Properties

Label 78.3.c.a.53.1
Level $78$
Weight $3$
Character 78.53
Analytic conductor $2.125$
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] = [78,3,Mod(53,78)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(78, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("78.53");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 78.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: \(2.12534606201\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.16845963264.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 6x^{6} + 15x^{4} + 8x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 53.1
Root \(-0.444099 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 78.53
Dual form 78.3.c.a.53.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-2.93352 + 0.628052i) q^{3} -2.00000 q^{4} +6.81894i q^{5} +(0.888199 + 4.14863i) q^{6} -9.58440 q^{7} +2.82843i q^{8} +(8.21110 - 3.68481i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-2.93352 + 0.628052i) q^{3} -2.00000 q^{4} +6.81894i q^{5} +(0.888199 + 4.14863i) q^{6} -9.58440 q^{7} +2.82843i q^{8} +(8.21110 - 3.68481i) q^{9} +9.64344 q^{10} +15.6028i q^{11} +(5.86704 - 1.25610i) q^{12} -3.60555 q^{13} +13.5544i q^{14} +(-4.28265 - 20.0035i) q^{15} +4.00000 q^{16} -15.6099i q^{17} +(-5.21110 - 11.6123i) q^{18} -24.1247 q^{19} -13.6379i q^{20} +(28.1160 - 6.01949i) q^{21} +22.0656 q^{22} -8.09698i q^{23} +(-1.77640 - 8.29725i) q^{24} -21.4980 q^{25} +5.09902i q^{26} +(-21.7732 + 15.9665i) q^{27} +19.1688 q^{28} +33.5148i q^{29} +(-28.2892 + 6.05658i) q^{30} +31.1754 q^{31} -5.65685i q^{32} +(-9.79934 - 45.7711i) q^{33} -22.0758 q^{34} -65.3555i q^{35} +(-16.4222 + 7.36961i) q^{36} +40.8558 q^{37} +34.1175i q^{38} +(10.5770 - 2.26447i) q^{39} -19.2869 q^{40} +60.5466i q^{41} +(-8.51285 - 39.7621i) q^{42} +18.6249 q^{43} -31.2055i q^{44} +(25.1265 + 55.9910i) q^{45} -11.4509 q^{46} +6.55340i q^{47} +(-11.7341 + 2.51221i) q^{48} +42.8607 q^{49} +30.4027i q^{50} +(9.80384 + 45.7921i) q^{51} +7.21110 q^{52} +39.5256i q^{53} +(22.5800 + 30.7920i) q^{54} -106.394 q^{55} -27.1088i q^{56} +(70.7703 - 15.1516i) q^{57} +47.3971 q^{58} -48.4157i q^{59} +(8.56530 + 40.0070i) q^{60} -33.4519 q^{61} -44.0887i q^{62} +(-78.6985 + 35.3166i) q^{63} -8.00000 q^{64} -24.5860i q^{65} +(-64.7301 + 13.8584i) q^{66} +0.352240 q^{67} +31.2199i q^{68} +(5.08532 + 23.7527i) q^{69} -92.4266 q^{70} +99.3891i q^{71} +(10.4222 + 23.2245i) q^{72} -94.9501 q^{73} -57.7789i q^{74} +(63.0648 - 13.5018i) q^{75} +48.2494 q^{76} -149.543i q^{77} +(-3.20245 - 14.9581i) q^{78} +51.4866 q^{79} +27.2758i q^{80} +(53.8444 - 60.5126i) q^{81} +85.6258 q^{82} +87.9015i q^{83} +(-56.2321 + 12.0390i) q^{84} +106.443 q^{85} -26.3396i q^{86} +(-21.0490 - 98.3165i) q^{87} -44.1313 q^{88} -108.309i q^{89} +(79.1833 - 35.5342i) q^{90} +34.5570 q^{91} +16.1940i q^{92} +(-91.4537 + 19.5798i) q^{93} +9.26791 q^{94} -164.505i q^{95} +(3.55280 + 16.5945i) q^{96} -82.7350 q^{97} -60.6141i q^{98} +(57.4932 + 128.116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 16 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 16 q^{4} - 8 q^{7} + 8 q^{9} + 16 q^{10} - 56 q^{15} + 32 q^{16} + 16 q^{18} - 24 q^{19} + 88 q^{21} + 8 q^{25} + 16 q^{28} - 64 q^{30} - 72 q^{31} - 56 q^{33} - 112 q^{34} - 16 q^{36} + 96 q^{37} - 32 q^{40} + 80 q^{42} + 208 q^{43} - 16 q^{45} + 32 q^{46} - 24 q^{49} + 112 q^{51} - 176 q^{55} + 40 q^{57} + 176 q^{58} + 112 q^{60} - 272 q^{61} - 216 q^{63} - 64 q^{64} - 64 q^{66} + 264 q^{67} - 240 q^{69} - 32 q^{70} - 32 q^{72} - 416 q^{73} + 128 q^{75} + 48 q^{76} + 160 q^{79} + 200 q^{81} + 176 q^{82} - 176 q^{84} + 464 q^{85} + 384 q^{87} + 16 q^{90} + 104 q^{91} - 264 q^{93} - 384 q^{94} - 16 q^{97} + 416 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −2.93352 + 0.628052i −0.977841 + 0.209351i
\(4\) −2.00000 −0.500000
\(5\) 6.81894i 1.36379i 0.731451 + 0.681894i \(0.238844\pi\)
−0.731451 + 0.681894i \(0.761156\pi\)
\(6\) 0.888199 + 4.14863i 0.148033 + 0.691438i
\(7\) −9.58440 −1.36920 −0.684600 0.728919i \(-0.740023\pi\)
−0.684600 + 0.728919i \(0.740023\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 8.21110 3.68481i 0.912345 0.409423i
\(10\) 9.64344 0.964344
\(11\) 15.6028i 1.41843i 0.704990 + 0.709217i \(0.250951\pi\)
−0.704990 + 0.709217i \(0.749049\pi\)
\(12\) 5.86704 1.25610i 0.488920 0.104675i
\(13\) −3.60555 −0.277350
\(14\) 13.5544i 0.968170i
\(15\) −4.28265 20.0035i −0.285510 1.33357i
\(16\) 4.00000 0.250000
\(17\) 15.6099i 0.918231i −0.888376 0.459116i \(-0.848166\pi\)
0.888376 0.459116i \(-0.151834\pi\)
\(18\) −5.21110 11.6123i −0.289506 0.645125i
\(19\) −24.1247 −1.26972 −0.634860 0.772627i \(-0.718942\pi\)
−0.634860 + 0.772627i \(0.718942\pi\)
\(20\) 13.6379i 0.681894i
\(21\) 28.1160 6.01949i 1.33886 0.286643i
\(22\) 22.0656 1.00298
\(23\) 8.09698i 0.352043i −0.984386 0.176021i \(-0.943677\pi\)
0.984386 0.176021i \(-0.0563228\pi\)
\(24\) −1.77640 8.29725i −0.0740166 0.345719i
\(25\) −21.4980 −0.859919
\(26\) 5.09902i 0.196116i
\(27\) −21.7732 + 15.9665i −0.806415 + 0.591350i
\(28\) 19.1688 0.684600
\(29\) 33.5148i 1.15568i 0.816149 + 0.577842i \(0.196105\pi\)
−0.816149 + 0.577842i \(0.803895\pi\)
\(30\) −28.2892 + 6.05658i −0.942975 + 0.201886i
\(31\) 31.1754 1.00566 0.502829 0.864386i \(-0.332293\pi\)
0.502829 + 0.864386i \(0.332293\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −9.79934 45.7711i −0.296950 1.38700i
\(34\) −22.0758 −0.649288
\(35\) 65.3555i 1.86730i
\(36\) −16.4222 + 7.36961i −0.456172 + 0.204711i
\(37\) 40.8558 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(38\) 34.1175i 0.897828i
\(39\) 10.5770 2.26447i 0.271204 0.0580634i
\(40\) −19.2869 −0.482172
\(41\) 60.5466i 1.47675i 0.674393 + 0.738373i \(0.264405\pi\)
−0.674393 + 0.738373i \(0.735595\pi\)
\(42\) −8.51285 39.7621i −0.202687 0.946716i
\(43\) 18.6249 0.433138 0.216569 0.976267i \(-0.430513\pi\)
0.216569 + 0.976267i \(0.430513\pi\)
\(44\) 31.2055i 0.709217i
\(45\) 25.1265 + 55.9910i 0.558366 + 1.24425i
\(46\) −11.4509 −0.248932
\(47\) 6.55340i 0.139434i 0.997567 + 0.0697170i \(0.0222096\pi\)
−0.997567 + 0.0697170i \(0.977790\pi\)
\(48\) −11.7341 + 2.51221i −0.244460 + 0.0523376i
\(49\) 42.8607 0.874707
\(50\) 30.4027i 0.608055i
