Properties

Label 105.4.q.b.4.19
Level $105$
Weight $4$
Character 105.4
Analytic conductor $6.195$
Analytic rank $0$
Dimension $44$
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] = [105,4,Mod(4,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.q (of order \(6\), 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: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.19
Character \(\chi\) \(=\) 105.4
Dual form 105.4.q.b.79.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.00489 - 1.73487i) q^{2} +(2.59808 + 1.50000i) q^{3} +(2.01958 - 3.49802i) q^{4} +(1.37289 - 11.0957i) q^{5} +10.4092 q^{6} +(12.4845 - 13.6798i) q^{7} +13.7431i q^{8} +(4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(3.00489 - 1.73487i) q^{2} +(2.59808 + 1.50000i) q^{3} +(2.01958 - 3.49802i) q^{4} +(1.37289 - 11.0957i) q^{5} +10.4092 q^{6} +(12.4845 - 13.6798i) q^{7} +13.7431i q^{8} +(4.50000 + 7.79423i) q^{9} +(-15.1243 - 35.7232i) q^{10} +(13.2857 - 23.0115i) q^{11} +(10.4940 - 6.05874i) q^{12} +8.46682i q^{13} +(13.7819 - 62.7654i) q^{14} +(20.2105 - 26.7682i) q^{15} +(39.9992 + 69.2807i) q^{16} +(-34.8477 - 20.1193i) q^{17} +(27.0440 + 15.6139i) q^{18} +(50.5336 + 87.5268i) q^{19} +(-36.0404 - 27.2111i) q^{20} +(52.9554 - 16.8143i) q^{21} -92.1959i q^{22} +(-123.891 + 71.5282i) q^{23} +(-20.6147 + 35.7057i) q^{24} +(-121.230 - 30.4663i) q^{25} +(14.6889 + 25.4419i) q^{26} +27.0000i q^{27} +(-22.6386 - 71.2985i) q^{28} -80.4405 q^{29} +(14.2907 - 115.498i) q^{30} +(20.1857 - 34.9627i) q^{31} +(145.172 + 83.8148i) q^{32} +(69.0344 - 39.8570i) q^{33} -139.618 q^{34} +(-134.647 - 157.306i) q^{35} +36.3524 q^{36} +(-252.167 + 145.589i) q^{37} +(303.696 + 175.339i) q^{38} +(-12.7002 + 21.9974i) q^{39} +(152.490 + 18.8677i) q^{40} -16.7260 q^{41} +(129.955 - 142.396i) q^{42} +435.792i q^{43} +(-53.6630 - 92.9470i) q^{44} +(92.6606 - 39.2302i) q^{45} +(-248.185 + 429.869i) q^{46} +(278.455 - 160.766i) q^{47} +239.995i q^{48} +(-31.2731 - 341.571i) q^{49} +(-417.139 + 118.771i) q^{50} +(-60.3580 - 104.543i) q^{51} +(29.6171 + 17.0994i) q^{52} +(187.426 + 108.210i) q^{53} +(46.8416 + 81.1321i) q^{54} +(-237.089 - 179.006i) q^{55} +(188.003 + 171.576i) q^{56} +303.202i q^{57} +(-241.715 + 139.554i) q^{58} +(246.925 - 427.686i) q^{59} +(-52.8190 - 124.757i) q^{60} +(392.971 + 680.646i) q^{61} -140.079i q^{62} +(162.804 + 35.7482i) q^{63} -58.3547 q^{64} +(93.9455 + 11.6240i) q^{65} +(138.294 - 239.532i) q^{66} +(-629.817 - 363.625i) q^{67} +(-140.756 + 81.2653i) q^{68} -429.169 q^{69} +(-677.506 - 239.090i) q^{70} +546.448 q^{71} +(-107.117 + 61.8440i) q^{72} +(-288.341 - 166.474i) q^{73} +(-505.157 + 874.958i) q^{74} +(-269.266 - 260.999i) q^{75} +408.227 q^{76} +(-148.926 - 469.032i) q^{77} +88.1332i q^{78} +(-385.859 - 668.327i) q^{79} +(823.634 - 348.706i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-50.2597 + 29.0174i) q^{82} -1025.32i q^{83} +(48.1310 - 219.197i) q^{84} +(-271.081 + 359.039i) q^{85} +(756.044 + 1309.51i) q^{86} +(-208.990 - 120.661i) q^{87} +(316.249 + 182.587i) q^{88} +(428.219 + 741.697i) q^{89} +(210.376 - 278.637i) q^{90} +(115.824 + 105.704i) q^{91} +577.828i q^{92} +(104.888 - 60.5571i) q^{93} +(557.817 - 966.167i) q^{94} +(1040.55 - 440.543i) q^{95} +(251.445 + 435.515i) q^{96} -127.420i q^{97} +(-686.556 - 972.130i) q^{98} +239.142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 62 q^{4} - 4 q^{5} + 108 q^{6} + 198 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 62 q^{4} - 4 q^{5} + 108 q^{6} + 198 q^{9} - 92 q^{10} - 174 q^{11} + 254 q^{14} + 48 q^{15} - 262 q^{16} + 38 q^{19} - 816 q^{20} - 174 q^{21} + 558 q^{24} - 24 q^{25} - 586 q^{26} - 1024 q^{29} + 84 q^{30} - 912 q^{31} + 1112 q^{34} - 690 q^{35} + 1116 q^{36} - 390 q^{39} + 552 q^{40} - 356 q^{41} + 1114 q^{44} + 36 q^{45} + 1502 q^{46} + 24 q^{49} + 5768 q^{50} - 516 q^{51} + 486 q^{54} + 2444 q^{55} + 972 q^{56} + 2200 q^{59} + 216 q^{60} - 1068 q^{61} - 13180 q^{64} - 154 q^{65} - 390 q^{66} - 1356 q^{69} - 5870 q^{70} + 4392 q^{71} - 2342 q^{74} - 576 q^{75} - 4948 q^{76} - 464 q^{79} - 5588 q^{80} - 1782 q^{81} + 4278 q^{84} + 6880 q^{85} - 2948 q^{86} + 5684 q^{89} - 1656 q^{90} - 4192 q^{91} + 8762 q^{94} + 5212 q^{95} - 5778 q^{96} - 3132 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00489 1.73487i 1.06239 0.613371i 0.136297 0.990668i \(-0.456480\pi\)
0.926092 + 0.377297i \(0.123146\pi\)
\(3\) 2.59808 + 1.50000i 0.500000 + 0.288675i
\(4\) 2.01958 3.49802i 0.252448 0.437252i
\(5\) 1.37289 11.0957i 0.122795 0.992432i
\(6\) 10.4092 0.708260
\(7\) 12.4845 13.6798i 0.674101 0.738639i
\(8\) 13.7431i 0.607366i
\(9\) 4.50000 + 7.79423i 0.166667 + 0.288675i
\(10\) −15.1243 35.7232i −0.478273 1.12967i
\(11\) 13.2857 23.0115i 0.364162 0.630747i −0.624479 0.781041i \(-0.714689\pi\)
0.988641 + 0.150294i \(0.0480222\pi\)
\(12\) 10.4940 6.05874i 0.252448 0.145751i
\(13\) 8.46682i 0.180636i 0.995913 + 0.0903182i \(0.0287884\pi\)
−0.995913 + 0.0903182i \(0.971212\pi\)
\(14\) 13.7819 62.7654i 0.263098 1.19820i
\(15\) 20.2105 26.7682i 0.347888 0.460768i
\(16\) 39.9992 + 69.2807i 0.624988 + 1.08251i
\(17\) −34.8477 20.1193i −0.497165 0.287039i 0.230377 0.973102i \(-0.426004\pi\)
−0.727542 + 0.686063i \(0.759337\pi\)
\(18\) 27.0440 + 15.6139i 0.354130 + 0.204457i
\(19\) 50.5336 + 87.5268i 0.610169 + 1.05684i 0.991212 + 0.132286i \(0.0422316\pi\)
−0.381043 + 0.924557i \(0.624435\pi\)
\(20\) −36.0404 27.2111i −0.402944 0.304229i
\(21\) 52.9554 16.8143i 0.550277 0.174723i
\(22\) 92.1959i 0.893465i
\(23\) −123.891 + 71.5282i −1.12317 + 0.648464i −0.942209 0.335026i \(-0.891255\pi\)
−0.180963 + 0.983490i \(0.557922\pi\)
\(24\) −20.6147 + 35.7057i −0.175331 + 0.303683i
\(25\) −121.230 30.4663i −0.969843 0.243731i
\(26\) 14.6889 + 25.4419i 0.110797 + 0.191906i
\(27\) 27.0000i 0.192450i
\(28\) −22.6386 71.2985i −0.152796 0.481220i
\(29\) −80.4405 −0.515083 −0.257542 0.966267i \(-0.582912\pi\)
−0.257542 + 0.966267i \(0.582912\pi\)
\(30\) 14.2907 115.498i 0.0869705 0.702900i
\(31\) 20.1857 34.9627i 0.116950 0.202564i −0.801607 0.597851i \(-0.796022\pi\)
0.918558 + 0.395287i \(0.129355\pi\)
\(32\) 145.172 + 83.8148i 0.801967 + 0.463016i
\(33\) 69.0344 39.8570i 0.364162 0.210249i
\(34\) −139.618 −0.704244
\(35\) −134.647 157.306i −0.650273 0.759701i
\(36\) 36.3524 0.168298
\(37\) −252.167 + 145.589i −1.12043 + 0.646883i −0.941512 0.336980i \(-0.890595\pi\)
−0.178923 + 0.983863i \(0.557261\pi\)
\(38\) 303.696 + 175.339i 1.29647 + 0.748519i
\(39\) −12.7002 + 21.9974i −0.0521452 + 0.0903182i
\(40\) 152.490 + 18.8677i 0.602769 + 0.0745813i
\(41\) −16.7260 −0.0637111 −0.0318556 0.999492i \(-0.510142\pi\)
−0.0318556 + 0.999492i \(0.510142\pi\)
\(42\) 129.955 142.396i 0.477439 0.523148i
\(43\) 435.792i 1.54553i 0.634695 + 0.772763i \(0.281126\pi\)
−0.634695 + 0.772763i \(0.718874\pi\)
\(44\) −53.6630 92.9470i −0.183864 0.318461i
\(45\) 92.6606 39.2302i 0.306956 0.129958i
\(46\) −248.185 + 429.869i −0.795497 + 1.37784i
\(47\) 278.455 160.766i 0.864187 0.498938i −0.00122547 0.999999i \(-0.500390\pi\)
0.865412 + 0.501061i \(0.167057\pi\)
\(48\) 239.995i 0.721674i
\(49\) −31.2731 341.571i −0.0911752 0.995835i
\(50\) −417.139 + 118.771i −1.17985 + 0.335936i
\(51\) −60.3580 104.543i −0.165722 0.287039i
\(52\) 29.6171 + 17.0994i 0.0789836 + 0.0456012i
\(53\) 187.426 + 108.210i 0.485753 + 0.280450i 0.722811 0.691046i \(-0.242850\pi\)
−0.237058 + 0.971496i \(0.576183\pi\)
\(54\) 46.8416 + 81.1321i 0.118043 + 0.204457i
