Properties

Label 245.4.e.l.226.2
Level $245$
Weight $4$
Character 245.226
Analytic conductor $14.455$
Analytic rank $0$
Dimension $4$
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] = [245,4,Mod(116,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("245.116");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.l.116.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.20711 - 3.82282i) q^{2} +(1.62132 + 2.80821i) q^{3} +(-5.74264 - 9.94655i) q^{4} +(2.50000 - 4.33013i) q^{5} +14.3137 q^{6} -15.3848 q^{8} +(8.24264 - 14.2767i) q^{9} +O(q^{10})\) \(q+(2.20711 - 3.82282i) q^{2} +(1.62132 + 2.80821i) q^{3} +(-5.74264 - 9.94655i) q^{4} +(2.50000 - 4.33013i) q^{5} +14.3137 q^{6} -15.3848 q^{8} +(8.24264 - 14.2767i) q^{9} +(-11.0355 - 19.1141i) q^{10} +(0.0710678 + 0.123093i) q^{11} +(18.6213 - 32.2531i) q^{12} +32.1421 q^{13} +16.2132 q^{15} +(11.9853 - 20.7591i) q^{16} +(-57.1838 - 99.0452i) q^{17} +(-36.3848 - 63.0203i) q^{18} +(21.6152 - 37.4387i) q^{19} -57.4264 q^{20} +0.627417 q^{22} +(-77.2315 + 133.769i) q^{23} +(-24.9437 - 43.2037i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(70.9411 - 122.874i) q^{26} +141.007 q^{27} -40.1472 q^{29} +(35.7843 - 61.9802i) q^{30} +(37.7107 + 65.3168i) q^{31} +(-114.445 - 198.224i) q^{32} +(-0.230447 + 0.399147i) q^{33} -504.843 q^{34} -189.338 q^{36} +(200.167 - 346.699i) q^{37} +(-95.4142 - 165.262i) q^{38} +(52.1127 + 90.2618i) q^{39} +(-38.4619 + 66.6180i) q^{40} +95.4264 q^{41} -340.071 q^{43} +(0.816234 - 1.41376i) q^{44} +(-41.2132 - 71.3834i) q^{45} +(340.916 + 590.484i) q^{46} +(-3.74517 + 6.48682i) q^{47} +77.7279 q^{48} -110.355 q^{50} +(185.426 - 321.168i) q^{51} +(-184.581 - 319.703i) q^{52} +(338.409 + 586.142i) q^{53} +(311.218 - 539.045i) q^{54} +0.710678 q^{55} +140.181 q^{57} +(-88.6091 + 153.476i) q^{58} +(398.090 + 689.513i) q^{59} +(-93.1066 - 161.265i) q^{60} +(-378.551 + 655.669i) q^{61} +332.926 q^{62} -818.602 q^{64} +(80.3553 - 139.180i) q^{65} +(1.01724 + 1.76192i) q^{66} +(370.290 + 641.362i) q^{67} +(-656.772 + 1137.56i) q^{68} -500.868 q^{69} +37.0253 q^{71} +(-126.811 + 219.643i) q^{72} +(40.4386 + 70.0417i) q^{73} +(-883.578 - 1530.40i) q^{74} +(40.5330 - 70.2052i) q^{75} -496.514 q^{76} +460.073 q^{78} +(158.679 - 274.840i) q^{79} +(-59.9264 - 103.796i) q^{80} +(6.06645 + 10.5074i) q^{81} +(210.616 - 364.798i) q^{82} +945.929 q^{83} -571.838 q^{85} +(-750.573 + 1300.03i) q^{86} +(-65.0914 - 112.742i) q^{87} +(-1.09336 - 1.89376i) q^{88} +(391.603 - 678.276i) q^{89} -363.848 q^{90} +1774.05 q^{92} +(-122.282 + 211.799i) q^{93} +(16.5320 + 28.6342i) q^{94} +(-108.076 - 187.193i) q^{95} +(371.103 - 642.769i) q^{96} -393.107 q^{97} +2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{2} - 2 q^{3} - 6 q^{4} + 10 q^{5} + 12 q^{6} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{2} - 2 q^{3} - 6 q^{4} + 10 q^{5} + 12 q^{6} + 12 q^{8} + 16 q^{9} - 30 q^{10} - 28 q^{11} + 66 q^{12} + 72 q^{13} - 20 q^{15} + 14 q^{16} - 76 q^{17} - 72 q^{18} + 160 q^{19} - 60 q^{20} - 88 q^{22} + 22 q^{23} - 162 q^{24} - 50 q^{25} + 148 q^{26} + 4 q^{27} - 500 q^{29} + 30 q^{30} - 132 q^{31} - 42 q^{32} - 148 q^{33} - 888 q^{34} - 384 q^{36} + 416 q^{37} - 376 q^{38} + 84 q^{39} + 30 q^{40} + 212 q^{41} - 1332 q^{43} + 156 q^{44} - 80 q^{45} + 402 q^{46} - 196 q^{47} + 260 q^{48} - 300 q^{50} + 572 q^{51} - 348 q^{52} + 952 q^{53} + 402 q^{54} - 280 q^{55} - 944 q^{57} - 510 q^{58} + 840 q^{59} - 330 q^{60} + 98 q^{61} + 8 q^{62} - 1204 q^{64} + 180 q^{65} + 236 q^{66} + 1286 q^{67} - 1524 q^{68} - 2852 q^{69} + 2128 q^{71} - 264 q^{72} - 172 q^{73} - 1792 q^{74} - 50 q^{75} + 288 q^{76} + 856 q^{78} + 1240 q^{79} - 70 q^{80} + 754 q^{81} + 438 q^{82} + 3812 q^{83} - 760 q^{85} - 2018 q^{86} + 970 q^{87} - 604 q^{88} + 650 q^{89} - 720 q^{90} + 5484 q^{92} - 1332 q^{93} + 332 q^{94} - 800 q^{95} + 1722 q^{96} + 1256 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.20711 3.82282i 0.780330 1.35157i −0.151419 0.988470i \(-0.548384\pi\)
0.931749 0.363102i \(-0.118282\pi\)
\(3\) 1.62132 + 2.80821i 0.312023 + 0.540440i 0.978800 0.204817i \(-0.0656600\pi\)
−0.666777 + 0.745257i \(0.732327\pi\)
\(4\) −5.74264 9.94655i −0.717830 1.24332i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 14.3137 0.973925
\(7\) 0 0
\(8\) −15.3848 −0.679917
\(9\) 8.24264 14.2767i 0.305283 0.528766i
\(10\) −11.0355 19.1141i −0.348974 0.604441i
\(11\) 0.0710678 + 0.123093i 0.00194798 + 0.00337400i 0.866998 0.498312i \(-0.166047\pi\)
−0.865050 + 0.501686i \(0.832713\pi\)
\(12\) 18.6213 32.2531i 0.447959 0.775888i
\(13\) 32.1421 0.685740 0.342870 0.939383i \(-0.388601\pi\)
0.342870 + 0.939383i \(0.388601\pi\)
\(14\) 0 0
\(15\) 16.2132 0.279082
\(16\) 11.9853 20.7591i 0.187270 0.324361i
\(17\) −57.1838 99.0452i −0.815829 1.41306i −0.908731 0.417383i \(-0.862947\pi\)
0.0929014 0.995675i \(-0.470386\pi\)
\(18\) −36.3848 63.0203i −0.476443 0.825223i
\(19\) 21.6152 37.4387i 0.260993 0.452054i −0.705513 0.708697i \(-0.749283\pi\)
0.966506 + 0.256643i \(0.0826166\pi\)
\(20\) −57.4264 −0.642047
\(21\) 0 0
\(22\) 0.627417 0.00608026
\(23\) −77.2315 + 133.769i −0.700169 + 1.21273i 0.268238 + 0.963353i \(0.413559\pi\)
−0.968407 + 0.249375i \(0.919775\pi\)
\(24\) −24.9437 43.2037i −0.212150 0.367455i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 70.9411 122.874i 0.535104 0.926827i
\(27\) 141.007 1.00507
\(28\) 0 0
\(29\) −40.1472 −0.257074 −0.128537 0.991705i \(-0.541028\pi\)
−0.128537 + 0.991705i \(0.541028\pi\)
\(30\) 35.7843 61.9802i 0.217776 0.377199i
\(31\) 37.7107 + 65.3168i 0.218485 + 0.378427i 0.954345 0.298707i \(-0.0965552\pi\)
−0.735860 + 0.677134i \(0.763222\pi\)
\(32\) −114.445 198.224i −0.632224 1.09504i
\(33\) −0.230447 + 0.399147i −0.00121563 + 0.00210553i
\(34\) −504.843 −2.54647
\(35\) 0 0
\(36\) −189.338 −0.876565
\(37\) 200.167 346.699i 0.889383 1.54046i 0.0487770 0.998810i \(-0.484468\pi\)
0.840606 0.541647i \(-0.182199\pi\)
\(38\) −95.4142 165.262i −0.407322 0.705502i
\(39\) 52.1127 + 90.2618i 0.213967 + 0.370602i
\(40\) −38.4619 + 66.6180i −0.152034 + 0.263331i
\(41\) 95.4264 0.363490 0.181745 0.983346i \(-0.441825\pi\)
0.181745 + 0.983346i \(0.441825\pi\)
\(42\) 0 0
\(43\) −340.071 −1.20605 −0.603027 0.797721i \(-0.706039\pi\)
−0.603027 + 0.797721i \(0.706039\pi\)
\(44\) 0.816234 1.41376i 0.00279663 0.00484391i
\(45\) −41.2132 71.3834i −0.136527 0.236471i
\(46\) 340.916 + 590.484i 1.09273 + 1.89266i
\(47\) −3.74517 + 6.48682i −0.0116232 + 0.0201319i −0.871778 0.489900i \(-0.837033\pi\)
0.860155 + 0.510032i \(0.170367\pi\)
\(48\) 77.7279 0.233730
\(49\) 0 0
\(50\) −110.355 −0.312132
\(51\) 185.426 321.168i 0.509115 0.881814i
\(52\) −184.581 319.703i −0.492245 0.852593i
\(53\) 338.409 + 586.142i 0.877058 + 1.51911i 0.854554 + 0.519362i \(0.173830\pi\)
