Properties

Label 105.3.k.d.83.5
Level $105$
Weight $3$
Character 105.83
Analytic conductor $2.861$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(62,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.62");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.5
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.d.62.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.88692 - 1.88692i) q^{2} +(-2.65373 + 1.39918i) q^{3} +3.12092i q^{4} +(4.96950 - 0.551428i) q^{5} +(7.64751 + 2.36725i) q^{6} +(2.09055 + 6.68054i) q^{7} +(-1.65875 + 1.65875i) q^{8} +(5.08462 - 7.42608i) q^{9} +O(q^{10})\) \(q+(-1.88692 - 1.88692i) q^{2} +(-2.65373 + 1.39918i) q^{3} +3.12092i q^{4} +(4.96950 - 0.551428i) q^{5} +(7.64751 + 2.36725i) q^{6} +(2.09055 + 6.68054i) q^{7} +(-1.65875 + 1.65875i) q^{8} +(5.08462 - 7.42608i) q^{9} +(-10.4175 - 8.33654i) q^{10} -17.9060i q^{11} +(-4.36672 - 8.28210i) q^{12} +(11.1383 - 11.1383i) q^{13} +(8.66093 - 16.5503i) q^{14} +(-12.4162 + 8.41655i) q^{15} +18.7435 q^{16} +(-0.666845 + 0.666845i) q^{17} +(-23.6067 + 4.41815i) q^{18} +10.8119 q^{19} +(1.72096 + 15.5094i) q^{20} +(-14.8950 - 14.8033i) q^{21} +(-33.7872 + 33.7872i) q^{22} +(2.20425 - 2.20425i) q^{23} +(2.08100 - 6.72276i) q^{24} +(24.3919 - 5.48064i) q^{25} -42.0343 q^{26} +(-3.10283 + 26.8211i) q^{27} +(-20.8494 + 6.52445i) q^{28} +22.9708 q^{29} +(39.3097 + 7.54700i) q^{30} +26.1094i q^{31} +(-28.7325 - 28.7325i) q^{32} +(25.0537 + 47.5179i) q^{33} +2.51656 q^{34} +(14.0728 + 32.0461i) q^{35} +(23.1762 + 15.8687i) q^{36} +(41.6663 - 41.6663i) q^{37} +(-20.4011 - 20.4011i) q^{38} +(-13.9737 + 45.1427i) q^{39} +(-7.32848 + 9.15784i) q^{40} +6.85976 q^{41} +(0.173022 + 56.0383i) q^{42} +(-37.6932 - 37.6932i) q^{43} +55.8834 q^{44} +(21.1730 - 39.7077i) q^{45} -8.31847 q^{46} +(5.55606 - 5.55606i) q^{47} +(-49.7404 + 26.2255i) q^{48} +(-40.2592 + 27.9320i) q^{49} +(-56.3670 - 35.6839i) q^{50} +(0.836596 - 2.70266i) q^{51} +(34.7619 + 34.7619i) q^{52} +(-32.4556 + 32.4556i) q^{53} +(56.4640 - 44.7545i) q^{54} +(-9.87390 - 88.9841i) q^{55} +(-14.5490 - 7.61364i) q^{56} +(-28.6918 + 15.1277i) q^{57} +(-43.3441 - 43.3441i) q^{58} +99.8940i q^{59} +(-26.2674 - 38.7499i) q^{60} -44.6768i q^{61} +(49.2664 - 49.2664i) q^{62} +(60.2399 + 18.4433i) q^{63} +33.4577i q^{64} +(49.2100 - 61.4940i) q^{65} +(42.3881 - 136.937i) q^{66} +(-18.0239 + 18.0239i) q^{67} +(-2.08117 - 2.08117i) q^{68} +(-2.76536 + 8.93362i) q^{69} +(33.9141 - 87.0228i) q^{70} +6.35575i q^{71} +(3.88391 + 20.7521i) q^{72} +(-55.3597 + 55.3597i) q^{73} -157.242 q^{74} +(-57.0611 + 48.6727i) q^{75} +33.7430i q^{76} +(119.622 - 37.4336i) q^{77} +(111.548 - 58.8133i) q^{78} +59.7832i q^{79} +(93.1460 - 10.3357i) q^{80} +(-29.2934 - 75.5175i) q^{81} +(-12.9438 - 12.9438i) q^{82} +(-42.2387 - 42.2387i) q^{83} +(46.2000 - 46.4862i) q^{84} +(-2.94617 + 3.68160i) q^{85} +142.248i q^{86} +(-60.9585 + 32.1402i) q^{87} +(29.7017 + 29.7017i) q^{88} -58.4197i q^{89} +(-114.877 + 34.9734i) q^{90} +(97.6954 + 51.1248i) q^{91} +(6.87928 + 6.87928i) q^{92} +(-36.5317 - 69.2875i) q^{93} -20.9677 q^{94} +(53.7296 - 5.96197i) q^{95} +(116.450 + 36.0466i) q^{96} +(-11.1921 - 11.1921i) q^{97} +(128.671 + 23.2603i) q^{98} +(-132.972 - 91.0454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 48 q^{15} - 24 q^{16} - 92 q^{18} - 60 q^{21} + 112 q^{22} - 72 q^{25} + 88 q^{28} - 108 q^{30} + 416 q^{36} + 72 q^{37} + 300 q^{42} - 328 q^{43} + 32 q^{46} + 148 q^{51} - 748 q^{57} - 392 q^{58} + 544 q^{60} - 220 q^{63} - 648 q^{67} - 8 q^{70} - 8 q^{72} + 500 q^{78} - 948 q^{81} + 672 q^{85} + 1288 q^{88} + 808 q^{91} + 292 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88692 1.88692i −0.943459 0.943459i 0.0550258 0.998485i \(-0.482476\pi\)
−0.998485 + 0.0550258i \(0.982476\pi\)
\(3\) −2.65373 + 1.39918i −0.884578 + 0.466392i
\(4\) 3.12092i 0.780230i
\(5\) 4.96950 0.551428i 0.993900 0.110286i
\(6\) 7.64751 + 2.36725i 1.27459 + 0.394542i
\(7\) 2.09055 + 6.68054i 0.298651 + 0.954363i
\(8\) −1.65875 + 1.65875i −0.207344 + 0.207344i
\(9\) 5.08462 7.42608i 0.564957 0.825120i
\(10\) −10.4175 8.33654i −1.04175 0.833654i
\(11\) 17.9060i 1.62782i −0.580989 0.813911i \(-0.697334\pi\)
0.580989 0.813911i \(-0.302666\pi\)
\(12\) −4.36672 8.28210i −0.363893 0.690175i
\(13\) 11.1383 11.1383i 0.856796 0.856796i −0.134164 0.990959i \(-0.542835\pi\)
0.990959 + 0.134164i \(0.0428348\pi\)
\(14\) 8.66093 16.5503i 0.618638 1.18217i
\(15\) −12.4162 + 8.41655i −0.827746 + 0.561103i
\(16\) 18.7435 1.17147
\(17\) −0.666845 + 0.666845i −0.0392262 + 0.0392262i −0.726448 0.687222i \(-0.758830\pi\)
0.687222 + 0.726448i \(0.258830\pi\)
\(18\) −23.6067 + 4.41815i −1.31148 + 0.245453i
\(19\) 10.8119 0.569046 0.284523 0.958669i \(-0.408165\pi\)
0.284523 + 0.958669i \(0.408165\pi\)
\(20\) 1.72096 + 15.5094i 0.0860482 + 0.775471i
\(21\) −14.8950 14.8033i −0.709287 0.704920i
\(22\) −33.7872 + 33.7872i −1.53578 + 1.53578i
\(23\) 2.20425 2.20425i 0.0958368 0.0958368i −0.657563 0.753400i \(-0.728413\pi\)
0.753400 + 0.657563i \(0.228413\pi\)
\(24\) 2.08100 6.72276i 0.0867083 0.280115i
\(25\) 24.3919 5.48064i 0.975674 0.219226i
\(26\) −42.0343 −1.61670
\(27\) −3.10283 + 26.8211i −0.114920 + 0.993375i
\(28\) −20.8494 + 6.52445i −0.744623 + 0.233016i
\(29\) 22.9708 0.792098 0.396049 0.918229i \(-0.370381\pi\)
0.396049 + 0.918229i \(0.370381\pi\)
\(30\) 39.3097 + 7.54700i 1.31032 + 0.251567i
\(31\) 26.1094i 0.842240i 0.907005 + 0.421120i \(0.138363\pi\)
−0.907005 + 0.421120i \(0.861637\pi\)
\(32\) −28.7325 28.7325i −0.897891 0.897891i
\(33\) 25.0537 + 47.5179i 0.759203 + 1.43994i
\(34\) 2.51656 0.0740166
\(35\) 14.0728 + 32.0461i 0.402081 + 0.915604i
\(36\) 23.1762 + 15.8687i 0.643784 + 0.440797i
\(37\) 41.6663 41.6663i 1.12612 1.12612i 0.135314 0.990803i \(-0.456796\pi\)
0.990803 0.135314i \(-0.0432044\pi\)
\(38\) −20.4011 20.4011i −0.536871 0.536871i
\(39\) −13.9737 + 45.1427i −0.358300 + 1.15751i
\(40\) −7.32848 + 9.15784i −0.183212 + 0.228946i
\(41\) 6.85976 0.167311 0.0836556 0.996495i \(-0.473340\pi\)
0.0836556 + 0.996495i \(0.473340\pi\)
\(42\) 0.173022 + 56.0383i 0.00411958 + 1.33425i
\(43\) −37.6932 37.6932i −0.876587 0.876587i 0.116593 0.993180i \(-0.462803\pi\)
−0.993180 + 0.116593i \(0.962803\pi\)
\(44\) 55.8834 1.27008
\(45\) 21.1730 39.7077i 0.470512 0.882394i
\(46\) −8.31847 −0.180836
\(47\) 5.55606 5.55606i 0.118214 0.118214i −0.645525 0.763739i \(-0.723361\pi\)
0.763739 + 0.645525i \(0.223361\pi\)
\(48\) −49.7404 + 26.2255i −1.03626 + 0.546364i
\(49\) −40.2592 + 27.9320i −0.821616 + 0.570042i
\(50\) −56.3670 35.6839i −1.12734 0.713678i
\(51\) 0.836596 2.70266i 0.0164038 0.0529934i
\(52\) 34.7619 + 34.7619i 0.668498 + 0.668498i
\(53\) −32.4556 + 32.4556i −0.612369 + 0.612369i −0.943563 0.331194i \(-0.892549\pi\)
0.331194 + 0.943563i \(0.392549\pi\)
\(54\) 56.4640 44.7545i 1.04563 0.828787i
\(55\) −9.87390 88.9841i −0.179525 1.61789i
\(56\) −14.5490 7.61364i −0.259804 0.135958i
\(57\) −28.6918 + 15.1277i −0.503365 + 0.265398i
\(58\) −43.3441 43.3441i −0.747312 0.747312i
\(59\) 99.8940i 1.69312i 0.532294 + 0.846559i \(0.321330\pi\)
−0.532294 + 0.846559i \(0.678670\pi\)
\(60\) −26.2674 38.7499i −0.437790 0.645832i
\(61\) 44.6768i 0.732406i −0.930535 0.366203i \(-0.880658\pi\)
0.930535 0.366203i \(-0.119342\pi\)
\(62\) 49.2664 49.2664i 0.794619 0.794619i
\(63\) 60.2399 + 18.4433i 0.956189 + 0.292752i
\(64\) 33.4577i 0.522776i