\(55\) −237.089 179.006i −0.581256 0.438858i
\(56\) 188.003 + 171.576i 0.448624 + 0.409426i
\(57\) 303.202i 0.704562i
\(58\) −241.715 + 139.554i −0.547219 + 0.315937i
\(59\) 246.925 427.686i 0.544862 0.943729i −0.453753 0.891127i \(-0.649915\pi\)
0.998616 0.0526020i \(-0.0167515\pi\)
\(60\) −52.8190 124.757i −0.113648 0.268434i
\(61\) 392.971 + 680.646i 0.824833 + 1.42865i 0.902047 + 0.431638i \(0.142064\pi\)
−0.0772143 + 0.997015i \(0.524603\pi\)
\(62\) 140.079i 0.286936i
\(63\) 162.804 + 35.7482i 0.325577 + 0.0714897i
\(64\) −58.3547 −0.113974
\(65\) 93.9455 + 11.6240i 0.179269 + 0.0221812i
\(66\) 138.294 239.532i 0.257921 0.446733i
\(67\) −629.817 363.625i −1.14842 0.663042i −0.199921 0.979812i \(-0.564068\pi\)
−0.948502 + 0.316770i \(0.897402\pi\)
\(68\) −140.756 + 81.2653i −0.251016 + 0.144924i
\(69\) −429.169 −0.748781
\(70\) −677.506 239.090i −1.15682 0.408239i
\(71\) 546.448 0.913400 0.456700 0.889621i \(-0.349031\pi\)
0.456700 + 0.889621i \(0.349031\pi\)
\(72\) −107.117 + 61.8440i −0.175331 + 0.101228i
\(73\) −288.341 166.474i −0.462298 0.266908i 0.250712 0.968062i \(-0.419335\pi\)
−0.713010 + 0.701154i \(0.752669\pi\)
\(74\) −505.157 + 874.958i −0.793559 + 1.37448i
\(75\) −269.266 260.999i −0.414562 0.401835i
\(76\) 408.227 0.616142
\(77\) −148.926 469.032i −0.220412 0.694171i
\(78\) 88.1332i 0.127937i
\(79\) −385.859 668.327i −0.549526 0.951806i −0.998307 0.0581646i \(-0.981475\pi\)
0.448781 0.893642i \(-0.351858\pi\)
\(80\) 823.634 348.706i 1.15106 0.487332i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −50.2597 + 29.0174i −0.0676860 + 0.0390785i
\(83\) 1025.32i 1.35595i −0.735084 0.677976i \(-0.762857\pi\)
0.735084 0.677976i \(-0.237143\pi\)
\(84\) 48.1310 219.197i 0.0625181 0.284718i
\(85\) −271.081 + 359.039i −0.345916 + 0.458156i
\(86\) 756.044 + 1309.51i 0.947980 + 1.64195i
\(87\) −208.990 120.661i −0.257542 0.148692i
\(88\) 316.249 + 182.587i 0.383094 + 0.221179i
\(89\) 428.219 + 741.697i 0.510012 + 0.883367i 0.999933 + 0.0116000i \(0.00369247\pi\)
−0.489920 + 0.871767i \(0.662974\pi\)
\(90\) 210.376 278.637i 0.246395 0.326344i
\(91\) 115.824 + 105.704i 0.133425 + 0.121767i
\(92\) 577.828i 0.654812i
\(93\) 104.888 60.5571i 0.116950 0.0675213i
\(94\) 557.817 966.167i 0.612068 1.06013i
\(95\) 1040.55 440.543i 1.12377 0.475776i
\(96\) 251.445 + 435.515i 0.267322 + 0.463016i
\(97\) 127.420i 0.133377i −0.997774 0.0666883i \(-0.978757\pi\)
0.997774 0.0666883i \(-0.0212433\pi\)
\(98\) −686.556 972.130i −0.707680 1.00204i
\(99\) 239.142 0.242775
\(100\) −351.406 + 362.537i −0.351406 + 0.362537i
\(101\) 450.729 780.686i 0.444052 0.769121i −0.553934 0.832561i \(-0.686874\pi\)
0.997986 + 0.0634402i \(0.0202072\pi\)
\(102\) −362.739 209.427i −0.352122 0.203298i
\(103\) 321.096 185.385i 0.307170 0.177345i −0.338489 0.940970i \(-0.609916\pi\)
0.645660 + 0.763625i \(0.276583\pi\)
\(104\) −116.360 −0.109712
\(105\) −113.866 610.663i −0.105830 0.567568i
\(106\) 750.926 0.688079
\(107\) −892.421 + 515.240i −0.806296 + 0.465515i −0.845668 0.533710i \(-0.820798\pi\)
0.0393722 + 0.999225i \(0.487464\pi\)
\(108\) 94.4464 + 54.5287i 0.0841492 + 0.0485836i
\(109\) 942.880 1633.12i 0.828546 1.43508i −0.0706330 0.997502i \(-0.522502\pi\)
0.899179 0.437581i \(-0.144165\pi\)
\(110\) −1022.98 126.574i −0.886703 0.109713i
\(111\) −873.534 −0.746956
\(112\) 1447.12 + 317.756i 1.22089 + 0.268081i
\(113\) 2054.47i 1.71034i −0.518349 0.855169i \(-0.673453\pi\)
0.518349 0.855169i \(-0.326547\pi\)
\(114\) 526.017 + 911.088i 0.432158 + 0.748519i
\(115\) 623.570 + 1472.86i 0.505637 + 1.19430i
\(116\) −162.456 + 281.382i −0.130032 + 0.225221i
\(117\) −65.9923 + 38.1007i −0.0521452 + 0.0301061i
\(118\) 1713.54i 1.33681i
\(119\) −710.286 + 225.529i −0.547158 + 0.173733i
\(120\) 367.879 + 277.755i 0.279855 + 0.211295i
\(121\) 312.482 + 541.235i 0.234772 + 0.406638i
\(122\) 2361.67 + 1363.51i 1.75259 + 1.01186i
\(123\) −43.4553 25.0889i −0.0318556 0.0183918i
\(124\) −81.5333 141.220i −0.0590476 0.102273i
\(125\) −504.482 + 1303.31i −0.360978 + 0.932574i
\(126\) 551.226 175.025i 0.389739 0.123749i
\(127\) 1203.95i 0.841206i 0.907245 + 0.420603i \(0.138181\pi\)
−0.907245 + 0.420603i \(0.861819\pi\)
\(128\) −1336.72 + 771.757i −0.923052 + 0.532924i
\(129\) −653.687 + 1132.22i −0.446155 + 0.772763i
\(130\) 302.462 128.055i 0.204059 0.0863935i
\(131\) −1435.56 2486.46i −0.957445 1.65834i −0.728670 0.684865i \(-0.759861\pi\)
−0.228775 0.973479i \(-0.573472\pi\)
\(132\) 321.978i 0.212307i
\(133\) 1828.24 + 401.441i 1.19194 + 0.261725i
\(134\) −2523.37 −1.62676
\(135\) 299.585 + 37.0679i 0.190994 + 0.0236318i
\(136\) 276.502 478.916i 0.174337 0.301961i
\(137\) −1556.12 898.427i −0.970427 0.560276i −0.0710604 0.997472i \(-0.522638\pi\)
−0.899366 + 0.437196i \(0.855972\pi\)
\(138\) −1289.61 + 744.555i −0.795497 + 0.459281i
\(139\) −7.88277 −0.00481013 −0.00240506 0.999997i \(-0.500766\pi\)
−0.00240506 + 0.999997i \(0.500766\pi\)
\(140\) −822.189 + 153.307i −0.496340 + 0.0925486i
\(141\) 964.595 0.576124
\(142\) 1642.02 948.018i 0.970387 0.560253i
\(143\) 194.834 + 112.487i 0.113936 + 0.0657809i
\(144\) −359.993 + 623.526i −0.208329 + 0.360837i
\(145\) −110.436 + 892.546i −0.0632495 + 0.511185i
\(146\) −1155.24 −0.654854
\(147\) 431.107 934.338i 0.241885 0.524237i
\(148\) 1176.11i 0.653216i
\(149\) 1178.71 + 2041.59i 0.648080 + 1.12251i 0.983581 + 0.180467i \(0.0577609\pi\)
−0.335501 + 0.942040i \(0.608906\pi\)
\(150\) −1261.92 317.132i −0.686901 0.172625i
\(151\) −1719.08 + 2977.53i −0.926468 + 1.60469i −0.137286 + 0.990532i \(0.543838\pi\)
−0.789183 + 0.614159i \(0.789496\pi\)
\(152\) −1202.89 + 694.489i −0.641890 + 0.370595i
\(153\) 362.148i 0.191359i
\(154\) −1261.22 1151.02i −0.659948 0.602286i
\(155\) −360.223 271.975i −0.186670 0.140939i
\(156\) 51.2982 + 88.8512i 0.0263279 + 0.0456012i
\(157\) −1030.91 595.196i −0.524048 0.302559i 0.214541 0.976715i \(-0.431174\pi\)
−0.738589 + 0.674156i \(0.764508\pi\)
\(158\) −2318.93 1338.83i −1.16762 0.674126i
\(159\) 324.631 + 562.277i 0.161918 + 0.280450i
\(160\) 1129.29 1495.72i 0.557989 0.739042i
\(161\) −568.224 + 2587.79i −0.278151 + 1.26675i
\(162\) 281.050i 0.136305i
\(163\) −2223.76 + 1283.89i −1.06858 + 0.616945i −0.927793 0.373095i \(-0.878297\pi\)
−0.140787 + 0.990040i \(0.544963\pi\)
\(164\) −33.7794 + 58.5077i −0.0160837 + 0.0278578i
\(165\) −347.466 820.706i −0.163941 0.387223i
\(166\) −1778.81 3080.99i −0.831701 1.44055i
\(167\) 2994.69i 1.38764i 0.720149 + 0.693820i \(0.244074\pi\)
−0.720149 + 0.693820i \(0.755926\pi\)
\(168\) 231.081 + 727.773i 0.106121 + 0.334220i
\(169\) 2125.31 0.967371
\(170\) −191.680 + 1549.16i −0.0864775 + 0.698915i
\(171\) −454.802 + 787.741i −0.203390 + 0.352281i
\(172\) 1524.41 + 880.116i 0.675784 + 0.390164i
\(173\) 1890.39 1091.41i 0.830771 0.479646i −0.0233456 0.999727i \(-0.507432\pi\)
0.854117 + 0.520082i \(0.174098\pi\)
\(174\) −837.325 −0.364813
\(175\) −1930.28 + 1278.05i −0.833801 + 0.552065i
\(176\) 2125.67 0.910387
\(177\) 1283.06 740.775i 0.544862 0.314576i
\(178\) 2573.50 + 1485.81i 1.08366 + 0.625653i
\(179\) 1057.95 1832.42i 0.441760 0.765150i −0.556061 0.831142i \(-0.687688\pi\)
0.997820 + 0.0659917i \(0.0210211\pi\)
\(180\) 49.9078 403.357i 0.0206661 0.167025i
\(181\) −102.107 −0.0419314 −0.0209657 0.999780i \(-0.506674\pi\)
−0.0209657 + 0.999780i \(0.506674\pi\)
\(182\) 531.423 + 116.689i 0.216438 + 0.0475251i
\(183\) 2357.83i 0.952435i
\(184\) −983.021 1702.64i −0.393855 0.682176i
