LMFDB - Embedded newform 43.6.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.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:	$6.89650425196$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 $ x^8 - 4x^7 - 173x^6 + 462x^5 + 9118x^4 - 14192x^3 - 167688x^2 + 106368*x + 681984
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$7.21373$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.21373 q^{2} -11.2683 q^{3} -4.81697 q^{4} -9.80186 q^{5} -58.7500 q^{6} -11.1041 q^{7} -191.954 q^{8} -116.025 q^{9} +O(q^{10})$	\(q+5.21373 q^{2} -11.2683 q^{3} -4.81697 q^{4} -9.80186 q^{5} -58.7500 q^{6} -11.1041 q^{7} -191.954 q^{8} -116.025 q^{9} -51.1043 q^{10} -557.274 q^{11} +54.2791 q^{12} +107.663 q^{13} -57.8938 q^{14} +110.450 q^{15} -846.654 q^{16} +329.005 q^{17} -604.924 q^{18} +2938.10 q^{19} +47.2153 q^{20} +125.124 q^{21} -2905.48 q^{22} -385.537 q^{23} +2163.00 q^{24} -3028.92 q^{25} +561.326 q^{26} +4045.61 q^{27} +53.4881 q^{28} -3309.15 q^{29} +575.859 q^{30} -5471.71 q^{31} +1728.30 q^{32} +6279.54 q^{33} +1715.34 q^{34} +108.841 q^{35} +558.890 q^{36} +4832.22 q^{37} +15318.5 q^{38} -1213.18 q^{39} +1881.51 q^{40} +1065.16 q^{41} +652.365 q^{42} -1849.00 q^{43} +2684.37 q^{44} +1137.26 q^{45} -2010.09 q^{46} -8991.95 q^{47} +9540.36 q^{48} -16683.7 q^{49} -15792.0 q^{50} -3707.33 q^{51} -518.609 q^{52} -10216.7 q^{53} +21092.7 q^{54} +5462.32 q^{55} +2131.47 q^{56} -33107.4 q^{57} -17253.0 q^{58} -27457.0 q^{59} -532.036 q^{60} -36692.9 q^{61} -28528.1 q^{62} +1288.35 q^{63} +36103.8 q^{64} -1055.30 q^{65} +32739.9 q^{66} -26272.2 q^{67} -1584.81 q^{68} +4344.35 q^{69} +567.467 q^{70} +55130.3 q^{71} +22271.5 q^{72} -9315.14 q^{73} +25193.9 q^{74} +34130.9 q^{75} -14152.7 q^{76} +6188.02 q^{77} -6325.20 q^{78} +56826.5 q^{79} +8298.78 q^{80} -17393.1 q^{81} +5553.44 q^{82} -5858.19 q^{83} -602.721 q^{84} -3224.86 q^{85} -9640.20 q^{86} +37288.5 q^{87} +106971. q^{88} -42815.7 q^{89} +5929.38 q^{90} -1195.50 q^{91} +1857.12 q^{92} +61657.0 q^{93} -46881.7 q^{94} -28798.8 q^{95} -19475.0 q^{96} -231.671 q^{97} -86984.4 q^{98} +64657.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) $ 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9} - 617 q^{10} - 532 q^{11} - 4195 q^{12} - 2492 q^{13} - 4240 q^{14} - 1780 q^{15} + 1882 q^{16} - 2534 q^{17} - 3711 q^{18} - 1678 q^{19} - 2607 q^{20} - 2256 q^{21} + 11502 q^{22} - 2488 q^{23} + 19953 q^{24} + 4378 q^{25} + 4586 q^{26} - 8960 q^{27} + 18640 q^{28} - 4360 q^{29} + 25092 q^{30} + 5704 q^{31} - 18294 q^{32} - 12852 q^{33} + 30007 q^{34} + 5640 q^{35} + 67969 q^{36} - 3772 q^{37} - 6559 q^{38} + 11120 q^{39} + 14869 q^{40} - 10698 q^{41} + 78698 q^{42} - 14792 q^{43} - 356 q^{44} - 44912 q^{45} - 19389 q^{46} - 77864 q^{47} - 118727 q^{48} + 7188 q^{49} + 26877 q^{50} - 80246 q^{51} - 60736 q^{52} - 62352 q^{53} + 61026 q^{54} - 49552 q^{55} - 144528 q^{56} - 808 q^{57} + 52951 q^{58} - 26224 q^{59} + 101500 q^{60} - 82540 q^{61} - 9023 q^{62} - 61768 q^{63} + 153858 q^{64} - 5000 q^{65} - 48516 q^{66} + 27784 q^{67} + 40507 q^{68} - 93776 q^{69} + 185910 q^{70} - 9504 q^{71} - 186687 q^{72} + 14260 q^{73} - 15239 q^{74} + 167420 q^{75} + 1279 q^{76} - 218140 q^{77} + 264170 q^{78} + 160248 q^{79} - 1291 q^{80} + 161076 q^{81} - 47781 q^{82} - 77176 q^{83} + 16382 q^{84} + 141096 q^{85} + 22188 q^{86} + 268136 q^{87} + 129544 q^{88} - 265692 q^{89} + 48990 q^{90} + 401148 q^{91} + 190391 q^{92} - 123860 q^{93} + 248737 q^{94} + 135884 q^{95} + 950817 q^{96} + 144742 q^{97} - 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9 - 617 * q^10 - 532 * q^11 - 4195 * q^12 - 2492 * q^13 - 4240 * q^14 - 1780 * q^15 + 1882 * q^16 - 2534 * q^17 - 3711 * q^18 - 1678 * q^19 - 2607 * q^20 - 2256 * q^21 + 11502 * q^22 - 2488 * q^23 + 19953 * q^24 + 4378 * q^25 + 4586 * q^26 - 8960 * q^27 + 18640 * q^28 - 4360 * q^29 + 25092 * q^30 + 5704 * q^31 - 18294 * q^32 - 12852 * q^33 + 30007 * q^34 + 5640 * q^35 + 67969 * q^36 - 3772 * q^37 - 6559 * q^38 + 11120 * q^39 + 14869 * q^40 - 10698 * q^41 + 78698 * q^42 - 14792 * q^43 - 356 * q^44 - 44912 * q^45 - 19389 * q^46 - 77864 * q^47 - 118727 * q^48 + 7188 * q^49 + 26877 * q^50 - 80246 * q^51 - 60736 * q^52 - 62352 * q^53 + 61026 * q^54 - 49552 * q^55 - 144528 * q^56 - 808 * q^57 + 52951 * q^58 - 26224 * q^59 + 101500 * q^60 - 82540 * q^61 - 9023 * q^62 - 61768 * q^63 + 153858 * q^64 - 5000 * q^65 - 48516 * q^66 + 27784 * q^67 + 40507 * q^68 - 93776 * q^69 + 185910 * q^70 - 9504 * q^71 - 186687 * q^72 + 14260 * q^73 - 15239 * q^74 + 167420 * q^75 + 1279 * q^76 - 218140 * q^77 + 264170 * q^78 + 160248 * q^79 - 1291 * q^80 + 161076 * q^81 - 47781 * q^82 - 77176 * q^83 + 16382 * q^84 + 141096 * q^85 + 22188 * q^86 + 268136 * q^87 + 129544 * q^88 - 265692 * q^89 + 48990 * q^90 + 401148 * q^91 + 190391 * q^92 - 123860 * q^93 + 248737 * q^94 + 135884 * q^95 + 950817 * q^96 + 144742 * q^97 - 292244 * q^98 + 239516 * 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 $

$2$	5.21373	0.921667	0.460833	−	0.887487i	$-0.347551\pi$
$2$	5.21373	0.921667	0.460833	+	0.887487i	$0.347551\pi$
$3$	−11.2683	−0.722863	−0.361431	−	0.932399i	$-0.617712\pi$
$3$	−11.2683	−0.722863	−0.361431	+	0.932399i	$0.617712\pi$
$4$	−4.81697	−0.150530
$5$	−9.80186	−0.175341	−0.0876705	−	0.996150i	$-0.527942\pi$
$5$	−9.80186	−0.175341	−0.0876705	+	0.996150i	$0.527942\pi$
$6$	−58.7500	−0.666239
$7$	−11.1041	−0.0856521	−0.0428260	−	0.999083i	$-0.513636\pi$
$7$	−11.1041	−0.0856521	−0.0428260	+	0.999083i	$0.513636\pi$
$8$	−191.954	−1.06041
$9$	−116.025	−0.477470
$10$	−51.1043	−0.161606
$11$	−557.274	−1.38863	−0.694316	−	0.719670i	$-0.744293\pi$
$11$	−557.274	−1.38863	−0.694316	+	0.719670i	$0.744293\pi$
$12$	54.2791	0.108813
$13$	107.663	0.176688	0.0883441	−	0.996090i	$-0.471842\pi$
$13$	107.663	0.176688	0.0883441	+	0.996090i	$0.471842\pi$
$14$	−57.8938	−0.0789427
$15$	110.450	0.126747
$16$	−846.654	−0.826810
$17$	329.005	0.276109	0.138054	−	0.990425i	$-0.455915\pi$
$17$	329.005	0.276109	0.138054	+	0.990425i	$0.455915\pi$
$18$	−604.924	−0.440068
$19$	2938.10	1.86716	0.933582	−	0.358365i	$-0.116666\pi$
$19$	2938.10	1.86716	0.933582	+	0.358365i	$0.116666\pi$
$20$	47.2153	0.0263941
$21$	125.124	0.0619147
$22$	−2905.48	−1.27986
$23$	−385.537	−0.151966	−0.0759830	−	0.997109i	$-0.524209\pi$
$23$	−385.537	−0.151966	−0.0759830	+	0.997109i	$0.524209\pi$
$24$	2163.00	0.766528
$25$	−3028.92	−0.969256
