Properties

Label 147.7.f.d.19.2
Level $147$
Weight $7$
Character 147.19
Analytic conductor $33.818$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,7,Mod(19,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.19");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 147.f (of order \(6\), degree \(2\), not 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: \(33.8179502921\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(2.26350 - 3.92050i\) of defining polynomial
Character \(\chi\) \(=\) 147.19
Dual form 147.7.f.d.31.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.76350 + 4.78652i) q^{2} +(13.5000 - 7.79423i) q^{3} +(16.7261 + 28.9705i) q^{4} +(57.9943 + 33.4830i) q^{5} +86.1574i q^{6} -538.619 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})\) \(q+(-2.76350 + 4.78652i) q^{2} +(13.5000 - 7.79423i) q^{3} +(16.7261 + 28.9705i) q^{4} +(57.9943 + 33.4830i) q^{5} +86.1574i q^{6} -538.619 q^{8} +(121.500 - 210.444i) q^{9} +(-320.535 + 185.061i) q^{10} +(-862.868 - 1494.53i) q^{11} +(451.605 + 260.734i) q^{12} -2807.43i q^{13} +1043.90 q^{15} +(418.002 - 724.000i) q^{16} +(5323.58 - 3073.57i) q^{17} +(671.531 + 1163.13i) q^{18} +(-7737.30 - 4467.13i) q^{19} +2240.17i q^{20} +9538.15 q^{22} +(-4950.64 + 8574.76i) q^{23} +(-7271.35 + 4198.12i) q^{24} +(-5570.27 - 9648.00i) q^{25} +(13437.8 + 7758.32i) q^{26} -3788.00i q^{27} -13610.4 q^{29} +(-2884.81 + 4996.64i) q^{30} +(21833.0 - 12605.3i) q^{31} +(-14925.5 - 25851.7i) q^{32} +(-23297.4 - 13450.8i) q^{33} +33975.2i q^{34} +8128.90 q^{36} +(-11366.4 + 19687.1i) q^{37} +(42764.1 - 24689.9i) q^{38} +(-21881.7 - 37900.2i) q^{39} +(-31236.8 - 18034.6i) q^{40} +37897.2i q^{41} +73646.2 q^{43} +(28864.9 - 49995.4i) q^{44} +(14092.6 - 8136.38i) q^{45} +(-27362.2 - 47392.7i) q^{46} +(-120523. - 69583.9i) q^{47} -13032.0i q^{48} +61573.8 q^{50} +(47912.2 - 82986.3i) q^{51} +(81332.5 - 46957.3i) q^{52} +(8258.79 + 14304.7i) q^{53} +(18131.3 + 10468.1i) q^{54} -115566. i q^{55} -139271. q^{57} +(37612.3 - 65146.4i) q^{58} +(61989.7 - 35789.8i) q^{59} +(17460.4 + 30242.2i) q^{60} +(228557. + 131958. i) q^{61} +139339. i q^{62} +218491. q^{64} +(94001.1 - 162815. i) q^{65} +(128765. - 74342.5i) q^{66} +(-274333. - 475159. i) q^{67} +(178086. + 102818. i) q^{68} +154346. i q^{69} +465655. q^{71} +(-65442.2 + 113349. i) q^{72} +(289020. - 166866. i) q^{73} +(-62821.9 - 108811. i) q^{74} +(-150397. - 86832.0i) q^{75} -298871. i q^{76} +241881. q^{78} +(205012. - 355091. i) q^{79} +(48483.5 - 27991.9i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(-181396. - 104729. i) q^{82} -71948.9i q^{83} +411649. q^{85} +(-203521. + 352509. i) q^{86} +(-183740. + 106082. i) q^{87} +(464757. + 804983. i) q^{88} +(141505. + 81698.0i) q^{89} +89939.6i q^{90} -331220. q^{92} +(196497. - 340342. i) q^{93} +(666130. - 384590. i) q^{94} +(-299146. - 518137. i) q^{95} +(-402989. - 232666. i) q^{96} -651914. i q^{97} -419354. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} + 294 q^{5} + 3326 q^{8} + 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} + 294 q^{5} + 3326 q^{8} + 972 q^{9} + 3411 q^{10} - 314 q^{11} - 4671 q^{12} + 5292 q^{15} - 12721 q^{16} + 5532 q^{17} + 1215 q^{18} + 18234 q^{19} + 86106 q^{22} + 3928 q^{23} + 44901 q^{24} - 17038 q^{25} - 12366 q^{26} - 8300 q^{29} + 30699 q^{30} + 89508 q^{31} - 186207 q^{32} - 8478 q^{33} - 84078 q^{36} + 64706 q^{37} + 77136 q^{38} + 29106 q^{39} - 221823 q^{40} + 45740 q^{43} + 92529 q^{44} + 71442 q^{45} - 111504 q^{46} - 483276 q^{47} + 967216 q^{50} + 49788 q^{51} + 1673988 q^{52} - 540974 q^{53} + 32805 q^{54} + 328212 q^{57} + 539799 q^{58} + 181770 q^{59} - 146367 q^{60} - 418224 q^{61} + 2378626 q^{64} - 414204 q^{65} + 1162431 q^{66} - 1158902 q^{67} + 821250 q^{68} + 1442344 q^{71} + 404109 q^{72} + 378666 q^{73} - 432940 q^{74} - 460026 q^{75} - 222588 q^{78} + 611452 q^{79} + 2094945 q^{80} - 236196 q^{81} + 1561266 q^{82} - 275112 q^{85} + 816224 q^{86} - 112050 q^{87} - 366441 q^{88} + 989196 q^{89} + 678720 q^{92} + 805572 q^{93} + 716148 q^{94} - 591792 q^{95} - 5027589 q^{96} - 152604 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76350 + 4.78652i −0.345438 + 0.598316i −0.985433 0.170063i \(-0.945603\pi\)
0.639996 + 0.768379i \(0.278936\pi\)
\(3\) 13.5000 7.79423i 0.500000 0.288675i
\(4\) 16.7261 + 28.9705i 0.261346 + 0.452664i
\(5\) 57.9943 + 33.4830i 0.463955 + 0.267864i 0.713706 0.700446i \(-0.247015\pi\)
−0.249751 + 0.968310i \(0.580349\pi\)
\(6\) 86.1574i 0.398877i
\(7\) 0 0
\(8\) −538.619 −1.05199
\(9\) 121.500 210.444i 0.166667 0.288675i
\(10\) −320.535 + 185.061i −0.320535 + 0.185061i
\(11\) −862.868 1494.53i −0.648285 1.12286i −0.983532 0.180733i \(-0.942153\pi\)
0.335247 0.942130i \(-0.391180\pi\)
\(12\) 451.605 + 260.734i 0.261346 + 0.150888i
\(13\) 2807.43i 1.27785i −0.769271 0.638923i \(-0.779380\pi\)
0.769271 0.638923i \(-0.220620\pi\)
\(14\) 0 0
\(15\) 1043.90 0.309303
\(16\) 418.002 724.000i 0.102051 0.176758i
\(17\) 5323.58 3073.57i 1.08357 0.625599i 0.151712 0.988425i \(-0.451521\pi\)
0.931857 + 0.362826i \(0.118188\pi\)
\(18\) 671.531 + 1163.13i 0.115146 + 0.199439i
\(19\) −7737.30 4467.13i −1.12805 0.651281i −0.184607 0.982812i \(-0.559101\pi\)
−0.943444 + 0.331532i \(0.892435\pi\)
\(20\) 2240.17i 0.280021i
\(21\) 0 0
\(22\) 9538.15 0.895769
\(23\) −4950.64 + 8574.76i −0.406891 + 0.704755i −0.994540 0.104361i \(-0.966720\pi\)
0.587649 + 0.809116i \(0.300054\pi\)
\(24\) −7271.35 + 4198.12i −0.525995 + 0.303683i
\(25\) −5570.27 9648.00i −0.356497 0.617472i
\(26\) 13437.8 + 7758.32i 0.764555 + 0.441416i
\(27\) 3788.00i 0.192450i
\(28\) 0 0
\(29\) −13610.4 −0.558054 −0.279027 0.960283i \(-0.590012\pi\)
−0.279027 + 0.960283i \(0.590012\pi\)
\(30\) −2884.81 + 4996.64i −0.106845 + 0.185061i
\(31\) 21833.0 12605.3i 0.732871 0.423123i −0.0866007 0.996243i \(-0.527600\pi\)
0.819472 + 0.573120i \(0.194267\pi\)
\(32\) −14925.5 25851.7i −0.455490 0.788932i
\(33\) −23297.4 13450.8i −0.648285 0.374288i
\(34\) 33975.2i 0.864422i
\(35\) 0 0
\(36\) 8128.90 0.174230
\(37\) −11366.4 + 19687.1i −0.224397 + 0.388666i −0.956138 0.292916i \(-0.905374\pi\)
0.731742 + 0.681582i \(0.238708\pi\)
\(38\) 42764.1 24689.9i 0.779343 0.449954i
\(39\) −21881.7 37900.2i −0.368882 0.638923i
\(40\) −31236.8 18034.6i −0.488075 0.281790i
\(41\) 37897.2i 0.549865i 0.961464 + 0.274932i \(0.0886554\pi\)
−0.961464 + 0.274932i \(0.911345\pi\)
\(42\) 0 0
\(43\) 73646.2 0.926286 0.463143 0.886284i \(-0.346722\pi\)
0.463143 + 0.886284i \(0.346722\pi\)
\(44\) 28864.9 49995.4i 0.338853 0.586911i
\(45\) 14092.6 8136.38i 0.154652 0.0892881i
\(46\) −27362.2 47392.7i −0.281111 0.486898i
\(47\) −120523. 69583.9i −1.16085 0.670216i −0.209342 0.977843i \(-0.567132\pi\)
−0.951507 + 0.307626i \(0.900465\pi\)
\(48\) 13032.0i 0.117839i
\(49\) 0 0
\(50\) 61573.8 0.492591
\(51\) 47912.2 82986.3i 0.361190 0.625599i
\(52\) 81332.5 46957.3i 0.578434 0.333959i
\(53\) 8258.79 + 14304.7i 0.0554739 + 0.0960837i 0.892429 0.451188i \(-0.149000\pi\)
