LMFDB - Embedded newform 354.6.a.i.1.7

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} - 17732 x^{6} - 152272 x^{5} + 93277609 x^{4} + 1554240404 x^{3} - 156444406614 x^{2} + \cdots + 6279664243680 $ x^8 - 17732x^6 - 152272x^5 + 93277609x^4 + 1554240404x^3 - 156444406614x^2 - 3720609623076x + 6279664243680
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			1.7
Root			$-59.0243$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +71.0243 q^{5} +36.0000 q^{6} +223.194 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +71.0243 q^{5} +36.0000 q^{6} +223.194 q^{7} +64.0000 q^{8} +81.0000 q^{9} +284.097 q^{10} +313.070 q^{11} +144.000 q^{12} -629.044 q^{13} +892.776 q^{14} +639.219 q^{15} +256.000 q^{16} +201.206 q^{17} +324.000 q^{18} +597.191 q^{19} +1136.39 q^{20} +2008.75 q^{21} +1252.28 q^{22} +3958.93 q^{23} +576.000 q^{24} +1919.45 q^{25} -2516.17 q^{26} +729.000 q^{27} +3571.10 q^{28} -7339.61 q^{29} +2556.87 q^{30} -9236.50 q^{31} +1024.00 q^{32} +2817.63 q^{33} +804.823 q^{34} +15852.2 q^{35} +1296.00 q^{36} -9172.71 q^{37} +2388.76 q^{38} -5661.39 q^{39} +4545.55 q^{40} -17105.8 q^{41} +8034.99 q^{42} -3595.70 q^{43} +5009.12 q^{44} +5752.97 q^{45} +15835.7 q^{46} -7284.15 q^{47} +2304.00 q^{48} +33008.6 q^{49} +7677.80 q^{50} +1810.85 q^{51} -10064.7 q^{52} -18470.4 q^{53} +2916.00 q^{54} +22235.6 q^{55} +14284.4 q^{56} +5374.72 q^{57} -29358.5 q^{58} +3481.00 q^{59} +10227.5 q^{60} -30032.4 q^{61} -36946.0 q^{62} +18078.7 q^{63} +4096.00 q^{64} -44677.4 q^{65} +11270.5 q^{66} +48716.6 q^{67} +3219.29 q^{68} +35630.4 q^{69} +63408.8 q^{70} +70041.9 q^{71} +5184.00 q^{72} +12526.1 q^{73} -36690.8 q^{74} +17275.0 q^{75} +9555.06 q^{76} +69875.3 q^{77} -22645.6 q^{78} -80296.6 q^{79} +18182.2 q^{80} +6561.00 q^{81} -68423.1 q^{82} +105203. q^{83} +32139.9 q^{84} +14290.5 q^{85} -14382.8 q^{86} -66056.5 q^{87} +20036.5 q^{88} +30298.2 q^{89} +23011.9 q^{90} -140399. q^{91} +63342.9 q^{92} -83128.5 q^{93} -29136.6 q^{94} +42415.1 q^{95} +9216.00 q^{96} +52436.6 q^{97} +132034. q^{98} +25358.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 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 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9} + 384 q^{10} + 897 q^{11} + 1152 q^{12} + 1743 q^{13} + 724 q^{14} + 864 q^{15} + 2048 q^{16} + 1861 q^{17} + 2592 q^{18} + 3154 q^{19} + 1536 q^{20} + 1629 q^{21} + 3588 q^{22} + 3808 q^{23} + 4608 q^{24} + 11616 q^{25} + 6972 q^{26} + 5832 q^{27} + 2896 q^{28} + 328 q^{29} + 3456 q^{30} + 570 q^{31} + 8192 q^{32} + 8073 q^{33} + 7444 q^{34} + 36086 q^{35} + 10368 q^{36} + 12777 q^{37} + 12616 q^{38} + 15687 q^{39} + 6144 q^{40} + 20167 q^{41} + 6516 q^{42} + 24579 q^{43} + 14352 q^{44} + 7776 q^{45} + 15232 q^{46} + 20490 q^{47} + 18432 q^{48} + 59391 q^{49} + 46464 q^{50} + 16749 q^{51} + 27888 q^{52} + 13404 q^{53} + 23328 q^{54} - 34588 q^{55} + 11584 q^{56} + 28386 q^{57} + 1312 q^{58} + 27848 q^{59} + 13824 q^{60} + 94944 q^{61} + 2280 q^{62} + 14661 q^{63} + 32768 q^{64} + 54560 q^{65} + 32292 q^{66} + 28838 q^{67} + 29776 q^{68} + 34272 q^{69} + 144344 q^{70} + 14983 q^{71} + 41472 q^{72} + 69384 q^{73} + 51108 q^{74} + 104544 q^{75} + 50464 q^{76} - 22359 q^{77} + 62748 q^{78} - 49199 q^{79} + 24576 q^{80} + 52488 q^{81} + 80668 q^{82} + 3995 q^{83} + 26064 q^{84} - 142290 q^{85} + 98316 q^{86} + 2952 q^{87} + 57408 q^{88} + 28722 q^{89} + 31104 q^{90} + 20815 q^{91} + 60928 q^{92} + 5130 q^{93} + 81960 q^{94} + 208010 q^{95} + 73728 q^{96} + 204150 q^{97} + 237564 q^{98} + 72657 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9 + 384 * q^10 + 897 * q^11 + 1152 * q^12 + 1743 * q^13 + 724 * q^14 + 864 * q^15 + 2048 * q^16 + 1861 * q^17 + 2592 * q^18 + 3154 * q^19 + 1536 * q^20 + 1629 * q^21 + 3588 * q^22 + 3808 * q^23 + 4608 * q^24 + 11616 * q^25 + 6972 * q^26 + 5832 * q^27 + 2896 * q^28 + 328 * q^29 + 3456 * q^30 + 570 * q^31 + 8192 * q^32 + 8073 * q^33 + 7444 * q^34 + 36086 * q^35 + 10368 * q^36 + 12777 * q^37 + 12616 * q^38 + 15687 * q^39 + 6144 * q^40 + 20167 * q^41 + 6516 * q^42 + 24579 * q^43 + 14352 * q^44 + 7776 * q^45 + 15232 * q^46 + 20490 * q^47 + 18432 * q^48 + 59391 * q^49 + 46464 * q^50 + 16749 * q^51 + 27888 * q^52 + 13404 * q^53 + 23328 * q^54 - 34588 * q^55 + 11584 * q^56 + 28386 * q^57 + 1312 * q^58 + 27848 * q^59 + 13824 * q^60 + 94944 * q^61 + 2280 * q^62 + 14661 * q^63 + 32768 * q^64 + 54560 * q^65 + 32292 * q^66 + 28838 * q^67 + 29776 * q^68 + 34272 * q^69 + 144344 * q^70 + 14983 * q^71 + 41472 * q^72 + 69384 * q^73 + 51108 * q^74 + 104544 * q^75 + 50464 * q^76 - 22359 * q^77 + 62748 * q^78 - 49199 * q^79 + 24576 * q^80 + 52488 * q^81 + 80668 * q^82 + 3995 * q^83 + 26064 * q^84 - 142290 * q^85 + 98316 * q^86 + 2952 * q^87 + 57408 * q^88 + 28722 * q^89 + 31104 * q^90 + 20815 * q^91 + 60928 * q^92 + 5130 * q^93 + 81960 * q^94 + 208010 * q^95 + 73728 * q^96 + 204150 * q^97 + 237564 * q^98 + 72657 * 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
$5$	71.0243	1.27052	0.635261	−	0.772298i	$-0.280893\pi$
$5$	71.0243	1.27052	0.635261	+	0.772298i	$0.280893\pi$
$6$	36.0000	0.408248
$7$	223.194	1.72162	0.860810	−	0.508926i	$-0.169957\pi$
$7$	223.194	1.72162	0.860810	+	0.508926i	$0.169957\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	284.097	0.898394
$11$	313.070	0.780116	0.390058	−	0.920790i	$-0.372455\pi$
$11$	313.070	0.780116	0.390058	+	0.920790i	$0.372455\pi$
$12$	144.000	0.288675
$13$	−629.044	−1.03234	−0.516170	−	0.856486i	$-0.672643\pi$
$13$	−629.044	−1.03234	−0.516170	+	0.856486i	$0.672643\pi$
$14$	892.776	1.21737
$15$	639.219	0.733536
$16$	256.000	0.250000
$17$	201.206	0.168857	0.0844283	−	0.996430i	$-0.473094\pi$
$17$	201.206	0.168857	0.0844283	+	0.996430i	$0.473094\pi$
$18$	324.000	0.235702
$19$	597.191	0.379515	0.189758	−	0.981831i	$-0.439230\pi$
$19$	597.191	0.379515	0.189758	+	0.981831i	$0.439230\pi$
$20$	1136.39	0.635261
$21$	2008.75	0.993978
$22$	1252.28	0.551625
$23$	3958.93	1.56048	0.780240	−	0.625480i	$-0.215097\pi$
$23$	3958.93	1.56048	0.780240	+	0.625480i	$0.215097\pi$
$24$	576.000	0.204124
$25$	1919.45	0.614224
$26$	−2516.17	−0.729974
$27$	729.000	0.192450
$28$	3571.10	0.860810
$29$	−7339.61	−1.62061	−0.810304	−	0.586009i	$-0.800698\pi$
$29$	−7339.61	−1.62061	−0.810304	+	0.586009i	$0.800698\pi$
$30$	2556.87	0.518688
$31$	−9236.50	−1.72625	−0.863124	−	0.504991i	$-0.831496\pi$
