LMFDB - Embedded newform 354.6.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, 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("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.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:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 17196 x^{6} - 154000 x^{5} + 98085975 x^{4} + 1816612536 x^{3} - 184506058580 x^{2} + \cdots - 7060184373200 $ x^8 - 17196x^6 - 154000x^5 + 98085975x^4 + 1816612536x^3 - 184506058580x^2 - 5340414471536x - 7060184373200
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$75.7365$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +80.7365 q^{5} -36.0000 q^{6} +18.8441 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +80.7365 q^{5} -36.0000 q^{6} +18.8441 q^{7} -64.0000 q^{8} +81.0000 q^{9} -322.946 q^{10} -625.051 q^{11} +144.000 q^{12} -1082.96 q^{13} -75.3765 q^{14} +726.629 q^{15} +256.000 q^{16} +469.911 q^{17} -324.000 q^{18} +2697.80 q^{19} +1291.78 q^{20} +169.597 q^{21} +2500.21 q^{22} +4017.69 q^{23} -576.000 q^{24} +3393.38 q^{25} +4331.85 q^{26} +729.000 q^{27} +301.506 q^{28} +1001.51 q^{29} -2906.51 q^{30} -7363.30 q^{31} -1024.00 q^{32} -5625.46 q^{33} -1879.64 q^{34} +1521.41 q^{35} +1296.00 q^{36} +14138.4 q^{37} -10791.2 q^{38} -9746.67 q^{39} -5167.14 q^{40} +14329.5 q^{41} -678.388 q^{42} +21707.7 q^{43} -10000.8 q^{44} +6539.66 q^{45} -16070.7 q^{46} -3809.82 q^{47} +2304.00 q^{48} -16451.9 q^{49} -13573.5 q^{50} +4229.20 q^{51} -17327.4 q^{52} +31460.9 q^{53} -2916.00 q^{54} -50464.5 q^{55} -1206.02 q^{56} +24280.2 q^{57} -4006.03 q^{58} -3481.00 q^{59} +11626.1 q^{60} +31106.0 q^{61} +29453.2 q^{62} +1526.37 q^{63} +4096.00 q^{64} -87434.7 q^{65} +22501.8 q^{66} +51188.5 q^{67} +7518.58 q^{68} +36159.2 q^{69} -6085.63 q^{70} -26720.0 q^{71} -5184.00 q^{72} -58290.0 q^{73} -56553.7 q^{74} +30540.5 q^{75} +43164.9 q^{76} -11778.5 q^{77} +38986.7 q^{78} -4811.15 q^{79} +20668.5 q^{80} +6561.00 q^{81} -57318.0 q^{82} -4782.89 q^{83} +2713.55 q^{84} +37939.0 q^{85} -86830.8 q^{86} +9013.57 q^{87} +40003.3 q^{88} +13333.2 q^{89} -26158.6 q^{90} -20407.5 q^{91} +64283.0 q^{92} -66269.7 q^{93} +15239.3 q^{94} +217811. q^{95} -9216.00 q^{96} -31742.0 q^{97} +65807.6 q^{98} -50629.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9}+O(q^{10}) $ 8 * q - 32 * q^2 + 72 * q^3 + 128 * q^4 + 40 * q^5 - 288 * q^6 + 181 * q^7 - 512 * q^8 + 648 * q^9	\( 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9} - 160 q^{10} - 349 q^{11} + 1152 q^{12} + 121 q^{13} - 724 q^{14} + 360 q^{15} + 2048 q^{16} + 437 q^{17} - 2592 q^{18} + 1314 q^{19} + 640 q^{20} + 1629 q^{21} + 1396 q^{22} + 1224 q^{23} - 4608 q^{24} + 9592 q^{25} - 484 q^{26} + 5832 q^{27} + 2896 q^{28} + 5276 q^{29} - 1440 q^{30} + 18332 q^{31} - 8192 q^{32} - 3141 q^{33} - 1748 q^{34} + 19518 q^{35} + 10368 q^{36} + 30331 q^{37} - 5256 q^{38} + 1089 q^{39} - 2560 q^{40} + 8323 q^{41} - 6516 q^{42} + 30851 q^{43} - 5584 q^{44} + 3240 q^{45} - 4896 q^{46} - 5730 q^{47} + 18432 q^{48} + 32295 q^{49} - 38368 q^{50} + 3933 q^{51} + 1936 q^{52} - 33524 q^{53} - 23328 q^{54} + 23660 q^{55} - 11584 q^{56} + 11826 q^{57} - 21104 q^{58} - 27848 q^{59} + 5760 q^{60} + 2692 q^{61} - 73328 q^{62} + 14661 q^{63} + 32768 q^{64} - 59892 q^{65} + 12564 q^{66} + 56244 q^{67} + 6992 q^{68} + 11016 q^{69} - 78072 q^{70} - 48473 q^{71} - 41472 q^{72} - 30796 q^{73} - 121324 q^{74} + 86328 q^{75} + 21024 q^{76} + 59683 q^{77} - 4356 q^{78} + 135513 q^{79} + 10240 q^{80} + 52488 q^{81} - 33292 q^{82} - 88111 q^{83} + 26064 q^{84} + 114418 q^{85} - 123404 q^{86} + 47484 q^{87} + 22336 q^{88} - 112196 q^{89} - 12960 q^{90} + 377433 q^{91} + 19584 q^{92} + 164988 q^{93} + 22920 q^{94} + 328146 q^{95} - 73728 q^{96} + 551378 q^{97} - 129180 q^{98} - 28269 q^{99}+O(q^{100}) \) 8 * q - 32 * q^2 + 72 * q^3 + 128 * q^4 + 40 * q^5 - 288 * q^6 + 181 * q^7 - 512 * q^8 + 648 * q^9 - 160 * q^10 - 349 * q^11 + 1152 * q^12 + 121 * q^13 - 724 * q^14 + 360 * q^15 + 2048 * q^16 + 437 * q^17 - 2592 * q^18 + 1314 * q^19 + 640 * q^20 + 1629 * q^21 + 1396 * q^22 + 1224 * q^23 - 4608 * q^24 + 9592 * q^25 - 484 * q^26 + 5832 * q^27 + 2896 * q^28 + 5276 * q^29 - 1440 * q^30 + 18332 * q^31 - 8192 * q^32 - 3141 * q^33 - 1748 * q^34 + 19518 * q^35 + 10368 * q^36 + 30331 * q^37 - 5256 * q^38 + 1089 * q^39 - 2560 * q^40 + 8323 * q^41 - 6516 * q^42 + 30851 * q^43 - 5584 * q^44 + 3240 * q^45 - 4896 * q^46 - 5730 * q^47 + 18432 * q^48 + 32295 * q^49 - 38368 * q^50 + 3933 * q^51 + 1936 * q^52 - 33524 * q^53 - 23328 * q^54 + 23660 * q^55 - 11584 * q^56 + 11826 * q^57 - 21104 * q^58 - 27848 * q^59 + 5760 * q^60 + 2692 * q^61 - 73328 * q^62 + 14661 * q^63 + 32768 * q^64 - 59892 * q^65 + 12564 * q^66 + 56244 * q^67 + 6992 * q^68 + 11016 * q^69 - 78072 * q^70 - 48473 * q^71 - 41472 * q^72 - 30796 * q^73 - 121324 * q^74 + 86328 * q^75 + 21024 * q^76 + 59683 * q^77 - 4356 * q^78 + 135513 * q^79 + 10240 * q^80 + 52488 * q^81 - 33292 * q^82 - 88111 * q^83 + 26064 * q^84 + 114418 * q^85 - 123404 * q^86 + 47484 * q^87 + 22336 * q^88 - 112196 * q^89 - 12960 * q^90 + 377433 * q^91 + 19584 * q^92 + 164988 * q^93 + 22920 * q^94 + 328146 * q^95 - 73728 * q^96 + 551378 * q^97 - 129180 * q^98 - 28269 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	80.7365	1.44426	0.722129	−	0.691758i	$-0.243164\pi$
$5$	80.7365	1.44426	0.722129	+	0.691758i	$0.243164\pi$
$6$	−36.0000	−0.408248
$7$	18.8441	0.145355	0.0726776	−	0.997355i	$-0.476846\pi$
$7$	18.8441	0.145355	0.0726776	+	0.997355i	$0.476846\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−322.946	−1.02125
$11$	−625.051	−1.55752	−0.778761	−	0.627321i	$-0.784151\pi$
$11$	−625.051	−1.55752	−0.778761	+	0.627321i	$0.784151\pi$
$12$	144.000	0.288675
$13$	−1082.96	−1.77728	−0.888639	−	0.458607i	$-0.848349\pi$
$13$	−1082.96	−1.77728	−0.888639	+	0.458607i	$0.848349\pi$
$14$	−75.3765	−0.102782
$15$	726.629	0.833843
$16$	256.000	0.250000
$17$	469.911	0.394361	0.197180	−	0.980367i	$-0.436822\pi$
$17$	469.911	0.394361	0.197180	+	0.980367i	$0.436822\pi$
$18$	−324.000	−0.235702
$19$	2697.80	1.71446	0.857228	−	0.514937i	$-0.172185\pi$
$19$	2697.80	1.71446	0.857228	+	0.514937i	$0.172185\pi$
$20$	1291.78	0.722129
$21$	169.597	0.0839209
$22$	2500.21	1.10133
$23$	4017.69	1.58364	0.791820	−	0.610755i	$-0.209134\pi$
$23$	4017.69	1.58364	0.791820	+	0.610755i	$0.209134\pi$
$24$	−576.000	−0.204124
$25$	3393.38	1.08588
$26$	4331.85	1.25673
