Properties

Label 300.5.c.b.151.5
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
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] = [300,5,Mod(151,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.151");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 300.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: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + \cdots + 4294967296 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.5
Root \(-1.06635 + 3.85524i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.b.151.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.80556 - 2.85111i) q^{2} -5.19615i q^{3} +(-0.257663 + 15.9979i) q^{4} +(-14.8148 + 14.5781i) q^{6} +63.6232i q^{7} +(46.3347 - 44.1485i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(-2.80556 - 2.85111i) q^{2} -5.19615i q^{3} +(-0.257663 + 15.9979i) q^{4} +(-14.8148 + 14.5781i) q^{6} +63.6232i q^{7} +(46.3347 - 44.1485i) q^{8} -27.0000 q^{9} -220.737i q^{11} +(83.1277 + 1.33886i) q^{12} -236.856 q^{13} +(181.397 - 178.499i) q^{14} +(-255.867 - 8.24415i) q^{16} +46.7414 q^{17} +(75.7501 + 76.9800i) q^{18} -195.899i q^{19} +330.596 q^{21} +(-629.345 + 619.291i) q^{22} +741.830i q^{23} +(-229.402 - 240.762i) q^{24} +(664.512 + 675.301i) q^{26} +140.296i q^{27} +(-1017.84 - 16.3934i) q^{28} +1059.06 q^{29} +1067.12i q^{31} +(694.346 + 752.635i) q^{32} -1146.98 q^{33} +(-131.136 - 133.265i) q^{34} +(6.95691 - 431.944i) q^{36} +2287.23 q^{37} +(-558.530 + 549.606i) q^{38} +1230.74i q^{39} -1141.57 q^{41} +(-927.506 - 942.565i) q^{42} +1245.24i q^{43} +(3531.33 + 56.8758i) q^{44} +(2115.04 - 2081.25i) q^{46} -406.719i q^{47} +(-42.8379 + 1329.53i) q^{48} -1646.91 q^{49} -242.875i q^{51} +(61.0290 - 3789.20i) q^{52} -1442.39 q^{53} +(400.000 - 393.609i) q^{54} +(2808.87 + 2947.96i) q^{56} -1017.92 q^{57} +(-2971.25 - 3019.49i) q^{58} +2472.02i q^{59} +4819.29 q^{61} +(3042.47 - 2993.86i) q^{62} -1717.83i q^{63} +(197.817 - 4091.22i) q^{64} +(3217.93 + 3270.17i) q^{66} +5792.14i q^{67} +(-12.0435 + 747.765i) q^{68} +3854.66 q^{69} -309.369i q^{71} +(-1251.04 + 1192.01i) q^{72} -996.733 q^{73} +(-6416.96 - 6521.15i) q^{74} +(3133.98 + 50.4759i) q^{76} +14044.0 q^{77} +(3508.97 - 3452.91i) q^{78} -1096.99i q^{79} +729.000 q^{81} +(3202.76 + 3254.76i) q^{82} +3097.31i q^{83} +(-85.1824 + 5288.85i) q^{84} +(3550.32 - 3493.60i) q^{86} -5503.02i q^{87} +(-9745.21 - 10227.8i) q^{88} +10965.3 q^{89} -15069.5i q^{91} +(-11867.7 - 191.142i) q^{92} +5544.91 q^{93} +(-1159.60 + 1141.07i) q^{94} +(3910.81 - 3607.93i) q^{96} +12339.0 q^{97} +(4620.50 + 4695.52i) q^{98} +5959.90i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} - 176 q^{13} + 78 q^{14} - 376 q^{16} + 162 q^{18} - 144 q^{21} + 788 q^{22} + 108 q^{24} + 678 q^{26} - 3368 q^{28} + 1728 q^{29} - 2016 q^{32} - 2932 q^{34} - 216 q^{36} + 1568 q^{37} + 6990 q^{38} + 1248 q^{41} - 162 q^{42} + 8088 q^{44} + 5956 q^{46} - 2088 q^{48} - 10720 q^{49} - 3128 q^{52} + 288 q^{53} - 486 q^{54} - 10236 q^{56} - 5616 q^{57} + 16164 q^{58} - 3760 q^{61} + 12714 q^{62} + 10544 q^{64} + 8100 q^{66} - 26136 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} - 17004 q^{74} - 28344 q^{76} - 768 q^{77} + 16830 q^{78} + 11664 q^{81} + 21280 q^{82} + 15120 q^{84} + 24414 q^{86} - 52840 q^{88} - 768 q^{89} - 23736 q^{92} + 9936 q^{93} - 45156 q^{94} - 11088 q^{96} - 7248 q^{97} + 58140 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.80556 2.85111i −0.701390 0.712778i
\(3\) 5.19615i 0.577350i
\(4\) −0.257663 + 15.9979i −0.0161040 + 0.999870i
\(5\) 0 0
\(6\) −14.8148 + 14.5781i −0.411522 + 0.404948i
\(7\) 63.6232i 1.29843i 0.760604 + 0.649216i \(0.224903\pi\)
−0.760604 + 0.649216i \(0.775097\pi\)
\(8\) 46.3347 44.1485i 0.723980 0.689821i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 220.737i 1.82427i −0.409888 0.912136i \(-0.634432\pi\)
0.409888 0.912136i \(-0.365568\pi\)
\(12\) 83.1277 + 1.33886i 0.577275 + 0.00929762i
\(13\) −236.856 −1.40151 −0.700756 0.713401i \(-0.747154\pi\)
−0.700756 + 0.713401i \(0.747154\pi\)
\(14\) 181.397 178.499i 0.925493 0.910707i
\(15\) 0 0
\(16\) −255.867 8.24415i −0.999481 0.0322037i
\(17\) 46.7414 0.161735 0.0808674 0.996725i \(-0.474231\pi\)
0.0808674 + 0.996725i \(0.474231\pi\)
\(18\) 75.7501 + 76.9800i 0.233797 + 0.237593i
\(19\) 195.899i 0.542656i −0.962487 0.271328i \(-0.912537\pi\)
0.962487 0.271328i \(-0.0874629\pi\)
\(20\) 0 0
\(21\) 330.596 0.749650
\(22\) −629.345 + 619.291i −1.30030 + 1.27953i
\(23\) 741.830i 1.40232i 0.713002 + 0.701162i \(0.247335\pi\)
−0.713002 + 0.701162i \(0.752665\pi\)
\(24\) −229.402 240.762i −0.398268 0.417990i
\(25\) 0 0
\(26\) 664.512 + 675.301i 0.983007 + 0.998966i
\(27\) 140.296i 0.192450i
\(28\) −1017.84 16.3934i −1.29826 0.0209099i
\(29\) 1059.06 1.25928 0.629641 0.776886i \(-0.283202\pi\)
0.629641 + 0.776886i \(0.283202\pi\)
\(30\) 0 0
\(31\) 1067.12i 1.11042i 0.831709 + 0.555212i \(0.187363\pi\)
−0.831709 + 0.555212i \(0.812637\pi\)
\(32\) 694.346 + 752.635i 0.678072 + 0.734995i
\(33\) −1146.98 −1.05324
\(34\) −131.136 133.265i −0.113439 0.115281i
\(35\) 0 0
\(36\) 6.95691 431.944i 0.00536798 0.333290i
\(37\) 2287.23 1.67073 0.835366 0.549695i \(-0.185256\pi\)
0.835366 + 0.549695i \(0.185256\pi\)
\(38\) −558.530 + 549.606i −0.386793 + 0.380614i
\(39\) 1230.74i 0.809163i
\(40\) 0 0
\(41\) −1141.57 −0.679105 −0.339552 0.940587i \(-0.610276\pi\)
−0.339552 + 0.940587i \(0.610276\pi\)
\(42\) −927.506 942.565i −0.525797 0.534334i
\(43\) 1245.24i 0.673468i 0.941600 + 0.336734i \(0.109322\pi\)
−0.941600 + 0.336734i \(0.890678\pi\)
\(44\) 3531.33 + 56.8758i 1.82404 + 0.0293780i
\(45\) 0 0
\(46\) 2115.04 2081.25i 0.999546 0.983577i
\(47\) 406.719i 0.184119i −0.995754 0.0920595i \(-0.970655\pi\)
0.995754 0.0920595i \(-0.0293450\pi\)
\(48\) −42.8379 + 1329.53i −0.0185928 + 0.577051i
\(49\) −1646.91 −0.685926
\(50\) 0 0
\(51\) 242.875i 0.0933777i
\(52\) 61.0290 3789.20i 0.0225699 1.40133i
\(53\) −1442.39 −0.513488 −0.256744 0.966479i \(-0.582650\pi\)
−0.256744 + 0.966479i \(0.582650\pi\)
