LMFDB - Embedded newform 354.6.a.f.1.3

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			1.3
Root			$-58.4572$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -9.89453 q^{5} +36.0000 q^{6} -127.898 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -9.89453 q^{5} +36.0000 q^{6} -127.898 q^{7} -64.0000 q^{8} +81.0000 q^{9} +39.5781 q^{10} +101.464 q^{11} -144.000 q^{12} -39.7326 q^{13} +511.592 q^{14} +89.0508 q^{15} +256.000 q^{16} +994.202 q^{17} -324.000 q^{18} -479.743 q^{19} -158.313 q^{20} +1151.08 q^{21} -405.855 q^{22} +2622.48 q^{23} +576.000 q^{24} -3027.10 q^{25} +158.930 q^{26} -729.000 q^{27} -2046.37 q^{28} -3663.10 q^{29} -356.203 q^{30} +8377.93 q^{31} -1024.00 q^{32} -913.173 q^{33} -3976.81 q^{34} +1265.49 q^{35} +1296.00 q^{36} +5623.43 q^{37} +1918.97 q^{38} +357.594 q^{39} +633.250 q^{40} -5288.34 q^{41} -4604.33 q^{42} +17470.5 q^{43} +1623.42 q^{44} -801.457 q^{45} -10489.9 q^{46} -15776.9 q^{47} -2304.00 q^{48} -449.071 q^{49} +12108.4 q^{50} -8947.81 q^{51} -635.722 q^{52} +29885.5 q^{53} +2916.00 q^{54} -1003.94 q^{55} +8185.48 q^{56} +4317.69 q^{57} +14652.4 q^{58} -3481.00 q^{59} +1424.81 q^{60} +41504.6 q^{61} -33511.7 q^{62} -10359.7 q^{63} +4096.00 q^{64} +393.136 q^{65} +3652.69 q^{66} -72837.5 q^{67} +15907.2 q^{68} -23602.4 q^{69} -5061.97 q^{70} +37373.7 q^{71} -5184.00 q^{72} +59567.1 q^{73} -22493.7 q^{74} +27243.9 q^{75} -7675.89 q^{76} -12977.0 q^{77} -1430.37 q^{78} -47045.6 q^{79} -2533.00 q^{80} +6561.00 q^{81} +21153.3 q^{82} -124624. q^{83} +18417.3 q^{84} -9837.16 q^{85} -69882.2 q^{86} +32967.9 q^{87} -6493.67 q^{88} -85797.2 q^{89} +3205.83 q^{90} +5081.73 q^{91} +41959.8 q^{92} -75401.3 q^{93} +63107.4 q^{94} +4746.83 q^{95} +9216.00 q^{96} -19781.9 q^{97} +1796.28 q^{98} +8218.56 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−9.89453	−0.176999	−0.0884994	−	0.996076i	$-0.528207\pi$
$5$	−9.89453	−0.176999	−0.0884994	+	0.996076i	$0.528207\pi$
$6$	36.0000	0.408248
$7$	−127.898	−0.986550	−0.493275	−	0.869873i	$-0.664200\pi$
$7$	−127.898	−0.986550	−0.493275	+	0.869873i	$0.664200\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	39.5781	0.125157
$11$	101.464	0.252830	0.126415	−	0.991977i	$-0.459653\pi$
$11$	101.464	0.252830	0.126415	+	0.991977i	$0.459653\pi$
$12$	−144.000	−0.288675
$13$	−39.7326	−0.0652062	−0.0326031	−	0.999468i	$-0.510380\pi$
$13$	−39.7326	−0.0652062	−0.0326031	+	0.999468i	$0.510380\pi$
$14$	511.592	0.697596
$15$	89.0508	0.102190
$16$	256.000	0.250000
$17$	994.202	0.834358	0.417179	−	0.908824i	$-0.363019\pi$
$17$	994.202	0.834358	0.417179	+	0.908824i	$0.363019\pi$
$18$	−324.000	−0.235702
$19$	−479.743	−0.304877	−0.152438	−	0.988313i	$-0.548713\pi$
$19$	−479.743	−0.304877	−0.152438	+	0.988313i	$0.548713\pi$
$20$	−158.313	−0.0884994
$21$	1151.08	0.569585
$22$	−405.855	−0.178778
$23$	2622.48	1.03370	0.516849	−	0.856077i	$-0.327105\pi$
$23$	2622.48	1.03370	0.516849	+	0.856077i	$0.327105\pi$
$24$	576.000	0.204124
$25$	−3027.10	−0.968671
$26$	158.930	0.0461077
$27$	−729.000	−0.192450
$28$	−2046.37	−0.493275
$29$	−3663.10	−0.808823	−0.404411	−	0.914577i	$-0.632524\pi$
$29$	−3663.10	−0.808823	−0.404411	+	0.914577i	$0.632524\pi$
$30$	−356.203	−0.0722594
$31$	8377.93	1.56579	0.782893	−	0.622157i	$-0.213743\pi$
$31$	8377.93	1.56579	0.782893	+	0.622157i	$0.213743\pi$
$32$	−1024.00	−0.176777
$33$	−913.173	−0.145972
$34$	−3976.81	−0.589980
$35$	1265.49	0.174618
$36$	1296.00	0.166667
$37$	5623.43	0.675301	0.337650	−	0.941272i	$-0.390368\pi$
$37$	5623.43	0.675301	0.337650	+	0.941272i	$0.390368\pi$
$38$	1918.97	0.215581
$39$	357.594	0.0376468
$40$	633.250	0.0625785
$41$	−5288.34	−0.491314	−0.245657	−	0.969357i	$-0.579004\pi$
$41$	−5288.34	−0.491314	−0.245657	+	0.969357i	$0.579004\pi$
$42$	−4604.33	−0.402757
$43$	17470.5	1.44090	0.720452	−	0.693505i	$-0.243934\pi$
$43$	17470.5	1.44090	0.720452	+	0.693505i	$0.243934\pi$
$44$	1623.42	0.126415
$45$	−801.457	−0.0589996
$46$	−10489.9	−0.730934
$47$	−15776.9	−1.04178	−0.520890	−	0.853624i	$-0.674400\pi$
$47$	−15776.9	−1.04178	−0.520890	+	0.853624i	$0.674400\pi$
$48$	−2304.00	−0.144338
$49$	−449.071	−0.0267193
$50$	12108.4	0.684954
$51$	−8947.81	−0.481717
$52$	−635.722	−0.0326031
$53$	29885.5	1.46141	0.730704	−	0.682695i	$-0.239192\pi$
$53$	29885.5	1.46141	0.730704	+	0.682695i	$0.239192\pi$
$54$	2916.00	0.136083
$55$	−1003.94	−0.0447506
$56$	8185.48	0.348798
$57$	4317.69	0.176021
$58$	14652.4	0.571924
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	1424.81	0.0510951
$61$	41504.6	1.42814	0.714071	−	0.700073i	$-0.246849\pi$
$61$	41504.6	1.42814	0.714071	+	0.700073i	$0.246849\pi$
$62$	−33511.7	−1.10718
$63$	−10359.7	−0.328850
$64$	4096.00	0.125000
$65$	393.136	0.0115414
$66$	3652.69	0.103217
$67$	−72837.5	−1.98230	−0.991148	−	0.132765i	$-0.957614\pi$
$67$	−72837.5	−1.98230	−0.991148	+	0.132765i	$0.957614\pi$
$68$	15907.2	0.417179
$69$	−23602.4	−0.596805
$70$	−5061.97	−0.123474
$71$	37373.7	0.879874	0.439937	−	0.898029i	$-0.355001\pi$
$71$	37373.7	0.879874	0.439937	+	0.898029i	$0.355001\pi$
$72$	−5184.00	−0.117851
$73$	59567.1	1.30828	0.654138	−	0.756376i	$-0.273032\pi$
$73$	59567.1	1.30828	0.654138	+	0.756376i	$0.273032\pi$
$74$	−22493.7	−0.477510
$75$	27243.9	0.559263
$76$	−7675.89	−0.152438
$77$	−12977.0	−0.249430
$78$	−1430.37	−0.0266203
$79$	−47045.6	−0.848109	−0.424054	−	0.905637i	$-0.639393\pi$
$79$	−47045.6	−0.848109	−0.424054	+	0.905637i	$0.639393\pi$
$80$	−2533.00	−0.0442497
$81$	6561.00	0.111111
$82$	21153.3	0.347412
$83$	−124624.	−1.98567	−0.992837	−	0.119478i	$-0.961878\pi$
$83$	−124624.	−1.98567	−0.992837	+	0.119478i	$0.961878\pi$
$84$	18417.3	0.284792
