Properties

Label 162.4.g.a.13.5
Level $162$
Weight $4$
Character 162.13
Analytic conductor $9.558$
Analytic rank $0$
Dimension $234$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,4,Mod(7,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 162.g (of order \(27\), degree \(18\), 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: \(9.55830942093\)
Analytic rank: \(0\)
Dimension: \(234\)
Relative dimension: \(13\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 13.5
Character \(\chi\) \(=\) 162.13
Dual form 162.4.g.a.25.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.78727 + 0.897598i) q^{2} +(-2.81153 - 4.36982i) q^{3} +(2.38863 + 3.20849i) q^{4} +(5.60704 + 18.7288i) q^{5} +(-1.10260 - 10.3336i) q^{6} +(-5.60229 - 12.9876i) q^{7} +(1.38919 + 7.87846i) q^{8} +(-11.1906 + 24.5717i) q^{9} +O(q^{10})\) \(q+(1.78727 + 0.897598i) q^{2} +(-2.81153 - 4.36982i) q^{3} +(2.38863 + 3.20849i) q^{4} +(5.60704 + 18.7288i) q^{5} +(-1.10260 - 10.3336i) q^{6} +(-5.60229 - 12.9876i) q^{7} +(1.38919 + 7.87846i) q^{8} +(-11.1906 + 24.5717i) q^{9} +(-6.78969 + 38.5062i) q^{10} +(-56.0898 + 13.2935i) q^{11} +(7.30482 - 19.4587i) q^{12} +(54.9819 + 36.1622i) q^{13} +(1.64484 - 28.2409i) q^{14} +(66.0772 - 77.1584i) q^{15} +(-4.58885 + 15.3278i) q^{16} +(-83.3537 + 30.3383i) q^{17} +(-42.0562 + 33.8715i) q^{18} +(127.507 + 46.4087i) q^{19} +(-46.6981 + 62.7265i) q^{20} +(-41.0023 + 60.9959i) q^{21} +(-112.180 - 26.5871i) q^{22} +(-22.8166 + 52.8949i) q^{23} +(30.5217 - 28.2210i) q^{24} +(-214.894 + 141.338i) q^{25} +(65.8082 + 113.983i) q^{26} +(138.837 - 20.1831i) q^{27} +(28.2887 - 48.9975i) q^{28} +(5.81662 + 99.8675i) q^{29} +(187.355 - 78.5917i) q^{30} +(132.595 - 15.4981i) q^{31} +(-21.9597 + 23.2760i) q^{32} +(215.788 + 207.727i) q^{33} +(-176.207 - 20.5956i) q^{34} +(211.830 - 177.746i) q^{35} +(-105.569 + 22.7879i) q^{36} +(-20.8373 - 17.4846i) q^{37} +(186.232 + 197.395i) q^{38} +(3.43894 - 341.932i) q^{39} +(-139.765 + 70.1927i) q^{40} +(75.7145 - 38.0253i) q^{41} +(-128.032 + 72.2123i) q^{42} +(-162.424 - 172.159i) q^{43} +(-176.630 - 148.210i) q^{44} +(-522.946 - 71.8124i) q^{45} +(-88.2577 + 74.0570i) q^{46} +(-388.495 - 45.4086i) q^{47} +(79.8815 - 23.0422i) q^{48} +(98.0894 - 103.969i) q^{49} +(-510.937 + 59.7200i) q^{50} +(366.924 + 278.944i) q^{51} +(15.3056 + 262.787i) q^{52} +(198.384 - 343.610i) q^{53} +(266.254 + 88.5470i) q^{54} +(-563.470 - 975.959i) q^{55} +(94.5395 - 62.1796i) q^{56} +(-155.692 - 687.662i) q^{57} +(-79.2451 + 183.711i) q^{58} +(-45.9039 - 10.8794i) q^{59} +(405.396 + 27.7051i) q^{60} +(526.358 - 707.022i) q^{61} +(250.894 + 91.3179i) q^{62} +(381.820 + 7.68099i) q^{63} +(-60.1403 + 21.8893i) q^{64} +(-368.989 + 1232.51i) q^{65} +(199.216 + 564.955i) q^{66} +(-1.72918 + 29.6889i) q^{67} +(-296.442 - 194.973i) q^{68} +(295.290 - 49.0109i) q^{69} +(538.141 - 127.542i) q^{70} +(96.0332 - 544.631i) q^{71} +(-209.133 - 54.0302i) q^{72} +(205.105 + 1163.21i) q^{73} +(-21.5477 - 49.9532i) q^{74} +(1221.80 + 541.672i) q^{75} +(155.665 + 519.959i) q^{76} +(486.882 + 653.997i) q^{77} +(313.064 - 608.037i) q^{78} +(40.5975 + 20.3888i) q^{79} -312.802 q^{80} +(-478.540 - 549.946i) q^{81} +169.453 q^{82} +(523.152 + 262.737i) q^{83} +(-293.645 + 14.1413i) q^{84} +(-1035.57 - 1391.01i) q^{85} +(-135.764 - 453.485i) q^{86} +(420.049 - 306.198i) q^{87} +(-182.652 - 423.434i) q^{88} +(55.0970 + 312.471i) q^{89} +(-870.184 - 597.743i) q^{90} +(161.634 - 916.673i) q^{91} +(-224.213 + 53.1395i) q^{92} +(-440.519 - 535.843i) q^{93} +(-653.586 - 429.870i) q^{94} +(-154.244 + 2648.27i) q^{95} +(163.452 + 30.5190i) q^{96} +(-16.3459 + 54.5990i) q^{97} +(268.634 - 97.7747i) q^{98} +(301.035 - 1526.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 234 q + 36 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 234 q + 36 q^{6} - 90 q^{13} - 162 q^{18} - 144 q^{20} - 405 q^{21} - 756 q^{23} - 846 q^{25} + 702 q^{26} + 702 q^{27} + 504 q^{28} + 540 q^{29} + 1098 q^{30} + 2214 q^{31} + 684 q^{33} - 1242 q^{35} - 576 q^{36} - 72 q^{38} - 927 q^{41} - 774 q^{42} + 900 q^{43} - 3843 q^{45} + 2088 q^{46} + 297 q^{47} + 144 q^{48} + 810 q^{51} + 720 q^{52} + 1431 q^{53} + 2970 q^{55} + 1485 q^{57} - 126 q^{58} - 1179 q^{59} - 2259 q^{63} + 3627 q^{65} + 4680 q^{66} - 8046 q^{67} + 2304 q^{68} - 594 q^{69} + 1530 q^{70} + 720 q^{71} + 864 q^{72} - 3204 q^{73} - 3384 q^{74} - 9918 q^{75} - 144 q^{76} - 9792 q^{77} - 7524 q^{78} + 4527 q^{79} - 1440 q^{80} + 5832 q^{81} - 5904 q^{82} - 9621 q^{83} - 1224 q^{84} + 4059 q^{85} - 3600 q^{86} - 117 q^{87} - 576 q^{88} + 531 q^{89} + 1440 q^{90} - 4473 q^{91} + 1872 q^{92} + 135 q^{93} + 666 q^{94} + 8037 q^{95} + 1728 q^{96} - 16560 q^{97} + 8136 q^{98} + 18567 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{4}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.78727 + 0.897598i 0.631894 + 0.317349i
\(3\) −2.81153 4.36982i −0.541079 0.840972i
\(4\) 2.38863 + 3.20849i 0.298579 + 0.401062i
\(5\) 5.60704 + 18.7288i 0.501509 + 1.67516i 0.715735 + 0.698372i \(0.246092\pi\)
−0.214226 + 0.976784i \(0.568723\pi\)
\(6\) −1.10260 10.3336i −0.0750227 0.703116i
\(7\) −5.60229 12.9876i −0.302495 0.701263i 0.697385 0.716696i \(-0.254347\pi\)
−0.999881 + 0.0154330i \(0.995087\pi\)
\(8\) 1.38919 + 7.87846i 0.0613939 + 0.348182i
\(9\) −11.1906 + 24.5717i −0.414467 + 0.910064i
\(10\) −6.78969 + 38.5062i −0.214709 + 1.21767i
\(11\) −56.0898 + 13.2935i −1.53743 + 0.364377i −0.910104 0.414380i \(-0.863998\pi\)
−0.627325 + 0.778758i \(0.715850\pi\)
\(12\) 7.30482 19.4587i 0.175727 0.468103i
\(13\) 54.9819 + 36.1622i 1.17302 + 0.771507i 0.977859 0.209265i \(-0.0671071\pi\)
0.195160 + 0.980771i \(0.437477\pi\)
\(14\) 1.64484 28.2409i 0.0314002 0.539120i
\(15\) 66.0772 77.1584i 1.13740 1.32815i
\(16\) −4.58885 + 15.3278i −0.0717008 + 0.239497i
\(17\) −83.3537 + 30.3383i −1.18919 + 0.432830i −0.859439 0.511238i \(-0.829187\pi\)
−0.329751 + 0.944068i \(0.606965\pi\)
\(18\) −42.0562 + 33.8715i −0.550707 + 0.443533i
\(19\) 127.507 + 46.4087i 1.53958 + 0.560363i 0.965946 0.258745i \(-0.0833090\pi\)
0.573639 + 0.819108i \(0.305531\pi\)
\(20\) −46.6981 + 62.7265i −0.522101 + 0.701303i
\(21\) −41.0023 + 60.9959i −0.426069 + 0.633829i
\(22\) −112.180 26.5871i −1.08713 0.257654i
\(23\) −22.8166 + 52.8949i −0.206852 + 0.479536i −0.989785 0.142570i \(-0.954464\pi\)
0.782933 + 0.622106i \(0.213723\pi\)
\(24\) 30.5217 28.2210i 0.259592 0.240025i
\(25\) −214.894 + 141.338i −1.71915 + 1.13070i
\(26\) 65.8082 + 113.983i 0.496386 + 0.859766i
\(27\) 138.837 20.1831i 0.989598 0.143861i
\(28\) 28.2887 48.9975i 0.190931 0.330702i
\(29\) 5.81662 + 99.8675i 0.0372455 + 0.639481i 0.964342 + 0.264658i \(0.0852592\pi\)
−0.927097 + 0.374822i \(0.877704\pi\)
\(30\) 187.355 78.5917i 1.14020 0.478294i
\(31\) 132.595 15.4981i 0.768219 0.0897919i 0.277049 0.960856i \(-0.410644\pi\)
0.491170 + 0.871064i \(0.336569\pi\)
\(32\) −21.9597 + 23.2760i −0.121312 + 0.128583i
\(33\) 215.788 + 207.727i 1.13830 + 1.09578i
\(34\) −176.207 20.5956i −0.888800 0.103886i
\(35\) 211.830 177.746i 1.02302 0.858417i
\(36\) −105.569 + 22.7879i −0.488743 + 0.105499i
\(37\) −20.8373 17.4846i −0.0925848 0.0776879i 0.595320 0.803488i \(-0.297025\pi\)
−0.687905 + 0.725801i \(0.741470\pi\)
\(38\) 186.232 + 197.395i 0.795023 + 0.842675i
\(39\) 3.43894 341.932i 0.0141198 1.40392i
\(40\) −139.765 + 70.1927i −0.552470 + 0.277461i
\(41\) 75.7145 38.0253i 0.288405 0.144843i −0.298715 0.954342i \(-0.596558\pi\)
0.587120 + 0.809500i \(0.300262\pi\)
\(42\) −128.032 + 72.2123i −0.470375 + 0.265300i
\(43\) −162.424 172.159i −0.576032 0.610558i 0.372194 0.928155i \(-0.378606\pi\)
−0.948226 + 0.317597i \(0.897124\pi\)
\(44\) −176.630 148.210i −0.605182 0.507808i
\(45\) −522.946 71.8124i −1.73236 0.237893i
\(46\) −88.2577 + 74.0570i −0.282889 + 0.237372i
\(47\) −388.495 45.4086i −1.20570 0.140926i −0.510586 0.859827i \(-0.670572\pi\)
−0.695113 + 0.718901i \(0.744646\pi\)
\(48\) 79.8815 23.0422i 0.240206 0.0692886i
\(49\) 98.0894 103.969i 0.285975 0.303116i
