Properties

Label 930.4.d.c.559.14
Level $930$
Weight $4$
Character 930.559
Analytic conductor $54.872$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,4,Mod(559,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.559");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.d (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: \(54.8717763053\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 2763 x^{18} + 2652899 x^{16} + 1161420105 x^{14} + 247831438280 x^{12} + 26461073949176 x^{10} + \cdots + 34\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{5}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 559.14
Root \(2.24994i\) of defining polynomial
Character \(\chi\) \(=\) 930.559
Dual form 930.4.d.c.559.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-6.23400 + 9.28102i) q^{5} +6.00000 q^{6} +2.24994i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-6.23400 + 9.28102i) q^{5} +6.00000 q^{6} +2.24994i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(-18.5620 - 12.4680i) q^{10} +10.8894 q^{11} +12.0000i q^{12} -9.95921i q^{13} -4.49987 q^{14} +(27.8430 + 18.7020i) q^{15} +16.0000 q^{16} +47.5791i q^{17} -18.0000i q^{18} +25.1773 q^{19} +(24.9360 - 37.1241i) q^{20} +6.74981 q^{21} +21.7789i q^{22} +205.260i q^{23} -24.0000 q^{24} +(-47.2745 - 115.716i) q^{25} +19.9184 q^{26} +27.0000i q^{27} -8.99974i q^{28} +98.6634 q^{29} +(-37.4040 + 55.6861i) q^{30} -31.0000 q^{31} +32.0000i q^{32} -32.6683i q^{33} -95.1582 q^{34} +(-20.8817 - 14.0261i) q^{35} +36.0000 q^{36} -131.000i q^{37} +50.3547i q^{38} -29.8776 q^{39} +(74.2481 + 49.8720i) q^{40} -482.771 q^{41} +13.4996i q^{42} +274.383i q^{43} -43.5578 q^{44} +(56.1060 - 83.5291i) q^{45} -410.521 q^{46} -155.090i q^{47} -48.0000i q^{48} +337.938 q^{49} +(231.431 - 94.5490i) q^{50} +142.737 q^{51} +39.8368i q^{52} -205.199i q^{53} -54.0000 q^{54} +(-67.8848 + 101.065i) q^{55} +17.9995 q^{56} -75.5320i q^{57} +197.327i q^{58} -449.126 q^{59} +(-111.372 - 74.8080i) q^{60} -402.422 q^{61} -62.0000i q^{62} -20.2494i q^{63} -64.0000 q^{64} +(92.4316 + 62.0857i) q^{65} +65.3367 q^{66} -709.830i q^{67} -190.316i q^{68} +615.781 q^{69} +(28.0522 - 41.7634i) q^{70} +92.4428 q^{71} +72.0000i q^{72} -207.183i q^{73} +262.000 q^{74} +(-347.147 + 141.824i) q^{75} -100.709 q^{76} +24.5006i q^{77} -59.7553i q^{78} -391.407 q^{79} +(-99.7440 + 148.496i) q^{80} +81.0000 q^{81} -965.542i q^{82} +936.113i q^{83} -26.9992 q^{84} +(-441.582 - 296.608i) q^{85} -548.766 q^{86} -295.990i q^{87} -87.1155i q^{88} +500.955 q^{89} +(167.058 + 112.212i) q^{90} +22.4076 q^{91} -821.041i q^{92} +93.0000i q^{93} +310.179 q^{94} +(-156.955 + 233.671i) q^{95} +96.0000 q^{96} +418.229i q^{97} +675.876i q^{98} -98.0050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9} + 8 q^{10} - 114 q^{11} + 52 q^{14} - 12 q^{15} + 320 q^{16} + 370 q^{19} + 8 q^{20} - 78 q^{21} - 480 q^{24} - 90 q^{25} - 368 q^{26} + 368 q^{29} - 12 q^{30} - 620 q^{31} + 712 q^{34} + 374 q^{35} + 720 q^{36} + 552 q^{39} - 32 q^{40} - 872 q^{41} + 456 q^{44} + 18 q^{45} - 1236 q^{46} + 1334 q^{49} + 416 q^{50} - 1068 q^{51} - 1080 q^{54} - 1290 q^{55} - 208 q^{56} + 3228 q^{59} + 48 q^{60} - 2604 q^{61} - 1280 q^{64} + 44 q^{65} - 684 q^{66} + 1854 q^{69} - 852 q^{70} - 2290 q^{71} + 2008 q^{74} - 624 q^{75} - 1480 q^{76} + 4342 q^{79} - 32 q^{80} + 1620 q^{81} + 312 q^{84} + 500 q^{85} - 4 q^{86} + 1390 q^{89} - 72 q^{90} - 5744 q^{91} + 2608 q^{94} - 1136 q^{95} + 1920 q^{96} + 1026 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 3.00000i 0.577350i
\(4\) −4.00000 −0.500000
\(5\) −6.23400 + 9.28102i −0.557586 + 0.830119i
\(6\) 6.00000 0.408248
\(7\) 2.24994i 0.121485i 0.998153 + 0.0607426i \(0.0193469\pi\)
−0.998153 + 0.0607426i \(0.980653\pi\)
\(8\) 8.00000i 0.353553i
\(9\) −9.00000 −0.333333
\(10\) −18.5620 12.4680i −0.586983 0.394273i
\(11\) 10.8894 0.298481 0.149240 0.988801i \(-0.452317\pi\)
0.149240 + 0.988801i \(0.452317\pi\)
\(12\) 12.0000i 0.288675i
\(13\) 9.95921i 0.212476i −0.994341 0.106238i \(-0.966119\pi\)
0.994341 0.106238i \(-0.0338805\pi\)
\(14\) −4.49987 −0.0859030
\(15\) 27.8430 + 18.7020i 0.479270 + 0.321922i
\(16\) 16.0000 0.250000
\(17\) 47.5791i 0.678801i 0.940642 + 0.339401i \(0.110224\pi\)
−0.940642 + 0.339401i \(0.889776\pi\)
\(18\) 18.0000i 0.235702i
\(19\) 25.1773 0.304004 0.152002 0.988380i \(-0.451428\pi\)
0.152002 + 0.988380i \(0.451428\pi\)
\(20\) 24.9360 37.1241i 0.278793 0.415060i
\(21\) 6.74981 0.0701395
\(22\) 21.7789i 0.211058i
\(23\) 205.260i 1.86086i 0.366473 + 0.930429i \(0.380565\pi\)
−0.366473 + 0.930429i \(0.619435\pi\)
\(24\) −24.0000 −0.204124
\(25\) −47.2745 115.716i −0.378196 0.925725i
\(26\) 19.9184 0.150243
\(27\) 27.0000i 0.192450i
\(28\) 8.99974i 0.0607426i
\(29\) 98.6634 0.631770 0.315885 0.948797i \(-0.397699\pi\)
0.315885 + 0.948797i \(0.397699\pi\)
\(30\) −37.4040 + 55.6861i −0.227633 + 0.338895i
\(31\) −31.0000 −0.179605
\(32\) 32.0000i 0.176777i
\(33\) 32.6683i 0.172328i
\(34\) −95.1582 −0.479985
\(35\) −20.8817 14.0261i −0.100847 0.0677384i
\(36\) 36.0000 0.166667
\(37\) 131.000i 0.582061i −0.956714 0.291031i \(-0.906002\pi\)
0.956714 0.291031i \(-0.0939982\pi\)
\(38\) 50.3547i 0.214963i
\(39\) −29.8776 −0.122673
\(40\) 74.2481 + 49.8720i 0.293492 + 0.197136i
\(41\) −482.771 −1.83893 −0.919465 0.393172i \(-0.871378\pi\)
−0.919465 + 0.393172i \(0.871378\pi\)
\(42\) 13.4996i 0.0495961i
\(43\) 274.383i 0.973094i 0.873654 + 0.486547i \(0.161744\pi\)
−0.873654 + 0.486547i \(0.838256\pi\)
\(44\) −43.5578 −0.149240
\(45\) 56.1060 83.5291i 0.185862 0.276706i
\(46\) −410.521 −1.31583
\(47\) 155.090i 0.481322i −0.970609 0.240661i \(-0.922636\pi\)
0.970609 0.240661i \(-0.0773642\pi\)
\(48\) 48.0000i 0.144338i
\(49\) 337.938 0.985241
\(50\) 231.431 94.5490i 0.654587 0.267425i
\(51\) 142.737 0.391906
\(52\) 39.8368i 0.106238i