\(65\) 49.2100 61.4940i 0.757077 0.946061i
\(66\) 42.3881 136.937i 0.642244 2.07480i
\(67\) −18.0239 + 18.0239i −0.269013 + 0.269013i −0.828702 0.559689i \(-0.810920\pi\)
0.559689 + 0.828702i \(0.310920\pi\)
\(68\) −2.08117 2.08117i −0.0306054 0.0306054i
\(69\) −2.76536 + 8.93362i −0.0400777 + 0.129473i
\(70\) 33.9141 87.0228i 0.484488 1.24318i
\(71\) 6.35575i 0.0895177i 0.998998 + 0.0447588i \(0.0142519\pi\)
−0.998998 + 0.0447588i \(0.985748\pi\)
\(72\) 3.88391 + 20.7521i 0.0539431 + 0.288224i
\(73\) −55.3597 + 55.3597i −0.758352 + 0.758352i −0.976022 0.217671i \(-0.930154\pi\)
0.217671 + 0.976022i \(0.430154\pi\)
\(74\) −157.242 −2.12489
\(75\) −57.0611 + 48.6727i −0.760815 + 0.648969i
\(76\) 33.7430i 0.443987i
\(77\) 119.622 37.4336i 1.55353 0.486150i
\(78\) 111.548 58.8133i 1.43010 0.754017i
\(79\) 59.7832i 0.756749i 0.925653 + 0.378375i \(0.123517\pi\)
−0.925653 + 0.378375i \(0.876483\pi\)
\(80\) 93.1460 10.3357i 1.16432 0.129196i
\(81\) −29.2934 75.5175i −0.361646 0.932315i
\(82\) −12.9438 12.9438i −0.157851 0.157851i
\(83\) −42.2387 42.2387i −0.508900 0.508900i 0.405289 0.914189i \(-0.367171\pi\)
−0.914189 + 0.405289i \(0.867171\pi\)
\(84\) 46.2000 46.4862i 0.550000 0.553407i
\(85\) −2.94617 + 3.68160i −0.0346608 + 0.0433130i
\(86\) 142.248i 1.65405i
\(87\) −60.9585 + 32.1402i −0.700673 + 0.369428i
\(88\) 29.7017 + 29.7017i 0.337519 + 0.337519i
\(89\) 58.4197i 0.656401i −0.944608 0.328200i \(-0.893558\pi\)
0.944608 0.328200i \(-0.106442\pi\)
\(90\) −114.877 + 34.9734i −1.27641 + 0.388593i
\(91\) 97.6954 + 51.1248i 1.07358 + 0.561811i
\(92\) 6.87928 + 6.87928i 0.0747748 + 0.0747748i
\(93\) −36.5317 69.2875i −0.392814 0.745027i
\(94\) −20.9677 −0.223060
\(95\) 53.7296 5.96197i 0.565574 0.0627576i
\(96\) 116.450 + 36.0466i 1.21302 + 0.375486i
\(97\) −11.1921 11.1921i −0.115383 0.115383i 0.647058 0.762441i \(-0.275999\pi\)
−0.762441 + 0.647058i \(0.775999\pi\)
\(98\) 128.671 + 23.2603i 1.31297 + 0.237350i
\(99\) −132.972 91.0454i −1.34315 0.919650i
\(100\) 17.1047 + 76.1251i 0.171047 + 0.761251i
\(101\) 11.9219 0.118038 0.0590191 0.998257i \(-0.481203\pi\)
0.0590191 + 0.998257i \(0.481203\pi\)
\(102\) −6.67829 + 3.52111i −0.0654734 + 0.0345207i
\(103\) 24.4345 24.4345i 0.237229 0.237229i −0.578473 0.815702i \(-0.696351\pi\)
0.815702 + 0.578473i \(0.196351\pi\)
\(104\) 36.9514i 0.355302i
\(105\) −82.1838 65.3516i −0.782703 0.622396i
\(106\) 122.482 1.15549
\(107\) 36.8755 + 36.8755i 0.344631 + 0.344631i 0.858105 0.513474i \(-0.171642\pi\)
−0.513474 + 0.858105i \(0.671642\pi\)
\(108\) −83.7066 9.68369i −0.775061 0.0896638i
\(109\) 53.8082i 0.493653i 0.969060 + 0.246827i \(0.0793879\pi\)
−0.969060 + 0.246827i \(0.920612\pi\)
\(110\) −149.274 + 186.537i −1.35704 + 1.69579i
\(111\) −52.2729 + 168.870i −0.470927 + 1.52135i
\(112\) 39.1844 + 125.217i 0.349860 + 1.11801i
\(113\) −83.5360 + 83.5360i −0.739257 + 0.739257i −0.972434 0.233177i \(-0.925088\pi\)
0.233177 + 0.972434i \(0.425088\pi\)
\(114\) 82.6839 + 25.5944i 0.725297 + 0.224512i
\(115\) 9.73852 12.1695i 0.0846828 0.105822i
\(116\) 71.6902i 0.618019i
\(117\) −26.0800 139.348i −0.222906 1.19101i
\(118\) 188.492 188.492i 1.59739 1.59739i
\(119\) −5.84896 3.06081i −0.0491509 0.0257211i
\(120\) 6.63441 34.5563i 0.0552867 0.287969i
\(121\) −199.627 −1.64981
\(122\) −84.3014 + 84.3014i −0.690995 + 0.690995i
\(123\) −18.2040 + 9.59801i −0.148000 + 0.0780326i
\(124\) −81.4855 −0.657141
\(125\) 118.193 40.6864i 0.945545 0.325491i
\(126\) −78.8666 148.469i −0.625926 1.17832i
\(127\) 147.690 147.690i 1.16291 1.16291i 0.179080 0.983835i \(-0.442688\pi\)
0.983835 0.179080i \(-0.0573121\pi\)
\(128\) −51.7981 + 51.7981i −0.404673 + 0.404673i
\(129\) 152.767 + 47.2884i 1.18424 + 0.366577i
\(130\) −208.889 + 23.1789i −1.60684 + 0.178299i
\(131\) −131.274 −1.00209 −0.501046 0.865421i \(-0.667051\pi\)
−0.501046 + 0.865421i \(0.667051\pi\)
\(132\) −148.300 + 78.1906i −1.12348 + 0.592353i
\(133\) 22.6028 + 72.2291i 0.169946 + 0.543076i
\(134\) 68.0192 0.507606
\(135\) −0.629594 + 134.999i −0.00466366 + 0.999989i
\(136\) 2.21226i 0.0162666i
\(137\) −68.1163 68.1163i −0.497199 0.497199i 0.413366 0.910565i \(-0.364353\pi\)
−0.910565 + 0.413366i \(0.864353\pi\)
\(138\) 22.0750 11.6390i 0.159964 0.0843406i
\(139\) 30.1138 0.216646 0.108323 0.994116i \(-0.465452\pi\)
0.108323 + 0.994116i \(0.465452\pi\)
\(140\) −100.013 + 43.9202i −0.714382 + 0.313716i
\(141\) −6.97041 + 22.5182i −0.0494355 + 0.159704i
\(142\) 11.9928 11.9928i 0.0844563 0.0844563i
\(143\) −199.444 199.444i −1.39471 1.39471i
\(144\) 95.3037 139.191i 0.661831 0.966604i
\(145\) 114.154 12.6668i 0.787266 0.0873570i
\(146\) 208.918 1.43095
\(147\) 67.7553 130.454i 0.460921 0.887441i
\(148\) 130.037 + 130.037i 0.878631 + 0.878631i
\(149\) −92.4633 −0.620559 −0.310280 0.950645i \(-0.600423\pi\)
−0.310280 + 0.950645i \(0.600423\pi\)
\(150\) 199.511 + 15.8283i 1.33007 + 0.105522i
\(151\) −12.2683 −0.0812472 −0.0406236 0.999175i \(-0.512934\pi\)
−0.0406236 + 0.999175i \(0.512934\pi\)
\(152\) −17.9342 + 17.9342i −0.117988 + 0.117988i
\(153\) 1.56139 + 8.34269i 0.0102052 + 0.0545274i
\(154\) −296.351 155.083i −1.92436 1.00703i
\(155\) 14.3975 + 129.751i 0.0928870 + 0.837102i
\(156\) −140.887 43.6108i −0.903121 0.279557i
\(157\) 63.9309 + 63.9309i 0.407203 + 0.407203i 0.880762 0.473559i \(-0.157031\pi\)
−0.473559 + 0.880762i \(0.657031\pi\)
\(158\) 112.806 112.806i 0.713962 0.713962i
\(159\) 40.7174 131.540i 0.256084 0.827292i
\(160\) −158.630 126.942i −0.991439 0.793390i
\(161\) 19.3337 + 10.1175i 0.120085 + 0.0628414i
\(162\) −87.2212 + 197.770i −0.538403 + 1.22080i
\(163\) −10.2931 10.2931i −0.0631481 0.0631481i 0.674827 0.737976i \(-0.264218\pi\)
−0.737976 + 0.674827i \(0.764218\pi\)
\(164\) 21.4088i 0.130541i
\(165\) 150.707 + 222.325i 0.913376 + 1.34742i
\(166\) 159.402i 0.960253i
\(167\) −57.7311 + 57.7311i −0.345695 + 0.345695i −0.858503 0.512808i \(-0.828605\pi\)
0.512808 + 0.858503i \(0.328605\pi\)
\(168\) 49.2621 0.152100i 0.293227 0.000905359i
\(169\) 79.1253i 0.468197i
\(170\) 12.5061 1.38770i 0.0735650 0.00816296i
\(171\) 54.9742 80.2898i 0.321487 0.469531i
\(172\) 117.638 117.638i 0.683940 0.683940i
\(173\) 179.111 + 179.111i 1.03532 + 1.03532i 0.999353 + 0.0359688i \(0.0114517\pi\)
0.0359688 + 0.999353i \(0.488548\pi\)
\(174\) 175.670 + 54.3777i 1.00960 + 0.312516i
\(175\) 87.6061 + 151.493i 0.500606 + 0.865675i
\(176\) 335.623i 1.90695i
\(177\) −139.769 265.092i −0.789657 1.49770i
\(178\) −110.233 + 110.233i −0.619287 + 0.619287i
\(179\) 307.914 1.72019 0.860095 0.510133i \(-0.170404\pi\)
0.860095 + 0.510133i \(0.170404\pi\)
\(180\) 123.925 + 66.0794i 0.688470 + 0.367108i
\(181\) 124.967i 0.690428i 0.938524 + 0.345214i \(0.112194\pi\)
−0.938524 + 0.345214i \(0.887806\pi\)
\(182\) −87.8749 280.812i −0.482829 1.54292i
\(183\) 62.5106 + 118.560i 0.341588 + 0.647870i
\(184\) 7.31259i 0.0397423i
\(185\) 184.085 230.037i 0.995053 1.24344i
\(186\) −61.8076 + 199.672i −0.332299 + 1.07351i
\(187\) 11.9406 + 11.9406i 0.0638532 + 0.0638532i
\(188\) 17.3400 + 17.3400i 0.0922342 + 0.0922342i
\(189\) −185.666 + 35.3424i −0.982361 + 0.186997i
\(190\) −112.633 90.1336i −0.592806 0.474387i
\(191\) 120.234i 0.629496i −0.949175 0.314748i \(-0.898080\pi\)
0.949175 0.314748i \(-0.101920\pi\)
\(192\) −46.8132 88.7878i −0.243819 0.462437i
\(193\) −12.8649 12.8649i −0.0666576 0.0666576i 0.672992 0.739650i \(-0.265009\pi\)
−0.739650 + 0.672992i \(0.765009\pi\)