$27$	729.000	0.192450
$28$	301.506	0.0726776
$29$	1001.51	0.221136	0.110568	−	0.993869i	$-0.464733\pi$
$29$	1001.51	0.221136	0.110568	+	0.993869i	$0.464733\pi$
$30$	−2906.51	−0.589616
$31$	−7363.30	−1.37616	−0.688079	−	0.725636i	$-0.741546\pi$
$31$	−7363.30	−1.37616	−0.688079	+	0.725636i	$0.741546\pi$
$32$	−1024.00	−0.176777
$33$	−5625.46	−0.899235
$34$	−1879.64	−0.278855
$35$	1521.41	0.209931
$36$	1296.00	0.166667
$37$	14138.4	1.69784	0.848920	−	0.528522i	$-0.177254\pi$
$37$	14138.4	1.69784	0.848920	+	0.528522i	$0.177254\pi$
$38$	−10791.2	−1.21230
$39$	−9746.67	−1.02611
$40$	−5167.14	−0.510623
$41$	14329.5	1.33129	0.665643	−	0.746271i	$-0.268157\pi$
$41$	14329.5	1.33129	0.665643	+	0.746271i	$0.268157\pi$
$42$	−678.388	−0.0593410
$43$	21707.7	1.79037	0.895185	−	0.445695i	$-0.147043\pi$
$43$	21707.7	1.79037	0.895185	+	0.445695i	$0.147043\pi$
$44$	−10000.8	−0.778761
$45$	6539.66	0.481420
$46$	−16070.7	−1.11980
$47$	−3809.82	−0.251571	−0.125785	−	0.992057i	$-0.540145\pi$
$47$	−3809.82	−0.251571	−0.125785	+	0.992057i	$0.540145\pi$
$48$	2304.00	0.144338
$49$	−16451.9	−0.978872
$50$	−13573.5	−0.767835
$51$	4229.20	0.227684
$52$	−17327.4	−0.888639
$53$	31460.9	1.53844	0.769222	−	0.638981i	$-0.220644\pi$
$53$	31460.9	1.53844	0.769222	+	0.638981i	$0.220644\pi$
$54$	−2916.00	−0.136083
$55$	−50464.5	−2.24946
$56$	−1206.02	−0.0513908
$57$	24280.2	0.989842
$58$	−4006.03	−0.156367
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	11626.1	0.416922
$61$	31106.0	1.07034	0.535168	−	0.844746i	$-0.320248\pi$
$61$	31106.0	1.07034	0.535168	+	0.844746i	$0.320248\pi$
$62$	29453.2	0.973090
$63$	1526.37	0.0484517
$64$	4096.00	0.125000
$65$	−87434.7	−2.56685
$66$	22501.8	0.635855
$67$	51188.5	1.39311	0.696555	−	0.717504i	$-0.254715\pi$
$67$	51188.5	1.39311	0.696555	+	0.717504i	$0.254715\pi$
$68$	7518.58	0.197180
$69$	36159.2	0.914315
$70$	−6085.63	−0.148443
$71$	−26720.0	−0.629058	−0.314529	−	0.949248i	$-0.601847\pi$
$71$	−26720.0	−0.629058	−0.314529	+	0.949248i	$0.601847\pi$
$72$	−5184.00	−0.117851
$73$	−58290.0	−1.28023	−0.640114	−	0.768280i	$-0.721113\pi$
$73$	−58290.0	−1.28023	−0.640114	+	0.768280i	$0.721113\pi$
$74$	−56553.7	−1.20055
$75$	30540.5	0.626935
$76$	43164.9	0.857228
$77$	−11778.5	−0.226394
$78$	38986.7	0.725571
$79$	−4811.15	−0.0867323	−0.0433661	−	0.999059i	$-0.513808\pi$
$79$	−4811.15	−0.0867323	−0.0433661	+	0.999059i	$0.513808\pi$
$80$	20668.5	0.361065
$81$	6561.00	0.111111
$82$	−57318.0	−0.941361
$83$	−4782.89	−0.0762071	−0.0381035	−	0.999274i	$-0.512132\pi$
$83$	−4782.89	−0.0762071	−0.0381035	+	0.999274i	$0.512132\pi$
$84$	2713.55	0.0419604
$85$	37939.0	0.569559
$86$	−86830.8	−1.26598
$87$	9013.57	0.127673
$88$	40003.3	0.550667
$89$	13333.2	0.178427	0.0892135	−	0.996013i	$-0.471565\pi$
$89$	13333.2	0.178427	0.0892135	+	0.996013i	$0.471565\pi$
$90$	−26158.6	−0.340415
$91$	−20407.5	−0.258337
$92$	64283.0	0.791820
$93$	−66269.7	−0.794525
$94$	15239.3	0.177887
$95$	217811.	2.47612
$96$	−9216.00	−0.102062
$97$	−31742.0	−0.342535	−0.171267	−	0.985225i	$-0.554786\pi$
$97$	−31742.0	−0.342535	−0.171267	+	0.985225i	$0.554786\pi$
$98$	65807.6	0.692167
$99$	−50629.2	−0.519174
$100$	54294.1	0.542941
$101$	117854.	1.14959	0.574793	−	0.818299i	$-0.305083\pi$
$101$	117854.	1.14959	0.574793	+	0.818299i	$0.305083\pi$
$102$	−16916.8	−0.160997
$103$	167775.	1.55824	0.779122	−	0.626873i	$-0.215665\pi$
$103$	167775.	1.55824	0.779122	+	0.626873i	$0.215665\pi$
$104$	69309.7	0.628363
$105$	13692.7	0.121203
$106$	−125844.	−1.08784
$107$	−38534.5	−0.325380	−0.162690	−	0.986677i	$-0.552017\pi$
$107$	−38534.5	−0.325380	−0.162690	+	0.986677i	$0.552017\pi$
$108$	11664.0	0.0962250
$109$	90161.2	0.726864	0.363432	−	0.931621i	$-0.381605\pi$
$109$	90161.2	0.726864	0.363432	+	0.931621i	$0.381605\pi$
$110$	201858.	1.59061
$111$	127246.	0.980248
$112$	4824.09	0.0363388
$113$	−164034.	−1.20848	−0.604238	−	0.796804i	$-0.706522\pi$
$113$	−164034.	−1.20848	−0.604238	+	0.796804i	$0.706522\pi$
$114$	−97121.0	−0.699924
$115$	324374.	2.28718
$116$	16024.1	0.110568
$117$	−87720.1	−0.592426
$118$	13924.0	0.0920575
$119$	8855.06	0.0573224
$120$	−46504.2	−0.294808
$121$	229638.	1.42587
$122$	−124424.	−0.756842
$123$	128965.	0.768618
$124$	−117813.	−0.688079
$125$	21668.4	0.124037
$126$	−6105.49	−0.0342606
$127$	−21170.1	−0.116470	−0.0582350	−	0.998303i	$-0.518547\pi$
$127$	−21170.1	−0.116470	−0.0582350	+	0.998303i	$0.518547\pi$
$128$	−16384.0	−0.0883883
$129$	195369.	1.03367
$130$	349739.	1.81504
$131$	39138.9	0.199265	0.0996325	−	0.995024i	$-0.468233\pi$
$131$	39138.9	0.199265	0.0996325	+	0.995024i	$0.468233\pi$
$132$	−90007.4	−0.449618
$133$	50837.7	0.249205
$134$	−204754.	−0.985077
$135$	58856.9	0.277948
$136$	−30074.3	−0.139427
$137$	−277583.	−1.26355	−0.631774	−	0.775152i	$-0.717673\pi$
$137$	−277583.	−1.26355	−0.631774	+	0.775152i	$0.717673\pi$
$138$	−144637.	−0.646518
$139$	97264.6	0.426990	0.213495	−	0.976944i	$-0.431515\pi$
$139$	97264.6	0.426990	0.213495	+	0.976944i	$0.431515\pi$
$140$	24342.5	0.104965
$141$	−34288.4	−0.145244
$142$	106880.	0.444811
$143$	676908.	2.76815
$144$	20736.0	0.0833333
$145$	80858.3	0.319378
$146$	233160.	0.905257
$147$	−148067.	−0.565152
$148$	226215.	0.848920
$149$	−378838.	−1.39794	−0.698969	−	0.715152i	$-0.746358\pi$
$149$	−378838.	−1.39794	−0.698969	+	0.715152i	$0.746358\pi$
$150$	−122162.	−0.443310
$151$	−36849.8	−0.131520	−0.0657601	−	0.997835i	$-0.520947\pi$
$151$	−36849.8	−0.131520	−0.0657601	+	0.997835i	$0.520947\pi$
$152$	−172659.	−0.606152
$153$	38062.8	0.131454
$154$	47114.1	0.160085
$155$	−594487.	−1.98753
$156$	−155947.	−0.513056
$157$	−141719.	−0.458859	−0.229430	−	0.973325i	$-0.573686\pi$
$157$	−141719.	−0.458859	−0.229430	+	0.973325i	$0.573686\pi$
$158$	19244.6	0.0613290
$159$	283148.	0.888221
$160$	−82674.2	−0.255311
$161$	75709.7	0.230190
$162$	−26244.0	−0.0785674
$163$	365134.	1.07642	0.538211	−	0.842810i	$-0.319100\pi$
$163$	365134.	1.07642	0.538211	+	0.842810i	$0.319100\pi$
$164$	229272.	0.665643
$165$	−454180.	−1.29873
$166$	19131.6	0.0538866
$167$	−271278.	−0.752701	−0.376351	−	0.926477i	$-0.622821\pi$
$167$	−271278.	−0.752701	−0.376351	+	0.926477i	$0.622821\pi$
$168$	−10854.2	−0.0296705
$169$	801517.	2.15872
$170$	−151756.	−0.402739
$171$	218522.	0.571485
$172$	347323.	0.895185
$173$	−599694.	−1.52340	−0.761701	−	0.647928i	$-0.775636\pi$
$173$	−599694.	−1.52340	−0.761701	+	0.647928i	$0.775636\pi$
$174$	−36054.3	−0.0902784
$175$	63945.3	0.157839
