LMFDB - Embedded newform 354.6.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 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			1.6
Root			$-50.6379$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +62.6379 q^{5} +36.0000 q^{6} -69.5352 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +62.6379 q^{5} +36.0000 q^{6} -69.5352 q^{7} +64.0000 q^{8} +81.0000 q^{9} +250.552 q^{10} -52.2538 q^{11} +144.000 q^{12} -61.0326 q^{13} -278.141 q^{14} +563.741 q^{15} +256.000 q^{16} +1815.93 q^{17} +324.000 q^{18} -962.387 q^{19} +1002.21 q^{20} -625.817 q^{21} -209.015 q^{22} +3399.34 q^{23} +576.000 q^{24} +798.510 q^{25} -244.130 q^{26} +729.000 q^{27} -1112.56 q^{28} +2501.25 q^{29} +2254.97 q^{30} +5850.84 q^{31} +1024.00 q^{32} -470.284 q^{33} +7263.74 q^{34} -4355.54 q^{35} +1296.00 q^{36} +4823.38 q^{37} -3849.55 q^{38} -549.294 q^{39} +4008.83 q^{40} +4997.88 q^{41} -2503.27 q^{42} -11195.8 q^{43} -836.060 q^{44} +5073.67 q^{45} +13597.4 q^{46} +3029.23 q^{47} +2304.00 q^{48} -11971.9 q^{49} +3194.04 q^{50} +16343.4 q^{51} -976.522 q^{52} +23863.7 q^{53} +2916.00 q^{54} -3273.07 q^{55} -4450.25 q^{56} -8661.48 q^{57} +10005.0 q^{58} +3481.00 q^{59} +9019.86 q^{60} -24221.5 q^{61} +23403.4 q^{62} -5632.35 q^{63} +4096.00 q^{64} -3822.96 q^{65} -1881.14 q^{66} -38833.4 q^{67} +29054.9 q^{68} +30594.1 q^{69} -17422.2 q^{70} +27839.3 q^{71} +5184.00 q^{72} -22911.1 q^{73} +19293.5 q^{74} +7186.59 q^{75} -15398.2 q^{76} +3633.47 q^{77} -2197.17 q^{78} -20265.3 q^{79} +16035.3 q^{80} +6561.00 q^{81} +19991.5 q^{82} -49517.8 q^{83} -10013.1 q^{84} +113746. q^{85} -44783.2 q^{86} +22511.3 q^{87} -3344.24 q^{88} +30749.7 q^{89} +20294.7 q^{90} +4243.91 q^{91} +54389.5 q^{92} +52657.6 q^{93} +12116.9 q^{94} -60281.9 q^{95} +9216.00 q^{96} +79454.8 q^{97} -47887.4 q^{98} -4232.55 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	62.6379	1.12050	0.560251	−	0.828323i	$-0.310705\pi$
$5$	62.6379	1.12050	0.560251	+	0.828323i	$0.310705\pi$
$6$	36.0000	0.408248
$7$	−69.5352	−0.536364	−0.268182	−	0.963368i	$-0.586423\pi$
$7$	−69.5352	−0.536364	−0.268182	+	0.963368i	$0.586423\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	250.552	0.792314
$11$	−52.2538	−0.130207	−0.0651037	−	0.997879i	$-0.520738\pi$
$11$	−52.2538	−0.130207	−0.0651037	+	0.997879i	$0.520738\pi$
$12$	144.000	0.288675
$13$	−61.0326	−0.100162	−0.0500811	−	0.998745i	$-0.515948\pi$
$13$	−61.0326	−0.100162	−0.0500811	+	0.998745i	$0.515948\pi$
$14$	−278.141	−0.379267
$15$	563.741	0.646922
$16$	256.000	0.250000
$17$	1815.93	1.52397	0.761987	−	0.647592i	$-0.224224\pi$
$17$	1815.93	1.52397	0.761987	+	0.647592i	$0.224224\pi$
$18$	324.000	0.235702
$19$	−962.387	−0.611597	−0.305799	−	0.952096i	$-0.598923\pi$
$19$	−962.387	−0.611597	−0.305799	+	0.952096i	$0.598923\pi$
$20$	1002.21	0.560251
$21$	−625.817	−0.309670
$22$	−209.015	−0.0920706
$23$	3399.34	1.33991	0.669954	−	0.742402i	$-0.266314\pi$
$23$	3399.34	1.33991	0.669954	+	0.742402i	$0.266314\pi$
$24$	576.000	0.204124
$25$	798.510	0.255523
$26$	−244.130	−0.0708253
$27$	729.000	0.192450
$28$	−1112.56	−0.268182
$29$	2501.25	0.552284	0.276142	−	0.961117i	$-0.410944\pi$
$29$	2501.25	0.552284	0.276142	+	0.961117i	$0.410944\pi$
$30$	2254.97	0.457443
$31$	5850.84	1.09349	0.546744	−	0.837300i	$-0.315867\pi$
$31$	5850.84	1.09349	0.546744	+	0.837300i	$0.315867\pi$
$32$	1024.00	0.176777
$33$	−470.284	−0.0751753
$34$	7263.74	1.07761
$35$	−4355.54	−0.600996
$36$	1296.00	0.166667
$37$	4823.38	0.579225	0.289612	−	0.957144i	$-0.406474\pi$
$37$	4823.38	0.579225	0.289612	+	0.957144i	$0.406474\pi$
$38$	−3849.55	−0.432465
$39$	−549.294	−0.0578286
$40$	4008.83	0.396157
$41$	4997.88	0.464329	0.232165	−	0.972677i	$-0.425419\pi$
$41$	4997.88	0.464329	0.232165	+	0.972677i	$0.425419\pi$
$42$	−2503.27	−0.218970
$43$	−11195.8	−0.923387	−0.461694	−	0.887039i	$-0.652758\pi$
$43$	−11195.8	−0.923387	−0.461694	+	0.887039i	$0.652758\pi$
$44$	−836.060	−0.0651037
$45$	5073.67	0.373500
$46$	13597.4	0.947458
$47$	3029.23	0.200027	0.100013	−	0.994986i	$-0.468111\pi$
$47$	3029.23	0.200027	0.100013	+	0.994986i	$0.468111\pi$
$48$	2304.00	0.144338
$49$	−11971.9	−0.712314
$50$	3194.04	0.180682
$51$	16343.4	0.879867
$52$	−976.522	−0.0500811
$53$	23863.7	1.16694	0.583470	−	0.812135i	$-0.301695\pi$
$53$	23863.7	1.16694	0.583470	+	0.812135i	$0.301695\pi$
$54$	2916.00	0.136083
$55$	−3273.07	−0.145898
$56$	−4450.25	−0.189633
$57$	−8661.48	−0.353106
$58$	10005.0	0.390524
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	9019.86	0.323461
$61$	−24221.5	−0.833444	−0.416722	−	0.909034i	$-0.636821\pi$
$61$	−24221.5	−0.833444	−0.416722	+	0.909034i	$0.636821\pi$
$62$	23403.4	0.773213
$63$	−5632.35	−0.178788
$64$	4096.00	0.125000
$65$	−3822.96	−0.112232
$66$	−1881.14	−0.0531570
$67$	−38833.4	−1.05686	−0.528431	−	0.848976i	$-0.677219\pi$
$67$	−38833.4	−1.05686	−0.528431	+	0.848976i	$0.677219\pi$
$68$	29054.9	0.761987
$69$	30594.1	0.773597
$70$	−17422.2	−0.424969
$71$	27839.3	0.655409	0.327705	−	0.944780i	$-0.393725\pi$
$71$	27839.3	0.655409	0.327705	+	0.944780i	$0.393725\pi$
$72$	5184.00	0.117851
$73$	−22911.1	−0.503198	−0.251599	−	0.967832i	$-0.580956\pi$
$73$	−22911.1	−0.503198	−0.251599	+	0.967832i	$0.580956\pi$
$74$	19293.5	0.409574
$75$	7186.59	0.147526
$76$	−15398.2	−0.305799
$77$	3633.47	0.0698386
$78$	−2197.17	−0.0408910
$79$	−20265.3	−0.365330	−0.182665	−	0.983175i	$-0.558472\pi$
$79$	−20265.3	−0.365330	−0.182665	+	0.983175i	$0.558472\pi$
$80$	16035.3	0.280125
$81$	6561.00	0.111111
$82$	19991.5	0.328330
$83$	−49517.8	−0.788980	−0.394490	−	0.918900i	$-0.629079\pi$
$83$	−49517.8	−0.788980	−0.394490	+	0.918900i	$0.629079\pi$