\(50\) −510.937 + 59.7200i −1.44515 + 0.168914i
\(51\) 366.924 + 278.944i 1.00744 + 0.765881i
\(52\) 15.3056 + 262.787i 0.0408175 + 0.700809i
\(53\) 198.384 343.610i 0.514152 0.890538i −0.485713 0.874118i \(-0.661440\pi\)
0.999865 0.0164196i \(-0.00522675\pi\)
\(54\) 266.254 + 88.5470i 0.670975 + 0.223143i
\(55\) −563.470 975.959i −1.38142 2.39270i
\(56\) 94.5395 62.1796i 0.225596 0.148377i
\(57\) −155.692 687.662i −0.361787 1.59795i
\(58\) −79.2451 + 183.711i −0.179403 + 0.415904i
\(59\) −45.9039 10.8794i −0.101291 0.0240064i 0.179658 0.983729i \(-0.442501\pi\)
−0.280949 + 0.959723i \(0.590649\pi\)
\(60\) 405.396 + 27.7051i 0.872274 + 0.0596119i
\(61\) 526.358 707.022i 1.10481 1.48401i 0.247729 0.968829i \(-0.420316\pi\)
0.857079 0.515185i \(-0.172277\pi\)
\(62\) 250.894 + 91.3179i 0.513928 + 0.187055i
\(63\) 381.820 + 7.68099i 0.763569 + 0.0153605i
\(64\) −60.1403 + 21.8893i −0.117462 + 0.0427525i
\(65\) −368.989 + 1232.51i −0.704115 + 2.35191i
\(66\) 199.216 + 564.955i 0.371541 + 1.05365i
\(67\) −1.72918 + 29.6889i −0.00315303 + 0.0541355i −0.999518 0.0310557i \(-0.990113\pi\)
0.996365 + 0.0851912i \(0.0271501\pi\)
\(68\) −296.442 194.973i −0.528659 0.347705i
\(69\) 295.290 49.0109i 0.515200 0.0855104i
\(70\) 538.141 127.542i 0.918859 0.217774i
\(71\) 96.0332 544.631i 0.160522 0.910364i −0.793041 0.609169i \(-0.791503\pi\)
0.953562 0.301195i \(-0.0973856\pi\)
\(72\) −209.133 54.0302i −0.342314 0.0884378i
\(73\) 205.105 + 1163.21i 0.328846 + 1.86498i 0.481139 + 0.876644i \(0.340223\pi\)
−0.152293 + 0.988335i \(0.548666\pi\)
\(74\) −21.5477 49.9532i −0.0338496 0.0784721i
\(75\) 1221.80 + 541.672i 1.88109 + 0.833958i
\(76\) 155.665 + 519.959i 0.234948 + 0.784781i
\(77\) 486.882 + 653.997i 0.720590 + 0.967920i
\(78\) 313.064 608.037i 0.454455 0.882648i
\(79\) 40.5975 + 20.3888i 0.0578174 + 0.0290370i 0.477473 0.878646i \(-0.341553\pi\)
−0.419656 + 0.907683i \(0.637849\pi\)
\(80\) −312.802 −0.437154
\(81\) −478.540 549.946i −0.656433 0.754384i
\(82\) 169.453 0.228207
\(83\) 523.152 + 262.737i 0.691847 + 0.347459i 0.759734 0.650234i \(-0.225329\pi\)
−0.0678864 + 0.997693i \(0.521626\pi\)
\(84\) −293.645 + 14.1413i −0.381420 + 0.0183683i
\(85\) −1035.57 1391.01i −1.32145 1.77501i
\(86\) −135.764 453.485i −0.170231 0.568611i
\(87\) 420.049 306.198i 0.517632 0.377332i
\(88\) −182.652 423.434i −0.221258 0.512935i
\(89\) 55.0970 + 312.471i 0.0656210 + 0.372155i 0.999879 + 0.0155573i \(0.00495224\pi\)
−0.934258 + 0.356598i \(0.883937\pi\)
\(90\) −870.184 597.743i −1.01917 0.700085i
\(91\) 161.634 916.673i 0.186196 1.05597i
\(92\) −224.213 + 53.1395i −0.254085 + 0.0602193i
\(93\) −440.519 535.843i −0.491179 0.597466i
\(94\) −653.586 429.870i −0.717151 0.471678i
\(95\) −154.244 + 2648.27i −0.166580 + 2.86007i
\(96\) 163.452 + 30.5190i 0.173774 + 0.0324462i
\(97\) −16.3459 + 54.5990i −0.0171100 + 0.0571514i −0.966118 0.258100i \(-0.916904\pi\)
0.949008 + 0.315251i \(0.102089\pi\)
\(98\) 268.634 97.7747i 0.276899 0.100783i
\(99\) 301.035 1526.99i 0.305607 1.55018i
\(100\) −966.784 351.881i −0.966784 0.351881i
\(101\) 232.413 312.184i 0.228970 0.307560i −0.672759 0.739861i \(-0.734891\pi\)
0.901729 + 0.432302i \(0.142298\pi\)
\(102\) 405.411 + 827.897i 0.393546 + 0.803667i
\(103\) 14.9014 + 3.53171i 0.0142552 + 0.00337854i 0.237737 0.971329i \(-0.423594\pi\)
−0.223482 + 0.974708i \(0.571742\pi\)
\(104\) −208.522 + 483.409i −0.196609 + 0.455790i
\(105\) −1372.28 425.919i −1.27544 0.395861i
\(106\) 662.988 436.054i 0.607501 0.399560i
\(107\) 673.271 + 1166.14i 0.608295 + 1.05360i 0.991521 + 0.129943i \(0.0414795\pi\)
−0.383227 + 0.923654i \(0.625187\pi\)
\(108\) 396.388 + 397.247i 0.353171 + 0.353936i
\(109\) −756.574 + 1310.43i −0.664832 + 1.15152i 0.314499 + 0.949258i \(0.398163\pi\)
−0.979331 + 0.202265i \(0.935170\pi\)
\(110\) −131.051 2250.07i −0.113593 1.95032i
\(111\) −17.8198 + 140.214i −0.0152376 + 0.119896i
\(112\) 224.780 26.2730i 0.189640 0.0221657i
\(113\) 430.088 455.866i 0.358046 0.379507i −0.523163 0.852232i \(-0.675248\pi\)
0.881210 + 0.472725i \(0.156730\pi\)
\(114\) 338.982 1368.78i 0.278496 1.12455i
\(115\) −1118.59 130.745i −0.907037 0.106017i
\(116\) −306.531 + 257.210i −0.245350 + 0.205873i
\(117\) −1503.85 + 946.324i −1.18830 + 0.747758i
\(118\) −72.2770 60.6476i −0.0563868 0.0473141i
\(119\) 860.993 + 912.599i 0.663253 + 0.703007i
\(120\) 699.683 + 413.399i 0.532267 + 0.314484i
\(121\) 1779.92 893.912i 1.33728 0.671609i
\(122\) 1575.36 791.177i 1.16907 0.587130i
\(123\) −379.037 223.950i −0.277859 0.164170i
\(124\) 366.447 + 388.411i 0.265386 + 0.281293i
\(125\) −1979.98 1661.40i −1.41676 1.18880i
\(126\) 675.520 + 356.449i 0.477620 + 0.252024i
\(127\) −1098.58 + 921.817i −0.767583 + 0.644079i −0.940089 0.340930i \(-0.889258\pi\)
0.172505 + 0.985009i \(0.444814\pi\)
\(128\) −127.135 14.8599i −0.0877907 0.0102613i
\(129\) −295.645 + 1193.79i −0.201783 + 0.814786i
\(130\) −1765.78 + 1871.62i −1.19130 + 1.26271i
\(131\) 756.752 88.4516i 0.504716 0.0589928i 0.140075 0.990141i \(-0.455266\pi\)
0.364641 + 0.931148i \(0.381192\pi\)
\(132\) −151.052 + 1188.54i −0.0996011 + 0.783705i
\(133\) −111.594 1916.00i −0.0727554 1.24916i
\(134\) −29.7392 + 51.5098i −0.0191722 + 0.0332073i
\(135\) 1156.47 + 2487.08i 0.737282 + 1.58558i
\(136\) −354.813 614.554i −0.223713 0.387482i
\(137\) 858.784 564.831i 0.535554 0.352239i −0.252744 0.967533i \(-0.581333\pi\)
0.788298 + 0.615294i \(0.210963\pi\)
\(138\) 571.754 + 177.457i 0.352688 + 0.109465i
\(139\) 24.0071 55.6547i 0.0146493 0.0339609i −0.910734 0.412993i \(-0.864484\pi\)
0.925384 + 0.379032i \(0.123743\pi\)
\(140\) 1076.28 + 255.083i 0.649731 + 0.153989i
\(141\) 893.838 + 1825.32i 0.533863 + 1.09021i
\(142\) 660.497 887.201i 0.390336 0.524312i
\(143\) −3564.65 1297.43i −2.08455 0.758715i
\(144\) −325.279 284.284i −0.188240 0.164516i
\(145\) −1837.79 + 668.900i −1.05255 + 0.383097i
\(146\) −677.518 + 2263.07i −0.384054 + 1.28283i
\(147\) −730.105 136.322i −0.409647 0.0764874i
\(148\) 6.32644 108.621i 0.00351372 0.0603282i
\(149\) 1011.21 + 665.080i 0.555981 + 0.365675i 0.796190 0.605047i \(-0.206846\pi\)
−0.240209 + 0.970721i \(0.577216\pi\)
\(150\) 1697.48 + 2064.80i 0.923991 + 1.12393i
\(151\) 3327.00 788.513i 1.79303 0.424955i 0.806865 0.590735i \(-0.201162\pi\)
0.986163 + 0.165780i \(0.0530142\pi\)
\(152\) −188.499 + 1069.03i −0.100587 + 0.570459i
\(153\) 187.316 2387.65i 0.0989778 1.26163i
\(154\) 283.162 + 1605.89i 0.148168 + 0.840301i
\(155\) 1033.73 + 2396.45i 0.535684 + 1.24186i
\(156\) 1105.30 805.717i 0.567275 0.413519i
\(157\) −91.5747 305.881i −0.0465507 0.155490i 0.931554 0.363602i \(-0.118453\pi\)
−0.978105 + 0.208112i \(0.933268\pi\)
\(158\) 54.2575 + 72.8805i 0.0273196 + 0.0366966i
\(159\) −2059.28 + 99.1702i −1.02711 + 0.0494636i
\(160\) −559.060 280.771i −0.276235 0.138730i
\(161\) 814.801 0.398853
\(162\) −361.647 1412.44i −0.175393 0.685009i
\(163\) −3104.98 −1.49203 −0.746014 0.665930i \(-0.768035\pi\)
−0.746014 + 0.665930i \(0.768035\pi\)
\(164\) 302.858 + 152.101i 0.144203 + 0.0724213i
\(165\) −2680.55 + 5206.20i −1.26473 + 2.45637i
\(166\) 699.179 + 939.160i 0.326908 + 0.439114i
\(167\) −125.376 418.784i −0.0580949 0.194051i 0.924016 0.382354i \(-0.124886\pi\)
−0.982111 + 0.188303i \(0.939701\pi\)
\(168\) −537.514 238.301i −0.246846 0.109436i
\(169\) 845.122 + 1959.21i 0.384671 + 0.891768i
\(170\) −602.267 3415.63i −0.271716 1.54098i
\(171\) −2567.23 + 2613.72i −1.14807 + 1.16887i
\(172\) 164.400 932.359i 0.0728802 0.413324i
\(173\) −1852.04 + 438.942i −0.813921 + 0.192903i −0.616438 0.787404i \(-0.711425\pi\)
−0.197483 + 0.980306i \(0.563277\pi\)
\(174\) 1025.58 170.221i 0.446835 0.0741635i
\(175\) 3039.54 + 1999.13i 1.31296 + 0.863545i
\(176\) 53.6268 920.737i 0.0229675 0.394336i
\(177\) 81.5189 + 231.179i 0.0346177 + 0.0981723i
\(178\) −182.000 + 607.923i −0.0766375 + 0.255987i
\(179\) 2221.99 808.737i 0.927816 0.337697i 0.166472 0.986046i \(-0.446762\pi\)
0.761344 + 0.648349i \(0.224540\pi\)
\(180\) −1018.72 1849.40i −0.421837 0.765813i