$176$	−160013.	−0.389380
$177$	−31329.0	−0.0751646
$178$	−53333.0	−0.126167
$179$	−108220.	−0.252450	−0.126225	−	0.992002i	$-0.540286\pi$
$179$	−108220.	−0.252450	−0.126225	+	0.992002i	$0.540286\pi$
$180$	104635.	0.240710
$181$	742887.	1.68549	0.842745	−	0.538313i	$-0.180938\pi$
$181$	742887.	1.68549	0.842745	+	0.538313i	$0.180938\pi$
$182$	81630.0	0.182672
$183$	279954.	0.617959
$184$	−257132.	−0.559901
$185$	1.14149e6	2.45212
$186$	265079.	0.561814
$187$	−293719.	−0.614225
$188$	−60957.1	−0.125785
$189$	13737.4	0.0279736
$190$	−871245.	−1.75088
$191$	−107271.	−0.212764	−0.106382	−	0.994325i	$-0.533927\pi$
$191$	−107271.	−0.212764	−0.106382	+	0.994325i	$0.533927\pi$
$192$	36864.0	0.0721688
$193$	403640.	0.780012	0.390006	−	0.920812i	$-0.372473\pi$
$193$	403640.	0.780012	0.390006	+	0.920812i	$0.372473\pi$
$194$	126968.	0.242209
$195$	−786912.	−1.48197
$196$	−263230.	−0.489436
$197$	−490619.	−0.900697	−0.450349	−	0.892853i	$-0.648700\pi$
$197$	−490619.	−0.900697	−0.450349	+	0.892853i	$0.648700\pi$
$198$	202517.	0.367111
$199$	−132706.	−0.237551	−0.118776	−	0.992921i	$-0.537897\pi$
$199$	−132706.	−0.237551	−0.118776	+	0.992921i	$0.537897\pi$
$200$	−217177.	−0.383918
$201$	460696.	0.804312
$202$	−471417.	−0.812880
$203$	18872.5	0.0321433
$204$	67667.2	0.113842
$205$	1.15691e6	1.92272
$206$	−671102.	−1.10184
$207$	325432.	0.527880
$208$	−277239.	−0.444320
$209$	−1.68627e6	−2.67030
$210$	−54770.7	−0.0857038
$211$	−514112.	−0.794971	−0.397486	−	0.917608i	$-0.630117\pi$
$211$	−514112.	−0.794971	−0.397486	+	0.917608i	$0.630117\pi$
$212$	503375.	0.769222
$213$	−240480.	−0.363187
$214$	154138.	0.230078
$215$	1.75260e6	2.58576
$216$	−46656.0	−0.0680414
$217$	−138755.	−0.200032
$218$	−360645.	−0.513971
$219$	−524610.	−0.739140
$220$	−807431.	−1.12473
$221$	−508897.	−0.700888
$222$	−508983.	−0.693140
$223$	281653.	0.379273	0.189637	−	0.981854i	$-0.439269\pi$
$223$	281653.	0.379273	0.189637	+	0.981854i	$0.439269\pi$
$224$	−19296.4	−0.0256954
$225$	274864.	0.361961
$226$	656136.	0.854521
$227$	871823.	1.12296	0.561480	−	0.827491i	$-0.310232\pi$
$227$	871823.	1.12296	0.561480	+	0.827491i	$0.310232\pi$
$228$	388484.	0.494921
$229$	1.24235e6	1.56551	0.782756	−	0.622329i	$-0.213813\pi$
$229$	1.24235e6	1.56551	0.782756	+	0.622329i	$0.213813\pi$
$230$	−1.29750e6	−1.61728
$231$	−106007.	−0.130709
$232$	−64096.5	−0.0781834
$233$	206066.	0.248666	0.124333	−	0.992241i	$-0.460321\pi$
$233$	206066.	0.248666	0.124333	+	0.992241i	$0.460321\pi$
$234$	350880.	0.418909
$235$	−307592.	−0.363333
$236$	−55696.0	−0.0650945
$237$	−43300.3	−0.0500749
$238$	−35420.2	−0.0405330
$239$	−1.34950e6	−1.52820	−0.764099	−	0.645099i	$-0.776816\pi$
$239$	−1.34950e6	−1.52820	−0.764099	+	0.645099i	$0.776816\pi$
$240$	186017.	0.208461
$241$	−1.10404e6	−1.22445	−0.612226	−	0.790683i	$-0.709726\pi$
$241$	−1.10404e6	−1.22445	−0.612226	+	0.790683i	$0.709726\pi$
$242$	−918552.	−1.00824
$243$	59049.0	0.0641500
$244$	497697.	0.535168
$245$	−1.32827e6	−1.41374
$246$	−515862.	−0.543495
$247$	−2.92162e6	−3.04707
$248$	471251.	0.486545
$249$	−43046.0	−0.0439982
$250$	−86673.4	−0.0877073
$251$	1.27550e6	1.27790	0.638948	−	0.769250i	$-0.279370\pi$
$251$	1.27550e6	1.27790	0.638948	+	0.769250i	$0.279370\pi$
$252$	24422.0	0.0242259
$253$	−2.51126e6	−2.46655
$254$	84680.4	0.0823567
$255$	341451.	0.328835
$256$	65536.0	0.0625000
$257$	−908454.	−0.857966	−0.428983	−	0.903313i	$-0.641128\pi$
$257$	−908454.	−0.857966	−0.428983	+	0.903313i	$0.641128\pi$
$258$	−781477.	−0.730916
$259$	266426.	0.246790
$260$	−1.39896e6	−1.28342
$261$	81122.2	0.0737120
$262$	−156556.	−0.140902
$263$	2.14790e6	1.91481	0.957404	−	0.288753i	$-0.0932405\pi$
$263$	2.14790e6	1.91481	0.957404	+	0.288753i	$0.0932405\pi$
$264$	360030.	0.317928
$265$	2.54005e6	2.22191
$266$	−203351.	−0.176215
$267$	119999.	0.103015
$268$	819015.	0.696555
$269$	−1.65376e6	−1.39345	−0.696725	−	0.717338i	$-0.745360\pi$
$269$	−1.65376e6	−1.39345	−0.696725	+	0.717338i	$0.745360\pi$
$270$	−235428.	−0.196539
$271$	−1.85042e6	−1.53055	−0.765276	−	0.643702i	$-0.777398\pi$
$271$	−1.85042e6	−1.53055	−0.765276	+	0.643702i	$0.777398\pi$
$272$	120297.	0.0985901
$273$	−183667.	−0.149151
$274$	1.11033e6	0.893464
$275$	−2.12104e6	−1.69129
$276$	578547.	0.457157
$277$	842837.	0.660001	0.330000	−	0.943981i	$-0.392951\pi$
$277$	842837.	0.660001	0.330000	+	0.943981i	$0.392951\pi$
$278$	−389058.	−0.301928
$279$	−596427.	−0.458719
$280$	−97370.1	−0.0742216
$281$	−436246.	−0.329584	−0.164792	−	0.986328i	$-0.552695\pi$
$281$	−436246.	−0.329584	−0.164792	+	0.986328i	$0.552695\pi$
$282$	137154.	0.102703
$283$	−843841.	−0.626317	−0.313159	−	0.949701i	$-0.601387\pi$
$283$	−843841.	−0.626317	−0.313159	+	0.949701i	$0.601387\pi$
$284$	−427520.	−0.314529
$285$	1.96030e6	1.42959
$286$	−2.70763e6	−1.95738
$287$	270027.	0.193509
$288$	−82944.0	−0.0589256
$289$	−1.19904e6	−0.844480
$290$	−323433.	−0.225834
$291$	−285678.	−0.197763
$292$	−932640.	−0.640114
$293$	−273139.	−0.185872	−0.0929361	−	0.995672i	$-0.529625\pi$
$293$	−273139.	−0.185872	−0.0929361	+	0.995672i	$0.529625\pi$
$294$	592268.	0.399623
$295$	−281044.	−0.188026
$296$	−904859.	−0.600277
$297$	−455662.	−0.299745
$298$	1.51535e6	0.988492
$299$	−4.35101e6	−2.81457
$300$	488647.	0.313467
$301$	409063.	0.260240
$302$	147399.	0.0929989
$303$	1.06069e6	0.663714
$304$	690638.	0.428614
$305$	2.51139e6	1.54584
$306$	−152251.	−0.0929517
$307$	1.10047e6	0.666395	0.333197	−	0.942857i	$-0.391872\pi$
$307$	1.10047e6	0.666395	0.333197	+	0.942857i	$0.391872\pi$
$308$	−188457.	−0.113197
$309$	1.50998e6	0.899652
$310$	2.37795e6	1.40539
$311$	1.83857e6	1.07790	0.538952	−	0.842337i	$-0.318821\pi$
$311$	1.83857e6	1.07790	0.538952	+	0.842337i	$0.318821\pi$
$312$	623787.	0.362785
$313$	2.60818e6	1.50479	0.752396	−	0.658711i	$-0.228898\pi$
$313$	2.60818e6	1.50479	0.752396	+	0.658711i	$0.228898\pi$
$314$	566876.	0.324462
$315$	123234.	0.0699768
$316$	−76978.3	−0.0433661
$317$	−1.12539e6	−0.629004	−0.314502	−	0.949257i	$-0.601837\pi$
$317$	−1.12539e6	−0.629004	−0.314502	+	0.949257i	$0.601837\pi$
$318$	−1.13259e6	−0.628067
$319$	−625994.	−0.344424
$320$	330697.	0.180532
$321$	−346811.	−0.187858
$322$	−302839.	−0.162769
$323$	1.26773e6	0.676114
$324$	104976.	0.0555556
$325$	−3.67491e6	−1.92992
$326$	−1.46053e6	−0.761146
$327$	811451.	0.419655
$328$	−917088.	−0.470680
$329$	−71792.7	−0.0365671
$330$	1.81672e6	0.918339
$331$	2.45875e6	1.23351	0.616757	−	0.787154i	$-0.288446\pi$