−0.836955 + 0.547272i \(0.815666\pi\)
\(54\) 18131.3 + 10468.1i 0.115146 + 0.0664795i
\(55\) 115566.i 0.694610i
\(56\) 0 0
\(57\) −139271. −0.752034
\(58\) 37612.3 65146.4i 0.192773 0.333892i
\(59\) 61989.7 35789.8i 0.301831 0.174262i −0.341434 0.939906i \(-0.610913\pi\)
0.643265 + 0.765644i \(0.277579\pi\)
\(60\) 17460.4 + 30242.2i 0.0808350 + 0.140010i
\(61\) 228557. + 131958.i 1.00695 + 0.581360i 0.910296 0.413958i \(-0.135854\pi\)
0.0966496 + 0.995318i \(0.469187\pi\)
\(62\) 139339.i 0.584651i
\(63\) 0 0
\(64\) 218491. 0.833476
\(65\) 94001.1 162815.i 0.342289 0.592862i
\(66\) 128765. 74342.5i 0.447884 0.258586i
\(67\) −274333. 475159.i −0.912125 1.57985i −0.811057 0.584967i \(-0.801107\pi\)
−0.101068 0.994880i \(-0.532226\pi\)
\(68\) 178086. + 102818.i 0.566372 + 0.326995i
\(69\) 154346.i 0.469837i
\(70\) 0 0
\(71\) 465655. 1.30103 0.650517 0.759491i \(-0.274552\pi\)
0.650517 + 0.759491i \(0.274552\pi\)
\(72\) −65442.2 + 113349.i −0.175332 + 0.303683i
\(73\) 289020. 166866.i 0.742950 0.428942i −0.0801910 0.996780i \(-0.525553\pi\)
0.823141 + 0.567837i \(0.192220\pi\)
\(74\) −62821.9 108811.i −0.155030 0.268520i
\(75\) −150397. 86832.0i −0.356497 0.205824i
\(76\) 298871.i 0.680837i
\(77\) 0 0
\(78\) 241881. 0.509703
\(79\) 205012. 355091.i 0.415813 0.720209i −0.579700 0.814830i \(-0.696830\pi\)
0.995513 + 0.0946203i \(0.0301637\pi\)
\(80\) 48483.5 27991.9i 0.0946942 0.0546717i
\(81\) −29524.5 51137.9i −0.0555556 0.0962250i
\(82\) −181396. 104729.i −0.328993 0.189944i
\(83\) 71948.9i 0.125832i −0.998019 0.0629158i \(-0.979960\pi\)
0.998019 0.0629158i \(-0.0200400\pi\)
\(84\) 0 0
\(85\) 411649. 0.670302
\(86\) −203521. + 352509.i −0.319974 + 0.554211i
\(87\) −183740. + 106082.i −0.279027 + 0.161096i
\(88\) 464757. + 804983.i 0.681990 + 1.18124i
\(89\) 141505. + 81698.0i 0.200725 + 0.115889i 0.596994 0.802246i \(-0.296362\pi\)
−0.396269 + 0.918135i \(0.629695\pi\)
\(90\) 89939.6i 0.123374i
\(91\) 0 0
\(92\) −331220. −0.425357
\(93\) 196497. 340342.i 0.244290 0.423123i
\(94\) 666130. 384590.i 0.802002 0.463036i
\(95\) −299146. 518137.i −0.348910 0.604329i
\(96\) −402989. 232666.i −0.455490 0.262977i
\(97\) 651914.i 0.714291i −0.934049 0.357146i \(-0.883750\pi\)
0.934049 0.357146i \(-0.116250\pi\)
\(98\) 0 0
\(99\) −419354. −0.432190
\(100\) 186338. 322747.i 0.186338 0.322747i
\(101\) −883850. + 510291.i −0.857856 + 0.495283i −0.863294 0.504702i \(-0.831602\pi\)
0.00543765 + 0.999985i \(0.498269\pi\)
\(102\) 264811. + 458666.i 0.249537 + 0.432211i
\(103\) −363147. 209663.i −0.332331 0.191871i 0.324545 0.945870i \(-0.394789\pi\)
−0.656875 + 0.753999i \(0.728122\pi\)
\(104\) 1.51213e6i 1.34428i
\(105\) 0 0
\(106\) −91292.8 −0.0766512
\(107\) −1.10621e6 + 1.91600e6i −0.902993 + 1.56403i −0.0794039 + 0.996843i \(0.525302\pi\)
−0.823589 + 0.567187i \(0.808032\pi\)
\(108\) 109740. 63358.5i 0.0871152 0.0502960i
\(109\) −382955. 663297.i −0.295711 0.512187i 0.679439 0.733732i \(-0.262223\pi\)
−0.975150 + 0.221545i \(0.928890\pi\)
\(110\) 553158. + 319366.i 0.415596 + 0.239944i
\(111\) 354368.i 0.259111i
\(112\) 0 0
\(113\) −2.66096e6 −1.84418 −0.922090 0.386976i \(-0.873520\pi\)
−0.922090 + 0.386976i \(0.873520\pi\)
\(114\) 384877. 666626.i 0.259781 0.449954i
\(115\) −574218. + 331525.i −0.377558 + 0.217983i
\(116\) −227649. 394299.i −0.145845 0.252611i
\(117\) −590806. 341102.i −0.368882 0.212974i
\(118\) 395620.i 0.240787i
\(119\) 0 0
\(120\) −562263. −0.325384
\(121\) −603302. + 1.04495e6i −0.340548 + 0.589847i
\(122\) −1.26324e6 + 729331.i −0.695674 + 0.401647i
\(123\) 295380. + 511612.i 0.158732 + 0.274932i
\(124\) 730361. + 421674.i 0.383065 + 0.221163i
\(125\) 1.79238e6i 0.917700i
\(126\) 0 0
\(127\) −1.11648e6 −0.545055 −0.272527 0.962148i \(-0.587859\pi\)
−0.272527 + 0.962148i \(0.587859\pi\)
\(128\) 351433. 608699.i 0.167576 0.290250i
\(129\) 994224. 574015.i 0.463143 0.267396i
\(130\) 519544. + 899877.i 0.236479 + 0.409594i
\(131\) −247826. 143083.i −0.110239 0.0636463i 0.443867 0.896093i \(-0.353606\pi\)
−0.554106 + 0.832446i \(0.686940\pi\)
\(132\) 899918.i 0.391274i
\(133\) 0 0
\(134\) 3.03248e6 1.26033
\(135\) 126834. 219682.i 0.0515505 0.0892881i
\(136\) −2.86738e6 + 1.65548e6i −1.13990 + 0.658124i
\(137\) 1.86697e6 + 3.23368e6i 0.726063 + 1.25758i 0.958535 + 0.284975i \(0.0919854\pi\)
−0.232472 + 0.972603i \(0.574681\pi\)
\(138\) −738779. 426534.i −0.281111 0.162299i
\(139\) 618216.i 0.230195i −0.993354 0.115097i \(-0.963282\pi\)
0.993354 0.115097i \(-0.0367180\pi\)
\(140\) 0 0
\(141\) −2.16941e6 −0.773899
\(142\) −1.28684e6 + 2.22887e6i −0.449426 + 0.778429i
\(143\) −4.19579e6 + 2.42244e6i −1.43485 + 0.828408i
\(144\) −101574. 175932.i −0.0340171 0.0589193i
\(145\) −789324. 455716.i −0.258911 0.149483i
\(146\) 1.84454e6i 0.592691i
\(147\) 0 0
\(148\) −760461. −0.234580
\(149\) −1.86160e6 + 3.22438e6i −0.562765 + 0.974737i 0.434489 + 0.900677i \(0.356929\pi\)
−0.997254 + 0.0740601i \(0.976404\pi\)
\(150\) 831247. 479920.i 0.246295 0.142199i
\(151\) 1.27599e6 + 2.21009e6i 0.370611 + 0.641917i 0.989660 0.143436i \(-0.0458151\pi\)
−0.619049 + 0.785352i \(0.712482\pi\)
\(152\) 4.16746e6 + 2.40608e6i 1.18670 + 0.685140i
\(153\) 1.49375e6i 0.417066i
\(154\) 0 0
\(155\) 1.68825e6 0.453358
\(156\) 731993. 1.26785e6i 0.192811 0.333959i
\(157\) 5.87057e6 3.38938e6i 1.51699 0.875832i 0.517186 0.855873i \(-0.326980\pi\)
0.999801 0.0199592i \(-0.00635363\pi\)
\(158\) 1.13310e6 + 1.96259e6i 0.287275 + 0.497575i
\(159\) 222987. + 128742.i 0.0554739 + 0.0320279i
\(160\) 1.99900e6i 0.488038i
\(161\) 0 0
\(162\) 326364. 0.0767639
\(163\) 4.13571e6 7.16325e6i 0.954964 1.65405i 0.220513 0.975384i \(-0.429227\pi\)
0.734451 0.678662i \(-0.237440\pi\)
\(164\) −1.09790e6 + 633874.i −0.248904 + 0.143705i
\(165\) −900746. 1.56014e6i −0.200517 0.347305i
\(166\) 344385. + 198831.i 0.0752871 + 0.0434670i
\(167\) 2.59960e6i 0.558158i 0.960268 + 0.279079i \(0.0900291\pi\)
−0.960268 + 0.279079i \(0.909971\pi\)
\(168\) 0 0
\(169\) −3.05483e6 −0.632888
\(170\) −1.13759e6 + 1.97037e6i −0.231548 + 0.401052i
\(171\) −1.88016e6 + 1.08551e6i −0.376017 + 0.217094i
\(172\) 1.23182e6 + 2.13357e6i 0.242081 + 0.419296i
\(173\) 7.10612e6 + 4.10272e6i 1.37244 + 0.792380i 0.991235 0.132109i \(-0.0421749\pi\)
0.381208 + 0.924489i \(0.375508\pi\)
\(174\) 1.17263e6i 0.222595i
\(175\) 0 0
\(176\) −1.44272e6 −0.264633
\(177\) 557907. 966324.i 0.100610 0.174262i
\(178\) −782099. + 451545.i −0.138676 + 0.0800647i
\(179\) −4.09401e6 7.09104e6i −0.713822 1.23638i −0.963412 0.268025i \(-0.913629\pi\)
0.249590 0.968352i \(-0.419704\pi\)
\(180\) 471430. + 272180.i 0.0808350 + 0.0466701i
\(181\) 3.25606e6i 0.549106i 0.961572 + 0.274553i \(0.0885298\pi\)
−0.961572 + 0.274553i \(0.911470\pi\)
\(182\) 0 0
\(183\) 4.11403e6 0.671297
\(184\) 2.66651e6 4.61853e6i 0.428045 0.741395i
\(185\) −1.31837e6 + 761161.i −0.208220 + 0.120216i
\(186\) 1.08604e6 + 1.88107e6i 0.168774 + 0.292325i
\(187\) −9.18709e6 5.30417e6i −1.40492 0.811133i
\(188\) 4.65547e6i 0.700633i
\(189\) 0 0
\(190\) 3.30677e6 0.482106