\(181\) 4023.45 + 1464.42i 1.65227 + 0.601377i 0.989120 0.147109i \(-0.0469967\pi\)
0.663151 + 0.748486i \(0.269219\pi\)
\(182\) 1111.69 1493.26i 0.452768 0.608173i
\(183\) −4569.43 312.278i −1.84580 0.126144i
\(184\) −448.427 106.279i −0.179665 0.0425815i
\(185\) 210.630 488.296i 0.0837072 0.194055i
\(186\) −306.352 1353.10i −0.120768 0.533410i
\(187\) 4271.99 2809.73i 1.67058 1.09876i
\(188\) −782.280 1354.95i −0.303477 0.525637i
\(189\) −1039.93 1690.08i −0.400233 0.650451i
\(190\) −2652.76 + 4594.71i −1.01290 + 1.75440i
\(191\) 138.029 + 2369.87i 0.0522903 + 0.897789i 0.917836 + 0.396959i \(0.129935\pi\)
−0.865546 + 0.500830i \(0.833028\pi\)
\(192\) 264.738 + 201.260i 0.0995096 + 0.0756494i
\(193\) 2640.62 308.644i 0.984850 0.115112i 0.391604 0.920134i \(-0.371920\pi\)
0.593246 + 0.805021i \(0.297846\pi\)
\(194\) −78.2223 + 82.9108i −0.0289486 + 0.0306838i
\(195\) 6423.27 1852.82i 2.35887 0.680427i
\(196\) 567.883 + 66.3759i 0.206954 + 0.0241895i
\(197\) −332.287 + 278.822i −0.120175 + 0.100839i −0.700895 0.713265i \(-0.747216\pi\)
0.580720 + 0.814104i \(0.302771\pi\)
\(198\) 1908.65 2458.92i 0.685060 0.882566i
\(199\) 205.253 + 172.227i 0.0731154 + 0.0613511i 0.678613 0.734496i \(-0.262581\pi\)
−0.605498 + 0.795847i \(0.707026\pi\)
\(200\) −1412.05 1496.69i −0.499236 0.529159i
\(201\) 134.597 75.9150i 0.0472325 0.0266400i
\(202\) 695.599 349.343i 0.242288 0.121682i
\(203\) 1264.45 635.031i 0.437178 0.219559i
\(204\) −18.5414 + 1843.57i −0.00636353 + 0.632723i
\(205\) 1136.70 + 1204.83i 0.387272 + 0.410484i
\(206\) 23.4628 + 19.6876i 0.00793558 + 0.00665874i
\(207\) −1044.39 1152.57i −0.350676 0.387001i
\(208\) −806.592 + 676.811i −0.268880 + 0.225617i
\(209\) −7768.78 908.040i −2.57119 0.300528i
\(210\) −2070.33 1992.99i −0.680316 0.654902i
\(211\) −3886.32 + 4119.26i −1.26799 + 1.34399i −0.355612 + 0.934634i \(0.615728\pi\)
−0.912375 + 0.409355i \(0.865754\pi\)
\(212\) 1576.34 184.247i 0.510676 0.0596894i
\(213\) −2649.94 + 1111.60i −0.852445 + 0.357584i
\(214\) 156.589 + 2688.53i 0.0500196 + 0.858804i
\(215\) 2313.62 4007.30i 0.733895 1.27114i
\(216\) 351.882 + 1065.78i 0.110845 + 0.335728i
\(217\) −944.120 1635.26i −0.295351 0.511562i
\(218\) −2528.43 + 1662.98i −0.785538 + 0.516656i
\(219\) 4506.36 4166.67i 1.39046 1.28565i
\(220\) 1785.43 4139.10i 0.547154 1.26845i
\(221\) −5680.05 1346.20i −1.72887 0.409751i
\(222\) −157.704 + 234.604i −0.0476776 + 0.0709262i
\(223\) −253.140 + 340.026i −0.0760156 + 0.102107i −0.838505 0.544894i \(-0.816570\pi\)
0.762489 + 0.647001i \(0.223977\pi\)
\(224\) 425.323 + 154.805i 0.126867 + 0.0461756i
\(225\) −1068.12 6861.97i −0.316480 2.03318i
\(226\) 1177.87 428.708i 0.346683 0.126182i
\(227\) 995.455 3325.05i 0.291060 0.972209i −0.679968 0.733242i \(-0.738006\pi\)
0.971028 0.238966i \(-0.0768086\pi\)
\(228\) 1834.47 2142.11i 0.532853 0.622213i
\(229\) −130.914 + 2247.71i −0.0377774 + 0.648614i 0.925275 + 0.379298i \(0.123835\pi\)
−0.963052 + 0.269316i \(0.913203\pi\)
\(230\) −1881.86 1237.72i −0.539506 0.354839i
\(231\) 1488.96 3966.32i 0.424098 1.12972i
\(232\) −778.722 + 184.561i −0.220369 + 0.0522284i
\(233\) 987.870 5602.49i 0.277758 1.57524i −0.452306 0.891863i \(-0.649399\pi\)
0.730064 0.683379i \(-0.239490\pi\)
\(234\) −3537.20 + 341.479i −0.988179 + 0.0953982i
\(235\) −1327.86 7530.67i −0.368596 2.09041i
\(236\) −74.7410 173.269i −0.0206154 0.0477918i
\(237\) −25.0455 234.727i −0.00686448 0.0643341i
\(238\) 719.675 + 2403.88i 0.196007 + 0.654708i
\(239\) 1654.81 + 2222.80i 0.447871 + 0.601595i 0.967523 0.252783i \(-0.0813460\pi\)
−0.519652 + 0.854378i \(0.673939\pi\)
\(240\) 879.452 + 1366.89i 0.236535 + 0.367634i
\(241\) −2687.05 1349.49i −0.718207 0.360697i 0.0518650 0.998654i \(-0.483483\pi\)
−0.770072 + 0.637957i \(0.779780\pi\)
\(242\) 3983.57 1.05816
\(243\) −1057.73 + 3637.32i −0.279233 + 0.960223i
\(244\) 3525.75 0.925054
\(245\) 2497.20 + 1254.14i 0.651185 + 0.327038i
\(246\) −476.423 740.480i −0.123478 0.191916i
\(247\) 5332.34 + 7162.57i 1.37364 + 1.84512i
\(248\) 306.301 + 1023.12i 0.0784279 + 0.261967i
\(249\) −322.744 3024.77i −0.0821409 0.769827i
\(250\) −2047.48 4746.58i −0.517975 1.20080i
\(251\) 172.413 + 977.803i 0.0433570 + 0.245890i 0.998782 0.0493447i \(-0.0157133\pi\)
−0.955425 + 0.295235i \(0.904602\pi\)
\(252\) 887.385 + 1243.42i 0.221825 + 0.310825i
\(253\) 576.620 3270.18i 0.143288 0.812625i
\(254\) −2790.87 + 661.449i −0.689429 + 0.163398i
\(255\) −3166.93 + 8436.10i −0.777728 + 2.07172i
\(256\) −213.885 140.674i −0.0522180 0.0343443i
\(257\) −332.280 + 5705.02i −0.0806499 + 1.38471i 0.678888 + 0.734242i \(0.262462\pi\)
−0.759538 + 0.650463i \(0.774575\pi\)
\(258\) −1599.94 + 1868.25i −0.386077 + 0.450822i
\(259\) −110.346 + 368.580i −0.0264732 + 0.0884265i
\(260\) −4835.88 + 1760.12i −1.15349 + 0.419838i
\(261\) −2519.01 974.655i −0.597405 0.231148i
\(262\) 1431.91 + 521.173i 0.337648 + 0.122894i
\(263\) 2325.72 3123.99i 0.545286 0.732447i −0.440997 0.897509i \(-0.645375\pi\)
0.986283 + 0.165062i \(0.0527824\pi\)
\(264\) −1336.80 + 1988.65i −0.311645 + 0.463610i
\(265\) 7547.76 + 1788.85i 1.74964 + 0.414673i
\(266\) 1520.35 3524.57i 0.350446 0.812426i
\(267\) 1210.53 1119.28i 0.277466 0.256551i
\(268\) −99.3870 + 65.3679i −0.0226531 + 0.0148992i
\(269\) −2266.24 3925.24i −0.513662 0.889689i −0.999874 0.0158482i \(-0.994955\pi\)
0.486212 0.873841i \(-0.338378\pi\)
\(270\) −165.482 + 5483.12i −0.0372996 + 1.23590i
\(271\) 1030.10 1784.18i 0.230901 0.399931i −0.727173 0.686454i \(-0.759166\pi\)
0.958073 + 0.286523i \(0.0924995\pi\)
\(272\) −82.5221 1416.85i −0.0183957 0.315842i
\(273\) −4460.14 + 1870.94i −0.988790 + 0.414778i
\(274\) 2041.87 238.660i 0.450196 0.0526203i
\(275\) 10174.5 10784.3i 2.23107 2.36480i
\(276\) 862.592 + 830.368i 0.188123 + 0.181095i
\(277\) −4160.08 486.244i −0.902365 0.105471i −0.347759 0.937584i \(-0.613057\pi\)
−0.554607 + 0.832113i \(0.687131\pi\)
\(278\) 92.8627 77.9210i 0.0200343 0.0168108i
\(279\) −1103.01 + 3431.53i −0.236685 + 0.736344i
\(280\) 1694.64 + 1421.97i 0.361693 + 0.303496i
\(281\) 5660.48 + 5999.76i 1.20169 + 1.27372i 0.952246 + 0.305333i \(0.0987676\pi\)
0.249448 + 0.968388i \(0.419751\pi\)
\(282\) −40.8796 + 4064.64i −0.00863243 + 0.858319i
\(283\) −4278.30 + 2148.64i −0.898651 + 0.451320i −0.837267 0.546795i \(-0.815848\pi\)
−0.0613845 + 0.998114i \(0.519552\pi\)
\(284\) 1976.83 992.803i 0.413041 0.207437i
\(285\) 12006.1 6771.67i 2.49537 1.40744i
\(286\) −5206.41 5518.47i −1.07644 1.14096i
\(287\) −918.031 770.320i −0.188814 0.158434i
\(288\) −326.188 800.061i −0.0667388 0.163695i
\(289\) 2263.85 1899.60i 0.460789 0.386647i
\(290\) −3885.02 454.093i −0.786676 0.0919492i
\(291\) 284.544 82.0781i 0.0573206 0.0165344i
\(292\) −3242.23 + 3436.56i −0.649785 + 0.688732i
\(293\) 61.3772 7.17397i 0.0122379 0.00143040i −0.109972 0.993935i \(-0.535076\pi\)
0.122210 + 0.992504i \(0.461002\pi\)
\(294\) −1182.53 898.985i −0.234580 0.178333i
\(295\) −53.6262 920.727i −0.0105839 0.181718i
\(296\) 108.805 188.456i 0.0213654 0.0370059i
\(297\) −7519.02 + 2977.70i −1.46902 + 0.581763i
\(298\) 1210.32 + 2096.33i 0.235275 + 0.407508i
\(299\) −3167.30 + 2083.16i −0.612607 + 0.402918i
\(300\) 1180.49 + 5213.99i 0.227185 + 1.00343i
\(301\) −1325.98 + 3073.97i −0.253915 + 0.588641i
\(302\) 6654.00 + 1577.03i 1.26786 + 0.300489i
\(303\) −2017.62 137.886i −0.382540 0.0261430i
\(304\) −1296.46 + 1741.44i −0.244595 + 0.328548i
\(305\) 16193.0 + 5893.77i 3.04003 + 1.10648i
\(306\) 2477.93 4099.23i 0.462922 0.765808i
\(307\) −1711.59 + 622.968i −0.318194 + 0.115813i −0.496180 0.868220i \(-0.665264\pi\)
0.177985 + 0.984033i \(0.443042\pi\)
\(308\) −935.359 + 3124.32i −0.173042 + 0.578002i
\(309\) −26.4629 75.0461i −0.00487191 0.0138162i
\(310\) −303.504 + 5210.97i −0.0556061 + 0.954720i
\(311\) −5803.20 3816.83i −1.05810 0.695924i −0.103748 0.994604i \(-0.533084\pi\)
−0.954354 + 0.298679i \(0.903454\pi\)
\(312\) 2698.68 447.914i 0.489687 0.0812760i
\(313\) −2502.02 + 592.991i −0.451830 + 0.107086i −0.450229 0.892913i \(-0.648658\pi\)
−0.00160085 + 0.999999i \(0.500510\pi\)