0.0225038 + 0.999747i \(0.492836\pi\)
\(54\) 311.218 539.045i 0.784285 1.35842i
\(55\) 0.710678 0.00174232
\(56\) 0 0
\(57\) 140.181 0.325744
\(58\) −88.6091 + 153.476i −0.200603 + 0.347454i
\(59\) 398.090 + 689.513i 0.878423 + 1.52147i 0.853071 + 0.521795i \(0.174737\pi\)
0.0253519 + 0.999679i \(0.491929\pi\)
\(60\) −93.1066 161.265i −0.200334 0.346988i
\(61\) −378.551 + 655.669i −0.794565 + 1.37623i 0.128550 + 0.991703i \(0.458968\pi\)
−0.923115 + 0.384524i \(0.874366\pi\)
\(62\) 332.926 0.681962
\(63\) 0 0
\(64\) −818.602 −1.59883
\(65\) 80.3553 139.180i 0.153336 0.265586i
\(66\) 1.01724 + 1.76192i 0.00189718 + 0.00328602i
\(67\) 370.290 + 641.362i 0.675197 + 1.16947i 0.976411 + 0.215918i \(0.0692745\pi\)
−0.301215 + 0.953556i \(0.597392\pi\)
\(68\) −656.772 + 1137.56i −1.17125 + 2.02867i
\(69\) −500.868 −0.873876
\(70\) 0 0
\(71\) 37.0253 0.0618886 0.0309443 0.999521i \(-0.490149\pi\)
0.0309443 + 0.999521i \(0.490149\pi\)
\(72\) −126.811 + 219.643i −0.207567 + 0.359517i
\(73\) 40.4386 + 70.0417i 0.0648353 + 0.112298i 0.896621 0.442799i \(-0.146014\pi\)
−0.831786 + 0.555097i \(0.812681\pi\)
\(74\) −883.578 1530.40i −1.38802 2.40413i
\(75\) 40.5330 70.2052i 0.0624046 0.108088i
\(76\) −496.514 −0.749395
\(77\) 0 0
\(78\) 460.073 0.667859
\(79\) 158.679 274.840i 0.225985 0.391417i −0.730630 0.682774i \(-0.760773\pi\)
0.956614 + 0.291357i \(0.0941067\pi\)
\(80\) −59.9264 103.796i −0.0837497 0.145059i
\(81\) 6.06645 + 10.5074i 0.00832161 + 0.0144134i
\(82\) 210.616 364.798i 0.283642 0.491283i
\(83\) 945.929 1.25095 0.625477 0.780243i \(-0.284904\pi\)
0.625477 + 0.780243i \(0.284904\pi\)
\(84\) 0 0
\(85\) −571.838 −0.729700
\(86\) −750.573 + 1300.03i −0.941121 + 1.63007i
\(87\) −65.0914 112.742i −0.0802131 0.138933i
\(88\) −1.09336 1.89376i −0.00132446 0.00229404i
\(89\) 391.603 678.276i 0.466402 0.807832i −0.532861 0.846203i \(-0.678883\pi\)
0.999264 + 0.0383703i \(0.0122166\pi\)
\(90\) −363.848 −0.426144
\(91\) 0 0
\(92\) 1774.05 2.01041
\(93\) −122.282 + 211.799i −0.136345 + 0.236156i
\(94\) 16.5320 + 28.6342i 0.0181398 + 0.0314191i
\(95\) −108.076 187.193i −0.116720 0.202165i
\(96\) 371.103 642.769i 0.394537 0.683358i
\(97\) −393.107 −0.411484 −0.205742 0.978606i \(-0.565961\pi\)
−0.205742 + 0.978606i \(0.565961\pi\)
\(98\) 0 0
\(99\) 2.34315 0.00237874
\(100\) −143.566 + 248.664i −0.143566 + 0.248664i
\(101\) 227.221 + 393.558i 0.223855 + 0.387728i 0.955975 0.293448i \(-0.0948026\pi\)
−0.732121 + 0.681175i \(0.761469\pi\)
\(102\) −818.512 1417.70i −0.794556 1.37621i
\(103\) −351.850 + 609.422i −0.336590 + 0.582991i −0.983789 0.179330i \(-0.942607\pi\)
0.647199 + 0.762321i \(0.275940\pi\)
\(104\) −494.500 −0.466247
\(105\) 0 0
\(106\) 2987.62 2.73758
\(107\) −477.499 + 827.052i −0.431416 + 0.747235i −0.996996 0.0774592i \(-0.975319\pi\)
0.565579 + 0.824694i \(0.308653\pi\)
\(108\) −809.753 1402.53i −0.721468 1.24962i
\(109\) −144.463 250.218i −0.126946 0.219876i 0.795546 0.605893i \(-0.207184\pi\)
−0.922492 + 0.386017i \(0.873851\pi\)
\(110\) 1.56854 2.71680i 0.00135959 0.00235488i
\(111\) 1298.14 1.11003
\(112\) 0 0
\(113\) 1251.24 1.04165 0.520826 0.853663i \(-0.325624\pi\)
0.520826 + 0.853663i \(0.325624\pi\)
\(114\) 309.394 535.886i 0.254188 0.440266i
\(115\) 386.157 + 668.844i 0.313125 + 0.542348i
\(116\) 230.551 + 399.326i 0.184535 + 0.319625i
\(117\) 264.936 458.883i 0.209345 0.362596i
\(118\) 3514.51 2.74184
\(119\) 0 0
\(120\) −249.437 −0.189753
\(121\) 665.490 1152.66i 0.499992 0.866012i
\(122\) 1671.00 + 2894.26i 1.24005 + 2.14782i
\(123\) 154.717 + 267.977i 0.113417 + 0.196445i
\(124\) 433.118 750.182i 0.313670 0.543293i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1947.62 −1.36082 −0.680408 0.732833i \(-0.738198\pi\)
−0.680408 + 0.732833i \(0.738198\pi\)
\(128\) −891.185 + 1543.58i −0.615393 + 1.06589i
\(129\) −551.364 954.991i −0.376317 0.651800i
\(130\) −354.706 614.368i −0.239306 0.414490i
\(131\) 530.823 919.412i 0.354032 0.613201i −0.632920 0.774217i \(-0.718144\pi\)
0.986952 + 0.161016i \(0.0514771\pi\)
\(132\) 5.29351 0.00349046
\(133\) 0 0
\(134\) 3269.08 2.10750
\(135\) 352.518 610.579i 0.224740 0.389261i
\(136\) 879.759 + 1523.79i 0.554697 + 0.960763i
\(137\) 719.671 + 1246.51i 0.448800 + 0.777345i 0.998308 0.0581435i \(-0.0185181\pi\)
−0.549508 + 0.835489i \(0.685185\pi\)
\(138\) −1105.47 + 1914.73i −0.681911 + 1.18111i
\(139\) −662.132 −0.404038 −0.202019 0.979382i \(-0.564750\pi\)
−0.202019 + 0.979382i \(0.564750\pi\)
\(140\) 0 0
\(141\) −24.2885 −0.0145068
\(142\) 81.7187 141.541i 0.0482935 0.0836468i
\(143\) 2.28427 + 3.95647i 0.00133581 + 0.00231369i
\(144\) −197.581 342.220i −0.114341 0.198044i
\(145\) −100.368 + 173.842i −0.0574835 + 0.0995643i
\(146\) 357.009 0.202372
\(147\) 0 0
\(148\) −4597.94 −2.55370
\(149\) 393.555 681.657i 0.216384 0.374789i −0.737315 0.675549i \(-0.763907\pi\)
0.953700 + 0.300760i \(0.0972402\pi\)
\(150\) −178.921 309.901i −0.0973925 0.168689i
\(151\) 424.177 + 734.697i 0.228603 + 0.395952i 0.957394 0.288784i \(-0.0932509\pi\)
−0.728791 + 0.684736i \(0.759918\pi\)
\(152\) −332.545 + 575.985i −0.177454 + 0.307359i
\(153\) −1885.38 −0.996235
\(154\) 0 0
\(155\) 377.107 0.195419
\(156\) 598.529 1036.68i 0.307184 0.532058i
\(157\) 477.461 + 826.987i 0.242710 + 0.420387i 0.961485 0.274856i \(-0.0886302\pi\)
−0.718775 + 0.695243i \(0.755297\pi\)
\(158\) −700.444 1213.20i −0.352685 0.610869i
\(159\) −1097.34 + 1900.65i −0.547325 + 0.947995i
\(160\) −1144.45 −0.565478
\(161\) 0 0
\(162\) 53.5572 0.0259744
\(163\) 3.68211 6.37760i 0.00176936 0.00306461i −0.865139 0.501532i \(-0.832770\pi\)
0.866909 + 0.498467i \(0.166103\pi\)
\(164\) −548.000 949.163i −0.260924 0.451934i
\(165\) 1.15224 + 1.99573i 0.000543646 + 0.000941622i
\(166\) 2087.77 3616.12i 0.976157 1.69075i
\(167\) −2921.40 −1.35368 −0.676841 0.736129i \(-0.736651\pi\)
−0.676841 + 0.736129i \(0.736651\pi\)
\(168\) 0 0
\(169\) −1163.88 −0.529760
\(170\) −1262.11 + 2186.03i −0.569407 + 0.986242i
\(171\) −356.333 617.187i −0.159354 0.276009i
\(172\) 1952.91 + 3382.53i 0.865742 + 1.49951i
\(173\) −1984.78 + 3437.75i −0.872256 + 1.51079i −0.0125990 + 0.999921i \(0.504011\pi\)
−0.859657 + 0.510871i \(0.829323\pi\)
\(174\) −574.655 −0.250371
\(175\) 0 0
\(176\) 3.40707 0.00145919
\(177\) −1290.86 + 2235.84i −0.548177 + 0.949470i
\(178\) −1728.62 2994.05i −0.727895 1.26075i
\(179\) 552.976 + 957.782i 0.230901 + 0.399933i 0.958074 0.286522i \(-0.0924992\pi\)
−0.727172 + 0.686455i \(0.759166\pi\)
\(180\) −473.345 + 819.858i −0.196006 + 0.339492i
\(181\) 117.214 0.0481349 0.0240674 0.999710i \(-0.492338\pi\)
0.0240674 + 0.999710i \(0.492338\pi\)
\(182\) 0 0
\(183\) −2455.01 −0.991691
\(184\) 1188.19 2058.00i 0.476057 0.824555i