$331$	2.45875e6	1.23351	0.616757	+	0.787154i	$0.288446\pi$
$332$	−76526.3	−0.0381035
$333$	1.14521e6	0.565946
$334$	1.08511e6	0.532240
$335$	4.13278e6	2.01201
$336$	43416.8	0.0209802
$337$	−2.73236e6	−1.31058	−0.655289	−	0.755378i	$-0.727453\pi$
$337$	−2.73236e6	−1.31058	−0.655289	+	0.755378i	$0.727453\pi$
$338$	−3.20607e6	−1.52644
$339$	−1.47631e6	−0.697714
$340$	607024.	0.284779
$341$	4.60244e6	2.14339
$342$	−874089.	−0.404101
$343$	−626735.	−0.287639
$344$	−1.38929e6	−0.632991
$345$	2.91936e6	1.32051
$346$	2.39878e6	1.07721
$347$	−152099.	−0.0678112	−0.0339056	−	0.999425i	$-0.510795\pi$
$347$	−152099.	−0.0678112	−0.0339056	+	0.999425i	$0.510795\pi$
$348$	144217.	0.0638365
$349$	−3.08112e6	−1.35408	−0.677040	−	0.735946i	$-0.736738\pi$
$349$	−3.08112e6	−1.35408	−0.677040	+	0.735946i	$0.736738\pi$
$350$	−255781.	−0.111609
$351$	−789480.	−0.342037
$352$	640052.	0.275333
$353$	−877601.	−0.374853	−0.187426	−	0.982279i	$-0.560015\pi$
$353$	−877601.	−0.374853	−0.187426	+	0.982279i	$0.560015\pi$
$354$	125316.	0.0531494
$355$	−2.15728e6	−0.908522
$356$	213332.	0.0892135
$357$	79695.5	0.0330951
$358$	432881.	0.178509
$359$	2.46578e6	1.00976	0.504880	−	0.863190i	$-0.331537\pi$
$359$	2.46578e6	1.00976	0.504880	+	0.863190i	$0.331537\pi$
$360$	−418538.	−0.170208
$361$	4.80205e6	1.93936
$362$	−2.97155e6	−1.19182
$363$	2.06674e6	0.823227
$364$	−326520.	−0.129168
$365$	−4.70613e6	−1.84898
$366$	−1.11982e6	−0.436963
$367$	965749.	0.374282	0.187141	−	0.982333i	$-0.440078\pi$
$367$	965749.	0.374282	0.187141	+	0.982333i	$0.440078\pi$
$368$	1.02853e6	0.395910
$369$	1.16069e6	0.443762
$370$	−4.56595e6	−1.73391
$371$	592853.	0.223621
$372$	−1.06031e6	−0.397262
$373$	−952121.	−0.354340	−0.177170	−	0.984180i	$-0.556694\pi$
$373$	−952121.	−0.354340	−0.177170	+	0.984180i	$0.556694\pi$
$374$	1.17487e6	0.434323
$375$	195015.	0.0716127
$376$	243828.	0.0889436
$377$	−1.08460e6	−0.393020
$378$	−54949.4	−0.0197803
$379$	4.70759e6	1.68345	0.841726	−	0.539905i	$-0.181540\pi$
$379$	4.70759e6	1.68345	0.841726	+	0.539905i	$0.181540\pi$
$380$	3.48498e6	1.23806
$381$	−190531.	−0.0672439
$382$	429084.	0.150447
$383$	−612265.	−0.213276	−0.106638	−	0.994298i	$-0.534009\pi$
$383$	−612265.	−0.213276	−0.106638	+	0.994298i	$0.534009\pi$
$384$	−147456.	−0.0510310
$385$	−950958.	−0.326971
$386$	−1.61456e6	−0.551552
$387$	1.75832e6	0.596790
$388$	−507872.	−0.171267
$389$	−694962.	−0.232856	−0.116428	−	0.993199i	$-0.537144\pi$
$389$	−694962.	−0.232856	−0.116428	+	0.993199i	$0.537144\pi$
$390$	3.14765e6	1.04791
$391$	1.88795e6	0.624525
$392$	1.05292e6	0.346083
$393$	352250.	0.115046
$394$	1.96248e6	0.636889
$395$	−388435.	−0.125264
$396$	−810066.	−0.259587
$397$	3.67028e6	1.16875	0.584377	−	0.811483i	$-0.301339\pi$
$397$	3.67028e6	1.16875	0.584377	+	0.811483i	$0.301339\pi$
$398$	530824.	0.167974
$399$	457540.	0.143879
$400$	868706.	0.271471
$401$	1.54767e6	0.480636	0.240318	−	0.970694i	$-0.422748\pi$
$401$	1.54767e6	0.480636	0.240318	+	0.970694i	$0.422748\pi$
$402$	−1.84278e6	−0.568734
$403$	7.97418e6	2.44581
$404$	1.88567e6	0.574793
$405$	529712.	0.160473
$406$	−75490.1	−0.0227287
$407$	−8.83724e6	−2.64442
$408$	−270669.	−0.0804985
$409$	−2.61795e6	−0.773844	−0.386922	−	0.922112i	$-0.626462\pi$
$409$	−2.61795e6	−0.773844	−0.386922	+	0.922112i	$0.626462\pi$
$410$	−4.62765e6	−1.35957
$411$	−2.49825e6	−0.729510
$412$	2.68441e6	0.779122
$413$	−65596.4	−0.0189236
$414$	−1.30173e6	−0.373267
$415$	−386154.	−0.110063
$416$	1.10895e6	0.314181
$417$	875382.	0.246523
$418$	6.74506e6	1.88819
$419$	−3.87843e6	−1.07925	−0.539623	−	0.841907i	$-0.681433\pi$
$419$	−3.87843e6	−1.07925	−0.539623	+	0.841907i	$0.681433\pi$
$420$	219083.	0.0606017
$421$	−5.44262e6	−1.49659	−0.748295	−	0.663366i	$-0.769127\pi$
$421$	−5.44262e6	−1.49659	−0.748295	+	0.663366i	$0.769127\pi$
$422$	2.05645e6	0.562130
$423$	−308595.	−0.0838568
$424$	−2.01350e6	−0.543922
$425$	1.59459e6	0.428229
$426$	961920.	0.256812
$427$	586166.	0.155579
$428$	−616552.	−0.162690
$429$	6.09217e6	1.59819
$430$	−7.01042e6	−1.82841
$431$	−2.63930e6	−0.684378	−0.342189	−	0.939631i	$-0.611168\pi$
$431$	−2.63930e6	−0.684378	−0.342189	+	0.939631i	$0.611168\pi$
$432$	186624.	0.0481125
$433$	3.86894e6	0.991681	0.495841	−	0.868414i	$-0.334860\pi$
$433$	3.86894e6	0.991681	0.495841	+	0.868414i	$0.334860\pi$
$434$	555019.	0.141444
$435$	727725.	0.184393
$436$	1.44258e6	0.363432
$437$	1.08389e7	2.71508
$438$	2.09844e6	0.522651
$439$	643286.	0.159310	0.0796550	−	0.996822i	$-0.474618\pi$
$439$	643286.	0.159310	0.0796550	+	0.996822i	$0.474618\pi$
$440$	3.22973e6	0.795305
$441$	−1.33260e6	−0.326291
$442$	2.03559e6	0.495603
$443$	−4.80104e6	−1.16232	−0.581160	−	0.813789i	$-0.697401\pi$
$443$	−4.80104e6	−1.16232	−0.581160	+	0.813789i	$0.697401\pi$
$444$	2.03593e6	0.490124
$445$	1.07648e6	0.257695
$446$	−1.12661e6	−0.268187
$447$	−3.40954e6	−0.807100
$448$	77185.5	0.0181694
$449$	−78306.0	−0.0183307	−0.00916536	−	0.999958i	$-0.502917\pi$
$449$	−78306.0	−0.0183307	−0.00916536	+	0.999958i	$0.502917\pi$
$450$	−1.09946e6	−0.255945
$451$	−8.95667e6	−2.07351
$452$	−2.62454e6	−0.604238
$453$	−331648.	−0.0759332
$454$	−3.48729e6	−0.794052
$455$	−1.64763e6	−0.373105
$456$	−1.55394e6	−0.349962
$457$	−585457.	−0.131131	−0.0655654	−	0.997848i	$-0.520885\pi$
$457$	−585457.	−0.131131	−0.0655654	+	0.997848i	$0.520885\pi$
$458$	−4.96941e6	−1.10698
$459$	342565.	0.0758947
$460$	5.18998e6	1.14359
$461$	−5.61184e6	−1.22985	−0.614926	−	0.788585i	$-0.710814\pi$
$461$	−5.61184e6	−1.22985	−0.614926	+	0.788585i	$0.710814\pi$
$462$	424027.	0.0924249
$463$	−4.30153e6	−0.932546	−0.466273	−	0.884641i	$-0.654404\pi$
$463$	−4.30153e6	−0.932546	−0.466273	+	0.884641i	$0.654404\pi$
$464$	256386.	0.0552840
$465$	−5.35038e6	−1.14750
$466$	−824263.	−0.175833
$467$	−73223.2	−0.0155366	−0.00776831	−	0.999970i	$-0.502473\pi$
$467$	−73223.2	−0.0155366	−0.00776831	+	0.999970i	$0.502473\pi$
$468$	−1.40352e6	−0.296213
$469$	964601.	0.202496
$470$	1.23037e6	0.256915
$471$	−1.27547e6	−0.264922
$472$	222784.	0.0460287
$473$	−1.35684e7	−2.78854
$474$	173201.	0.0354083
$475$	9.15468e6	1.86170
$476$	141681.	0.0286612
$477$	2.54833e6	0.512815
$478$	5.39802e6	1.08060
$479$	4.48812e6	0.893769	0.446885	−	0.894592i	$-0.352533\pi$
$479$	4.48812e6	0.893769	0.446885	+	0.894592i	$0.352533\pi$
$480$	−744068.	−0.147404
$481$	−1.53114e7	−3.01753
$482$	4.41616e6	0.865819
$483$	681387.	0.132900
$484$	3.67421e6	0.712936
$485$	−2.56274e6	−0.494709