$85$	−9837.16	−0.147680
$86$	−69882.2	−1.01887
$87$	32967.9	0.466974
$88$	−6493.67	−0.0893889
$89$	−85797.2	−1.14815	−0.574074	−	0.818803i	$-0.694638\pi$
$89$	−85797.2	−1.14815	−0.574074	+	0.818803i	$0.694638\pi$
$90$	3205.83	0.0417190
$91$	5081.73	0.0643291
$92$	41959.8	0.516849
$93$	−75401.3	−0.904007
$94$	63107.4	0.736649
$95$	4746.83	0.0539628
$96$	9216.00	0.102062
$97$	−19781.9	−0.213471	−0.106736	−	0.994287i	$-0.534040\pi$
$97$	−19781.9	−0.213471	−0.106736	+	0.994287i	$0.534040\pi$
$98$	1796.28	0.0188934
$99$	8218.56	0.0842767
$100$	−48433.6	−0.484336
$101$	−133985.	−1.30693	−0.653464	−	0.756958i	$-0.726685\pi$
$101$	−133985.	−1.30693	−0.653464	+	0.756958i	$0.726685\pi$
$102$	35791.3	0.340625
$103$	−119734.	−1.11205	−0.556025	−	0.831166i	$-0.687674\pi$
$103$	−119734.	−1.11205	−0.556025	+	0.831166i	$0.687674\pi$
$104$	2542.89	0.0230539
$105$	−11389.4	−0.100816
$106$	−119542.	−1.03337
$107$	−166409.	−1.40514	−0.702568	−	0.711616i	$-0.747964\pi$
$107$	−166409.	−1.40514	−0.702568	+	0.711616i	$0.747964\pi$
$108$	−11664.0	−0.0962250
$109$	29896.6	0.241021	0.120511	−	0.992712i	$-0.461547\pi$
$109$	29896.6	0.241021	0.120511	+	0.992712i	$0.461547\pi$
$110$	4015.74	0.0316435
$111$	−50610.9	−0.389885
$112$	−32741.9	−0.246637
$113$	−72313.2	−0.532748	−0.266374	−	0.963870i	$-0.585826\pi$
$113$	−72313.2	−0.532748	−0.266374	+	0.963870i	$0.585826\pi$
$114$	−17270.7	−0.124465
$115$	−25948.3	−0.182963
$116$	−58609.5	−0.404411
$117$	−3218.34	−0.0217354
$118$	13924.0	0.0920575
$119$	−127157.	−0.823135
$120$	−5699.25	−0.0361297
$121$	−150756.	−0.936077
$122$	−166018.	−1.00985
$123$	47595.0	0.283660
$124$	134047.	0.782893
$125$	60872.1	0.348452
$126$	41439.0	0.232532
$127$	267326.	1.47073	0.735363	−	0.677674i	$-0.237012\pi$
$127$	267326.	1.47073	0.735363	+	0.677674i	$0.237012\pi$
$128$	−16384.0	−0.0883883
$129$	−157235.	−0.831907
$130$	−1572.54	−0.00816101
$131$	−255994.	−1.30332	−0.651660	−	0.758512i	$-0.725927\pi$
$131$	−255994.	−1.30332	−0.651660	+	0.758512i	$0.725927\pi$
$132$	−14610.8	−0.0729858
$133$	61358.2	0.300776
$134$	291350.	1.40169
$135$	7213.11	0.0340634
$136$	−63628.9	−0.294990
$137$	67124.9	0.305550	0.152775	−	0.988261i	$-0.451179\pi$
$137$	67124.9	0.305550	0.152775	+	0.988261i	$0.451179\pi$
$138$	94409.4	0.422005
$139$	104043.	0.456748	0.228374	−	0.973574i	$-0.426659\pi$
$139$	104043.	0.456748	0.228374	+	0.973574i	$0.426659\pi$
$140$	20247.9	0.0873091
$141$	141992.	0.601472
$142$	−149495.	−0.622165
$143$	−4031.42	−0.0164861
$144$	20736.0	0.0833333
$145$	36244.6	0.143161
$146$	−238268.	−0.925090
$147$	4041.64	0.0154264
$148$	89974.9	0.337650
$149$	−66991.0	−0.247201	−0.123601	−	0.992332i	$-0.539444\pi$
$149$	−66991.0	−0.247201	−0.123601	+	0.992332i	$0.539444\pi$
$150$	−108976.	−0.395458
$151$	−332250.	−1.18583	−0.592916	−	0.805265i	$-0.702023\pi$
$151$	−332250.	−1.18583	−0.592916	+	0.805265i	$0.702023\pi$
$152$	30703.5	0.107790
$153$	80530.3	0.278119
$154$	51908.0	0.176373
$155$	−82895.7	−0.277142
$156$	5721.50	0.0188234
$157$	−137962.	−0.446694	−0.223347	−	0.974739i	$-0.571698\pi$
$157$	−137962.	−0.446694	−0.223347	+	0.974739i	$0.571698\pi$
$158$	188182.	0.599703
$159$	−268970.	−0.843744
$160$	10132.0	0.0312893
$161$	−335411.	−1.01979
$162$	−26244.0	−0.0785674
$163$	188239.	0.554934	0.277467	−	0.960735i	$-0.410505\pi$
$163$	188239.	0.554934	0.277467	+	0.960735i	$0.410505\pi$
$164$	−84613.4	−0.245657
$165$	9035.42	0.0258368
$166$	498498.	1.40408
$167$	−521907.	−1.44811	−0.724056	−	0.689741i	$-0.757724\pi$
$167$	−521907.	−1.44811	−0.724056	+	0.689741i	$0.757724\pi$
$168$	−73669.3	−0.201379
$169$	−369714.	−0.995748
$170$	39348.6	0.104426
$171$	−38859.2	−0.101626
$172$	279529.	0.720452
$173$	40104.8	0.101878	0.0509391	−	0.998702i	$-0.483779\pi$
$173$	40104.8	0.101878	0.0509391	+	0.998702i	$0.483779\pi$
$174$	−131871.	−0.330200
$175$	387160.	0.955643
$176$	25974.7	0.0632075
$177$	31329.0	0.0751646
$178$	343189.	0.811864
$179$	−54672.0	−0.127536	−0.0637680	−	0.997965i	$-0.520312\pi$
$179$	−54672.0	−0.127536	−0.0637680	+	0.997965i	$0.520312\pi$
$180$	−12823.3	−0.0294998
$181$	248812.	0.564513	0.282257	−	0.959339i	$-0.408917\pi$
$181$	248812.	0.564513	0.282257	+	0.959339i	$0.408917\pi$
$182$	−20326.9	−0.0454876
$183$	−373541.	−0.824538
$184$	−167839.	−0.365467
$185$	−55641.2	−0.119527
$186$	301605.	0.639229
$187$	100875.	0.210951
$188$	−252430.	−0.520890
$189$	93237.7	0.189862
$190$	−18987.3	−0.0381575
$191$	−154677.	−0.306790	−0.153395	−	0.988165i	$-0.549021\pi$
$191$	−154677.	−0.306790	−0.153395	+	0.988165i	$0.549021\pi$
$192$	−36864.0	−0.0721688
$193$	233117.	0.450485	0.225242	−	0.974303i	$-0.427683\pi$
$193$	233117.	0.450485	0.225242	+	0.974303i	$0.427683\pi$
$194$	79127.7	0.150947
$195$	−3538.22	−0.00666344
$196$	−7185.13	−0.0133596
$197$	645409.	1.18487	0.592434	−	0.805619i	$-0.298167\pi$
$197$	645409.	1.18487	0.592434	+	0.805619i	$0.298167\pi$
$198$	−32874.2	−0.0595926
$199$	−1.05358e6	−1.88598	−0.942989	−	0.332825i	$-0.891998\pi$
$199$	−1.05358e6	−1.88598	−0.942989	+	0.332825i	$0.891998\pi$
$200$	193734.	0.342477
$201$	655538.	1.14448
$202$	535938.	0.924137
$203$	468503.	0.797944
$204$	−143165.	−0.240858
$205$	52325.6	0.0869620
$206$	478936.	0.786338
$207$	212421.	0.344566
$208$	−10171.5	−0.0163015
$209$	−48676.5	−0.0770821
$210$	45557.7	0.0712876
$211$	−755128.	−1.16765	−0.583827	−	0.811878i	$-0.698446\pi$
$211$	−755128.	−1.16765	−0.583827	+	0.811878i	$0.698446\pi$
$212$	478169.	0.730704
$213$	−336363.	−0.507995
$214$	665638.	0.993582
$215$	−172863.	−0.255038
$216$	46656.0	0.0680414
$217$	−1.07152e6	−1.54473
$218$	−119586.	−0.170428
$219$	−536104.	−0.755333