\(314\) 110.890 628.887i 0.0199295 0.113026i
\(315\) 1997.03 + 7194.11i 0.357205 + 1.28680i
\(316\) 31.5552 + 178.958i 0.00561746 + 0.0318582i
\(317\) 1901.99 + 4409.30i 0.336991 + 0.781234i 0.999483 + 0.0321641i \(0.0102399\pi\)
−0.662491 + 0.749070i \(0.730501\pi\)
\(318\) −3769.49 1671.16i −0.664724 0.294698i
\(319\) −1653.85 5524.23i −0.290275 0.969584i
\(320\) −747.170 1003.62i −0.130525 0.175326i
\(321\) 3202.90 6220.71i 0.556911 1.08164i
\(322\) 1456.27 + 731.364i 0.252033 + 0.126576i
\(323\) −12036.1 −2.07340
\(324\) 621.440 2849.01i 0.106557 0.488514i
\(325\) −16926.4 −2.88894
\(326\) −5549.42 2787.02i −0.942804 0.473494i
\(327\) 7853.45 378.205i 1.32812 0.0639595i
\(328\) 404.762 + 543.690i 0.0681380 + 0.0915252i
\(329\) 1586.72 + 5300.01i 0.265892 + 0.888142i
\(330\) −9463.93 + 6898.80i −1.57870 + 1.15081i
\(331\) 1769.58 + 4102.35i 0.293852 + 0.681225i 0.999630 0.0272083i \(-0.00866173\pi\)
−0.705778 + 0.708433i \(0.749402\pi\)
\(332\) 406.629 + 2306.11i 0.0672189 + 0.381217i
\(333\) 662.810 316.346i 0.109074 0.0520590i
\(334\) 151.820 861.014i 0.0248719 0.141056i
\(335\) −565.734 + 134.081i −0.0922667 + 0.0218676i
\(336\) −746.782 908.378i −0.121251 0.147488i
\(337\) −2078.31 1366.92i −0.335942 0.220953i 0.370318 0.928905i \(-0.379249\pi\)
−0.706260 + 0.707952i \(0.749619\pi\)
\(338\) −248.129 + 4260.21i −0.0399303 + 0.685577i
\(339\) −3201.26 597.724i −0.512886 0.0957637i
\(340\) 1989.45 6645.22i 0.317332 1.05996i
\(341\) −7231.21 + 2631.95i −1.14836 + 0.417970i
\(342\) −6934.39 + 2367.08i −1.09640 + 0.374261i
\(343\) −6458.76 2350.80i −1.01674 0.370061i
\(344\) 1130.71 1518.81i 0.177220 0.238048i
\(345\) 2573.62 + 5255.64i 0.401621 + 0.820156i
\(346\) −3704.09 877.885i −0.575529 0.136403i
\(347\) 1299.12 3011.71i 0.200982 0.465928i −0.787681 0.616084i \(-0.788718\pi\)
0.988662 + 0.150156i \(0.0479776\pi\)
\(348\) 1985.78 + 616.331i 0.305888 + 0.0949390i
\(349\) 4555.84 2996.43i 0.698764 0.459584i −0.149773 0.988720i \(-0.547854\pi\)
0.848537 + 0.529136i \(0.177484\pi\)
\(350\) 3638.04 + 6301.26i 0.555604 + 0.962334i
\(351\) 8363.38 + 3910.93i 1.27181 + 0.594730i
\(352\) 922.298 1597.47i 0.139655 0.241890i
\(353\) −537.975 9236.67i −0.0811148 1.39269i −0.755907 0.654679i \(-0.772804\pi\)
0.674792 0.738008i \(-0.264233\pi\)
\(354\) −61.8102 + 486.350i −0.00928016 + 0.0730204i
\(355\) 10738.8 1255.18i 1.60551 0.187657i
\(356\) −870.953 + 923.156i −0.129664 + 0.137436i
\(357\) 1567.19 6328.18i 0.232337 0.938159i
\(358\) 4697.20 + 549.024i 0.693449 + 0.0810526i
\(359\) 3777.09 3169.35i 0.555284 0.465939i −0.321442 0.946929i \(-0.604167\pi\)
0.876726 + 0.480991i \(0.159723\pi\)
\(360\) −160.697 4219.77i −0.0235263 0.617782i
\(361\) 8849.96 + 7426.00i 1.29027 + 1.08267i
\(362\) 5876.52 + 6228.75i 0.853213 + 0.904353i
\(363\) −8910.54 5264.69i −1.28838 0.761224i
\(364\) 3327.23 1671.00i 0.479104 0.240615i
\(365\) −20635.5 + 10363.6i −2.95921 + 1.48617i
\(366\) −7886.48 4659.64i −1.12632 0.665473i
\(367\) 2916.06 + 3090.84i 0.414760 + 0.439620i 0.900746 0.434347i \(-0.143021\pi\)
−0.485986 + 0.873967i \(0.661539\pi\)
\(368\) −706.061 592.456i −0.100016 0.0839236i
\(369\) 87.0540 + 2285.96i 0.0122814 + 0.322500i
\(370\) 814.745 683.652i 0.114477 0.0960578i
\(371\) −5574.07 651.515i −0.780030 0.0911725i
\(372\) 667.010 2693.34i 0.0929647 0.375384i
\(373\) 7368.82 7810.49i 1.02290 1.08421i 0.0264855 0.999649i \(-0.491568\pi\)
0.996418 0.0845651i \(-0.0269501\pi\)
\(374\) 10157.2 1187.21i 1.40432 0.164142i
\(375\) −1693.25 + 13323.2i −0.233170 + 1.83469i
\(376\) −181.942 3123.83i −0.0249547 0.428455i
\(377\) −3291.62 + 5701.25i −0.449674 + 0.778858i
\(378\) −341.624 3954.07i −0.0464848 0.538030i
\(379\) 101.747 + 176.231i 0.0137900 + 0.0238849i 0.872838 0.488010i \(-0.162277\pi\)
−0.859048 + 0.511895i \(0.828944\pi\)
\(380\) −8865.39 + 5830.86i −1.19680 + 0.787150i
\(381\) 7116.86 + 2208.87i 0.956975 + 0.297019i
\(382\) −1880.50 + 4359.48i −0.251870 + 0.583901i
\(383\) 13645.7 + 3234.08i 1.82052 + 0.431472i 0.991758 0.128124i \(-0.0408955\pi\)
0.828766 + 0.559596i \(0.189044\pi\)
\(384\) 292.507 + 597.334i 0.0388723 + 0.0793817i
\(385\) −9518.61 + 12785.7i −1.26004 + 1.69252i
\(386\) 4996.53 + 1818.59i 0.658851 + 0.239802i
\(387\) 6047.86 2064.46i 0.794393 0.271169i
\(388\) −214.225 + 77.9714i −0.0280299 + 0.0102021i
\(389\) −1159.78 + 3873.94i −0.151165 + 0.504927i −0.999707 0.0242013i \(-0.992296\pi\)
0.848542 + 0.529128i \(0.177481\pi\)
\(390\) 13143.2 + 2454.03i 1.70649 + 0.318628i
\(391\) 297.111 5101.20i 0.0384285 0.659792i
\(392\) 955.378 + 628.362i 0.123097 + 0.0809619i
\(393\) −2514.15 3058.18i −0.322702 0.392532i
\(394\) −844.155 + 200.069i −0.107939 + 0.0255820i
\(395\) −154.227 + 874.664i −0.0196456 + 0.111416i
\(396\) 5618.39 2681.54i 0.712966 0.340285i
\(397\) −2203.56 12497.0i −0.278573 1.57987i −0.727378 0.686237i \(-0.759261\pi\)
0.448805 0.893630i \(-0.351850\pi\)
\(398\) 212.250 + 492.050i 0.0267315 + 0.0619705i
\(399\) −8058.83 + 5874.54i −1.01114 + 0.737080i
\(400\) −1180.29 3942.44i −0.147536 0.492804i
\(401\) −192.053 257.972i −0.0239169 0.0321259i 0.790004 0.613102i \(-0.210078\pi\)
−0.813921 + 0.580976i \(0.802671\pi\)
\(402\) 308.701 14.8664i 0.0383001 0.00184445i
\(403\) 7850.78 + 3942.81i 0.970410 + 0.487358i
\(404\) 1556.79 0.191716
\(405\) 7616.64 12046.1i 0.934504 1.47796i
\(406\) 2829.91 0.345927
\(407\) 1401.19 + 703.706i 0.170650 + 0.0857037i
\(408\) −1687.92 + 3278.30i −0.204815 + 0.397794i
\(409\) −2267.24 3045.43i −0.274102 0.368183i 0.643661 0.765311i \(-0.277415\pi\)
−0.917764 + 0.397127i \(0.870007\pi\)
\(410\) 950.132 + 3173.66i 0.114448 + 0.382283i
\(411\) −4882.70 2164.69i −0.586000 0.259796i
\(412\) 24.2626 + 56.2471i 0.00290130 + 0.00672596i
\(413\) 115.870 + 657.130i 0.0138053 + 0.0782936i
\(414\) −832.050 2997.39i −0.0987754 0.355830i
\(415\) −1987.41 + 11271.2i −0.235080 + 1.33321i
\(416\) −2049.10 + 485.645i −0.241503 + 0.0572373i
\(417\) −310.698 + 51.5681i −0.0364866 + 0.00605588i
\(418\) −13069.8 8596.15i −1.52934 1.00586i
\(419\) −85.3117 + 1464.74i −0.00994689 + 0.170782i 0.989676 + 0.143323i \(0.0457786\pi\)
−0.999623 + 0.0274590i \(0.991258\pi\)
\(420\) −1911.33 5420.33i −0.222055 0.629726i
\(421\) 1774.65 5927.75i 0.205443 0.686226i −0.791716 0.610890i \(-0.790812\pi\)
0.997158 0.0753360i \(-0.0240029\pi\)
\(422\) −10643.3 + 3873.85i −1.22775 + 0.446863i
\(423\) 5463.27 9037.85i 0.627975 1.03885i
\(424\) 2982.71 + 1085.62i 0.341635 + 0.124345i
\(425\) 13624.3 18300.5i 1.55500 2.08872i
\(426\) −5733.91 391.860i −0.652134 0.0445673i
\(427\) −12131.3 2875.18i −1.37488 0.325854i
\(428\) −2133.35 + 4945.67i −0.240933 + 0.558546i
\(429\) 4352.59 + 19224.6i 0.489849 + 2.16357i
\(430\) 7732.00 5085.41i 0.867139 0.570327i
\(431\) −3537.72 6127.51i −0.395373 0.684807i 0.597776 0.801664i \(-0.296051\pi\)
−0.993149 + 0.116857i \(0.962718\pi\)
\(432\) −327.738 + 2220.68i −0.0365007 + 0.247321i
\(433\) 631.789 1094.29i 0.0701197 0.121451i −0.828834 0.559495i \(-0.810995\pi\)
0.898954 + 0.438044i \(0.144329\pi\)
\(434\) −219.583 3770.09i −0.0242864 0.416982i
\(435\) 8089.96 + 6150.17i 0.891687 + 0.677880i
\(436\) −6011.67 + 702.663i −0.660337 + 0.0771823i
\(437\) −5364.06 + 5685.57i −0.587180 + 0.622375i
\(438\) 11794.1 3402.05i 1.28663 0.371133i
\(439\) −11643.3 1360.91i −1.26584 0.147956i −0.543453 0.839440i \(-0.682883\pi\)
−0.722392 + 0.691484i \(0.756957\pi\)
\(440\) 6906.29 5795.06i 0.748283 0.627884i
\(441\) 1457.01 + 3573.70i 0.157327 + 0.385887i
\(442\) −8943.41 7504.41i −0.962431 0.807575i
\(443\) −2726.32 2889.73i −0.292396 0.309922i 0.564477 0.825449i \(-0.309078\pi\)
−0.856874 + 0.515527i \(0.827596\pi\)
\(444\) −492.440 + 277.745i −0.0526355 + 0.0296874i
\(445\) −5543.27 + 2783.94i −0.590509 + 0.296565i
\(446\) −757.634 + 380.498i −0.0804373 + 0.0403971i
\(447\) 63.2475 6288.68i 0.00669241 0.665423i
\(448\) 621.213 + 658.447i 0.0655124 + 0.0694391i
\(449\) −7264.00 6095.22i −0.763495 0.640649i 0.175539 0.984473i \(-0.443833\pi\)
−0.939034 + 0.343824i \(0.888278\pi\)