$26$	561.326	0.162848
$27$	4045.61	1.06801
$28$	53.4881	0.0128932
$29$	−3309.15	−0.730670	−0.365335	−	0.930876i	$-0.619046\pi$
$29$	−3309.15	−0.730670	−0.365335	+	0.930876i	$0.619046\pi$
$30$	575.859	0.116819
$31$	−5471.71	−1.02263	−0.511316	−	0.859393i	$-0.670842\pi$
$31$	−5471.71	−1.02263	−0.511316	+	0.859393i	$0.670842\pi$
$32$	1728.30	0.298362
$33$	6279.54	1.00379
$34$	1715.34	0.254480
$35$	108.841	0.0150183
$36$	558.890	0.0718737
$37$	4832.22	0.580286	0.290143	−	0.956983i	$-0.406297\pi$
$37$	4832.22	0.580286	0.290143	+	0.956983i	$0.406297\pi$
$38$	15318.5	1.72090
$39$	−1213.18	−0.127721
$40$	1881.51	0.185933
$41$	1065.16	0.0989587	0.0494793	−	0.998775i	$-0.484244\pi$
$41$	1065.16	0.0989587	0.0494793	+	0.998775i	$0.484244\pi$
$42$	652.365	0.0570647
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	2684.37	0.209031
$45$	1137.26	0.0837200
$46$	−2010.09	−0.140062
$47$	−8991.95	−0.593758	−0.296879	−	0.954915i	$-0.595946\pi$
$47$	−8991.95	−0.593758	−0.296879	+	0.954915i	$0.595946\pi$
$48$	9540.36	0.597670
$49$	−16683.7	−0.992664
$50$	−15792.0	−0.893331
$51$	−3707.33	−0.199589
$52$	−518.609	−0.0265969
$53$	−10216.7	−0.499598	−0.249799	−	0.968298i	$-0.580365\pi$
$53$	−10216.7	−0.499598	−0.249799	+	0.968298i	$0.580365\pi$
$54$	21092.7	0.984347
$55$	5462.32	0.243484
$56$	2131.47	0.0908260
$57$	−33107.4	−1.34970
$58$	−17253.0	−0.673434
$59$	−27457.0	−1.02689	−0.513444	−	0.858123i	$-0.671631\pi$
$59$	−27457.0	−1.02689	−0.513444	+	0.858123i	$0.671631\pi$
$60$	−532.036	−0.0190793
$61$	−36692.9	−1.26258	−0.631288	−	0.775548i	$-0.717473\pi$
$61$	−36692.9	−1.26258	−0.631288	+	0.775548i	$0.717473\pi$
$62$	−28528.1	−0.942525
$63$	1288.35	0.0408963
$64$	36103.8	1.10180
$65$	−1055.30	−0.0309807
$66$	32739.9	0.925160
$67$	−26272.2	−0.715004	−0.357502	−	0.933912i	$-0.616372\pi$
$67$	−26272.2	−0.715004	−0.357502	+	0.933912i	$0.616372\pi$
$68$	−1584.81	−0.0415627
$69$	4344.35	0.109851
$70$	567.467	0.0138419
$71$	55130.3	1.29791	0.648955	−	0.760827i	$-0.275206\pi$
$71$	55130.3	1.29791	0.648955	+	0.760827i	$0.275206\pi$
$72$	22271.5	0.506311
$73$	−9315.14	−0.204589	−0.102294	−	0.994754i	$-0.532618\pi$
$73$	−9315.14	−0.204589	−0.102294	+	0.994754i	$0.532618\pi$
$74$	25193.9	0.534830
$75$	34130.9	0.700639
$76$	−14152.7	−0.281065
$77$	6188.02	0.118939
$78$	−6325.20	−0.117717
$79$	56826.5	1.02443	0.512216	−	0.858856i	$-0.328825\pi$
$79$	56826.5	1.02443	0.512216	+	0.858856i	$0.328825\pi$
$80$	8298.78	0.144974
$81$	−17393.1	−0.294553
$82$	5553.44	0.0912069
$83$	−5858.19	−0.0933401	−0.0466700	−	0.998910i	$-0.514861\pi$
$83$	−5858.19	−0.0933401	−0.0466700	+	0.998910i	$0.514861\pi$
$84$	−602.721	−0.00932004
$85$	−3224.86	−0.0484132
$86$	−9640.20	−0.140553
$87$	37288.5	0.528174
$88$	106971.	1.47251
$89$	−42815.7	−0.572965	−0.286483	−	0.958085i	$-0.592486\pi$
$89$	−42815.7	−0.572965	−0.286483	+	0.958085i	$0.592486\pi$
$90$	5929.38	0.0771619
$91$	−1195.50	−0.0151337
$92$	1857.12	0.0228755
$93$	61657.0	0.739222
$94$	−46881.7	−0.547247
$95$	−28798.8	−0.327390
$96$	−19475.0	−0.215675
$97$	−231.671	−0.00250002	−0.00125001	−	0.999999i	$-0.500398\pi$
$97$	−231.671	−0.00250002	−0.00125001	+	0.999999i	$0.500398\pi$
$98$	−86984.4	−0.914905
$99$	64657.8	0.663029
$100$	14590.2	0.145902
$101$	−65329.5	−0.637245	−0.318622	−	0.947882i	$-0.603220\pi$
$101$	−65329.5	−0.637245	−0.318622	+	0.947882i	$0.603220\pi$
$102$	−19329.0	−0.183954
$103$	210856.	1.95837	0.979183	−	0.202980i	$-0.0650628\pi$
$103$	210856.	1.95837	0.979183	+	0.202980i	$0.0650628\pi$
$104$	−20666.3	−0.187361
$105$	−1226.45	−0.0108562
$106$	−53267.2	−0.460463
$107$	−158342.	−1.33702	−0.668508	−	0.743705i	$-0.733067\pi$
$107$	−158342.	−1.33702	−0.668508	+	0.743705i	$0.733067\pi$
$108$	−19487.6	−0.160768
$109$	−85822.7	−0.691888	−0.345944	−	0.938255i	$-0.612441\pi$
$109$	−85822.7	−0.691888	−0.345944	+	0.938255i	$0.612441\pi$
$110$	28479.1	0.224411
$111$	−54450.9	−0.419467
$112$	9401.32	0.0708180
$113$	101903.	0.750745	0.375372	−	0.926874i	$-0.377515\pi$
$113$	101903.	0.750745	0.375372	+	0.926874i	$0.377515\pi$
$114$	−172613.	−1.24398
$115$	3778.98	0.0266459
$116$	15940.1	0.109988
$117$	−12491.6	−0.0843633
$118$	−143153.	−0.946448
$119$	−3653.30	−0.0236493
$120$	−21201.4	−0.134404
$121$	149503.	0.928299
$122$	−191307.	−1.16367
$123$	−12002.5	−0.0715335
$124$	26357.1	0.153937
$125$	60319.9	0.345291
$126$	6717.13	0.0376927
$127$	109901.	0.604635	0.302318	−	0.953207i	$-0.402240\pi$
$127$	109901.	0.604635	0.302318	+	0.953207i	$0.402240\pi$
$128$	132930.	0.717131
$129$	20835.1	0.110236
$130$	−5502.04	−0.0285539
$131$	−79310.4	−0.403787	−0.201893	−	0.979408i	$-0.564709\pi$
$131$	−79310.4	−0.403787	−0.201893	+	0.979408i	$0.564709\pi$
$132$	−30248.4	−0.151101
$133$	−32624.9	−0.159926
$134$	−136976.	−0.658996
$135$	−39654.5	−0.187266
$136$	−63153.8	−0.292787
$137$	−360169.	−1.63948	−0.819738	−	0.572738i	$-0.805881\pi$
$137$	−360169.	−1.63948	−0.819738	+	0.572738i	$0.805881\pi$
$138$	22650.3	0.101246
$139$	330826.	1.45232	0.726160	−	0.687525i	$-0.241303\pi$
$139$	330826.	1.45232	0.726160	+	0.687525i	$0.241303\pi$
$140$	−524.283	−0.00226071
$141$	101324.	0.429205
$142$	287435.	1.19624
$143$	−59997.8	−0.245355
$144$	98233.1	0.394777
$145$	32435.8	0.128116
$146$	−48566.7	−0.188563
$147$	187997.	0.717560
$148$	−23276.6	−0.0873506
$149$	24179.7	0.0892249	0.0446125	−	0.999004i	$-0.485795\pi$
$149$	24179.7	0.0892249	0.0446125	+	0.999004i	$0.485795\pi$
$150$	177949.	0.645755
$151$	278667.	0.994589	0.497295	−	0.867582i	$-0.334327\pi$
$151$	278667.	0.994589	0.497295	+	0.867582i	$0.334327\pi$
$152$	−563979.	−1.97995
$153$	−38172.8	−0.131833
$154$	32262.7	0.109622
$155$	53633.0	0.179309
$156$	5843.85	0.0192259
$157$	−102228.	−0.330995	−0.165497	−	0.986210i	$-0.552923\pi$
$157$	−102228.	−0.330995	−0.165497	+	0.986210i	$0.552923\pi$
$158$	296279.	0.944186
$159$	115125.	0.361141
$160$	−16940.5	−0.0523151
$161$	4281.04	0.0130162
$162$	−90682.9	−0.271480
$163$	444216.	1.30956	0.654780	−	0.755819i	$-0.272761\pi$
$163$	444216.	1.30956	0.654780	+	0.755819i	$0.272761\pi$
$164$	−5130.83	−0.0148963
$165$	−61551.2	−0.176006
$166$	−30543.0	−0.0860285
$167$	−467231.	−1.29640	−0.648202	−	0.761469i	$-0.724479\pi$
$167$	−467231.	−1.29640	−0.648202	+	0.761469i	$0.724479\pi$
$168$	−24018.1	−0.0656547
$169$	−359702.	−0.968781
$170$	−16813.6	−0.0446208
$171$	−340893.	−0.891514
$172$	8906.58	0.0229557
$173$	296435.	0.753033	0.376516	−	0.926410i	$-0.377122\pi$
$173$	296435.	0.753033	0.376516	+	0.926410i	$0.377122\pi$
