Properties

Label 16.7.f.a.11.8
Level $16$
Weight $7$
Character 16.11
Analytic conductor $3.681$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,7,Mod(3,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68086533792\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.8
Character \(\chi\) \(=\) 16.11
Dual form 16.7.f.a.3.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.82644 + 5.48203i) q^{2} +(-6.79913 - 6.79913i) q^{3} +(3.89476 + 63.8814i) q^{4} +(158.437 + 158.437i) q^{5} +(-2.34170 - 76.8878i) q^{6} -213.507 q^{7} +(-327.507 + 393.552i) q^{8} -636.544i q^{9} +O(q^{10})\) \(q+(5.82644 + 5.48203i) q^{2} +(-6.79913 - 6.79913i) q^{3} +(3.89476 + 63.8814i) q^{4} +(158.437 + 158.437i) q^{5} +(-2.34170 - 76.8878i) q^{6} -213.507 q^{7} +(-327.507 + 393.552i) q^{8} -636.544i q^{9} +(54.5675 + 1791.68i) q^{10} +(1309.41 - 1309.41i) q^{11} +(407.857 - 460.819i) q^{12} +(11.6360 - 11.6360i) q^{13} +(-1243.99 - 1170.45i) q^{14} -2154.47i q^{15} +(-4065.66 + 497.605i) q^{16} +2834.10 q^{17} +(3489.55 - 3708.78i) q^{18} +(-7194.40 - 7194.40i) q^{19} +(-9504.10 + 10738.3i) q^{20} +(1451.67 + 1451.67i) q^{21} +(14807.4 - 450.974i) q^{22} +7839.29 q^{23} +(4902.58 - 449.050i) q^{24} +34579.6i q^{25} +(131.585 - 4.00756i) q^{26} +(-9284.51 + 9284.51i) q^{27} +(-831.561 - 13639.2i) q^{28} +(-112.081 + 112.081i) q^{29} +(11810.9 - 12552.9i) q^{30} -7877.51i q^{31} +(-26416.2 - 19388.8i) q^{32} -17805.7 q^{33} +(16512.7 + 15536.6i) q^{34} +(-33827.5 - 33827.5i) q^{35} +(40663.3 - 2479.19i) q^{36} +(22766.4 + 22766.4i) q^{37} +(-2477.83 - 81357.6i) q^{38} -158.229 q^{39} +(-114242. + 10464.0i) q^{40} +20200.8i q^{41} +(499.970 + 16416.1i) q^{42} +(29632.7 - 29632.7i) q^{43} +(88746.6 + 78546.9i) q^{44} +(100852. - 100852. i) q^{45} +(45675.2 + 42975.2i) q^{46} +79640.8i q^{47} +(31026.3 + 24259.7i) q^{48} -72063.5 q^{49} +(-189566. + 201476. i) q^{50} +(-19269.4 - 19269.4i) q^{51} +(788.641 + 698.002i) q^{52} +(-189013. - 189013. i) q^{53} +(-104994. + 3197.69i) q^{54} +414917. q^{55} +(69925.2 - 84026.3i) q^{56} +97831.3i q^{57} +(-1267.46 + 38.6018i) q^{58} +(-251413. + 251413. i) q^{59} +(137630. - 8391.14i) q^{60} +(197272. - 197272. i) q^{61} +(43184.7 - 45897.8i) q^{62} +135907. i q^{63} +(-47622.5 - 257782. i) q^{64} +3687.14 q^{65} +(-103744. - 97611.1i) q^{66} +(-214576. - 214576. i) q^{67} +(11038.1 + 181046. i) q^{68} +(-53300.4 - 53300.4i) q^{69} +(-11650.6 - 382537. i) q^{70} -275257. q^{71} +(250513. + 208472. i) q^{72} +106038. i