$152$	−190145.	−0.667538
$153$	35348.0	0.122078
$154$	270520.	0.919174
$155$	4597.29	0.0153700
$156$	714530.	2.35076
$157$	−281464.	−0.911327	−0.455664	−	0.890152i	$-0.650598\pi$
$157$	−281464.	−0.911327	−0.455664	+	0.890152i	$0.650598\pi$
$158$	−167678.	−0.534361
$159$	−270141.	−0.847417
$160$	27000.5	0.0833819
$161$	−2588.03	−0.00786872
$162$	−15020.5	−0.0449674
$163$	−357399.	−1.05362	−0.526810	−	0.849983i	$-0.676612\pi$
$163$	−357399.	−1.05362	−0.526810	+	0.849983i	$0.676612\pi$
$164$	−564787.	−1.63974
$165$	−228795.	−0.654239
$166$	1845.56	0.00519825
$167$	436970.	1.21244	0.606220	−	0.795297i	$-0.292685\pi$
$167$	436970.	1.21244	0.606220	+	0.795297i	$0.292685\pi$
$168$	151002.	0.412772
$169$	971798.	2.61734
$170$	−97879.5	−0.259758
$171$	−89557.0	−0.234212
$172$	−935372.	−2.41081
$173$	678550.	1.72372	0.861860	−	0.507146i	$-0.169299\pi$
$173$	678550.	1.72372	0.861860	+	0.507146i	$0.169299\pi$
$174$	393253.	0.984689
$175$	−62467.2	−0.154190
$176$	−627395.	−1.52672
$177$	−274737.	−0.659149
$178$	−370036.	−0.875375
$179$	−209352.	−0.488364	−0.244182	−	0.969729i	$-0.578519\pi$
$179$	−209352.	−0.488364	−0.244182	+	0.969729i	$0.578519\pi$
$180$	427574.	0.983625
$181$	−203156.	−0.460928	−0.230464	−	0.973081i	$-0.574024\pi$
$181$	−203156.	−0.460928	−0.230464	+	0.973081i	$0.574024\pi$
$182$	559232.	1.25145
$183$	172041.	0.379756
$184$	17154.5	0.0373538
$185$	−190826.	−0.409929
$186$	−9986.70	−0.0211661
$187$	129540.	0.270894
$188$	126242.	0.260500
$189$	184096.	0.374879
$190$	247986.	0.498360
$191$	−671304.	−1.33148	−0.665742	−	0.746182i	$-0.731885\pi$
$191$	−671304.	−1.33148	−0.665742	+	0.746182i	$0.731885\pi$
$192$	281138.	0.550386
$193$	114729.	0.221707	0.110853	−	0.993837i	$-0.464642\pi$
$193$	114729.	0.221707	0.110853	+	0.993837i	$0.464642\pi$
$194$	−198919.	−0.379465
$195$	−472976.	−0.890743
$196$	156019.	0.290093
$197$	528217.	0.969721	0.484860	−	0.874592i	$-0.338870\pi$
$197$	528217.	0.969721	0.484860	+	0.874592i	$0.338870\pi$
$198$	−844547.	−1.53095
$199$	723335.	1.29481	0.647406	−	0.762145i	$-0.275854\pi$
$199$	723335.	1.29481	0.647406	+	0.762145i	$0.275854\pi$
$200$	414059.	0.731959
$201$	19523.0	0.0340844
$202$	209279.	0.360867
$203$	206226.	0.351239
$204$	142466.	0.239682
$205$	373855.	0.621325
$206$	−234499.	−0.385011
$207$	8079.66	0.0131059
$208$	−1.29698e6	−2.07862
$209$	−328200.	−0.519725
$210$	−196936.	−0.308161
$211$	1.20823e6	1.86829	0.934145	−	0.356895i	$-0.116164\pi$
$211$	1.20823e6	1.86829	0.934145	+	0.356895i	$0.116164\pi$
$212$	1.85010e6	2.82719
$213$	−47956.2	−0.0724262
$214$	−535367.	−0.799129
$215$	619160.	0.913496
$216$	−1.22027e6	−1.77959
$217$	−5237.13	−0.00754995
$218$	348121.	0.496123
$219$	166423.	0.234478
$220$	1.56693e6	2.18270
$221$	267791.	0.368821
$222$	414532.	0.564515
$223$	640844.	0.862959	0.431480	−	0.902123i	$-0.357992\pi$
$223$	640844.	0.862959	0.431480	+	0.902123i	$0.357992\pi$
$224$	−30758.4	−0.0409584
$225$	195019.	0.256815
$226$	1.04322e6	1.35864
$227$	−1.21706e6	−1.56764	−0.783820	−	0.620988i	$-0.786732\pi$
$227$	−1.21706e6	−1.56764	−0.783820	+	0.620988i	$0.786732\pi$
$228$	−360950.	−0.459843
$229$	204192.	0.257306	0.128653	−	0.991690i	$-0.458935\pi$
$229$	204192.	0.257306	0.128653	+	0.991690i	$0.458935\pi$
$230$	−22372.8	−0.0278870
$231$	260638.	0.321372
$232$	−1.36695e6	−1.66738
$233$	1.00778e6	1.21612	0.608062	−	0.793890i	$-0.291947\pi$
$233$	1.00778e6	1.21612	0.608062	+	0.793890i	$0.291947\pi$
$234$	−1.74589e6	−2.08438
$235$	−83564.5	−0.0987079
$236$	1.88157e6	2.19908
$237$	−161553.	−0.186829
$238$	111502.	0.127597
$239$	569149.	0.644512	0.322256	−	0.946653i	$-0.395559\pi$
$239$	569149.	0.644512	0.322256	+	0.946653i	$0.395559\pi$
$240$	456738.	0.511846
$241$	57181.4	0.0634179	0.0317090	−	0.999497i	$-0.489905\pi$
$241$	57181.4	0.0634179	0.0317090	+	0.999497i	$0.489905\pi$
$242$	−1.50901e6	−1.65635
$243$	−927440.	−1.00756
$244$	−1.17825e6	−1.26696
$245$	−103275.	−0.109921
$246$	−812127.	−0.855630
$247$	−678472.	−0.707603
$248$	34713.9	0.0358405
$249$	1778.14	0.00181747
$250$	−1.86374e6	−1.88597
$251$	−1.06738e6	−1.06939	−0.534693	−	0.845046i	$-0.679573\pi$
$251$	−1.06738e6	−1.06939	−0.534693	+	0.845046i	$0.679573\pi$
$252$	−487082.	−0.483171
$253$	29609.6	0.0290825
$254$	−723240.	−0.703393
$255$	−94304.0	−0.0908196
$256$	−2.12323e6	−2.02487
$257$	1.14199e6	1.07852	0.539260	−	0.842139i	$-0.318704\pi$
$257$	1.14199e6	1.07852	0.539260	+	0.842139i	$0.318704\pi$
$258$	−1.34500e6	−1.25798
$259$	217385.	0.201363
$260$	3.23924e6	2.97173
$261$	−643825.	−0.585014
$262$	−2.03735e6	−1.83364
$263$	−495917.	−0.442099	−0.221050	−	0.975263i	$-0.570948\pi$
$263$	−495917.	−0.442099	−0.221050	+	0.975263i	$0.570948\pi$
$264$	−1.72762e6	−1.52559
$265$	−1.22465e6	−1.07127
$266$	−282500.	−0.244802
$267$	−356519.	−0.306059
$268$	−133706.	−0.113714
$269$	−819861.	−0.690811	−0.345406	−	0.938453i	$-0.612259\pi$
$269$	−819861.	−0.690811	−0.345406	+	0.938453i	$0.612259\pi$
$270$	1.59147e6	1.32858
