LMFDB - Embedded newform 354.6.a.d.1.2

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:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 835x^{3} + 14269x^{2} - 82497x + 143433 $ x^5 - x^4 - 835x^3 + 14269x^2 - 82497*x + 143433
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$10.1932$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -21.6596 q^{5} -36.0000 q^{6} -77.1916 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -21.6596 q^{5} -36.0000 q^{6} -77.1916 q^{7} +64.0000 q^{8} +81.0000 q^{9} -86.6382 q^{10} -128.442 q^{11} -144.000 q^{12} +503.952 q^{13} -308.766 q^{14} +194.936 q^{15} +256.000 q^{16} +1619.88 q^{17} +324.000 q^{18} +2073.10 q^{19} -346.553 q^{20} +694.724 q^{21} -513.767 q^{22} -4009.85 q^{23} -576.000 q^{24} -2655.86 q^{25} +2015.81 q^{26} -729.000 q^{27} -1235.07 q^{28} -5400.85 q^{29} +779.744 q^{30} -3186.45 q^{31} +1024.00 q^{32} +1155.98 q^{33} +6479.52 q^{34} +1671.94 q^{35} +1296.00 q^{36} -9096.72 q^{37} +8292.39 q^{38} -4535.56 q^{39} -1386.21 q^{40} -2547.82 q^{41} +2778.90 q^{42} +9653.45 q^{43} -2055.07 q^{44} -1754.42 q^{45} -16039.4 q^{46} +11304.0 q^{47} -2304.00 q^{48} -10848.5 q^{49} -10623.5 q^{50} -14578.9 q^{51} +8063.23 q^{52} -27741.1 q^{53} -2916.00 q^{54} +2781.99 q^{55} -4940.26 q^{56} -18657.9 q^{57} -21603.4 q^{58} +3481.00 q^{59} +3118.98 q^{60} +615.936 q^{61} -12745.8 q^{62} -6252.52 q^{63} +4096.00 q^{64} -10915.4 q^{65} +4623.91 q^{66} -11719.6 q^{67} +25918.1 q^{68} +36088.7 q^{69} +6687.74 q^{70} -5850.85 q^{71} +5184.00 q^{72} -60564.3 q^{73} -36386.9 q^{74} +23902.8 q^{75} +33169.6 q^{76} +9914.63 q^{77} -18142.3 q^{78} +2865.64 q^{79} -5544.85 q^{80} +6561.00 q^{81} -10191.3 q^{82} -63356.1 q^{83} +11115.6 q^{84} -35085.9 q^{85} +38613.8 q^{86} +48607.7 q^{87} -8220.28 q^{88} -100326. q^{89} -7017.70 q^{90} -38900.8 q^{91} -64157.7 q^{92} +28678.1 q^{93} +45216.1 q^{94} -44902.4 q^{95} -9216.00 q^{96} -52037.8 q^{97} -43393.8 q^{98} -10403.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} - 24 q^{5} - 180 q^{6} - 103 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 - 24 * q^5 - 180 * q^6 - 103 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} - 24 q^{5} - 180 q^{6} - 103 q^{7} + 320 q^{8} + 405 q^{9} - 96 q^{10} - 211 q^{11} - 720 q^{12} - 97 q^{13} - 412 q^{14} + 216 q^{15} + 1280 q^{16} - 933 q^{17} + 1620 q^{18} - 218 q^{19} - 384 q^{20} + 927 q^{21} - 844 q^{22} - 1820 q^{23} - 2880 q^{24} + 1515 q^{25} - 388 q^{26} - 3645 q^{27} - 1648 q^{28} - 6464 q^{29} + 864 q^{30} - 9270 q^{31} + 5120 q^{32} + 1899 q^{33} - 3732 q^{34} + 11978 q^{35} + 6480 q^{36} - 7639 q^{37} - 872 q^{38} + 873 q^{39} - 1536 q^{40} - 39103 q^{41} + 3708 q^{42} - 8183 q^{43} - 3376 q^{44} - 1944 q^{45} - 7280 q^{46} - 36178 q^{47} - 11520 q^{48} - 63156 q^{49} + 6060 q^{50} + 8397 q^{51} - 1552 q^{52} - 29228 q^{53} - 14580 q^{54} - 120292 q^{55} - 6592 q^{56} + 1962 q^{57} - 25856 q^{58} + 17405 q^{59} + 3456 q^{60} - 112 q^{61} - 37080 q^{62} - 8343 q^{63} + 20480 q^{64} - 198752 q^{65} + 7596 q^{66} - 21384 q^{67} - 14928 q^{68} + 16380 q^{69} + 47912 q^{70} - 71819 q^{71} + 25920 q^{72} - 61382 q^{73} - 30556 q^{74} - 13635 q^{75} - 3488 q^{76} - 103107 q^{77} + 3492 q^{78} - 13243 q^{79} - 6144 q^{80} + 32805 q^{81} - 156412 q^{82} - 74321 q^{83} + 14832 q^{84} + 45950 q^{85} - 32732 q^{86} + 58176 q^{87} - 13504 q^{88} - 91334 q^{89} - 7776 q^{90} - 132237 q^{91} - 29120 q^{92} + 83430 q^{93} - 144712 q^{94} - 154198 q^{95} - 46080 q^{96} - 402052 q^{97} - 252624 q^{98} - 17091 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 - 24 * q^5 - 180 * q^6 - 103 * q^7 + 320 * q^8 + 405 * q^9 - 96 * q^10 - 211 * q^11 - 720 * q^12 - 97 * q^13 - 412 * q^14 + 216 * q^15 + 1280 * q^16 - 933 * q^17 + 1620 * q^18 - 218 * q^19 - 384 * q^20 + 927 * q^21 - 844 * q^22 - 1820 * q^23 - 2880 * q^24 + 1515 * q^25 - 388 * q^26 - 3645 * q^27 - 1648 * q^28 - 6464 * q^29 + 864 * q^30 - 9270 * q^31 + 5120 * q^32 + 1899 * q^33 - 3732 * q^34 + 11978 * q^35 + 6480 * q^36 - 7639 * q^37 - 872 * q^38 + 873 * q^39 - 1536 * q^40 - 39103 * q^41 + 3708 * q^42 - 8183 * q^43 - 3376 * q^44 - 1944 * q^45 - 7280 * q^46 - 36178 * q^47 - 11520 * q^48 - 63156 * q^49 + 6060 * q^50 + 8397 * q^51 - 1552 * q^52 - 29228 * q^53 - 14580 * q^54 - 120292 * q^55 - 6592 * q^56 + 1962 * q^57 - 25856 * q^58 + 17405 * q^59 + 3456 * q^60 - 112 * q^61 - 37080 * q^62 - 8343 * q^63 + 20480 * q^64 - 198752 * q^65 + 7596 * q^66 - 21384 * q^67 - 14928 * q^68 + 16380 * q^69 + 47912 * q^70 - 71819 * q^71 + 25920 * q^72 - 61382 * q^73 - 30556 * q^74 - 13635 * q^75 - 3488 * q^76 - 103107 * q^77 + 3492 * q^78 - 13243 * q^79 - 6144 * q^80 + 32805 * q^81 - 156412 * q^82 - 74321 * q^83 + 14832 * q^84 + 45950 * q^85 - 32732 * q^86 + 58176 * q^87 - 13504 * q^88 - 91334 * q^89 - 7776 * q^90 - 132237 * q^91 - 29120 * q^92 + 83430 * q^93 - 144712 * q^94 - 154198 * q^95 - 46080 * q^96 - 402052 * q^97 - 252624 * q^98 - 17091 * 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
$5$	−21.6596	−0.387458	−0.193729	−	0.981055i	$-0.562058\pi$
$5$	−21.6596	−0.387458	−0.193729	+	0.981055i	$0.562058\pi$
$6$	−36.0000	−0.408248
$7$	−77.1916	−0.595422	−0.297711	−	0.954656i	$-0.596223\pi$
$7$	−77.1916	−0.595422	−0.297711	+	0.954656i	$0.596223\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−86.6382	−0.273974
$11$	−128.442	−0.320055	−0.160028	−	0.987113i	$-0.551158\pi$
$11$	−128.442	−0.320055	−0.160028	+	0.987113i	$0.551158\pi$
$12$	−144.000	−0.288675
$13$	503.952	0.827048	0.413524	−	0.910493i	$-0.364298\pi$
$13$	503.952	0.827048	0.413524	+	0.910493i	$0.364298\pi$
$14$	−308.766	−0.421027
$15$	194.936	0.223699
$16$	256.000	0.250000
$17$	1619.88	1.35944	0.679721	−	0.733471i	$-0.262101\pi$
$17$	1619.88	1.35944	0.679721	+	0.733471i	$0.262101\pi$
$18$	324.000	0.235702
$19$	2073.10	1.31745	0.658727	−	0.752382i	$-0.271095\pi$
$19$	2073.10	1.31745	0.658727	+	0.752382i	$0.271095\pi$
$20$	−346.553	−0.193729
$21$	694.724	0.343767
$22$	−513.767	−0.226313
$23$	−4009.85	−1.58055	−0.790276	−	0.612751i	$-0.790063\pi$
$23$	−4009.85	−1.58055	−0.790276	+	0.612751i	$0.790063\pi$
$24$	−576.000	−0.204124
$25$	−2655.86	−0.849876
$26$	2015.81	0.584811
$27$	−729.000	−0.192450
$28$	−1235.07	−0.297711
$29$	−5400.85	−1.19252	−0.596262	−	0.802790i	$-0.703348\pi$
$29$	−5400.85	−1.19252	−0.596262	+	0.802790i	$0.703348\pi$
$30$	779.744	0.158179