$31$	−9236.50	−1.72625	−0.863124	+	0.504991i	$0.831496\pi$
$32$	1024.00	0.176777
$33$	2817.63	0.450400
$34$	804.823	0.119400
$35$	15852.2	2.18736
$36$	1296.00	0.166667
$37$	−9172.71	−1.10152	−0.550761	−	0.834663i	$-0.685662\pi$
$37$	−9172.71	−1.10152	−0.550761	+	0.834663i	$0.685662\pi$
$38$	2388.76	0.268358
$39$	−5661.39	−0.596021
$40$	4545.55	0.449197
$41$	−17105.8	−1.58922	−0.794608	−	0.607123i	$-0.792324\pi$
$41$	−17105.8	−1.58922	−0.794608	+	0.607123i	$0.792324\pi$
$42$	8034.99	0.702849
$43$	−3595.70	−0.296559	−0.148280	−	0.988945i	$-0.547374\pi$
$43$	−3595.70	−0.296559	−0.148280	+	0.988945i	$0.547374\pi$
$44$	5009.12	0.390058
$45$	5752.97	0.423507
$46$	15835.7	1.10343
$47$	−7284.15	−0.480988	−0.240494	−	0.970651i	$-0.577309\pi$
$47$	−7284.15	−0.480988	−0.240494	+	0.970651i	$0.577309\pi$
$48$	2304.00	0.144338
$49$	33008.6	1.96398
$50$	7677.80	0.434322
$51$	1810.85	0.0974895
$52$	−10064.7	−0.516170
$53$	−18470.4	−0.903205	−0.451602	−	0.892219i	$-0.649147\pi$
$53$	−18470.4	−0.903205	−0.451602	+	0.892219i	$0.649147\pi$
$54$	2916.00	0.136083
$55$	22235.6	0.991154
$56$	14284.4	0.608685
$57$	5374.72	0.219113
$58$	−29358.5	−1.14594
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	10227.5	0.366768
$61$	−30032.4	−1.03339	−0.516697	−	0.856168i	$-0.672839\pi$
$61$	−30032.4	−1.03339	−0.516697	+	0.856168i	$0.672839\pi$
$62$	−36946.0	−1.22064
$63$	18078.7	0.573874
$64$	4096.00	0.125000
$65$	−44677.4	−1.31161
$66$	11270.5	0.318481
$67$	48716.6	1.32584	0.662918	−	0.748692i	$-0.269318\pi$
$67$	48716.6	1.32584	0.662918	+	0.748692i	$0.269318\pi$
$68$	3219.29	0.0844283
$69$	35630.4	0.900944
$70$	63408.8	1.54669
$71$	70041.9	1.64897	0.824483	−	0.565886i	$-0.191466\pi$
$71$	70041.9	1.64897	0.824483	+	0.565886i	$0.191466\pi$
$72$	5184.00	0.117851
$73$	12526.1	0.275112	0.137556	−	0.990494i	$-0.456075\pi$
$73$	12526.1	0.275112	0.137556	+	0.990494i	$0.456075\pi$
$74$	−36690.8	−0.778894
$75$	17275.0	0.354622
$76$	9555.06	0.189758
$77$	69875.3	1.34306
$78$	−22645.6	−0.421451
$79$	−80296.6	−1.44754	−0.723768	−	0.690043i	$-0.757592\pi$
$79$	−80296.6	−1.44754	−0.723768	+	0.690043i	$0.757592\pi$
$80$	18182.2	0.317630
$81$	6561.00	0.111111
$82$	−68423.1	−1.12375
$83$	105203.	1.67623	0.838115	−	0.545494i	$-0.183658\pi$
$83$	105203.	1.67623	0.838115	+	0.545494i	$0.183658\pi$
$84$	32139.9	0.496989
$85$	14290.5	0.214536
$86$	−14382.8	−0.209699
$87$	−66056.5	−0.935659
$88$	20036.5	0.275813
$89$	30298.2	0.405454	0.202727	−	0.979235i	$-0.435020\pi$
$89$	30298.2	0.405454	0.202727	+	0.979235i	$0.435020\pi$
$90$	23011.9	0.299465
$91$	−140399.	−1.77730
$92$	63342.9	0.780240
$93$	−83128.5	−0.996650
$94$	−29136.6	−0.340110
$95$	42415.1	0.482182
$96$	9216.00	0.102062
$97$	52436.6	0.565855	0.282928	−	0.959141i	$-0.408694\pi$
$97$	52436.6	0.565855	0.282928	+	0.959141i	$0.408694\pi$
$98$	132034.	1.38874
$99$	25358.6	0.260039
$100$	30711.2	0.307112
$101$	−183342.	−1.78838	−0.894188	−	0.447692i	$-0.852246\pi$
$101$	−183342.	−1.78838	−0.894188	+	0.447692i	$0.852246\pi$
$102$	7243.41	0.0689355
$103$	154031.	1.43059	0.715295	−	0.698823i	$-0.246292\pi$
$103$	154031.	1.43059	0.715295	+	0.698823i	$0.246292\pi$
$104$	−40258.8	−0.364987
$105$	142670.	1.26287
$106$	−73881.5	−0.638662
$107$	124601.	1.05211	0.526056	−	0.850450i	$-0.323670\pi$
$107$	124601.	1.05211	0.526056	+	0.850450i	$0.323670\pi$
$108$	11664.0	0.0962250
$109$	271.632	0.00218985	0.00109493	−	0.999999i	$-0.499651\pi$
$109$	271.632	0.00218985	0.00109493	+	0.999999i	$0.499651\pi$
$110$	88942.2	0.700852
$111$	−82554.4	−0.635964
$112$	57137.7	0.430405
$113$	−16139.5	−0.118904	−0.0594518	−	0.998231i	$-0.518935\pi$
$113$	−16139.5	−0.118904	−0.0594518	+	0.998231i	$0.518935\pi$
$114$	21498.9	0.154936
$115$	281180.	1.98262
$116$	−117434.	−0.810304
$117$	−50952.5	−0.344113
$118$	13924.0	0.0920575
$119$	44907.9	0.290707
$120$	40910.0	0.259344
$121$	−63038.4	−0.391419
$122$	−120130.	−0.730720
$123$	−153952.	−0.917534
$124$	−147784.	−0.863124
$125$	−85623.4	−0.490137
$126$	72314.9	0.405790
$127$	−217196.	−1.19493	−0.597464	−	0.801895i	$-0.703825\pi$
$127$	−217196.	−1.19493	−0.597464	+	0.801895i	$0.703825\pi$
$128$	16384.0	0.0883883
$129$	−32361.3	−0.171219
$130$	−178709.	−0.927447
$131$	213005.	1.08446	0.542228	−	0.840231i	$-0.317581\pi$
$131$	213005.	1.08446	0.542228	+	0.840231i	$0.317581\pi$
$132$	45082.0	0.225200
$133$	133289.	0.653381
$134$	194866.	0.937507
$135$	51776.7	0.244512
$136$	12877.2	0.0596999
$137$	164592.	0.749215	0.374608	−	0.927183i	$-0.377777\pi$
$137$	164592.	0.749215	0.374608	+	0.927183i	$0.377777\pi$
$138$	142522.	0.637064
$139$	−75385.7	−0.330942	−0.165471	−	0.986215i	$-0.552914\pi$
$139$	−75385.7	−0.330942	−0.165471	+	0.986215i	$0.552914\pi$
$140$	253635.	1.09368
$141$	−65557.3	−0.277698
$142$	280168.	1.16600
$143$	−196934.	−0.805345
$144$	20736.0	0.0833333
$145$	−521291.	−2.05902
$146$	50104.4	0.194533
$147$	297077.	1.13390
$148$	−146763.	−0.550761
$149$	−290101.	−1.07049	−0.535247	−	0.844696i	$-0.679781\pi$
$149$	−290101.	−1.07049	−0.535247	+	0.844696i	$0.679781\pi$
$150$	69100.2	0.250756
$151$	−165279.	−0.589896	−0.294948	−	0.955513i	$-0.595302\pi$
$151$	−165279.	−0.589896	−0.294948	+	0.955513i	$0.595302\pi$
$152$	38220.2	0.134179
$153$	16297.7	0.0562856
$154$	279501.	0.949690
$155$	−656016.	−2.19324
$156$	−90582.3	−0.298011
$157$	605495.	1.96048	0.980238	−	0.197822i	$-0.0633869\pi$
$157$	605495.	1.96048	0.980238	+	0.197822i	$0.0633869\pi$
$158$	−321187.	−1.02356
$159$	−166233.	−0.521465
$160$	72728.9	0.224599
$161$	883610.	2.68656
$162$	26244.0	0.0785674
$163$	212605.	0.626766	0.313383	−	0.949627i	$-0.398538\pi$
$163$	212605.	0.626766	0.313383	+	0.949627i	$0.398538\pi$
$164$	−273692.	−0.794608
$165$	200120.	0.572243
$166$	420813.	1.18527
$167$	−658885.	−1.82818	−0.914089	−	0.405514i	$-0.867092\pi$
$167$	−658885.	−1.82818	−0.914089	+	0.405514i	$0.867092\pi$
$168$	128560.	0.351424
$169$	24402.9	0.0657241
$170$	57162.0	0.151700
$171$	48372.5	0.126505
$172$	−57531.1	−0.148280
$173$	533464.	1.35516	0.677579	−	0.735450i	$-0.263029\pi$
$173$	533464.	1.35516	0.677579	+	0.735450i	$0.263029\pi$
$174$	−264226.	−0.661611
$175$	428410.	1.05746
$176$	80145.8	0.195029
$177$	31329.0	0.0751646
$178$	121193.	0.286699
$179$	−117757.	−0.274697	−0.137348	−	0.990523i	$-0.543858\pi$
$179$	−117757.	−0.274697	−0.137348	+	0.990523i	$0.543858\pi$
$180$	92047.5	0.211754