$271$	−2.21381e6	−1.83112	−0.915562	−	0.402178i	$-0.868253\pi$
$271$	−2.21381e6	−1.83112	−0.915562	+	0.402178i	$0.868253\pi$
$272$	−258598.	−0.211935
$273$	538804.	0.437546
$274$	−184835.	−0.148733
$275$	714687.	0.569881
$276$	32564.2	0.0257317
$277$	−79140.6	−0.0619726	−0.0309863	−	0.999520i	$-0.509865\pi$
$277$	−79140.6	−0.0619726	−0.0309863	+	0.999520i	$0.509865\pi$
$278$	−2.00909e6	−1.55915
$279$	16350.0	0.0125750
$280$	684553.	0.521809
$281$	1.37293e6	1.03725	0.518624	−	0.855002i	$-0.326444\pi$
$281$	1.37293e6	1.03725	0.518624	+	0.855002i	$0.326444\pi$
$282$	181527.	0.135931
$283$	−1.47907e6	−1.09780	−0.548899	−	0.835888i	$-0.684953\pi$
$283$	−1.47907e6	−1.09780	−0.548899	+	0.835888i	$0.684953\pi$
$284$	328435.	0.241631
$285$	238927.	0.174242
$286$	−6.39817e6	−4.62531
$287$	−425888.	−0.305204
$288$	96025.7	0.0682191
$289$	−1.36646e6	−0.962395
$290$	1.78277e6	1.24480
$291$	−191653.	−0.132673
$292$	−1.13977e6	−0.782276
$293$	−1.02940e6	−0.700513	−0.350257	−	0.936654i	$-0.613906\pi$
$293$	−1.02940e6	−0.700513	−0.350257	+	0.936654i	$0.613906\pi$
$294$	224345.	0.151373
$295$	−1.24549e6	−0.833268
$296$	−1.44092e6	−0.955894
$297$	−2.10625e6	−1.38554
$298$	−1.40874e6	−0.918948
$299$	61210.4	0.0395957
$300$	786001.	0.504220
$301$	−705333.	−0.448723
$302$	3.17275e6	2.00179
$303$	201634.	0.126170
$304$	655179.	0.406608
$305$	779930.	0.480071
$306$	−348103.	−0.212522
$307$	−1.37028e6	−0.829780	−0.414890	−	0.909871i	$-0.636180\pi$
$307$	−1.37028e6	−0.829780	−0.414890	+	0.909871i	$0.636180\pi$
$308$	−1.78502e6	−1.07217
$309$	−225933.	−0.134612
$310$	−45273.6	−0.0267572
$311$	−1.16857e6	−0.685102	−0.342551	−	0.939499i	$-0.611291\pi$
$311$	−1.16857e6	−0.685102	−0.342551	+	0.939499i	$0.611291\pi$
$312$	−3.57142e6	−2.07708
$313$	−411246.	−0.237269	−0.118634	−	0.992938i	$-0.537852\pi$
$313$	−411246.	−0.237269	−0.118634	+	0.992938i	$0.537852\pi$
$314$	2.77183e6	1.58651
$315$	322419.	0.183082
$316$	1.10642e6	0.623307
$317$	236234.	0.132036	0.0660182	−	0.997818i	$-0.478970\pi$
$317$	236234.	0.132036	0.0660182	+	0.997818i	$0.478970\pi$
$318$	2.66032e6	1.47525
$319$	−2.35943e6	−1.29817
$320$	1.27451e6	0.695774
$321$	−515810.	−0.279401
$322$	25486.6	0.0136985
$323$	−135277.	−0.0721467
$324$	99112.5	0.0524525
$325$	1.47744e6	0.775890
$326$	3.51963e6	1.83422
$327$	335404.	0.173460
$328$	2.82296e6	1.44884
$329$	95194.8	0.0484868
$330$	2.25315e6	1.13895
$331$	−1.60026e6	−0.802823	−0.401412	−	0.915898i	$-0.631480\pi$
$331$	−1.60026e6	−0.802823	−0.401412	+	0.915898i	$0.631480\pi$
$332$	−12177.8	−0.00606352
$333$	−678662.	−0.335384
$334$	−4.30323e6	−2.11071
$335$	88505.2	0.0430880
$336$	−520306.	−0.251426
$337$	3.40842e6	1.63485	0.817427	−	0.576032i	$-0.195400\pi$
$337$	3.40842e6	1.63485	0.817427	+	0.576032i	$0.195400\pi$
$338$	−9.57016e6	−4.55646
$339$	1.00511e6	0.475022
$340$	645854.	0.302996
$341$	59918.0	0.0279043
$342$	881947.	0.407734
$343$	117649.	0.0539949
$344$	4.67524e6	2.13014
$345$	−21555.5	−0.00975015
$346$	−6.68229e6	−3.00079
$347$	1.65302e6	0.736976	0.368488	−	0.929632i	$-0.379876\pi$
$347$	1.65302e6	0.736976	0.368488	+	0.929632i	$0.379876\pi$
$348$	−2.59486e6	−1.14859
$349$	2.96799e6	1.30436	0.652182	−	0.758062i	$-0.273854\pi$
$349$	2.96799e6	1.30436	0.652182	+	0.758062i	$0.273854\pi$
$350$	615170.	0.268426
$351$	−4.35414e6	−1.88640
$352$	351906.	0.151381
$353$	−595172.	−0.254218	−0.127109	−	0.991889i	$-0.540570\pi$
$353$	−595172.	−0.254218	−0.127109	+	0.991889i	$0.540570\pi$
$354$	2.70558e6	1.14750
$355$	−217404.	−0.0915582
$356$	2.44167e6	1.02109
$357$	107429.	0.0446119
$358$	2.06167e6	0.850182
$359$	−4.14236e6	−1.69634	−0.848168	−	0.529727i	$-0.822294\pi$
$359$	−4.14236e6	−1.69634	−0.848168	+	0.529727i	$0.822294\pi$
$360$	−2.13713e6	−0.869110
$361$	−2.13336e6	−0.861583
$362$	2.00066e6	0.802419
$363$	−1.45388e6	−0.579113
$364$	−3.69007e6	−1.45976
$365$	754459.	0.296417
$366$	−1.69424e6	−0.661109
$367$	−2.43683e6	−0.944407	−0.472204	−	0.881489i	$-0.656541\pi$
$367$	−2.43683e6	−0.944407	−0.472204	+	0.881489i	$0.656541\pi$
$368$	−59109.0	−0.0227528
$369$	1.32960e6	0.508339
$370$	1.87923e6	0.713636
$371$	1.39510e6	0.526223
$372$	65896.9	0.0246892
$373$	1.04199e6	0.387785	0.193892	−	0.981023i	$-0.437889\pi$
$373$	1.04199e6	0.387785	0.193892	+	0.981023i	$0.437889\pi$
$374$	−1.27570e6	−0.471594
$375$	−1.79566e6	−0.659394
$376$	−630991.	−0.230172
$377$	−4.87753e6	−1.76745
$378$	−1.81296e6	−0.652618
$379$	1.69290e6	0.605388	0.302694	−	0.953088i	$-0.402114\pi$
$379$	1.69290e6	0.605388	0.302694	+	0.953088i	$0.402114\pi$
$380$	−1.63633e6	−0.581314
$381$	−696820.	−0.245928
$382$	6.61093e6	2.31795
$383$	4.86543e6	1.69482	0.847411	−	0.530938i	$-0.178160\pi$
$383$	4.86543e6	1.69482	0.847411	+	0.530938i	$0.178160\pi$
$384$	−2.95921e6	−1.02411
$385$	1.18157e6	0.406265
$386$	−1.12984e6	−0.385964
$387$	2.20201e6	0.747380
$388$	1.31256e6	0.442629
$389$	695182.	0.232930	0.116465	−	0.993195i	$-0.462844\pi$
$389$	695182.	0.232930	0.116465	+	0.993195i	$0.462844\pi$