\(185\) 1269.22 + 2997.86i 0.504404 + 1.19139i
\(186\) 210.118 363.935i 0.0828312 0.143468i
\(187\) −925.951 + 534.598i −0.362097 + 0.209057i
\(188\) 1298.72i 0.503823i
\(189\) 369.354 + 337.082i 0.142151 + 0.129731i
\(190\) 2362.45 3129.01i 0.902054 1.19475i
\(191\) −374.792 649.158i −0.141984 0.245924i 0.786260 0.617896i \(-0.212015\pi\)
−0.928244 + 0.371973i \(0.878682\pi\)
\(192\) −151.610 87.5321i −0.0569871 0.0329015i
\(193\) 1215.06 + 701.516i 0.453171 + 0.261638i 0.709168 0.705039i \(-0.249071\pi\)
−0.255998 + 0.966677i \(0.582404\pi\)
\(194\) −221.058 382.883i −0.0818094 0.141698i
\(195\) 226.642 + 171.118i 0.0832315 + 0.0628412i
\(196\) −1257.98 580.437i −0.458448 0.211530i
\(197\) 1258.07i 0.454995i −0.973779 0.227498i \(-0.926946\pi\)
0.973779 0.227498i \(-0.0730544\pi\)
\(198\) 718.596 414.882i 0.257921 0.148911i
\(199\) 1524.75 2640.94i 0.543149 0.940761i −0.455572 0.890199i \(-0.650565\pi\)
0.998721 0.0505624i \(-0.0161014\pi\)
\(200\) 418.703 1666.08i 0.148034 0.589049i
\(201\) −1090.87 1889.45i −0.382808 0.663042i
\(202\) 3127.84i 1.08947i
\(203\) −1004.26 + 1100.41i −0.347218 + 0.380461i
\(204\) −487.592 −0.167344
\(205\) −22.9628 + 185.587i −0.00782338 + 0.0632289i
\(206\) 643.240 1114.12i 0.217556 0.376819i
\(207\) −1115.01 643.754i −0.374391 0.216155i
\(208\) −586.587 + 338.666i −0.195541 + 0.112896i
\(209\) 2685.49 0.888800
\(210\) −1401.58 1637.43i −0.460562 0.538065i
\(211\) 4241.89 1.38400 0.691999 0.721898i \(-0.256730\pi\)
0.691999 + 0.721898i \(0.256730\pi\)
\(212\) 757.043 437.079i 0.245254 0.141598i
\(213\) 1419.71 + 819.672i 0.456700 + 0.263676i
\(214\) −1787.75 + 3096.48i −0.571067 + 0.989116i
\(215\) 4835.43 + 598.292i 1.53383 + 0.189782i
\(216\) −371.064 −0.116888
\(217\) −226.273 712.628i −0.0707852 0.222933i
\(218\) 6543.11i 2.03282i
\(219\) −499.421 865.022i −0.154099 0.266908i
\(220\) −1104.99 + 467.824i −0.338628 + 0.143367i
\(221\) 170.347 295.049i 0.0518496 0.0898061i
\(222\) −2624.87 + 1515.47i −0.793559 + 0.458161i
\(223\) 2842.48i 0.853573i 0.904352 + 0.426786i \(0.140354\pi\)
−0.904352 + 0.426786i \(0.859646\pi\)
\(224\) 2958.97 939.527i 0.882609 0.280245i
\(225\) −308.075 1082.00i −0.0912815 0.320591i
\(226\) −3564.25 6173.46i −1.04907 1.81705i
\(227\) −1164.18 672.137i −0.340392 0.196526i 0.320053 0.947400i \(-0.396299\pi\)
−0.660446 + 0.750874i \(0.729633\pi\)
\(228\) 1060.60 + 612.340i 0.308071 + 0.177865i
\(229\) 2688.97 + 4657.43i 0.775947 + 1.34398i 0.934261 + 0.356591i \(0.116061\pi\)
−0.158313 + 0.987389i \(0.550606\pi\)
\(230\) 4428.98 + 3343.95i 1.26973 + 0.958669i
\(231\) 316.626 1441.97i 0.0901838 0.410713i
\(232\) 1105.50i 0.312844i
\(233\) 2020.02 1166.26i 0.567964 0.327914i −0.188372 0.982098i \(-0.560321\pi\)
0.756336 + 0.654184i \(0.226988\pi\)
\(234\) −132.200 + 228.977i −0.0369324 + 0.0639687i
\(235\) −1401.53 3310.37i −0.389045 0.918913i
\(236\) −997.369 1727.49i −0.275098 0.476484i
\(237\) 2315.15i 0.634537i
\(238\) −1743.07 + 1909.95i −0.474732 + 0.520182i
\(239\) −1637.91 −0.443295 −0.221647 0.975127i \(-0.571143\pi\)
−0.221647 + 0.975127i \(0.571143\pi\)
\(240\) 2662.92 + 329.486i 0.716212 + 0.0886177i
\(241\) −634.373 + 1098.77i −0.169558 + 0.293684i −0.938265 0.345918i \(-0.887567\pi\)
0.768706 + 0.639602i \(0.220901\pi\)
\(242\) 1877.95 + 1084.23i 0.498839 + 0.288005i
\(243\) −210.444 + 121.500i −0.0555556 + 0.0320750i
\(244\) 3174.55 0.832908
\(245\) −3832.92 121.941i −0.999494 0.0317980i
\(246\) −174.105 −0.0451240
\(247\) −741.073 + 427.859i −0.190904 + 0.110219i
\(248\) 480.496 + 277.414i 0.123030 + 0.0710316i
\(249\) 1537.99 2663.87i 0.391429 0.677976i
\(250\) 745.171 + 4791.52i 0.188515 + 1.21217i
\(251\) −7277.29 −1.83003 −0.915017 0.403416i \(-0.867823\pi\)
−0.915017 + 0.403416i \(0.867823\pi\)
\(252\) 453.843 497.294i 0.113450 0.124312i
\(253\) 3801.20i 0.944583i
\(254\) 2088.70 + 3617.73i 0.515971 + 0.893688i
\(255\) −1242.85 + 526.190i −0.305216 + 0.129221i
\(256\) −2444.38 + 4233.80i −0.596773 + 1.03364i
\(257\) 156.196 90.1797i 0.0379114 0.0218882i −0.480925 0.876762i \(-0.659699\pi\)
0.518836 + 0.854874i \(0.326366\pi\)
\(258\) 4536.26i 1.09463i
\(259\) −1156.57 + 5267.21i −0.277473 + 1.26366i
\(260\) 230.391 305.147i 0.0549549 0.0727863i
\(261\) −361.982 626.971i −0.0858472 0.148692i
\(262\) −8627.39 4981.03i −2.03436 1.17454i
\(263\) 589.122 + 340.130i 0.138125 + 0.0797464i 0.567470 0.823394i \(-0.307922\pi\)
−0.429345 + 0.903140i \(0.641256\pi\)
\(264\) 547.760 + 948.748i 0.127698 + 0.221179i
\(265\) 1457.99 1931.07i 0.337975 0.447639i
\(266\) 6190.10 1965.47i 1.42684 0.453048i
\(267\) 2569.31i 0.588911i
\(268\) −2543.93 + 1468.74i −0.579833 + 0.334767i
\(269\) −645.815 + 1118.58i −0.146379 + 0.253536i −0.929887 0.367846i \(-0.880095\pi\)
0.783507 + 0.621383i \(0.213429\pi\)
\(270\) 964.527 408.357i 0.217405 0.0920437i
\(271\) −2831.37 4904.08i −0.634663 1.09927i −0.986586 0.163240i \(-0.947806\pi\)
0.351923 0.936029i \(-0.385528\pi\)
\(272\) 3219.03i 0.717583i
\(273\) 142.364 + 448.364i 0.0315614 + 0.0994001i
\(274\) −6234.64 −1.37463
\(275\) −2311.70 + 2384.92i −0.506912 + 0.522968i
\(276\) −866.742 + 1501.24i −0.189028 + 0.327406i
\(277\) 1212.47 + 700.021i 0.262998 + 0.151842i 0.625701 0.780063i \(-0.284813\pi\)
−0.362704 + 0.931905i \(0.618146\pi\)
\(278\) −23.6869 + 13.6756i −0.00511023 + 0.00295039i
\(279\) 363.343 0.0779669
\(280\) 2161.87 1850.47i 0.461416 0.394954i
\(281\) −4965.18 −1.05408 −0.527042 0.849839i \(-0.676699\pi\)
−0.527042 + 0.849839i \(0.676699\pi\)
\(282\) 2898.50 1673.45i 0.612068 0.353378i
\(283\) −6502.86 3754.43i −1.36592 0.788613i −0.375514 0.926817i \(-0.622534\pi\)
−0.990404 + 0.138204i \(0.955867\pi\)
\(284\) 1103.60 1911.48i 0.230586 0.399386i
\(285\) 3364.24 + 416.261i 0.699230 + 0.0865164i
\(286\) 780.606 0.161392
\(287\) −208.816 + 228.808i −0.0429477 + 0.0470595i
\(288\) 1508.67i 0.308677i
\(289\) −1646.92 2852.56i −0.335218 0.580614i
\(290\) 1216.61 + 2873.59i 0.246351 + 0.581873i
\(291\) 191.130 331.047i 0.0385025 0.0666883i
\(292\) −1164.65 + 672.414i −0.233412 + 0.134760i
\(293\) 5927.86i 1.18194i 0.806693 + 0.590971i \(0.201255\pi\)
−0.806693 + 0.590971i \(0.798745\pi\)
\(294\) −325.530 3555.50i −0.0645757 0.705310i
\(295\) −4406.49 3326.98i −0.869681 0.656624i
\(296\) −2000.85 3465.57i −0.392895 0.680514i
\(297\) 621.309 + 358.713i 0.121387 + 0.0700830i
\(298\) 7083.80 + 4089.84i 1.37703 + 0.795026i
\(299\) −605.616 1048.96i −0.117136 0.202886i
\(300\) −1456.78 + 414.788i −0.280358 + 0.0798260i
\(301\) 5961.54 + 5440.65i 1.14159 + 1.04184i
\(302\) 11929.6i 2.27307i
\(303\) 2342.06 1352.19i 0.444052 0.256374i
\(304\) −4042.61 + 7002.01i −0.762696 + 1.32103i
\(305\) 8091.77 3425.85i 1.51913 0.643160i
\(306\) −628.282 1088.22i −0.117374 0.203298i
\(307\) 2756.38i 0.512426i −0.966620 0.256213i \(-0.917525\pi\)
0.966620 0.256213i \(-0.0824749\pi\)
\(308\) −1941.45 426.301i −0.359170 0.0788661i
\(309\) 1112.31 0.204780
\(310\) −1554.27 192.312i −0.284764 0.0352342i
\(311\) 1991.81 3449.92i 0.363168 0.629026i −0.625312 0.780375i \(-0.715028\pi\)
0.988480 + 0.151349i \(0.0483617\pi\)
\(312\) −302.313 174.541i −0.0548562 0.0316712i
\(313\) 7472.28 4314.12i 1.34939 0.779069i 0.361225 0.932479i \(-0.382359\pi\)
0.988163 + 0.153409i \(0.0490253\pi\)
\(314\) −4130.36 −0.742325
\(315\) 620.164 1757.35i 0.110928 0.314334i
\(316\) −3117.09 −0.554906
\(317\) 4544.63 2623.85i 0.805211 0.464889i −0.0400788 0.999197i \(-0.512761\pi\)