$181$	97526.7	0.221272	0.110636	−	0.993861i	$-0.464711\pi$
$181$	97526.7	0.221272	0.110636	+	0.993861i	$0.464711\pi$
$182$	−561595.	−1.25674
$183$	−270292.	−0.596630
$184$	253372.	0.551713
$185$	−651485.	−1.39951
$186$	−332514.	−0.704738
$187$	62991.5	0.131728
$188$	−116546.	−0.240494
$189$	162708.	0.331326
$190$	169660.	0.340954
$191$	702736.	1.39383	0.696913	−	0.717156i	$-0.254556\pi$
$191$	702736.	1.39383	0.696913	+	0.717156i	$0.254556\pi$
$192$	36864.0	0.0721688
$193$	−695321.	−1.34367	−0.671834	−	0.740702i	$-0.734493\pi$
$193$	−695321.	−1.34367	−0.671834	+	0.740702i	$0.734493\pi$
$194$	209746.	0.400120
$195$	−402096.	−0.757258
$196$	528137.	0.981989
$197$	−667332.	−1.22511	−0.612557	−	0.790427i	$-0.709859\pi$
$197$	−667332.	−1.22511	−0.612557	+	0.790427i	$0.709859\pi$
$198$	101435.	0.183875
$199$	58098.1	0.103999	0.0519995	−	0.998647i	$-0.483441\pi$
$199$	58098.1	0.103999	0.0519995	+	0.998647i	$0.483441\pi$
$200$	122845.	0.217161
$201$	438449.	0.765471
$202$	−733368.	−1.26457
$203$	−1.63816e6	−2.79007
$204$	28973.6	0.0487447
$205$	−1.21492e6	−2.01913
$206$	616124.	1.01158
$207$	320674.	0.520160
$208$	−161035.	−0.258085
$209$	186962.	0.296066
$210$	570679.	0.892984
$211$	492086.	0.760912	0.380456	−	0.924799i	$-0.375767\pi$
$211$	492086.	0.760912	0.380456	+	0.924799i	$0.375767\pi$
$212$	−295526.	−0.451602
$213$	630377.	0.952032
$214$	498404.	0.743956
$215$	−255382.	−0.376785
$216$	46656.0	0.0680414
$217$	−2.06153e6	−2.97195
$218$	1086.53	0.00154846
$219$	112735.	0.158836
$220$	355769.	0.495577
$221$	−126567.	−0.174317
$222$	−330218.	−0.449695
$223$	332446.	0.447671	0.223836	−	0.974627i	$-0.428142\pi$
$223$	332446.	0.447671	0.223836	+	0.974627i	$0.428142\pi$
$224$	228551.	0.304342
$225$	155475.	0.204741
$226$	−64558.2	−0.0840776
$227$	760231.	0.979221	0.489611	−	0.871941i	$-0.337139\pi$
$227$	760231.	0.979221	0.489611	+	0.871941i	$0.337139\pi$
$228$	85995.5	0.109557
$229$	988392.	1.24549	0.622746	−	0.782424i	$-0.286017\pi$
$229$	988392.	1.24549	0.622746	+	0.782424i	$0.286017\pi$
$230$	1.12472e6	1.40193
$231$	628878.	0.775419
$232$	−469735.	−0.572972
$233$	814356.	0.982708	0.491354	−	0.870960i	$-0.336502\pi$
$233$	814356.	0.982708	0.491354	+	0.870960i	$0.336502\pi$
$234$	−203810.	−0.243325
$235$	−517351.	−0.611105
$236$	55696.0	0.0650945
$237$	−722670.	−0.835736
$238$	179632.	0.205561
$239$	−945619.	−1.07083	−0.535416	−	0.844588i	$-0.679845\pi$
$239$	−945619.	−1.07083	−0.535416	+	0.844588i	$0.679845\pi$
$240$	163640.	0.183384
$241$	−400683.	−0.444384	−0.222192	−	0.975003i	$-0.571321\pi$
$241$	−400683.	−0.444384	−0.222192	+	0.975003i	$0.571321\pi$
$242$	−252153.	−0.276775
$243$	59049.0	0.0641500
$244$	−480519.	−0.516697
$245$	2.34441e6	2.49528
$246$	−615808.	−0.648795
$247$	−375659.	−0.391789
$248$	−591136.	−0.610321
$249$	946828.	0.967771
$250$	−342494.	−0.346579
$251$	−73091.0	−0.0732284	−0.0366142	−	0.999329i	$-0.511657\pi$
$251$	−73091.0	−0.0732284	−0.0366142	+	0.999329i	$0.511657\pi$
$252$	289259.	0.286937
$253$	1.23942e6	1.21736
$254$	−868783.	−0.844942
$255$	128615.	0.123862
$256$	65536.0	0.0625000
$257$	−894014.	−0.844328	−0.422164	−	0.906519i	$-0.638729\pi$
$257$	−894014.	−0.844328	−0.422164	+	0.906519i	$0.638729\pi$
$258$	−129445.	−0.121070
$259$	−2.04729e6	−1.89640
$260$	−714838.	−0.655804
$261$	−594509.	−0.540203
$262$	852020.	0.766826
$263$	−1.12922e6	−1.00667	−0.503337	−	0.864090i	$-0.667895\pi$
$263$	−1.12922e6	−1.00667	−0.503337	+	0.864090i	$0.667895\pi$
$264$	180328.	0.159241
$265$	−1.31185e6	−1.14754
$266$	533158.	0.462010
$267$	272684.	0.234089
$268$	779465.	0.662918
$269$	−1.53929e6	−1.29700	−0.648500	−	0.761215i	$-0.724603\pi$
$269$	−1.53929e6	−1.29700	−0.648500	+	0.761215i	$0.724603\pi$
$270$	207107.	0.172896
$271$	1.23052e6	1.01781	0.508905	−	0.860823i	$-0.330050\pi$
$271$	1.23052e6	1.01781	0.508905	+	0.860823i	$0.330050\pi$
$272$	51508.7	0.0422142
$273$	−1.26359e6	−1.02612
$274$	658367.	0.529775
$275$	600921.	0.479166
$276$	570086.	0.450472
$277$	489684.	0.383457	0.191729	−	0.981448i	$-0.438591\pi$
$277$	489684.	0.383457	0.191729	+	0.981448i	$0.438591\pi$
$278$	−301543.	−0.234011
$279$	−748157.	−0.575416
$280$	1.01454e6	0.773347
$281$	−1.36139e6	−1.02853	−0.514265	−	0.857631i	$-0.671935\pi$
$281$	−1.36139e6	−1.02853	−0.514265	+	0.857631i	$0.671935\pi$
$282$	−262229.	−0.196362
$283$	381461.	0.283129	0.141565	−	0.989929i	$-0.454787\pi$
$283$	381461.	0.283129	0.141565	+	0.989929i	$0.454787\pi$
$284$	1.12067e6	0.824483
$285$	381736.	0.278388
$286$	−787738.	−0.569465
$287$	−3.81790e6	−2.73603
$288$	82944.0	0.0589256
$289$	−1.37937e6	−0.971487
$290$	−2.08516e6	−1.45595
$291$	471929.	0.326697
$292$	200418.	0.137556
$293$	1.23164e6	0.838134	0.419067	−	0.907955i	$-0.362357\pi$
$293$	1.23164e6	0.838134	0.419067	+	0.907955i	$0.362357\pi$
$294$	1.18831e6	0.801791
$295$	247236.	0.165408
$296$	−587053.	−0.389447
$297$	228228.	0.150133
$298$	−1.16041e6	−0.756954
$299$	−2.49034e6	−1.61095
$300$	276401.	0.177311
$301$	−802538.	−0.510563
$302$	−661116.	−0.417119
$303$	−1.65008e6	−1.03252
$304$	152881.	0.0948788
$305$	−2.13303e6	−1.31295
$306$	65190.7	0.0397999
$307$	−775430.	−0.469566	−0.234783	−	0.972048i	$-0.575438\pi$
$307$	−775430.	−0.469566	−0.234783	+	0.972048i	$0.575438\pi$
$308$	1.11800e6	0.671532
$309$	1.38628e6	0.825951
$310$	−2.62406e6	−1.55085
$311$	651185.	0.381771	0.190886	−	0.981612i	$-0.438864\pi$
$311$	651185.	0.381771	0.190886	+	0.981612i	$0.438864\pi$
$312$	−362329.	−0.210725
$313$	1.15596e6	0.666931	0.333465	−	0.942762i	$-0.391782\pi$
$313$	1.15596e6	0.666931	0.333465	+	0.942762i	$0.391782\pi$
$314$	2.42198e6	1.38627
$315$	1.28403e6	0.729118
$316$	−1.28475e6	−0.723768
$317$	−701918.	−0.392318	−0.196159	−	0.980572i	$-0.562847\pi$
$317$	−701918.	−0.392318	−0.196159	+	0.980572i	$0.562847\pi$
$318$	−664934.	−0.368732
$319$	−2.29781e6	−1.26426
$320$	290915.	0.158815
$321$	1.12141e6	0.607438
$322$	3.53444e6	1.89968
$323$	120158.	0.0640837
$324$	104976.	0.0555556
$325$	−1.20742e6	−0.634087
$326$	850422.	0.443190
$327$	2444.69	0.00126431
$328$	−1.09477e6	−0.561873
$329$	−1.62578e6	−0.828079
$330$	800480.	0.404637
$331$	3.31330e6	1.66223	0.831113	−	0.556103i	$-0.187704\pi$
$331$	3.31330e6	1.66223	0.831113	+	0.556103i	$0.187704\pi$
$332$	1.68325e6	0.838115
$333$	−742989.	−0.367174
$334$	−2.63554e6	−1.29272
$335$	3.46006e6	1.68450
$336$	514239.	0.248495