\(54\) 400.000 393.609i 0.137174 0.134983i
\(55\) 0 0
\(56\) 2808.87 + 2947.96i 0.895685 + 0.940039i
\(57\) −1017.92 −0.313303
\(58\) −2971.25 3019.49i −0.883248 0.897588i
\(59\) 2472.02i 0.710147i 0.934838 + 0.355074i \(0.115544\pi\)
−0.934838 + 0.355074i \(0.884456\pi\)
\(60\) 0 0
\(61\) 4819.29 1.29516 0.647579 0.761998i \(-0.275781\pi\)
0.647579 + 0.761998i \(0.275781\pi\)
\(62\) 3042.47 2993.86i 0.791486 0.778841i
\(63\) 1717.83i 0.432811i
\(64\) 197.817 4091.22i 0.0482951 0.998833i
\(65\) 0 0
\(66\) 3217.93 + 3270.17i 0.738735 + 0.750729i
\(67\) 5792.14i 1.29030i 0.764057 + 0.645149i \(0.223205\pi\)
−0.764057 + 0.645149i \(0.776795\pi\)
\(68\) −12.0435 + 747.765i −0.00260457 + 0.161714i
\(69\) 3854.66 0.809633
\(70\) 0 0
\(71\) 309.369i 0.0613706i −0.999529 0.0306853i \(-0.990231\pi\)
0.999529 0.0306853i \(-0.00976897\pi\)
\(72\) −1251.04 + 1192.01i −0.241327 + 0.229940i
\(73\) −996.733 −0.187039 −0.0935197 0.995617i \(-0.529812\pi\)
−0.0935197 + 0.995617i \(0.529812\pi\)
\(74\) −6416.96 6521.15i −1.17183 1.19086i
\(75\) 0 0
\(76\) 3133.98 + 50.4759i 0.542586 + 0.00873891i
\(77\) 14044.0 2.36869
\(78\) 3508.97 3452.91i 0.576754 0.567539i
\(79\) 1096.99i 0.175772i −0.996131 0.0878860i \(-0.971989\pi\)
0.996131 0.0878860i \(-0.0280111\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) 3202.76 + 3254.76i 0.476317 + 0.484051i
\(83\) 3097.31i 0.449603i 0.974405 + 0.224801i \(0.0721733\pi\)
−0.974405 + 0.224801i \(0.927827\pi\)
\(84\) −85.1824 + 5288.85i −0.0120723 + 0.749553i
\(85\) 0 0
\(86\) 3550.32 3493.60i 0.480033 0.472364i
\(87\) 5503.02i 0.727047i
\(88\) −9745.21 10227.8i −1.25842 1.32074i
\(89\) 10965.3 1.38433 0.692167 0.721738i \(-0.256656\pi\)
0.692167 + 0.721738i \(0.256656\pi\)
\(90\) 0 0
\(91\) 15069.5i 1.81977i
\(92\) −11867.7 191.142i −1.40214 0.0225830i
\(93\) 5544.91 0.641104
\(94\) −1159.60 + 1141.07i −0.131236 + 0.129139i
\(95\) 0 0
\(96\) 3910.81 3607.93i 0.424350 0.391485i
\(97\) 12339.0 1.31140 0.655701 0.755020i \(-0.272373\pi\)
0.655701 + 0.755020i \(0.272373\pi\)
\(98\) 4620.50 + 4695.52i 0.481102 + 0.488913i
\(99\) 5959.90i 0.608091i
\(100\) 0 0
\(101\) 14918.3 1.46244 0.731219 0.682143i \(-0.238952\pi\)
0.731219 + 0.682143i \(0.238952\pi\)
\(102\) −692.464 + 681.401i −0.0665575 + 0.0654942i
\(103\) 10083.1i 0.950433i −0.879869 0.475216i \(-0.842370\pi\)
0.879869 0.475216i \(-0.157630\pi\)
\(104\) −10974.6 + 10456.8i −1.01467 + 0.966792i
\(105\) 0 0
\(106\) 4046.71 + 4112.41i 0.360155 + 0.366003i
\(107\) 18475.7i 1.61374i 0.590731 + 0.806869i \(0.298839\pi\)
−0.590731 + 0.806869i \(0.701161\pi\)
\(108\) −2244.45 36.1491i −0.192425 0.00309921i
\(109\) −676.882 −0.0569718 −0.0284859 0.999594i \(-0.509069\pi\)
−0.0284859 + 0.999594i \(0.509069\pi\)
\(110\) 0 0
\(111\) 11884.8i 0.964597i
\(112\) 524.519 16279.1i 0.0418144 1.29776i
\(113\) 5693.92 0.445917 0.222959 0.974828i \(-0.428429\pi\)
0.222959 + 0.974828i \(0.428429\pi\)
\(114\) 2855.84 + 2902.20i 0.219747 + 0.223315i
\(115\) 0 0
\(116\) −272.880 + 16942.7i −0.0202794 + 1.25912i
\(117\) 6395.10 0.467171
\(118\) 7048.01 6935.41i 0.506177 0.498090i
\(119\) 2973.83i 0.210002i
\(120\) 0 0
\(121\) −34083.8 −2.32797
\(122\) −13520.8 13740.3i −0.908412 0.923160i
\(123\) 5931.80i 0.392081i
\(124\) −17071.7 274.957i −1.11028 0.0178822i
\(125\) 0 0
\(126\) −4897.71 + 4819.46i −0.308498 + 0.303569i
\(127\) 21834.4i 1.35374i 0.736103 + 0.676869i \(0.236664\pi\)
−0.736103 + 0.676869i \(0.763336\pi\)
\(128\) −12219.5 + 10914.2i −0.745820 + 0.666148i
\(129\) 6470.47 0.388827
\(130\) 0 0
\(131\) 6919.28i 0.403198i 0.979468 + 0.201599i \(0.0646138\pi\)
−0.979468 + 0.201599i \(0.935386\pi\)
\(132\) 295.535 18349.3i 0.0169614 1.05311i
\(133\) 12463.7 0.704602
\(134\) 16514.0 16250.2i 0.919695 0.905002i
\(135\) 0 0
\(136\) 2165.75 2063.56i 0.117093 0.111568i
\(137\) −24619.2 −1.31169 −0.655846 0.754895i \(-0.727688\pi\)
−0.655846 + 0.754895i \(0.727688\pi\)
\(138\) −10814.5 10990.1i −0.567868 0.577088i
\(139\) 18767.2i 0.971336i 0.874143 + 0.485668i \(0.161424\pi\)
−0.874143 + 0.485668i \(0.838576\pi\)
\(140\) 0 0
\(141\) −2113.37 −0.106301
\(142\) −882.046 + 867.954i −0.0437436 + 0.0430447i
\(143\) 52282.8i 2.55674i
\(144\) 6908.41 + 222.592i 0.333160 + 0.0107346i
\(145\) 0 0
\(146\) 2796.39 + 2841.80i 0.131188 + 0.133318i
\(147\) 8557.59i 0.396020i
\(148\) −589.335 + 36590.9i −0.0269054 + 1.67051i
\(149\) 6573.00 0.296068 0.148034 0.988982i \(-0.452706\pi\)
0.148034 + 0.988982i \(0.452706\pi\)
\(150\) 0 0
\(151\) 7823.28i 0.343111i 0.985174 + 0.171556i \(0.0548793\pi\)
−0.985174 + 0.171556i \(0.945121\pi\)
\(152\) −8648.65 9076.93i −0.374335 0.392873i
\(153\) −1262.02 −0.0539116
\(154\) −39401.2 40041.0i −1.66138 1.68835i
\(155\) 0 0
\(156\) −19689.2 317.116i −0.809058 0.0130307i
\(157\) 9202.59 0.373346 0.186673 0.982422i \(-0.440230\pi\)
0.186673 + 0.982422i \(0.440230\pi\)
\(158\) −3127.65 + 3077.68i −0.125286 + 0.123285i
\(159\) 7494.87i 0.296462i
\(160\) 0 0
\(161\) −47197.6 −1.82082
\(162\) −2045.25 2078.46i −0.0779322 0.0791975i
\(163\) 43667.2i 1.64354i −0.569820 0.821769i \(-0.692987\pi\)
0.569820 0.821769i \(-0.307013\pi\)
\(164\) 294.142 18262.8i 0.0109363 0.679017i
\(165\) 0 0
\(166\) 8830.78 8689.70i 0.320467 0.315347i
\(167\) 19662.7i 0.705034i 0.935805 + 0.352517i \(0.114674\pi\)
−0.935805 + 0.352517i \(0.885326\pi\)
\(168\) 15318.1 14595.3i 0.542732 0.517124i
\(169\) 27539.5 0.964236
\(170\) 0 0
\(171\) 5289.27i 0.180885i
\(172\) −19921.3 320.853i −0.673381 0.0108455i
\(173\) 31871.9 1.06492 0.532459 0.846456i \(-0.321268\pi\)
0.532459 + 0.846456i \(0.321268\pi\)
\(174\) −15689.7 + 15439.1i −0.518223 + 0.509944i
\(175\) 0 0
\(176\) −1819.79 + 56479.3i −0.0587484 + 1.82333i
\(177\) 12845.0 0.410004
\(178\) −30763.8 31263.3i −0.970958 0.986722i
\(179\) 52843.2i 1.64924i −0.565689 0.824619i \(-0.691390\pi\)
0.565689 0.824619i \(-0.308610\pi\)
\(180\) 0 0
\(181\) −63045.0 −1.92439 −0.962197 0.272356i \(-0.912197\pi\)
−0.962197 + 0.272356i \(0.912197\pi\)
\(182\) −42964.8 + 42278.4i −1.29709 + 1.27637i
\(183\) 25041.7i 0.747760i