$174$	194412.	0.486801
$175$	33633.5	0.0830188
$176$	471818.	1.14814
$177$	309394.	0.742299
$178$	−223230.	−0.528083
$179$	211576.	0.493553	0.246777	−	0.969072i	$-0.420629\pi$
$179$	211576.	0.493553	0.246777	+	0.969072i	$0.420629\pi$
$180$	−5478.16	−0.0126024
$181$	−187769.	−0.426018	−0.213009	−	0.977050i	$-0.568326\pi$
$181$	−187769.	−0.426018	−0.213009	+	0.977050i	$0.568326\pi$
$182$	−6233.01	−0.0139482
$183$	413467.	0.912669
$184$	74005.3	0.161146
$185$	−47364.7	−0.101748
$186$	321463.	0.681316
$187$	−183346.	−0.383413
$188$	43314.0	0.0893786
$189$	−44922.8	−0.0914771
$190$	−150149.	−0.301745
$191$	−655959.	−1.30105	−0.650524	−	0.759486i	$-0.725450\pi$
$191$	−655959.	−1.30105	−0.650524	+	0.759486i	$0.725450\pi$
$192$	−406829.	−0.796451
$193$	450394.	0.870361	0.435180	−	0.900343i	$-0.356685\pi$
$193$	450394.	0.870361	0.435180	+	0.900343i	$0.356685\pi$
$194$	−1207.87	−0.00230418
$195$	11891.4	0.0223948
$196$	80364.9	0.149426
$197$	−973133.	−1.78652	−0.893258	−	0.449545i	$-0.851586\pi$
$197$	−973133.	−1.78652	−0.893258	+	0.449545i	$0.851586\pi$
$198$	337109.	0.611092
$199$	259840.	0.465129	0.232564	−	0.972581i	$-0.425288\pi$
$199$	259840.	0.465129	0.232564	+	0.972581i	$0.425288\pi$
$200$	581414.	1.02780
$201$	296043.	0.516850
$202$	−340611.	−0.587327
$203$	36745.1	0.0625834
$204$	17858.1	0.0300441
$205$	−10440.5	−0.0173515
$206$	1.09935e6	1.80496
$207$	44732.0	0.0725591
$208$	−91153.2	−0.146088
$209$	−1.63733e6	−2.59280
$210$	−6394.39	−0.0100058
$211$	−621161.	−0.960502	−0.480251	−	0.877131i	$-0.659454\pi$
$211$	−621161.	−0.960502	−0.480251	+	0.877131i	$0.659454\pi$
$212$	49213.5	0.0752047
$213$	−621226.	−0.938211
$214$	−825553.	−1.23228
$215$	18123.6	0.0267392
$216$	−776570.	−1.13252
$217$	60758.4	0.0875905
$218$	−447457.	−0.637690
$219$	104966.	0.147890
$220$	−26311.8	−0.0366517
$221$	35421.6	0.0487852
$222$	−283893.	−0.386609
$223$	−779614.	−1.04983	−0.524913	−	0.851156i	$-0.675902\pi$
$223$	−779614.	−1.04983	−0.524913	+	0.851156i	$0.675902\pi$
$224$	−19191.2	−0.0255553
$225$	351431.	0.462790
$226$	531297.	0.691937
$227$	795424.	1.02455	0.512276	−	0.858821i	$-0.328803\pi$
$227$	795424.	1.02455	0.512276	+	0.858821i	$0.328803\pi$
$228$	159477.	0.203171
$229$	−702980.	−0.885838	−0.442919	−	0.896562i	$-0.646057\pi$
$229$	−702980.	−0.885838	−0.442919	+	0.896562i	$0.646057\pi$
$230$	19702.6	0.0245586
$231$	−69728.6	−0.0859767
$232$	635204.	0.774807
$233$	−219327.	−0.264669	−0.132334	−	0.991205i	$-0.542247\pi$
$233$	−219327.	−0.264669	−0.132334	+	0.991205i	$0.542247\pi$
$234$	−65127.9	−0.0777548
$235$	88137.9	0.104110
$236$	132260.	0.154578
$237$	−640339.	−0.740524
$238$	−19047.3	−0.0217968
$239$	1.75148e6	1.98340	0.991701	−	0.128565i	$-0.0410372\pi$
$239$	1.75148e6	1.98340	0.991701	+	0.128565i	$0.0410372\pi$
$240$	−93513.3	−0.104796
$241$	985600.	1.09310	0.546548	−	0.837428i	$-0.315942\pi$
$241$	985600.	1.09310	0.546548	+	0.837428i	$0.315942\pi$
$242$	779471.	0.855582
$243$	−787092.	−0.855086
$244$	176749.	0.190056
$245$	163531.	0.174055
$246$	−62578.0	−0.0659301
$247$	316324.	0.329906
$248$	1.05032e6	1.08440
$249$	66011.9	0.0674721
$250$	314492.	0.318243
$251$	126142.	0.126379	0.0631894	−	0.998002i	$-0.479873\pi$
$251$	126142.	0.126379	0.0631894	+	0.998002i	$0.479873\pi$
$252$	−6205.96	−0.00615613
$253$	214850.	0.211025
$254$	572996.	0.557272
$255$	36338.7	0.0349961
$256$	−462259.	−0.440845
$257$	1.55933e6	1.47267	0.736335	−	0.676617i	$-0.236555\pi$
$257$	1.55933e6	1.47267	0.736335	+	0.676617i	$0.236555\pi$
$258$	108629.	0.101600
$259$	−53657.4	−0.0497027
$260$	5083.33	0.00466353
$261$	383944.	0.348873
$262$	−413503.	−0.372157
$263$	−107289.	−0.0956460	−0.0478230	−	0.998856i	$-0.515228\pi$
$263$	−107289.	−0.0956460	−0.0478230	+	0.998856i	$0.515228\pi$
$264$	−1.20538e6	−1.06442
$265$	100143.	0.0876001
$266$	−170098.	−0.147399
$267$	482461.	0.414175
$268$	126552.	0.107630
$269$	829468.	0.698906	0.349453	−	0.936954i	$-0.386367\pi$
$269$	829468.	0.698906	0.349453	+	0.936954i	$0.386367\pi$
$270$	−206748.	−0.172596
$271$	2.22835e6	1.84315	0.921575	−	0.388200i	$-0.126903\pi$
$271$	2.22835e6	1.84315	0.921575	+	0.388200i	$0.126903\pi$
$272$	−278553.	−0.228289
$273$	13471.3	0.0109396
$274$	−1.87783e6	−1.51105
$275$	1.68794e6	1.34594
$276$	−20926.6	−0.0165358
$277$	−1.57467e6	−1.23308	−0.616538	−	0.787325i	$-0.711465\pi$
$277$	−1.57467e6	−1.23308	−0.616538	+	0.787325i	$0.711465\pi$
$278$	1.72484e6	1.33856
$279$	634856.	0.488275
$280$	−20892.4	−0.0159255
$281$	−2.26025e6	−1.70762	−0.853809	−	0.520586i	$-0.825713\pi$
$281$	−2.26025e6	−1.70762	−0.853809	+	0.520586i	$0.825713\pi$
$282$	528277.	0.395584
$283$	−1.81290e6	−1.34558	−0.672789	−	0.739835i	$-0.734904\pi$
$283$	−1.81290e6	−1.34558	−0.672789	+	0.739835i	$0.734904\pi$
$284$	−265561.	−0.195375
$285$	324514.	0.236658
$286$	−312812.	−0.226136
$287$	−11827.6	−0.00847602
$288$	−200526.	−0.142459
$289$	−1.31161e6	−0.923764
$290$	169112.	0.118081
$291$	2610.55	0.00180717
$292$	44870.7	0.0307968
$293$	−1.92999e6	−1.31336	−0.656682	−	0.754168i	$-0.728041\pi$
$293$	−1.92999e6	−1.31336	−0.656682	+	0.754168i	$0.728041\pi$
$294$	980167.	0.661351
$295$	269130.	0.180056
$296$	−927563.	−0.615338
$297$	−2.25451e6	−1.48307
$298$	126067.	0.0822356
$299$	−41508.0	−0.0268506
$300$	−164407.	−0.105467
$301$	20531.5	0.0130618
$302$	1.45290e6	0.916680
$303$	736154.	0.460640
$304$	−2.48755e6	−1.54379
$305$	359659.	0.221381
$306$	−199023.	−0.121507
$307$	−2.35372e6	−1.42531	−0.712654	−	0.701515i	$-0.752507\pi$
$307$	−2.35372e6	−1.42531	−0.712654	+	0.701515i	$0.752507\pi$
$308$	−29807.5	−0.0179040
$309$	−2.37600e6	−1.41563
$310$	279628.	0.165263
$311$	1.25933e6	0.738312	0.369156	−	0.929367i	$-0.379647\pi$
$311$	1.25933e6	0.738312	0.369156	+	0.929367i	$0.379647\pi$
$312$	232875.	0.135436
$313$	−1.21791e6	−0.702676	−0.351338	−	0.936249i	$-0.614273\pi$
$313$	−1.21791e6	−0.702676	−0.351338	+	0.936249i	$0.614273\pi$
$314$	−532990.	−0.305067
$315$	−12628.3	−0.00717079
$316$	−273732.	−0.154208
$317$	689890.	0.385595	0.192798	−	0.981239i	$-0.438244\pi$
$317$	689890.	0.385595	0.192798	+	0.981239i	$0.438244\pi$
$318$	600231.	0.332852
$319$	1.84410e6	1.01463
$320$	−353884.	−0.193191
$321$	1.78425e6	0.966480
$322$	22320.2	0.0119966
$323$	966649.	0.515540
$324$	83782.0	0.0443392
$325$	−326103.	−0.171256
$326$	2.31603e6	1.20698
$327$	967077.	0.500140
$328$	−204461.	−0.104936
$329$	99847.5	0.0508566
$330$	−320911.	−0.162218