$31$	−3186.45	−0.595529	−0.297765	−	0.954639i	$-0.596241\pi$
$31$	−3186.45	−0.595529	−0.297765	+	0.954639i	$0.596241\pi$
$32$	1024.00	0.176777
$33$	1155.98	0.184784
$34$	6479.52	0.961271
$35$	1671.94	0.230701
$36$	1296.00	0.166667
$37$	−9096.72	−1.09240	−0.546198	−	0.837656i	$-0.683925\pi$
$37$	−9096.72	−1.09240	−0.546198	+	0.837656i	$0.683925\pi$
$38$	8292.39	0.931581
$39$	−4535.56	−0.477496
$40$	−1386.21	−0.136987
$41$	−2547.82	−0.236706	−0.118353	−	0.992972i	$-0.537761\pi$
$41$	−2547.82	−0.236706	−0.118353	+	0.992972i	$0.537761\pi$
$42$	2778.90	0.243080
$43$	9653.45	0.796180	0.398090	−	0.917346i	$-0.369673\pi$
$43$	9653.45	0.796180	0.398090	+	0.917346i	$0.369673\pi$
$44$	−2055.07	−0.160028
$45$	−1754.42	−0.129153
$46$	−16039.4	−1.11762
$47$	11304.0	0.746429	0.373214	−	0.927745i	$-0.378256\pi$
$47$	11304.0	0.746429	0.373214	+	0.927745i	$0.378256\pi$
$48$	−2304.00	−0.144338
$49$	−10848.5	−0.645473
$50$	−10623.5	−0.600953
$51$	−14578.9	−0.784874
$52$	8063.23	0.413524
$53$	−27741.1	−1.35655	−0.678273	−	0.734810i	$-0.737271\pi$
$53$	−27741.1	−1.35655	−0.678273	+	0.734810i	$0.737271\pi$
$54$	−2916.00	−0.136083
$55$	2781.99	0.124008
$56$	−4940.26	−0.210513
$57$	−18657.9	−0.760633
$58$	−21603.4	−0.843242
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	3118.98	0.111849
$61$	615.936	0.0211939	0.0105970	−	0.999944i	$-0.496627\pi$
$61$	615.936	0.0211939	0.0105970	+	0.999944i	$0.496627\pi$
$62$	−12745.8	−0.421103
$63$	−6252.52	−0.198474
$64$	4096.00	0.125000
$65$	−10915.4	−0.320446
$66$	4623.91	0.130662
$67$	−11719.6	−0.318952	−0.159476	−	0.987202i	$-0.550980\pi$
$67$	−11719.6	−0.318952	−0.159476	+	0.987202i	$0.550980\pi$
$68$	25918.1	0.679721
$69$	36088.7	0.912532
$70$	6687.74	0.163130
$71$	−5850.85	−0.137744	−0.0688721	−	0.997626i	$-0.521940\pi$
$71$	−5850.85	−0.137744	−0.0688721	+	0.997626i	$0.521940\pi$
$72$	5184.00	0.117851
$73$	−60564.3	−1.33018	−0.665089	−	0.746764i	$-0.731606\pi$
$73$	−60564.3	−1.33018	−0.665089	+	0.746764i	$0.731606\pi$
$74$	−36386.9	−0.772441
$75$	23902.8	0.490676
$76$	33169.6	0.658727
$77$	9914.63	0.190568
$78$	−18142.3	−0.337641
$79$	2865.64	0.0516600	0.0258300	−	0.999666i	$-0.491777\pi$
$79$	2865.64	0.0516600	0.0258300	+	0.999666i	$0.491777\pi$
$80$	−5544.85	−0.0968645
$81$	6561.00	0.111111
$82$	−10191.3	−0.167376
$83$	−63356.1	−1.00947	−0.504735	−	0.863274i	$-0.668410\pi$
$83$	−63356.1	−1.00947	−0.504735	+	0.863274i	$0.668410\pi$
$84$	11115.6	0.171884
$85$	−35085.9	−0.526727
$86$	38613.8	0.562984
$87$	48607.7	0.688504
$88$	−8220.28	−0.113157
$89$	−100326.	−1.34258	−0.671289	−	0.741196i	$-0.734259\pi$
$89$	−100326.	−1.34258	−0.671289	+	0.741196i	$0.734259\pi$
$90$	−7017.70	−0.0913247
$91$	−38900.8	−0.492442
$92$	−64157.7	−0.790276
$93$	28678.1	0.343829
$94$	45216.1	0.527805
$95$	−44902.4	−0.510458
$96$	−9216.00	−0.102062
$97$	−52037.8	−0.561552	−0.280776	−	0.959773i	$-0.590592\pi$
$97$	−52037.8	−0.561552	−0.280776	+	0.959773i	$0.590592\pi$
$98$	−43393.8	−0.456418
$99$	−10403.8	−0.106685
$100$	−42493.8	−0.424938
$101$	12921.2	0.126037	0.0630185	−	0.998012i	$-0.479927\pi$
$101$	12921.2	0.126037	0.0630185	+	0.998012i	$0.479927\pi$
$102$	−58315.7	−0.554990
$103$	75510.1	0.701313	0.350657	−	0.936504i	$-0.385958\pi$
$103$	75510.1	0.701313	0.350657	+	0.936504i	$0.385958\pi$
$104$	32252.9	0.292405
$105$	−15047.4	−0.133195
$106$	−110965.	−0.959223
$107$	−174037.	−1.46954	−0.734770	−	0.678316i	$-0.762710\pi$
$107$	−174037.	−1.46954	−0.734770	+	0.678316i	$0.762710\pi$
$108$	−11664.0	−0.0962250
$109$	−28622.3	−0.230749	−0.115374	−	0.993322i	$-0.536807\pi$
$109$	−28622.3	−0.230749	−0.115374	+	0.993322i	$0.536807\pi$
$110$	11128.0	0.0876869
$111$	81870.4	0.630695
$112$	−19761.0	−0.148855
$113$	82618.1	0.608666	0.304333	−	0.952566i	$-0.401566\pi$
$113$	82618.1	0.608666	0.304333	+	0.952566i	$0.401566\pi$
$114$	−74631.5	−0.537849
$115$	86851.7	0.612398
$116$	−86413.6	−0.596262
$117$	40820.1	0.275683
$118$	13924.0	0.0920575
$119$	−125041.	−0.809442
$120$	12475.9	0.0790895
$121$	−144554.	−0.897565
$122$	2463.74	0.0149864
$123$	22930.3	0.136662
$124$	−50983.2	−0.297765
$125$	125211.	0.716749
$126$	−25010.1	−0.140342
$127$	194318.	1.06906	0.534532	−	0.845148i	$-0.320488\pi$
$127$	194318.	1.06906	0.534532	+	0.845148i	$0.320488\pi$
$128$	16384.0	0.0883883
$129$	−86881.0	−0.459675
$130$	−43661.5	−0.226590
$131$	34203.4	0.174137	0.0870685	−	0.996202i	$-0.472250\pi$
$131$	34203.4	0.174137	0.0870685	+	0.996202i	$0.472250\pi$
$132$	18495.6	0.0923920
$133$	−160026.	−0.784441
$134$	−46878.3	−0.225533
$135$	15789.8	0.0745663
$136$	103672.	0.480635
$137$	−383726.	−1.74671	−0.873353	−	0.487088i	$-0.838059\pi$
$137$	−383726.	−1.74671	−0.873353	+	0.487088i	$0.838059\pi$
$138$	144355.	0.645258
$139$	−158558.	−0.696069	−0.348034	−	0.937482i	$-0.613151\pi$
$139$	−158558.	−0.696069	−0.348034	+	0.937482i	$0.613151\pi$
$140$	26751.0	0.115350
$141$	−101736.	−0.430951
$142$	−23403.4	−0.0973998
$143$	−64728.5	−0.264701
$144$	20736.0	0.0833333
$145$	116980.	0.462053
$146$	−242257.	−0.940578
$147$	97636.1	0.372664
$148$	−145547.	−0.546198
$149$	499206.	1.84210	0.921052	−	0.389440i	$-0.127332\pi$
$149$	499206.	1.84210	0.921052	+	0.389440i	$0.127332\pi$
$150$	95611.1	0.346961
$151$	−267380.	−0.954303	−0.477152	−	0.878821i	$-0.658331\pi$
$151$	−267380.	−0.954303	−0.477152	+	0.878821i	$0.658331\pi$
$152$	132678.	0.465791
$153$	131210.	0.453147
$154$	39658.5	0.134752
$155$	69017.2	0.230743
$156$	−72569.0	−0.238748
$157$	584759.	1.89334	0.946668	−	0.322210i	$-0.104426\pi$
$157$	584759.	1.89334	0.946668	+	0.322210i	$0.104426\pi$
$158$	11462.6	0.0365291
$159$	249670.	0.783202
$160$	−22179.4	−0.0684935
$161$	309527.	0.941096
$162$	26244.0	0.0785674
$163$	8973.65	0.0264545	0.0132273	−	0.999913i	$-0.495790\pi$
$163$	8973.65	0.0264545	0.0132273	+	0.999913i	$0.495790\pi$
$164$	−40765.1	−0.118353
$165$	−25037.9	−0.0715960
$166$	−253424.	−0.713803
$167$	459147.	1.27397	0.636987	−	0.770875i	$-0.280181\pi$
$167$	459147.	1.27397	0.636987	+	0.770875i	$0.280181\pi$
$168$	44462.4	0.121540
$169$	−117326.	−0.315992
$170$	−140344.	−0.372452
$171$	167921.	0.439152
$172$	154455.	0.398090
$173$	139529.	0.354445	0.177222	−	0.984171i	$-0.443289\pi$
$173$	139529.	0.354445	0.177222	+	0.984171i	$0.443289\pi$
$174$	194431.	0.486846
$175$	205010.	0.506035
$176$	−32881.1	−0.0800138
$177$	−31329.0	−0.0751646
$178$	−401305.	−0.949346
$179$	−32783.4	−0.0764754	−0.0382377	−	0.999269i	$-0.512174\pi$