\(53\) 205.199i 0.531815i −0.963999 0.265908i \(-0.914328\pi\)
0.963999 0.265908i \(-0.0856716\pi\)
\(54\) −54.0000 −0.136083
\(55\) −67.8848 + 101.065i −0.166429 + 0.247775i
\(56\) 17.9995 0.0429515
\(57\) 75.5320i 0.175517i
\(58\) 197.327i 0.446729i
\(59\) −449.126 −0.991039 −0.495519 0.868597i \(-0.665022\pi\)
−0.495519 + 0.868597i \(0.665022\pi\)
\(60\) −111.372 74.8080i −0.239635 0.160961i
\(61\) −402.422 −0.844670 −0.422335 0.906440i \(-0.638789\pi\)
−0.422335 + 0.906440i \(0.638789\pi\)
\(62\) 62.0000i 0.127000i
\(63\) 20.2494i 0.0404950i
\(64\) −64.0000 −0.125000
\(65\) 92.4316 + 62.0857i 0.176380 + 0.118474i
\(66\) 65.3367 0.121854
\(67\) 709.830i 1.29432i −0.762354 0.647161i \(-0.775956\pi\)
0.762354 0.647161i \(-0.224044\pi\)
\(68\) 190.316i 0.339401i
\(69\) 615.781 1.07437
\(70\) 28.0522 41.7634i 0.0478983 0.0713097i
\(71\) 92.4428 0.154520 0.0772602 0.997011i \(-0.475383\pi\)
0.0772602 + 0.997011i \(0.475383\pi\)
\(72\) 72.0000i 0.117851i
\(73\) 207.183i 0.332177i −0.986111 0.166088i \(-0.946886\pi\)
0.986111 0.166088i \(-0.0531137\pi\)
\(74\) 262.000 0.411579
\(75\) −347.147 + 141.824i −0.534468 + 0.218352i
\(76\) −100.709 −0.152002
\(77\) 24.5006i 0.0362610i
\(78\) 59.7553i 0.0867429i
\(79\) −391.407 −0.557426 −0.278713 0.960374i \(-0.589908\pi\)
−0.278713 + 0.960374i \(0.589908\pi\)
\(80\) −99.7440 + 148.496i −0.139396 + 0.207530i
\(81\) 81.0000 0.111111
\(82\) 965.542i 1.30032i
\(83\) 936.113i 1.23797i 0.785402 + 0.618986i \(0.212456\pi\)
−0.785402 + 0.618986i \(0.787544\pi\)
\(84\) −26.9992 −0.0350697
\(85\) −441.582 296.608i −0.563486 0.378490i
\(86\) −548.766 −0.688081
\(87\) 295.990i 0.364753i
\(88\) 87.1155i 0.105529i
\(89\) 500.955 0.596642 0.298321 0.954466i \(-0.403573\pi\)
0.298321 + 0.954466i \(0.403573\pi\)
\(90\) 167.058 + 112.212i 0.195661 + 0.131424i
\(91\) 22.4076 0.0258127
\(92\) 821.041i 0.930429i
\(93\) 93.0000i 0.103695i
\(94\) 310.179 0.340346
\(95\) −156.955 + 233.671i −0.169508 + 0.252360i
\(96\) 96.0000 0.102062
\(97\) 418.229i 0.437780i 0.975750 + 0.218890i \(0.0702436\pi\)
−0.975750 + 0.218890i \(0.929756\pi\)
\(98\) 675.876i 0.696671i
\(99\) −98.0050 −0.0994936
\(100\) 189.098 + 462.863i 0.189098 + 0.462863i
\(101\) −293.770 −0.289418 −0.144709 0.989474i \(-0.546225\pi\)
−0.144709 + 0.989474i \(0.546225\pi\)
\(102\) 285.474i 0.277119i
\(103\) 1903.51i 1.82095i −0.413563 0.910476i \(-0.635716\pi\)
0.413563 0.910476i \(-0.364284\pi\)
\(104\) −79.6737 −0.0751216
\(105\) −42.0783 + 62.6451i −0.0391088 + 0.0582241i
\(106\) 410.397 0.376050
\(107\) 1517.88i 1.37139i −0.727887 0.685697i \(-0.759497\pi\)
0.727887 0.685697i \(-0.240503\pi\)
\(108\) 108.000i 0.0962250i
\(109\) −1875.15 −1.64777 −0.823883 0.566760i \(-0.808197\pi\)
−0.823883 + 0.566760i \(0.808197\pi\)
\(110\) −202.130 135.770i −0.175203 0.117683i
\(111\) −393.000 −0.336053
\(112\) 35.9990i 0.0303713i
\(113\) 1711.38i 1.42472i −0.701814 0.712360i \(-0.747626\pi\)
0.701814 0.712360i \(-0.252374\pi\)
\(114\) 151.064 0.124109
\(115\) −1905.02 1279.59i −1.54473 1.03759i
\(116\) −394.654 −0.315885
\(117\) 89.6329i 0.0708253i
\(118\) 898.253i 0.700770i
\(119\) −107.050 −0.0824643
\(120\) 149.616 222.744i 0.113817 0.169447i
\(121\) −1212.42 −0.910909
\(122\) 804.844i 0.597272i
\(123\) 1448.31i 1.06171i
\(124\) 124.000 0.0898027
\(125\) 1368.67 + 282.616i 0.979339 + 0.202223i
\(126\) 40.4989 0.0286343
\(127\) 254.670i 0.177940i −0.996034 0.0889698i \(-0.971643\pi\)
0.996034 0.0889698i \(-0.0283575\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 823.150 0.561816
\(130\) −124.171 + 184.863i −0.0837735 + 0.124720i
\(131\) −2563.41 −1.70967 −0.854833 0.518903i \(-0.826341\pi\)
−0.854833 + 0.518903i \(0.826341\pi\)
\(132\) 130.673i 0.0861640i
\(133\) 56.6474i 0.0369320i
\(134\) 1419.66 0.915223
\(135\) −250.587 168.318i −0.159757 0.107307i
\(136\) 380.633 0.239993
\(137\) 1134.23i 0.707329i 0.935372 + 0.353664i \(0.115064\pi\)
−0.935372 + 0.353664i \(0.884936\pi\)
\(138\) 1231.56i 0.759692i
\(139\) −2489.71 −1.51924 −0.759620 0.650367i \(-0.774615\pi\)
−0.759620 + 0.650367i \(0.774615\pi\)
\(140\) 83.5268 + 56.1044i 0.0504236 + 0.0338692i
\(141\) −465.269 −0.277892
\(142\) 184.886i 0.109262i
\(143\) 108.450i 0.0634200i
\(144\) −144.000 −0.0833333
\(145\) −615.068 + 915.697i −0.352266 + 0.524445i
\(146\) 414.366 0.234885
\(147\) 1013.81i 0.568829i
\(148\) 524.000i 0.291031i
\(149\) −1456.20 −0.800649 −0.400324 0.916373i \(-0.631103\pi\)
−0.400324 + 0.916373i \(0.631103\pi\)
\(150\) −283.647 694.294i −0.154398 0.377926i
\(151\) −1902.46 −1.02530 −0.512648 0.858599i \(-0.671335\pi\)
−0.512648 + 0.858599i \(0.671335\pi\)
\(152\) 201.419i 0.107482i
\(153\) 428.212i 0.226267i
\(154\) −49.0011 −0.0256404
\(155\) 193.254 287.712i 0.100145 0.149094i
\(156\) 119.511 0.0613365
\(157\) 2174.76i 1.10551i −0.833345 0.552754i \(-0.813577\pi\)
0.833345 0.552754i \(-0.186423\pi\)
\(158\) 782.813i 0.394160i
\(159\) −615.596 −0.307044
\(160\) −296.993 199.488i −0.146746 0.0985682i
\(161\) −461.823 −0.226067
\(162\) 162.000i 0.0785674i
\(163\) 287.277i 0.138045i 0.997615 + 0.0690224i \(0.0219880\pi\)
−0.997615 + 0.0690224i \(0.978012\pi\)
\(164\) 1931.08 0.919465
\(165\) 303.195 + 203.654i 0.143053 + 0.0960877i
\(166\) −1872.23 −0.875379
\(167\) 729.658i 0.338099i −0.985608 0.169050i \(-0.945930\pi\)
0.985608 0.169050i \(-0.0540698\pi\)
\(168\) 53.9985i 0.0247980i
\(169\) 2097.81 0.954854
\(170\) 593.216 883.164i 0.267633 0.398445i
\(171\) −226.596 −0.101335
\(172\) 1097.53i 0.486547i
\(173\) 618.987i 0.272027i −0.990707 0.136014i \(-0.956571\pi\)
0.990707 0.136014i \(-0.0434291\pi\)
\(174\) 591.980 0.257919
\(175\) 260.353 106.365i 0.112462 0.0459452i
\(176\) 174.231 0.0746202
\(177\) 1347.38i 0.572176i
\(178\) 1001.91i 0.421890i
\(179\) −1675.34 −0.699558 −0.349779 0.936832i \(-0.613743\pi\)
−0.349779 + 0.936832i \(0.613743\pi\)
\(180\) −224.424 + 334.117i −0.0929310 + 0.138353i