\(51\) 9.80384 + 45.7921i 0.192232 + 0.897884i
\(52\) 7.21110 0.138675
\(53\) 39.5256i 0.745767i 0.927878 + 0.372883i \(0.121631\pi\)
−0.927878 + 0.372883i \(0.878369\pi\)
\(54\) 22.5800 + 30.7920i 0.418148 + 0.570221i
\(55\) −106.394 −1.93444
\(56\) 27.1088i 0.484085i
\(57\) 70.7703 15.1516i 1.24158 0.265817i
\(58\) 47.3971 0.817192
\(59\) 48.4157i 0.820606i −0.911949 0.410303i \(-0.865423\pi\)
0.911949 0.410303i \(-0.134577\pi\)
\(60\) 8.56530 + 40.0070i 0.142755 + 0.666784i
\(61\) −33.4519 −0.548391 −0.274196 0.961674i \(-0.588412\pi\)
−0.274196 + 0.961674i \(0.588412\pi\)
\(62\) 44.0887i 0.711107i
\(63\) −78.6985 + 35.3166i −1.24918 + 0.560582i
\(64\) −8.00000 −0.125000
\(65\) 24.5860i 0.378247i
\(66\) −64.7301 + 13.8584i −0.980758 + 0.209975i
\(67\) 0.352240 0.00525732 0.00262866 0.999997i \(-0.499163\pi\)
0.00262866 + 0.999997i \(0.499163\pi\)
\(68\) 31.2199i 0.459116i
\(69\) 5.08532 + 23.7527i 0.0737003 + 0.344242i
\(70\) −92.4266 −1.32038
\(71\) 99.3891i 1.39985i 0.714218 + 0.699923i \(0.246782\pi\)
−0.714218 + 0.699923i \(0.753218\pi\)
\(72\) 10.4222 + 23.2245i 0.144753 + 0.322563i
\(73\) −94.9501 −1.30069 −0.650343 0.759641i \(-0.725375\pi\)
−0.650343 + 0.759641i \(0.725375\pi\)
\(74\) 57.7789i 0.780796i
\(75\) 63.0648 13.5018i 0.840864 0.180025i
\(76\) 48.2494 0.634860
\(77\) 149.543i 1.94212i
\(78\) −3.20245 14.9581i −0.0410570 0.191770i
\(79\) 51.4866 0.651729 0.325865 0.945416i \(-0.394345\pi\)
0.325865 + 0.945416i \(0.394345\pi\)
\(80\) 27.2758i 0.340947i
\(81\) 53.8444 60.5126i 0.664746 0.747070i
\(82\) 85.6258 1.04422
\(83\) 87.9015i 1.05905i 0.848293 + 0.529527i \(0.177631\pi\)
−0.848293 + 0.529527i \(0.822369\pi\)
\(84\) −56.2321 + 12.0390i −0.669429 + 0.143321i
\(85\) 106.443 1.25227
\(86\) 26.3396i 0.306275i
\(87\) −21.0490 98.3165i −0.241943 1.13007i
\(88\) −44.1313 −0.501492
\(89\) 108.309i 1.21696i −0.793569 0.608480i \(-0.791780\pi\)
0.793569 0.608480i \(-0.208220\pi\)
\(90\) 79.1833 35.5342i 0.879814 0.394825i
\(91\) 34.5570 0.379748
\(92\) 16.1940i 0.176021i
\(93\) −91.4537 + 19.5798i −0.983373 + 0.210535i
\(94\) 9.26791 0.0985948
\(95\) 164.505i 1.73163i
\(96\) 3.55280 + 16.5945i 0.0370083 + 0.172859i
\(97\) −82.7350 −0.852938 −0.426469 0.904502i \(-0.640243\pi\)
−0.426469 + 0.904502i \(0.640243\pi\)
\(98\) 60.6141i 0.618511i
\(99\) 57.4932 + 128.116i 0.580739 + 1.29410i
\(100\) 42.9960 0.429960
\(101\) 43.6823i 0.432498i −0.976338 0.216249i \(-0.930618\pi\)
0.976338 0.216249i \(-0.0693822\pi\)
\(102\) 64.7598 13.8647i 0.634900 0.135929i
\(103\) −79.9691 −0.776399 −0.388200 0.921575i \(-0.626903\pi\)
−0.388200 + 0.921575i \(0.626903\pi\)
\(104\) 10.1980i 0.0980581i
\(105\) 41.0466 + 191.722i 0.390920 + 1.82592i
\(106\) 55.8977 0.527337
\(107\) 123.680i 1.15588i −0.816078 0.577942i \(-0.803856\pi\)
0.816078 0.577942i \(-0.196144\pi\)
\(108\) 43.5464 31.9329i 0.403207 0.295675i
\(109\) 42.8003 0.392664 0.196332 0.980538i \(-0.437097\pi\)
0.196332 + 0.980538i \(0.437097\pi\)
\(110\) 150.464i 1.36786i
\(111\) −119.852 + 25.6596i −1.07974 + 0.231167i
\(112\) −38.3376 −0.342300
\(113\) 84.5000i 0.747787i 0.927472 + 0.373894i \(0.121977\pi\)
−0.927472 + 0.373894i \(0.878023\pi\)
\(114\) −21.4275 100.084i −0.187961 0.877933i
\(115\) 55.2129 0.480112
\(116\) 67.0297i 0.577842i
\(117\) −29.6056 + 13.2858i −0.253039 + 0.113553i
\(118\) −68.4702 −0.580256
\(119\) 149.612i 1.25724i
\(120\) 56.5785 12.1132i 0.471487 0.100943i
\(121\) −122.446 −1.01195
\(122\) 47.3081i 0.387771i
\(123\) −38.0264 177.615i −0.309157 1.44402i
\(124\) −62.3508 −0.502829
\(125\) 23.8800i 0.191040i
\(126\) 49.9453 + 111.296i 0.396391 + 0.883305i
\(127\) −13.2028 −0.103959 −0.0519794 0.998648i \(-0.516553\pi\)
−0.0519794 + 0.998648i \(0.516553\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −54.6366 + 11.6974i −0.423540 + 0.0906776i
\(130\) −34.7699 −0.267461
\(131\) 164.929i 1.25900i 0.777000 + 0.629501i \(0.216740\pi\)
−0.777000 + 0.629501i \(0.783260\pi\)
\(132\) 19.5987 + 91.5421i 0.148475 + 0.693501i
\(133\) 231.221 1.73850
\(134\) 0.498143i 0.00371749i
\(135\) −108.874 148.470i −0.806477 1.09978i
\(136\) 44.1516 0.324644
\(137\) 48.3810i 0.353146i −0.984288 0.176573i \(-0.943499\pi\)
0.984288 0.176573i \(-0.0565011\pi\)
\(138\) 33.5914 7.19173i 0.243416 0.0521140i
\(139\) −40.5641 −0.291828 −0.145914 0.989297i \(-0.546612\pi\)
−0.145914 + 0.989297i \(0.546612\pi\)
\(140\) 130.711i 0.933649i
\(141\) −4.11587 19.2246i −0.0291906 0.136344i
\(142\) 140.557 0.989841
\(143\) 56.2566i 0.393403i
\(144\) 32.8444 14.7392i 0.228086 0.102356i
\(145\) −228.536 −1.57611
\(146\) 134.280i 0.919724i
\(147\) −125.733 + 26.9187i −0.855324 + 0.183120i
\(148\) −81.7117 −0.552106
\(149\) 193.107i 1.29602i 0.761630 + 0.648012i \(0.224399\pi\)
−0.761630 + 0.648012i \(0.775601\pi\)
\(150\) −19.0945 89.1871i −0.127297 0.594581i
\(151\) 155.839 1.03205 0.516023 0.856575i \(-0.327412\pi\)
0.516023 + 0.856575i \(0.327412\pi\)
\(152\) 68.2349i 0.448914i
\(153\) −57.5196 128.175i −0.375945 0.837744i
\(154\) −211.486 −1.37329
\(155\) 212.583i 1.37150i
\(156\) −21.1539 + 4.52894i −0.135602 + 0.0290317i
\(157\) 64.8982 0.413365 0.206682 0.978408i \(-0.433733\pi\)
0.206682 + 0.978408i \(0.433733\pi\)
\(158\) 72.8131i 0.460842i
\(159\) −24.8241 115.949i −0.156127 0.729241i
\(160\) 38.5738 0.241086
\(161\) 77.6047i 0.482017i
\(162\) −85.5778 76.1475i −0.528258 0.470046i
\(163\) 295.523 1.81303 0.906513 0.422177i \(-0.138734\pi\)
0.906513 + 0.422177i \(0.138734\pi\)
\(164\) 121.093i 0.738373i
\(165\) 312.110 66.8212i 1.89158 0.404977i
\(166\) 124.311 0.748864
\(167\) 86.5149i 0.518053i 0.965870 + 0.259027i \(0.0834017\pi\)
−0.965870 + 0.259027i \(0.916598\pi\)
\(168\) 17.0257 + 79.5242i 0.101343 + 0.473358i
\(169\) 13.0000 0.0769231
\(170\) 150.533i 0.885491i
\(171\) −198.090 + 88.8948i −1.15842 + 0.519853i
\(172\) −37.2498 −0.216569
\(173\) 79.8623i 0.461632i 0.972997 + 0.230816i \(0.0741395\pi\)
−0.972997 + 0.230816i \(0.925861\pi\)
\(174\) −139.041 + 29.7678i −0.799083 + 0.171080i
\(175\) 206.045 1.17740
\(176\) 62.4111i 0.354608i
\(177\) 30.4076 + 142.029i 0.171794 + 0.802421i
\(178\) −153.173 −0.860520
\(179\) 200.837i 1.12199i −0.827818 0.560996i \(-0.810418\pi\)
0.827818 0.560996i \(-0.189582\pi\)
