Properties

Label 225.4.k.c.124.5
Level $225$
Weight $4$
Character 225.124
Analytic conductor $13.275$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(49,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 23x^{10} + 198x^{8} - 719x^{6} + 886x^{4} + 585x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.5
Root \(0.0378788 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.4.k.c.49.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.24635 + 1.87428i) q^{2} +(3.24635 - 4.05724i) q^{3} +(3.02587 + 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(-27.1492 - 15.6746i) q^{7} -7.30318i q^{8} +(-5.92239 - 26.3425i) q^{9} +O(q^{10})\) \(q+(3.24635 + 1.87428i) q^{2} +(3.24635 - 4.05724i) q^{3} +(3.02587 + 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(-27.1492 - 15.6746i) q^{7} -7.30318i q^{8} +(-5.92239 - 26.3425i) q^{9} +(10.4166 - 18.0422i) q^{11} +(31.0869 + 4.73733i) q^{12} +(51.9018 - 29.9655i) q^{13} +(-58.7572 - 101.770i) q^{14} +(37.8952 - 65.6364i) q^{16} +74.0460i q^{17} +(30.1471 - 96.6172i) q^{18} +63.8390 q^{19} +(-151.731 + 59.2655i) q^{21} +(67.6322 - 39.0475i) q^{22} +(-28.4484 + 16.4247i) q^{23} +(-29.6307 - 23.7087i) q^{24} +224.655 q^{26} +(-126.104 - 61.4884i) q^{27} -189.717i q^{28} +(-80.0044 + 138.572i) q^{29} +(127.187 + 220.294i) q^{31} +(195.444 - 112.840i) q^{32} +(-39.3853 - 100.834i) q^{33} +(-138.783 + 240.379i) q^{34} +(120.139 - 110.748i) q^{36} -215.365i q^{37} +(207.244 + 119.652i) q^{38} +(46.9143 - 307.857i) q^{39} +(-70.8407 - 122.700i) q^{41} +(-603.654 - 91.9908i) q^{42} +(-119.430 - 68.9529i) q^{43} +126.078 q^{44} -123.138 q^{46} +(29.0803 + 16.7895i) q^{47} +(-143.281 - 366.829i) q^{48} +(319.885 + 554.058i) q^{49} +(300.422 + 240.379i) q^{51} +(314.096 + 181.344i) q^{52} -41.9914i q^{53} +(-294.131 - 435.967i) q^{54} +(-114.474 + 198.275i) q^{56} +(207.244 - 259.010i) q^{57} +(-519.445 + 299.902i) q^{58} +(307.571 + 532.728i) q^{59} +(67.1535 - 116.313i) q^{61} +953.535i q^{62} +(-252.119 + 808.007i) q^{63} +239.652 q^{64} +(61.1331 - 401.162i) q^{66} +(742.646 - 428.767i) q^{67} +(-388.072 + 224.054i) q^{68} +(-25.7146 + 168.742i) q^{69} +588.665 q^{71} +(-192.384 + 43.2522i) q^{72} -618.191i q^{73} +(403.655 - 699.152i) q^{74} +(193.169 + 334.578i) q^{76} +(-565.607 + 326.553i) q^{77} +(729.311 - 911.481i) q^{78} +(-172.644 + 299.029i) q^{79} +(-658.851 + 312.021i) q^{81} -531.102i q^{82} +(946.711 + 546.584i) q^{83} +(-769.728 - 615.889i) q^{84} +(-258.474 - 447.691i) q^{86} +(302.496 + 774.450i) q^{87} +(-131.765 - 76.0746i) q^{88} -414.849 q^{89} -1878.79 q^{91} +(-172.162 - 99.3979i) q^{92} +(1306.68 + 199.125i) q^{93} +(62.9366 + 109.009i) q^{94} +(176.663 - 1159.28i) q^{96} +(-174.427 - 100.705i) q^{97} +2398.22i q^{98} +(-536.967 - 167.547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.24635 + 1.87428i 1.14776 + 0.662659i 0.948340 0.317255i \(-0.102761\pi\)
0.199419 + 0.979914i \(0.436095\pi\)
\(3\) 3.24635 4.05724i 0.624761 0.780816i
\(4\) 3.02587 + 5.24096i 0.378234 + 0.655120i
\(5\) 0 0
\(6\) 18.1432 7.08665i 1.23449 0.482185i
\(7\) −27.1492 15.6746i −1.46592 0.846348i −0.466644 0.884445i \(-0.654537\pi\)
−0.999274 + 0.0380969i \(0.987870\pi\)
\(8\) 7.30318i 0.322758i
\(9\) −5.92239 26.3425i −0.219348 0.975647i
\(10\) 0 0
\(11\) 10.4166 18.0422i 0.285522 0.494538i −0.687214 0.726455i \(-0.741166\pi\)
0.972736 + 0.231917i \(0.0744998\pi\)
\(12\) 31.0869 + 4.73733i 0.747834 + 0.113962i
\(13\) 51.9018 29.9655i 1.10731 0.639303i 0.169175 0.985586i \(-0.445890\pi\)
0.938130 + 0.346283i \(0.112556\pi\)
\(14\) −58.7572 101.770i −1.12168 1.94281i
\(15\) 0 0
\(16\) 37.8952 65.6364i 0.592112 1.02557i
\(17\) 74.0460i 1.05640i 0.849120 + 0.528200i \(0.177133\pi\)
−0.849120 + 0.528200i \(0.822867\pi\)
\(18\) 30.1471 96.6172i 0.394763 1.26516i
\(19\) 63.8390 0.770825 0.385413 0.922744i \(-0.374059\pi\)
0.385413 + 0.922744i \(0.374059\pi\)
\(20\) 0 0
\(21\) −151.731 + 59.2655i −1.57669 + 0.615847i
\(22\) 67.6322 39.0475i 0.655420 0.378407i
\(23\) −28.4484 + 16.4247i −0.257909 + 0.148904i −0.623380 0.781919i \(-0.714241\pi\)
0.365472 + 0.930823i \(0.380908\pi\)
\(24\) −29.6307 23.7087i −0.252015 0.201646i
\(25\) 0 0
\(26\) 224.655 1.69456
\(27\) −126.104 61.4884i −0.898841 0.438276i
\(28\) 189.717i 1.28047i
\(29\) −80.0044 + 138.572i −0.512291 + 0.887314i 0.487607 + 0.873063i \(0.337870\pi\)
−0.999898 + 0.0142513i \(0.995464\pi\)
\(30\) 0 0
\(31\) 127.187 + 220.294i 0.736884 + 1.27632i 0.953892 + 0.300151i \(0.0970371\pi\)
−0.217007 + 0.976170i \(0.569630\pi\)
\(32\) 195.444 112.840i 1.07969 0.623358i
\(33\) −39.3853 100.834i −0.207760 0.531908i
\(34\) −138.783 + 240.379i −0.700033 + 1.21249i
\(35\) 0 0
\(36\) 120.139 110.748i 0.556201 0.512722i
\(37\) 215.365i 0.956914i −0.878111 0.478457i \(-0.841196\pi\)
0.878111 0.478457i \(-0.158804\pi\)
\(38\) 207.244 + 119.652i 0.884722 + 0.510794i
\(39\) 46.9143 307.857i 0.192623 1.26401i
\(40\) 0 0
\(41\) −70.8407 122.700i −0.269841 0.467377i 0.698980 0.715141i \(-0.253638\pi\)
−0.968820 + 0.247764i \(0.920304\pi\)
\(42\) −603.654 91.9908i −2.21776 0.337964i
\(43\) −119.430 68.9529i −0.423556 0.244540i 0.273042 0.962002i \(-0.411970\pi\)
−0.696597 + 0.717462i \(0.745304\pi\)
\(44\) 126.078 0.431976
\(45\) 0 0
\(46\) −123.138 −0.394689
\(47\) 29.0803 + 16.7895i 0.0902509 + 0.0521064i 0.544446 0.838796i \(-0.316740\pi\)
−0.454195 + 0.890902i \(0.650073\pi\)
\(48\) −143.281 366.829i −0.430852 1.10307i
\(49\) 319.885 + 554.058i 0.932611 + 1.61533i
\(50\) 0 0
\(51\) 300.422 + 240.379i 0.824854 + 0.659997i
\(52\) 314.096 + 181.344i 0.837641 + 0.483612i
\(53\) 41.9914i 0.108829i −0.998518 0.0544147i \(-0.982671\pi\)
0.998518 0.0544147i \(-0.0173293\pi\)
\(54\) −294.131 435.967i −0.741225 1.09866i
\(55\) 0 0
\(56\) −114.474 + 198.275i −0.273166 + 0.473137i
\(57\) 207.244 259.010i 0.481581 0.601873i
\(58\) −519.445 + 299.902i −1.17597 + 0.678949i
\(59\) 307.571 + 532.728i 0.678683 + 1.17551i 0.975378 + 0.220541i \(0.0707824\pi\)
−0.296694 + 0.954973i \(0.595884\pi\)
\(60\) 0 0
\(61\) 67.1535 116.313i 0.140953 0.244137i −0.786903 0.617077i \(-0.788317\pi\)
0.927856 + 0.372939i \(0.121650\pi\)
\(62\) 953.535i 1.95321i
\(63\) −252.119 + 808.007i −0.504191 + 1.61586i
\(64\) 239.652 0.468071
\(65\) 0 0
\(66\) 61.1331 401.162i 0.114015 0.748176i
\(67\) 742.646 428.767i 1.35416 0.781824i 0.365329 0.930878i \(-0.380956\pi\)
0.988829 + 0.149055i \(0.0476231\pi\)
\(68\) −388.072 + 224.054i −0.692069 + 0.399566i
\(69\) −25.7146 + 168.742i −0.0448649 + 0.294408i
\(70\) 0 0
\(71\) 588.665 0.983968 0.491984 0.870604i \(-0.336272\pi\)