\(181\) −1059.19 −0.434967 −0.217483 0.976064i \(-0.569785\pi\)
−0.217483 + 0.976064i \(0.569785\pi\)
\(182\) 44.8152i 0.0182523i
\(183\) 1207.27i 0.487670i
\(184\) 1642.08 0.657913
\(185\) 1215.81 + 816.654i 0.483180 + 0.324549i
\(186\) −186.000 −0.0733236
\(187\) 518.110i 0.202609i
\(188\) 620.358i 0.240661i
\(189\) −60.7483 −0.0233798
\(190\) −467.342 313.911i −0.178445 0.119860i
\(191\) 2708.30 1.02600 0.512999 0.858389i \(-0.328534\pi\)
0.512999 + 0.858389i \(0.328534\pi\)
\(192\) 192.000i 0.0721688i
\(193\) 1465.36i 0.546524i 0.961940 + 0.273262i \(0.0881026\pi\)
−0.961940 + 0.273262i \(0.911897\pi\)
\(194\) −836.457 −0.309557
\(195\) 186.257 277.295i 0.0684008 0.101833i
\(196\) −1351.75 −0.492621
\(197\) 1816.44i 0.656933i 0.944516 + 0.328466i \(0.106532\pi\)
−0.944516 + 0.328466i \(0.893468\pi\)
\(198\) 196.010i 0.0703526i
\(199\) 1278.12 0.455295 0.227648 0.973744i \(-0.426897\pi\)
0.227648 + 0.973744i \(0.426897\pi\)
\(200\) −925.725 + 378.196i −0.327293 + 0.133713i
\(201\) −2129.49 −0.747277
\(202\) 587.540i 0.204650i
\(203\) 221.986i 0.0767507i
\(204\) −570.949 −0.195953
\(205\) 3009.59 4480.60i 1.02536 1.52653i
\(206\) 3807.01 1.28761
\(207\) 1847.34i 0.620286i
\(208\) 159.347i 0.0531190i
\(209\) 274.167 0.0907394
\(210\) −125.290 84.1566i −0.0411707 0.0276541i
\(211\) 1969.15 0.642474 0.321237 0.946999i \(-0.395901\pi\)
0.321237 + 0.946999i \(0.395901\pi\)
\(212\) 820.794i 0.265908i
\(213\) 277.328i 0.0892124i
\(214\) 3035.76 0.969722
\(215\) −2546.56 1710.50i −0.807784 0.542583i
\(216\) 216.000 0.0680414
\(217\) 69.7480i 0.0218194i
\(218\) 3750.29i 1.16515i
\(219\) −621.548 −0.191782
\(220\) 271.539 404.260i 0.0832144 0.123887i
\(221\) 473.850 0.144229
\(222\) 786.000i 0.237626i
\(223\) 3020.81i 0.907122i −0.891225 0.453561i \(-0.850153\pi\)
0.891225 0.453561i \(-0.149847\pi\)
\(224\) −71.9980 −0.0214757
\(225\) 425.471 + 1041.44i 0.126065 + 0.308575i
\(226\) 3422.77 1.00743
\(227\) 1509.70i 0.441420i 0.975339 + 0.220710i \(0.0708375\pi\)
−0.975339 + 0.220710i \(0.929162\pi\)
\(228\) 302.128i 0.0877584i
\(229\) −4937.81 −1.42489 −0.712444 0.701729i \(-0.752412\pi\)
−0.712444 + 0.701729i \(0.752412\pi\)
\(230\) 2559.18 3810.05i 0.733685 1.09229i
\(231\) 73.5017 0.0209353
\(232\) 789.307i 0.223364i
\(233\) 6055.71i 1.70267i 0.524621 + 0.851336i \(0.324207\pi\)
−0.524621 + 0.851336i \(0.675793\pi\)
\(234\) −179.266 −0.0500811
\(235\) 1439.39 + 966.828i 0.399555 + 0.268378i
\(236\) 1796.51 0.495519
\(237\) 1174.22i 0.321830i
\(238\) 214.100i 0.0583110i
\(239\) 2028.23 0.548935 0.274467 0.961596i \(-0.411498\pi\)
0.274467 + 0.961596i \(0.411498\pi\)
\(240\) 445.489 + 299.232i 0.119817 + 0.0804806i
\(241\) −1848.47 −0.494067 −0.247033 0.969007i \(-0.579456\pi\)
−0.247033 + 0.969007i \(0.579456\pi\)
\(242\) 2424.84i 0.644110i
\(243\) 243.000i 0.0641500i
\(244\) 1609.69 0.422335
\(245\) −2106.70 + 3136.41i −0.549357 + 0.817868i
\(246\) −2896.63 −0.750740
\(247\) 250.746i 0.0645935i
\(248\) 248.000i 0.0635001i
\(249\) 2808.34 0.714744
\(250\) −565.232 + 2737.34i −0.142994 + 0.692498i
\(251\) 4491.18 1.12941 0.564703 0.825294i \(-0.308991\pi\)
0.564703 + 0.825294i \(0.308991\pi\)
\(252\) 80.9977i 0.0202475i
\(253\) 2235.17i 0.555431i
\(254\) 509.340 0.125822
\(255\) −889.824 + 1324.75i −0.218521 + 0.325329i
\(256\) 256.000 0.0625000
\(257\) 7305.07i 1.77306i −0.462667 0.886532i \(-0.653107\pi\)
0.462667 0.886532i \(-0.346893\pi\)
\(258\) 1646.30i 0.397264i
\(259\) 294.742 0.0707118
\(260\) −369.726 248.343i −0.0881902 0.0592368i
\(261\) −887.971 −0.210590
\(262\) 5126.82i 1.20892i
\(263\) 91.2037i 0.0213835i −0.999943 0.0106918i \(-0.996597\pi\)
0.999943 0.0106918i \(-0.00340335\pi\)
\(264\) −261.347 −0.0609272
\(265\) 1904.45 + 1279.21i 0.441470 + 0.296533i
\(266\) −113.295 −0.0261148
\(267\) 1502.87i 0.344471i
\(268\) 2839.32i 0.647161i
\(269\) 6053.61 1.37210 0.686050 0.727555i \(-0.259343\pi\)
0.686050 + 0.727555i \(0.259343\pi\)
\(270\) 336.636 501.175i 0.0758778 0.112965i
\(271\) −7739.32 −1.73480 −0.867399 0.497614i \(-0.834210\pi\)
−0.867399 + 0.497614i \(0.834210\pi\)
\(272\) 761.265i 0.169700i
\(273\) 67.2228i 0.0149030i
\(274\) −2268.46 −0.500157
\(275\) −514.793 1260.08i −0.112884 0.276311i
\(276\) −2463.12 −0.537183
\(277\) 3573.85i 0.775206i −0.921826 0.387603i \(-0.873303\pi\)
0.921826 0.387603i \(-0.126697\pi\)
\(278\) 4979.42i 1.07427i
\(279\) 279.000 0.0598684
\(280\) −112.209 + 167.054i −0.0239491 + 0.0356549i
\(281\) 2091.82 0.444083 0.222042 0.975037i \(-0.428728\pi\)
0.222042 + 0.975037i \(0.428728\pi\)
\(282\) 930.538i 0.196499i
\(283\) 2554.99i 0.536672i −0.963325 0.268336i \(-0.913526\pi\)
0.963325 0.268336i \(-0.0864737\pi\)
\(284\) −369.771 −0.0772602
\(285\) 701.014 + 470.866i 0.145700 + 0.0978656i
\(286\) 216.900 0.0448447
\(287\) 1086.20i 0.223403i
\(288\) 288.000i 0.0589256i
\(289\) 2649.23 0.539229
\(290\) −1831.39 1230.14i −0.370838 0.249090i
\(291\) 1254.69 0.252752
\(292\) 828.731i 0.166088i
\(293\) 3574.07i 0.712625i 0.934367 + 0.356313i \(0.115966\pi\)
−0.934367 + 0.356313i \(0.884034\pi\)
\(294\) 2027.63 0.402223
\(295\) 2799.85 4168.35i 0.552589 0.822680i
\(296\) −1048.00 −0.205790
\(297\) 294.015i 0.0574427i
\(298\) 2912.40i 0.566144i
\(299\) 2044.23 0.395388
\(300\) 1388.59 567.294i 0.267234 0.109176i
\(301\) −617.345 −0.118216
\(302\) 3804.91i 0.724994i
\(303\) 881.311i 0.167096i
\(304\) 402.837 0.0760010
\(305\) 2508.70 3734.89i 0.470976 0.701177i
\(306\) 856.423 0.159995
\(307\) 1272.37i 0.236541i 0.992981 + 0.118270i \(0.0377350\pi\)
−0.992981 + 0.118270i \(0.962265\pi\)
\(308\) 98.0022i 0.0181305i
\(309\) −5710.52 −1.05133
\(310\) 575.423 + 386.508i 0.105425 + 0.0708135i
\(311\) −211.004 −0.0384725 −0.0192362 0.999815i \(-0.506123\pi\)
−0.0192362 + 0.999815i \(0.506123\pi\)
\(312\) 239.021i 0.0433715i
\(313\) 7743.12i 1.39830i 0.714976 + 0.699149i \(0.246437\pi\)
