Properties

Label 147.6.c.d.146.13
Level $147$
Weight $6$
Character 147.146
Analytic conductor $23.576$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,6,Mod(146,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.146");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.13
Character \(\chi\) \(=\) 147.146
Dual form 147.6.c.d.146.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-10.7583i q^{2} +(14.9806 - 4.31048i) q^{3} -83.7406 q^{4} -26.3120 q^{5} +(-46.3734 - 161.166i) q^{6} +556.640i q^{8} +(205.839 - 129.148i) q^{9} +O(q^{10})\) \(q-10.7583i q^{2} +(14.9806 - 4.31048i) q^{3} -83.7406 q^{4} -26.3120 q^{5} +(-46.3734 - 161.166i) q^{6} +556.640i q^{8} +(205.839 - 129.148i) q^{9} +283.072i q^{10} +604.422i q^{11} +(-1254.49 + 360.963i) q^{12} +732.880i q^{13} +(-394.170 + 113.417i) q^{15} +3308.79 q^{16} -1696.88 q^{17} +(-1389.41 - 2214.48i) q^{18} +211.839i q^{19} +2203.38 q^{20} +6502.54 q^{22} +966.176i q^{23} +(2399.39 + 8338.83i) q^{24} -2432.68 q^{25} +7884.53 q^{26} +(2526.92 - 2821.98i) q^{27} -764.382i q^{29} +(1220.18 + 4240.60i) q^{30} +79.9439i q^{31} -17784.4i q^{32} +(2605.35 + 9054.63i) q^{33} +18255.5i q^{34} +(-17237.1 + 10814.9i) q^{36} -643.992 q^{37} +2279.03 q^{38} +(3159.07 + 10979.0i) q^{39} -14646.3i q^{40} -5200.75 q^{41} +5841.96 q^{43} -50614.7i q^{44} +(-5416.04 + 3398.13i) q^{45} +10394.4 q^{46} -10774.3 q^{47} +(49567.9 - 14262.5i) q^{48} +26171.5i q^{50} +(-25420.3 + 7314.37i) q^{51} -61371.9i q^{52} -9768.69i q^{53} +(-30359.7 - 27185.3i) q^{54} -15903.5i q^{55} +(913.130 + 3173.49i) q^{57} -8223.44 q^{58} -10491.3 q^{59} +(33008.1 - 9497.64i) q^{60} +47115.9i q^{61} +860.059 q^{62} -85448.6 q^{64} -19283.5i q^{65} +(97412.3 - 28029.1i) q^{66} +48582.8 q^{67} +142098. q^{68} +(4164.69 + 14473.9i) q^{69} -28803.7i q^{71} +(71888.8 + 114579. i) q^{72} +72915.2i q^{73} +6928.25i q^{74} +(-36443.1 + 10486.0i) q^{75} -17739.6i q^{76} +(118115. - 33986.2i) q^{78} -70838.8 q^{79} -87060.9 q^{80} +(25690.7 - 53167.4i) q^{81} +55951.1i q^{82} -33914.5 q^{83} +44648.2 q^{85} -62849.5i q^{86} +(-3294.86 - 11450.9i) q^{87} -336446. q^{88} -84328.4 q^{89} +(36558.1 + 58267.3i) q^{90} -80908.2i q^{92} +(344.597 + 1197.61i) q^{93} +115913. i q^{94} -5573.91i q^{95} +(-76659.6 - 266422. i) q^{96} +17034.2i q^{97} +(78059.7 + 124414. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.7583i 1.90181i −0.309478 0.950907i \(-0.600154\pi\)
0.309478 0.950907i \(-0.399846\pi\)
\(3\) 14.9806 4.31048i 0.961009 0.276518i
\(4\) −83.7406 −2.61689
\(5\) −26.3120 −0.470683 −0.235342 0.971913i \(-0.575621\pi\)
−0.235342 + 0.971913i \(0.575621\pi\)
\(6\) −46.3734 161.166i −0.525885 1.82766i
\(7\) 0 0
\(8\) 556.640i 3.07503i
\(9\) 205.839 129.148i 0.847076 0.531472i
\(10\) 283.072i 0.895151i
\(11\) 604.422i 1.50612i 0.657954 + 0.753058i \(0.271422\pi\)
−0.657954 + 0.753058i \(0.728578\pi\)
\(12\) −1254.49 + 360.963i −2.51486 + 0.723618i
\(13\) 732.880i 1.20275i 0.798968 + 0.601374i \(0.205380\pi\)
−0.798968 + 0.601374i \(0.794620\pi\)
\(14\) 0 0
\(15\) −394.170 + 113.417i −0.452331 + 0.130152i
\(16\) 3308.79 3.23124
\(17\) −1696.88 −1.42406 −0.712030 0.702149i \(-0.752224\pi\)
−0.712030 + 0.702149i \(0.752224\pi\)
\(18\) −1389.41 2214.48i −1.01076 1.61098i
\(19\) 211.839i 0.134624i 0.997732 + 0.0673120i \(0.0214423\pi\)
−0.997732 + 0.0673120i \(0.978558\pi\)
\(20\) 2203.38 1.23173
\(21\) 0 0
\(22\) 6502.54 2.86435
\(23\) 966.176i 0.380835i 0.981703 + 0.190417i \(0.0609842\pi\)
−0.981703 + 0.190417i \(0.939016\pi\)
\(24\) 2399.39 + 8338.83i 0.850301 + 2.95513i
\(25\) −2432.68 −0.778457
\(26\) 7884.53 2.28740
\(27\) 2526.92 2821.98i 0.667086 0.744981i
\(28\) 0 0
\(29\) 764.382i 0.168778i −0.996433 0.0843889i \(-0.973106\pi\)
0.996433 0.0843889i \(-0.0268938\pi\)
\(30\) 1220.18 + 4240.60i 0.247525 + 0.860248i
\(31\) 79.9439i 0.0149410i 0.999972 + 0.00747052i \(0.00237796\pi\)
−0.999972 + 0.00747052i \(0.997622\pi\)
\(32\) 17784.4i 3.07019i
\(33\) 2605.35 + 9054.63i 0.416468 + 1.44739i
\(34\) 18255.5i 2.70830i
\(35\) 0 0
\(36\) −17237.1 + 10814.9i −2.21671 + 1.39081i
\(37\) −643.992 −0.0773350 −0.0386675 0.999252i \(-0.512311\pi\)
−0.0386675 + 0.999252i \(0.512311\pi\)
\(38\) 2279.03 0.256030
\(39\) 3159.07 + 10979.0i 0.332581 + 1.15585i
\(40\) 14646.3i 1.44737i
\(41\) −5200.75 −0.483177 −0.241589 0.970379i \(-0.577668\pi\)
−0.241589 + 0.970379i \(0.577668\pi\)
\(42\) 0 0
\(43\) 5841.96 0.481823 0.240912 0.970547i \(-0.422554\pi\)
0.240912 + 0.970547i \(0.422554\pi\)
\(44\) 50614.7i 3.94135i
\(45\) −5416.04 + 3398.13i −0.398704 + 0.250155i
\(46\) 10394.4 0.724277
\(47\) −10774.3 −0.711449 −0.355724 0.934591i \(-0.615766\pi\)
−0.355724 + 0.934591i \(0.615766\pi\)
\(48\) 49567.9 14262.5i 3.10525 0.893496i
\(49\) 0 0
\(50\) 26171.5i 1.48048i
\(51\) −25420.3 + 7314.37i −1.36854 + 0.393778i
\(52\) 61371.9i 3.14747i
\(53\) 9768.69i 0.477691i −0.971058 0.238845i \(-0.923231\pi\)
0.971058 0.238845i \(-0.0767689\pi\)
\(54\) −30359.7 27185.3i −1.41681 1.26867i
\(55\) 15903.5i 0.708904i
\(56\) 0 0
\(57\) 913.130 + 3173.49i 0.0372259 + 0.129375i
\(58\) −8223.44 −0.320984
\(59\) −10491.3 −0.392374 −0.196187 0.980566i \(-0.562856\pi\)
−0.196187 + 0.980566i \(0.562856\pi\)
\(60\) 33008.1 9497.64i 1.18370 0.340595i
\(61\) 47115.9i 1.62122i 0.585585 + 0.810611i \(0.300865\pi\)
−0.585585 + 0.810611i \(0.699135\pi\)
\(62\) 860.059 0.0284151
\(63\) 0 0
\(64\) −85448.6 −2.60769
\(65\) 19283.5i 0.566113i
\(66\) 97412.3 28029.1i 2.75267 0.792044i
\(67\) 48582.8 1.32219 0.661097 0.750300i \(-0.270091\pi\)
0.661097 + 0.750300i \(0.270091\pi\)
\(68\) 142098. 3.72662
\(69\) 4164.69 + 14473.9i 0.105308 + 0.365986i
\(70\) 0 0
\(71\) 28803.7i 0.678113i −0.940766 0.339056i \(-0.889892\pi\)
0.940766 0.339056i \(-0.110108\pi\)
\(72\) 71888.8 + 114579.i 1.63429 + 2.60479i
\(73\) 72915.2i 1.60144i 0.599038 + 0.800721i \(0.295550\pi\)