\(180\) −50.2530 111.982i −0.279183 0.622123i
\(181\) −46.9661 −0.259481 −0.129741 0.991548i \(-0.541414\pi\)
−0.129741 + 0.991548i \(0.541414\pi\)
\(182\) 48.8710i 0.268522i
\(183\) 98.1317 21.0095i 0.536239 0.114806i
\(184\) 22.9017 0.124466
\(185\) 278.594i 1.50591i
\(186\) 27.6900 + 129.335i 0.148871 + 0.695350i
\(187\) 243.558 1.30245
\(188\) 13.1068i 0.0697170i
\(189\) 208.683 153.029i 1.10414 0.809676i
\(190\) −232.645 −1.22445
\(191\) 12.0342i 0.0630062i −0.999504 0.0315031i \(-0.989971\pi\)
0.999504 0.0315031i \(-0.0100294\pi\)
\(192\) 23.4682 5.02441i 0.122230 0.0261688i
\(193\) −265.711 −1.37674 −0.688369 0.725360i \(-0.741673\pi\)
−0.688369 + 0.725360i \(0.741673\pi\)
\(194\) 117.005i 0.603118i
\(195\) 15.4413 + 72.1237i 0.0791862 + 0.369865i
\(196\) −85.7213 −0.437354
\(197\) 324.865i 1.64906i −0.565817 0.824531i \(-0.691439\pi\)
0.565817 0.824531i \(-0.308561\pi\)
\(198\) 181.183 81.3076i 0.915067 0.410645i
\(199\) 266.613 1.33976 0.669882 0.742468i \(-0.266345\pi\)
0.669882 + 0.742468i \(0.266345\pi\)
\(200\) 60.8055i 0.304027i
\(201\) −1.03331 + 0.221225i −0.00514082 + 0.00110062i
\(202\) −61.7760 −0.305822
\(203\) 321.219i 1.58236i
\(204\) −19.6077 91.5842i −0.0961161 0.448942i
\(205\) −412.864 −2.01397
\(206\) 113.093i 0.548997i
\(207\) −29.8358 66.4852i −0.144134 0.321184i
\(208\) −14.4222 −0.0693375
\(209\) 376.412i 1.80101i
\(210\) 271.135 58.0486i 1.29112 0.276422i
\(211\) −302.781 −1.43498 −0.717491 0.696568i \(-0.754710\pi\)
−0.717491 + 0.696568i \(0.754710\pi\)
\(212\) 79.0513i 0.372883i
\(213\) −62.4215 291.560i −0.293059 1.36883i
\(214\) −174.909 −0.817334
\(215\) 127.002i 0.590708i
\(216\) −45.1600 61.5839i −0.209074 0.285111i
\(217\) −298.797 −1.37695
\(218\) 60.5288i 0.277655i
\(219\) 278.538 59.6335i 1.27186 0.272299i
\(220\) 212.789 0.967222
\(221\) 56.2824i 0.254672i
\(222\) 36.2881 + 169.496i 0.163460 + 0.763494i
\(223\) 299.147 1.34147 0.670733 0.741699i \(-0.265980\pi\)
0.670733 + 0.741699i \(0.265980\pi\)
\(224\) 54.2175i 0.242043i
\(225\) −176.522 + 79.2159i −0.784543 + 0.352071i
\(226\) 119.501 0.528765
\(227\) 26.9489i 0.118718i 0.998237 + 0.0593588i \(0.0189056\pi\)
−0.998237 + 0.0593588i \(0.981094\pi\)
\(228\) −141.541 + 30.3031i −0.620792 + 0.132908i
\(229\) 268.170 1.17105 0.585523 0.810655i \(-0.300889\pi\)
0.585523 + 0.810655i \(0.300889\pi\)
\(230\) 78.0828i 0.339490i
\(231\) 93.9208 + 438.688i 0.406583 + 1.89908i
\(232\) −94.7942 −0.408596
\(233\) 307.370i 1.31919i −0.751623 0.659593i \(-0.770729\pi\)
0.751623 0.659593i \(-0.229271\pi\)
\(234\) 18.7889 + 41.8686i 0.0802944 + 0.178926i
\(235\) −44.6873 −0.190159
\(236\) 96.8314i 0.410303i
\(237\) −151.037 + 32.3363i −0.637287 + 0.136440i
\(238\) 211.583 0.889004
\(239\) 394.784i 1.65181i 0.563806 + 0.825907i \(0.309337\pi\)
−0.563806 + 0.825907i \(0.690663\pi\)
\(240\) −17.1306 80.0141i −0.0713775 0.333392i
\(241\) 4.44186 0.0184309 0.00921547 0.999958i \(-0.497067\pi\)
0.00921547 + 0.999958i \(0.497067\pi\)
\(242\) 173.165i 0.715559i
\(243\) −119.949 + 211.332i −0.493616 + 0.869680i
\(244\) 66.9037 0.274196
\(245\) 292.264i 1.19292i
\(246\) −251.185 + 53.7774i −1.02108 + 0.218607i
\(247\) 86.9828 0.352157
\(248\) 88.1773i 0.355554i
\(249\) −55.2067 257.861i −0.221713 1.03559i
\(250\) 33.7715 0.135086
\(251\) 188.722i 0.751882i −0.926644 0.375941i \(-0.877320\pi\)
0.926644 0.375941i \(-0.122680\pi\)
\(252\) 157.397 70.6333i 0.624591 0.280291i
\(253\) 126.335 0.499349
\(254\) 18.6715i 0.0735100i
\(255\) −312.254 + 66.8519i −1.22452 + 0.262164i
\(256\) 16.0000 0.0625000
\(257\) 288.936i 1.12426i 0.827047 + 0.562132i \(0.190019\pi\)
−0.827047 + 0.562132i \(0.809981\pi\)
\(258\) 16.5426 + 77.2678i 0.0641187 + 0.299488i
\(259\) −391.579 −1.51189
\(260\) 49.1721i 0.189123i
\(261\) 123.496 + 275.194i 0.473163 + 1.05438i
\(262\) 233.245 0.890248
\(263\) 292.966i 1.11394i 0.830533 + 0.556969i \(0.188036\pi\)
−0.830533 + 0.556969i \(0.811964\pi\)
\(264\) 129.460 27.7167i 0.490379 0.104988i
\(265\) −269.523 −1.01707
\(266\) 326.995i 1.22931i
\(267\) 68.0239 + 317.728i 0.254771 + 1.18999i
\(268\) −0.704481 −0.00262866
\(269\) 205.144i 0.762617i −0.924448 0.381308i \(-0.875474\pi\)
0.924448 0.381308i \(-0.124526\pi\)
\(270\) −209.969 + 153.972i −0.777662 + 0.570265i
\(271\) 212.721 0.784949 0.392475 0.919763i \(-0.371619\pi\)
0.392475 + 0.919763i \(0.371619\pi\)
\(272\) 62.4397i 0.229558i
\(273\) −101.374 + 21.7036i −0.371333 + 0.0795004i
\(274\) −68.4210 −0.249712
\(275\) 335.428i 1.21974i
\(276\) −10.1706 47.5054i −0.0368502 0.172121i
\(277\) −275.738 −0.995443 −0.497721 0.867337i \(-0.665830\pi\)
−0.497721 + 0.867337i \(0.665830\pi\)
\(278\) 57.3664i 0.206354i
\(279\) 255.984 114.875i 0.917507 0.411739i
\(280\) 184.853 0.660190
\(281\) 143.542i 0.510825i −0.966832 0.255412i \(-0.917789\pi\)
0.966832 0.255412i \(-0.0822113\pi\)
\(282\) −27.1876 + 5.82073i −0.0964100 + 0.0206409i
\(283\) 91.9591 0.324944 0.162472 0.986713i \(-0.448053\pi\)
0.162472 + 0.986713i \(0.448053\pi\)
\(284\) 198.778i 0.699923i
\(285\) 103.318 + 482.579i 0.362518 + 1.69326i
\(286\) −79.5588 −0.278178
\(287\) 580.302i 2.02196i
\(288\) −20.8444 46.4490i −0.0723764 0.161281i
\(289\) 45.3299 0.156851
\(290\) 323.198i 1.11448i
\(291\) 242.705 51.9618i 0.834037 0.178563i
\(292\) 189.900 0.650343
\(293\) 475.059i 1.62136i 0.585489 + 0.810681i \(0.300903\pi\)
−0.585489 + 0.810681i \(0.699097\pi\)
\(294\) 38.0688 + 177.813i 0.129486 + 0.604806i
\(295\) 330.144 1.11913
\(296\) 115.558i 0.390398i
\(297\) −249.121 339.722i −0.838791 1.14385i
\(298\) 273.095 0.916427
\(299\) 29.1941i 0.0976391i
\(300\) −126.130 + 27.0037i −0.420432 + 0.0900123i
\(301\) −178.509 −0.593052
\(302\) 220.390i 0.729767i
\(303\) 27.4347 + 128.143i 0.0905436 + 0.422914i
\(304\) −96.4988 −0.317430
\(305\) 228.106i 0.747889i
\(306\) −181.267 + 81.3450i −0.592374 + 0.265833i
\(307\) −455.182 −1.48268 −0.741338 0.671131i \(-0.765809\pi\)
−0.741338 + 0.671131i \(0.765809\pi\)
\(308\) 299.086i 0.971059i
\(309\) 234.591 50.2247i 0.759195 0.162540i
\(310\) 300.638 0.969800
\(311\) 436.493i 1.40352i −0.712416 0.701758i \(-0.752399\pi\)
0.712416 0.701758i \(-0.247601\pi\)
\(312\) 6.40489 + 29.9162i 0.0205285 + 0.0958852i