$390$	4.65782e6	1.55067
$391$	12204.4	0.00403715
$392$	−779827.	−0.256320
$393$	−1.96293e6	−0.641097
$394$	−5.20182e6	−1.68816
$395$	−732384.	−0.236182
$396$	5.57271e6	1.78578
$397$	2.40473e6	0.765757	0.382878	−	0.923799i	$-0.374933\pi$
$397$	2.40473e6	0.765757	0.382878	+	0.923799i	$0.374933\pi$
$398$	−7.12332e6	−2.25411
$399$	−272180.	−0.0855903
$400$	−1.42671e6	−0.445848
$401$	3.24708e6	1.00840	0.504200	−	0.863587i	$-0.331788\pi$
$401$	3.24708e6	1.00840	0.504200	+	0.863587i	$0.331788\pi$
$402$	−192260.	−0.0593368
$403$	123865.	0.0379916
$404$	−1.38092e6	−0.420935
$405$	−65606.6	−0.0198751
$406$	−2.03089e6	−0.611465
$407$	−2.48710e6	−0.744230
$408$	−712085.	−0.211778
$409$	91808.3	0.0271377	0.0135689	−	0.999908i	$-0.495681\pi$
$409$	91808.3	0.0271377	0.0135689	+	0.999908i	$0.495681\pi$
$410$	−3.68169e6	−1.08165
$411$	−178083.	−0.0520018
$412$	1.54733e6	0.449098
$413$	1.41883e6	0.409313
$414$	−79567.6	−0.0228158
$415$	8061.00	0.00229757
$416$	727478.	0.206104
$417$	−1.93570e6	−0.545126
$418$	3.23208e6	0.904777
$419$	1.10166e6	0.306559	0.153279	−	0.988183i	$-0.451017\pi$
$419$	1.10166e6	0.306559	0.153279	+	0.988183i	$0.451017\pi$
$420$	1.29948e6	0.359455
$421$	−6.61070e6	−1.81778	−0.908891	−	0.417033i	$-0.863070\pi$
$421$	−6.61070e6	−1.81778	−0.908891	+	0.417033i	$0.863070\pi$
$422$	−1.18985e7	−3.25246
$423$	−297192.	−0.0807582
$424$	−9.24729e6	−2.49804
$425$	294578.	0.0791092
$426$	472268.	0.126085
$427$	−888478.	−0.235818
$428$	3.53260e6	0.932148
$429$	−6.16445e6	−1.61715
$430$	−6.09742e6	−1.59028
$431$	−3.46738e6	−0.899099	−0.449550	−	0.893255i	$-0.648416\pi$
$431$	−3.46738e6	−0.899099	−0.449550	+	0.893255i	$0.648416\pi$
$432$	4.20466e6	1.08398
$433$	2.29073e6	0.587156	0.293578	−	0.955935i	$-0.405154\pi$
$433$	2.29073e6	0.587156	0.293578	+	0.955935i	$0.405154\pi$
$434$	51574.7	0.0131435
$435$	1.71765e6	0.435222
$436$	−2.29706e6	−0.578704
$437$	−30920.9	−0.00774548
$438$	−1.63891e6	−0.408198
$439$	223004.	0.0552270	0.0276135	−	0.999619i	$-0.491209\pi$
$439$	223004.	0.0552270	0.0276135	+	0.999619i	$0.491209\pi$
$440$	−7.83197e6	−1.92859
$441$	−367293.	−0.0899324
$442$	−2.63718e6	−0.642073
$443$	−1.21301e6	−0.293668	−0.146834	−	0.989161i	$-0.546908\pi$
$443$	−1.21301e6	−0.293668	−0.146834	+	0.989161i	$0.546908\pi$
$444$	−2.73527e6	−0.658481
$445$	−1.61624e6	−0.386906
$446$	−6.31096e6	−1.50231
$447$	−1.35728e6	−0.321293
$448$	−1.45189e6	−0.341774
$449$	5.80926e6	1.35989	0.679947	−	0.733261i	$-0.262003\pi$
$449$	5.80926e6	1.35989	0.679947	+	0.733261i	$0.262003\pi$
$450$	−1.92052e6	−0.447083
$451$	4.87258e6	1.12802
$452$	−6.88363e6	−1.58479
$453$	3.05685e6	0.699888
$454$	1.19855e7	2.72907
$455$	2.44261e6	0.553127
$456$	1.80413e6	0.406307
$457$	2.67914e6	0.600074	0.300037	−	0.953928i	$-0.403001\pi$
$457$	2.67914e6	0.600074	0.300037	+	0.953928i	$0.403001\pi$
$458$	−2.01086e6	−0.447939
$459$	−868147.	−0.192336
$460$	147626.	0.0325289
$461$	−3.50373e6	−0.767854	−0.383927	−	0.923363i	$-0.625429\pi$
$461$	−3.50373e6	−0.767854	−0.383927	+	0.923363i	$0.625429\pi$
$462$	−2.56673e6	−0.559469
$463$	5.36755e6	1.16365	0.581826	−	0.813313i	$-0.302338\pi$
$463$	5.36755e6	1.16365	0.581826	+	0.813313i	$0.302338\pi$
$464$	4.71008e6	1.01562
$465$	−43619.8	−0.00935516
$466$	−9.92455e6	−2.11712
$467$	5.11673e6	1.08568	0.542838	−	0.839838i	$-0.317350\pi$
$467$	5.11673e6	1.08568	0.542838	+	0.839838i	$0.317350\pi$
$468$	1.15202e7	2.43133
$469$	−100823.	−0.0211655
$470$	822934.	0.171838
$471$	2.67058e6	0.554693
$472$	−9.40461e6	−1.94306
$473$	8.06972e6	1.65846
$474$	1.59096e6	0.325247
$475$	−746337.	−0.151775
$476$	−735743.	−0.148836
$477$	−4.35541e6	−0.876462
$478$	−5.60492e6	−1.12202
$479$	3.15338e6	0.627968	0.313984	−	0.949428i	$-0.398336\pi$
$479$	3.15338e6	0.627968	0.313984	+	0.949428i	$0.398336\pi$
$480$	−256185.	−0.0507517
$481$	−5.14145e6	−1.01327
$482$	−563116.	−0.110403
$483$	24555.6	0.00478942
$484$	9.95712e6	1.93206
$485$	−868835.	−0.167719
$486$	9.13333e6	1.75404
$487$	1.45205e6	0.277433	0.138717	−	0.990332i	$-0.455702\pi$
$487$	1.45205e6	0.277433	0.138717	+	0.990332i	$0.455702\pi$
$488$	5.88921e6	1.11946
$489$	3.39106e6	0.641302
$490$	1.01704e6	0.191359
$491$	1.13148e6	0.211809	0.105905	−	0.994376i	$-0.466226\pi$
$491$	1.13148e6	0.211809	0.105905	+	0.994376i	$0.466226\pi$
$492$	5.35879e6	0.998054
$493$	−972503.	−0.180208
$494$	6.68152e6	1.23185
$495$	−3.68880e6	−0.676662
$496$	−119613.	−0.0218310
$497$	247662.	0.0449747
$498$	−17510.9	−0.00316399
$499$	−9.81257e6	−1.76413	−0.882067	−	0.471124i	$-0.843848\pi$
$499$	−9.81257e6	−1.76413	−0.882067	+	0.471124i	$0.843848\pi$
$500$	1.22978e7	2.19990
$501$	−4.14604e6	−0.737970
$502$	1.05114e7	1.86167
$503$	−1.06895e7	−1.88382	−0.941910	−	0.335866i	$-0.890971\pi$
$503$	−1.06895e7	−1.88382	−0.941910	+	0.335866i	$0.890971\pi$
$504$	2.43457e6	0.426920
$505$	914086.	0.159499
$506$	−291592.	−0.0506290
$507$	−9.22057e6	−1.59308
$508$	4.77227e6	0.820476
$509$	3.34334e6	0.571988	0.285994	−	0.958231i	$-0.407676\pi$