\(184\) 32750.7 + 34372.5i 0.967352 + 1.01526i
\(185\) 0 0
\(186\) −15556.6 15809.1i −0.449664 0.456964i
\(187\) 10317.5i 0.295048i
\(188\) 6506.66 + 104.796i 0.184095 + 0.00296504i
\(189\) −8926.08 −0.249883
\(190\) 0 0
\(191\) 20730.2i 0.568246i −0.958788 0.284123i \(-0.908298\pi\)
0.958788 0.284123i \(-0.0917024\pi\)
\(192\) −21258.6 1027.89i −0.576677 0.0278832i
\(193\) −17567.6 −0.471627 −0.235813 0.971798i \(-0.575775\pi\)
−0.235813 + 0.971798i \(0.575775\pi\)
\(194\) −34617.8 35179.8i −0.919805 0.934739i
\(195\) 0 0
\(196\) 424.348 26347.1i 0.0110461 0.685837i
\(197\) 50800.9 1.30900 0.654499 0.756063i \(-0.272880\pi\)
0.654499 + 0.756063i \(0.272880\pi\)
\(198\) 16992.3 16720.8i 0.433433 0.426509i
\(199\) 32141.3i 0.811629i 0.913955 + 0.405814i \(0.133012\pi\)
−0.913955 + 0.405814i \(0.866988\pi\)
\(200\) 0 0
\(201\) 30096.9 0.744953
\(202\) −41854.3 42533.8i −1.02574 1.04239i
\(203\) 67380.5i 1.63509i
\(204\) 3885.50 + 62.5800i 0.0933656 + 0.00150375i
\(205\) 0 0
\(206\) −28748.1 + 28288.9i −0.677447 + 0.666624i
\(207\) 20029.4i 0.467442i
\(208\) 60603.6 + 1952.67i 1.40079 + 0.0451339i
\(209\) −43242.1 −0.989953
\(210\) 0 0
\(211\) 9541.34i 0.214311i −0.994242 0.107156i \(-0.965826\pi\)
0.994242 0.107156i \(-0.0341743\pi\)
\(212\) 371.650 23075.2i 0.00826919 0.513421i
\(213\) −1607.53 −0.0354323
\(214\) 52676.2 51834.6i 1.15024 1.13186i
\(215\) 0 0
\(216\) 6193.87 + 6500.58i 0.132756 + 0.139330i
\(217\) −67893.4 −1.44181
\(218\) 1899.03 + 1929.86i 0.0399594 + 0.0406082i
\(219\) 5179.18i 0.107987i
\(220\) 0 0
\(221\) −11071.0 −0.226673
\(222\) −33884.9 + 33343.5i −0.687543 + 0.676559i
\(223\) 33469.4i 0.673037i 0.941677 + 0.336518i \(0.109249\pi\)
−0.941677 + 0.336518i \(0.890751\pi\)
\(224\) −47885.0 + 44176.5i −0.954342 + 0.880431i
\(225\) 0 0
\(226\) −15974.6 16234.0i −0.312762 0.317840i
\(227\) 1149.27i 0.0223033i 0.999938 + 0.0111517i \(0.00354976\pi\)
−0.999938 + 0.0111517i \(0.996450\pi\)
\(228\) 262.281 16284.6i 0.00504541 0.313262i
\(229\) −49392.2 −0.941863 −0.470931 0.882170i \(-0.656082\pi\)
−0.470931 + 0.882170i \(0.656082\pi\)
\(230\) 0 0
\(231\) 72974.7i 1.36757i
\(232\) 49071.1 46755.8i 0.911696 0.868679i
\(233\) −42084.0 −0.775184 −0.387592 0.921831i \(-0.626693\pi\)
−0.387592 + 0.921831i \(0.626693\pi\)
\(234\) −17941.8 18233.1i −0.327669 0.332989i
\(235\) 0 0
\(236\) −39547.2 636.949i −0.710055 0.0114362i
\(237\) −5700.14 −0.101482
\(238\) 8478.73 8343.27i 0.149685 0.147293i
\(239\) 34540.4i 0.604689i 0.953199 + 0.302345i \(0.0977693\pi\)
−0.953199 + 0.302345i \(0.902231\pi\)
\(240\) 0 0
\(241\) 68666.9 1.18226 0.591131 0.806576i \(-0.298682\pi\)
0.591131 + 0.806576i \(0.298682\pi\)
\(242\) 95624.1 + 97176.6i 1.63281 + 1.65932i
\(243\) 3788.00i 0.0641500i
\(244\) −1241.75 + 77098.6i −0.0208572 + 1.29499i
\(245\) 0 0
\(246\) 16912.2 16642.0i 0.279467 0.275002i
\(247\) 46399.7i 0.760539i
\(248\) 47111.7 + 49444.6i 0.765994 + 0.803925i
\(249\) 16094.1 0.259578
\(250\) 0 0
\(251\) 62003.3i 0.984163i 0.870549 + 0.492082i \(0.163764\pi\)
−0.870549 + 0.492082i \(0.836236\pi\)
\(252\) 27481.6 + 442.621i 0.432755 + 0.00696996i
\(253\) 163749. 2.55822
\(254\) 62252.4 61257.9i 0.964914 0.949499i
\(255\) 0 0
\(256\) 65400.1 + 4218.82i 0.997926 + 0.0643740i
\(257\) 65977.4 0.998916 0.499458 0.866338i \(-0.333532\pi\)
0.499458 + 0.866338i \(0.333532\pi\)
\(258\) −18153.3 18448.0i −0.272719 0.277147i
\(259\) 145521.i 2.16933i
\(260\) 0 0
\(261\) −28594.5 −0.419761
\(262\) 19727.6 19412.5i 0.287391 0.282799i
\(263\) 45889.4i 0.663439i −0.943378 0.331719i \(-0.892371\pi\)
0.943378 0.331719i \(-0.107629\pi\)
\(264\) −53145.1 + 50637.6i −0.762528 + 0.726549i
\(265\) 0 0
\(266\) −34967.7 35535.4i −0.494201 0.502225i
\(267\) 56977.4i 0.799245i
\(268\) −92662.3 1492.42i −1.29013 0.0207789i
\(269\) 66600.2 0.920388 0.460194 0.887818i \(-0.347780\pi\)
0.460194 + 0.887818i \(0.347780\pi\)
\(270\) 0 0
\(271\) 107846.i 1.46848i 0.678892 + 0.734239i \(0.262461\pi\)
−0.678892 + 0.734239i \(0.737539\pi\)
\(272\) −11959.6 385.343i −0.161651 0.00520847i
\(273\) −78303.4 −1.05064
\(274\) 69070.5 + 70191.9i 0.920008 + 0.934945i
\(275\) 0 0
\(276\) −993.204 + 61666.6i −0.0130383 + 0.809528i
\(277\) −76120.9 −0.992074 −0.496037 0.868301i \(-0.665212\pi\)
−0.496037 + 0.868301i \(0.665212\pi\)
\(278\) 53507.3 52652.5i 0.692347 0.681286i
\(279\) 28812.2i 0.370141i
\(280\) 0 0
\(281\) 127936. 1.62024 0.810120 0.586264i \(-0.199402\pi\)
0.810120 + 0.586264i \(0.199402\pi\)
\(282\) 5929.19 + 6025.46i 0.0745586 + 0.0757691i
\(283\) 117792.i 1.47076i −0.677655 0.735380i \(-0.737004\pi\)
0.677655 0.735380i \(-0.262996\pi\)
\(284\) 4949.27 + 79.7131i 0.0613627 + 0.000988310i
\(285\) 0 0
\(286\) 149064. 146682.i 1.82239 1.79327i
\(287\) 72630.6i 0.881771i
\(288\) −18747.3 20321.2i −0.226024 0.244998i
\(289\) −81336.2 −0.973842
\(290\) 0 0
\(291\) 64115.3i 0.757139i
\(292\) 256.821 15945.7i 0.00301207 0.187015i
\(293\) −120518. −1.40384 −0.701918 0.712258i \(-0.747673\pi\)
−0.701918 + 0.712258i \(0.747673\pi\)
\(294\) 24398.6 24008.8i 0.282274 0.277764i
\(295\) 0 0
\(296\) 105978. 100978.i 1.20958 1.15250i
\(297\) 30968.5 0.351081
\(298\) −18441.0 18740.4i −0.207659 0.211031i
\(299\) 175706.i 1.96537i
\(300\) 0 0
\(301\) −79226.3 −0.874453
\(302\) 22305.0 21948.7i 0.244562 0.240655i
\(303\) 77517.9i 0.844339i
\(304\) −1615.02 + 50124.1i −0.0174756 + 0.542375i
\(305\) 0 0
\(306\) 3540.67 + 3598.15i 0.0378131 + 0.0384270i
\(307\) 90003.1i 0.954950i −0.878645 0.477475i \(-0.841552\pi\)
0.878645 0.477475i \(-0.158448\pi\)
\(308\) −3618.62 + 224675.i −0.0381453 + 2.36839i
\(309\) −52393.5 −0.548732
\(310\) 0 0
\(311\) 35944.1i 0.371627i −0.982585 0.185813i \(-0.940508\pi\)
0.982585 0.185813i \(-0.0594920\pi\)
\(312\) 54335.2 + 57025.9i 0.558178 + 0.585818i
\(313\) 10420.7 0.106368 0.0531838 0.998585i \(-0.483063\pi\)
0.0531838 + 0.998585i \(0.483063\pi\)
\(314\) −25818.4 26237.6i −0.261861 0.266112i
\(315\) 0 0
\(316\) 17549.6 + 282.655i 0.175749 + 0.00283062i
\(317\) −44276.9 −0.440614 −0.220307 0.975431i \(-0.570706\pi\)