\(313\) 191.914 0.613144 0.306572 0.951847i \(-0.400818\pi\)
0.306572 + 0.951847i \(0.400818\pi\)
\(314\) 91.7800i 0.292293i
\(315\) −240.822 536.640i −0.764515 1.70362i
\(316\) −102.973 −0.325865
\(317\) 239.722i 0.756221i −0.925761 0.378110i \(-0.876574\pi\)
0.925761 0.378110i \(-0.123426\pi\)
\(318\) −163.977 + 35.1066i −0.515651 + 0.110398i
\(319\) −522.924 −1.63926
\(320\) 54.5515i 0.170474i
\(321\) 77.6772 + 362.817i 0.241985 + 1.13027i
\(322\) 109.750 0.340837
\(323\) 376.585i 1.16590i
\(324\) −107.689 + 121.025i −0.332373 + 0.373535i
\(325\) 77.5121 0.238499
\(326\) 417.933i 1.28200i
\(327\) −125.556 + 26.8808i −0.383962 + 0.0822043i
\(328\) −171.252 −0.522108
\(329\) 62.8104i 0.190913i
\(330\) −94.4994 441.391i −0.286362 1.33755i
\(331\) −262.349 −0.792594 −0.396297 0.918122i \(-0.629705\pi\)
−0.396297 + 0.918122i \(0.629705\pi\)
\(332\) 175.803i 0.529527i
\(333\) 335.471 150.546i 1.00742 0.452090i
\(334\) 122.350 0.366319
\(335\) 2.40191i 0.00716987i
\(336\) 112.464 24.0780i 0.334715 0.0716607i
\(337\) 108.189 0.321037 0.160518 0.987033i \(-0.448683\pi\)
0.160518 + 0.987033i \(0.448683\pi\)
\(338\) 18.3848i 0.0543928i
\(339\) −53.0703 247.882i −0.156550 0.731217i
\(340\) −212.887 −0.626137
\(341\) 486.422i 1.42646i
\(342\) 125.716 + 280.142i 0.367591 + 0.819129i
\(343\) 58.8419 0.171551
\(344\) 52.6792i 0.153137i
\(345\) −161.968 + 34.6765i −0.469473 + 0.100512i
\(346\) 112.942 0.326423
\(347\) 371.606i 1.07091i 0.844564 + 0.535455i \(0.179860\pi\)
−0.844564 + 0.535455i \(0.820140\pi\)
\(348\) 42.0981 + 196.633i 0.120971 + 0.565037i
\(349\) 187.750 0.537966 0.268983 0.963145i \(-0.413312\pi\)
0.268983 + 0.963145i \(0.413312\pi\)
\(350\) 291.392i 0.832548i
\(351\) 78.5044 57.5679i 0.223659 0.164011i
\(352\) 88.2626 0.250746
\(353\) 258.521i 0.732354i 0.930545 + 0.366177i \(0.119334\pi\)
−0.930545 + 0.366177i \(0.880666\pi\)
\(354\) 200.859 43.0028i 0.567398 0.121477i
\(355\) −677.728 −1.90909
\(356\) 216.619i 0.608480i
\(357\) −93.9639 438.890i −0.263204 1.22938i
\(358\) −284.026 −0.793369
\(359\) 134.918i 0.375816i −0.982187 0.187908i \(-0.939829\pi\)
0.982187 0.187908i \(-0.0601707\pi\)
\(360\) −158.367 + 71.0684i −0.439907 + 0.197412i
\(361\) 221.001 0.612191
\(362\) 66.4201i 0.183481i
\(363\) 359.199 76.9026i 0.989529 0.211853i
\(364\) −69.1141 −0.189874
\(365\) 647.459i 1.77386i
\(366\) −29.7119 138.779i −0.0811801 0.379178i
\(367\) 354.929 0.967109 0.483554 0.875314i \(-0.339346\pi\)
0.483554 + 0.875314i \(0.339346\pi\)
\(368\) 32.3879i 0.0880107i
\(369\) 223.102 + 497.154i 0.604613 + 1.34730i
\(370\) 393.991 1.06484
\(371\) 378.829i 1.02110i
\(372\) 182.907 39.1595i 0.491687 0.105267i
\(373\) 355.525 0.953149 0.476575 0.879134i \(-0.341878\pi\)
0.476575 + 0.879134i \(0.341878\pi\)
\(374\) 344.443i 0.920971i
\(375\) −14.9979 70.0526i −0.0399944 0.186807i
\(376\) −18.5358 −0.0492974
\(377\) 120.839i 0.320529i
\(378\) −216.415 295.122i −0.572528 0.780747i
\(379\) 490.270 1.29359 0.646794 0.762665i \(-0.276110\pi\)
0.646794 + 0.762665i \(0.276110\pi\)
\(380\) 329.010i 0.865815i
\(381\) 38.7306 8.29202i 0.101655 0.0217638i
\(382\) −17.0189 −0.0445521
\(383\) 102.395i 0.267351i −0.991025 0.133675i \(-0.957322\pi\)
0.991025 0.133675i \(-0.0426780\pi\)
\(384\) −7.10559 33.1890i −0.0185041 0.0864297i
\(385\) 1019.73 2.64864
\(386\) 375.771i 0.973501i
\(387\) 152.931 68.6292i 0.395171 0.177336i
\(388\) 165.470 0.426469
\(389\) 365.422i 0.939389i 0.882829 + 0.469694i \(0.155636\pi\)
−0.882829 + 0.469694i \(0.844364\pi\)
\(390\) 101.998 21.8373i 0.261534 0.0559931i
\(391\) −126.393 −0.323257
\(392\) 121.228i 0.309256i
\(393\) −103.584 483.823i −0.263573 1.23110i
\(394\) −459.429 −1.16606
\(395\) 351.084i 0.888821i
\(396\) −114.986 256.232i −0.290370 0.647050i
\(397\) −497.163 −1.25230 −0.626149 0.779703i \(-0.715370\pi\)
−0.626149 + 0.779703i \(0.715370\pi\)
\(398\) 377.048i 0.947356i
\(399\) −678.291 + 145.218i −1.69998 + 0.363956i
\(400\) −85.9919 −0.214980
\(401\) 563.415i 1.40502i −0.711672 0.702512i \(-0.752062\pi\)
0.711672 0.702512i \(-0.247938\pi\)
\(402\) 0.312860 + 1.46131i 0.000778258 + 0.00363511i
\(403\) −112.404 −0.278919
\(404\) 87.3645i 0.216249i
\(405\) 412.632 + 367.162i 1.01885 + 0.906573i
\(406\) −454.273 −1.11890
\(407\) 637.464i 1.56625i
\(408\) −129.520 + 27.7295i −0.317450 + 0.0679644i
\(409\) −734.959 −1.79696 −0.898482 0.439010i \(-0.855329\pi\)
−0.898482 + 0.439010i \(0.855329\pi\)
\(410\) 583.877i 1.42409i
\(411\) 30.3857 + 141.927i 0.0739313 + 0.345320i
\(412\) 159.938 0.388200
\(413\) 464.035i 1.12357i
\(414\) −94.0242 + 42.1942i −0.227112 + 0.101918i
\(415\) −599.395 −1.44433
\(416\) 20.3961i 0.0490290i
\(417\) 118.996 25.4764i 0.285362 0.0610944i
\(418\) −532.327 −1.27351
\(419\) 301.483i 0.719529i 0.933043 + 0.359765i \(0.117143\pi\)
−0.933043 + 0.359765i \(0.882857\pi\)
\(420\) −82.0932 383.443i −0.195460 0.912960i
\(421\) 50.6030 0.120197 0.0600986 0.998192i \(-0.480858\pi\)
0.0600986 + 0.998192i \(0.480858\pi\)
\(422\) 428.197i 1.01469i
\(423\) 24.1480 + 53.8107i 0.0570875 + 0.127212i
\(424\) −111.795 −0.263668
\(425\) 335.582i 0.789605i
\(426\) −412.328 + 88.2773i −0.967907 + 0.207224i
\(427\) 320.616 0.750857
\(428\) 247.359i 0.577942i
\(429\) 35.3320 + 165.030i 0.0823591 + 0.384685i
\(430\) 179.608 0.417694
\(431\) 57.2102i 0.132738i −0.997795 0.0663691i \(-0.978859\pi\)
0.997795 0.0663691i \(-0.0211415\pi\)
\(432\) −87.0928 + 63.8658i −0.201604 + 0.147838i
\(433\) 697.010 1.60972 0.804862 0.593462i \(-0.202239\pi\)
0.804862 + 0.593462i \(0.202239\pi\)
\(434\) 422.563i 0.973648i
\(435\) 670.415 143.532i 1.54118 0.329959i
\(436\) −85.6007 −0.196332
\(437\) 195.337i 0.446996i
\(438\) −84.3346 393.912i −0.192545 0.899343i
\(439\) −89.8292 −0.204622 −0.102311 0.994752i \(-0.532624\pi\)
−0.102311 + 0.994752i \(0.532624\pi\)
\(440\) 300.929i 0.683929i
\(441\) 351.933 157.933i 0.798034 0.358125i
\(442\) 79.5954 0.180080
\(443\) 327.588i 0.739476i 0.929136 + 0.369738i \(0.120553\pi\)
−0.929136 + 0.369738i \(0.879447\pi\)
\(444\) 239.703 51.3191i 0.539872 0.115584i
\(445\) 738.556 1.65968
\(446\) 423.058i 0.948560i
\(447\) −121.281 566.485i −0.271323 1.26730i
\(448\) 76.6752 0.171150
\(449\) 590.940i 1.31612i 0.752964 + 0.658062i \(0.228624\pi\)