$509$	3.34334e6	0.571988	0.285994	+	0.958231i	$0.407676\pi$
$510$	928696.	0.158106
$511$	−859463.	−0.145605
$512$	1.09290e7	1.84250
$513$	2.19952e6	0.369007
$514$	−1.12462e7	−1.87757
$515$	−1.02424e6	−0.170171
$516$	8.87495e6	1.46738
$517$	−1.08912e6	−0.179205
$518$	−2.14078e6	−0.350548
$519$	−6.43819e6	−1.04917
$520$	−1.61906e7	−2.62576
$521$	1.35719e6	0.219051	0.109526	−	0.993984i	$-0.465067\pi$
$521$	1.35719e6	0.219051	0.109526	+	0.993984i	$0.465067\pi$
$522$	6.34031e6	1.01844
$523$	1.03410e7	1.65314	0.826571	−	0.562833i	$-0.190289\pi$
$523$	1.03410e7	1.65314	0.826571	+	0.562833i	$0.190289\pi$
$524$	1.34434e7	2.13885
$525$	592698.	0.0938502
$526$	4.88374e6	0.769640
$527$	24696.8	0.00387360
$528$	5.95282e6	0.929262
$529$	−6.43355e6	−0.999567
$530$	1.20603e7	1.86495
$531$	−4.42951e6	−0.681740
$532$	1.86407e6	0.285550
$533$	1.00728e7	1.53580
$534$	3.51096e6	0.532811
$535$	−2.33837e6	−0.353206
$536$	668298.	0.100475
$537$	1.98636e6	0.297250
$538$	8.07390e6	1.20262
$539$	−1.34602e6	−0.199563
$540$	−1.05012e7	−1.54973
$541$	−1.02452e7	−1.50497	−0.752485	−	0.658609i	$-0.771145\pi$
$541$	−1.02452e7	−1.50497	−0.752485	+	0.658609i	$0.771145\pi$
$542$	2.18014e7	3.18776
$543$	1.92757e6	0.280551
$544$	145048.	0.0210142
$545$	1.52052e6	0.219281
$546$	−5.30608e6	−0.761714
$547$	4.72923e6	0.675806	0.337903	−	0.941181i	$-0.390282\pi$
$547$	4.72923e6	0.675806	0.337903	+	0.941181i	$0.390282\pi$
$548$	1.21963e6	0.173490
$549$	2.77377e6	0.392772
$550$	−7.03816e6	−0.992093
$551$	2.46392e6	0.345738
$552$	−162765.	−0.0227359
$553$	834315.	0.116016
$554$	779368.	0.107887
$555$	1.81059e6	0.249509
$556$	1.32569e7	1.81867
$557$	−6.07781e6	−0.830060	−0.415030	−	0.909808i	$-0.636229\pi$
$557$	−6.07781e6	−0.830060	−0.415030	+	0.909808i	$0.636229\pi$
$558$	−161013.	−0.0218915
$559$	1.66821e7	2.25799
$560$	−2.35875e6	−0.317842
$561$	−1.22910e6	−0.164884
$562$	−1.35205e7	−1.80572
$563$	6.42236e6	0.853932	0.426966	−	0.904268i	$-0.359582\pi$
$563$	6.42236e6	0.853932	0.426966	+	0.904268i	$0.359582\pi$
$564$	−1.19780e6	−0.158557
$565$	4.55655e6	0.600503
$566$	1.45657e7	1.91113
$567$	74737.5	0.00976295
$568$	−1.64161e6	−0.213500
$569$	4.95052e6	0.641018	0.320509	−	0.947245i	$-0.396146\pi$
$569$	4.95052e6	0.641018	0.320509	+	0.947245i	$0.396146\pi$
$570$	−2.35293e6	−0.303334
$571$	−9.37371e6	−1.20315	−0.601577	−	0.798815i	$-0.705461\pi$
$571$	−9.37371e6	−1.20315	−0.601577	+	0.798815i	$0.705461\pi$
$572$	4.22181e7	5.39521
$573$	6.36944e6	0.810428
$574$	4.19410e6	0.531323
$575$	67333.1	0.00849296
$576$	4.53272e6	0.569250
$577$	5.34296e6	0.668101	0.334051	−	0.942555i	$-0.391584\pi$
$577$	5.34296e6	0.668101	0.334051	+	0.942555i	$0.391584\pi$
$578$	1.34568e7	1.67541
$579$	−1.08856e6	−0.134945
$580$	−1.17635e7	−1.45200
$581$	−9182.91	−0.00112860
$582$	1.88737e6	0.230967
$583$	−1.59613e7	−1.94490
$584$	5.69688e6	0.691202
$585$	−7.62567e6	−0.921273
$586$	1.01374e7	1.21951
$587$	−2.85180e6	−0.341604	−0.170802	−	0.985305i	$-0.554636\pi$
$587$	−2.85180e6	−0.341604	−0.170802	+	0.985305i	$0.554636\pi$
$588$	−1.48033e6	−0.176570
$589$	−62571.5	−0.00743170
$590$	1.22654e7	1.45062
$591$	−5.01180e6	−0.590235
$592$	4.96494e6	0.582251
$593$	−1.31653e7	−1.53742	−0.768711	−	0.639597i	$-0.779101\pi$
$593$	−1.31653e7	−1.53742	−0.768711	+	0.639597i	$0.779101\pi$
$594$	2.07421e7	2.41205
$595$	487018.	0.0563965
$596$	9.29553e6	1.07191
$597$	−6.86311e6	−0.788107
$598$	−602794.	−0.0689312
$599$	3.61831e6	0.412040	0.206020	−	0.978548i	$-0.433949\pi$
$599$	3.61831e6	0.412040	0.206020	+	0.978548i	$0.433949\pi$
$600$	−3.92865e6	−0.445518
$601$	2.88252e6	0.325526	0.162763	−	0.986665i	$-0.447959\pi$
$601$	2.88252e6	0.325526	0.162763	+	0.986665i	$0.447959\pi$
$602$	6.94604e6	0.781171
$603$	314764.	0.0352526
$604$	−2.09352e7	−2.33499
$605$	−6.59102e6	−0.732089
$606$	−1.98567e6	−0.219647
$607$	5.01887e6	0.552884	0.276442	−	0.961031i	$-0.410845\pi$
$607$	5.01887e6	0.552884	0.276442	+	0.961031i	$0.410845\pi$
$608$	−367491.	−0.0403169
$609$	−1.95670e6	−0.213787
$610$	−7.68066e6	−0.835745
$611$	−2.25149e6	−0.243987
$612$	2.29694e6	0.247897
$613$	−1.56247e6	−0.167943	−0.0839714	−	0.996468i	$-0.526760\pi$
$613$	−1.56247e6	−0.167943	−0.0839714	+	0.996468i	$0.526760\pi$
$614$	1.34944e7	1.44455
$615$	−3.54720e6	−0.378179
$616$	8.92200e6	0.947350
$617$	709146.	0.0749934	0.0374967	−	0.999297i	$-0.488062\pi$
$617$	709146.	0.0749934	0.0374967	+	0.999297i	$0.488062\pi$
$618$	2.22496e6	0.234343
$619$	1.24471e7	1.30569	0.652847	−	0.757490i	$-0.273575\pi$
$619$	1.24471e7	1.30569	0.652847	+	0.757490i	$0.273575\pi$
$620$	298736.	0.0312111
$621$	−198437.	−0.0206487
$622$	1.15080e7	1.19268
$623$	1.84118e6	0.190054
$624$	1.23060e7	1.26519
$625$	−4.15653e6	−0.425629
$626$	4.04991e6	0.413056
$627$	3.11402e6	0.316338
$628$	−1.82898e7	−1.85059
$629$	−1.02513e6	−0.103312
$630$	−3.17515e6	−0.318723
$631$	−1.84328e6	−0.184297	−0.0921484	−	0.995745i	$-0.529373\pi$