$220$	−16063.0	−0.0223753
$221$	−39502.2	−0.0544053
$222$	202444.	0.275690
$223$	1.06800e6	1.43817	0.719084	−	0.694923i	$-0.244561\pi$
$223$	1.06800e6	1.43817	0.719084	+	0.694923i	$0.244561\pi$
$224$	130968.	0.174399
$225$	−245195.	−0.322890
$226$	289253.	0.376709
$227$	1.10400e6	1.42202	0.711010	−	0.703182i	$-0.248238\pi$
$227$	1.10400e6	1.42202	0.711010	+	0.703182i	$0.248238\pi$
$228$	69083.0	0.0880104
$229$	706261.	0.889972	0.444986	−	0.895538i	$-0.353209\pi$
$229$	706261.	0.889972	0.444986	+	0.895538i	$0.353209\pi$
$230$	103793.	0.129374
$231$	116793.	0.144008
$232$	234438.	0.285962
$233$	−674116.	−0.813476	−0.406738	−	0.913545i	$-0.633334\pi$
$233$	−674116.	−0.813476	−0.406738	+	0.913545i	$0.633334\pi$
$234$	12873.4	0.0153692
$235$	156105.	0.184394
$236$	−55696.0	−0.0650945
$237$	423411.	0.489656
$238$	508626.	0.582045
$239$	−713460.	−0.807932	−0.403966	−	0.914774i	$-0.632369\pi$
$239$	−713460.	−0.807932	−0.403966	+	0.914774i	$0.632369\pi$
$240$	22797.0	0.0255476
$241$	1.56291e6	1.73337	0.866684	−	0.498858i	$-0.166247\pi$
$241$	1.56291e6	1.73337	0.866684	+	0.498858i	$0.166247\pi$
$242$	603025.	0.661906
$243$	−59049.0	−0.0641500
$244$	664073.	0.714071
$245$	4443.35	0.00472928
$246$	−190380.	−0.200578
$247$	19061.4	0.0198799
$248$	−536187.	−0.553589
$249$	1.12162e6	1.14643
$250$	−243489.	−0.246393
$251$	−841208.	−0.842789	−0.421395	−	0.906877i	$-0.638459\pi$
$251$	−841208.	−0.842789	−0.421395	+	0.906877i	$0.638459\pi$
$252$	−165756.	−0.164425
$253$	266087.	0.261350
$254$	−1.06930e6	−1.03996
$255$	88534.4	0.0852632
$256$	65536.0	0.0625000
$257$	−201368.	−0.190177	−0.0950885	−	0.995469i	$-0.530313\pi$
$257$	−201368.	−0.190177	−0.0950885	+	0.995469i	$0.530313\pi$
$258$	628939.	0.588247
$259$	−719226.	−0.666218
$260$	6290.17	0.00577071
$261$	−296711.	−0.269608
$262$	1.02397e6	0.921586
$263$	−632284.	−0.563667	−0.281834	−	0.959463i	$-0.590943\pi$
$263$	−632284.	−0.563667	−0.281834	+	0.959463i	$0.590943\pi$
$264$	58443.1	0.0516087
$265$	−295703.	−0.258667
$266$	−245433.	−0.212681
$267$	772175.	0.662884
$268$	−1.16540e6	−0.991148
$269$	−566711.	−0.477508	−0.238754	−	0.971080i	$-0.576739\pi$
$269$	−566711.	−0.477508	−0.238754	+	0.971080i	$0.576739\pi$
$270$	−28852.5	−0.0240865
$271$	1.17169e6	0.969146	0.484573	−	0.874751i	$-0.338975\pi$
$271$	1.17169e6	0.969146	0.484573	+	0.874751i	$0.338975\pi$
$272$	254516.	0.208589
$273$	−45735.5	−0.0371405
$274$	−268500.	−0.216057
$275$	−307140.	−0.244909
$276$	−377638.	−0.298403
$277$	363720.	0.284819	0.142409	−	0.989808i	$-0.454515\pi$
$277$	363720.	0.284819	0.142409	+	0.989808i	$0.454515\pi$
$278$	−416172.	−0.322969
$279$	678612.	0.521929
$280$	−80991.5	−0.0617368
$281$	2.18129e6	1.64796	0.823981	−	0.566618i	$-0.191748\pi$
$281$	2.18129e6	1.64796	0.823981	+	0.566618i	$0.191748\pi$
$282$	−567967.	−0.425305
$283$	1.38985e6	1.03158	0.515788	−	0.856717i	$-0.327499\pi$
$283$	1.38985e6	1.03158	0.515788	+	0.856717i	$0.327499\pi$
$284$	597979.	0.439937
$285$	−42721.5	−0.0311555
$286$	16125.7	0.0116574
$287$	676368.	0.484706
$288$	−82944.0	−0.0589256
$289$	−431420.	−0.303848
$290$	−144978.	−0.101230
$291$	178037.	0.123248
$292$	953073.	0.654138
$293$	−2.56467e6	−1.74527	−0.872635	−	0.488373i	$-0.837590\pi$
$293$	−2.56467e6	−1.74527	−0.872635	+	0.488373i	$0.837590\pi$
$294$	−16166.6	−0.0109081
$295$	34442.9	0.0230433
$296$	−359900.	−0.238755
$297$	−73967.0	−0.0486572
$298$	267964.	0.174798
$299$	−104198.	−0.0674034
$300$	435902.	0.279631
$301$	−2.23445e6	−1.42152
$302$	1.32900e6	0.838509
$303$	1.20586e6	0.754555
$304$	−122814.	−0.0762192
$305$	−410668.	−0.252779
$306$	−322121.	−0.196660
$307$	1.56478e6	0.947562	0.473781	−	0.880643i	$-0.342889\pi$
$307$	1.56478e6	0.947562	0.473781	+	0.880643i	$0.342889\pi$
$308$	−207632.	−0.124715
$309$	1.07760e6	0.642042
$310$	331583.	0.195969
$311$	−766210.	−0.449208	−0.224604	−	0.974450i	$-0.572109\pi$
$311$	−766210.	−0.449208	−0.224604	+	0.974450i	$0.572109\pi$
$312$	−22886.0	−0.0133102
$313$	664734.	0.383519	0.191760	−	0.981442i	$-0.438581\pi$
$313$	664734.	0.383519	0.191760	+	0.981442i	$0.438581\pi$
$314$	551847.	0.315860
$315$	102505.	0.0582060
$316$	−752730.	−0.424054
$317$	−3.28159e6	−1.83415	−0.917076	−	0.398711i	$-0.869458\pi$
$317$	−3.28159e6	−1.83415	−0.917076	+	0.398711i	$0.869458\pi$
$318$	1.07588e6	0.596617
$319$	−371671.	−0.204495
$320$	−40528.0	−0.0221248
$321$	1.49769e6	0.811256
$322$	1.34164e6	0.721103
$323$	−476961.	−0.254376
$324$	104976.	0.0555556
$325$	120275.	0.0631634
$326$	−752958.	−0.392398
$327$	−269069.	−0.139154
$328$	338454.	0.173706
$329$	2.01783e6	1.02777
$330$	−36141.7	−0.0182694
$331$	219823.	0.110281	0.0551407	−	0.998479i	$-0.482439\pi$
$331$	219823.	0.110281	0.0551407	+	0.998479i	$0.482439\pi$
$332$	−1.99399e6	−0.992837
$333$	455498.	0.225100
$334$	2.08763e6	1.02397
$335$	720693.	0.350864
$336$	294677.	0.142396
$337$	2.03976e6	0.978375	0.489187	−	0.872179i	$-0.337293\pi$
$337$	2.03976e6	0.978375	0.489187	+	0.872179i	$0.337293\pi$
$338$	1.47886e6	0.704100
$339$	650819.	0.307582
$340$	−157395.	−0.0738401
$341$	850055.	0.395878
$342$	155437.	0.0718602
$343$	2.20702e6	1.01291
$344$	−1.11811e6	−0.509437
$345$	233534.	0.105634
$346$	−160419.	−0.0720388
$347$	279306.	0.124525	0.0622625	−	0.998060i	$-0.480168\pi$
$347$	279306.	0.124525	0.0622625	+	0.998060i	$0.480168\pi$
$348$	527486.	0.233487
$349$	−3.93497e6	−1.72933	−0.864665	−	0.502350i	$-0.832469\pi$
$349$	−3.93497e6	−1.72933	−0.864665	+	0.502350i	$0.832469\pi$
$350$	−1.54864e6	−0.675741
$351$	28965.1	0.0125489
$352$	−103899.	−0.0446945
$353$	4.46787e6	1.90838	0.954188	−	0.299208i	$-0.0967225\pi$
$353$	4.46787e6	1.90838	0.954188	+	0.299208i	$0.0967225\pi$