−0.220307 + 0.975431i \(0.570706\pi\)
\(318\) 21368.7 21027.3i 0.211312 0.207936i
\(319\) 233773.i 2.29727i
\(320\) 0 0
\(321\) 96002.4 0.931692
\(322\) 132416. + 134565.i 1.27711 + 1.29784i
\(323\) 9156.59i 0.0877664i
\(324\) −187.836 + 11662.5i −0.00178933 + 0.111097i
\(325\) 0 0
\(326\) −124500. + 122511.i −1.17148 + 1.15276i
\(327\) 3517.18i 0.0328927i
\(328\) −52894.6 + 50398.8i −0.491658 + 0.468460i
\(329\) 25876.7 0.239066
\(330\) 0 0
\(331\) 219017.i 1.99904i 0.0309493 + 0.999521i \(0.490147\pi\)
−0.0309493 + 0.999521i \(0.509853\pi\)
\(332\) −49550.6 798.064i −0.449544 0.00724038i
\(333\) −61755.2 −0.556910
\(334\) 56060.5 55164.9i 0.502533 0.494504i
\(335\) 0 0
\(336\) −84588.6 2725.48i −0.749261 0.0241415i
\(337\) −51173.5 −0.450594 −0.225297 0.974290i \(-0.572335\pi\)
−0.225297 + 0.974290i \(0.572335\pi\)
\(338\) −77263.9 78518.3i −0.676306 0.687286i
\(339\) 29586.5i 0.257450i
\(340\) 0 0
\(341\) 235552. 2.02572
\(342\) 15080.3 14839.4i 0.128931 0.126871i
\(343\) 47977.7i 0.407804i
\(344\) 54975.6 + 57698.0i 0.464572 + 0.487578i
\(345\) 0 0
\(346\) −89418.7 90870.4i −0.746923 0.759050i
\(347\) 78897.6i 0.655247i 0.944808 + 0.327623i \(0.106248\pi\)
−0.944808 + 0.327623i \(0.893752\pi\)
\(348\) 88036.9 + 1417.93i 0.726953 + 0.0117083i
\(349\) 187086. 1.53599 0.767997 0.640454i \(-0.221254\pi\)
0.767997 + 0.640454i \(0.221254\pi\)
\(350\) 0 0
\(351\) 33229.9i 0.269721i
\(352\) 166134. 153268.i 1.34083 1.23699i
\(353\) −26576.3 −0.213278 −0.106639 0.994298i \(-0.534009\pi\)
−0.106639 + 0.994298i \(0.534009\pi\)
\(354\) −36037.4 36622.5i −0.287573 0.292242i
\(355\) 0 0
\(356\) −2825.36 + 175422.i −0.0222932 + 1.38415i
\(357\) 15452.5 0.121245
\(358\) −150662. + 148255.i −1.17554 + 1.15676i
\(359\) 13211.6i 0.102510i −0.998686 0.0512552i \(-0.983678\pi\)
0.998686 0.0512552i \(-0.0163222\pi\)
\(360\) 0 0
\(361\) 91944.6 0.705524
\(362\) 176877. + 179748.i 1.34975 + 1.37166i
\(363\) 177105.i 1.34405i
\(364\) 241081. + 3882.86i 1.81953 + 0.0293055i
\(365\) 0 0
\(366\) −71396.8 + 70256.1i −0.532987 + 0.524472i
\(367\) 46921.2i 0.348367i −0.984713 0.174184i \(-0.944271\pi\)
0.984713 0.174184i \(-0.0557286\pi\)
\(368\) 6115.76 189810.i 0.0451601 1.40160i
\(369\) 30822.5 0.226368
\(370\) 0 0
\(371\) 91769.3i 0.666729i
\(372\) −1428.72 + 88707.0i −0.0103243 + 0.641021i
\(373\) −237489. −1.70697 −0.853487 0.521115i \(-0.825516\pi\)
−0.853487 + 0.521115i \(0.825516\pi\)
\(374\) −29416.5 + 28946.5i −0.210304 + 0.206944i
\(375\) 0 0
\(376\) −17956.0 18845.2i −0.127009 0.133299i
\(377\) −250843. −1.76490
\(378\) 25042.7 + 25449.3i 0.175266 + 0.178111i
\(379\) 108145.i 0.752885i 0.926440 + 0.376442i \(0.122853\pi\)
−0.926440 + 0.376442i \(0.877147\pi\)
\(380\) 0 0
\(381\) 113455. 0.781581
\(382\) −59104.0 + 58159.8i −0.405033 + 0.398562i
\(383\) 143109.i 0.975594i 0.872957 + 0.487797i \(0.162199\pi\)
−0.872957 + 0.487797i \(0.837801\pi\)
\(384\) 56711.7 + 63494.4i 0.384601 + 0.430599i
\(385\) 0 0
\(386\) 49287.0 + 50087.3i 0.330794 + 0.336165i
\(387\) 33621.6i 0.224489i
\(388\) −3179.30 + 197398.i −0.0211188 + 1.31123i
\(389\) −132061. −0.872720 −0.436360 0.899772i \(-0.643733\pi\)
−0.436360 + 0.899772i \(0.643733\pi\)
\(390\) 0 0
\(391\) 34674.1i 0.226805i
\(392\) −76309.1 + 72708.6i −0.496597 + 0.473166i
\(393\) 35953.6 0.232787
\(394\) −142525. 144839.i −0.918118 0.933024i
\(395\) 0 0
\(396\) −95346.0 1535.65i −0.608012 0.00979266i
\(397\) −46139.3 −0.292745 −0.146373 0.989230i \(-0.546760\pi\)
−0.146373 + 0.989230i \(0.546760\pi\)
\(398\) 91638.5 90174.4i 0.578511 0.569269i
\(399\) 64763.3i 0.406802i
\(400\) 0 0
\(401\) 3244.97 0.0201800 0.0100900 0.999949i \(-0.496788\pi\)
0.0100900 + 0.999949i \(0.496788\pi\)
\(402\) −84438.6 85809.5i −0.522503 0.530986i
\(403\) 252753.i 1.55627i
\(404\) −3843.90 + 238662.i −0.0235510 + 1.46225i
\(405\) 0 0
\(406\) 192109. 189040.i 1.16546 1.14684i
\(407\) 504876.i 3.04787i
\(408\) −10722.6 11253.6i −0.0644138 0.0676036i
\(409\) −190227. −1.13717 −0.568585 0.822625i \(-0.692509\pi\)
−0.568585 + 0.822625i \(0.692509\pi\)
\(410\) 0 0
\(411\) 127925.i 0.757306i
\(412\) 161309. + 2598.05i 0.950309 + 0.0153057i
\(413\) −157278. −0.922078
\(414\) −57106.0 + 56193.7i −0.333182 + 0.327859i
\(415\) 0 0
\(416\) −164460. 178266.i −0.950326 1.03010i
\(417\) 97517.2 0.560801
\(418\) 121318. + 123288.i 0.694343 + 0.705616i
\(419\) 38663.2i 0.220226i −0.993919 0.110113i \(-0.964879\pi\)
0.993919 0.110113i \(-0.0351213\pi\)
\(420\) 0 0
\(421\) −215220. −1.21428 −0.607140 0.794595i \(-0.707683\pi\)
−0.607140 + 0.794595i \(0.707683\pi\)
\(422\) −27203.4 + 26768.8i −0.152756 + 0.150316i
\(423\) 10981.4i 0.0613730i
\(424\) −66832.7 + 63679.3i −0.371755 + 0.354215i
\(425\) 0 0
\(426\) 4510.02 + 4583.25i 0.0248519 + 0.0252554i
\(427\) 306618.i 1.68168i
\(428\) −295572. 4760.50i −1.61353 0.0259875i
\(429\) 271669. 1.47613
\(430\) 0 0
\(431\) 12832.4i 0.0690804i −0.999403 0.0345402i \(-0.989003\pi\)
0.999403 0.0345402i \(-0.0109967\pi\)
\(432\) 1156.62 35897.2i 0.00619761 0.192350i
\(433\) 245264. 1.30815 0.654076 0.756429i \(-0.273058\pi\)
0.654076 + 0.756429i \(0.273058\pi\)
\(434\) 190479. + 193572.i 1.01127 + 1.02769i
\(435\) 0 0
\(436\) 174.408 10828.7i 0.000917471 0.0569644i
\(437\) 145324. 0.760980
\(438\) 14766.4 14530.5i 0.0769709 0.0757412i
\(439\) 8320.58i 0.0431742i 0.999767 + 0.0215871i \(0.00687192\pi\)
−0.999767 + 0.0215871i \(0.993128\pi\)
\(440\) 0 0
\(441\) 44466.5 0.228642
\(442\) 31060.2 + 31564.5i 0.158986 + 0.161568i
\(443\) 141239.i 0.719695i −0.933011 0.359847i \(-0.882829\pi\)
0.933011 0.359847i \(-0.117171\pi\)
\(444\) 190132. + 3062.28i 0.964472 + 0.0155338i
\(445\) 0 0
\(446\) 95425.1 93900.6i 0.479726 0.472061i
\(447\) 34154.3i 0.170935i
\(448\) 260296. + 12585.7i 1.29692 + 0.0627080i
\(449\) −197626. −0.980282 −0.490141 0.871643i \(-0.663055\pi\)
−0.490141 + 0.871643i \(0.663055\pi\)
\(450\) 0 0
\(451\) 251988.i 1.23887i
\(452\) −1467.11 + 91090.9i −0.00718103 + 0.445859i
\(453\) 40651.0 0.198095
\(454\) 3276.69 3224.34i 0.0158973 0.0156433i
\(455\) 0 0
