LMFDB - Embedded newform 354.6.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.7758722138$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6296x^{4} - 192180x^{3} - 1919598x^{2} - 7344954x - 8433643 $ x^6 - 2x^5 - 6296x^4 - 192180x^3 - 1919598x^2 - 7344954*x - 8433643
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-17.9445$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +17.9373 q^{5} +36.0000 q^{6} +177.055 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +17.9373 q^{5} +36.0000 q^{6} +177.055 q^{7} -64.0000 q^{8} +81.0000 q^{9} -71.7490 q^{10} +129.074 q^{11} -144.000 q^{12} -1171.27 q^{13} -708.221 q^{14} -161.435 q^{15} +256.000 q^{16} +756.475 q^{17} -324.000 q^{18} -227.613 q^{19} +286.996 q^{20} -1593.50 q^{21} -516.297 q^{22} -3364.96 q^{23} +576.000 q^{24} -2803.25 q^{25} +4685.08 q^{26} -729.000 q^{27} +2832.88 q^{28} -450.000 q^{29} +645.741 q^{30} +4615.07 q^{31} -1024.00 q^{32} -1161.67 q^{33} -3025.90 q^{34} +3175.89 q^{35} +1296.00 q^{36} +14879.9 q^{37} +910.451 q^{38} +10541.4 q^{39} -1147.98 q^{40} -6233.02 q^{41} +6373.99 q^{42} +1391.12 q^{43} +2065.19 q^{44} +1452.92 q^{45} +13459.8 q^{46} -2197.52 q^{47} -2304.00 q^{48} +14541.5 q^{49} +11213.0 q^{50} -6808.27 q^{51} -18740.3 q^{52} -25356.1 q^{53} +2916.00 q^{54} +2315.24 q^{55} -11331.5 q^{56} +2048.51 q^{57} +1800.00 q^{58} -3481.00 q^{59} -2582.97 q^{60} -46047.3 q^{61} -18460.3 q^{62} +14341.5 q^{63} +4096.00 q^{64} -21009.4 q^{65} +4646.67 q^{66} +57443.2 q^{67} +12103.6 q^{68} +30284.6 q^{69} -12703.5 q^{70} -40949.1 q^{71} -5184.00 q^{72} +30257.8 q^{73} -59519.5 q^{74} +25229.3 q^{75} -3641.80 q^{76} +22853.3 q^{77} -42165.7 q^{78} +10832.9 q^{79} +4591.94 q^{80} +6561.00 q^{81} +24932.1 q^{82} +69109.5 q^{83} -25495.9 q^{84} +13569.1 q^{85} -5564.47 q^{86} +4050.00 q^{87} -8260.75 q^{88} -104198. q^{89} -5811.67 q^{90} -207379. q^{91} -53839.3 q^{92} -41535.7 q^{93} +8790.10 q^{94} -4082.75 q^{95} +9216.00 q^{96} -141345. q^{97} -58166.2 q^{98} +10455.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9} + 184 q^{10} - 653 q^{11} - 864 q^{12} + 647 q^{13} + 412 q^{14} + 414 q^{15} + 1536 q^{16} + 621 q^{17} - 1944 q^{18} - 454 q^{19} - 736 q^{20} + 927 q^{21} + 2612 q^{22} - 3412 q^{23} + 3456 q^{24} + 3866 q^{25} - 2588 q^{26} - 4374 q^{27} - 1648 q^{28} + 1526 q^{29} - 1656 q^{30} + 5976 q^{31} - 6144 q^{32} + 5877 q^{33} - 2484 q^{34} + 8098 q^{35} + 7776 q^{36} + 37033 q^{37} + 1816 q^{38} - 5823 q^{39} + 2944 q^{40} + 13983 q^{41} - 3708 q^{42} + 11521 q^{43} - 10448 q^{44} - 3726 q^{45} + 13648 q^{46} + 12434 q^{47} - 13824 q^{48} + 54237 q^{49} - 15464 q^{50} - 5589 q^{51} + 10352 q^{52} + 21310 q^{53} + 17496 q^{54} + 57468 q^{55} + 6592 q^{56} + 4086 q^{57} - 6104 q^{58} - 20886 q^{59} + 6624 q^{60} - 23030 q^{61} - 23904 q^{62} - 8343 q^{63} + 24576 q^{64} - 37368 q^{65} - 23508 q^{66} + 24342 q^{67} + 9936 q^{68} + 30708 q^{69} - 32392 q^{70} - 184375 q^{71} - 31104 q^{72} - 24512 q^{73} - 148132 q^{74} - 34794 q^{75} - 7264 q^{76} - 46529 q^{77} + 23292 q^{78} - 17987 q^{79} - 11776 q^{80} + 39366 q^{81} - 55932 q^{82} - 46687 q^{83} + 14832 q^{84} - 29706 q^{85} - 46084 q^{86} - 13734 q^{87} + 41792 q^{88} - 178946 q^{89} + 14904 q^{90} - 340179 q^{91} - 54592 q^{92} - 53784 q^{93} - 49736 q^{94} - 532190 q^{95} + 55296 q^{96} - 214638 q^{97} - 216948 q^{98} - 52893 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9 + 184 * q^10 - 653 * q^11 - 864 * q^12 + 647 * q^13 + 412 * q^14 + 414 * q^15 + 1536 * q^16 + 621 * q^17 - 1944 * q^18 - 454 * q^19 - 736 * q^20 + 927 * q^21 + 2612 * q^22 - 3412 * q^23 + 3456 * q^24 + 3866 * q^25 - 2588 * q^26 - 4374 * q^27 - 1648 * q^28 + 1526 * q^29 - 1656 * q^30 + 5976 * q^31 - 6144 * q^32 + 5877 * q^33 - 2484 * q^34 + 8098 * q^35 + 7776 * q^36 + 37033 * q^37 + 1816 * q^38 - 5823 * q^39 + 2944 * q^40 + 13983 * q^41 - 3708 * q^42 + 11521 * q^43 - 10448 * q^44 - 3726 * q^45 + 13648 * q^46 + 12434 * q^47 - 13824 * q^48 + 54237 * q^49 - 15464 * q^50 - 5589 * q^51 + 10352 * q^52 + 21310 * q^53 + 17496 * q^54 + 57468 * q^55 + 6592 * q^56 + 4086 * q^57 - 6104 * q^58 - 20886 * q^59 + 6624 * q^60 - 23030 * q^61 - 23904 * q^62 - 8343 * q^63 + 24576 * q^64 - 37368 * q^65 - 23508 * q^66 + 24342 * q^67 + 9936 * q^68 + 30708 * q^69 - 32392 * q^70 - 184375 * q^71 - 31104 * q^72 - 24512 * q^73 - 148132 * q^74 - 34794 * q^75 - 7264 * q^76 - 46529 * q^77 + 23292 * q^78 - 17987 * q^79 - 11776 * q^80 + 39366 * q^81 - 55932 * q^82 - 46687 * q^83 + 14832 * q^84 - 29706 * q^85 - 46084 * q^86 - 13734 * q^87 + 41792 * q^88 - 178946 * q^89 + 14904 * q^90 - 340179 * q^91 - 54592 * q^92 - 53784 * q^93 - 49736 * q^94 - 532190 * q^95 + 55296 * q^96 - 214638 * q^97 - 216948 * q^98 - 52893 * 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
$5$	17.9373	0.320871	0.160436	−	0.987046i	$-0.448710\pi$
$5$	17.9373	0.320871	0.160436	+	0.987046i	$0.448710\pi$
$6$	36.0000	0.408248
$7$	177.055	1.36573	0.682863	−	0.730546i	$-0.260735\pi$
$7$	177.055	1.36573	0.682863	+	0.730546i	$0.260735\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−71.7490	−0.226890
$11$	129.074	0.321631	0.160816	−	0.986984i	$-0.448588\pi$
$11$	129.074	0.321631	0.160816	+	0.986984i	$0.448588\pi$
$12$	−144.000	−0.288675
$13$	−1171.27	−1.92220	−0.961100	−	0.276202i	$-0.910924\pi$
$13$	−1171.27	−1.92220	−0.961100	+	0.276202i	$0.910924\pi$
$14$	−708.221	−0.965714
$15$	−161.435	−0.185255
$16$	256.000	0.250000
$17$	756.475	0.634852	0.317426	−	0.948283i	$-0.397182\pi$
$17$	756.475	0.634852	0.317426	+	0.948283i	$0.397182\pi$
$18$	−324.000	−0.235702
$19$	−227.613	−0.144648	−0.0723240	−	0.997381i	$-0.523042\pi$
$19$	−227.613	−0.144648	−0.0723240	+	0.997381i	$0.523042\pi$
$20$	286.996	0.160436
$21$	−1593.50	−0.788502
$22$	−516.297	−0.227428
$23$	−3364.96	−1.32635	−0.663177	−	0.748462i	$-0.730793\pi$
$23$	−3364.96	−1.32635	−0.663177	+	0.748462i	$0.730793\pi$
$24$	576.000	0.204124
$25$	−2803.25	−0.897042
$26$	4685.08	1.35920
$27$	−729.000	−0.192450
$28$	2832.88	0.682863
$29$	−450.000	−0.0993613	−0.0496806	−	0.998765i	$-0.515820\pi$
$29$	−450.000	−0.0993613	−0.0496806	+	0.998765i	$0.515820\pi$
$30$	645.741	0.130995
$31$	4615.07	0.862530	0.431265	−	0.902225i	$-0.358067\pi$
$31$	4615.07	0.862530	0.431265	+	0.902225i	$0.358067\pi$
$32$	−1024.00	−0.176777
$33$	−1161.67	−0.185694
$34$	−3025.90	−0.448908