0.491984 + 0.870604i \(0.336272\pi\)
\(72\) −192.384 + 43.2522i −0.314898 + 0.0707962i
\(73\) 618.191i 0.991148i −0.868566 0.495574i \(-0.834958\pi\)
0.868566 0.495574i \(-0.165042\pi\)
\(74\) 403.655 699.152i 0.634108 1.09831i
\(75\) 0 0
\(76\) 193.169 + 334.578i 0.291552 + 0.504983i
\(77\) −565.607 + 326.553i −0.837103 + 0.483301i
\(78\) 729.311 911.481i 1.05869 1.32314i
\(79\) −172.644 + 299.029i −0.245873 + 0.425865i −0.962377 0.271718i \(-0.912408\pi\)
0.716503 + 0.697584i \(0.245741\pi\)
\(80\) 0 0
\(81\) −658.851 + 312.021i −0.903773 + 0.428012i
\(82\) 531.102i 0.715249i
\(83\) 946.711 + 546.584i 1.25199 + 0.722836i 0.971504 0.237023i \(-0.0761717\pi\)
0.280484 + 0.959859i \(0.409505\pi\)
\(84\) −769.728 615.889i −0.999812 0.799988i
\(85\) 0 0
\(86\) −258.474 447.691i −0.324093 0.561346i
\(87\) 302.496 + 774.450i 0.372770 + 0.954365i
\(88\) −131.765 76.0746i −0.159616 0.0921543i
\(89\) −414.849 −0.494089 −0.247045 0.969004i \(-0.579459\pi\)
−0.247045 + 0.969004i \(0.579459\pi\)
\(90\) 0 0
\(91\) −1878.79 −2.16429
\(92\) −172.162 99.3979i −0.195100 0.112641i
\(93\) 1306.68 + 199.125i 1.45695 + 0.222024i
\(94\) 62.9366 + 109.009i 0.0690576 + 0.119611i
\(95\) 0 0
\(96\) 176.663 1159.28i 0.187819 1.23249i
\(97\) −174.427 100.705i −0.182581 0.105413i 0.405924 0.913907i \(-0.366950\pi\)
−0.588505 + 0.808494i \(0.700283\pi\)
\(98\) 2398.22i 2.47201i
\(99\) −536.967 167.547i −0.545123 0.170092i
\(100\) 0 0
\(101\) −132.691 + 229.828i −0.130726 + 0.226424i −0.923957 0.382498i \(-0.875064\pi\)
0.793231 + 0.608921i \(0.208397\pi\)
\(102\) 524.738 + 1343.43i 0.509380 + 1.30411i
\(103\) −456.931 + 263.809i −0.437114 + 0.252368i −0.702373 0.711810i \(-0.747876\pi\)
0.265259 + 0.964177i \(0.414543\pi\)
\(104\) −218.843 379.048i −0.206340 0.357391i
\(105\) 0 0
\(106\) 78.7038 136.319i 0.0721168 0.124910i
\(107\) 2084.24i 1.88310i −0.336877 0.941549i \(-0.609371\pi\)
0.336877 0.941549i \(-0.390629\pi\)
\(108\) −59.3157 846.961i −0.0528487 0.754619i
\(109\) −925.651 −0.813406 −0.406703 0.913560i \(-0.633322\pi\)
−0.406703 + 0.913560i \(0.633322\pi\)
\(110\) 0 0
\(111\) −873.788 699.152i −0.747174 0.597843i
\(112\) −2057.65 + 1187.98i −1.73598 + 1.00227i
\(113\) 472.866 273.009i 0.393659 0.227279i −0.290085 0.957001i \(-0.593684\pi\)
0.683745 + 0.729721i \(0.260350\pi\)
\(114\) 1158.25 452.405i 0.951576 0.371681i
\(115\) 0 0
\(116\) −968.332 −0.775063
\(117\) −1096.75 1189.75i −0.866619 0.940109i
\(118\) 2305.90i 1.79894i
\(119\) 1160.64 2010.29i 0.894082 1.54860i
\(120\) 0 0
\(121\) 448.487 + 776.802i 0.336955 + 0.583623i
\(122\) 436.008 251.729i 0.323560 0.186807i
\(123\) −727.796 110.909i −0.533522 0.0813033i
\(124\) −769.701 + 1333.16i −0.557429 + 0.965495i
\(125\) 0 0
\(126\) −2332.90 + 2150.53i −1.64946 + 1.52051i
\(127\) 975.972i 0.681918i 0.940078 + 0.340959i \(0.110752\pi\)
−0.940078 + 0.340959i \(0.889248\pi\)
\(128\) −785.559 453.543i −0.542455 0.313187i
\(129\) −667.470 + 260.710i −0.455562 + 0.177940i
\(130\) 0 0
\(131\) 814.614 + 1410.95i 0.543307 + 0.941035i 0.998711 + 0.0507502i \(0.0161612\pi\)
−0.455405 + 0.890285i \(0.650505\pi\)
\(132\) 409.293 511.528i 0.269882 0.337294i
\(133\) −1733.18 1000.65i −1.12997 0.652387i
\(134\) 3214.52 2.07233
\(135\) 0 0
\(136\) 540.771 0.340961
\(137\) 572.833 + 330.725i 0.357229 + 0.206246i 0.667865 0.744283i \(-0.267208\pi\)
−0.310635 + 0.950529i \(0.600542\pi\)
\(138\) −399.749 + 499.600i −0.246586 + 0.308180i
\(139\) 691.495 + 1197.70i 0.421955 + 0.730848i 0.996131 0.0878842i \(-0.0280105\pi\)
−0.574175 + 0.818732i \(0.694677\pi\)
\(140\) 0 0
\(141\) 162.524 63.4810i 0.0970708 0.0379153i
\(142\) 1911.02 + 1103.33i 1.12936 + 0.652035i
\(143\) 1248.56i 0.730139i
\(144\) −1953.45 609.528i −1.13047 0.352736i
\(145\) 0 0
\(146\) 1158.66 2006.87i 0.656793 1.13760i
\(147\) 3286.41 + 500.815i 1.84393 + 0.280997i
\(148\) 1128.72 651.667i 0.626894 0.361937i
\(149\) 1581.75 + 2739.66i 0.869676 + 1.50632i 0.862328 + 0.506349i \(0.169005\pi\)
0.00734719 + 0.999973i \(0.497661\pi\)
\(150\) 0 0
\(151\) 1279.40 2215.98i 0.689509 1.19427i −0.282488 0.959271i \(-0.591160\pi\)
0.971997 0.234994i \(-0.0755071\pi\)
\(152\) 466.228i 0.248790i
\(153\) 1950.55 438.529i 1.03067 0.231719i
\(154\) −2448.21 −1.28106
\(155\) 0 0
\(156\) 1755.42 685.659i 0.900937 0.351901i
\(157\) −3031.92 + 1750.48i −1.54123 + 0.889832i −0.542474 + 0.840073i \(0.682512\pi\)
−0.998761 + 0.0497594i \(0.984155\pi\)
\(158\) −1120.93 + 647.168i −0.564407 + 0.325860i
\(159\) −170.369 136.319i −0.0849758 0.0679924i
\(160\) 0 0
\(161\) 1029.80 0.504097
\(162\) −2723.68 221.943i −1.32094 0.107639i
\(163\) 263.950i 0.126835i 0.997987 + 0.0634176i \(0.0202000\pi\)
−0.997987 + 0.0634176i \(0.979800\pi\)
\(164\) 428.710 742.547i 0.204126 0.353556i
\(165\) 0 0
\(166\) 2048.90 + 3548.81i 0.957987 + 1.65928i
\(167\) 3108.21 1794.53i 1.44024 0.831524i 0.442377 0.896829i \(-0.354135\pi\)
0.997865 + 0.0653054i \(0.0208021\pi\)
\(168\) 432.826 + 1108.12i 0.198770 + 0.508889i
\(169\) 697.365 1207.87i 0.317417 0.549782i
\(170\) 0 0
\(171\) −378.080 1681.68i −0.169079 0.752053i
\(172\) 834.570i 0.369973i
\(173\) −320.824 185.228i −0.140993 0.0814024i 0.427844 0.903853i \(-0.359273\pi\)
−0.568837 + 0.822450i \(0.692607\pi\)
\(174\) −469.529 + 3081.10i −0.204568 + 1.34240i
\(175\) 0 0
\(176\) −789.482 1367.42i −0.338122 0.585644i
\(177\) 3159.89 + 481.535i 1.34188 + 0.204488i
\(178\) −1346.75 777.545i −0.567095 0.327413i
\(179\) −446.898 −0.186607 −0.0933036 0.995638i \(-0.529743\pi\)
−0.0933036 + 0.995638i \(0.529743\pi\)
\(180\) 0 0
\(181\) −904.046 −0.371255 −0.185628 0.982620i \(-0.559432\pi\)
−0.185628 + 0.982620i \(0.559432\pi\)
\(182\) −6099.21 3521.38i −2.48409 1.43419i
\(183\) −253.907 650.051i −0.102565 0.262586i
\(184\) 119.952 + 207.764i 0.0480598 + 0.0832420i
\(185\) 0 0
\(186\) 3868.72 + 3095.51i 1.52510 + 1.22029i
\(187\) 1335.95 + 771.311i 0.522430 + 0.301625i
\(188\) 203.211i 0.0788336i
\(189\) 2459.81 + 3645.99i 0.946693 + 1.40321i
\(190\) 0 0
\(191\) 299.793 519.257i 0.113572 0.196713i −0.803636 0.595121i \(-0.797104\pi\)
0.917208 + 0.398409i \(0.130437\pi\)
\(192\) 777.995 972.326i 0.292432 0.365477i
\(193\) −3822.40 + 2206.87i −1.42561 + 0.823076i −0.996770 0.0803048i \(-0.974411\pi\)
−0.428839 + 0.903381i \(0.641077\pi\)
\(194\) −377.500 653.850i −0.139706 0.241978i
\(195\) 0 0
\(196\) −1935.86 + 3353.01i −0.705490 + 1.22194i
\(197\) 4807.15i 1.73855i 0.494325 + 0.869277i \(0.335415\pi\)
−0.494325 + 0.869277i \(0.664585\pi\)
\(198\) −1429.15 1550.35i −0.512956 0.556456i