$631$	−1.84328e6	−0.184297	−0.0921484	+	0.995745i	$0.529373\pi$
$632$	−5.53019e6	−0.550741
$633$	−1.14639e7	−1.13716
$634$	−2.32640e6	−0.229859
$635$	−3.15896e6	−0.310892
$636$	−1.75540e7	−1.72081
$637$	−2.78256e6	−0.271704
$638$	2.32354e7	2.25995
$639$	−773185.	−0.0749086
$640$	−1.34153e7	−1.29464
$641$	−1.11187e7	−1.06883	−0.534414	−	0.845223i	$-0.679468\pi$
$641$	−1.11187e7	−1.06883	−0.534414	+	0.845223i	$0.679468\pi$
$642$	5.07964e6	0.486402
$643$	2.76977e6	0.264189	0.132095	−	0.991237i	$-0.457830\pi$
$643$	2.76977e6	0.264189	0.132095	+	0.991237i	$0.457830\pi$
$644$	−168172.	−0.0159787
$645$	−5.87468e6	−0.556013
$646$	1.33219e6	0.125599
$647$	−1.51870e7	−1.42630	−0.713151	−	0.701011i	$-0.752732\pi$
$647$	−1.51870e7	−1.42630	−0.713151	+	0.701011i	$0.752732\pi$
$648$	−495392.	−0.0463459
$649$	−1.62329e7	−1.51281
$650$	−1.45496e7	−1.35073
$651$	49690.7	0.00459539
$652$	−2.32241e7	−2.13954
$653$	4.74478e6	0.435445	0.217722	−	0.976011i	$-0.430137\pi$
$653$	4.74478e6	0.435445	0.217722	+	0.976011i	$0.430137\pi$
$654$	−3.30303e6	−0.301973
$655$	−8.89873e6	−0.810447
$656$	−9.72703e6	−0.882512
$657$	2.68319e6	0.242515
$658$	−937467.	−0.0844095
$659$	1.97055e6	0.176755	0.0883777	−	0.996087i	$-0.471832\pi$
$659$	1.97055e6	0.176755	0.0883777	+	0.996087i	$0.471832\pi$
$660$	−1.48673e7	−1.32853
$661$	−7.51404e6	−0.668913	−0.334457	−	0.942411i	$-0.608553\pi$
$661$	−7.51404e6	−0.668913	−0.334457	+	0.942411i	$0.608553\pi$
$662$	1.57592e7	1.39762
$663$	−2.54085e6	−0.224489
$664$	60868.2	0.00535760
$665$	−1.23390e6	−0.108200
$666$	6.68339e6	0.583863
$667$	−222290.	−0.0193466
$668$	2.83947e7	2.46205
$669$	−6.08043e6	−0.525253
$670$	−871589.	−0.0750110
$671$	1.01651e7	0.871575
$672$	291840.	0.0249300
$673$	1.44500e7	1.22979	0.614894	−	0.788610i	$-0.289199\pi$
$673$	1.44500e7	1.22979	0.614894	+	0.788610i	$0.289199\pi$
$674$	−3.35658e7	−2.84608
$675$	−4.78966e6	−0.404618
$676$	6.31484e7	5.31490
$677$	−2.24975e6	−0.188652	−0.0943261	−	0.995541i	$-0.530070\pi$
$677$	−2.24975e6	−0.188652	−0.0943261	+	0.995541i	$0.530070\pi$
$678$	−9.89820e6	−0.826955
$679$	989758.	0.0823862
$680$	−3.22816e6	−0.267721
$681$	1.15476e7	0.954168
$682$	−590066.	−0.0485780
$683$	910745.	0.0747042	0.0373521	−	0.999302i	$-0.488108\pi$
$683$	910745.	0.0747042	0.0373521	+	0.999302i	$0.488108\pi$
$684$	−5.81950e6	−0.475604
$685$	−807320.	−0.0657384
$686$	−1.15859e6	−0.0939985
$687$	−1.93741e6	−0.156613
$688$	−1.61094e7	−1.29750
$689$	−3.29960e7	−2.64797
$690$	212277.	0.0169738
$691$	−1.45001e7	−1.15525	−0.577626	−	0.816302i	$-0.696021\pi$
$691$	−1.45001e7	−1.15525	−0.577626	+	0.816302i	$0.696021\pi$
$692$	4.40928e7	3.50028
$693$	4.20220e6	0.332387
$694$	−1.62787e7	−1.28299
$695$	−8.77526e6	−0.689125
$696$	1.29698e7	1.01487
$697$	2.00837e6	0.156589
$698$	−2.92284e7	−2.27074
$699$	−9.56201e6	−0.740212
$700$	−4.05917e6	−0.313107
$701$	−1.48298e7	−1.13983	−0.569917	−	0.821702i	$-0.693025\pi$
$701$	−1.48298e7	−1.13983	−0.569917	+	0.821702i	$0.693025\pi$
$702$	4.28791e7	3.28400
$703$	2.59724e6	0.198209
$704$	1.66111e7	1.26319
$705$	792872.	0.0600801
$706$	5.86118e6	0.442562
$707$	−1.04131e6	−0.0783483
$708$	−1.78526e7	−1.33850
$709$	1.61993e7	1.21027	0.605134	−	0.796124i	$-0.293120\pi$
$709$	1.61993e7	1.21027	0.605134	+	0.796124i	$0.293120\pi$
$710$	2.14097e6	0.159392
$711$	−2.60468e6	−0.193233
$712$	−1.22041e7	−0.902209
$713$	5645.08	0.000415859 0
$714$	−1.05795e6	−0.0776639
$715$	−2.79459e7	−2.04434
$716$	−1.36039e7	−0.991698
$717$	−5.40017e6	−0.392292
$718$	4.07935e7	2.95311
$719$	−7.20949e6	−0.520095	−0.260047	−	0.965596i	$-0.583738\pi$
$719$	−7.20949e6	−0.520095	−0.260047	+	0.965596i	$0.583738\pi$
$720$	7.36387e6	0.529389
$721$	1.16679e6	0.0835903
$722$	2.10091e7	1.49991
$723$	−542546.	−0.0386003
$724$	−1.32013e7	−0.935985
$725$	−5.36541e6	−0.379104
$726$	1.43177e7	1.00816
$727$	−7.43790e6	−0.521932	−0.260966	−	0.965348i	$-0.584041\pi$
$727$	−7.43790e6	−0.521932	−0.260966	+	0.965348i	$0.584041\pi$
$728$	1.84440e7	1.28981
$729$	8.42906e6	0.587435
$730$	−7.42983e6	−0.516026
$731$	3.32615e6	0.230223
$732$	1.11794e7	0.771153
$733$	1.60482e6	0.110323	0.0551616	−	0.998477i	$-0.482433\pi$
$733$	1.60482e6	0.110323	0.0551616	+	0.998477i	$0.482433\pi$
$734$	2.39976e7	1.64410
$735$	979893.	0.0669052
$736$	33154.3	0.00225603
$737$	1.15352e6	0.0782268
$738$	−1.30937e7	−0.884956
$739$	−2.24574e7	−1.51268	−0.756341	−	0.654178i	$-0.773015\pi$
$739$	−2.24574e7	−1.51268	−0.756341	+	0.654178i	$0.773015\pi$
$740$	−1.24001e7	−0.832423
$741$	6.43744e6	0.430693
$742$	−1.37388e7	−0.916090
$743$	1.56980e7	1.04321	0.521607	−	0.853186i	$-0.325333\pi$
$743$	1.56980e7	1.04321	0.521607	+	0.853186i	$0.325333\pi$
$744$	−329371.	−0.0218149
$745$	−6.15309e6	−0.406165
$746$	−1.02614e7	−0.675086
$747$	28668.5	0.00187976
$748$	8.41763e6	0.550093
$749$	2.66382e6	0.173500
$750$	1.76834e7	1.14792
$751$	−1.21062e7	−0.783263	−0.391631	−	0.920122i	$-0.628089\pi$
$751$	−1.21062e7	−0.783263	−0.391631	+	0.920122i	$0.628089\pi$
$752$	2.17419e6	0.140202