\(185\) −1000.83 1733.49i −0.397744 0.688913i
\(186\) 539.780 + 934.926i 0.212788 + 0.368560i
\(187\) 8.12785 14.0778i 0.00317843 0.00550521i
\(188\) 86.0286 0.0333738
\(189\) 0 0
\(190\) −954.142 −0.364320
\(191\) −501.300 + 868.277i −0.189910 + 0.328933i −0.945220 0.326434i \(-0.894153\pi\)
0.755310 + 0.655368i \(0.227486\pi\)
\(192\) −1327.22 2298.81i −0.498873 0.864073i
\(193\) −1628.88 2821.30i −0.607510 1.05224i −0.991649 0.128963i \(-0.958835\pi\)
0.384140 0.923275i \(-0.374498\pi\)
\(194\) −867.629 + 1502.78i −0.321093 + 0.556150i
\(195\) 521.127 0.191378
\(196\) 0 0
\(197\) −41.6955 −0.0150796 −0.00753981 0.999972i \(-0.502400\pi\)
−0.00753981 + 0.999972i \(0.502400\pi\)
\(198\) 5.17157 8.95743i 0.00185620 0.00321503i
\(199\) 1202.81 + 2083.32i 0.428466 + 0.742125i 0.996737 0.0807167i \(-0.0257209\pi\)
−0.568271 + 0.822841i \(0.692388\pi\)
\(200\) 192.310 + 333.090i 0.0679917 + 0.117765i
\(201\) −1200.72 + 2079.71i −0.421354 + 0.729807i
\(202\) 2006.00 0.698722
\(203\) 0 0
\(204\) −4259.35 −1.46183
\(205\) 238.566 413.208i 0.0812789 0.140779i
\(206\) 1553.14 + 2690.12i 0.525303 + 0.909851i
\(207\) 1273.18 + 2205.22i 0.427499 + 0.740450i
\(208\) 385.233 667.242i 0.128419 0.222428i
\(209\) 6.14459 0.00203364
\(210\) 0 0
\(211\) 1211.24 0.395190 0.197595 0.980284i \(-0.436687\pi\)
0.197595 + 0.980284i \(0.436687\pi\)
\(212\) 3886.72 6732.00i 1.25916 2.18092i
\(213\) 60.0298 + 103.975i 0.0193107 + 0.0334471i
\(214\) 2107.78 + 3650.78i 0.673294 + 1.16618i
\(215\) −850.178 + 1472.55i −0.269682 + 0.467103i
\(216\) −2169.36 −0.683363
\(217\) 0 0
\(218\) −1275.38 −0.396238
\(219\) −131.128 + 227.120i −0.0404603 + 0.0700792i
\(220\) −4.08117 7.06879i −0.00125069 0.00216626i
\(221\) −1838.01 3183.52i −0.559447 0.968991i
\(222\) 2865.13 4962.54i 0.866192 1.50029i
\(223\) −4164.99 −1.25071 −0.625354 0.780341i \(-0.715046\pi\)
−0.625354 + 0.780341i \(0.715046\pi\)
\(224\) 0 0
\(225\) −412.132 −0.122113
\(226\) 2761.62 4783.26i 0.812832 1.40787i
\(227\) 1178.12 + 2040.57i 0.344470 + 0.596639i 0.985257 0.171079i \(-0.0547254\pi\)
−0.640788 + 0.767718i \(0.721392\pi\)
\(228\) −805.008 1394.31i −0.233829 0.405003i
\(229\) 2172.58 3763.02i 0.626935 1.08588i −0.361228 0.932477i \(-0.617642\pi\)
0.988163 0.153406i \(-0.0490242\pi\)
\(230\) 3409.16 0.977363
\(231\) 0 0
\(232\) 617.655 0.174789
\(233\) −1229.12 + 2128.91i −0.345591 + 0.598581i −0.985461 0.169902i \(-0.945655\pi\)
0.639870 + 0.768483i \(0.278988\pi\)
\(234\) −1169.48 2025.61i −0.326716 0.565889i
\(235\) 18.7258 + 32.4341i 0.00519804 + 0.00900326i
\(236\) 4572.18 7919.25i 1.26112 2.18432i
\(237\) 1029.08 0.282050
\(238\) 0 0
\(239\) 322.304 0.0872307 0.0436154 0.999048i \(-0.486112\pi\)
0.0436154 + 0.999048i \(0.486112\pi\)
\(240\) 194.320 336.572i 0.0522637 0.0905234i
\(241\) −2505.62 4339.86i −0.669714 1.15998i −0.977984 0.208680i \(-0.933083\pi\)
0.308270 0.951299i \(-0.400250\pi\)
\(242\) −2937.61 5088.10i −0.780318 1.35155i
\(243\) 1883.93 3263.05i 0.497341 0.861420i
\(244\) 8695.53 2.28145
\(245\) 0 0
\(246\) 1365.91 0.354012
\(247\) 694.759 1203.36i 0.178974 0.309991i
\(248\) −580.170 1004.88i −0.148552 0.257299i
\(249\) 1533.65 + 2656.37i 0.390327 + 0.676066i
\(250\) −275.888 + 477.853i −0.0697948 + 0.120888i
\(251\) −3936.95 −0.990031 −0.495015 0.868884i \(-0.664838\pi\)
−0.495015 + 0.868884i \(0.664838\pi\)
\(252\) 0 0
\(253\) −21.9547 −0.00545565
\(254\) −4298.62 + 7445.42i −1.06189 + 1.83924i
\(255\) −927.132 1605.84i −0.227683 0.394359i
\(256\) 659.471 + 1142.24i 0.161004 + 0.278867i
\(257\) −1813.08 + 3140.35i −0.440066 + 0.762216i −0.997694 0.0678748i \(-0.978378\pi\)
0.557628 + 0.830091i \(0.311711\pi\)
\(258\) −4867.68 −1.17461
\(259\) 0 0
\(260\) −1845.81 −0.440277
\(261\) −330.919 + 573.168i −0.0784803 + 0.135932i
\(262\) −2343.16 4058.48i −0.552523 0.956999i
\(263\) 393.278 + 681.177i 0.0922074 + 0.159708i 0.908440 0.418016i \(-0.137274\pi\)
−0.816232 + 0.577724i \(0.803941\pi\)
\(264\) 3.54538 6.14078i 0.000826527 0.00143159i
\(265\) 3384.09 0.784465
\(266\) 0 0
\(267\) 2539.65 0.582113
\(268\) 4252.89 7366.22i 0.969353 1.67897i
\(269\) 2028.97 + 3514.28i 0.459883 + 0.796541i 0.998954 0.0457192i \(-0.0145580\pi\)
−0.539071 + 0.842260i \(0.681225\pi\)
\(270\) −1556.09 2695.23i −0.350743 0.607504i
\(271\) 1449.71 2510.97i 0.324958 0.562844i −0.656546 0.754286i \(-0.727983\pi\)
0.981504 + 0.191442i \(0.0613165\pi\)
\(272\) −2741.45 −0.611122
\(273\) 0 0
\(274\) 6353.56 1.40085
\(275\) 1.77670 3.07733i 0.000389595 0.000674799i
\(276\) 2876.30 + 4981.91i 0.627294 + 1.08651i
\(277\) −2646.98 4584.70i −0.574157 0.994470i −0.996133 0.0878623i \(-0.971996\pi\)
0.421975 0.906607i \(-0.361337\pi\)
\(278\) −1461.40 + 2531.21i −0.315283 + 0.546086i
\(279\) 1243.34 0.266799
\(280\) 0 0
\(281\) 2359.40 0.500890 0.250445 0.968131i \(-0.419423\pi\)
0.250445 + 0.968131i \(0.419423\pi\)
\(282\) −53.6072 + 92.8504i −0.0113201 + 0.0196070i
\(283\) −1440.67 2495.32i −0.302612 0.524139i 0.674115 0.738626i \(-0.264525\pi\)
−0.976727 + 0.214487i \(0.931192\pi\)
\(284\) −212.623 368.273i −0.0444255 0.0769472i
\(285\) 350.452 607.001i 0.0728385 0.126160i
\(286\) 20.1665 0.00416948
\(287\) 0 0
\(288\) −3773.31 −0.772028
\(289\) −4083.47 + 7072.77i −0.831155 + 1.43960i
\(290\) 443.046 + 767.378i 0.0897122 + 0.155386i
\(291\) −637.352 1103.93i −0.128393 0.222382i
\(292\) 464.449 804.449i 0.0930815 0.161222i
\(293\) −760.730 −0.151680 −0.0758402 0.997120i \(-0.524164\pi\)
−0.0758402 + 0.997120i \(0.524164\pi\)
\(294\) 0 0
\(295\) 3980.90 0.785685
\(296\) −3079.52 + 5333.88i −0.604707 + 1.04738i
\(297\) 10.0211 + 17.3570i 0.00195785 + 0.00339110i
\(298\) −1737.24 3008.98i −0.337703 0.584918i
\(299\) −2482.39 + 4299.62i −0.480134 + 0.831616i
\(300\) −931.066 −0.179184
\(301\) 0 0
\(302\) 3744.82 0.713544
\(303\) −736.795 + 1276.17i −0.139696 + 0.241960i
\(304\) −518.129 897.426i −0.0977524 0.169312i
\(305\) 1892.75 + 3278.35i 0.355340 + 0.615467i
\(306\) −4161.24 + 7207.47i −0.777392 + 1.34648i
\(307\) 4968.57 0.923685 0.461842 0.886962i \(-0.347189\pi\)
0.461842 + 0.886962i \(0.347189\pi\)
\(308\) 0 0
\(309\) −2281.84 −0.420096
\(310\) 832.315 1441.61i 0.152491 0.264123i
\(311\) −2516.98 4359.54i −0.458922 0.794877i 0.539982 0.841677i \(-0.318431\pi\)
−0.998904 + 0.0467998i \(0.985098\pi\)
\(312\) −801.742 1388.66i −0.145480 0.251978i
\(313\) 1799.60 3117.00i 0.324983 0.562886i −0.656526 0.754303i \(-0.727975\pi\)
0.981509 + 0.191417i \(0.0613082\pi\)
\(314\) 4215.23 0.757577
\(315\) 0 0
\(316\) −3644.95 −0.648875
\(317\) −1770.78 + 3067.08i −0.313744 + 0.543420i −0.979170 0.203044i \(-0.934917\pi\)
0.665426 + 0.746464i \(0.268250\pi\)
\(318\) 4843.89 + 8389.86i 0.854188 + 1.47950i
\(319\) −2.85317 4.94184i −0.000500774 0.000867367i