−0.599038 + 0.800721i \(0.704450\pi\)
\(74\) 6928.25i 0.147077i
\(75\) −36443.1 + 10486.0i −0.748104 + 0.215257i
\(76\) 17739.6i 0.352297i
\(77\) 0 0
\(78\) 118115. 33986.2i 2.19821 0.632508i
\(79\) −70838.8 −1.27704 −0.638518 0.769607i \(-0.720452\pi\)
−0.638518 + 0.769607i \(0.720452\pi\)
\(80\) −87060.9 −1.52089
\(81\) 25690.7 53167.4i 0.435075 0.900394i
\(82\) 55951.1i 0.918913i
\(83\) −33914.5 −0.540368 −0.270184 0.962809i \(-0.587085\pi\)
−0.270184 + 0.962809i \(0.587085\pi\)
\(84\) 0 0
\(85\) 44648.2 0.670281
\(86\) 62849.5i 0.916338i
\(87\) −3294.86 11450.9i −0.0466701 0.162197i
\(88\) −336446. −4.63136
\(89\) −84328.4 −1.12849 −0.564247 0.825606i \(-0.690833\pi\)
−0.564247 + 0.825606i \(0.690833\pi\)
\(90\) 36558.1 + 58267.3i 0.475748 + 0.758261i
\(91\) 0 0
\(92\) 80908.2i 0.996605i
\(93\) 344.597 + 1197.61i 0.00413147 + 0.0143585i
\(94\) 115913.i 1.35304i
\(95\) 5573.91i 0.0633652i
\(96\) −76659.6 266422.i −0.848962 2.95048i
\(97\) 17034.2i 0.183819i 0.995767 + 0.0919097i \(0.0292971\pi\)
−0.995767 + 0.0919097i \(0.970703\pi\)
\(98\) 0 0
\(99\) 78059.7 + 124414.i 0.800459 + 1.27580i
\(100\) 203714. 2.03714
\(101\) −120183. −1.17230 −0.586151 0.810202i \(-0.699357\pi\)
−0.586151 + 0.810202i \(0.699357\pi\)
\(102\) 78690.1 + 273479.i 0.748892 + 2.60270i
\(103\) 94611.9i 0.878725i 0.898310 + 0.439362i \(0.144796\pi\)
−0.898310 + 0.439362i \(0.855204\pi\)
\(104\) −407951. −3.69849
\(105\) 0 0
\(106\) −105094. −0.908479
\(107\) 17922.6i 0.151335i 0.997133 + 0.0756677i \(0.0241088\pi\)
−0.997133 + 0.0756677i \(0.975891\pi\)
\(108\) −211606. + 236315.i −1.74569 + 1.94954i
\(109\) 66214.4 0.533809 0.266905 0.963723i \(-0.413999\pi\)
0.266905 + 0.963723i \(0.413999\pi\)
\(110\) −171095. −1.34820
\(111\) −9647.42 + 2775.92i −0.0743196 + 0.0213845i
\(112\) 0 0
\(113\) 138434.i 1.01988i 0.860211 + 0.509938i \(0.170332\pi\)
−0.860211 + 0.509938i \(0.829668\pi\)
\(114\) 34141.3 9823.71i 0.246047 0.0707968i
\(115\) 25422.0i 0.179253i
\(116\) 64009.8i 0.441674i
\(117\) 94649.8 + 150856.i 0.639227 + 1.01882i
\(118\) 112869.i 0.746223i
\(119\) 0 0
\(120\) −63132.7 219411.i −0.400222 1.39093i
\(121\) −204275. −1.26839
\(122\) 506886. 3.08326
\(123\) −77910.6 + 22417.8i −0.464338 + 0.133607i
\(124\) 6694.55i 0.0390992i
\(125\) 146234. 0.837090
\(126\) 0 0
\(127\) 207046. 1.13909 0.569545 0.821960i \(-0.307119\pi\)
0.569545 + 0.821960i \(0.307119\pi\)
\(128\) 350178.i 1.88914i
\(129\) 87516.4 25181.7i 0.463036 0.133233i
\(130\) −207458. −1.07664
\(131\) 202375. 1.03033 0.515167 0.857090i \(-0.327730\pi\)
0.515167 + 0.857090i \(0.327730\pi\)
\(132\) −218174. 758241.i −1.08985 3.78767i
\(133\) 0 0
\(134\) 522667.i 2.51457i
\(135\) −66488.2 + 74252.0i −0.313986 + 0.350650i
\(136\) 944551.i 4.37903i
\(137\) 1182.37i 0.00538211i 0.999996 + 0.00269106i \(0.000856591\pi\)
−0.999996 + 0.00269106i \(0.999143\pi\)
\(138\) 155715. 44804.9i 0.696037 0.200275i
\(139\) 103308.i 0.453519i 0.973951 + 0.226760i \(0.0728132\pi\)
−0.973951 + 0.226760i \(0.927187\pi\)
\(140\) 0 0
\(141\) −161406. + 46442.4i −0.683709 + 0.196728i
\(142\) −309878. −1.28964
\(143\) −442969. −1.81148
\(144\) 681080. 427323.i 2.73711 1.71732i
\(145\) 20112.4i 0.0794409i
\(146\) 784443. 3.04564
\(147\) 0 0
\(148\) 53928.3 0.202378
\(149\) 383207.i 1.41406i 0.707184 + 0.707029i \(0.249965\pi\)
−0.707184 + 0.707029i \(0.750035\pi\)
\(150\) 112812. + 392065.i 0.409379 + 1.42276i
\(151\) 411512. 1.46872 0.734361 0.678759i \(-0.237482\pi\)
0.734361 + 0.678759i \(0.237482\pi\)
\(152\) −117918. −0.413973
\(153\) −349285. + 219148.i −1.20629 + 0.756848i
\(154\) 0 0
\(155\) 2103.48i 0.00703250i
\(156\) −264543. 919390.i −0.870330 3.02474i
\(157\) 560413.i 1.81451i −0.420582 0.907255i \(-0.638174\pi\)
0.420582 0.907255i \(-0.361826\pi\)
\(158\) 762103.i 2.42868i
\(159\) −42107.8 146341.i −0.132090 0.459065i
\(160\) 467944.i 1.44509i
\(161\) 0 0
\(162\) −571990. 276388.i −1.71238 0.827432i
\(163\) 575063. 1.69530 0.847650 0.530556i \(-0.178017\pi\)
0.847650 + 0.530556i \(0.178017\pi\)
\(164\) 435514. 1.26442
\(165\) −68552.0 238245.i −0.196024 0.681263i
\(166\) 364861.i 1.02768i
\(167\) −101689. −0.282151 −0.141076 0.989999i \(-0.545056\pi\)
−0.141076 + 0.989999i \(0.545056\pi\)
\(168\) 0 0
\(169\) −165821. −0.446604
\(170\) 480338.i 1.27475i
\(171\) 27358.6 + 43604.9i 0.0715489 + 0.114037i
\(172\) −489210. −1.26088
\(173\) −741653. −1.88402 −0.942011 0.335583i \(-0.891067\pi\)
−0.942011 + 0.335583i \(0.891067\pi\)
\(174\) −123192. + 35447.0i −0.308469 + 0.0887578i
\(175\) 0 0
\(176\) 1.99991e6i 4.86663i
\(177\) −157167. + 45222.7i −0.377075 + 0.108499i
\(178\) 907229.i 2.14618i
\(179\) 383196.i 0.893900i −0.894559 0.446950i \(-0.852510\pi\)
0.894559 0.446950i \(-0.147490\pi\)
\(180\) 453543. 284562.i 1.04337 0.654629i
\(181\) 549563.i 1.24687i −0.781875 0.623435i \(-0.785736\pi\)
0.781875 0.623435i \(-0.214264\pi\)
\(182\) 0 0
\(183\) 203092. + 705826.i 0.448297 + 1.55801i
\(184\) −537813. −1.17108
\(185\) 16944.7 0.0364003
\(186\) 12884.2 3707.27i 0.0273072 0.00785728i
\(187\) 1.02563e6i 2.14480i
\(188\) 902245. 1.86179
\(189\) 0 0
\(190\) −59965.7 −0.120509
\(191\) 477.490i 0.000947068i 1.00000 0.000473534i \(0.000150731\pi\)
−1.00000 0.000473534i \(0.999849\pi\)
\(192\) −1.28008e6 + 368325.i −2.50601 + 0.721071i
\(193\) −853061. −1.64849 −0.824246 0.566232i \(-0.808401\pi\)
−0.824246 + 0.566232i \(0.808401\pi\)
\(194\) 183258. 0.349590
\(195\) −83121.4 288880.i −0.156540 0.544040i
\(196\) 0 0
\(197\) 859613.i 1.57811i −0.614322 0.789056i \(-0.710570\pi\)
0.614322 0.789056i \(-0.289430\pi\)
\(198\) 1.33848e6 839788.i 2.42632 1.52232i
\(199\) 468982.i 0.839506i 0.907638 + 0.419753i \(0.137883\pi\)
−0.907638 + 0.419753i \(0.862117\pi\)
\(200\) 1.35413e6i 2.39378i
\(201\) 727802. 209415.i 1.27064 0.365610i
\(202\) 1.29296e6i 2.22950i
\(203\) 0 0