\(191\) −4.30425e6 + 7.45518e6i −0.617728 + 1.06994i 0.372171 + 0.928164i \(0.378614\pi\)
−0.989899 + 0.141773i \(0.954720\pi\)
\(192\) 2.94963e6 1.70297e6i 0.416738 0.240604i
\(193\) 89943.0 + 155786.i 0.0125111 + 0.0216699i 0.872213 0.489126i \(-0.162684\pi\)
−0.859702 + 0.510796i \(0.829351\pi\)
\(194\) 3.12040e6 + 1.80157e6i 0.427372 + 0.246743i
\(195\) 2.93067e6i 0.395241i
\(196\) 0 0
\(197\) 2.69333e6 0.352283 0.176141 0.984365i \(-0.443638\pi\)
0.176141 + 0.984365i \(0.443638\pi\)
\(198\) 1.15888e6 2.00725e6i 0.149295 0.258586i
\(199\) −5.23271e6 + 3.02111e6i −0.663999 + 0.383360i −0.793799 0.608180i \(-0.791900\pi\)
0.129800 + 0.991540i \(0.458566\pi\)
\(200\) 3.00025e6 + 5.19659e6i 0.375032 + 0.649574i
\(201\) −7.40700e6 4.27643e6i −0.912125 0.526616i
\(202\) 5.64076e6i 0.684358i
\(203\) 0 0
\(204\) 3.20554e6 0.377581
\(205\) −1.26891e6 + 2.19782e6i −0.147289 + 0.255112i
\(206\) 2.00711e6 1.15881e6i 0.229599 0.132559i
\(207\) 1.20301e6 + 2.08367e6i 0.135630 + 0.234918i
\(208\) −2.03258e6 1.17351e6i −0.225869 0.130406i
\(209\) 1.54182e7i 1.68886i
\(210\) 0 0
\(211\) −1.38113e7 −1.47024 −0.735118 0.677939i \(-0.762873\pi\)
−0.735118 + 0.677939i \(0.762873\pi\)
\(212\) −276275. + 478523.i −0.0289958 + 0.0502221i
\(213\) 6.28634e6 3.62942e6i 0.650517 0.375576i
\(214\) −6.11400e6 1.05898e7i −0.623855 1.08055i
\(215\) 4.27106e6 + 2.46590e6i 0.429755 + 0.248119i
\(216\) 2.04029e6i 0.202456i
\(217\) 0 0
\(218\) 4.23318e6 0.408599
\(219\) 2.60118e6 4.50538e6i 0.247650 0.428942i
\(220\) 3.34800e6 1.93297e6i 0.314425 0.181533i
\(221\) −8.62881e6 1.49455e7i −0.799419 1.38463i
\(222\) −1.69619e6 979297.i −0.155030 0.0895067i
\(223\) 9.81400e6i 0.884976i 0.896774 + 0.442488i \(0.145904\pi\)
−0.896774 + 0.442488i \(0.854096\pi\)
\(224\) 0 0
\(225\) −2.70715e6 −0.237665
\(226\) 7.35357e6 1.27368e7i 0.637049 1.10340i
\(227\) 1.26217e7 7.28715e6i 1.07905 0.622989i 0.148408 0.988926i \(-0.452585\pi\)
0.930639 + 0.365938i \(0.119252\pi\)
\(228\) −2.32947e6 4.03476e6i −0.196541 0.340419i
\(229\) −1.27292e7 7.34923e6i −1.05998 0.611978i −0.134551 0.990907i \(-0.542959\pi\)
−0.925426 + 0.378929i \(0.876292\pi\)
\(230\) 3.66468e6i 0.301198i
\(231\) 0 0
\(232\) 7.33080e6 0.587067
\(233\) −2.87597e6 + 4.98133e6i −0.227362 + 0.393802i −0.957025 0.290004i \(-0.906343\pi\)
0.729664 + 0.683806i \(0.239677\pi\)
\(234\) 3.26539e6 1.88527e6i 0.254852 0.147139i
\(235\) −4.65976e6 8.07094e6i −0.359054 0.621900i
\(236\) 2.07369e6 + 1.19725e6i 0.157764 + 0.0910853i
\(237\) 6.39164e6i 0.480140i
\(238\) 0 0
\(239\) 1.60167e7 1.17322 0.586610 0.809869i \(-0.300462\pi\)
0.586610 + 0.809869i \(0.300462\pi\)
\(240\) 436351. 755782.i 0.0315647 0.0546717i
\(241\) 2.23613e7 1.29103e7i 1.59752 0.922327i 0.605553 0.795805i \(-0.292952\pi\)
0.991964 0.126522i \(-0.0403816\pi\)
\(242\) −3.33445e6 5.77544e6i −0.235276 0.407510i
\(243\) −797162. 460241.i −0.0555556 0.0320750i
\(244\) 8.82856e6i 0.607744i
\(245\) 0 0
\(246\) −3.26513e6 −0.219328
\(247\) −1.25411e7 + 2.17219e7i −0.832236 + 1.44147i
\(248\) −1.17596e7 + 6.78943e6i −0.770973 + 0.445121i
\(249\) −560786. 971311.i −0.0363245 0.0629158i
\(250\) 8.57929e6 + 4.95325e6i 0.549074 + 0.317008i
\(251\) 9.51912e6i 0.601971i −0.953629 0.300985i \(-0.902684\pi\)
0.953629 0.300985i \(-0.0973156\pi\)
\(252\) 0 0
\(253\) 1.70870e7 1.05513
\(254\) 3.08539e6 5.34406e6i 0.188282 0.326115i
\(255\) 5.55727e6 3.20849e6i 0.335151 0.193500i
\(256\) 8.93408e6 + 1.54743e7i 0.532512 + 0.922339i
\(257\) −1.93872e7 1.11932e7i −1.14213 0.659408i −0.195171 0.980769i \(-0.562526\pi\)
−0.946957 + 0.321361i \(0.895860\pi\)
\(258\) 6.34517e6i 0.369474i
\(259\) 0 0
\(260\) 6.28910e6 0.357823
\(261\) −1.65366e6 + 2.86422e6i −0.0930089 + 0.161096i
\(262\) 1.36974e6 790818.i 0.0761612 0.0439717i
\(263\) −5.24659e6 9.08736e6i −0.288410 0.499540i 0.685021 0.728524i \(-0.259793\pi\)
−0.973430 + 0.228983i \(0.926460\pi\)
\(264\) 1.25484e7 + 7.24484e6i 0.681990 + 0.393747i
\(265\) 1.10612e6i 0.0594380i
\(266\) 0 0
\(267\) 2.54709e6 0.133817
\(268\) 9.17707e6 1.58951e7i 0.476760 0.825772i
\(269\) −2.33663e7 + 1.34905e7i −1.20042 + 0.693063i −0.960649 0.277766i \(-0.910406\pi\)
−0.239772 + 0.970829i \(0.577073\pi\)
\(270\) 701009. + 1.21418e6i 0.0356150 + 0.0616869i
\(271\) 1.09955e6 + 634826.i 0.0552468 + 0.0318968i 0.527369 0.849636i \(-0.323179\pi\)
−0.472122 + 0.881533i \(0.656512\pi\)
\(272\) 5.13903e6i 0.255373i
\(273\) 0 0
\(274\) −2.06374e7 −1.00324
\(275\) −9.61282e6 + 1.66499e7i −0.462224 + 0.800596i
\(276\) −4.47147e6 + 2.58160e6i −0.212678 + 0.122790i
\(277\) 3.35016e6 + 5.80265e6i 0.157626 + 0.273016i 0.934012 0.357242i \(-0.116283\pi\)
−0.776386 + 0.630257i \(0.782949\pi\)
\(278\) 2.95911e6 + 1.70844e6i 0.137729 + 0.0795180i
\(279\) 6.12616e6i 0.282082i
\(280\) 0 0
\(281\) −321000. −0.0144673 −0.00723363 0.999974i \(-0.502303\pi\)
−0.00723363 + 0.999974i \(0.502303\pi\)
\(282\) 5.99517e6 1.03839e7i 0.267334 0.463036i
\(283\) −2.77311e6 + 1.60105e6i −0.122351 + 0.0706394i −0.559926 0.828542i \(-0.689171\pi\)
0.437575 + 0.899182i \(0.355837\pi\)
\(284\) 7.78860e6 + 1.34902e7i 0.340020 + 0.588931i
\(285\) −8.07695e6 4.66323e6i −0.348910 0.201443i
\(286\) 2.67776e7i 1.14465i
\(287\) 0 0
\(288\) −7.25380e6 −0.303660
\(289\) 6.82485e6 1.18210e7i 0.282748 0.489734i
\(290\) 4.36260e6 2.51875e6i 0.178876 0.103274i
\(291\) −5.08117e6 8.80084e6i −0.206198 0.357146i
\(292\) 9.66837e6 + 5.58204e6i 0.388333 + 0.224204i
\(293\) 2.67440e6i 0.106322i −0.998586 0.0531610i \(-0.983070\pi\)
0.998586 0.0531610i \(-0.0169297\pi\)
\(294\) 0 0
\(295\) 4.79340e6 0.186714
\(296\) 6.12214e6 1.06039e7i 0.236063 0.408873i
\(297\) −5.66128e6 + 3.26854e6i −0.216095 + 0.124763i
\(298\) −1.02891e7 1.78212e7i −0.388800 0.673422i
\(299\) 2.40730e7 + 1.38986e7i 0.900568 + 0.519943i
\(300\) 5.80945e6i 0.215165i
\(301\) 0 0
\(302\) −1.41048e7 −0.512092
\(303\) −7.95465e6 + 1.37779e7i −0.285952 + 0.495283i
\(304\) −6.46841e6 + 3.73454e6i −0.230238 + 0.132928i
\(305\) 8.83669e6 + 1.53056e7i 0.311451 + 0.539449i
\(306\) 7.14989e6 + 4.12799e6i 0.249537 + 0.144070i
\(307\) 1.98765e7i 0.686950i 0.939162 + 0.343475i \(0.111604\pi\)
−0.939162 + 0.343475i \(0.888396\pi\)
\(308\) 0 0
\(309\) −6.53664e6 −0.221554
\(310\) −4.66548e6 + 8.08085e6i −0.156607 + 0.271251i
\(311\) 1.36580e7 7.88548e6i 0.454054 0.262148i −0.255487 0.966813i \(-0.582236\pi\)
0.709541 + 0.704664i \(0.248902\pi\)
\(312\) 1.17859e7 + 2.04138e7i 0.388060 + 0.672140i
\(313\) 9.13939e6 + 5.27663e6i 0.298047 + 0.172077i 0.641565 0.767069i \(-0.278285\pi\)
−0.343518 + 0.939146i \(0.611619\pi\)
\(314\) 3.74662e7i 1.21018i
\(315\) 0 0
\(316\) 1.37162e7 0.434684
\(317\) 1.61613e7 2.79923e7i 0.507341 0.878740i −0.492623 0.870243i \(-0.663962\pi\)
0.999964 0.00849733i \(-0.00270482\pi\)
\(318\) −1.23245e6 + 711557.i −0.0383256 + 0.0221273i
\(319\) 1.17440e7 + 2.03411e7i 0.361778 + 0.626618i
\(320\) 1.26712e7 + 7.31574e6i 0.386695 + 0.223259i
\(321\) 3.44881e7i 1.04269i
\(322\) 0 0
\(323\) −5.49201e7 −1.62976
\(324\) 987661. 1.71068e6i 0.0290384 0.0502960i