\(450\) 4250.28 13222.9i 0.445245 1.38519i
\(451\) −3741.32 + 3139.34i −0.390625 + 0.327774i
\(452\) 2489.97 + 291.035i 0.259111 + 0.0302857i
\(453\) −12799.6 12321.4i −1.32755 1.27795i
\(454\) 4763.70 5049.23i 0.492448 0.521965i
\(455\) 18074.5 2112.61i 1.86230 0.217671i
\(456\) 5201.43 2181.90i 0.534165 0.224072i
\(457\) 164.710 + 2827.96i 0.0168596 + 0.289467i 0.996191 + 0.0872032i \(0.0277929\pi\)
−0.979331 + 0.202264i \(0.935170\pi\)
\(458\) −2251.51 + 3899.74i −0.229708 + 0.397866i
\(459\) −10960.2 + 5894.41i −1.11455 + 0.599406i
\(460\) −2252.41 3901.30i −0.228303 0.395432i
\(461\) −11933.7 + 7848.91i −1.20566 + 0.792972i −0.983300 0.181993i \(-0.941745\pi\)
−0.222356 + 0.974966i \(0.571375\pi\)
\(462\) 6221.33 5752.37i 0.626499 0.579274i
\(463\) 593.613 1376.15i 0.0595844 0.138132i −0.885823 0.464024i \(-0.846405\pi\)
0.945407 + 0.325892i \(0.105664\pi\)
\(464\) −1557.44 369.121i −0.155824 0.0369311i
\(465\) 7565.70 11254.9i 0.754518 1.12244i
\(466\) 6794.37 9126.42i 0.675415 0.907239i
\(467\) −6080.97 2213.29i −0.602556 0.219313i 0.0226867 0.999743i \(-0.492778\pi\)
−0.625243 + 0.780430i \(0.715000\pi\)
\(468\) −6628.42 2564.67i −0.654698 0.253316i
\(469\) 395.274 143.868i 0.0389170 0.0141646i
\(470\) 4386.28 14651.2i 0.430476 1.43789i
\(471\) −1079.18 + 1260.16i −0.105575 + 0.123280i
\(472\) 21.9441 376.765i 0.00213995 0.0367416i
\(473\) 11398.9 + 7497.18i 1.10808 + 0.728796i
\(474\) 165.928 442.001i 0.0160787 0.0428308i
\(475\) −33959.8 + 8048.62i −3.28038 + 0.777465i
\(476\) −871.470 + 4942.35i −0.0839155 + 0.475908i
\(477\) 6223.07 + 8719.84i 0.597347 + 0.837011i
\(478\) 962.409 + 5458.10i 0.0920912 + 0.522275i
\(479\) 2897.34 + 6716.79i 0.276373 + 0.640706i 0.998707 0.0508393i \(-0.0161896\pi\)
−0.722333 + 0.691545i \(0.756930\pi\)
\(480\) 344.897 + 3232.39i 0.0327965 + 0.307370i
\(481\) −513.396 1714.86i −0.0486670 0.162559i
\(482\) −3591.17 4823.78i −0.339364 0.455844i
\(483\) −2290.84 3560.53i −0.215811 0.335424i
\(484\) 7119.70 + 3575.65i 0.668642 + 0.335804i
\(485\) −1114.23 −0.104318
\(486\) −5155.31 + 5551.44i −0.481172 + 0.518145i
\(487\) 4978.72 0.463259 0.231630 0.972804i \(-0.425594\pi\)
0.231630 + 0.972804i \(0.425594\pi\)
\(488\) 6301.46 + 3164.71i 0.584536 + 0.293565i
\(489\) 8729.73 + 13568.2i 0.807305 + 1.25475i
\(490\) 3337.45 + 4482.97i 0.307695 + 0.413306i
\(491\) −3144.78 10504.3i −0.289047 0.965484i −0.971992 0.235014i \(-0.924486\pi\)
0.682945 0.730470i \(-0.260699\pi\)
\(492\) −186.840 1751.07i −0.0171207 0.160456i
\(493\) −3514.65 8147.86i −0.321078 0.744344i
\(494\) 3101.19 + 17587.7i 0.282448 + 1.60184i
\(495\) 30286.6 2923.85i 2.75006 0.265489i
\(496\) −370.906 + 2103.51i −0.0335770 + 0.190425i
\(497\) −7611.45 + 1803.95i −0.686962 + 0.162813i
\(498\) 2138.20 5695.76i 0.192399 0.512516i
\(499\) 292.394 + 192.310i 0.0262312 + 0.0172525i 0.562557 0.826759i \(-0.309818\pi\)
−0.536326 + 0.844011i \(0.680188\pi\)
\(500\) 601.142 10321.2i 0.0537678 0.923158i
\(501\) −1477.51 + 1725.29i −0.131757 + 0.153853i
\(502\) −569.527 + 1902.35i −0.0506359 + 0.169136i
\(503\) 4733.36 1722.80i 0.419583 0.152716i −0.123596 0.992333i \(-0.539443\pi\)
0.543179 + 0.839617i \(0.317220\pi\)
\(504\) 469.905 + 3018.83i 0.0415302 + 0.266804i
\(505\) 7149.99 + 2602.39i 0.630041 + 0.229316i
\(506\) 3965.88 5327.10i 0.348428 0.468021i
\(507\) 6185.32 9201.41i 0.541814 0.806014i
\(508\) −5581.75 1322.90i −0.487500 0.115540i
\(509\) −3763.48 + 8724.72i −0.327727 + 0.759757i 0.672087 + 0.740472i \(0.265398\pi\)
−0.999814 + 0.0192849i \(0.993861\pi\)
\(510\) −13232.4 + 12234.9i −1.14890 + 1.06230i
\(511\) 13958.2 9180.47i 1.20837 0.794756i
\(512\) −256.000 443.405i −0.0220971 0.0382733i
\(513\) 18639.3 + 3869.75i 1.60418 + 0.333048i
\(514\) −5714.69 + 9898.13i −0.490397 + 0.849393i
\(515\) 17.4083 + 298.889i 0.00148952 + 0.0255740i
\(516\) −4536.46 + 1902.96i −0.387028 + 0.162351i
\(517\) 22394.3 2617.51i 1.90503 0.222666i
\(518\) −528.054 + 559.705i −0.0447903 + 0.0474749i
\(519\) 7125.17 + 6858.99i 0.602621 + 0.580109i
\(520\) −10222.9 1194.88i −0.862121 0.100767i
\(521\) 6265.22 5257.14i 0.526841 0.442072i −0.340168 0.940365i \(-0.610484\pi\)
0.867009 + 0.498292i \(0.166039\pi\)
\(522\) −3627.29 4003.03i −0.304142 0.335647i
\(523\) −14534.8 12196.2i −1.21523 1.01970i −0.999060 0.0433418i \(-0.986200\pi\)
−0.216168 0.976356i \(-0.569356\pi\)
\(524\) 2091.40 + 2216.76i 0.174357 + 0.184808i
\(525\) 190.113 18902.8i 0.0158042 1.57140i
\(526\) 6960.77 3495.83i 0.577004 0.289782i
\(527\) −10582.1 + 5314.53i −0.874694 + 0.439288i
\(528\) −4174.23 + 2354.34i −0.344053 + 0.194052i
\(529\) 6072.23 + 6436.19i 0.499074 + 0.528988i
\(530\) 11884.2 + 9972.01i 0.973992 + 0.817277i
\(531\) 781.019 1006.19i 0.0638293 0.0822315i
\(532\) 5880.92 4934.68i 0.479267 0.402153i
\(533\) 5538.01 + 647.300i 0.450052 + 0.0526035i
\(534\) 3168.21 913.884i 0.256745 0.0740592i
\(535\) −18065.4 + 19148.2i −1.45988 + 1.54738i
\(536\) −236.305 + 27.6201i −0.0190426 + 0.00222576i
\(537\) −9781.21 7435.89i −0.786016 0.597546i
\(538\) −527.081 9049.63i −0.0422380 0.725199i
\(539\) −4119.71 + 7135.54i −0.329218 + 0.570222i
\(540\) −5217.40 + 9651.25i −0.415780 + 0.769118i
\(541\) 7124.13 + 12339.4i 0.566156 + 0.980611i 0.996941 + 0.0781562i \(0.0249033\pi\)
−0.430785 + 0.902454i \(0.641763\pi\)
\(542\) 3442.54 2264.19i 0.272822 0.179438i
\(543\) −4912.82 21699.0i −0.388267 1.71491i
\(544\) 1124.27 2606.36i 0.0886081 0.205417i
\(545\) −28784.9 6822.14i −2.26240 0.536199i
\(546\) −9650.80 659.543i −0.756440 0.0516957i
\(547\) −4795.57 + 6441.57i −0.374852 + 0.503513i −0.949016 0.315227i \(-0.897919\pi\)
0.574165 + 0.818740i \(0.305327\pi\)
\(548\) 3863.58 + 1406.23i 0.301175 + 0.109619i
\(549\) 11482.5 + 20845.6i 0.892642 + 1.62052i
\(550\) 27864.5 10141.8i 2.16026 0.786272i
\(551\) −3893.07 + 13003.8i −0.300999 + 1.00541i
\(552\) 796.344 + 2258.35i 0.0614033 + 0.174134i
\(553\) 37.3624 641.487i 0.00287307 0.0493288i
\(554\) −6998.72 4603.13i −0.536728 0.353011i
\(555\) −2725.96 + 452.441i −0.208487 + 0.0346037i
\(556\) 235.912 55.9122i 0.0179944 0.00426476i
\(557\) −606.007 + 3436.84i −0.0460994 + 0.261443i −0.999143 0.0413903i \(-0.986821\pi\)
0.953044 + 0.302833i \(0.0979324\pi\)
\(558\) −5051.50 + 5142.99i −0.383238 + 0.390180i
\(559\) −2704.72 15339.2i −0.204646 1.16061i
\(560\) 1752.41 + 4062.54i 0.132237 + 0.306560i
\(561\) −24288.8 10768.2i −1.82794 0.810398i
\(562\) 4731.41 + 15804.0i 0.355129 + 1.18621i
\(563\) −11629.1 15620.6i −0.870533 1.16933i −0.984420 0.175835i \(-0.943738\pi\)
0.113887 0.993494i \(-0.463670\pi\)
\(564\) −3721.48 + 7227.90i −0.277841 + 0.539627i
\(565\) 10949.4 + 5498.97i 0.815297 + 0.409458i
\(566\) −9575.07 −0.711078
\(567\) −4461.54 + 9296.03i −0.330454 + 0.688530i
\(568\) 4424.27 0.326828
\(569\) 8729.55 + 4384.14i 0.643166 + 0.323010i 0.740316 0.672260i \(-0.234676\pi\)
−0.0971491 + 0.995270i \(0.530972\pi\)
\(570\) 27536.4 1326.09i 2.02346 0.0974453i
\(571\) −8404.90 11289.7i −0.615996 0.827427i 0.379201 0.925314i \(-0.376199\pi\)
−0.995197 + 0.0978875i \(0.968791\pi\)
\(572\) −4351.86 14536.2i −0.318113 1.06257i
\(573\) 9967.82 7266.11i 0.726722 0.529749i
\(574\) −949.328 2200.79i −0.0690317 0.160033i
\(575\) −2572.90 14591.6i −0.186604 1.05828i
\(576\) 135.150 1722.71i 0.00977647 0.124617i
\(577\) −3133.37 + 17770.2i −0.226073 + 1.28212i 0.634551 + 0.772881i \(0.281185\pi\)
−0.860624 + 0.509242i \(0.829926\pi\)
\(578\) 5751.18 1363.06i 0.413872 0.0980894i
\(579\) −8772.90 10671.3i −0.629688 0.765946i
\(580\) −6535.96 4298.77i −0.467916 0.307753i
\(581\) 481.463 8266.40i 0.0343794 0.590272i
\(582\) 582.230 + 108.711i 0.0414677 + 0.00774266i
\(583\) −6559.50 + 21910.3i −0.465981 + 1.55648i
\(584\) −8879.38 + 3231.83i −0.629163 + 0.228997i
\(585\) −26155.7 22859.3i −1.84855 1.61558i
\(586\) 116.137 + 42.2703i 0.00818697 + 0.00297981i
\(587\) 11459.6 15392.9i 0.805774 1.08234i −0.189173 0.981944i \(-0.560581\pi\)
0.994947 0.100399i \(-0.0320118\pi\)
\(588\) −1306.57 2668.16i −0.0916359 0.187131i
\(589\) 17626.1 + 4177.45i 1.23305 + 0.292239i