\(204\) 2.12872e6 612510.i 3.58131 1.03048i
\(205\) 136842. 0.227423
\(206\) 1.01786e6 1.67117
\(207\) 124779. + 198877.i 0.202403 + 0.322596i
\(208\) 2.42495e6i 3.88637i
\(209\) −128040. −0.202759
\(210\) 0 0
\(211\) −961141. −1.48621 −0.743106 0.669174i \(-0.766648\pi\)
−0.743106 + 0.669174i \(0.766648\pi\)
\(212\) 818037.i 1.25007i
\(213\) −124158. 431498.i −0.187510 0.651672i
\(214\) 192816. 0.287812
\(215\) −153714. −0.226786
\(216\) 1.57083e6 + 1.40658e6i 2.29084 + 2.05131i
\(217\) 0 0
\(218\) 712353.i 1.01521i
\(219\) 314300. + 1.09232e6i 0.442827 + 1.53900i
\(220\) 1.33177e6i 1.85513i
\(221\) 1.24361e6i 1.71279i
\(222\) 29864.1 + 103790.i 0.0406693 + 0.141342i
\(223\) 74345.3i 0.100113i −0.998746 0.0500566i \(-0.984060\pi\)
0.998746 0.0500566i \(-0.0159402\pi\)
\(224\) 0 0
\(225\) −500741. + 314175.i −0.659413 + 0.413728i
\(226\) 1.48931e6 1.93961
\(227\) −1.00173e6 −1.29029 −0.645146 0.764060i \(-0.723203\pi\)
−0.645146 + 0.764060i \(0.723203\pi\)
\(228\) −76466.1 265750.i −0.0974163 0.338560i
\(229\) 185220.i 0.233400i 0.993167 + 0.116700i \(0.0372316\pi\)
−0.993167 + 0.116700i \(0.962768\pi\)
\(230\) −273497. −0.340905
\(231\) 0 0
\(232\) 425486. 0.518997
\(233\) 483434.i 0.583375i 0.956514 + 0.291687i \(0.0942167\pi\)
−0.956514 + 0.291687i \(0.905783\pi\)
\(234\) 1.62295e6 1.01827e6i 1.93760 1.21569i
\(235\) 283493. 0.334867
\(236\) 878551. 1.02680
\(237\) −1.06121e6 + 305349.i −1.22724 + 0.353123i
\(238\) 0 0
\(239\) 305349.i 0.345782i −0.984941 0.172891i \(-0.944689\pi\)
0.984941 0.172891i \(-0.0553108\pi\)
\(240\) −1.30423e6 + 375275.i −1.46159 + 0.420553i
\(241\) 141408.i 0.156831i 0.996921 + 0.0784157i \(0.0249861\pi\)
−0.996921 + 0.0784157i \(0.975014\pi\)
\(242\) 2.19765e6i 2.41224i
\(243\) 155687. 907221.i 0.169136 0.985593i
\(244\) 3.94551e6i 4.24257i
\(245\) 0 0
\(246\) 241177. + 838184.i 0.254096 + 0.883083i
\(247\) −155253. −0.161919
\(248\) −44500.0 −0.0459442
\(249\) −508060. + 146188.i −0.519298 + 0.149421i
\(250\) 1.57322e6i 1.59199i
\(251\) 1.49757e6 1.50039 0.750194 0.661218i \(-0.229960\pi\)
0.750194 + 0.661218i \(0.229960\pi\)
\(252\) 0 0
\(253\) −583978. −0.573582
\(254\) 2.22746e6i 2.16634i
\(255\) 668860. 192456.i 0.644146 0.185345i
\(256\) 1.03296e6 0.985109
\(257\) 408325. 0.385632 0.192816 0.981235i \(-0.438238\pi\)
0.192816 + 0.981235i \(0.438238\pi\)
\(258\) −270912. 941526.i −0.253384 0.880609i
\(259\) 0 0
\(260\) 1.61482e6i 1.48146i
\(261\) −98718.2 157340.i −0.0897007 0.142968i
\(262\) 2.17721e6i 1.95950i
\(263\) 777076.i 0.692746i 0.938097 + 0.346373i \(0.112587\pi\)
−0.938097 + 0.346373i \(0.887413\pi\)
\(264\) −5.04017e6 + 1.45024e6i −4.45077 + 1.28065i
\(265\) 257034.i 0.224841i
\(266\) 0 0
\(267\) −1.26329e6 + 363496.i −1.08449 + 0.312048i
\(268\) −4.06835e6 −3.46004
\(269\) −1.81934e6 −1.53297 −0.766483 0.642264i \(-0.777995\pi\)
−0.766483 + 0.642264i \(0.777995\pi\)
\(270\) 798824. + 715299.i 0.666871 + 0.597143i
\(271\) 472882.i 0.391137i 0.980690 + 0.195569i \(0.0626552\pi\)
−0.980690 + 0.195569i \(0.937345\pi\)
\(272\) −5.61462e6 −4.60149
\(273\) 0 0
\(274\) 12720.3 0.0102358
\(275\) 1.47037e6i 1.17245i
\(276\) −348754. 1.21206e6i −0.275579 0.957746i
\(277\) −623772. −0.488457 −0.244229 0.969718i \(-0.578535\pi\)
−0.244229 + 0.969718i \(0.578535\pi\)
\(278\) 1.11141e6 0.862509
\(279\) 10324.6 + 16455.6i 0.00794075 + 0.0126562i
\(280\) 0 0
\(281\) 827985.i 0.625542i −0.949828 0.312771i \(-0.898743\pi\)
0.949828 0.312771i \(-0.101257\pi\)
\(282\) 499640. + 1.73645e6i 0.374140 + 1.30029i
\(283\) 1.28739e6i 0.955527i −0.878488 0.477764i \(-0.841448\pi\)
0.878488 0.477764i \(-0.158552\pi\)
\(284\) 2.41204e6i 1.77455i
\(285\) −24026.3 83500.8i −0.0175216 0.0608946i
\(286\) 4.76559e6i 3.44510i
\(287\) 0 0
\(288\) −2.29682e6 3.66074e6i −1.63172 2.60068i
\(289\) 1.45954e6 1.02795
\(290\) 216375. 0.151082
\(291\) 73425.5 + 255183.i 0.0508293 + 0.176652i
\(292\) 6.10597e6i 4.19080i
\(293\) 1.78967e6 1.21788 0.608940 0.793217i \(-0.291595\pi\)
0.608940 + 0.793217i \(0.291595\pi\)
\(294\) 0 0
\(295\) 276048. 0.184684
\(296\) 358472.i 0.237808i
\(297\) 1.70567e6 + 1.52733e6i 1.12203 + 1.00471i
\(298\) 4.12265e6 2.68928
\(299\) −708092. −0.458049
\(300\) 3.05177e6 878107.i 1.95771 0.563306i
\(301\) 0 0
\(302\) 4.42716e6i 2.79324i
\(303\) −1.80042e6 + 518047.i −1.12659 + 0.324162i
\(304\) 700932.i 0.435003i
\(305\) 1.23971e6i 0.763082i
\(306\) 2.35766e6 + 3.75770e6i 1.43938 + 2.29413i
\(307\) 2.36447e6i 1.43182i −0.698195 0.715908i \(-0.746013\pi\)
0.698195 0.715908i \(-0.253987\pi\)
\(308\) 0 0
\(309\) 407823. + 1.41735e6i 0.242983 + 0.844462i
\(310\) −22629.9 −0.0133745
\(311\) −1.75107e6 −1.02660 −0.513302 0.858208i \(-0.671578\pi\)
−0.513302 + 0.858208i \(0.671578\pi\)
\(312\) −6.11137e6 + 1.75847e6i −3.55428 + 1.02270i
\(313\) 1.75907e6i 1.01490i 0.861682 + 0.507449i \(0.169412\pi\)
−0.861682 + 0.507449i \(0.830588\pi\)
\(314\) −6.02908e6 −3.45086
\(315\) 0 0
\(316\) 5.93208e6 3.34187
\(317\) 879467.i 0.491554i 0.969326 + 0.245777i \(0.0790431\pi\)
−0.969326 + 0.245777i \(0.920957\pi\)
\(318\) −1.57438e6 + 453008.i −0.873056 + 0.251210i
\(319\) 462009. 0.254199
\(320\) 2.24832e6 1.22739
\(321\) 77254.9 + 268492.i 0.0418469 + 0.145435i
\(322\) 0 0
\(323\) 359466.i 0.191713i
\(324\) −2.15136e6 + 4.45227e6i −1.13855 + 2.35624i
\(325\) 1.78286e6i 0.936288i
\(326\) 6.18669e6i 3.22414i
\(327\) 991934. 285416.i 0.512995 0.147608i
\(328\) 2.89495e6i 1.48579i
\(329\) 0 0
\(330\) −2.56311e6 + 737502.i −1.29563 + 0.372802i
\(331\) 450960. 0.226239 0.113120 0.993581i \(-0.463916\pi\)
0.113120 + 0.993581i \(0.463916\pi\)
\(332\) 2.84002e6 1.41409
\(333\) −132559. + 83170.1i −0.0655086 + 0.0411014i
\(334\) 1.09400e6i 0.536599i
\(335\) −1.27831e6 −0.622335
\(336\) 0 0
\(337\) 2.01453e6 0.966273 0.483136 0.875545i \(-0.339498\pi\)
0.483136 + 0.875545i \(0.339498\pi\)
\(338\) 1.78395e6i 0.849357i