−0.714976 + 0.699149i \(0.753563\pi\)
\(314\) 4349.52 0.781712
\(315\) 187.935 + 126.235i 0.0336157 + 0.0225795i
\(316\) 1565.63 0.278713
\(317\) 5554.49i 0.984137i −0.870556 0.492068i \(-0.836241\pi\)
0.870556 0.492068i \(-0.163759\pi\)
\(318\) 1231.19i 0.217113i
\(319\) 1074.39 0.188571
\(320\) 398.976 593.985i 0.0696982 0.103765i
\(321\) −4553.65 −0.791775
\(322\) 923.645i 0.159853i
\(323\) 1197.91i 0.206358i
\(324\) −324.000 −0.0555556
\(325\) −1152.44 + 470.817i −0.196694 + 0.0803576i
\(326\) −574.555 −0.0976124
\(327\) 5625.44i 0.951338i
\(328\) 3862.17i 0.650160i
\(329\) 348.942 0.0584735
\(330\) −407.309 + 606.391i −0.0679442 + 0.101154i
\(331\) −3684.80 −0.611888 −0.305944 0.952050i \(-0.598972\pi\)
−0.305944 + 0.952050i \(0.598972\pi\)
\(332\) 3744.45i 0.618986i
\(333\) 1179.00i 0.194020i
\(334\) 1459.32 0.239072
\(335\) 6587.94 + 4425.08i 1.07444 + 0.721695i
\(336\) 107.997 0.0175349
\(337\) 8299.86i 1.34161i 0.741634 + 0.670804i \(0.234051\pi\)
−0.741634 + 0.670804i \(0.765949\pi\)
\(338\) 4195.63i 0.675184i
\(339\) −5134.15 −0.822563
\(340\) 1766.33 + 1186.43i 0.281743 + 0.189245i
\(341\) −337.573 −0.0536088
\(342\) 453.192i 0.0716544i
\(343\) 1532.07i 0.241177i
\(344\) 2195.07 0.344041
\(345\) −3838.78 + 5715.07i −0.599052 + 0.891853i
\(346\) 1237.97 0.192352
\(347\) 762.646i 0.117985i −0.998258 0.0589927i \(-0.981211\pi\)
0.998258 0.0589927i \(-0.0187889\pi\)
\(348\) 1183.96i 0.182376i
\(349\) −2941.61 −0.451177 −0.225589 0.974223i \(-0.572431\pi\)
−0.225589 + 0.974223i \(0.572431\pi\)
\(350\) 212.729 + 520.706i 0.0324882 + 0.0795226i
\(351\) 268.899 0.0408910
\(352\) 348.462i 0.0527645i
\(353\) 815.296i 0.122929i 0.998109 + 0.0614643i \(0.0195770\pi\)
−0.998109 + 0.0614643i \(0.980423\pi\)
\(354\) −2694.76 −0.404590
\(355\) −576.288 + 857.963i −0.0861583 + 0.128270i
\(356\) −2003.82 −0.298321
\(357\) 321.150i 0.0476108i
\(358\) 3350.68i 0.494662i
\(359\) −8579.01 −1.26123 −0.630617 0.776094i \(-0.717198\pi\)
−0.630617 + 0.776094i \(0.717198\pi\)
\(360\) −668.233 448.848i −0.0978305 0.0657121i
\(361\) −6225.10 −0.907582
\(362\) 2118.38i 0.307568i
\(363\) 3637.26i 0.525914i
\(364\) −89.6303 −0.0129063
\(365\) 1922.87 + 1291.58i 0.275746 + 0.185217i
\(366\) −2414.53 −0.344835
\(367\) 11319.4i 1.60999i 0.593280 + 0.804996i \(0.297833\pi\)
−0.593280 + 0.804996i \(0.702167\pi\)
\(368\) 3284.16i 0.465214i
\(369\) 4344.94 0.612977
\(370\) −1633.31 + 2431.63i −0.229491 + 0.341660i
\(371\) 461.684 0.0646076
\(372\) 372.000i 0.0518476i
\(373\) 4921.92i 0.683237i 0.939839 + 0.341619i \(0.110975\pi\)
−0.939839 + 0.341619i \(0.889025\pi\)
\(374\) −1036.22 −0.143266
\(375\) 847.847 4106.01i 0.116754 0.565422i
\(376\) −1240.72 −0.170173
\(377\) 982.609i 0.134236i
\(378\) 121.497i 0.0165320i
\(379\) 6361.23 0.862149 0.431075 0.902316i \(-0.358135\pi\)
0.431075 + 0.902316i \(0.358135\pi\)
\(380\) 627.822 934.685i 0.0847541 0.126180i
\(381\) −764.011 −0.102733
\(382\) 5416.60i 0.725490i
\(383\) 6047.87i 0.806871i 0.915008 + 0.403436i \(0.132184\pi\)
−0.915008 + 0.403436i \(0.867816\pi\)
\(384\) −384.000 −0.0510310
\(385\) −227.390 152.736i −0.0301010 0.0202186i
\(386\) −2930.73 −0.386451
\(387\) 2469.45i 0.324365i
\(388\) 1672.91i 0.218890i
\(389\) 6144.42 0.800860 0.400430 0.916327i \(-0.368861\pi\)
0.400430 + 0.916327i \(0.368861\pi\)
\(390\) 554.589 + 372.514i 0.0720070 + 0.0483666i
\(391\) −9766.10 −1.26315
\(392\) 2703.50i 0.348335i
\(393\) 7690.23i 0.987076i
\(394\) −3632.87 −0.464521
\(395\) 2440.03 3632.65i 0.310813 0.462730i
\(396\) 392.020 0.0497468
\(397\) 7404.02i 0.936013i 0.883725 + 0.468006i \(0.155028\pi\)
−0.883725 + 0.468006i \(0.844972\pi\)
\(398\) 2556.25i 0.321942i
\(399\) 169.942 0.0213227
\(400\) −756.392 1851.45i −0.0945490 0.231431i
\(401\) 9297.88 1.15789 0.578945 0.815366i \(-0.303465\pi\)
0.578945 + 0.815366i \(0.303465\pi\)
\(402\) 4258.98i 0.528404i
\(403\) 308.735i 0.0381618i
\(404\) 1175.08 0.144709
\(405\) −504.954 + 751.762i −0.0619540 + 0.0922355i
\(406\) −443.973 −0.0542709
\(407\) 1426.52i 0.173734i
\(408\) 1141.90i 0.138560i
\(409\) −1759.08 −0.212668 −0.106334 0.994330i \(-0.533911\pi\)
−0.106334 + 0.994330i \(0.533911\pi\)
\(410\) 8961.21 + 6019.19i 1.07942 + 0.725040i
\(411\) 3402.70 0.408376
\(412\) 7614.02i 0.910476i
\(413\) 1010.51i 0.120396i
\(414\) 3694.68 0.438608
\(415\) −8688.08 5835.73i −1.02767 0.690276i
\(416\) 318.695 0.0375608
\(417\) 7469.13i 0.877134i
\(418\) 548.334i 0.0641624i
\(419\) −2560.32 −0.298520 −0.149260 0.988798i \(-0.547689\pi\)
−0.149260 + 0.988798i \(0.547689\pi\)
\(420\) 168.313 250.580i 0.0195544 0.0291121i
\(421\) −521.060 −0.0603204 −0.0301602 0.999545i \(-0.509602\pi\)
−0.0301602 + 0.999545i \(0.509602\pi\)
\(422\) 3938.30i 0.454298i
\(423\) 1395.81i 0.160441i
\(424\) −1641.59 −0.188025
\(425\) 5505.65 2249.28i 0.628384 0.256720i
\(426\) 554.657 0.0630827
\(427\) 905.424i 0.102615i
\(428\) 6071.53i 0.685697i
\(429\) −325.351 −0.0366156
\(430\) 3421.01 5093.11i 0.383664 0.571190i
\(431\) 9908.05 1.10732 0.553659 0.832743i \(-0.313231\pi\)
0.553659 + 0.832743i \(0.313231\pi\)
\(432\) 432.000i 0.0481125i
\(433\) 6923.06i 0.768363i 0.923258 + 0.384181i \(0.125516\pi\)
−0.923258 + 0.384181i \(0.874484\pi\)
\(434\) 139.496 0.0154286
\(435\) 2747.09 + 1845.20i 0.302788 + 0.203381i
\(436\) 7500.59 0.823883
\(437\) 5167.90i 0.565708i
\(438\) 1243.10i 0.135611i
\(439\) −9678.94 −1.05228 −0.526140 0.850398i \(-0.676361\pi\)
−0.526140 + 0.850398i \(0.676361\pi\)
\(440\) 808.521 + 543.078i 0.0876016 + 0.0588414i
\(441\) −3041.44 −0.328414
\(442\) 947.700i 0.101985i
\(443\) 5777.93i 0.619679i −0.950789 0.309839i \(-0.899725\pi\)
0.950789 0.309839i \(-0.100275\pi\)
\(444\) 1572.00 0.168027
\(445\) −3122.95 + 4649.37i −0.332679 + 0.495284i
\(446\) 6041.62 0.641432
\(447\) 4368.61i 0.462255i
\(448\) 143.996i 0.0151856i