$337$	1.64284e6	0.787988	0.393994	−	0.919113i	$-0.371093\pi$
$337$	1.64284e6	0.787988	0.393994	+	0.919113i	$0.371093\pi$
$338$	97611.6	0.0464740
$339$	−145256.	−0.0686490
$340$	228648.	0.107268
$341$	−2.89167e6	−1.34667
$342$	193490.	0.0894526
$343$	3.61610e6	1.65960
$344$	−230125.	−0.104850
$345$	2.53062e6	1.14467
$346$	2.13386e6	0.958241
$347$	−1.77624e6	−0.791913	−0.395956	−	0.918269i	$-0.629587\pi$
$347$	−1.77624e6	−0.791913	−0.395956	+	0.918269i	$0.629587\pi$
$348$	−1.05690e6	−0.467829
$349$	40388.6	0.0177499	0.00887493	−	0.999961i	$-0.497175\pi$
$349$	40388.6	0.0177499	0.00887493	+	0.999961i	$0.497175\pi$
$350$	1.71364e6	0.747737
$351$	−458573.	−0.198674
$352$	320583.	0.137906
$353$	−4.20338e6	−1.79540	−0.897702	−	0.440604i	$-0.854764\pi$
$353$	−4.20338e6	−1.79540	−0.897702	+	0.440604i	$0.854764\pi$
$354$	125316.	0.0531494
$355$	4.97467e6	2.09505
$356$	484771.	0.202727
$357$	404171.	0.167840
$358$	−471027.	−0.194240
$359$	−1.73147e6	−0.709053	−0.354527	−	0.935046i	$-0.615358\pi$
$359$	−1.73147e6	−0.709053	−0.354527	+	0.935046i	$0.615358\pi$
$360$	368190.	0.149732
$361$	−2.11946e6	−0.855968
$362$	390107.	0.156463
$363$	−567345.	−0.225986
$364$	−2.24638e6	−0.888648
$365$	889658.	0.349535
$366$	−1.08117e6	−0.421881
$367$	262543.	0.101750	0.0508750	−	0.998705i	$-0.483799\pi$
$367$	262543.	0.101750	0.0508750	+	0.998705i	$0.483799\pi$
$368$	1.01349e6	0.390120
$369$	−1.38557e6	−0.529739
$370$	−2.60594e6	−0.989601
$371$	−4.12248e6	−1.55498
$372$	−1.33006e6	−0.498325
$373$	3.05265e6	1.13607	0.568034	−	0.823005i	$-0.307704\pi$
$373$	3.05265e6	1.13607	0.568034	+	0.823005i	$0.307704\pi$
$374$	251966.	0.0931457
$375$	−770611.	−0.282981
$376$	−466185.	−0.170055
$377$	4.61694e6	1.67302
$378$	650834.	0.234283
$379$	543585.	0.194388	0.0971940	−	0.995265i	$-0.469013\pi$
$379$	543585.	0.194388	0.0971940	+	0.995265i	$0.469013\pi$
$380$	678641.	0.241091
$381$	−1.95476e6	−0.689893
$382$	2.81094e6	0.985584
$383$	−1.45636e6	−0.507307	−0.253653	−	0.967295i	$-0.581632\pi$
$383$	−1.45636e6	−0.507307	−0.253653	+	0.967295i	$0.581632\pi$
$384$	147456.	0.0510310
$385$	4.96284e6	1.70639
$386$	−2.78128e6	−0.950117
$387$	−291251.	−0.0988532
$388$	838986.	0.282928
$389$	−2.17165e6	−0.727639	−0.363819	−	0.931469i	$-0.618527\pi$
$389$	−2.17165e6	−0.727639	−0.363819	+	0.931469i	$0.618527\pi$
$390$	−1.60839e6	−0.535462
$391$	796560.	0.263498
$392$	2.11255e6	0.694371
$393$	1.91705e6	0.626111
$394$	−2.66933e6	−0.866286
$395$	−5.70301e6	−1.83913
$396$	405738.	0.130019
$397$	−1.65420e6	−0.526758	−0.263379	−	0.964692i	$-0.584837\pi$
$397$	−1.65420e6	−0.526758	−0.263379	+	0.964692i	$0.584837\pi$
$398$	232392.	0.0735384
$399$	1.19961e6	0.377230
$400$	491379.	0.153556
$401$	−150949.	−0.0468779	−0.0234389	−	0.999725i	$-0.507462\pi$
$401$	−150949.	−0.0468779	−0.0234389	+	0.999725i	$0.507462\pi$
$402$	1.75380e6	0.541270
$403$	5.81016e6	1.78207
$404$	−2.93347e6	−0.894188
$405$	465990.	0.141169
$406$	−6.55263e6	−1.97288
$407$	−2.87170e6	−0.859315
$408$	115895.	0.0344677
$409$	3.26987e6	0.966546	0.483273	−	0.875470i	$-0.339448\pi$
$409$	3.26987e6	0.966546	0.483273	+	0.875470i	$0.339448\pi$
$410$	−4.85970e6	−1.42774
$411$	1.48133e6	0.432560
$412$	2.46450e6	0.715295
$413$	776938.	0.224136
$414$	1.28269e6	0.367809
$415$	7.47198e6	2.12968
$416$	−644141.	−0.182494
$417$	−678472.	−0.191070
$418$	747850.	0.209350
$419$	28633.0	0.00796769	0.00398384	−	0.999992i	$-0.498732\pi$
$419$	28633.0	0.00796769	0.00398384	+	0.999992i	$0.498732\pi$
$420$	2.28272e6	0.631435
$421$	−1.89228e6	−0.520332	−0.260166	−	0.965564i	$-0.583777\pi$
$421$	−1.89228e6	−0.520332	−0.260166	+	0.965564i	$0.583777\pi$
$422$	1.96834e6	0.538046
$423$	−590016.	−0.160329
$424$	−1.18210e6	−0.319331
$425$	386204.	0.103716
$426$	2.52151e6	0.673188
$427$	−6.70306e6	−1.77911
$428$	1.99362e6	0.526056
$429$	−1.77241e6	−0.464966
$430$	−1.02153e6	−0.266427
$431$	6.68847e6	1.73434	0.867168	−	0.498015i	$-0.165938\pi$
$431$	6.68847e6	1.73434	0.867168	+	0.498015i	$0.165938\pi$
$432$	186624.	0.0481125
$433$	6.05316e6	1.55154	0.775769	−	0.631017i	$-0.217362\pi$
$433$	6.05316e6	1.55154	0.775769	+	0.631017i	$0.217362\pi$
$434$	−8.24613e6	−2.10148
$435$	−4.69162e6	−1.18877
$436$	4346.12	0.00109493
$437$	2.36424e6	0.592226
$438$	450940.	0.112314
$439$	5.45370e6	1.35061	0.675306	−	0.737538i	$-0.264012\pi$
$439$	5.45370e6	1.35061	0.675306	+	0.737538i	$0.264012\pi$
$440$	1.42308e6	0.350426
$441$	2.67369e6	0.654659
$442$	−506269.	−0.123261
$443$	−947176.	−0.229309	−0.114655	−	0.993405i	$-0.536576\pi$
$443$	−947176.	−0.229309	−0.114655	+	0.993405i	$0.536576\pi$
$444$	−1.32087e6	−0.317982
$445$	2.15191e6	0.515138
$446$	1.32978e6	0.316551
$447$	−2.61091e6	−0.618050
$448$	914203.	0.215203
$449$	−3.79669e6	−0.888770	−0.444385	−	0.895836i	$-0.646578\pi$
$449$	−3.79669e6	−0.888770	−0.444385	+	0.895836i	$0.646578\pi$
$450$	621901.	0.144774
$451$	−5.35530e6	−1.23977
$452$	−258233.	−0.0594518
$453$	−1.48751e6	−0.340577
$454$	3.04092e6	0.692414
$455$	−9.97172e6	−2.25809
$456$	343982.	0.0774682
$457$	1.89716e6	0.424926	0.212463	−	0.977169i	$-0.431852\pi$
$457$	1.89716e6	0.424926	0.212463	+	0.977169i	$0.431852\pi$
$458$	3.95357e6	0.880695
$459$	146679.	0.0324965
$460$	4.49889e6	0.991312
$461$	−3.88561e6	−0.851544	−0.425772	−	0.904830i	$-0.639997\pi$
$461$	−3.88561e6	−0.851544	−0.425772	+	0.904830i	$0.639997\pi$
$462$	2.51551e6	0.548304
$463$	−1.08855e6	−0.235991	−0.117996	−	0.993014i	$-0.537647\pi$
$463$	−1.08855e6	−0.235991	−0.117996	+	0.993014i	$0.537647\pi$
$464$	−1.87894e6	−0.405152
$465$	−5.90414e6	−1.26626
$466$	3.25742e6	0.694880
$467$	8.50909e6	1.80547	0.902736	−	0.430194i	$-0.141555\pi$
$467$	8.50909e6	1.80547	0.902736	+	0.430194i	$0.141555\pi$
$468$	−815241.	−0.172057
$469$	1.08732e7	2.28259
$470$	−2.06941e6	−0.432117
$471$	5.44946e6	1.13188
$472$	222784.	0.0460287
$473$	−1.12570e6	−0.231351
$474$	−2.89068e6	−0.590954
$475$	1.14628e6	0.233107
$476$	718527.	0.145354
$477$	−1.49610e6	−0.301068
$478$	−3.78248e6	−0.757193
$479$	737783.	0.146923	0.0734615	−	0.997298i	$-0.476595\pi$
$479$	737783.	0.146923	0.0734615	+	0.997298i	$0.476595\pi$
$480$	654560.	0.129672
$481$	5.77003e6	1.13714
$482$	−1.60273e6	−0.314227
$483$	7.95249e6	1.55108
$484$	−1.00861e6	−0.195709
$485$	3.72427e6	0.718931
$486$	236196.	0.0453609
$487$	261122.	0.0498909	0.0249454	−	0.999689i	$-0.492059\pi$
$487$	261122.	0.0498909	0.0249454	+	0.999689i	$0.492059\pi$