0.845290 + 0.534308i \(0.179428\pi\)
\(318\) 1950.96 + 1126.39i 0.344039 + 0.198631i
\(319\) −1068.71 + 1851.05i −0.187574 + 0.324887i
\(320\) −80.1144 + 647.488i −0.0139954 + 0.113112i
\(321\) −3091.44 −0.537530
\(322\) 2782.04 + 8761.83i 0.481482 + 1.51639i
\(323\) 4066.81i 0.700568i
\(324\) 163.586 + 283.339i 0.0280497 + 0.0485836i
\(325\) 257.953 1026.44i 0.0440266 0.175189i
\(326\) −4454.78 + 7715.90i −0.756832 + 1.31087i
\(327\) 4899.35 2828.64i 0.828546 0.478361i
\(328\) 229.867i 0.0386959i
\(329\) 1277.13 5816.28i 0.214014 0.974657i
\(330\) −2467.92 1863.32i −0.411680 0.310826i
\(331\) −2244.31 3887.26i −0.372684 0.645507i 0.617294 0.786733i \(-0.288229\pi\)
−0.989977 + 0.141225i \(0.954896\pi\)
\(332\) −3586.60 2070.73i −0.592893 0.342307i
\(333\) −2269.51 1310.30i −0.373478 0.215628i
\(334\) 5195.41 + 8998.71i 0.851138 + 1.47421i
\(335\) −4899.35 + 6489.06i −0.799045 + 1.05831i
\(336\) 3283.09 + 2996.23i 0.533057 + 0.486481i
\(337\) 5703.77i 0.921971i 0.887408 + 0.460986i \(0.152504\pi\)
−0.887408 + 0.460986i \(0.847496\pi\)
\(338\) 6386.33 3687.15i 1.02772 0.593357i
\(339\) 3081.70 5337.67i 0.493732 0.855169i
\(340\) 708.456 + 1673.35i 0.113004 + 0.266913i
\(341\) −536.361 929.005i −0.0851777 0.147532i
\(342\) 3156.10i 0.499013i
\(343\) −5063.05 3836.55i −0.797024 0.603948i
\(344\) −5989.14 −0.938699
\(345\) −589.201 + 4761.95i −0.0919464 + 0.743115i
\(346\) 3786.94 6559.16i 0.588402 1.01914i
\(347\) 3987.06 + 2301.93i 0.616820 + 0.356121i 0.775630 0.631188i \(-0.217432\pi\)
−0.158810 + 0.987309i \(0.550766\pi\)
\(348\) −844.146 + 487.368i −0.130032 + 0.0750738i
\(349\) 4802.77 0.736638 0.368319 0.929700i \(-0.379933\pi\)
0.368319 + 0.929700i \(0.379933\pi\)
\(350\) −3583.02 + 7189.18i −0.547201 + 1.09794i
\(351\) −228.604 −0.0347635
\(352\) 3857.40 2227.07i 0.584092 0.337225i
\(353\) −8996.88 5194.35i −1.35653 0.783194i −0.367377 0.930072i \(-0.619744\pi\)
−0.989155 + 0.146878i \(0.953078\pi\)
\(354\) 2570.30 4451.89i 0.385904 0.668405i
\(355\) 750.211 6063.24i 0.112161 0.906488i
\(356\) 3459.29 0.515005
\(357\) −2183.67 479.487i −0.323731 0.0710845i
\(358\) 7341.65i 1.08385i
\(359\) −2265.55 3924.04i −0.333067 0.576889i 0.650045 0.759896i \(-0.274750\pi\)
−0.983112 + 0.183007i \(0.941417\pi\)
\(360\) 539.145 + 1273.45i 0.0789318 + 0.186435i
\(361\) −1677.79 + 2906.01i −0.244611 + 0.423679i
\(362\) −306.821 + 177.143i −0.0445474 + 0.0257195i
\(363\) 1874.89i 0.271092i
\(364\) 603.671 191.677i 0.0869258 0.0276005i
\(365\) −2243.01 + 2970.80i −0.321656 + 0.426024i
\(366\) 4090.53 + 7085.01i 0.584196 + 1.01186i
\(367\) −4449.31 2568.81i −0.632840 0.365370i 0.149011 0.988836i \(-0.452391\pi\)
−0.781851 + 0.623465i \(0.785724\pi\)
\(368\) −9911.05 5722.15i −1.40394 0.810564i
\(369\) −75.2668 130.366i −0.0106185 0.0183918i
\(370\) 9014.77 + 6806.30i 1.26664 + 0.956332i
\(371\) 3820.22 1212.99i 0.534598 0.169745i
\(372\) 489.200i 0.0681823i
\(373\) −4685.97 + 2705.44i −0.650483 + 0.375557i −0.788641 0.614854i \(-0.789215\pi\)
0.138158 + 0.990410i \(0.455882\pi\)
\(374\) −1854.92 + 3212.82i −0.256459 + 0.444200i
\(375\) −3265.65 + 2629.38i −0.449700 + 0.362082i
\(376\) 2209.42 + 3826.83i 0.303038 + 0.524877i
\(377\) 681.075i 0.0930428i
\(378\) 1694.66 + 372.112i 0.230593 + 0.0506333i
\(379\) 1905.38 0.258239 0.129120 0.991629i \(-0.458785\pi\)
0.129120 + 0.991629i \(0.458785\pi\)
\(380\) 560.449 4529.57i 0.0756590 0.611479i
\(381\) −1805.92 + 3127.95i −0.242835 + 0.420603i
\(382\) −2252.42 1300.43i −0.301685 0.174178i
\(383\) −4233.89 + 2444.44i −0.564860 + 0.326122i −0.755094 0.655617i \(-0.772409\pi\)
0.190234 + 0.981739i \(0.439075\pi\)
\(384\) −4630.54 −0.615368
\(385\) −5408.71 + 1008.52i −0.715983 + 0.133504i
\(386\) 4868.17 0.641925
\(387\) −3396.66 + 1961.06i −0.446155 + 0.257588i
\(388\) −445.717 257.335i −0.0583192 0.0336706i
\(389\) 2266.47 3925.64i 0.295410 0.511665i −0.679670 0.733518i \(-0.737877\pi\)
0.975080 + 0.221853i \(0.0712104\pi\)
\(390\) 977.902 + 120.997i 0.126969 + 0.0157100i
\(391\) 5756.40 0.744537
\(392\) 4694.26 429.790i 0.604836 0.0553767i
\(393\) 8613.35i 1.10556i
\(394\) −2182.60 3780.38i −0.279081 0.483382i
\(395\) −7945.32 + 3363.85i −1.01208 + 0.428490i
\(396\) 482.967 836.523i 0.0612878 0.106154i
\(397\) 1922.70 1110.07i 0.243067 0.140335i −0.373519 0.927623i \(-0.621849\pi\)
0.616586 + 0.787288i \(0.288515\pi\)
\(398\) 10581.0i 1.33261i
\(399\) 4147.73 + 3785.33i 0.520417 + 0.474946i
\(400\) −2738.39 9617.56i −0.342299 1.20219i
\(401\) 4071.07 + 7051.30i 0.506981 + 0.878117i 0.999967 + 0.00807997i \(0.00257196\pi\)
−0.492986 + 0.870037i \(0.664095\pi\)
\(402\) −6555.92 3785.06i −0.813382 0.469606i
\(403\) 296.022 + 170.909i 0.0365904 + 0.0211255i
\(404\) −1820.57 3153.32i −0.224200 0.388325i
\(405\) 722.742 + 545.682i 0.0886749 + 0.0669510i
\(406\) −1108.63 + 5048.88i −0.135518 + 0.617171i
\(407\) 7736.99i 0.942281i
\(408\) 1436.75 829.507i 0.174337 0.100654i
\(409\) 993.077 1720.06i 0.120060 0.207950i −0.799731 0.600358i \(-0.795025\pi\)
0.919791 + 0.392408i \(0.128358\pi\)
\(410\) 252.969 + 597.505i 0.0304713 + 0.0719724i
\(411\) −2695.28 4668.37i −0.323476 0.560276i
\(412\) 1497.60i 0.179081i
\(413\) −2767.92 8717.34i −0.329783 1.03863i
\(414\) −4467.33 −0.530332
\(415\) −11376.7 1407.65i −1.34569 0.166504i
\(416\) −709.645 + 1229.14i −0.0836375 + 0.144864i
\(417\) −20.4800 11.8242i −0.00240506 0.00138856i
\(418\) 8069.61 4658.99i 0.944252 0.545164i
\(419\) 14976.8 1.74621 0.873107 0.487529i \(-0.162102\pi\)
0.873107 + 0.487529i \(0.162102\pi\)
\(420\) −2366.07 834.980i −0.274887 0.0970068i
\(421\) 8004.99 0.926697 0.463348 0.886176i \(-0.346648\pi\)
0.463348 + 0.886176i \(0.346648\pi\)
\(422\) 12746.4 7359.15i 1.47035 0.848905i
\(423\) 2506.09 + 1446.89i 0.288062 + 0.166313i
\(424\) −1487.15 + 2575.82i −0.170336 + 0.295030i
\(425\) 3611.64 + 3500.76i 0.412212 + 0.399557i
\(426\) 5688.11 0.646925
\(427\) 14217.2 + 3121.78i 1.61128 + 0.353802i
\(428\) 4162.27i 0.470072i
\(429\) 337.462 + 584.501i 0.0379786 + 0.0657809i
\(430\) 15567.9 6591.05i 1.74593 0.739183i
\(431\) −2966.24 + 5137.68i −0.331505 + 0.574184i −0.982807 0.184635i \(-0.940890\pi\)
0.651302 + 0.758819i \(0.274223\pi\)
\(432\) −1870.58 + 1079.98i −0.208329 + 0.120279i
\(433\) 7966.33i 0.884151i 0.896978 + 0.442075i \(0.145758\pi\)
−0.896978 + 0.442075i \(0.854242\pi\)
\(434\) −1916.25 1748.82i −0.211942 0.193424i
\(435\) −1625.74 + 2153.25i −0.179191 + 0.237334i
\(436\) −3808.44 6596.42i −0.418329 0.724567i
\(437\) −12521.3 7229.16i −1.37065 0.791344i
\(438\) −3001.41 1732.87i −0.327427 0.189040i
\(439\) −4873.43 8441.03i −0.529832 0.917696i −0.999394 0.0347966i \(-0.988922\pi\)
0.469563 0.882899i \(-0.344412\pi\)
\(440\) 2460.10 3258.34i 0.266547 0.353035i
\(441\) 2521.56 1780.82i 0.272277 0.192293i
\(442\) 1182.12i 0.127212i
\(443\) 3808.48 2198.82i 0.408456 0.235822i −0.281670 0.959511i \(-0.590888\pi\)
0.690126 + 0.723689i \(0.257555\pi\)
\(444\) −1764.17 + 3055.64i −0.188567 + 0.326608i
\(445\) 8817.56 3733.13i 0.939309 0.397680i
\(446\) 4931.35 + 8541.35i 0.523557 + 0.906827i
\(447\) 7072.27i 0.748338i
\(448\) −728.531 + 798.280i −0.0768301 + 0.0841857i
\(449\) 13617.5 1.43129 0.715645 0.698464i \(-0.246133\pi\)
0.715645 + 0.698464i \(0.246133\pi\)
\(450\) −2802.86 2716.81i −0.293618 0.284603i
\(451\) −222.216 + 384.889i −0.0232012 + 0.0401856i
\(452\) −7186.57 4149.17i −0.747849 0.431771i
\(453\) −8932.60 + 5157.24i −0.926468 + 0.534897i