\(449\) 5492.87 0.577337 0.288669 0.957429i \(-0.406787\pi\)
0.288669 + 0.957429i \(0.406787\pi\)
\(450\) −2082.88 + 850.941i −0.218196 + 0.0891417i
\(451\) −5257.11 −0.548886
\(452\) 6845.54i 0.712360i
\(453\) 5707.37i 0.591955i
\(454\) −3019.40 −0.312131
\(455\) −139.689 + 207.965i −0.0143928 + 0.0214276i
\(456\) −604.256 −0.0620545
\(457\) 15965.8i 1.63424i 0.576469 + 0.817119i \(0.304430\pi\)
−0.576469 + 0.817119i \(0.695570\pi\)
\(458\) 9875.61i 1.00755i
\(459\) −1284.64 −0.130635
\(460\) 7620.10 + 5118.37i 0.772367 + 0.518794i
\(461\) −2081.38 −0.210281 −0.105141 0.994457i \(-0.533529\pi\)
−0.105141 + 0.994457i \(0.533529\pi\)
\(462\) 147.003i 0.0148035i
\(463\) 297.022i 0.0298138i 0.999889 + 0.0149069i \(0.00474518\pi\)
−0.999889 + 0.0149069i \(0.995255\pi\)
\(464\) 1578.61 0.157943
\(465\) −863.135 579.762i −0.0860794 0.0578190i
\(466\) −12111.4 −1.20397
\(467\) 13958.1i 1.38309i 0.722334 + 0.691545i \(0.243069\pi\)
−0.722334 + 0.691545i \(0.756931\pi\)
\(468\) 358.532i 0.0354127i
\(469\) 1597.07 0.157241
\(470\) −1933.66 + 2878.78i −0.189772 + 0.282528i
\(471\) −6524.28 −0.638265
\(472\) 3593.01i 0.350385i
\(473\) 2987.88i 0.290450i
\(474\) −2348.44 −0.227568
\(475\) −1190.25 2913.41i −0.114973 0.281424i
\(476\) 428.200 0.0412321
\(477\) 1846.79i 0.177272i
\(478\) 4056.46i 0.388155i
\(479\) 9196.23 0.877216 0.438608 0.898678i \(-0.355472\pi\)
0.438608 + 0.898678i \(0.355472\pi\)
\(480\) −598.464 + 890.978i −0.0569084 + 0.0847237i
\(481\) −1304.66 −0.123674
\(482\) 3696.93i 0.349358i
\(483\) 1385.47i 0.130520i
\(484\) 4849.68 0.455455
\(485\) −3881.59 2607.24i −0.363410 0.244100i
\(486\) 486.000 0.0453609
\(487\) 19063.6i 1.77383i −0.461936 0.886913i \(-0.652845\pi\)
0.461936 0.886913i \(-0.347155\pi\)
\(488\) 3219.38i 0.298636i
\(489\) 861.832 0.0797002
\(490\) −6272.81 4213.41i −0.578320 0.388454i
\(491\) −13964.5 −1.28352 −0.641760 0.766906i \(-0.721795\pi\)
−0.641760 + 0.766906i \(0.721795\pi\)
\(492\) 5793.25i 0.530853i
\(493\) 4694.31i 0.428846i
\(494\) 501.492 0.0456745
\(495\) 610.963 909.586i 0.0554762 0.0825916i
\(496\) −496.000 −0.0449013
\(497\) 207.990i 0.0187719i
\(498\) 5616.68i 0.505400i
\(499\) 9699.36 0.870146 0.435073 0.900395i \(-0.356723\pi\)
0.435073 + 0.900395i \(0.356723\pi\)
\(500\) −5474.67 1130.46i −0.489670 0.101112i
\(501\) −2188.97 −0.195202
\(502\) 8982.37i 0.798611i
\(503\) 2300.90i 0.203960i 0.994786 + 0.101980i \(0.0325178\pi\)
−0.994786 + 0.101980i \(0.967482\pi\)
\(504\) −161.995 −0.0143172
\(505\) 1831.36 2726.49i 0.161375 0.240252i
\(506\) −4470.34 −0.392749
\(507\) 6293.44i 0.551285i
\(508\) 1018.68i 0.0889698i
\(509\) 4600.37 0.400605 0.200302 0.979734i \(-0.435808\pi\)
0.200302 + 0.979734i \(0.435808\pi\)
\(510\) −2649.49 1779.65i −0.230042 0.154518i
\(511\) 466.148 0.0403546
\(512\) 512.000i 0.0441942i
\(513\) 679.788i 0.0585056i
\(514\) 14610.1 1.25375
\(515\) 17666.5 + 11866.5i 1.51161 + 1.01534i
\(516\) −3292.60 −0.280908
\(517\) 1688.84i 0.143666i
\(518\) 589.483i 0.0500008i
\(519\) −1856.96 −0.157055
\(520\) 496.686 739.453i 0.0418867 0.0623599i
\(521\) −21170.9 −1.78025 −0.890127 0.455712i \(-0.849385\pi\)
−0.890127 + 0.455712i \(0.849385\pi\)
\(522\) 1775.94i 0.148910i
\(523\) 11372.5i 0.950834i −0.879761 0.475417i \(-0.842297\pi\)
0.879761 0.475417i \(-0.157703\pi\)
\(524\) 10253.6 0.854833
\(525\) −319.094 781.059i −0.0265265 0.0649299i
\(526\) 182.407 0.0151204
\(527\) 1474.95i 0.121916i
\(528\) 522.693i 0.0430820i
\(529\) −29964.8 −2.46279
\(530\) −2558.42 + 3808.90i −0.209680 + 0.312166i
\(531\) 4042.14 0.330346
\(532\) 226.590i 0.0184660i
\(533\) 4808.02i 0.390728i
\(534\) 3005.73 0.243578
\(535\) 14087.5 + 9462.48i 1.13842 + 0.764670i
\(536\) −5678.64 −0.457612
\(537\) 5026.02i 0.403890i
\(538\) 12107.2i 0.970221i
\(539\) 3679.95 0.294076
\(540\) 1002.35 + 673.272i 0.0798783 + 0.0536537i
\(541\) −11362.4 −0.902971 −0.451485 0.892279i \(-0.649106\pi\)
−0.451485 + 0.892279i \(0.649106\pi\)
\(542\) 15478.6i 1.22669i
\(543\) 3177.57i 0.251128i
\(544\) −1522.53 −0.119996
\(545\) 11689.7 17403.3i 0.918771 1.36784i
\(546\) 134.446 0.0105380
\(547\) 15087.7i 1.17934i −0.807643 0.589672i \(-0.799257\pi\)
0.807643 0.589672i \(-0.200743\pi\)
\(548\) 4536.93i 0.353664i
\(549\) 3621.80 0.281557
\(550\) 2520.16 1029.59i 0.195382 0.0798213i
\(551\) 2484.08 0.192061
\(552\) 4926.25i 0.379846i
\(553\) 880.640i 0.0677190i
\(554\) 7147.71 0.548153
\(555\) 2449.96 3647.44i 0.187379 0.278964i
\(556\) 9958.84 0.759620
\(557\) 14350.8i 1.09167i −0.837891 0.545837i \(-0.816212\pi\)
0.837891 0.545837i \(-0.183788\pi\)
\(558\) 558.000i 0.0423334i
\(559\) 2732.64 0.206759
\(560\) −334.107 224.418i −0.0252118 0.0169346i
\(561\) 1554.33 0.116977
\(562\) 4183.64i 0.314014i
\(563\) 4772.13i 0.357232i 0.983919 + 0.178616i \(0.0571619\pi\)
−0.983919 + 0.178616i \(0.942838\pi\)
\(564\) 1861.08 0.138946
\(565\) 15883.4 + 10668.8i 1.18269 + 0.794404i
\(566\) 5109.97 0.379484
\(567\) 182.245i 0.0134983i
\(568\) 739.542i 0.0546312i
\(569\) −21931.0 −1.61581 −0.807906 0.589311i \(-0.799399\pi\)
−0.807906 + 0.589311i \(0.799399\pi\)
\(570\) −941.732 + 1402.03i −0.0692015 + 0.103025i
\(571\) 12783.4 0.936897 0.468449 0.883491i \(-0.344813\pi\)
0.468449 + 0.883491i \(0.344813\pi\)
\(572\) 433.801i 0.0317100i
\(573\) 8124.90i 0.592360i
\(574\) 2172.41 0.157970
\(575\) 23751.8 9703.58i 1.72264 0.703769i
\(576\) 576.000 0.0416667
\(577\) 17598.4i 1.26973i −0.772625 0.634863i \(-0.781056\pi\)
0.772625 0.634863i \(-0.218944\pi\)
\(578\) 5298.46i 0.381292i
\(579\) 4396.09 0.315536
\(580\) 2460.27 3662.79i 0.176133 0.262222i
\(581\) −2106.19 −0.150395
\(582\) 2509.37i 0.178723i
\(583\) 2234.50i 0.158737i
\(584\) −1657.46 −0.117442
\(585\) −831.884 558.771i −0.0587935 0.0394912i
\(586\) −7148.13 −0.503902
\(587\) 7068.88i 0.497042i −0.968626 0.248521i \(-0.920055\pi\)
0.968626 0.248521i \(-0.0799446\pi\)
\(588\) 4055.25i 0.284415i