$331$	1.93331e6	0.969912	0.484956	−	0.874538i	$-0.338836\pi$
$331$	1.93331e6	0.969912	0.484956	+	0.874538i	$0.338836\pi$
$332$	28218.7	0.0140505
$333$	−560658.	−0.277069
$334$	−2.43602e6	−1.19485
$335$	257516.	0.125370
$336$	−105937.	−0.0511917
$337$	347418.	0.166639	0.0833196	−	0.996523i	$-0.473448\pi$
$337$	347418.	0.166639	0.0833196	+	0.996523i	$0.473448\pi$
$338$	−1.87539e6	−0.892893
$339$	−1.14828e6	−0.542686
$340$	15534.1	0.00728765
$341$	3.04924e6	1.42006
$342$	−1.77733e6	−0.821678
$343$	371884.	0.170676
$344$	354923.	0.161710
$345$	−42582.7	−0.0192613
$346$	1.54553e6	0.694045
$347$	−4.28700e6	−1.91130	−0.955652	−	0.294498i	$-0.904847\pi$
$347$	−4.28700e6	−1.91130	−0.955652	+	0.294498i	$0.904847\pi$
$348$	−179618.	−0.0795062
$349$	2.58234e6	1.13488	0.567439	−	0.823415i	$-0.307934\pi$
$349$	2.58234e6	1.13488	0.567439	+	0.823415i	$0.307934\pi$
$350$	175356.	0.0765156
$351$	435562.	0.188704
$352$	−963136.	−0.414315
$353$	−2.31876e6	−0.990419	−0.495210	−	0.868774i	$-0.664909\pi$
$353$	−2.31876e6	−0.990419	−0.495210	+	0.868774i	$0.664909\pi$
$354$	1.61310e6	0.684152
$355$	−540380.	−0.227577
$356$	206242.	0.0862486
$357$	41166.5	0.0170952
$358$	1.10310e6	0.454892
$359$	−1.41572e6	−0.579752	−0.289876	−	0.957064i	$-0.593614\pi$
$359$	−1.41572e6	−0.579752	−0.289876	+	0.957064i	$0.593614\pi$
$360$	−218302.	−0.0887771
$361$	6.15632e6	2.48630
$362$	−978979.	−0.392647
$363$	−1.68465e6	−0.671033
$364$	5758.68	0.00227808
$365$	91305.7	0.0358728
$366$	2.15571e6	0.841177
$367$	2.64620e6	1.02555	0.512776	−	0.858523i	$-0.328617\pi$
$367$	2.64620e6	1.02555	0.512776	+	0.858523i	$0.328617\pi$
$368$	326416.	0.125647
$369$	−123585.	−0.0472498
$370$	−246947.	−0.0937777
$371$	113447.	0.0427916
$372$	−297000.	−0.111275
$373$	3.49265e6	1.29982	0.649910	−	0.760011i	$-0.274806\pi$
$373$	3.49265e6	1.29982	0.649910	+	0.760011i	$0.274806\pi$
$374$	−955917.	−0.353379
$375$	−679703.	−0.249598
$376$	1.72604e6	0.629624
$377$	−356273.	−0.129101
$378$	−234216.	−0.0843114
$379$	1.42204e6	0.508526	0.254263	−	0.967135i	$-0.418167\pi$
$379$	1.42204e6	0.508526	0.254263	+	0.967135i	$0.418167\pi$
$380$	138723.	0.0492822
$381$	−1.23840e6	−0.437068
$382$	−3.41999e6	−1.19913
$383$	−2.81442e6	−0.980373	−0.490187	−	0.871618i	$-0.663071\pi$
$383$	−2.81442e6	−0.980373	−0.490187	+	0.871618i	$0.663071\pi$
$384$	−1.49790e6	−0.518387
$385$	−60654.1	−0.0208549
$386$	2.34823e6	0.802182
$387$	214530.	0.0728134
$388$	1115.95	0.000376329 0
$389$	−165325.	−0.0553943	−0.0276971	−	0.999616i	$-0.508817\pi$
$389$	−165325.	−0.0553943	−0.0276971	+	0.999616i	$0.508817\pi$
$390$	61998.7	0.0206405
$391$	−126844.	−0.0419591
$392$	3.20250e6	1.05263
$393$	893695.	0.291882
$394$	−5.07366e6	−1.64657
$395$	−557006.	−0.179625
$396$	−311455.	−0.0998061
$397$	−3.79445e6	−1.20830	−0.604148	−	0.796872i	$-0.706486\pi$
$397$	−3.79445e6	−1.20830	−0.604148	+	0.796872i	$0.706486\pi$
$398$	1.35474e6	0.428694
$399$	367628.	0.115605
$400$	2.56445e6	0.801390
$401$	4.59396e6	1.42668	0.713339	−	0.700819i	$-0.247182\pi$
$401$	4.59396e6	1.42668	0.713339	+	0.700819i	$0.247182\pi$
$402$	1.54349e6	0.476363
$403$	−589100.	−0.180687
$404$	314690.	0.0959246
$405$	170485.	0.0516473
$406$	191579.	0.0576811
$407$	−2.69287e6	−0.805804
$408$	711637.	0.211645
$409$	3.83956e6	1.13494	0.567471	−	0.823393i	$-0.307922\pi$
$409$	3.83956e6	1.13494	0.567471	+	0.823393i	$0.307922\pi$
$410$	−54434.1	−0.0159923
$411$	4.05850e6	1.18512
$412$	−1.01569e6	−0.294793
$413$	304885.	0.0879551
$414$	233221.	0.0668753
$415$	57421.2	0.0163663
$416$	186074.	0.0527171
$417$	−3.72785e6	−1.04983
$418$	−8.53658e6	−2.38970
$419$	2.87922e6	0.801199	0.400600	−	0.916253i	$-0.368802\pi$
$419$	2.87922e6	0.801199	0.400600	+	0.916253i	$0.368802\pi$
$420$	5907.78	0.00163419
$421$	1.41982e6	0.390417	0.195208	−	0.980762i	$-0.437462\pi$
$421$	1.41982e6	0.390417	0.195208	+	0.980762i	$0.437462\pi$
$422$	−3.23857e6	−0.885262
$423$	1.04329e6	0.283501
$424$	1.96114e6	0.529777
$425$	−996531.	−0.267620
$426$	−3.23891e6	−0.864718
$427$	407441.	0.108142
$428$	762729.	0.201262
$429$	676074.	0.177358
$430$	94491.8	0.0246447
$431$	−4.77968e6	−1.23938	−0.619691	−	0.784846i	$-0.712742\pi$
$431$	−4.77968e6	−1.23938	−0.619691	+	0.784846i	$0.712742\pi$
$432$	−3.42523e6	−0.883040
$433$	213516.	0.0547282	0.0273641	−	0.999626i	$-0.491289\pi$
$433$	213516.	0.0547282	0.0273641	+	0.999626i	$0.491289\pi$
$434$	316778.	0.0807293
$435$	−365497.	−0.0926106
$436$	413405.	0.104150
$437$	−1.13275e6	−0.283745
$438$	547264.	0.136305
$439$	555761.	0.137634	0.0688172	−	0.997629i	$-0.478077\pi$
$439$	555761.	0.137634	0.0688172	+	0.997629i	$0.478077\pi$
$440$	−1.04851e6	−0.258192
$441$	1.93573e6	0.473967
$442$	184679.	0.0449637
$443$	−1.23542e6	−0.299092	−0.149546	−	0.988755i	$-0.547781\pi$
$443$	−1.23542e6	−0.299092	−0.149546	+	0.988755i	$0.547781\pi$
$444$	262289.	0.0631425
$445$	419674.	0.100464
$446$	−4.06470e6	−0.967591
$447$	−272465.	−0.0644974
$448$	−400900.	−0.0943715
$449$	1.61043e6	0.376986	0.188493	−	0.982074i	$-0.439640\pi$
$449$	1.61043e6	0.376986	0.188493	+	0.982074i	$0.439640\pi$
$450$	1.83227e6	0.426538
$451$	−593584.	−0.137417
$452$	−490866.	−0.113010
$453$	−3.14011e6	−0.718951
$454$	4.14713e6	0.944295
$455$	11718.1	0.00265356
$456$	6.35510e6	1.43123
$457$	4.44189e6	0.994894	0.497447	−	0.867494i	$-0.334271\pi$
$457$	4.44189e6	0.994894	0.497447	+	0.867494i	$0.334271\pi$
$458$	−3.66515e6	−0.816447
$459$	1.33102e6	0.294886
$460$	−18203.2	−0.00401101
$461$	−8.65627e6	−1.89705	−0.948524	−	0.316705i	$-0.897423\pi$
$461$	−8.65627e6	−1.89705	−0.948524	+	0.316705i	$0.897423\pi$
$462$	−363546.	−0.0792419
$463$	−8.50880e6	−1.84466	−0.922329	−	0.386404i	$-0.873717\pi$
$463$	−8.50880e6	−1.84466	−0.922329	+	0.386404i	$0.873717\pi$
$464$	2.80170e6	0.604126
$465$	−604353.	−0.129616
$466$	−1.14351e6	−0.243936
$467$	−692449.	−0.146925	−0.0734625	−	0.997298i	$-0.523405\pi$
$467$	−692449.	−0.146925	−0.0734625	+	0.997298i	$0.523405\pi$
$468$	60171.7	0.0126992
$469$	291728.	0.0612416
$470$	459527.	0.0959548
$471$	1.15194e6	0.239264
$472$	5.27048e6	1.08892
$473$	1.03040e6	0.211764
$474$	−3.33856e6	−0.682517
$475$	−8.89927e6	−1.80976
$476$	17597.8	0.00355993
$477$	1.18539e6	0.238543
$478$	9.13176e6	1.82804
$479$	−7.63881e6	−1.52120	−0.760601	−	0.649220i	$-0.775095\pi$
$479$	−7.63881e6	−1.52120	−0.760601	+	0.649220i	$0.775095\pi$
$480$	190891.	0.0378166
$481$	520250.	0.102530
$482$	5.13865e6	1.00747
$483$	−48240.1	−0.00940893
$484$	−720154.	−0.139737