\(320\) −2046.51 + 3544.65i −0.357510 + 0.619225i
\(321\) −3096.71 −0.538447
\(322\) 0 0
\(323\) −4944.16 −0.851704
\(324\) 69.6749 120.680i 0.0119470 0.0206928i
\(325\) −401.777 695.898i −0.0685740 0.118774i
\(326\) −16.2536 28.1521i −0.00276136 0.00478282i
\(327\) 468.443 811.367i 0.0792200 0.137213i
\(328\) −1468.11 −0.247143
\(329\) 0 0
\(330\) 10.1724 0.00169689
\(331\) 3678.98 6372.18i 0.610922 1.05815i −0.380164 0.924919i \(-0.624132\pi\)
0.991085 0.133228i \(-0.0425342\pi\)
\(332\) −5432.13 9408.73i −0.897972 1.55533i
\(333\) −3299.80 5715.42i −0.543027 0.940550i
\(334\) −6447.85 + 11168.0i −1.05632 + 1.82960i
\(335\) 3702.90 0.603914
\(336\) 0 0
\(337\) −2323.24 −0.375534 −0.187767 0.982214i \(-0.560125\pi\)
−0.187767 + 0.982214i \(0.560125\pi\)
\(338\) −2568.81 + 4449.32i −0.413388 + 0.716009i
\(339\) 2028.66 + 3513.74i 0.325020 + 0.562950i
\(340\) 3283.86 + 5687.81i 0.523801 + 0.907249i
\(341\) −5.36003 + 9.28385i −0.000851208 + 0.00147434i
\(342\) −3145.86 −0.497394
\(343\) 0 0
\(344\) 5231.92 0.820018
\(345\) −1252.17 + 2168.82i −0.195405 + 0.338451i
\(346\) 8761.26 + 15174.9i 1.36130 + 2.35783i
\(347\) 2723.89 + 4717.92i 0.421401 + 0.729889i 0.996077 0.0884927i \(-0.0282050\pi\)
−0.574675 + 0.818381i \(0.694872\pi\)
\(348\) −747.594 + 1294.87i −0.115159 + 0.199461i
\(349\) 1227.84 0.188324 0.0941618 0.995557i \(-0.469983\pi\)
0.0941618 + 0.995557i \(0.469983\pi\)
\(350\) 0 0
\(351\) 4532.27 0.689216
\(352\) 16.2667 28.1747i 0.00246311 0.00426624i
\(353\) 990.931 + 1716.34i 0.149411 + 0.258787i 0.931010 0.364994i \(-0.118929\pi\)
−0.781599 + 0.623781i \(0.785596\pi\)
\(354\) 5698.15 + 9869.49i 0.855518 + 1.48180i
\(355\) 92.5631 160.324i 0.0138387 0.0239693i
\(356\) −8995.33 −1.33919
\(357\) 0 0
\(358\) 4881.90 0.720717
\(359\) 6109.03 10581.1i 0.898112 1.55557i 0.0682058 0.997671i \(-0.478273\pi\)
0.829906 0.557904i \(-0.188394\pi\)
\(360\) 634.056 + 1098.22i 0.0928269 + 0.160781i
\(361\) 2495.06 + 4321.58i 0.363765 + 0.630059i
\(362\) 258.703 448.086i 0.0375611 0.0650577i
\(363\) 4315.89 0.624037
\(364\) 0 0
\(365\) 404.386 0.0579905
\(366\) −5418.47 + 9385.06i −0.773846 + 1.34034i
\(367\) 6823.85 + 11819.3i 0.970577 + 1.68109i 0.693818 + 0.720150i \(0.255927\pi\)
0.276759 + 0.960939i \(0.410740\pi\)
\(368\) 1851.28 + 3206.52i 0.262241 + 0.454215i
\(369\) 786.566 1362.37i 0.110967 0.192201i
\(370\) −8835.78 −1.24149
\(371\) 0 0
\(372\) 2808.89 0.391490
\(373\) 2772.01 4801.27i 0.384797 0.666488i −0.606944 0.794745i \(-0.707605\pi\)
0.991741 + 0.128256i \(0.0409380\pi\)
\(374\) −35.8781 62.1426i −0.00496046 0.00859176i
\(375\) −202.665 351.026i −0.0279082 0.0483384i
\(376\) 57.6185 99.7982i 0.00790279 0.0136880i
\(377\) −1290.42 −0.176286
\(378\) 0 0
\(379\) −634.243 −0.0859601 −0.0429801 0.999076i \(-0.513685\pi\)
−0.0429801 + 0.999076i \(0.513685\pi\)
\(380\) −1241.28 + 2149.97i −0.167570 + 0.290240i
\(381\) −3157.72 5469.34i −0.424607 0.735440i
\(382\) 2212.84 + 3832.76i 0.296385 + 0.513353i
\(383\) 2895.47 5015.09i 0.386296 0.669084i −0.605652 0.795730i \(-0.707088\pi\)
0.991948 + 0.126645i \(0.0404210\pi\)
\(384\) −5779.58 −0.768068
\(385\) 0 0
\(386\) −14380.5 −1.89623
\(387\) −2803.08 + 4855.08i −0.368188 + 0.637720i
\(388\) 2257.47 + 3910.05i 0.295376 + 0.511606i
\(389\) −758.496 1313.75i −0.0988619 0.171234i 0.812352 0.583168i \(-0.198187\pi\)
−0.911214 + 0.411934i \(0.864854\pi\)
\(390\) 1150.18 1992.18i 0.149338 0.258661i
\(391\) 17665.6 2.28487
\(392\) 0 0
\(393\) 3442.53 0.441865
\(394\) −92.0265 + 159.395i −0.0117671 + 0.0203812i
\(395\) −793.396 1374.20i −0.101063 0.175047i
\(396\) −13.4558 23.3062i −0.00170753 0.00295753i
\(397\) −3937.47 + 6819.90i −0.497773 + 0.862169i −0.999997 0.00256925i \(-0.999182\pi\)
0.502223 + 0.864738i \(0.332516\pi\)
\(398\) 10618.9 1.33738
\(399\) 0 0
\(400\) −599.264 −0.0749080
\(401\) 5555.64 9622.65i 0.691859 1.19833i −0.279369 0.960184i \(-0.590125\pi\)
0.971228 0.238151i \(-0.0765412\pi\)
\(402\) 5300.23 + 9180.26i 0.657590 + 1.13898i
\(403\) 1212.10 + 2099.42i 0.149824 + 0.259503i
\(404\) 2609.69 4520.12i 0.321379 0.556645i
\(405\) 60.6645 0.00744307
\(406\) 0 0
\(407\) 56.9016 0.00692999
\(408\) −2852.74 + 4941.10i −0.346157 + 0.599561i
\(409\) −5355.07 9275.25i −0.647411 1.12135i −0.983739 0.179603i \(-0.942519\pi\)
0.336328 0.941745i \(-0.390815\pi\)
\(410\) −1053.08 1823.99i −0.126849 0.219708i
\(411\) −2333.63 + 4041.97i −0.280072 + 0.485099i
\(412\) 8082.19 0.966458
\(413\) 0 0
\(414\) 11240.2 1.33436
\(415\) 2364.82 4095.99i 0.279722 0.484492i
\(416\) −3678.50 6371.34i −0.433541 0.750915i
\(417\) −1073.53 1859.41i −0.126069 0.218358i
\(418\) 13.5618 23.4897i 0.00158691 0.00274860i
\(419\) −8615.98 −1.00458 −0.502289 0.864700i \(-0.667509\pi\)
−0.502289 + 0.864700i \(0.667509\pi\)
\(420\) 0 0
\(421\) 6689.72 0.774435 0.387217 0.921988i \(-0.373436\pi\)
0.387217 + 0.921988i \(0.373436\pi\)
\(422\) 2673.33 4630.35i 0.308379 0.534128i
\(423\) 61.7401 + 106.937i 0.00709671 + 0.0122919i
\(424\) −5206.35 9017.66i −0.596327 1.03287i
\(425\) −1429.59 + 2476.13i −0.163166 + 0.282612i
\(426\) 529.969 0.0602748
\(427\) 0 0
\(428\) 10968.4 1.23873
\(429\) −7.40707 + 12.8294i −0.000833605 + 0.00144385i
\(430\) 3752.87 + 6500.15i 0.420882 + 0.728989i
\(431\) −3085.32 5343.93i −0.344814 0.597235i 0.640506 0.767953i \(-0.278725\pi\)
−0.985320 + 0.170718i \(0.945391\pi\)
\(432\) 1690.01 2927.18i 0.188219 0.326005i
\(433\) −14001.1 −1.55392 −0.776961 0.629548i \(-0.783240\pi\)
−0.776961 + 0.629548i \(0.783240\pi\)
\(434\) 0 0
\(435\) −650.914 −0.0717447
\(436\) −1659.20 + 2873.82i −0.182251 + 0.315668i
\(437\) 3338.75 + 5782.89i 0.365479 + 0.633028i
\(438\) 578.826 + 1002.56i 0.0631447 + 0.109370i
\(439\) 6103.49 10571.6i 0.663562 1.14932i −0.316111 0.948722i \(-0.602377\pi\)
0.979673 0.200601i \(-0.0642893\pi\)
\(440\) −10.9336 −0.00118464
\(441\) 0 0
\(442\) −16226.7 −1.74621
\(443\) −613.882 + 1063.27i −0.0658384 + 0.114035i −0.897066 0.441897i \(-0.854306\pi\)
0.831227 + 0.555933i \(0.187639\pi\)
\(444\) −7454.73 12912.0i −0.796815 1.38012i
\(445\) −1958.01 3391.38i −0.208581 0.361274i
\(446\) −9192.57 + 15922.0i −0.975966 + 1.69042i
\(447\) 2552.32 0.270068
\(448\) 0 0
\(449\) −1151.70 −0.121051 −0.0605257 0.998167i \(-0.519278\pi\)
−0.0605257 + 0.998167i \(0.519278\pi\)
\(450\) −909.619 + 1575.51i −0.0952886 + 0.165045i
\(451\) 6.78175 + 11.7463i 0.000708071 + 0.00122641i
\(452\) −7185.41 12445.5i −0.747729 1.29510i
\(453\) −1375.46 + 2382.36i −0.142659 + 0.247093i
\(454\) 10401.0 1.07520
\(455\) 0 0
\(456\) −2156.65 −0.221479
\(457\) −9356.91 + 16206.6i −0.957763 + 1.65889i −0.229849 + 0.973226i \(0.573823\pi\)
−0.727914 + 0.685668i \(0.759510\pi\)
\(458\) −9590.23 16610.8i −0.978433 1.69470i
\(459\) −8063.32 13966.1i −0.819964 1.42022i