\(589\) −780.497 −0.0546007
\(590\) 8336.70 + 5599.71i 0.581723 + 0.390739i
\(591\) 5449.31 0.379280
\(592\) 2096.00i 0.145515i
\(593\) 22007.7i 1.52402i −0.647563 0.762012i \(-0.724212\pi\)
0.647563 0.762012i \(-0.275788\pi\)
\(594\) −588.030 −0.0406181
\(595\) 667.349 993.532i 0.0459809 0.0684552i
\(596\) 5824.81 0.400324
\(597\) 3834.37i 0.262865i
\(598\) 4088.46i 0.279581i
\(599\) −11236.2 −0.766444 −0.383222 0.923656i \(-0.625186\pi\)
−0.383222 + 0.923656i \(0.625186\pi\)
\(600\) 1134.59 + 2777.18i 0.0771990 + 0.188963i
\(601\) 15445.9 1.04834 0.524168 0.851615i \(-0.324376\pi\)
0.524168 + 0.851615i \(0.324376\pi\)
\(602\) 1234.69i 0.0835917i
\(603\) 6388.47i 0.431440i
\(604\) 7609.83 0.512648
\(605\) 7558.22 11252.5i 0.507910 0.756163i
\(606\) −1762.62 −0.118154
\(607\) 22777.7i 1.52309i 0.648111 + 0.761546i \(0.275559\pi\)
−0.648111 + 0.761546i \(0.724441\pi\)
\(608\) 805.674i 0.0537408i
\(609\) 665.959 0.0443120
\(610\) 7469.77 + 5017.40i 0.495807 + 0.333030i
\(611\) −1544.57 −0.102269
\(612\) 1712.85i 0.113134i
\(613\) 5876.19i 0.387173i 0.981083 + 0.193587i \(0.0620120\pi\)
−0.981083 + 0.193587i \(0.937988\pi\)
\(614\) −2544.74 −0.167260
\(615\) −13441.8 9028.78i −0.881343 0.591993i
\(616\) 196.004 0.0128202
\(617\) 8356.68i 0.545263i 0.962119 + 0.272631i \(0.0878940\pi\)
−0.962119 + 0.272631i \(0.912106\pi\)
\(618\) 11421.0i 0.743400i
\(619\) −2054.93 −0.133433 −0.0667163 0.997772i \(-0.521252\pi\)
−0.0667163 + 0.997772i \(0.521252\pi\)
\(620\) −773.016 + 1150.85i −0.0500727 + 0.0745469i
\(621\) −5542.03 −0.358122
\(622\) 422.008i 0.0272042i
\(623\) 1127.12i 0.0724831i
\(624\) −478.042 −0.0306683
\(625\) −11155.2 + 10940.8i −0.713935 + 0.700212i
\(626\) −15486.2 −0.988746
\(627\) 822.501i 0.0523884i
\(628\) 8699.04i 0.552754i
\(629\) 6232.86 0.395104
\(630\) −252.470 + 375.871i −0.0159661 + 0.0237699i
\(631\) −15517.2 −0.978972 −0.489486 0.872011i \(-0.662816\pi\)
−0.489486 + 0.872011i \(0.662816\pi\)
\(632\) 3131.25i 0.197080i
\(633\) 5907.46i 0.370933i
\(634\) 11109.0 0.695890
\(635\) 2363.60 + 1587.61i 0.147711 + 0.0992166i
\(636\) 2462.38 0.153522
\(637\) 3365.59i 0.209340i
\(638\) 2148.78i 0.133340i
\(639\) −831.985 −0.0515068
\(640\) 1187.97 + 797.952i 0.0733729 + 0.0492841i
\(641\) 21451.8 1.32183 0.660917 0.750459i \(-0.270167\pi\)
0.660917 + 0.750459i \(0.270167\pi\)
\(642\) 9107.29i 0.559869i
\(643\) 29219.0i 1.79204i −0.444012 0.896021i \(-0.646445\pi\)
0.444012 0.896021i \(-0.353555\pi\)
\(644\) 1847.29 0.113033
\(645\) −5131.51 + 7639.67i −0.313261 + 0.466374i
\(646\) −2395.83 −0.145917
\(647\) 17654.3i 1.07274i −0.843982 0.536371i \(-0.819795\pi\)
0.843982 0.536371i \(-0.180205\pi\)
\(648\) 648.000i 0.0392837i
\(649\) −4890.74 −0.295806
\(650\) −941.634 2304.87i −0.0568214 0.139084i
\(651\) −209.244 −0.0125974
\(652\) 1149.11i 0.0690224i
\(653\) 5833.34i 0.349581i 0.984606 + 0.174790i \(0.0559248\pi\)
−0.984606 + 0.174790i \(0.944075\pi\)
\(654\) −11250.9 −0.672698
\(655\) 15980.3 23791.1i 0.953286 1.41923i
\(656\) −7724.33 −0.459733
\(657\) 1864.65i 0.110726i
\(658\) 697.883i 0.0413470i
\(659\) 16793.6 0.992697 0.496349 0.868123i \(-0.334674\pi\)
0.496349 + 0.868123i \(0.334674\pi\)
\(660\) −1212.78 814.617i −0.0715264 0.0480438i
\(661\) −28701.3 −1.68888 −0.844442 0.535647i \(-0.820068\pi\)
−0.844442 + 0.535647i \(0.820068\pi\)
\(662\) 7369.59i 0.432670i
\(663\) 1421.55i 0.0832706i
\(664\) 7488.90 0.437689
\(665\) −525.745 353.140i −0.0306579 0.0205927i
\(666\) −2358.00 −0.137193
\(667\) 20251.7i 1.17563i
\(668\) 2918.63i 0.169050i
\(669\) −9062.42 −0.523727
\(670\) −8850.16 + 13175.9i −0.510315 + 0.759745i
\(671\) −4382.15 −0.252118
\(672\) 215.994i 0.0123990i
\(673\) 24650.9i 1.41192i −0.708251 0.705961i \(-0.750515\pi\)
0.708251 0.705961i \(-0.249485\pi\)
\(674\) −16599.7 −0.948661
\(675\) 3124.32 1276.41i 0.178156 0.0727839i
\(676\) −8391.26 −0.477427
\(677\) 30639.7i 1.73941i 0.493575 + 0.869703i \(0.335690\pi\)
−0.493575 + 0.869703i \(0.664310\pi\)
\(678\) 10268.3i 0.581640i
\(679\) −940.988 −0.0531838
\(680\) −2372.86 + 3532.66i −0.133816 + 0.199222i
\(681\) 4529.11 0.254854
\(682\) 675.145i 0.0379071i
\(683\) 18339.0i 1.02741i 0.857966 + 0.513706i \(0.171728\pi\)
−0.857966 + 0.513706i \(0.828272\pi\)
\(684\) 906.384 0.0506673
\(685\) −10526.8 7070.80i −0.587167 0.394396i
\(686\) −3064.13 −0.170538
\(687\) 14813.4i 0.822660i
\(688\) 4390.13i 0.243274i
\(689\) −2043.62 −0.112998
\(690\) −11430.1 7677.55i −0.630635 0.423593i
\(691\) 17528.7 0.965014 0.482507 0.875892i \(-0.339726\pi\)
0.482507 + 0.875892i \(0.339726\pi\)
\(692\) 2475.95i 0.136014i
\(693\) 220.505i 0.0120870i
\(694\) 1525.29 0.0834283
\(695\) 15520.8 23107.0i 0.847107 1.26115i
\(696\) −2367.92 −0.128960
\(697\) 22969.8i 1.24827i
\(698\) 5883.22i 0.319030i
\(699\) 18167.1 0.983038
\(700\) −1041.41 + 425.459i −0.0562309 + 0.0229726i
\(701\) −12315.1 −0.663531 −0.331766 0.943362i \(-0.607644\pi\)
−0.331766 + 0.943362i \(0.607644\pi\)
\(702\) 537.797i 0.0289143i
\(703\) 3298.23i 0.176949i
\(704\) −696.924 −0.0373101
\(705\) 2900.49 4318.17i 0.154948 0.230683i
\(706\) −1630.59 −0.0869237
\(707\) 660.964i 0.0351600i
\(708\) 5389.52i 0.286088i
\(709\) 25804.0 1.36684 0.683419 0.730026i \(-0.260492\pi\)
0.683419 + 0.730026i \(0.260492\pi\)
\(710\) −1715.93 1152.58i −0.0907008 0.0609231i
\(711\) 3522.66 0.185809
\(712\) 4007.64i 0.210945i
\(713\) 6363.07i 0.334220i
\(714\) −642.299 −0.0336659
\(715\) 1006.53 + 676.079i 0.0526462 + 0.0353621i
\(716\) 6701.36 0.349779
\(717\) 6084.69i 0.316928i
\(718\) 17158.0i 0.891827i
\(719\) 7816.03 0.405408 0.202704 0.979240i \(-0.435027\pi\)
0.202704 + 0.979240i \(0.435027\pi\)
\(720\) 897.696 1336.47i 0.0464655 0.0691766i
\(721\) 4282.77 0.221219
\(722\) 12450.2i 0.641757i
\(723\) 5545.40i 0.285250i
\(724\) 4236.76 0.217483
\(725\) −4664.27 11416.9i −0.238933 0.584846i