$354$	−125316.	−0.0531494
$355$	−369795.	−0.155737
$356$	−1.37276e6	−0.574074
$357$	1.14441e6	0.475237
$358$	218688.	0.0901815
$359$	−4.25491e6	−1.74243	−0.871213	−	0.490904i	$-0.836666\pi$
$359$	−4.25491e6	−1.74243	−0.871213	+	0.490904i	$0.836666\pi$
$360$	51293.3	0.0208595
$361$	−2.24595e6	−0.907050
$362$	−995246.	−0.399171
$363$	1.35681e6	0.540444
$364$	81307.6	0.0321646
$365$	−589388.	−0.231563
$366$	1.49416e6	0.583037
$367$	−3.98841e6	−1.54573	−0.772867	−	0.634568i	$-0.781178\pi$
$367$	−3.98841e6	−1.54573	−0.772867	+	0.634568i	$0.781178\pi$
$368$	671356.	0.258424
$369$	−428355.	−0.163771
$370$	222565.	0.0845186
$371$	−3.82230e6	−1.44175
$372$	−1.20642e6	−0.452003
$373$	3.83713e6	1.42802	0.714010	−	0.700135i	$-0.246877\pi$
$373$	3.83713e6	1.42802	0.714010	+	0.700135i	$0.246877\pi$
$374$	−403501.	−0.149165
$375$	−547849.	−0.201179
$376$	1.00972e6	0.368325
$377$	145544.	0.0527402
$378$	−372951.	−0.134252
$379$	670319.	0.239708	0.119854	−	0.992792i	$-0.461757\pi$
$379$	670319.	0.239708	0.119854	+	0.992792i	$0.461757\pi$
$380$	75949.3	0.0269814
$381$	−2.40593e6	−0.849124
$382$	618706.	0.216933
$383$	−4.61089e6	−1.60616	−0.803078	−	0.595873i	$-0.796806\pi$
$383$	−4.61089e6	−1.60616	−0.803078	+	0.595873i	$0.796806\pi$
$384$	147456.	0.0510310
$385$	128401.	0.0441487
$386$	−932466.	−0.318541
$387$	1.41511e6	0.480301
$388$	−316511.	−0.106736
$389$	−418648.	−0.140273	−0.0701366	−	0.997537i	$-0.522344\pi$
$389$	−418648.	−0.140273	−0.0701366	+	0.997537i	$0.522344\pi$
$390$	14152.9	0.00471176
$391$	2.60728e6	0.862473
$392$	28740.5	0.00944669
$393$	2.30394e6	0.752472
$394$	−2.58164e6	−0.837828
$395$	465494.	0.150114
$396$	131497.	0.0421383
$397$	3.47840e6	1.10765	0.553826	−	0.832632i	$-0.313167\pi$
$397$	3.47840e6	1.10765	0.553826	+	0.832632i	$0.313167\pi$
$398$	4.21434e6	1.33359
$399$	−552224.	−0.173653
$400$	−774937.	−0.242168
$401$	2.53861e6	0.788379	0.394190	−	0.919029i	$-0.371025\pi$
$401$	2.53861e6	0.788379	0.394190	+	0.919029i	$0.371025\pi$
$402$	−2.62215e6	−0.809269
$403$	−332877.	−0.102099
$404$	−2.14375e6	−0.653464
$405$	−64918.0	−0.0196665
$406$	−1.87401e6	−0.564232
$407$	570574.	0.170736
$408$	572660.	0.170313
$409$	−4.03886e6	−1.19385	−0.596926	−	0.802296i	$-0.703611\pi$
$409$	−4.03886e6	−1.19385	−0.596926	+	0.802296i	$0.703611\pi$
$410$	−209302.	−0.0614914
$411$	−604124.	−0.176409
$412$	−1.91574e6	−0.556025
$413$	445213.	0.128438
$414$	−849685.	−0.243645
$415$	1.23310e6	0.351462
$416$	40686.2	0.0115269
$417$	−936388.	−0.263703
$418$	194706.	0.0545052
$419$	−3.24820e6	−0.903874	−0.451937	−	0.892050i	$-0.649267\pi$
$419$	−3.24820e6	−0.903874	−0.451937	+	0.892050i	$0.649267\pi$
$420$	−182231.	−0.0504079
$421$	−6.23050e6	−1.71324	−0.856619	−	0.515950i	$-0.827439\pi$
$421$	−6.23050e6	−1.71324	−0.856619	+	0.515950i	$0.827439\pi$
$422$	3.02051e6	0.825657
$423$	−1.27793e6	−0.347260
$424$	−1.91267e6	−0.516686
$425$	−3.00955e6	−0.808218
$426$	1.34545e6	0.359207
$427$	−5.30836e6	−1.40893
$428$	−2.66255e6	−0.702568
$429$	36282.7	0.00951824
$430$	691451.	0.180339
$431$	−3.74967e6	−0.972300	−0.486150	−	0.873875i	$-0.661599\pi$
$431$	−3.74967e6	−0.972300	−0.486150	+	0.873875i	$0.661599\pi$
$432$	−186624.	−0.0481125
$433$	−2.83760e6	−0.727331	−0.363665	−	0.931530i	$-0.618475\pi$
$433$	−2.83760e6	−0.727331	−0.363665	+	0.931530i	$0.618475\pi$
$434$	4.28608e6	1.09229
$435$	−326202.	−0.0826538
$436$	478345.	0.120511
$437$	−1.25812e6	−0.315150
$438$	2.14441e6	0.534101
$439$	−7.31609e6	−1.81183	−0.905915	−	0.423459i	$-0.860816\pi$
$439$	−7.31609e6	−1.81183	−0.905915	+	0.423459i	$0.860816\pi$
$440$	64251.9	0.0158217
$441$	−36374.7	−0.00890643
$442$	158009.	0.0384703
$443$	927328.	0.224504	0.112252	−	0.993680i	$-0.464194\pi$
$443$	927328.	0.224504	0.112252	+	0.993680i	$0.464194\pi$
$444$	−809774.	−0.194943
$445$	848923.	0.203221
$446$	−4.27201e6	−1.01694
$447$	602919.	0.142722
$448$	−523871.	−0.123319
$449$	3.99770e6	0.935825	0.467913	−	0.883775i	$-0.345006\pi$
$449$	3.99770e6	0.935825	0.467913	+	0.883775i	$0.345006\pi$
$450$	980780.	0.228318
$451$	−536574.	−0.124219
$452$	−1.15701e6	−0.266374
$453$	2.99025e6	0.684640
$454$	−4.41601e6	−1.00552
$455$	−50281.3	−0.0113862
$456$	−276332.	−0.0622327
$457$	3.04010e6	0.680922	0.340461	−	0.940259i	$-0.389417\pi$
$457$	3.04010e6	0.680922	0.340461	+	0.940259i	$0.389417\pi$
$458$	−2.82504e6	−0.629305
$459$	−724773.	−0.160572
$460$	−415172.	−0.0914816
$461$	−1.10200e6	−0.241507	−0.120753	−	0.992683i	$-0.538531\pi$
$461$	−1.10200e6	−0.241507	−0.120753	+	0.992683i	$0.538531\pi$
$462$	−467172.	−0.101829
$463$	−9.13646e6	−1.98073	−0.990365	−	0.138479i	$-0.955779\pi$
$463$	−9.13646e6	−1.98073	−0.990365	+	0.138479i	$0.955779\pi$
$464$	−937753.	−0.202206
$465$	746061.	0.160008
$466$	2.69646e6	0.575214
$467$	184302.	0.0391055	0.0195528	−	0.999809i	$-0.493776\pi$
$467$	184302.	0.0391055	0.0195528	+	0.999809i	$0.493776\pi$
$468$	−51493.5	−0.0108677
$469$	9.31579e6	1.95563
$470$	−624418.	−0.130386
$471$	1.24166e6	0.257899
$472$	222784.	0.0460287
$473$	1.77262e6	0.364304
$474$	−1.69364e6	−0.346239
$475$	1.45223e6	0.295326
$476$	−2.03450e6	−0.411568
$477$	2.42073e6	0.487136
$478$	2.85384e6	0.571295
$479$	3.79385e6	0.755511	0.377756	−	0.925905i	$-0.376696\pi$
$479$	3.79385e6	0.755511	0.377756	+	0.925905i	$0.376696\pi$
$480$	−91188.0	−0.0180649
$481$	−223434.	−0.0440338
$482$	−6.25163e6	−1.22568
$483$	3.01870e6	0.588778
$484$	−2.41210e6	−0.468038
$485$	195733.	0.0377841
$486$	236196.	0.0453609
$487$	7.64336e6	1.46037	0.730183	−	0.683251i	$-0.239435\pi$
$487$	7.64336e6	1.46037	0.730183	+	0.683251i	$0.239435\pi$
$488$	−2.65629e6	−0.504925
$489$	−1.69415e6	−0.320391