$485$	2270.81	0.000438356 0
$486$	−4.10369e6	−0.788104
$487$	4.82019e6	0.920962	0.460481	−	0.887670i	$-0.347677\pi$
$487$	4.82019e6	0.920962	0.460481	+	0.887670i	$0.347677\pi$
$488$	7.04335e6	1.33884
$489$	−5.00557e6	−0.946633
$490$	852609.	0.160420
$491$	66664.0	0.0124792	0.00623961	−	0.999981i	$-0.498014\pi$
$491$	66664.0	0.0124792	0.00623961	+	0.999981i	$0.498014\pi$
$492$	57815.8	0.0107680
$493$	−1.08873e6	−0.201744
$494$	1.64923e6	0.304063
$495$	−633767.	−0.116256
$496$	4.63265e6	0.845522
$497$	−612172.	−0.111169
$498$	344169.	0.0621868
$499$	−2.93211e6	−0.527144	−0.263572	−	0.964640i	$-0.584901\pi$
$499$	−2.93211e6	−0.527144	−0.263572	+	0.964640i	$0.584901\pi$
$500$	−290559.	−0.0519768
$501$	5.26490e6	0.937122
$502$	657669.	0.116479
$503$	−3.90093e6	−0.687462	−0.343731	−	0.939068i	$-0.611691\pi$
$503$	−3.90093e6	−0.687462	−0.343731	+	0.939068i	$0.611691\pi$
$504$	−247305.	−0.0433666
$505$	640351.	0.111735
$506$	1.12017e6	0.194495
$507$	4.05323e6	0.700296
$508$	−529391.	−0.0910159
$509$	2.09591e6	0.358573	0.179287	−	0.983797i	$-0.442621\pi$
$509$	2.09591e6	0.358573	0.179287	+	0.983797i	$0.442621\pi$
$510$	189460.	0.0322547
$511$	103436.	0.0175235
$512$	−6.66386e6	−1.12344
$513$	1.18864e7	1.99414
$514$	8.12994e6	1.35731
$515$	−2.06678e6	−0.343382
$516$	−100362.	−0.0165938
$517$	5.01098e6	0.824511
$518$	−279755.	−0.0458093
$519$	−3.34032e6	−0.544339
$520$	202568.	0.0328521
$521$	3.34502e6	0.539889	0.269944	−	0.962876i	$-0.412995\pi$
$521$	3.34502e6	0.539889	0.269944	+	0.962876i	$0.412995\pi$
$522$	2.00178e6	0.321544
$523$	−1.04450e7	−1.66976	−0.834878	−	0.550434i	$-0.814462\pi$
$523$	−1.04450e7	−1.66976	−0.834878	+	0.550434i	$0.814462\pi$
$524$	382036.	0.0607821
$525$	−378992.	−0.0600112
$526$	−559378.	−0.0881538
$527$	−1.80022e6	−0.282357
$528$	−5.31660e6	−0.829944
$529$	−6.28770e6	−0.976906
$530$	522117.	0.0807381
$531$	3.18570e6	0.490308
$532$	157153.	0.0240738
$533$	114678.	0.0174848
$534$	2.51542e6	0.381731
$535$	1.55205e6	0.234434
$536$	5.04304e6	0.758195
$537$	−2.38411e6	−0.356771
$538$	4.32463e6	0.644159
$539$	9.29739e6	1.37844
$540$	191014.	0.0281891
$541$	5.88573e6	0.864584	0.432292	−	0.901734i	$-0.357705\pi$
$541$	5.88573e6	0.864584	0.432292	+	0.901734i	$0.357705\pi$
$542$	1.16180e7	1.69877
$543$	2.11584e6	0.307952
$544$	568618.	0.0823803
$545$	841222.	0.121316
$546$	70235.6	0.0100827
$547$	−2.94922e6	−0.421444	−0.210722	−	0.977546i	$-0.567581\pi$
$547$	−2.94922e6	−0.421444	−0.210722	+	0.977546i	$0.567581\pi$
$548$	1.73492e6	0.246791
$549$	4.25730e6	0.602842
$550$	8.80048e6	1.24051
$551$	−9.72260e6	−1.36428
$552$	−833915.	−0.116486
$553$	−631007.	−0.0877448
$554$	−8.20990e6	−1.13648
$555$	533720.	0.0735498
$556$	−1.59358e6	−0.218618
$557$	−1.44836e7	−1.97806	−0.989029	−	0.147723i	$-0.952805\pi$
$557$	−1.44836e7	−1.97806	−0.989029	+	0.147723i	$0.952805\pi$
$558$	3.30997e6	0.450027
$559$	−199069.	−0.0269447
$560$	−92150.4	−0.0124173
$561$	2.06600e6	0.277155
$562$	−1.17843e7	−1.57385
$563$	6.77740e6	0.901139	0.450570	−	0.892741i	$-0.351221\pi$
$563$	6.77740e6	0.901139	0.450570	+	0.892741i	$0.351221\pi$
$564$	−488076.	−0.0646084
$565$	−998842.	−0.131636
$566$	−9.45200e6	−1.24017
$567$	193134.	0.0252291
$568$	−1.05825e7	−1.37631
$569$	1.03288e7	1.33742	0.668710	−	0.743523i	$-0.266847\pi$
$569$	1.03288e7	1.33742	0.668710	+	0.743523i	$0.266847\pi$
$570$	1.69193e6	0.218120
$571$	−9.52868e6	−1.22304	−0.611522	−	0.791227i	$-0.709443\pi$
$571$	−9.52868e6	−1.22304	−0.611522	+	0.791227i	$0.709443\pi$
$572$	289007.	0.0369334
$573$	7.39155e6	0.940478
$574$	−61666.0	−0.00781206
$575$	1.16776e6	0.147294
$576$	−4.18895e6	−0.526076
$577$	5.58573e6	0.698458	0.349229	−	0.937037i	$-0.386444\pi$
$577$	5.58573e6	0.698458	0.349229	+	0.937037i	$0.386444\pi$
$578$	−6.83840e6	−0.851403
$579$	−5.07518e6	−0.629151
$580$	−156242.	−0.0192854
$581$	65049.9	0.00799478
$582$	13610.7	0.00166561
$583$	5.69350e6	0.693758
$584$	1.78808e6	0.216947
$585$	122441.	0.0147923
$586$	−1.00624e7	−1.21048
$587$	−1.34089e7	−1.60619	−0.803096	−	0.595849i	$-0.796816\pi$
$587$	−1.34089e7	−1.60619	−0.803096	+	0.595849i	$0.796816\pi$
$588$	−905577.	−0.108014
$589$	−1.60764e7	−1.90942
$590$	1.40317e6	0.165951
$591$	1.09656e7	1.29141
$592$	−4.09121e6	−0.479786
$593$	−1.46278e7	−1.70821	−0.854106	−	0.520099i	$-0.825895\pi$
$593$	−1.46278e7	−1.70821	−0.854106	+	0.520099i	$0.825895\pi$
$594$	−1.17544e7	−1.36690
$595$	35809.1	0.00414669
$596$	−116473.	−0.0134311
$597$	−2.92796e6	−0.336224
$598$	−216412.	−0.0247473
$599$	1.02632e7	1.16873	0.584367	−	0.811489i	$-0.301343\pi$
$599$	1.02632e7	1.16873	0.584367	+	0.811489i	$0.301343\pi$
$600$	−6.55155e6	−0.742961
$601$	9.07707e6	1.02508	0.512542	−	0.858662i	$-0.328704\pi$
$601$	9.07707e6	1.02508	0.512542	+	0.858662i	$0.328704\pi$
$602$	107046.	0.0120386
$603$	3.04823e6	0.341393
$604$	−1.34233e6	−0.149716
$605$	−1.46541e6	−0.162769
$606$	3.83811e6	0.424557
$607$	−1.20707e7	−1.32972	−0.664862	−	0.746966i	$-0.731510\pi$
$607$	−1.20707e7	−1.32972	−0.664862	+	0.746966i	$0.731510\pi$
$608$	5.07791e6	0.557091
$609$	−414055.	−0.0452392
$610$	1.87517e6	0.204040
$611$	−968100.	−0.104910
$612$	183877.	0.0198449
$613$	1.40958e6	0.151509	0.0757544	−	0.997127i	$-0.475864\pi$
$613$	1.40958e6	0.151509	0.0757544	+	0.997127i	$0.475864\pi$
$614$	−1.22717e7	−1.31366
$615$	117647.	0.0125428
$616$	−1.18782e6	−0.126124
$617$	1.51488e7	1.60201	0.801005	−	0.598658i	$-0.204299\pi$
$617$	1.51488e7	1.60201	0.801005	+	0.598658i	$0.204299\pi$
$618$	−1.23878e7	−1.30474
$619$	1.58021e7	1.65763	0.828816	−	0.559521i	$-0.189015\pi$
$619$	1.58021e7	1.65763	0.828816	+	0.559521i	$0.189015\pi$
$620$	−258348.	−0.0269915
$621$	−1.55973e6	−0.162301
$622$	6.56584e6	0.680478
$623$	475430.	0.0490757
$624$	1.02714e6	0.105601
$625$	8.87414e6	0.908712
$626$	−6.34988e6	−0.647634
$627$	1.84499e7	1.87424
$628$	492430.	0.0498247
$629$	1.58982e6	0.160222
$630$	−65840.4	−0.00660908
$631$	−1.08922e7	−1.08904	−0.544519	−	0.838749i	$-0.683288\pi$
$631$	−1.08922e7	−1.08904	−0.544519	+	0.838749i	$0.683288\pi$
$632$	−1.09081e7	−1.08631
$633$	6.99944e6	0.694311
$634$	3.59690e6	0.355390
$635$	−1.07724e6	−0.106017
$636$	−554554.	−0.0543627
$637$	−1.79622e6	−0.175392
$638$	9.61466e6	0.935152
$639$	−6.39650e6	−0.619712
$640$	−1.30296e6	−0.125742
$641$	2.41942e6	0.232577	0.116289	−	0.993215i	$-0.462900\pi$
$641$	2.41942e6	0.232577	0.116289	+	0.993215i	$0.462900\pi$
$642$	9.30260e6	0.890772
$643$	1.38769e7	1.32363	0.661814	−	0.749668i	$-0.269787\pi$