$486$	−236196.	−0.0453609
$487$	2.28143e6	0.435898	0.217949	−	0.975960i	$-0.430063\pi$
$487$	2.28143e6	0.435898	0.217949	+	0.975960i	$0.430063\pi$
$488$	−1.99079e6	−0.378421
$489$	3.28620e6	0.621473
$490$	5.31308e6	0.999668
$491$	3.36442e6	0.629805	0.314903	−	0.949124i	$-0.398028\pi$
$491$	3.36442e6	0.629805	0.314903	+	0.949124i	$0.398028\pi$
$492$	2.06345e6	0.384309
$493$	470620.	0.0872073
$494$	1.16865e7	2.15460
$495$	−4.08762e6	−0.749821
$496$	−1.88500e6	−0.344039
$497$	−503515.	−0.0914368
$498$	172184.	0.0311114
$499$	−3.78225e6	−0.679985	−0.339992	−	0.940428i	$-0.610425\pi$
$499$	−3.78225e6	−0.679985	−0.339992	+	0.940428i	$0.610425\pi$
$500$	346694.	0.0620185
$501$	−2.44150e6	−0.434572
$502$	−5.10199e6	−0.903609
$503$	3.06123e6	0.539481	0.269740	−	0.962933i	$-0.413062\pi$
$503$	3.06123e6	0.539481	0.269740	+	0.962933i	$0.413062\pi$
$504$	−97687.9	−0.0171303
$505$	9.51513e6	1.66030
$506$	1.00450e7	1.74412
$507$	7.21366e6	1.24634
$508$	−338722.	−0.0582350
$509$	2.52603e6	0.432159	0.216079	−	0.976376i	$-0.430673\pi$
$509$	2.52603e6	0.432159	0.216079	+	0.976376i	$0.430673\pi$
$510$	−1.36580e6	−0.232521
$511$	−1.09842e6	−0.186088
$512$	−262144.	−0.0441942
$513$	1.96670e6	0.329947
$514$	3.63382e6	0.606674
$515$	1.35456e7	2.25051
$516$	3.12591e6	0.516835
$517$	2.38133e6	0.391826
$518$	−1.06570e6	−0.174507
$519$	−5.39725e6	−0.879537
$520$	5.59582e6	0.907518
$521$	7.64614e6	1.23409	0.617046	−	0.786927i	$-0.288329\pi$
$521$	7.64614e6	1.23409	0.617046	+	0.786927i	$0.288329\pi$
$522$	−324489.	−0.0521223
$523$	8.71406e6	1.39305	0.696525	−	0.717533i	$-0.254729\pi$
$523$	8.71406e6	1.39305	0.696525	+	0.717533i	$0.254729\pi$
$524$	626223.	0.0996325
$525$	575508.	0.0911282
$526$	−8.59161e6	−1.35397
$527$	−3.46009e6	−0.542702
$528$	−1.44012e6	−0.224809
$529$	9.70545e6	1.50791
$530$	−1.01602e7	−1.57113
$531$	−281961.	−0.0433963
$532$	813404.	0.124603
$533$	−1.55183e7	−2.36607
$534$	−479997.	−0.0728425
$535$	−3.11114e6	−0.469932
$536$	−3.27606e6	−0.492538
$537$	−973982.	−0.145752
$538$	6.61504e6	0.985318
$539$	1.02833e7	1.52461
$540$	941711.	0.138974
$541$	−7.47853e6	−1.09856	−0.549279	−	0.835639i	$-0.685098\pi$
$541$	−7.47853e6	−1.09856	−0.549279	+	0.835639i	$0.685098\pi$
$542$	7.40170e6	1.08226
$543$	6.68598e6	0.973118
$544$	−481189.	−0.0697137
$545$	7.27930e6	1.04978
$546$	734670.	0.105466
$547$	−7.75529e6	−1.10823	−0.554115	−	0.832440i	$-0.686943\pi$
$547$	−7.75529e6	−1.10823	−0.554115	+	0.832440i	$0.686943\pi$
$548$	−4.44133e6	−0.631774
$549$	2.51959e6	0.356779
$550$	8.48415e6	1.19592
$551$	2.70187e6	0.379128
$552$	−2.31419e6	−0.323259
$553$	−90661.8	−0.0126070
$554$	−3.37135e6	−0.466691
$555$	1.02734e7	1.41573
$556$	1.55623e6	0.213495
$557$	−2.19074e6	−0.299194	−0.149597	−	0.988747i	$-0.547798\pi$
$557$	−2.19074e6	−0.299194	−0.149597	+	0.988747i	$0.547798\pi$
$558$	2.38571e6	0.324363
$559$	−2.35087e7	−3.18199
$560$	389480.	0.0524826
$561$	−2.64347e6	−0.354623
$562$	1.74499e6	0.233051
$563$	−1.48353e7	−1.97254	−0.986268	−	0.165151i	$-0.947189\pi$
$563$	−1.48353e7	−1.97254	−0.986268	+	0.165151i	$0.947189\pi$
$564$	−548614.	−0.0726222
$565$	−1.32435e7	−1.74535
$566$	3.37536e6	0.442873
$567$	123636.	0.0161506
$568$	1.71008e6	0.222406
$569$	1.19609e7	1.54875	0.774376	−	0.632725i	$-0.218064\pi$
$569$	1.19609e7	1.54875	0.774376	+	0.632725i	$0.218064\pi$
$570$	−7.84121e6	−1.01087
$571$	−9.56361e6	−1.22753	−0.613764	−	0.789489i	$-0.710345\pi$
$571$	−9.56361e6	−1.22753	−0.613764	+	0.789489i	$0.710345\pi$
$572$	1.08305e7	1.38407
$573$	−965439.	−0.122840
$574$	−1.08011e6	−0.136832
$575$	1.36335e7	1.71965
$576$	331776.	0.0416667
$577$	1.04127e7	1.30204	0.651018	−	0.759062i	$-0.274342\pi$
$577$	1.04127e7	1.30204	0.651018	+	0.759062i	$0.274342\pi$
$578$	4.79616e6	0.597137
$579$	3.63276e6	0.450340
$580$	1.29373e6	0.159689
$581$	−90129.4	−0.0110771
$582$	1.14271e6	0.139839
$583$	−1.96647e7	−2.39616
$584$	3.73056e6	0.452629
$585$	−7.08221e6	−0.855617
$586$	1.09256e6	0.131431
$587$	−8.16423e6	−0.977957	−0.488979	−	0.872296i	$-0.662630\pi$
$587$	−8.16423e6	−0.977957	−0.488979	+	0.872296i	$0.662630\pi$
$588$	−2.36907e6	−0.282576
$589$	−1.98647e7	−2.35936
$590$	1.12418e6	0.132955
$591$	−4.41557e6	−0.520018
$592$	3.61944e6	0.424460
$593$	−1.24728e7	−1.45655	−0.728277	−	0.685283i	$-0.759678\pi$
$593$	−1.24728e7	−1.45655	−0.728277	+	0.685283i	$0.759678\pi$
$594$	1.82265e6	0.211952
$595$	714927.	0.0827883
$596$	−6.06141e6	−0.698969
$597$	−1.19435e6	−0.137150
$598$	1.74040e7	1.99020
$599$	2.35718e6	0.268427	0.134214	−	0.990952i	$-0.457149\pi$
$599$	2.35718e6	0.268427	0.134214	+	0.990952i	$0.457149\pi$
$600$	−1.95459e6	−0.221655
$601$	−324771.	−0.0366768	−0.0183384	−	0.999832i	$-0.505838\pi$
$601$	−324771.	−0.0366768	−0.0183384	+	0.999832i	$0.505838\pi$
$602$	−1.63625e6	−0.184017
$603$	4.14627e6	0.464370
$604$	−589597.	−0.0657601
$605$	1.85402e7	2.05933
$606$	−4.24275e6	−0.469316
$607$	−6.81064e6	−0.750268	−0.375134	−	0.926971i	$-0.622403\pi$
$607$	−6.81064e6	−0.750268	−0.375134	+	0.926971i	$0.622403\pi$
$608$	−2.76255e6	−0.303076
$609$	169853.	0.0185579
$610$	−1.00456e7	−1.09308
$611$	4.12590e6	0.447111
$612$	609005.	0.0657268
$613$	−3.68586e6	−0.396175	−0.198088	−	0.980184i	$-0.563473\pi$
$613$	−3.68586e6	−0.396175	−0.198088	+	0.980184i	$0.563473\pi$
$614$	−4.40187e6	−0.471212
$615$	1.04122e7	1.11008
$616$	753826.	0.0800423
$617$	−1.00450e7	−1.06227	−0.531135	−	0.847287i	$-0.678234\pi$
$617$	−1.00450e7	−1.06227	−0.531135	+	0.847287i	$0.678234\pi$
$618$	−6.03991e6	−0.636150
$619$	3.93530e6	0.412811	0.206406	−	0.978466i	$-0.433823\pi$
$619$	3.93530e6	0.412811	0.206406	+	0.978466i	$0.433823\pi$
$620$	−9.51179e6	−0.993763
$621$	2.92889e6	0.304772
$622$	−7.35429e6	−0.762193
$623$	251253.	0.0259353
$624$	−2.49515e6	−0.256528
$625$	−8.85490e6	−0.906741
$626$	−1.04327e7	−1.06405
$627$	−1.51764e7	−1.54170
$628$	−2.26751e6	−0.229430
$629$	6.64380e6	0.669561
$630$	−492936.	−0.0494811
$631$	1.42610e7	1.42586	0.712931	−	0.701234i	$-0.247367\pi$
$631$	1.42610e7	1.42586	0.712931	+	0.701234i	$0.247367\pi$
$632$	307913.	0.0306645
$633$	−4.62701e6	−0.458977
$634$	4.50154e6	0.444773
$635$	−1.70920e6	−0.168213
$636$	4.53037e6	0.444111
$637$	1.78168e7	1.73973
$638$	2.50398e6	0.243545
$639$	−2.16432e6	−0.209686
$640$	−1.32279e6	−0.127656
$641$	−3.67742e6	−0.353507	−0.176754	−	0.984255i	$-0.556560\pi$
$641$	−3.67742e6	−0.353507	−0.176754	+	0.984255i	$0.556560\pi$
$642$	1.38724e6	0.132836