$84$	−10013.1	−0.154835
$85$	113746.	1.70762
$86$	−44783.2	−0.652934
$87$	22511.3	0.318861
$88$	−3344.24	−0.0460353
$89$	30749.7	0.411497	0.205748	−	0.978605i	$-0.434037\pi$
$89$	30749.7	0.411497	0.205748	+	0.978605i	$0.434037\pi$
$90$	20294.7	0.264105
$91$	4243.91	0.0537234
$92$	54389.5	0.669954
$93$	52657.6	0.631326
$94$	12116.9	0.141440
$95$	−60281.9	−0.685296
$96$	9216.00	0.102062
$97$	79454.8	0.857415	0.428707	−	0.903443i	$-0.358969\pi$
$97$	79454.8	0.857415	0.428707	+	0.903443i	$0.358969\pi$
$98$	−47887.4	−0.503682
$99$	−4232.55	−0.0434025
$100$	12776.2	0.127762
$101$	184364.	1.79835	0.899174	−	0.437591i	$-0.144168\pi$
$101$	184364.	1.79835	0.899174	+	0.437591i	$0.144168\pi$
$102$	65373.6	0.622160
$103$	16084.2	0.149384	0.0746922	−	0.997207i	$-0.476203\pi$
$103$	16084.2	0.149384	0.0746922	+	0.997207i	$0.476203\pi$
$104$	−3906.09	−0.0354127
$105$	−39199.9	−0.346985
$106$	95454.8	0.825151
$107$	65786.6	0.555492	0.277746	−	0.960655i	$-0.410413\pi$
$107$	65786.6	0.555492	0.277746	+	0.960655i	$0.410413\pi$
$108$	11664.0	0.0962250
$109$	−50336.5	−0.405804	−0.202902	−	0.979199i	$-0.565037\pi$
$109$	−50336.5	−0.405804	−0.202902	+	0.979199i	$0.565037\pi$
$110$	−13092.3	−0.103165
$111$	43410.4	0.334416
$112$	−17801.0	−0.134091
$113$	76494.0	0.563549	0.281774	−	0.959481i	$-0.409077\pi$
$113$	76494.0	0.563549	0.281774	+	0.959481i	$0.409077\pi$
$114$	−34645.9	−0.249684
$115$	212928.	1.50137
$116$	40020.0	0.276142
$117$	−4943.64	−0.0333874
$118$	13924.0	0.0920575
$119$	−126271.	−0.817405
$120$	36079.4	0.228721
$121$	−158321.	−0.983046
$122$	−96886.0	−0.589334
$123$	44980.9	0.268081
$124$	93613.5	0.546744
$125$	−145727.	−0.834187
$126$	−22529.4	−0.126422
$127$	−84160.5	−0.463019	−0.231509	−	0.972833i	$-0.574366\pi$
$127$	−84160.5	−0.463019	−0.231509	+	0.972833i	$0.574366\pi$
$128$	16384.0	0.0883883
$129$	−100762.	−0.533118
$130$	−15291.8	−0.0793599
$131$	−25742.1	−0.131059	−0.0655294	−	0.997851i	$-0.520874\pi$
$131$	−25742.1	−0.131059	−0.0655294	+	0.997851i	$0.520874\pi$
$132$	−7524.54	−0.0375876
$133$	66919.7	0.328039
$134$	−155333.	−0.747314
$135$	45663.1	0.215641
$136$	116220.	0.538806
$137$	−212197.	−0.965911	−0.482955	−	0.875645i	$-0.660437\pi$
$137$	−212197.	−0.965911	−0.482955	+	0.875645i	$0.660437\pi$
$138$	122376.	0.547015
$139$	−351792.	−1.54436	−0.772181	−	0.635402i	$-0.780834\pi$
$139$	−351792.	−1.54436	−0.772181	+	0.635402i	$0.780834\pi$
$140$	−69688.6	−0.300498
$141$	27263.1	0.115485
$142$	111357.	0.463444
$143$	3189.18	0.0130419
$144$	20736.0	0.0833333
$145$	156673.	0.618835
$146$	−91644.4	−0.355815
$147$	−107747.	−0.411255
$148$	77174.1	0.289612
$149$	373629.	1.37872	0.689358	−	0.724421i	$-0.257893\pi$
$149$	373629.	1.37872	0.689358	+	0.724421i	$0.257893\pi$
$150$	28746.4	0.104317
$151$	−404273.	−1.44289	−0.721443	−	0.692474i	$-0.756521\pi$
$151$	−404273.	−1.44289	−0.721443	+	0.692474i	$0.756521\pi$
$152$	−61592.7	−0.216232
$153$	147091.	0.507992
$154$	14533.9	0.0493833
$155$	366485.	1.22526
$156$	−8788.70	−0.0289143
$157$	294774.	0.954420	0.477210	−	0.878789i	$-0.341648\pi$
$157$	294774.	0.954420	0.477210	+	0.878789i	$0.341648\pi$
$158$	−81061.2	−0.258327
$159$	214773.	0.673733
$160$	64141.2	0.198079
$161$	−236374.	−0.718679
$162$	26244.0	0.0785674
$163$	472053.	1.39162	0.695811	−	0.718225i	$-0.255045\pi$
$163$	472053.	1.39162	0.695811	+	0.718225i	$0.255045\pi$
$164$	79966.0	0.232165
$165$	−29457.6	−0.0842340
$166$	−198071.	−0.557893
$167$	63192.7	0.175338	0.0876689	−	0.996150i	$-0.472058\pi$
$167$	63192.7	0.175338	0.0876689	+	0.996150i	$0.472058\pi$
$168$	−40052.3	−0.109485
$169$	−367568.	−0.989968
$170$	454985.	1.20747
$171$	−77953.3	−0.203866
$172$	−179133.	−0.461694
$173$	−365026.	−0.927274	−0.463637	−	0.886025i	$-0.653456\pi$
$173$	−365026.	−0.927274	−0.463637	+	0.886025i	$0.653456\pi$
$174$	90045.0	0.225469
$175$	−55524.6	−0.137053
$176$	−13377.0	−0.0325519
$177$	31329.0	0.0751646
$178$	122999.	0.290972
$179$	−189024.	−0.440946	−0.220473	−	0.975393i	$-0.570760\pi$
$179$	−189024.	−0.440946	−0.220473	+	0.975393i	$0.570760\pi$
$180$	81178.8	0.186750
$181$	−50995.0	−0.115700	−0.0578498	−	0.998325i	$-0.518424\pi$
$181$	−50995.0	−0.115700	−0.0578498	+	0.998325i	$0.518424\pi$
$182$	16975.7	0.0379882
$183$	−217993.	−0.481189
$184$	217558.	0.473729
$185$	302127.	0.649022
$186$	210630.	0.446415
$187$	−94889.4	−0.198433
$188$	48467.7	0.100013
$189$	−50691.2	−0.103223
$190$	−241128.	−0.484577
$191$	−669052.	−1.32702	−0.663509	−	0.748169i	$-0.730933\pi$
$191$	−669052.	−1.32702	−0.663509	+	0.748169i	$0.730933\pi$
$192$	36864.0	0.0721688
$193$	120605.	0.233062	0.116531	−	0.993187i	$-0.462823\pi$
$193$	120605.	0.233062	0.116531	+	0.993187i	$0.462823\pi$
$194$	317819.	0.606284
$195$	−34406.6	−0.0647971
$196$	−191550.	−0.356157
$197$	915261.	1.68027	0.840135	−	0.542377i	$-0.182476\pi$
$197$	915261.	1.68027	0.840135	+	0.542377i	$0.182476\pi$
$198$	−16930.2	−0.0306902
$199$	−635762.	−1.13805	−0.569026	−	0.822319i	$-0.692680\pi$
$199$	−635762.	−1.13805	−0.569026	+	0.822319i	$0.692680\pi$
$200$	51104.6	0.0903411
$201$	−349500.	−0.610179
$202$	737458.	1.27162
$203$	−173925.	−0.296225
$204$	261494.	0.439934
$205$	313057.	0.520281
$206$	64336.7	0.105631
$207$	275347.	0.446636
$208$	−15624.4	−0.0250405
$209$	50288.3	0.0796345
$210$	−156799.	−0.245356
$211$	256567.	0.396730	0.198365	−	0.980128i	$-0.436437\pi$
$211$	256567.	0.396730	0.198365	+	0.980128i	$0.436437\pi$
$212$	381819.	0.583470
$213$	250554.	0.378401
$214$	263146.	0.392792
$215$	−701282.	−1.03466
$216$	46656.0	0.0680414
$217$	−406839.	−0.586508
$218$	−201346.	−0.286947
$219$	−206200.	−0.290521