$643$	1.38769e7	1.32363	0.661814	+	0.749668i	$0.269787\pi$
$644$	−20621.6	−0.00195933
$645$	−204223.	−0.0193288
$646$	5.03985e6	0.475156
$647$	−7.58249e6	−0.712116	−0.356058	−	0.934464i	$-0.615880\pi$
$647$	−7.58249e6	−0.712116	−0.356058	+	0.934464i	$0.615880\pi$
$648$	3.33867e6	0.312346
$649$	1.53011e7	1.42597
$650$	−1.70021e6	−0.157841
$651$	−684645.	−0.0633159
$652$	−2.13978e6	−0.197129
$653$	3.26919e6	0.300025	0.150012	−	0.988684i	$-0.452069\pi$
$653$	3.26919e6	0.300025	0.150012	+	0.988684i	$0.452069\pi$
$654$	5.04208e6	0.460962
$655$	777389.	0.0708003
$656$	−901819.	−0.0818201
$657$	1.08079e6	0.0976850
$658$	520578.	0.0468728
$659$	1.94787e6	0.174721	0.0873606	−	0.996177i	$-0.472157\pi$
$659$	1.94787e6	0.174721	0.0873606	+	0.996177i	$0.472157\pi$
$660$	296490.	0.0264942
$661$	−1.04897e7	−0.933810	−0.466905	−	0.884307i	$-0.654631\pi$
$661$	−1.04897e7	−0.933810	−0.466905	+	0.884307i	$0.654631\pi$
$662$	1.00798e7	0.893936
$663$	−399142.	−0.0352650
$664$	1.12450e6	0.0989784
$665$	319785.	0.0280417
$666$	−2.92312e6	−0.255365
$667$	1.27580e6	0.111037
$668$	2.25064e6	0.195148
$669$	8.78494e6	0.758881
$670$	1.34262e6	0.115549
$671$	2.04480e7	1.75325
$672$	216252.	0.0184730
$673$	−1.81198e6	−0.154211	−0.0771054	−	0.997023i	$-0.524568\pi$
$673$	−1.81198e6	−0.154211	−0.0771054	+	0.997023i	$0.524568\pi$
$674$	1.81134e6	0.153586
$675$	−1.22538e7	−1.03517
$676$	1.73267e6	0.145831
$677$	−1.71538e7	−1.43843	−0.719216	−	0.694786i	$-0.755499\pi$
$677$	−1.71538e7	−1.43843	−0.719216	+	0.694786i	$0.755499\pi$
$678$	−5.98682e6	−0.500175
$679$	2572.50	0.000214132 0
$680$	619024.	0.0513376
$681$	−8.96308e6	−0.740610
$682$	1.58979e7	1.30882
$683$	1.80610e7	1.48146	0.740732	−	0.671801i	$-0.234479\pi$
$683$	1.80610e7	1.48146	0.740732	+	0.671801i	$0.234479\pi$
$684$	1.64207e6	0.134200
$685$	3.53033e6	0.287467
$686$	1.93890e6	0.157306
$687$	7.92140e6	0.640339
$688$	1.56546e6	0.126087
$689$	−1.09996e6	−0.0882732
$690$	−222015.	−0.0177525
$691$	−1.44368e7	−1.15021	−0.575105	−	0.818080i	$-0.695039\pi$
$691$	−1.44368e7	−1.15021	−0.575105	+	0.818080i	$0.695039\pi$
$692$	−1.42792e6	−0.113354
$693$	−717966.	−0.0567899
$694$	−2.23513e7	−1.76159
$695$	−3.24271e6	−0.254651
$696$	−7.15768e6	−0.560079
$697$	350442.	0.0273233
$698$	1.34636e7	1.04598
$699$	2.47145e6	0.191319
$700$	−162011.	−0.0124968
$701$	−1.39926e7	−1.07549	−0.537743	−	0.843109i	$-0.680723\pi$
$701$	−1.39926e7	−1.07549	−0.537743	+	0.843109i	$0.680723\pi$
$702$	2.27090e6	0.173923
$703$	1.41975e7	1.08349
$704$	−2.01197e7	−1.53000
$705$	−993165.	−0.0752573
$706$	−1.20894e7	−0.912836
$707$	725425.	0.0545813
$708$	−1.49034e6	−0.111738
$709$	−1.37678e7	−1.02860	−0.514302	−	0.857609i	$-0.671949\pi$
$709$	−1.37678e7	−1.02860	−0.514302	+	0.857609i	$0.671949\pi$
$710$	−2.81740e6	−0.209750
$711$	−6.59331e6	−0.489136
$712$	8.21864e6	0.607575
$713$	2.10955e6	0.155405
$714$	214631.	0.0157561
$715$	588090.	0.0430208
$716$	−1.01916e6	−0.0742947
$717$	−1.97362e7	−1.43373
$718$	−7.38120e6	−0.534338
$719$	−8.26505e6	−0.596243	−0.298121	−	0.954528i	$-0.596360\pi$
$719$	−8.26505e6	−0.596243	−0.298121	+	0.954528i	$0.596360\pi$
$720$	−962867.	−0.0692205
$721$	−2.34137e6	−0.167738
$722$	3.20974e7	2.29154
$723$	−1.11060e7	−0.790158
$724$	904479.	0.0641286
$725$	1.00232e7	0.708206
$726$	−8.78333e6	−0.618469
$727$	7.18688e6	0.504318	0.252159	−	0.967686i	$-0.418859\pi$
$727$	7.18688e6	0.504318	0.252159	+	0.967686i	$0.418859\pi$
$728$	229481.	0.0160479
$729$	1.30957e7	0.912663
$730$	476043.	0.0330628
$731$	−608330.	−0.0421062
$732$	−1.99166e6	−0.137384
$733$	−1.10728e6	−0.0761196	−0.0380598	−	0.999275i	$-0.512118\pi$
$733$	−1.10728e6	−0.0761196	−0.0380598	+	0.999275i	$0.512118\pi$
$734$	1.37966e7	0.945217
$735$	−1.84272e6	−0.125818
$736$	−666322.	−0.0453409
$737$	1.46408e7	0.992878
$738$	−644339.	−0.0435485
$739$	1.98449e7	1.33671	0.668356	−	0.743841i	$-0.266998\pi$
$739$	1.98449e7	1.33671	0.668356	+	0.743841i	$0.266998\pi$
$740$	228154.	0.0153161
$741$	−3.56444e6	−0.238477
$742$	591484.	0.0394396
$743$	−2.19204e7	−1.45672	−0.728360	−	0.685194i	$-0.759717\pi$
$743$	−2.19204e7	−1.45672	−0.728360	+	0.685194i	$0.759717\pi$
$744$	−1.18353e7	−0.783875
$745$	−237006.	−0.0156448
$746$	1.82098e7	1.19800
$747$	679697.	0.0445671
$748$	883172.	0.0577153
$749$	1.75825e6	0.114518
$750$	−3.54379e6	−0.230046
$751$	−1.62135e7	−1.04900	−0.524502	−	0.851409i	$-0.675748\pi$
$751$	−1.62135e7	−1.04900	−0.524502	+	0.851409i	$0.675748\pi$
$752$	7.61307e6	0.490925
$753$	−1.42140e6	−0.0913545
$754$	−1.85751e6	−0.118988
$755$	−2.73146e6	−0.174392
$756$	216392.	0.0137701
$757$	1.31863e7	0.836342	0.418171	−	0.908368i	$-0.362671\pi$
$757$	1.31863e7	0.836342	0.418171	+	0.908368i	$0.362671\pi$
$758$	7.41412e6	0.468691
$759$	−2.42099e6	−0.152542
$760$	5.52805e6	0.347166
$761$	−1.92620e7	−1.20570	−0.602851	−	0.797854i	$-0.705969\pi$
$761$	−1.92620e7	−1.20570	−0.602851	+	0.797854i	$0.705969\pi$
$762$	−6.45670e6	−0.402831
$763$	952983.	0.0592617
$764$	3.15973e6	0.195847
$765$	374165.	0.0231158
$766$	−1.46736e7	−0.903577
$767$	−2.95610e6	−0.181439
$768$	5.20888e6	0.318670
$769$	−456438.	−0.0278334	−0.0139167	−	0.999903i	$-0.504430\pi$
$769$	−456438.	−0.0278334	−0.0139167	+	0.999903i	$0.504430\pi$
$770$	−316235.	−0.0192213
$771$	−1.75710e7	−1.06454
$772$	−2.16953e6	−0.131016
$773$	−6.14461e6	−0.369867	−0.184933	−	0.982751i	$-0.559207\pi$
$773$	−6.14461e6	−0.369867	−0.184933	+	0.982751i	$0.559207\pi$
$774$	1.11850e6	0.0671097
$775$	1.65734e7	0.991191
$776$	44470.2	0.00265103
$777$	604628.	0.0359282
$778$	−861961.	−0.0510551
$779$	3.12953e6	0.184772
$780$	−57280.6	−0.00337110
$781$	−3.07227e7	−1.80232
$782$	−661328.	−0.0386723
$783$	−1.33875e7	−0.780361
$784$	1.41253e7	0.820745
$785$	1.00203e6	0.0580369
$786$	4.65949e6	0.269018
$787$	8.50558e6	0.489516	0.244758	−	0.969584i	$-0.421291\pi$
$787$	8.50558e6	0.489516	0.244758	+	0.969584i	$0.421291\pi$
$788$	4.68755e6	0.268925
$789$	1.20897e6	0.0691389
$790$	−2.90408e6	−0.165554
$791$	−1.13154e6	−0.0643029
$792$	−1.24113e7	−0.703080
$793$	−3.95047e6	−0.223082
$794$	−1.97833e7	−1.11365
$795$	−1.12844e6	−0.0633228
$796$	−1.25164e6	−0.0700160
$797$	1.28439e7	0.716227	0.358113	−	0.933678i	$-0.383420\pi$
$797$	1.28439e7	0.716227	0.358113	+	0.933678i	$0.383420\pi$
$798$	1.91671e6	0.106549
$799$	−2.95840e6	−0.163942
$800$	−5.23488e6	−0.289189
$801$	4.96770e6	0.273573
$802$	2.39517e7	1.31492
$803$	5.19108e6	0.284099
$804$	−1.42603e6	−0.0778016