\(325\) −2.70860e7 + 1.56381e7i −0.789033 + 0.455549i
\(326\) 2.28581e7 + 3.95913e7i 0.659761 + 1.14274i
\(327\) −1.03398e7 5.96968e6i −0.295711 0.170729i
\(328\) 2.04122e7i 0.578452i
\(329\) 0 0
\(330\) 9.95685e6 0.277064
\(331\) −1.00165e7 + 1.73490e7i −0.276205 + 0.478400i −0.970438 0.241349i \(-0.922410\pi\)
0.694234 + 0.719750i \(0.255743\pi\)
\(332\) 2.08440e6 1.20343e6i 0.0569595 0.0328856i
\(333\) 2.76203e6 + 4.78397e6i 0.0747989 + 0.129555i
\(334\) −1.24430e7 7.18400e6i −0.333955 0.192809i
\(335\) 3.67421e7i 0.977303i
\(336\) 0 0
\(337\) −3.66702e6 −0.0958128 −0.0479064 0.998852i \(-0.515255\pi\)
−0.0479064 + 0.998852i \(0.515255\pi\)
\(338\) 8.44203e6 1.46220e7i 0.218623 0.378667i
\(339\) −3.59230e7 + 2.07401e7i −0.922090 + 0.532369i
\(340\) 6.88530e6 + 1.19257e7i 0.175181 + 0.303422i
\(341\) −3.76779e7 2.17534e7i −0.950219 0.548609i
\(342\) 1.19993e7i 0.299969i
\(343\) 0 0
\(344\) −3.96672e7 −0.974443
\(345\) −5.16796e6 + 8.95117e6i −0.125853 + 0.217983i
\(346\) −3.92756e7 + 2.26758e7i −0.948187 + 0.547436i
\(347\) −3.22802e6 5.59109e6i −0.0772587 0.133816i 0.824808 0.565414i \(-0.191283\pi\)
−0.902066 + 0.431598i \(0.857950\pi\)
\(348\) −6.14652e6 3.54869e6i −0.145845 0.0842036i
\(349\) 4.01536e7i 0.944600i −0.881438 0.472300i \(-0.843424\pi\)
0.881438 0.472300i \(-0.156576\pi\)
\(350\) 0 0
\(351\) −1.06345e7 −0.245921
\(352\) −2.57575e7 + 4.46133e7i −0.590575 + 1.02291i
\(353\) −7.02915e6 + 4.05828e6i −0.159801 + 0.0922610i −0.577768 0.816201i \(-0.696076\pi\)
0.417967 + 0.908462i \(0.362743\pi\)
\(354\) 3.08356e6 + 5.34087e6i 0.0695091 + 0.120393i
\(355\) 2.70053e7 + 1.55915e7i 0.603621 + 0.348501i
\(356\) 5.46596e6i 0.121148i
\(357\) 0 0
\(358\) 4.52552e7 0.986324
\(359\) −1.84586e7 + 3.19712e7i −0.398946 + 0.690996i −0.993596 0.112989i \(-0.963957\pi\)
0.594650 + 0.803985i \(0.297291\pi\)
\(360\) −7.59055e6 + 4.38241e6i −0.162692 + 0.0939302i
\(361\) 1.63876e7 + 2.83842e7i 0.348333 + 0.603330i
\(362\) −1.55852e7 8.99811e6i −0.328539 0.189682i
\(363\) 1.88091e7i 0.393231i
\(364\) 0 0
\(365\) 2.23487e7 0.459593
\(366\) −1.13691e7 + 1.96919e7i −0.231891 + 0.401647i
\(367\) −1.70742e7 + 9.85777e6i −0.345415 + 0.199425i −0.662664 0.748917i \(-0.730574\pi\)
0.317249 + 0.948342i \(0.397241\pi\)
\(368\) 4.13875e6 + 7.16853e6i 0.0830474 + 0.143842i
\(369\) 7.97525e6 + 4.60451e6i 0.158732 + 0.0916441i
\(370\) 8.41387e6i 0.166108i
\(371\) 0 0
\(372\) 1.31465e7 0.255377
\(373\) −5.21653e6 + 9.03530e6i −0.100521 + 0.174107i −0.911899 0.410414i \(-0.865384\pi\)
0.811379 + 0.584521i \(0.198718\pi\)
\(374\) 5.07770e7 2.93161e7i 0.970627 0.560392i
\(375\) −1.39702e7 2.41972e7i −0.264917 0.458850i
\(376\) 6.49158e7 + 3.74792e7i 1.22120 + 0.705061i
\(377\) 3.82101e7i 0.713106i
\(378\) 0 0
\(379\) −5.26018e7 −0.966235 −0.483118 0.875556i \(-0.660496\pi\)
−0.483118 + 0.875556i \(0.660496\pi\)
\(380\) 1.00071e7 1.73328e7i 0.182372 0.315878i
\(381\) −1.50725e7 + 8.70210e6i −0.272527 + 0.157344i
\(382\) −2.37896e7 4.12048e7i −0.426773 0.739193i
\(383\) −6.36846e7 3.67683e7i −1.13354 0.654451i −0.188719 0.982031i \(-0.560434\pi\)
−0.944823 + 0.327580i \(0.893767\pi\)
\(384\) 1.09566e7i 0.193500i
\(385\) 0 0
\(386\) −994230. −0.0172872
\(387\) 8.94802e6 1.54984e7i 0.154381 0.267396i
\(388\) 1.88863e7 1.09040e7i 0.323334 0.186677i
\(389\) −8.60695e6 1.49077e7i −0.146218 0.253257i 0.783609 0.621255i \(-0.213377\pi\)
−0.929827 + 0.367998i \(0.880043\pi\)
\(390\) 1.40277e7 + 8.09890e6i 0.236479 + 0.136531i
\(391\) 6.08645e7i 1.01820i
\(392\) 0 0
\(393\) −4.46088e6 −0.0734924
\(394\) −7.44303e6 + 1.28917e7i −0.121692 + 0.210776i
\(395\) 2.37791e7 1.37289e7i 0.385837 0.222763i
\(396\) −7.01416e6 1.21489e7i −0.112951 0.195637i
\(397\) 5.31024e7 + 3.06587e7i 0.848678 + 0.489984i 0.860205 0.509949i \(-0.170336\pi\)
−0.0115267 + 0.999934i \(0.503669\pi\)
\(398\) 3.33953e7i 0.529708i
\(399\) 0 0
\(400\) −9.31354e6 −0.145524
\(401\) 2.30735e7 3.99645e7i 0.357833 0.619785i −0.629765 0.776785i \(-0.716849\pi\)
0.987599 + 0.157000i \(0.0501823\pi\)
\(402\) 4.09385e7 2.36359e7i 0.630165 0.363826i
\(403\) −3.53883e7 6.12944e7i −0.540686 0.936495i
\(404\) −2.95668e7 1.70704e7i −0.448394 0.258880i
\(405\) 3.95428e6i 0.0595254i
\(406\) 0 0
\(407\) 3.92307e7 0.581892
\(408\) −2.58064e7 + 4.46980e7i −0.379968 + 0.658124i
\(409\) 5.25613e7 3.03463e7i 0.768239 0.443543i −0.0640071 0.997949i \(-0.520388\pi\)
0.832246 + 0.554406i \(0.187055\pi\)
\(410\) −7.01329e6 1.21474e7i −0.101758 0.176251i
\(411\) 5.04081e7 + 2.91031e7i 0.726063 + 0.419193i
\(412\) 1.40274e7i 0.200579i
\(413\) 0 0
\(414\) −1.32980e7 −0.187407
\(415\) 2.40907e6 4.17263e6i 0.0337058 0.0583802i
\(416\) −7.25768e7 + 4.19022e7i −1.00813 + 0.582046i
\(417\) −4.81852e6 8.34592e6i −0.0664516 0.115097i
\(418\) −7.37995e7 4.26082e7i −1.01047 0.583397i
\(419\) 1.17371e8i 1.59558i −0.602939 0.797788i \(-0.706004\pi\)
0.602939 0.797788i \(-0.293996\pi\)
\(420\) 0 0
\(421\) −1.28510e7 −0.172222 −0.0861111 0.996286i \(-0.527444\pi\)
−0.0861111 + 0.996286i \(0.527444\pi\)
\(422\) 3.81676e7 6.61081e7i 0.507875 0.879666i
\(423\) −2.92870e7 + 1.69089e7i −0.386950 + 0.223405i
\(424\) −4.44834e6 7.70475e6i −0.0583580 0.101079i
\(425\) −5.93075e7 3.42412e7i −0.772579 0.446049i
\(426\) 4.01196e7i 0.518953i
\(427\) 0 0
\(428\) −7.40101e7 −0.943973
\(429\) −3.77621e7 + 6.54058e7i −0.478282 + 0.828408i
\(430\) −2.36062e7 + 1.36290e7i −0.296907 + 0.171419i
\(431\) 5.69282e7 + 9.86026e7i 0.711043 + 1.23156i 0.964466 + 0.264207i \(0.0851102\pi\)
−0.253423 + 0.967356i \(0.581556\pi\)
\(432\) −2.74251e6 1.58339e6i −0.0340171 0.0196398i
\(433\) 2.76112e7i 0.340111i −0.985434 0.170056i \(-0.945605\pi\)
0.985434 0.170056i \(-0.0543947\pi\)
\(434\) 0 0
\(435\) −1.42078e7 −0.172608
\(436\) 1.28107e7 2.21888e7i 0.154566 0.267716i
\(437\) 7.66092e7 4.42303e7i 0.917987 0.530000i
\(438\) 1.43767e7 + 2.49012e7i 0.171095 + 0.296346i
\(439\) −6.22452e7 3.59373e7i −0.735720 0.424768i 0.0847914 0.996399i \(-0.472978\pi\)
−0.820511 + 0.571631i \(0.806311\pi\)
\(440\) 6.22459e7i 0.730723i
\(441\) 0 0
\(442\) 9.53829e7 1.10460
\(443\) 4.75145e7 8.22975e7i 0.546531 0.946620i −0.451978 0.892029i \(-0.649281\pi\)
0.998509 0.0545904i \(-0.0173853\pi\)
\(444\) −1.02662e7 + 5.92721e6i −0.117290 + 0.0677175i
\(445\) 5.47099e6 + 9.47603e6i 0.0620849 + 0.107534i
\(446\) −4.69750e7 2.71210e7i −0.529495 0.305704i
\(447\) 5.80389e7i 0.649825i
\(448\) 0 0
\(449\) 1.15401e8 1.27488 0.637440 0.770500i \(-0.279993\pi\)
0.637440 + 0.770500i \(0.279993\pi\)
\(450\) 7.48122e6 1.29579e7i 0.0820984 0.142199i
\(451\) 5.66386e7 3.27003e7i 0.617423 0.356469i
\(452\) −4.45076e7 7.70894e7i −0.481968 0.834794i
\(453\) 3.44518e7 + 1.98908e7i 0.370611 + 0.213972i
\(454\) 8.05522e7i 0.860815i
\(455\) 0 0
\(456\) 7.50142e7 0.791132
\(457\) −4.58763e6 + 7.94601e6i −0.0480662 + 0.0832531i −0.889058 0.457796i \(-0.848639\pi\)
0.840991 + 0.541049i \(0.181973\pi\)
\(458\) 7.03546e7 4.06192e7i 0.732311 0.422800i
\(459\) −1.16427e7 2.01657e7i −0.120397 0.208533i
\(460\) −1.92089e7 1.10903e7i −0.197346 0.113938i