$490$	−17773.4	−0.00334411
$491$	−950703.	−0.177968	−0.0889838	−	0.996033i	$-0.528362\pi$
$491$	−950703.	−0.177968	−0.0889838	+	0.996033i	$0.528362\pi$
$492$	761520.	0.141830
$493$	−3.64186e6	−0.674847
$494$	−76245.7	−0.0140572
$495$	−81318.8	−0.0149169
$496$	2.14475e6	0.391446
$497$	−4.78003e6	−0.868039
$498$	−4.48648e6	−0.810648
$499$	−3.59772e6	−0.646809	−0.323404	−	0.946261i	$-0.604827\pi$
$499$	−3.59772e6	−0.646809	−0.323404	+	0.946261i	$0.604827\pi$
$500$	973954.	0.174226
$501$	4.69716e6	0.836068
$502$	3.36483e6	0.595942
$503$	4.71522e6	0.830964	0.415482	−	0.909601i	$-0.363613\pi$
$503$	4.71522e6	0.830964	0.415482	+	0.909601i	$0.363613\pi$
$504$	663024.	0.116266
$505$	1.32571e6	0.231325
$506$	−1.06435e6	−0.184802
$507$	3.32743e6	0.574895
$508$	4.27721e6	0.735363
$509$	6.49637e6	1.11142	0.555708	−	0.831378i	$-0.312447\pi$
$509$	6.49637e6	1.11142	0.555708	+	0.831378i	$0.312447\pi$
$510$	−354138.	−0.0602902
$511$	−7.61852e6	−1.29068
$512$	−262144.	−0.0441942
$513$	349733.	0.0586736
$514$	805472.	0.134475
$515$	1.18471e6	0.196831
$516$	−2.51576e6	−0.415953
$517$	−1.60078e6	−0.263393
$518$	2.87691e6	0.471087
$519$	−360944.	−0.0588194
$520$	−25160.7	−0.00408051
$521$	1.11103e7	1.79321	0.896605	−	0.442832i	$-0.146026\pi$
$521$	1.11103e7	1.79321	0.896605	+	0.442832i	$0.146026\pi$
$522$	1.18684e6	0.190641
$523$	−3.89188e6	−0.622165	−0.311082	−	0.950383i	$-0.600691\pi$
$523$	−3.89188e6	−0.622165	−0.311082	+	0.950383i	$0.600691\pi$
$524$	−4.09590e6	−0.651660
$525$	−3.48444e6	−0.551741
$526$	2.52913e6	0.398573
$527$	8.32935e6	1.30643
$528$	−233772.	−0.0364929
$529$	441083.	0.0685300
$530$	1.18281e6	0.182905
$531$	−281961.	−0.0433963
$532$	981731.	0.150388
$533$	210119.	0.0320367
$534$	−3.08870e6	−0.468730
$535$	1.64654e6	0.248707
$536$	4.66160e6	0.700847
$537$	492048.	0.0736329
$538$	2.26684e6	0.337649
$539$	−45564.4	−0.00675544
$540$	115410.	0.0170317
$541$	3.55799e6	0.522650	0.261325	−	0.965251i	$-0.415840\pi$
$541$	3.55799e6	0.522650	0.261325	+	0.965251i	$0.415840\pi$
$542$	−4.68676e6	−0.685290
$543$	−2.23930e6	−0.325922
$544$	−1.01806e6	−0.147495
$545$	−295813.	−0.0426605
$546$	182942.	0.0262623
$547$	6.42512e6	0.918149	0.459074	−	0.888398i	$-0.348181\pi$
$547$	6.42512e6	0.918149	0.459074	+	0.888398i	$0.348181\pi$
$548$	1.07400e6	0.152775
$549$	3.36187e6	0.476047
$550$	1.22856e6	0.173177
$551$	1.75734e6	0.246591
$552$	1.51055e6	0.211003
$553$	6.01705e6	0.836701
$554$	−1.45488e6	−0.201397
$555$	500771.	0.0690092
$556$	1.66469e6	0.228374
$557$	−1.04921e7	−1.43293	−0.716463	−	0.697625i	$-0.754240\pi$
$557$	−1.04921e7	−1.43293	−0.716463	+	0.697625i	$0.754240\pi$
$558$	−2.71445e6	−0.369059
$559$	−694150.	−0.0939559
$560$	323966.	0.0436545
$561$	−907878.	−0.121792
$562$	−8.72515e6	−1.16528
$563$	−8.88837e6	−1.18182	−0.590910	−	0.806738i	$-0.701231\pi$
$563$	−8.88837e6	−1.18182	−0.590910	+	0.806738i	$0.701231\pi$
$564$	2.27187e6	0.300736
$565$	715505.	0.0942957
$566$	−5.55939e6	−0.729434
$567$	−839140.	−0.109617
$568$	−2.39192e6	−0.311082
$569$	2.60182e6	0.336897	0.168448	−	0.985710i	$-0.446124\pi$
$569$	2.60182e6	0.336897	0.168448	+	0.985710i	$0.446124\pi$
$570$	170886.	0.0220302
$571$	6.74309e6	0.865503	0.432752	−	0.901513i	$-0.357543\pi$
$571$	6.74309e6	0.865503	0.432752	+	0.901513i	$0.357543\pi$
$572$	−64502.7	−0.00824304
$573$	1.39209e6	0.177125
$574$	−2.70547e6	−0.342739
$575$	−7.93852e6	−1.00131
$576$	331776.	0.0416667
$577$	−8.99008e6	−1.12415	−0.562074	−	0.827087i	$-0.689997\pi$
$577$	−8.99008e6	−1.12415	−0.562074	+	0.827087i	$0.689997\pi$
$578$	1.72568e6	0.214853
$579$	−2.09805e6	−0.260087
$580$	579914.	0.0715803
$581$	1.59392e7	1.95897
$582$	−712149.	−0.0871493
$583$	3.03230e6	0.369488
$584$	−3.81229e6	−0.462545
$585$	31844.0	0.00384714
$586$	1.02587e7	1.23409
$587$	−1.00623e7	−1.20532	−0.602658	−	0.797999i	$-0.705892\pi$
$587$	−1.00623e7	−1.20532	−0.602658	+	0.797999i	$0.705892\pi$
$588$	64666.2	0.00771319
$589$	−4.01925e6	−0.477372
$590$	−137771.	−0.0162941
$591$	−5.80868e6	−0.684083
$592$	1.43960e6	0.168825
$593$	1.10411e7	1.28937	0.644684	−	0.764449i	$-0.276989\pi$
$593$	1.10411e7	1.28937	0.644684	+	0.764449i	$0.276989\pi$
$594$	295868.	0.0344058
$595$	1.25815e6	0.145694
$596$	−1.07186e6	−0.123601
$597$	9.48226e6	1.08887
$598$	416793.	0.0476614
$599$	−1.11931e7	−1.27463	−0.637314	−	0.770604i	$-0.719954\pi$
$599$	−1.11931e7	−1.27463	−0.637314	+	0.770604i	$0.719954\pi$
$600$	−1.74361e6	−0.197729
$601$	−1.58301e7	−1.78771	−0.893856	−	0.448355i	$-0.852010\pi$
$601$	−1.58301e7	−1.78771	−0.893856	+	0.448355i	$0.852010\pi$
$602$	8.93780e6	1.00517
$603$	−5.89984e6	−0.660765
$604$	−5.31600e6	−0.592916
$605$	1.49166e6	0.165684
$606$	−4.82344e6	−0.533551
$607$	2.08192e6	0.229347	0.114674	−	0.993403i	$-0.463418\pi$
$607$	2.08192e6	0.229347	0.114674	+	0.993403i	$0.463418\pi$
$608$	491257.	0.0538951
$609$	−4.21653e6	−0.460693
$610$	1.64267e6	0.178742
$611$	626856.	0.0679305
$612$	1.28849e6	0.139060
$613$	−6.67368e6	−0.717322	−0.358661	−	0.933468i	$-0.616767\pi$
$613$	−6.67368e6	−0.717322	−0.358661	+	0.933468i	$0.616767\pi$
$614$	−6.25912e6	−0.670027
$615$	−470931.	−0.0502076
$616$	830529.	0.0881866
$617$	6.45622e6	0.682756	0.341378	−	0.939926i	$-0.389106\pi$
$617$	6.45622e6	0.682756	0.341378	+	0.939926i	$0.389106\pi$
$618$	−4.31042e6	−0.453992
$619$	1.36659e6	0.143355	0.0716776	−	0.997428i	$-0.477165\pi$
$619$	1.36659e6	0.143355	0.0716776	+	0.997428i	$0.477165\pi$
$620$	−1.32633e6	−0.138571
$621$	−1.91179e6	−0.198935
$622$	3.06484e6	0.317638
$623$	1.09733e7	1.13271
$624$	91543.9	0.00941170
$625$	8.85738e6	0.906996
$626$	−2.65894e6	−0.271189
$627$	438088.	0.0445033