$179$	−32783.4	−0.0764754	−0.0382377	+	0.999269i	$0.512174\pi$
$180$	−28070.8	−0.0645763
$181$	−534516.	−1.21273	−0.606365	−	0.795186i	$-0.707373\pi$
$181$	−534516.	−1.21273	−0.606365	+	0.795186i	$0.707373\pi$
$182$	−155603.	−0.348209
$183$	−5543.43	−0.0122363
$184$	−256631.	−0.558810
$185$	197031.	0.423258
$186$	114712.	0.243124
$187$	−208061.	−0.435097
$188$	180864.	0.373214
$189$	56272.7	0.114589
$190$	−179609.	−0.360949
$191$	−205213.	−0.407025	−0.203513	−	0.979072i	$-0.565236\pi$
$191$	−205213.	−0.407025	−0.203513	+	0.979072i	$0.565236\pi$
$192$	−36864.0	−0.0721688
$193$	−200077.	−0.386637	−0.193318	−	0.981136i	$-0.561925\pi$
$193$	−200077.	−0.386637	−0.193318	+	0.981136i	$0.561925\pi$
$194$	−208151.	−0.397077
$195$	98238.3	0.185010
$196$	−173575.	−0.322736
$197$	−17387.7	−0.0319210	−0.0159605	−	0.999873i	$-0.505081\pi$
$197$	−17387.7	−0.0319210	−0.0159605	+	0.999873i	$0.505081\pi$
$198$	−41615.2	−0.0754377
$199$	230786.	0.413121	0.206560	−	0.978434i	$-0.433773\pi$
$199$	230786.	0.413121	0.206560	+	0.978434i	$0.433773\pi$
$200$	−169975.	−0.300477
$201$	105476.	0.184147
$202$	51684.6	0.0891216
$203$	416900.	0.710055
$204$	−233263.	−0.392437
$205$	55184.6	0.0917135
$206$	302040.	0.495903
$207$	−324798.	−0.526851
$208$	129012.	0.206762
$209$	−266272.	−0.421658
$210$	−60189.7	−0.0941833
$211$	724615.	1.12047	0.560236	−	0.828333i	$-0.310710\pi$
$211$	724615.	1.12047	0.560236	+	0.828333i	$0.310710\pi$
$212$	−443858.	−0.678273
$213$	52657.6	0.0795266
$214$	−696147.	−1.03912
$215$	−209089.	−0.308486
$216$	−46656.0	−0.0680414
$217$	245967.	0.354591
$218$	−114489.	−0.163164
$219$	545079.	0.767979
$220$	44511.9	0.0620040
$221$	816342.	1.12432
$222$	327482.	0.445969
$223$	−361244.	−0.486450	−0.243225	−	0.969970i	$-0.578205\pi$
$223$	−361244.	−0.486450	−0.243225	+	0.969970i	$0.578205\pi$
$224$	−79044.2	−0.105257
$225$	−215125.	−0.283292
$226$	330473.	0.430392
$227$	−251733.	−0.324246	−0.162123	−	0.986771i	$-0.551834\pi$
$227$	−251733.	−0.324246	−0.162123	+	0.986771i	$0.551834\pi$
$228$	−298526.	−0.380316
$229$	371899.	0.468636	0.234318	−	0.972160i	$-0.424714\pi$
$229$	371899.	0.468636	0.234318	+	0.972160i	$0.424714\pi$
$230$	347407.	0.433031
$231$	−89231.7	−0.110024
$232$	−345655.	−0.421621
$233$	−1.51927e6	−1.83335	−0.916675	−	0.399632i	$-0.869138\pi$
$233$	−1.51927e6	−1.83335	−0.916675	+	0.399632i	$0.869138\pi$
$234$	163280.	0.194937
$235$	−244840.	−0.289210
$236$	55696.0	0.0650945
$237$	−25790.8	−0.0298259
$238$	−500165.	−0.572362
$239$	−1.03167e6	−1.16827	−0.584137	−	0.811655i	$-0.698567\pi$
$239$	−1.03167e6	−1.16827	−0.584137	+	0.811655i	$0.698567\pi$
$240$	49903.6	0.0559247
$241$	1.61536e6	1.79154	0.895771	−	0.444517i	$-0.146625\pi$
$241$	1.61536e6	1.79154	0.895771	+	0.444517i	$0.146625\pi$
$242$	−578215.	−0.634674
$243$	−59049.0	−0.0641500
$244$	9854.98	0.0105970
$245$	234973.	0.250094
$246$	91721.4	0.0966347
$247$	1.04474e6	1.08960
$248$	−203933.	−0.210551
$249$	570205.	0.582818
$250$	500844.	0.506818
$251$	450196.	0.451042	0.225521	−	0.974238i	$-0.427592\pi$
$251$	450196.	0.451042	0.225521	+	0.974238i	$0.427592\pi$
$252$	−100040.	−0.0992370
$253$	515033.	0.505864
$254$	777273.	0.755943
$255$	315773.	0.304106
$256$	65536.0	0.0625000
$257$	−1.64191e6	−1.55066	−0.775331	−	0.631555i	$-0.782417\pi$
$257$	−1.64191e6	−1.55066	−0.775331	+	0.631555i	$0.782417\pi$
$258$	−347524.	−0.325039
$259$	702190.	0.650437
$260$	−174646.	−0.160223
$261$	−437469.	−0.397508
$262$	136814.	0.123134
$263$	856037.	0.763138	0.381569	−	0.924340i	$-0.375384\pi$
$263$	856037.	0.763138	0.381569	+	0.924340i	$0.375384\pi$
$264$	73982.5	0.0653310
$265$	600861.	0.525604
$266$	−640103.	−0.554684
$267$	902936.	0.775137
$268$	−187513.	−0.159476
$269$	−1.84037e6	−1.55069	−0.775345	−	0.631538i	$-0.782424\pi$
$269$	−1.84037e6	−1.55069	−0.775345	+	0.631538i	$0.782424\pi$
$270$	63159.3	0.0527264
$271$	1.06485e6	0.880774	0.440387	−	0.897808i	$-0.354841\pi$
$271$	1.06485e6	0.880774	0.440387	+	0.897808i	$0.354841\pi$
$272$	414689.	0.339861
$273$	350107.	0.284312
$274$	−1.53490e6	−1.23511
$275$	341124.	0.272007
$276$	577419.	0.456266
$277$	1.29712e6	1.01574	0.507869	−	0.861434i	$-0.330433\pi$
$277$	1.29712e6	1.01574	0.507869	+	0.861434i	$0.330433\pi$
$278$	−634233.	−0.492195
$279$	−258103.	−0.198510
$280$	107004.	0.0815651
$281$	1.01030e6	0.763280	0.381640	−	0.924311i	$-0.375359\pi$
$281$	1.01030e6	0.763280	0.381640	+	0.924311i	$0.375359\pi$
$282$	−406945.	−0.304728
$283$	−2.21030e6	−1.64053	−0.820266	−	0.571982i	$-0.806175\pi$
$283$	−2.21030e6	−1.64053	−0.820266	+	0.571982i	$0.806175\pi$
$284$	−93613.6	−0.0688721
$285$	404121.	0.294713
$286$	−258914.	−0.187172
$287$	196670.	0.140940
$288$	82944.0	0.0589256
$289$	1.20416e6	0.848083
$290$	467920.	0.326721
$291$	468341.	0.324212
$292$	−969029.	−0.665089
$293$	445187.	0.302952	0.151476	−	0.988461i	$-0.451597\pi$
$293$	445187.	0.302952	0.151476	+	0.988461i	$0.451597\pi$
$294$	390545.	0.263513
$295$	−75396.9	−0.0504427
$296$	−582190.	−0.386221
$297$	93634.1	0.0615947
$298$	1.99682e6	1.30256
$299$	−2.02077e6	−1.30719
$300$	382444.	0.245338
$301$	−745165.	−0.474063
$302$	−1.06952e6	−0.674794
$303$	−116290.	−0.0727675
$304$	530713.	0.329364
$305$	−13340.9	−0.00821175
$306$	524841.	0.320424
$307$	179838.	0.108902	0.0544511	−	0.998516i	$-0.482659\pi$
$307$	179838.	0.108902	0.0544511	+	0.998516i	$0.482659\pi$
$308$	158634.	0.0952839
$309$	−679591.	−0.404903
$310$	276069.	0.163160
$311$	2.88520e6	1.69151	0.845757	−	0.533568i	$-0.179149\pi$
$311$	2.88520e6	1.69151	0.845757	+	0.533568i	$0.179149\pi$
$312$	−290276.	−0.168820
$313$	−183169.	−0.105680	−0.0528399	−	0.998603i	$-0.516827\pi$
$313$	−183169.	−0.105680	−0.0528399	+	0.998603i	$0.516827\pi$
$314$	2.33904e6	1.33879
$315$	135427.	0.0769003
$316$	45850.3	0.0258300
$317$	−2.34774e6	−1.31221	−0.656104	−	0.754671i	$-0.727797\pi$
$317$	−2.34774e6	−1.31221	−0.656104	+	0.754671i	$0.727797\pi$
$318$	998681.	0.553807
$319$	693695.	0.381674
$320$	−88717.6	−0.0484322
$321$	1.56633e6	0.848439
$322$	1.23811e6	0.665455
$323$	3.35817e6	1.79100
$324$	104976.	0.0555556
$325$	−1.33843e6	−0.702888
$326$	35894.6	0.0187062
$327$	257601.	0.133223
$328$	−163060.	−0.0836881
$329$	−872576.	−0.444440
$330$	−100152.	−0.0506260
$331$	3.56234e6	1.78717	0.893584	−	0.448895i	$-0.148182\pi$
$331$	3.56234e6	1.78717	0.893584	+	0.448895i	$0.148182\pi$
$332$	−1.01370e6	−0.504735
$333$	−736834.	−0.364132
$334$	1.83659e6	0.900835
$335$	253841.	0.123580