\(461\) 5.79354e7i 0.591346i −0.955289 0.295673i \(-0.904456\pi\)
0.955289 0.295673i \(-0.0955438\pi\)
\(462\) 0 0
\(463\) 6.51781e7 0.656687 0.328344 0.944558i \(-0.393510\pi\)
0.328344 + 0.944558i \(0.393510\pi\)
\(464\) −5.68916e6 + 9.85391e6i −0.0569500 + 0.0986404i
\(465\) 2.27914e7 1.31586e7i 0.226679 0.130873i
\(466\) −1.58955e7 2.75318e7i −0.157079 0.272068i
\(467\) 1.46749e8 + 8.47258e7i 1.44087 + 0.831888i 0.997908 0.0646508i \(-0.0205933\pi\)
0.442965 + 0.896539i \(0.353927\pi\)
\(468\) 2.28213e7i 0.222640i
\(469\) 0 0
\(470\) 5.15090e7 0.496123
\(471\) 5.28352e7 9.15132e7i 0.505662 0.875832i
\(472\) −3.33888e7 + 1.92770e7i −0.317523 + 0.183322i
\(473\) −6.35470e7 1.10067e8i −0.600498 1.04009i
\(474\) 3.05938e7 + 1.76633e7i 0.287275 + 0.165858i
\(475\) 9.95326e7i 0.928719i
\(476\) 0 0
\(477\) 4.01377e6 0.0369826
\(478\) −4.42622e7 + 7.66644e7i −0.405275 + 0.701956i
\(479\) 7.92689e7 4.57659e7i 0.721268 0.416424i −0.0939514 0.995577i \(-0.529950\pi\)
0.815219 + 0.579153i \(0.196617\pi\)
\(480\) −1.55807e7 2.69866e7i −0.140885 0.244019i
\(481\) 5.52701e7 + 3.19102e7i 0.496656 + 0.286744i
\(482\) 1.42710e8i 1.27443i
\(483\) 0 0
\(484\) −4.03636e7 −0.356003
\(485\) 2.18281e7 3.78073e7i 0.191333 0.331399i
\(486\) 4.40591e6 2.54376e6i 0.0383820 0.0221598i
\(487\) 6.56199e7 + 1.13657e8i 0.568131 + 0.984032i 0.996751 + 0.0805467i \(0.0256666\pi\)
−0.428620 + 0.903485i \(0.641000\pi\)
\(488\) −1.23105e8 7.10749e7i −1.05930 0.611585i
\(489\) 1.28939e8i 1.10270i
\(490\) 0 0
\(491\) −8.81776e7 −0.744927 −0.372463 0.928047i \(-0.621487\pi\)
−0.372463 + 0.928047i \(0.621487\pi\)
\(492\) −9.88111e6 + 1.71146e7i −0.0829680 + 0.143705i
\(493\) −7.24558e7 + 4.18324e7i −0.604690 + 0.349118i
\(494\) −6.93149e7 1.20057e8i −0.574971 0.995879i
\(495\) −2.43201e7 1.40412e7i −0.200517 0.115768i
\(496\) 2.10761e7i 0.172721i
\(497\) 0 0
\(498\) 6.19894e6 0.0501914
\(499\) 1.14235e8 1.97862e8i 0.919389 1.59243i 0.119043 0.992889i \(-0.462017\pi\)
0.800346 0.599539i \(-0.204649\pi\)
\(500\) 5.19262e7 2.99796e7i 0.415410 0.239837i
\(501\) 2.02619e7 + 3.50946e7i 0.161126 + 0.279079i
\(502\) 4.55635e7 + 2.63061e7i 0.360169 + 0.207943i
\(503\) 2.07735e8i 1.63232i −0.577824 0.816161i \(-0.696098\pi\)
0.577824 0.816161i \(-0.303902\pi\)
\(504\) 0 0
\(505\) −6.83444e7 −0.530675
\(506\) −4.72199e7 + 8.17873e7i −0.364480 + 0.631298i
\(507\) −4.12402e7 + 2.38100e7i −0.316444 + 0.182699i
\(508\) −1.86744e7 3.23450e7i −0.142448 0.246727i
\(509\) 4.74960e7 + 2.74218e7i 0.360167 + 0.207942i 0.669154 0.743124i \(-0.266657\pi\)
−0.308987 + 0.951066i \(0.599990\pi\)
\(510\) 3.54667e7i 0.267368i
\(511\) 0 0
\(512\) −5.37739e7 −0.400647
\(513\) −1.69215e7 + 2.93089e7i −0.125339 + 0.217094i
\(514\) 1.07153e8 6.18647e7i 0.789068 0.455569i
\(515\) −1.40403e7 2.43185e7i −0.102791 0.178039i
\(516\) 3.32590e7 + 1.92021e7i 0.242081 + 0.139765i
\(517\) 2.40167e8i 1.73797i
\(518\) 0 0
\(519\) 1.27910e8 0.914962
\(520\) −5.06308e7 + 8.76951e7i −0.360085 + 0.623685i
\(521\) 2.47035e7 1.42626e7i 0.174681 0.100852i −0.410110 0.912036i \(-0.634510\pi\)
0.584791 + 0.811184i \(0.301176\pi\)
\(522\) −9.13978e6 1.58306e7i −0.0642576 0.111297i
\(523\) 9.32394e7 + 5.38318e7i 0.651770 + 0.376300i 0.789134 0.614221i \(-0.210530\pi\)
−0.137364 + 0.990521i \(0.543863\pi\)
\(524\) 9.57287e6i 0.0665347i
\(525\) 0 0
\(526\) 5.79958e7 0.398510
\(527\) 7.74863e7 1.34210e8i 0.529411 0.916966i
\(528\) −1.94767e7 + 1.12449e7i −0.132317 + 0.0763930i
\(529\) 2.50003e7 + 4.33018e7i 0.168880 + 0.292509i
\(530\) −5.29446e6 3.05676e6i −0.0355627 0.0205321i
\(531\) 1.73938e7i 0.116175i
\(532\) 0 0
\(533\) 1.06394e8 0.702642
\(534\) −7.03889e6 + 1.21917e7i −0.0462253 + 0.0800647i
\(535\) −1.28307e8 + 7.40782e7i −0.837895 + 0.483759i
\(536\) 1.47761e8 + 2.55930e8i 0.959546 + 1.66198i
\(537\) −1.10538e8 6.38193e7i −0.713822 0.412125i
\(538\) 1.49125e8i 0.957640i
\(539\) 0 0
\(540\) 8.48574e6 0.0538900
\(541\) −2.77877e7 + 4.81297e7i −0.175493 + 0.303963i −0.940332 0.340259i \(-0.889485\pi\)
0.764839 + 0.644222i \(0.222819\pi\)
\(542\) −6.07722e6 + 3.50868e6i −0.0381686 + 0.0220367i
\(543\) 2.53784e7 + 4.39567e7i 0.158513 + 0.274553i
\(544\) −1.58914e8 9.17491e7i −0.987110 0.569908i
\(545\) 5.12900e7i 0.316842i
\(546\) 0 0
\(547\) 5.44170e7 0.332485 0.166243 0.986085i \(-0.446837\pi\)
0.166243 + 0.986085i \(0.446837\pi\)
\(548\) −6.24542e7 + 1.08174e8i −0.379507 + 0.657325i
\(549\) 5.55395e7 3.20657e7i 0.335648 0.193787i
\(550\) −5.31301e7 9.20240e7i −0.319339 0.553112i
\(551\) 1.05308e8 + 6.07993e7i 0.629513 + 0.363449i
\(552\) 8.31335e7i 0.494264i
\(553\) 0 0
\(554\) −3.70327e7 −0.217799
\(555\) −1.18653e7 + 2.05513e7i −0.0694066 + 0.120216i
\(556\) 1.79100e7 1.03404e7i 0.104201 0.0601605i
\(557\) −6.26135e6 1.08450e7i −0.0362329 0.0627571i 0.847340 0.531050i \(-0.178202\pi\)
−0.883573 + 0.468293i \(0.844869\pi\)
\(558\) 2.93230e7 + 1.69296e7i 0.168774 + 0.0974418i
\(559\) 2.06756e8i 1.18365i
\(560\) 0 0
\(561\) −1.65368e8 −0.936616
\(562\) 887085. 1.53648e6i 0.00499754 0.00865599i
\(563\) −1.50742e8 + 8.70310e7i −0.844713 + 0.487695i −0.858864 0.512204i \(-0.828829\pi\)
0.0141502 + 0.999900i \(0.495496\pi\)
\(564\) −3.62858e7 6.28489e7i −0.202255 0.350316i
\(565\) −1.54321e8 8.90971e7i −0.855616 0.493990i
\(566\) 1.76981e7i 0.0976060i
\(567\) 0 0
\(568\) −2.50810e8 −1.36868
\(569\) −2.37803e7 + 4.11886e7i −0.129086 + 0.223584i −0.923323 0.384025i \(-0.874538\pi\)
0.794237 + 0.607609i \(0.207871\pi\)
\(570\) 4.46413e7 2.57737e7i 0.241053 0.139172i
\(571\) −8.27707e7 1.43363e8i −0.444599 0.770068i 0.553425 0.832899i \(-0.313320\pi\)
−0.998024 + 0.0628311i \(0.979987\pi\)
\(572\) −1.40358e8 8.10360e7i −0.749981 0.433002i
\(573\) 1.34193e8i 0.713291i
\(574\) 0 0
\(575\) 1.10306e8 0.580222
\(576\) 2.65466e7 4.59801e7i 0.138913 0.240604i
\(577\) 4.44692e7 2.56743e7i 0.231490 0.133651i −0.379769 0.925081i \(-0.623997\pi\)
0.611259 + 0.791431i \(0.290663\pi\)
\(578\) 3.77210e7 + 6.53346e7i 0.195344 + 0.338345i
\(579\) 2.42846e6 + 1.40207e6i 0.0125111 + 0.00722328i
\(580\) 3.04895e7i 0.156267i
\(581\) 0 0
\(582\) 5.61673e7 0.284914
\(583\) 1.42525e7 2.46861e7i 0.0719259 0.124579i
\(584\) −1.55672e8 + 8.98771e7i −0.781576 + 0.451243i
\(585\) −2.28423e7 3.95640e7i −0.114096 0.197621i
\(586\) 1.28011e7 + 7.39070e6i 0.0636141 + 0.0367276i
\(587\) 2.37624e8i 1.17483i 0.809285 + 0.587416i \(0.199855\pi\)
−0.809285 + 0.587416i \(0.800145\pi\)
\(588\) 0 0
\(589\) −2.25238e8 −1.10229
\(590\) −1.32466e7 + 2.29437e7i −0.0644982 + 0.111714i
\(591\) 3.63600e7 2.09925e7i 0.176141 0.101695i
\(592\) 9.50232e6 + 1.64585e7i 0.0457999 + 0.0793278i
\(593\) 3.20624e8 + 1.85112e8i 1.53756 + 0.887711i 0.998981 + 0.0451361i \(0.0143722\pi\)
0.538579 + 0.842575i \(0.318961\pi\)
\(594\) 3.61305e7i 0.172391i
\(595\) 0 0
\(596\) −1.24549e8 −0.588305
\(597\) −4.70944e7 + 8.15699e7i −0.221333 + 0.383360i
\(598\) −1.33052e8 + 7.68173e7i −0.622180 + 0.359216i
\(599\) 1.87938e7 + 3.25519e7i 0.0874451 + 0.151459i 0.906430 0.422355i \(-0.138796\pi\)