$805$	−41962.1	−0.00228227
$806$	−3.07141e6	−0.166533
$807$	−9.34670e6	−0.505213
$808$	1.25403e7	0.675738
$809$	2.98801e7	1.60513	0.802567	−	0.596562i	$-0.203467\pi$
$809$	2.98801e7	1.60513	0.802567	+	0.596562i	$0.203467\pi$
$810$	888861.	0.0476016
$811$	−2.05001e7	−1.09447	−0.547234	−	0.836980i	$-0.684319\pi$
$811$	−2.05001e7	−1.09447	−0.547234	+	0.836980i	$0.684319\pi$
$812$	−177000.	−0.00942070
$813$	−2.51098e7	−1.33234
$814$	−1.40399e7	−0.742682
$815$	−4.35415e6	−0.229620
$816$	3.13882e6	0.165022
$817$	−5.43254e6	−0.284740
$818$	2.00185e7	1.04604
$819$	138708.	0.00722589
$820$	50291.7	0.00261193
$821$	2.20698e7	1.14272	0.571360	−	0.820699i	$-0.306416\pi$
$821$	2.20698e7	1.14272	0.571360	+	0.820699i	$0.306416\pi$
$822$	2.11599e7	1.09228
$823$	1.59817e6	0.0822476	0.0411238	−	0.999154i	$-0.486906\pi$
$823$	1.59817e6	0.0822476	0.0411238	+	0.999154i	$0.486906\pi$
$824$	−4.04747e7	−2.07666
$825$	−1.90202e7	−0.972929
$826$	1.58959e6	0.0810653
$827$	−1.49218e7	−0.758680	−0.379340	−	0.925257i	$-0.623849\pi$
$827$	−1.49218e7	−0.758680	−0.379340	+	0.925257i	$0.623849\pi$
$828$	−215473.	−0.0109223
$829$	7.71986e6	0.390142	0.195071	−	0.980789i	$-0.437506\pi$
$829$	7.71986e6	0.390142	0.195071	+	0.980789i	$0.437506\pi$
$830$	299379.	0.0150843
$831$	1.77439e7	0.891344
$832$	3.88704e6	0.194675
$833$	−5.48902e6	−0.274083
$834$	−1.94360e7	−0.967592
$835$	4.57973e6	0.227313
$836$	7.88695e6	0.390295
$837$	−2.21364e7	−1.09218
$838$	1.50115e7	0.738439
$839$	3.50556e7	1.71930	0.859652	−	0.510880i	$-0.170680\pi$
$839$	3.50556e7	1.71930	0.859652	+	0.510880i	$0.170680\pi$
$840$	235422.	0.0115120
$841$	−9.56068e6	−0.466121
$842$	7.40258e6	0.359834
$843$	2.54692e7	1.23437
$844$	2.99211e6	0.144585
$845$	3.52575e6	0.169867
$846$	5.43945e6	0.261294
$847$	−1.66010e6	−0.0795108
$848$	8.65001e6	0.413073
$849$	2.04284e7	0.972668
$850$	−5.19565e6	−0.246656
$851$	−1.86300e6	−0.0881837
$852$	2.99243e6	0.141229
$853$	−2.21072e7	−1.04031	−0.520153	−	0.854073i	$-0.674125\pi$
$853$	−2.21072e7	−1.04031	−0.520153	+	0.854073i	$0.674125\pi$
$854$	2.12429e6	0.0996712
$855$	3.34139e6	0.156319
$856$	3.03944e7	1.41778
$857$	1.60053e7	0.744410	0.372205	−	0.928151i	$-0.378602\pi$
$857$	1.60053e7	0.744410	0.372205	+	0.928151i	$0.378602\pi$
$858$	3.52487e6	0.163465
$859$	−2.09057e7	−0.966677	−0.483338	−	0.875434i	$-0.660576\pi$
$859$	−2.09057e7	−0.966677	−0.483338	+	0.875434i	$0.660576\pi$
$860$	−87301.0	−0.00402507
$861$	133277.	0.00612700
$862$	−2.49200e7	−1.14230
$863$	1.41874e7	0.648449	0.324224	−	0.945980i	$-0.394897\pi$
$863$	1.41874e7	0.648449	0.324224	+	0.945980i	$0.394897\pi$
$864$	6.99201e6	0.318653
$865$	−2.90561e6	−0.132037
$866$	1.11322e6	0.0504412
$867$	1.47797e7	0.667755
$868$	−292671.	−0.0131850
$869$	−3.16680e7	−1.42256
$870$	−1.90560e6	−0.0853561
$871$	−2.82854e6	−0.126333
$872$	1.64740e7	0.733682
$873$	26879.7	0.00119368
$874$	−5.90583e6	−0.261519
$875$	−669798.	−0.0295749
$876$	−505618.	−0.0222619
$877$	2.06566e7	0.906901	0.453450	−	0.891282i	$-0.350193\pi$
$877$	2.06566e7	0.906901	0.453450	+	0.891282i	$0.350193\pi$
$878$	2.89759e6	0.126853
$879$	2.17477e7	0.949382
$880$	−4.62470e6	−0.201315
$881$	−1.35902e7	−0.589909	−0.294955	−	0.955511i	$-0.595305\pi$
$881$	−1.35902e7	−0.589909	−0.294955	+	0.955511i	$0.595305\pi$
$882$	1.00924e7	0.436839
$883$	1.20900e7	0.521824	0.260912	−	0.965363i	$-0.415977\pi$
$883$	1.20900e7	0.521824	0.260912	+	0.965363i	$0.415977\pi$
$884$	−170625.	−0.00734365
$885$	−3.03264e6	−0.130155
$886$	−6.44115e6	−0.275663
$887$	1.83559e7	0.783371	0.391685	−	0.920099i	$-0.371892\pi$
$887$	1.83559e7	0.783371	0.391685	+	0.920099i	$0.371892\pi$
$888$	1.04521e7	0.444805
$889$	−1.22035e6	−0.0517883
$890$	2.18807e6	0.0925946
$891$	9.69271e6	0.409026
$892$	3.75538e6	0.158031
$893$	−2.64192e7	−1.10864
$894$	−1.42056e6	−0.0594451
$895$	−2.07384e6	−0.0865401
$896$	−1.47607e6	−0.0614238
$897$	467725.	0.0194093
$898$	8.39635e6	0.347456
$899$	1.81067e7	0.747206
$900$	−1.69283e6	−0.0696639
$901$	−3.36134e6	−0.137943
$902$	−3.09479e6	−0.126653
$903$	−231355.	−0.00944190
$904$	−1.95608e7	−0.796094
$905$	1.84049e6	0.0746984
$906$	−1.63717e7	−0.662634
$907$	1.78761e7	0.721531	0.360765	−	0.932657i	$-0.382515\pi$
$907$	1.78761e7	0.721531	0.360765	+	0.932657i	$0.382515\pi$
$908$	−3.83153e6	−0.154226
$909$	7.57987e6	0.304265
$910$	61095.1	0.00244570
$911$	−1.47994e7	−0.590809	−0.295405	−	0.955372i	$-0.595454\pi$
$911$	−1.47994e7	−0.590809	−0.295405	+	0.955372i	$0.595454\pi$
$912$	2.80305e7	1.11595
$913$	3.26462e6	0.129615
$914$	2.31588e7	0.916961
$915$	−4.05275e6	−0.160028
$916$	3.38623e6	0.133345
$917$	880670.	0.0345852
$918$	6.93961e6	0.271787
$919$	−2.50852e6	−0.0979780	−0.0489890	−	0.998799i	$-0.515600\pi$
$919$	−2.50852e6	−0.0979780	−0.0489890	+	0.998799i	$0.515600\pi$
$920$	−725390.	−0.0282554
$921$	2.65225e7	1.03030
$922$	−4.51315e7	−1.74845
$923$	5.93549e6	0.229325
$924$	335881.	0.0129421
$925$	−1.46364e7	−0.562445
$926$	−4.43626e7	−1.70016
$927$	−2.44646e7	−0.935060
$928$	−5.71919e6	−0.218004
$929$	−9.51733e6	−0.361806	−0.180903	−	0.983501i	$-0.557902\pi$
$929$	−9.51733e6	−0.361806	−0.180903	+	0.983501i	$0.557902\pi$
$930$	−3.15094e6	−0.119463
$931$	−4.90183e7	−1.85347
$932$	1.05649e6	0.0398407
$933$	−1.41906e7	−0.533698
$934$	−3.61025e6	−0.135416
$935$	1.79713e6	0.0672281
$936$	2.39781e6	0.0894593
$937$	4.27838e6	0.159195	0.0795977	−	0.996827i	$-0.474636\pi$
$937$	4.27838e6	0.159195	0.0795977	+	0.996827i	$0.474636\pi$
$938$	1.52099e6	0.0564444
$939$	1.37238e7	0.507939
$940$	−424557.	−0.0156717
$941$	−3.20489e7	−1.17988	−0.589941	−	0.807446i	$-0.700849\pi$
$941$	−3.20489e7	−1.17988	−0.589941	+	0.807446i	$0.700849\pi$
$942$	6.00590e6	0.220521
$943$	−410657.	−0.0150384
$944$	2.32466e7	0.849041
$945$	440327.	0.0160397
$946$	5.37223e6	0.195176
$947$	1.34081e7	0.485841	0.242920	−	0.970046i	$-0.421895\pi$
$947$	1.34081e7	0.485841	0.242920	+	0.970046i	$0.421895\pi$
$948$	3.08450e6	0.111471
$949$	−1.00289e6	−0.0361485
$950$	−4.63985e7	−1.66799
$951$	−7.77389e6	−0.278732
$952$	701265.	0.0250778
$953$	4.23589e7	1.51082	0.755409	−	0.655254i	$-0.227438\pi$
$953$	4.23589e7	1.51082	0.755409	+	0.655254i	$0.227438\pi$
$954$	6.18033e6	0.219857
$955$	6.42961e6	0.228127
$956$	−8.43683e6	−0.298562
$957$	−2.07799e7	−0.733440
$958$	−3.98267e7	−1.40204
$959$	3.99935e6	0.140425
$960$	3.98768e6	0.139650
$961$	1.31048e6	0.0457745
$962$	2.71245e6	0.0944982
$963$	1.83717e7	0.638385
$964$	−4.74760e6	−0.164544