$35$	3175.89	0.438222
$36$	1296.00	0.166667
$37$	14879.9	1.78688	0.893440	−	0.449183i	$-0.148285\pi$
$37$	14879.9	1.78688	0.893440	+	0.449183i	$0.148285\pi$
$38$	910.451	0.102282
$39$	10541.4	1.10978
$40$	−1147.98	−0.113445
$41$	−6233.02	−0.579081	−0.289540	−	0.957166i	$-0.593502\pi$
$41$	−6233.02	−0.579081	−0.289540	+	0.957166i	$0.593502\pi$
$42$	6373.99	0.557555
$43$	1391.12	0.114734	0.0573671	−	0.998353i	$-0.481729\pi$
$43$	1391.12	0.114734	0.0573671	+	0.998353i	$0.481729\pi$
$44$	2065.19	0.160816
$45$	1452.92	0.106957
$46$	13459.8	0.937875
$47$	−2197.52	−0.145107	−0.0725536	−	0.997365i	$-0.523115\pi$
$47$	−2197.52	−0.145107	−0.0725536	+	0.997365i	$0.523115\pi$
$48$	−2304.00	−0.144338
$49$	14541.5	0.865208
$50$	11213.0	0.634304
$51$	−6808.27	−0.366532
$52$	−18740.3	−0.961100
$53$	−25356.1	−1.23992	−0.619960	−	0.784634i	$-0.712851\pi$
$53$	−25356.1	−1.23992	−0.619960	+	0.784634i	$0.712851\pi$
$54$	2916.00	0.136083
$55$	2315.24	0.103202
$56$	−11331.5	−0.482857
$57$	2048.51	0.0835126
$58$	1800.00	0.0702590
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−2582.97	−0.0926276
$61$	−46047.3	−1.58445	−0.792226	−	0.610227i	$-0.791078\pi$
$61$	−46047.3	−1.58445	−0.792226	+	0.610227i	$0.791078\pi$
$62$	−18460.3	−0.609901
$63$	14341.5	0.455242
$64$	4096.00	0.125000
$65$	−21009.4	−0.616779
$66$	4646.67	0.131305
$67$	57443.2	1.56333	0.781667	−	0.623696i	$-0.214370\pi$
$67$	57443.2	1.56333	0.781667	+	0.623696i	$0.214370\pi$
$68$	12103.6	0.317426
$69$	30284.6	0.765771
$70$	−12703.5	−0.309870
$71$	−40949.1	−0.964048	−0.482024	−	0.876158i	$-0.660098\pi$
$71$	−40949.1	−0.964048	−0.482024	+	0.876158i	$0.660098\pi$
$72$	−5184.00	−0.117851
$73$	30257.8	0.664553	0.332277	−	0.943182i	$-0.392183\pi$
$73$	30257.8	0.664553	0.332277	+	0.943182i	$0.392183\pi$
$74$	−59519.5	−1.26351
$75$	25229.3	0.517907
$76$	−3641.80	−0.0723240
$77$	22853.3	0.439260
$78$	−42165.7	−0.784734
$79$	10832.9	0.195288	0.0976441	−	0.995221i	$-0.468869\pi$
$79$	10832.9	0.195288	0.0976441	+	0.995221i	$0.468869\pi$
$80$	4591.94	0.0802179
$81$	6561.00	0.111111
$82$	24932.1	0.409472
$83$	69109.5	1.10114	0.550570	−	0.834789i	$-0.314410\pi$
$83$	69109.5	1.10114	0.550570	+	0.834789i	$0.314410\pi$
$84$	−25495.9	−0.394251
$85$	13569.1	0.203706
$86$	−5564.47	−0.0811293
$87$	4050.00	0.0573663
$88$	−8260.75	−0.113714
$89$	−104198.	−1.39440	−0.697198	−	0.716879i	$-0.745570\pi$
$89$	−104198.	−1.39440	−0.697198	+	0.716879i	$0.745570\pi$
$90$	−5811.67	−0.0756301
$91$	−207379.	−2.62520
$92$	−53839.3	−0.663177
$93$	−41535.7	−0.497982
$94$	8790.10	0.102606
$95$	−4082.75	−0.0464134
$96$	9216.00	0.102062
$97$	−141345.	−1.52528	−0.762641	−	0.646822i	$-0.776098\pi$
$97$	−141345.	−1.52528	−0.762641	+	0.646822i	$0.776098\pi$
$98$	−58166.2	−0.611794
$99$	10455.0	0.107210
$100$	−44852.1	−0.448521
$101$	−152774.	−1.49020	−0.745101	−	0.666951i	$-0.767599\pi$
$101$	−152774.	−1.49020	−0.745101	+	0.666951i	$0.767599\pi$
$102$	27233.1	0.259177
$103$	1917.32	0.0178074	0.00890372	−	0.999960i	$-0.497166\pi$
$103$	1917.32	0.0178074	0.00890372	+	0.999960i	$0.497166\pi$
$104$	74961.2	0.679600
$105$	−28583.0	−0.253008
$106$	101425.	0.876756
$107$	−51979.6	−0.438908	−0.219454	−	0.975623i	$-0.570428\pi$
$107$	−51979.6	−0.438908	−0.219454	+	0.975623i	$0.570428\pi$
$108$	−11664.0	−0.0962250
$109$	38295.1	0.308729	0.154364	−	0.988014i	$-0.450667\pi$
$109$	38295.1	0.308729	0.154364	+	0.988014i	$0.450667\pi$
$110$	−9260.96	−0.0729750
$111$	−133919.	−1.03166
$112$	45326.1	0.341432
$113$	81004.0	0.596775	0.298387	−	0.954445i	$-0.403551\pi$
$113$	81004.0	0.596775	0.298387	+	0.954445i	$0.403551\pi$
$114$	−8194.06	−0.0590523
$115$	−60358.1	−0.425589
$116$	−7199.99	−0.0496806
$117$	−94872.8	−0.640733
$118$	13924.0	0.0920575
$119$	133938.	0.867033
$120$	10331.9	0.0654976
$121$	−144391.	−0.896553
$122$	184189.	1.12038
$123$	56097.2	0.334332
$124$	73841.2	0.431265
$125$	−106337.	−0.608706
$126$	−57365.9	−0.321905
$127$	−143563.	−0.789828	−0.394914	−	0.918718i	$-0.629226\pi$
$127$	−143563.	−0.789828	−0.394914	+	0.918718i	$0.629226\pi$
$128$	−16384.0	−0.0883883
$129$	−12520.1	−0.0662418
$130$	84037.4	0.436128
$131$	24923.2	0.126889	0.0634447	−	0.997985i	$-0.479791\pi$
$131$	24923.2	0.126889	0.0634447	+	0.997985i	$0.479791\pi$
$132$	−18586.7	−0.0928469
$133$	−40300.0	−0.197550
$134$	−229773.	−1.10544
$135$	−13076.3	−0.0617517
$136$	−48414.4	−0.224454
$137$	−305691.	−1.39150	−0.695748	−	0.718286i	$-0.744927\pi$
$137$	−305691.	−1.39150	−0.695748	+	0.718286i	$0.744927\pi$
$138$	−121138.	−0.541482
$139$	−79638.6	−0.349612	−0.174806	−	0.984603i	$-0.555930\pi$
$139$	−79638.6	−0.349612	−0.174806	+	0.984603i	$0.555930\pi$
$140$	50814.2	0.219111
$141$	19777.7	0.0837777
$142$	163796.	0.681685
$143$	−151181.	−0.618239
$144$	20736.0	0.0833333
$145$	−8071.76	−0.0318822
$146$	−121031.	−0.469910
$147$	−130874.	−0.499528
$148$	238078.	0.893440
$149$	−36015.6	−0.132900	−0.0664500	−	0.997790i	$-0.521167\pi$
$149$	−36015.6	−0.132900	−0.0664500	+	0.997790i	$0.521167\pi$
$150$	−100917.	−0.366216
$151$	−115452.	−0.412060	−0.206030	−	0.978546i	$-0.566054\pi$
$151$	−115452.	−0.412060	−0.206030	+	0.978546i	$0.566054\pi$
$152$	14567.2	0.0511408
$153$	61274.5	0.211617
$154$	−91413.1	−0.310604
$155$	82781.8	0.276761
$156$	168663.	0.554891
$157$	241308.	0.781310	0.390655	−	0.920537i	$-0.372249\pi$
$157$	241308.	0.781310	0.390655	+	0.920537i	$0.372249\pi$
$158$	−43331.5	−0.138090
$159$	228205.	0.715868
$160$	−18367.8	−0.0567226
$161$	−595783.	−1.81144
$162$	−26244.0	−0.0785674
$163$	−466745.	−1.37598	−0.687988	−	0.725722i	$-0.741506\pi$
$163$	−466745.	−1.37598	−0.687988	+	0.725722i	$0.741506\pi$
$164$	−99728.4	−0.289540
$165$	−20837.1	−0.0595838
$166$	−276438.	−0.778623
$167$	−510227.	−1.41570	−0.707852	−	0.706361i	$-0.750335\pi$
$167$	−510227.	−1.41570	−0.707852	+	0.706361i	$0.750335\pi$
$168$	101984.	0.278778
$169$	1.00058e6	2.69485
$170$	−54276.3	−0.144042
$171$	−18436.6	−0.0482160
$172$	22257.9	0.0573671
$173$	−469483.	−1.19263	−0.596313	−	0.802752i	$-0.703368\pi$
$173$	−469483.	−1.19263	−0.596313	+	0.802752i	$0.703368\pi$
$174$	−16200.0	−0.0405641
$175$	−496331.	−1.22511
$176$	33043.0	0.0804078
$177$	31329.0	0.0751646
$178$	416794.	0.985987
$179$	51292.9	0.119653	0.0598266	−	0.998209i	$-0.480945\pi$
$179$	51292.9	0.119653	0.0598266	+	0.998209i	$0.480945\pi$
$180$	23246.7	0.0534786