$220$	−52369.1	−0.0729488
$221$	−110831.	−0.152645
$222$	173642.	0.236468
$223$	−85346.9	−0.114928	−0.0574640	−	0.998348i	$-0.518301\pi$
$223$	−85346.9	−0.114928	−0.0574640	+	0.998348i	$0.518301\pi$
$224$	−71204.0	−0.0948166
$225$	64679.3	0.0851744
$226$	305976.	0.398489
$227$	−918305.	−1.18283	−0.591415	−	0.806368i	$-0.701430\pi$
$227$	−918305.	−1.18283	−0.591415	+	0.806368i	$0.701430\pi$
$228$	−138584.	−0.176553
$229$	−606529.	−0.764299	−0.382149	−	0.924101i	$-0.624816\pi$
$229$	−606529.	−0.764299	−0.382149	+	0.924101i	$0.624816\pi$
$230$	851711.	1.06163
$231$	32701.3	0.0403213
$232$	160080.	0.195262
$233$	−647631.	−0.781516	−0.390758	−	0.920493i	$-0.627787\pi$
$233$	−647631.	−0.781516	−0.390758	+	0.920493i	$0.627787\pi$
$234$	−19774.6	−0.0236084
$235$	189745.	0.224130
$236$	55696.0	0.0650945
$237$	−182388.	−0.210923
$238$	−505085.	−0.577993
$239$	−931073.	−1.05436	−0.527180	−	0.849754i	$-0.676751\pi$
$239$	−931073.	−1.05436	−0.527180	+	0.849754i	$0.676751\pi$
$240$	144318.	0.161730
$241$	−560209.	−0.621309	−0.310655	−	0.950523i	$-0.600548\pi$
$241$	−560209.	−0.621309	−0.310655	+	0.950523i	$0.600548\pi$
$242$	−633282.	−0.695119
$243$	59049.0	0.0641500
$244$	−387544.	−0.416722
$245$	−749892.	−0.798149
$246$	179924.	0.189562
$247$	58737.0	0.0612589
$248$	374454.	0.386607
$249$	−445660.	−0.455518
$250$	−582906.	−0.589859
$251$	485697.	0.486610	0.243305	−	0.969950i	$-0.421768\pi$
$251$	485697.	0.486610	0.243305	+	0.969950i	$0.421768\pi$
$252$	−90117.6	−0.0893940
$253$	−177628.	−0.174466
$254$	−336642.	−0.327404
$255$	1.02372e6	0.985892
$256$	65536.0	0.0625000
$257$	18420.3	0.0173966	0.00869830	−	0.999962i	$-0.497231\pi$
$257$	18420.3	0.0173966	0.00869830	+	0.999962i	$0.497231\pi$
$258$	−403049.	−0.376971
$259$	−335395.	−0.310675
$260$	−61167.3	−0.0561159
$261$	202601.	0.184095
$262$	−102968.	−0.0926725
$263$	−720286.	−0.642119	−0.321059	−	0.947059i	$-0.604039\pi$
$263$	−720286.	−0.642119	−0.321059	+	0.947059i	$0.604039\pi$
$264$	−30098.2	−0.0265785
$265$	1.49477e6	1.30756
$266$	267679.	0.231958
$267$	276748.	0.237578
$268$	−621334.	−0.528431
$269$	−632183.	−0.532674	−0.266337	−	0.963880i	$-0.585813\pi$
$269$	−632183.	−0.532674	−0.266337	+	0.963880i	$0.585813\pi$
$270$	182652.	0.152481
$271$	−763515.	−0.631531	−0.315765	−	0.948837i	$-0.602261\pi$
$271$	−763515.	−0.631531	−0.315765	+	0.948837i	$0.602261\pi$
$272$	464879.	0.380994
$273$	38195.2	0.0310172
$274$	−848786.	−0.683002
$275$	−41725.2	−0.0332710
$276$	489505.	0.386798
$277$	−1.79852e6	−1.40837	−0.704184	−	0.710018i	$-0.748687\pi$
$277$	−1.79852e6	−1.40837	−0.704184	+	0.710018i	$0.748687\pi$
$278$	−1.40717e6	−1.09203
$279$	473918.	0.364496
$280$	−278755.	−0.212484
$281$	−503389.	−0.380310	−0.190155	−	0.981754i	$-0.560899\pi$
$281$	−503389.	−0.380310	−0.190155	+	0.981754i	$0.560899\pi$
$282$	109052.	0.0816605
$283$	965563.	0.716662	0.358331	−	0.933595i	$-0.383346\pi$
$283$	965563.	0.716662	0.358331	+	0.933595i	$0.383346\pi$
$284$	445429.	0.327705
$285$	−542537.	−0.395656
$286$	12756.7	0.00922199
$287$	−347528.	−0.249049
$288$	82944.0	0.0589256
$289$	1.87776e6	1.32250
$290$	626693.	0.437582
$291$	715094.	0.495029
$292$	−366578.	−0.251599
$293$	−1.89882e6	−1.29216	−0.646079	−	0.763271i	$-0.723592\pi$
$293$	−1.89882e6	−1.29216	−0.646079	+	0.763271i	$0.723592\pi$
$294$	−430987.	−0.290801
$295$	218043.	0.145877
$296$	308696.	0.204787
$297$	−38093.0	−0.0250584
$298$	1.49452e6	0.974899
$299$	−207471.	−0.134208
$300$	114985.	0.0737632
$301$	778502.	0.495272
$302$	−1.61709e6	−1.02027
$303$	1.65928e6	1.03828
$304$	−246371.	−0.152899
$305$	−1.51718e6	−0.933875
$306$	588363.	0.359204
$307$	454728.	0.275363	0.137682	−	0.990477i	$-0.456035\pi$
$307$	454728.	0.275363	0.137682	+	0.990477i	$0.456035\pi$
$308$	58135.6	0.0349193
$309$	144757.	0.0862472
$310$	1.46594e6	0.866386
$311$	−1.28465e6	−0.753152	−0.376576	−	0.926386i	$-0.622899\pi$
$311$	−1.28465e6	−0.753152	−0.376576	+	0.926386i	$0.622899\pi$
$312$	−35154.8	−0.0204455
$313$	−2.42519e6	−1.39922	−0.699609	−	0.714526i	$-0.746642\pi$
$313$	−2.42519e6	−1.39922	−0.699609	+	0.714526i	$0.746642\pi$
$314$	1.17909e6	0.674877
$315$	−352799.	−0.200332
$316$	−324245.	−0.182665
$317$	−2.28438e6	−1.27679	−0.638395	−	0.769709i	$-0.720401\pi$
$317$	−2.28438e6	−1.27679	−0.638395	+	0.769709i	$0.720401\pi$
$318$	859093.	0.476401
$319$	−130700.	−0.0719114
$320$	256565.	0.140063
$321$	592079.	0.320713
$322$	−945495.	−0.508182
$323$	−1.74763e6	−0.932059
$324$	104976.	0.0555556
$325$	−48735.2	−0.0255938
$326$	1.88821e6	0.984025
$327$	−453028.	−0.234291
$328$	319864.	0.164165
$329$	−210638.	−0.107287
$330$	−117830.	−0.0595624
$331$	178269.	0.0894349	0.0447174	−	0.999000i	$-0.485761\pi$
$331$	178269.	0.0894349	0.0447174	+	0.999000i	$0.485761\pi$
$332$	−792284.	−0.394490
$333$	390694.	0.193075
$334$	252771.	0.123983
$335$	−2.43244e6	−1.18421
$336$	−160209.	−0.0774175
$337$	1.31410e6	0.630312	0.315156	−	0.949040i	$-0.397943\pi$
$337$	1.31410e6	0.630312	0.315156	+	0.949040i	$0.397943\pi$
$338$	−1.47027e6	−0.700013
$339$	688446.	0.325365
$340$	1.81994e6	0.853808
$341$	−305729.	−0.142380
$342$	−311813.	−0.144155
$343$	2.00114e6	0.918423
$344$	−716531.	−0.326467
$345$	1.91635e6	0.866816
$346$	−1.46010e6	−0.655682
$347$	−2.01558e6	−0.898619	−0.449309	−	0.893376i	$-0.648330\pi$
$347$	−2.01558e6	−0.898619	−0.449309	+	0.893376i	$0.648330\pi$
$348$	360180.	0.159431
$349$	190287.	0.0836269	0.0418135	−	0.999125i	$-0.486686\pi$
$349$	190287.	0.0836269	0.0418135	+	0.999125i	$0.486686\pi$
$350$	−222098.	−0.0969114
$351$	−44492.8	−0.0192762
$352$	−53507.8	−0.0230176
$353$	−1.29310e6	−0.552327	−0.276164	−	0.961111i	$-0.589063\pi$