$643$	3.37410e6	0.321833	0.160916	−	0.986968i	$-0.448555\pi$
$643$	3.37410e6	0.321833	0.160916	+	0.986968i	$0.448555\pi$
$644$	1.21136e6	0.115095
$645$	1.57734e7	1.49289
$646$	−5.07091e6	−0.478085
$647$	1.00171e7	0.940765	0.470383	−	0.882463i	$-0.344116\pi$
$647$	1.00171e7	0.940765	0.470383	+	0.882463i	$0.344116\pi$
$648$	−419904.	−0.0392837
$649$	2.17580e6	0.202772
$650$	1.46996e7	1.36466
$651$	−1.24879e6	−0.115488
$652$	5.84214e6	0.538211
$653$	−510352.	−0.0468368	−0.0234184	−	0.999726i	$-0.507455\pi$
$653$	−510352.	−0.0468368	−0.0234184	+	0.999726i	$0.507455\pi$
$654$	−3.24580e6	−0.296741
$655$	3.15994e6	0.287790
$656$	3.66835e6	0.332821
$657$	−4.72149e6	−0.426742
$658$	287171.	0.0258568
$659$	−8.19008e6	−0.734640	−0.367320	−	0.930095i	$-0.619725\pi$
$659$	−8.19008e6	−0.734640	−0.367320	+	0.930095i	$0.619725\pi$
$660$	−7.26688e6	−0.649364
$661$	1.51238e7	1.34635	0.673173	−	0.739485i	$-0.264931\pi$
$661$	1.51238e7	1.34635	0.673173	+	0.739485i	$0.264931\pi$
$662$	−9.83499e6	−0.872226
$663$	−4.58007e6	−0.404658
$664$	306105.	0.0269433
$665$	4.10446e6	0.359917
$666$	−4.58085e6	−0.400185
$667$	4.02375e6	0.350200
$668$	−4.34044e6	−0.376351
$669$	2.53488e6	0.218974
$670$	−1.65311e7	−1.42271
$671$	−1.94429e7	−1.66707
$672$	−173667.	−0.0148353
$673$	−1.67972e7	−1.42955	−0.714775	−	0.699355i	$-0.753471\pi$
$673$	−1.67972e7	−1.42955	−0.714775	+	0.699355i	$0.753471\pi$
$674$	1.09294e7	0.926719
$675$	2.47378e6	0.208978
$676$	1.28243e7	1.07936
$677$	−4.54835e6	−0.381402	−0.190701	−	0.981648i	$-0.561076\pi$
$677$	−4.54835e6	−0.381402	−0.190701	+	0.981648i	$0.561076\pi$
$678$	5.90523e6	0.493358
$679$	−598149.	−0.0497892
$680$	−2.42809e6	−0.201369
$681$	7.84641e6	0.648341
$682$	−1.84098e7	−1.51561
$683$	1.60260e7	1.31454	0.657268	−	0.753657i	$-0.271712\pi$
$683$	1.60260e7	1.31454	0.657268	+	0.753657i	$0.271712\pi$
$684$	3.49635e6	0.285743
$685$	−2.24111e7	−1.82489
$686$	2.50694e6	0.203392
$687$	1.11812e7	0.903848
$688$	5.55717e6	0.447593
$689$	−3.40710e7	−2.73424
$690$	−1.16775e7	−0.933739
$691$	1.64735e7	1.31247	0.656236	−	0.754555i	$-0.272147\pi$
$691$	1.64735e7	1.31247	0.656236	+	0.754555i	$0.272147\pi$
$692$	−9.59511e6	−0.761701
$693$	−954062.	−0.0754646
$694$	608394.	0.0479498
$695$	7.85281e6	0.616684
$696$	−576869.	−0.0451392
$697$	6.73359e6	0.525006
$698$	1.23245e7	0.957479
$699$	1.85459e6	0.143567
$700$	1.02312e6	0.0789194
$701$	2.38198e7	1.83081	0.915405	−	0.402535i	$-0.131871\pi$
$701$	2.38198e7	1.83081	0.915405	+	0.402535i	$0.131871\pi$
$702$	3.15792e6	0.241857
$703$	3.81427e7	2.91087
$704$	−2.56021e6	−0.194690
$705$	−2.76832e6	−0.209770
$706$	3.51041e6	0.265061
$707$	2.22086e6	0.167098
$708$	−501264.	−0.0375823
$709$	−2.54146e7	−1.89875	−0.949375	−	0.314144i	$-0.898283\pi$
$709$	−2.54146e7	−1.89875	−0.949375	+	0.314144i	$0.898283\pi$
$710$	8.62912e6	0.642422
$711$	−389703.	−0.0289108
$712$	−853327.	−0.0630835
$713$	−2.95834e7	−2.17934
$714$	−318782.	−0.0234018
$715$	5.46512e7	3.99792
$716$	−1.73152e6	−0.126225
$717$	−1.21455e7	−0.882305
$718$	−9.86311e6	−0.714008
$719$	1.07698e7	0.776933	0.388466	−	0.921463i	$-0.373005\pi$
$719$	1.07698e7	0.776933	0.388466	+	0.921463i	$0.373005\pi$
$720$	1.67415e6	0.120355
$721$	3.16158e6	0.226499
$722$	−1.92082e7	−1.37133
$723$	−9.93636e6	−0.706938
$724$	1.18862e7	0.842745
$725$	3.39850e6	0.240128
$726$	−8.26697e6	−0.582110
$727$	−1.81058e7	−1.27052	−0.635261	−	0.772298i	$-0.719107\pi$
$727$	−1.81058e7	−1.27052	−0.635261	+	0.772298i	$0.719107\pi$
$728$	1.30608e6	0.0913358
$729$	531441.	0.0370370
$730$	1.88245e7	1.30743
$731$	1.02007e7	0.706051
$732$	4.47927e6	0.308979
$733$	−7.00979e6	−0.481887	−0.240943	−	0.970539i	$-0.577457\pi$
$733$	−7.00979e6	−0.481887	−0.240943	+	0.970539i	$0.577457\pi$
$734$	−3.86300e6	−0.264658
$735$	−1.19544e7	−0.816226
$736$	−4.11411e6	−0.279951
$737$	−3.19954e7	−2.16980
$738$	−4.64276e6	−0.313787
$739$	5.80778e6	0.391200	0.195600	−	0.980684i	$-0.437335\pi$
$739$	5.80778e6	0.391200	0.195600	+	0.980684i	$0.437335\pi$
$740$	1.82638e7	1.22606
$741$	−2.62946e7	−1.75922
$742$	−2.37141e6	−0.158124
$743$	1.40031e7	0.930576	0.465288	−	0.885159i	$-0.345951\pi$
$743$	1.40031e7	0.930576	0.465288	+	0.885159i	$0.345951\pi$
$744$	4.24126e6	0.280907
$745$	−3.05861e7	−2.01898
$746$	3.80848e6	0.250556
$747$	−387414.	−0.0254024
$748$	−4.69950e6	−0.307112
$749$	−726149.	−0.0472956
$750$	−780061.	−0.0506379
$751$	4.82662e6	0.312279	0.156140	−	0.987735i	$-0.450095\pi$
$751$	4.82662e6	0.312279	0.156140	+	0.987735i	$0.450095\pi$
$752$	−975314.	−0.0628926
$753$	1.14795e7	0.737794
$754$	4.33839e6	0.277907
$755$	−2.97512e6	−0.189949
$756$	219798.	0.0139868
$757$	−1.72362e7	−1.09321	−0.546604	−	0.837391i	$-0.684080\pi$
$757$	−1.72362e7	−1.09321	−0.546604	+	0.837391i	$0.684080\pi$
$758$	−1.88304e7	−1.19038
$759$	−2.26013e7	−1.42406
$760$	−1.39399e7	−0.875440
$761$	−1.81912e7	−1.13868	−0.569339	−	0.822103i	$-0.692801\pi$
$761$	−1.81912e7	−1.13868	−0.569339	+	0.822103i	$0.692801\pi$
$762$	762124.	0.0475486
$763$	1.69901e6	0.105654
$764$	−1.71634e6	−0.106382
$765$	3.07306e6	0.189853
$766$	2.44906e6	0.150809
$767$	3.76980e6	0.231382
$768$	589824.	0.0360844
$769$	4.08396e6	0.249038	0.124519	−	0.992217i	$-0.460261\pi$
$769$	4.08396e6	0.249038	0.124519	+	0.992217i	$0.460261\pi$
$770$	3.80383e6	0.231204
$771$	−8.17608e6	−0.495347
$772$	6.45825e6	0.390006
$773$	−2.51696e7	−1.51505	−0.757527	−	0.652804i	$-0.773592\pi$
$773$	−2.51696e7	−1.51505	−0.757527	+	0.652804i	$0.773592\pi$
$774$	−7.03330e6	−0.421994
$775$	−2.49865e7	−1.49435
$776$	2.03149e6	0.121104
$777$	2.39783e6	0.142484
$778$	2.77985e6	0.164654
$779$	3.86582e7	2.28243
$780$	−1.25906e7	−0.740986
$781$	1.67014e7	0.979771
$782$	−7.55182e6	−0.441606
$783$	730100.	0.0425577
$784$	−4.21169e6	−0.244718
$785$	−1.14419e7	−0.662711
$786$	−1.40900e6	−0.0813496
$787$	−3.90725e6	−0.224871	−0.112436	−	0.993659i	$-0.535865\pi$
$787$	−3.90725e6	−0.224871	−0.112436	+	0.993659i	$0.535865\pi$
$788$	−7.84991e6	−0.450349
$789$	1.93311e7	1.10551
$790$	1.55374e6	0.0885749
$791$	−3.09108e6	−0.175658
$792$	3.24027e6	0.183556
$793$	−3.36867e7	−1.90229
$794$	−1.46811e7	−0.826433
$795$	2.28604e7	1.28282
$796$	−2.12329e6	−0.118776
$797$	1.80649e7	1.00737	0.503685	−	0.863888i	$-0.331977\pi$
$797$	1.80649e7	1.00737	0.503685	+	0.863888i	$0.331977\pi$
$798$	−1.83016e6	−0.101738
$799$	−1.79028e6	−0.0992095
$800$	−3.47482e6	−0.191959
$801$	1.07999e6	0.0594757
$802$	−6.19067e6	−0.339861
$803$	3.64343e7	1.99398