$336$	177849.	0.0859418
$337$	3.88763e6	1.86470	0.932352	−	0.361553i	$-0.117753\pi$
$337$	3.88763e6	1.86470	0.932352	+	0.361553i	$0.117753\pi$
$338$	−469303.	−0.223440
$339$	−743563.	−0.351414
$340$	−561374.	−0.263363
$341$	409274.	0.190602
$342$	671684.	0.310527
$343$	2.13477e6	0.979751
$344$	617821.	0.281492
$345$	−781665.	−0.353568
$346$	558115.	0.250630
$347$	−2.51278e6	−1.12029	−0.560145	−	0.828395i	$-0.689255\pi$
$347$	−2.51278e6	−1.12029	−0.560145	+	0.828395i	$0.689255\pi$
$348$	777723.	0.344252
$349$	887421.	0.390001	0.195001	−	0.980803i	$-0.437529\pi$
$349$	887421.	0.390001	0.195001	+	0.980803i	$0.437529\pi$
$350$	820041.	0.357821
$351$	−367381.	−0.159165
$352$	−131524.	−0.0565783
$353$	−2.15798e6	−0.921745	−0.460872	−	0.887466i	$-0.652463\pi$
$353$	−2.15798e6	−0.921745	−0.460872	+	0.887466i	$0.652463\pi$
$354$	−125316.	−0.0531494
$355$	126727.	0.0533700
$356$	−1.60522e6	−0.671289
$357$	1.12537e6	0.467331
$358$	−131134.	−0.0540763
$359$	−2.87295e6	−1.17650	−0.588249	−	0.808680i	$-0.700183\pi$
$359$	−2.87295e6	−1.17650	−0.588249	+	0.808680i	$0.700183\pi$
$360$	−112283.	−0.0456624
$361$	1.82163e6	0.735687
$362$	−2.13806e6	−0.857530
$363$	1.30098e6	0.518209
$364$	−622413.	−0.246221
$365$	1.31180e6	0.515388
$366$	−22173.7	−0.00865238
$367$	4.62685e6	1.79317	0.896583	−	0.442877i	$-0.146042\pi$
$367$	4.62685e6	1.79317	0.896583	+	0.442877i	$0.146042\pi$
$368$	−1.02652e6	−0.395138
$369$	−206373.	−0.0789019
$370$	788123.	0.299288
$371$	2.14138e6	0.807717
$372$	458849.	0.171915
$373$	1.71103e6	0.636774	0.318387	−	0.947961i	$-0.396859\pi$
$373$	1.71103e6	0.636774	0.318387	+	0.947961i	$0.396859\pi$
$374$	−832242.	−0.307660
$375$	−1.12690e6	−0.413815
$376$	723458.	0.263902
$377$	−2.72177e6	−0.986274
$378$	225091.	0.0810267
$379$	−2.67669e6	−0.957194	−0.478597	−	0.878035i	$-0.658855\pi$
$379$	−2.67669e6	−0.957194	−0.478597	+	0.878035i	$0.658855\pi$
$380$	−718438.	−0.255229
$381$	−1.74886e6	−0.617225
$382$	−820852.	−0.287810
$383$	2.72225e6	0.948269	0.474135	−	0.880452i	$-0.342761\pi$
$383$	2.72225e6	0.948269	0.474135	+	0.880452i	$0.342761\pi$
$384$	−147456.	−0.0510310
$385$	−214747.	−0.0738370
$386$	−800307.	−0.273394
$387$	781929.	0.265393
$388$	−832605.	−0.280776
$389$	−4.44255e6	−1.48853	−0.744267	−	0.667882i	$-0.767201\pi$
$389$	−4.44255e6	−1.48853	−0.744267	+	0.667882i	$0.767201\pi$
$390$	392953.	0.130822
$391$	−6.49548e6	−2.14867
$392$	−694301.	−0.228209
$393$	−307831.	−0.100538
$394$	−69550.8	−0.0225716
$395$	−62068.6	−0.0200161
$396$	−166461.	−0.0533425
$397$	2.28358e6	0.727178	0.363589	−	0.931559i	$-0.381551\pi$
$397$	2.28358e6	0.727178	0.363589	+	0.931559i	$0.381551\pi$
$398$	923144.	0.292120
$399$	1.44023e6	0.452897
$400$	−679901.	−0.212469
$401$	−1.10996e6	−0.344706	−0.172353	−	0.985035i	$-0.555137\pi$
$401$	−1.10996e6	−0.344706	−0.172353	+	0.985035i	$0.555137\pi$
$402$	421905.	0.130211
$403$	−1.60582e6	−0.492531
$404$	206739.	0.0630185
$405$	−142108.	−0.0430509
$406$	1.66760e6	0.502085
$407$	1.16840e6	0.349627
$408$	−933051.	−0.277495
$409$	132134.	0.0390578	0.0195289	−	0.999809i	$-0.493783\pi$
$409$	132134.	0.0390578	0.0195289	+	0.999809i	$0.493783\pi$
$410$	220738.	0.0648512
$411$	3.45353e6	1.00846
$412$	1.20816e6	0.350657
$413$	−268704.	−0.0775173
$414$	−1.29919e6	−0.372540
$415$	1.37227e6	0.391127
$416$	516046.	0.146203
$417$	1.42702e6	0.401875
$418$	−1.06509e6	−0.298157
$419$	−2.87598e6	−0.800296	−0.400148	−	0.916450i	$-0.631041\pi$
$419$	−2.87598e6	−0.800296	−0.400148	+	0.916450i	$0.631041\pi$
$420$	−240759.	−0.0665976
$421$	−5.73451e6	−1.57685	−0.788427	−	0.615128i	$-0.789104\pi$
$421$	−5.73451e6	−1.57685	−0.788427	+	0.615128i	$0.789104\pi$
$422$	2.89846e6	0.792293
$423$	915626.	0.248810
$424$	−1.77543e6	−0.479611
$425$	−4.30218e6	−1.15536
$426$	210631.	0.0562338
$427$	−47545.1	−0.0126193
$428$	−2.78459e6	−0.734770
$429$	582556.	0.152825
$430$	−836358.	−0.218133
$431$	−1.11655e6	−0.289523	−0.144762	−	0.989467i	$-0.546242\pi$
$431$	−1.11655e6	−0.289523	−0.144762	+	0.989467i	$0.546242\pi$
$432$	−186624.	−0.0481125
$433$	−3.62335e6	−0.928733	−0.464366	−	0.885643i	$-0.653718\pi$
$433$	−3.62335e6	−0.928733	−0.464366	+	0.885643i	$0.653718\pi$
$434$	983869.	0.250734
$435$	−1.05282e6	−0.266766
$436$	−457957.	−0.115374
$437$	−8.31282e6	−2.08231
$438$	2.18032e6	0.543043
$439$	−3.83526e6	−0.949804	−0.474902	−	0.880039i	$-0.657516\pi$
$439$	−3.83526e6	−0.949804	−0.474902	+	0.880039i	$0.657516\pi$
$440$	178048.	0.0438434
$441$	−878725.	−0.215158
$442$	3.26537e6	0.795017
$443$	−3.94768e6	−0.955724	−0.477862	−	0.878435i	$-0.658588\pi$
$443$	−3.94768e6	−0.955724	−0.477862	+	0.878435i	$0.658588\pi$
$444$	1.30993e6	0.315348
$445$	2.17302e6	0.520192
$446$	−1.44497e6	−0.343972
$447$	−4.49285e6	−1.06354
$448$	−316177.	−0.0744277
$449$	−3.50275e6	−0.819962	−0.409981	−	0.912094i	$-0.634465\pi$
$449$	−3.50275e6	−0.819962	−0.409981	+	0.912094i	$0.634465\pi$
$450$	−860500.	−0.200318
$451$	327246.	0.0757589
$452$	1.32189e6	0.304333
$453$	2.40642e6	0.550967
$454$	−1.00693e6	−0.229277
$455$	842575.	0.190801
$456$	−1.19410e6	−0.268924
$457$	2.75689e6	0.617489	0.308745	−	0.951145i	$-0.400091\pi$
$457$	2.75689e6	0.617489	0.308745	+	0.951145i	$0.400091\pi$
$458$	1.48759e6	0.331376
$459$	−1.18089e6	−0.261625
$460$	1.38963e6	0.306199
$461$	−1.88180e6	−0.412403	−0.206201	−	0.978510i	$-0.566110\pi$
$461$	−1.88180e6	−0.412403	−0.206201	+	0.978510i	$0.566110\pi$
$462$	−356927.	−0.0777990
$463$	5.04122e6	1.09291	0.546454	−	0.837489i	$-0.315977\pi$
$463$	5.04122e6	1.09291	0.546454	+	0.837489i	$0.315977\pi$
$464$	−1.38262e6	−0.298131
$465$	−621154.	−0.133219
$466$	−6.07709e6	−1.29637
$467$	−1.85991e6	−0.394638	−0.197319	−	0.980339i	$-0.563223\pi$
$467$	−1.85991e6	−0.394638	−0.197319	+	0.980339i	$0.563223\pi$
$468$	653121.	0.137841
$469$	904652.	0.189911
$470$	−979361.	−0.204502
$471$	−5.26283e6	−1.09312
$472$	222784.	0.0460287
$473$	−1.23991e6	−0.254822
$474$	−103163.	−0.0210901
$475$	−5.50586e6	−1.11967
$476$	−2.00066e6	−0.404721
$477$	−2.24703e6	−0.452182
$478$	−4.12666e6	−0.826094
$479$	4.30254e6	0.856813	0.428406	−	0.903586i	$-0.359075\pi$
$479$	4.30254e6	0.856813	0.428406	+	0.903586i	$0.359075\pi$
$480$	199614.	0.0395448
$481$	−4.58430e6	−0.903464
$482$	6.46144e6	1.26681
$483$	−2.78574e6	−0.543342
$484$	−2.31286e6	−0.448782
$485$	1.12712e6	0.217578
$486$	−236196.	−0.0453609
$487$	3.70305e6	0.707517	0.353759	−	0.935337i	$-0.384903\pi$