$353$	−1.29310e6	−0.552327	−0.276164	+	0.961111i	$0.589063\pi$
$354$	125316.	0.0531494
$355$	1.74380e6	0.734387
$356$	491996.	0.205748
$357$	−1.13644e6	−0.471929
$358$	−756098.	−0.311796
$359$	3.61757e6	1.48143	0.740714	−	0.671821i	$-0.234488\pi$
$359$	3.61757e6	1.48143	0.740714	+	0.671821i	$0.234488\pi$
$360$	324715.	0.132052
$361$	−1.54991e6	−0.625949
$362$	−203980.	−0.0818119
$363$	−1.42488e6	−0.567562
$364$	67902.6	0.0268617
$365$	−1.43510e6	−0.563834
$366$	−871974.	−0.340252
$367$	1.25588e6	0.486726	0.243363	−	0.969935i	$-0.421749\pi$
$367$	1.25588e6	0.486726	0.243363	+	0.969935i	$0.421749\pi$
$368$	870231.	0.334977
$369$	404828.	0.154776
$370$	1.20851e6	0.458928
$371$	−1.65937e6	−0.625904
$372$	842521.	0.315663
$373$	−2.58051e6	−0.960359	−0.480180	−	0.877170i	$-0.659429\pi$
$373$	−2.58051e6	−0.960359	−0.480180	+	0.877170i	$0.659429\pi$
$374$	−379557.	−0.140313
$375$	−1.31154e6	−0.481618
$376$	193871.	0.0707201
$377$	−152658.	−0.0553179
$378$	−202765.	−0.0729899
$379$	790035.	0.282519	0.141260	−	0.989973i	$-0.454885\pi$
$379$	790035.	0.282519	0.141260	+	0.989973i	$0.454885\pi$
$380$	−964510.	−0.342648
$381$	−757444.	−0.267324
$382$	−2.67621e6	−0.938343
$383$	460166.	0.160294	0.0801471	−	0.996783i	$-0.474461\pi$
$383$	460166.	0.160294	0.0801471	+	0.996783i	$0.474461\pi$
$384$	147456.	0.0510310
$385$	227593.	0.0782542
$386$	482419.	0.164799
$387$	−906860.	−0.307796
$388$	1.27128e6	0.428707
$389$	3.29689e6	1.10466	0.552332	−	0.833624i	$-0.313738\pi$
$389$	3.29689e6	1.10466	0.552332	+	0.833624i	$0.313738\pi$
$390$	−137626.	−0.0458184
$391$	6.17298e6	2.04199
$392$	−766199.	−0.251841
$393$	−231679.	−0.0756668
$394$	3.66104e6	1.18813
$395$	−1.26938e6	−0.409353
$396$	−67720.9	−0.0217012
$397$	3.69776e6	1.17750	0.588752	−	0.808314i	$-0.299619\pi$
$397$	3.69776e6	1.17750	0.588752	+	0.808314i	$0.299619\pi$
$398$	−2.54305e6	−0.804724
$399$	602278.	0.189393
$400$	204419.	0.0638808
$401$	−4.26580e6	−1.32477	−0.662383	−	0.749165i	$-0.730455\pi$
$401$	−4.26580e6	−1.32477	−0.662383	+	0.749165i	$0.730455\pi$
$402$	−1.39800e6	−0.431462
$403$	−357092.	−0.109526
$404$	2.94983e6	0.899174
$405$	410967.	0.124500
$406$	−695700.	−0.209463
$407$	−252040.	−0.0754194
$408$	1.04598e6	0.311080
$409$	2.54340e6	0.751807	0.375904	−	0.926659i	$-0.377332\pi$
$409$	2.54340e6	0.751807	0.375904	+	0.926659i	$0.377332\pi$
$410$	1.25223e6	0.367895
$411$	−1.90977e6	−0.557669
$412$	257347.	0.0746922
$413$	−242052.	−0.0698286
$414$	1.10139e6	0.315819
$415$	−3.10169e6	−0.884053
$416$	−62497.4	−0.0177063
$417$	−3.16613e6	−0.891638
$418$	201153.	0.0563101
$419$	−3.74555e6	−1.04227	−0.521135	−	0.853474i	$-0.674491\pi$
$419$	−3.74555e6	−1.04227	−0.521135	+	0.853474i	$0.674491\pi$
$420$	−627198.	−0.173493
$421$	2.19338e6	0.603126	0.301563	−	0.953446i	$-0.402492\pi$
$421$	2.19338e6	0.603126	0.301563	+	0.953446i	$0.402492\pi$
$422$	1.02627e6	0.280531
$423$	245368.	0.0666755
$424$	1.52728e6	0.412575
$425$	1.45004e6	0.389411
$426$	1.00222e6	0.267570
$427$	1.68425e6	0.447029
$428$	1.05258e6	0.277746
$429$	28702.7	0.00752972
$430$	−2.80513e6	−0.731613
$431$	−4.62476e6	−1.19921	−0.599606	−	0.800295i	$-0.704676\pi$
$431$	−4.62476e6	−1.19921	−0.599606	+	0.800295i	$0.704676\pi$
$432$	186624.	0.0481125
$433$	4.53241e6	1.16174	0.580871	−	0.813996i	$-0.302712\pi$
$433$	4.53241e6	1.16174	0.580871	+	0.813996i	$0.302712\pi$
$434$	−1.62736e6	−0.414724
$435$	1.41006e6	0.357284
$436$	−805384.	−0.202902
$437$	−3.27148e6	−0.819484
$438$	−824800.	−0.205430
$439$	−1.30519e6	−0.323230	−0.161615	−	0.986854i	$-0.551670\pi$
$439$	−1.30519e6	−0.323230	−0.161615	+	0.986854i	$0.551670\pi$
$440$	−209476.	−0.0515826
$441$	−969720.	−0.237438
$442$	−443325.	−0.107936
$443$	7.62952e6	1.84709	0.923545	−	0.383490i	$-0.125278\pi$
$443$	7.62952e6	1.84709	0.923545	+	0.383490i	$0.125278\pi$
$444$	694567.	0.167208
$445$	1.92610e6	0.461082
$446$	−341388.	−0.0812664
$447$	3.36266e6	0.796002
$448$	−284816.	−0.0670455
$449$	6.16668e6	1.44356	0.721781	−	0.692122i	$-0.243324\pi$
$449$	6.16668e6	1.44356	0.721781	+	0.692122i	$0.243324\pi$
$450$	258717.	0.0602274
$451$	−261158.	−0.0604591
$452$	1.22390e6	0.281774
$453$	−3.63845e6	−0.833051
$454$	−3.67322e6	−0.836387
$455$	265830.	0.0601971
$456$	−554335.	−0.124842
$457$	6.62277e6	1.48337	0.741684	−	0.670749i	$-0.234027\pi$
$457$	6.62277e6	1.48337	0.741684	+	0.670749i	$0.234027\pi$
$458$	−2.42612e6	−0.540441
$459$	1.32382e6	0.293289
$460$	3.40684e6	0.750685
$461$	2.16812e6	0.475151	0.237575	−	0.971369i	$-0.423647\pi$
$461$	2.16812e6	0.475151	0.237575	+	0.971369i	$0.423647\pi$
$462$	130805.	0.0285115
$463$	3.21190e6	0.696322	0.348161	−	0.937435i	$-0.386806\pi$
$463$	3.21190e6	0.696322	0.348161	+	0.937435i	$0.386806\pi$
$464$	640320.	0.138071
$465$	3.29836e6	0.707401
$466$	−2.59053e6	−0.552615
$467$	1.41654e6	0.300565	0.150282	−	0.988643i	$-0.451982\pi$
$467$	1.41654e6	0.300565	0.150282	+	0.988643i	$0.451982\pi$
$468$	−79098.3	−0.0166937
$469$	2.70029e6	0.566862
$470$	758979.	0.158484
$471$	2.65296e6	0.551035
$472$	222784.	0.0460287
$473$	585023.	0.120232
$474$	−729551.	−0.149145
$475$	−768475.	−0.156277
$476$	−2.02034e6	−0.408703
$477$	1.93296e6	0.388980
$478$	−3.72429e6	−0.745545
$479$	1.12653e6	0.224338	0.112169	−	0.993689i	$-0.464220\pi$
$479$	1.12653e6	0.224338	0.112169	+	0.993689i	$0.464220\pi$
$480$	577271.	0.114361
$481$	−294384.	−0.0580164
$482$	−2.24084e6	−0.439332
$483$	−2.12736e6	−0.414929
$484$	−2.53313e6	−0.491523
$485$	4.97689e6	0.960735
$486$	236196.	0.0453609
$487$	8.12670e6	1.55272	0.776358	−	0.630293i	$-0.217065\pi$
$487$	8.12670e6	1.55272	0.776358	+	0.630293i	$0.217065\pi$