$181$	612199.	1.38898	0.694491	−	0.719502i	$-0.255630\pi$
$181$	612199.	1.38898	0.694491	+	0.719502i	$0.255630\pi$
$182$	829517.	1.85629
$183$	414425.	0.914784
$184$	215357.	0.468937
$185$	266904.	0.573359
$186$	166143.	0.352127
$187$	97641.5	0.204188
$188$	−35160.4	−0.0725536
$189$	−129073.	−0.262834
$190$	16331.0	0.0328192
$191$	−676635.	−1.34206	−0.671029	−	0.741431i	$-0.734147\pi$
$191$	−676635.	−1.34206	−0.671029	+	0.741431i	$0.734147\pi$
$192$	−36864.0	−0.0721688
$193$	659804.	1.27503	0.637517	−	0.770436i	$-0.279961\pi$
$193$	659804.	1.27503	0.637517	+	0.770436i	$0.279961\pi$
$194$	565379.	1.07854
$195$	189084.	0.356097
$196$	232665.	0.432604
$197$	−87290.0	−0.160250	−0.0801252	−	0.996785i	$-0.525532\pi$
$197$	−87290.0	−0.160250	−0.0801252	+	0.996785i	$0.525532\pi$
$198$	−41820.1	−0.0758092
$199$	−73397.9	−0.131387	−0.0656933	−	0.997840i	$-0.520926\pi$
$199$	−73397.9	−0.131387	−0.0656933	+	0.997840i	$0.520926\pi$
$200$	179408.	0.317152
$201$	−516989.	−0.902592
$202$	611095.	1.05373
$203$	−79674.8	−0.135700
$204$	−108932.	−0.183266
$205$	−111803.	−0.185811
$206$	−7669.28	−0.0125918
$207$	−272561.	−0.442118
$208$	−299845.	−0.480550
$209$	−29378.9	−0.0465233
$210$	114332.	0.178904
$211$	792977.	1.22618	0.613090	−	0.790013i	$-0.289926\pi$
$211$	792977.	1.22618	0.613090	+	0.790013i	$0.289926\pi$
$212$	−405698.	−0.619960
$213$	368542.	0.556593
$214$	207919.	0.310355
$215$	24952.8	0.0368149
$216$	46656.0	0.0680414
$217$	817123.	1.17798
$218$	−153180.	−0.218304
$219$	−272320.	−0.383680
$220$	37043.8	0.0516011
$221$	−886036.	−1.22031
$222$	535676.	0.729490
$223$	−283956.	−0.382375	−0.191187	−	0.981554i	$-0.561234\pi$
$223$	−283956.	−0.382375	−0.191187	+	0.981554i	$0.561234\pi$
$224$	−181305.	−0.241429
$225$	−227064.	−0.299014
$226$	−324016.	−0.421984
$227$	892072.	1.14904	0.574520	−	0.818490i	$-0.305189\pi$
$227$	892072.	1.14904	0.574520	+	0.818490i	$0.305189\pi$
$228$	32776.2	0.0417563
$229$	−48604.0	−0.0612467	−0.0306234	−	0.999531i	$-0.509749\pi$
$229$	−48604.0	−0.0612467	−0.0306234	+	0.999531i	$0.509749\pi$
$230$	241432.	0.300937
$231$	−205679.	−0.253607
$232$	28800.0	0.0351295
$233$	114970.	0.138738	0.0693689	−	0.997591i	$-0.477901\pi$
$233$	114970.	0.138738	0.0693689	+	0.997591i	$0.477901\pi$
$234$	379491.	0.453067
$235$	−39417.6	−0.0465608
$236$	−55696.0	−0.0650945
$237$	−97495.9	−0.112750
$238$	−535751.	−0.613085
$239$	−1.47234e6	−1.66729	−0.833647	−	0.552298i	$-0.813751\pi$
$239$	−1.47234e6	−1.66729	−0.833647	+	0.552298i	$0.813751\pi$
$240$	−41327.4	−0.0463138
$241$	416424.	0.461842	0.230921	−	0.972973i	$-0.425826\pi$
$241$	416424.	0.461842	0.230921	+	0.972973i	$0.425826\pi$
$242$	577563.	0.633959
$243$	−59049.0	−0.0641500
$244$	−736756.	−0.792226
$245$	260835.	0.277620
$246$	−224389.	−0.236409
$247$	266596.	0.278042
$248$	−295365.	−0.304951
$249$	−621985.	−0.635743
$250$	425347.	0.430420
$251$	−269053.	−0.269559	−0.134779	−	0.990876i	$-0.543033\pi$
$251$	−269053.	−0.269559	−0.134779	+	0.990876i	$0.543033\pi$
$252$	229464.	0.227621
$253$	−434329.	−0.426597
$254$	574251.	0.558493
$255$	−122122.	−0.117610
$256$	65536.0	0.0625000
$257$	1.10658e6	1.04508	0.522542	−	0.852613i	$-0.324984\pi$
$257$	1.10658e6	1.04508	0.522542	+	0.852613i	$0.324984\pi$
$258$	50080.2	0.0468400
$259$	2.63456e6	2.44039
$260$	−336150.	−0.308389
$261$	−36450.0	−0.0331204
$262$	−99692.8	−0.0897244
$263$	−1.13388e6	−1.01083	−0.505416	−	0.862876i	$-0.668661\pi$
$263$	−1.13388e6	−1.01083	−0.505416	+	0.862876i	$0.668661\pi$
$264$	74346.8	0.0656527
$265$	−454820.	−0.397855
$266$	161200.	0.139689
$267$	937786.	0.805055
$268$	919092.	0.781667
$269$	1.86128e6	1.56831	0.784155	−	0.620566i	$-0.213097\pi$
$269$	1.86128e6	1.56831	0.784155	+	0.620566i	$0.213097\pi$
$270$	52305.0	0.0436651
$271$	−2.26306e6	−1.87186	−0.935928	−	0.352191i	$-0.885437\pi$
$271$	−2.26306e6	−1.87186	−0.935928	+	0.352191i	$0.885437\pi$
$272$	193658.	0.158713
$273$	1.86641e6	1.51566
$274$	1.22277e6	0.983936
$275$	−361828.	−0.288516
$276$	484554.	0.382886
$277$	347075.	0.271784	0.135892	−	0.990724i	$-0.456610\pi$
$277$	347075.	0.271784	0.135892	+	0.990724i	$0.456610\pi$
$278$	318554.	0.247213
$279$	373821.	0.287510
$280$	−203257.	−0.154935
$281$	−216216.	−0.163351	−0.0816754	−	0.996659i	$-0.526027\pi$
$281$	−216216.	−0.163351	−0.0816754	+	0.996659i	$0.526027\pi$
$282$	−79110.9	−0.0592398
$283$	−329179.	−0.244324	−0.122162	−	0.992510i	$-0.538983\pi$
$283$	−329179.	−0.244324	−0.122162	+	0.992510i	$0.538983\pi$
$284$	−655186.	−0.482024
$285$	36744.7	0.0267968
$286$	604723.	0.437161
$287$	−1.10359e6	−0.790866
$288$	−82944.0	−0.0589256
$289$	−847603.	−0.596963
$290$	32287.0	0.0225441
$291$	1.27210e6	0.880622
$292$	484124.	0.332277
$293$	1.93740e6	1.31841	0.659205	−	0.751963i	$-0.270893\pi$
$293$	1.93740e6	1.31841	0.659205	+	0.751963i	$0.270893\pi$
$294$	523496.	0.353220
$295$	−62439.6	−0.0417739
$296$	−952313.	−0.631757
$297$	−94095.1	−0.0618979
$298$	144062.	0.0939745
$299$	3.94127e6	2.54952
$300$	403669.	0.258954
$301$	246305.	0.156695
$302$	461810.	0.291371
$303$	1.37496e6	0.860369
$304$	−58268.9	−0.0361620
$305$	−825962.	−0.508406
$306$	−245098.	−0.149636
$307$	−2.12186e6	−1.28490	−0.642452	−	0.766326i	$-0.722083\pi$
$307$	−2.12186e6	−1.28490	−0.642452	+	0.766326i	$0.722083\pi$
$308$	365652.	0.219630
$309$	−17255.9	−0.0102811
$310$	−331127.	−0.195700
$311$	−1.86690e6	−1.09451	−0.547254	−	0.836967i	$-0.684327\pi$
$311$	−1.86690e6	−1.09451	−0.547254	+	0.836967i	$0.684327\pi$
$312$	−674651.	−0.392367
$313$	−1.91650e6	−1.10573	−0.552863	−	0.833272i	$-0.686465\pi$
$313$	−1.91650e6	−1.10573	−0.552863	+	0.833272i	$0.686465\pi$
$314$	−965234.	−0.552470
$315$	257247.	0.146074
$316$	173326.	0.0976441
$317$	−3.26042e6	−1.82232	−0.911162	−	0.412048i	$-0.864814\pi$
$317$	−3.26042e6	−1.82232	−0.911162	+	0.412048i	$0.864814\pi$
$318$	−912821.	−0.506195
$319$	−58083.4	−0.0319577
$320$	73471.0	0.0401089
$321$	467817.	0.253404
$322$	2.38313e6	1.28088
$323$	−172183.	−0.0918300
$324$	104976.	0.0555556
$325$	3.28337e6	1.72429
$326$	1.86698e6	0.972961
$327$	−344656.	−0.178245
$328$	398914.	0.204736
$329$	−389083.	−0.198177
$330$	83348.6	0.0421321
$331$	−482525.	−0.242075	−0.121037	−	0.992648i	$-0.538622\pi$
$331$	−482525.	−0.242075	−0.121037	+	0.992648i	$0.538622\pi$
$332$	1.10575e6	0.550570
$333$	1.20527e6	0.595626
$334$	2.04091e6	1.00105
$335$	1.03037e6	0.501629