$488$	−1.92208e6	−0.365360
$489$	1.91345e6	0.361864
$490$	9.37764e6	1.76443
$491$	−5.88599e6	−1.10183	−0.550916	−	0.834561i	$-0.685722\pi$
$491$	−5.88599e6	−1.10183	−0.550916	+	0.834561i	$0.685722\pi$
$492$	−2.46323e6	−0.458767
$493$	−1.47677e6	−0.273651
$494$	−1.50264e6	−0.277036
$495$	1.80108e6	0.330385
$496$	−2.36454e6	−0.431562
$497$	1.56329e7	2.83890
$498$	3.78731e6	0.684318
$499$	3.30684e6	0.594514	0.297257	−	0.954797i	$-0.403928\pi$
$499$	3.30684e6	0.594514	0.297257	+	0.954797i	$0.403928\pi$
$500$	−1.36997e6	−0.245068
$501$	−5.92996e6	−1.05550
$502$	−292364.	−0.0517803
$503$	309897.	0.0546132	0.0273066	−	0.999627i	$-0.491307\pi$
$503$	309897.	0.0546132	0.0273066	+	0.999627i	$0.491307\pi$
$504$	1.15704e6	0.202895
$505$	−1.30217e7	−2.27217
$506$	4.95769e6	0.860801
$507$	219626.	0.0379458
$508$	−3.47513e6	−0.597464
$509$	−90078.2	−0.0154108	−0.00770540	−	0.999970i	$-0.502453\pi$
$509$	−90078.2	−0.0154108	−0.00770540	+	0.999970i	$0.502453\pi$
$510$	514458.	0.0875839
$511$	2.79575e6	0.473638
$512$	262144.	0.0441942
$513$	435352.	0.0730378
$514$	−3.57605e6	−0.597030
$515$	1.09399e7	1.81759
$516$	−517780.	−0.0856093
$517$	−2.28045e6	−0.375226
$518$	−8.18918e6	−1.34096
$519$	4.80118e6	0.782401
$520$	−2.85935e6	−0.463724
$521$	−740001.	−0.119437	−0.0597184	−	0.998215i	$-0.519020\pi$
$521$	−740001.	−0.119437	−0.0597184	+	0.998215i	$0.519020\pi$
$522$	−2.37803e6	−0.381981
$523$	9.89343e6	1.58159	0.790793	−	0.612084i	$-0.209668\pi$
$523$	9.89343e6	1.58159	0.790793	+	0.612084i	$0.209668\pi$
$524$	3.40808e6	0.542228
$525$	3.85569e6	0.610525
$526$	−4.51688e6	−0.711826
$527$	−1.85844e6	−0.291489
$528$	721313.	0.112600
$529$	9.23680e6	1.43510
$530$	−5.24738e6	−0.811434
$531$	281961.	0.0433963
$532$	2.13263e6	0.326691
$533$	1.07603e7	1.64061
$534$	1.09073e6	0.165526
$535$	8.84970e6	1.33673
$536$	3.11786e6	0.468754
$537$	−1.05981e6	−0.158596
$538$	−6.15716e6	−0.917117
$539$	1.03340e7	1.53213
$540$	828427.	0.122256
$541$	7.13925e6	1.04872	0.524360	−	0.851497i	$-0.324305\pi$
$541$	7.13925e6	1.04872	0.524360	+	0.851497i	$0.324305\pi$
$542$	4.92210e6	0.719701
$543$	877740.	0.127752
$544$	206035.	0.0298499
$545$	19292.5	0.00278225
$546$	−5.05436e6	−0.725578
$547$	1.33987e7	1.91467	0.957335	−	0.288981i	$-0.0933166\pi$
$547$	1.33987e7	1.91467	0.957335	+	0.288981i	$0.0933166\pi$
$548$	2.63347e6	0.374608
$549$	−2.43263e6	−0.344465
$550$	2.40368e6	0.338821
$551$	−4.38315e6	−0.615046
$552$	2.28034e6	0.318532
$553$	−1.79217e7	−2.49211
$554$	1.95874e6	0.271145
$555$	−5.86337e6	−0.808006
$556$	−1.20617e6	−0.165471
$557$	4.62286e6	0.631354	0.315677	−	0.948867i	$-0.397768\pi$
$557$	4.62286e6	0.631354	0.315677	+	0.948867i	$0.397768\pi$
$558$	−2.99263e6	−0.406881
$559$	2.26185e6	0.306150
$560$	4.05816e6	0.546839
$561$	566923.	0.0760531
$562$	−5.44556e6	−0.727281
$563$	−1.28413e7	−1.70742	−0.853708	−	0.520751i	$-0.825652\pi$
$563$	−1.28413e7	−1.70742	−0.853708	+	0.520751i	$0.825652\pi$
$564$	−1.04892e6	−0.138849
$565$	−1.14630e6	−0.151070
$566$	1.52585e6	0.200202
$567$	1.46438e6	0.191291
$568$	4.48268e6	0.582998
$569$	−4.54183e6	−0.588099	−0.294050	−	0.955790i	$-0.595003\pi$
$569$	−4.54183e6	−0.588099	−0.294050	+	0.955790i	$0.595003\pi$
$570$	1.52694e6	0.196850
$571$	−5.85422e6	−0.751413	−0.375707	−	0.926739i	$-0.622600\pi$
$571$	−5.85422e6	−0.751413	−0.375707	+	0.926739i	$0.622600\pi$
$572$	−3.15095e6	−0.402672
$573$	6.32462e6	0.804726
$574$	−1.52716e7	−1.93466
$575$	7.59897e6	0.958484
$576$	331776.	0.0416667
$577$	−1.01301e7	−1.26670	−0.633350	−	0.773866i	$-0.718321\pi$
$577$	−1.01301e7	−1.26670	−0.633350	+	0.773866i	$0.718321\pi$
$578$	−5.51749e6	−0.686945
$579$	−6.25789e6	−0.775767
$580$	−8.34065e6	−1.02951
$581$	2.34807e7	2.88583
$582$	1.88772e6	0.231009
$583$	−5.78252e6	−0.704605
$584$	801671.	0.0972667
$585$	−3.61887e6	−0.437203
$586$	4.92654e6	0.592650
$587$	1.35831e7	1.62706	0.813528	−	0.581525i	$-0.197544\pi$
$587$	1.35831e7	1.62706	0.813528	+	0.581525i	$0.197544\pi$
$588$	4.75324e6	0.566952
$589$	−5.51596e6	−0.655138
$590$	988942.	0.116961
$591$	−6.00599e6	−0.707319
$592$	−2.34821e6	−0.275381
$593$	7.79306e6	0.910063	0.455031	−	0.890475i	$-0.349628\pi$
$593$	7.79306e6	0.910063	0.455031	+	0.890475i	$0.349628\pi$
$594$	912911.	0.106160
$595$	3.18955e6	0.369350
$596$	−4.64162e6	−0.535247
$597$	522882.	0.0600438
$598$	−9.96136e6	−1.13911
$599$	−3.66870e6	−0.417777	−0.208889	−	0.977939i	$-0.566985\pi$
$599$	−3.66870e6	−0.417777	−0.208889	+	0.977939i	$0.566985\pi$
$600$	1.10560e6	0.125378
$601$	316697.	0.0357650	0.0178825	−	0.999840i	$-0.494308\pi$
$601$	316697.	0.0357650	0.0178825	+	0.999840i	$0.494308\pi$
$602$	−3.21015e6	−0.361023
$603$	3.94604e6	0.441945
$604$	−2.64446e6	−0.294948
$605$	−4.47726e6	−0.497306
$606$	−6.60031e6	−0.730101
$607$	−1.64727e7	−1.81465	−0.907326	−	0.420427i	$-0.861880\pi$
$607$	−1.64727e7	−1.81465	−0.907326	+	0.420427i	$0.861880\pi$
$608$	611524.	0.0670895
$609$	−1.47434e7	−1.61085
$610$	−8.53213e6	−0.928395
$611$	4.58205e6	0.496543
$612$	260763.	0.0281428
$613$	1.53009e7	1.64462	0.822311	−	0.569039i	$-0.192685\pi$
$613$	1.53009e7	1.64462	0.822311	+	0.569039i	$0.192685\pi$
$614$	−3.10172e6	−0.332034
$615$	−1.09343e7	−1.16575
$616$	4.47202e6	0.474845
$617$	920840.	0.0973803	0.0486901	−	0.998814i	$-0.484495\pi$
$617$	920840.	0.0973803	0.0486901	+	0.998814i	$0.484495\pi$
$618$	5.54511e6	0.584036
$619$	−1.16294e7	−1.21992	−0.609958	−	0.792434i	$-0.708814\pi$
$619$	−1.16294e7	−1.21992	−0.609958	+	0.792434i	$0.708814\pi$
$620$	−1.04963e7	−1.09662
$621$	2.88606e6	0.300315
$622$	2.60474e6	0.269953
$623$	6.76237e6	0.698038
$624$	−1.44932e6	−0.149005
$625$	−1.20796e7	−1.23695
$626$	4.62383e6	0.471591
$627$	1.68266e6	0.170934
$628$	9.68792e6	0.980238
$629$	−1.84560e6	−0.185999
$630$	5.13611e6	0.515565
$631$	−5.15263e6	−0.515176	−0.257588	−	0.966255i	$-0.582928\pi$
$631$	−5.15263e6	−0.515176	−0.257588	+	0.966255i	$0.582928\pi$
$632$	−5.13898e6	−0.511782
$633$	4.42877e6	0.439313
$634$	−2.80767e6	−0.277411
$635$	−1.54262e7	−1.51818
$636$	−2.65974e6	−0.260733
$637$	−2.07638e7	−2.02749
$638$	−9.19124e6	−0.893969
$639$	5.67339e6	0.549656
$640$	1.16366e6	0.112299
$641$	−4.33605e6	−0.416820	−0.208410	−	0.978042i	$-0.566829\pi$
$641$	−4.33605e6	−0.416820	−0.208410	+	0.978042i	$0.566829\pi$
$642$	4.48564e6	0.429523
$643$	−1.39861e7	−1.33404	−0.667020	−	0.745040i	$-0.732430\pi$
$643$	−1.39861e7	−1.33404	−0.667020	+	0.745040i	$0.732430\pi$