$753$	1.01275e7	0.650898
$754$	4.80334e7	3.07691
$755$	1.38579e7	0.884768
$756$	1.19628e7	0.761249
$757$	−2.68176e7	−1.70091	−0.850453	−	0.526052i	$-0.823672\pi$
$757$	−2.68176e7	−1.70091	−0.850453	+	0.526052i	$0.823672\pi$
$758$	−1.66715e7	−1.05391
$759$	−280941.	−0.0177015
$760$	8.17880e6	0.513636
$761$	−2.28158e7	−1.42815	−0.714075	−	0.700069i	$-0.753152\pi$
$761$	−2.28158e7	−1.42815	−0.714075	+	0.700069i	$0.753152\pi$
$762$	6.86221e6	0.428131
$763$	−1.73214e6	−0.107714
$764$	−4.36220e7	−2.70378
$765$	−1.52044e6	−0.0939324
$766$	−4.79142e7	−2.95048
$767$	−3.35573e7	−2.05968
$768$	2.01455e7	1.23247
$769$	1.97103e7	1.20192	0.600962	−	0.799278i	$-0.294784\pi$
$769$	1.97103e7	1.20192	0.600962	+	0.799278i	$0.294784\pi$
$770$	−1.16360e7	−0.707257
$771$	−1.08353e7	−0.656457
$772$	7.45517e6	0.450209
$773$	−1.35016e7	−0.812713	−0.406356	−	0.913715i	$-0.633201\pi$
$773$	−1.35016e7	−0.812713	−0.406356	+	0.913715i	$0.633201\pi$
$774$	−2.16851e7	−1.30110
$775$	136255.	0.00814890
$776$	−6.56053e6	−0.391097
$777$	−2.06258e6	−0.122563
$778$	−6.84608e6	−0.405502
$779$	−5.08836e6	−0.300424
$780$	−3.07344e7	−1.80879
$781$	−2.83350e6	−0.166225
$782$	−120188.	−0.00702818
$783$	1.58124e7	0.921705
$784$	2.68703e6	0.156129
$785$	1.21068e7	0.701219
$786$	1.93307e7	1.11607
$787$	−2.36060e7	−1.35858	−0.679291	−	0.733869i	$-0.737713\pi$
$787$	−2.36060e7	−1.35858	−0.679291	+	0.733869i	$0.737713\pi$
$788$	3.43240e7	1.96917
$789$	4.70534e6	0.269090
$790$	7.21244e6	0.411163
$791$	−5.19072e6	−0.294976
$792$	−2.78539e7	−1.57788
$793$	2.10137e7	1.18664
$794$	−2.36816e7	−1.33309
$795$	1.16197e7	0.652044
$796$	4.70030e7	2.62932
$797$	−1.34192e7	−0.748309	−0.374154	−	0.927366i	$-0.622067\pi$
$797$	−1.34192e7	−0.748309	−0.374154	+	0.927366i	$0.622067\pi$
$798$	2.68040e6	0.149002
$799$	−448912.	−0.0248768
$800$	800245.	0.0442077
$801$	−5.74806e6	−0.316548
$802$	−3.19769e7	−1.75550
$803$	9.83312e6	0.538149
$804$	1.26862e6	0.0692136
$805$	111320.	0.00605458
$806$	−1.21981e6	−0.0661387
$807$	7.77896e6	0.420473
$808$	6.90221e6	0.371929
$809$	−306511.	−0.0164655	−0.00823275	−	0.999966i	$-0.502621\pi$
$809$	−306511.	−0.0164655	−0.00823275	+	0.999966i	$0.502621\pi$
$810$	646086.	0.0346001
$811$	1.07206e7	0.572355	0.286178	−	0.958177i	$-0.407615\pi$
$811$	1.07206e7	0.572355	0.286178	+	0.958177i	$0.407615\pi$
$812$	1.34008e7	0.713246
$813$	2.10050e7	1.11454
$814$	2.44927e7	1.29561
$815$	1.53730e7	0.810707
$816$	2.45362e6	0.128998
$817$	−8.42708e6	−0.441695
$818$	−904118.	−0.0472435
$819$	8.68699e6	0.452543
$820$	2.42935e7	1.26170
$821$	1.01744e7	0.526808	0.263404	−	0.964686i	$-0.415155\pi$
$821$	1.01744e7	0.526808	0.263404	+	0.964686i	$0.415155\pi$
$822$	1.75374e6	0.0905287
$823$	−3.34132e6	−0.171956	−0.0859782	−	0.996297i	$-0.527402\pi$
$823$	−3.34132e6	−0.171956	−0.0859782	+	0.996297i	$0.527402\pi$
$824$	−7.73400e6	−0.396813
$825$	−6.78106e6	−0.346867
$826$	−1.39725e7	−0.712564
$827$	3.57710e7	1.81873	0.909363	−	0.416003i	$-0.136569\pi$
$827$	3.57710e7	1.81873	0.909363	+	0.416003i	$0.136569\pi$
$828$	525024.	0.0266136
$829$	3.22764e7	1.63117	0.815584	−	0.578639i	$-0.196416\pi$
$829$	3.22764e7	1.63117	0.815584	+	0.578639i	$0.196416\pi$
$830$	−79383.8	−0.00399979
$831$	750898.	0.0377206
$832$	3.43393e7	1.71982
$833$	−554800.	−0.0277028
$834$	1.90625e7	0.948998
$835$	−1.87956e7	−0.932910
$836$	−2.13268e7	−1.05538
$837$	−401557.	−0.0198122
$838$	−1.08491e7	−0.533681
$839$	2.07196e7	1.01620	0.508098	−	0.861299i	$-0.330349\pi$
$839$	2.07196e7	1.01620	0.508098	+	0.861299i	$0.330349\pi$
$840$	−6.49514e6	−0.317607
$841$	−2.79806e6	−0.136416
$842$	6.51014e7	3.16454
$843$	−1.30266e7	−0.631337
$844$	7.85120e7	3.79385
$845$	−4.18004e7	−2.01391
$846$	2.92672e6	0.140590
$847$	7.50834e6	0.359613
$848$	3.18632e7	1.52160
$849$	1.40336e7	0.668192
$850$	−2.90097e6	−0.137719
$851$	−234318.	−0.0110913
$852$	−3.11624e6	−0.147073
$853$	−2.94258e7	−1.38470	−0.692351	−	0.721561i	$-0.743425\pi$
$853$	−2.94258e7	−1.38470	−0.692351	+	0.721561i	$0.743425\pi$
$854$	8.74964e6	0.410530
$855$	3.85216e6	0.180214
$856$	−1.76569e7	−0.823626
$857$	5.21841e6	0.242709	0.121355	−	0.992609i	$-0.461276\pi$
$857$	5.21841e6	0.242709	0.121355	+	0.992609i	$0.461276\pi$
$858$	6.07068e7	2.81527
$859$	1.97131e7	0.911531	0.455766	−	0.890100i	$-0.349366\pi$
$859$	1.97131e7	0.911531	0.455766	+	0.890100i	$0.349366\pi$
$860$	4.02336e7	1.85499
$861$	4.04089e6	0.185767
$862$	3.41463e7	1.56522
$863$	−2.25068e7	−1.02869	−0.514347	−	0.857582i	$-0.671966\pi$
$863$	−2.25068e7	−1.02869	−0.514347	+	0.857582i	$0.671966\pi$
$864$	−2.35839e6	−0.107481
$865$	−2.91868e7	−1.32631
$866$	−2.25588e7	−1.02217
$867$	1.29652e7	0.585777
$868$	−340314.	−0.0153313
$869$	−9.54540e6	−0.428790
$870$	−1.69152e7	−0.757667
$871$	2.38461e6	0.106505
$872$	1.14814e7	0.511331
$873$	−3.08996e6	−0.137220
$874$	304505.	0.0134839
$875$	9.27337e6	0.409466
$876$	1.08143e7	0.476144
$877$	3.12030e7	1.36993	0.684963	−	0.728578i	$-0.259819\pi$