\(199\) −313.833 −0.111794 −0.0558970 0.998437i \(-0.517802\pi\)
−0.0558970 + 0.998437i \(0.517802\pi\)
\(200\) 0 0
\(201\) 671.281 4405.02i 0.235565 1.54580i
\(202\) −861.527 + 497.403i −0.300083 + 0.173253i
\(203\) 4344.11 2508.07i 1.50195 0.867153i
\(204\) −350.780 + 2301.86i −0.120390 + 0.790012i
\(205\) 0 0
\(206\) −1977.81 −0.668935
\(207\) 601.149 + 652.127i 0.201849 + 0.218966i
\(208\) 4542.20i 1.51416i
\(209\) 664.989 1151.79i 0.220087 0.381202i
\(210\) 0 0
\(211\) −1219.41 2112.08i −0.397856 0.689106i 0.595605 0.803277i \(-0.296912\pi\)
−0.993461 + 0.114171i \(0.963579\pi\)
\(212\) 220.075 127.061i 0.0712964 0.0411630i
\(213\) 1911.02 2388.36i 0.614745 0.768298i
\(214\) 3906.46 6766.19i 1.24785 2.16134i
\(215\) 0 0
\(216\) −449.060 + 920.959i −0.141457 + 0.290108i
\(217\) 7974.40i 2.49464i
\(218\) −3004.99 1734.93i −0.933594 0.539011i
\(219\) −2508.15 2006.87i −0.773904 0.619230i
\(220\) 0 0
\(221\) 2218.83 + 3843.12i 0.675360 + 1.16976i
\(222\) −1526.22 3907.42i −0.461410 1.18130i
\(223\) 2020.79 + 1166.71i 0.606827 + 0.350352i 0.771722 0.635959i \(-0.219395\pi\)
−0.164896 + 0.986311i \(0.552729\pi\)
\(224\) −7074.87 −2.11031
\(225\) 0 0
\(226\) 2046.79 0.602435
\(227\) −2358.79 1361.85i −0.689684 0.398189i 0.113810 0.993503i \(-0.463695\pi\)
−0.803494 + 0.595313i \(0.797028\pi\)
\(228\) 1984.56 + 302.426i 0.576449 + 0.0878451i
\(229\) −1657.08 2870.15i −0.478179 0.828230i 0.521508 0.853246i \(-0.325370\pi\)
−0.999687 + 0.0250162i \(0.992036\pi\)
\(230\) 0 0
\(231\) −511.255 + 3354.91i −0.145619 + 0.955571i
\(232\) 1012.01 + 584.286i 0.286388 + 0.165346i
\(233\) 3175.44i 0.892833i −0.894825 0.446416i \(-0.852700\pi\)
0.894825 0.446416i \(-0.147300\pi\)
\(234\) −1330.50 5917.98i −0.371698 1.65329i
\(235\) 0 0
\(236\) −1861.34 + 3223.93i −0.513402 + 0.889238i
\(237\) 652.767 + 1671.21i 0.178910 + 0.458046i
\(238\) 7535.70 4350.74i 2.05238 1.18494i
\(239\) −123.062 213.150i −0.0333064 0.0576884i 0.848892 0.528567i \(-0.177270\pi\)
−0.882198 + 0.470878i \(0.843937\pi\)
\(240\) 0 0
\(241\) 2643.87 4579.31i 0.706666 1.22398i −0.259421 0.965764i \(-0.583532\pi\)
0.966087 0.258217i \(-0.0831349\pi\)
\(242\) 3362.36i 0.893144i
\(243\) −872.919 + 3686.04i −0.230444 + 0.973086i
\(244\) 812.791 0.213252
\(245\) 0 0
\(246\) −2154.81 1724.14i −0.558478 0.446860i
\(247\) 3313.36 1912.97i 0.853539 0.492791i
\(248\) 1608.84 928.867i 0.411943 0.237835i
\(249\) 5290.98 2066.63i 1.34659 0.525973i
\(250\) 0 0
\(251\) 2821.23 0.709459 0.354730 0.934969i \(-0.384573\pi\)
0.354730 + 0.934969i \(0.384573\pi\)
\(252\) −4997.62 + 1123.58i −1.24929 + 0.280868i
\(253\) 684.361i 0.170061i
\(254\) −1829.25 + 3168.35i −0.451879 + 0.782677i
\(255\) 0 0
\(256\) −2658.74 4605.08i −0.649107 1.12429i
\(257\) 1631.76 942.096i 0.396056 0.228663i −0.288725 0.957412i \(-0.593231\pi\)
0.684781 + 0.728749i \(0.259898\pi\)
\(258\) −2655.49 404.670i −0.640789 0.0976497i
\(259\) −3375.76 + 5846.99i −0.809883 + 1.40276i
\(260\) 0 0
\(261\) 4124.14 + 1286.84i 0.978075 + 0.305185i
\(262\) 6107.27i 1.44011i
\(263\) −478.922 276.506i −0.112287 0.0648292i 0.442804 0.896618i \(-0.353984\pi\)
−0.555092 + 0.831789i \(0.687317\pi\)
\(264\) −736.409 + 287.638i −0.171677 + 0.0670563i
\(265\) 0 0
\(266\) −3751.00 6496.93i −0.864620 1.49757i
\(267\) −1346.75 + 1683.14i −0.308688 + 0.385793i
\(268\) 4494.30 + 2594.78i 1.02438 + 0.591424i
\(269\) −3363.48 −0.762361 −0.381180 0.924501i \(-0.624482\pi\)
−0.381180 + 0.924501i \(0.624482\pi\)
\(270\) 0 0
\(271\) −3333.85 −0.747295 −0.373648 0.927571i \(-0.621893\pi\)
−0.373648 + 0.927571i \(0.621893\pi\)
\(272\) 4860.11 + 2805.99i 1.08341 + 0.625507i
\(273\) −6099.21 + 7622.70i −1.35217 + 1.68991i
\(274\) 1239.75 + 2147.30i 0.273342 + 0.473443i
\(275\) 0 0
\(276\) −962.181 + 375.823i −0.209842 + 0.0819633i
\(277\) −4665.50 2693.63i −1.01199 0.584275i −0.100220 0.994965i \(-0.531955\pi\)
−0.911775 + 0.410690i \(0.865288\pi\)
\(278\) 5184.23i 1.11845i
\(279\) 5049.83 4655.08i 1.08360 0.998897i
\(280\) 0 0
\(281\) −1858.35 + 3218.76i −0.394519 + 0.683327i −0.993040 0.117781i \(-0.962422\pi\)
0.598521 + 0.801107i \(0.295755\pi\)
\(282\) 646.591 + 98.5340i 0.136539 + 0.0208071i
\(283\) 2397.81 1384.38i 0.503658 0.290787i −0.226565 0.973996i \(-0.572750\pi\)
0.730223 + 0.683209i \(0.239416\pi\)
\(284\) 1781.23 + 3085.17i 0.372170 + 0.644617i
\(285\) 0 0
\(286\) 2340.16 4053.27i 0.483833 0.838024i
\(287\) 4441.60i 0.913516i
\(288\) −4129.98 4480.20i −0.845004 0.916662i
\(289\) −569.810 −0.115980
\(290\) 0 0
\(291\) −974.836 + 380.766i −0.196378 + 0.0767041i
\(292\) 3239.91 1870.57i 0.649321 0.374886i
\(293\) −3013.76 + 1740.00i −0.600907 + 0.346934i −0.769398 0.638769i \(-0.779444\pi\)
0.168491 + 0.985703i \(0.446110\pi\)
\(294\) 9730.17 + 7785.48i 1.93019 + 1.54442i
\(295\) 0 0
\(296\) −1572.85 −0.308852
\(297\) −2422.96 + 1634.68i −0.473382 + 0.319374i
\(298\) 11858.6i 2.30519i
\(299\) −984.348 + 1704.94i −0.190389 + 0.329764i
\(300\) 0 0
\(301\) 2161.62 + 3744.03i 0.413932 + 0.716951i
\(302\) 8306.75 4795.91i 1.58278 0.913819i
\(303\) 501.705 + 1284.47i 0.0951229 + 0.243533i
\(304\) 2419.19 4190.16i 0.456415 0.790534i
\(305\) 0 0
\(306\) 7154.11 + 2232.27i 1.33651 + 0.417027i
\(307\) 1810.36i 0.336555i 0.985740 + 0.168278i \(0.0538205\pi\)
−0.985740 + 0.168278i \(0.946179\pi\)
\(308\) −3422.91 1976.22i −0.633241 0.365602i
\(309\) −413.021 + 2710.29i −0.0760387 + 0.498975i
\(310\) 0 0
\(311\) 443.649 + 768.422i 0.0808907 + 0.140107i 0.903633 0.428308i \(-0.140890\pi\)
−0.822742 + 0.568415i \(0.807557\pi\)
\(312\) −2248.33 342.623i −0.407970 0.0621706i
\(313\) 1918.36 + 1107.57i 0.346429 + 0.200011i 0.663111 0.748521i \(-0.269236\pi\)
−0.316682 + 0.948532i \(0.602569\pi\)
\(314\) −13123.6 −2.35862
\(315\) 0 0
\(316\) −2089.60 −0.371990
\(317\) −569.884 329.023i −0.100971 0.0582958i 0.448664 0.893700i \(-0.351900\pi\)
−0.549635 + 0.835405i \(0.685233\pi\)
\(318\) −297.578 761.859i −0.0524760 0.134349i
\(319\) 1666.76 + 2886.91i 0.292540 + 0.506695i
\(320\) 0 0
\(321\) −8456.28 6766.19i −1.47035 1.17649i
\(322\) 3343.10 + 1930.14i 0.578582 + 0.334045i
\(323\) 4727.03i 0.814299i
\(324\) −3628.88 2508.88i −0.622237 0.430192i
\(325\) 0 0
\(326\) −494.717 + 856.875i −0.0840485 + 0.145576i
\(327\) −3004.99 + 3755.59i −0.508184 + 0.635121i
\(328\) −896.098 + 517.362i −0.150850 + 0.0870931i
\(329\) −526.337 911.643i −0.0882003 0.152767i
\(330\) 0 0
\(331\) −2638.22 + 4569.53i −0.438096 + 0.758804i −0.997543 0.0700619i \(-0.977680\pi\)
0.559447 + 0.828866i \(0.311014\pi\)
\(332\) 6615.57i 1.09360i
\(333\) −5673.25 + 1275.48i −0.933610 + 0.209897i