−0.818985 + 0.573814i \(0.805463\pi\)
\(600\) 8.10068e7 + 4.67693e7i 0.375032 + 0.216525i
\(601\) 2.67605e7i 0.123274i 0.998099 + 0.0616369i \(0.0196321\pi\)
−0.998099 + 0.0616369i \(0.980368\pi\)
\(602\) 0 0
\(603\) −1.33326e8 −0.608083
\(604\) −4.26849e7 + 7.39324e7i −0.193715 + 0.335524i
\(605\) −6.99761e7 + 4.04007e7i −0.315998 + 0.182441i
\(606\) −4.39654e7 7.61503e7i −0.197557 0.342179i
\(607\) −6.69071e7 3.86288e7i −0.299162 0.172721i 0.342905 0.939370i \(-0.388589\pi\)
−0.642066 + 0.766649i \(0.721923\pi\)
\(608\) 2.66697e8i 1.18661i
\(609\) 0 0
\(610\) −9.76808e7 −0.430348
\(611\) −1.95352e8 + 3.38359e8i −0.856433 + 1.48338i
\(612\) 4.32748e7 2.49847e7i 0.188791 0.108998i
\(613\) 1.76486e8 + 3.05682e8i 0.766174 + 1.32705i 0.939623 + 0.342210i \(0.111175\pi\)
−0.173449 + 0.984843i \(0.555491\pi\)
\(614\) −9.51394e7 5.49288e7i −0.411013 0.237298i
\(615\) 3.95608e7i 0.170075i
\(616\) 0 0
\(617\) 1.82109e8 0.775310 0.387655 0.921805i \(-0.373285\pi\)
0.387655 + 0.921805i \(0.373285\pi\)
\(618\) 1.80640e7 3.12878e7i 0.0765330 0.132559i
\(619\) −8.43335e7 + 4.86900e7i −0.355573 + 0.205290i −0.667137 0.744935i \(-0.732480\pi\)
0.311564 + 0.950225i \(0.399147\pi\)
\(620\) 2.82379e7 + 4.89094e7i 0.118483 + 0.205219i
\(621\) 3.24811e7 + 1.87530e7i 0.135630 + 0.0783062i
\(622\) 8.71661e7i 0.362223i
\(623\) 0 0
\(624\) −3.65864e7 −0.150579
\(625\) −2.70211e7 + 4.68019e7i −0.110678 + 0.191701i
\(626\) −5.05134e7 + 2.91639e7i −0.205913 + 0.118884i
\(627\) 1.20173e8 + 2.08145e8i 0.487533 + 0.844431i
\(628\) 1.96384e8 + 1.13382e8i 0.792916 + 0.457790i
\(629\) 1.39741e8i 0.561529i
\(630\) 0 0
\(631\) −1.37285e8 −0.546430 −0.273215 0.961953i \(-0.588087\pi\)
−0.273215 + 0.961953i \(0.588087\pi\)
\(632\) −1.10423e8 + 1.91259e8i −0.437431 + 0.757653i
\(633\) −1.86453e8 + 1.07648e8i −0.735118 + 0.424421i
\(634\) 8.93238e7 + 1.54713e8i 0.350509 + 0.607100i
\(635\) −6.47495e7 3.73832e7i −0.252881 0.146001i
\(636\) 8.61341e6i 0.0334814i
\(637\) 0 0
\(638\) −1.29818e8 −0.499887
\(639\) 5.65770e7 9.79943e7i 0.216839 0.375576i
\(640\) 4.07622e7 2.35341e7i 0.155495 0.0897753i
\(641\) 1.04673e8 + 1.81298e8i 0.397428 + 0.688366i 0.993408 0.114633i \(-0.0365693\pi\)
−0.595979 + 0.803000i \(0.703236\pi\)
\(642\) −1.65078e8 9.53078e7i −0.623855 0.360183i
\(643\) 3.49818e8i 1.31586i −0.753079 0.657930i \(-0.771432\pi\)
0.753079 0.657930i \(-0.228568\pi\)
\(644\) 0 0
\(645\) 7.68791e7 0.286503
\(646\) 1.51772e8 2.62877e8i 0.562981 0.975112i
\(647\) −3.20197e8 + 1.84866e8i −1.18224 + 0.682566i −0.956531 0.291630i \(-0.905803\pi\)
−0.225707 + 0.974195i \(0.572469\pi\)
\(648\) 1.59025e7 + 2.75439e7i 0.0584439 + 0.101228i
\(649\) −1.06978e8 6.17637e7i −0.391345 0.225943i
\(650\) 1.72864e8i 0.629454i
\(651\) 0 0
\(652\) 2.76697e8 0.998303
\(653\) 1.97623e7 3.42293e7i 0.0709737 0.122930i −0.828355 0.560204i \(-0.810723\pi\)
0.899328 + 0.437274i \(0.144056\pi\)
\(654\) 5.71480e7 3.29944e7i 0.204300 0.117952i
\(655\) −9.58169e6 1.65960e7i −0.0340971 0.0590580i
\(656\) 2.74376e7 + 1.58411e7i 0.0971929 + 0.0561144i
\(657\) 8.10968e7i 0.285962i
\(658\) 0 0
\(659\) −3.29124e8 −1.15002 −0.575008 0.818148i \(-0.695001\pi\)
−0.575008 + 0.818148i \(0.695001\pi\)
\(660\) 3.01320e7 5.21901e7i 0.104808 0.181533i
\(661\) 1.39292e8 8.04205e7i 0.482306 0.278460i −0.239071 0.971002i \(-0.576843\pi\)
0.721377 + 0.692543i \(0.243509\pi\)
\(662\) −5.53611e7 9.58882e7i −0.190823 0.330515i
\(663\) −2.32978e8 1.34510e8i −0.799419 0.461545i
\(664\) 3.87530e7i 0.132374i
\(665\) 0 0
\(666\) −3.05315e7 −0.103353
\(667\) 6.73800e7 1.16706e8i 0.227067 0.393291i
\(668\) −7.53117e7 + 4.34812e7i −0.252658 + 0.145872i
\(669\) 7.64926e7 + 1.32489e8i 0.255471 + 0.442488i
\(670\) 1.75867e8 + 1.01537e8i 0.584735 + 0.337597i
\(671\) 4.55448e8i 1.50755i
\(672\) 0 0
\(673\) 5.32162e8 1.74582 0.872908 0.487886i \(-0.162232\pi\)
0.872908 + 0.487886i \(0.162232\pi\)
\(674\) 1.01338e7 1.75523e7i 0.0330974 0.0573263i
\(675\) −3.65466e7 + 2.11002e7i −0.118832 + 0.0686080i
\(676\) −5.10955e7 8.84999e7i −0.165403 0.286486i
\(677\) 4.68878e8 + 2.70707e8i 1.51110 + 0.872435i 0.999916 + 0.0129645i \(0.00412684\pi\)
0.511186 + 0.859470i \(0.329206\pi\)
\(678\) 2.29262e8i 0.735601i
\(679\) 0 0
\(680\) −2.21722e8 −0.705151
\(681\) 1.13595e8 1.96753e8i 0.359683 0.622989i
\(682\) 2.08246e8 1.20231e8i 0.656483 0.379021i
\(683\) −1.24469e8 2.15587e8i −0.390662 0.676646i 0.601875 0.798590i \(-0.294420\pi\)
−0.992537 + 0.121944i \(0.961087\pi\)
\(684\) −6.28957e7 3.63129e7i −0.196541 0.113473i
\(685\) 2.50047e8i 0.777946i
\(686\) 0 0
\(687\) −2.29126e8 −0.706651
\(688\) 3.07843e7 5.33199e7i 0.0945286 0.163728i
\(689\) 4.01592e7 2.31860e7i 0.122780 0.0708871i
\(690\) −2.85633e7 4.94731e7i −0.0869484 0.150599i
\(691\) −8.00565e7 4.62206e7i −0.242640 0.140088i 0.373749 0.927530i \(-0.378072\pi\)
−0.616390 + 0.787441i \(0.711405\pi\)
\(692\) 2.74491e8i 0.828341i
\(693\) 0 0
\(694\) 3.56825e7 0.106752
\(695\) 2.06997e7 3.58530e7i 0.0616610 0.106800i
\(696\) 9.89658e7 5.71379e7i 0.293533 0.169472i
\(697\) 1.16480e8 + 2.01749e8i 0.343995 + 0.595816i
\(698\) 1.92196e8 + 1.10964e8i 0.565169 + 0.326300i
\(699\) 8.96640e7i 0.262535i
\(700\) 0 0
\(701\) 5.38435e8 1.56307 0.781537 0.623859i \(-0.214436\pi\)
0.781537 + 0.623859i \(0.214436\pi\)
\(702\) 2.93885e7 5.09024e7i 0.0849505 0.147139i
\(703\) 1.75890e8 1.01550e8i 0.506262 0.292290i
\(704\) −1.88529e8 3.26541e8i −0.540331 0.935880i
\(705\) −1.25813e8 7.26384e7i −0.359054 0.207300i
\(706\) 4.48603e7i 0.127482i
\(707\) 0 0
\(708\) 3.73265e7 0.105176
\(709\) −3.53455e7 + 6.12202e7i −0.0991735 + 0.171773i −0.911343 0.411648i \(-0.864953\pi\)
0.812169 + 0.583422i \(0.198287\pi\)
\(710\) −1.49258e8 + 8.61744e7i −0.417027 + 0.240771i
\(711\) −4.98179e7 8.62872e7i −0.138604 0.240070i
\(712\) −7.62173e7 4.40041e7i −0.211161 0.121914i
\(713\) 2.49616e8i 0.688660i
\(714\) 0 0
\(715\) −3.24442e8 −0.887604
\(716\) 1.36954e8 2.37211e8i 0.373109 0.646243i
\(717\) 2.16226e8 1.24838e8i 0.586610 0.338680i
\(718\) −1.02021e8 1.76705e8i −0.275622 0.477392i
\(719\) 3.38940e8 + 1.95687e8i 0.911876 + 0.526472i 0.881034 0.473053i \(-0.156848\pi\)
0.0308415 + 0.999524i \(0.490181\pi\)
\(720\) 1.36041e7i 0.0364478i
\(721\) 0 0
\(722\) −1.81149e8 −0.481309
\(723\) 2.01252e8 3.48578e8i 0.532506 0.922327i
\(724\) −9.43295e7 + 5.44612e7i −0.248560 + 0.143506i
\(725\) 7.58135e7 + 1.31313e8i 0.198945 + 0.344582i
\(726\) −9.00302e7 5.19789e7i −0.235276 0.135837i
\(727\) 4.83550e8i 1.25846i −0.777221 0.629228i \(-0.783371\pi\)
0.777221 0.629228i \(-0.216629\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −0.0370370
\(730\) −6.17607e7 + 1.06973e8i −0.158761 + 0.274982i
\(731\) 3.92061e8 2.26357e8i 1.00369 0.579484i
\(732\) 6.88118e7 + 1.19186e8i 0.175441 + 0.303872i
\(733\) 2.76711e8 + 1.59759e8i 0.702611 + 0.405653i 0.808319 0.588745i \(-0.200378\pi\)
−0.105708 + 0.994397i \(0.533711\pi\)
\(734\) 1.08968e8i 0.275556i
\(735\) 0 0
\(736\) 2.95563e8 0.741339
\(737\) −4.73427e8 + 8.20000e8i −1.18263 + 2.04838i