$877$	3.12030e7	1.36993	0.684963	+	0.728578i	$0.259819\pi$
$878$	−2.19612e6	−0.0961434
$879$	9.76713e6	0.426378
$880$	2.69865e7	1.17473
$881$	1.81502e7	0.787847	0.393923	−	0.919143i	$-0.371117\pi$
$881$	1.81502e7	0.787847	0.393923	+	0.919143i	$0.371117\pi$
$882$	3.61706e6	0.156561
$883$	−2.14832e7	−0.927249	−0.463624	−	0.886032i	$-0.653451\pi$
$883$	−2.14832e7	−0.927249	−0.463624	+	0.886032i	$0.653451\pi$
$884$	1.74013e7	0.748949
$885$	1.18174e7	0.507181
$886$	1.19456e7	0.511240
$887$	9.65327e6	0.411970	0.205985	−	0.978555i	$-0.433960\pi$
$887$	9.65327e6	0.411970	0.205985	+	0.978555i	$0.433960\pi$
$888$	1.36716e7	0.581820
$889$	3.59861e6	0.152715
$890$	1.59166e7	0.673556
$891$	−855072.	−0.0360835
$892$	4.16426e7	1.75237
$893$	1.13735e6	0.0477274
$894$	1.33664e7	0.559332
$895$	9.00494e6	0.375771
$896$	1.52824e7	0.635946
$897$	−580774.	−0.0241005
$898$	−5.72090e7	−2.36741
$899$	−449826.	−0.0185629
$900$	1.26725e7	0.521502
$901$	−6.57889e6	−0.269986
$902$	−4.79846e7	−1.96375
$903$	6.69231e6	0.273122
$904$	3.44063e7	1.40028
$905$	8.73844e6	0.354660
$906$	−3.01035e7	−1.21842
$907$	1.19015e7	0.480378	0.240189	−	0.970726i	$-0.422791\pi$
$907$	1.19015e7	0.480378	0.240189	+	0.970726i	$0.422791\pi$
$908$	−7.90855e7	−3.18334
$909$	3.25089e6	0.130495
$910$	−2.40545e7	−0.962927
$911$	−2.91763e7	−1.16475	−0.582377	−	0.812919i	$-0.697877\pi$
$911$	−2.91763e7	−1.16475	−0.582377	+	0.812919i	$0.697877\pi$
$912$	−6.21644e6	−0.247488
$913$	105062.	0.00417126
$914$	−2.63839e7	−1.04466
$915$	−7.40009e6	−0.292203
$916$	1.32686e7	0.522500
$917$	1.01372e7	0.398104
$918$	8.54942e6	0.334834
$919$	−1.27117e7	−0.496494	−0.248247	−	0.968697i	$-0.579854\pi$
$919$	−1.27117e7	−0.496494	−0.248247	+	0.968697i	$0.579854\pi$
$920$	−737876.	−0.0287418
$921$	1.30014e7	0.505058
$922$	3.45044e7	1.33674
$923$	−5.85755e6	−0.226314
$924$	1.69365e7	0.652595
$925$	−5.65573e6	−0.217337
$926$	−5.28590e7	−2.02578
$927$	−3.64266e6	−0.139226
$928$	−2.64189e6	−0.100703
$929$	−3.35158e7	−1.27412	−0.637060	−	0.770814i	$-0.719850\pi$
$929$	−3.35158e7	−1.27412	−0.637060	+	0.770814i	$0.719850\pi$
$930$	429563.	0.0162862
$931$	1.40563e6	0.0531492
$932$	6.54868e7	2.46953
$933$	1.10876e7	0.416998
$934$	−5.03889e7	−1.89003
$935$	−5.57197e6	−0.208439
$936$	−5.75810e7	−2.14827
$937$	−502740.	−0.0187066	−0.00935329	−	0.999956i	$-0.502977\pi$
$937$	−502740.	−0.0187066	−0.00935329	+	0.999956i	$0.502977\pi$
$938$	992895.	0.0368465
$939$	3.90197e6	0.144417
$940$	−5.43010e6	−0.200442
$941$	−9.99890e6	−0.368111	−0.184055	−	0.982916i	$-0.558923\pi$
$941$	−9.99890e6	−0.368111	−0.184055	+	0.982916i	$0.558923\pi$
$942$	−2.62995e7	−0.965653
$943$	459063.	0.0168110
$944$	3.24053e7	1.18355
$945$	−7.91863e6	−0.288450
$946$	−7.94697e7	−2.88718
$947$	−3.75085e7	−1.35911	−0.679555	−	0.733625i	$-0.737827\pi$
$947$	−3.75085e7	−1.35911	−0.679555	+	0.733625i	$0.737827\pi$
$948$	−1.04979e7	−0.379386
$949$	2.03275e7	0.732687
$950$	7.34984e6	0.264222
$951$	−2.24142e6	−0.0803660
$952$	3.67744e6	0.131508
$953$	−3.86996e7	−1.38030	−0.690151	−	0.723665i	$-0.742456\pi$
$953$	−3.86996e7	−1.38030	−0.690151	+	0.723665i	$0.742456\pi$
$954$	4.28916e7	1.52581
$955$	2.88751e7	1.02451
$956$	3.69838e7	1.30878
$957$	2.23866e7	0.790149
$958$	−3.10542e7	−1.09322
$959$	919681.	0.0322917
$960$	−1.20927e7	−0.423494
$961$	−2.86177e7	−0.999601
$962$	5.06325e7	1.76397
$963$	−8.31627e6	−0.288977
$964$	3.71570e6	0.128780
$965$	−4.93488e6	−0.170592
$966$	−241821.	−0.00833779
$967$	2.55053e7	0.877131	0.438565	−	0.898699i	$-0.355487\pi$
$967$	2.55053e7	0.877131	0.438565	+	0.898699i	$0.355487\pi$
$968$	−4.97684e7	−1.70713
$969$	1.28353e6	0.0439132
$970$	8.55620e6	0.291979
$971$	4.02894e7	1.37133	0.685666	−	0.727916i	$-0.259511\pi$
$971$	4.02894e7	1.37133	0.685666	+	0.727916i	$0.259511\pi$
$972$	−6.02659e7	−2.04600
$973$	9.99658e6	0.338508
$974$	−1.42996e7	−0.482977
$975$	−1.40181e7	−0.472257
$976$	−2.02923e7	−0.681879
$977$	−1.04511e7	−0.350288	−0.175144	−	0.984543i	$-0.556039\pi$
$977$	−1.04511e7	−0.350288	−0.175144	+	0.984543i	$0.556039\pi$
$978$	−3.33947e7	−1.11643
$979$	−2.10650e7	−0.702432
$980$	−6.71093e6	−0.223212
$981$	5.40764e6	0.179405
$982$	−1.11427e7	−0.368734
$983$	4.27191e7	1.41006	0.705032	−	0.709176i	$-0.250933\pi$
$983$	4.27191e7	1.41006	0.705032	+	0.709176i	$0.250933\pi$
$984$	−2.67847e7	−0.881859
$985$	−2.27204e7	−0.746150
$986$	9.57711e6	0.313720
$987$	−903222.	−0.0295122
$988$	−4.40877e7	−1.43690
$989$	760276.	0.0247161
$990$	3.63269e7	1.17799
$991$	−4.52698e7	−1.46428	−0.732140	−	0.681154i	$-0.761478\pi$
$991$	−4.52698e7	−1.46428	−0.732140	+	0.681154i	$0.761478\pi$
$992$	67091.0	0.00216464
$993$	1.51835e7	0.488651
$994$	−2.43895e6	−0.0782955
$995$	−3.11132e7	−0.996292
$996$	115545.	0.00369066
$997$	−7.19964e6	−0.229389	−0.114695	−	0.993401i	$-0.536589\pi$
$997$	−7.19964e6	−0.229389	−0.114695	+	0.993401i	$0.536589\pi$
$998$	9.66331e7	3.07114