\(334\) 13453.8 2.20407
\(335\) 0 0
\(336\) −1859.92 + 12205.0i −0.301984 + 1.98165i
\(337\) 2910.95 1680.64i 0.470532 0.271662i −0.245930 0.969288i \(-0.579093\pi\)
0.716462 + 0.697626i \(0.245760\pi\)
\(338\) 4527.78 2614.12i 0.728636 0.420678i
\(339\) 427.426 2804.82i 0.0684796 0.449371i
\(340\) 0 0
\(341\) 5299.44 0.841586
\(342\) 1924.56 6167.95i 0.304293 0.975217i
\(343\) 9303.52i 1.46456i
\(344\) −503.575 + 872.218i −0.0789272 + 0.136706i
\(345\) 0 0
\(346\) −694.339 1202.63i −0.107884 0.186861i
\(347\) −8102.13 + 4677.77i −1.25344 + 0.723677i −0.971792 0.235840i \(-0.924216\pi\)
−0.281653 + 0.959516i \(0.590883\pi\)
\(348\) −3143.55 + 3928.75i −0.484229 + 0.605182i
\(349\) 3519.65 6096.22i 0.539836 0.935023i −0.459077 0.888397i \(-0.651820\pi\)
0.998912 0.0466263i \(-0.0148470\pi\)
\(350\) 0 0
\(351\) −8387.55 + 587.410i −1.27548 + 0.0893266i
\(352\) 4701.65i 0.711929i
\(353\) −3639.19 2101.09i −0.548710 0.316798i 0.199891 0.979818i \(-0.435941\pi\)
−0.748602 + 0.663020i \(0.769274\pi\)
\(354\) 9355.58 + 7485.76i 1.40464 + 1.12391i
\(355\) 0 0
\(356\) −1255.28 2174.21i −0.186881 0.323688i
\(357\) −4388.37 11235.1i −0.650581 1.66562i
\(358\) −1450.79 837.612i −0.214180 0.123657i
\(359\) −588.013 −0.0864461 −0.0432230 0.999065i \(-0.513763\pi\)
−0.0432230 + 0.999065i \(0.513763\pi\)
\(360\) 0 0
\(361\) −2783.58 −0.405828
\(362\) −2934.85 1694.44i −0.426112 0.246016i
\(363\) 4607.62 + 702.155i 0.666218 + 0.101525i
\(364\) −5684.97 9846.66i −0.818608 1.41787i
\(365\) 0 0
\(366\) 394.109 2586.19i 0.0562853 0.369350i
\(367\) −6742.10 3892.55i −0.958950 0.553650i −0.0631004 0.998007i \(-0.520099\pi\)
−0.895850 + 0.444357i \(0.853432\pi\)
\(368\) 2489.67i 0.352671i
\(369\) −2812.67 + 2592.79i −0.396806 + 0.365787i
\(370\) 0 0
\(371\) −658.198 + 1140.03i −0.0921077 + 0.159535i
\(372\) 2910.23 + 7450.77i 0.405615 + 1.03845i
\(373\) −6775.81 + 3912.02i −0.940585 + 0.543047i −0.890144 0.455680i \(-0.849396\pi\)
−0.0504412 + 0.998727i \(0.516063\pi\)
\(374\) 2891.31 + 5007.90i 0.399749 + 0.692385i
\(375\) 0 0
\(376\) 122.617 212.378i 0.0168177 0.0291292i
\(377\) 9589.49i 1.31004i
\(378\) 1151.81 + 16446.5i 0.156727 + 2.23788i
\(379\) 4679.90 0.634275 0.317138 0.948379i \(-0.397278\pi\)
0.317138 + 0.948379i \(0.397278\pi\)
\(380\) 0 0
\(381\) 3959.75 + 3168.35i 0.532452 + 0.426036i
\(382\) 1946.47 1123.79i 0.260707 0.150519i
\(383\) −5826.31 + 3363.82i −0.777313 + 0.448782i −0.835477 0.549525i \(-0.814809\pi\)
0.0581644 + 0.998307i \(0.481475\pi\)
\(384\) −4390.33 + 1714.84i −0.583446 + 0.227891i
\(385\) 0 0
\(386\) −16545.2 −2.18167
\(387\) −1109.08 + 3554.44i −0.145679 + 0.466880i
\(388\) 1218.89i 0.159483i
\(389\) −2386.44 + 4133.43i −0.311047 + 0.538749i −0.978589 0.205823i \(-0.934013\pi\)
0.667542 + 0.744572i \(0.267346\pi\)
\(390\) 0 0
\(391\) −1216.18 2106.49i −0.157302 0.272455i
\(392\) 4046.38 2336.18i 0.521360 0.301007i
\(393\) 8369.10 + 1275.37i 1.07421 + 0.163699i
\(394\) −9009.95 + 15605.7i −1.15207 + 1.99544i
\(395\) 0 0
\(396\) −746.681 3321.20i −0.0947529 0.421456i
\(397\) 4688.95i 0.592775i 0.955068 + 0.296388i \(0.0957820\pi\)
−0.955068 + 0.296388i \(0.904218\pi\)
\(398\) −1018.81 588.211i −0.128313 0.0740813i
\(399\) −9686.39 + 3783.45i −1.21535 + 0.474711i
\(400\) 0 0
\(401\) −766.916 1328.34i −0.0955061 0.165421i 0.814314 0.580425i \(-0.197114\pi\)
−0.909820 + 0.415004i \(0.863780\pi\)
\(402\) 10435.5 13042.1i 1.29471 1.61811i
\(403\) 13202.4 + 7622.43i 1.63191 + 0.942185i
\(404\) −1606.03 −0.197780
\(405\) 0 0
\(406\) 18803.3 2.29851
\(407\) −3885.66 2243.38i −0.473230 0.273220i
\(408\) 1755.53 2194.04i 0.213019 0.266228i
\(409\) −4389.41 7602.68i −0.530666 0.919140i −0.999360 0.0357796i \(-0.988609\pi\)
0.468694 0.883361i \(-0.344725\pi\)
\(410\) 0 0
\(411\) 3201.45 1250.47i 0.384224 0.150076i
\(412\) −2765.23 1596.50i −0.330662 0.190908i
\(413\) 19284.2i 2.29761i
\(414\) 729.271 + 3243.76i 0.0865742 + 0.385077i
\(415\) 0 0
\(416\) 6762.61 11713.2i 0.797029 1.38050i
\(417\) 7104.21 + 1082.61i 0.834279 + 0.127136i
\(418\) 4317.58 2492.75i 0.505214 0.291686i
\(419\) −2138.02 3703.17i −0.249282 0.431770i 0.714044 0.700100i \(-0.246861\pi\)
−0.963327 + 0.268330i \(0.913528\pi\)
\(420\) 0 0
\(421\) −7231.64 + 12525.6i −0.837169 + 1.45002i 0.0550823 + 0.998482i \(0.482458\pi\)
−0.892252 + 0.451538i \(0.850875\pi\)
\(422\) 9142.07i 1.05457i
\(423\) 270.052 865.480i 0.0310411 0.0994825i
\(424\) −306.671 −0.0351256
\(425\) 0 0
\(426\) 10680.3 4171.66i 1.21470 0.474455i
\(427\) −3646.32 + 2105.21i −0.413250 + 0.238590i
\(428\) 10923.4 6306.65i 1.23366 0.712251i
\(429\) −5065.71 4053.27i −0.570105 0.456163i
\(430\) 0 0
\(431\) −2208.11 −0.246777 −0.123389 0.992358i \(-0.539376\pi\)
−0.123389 + 0.992358i \(0.539376\pi\)
\(432\) −8814.60 + 5946.89i −0.981696 + 0.662314i
\(433\) 10062.3i 1.11677i −0.829581 0.558386i \(-0.811421\pi\)
0.829581 0.558386i \(-0.188579\pi\)
\(434\) 14946.3 25887.7i 1.65310 2.86325i
\(435\) 0 0
\(436\) −2800.90 4851.30i −0.307658 0.532879i
\(437\) −1816.12 + 1048.54i −0.198803 + 0.114779i
\(438\) −4380.90 11216.0i −0.477917 1.22356i
\(439\) 6658.62 11533.1i 0.723915 1.25386i −0.235504 0.971873i \(-0.575674\pi\)
0.959419 0.281984i \(-0.0909925\pi\)
\(440\) 0 0
\(441\) 12700.8 11707.9i 1.37142 1.26422i
\(442\) 16634.8i 1.79013i
\(443\) 12362.6 + 7137.55i 1.32588 + 0.765497i 0.984660 0.174486i \(-0.0558265\pi\)
0.341220 + 0.939983i \(0.389160\pi\)
\(444\) 1020.26 6695.03i 0.109052 0.715613i
\(445\) 0 0
\(446\) 4373.47 + 7575.08i 0.464327 + 0.804238i
\(447\) 16250.4 + 2476.39i 1.71950 + 0.262034i
\(448\) −6506.36 3756.45i −0.686153 0.396151i
\(449\) 1690.02 0.177632 0.0888162 0.996048i \(-0.471692\pi\)
0.0888162 + 0.996048i \(0.471692\pi\)
\(450\) 0 0
\(451\) −2951.69 −0.308181
\(452\) 2861.66 + 1652.18i 0.297791 + 0.171929i
\(453\) −4837.39 12384.7i −0.501723 1.28451i
\(454\) −5104.97 8842.07i −0.527727 0.914051i
\(455\) 0 0
\(456\) −1891.60 1513.54i −0.194259 0.155434i
\(457\) −5771.53 3332.19i −0.590767 0.341080i 0.174633 0.984634i \(-0.444126\pi\)
−0.765401 + 0.643554i \(0.777459\pi\)
\(458\) 12423.3i 1.26748i
\(459\) 4552.97 9337.49i 0.462994 0.949535i
\(460\) 0 0
\(461\) −833.712 + 1444.03i −0.0842295 + 0.145890i −0.905063 0.425278i \(-0.860176\pi\)
0.820833 + 0.571168i \(0.193510\pi\)
\(462\) −7947.76 + 9932.99i −0.800354 + 1.00027i
\(463\) −5050.68 + 2916.01i −0.506966 + 0.292697i −0.731585 0.681750i \(-0.761219\pi\)
0.224620 + 0.974446i \(0.427886\pi\)
\(464\) 6063.56 + 10502.4i 0.606668 + 1.05078i
\(465\) 0 0
\(466\) 5951.67 10308.6i 0.591644 1.02476i