\(339\) 596719. + 2.07383e6i 0.282014 + 0.980110i
\(340\) −3.73887e6 −1.75406
\(341\) −48319.9 −0.0225030
\(342\) 469114. 294331.i 0.216877 0.136073i
\(343\) 0 0
\(344\) 3.25187e6i 1.48162i
\(345\) −109581. 380838.i −0.0495665 0.172263i
\(346\) 7.97892e6i 3.58306i
\(347\) 2.27813e6i 1.01568i 0.861453 + 0.507838i \(0.169555\pi\)
−0.861453 + 0.507838i \(0.830445\pi\)
\(348\) 275913. + 958909.i 0.122131 + 0.424453i
\(349\) 3.15486e6i 1.38649i 0.720701 + 0.693246i \(0.243820\pi\)
−0.720701 + 0.693246i \(0.756180\pi\)
\(350\) 0 0
\(351\) 2.06818e6 + 1.85193e6i 0.896024 + 0.802337i
\(352\) 1.07493e7 4.62406
\(353\) 3.04877e6 1.30223 0.651115 0.758979i \(-0.274302\pi\)
0.651115 + 0.758979i \(0.274302\pi\)
\(354\) 486519. + 1.69085e6i 0.206344 + 0.717127i
\(355\) 757882.i 0.319176i
\(356\) 7.06172e6 2.95315
\(357\) 0 0
\(358\) −4.12253e6 −1.70003
\(359\) 3.19970e6i 1.31031i −0.755496 0.655154i \(-0.772604\pi\)
0.755496 0.655154i \(-0.227396\pi\)
\(360\) −1.89154e6 3.01479e6i −0.769234 1.22603i
\(361\) 2.43122e6 0.981876
\(362\) −5.91236e6 −2.37132
\(363\) −3.06017e6 + 880524.i −1.21893 + 0.350732i
\(364\) 0 0
\(365\) 1.91854e6i 0.753771i
\(366\) 7.59348e6 2.18492e6i 2.96304 0.852577i
\(367\) 2.78935e6i 1.08103i 0.841334 + 0.540515i \(0.181771\pi\)
−0.841334 + 0.540515i \(0.818229\pi\)
\(368\) 3.19688e6i 1.23057i
\(369\) −1.07052e6 + 671665.i −0.409288 + 0.256795i
\(370\) 182296.i 0.0692266i
\(371\) 0 0
\(372\) −28856.8 100289.i −0.0108116 0.0375746i
\(373\) −2.57875e6 −0.959703 −0.479852 0.877350i \(-0.659310\pi\)
−0.479852 + 0.877350i \(0.659310\pi\)
\(374\) −1.10340e7 −4.07901
\(375\) 2.19067e6 630338.i 0.804451 0.231470i
\(376\) 5.99740e6i 2.18773i
\(377\) 560201. 0.202997
\(378\) 0 0
\(379\) 2.95401e6 1.05636 0.528182 0.849131i \(-0.322874\pi\)
0.528182 + 0.849131i \(0.322874\pi\)
\(380\) 466763.i 0.165820i
\(381\) 3.10169e6 892469.i 1.09468 0.314979i
\(382\) 5136.97 0.00180115
\(383\) −3.98378e6 −1.38771 −0.693854 0.720116i \(-0.744089\pi\)
−0.693854 + 0.720116i \(0.744089\pi\)
\(384\) 1.50944e6 + 5.24590e6i 0.522381 + 1.81548i
\(385\) 0 0
\(386\) 9.17747e6i 3.13513i
\(387\) 1.20251e6 754476.i 0.408141 0.256075i
\(388\) 1.42645e6i 0.481036i
\(389\) 623403.i 0.208879i −0.994531 0.104440i \(-0.966695\pi\)
0.994531 0.104440i \(-0.0333049\pi\)
\(390\) −3.10785e6 + 894243.i −1.03466 + 0.297711i
\(391\) 1.63948e6i 0.542332i
\(392\) 0 0
\(393\) 3.03171e6 872334.i 0.990161 0.284906i
\(394\) −9.24796e6 −3.00127
\(395\) 1.86391e6 0.601079
\(396\) −6.53677e6 1.04185e7i −2.09472 3.33862i
\(397\) 3.52878e6i 1.12370i 0.827240 + 0.561848i \(0.189909\pi\)
−0.827240 + 0.561848i \(0.810091\pi\)
\(398\) 5.04544e6 1.59658
\(399\) 0 0
\(400\) −8.04923e6 −2.51539
\(401\) 1.29986e6i 0.403679i −0.979419 0.201840i \(-0.935308\pi\)
0.979419 0.201840i \(-0.0646919\pi\)
\(402\) −2.25295e6 7.82989e6i −0.695323 2.41652i
\(403\) −58589.3 −0.0179703
\(404\) 1.00642e7 3.06779
\(405\) −675975. + 1.39894e6i −0.204782 + 0.423800i
\(406\) 0 0
\(407\) 389243.i 0.116476i
\(408\) −4.07147e6 1.41500e7i −1.21088 4.20829i
\(409\) 227103.i 0.0671297i −0.999437 0.0335648i \(-0.989314\pi\)
0.999437 0.0335648i \(-0.0106860\pi\)
\(410\) 1.47219e6i 0.432517i
\(411\) 5096.60 + 17712.7i 0.00148825 + 0.00517226i
\(412\) 7.92286e6i 2.29953i
\(413\) 0 0
\(414\) 2.13958e6 1.34241e6i 0.613518 0.384933i
\(415\) 892356. 0.254342
\(416\) 1.30339e7 3.69267
\(417\) 445306. + 1.54762e6i 0.125406 + 0.435836i
\(418\) 1.37749e6i 0.385611i
\(419\) 2.43482e6 0.677536 0.338768 0.940870i \(-0.389990\pi\)
0.338768 + 0.940870i \(0.389990\pi\)
\(420\) 0 0
\(421\) 566569. 0.155793 0.0778965 0.996961i \(-0.475180\pi\)
0.0778965 + 0.996961i \(0.475180\pi\)
\(422\) 1.03402e7i 2.82650i
\(423\) −2.21777e6 + 1.39147e6i −0.602651 + 0.378115i
\(424\) 5.43765e6 1.46891
\(425\) 4.12796e6 1.10857
\(426\) −4.64217e6 + 1.33572e6i −1.23936 + 0.356609i
\(427\) 0 0
\(428\) 1.50085e6i 0.396029i
\(429\) −6.63596e6 + 1.90941e6i −1.74085 + 0.500906i
\(430\) 1.65369e6i 0.431305i
\(431\) 4.48198e6i 1.16219i 0.813836 + 0.581094i \(0.197375\pi\)
−0.813836 + 0.581094i \(0.802625\pi\)
\(432\) 8.36105e6 9.33736e6i 2.15552 2.40721i
\(433\) 1.44259e6i 0.369762i −0.982761 0.184881i \(-0.940810\pi\)
0.982761 0.184881i \(-0.0591899\pi\)
\(434\) 0 0
\(435\) 86694.2 + 301297.i 0.0219668 + 0.0763434i
\(436\) −5.54483e6 −1.39692
\(437\) −204674. −0.0512695
\(438\) 1.17515e7 3.38133e6i 2.92689 0.842174i
\(439\) 2.95219e6i 0.731110i 0.930790 + 0.365555i \(0.119121\pi\)
−0.930790 + 0.365555i \(0.880879\pi\)
\(440\) 8.85255e6 2.17990
\(441\) 0 0
\(442\) −1.33791e7 −3.25740
\(443\) 31430.0i 0.00760914i −0.999993 0.00380457i \(-0.998789\pi\)
0.999993 0.00380457i \(-0.00121103\pi\)
\(444\) 807881. 232457.i 0.194487 0.0559610i
\(445\) 2.21885e6 0.531163
\(446\) −799828. −0.190397
\(447\) 1.65181e6 + 5.74068e6i 0.391012 + 1.35892i
\(448\) 0 0
\(449\) 3.65589e6i 0.855810i −0.903824 0.427905i \(-0.859252\pi\)
0.903824 0.427905i \(-0.140748\pi\)
\(450\) 3.37998e6 + 5.38712e6i 0.786834 + 1.25408i
\(451\) 3.14345e6i 0.727721i
\(452\) 1.15926e7i 2.66891i
\(453\) 6.16471e6 1.77382e6i 1.41146 0.406128i
\(454\) 1.07769e7i 2.45389i
\(455\) 0 0
\(456\) −1.76649e6 + 508285.i −0.397832 + 0.114471i
\(457\) 3.57735e6 0.801255 0.400627 0.916241i \(-0.368792\pi\)
0.400627 + 0.916241i \(0.368792\pi\)
\(458\) 1.99265e6 0.443883
\(459\) −4.28787e6 + 4.78856e6i −0.949971 + 1.06090i
\(460\) 2.12886e6i 0.469085i
\(461\) −3.57853e6 −0.784247 −0.392124 0.919913i \(-0.628259\pi\)
−0.392124 + 0.919913i \(0.628259\pi\)
\(462\) 0 0
\(463\) 463276. 0.100436 0.0502178 0.998738i \(-0.484008\pi\)
0.0502178 + 0.998738i \(0.484008\pi\)
\(464\) 2.52918e6i 0.545362i
\(465\) −9067.03 31511.5i −0.00194461 0.00675829i
\(466\) 5.20092e6 1.10947
\(467\) −5.32694e6 −1.13028 −0.565140 0.824995i \(-0.691178\pi\)
−0.565140 + 0.824995i \(0.691178\pi\)