q^{73} +(7840.99 + 257453. i) q^{74} +(235111. - 235111. i) q^{75} +(431568. - 487609. i) q^{76} +(-279568. + 279568. i) q^{77} +(-921.911 - 867.415i) q^{78} +637548. i q^{79} +(-722990. - 565312. i) q^{80} -337787. q^{81} +(-110742. + 117699. i) q^{82} +(467104. + 467104. i) q^{83} +(-87080.5 + 98388.3i) q^{84} +(449026. + 449026. i) q^{85} +(335100. - 10205.8i) q^{86} +1524.10 q^{87} +(86480.1 + 944160. i) q^{88} -240298. i q^{89} +(1.14048e6 - 34734.6i) q^{90} +(-2484.37 + 2484.37i) q^{91} +(30532.2 + 500785. i) q^{92} +(-53560.2 + 53560.2i) q^{93} +(-436593. + 464022. i) q^{94} -2.27972e6i q^{95} +(47780.3 + 311434. i) q^{96} +869115. q^{97} +(-419874. - 395054. i) q^{98} +(-833495. - 833495. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.82644 + 5.48203i 0.728305 + 0.685253i
\(3\) −6.79913 6.79913i −0.251820 0.251820i 0.569897 0.821716i \(-0.306983\pi\)
−0.821716 + 0.569897i \(0.806983\pi\)
\(4\) 3.89476 + 63.8814i 0.0608556 + 0.998147i
\(5\) 158.437 + 158.437i 1.26750 + 1.26750i 0.947377 + 0.320119i \(0.103723\pi\)
0.320119 + 0.947377i \(0.396277\pi\)
\(6\) −2.34170 76.8878i −0.0108412 0.355962i
\(7\) −213.507 −0.622471 −0.311235 0.950333i \(-0.600743\pi\)
−0.311235 + 0.950333i \(0.600743\pi\)
\(8\) −327.507 + 393.552i −0.639662 + 0.768656i
\(9\) 636.544i 0.873174i
\(10\) 54.5675 + 1791.68i 0.0545675 + 1.79168i
\(11\) 1309.41 1309.41i 0.983777 0.983777i −0.0160934 0.999870i \(-0.505123\pi\)
0.999870 + 0.0160934i \(0.00512291\pi\)
\(12\) 407.857 460.819i 0.236028 0.266678i
\(13\) 11.6360 11.6360i 0.00529630 0.00529630i −0.704454 0.709750i \(-0.748808\pi\)
0.709750 + 0.704454i \(0.248808\pi\)
\(14\) −1243.99 1170.45i −0.453348 0.426550i
\(15\) 2154.47i 0.638361i
\(16\) −4065.66 + 497.605i −0.992593 + 0.121486i
\(17\) 2834.10 0.576857 0.288429 0.957501i \(-0.406867\pi\)
0.288429 + 0.957501i \(0.406867\pi\)
\(18\) 3489.55 3708.78i 0.598345 0.635937i
\(19\) −7194.40 7194.40i −1.04890 1.04890i −0.998741 0.0501577i \(-0.984028\pi\)
−0.0501577 0.998741i \(-0.515972\pi\)
\(20\) −9504.10 + 10738.3i −1.18801 + 1.34228i
\(21\) 1451.67 + 1451.67i 0.156750 + 0.156750i
\(22\) 14807.4 450.974i 1.39063 0.0423530i
\(23\) 7839.29 0.644308 0.322154 0.946687i \(-0.395593\pi\)
0.322154 + 0.946687i \(0.395593\pi\)
\(24\) 4902.58 449.050i 0.354642 0.0324834i
\(25\) 34579.6i 2.21309i
\(26\) 131.585 4.00756i 0.00748662 0.000228013i
\(27\) −9284.51 + 9284.51i −0.471702 + 0.471702i
\(28\) −831.561 13639.2i −0.0378809 0.621317i