\(194\) 42.2372i 0.217718i
\(195\) −44.5494 + 232.042i −0.228458 + 1.18996i
\(196\) −87.1737 125.646i −0.444764 0.641050i
\(197\) 7.82035 + 7.82035i 0.0396972 + 0.0396972i 0.726677 0.686980i \(-0.241064\pi\)
−0.686980 + 0.726677i \(0.741064\pi\)
\(198\) 79.1117 + 422.702i 0.399554 + 2.13486i
\(199\) −301.160 −1.51336 −0.756682 0.653783i \(-0.773181\pi\)
−0.756682 + 0.653783i \(0.773181\pi\)
\(200\) −31.3690 + 49.5510i −0.156845 + 0.247755i
\(201\) 22.6120 73.0491i 0.112498 0.363429i
\(202\) −22.4956 22.4956i −0.111364 0.111364i
\(203\) 48.0218 + 153.458i 0.236560 + 0.755949i
\(204\) 8.43479 + 2.61095i 0.0413470 + 0.0127988i
\(205\) 34.0896 3.78266i 0.166291 0.0184520i
\(206\) −92.2120 −0.447631
\(207\) −5.16117 27.5767i −0.0249332 0.133221i
\(208\) 208.772 208.772i 1.00371 1.00371i
\(209\) 193.598i 0.926305i
\(210\) 31.7610 + 278.387i 0.151243 + 1.32565i
\(211\) −363.605 −1.72325 −0.861623 0.507549i \(-0.830552\pi\)
−0.861623 + 0.507549i \(0.830552\pi\)
\(212\) −101.291 101.291i −0.477789 0.477789i
\(213\) −8.89282 16.8665i −0.0417503 0.0791854i
\(214\) 139.162i 0.650291i
\(215\) −208.102 166.531i −0.967915 0.774565i
\(216\) −39.3427 49.6363i −0.182142 0.229798i
\(217\) −174.425 + 54.5832i −0.803802 + 0.251535i
\(218\) 101.532 101.532i 0.465742 0.465742i
\(219\) 69.4520 224.368i 0.317132 1.02451i
\(220\) 277.712 30.8157i 1.26233 0.140071i
\(221\) 14.8551i 0.0672176i
\(222\) 417.278 220.009i 1.87963 0.991032i
\(223\) 21.1671 21.1671i 0.0949198 0.0949198i −0.658052 0.752972i \(-0.728619\pi\)
0.752972 + 0.658052i \(0.228619\pi\)
\(224\) 131.882 252.016i 0.588758 1.12507i
\(225\) 83.3235 209.003i 0.370327 0.928902i
\(226\) 315.251 1.39492
\(227\) −190.960 + 190.960i −0.841234 + 0.841234i −0.989019 0.147785i \(-0.952785\pi\)
0.147785 + 0.989019i \(0.452785\pi\)
\(228\) −47.2124 89.5449i −0.207072 0.392741i
\(229\) −84.1627 −0.367523 −0.183761 0.982971i \(-0.558827\pi\)
−0.183761 + 0.982971i \(0.558827\pi\)
\(230\) −41.3386 + 4.58704i −0.179733 + 0.0199436i
\(231\) −265.069 + 266.711i −1.14748 + 1.15459i
\(232\) −38.1029 + 38.1029i −0.164237 + 0.164237i
\(233\) 227.465 227.465i 0.976246 0.976246i −0.0234784 0.999724i \(-0.507474\pi\)
0.999724 + 0.0234784i \(0.00747408\pi\)
\(234\) −213.728 + 312.150i −0.913368 + 1.33397i
\(235\) 24.5471 30.6746i 0.104456 0.130530i
\(236\) −311.761 −1.32102
\(237\) −83.6472 158.649i −0.352942 0.669404i
\(238\) 5.26101 + 16.8120i 0.0221051 + 0.0706386i
\(239\) −19.0852 −0.0798543 −0.0399272 0.999203i \(-0.512713\pi\)
−0.0399272 + 0.999203i \(0.512713\pi\)
\(240\) −232.723 + 157.756i −0.969680 + 0.657316i
\(241\) 345.423i 1.43329i −0.697438 0.716645i \(-0.745677\pi\)
0.697438 0.716645i \(-0.254323\pi\)
\(242\) 376.679 + 376.679i 1.55652 + 1.55652i
\(243\) 183.399 + 159.417i 0.754729 + 0.656037i
\(244\) 139.433 0.571445
\(245\) −184.665 + 161.008i −0.753736 + 0.657177i
\(246\) 52.4601 + 16.2388i 0.213252 + 0.0660112i
\(247\) 120.426 120.426i 0.487556 0.487556i
\(248\) −43.3090 43.3090i −0.174633 0.174633i
\(249\) 171.190 + 52.9910i 0.687509 + 0.212815i
\(250\) −299.793 146.249i −1.19917 0.584995i
\(251\) 253.938 1.01170 0.505852 0.862620i \(-0.331178\pi\)
0.505852 + 0.862620i \(0.331178\pi\)
\(252\) −57.5602 + 188.004i −0.228414 + 0.746047i
\(253\) −39.4694 39.4694i −0.156005 0.156005i
\(254\) −557.358 −2.19432
\(255\) 2.66714 13.8922i 0.0104594 0.0544792i
\(256\) 329.309 1.28636
\(257\) −295.955 + 295.955i −1.15158 + 1.15158i −0.165340 + 0.986237i \(0.552872\pi\)
−0.986237 + 0.165340i \(0.947128\pi\)
\(258\) −199.030 377.489i −0.771435 1.46313i
\(259\) 365.459 + 191.248i 1.41104 + 0.738408i
\(260\) 191.918 + 153.581i 0.738146 + 0.590694i
\(261\) 116.798 170.583i 0.447502 0.653576i
\(262\) 247.703 + 247.703i 0.945433 + 0.945433i
\(263\) 1.73180 1.73180i 0.00658477 0.00658477i −0.703807 0.710392i \(-0.748518\pi\)
0.710392 + 0.703807i \(0.248518\pi\)
\(264\) −120.378 37.2625i −0.455978 0.141146i
\(265\) −143.391 + 179.185i −0.541098 + 0.676169i
\(266\) 93.6408 178.940i 0.352033 0.672707i
\(267\) 81.7394 + 155.030i 0.306140 + 0.580638i
\(268\) −56.2511 56.2511i −0.209892 0.209892i
\(269\) 400.956i 1.49054i 0.666761 + 0.745272i \(0.267680\pi\)
−0.666761 + 0.745272i \(0.732320\pi\)
\(270\) 255.919 253.543i 0.947849 0.939049i
\(271\) 395.831i 1.46063i 0.683109 + 0.730316i \(0.260627\pi\)
−0.683109 + 0.730316i \(0.739373\pi\)
\(272\) −12.4990 + 12.4990i −0.0459523 + 0.0459523i
\(273\) −330.790 + 1.02134i −1.21169 + 0.00374117i
\(274\) 257.060i 0.938174i
\(275\) −98.1367 436.762i −0.356861 1.58822i
\(276\) −27.8811 8.63047i −0.101019 0.0312698i
\(277\) −40.6213 + 40.6213i −0.146647 + 0.146647i −0.776618 0.629971i \(-0.783067\pi\)
0.629971 + 0.776618i \(0.283067\pi\)
\(278\) −56.8222 56.8222i −0.204397 0.204397i
\(279\) 193.891 + 132.756i 0.694949 + 0.475830i
\(280\) −76.4999 29.8132i −0.273214 0.106476i
\(281\) 284.890i 1.01384i 0.861992 + 0.506922i \(0.169217\pi\)
−0.861992 + 0.506922i \(0.830783\pi\)
\(282\) 55.6426 29.3374i 0.197314 0.104033i
\(283\) −102.657 + 102.657i −0.362744 + 0.362744i −0.864822 0.502078i \(-0.832569\pi\)
0.502078 + 0.864822i \(0.332569\pi\)
\(284\) −19.8358 −0.0698444
\(285\) −134.242 + 90.9986i −0.471025 + 0.319293i
\(286\) 752.668i 2.63171i
\(287\) 14.3407 + 45.8269i 0.0499676 + 0.159676i
\(288\) −359.464 + 67.2762i −1.24814 + 0.233598i
\(289\) 288.111i 0.996923i
\(290\) −239.300 191.497i −0.825171 0.660336i
\(291\) 45.3606 + 14.0412i 0.155879 + 0.0482515i
\(292\) −172.773 172.773i −0.591689 0.591689i
\(293\) −204.227 204.227i −0.697021 0.697021i 0.266746 0.963767i \(-0.414052\pi\)
−0.963767 + 0.266746i \(0.914052\pi\)
\(294\) −374.005 + 118.307i −1.27212 + 0.402405i
\(295\) 55.0844 + 496.423i 0.186727 + 1.68279i
\(296\) 138.228i 0.466987i
\(297\) 480.260 + 55.5594i 1.61704 + 0.187069i
\(298\) 174.471 + 174.471i 0.585472 + 0.585472i
\(299\) 49.1033i 0.164225i
\(300\) −151.904 178.083i −0.506345 0.593611i
\(301\) 173.011 330.611i 0.574789 1.09838i
\(302\) 23.1493 + 23.1493i 0.0766534 + 0.0766534i
\(303\) −31.6374 + 16.6808i −0.104414 + 0.0550520i
\(304\) 202.653 0.666621
\(305\) −24.6360 222.021i −0.0807738 0.727938i
\(306\) 12.7958 18.6882i 0.0418162 0.0610725i
\(307\) −209.811 209.811i −0.683425 0.683425i 0.277345 0.960770i \(-0.410545\pi\)
−0.960770 + 0.277345i \(0.910545\pi\)
\(308\) 116.827 + 373.331i 0.379309 + 1.21211i
\(309\) −30.6546 + 99.0310i −0.0992058 + 0.320489i
\(310\) 217.662 271.996i 0.702137 0.877407i
\(311\) 414.961 1.33428 0.667141 0.744932i \(-0.267518\pi\)
0.667141 + 0.744932i \(0.267518\pi\)
\(312\) −51.7016 98.0593i −0.165710 0.314293i
\(313\) −6.05318 + 6.05318i −0.0193392 + 0.0193392i −0.716710 0.697371i \(-0.754353\pi\)
0.697371 + 0.716710i \(0.254353\pi\)
\(314\) 241.265i 0.768359i
\(315\) 309.532 + 58.4362i 0.982642 + 0.185512i
\(316\) −186.579 −0.590439
\(317\) 255.502 + 255.502i 0.805999 + 0.805999i 0.984026 0.178027i \(-0.0569714\pi\)
−0.178027 + 0.984026i \(0.556971\pi\)
\(318\) −325.035 + 171.374i −1.02212 + 0.538911i
\(319\) 411.317i 1.28939i
\(320\) 18.4495 + 166.268i 0.0576547 + 0.519588i
\(321\) −149.453 46.2625i −0.465586 0.144120i
\(322\) −17.3902 55.5719i −0.0540069 0.172583i
\(323\) −7.20984 + 7.20984i −0.0223215 + 0.0223215i
\(324\) 235.684 91.4223i 0.727421 0.282168i
\(325\) 210.640 332.730i 0.648122 1.02378i
\(326\) 38.8446i 0.119155i
\(327\) −75.2872 142.793i −0.230236 0.436675i
\(328\) −11.3786 + 11.3786i −0.0346909 + 0.0346909i