\(590\) 730.598 1693.72i 0.0509801 0.118185i
\(591\) 2152.64 + 668.118i 0.149827 + 0.0465021i
\(592\) 363.620 239.157i 0.0252444 0.0166035i
\(593\) 10014.9 + 17346.3i 0.693528 + 1.20123i 0.970674 + 0.240398i \(0.0772779\pi\)
−0.277147 + 0.960828i \(0.589389\pi\)
\(594\) −16111.3 1427.12i −1.11288 0.0985785i
\(595\) −12264.3 + 21242.4i −0.845019 + 1.46362i
\(596\) 281.495 + 4833.08i 0.0193464 + 0.332166i
\(597\) 175.529 1381.14i 0.0120334 0.0946838i
\(598\) −7530.64 + 880.206i −0.514968 + 0.0601911i
\(599\) −6103.89 + 6469.74i −0.416357 + 0.441313i −0.901275 0.433246i \(-0.857368\pi\)
0.484918 + 0.874560i \(0.338849\pi\)
\(600\) −2570.23 + 10378.4i −0.174882 + 0.706160i
\(601\) −5284.10 617.623i −0.358641 0.0419191i −0.0651351 0.997876i \(-0.520748\pi\)
−0.293506 + 0.955957i \(0.594822\pi\)
\(602\) −5129.08 + 4303.81i −0.347252 + 0.291379i
\(603\) −710.157 374.726i −0.0479599 0.0253069i
\(604\) 10476.9 + 8791.18i 0.705794 + 0.592232i
\(605\) 26722.0 + 28323.7i 1.79571 + 1.90334i
\(606\) −3482.26 2057.46i −0.233428 0.137918i
\(607\) −7974.42 + 4004.90i −0.533232 + 0.267799i −0.694975 0.719034i \(-0.744585\pi\)
0.161743 + 0.986833i \(0.448288\pi\)
\(608\) −3880.23 + 1948.72i −0.258822 + 0.129985i
\(609\) −6330.01 3740.01i −0.421190 0.248855i
\(610\) 23651.0 + 25068.5i 1.56983 + 1.66393i
\(611\) −19718.2 16545.5i −1.30558 1.09551i
\(612\) 8108.18 5102.22i 0.535546 0.337002i
\(613\) 20129.4 16890.6i 1.32630 1.11290i 0.341370 0.939929i \(-0.389109\pi\)
0.984928 0.172967i \(-0.0553353\pi\)
\(614\) −3618.24 422.912i −0.237818 0.0277969i
\(615\) 2069.04 8354.61i 0.135661 0.547789i
\(616\) −4476.12 + 4744.41i −0.292773 + 0.310321i
\(617\) −7712.13 + 901.419i −0.503207 + 0.0588164i −0.363910 0.931434i \(-0.618558\pi\)
−0.139297 + 0.990251i \(0.544484\pi\)
\(618\) 20.0650 157.880i 0.00130604 0.0102765i
\(619\) −64.2295 1102.78i −0.00417060 0.0716065i 0.995581 0.0939107i \(-0.0299368\pi\)
−0.999751 + 0.0223042i \(0.992900\pi\)
\(620\) −5219.80 + 9040.96i −0.338116 + 0.585635i
\(621\) −2100.20 + 7804.26i −0.135714 + 0.504306i
\(622\) −6945.89 12030.6i −0.447757 0.775538i
\(623\) 3749.57 2466.13i 0.241129 0.158593i
\(624\) 5225.30 + 1621.79i 0.335223 + 0.104044i
\(625\) 7279.87 16876.6i 0.465912 1.08010i
\(626\) −5004.05 1185.98i −0.319492 0.0757210i
\(627\) 17874.2 + 36501.1i 1.13848 + 2.32490i
\(628\) 762.678 1024.45i 0.0484620 0.0650958i
\(629\) 2267.32 + 825.238i 0.143727 + 0.0523122i
\(630\) −2888.21 + 14650.3i −0.182649 + 0.926480i
\(631\) 21471.9 7815.15i 1.35465 0.493053i 0.440255 0.897873i \(-0.354888\pi\)
0.914396 + 0.404820i \(0.132666\pi\)
\(632\) −104.235 + 348.170i −0.00656053 + 0.0219137i
\(633\) 28926.9 + 5401.10i 1.81634 + 0.339138i
\(634\) −558.427 + 9587.81i −0.0349810 + 0.600600i
\(635\) −23424.3 15406.4i −1.46388 0.962811i
\(636\) −5237.04 6370.29i −0.326513 0.397167i
\(637\) 9152.88 2169.27i 0.569310 0.134929i
\(638\) 2002.68 11357.8i 0.124274 0.704793i
\(639\) 12307.9 + 8454.46i 0.761959 + 0.523401i
\(640\) −434.540 2464.40i −0.0268386 0.152209i
\(641\) −3954.14 9166.73i −0.243649 0.564843i 0.751880 0.659301i \(-0.229147\pi\)
−0.995529 + 0.0944579i \(0.969888\pi\)
\(642\) 11308.1 8243.13i 0.695165 0.506745i
\(643\) −173.751 580.368i −0.0106564 0.0355948i 0.952496 0.304551i \(-0.0985065\pi\)
−0.963152 + 0.268956i \(0.913321\pi\)
\(644\) 1946.26 + 2614.28i 0.119089 + 0.159965i
\(645\) −24016.0 + 1156.56i −1.46609 + 0.0706037i
\(646\) −21511.8 10803.6i −1.31017 0.657992i
\(647\) 27732.2 1.68511 0.842553 0.538613i \(-0.181052\pi\)
0.842553 + 0.538613i \(0.181052\pi\)
\(648\) 3667.95 4534.14i 0.222362 0.274873i
\(649\) 2719.37 0.164475
\(650\) −30251.9 15193.1i −1.82550 0.916802i
\(651\) −4491.39 + 8723.23i −0.270401 + 0.525177i
\(652\) −7416.66 9962.30i −0.445489 0.598395i
\(653\) 763.867 + 2551.49i 0.0457771 + 0.152906i 0.977822 0.209435i \(-0.0671626\pi\)
−0.932045 + 0.362342i \(0.881977\pi\)
\(654\) 14375.7 + 6373.29i 0.859531 + 0.381063i
\(655\) 5899.73 + 13677.1i 0.351942 + 0.815892i
\(656\) 235.402 + 1335.03i 0.0140105 + 0.0794577i
\(657\) −30877.4 7977.26i −1.83355 0.473702i
\(658\) −1921.39 + 10896.8i −0.113835 + 0.645592i
\(659\) 17087.9 4049.90i 1.01009 0.239395i 0.307925 0.951411i \(-0.400366\pi\)
0.702164 + 0.712015i \(0.252217\pi\)
\(660\) −23106.9 + 3835.17i −1.36278 + 0.226188i
\(661\) 4771.99 + 3138.59i 0.280800 + 0.184685i 0.682095 0.731264i \(-0.261069\pi\)
−0.401294 + 0.915949i \(0.631440\pi\)
\(662\) −519.551 + 8920.35i −0.0305029 + 0.523715i
\(663\) 10087.0 + 28605.6i 0.590868 + 1.67564i
\(664\) −1343.21 + 4486.62i −0.0785037 + 0.262221i
\(665\) 35258.8 12833.1i 2.05605 0.748342i
\(666\) 1468.57 + 29.5428i 0.0854442 + 0.00171886i
\(667\) −5415.19 1970.97i −0.314359 0.114417i
\(668\) 1044.19 1402.59i 0.0604803 0.0812391i
\(669\) 2197.56 + 150.183i 0.126999 + 0.00867923i
\(670\) −1131.47 268.163i −0.0652424 0.0154627i
\(671\) −20124.5 + 46653.9i −1.15782 + 2.68413i
\(672\) −519.338 2293.82i −0.0298124 0.131676i
\(673\) 676.348 444.841i 0.0387389 0.0254790i −0.529992 0.848003i \(-0.677805\pi\)
0.568731 + 0.822524i \(0.307435\pi\)
\(674\) −2487.54 4308.54i −0.142161 0.246230i
\(675\) −26982.5 + 23960.1i −1.53860 + 1.36626i
\(676\) −4267.43 + 7391.41i −0.242799 + 0.420540i
\(677\) −1511.51 25951.6i −0.0858080 1.47327i −0.716693 0.697389i \(-0.754345\pi\)
0.630885 0.775877i \(-0.282692\pi\)
\(678\) −5184.98 3941.73i −0.293699 0.223276i
\(679\) 800.683 93.5864i 0.0452539 0.00528942i
\(680\) 9520.41 10091.0i 0.536899 0.569080i
\(681\) −17328.6 + 4998.52i −0.975087 + 0.281268i
\(682\) −15286.5 1786.74i −0.858286 0.100319i
\(683\) 19459.5 16328.5i 1.09019 0.914777i 0.0934618 0.995623i \(-0.470207\pi\)
0.996727 + 0.0808462i \(0.0257623\pi\)
\(684\) −14518.3 1993.69i −0.811579 0.111448i
\(685\) 15393.9 + 12917.0i 0.858641 + 0.720485i
\(686\) −9433.45 9998.87i −0.525030 0.556499i
\(687\) 10190.1 5747.42i 0.565906 0.319181i
\(688\) 3384.16 1699.59i 0.187529 0.0941806i
\(689\) 23333.2 11718.4i 1.29017 0.647946i
\(690\) −117.704 + 11703.3i −0.00649410 + 0.645705i
\(691\) 4468.16 + 4735.98i 0.245987 + 0.260731i 0.838589 0.544764i \(-0.183381\pi\)
−0.592602 + 0.805495i \(0.701899\pi\)
\(692\) −5832.20 4893.80i −0.320386 0.268836i
\(693\) −21518.3 + 4644.92i −1.17953 + 0.254611i
\(694\) 5025.18 4216.63i 0.274861 0.230635i
\(695\) 1176.96 + 137.566i 0.0642367 + 0.00750819i
\(696\) 2995.90 + 2883.98i 0.163160 + 0.157064i
\(697\) −5157.47 + 5466.60i −0.280277 + 0.297076i
\(698\) 10832.1 1266.09i 0.587393 0.0686564i
\(699\) −27259.3 + 11434.7i −1.47502 + 0.618744i
\(700\) 846.132 + 14527.5i 0.0456868 + 0.784413i
\(701\) −5250.27 + 9093.73i −0.282881 + 0.489965i −0.972093 0.234595i \(-0.924624\pi\)
0.689212 + 0.724560i \(0.257957\pi\)
\(702\) 11437.1 + 14496.8i 0.614910 + 0.779413i
\(703\) −1845.47 3196.44i −0.0990087 0.171488i
\(704\) 3082.27 2027.24i 0.165011 0.108529i
\(705\) −29174.3 + 26975.2i −1.55854 + 1.44106i
\(706\) 7329.32 16991.3i 0.390712 0.905772i
\(707\) −5356.56 1269.53i −0.284943 0.0675326i
\(708\) −547.018 + 813.756i −0.0290370 + 0.0431961i
\(709\) 7311.83 9821.49i 0.387308 0.520245i −0.565120 0.825009i \(-0.691170\pi\)
0.952428 + 0.304764i \(0.0985775\pi\)
\(710\) 20319.7 + 7395.76i 1.07406 + 0.390926i
\(711\) −955.300 + 769.387i −0.0503890 + 0.0405827i
\(712\) −2385.25 + 868.159i −0.125549 + 0.0456961i
\(713\) −2205.60 + 7367.21i −0.115849 + 0.386963i
\(714\) 8481.14 9903.43i 0.444536 0.519085i
\(715\) 4312.13 74036.4i 0.225545 3.87245i
\(716\) 7902.34 + 5197.45i 0.412464 + 0.271282i
\(717\) 5060.68 13480.7i 0.263591 0.702157i
\(718\) 9595.46 2274.17i 0.498746 0.118205i
\(719\) 1879.53 10659.3i 0.0974889 0.552887i −0.896467 0.443110i \(-0.853875\pi\)
0.993956 0.109777i \(-0.0350137\pi\)
\(720\) 3500.45 7686.09i 0.181186 0.397838i
\(721\) −37.6139 213.319i −0.00194288 0.0110186i
\(722\) 9151.66 + 21215.9i 0.471731 + 1.09360i
\(723\) 1657.70 + 15536.0i 0.0852704 + 0.799157i
\(724\) 4911.99 + 16407.2i 0.252144 + 0.842221i
\(725\) −15365.0 20638.8i −0.787093 1.05725i
\(726\) −11199.9 17407.5i −0.572545 0.889879i