$628$	−2.20739e6	−0.223347
$629$	5.59083e6	0.563442
$630$	−410019.	−0.0411579
$631$	8.39810e6	0.839669	0.419834	−	0.907601i	$-0.362088\pi$
$631$	8.39810e6	0.839669	0.419834	+	0.907601i	$0.362088\pi$
$632$	3.01092e6	0.299852
$633$	6.79615e6	0.674146
$634$	1.31263e7	1.29694
$635$	−2.64506e6	−0.260317
$636$	−4.30352e6	−0.421872
$637$	17842.8	0.00174226
$638$	1.48668e6	0.144600
$639$	3.02727e6	0.293291
$640$	162112.	0.0156446
$641$	−1.11476e7	−1.07161	−0.535803	−	0.844343i	$-0.679991\pi$
$641$	−1.11476e7	−1.07161	−0.535803	+	0.844343i	$0.679991\pi$
$642$	−5.99074e6	−0.573645
$643$	−4.48334e6	−0.427636	−0.213818	−	0.976874i	$-0.568590\pi$
$643$	−4.48334e6	−0.427636	−0.213818	+	0.976874i	$0.568590\pi$
$644$	−5.36657e6	−0.509897
$645$	1.55577e6	0.147246
$646$	1.90784e6	0.179871
$647$	1.44601e7	1.35803	0.679016	−	0.734124i	$-0.262407\pi$
$647$	1.44601e7	1.35803	0.679016	+	0.734124i	$0.262407\pi$
$648$	−419904.	−0.0392837
$649$	−353195.	−0.0329157
$650$	−481098.	−0.0446632
$651$	9.64369e6	0.891848
$652$	3.01183e6	0.277467
$653$	−4.62962e6	−0.424876	−0.212438	−	0.977175i	$-0.568140\pi$
$653$	−4.62962e6	−0.424876	−0.212438	+	0.977175i	$0.568140\pi$
$654$	1.07628e6	0.0983965
$655$	2.53294e6	0.230686
$656$	−1.35381e6	−0.122829
$657$	4.82493e6	0.436092
$658$	−8.07132e6	−0.726741
$659$	6.94837e6	0.623260	0.311630	−	0.950203i	$-0.399125\pi$
$659$	6.94837e6	0.623260	0.311630	+	0.950203i	$0.399125\pi$
$660$	144567.	0.0129184
$661$	2.46263e6	0.219228	0.109614	−	0.993974i	$-0.465039\pi$
$661$	2.46263e6	0.219228	0.109614	+	0.993974i	$0.465039\pi$
$662$	−879290.	−0.0779807
$663$	355520.	0.0314109
$664$	7.97596e6	0.702042
$665$	−607111.	−0.0532370
$666$	−1.82199e6	−0.159170
$667$	−9.60641e6	−0.836078
$668$	−8.35052e6	−0.724056
$669$	−9.61202e6	−0.830327
$670$	−2.88277e6	−0.248098
$671$	4.21121e6	0.361077
$672$	−1.17871e6	−0.100689
$673$	7.21308e6	0.613879	0.306940	−	0.951729i	$-0.400695\pi$
$673$	7.21308e6	0.613879	0.306940	+	0.951729i	$0.400695\pi$
$674$	−8.15906e6	−0.691815
$675$	2.20675e6	0.186421
$676$	−5.91543e6	−0.497874
$677$	−2.55470e6	−0.214224	−0.107112	−	0.994247i	$-0.534160\pi$
$677$	−2.55470e6	−0.214224	−0.107112	+	0.994247i	$0.534160\pi$
$678$	−2.60328e6	−0.217493
$679$	2.53007e6	0.210600
$680$	629578.	0.0522129
$681$	−9.93602e6	−0.821003
$682$	−3.40022e6	−0.279928
$683$	4.87856e6	0.400165	0.200083	−	0.979779i	$-0.435879\pi$
$683$	4.87856e6	0.400165	0.200083	+	0.979779i	$0.435879\pi$
$684$	−621747.	−0.0508128
$685$	−664170.	−0.0540820
$686$	−8.82808e6	−0.716235
$687$	−6.35635e6	−0.513825
$688$	4.47246e6	0.360226
$689$	−1.18743e6	−0.0952928
$690$	−934137.	−0.0746944
$691$	−1.34776e7	−1.07378	−0.536892	−	0.843651i	$-0.680402\pi$
$691$	−1.34776e7	−1.07378	−0.536892	+	0.843651i	$0.680402\pi$
$692$	641677.	0.0509391
$693$	−1.05114e6	−0.0831432
$694$	−1.11722e6	−0.0880525
$695$	−1.02946e6	−0.0808438
$696$	−2.10994e6	−0.165100
$697$	−5.25767e6	−0.409932
$698$	1.57399e7	1.22282
$699$	6.06704e6	0.469660
$700$	6.19456e6	0.477821
$701$	−1.15500e7	−0.887740	−0.443870	−	0.896091i	$-0.646395\pi$
$701$	−1.15500e7	−0.887740	−0.443870	+	0.896091i	$0.646395\pi$
$702$	−115860.	−0.00887344
$703$	−2.69780e6	−0.205884
$704$	415595.	0.0316038
$705$	−1.40494e6	−0.106460
$706$	−1.78715e7	−1.34943
$707$	1.71364e7	1.28935
$708$	501264.	0.0375823
$709$	2.43991e6	0.182288	0.0911439	−	0.995838i	$-0.470948\pi$
$709$	2.43991e6	0.182288	0.0911439	+	0.995838i	$0.470948\pi$
$710$	1.47918e6	0.110122
$711$	−3.81070e6	−0.282703
$712$	5.49102e6	0.405932
$713$	2.19710e7	1.61855
$714$	−4.57763e6	−0.336044
$715$	39889.0	0.00291802
$716$	−874752.	−0.0637680
$717$	6.42114e6	0.466460
$718$	1.70197e7	1.23208
$719$	1.57071e7	1.13312	0.566558	−	0.824022i	$-0.308275\pi$
$719$	1.57071e7	1.13312	0.566558	+	0.824022i	$0.308275\pi$
$720$	−205173.	−0.0147499
$721$	1.53137e7	1.09709
$722$	8.98378e6	0.641381
$723$	−1.40662e7	−1.00076
$724$	3.98098e6	0.282257
$725$	1.10886e7	0.783483
$726$	−5.42722e6	−0.382152
$727$	1.24913e7	0.876542	0.438271	−	0.898843i	$-0.355591\pi$
$727$	1.24913e7	0.876542	0.438271	+	0.898843i	$0.355591\pi$
$728$	−325230.	−0.0227438
$729$	531441.	0.0370370
$730$	2.35755e6	0.163740
$731$	1.73692e7	1.20223
$732$	−5.97666e6	−0.412269
$733$	4.76967e6	0.327890	0.163945	−	0.986469i	$-0.447578\pi$
$733$	4.76967e6	0.327890	0.163945	+	0.986469i	$0.447578\pi$
$734$	1.59536e7	1.09300
$735$	−39990.1	−0.00273045
$736$	−2.68542e6	−0.182734
$737$	−7.39036e6	−0.501184
$738$	1.71342e6	0.115804
$739$	5.84320e6	0.393586	0.196793	−	0.980445i	$-0.436947\pi$
$739$	5.84320e6	0.393586	0.196793	+	0.980445i	$0.436947\pi$
$740$	−890260.	−0.0597637
$741$	−171553.	−0.0114776
$742$	1.52892e7	1.01947
$743$	−1.75343e7	−1.16524	−0.582620	−	0.812745i	$-0.697972\pi$
$743$	−1.75343e7	−1.16524	−0.582620	+	0.812745i	$0.697972\pi$
$744$	4.82569e6	0.319615
$745$	662844.	0.0437543
$746$	−1.53485e7	−1.00976
$747$	−1.00946e7	−0.661891
$748$	1.61401e6	0.105475
$749$	2.12835e7	1.38624
$750$	2.19140e6	0.142255
$751$	−2.05590e7	−1.33016	−0.665078	−	0.746774i	$-0.731602\pi$
$751$	−2.05590e7	−1.33016	−0.665078	+	0.746774i	$0.731602\pi$
$752$	−4.03888e6	−0.260445
$753$	7.57087e6	0.486585
$754$	−582178.	−0.0372930
$755$	3.28746e6	0.209891
$756$	1.49180e6	0.0949308
$757$	−6.79184e6	−0.430772	−0.215386	−	0.976529i	$-0.569101\pi$
$757$	−6.79184e6	−0.430772	−0.215386	+	0.976529i	$0.569101\pi$
$758$	−2.68127e6	−0.169499
$759$	−2.39478e6	−0.150890
$760$	−303797.	−0.0190787
$761$	3.84017e6	0.240375	0.120187	−	0.992751i	$-0.461650\pi$
$761$	3.84017e6	0.240375	0.120187	+	0.992751i	$0.461650\pi$
$762$	9.62373e6	0.600421
$763$	−3.82372e6	−0.237780
$764$	−2.47483e6	−0.153395