$488$	−1.55018e6	−0.294667
$489$	4.24847e6	0.803453
$490$	−2.99957e6	−0.564376
$491$	−4.35407e6	−0.815064	−0.407532	−	0.913191i	$-0.633610\pi$
$491$	−4.35407e6	−0.815064	−0.407532	+	0.913191i	$0.633610\pi$
$492$	719694.	0.134040
$493$	4.54211e6	0.841666
$494$	234948.	0.0433166
$495$	−265118.	−0.0486325
$496$	1.49782e6	0.273372
$497$	−1.93581e6	−0.351538
$498$	−1.78264e6	−0.322100
$499$	2.13499e6	0.383835	0.191917	−	0.981411i	$-0.438529\pi$
$499$	2.13499e6	0.383835	0.191917	+	0.981411i	$0.438529\pi$
$500$	−2.33162e6	−0.417094
$501$	568734.	0.101231
$502$	1.94279e6	0.344085
$503$	−1.00884e6	−0.177787	−0.0888936	−	0.996041i	$-0.528333\pi$
$503$	−1.00884e6	−0.177787	−0.0888936	+	0.996041i	$0.528333\pi$
$504$	−360470.	−0.0632111
$505$	1.15482e7	2.01505
$506$	−710513.	−0.123366
$507$	−3.30811e6	−0.571558
$508$	−1.34657e6	−0.231509
$509$	2.56091e6	0.438127	0.219064	−	0.975711i	$-0.429700\pi$
$509$	2.56091e6	0.438127	0.219064	+	0.975711i	$0.429700\pi$
$510$	4.09487e6	0.697131
$511$	1.59313e6	0.269897
$512$	262144.	0.0441942
$513$	−701580.	−0.117702
$514$	73681.3	0.0123012
$515$	1.00748e6	0.167386
$516$	−1.61220e6	−0.266559
$517$	−158289.	−0.0260450
$518$	−1.34158e6	−0.219681
$519$	−3.28523e6	−0.535362
$520$	−244669.	−0.0396799
$521$	5.47857e6	0.884246	0.442123	−	0.896954i	$-0.354225\pi$
$521$	5.47857e6	0.884246	0.442123	+	0.896954i	$0.354225\pi$
$522$	810405.	0.130175
$523$	−629588.	−0.100647	−0.0503237	−	0.998733i	$-0.516025\pi$
$523$	−629588.	−0.100647	−0.0503237	+	0.998733i	$0.516025\pi$
$524$	−411874.	−0.0655294
$525$	−499721.	−0.0791278
$526$	−2.88114e6	−0.454047
$527$	1.06247e7	1.66645
$528$	−120393.	−0.0187938
$529$	5.11918e6	0.795355
$530$	5.97909e6	0.924582
$531$	281961.	0.0433963
$532$	1.07072e6	0.164019
$533$	−305034.	−0.0465082
$534$	1.10699e6	0.167993
$535$	4.12073e6	0.622429
$536$	−2.48534e6	−0.373657
$537$	−1.70122e6	−0.254580
$538$	−2.52873e6	−0.376658
$539$	625575.	0.0927486
$540$	730609.	0.107820
$541$	−6.47786e6	−0.951565	−0.475783	−	0.879563i	$-0.657835\pi$
$541$	−6.47786e6	−0.951565	−0.475783	+	0.879563i	$0.657835\pi$
$542$	−3.05406e6	−0.446560
$543$	−458955.	−0.0667991
$544$	1.85952e6	0.269403
$545$	−3.15297e6	−0.454704
$546$	152781.	0.0219325
$547$	−8.45158e6	−1.20773	−0.603865	−	0.797087i	$-0.706373\pi$
$547$	−8.45158e6	−1.20773	−0.603865	+	0.797087i	$0.706373\pi$
$548$	−3.39514e6	−0.482955
$549$	−1.96194e6	−0.277815
$550$	−166901.	−0.0235262
$551$	−2.40717e6	−0.337775
$552$	1.95802e6	0.273508
$553$	1.40915e6	0.195950
$554$	−7.19408e6	−0.995866
$555$	2.71914e6	0.374713
$556$	−5.62868e6	−0.772181
$557$	4.01428e6	0.548238	0.274119	−	0.961696i	$-0.411614\pi$
$557$	4.01428e6	0.548238	0.274119	+	0.961696i	$0.411614\pi$
$558$	1.89567e6	0.257738
$559$	683309.	0.0924885
$560$	−1.11502e6	−0.150249
$561$	−854004.	−0.114565
$562$	−2.01355e6	−0.268920
$563$	170359.	0.0226514	0.0113257	−	0.999936i	$-0.496395\pi$
$563$	170359.	0.0226514	0.0113257	+	0.999936i	$0.496395\pi$
$564$	436209.	0.0577427
$565$	4.79143e6	0.631457
$566$	3.86225e6	0.506757
$567$	−456220.	−0.0595960
$568$	1.78172e6	0.231722
$569$	5.68664e6	0.736335	0.368167	−	0.929760i	$-0.379985\pi$
$569$	5.68664e6	0.736335	0.368167	+	0.929760i	$0.379985\pi$
$570$	−2.17015e6	−0.279771
$571$	4.25187e6	0.545745	0.272873	−	0.962050i	$-0.412026\pi$
$571$	4.25187e6	0.545745	0.272873	+	0.962050i	$0.412026\pi$
$572$	51026.9	0.00652093
$573$	−6.02147e6	−0.766154
$574$	−1.39011e6	−0.176105
$575$	2.71441e6	0.342378
$576$	331776.	0.0416667
$577$	3.97345e6	0.496853	0.248427	−	0.968651i	$-0.420086\pi$
$577$	3.97345e6	0.496853	0.248427	+	0.968651i	$0.420086\pi$
$578$	7.51104e6	0.935148
$579$	1.08544e6	0.134558
$580$	2.50677e6	0.309417
$581$	3.44323e6	0.423180
$582$	2.86037e6	0.350038
$583$	−1.24697e6	−0.151944
$584$	−1.46631e6	−0.177907
$585$	−309659.	−0.0374106
$586$	−7.59530e6	−0.913694
$587$	−1.51745e6	−0.181769	−0.0908846	−	0.995861i	$-0.528969\pi$
$587$	−1.51745e6	−0.181769	−0.0908846	+	0.995861i	$0.528969\pi$
$588$	−1.72395e6	−0.205627
$589$	−5.63077e6	−0.668775
$590$	872171.	0.103151
$591$	8.23734e6	0.970105
$592$	1.23479e6	0.144806
$593$	4.85281e6	0.566705	0.283352	−	0.959016i	$-0.408553\pi$
$593$	4.85281e6	0.566705	0.283352	+	0.959016i	$0.408553\pi$
$594$	−152372.	−0.0177190
$595$	−7.90937e6	−0.915903
$596$	5.97806e6	0.689358
$597$	−5.72186e6	−0.657055
$598$	−829883.	−0.0948995
$599$	1.27306e6	0.144971	0.0724855	−	0.997369i	$-0.476907\pi$
$599$	1.27306e6	0.144971	0.0724855	+	0.997369i	$0.476907\pi$
$600$	459942.	0.0521585
$601$	−2.89117e6	−0.326503	−0.163252	−	0.986584i	$-0.552198\pi$
$601$	−2.89117e6	−0.326503	−0.163252	+	0.986584i	$0.552198\pi$
$602$	3.11401e6	0.350210
$603$	−3.14550e6	−0.352287
$604$	−6.46836e6	−0.721443
$605$	−9.91687e6	−1.10150
$606$	6.63712e6	0.734173
$607$	−3.78663e6	−0.417139	−0.208569	−	0.978008i	$-0.566881\pi$
$607$	−3.78663e6	−0.417139	−0.208569	+	0.978008i	$0.566881\pi$
$608$	−985484.	−0.108116
$609$	−1.56532e6	−0.171026
$610$	−6.06874e6	−0.660349
$611$	−184882.	−0.0200351
$612$	2.35345e6	0.253996
$613$	3.59276e6	0.386168	0.193084	−	0.981182i	$-0.438151\pi$
$613$	3.59276e6	0.386168	0.193084	+	0.981182i	$0.438151\pi$
$614$	1.81891e6	0.194711
$615$	2.81751e6	0.300385
$616$	232542.	0.0246917
$617$	−4.01812e6	−0.424923	−0.212462	−	0.977169i	$-0.568148\pi$
$617$	−4.01812e6	−0.424923	−0.212462	+	0.977169i	$0.568148\pi$
$618$	579030.	0.0609860
$619$	−1.46678e7	−1.53864	−0.769321	−	0.638863i	$-0.779405\pi$
$619$	−1.46678e7	−1.53864	−0.769321	+	0.638863i	$0.779405\pi$
$620$	5.86375e6	0.612628
$621$	2.47812e6	0.257866
$622$	−5.13859e6	−0.532559
$623$	−2.13819e6	−0.220712
$624$	−140619.	−0.0144572