\(329\) 48.7327 + 25.5022i 0.148124 + 0.0775144i
\(330\) 135.137 703.881i 0.409506 2.13297i
\(331\) 148.520 0.448702 0.224351 0.974508i \(-0.427974\pi\)
0.224351 + 0.974508i \(0.427974\pi\)
\(332\) 131.824 131.824i 0.397059 0.397059i
\(333\) −97.5603 521.275i −0.292974 1.56539i
\(334\) 217.868 0.652299
\(335\) −79.6308 + 99.5085i −0.237704 + 0.297040i
\(336\) −279.185 277.467i −0.830909 0.825794i
\(337\) 225.218 225.218i 0.668303 0.668303i −0.289020 0.957323i \(-0.593329\pi\)
0.957323 + 0.289020i \(0.0933294\pi\)
\(338\) −149.303 + 149.303i −0.441725 + 0.441725i
\(339\) 104.801 338.564i 0.309147 0.998714i
\(340\) −11.4900 9.19476i −0.0337941 0.0270434i
\(341\) 467.517 1.37102
\(342\) −255.232 + 47.7685i −0.746293 + 0.139674i
\(343\) −270.765 210.559i −0.789402 0.613876i
\(344\) 125.047 0.363510
\(345\) −8.81620 + 45.9205i −0.0255542 + 0.133103i
\(346\) 675.934i 1.95357i
\(347\) 81.8789 + 81.8789i 0.235962 + 0.235962i 0.815176 0.579214i \(-0.196640\pi\)
−0.579214 + 0.815176i \(0.696640\pi\)
\(348\) −100.307 190.247i −0.288239 0.546686i
\(349\) 356.670 1.02198 0.510989 0.859587i \(-0.329279\pi\)
0.510989 + 0.859587i \(0.329279\pi\)
\(350\) 120.550 451.161i 0.344427 1.28903i
\(351\) 264.182 + 333.303i 0.752656 + 0.949582i
\(352\) −514.486 + 514.486i −1.46161 + 1.46161i
\(353\) 305.766 + 305.766i 0.866191 + 0.866191i 0.992048 0.125857i \(-0.0401681\pi\)
−0.125857 + 0.992048i \(0.540168\pi\)
\(354\) −236.474 + 763.940i −0.668006 + 2.15802i
\(355\) 3.50474 + 31.5849i 0.00987251 + 0.0889716i
\(356\) 182.323 0.512144
\(357\) 19.8042 0.0611469i 0.0554739 0.000171280i
\(358\) −581.009 581.009i −1.62293 1.62293i
\(359\) −356.776 −0.993806 −0.496903 0.867806i \(-0.665530\pi\)
−0.496903 + 0.867806i \(0.665530\pi\)
\(360\) 30.7444 + 100.986i 0.0854010 + 0.280516i
\(361\) −244.103 −0.676187
\(362\) 235.803 235.803i 0.651390 0.651390i
\(363\) 529.756 279.313i 1.45938 0.769456i
\(364\) −159.557 + 304.900i −0.438342 + 0.837637i
\(365\) −244.583 + 305.637i −0.670090 + 0.837361i
\(366\) 105.761 341.666i 0.288965 0.933514i
\(367\) −185.321 185.321i −0.504963 0.504963i 0.408013 0.912976i \(-0.366222\pi\)
−0.912976 + 0.408013i \(0.866222\pi\)
\(368\) 41.3154 41.3154i 0.112270 0.112270i
\(369\) 34.8792 50.9411i 0.0945237 0.138052i
\(370\) −781.414 + 86.7076i −2.11193 + 0.234345i
\(371\) −284.671 148.971i −0.767307 0.401538i
\(372\) 216.241 114.013i 0.581293 0.306485i
\(373\) −231.949 231.949i −0.621848 0.621848i 0.324155 0.946004i \(-0.394920\pi\)
−0.946004 + 0.324155i \(0.894920\pi\)
\(374\) 45.0617i 0.120486i
\(375\) −256.726 + 273.344i −0.684602 + 0.728917i
\(376\) 18.4322i 0.0490219i
\(377\) 255.857 255.857i 0.678666 0.678666i
\(378\) 417.025 + 283.649i 1.10324 + 0.750393i
\(379\) 33.7232i 0.0889794i 0.999010 + 0.0444897i \(0.0141662\pi\)
−0.999010 + 0.0444897i \(0.985834\pi\)
\(380\) 18.6068 + 167.686i 0.0489654 + 0.441278i
\(381\) −185.286 + 598.575i −0.486315 + 1.57106i
\(382\) −226.871 + 226.871i −0.593904 + 0.593904i
\(383\) −353.025 353.025i −0.921735 0.921735i 0.0754169 0.997152i \(-0.475971\pi\)
−0.997152 + 0.0754169i \(0.975971\pi\)
\(384\) 64.9838 209.933i 0.169229 0.546701i
\(385\) 573.820 251.989i 1.49044 0.654517i
\(386\) 48.5501i 0.125777i
\(387\) −471.569 + 88.2574i −1.21852 + 0.228055i
\(388\) 34.9297 34.9297i 0.0900250 0.0900250i
\(389\) −222.963 −0.573170 −0.286585 0.958055i \(-0.592520\pi\)
−0.286585 + 0.958055i \(0.592520\pi\)
\(390\) 521.906 353.783i 1.33822 0.907137i
\(391\) 2.93978i 0.00751862i
\(392\) 20.4476 113.112i 0.0521623 0.288551i
\(393\) 348.366 183.675i 0.886429 0.467367i
\(394\) 29.5127i 0.0749054i
\(395\) 32.9661 + 297.093i 0.0834586 + 0.752133i
\(396\) 284.145 414.994i 0.717539 1.04797i
\(397\) 518.609 + 518.609i 1.30632 + 1.30632i 0.924051 + 0.382270i \(0.124857\pi\)
0.382270 + 0.924051i \(0.375143\pi\)
\(398\) 568.264 + 568.264i 1.42780 + 1.42780i
\(399\) −161.043 160.052i −0.403617 0.401132i
\(400\) 457.190 102.727i 1.14297 0.256817i
\(401\) 333.028i 0.830494i 0.909709 + 0.415247i \(0.136305\pi\)
−0.909709 + 0.415247i \(0.863695\pi\)
\(402\) −180.505 + 95.1707i −0.449017 + 0.236743i
\(403\) 290.816 + 290.816i 0.721628 + 0.721628i
\(404\) 37.2072i 0.0920969i
\(405\) −187.216 359.131i −0.462261 0.886744i
\(406\) 198.949 380.175i 0.490022 0.936392i
\(407\) −746.079 746.079i −1.83312 1.83312i
\(408\) 3.09534 + 5.87074i 0.00758661 + 0.0143891i
\(409\) −634.549 −1.55146 −0.775732 0.631062i \(-0.782619\pi\)
−0.775732 + 0.631062i \(0.782619\pi\)
\(410\) −71.4618 57.1866i −0.174297 0.139480i
\(411\) 276.069 + 85.4559i 0.671701 + 0.207922i
\(412\) 76.2583 + 76.2583i 0.185093 + 0.185093i
\(413\) −667.346 + 208.834i −1.61585 + 0.505651i
\(414\) −42.2962 + 61.7736i −0.102165 + 0.149212i
\(415\) −233.197 186.614i −0.561920 0.449671i
\(416\) −640.065 −1.53862
\(417\) −79.9140 + 42.1345i −0.191640 + 0.101042i
\(418\) −365.303 + 365.303i −0.873931 + 0.873931i
\(419\) 415.098i 0.990687i 0.868697 + 0.495343i \(0.164958\pi\)
−0.868697 + 0.495343i \(0.835042\pi\)
\(420\) 203.957 256.489i 0.485612 0.610688i
\(421\) 425.874 1.01158 0.505789 0.862657i \(-0.331201\pi\)
0.505789 + 0.862657i \(0.331201\pi\)
\(422\) 686.093 + 686.093i 1.62581 + 1.62581i
\(423\) −13.0093 69.5102i −0.0307549 0.164327i
\(424\) 107.671i 0.253942i
\(425\) −12.6108 + 19.9203i −0.0296726 + 0.0468713i
\(426\) −15.0457 + 48.6057i −0.0353185 + 0.114098i
\(427\) 298.465 93.3992i 0.698981 0.218733i
\(428\) −115.086 + 115.086i −0.268892 + 0.268892i
\(429\) 808.327 + 250.214i 1.88421 + 0.583249i
\(430\) 78.4396 + 706.902i 0.182418 + 1.64396i
\(431\) 217.914i 0.505600i −0.967519 0.252800i \(-0.918649\pi\)
0.967519 0.252800i \(-0.0813514\pi\)
\(432\) −58.1580 + 502.723i −0.134625 + 1.16371i
\(433\) −377.736 + 377.736i −0.872369 + 0.872369i −0.992730 0.120361i \(-0.961595\pi\)
0.120361 + 0.992730i \(0.461595\pi\)
\(434\) 432.120 + 226.132i 0.995668 + 0.521041i
\(435\) −285.210 + 193.335i −0.655656 + 0.444449i
\(436\) −167.931 −0.385163
\(437\) 23.8320 23.8320i 0.0545355 0.0545355i
\(438\) −554.414 + 292.313i −1.26579 + 0.667382i
\(439\) −18.8677 −0.0429789 −0.0214894 0.999769i \(-0.506841\pi\)
−0.0214894 + 0.999769i \(0.506841\pi\)
\(440\) 163.981 + 131.224i 0.372683 + 0.298236i
\(441\) 2.72321 + 440.992i 0.00617509 + 0.999981i
\(442\) 28.0303 28.0303i 0.0634171 0.0634171i
\(443\) 484.487 484.487i 1.09365 1.09365i 0.0985149 0.995136i \(-0.468591\pi\)
0.995136 0.0985149i \(-0.0314092\pi\)
\(444\) −527.030 163.140i −1.18700 0.367431i
\(445\) −32.2143 290.317i −0.0723916 0.652397i
\(446\) −79.8812 −0.179106
\(447\) 245.373 129.372i 0.548933 0.289424i
\(448\) −223.515 + 69.9451i −0.498918 + 0.156127i
\(449\) 801.204 1.78442 0.892209 0.451623i \(-0.149155\pi\)
0.892209 + 0.451623i \(0.149155\pi\)
\(450\) −551.596 + 237.147i −1.22577 + 0.526993i
\(451\) 122.831i 0.272353i
\(452\) −260.709 260.709i −0.576791 0.576791i
\(453\) 32.5569 17.1655i 0.0718695 0.0378930i
\(454\) 720.652 1.58734
\(455\) 513.689 + 200.193i 1.12899 + 0.439984i
\(456\) 22.4995 72.6856i 0.0493410 0.159398i
\(457\) −407.879 + 407.879i −0.892515 + 0.892515i −0.994759 0.102244i \(-0.967398\pi\)
0.102244 + 0.994759i \(0.467398\pi\)
\(458\) 158.808 + 158.808i 0.346743 + 0.346743i
\(459\) −15.8164 19.9546i −0.0344584 0.0434741i
\(460\) 37.9800 + 30.3932i 0.0825653 + 0.0660721i
\(461\) −627.296 −1.36073 −0.680365 0.732874i \(-0.738179\pi\)
−0.680365 + 0.732874i \(0.738179\pi\)