\(456\) −47165.1 + 44939.7i −0.226825 + 0.216123i
\(457\) −331333. −1.58647 −0.793236 0.608915i \(-0.791605\pi\)
−0.793236 + 0.608915i \(0.791605\pi\)
\(458\) 138573. + 140823.i 0.660613 + 0.671339i
\(459\) 6557.63i 0.0311259i
\(460\) 0 0
\(461\) −196090. −0.922687 −0.461343 0.887222i \(-0.652632\pi\)
−0.461343 + 0.887222i \(0.652632\pi\)
\(462\) −208059. + 204735.i −0.974770 + 0.959197i
\(463\) 168744.i 0.787164i −0.919289 0.393582i \(-0.871236\pi\)
0.919289 0.393582i \(-0.128764\pi\)
\(464\) −270978. 8731.03i −1.25863 0.0405536i
\(465\) 0 0
\(466\) 118069. + 119986.i 0.543706 + 0.552534i
\(467\) 58203.8i 0.266881i 0.991057 + 0.133440i \(0.0426025\pi\)
−0.991057 + 0.133440i \(0.957398\pi\)
\(468\) −1647.78 + 102308.i −0.00752329 + 0.467110i
\(469\) −368515. −1.67536
\(470\) 0 0
\(471\) 47818.1i 0.215551i
\(472\) 109136. + 114541.i 0.489874 + 0.514133i
\(473\) 274871. 1.22859
\(474\) 15992.1 + 16251.7i 0.0711785 + 0.0723341i
\(475\) 0 0
\(476\) −47575.2 766.248i −0.209975 0.00338186i
\(477\) 38944.5 0.171163
\(478\) 98478.6 96905.3i 0.431009 0.424123i
\(479\) 221700.i 0.966260i 0.875549 + 0.483130i \(0.160500\pi\)
−0.875549 + 0.483130i \(0.839500\pi\)
\(480\) 0 0
\(481\) −541743. −2.34155
\(482\) −192649. 195777.i −0.829227 0.842690i
\(483\) 245246.i 1.05125i
\(484\) 8782.14 545270.i 0.0374895 2.32767i
\(485\) 0 0
\(486\) −10800.0 + 10627.4i −0.0457247 + 0.0449942i
\(487\) 145571.i 0.613788i 0.951744 + 0.306894i \(0.0992897\pi\)
−0.951744 + 0.306894i \(0.900710\pi\)
\(488\) 223300. 212764.i 0.937670 0.893427i
\(489\) −226901. −0.948897
\(490\) 0 0
\(491\) 244597.i 1.01458i −0.861774 0.507292i \(-0.830646\pi\)
0.861774 0.507292i \(-0.169354\pi\)
\(492\) −94896.4 1528.41i −0.392030 0.00631406i
\(493\) 49501.8 0.203670
\(494\) 132291. 130177.i 0.542095 0.533435i
\(495\) 0 0
\(496\) 8797.48 273040.i 0.0357598 1.10985i
\(497\) 19683.1 0.0796856
\(498\) −45153.0 45886.1i −0.182066 0.185022i
\(499\) 113422.i 0.455507i 0.973719 + 0.227754i \(0.0731381\pi\)
−0.973719 + 0.227754i \(0.926862\pi\)
\(500\) 0 0
\(501\) 102170. 0.407052
\(502\) 176778. 173954.i 0.701490 0.690282i
\(503\) 135516.i 0.535616i −0.963472 0.267808i \(-0.913701\pi\)
0.963472 0.267808i \(-0.0862993\pi\)
\(504\) −75839.5 79595.0i −0.298562 0.313346i
\(505\) 0 0
\(506\) −459408. 466867.i −1.79431 1.82344i
\(507\) 143100.i 0.556702i
\(508\) −349306. 5625.93i −1.35356 0.0218005i
\(509\) 393520. 1.51891 0.759454 0.650561i \(-0.225466\pi\)
0.759454 + 0.650561i \(0.225466\pi\)
\(510\) 0 0
\(511\) 63415.3i 0.242858i
\(512\) −171456. 198299.i −0.654051 0.756451i
\(513\) 27483.9 0.104434
\(514\) −185104. 188109.i −0.700630 0.712005i
\(515\) 0 0
\(516\) −1667.20 + 103514.i −0.00626165 + 0.388777i
\(517\) −89777.9 −0.335883
\(518\) 414896. 408268.i 1.54625 1.52155i
\(519\) 165611.i 0.614831i
\(520\) 0 0
\(521\) 309126. 1.13883 0.569416 0.822049i \(-0.307169\pi\)
0.569416 + 0.822049i \(0.307169\pi\)
\(522\) 80223.7 + 81526.2i 0.294416 + 0.299196i
\(523\) 49369.3i 0.180490i 0.995920 + 0.0902452i \(0.0287651\pi\)
−0.995920 + 0.0902452i \(0.971235\pi\)
\(524\) −110694. 1782.84i −0.403146 0.00649308i
\(525\) 0 0
\(526\) −130836. + 128745.i −0.472884 + 0.465329i
\(527\) 49878.6i 0.179594i
\(528\) 293475. + 9455.90i 1.05270 + 0.0339184i
\(529\) −270470. −0.966514
\(530\) 0 0
\(531\) 66744.6i 0.236716i
\(532\) −3211.44 + 199394.i −0.0113469 + 0.704511i
\(533\) 270388. 0.951773
\(534\) −162449. + 159854.i −0.569684 + 0.560583i
\(535\) 0 0
\(536\) 255715. + 268377.i 0.890073 + 0.934150i
\(537\) −274581. −0.952188
\(538\) −186851. 189885.i −0.645551 0.656032i
\(539\) 363533.i 1.25132i
\(540\) 0 0
\(541\) −102454. −0.350053 −0.175027 0.984564i \(-0.556001\pi\)
−0.175027 + 0.984564i \(0.556001\pi\)
\(542\) 307482. 302570.i 1.04670 1.02998i
\(543\) 327592.i 1.11105i
\(544\) 32454.7 + 35179.2i 0.109668 + 0.118874i
\(545\) 0 0
\(546\) 219685. + 223252.i 0.736911 + 0.748875i
\(547\) 66168.6i 0.221145i −0.993868 0.110573i \(-0.964732\pi\)
0.993868 0.110573i \(-0.0352685\pi\)
\(548\) 6343.45 393855.i 0.0211234 1.31152i
\(549\) −130121. −0.431720
\(550\) 0 0
\(551\) 207468.i 0.683358i
\(552\) 178605. 170178.i 0.586158 0.558501i
\(553\) 69794.2 0.228228
\(554\) 213562. + 217029.i 0.695831 + 0.707128i
\(555\) 0 0
\(556\) −300236. 4835.61i −0.971210 0.0156424i
\(557\) 344220. 1.10950 0.554749 0.832018i \(-0.312814\pi\)
0.554749 + 0.832018i \(0.312814\pi\)
\(558\) −82146.7 + 80834.3i −0.263829 + 0.259614i
\(559\) 294943.i 0.943874i
\(560\) 0 0
\(561\) −53611.6 −0.170346
\(562\) −358931. 364759.i −1.13642 1.15487i
\(563\) 581940.i 1.83595i −0.396637 0.917976i \(-0.629823\pi\)
0.396637 0.917976i \(-0.370177\pi\)
\(564\) 544.538 33809.6i 0.00171187 0.106287i
\(565\) 0 0
\(566\) −335837. + 330472.i −1.04833 + 1.03158i
\(567\) 46381.3i 0.144270i
\(568\) −13658.2 14334.5i −0.0423347 0.0444311i
\(569\) 269874. 0.833559 0.416779 0.909008i \(-0.363159\pi\)
0.416779 + 0.909008i \(0.363159\pi\)
\(570\) 0 0
\(571\) 248959.i 0.763581i 0.924249 + 0.381790i \(0.124692\pi\)
−0.924249 + 0.381790i \(0.875308\pi\)
\(572\) −836416. 13471.3i −2.55641 0.0411736i
\(573\) −107717. −0.328077
\(574\) −207078. + 203770.i −0.628507 + 0.618466i
\(575\) 0 0
\(576\) −5341.06 + 110463.i −0.0160984 + 0.332944i
\(577\) 389168. 1.16892 0.584461 0.811422i \(-0.301306\pi\)
0.584461 + 0.811422i \(0.301306\pi\)
\(578\) 228194. + 231899.i 0.683043 + 0.694133i
\(579\) 91284.1i 0.272294i
\(580\) 0 0
\(581\) −197061. −0.583779
\(582\) −182800. + 179879.i −0.539672 + 0.531050i
\(583\) 318388.i 0.936742i
\(584\) −46183.4 + 44004.3i −0.135413 + 0.129024i
\(585\) 0 0
\(586\) 338120. + 343610.i 0.984636 + 1.00062i
\(587\) 67273.5i 0.195240i −0.995224 0.0976198i \(-0.968877\pi\)
0.995224 0.0976198i \(-0.0311229\pi\)
\(588\) −136904. 2204.98i −0.395968 0.00637748i
\(589\) 209047. 0.602579
\(590\) 0 0
\(591\) 263969.i 0.755750i
\(592\) −585227. 18856.3i −1.66986 0.0538038i
\(593\) −483157. −1.37398 −0.686988 0.726669i \(-0.741067\pi\)
−0.686988 + 0.726669i \(0.741067\pi\)
\(594\) −86884.1 88294.7i −0.246245 0.250243i
\(595\) 0 0