\(460\) 4435.13 7681.87i 0.449541 0.778628i
\(461\) 3154.57 0.318705 0.159352 0.987222i \(-0.449059\pi\)
0.159352 + 0.987222i \(0.449059\pi\)
\(462\) 0 0
\(463\) 4051.11 0.406633 0.203316 0.979113i \(-0.434828\pi\)
0.203316 + 0.979113i \(0.434828\pi\)
\(464\) −481.175 + 833.420i −0.0481422 + 0.0833848i
\(465\) 611.411 + 1058.99i 0.0609753 + 0.105612i
\(466\) 5425.62 + 9397.45i 0.539350 + 0.934181i
\(467\) 8170.80 14152.2i 0.809635 1.40233i −0.103482 0.994631i \(-0.532998\pi\)
0.913117 0.407697i \(-0.133668\pi\)
\(468\) −6085.73 −0.601096
\(469\) 0 0
\(470\) 165.320 0.0162247
\(471\) −1548.23 + 2681.62i −0.151463 + 0.262341i
\(472\) −6124.53 10608.0i −0.597255 1.03448i
\(473\) −24.1681 41.8604i −0.00234937 0.00406922i
\(474\) 2271.29 3933.98i 0.220092 0.381211i
\(475\) −1080.76 −0.104397
\(476\) 0 0
\(477\) 11157.5 1.07100
\(478\) 711.360 1232.11i 0.0680688 0.117899i
\(479\) 1265.72 + 2192.30i 0.120736 + 0.209121i 0.920058 0.391782i \(-0.128141\pi\)
−0.799322 + 0.600903i \(0.794808\pi\)
\(480\) −1855.52 3213.85i −0.176442 0.305607i
\(481\) 6433.78 11143.6i 0.609886 1.05635i
\(482\) −22120.7 −2.09039
\(483\) 0 0
\(484\) −15286.7 −1.43564
\(485\) −982.767 + 1702.20i −0.0920106 + 0.159367i
\(486\) −8316.05 14403.8i −0.776180 1.34438i
\(487\) 4221.09 + 7311.14i 0.392763 + 0.680286i 0.992813 0.119677i \(-0.0381858\pi\)
−0.600050 + 0.799963i \(0.704852\pi\)
\(488\) 5823.92 10087.3i 0.540239 0.935721i
\(489\) 23.8795 0.00220832
\(490\) 0 0
\(491\) −15223.9 −1.39928 −0.699640 0.714496i \(-0.746656\pi\)
−0.699640 + 0.714496i \(0.746656\pi\)
\(492\) 1776.97 3077.79i 0.162829 0.282028i
\(493\) 2295.77 + 3976.39i 0.209729 + 0.363260i
\(494\) −3066.82 5311.88i −0.279317 0.483791i
\(495\) 5.85786 10.1461i 0.000531902 0.000921281i
\(496\) 1807.89 0.163663
\(497\) 0 0
\(498\) 13539.8 1.21833
\(499\) 8311.32 14395.6i 0.745623 1.29146i −0.204280 0.978913i \(-0.565485\pi\)
0.949903 0.312545i \(-0.101181\pi\)
\(500\) 717.830 + 1243.32i 0.0642047 + 0.111206i
\(501\) −4736.53 8203.91i −0.422380 0.731584i
\(502\) −8689.26 + 15050.2i −0.772551 + 1.33810i
\(503\) 17506.6 1.55185 0.775923 0.630828i \(-0.217285\pi\)
0.775923 + 0.630828i \(0.217285\pi\)
\(504\) 0 0
\(505\) 2272.21 0.200222
\(506\) −48.4564 + 83.9289i −0.00425721 + 0.00737370i
\(507\) −1887.03 3268.43i −0.165297 0.286304i
\(508\) 11184.5 + 19372.1i 0.976835 + 1.69193i
\(509\) 6191.58 10724.1i 0.539169 0.933867i −0.459780 0.888033i \(-0.652072\pi\)
0.998949 0.0458348i \(-0.0145948\pi\)
\(510\) −8185.12 −0.710673
\(511\) 0 0
\(512\) −8436.86 −0.728242
\(513\) 3047.90 5279.12i 0.262316 0.454345i
\(514\) 8003.33 + 13862.2i 0.686793 + 1.18956i
\(515\) 1759.25 + 3047.11i 0.150528 + 0.260722i
\(516\) −6332.57 + 10968.3i −0.540263 + 0.935764i
\(517\) −1.06464 −9.05666e−5
\(518\) 0 0
\(519\) −12871.9 −1.08866
\(520\) −1236.25 + 2141.25i −0.104256 + 0.180577i
\(521\) −7489.50 12972.2i −0.629790 1.09083i −0.987594 0.157032i \(-0.949807\pi\)
0.357803 0.933797i \(-0.383526\pi\)
\(522\) 1460.75 + 2530.09i 0.122481 + 0.212143i
\(523\) 1859.56 3220.85i 0.155474 0.269288i −0.777758 0.628564i \(-0.783643\pi\)
0.933231 + 0.359276i \(0.116976\pi\)
\(524\) −12193.3 −1.01654
\(525\) 0 0
\(526\) 3472.02 0.287809
\(527\) 4312.88 7470.12i 0.356493 0.617464i
\(528\) 5.52395 + 9.56777i 0.000455302 + 0.000788605i
\(529\) −5845.91 10125.4i −0.480472 0.832203i
\(530\) 7469.05 12936.8i 0.612141 1.06026i
\(531\) 13125.3 1.07267
\(532\) 0 0
\(533\) 3067.21 0.249260
\(534\) 5605.29 9708.64i 0.454240 0.786768i
\(535\) 2387.49 + 4135.26i 0.192935 + 0.334173i
\(536\) −5696.83 9867.21i −0.459078 0.795146i
\(537\) −1793.10 + 3105.74i −0.144093 + 0.249577i
\(538\) 17912.6 1.43544
\(539\) 0 0
\(540\) −8097.53 −0.645301
\(541\) 122.363 211.939i 0.00972420 0.0168428i −0.861122 0.508398i \(-0.830238\pi\)
0.870847 + 0.491555i \(0.163571\pi\)
\(542\) −6399.33 11084.0i −0.507149 0.878408i
\(543\) 190.041 + 329.160i 0.0150192 + 0.0260140i
\(544\) −13088.8 + 22670.4i −1.03157 + 1.78674i
\(545\) −1444.63 −0.113544
\(546\) 0 0
\(547\) −12685.4 −0.991568 −0.495784 0.868446i \(-0.665119\pi\)
−0.495784 + 0.868446i \(0.665119\pi\)
\(548\) 8265.63 14316.5i 0.644325 1.11600i
\(549\) 6240.52 + 10808.9i 0.485134 + 0.840277i
\(550\) −7.84271 13.5840i −0.000608026 0.00105313i
\(551\) −867.790 + 1503.06i −0.0670946 + 0.116211i
\(552\) 7705.74 0.594163
\(553\) 0 0
\(554\) −23368.7 −1.79213
\(555\) 3245.34 5621.09i 0.248211 0.429914i
\(556\) 3802.39 + 6585.93i 0.290031 + 0.502348i
\(557\) 11031.4 + 19106.9i 0.839164 + 1.45347i 0.890595 + 0.454798i \(0.150289\pi\)
−0.0514307 + 0.998677i \(0.516378\pi\)
\(558\) 2744.19 4753.08i 0.208191 0.360598i
\(559\) −10930.6 −0.827040
\(560\) 0 0
\(561\) 52.7114 0.00396698
\(562\) 5207.45 9019.57i 0.390859 0.676988i
\(563\) 3931.10 + 6808.86i 0.294274 + 0.509697i 0.974816 0.223012i \(-0.0715890\pi\)
−0.680542 + 0.732709i \(0.738256\pi\)
\(564\) 139.480 + 241.586i 0.0104134 + 0.0180366i
\(565\) 3128.10 5418.02i 0.232920 0.403430i
\(566\) −12718.9 −0.944549
\(567\) 0 0
\(568\) −569.625 −0.0420791
\(569\) −10470.8 + 18135.9i −0.771453 + 1.33620i 0.165313 + 0.986241i \(0.447136\pi\)
−0.936766 + 0.349955i \(0.886197\pi\)
\(570\) −1546.97 2679.43i −0.113676 0.196893i
\(571\) 3565.83 + 6176.20i 0.261341 + 0.452655i 0.966598 0.256296i \(-0.0825021\pi\)
−0.705258 + 0.708951i \(0.749169\pi\)
\(572\) 26.2355 45.4412i 0.00191776 0.00332167i
\(573\) −3251.07 −0.237025
\(574\) 0 0
\(575\) 3861.57 0.280067
\(576\) −6747.44 + 11686.9i −0.488096 + 0.845408i
\(577\) −7816.51 13538.6i −0.563961 0.976809i −0.997146 0.0755039i \(-0.975943\pi\)
0.433184 0.901305i \(-0.357390\pi\)
\(578\) 18025.3 + 31220.7i 1.29715 + 2.24673i
\(579\) 5281.87 9148.47i 0.379114 0.656645i
\(580\) 2305.51 0.165054
\(581\) 0 0
\(582\) −5626.82 −0.400754
\(583\) −48.1000 + 83.3116i −0.00341698 + 0.00591838i
\(584\) −622.139 1077.58i −0.0440827 0.0763534i
\(585\) −1324.68 2294.41i −0.0936219 0.162158i
\(586\) −1679.01 + 2908.14i −0.118361 + 0.205007i
\(587\) 19406.2 1.36453 0.682266 0.731104i \(-0.260995\pi\)
0.682266 + 0.731104i \(0.260995\pi\)
\(588\) 0 0
\(589\) 3260.50 0.228093
\(590\) 8786.28 15218.3i 0.613094 1.06191i
\(591\) −67.6018 117.090i −0.00470519 0.00814963i
\(592\) −4798.10 8310.56i −0.333110 0.576963i
\(593\) −7429.82 + 12868.8i −0.514513 + 0.891162i 0.485346 + 0.874322i \(0.338694\pi\)
−0.999858 + 0.0168395i \(0.994640\pi\)
\(594\) 88.4703 0.00611108
\(595\) 0 0
\(596\) −9040.18 −0.621309
\(597\) −3900.27 + 6755.46i −0.267383 + 0.463120i
\(598\) 10957.8 + 18979.4i 0.749326 + 1.29787i
\(599\) 5264.93 + 9119.13i 0.359131 + 0.622032i 0.987816 0.155627i \(-0.0497399\pi\)
−0.628685 + 0.777660i \(0.716407\pi\)
\(600\) −623.591 + 1080.09i −0.0424300 + 0.0734909i
\(601\) −11595.2 −0.786984 −0.393492 0.919328i \(-0.628733\pi\)