\(454\) −4664.30 −0.482172
\(455\) 1331.88 1140.03i 0.137230 0.117463i
\(456\) −4166.94 −0.427927
\(457\) 5750.26 3319.92i 0.588591 0.339823i −0.175949 0.984399i \(-0.556299\pi\)
0.764540 + 0.644576i \(0.222966\pi\)
\(458\) 16160.1 + 9330.04i 1.64872 + 0.951887i
\(459\) 543.222 940.888i 0.0552406 0.0956795i
\(460\) 6411.42 + 793.292i 0.649857 + 0.0804075i
\(461\) −3346.60 −0.338106 −0.169053 0.985607i \(-0.554071\pi\)
−0.169053 + 0.985607i \(0.554071\pi\)
\(462\) −1550.21 4882.27i −0.156109 0.491654i
\(463\) 4620.72i 0.463808i 0.972739 + 0.231904i \(0.0744955\pi\)
−0.972739 + 0.231904i \(0.925505\pi\)
\(464\) −3217.56 5572.97i −0.321921 0.557584i
\(465\) −527.926 1246.95i −0.0526494 0.124356i
\(466\) 4046.62 7008.95i 0.402266 0.696745i
\(467\) −11032.0 + 6369.32i −1.09315 + 0.631129i −0.934413 0.356193i \(-0.884075\pi\)
−0.158735 + 0.987321i \(0.550741\pi\)
\(468\) 307.789i 0.0304008i
\(469\) −12837.3 + 4076.07i −1.26390 + 0.401313i
\(470\) −9954.51 7515.82i −0.976952 0.737615i
\(471\) −1785.59 3092.73i −0.174683 0.302559i
\(472\) 5877.75 + 3393.52i 0.573189 + 0.330931i
\(473\) 10028.2 + 5789.78i 0.974835 + 0.562821i
\(474\) −4016.50 6956.78i −0.389207 0.674126i
\(475\) −3459.59 12150.5i −0.334183 1.17369i
\(476\) −645.575 + 2940.06i −0.0621636 + 0.283104i
\(477\) 1947.79i 0.186966i
\(478\) −4921.74 + 2841.57i −0.470952 + 0.271904i
\(479\) −6797.08 + 11772.9i −0.648365 + 1.12300i 0.335149 + 0.942165i \(0.391213\pi\)
−0.983513 + 0.180835i \(0.942120\pi\)
\(480\) 5177.56 2192.05i 0.492338 0.208443i
\(481\) −1232.67 2135.06i −0.116851 0.202391i
\(482\) 4402.23i 0.416009i
\(483\) −5357.98 + 5870.94i −0.504754 + 0.553079i
\(484\) 2524.33 0.237071
\(485\) −1413.82 174.933i −0.132367 0.0163779i
\(486\) −421.575 + 730.189i −0.0393478 + 0.0681523i
\(487\) 2197.37 + 1268.65i 0.204461 + 0.118046i 0.598735 0.800948i \(-0.295670\pi\)
−0.394274 + 0.918993i \(0.629004\pi\)
\(488\) −9354.20 + 5400.65i −0.867714 + 0.500975i
\(489\) −7703.34 −0.712387
\(490\) −11729.1 + 6283.21i −1.08136 + 0.579279i
\(491\) 19203.4 1.76504 0.882522 0.470272i \(-0.155844\pi\)
0.882522 + 0.470272i \(0.155844\pi\)
\(492\) −175.523 + 101.338i −0.0160837 + 0.00928594i
\(493\) 2803.17 + 1618.41i 0.256082 + 0.147849i
\(494\) −1484.56 + 2571.34i −0.135210 + 0.234190i
\(495\) 328.315 2653.46i 0.0298114 0.240937i
\(496\) 3229.65 0.292370
\(497\) 6822.14 7475.29i 0.615724 0.674673i
\(498\) 10672.9i 0.960366i
\(499\) 3253.29 + 5634.86i 0.291858 + 0.505513i 0.974249 0.225475i \(-0.0723932\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(500\) 3540.17 + 4396.83i 0.316642 + 0.393264i
\(501\) −4492.03 + 7780.42i −0.400577 + 0.693820i
\(502\) −21867.5 + 12625.2i −1.94421 + 1.12249i
\(503\) 3373.80i 0.299066i 0.988757 + 0.149533i \(0.0477770\pi\)
−0.988757 + 0.149533i \(0.952223\pi\)
\(504\) −491.292 + 2237.43i −0.0434204 + 0.197744i
\(505\) −8043.48 6072.96i −0.708773 0.535135i
\(506\) 6594.61 + 11422.2i 0.579380 + 1.00351i
\(507\) 5521.73 + 3187.97i 0.483685 + 0.279256i
\(508\) 4211.43 + 2431.47i 0.367819 + 0.212360i
\(509\) −1661.50 2877.80i −0.144685 0.250602i 0.784570 0.620040i \(-0.212884\pi\)
−0.929255 + 0.369438i \(0.879550\pi\)
\(510\) −2821.75 + 3737.33i −0.244998 + 0.324494i
\(511\) −5877.12 + 1866.10i −0.508784 + 0.161548i
\(512\) 4614.69i 0.398325i
\(513\) −2363.22 + 1364.41i −0.203390 + 0.117427i
\(514\) 312.901 541.960i 0.0268511 0.0465075i
\(515\) −1616.15 3817.31i −0.138284 0.326623i
\(516\) 2640.35 + 4573.22i 0.225261 + 0.390164i
\(517\) 8543.53i 0.726777i
\(518\) 5662.59 + 17833.9i 0.480309 + 1.51269i
\(519\) 6548.49 0.553847
\(520\) −159.750 + 1291.10i −0.0134721 + 0.108882i
\(521\) −7755.66 + 13433.2i −0.652172 + 1.12959i 0.330423 + 0.943833i \(0.392809\pi\)
−0.982595 + 0.185762i \(0.940525\pi\)
\(522\) −2175.43 1255.99i −0.182406 0.105312i
\(523\) 16832.0 9717.97i 1.40729 0.812499i 0.412164 0.911110i \(-0.364773\pi\)
0.995126 + 0.0986106i \(0.0314398\pi\)
\(524\) −11596.9 −0.966819
\(525\) −6932.08 + 425.050i −0.576268 + 0.0353346i
\(526\) 2360.33 0.195656
\(527\) −1406.85 + 812.246i −0.116287 + 0.0671385i
\(528\) 5522.64 + 3188.50i 0.455194 + 0.262806i
\(529\) 4149.07 7186.41i 0.341010 0.590647i
\(530\) 1030.94 8332.07i 0.0844924 0.682871i
\(531\) 4444.65 0.363242
\(532\) 5096.52 5584.45i 0.415342 0.455107i
\(533\) 141.616i 0.0115085i
\(534\) 4457.43 + 7720.50i 0.361221 + 0.625653i
\(535\) 4491.77 + 10609.4i 0.362983 + 0.857356i
\(536\) 4997.34 8655.65i 0.402709 0.697513i
\(537\) 5497.27 3173.85i 0.441760 0.255050i
\(538\) 4481.63i 0.359139i
\(539\) −8275.54 3818.36i −0.661322 0.305137i
\(540\) 734.700 973.090i 0.0585490 0.0775466i
\(541\) 7151.98 + 12387.6i 0.568369 + 0.984445i 0.996727 + 0.0808355i \(0.0257589\pi\)
−0.428358 + 0.903609i \(0.640908\pi\)
\(542\) −17015.9 9824.16i −1.34852 0.778568i
\(543\) −265.283 153.161i −0.0209657 0.0121045i
\(544\) −3372.60 5841.51i −0.265807 0.460391i
\(545\) −16826.1 12704.0i −1.32248 0.998496i
\(546\) 1205.64 + 1100.30i 0.0944996 + 0.0862428i
\(547\) 596.885i 0.0466562i 0.999728 + 0.0233281i \(0.00742624\pi\)
−0.999728 + 0.0233281i \(0.992574\pi\)
\(548\) −6285.43 + 3628.89i −0.489964 + 0.282881i
\(549\) −3536.74 + 6125.81i −0.274944 + 0.476217i
\(550\) −2808.87 + 11176.9i −0.217765 + 0.866521i
\(551\) −4064.95 7040.69i −0.314288 0.544362i
\(552\) 5898.13i 0.454784i
\(553\) −13959.8 3065.28i −1.07348 0.235713i
\(554\) 4857.79 0.372541
\(555\) −1199.26 + 9692.49i −0.0917223 + 0.741303i
\(556\) −15.9199 + 27.5740i −0.00121430 + 0.00210324i
\(557\) −4741.31 2737.40i −0.360675 0.208236i 0.308702 0.951159i \(-0.400105\pi\)
−0.669377 + 0.742923i \(0.733439\pi\)
\(558\) 1091.80 630.354i 0.0828312 0.0478226i
\(559\) −3689.77 −0.279178
\(560\) 5512.46 15620.6i 0.415971 1.17873i
\(561\) −3207.59 −0.241398
\(562\) −14919.8 + 8613.96i −1.11985 + 0.646545i
\(563\) 13236.2 + 7641.93i 0.990835 + 0.572059i 0.905524 0.424296i \(-0.139478\pi\)
0.0853110 + 0.996354i \(0.472812\pi\)
\(564\) 1948.08 3374.17i 0.145441 0.251912i
\(565\) −22795.8 2820.55i −1.69739 0.210020i
\(566\) −26053.8 −1.93485
\(567\) 453.987 + 1429.80i 0.0336255 + 0.105901i
\(568\) 7509.90i 0.554768i
\(569\) −1060.65 1837.10i −0.0781454 0.135352i 0.824304 0.566147i \(-0.191566\pi\)
−0.902450 + 0.430795i \(0.858233\pi\)
\(570\) 10831.3 4585.72i 0.795921 0.336973i
\(571\) −3615.00 + 6261.36i −0.264944 + 0.458896i −0.967549 0.252684i \(-0.918687\pi\)
0.702605 + 0.711580i \(0.252020\pi\)
\(572\) 786.965 454.354i 0.0575256 0.0332124i
\(573\) 2248.75i 0.163949i
\(574\) −230.516 + 1049.81i −0.0167623 + 0.0763384i
\(575\) 17198.5 4896.90i 1.24735 0.355156i
\(576\) −262.596 454.830i −0.0189957 0.0329015i
\(577\) 11534.0 + 6659.17i 0.832180 + 0.480459i 0.854598 0.519289i \(-0.173803\pi\)
−0.0224187 + 0.999749i \(0.507137\pi\)
\(578\) −9897.66 5714.41i −0.712263 0.411225i
\(579\) 2104.55 + 3645.18i 0.151057 + 0.261638i
\(580\) 2899.11 + 2188.87i 0.207550 + 0.156703i
\(581\) −14026.2 12800.7i −1.00156 0.914049i
\(582\) 1326.35i 0.0944653i
\(583\) 4980.16 2875.29i 0.353786 0.204258i
\(584\) 2287.87 3962.70i 0.162111 0.280784i
\(585\) 332.155 + 784.541i 0.0234751 + 0.0554474i
\(586\) 10284.1 + 17812.6i 0.724969 + 1.25568i
\(587\) 10809.0i 0.760026i −0.924981 0.380013i \(-0.875919\pi\)
0.924981 0.380013i \(-0.124081\pi\)
\(588\) −2397.67 3394.99i −0.168161 0.238107i
\(589\) 4080.22 0.285438
\(590\) −19012.9 2352.49i −1.32669 0.164153i
\(591\) 1887.11 3268.57i 0.131346 0.227498i
\(592\) −20173.0 11646.9i −1.40052 0.808588i