\(468\) −7.92604e6 1.26328e7i −1.67279 2.66614i
\(469\) 0 0
\(470\) 3.04989e6i 0.636855i
\(471\) −2.41565e6 8.39535e6i −0.501744 1.74376i
\(472\) 5.83990e6i 1.20656i
\(473\) 3.53101e6i 0.725682i
\(474\) 3.28503e6 + 1.14168e7i 0.671574 + 2.33399i
\(475\) 515337.i 0.104799i
\(476\) 0 0
\(477\) −1.26160e6 2.01078e6i −0.253879 0.404640i
\(478\) −3.28503e6 −0.657612
\(479\) 6.34325e6 1.26320 0.631602 0.775293i \(-0.282398\pi\)
0.631602 + 0.775293i \(0.282398\pi\)
\(480\) 2.01706e6 + 7.01010e6i 0.399592 + 1.38874i
\(481\) 471969.i 0.0930146i
\(482\) 1.52131e6 0.298264
\(483\) 0 0
\(484\) 1.71061e7 3.31924
\(485\) 448203.i 0.0865207i
\(486\) −9.76014e6 1.67492e6i −1.87441 0.321665i
\(487\) −8.17845e6 −1.56260 −0.781301 0.624154i \(-0.785444\pi\)
−0.781301 + 0.624154i \(0.785444\pi\)
\(488\) −2.62266e7 −4.98531
\(489\) 8.61481e6 2.47880e6i 1.62920 0.468780i
\(490\) 0 0
\(491\) 6.14286e6i 1.14992i 0.818182 + 0.574959i \(0.194982\pi\)
−0.818182 + 0.574959i \(0.805018\pi\)
\(492\) 6.52428e6 1.87728e6i 1.21512 0.349636i
\(493\) 1.29706e6i 0.240350i
\(494\) 1.67025e6i 0.307939i
\(495\) −2.05391e6 3.27358e6i −0.376762 0.600495i
\(496\) 264518.i 0.0482782i
\(497\) 0 0
\(498\) 1.57273e6 + 5.46586e6i 0.284172 + 0.987609i
\(499\) 4.97666e6 0.894718 0.447359 0.894354i \(-0.352365\pi\)
0.447359 + 0.894354i \(0.352365\pi\)
\(500\) −1.22457e7 −2.19058
\(501\) −1.52336e6 + 438328.i −0.271150 + 0.0780199i
\(502\) 1.61113e7i 2.85346i
\(503\) 1.01525e6 0.178918 0.0894588 0.995991i \(-0.471486\pi\)
0.0894588 + 0.995991i \(0.471486\pi\)
\(504\) 0 0
\(505\) 3.16225e6 0.551782
\(506\) 6.28260e6i 1.09085i
\(507\) −2.48410e6 + 714768.i −0.429190 + 0.123494i
\(508\) −1.73382e7 −2.98088
\(509\) 6.31706e6 1.08074 0.540369 0.841428i \(-0.318284\pi\)
0.540369 + 0.841428i \(0.318284\pi\)
\(510\) −2.07049e6 7.19578e6i −0.352491 1.22505i
\(511\) 0 0
\(512\) 92813.9i 0.0156472i
\(513\) 597807. + 535301.i 0.100292 + 0.0898058i
\(514\) 4.39287e6i 0.733400i
\(515\) 2.48943e6i 0.413601i
\(516\) −7.32868e6 + 2.10873e6i −1.21172 + 0.348656i
\(517\) 6.51221e6i 1.07153i
\(518\) 0 0
\(519\) −1.11104e7 + 3.19689e6i −1.81056 + 0.520965i
\(520\) 1.07340e7 1.74082
\(521\) −3.69216e6 −0.595917 −0.297959 0.954579i \(-0.596306\pi\)
−0.297959 + 0.954579i \(0.596306\pi\)
\(522\) −1.69271e6 + 1.06204e6i −0.271898 + 0.170594i
\(523\) 3.25116e6i 0.519737i 0.965644 + 0.259869i \(0.0836793\pi\)
−0.965644 + 0.259869i \(0.916321\pi\)
\(524\) −1.69470e7 −2.69628
\(525\) 0 0
\(526\) 8.36000e6 1.31747
\(527\) 135655.i 0.0212770i
\(528\) 8.62057e6 + 2.99599e7i 1.34571 + 4.67687i
\(529\) 5.50285e6 0.854965
\(530\) 2.76524e6 0.427606
\(531\) −2.15953e6 + 1.35493e6i −0.332371 + 0.208536i
\(532\) 0 0
\(533\) 3.81153e6i 0.581141i
\(534\) 3.91060e6 + 1.35909e7i 0.593458 + 2.06250i
\(535\) 471578.i 0.0712310i
\(536\) 2.70431e7i 4.06579i
\(537\) −1.65176e6 5.74053e6i −0.247179 0.859045i
\(538\) 1.95730e7i 2.91542i
\(539\) 0 0
\(540\) 5.56777e6 6.21791e6i 0.821668 0.917614i
\(541\) 7.51164e6 1.10342 0.551711 0.834036i \(-0.313975\pi\)
0.551711 + 0.834036i \(0.313975\pi\)
\(542\) 5.08739e6 0.743870
\(543\) −2.36889e6 8.23282e6i −0.344782 1.19825i
\(544\) 3.01780e7i 4.37214i
\(545\) −1.74223e6 −0.251255
\(546\) 0 0
\(547\) −8.99855e6 −1.28589 −0.642945 0.765912i \(-0.722288\pi\)
−0.642945 + 0.765912i \(0.722288\pi\)
\(548\) 99012.6i 0.0140844i
\(549\) 6.08490e6 + 9.69830e6i 0.861634 + 1.37330i
\(550\) −1.58186e7 −2.22978
\(551\) 161926. 0.0227216
\(552\) −8.05678e6 + 2.31823e6i −1.12542 + 0.323824i
\(553\) 0 0
\(554\) 6.71072e6i 0.928955i
\(555\) 253843. 73039.9i 0.0349810 0.0100653i
\(556\) 8.65105e6i 1.18681i
\(557\) 3.95822e6i 0.540583i −0.962779 0.270291i \(-0.912880\pi\)
0.962779 0.270291i \(-0.0871200\pi\)
\(558\) 177034. 111075.i 0.0240697 0.0151018i
\(559\) 4.28146e6i 0.579512i
\(560\) 0 0
\(561\) −4.42097e6 1.53646e7i −0.593076 2.06117i
\(562\) −8.90770e6 −1.18967
\(563\) 7.70908e6 1.02502 0.512509 0.858682i \(-0.328716\pi\)
0.512509 + 0.858682i \(0.328716\pi\)
\(564\) 1.35162e7 3.88911e6i 1.78919 0.514817i
\(565\) 3.64248e6i 0.480038i
\(566\) −1.38501e7 −1.81723
\(567\) 0 0
\(568\) 1.60333e7 2.08522
\(569\) 3.88317e6i 0.502812i 0.967882 + 0.251406i \(0.0808930\pi\)
−0.967882 + 0.251406i \(0.919107\pi\)
\(570\) −898325. + 258481.i −0.115810 + 0.0333228i
\(571\) 5.43972e6 0.698210 0.349105 0.937084i \(-0.386486\pi\)
0.349105 + 0.937084i \(0.386486\pi\)
\(572\) 3.70945e7 4.74045
\(573\) 2058.21 + 7153.11i 0.000261881 + 0.000910141i
\(574\) 0 0
\(575\) 2.35040e6i 0.296464i
\(576\) −1.75887e7 + 1.10355e7i −2.20891 + 1.38591i
\(577\) 7.58538e6i 0.948501i 0.880390 + 0.474251i \(0.157281\pi\)
−0.880390 + 0.474251i \(0.842719\pi\)
\(578\) 1.57022e7i 1.95497i
\(579\) −1.27794e7 + 3.67711e6i −1.58422 + 0.455837i
\(580\) 1.68423e6i 0.207888i
\(581\) 0 0
\(582\) 2.74533e6 789932.i 0.335959 0.0966679i
\(583\) 5.90441e6 0.719458
\(584\) −4.05876e7 −4.92448
\(585\) −2.49042e6 3.96931e6i −0.300873 0.479541i
\(586\) 1.92538e7i 2.31618i
\(587\) 3.48485e6 0.417435 0.208718 0.977976i \(-0.433071\pi\)
0.208718 + 0.977976i \(0.433071\pi\)
\(588\) 0 0
\(589\) −16935.3 −0.00201142
\(590\) 2.96980e6i 0.351235i
\(591\) −3.70535e6 1.28776e7i −0.436376 1.51658i
\(592\) −2.13084e6 −0.249888
\(593\) 1.35189e7 1.57872 0.789360 0.613930i \(-0.210412\pi\)
0.789360 + 0.613930i \(0.210412\pi\)
\(594\) 1.64314e7 1.83501e7i 1.91077 2.13389i
\(595\) 0 0
\(596\) 3.20900e7i 3.70044i
\(597\) 2.02154e6 + 7.02566e6i 0.232138 + 0.806773i
\(598\) 7.61785e6i 0.871123i
\(599\) 3.91308e6i 0.445607i 0.974863 + 0.222804i \(0.0715208\pi\)
−0.974863 + 0.222804i \(0.928479\pi\)
\(600\) −5.83695e6 2.02857e7i −0.661923 2.30045i
\(601\) 1.14323e7i 1.29106i −0.763734 0.645531i \(-0.776636\pi\)
0.763734 0.645531i \(-0.223364\pi\)
\(602\) 0 0
\(603\) 1.00003e7 6.27436e6i 1.12000 0.702710i
\(604\) −3.44603e7 −3.84349
\(605\) 5.37488e6 0.597008