$625$	−1.16234e7	−1.19023
$626$	−9.70077e6	−0.989396
$627$	452595.	0.0459770
$628$	4.71638e6	0.477210
$629$	8.75894e6	0.882724
$630$	−1.41120e6	−0.141656
$631$	−1.12626e6	−0.112607	−0.0563033	−	0.998414i	$-0.517931\pi$
$631$	−1.12626e6	−0.112607	−0.0563033	+	0.998414i	$0.517931\pi$
$632$	−1.29698e6	−0.129164
$633$	2.30911e6	0.229052
$634$	−9.13751e6	−0.902827
$635$	−5.27164e6	−0.518813
$636$	3.43637e6	0.336866
$637$	730674.	0.0713469
$638$	−522799.	−0.0508491
$639$	2.25498e6	0.218470
$640$	1.02626e6	0.0990393
$641$	1.27207e7	1.22283	0.611414	−	0.791311i	$-0.290601\pi$
$641$	1.27207e7	1.22283	0.611414	+	0.791311i	$0.290601\pi$
$642$	2.36832e6	0.226779
$643$	−1.49178e7	−1.42291	−0.711455	−	0.702732i	$-0.751963\pi$
$643$	−1.49178e7	−1.42291	−0.711455	+	0.702732i	$0.751963\pi$
$644$	−3.78198e6	−0.359339
$645$	−6.31153e6	−0.597359
$646$	−6.99052e6	−0.659065
$647$	−4.23839e6	−0.398052	−0.199026	−	0.979994i	$-0.563778\pi$
$647$	−4.23839e6	−0.398052	−0.199026	+	0.979994i	$0.563778\pi$
$648$	419904.	0.0392837
$649$	−181895.	−0.0169516
$650$	−194941.	−0.0180975
$651$	−3.66156e6	−0.338620
$652$	7.55284e6	0.695811
$653$	7.27327e6	0.667493	0.333747	−	0.942663i	$-0.391687\pi$
$653$	7.27327e6	0.667493	0.333747	+	0.942663i	$0.391687\pi$
$654$	−1.81211e6	−0.165669
$655$	−1.61243e6	−0.146852
$656$	1.27946e6	0.116082
$657$	−1.85580e6	−0.167733
$658$	−842553.	−0.0758634
$659$	2.96978e6	0.266385	0.133193	−	0.991090i	$-0.457477\pi$
$659$	2.96978e6	0.266385	0.133193	+	0.991090i	$0.457477\pi$
$660$	−471322.	−0.0421170
$661$	−6.19035e6	−0.551076	−0.275538	−	0.961290i	$-0.588856\pi$
$661$	−6.19035e6	−0.551076	−0.275538	+	0.961290i	$0.588856\pi$
$662$	713078.	0.0632400
$663$	−997481.	−0.0881294
$664$	−3.16914e6	−0.278946
$665$	4.19171e6	0.367568
$666$	1.56278e6	0.136525
$667$	8.50260e6	0.740010
$668$	1.01108e6	0.0876689
$669$	−768122.	−0.0663537
$670$	−9.72977e6	−0.837366
$671$	1.26566e6	0.108521
$672$	−640836.	−0.0547424
$673$	−9.01195e6	−0.766975	−0.383487	−	0.923546i	$-0.625277\pi$
$673$	−9.01195e6	−0.766975	−0.383487	+	0.923546i	$0.625277\pi$
$674$	5.25642e6	0.445698
$675$	582114.	0.0491755
$676$	−5.88109e6	−0.494984
$677$	−5.17917e6	−0.434299	−0.217149	−	0.976138i	$-0.569676\pi$
$677$	−5.17917e6	−0.434299	−0.217149	+	0.976138i	$0.569676\pi$
$678$	2.75379e6	0.230068
$679$	−5.52491e6	−0.459886
$680$	7.27977e6	0.603733
$681$	−8.26474e6	−0.682907
$682$	−1.22291e6	−0.100678
$683$	−8.47335e6	−0.695029	−0.347515	−	0.937675i	$-0.612974\pi$
$683$	−8.47335e6	−0.695029	−0.347515	+	0.937675i	$0.612974\pi$
$684$	−1.24725e6	−0.101933
$685$	−1.32916e7	−1.08230
$686$	8.00457e6	0.649423
$687$	−5.45876e6	−0.441268
$688$	−2.86612e6	−0.230847
$689$	−1.45646e6	−0.116883
$690$	7.66540e6	0.612931
$691$	−3.59584e6	−0.286487	−0.143244	−	0.989687i	$-0.545753\pi$
$691$	−3.59584e6	−0.286487	−0.143244	+	0.989687i	$0.545753\pi$
$692$	−5.84041e6	−0.463637
$693$	294311.	0.0232795
$694$	−8.06230e6	−0.635419
$695$	−2.20355e7	−1.73046
$696$	1.44072e6	0.112734
$697$	9.07582e6	0.707626
$698$	761149.	0.0591332
$699$	−5.82868e6	−0.451209
$700$	−888393.	−0.0685267
$701$	1.09587e7	0.842294	0.421147	−	0.906992i	$-0.361628\pi$
$701$	1.09587e7	0.842294	0.421147	+	0.906992i	$0.361628\pi$
$702$	−177971.	−0.0136303
$703$	−4.64196e6	−0.354252
$704$	−214031.	−0.0162759
$705$	1.70770e6	0.129402
$706$	−5.17241e6	−0.390554
$707$	−1.28198e7	−0.964569
$708$	501264.	0.0375823
$709$	2.03920e6	0.152351	0.0761754	−	0.997094i	$-0.475729\pi$
$709$	2.03920e6	0.152351	0.0761754	+	0.997094i	$0.475729\pi$
$710$	6.97519e6	0.519290
$711$	−1.64149e6	−0.121777
$712$	1.96798e6	0.145486
$713$	1.98890e7	1.46517
$714$	−4.54577e6	−0.333704
$715$	199764.	0.0146134
$716$	−3.02439e6	−0.220473
$717$	−8.37965e6	−0.608735
$718$	1.44703e7	1.04753
$719$	−1.96199e7	−1.41538	−0.707692	−	0.706521i	$-0.750264\pi$
$719$	−1.96199e7	−1.41538	−0.707692	+	0.706521i	$0.750264\pi$
$720$	1.29886e6	0.0933751
$721$	−1.11842e6	−0.0801244
$722$	−6.19964e6	−0.442613
$723$	−5.04188e6	−0.358713
$724$	−815921.	−0.0578498
$725$	1.99727e6	0.141121
$726$	−5.69954e6	−0.401327
$727$	−1.91389e7	−1.34301	−0.671507	−	0.740998i	$-0.734353\pi$
$727$	−1.91389e7	−1.34301	−0.671507	+	0.740998i	$0.734353\pi$
$728$	271611.	0.0189941
$729$	531441.	0.0370370
$730$	−5.74042e6	−0.398691
$731$	−2.03308e7	−1.40722
$732$	−3.48789e6	−0.240594
$733$	−3.91683e6	−0.269262	−0.134631	−	0.990896i	$-0.542985\pi$
$733$	−3.91683e6	−0.269262	−0.134631	+	0.990896i	$0.542985\pi$
$734$	5.02353e6	0.344167
$735$	−6.74903e6	−0.460811
$736$	3.48093e6	0.236865
$737$	2.02919e6	0.137611
$738$	1.61931e6	0.109443
$739$	−4.69523e6	−0.316261	−0.158131	−	0.987418i	$-0.550547\pi$
$739$	−4.69523e6	−0.316261	−0.158131	+	0.987418i	$0.550547\pi$
$740$	4.83403e6	0.324511
$741$	528633.	0.0353678
$742$	−6.63747e6	−0.442581
$743$	−1.52555e7	−1.01380	−0.506902	−	0.862004i	$-0.669209\pi$
$743$	−1.52555e7	−1.01380	−0.506902	+	0.862004i	$0.669209\pi$
$744$	3.37009e6	0.223207
$745$	2.34033e7	1.54485
$746$	−1.03220e7	−0.679077
$747$	−4.01094e6	−0.262993
$748$	−1.51823e6	−0.0992164
$749$	−4.57448e6	−0.297946
$750$	−5.24615e6	−0.340555
$751$	1.91358e7	1.23807	0.619036	−	0.785363i	$-0.287523\pi$
$751$	1.91358e7	1.23807	0.619036	+	0.785363i	$0.287523\pi$
$752$	775483.	0.0500066
$753$	4.37128e6	0.280945
$754$	−610631.	−0.0391157
$755$	−2.53228e7	−1.61676
$756$	−811058.	−0.0516116
$757$	2.89626e7	1.83695	0.918477	−	0.395474i	$-0.129420\pi$
$757$	2.89626e7	1.83695	0.918477	+	0.395474i	$0.129420\pi$
$758$	3.16014e6	0.199771
$759$	−1.59865e6	−0.100728
$760$	−3.85804e6	−0.242289
$761$	1.46994e6	0.0920105	0.0460052	−	0.998941i	$-0.485351\pi$