\(462\) 1003.43 3.09815i 2.17192 0.00670595i
\(463\) 576.012 + 576.012i 1.24409 + 1.24409i 0.958290 + 0.285797i \(0.0922584\pi\)
0.285797 + 0.958290i \(0.407742\pi\)
\(464\) 430.555 0.927920
\(465\) −219.751 324.180i −0.472584 0.697161i
\(466\) −858.417 −1.84210
\(467\) −239.537 + 239.537i −0.512928 + 0.512928i −0.915422 0.402495i \(-0.868143\pi\)
0.402495 + 0.915422i \(0.368143\pi\)
\(468\) 434.895 81.3938i 0.929264 0.173918i
\(469\) −158.089 82.7293i −0.337077 0.176395i
\(470\) −104.199 + 11.5622i −0.221700 + 0.0246003i
\(471\) −259.106 80.2051i −0.550119 0.170287i
\(472\) −165.699 165.699i −0.351058 0.351058i
\(473\) −674.937 + 674.937i −1.42693 + 1.42693i
\(474\) −141.522 + 457.193i −0.298569 + 0.964542i
\(475\) 263.722 59.2560i 0.555203 0.124749i
\(476\) 9.55254 18.2541i 0.0200684 0.0383490i
\(477\) 75.9936 + 406.042i 0.159316 + 0.851241i
\(478\) 36.0122 + 36.0122i 0.0753393 + 0.0753393i
\(479\) 868.698i 1.81357i −0.421598 0.906783i \(-0.638531\pi\)
0.421598 0.906783i \(-0.361469\pi\)
\(480\) 598.577 + 114.920i 1.24704 + 0.239416i
\(481\) 928.188i 1.92970i
\(482\) −651.785 + 651.785i −1.35225 + 1.35225i
\(483\) −65.4625 + 0.202120i −0.135533 + 0.000418468i
\(484\) 623.019i 1.28723i
\(485\) −61.7909 49.4476i −0.127404 0.101954i
\(486\) −45.2524 646.866i −0.0931119 1.33100i
\(487\) 1.87718 1.87718i 0.00385458 0.00385458i −0.705177 0.709031i \(-0.749132\pi\)
0.709031 + 0.705177i \(0.249132\pi\)
\(488\) 74.1076 + 74.1076i 0.151860 + 0.151860i
\(489\) 41.7171 + 12.9133i 0.0853111 + 0.0264077i
\(490\) 652.258 + 44.6390i 1.33114 + 0.0911000i
\(491\) 125.302i 0.255198i −0.991826 0.127599i \(-0.959273\pi\)
0.991826 0.127599i \(-0.0407270\pi\)
\(492\) −29.9546 56.8132i −0.0608834 0.115474i
\(493\) −15.3180 + 15.3180i −0.0310710 + 0.0310710i
\(494\) −454.469 −0.919978
\(495\) −711.008 379.126i −1.43638 0.765910i
\(496\) 489.383i 0.986660i
\(497\) −42.4599 + 13.2870i −0.0854323 + 0.0267345i
\(498\) −223.031 423.011i −0.447854 0.849419i
\(499\) 426.549i 0.854807i −0.904061 0.427403i \(-0.859428\pi\)
0.904061 0.427403i \(-0.140572\pi\)
\(500\) 126.979 + 368.871i 0.253958 + 0.737743i
\(501\) 72.4271 233.979i 0.144565 0.467024i
\(502\) −479.160 479.160i −0.954502 0.954502i
\(503\) −606.100 606.100i −1.20497 1.20497i −0.972636 0.232335i \(-0.925364\pi\)
−0.232335 0.972636i \(-0.574636\pi\)
\(504\) −130.516 + 69.3300i −0.258960 + 0.137559i
\(505\) 59.2456 6.57404i 0.117318 0.0130179i
\(506\) 148.951i 0.294369i
\(507\) 110.710 + 209.978i 0.218363 + 0.414157i
\(508\) 460.929 + 460.929i 0.907341 + 0.907341i
\(509\) 3.90604i 0.00767394i 0.999993 + 0.00383697i \(0.00122135\pi\)
−0.999993 + 0.00383697i \(0.998779\pi\)
\(510\) −31.2461 + 21.1808i −0.0612669 + 0.0415309i
\(511\) −485.565 254.100i −0.950225 0.497260i
\(512\) −414.186 414.186i −0.808956 0.808956i
\(513\) −33.5474 + 289.986i −0.0653945 + 0.565276i
\(514\) 1116.89 2.17293
\(515\) 107.954 134.901i 0.209619 0.261944i
\(516\) −147.583 + 476.775i −0.286014 + 0.923982i
\(517\) −99.4871 99.4871i −0.192431 0.192431i
\(518\) −328.723 1050.46i −0.634600 2.02792i
\(519\) −725.919 224.705i −1.39869 0.432957i
\(520\) 20.3761 + 183.630i 0.0391847 + 0.353135i
\(521\) −556.444 −1.06803 −0.534015 0.845475i \(-0.679317\pi\)
−0.534015 + 0.845475i \(0.679317\pi\)
\(522\) −542.265 + 101.489i −1.03882 + 0.194423i
\(523\) 241.019 241.019i 0.460839 0.460839i −0.438092 0.898930i \(-0.644345\pi\)
0.898930 + 0.438092i \(0.144345\pi\)
\(524\) 409.696i 0.781862i
\(525\) −444.449 279.446i −0.846569 0.532278i
\(526\) −6.53551 −0.0124249
\(527\) −17.4109 17.4109i −0.0330378 0.0330378i
\(528\) 469.595 + 890.653i 0.889384 + 1.68684i
\(529\) 519.283i 0.981631i
\(530\) 608.674 67.5400i 1.14844 0.127434i
\(531\) 741.821 + 507.923i 1.39703 + 0.956540i
\(532\) −225.421 + 70.5415i −0.423724 + 0.132597i
\(533\) 76.4063 76.4063i 0.143351 0.143351i
\(534\) 138.294 446.765i 0.258978 0.836639i
\(535\) 203.587 + 162.919i 0.380537 + 0.304521i
\(536\) 59.7942i 0.111556i
\(537\) −817.122 + 430.826i −1.52164 + 0.802283i
\(538\) 756.572 756.572i 1.40627 1.40627i
\(539\) 500.153 + 720.883i 0.927927 + 1.33744i
\(540\) −421.320 1.96491i −0.780222 0.00363873i
\(541\) 255.515 0.472302 0.236151 0.971716i \(-0.424114\pi\)
0.236151 + 0.971716i \(0.424114\pi\)
\(542\) 746.901 746.901i 1.37805 1.37805i
\(543\) −174.851 331.630i −0.322010 0.610737i
\(544\) 38.3203 0.0704416
\(545\) 29.6714 + 267.400i 0.0544429 + 0.490642i
\(546\) 626.101 + 622.247i 1.14671 + 1.13965i
\(547\) −80.6313 + 80.6313i −0.147406 + 0.147406i −0.776958 0.629552i \(-0.783238\pi\)
0.629552 + 0.776958i \(0.283238\pi\)
\(548\) 212.586 212.586i 0.387930 0.387930i
\(549\) −331.773 227.164i −0.604323 0.413778i
\(550\) −638.958 + 1009.31i −1.16174 + 1.83511i
\(551\) 248.358 0.450740
\(552\) −10.2316 19.4057i −0.0185355 0.0351552i
\(553\) −399.384 + 124.980i −0.722213 + 0.226004i
\(554\) 153.298 0.276711
\(555\) −166.650 + 868.024i −0.300271 + 1.56401i
\(556\) 93.9827i 0.169034i
\(557\) −452.948 452.948i −0.813192 0.813192i 0.171919 0.985111i \(-0.445003\pi\)
−0.985111 + 0.171919i \(0.945003\pi\)
\(558\) −115.356 616.357i −0.206730 1.10458i
\(559\) −839.680 −1.50211
\(560\) 263.775 + 600.658i 0.471026 + 1.07260i
\(561\) −48.3940 14.9801i −0.0862638 0.0267025i
\(562\) 537.564 537.564i 0.956520 0.956520i
\(563\) 534.797 + 534.797i 0.949906 + 0.949906i 0.998804 0.0488978i \(-0.0155709\pi\)
−0.0488978 + 0.998804i \(0.515571\pi\)
\(564\) −70.2776 21.7541i −0.124606 0.0385711i
\(565\) −369.068 + 461.196i −0.653218 + 0.816277i
\(566\) 387.409 0.684468
\(567\) 443.258 353.569i 0.781761 0.623578i
\(568\) −10.5426 10.5426i −0.0185609 0.0185609i
\(569\) −527.903 −0.927773 −0.463886 0.885895i \(-0.653545\pi\)
−0.463886 + 0.885895i \(0.653545\pi\)
\(570\) 425.011 + 81.5972i 0.745633 + 0.143153i
\(571\) 249.965 0.437767 0.218884 0.975751i \(-0.429759\pi\)
0.218884 + 0.975751i \(0.429759\pi\)
\(572\) 622.448 622.448i 1.08820 1.08820i
\(573\) 168.228 + 319.069i 0.293592 + 0.556839i
\(574\) 59.4118 113.531i 0.103505 0.197790i
\(575\) 41.6850 65.8464i 0.0724956 0.114515i
\(576\) 248.460 + 170.120i 0.431353 + 0.295346i
\(577\) 63.8107 + 63.8107i 0.110590 + 0.110590i 0.760237 0.649646i \(-0.225083\pi\)
−0.649646 + 0.760237i \(0.725083\pi\)
\(578\) 543.641 543.641i 0.940556 0.940556i
\(579\) 52.1404 + 16.1398i 0.0900524 + 0.0278753i
\(580\) 39.5320 + 356.264i 0.0681586 + 0.614249i
\(581\) 193.875 370.480i 0.333692 0.637658i
\(582\) −59.0973 112.086i −0.101542 0.192588i
\(583\) 581.151 + 581.151i 0.996828 + 0.996828i
\(584\) 183.656i 0.314479i
\(585\) −206.445 678.111i −0.352898 1.15916i
\(586\) 770.720i 1.31522i
\(587\) 748.348 748.348i 1.27487 1.27487i 0.331366 0.943502i \(-0.392491\pi\)
0.943502 0.331366i \(-0.107509\pi\)
\(588\) 407.136 + 211.459i 0.692409 + 0.359624i
\(589\) 282.292i 0.479273i
\(590\) 832.770 1040.65i 1.41148 1.76381i
\(591\) −31.6952 9.81110i −0.0536298 0.0166008i
\(592\) 780.974 780.974i 1.31921 1.31921i
\(593\) −88.6544 88.6544i −0.149502 0.149502i 0.628394 0.777895i \(-0.283713\pi\)
−0.777895 + 0.628394i \(0.783713\pi\)
\(594\) −801.376 1011.05i −1.34912 1.70210i
\(595\) −30.7542 11.9854i −0.0516877 0.0201435i
\(596\) 288.571i 0.484179i
\(597\) 799.198 421.375i 1.33869 0.705821i
\(598\) −92.6540 + 92.6540i −0.154940 + 0.154940i
\(599\) −512.160 −0.855025 −0.427512 0.904009i \(-0.640610\pi\)
−0.427512 + 0.904009i \(0.640610\pi\)
\(600\) 13.9144 175.386i 0.0231906 0.292310i