\(596\) −1693.62 + 105154.i −0.00476786 + 0.296029i
\(597\) 167011. 0.468594
\(598\) −500959. + 492955.i −1.40088 + 1.37849i
\(599\) 361016.i 1.00617i 0.864236 + 0.503086i \(0.167802\pi\)
−0.864236 + 0.503086i \(0.832198\pi\)
\(600\) 0 0
\(601\) −329300. −0.911681 −0.455841 0.890061i \(-0.650661\pi\)
−0.455841 + 0.890061i \(0.650661\pi\)
\(602\) 222274. + 225883.i 0.613333 + 0.623290i
\(603\) 156388.i 0.430099i
\(604\) −125156. 2015.77i −0.343067 0.00552545i
\(605\) 0 0
\(606\) −221012. + 217481.i −0.601826 + 0.592211i
\(607\) 347112.i 0.942090i 0.882109 + 0.471045i \(0.156123\pi\)
−0.882109 + 0.471045i \(0.843877\pi\)
\(608\) 147440. 136022.i 0.398850 0.367960i
\(609\) 350120. 0.944021
\(610\) 0 0
\(611\) 96333.6i 0.258045i
\(612\) 325.175 20189.7i 0.000868190 0.0539046i
\(613\) 315831. 0.840492 0.420246 0.907410i \(-0.361944\pi\)
0.420246 + 0.907410i \(0.361944\pi\)
\(614\) −256609. + 252509.i −0.680667 + 0.669792i
\(615\) 0 0
\(616\) 650724. 620021.i 1.71489 1.63397i
\(617\) 302237. 0.793920 0.396960 0.917836i \(-0.370065\pi\)
0.396960 + 0.917836i \(0.370065\pi\)
\(618\) 146993. + 149380.i 0.384876 + 0.391124i
\(619\) 367141.i 0.958190i −0.877763 0.479095i \(-0.840965\pi\)
0.877763 0.479095i \(-0.159035\pi\)
\(620\) 0 0
\(621\) −104076. −0.269878
\(622\) −102481. + 100843.i −0.264887 + 0.260655i
\(623\) 697647.i 1.79746i
\(624\) 10146.4 314905.i 0.0260581 0.808744i
\(625\) 0 0
\(626\) −29236.0 29710.7i −0.0746052 0.0758165i
\(627\) 224693.i 0.571549i
\(628\) −2371.17 + 147222.i −0.00601234 + 0.373297i
\(629\) 106908. 0.270215
\(630\) 0 0
\(631\) 210709.i 0.529206i −0.964357 0.264603i \(-0.914759\pi\)
0.964357 0.264603i \(-0.0852409\pi\)
\(632\) −48430.6 50828.9i −0.121251 0.127255i
\(633\) −49578.3 −0.123733
\(634\) 124221. + 126238.i 0.309043 + 0.314060i
\(635\) 0 0
\(636\) −119902. 1931.15i −0.296424 0.00477422i
\(637\) 390079. 0.961334
\(638\) −666512. + 655864.i −1.63745 + 1.61129i
\(639\) 8352.97i 0.0204569i
\(640\) 0 0
\(641\) −415962. −1.01237 −0.506183 0.862426i \(-0.668944\pi\)
−0.506183 + 0.862426i \(0.668944\pi\)
\(642\) −269341. 273714.i −0.653479 0.664089i
\(643\) 732294.i 1.77118i 0.464465 + 0.885592i \(0.346247\pi\)
−0.464465 + 0.885592i \(0.653753\pi\)
\(644\) 12161.1 755063.i 0.0293225 1.82059i
\(645\) 0 0
\(646\) −26106.4 + 25689.4i −0.0625580 + 0.0615585i
\(647\) 96321.2i 0.230098i 0.993360 + 0.115049i \(0.0367025\pi\)
−0.993360 + 0.115049i \(0.963297\pi\)
\(648\) 33778.0 32184.3i 0.0804423 0.0766467i
\(649\) 545667. 1.29550
\(650\) 0 0
\(651\) 352785.i 0.832430i
\(652\) 698584. + 11251.4i 1.64333 + 0.0264675i
\(653\) 274691. 0.644196 0.322098 0.946706i \(-0.395612\pi\)
0.322098 + 0.946706i \(0.395612\pi\)
\(654\) 10027.9 9867.66i 0.0234452 0.0230706i
\(655\) 0 0
\(656\) 292092. + 9411.32i 0.678752 + 0.0218697i
\(657\) 26911.8 0.0623465
\(658\) −72598.8 73777.5i −0.167679 0.170401i
\(659\) 360421.i 0.829927i −0.909838 0.414963i \(-0.863794\pi\)
0.909838 0.414963i \(-0.136206\pi\)
\(660\) 0 0
\(661\) 461663. 1.05663 0.528314 0.849049i \(-0.322824\pi\)
0.528314 + 0.849049i \(0.322824\pi\)
\(662\) 624442. 614465.i 1.42487 1.40211i
\(663\) 57526.4i 0.130870i
\(664\) 136742. + 143513.i 0.310145 + 0.325504i
\(665\) 0 0
\(666\) 173258. + 176071.i 0.390611 + 0.396953i
\(667\) 785640.i 1.76592i
\(668\) −314562. 5066.35i −0.704943 0.0113538i
\(669\) 173912. 0.388578
\(670\) 0 0
\(671\) 1.06379e6i 2.36272i
\(672\) 229548. + 248818.i 0.508317 + 0.550989i
\(673\) 295518. 0.652459 0.326230 0.945291i \(-0.394222\pi\)
0.326230 + 0.945291i \(0.394222\pi\)
\(674\) 143570. + 145901.i 0.316042 + 0.321173i
\(675\) 0 0
\(676\) −7095.93 + 440576.i −0.0155280 + 0.964111i
\(677\) −865789. −1.88901 −0.944506 0.328494i \(-0.893459\pi\)
−0.944506 + 0.328494i \(0.893459\pi\)
\(678\) −84354.3 + 83006.6i −0.183505 + 0.180573i
\(679\) 785046.i 1.70277i
\(680\) 0 0
\(681\) 5971.77 0.0128768
\(682\) −660856. 671586.i −1.42082 1.44389i
\(683\) 631289.i 1.35328i −0.736316 0.676638i \(-0.763436\pi\)
0.736316 0.676638i \(-0.236564\pi\)
\(684\) −84617.4 1362.85i −0.180862 0.00291297i
\(685\) 0 0
\(686\) 136790. 134604.i 0.290673 0.286029i
\(687\) 256650.i 0.543785i
\(688\) 10266.0 318617.i 0.0216882 0.673119i
\(689\) 341638. 0.719660
\(690\) 0 0
\(691\) 692970.i 1.45130i 0.688062 + 0.725652i \(0.258462\pi\)
−0.688062 + 0.725652i \(0.741538\pi\)
\(692\) −8212.23 + 509885.i −0.0171494 + 1.06478i
\(693\) −379188. −0.789564
\(694\) 224946. 221352.i 0.467045 0.459584i
\(695\) 0 0
\(696\) −242950. 254981.i −0.501532 0.526368i
\(697\) −53358.8 −0.109835
\(698\) −524880. 533402.i −1.07733 1.09482i
\(699\) 218675.i 0.447553i
\(700\) 0 0
\(701\) −106868. −0.217477 −0.108739 0.994070i \(-0.534681\pi\)
−0.108739 + 0.994070i \(0.534681\pi\)
\(702\) −94742.2 + 93228.5i −0.192251 + 0.189180i
\(703\) 448066.i 0.906633i
\(704\) −903083. 43665.5i −1.82214 0.0881035i
\(705\) 0 0
\(706\) 74561.4 + 75772.0i 0.149591 + 0.152020i
\(707\) 949151.i 1.89888i
\(708\) −3309.69 + 205493.i −0.00660268 + 0.409951i
\(709\) 71602.5 0.142441 0.0712207 0.997461i \(-0.477311\pi\)
0.0712207 + 0.997461i \(0.477311\pi\)
\(710\) 0 0
\(711\) 29618.8i 0.0585906i
\(712\) 508075. 484102.i 1.00223 0.954942i
\(713\) −791620. −1.55718
\(714\) −43352.9 44056.8i −0.0850397 0.0864204i
\(715\) 0 0
\(716\) 845382. + 13615.8i 1.64902 + 0.0265592i
\(717\) 179477. 0.349117
\(718\) −37667.8 + 37066.0i −0.0730671 + 0.0718997i
\(719\) 84839.0i 0.164111i −0.996628 0.0820555i \(-0.973852\pi\)
0.996628 0.0820555i \(-0.0261485\pi\)
\(720\) 0 0
\(721\) 641521. 1.23407
\(722\) −257956. 262144.i −0.494848 0.502882i
\(723\) 356804.i 0.682579i
\(724\) 16244.4 1.00859e6i 0.0309903 1.92414i
\(725\) 0 0
\(726\) 504945. 496877.i 0.958011 0.942706i
\(727\) 80916.8i 0.153098i −0.997066 0.0765491i \(-0.975610\pi\)
0.997066 0.0765491i \(-0.0243902\pi\)
\(728\) −665296. 698241.i −1.25531 1.31748i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 58204.4i 0.108923i
\(732\) 400616. + 6452.34i 0.747663 + 0.0120419i
\(733\) 62103.9 0.115588 0.0577938 0.998329i \(-0.481593\pi\)
0.0577938 + 0.998329i \(0.481593\pi\)