$644$	1.41378e7	1.34328
$645$	−2.29844e6	−0.217537
$646$	480633.	0.0453140
$647$	2.73516e6	0.256875	0.128437	−	0.991718i	$-0.459004\pi$
$647$	2.73516e6	0.256875	0.128437	+	0.991718i	$0.459004\pi$
$648$	419904.	0.0392837
$649$	1.08980e6	0.101562
$650$	−4.82967e6	−0.448367
$651$	−1.85538e7	−1.71585
$652$	3.40169e6	0.313383
$653$	1.84532e7	1.69351	0.846756	−	0.531982i	$-0.178553\pi$
$653$	1.84532e7	1.69351	0.846756	+	0.531982i	$0.178553\pi$
$654$	9778.76	0.000894004 0
$655$	1.51285e7	1.37782
$656$	−4.37908e6	−0.397304
$657$	1.01461e6	0.0917039
$658$	−6.50311e6	−0.585540
$659$	−1.35535e7	−1.21573	−0.607867	−	0.794039i	$-0.707975\pi$
$659$	−1.35535e7	−1.21573	−0.607867	+	0.794039i	$0.707975\pi$
$660$	3.20192e6	0.286122
$661$	−1.38818e7	−1.23578	−0.617892	−	0.786263i	$-0.712013\pi$
$661$	−1.38818e7	−1.23578	−0.617892	+	0.786263i	$0.712013\pi$
$662$	1.32532e7	1.17537
$663$	−1.13911e6	−0.100642
$664$	6.73300e6	0.592637
$665$	9.46679e6	0.830135
$666$	−2.97196e6	−0.259631
$667$	−2.90570e7	−2.52893
$668$	−1.05422e7	−0.914089
$669$	2.99202e6	0.258463
$670$	1.38402e7	1.19112
$671$	−9.40225e6	−0.806168
$672$	2.05696e6	0.175712
$673$	1.03382e7	0.879845	0.439922	−	0.898036i	$-0.355006\pi$
$673$	1.03382e7	0.879845	0.439922	+	0.898036i	$0.355006\pi$
$674$	6.57135e6	0.557192
$675$	1.39928e6	0.118207
$676$	390447.	0.0328621
$677$	1.54109e7	1.29228	0.646141	−	0.763218i	$-0.276382\pi$
$677$	1.54109e7	1.29228	0.646141	+	0.763218i	$0.276382\pi$
$678$	−581023.	−0.0485422
$679$	1.17035e7	0.974188
$680$	914592.	0.0758499
$681$	6.84208e6	0.565354
$682$	−1.15667e7	−0.952243
$683$	−8.80251e6	−0.722029	−0.361015	−	0.932560i	$-0.617570\pi$
$683$	−8.80251e6	−0.722029	−0.361015	+	0.932560i	$0.617570\pi$
$684$	773960.	0.0632526
$685$	1.16900e7	0.951894
$686$	1.44644e7	1.17352
$687$	8.89553e6	0.719085
$688$	−920498.	−0.0741399
$689$	1.16187e7	0.932414
$690$	1.01225e7	0.809403
$691$	−6.74766e6	−0.537599	−0.268799	−	0.963196i	$-0.586627\pi$
$691$	−6.74766e6	−0.537599	−0.268799	+	0.963196i	$0.586627\pi$
$692$	8.53542e6	0.677579
$693$	5.65990e6	0.447688
$694$	−7.10495e6	−0.559967
$695$	−5.35422e6	−0.420469
$696$	−4.22762e6	−0.330805
$697$	−3.44178e6	−0.268350
$698$	161554.	0.0125510
$699$	7.32921e6	0.567367
$700$	6.85455e6	0.528730
$701$	−2.27614e7	−1.74946	−0.874728	−	0.484614i	$-0.838960\pi$
$701$	−2.27614e7	−1.74946	−0.874728	+	0.484614i	$0.838960\pi$
$702$	−1.83429e6	−0.140484
$703$	−5.47786e6	−0.418045
$704$	1.28233e6	0.0975145
$705$	−4.65616e6	−0.352822
$706$	−1.68135e7	−1.26954
$707$	−4.09209e7	−3.07890
$708$	501264.	0.0375823
$709$	1.02432e7	0.765282	0.382641	−	0.923897i	$-0.375015\pi$
$709$	1.02432e7	0.765282	0.382641	+	0.923897i	$0.375015\pi$
$710$	1.98987e7	1.48142
$711$	−6.50403e6	−0.482512
$712$	1.93908e6	0.143350
$713$	−3.65667e7	−2.69378
$714$	1.61669e6	0.118681
$715$	−1.39871e7	−1.02321
$716$	−1.88411e6	−0.137348
$717$	−8.51057e6	−0.618246
$718$	−6.92588e6	−0.501376
$719$	−2.11734e7	−1.52745	−0.763726	−	0.645541i	$-0.776632\pi$
$719$	−2.11734e7	−1.52745	−0.763726	+	0.645541i	$0.776632\pi$
$720$	1.47276e6	0.105877
$721$	3.43788e7	2.46293
$722$	−8.47785e6	−0.605261
$723$	−3.60615e6	−0.256565
$724$	1.56043e6	0.110636
$725$	−1.40880e7	−0.995416
$726$	−2.26938e6	−0.159796
$727$	1.81721e7	1.27518	0.637588	−	0.770377i	$-0.279932\pi$
$727$	1.81721e7	1.27518	0.637588	+	0.770377i	$0.279932\pi$
$728$	−8.98552e6	−0.628369
$729$	531441.	0.0370370
$730$	3.55863e6	0.247159
$731$	−723475.	−0.0500761
$732$	−4.32467e6	−0.298315
$733$	1.11265e7	0.764890	0.382445	−	0.923978i	$-0.375082\pi$
$733$	1.11265e7	0.764890	0.382445	+	0.923978i	$0.375082\pi$
$734$	1.05017e6	0.0719481
$735$	2.10997e7	1.44065
$736$	4.05395e6	0.275857
$737$	1.52517e7	1.03431
$738$	−5.54227e6	−0.374582
$739$	−1.78015e7	−1.19907	−0.599536	−	0.800348i	$-0.704648\pi$
$739$	−1.78015e7	−1.19907	−0.599536	+	0.800348i	$0.704648\pi$
$740$	−1.04238e7	−0.699754
$741$	−3.38093e6	−0.226199
$742$	−1.64899e7	−1.09953
$743$	−948812.	−0.0630534	−0.0315267	−	0.999503i	$-0.510037\pi$
$743$	−948812.	−0.0630534	−0.0315267	+	0.999503i	$0.510037\pi$
$744$	−5.32023e6	−0.352369
$745$	−2.06043e7	−1.36009
$746$	1.22106e7	0.803322
$747$	8.52145e6	0.558743
$748$	1.00786e6	0.0658639
$749$	2.78102e7	1.81134
$750$	−3.08244e6	−0.200098
$751$	−171199.	−0.0110765	−0.00553825	−	0.999985i	$-0.501763\pi$
$751$	−171199.	−0.0110765	−0.00553825	+	0.999985i	$0.501763\pi$
$752$	−1.86474e6	−0.120247
$753$	−657819.	−0.0422784
$754$	1.84677e7	1.18300
$755$	−1.17388e7	−0.749475
$756$	2.60334e6	0.165663
$757$	−1.46080e6	−0.0926511	−0.0463256	−	0.998926i	$-0.514751\pi$
$757$	−1.46080e6	−0.0926511	−0.0463256	+	0.998926i	$0.514751\pi$
$758$	2.17434e6	0.137453
$759$	1.11548e7	0.702841
$760$	2.71456e6	0.170477
$761$	−8.51771e6	−0.533165	−0.266582	−	0.963812i	$-0.585894\pi$
$761$	−8.51771e6	−0.533165	−0.266582	+	0.963812i	$0.585894\pi$
$762$	−7.81905e6	−0.487828
$763$	60626.7	0.00377010
$764$	1.12438e7	0.696913
$765$	1.15753e6	0.0715120
$766$	−5.82542e6	−0.358720
$767$	−2.18970e6	−0.134399
$768$	589824.	0.0360844
$769$	−3.11775e7	−1.90119	−0.950595	−	0.310434i	$-0.899525\pi$
$769$	−3.11775e7	−1.90119	−0.950595	+	0.310434i	$0.899525\pi$
$770$	1.98514e7	1.20660
$771$	−8.04612e6	−0.487473
$772$	−1.11251e7	−0.671834
$773$	−1.45045e7	−0.873078	−0.436539	−	0.899685i	$-0.643796\pi$
$773$	−1.45045e7	−0.873078	−0.436539	+	0.899685i	$0.643796\pi$
$774$	−1.16501e6	−0.0698997
$775$	−1.77290e7	−1.06030
$776$	3.35594e6	0.200060
$777$	−1.84256e7	−1.09489
$778$	−8.68660e6	−0.514518
$779$	−1.02154e7	−0.603132
$780$	−6.43354e6	−0.378629
$781$	2.19280e7	1.28639
$782$	3.18624e6	0.186321
$783$	−5.35058e6	−0.311886
$784$	8.45020e6	0.490994
$785$	4.30049e7	2.49083
$786$	7.66818e6	0.442727
$787$	7.20758e6	0.414813	0.207407	−	0.978255i	$-0.433498\pi$
$787$	7.20758e6	0.414813	0.207407	+	0.978255i	$0.433498\pi$
$788$	−1.06773e7	−0.612557
$789$	−1.01630e7	−0.581204
$790$	−2.28120e7	−1.30046
$791$	−3.60225e6	−0.204707
$792$	1.62295e6	0.0919376
$793$	1.88917e7	1.06681
$794$	−6.61679e6	−0.372474
$795$	−1.18066e7	−0.662533
$796$	929569.	0.0519995
$797$	4.68685e6	0.261358	0.130679	−	0.991425i	$-0.458284\pi$
$797$	4.68685e6	0.261358	0.130679	+	0.991425i	$0.458284\pi$
$798$	4.79842e6	0.266742
$799$	−1.46561e6	−0.0812180
$800$	1.96552e6	0.108580
$801$	2.45415e6	0.135151
$802$	−603794.	−0.0331477
$803$	3.92154e6	0.214619