\(601\) 148.766i 0.247530i 0.992312 + 0.123765i \(0.0394969\pi\)
−0.992312 + 0.123765i \(0.960503\pi\)
\(602\) −950.294 + 297.377i −1.57856 + 0.493982i
\(603\) 42.2023 + 225.491i 0.0699872 + 0.373949i
\(604\) 38.2885i 0.0633915i
\(605\) −992.044 + 110.080i −1.63974 + 0.181950i
\(606\) 91.1725 + 28.2220i 0.150450 + 0.0465710i
\(607\) −336.268 336.268i −0.553984 0.553984i 0.373604 0.927588i \(-0.378122\pi\)
−0.927588 + 0.373604i \(0.878122\pi\)
\(608\) −310.652 310.652i −0.510941 0.510941i
\(609\) −342.151 340.045i −0.561825 0.558366i
\(610\) −372.450 + 465.422i −0.610573 + 0.762987i
\(611\) 123.771i 0.202571i
\(612\) −26.0369 + 4.87299i −0.0425439 + 0.00796240i
\(613\) −289.428 289.428i −0.472151 0.472151i 0.430459 0.902610i \(-0.358352\pi\)
−0.902610 + 0.430459i \(0.858352\pi\)
\(614\) 791.794i 1.28957i
\(615\) −85.1720 + 57.7355i −0.138491 + 0.0938788i
\(616\) −136.330 + 260.516i −0.221315 + 0.422915i
\(617\) 759.979 + 759.979i 1.23173 + 1.23173i 0.963298 + 0.268434i \(0.0865062\pi\)
0.268434 + 0.963298i \(0.413494\pi\)
\(618\) 244.706 129.021i 0.395965 0.208771i
\(619\) −509.592 −0.823251 −0.411626 0.911353i \(-0.635039\pi\)
−0.411626 + 0.911353i \(0.635039\pi\)
\(620\) −404.942 + 44.9334i −0.653133 + 0.0724732i
\(621\) 52.2810 + 65.9598i 0.0841884 + 0.106215i
\(622\) −782.998 782.998i −1.25884 1.25884i
\(623\) 390.275 122.129i 0.626444 0.196034i
\(624\) −261.917 + 846.134i −0.419738 + 1.35598i
\(625\) 564.925 267.366i 0.903880 0.427786i
\(626\) 22.8437 0.0364915
\(627\) 270.877 + 513.757i 0.432021 + 0.819390i
\(628\) −199.523 + 199.523i −0.317712 + 0.317712i
\(629\) 55.5699i 0.0883465i
\(630\) −473.798 694.326i −0.752060 1.10211i
\(631\) −647.514 −1.02617 −0.513086 0.858337i \(-0.671498\pi\)
−0.513086 + 0.858337i \(0.671498\pi\)
\(632\) −99.1654 99.1654i −0.156907 0.156907i
\(633\) 964.911 508.747i 1.52435 0.803708i
\(634\) 964.221i 1.52085i
\(635\) 652.506 815.387i 1.02757 1.28407i
\(636\) 410.524 + 127.076i 0.645479 + 0.199805i
\(637\) −137.304 + 759.537i −0.215547 + 1.19237i
\(638\) −776.122 + 776.122i −1.21649 + 1.21649i
\(639\) 47.1983 + 32.3166i 0.0738628 + 0.0505737i
\(640\) −228.848 + 285.974i −0.357575 + 0.446834i
\(641\) 428.281i 0.668145i 0.942547 + 0.334072i \(0.108423\pi\)
−0.942547 + 0.334072i \(0.891577\pi\)
\(642\) 194.712 + 369.300i 0.303290 + 0.575233i
\(643\) 251.455 251.455i 0.391065 0.391065i −0.484002 0.875067i \(-0.660817\pi\)
0.875067 + 0.484002i \(0.160817\pi\)
\(644\) −31.5758 + 60.3388i −0.0490307 + 0.0936938i
\(645\) 785.253 + 150.760i 1.21745 + 0.233736i
\(646\) 27.2087 0.0421188
\(647\) 245.105 245.105i 0.378832 0.378832i −0.491848 0.870681i \(-0.663679\pi\)
0.870681 + 0.491848i \(0.163679\pi\)
\(648\) 173.855 + 76.6743i 0.268295 + 0.118325i
\(649\) 1788.71 2.75610
\(650\) −1025.29 + 230.375i −1.57738 + 0.354423i
\(651\) 386.507 388.901i 0.593712 0.597390i
\(652\) 32.1241 32.1241i 0.0492700 0.0492700i
\(653\) −253.883 + 253.883i −0.388794 + 0.388794i −0.874257 0.485463i \(-0.838651\pi\)
0.485463 + 0.874257i \(0.338651\pi\)
\(654\) −127.378 + 411.499i −0.194767 + 0.629203i
\(655\) −652.366 + 72.3882i −0.995979 + 0.110516i
\(656\) 128.576 0.196000
\(657\) 129.623 + 692.588i 0.197295 + 1.05417i
\(658\) −43.8340 140.075i −0.0666170 0.212880i
\(659\) −508.205 −0.771176 −0.385588 0.922671i \(-0.626001\pi\)
−0.385588 + 0.922671i \(0.626001\pi\)
\(660\) −693.858 + 470.345i −1.05130 + 0.712644i
\(661\) 392.220i 0.593373i 0.954975 + 0.296687i \(0.0958817\pi\)
−0.954975 + 0.296687i \(0.904118\pi\)
\(662\) −280.246 280.246i −0.423332 0.423332i
\(663\) −20.7849 39.4215i −0.0313497 0.0594592i
\(664\) 140.127 0.211034
\(665\) 152.154 + 346.479i 0.228803 + 0.521021i
\(666\) −799.515 + 1167.69i −1.20047 + 1.75329i
\(667\) 50.6334 50.6334i 0.0759122 0.0759122i
\(668\) −180.174 180.174i −0.269722 0.269722i
\(669\) −26.5554 + 85.7884i −0.0396942 + 0.128234i
\(670\) 338.021 37.5077i 0.504509 0.0559816i
\(671\) −799.984 −1.19223
\(672\) 2.63465 + 853.308i 0.00392061 + 1.26980i
\(673\) 335.327 + 335.327i 0.498257 + 0.498257i 0.910895 0.412638i \(-0.135393\pi\)
−0.412638 + 0.910895i \(0.635393\pi\)
\(674\) −849.936 −1.26103
\(675\) 71.3132 + 671.222i 0.105649 + 0.994403i
\(676\) 246.944 0.365302
\(677\) −164.817 + 164.817i −0.243452 + 0.243452i −0.818277 0.574825i \(-0.805070\pi\)
0.574825 + 0.818277i \(0.305070\pi\)
\(678\) −836.593 + 441.092i −1.23391 + 0.650578i
\(679\) 51.3716 98.1671i 0.0756578 0.144576i
\(680\) −1.21990 10.9938i −0.00179397 0.0161674i
\(681\) 239.571 773.944i 0.351793 1.13648i
\(682\) −882.166 882.166i −1.29350 1.29350i
\(683\) 707.818 707.818i 1.03634 1.03634i 0.0370224 0.999314i \(-0.488213\pi\)
0.999314 0.0370224i \(-0.0117873\pi\)
\(684\) 250.578 + 171.570i 0.366342 + 0.250834i
\(685\) −376.065 300.943i −0.549000 0.439332i
\(686\) 113.603 + 908.220i 0.165602 + 1.32394i
\(687\) 223.346 117.758i 0.325103 0.171410i
\(688\) −706.505 706.505i −1.02690 1.02690i
\(689\) 723.002i 1.04935i
\(690\) 103.284 70.0128i 0.149687 0.101468i
\(691\) 603.312i 0.873101i −0.899680 0.436550i \(-0.856200\pi\)
0.899680 0.436550i \(-0.143800\pi\)
\(692\) −558.990 + 558.990i −0.807789 + 0.807789i
\(693\) 330.247 1078.66i 0.476548 1.55651i
\(694\) 308.998i 0.445242i
\(695\) 149.650 16.6056i 0.215324 0.0238929i
\(696\) 47.8023 154.428i 0.0686815 0.221879i
\(697\) −4.57439 + 4.57439i −0.00656297 + 0.00656297i
\(698\) −673.008 673.008i −0.964195 0.964195i
\(699\) −285.369 + 921.896i −0.408253 + 1.31888i
\(700\) −472.798 + 273.412i −0.675426 + 0.390588i
\(701\) 354.991i 0.506406i −0.967413 0.253203i \(-0.918516\pi\)
0.967413 0.253203i \(-0.0814841\pi\)
\(702\) 130.425 1127.41i 0.185791 1.60599i
\(703\) 450.491 450.491i 0.640812 0.640812i
\(704\) 599.095 0.850987
\(705\) −22.2223 + 115.748i −0.0315209 + 0.164181i
\(706\) 1153.91i 1.63443i
\(707\) 24.9233 + 79.6444i 0.0352521 + 0.112651i
\(708\) 827.332 436.209i 1.16855 0.616114i
\(709\) 637.022i 0.898479i −0.893411 0.449240i \(-0.851695\pi\)
0.893411 0.449240i \(-0.148305\pi\)
\(710\) 52.9850 66.2113i 0.0746268 0.0932554i
\(711\) 443.955 + 303.975i 0.624409 + 0.427531i
\(712\) 96.9036 + 96.9036i 0.136101 + 0.136101i
\(713\) 57.5517 + 57.5517i 0.0807176 + 0.0807176i
\(714\) −37.4843 37.2535i −0.0524990 0.0521758i
\(715\) −1101.11 881.156i −1.54002 1.23239i
\(716\) 960.976i 1.34215i
\(717\) 50.6470 26.7035i 0.0706374 0.0372434i
\(718\) 673.208 + 673.208i 0.937616 + 0.937616i
\(719\) 435.697i 0.605976i −0.952994 0.302988i \(-0.902016\pi\)
0.952994 0.302988i \(-0.0979843\pi\)
\(720\) 396.858 744.263i 0.551191 1.03370i
\(721\) 214.318 + 112.154i 0.297251 + 0.155554i
\(722\) 460.603 + 460.603i 0.637955 + 0.637955i
\(723\) 483.307 + 916.661i 0.668475 + 1.26786i
\(724\) −390.014 −0.538693
\(725\) 560.301 125.895i 0.772830 0.173648i
\(726\) −1526.65 472.566i −2.10282 0.650917i
\(727\) 757.367 + 757.367i 1.04177 + 1.04177i 0.999089 + 0.0426819i \(0.0135902\pi\)
0.0426819 + 0.999089i \(0.486410\pi\)
\(728\) −246.856 + 77.2490i −0.339087 + 0.106111i
\(729\) −709.745 166.443i −0.973587 0.228317i
\(730\) 1038.22 115.203i 1.42222 0.157813i
\(731\) 50.2711 0.0687703
\(732\) −370.017 + 195.091i −0.505488 + 0.266517i
\(733\) −672.443 + 672.443i −0.917385 + 0.917385i −0.996839 0.0794540i \(-0.974682\pi\)
0.0794540 + 0.996839i \(0.474682\pi\)
\(734\) 699.372i 0.952823i
\(735\) 264.774 685.653i 0.360237 0.932861i
\(736\) −126.667 −0.172102
\(737\) 322.736 + 322.736i 0.437906 + 0.437906i