\(738\) −4.40792e7 + 2.54491e7i −0.109664 + 0.0633146i
\(739\) −1.76757e8 3.06151e8i −0.437968 0.758582i 0.559565 0.828787i \(-0.310968\pi\)
−0.997533 + 0.0702042i \(0.977635\pi\)
\(740\) −4.41024e7 2.54625e7i −0.108835 0.0628357i
\(741\) 3.90994e8i 0.960983i
\(742\) 0 0
\(743\) 4.63396e8 1.12976 0.564880 0.825173i \(-0.308923\pi\)
0.564880 + 0.825173i \(0.308923\pi\)
\(744\) −1.05837e8 + 1.83315e8i −0.256991 + 0.445121i
\(745\) −2.15924e8 + 1.24664e8i −0.522195 + 0.301489i
\(746\) −2.88318e7 4.99381e7i −0.0694472 0.120286i
\(747\) −1.51412e7 8.74179e6i −0.0363245 0.0209719i
\(748\) 3.54873e8i 0.847945i
\(749\) 0 0
\(750\) 1.54427e8 0.366050
\(751\) 1.48510e7 2.57226e7i 0.0350618 0.0607289i −0.847962 0.530057i \(-0.822171\pi\)
0.883024 + 0.469328i \(0.155504\pi\)
\(752\) −1.00757e8 + 5.81724e7i −0.236932 + 0.136793i
\(753\) −7.41942e7 1.28508e8i −0.173774 0.300985i
\(754\) −1.82894e8 1.05594e8i −0.426662 0.246334i
\(755\) 1.70897e8i 0.397093i
\(756\) 0 0
\(757\) 7.11235e8 1.63955 0.819776 0.572684i \(-0.194098\pi\)
0.819776 + 0.572684i \(0.194098\pi\)
\(758\) 1.45365e8 2.51780e8i 0.333774 0.578113i
\(759\) 2.30674e8 1.33180e8i 0.527563 0.304588i
\(760\) 1.61126e8 + 2.79078e8i 0.367049 + 0.635748i
\(761\) −3.18255e8 1.83745e8i −0.722140 0.416928i 0.0933998 0.995629i \(-0.470227\pi\)
−0.815540 + 0.578701i \(0.803560\pi\)
\(762\) 9.61931e7i 0.217410i
\(763\) 0 0
\(764\) −2.87974e8 −0.645763
\(765\) 5.00154e7 8.66292e7i 0.111717 0.193500i
\(766\) 3.51985e8 2.03218e8i 0.783137 0.452144i
\(767\) −1.00477e8 1.74031e8i −0.222680 0.385693i
\(768\) 2.41220e8 + 1.39268e8i 0.532512 + 0.307446i
\(769\) 3.18891e8i 0.701235i 0.936519 + 0.350617i \(0.114028\pi\)
−0.936519 + 0.350617i \(0.885972\pi\)
\(770\) 0 0
\(771\) −3.48969e8 −0.761419
\(772\) −3.00879e6 + 5.21138e6i −0.00653944 + 0.0113266i
\(773\) −1.35153e8 + 7.80307e7i −0.292609 + 0.168938i −0.639118 0.769109i \(-0.720700\pi\)
0.346509 + 0.938047i \(0.387367\pi\)
\(774\) 4.94557e7 + 8.56598e7i 0.106658 + 0.184737i
\(775\) −2.43231e8 1.40430e8i −0.522533 0.301685i
\(776\) 3.51133e8i 0.751427i
\(777\) 0 0
\(778\) 9.51413e7 0.202037
\(779\) 1.69292e8 2.93222e8i 0.358116 0.620275i
\(780\) 8.49028e7 4.90187e7i 0.178912 0.103295i
\(781\) −4.01798e8 6.95935e8i −0.843442 1.46088i
\(782\) −2.91329e8 1.68199e8i −0.609206 0.351725i
\(783\) 5.15560e7i 0.107397i
\(784\) 0 0
\(785\) 4.53947e8 0.938417
\(786\) 1.23276e7 2.13521e7i 0.0253871 0.0439717i
\(787\) 6.50044e8 3.75303e8i 1.33358 0.769942i 0.347733 0.937594i \(-0.386952\pi\)
0.985846 + 0.167651i \(0.0536183\pi\)
\(788\) 4.50490e7 + 7.80272e7i 0.0920676 + 0.159466i
\(789\) −1.41658e8 8.17862e7i −0.288410 0.166513i
\(790\) 1.51759e8i 0.307803i
\(791\) 0 0
\(792\) 2.25872e8 0.454660
\(793\) 3.70462e8 6.41658e8i 0.742888 1.28672i
\(794\) −2.93497e8 + 1.69451e8i −0.586331 + 0.338518i
\(795\) 8.62134e6 + 1.49326e7i 0.0171583 + 0.0297190i
\(796\) −1.75046e8 1.01063e8i −0.347067 0.200379i
\(797\) 1.08408e6i 0.00214134i −0.999999 0.00107067i \(-0.999659\pi\)
0.999999 0.00107067i \(-0.000340806\pi\)
\(798\) 0 0
\(799\) −8.55483e8 −1.67715
\(800\) −1.66278e8 + 2.88002e8i −0.324762 + 0.562505i
\(801\) 3.43857e7 1.98526e7i 0.0669084 0.0386296i
\(802\) 1.27527e8 + 2.20884e8i 0.247218 + 0.428194i
\(803\) −4.98772e8 2.87966e8i −0.963287 0.556154i
\(804\) 2.86113e8i 0.550515i
\(805\) 0 0
\(806\) 3.91183e8 0.747093
\(807\) −2.10297e8 + 3.64245e8i −0.400140 + 0.693063i
\(808\) 4.76058e8 2.74852e8i 0.902456 0.521033i
\(809\) −2.23887e8 3.87784e8i −0.422847 0.732392i 0.573370 0.819297i \(-0.305636\pi\)
−0.996217 + 0.0869044i \(0.972303\pi\)
\(810\) 1.89273e7 + 1.09277e7i 0.0356150 + 0.0205623i
\(811\) 7.02416e8i 1.31684i 0.752652 + 0.658418i \(0.228774\pi\)
−0.752652 + 0.658418i \(0.771226\pi\)
\(812\) 0 0
\(813\) 1.97919e7 0.0368312
\(814\) −1.08414e8 + 1.87779e8i −0.201008 + 0.348155i
\(815\) 4.79695e8 2.76952e8i 0.886120 0.511601i
\(816\) −4.00548e7 6.93769e7i −0.0737197 0.127686i
\(817\) −5.69823e8 3.28987e8i −1.04490 0.603272i
\(818\) 3.35448e8i 0.612866i
\(819\) 0 0
\(820\) −8.48960e7 −0.153973
\(821\) −3.31937e8 + 5.74932e8i −0.599828 + 1.03893i 0.393018 + 0.919531i \(0.371431\pi\)
−0.992846 + 0.119402i \(0.961902\pi\)
\(822\) −2.78605e8 + 1.60853e8i −0.501619 + 0.289610i
\(823\) −2.08427e8 3.61007e8i −0.373900 0.647614i 0.616262 0.787541i \(-0.288646\pi\)
−0.990162 + 0.139928i \(0.955313\pi\)
\(824\) 1.95598e8 + 1.12928e8i 0.349609 + 0.201847i
\(825\) 2.99698e8i 0.533731i
\(826\) 0 0
\(827\) 1.14598e8 0.202609 0.101305 0.994855i \(-0.467698\pi\)
0.101305 + 0.994855i \(0.467698\pi\)
\(828\) −4.02432e7 + 6.97033e7i −0.0708928 + 0.122790i
\(829\) −4.05381e8 + 2.34047e8i −0.711541 + 0.410808i −0.811631 0.584170i \(-0.801420\pi\)
0.100090 + 0.994978i \(0.468087\pi\)
\(830\) 1.33149e7 + 2.30621e7i 0.0232865 + 0.0403334i
\(831\) 9.04544e7 + 5.22239e7i 0.157626 + 0.0910052i
\(832\) 6.13397e8i 1.06505i
\(833\) 0 0
\(834\) 5.32639e7 0.0918195
\(835\) −8.70425e7 + 1.50762e8i −0.149511 + 0.258960i
\(836\) −4.46672e8 + 2.57886e8i −0.764487 + 0.441377i
\(837\) −4.77487e7 8.27031e7i −0.0814301 0.141041i
\(838\) 5.61797e8 + 3.24354e8i 0.954657 + 0.551172i
\(839\) 6.49855e8i 1.10035i −0.835050 0.550174i \(-0.814561\pi\)
0.835050 0.550174i \(-0.185439\pi\)
\(840\) 0 0
\(841\) −4.09581e8 −0.688576
\(842\) 3.55136e7 6.15114e7i 0.0594920 0.103043i
\(843\) −4.33350e6 + 2.50195e6i −0.00723363 + 0.00417634i
\(844\) −2.31010e8 4.00120e8i −0.384240 0.665523i
\(845\) −1.77163e8 1.02285e8i −0.293631 0.169528i
\(846\) 1.86911e8i 0.308691i
\(847\) 0 0
\(848\) 1.38088e7 0.0226447
\(849\) −2.49580e7 + 4.32285e7i −0.0407837 + 0.0706394i
\(850\) 3.27793e8 1.89251e8i 0.533756 0.308164i
\(851\) −1.12542e8 1.94928e8i −0.182610 0.316290i
\(852\) 2.10292e8 + 1.21412e8i 0.340020 + 0.196310i
\(853\) 7.47082e7i 0.120371i 0.998187 + 0.0601854i \(0.0191692\pi\)
−0.998187 + 0.0601854i \(0.980831\pi\)
\(854\) 0 0
\(855\) −1.45385e8 −0.232606
\(856\) 5.95823e8 1.03200e9i 0.949939 1.64534i
\(857\) 7.50588e8 4.33352e8i 1.19250 0.688491i 0.233629 0.972326i \(-0.424940\pi\)
0.958873 + 0.283835i \(0.0916066\pi\)
\(858\) −2.08711e8 3.61498e8i −0.330433 0.572327i
\(859\) 1.51273e7 + 8.73376e6i 0.0238662 + 0.0137791i 0.511886 0.859054i \(-0.328947\pi\)
−0.488019 + 0.872833i \(0.662280\pi\)
\(860\) 1.64980e8i 0.259379i
\(861\) 0 0
\(862\) −6.29285e8 −0.982484
\(863\) 5.59542e8 9.69155e8i 0.870563 1.50786i 0.00914866 0.999958i \(-0.497088\pi\)
0.861415 0.507902i \(-0.169579\pi\)
\(864\) −9.79262e7 + 5.65377e7i −0.151830 + 0.0876591i
\(865\) 2.74743e8 + 4.75869e8i 0.424501 + 0.735257i
\(866\) 1.32161e8 + 7.63035e7i 0.203494 + 0.117487i
\(867\) 2.12778e8i 0.326489i
\(868\) 0 0
\(869\) −7.07593e8 −1.07826
\(870\) 3.92634e7 6.80061e7i 0.0596252 0.103274i
\(871\) −1.33397e9 + 7.70171e8i −2.01880 + 1.16555i
\(872\) 2.06267e8 + 3.57264e8i 0.311085 + 0.538816i
\(873\) −1.37192e8 7.92076e7i −0.206198 0.119049i
\(874\) 4.88922e8i 0.732328i
\(875\) 0 0
\(876\) 1.74031e8 0.258889
\(877\) −5.82730e8 + 1.00932e9i −0.863910 + 1.49634i 0.00421521 + 0.999991i \(0.498658\pi\)