$761$	1.46994e6	0.0920105	0.0460052	+	0.998941i	$0.485351\pi$
$762$	−3.02978e6	−0.189027
$763$	3.50016e6	0.217659
$764$	−1.07048e7	−0.663509
$765$	9.21345e6	0.569205
$766$	1.84066e6	0.113345
$767$	−212455.	−0.0130400
$768$	589824.	0.0360844
$769$	−7.90548e6	−0.482073	−0.241036	−	0.970516i	$-0.577487\pi$
$769$	−7.90548e6	−0.482073	−0.241036	+	0.970516i	$0.577487\pi$
$770$	910373.	0.0553341
$771$	165783.	0.0100439
$772$	1.92967e6	0.116531
$773$	2.15146e7	1.29504	0.647522	−	0.762047i	$-0.275805\pi$
$773$	2.15146e7	1.29504	0.647522	+	0.762047i	$0.275805\pi$
$774$	−3.62744e6	−0.217645
$775$	4.67196e6	0.279412
$776$	5.08511e6	0.303142
$777$	−3.01855e6	−0.179368
$778$	1.31875e7	0.781115
$779$	−4.80989e6	−0.283982
$780$	−550506.	−0.0323985
$781$	−1.45471e6	−0.0853392
$782$	2.46919e7	1.44390
$783$	1.82341e6	0.106287
$784$	−3.06480e6	−0.178078
$785$	1.84640e7	1.06943
$786$	−926716.	−0.0535045
$787$	−2.19956e7	−1.26590	−0.632948	−	0.774194i	$-0.718155\pi$
$787$	−2.19956e7	−1.26590	−0.632948	+	0.774194i	$0.718155\pi$
$788$	1.46442e7	0.840135
$789$	−6.48257e6	−0.370728
$790$	−5.07751e6	−0.289456
$791$	−5.31903e6	−0.302267
$792$	−270883.	−0.0153451
$793$	1.47830e6	0.0834795
$794$	1.47910e7	0.832621
$795$	1.34530e7	0.754918
$796$	−1.01722e7	−0.569026
$797$	3.03936e7	1.69487	0.847435	−	0.530899i	$-0.178145\pi$
$797$	3.03936e7	1.69487	0.847435	+	0.530899i	$0.178145\pi$
$798$	2.40911e6	0.133921
$799$	5.50088e6	0.304835
$800$	817674.	0.0451706
$801$	2.49073e6	0.137166
$802$	−1.70632e7	−0.936751
$803$	1.19719e6	0.0655201
$804$	−5.59201e6	−0.305090
$805$	−1.48060e7	−0.805280
$806$	−1.42837e6	−0.0774467
$807$	−5.68964e6	−0.307540
$808$	1.17993e7	0.635812
$809$	2.55004e6	0.136986	0.0684929	−	0.997652i	$-0.478181\pi$
$809$	2.55004e6	0.136986	0.0684929	+	0.997652i	$0.478181\pi$
$810$	1.64387e6	0.0880349
$811$	2.68430e7	1.43311	0.716554	−	0.697532i	$-0.245718\pi$
$811$	2.68430e7	1.43311	0.716554	+	0.697532i	$0.245718\pi$
$812$	−2.78280e6	−0.148113
$813$	−6.87164e6	−0.364614
$814$	−1.00816e6	−0.0533296
$815$	2.95684e7	1.55931
$816$	4.18391e6	0.219967
$817$	1.07747e7	0.564741
$818$	1.01736e7	0.531608
$819$	343757.	0.0179078
$820$	5.00891e6	0.260141
$821$	1.62469e7	0.841224	0.420612	−	0.907241i	$-0.361815\pi$
$821$	1.62469e7	0.841224	0.420612	+	0.907241i	$0.361815\pi$
$822$	−7.63908e6	−0.394331
$823$	−1.54477e7	−0.794996	−0.397498	−	0.917603i	$-0.630121\pi$
$823$	−1.54477e7	−0.794996	−0.397498	+	0.917603i	$0.630121\pi$
$824$	1.02939e6	0.0528154
$825$	−375526.	−0.0192090
$826$	−968208.	−0.0493763
$827$	−4.34385e6	−0.220857	−0.110428	−	0.993884i	$-0.535222\pi$
$827$	−4.34385e6	−0.220857	−0.110428	+	0.993884i	$0.535222\pi$
$828$	4.40555e6	0.223318
$829$	3.36168e7	1.69891	0.849454	−	0.527662i	$-0.176931\pi$
$829$	3.36168e7	1.69891	0.849454	+	0.527662i	$0.176931\pi$
$830$	−1.24068e7	−0.625120
$831$	−1.61867e7	−0.813121
$832$	−249990.	−0.0125203
$833$	−2.17401e7	−1.08555
$834$	−1.26645e7	−0.630483
$835$	3.95826e6	0.196466
$836$	804613.	0.0398173
$837$	4.26526e6	0.210442
$838$	−1.49822e7	−0.736996
$839$	−2.60524e7	−1.27774	−0.638870	−	0.769315i	$-0.720598\pi$
$839$	−2.60524e7	−1.27774	−0.638870	+	0.769315i	$0.720598\pi$
$840$	−2.50879e6	−0.122678
$841$	−1.42549e7	−0.694983
$842$	8.77351e6	0.426474
$843$	−4.53050e6	−0.219572
$844$	4.10508e6	0.198365
$845$	−2.30237e7	−1.10926
$846$	981471.	0.0471467
$847$	1.10088e7	0.527270
$848$	6.10911e6	0.291735
$849$	8.69007e6	0.413765
$850$	5.80017e6	0.275355
$851$	1.63963e7	0.776108
$852$	4.00886e6	0.189200
$853$	−1.85449e7	−0.872672	−0.436336	−	0.899784i	$-0.643724\pi$
$853$	−1.85449e7	−0.872672	−0.436336	+	0.899784i	$0.643724\pi$
$854$	6.73698e6	0.316097
$855$	−4.88283e6	−0.228432
$856$	4.21034e6	0.196396
$857$	−1.37110e7	−0.637700	−0.318850	−	0.947805i	$-0.603297\pi$
$857$	−1.37110e7	−0.637700	−0.318850	+	0.947805i	$0.603297\pi$
$858$	114811.	0.00532432
$859$	−1.05457e7	−0.487634	−0.243817	−	0.969821i	$-0.578400\pi$
$859$	−1.05457e7	−0.487634	−0.243817	+	0.969821i	$0.578400\pi$
$860$	−1.12205e7	−0.517328
$861$	−3.12776e6	−0.143789
$862$	−1.84990e7	−0.847971
$863$	−2.82316e7	−1.29035	−0.645176	−	0.764034i	$-0.723216\pi$
$863$	−2.82316e7	−1.29035	−0.645176	+	0.764034i	$0.723216\pi$
$864$	746496.	0.0340207
$865$	−2.28644e7	−1.03901
$866$	1.81297e7	0.821476
$867$	1.68998e7	0.763545
$868$	−6.50943e6	−0.293254
$869$	1.05894e6	0.0475687
$870$	5.64023e6	0.252638
$871$	2.37010e6	0.105858
$872$	−3.22154e6	−0.143473
$873$	6.43584e6	0.285805
$874$	−1.30859e7	−0.579463
$875$	1.01331e7	0.447428
$876$	−3.29920e6	−0.145261
$877$	3.02313e6	0.132727	0.0663633	−	0.997796i	$-0.478860\pi$
$877$	3.02313e6	0.132727	0.0663633	+	0.997796i	$0.478860\pi$
$878$	−5.22074e6	−0.228558
$879$	−1.70894e7	−0.746028
$880$	−837905.	−0.0364744
$881$	2.95966e7	1.28470	0.642351	−	0.766411i	$-0.277959\pi$
$881$	2.95966e7	1.28470	0.642351	+	0.766411i	$0.277959\pi$
$882$	−3.87888e6	−0.167894
$883$	−2.34322e7	−1.01137	−0.505687	−	0.862717i	$-0.668761\pi$
$883$	−2.34322e7	−1.01137	−0.505687	+	0.862717i	$0.668761\pi$
$884$	−1.77330e6	−0.0763223
$885$	1.96238e6	0.0842220
$886$	3.05181e7	1.30609
$887$	4.43337e7	1.89202	0.946008	−	0.324144i	$-0.105076\pi$
$887$	4.43337e7	1.89202	0.946008	+	0.324144i	$0.105076\pi$
$888$	2.77827e6	0.118234
$889$	5.85211e6	0.248347
$890$	7.70440e6	0.326035
$891$	−342837.	−0.0144675
$892$	−1.36555e6	−0.0574640
$893$	−2.91529e6	−0.122336
$894$	1.34506e7	0.562858
$895$	−1.18401e7	−0.494081
$896$	−1.13926e6	−0.0474083
$897$	−1.86724e6	−0.0774851
$898$	2.46667e7	1.02075
$899$	1.46344e7	0.603916
$900$	1.03487e6	0.0425872
$901$	4.33349e7	1.77839
$902$	−1.04463e6	−0.0427510