\(738\) −161.936 + 30.3075i −0.219425 + 0.0410670i
\(739\) 540.207i 0.730997i −0.930812 0.365498i \(-0.880899\pi\)
0.930812 0.365498i \(-0.119101\pi\)
\(740\) 717.927 + 574.514i 0.970171 + 0.776371i
\(741\) −151.082 + 488.077i −0.203889 + 0.658673i
\(742\) 256.055 + 818.246i 0.345088 + 1.10276i
\(743\) 164.151 164.151i 0.220931 0.220931i −0.587960 0.808890i \(-0.700069\pi\)
0.808890 + 0.587960i \(0.200069\pi\)
\(744\) 175.528 + 54.3337i 0.235924 + 0.0730292i
\(745\) −459.497 + 50.9869i −0.616774 + 0.0684388i
\(746\) 875.339i 1.17338i
\(747\) −528.436 + 98.9005i −0.707411 + 0.132397i
\(748\) −37.2655 + 37.2655i −0.0498202 + 0.0498202i
\(749\) −169.258 + 323.439i −0.225979 + 0.431827i
\(750\) 1000.20 31.3570i 1.33360 0.0418094i
\(751\) −12.8996 −0.0171766 −0.00858830 0.999963i \(-0.502734\pi\)
−0.00858830 + 0.999963i \(0.502734\pi\)
\(752\) 104.140 104.140i 0.138484 0.138484i
\(753\) −673.883 + 355.304i −0.894932 + 0.471851i
\(754\) −965.563 −1.28059
\(755\) −60.9674 + 6.76510i −0.0807515 + 0.00896039i
\(756\) −110.301 579.449i −0.145901 0.766467i
\(757\) −328.630 + 328.630i −0.434121 + 0.434121i −0.890028 0.455906i \(-0.849315\pi\)
0.455906 + 0.890028i \(0.349315\pi\)
\(758\) 63.6329 63.6329i 0.0839484 0.0839484i
\(759\) 159.966 + 49.5166i 0.210759 + 0.0652393i
\(760\) −79.2345 + 99.0133i −0.104256 + 0.130281i
\(761\) 984.602 1.29383 0.646913 0.762564i \(-0.276060\pi\)
0.646913 + 0.762564i \(0.276060\pi\)
\(762\) 1479.08 779.842i 1.94105 1.02342i
\(763\) −359.468 + 112.489i −0.471124 + 0.147430i
\(764\) 375.240 0.491152
\(765\) 12.3597 + 40.5980i 0.0161565 + 0.0530693i
\(766\) 1332.26i 1.73924i
\(767\) 1112.65 + 1112.65i 1.45066 + 1.45066i
\(768\) −873.897 + 460.760i −1.13789 + 0.599948i
\(769\) 293.762 0.382006 0.191003 0.981589i \(-0.438826\pi\)
0.191003 + 0.981589i \(0.438826\pi\)
\(770\) −1558.23 607.268i −2.02368 0.788660i
\(771\) 371.293 1199.48i 0.481574 1.55575i
\(772\) 40.1504 40.1504i 0.0520083 0.0520083i
\(773\) 400.965 + 400.965i 0.518712 + 0.518712i 0.917182 0.398469i \(-0.130458\pi\)
−0.398469 + 0.917182i \(0.630458\pi\)
\(774\) 1056.35 + 723.277i 1.36479 + 0.934467i
\(775\) 143.097 + 636.858i 0.184641 + 0.821752i
\(776\) 37.1298 0.0478477
\(777\) −1237.42 + 3.82063i −1.59256 + 0.00491715i
\(778\) 420.713 + 420.713i 0.540763 + 0.540763i
\(779\) 74.1668 0.0952077
\(780\) −724.185 139.035i −0.928443 0.178250i
\(781\) 113.806 0.145719
\(782\) 5.54713 5.54713i 0.00709351 0.00709351i
\(783\) −71.2746 + 616.104i −0.0910276 + 0.786850i
\(784\) −754.599 + 523.545i −0.962499 + 0.667787i
\(785\) 352.958 + 282.451i 0.449628 + 0.359810i
\(786\) −1003.92 310.759i −1.27725 0.395367i
\(787\) 988.607 + 988.607i 1.25617 + 1.25617i 0.952906 + 0.303265i \(0.0980766\pi\)
0.303265 + 0.952906i \(0.401923\pi\)
\(788\) −24.4067 + 24.4067i −0.0309730 + 0.0309730i
\(789\) −2.17264 + 7.01881i −0.00275366 + 0.00889583i
\(790\) 498.385 622.794i 0.630867 0.788347i
\(791\) −732.702 383.429i −0.926299 0.484740i
\(792\) 371.588 69.5454i 0.469177 0.0878098i
\(793\) −497.625 497.625i −0.627522 0.627522i
\(794\) 1957.15i 2.46492i
\(795\) 129.811 676.138i 0.163284 0.850488i
\(796\) 939.895i 1.18077i
\(797\) −0.660026 + 0.660026i −0.000828138 + 0.000828138i −0.707521 0.706693i \(-0.750186\pi\)
0.706693 + 0.707521i \(0.250186\pi\)
\(798\) 1.87070 + 605.879i 0.00234423 + 0.759247i
\(799\) 7.41006i 0.00927416i
\(800\) −858.312 543.367i −1.07289 0.679208i
\(801\) −433.829 297.042i −0.541610 0.370838i
\(802\) 628.397 628.397i 0.783538 0.783538i
\(803\) 991.273 + 991.273i 1.23446 + 1.23446i
\(804\) 227.981 + 70.5703i 0.283558 + 0.0877740i
\(805\) 101.658 + 39.6176i 0.126283 + 0.0492144i
\(806\) 1097.49i 1.36165i
\(807\) −561.008 1064.03i −0.695178 1.31850i
\(808\) −19.7754 + 19.7754i −0.0244745 + 0.0244745i
\(809\) −327.649 −0.405006 −0.202503 0.979282i \(-0.564908\pi\)
−0.202503 + 0.979282i \(0.564908\pi\)
\(810\) −324.390 + 1030.91i −0.400482 + 1.27273i
\(811\) 729.399i 0.899382i −0.893184 0.449691i \(-0.851534\pi\)
0.893184 0.449691i \(-0.148466\pi\)
\(812\) −478.929 + 149.872i −0.589814 + 0.184572i
\(813\) −553.837 1050.43i −0.681227 1.29204i
\(814\) 2815.58i 3.45894i
\(815\) −56.8276 45.4758i −0.0697272 0.0557985i
\(816\) 15.6808 50.6574i 0.0192166 0.0620802i
\(817\) −407.534 407.534i −0.498818 0.498818i
\(818\) 1197.34 + 1197.34i 1.46374 + 1.46374i
\(819\) 876.401 465.544i 1.07009 0.568430i
\(820\) 11.8054 + 106.391i 0.0143968 + 0.129745i
\(821\) 413.667i 0.503858i 0.967746 + 0.251929i \(0.0810649\pi\)
−0.967746 + 0.251929i \(0.918935\pi\)
\(822\) −359.672 682.168i −0.437557 0.829888i
\(823\) 537.571 + 537.571i 0.653184 + 0.653184i 0.953758 0.300574i \(-0.0971783\pi\)
−0.300574 + 0.953758i \(0.597178\pi\)
\(824\) 81.0616i 0.0983757i
\(825\) 871.535 + 1021.74i 1.05641 + 1.23847i
\(826\) 1653.28 + 865.175i 2.00155 + 1.04743i
\(827\) −652.909 652.909i −0.789491 0.789491i 0.191920 0.981411i \(-0.438529\pi\)
−0.981411 + 0.191920i \(0.938529\pi\)
\(828\) 86.0646 16.1076i 0.103943 0.0194536i
\(829\) −167.399 −0.201928 −0.100964 0.994890i \(-0.532193\pi\)
−0.100964 + 0.994890i \(0.532193\pi\)
\(830\) 87.8987 + 792.148i 0.105902 + 0.954395i
\(831\) 50.9618 164.634i 0.0613259 0.198116i
\(832\) 372.663 + 372.663i 0.447913 + 0.447913i
\(833\) 8.22028 45.4729i 0.00986828 0.0545894i
\(834\) 230.295 + 71.2869i 0.276134 + 0.0854759i
\(835\) −255.060 + 318.729i −0.305461 + 0.381712i
\(836\) 604.204 0.722732
\(837\) −700.284 81.0132i −0.836660 0.0967899i
\(838\) 783.255 783.255i 0.934672 0.934672i
\(839\) 906.507i 1.08046i −0.841517 0.540231i \(-0.818337\pi\)
0.841517 0.540231i \(-0.181663\pi\)
\(840\) 244.724 27.9204i 0.291338 0.0332386i
\(841\) −313.340 −0.372581
\(842\) −803.590 803.590i −0.954383 0.954383i
\(843\) −398.611 756.023i −0.472848 0.896824i
\(844\) 1134.78i 1.34453i
\(845\) −43.6319 393.213i −0.0516354 0.465341i
\(846\) −106.612 + 155.708i −0.126020 + 0.184051i
\(847\) −417.330 1333.61i −0.492715 1.57451i
\(848\) −608.332 + 608.332i −0.717373 + 0.717373i
\(849\) 128.789 416.058i 0.151695 0.490056i
\(850\) 61.3836 13.7924i 0.0722160 0.0162263i
\(851\) 183.686i 0.215847i
\(852\) 52.6390 27.7538i 0.0617828 0.0325749i
\(853\) 759.174 759.174i 0.890005 0.890005i −0.104518 0.994523i \(-0.533330\pi\)
0.994523 + 0.104518i \(0.0333301\pi\)
\(854\) −739.415 386.942i −0.865826 0.453094i
\(855\) 228.920 429.315i 0.267743 0.502122i
\(856\) −122.335 −0.142914
\(857\) 188.854 188.854i 0.220366 0.220366i −0.588287 0.808652i \(-0.700197\pi\)
0.808652 + 0.588287i \(0.200197\pi\)
\(858\) −1053.11 1997.38i −1.22741 2.32795i
\(859\) −997.171 −1.16085 −0.580425 0.814313i \(-0.697114\pi\)
−0.580425 + 0.814313i \(0.697114\pi\)
\(860\) 519.732 649.469i 0.604339 0.755196i
\(861\) −102.176 101.547i −0.118672 0.117941i
\(862\) −411.185 + 411.185i −0.477013 + 0.477013i
\(863\) −1003.10 + 1003.10i −1.16234 + 1.16234i −0.178383 + 0.983961i \(0.557087\pi\)
−0.983961 + 0.178383i \(0.942913\pi\)
\(864\) 859.791 681.486i 0.995128 0.788757i
\(865\) 988.857 + 791.324i 1.14319 + 0.914825i
\(866\) 1425.51 1.64609
\(867\) −403.117 764.569i −0.464957 0.881856i
\(868\) −170.350 544.367i −0.196256 0.627151i
\(869\) 1070.48 1.23185
\(870\) 902.976 + 173.361i 1.03790 + 0.199265i
\(871\) 401.512i 0.460978i
\(872\) −89.2544 89.2544i −0.102356 0.102356i
\(873\) −140.021 + 26.2060i −0.160391 + 0.0300183i
\(874\) −89.9382 −0.102904
\(875\) 518.896 + 704.537i 0.593024 + 0.805185i
\(876\) 700.234 + 216.754i 0.799354 + 0.247436i