−0.752964 + 0.658062i \(0.771376\pi\)
\(450\) 112.028 + 249.640i 0.248952 + 0.554756i
\(451\) −944.694 −2.09467
\(452\) 169.000i 0.373894i
\(453\) −457.157 + 97.8749i −1.00918 + 0.216059i
\(454\) 38.1115 0.0839461
\(455\) 235.642i 0.517895i
\(456\) 42.8551 + 200.169i 0.0939804 + 0.438966i
\(457\) −584.524 −1.27905 −0.639523 0.768772i \(-0.720868\pi\)
−0.639523 + 0.768772i \(0.720868\pi\)
\(458\) 379.249i 0.828055i
\(459\) 249.235 + 339.878i 0.542996 + 0.740476i
\(460\) −110.426 −0.240056
\(461\) 183.062i 0.397097i −0.980091 0.198548i \(-0.936377\pi\)
0.980091 0.198548i \(-0.0636227\pi\)
\(462\) 620.399 132.824i 1.34285 0.287498i
\(463\) −752.102 −1.62441 −0.812205 0.583372i \(-0.801733\pi\)
−0.812205 + 0.583372i \(0.801733\pi\)
\(464\) 134.059i 0.288921i
\(465\) −133.513 623.618i −0.287125 1.34111i
\(466\) −434.687 −0.932806
\(467\) 46.3727i 0.0992991i −0.998767 0.0496495i \(-0.984190\pi\)
0.998767 0.0496495i \(-0.0158104\pi\)
\(468\) 59.2111 26.5715i 0.126519 0.0567767i
\(469\) −3.37601 −0.00719832
\(470\) 63.1974i 0.134462i
\(471\) −190.380 + 40.7594i −0.404205 + 0.0865381i
\(472\) 136.940 0.290128
\(473\) 290.600i 0.614377i
\(474\) 45.7304 + 213.599i 0.0964776 + 0.450630i
\(475\) 518.632 1.09186
\(476\) 299.224i 0.628621i
\(477\) 145.644 + 324.549i 0.305334 + 0.680396i
\(478\) 558.309 1.16801
\(479\) 338.396i 0.706464i −0.935536 0.353232i \(-0.885083\pi\)
0.935536 0.353232i \(-0.114917\pi\)
\(480\) −113.157 + 24.2263i −0.235744 + 0.0504715i
\(481\) −147.308 −0.306253
\(482\) 6.28174i 0.0130326i
\(483\) −48.7398 227.655i −0.100910 0.471336i
\(484\) 244.893 0.505977
\(485\) 564.165i 1.16323i
\(486\) 298.869 + 169.633i 0.614957 + 0.349039i
\(487\) −104.632 −0.214850 −0.107425 0.994213i \(-0.534261\pi\)
−0.107425 + 0.994213i \(0.534261\pi\)
\(488\) 94.6161i 0.193886i
\(489\) −866.924 + 185.604i −1.77285 + 0.379558i
\(490\) 413.324 0.843519
\(491\) 204.874i 0.417259i 0.977995 + 0.208630i \(0.0669004\pi\)
−0.977995 + 0.208630i \(0.933100\pi\)
\(492\) 76.0527 + 355.229i 0.154579 + 0.722011i
\(493\) 523.164 1.06119
\(494\) 123.012i 0.249013i
\(495\) −873.615 + 392.043i −1.76488 + 0.792005i
\(496\) 124.702 0.251414
\(497\) 952.584i 1.91667i
\(498\) −364.670 + 78.0740i −0.732270 + 0.156775i
\(499\) 398.915 0.799430 0.399715 0.916640i \(-0.369109\pi\)
0.399715 + 0.916640i \(0.369109\pi\)
\(500\) 47.7601i 0.0955201i
\(501\) −54.3358 253.793i −0.108455 0.506573i
\(502\) −266.894 −0.531661
\(503\) 412.934i 0.820943i −0.911873 0.410472i \(-0.865364\pi\)
0.911873 0.410472i \(-0.134636\pi\)
\(504\) −99.8905 222.593i −0.198196 0.441653i
\(505\) 297.867 0.589835
\(506\) 178.665i 0.353093i
\(507\) −38.1358 + 8.16467i −0.0752185 + 0.0161039i
\(508\) 26.4055 0.0519794
\(509\) 731.331i 1.43680i −0.695630 0.718400i \(-0.744875\pi\)
0.695630 0.718400i \(-0.255125\pi\)
\(510\) 94.5428 + 441.593i 0.185378 + 0.865869i
\(511\) 910.039 1.78090
\(512\) 22.6274i 0.0441942i
\(513\) 525.272 385.186i 1.02392 0.750850i
\(514\) 408.617 0.794975
\(515\) 545.305i 1.05884i
\(516\) 109.273 23.3948i 0.211770 0.0453388i
\(517\) −102.251 −0.197778
\(518\) 553.776i 1.06907i
\(519\) −50.1576 234.278i −0.0966428 0.451402i
\(520\) 69.5398 0.133730
\(521\) 802.622i 1.54054i 0.637717 + 0.770271i \(0.279879\pi\)
−0.637717 + 0.770271i \(0.720121\pi\)
\(522\) 389.183 174.649i 0.745561 0.334577i
\(523\) −832.197 −1.59120 −0.795599 0.605823i \(-0.792844\pi\)
−0.795599 + 0.605823i \(0.792844\pi\)
\(524\) 329.858i 0.629501i
\(525\) −604.438 + 129.407i −1.15131 + 0.246490i
\(526\) 414.316 0.787673
\(527\) 486.646i 0.923427i
\(528\) −39.1974 183.084i −0.0742374 0.346750i
\(529\) 463.439 0.876066
\(530\) 381.163i 0.719176i
\(531\) −178.403 397.546i −0.335975 0.748675i
\(532\) −462.441 −0.869250
\(533\) 218.304i 0.409575i
\(534\) 449.335 96.2003i 0.841452 0.180150i
\(535\) 843.364 1.57638
\(536\) 0.996287i 0.00185874i
\(537\) 126.136 + 589.159i 0.234890 + 1.09713i
\(538\) −290.117 −0.539251
\(539\) 668.745i 1.24071i
\(540\) 217.749 + 296.940i 0.403238 + 0.549890i
\(541\) 304.987 0.563747 0.281873 0.959452i \(-0.409044\pi\)
0.281873 + 0.959452i \(0.409044\pi\)
\(542\) 300.833i 0.555043i
\(543\) 137.776 29.4971i 0.253731 0.0543225i
\(544\) −88.3031 −0.162322
\(545\) 291.853i 0.535510i
\(546\) 30.6935 + 143.364i 0.0562152 + 0.262572i
\(547\) 462.958 0.846359 0.423180 0.906046i \(-0.360914\pi\)
0.423180 + 0.906046i \(0.360914\pi\)
\(548\) 96.7620i 0.176573i
\(549\) −274.677 + 123.264i −0.500322 + 0.224524i
\(550\) −474.367 −0.862485
\(551\) 808.535i 1.46740i
\(552\) −67.1827 + 14.3835i −0.121708 + 0.0260570i
\(553\) −493.468 −0.892348
\(554\) 389.952i 0.703884i
\(555\) −174.971 817.261i −0.315263 1.47254i
\(556\) 81.1283 0.145914
\(557\) 776.893i 1.39478i 0.716691 + 0.697391i \(0.245656\pi\)
−0.716691 + 0.697391i \(0.754344\pi\)
\(558\) −162.458 362.017i −0.291144 0.648775i
\(559\) −67.1531 −0.120131
\(560\) 261.422i 0.466825i
\(561\) −714.483 + 152.967i −1.27359 + 0.272669i
\(562\) −202.999 −0.361208
\(563\) 51.4872i 0.0914516i 0.998954 + 0.0457258i \(0.0145600\pi\)
−0.998954 + 0.0457258i \(0.985440\pi\)
\(564\) 8.23175 + 38.4491i 0.0145953 + 0.0681722i
\(565\) −576.200 −1.01982
\(566\) 130.050i 0.229770i
\(567\) −516.066 + 579.977i −0.910170 + 1.02289i
\(568\) −281.115 −0.494920
\(569\) 172.306i 0.302823i −0.988471 0.151412i \(-0.951618\pi\)
0.988471 0.151412i \(-0.0483819\pi\)
\(570\) 682.469 146.113i 1.19731 0.256339i
\(571\) 190.675 0.333932 0.166966 0.985963i \(-0.446603\pi\)
0.166966 + 0.985963i \(0.446603\pi\)
\(572\) 112.513i 0.196701i
\(573\) 7.55809 + 35.3026i 0.0131904 + 0.0616100i
\(574\) −820.671 −1.42974
\(575\) 174.069i 0.302728i
\(576\) −65.6888 + 29.4784i −0.114043 + 0.0511779i
\(577\) −279.690 −0.484732 −0.242366 0.970185i \(-0.577924\pi\)
−0.242366 + 0.970185i \(0.577924\pi\)
\(578\) 64.1062i 0.110910i
\(579\) 779.468 166.880i 1.34623 0.288221i
\(580\) 457.071 0.788054
\(581\) 842.483i 1.45006i
\(582\) −73.4851 343.236i −0.126263 0.589753i
\(583\) −616.709 −1.05782
\(584\) 268.559i 0.459862i
\(585\) −90.5948 201.879i −0.154863 0.345092i
\(586\) 671.835 1.14648
\(587\) 263.161i 0.448315i 0.974553 + 0.224157i \(0.0719629\pi\)
−0.974553 + 0.224157i \(0.928037\pi\)
\(588\) 251.465 53.8374i 0.427662 0.0915602i