\(606\) 5.57329e6 + 1.93694e7i 0.616496 + 2.14257i
\(607\) 1.63986e7i 1.80648i −0.429133 0.903241i \(-0.641181\pi\)
0.429133 0.903241i \(-0.358819\pi\)
\(608\) 3.76744e6 0.413321
\(609\) 0 0
\(610\) −1.33372e7 −1.45124
\(611\) 7.89626e6i 0.855694i
\(612\) 2.92493e7 1.83516e7i 3.15673 1.98059i
\(613\) −6.33447e6 −0.680862 −0.340431 0.940270i \(-0.610573\pi\)
−0.340431 + 0.940270i \(0.610573\pi\)
\(614\) −2.54376e7 −2.72305
\(615\) 2.04998e6 589856.i 0.218556 0.0628866i
\(616\) 0 0
\(617\) 9.24609e6i 0.977790i 0.872343 + 0.488895i \(0.162600\pi\)
−0.872343 + 0.488895i \(0.837400\pi\)
\(618\) 1.52482e7 4.38748e6i 1.60601 0.462108i
\(619\) 1.53014e7i 1.60511i −0.596581 0.802553i \(-0.703474\pi\)
0.596581 0.802553i \(-0.296526\pi\)
\(620\) 176147.i 0.0184033i
\(621\) 2.72653e6 + 2.44145e6i 0.283715 + 0.254050i
\(622\) 1.88385e7i 1.95241i
\(623\) 0 0
\(624\) 1.04527e7 + 3.63273e7i 1.07465 + 3.73484i
\(625\) 3.75443e6 0.384454
\(626\) 1.89246e7 1.93015
\(627\) −1.91813e6 + 551916.i −0.194854 + 0.0560666i
\(628\) 4.69293e7i 4.74838i
\(629\) 1.09278e6 0.110130
\(630\) 0 0
\(631\) −1.50234e7 −1.50209 −0.751043 0.660253i \(-0.770449\pi\)
−0.751043 + 0.660253i \(0.770449\pi\)
\(632\) 3.94317e7i 3.92693i
\(633\) −1.43985e7 + 4.14298e6i −1.42826 + 0.410964i
\(634\) 9.46155e6 0.934844
\(635\) −5.44780e6 −0.536150
\(636\) 3.52613e6 + 1.22547e7i 0.345666 + 1.20132i
\(637\) 0 0
\(638\) 4.97043e6i 0.483439i
\(639\) −3.71993e6 5.92893e6i −0.360398 0.574413i
\(640\) 9.21389e6i 0.889187i
\(641\) 7.78350e6i 0.748221i −0.927384 0.374110i \(-0.877948\pi\)
0.927384 0.374110i \(-0.122052\pi\)
\(642\) 2.88851e6 831131.i 0.276590 0.0795851i
\(643\) 1.30114e7i 1.24107i −0.784178 0.620536i \(-0.786915\pi\)
0.784178 0.620536i \(-0.213085\pi\)
\(644\) 0 0
\(645\) −2.30273e6 + 662580.i −0.217943 + 0.0627103i
\(646\) −3.86723e6 −0.364602
\(647\) −5.03966e6 −0.473304 −0.236652 0.971594i \(-0.576050\pi\)
−0.236652 + 0.971594i \(0.576050\pi\)
\(648\) 2.95951e7 + 1.43005e7i 2.76874 + 1.33787i
\(649\) 6.34119e6i 0.590962i
\(650\) −1.91805e7 −1.78065
\(651\) 0 0
\(652\) −4.81561e7 −4.43642
\(653\) 1.32180e7i 1.21306i 0.795060 + 0.606531i \(0.207439\pi\)
−0.795060 + 0.606531i \(0.792561\pi\)
\(654\) −3.07059e6 1.06715e7i −0.280722 0.975621i
\(655\) −5.32488e6 −0.484961
\(656\) −1.72082e7 −1.56126
\(657\) 9.41683e6 + 1.50088e7i 0.851121 + 1.35654i
\(658\) 0 0
\(659\) 2.02891e7i 1.81991i 0.414706 + 0.909956i \(0.363885\pi\)
−0.414706 + 0.909956i \(0.636115\pi\)
\(660\) 5.74059e6 + 1.99508e7i 0.512975 + 1.78279i
\(661\) 5.77967e6i 0.514517i −0.966343 0.257258i \(-0.917181\pi\)
0.966343 0.257258i \(-0.0828192\pi\)
\(662\) 4.85156e6i 0.430265i
\(663\) −5.36056e6 1.86301e7i −0.473616 1.64600i
\(664\) 1.88782e7i 1.66165i
\(665\) 0 0
\(666\) 894767. + 1.42611e6i 0.0781672 + 0.124585i
\(667\) 738528. 0.0642765
\(668\) 8.51549e6 0.738361
\(669\) −320464. 1.11374e6i −0.0276831 0.0962097i
\(670\) 1.37524e7i 1.18356i
\(671\) −2.84779e7 −2.44175
\(672\) 0 0
\(673\) −959659. −0.0816732 −0.0408366 0.999166i \(-0.513002\pi\)
−0.0408366 + 0.999166i \(0.513002\pi\)
\(674\) 2.16729e7i 1.83767i
\(675\) −6.14718e6 + 6.86498e6i −0.519298 + 0.579936i
\(676\) 1.38859e7 1.16871
\(677\) 6.45075e6 0.540927 0.270464 0.962730i \(-0.412823\pi\)
0.270464 + 0.962730i \(0.412823\pi\)
\(678\) 2.23109e7 6.41967e6i 1.86399 0.536338i
\(679\) 0 0
\(680\) 2.48530e7i 2.06114i
\(681\) −1.50066e7 + 4.31796e6i −1.23998 + 0.356788i
\(682\) 519839.i 0.0427964i
\(683\) 8.28136e6i 0.679282i 0.940555 + 0.339641i \(0.110305\pi\)
−0.940555 + 0.339641i \(0.889695\pi\)
\(684\) −2.29102e6 3.65150e6i −0.187236 0.298422i
\(685\) 31110.5i 0.00253327i
\(686\) 0 0
\(687\) 798390. + 2.77472e6i 0.0645392 + 0.224299i
\(688\) 1.93298e7 1.55689
\(689\) 7.15929e6 0.574542
\(690\) −4.09716e6 + 1.17891e6i −0.327613 + 0.0942663i
\(691\) 1.95993e7i 1.56151i 0.624837 + 0.780755i \(0.285165\pi\)
−0.624837 + 0.780755i \(0.714835\pi\)
\(692\) 6.21065e7 4.93028
\(693\) 0 0
\(694\) 2.45088e7 1.93163
\(695\) 2.71823e6i 0.213464i
\(696\) 6.37405e6 1.83405e6i 0.498761 0.143512i
\(697\) 8.82504e6 0.688074
\(698\) 3.39409e7 2.63685
\(699\) 2.08384e6 + 7.24215e6i 0.161313 + 0.560628i
\(700\) 0 0
\(701\) 7.77783e6i 0.597810i −0.954283 0.298905i \(-0.903379\pi\)
0.954283 0.298905i \(-0.0966214\pi\)
\(702\) 1.99236e7 2.22500e7i 1.52589 1.70407i
\(703\) 136423.i 0.0104112i
\(704\) 5.16470e7i 3.92748i
\(705\) 4.24690e6 1.22199e6i 0.321810 0.0925967i
\(706\) 3.27995e7i 2.47660i
\(707\) 0 0
\(708\) 1.31613e7 3.78698e6i 0.986766 0.283929i
\(709\) −404.312 −3.02066e−5 −1.51033e−5 1.00000i \(-0.500005\pi\)
−1.51033e−5 1.00000i \(0.500005\pi\)
\(710\) 8.15350e6 0.607014
\(711\) −1.45814e7 + 9.14866e6i −1.08175 + 0.678709i
\(712\) 4.69406e7i 3.47015i
\(713\) −77239.9 −0.00569007
\(714\) 0 0
\(715\) 1.16554e7 0.852633
\(716\) 3.20891e7i 2.33924i
\(717\) −1.31620e6 4.57433e6i −0.0956148 0.332299i
\(718\) −3.44233e7 −2.49196
\(719\) 2.28281e6 0.164683 0.0823413 0.996604i \(-0.473760\pi\)
0.0823413 + 0.996604i \(0.473760\pi\)
\(720\) −1.79206e7 + 1.12437e7i −1.28831 + 0.808311i
\(721\) 0 0
\(722\) 2.61558e7i 1.86735i
\(723\) 609539. + 2.11839e6i 0.0433666 + 0.150716i
\(724\) 4.60208e7i 3.26293i
\(725\) 1.85950e6i 0.131386i
\(726\) 9.47293e6 + 3.29222e7i 0.667026 + 2.31818i
\(727\) 1.14126e7i 0.800845i 0.916331 + 0.400422i \(0.131137\pi\)
−0.916331 + 0.400422i \(0.868863\pi\)
\(728\) 0 0
\(729\) −1.57827e6 1.42618e7i −0.109993 0.993932i
\(730\) −2.06402e7 −1.43353
\(731\) −9.91310e6 −0.686145
\(732\) −1.70071e7 5.91063e7i −1.17315 4.07715i
\(733\) 1.81527e7i 1.24790i 0.781464 + 0.623951i \(0.214473\pi\)
−0.781464 + 0.623951i \(0.785527\pi\)
\(734\) 3.00086e7 2.05592
\(735\) 0 0
\(736\) 1.71829e7 1.16924
\(737\) 2.93645e7i 1.99138i
\(738\) 7.22596e6 + 1.15170e7i 0.488376 + 0.778389i
\(739\) 4.72208e6 0.318070 0.159035 0.987273i \(-0.449162\pi\)