$487$	3.70305e6	0.707517	0.353759	+	0.935337i	$0.384903\pi$
$488$	39419.9	0.00749318
$489$	−80762.8	−0.0152735
$490$	939891.	0.176843
$491$	−546082.	−0.102224	−0.0511121	−	0.998693i	$-0.516277\pi$
$491$	−546082.	−0.102224	−0.0511121	+	0.998693i	$0.516277\pi$
$492$	366886.	0.0683310
$493$	−8.74874e6	−1.62117
$494$	4.17896e6	0.770462
$495$	225342.	0.0413360
$496$	−815732.	−0.148882
$497$	451636.	0.0820159
$498$	2.28082e6	0.412114
$499$	1.51200e6	0.271832	0.135916	−	0.990720i	$-0.456602\pi$
$499$	1.51200e6	0.271832	0.135916	+	0.990720i	$0.456602\pi$
$500$	2.00338e6	0.358375
$501$	−4.13232e6	−0.735529
$502$	1.80078e6	0.318935
$503$	−7.95851e6	−1.40253	−0.701265	−	0.712901i	$-0.747381\pi$
$503$	−7.95851e6	−1.40253	−0.701265	+	0.712901i	$0.747381\pi$
$504$	−400161.	−0.0701711
$505$	−279867.	−0.0488340
$506$	2.06013e6	0.357700
$507$	1.05593e6	0.182438
$508$	3.10909e6	0.534532
$509$	8.23938e6	1.40961	0.704807	−	0.709400i	$-0.251034\pi$
$509$	8.23938e6	1.40961	0.704807	+	0.709400i	$0.251034\pi$
$510$	1.26309e6	0.215035
$511$	4.67506e6	0.792017
$512$	262144.	0.0441942
$513$	−1.51129e6	−0.253544
$514$	−6.56765e6	−1.09648
$515$	−1.63552e6	−0.271729
$516$	−1.39010e6	−0.229837
$517$	−1.45191e6	−0.238898
$518$	2.80876e6	0.459928
$519$	−1.25576e6	−0.204639
$520$	−698584.	−0.113295
$521$	−1.07297e7	−1.73179	−0.865894	−	0.500227i	$-0.833250\pi$
$521$	−1.07297e7	−1.73179	−0.865894	+	0.500227i	$0.833250\pi$
$522$	−1.74988e6	−0.281081
$523$	1.02869e7	1.64449	0.822244	−	0.569136i	$-0.192722\pi$
$523$	1.02869e7	1.64449	0.822244	+	0.569136i	$0.192722\pi$
$524$	547255.	0.0870685
$525$	−1.84509e6	−0.292159
$526$	3.42415e6	0.539620
$527$	−5.16167e6	−0.809588
$528$	295930.	0.0461960
$529$	9.64258e6	1.49815
$530$	2.40344e6	0.371658
$531$	281961.	0.0433963
$532$	−2.56041e6	−0.392221
$533$	−1.28398e6	−0.195767
$534$	3.61174e6	0.548105
$535$	3.76956e6	0.569385
$536$	−750052.	−0.112766
$537$	295051.	0.0441531
$538$	−7.36149e6	−1.09650
$539$	1.39340e6	0.206587
$540$	252637.	0.0372832
$541$	−4.20979e6	−0.618397	−0.309199	−	0.950997i	$-0.600061\pi$
$541$	−4.20979e6	−0.618397	−0.309199	+	0.950997i	$0.600061\pi$
$542$	4.25939e6	0.622801
$543$	4.81065e6	0.700170
$544$	1.65876e6	0.240318
$545$	619947.	0.0894054
$546$	1.40043e6	0.201039
$547$	1.85114e6	0.264527	0.132264	−	0.991215i	$-0.457775\pi$
$547$	1.85114e6	0.264527	0.132264	+	0.991215i	$0.457775\pi$
$548$	−6.13961e6	−0.873353
$549$	49890.8	0.00706464
$550$	1.36450e6	0.192338
$551$	−1.11965e7	−1.57110
$552$	2.30968e6	0.322629
$553$	−221203.	−0.0307595
$554$	5.18849e6	0.718235
$555$	−1.77328e6	−0.244368
$556$	−2.53693e6	−0.348034
$557$	6.03571e6	0.824309	0.412155	−	0.911114i	$-0.364776\pi$
$557$	6.03571e6	0.824309	0.412155	+	0.911114i	$0.364776\pi$
$558$	−1.03241e6	−0.140368
$559$	4.86487e6	0.658479
$560$	428016.	0.0576752
$561$	1.87254e6	0.251203
$562$	4.04120e6	0.539721
$563$	−8.40073e6	−1.11698	−0.558491	−	0.829511i	$-0.688619\pi$
$563$	−8.40073e6	−1.11698	−0.558491	+	0.829511i	$0.688619\pi$
$564$	−1.62778e6	−0.215475
$565$	−1.78947e6	−0.235833
$566$	−8.84120e6	−1.16003
$567$	−506454.	−0.0661580
$568$	−374454.	−0.0486999
$569$	−1.33517e6	−0.172885	−0.0864423	−	0.996257i	$-0.527550\pi$
$569$	−1.33517e6	−0.172885	−0.0864423	+	0.996257i	$0.527550\pi$
$570$	1.61649e6	0.208394
$571$	5.90428e6	0.757838	0.378919	−	0.925430i	$-0.376296\pi$
$571$	5.90428e6	0.757838	0.378919	+	0.925430i	$0.376296\pi$
$572$	−1.03566e6	−0.132350
$573$	1.84692e6	0.234996
$574$	786680.	0.0996594
$575$	1.06496e7	1.34327
$576$	331776.	0.0416667
$577$	−2.97450e6	−0.371941	−0.185971	−	0.982555i	$-0.559543\pi$
$577$	−2.97450e6	−0.371941	−0.185971	+	0.982555i	$0.559543\pi$
$578$	4.81663e6	0.599685
$579$	1.80069e6	0.223225
$580$	1.87168e6	0.231027
$581$	4.89056e6	0.601060
$582$	1.87336e6	0.229253
$583$	3.56312e6	0.434170
$584$	−3.87612e6	−0.470289
$585$	−884145.	−0.106815
$586$	1.78075e6	0.214219
$587$	9.39558e6	1.12546	0.562728	−	0.826642i	$-0.309752\pi$
$587$	9.39558e6	1.12546	0.562728	+	0.826642i	$0.309752\pi$
$588$	1.56218e6	0.186332
$589$	−6.60583e6	−0.784583
$590$	−301588.	−0.0356684
$591$	156489.	0.0184296
$592$	−2.32876e6	−0.273099
$593$	−8.93278e6	−1.04316	−0.521579	−	0.853203i	$-0.674657\pi$
$593$	−8.93278e6	−1.04316	−0.521579	+	0.853203i	$0.674657\pi$
$594$	374536.	0.0435540
$595$	2.70834e6	0.313625
$596$	7.98729e6	0.921052
$597$	−2.07707e6	−0.238515
$598$	−8.08309e6	−0.924324
$599$	6.34033e6	0.722013	0.361006	−	0.932563i	$-0.382433\pi$
$599$	6.34033e6	0.722013	0.361006	+	0.932563i	$0.382433\pi$
$600$	1.52978e6	0.173480
$601$	−5.69381e6	−0.643008	−0.321504	−	0.946908i	$-0.604188\pi$
$601$	−5.69381e6	−0.643008	−0.321504	+	0.946908i	$0.604188\pi$
$602$	−2.98066e6	−0.335213
$603$	−949285.	−0.106317
$604$	−4.27808e6	−0.477152
$605$	3.13097e6	0.347769
$606$	−465162.	−0.0514544
$607$	−2.78296e6	−0.306574	−0.153287	−	0.988182i	$-0.548986\pi$
$607$	−2.78296e6	−0.306574	−0.153287	+	0.988182i	$0.548986\pi$
$608$	2.12285e6	0.232895
$609$	−3.75210e6	−0.409951
$610$	−53363.6	−0.00580658
$611$	5.69668e6	0.617332
$612$	2.09937e6	0.226574
$613$	−8.57651e6	−0.921848	−0.460924	−	0.887440i	$-0.652482\pi$
$613$	−8.57651e6	−0.921848	−0.460924	+	0.887440i	$0.652482\pi$
$614$	719354.	0.0770055
$615$	−496661.	−0.0529508
$616$	634536.	0.0673759
$617$	3.81595e6	0.403543	0.201771	−	0.979433i	$-0.435330\pi$
$617$	3.81595e6	0.403543	0.201771	+	0.979433i	$0.435330\pi$
$618$	−2.71836e6	−0.286310
$619$	−1.86803e7	−1.95955	−0.979776	−	0.200096i	$-0.935874\pi$
$619$	−1.86803e7	−1.95955	−0.979776	+	0.200096i	$0.935874\pi$
$620$	1.10427e6	0.115371
$621$	2.92318e6	0.304177
$622$	1.15408e7	1.19608
$623$	7.74434e6	0.799400
$624$	−1.16110e6	−0.119374
$625$	5.58756e6	0.572166
$626$	−732677.	−0.0747269
$627$	2.39645e6	0.243444
$628$	9.35614e6	0.946668
$629$	−1.47356e7	−1.48505
$630$	541707.	0.0543767
$631$	4.50388e6	0.450312	0.225156	−	0.974323i	$-0.427711\pi$
$631$	4.50388e6	0.450312	0.225156	+	0.974323i	$0.427711\pi$
$632$	183401.	0.0182646
$633$	−6.52153e6	−0.646905
$634$	−9.39097e6	−0.927871
$635$	−4.20885e6	−0.414218
$636$	3.99472e6	0.391601
$637$	−5.46710e6	−0.533837
$638$	2.77478e6	0.269884
$639$	−473919.	−0.0459147
$640$	−354870.	−0.0342468
$641$	9.29996e6	0.893997	0.446998	−	0.894535i	$-0.352493\pi$
$641$	9.29996e6	0.893997	0.446998	+	0.894535i	$0.352493\pi$
$642$	6.26532e6	0.599937
$643$	1.66366e6	0.158685	0.0793427	−	0.996847i	$-0.474718\pi$
$643$	1.66366e6	0.158685	0.0793427	+	0.996847i	$0.474718\pi$