$765$	−796810.	−0.0492268
$766$	1.84436e7	1.13572
$767$	138309.	0.00848912
$768$	−589824.	−0.0360844
$769$	1.59227e7	0.970958	0.485479	−	0.874248i	$-0.338645\pi$
$769$	1.59227e7	0.970958	0.485479	+	0.874248i	$0.338645\pi$
$770$	−513606.	−0.0312179
$771$	1.81231e6	0.109799
$772$	3.72987e6	0.225242
$773$	−1.29273e7	−0.778140	−0.389070	−	0.921208i	$-0.627204\pi$
$773$	−1.29273e7	−0.778140	−0.389070	+	0.921208i	$0.627204\pi$
$774$	−5.66045e6	−0.339624
$775$	−2.53608e7	−1.51673
$776$	1.26604e6	0.0754735
$777$	6.47304e6	0.384641
$778$	1.67459e6	0.0991881
$779$	2.53704e6	0.149790
$780$	−56611.5	−0.00333172
$781$	3.79207e6	0.222459
$782$	−1.04291e7	−0.609861
$783$	2.67040e6	0.155658
$784$	−114962.	−0.00667982
$785$	1.36507e6	0.0790642
$786$	−9.21577e6	−0.532078
$787$	−5.03670e6	−0.289874	−0.144937	−	0.989441i	$-0.546298\pi$
$787$	−5.03670e6	−0.289874	−0.144937	+	0.989441i	$0.546298\pi$
$788$	1.03266e7	0.592434
$789$	5.69055e6	0.325433
$790$	−1.86198e6	−0.106147
$791$	9.24872e6	0.525582
$792$	−525988.	−0.0297963
$793$	−1.64909e6	−0.0931237
$794$	−1.39136e7	−0.783228
$795$	2.66133e6	0.149342
$796$	−1.68573e7	−0.942989
$797$	1.97261e7	1.10000	0.550002	−	0.835163i	$-0.314627\pi$
$797$	1.97261e7	1.10000	0.550002	+	0.835163i	$0.314627\pi$
$798$	2.20890e6	0.122791
$799$	−1.56854e7	−0.869217
$800$	3.09975e6	0.171239
$801$	−6.94957e6	−0.382716
$802$	−1.01544e7	−0.557468
$803$	6.04389e6	0.330771
$804$	1.04886e7	0.572239
$805$	3.31873e6	0.180502
$806$	1.33151e6	0.0721948
$807$	5.10040e6	0.275689
$808$	8.57501e6	0.462069
$809$	3.30421e7	1.77499	0.887497	−	0.460814i	$-0.152442\pi$
$809$	3.30421e7	1.77499	0.887497	+	0.460814i	$0.152442\pi$
$810$	259672.	0.0139063
$811$	1.81419e7	0.968570	0.484285	−	0.874910i	$-0.339080\pi$
$811$	1.81419e7	0.968570	0.484285	+	0.874910i	$0.339080\pi$
$812$	7.49605e6	0.398972
$813$	−1.05452e7	−0.559537
$814$	−2.28230e6	−0.120729
$815$	−1.86254e6	−0.0982227
$816$	−2.29064e6	−0.120429
$817$	−8.38137e6	−0.439298
$818$	1.61554e7	0.844181
$819$	411620.	0.0214430
$820$	837210.	0.0434810
$821$	−1.58973e7	−0.823125	−0.411562	−	0.911382i	$-0.635017\pi$
$821$	−1.58973e7	−0.823125	−0.411562	+	0.911382i	$0.635017\pi$
$822$	2.41650e6	0.124740
$823$	−2.01823e7	−1.03866	−0.519328	−	0.854575i	$-0.673818\pi$
$823$	−2.01823e7	−1.03866	−0.519328	+	0.854575i	$0.673818\pi$
$824$	7.66297e6	0.393169
$825$	2.76426e6	0.141398
$826$	−1.78085e6	−0.0908193
$827$	1.85607e6	0.0943695	0.0471847	−	0.998886i	$-0.484975\pi$
$827$	1.85607e6	0.0943695	0.0471847	+	0.998886i	$0.484975\pi$
$828$	3.39874e6	0.172283
$829$	7.99898e6	0.404248	0.202124	−	0.979360i	$-0.435216\pi$
$829$	7.99898e6	0.404248	0.202124	+	0.979360i	$0.435216\pi$
$830$	−4.93240e6	−0.248521
$831$	−3.27348e6	−0.164440
$832$	−162745.	−0.00815077
$833$	−446467.	−0.0222934
$834$	3.74555e6	0.186466
$835$	5.16403e6	0.256314
$836$	−778823.	−0.0385410
$837$	−6.10751e6	−0.301336
$838$	1.29928e7	0.639135
$839$	−3.54479e7	−1.73855	−0.869273	−	0.494333i	$-0.835412\pi$
$839$	−3.54479e7	−1.73855	−0.869273	+	0.494333i	$0.835412\pi$
$840$	728923.	0.0356438
$841$	−7.09287e6	−0.345806
$842$	2.49220e7	1.21144
$843$	−1.96316e7	−0.951451
$844$	−1.20821e7	−0.583827
$845$	3.65815e6	0.176246
$846$	5.11170e6	0.245550
$847$	1.92814e7	0.923487
$848$	7.65070e6	0.365352
$849$	−1.25086e7	−0.595580
$850$	1.20382e7	0.571497
$851$	1.47474e7	0.698056
$852$	−5.38181e6	−0.253998
$853$	−9.29249e6	−0.437280	−0.218640	−	0.975806i	$-0.570162\pi$
$853$	−9.29249e6	−0.437280	−0.218640	+	0.975806i	$0.570162\pi$
$854$	2.12334e7	0.996266
$855$	384493.	0.0179876
$856$	1.06502e7	0.496791
$857$	−2.38636e7	−1.10990	−0.554951	−	0.831883i	$-0.687263\pi$
$857$	−2.38636e7	−1.10990	−0.554951	+	0.831883i	$0.687263\pi$
$858$	−145131.	−0.00673042
$859$	−2.11086e7	−0.976061	−0.488031	−	0.872826i	$-0.662285\pi$
$859$	−2.11086e7	−0.976061	−0.488031	+	0.872826i	$0.662285\pi$
$860$	−2.76581e6	−0.127519
$861$	−6.08731e6	−0.279845
$862$	1.49987e7	0.687520
$863$	3.60663e7	1.64845	0.824223	−	0.566265i	$-0.191612\pi$
$863$	3.60663e7	1.64845	0.824223	+	0.566265i	$0.191612\pi$
$864$	746496.	0.0340207
$865$	−396819.	−0.0180323
$866$	1.13504e7	0.514301
$867$	3.88278e6	0.175426
$868$	−1.71443e7	−0.772363
$869$	−4.77342e6	−0.214427
$870$	1.30481e6	0.0584451
$871$	2.89403e6	0.129258
$872$	−1.91338e6	−0.0852139
$873$	−1.60234e6	−0.0711571
$874$	5.03247e6	0.222845
$875$	−7.78543e6	−0.343766
$876$	−8.57766e6	−0.377666
$877$	2.15647e7	0.946769	0.473384	−	0.880856i	$-0.343032\pi$
$877$	2.15647e7	0.946769	0.473384	+	0.880856i	$0.343032\pi$
$878$	2.92644e7	1.28116
$879$	2.30820e7	1.00763
$880$	−257007.	−0.0111877
$881$	−4.25473e7	−1.84685	−0.923426	−	0.383778i	$-0.874623\pi$
$881$	−4.25473e7	−1.84685	−0.923426	+	0.383778i	$0.874623\pi$
$882$	145499.	0.00629779
$883$	−2.49675e7	−1.07764	−0.538820	−	0.842421i	$-0.681130\pi$
$883$	−2.49675e7	−1.07764	−0.538820	+	0.842421i	$0.681130\pi$
$884$	−632036.	−0.0272026
$885$	−309986.	−0.0133040
$886$	−3.70931e6	−0.158748
$887$	−2.79339e7	−1.19213	−0.596064	−	0.802937i	$-0.703270\pi$
$887$	−2.79339e7	−1.19213	−0.596064	+	0.802937i	$0.703270\pi$
$888$	3.23910e6	0.137845
$889$	−3.41905e7	−1.45094
$890$	−3.39569e6	−0.143699
$891$	665703.	0.0280922
$892$	1.70880e7	0.719084
$893$	7.56883e6	0.317615
$894$	−2.41167e6	−0.100919
$895$	540954.	0.0225737
$896$	2.09548e6	0.0871995
$897$	937783.	0.0389154
$898$	−1.59908e7	−0.661728
$899$	−3.06892e7	−1.26644
$900$	−3.92312e6	−0.161445
$901$	2.97122e7	1.21934
$902$	2.14630e6	0.0878361
$903$	2.01100e7	0.820717
$904$	4.62804e6	0.188355
$905$	−2.46187e6	−0.0999181
$906$	−1.19610e7	−0.484114
$907$	1.94961e7	0.786920	0.393460	−	0.919342i	$-0.371278\pi$