$804$	7.01518e6	0.382736
$805$	6.27578e7	3.41333
$806$	2.32407e7	1.26012
$807$	−1.38536e7	−0.748823
$808$	−1.17339e7	−0.632286
$809$	−9.59860e6	−0.515628	−0.257814	−	0.966195i	$-0.583002\pi$
$809$	−9.59860e6	−0.515628	−0.257814	+	0.966195i	$0.583002\pi$
$810$	1.86396e6	0.0998216
$811$	−3.05478e7	−1.63090	−0.815452	−	0.578825i	$-0.803511\pi$
$811$	−3.05478e7	−1.63090	−0.815452	+	0.578825i	$0.803511\pi$
$812$	−2.62105e7	−1.39504
$813$	1.10747e7	0.587633
$814$	−1.14868e7	−0.607628
$815$	1.51002e7	0.796319
$816$	463578.	0.0243724
$817$	−2.14732e6	−0.112549
$818$	1.30795e7	0.683451
$819$	−1.13723e7	−0.592432
$820$	−1.94388e7	−1.00957
$821$	−843027.	−0.0436500	−0.0218250	−	0.999762i	$-0.506948\pi$
$821$	−843027.	−0.0436500	−0.0218250	+	0.999762i	$0.506948\pi$
$822$	5.92530e6	0.305866
$823$	−328045.	−0.0168824	−0.00844120	−	0.999964i	$-0.502687\pi$
$823$	−328045.	−0.0168824	−0.00844120	+	0.999964i	$0.502687\pi$
$824$	9.85798e6	0.505790
$825$	5.40829e6	0.276647
$826$	3.10775e6	0.158488
$827$	−8.51344e6	−0.432854	−0.216427	−	0.976299i	$-0.569440\pi$
$827$	−8.51344e6	−0.432854	−0.216427	+	0.976299i	$0.569440\pi$
$828$	5.13078e6	0.260080
$829$	5.93255e6	0.299816	0.149908	−	0.988700i	$-0.452102\pi$
$829$	5.93255e6	0.299816	0.149908	+	0.988700i	$0.452102\pi$
$830$	2.98879e7	1.50591
$831$	4.40716e6	0.221389
$832$	−2.57656e6	−0.129042
$833$	6.64152e6	0.331631
$834$	−2.71389e6	−0.135107
$835$	−4.67968e7	−2.32274
$836$	2.99140e6	0.148033
$837$	−6.73341e6	−0.332217
$838$	114532.	0.00563400
$839$	9.05213e6	0.443962	0.221981	−	0.975051i	$-0.428748\pi$
$839$	9.05213e6	0.443962	0.221981	+	0.975051i	$0.428748\pi$
$840$	9.13087e6	0.446492
$841$	3.33588e7	1.62637
$842$	−7.56912e6	−0.367930
$843$	−1.22525e7	−0.593822
$844$	7.87337e6	0.380456
$845$	1.73320e6	0.0835039
$846$	−2.36006e6	−0.113370
$847$	−1.40698e7	−0.673875
$848$	−4.72842e6	−0.225801
$849$	3.43315e6	0.163465
$850$	1.54482e6	0.0733381
$851$	−3.63141e7	−1.71890
$852$	1.00860e7	0.476016
$853$	3.37689e7	1.58908	0.794538	−	0.607214i	$-0.207713\pi$
$853$	3.37689e7	1.58908	0.794538	+	0.607214i	$0.207713\pi$
$854$	−2.68122e7	−1.25802
$855$	3.43562e6	0.160727
$856$	7.97447e6	0.371978
$857$	2.11266e7	0.982602	0.491301	−	0.870990i	$-0.336522\pi$
$857$	2.11266e7	0.982602	0.491301	+	0.870990i	$0.336522\pi$
$858$	−7.08964e6	−0.328781
$859$	3.89769e7	1.80229	0.901145	−	0.433518i	$-0.142728\pi$
$859$	3.89769e7	1.80229	0.901145	+	0.433518i	$0.142728\pi$
$860$	−4.08611e6	−0.188393
$861$	−3.43611e7	−1.57965
$862$	2.67539e7	1.22636
$863$	2.58489e7	1.18145	0.590725	−	0.806873i	$-0.298842\pi$
$863$	2.58489e7	1.18145	0.590725	+	0.806873i	$0.298842\pi$
$864$	746496.	0.0340207
$865$	3.78889e7	1.72176
$866$	2.42126e7	1.09710
$867$	−1.24144e7	−0.560889
$868$	−3.29845e7	−1.48597
$869$	−2.51384e7	−1.12925
$870$	−1.87665e7	−0.840590
$871$	−3.06448e7	−1.36871
$872$	17384.5	0.000774230 0
$873$	4.24737e6	0.188618
$874$	9.45696e6	0.418767
$875$	−1.91106e7	−0.843830
$876$	1.80376e6	0.0794179
$877$	4.24755e7	1.86483	0.932415	−	0.361389i	$-0.117697\pi$
$877$	4.24755e7	1.86483	0.932415	+	0.361389i	$0.117697\pi$
$878$	2.18148e7	0.955026
$879$	1.10847e7	0.483897
$880$	5.69230e6	0.247789
$881$	3.33434e7	1.44734	0.723669	−	0.690148i	$-0.242454\pi$
$881$	3.33434e7	1.44734	0.723669	+	0.690148i	$0.242454\pi$
$882$	1.06948e7	0.462914
$883$	4.33582e7	1.87141	0.935707	−	0.352779i	$-0.114763\pi$
$883$	4.33582e7	1.87141	0.935707	+	0.352779i	$0.114763\pi$
$884$	−2.02508e6	−0.0871587
$885$	2.22512e6	0.0954982
$886$	−3.78870e6	−0.162146
$887$	1.82161e7	0.777404	0.388702	−	0.921363i	$-0.372923\pi$
$887$	1.82161e7	0.777404	0.388702	+	0.921363i	$0.372923\pi$
$888$	−5.28348e6	−0.224847
$889$	−4.84768e7	−2.05721
$890$	8.60762e6	0.364257
$891$	2.05405e6	0.0866796
$892$	5.31914e6	0.223836
$893$	−4.35003e6	−0.182542
$894$	−1.04437e7	−0.437027
$895$	−8.36359e6	−0.349008
$896$	3.65681e6	0.152171
$897$	−2.24131e7	−0.930080
$898$	−1.51868e7	−0.628455
$899$	6.77924e7	2.79757
$900$	2.48761e6	0.102371
$901$	−3.71635e6	−0.152512
$902$	−2.14212e7	−0.876652
$903$	−7.22284e6	−0.294774
$904$	−1.03293e6	−0.0420388
$905$	6.92676e6	0.281131
$906$	−5.95005e6	−0.240824
$907$	−8.20429e6	−0.331149	−0.165574	−	0.986197i	$-0.552948\pi$
$907$	−8.20429e6	−0.331149	−0.165574	+	0.986197i	$0.552948\pi$
$908$	1.21637e7	0.489611
$909$	−1.48507e7	−0.596125
$910$	−3.98869e7	−1.59671
$911$	3.08923e7	1.23326	0.616629	−	0.787254i	$-0.288498\pi$
$911$	3.08923e7	1.23326	0.616629	+	0.787254i	$0.288498\pi$
$912$	1.37593e6	0.0547783
$913$	3.29359e7	1.30765
$914$	7.58863e6	0.300468
$915$	−1.91973e7	−0.758031
$916$	1.58143e7	0.622746
$917$	4.75415e7	1.86702
$918$	586716.	0.0229785
$919$	−2.30162e7	−0.898969	−0.449485	−	0.893288i	$-0.648392\pi$
$919$	−2.30162e7	−0.898969	−0.449485	+	0.893288i	$0.648392\pi$
$920$	1.79955e7	0.700963
$921$	−6.97887e6	−0.271104
$922$	−1.55424e7	−0.602133
$923$	−4.40594e7	−1.70229
$924$	1.00620e7	0.387709
$925$	−1.76065e7	−0.676581
$926$	−4.35420e6	−0.166871
$927$	1.24765e7	0.476863
$928$	−7.51576e6	−0.286486
$929$	5.07543e7	1.92945	0.964726	−	0.263256i	$-0.0847965\pi$
$929$	5.07543e7	1.92945	0.964726	+	0.263256i	$0.0847965\pi$
$930$	−2.36166e7	−0.895385
$931$	1.97124e7	0.745360
$932$	1.30297e7	0.491354
$933$	5.86066e6	0.220416
$934$	3.40364e7	1.27666
$935$	4.47392e6	0.167363
$936$	−3.26096e6	−0.121662
$937$	2.52453e7	0.939359	0.469679	−	0.882837i	$-0.344370\pi$
$937$	2.52453e7	0.939359	0.469679	+	0.882837i	$0.344370\pi$
$938$	4.34930e7	1.61403
$939$	1.04036e7	0.385053
$940$	−8.27762e6	−0.305553
$941$	−1.62682e7	−0.598917	−0.299458	−	0.954109i	$-0.596806\pi$
$941$	−1.62682e7	−0.598917	−0.299458	+	0.954109i	$0.596806\pi$
$942$	2.17978e7	0.800361
$943$	−6.77206e7	−2.47994
$944$	891136.	0.0325472
$945$	1.15563e7	0.420957
$946$	−4.50281e6	−0.163590
$947$	1.99694e6	0.0723587	0.0361794	−	0.999345i	$-0.488481\pi$
$947$	1.99694e6	0.0723587	0.0361794	+	0.999345i	$0.488481\pi$
$948$	−1.15627e7	−0.417868
$949$	−7.87947e6	−0.284009
$950$	4.58511e6	0.164832
$951$	−6.31726e6	−0.226505
$952$	2.87411e6	0.102781
$953$	2.06218e7	0.735520	0.367760	−	0.929921i	$-0.380125\pi$
$953$	2.06218e7	0.735520	0.367760	+	0.929921i	$0.380125\pi$
$954$	−5.98440e6	−0.212887
$955$	4.99113e7	1.77089
$956$	−1.51299e7	−0.535416
$957$	−2.06803e7	−0.729923
$958$	2.95113e6	0.103890
$959$	3.67359e7	1.28986
$960$	2.61824e6	0.0916920
$961$	5.66839e7	1.97993