\(589\) −752.097 −1.27690
\(590\) 466.894i 0.791346i
\(591\) 204.032 + 952.999i 0.345232 + 1.61252i
\(592\) 163.423 0.276053
\(593\) 316.144i 0.533126i 0.963817 + 0.266563i \(0.0858881\pi\)
−0.963817 + 0.266563i \(0.914112\pi\)
\(594\) −480.440 + 352.310i −0.808821 + 0.593115i
\(595\) −1020.19 −1.71461
\(596\) 386.215i 0.648012i
\(597\) −782.115 + 167.447i −1.31008 + 0.280480i
\(598\) 41.2867 0.0690413
\(599\) 159.206i 0.265787i −0.991130 0.132893i \(-0.957573\pi\)
0.991130 0.132893i \(-0.0424268\pi\)
\(600\) 38.1890 + 178.374i 0.0636483 + 0.297290i
\(601\) 1032.53 1.71801 0.859006 0.511965i \(-0.171082\pi\)
0.859006 + 0.511965i \(0.171082\pi\)
\(602\) 252.449i 0.419351i
\(603\) 2.89228 1.29794i 0.00479649 0.00215247i
\(604\) −311.678 −0.516023
\(605\) 834.955i 1.38009i
\(606\) 181.221 38.7985i 0.299045 0.0640240i
\(607\) 272.955 0.449679 0.224840 0.974396i \(-0.427814\pi\)
0.224840 + 0.974396i \(0.427814\pi\)
\(608\) 136.470i 0.224457i
\(609\) 201.742 + 942.304i 0.331268 + 1.54730i
\(610\) −322.591 −0.528838
\(611\) 23.6286i 0.0386721i
\(612\) 115.039 + 256.350i 0.187972 + 0.418872i
\(613\) 909.866 1.48428 0.742142 0.670243i \(-0.233810\pi\)
0.742142 + 0.670243i \(0.233810\pi\)
\(614\) 643.724i 1.04841i
\(615\) 1211.14 259.300i 1.96934 0.421625i
\(616\) 422.972 0.686643
\(617\) 299.087i 0.484744i 0.970183 + 0.242372i \(0.0779255\pi\)
−0.970183 + 0.242372i \(0.922074\pi\)
\(618\) −71.0285 331.762i −0.114933 0.536832i
\(619\) 175.344 0.283269 0.141635 0.989919i \(-0.454764\pi\)
0.141635 + 0.989919i \(0.454764\pi\)
\(620\) 425.166i 0.685752i
\(621\) 129.280 + 176.297i 0.208181 + 0.283893i
\(622\) −617.295 −0.992435
\(623\) 1038.08i 1.66626i
\(624\) 42.3079 9.05789i 0.0678011 0.0145158i
\(625\) −700.286 −1.12046
\(626\) 271.407i 0.433558i
\(627\) 236.406 + 1104.21i 0.377043 + 1.76111i
\(628\) −129.796 −0.206682
\(629\) 637.757i 1.01392i
\(630\) −758.924 + 340.574i −1.20464 + 0.540594i
\(631\) 821.692 1.30221 0.651103 0.758989i \(-0.274307\pi\)
0.651103 + 0.758989i \(0.274307\pi\)
\(632\) 145.626i 0.230421i
\(633\) 888.215 190.162i 1.40318 0.300414i
\(634\) −339.018 −0.534729
\(635\) 90.0290i 0.141778i
\(636\) 49.6483 + 231.899i 0.0780633 + 0.364621i
\(637\) −154.536 −0.242600
\(638\) 739.526i 1.15913i
\(639\) 366.229 + 816.094i 0.573129 + 1.27714i
\(640\) −77.1475 −0.120543
\(641\) 774.943i 1.20896i −0.796621 0.604480i \(-0.793381\pi\)
0.796621 0.604480i \(-0.206619\pi\)
\(642\) 513.101 109.852i 0.799222 0.171109i
\(643\) −582.871 −0.906487 −0.453244 0.891387i \(-0.649733\pi\)
−0.453244 + 0.891387i \(0.649733\pi\)
\(644\) 155.209i 0.241008i
\(645\) −79.7640 372.564i −0.123665 0.577618i
\(646\) 532.571 0.824414
\(647\) 467.365i 0.722358i −0.932497 0.361179i \(-0.882374\pi\)
0.932497 0.361179i \(-0.117626\pi\)
\(648\) 171.156 + 152.295i 0.264129 + 0.235023i
\(649\) 755.419 1.16397
\(650\) 109.619i 0.168644i
\(651\) 876.529 187.660i 1.34643 0.288264i
\(652\) −591.047 −0.906513
\(653\) 485.145i 0.742948i 0.928443 + 0.371474i \(0.121147\pi\)
−0.928443 + 0.371474i \(0.878853\pi\)
\(654\) 38.0152 + 177.563i 0.0581272 + 0.271502i
\(655\) −1124.64 −1.71701
\(656\) 242.186i 0.369186i
\(657\) −779.645 + 349.873i −1.18667 + 0.532531i
\(658\) −88.8273 −0.134996
\(659\) 545.968i 0.828480i −0.910168 0.414240i \(-0.864047\pi\)
0.910168 0.414240i \(-0.135953\pi\)
\(660\) −624.221 + 133.642i −0.945789 + 0.202488i
\(661\) −368.850 −0.558019 −0.279009 0.960288i \(-0.590006\pi\)
−0.279009 + 0.960288i \(0.590006\pi\)
\(662\) 371.017i 0.560449i
\(663\) −35.3483 165.106i −0.0533156 0.249028i
\(664\) −248.623 −0.374432
\(665\) 1576.68i 2.37095i
\(666\) −212.904 474.428i −0.319676 0.712355i
\(667\) 271.369 0.406850
\(668\) 173.030i 0.259027i
\(669\) −877.554 + 187.880i −1.31174 + 0.280837i
\(670\) 3.39681 0.00506987
\(671\) 521.942i 0.777856i
\(672\) −34.0514 159.048i −0.0506717 0.236679i
\(673\) 231.121 0.343418 0.171709 0.985148i \(-0.445071\pi\)
0.171709 + 0.985148i \(0.445071\pi\)
\(674\) 153.003i 0.227007i
\(675\) 468.080 343.247i 0.693452 0.508514i
\(676\) −26.0000 −0.0384615
\(677\) 882.725i 1.30388i 0.758271 + 0.651939i \(0.226044\pi\)
−0.758271 + 0.651939i \(0.773956\pi\)
\(678\) −350.559 + 75.0528i −0.517048 + 0.110697i
\(679\) 792.965 1.16784
\(680\) 301.067i 0.442746i
\(681\) −16.9253 79.0552i −0.0248536 0.116087i
\(682\) 687.905 1.00866
\(683\) 163.689i 0.239661i 0.992794 + 0.119831i \(0.0382351\pi\)
−0.992794 + 0.119831i \(0.961765\pi\)
\(684\) 396.181 177.790i 0.579211 0.259926i
\(685\) 329.907 0.481616
\(686\) 83.2151i 0.121305i
\(687\) −786.682 + 168.424i −1.14510 + 0.245159i
\(688\) 74.4997 0.108284
\(689\) 142.512i 0.206839i
\(690\) 49.0400 + 229.058i 0.0710725 + 0.331968i
\(691\) −940.426 −1.36096 −0.680482 0.732765i \(-0.738230\pi\)
−0.680482 + 0.732765i \(0.738230\pi\)
\(692\) 159.725i 0.230816i
\(693\) −551.037 1227.91i −0.795148 1.77188i
\(694\) 525.530 0.757248
\(695\) 276.605i 0.397992i
\(696\) 278.081 59.5357i 0.399542 0.0855398i
\(697\) 945.128 1.35599
\(698\) 265.519i 0.380400i
\(699\) 193.044 + 901.678i 0.276172 + 1.28995i
\(700\) −412.090 −0.588701
\(701\) 394.213i 0.562357i −0.959655 0.281179i \(-0.909275\pi\)
0.959655 0.281179i \(-0.0907254\pi\)
\(702\) −81.4133 111.022i −0.115973 0.158151i
\(703\) −985.635 −1.40204
\(704\) 124.822i 0.177304i
\(705\) 131.091 28.0659i 0.185945 0.0398098i
\(706\) 365.604 0.517853
\(707\) 418.668i 0.592175i
\(708\) −60.8151 284.057i −0.0858971 0.401211i
\(709\) −433.261 −0.611087 −0.305544 0.952178i \(-0.598838\pi\)
−0.305544 + 0.952178i \(0.598838\pi\)
\(710\) 958.453i 1.34993i
\(711\) 422.762 189.718i 0.594602 0.266833i
\(712\) 306.345 0.430260
\(713\) 252.427i 0.354035i
\(714\) −620.683 + 132.885i −0.869305 + 0.186114i
\(715\) 383.610 0.536518
\(716\) 401.673i 0.560996i
\(717\) −247.945 1158.11i −0.345808 1.61521i
\(718\) −190.803 −0.265742
\(719\) 289.992i 0.403326i 0.979455 + 0.201663i \(0.0646346\pi\)
−0.979455 + 0.201663i \(0.935365\pi\)
\(720\) 100.506 + 223.964i 0.139592 + 0.311061i
\(721\) 766.456 1.06305
\(722\) 312.542i 0.432884i
\(723\) −13.0303 + 2.78972i −0.0180225 + 0.00385853i
\(724\) 93.9322 0.129741
\(725\) 720.501i 0.993795i
\(726\) −108.757 507.984i −0.149803 0.699703i
\(727\) 1161.84 1.59813 0.799067 0.601241i \(-0.205327\pi\)