−0.393492 + 0.919328i \(0.628733\pi\)
\(602\) 0 0
\(603\) 12208.7 0.824504
\(604\) 4871.80 8438.20i 0.328196 0.568453i
\(605\) −3327.45 5763.31i −0.223603 0.387292i
\(606\) 3252.37 + 5633.27i 0.218017 + 0.377617i
\(607\) −11641.0 + 20162.9i −0.778411 + 1.34825i 0.154446 + 0.988001i \(0.450641\pi\)
−0.932857 + 0.360246i \(0.882693\pi\)
\(608\) −9894.99 −0.660024
\(609\) 0 0
\(610\) 16710.0 1.10913
\(611\) −120.378 + 208.500i −0.00797047 + 0.0138053i
\(612\) 10827.1 + 18753.0i 0.715128 + 1.23864i
\(613\) 3693.99 + 6398.18i 0.243391 + 0.421566i 0.961678 0.274181i \(-0.0884068\pi\)
−0.718287 + 0.695747i \(0.755073\pi\)
\(614\) 10966.2 18993.9i 0.720779 1.24843i
\(615\) 1547.17 0.101444
\(616\) 0 0
\(617\) 667.085 0.0435265 0.0217632 0.999763i \(-0.493072\pi\)
0.0217632 + 0.999763i \(0.493072\pi\)
\(618\) −5036.27 + 8723.08i −0.327813 + 0.567789i
\(619\) −4712.89 8162.96i −0.306021 0.530044i 0.671467 0.741034i \(-0.265664\pi\)
−0.977488 + 0.210990i \(0.932331\pi\)
\(620\) −2165.59 3750.91i −0.140278 0.242968i
\(621\) −10890.2 + 18862.4i −0.703717 + 1.21887i
\(622\) −22221.0 −1.43244
\(623\) 0 0
\(624\) 2498.34 0.160278
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −7943.83 13759.1i −0.507187 0.878474i
\(627\) 9.96234 + 17.2553i 0.000634542 + 0.00109906i
\(628\) 5483.77 9498.17i 0.348450 0.603532i
\(629\) −45785.1 −2.90234
\(630\) 0 0
\(631\) 28047.3 1.76949 0.884744 0.466078i \(-0.154333\pi\)
0.884744 + 0.466078i \(0.154333\pi\)
\(632\) −2441.24 + 4228.36i −0.153651 + 0.266131i
\(633\) 1963.81 + 3401.41i 0.123309 + 0.213577i
\(634\) 7816.59 + 13538.7i 0.489647 + 0.848094i
\(635\) −4869.06 + 8433.46i −0.304288 + 0.527042i
\(636\) 25206.5 1.57155
\(637\) 0 0
\(638\) −25.1890 −0.00156308
\(639\) 305.186 528.597i 0.0188935 0.0327246i
\(640\) 4455.92 + 7717.89i 0.275212 + 0.476682i
\(641\) −11604.2 20099.0i −0.715034 1.23847i −0.962947 0.269692i \(-0.913078\pi\)
0.247913 0.968782i \(-0.420255\pi\)
\(642\) −6834.77 + 11838.2i −0.420167 + 0.727750i
\(643\) 4294.22 0.263371 0.131686 0.991292i \(-0.457961\pi\)
0.131686 + 0.991292i \(0.457961\pi\)
\(644\) 0 0
\(645\) −5513.64 −0.336588
\(646\) −10912.3 + 18900.6i −0.664610 + 1.15114i
\(647\) −8696.69 15063.1i −0.528443 0.915289i −0.999450 0.0331602i \(-0.989443\pi\)
0.471007 0.882129i \(-0.343890\pi\)
\(648\) −93.3310 161.654i −0.00565801 0.00979995i
\(649\) −56.5828 + 98.0043i −0.00342230 + 0.00592759i
\(650\) −3547.06 −0.214042
\(651\) 0 0
\(652\) −84.5801 −0.00508039
\(653\) −7237.72 + 12536.1i −0.433743 + 0.751265i −0.997192 0.0748861i \(-0.976141\pi\)
0.563449 + 0.826151i \(0.309474\pi\)
\(654\) −2067.81 3581.55i −0.123636 0.214143i
\(655\) −2654.11 4597.06i −0.158328 0.274232i
\(656\) 1143.71 1980.97i 0.0680708 0.117902i
\(657\) 1333.28 0.0791725
\(658\) 0 0
\(659\) 620.113 0.0366558 0.0183279 0.999832i \(-0.494166\pi\)
0.0183279 + 0.999832i \(0.494166\pi\)
\(660\) 13.2338 22.9216i 0.000780490 0.00135185i
\(661\) 3052.75 + 5287.52i 0.179634 + 0.311135i 0.941755 0.336299i \(-0.109175\pi\)
−0.762121 + 0.647434i \(0.775842\pi\)
\(662\) −16239.8 28128.2i −0.953441 1.65141i
\(663\) 5960.00 10323.0i 0.349121 0.604695i
\(664\) −14552.9 −0.850546
\(665\) 0 0
\(666\) −29132.1 −1.69496
\(667\) 3100.63 5370.44i 0.179995 0.311761i
\(668\) 16776.6 + 29057.9i 0.971713 + 1.68306i
\(669\) −6752.78 11696.2i −0.390250 0.675933i
\(670\) 8172.70 14155.5i 0.471252 0.816233i
\(671\) −107.611 −0.00619118
\(672\) 0 0
\(673\) −16302.5 −0.933754 −0.466877 0.884322i \(-0.654621\pi\)
−0.466877 + 0.884322i \(0.654621\pi\)
\(674\) −5127.64 + 8881.33i −0.293040 + 0.507561i
\(675\) −1762.59 3052.89i −0.100507 0.174083i
\(676\) 6683.76 + 11576.6i 0.380278 + 0.658660i
\(677\) −2409.55 + 4173.46i −0.136789 + 0.236926i −0.926280 0.376837i \(-0.877012\pi\)
0.789490 + 0.613763i \(0.210345\pi\)
\(678\) 17909.9 1.01449
\(679\) 0 0
\(680\) 8797.59 0.496136
\(681\) −3820.22 + 6616.82i −0.214965 + 0.372331i
\(682\) 23.6603 + 40.9809i 0.00132845 + 0.00230094i
\(683\) 4095.16 + 7093.03i 0.229425 + 0.397375i 0.957638 0.287976i \(-0.0929822\pi\)
−0.728213 + 0.685351i \(0.759649\pi\)
\(684\) −4092.59 + 7088.57i −0.228778 + 0.396255i
\(685\) 7196.71 0.401419
\(686\) 0 0
\(687\) 14089.8 0.782473
\(688\) −4075.85 + 7059.57i −0.225858 + 0.391197i
\(689\) 10877.2 + 18839.9i 0.601434 + 1.04171i
\(690\) 5527.35 + 9573.64i 0.304960 + 0.528206i
\(691\) 238.487 413.071i 0.0131295 0.0227409i −0.859386 0.511327i \(-0.829154\pi\)
0.872515 + 0.488586i \(0.162487\pi\)
\(692\) 45591.6 2.50453
\(693\) 0 0
\(694\) 24047.7 1.31533
\(695\) −1655.33 + 2867.12i −0.0903457 + 0.156483i
\(696\) 1001.42 + 1734.51i 0.0545383 + 0.0944630i
\(697\) −5456.84 9451.53i −0.296546 0.513633i
\(698\) 2709.98 4693.82i 0.146955 0.254533i
\(699\) −7971.22 −0.431329
\(700\) 0 0
\(701\) −20366.7 −1.09735 −0.548673 0.836037i \(-0.684867\pi\)
−0.548673 + 0.836037i \(0.684867\pi\)
\(702\) 10003.2 17326.1i 0.537816 0.931524i
\(703\) −8653.29 14987.9i −0.464246 0.804098i
\(704\) −58.1763 100.764i −0.00311449 0.00539445i
\(705\) −60.7211 + 105.172i −0.00324382 + 0.00561845i
\(706\) 8748.36 0.466358
\(707\) 0 0
\(708\) 29651.9 1.57399
\(709\) −11207.5 + 19412.0i −0.593664 + 1.02826i 0.400070 + 0.916484i \(0.368986\pi\)
−0.993734 + 0.111771i \(0.964348\pi\)
\(710\) −408.593 707.705i −0.0215975 0.0374080i
\(711\) −2615.87 4530.82i −0.137979 0.238986i
\(712\) −6024.72 + 10435.1i −0.317115 + 0.549259i
\(713\) −11649.8 −0.611906
\(714\) 0 0
\(715\) 22.8427 0.00119478
\(716\) 6351.08 11000.4i 0.331496 0.574168i
\(717\) 522.559 + 905.098i 0.0272180 + 0.0471430i
\(718\) −26966.5 46707.4i −1.40165 2.42772i
\(719\) −13078.0 + 22651.7i −0.678340 + 1.17492i 0.297141 + 0.954834i \(0.403967\pi\)
−0.975481 + 0.220085i \(0.929366\pi\)
\(720\) −1975.81 −0.102269
\(721\) 0 0
\(722\) 22027.5 1.13543
\(723\) 8124.82 14072.6i 0.417933 0.723881i
\(724\) −673.115 1165.87i −0.0345527 0.0598470i
\(725\) 501.840 + 869.212i 0.0257074 + 0.0445265i
\(726\) 9525.63 16498.9i 0.486955 0.843431i
\(727\) 13666.2 0.697184 0.348592 0.937275i \(-0.386660\pi\)
0.348592 + 0.937275i \(0.386660\pi\)
\(728\) 0 0
\(729\) 12545.4 0.637371
\(730\) 892.523 1545.90i 0.0452517 0.0783783i
\(731\) 19446.5 + 33682.4i 0.983935 + 1.70423i
\(732\) 14098.2 + 24418.9i 0.711866 + 1.23299i
\(733\) 12519.1 21683.7i 0.630836 1.09264i −0.356545 0.934278i \(-0.616045\pi\)
0.987381 0.158362i \(-0.0506213\pi\)
\(734\) 60243.8 3.02948
\(735\) 0 0
\(736\) 35354.9 1.77065
\(737\) −52.6315 + 91.1603i −0.00263054 + 0.00455622i
\(738\) −3472.07 6013.80i −0.173182 0.299961i
\(739\) −1627.60 2819.08i −0.0810178 0.140327i 0.822670 0.568520i \(-0.192484\pi\)
−0.903687 + 0.428193i \(0.859150\pi\)
\(740\) −11494.8 + 19909.7i −0.571026 + 0.989045i
\(741\) 4505.71 0.223376