$804$	7.37114e6	0.402156
$805$	6.11254e6	0.332454
$806$	−3.18967e7	−1.72945
$807$	−1.48838e7	−0.804509
$808$	−7.54267e6	−0.406440
$809$	1.15951e7	0.622879	0.311439	−	0.950266i	$-0.399189\pi$
$809$	1.15951e7	0.622879	0.311439	+	0.950266i	$0.399189\pi$
$810$	−2.11885e6	−0.113472
$811$	−8.03253e6	−0.428845	−0.214422	−	0.976741i	$-0.568787\pi$
$811$	−8.03253e6	−0.428845	−0.214422	+	0.976741i	$0.568787\pi$
$812$	301961.	0.0160716
$813$	−1.66538e7	−0.883665
$814$	3.53489e7	1.86989
$815$	2.94796e7	1.55463
$816$	1.08268e6	0.0569210
$817$	5.85631e7	3.06951
$818$	1.04718e7	0.547190
$819$	−1.65301e6	−0.0861122
$820$	1.85106e7	0.961360
$821$	−2.08438e7	−1.07924	−0.539621	−	0.841908i	$-0.681432\pi$
$821$	−2.08438e7	−1.07924	−0.539621	+	0.841908i	$0.681432\pi$
$822$	9.99300e6	0.515842
$823$	−2.60957e7	−1.34298	−0.671490	−	0.741013i	$-0.734346\pi$
$823$	−2.60957e7	−1.34298	−0.671490	+	0.741013i	$0.734346\pi$
$824$	−1.07376e7	−0.550922
$825$	−1.90893e7	−0.976464
$826$	262385.	0.0133810
$827$	−2.89971e7	−1.47432	−0.737159	−	0.675720i	$-0.763833\pi$
$827$	−2.89971e7	−1.47432	−0.737159	+	0.675720i	$0.763833\pi$
$828$	5.20692e6	0.263940
$829$	−1.87538e7	−0.947769	−0.473885	−	0.880587i	$-0.657149\pi$
$829$	−1.87538e7	−0.947769	−0.473885	+	0.880587i	$0.657149\pi$
$830$	1.54462e6	0.0778261
$831$	7.58554e6	0.381052
$832$	−4.43582e6	−0.222160
$833$	−7.73093e6	−0.386028
$834$	−3.50153e6	−0.174318
$835$	−2.19020e7	−1.08710
$836$	−2.69803e7	−1.33515
$837$	−5.36784e6	−0.264842
$838$	1.55137e7	0.763143
$839$	2.88718e7	1.41602	0.708008	−	0.706204i	$-0.249594\pi$
$839$	2.88718e7	1.41602	0.708008	+	0.706204i	$0.249594\pi$
$840$	−876331.	−0.0428519
$841$	−1.95081e7	−0.951099
$842$	2.17705e7	1.05825
$843$	−3.92622e6	−0.190285
$844$	−8.22579e6	−0.397486
$845$	6.47117e7	3.11775
$846$	1.23438e6	0.0592957
$847$	4.32733e6	0.207258
$848$	8.05400e6	0.384611
$849$	−7.59457e6	−0.361605
$850$	−6.37835e6	−0.302804
$851$	5.68037e7	2.68877
$852$	−3.84768e6	−0.181593
$853$	−3.45782e7	−1.62716	−0.813578	−	0.581455i	$-0.802484\pi$
$853$	−3.45782e7	−1.62716	−0.813578	+	0.581455i	$0.802484\pi$
$854$	−2.34466e6	−0.110011
$855$	1.76427e7	0.825373
$856$	2.46621e6	0.115039
$857$	801420.	0.0372742	0.0186371	−	0.999826i	$-0.494067\pi$
$857$	801420.	0.0372742	0.0186371	+	0.999826i	$0.494067\pi$
$858$	−2.43687e7	−1.13009
$859$	3.71649e7	1.71850	0.859250	−	0.511555i	$-0.170930\pi$
$859$	3.71649e7	1.71850	0.859250	+	0.511555i	$0.170930\pi$
$860$	2.80417e7	1.29288
$861$	2.43024e6	0.111723
$862$	1.05572e7	0.483928
$863$	−9.79140e6	−0.447525	−0.223763	−	0.974644i	$-0.571834\pi$
$863$	−9.79140e6	−0.447525	−0.223763	+	0.974644i	$0.571834\pi$
$864$	−746496.	−0.0340207
$865$	−4.84172e7	−2.20019
$866$	−1.54758e7	−0.701225
$867$	−1.07914e7	−0.487561
$868$	−2.22008e6	−0.100016
$869$	3.00721e6	0.135087
$870$	−2.91090e6	−0.130385
$871$	−5.54352e7	−2.47594
$872$	−5.77032e6	−0.256985
$873$	−2.57110e6	−0.114178
$874$	−4.33557e7	−1.91985
$875$	408321.	0.0180294
$876$	−8.39376e6	−0.369570
$877$	−2.67998e7	−1.17661	−0.588304	−	0.808640i	$-0.700204\pi$
$877$	−2.67998e7	−1.17661	−0.588304	+	0.808640i	$0.700204\pi$
$878$	−2.57314e6	−0.112649
$879$	−2.45825e6	−0.107313
$880$	−1.29189e7	−0.562366
$881$	−2.74718e7	−1.19247	−0.596236	−	0.802809i	$-0.703338\pi$
$881$	−2.74718e7	−1.19247	−0.596236	+	0.802809i	$0.703338\pi$
$882$	5.33042e6	0.230722
$883$	2.70645e7	1.16815	0.584075	−	0.811700i	$-0.301457\pi$
$883$	2.70645e7	1.16815	0.584075	+	0.811700i	$0.301457\pi$
$884$	−8.14235e6	−0.350444
$885$	−2.52939e6	−0.108557
$886$	1.92042e7	0.821885
$887$	−5.86932e6	−0.250483	−0.125242	−	0.992126i	$-0.539971\pi$
$887$	−5.86932e6	−0.250483	−0.125242	+	0.992126i	$0.539971\pi$
$888$	−8.14373e6	−0.346570
$889$	−398932.	−0.0169295
$890$	−4.30592e6	−0.182218
$891$	−4.10096e6	−0.173058
$892$	4.50645e6	0.189637
$893$	−1.02781e7	−0.431307
$894$	1.36382e7	0.570706
$895$	−8.73733e6	−0.364604
$896$	−308742.	−0.0128477
$897$	−3.91591e7	−1.62499
$898$	313224.	0.0129618
$899$	−7.37440e6	−0.304318
$900$	4.39783e6	0.180980
$901$	1.47838e7	0.606702
$902$	3.58267e7	1.46619
$903$	3.68156e6	0.150249
$904$	1.04982e7	0.427261
$905$	5.99781e7	2.43428
$906$	1.32659e6	0.0536929
$907$	−135033.	−0.00545033	−0.00272516	−	0.999996i	$-0.500867\pi$
$907$	−135033.	−0.00545033	−0.00272516	+	0.999996i	$0.500867\pi$
$908$	1.39492e7	0.561480
$909$	9.54619e6	0.383195
$910$	6.59052e6	0.263825
$911$	2.95411e7	1.17932	0.589658	−	0.807653i	$-0.299263\pi$
$911$	2.95411e7	1.17932	0.589658	+	0.807653i	$0.299263\pi$
$912$	6.21574e6	0.247460
$913$	2.98955e6	0.118694
$914$	2.34183e6	0.0927235
$915$	2.26025e7	0.892492
$916$	1.98776e7	0.782756
$917$	737539.	0.0289642
$918$	−1.37026e6	−0.0536657
$919$	7.84760e6	0.306513	0.153256	−	0.988186i	$-0.451024\pi$
$919$	7.84760e6	0.306513	0.153256	+	0.988186i	$0.451024\pi$
$920$	−2.07599e7	−0.808642
$921$	9.90422e6	0.384743
$922$	2.24473e7	0.869636
$923$	2.89368e7	1.11801
$924$	−1.69611e6	−0.0653543
$925$	4.79771e7	1.84365
$926$	1.72061e7	0.659410
$927$	1.35898e7	0.519414
$928$	−1.02554e6	−0.0390917
$929$	6.87820e6	0.261478	0.130739	−	0.991417i	$-0.458265\pi$
$929$	6.87820e6	0.261478	0.130739	+	0.991417i	$0.458265\pi$
$930$	2.14015e7	0.811404
$931$	−4.43840e7	−1.67823
$932$	3.29705e6	0.124333
$933$	1.65471e7	0.622328
$934$	292893.	0.0109860
$935$	−2.37138e7	−0.887099
$936$	5.61408e6	0.209454
$937$	7.83325e6	0.291469	0.145735	−	0.989324i	$-0.453445\pi$
$937$	7.83325e6	0.291469	0.145735	+	0.989324i	$0.453445\pi$
$938$	−3.85841e6	−0.143186
$939$	2.34736e7	0.868792
$940$	−4.92146e6	−0.181666
$941$	−2.72700e7	−1.00395	−0.501973	−	0.864883i	$-0.667392\pi$
$941$	−2.72700e7	−1.00395	−0.501973	+	0.864883i	$0.667392\pi$
$942$	5.10189e6	0.187328
$943$	5.75714e7	2.10828
$944$	−891136.	−0.0325472
$945$	1.10911e6	0.0404011
$946$	5.42737e7	1.97179
$947$	−8.55332e6	−0.309927	−0.154964	−	0.987920i	$-0.549526\pi$
$947$	−8.55332e6	−0.309927	−0.154964	+	0.987920i	$0.549526\pi$
$948$	−692805.	−0.0250375
$949$	6.31260e7	2.27532
$950$	−3.66187e7	−1.31642
$951$	−1.01285e7	−0.363155
$952$	−566724.	−0.0202665
$953$	−2.85794e7	−1.01934	−0.509672	−	0.860369i	$-0.670233\pi$
$953$	−2.85794e7	−1.01934	−0.509672	+	0.860369i	$0.670233\pi$
$954$	−1.01933e7	−0.362615
$955$	−8.66068e6	−0.307287
$956$	−2.15921e7	−0.764099
$957$	−5.63395e6	−0.198853
$958$	−1.79525e7	−0.631990
$959$	−5.23081e6	−0.183663
$960$	2.97627e6	0.104230
$961$	2.55890e7	0.893809
$962$	6.12456e7	2.13372
$963$	−3.12129e6	−0.108460