0.799067 + 0.601241i \(0.205327\pi\)
\(728\) 97.7420i 0.134261i
\(729\) 219.145 695.282i 0.300610 0.953747i
\(730\) −915.646 −1.25431
\(731\) 290.734i 0.397721i
\(732\) −196.263 + 42.0190i −0.268120 + 0.0574030i
\(733\) 573.124 0.781888 0.390944 0.920414i \(-0.372149\pi\)
0.390944 + 0.920414i \(0.372149\pi\)
\(734\) 501.945i 0.683849i
\(735\) −183.557 857.364i −0.249738 1.16648i
\(736\) −45.8035 −0.0622330
\(737\) 5.49593i 0.00745716i
\(738\) 703.082 315.514i 0.952686 0.427526i
\(739\) 351.285 0.475352 0.237676 0.971344i \(-0.423614\pi\)
0.237676 + 0.971344i \(0.423614\pi\)
\(740\) 557.187i 0.752956i
\(741\) −255.166 + 54.6297i −0.344354 + 0.0737243i
\(742\) −535.746 −0.722029
\(743\) 76.8398i 0.103418i 0.998662 + 0.0517092i \(0.0164669\pi\)
−0.998662 + 0.0517092i \(0.983533\pi\)
\(744\) −55.3799 258.670i −0.0744354 0.347675i
\(745\) −1316.79 −1.76750
\(746\) 502.788i 0.673978i
\(747\) 323.900 + 721.768i 0.433601 + 0.966222i
\(748\) −487.116 −0.651225
\(749\) 1185.39i 1.58264i
\(750\) −99.0693 + 21.2102i −0.132092 + 0.0282803i
\(751\) −74.4474 −0.0991311 −0.0495655 0.998771i \(-0.515784\pi\)
−0.0495655 + 0.998771i \(0.515784\pi\)
\(752\) 26.2136i 0.0348585i
\(753\) 118.527 + 553.621i 0.157407 + 0.735221i
\(754\) −170.893 −0.226648
\(755\) 1062.66i 1.40749i
\(756\) −417.366 + 306.058i −0.552071 + 0.404838i
\(757\) 344.312 0.454838 0.227419 0.973797i \(-0.426971\pi\)
0.227419 + 0.973797i \(0.426971\pi\)
\(758\) 693.346i 0.914704i
\(759\) −370.608 + 79.3451i −0.488284 + 0.104539i
\(760\) 465.290 0.612224
\(761\) 742.341i 0.975480i −0.872989 0.487740i \(-0.837821\pi\)
0.872989 0.487740i \(-0.162179\pi\)
\(762\) −11.7267 54.7734i −0.0153894 0.0718811i
\(763\) −410.215 −0.537635
\(764\) 24.0684i 0.0315031i
\(765\) 874.017 392.223i 1.14251 0.512709i
\(766\) −144.809 −0.189046
\(767\) 174.565i 0.227595i
\(768\) −46.9364 + 10.0488i −0.0611150 + 0.0130844i
\(769\) 1264.66 1.64455 0.822275 0.569091i \(-0.192705\pi\)
0.822275 + 0.569091i \(0.192705\pi\)
\(770\) 1442.11i 1.87287i
\(771\) −181.467 847.600i −0.235365 1.09935i
\(772\) 531.421 0.688369
\(773\) 695.508i 0.899752i 0.893091 + 0.449876i \(0.148532\pi\)
−0.893091 + 0.449876i \(0.851468\pi\)
\(774\) −97.0564 216.277i −0.125396 0.279428i
\(775\) −670.208 −0.864785
\(776\) 234.010i 0.301559i
\(777\) 1148.70 245.932i 1.47838 0.316514i
\(778\) 516.785 0.664248
\(779\) 1460.67i 1.87505i
\(780\) −30.8826 144.247i −0.0395931 0.184933i
\(781\) −1550.74 −1.98559
\(782\) 178.747i 0.228577i
\(783\) −535.113 729.725i −0.683414 0.931961i
\(784\) 171.443 0.218677
\(785\) 442.537i 0.563742i
\(786\) −684.229 + 146.490i −0.870521 + 0.186374i
\(787\) 413.104 0.524910 0.262455 0.964944i \(-0.415468\pi\)
0.262455 + 0.964944i \(0.415468\pi\)
\(788\) 649.730i 0.824531i
\(789\) −183.997 859.421i −0.233203 1.08925i
\(790\) 496.508 0.628491
\(791\) 809.881i 1.02387i
\(792\) −362.367 + 162.615i −0.457534 + 0.205322i
\(793\) 120.612 0.152096
\(794\) 703.094i 0.885509i
\(795\) 790.652 169.274i 0.994531 0.212924i
\(796\) −533.226 −0.669882
\(797\) 1085.67i 1.36219i 0.732194 + 0.681096i \(0.238496\pi\)
−0.732194 + 0.681096i \(0.761504\pi\)
\(798\) 205.370 + 959.248i 0.257356 + 1.20207i
\(799\) 102.298 0.128033
\(800\) 121.611i 0.152014i
\(801\) −399.099 889.340i −0.498251 1.11029i
\(802\) −796.789 −0.993502
\(803\) 1481.48i 1.84494i
\(804\) 2.06661 0.442450i 0.00257041 0.000550311i
\(805\) −529.182 −0.657369
\(806\) 158.964i 0.197226i
\(807\) 128.841 + 601.794i 0.159654 + 0.745718i
\(808\) 123.552 0.152911
\(809\) 415.510i 0.513609i −0.966463 0.256805i \(-0.917330\pi\)
0.966463 0.256805i \(-0.0826697\pi\)
\(810\) 519.245 583.550i 0.641044 0.720432i
\(811\) −720.055 −0.887861 −0.443930 0.896061i \(-0.646416\pi\)
−0.443930 + 0.896061i \(0.646416\pi\)
\(812\) 642.439i 0.791181i
\(813\) −624.023 + 133.600i −0.767555 + 0.164330i
\(814\) 901.511 1.10751
\(815\) 2015.16i 2.47258i
\(816\) 39.2154 + 183.168i 0.0480581 + 0.224471i
\(817\) −449.320 −0.549964
\(818\) 1039.39i 1.27065i
\(819\) 283.751 127.336i 0.346461 0.155477i
\(820\) 825.727 1.00698
\(821\) 725.813i 0.884059i 0.897000 + 0.442030i \(0.145741\pi\)
−0.897000 + 0.442030i \(0.854259\pi\)
\(822\) 200.715 42.9719i 0.244178 0.0522773i
\(823\) 1122.02 1.36333 0.681663 0.731666i \(-0.261257\pi\)
0.681663 + 0.731666i \(0.261257\pi\)
\(824\) 226.187i 0.274499i
\(825\) 210.666 + 983.986i 0.255353 + 1.19271i
\(826\) 656.245 0.794486
\(827\) 1451.22i 1.75480i 0.479758 + 0.877401i \(0.340724\pi\)
−0.479758 + 0.877401i \(0.659276\pi\)
\(828\) 59.6716 + 132.970i 0.0720672 + 0.160592i
\(829\) −1099.31 −1.32607 −0.663037 0.748587i \(-0.730733\pi\)
−0.663037 + 0.748587i \(0.730733\pi\)
\(830\) 847.673i 1.02129i
\(831\) 808.883 173.177i 0.973385 0.208396i
\(832\) 28.8444 0.0346688
\(833\) 669.052i 0.803184i
\(834\) −36.0290 168.285i −0.0432003 0.201781i
\(835\) −589.940 −0.706515
\(836\) 752.824i 0.900507i
\(837\) −678.788 + 497.761i −0.810977 + 0.594696i
\(838\) 426.361 0.508784
\(839\) 714.937i 0.852130i 0.904693 + 0.426065i \(0.140100\pi\)
−0.904693 + 0.426065i \(0.859900\pi\)
\(840\) −542.271 + 116.097i −0.645560 + 0.138211i
\(841\) −282.244 −0.335605
\(842\) 71.5635i 0.0849923i
\(843\) 90.1516 + 421.083i 0.106941 + 0.499505i
\(844\) 605.562 0.717491
\(845\) 88.6463i 0.104907i
\(846\) 76.0998 34.1505i 0.0899524 0.0403670i
\(847\) 1173.57 1.38557
\(848\) 158.103i 0.186442i
\(849\) −269.764 + 57.7550i −0.317743 + 0.0680271i
\(850\) 474.585 0.558335
\(851\) 330.809i 0.388730i
\(852\) 124.843 + 583.120i 0.146529 + 0.684413i
\(853\) −619.594 −0.726370 −0.363185 0.931717i \(-0.618311\pi\)
−0.363185 + 0.931717i \(0.618311\pi\)
\(854\) 453.419i 0.530936i
\(855\) −606.169 1350.77i −0.708969 1.57984i
\(856\) 349.819 0.408667
\(857\) 603.166i 0.703811i −0.936035 0.351906i \(-0.885534\pi\)
0.936035 0.351906i \(-0.114466\pi\)
\(858\) 233.388 49.9670i 0.272013 0.0582366i
\(859\) 917.890 1.06856 0.534278 0.845309i \(-0.320583\pi\)
0.534278 + 0.845309i \(0.320583\pi\)
\(860\) 254.004i 0.295354i
\(861\) 364.460 + 1702.33i 0.423298 + 1.97715i
\(862\) −80.9074 −0.0938601
\(863\) 144.641i 0.167602i 0.996483 + 0.0838010i \(0.0267060\pi\)
−0.996483 + 0.0838010i \(0.973294\pi\)
\(864\) 90.3199 + 123.168i 0.104537 + 0.142555i