$644$	4.95243e6	0.470548
$645$	1.88181e6	0.178105
$646$	1.34327e7	1.26643
$647$	−803956.	−0.0755043	−0.0377521	−	0.999287i	$-0.512020\pi$
$647$	−803956.	−0.0755043	−0.0377521	+	0.999287i	$0.512020\pi$
$648$	419904.	0.0392837
$649$	−447106.	−0.0416676
$650$	−5.35371e6	−0.497017
$651$	−2.21371e6	−0.204723
$652$	143578.	0.0132273
$653$	2.07948e7	1.90841	0.954205	−	0.299154i	$-0.0967046\pi$
$653$	2.07948e7	1.90841	0.954205	+	0.299154i	$0.0967046\pi$
$654$	1.03040e6	0.0942027
$655$	−740831.	−0.0674708
$656$	−652241.	−0.0591764
$657$	−4.90571e6	−0.443393
$658$	−3.49030e6	−0.314267
$659$	−4.69572e6	−0.421200	−0.210600	−	0.977572i	$-0.567542\pi$
$659$	−4.69572e6	−0.421200	−0.210600	+	0.977572i	$0.567542\pi$
$660$	−400607.	−0.0357980
$661$	−3.23621e6	−0.288093	−0.144047	−	0.989571i	$-0.546012\pi$
$661$	−3.23621e6	−0.288093	−0.144047	+	0.989571i	$0.546012\pi$
$662$	1.42494e7	1.26372
$663$	−7.34707e6	−0.649128
$664$	−4.05479e6	−0.356901
$665$	3.46609e6	0.303938
$666$	−2.94734e6	−0.257480
$667$	2.16566e7	1.88485
$668$	7.34635e6	0.636987
$669$	3.25119e6	0.280852
$670$	1.01536e6	0.0873845
$671$	−79112.0	−0.00678322
$672$	711398.	0.0607700
$673$	1.35095e7	1.14974	0.574872	−	0.818244i	$-0.305052\pi$
$673$	1.35095e7	1.14974	0.574872	+	0.818244i	$0.305052\pi$
$674$	1.55505e7	1.31854
$675$	1.93612e6	0.163559
$676$	−1.87721e6	−0.157996
$677$	−3.12855e6	−0.262344	−0.131172	−	0.991360i	$-0.541874\pi$
$677$	−3.12855e6	−0.262344	−0.131172	+	0.991360i	$0.541874\pi$
$678$	−2.97425e6	−0.248487
$679$	4.01688e6	0.334360
$680$	−2.24550e6	−0.186226
$681$	2.26559e6	0.187204
$682$	1.63710e6	0.134776
$683$	2.88511e6	0.236652	0.118326	−	0.992975i	$-0.462247\pi$
$683$	2.88511e6	0.236652	0.118326	+	0.992975i	$0.462247\pi$
$684$	2.68673e6	0.219576
$685$	8.31133e6	0.676775
$686$	8.53907e6	0.692788
$687$	−3.34709e6	−0.270567
$688$	2.47128e6	0.199045
$689$	−1.39802e7	−1.12193
$690$	−3.12666e6	−0.250010
$691$	−1.86565e7	−1.48640	−0.743201	−	0.669068i	$-0.766693\pi$
$691$	−1.86565e7	−1.48640	−0.743201	+	0.669068i	$0.766693\pi$
$692$	2.23246e6	0.177222
$693$	803085.	0.0635226
$694$	−1.00511e7	−0.792164
$695$	3.43430e6	0.269697
$696$	3.11089e6	0.243423
$697$	−4.12716e6	−0.321788
$698$	3.54968e6	0.275773
$699$	1.36734e7	1.05849
$700$	3.28016e6	0.253018
$701$	−2.18409e7	−1.67871	−0.839354	−	0.543586i	$-0.817066\pi$
$701$	−2.18409e7	−1.67871	−0.839354	+	0.543586i	$0.817066\pi$
$702$	−1.46952e6	−0.112547
$703$	−1.88584e7	−1.43918
$704$	−526098.	−0.0400069
$705$	2.20356e6	0.166975
$706$	−8.63192e6	−0.651772
$707$	−997405.	−0.0750452
$708$	−501264.	−0.0375823
$709$	2.33017e7	1.74089	0.870446	−	0.492265i	$-0.163831\pi$
$709$	2.33017e7	1.74089	0.870446	+	0.492265i	$0.163831\pi$
$710$	506907.	0.0377383
$711$	232117.	0.0172200
$712$	−6.42088e6	−0.474673
$713$	1.27772e7	0.941266
$714$	4.50148e6	0.330453
$715$	1.40199e6	0.102560
$716$	−524535.	−0.0382377
$717$	9.28499e6	0.674503
$718$	−1.14918e7	−0.831910
$719$	2.25652e7	1.62786	0.813931	−	0.580961i	$-0.197323\pi$
$719$	2.25652e7	1.62786	0.813931	+	0.580961i	$0.197323\pi$
$720$	−449133.	−0.0322882
$721$	−5.82875e6	−0.417577
$722$	7.28653e6	0.520209
$723$	−1.45382e7	−1.03435
$724$	−8.55226e6	−0.606365
$725$	1.43439e7	1.01350
$726$	5.20393e6	0.366429
$727$	−1.30708e7	−0.917204	−0.458602	−	0.888642i	$-0.651650\pi$
$727$	−1.30708e7	−0.917204	−0.458602	+	0.888642i	$0.651650\pi$
$728$	−2.48965e6	−0.174105
$729$	531441.	0.0370370
$730$	5.24719e6	0.364434
$731$	1.56374e7	1.08236
$732$	−88694.8	−0.00611816
$733$	9.25040e6	0.635917	0.317959	−	0.948105i	$-0.397003\pi$
$733$	9.25040e6	0.635917	0.317959	+	0.948105i	$0.397003\pi$
$734$	1.85074e7	1.26796
$735$	−2.11476e6	−0.144392
$736$	−4.10609e6	−0.279405
$737$	1.50528e6	0.102082
$738$	−825493.	−0.0557920
$739$	−6.85807e6	−0.461946	−0.230973	−	0.972960i	$-0.574191\pi$
$739$	−6.85807e6	−0.461946	−0.230973	+	0.972960i	$0.574191\pi$
$740$	3.15249e6	0.211629
$741$	−9.40267e6	−0.629079
$742$	8.56553e6	0.571142
$743$	3.81790e6	0.253719	0.126859	−	0.991921i	$-0.459510\pi$
$743$	3.81790e6	0.253719	0.126859	+	0.991921i	$0.459510\pi$
$744$	1.83540e6	0.121562
$745$	−1.08126e7	−0.713738
$746$	6.84412e6	0.450268
$747$	−5.13184e6	−0.336490
$748$	−3.32897e6	−0.217548
$749$	1.34342e7	0.874996
$750$	−4.50759e6	−0.292612
$751$	1.88103e7	1.21701	0.608506	−	0.793549i	$-0.291769\pi$
$751$	1.88103e7	1.21701	0.608506	+	0.793549i	$0.291769\pi$
$752$	2.89383e6	0.186607
$753$	−4.05176e6	−0.260409
$754$	−1.08871e7	−0.697401
$755$	5.79133e6	0.369752
$756$	900363.	0.0572945
$757$	−3.38802e6	−0.214885	−0.107442	−	0.994211i	$-0.534266\pi$
$757$	−3.38802e6	−0.214885	−0.107442	+	0.994211i	$0.534266\pi$
$758$	−1.07068e7	−0.676839
$759$	−4.63530e6	−0.292061
$760$	−2.87375e6	−0.180474
$761$	−1.91972e7	−1.20165	−0.600824	−	0.799382i	$-0.705161\pi$
$761$	−1.91972e7	−1.20165	−0.600824	+	0.799382i	$0.705161\pi$
$762$	−6.99545e6	−0.436444
$763$	2.20940e6	0.137393
$764$	−3.28341e6	−0.203513
$765$	−2.84196e6	−0.175576
$766$	1.08890e7	0.670528
$767$	1.75426e6	0.107672
$768$	−589824.	−0.0360844
$769$	2.42030e7	1.47589	0.737943	−	0.674863i	$-0.235797\pi$
$769$	2.42030e7	1.47589	0.737943	+	0.674863i	$0.235797\pi$
$770$	−858986.	−0.0522107
$771$	1.47772e7	0.895275
$772$	−3.20123e6	−0.193318
$773$	2.18974e7	1.31809	0.659043	−	0.752105i	$-0.270962\pi$
$773$	2.18974e7	1.31809	0.659043	+	0.752105i	$0.270962\pi$
$774$	3.12772e6	0.187661
$775$	8.46278e6	0.506126
$776$	−3.33042e6	−0.198539
$777$	−6.31971e6	−0.375530
$778$	−1.77702e7	−1.05255
$779$	−5.28187e6	−0.311849
$780$	1.57181e6	0.0925048
$781$	751494.	0.0440857
$782$	−2.59819e7	−1.51934
$783$	3.93722e6	0.229501
$784$	−2.77721e6	−0.161368
$785$	−1.26656e7	−0.733588
$786$	−1.23132e6	−0.0710912
$787$	629412.	0.0362242	0.0181121	−	0.999836i	$-0.494234\pi$
$787$	629412.	0.0362242	0.0181121	+	0.999836i	$0.494234\pi$
$788$	−278203.	−0.0159605
$789$	−7.70433e6	−0.440598
$790$	−248274.	−0.0141535
$791$	−6.37742e6	−0.362413
$792$	−665843.	−0.0377189
$793$	310402.	0.0175284
$794$	9.13433e6	0.514192
$795$	−5.40775e6	−0.303458
$796$	3.69258e6	0.206560
$797$	2.56846e7	1.43228	0.716138	−	0.697959i	$-0.245908\pi$
$797$	2.56846e7	1.43228	0.716138	+	0.697959i	$0.245908\pi$
$798$	5.76092e6	0.320247
$799$	1.83112e7	1.01473
$800$	−2.71960e6	−0.150238
$801$	−8.12642e6	−0.447526
$802$	−4.43986e6	−0.243744
$803$	7.77900e6	0.425730
$804$	1.68762e6	0.0920734
$805$	−6.70422e6	−0.364635
$806$	−6.42327e6	−0.348272