\(742\) 0 0
\(743\) −8366.48 −0.413104 −0.206552 0.978436i \(-0.566224\pi\)
−0.206552 + 0.978436i \(0.566224\pi\)
\(744\) 1881.28 3258.48i 0.0927032 0.160567i
\(745\) −1967.78 3408.29i −0.0967701 0.167611i
\(746\) −12236.3 21193.8i −0.600538 1.04016i
\(747\) 7796.95 13504.7i 0.381895 0.661462i
\(748\) −186.701 −0.00912630
\(749\) 0 0
\(750\) −1789.21 −0.0871105
\(751\) 5082.23 8802.69i 0.246942 0.427716i −0.715734 0.698373i \(-0.753908\pi\)
0.962676 + 0.270657i \(0.0872410\pi\)
\(752\) 89.7737 + 155.493i 0.00435334 + 0.00754021i
\(753\) −6383.05 11055.8i −0.308913 0.535052i
\(754\) −2848.09 + 4933.03i −0.137561 + 0.238263i
\(755\) 4241.77 0.204469
\(756\) 0 0
\(757\) 9031.23 0.433614 0.216807 0.976214i \(-0.430436\pi\)
0.216807 + 0.976214i \(0.430436\pi\)
\(758\) −1399.84 + 2424.60i −0.0670773 + 0.116181i
\(759\) −35.5956 61.6534i −0.00170229 0.00294845i
\(760\) 1662.73 + 2879.93i 0.0793598 + 0.137455i
\(761\) −16217.3 + 28089.3i −0.772508 + 1.33802i 0.163677 + 0.986514i \(0.447665\pi\)
−0.936185 + 0.351509i \(0.885669\pi\)
\(762\) −27877.7 −1.32533
\(763\) 0 0
\(764\) 11515.1 0.545292
\(765\) −4713.45 + 8163.94i −0.222765 + 0.385840i
\(766\) −12781.2 22137.7i −0.602877 1.04421i
\(767\) 12795.5 + 22162.4i 0.602370 + 1.04334i
\(768\) −2138.43 + 3703.87i −0.100474 + 0.174026i
\(769\) 22629.4 1.06117 0.530583 0.847633i \(-0.321973\pi\)
0.530583 + 0.847633i \(0.321973\pi\)
\(770\) 0 0
\(771\) −11758.3 −0.549243
\(772\) −18708.2 + 32403.5i −0.872178 + 1.51066i
\(773\) 1353.50 + 2344.34i 0.0629782 + 0.109081i 0.895795 0.444467i \(-0.146607\pi\)
−0.832817 + 0.553548i \(0.813273\pi\)
\(774\) 12373.4 + 21431.4i 0.574616 + 0.995265i
\(775\) 942.767 1632.92i 0.0436970 0.0756855i
\(776\) 6047.86 0.279775
\(777\) 0 0
\(778\) −6696.33 −0.308580
\(779\) 2062.66 3572.64i 0.0948685 0.164317i
\(780\) −2992.65 5183.41i −0.137377 0.237944i
\(781\) 2.63130 + 4.55755i 0.000120558 + 0.000208812i
\(782\) 38989.8 67532.2i 1.78296 3.08817i
\(783\) −5661.04 −0.258377
\(784\) 0 0
\(785\) 4774.61 0.217087
\(786\) 7598.04 13160.2i 0.344800 0.597212i
\(787\) −12542.3 21723.9i −0.568088 0.983958i −0.996755 0.0804951i \(-0.974350\pi\)
0.428667 0.903463i \(-0.358983\pi\)
\(788\) 239.442 + 414.726i 0.0108246 + 0.0187488i
\(789\) −1275.26 + 2208.81i −0.0575417 + 0.0996651i
\(790\) −7004.44 −0.315451
\(791\) 0 0
\(792\) −36.0488 −0.00161735
\(793\) −12167.4 + 21074.6i −0.544865 + 0.943734i
\(794\) 17380.8 + 30104.5i 0.776855 + 1.34555i
\(795\) 5486.70 + 9503.24i 0.244771 + 0.423956i
\(796\) 13814.6 23927.5i 0.615131 1.06544i
\(797\) −7374.99 −0.327774 −0.163887 0.986479i \(-0.552403\pi\)
−0.163887 + 0.986479i \(0.552403\pi\)
\(798\) 0 0
\(799\) 856.651 0.0379301
\(800\) −2861.12 + 4955.60i −0.126445 + 0.219009i
\(801\) −6455.68 11181.6i −0.284769 0.493235i
\(802\) −24523.8 42476.4i −1.07976 1.87019i
\(803\) −5.74777 + 9.95542i −0.000252596 + 0.000437508i
\(804\) 27581.2 1.20984
\(805\) 0 0
\(806\) 10701.0 0.467649
\(807\) −6579.23 + 11395.6i −0.286988 + 0.497079i
\(808\) −3495.74 6054.80i −0.152203 0.263623i
\(809\) −1157.19 2004.30i −0.0502899 0.0871046i 0.839785 0.542920i \(-0.182681\pi\)
−0.890075 + 0.455815i \(0.849348\pi\)
\(810\) 133.893 231.910i 0.00580805 0.0100598i
\(811\) −38300.1 −1.65832 −0.829160 0.559011i \(-0.811181\pi\)
−0.829160 + 0.559011i \(0.811181\pi\)
\(812\) 0 0
\(813\) 9401.78 0.405578
\(814\) 125.588 217.525i 0.00540768 0.00936638i
\(815\) −18.4105 31.8880i −0.000791280 0.00137054i
\(816\) −4444.78 7698.58i −0.190684 0.330275i
\(817\) −7350.71 + 12731.8i −0.314772 + 0.545201i
\(818\) −47276.8 −2.02078
\(819\) 0 0
\(820\) −5480.00 −0.233378
\(821\) −1971.47 + 3414.68i −0.0838059 + 0.145156i −0.904882 0.425663i \(-0.860041\pi\)
0.821076 + 0.570819i \(0.193374\pi\)
\(822\) 10301.2 + 17842.1i 0.437098 + 0.757075i
\(823\) −9251.41 16023.9i −0.391839 0.678686i 0.600853 0.799360i \(-0.294828\pi\)
−0.992692 + 0.120674i \(0.961494\pi\)
\(824\) 5413.13 9375.81i 0.228853 0.396386i
\(825\) 11.5224 0.000486251
\(826\) 0 0
\(827\) −11965.2 −0.503110 −0.251555 0.967843i \(-0.580942\pi\)
−0.251555 + 0.967843i \(0.580942\pi\)
\(828\) 14622.9 25327.5i 0.613744 1.06303i
\(829\) −17981.5 31144.8i −0.753344 1.30483i −0.946193 0.323602i \(-0.895106\pi\)
0.192849 0.981228i \(-0.438227\pi\)
\(830\) −10438.8 18080.6i −0.436551 0.756128i
\(831\) 8583.20 14866.5i 0.358301 0.620595i
\(832\) −26311.6 −1.09638
\(833\) 0 0
\(834\) −9477.56 −0.393503
\(835\) −7303.50 + 12650.0i −0.302692 + 0.524279i
\(836\) −35.2862 61.1174i −0.00145981 0.00252846i
\(837\) 5317.47 + 9210.14i 0.219592 + 0.380345i
\(838\) −19016.4 + 32937.3i −0.783902 + 1.35776i
\(839\) 20174.0 0.830137 0.415069 0.909790i \(-0.363758\pi\)
0.415069 + 0.909790i \(0.363758\pi\)
\(840\) 0 0
\(841\) −22777.2 −0.933913
\(842\) 14764.9 25573.6i 0.604315 1.04670i
\(843\) 3825.35 + 6625.69i 0.156289 + 0.270701i
\(844\) −6955.71 12047.6i −0.283679 0.491347i
\(845\) −2909.71 + 5039.76i −0.118458 + 0.205175i
\(846\) 545.068 0.0221511
\(847\) 0 0
\(848\) 16223.7 0.656987
\(849\) 4671.59 8091.43i 0.188844 0.327087i
\(850\) 6310.53 + 10930.2i 0.254647 + 0.441061i
\(851\) 30918.3 + 53552.1i 1.24544 + 2.15716i
\(852\) 689.459 1194.18i 0.0277236 0.0480186i
\(853\) −25297.5 −1.01544 −0.507719 0.861523i \(-0.669511\pi\)
−0.507719 + 0.861523i \(0.669511\pi\)
\(854\) 0 0
\(855\) −3563.33 −0.142530
\(856\) 7346.21 12724.0i 0.293327 0.508058i
\(857\) 19634.5 + 34008.0i 0.782617 + 1.35553i 0.930412 + 0.366514i \(0.119449\pi\)
−0.147795 + 0.989018i \(0.547218\pi\)
\(858\) 32.6964 + 56.6318i 0.00130097 + 0.00225335i
\(859\) −7249.55 + 12556.6i −0.287953 + 0.498749i −0.973321 0.229448i \(-0.926308\pi\)
0.685368 + 0.728197i \(0.259641\pi\)
\(860\) 19529.1 0.774343
\(861\) 0 0
\(862\) −27238.5 −1.07627
\(863\) 12205.6 21140.8i 0.481442 0.833882i −0.518331 0.855180i \(-0.673447\pi\)
0.999773 + 0.0212980i \(0.00677986\pi\)
\(864\) −16137.5 27951.0i −0.635428 1.10059i
\(865\) 9923.92 + 17188.7i 0.390085 + 0.675647i
\(866\) −30901.9 + 53523.6i −1.21257 + 2.10024i
\(867\) −26482.4 −1.03736
\(868\) 0 0
\(869\) 45.1079 0.00176085
\(870\) −1436.64 + 2488.33i −0.0559846 + 0.0969681i
\(871\) 11901.9 + 20614.7i 0.463010 + 0.801956i
\(872\) 2222.54 + 3849.55i 0.0863126 + 0.149498i
\(873\) −3240.24 + 5612.26i −0.125619 + 0.217579i
\(874\) 29475.9 1.14078
\(875\) 0 0
\(876\) 3012.08 0.116174
\(877\) 2528.32 4379.18i 0.0973494 0.168614i −0.813237 0.581932i \(-0.802297\pi\)
0.910587 + 0.413318i \(0.135630\pi\)
\(878\) −26942.1 46665.1i −1.03559 1.79370i
\(879\) −1233.39 2136.29i −0.0473278 0.0819741i
\(880\) 8.51768 14.7530i 0.000326285 0.000565142i
\(881\) −13233.9 −0.506086 −0.253043 0.967455i \(-0.581431\pi\)
−0.253043 + 0.967455i \(0.581431\pi\)
\(882\) 0 0
\(883\) −13824.2 −0.526866 −0.263433 0.964678i \(-0.584855\pi\)