\(467\) 17410.6i 1.72519i −0.505892 0.862597i \(-0.668837\pi\)
0.505892 0.862597i \(-0.331163\pi\)
\(468\) 2916.84 9348.06i 0.288100 0.923321i
\(469\) −26883.0 −2.64678
\(470\) 0 0
\(471\) −2740.57 + 17983.9i −0.268108 + 1.75935i
\(472\) 3890.61 2246.24i 0.379406 0.219050i
\(473\) −2488.12 + 1436.52i −0.241869 + 0.139643i
\(474\) −1013.21 + 6648.81i −0.0981822 + 0.644283i
\(475\) 0 0
\(476\) 14047.8 1.35269
\(477\) −1106.16 + 248.689i −0.106179 + 0.0238715i
\(478\) 922.614i 0.0882832i
\(479\) −1639.67 + 2839.99i −0.156406 + 0.270903i −0.933570 0.358395i \(-0.883324\pi\)
0.777164 + 0.629298i \(0.216657\pi\)
\(480\) 0 0
\(481\) −6453.53 11177.8i −0.611758 1.05960i
\(482\) 17165.9 9910.71i 1.62216 0.936557i
\(483\) 3343.10 4178.15i 0.314940 0.393607i
\(484\) −2714.13 + 4701.00i −0.254895 + 0.441492i
\(485\) 0 0
\(486\) −9742.49 + 10330.1i −0.909318 + 0.964162i
\(487\) 10506.7i 0.977624i 0.872389 + 0.488812i \(0.162570\pi\)
−0.872389 + 0.488812i \(0.837430\pi\)
\(488\) −849.456 490.433i −0.0787972 0.0454936i
\(489\) 1070.91 + 856.875i 0.0990350 + 0.0792417i
\(490\) 0 0
\(491\) 7132.25 + 12353.4i 0.655548 + 1.13544i 0.981756 + 0.190144i \(0.0608956\pi\)
−0.326208 + 0.945298i \(0.605771\pi\)
\(492\) −1620.95 4149.95i −0.148532 0.380272i
\(493\) −10260.7 5924.01i −0.937359 0.541184i
\(494\) 14341.8 1.30621
\(495\) 0 0
\(496\) 19279.1 1.74527
\(497\) −15981.8 9227.09i −1.44242 0.832780i
\(498\) 21049.8 + 3207.78i 1.89411 + 0.288643i
\(499\) 4723.70 + 8181.68i 0.423771 + 0.733993i 0.996305 0.0858882i \(-0.0273728\pi\)
−0.572534 + 0.819881i \(0.694039\pi\)
\(500\) 0 0
\(501\) 2809.52 18436.4i 0.250539 1.64407i
\(502\) 9158.70 + 5287.78i 0.814288 + 0.470130i
\(503\) 14579.2i 1.29235i 0.763188 + 0.646177i \(0.223633\pi\)
−0.763188 + 0.646177i \(0.776367\pi\)
\(504\) 5901.02 + 1841.27i 0.521532 + 0.162732i
\(505\) 0 0
\(506\) −1282.69 + 2221.68i −0.112692 + 0.195189i
\(507\) −2636.73 6750.55i −0.230969 0.591327i
\(508\) −5115.03 + 2953.17i −0.446738 + 0.257924i
\(509\) 4205.32 + 7283.83i 0.366204 + 0.634283i 0.988969 0.148126i \(-0.0473240\pi\)
−0.622765 + 0.782409i \(0.713991\pi\)
\(510\) 0 0
\(511\) −9689.89 + 16783.4i −0.838856 + 1.45294i
\(512\) 12676.3i 1.09417i
\(513\) −8050.35 3925.36i −0.692849 0.337834i
\(514\) 7063.02 0.606102
\(515\) 0 0
\(516\) −3386.05 2709.31i −0.288881 0.231145i
\(517\) 605.838 349.781i 0.0515372 0.0297550i
\(518\) −21917.8 + 12654.3i −1.85910 + 1.07335i
\(519\) −1793.02 + 700.345i −0.151647 + 0.0592327i
\(520\) 0 0
\(521\) 10058.1 0.845781 0.422890 0.906181i \(-0.361016\pi\)
0.422890 + 0.906181i \(0.361016\pi\)
\(522\) 10976.5 + 11907.3i 0.920361 + 0.998409i
\(523\) 20006.3i 1.67269i 0.548205 + 0.836344i \(0.315312\pi\)
−0.548205 + 0.836344i \(0.684688\pi\)
\(524\) −4929.83 + 8538.72i −0.410994 + 0.711862i
\(525\) 0 0
\(526\) −1036.50 1795.27i −0.0859192 0.148817i
\(527\) −16311.9 + 9417.67i −1.34830 + 0.778444i
\(528\) −8110.90 1236.02i −0.668525 0.101877i
\(529\) −5543.96 + 9602.42i −0.455655 + 0.789218i
\(530\) 0 0
\(531\) 12211.8 11257.2i 0.998019 0.920001i
\(532\) 12111.4i 0.987019i
\(533\) −7353.52 4245.56i −0.597592 0.345020i
\(534\) −7526.70 + 2939.89i −0.609948 + 0.238243i
\(535\) 0 0
\(536\) −3131.36 5423.67i −0.252340 0.437065i
\(537\) −1450.79 + 1813.17i −0.116585 + 0.145706i
\(538\) −10919.0 6304.11i −0.875006 0.505185i
\(539\) 13328.5 1.06512
\(540\) 0 0
\(541\) −1884.15 −0.149734 −0.0748668 0.997194i \(-0.523853\pi\)
−0.0748668 + 0.997194i \(0.523853\pi\)
\(542\) −10822.9 6248.58i −0.857715 0.495202i
\(543\) −2934.85 + 3667.93i −0.231946 + 0.289882i
\(544\) 8355.34 + 14471.9i 0.658515 + 1.14058i
\(545\) 0 0
\(546\) −34087.3 + 13314.3i −2.67180 + 1.04359i
\(547\) −15585.4 8998.24i −1.21825 0.703358i −0.253708 0.967281i \(-0.581650\pi\)
−0.964544 + 0.263922i \(0.914984\pi\)
\(548\) 4002.93i 0.312038i
\(549\) −3461.68 1080.14i −0.269109 0.0839691i
\(550\) 0 0
\(551\) −5107.40 + 8846.28i −0.394887 + 0.683964i
\(552\) 1232.35 + 187.798i 0.0950226 + 0.0144805i
\(553\) 9374.30 5412.25i 0.720860 0.416189i
\(554\) −10097.2 17488.9i −0.774351 1.34121i
\(555\) 0 0
\(556\) −4184.75 + 7248.19i −0.319196 + 0.552863i
\(557\) 3615.76i 0.275054i 0.990498 + 0.137527i \(0.0439153\pi\)
−0.990498 + 0.137527i \(0.956085\pi\)
\(558\) 25118.5 5647.21i 1.90564 0.428433i
\(559\) −8264.84 −0.625341
\(560\) 0 0
\(561\) 7466.36 2916.32i 0.561907 0.219478i
\(562\) −12065.7 + 6966.14i −0.905625 + 0.522863i
\(563\) 12836.1 7410.91i 0.960881 0.554765i 0.0644370 0.997922i \(-0.479475\pi\)
0.896444 + 0.443157i \(0.146142\pi\)
\(564\) 824.478 + 659.696i 0.0615546 + 0.0492522i
\(565\) 0 0
\(566\) 10378.9 0.770771
\(567\) 22778.1 + 1856.11i 1.68710 + 0.137477i
\(568\) 4299.13i 0.317583i
\(569\) 11224.7 19441.8i 0.827005 1.43241i −0.0733726 0.997305i \(-0.523376\pi\)
0.900377 0.435110i \(-0.143290\pi\)
\(570\) 0 0
\(571\) 8006.75 + 13868.1i 0.586817 + 1.01640i 0.994646 + 0.103338i \(0.0329523\pi\)
−0.407830 + 0.913058i \(0.633714\pi\)
\(572\) 6543.66 3777.98i 0.478329 0.276163i
\(573\) −1133.52 2902.03i −0.0826410 0.211577i
\(574\) −8324.81 + 14419.0i −0.605350 + 1.04850i
\(575\) 0 0
\(576\) −1419.31 6313.03i −0.102670 0.456672i
\(577\) 3096.97i 0.223446i −0.993739 0.111723i \(-0.964363\pi\)
0.993739 0.111723i \(-0.0356370\pi\)
\(578\) −1849.81 1067.99i −0.133117 0.0768553i
\(579\) −3455.09 + 22672.7i −0.247994 + 1.62736i
\(580\) 0 0
\(581\) −17135.0 29678.6i −1.22354 2.11924i
\(582\) −3878.33 591.018i −0.276223 0.0420936i
\(583\) −757.616 437.410i −0.0538203 0.0310732i
\(584\) −4514.76 −0.319901
\(585\) 0 0
\(586\) −13045.0 −0.919595
\(587\) 21325.7 + 12312.4i 1.49950 + 0.865734i 1.00000 0.000582275i \(-0.000185344\pi\)
0.499496 + 0.866316i \(0.333519\pi\)
\(588\) 7319.49 + 18739.3i 0.513351 + 1.31428i
\(589\) 8119.48 + 14063.3i 0.568009 + 0.983820i
\(590\) 0 0
\(591\) 19503.8 + 15605.7i 1.35749 + 1.08618i
\(592\) −14135.8 8161.30i −0.981381 0.566601i
\(593\) 27128.8i 1.87866i 0.343014 + 0.939330i \(0.388552\pi\)
−0.343014 + 0.939330i \(0.611448\pi\)
\(594\) −10929.7 + 765.442i −0.754965 + 0.0528729i
\(595\) 0 0
\(596\) −9572.32 + 16579.7i −0.657881 + 1.13948i
\(597\) −1018.81 + 1273.29i −0.0698445 + 0.0872906i
\(598\) −6391.08 + 3689.89i −0.437042 + 0.252326i
\(599\) 2815.87 + 4877.24i 0.192076 + 0.332685i 0.945938 0.324347i \(-0.105145\pi\)
−0.753862 + 0.657033i \(0.771811\pi\)
\(600\) 0 0
\(601\) 7375.88 12775.4i 0.500613 0.867087i −0.499387 0.866379i \(-0.666441\pi\)
1.00000 0.000707853i \(-0.000225317\pi\)
\(602\) 16205.9i 1.09718i
\(603\) −15693.0 17023.8i −1.05982 1.14969i
\(604\) 15485.2 1.04318
\(605\) 0 0