0.159035 + 0.987273i \(0.449162\pi\)
\(740\) −1.41896e6 −0.0952557
\(741\) −2.32579e6 + 669215.i −0.155605 + 0.0447734i
\(742\) 0 0
\(743\) 2.37693e7i 1.57959i 0.613372 + 0.789794i \(0.289813\pi\)
−0.613372 + 0.789794i \(0.710187\pi\)
\(744\) −666639. + 191817.i −0.0441528 + 0.0127044i
\(745\) 1.00829e7i 0.665574i
\(746\) 2.77429e7i 1.82518i
\(747\) −6.98093e6 + 4.37997e6i −0.457733 + 0.287190i
\(748\) 8.58870e7i 5.61272i
\(749\) 0 0
\(750\) −6.78135e6 2.35679e7i −0.440213 1.52992i
\(751\) 8.55543e6 0.553531 0.276765 0.960937i \(-0.410737\pi\)
0.276765 + 0.960937i \(0.410737\pi\)
\(752\) −3.56499e7 −2.29886
\(753\) 2.24346e7 6.45526e6i 1.44189 0.414884i
\(754\) 6.02680e6i 0.386063i
\(755\) −1.08277e7 −0.691303
\(756\) 0 0
\(757\) 1.81552e7 1.15149 0.575745 0.817629i \(-0.304712\pi\)
0.575745 + 0.817629i \(0.304712\pi\)
\(758\) 3.17801e7i 2.00901i
\(759\) −8.74837e6 + 2.51723e6i −0.551217 + 0.158606i
\(760\) 3.10266e6 0.194850
\(761\) 2.00423e7 1.25454 0.627271 0.778801i \(-0.284172\pi\)
0.627271 + 0.778801i \(0.284172\pi\)
\(762\) −9.60144e6 3.33688e7i −0.599030 2.08187i
\(763\) 0 0
\(764\) 39985.3i 0.00247838i
\(765\) 9.19037e6 5.76622e6i 0.567779 0.356236i
\(766\) 4.28586e7i 2.63916i
\(767\) 7.68890e6i 0.471928i
\(768\) 1.54744e7 4.45257e6i 0.946699 0.272400i
\(769\) 1.58687e7i 0.967666i 0.875160 + 0.483833i \(0.160756\pi\)
−0.875160 + 0.483833i \(0.839244\pi\)
\(770\) 0 0
\(771\) 6.11697e6 1.76008e6i 0.370596 0.106634i
\(772\) 7.14359e7 4.31393
\(773\) −213540. −0.0128538 −0.00642689 0.999979i \(-0.502046\pi\)
−0.00642689 + 0.999979i \(0.502046\pi\)
\(774\) −8.11686e6 1.29369e7i −0.487008 0.776208i
\(775\) 194478.i 0.0116310i
\(776\) −9.48190e6 −0.565251
\(777\) 0 0
\(778\) −6.70674e6 −0.397249
\(779\) 1.10172e6i 0.0650472i
\(780\) 6.96064e6 + 2.41910e7i 0.409650 + 1.42369i
\(781\) 1.74096e7 1.02132
\(782\) −1.76380e7 −1.03141
\(783\) −2.15707e6 1.93153e6i −0.125736 0.112589i
\(784\) 0 0
\(785\) 1.47456e7i 0.854059i
\(786\) −9.38481e6 3.26160e7i −0.541838 1.88310i
\(787\) 1.33401e6i 0.0767752i −0.999263 0.0383876i \(-0.987778\pi\)
0.999263 0.0383876i \(-0.0122222\pi\)
\(788\) 7.19846e7i 4.12975i
\(789\) 3.34957e6 + 1.16411e7i 0.191557 + 0.665735i
\(790\) 2.00524e7i 1.14314i
\(791\) 0 0
\(792\) −6.92538e7 + 4.34512e7i −3.92311 + 2.46144i
\(793\) −3.45303e7 −1.94992
\(794\) 3.79637e7 2.13706
\(795\) 1.10794e6 + 3.85053e6i 0.0621725 + 0.216074i
\(796\) 3.92729e7i 2.19690i
\(797\) 1.62474e7 0.906019 0.453009 0.891506i \(-0.350350\pi\)
0.453009 + 0.891506i \(0.350350\pi\)
\(798\) 0 0
\(799\) 1.82827e7 1.01315
\(800\) 4.32638e7i 2.39001i
\(801\) −1.73581e7 + 1.08908e7i −0.955920 + 0.599763i
\(802\) −1.39843e7 −0.767722
\(803\) −4.40716e7 −2.41196
\(804\) −6.09466e7 + 1.75366e7i −3.32513 + 0.956764i
\(805\) 0 0
\(806\) 630320.i 0.0341762i
\(807\) −2.72549e7 + 7.84223e6i −1.47319 + 0.423893i
\(808\) 6.68987e7i 3.60487i
\(809\) 2.90690e7i 1.56156i −0.624807 0.780779i \(-0.714822\pi\)
0.624807 0.780779i \(-0.285178\pi\)
\(810\) 1.50502e7 + 7.27232e6i 0.805989 + 0.389458i
\(811\) 9.68866e6i 0.517263i −0.965976 0.258631i \(-0.916728\pi\)
0.965976 0.258631i \(-0.0832715\pi\)
\(812\) 0 0
\(813\) 2.03835e6 + 7.08407e6i 0.108156 + 0.375886i
\(814\) −4.18759e6 −0.221515
\(815\) −1.51310e7 −0.797949
\(816\) −8.41106e7 + 2.42017e7i −4.42207 + 1.27239i
\(817\) 1.23756e6i 0.0648650i
\(818\) −2.44324e6 −0.127668
\(819\) 0 0
\(820\) −1.14592e7 −0.595143
\(821\) 4.08927e6i 0.211733i 0.994380 + 0.105866i \(0.0337616\pi\)
−0.994380 + 0.105866i \(0.966238\pi\)
\(822\) 190558. 54830.6i 0.00983667 0.00283037i
\(823\) −1.51161e7 −0.777931 −0.388965 0.921252i \(-0.627167\pi\)
−0.388965 + 0.921252i \(0.627167\pi\)
\(824\) −5.26648e7 −2.70211
\(825\) −6.33799e6 2.20270e7i −0.324203 1.12673i
\(826\) 0 0
\(827\) 2.42352e7i 1.23220i 0.787667 + 0.616101i \(0.211289\pi\)
−0.787667 + 0.616101i \(0.788711\pi\)
\(828\) −1.04491e7 1.66541e7i −0.529668 0.844200i
\(829\) 1.29487e6i 0.0654396i 0.999465 + 0.0327198i \(0.0104169\pi\)
−0.999465 + 0.0327198i \(0.989583\pi\)
\(830\) 9.60022e6i 0.483711i
\(831\) −9.34451e6 + 2.68876e6i −0.469412 + 0.135067i
\(832\) 6.26236e7i 3.13639i
\(833\) 0 0
\(834\) 1.66497e7 4.79073e6i 0.828879 0.238499i
\(835\) 2.67564e6 0.132804
\(836\) 1.07222e7 0.530600
\(837\) 225600. + 202012.i 0.0111308 + 0.00996696i
\(838\) 2.61945e7i 1.28855i
\(839\) −2.38737e6 −0.117089 −0.0585443 0.998285i \(-0.518646\pi\)
−0.0585443 + 0.998285i \(0.518646\pi\)
\(840\) 0 0
\(841\) 1.99269e7 0.971514
\(842\) 6.09531e6i 0.296289i
\(843\) −3.56902e6 1.24038e7i −0.172974 0.601152i
\(844\) 8.04865e7 3.88926
\(845\) 4.36307e6 0.210209
\(846\) 1.49699e7 + 2.38594e7i 0.719105 + 1.14613i
\(847\) 0 0
\(848\) 3.23226e7i 1.54353i
\(849\) −5.54926e6 1.92859e7i −0.264220 0.918270i
\(850\) 4.44098e7i 2.10829i
\(851\) 622210.i 0.0294519i
\(852\) 1.03971e7 + 3.61339e7i 0.490695 + 1.70536i
\(853\) 8.94330e6i 0.420848i −0.977610 0.210424i \(-0.932516\pi\)
0.977610 0.210424i \(-0.0674845\pi\)
\(854\) 0 0
\(855\) −719858. 1.14733e6i −0.0336768 0.0536752i
\(856\) −9.97642e6 −0.465361
\(857\) 2.97785e7 1.38501 0.692503 0.721415i \(-0.256508\pi\)
0.692503 + 0.721415i \(0.256508\pi\)
\(858\) 2.05420e7 + 7.13916e7i 0.952630 + 3.31077i
\(859\) 2.15240e7i 0.995268i 0.867387 + 0.497634i \(0.165798\pi\)
−0.867387 + 0.497634i \(0.834202\pi\)
\(860\) 1.28721e7 0.593475
\(861\) 0 0
\(862\) 4.82184e7 2.21027
\(863\) 2.74455e7i 1.25442i −0.778848 0.627212i \(-0.784196\pi\)
0.778848 0.627212i \(-0.215804\pi\)
\(864\) −5.01874e7 4.49398e7i −2.28723 2.04808i
\(865\) 1.95144e7 0.886777
\(866\) −1.55197e7 −0.703218
\(867\) 2.18649e7 6.29133e6i 0.987868 0.284246i
\(868\) 0 0
\(869\) 4.28165e7i 1.92337i
\(870\) 3.24144e6 932681.i 0.145191 0.0417768i
\(871\) 3.56054e7i 1.59027i
\(872\) 3.68576e7i 1.64148i
\(873\) 2.19992e6 + 3.50630e6i 0.0976949 + 0.155709i