$336$	−407935.	−0.197126
$337$	301253.	0.144496	0.0722482	−	0.997387i	$-0.476983\pi$
$337$	301253.	0.144496	0.0722482	+	0.997387i	$0.476983\pi$
$338$	−4.00231e6	−1.90555
$339$	−729036.	−0.344548
$340$	217105.	0.101853
$341$	595687.	0.277417
$342$	73746.5	0.0340939
$343$	−401111.	−0.184089
$344$	−89031.5	−0.0405646
$345$	543223.	0.245714
$346$	1.87793e6	0.843314
$347$	51889.7	0.0231343	0.0115672	−	0.999933i	$-0.496318\pi$
$347$	51889.7	0.0231343	0.0115672	+	0.999933i	$0.496318\pi$
$348$	64799.9	0.0286831
$349$	3.68029e6	1.61740	0.808702	−	0.588218i	$-0.200170\pi$
$349$	3.68029e6	1.61740	0.808702	+	0.588218i	$0.200170\pi$
$350$	1.98532e6	0.866286
$351$	853855.	0.369927
$352$	−132172.	−0.0568569
$353$	−2.00577e6	−0.856732	−0.428366	−	0.903605i	$-0.640911\pi$
$353$	−2.00577e6	−0.856732	−0.428366	+	0.903605i	$0.640911\pi$
$354$	−125316.	−0.0531494
$355$	−734515.	−0.309336
$356$	−1.66717e6	−0.697198
$357$	−1.20544e6	−0.500582
$358$	−205171.	−0.0846076
$359$	−97002.9	−0.0397236	−0.0198618	−	0.999803i	$-0.506323\pi$
$359$	−97002.9	−0.0397236	−0.0198618	+	0.999803i	$0.506323\pi$
$360$	−92986.7	−0.0378151
$361$	−2.42429e6	−0.979077
$362$	−2.44880e6	−0.982158
$363$	1.29952e6	0.517625
$364$	−3.31807e6	−1.31260
$365$	542742.	0.213236
$366$	−1.65770e6	−0.646850
$367$	709483.	0.274965	0.137482	−	0.990504i	$-0.456099\pi$
$367$	709483.	0.274965	0.137482	+	0.990504i	$0.456099\pi$
$368$	−861429.	−0.331589
$369$	−504875.	−0.193027
$370$	−1.06762e6	−0.405426
$371$	−4.48944e6	−1.69339
$372$	−664571.	−0.248991
$373$	4.77061e6	1.77542	0.887712	−	0.460399i	$-0.152294\pi$
$373$	4.77061e6	1.77542	0.887712	+	0.460399i	$0.152294\pi$
$374$	−390566.	−0.144383
$375$	957030.	0.351437
$376$	140642.	0.0513031
$377$	527071.	0.190992
$378$	516293.	0.185852
$379$	−2.21714e6	−0.792856	−0.396428	−	0.918066i	$-0.629750\pi$
$379$	−2.21714e6	−0.792856	−0.396428	+	0.918066i	$0.629750\pi$
$380$	−65324.0	−0.0232067
$381$	1.29207e6	0.456008
$382$	2.70654e6	0.948978
$383$	−1.42655e6	−0.496924	−0.248462	−	0.968642i	$-0.579925\pi$
$383$	−1.42655e6	−0.496924	−0.248462	+	0.968642i	$0.579925\pi$
$384$	147456.	0.0510310
$385$	409925.	0.140946
$386$	−2.63922e6	−0.901586
$387$	112680.	0.0382447
$388$	−2.26151e6	−0.762641
$389$	−964763.	−0.323256	−0.161628	−	0.986852i	$-0.551674\pi$
$389$	−964763.	−0.323256	−0.161628	+	0.986852i	$0.551674\pi$
$390$	−756337.	−0.251799
$391$	−2.54550e6	−0.842039
$392$	−930659.	−0.305897
$393$	−224309.	−0.0732597
$394$	349160.	0.113314
$395$	194312.	0.0626624
$396$	167280.	0.0536052
$397$	−1.06320e6	−0.338563	−0.169282	−	0.985568i	$-0.554145\pi$
$397$	−1.06320e6	−0.338563	−0.169282	+	0.985568i	$0.554145\pi$
$398$	293592.	0.0929043
$399$	362700.	0.114055
$400$	−717633.	−0.224260
$401$	1.80506e6	0.560571	0.280286	−	0.959917i	$-0.409571\pi$
$401$	1.80506e6	0.560571	0.280286	+	0.959917i	$0.409571\pi$
$402$	2.06796e6	0.638229
$403$	−5.40549e6	−1.65796
$404$	−2.44438e6	−0.745101
$405$	117686.	0.0356524
$406$	318699.	0.0959546
$407$	1.92061e6	0.574716
$408$	435730.	0.129589
$409$	7056.72	0.00208590	0.00104295	−	0.999999i	$-0.499668\pi$
$409$	7056.72	0.00208590	0.00104295	+	0.999999i	$0.499668\pi$
$410$	447214.	0.131388
$411$	2.75122e6	0.803380
$412$	30677.1	0.00890372
$413$	−616329.	−0.177802
$414$	1.09025e6	0.312625
$415$	1.23963e6	0.353324
$416$	1.19938e6	0.339800
$417$	716747.	0.201849
$418$	117516.	0.0328969
$419$	−7.14594e6	−1.98850	−0.994248	−	0.107106i	$-0.965842\pi$
$419$	−7.14594e6	−1.98850	−0.994248	+	0.107106i	$0.965842\pi$
$420$	−457327.	−0.126504
$421$	−2.22390e6	−0.611520	−0.305760	−	0.952109i	$-0.598911\pi$
$421$	−2.22390e6	−0.611520	−0.305760	+	0.952109i	$0.598911\pi$
$422$	−3.17191e6	−0.867041
$423$	−177999.	−0.0483691
$424$	1.62279e6	0.438378
$425$	−2.12059e6	−0.569488
$426$	−1.47417e6	−0.393571
$427$	−8.15291e6	−2.16393
$428$	−831674.	−0.219454
$429$	1.36063e6	0.356940
$430$	−99811.3	−0.0260321
$431$	3.77074e6	0.977762	0.488881	−	0.872350i	$-0.337405\pi$
$431$	3.77074e6	0.977762	0.488881	+	0.872350i	$0.337405\pi$
$432$	−186624.	−0.0481125
$433$	−1.45537e6	−0.373039	−0.186519	−	0.982451i	$-0.559721\pi$
$433$	−1.45537e6	−0.373039	−0.186519	+	0.982451i	$0.559721\pi$
$434$	−3.26849e6	−0.832958
$435$	72645.8	0.0184072
$436$	612722.	0.154364
$437$	765907.	0.191855
$438$	1.08928e6	0.271303
$439$	−4.42056e6	−1.09475	−0.547376	−	0.836887i	$-0.684373\pi$
$439$	−4.42056e6	−1.09475	−0.547376	+	0.836887i	$0.684373\pi$
$440$	−148175.	−0.0364875
$441$	1.17787e6	0.288403
$442$	3.54414e6	0.862890
$443$	3.26090e6	0.789457	0.394729	−	0.918798i	$-0.370839\pi$
$443$	3.26090e6	0.789457	0.394729	+	0.918798i	$0.370839\pi$
$444$	−2.14270e6	−0.515828
$445$	−1.86903e6	−0.447422
$446$	1.13583e6	0.270380
$447$	324140.	0.0767298
$448$	725218.	0.170716
$449$	3.60837e6	0.844685	0.422343	−	0.906436i	$-0.361208\pi$
$449$	3.60837e6	0.844685	0.422343	+	0.906436i	$0.361208\pi$
$450$	908255.	0.211435
$451$	−804523.	−0.186250
$452$	1.29606e6	0.298387
$453$	1.03907e6	0.237903
$454$	−3.56829e6	−0.812494
$455$	−3.71982e6	−0.842351
$456$	−131105.	−0.0295262
$457$	5.22448e6	1.17018	0.585090	−	0.810968i	$-0.301059\pi$
$457$	5.22448e6	1.17018	0.585090	+	0.810968i	$0.301059\pi$
$458$	194416.	0.0433080
$459$	−551470.	−0.122177
$460$	−965729.	−0.212795
$461$	−4.26501e6	−0.934691	−0.467346	−	0.884075i	$-0.654790\pi$
$461$	−4.26501e6	−0.934691	−0.467346	+	0.884075i	$0.654790\pi$
$462$	822718.	0.179327
$463$	3.88520e6	0.842288	0.421144	−	0.906994i	$-0.361629\pi$
$463$	3.88520e6	0.842288	0.421144	+	0.906994i	$0.361629\pi$
$464$	−115200.	−0.0248403
$465$	−745036.	−0.159788
$466$	−459880.	−0.0981024
$467$	2.26688e6	0.480991	0.240495	−	0.970650i	$-0.422690\pi$
$467$	2.26688e6	0.480991	0.240495	+	0.970650i	$0.422690\pi$
$468$	−1.51796e6	−0.320367
$469$	1.01706e7	2.13509
$470$	157670.	0.0329234
$471$	−2.17178e6	−0.451089
$472$	222784.	0.0460287
$473$	179557.	0.0369021
$474$	389983.	0.0797261
$475$	638056.	0.129755
$476$	2.14301e6	0.433517
$477$	−2.05385e6	−0.413307
$478$	5.88934e6	1.17895
$479$	−9.60722e6	−1.91319	−0.956597	−	0.291414i	$-0.905874\pi$
$479$	−9.60722e6	−1.91319	−0.956597	+	0.291414i	$0.905874\pi$
$480$	165310.	0.0327488
$481$	−1.74283e7	−3.43474
$482$	−1.66570e6	−0.326571
$483$	5.36205e6	1.04583
$484$	−2.31025e6	−0.448277
$485$	−2.53534e6	−0.489419
$486$	236196.	0.0453609
$487$	9.02101e6	1.72358	0.861792	−	0.507262i	$-0.169342\pi$