\(29\) −112.081 + 112.081i −0.00459554 + 0.00459554i −0.709401 0.704805i \(-0.751034\pi\)
0.704805 + 0.709401i \(0.251034\pi\)
\(30\) 11810.9 12552.9i 0.437439 0.464921i
\(31\) 7877.51i 0.264426i −0.991221 0.132213i \(-0.957792\pi\)
0.991221 0.132213i \(-0.0422083\pi\)
\(32\) −26416.2 19388.8i −0.806159 0.591699i
\(33\) −17805.7 −0.495469
\(34\) 16512.7 + 15536.6i 0.420128 + 0.395293i
\(35\) −33827.5 33827.5i −0.788979 0.788979i
\(36\) 40663.3 2479.19i 0.871555 0.0531375i
\(37\) 22766.4 + 22766.4i 0.449457 + 0.449457i 0.895174 0.445717i \(-0.147051\pi\)
−0.445717 + 0.895174i \(0.647051\pi\)
\(38\) −2477.83 81357.6i −0.0451566 1.48268i
\(39\) −158.229 −0.00266742
\(40\) −114242. + 10464.0i −1.78504 + 0.163500i
\(41\) 20200.8i 0.293101i 0.989203 + 0.146551i \(0.0468172\pi\)
−0.989203 + 0.146551i \(0.953183\pi\)
\(42\) 499.970 + 16416.1i 0.00674833 + 0.221576i
\(43\) 29632.7 29632.7i 0.372705 0.372705i −0.495756 0.868462i \(-0.665109\pi\)
0.868462 + 0.495756i \(0.165109\pi\)
\(44\) 88746.6 + 78546.9i 1.04182 + 0.922085i
\(45\) 100852. 100852.i 1.10674 1.10674i
\(46\) 45675.2 + 42975.2i 0.469252 + 0.441514i
\(47\) 79640.8i 0.767083i 0.923524 + 0.383541i \(0.125296\pi\)
−0.923524 + 0.383541i \(0.874704\pi\)
\(48\) 31026.3 + 24259.7i 0.280547 + 0.219362i
\(49\) −72063.5 −0.612530
\(50\) −189566. + 201476.i −1.51653 + 1.61181i
\(51\) −19269.4 19269.4i −0.145264 0.145264i
\(52\) 788.641 + 698.002i 0.00560879 + 0.00496417i
\(53\) −189013. 189013.i −1.26959 1.26959i −0.946299 0.323292i \(-0.895210\pi\)
−0.323292 0.946299i \(-0.604790\pi\)
\(54\) −104994. + 3197.69i −0.666778 + 0.0203074i
\(55\) 414917. 2.49387
\(56\) 69925.2 84026.3i 0.398171 0.478466i
\(57\) 97831.3i 0.528267i
\(58\) −1267.46 + 38.6018i −0.00649606 + 0.000197844i
\(59\) −251413. + 251413.i −1.22414 + 1.22414i −0.257998 + 0.966145i \(0.583063\pi\)
−0.966145 + 0.257998i \(0.916937\pi\)
\(60\) 137630. 8391.14i 0.637178 0.0388479i
\(61\) 197272. 197272.i 0.869113 0.869113i −0.123261 0.992374i \(-0.539335\pi\)
0.992374 + 0.123261i \(0.0393353\pi\)
\(62\) 43184.7 45897.8i 0.181199 0.192583i
\(63\) 135907.i 0.543525i
\(64\) −47622.5 257782.i −0.181665 0.983360i
\(65\) 3687.14 0.0134261
\(66\) −103744. 97611.1i −0.360852 0.339522i
\(67\) −214576. 214576.i −0.713439 0.713439i 0.253814 0.967253i \(-0.418315\pi\)
−0.967253 + 0.253814i \(0.918315\pi\)
\(68\) 11038.1 + 181046.i 0.0351050 + 0.575788i
\(69\) −53300.4 53300.4i −0.162249 0.162249i
\(70\) −11650.6 382537.i −0.0339667 1.11527i
\(71\) −275257. −0.769066 −0.384533 0.923111i \(-0.625638\pi\)