\(865\) −544.576 −0.629568
\(866\) 985.721i 1.13825i
\(867\) −132.976 + 28.4695i −0.153375 + 0.0328368i
\(868\) 597.595 0.688473
\(869\) 803.334i 0.924435i
\(870\) −202.985 948.109i −0.233316 1.08978i
\(871\) −1.27002 −0.00145812
\(872\) 121.058i 0.138828i
\(873\) −679.345 + 304.862i −0.778173 + 0.349212i
\(874\) 276.249 0.316074
\(875\) 228.876i 0.261572i
\(876\) −557.076 + 119.267i −0.635932 + 0.136150i
\(877\) −1102.64 −1.25728 −0.628641 0.777695i \(-0.716389\pi\)
−0.628641 + 0.777695i \(0.716389\pi\)
\(878\) 127.038i 0.144690i
\(879\) −298.361 1393.60i −0.339433 1.58543i
\(880\) −425.578 −0.483611
\(881\) 458.046i 0.519916i 0.965620 + 0.259958i \(0.0837088\pi\)
−0.965620 + 0.259958i \(0.916291\pi\)
\(882\) −223.351 497.709i −0.253233 0.564296i
\(883\) −1578.69 −1.78787 −0.893935 0.448197i \(-0.852066\pi\)
−0.893935 + 0.448197i \(0.852066\pi\)
\(884\) 112.565i 0.127336i
\(885\) −968.485 + 207.347i −1.09433 + 0.234291i
\(886\) 463.279 0.522889
\(887\) 1322.77i 1.49128i −0.666349 0.745640i \(-0.732144\pi\)
0.666349 0.745640i \(-0.267856\pi\)
\(888\) −72.5762 338.991i −0.0817300 0.381747i
\(889\) 126.541 0.142340
\(890\) 1044.48i 1.17357i
\(891\) 944.165 + 840.122i 1.05967 + 0.942898i
\(892\) −598.294 −0.670733
\(893\) 158.099i 0.177042i
\(894\) −801.131 + 171.518i −0.896119 + 0.191854i
\(895\) 1369.49 1.53016
\(896\) 108.435i 0.121021i
\(897\) −18.3354 85.6415i −0.0204408 0.0954755i
\(898\) 835.715 0.930640
\(899\) 1044.84i 1.16222i
\(900\) 353.044 158.432i 0.392271 0.176035i
\(901\) 616.993 0.684787
\(902\) 1336.00i 1.48115i
\(903\) 523.659 112.113i 0.579910 0.124156i
\(904\) −239.002 −0.264383
\(905\) 320.259i 0.353877i
\(906\) 138.416 + 646.518i 0.152777 + 0.713596i
\(907\) 183.989 0.202854 0.101427 0.994843i \(-0.467659\pi\)
0.101427 + 0.994843i \(0.467659\pi\)
\(908\) 53.8978i 0.0593588i
\(909\) −160.961 358.679i −0.177074 0.394587i
\(910\) 333.249 0.366207
\(911\) 662.881i 0.727641i 0.931469 + 0.363821i \(0.118528\pi\)
−0.931469 + 0.363821i \(0.881472\pi\)
\(912\) 283.081 60.6062i 0.310396 0.0664542i
\(913\) −1371.51 −1.50220
\(914\) 826.642i 0.904422i
\(915\) 143.263 + 669.155i 0.156571 + 0.731317i
\(916\) −536.339 −0.585523
\(917\) 1580.75i 1.72382i
\(918\) 480.660 352.472i 0.523595 0.383956i
\(919\) −1062.65 −1.15631 −0.578153 0.815928i \(-0.696226\pi\)
−0.578153 + 0.815928i \(0.696226\pi\)
\(920\) 156.166i 0.169745i
\(921\) 1335.29 285.878i 1.44982 0.310399i
\(922\) −258.888 −0.280790
\(923\) 358.352i 0.388247i
\(924\) −187.842 877.376i −0.203292 0.949541i
\(925\) −878.318 −0.949533
\(926\) 1063.63i 1.14863i
\(927\) −656.635 + 294.671i −0.708344 + 0.317876i
\(928\) 189.588 0.204298
\(929\) 584.511i 0.629183i −0.949227 0.314591i \(-0.898133\pi\)
0.949227 0.314591i \(-0.101867\pi\)
\(930\) −881.928 + 188.816i −0.948310 + 0.203028i
\(931\) −1034.00 −1.11063
\(932\) 614.741i 0.659593i
\(933\) 274.140 + 1280.46i 0.293827 + 1.37241i
\(934\) −65.5809 −0.0702151
\(935\) 1660.81i 1.77627i
\(936\) −37.5778 83.7371i −0.0401472 0.0894628i
\(937\) −779.887 −0.832323 −0.416162 0.909291i \(-0.636625\pi\)
−0.416162 + 0.909291i \(0.636625\pi\)
\(938\) 4.77440i 0.00508998i
\(939\) −562.984 + 120.532i −0.599557 + 0.128362i
\(940\) 89.3746 0.0950793
\(941\) 1016.41i 1.08013i −0.841622 0.540067i \(-0.818399\pi\)
0.841622 0.540067i \(-0.181601\pi\)
\(942\) 57.6426 + 269.239i 0.0611917 + 0.285816i
\(943\) 490.245 0.519878
\(944\) 193.663i 0.205151i
\(945\) 1043.49 + 1423.00i 1.10423 + 1.50582i
\(946\) 410.971 0.434430
\(947\) 360.349i 0.380516i −0.981734 0.190258i \(-0.939068\pi\)
0.981734 0.190258i \(-0.0609324\pi\)
\(948\) 302.074 64.6725i 0.318644 0.0682199i
\(949\) 342.347 0.360745
\(950\) 733.457i 0.772060i
\(951\) 150.558 + 703.230i 0.158315 + 0.739463i
\(952\) −423.166 −0.444502
\(953\) 733.168i 0.769327i −0.923057 0.384663i \(-0.874318\pi\)
0.923057 0.384663i \(-0.125682\pi\)
\(954\) 458.982 205.972i 0.481113 0.215904i
\(955\) 82.0604 0.0859272
\(956\) 789.568i 0.825907i
\(957\) 1534.01 328.423i 1.60294 0.343180i
\(958\) −478.565 −0.499546
\(959\) 463.702i 0.483527i
\(960\) 34.2612 + 160.028i 0.0356887 + 0.166696i
\(961\) 10.9052 0.0113477
\(962\) 208.325i 0.216554i
\(963\) −455.736 1015.55i −0.473246 1.05457i
\(964\) −8.88372 −0.00921547
\(965\) 1811.87i 1.87758i
\(966\) −321.953 + 68.9284i −0.333285 + 0.0713545i
\(967\) −841.679 −0.870402 −0.435201 0.900333i \(-0.643323\pi\)
−0.435201 + 0.900333i \(0.643323\pi\)
\(968\) 346.331i 0.357780i
\(969\) −236.515 1104.72i −0.244081 1.14006i
\(970\) −797.850 −0.822525
\(971\) 536.293i 0.552310i −0.961113 0.276155i \(-0.910940\pi\)
0.961113 0.276155i \(-0.0890604\pi\)
\(972\) 239.897 422.664i 0.246808 0.434840i
\(973\) 388.783 0.399571
\(974\) 147.972i 0.151922i
\(975\) −227.383 + 48.6816i −0.233214 + 0.0499298i
\(976\) −133.807 −0.137098
\(977\) 679.462i 0.695457i −0.937595 0.347729i \(-0.886953\pi\)
0.937595 0.347729i \(-0.113047\pi\)
\(978\) 262.484 + 1226.02i 0.268388 + 1.25359i
\(979\) 1689.93 1.72618
\(980\) 584.529i 0.596458i
\(981\) 351.438 157.711i 0.358245 0.160765i
\(982\) 289.736 0.295047
\(983\) 462.786i 0.470790i 0.971900 + 0.235395i \(0.0756383\pi\)
−0.971900 + 0.235395i \(0.924362\pi\)
\(984\) 502.370 107.555i 0.510539 0.109304i
\(985\) 2215.24 2.24897
\(986\) 739.866i 0.750371i
\(987\) 39.4482 + 184.256i 0.0399678 + 0.186683i
\(988\) −173.966 −0.176079
\(989\) 150.806i 0.152483i
\(990\) 554.432 + 1235.48i 0.560032 + 1.24796i
\(991\) −645.895 −0.651760 −0.325880 0.945411i \(-0.605661\pi\)
−0.325880 + 0.945411i \(0.605661\pi\)
\(992\) 176.355i 0.177777i
\(993\) 769.606 164.768i 0.775031 0.165930i
\(994\) −1347.16 −1.35529
\(995\) 1818.02i 1.82715i
\(996\) 110.413 + 515.722i 0.110857 + 0.517793i
\(997\) 761.944 0.764236 0.382118 0.924113i \(-0.375195\pi\)
0.382118 + 0.924113i \(0.375195\pi\)
\(998\) 564.151i 0.565282i
\(999\) −889.562 + 652.323i −0.890453 + 0.652976i
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 78.3.c.a.53.1 8
3.2 odd 2 inner 78.3.c.a.53.5 yes 8
4.3 odd 2 624.3.f.b.209.7 8
12.11 even 2 624.3.f.b.209.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.3.c.a.53.1 8 1.1 even 1 trivial
78.3.c.a.53.5 yes 8 3.2 odd 2 inner
624.3.f.b.209.7 8 4.3 odd 2
624.3.f.b.209.8 8 12.11 even 2