$487$	9.02101e6	1.72358	0.861792	+	0.507262i	$0.169342\pi$
$488$	2.94703e6	0.560189
$489$	4.20070e6	0.794420
$490$	−1.04334e6	−0.196307
$491$	4.09612e6	0.766777	0.383388	−	0.923587i	$-0.374757\pi$
$491$	4.09612e6	0.766777	0.383388	+	0.923587i	$0.374757\pi$
$492$	897556.	0.167166
$493$	−340413.	−0.0630797
$494$	−1.06638e6	−0.196606
$495$	187534.	0.0344007
$496$	1.18146e6	0.215633
$497$	−7.25026e6	−1.31663
$498$	2.48794e6	0.449538
$499$	1.07181e6	0.192694	0.0963470	−	0.995348i	$-0.469284\pi$
$499$	1.07181e6	0.192694	0.0963470	+	0.995348i	$0.469284\pi$
$500$	−1.70139e6	−0.304353
$501$	4.59204e6	0.817357
$502$	1.07621e6	0.190607
$503$	−3.28877e6	−0.579580	−0.289790	−	0.957090i	$-0.593585\pi$
$503$	−3.28877e6	−0.579580	−0.289790	+	0.957090i	$0.593585\pi$
$504$	−917854.	−0.160952
$505$	−2.74034e6	−0.478164
$506$	1.73732e6	0.301650
$507$	−9.00521e6	−1.55587
$508$	−2.29701e6	−0.394914
$509$	−651077.	−0.111388	−0.0556939	−	0.998448i	$-0.517737\pi$
$509$	−651077.	−0.111388	−0.0556939	+	0.998448i	$0.517737\pi$
$510$	488487.	0.0831625
$511$	5.35730e6	0.907598
$512$	−262144.	−0.0441942
$513$	165930.	0.0278375
$514$	−4.42633e6	−0.738986
$515$	34391.5	0.00571390
$516$	−200321.	−0.0331209
$517$	−283644.	−0.0466710
$518$	−1.05382e7	−1.72561
$519$	4.22535e6	0.688563
$520$	1.34460e6	0.218064
$521$	3.75752e6	0.606466	0.303233	−	0.952916i	$-0.401934\pi$
$521$	3.75752e6	0.606466	0.303233	+	0.952916i	$0.401934\pi$
$522$	145800.	0.0234197
$523$	−6.07184e6	−0.970658	−0.485329	−	0.874332i	$-0.661300\pi$
$523$	−6.07184e6	−0.970658	−0.485329	+	0.874332i	$0.661300\pi$
$524$	398771.	0.0634447
$525$	4.46698e6	0.707319
$526$	4.53553e6	0.714766
$527$	3.49119e6	0.547579
$528$	−297387.	−0.0464234
$529$	4.88658e6	0.759217
$530$	1.81928e6	0.281326
$531$	−281961.	−0.0433963
$532$	−644800.	−0.0987748
$533$	7.30055e6	1.11311
$534$	−3.75114e6	−0.569260
$535$	−932372.	−0.140833
$536$	−3.67637e6	−0.552722
$537$	−461636.	−0.0690818
$538$	−7.44513e6	−1.10896
$539$	1.87694e6	0.278278
$540$	−209220.	−0.0308759
$541$	−6.37512e6	−0.936472	−0.468236	−	0.883603i	$-0.655110\pi$
$541$	−6.37512e6	−0.936472	−0.468236	+	0.883603i	$0.655110\pi$
$542$	9.05223e6	1.32360
$543$	−5.50979e6	−0.801929
$544$	−774630.	−0.112227
$545$	686909.	0.0990622
$546$	−7.46566e6	−1.07173
$547$	−3.35311e6	−0.479158	−0.239579	−	0.970877i	$-0.577009\pi$
$547$	−3.35311e6	−0.479158	−0.239579	+	0.970877i	$0.577009\pi$
$548$	−4.89106e6	−0.695748
$549$	−3.72983e6	−0.528151
$550$	1.44731e6	0.204012
$551$	102426.	0.0143724
$552$	−1.93821e6	−0.270741
$553$	1.91802e6	0.266710
$554$	−1.38830e6	−0.192180
$555$	−2.40214e6	−0.331029
$556$	−1.27422e6	−0.174806
$557$	1.41555e7	1.93324	0.966621	−	0.256211i	$-0.0824742\pi$
$557$	1.41555e7	1.93324	0.966621	+	0.256211i	$0.0824742\pi$
$558$	−1.49528e6	−0.203300
$559$	−1.62937e6	−0.220542
$560$	813027.	0.109556
$561$	−878773.	−0.117888
$562$	864863.	0.115506
$563$	1.32605e7	1.76315	0.881575	−	0.472045i	$-0.156484\pi$
$563$	1.32605e7	1.76315	0.881575	+	0.472045i	$0.156484\pi$
$564$	316443.	0.0418888
$565$	1.45299e6	0.191488
$566$	1.31672e6	0.172763
$567$	1.16166e6	0.151747
$568$	2.62074e6	0.340843
$569$	−487891.	−0.0631745	−0.0315872	−	0.999501i	$-0.510056\pi$
$569$	−487891.	−0.0631745	−0.0315872	+	0.999501i	$0.510056\pi$
$570$	−146979.	−0.0189482
$571$	−6.58708e6	−0.845479	−0.422739	−	0.906251i	$-0.638931\pi$
$571$	−6.58708e6	−0.845479	−0.422739	+	0.906251i	$0.638931\pi$
$572$	−2.41889e6	−0.309119
$573$	6.08972e6	0.774837
$574$	4.41436e6	0.559227
$575$	9.43283e6	1.18980
$576$	331776.	0.0416667
$577$	−586957.	−0.0733951	−0.0366975	−	0.999326i	$-0.511684\pi$
$577$	−586957.	−0.0733951	−0.0366975	+	0.999326i	$0.511684\pi$
$578$	3.39041e6	0.422117
$579$	−5.93824e6	−0.736142
$580$	−129148.	−0.0159411
$581$	1.22362e7	1.50386
$582$	−5.08841e6	−0.622694
$583$	−3.27283e6	−0.398797
$584$	−1.93650e6	−0.234955
$585$	−1.70176e6	−0.205593
$586$	−7.74960e6	−0.932256
$587$	1.27863e7	1.53162	0.765808	−	0.643069i	$-0.222339\pi$
$587$	1.27863e7	1.53162	0.765808	+	0.643069i	$0.222339\pi$
$588$	−2.09398e6	−0.249764
$589$	−1.05045e6	−0.124763
$590$	249758.	0.0295386
$591$	785610.	0.0925206
$592$	3.80925e6	0.446720
$593$	−1.59425e7	−1.86175	−0.930873	−	0.365342i	$-0.880952\pi$
$593$	−1.59425e7	−1.86175	−0.930873	+	0.365342i	$0.880952\pi$
$594$	376381.	0.0437684
$595$	2.40248e6	0.278206
$596$	−576249.	−0.0664500
$597$	660581.	0.0758560
$598$	−1.57651e7	−1.80278
$599$	1.58353e7	1.80327	0.901633	−	0.432502i	$-0.142369\pi$
$599$	1.58353e7	1.80327	0.901633	+	0.432502i	$0.142369\pi$
$600$	−1.61467e6	−0.183108
$601$	1.39014e7	1.56991	0.784953	−	0.619555i	$-0.212687\pi$
$601$	1.39014e7	1.56991	0.784953	+	0.619555i	$0.212687\pi$
$602$	−985218.	−0.110800
$603$	4.65290e6	0.521112
$604$	−1.84724e6	−0.206030
$605$	−2.58998e6	−0.287678
$606$	−5.49986e6	−0.608373
$607$	1.30722e7	1.44005	0.720027	−	0.693947i	$-0.244130\pi$
$607$	1.30722e7	1.44005	0.720027	+	0.693947i	$0.244130\pi$
$608$	233075.	0.0255704
$609$	717073.	0.0783466
$610$	3.30385e6	0.359497
$611$	2.57389e6	0.278925
$612$	980392.	0.105809
$613$	673698.	0.0724126	0.0362063	−	0.999344i	$-0.488473\pi$
$613$	673698.	0.0724126	0.0362063	+	0.999344i	$0.488473\pi$
$614$	8.48744e6	0.908564
$615$	1.00623e6	0.107278
$616$	−1.46261e6	−0.155302
$617$	−1.47407e7	−1.55885	−0.779424	−	0.626497i	$-0.784488\pi$
$617$	−1.47407e7	−1.55885	−0.779424	+	0.626497i	$0.784488\pi$
$618$	69023.5	0.00726986
$619$	−831351.	−0.0872082	−0.0436041	−	0.999049i	$-0.513884\pi$
$619$	−831351.	−0.0872082	−0.0436041	+	0.999049i	$0.513884\pi$
$620$	1.32451e6	0.138381
$621$	2.45305e6	0.255257
$622$	7.46758e6	0.773934
$623$	−1.84489e7	−1.90436
$624$	2.69860e6	0.277446
$625$	6.85278e6	0.701725
$626$	7.66599e6	0.781866
$627$	264411.	0.0268602
$628$	3.86093e6	0.390655
$629$	1.12563e7	1.13440
$630$	−1.02899e6	−0.103290
$631$	8.64886e6	0.864739	0.432370	−	0.901696i	$-0.357678\pi$
$631$	8.64886e6	0.864739	0.432370	+	0.901696i	$0.357678\pi$
$632$	−693304.	−0.0690448
$633$	−7.13679e6	−0.707936
$634$	1.30417e7	1.28858
$635$	−2.57512e6	−0.253433
$636$	3.65129e6	0.357934
$637$	−1.70321e7	−1.66310
$638$	232334.	0.0225975
$639$	−3.31688e6	−0.321349
$640$	−293884.	−0.0283613
$641$	2.02662e6	0.194817	0.0974086	−	0.995244i	$-0.468945\pi$
$641$	2.02662e6	0.194817	0.0974086	+	0.995244i	$0.468945\pi$
$642$	−1.87127e6	−0.179184