$965$	−4.41470e6	−0.152610
$966$	−251511.	−0.00867190
$967$	−4.12202e7	−1.41757	−0.708785	−	0.705425i	$-0.750756\pi$
$967$	−4.12202e7	−1.41757	−0.708785	+	0.705425i	$0.750756\pi$
$968$	−2.86978e7	−0.984373
$969$	−1.08925e7	−0.372665
$970$	11839.4	0.000404018 0
$971$	−1.13026e7	−0.384708	−0.192354	−	0.981326i	$-0.561612\pi$
$971$	−1.13026e7	−0.384708	−0.192354	+	0.981326i	$0.561612\pi$
$972$	3.79140e6	0.128716
$973$	−3.67352e6	−0.124394
$974$	2.51312e7	0.848820
$975$	3.67463e6	0.123795
$976$	3.10662e7	1.04391
$977$	−2.79073e7	−0.935367	−0.467684	−	0.883896i	$-0.654911\pi$
$977$	−2.79073e7	−0.935367	−0.467684	+	0.883896i	$0.654911\pi$
$978$	−2.60977e7	−0.872480
$979$	2.38601e7	0.795638
$980$	−787725.	−0.0262005
$981$	9.95758e6	0.330355
$982$	347568.	0.0115017
$983$	−1.22161e7	−0.403226	−0.201613	−	0.979465i	$-0.564618\pi$
$983$	−1.22161e7	−0.403226	−0.201613	+	0.979465i	$0.564618\pi$
$984$	2.30393e6	0.0758546
$985$	9.53852e6	0.313249
$986$	−5.67633e6	−0.185941
$987$	−1.12511e6	−0.0367623
$988$	−1.52372e6	−0.0496608
$989$	712858.	0.0231746
$990$	−3.30429e6	−0.107150
$991$	2.47723e7	0.801277	0.400638	−	0.916236i	$-0.368788\pi$
$991$	2.47723e7	0.801277	0.400638	+	0.916236i	$0.368788\pi$
$992$	−9.45675e6	−0.305114
$993$	−2.17852e7	−0.701113
$994$	−3.19170e6	−0.102461
$995$	−2.54691e6	−0.0815561
$996$	−317978.	−0.0101566
$997$	2.12381e7	0.676670	0.338335	−	0.941026i	$-0.390136\pi$
$997$	2.12381e7	0.676670	0.338335	+	0.941026i	$0.390136\pi$
$998$	−1.52873e7	−0.485851
$999$	1.95493e7	0.619750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.a.1.7	✓	8
3.2	odd	2		387.6.a.c.1.2		8
4.3	odd	2		688.6.a.e.1.6		8
5.4	even	2		1075.6.a.a.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.a.1.7	✓	8	1.1	even	1	trivial
387.6.a.c.1.2		8	3.2	odd	2
688.6.a.e.1.6		8	4.3	odd	2
1075.6.a.a.1.2		8	5.4	even	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q+5.21373 q^{2} -11.2683 q^{3} -4.81697 q^{4} -9.80186 q^{5} -58.7500 q^{6} -11.1041 q^{7} -191.954 q^{8} -116.025 q^{9} +O(q^{10})\)	\(q+5.21373 q^{2} -11.2683 q^{3} -4.81697 q^{4} -9.80186 q^{5} -58.7500 q^{6} -11.1041 q^{7} -191.954 q^{8} -116.025 q^{9} -51.1043 q^{10} -557.274 q^{11} +54.2791 q^{12} +107.663 q^{13} -57.8938 q^{14} +110.450 q^{15} -846.654 q^{16} +329.005 q^{17} -604.924 q^{18} +2938.10 q^{19} +47.2153 q^{20} +125.124 q^{21} -2905.48 q^{22} -385.537 q^{23} +2163.00 q^{24} -3028.92 q^{25} +561.326 q^{26} +4045.61 q^{27} +53.4881 q^{28} -3309.15 q^{29} +575.859 q^{30} -5471.71 q^{31} +1728.30 q^{32} +6279.54 q^{33} +1715.34 q^{34} +108.841 q^{35} +558.890 q^{36} +4832.22 q^{37} +15318.5 q^{38} -1213.18 q^{39} +1881.51 q^{40} +1065.16 q^{41} +652.365 q^{42} -1849.00 q^{43} +2684.37 q^{44} +1137.26 q^{45} -2010.09 q^{46} -8991.95 q^{47} +9540.36 q^{48} -16683.7 q^{49} -15792.0 q^{50} -3707.33 q^{51} -518.609 q^{52} -10216.7 q^{53} +21092.7 q^{54} +5462.32 q^{55} +2131.47 q^{56} -33107.4 q^{57} -17253.0 q^{58} -27457.0 q^{59} -532.036 q^{60} -36692.9 q^{61} -28528.1 q^{62} +1288.35 q^{63} +36103.8 q^{64} -1055.30 q^{65} +32739.9 q^{66} -26272.2 q^{67} -1584.81 q^{68} +4344.35 q^{69} +567.467 q^{70} +55130.3 q^{71} +22271.5 q^{72} -9315.14 q^{73} +25193.9 q^{74} +34130.9 q^{75} -14152.7 q^{76} +6188.02 q^{77} -6325.20 q^{78} +56826.5 q^{79} +8298.78 q^{80} -17393.1 q^{81} +5553.44 q^{82} -5858.19 q^{83} -602.721 q^{84} -3224.86 q^{85} -9640.20 q^{86} +37288.5 q^{87} +106971. q^{88} -42815.7 q^{89} +5929.38 q^{90} -1195.50 q^{91} +1857.12 q^{92} +61657.0 q^{93} -46881.7 q^{94} -28798.8 q^{95} -19475.0 q^{96} -231.671 q^{97} -86984.4 q^{98} +64657.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9} - 617 q^{10} - 532 q^{11} - 4195 q^{12} - 2492 q^{13} - 4240 q^{14} - 1780 q^{15} + 1882 q^{16} - 2534 q^{17} - 3711 q^{18} - 1678 q^{19} - 2607 q^{20} - 2256 q^{21} + 11502 q^{22} - 2488 q^{23} + 19953 q^{24} + 4378 q^{25} + 4586 q^{26} - 8960 q^{27} + 18640 q^{28} - 4360 q^{29} + 25092 q^{30} + 5704 q^{31} - 18294 q^{32} - 12852 q^{33} + 30007 q^{34} + 5640 q^{35} + 67969 q^{36} - 3772 q^{37} - 6559 q^{38} + 11120 q^{39} + 14869 q^{40} - 10698 q^{41} + 78698 q^{42} - 14792 q^{43} - 356 q^{44} - 44912 q^{45} - 19389 q^{46} - 77864 q^{47} - 118727 q^{48} + 7188 q^{49} + 26877 q^{50} - 80246 q^{51} - 60736 q^{52} - 62352 q^{53} + 61026 q^{54} - 49552 q^{55} - 144528 q^{56} - 808 q^{57} + 52951 q^{58} - 26224 q^{59} + 101500 q^{60} - 82540 q^{61} - 9023 q^{62} - 61768 q^{63} + 153858 q^{64} - 5000 q^{65} - 48516 q^{66} + 27784 q^{67} + 40507 q^{68} - 93776 q^{69} + 185910 q^{70} - 9504 q^{71} - 186687 q^{72} + 14260 q^{73} - 15239 q^{74} + 167420 q^{75} + 1279 q^{76} - 218140 q^{77} + 264170 q^{78} + 160248 q^{79} - 1291 q^{80} + 161076 q^{81} - 47781 q^{82} - 77176 q^{83} + 16382 q^{84} + 141096 q^{85} + 22188 q^{86} + 268136 q^{87} + 129544 q^{88} - 265692 q^{89} + 48990 q^{90} + 401148 q^{91} + 190391 q^{92} - 123860 q^{93} + 248737 q^{94} + 135884 q^{95} + 950817 q^{96} + 144742 q^{97} - 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9 - 617 * q^10 - 532 * q^11 - 4195 * q^12 - 2492 * q^13 - 4240 * q^14 - 1780 * q^15 + 1882 * q^16 - 2534 * q^17 - 3711 * q^18 - 1678 * q^19 - 2607 * q^20 - 2256 * q^21 + 11502 * q^22 - 2488 * q^23 + 19953 * q^24 + 4378 * q^25 + 4586 * q^26 - 8960 * q^27 + 18640 * q^28 - 4360 * q^29 + 25092 * q^30 + 5704 * q^31 - 18294 * q^32 - 12852 * q^33 + 30007 * q^34 + 5640 * q^35 + 67969 * q^36 - 3772 * q^37 - 6559 * q^38 + 11120 * q^39 + 14869 * q^40 - 10698 * q^41 + 78698 * q^42 - 14792 * q^43 - 356 * q^44 - 44912 * q^45 - 19389 * q^46 - 77864 * q^47 - 118727 * q^48 + 7188 * q^49 + 26877 * q^50 - 80246 * q^51 - 60736 * q^52 - 62352 * q^53 + 61026 * q^54 - 49552 * q^55 - 144528 * q^56 - 808 * q^57 + 52951 * q^58 - 26224 * q^59 + 101500 * q^60 - 82540 * q^61 - 9023 * q^62 - 61768 * q^63 + 153858 * q^64 - 5000 * q^65 - 48516 * q^66 + 27784 * q^67 + 40507 * q^68 - 93776 * q^69 + 185910 * q^70 - 9504 * q^71 - 186687 * q^72 + 14260 * q^73 - 15239 * q^74 + 167420 * q^75 + 1279 * q^76 - 218140 * q^77 + 264170 * q^78 + 160248 * q^79 - 1291 * q^80 + 161076 * q^81 - 47781 * q^82 - 77176 * q^83 + 16382 * q^84 + 141096 * q^85 + 22188 * q^86 + 268136 * q^87 + 129544 * q^88 - 265692 * q^89 + 48990 * q^90 + 401148 * q^91 + 190391 * q^92 - 123860 * q^93 + 248737 * q^94 + 135884 * q^95 + 950817 * q^96 + 144742 * q^97 - 292244 * q^98 + 239516 * q^99

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