$907$	1.94961e7	0.786920	0.393460	+	0.919342i	$0.371278\pi$
$908$	1.76640e7	0.711010
$909$	−1.08528e7	−0.435642
$910$	201125.	0.00805125
$911$	1.10405e7	0.440749	0.220375	−	0.975415i	$-0.429272\pi$
$911$	1.10405e7	0.440749	0.220375	+	0.975415i	$0.429272\pi$
$912$	1.10533e6	0.0440052
$913$	−1.26448e7	−0.502038
$914$	−1.21604e7	−0.481484
$915$	3.69602e6	0.145942
$916$	1.13002e7	0.444986
$917$	3.27411e7	1.28579
$918$	2.89909e6	0.113542
$919$	−2.05689e7	−0.803381	−0.401691	−	0.915775i	$-0.631577\pi$
$919$	−2.05689e7	−0.803381	−0.401691	+	0.915775i	$0.631577\pi$
$920$	1.66069e6	0.0646872
$921$	−1.40830e7	−0.547075
$922$	4.40800e6	0.170771
$923$	−1.48496e6	−0.0573732
$924$	1.86869e6	0.0720041
$925$	−1.70227e7	−0.654144
$926$	3.65458e7	1.40059
$927$	−9.69844e6	−0.370683
$928$	3.75101e6	0.142981
$929$	−2.52687e7	−0.960601	−0.480301	−	0.877104i	$-0.659472\pi$
$929$	−2.52687e7	−0.960601	−0.480301	+	0.877104i	$0.659472\pi$
$930$	−2.98424e6	−0.113143
$931$	215439.	0.00814609
$932$	−1.07858e7	−0.406738
$933$	6.89589e6	0.259350
$934$	−737208.	−0.0276518
$935$	−998114.	−0.0373380
$936$	205974.	0.00768462
$937$	−1.95081e7	−0.725883	−0.362941	−	0.931812i	$-0.618227\pi$
$937$	−1.95081e7	−0.725883	−0.362941	+	0.931812i	$0.618227\pi$
$938$	−3.72631e7	−1.38284
$939$	−5.98261e6	−0.221425
$940$	2.49767e6	0.0921968
$941$	8.65323e6	0.318570	0.159285	−	0.987233i	$-0.449081\pi$
$941$	8.65323e6	0.318570	0.159285	+	0.987233i	$0.449081\pi$
$942$	−4.96662e6	−0.182362
$943$	−1.38686e7	−0.507870
$944$	−891136.	−0.0325472
$945$	−922544.	−0.0336053
$946$	−7.09050e6	−0.257602
$947$	−8.77490e6	−0.317956	−0.158978	−	0.987282i	$-0.550820\pi$
$947$	−8.77490e6	−0.317956	−0.158978	+	0.987282i	$0.550820\pi$
$948$	6.77457e6	0.244828
$949$	−2.36676e6	−0.0853076
$950$	−5.80892e6	−0.208827
$951$	2.95343e7	1.05895
$952$	8.13802e6	0.291022
$953$	2.25828e7	0.805464	0.402732	−	0.915318i	$-0.368061\pi$
$953$	2.25828e7	0.805464	0.402732	+	0.915318i	$0.368061\pi$
$954$	−9.68291e6	−0.344457
$955$	1.53045e6	0.0543015
$956$	−1.14154e7	−0.403966
$957$	3.34504e6	0.118065
$958$	−1.51754e7	−0.534227
$959$	−8.58515e6	−0.301440
$960$	364752.	0.0127738
$961$	4.15605e7	1.45169
$962$	893735.	0.0311366
$963$	−1.34792e7	−0.468379
$964$	2.50065e7	0.866684
$965$	−2.30658e6	−0.0797352
$966$	−1.20748e7	−0.416329
$967$	−3.35996e7	−1.15550	−0.577748	−	0.816215i	$-0.696068\pi$
$967$	−3.35996e7	−1.15550	−0.577748	+	0.816215i	$0.696068\pi$
$968$	9.64839e6	0.330953
$969$	4.29265e6	0.146864
$970$	−782932.	−0.0267174
$971$	−4.70990e7	−1.60311	−0.801556	−	0.597920i	$-0.795994\pi$
$971$	−4.70990e7	−1.60311	−0.801556	+	0.597920i	$0.795994\pi$
$972$	−944784.	−0.0320750
$973$	−1.33069e7	−0.450604
$974$	−3.05734e7	−1.03264
$975$	−1.08247e6	−0.0364674
$976$	1.06252e7	0.357036
$977$	1.70976e6	0.0573058	0.0286529	−	0.999589i	$-0.490878\pi$
$977$	1.70976e6	0.0573058	0.0286529	+	0.999589i	$0.490878\pi$
$978$	6.77662e6	0.226551
$979$	−8.70530e6	−0.290287
$980$	71093.5	0.00236464
$981$	2.42162e6	0.0803404
$982$	3.80281e6	0.125842
$983$	−1.14970e7	−0.379490	−0.189745	−	0.981833i	$-0.560766\pi$
$983$	−1.14970e7	−0.379490	−0.189745	+	0.981833i	$0.560766\pi$
$984$	−3.04608e6	−0.100289
$985$	−6.38602e6	−0.209720
$986$	1.45674e7	0.477189
$987$	−1.81605e7	−0.593382
$988$	304983.	0.00993993
$989$	4.58162e7	1.48946
$990$	325275.	0.0105478
$991$	−4.53507e7	−1.46690	−0.733449	−	0.679745i	$-0.762090\pi$
$991$	−4.53507e7	−1.46690	−0.733449	+	0.679745i	$0.762090\pi$
$992$	−8.57900e6	−0.276794
$993$	−1.97840e6	−0.0636710
$994$	1.91201e7	0.613796
$995$	1.04247e7	0.333816
$996$	1.79459e7	0.573215
$997$	−3.25055e7	−1.03567	−0.517833	−	0.855482i	$-0.673261\pi$
$997$	−3.25055e7	−1.03567	−0.517833	+	0.855482i	$0.673261\pi$
$998$	1.43909e7	0.457363
$999$	−4.09948e6	−0.129962

Twists

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -9.89453 q^{5} +36.0000 q^{6} -127.898 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -9.89453 q^{5} +36.0000 q^{6} -127.898 q^{7} -64.0000 q^{8} +81.0000 q^{9} +39.5781 q^{10} +101.464 q^{11} -144.000 q^{12} -39.7326 q^{13} +511.592 q^{14} +89.0508 q^{15} +256.000 q^{16} +994.202 q^{17} -324.000 q^{18} -479.743 q^{19} -158.313 q^{20} +1151.08 q^{21} -405.855 q^{22} +2622.48 q^{23} +576.000 q^{24} -3027.10 q^{25} +158.930 q^{26} -729.000 q^{27} -2046.37 q^{28} -3663.10 q^{29} -356.203 q^{30} +8377.93 q^{31} -1024.00 q^{32} -913.173 q^{33} -3976.81 q^{34} +1265.49 q^{35} +1296.00 q^{36} +5623.43 q^{37} +1918.97 q^{38} +357.594 q^{39} +633.250 q^{40} -5288.34 q^{41} -4604.33 q^{42} +17470.5 q^{43} +1623.42 q^{44} -801.457 q^{45} -10489.9 q^{46} -15776.9 q^{47} -2304.00 q^{48} -449.071 q^{49} +12108.4 q^{50} -8947.81 q^{51} -635.722 q^{52} +29885.5 q^{53} +2916.00 q^{54} -1003.94 q^{55} +8185.48 q^{56} +4317.69 q^{57} +14652.4 q^{58} -3481.00 q^{59} +1424.81 q^{60} +41504.6 q^{61} -33511.7 q^{62} -10359.7 q^{63} +4096.00 q^{64} +393.136 q^{65} +3652.69 q^{66} -72837.5 q^{67} +15907.2 q^{68} -23602.4 q^{69} -5061.97 q^{70} +37373.7 q^{71} -5184.00 q^{72} +59567.1 q^{73} -22493.7 q^{74} +27243.9 q^{75} -7675.89 q^{76} -12977.0 q^{77} -1430.37 q^{78} -47045.6 q^{79} -2533.00 q^{80} +6561.00 q^{81} +21153.3 q^{82} -124624. q^{83} +18417.3 q^{84} -9837.16 q^{85} -69882.2 q^{86} +32967.9 q^{87} -6493.67 q^{88} -85797.2 q^{89} +3205.83 q^{90} +5081.73 q^{91} +41959.8 q^{92} -75401.3 q^{93} +63107.4 q^{94} +4746.83 q^{95} +9216.00 q^{96} -19781.9 q^{97} +1796.28 q^{98} +8218.56 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) \) 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

Introduction

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