$643$	1.79287e7	1.71010	0.855050	−	0.518546i	$-0.173527\pi$
$643$	1.79287e7	1.71010	0.855050	+	0.518546i	$0.173527\pi$
$644$	−9.53253e6	−0.905719
$645$	−224575.	−0.0212551
$646$	688733.	0.0649336
$647$	1.06475e7	0.999966	0.499983	−	0.866035i	$-0.333340\pi$
$647$	1.06475e7	0.999966	0.499983	+	0.866035i	$0.333340\pi$
$648$	−419904.	−0.0392837
$649$	−449308.	−0.0418728
$650$	−1.31335e7	−1.21926
$651$	−7.35411e6	−0.680107
$652$	−7.46792e6	−0.687988
$653$	1.96514e6	0.180348	0.0901740	−	0.995926i	$-0.471258\pi$
$653$	1.96514e6	0.180348	0.0901740	+	0.995926i	$0.471258\pi$
$654$	1.37862e6	0.126038
$655$	447054.	0.0407152
$656$	−1.59565e6	−0.144770
$657$	2.45088e6	0.221518
$658$	1.55633e6	0.140132
$659$	−9.99801e6	−0.896809	−0.448405	−	0.893831i	$-0.648008\pi$
$659$	−9.99801e6	−0.896809	−0.448405	+	0.893831i	$0.648008\pi$
$660$	−333394.	−0.0297919
$661$	−1.38512e7	−1.23306	−0.616529	−	0.787333i	$-0.711462\pi$
$661$	−1.38512e7	−1.23306	−0.616529	+	0.787333i	$0.711462\pi$
$662$	1.93010e6	0.171173
$663$	7.97432e6	0.704547
$664$	−4.42301e6	−0.389312
$665$	−722872.	−0.0633880
$666$	−4.82108e6	−0.421171
$667$	1.51423e6	0.131788
$668$	−8.16363e6	−0.707852
$669$	2.55561e6	0.220764
$670$	−4.12150e6	−0.354706
$671$	−5.94352e6	−0.509609
$672$	1.63174e6	0.139389
$673$	−2.79500e6	−0.237873	−0.118936	−	0.992902i	$-0.537948\pi$
$673$	−2.79500e6	−0.237873	−0.118936	+	0.992902i	$0.537948\pi$
$674$	−1.20501e6	−0.102174
$675$	2.04357e6	0.172636
$676$	1.60093e7	1.34742
$677$	−1.51444e6	−0.126993	−0.0634966	−	0.997982i	$-0.520225\pi$
$677$	−1.51444e6	−0.126993	−0.0634966	+	0.997982i	$0.520225\pi$
$678$	2.91614e6	0.243632
$679$	−2.50258e7	−2.08312
$680$	−868422.	−0.0720209
$681$	−8.02865e6	−0.663399
$682$	−2.38275e6	−0.196163
$683$	1.67217e6	0.137161	0.0685803	−	0.997646i	$-0.478153\pi$
$683$	1.67217e6	0.137161	0.0685803	+	0.997646i	$0.478153\pi$
$684$	−294986.	−0.0241080
$685$	−5.48327e6	−0.446491
$686$	1.60444e6	0.130171
$687$	437436.	0.0353608
$688$	356126.	0.0286835
$689$	2.96989e7	2.38337
$690$	−2.17289e6	−0.173746
$691$	−2.95289e6	−0.235262	−0.117631	−	0.993057i	$-0.537530\pi$
$691$	−2.95289e6	−0.235262	−0.117631	+	0.993057i	$0.537530\pi$
$692$	−7.51172e6	−0.596313
$693$	1.85112e6	0.146420
$694$	−207559.	−0.0163585
$695$	−1.42850e6	−0.112181
$696$	−259200.	−0.0202820
$697$	−4.71513e6	−0.367630
$698$	−1.47212e7	−1.14368
$699$	−1.03473e6	−0.0801003
$700$	−7.94129e6	−0.612556
$701$	1.17592e7	0.903823	0.451912	−	0.892063i	$-0.350742\pi$
$701$	1.17592e7	0.903823	0.451912	+	0.892063i	$0.350742\pi$
$702$	−3.41542e6	−0.261578
$703$	−3.38685e6	−0.258469
$704$	528688.	0.0402039
$705$	354758.	0.0268819
$706$	8.02309e6	0.605801
$707$	−2.70494e7	−2.03521
$708$	501264.	0.0375823
$709$	3.00008e6	0.224139	0.112069	−	0.993700i	$-0.464252\pi$
$709$	3.00008e6	0.224139	0.112069	+	0.993700i	$0.464252\pi$
$710$	2.93806e6	0.218733
$711$	877463.	0.0650961
$712$	6.66870e6	0.492993
$713$	−1.55295e7	−1.14402
$714$	4.82176e6	0.353965
$715$	−2.71177e6	−0.198375
$716$	820686.	0.0598266
$717$	1.32510e7	0.962612
$718$	388012.	0.0280888
$719$	−5.75228e6	−0.414971	−0.207485	−	0.978238i	$-0.566528\pi$
$719$	−5.75228e6	−0.414971	−0.207485	+	0.978238i	$0.566528\pi$
$720$	371947.	0.0267393
$721$	339471.	0.0243201
$722$	9.69717e6	0.692312
$723$	−3.74782e6	−0.266644
$724$	9.79519e6	0.694491
$725$	1.26146e6	0.0891312
$726$	−5.19807e6	−0.366016
$727$	1.95045e7	1.36867	0.684333	−	0.729169i	$-0.260093\pi$
$727$	1.95045e7	1.36867	0.684333	+	0.729169i	$0.260093\pi$
$728$	1.32723e7	0.928147
$729$	531441.	0.0370370
$730$	−2.17097e6	−0.150781
$731$	1.05235e6	0.0728391
$732$	6.63081e6	0.457392
$733$	1.14697e6	0.0788480	0.0394240	−	0.999223i	$-0.487448\pi$
$733$	1.14697e6	0.0788480	0.0394240	+	0.999223i	$0.487448\pi$
$734$	−2.83793e6	−0.194429
$735$	−2.34752e6	−0.160284
$736$	3.44571e6	0.234469
$737$	7.41445e6	0.502817
$738$	2.01950e6	0.136491
$739$	−5.23498e6	−0.352617	−0.176309	−	0.984335i	$-0.556416\pi$
$739$	−5.23498e6	−0.352617	−0.176309	+	0.984335i	$0.556416\pi$
$740$	4.27047e6	0.286679
$741$	−2.39936e6	−0.160528
$742$	1.79578e7	1.19741
$743$	1.12611e7	0.748357	0.374179	−	0.927357i	$-0.377925\pi$
$743$	1.12611e7	0.748357	0.374179	+	0.927357i	$0.377925\pi$
$744$	2.65828e6	0.176063
$745$	−646021.	−0.0426438
$746$	−1.90824e7	−1.25541
$747$	5.59787e6	0.367047
$748$	1.56226e6	0.102094
$749$	−9.20326e6	−0.599428
$750$	−3.82812e6	−0.248503
$751$	4.34861e6	0.281353	0.140676	−	0.990056i	$-0.455072\pi$
$751$	4.34861e6	0.281353	0.140676	+	0.990056i	$0.455072\pi$
$752$	−562566.	−0.0362768
$753$	2.42148e6	0.155630
$754$	−2.10828e6	−0.135052
$755$	−2.07090e6	−0.132218
$756$	−2.06517e6	−0.131417
$757$	9.05995e6	0.574627	0.287314	−	0.957837i	$-0.407238\pi$
$757$	9.05995e6	0.574627	0.287314	+	0.957837i	$0.407238\pi$
$758$	8.86854e6	0.560634
$759$	3.90896e6	0.246296
$760$	261296.	0.0164096
$761$	2.19264e7	1.37248	0.686238	−	0.727377i	$-0.259261\pi$
$761$	2.19264e7	1.37248	0.686238	+	0.727377i	$0.259261\pi$
$762$	−5.16826e6	−0.322446
$763$	6.78035e6	0.421639
$764$	−1.08262e7	−0.671029
$765$	1.09910e6	0.0679019
$766$	5.70620e6	0.351378
$767$	4.07719e6	0.250249
$768$	−589824.	−0.0360844
$769$	3.18958e7	1.94499	0.972495	−	0.232923i	$-0.0748291\pi$
$769$	3.18958e7	1.94499	0.972495	+	0.232923i	$0.0748291\pi$
$770$	−1.63970e6	−0.0996638
$771$	−9.95925e6	−0.603380
$772$	1.05569e7	0.637517
$773$	1.23772e7	0.745028	0.372514	−	0.928027i	$-0.378496\pi$
$773$	1.23772e7	0.745028	0.372514	+	0.928027i	$0.378496\pi$
$774$	−450722.	−0.0270431
$775$	−1.29372e7	−0.773726
$776$	9.04606e6	0.539268
$777$	−2.37110e7	−1.40896
$778$	3.85905e6	0.228576
$779$	1.41872e6	0.0837629
$780$	3.02535e6	0.178049
$781$	−5.28548e6	−0.310068
$782$	1.01820e7	0.595411
$783$	328050.	0.0191221
$784$	3.72264e6	0.216302
$785$	4.32841e6	0.250700
$786$	897235.	0.0518024
$787$	−1.81664e7	−1.04552	−0.522758	−	0.852481i	$-0.675097\pi$
$787$	−1.81664e7	−1.04552	−0.522758	+	0.852481i	$0.675097\pi$
$788$	−1.39664e6	−0.0801252
$789$	1.02049e7	0.583604
$790$	−777248.	−0.0443090
$791$	1.43422e7	0.815031
$792$	−669121.	−0.0379046
$793$	5.39338e7	3.04563
$794$	4.25281e6	0.239400
$795$	4.09338e6	0.229702
$796$	−1.17437e6	−0.0656933
$797$	1.06279e7	0.592657	0.296329	−	0.955086i	$-0.404238\pi$
$797$	1.06279e7	0.592657	0.296329	+	0.955086i	$0.404238\pi$
$798$	−1.45080e6	−0.0806493
$799$	−1.66237e6	−0.0921215
$800$	2.87053e6	0.158576