\(877\) −1130.81 + 1130.81i −1.28940 + 1.28940i −0.354252 + 0.935150i \(0.615264\pi\)
−0.935150 + 0.354252i \(0.884736\pi\)
\(878\) 35.6018 + 35.6018i 0.0405488 + 0.0405488i
\(879\) 827.715 + 256.215i 0.941655 + 0.291485i
\(880\) −185.072 1667.88i −0.210309 1.89531i
\(881\) −778.866 −0.884071 −0.442035 0.896998i \(-0.645743\pi\)
−0.442035 + 0.896998i \(0.645743\pi\)
\(882\) 826.977 837.254i 0.937615 0.949267i
\(883\) 311.479 + 311.479i 0.352751 + 0.352751i 0.861132 0.508381i \(-0.169756\pi\)
−0.508381 + 0.861132i \(0.669756\pi\)
\(884\) −46.3616 −0.0524452
\(885\) −840.763 1240.30i −0.950014 1.40147i
\(886\) −1828.38 −2.06363
\(887\) −534.557 + 534.557i −0.602657 + 0.602657i −0.941017 0.338360i \(-0.890128\pi\)
0.338360 + 0.941017i \(0.390128\pi\)
\(888\) −193.405 366.820i −0.217799 0.413086i
\(889\) 1295.40 + 677.895i 1.45715 + 0.762537i
\(890\) −487.018 + 608.589i −0.547211 + 0.683808i
\(891\) −1352.22 + 524.528i −1.51764 + 0.588696i
\(892\) 66.0609 + 66.0609i 0.0740593 + 0.0740593i
\(893\) 60.0714 60.0714i 0.0672692 0.0672692i
\(894\) −707.114 218.884i −0.790956 0.244837i
\(895\) 1530.18 169.793i 1.70970 0.189712i
\(896\) −454.326 237.753i −0.507061 0.265349i
\(897\) 68.7042 + 130.307i 0.0765933 + 0.145270i
\(898\) −1511.81 1511.81i −1.68353 1.68353i
\(899\) 599.756i 0.667137i
\(900\) 652.281 + 260.046i 0.724757 + 0.288940i
\(901\) 43.2856i 0.0480418i
\(902\) −231.772 + 231.772i −0.256954 + 0.256954i
\(903\) 3.45631 + 1119.43i 0.00382759 + 1.23968i
\(904\) 277.131i 0.306561i
\(905\) 68.9106 + 621.026i 0.0761443 + 0.686216i
\(906\) −93.8221 29.0422i −0.103556 0.0320554i
\(907\) 228.099 228.099i 0.251487 0.251487i −0.570093 0.821580i \(-0.693093\pi\)
0.821580 + 0.570093i \(0.193093\pi\)
\(908\) −595.971 595.971i −0.656356 0.656356i
\(909\) 60.6180 88.5326i 0.0666865 0.0973956i
\(910\) −591.542 1347.04i −0.650046 1.48026i
\(911\) 4.69642i 0.00515524i −0.999997 0.00257762i \(-0.999180\pi\)
0.999997 0.00257762i \(-0.000820483\pi\)
\(912\) −537.786 + 283.547i −0.589678 + 0.310906i
\(913\) −756.328 + 756.328i −0.828399 + 0.828399i
\(914\) 1539.27 1.68410
\(915\) 376.024 + 554.715i 0.410955 + 0.606246i
\(916\) 262.665i 0.286752i
\(917\) −274.435 876.981i −0.299275 0.956359i
\(918\) −7.80847 + 67.4970i −0.00850596 + 0.0735262i
\(919\) 920.349i 1.00147i 0.865601 + 0.500734i \(0.166937\pi\)
−0.865601 + 0.500734i \(0.833063\pi\)
\(920\) 4.03237 + 36.3399i 0.00438301 + 0.0394999i
\(921\) 850.347 + 263.221i 0.923286 + 0.285799i
\(922\) 1183.66 + 1183.66i 1.28379 + 1.28379i
\(923\) 70.7926 + 70.7926i 0.0766983 + 0.0766983i
\(924\) −832.384 827.260i −0.900848 0.895303i
\(925\) 787.961 1244.68i 0.851849 1.34560i
\(926\) 2173.78i 2.34749i
\(927\) −57.2126 305.693i −0.0617181 0.329766i
\(928\) −660.010 660.010i −0.711218 0.711218i
\(929\) 1603.42i 1.72597i −0.505233 0.862983i \(-0.668593\pi\)
0.505233 0.862983i \(-0.331407\pi\)
\(930\) −197.048 + 1026.35i −0.211879 + 1.10361i
\(931\) −435.277 + 301.998i −0.467537 + 0.324380i
\(932\) 709.901 + 709.901i 0.761697 + 0.761697i
\(933\) −1101.20 + 580.604i −1.18028 + 0.622298i
\(934\) 903.974 0.967853
\(935\) 65.9229 + 52.7542i 0.0705058 + 0.0564216i
\(936\) 274.404 + 187.884i 0.293167 + 0.200731i
\(937\) −858.211 858.211i −0.915914 0.915914i 0.0808153 0.996729i \(-0.474248\pi\)
−0.996729 + 0.0808153i \(0.974248\pi\)
\(938\) 142.198 + 454.405i 0.151597 + 0.484440i
\(939\) 7.59407 24.5330i 0.00808740 0.0261267i
\(940\) 95.7330 + 76.6095i 0.101844 + 0.0814994i
\(941\) 1155.36 1.22780 0.613900 0.789384i \(-0.289600\pi\)
0.613900 + 0.789384i \(0.289600\pi\)
\(942\) 337.572 + 640.253i 0.358356 + 0.679674i
\(943\) 15.1206 15.1206i 0.0160346 0.0160346i
\(944\) 1872.37i 1.98344i
\(945\) −903.179 + 278.016i −0.955745 + 0.294196i
\(946\) 2547.10 2.69250
\(947\) 119.546 + 119.546i 0.126236 + 0.126236i 0.767402 0.641166i \(-0.221549\pi\)
−0.641166 + 0.767402i \(0.721549\pi\)
\(948\) 495.130 261.056i 0.522289 0.275376i
\(949\) 1233.23i 1.29950i
\(950\) −609.432 385.810i −0.641508 0.406115i
\(951\) −1035.53 320.542i −1.08888 0.337058i
\(952\) 14.7791 4.62484i 0.0155242 0.00485803i
\(953\) 567.636 567.636i 0.595631 0.595631i −0.343516 0.939147i \(-0.611618\pi\)
0.939147 + 0.343516i \(0.111618\pi\)
\(954\) 622.774 909.561i 0.652803 0.953419i
\(955\) −66.3003 597.502i −0.0694244 0.625657i
\(956\) 59.5634i 0.0623048i
\(957\) 575.505 + 1091.53i 0.601363 + 1.14057i
\(958\) −1639.16 + 1639.16i −1.71102 + 1.71102i
\(959\) 312.653 597.454i 0.326019 0.622997i
\(960\) −281.598 415.417i −0.293332 0.432726i
\(961\) 279.297 0.290632
\(962\) −1751.41 + 1751.41i −1.82060 + 1.82060i
\(963\) 461.339 86.3428i 0.479064 0.0896602i
\(964\) 1078.04 1.11830
\(965\) −71.0263 56.8381i −0.0736024 0.0588996i
\(966\) 123.904 + 123.141i 0.128265 + 0.127475i
\(967\) −102.432 + 102.432i −0.105928 + 0.105928i −0.758084 0.652157i \(-0.773864\pi\)
0.652157 + 0.758084i \(0.273864\pi\)
\(968\) 331.130 331.130i 0.342077 0.342077i
\(969\) 9.04517 29.2208i 0.00933454 0.0301556i
\(970\) 23.2908 + 209.898i 0.0240111 + 0.216390i
\(971\) −753.100 −0.775592 −0.387796 0.921745i \(-0.626764\pi\)
−0.387796 + 0.921745i \(0.626764\pi\)
\(972\) −497.528 + 572.374i −0.511860 + 0.588862i
\(973\) 62.9545 + 201.176i 0.0647014 + 0.206759i
\(974\) −7.08418 −0.00727328
\(975\) −93.4336 + 1177.70i −0.0958293 + 1.20790i
\(976\) 837.400i 0.857992i
\(977\) 755.362 + 755.362i 0.773145 + 0.773145i 0.978655 0.205510i \(-0.0658854\pi\)
−0.205510 + 0.978655i \(0.565885\pi\)
\(978\) −54.3504 103.083i −0.0555730 0.105402i
\(979\) −1046.07 −1.06850
\(980\) −502.494 576.326i −0.512749 0.588088i
\(981\) 399.584 + 273.594i 0.407323 + 0.278893i
\(982\) −236.435 + 236.435i −0.240769 + 0.240769i
\(983\) −224.108 224.108i −0.227984 0.227984i 0.583866 0.811850i \(-0.301539\pi\)
−0.811850 + 0.583866i \(0.801539\pi\)
\(984\) 14.2752 46.1165i 0.0145073 0.0468664i
\(985\) 43.1756 + 34.5509i 0.0438331 + 0.0350770i
\(986\) 57.8076 0.0586284
\(987\) −165.006 + 0.509467i −0.167179 + 0.000516178i
\(988\) 375.841 + 375.841i 0.380406 + 0.380406i
\(989\) −166.170 −0.168019
\(990\) 626.235 + 2056.99i 0.632561 + 2.07777i
\(991\) −175.163 −0.176753 −0.0883767 0.996087i \(-0.528168\pi\)
−0.0883767 + 0.996087i \(0.528168\pi\)
\(992\) 750.190 750.190i 0.756240 0.756240i
\(993\) −394.134 + 207.806i −0.396912 + 0.209271i
\(994\) 105.190 + 55.0467i 0.105825 + 0.0553790i
\(995\) −1496.61 + 166.068i −1.50413 + 0.166902i
\(996\) −165.381 + 534.270i −0.166045 + 0.536415i
\(997\) 265.876 + 265.876i 0.266676 + 0.266676i 0.827759 0.561084i \(-0.189615\pi\)
−0.561084 + 0.827759i \(0.689615\pi\)
\(998\) −804.862 + 804.862i −0.806475 + 0.806475i
\(999\) 988.254 + 1246.82i 0.989243 + 1.24807i
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 105.3.k.d.83.5 yes 32
3.2 odd 2 inner 105.3.k.d.83.11 yes 32
5.2 odd 4 inner 105.3.k.d.62.12 yes 32
7.6 odd 2 inner 105.3.k.d.83.6 yes 32
15.2 even 4 inner 105.3.k.d.62.6 yes 32
21.20 even 2 inner 105.3.k.d.83.12 yes 32
35.27 even 4 inner 105.3.k.d.62.11 yes 32
105.62 odd 4 inner 105.3.k.d.62.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.k.d.62.5 32 105.62 odd 4 inner
105.3.k.d.62.6 yes 32 15.2 even 4 inner
105.3.k.d.62.11 yes 32 35.27 even 4 inner
105.3.k.d.62.12 yes 32 5.2 odd 4 inner
105.3.k.d.83.5 yes 32 1.1 even 1 trivial
105.3.k.d.83.6 yes 32 7.6 odd 2 inner
105.3.k.d.83.11 yes 32 3.2 odd 2 inner
105.3.k.d.83.12 yes 32 21.20 even 2 inner