\(726\) −7274.52 −0.371877
\(727\) 31359.8i 1.59982i 0.600120 + 0.799910i \(0.295119\pi\)
−0.600120 + 0.799910i \(0.704881\pi\)
\(728\) 179.261i 0.00912616i
\(729\) −729.000 −0.0370370
\(730\) −2583.15 + 3845.73i −0.130968 + 0.194982i
\(731\) −13054.9 −0.660538
\(732\) 4829.07i 0.243835i
\(733\) 17990.0i 0.906516i −0.891379 0.453258i \(-0.850262\pi\)
0.891379 0.453258i \(-0.149738\pi\)
\(734\) −22638.8 −1.13844
\(735\) 9409.22 + 6320.11i 0.472196 + 0.317171i
\(736\) −6568.33 −0.328956
\(737\) 7729.65i 0.386330i
\(738\) 8689.88i 0.433440i
\(739\) 29472.2 1.46706 0.733528 0.679660i \(-0.237873\pi\)
0.733528 + 0.679660i \(0.237873\pi\)
\(740\) −4863.25 3266.62i −0.241590 0.162275i
\(741\) −752.239 −0.0372931
\(742\) 923.368i 0.0456845i
\(743\) 12651.6i 0.624687i −0.949969 0.312343i \(-0.898886\pi\)
0.949969 0.312343i \(-0.101114\pi\)
\(744\) 744.000 0.0366618
\(745\) 9077.96 13515.0i 0.446430 0.664634i
\(746\) −9843.85 −0.483122
\(747\) 8425.02i 0.412658i
\(748\) 2072.44i 0.101305i
\(749\) 3415.14 0.166604
\(750\) 8212.01 + 1695.69i 0.399814 + 0.0825574i
\(751\) −19116.4 −0.928850 −0.464425 0.885613i \(-0.653739\pi\)
−0.464425 + 0.885613i \(0.653739\pi\)
\(752\) 2481.43i 0.120331i
\(753\) 13473.6i 0.652063i
\(754\) 1965.22 0.0949192
\(755\) 11859.9 17656.7i 0.571691 0.851118i
\(756\) 242.993 0.0116899
\(757\) 29764.7i 1.42908i 0.699594 + 0.714541i \(0.253364\pi\)
−0.699594 + 0.714541i \(0.746636\pi\)
\(758\) 12722.5i 0.609632i
\(759\) 6705.51 0.320678
\(760\) 1869.37 + 1255.64i 0.0892226 + 0.0599302i
\(761\) −17484.0 −0.832845 −0.416422 0.909171i \(-0.636716\pi\)
−0.416422 + 0.909171i \(0.636716\pi\)
\(762\) 1528.02i 0.0726435i
\(763\) 4218.96i 0.200179i
\(764\) −10833.2 −0.512999
\(765\) 3974.24 + 2669.47i 0.187829 + 0.126163i
\(766\) −12095.7 −0.570544
\(767\) 4472.94i 0.210572i
\(768\) 768.000i 0.0360844i
\(769\) −11594.0 −0.543681 −0.271841 0.962342i \(-0.587632\pi\)
−0.271841 + 0.962342i \(0.587632\pi\)
\(770\) 305.473 454.780i 0.0142967 0.0212846i
\(771\) −21915.2 −1.02368
\(772\) 5861.45i 0.273262i
\(773\) 35985.8i 1.67441i −0.546888 0.837206i \(-0.684188\pi\)
0.546888 0.837206i \(-0.315812\pi\)
\(774\) 4938.90 0.229360
\(775\) 1465.51 + 3587.19i 0.0679260 + 0.166265i
\(776\) 3345.83 0.154779
\(777\) 884.225i 0.0408255i
\(778\) 12288.8i 0.566294i
\(779\) −12154.9 −0.559042
\(780\) −745.028 + 1109.18i −0.0342004 + 0.0509166i
\(781\) 1006.65 0.0461214
\(782\) 19532.2i 0.893184i
\(783\) 2663.91i 0.121584i
\(784\) 5407.00 0.246310
\(785\) 20184.0 + 13557.4i 0.917703 + 0.616415i
\(786\) −15380.5 −0.697968
\(787\) 18812.4i 0.852084i 0.904704 + 0.426042i \(0.140092\pi\)
−0.904704 + 0.426042i \(0.859908\pi\)
\(788\) 7265.74i 0.328466i
\(789\) −273.611 −0.0123458
\(790\) 7265.30 + 4880.06i 0.327200 + 0.219778i
\(791\) 3850.50 0.173082
\(792\) 784.040i 0.0351763i
\(793\) 4007.81i 0.179472i
\(794\) −14808.0 −0.661861
\(795\) 3837.62 5713.36i 0.171203 0.254883i
\(796\) −5112.49 −0.227648
\(797\) 7366.19i 0.327383i −0.986512 0.163691i \(-0.947660\pi\)
0.986512 0.163691i \(-0.0523401\pi\)
\(798\) 339.884i 0.0150774i
\(799\) 7379.02 0.326722
\(800\) 3702.90 1512.78i 0.163647 0.0668563i
\(801\) −4508.60 −0.198881
\(802\) 18595.8i 0.818752i
\(803\) 2256.11i 0.0991485i
\(804\) 8517.96 0.373638
\(805\) 2879.00 4286.18i 0.126051 0.187662i
\(806\) −617.471 −0.0269845
\(807\) 18160.8i 0.792182i
\(808\) 2350.16i 0.102325i
\(809\) −23990.8 −1.04261 −0.521304 0.853371i \(-0.674554\pi\)
−0.521304 + 0.853371i \(0.674554\pi\)
\(810\) −1503.52 1009.91i −0.0652203 0.0438081i
\(811\) −15345.3 −0.664420 −0.332210 0.943205i \(-0.607794\pi\)
−0.332210 + 0.943205i \(0.607794\pi\)
\(812\) 887.945i 0.0383753i
\(813\) 23218.0i 1.00159i
\(814\) 2853.03 0.122849
\(815\) −2666.23 1790.89i −0.114594 0.0769718i
\(816\) 2283.80 0.0979765
\(817\) 6908.24i 0.295824i
\(818\) 3518.17i 0.150379i
\(819\) −201.668 −0.00860422
\(820\) −12038.4 + 17922.4i −0.512681 + 0.763266i
\(821\) −14196.0 −0.603464 −0.301732 0.953393i \(-0.597565\pi\)
−0.301732 + 0.953393i \(0.597565\pi\)
\(822\) 6805.39i 0.288766i
\(823\) 27097.9i 1.14772i −0.818953 0.573860i \(-0.805445\pi\)
0.818953 0.573860i \(-0.194555\pi\)
\(824\) −15228.0 −0.643804
\(825\) −3780.24 + 1544.38i −0.159528 + 0.0651738i
\(826\) 2021.01 0.0851332
\(827\) 11753.8i 0.494219i 0.968988 + 0.247110i \(0.0794808\pi\)
−0.968988 + 0.247110i \(0.920519\pi\)
\(828\) 7389.37i 0.310143i
\(829\) 14701.0 0.615909 0.307954 0.951401i \(-0.400356\pi\)
0.307954 + 0.951401i \(0.400356\pi\)
\(830\) 11671.5 17376.2i 0.488099 0.726669i
\(831\) −10721.6 −0.447565
\(832\) 637.389i 0.0265595i
\(833\) 16078.8i 0.668783i
\(834\) −14938.3 −0.620227
\(835\) 6771.96 + 4548.68i 0.280663 + 0.188519i
\(836\) −1096.67 −0.0453697
\(837\) 837.000i 0.0345651i
\(838\) 5120.65i 0.211086i
\(839\) 27540.0 1.13324 0.566619 0.823980i \(-0.308251\pi\)
0.566619 + 0.823980i \(0.308251\pi\)
\(840\) 501.161 + 336.626i 0.0205853 + 0.0138270i
\(841\) −14654.5 −0.600866
\(842\) 1042.12i 0.0426530i
\(843\) 6275.45i 0.256392i
\(844\) −7876.61 −0.321237
\(845\) −13077.8 + 19469.8i −0.532413 + 0.792643i
\(846\) −2791.61 −0.113449
\(847\) 2727.87i 0.110662i
\(848\) 3283.18i 0.132954i
\(849\) −7664.96 −0.309848
\(850\) 4498.56 + 11011.3i 0.181528 + 0.444334i
\(851\) 26889.1 1.08313
\(852\) 1109.31i 0.0446062i
\(853\) 21437.7i 0.860509i −0.902708 0.430254i \(-0.858424\pi\)
0.902708 0.430254i \(-0.141576\pi\)
\(854\) 1810.85 0.0725597
\(855\) 1412.60 2103.04i 0.0565028 0.0841198i
\(856\) −12143.1 −0.484861
\(857\) 36381.2i 1.45013i 0.688682 + 0.725063i \(0.258189\pi\)
−0.688682 + 0.725063i \(0.741811\pi\)
\(858\) 650.701i 0.0258911i
\(859\) 28100.8 1.11616 0.558082 0.829786i \(-0.311537\pi\)
0.558082 + 0.829786i \(0.311537\pi\)
\(860\) 10186.2 + 6842.02i 0.403892 + 0.271292i
\(861\) −3258.61 −0.128982
\(862\) 19816.1i 0.782992i
\(863\) 25051.6i 0.988140i −0.869422 0.494070i \(-0.835509\pi\)