\(727\) −21374.2 10734.5i −1.09041 0.547622i −0.189608 0.981860i \(-0.560722\pi\)
−0.900798 + 0.434237i \(0.857018\pi\)
\(728\) 7446.52 0.379102
\(729\) 18868.3 5604.32i 0.958608 0.284729i
\(730\) −46183.5 −2.34154
\(731\) 18761.6 + 9422.43i 0.949279 + 0.476746i
\(732\) −9912.75 15406.9i −0.500527 0.777944i
\(733\) 8495.65 + 11411.6i 0.428095 + 0.575032i 0.962871 0.269962i \(-0.0870112\pi\)
−0.534775 + 0.844994i \(0.679604\pi\)
\(734\) 2437.43 + 8141.59i 0.122571 + 0.409417i
\(735\) −1540.58 14438.4i −0.0773132 0.724582i
\(736\) −730.132 1692.64i −0.0365666 0.0847709i
\(737\) −297.681 1688.23i −0.0148782 0.0843783i
\(738\) −1896.29 + 4163.76i −0.0945845 + 0.207683i
\(739\) 253.677 1438.67i 0.0126274 0.0716136i −0.977843 0.209340i \(-0.932868\pi\)
0.990470 + 0.137727i \(0.0439795\pi\)
\(740\) 2069.81 490.554i 0.102821 0.0243691i
\(741\) 16307.1 43439.1i 0.808444 2.15354i
\(742\) −9377.54 6167.71i −0.463963 0.305153i
\(743\) −244.524 + 4198.32i −0.0120737 + 0.207297i 0.986876 + 0.161479i \(0.0516264\pi\)
−0.998950 + 0.0458177i \(0.985411\pi\)
\(744\) 3609.66 4215.00i 0.177872 0.207701i
\(745\) −6786.30 + 22667.8i −0.333733 + 1.11474i
\(746\) 20180.7 7345.18i 0.990440 0.360491i
\(747\) −12310.3 + 9914.55i −0.602958 + 0.485615i
\(748\) 19219.2 + 6995.23i 0.939472 + 0.341940i
\(749\) 11373.5 15277.2i 0.554843 0.745283i
\(750\) −14985.2 + 22292.3i −0.729575 + 1.08533i
\(751\) −25160.0 5963.03i −1.22250 0.289739i −0.431818 0.901961i \(-0.642128\pi\)
−0.790686 + 0.612222i \(0.790276\pi\)
\(752\) 2478.76 5746.42i 0.120201 0.278657i
\(753\) 3788.08 3502.53i 0.183327 0.169508i
\(754\) −11000.4 + 7235.10i −0.531316 + 0.349452i
\(755\) 33422.5 + 57889.5i 1.61109 + 2.79048i
\(756\) 2938.59 7373.61i 0.141370 0.354730i
\(757\) 14055.9 24345.5i 0.674862 1.16890i −0.301647 0.953420i \(-0.597537\pi\)
0.976509 0.215475i \(-0.0691301\pi\)
\(758\) 23.6643 + 406.300i 0.00113394 + 0.0194690i
\(759\) −15911.3 + 6674.47i −0.760925 + 0.319193i
\(760\) −21078.6 + 2463.73i −1.00605 + 0.117591i
\(761\) 17146.5 18174.2i 0.816766 0.865721i −0.176172 0.984359i \(-0.556371\pi\)
0.992938 + 0.118638i \(0.0378529\pi\)
\(762\) 10737.0 + 10335.9i 0.510448 + 0.491379i
\(763\) 21257.8 + 2484.68i 1.00863 + 0.117892i
\(764\) −7274.01 + 6103.62i −0.344456 + 0.289033i
\(765\) 45768.1 9879.44i 2.16307 0.466917i
\(766\) 21485.5 + 18028.5i 1.01345 + 0.850386i
\(767\) −2130.46 2258.16i −0.100295 0.106307i
\(768\) −13.3778 + 1330.15i −0.000628554 + 0.0624968i
\(769\) −35410.3 + 17783.7i −1.66051 + 0.833937i −0.664247 + 0.747513i \(0.731248\pi\)
−0.996258 + 0.0864237i \(0.972456\pi\)
\(770\) −28488.7 + 14307.6i −1.33333 + 0.669622i
\(771\) 25864.1 14587.8i 1.20814 0.681410i
\(772\) 7297.76 + 7735.17i 0.340223 + 0.360615i
\(773\) −27917.4 23425.5i −1.29899 1.08998i −0.990319 0.138811i \(-0.955672\pi\)
−0.308669 0.951169i \(-0.599884\pi\)
\(774\) 12662.2 + 1738.81i 0.588027 + 0.0807496i
\(775\) −26303.4 + 22071.2i −1.21916 + 1.02299i
\(776\) −452.863 52.9321i −0.0209495 0.00244865i
\(777\) 1920.87 554.083i 0.0886883 0.0255825i
\(778\) −5550.08 + 5882.74i −0.255758 + 0.271088i
\(779\) 11418.8 1334.67i 0.525189 0.0613858i
\(780\) 21287.6 + 16183.3i 0.977203 + 0.742891i
\(781\) 1853.59 + 31824.9i 0.0849253 + 1.45811i
\(782\) 5109.84 8850.51i 0.233667 0.404723i
\(783\) 2823.20 + 13747.9i 0.128854 + 0.627471i
\(784\) 1143.50 + 1980.59i 0.0520908 + 0.0902239i
\(785\) 5215.32 3430.17i 0.237125 0.155959i
\(786\) −1748.43 7722.48i −0.0793439 0.350448i
\(787\) 8173.43 18948.1i 0.370205 0.858232i −0.626673 0.779282i \(-0.715584\pi\)
0.996879 0.0789499i \(-0.0251567\pi\)
\(788\) −1688.31 400.137i −0.0763243 0.0180892i
\(789\) −20190.1 1379.81i −0.911010 0.0622591i
\(790\) −1060.74 + 1424.82i −0.0477715 + 0.0641683i
\(791\) −8330.07 3031.90i −0.374442 0.136286i
\(792\) 12448.5 + 250.424i 0.558508 + 0.0112354i
\(793\) 54507.7 19839.2i 2.44089 0.888410i
\(794\) 7278.95 24313.4i 0.325341 1.08671i
\(795\) −13403.8 38011.8i −0.597966 1.69577i
\(796\) −62.3169 + 1069.94i −0.00277483 + 0.0476420i
\(797\) 15852.8 + 10426.5i 0.704560 + 0.463397i 0.850553 0.525889i \(-0.176267\pi\)
−0.145993 + 0.989286i \(0.546638\pi\)
\(798\) −19676.2 + 3265.77i −0.872847 + 0.144871i
\(799\) 33760.1 8001.30i 1.49480 0.354275i
\(800\) 1429.24 8105.60i 0.0631639 0.358220i
\(801\) −8294.51 2142.91i −0.365883 0.0945269i
\(802\) −111.694 633.451i −0.00491779 0.0278902i
\(803\) −26967.5 62517.7i −1.18513 2.74745i
\(804\) 565.075 + 250.520i 0.0247869 + 0.0109890i
\(805\) 4568.62 + 15260.3i 0.200028 + 0.668141i
\(806\) 10492.4 + 14093.7i 0.458534 + 0.615917i
\(807\) −10781.0 + 20939.0i −0.470272 + 0.913367i
\(808\) 2782.40 + 1397.37i 0.121144 + 0.0608408i
\(809\) −26672.0 −1.15913 −0.579566 0.814925i \(-0.696778\pi\)
−0.579566 + 0.814925i \(0.696778\pi\)
\(810\) 24425.5 14692.8i 1.05954 0.637349i
\(811\) 30342.5 1.31377 0.656887 0.753989i \(-0.271873\pi\)
0.656887 + 0.753989i \(0.271873\pi\)
\(812\) 5057.80 + 2540.12i 0.218589 + 0.109779i
\(813\) −10692.7 + 514.937i −0.461267 + 0.0222136i
\(814\) 1872.66 + 2515.42i 0.0806348 + 0.108311i
\(815\) −17409.7 58152.6i −0.748266 2.49938i
\(816\) −5959.36 + 4344.12i −0.255661 + 0.186366i
\(817\) −12720.5 29489.3i −0.544715 1.26279i
\(818\) −1318.59 7478.07i −0.0563609 0.319639i
\(819\) 20715.5 + 14229.8i 0.883830 + 0.607117i
\(820\) −1150.54 + 6525.01i −0.0489981 + 0.277882i
\(821\) 29376.5 6962.36i 1.24878 0.295966i 0.447515 0.894277i \(-0.352309\pi\)
0.801264 + 0.598311i \(0.204161\pi\)
\(822\) −6783.66 8251.59i −0.287844 0.350130i
\(823\) −4781.22 3144.66i −0.202507 0.133191i 0.444205 0.895925i \(-0.353486\pi\)
−0.646712 + 0.762734i \(0.723856\pi\)
\(824\) −7.12355 + 122.307i −0.000301166 + 0.00517082i
\(825\) −75731.3 14140.2i −3.19591 0.596726i
\(826\) −382.749 + 1278.47i −0.0161229 + 0.0538543i
\(827\) −39503.0 + 14377.9i −1.66101 + 0.604558i −0.990521 0.137362i \(-0.956138\pi\)
−0.670489 + 0.741920i \(0.733915\pi\)
\(828\) 1203.36 6103.97i 0.0505067 0.256193i
\(829\) 24903.1 + 9063.99i 1.04333 + 0.379741i 0.806142 0.591723i \(-0.201552\pi\)
0.237188 + 0.971464i \(0.423774\pi\)
\(830\) −13669.0 + 18360.7i −0.571637 + 0.767842i
\(831\) 9571.39 + 19545.9i 0.399552 + 0.815932i
\(832\) −4098.20 971.290i −0.170768 0.0404729i
\(833\) −5021.89 + 11642.0i −0.208881 + 0.484241i
\(834\) −601.587 186.716i −0.0249775 0.00775232i
\(835\) 7140.34 4696.27i 0.295930 0.194636i
\(836\) −15643.3 27095.0i −0.647172 1.12094i
\(837\) 18096.3 4827.90i 0.747310 0.199375i
\(838\) −1467.23 + 2541.31i −0.0604827 + 0.104759i
\(839\) 345.924 + 5939.29i 0.0142344 + 0.244395i 0.997918 + 0.0644897i \(0.0205420\pi\)
−0.983684 + 0.179905i \(0.942421\pi\)
\(840\) 1449.23 11403.2i 0.0595275 0.468389i
\(841\) 14284.4 1669.61i 0.585690 0.0684574i
\(842\) 8492.52 9001.54i 0.347591 0.368425i
\(843\) 10303.3 41603.8i 0.420952 1.69977i
\(844\) −22499.6 2629.83i −0.917617 0.107254i
\(845\) −31955.1 + 26813.5i −1.30093 + 1.09161i
\(846\) 17876.7 11249.2i 0.726493 0.457158i
\(847\) −21581.4 18108.9i −0.875497 0.734629i
\(848\) 4356.45 + 4617.57i 0.176416 + 0.186990i
\(849\) 21417.7 + 12654.4i 0.865788 + 0.511541i
\(850\) 40776.7 20478.8i 1.64545 0.826374i
\(851\) 1400.28 703.248i 0.0564055 0.0283279i
\(852\) −9896.29 5847.11i −0.397936 0.235116i
\(853\) −10927.3 11582.2i −0.438619 0.464909i 0.469920 0.882709i \(-0.344283\pi\)
−0.908539 + 0.417800i \(0.862801\pi\)
\(854\) −19101.1 16027.8i −0.765371 0.642223i
\(855\) −63346.5 33425.8i −2.53381 1.33701i
\(856\) −8252.09 + 6924.32i −0.329498 + 0.276482i
\(857\) 10002.0 + 1169.07i 0.398672 + 0.0465980i 0.313067 0.949731i \(-0.398644\pi\)
0.0856048 + 0.996329i \(0.472718\pi\)
\(858\) −9476.75 + 38266.4i −0.377076 + 1.52260i
\(859\) 15040.5 15942.0i 0.597411 0.633219i −0.356146 0.934430i \(-0.615909\pi\)
0.953557 + 0.301211i \(0.0973909\pi\)
\(860\) 18383.8 2148.76i 0.728933 0.0852000i
\(861\) −785.086 + 6177.40i −0.0310751 + 0.244513i
\(862\) −822.800 14126.9i −0.0325112 0.558196i
\(863\) −18314.3 + 31721.4i −0.722395 + 1.25123i 0.237642 + 0.971353i \(0.423626\pi\)