\(593\) −13017.2 + 7515.46i −0.901434 + 0.520443i −0.877665 0.479274i \(-0.840900\pi\)
−0.0237691 + 0.999717i \(0.507567\pi\)
\(594\) 2489.29 0.171947
\(595\) 1527.27 + 8190.76i 0.105230 + 0.564350i
\(596\) 9522.02 0.654424
\(597\) 7922.83 4574.25i 0.543149 0.313587i
\(598\) −3639.62 2101.34i −0.248888 0.143696i
\(599\) −6994.92 + 12115.6i −0.477136 + 0.826424i −0.999657 0.0262026i \(-0.991659\pi\)
0.522520 + 0.852627i \(0.324992\pi\)
\(600\) 3586.95 3700.56i 0.244061 0.251791i
\(601\) 13467.0 0.914024 0.457012 0.889461i \(-0.348920\pi\)
0.457012 + 0.889461i \(0.348920\pi\)
\(602\) 27352.6 + 6006.05i 1.85184 + 0.406625i
\(603\) 6545.25i 0.442028i
\(604\) 6943.64 + 12026.7i 0.467769 + 0.810200i
\(605\) 6434.39 2724.16i 0.432389 0.183063i
\(606\) 4691.75 8126.36i 0.314504 0.544737i
\(607\) 13344.4 7704.38i 0.892308 0.515175i 0.0176116 0.999845i \(-0.494394\pi\)
0.874697 + 0.484670i \(0.161060\pi\)
\(608\) 16941.9i 1.13007i
\(609\) −4259.76 + 1352.55i −0.283439 + 0.0899971i
\(610\) 18371.5 24332.5i 1.21941 1.61507i
\(611\) 1361.17 + 2357.62i 0.0901264 + 0.156103i
\(612\) −1266.80 731.387i −0.0836721 0.0483081i
\(613\) 5811.39 + 3355.21i 0.382903 + 0.221069i 0.679081 0.734064i \(-0.262379\pi\)
−0.296177 + 0.955133i \(0.595712\pi\)
\(614\) −4781.97 8282.62i −0.314307 0.544396i
\(615\) −338.039 + 447.724i −0.0221643 + 0.0293561i
\(616\) 6445.97 2046.71i 0.421616 0.133871i
\(617\) 24471.6i 1.59674i 0.602166 + 0.798371i \(0.294305\pi\)
−0.602166 + 0.798371i \(0.705695\pi\)
\(618\) 3342.37 1929.72i 0.217556 0.125606i
\(619\) 9445.87 16360.7i 0.613346 1.06235i −0.377326 0.926081i \(-0.623156\pi\)
0.990672 0.136267i \(-0.0435104\pi\)
\(620\) −1678.87 + 710.793i −0.108750 + 0.0460421i
\(621\) −1931.26 3345.04i −0.124797 0.216155i
\(622\) 13822.2i 0.891027i
\(623\) 15492.4 + 3401.79i 0.996289 + 0.218764i
\(624\) −2032.00 −0.130361
\(625\) 13768.6 + 7386.89i 0.881191 + 0.472761i
\(626\) 14968.9 25926.9i 0.955717 1.65535i
\(627\) 6977.11 + 4028.24i 0.444400 + 0.256575i
\(628\) −4164.01 + 2404.09i −0.264589 + 0.152761i
\(629\) 11716.6 0.742722
\(630\) −1185.25 6356.55i −0.0749550 0.401985i
\(631\) −24768.0 −1.56259 −0.781297 0.624159i \(-0.785442\pi\)
−0.781297 + 0.624159i \(0.785442\pi\)
\(632\) 9184.90 5302.90i 0.578095 0.333763i
\(633\) 11020.8 + 6362.84i 0.691999 + 0.399526i
\(634\) 9104.08 15768.7i 0.570299 0.987786i
\(635\) 13358.7 + 1652.88i 0.834840 + 0.103296i
\(636\) 2622.47 0.163503
\(637\) 2892.02 264.784i 0.179884 0.0164696i
\(638\) 7416.28i 0.460209i
\(639\) 2459.02 + 4259.14i 0.152233 + 0.263676i
\(640\) 6728.04 + 15891.4i 0.415545 + 0.981507i
\(641\) 7719.40 13370.4i 0.475660 0.823867i −0.523951 0.851748i \(-0.675543\pi\)
0.999611 + 0.0278812i \(0.00887601\pi\)
\(642\) −9289.43 + 5363.26i −0.571067 + 0.329705i
\(643\) 27970.2i 1.71545i −0.514107 0.857726i \(-0.671877\pi\)
0.514107 0.857726i \(-0.328123\pi\)
\(644\) 7904.56 + 7213.91i 0.483670 + 0.441410i
\(645\) 11665.4 + 8807.55i 0.712129 + 0.537669i
\(646\) −7055.41 12220.3i −0.429708 0.744276i
\(647\) −8548.58 4935.52i −0.519442 0.299900i 0.217264 0.976113i \(-0.430287\pi\)
−0.736707 + 0.676213i \(0.763620\pi\)
\(648\) −964.053 556.596i −0.0584438 0.0337425i
\(649\) −6561.13 11364.2i −0.396836 0.687341i
\(650\) −1005.62 3531.84i −0.0606823 0.213123i
\(651\) 481.069 2190.87i 0.0289625 0.131900i
\(652\) 10371.7i 0.622985i
\(653\) −9403.83 + 5429.30i −0.563553 + 0.325367i −0.754570 0.656219i \(-0.772155\pi\)
0.191017 + 0.981587i \(0.438821\pi\)
\(654\) 9814.67 16999.5i 0.586826 1.01641i
\(655\) −29559.9 + 12514.9i −1.76336 + 0.746564i
\(656\) −669.025 1158.79i −0.0398187 0.0689680i
\(657\) 2996.53i 0.177939i
\(658\) −6252.88 19693.0i −0.370460 1.16673i
\(659\) −4519.16 −0.267134 −0.133567 0.991040i \(-0.542643\pi\)
−0.133567 + 0.991040i \(0.542643\pi\)
\(660\) −3572.58 442.039i −0.210701 0.0260702i
\(661\) −5891.72 + 10204.8i −0.346689 + 0.600483i −0.985659 0.168749i \(-0.946027\pi\)
0.638970 + 0.769231i \(0.279361\pi\)
\(662\) −13487.8 7787.19i −0.791871 0.457187i
\(663\) 885.148 511.040i 0.0518496 0.0299354i
\(664\) 14091.2 0.823559
\(665\) 6964.24 19734.5i 0.406108 1.15078i
\(666\) −9092.83 −0.529039
\(667\) 9965.81 5753.76i 0.578527 0.334013i
\(668\) 10475.5 + 6048.01i 0.606748 + 0.350306i
\(669\) −4263.72 + 7384.99i −0.246405 + 0.426786i
\(670\) −3464.31 + 27998.7i −0.199758 + 1.61445i
\(671\) 20883.5 1.20149
\(672\) 9096.91 + 1997.49i 0.522204 + 0.114665i
\(673\) 11910.6i 0.682197i 0.940028 + 0.341098i \(0.110799\pi\)
−0.940028 + 0.341098i \(0.889201\pi\)
\(674\) 9895.33 + 17139.2i 0.565510 + 0.979492i
\(675\) 822.591 3273.22i 0.0469060 0.186646i
\(676\) 4292.24 7434.38i 0.244210 0.422985i
\(677\) 2628.33 1517.47i 0.149210 0.0861463i −0.423536 0.905879i \(-0.639211\pi\)
0.572746 + 0.819733i \(0.305878\pi\)
\(678\) 21385.5i 1.21136i
\(679\) −1743.08 1590.78i −0.0985172 0.0899094i
\(680\) −4934.32 3725.49i −0.278268 0.210097i
\(681\) −2016.41 3492.53i −0.113464 0.196526i
\(682\) −3223.41 1861.04i −0.180984 0.104491i
\(683\) 11281.6 + 6513.46i 0.632035 + 0.364906i 0.781540 0.623855i \(-0.214435\pi\)
−0.149505 + 0.988761i \(0.547768\pi\)
\(684\) 1837.02 + 3181.81i 0.102690 + 0.177865i
\(685\) −12105.1 + 16032.9i −0.675199 + 0.894284i
\(686\) −21869.9 2744.65i −1.21719 0.152757i
\(687\) 16133.8i 0.895987i
\(688\) −30192.0 + 17431.3i −1.67305 + 0.965935i
\(689\) −916.197 + 1586.90i −0.0506594 + 0.0877447i
\(690\) 6490.90 + 15331.3i 0.358122 + 0.845874i
\(691\) 2249.56 + 3896.35i 0.123846 + 0.214507i 0.921281 0.388897i \(-0.127144\pi\)
−0.797436 + 0.603404i \(0.793811\pi\)
\(692\) 8816.80i 0.484342i
\(693\) 2985.58 3271.41i 0.163655 0.179323i
\(694\) 15974.2 0.873738
\(695\) −10.8221 + 87.4650i −0.000590658 + 0.00477372i
\(696\) 1658.25 2872.18i 0.0903103 0.156422i
\(697\) 582.861 + 336.515i 0.0316750 + 0.0182875i
\(698\) 14431.8 8332.21i 0.782596 0.451832i
\(699\) 6997.54 0.378643
\(700\) 572.281 + 9333.26i 0.0309003 + 0.503949i
\(701\) −26886.9 −1.44865 −0.724327 0.689457i \(-0.757849\pi\)
−0.724327 + 0.689457i \(0.757849\pi\)
\(702\) −686.930 + 396.599i −0.0369324 + 0.0213229i
\(703\) −25485.9 14714.3i −1.36731 0.789415i
\(704\) −775.282 + 1342.83i −0.0415050 + 0.0718888i
\(705\) 1324.28 10702.9i 0.0707450 0.571764i
\(706\) −36046.2 −1.92155
\(707\) −5052.48 15912.4i −0.268767 0.846459i
\(708\) 5984.22i 0.317656i
\(709\) −11091.9 19211.7i −0.587537 1.01764i −0.994554 0.104223i \(-0.966764\pi\)
0.407017 0.913421i \(-0.366569\pi\)
\(710\) −8264.65 19520.9i −0.436855 1.03184i
\(711\) 3472.73 6014.95i 0.183175 0.317269i
\(712\) −10193.2 + 5885.06i −0.536527 + 0.309764i
\(713\) 5775.39i 0.303352i
\(714\) −7393.54 + 2347.59i −0.387530 + 0.123048i
\(715\) 1515.61 2007.39i 0.0792737 0.104996i
\(716\) −4273.23 7401.46i −0.223042 0.386321i
\(717\) −4255.41 2456.86i −0.221647 0.127968i
\(718\) −13615.5 7860.88i −0.707694 0.408587i
\(719\) 9093.48 + 15750.4i 0.471669 + 0.816954i 0.999475 0.0324111i \(-0.0103186\pi\)
−0.527806 + 0.849365i \(0.676985\pi\)
\(720\) 6424.25 + 4850.42i 0.332524 + 0.251062i
\(721\) 1472.71 6706.97i 0.0760701 0.346437i
\(722\) 11643.0i 0.600150i
\(723\) −3296.30 + 1903.12i −0.169558 + 0.0978946i
\(724\) −206.214 + 357.173i −0.0105855 + 0.0183346i
\(725\) 9751.83 + 2450.73i 0.499550 + 0.125542i
\(726\) 3252.70 + 5633.85i 0.166280 + 0.288005i
\(727\) 15799.4i 0.806009i 0.915198 + 0.403004i \(0.132034\pi\)
−0.915198 + 0.403004i \(0.867966\pi\)
\(728\) −1452.71 + 1591.79i −0.0739572 + 0.0810378i