$807$	1.65633e7	0.895291
$808$	826954.	0.0445608
$809$	9.58648e6	0.514977	0.257489	−	0.966281i	$-0.417105\pi$
$809$	9.58648e6	0.514977	0.257489	+	0.966281i	$0.417105\pi$
$810$	−568433.	−0.0304416
$811$	−1.97330e7	−1.05352	−0.526758	−	0.850015i	$-0.676593\pi$
$811$	−1.97330e7	−1.05352	−0.526758	+	0.850015i	$0.676593\pi$
$812$	6.67040e6	0.355028
$813$	−9.58363e6	−0.508515
$814$	4.67360e6	0.247224
$815$	−194365.	−0.0102500
$816$	−3.73221e6	−0.196219
$817$	2.00125e7	1.04893
$818$	528537.	0.0276180
$819$	−3.15097e6	−0.164147
$820$	882953.	0.0458567
$821$	−2.10816e7	−1.09156	−0.545778	−	0.837930i	$-0.683766\pi$
$821$	−2.10816e7	−1.09156	−0.545778	+	0.837930i	$0.683766\pi$
$822$	1.38141e7	0.713090
$823$	−1.05686e7	−0.543900	−0.271950	−	0.962311i	$-0.587668\pi$
$823$	−1.05686e7	−0.543900	−0.271950	+	0.962311i	$0.587668\pi$
$824$	4.83265e6	0.247952
$825$	−3.07012e6	−0.157044
$826$	−1.07482e6	−0.0548130
$827$	1.40489e7	0.714298	0.357149	−	0.934047i	$-0.383749\pi$
$827$	1.40489e7	0.714298	0.357149	+	0.934047i	$0.383749\pi$
$828$	−5.19677e6	−0.263425
$829$	1.26072e7	0.637139	0.318569	−	0.947900i	$-0.396798\pi$
$829$	1.26072e7	0.637139	0.318569	+	0.947900i	$0.396798\pi$
$830$	5.48906e6	0.276569
$831$	−1.16741e7	−0.586436
$832$	2.06419e6	0.103381
$833$	−1.75732e7	−0.877483
$834$	5.70810e6	0.284169
$835$	−9.94492e6	−0.493611
$836$	−4.26036e6	−0.210829
$837$	2.32292e6	0.114610
$838$	−1.15039e7	−0.565895
$839$	1.42212e7	0.697481	0.348741	−	0.937219i	$-0.386609\pi$
$839$	1.42212e7	0.697481	0.348741	+	0.937219i	$0.386609\pi$
$840$	−963035.	−0.0470916
$841$	8.65805e6	0.422114
$842$	−2.29381e7	−1.11500
$843$	−9.09269e6	−0.440680
$844$	1.15938e7	0.560236
$845$	2.54122e6	0.122434
$846$	3.66250e6	0.175935
$847$	1.11583e7	0.534430
$848$	−7.10173e6	−0.339136
$849$	1.98927e7	0.947162
$850$	−1.72087e7	−0.816961
$851$	3.64765e7	1.72659
$852$	842522.	0.0397633
$853$	−1.78437e6	−0.0839676	−0.0419838	−	0.999118i	$-0.513368\pi$
$853$	−1.78437e6	−0.0839676	−0.0419838	+	0.999118i	$0.513368\pi$
$854$	−190180.	−0.00892321
$855$	−3.63709e6	−0.170153
$856$	−1.11384e7	−0.519561
$857$	−1.90948e7	−0.888102	−0.444051	−	0.896001i	$-0.646459\pi$
$857$	−1.90948e7	−0.888102	−0.444051	+	0.896001i	$0.646459\pi$
$858$	2.33023e6	0.108064
$859$	−1.13567e7	−0.525132	−0.262566	−	0.964914i	$-0.584569\pi$
$859$	−1.13567e7	−0.525132	−0.262566	+	0.964914i	$0.584569\pi$
$860$	−3.34543e6	−0.154243
$861$	−1.77003e6	−0.0813716
$862$	−4.46618e6	−0.204724
$863$	1.46123e7	0.667867	0.333934	−	0.942597i	$-0.391624\pi$
$863$	1.46123e7	0.667867	0.333934	+	0.942597i	$0.391624\pi$
$864$	−746496.	−0.0340207
$865$	−3.02213e6	−0.137332
$866$	−1.44934e7	−0.656713
$867$	−1.08374e7	−0.489641
$868$	3.93548e6	0.177296
$869$	−368069.	−0.0165340
$870$	−4.21128e6	−0.188632
$871$	−5.90610e6	−0.263788
$872$	−1.83183e6	−0.0815819
$873$	−4.21506e6	−0.187184
$874$	−3.32513e7	−1.47241
$875$	−9.66523e6	−0.426768
$876$	8.72126e6	0.383989
$877$	−3.88421e7	−1.70531	−0.852655	−	0.522475i	$-0.825009\pi$
$877$	−3.88421e7	−1.70531	−0.852655	+	0.522475i	$0.825009\pi$
$878$	−1.53411e7	−0.671613
$879$	−4.00669e6	−0.174909
$880$	712190.	0.0310020
$881$	−1.66067e7	−0.720847	−0.360423	−	0.932789i	$-0.617368\pi$
$881$	−1.66067e7	−0.720847	−0.360423	+	0.932789i	$0.617368\pi$
$882$	−3.51490e6	−0.152139
$883$	2.73002e7	1.17832	0.589162	−	0.808015i	$-0.299458\pi$
$883$	2.73002e7	1.17832	0.589162	+	0.808015i	$0.299458\pi$
$884$	1.30615e7	0.562162
$885$	678572.	0.0291231
$886$	−1.57907e7	−0.675799
$887$	−9.69238e6	−0.413639	−0.206819	−	0.978379i	$-0.566311\pi$
$887$	−9.69238e6	−0.413639	−0.206819	+	0.978379i	$0.566311\pi$
$888$	5.23971e6	0.222985
$889$	−1.49997e7	−0.636545
$890$	8.69209e6	0.367832
$891$	−842707.	−0.0355617
$892$	−5.77990e6	−0.243225
$893$	2.34343e7	0.983386
$894$	−1.79714e7	−0.752036
$895$	710075.	0.0296310
$896$	−1.26471e6	−0.0526284
$897$	1.81869e7	0.754708
$898$	−1.40110e7	−0.579801
$899$	1.72096e7	0.710183
$900$	−3.44200e6	−0.141646
$901$	−4.49373e7	−1.84415
$902$	1.30899e6	0.0535696
$903$	6.70649e6	0.273701
$904$	5.28756e6	0.215196
$905$	1.15774e7	0.469882
$906$	9.62568e6	0.389593
$907$	−2.03756e7	−0.822415	−0.411208	−	0.911542i	$-0.634893\pi$
$907$	−2.03756e7	−0.822415	−0.411208	+	0.911542i	$0.634893\pi$
$908$	−4.02772e6	−0.162123
$909$	1.04661e6	0.0420123
$910$	3.37030e6	0.134916
$911$	2.97191e7	1.18643	0.593213	−	0.805046i	$-0.297859\pi$
$911$	2.97191e7	1.18643	0.593213	+	0.805046i	$0.297859\pi$
$912$	−4.77642e6	−0.190158
$913$	8.13758e6	0.323086
$914$	1.10276e7	0.436631
$915$	120068.	0.00474106
$916$	5.95038e6	0.234318
$917$	−2.64022e6	−0.103685
$918$	−4.72357e6	−0.184997
$919$	2.94070e7	1.14858	0.574291	−	0.818651i	$-0.305278\pi$
$919$	2.94070e7	1.14858	0.574291	+	0.818651i	$0.305278\pi$
$920$	5.55851e6	0.216515
$921$	−1.61855e6	−0.0628747
$922$	−7.52721e6	−0.291613
$923$	−2.94854e6	−0.113921
$924$	−1.42771e6	−0.0550122
$925$	2.41596e7	0.928402
$926$	2.01649e7	0.772802
$927$	6.11632e6	0.233771
$928$	−5.53047e6	−0.210811
$929$	4.72194e6	0.179507	0.0897535	−	0.995964i	$-0.471392\pi$
$929$	4.72194e6	0.179507	0.0897535	+	0.995964i	$0.471392\pi$
$930$	−2.48462e6	−0.0942003
$931$	−2.24899e7	−0.850381
$932$	−2.43083e7	−0.916675
$933$	−2.59668e7	−0.976596
$934$	−7.43962e6	−0.279051
$935$	4.50650e6	0.168582
$936$	2.61249e6	0.0974685
$937$	5.95544e6	0.221598	0.110799	−	0.993843i	$-0.464659\pi$
$937$	5.95544e6	0.221598	0.110799	+	0.993843i	$0.464659\pi$
$938$	3.61861e6	0.134287
$939$	1.64852e6	0.0610143
$940$	−3.91744e6	−0.144605
$941$	−2.68418e7	−0.988185	−0.494092	−	0.869409i	$-0.664500\pi$
$941$	−2.68418e7	−0.988185	−0.494092	+	0.869409i	$0.664500\pi$
$942$	−2.10513e7	−0.772951
$943$	1.02164e7	0.374126
$944$	891136.	0.0325472
$945$	−1.21884e6	−0.0443984
$946$	−4.95963e6	−0.180186
$947$	−1.58430e7	−0.574065	−0.287033	−	0.957921i	$-0.592669\pi$
$947$	−1.58430e7	−0.574065	−0.287033	+	0.957921i	$0.592669\pi$
$948$	−412653.	−0.0149130
$949$	−3.05215e7	−1.10012
$950$	−2.20235e7	−0.791729
$951$	2.11297e7	0.757603
$952$	−8.00263e6	−0.286181
$953$	−2.91598e7	−1.04005	−0.520023	−	0.854153i	$-0.674076\pi$
$953$	−2.91598e7	−1.04005	−0.520023	+	0.854153i	$0.674076\pi$
$954$	−8.98813e6	−0.319741
$955$	4.44482e6	0.157705
$956$	−1.65067e7	−0.584137
$957$	−6.24326e6	−0.220359
$958$	1.72102e7	0.605858
$959$	2.96204e7	1.04003
$960$	798458.	0.0279624
$961$	−1.84757e7	−0.645345
$962$	−1.83372e7	−0.638845
$963$	−1.40970e7	−0.489847