\(874\) 2.20194e6i 0.0975051i
\(875\) 0 0
\(876\) −2.63197e7 9.14713e7i −1.15883 4.02740i
\(877\) 983504. 0.0431794 0.0215897 0.999767i \(-0.493127\pi\)
0.0215897 + 0.999767i \(0.493127\pi\)
\(878\) 3.17605e7 1.39044
\(879\) 2.68104e7 7.71435e6i 1.17039 0.336765i
\(880\) 5.26215e7i 2.29064i
\(881\) −2.41287e7 −1.04736 −0.523678 0.851917i \(-0.675440\pi\)
−0.523678 + 0.851917i \(0.675440\pi\)
\(882\) 0 0
\(883\) −3.21508e7 −1.38768 −0.693842 0.720127i \(-0.744083\pi\)
−0.693842 + 0.720127i \(0.744083\pi\)
\(884\) 1.04141e8i 4.48218i
\(885\) 4.13537e6 1.18990e6i 0.177483 0.0510684i
\(886\) −338133. −0.0144712
\(887\) −1.97916e7 −0.844641 −0.422321 0.906447i \(-0.638784\pi\)
−0.422321 + 0.906447i \(0.638784\pi\)
\(888\) −1.54519e6 5.37014e6i −0.0657580 0.228535i
\(889\) 0 0
\(890\) 2.38710e7i 1.01017i
\(891\) 3.21355e7 + 1.55281e7i 1.35610 + 0.655274i
\(892\) 6.22572e6i 0.261986i
\(893\) 2.28242e6i 0.0957781i
\(894\) 6.17599e7 1.77706e7i 2.58442 0.743633i
\(895\) 1.00827e7i 0.420743i
\(896\) 0 0
\(897\) −1.06077e7 + 3.05222e6i −0.440189 + 0.126659i
\(898\) −3.93311e7 −1.62759
\(899\) 61107.7 0.00252172
\(900\) 4.19324e7 2.63092e7i 1.72561 1.08268i
\(901\) 1.65763e7i 0.680261i
\(902\) −3.38181e7 −1.38399
\(903\) 0 0
\(904\) −7.70581e7 −3.13615
\(905\) 1.44601e7i 0.586881i
\(906\) −1.90832e7 6.63217e7i −0.772380 2.68433i
\(907\) 2.58958e7 1.04523 0.522615 0.852569i \(-0.324957\pi\)
0.522615 + 0.852569i \(0.324957\pi\)
\(908\) 8.38858e7 3.37656
\(909\) −2.47384e7 + 1.55213e7i −0.993028 + 0.623045i
\(910\) 0 0
\(911\) 3.95347e6i 0.157827i 0.996881 + 0.0789137i \(0.0251452\pi\)
−0.996881 + 0.0789137i \(0.974855\pi\)
\(912\) 3.02136e6 + 1.05004e7i 0.120286 + 0.418042i
\(913\) 2.04986e7i 0.813857i
\(914\) 3.84861e7i 1.52384i
\(915\) −5.34376e6 1.85717e7i −0.211006 0.733328i
\(916\) 1.55105e7i 0.610782i
\(917\) 0 0
\(918\) 5.15167e7 + 4.61302e7i 2.01763 + 1.80667i
\(919\) −2.46305e7 −0.962022 −0.481011 0.876715i \(-0.659730\pi\)
−0.481011 + 0.876715i \(0.659730\pi\)
\(920\) 1.41509e7 0.551207
\(921\) −1.01920e7 3.54212e7i −0.395922 1.37599i
\(922\) 3.84989e7i 1.49149i
\(923\) 2.11096e7 0.815599
\(924\) 0 0
\(925\) 1.56663e6 0.0602020
\(926\) 4.98405e6i 0.191010i
\(927\) 1.22189e7 + 1.94749e7i 0.467018 + 0.744346i
\(928\) −1.35941e7 −0.518180
\(929\) 7.12147e6 0.270726 0.135363 0.990796i \(-0.456780\pi\)
0.135363 + 0.990796i \(0.456780\pi\)
\(930\) −339010. + 97545.7i −0.0128530 + 0.00369829i
\(931\) 0 0
\(932\) 4.04831e7i 1.52663i
\(933\) −2.62322e7 + 7.54797e6i −0.986575 + 0.283874i
\(934\) 5.73088e7i 2.14958i
\(935\) 2.69864e7i 1.00952i
\(936\) −8.39724e7 + 5.26859e7i −3.13290 + 1.96564i
\(937\) 1.08826e6i 0.0404933i −0.999795 0.0202467i \(-0.993555\pi\)
0.999795 0.0202467i \(-0.00644516\pi\)
\(938\) 0 0
\(939\) 7.58245e6 + 2.63520e7i 0.280638 + 0.975327i
\(940\) −2.37399e7 −0.876312
\(941\) −3.05310e7 −1.12400 −0.562000 0.827137i \(-0.689968\pi\)
−0.562000 + 0.827137i \(0.689968\pi\)
\(942\) −9.03195e7 + 2.59883e7i −3.31630 + 0.954223i
\(943\) 5.02484e6i 0.184011i
\(944\) −3.47137e7 −1.26786
\(945\) 0 0
\(946\) 3.79876e7 1.38011
\(947\) 5.78796e6i 0.209725i 0.994487 + 0.104863i \(0.0334403\pi\)
−0.994487 + 0.104863i \(0.966560\pi\)
\(948\) 8.88664e7 2.55702e7i 3.21157 0.924086i
\(949\) −5.34382e7 −1.92613
\(950\) −5.54414e6 −0.199308
\(951\) 3.79093e6 + 1.31750e7i 0.135923 + 0.472388i
\(952\) 0 0
\(953\) 1.14506e7i 0.408410i 0.978928 + 0.204205i \(0.0654609\pi\)
−0.978928 + 0.204205i \(0.934539\pi\)
\(954\) −2.16326e7 + 1.35727e7i −0.769550 + 0.482831i
\(955\) 12563.7i 0.000445769i
\(956\) 2.55701e7i 0.904874i
\(957\) 6.92120e6 1.99148e6i 0.244288 0.0702906i
\(958\) 6.82425e7i 2.40238i
\(959\) 0 0
\(960\) 3.36813e7 9.69136e6i 1.17954 0.339396i
\(961\) 2.86228e7 0.999777
\(962\) −5.07758e6 −0.176896
\(963\) 2.31466e6 + 3.68917e6i 0.0804306 + 0.128193i
\(964\) 1.18416e7i 0.410411i
\(965\) 2.24457e7 0.775917
\(966\) 0 0
\(967\) −3.20783e7 −1.10318 −0.551588 0.834117i \(-0.685978\pi\)
−0.551588 + 0.834117i \(0.685978\pi\)
\(968\) 1.13708e8i 3.90033i
\(969\) −1.54947e6 5.38503e6i −0.0530120 0.184238i
\(970\) −4.82189e6 −0.164546
\(971\) 3.91845e7 1.33373 0.666863 0.745181i \(-0.267637\pi\)
0.666863 + 0.745181i \(0.267637\pi\)
\(972\) −1.30373e7 + 7.59713e7i −0.442611 + 2.57919i
\(973\) 0 0
\(974\) 8.79861e7i 2.97178i
\(975\) −7.68501e6 2.67084e7i −0.258900 0.899781i
\(976\) 1.55897e8i 5.23856i
\(977\) 2.62234e7i 0.878925i 0.898261 + 0.439462i \(0.144831\pi\)
−0.898261 + 0.439462i \(0.855169\pi\)
\(978\) −2.66676e7 9.26806e7i −0.891533 3.09843i
\(979\) 5.09700e7i 1.69964i
\(980\) 0 0
\(981\) 1.36295e7 8.55143e6i 0.452177 0.283705i
\(982\) 6.60866e7 2.18693
\(983\) −5.16857e7 −1.70603 −0.853015 0.521886i \(-0.825229\pi\)
−0.853015 + 0.521886i \(0.825229\pi\)
\(984\) −1.24786e7 4.33682e7i −0.410846 1.42785i
\(985\) 2.26181e7i 0.742790i
\(986\) 1.39542e7 0.457101
\(987\) 0 0
\(988\) 1.30010e7 0.423724
\(989\) 5.64437e6i 0.183495i
\(990\) −3.52181e7 + 2.20965e7i −1.14203 + 0.716532i
\(991\) 8.92621e6 0.288724 0.144362 0.989525i \(-0.453887\pi\)
0.144362 + 0.989525i \(0.453887\pi\)
\(992\) 1.42176e6 0.0458719
\(993\) 6.75567e6 1.94386e6i 0.217418 0.0625592i
\(994\) 0 0
\(995\) 1.23399e7i 0.395141i
\(996\) 4.25453e7 1.22419e7i 1.35895 0.391020i
\(997\) 2.54875e6i 0.0812061i −0.999175 0.0406031i \(-0.987072\pi\)
0.999175 0.0406031i \(-0.0129279\pi\)
\(998\) 5.35403e7i 1.70159i
\(999\) −1.62732e6 + 1.81733e6i −0.0515891 + 0.0576131i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 147.6.c.d.146.13 40
3.2 odd 2 inner 147.6.c.d.146.28 yes 40
7.6 odd 2 inner 147.6.c.d.146.27 yes 40
21.20 even 2 inner 147.6.c.d.146.14 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.6.c.d.146.13 40 1.1 even 1 trivial
147.6.c.d.146.14 yes 40 21.20 even 2 inner
147.6.c.d.146.27 yes 40 7.6 odd 2 inner
147.6.c.d.146.28 yes 40 3.2 odd 2 inner