0.869422 0.494070i \(-0.164491\pi\)
\(864\) −864.000 −0.0340207
\(865\) 5744.83 + 3858.77i 0.225815 + 0.151679i
\(866\) −13846.1 −0.543315
\(867\) 7947.69i 0.311324i
\(868\) 278.992i 0.0109097i
\(869\) −4262.20 −0.166381
\(870\) −3690.41 + 5494.18i −0.143812 + 0.214104i
\(871\) −7069.34 −0.275012
\(872\) 15001.2i 0.582573i
\(873\) 3764.06i 0.145927i
\(874\) −10335.8 −0.400016
\(875\) −635.868 + 3079.42i −0.0245671 + 0.118975i
\(876\) 2486.19 0.0958912
\(877\) 6588.69i 0.253688i 0.991923 + 0.126844i \(0.0404847\pi\)
−0.991923 + 0.126844i \(0.959515\pi\)
\(878\) 19357.9i 0.744074i
\(879\) 10722.2 0.411434
\(880\) −1086.16 + 1617.04i −0.0416072 + 0.0619437i
\(881\) −1395.81 −0.0533779 −0.0266890 0.999644i \(-0.508496\pi\)
−0.0266890 + 0.999644i \(0.508496\pi\)
\(882\) 6082.88i 0.232224i
\(883\) 9799.28i 0.373468i −0.982411 0.186734i \(-0.940210\pi\)
0.982411 0.186734i \(-0.0597902\pi\)
\(884\) −1895.40 −0.0721145
\(885\) −12505.0 8399.56i −0.474975 0.319037i
\(886\) 11555.9 0.438179
\(887\) 44139.7i 1.67087i −0.549586 0.835437i \(-0.685215\pi\)
0.549586 0.835437i \(-0.314785\pi\)
\(888\) 3144.00i 0.118813i
\(889\) 572.992 0.0216170
\(890\) −9298.74 6245.91i −0.350219 0.235240i
\(891\) 882.045 0.0331645
\(892\) 12083.2i 0.453561i
\(893\) 3904.74i 0.146324i
\(894\) −8737.21 −0.326864
\(895\) 10444.1 15548.9i 0.390064 0.580717i
\(896\) 287.992 0.0107379
\(897\) 6132.69i 0.228277i
\(898\) 10985.7i 0.408239i
\(899\) −3058.57 −0.113469
\(900\) −1701.88 4165.76i −0.0630327 0.154288i
\(901\) 9763.16 0.360997
\(902\) 10514.2i 0.388121i
\(903\) 1852.03i 0.0682523i
\(904\) −13691.1 −0.503715
\(905\) 6602.99 9830.36i 0.242531 0.361074i
\(906\) −11414.7 −0.418575
\(907\) 37360.8i 1.36775i −0.729601 0.683874i \(-0.760294\pi\)
0.729601 0.683874i \(-0.239706\pi\)
\(908\) 6038.81i 0.220710i
\(909\) 2643.93 0.0964727
\(910\) −415.930 279.378i −0.0151516 0.0101772i
\(911\) −47104.8 −1.71312 −0.856560 0.516048i \(-0.827403\pi\)
−0.856560 + 0.516048i \(0.827403\pi\)
\(912\) 1208.51i 0.0438792i
\(913\) 10193.7i 0.369511i
\(914\) −31931.5 −1.15558
\(915\) −11204.7 7526.10i −0.404825 0.271918i
\(916\) 19751.2 0.712444
\(917\) 5767.51i 0.207699i
\(918\) 2569.27i 0.0923732i
\(919\) 41188.0 1.47842 0.739210 0.673475i \(-0.235199\pi\)
0.739210 + 0.673475i \(0.235199\pi\)
\(920\) −10236.7 + 15240.2i −0.366843 + 0.546146i
\(921\) 3817.11 0.136567
\(922\) 4162.76i 0.148691i
\(923\) 920.657i 0.0328319i
\(924\) −294.007 −0.0104676
\(925\) −15158.8 + 6192.96i −0.538829 + 0.220133i
\(926\) −594.044 −0.0210815
\(927\) 17131.6i 0.606984i
\(928\) 3157.23i 0.111682i
\(929\) −1742.42 −0.0615359 −0.0307680 0.999527i \(-0.509795\pi\)
−0.0307680 + 0.999527i \(0.509795\pi\)
\(930\) 1159.52 1726.27i 0.0408842 0.0608673i
\(931\) 8508.37 0.299517
\(932\) 24222.8i 0.851336i
\(933\) 633.012i 0.0222121i
\(934\) −27916.2 −0.977992
\(935\) −4808.58 3229.89i −0.168190 0.112972i
\(936\) 717.063 0.0250405
\(937\) 36994.2i 1.28981i 0.764265 + 0.644903i \(0.223102\pi\)
−0.764265 + 0.644903i \(0.776898\pi\)
\(938\) 3194.14i 0.111186i
\(939\) 23229.4 0.807307
\(940\) −5757.56 3867.31i −0.199777 0.134189i
\(941\) −11226.0 −0.388904 −0.194452 0.980912i \(-0.562293\pi\)
−0.194452 + 0.980912i \(0.562293\pi\)
\(942\) 13048.6i 0.451322i
\(943\) 99093.7i 3.42199i
\(944\) −7186.02 −0.247760
\(945\) 378.705 563.806i 0.0130363 0.0194080i
\(946\) −5975.76 −0.205379
\(947\) 46538.4i 1.59693i 0.602040 + 0.798466i \(0.294355\pi\)
−0.602040 + 0.798466i \(0.705645\pi\)
\(948\) 4696.88i 0.160915i
\(949\) −2063.38 −0.0705796
\(950\) 5826.82 2380.49i 0.198997 0.0812983i
\(951\) −16663.5 −0.568192
\(952\) 856.399i 0.0291555i
\(953\) 34396.9i 1.16918i 0.811330 + 0.584588i \(0.198744\pi\)
−0.811330 + 0.584588i \(0.801256\pi\)
\(954\) −3693.58 −0.125350
\(955\) −16883.5 + 25135.8i −0.572082 + 0.851701i
\(956\) −8112.93 −0.274467
\(957\) 3223.17i 0.108872i
\(958\) 18392.5i 0.620286i
\(959\) −2551.95 −0.0859299
\(960\) −1781.96 1196.93i −0.0599087 0.0402403i
\(961\) 961.000 0.0322581
\(962\) 2609.31i 0.0874507i
\(963\) 13660.9i 0.457131i
\(964\) 7393.86 0.247033
\(965\) −13600.1 9135.07i −0.453680 0.304734i
\(966\) −2770.94 −0.0922913
\(967\) 23605.6i 0.785010i −0.919750 0.392505i \(-0.871609\pi\)
0.919750 0.392505i \(-0.128391\pi\)
\(968\) 9699.36i 0.322055i
\(969\) 3593.74 0.119141
\(970\) 5214.47 7763.17i 0.172605 0.256970i
\(971\) 42252.5 1.39644 0.698222 0.715882i \(-0.253975\pi\)
0.698222 + 0.715882i \(0.253975\pi\)
\(972\) 972.000i 0.0320750i
\(973\) 5601.69i 0.184565i
\(974\) 38127.2 1.25428
\(975\) 1412.45 + 3457.31i 0.0463945 + 0.113562i
\(976\) −6438.75 −0.211168
\(977\) 29549.0i 0.967611i 0.875175 + 0.483806i \(0.160746\pi\)
−0.875175 + 0.483806i \(0.839254\pi\)
\(978\) 1723.66i 0.0563565i
\(979\) 5455.12 0.178086
\(980\) 8426.81 12545.6i 0.274678 0.408934i
\(981\) 16876.3 0.549255
\(982\) 27929.0i 0.907586i
\(983\) 39496.9i 1.28154i 0.767733 + 0.640770i \(0.221385\pi\)
−0.767733 + 0.640770i \(0.778615\pi\)
\(984\) 11586.5 0.375370
\(985\) −16858.4 11323.7i −0.545332 0.366296i
\(986\) −9388.63 −0.303240
\(987\) 1046.83i 0.0337597i
\(988\) 1002.98i 0.0322968i
\(989\) −56320.0 −1.81079
\(990\) 1819.17 + 1221.93i 0.0584011 + 0.0392276i
\(991\) −45557.2 −1.46032 −0.730158 0.683278i \(-0.760554\pi\)
−0.730158 + 0.683278i \(0.760554\pi\)
\(992\) 992.000i 0.0317500i
\(993\) 11054.4i 0.353273i
\(994\) −415.981 −0.0132738
\(995\) −7967.81 + 11862.3i −0.253866 + 0.377949i
\(996\) −11233.4 −0.357372
\(997\) 29562.1i 0.939058i −0.882917 0.469529i \(-0.844424\pi\)
0.882917 0.469529i \(-0.155576\pi\)
\(998\) 19398.7i 0.615286i
\(999\) 3537.00 0.112018
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 930.4.d.c.559.14 yes 20
5.4 even 2 inner 930.4.d.c.559.4 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.4.d.c.559.4 20 5.4 even 2 inner
930.4.d.c.559.14 yes 20 1.1 even 1 trivial