\(734\) −133778. + 131640.i −0.248308 + 0.244341i
\(735\) 0 0
\(736\) −558327. + 515086.i −1.03070 + 0.950877i
\(737\) 1.27854e6 2.35385
\(738\) −86474.4 87878.4i −0.158772 0.161350i
\(739\) 268031.i 0.490790i 0.969423 + 0.245395i \(0.0789176\pi\)
−0.969423 + 0.245395i \(0.921082\pi\)
\(740\) 0 0
\(741\) 241100. 0.439098
\(742\) −261644. + 257464.i −0.475230 + 0.467637i
\(743\) 348633.i 0.631525i 0.948838 + 0.315763i \(0.102260\pi\)
−0.948838 + 0.315763i \(0.897740\pi\)
\(744\) 256922. 244799.i 0.464147 0.442247i
\(745\) 0 0
\(746\) 666291. + 677109.i 1.19725 + 1.21669i
\(747\) 83627.5i 0.149868i
\(748\) 165059. + 2658.45i 0.295010 + 0.00475145i
\(749\) −1.17548e6 −2.09533
\(750\) 0 0
\(751\) 757069.i 1.34232i −0.741313 0.671159i \(-0.765797\pi\)
0.741313 0.671159i \(-0.234203\pi\)
\(752\) −3353.05 + 104066.i −0.00592932 + 0.184023i
\(753\) 322179. 0.568207
\(754\) 703756. + 715182.i 1.23788 + 1.25798i
\(755\) 0 0
\(756\) 2299.92 142799.i 0.00402411 0.249851i
\(757\) 128542. 0.224312 0.112156 0.993691i \(-0.464224\pi\)
0.112156 + 0.993691i \(0.464224\pi\)
\(758\) 308334. 303408.i 0.536639 0.528066i
\(759\) 850866.i 1.47699i
\(760\) 0 0
\(761\) 460176. 0.794611 0.397306 0.917686i \(-0.369945\pi\)
0.397306 + 0.917686i \(0.369945\pi\)
\(762\) −318305. 323473.i −0.548193 0.557094i
\(763\) 43065.4i 0.0739740i
\(764\) 331640. + 5341.40i 0.568172 + 0.00915100i
\(765\) 0 0
\(766\) 408019. 401501.i 0.695382 0.684272i
\(767\) 585512.i 0.995280i
\(768\) 21921.6 339829.i 0.0371664 0.576153i
\(769\) 1.10194e6 1.86340 0.931701 0.363226i \(-0.118325\pi\)
0.931701 + 0.363226i \(0.118325\pi\)
\(770\) 0 0
\(771\) 342829.i 0.576725i
\(772\) 4526.53 281046.i 0.00759506 0.471566i
\(773\) 809541. 1.35481 0.677407 0.735608i \(-0.263103\pi\)
0.677407 + 0.735608i \(0.263103\pi\)
\(774\) −95858.8 + 94327.3i −0.160011 + 0.157455i
\(775\) 0 0
\(776\) 571724. 544748.i 0.949430 0.904633i
\(777\) 756149. 1.25246
\(778\) 370505. + 376520.i 0.612117 + 0.622055i
\(779\) 223633.i 0.368520i
\(780\) 0 0
\(781\) −68289.2 −0.111957
\(782\) 98859.8 97280.4i 0.161661 0.159079i
\(783\) 148582.i 0.242349i
\(784\) 421390. + 13577.4i 0.685570 + 0.0220894i
\(785\) 0 0
\(786\) −100870. 102508.i −0.163274 0.165925i
\(787\) 363079.i 0.586207i −0.956081 0.293104i \(-0.905312\pi\)
0.956081 0.293104i \(-0.0946881\pi\)
\(788\) −13089.5 + 812709.i −0.0210800 + 1.30883i
\(789\) −238448. −0.383036
\(790\) 0 0
\(791\) 362265.i 0.578993i
\(792\) 263121. + 276150.i 0.419473 + 0.440246i
\(793\) −1.14147e6 −1.81518
\(794\) 129446. + 131548.i 0.205328 + 0.208662i
\(795\) 0 0
\(796\) −514194. 8281.64i −0.811524 0.0130704i
\(797\) 483796. 0.761633 0.380816 0.924651i \(-0.375643\pi\)
0.380816 + 0.924651i \(0.375643\pi\)
\(798\) −184647. + 181697.i −0.289960 + 0.285327i
\(799\) 19010.6i 0.0297785i
\(800\) 0 0
\(801\) −296063. −0.461444
\(802\) −9103.96 9251.77i −0.0141541 0.0143839i
\(803\) 220016.i 0.341211i
\(804\) −7754.85 + 481487.i −0.0119967 + 0.744857i
\(805\) 0 0
\(806\) −720626. + 709113.i −1.10928 + 1.09155i
\(807\) 346065.i 0.531386i
\(808\) 691237. 658622.i 1.05878 1.00882i
\(809\) 483640. 0.738966 0.369483 0.929237i \(-0.379535\pi\)
0.369483 + 0.929237i \(0.379535\pi\)
\(810\) 0 0
\(811\) 406318.i 0.617767i −0.951100 0.308883i \(-0.900045\pi\)
0.951100 0.308883i \(-0.0999553\pi\)
\(812\) −1.07795e6 17361.5i −1.63488 0.0263315i
\(813\) 560386. 0.847826
\(814\) −1.43946e6 + 1.41646e6i −2.17245 + 2.13774i
\(815\) 0 0
\(816\) −2002.30 + 62143.8i −0.00300711 + 0.0933292i
\(817\) 243942. 0.365462
\(818\) 533693. + 542358.i 0.797599 + 0.810549i
\(819\) 406877.i 0.606589i
\(820\) 0 0
\(821\) 489931. 0.726857 0.363428 0.931622i \(-0.381606\pi\)
0.363428 + 0.931622i \(0.381606\pi\)
\(822\) 364728. 358901.i 0.539791 0.531167i
\(823\) 372808.i 0.550408i 0.961386 + 0.275204i \(0.0887455\pi\)
−0.961386 + 0.275204i \(0.911255\pi\)
\(824\) −445156. 467200.i −0.655628 0.688095i
\(825\) 0 0
\(826\) 441253. + 448417.i 0.646736 + 0.657237i
\(827\) 222364.i 0.325127i −0.986698 0.162563i \(-0.948024\pi\)
0.986698 0.162563i \(-0.0519762\pi\)
\(828\) 320429. + 5160.84i 0.467381 + 0.00752766i
\(829\) 127764. 0.185908 0.0929542 0.995670i \(-0.470369\pi\)
0.0929542 + 0.995670i \(0.470369\pi\)
\(830\) 0 0
\(831\) 395536.i 0.572774i
\(832\) −46854.0 + 969028.i −0.0676862 + 1.39988i
\(833\) −76978.8 −0.110938
\(834\) −273590. 278032.i −0.393341 0.399727i
\(835\) 0 0
\(836\) 11141.9 691784.i 0.0159422 0.989824i
\(837\) −149712. −0.213701
\(838\) −110233. + 108472.i −0.156972 + 0.154465i
\(839\) 981082.i 1.39374i −0.717198 0.696870i \(-0.754576\pi\)
0.717198 0.696870i \(-0.245424\pi\)
\(840\) 0 0
\(841\) 414320. 0.585793
\(842\) 603814. + 613617.i 0.851684 + 0.865512i
\(843\) 664774.i 0.935446i
\(844\) 152642. + 2458.45i 0.214283 + 0.00345125i
\(845\) 0 0
\(846\) 31309.2 30809.0i 0.0437453 0.0430464i
\(847\) 2.16852e6i 3.02271i
\(848\) 369060. + 11891.3i 0.513222 + 0.0165362i
\(849\) −612064. −0.849144
\(850\) 0 0
\(851\) 1.69674e6i 2.34291i
\(852\) 414.201 25717.1i 0.000570601 0.0354278i
\(853\) −192525. −0.264599 −0.132299 0.991210i \(-0.542236\pi\)
−0.132299 + 0.991210i \(0.542236\pi\)
\(854\) 874203. 860236.i 1.19866 1.17951i
\(855\) 0 0
\(856\) 815674. + 856066.i 1.11319 + 1.16831i
\(857\) −1.20031e6 −1.63430 −0.817151 0.576424i \(-0.804448\pi\)
−0.817151 + 0.576424i \(0.804448\pi\)
\(858\) −762184. 774559.i −1.03535 1.05216i
\(859\) 1.29982e6i 1.76156i 0.473529 + 0.880778i \(0.342980\pi\)
−0.473529 + 0.880778i \(0.657020\pi\)
\(860\) 0 0
\(861\) −377400. −0.509091
\(862\) −36586.7 + 36002.2i −0.0492390 + 0.0484523i
\(863\) 148386.i 0.199238i 0.995026 + 0.0996188i \(0.0317623\pi\)
−0.995026 + 0.0996188i \(0.968238\pi\)
\(864\) −105592. + 97414.0i −0.141450 + 0.130495i
\(865\) 0 0
\(866\) −688103. 699275.i −0.917525 0.932421i
\(867\) 422636.i 0.562248i
\(868\) 17493.6 1.08615e6i 0.0232188 1.44162i
\(869\) −242147. −0.320656
\(870\) 0 0
\(871\) 1.37190e6i 1.80837i
\(872\) −31363.1 + 29883.3i −0.0412465 + 0.0393003i
\(873\) −333153. −0.437134
\(874\) −407714. 414334.i −0.533744 0.542410i