−0.960037 + 0.279873i \(0.909708\pi\)
\(864\) −2579.04 + 3674.77i −0.101552 + 0.144697i
\(865\) −18605.4 32225.4i −0.731331 1.26670i
\(866\) 2111.41 1388.70i 0.0828506 0.0544917i
\(867\) −14665.8 4551.85i −0.574483 0.178303i
\(868\) 2991.58 6935.25i 0.116982 0.271196i
\(869\) −2548.15 603.922i −0.0994706 0.0235750i
\(870\) 8938.53 + 18253.5i 0.348327 + 0.711324i
\(871\) −1168.69 + 1569.82i −0.0454645 + 0.0610694i
\(872\) −11375.2 4140.22i −0.441756 0.160786i
\(873\) −1158.67 1012.64i −0.0449199 0.0392586i
\(874\) −14690.4 + 5346.85i −0.568546 + 0.206934i
\(875\) −10485.1 + 35022.7i −0.405099 + 1.35313i
\(876\) 24132.8 + 4505.96i 0.930789 + 0.173793i
\(877\) 1860.80 31948.7i 0.0716473 1.23014i −0.750503 0.660867i \(-0.770189\pi\)
0.822151 0.569270i \(-0.192774\pi\)
\(878\) −19588.2 12883.3i −0.752926 0.495207i
\(879\) −203.913 248.038i −0.00782458 0.00951774i
\(880\) 17545.0 4158.24i 0.672093 0.159289i
\(881\) −2430.98 + 13786.8i −0.0929645 + 0.527228i 0.902388 + 0.430925i \(0.141813\pi\)
−0.995352 + 0.0963025i \(0.969298\pi\)
\(882\) −603.685 + 7694.96i −0.0230467 + 0.293767i
\(883\) −1805.84 10241.4i −0.0688238 0.390319i −0.999689 0.0249551i \(-0.992056\pi\)
0.930865 0.365364i \(-0.119055\pi\)
\(884\) −9248.30 21440.0i −0.351871 0.815728i
\(885\) −3872.64 + 2822.99i −0.147093 + 0.107224i
\(886\) −2278.84 7611.86i −0.0864099 0.288629i
\(887\) 30042.1 + 40353.5i 1.13722 + 1.52755i 0.813656 + 0.581347i \(0.197474\pi\)
0.323565 + 0.946206i \(0.395119\pi\)
\(888\) −1129.42 + 54.3906i −0.0426813 + 0.00205544i
\(889\) 18126.7 + 9103.59i 0.683859 + 0.343447i
\(890\) −12406.2 −0.467253
\(891\) 34151.9 + 24484.9i 1.28410 + 0.920622i
\(892\) −1695.63 −0.0636478
\(893\) −47428.5 23819.5i −1.77731 0.892597i
\(894\) 5757.75 11182.8i 0.215400 0.418353i
\(895\) 27605.5 + 37080.6i 1.03100 + 1.38488i
\(896\) 519.251 + 1734.42i 0.0193604 + 0.0646684i
\(897\) 18008.0 + 7983.63i 0.670311 + 0.297175i
\(898\) −7511.64 17413.9i −0.279139 0.647116i
\(899\) 2319.02 + 13151.8i 0.0860329 + 0.487917i
\(900\) 19465.2 19817.8i 0.720935 0.733993i
\(901\) −6111.46 + 34659.8i −0.225974 + 1.28156i
\(902\) −9504.61 + 2252.63i −0.350852 + 0.0831535i
\(903\) 17160.7 2848.26i 0.632418 0.104966i
\(904\) 4189.00 + 2755.15i 0.154119 + 0.101366i
\(905\) −4867.14 + 83565.6i −0.178773 + 3.06941i
\(906\) −11816.6 33510.6i −0.433311 1.22882i
\(907\) −7082.35 + 23656.7i −0.259278 + 0.866050i 0.724898 + 0.688857i \(0.241887\pi\)
−0.984176 + 0.177193i \(0.943298\pi\)
\(908\) 13046.2 4748.42i 0.476820 0.173548i
\(909\) 5070.07 + 9204.32i 0.184998 + 0.335850i
\(910\) 34200.2 + 12447.9i 1.24585 + 0.453453i
\(911\) −455.578 + 611.947i −0.0165686 + 0.0222555i −0.810330 0.585973i \(-0.800712\pi\)
0.793762 + 0.608229i \(0.208120\pi\)
\(912\) 11254.8 + 769.162i 0.408645 + 0.0279271i
\(913\) −32836.2 7782.31i −1.19027 0.282100i
\(914\) −2244.00 + 5202.17i −0.0812087 + 0.188263i
\(915\) −19772.4 87331.0i −0.714376 3.15527i
\(916\) −7524.45 + 4948.91i −0.271414 + 0.178512i
\(917\) −5388.32 9332.85i −0.194044 0.336093i
\(918\) −24879.7 + 696.976i −0.894500 + 0.0250584i
\(919\) −15717.8 + 27224.0i −0.564180 + 0.977188i 0.432946 + 0.901420i \(0.357474\pi\)
−0.997125 + 0.0757681i \(0.975859\pi\)
\(920\) −523.865 8994.41i −0.0187732 0.322323i
\(921\) 7534.44 + 5727.84i 0.269564 + 0.204928i
\(922\) −28373.8 + 3316.43i −1.01350 + 0.118461i
\(923\) 24975.2 26472.1i 0.890647 0.944031i
\(924\) 16282.5 4696.76i 0.579713 0.167221i
\(925\) 6949.05 + 812.228i 0.247009 + 0.0288712i
\(926\) 2296.18 1926.72i 0.0814870 0.0683757i
\(927\) −253.536 + 326.632i −0.00898299 + 0.0115728i
\(928\) −2452.24 2057.68i −0.0867445 0.0727872i
\(929\) −4349.25 4609.94i −0.153600 0.162806i 0.646004 0.763334i \(-0.276439\pi\)
−0.799604 + 0.600527i \(0.794957\pi\)
\(930\) 23624.3 13324.5i 0.832980 0.469815i
\(931\) 17332.1 8704.53i 0.610137 0.306423i
\(932\) 20335.2 10212.7i 0.714702 0.358937i
\(933\) −362.971 + 36090.1i −0.0127365 + 1.26638i
\(934\) −8881.66 9414.01i −0.311153 0.329803i
\(935\) 76576.2 + 64255.1i 2.67841 + 2.24745i
\(936\) −9544.70 10533.4i −0.333310 0.367837i
\(937\) −24974.4 + 20956.0i −0.870736 + 0.730634i −0.964253 0.264984i \(-0.914633\pi\)
0.0935170 + 0.995618i \(0.470189\pi\)
\(938\) 835.596 + 97.6672i 0.0290865 + 0.00339973i
\(939\) 9625.77 + 9266.18i 0.334532 + 0.322035i
\(940\) 20990.3 22248.4i 0.728328 0.771983i
\(941\) −7393.21 + 864.142i −0.256123 + 0.0299365i −0.243185 0.969980i \(-0.578192\pi\)
−0.0129375 + 0.999916i \(0.504118\pi\)
\(942\) −3059.89 + 1283.57i −0.105835 + 0.0443958i
\(943\) 283.792 + 4872.52i 0.00980014 + 0.168262i
\(944\) 377.404 653.683i 0.0130121 0.0225377i
\(945\) 25822.3 28953.1i 0.888887 0.996661i
\(946\) 13643.4 + 23631.1i 0.468907 + 0.812170i
\(947\) 27585.6 18143.3i 0.946579 0.622575i 0.0204537 0.999791i \(-0.493489\pi\)
0.926125 + 0.377216i \(0.123119\pi\)
\(948\) 693.297 641.036i 0.0237524 0.0219619i
\(949\) −30787.2 + 71372.6i −1.05310 + 2.44136i
\(950\) −67919.6 16097.2i −2.31958 0.549751i
\(951\) 13920.4 20708.2i 0.474657 0.706109i
\(952\) −5993.80 + 8051.07i −0.204055 + 0.274093i
\(953\) −40123.9 14603.9i −1.36384 0.496397i −0.446601 0.894733i \(-0.647366\pi\)
−0.917240 + 0.398336i \(0.869588\pi\)
\(954\) 3295.36 + 21170.5i 0.111836 + 0.718469i
\(955\) −43610.9 + 15873.1i −1.47771 + 0.537844i
\(956\) −3179.10 + 10618.9i −0.107552 + 0.359247i
\(957\) −19490.0 + 22758.5i −0.658332 + 0.768734i
\(958\) −850.664 + 14605.3i −0.0286886 + 0.492565i
\(959\) −12146.9 7989.17i −0.409015 0.269013i
\(960\) −2284.96 + 6086.71i −0.0768196 + 0.204633i
\(961\) −11646.7 + 2760.32i −0.390947 + 0.0926562i
\(962\) 621.682 3525.73i 0.0208356 0.118164i
\(963\) −36188.4 + 3493.61i −1.21096 + 0.116905i
\(964\) −2088.56 11844.8i −0.0697800 0.395742i
\(965\) 20586.6 + 47725.1i 0.686742 + 1.59205i
\(966\) −898.404 8419.87i −0.0299231 0.280440i
\(967\) −2281.88 7622.02i −0.0758846 0.253472i 0.911627 0.411018i \(-0.134827\pi\)
−0.987512 + 0.157546i \(0.949642\pi\)
\(968\) 9515.29 + 12781.3i 0.315943 + 0.424385i
\(969\) 33839.9 + 52595.8i 1.12187 + 1.74367i
\(970\) −1991.42 1000.13i −0.0659181 0.0331053i
\(971\) 12674.8 0.418903 0.209451 0.977819i \(-0.432832\pi\)
0.209451 + 0.977819i \(0.432832\pi\)
\(972\) −14196.9 + 5294.49i −0.468482 + 0.174713i
\(973\) −857.315 −0.0282469
\(974\) 8898.29 + 4468.89i 0.292731 + 0.147015i
\(975\) 47589.0 + 73965.1i 1.56314 + 2.42952i
\(976\) 8421.73 + 11312.4i 0.276202 + 0.371004i
\(977\) 7744.25 + 25867.6i 0.253593 + 0.847060i 0.986079 + 0.166278i \(0.0531748\pi\)
−0.732486 + 0.680782i \(0.761640\pi\)
\(978\) 3423.56 + 32085.8i 0.111936 + 1.04907i
\(979\) −7244.22 16794.0i −0.236492 0.548251i
\(980\) 1941.00 + 11007.9i 0.0632682 + 0.358812i
\(981\) −23732.9 33254.8i −0.772408 1.08231i
\(982\) 3808.09 21596.7i 0.123748 0.701812i
\(983\) −23984.6 + 5684.45i −0.778219 + 0.184441i −0.600484 0.799637i \(-0.705025\pi\)
−0.177735 + 0.984078i \(0.556877\pi\)
\(984\) 1237.83 3297.34i 0.0401021 0.106824i
\(985\) −7085.15 4659.98i −0.229190 0.150740i
\(986\) 1031.91 17717.1i 0.0333292 0.572240i
\(987\) 18699.0 21834.8i 0.603034 0.704163i
\(988\) −10244.1 + 34217.5i −0.329865 + 1.10183i
\(989\) 12812.3 4663.29i 0.411938 0.149933i
\(990\) 56754.6 + 21959.5i 1.82200 + 0.704968i
\(991\) −20904.3 7608.53i −0.670077 0.243888i −0.0154957 0.999880i \(-0.504933\pi\)
−0.654581 + 0.755992i \(0.727155\pi\)
\(992\) −2551.02 + 3426.61i −0.0816481 + 0.109672i
\(993\) 12951.3 19266.6i 0.413894 0.615717i
\(994\) −15222.9 3607.89i −0.485755 0.115126i
\(995\) −2074.76 + 4809.83i −0.0661047 + 0.153248i
\(996\) 8934.03 8260.59i 0.284222 0.262798i
\(997\) −24887.3 + 16368.6i −0.790559 + 0.519959i −0.879398 0.476087i \(-0.842055\pi\)
0.0888392 + 0.996046i \(0.471684\pi\)
\(998\) 349.968 + 606.162i 0.0111002 + 0.0192262i
\(999\) −3245.88 2006.94i −0.102798 0.0635604i
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 162.4.g.a.13.5 234
81.25 even 27 inner 162.4.g.a.25.5 yes 234
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.4.g.a.13.5 234 1.1 even 1 trivial
162.4.g.a.25.5 yes 234 81.25 even 27 inner