\(606\) −778.738 + 5110.16i −0.0522014 + 0.342552i
\(607\) 12801.7 7391.04i 0.856018 0.494222i −0.00665872 0.999978i \(-0.502120\pi\)
0.862677 + 0.505756i \(0.168786\pi\)
\(608\) 12477.0 7203.59i 0.832251 0.480500i
\(609\) 3926.66 25767.2i 0.261275 1.71451i
\(610\) 0 0
\(611\) 2012.43 0.133247
\(612\) 8200.44 + 8895.85i 0.541639 + 0.587571i
\(613\) 4947.28i 0.325969i 0.986629 + 0.162984i \(0.0521120\pi\)
−0.986629 + 0.162984i \(0.947888\pi\)
\(614\) −3393.12 + 5877.06i −0.223021 + 0.386284i
\(615\) 0 0
\(616\) 2384.88 + 4130.73i 0.155989 + 0.270181i
\(617\) 3242.09 1871.82i 0.211543 0.122134i −0.390485 0.920609i \(-0.627693\pi\)
0.602028 + 0.798475i \(0.294360\pi\)
\(618\) −6420.67 + 8024.45i −0.417924 + 0.522315i
\(619\) 3069.37 5316.30i 0.199303 0.345202i −0.749000 0.662570i \(-0.769466\pi\)
0.948303 + 0.317368i \(0.102799\pi\)
\(620\) 0 0
\(621\) 4597.38 321.971i 0.297080 0.0208055i
\(622\) 3326.09i 0.214412i
\(623\) 11262.8 + 6502.59i 0.724294 + 0.418171i
\(624\) −18428.8 14745.6i −1.18228 0.945986i
\(625\) 0 0
\(626\) 4151.79 + 7191.11i 0.265078 + 0.459128i
\(627\) −2514.32 6437.15i −0.160147 0.410008i
\(628\) −18348.4 10593.5i −1.16589 0.673129i
\(629\) 15946.9 1.01088
\(630\) 0 0
\(631\) −5548.00 −0.350019 −0.175010 0.984567i \(-0.555996\pi\)
−0.175010 + 0.984567i \(0.555996\pi\)
\(632\) 2183.86 + 1260.85i 0.137451 + 0.0793575i
\(633\) −12527.8 1909.12i −0.786630 0.119874i
\(634\) −1233.36 2136.25i −0.0772605 0.133819i
\(635\) 0 0
\(636\) 198.927 1305.38i 0.0124025 0.0813864i
\(637\) 33205.3 + 19171.1i 2.06537 + 1.19244i
\(638\) 12495.9i 0.775418i
\(639\) −3486.31 15506.9i −0.215831 0.960005i
\(640\) 0 0
\(641\) 5804.05 10052.9i 0.357639 0.619448i −0.629927 0.776654i \(-0.716915\pi\)
0.987566 + 0.157206i \(0.0502487\pi\)
\(642\) −14770.3 37814.9i −0.908002 2.32466i
\(643\) −11017.3 + 6360.85i −0.675708 + 0.390120i −0.798236 0.602345i \(-0.794233\pi\)
0.122528 + 0.992465i \(0.460900\pi\)
\(644\) 3116.04 + 5397.15i 0.190667 + 0.330244i
\(645\) 0 0
\(646\) −8859.78 + 15345.6i −0.539603 + 0.934620i
\(647\) 28203.7i 1.71376i 0.515518 + 0.856879i \(0.327600\pi\)
−0.515518 + 0.856879i \(0.672400\pi\)
\(648\) 2278.74 + 4811.70i 0.138144 + 0.291700i
\(649\) 12815.4 0.775115
\(650\) 0 0
\(651\) −32354.0 25887.7i −1.94786 1.55856i
\(652\) −1383.35 + 798.678i −0.0830924 + 0.0479734i
\(653\) −19652.5 + 11346.4i −1.17774 + 0.679966i −0.955490 0.295024i \(-0.904672\pi\)
−0.222247 + 0.974991i \(0.571339\pi\)
\(654\) −16794.3 + 6559.76i −1.00414 + 0.392213i
\(655\) 0 0
\(656\) −10738.1 −0.639103
\(657\) −16284.7 + 3661.17i −0.967010 + 0.217406i
\(658\) 3946.02i 0.233787i
\(659\) 3002.00 5199.61i 0.177453 0.307357i −0.763555 0.645743i \(-0.776548\pi\)
0.941007 + 0.338386i \(0.109881\pi\)
\(660\) 0 0
\(661\) −5958.18 10319.9i −0.350600 0.607256i 0.635755 0.771891i \(-0.280689\pi\)
−0.986355 + 0.164635i \(0.947356\pi\)
\(662\) −17129.2 + 9889.54i −1.00566 + 0.580616i
\(663\) 22795.6 + 3473.81i 1.33530 + 0.203487i
\(664\) 3991.80 6914.00i 0.233301 0.404089i
\(665\) 0 0
\(666\) −20808.0 6492.63i −1.21065 0.377754i
\(667\) 5256.19i 0.305128i
\(668\) 18810.1 + 10860.0i 1.08950 + 0.629021i
\(669\) 11293.8 4411.31i 0.652682 0.254934i
\(670\) 0 0
\(671\) −1399.03 2423.19i −0.0804901 0.139413i
\(672\) −22967.5 + 28704.5i −1.31844 + 1.64777i
\(673\) 13885.6 + 8016.85i 0.795319 + 0.459178i 0.841832 0.539740i \(-0.181477\pi\)
−0.0465125 + 0.998918i \(0.514811\pi\)
\(674\) 12599.9 0.720077
\(675\) 0 0
\(676\) 8440.54 0.480231
\(677\) 9796.38 + 5655.94i 0.556138 + 0.321086i 0.751594 0.659626i \(-0.229285\pi\)
−0.195456 + 0.980712i \(0.562619\pi\)
\(678\) 6644.59 8304.31i 0.376378 0.470391i
\(679\) 3157.03 + 5468.14i 0.178432 + 0.309054i
\(680\) 0 0
\(681\) −13182.8 + 5149.13i −0.741800 + 0.289743i
\(682\) 17203.8 + 9932.64i 0.965937 + 0.557684i
\(683\) 652.395i 0.0365493i −0.999833 0.0182747i \(-0.994183\pi\)
0.999833 0.0182747i \(-0.00581733\pi\)
\(684\) 7669.59 7070.04i 0.428734 0.395219i
\(685\) 0 0
\(686\) 17437.4 30202.5i 0.970502 1.68096i
\(687\) −17024.3 2594.34i −0.945443 0.144076i
\(688\) −9051.64 + 5225.96i −0.501585 + 0.289590i
\(689\) −1258.29 2179.43i −0.0695750 0.120507i
\(690\) 0 0
\(691\) −6268.93 + 10858.1i −0.345125 + 0.597774i −0.985376 0.170392i \(-0.945497\pi\)
0.640252 + 0.768165i \(0.278830\pi\)
\(692\) 2241.90i 0.123157i
\(693\) 11952.0 + 12965.5i 0.655148 + 0.710705i
\(694\) −35069.8 −1.91820
\(695\) 0 0
\(696\) 5655.94 2209.18i 0.308029 0.120314i
\(697\) 9085.42 5245.47i 0.493737 0.285059i
\(698\) 22852.1 13193.6i 1.23920 0.715454i
\(699\) −12883.5 10308.6i −0.697138 0.557807i
\(700\) 0 0
\(701\) 5880.60 0.316844 0.158422 0.987372i \(-0.449359\pi\)
0.158422 + 0.987372i \(0.449359\pi\)
\(702\) −28329.9 13813.7i −1.52314 0.742684i
\(703\) 13748.7i 0.737614i
\(704\) 2496.37 4323.84i 0.133644 0.231479i
\(705\) 0 0
\(706\) −7876.07 13641.8i −0.419858 0.727216i
\(707\) 7204.93 4159.77i 0.383266 0.221279i
\(708\) 7037.71 + 18017.9i 0.373578 + 0.956434i
\(709\) 3203.33 5548.33i 0.169681 0.293895i −0.768627 0.639697i \(-0.779060\pi\)
0.938308 + 0.345802i \(0.112393\pi\)
\(710\) 0 0
\(711\) 8899.62 + 2776.91i 0.469426 + 0.146473i
\(712\) 3029.72i 0.159471i
\(713\) −7236.52 4178.00i −0.380098 0.219449i
\(714\) 6811.55 44698.2i 0.357025 2.34284i
\(715\) 0 0
\(716\) −1352.25 2342.17i −0.0705812 0.122250i
\(717\) −1264.30 192.667i −0.0658526 0.0100353i
\(718\) −1908.90 1102.10i −0.0992193 0.0572843i
\(719\) −21907.0 −1.13629 −0.568144 0.822929i \(-0.692338\pi\)
−0.568144 + 0.822929i \(0.692338\pi\)
\(720\) 0 0
\(721\) 16540.4 0.854364
\(722\) −9036.47 5217.21i −0.465793 0.268926i
\(723\) −9996.44 25592.9i −0.514207 1.31647i
\(724\) −2735.53 4738.07i −0.140421 0.243217i
\(725\) 0 0
\(726\) 13641.9 + 10915.4i 0.697382 + 0.558002i
\(727\) 11579.6 + 6685.46i 0.590732 + 0.341059i 0.765387 0.643571i \(-0.222548\pi\)
−0.174655 + 0.984630i \(0.555881\pi\)
\(728\) 13721.1i 0.698542i
\(729\) 12121.4 + 15507.8i 0.615829 + 0.787880i
\(730\) 0 0
\(731\) 5105.69 8843.31i 0.258332 0.447444i
\(732\) 2638.61 3297.69i 0.133232 0.166511i
\(733\) 26146.2 15095.5i 1.31751 0.760663i 0.334181 0.942509i \(-0.391540\pi\)
0.983327 + 0.181846i \(0.0582071\pi\)
\(734\) −14591.5 25273.2i −0.733762 1.27091i
\(735\) 0 0
\(736\) −3706.72 + 6420.22i −0.185641 + 0.321539i
\(737\) 17865.2i 0.892910i
\(738\) −13990.5 + 3145.39i −0.697830 + 0.156888i
\(739\) 11624.7 0.578650 0.289325 0.957231i \(-0.406569\pi\)
0.289325 + 0.957231i \(0.406569\pi\)
\(740\) 0 0
\(741\) 2994.96 19653.3i 0.148479 0.974334i
\(742\) −4273.49 + 2467.30i −0.211435 + 0.122072i