−0.868125 + 0.496345i \(0.834675\pi\)
\(878\) 3.44029e8 1.98625e8i 0.508290 0.293462i
\(879\) −2.08449e7 3.61044e7i −0.0306925 0.0531610i
\(880\) −8.36696e7 4.83067e7i −0.122778 0.0708858i
\(881\) 2.07806e8i 0.303900i −0.988388 0.151950i \(-0.951445\pi\)
0.988388 0.151950i \(-0.0485553\pi\)
\(882\) 0 0
\(883\) −3.48816e8 −0.506657 −0.253329 0.967380i \(-0.581525\pi\)
−0.253329 + 0.967380i \(0.581525\pi\)
\(884\) 2.88653e8 4.99962e8i 0.417849 0.723736i
\(885\) 6.47109e7 3.73609e7i 0.0933572 0.0538998i
\(886\) 2.62613e8 + 4.54859e8i 0.377585 + 0.653996i
\(887\) 7.31382e8 + 4.22263e8i 1.04803 + 0.605080i 0.922097 0.386959i \(-0.126475\pi\)
0.125932 + 0.992039i \(0.459808\pi\)
\(888\) 1.90869e8i 0.272582i
\(889\) 0 0
\(890\) −6.04764e7 −0.0857858
\(891\) −5.09515e7 + 8.82506e7i −0.0720317 + 0.124763i
\(892\) −2.84317e8 + 1.64150e8i −0.400597 + 0.231285i
\(893\) 6.21681e8 + 1.07678e9i 0.872998 + 1.51208i
\(894\) −2.77804e8 1.60390e8i −0.388800 0.224474i
\(895\) 5.48320e8i 0.764830i
\(896\) 0 0
\(897\) 4.33314e8 0.600379
\(898\) −3.18910e8 + 5.52368e8i −0.440391 + 0.762780i
\(899\) −2.97155e8 + 1.71562e8i −0.408981 + 0.236125i
\(900\) −4.52802e7 7.84276e7i −0.0621127 0.107582i
\(901\) 8.79326e7 + 5.07679e7i 0.120220 + 0.0694089i
\(902\) 3.61469e8i 0.492552i
\(903\) 0 0
\(904\) 1.43324e9 1.94006
\(905\) −1.09023e8 + 1.88833e8i −0.147086 + 0.254760i
\(906\) −1.90415e8 + 1.09936e8i −0.256046 + 0.147828i
\(907\) 3.99924e8 + 6.92689e8i 0.535989 + 0.928360i 0.999115 + 0.0420677i \(0.0133945\pi\)
−0.463126 + 0.886293i \(0.653272\pi\)
\(908\) 4.22225e8 + 2.43771e8i 0.564009 + 0.325631i
\(909\) 2.48001e8i 0.330189i
\(910\) 0 0
\(911\) 1.54047e8 0.203750 0.101875 0.994797i \(-0.467516\pi\)
0.101875 + 0.994797i \(0.467516\pi\)
\(912\) −5.82157e7 + 1.00833e8i −0.0767460 + 0.132928i
\(913\) −1.07530e8 + 6.20824e7i −0.141292 + 0.0815749i
\(914\) −2.53559e7 4.39176e7i −0.0332078 0.0575175i
\(915\) 2.38591e8 + 1.37750e8i 0.311451 + 0.179816i
\(916\) 4.91697e8i 0.639751i
\(917\) 0 0
\(918\) 1.28698e8 0.166358
\(919\) −3.43544e8 + 5.95036e8i −0.442625 + 0.766649i −0.997883 0.0650288i \(-0.979286\pi\)
0.555258 + 0.831678i \(0.312619\pi\)
\(920\) 3.09285e8 1.78566e8i 0.397187 0.229316i
\(921\) 1.54922e8 + 2.68333e8i 0.198305 + 0.343475i
\(922\) 2.77309e8 + 1.60105e8i 0.353811 + 0.204273i
\(923\) 1.30729e9i 1.66252i
\(924\) 0 0
\(925\) 2.53255e8 0.319987
\(926\) −1.80120e8 + 3.11977e8i −0.226845 + 0.392906i
\(927\) −8.82447e7 + 5.09481e7i −0.110777 + 0.0639571i
\(928\) 2.03142e8 + 3.51852e8i 0.254188 + 0.440266i
\(929\) −3.27395e8 1.89021e8i −0.408342 0.235757i 0.281735 0.959492i \(-0.409090\pi\)
−0.690077 + 0.723736i \(0.742423\pi\)
\(930\) 1.45455e8i 0.180834i
\(931\) 0 0
\(932\) −1.92416e8 −0.237680
\(933\) 1.22922e8 2.12908e8i 0.151351 0.262148i
\(934\) −8.11084e8 + 4.68280e8i −0.995463 + 0.574731i
\(935\) −3.55199e8 6.15223e8i −0.434547 0.752658i
\(936\) 3.18219e8 + 1.83724e8i 0.388060 + 0.224047i
\(937\) 1.27190e9i 1.54609i 0.634351 + 0.773045i \(0.281268\pi\)
−0.634351 + 0.773045i \(0.718732\pi\)
\(938\) 0 0
\(939\) 1.64509e8 0.198698
\(940\) 1.55879e8 2.69991e8i 0.187674 0.325062i
\(941\) 6.05181e8 3.49402e8i 0.726301 0.419330i −0.0907665 0.995872i \(-0.528932\pi\)
0.817067 + 0.576542i \(0.195598\pi\)
\(942\) 2.92020e8 + 5.05794e8i 0.349349 + 0.605091i
\(943\) −3.24960e8 1.87615e8i −0.387520 0.223735i
\(944\) 5.98408e7i 0.0711346i
\(945\) 0 0
\(946\) 7.02448e8 0.829738
\(947\) 1.95719e8 3.38995e8i 0.230453 0.399157i −0.727488 0.686120i \(-0.759312\pi\)
0.957942 + 0.286963i \(0.0926458\pi\)
\(948\) 1.85169e8 1.06907e8i 0.217342 0.125482i
\(949\) −4.68464e8 8.11403e8i −0.548122 0.949375i
\(950\) −4.76415e8 2.75058e8i −0.555667 0.320815i
\(951\) 5.03861e8i 0.585827i
\(952\) 0 0
\(953\) −9.05418e8 −1.04609 −0.523047 0.852304i \(-0.675205\pi\)
−0.523047 + 0.852304i \(0.675205\pi\)
\(954\) −1.10921e7 + 1.92120e7i −0.0127752 + 0.0221273i
\(955\) −4.99244e8 + 2.88239e8i −0.573196 + 0.330935i
\(956\) 2.67897e8 + 4.64012e8i 0.306616 + 0.531075i
\(957\) 3.17087e8 + 1.83070e8i 0.361778 + 0.208873i
\(958\) 5.05897e8i 0.575394i
\(959\) 0 0
\(960\) 2.28082e8 0.257797
\(961\) −1.25967e8 + 2.18180e8i −0.141934 + 0.245836i
\(962\) −3.05478e8 + 1.76368e8i −0.343127 + 0.198104i
\(963\) 2.68808e8 + 4.65589e8i 0.300998 + 0.521343i
\(964\) 7.48035e8 + 4.31878e8i 0.835008 + 0.482092i
\(965\) 1.20463e7i 0.0134051i
\(966\) 0 0
\(967\) −1.33523e9 −1.47665 −0.738323 0.674448i \(-0.764382\pi\)
−0.738323 + 0.674448i \(0.764382\pi\)
\(968\) 3.24950e8 5.62829e8i 0.358253 0.620513i
\(969\) −7.41422e8 + 4.28060e8i −0.814881 + 0.470472i
\(970\) 1.20644e8 + 2.08961e8i 0.132187 + 0.228955i
\(971\) 5.45806e8 + 3.15121e8i 0.596184 + 0.344207i 0.767539 0.641002i \(-0.221481\pi\)
−0.171355 + 0.985209i \(0.554814\pi\)
\(972\) 3.07922e7i 0.0335307i
\(973\) 0 0
\(974\) −7.25362e8 −0.785015
\(975\) −2.43774e8 + 4.22229e8i −0.263011 + 0.455549i
\(976\) 1.91075e8 1.10317e8i 0.205520 0.118657i
\(977\) 2.04552e8 + 3.54294e8i 0.219341 + 0.379910i 0.954607 0.297869i \(-0.0962760\pi\)
−0.735266 + 0.677779i \(0.762943\pi\)
\(978\) 6.17168e8 + 3.56322e8i 0.659761 + 0.380913i
\(979\) 2.81978e8i 0.300516i
\(980\) 0 0
\(981\) −1.86116e8 −0.197141
\(982\) 2.43679e8 4.22064e8i 0.257326 0.445701i
\(983\) −7.95291e8 + 4.59161e8i −0.837270 + 0.483398i −0.856335 0.516420i \(-0.827264\pi\)
0.0190654 + 0.999818i \(0.493931\pi\)
\(984\) −1.59097e8 2.75564e8i −0.166985 0.289226i
\(985\) 1.56198e8 + 9.01810e7i 0.163443 + 0.0943640i
\(986\) 4.62415e8i 0.482394i
\(987\) 0 0
\(988\) −8.39059e8 −0.870005
\(989\) −3.64596e8 + 6.31499e8i −0.376897 + 0.652805i
\(990\) 1.34417e8 7.76060e7i 0.138532 0.0799815i
\(991\) 2.59369e8 + 4.49241e8i 0.266500 + 0.461592i 0.967956 0.251122i \(-0.0807994\pi\)
−0.701455 + 0.712713i \(0.747466\pi\)
\(992\) −6.51736e8 3.76280e8i −0.667631 0.385457i
\(993\) 3.12283e8i 0.318934i
\(994\) 0 0
\(995\) −4.04623e8 −0.410754
\(996\) 1.87596e7 3.24925e7i 0.0189865 0.0328856i
\(997\) −3.12596e8 + 1.80477e8i −0.315426 + 0.182111i −0.649352 0.760488i \(-0.724960\pi\)
0.333926 + 0.942599i \(0.391626\pi\)
\(998\) 6.31379e8 + 1.09358e9i 0.635183 + 1.10017i
\(999\) 7.45747e7 + 4.30557e7i 0.0747989 + 0.0431852i
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 147.7.f.d.19.2 8
7.2 even 3 147.7.d.b.97.6 8
7.3 odd 6 inner 147.7.f.d.31.2 8
7.4 even 3 21.7.f.a.10.2 8
7.5 odd 6 147.7.d.b.97.5 8
7.6 odd 2 21.7.f.a.19.2 yes 8
21.2 odd 6 441.7.d.c.244.4 8
21.5 even 6 441.7.d.c.244.3 8
21.11 odd 6 63.7.m.d.10.3 8
21.20 even 2 63.7.m.d.19.3 8
28.11 odd 6 336.7.bh.d.241.2 8
28.27 even 2 336.7.bh.d.145.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.7.f.a.10.2 8 7.4 even 3
21.7.f.a.19.2 yes 8 7.6 odd 2
63.7.m.d.10.3 8 21.11 odd 6
63.7.m.d.19.3 8 21.20 even 2
147.7.d.b.97.5 8 7.5 odd 6
147.7.d.b.97.6 8 7.2 even 3
147.7.f.d.19.2 8 1.1 even 1 trivial
147.7.f.d.31.2 8 7.3 odd 6 inner
336.7.bh.d.145.2 8 28.27 even 2
336.7.bh.d.241.2 8 28.11 odd 6
441.7.d.c.244.3 8 21.5 even 6
441.7.d.c.244.4 8 21.2 odd 6