$903$	7.00652e6	0.285945
$904$	4.89562e6	0.199245
$905$	−3.19422e6	−0.129641
$906$	−1.45538e7	−0.589056
$907$	1.99260e7	0.804271	0.402135	−	0.915580i	$-0.368268\pi$
$907$	1.99260e7	0.804271	0.402135	+	0.915580i	$0.368268\pi$
$908$	−1.46929e7	−0.591415
$909$	1.49335e7	0.599449
$910$	1.06332e6	0.0425658
$911$	2.65918e7	1.06158	0.530790	−	0.847504i	$-0.321895\pi$
$911$	2.65918e7	1.06158	0.530790	+	0.847504i	$0.321895\pi$
$912$	−2.21734e6	−0.0882765
$913$	2.58749e6	0.102731
$914$	2.64911e7	1.04890
$915$	−1.36547e7	−0.539173
$916$	−9.70447e6	−0.382149
$917$	1.78998e6	0.0702952
$918$	5.29526e6	0.207387
$919$	−2.14288e7	−0.836969	−0.418485	−	0.908224i	$-0.637439\pi$
$919$	−2.14288e7	−0.836969	−0.418485	+	0.908224i	$0.637439\pi$
$920$	1.36274e7	0.530814
$921$	4.09255e6	0.158981
$922$	8.67249e6	0.335982
$923$	−1.69911e6	−0.0656472
$924$	523220.	0.0201607
$925$	3.85152e6	0.148005
$926$	1.28476e7	0.492374
$927$	1.30282e6	0.0497948
$928$	2.56128e6	0.0976309
$929$	1.52940e7	0.581407	0.290704	−	0.956813i	$-0.406111\pi$
$929$	1.52940e7	0.581407	0.290704	+	0.956813i	$0.406111\pi$
$930$	1.31934e7	0.500208
$931$	1.15216e7	0.435649
$932$	−1.03621e7	−0.390758
$933$	−1.15618e7	−0.434833
$934$	5.66617e6	0.212531
$935$	−5.94367e6	−0.222344
$936$	−316393.	−0.0118042
$937$	2.02169e7	0.752256	0.376128	−	0.926568i	$-0.377255\pi$
$937$	2.02169e7	0.752256	0.376128	+	0.926568i	$0.377255\pi$
$938$	1.08011e7	0.400832
$939$	−2.18267e7	−0.807839
$940$	3.03592e6	0.112065
$941$	−3.42263e7	−1.26005	−0.630023	−	0.776577i	$-0.716954\pi$
$941$	−3.42263e7	−1.26005	−0.630023	+	0.776577i	$0.716954\pi$
$942$	1.06119e7	0.389640
$943$	1.69895e7	0.622159
$944$	891136.	0.0325472
$945$	−3.17519e6	−0.115662
$946$	2.34009e6	0.0850168
$947$	2.42870e7	0.880032	0.440016	−	0.897990i	$-0.354973\pi$
$947$	2.42870e7	0.880032	0.440016	+	0.897990i	$0.354973\pi$
$948$	−2.91820e6	−0.105462
$949$	1.39832e6	0.0504014
$950$	−3.07390e6	−0.110505
$951$	−2.05594e7	−0.737155
$952$	−8.08136e6	−0.288996
$953$	3.65845e7	1.30486	0.652432	−	0.757847i	$-0.273749\pi$
$953$	3.65845e7	1.30486	0.652432	+	0.757847i	$0.273749\pi$
$954$	7.73184e6	0.275050
$955$	−4.19080e7	−1.48692
$956$	−1.48972e7	−0.527180
$957$	−1.17630e6	−0.0415181
$958$	4.50611e6	0.158631
$959$	1.47551e7	0.518080
$960$	2.30908e6	0.0808652
$961$	5.60321e6	0.195717
$962$	−1.17753e6	−0.0410238
$963$	5.32871e6	0.185164
$964$	−8.96335e6	−0.310655
$965$	7.55443e6	0.261146
$966$	−8.50946e6	−0.293399
$967$	3.11235e7	1.07034	0.535171	−	0.844744i	$-0.320247\pi$
$967$	3.11235e7	1.07034	0.535171	+	0.844744i	$0.320247\pi$
$968$	−1.01325e7	−0.347559
$969$	−1.57287e7	−0.538124
$970$	1.99075e7	0.679342
$971$	2.27733e7	0.775137	0.387568	−	0.921841i	$-0.373315\pi$
$971$	2.27733e7	0.775137	0.387568	+	0.921841i	$0.373315\pi$
$972$	944784.	0.0320750
$973$	2.44619e7	0.828340
$974$	3.25068e7	1.09794
$975$	−438616.	−0.0147766
$976$	−6.20070e6	−0.208361
$977$	−2.57158e7	−0.861912	−0.430956	−	0.902373i	$-0.641824\pi$
$977$	−2.57158e7	−0.861912	−0.430956	+	0.902373i	$0.641824\pi$
$978$	1.69939e7	0.568127
$979$	−1.60679e6	−0.0535799
$980$	−1.19983e7	−0.399074
$981$	−4.07726e6	−0.135268
$982$	−1.74163e7	−0.576337
$983$	4.18817e7	1.38242	0.691211	−	0.722653i	$-0.257077\pi$
$983$	4.18817e7	1.38242	0.691211	+	0.722653i	$0.257077\pi$
$984$	2.87878e6	0.0947808
$985$	5.73300e7	1.88275
$986$	1.81684e7	0.595148
$987$	−1.89574e6	−0.0619422
$988$	939792.	0.0306294
$989$	−3.80583e7	−1.23725
$990$	−1.06047e6	−0.0343884
$991$	−2.49348e7	−0.806533	−0.403267	−	0.915083i	$-0.632125\pi$
$991$	−2.49348e7	−0.806533	−0.403267	+	0.915083i	$0.632125\pi$
$992$	5.99126e6	0.193303
$993$	1.60442e6	0.0516352
$994$	−7.74325e6	−0.248575
$995$	−3.98228e7	−1.27519
$996$	−7.13056e6	−0.227759
$997$	−6.03007e7	−1.92125	−0.960627	−	0.277841i	$-0.910381\pi$
$997$	−6.03007e7	−1.92125	−0.960627	+	0.277841i	$0.910381\pi$
$998$	8.53996e6	0.271412
$999$	3.51624e6	0.111472

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +62.6379 q^{5} +36.0000 q^{6} -69.5352 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +62.6379 q^{5} +36.0000 q^{6} -69.5352 q^{7} +64.0000 q^{8} +81.0000 q^{9} +250.552 q^{10} -52.2538 q^{11} +144.000 q^{12} -61.0326 q^{13} -278.141 q^{14} +563.741 q^{15} +256.000 q^{16} +1815.93 q^{17} +324.000 q^{18} -962.387 q^{19} +1002.21 q^{20} -625.817 q^{21} -209.015 q^{22} +3399.34 q^{23} +576.000 q^{24} +798.510 q^{25} -244.130 q^{26} +729.000 q^{27} -1112.56 q^{28} +2501.25 q^{29} +2254.97 q^{30} +5850.84 q^{31} +1024.00 q^{32} -470.284 q^{33} +7263.74 q^{34} -4355.54 q^{35} +1296.00 q^{36} +4823.38 q^{37} -3849.55 q^{38} -549.294 q^{39} +4008.83 q^{40} +4997.88 q^{41} -2503.27 q^{42} -11195.8 q^{43} -836.060 q^{44} +5073.67 q^{45} +13597.4 q^{46} +3029.23 q^{47} +2304.00 q^{48} -11971.9 q^{49} +3194.04 q^{50} +16343.4 q^{51} -976.522 q^{52} +23863.7 q^{53} +2916.00 q^{54} -3273.07 q^{55} -4450.25 q^{56} -8661.48 q^{57} +10005.0 q^{58} +3481.00 q^{59} +9019.86 q^{60} -24221.5 q^{61} +23403.4 q^{62} -5632.35 q^{63} +4096.00 q^{64} -3822.96 q^{65} -1881.14 q^{66} -38833.4 q^{67} +29054.9 q^{68} +30594.1 q^{69} -17422.2 q^{70} +27839.3 q^{71} +5184.00 q^{72} -22911.1 q^{73} +19293.5 q^{74} +7186.59 q^{75} -15398.2 q^{76} +3633.47 q^{77} -2197.17 q^{78} -20265.3 q^{79} +16035.3 q^{80} +6561.00 q^{81} +19991.5 q^{82} -49517.8 q^{83} -10013.1 q^{84} +113746. q^{85} -44783.2 q^{86} +22511.3 q^{87} -3344.24 q^{88} +30749.7 q^{89} +20294.7 q^{90} +4243.91 q^{91} +54389.5 q^{92} +52657.6 q^{93} +12116.9 q^{94} -60281.9 q^{95} +9216.00 q^{96} +79454.8 q^{97} -47887.4 q^{98} -4232.55 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more