\(743\) −4550.42 + 2627.19i −0.224682 + 0.129720i −0.608116 0.793848i \(-0.708075\pi\)
0.383434 + 0.923568i \(0.374741\pi\)
\(744\) 1454.24 9542.90i 0.0716601 0.470241i
\(745\) 0 0
\(746\) −29328.9 −1.43942
\(747\) 8791.57 28175.8i 0.430612 1.38005i
\(748\) 9335.55i 0.456339i
\(749\) −32669.7 + 56585.5i −1.59376 + 2.76047i
\(750\) 0 0
\(751\) 14614.4 + 25312.9i 0.710102 + 1.22993i 0.964819 + 0.262917i \(0.0846844\pi\)
−0.254717 + 0.967016i \(0.581982\pi\)
\(752\) 2204.00 1272.48i 0.106877 0.0617057i
\(753\) 9158.70 11446.4i 0.443242 0.553957i
\(754\) −17973.4 + 31130.9i −0.868108 + 1.50361i
\(755\) 0 0
\(756\) −11665.4 + 23924.1i −0.561199 + 1.15094i
\(757\) 32885.9i 1.57894i −0.613789 0.789470i \(-0.710355\pi\)
0.613789 0.789470i \(-0.289645\pi\)
\(758\) 15192.6 + 8771.46i 0.727995 + 0.420308i
\(759\) 2776.62 + 2221.68i 0.132786 + 0.106247i
\(760\) 0 0
\(761\) 6634.11 + 11490.6i 0.316014 + 0.547352i 0.979652 0.200702i \(-0.0643221\pi\)
−0.663639 + 0.748053i \(0.730989\pi\)
\(762\) 6916.37 + 17707.3i 0.328811 + 0.841820i
\(763\) 25130.7 + 14509.2i 1.19239 + 0.688425i
\(764\) 3628.54 0.171827
\(765\) 0 0
\(766\) −25219.0 −1.18956
\(767\) 31927.0 + 18433.0i 1.50302 + 0.867769i
\(768\) −27315.1 4162.55i −1.28340 0.195577i
\(769\) 17142.9 + 29692.4i 0.803887 + 1.39237i 0.917040 + 0.398796i \(0.130572\pi\)
−0.113153 + 0.993578i \(0.536095\pi\)
\(770\) 0 0
\(771\) 1474.95 9678.81i 0.0688964 0.452106i
\(772\) −23132.2 13355.4i −1.07843 0.622630i
\(773\) 27987.1i 1.30223i −0.758978 0.651117i \(-0.774301\pi\)
0.758978 0.651117i \(-0.225699\pi\)
\(774\) −10262.5 + 9460.25i −0.476586 + 0.439330i
\(775\) 0 0
\(776\) −735.469 + 1273.87i −0.0340229 + 0.0589294i
\(777\) 12763.7 + 32677.7i 0.589313 + 1.50876i
\(778\) −15494.4 + 8945.72i −0.714014 + 0.412236i
\(779\) −4522.40 7833.03i −0.208000 0.360266i
\(780\) 0 0
\(781\) 6131.92 10620.8i 0.280944 0.486610i
\(782\) 9117.88i 0.416950i
\(783\) 18609.4 12555.1i 0.849356 0.573029i
\(784\) 48488.5 2.20884
\(785\) 0 0
\(786\) 24778.7 + 19826.3i 1.12446 + 0.899723i
\(787\) −307.265 + 177.400i −0.0139172 + 0.00803509i −0.506942 0.861980i \(-0.669224\pi\)
0.493025 + 0.870015i \(0.335891\pi\)
\(788\) −25194.1 + 14545.8i −1.13896 + 0.657580i
\(789\) −2676.60 + 1045.47i −0.120772 + 0.0471731i
\(790\) 0 0
\(791\) −17117.2 −0.769430
\(792\) −1223.63 + 3921.56i −0.0548987 + 0.175943i
\(793\) 8049.15i 0.360446i
\(794\) −8788.42 + 15222.0i −0.392808 + 0.680363i
\(795\) 0 0
\(796\) −949.617 1644.78i −0.0422843 0.0732385i
\(797\) −11086.2 + 6400.65i −0.492717 + 0.284470i −0.725701 0.688011i \(-0.758484\pi\)
0.232984 + 0.972481i \(0.425151\pi\)
\(798\) −38536.7 5872.60i −1.70950 0.260511i
\(799\) −1243.20 + 2153.28i −0.0550452 + 0.0953411i
\(800\) 0 0
\(801\) 2456.90 + 10928.2i 0.108377 + 0.482056i
\(802\) 5749.67i 0.253152i
\(803\) −11153.5 6439.48i −0.490160 0.282994i
\(804\) 25117.7 9810.86i 1.10178 0.430351i
\(805\) 0 0
\(806\) 28573.2 + 49490.2i 1.24869 + 2.16280i
\(807\) −10919.0 + 13646.4i −0.476293 + 0.595264i
\(808\) 1678.48 + 969.069i 0.0730800 + 0.0421927i
\(809\) 16374.9 0.711632 0.355816 0.934556i \(-0.384203\pi\)
0.355816 + 0.934556i \(0.384203\pi\)
\(810\) 0 0
\(811\) −35518.2 −1.53787 −0.768936 0.639326i \(-0.779214\pi\)
−0.768936 + 0.639326i \(0.779214\pi\)
\(812\) 26289.4 + 15178.2i 1.13618 + 0.655974i
\(813\) −10822.9 + 13526.2i −0.466881 + 0.583500i
\(814\) −8409.47 14565.6i −0.362103 0.627181i
\(815\) 0 0
\(816\) 27162.2 10609.4i 1.16528 0.455152i
\(817\) −7624.29 4401.89i −0.326487 0.188498i
\(818\) 32908.0i 1.40660i
\(819\) 11126.9 + 49491.9i 0.474733 + 2.11158i
\(820\) 0 0
\(821\) −21471.9 + 37190.5i −0.912760 + 1.58095i −0.102612 + 0.994721i \(0.532720\pi\)
−0.810148 + 0.586226i \(0.800613\pi\)
\(822\) 12736.8 + 1940.96i 0.540445 + 0.0823584i
\(823\) −6856.26 + 3958.46i −0.290394 + 0.167659i −0.638119 0.769937i \(-0.720287\pi\)
0.347726 + 0.937596i \(0.386954\pi\)
\(824\) 1926.64 + 3337.04i 0.0814536 + 0.141082i
\(825\) 0 0
\(826\) 36144.0 62603.3i 1.52253 2.63710i
\(827\) 18774.4i 0.789421i −0.918806 0.394710i \(-0.870845\pi\)
0.918806 0.394710i \(-0.129155\pi\)
\(828\) −1598.77 + 5123.85i −0.0671030 + 0.215056i
\(829\) −22166.1 −0.928661 −0.464330 0.885662i \(-0.653705\pi\)
−0.464330 + 0.885662i \(0.653705\pi\)
\(830\) 0 0
\(831\) −26074.5 + 10184.6i −1.08847 + 0.425149i
\(832\) 12438.4 7181.30i 0.518297 0.299239i
\(833\) −41025.8 + 23686.2i −1.70643 + 0.985210i
\(834\) 21033.6 + 16829.8i 0.873304 + 0.698764i
\(835\) 0 0
\(836\) 8048.68 0.332978
\(837\) −2493.22 35600.4i −0.102961 1.47017i
\(838\) 16029.1i 0.660757i
\(839\) 21295.4 36884.7i 0.876279 1.51776i 0.0208849 0.999782i \(-0.493352\pi\)
0.855394 0.517978i \(-0.173315\pi\)
\(840\) 0 0
\(841\) −606.908 1051.20i −0.0248845 0.0431012i
\(842\) −46952.9 + 27108.3i −1.92174 + 1.10952i
\(843\) 7026.40 + 17989.0i 0.287073 + 0.734963i
\(844\) 7379.55 12781.7i 0.300965 0.521287i
\(845\) 0 0
\(846\) 2498.84 2303.50i 0.101551 0.0936122i
\(847\) 28119.4i 1.14072i
\(848\) −2756.16 1591.27i −0.111612 0.0644393i
\(849\) 2167.39 14222.7i 0.0876145 0.574937i
\(850\) 0 0
\(851\) 3537.31 + 6126.79i 0.142488 + 0.246796i
\(852\) 18299.8 + 2788.70i 0.735845 + 0.112135i
\(853\) −22916.0 13230.6i −0.919847 0.531074i −0.0362605 0.999342i \(-0.511545\pi\)
−0.883586 + 0.468269i \(0.844878\pi\)
\(854\) −15783.0 −0.632416
\(855\) 0 0
\(856\) −15221.6 −0.607784
\(857\) −17328.3 10004.5i −0.690693 0.398772i 0.113179 0.993575i \(-0.463897\pi\)
−0.803871 + 0.594803i \(0.797230\pi\)
\(858\) −8848.12 22652.9i −0.352063 0.901350i
\(859\) −8909.03 15430.9i −0.353868 0.612917i 0.633056 0.774106i \(-0.281800\pi\)
−0.986923 + 0.161189i \(0.948467\pi\)
\(860\) 0 0
\(861\) 18020.6 + 14419.0i 0.713288 + 0.570729i
\(862\) −7168.31 4138.63i −0.283241 0.163529i
\(863\) 12769.5i 0.503683i 0.967769 + 0.251841i \(0.0810361\pi\)
−0.967769 + 0.251841i \(0.918964\pi\)
\(864\) −31584.6 + 2211.98i −1.24367 + 0.0870986i
\(865\) 0 0
\(866\) 18859.6 32665.7i 0.740039 1.28179i
\(867\) −1849.81 + 2311.86i −0.0724598 + 0.0905592i
\(868\) 41793.5 24129.5i 1.63429 0.943558i
\(869\) 3596.75 + 6229.75i 0.140404 + 0.243187i
\(870\) 0 0
\(871\) 25696.4 44507.5i 0.999644 1.73144i
\(872\) 6760.19i 0.262533i
\(873\) −1619.80 + 5191.25i −0.0627973 + 0.201257i
\(874\) −7861.01 −0.304236
\(875\) 0 0
\(876\) 2928.57 19217.6i 0.112954 0.741214i
\(877\) −23796.0 + 13738.6i −0.916231 + 0.528986i −0.882431 0.470442i \(-0.844094\pi\)
−0.0338003 + 0.999429i \(0.510761\pi\)
\(878\) 43232.5 24960.3i 1.66176 0.959417i
\(879\) −2724.15 + 17876.2i −0.104532 + 0.685948i
\(880\) 0 0