$801$	−8.44007e6	−0.464799
$802$	−7.22024e6	−0.396384
$803$	3.90550e6	0.213741
$804$	−8.27183e6	−0.451296
$805$	−1.06867e7	−0.581239
$806$	2.16220e7	1.17235
$807$	−1.67515e7	−0.905464
$808$	9.77752e6	0.526866
$809$	−8.62377e6	−0.463261	−0.231630	−	0.972804i	$-0.574406\pi$
$809$	−8.62377e6	−0.463261	−0.231630	+	0.972804i	$0.574406\pi$
$810$	−470745.	−0.0252100
$811$	−1.95998e7	−1.04641	−0.523203	−	0.852208i	$-0.675263\pi$
$811$	−1.95998e7	−1.04641	−0.523203	+	0.852208i	$0.675263\pi$
$812$	−1.27480e6	−0.0678501
$813$	2.03675e7	1.08072
$814$	−7.68244e6	−0.406385
$815$	−8.37212e6	−0.441511
$816$	−1.74292e6	−0.0916329
$817$	−316636.	−0.0165961
$818$	−28226.9	−0.00147496
$819$	−1.67977e7	−0.875066
$820$	−1.78885e6	−0.0929053
$821$	2.85532e7	1.47842	0.739210	−	0.673476i	$-0.235199\pi$
$821$	2.85532e7	1.47842	0.739210	+	0.673476i	$0.235199\pi$
$822$	−1.10049e7	−0.568076
$823$	1.45951e7	0.751119	0.375559	−	0.926798i	$-0.377451\pi$
$823$	1.45951e7	0.751119	0.375559	+	0.926798i	$0.377451\pi$
$824$	−122708.	−0.00629588
$825$	3.25645e6	0.166575
$826$	2.46532e6	0.125725
$827$	612107.	0.0311217	0.0155609	−	0.999879i	$-0.495047\pi$
$827$	612107.	0.0311217	0.0155609	+	0.999879i	$0.495047\pi$
$828$	−4.36098e6	−0.221059
$829$	−2.37608e6	−0.120081	−0.0600406	−	0.998196i	$-0.519123\pi$
$829$	−2.37608e6	−0.120081	−0.0600406	+	0.998196i	$0.519123\pi$
$830$	−4.95854e6	−0.249838
$831$	−3.12367e6	−0.156914
$832$	−4.79752e6	−0.240275
$833$	1.10003e7	0.549279
$834$	−2.86699e6	−0.142729
$835$	−9.15207e6	−0.454259
$836$	−470063.	−0.0232617
$837$	−3.36439e6	−0.165994
$838$	2.85838e7	1.40608
$839$	−3.87213e6	−0.189909	−0.0949545	−	0.995482i	$-0.530271\pi$
$839$	−3.87213e6	−0.189909	−0.0949545	+	0.995482i	$0.530271\pi$
$840$	1.82931e6	0.0894518
$841$	−2.03086e7	−0.990127
$842$	8.89561e6	0.432410
$843$	1.94594e6	0.0943106
$844$	1.26876e7	0.613090
$845$	1.79476e7	0.864700
$846$	711998.	0.0342021
$847$	−2.55651e7	−1.22445
$848$	−6.49117e6	−0.309980
$849$	2.96261e6	0.141060
$850$	8.48237e6	0.402689
$851$	−5.00701e7	−2.37004
$852$	5.89667e6	0.278297
$853$	2.27953e7	1.07269	0.536343	−	0.844000i	$-0.319806\pi$
$853$	2.27953e7	1.07269	0.536343	+	0.844000i	$0.319806\pi$
$854$	3.26116e7	1.53013
$855$	−330703.	−0.0154711
$856$	3.32670e6	0.155178
$857$	3.33059e7	1.54906	0.774531	−	0.632536i	$-0.217986\pi$
$857$	3.33059e7	1.54906	0.774531	+	0.632536i	$0.217986\pi$
$858$	−5.44251e6	−0.252395
$859$	−2.20379e7	−1.01903	−0.509516	−	0.860461i	$-0.670175\pi$
$859$	−2.20379e7	−1.01903	−0.509516	+	0.860461i	$0.670175\pi$
$860$	399245.	0.0184074
$861$	9.93231e6	0.456607
$862$	−1.50830e7	−0.691382
$863$	8.76342e6	0.400541	0.200270	−	0.979741i	$-0.435818\pi$
$863$	8.76342e6	0.400541	0.200270	+	0.979741i	$0.435818\pi$
$864$	746496.	0.0340207
$865$	−8.42123e6	−0.382680
$866$	5.82148e6	0.263778
$867$	7.62842e6	0.344657
$868$	1.30740e7	0.588990
$869$	1.39825e6	0.0628107
$870$	−290583.	−0.0130159
$871$	−6.72815e7	−3.00504
$872$	−2.45089e6	−0.109152
$873$	−1.14489e7	−0.508427
$874$	−3.06363e6	−0.135662
$875$	−1.88275e7	−0.831326
$876$	−4.35712e6	−0.191840
$877$	3.39809e7	1.49189	0.745943	−	0.666010i	$-0.231999\pi$
$877$	3.39809e7	1.49189	0.745943	+	0.666010i	$0.231999\pi$
$878$	1.76822e7	0.774106
$879$	−1.74366e7	−0.761184
$880$	592701.	0.0258006
$881$	8.55016e6	0.371137	0.185569	−	0.982631i	$-0.440587\pi$
$881$	8.55016e6	0.371137	0.185569	+	0.982631i	$0.440587\pi$
$882$	−4.71146e6	−0.203931
$883$	8.43785e6	0.364192	0.182096	−	0.983281i	$-0.441712\pi$
$883$	8.43785e6	0.364192	0.182096	+	0.983281i	$0.441712\pi$
$884$	−1.41766e7	−0.610156
$885$	561956.	0.0241182
$886$	−1.30436e7	−0.558231
$887$	3.45863e7	1.47603	0.738015	−	0.674784i	$-0.235763\pi$
$887$	3.45863e7	1.47603	0.738015	+	0.674784i	$0.235763\pi$
$888$	8.57081e6	0.364745
$889$	−2.54185e7	−1.07869
$890$	7.47613e6	0.316375
$891$	846856.	0.0357368
$892$	−4.54330e6	−0.191187
$893$	500184.	0.0209895
$894$	−1.29656e6	−0.0542562
$895$	920053.	0.0383933
$896$	−2.90087e6	−0.120714
$897$	−3.54714e7	−1.47196
$898$	−1.44335e7	−0.597283
$899$	−2.07678e6	−0.0857021
$900$	−3.63302e6	−0.149507
$901$	−1.91813e7	−0.787165
$902$	3.21809e6	0.131699
$903$	−2.21674e6	−0.0904681
$904$	−5.18426e6	−0.210992
$905$	1.09812e7	0.445684
$906$	−4.15629e6	−0.168223
$907$	−3.13405e7	−1.26499	−0.632497	−	0.774563i	$-0.717970\pi$
$907$	−3.13405e7	−1.26499	−0.632497	+	0.774563i	$0.717970\pi$
$908$	1.42732e7	0.574520
$909$	−1.23747e7	−0.496734
$910$	1.48793e7	0.595632
$911$	5.53480e6	0.220956	0.110478	−	0.993879i	$-0.464762\pi$
$911$	5.53480e6	0.220956	0.110478	+	0.993879i	$0.464762\pi$
$912$	524420.	0.0208781
$913$	8.92026e6	0.354161
$914$	−2.08979e7	−0.827442
$915$	7.43366e6	0.293528
$916$	−777663.	−0.0306234
$917$	4.41278e6	0.173296
$918$	2.20588e6	0.0863924
$919$	−1.62062e7	−0.632984	−0.316492	−	0.948595i	$-0.602505\pi$
$919$	−1.62062e7	−0.632984	−0.316492	+	0.948595i	$0.602505\pi$
$920$	3.86292e6	0.150469
$921$	1.90967e7	0.741840
$922$	1.70601e7	0.660927
$923$	4.79624e7	1.85309
$924$	−3.29087e6	−0.126803
$925$	−4.17121e7	−1.60290
$926$	−1.55408e7	−0.595588
$927$	155303.	0.00593581
$928$	460800.	0.0175648
$929$	−4.17835e7	−1.58842	−0.794210	−	0.607643i	$-0.792115\pi$
$929$	−4.17835e7	−1.58842	−0.794210	+	0.607643i	$0.792115\pi$
$930$	2.98014e6	0.112987
$931$	−3.30984e6	−0.125151
$932$	1.83952e6	0.0693689
$933$	1.68021e7	0.631915
$934$	−9.06753e6	−0.340112
$935$	1.75142e6	0.0655181
$936$	6.07186e6	0.226533
$937$	−4.48196e7	−1.66770	−0.833852	−	0.551988i	$-0.813869\pi$
$937$	−4.48196e7	−1.66770	−0.833852	+	0.551988i	$0.813869\pi$
$938$	−4.06825e7	−1.50973
$939$	1.72485e7	0.638391
$940$	−630681.	−0.0232804
$941$	6.67255e6	0.245651	0.122825	−	0.992428i	$-0.460805\pi$
$941$	6.67255e6	0.245651	0.122825	+	0.992428i	$0.460805\pi$
$942$	8.68710e6	0.318968
$943$	2.09739e7	0.768067
$944$	−891136.	−0.0325472
$945$	−2.31522e6	−0.0843360
$946$	−718230.	−0.0260937
$947$	4.65602e7	1.68710	0.843548	−	0.537054i	$-0.180463\pi$
$947$	4.65602e7	1.68710	0.843548	+	0.537054i	$0.180463\pi$
$948$	−1.55993e6	−0.0563748
$949$	−3.54400e7	−1.27740
$950$	−2.55223e6	−0.0917508
$951$	2.93438e7	1.05212
$952$	−8.57202e6	−0.306543
$953$	−3.32352e7	−1.18540	−0.592702	−	0.805422i	$-0.701939\pi$
$953$	−3.32352e7	−1.18540	−0.592702	+	0.805422i	$0.701939\pi$
$954$	8.21539e6	0.292252
$955$	−1.21370e7	−0.430628
$956$	−2.35574e7	−0.833647
$957$	522750.	0.0184508