$964$	2.58458e7	0.895771
$965$	4.33357e6	0.149806
$966$	−1.11430e7	−0.384201
$967$	−2.07514e7	−0.713643	−0.356822	−	0.934173i	$-0.616140\pi$
$967$	−2.07514e7	−0.713643	−0.356822	+	0.934173i	$0.616140\pi$
$968$	−9.25144e6	−0.317337
$969$	−3.02235e7	−1.03404
$970$	4.50847e6	0.153851
$971$	2.39804e7	0.816223	0.408111	−	0.912932i	$-0.366187\pi$
$971$	2.39804e7	0.816223	0.408111	+	0.912932i	$0.366187\pi$
$972$	−944784.	−0.0320750
$973$	1.22394e7	0.414455
$974$	1.48122e7	0.500290
$975$	1.20458e7	0.405813
$976$	157680.	0.00529848
$977$	3.94396e7	1.32189	0.660946	−	0.750434i	$-0.270155\pi$
$977$	3.94396e7	1.32189	0.660946	+	0.750434i	$0.270155\pi$
$978$	−323051.	−0.0108000
$979$	1.28861e7	0.429699
$980$	3.75957e6	0.125047
$981$	−2.31841e6	−0.0769162
$982$	−2.18433e6	−0.0722834
$983$	−1.36563e7	−0.450765	−0.225383	−	0.974270i	$-0.572363\pi$
$983$	−1.36563e7	−0.450765	−0.225383	+	0.974270i	$0.572363\pi$
$984$	1.46754e6	0.0483173
$985$	376610.	0.0123680
$986$	−3.49949e7	−1.14634
$987$	7.85318e6	0.256598
$988$	1.67159e7	0.544799
$989$	−3.87089e7	−1.25840
$990$	901366.	0.0292290
$991$	4.88196e7	1.57910	0.789551	−	0.613685i	$-0.210314\pi$
$991$	4.88196e7	1.57910	0.789551	+	0.613685i	$0.210314\pi$
$992$	−3.26293e6	−0.105276
$993$	−3.20611e7	−1.03182
$994$	1.80655e6	0.0579940
$995$	−4.99872e6	−0.160067
$996$	9.12328e6	0.291409
$997$	5.00478e7	1.59458	0.797291	−	0.603595i	$-0.206266\pi$
$997$	5.00478e7	1.59458	0.797291	+	0.603595i	$0.206266\pi$
$998$	6.04800e6	0.192214
$999$	6.63151e6	0.210232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.d.1.2	✓	5
3.2	odd	2		1062.6.a.d.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.d.1.2	✓	5	1.1	even	1	trivial
1062.6.a.d.1.4		5	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -21.6596 q^{5} -36.0000 q^{6} -77.1916 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -21.6596 q^{5} -36.0000 q^{6} -77.1916 q^{7} +64.0000 q^{8} +81.0000 q^{9} -86.6382 q^{10} -128.442 q^{11} -144.000 q^{12} +503.952 q^{13} -308.766 q^{14} +194.936 q^{15} +256.000 q^{16} +1619.88 q^{17} +324.000 q^{18} +2073.10 q^{19} -346.553 q^{20} +694.724 q^{21} -513.767 q^{22} -4009.85 q^{23} -576.000 q^{24} -2655.86 q^{25} +2015.81 q^{26} -729.000 q^{27} -1235.07 q^{28} -5400.85 q^{29} +779.744 q^{30} -3186.45 q^{31} +1024.00 q^{32} +1155.98 q^{33} +6479.52 q^{34} +1671.94 q^{35} +1296.00 q^{36} -9096.72 q^{37} +8292.39 q^{38} -4535.56 q^{39} -1386.21 q^{40} -2547.82 q^{41} +2778.90 q^{42} +9653.45 q^{43} -2055.07 q^{44} -1754.42 q^{45} -16039.4 q^{46} +11304.0 q^{47} -2304.00 q^{48} -10848.5 q^{49} -10623.5 q^{50} -14578.9 q^{51} +8063.23 q^{52} -27741.1 q^{53} -2916.00 q^{54} +2781.99 q^{55} -4940.26 q^{56} -18657.9 q^{57} -21603.4 q^{58} +3481.00 q^{59} +3118.98 q^{60} +615.936 q^{61} -12745.8 q^{62} -6252.52 q^{63} +4096.00 q^{64} -10915.4 q^{65} +4623.91 q^{66} -11719.6 q^{67} +25918.1 q^{68} +36088.7 q^{69} +6687.74 q^{70} -5850.85 q^{71} +5184.00 q^{72} -60564.3 q^{73} -36386.9 q^{74} +23902.8 q^{75} +33169.6 q^{76} +9914.63 q^{77} -18142.3 q^{78} +2865.64 q^{79} -5544.85 q^{80} +6561.00 q^{81} -10191.3 q^{82} -63356.1 q^{83} +11115.6 q^{84} -35085.9 q^{85} +38613.8 q^{86} +48607.7 q^{87} -8220.28 q^{88} -100326. q^{89} -7017.70 q^{90} -38900.8 q^{91} -64157.7 q^{92} +28678.1 q^{93} +45216.1 q^{94} -44902.4 q^{95} -9216.00 q^{96} -52037.8 q^{97} -43393.8 q^{98} -10403.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} - 24 q^{5} - 180 q^{6} - 103 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 - 24 * q^5 - 180 * q^6 - 103 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} - 24 q^{5} - 180 q^{6} - 103 q^{7} + 320 q^{8} + 405 q^{9} - 96 q^{10} - 211 q^{11} - 720 q^{12} - 97 q^{13} - 412 q^{14} + 216 q^{15} + 1280 q^{16} - 933 q^{17} + 1620 q^{18} - 218 q^{19} - 384 q^{20} + 927 q^{21} - 844 q^{22} - 1820 q^{23} - 2880 q^{24} + 1515 q^{25} - 388 q^{26} - 3645 q^{27} - 1648 q^{28} - 6464 q^{29} + 864 q^{30} - 9270 q^{31} + 5120 q^{32} + 1899 q^{33} - 3732 q^{34} + 11978 q^{35} + 6480 q^{36} - 7639 q^{37} - 872 q^{38} + 873 q^{39} - 1536 q^{40} - 39103 q^{41} + 3708 q^{42} - 8183 q^{43} - 3376 q^{44} - 1944 q^{45} - 7280 q^{46} - 36178 q^{47} - 11520 q^{48} - 63156 q^{49} + 6060 q^{50} + 8397 q^{51} - 1552 q^{52} - 29228 q^{53} - 14580 q^{54} - 120292 q^{55} - 6592 q^{56} + 1962 q^{57} - 25856 q^{58} + 17405 q^{59} + 3456 q^{60} - 112 q^{61} - 37080 q^{62} - 8343 q^{63} + 20480 q^{64} - 198752 q^{65} + 7596 q^{66} - 21384 q^{67} - 14928 q^{68} + 16380 q^{69} + 47912 q^{70} - 71819 q^{71} + 25920 q^{72} - 61382 q^{73} - 30556 q^{74} - 13635 q^{75} - 3488 q^{76} - 103107 q^{77} + 3492 q^{78} - 13243 q^{79} - 6144 q^{80} + 32805 q^{81} - 156412 q^{82} - 74321 q^{83} + 14832 q^{84} + 45950 q^{85} - 32732 q^{86} + 58176 q^{87} - 13504 q^{88} - 91334 q^{89} - 7776 q^{90} - 132237 q^{91} - 29120 q^{92} + 83430 q^{93} - 144712 q^{94} - 154198 q^{95} - 46080 q^{96} - 402052 q^{97} - 252624 q^{98} - 17091 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 - 24 * q^5 - 180 * q^6 - 103 * q^7 + 320 * q^8 + 405 * q^9 - 96 * q^10 - 211 * q^11 - 720 * q^12 - 97 * q^13 - 412 * q^14 + 216 * q^15 + 1280 * q^16 - 933 * q^17 + 1620 * q^18 - 218 * q^19 - 384 * q^20 + 927 * q^21 - 844 * q^22 - 1820 * q^23 - 2880 * q^24 + 1515 * q^25 - 388 * q^26 - 3645 * q^27 - 1648 * q^28 - 6464 * q^29 + 864 * q^30 - 9270 * q^31 + 5120 * q^32 + 1899 * q^33 - 3732 * q^34 + 11978 * q^35 + 6480 * q^36 - 7639 * q^37 - 872 * q^38 + 873 * q^39 - 1536 * q^40 - 39103 * q^41 + 3708 * q^42 - 8183 * q^43 - 3376 * q^44 - 1944 * q^45 - 7280 * q^46 - 36178 * q^47 - 11520 * q^48 - 63156 * q^49 + 6060 * q^50 + 8397 * q^51 - 1552 * q^52 - 29228 * q^53 - 14580 * q^54 - 120292 * q^55 - 6592 * q^56 + 1962 * q^57 - 25856 * q^58 + 17405 * q^59 + 3456 * q^60 - 112 * q^61 - 37080 * q^62 - 8343 * q^63 + 20480 * q^64 - 198752 * q^65 + 7596 * q^66 - 21384 * q^67 - 14928 * q^68 + 16380 * q^69 + 47912 * q^70 - 71819 * q^71 + 25920 * q^72 - 61382 * q^73 - 30556 * q^74 - 13635 * q^75 - 3488 * q^76 - 103107 * q^77 + 3492 * q^78 - 13243 * q^79 - 6144 * q^80 + 32805 * q^81 - 156412 * q^82 - 74321 * q^83 + 14832 * q^84 + 45950 * q^85 - 32732 * q^86 + 58176 * q^87 - 13504 * q^88 - 91334 * q^89 - 7776 * q^90 - 132237 * q^91 - 29120 * q^92 + 83430 * q^93 - 144712 * q^94 - 154198 * q^95 - 46080 * q^96 - 402052 * q^97 - 252624 * q^98 - 17091 * q^99

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