\(881\) 31509.1 1.20496 0.602480 0.798134i \(-0.294179\pi\)
0.602480 + 0.798134i \(0.294179\pi\)
\(882\) 63175.1 14203.2i 2.41181 0.542230i
\(883\) 5271.46i 0.200905i 0.994942 + 0.100452i \(0.0320290\pi\)
−0.994942 + 0.100452i \(0.967971\pi\)
\(884\) −13427.8 + 23257.6i −0.510888 + 0.884883i
\(885\) 0 0
\(886\) 26755.6 + 46342.0i 1.01453 + 1.75721i
\(887\) −9035.91 + 5216.89i −0.342048 + 0.197481i −0.661177 0.750230i \(-0.729943\pi\)
0.319130 + 0.947711i \(0.396609\pi\)
\(888\) −5106.03 + 6381.43i −0.192958 + 0.241156i
\(889\) 15298.0 26496.9i 0.577140 0.999636i
\(890\) 0 0
\(891\) −1233.49 + 15137.3i −0.0463787 + 0.569157i
\(892\) 14121.2i 0.530059i
\(893\) 1856.46 + 1071.83i 0.0695677 + 0.0401649i
\(894\) 48113.0 + 38497.1i 1.79993 + 1.44019i
\(895\) 0 0
\(896\) 14218.2 + 24626.6i 0.530130 + 0.918212i
\(897\) 3721.81 + 9528.58i 0.138537 + 0.354682i
\(898\) 5486.40 + 3167.57i 0.203879 + 0.117710i
\(899\) −40702.0 −1.51000
\(900\) 0 0
\(901\) 3109.30 0.114967
\(902\) −9582.23 5532.30i −0.353718 0.204219i
\(903\) 22207.8 + 3384.24i 0.818415 + 0.124718i
\(904\) −1993.84 3453.43i −0.0733562 0.127057i
\(905\) 0 0
\(906\) 7508.51 49271.7i 0.275335 1.80678i
\(907\) 17915.1 + 10343.3i 0.655856 + 0.378659i 0.790696 0.612209i \(-0.209719\pi\)
−0.134840 + 0.990867i \(0.543052\pi\)
\(908\) 16483.1i 0.602434i
\(909\) 6840.10 + 2134.29i 0.249584 + 0.0778766i
\(910\) 0 0
\(911\) 11820.0 20472.9i 0.429874 0.744563i −0.566988 0.823726i \(-0.691891\pi\)
0.996862 + 0.0791627i \(0.0252247\pi\)
\(912\) −9146.95 23418.0i −0.332111 0.850271i
\(913\) 19723.1 11387.1i 0.714939 0.412770i
\(914\) −12490.9 21635.0i −0.452039 0.782955i
\(915\) 0 0
\(916\) 10028.2 17369.4i 0.361727 0.626529i
\(917\) 51075.0i 1.83931i
\(918\) 32281.6 21779.2i 1.16062 0.783030i
\(919\) −27335.2 −0.981180 −0.490590 0.871390i \(-0.663219\pi\)
−0.490590 + 0.871390i \(0.663219\pi\)
\(920\) 0 0
\(921\) 7345.05 + 5877.06i 0.262788 + 0.210267i
\(922\) −5413.04 + 3125.22i −0.193350 + 0.111631i
\(923\) 30552.8 17639.7i 1.08955 0.629054i
\(924\) −19129.9 + 7472.06i −0.681092 + 0.266031i
\(925\) 0 0
\(926\) −21861.7 −0.775832
\(927\) 9655.50 + 10474.3i 0.342102 + 0.371112i
\(928\) 36110.7i 1.27736i
\(929\) −6614.28 + 11456.3i −0.233593 + 0.404594i −0.958863 0.283870i \(-0.908382\pi\)
0.725270 + 0.688464i \(0.241715\pi\)
\(930\) 0 0
\(931\) 20421.2 + 35370.5i 0.718880 + 1.24514i
\(932\) 16642.4 9608.47i 0.584913 0.337700i
\(933\) 4557.91 + 694.580i 0.159935 + 0.0243725i
\(934\) 32632.3 56520.9i 1.14321 1.98011i
\(935\) 0 0
\(936\) −8688.98 + 8009.75i −0.303428 + 0.279708i
\(937\) 18740.4i 0.653387i 0.945130 + 0.326693i \(0.105934\pi\)
−0.945130 + 0.326693i \(0.894066\pi\)
\(938\) −87271.6 50386.3i −3.03787 1.75391i
\(939\) 10721.3 4187.70i 0.372607 0.145538i
\(940\) 0 0
\(941\) −27244.5 47188.9i −0.943832 1.63476i −0.758074 0.652169i \(-0.773859\pi\)
−0.185758 0.982596i \(-0.559474\pi\)
\(942\) −42603.8 + 53245.6i −1.47357 + 1.84165i
\(943\) 4030.61 + 2327.07i 0.139188 + 0.0803605i
\(944\) 46621.8 1.60743
\(945\) 0 0
\(946\) −10769.7 −0.370142
\(947\) −9771.11 5641.35i −0.335289 0.193579i 0.322898 0.946434i \(-0.395343\pi\)
−0.658187 + 0.752855i \(0.728676\pi\)
\(948\) −6783.57 + 8477.99i −0.232405 + 0.290456i
\(949\) −18524.4 32085.2i −0.633644 1.09750i
\(950\) 0 0
\(951\) −3184.97 + 1244.03i −0.108601 + 0.0424191i
\(952\) −14681.5 8476.36i −0.499821 0.288572i
\(953\) 51190.0i 1.73999i −0.493063 0.869994i \(-0.664123\pi\)
0.493063 0.869994i \(-0.335877\pi\)
\(954\) −4057.09 1265.92i −0.137687 0.0429618i
\(955\) 0 0
\(956\) 744.741 1289.93i 0.0251952 0.0436394i
\(957\) 17123.7 + 2609.49i 0.578403 + 0.0881428i
\(958\) −10645.9 + 6146.41i −0.359033 + 0.207288i
\(959\) −10368.0 17957.8i −0.349113 0.604681i
\(960\) 0 0
\(961\) −17457.4 + 30237.2i −0.585997 + 1.01498i
\(962\) 48383.0i 1.62155i
\(963\) −54904.1 + 12343.7i −1.83724 + 0.413053i
\(964\) 32000.0 1.06914
\(965\) 0 0
\(966\) 18683.9 7297.84i 0.622303 0.243068i
\(967\) −20042.9 + 11571.8i −0.666530 + 0.384822i −0.794761 0.606923i \(-0.792404\pi\)
0.128230 + 0.991744i \(0.459070\pi\)
\(968\) 5673.12 3275.38i 0.188369 0.108755i
\(969\) 19178.7 + 15345.6i 0.635818 + 0.508742i
\(970\) 0 0
\(971\) −34124.5 −1.12782 −0.563908 0.825838i \(-0.690703\pi\)
−0.563908 + 0.825838i \(0.690703\pi\)
\(972\) −21959.8 + 6578.56i −0.724650 + 0.217086i
\(973\) 43355.6i 1.42848i
\(974\) −19692.5 + 34108.4i −0.647831 + 1.12208i
\(975\) 0 0
\(976\) −5089.58 8815.42i −0.166920 0.289113i
\(977\) 31578.5 18231.8i 1.03407 0.597020i 0.115921 0.993258i \(-0.463018\pi\)
0.918148 + 0.396239i \(0.129685\pi\)
\(978\) 1870.52 + 4788.90i 0.0611581 + 0.156577i
\(979\) −4321.34 + 7484.78i −0.141073 + 0.244346i
\(980\) 0 0
\(981\) 5482.06 + 24383.9i 0.178419 + 0.793597i
\(982\) 53471.4i 1.73762i
\(983\) 44636.3 + 25770.8i 1.44830 + 0.836176i 0.998380 0.0568941i \(-0.0181197\pi\)
0.449918 + 0.893070i \(0.351453\pi\)
\(984\) −809.986 + 5315.22i −0.0262413 + 0.172198i
\(985\) 0 0
\(986\) −22206.5 38462.8i −0.717241 1.24230i
\(987\) −5407.43 824.038i −0.174387 0.0265749i
\(988\) 20051.6 + 11576.8i 0.645675 + 0.372780i
\(989\) 4530.12 0.145652
\(990\) 0 0
\(991\) 34299.1 1.09944 0.549721 0.835348i \(-0.314734\pi\)
0.549721 + 0.835348i \(0.314734\pi\)
\(992\) 49715.9 + 28703.5i 1.59121 + 0.918685i
\(993\) 9975.10 + 25538.2i 0.318782 + 0.816144i
\(994\) −34588.3 59908.8i −1.10370 1.91166i
\(995\) 0 0
\(996\) 26840.9 + 21476.5i 0.853903 + 0.683241i
\(997\) 18443.7 + 10648.5i 0.585877 + 0.338256i 0.763465 0.645849i \(-0.223496\pi\)
−0.177589 + 0.984105i \(0.556830\pi\)
\(998\) 35414.2i 1.12326i
\(999\) −13242.5 + 27158.4i −0.419392 + 0.860113i
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 225.4.k.c.124.5 12
5.2 odd 4 45.4.e.b.16.1 6
5.3 odd 4 225.4.e.c.151.3 6
5.4 even 2 inner 225.4.k.c.124.2 12
9.4 even 3 inner 225.4.k.c.49.2 12
15.2 even 4 135.4.e.b.46.3 6
45.2 even 12 405.4.a.j.1.1 3
45.4 even 6 inner 225.4.k.c.49.5 12
45.7 odd 12 405.4.a.h.1.3 3
45.13 odd 12 225.4.e.c.76.3 6
45.22 odd 12 45.4.e.b.31.1 yes 6
45.32 even 12 135.4.e.b.91.3 6
45.38 even 12 2025.4.a.q.1.3 3
45.43 odd 12 2025.4.a.s.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.b.16.1 6 5.2 odd 4
45.4.e.b.31.1 yes 6 45.22 odd 12
135.4.e.b.46.3 6 15.2 even 4
135.4.e.b.91.3 6 45.32 even 12
225.4.e.c.76.3 6 45.13 odd 12
225.4.e.c.151.3 6 5.3 odd 4
225.4.k.c.49.2 12 9.4 even 3 inner
225.4.k.c.49.5 12 45.4 even 6 inner
225.4.k.c.124.2 12 5.4 even 2 inner
225.4.k.c.124.5 12 1.1 even 1 trivial
405.4.a.h.1.3 3 45.7 odd 12
405.4.a.j.1.1 3 45.2 even 12
2025.4.a.q.1.3 3 45.38 even 12
2025.4.a.s.1.1 3 45.43 odd 12