$999$	1.66680e7	0.528407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	959.6.a.a.1.6	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.6.a.a.1.6	✓	74	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:	\( N \)	\(=\)	\( 959 = 7 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	959.a (trivial)

\(f(q)\)	\(=\)	\(q-9.84789 q^{2} -9.48815 q^{3} +64.9809 q^{4} -43.0135 q^{5} +93.4383 q^{6} +49.0000 q^{7} -324.793 q^{8} -152.975 q^{9} +O(q^{10})\)	\(q-9.84789 q^{2} -9.48815 q^{3} +64.9809 q^{4} -43.0135 q^{5} +93.4383 q^{6} +49.0000 q^{7} -324.793 q^{8} -152.975 q^{9} +423.592 q^{10} -560.609 q^{11} -616.549 q^{12} -1158.92 q^{13} -482.547 q^{14} +408.119 q^{15} +1119.13 q^{16} -231.070 q^{17} +1506.48 q^{18} +585.435 q^{19} -2795.06 q^{20} -464.919 q^{21} +5520.82 q^{22} -52.8169 q^{23} +3081.68 q^{24} -1274.84 q^{25} +11412.9 q^{26} +3757.07 q^{27} +3184.07 q^{28} +4208.69 q^{29} -4019.11 q^{30} -106.880 q^{31} -627.722 q^{32} +5319.14 q^{33} +2275.55 q^{34} -2107.66 q^{35} -9940.46 q^{36} +4436.42 q^{37} -5765.30 q^{38} +10996.0 q^{39} +13970.5 q^{40} -8691.59 q^{41} +4578.48 q^{42} -14394.6 q^{43} -36428.9 q^{44} +6579.99 q^{45} +520.135 q^{46} +1942.75 q^{47} -10618.5 q^{48} +2401.00 q^{49} +12554.5 q^{50} +2192.43 q^{51} -75307.6 q^{52} +28471.4 q^{53} -36999.2 q^{54} +24113.7 q^{55} -15914.8 q^{56} -5554.70 q^{57} -41446.7 q^{58} +28955.8 q^{59} +26519.9 q^{60} -18132.2 q^{61} +1052.54 q^{62} -7495.77 q^{63} -29630.5 q^{64} +49849.1 q^{65} -52382.3 q^{66} -2057.61 q^{67} -15015.2 q^{68} +501.135 q^{69} +20756.0 q^{70} +5054.33 q^{71} +49685.1 q^{72} -17540.1 q^{73} -43689.4 q^{74} +12095.9 q^{75} +38042.1 q^{76} -27469.8 q^{77} -108287. q^{78} +17026.8 q^{79} -48137.7 q^{80} +1525.26 q^{81} +85593.8 q^{82} -187.406 q^{83} -30210.9 q^{84} +9939.13 q^{85} +141756. q^{86} -39932.7 q^{87} +182082. q^{88} +37575.2 q^{89} -64799.0 q^{90} -56787.0 q^{91} -3432.09 q^{92} +1014.10 q^{93} -19132.0 q^{94} -25181.6 q^{95} +5955.92 q^{96} +20199.1 q^{97} -23644.8 q^{98} +85759.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9}+O(q^{10}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9} - 1322 q^{10} - 1446 q^{11} - 1466 q^{12} - 1746 q^{13} - 980 q^{14} - 4313 q^{15} + 9208 q^{16} - 3681 q^{17} - 10234 q^{18} - 2860 q^{19} - 7308 q^{20} - 2401 q^{21} - 13879 q^{22} - 13685 q^{23} - 13424 q^{24} + 18155 q^{25} - 9144 q^{26} - 6865 q^{27} + 47824 q^{28} - 19489 q^{29} + 2307 q^{30} - 33560 q^{31} - 27274 q^{32} - 40132 q^{33} - 35811 q^{34} - 8281 q^{35} - 27689 q^{36} - 70663 q^{37} - 37203 q^{38} - 51201 q^{39} - 86817 q^{40} - 67917 q^{41} - 13377 q^{42} - 104475 q^{43} - 45827 q^{44} - 93598 q^{45} - 137776 q^{46} - 43192 q^{47} - 135425 q^{48} + 177674 q^{49} - 73802 q^{50} - 110795 q^{51} - 107131 q^{52} - 99015 q^{53} - 46226 q^{54} - 71678 q^{55} - 36603 q^{56} - 146490 q^{57} - 143069 q^{58} - 12512 q^{59} - 177875 q^{60} - 125581 q^{61} - 75283 q^{62} + 209475 q^{63} - 8449 q^{64} - 95447 q^{65} + 213311 q^{66} - 282713 q^{67} + 191684 q^{68} - 171171 q^{69} - 64778 q^{70} - 189029 q^{71} + 20181 q^{72} - 96401 q^{73} - 96089 q^{74} - 21522 q^{75} - 276776 q^{76} - 70854 q^{77} + 106155 q^{78} - 454125 q^{79} + 253095 q^{80} + 12226 q^{81} + 107086 q^{82} - 168146 q^{83} - 71834 q^{84} - 329524 q^{85} + 191853 q^{86} + 61244 q^{87} - 505209 q^{88} - 325374 q^{89} - 277645 q^{90} - 85554 q^{91} - 189827 q^{92} - 347054 q^{93} - 125581 q^{94} - 343566 q^{95} + 289017 q^{96} - 844266 q^{97} - 48020 q^{98} - 490575 q^{99}+O(q^{100}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9 - 1322 * q^10 - 1446 * q^11 - 1466 * q^12 - 1746 * q^13 - 980 * q^14 - 4313 * q^15 + 9208 * q^16 - 3681 * q^17 - 10234 * q^18 - 2860 * q^19 - 7308 * q^20 - 2401 * q^21 - 13879 * q^22 - 13685 * q^23 - 13424 * q^24 + 18155 * q^25 - 9144 * q^26 - 6865 * q^27 + 47824 * q^28 - 19489 * q^29 + 2307 * q^30 - 33560 * q^31 - 27274 * q^32 - 40132 * q^33 - 35811 * q^34 - 8281 * q^35 - 27689 * q^36 - 70663 * q^37 - 37203 * q^38 - 51201 * q^39 - 86817 * q^40 - 67917 * q^41 - 13377 * q^42 - 104475 * q^43 - 45827 * q^44 - 93598 * q^45 - 137776 * q^46 - 43192 * q^47 - 135425 * q^48 + 177674 * q^49 - 73802 * q^50 - 110795 * q^51 - 107131 * q^52 - 99015 * q^53 - 46226 * q^54 - 71678 * q^55 - 36603 * q^56 - 146490 * q^57 - 143069 * q^58 - 12512 * q^59 - 177875 * q^60 - 125581 * q^61 - 75283 * q^62 + 209475 * q^63 - 8449 * q^64 - 95447 * q^65 + 213311 * q^66 - 282713 * q^67 + 191684 * q^68 - 171171 * q^69 - 64778 * q^70 - 189029 * q^71 + 20181 * q^72 - 96401 * q^73 - 96089 * q^74 - 21522 * q^75 - 276776 * q^76 - 70854 * q^77 + 106155 * q^78 - 454125 * q^79 + 253095 * q^80 + 12226 * q^81 + 107086 * q^82 - 168146 * q^83 - 71834 * q^84 - 329524 * q^85 + 191853 * q^86 + 61244 * q^87 - 505209 * q^88 - 325374 * q^89 - 277645 * q^90 - 85554 * q^91 - 189827 * q^92 - 347054 * q^93 - 125581 * q^94 - 343566 * q^95 + 289017 * q^96 - 844266 * q^97 - 48020 * q^98 - 490575 * q^99

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