$958$	3.84289e7	1.35283
$959$	−5.41243e7	−1.90040
$960$	−661239.	−0.0231569
$961$	−7.33024e6	−0.256041
$962$	6.97134e7	2.42873
$963$	−4.21035e6	−0.146303
$964$	6.66278e6	0.230921
$965$	1.18351e7	0.409122
$966$	−2.14482e7	−0.739516
$967$	−1.97095e7	−0.677812	−0.338906	−	0.940820i	$-0.610057\pi$
$967$	−1.97095e7	−0.677812	−0.338906	+	0.940820i	$0.610057\pi$
$968$	9.24101e6	0.316980
$969$	1.54965e6	0.0530181
$970$	1.01413e7	0.346072
$971$	−1.68304e7	−0.572857	−0.286429	−	0.958102i	$-0.592468\pi$
$971$	−1.68304e7	−0.572857	−0.286429	+	0.958102i	$0.592468\pi$
$972$	−944784.	−0.0320750
$973$	−1.41004e7	−0.477474
$974$	−3.60840e7	−1.21876
$975$	−2.95503e7	−0.995521
$976$	−1.17881e7	−0.396113
$977$	2.10662e7	0.706073	0.353037	−	0.935609i	$-0.385149\pi$
$977$	2.10662e7	0.706073	0.353037	+	0.935609i	$0.385149\pi$
$978$	−1.68028e7	−0.561740
$979$	−1.34493e7	−0.448481
$980$	4.17337e6	0.138810
$981$	3.10190e6	0.102910
$982$	−1.63845e7	−0.542193
$983$	−5.73357e7	−1.89252	−0.946261	−	0.323404i	$-0.895173\pi$
$983$	−5.73357e7	−1.89252	−0.946261	+	0.323404i	$0.895173\pi$
$984$	−3.59022e6	−0.118204
$985$	−1.56574e6	−0.0514198
$986$	1.36165e6	0.0446041
$987$	3.50175e6	0.114417
$988$	4.26553e6	0.139021
$989$	−4.68105e6	−0.152178
$990$	−750137.	−0.0243250
$991$	1.70841e7	0.552595	0.276298	−	0.961072i	$-0.410892\pi$
$991$	1.70841e7	0.552595	0.276298	+	0.961072i	$0.410892\pi$
$992$	−4.72584e6	−0.152475
$993$	4.34272e6	0.139762
$994$	2.90010e7	0.930995
$995$	−1.31656e6	−0.0421582
$996$	−9.95177e6	−0.317872
$997$	3.42297e7	1.09060	0.545299	−	0.838241i	$-0.316416\pi$
$997$	3.42297e7	1.09060	0.545299	+	0.838241i	$0.316416\pi$
$998$	−4.28726e6	−0.136255
$999$	−1.08474e7	−0.343885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.f.1.4	✓	6
3.2	odd	2		1062.6.a.i.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.f.1.4	✓	6	1.1	even	1	trivial
1062.6.a.i.1.3		6	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +17.9373 q^{5} +36.0000 q^{6} +177.055 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +17.9373 q^{5} +36.0000 q^{6} +177.055 q^{7} -64.0000 q^{8} +81.0000 q^{9} -71.7490 q^{10} +129.074 q^{11} -144.000 q^{12} -1171.27 q^{13} -708.221 q^{14} -161.435 q^{15} +256.000 q^{16} +756.475 q^{17} -324.000 q^{18} -227.613 q^{19} +286.996 q^{20} -1593.50 q^{21} -516.297 q^{22} -3364.96 q^{23} +576.000 q^{24} -2803.25 q^{25} +4685.08 q^{26} -729.000 q^{27} +2832.88 q^{28} -450.000 q^{29} +645.741 q^{30} +4615.07 q^{31} -1024.00 q^{32} -1161.67 q^{33} -3025.90 q^{34} +3175.89 q^{35} +1296.00 q^{36} +14879.9 q^{37} +910.451 q^{38} +10541.4 q^{39} -1147.98 q^{40} -6233.02 q^{41} +6373.99 q^{42} +1391.12 q^{43} +2065.19 q^{44} +1452.92 q^{45} +13459.8 q^{46} -2197.52 q^{47} -2304.00 q^{48} +14541.5 q^{49} +11213.0 q^{50} -6808.27 q^{51} -18740.3 q^{52} -25356.1 q^{53} +2916.00 q^{54} +2315.24 q^{55} -11331.5 q^{56} +2048.51 q^{57} +1800.00 q^{58} -3481.00 q^{59} -2582.97 q^{60} -46047.3 q^{61} -18460.3 q^{62} +14341.5 q^{63} +4096.00 q^{64} -21009.4 q^{65} +4646.67 q^{66} +57443.2 q^{67} +12103.6 q^{68} +30284.6 q^{69} -12703.5 q^{70} -40949.1 q^{71} -5184.00 q^{72} +30257.8 q^{73} -59519.5 q^{74} +25229.3 q^{75} -3641.80 q^{76} +22853.3 q^{77} -42165.7 q^{78} +10832.9 q^{79} +4591.94 q^{80} +6561.00 q^{81} +24932.1 q^{82} +69109.5 q^{83} -25495.9 q^{84} +13569.1 q^{85} -5564.47 q^{86} +4050.00 q^{87} -8260.75 q^{88} -104198. q^{89} -5811.67 q^{90} -207379. q^{91} -53839.3 q^{92} -41535.7 q^{93} +8790.10 q^{94} -4082.75 q^{95} +9216.00 q^{96} -141345. q^{97} -58166.2 q^{98} +10455.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9} + 184 q^{10} - 653 q^{11} - 864 q^{12} + 647 q^{13} + 412 q^{14} + 414 q^{15} + 1536 q^{16} + 621 q^{17} - 1944 q^{18} - 454 q^{19} - 736 q^{20} + 927 q^{21} + 2612 q^{22} - 3412 q^{23} + 3456 q^{24} + 3866 q^{25} - 2588 q^{26} - 4374 q^{27} - 1648 q^{28} + 1526 q^{29} - 1656 q^{30} + 5976 q^{31} - 6144 q^{32} + 5877 q^{33} - 2484 q^{34} + 8098 q^{35} + 7776 q^{36} + 37033 q^{37} + 1816 q^{38} - 5823 q^{39} + 2944 q^{40} + 13983 q^{41} - 3708 q^{42} + 11521 q^{43} - 10448 q^{44} - 3726 q^{45} + 13648 q^{46} + 12434 q^{47} - 13824 q^{48} + 54237 q^{49} - 15464 q^{50} - 5589 q^{51} + 10352 q^{52} + 21310 q^{53} + 17496 q^{54} + 57468 q^{55} + 6592 q^{56} + 4086 q^{57} - 6104 q^{58} - 20886 q^{59} + 6624 q^{60} - 23030 q^{61} - 23904 q^{62} - 8343 q^{63} + 24576 q^{64} - 37368 q^{65} - 23508 q^{66} + 24342 q^{67} + 9936 q^{68} + 30708 q^{69} - 32392 q^{70} - 184375 q^{71} - 31104 q^{72} - 24512 q^{73} - 148132 q^{74} - 34794 q^{75} - 7264 q^{76} - 46529 q^{77} + 23292 q^{78} - 17987 q^{79} - 11776 q^{80} + 39366 q^{81} - 55932 q^{82} - 46687 q^{83} + 14832 q^{84} - 29706 q^{85} - 46084 q^{86} - 13734 q^{87} + 41792 q^{88} - 178946 q^{89} + 14904 q^{90} - 340179 q^{91} - 54592 q^{92} - 53784 q^{93} - 49736 q^{94} - 532190 q^{95} + 55296 q^{96} - 214638 q^{97} - 216948 q^{98} - 52893 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9 + 184 * q^10 - 653 * q^11 - 864 * q^12 + 647 * q^13 + 412 * q^14 + 414 * q^15 + 1536 * q^16 + 621 * q^17 - 1944 * q^18 - 454 * q^19 - 736 * q^20 + 927 * q^21 + 2612 * q^22 - 3412 * q^23 + 3456 * q^24 + 3866 * q^25 - 2588 * q^26 - 4374 * q^27 - 1648 * q^28 + 1526 * q^29 - 1656 * q^30 + 5976 * q^31 - 6144 * q^32 + 5877 * q^33 - 2484 * q^34 + 8098 * q^35 + 7776 * q^36 + 37033 * q^37 + 1816 * q^38 - 5823 * q^39 + 2944 * q^40 + 13983 * q^41 - 3708 * q^42 + 11521 * q^43 - 10448 * q^44 - 3726 * q^45 + 13648 * q^46 + 12434 * q^47 - 13824 * q^48 + 54237 * q^49 - 15464 * q^50 - 5589 * q^51 + 10352 * q^52 + 21310 * q^53 + 17496 * q^54 + 57468 * q^55 + 6592 * q^56 + 4086 * q^57 - 6104 * q^58 - 20886 * q^59 + 6624 * q^60 - 23030 * q^61 - 23904 * q^62 - 8343 * q^63 + 24576 * q^64 - 37368 * q^65 - 23508 * q^66 + 24342 * q^67 + 9936 * q^68 + 30708 * q^69 - 32392 * q^70 - 184375 * q^71 - 31104 * q^72 - 24512 * q^73 - 148132 * q^74 - 34794 * q^75 - 7264 * q^76 - 46529 * q^77 + 23292 * q^78 - 17987 * q^79 - 11776 * q^80 + 39366 * q^81 - 55932 * q^82 - 46687 * q^83 + 14832 * q^84 - 29706 * q^85 - 46084 * q^86 - 13734 * q^87 + 41792 * q^88 - 178946 * q^89 + 14904 * q^90 - 340179 * q^91 - 54592 * q^92 - 53784 * q^93 - 49736 * q^94 - 532190 * q^95 + 55296 * q^96 - 214638 * q^97 - 216948 * q^98 - 52893 * q^99

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