\(875\) 0 0
\(876\) −82856.1 1334.48i −0.107973 0.00173902i
\(877\) −144747. −0.188196 −0.0940981 0.995563i \(-0.529997\pi\)
−0.0940981 + 0.995563i \(0.529997\pi\)
\(878\) 23722.9 23343.9i 0.0307736 0.0302820i
\(879\) 626229.i 0.810505i
\(880\) 0 0
\(881\) 281633. 0.362853 0.181427 0.983404i \(-0.441928\pi\)
0.181427 + 0.983404i \(0.441928\pi\)
\(882\) −124754. 126779.i −0.160367 0.162971i
\(883\) 334210.i 0.428645i −0.976763 0.214323i \(-0.931246\pi\)
0.976763 0.214323i \(-0.0687544\pi\)
\(884\) 2852.58 177112.i 0.00365034 0.226644i
\(885\) 0 0
\(886\) −402689. + 396255.i −0.512982 + 0.504787i
\(887\) 504313.i 0.640992i 0.947250 + 0.320496i \(0.103850\pi\)
−0.947250 + 0.320496i \(0.896150\pi\)
\(888\) −524696. 550679.i −0.665399 0.698349i
\(889\) −1.38918e6 −1.75774
\(890\) 0 0
\(891\) 160917.i 0.202697i
\(892\) −535442. 8623.85i −0.672950 0.0108386i
\(893\) −79675.8 −0.0999133
\(894\) −97377.7 + 95822.0i −0.121839 + 0.119892i
\(895\) 0 0
\(896\) −694394. 777444.i −0.864948 0.968396i
\(897\) −912998. −1.13471
\(898\) 554451. + 563453.i 0.687560 + 0.698723i
\(899\) 1.13014e6i 1.39834i
\(900\) 0 0
\(901\) −67419.2 −0.0830489
\(902\) 718445. 706967.i 0.883040 0.868932i
\(903\) 411672.i 0.504866i
\(904\) 263826. 251378.i 0.322835 0.307603i
\(905\) 0 0
\(906\) −114049. 115900.i −0.138942 0.141198i
\(907\) 83306.2i 0.101266i 0.998717 + 0.0506329i \(0.0161239\pi\)
−0.998717 + 0.0506329i \(0.983876\pi\)
\(908\) −18385.9 296.124i −0.0223004 0.000359172i
\(909\) −402795. −0.487479
\(910\) 0 0
\(911\) 115795.i 0.139525i −0.997564 0.0697626i \(-0.977776\pi\)
0.997564 0.0697626i \(-0.0222242\pi\)
\(912\) 260453. + 8391.89i 0.313140 + 0.0100895i
\(913\) 683691. 0.820198
\(914\) 929574. + 944667.i 1.11274 + 1.13080i
\(915\) 0 0
\(916\) 12726.6 790173.i 0.0151677 0.941741i
\(917\) −440227. −0.523525
\(918\) 18696.5 18397.8i 0.0221858 0.0218314i
\(919\) 788234.i 0.933306i −0.884441 0.466653i \(-0.845460\pi\)
0.884441 0.466653i \(-0.154540\pi\)
\(920\) 0 0
\(921\) −467670. −0.551341
\(922\) 550143. + 559075.i 0.647163 + 0.657671i
\(923\) 73275.8i 0.0860117i
\(924\) 1.16744e6 + 18802.9i 1.36739 + 0.0220232i
\(925\) 0 0
\(926\) −481107. + 473420.i −0.561073 + 0.552109i
\(927\) 272245.i 0.316811i
\(928\) 735352. + 797083.i 0.853884 + 0.925567i
\(929\) −15865.8 −0.0183837 −0.00919183 0.999958i \(-0.502926\pi\)
−0.00919183 + 0.999958i \(0.502926\pi\)
\(930\) 0 0
\(931\) 322628.i 0.372222i
\(932\) 10843.5 673256.i 0.0124835 0.775084i
\(933\) −186771. −0.214559
\(934\) 165945. 163294.i 0.190227 0.187188i
\(935\) 0 0
\(936\) 296315. 282334.i 0.338222 0.322264i
\(937\) −15433.2 −0.0175783 −0.00878913 0.999961i \(-0.502798\pi\)
−0.00878913 + 0.999961i \(0.502798\pi\)
\(938\) 1.03389e6 + 1.05068e6i 1.17508 + 1.19416i
\(939\) 54147.7i 0.0614114i
\(940\) 0 0
\(941\) −550507. −0.621704 −0.310852 0.950458i \(-0.600614\pi\)
−0.310852 + 0.950458i \(0.600614\pi\)
\(942\) −136335. + 134157.i −0.153640 + 0.151185i
\(943\) 846854.i 0.952325i
\(944\) 20379.7 632510.i 0.0228694 0.709779i
\(945\) 0 0
\(946\) −771167. 783688.i −0.861720 0.875711i
\(947\) 1.27984e6i 1.42710i 0.700602 + 0.713552i \(0.252915\pi\)
−0.700602 + 0.713552i \(0.747085\pi\)
\(948\) 1468.72 91190.4i 0.00163426 0.101469i
\(949\) 236082. 0.262138
\(950\) 0 0
\(951\) 230069.i 0.254389i
\(952\) 131290. + 137792.i 0.144864 + 0.152037i
\(953\) 491859. 0.541571 0.270785 0.962640i \(-0.412717\pi\)
0.270785 + 0.962640i \(0.412717\pi\)
\(954\) −109261. 111035.i −0.120052 0.122001i
\(955\) 0 0
\(956\) −552575. 8899.80i −0.604611 0.00973788i
\(957\) −1.21472e6 −1.32633
\(958\) 632090. 621992.i 0.688729 0.677725i
\(959\) 1.56635e6i 1.70314i
\(960\) 0 0
\(961\) −215219. −0.233042
\(962\) 1.51989e6 + 1.54457e6i 1.64234 + 1.66900i
\(963\) 498843.i 0.537912i
\(964\) −17692.9 + 1.09853e6i −0.0190391 + 1.18211i
\(965\) 0 0
\(966\) 699223. 688052.i 0.749310 0.737338i
\(967\) 628976.i 0.672638i −0.941748 0.336319i \(-0.890818\pi\)
0.941748 0.336319i \(-0.109182\pi\)
\(968\) −1.57926e6 + 1.50475e6i −1.68540 + 1.60588i
\(969\) −47579.0 −0.0506720
\(970\) 0 0
\(971\) 1.78700e6i 1.89533i 0.319264 + 0.947666i \(0.396564\pi\)
−0.319264 + 0.947666i \(0.603436\pi\)
\(972\) 60600.1 + 976.027i 0.0641417 + 0.00103307i
\(973\) −1.19403e6 −1.26121
\(974\) 415040. 408409.i 0.437494 0.430505i
\(975\) 0 0
\(976\) −1.23310e6 39730.9i −1.29449 0.0417089i
\(977\) −842171. −0.882289 −0.441145 0.897436i \(-0.645427\pi\)
−0.441145 + 0.897436i \(0.645427\pi\)
\(978\) 636585. + 646921.i 0.665547 + 0.676353i
\(979\) 2.42045e6i 2.52540i
\(980\) 0 0
\(981\) 18275.8 0.0189906
\(982\) −697373. + 686232.i −0.723173 + 0.711620i
\(983\) 877633.i 0.908251i 0.890938 + 0.454125i \(0.150048\pi\)
−0.890938 + 0.454125i \(0.849952\pi\)
\(984\) 261880. + 274848.i 0.270466 + 0.283859i
\(985\) 0 0
\(986\) −138880. 141135.i −0.142852 0.145171i
\(987\) 134459.i 0.138025i
\(988\) −742300. 11955.5i −0.760441 0.0122477i
\(989\) −923758. −0.944421
\(990\) 0 0
\(991\) 326910.i 0.332875i −0.986052 0.166437i \(-0.946774\pi\)
0.986052 0.166437i \(-0.0532264\pi\)
\(992\) −803150. + 740949.i −0.816157 + 0.752948i
\(993\) 1.13805e6 1.15415
\(994\) −55222.0 56118.6i −0.0558907 0.0567981i
\(995\) 0 0
\(996\) −4146.86 + 257472.i −0.00418024 + 0.259545i
\(997\) −935659. −0.941298 −0.470649 0.882320i \(-0.655980\pi\)
−0.470649 + 0.882320i \(0.655980\pi\)
\(998\) 323378. 318212.i 0.324676 0.319488i
\(999\) 320890.i 0.321532i
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 300.5.c.b.151.5 16
4.3 odd 2 inner 300.5.c.b.151.6 yes 16
5.2 odd 4 300.5.f.c.199.25 32
5.3 odd 4 300.5.f.c.199.8 32
5.4 even 2 300.5.c.c.151.12 yes 16
20.3 even 4 300.5.f.c.199.26 32
20.7 even 4 300.5.f.c.199.7 32
20.19 odd 2 300.5.c.c.151.11 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.5.c.b.151.5 16 1.1 even 1 trivial
300.5.c.b.151.6 yes 16 4.3 odd 2 inner
300.5.c.c.151.11 yes 16 20.19 odd 2
300.5.c.c.151.12 yes 16 5.4 even 2
300.5.f.c.199.7 32 20.7 even 4
300.5.f.c.199.8 32 5.3 odd 4
300.5.f.c.199.25 32 5.2 odd 4
300.5.f.c.199.26 32 20.3 even 4