−0.263433 + 0.964678i \(0.584855\pi\)
\(884\) −21110.0 + 36563.7i −0.803176 + 1.39114i
\(885\) 6454.32 + 11179.2i 0.245152 + 0.424616i
\(886\) 2709.81 + 4693.52i 0.102751 + 0.177971i
\(887\) −18909.7 + 32752.5i −0.715811 + 1.23982i 0.246835 + 0.969057i \(0.420609\pi\)
−0.962646 + 0.270763i \(0.912724\pi\)
\(888\) −19971.5 −0.754731
\(889\) 0 0
\(890\) −17286.2 −0.651049
\(891\) −0.862259 + 1.49348i −3.24206e−5 + 5.61541e-5i
\(892\) 23918.0 + 41427.2i 0.897796 + 1.55503i
\(893\) 161.905 + 280.428i 0.00606713 + 0.0105086i
\(894\) 5633.23 9757.04i 0.210742 0.365016i
\(895\) 5529.76 0.206524
\(896\) 0 0
\(897\) −16099.0 −0.599252
\(898\) −2541.92 + 4402.74i −0.0944600 + 0.163609i
\(899\) −1513.98 2622.29i −0.0561668 0.0972838i
\(900\) 2366.73 + 4099.29i 0.0876565 + 0.151826i
\(901\) 38703.0 67035.6i 1.43106 2.47867i
\(902\) 59.8721 0.00221012
\(903\) 0 0
\(904\) −19250.0 −0.708237
\(905\) 293.034 507.550i 0.0107633 0.0186426i
\(906\) 6071.55 + 10516.2i 0.222642 + 0.385628i
\(907\) −526.377 911.711i −0.0192702 0.0333769i 0.856230 0.516596i \(-0.172801\pi\)
−0.875500 + 0.483219i \(0.839468\pi\)
\(908\) 13531.1 23436.5i 0.494542 0.856571i
\(909\) 7491.60 0.273356
\(910\) 0 0
\(911\) 7854.40 0.285651 0.142825 0.989748i \(-0.454381\pi\)
0.142825 + 0.989748i \(0.454381\pi\)
\(912\) 1680.11 2910.03i 0.0610021 0.105659i
\(913\) 67.2251 + 116.437i 0.00243683 + 0.00422071i
\(914\) 41303.4 + 71539.6i 1.49474 + 2.58897i
\(915\) −6137.52 + 10630.5i −0.221749 + 0.384080i
\(916\) −49905.4 −1.80013
\(917\) 0 0
\(918\) −71186.4 −2.55937
\(919\) −2467.92 + 4274.57i −0.0885846 + 0.153433i −0.906913 0.421318i \(-0.861568\pi\)
0.818328 + 0.574751i \(0.194901\pi\)
\(920\) −5940.95 10290.0i −0.212899 0.368752i
\(921\) 8055.64 + 13952.8i 0.288211 + 0.499196i
\(922\) 6962.47 12059.4i 0.248695 0.430752i
\(923\) 1190.07 0.0424395
\(924\) 0 0
\(925\) −10008.3 −0.355753
\(926\) 8941.22 15486.7i 0.317308 0.549593i
\(927\) 5800.34 + 10046.5i 0.205510 + 0.355955i
\(928\) 4594.63 + 7958.14i 0.162528 + 0.281507i
\(929\) −7852.51 + 13600.9i −0.277322 + 0.480336i −0.970718 0.240220i \(-0.922780\pi\)
0.693396 + 0.720557i \(0.256114\pi\)
\(930\) 5397.80 0.190323
\(931\) 0 0
\(932\) 28233.7 0.992302
\(933\) 8161.66 14136.4i 0.286389 0.496040i
\(934\) −36067.7 62471.0i −1.26356 2.18856i
\(935\) −40.6393 70.3892i −0.00142144 0.00246200i
\(936\) −4075.98 + 7059.81i −0.142337 + 0.246535i
\(937\) 43806.5 1.52732 0.763658 0.645621i \(-0.223401\pi\)
0.763658 + 0.645621i \(0.223401\pi\)
\(938\) 0 0
\(939\) 11670.9 0.405608
\(940\) 215.071 372.515i 0.00746261 0.0129256i
\(941\) 2031.21 + 3518.16i 0.0703672 + 0.121880i 0.899062 0.437821i \(-0.144250\pi\)
−0.828695 + 0.559700i \(0.810916\pi\)
\(942\) 6834.24 + 11837.2i 0.236382 + 0.409425i
\(943\) −7369.92 + 12765.1i −0.254504 + 0.440815i
\(944\) 19084.9 0.658009
\(945\) 0 0
\(946\) −213.366 −0.00733313
\(947\) 2430.06 4208.99i 0.0833859 0.144429i −0.821316 0.570473i \(-0.806760\pi\)
0.904702 + 0.426044i \(0.140093\pi\)
\(948\) −5909.63 10235.8i −0.202464 0.350678i
\(949\) 1299.78 + 2251.29i 0.0444602 + 0.0770073i
\(950\) −2385.36 + 4131.56i −0.0814644 + 0.141100i
\(951\) −11484.0 −0.391581
\(952\) 0 0
\(953\) −18999.6 −0.645811 −0.322906 0.946431i \(-0.604660\pi\)
−0.322906 + 0.946431i \(0.604660\pi\)
\(954\) 24625.9 42653.3i 0.835736 1.44754i
\(955\) 2506.50 + 4341.38i 0.0849303 + 0.147104i
\(956\) −1850.88 3205.82i −0.0626168 0.108456i
\(957\) 9.25181 16.0246i 0.000312506 0.000541277i
\(958\) 11174.4 0.376855
\(959\) 0 0
\(960\) −13272.2 −0.446205
\(961\) 12051.3 20873.5i 0.404529 0.700664i
\(962\) −28400.1 49190.4i −0.951825 1.64861i
\(963\) 7871.70 + 13634.2i 0.263408 + 0.456236i
\(964\) −28777.7 + 49844.5i −0.961482 + 1.66534i
\(965\) −16288.8 −0.543373
\(966\) 0 0
\(967\) −32695.1 −1.08728 −0.543641 0.839318i \(-0.682955\pi\)
−0.543641 + 0.839318i \(0.682955\pi\)
\(968\) −10238.4 + 17733.5i −0.339954 + 0.588817i
\(969\) −8016.07 13884.2i −0.265751 0.460295i
\(970\) 4338.14 + 7513.88i 0.143597 + 0.248718i
\(971\) −3094.85 + 5360.43i −0.102285 + 0.177162i −0.912626 0.408797i \(-0.865949\pi\)
0.810341 + 0.585959i \(0.199282\pi\)
\(972\) −43274.8 −1.42803
\(973\) 0 0
\(974\) 37265.6 1.22594
\(975\) 1302.82 2256.55i 0.0427934 0.0741203i
\(976\) 9074.08 + 15716.8i 0.297596 + 0.515452i
\(977\) −1071.22 1855.41i −0.0350782 0.0607572i 0.847953 0.530071i \(-0.177835\pi\)
−0.883032 + 0.469314i \(0.844501\pi\)
\(978\) 52.7046 91.2871i 0.00172322 0.00298470i
\(979\) 111.321 0.00363416
\(980\) 0 0
\(981\) −4763.04 −0.155018
\(982\) −33600.8 + 58198.4i −1.09190 + 1.89123i
\(983\) 8404.11 + 14556.4i 0.272685 + 0.472305i 0.969549 0.244899i \(-0.0787549\pi\)
−0.696863 + 0.717204i \(0.745422\pi\)
\(984\) −2380.28 4122.77i −0.0771145 0.133566i
\(985\) −104.239 + 180.547i −0.00337190 + 0.00584031i
\(986\) 20268.0 0.654630
\(987\) 0 0
\(988\) −15959.0 −0.513891
\(989\) 26264.2 45490.9i 0.844442 1.46262i
\(990\) −25.8579 44.7871i −0.000830118 0.00143781i
\(991\) −10625.4 18403.7i −0.340593 0.589924i 0.643950 0.765067i \(-0.277294\pi\)
−0.984543 + 0.175144i \(0.943961\pi\)
\(992\) 8631.57 14950.3i 0.276263 0.478501i
\(993\) 23859.2 0.762487
\(994\) 0 0
\(995\) 12028.1 0.383231
\(996\) 17614.4 30509.1i 0.560377 0.970601i
\(997\) −18820.0 32597.1i −0.597828 1.03547i −0.993141 0.116922i \(-0.962697\pi\)
0.395313 0.918546i \(-0.370636\pi\)
\(998\) −36688.0 63545.4i −1.16366 2.01553i
\(999\) 28224.9 48887.0i 0.893891 1.54826i
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 245.4.e.l.226.2 4
7.2 even 3 245.4.a.h.1.1 2
7.3 odd 6 35.4.e.b.11.2 4
7.4 even 3 inner 245.4.e.l.116.2 4
7.5 odd 6 245.4.a.g.1.1 2
7.6 odd 2 35.4.e.b.16.2 yes 4
21.2 odd 6 2205.4.a.bg.1.2 2
21.5 even 6 2205.4.a.bf.1.2 2
21.17 even 6 315.4.j.c.46.1 4
21.20 even 2 315.4.j.c.226.1 4
28.3 even 6 560.4.q.i.81.2 4
28.27 even 2 560.4.q.i.401.2 4
35.3 even 12 175.4.k.c.74.4 8
35.9 even 6 1225.4.a.v.1.2 2
35.13 even 4 175.4.k.c.149.1 8
35.17 even 12 175.4.k.c.74.1 8
35.19 odd 6 1225.4.a.x.1.2 2
35.24 odd 6 175.4.e.c.151.1 4
35.27 even 4 175.4.k.c.149.4 8
35.34 odd 2 175.4.e.c.51.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.4.e.b.11.2 4 7.3 odd 6
35.4.e.b.16.2 yes 4 7.6 odd 2
175.4.e.c.51.1 4 35.34 odd 2
175.4.e.c.151.1 4 35.24 odd 6
175.4.k.c.74.1 8 35.17 even 12
175.4.k.c.74.4 8 35.3 even 12
175.4.k.c.149.1 8 35.13 even 4
175.4.k.c.149.4 8 35.27 even 4
245.4.a.g.1.1 2 7.5 odd 6
245.4.a.h.1.1 2 7.2 even 3
245.4.e.l.116.2 4 7.4 even 3 inner
245.4.e.l.226.2 4 1.1 even 1 trivial
315.4.j.c.46.1 4 21.17 even 6
315.4.j.c.226.1 4 21.20 even 2
560.4.q.i.81.2 4 28.3 even 6
560.4.q.i.401.2 4 28.27 even 2
1225.4.a.v.1.2 2 35.9 even 6
1225.4.a.x.1.2 2 35.19 odd 6
2205.4.a.bf.1.2 2 21.5 even 6
2205.4.a.bg.1.2 2 21.2 odd 6