$964$	−1.76646e7	−0.612226
$965$	3.25885e7	1.12654
$966$	−2.72555e6	−0.0939748
$967$	3.43115e7	1.17998	0.589989	−	0.807411i	$-0.299132\pi$
$967$	3.43115e7	1.17998	0.589989	+	0.807411i	$0.299132\pi$
$968$	−1.46968e7	−0.504122
$969$	1.14096e7	0.390355
$970$	1.02509e7	0.349812
$971$	9.79042e6	0.333237	0.166619	−	0.986021i	$-0.446715\pi$
$971$	9.79042e6	0.333237	0.166619	+	0.986021i	$0.446715\pi$
$972$	944784.	0.0320750
$973$	1.83287e6	0.0620653
$974$	−9.12572e6	−0.308226
$975$	−3.30742e7	−1.11424
$976$	7.96315e6	0.267584
$977$	−1.43734e6	−0.0481753	−0.0240876	−	0.999710i	$-0.507668\pi$
$977$	−1.43734e6	−0.0481753	−0.0240876	+	0.999710i	$0.507668\pi$
$978$	−1.31448e7	−0.439448
$979$	−8.33396e6	−0.277904
$980$	−2.12523e7	−0.706872
$981$	7.30306e6	0.242288
$982$	−1.34577e7	−0.445340
$983$	−7.13807e6	−0.235612	−0.117806	−	0.993037i	$-0.537586\pi$
$983$	−7.13807e6	−0.235612	−0.117806	+	0.993037i	$0.537586\pi$
$984$	−8.25379e6	−0.271748
$985$	−3.96109e7	−1.30084
$986$	−1.88248e6	−0.0616649
$987$	−646134.	−0.0211120
$988$	−4.67460e7	−1.52353
$989$	8.72147e7	2.83530
$990$	1.63505e7	0.530204
$991$	2.13936e6	0.0691991	0.0345995	−	0.999401i	$-0.488984\pi$
$991$	2.13936e6	0.0691991	0.0345995	+	0.999401i	$0.488984\pi$
$992$	7.54002e6	0.243273
$993$	2.21287e7	0.712170
$994$	2.01406e6	0.0646556
$995$	−1.07142e7	−0.343086
$996$	−688737.	−0.0219991
$997$	1.46533e7	0.466871	0.233435	−	0.972372i	$-0.425003\pi$
$997$	1.46533e7	0.466871	0.233435	+	0.972372i	$0.425003\pi$
$998$	1.51290e7	0.480822
$999$	1.03069e7	0.326749

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.h.1.6	✓	8
3.2	odd	2		1062.6.a.m.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.h.1.6	✓	8	1.1	even	1	trivial
1062.6.a.m.1.3		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +80.7365 q^{5} -36.0000 q^{6} +18.8441 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +80.7365 q^{5} -36.0000 q^{6} +18.8441 q^{7} -64.0000 q^{8} +81.0000 q^{9} -322.946 q^{10} -625.051 q^{11} +144.000 q^{12} -1082.96 q^{13} -75.3765 q^{14} +726.629 q^{15} +256.000 q^{16} +469.911 q^{17} -324.000 q^{18} +2697.80 q^{19} +1291.78 q^{20} +169.597 q^{21} +2500.21 q^{22} +4017.69 q^{23} -576.000 q^{24} +3393.38 q^{25} +4331.85 q^{26} +729.000 q^{27} +301.506 q^{28} +1001.51 q^{29} -2906.51 q^{30} -7363.30 q^{31} -1024.00 q^{32} -5625.46 q^{33} -1879.64 q^{34} +1521.41 q^{35} +1296.00 q^{36} +14138.4 q^{37} -10791.2 q^{38} -9746.67 q^{39} -5167.14 q^{40} +14329.5 q^{41} -678.388 q^{42} +21707.7 q^{43} -10000.8 q^{44} +6539.66 q^{45} -16070.7 q^{46} -3809.82 q^{47} +2304.00 q^{48} -16451.9 q^{49} -13573.5 q^{50} +4229.20 q^{51} -17327.4 q^{52} +31460.9 q^{53} -2916.00 q^{54} -50464.5 q^{55} -1206.02 q^{56} +24280.2 q^{57} -4006.03 q^{58} -3481.00 q^{59} +11626.1 q^{60} +31106.0 q^{61} +29453.2 q^{62} +1526.37 q^{63} +4096.00 q^{64} -87434.7 q^{65} +22501.8 q^{66} +51188.5 q^{67} +7518.58 q^{68} +36159.2 q^{69} -6085.63 q^{70} -26720.0 q^{71} -5184.00 q^{72} -58290.0 q^{73} -56553.7 q^{74} +30540.5 q^{75} +43164.9 q^{76} -11778.5 q^{77} +38986.7 q^{78} -4811.15 q^{79} +20668.5 q^{80} +6561.00 q^{81} -57318.0 q^{82} -4782.89 q^{83} +2713.55 q^{84} +37939.0 q^{85} -86830.8 q^{86} +9013.57 q^{87} +40003.3 q^{88} +13333.2 q^{89} -26158.6 q^{90} -20407.5 q^{91} +64283.0 q^{92} -66269.7 q^{93} +15239.3 q^{94} +217811. q^{95} -9216.00 q^{96} -31742.0 q^{97} +65807.6 q^{98} -50629.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9}+O(q^{10}) \) 8 * q - 32 * q^2 + 72 * q^3 + 128 * q^4 + 40 * q^5 - 288 * q^6 + 181 * q^7 - 512 * q^8 + 648 * q^9	\( 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9} - 160 q^{10} - 349 q^{11} + 1152 q^{12} + 121 q^{13} - 724 q^{14} + 360 q^{15} + 2048 q^{16} + 437 q^{17} - 2592 q^{18} + 1314 q^{19} + 640 q^{20} + 1629 q^{21} + 1396 q^{22} + 1224 q^{23} - 4608 q^{24} + 9592 q^{25} - 484 q^{26} + 5832 q^{27} + 2896 q^{28} + 5276 q^{29} - 1440 q^{30} + 18332 q^{31} - 8192 q^{32} - 3141 q^{33} - 1748 q^{34} + 19518 q^{35} + 10368 q^{36} + 30331 q^{37} - 5256 q^{38} + 1089 q^{39} - 2560 q^{40} + 8323 q^{41} - 6516 q^{42} + 30851 q^{43} - 5584 q^{44} + 3240 q^{45} - 4896 q^{46} - 5730 q^{47} + 18432 q^{48} + 32295 q^{49} - 38368 q^{50} + 3933 q^{51} + 1936 q^{52} - 33524 q^{53} - 23328 q^{54} + 23660 q^{55} - 11584 q^{56} + 11826 q^{57} - 21104 q^{58} - 27848 q^{59} + 5760 q^{60} + 2692 q^{61} - 73328 q^{62} + 14661 q^{63} + 32768 q^{64} - 59892 q^{65} + 12564 q^{66} + 56244 q^{67} + 6992 q^{68} + 11016 q^{69} - 78072 q^{70} - 48473 q^{71} - 41472 q^{72} - 30796 q^{73} - 121324 q^{74} + 86328 q^{75} + 21024 q^{76} + 59683 q^{77} - 4356 q^{78} + 135513 q^{79} + 10240 q^{80} + 52488 q^{81} - 33292 q^{82} - 88111 q^{83} + 26064 q^{84} + 114418 q^{85} - 123404 q^{86} + 47484 q^{87} + 22336 q^{88} - 112196 q^{89} - 12960 q^{90} + 377433 q^{91} + 19584 q^{92} + 164988 q^{93} + 22920 q^{94} + 328146 q^{95} - 73728 q^{96} + 551378 q^{97} - 129180 q^{98} - 28269 q^{99}+O(q^{100}) \) 8 * q - 32 * q^2 + 72 * q^3 + 128 * q^4 + 40 * q^5 - 288 * q^6 + 181 * q^7 - 512 * q^8 + 648 * q^9 - 160 * q^10 - 349 * q^11 + 1152 * q^12 + 121 * q^13 - 724 * q^14 + 360 * q^15 + 2048 * q^16 + 437 * q^17 - 2592 * q^18 + 1314 * q^19 + 640 * q^20 + 1629 * q^21 + 1396 * q^22 + 1224 * q^23 - 4608 * q^24 + 9592 * q^25 - 484 * q^26 + 5832 * q^27 + 2896 * q^28 + 5276 * q^29 - 1440 * q^30 + 18332 * q^31 - 8192 * q^32 - 3141 * q^33 - 1748 * q^34 + 19518 * q^35 + 10368 * q^36 + 30331 * q^37 - 5256 * q^38 + 1089 * q^39 - 2560 * q^40 + 8323 * q^41 - 6516 * q^42 + 30851 * q^43 - 5584 * q^44 + 3240 * q^45 - 4896 * q^46 - 5730 * q^47 + 18432 * q^48 + 32295 * q^49 - 38368 * q^50 + 3933 * q^51 + 1936 * q^52 - 33524 * q^53 - 23328 * q^54 + 23660 * q^55 - 11584 * q^56 + 11826 * q^57 - 21104 * q^58 - 27848 * q^59 + 5760 * q^60 + 2692 * q^61 - 73328 * q^62 + 14661 * q^63 + 32768 * q^64 - 59892 * q^65 + 12564 * q^66 + 56244 * q^67 + 6992 * q^68 + 11016 * q^69 - 78072 * q^70 - 48473 * q^71 - 41472 * q^72 - 30796 * q^73 - 121324 * q^74 + 86328 * q^75 + 21024 * q^76 + 59683 * q^77 - 4356 * q^78 + 135513 * q^79 + 10240 * q^80 + 52488 * q^81 - 33292 * q^82 - 88111 * q^83 + 26064 * q^84 + 114418 * q^85 - 123404 * q^86 + 47484 * q^87 + 22336 * q^88 - 112196 * q^89 - 12960 * q^90 + 377433 * q^91 + 19584 * q^92 + 164988 * q^93 + 22920 * q^94 + 328146 * q^95 - 73728 * q^96 + 551378 * q^97 - 129180 * q^98 - 28269 * q^99

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