\(729\) −729.000 −0.0370370
\(730\) −1586.02 + 12818.3i −0.0804125 + 0.649898i
\(731\) 8767.84 15186.3i 0.443626 0.768382i
\(732\) 8247.72 + 4761.82i 0.416454 + 0.240440i
\(733\) 12603.4 7276.60i 0.635087 0.366668i −0.147632 0.989042i \(-0.547165\pi\)
0.782720 + 0.622375i \(0.213832\pi\)
\(734\) −17826.3 −0.896430
\(735\) −9775.30 6066.19i −0.490568 0.304428i
\(736\) −23980.5 −1.20100
\(737\) −16735.1 + 9662.00i −0.836424 + 0.482910i
\(738\) −452.337 261.157i −0.0225620 0.0130262i
\(739\) −15544.2 + 26923.4i −0.773752 + 1.34018i 0.161741 + 0.986833i \(0.448289\pi\)
−0.935493 + 0.353345i \(0.885044\pi\)
\(740\) 13049.8 + 1614.67i 0.648273 + 0.0802115i
\(741\) −2567.15 −0.127269
\(742\) 9374.95 10272.5i 0.463835 0.508242i
\(743\) 20776.5i 1.02586i −0.858430 0.512931i \(-0.828559\pi\)
0.858430 0.512931i \(-0.171441\pi\)
\(744\) 832.243 + 1441.49i 0.0410101 + 0.0710316i
\(745\) 24271.2 10275.8i 1.19359 0.505337i
\(746\) −9387.21 + 16259.1i −0.460711 + 0.797975i
\(747\) 7991.61 4613.96i 0.391429 0.225992i
\(748\) 4318.65i 0.211104i
\(749\) −4093.09 + 18640.7i −0.199677 + 0.909366i
\(750\) −5251.28 + 13566.5i −0.255666 + 0.660505i
\(751\) 9390.12 + 16264.2i 0.456259 + 0.790263i 0.998760 0.0497920i \(-0.0158558\pi\)
−0.542501 + 0.840055i \(0.682523\pi\)
\(752\) 22275.9 + 12861.0i 1.08021 + 0.623661i
\(753\) −18906.9 10915.9i −0.915017 0.528285i
\(754\) −1181.58 2046.56i −0.0570697 0.0988477i
\(755\) 30677.8 + 23162.3i 1.47878 + 1.11650i
\(756\) 1925.06 611.242i 0.0926108 0.0294056i
\(757\) 33774.4i 1.62160i 0.585323 + 0.810800i \(0.300968\pi\)
−0.585323 + 0.810800i \(0.699032\pi\)
\(758\) 5725.46 3305.59i 0.274351 0.158397i
\(759\) −5701.80 + 9875.81i −0.272678 + 0.472291i
\(760\) 6054.43 + 14300.4i 0.288970 + 0.682540i
\(761\) 14123.3 + 24462.2i 0.672757 + 1.16525i 0.977119 + 0.212693i \(0.0682236\pi\)
−0.304362 + 0.952557i \(0.598443\pi\)
\(762\) 12532.2i 0.595792i
\(763\) −10569.3 33287.1i −0.501485 1.57939i
\(764\) −3027.69 −0.143374
\(765\) −4018.30 497.188i −0.189911 0.0234979i
\(766\) −8481.58 + 14690.5i −0.400068 + 0.692938i
\(767\) 3621.14 + 2090.67i 0.170472 + 0.0984220i
\(768\) −12701.4 + 7333.15i −0.596773 + 0.344547i
\(769\) −15646.0 −0.733690 −0.366845 0.930282i \(-0.619562\pi\)
−0.366845 + 0.930282i \(0.619562\pi\)
\(770\) −14502.9 + 12413.9i −0.678766 + 0.580996i
\(771\) 541.078 0.0252743
\(772\) 4907.83 2833.53i 0.228804 0.132100i
\(773\) 18128.6 + 10466.6i 0.843521 + 0.487007i 0.858459 0.512881i \(-0.171422\pi\)
−0.0149387 + 0.999888i \(0.504755\pi\)
\(774\) −6804.39 + 11785.6i −0.315993 + 0.547317i
\(775\) −3512.30 + 3623.55i −0.162794 + 0.167951i
\(776\) 1751.15 0.0810084
\(777\) −10905.7 + 11949.8i −0.503524 + 0.551731i
\(778\) 15728.2i 0.724784i
\(779\) −845.223 1463.97i −0.0388745 0.0673326i
\(780\) 1056.30 447.209i 0.0484890 0.0205290i
\(781\) 7259.93 12574.6i 0.332626 0.576124i
\(782\) 17297.4 9986.64i 0.790988 0.456677i
\(783\) 2171.89i 0.0991279i
\(784\) 22413.4 15829.2i 1.02102 0.721083i
\(785\) −8019.46 + 10621.6i −0.364620 + 0.482930i
\(786\) −14943.1 25882.2i −0.678120 1.17454i
\(787\) −21731.7 12546.8i −0.984311 0.568292i −0.0807424 0.996735i \(-0.525729\pi\)
−0.903569 + 0.428443i \(0.859062\pi\)
\(788\) −4400.77 2540.78i −0.198948 0.114862i
\(789\) 1020.39 + 1767.37i 0.0460416 + 0.0797464i
\(790\) −18039.0 + 23892.1i −0.812402 + 1.07600i
\(791\) −28104.7 25649.1i −1.26332 1.15294i
\(792\) 3286.56i 0.147453i
\(793\) −5762.90 + 3327.21i −0.258066 + 0.148995i
\(794\) 3851.67 6671.29i 0.172154 0.298180i
\(795\) 6684.56 2830.08i 0.298210 0.126255i
\(796\) −6158.71 10667.2i −0.274233 0.474986i
\(797\) 23043.6i 1.02415i −0.858942 0.512073i \(-0.828878\pi\)
0.858942 0.512073i \(-0.171122\pi\)
\(798\) 19030.6 + 4178.70i 0.844203 + 0.185369i
\(799\) −12938.0 −0.572858
\(800\) −15045.7 14583.8i −0.664931 0.644517i
\(801\) −3853.97 + 6675.27i −0.170004 + 0.294456i
\(802\) 24466.2 + 14125.6i 1.07722 + 0.621935i
\(803\) −7661.60 + 4423.43i −0.336702 + 0.194395i
\(804\) −8812.44 −0.386556
\(805\) 27933.3 + 9857.60i 1.22301 + 0.431596i
\(806\) 1186.02 0.0518310
\(807\) −3355.75 + 1937.45i −0.146379 + 0.0845122i
\(808\) 10729.1 + 6194.43i 0.467138 + 0.269702i
\(809\) −9265.72 + 16048.7i −0.402676 + 0.697456i −0.994048 0.108943i \(-0.965253\pi\)
0.591371 + 0.806399i \(0.298587\pi\)
\(810\) 3118.45 + 385.849i 0.135273 + 0.0167375i
\(811\) 20005.9 0.866218 0.433109 0.901342i \(-0.357417\pi\)
0.433109 + 0.901342i \(0.357417\pi\)
\(812\) 1821.06 + 5735.29i 0.0787028 + 0.247868i
\(813\) 16988.2i 0.732846i
\(814\) 13422.7 + 23248.8i 0.577967 + 1.00107i
\(815\) 11192.7 + 26436.9i 0.481060 + 1.13625i
\(816\) 4828.55 8363.29i 0.207148 0.358791i
\(817\) −38143.4 + 22022.1i −1.63338 + 0.943031i
\(818\) 6891.46i 0.294565i
\(819\) −302.674 + 1378.43i −0.0129136 + 0.0588110i
\(820\) 602.810 + 455.132i 0.0256720 + 0.0193828i
\(821\) 2726.58 + 4722.58i 0.115905 + 0.200754i 0.918141 0.396253i \(-0.129690\pi\)
−0.802236 + 0.597007i \(0.796356\pi\)
\(822\) −16198.1 9351.95i −0.687314 0.396821i
\(823\) 24933.9 + 14395.6i 1.05606 + 0.609719i 0.924341 0.381568i \(-0.124616\pi\)
0.131723 + 0.991287i \(0.457949\pi\)
\(824\) 2547.77 + 4412.86i 0.107713 + 0.186565i
\(825\) −9583.36 + 2728.66i −0.404424 + 0.115151i
\(826\) −23440.8 21392.7i −0.987421 0.901146i
\(827\) 17303.1i 0.727556i −0.931486 0.363778i \(-0.881487\pi\)
0.931486 0.363778i \(-0.118513\pi\)
\(828\) −4503.72 + 2600.23i −0.189028 + 0.109135i
\(829\) 19897.6 34463.6i 0.833621 1.44387i −0.0615270 0.998105i \(-0.519597\pi\)
0.895148 0.445769i \(-0.147070\pi\)
\(830\) −36627.9 + 15507.3i −1.53178 + 0.648515i
\(831\) 2100.06 + 3637.41i 0.0876659 + 0.151842i
\(832\) 494.079i 0.0205879i
\(833\) −5782.39 + 12532.2i −0.240514 + 0.521266i
\(834\) −82.0537 −0.00340682
\(835\) 33228.2 + 4111.36i 1.37714 + 0.170395i
\(836\) 5423.56 9393.89i 0.224375 0.388630i
\(837\) 943.992 + 545.014i 0.0389834 + 0.0225071i
\(838\) 45003.6 25982.8i 1.85516 1.07108i
\(839\) 11244.8 0.462710 0.231355 0.972869i \(-0.425684\pi\)
0.231355 + 0.972869i \(0.425684\pi\)
\(840\) 8392.42 1564.87i 0.344721 0.0642774i
\(841\) −17918.3 −0.734689
\(842\) 24054.1 13887.7i 0.984513 0.568409i
\(843\) −12899.9 7447.77i −0.527042 0.304288i
\(844\) 8566.84 14838.2i 0.349387 0.605156i
\(845\) 2917.81 23581.9i 0.118788 0.960050i
\(846\) 10040.7 0.408046
\(847\) 11305.2 + 2482.37i 0.458619 + 0.100703i
\(848\) 17313.3i 0.701111i
\(849\) −11263.3 19508.6i −0.455306 0.788613i
\(850\) 16926.0 + 4253.65i 0.683007 + 0.171646i
\(851\) 20827.4 36074.2i 0.838961 1.45312i
\(852\) 5734.45 3310.79i 0.230586 0.133129i
\(853\) 4171.88i 0.167459i 0.996489 + 0.0837295i \(0.0266832\pi\)
−0.996489 + 0.0837295i \(0.973317\pi\)
\(854\) 48136.9 15284.4i 1.92882 0.612436i
\(855\) 8116.17 + 6127.84i 0.324640 + 0.245108i
\(856\) −7081.00 12264.7i −0.282738 0.489716i
\(857\) −23079.8 13325.1i −0.919943 0.531129i −0.0363261 0.999340i \(-0.511565\pi\)
−0.883617 + 0.468211i \(0.844899\pi\)
\(858\) 2028.07 + 1170.91i 0.0806961 + 0.0465899i
\(859\) 2088.24 + 3616.93i 0.0829449 + 0.143665i 0.904514 0.426445i \(-0.140234\pi\)
−0.821569 + 0.570109i \(0.806901\pi\)
\(860\) 11858.4 15706.1i 0.470194 0.622760i
\(861\) −885.730 + 281.236i −0.0350588 + 0.0111318i
\(862\) 20584.2i 0.813343i
\(863\) −29419.7 + 16985.5i −1.16044 + 0.669980i −0.951409 0.307929i \(-0.900364\pi\)
−0.209031 + 0.977909i \(0.567031\pi\)
\(864\) −2263.00 + 3919.63i −0.0891075 + 0.154339i