$962$	2.30801e7	0.804083
$963$	1.00927e7	0.350704
$964$	−6.41093e6	−0.222192
$965$	−4.93847e7	−1.70716
$966$	3.18100e7	1.09678
$967$	−1.82213e7	−0.626633	−0.313317	−	0.949649i	$-0.601440\pi$
$967$	−1.82213e7	−0.626633	−0.313317	+	0.949649i	$0.601440\pi$
$968$	−4.03446e6	−0.138387
$969$	1.08143e6	0.0369987
$970$	1.48971e7	0.508361
$971$	2.32561e7	0.791569	0.395784	−	0.918344i	$-0.370473\pi$
$971$	2.32561e7	0.791569	0.395784	+	0.918344i	$0.370473\pi$
$972$	944784.	0.0320750
$973$	−1.68256e7	−0.569757
$974$	1.04449e6	0.0352782
$975$	−1.08668e7	−0.366090
$976$	−7.68830e6	−0.258349
$977$	1.59994e7	0.536250	0.268125	−	0.963384i	$-0.413596\pi$
$977$	1.59994e7	0.536250	0.268125	+	0.963384i	$0.413596\pi$
$978$	7.65380e6	0.255876
$979$	9.48544e6	0.316301
$980$	3.75106e7	1.24764
$981$	22002.2	0.000729951 0
$982$	−2.35439e7	−0.779113
$983$	1.44660e7	0.477491	0.238746	−	0.971082i	$-0.423264\pi$
$983$	1.44660e7	0.477491	0.238746	+	0.971082i	$0.423264\pi$
$984$	−9.85292e6	−0.324397
$985$	−4.73968e7	−1.55653
$986$	−5.90709e6	−0.193500
$987$	−1.46320e7	−0.478091
$988$	−6.01055e6	−0.195894
$989$	−1.42351e7	−0.462775
$990$	7.20432e6	0.233617
$991$	808993.	0.0261674	0.0130837	−	0.999914i	$-0.495835\pi$
$991$	808993.	0.0261674	0.0130837	+	0.999914i	$0.495835\pi$
$992$	−9.45818e6	−0.305161
$993$	2.98197e7	0.959687
$994$	6.25317e7	2.00740
$995$	4.12637e6	0.132133
$996$	1.51493e7	0.483886
$997$	−4.25822e7	−1.35672	−0.678360	−	0.734730i	$-0.737309\pi$
$997$	−4.25822e7	−1.35672	−0.678360	+	0.734730i	$0.737309\pi$
$998$	1.32274e7	0.420385
$999$	−6.68690e6	−0.211988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.i.1.7	✓	8
3.2	odd	2		1062.6.a.k.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.i.1.7	✓	8	1.1	even	1	trivial
1062.6.a.k.1.2		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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +71.0243 q^{5} +36.0000 q^{6} +223.194 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +71.0243 q^{5} +36.0000 q^{6} +223.194 q^{7} +64.0000 q^{8} +81.0000 q^{9} +284.097 q^{10} +313.070 q^{11} +144.000 q^{12} -629.044 q^{13} +892.776 q^{14} +639.219 q^{15} +256.000 q^{16} +201.206 q^{17} +324.000 q^{18} +597.191 q^{19} +1136.39 q^{20} +2008.75 q^{21} +1252.28 q^{22} +3958.93 q^{23} +576.000 q^{24} +1919.45 q^{25} -2516.17 q^{26} +729.000 q^{27} +3571.10 q^{28} -7339.61 q^{29} +2556.87 q^{30} -9236.50 q^{31} +1024.00 q^{32} +2817.63 q^{33} +804.823 q^{34} +15852.2 q^{35} +1296.00 q^{36} -9172.71 q^{37} +2388.76 q^{38} -5661.39 q^{39} +4545.55 q^{40} -17105.8 q^{41} +8034.99 q^{42} -3595.70 q^{43} +5009.12 q^{44} +5752.97 q^{45} +15835.7 q^{46} -7284.15 q^{47} +2304.00 q^{48} +33008.6 q^{49} +7677.80 q^{50} +1810.85 q^{51} -10064.7 q^{52} -18470.4 q^{53} +2916.00 q^{54} +22235.6 q^{55} +14284.4 q^{56} +5374.72 q^{57} -29358.5 q^{58} +3481.00 q^{59} +10227.5 q^{60} -30032.4 q^{61} -36946.0 q^{62} +18078.7 q^{63} +4096.00 q^{64} -44677.4 q^{65} +11270.5 q^{66} +48716.6 q^{67} +3219.29 q^{68} +35630.4 q^{69} +63408.8 q^{70} +70041.9 q^{71} +5184.00 q^{72} +12526.1 q^{73} -36690.8 q^{74} +17275.0 q^{75} +9555.06 q^{76} +69875.3 q^{77} -22645.6 q^{78} -80296.6 q^{79} +18182.2 q^{80} +6561.00 q^{81} -68423.1 q^{82} +105203. q^{83} +32139.9 q^{84} +14290.5 q^{85} -14382.8 q^{86} -66056.5 q^{87} +20036.5 q^{88} +30298.2 q^{89} +23011.9 q^{90} -140399. q^{91} +63342.9 q^{92} -83128.5 q^{93} -29136.6 q^{94} +42415.1 q^{95} +9216.00 q^{96} +52436.6 q^{97} +132034. q^{98} +25358.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9}+O(q^{10}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9} + 384 q^{10} + 897 q^{11} + 1152 q^{12} + 1743 q^{13} + 724 q^{14} + 864 q^{15} + 2048 q^{16} + 1861 q^{17} + 2592 q^{18} + 3154 q^{19} + 1536 q^{20} + 1629 q^{21} + 3588 q^{22} + 3808 q^{23} + 4608 q^{24} + 11616 q^{25} + 6972 q^{26} + 5832 q^{27} + 2896 q^{28} + 328 q^{29} + 3456 q^{30} + 570 q^{31} + 8192 q^{32} + 8073 q^{33} + 7444 q^{34} + 36086 q^{35} + 10368 q^{36} + 12777 q^{37} + 12616 q^{38} + 15687 q^{39} + 6144 q^{40} + 20167 q^{41} + 6516 q^{42} + 24579 q^{43} + 14352 q^{44} + 7776 q^{45} + 15232 q^{46} + 20490 q^{47} + 18432 q^{48} + 59391 q^{49} + 46464 q^{50} + 16749 q^{51} + 27888 q^{52} + 13404 q^{53} + 23328 q^{54} - 34588 q^{55} + 11584 q^{56} + 28386 q^{57} + 1312 q^{58} + 27848 q^{59} + 13824 q^{60} + 94944 q^{61} + 2280 q^{62} + 14661 q^{63} + 32768 q^{64} + 54560 q^{65} + 32292 q^{66} + 28838 q^{67} + 29776 q^{68} + 34272 q^{69} + 144344 q^{70} + 14983 q^{71} + 41472 q^{72} + 69384 q^{73} + 51108 q^{74} + 104544 q^{75} + 50464 q^{76} - 22359 q^{77} + 62748 q^{78} - 49199 q^{79} + 24576 q^{80} + 52488 q^{81} + 80668 q^{82} + 3995 q^{83} + 26064 q^{84} - 142290 q^{85} + 98316 q^{86} + 2952 q^{87} + 57408 q^{88} + 28722 q^{89} + 31104 q^{90} + 20815 q^{91} + 60928 q^{92} + 5130 q^{93} + 81960 q^{94} + 208010 q^{95} + 73728 q^{96} + 204150 q^{97} + 237564 q^{98} + 72657 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9 + 384 * q^10 + 897 * q^11 + 1152 * q^12 + 1743 * q^13 + 724 * q^14 + 864 * q^15 + 2048 * q^16 + 1861 * q^17 + 2592 * q^18 + 3154 * q^19 + 1536 * q^20 + 1629 * q^21 + 3588 * q^22 + 3808 * q^23 + 4608 * q^24 + 11616 * q^25 + 6972 * q^26 + 5832 * q^27 + 2896 * q^28 + 328 * q^29 + 3456 * q^30 + 570 * q^31 + 8192 * q^32 + 8073 * q^33 + 7444 * q^34 + 36086 * q^35 + 10368 * q^36 + 12777 * q^37 + 12616 * q^38 + 15687 * q^39 + 6144 * q^40 + 20167 * q^41 + 6516 * q^42 + 24579 * q^43 + 14352 * q^44 + 7776 * q^45 + 15232 * q^46 + 20490 * q^47 + 18432 * q^48 + 59391 * q^49 + 46464 * q^50 + 16749 * q^51 + 27888 * q^52 + 13404 * q^53 + 23328 * q^54 - 34588 * q^55 + 11584 * q^56 + 28386 * q^57 + 1312 * q^58 + 27848 * q^59 + 13824 * q^60 + 94944 * q^61 + 2280 * q^62 + 14661 * q^63 + 32768 * q^64 + 54560 * q^65 + 32292 * q^66 + 28838 * q^67 + 29776 * q^68 + 34272 * q^69 + 144344 * q^70 + 14983 * q^71 + 41472 * q^72 + 69384 * q^73 + 51108 * q^74 + 104544 * q^75 + 50464 * q^76 - 22359 * q^77 + 62748 * q^78 - 49199 * q^79 + 24576 * q^80 + 52488 * q^81 + 80668 * q^82 + 3995 * q^83 + 26064 * q^84 - 142290 * q^85 + 98316 * q^86 + 2952 * q^87 + 57408 * q^88 + 28722 * q^89 + 31104 * q^90 + 20815 * q^91 + 60928 * q^92 + 5130 * q^93 + 81960 * q^94 + 208010 * q^95 + 73728 * q^96 + 204150 * q^97 + 237564 * q^98 + 72657 * q^99

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