\(865\) −9514.76 22473.6i −0.374002 0.883382i
\(866\) 13820.6 + 23938.0i 0.542312 + 0.939313i
\(867\) 9881.55i 0.387076i
\(868\) −2949.76 647.705i −0.115347 0.0253278i
\(869\) −20505.6 −0.800465
\(870\) −1149.55 + 9290.73i −0.0447971 + 0.362052i
\(871\) 3078.74 5332.54i 0.119770 0.207447i
\(872\) 22444.1 + 12958.1i 0.871621 + 0.503230i
\(873\) 993.140 573.390i 0.0385025 0.0222294i
\(874\) −50166.7 −1.94155
\(875\) 11530.8 + 23172.4i 0.445500 + 0.895282i
\(876\) −4034.48 −0.155608
\(877\) 22706.9 13109.9i 0.874298 0.504776i 0.00552360 0.999985i \(-0.498242\pi\)
0.868774 + 0.495209i \(0.164908\pi\)
\(878\) −29288.3 16909.6i −1.12578 0.649967i
\(879\) −8891.78 + 15401.0i −0.341197 + 0.590971i
\(880\) 2918.30 23585.8i 0.111791 0.903497i
\(881\) −30831.5 −1.17905 −0.589523 0.807752i \(-0.700684\pi\)
−0.589523 + 0.807752i \(0.700684\pi\)
\(882\) 4487.50 9725.76i 0.171317 0.371296i
\(883\) 29303.3i 1.11680i 0.829572 + 0.558399i \(0.188584\pi\)
−0.829572 + 0.558399i \(0.811416\pi\)
\(884\) −688.058 1191.75i −0.0261786 0.0453427i
\(885\) −6457.94 15253.5i −0.245290 0.579367i
\(886\) 7629.37 13214.5i 0.289293 0.501070i
\(887\) −14759.8 + 8521.55i −0.558719 + 0.322577i −0.752631 0.658442i \(-0.771216\pi\)
0.193912 + 0.981019i \(0.437882\pi\)
\(888\) 12005.1i 0.453676i
\(889\) 16469.8 + 15030.7i 0.621348 + 0.567058i
\(890\) 20019.3 26515.0i 0.753986 0.998635i
\(891\) 1076.14 + 1863.93i 0.0404624 + 0.0700830i
\(892\) 9943.05 + 5740.62i 0.373226 + 0.215482i
\(893\) 28142.6 + 16248.1i 1.05460 + 0.608873i
\(894\) 12269.5 + 21251.4i 0.459009 + 0.795026i
\(895\) −18879.6 14254.4i −0.705114 0.532373i
\(896\) −6130.88 + 27921.1i −0.228592 + 1.04105i
\(897\) 3633.70i 0.135257i
\(898\) 40919.1 23624.6i 1.52059 0.877911i
\(899\) −1623.75 + 2812.41i −0.0602392 + 0.104337i
\(900\) −4407.02 1107.53i −0.163223 0.0410195i
\(901\) −4354.24 7541.77i −0.161000 0.278860i
\(902\) 1542.06i 0.0569236i
\(903\) 7327.55 + 23077.5i 0.270039 + 0.850468i
\(904\) 28234.8 1.03880
\(905\) −140.182 + 1132.96i −0.00514895 + 0.0416140i
\(906\) −17894.3 + 30993.9i −0.656180 + 1.13654i
\(907\) −38499.2 22227.5i −1.40942 0.813729i −0.414088 0.910237i \(-0.635900\pi\)
−0.995332 + 0.0965073i \(0.969233\pi\)
\(908\) −4702.29 + 2714.87i −0.171862 + 0.0992249i
\(909\) 8113.13 0.296035
\(910\) 2024.33 5736.32i 0.0737429 0.208964i
\(911\) −24316.4 −0.884344 −0.442172 0.896930i \(-0.645792\pi\)
−0.442172 + 0.896930i \(0.645792\pi\)
\(912\) −21006.0 + 12127.8i −0.762696 + 0.440343i
\(913\) −23594.2 13622.1i −0.855262 0.493786i
\(914\) 11519.3 19952.0i 0.416875 0.722049i
\(915\) 26161.8 + 3237.03i 0.945227 + 0.116954i
\(916\) 21722.3 0.783544
\(917\) −51936.5 11404.2i −1.87033 0.410685i
\(918\) 3769.69i 0.135532i
\(919\) −3038.65 5263.09i −0.109070 0.188915i 0.806324 0.591475i \(-0.201454\pi\)
−0.915394 + 0.402559i \(0.868121\pi\)
\(920\) −20241.6 + 8569.80i −0.725377 + 0.307106i
\(921\) 4134.57 7161.28i 0.147925 0.256213i
\(922\) −10056.2 + 5805.93i −0.359200 + 0.207384i
\(923\) 4626.67i 0.164993i
\(924\) −4404.59 4019.74i −0.156818 0.143117i
\(925\) 35005.9 9967.18i 1.24431 0.354291i
\(926\) 8016.37 + 13884.8i 0.284486 + 0.492744i
\(927\) 2889.87 + 1668.47i 0.102390 + 0.0591150i
\(928\) −11677.7 6742.11i −0.413080 0.238492i
\(929\) −11500.2 19919.0i −0.406147 0.703467i 0.588307 0.808638i \(-0.299795\pi\)
−0.994454 + 0.105170i \(0.966461\pi\)
\(930\) −3749.66 2831.05i −0.132211 0.0998214i
\(931\) 28316.3 19998.1i 0.996809 0.703985i
\(932\) 9421.39i 0.331124i
\(933\) 10349.8 5975.44i 0.363168 0.209675i
\(934\) −22100.0 + 38278.2i −0.774232 + 1.34101i
\(935\) 4660.53 + 11008.0i 0.163011 + 0.385028i
\(936\) −523.622 906.940i −0.0182854 0.0316712i
\(937\) 19259.6i 0.671489i −0.941953 0.335744i \(-0.891012\pi\)
0.941953 0.335744i \(-0.108988\pi\)
\(938\) −31503.1 + 34519.2i −1.09660 + 1.20159i
\(939\) 25884.7 0.899592
\(940\) −14410.2 1782.99i −0.500010 0.0618668i
\(941\) 3051.64 5285.59i 0.105718 0.183109i −0.808313 0.588752i \(-0.799619\pi\)
0.914031 + 0.405644i \(0.132953\pi\)
\(942\) −10731.0 6195.55i −0.371162 0.214291i
\(943\) 2072.19 1196.38i 0.0715585 0.0413143i
\(944\) 39507.2 1.36213
\(945\) 4247.25 3635.48i 0.146204 0.125145i
\(946\) 40178.2 1.38087
\(947\) −17922.5 + 10347.6i −0.614998 + 0.355069i −0.774919 0.632061i \(-0.782209\pi\)
0.159921 + 0.987130i \(0.448876\pi\)
\(948\) −8098.44 4675.64i −0.277453 0.160187i
\(949\) 1409.50 2441.33i 0.0482132 0.0835078i
\(950\) −31475.2 30508.9i −1.07494 1.04194i
\(951\) 15743.1 0.536808
\(952\) −3099.47 9761.54i −0.105519 0.332325i
\(953\) 35769.9i 1.21585i −0.793996 0.607923i \(-0.792003\pi\)
0.793996 0.607923i \(-0.207997\pi\)
\(954\) 3379.17 + 5852.89i 0.114680 + 0.198631i
\(955\) −7717.43 + 3267.37i −0.261498 + 0.110711i
\(956\) −3307.89 + 5729.43i −0.111909 + 0.193832i
\(957\) −5553.16 + 3206.12i −0.187574 + 0.108296i
\(958\) 47168.4i 1.59075i
\(959\) −31717.7 + 10071.0i −1.06801 + 0.339112i
\(960\) −1179.38 + 1562.05i −0.0396502 + 0.0525157i
\(961\) 14080.6 + 24388.3i 0.472645 + 0.818646i
\(962\) −7408.11 4277.07i −0.248282 0.143346i
\(963\) −8031.79 4637.16i −0.268765 0.155172i
\(964\) 2562.34 + 4438.10i 0.0856092 + 0.148280i
\(965\) 9451.97 12518.9i 0.315305 0.417614i
\(966\) −5914.78 + 26937.0i −0.197003 + 0.897187i
\(967\) 39785.2i 1.32307i −0.749915 0.661534i \(-0.769906\pi\)
0.749915 0.661534i \(-0.230094\pi\)
\(968\) −7438.25 + 4294.48i −0.246978 + 0.142593i
\(969\) 6100.22 10565.9i 0.202236 0.350284i
\(970\) −4551.85 + 1927.14i −0.150671 + 0.0637905i
\(971\) −1036.55 1795.36i −0.0342580 0.0593365i 0.848388 0.529375i \(-0.177573\pi\)
−0.882646 + 0.470038i \(0.844240\pi\)
\(972\) 981.516i 0.0323890i
\(973\) −98.4126 + 107.835i −0.00324251 + 0.00355295i
\(974\) 8803.82 0.289623
\(975\) 2209.83 2279.83i 0.0725860 0.0748850i
\(976\) −31437.1 + 54450.6i −1.03102 + 1.78578i
\(977\) −3040.16 1755.24i −0.0995532 0.0574771i 0.449397 0.893332i \(-0.351639\pi\)
−0.548950 + 0.835855i \(0.684972\pi\)
\(978\) −23147.7 + 13364.3i −0.756832 + 0.436957i
\(979\) 22756.7 0.742908
\(980\) −8167.44 + 13161.3i −0.266224 + 0.429004i
\(981\) 16971.8 0.552364
\(982\) 57704.1 33315.5i 1.87516 1.08263i
\(983\) 48756.7 + 28149.7i 1.58199 + 0.913363i 0.994569 + 0.104083i \(0.0331908\pi\)
0.587423 + 0.809280i \(0.300143\pi\)
\(984\) 344.800 597.211i 0.0111706 0.0193480i
\(985\) −13959.3 1727.19i −0.451552 0.0558710i
\(986\) 11230.9 0.362745
\(987\) 12042.5 13195.5i 0.388366 0.425548i
\(988\) 3456.38i 0.111298i
\(989\) −31171.4 53990.5i −1.00222 1.73589i
\(990\) −3616.86 8542.93i −0.116113 0.274255i
\(991\) 29627.3 51315.9i 0.949689 1.64491i 0.203609 0.979052i \(-0.434733\pi\)
0.746080 0.665857i \(-0.231934\pi\)
\(992\) 5860.78 3383.72i 0.187581 0.108300i
\(993\) 13465.9i 0.430338i
\(994\) 7531.11 34298.0i 0.240314 1.09443i
\(995\) −27209.9 20543.9i −0.866946 0.654559i
\(996\) −6212.18 10759.8i −0.197631 0.342307i
\(997\) 39165.5 + 22612.2i 1.24412 + 0.718291i 0.969930 0.243386i \(-0.0782582\pi\)
0.274186 + 0.961677i \(0.411591\pi\)
\(998\) 19551.5 + 11288.1i 0.620133 + 0.358034i
\(999\) −3930.90 6808.52i −0.124493 0.215628i
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 105.4.q.b.4.19 yes 44
5.4 even 2 inner 105.4.q.b.4.4 44
7.2 even 3 inner 105.4.q.b.79.4 yes 44
35.9 even 6 inner 105.4.q.b.79.19 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.q.b.4.4 44 5.4 even 2 inner
105.4.q.b.4.19 yes 44 1.1 even 1 trivial
105.4.q.b.79.4 yes 44 7.2 even 3 inner
105.4.q.b.79.19 yes 44 35.9 even 6 inner