−0.384533 + 0.923111i \(0.625638\pi\)
\(72\) 250513. + 208472.i 0.671171 + 0.558536i
\(73\) 106038.i 0.272580i 0.990669 + 0.136290i \(0.0435179\pi\)
−0.990669 + 0.136290i \(0.956482\pi\)
\(74\) 7840.99 + 257453.i 0.0193498 + 0.635334i
\(75\) 235111. 235111.i 0.557301 0.557301i
\(76\) 431568. 487609.i 0.983124 1.11079i
\(77\) −279568. + 279568.i −0.612373 + 0.612373i
\(78\) −921.911 867.415i −0.00194270 0.00182786i
\(79\) 637548.i 1.29310i 0.762873 + 0.646549i \(0.223788\pi\)
−0.762873 + 0.646549i \(0.776212\pi\)
\(80\) −722990. 565312.i −1.41209 1.10413i
\(81\) −337787. −0.635606
\(82\) −110742. + 117699.i −0.200849 + 0.213467i
\(83\) 467104. + 467104.i 0.816919 + 0.816919i 0.985660 0.168741i \(-0.0539702\pi\)
−0.168741 + 0.985660i \(0.553970\pi\)
\(84\) −87080.5 + 98388.3i −0.146921 + 0.165999i
\(85\) 449026. + 449026.i 0.731164 + 0.731164i
\(86\) 335100. 10205.8i 0.526841 0.0160455i
\(87\) 1524.10 0.00231449
\(88\) 86480.1 + 944160.i 0.126902 + 1.38547i
\(89\) 240298.i 0.340863i −0.985370 0.170432i \(-0.945484\pi\)
0.985370 0.170432i \(-0.0545162\pi\)
\(90\) 1.14048e6 34734.6i 1.56445 0.0476469i
\(91\) −2484.37 + 2484.37i −0.00329679 + 0.00329679i
\(92\) 30532.2 + 500785.i 0.0392098 + 0.643114i
\(93\) −53560.2 + 53560.2i −0.0665876 + 0.0665876i
\(94\) −436593. + 464022.i −0.525646 + 0.558670i
\(95\) 2.27972e6i 2.65895i
\(96\) 47780.3 + 311434.i 0.0540052 + 0.352008i
\(97\) 869115. 0.952274 0.476137 0.879371i \(-0.342037\pi\)
0.476137 + 0.879371i \(0.342037\pi\)
\(98\) −419874. 395054.i −0.446109 0.419738i
\(99\) −833495. 833495.i −0.859008 0.859008i
\(100\) −2.20899e6 + 134679.i −2.20899 + 0.134679i
\(101\) 81235.1 + 81235.1i 0.0788459 + 0.0788459i 0.745430 0.666584i \(-0.232244\pi\)
−0.666584 + 0.745430i \(0.732244\pi\)
\(102\) −6636.60 217908.i −0.00625382 0.205339i
\(103\) −738426. −0.675764 −0.337882 0.941188i \(-0.609711\pi\)
−0.337882 + 0.941188i \(0.609711\pi\)
\(104\) 768.500 + 8390.22i 0.000683194 + 0.00745887i
\(105\) 459995.i 0.397361i
\(106\) −65098.2 2.13745e6i −0.0546577 1.79464i
\(107\) 498199. 498199.i 0.406679 0.406679i −0.473900 0.880579i \(-0.657154\pi\)
0.880579 + 0.473900i \(0.157154\pi\)
\(108\) −629268. 556946.i −0.499534 0.442122i
\(109\) 113037. 113037.i 0.0872849 0.0872849i −0.662116 0.749401i \(-0.730341\pi\)
0.749401 + 0.662116i \(0.230341\pi\)
\(110\) 2.41749e6 + 2.27459e6i 1.81630 + 1.70893i
\(111\) 309583.i 0.226364i
\(112\) 868049. 106243.i 0.617860 0.0756213i
\(113\) 623127. 0.431858 0.215929 0.976409i \(-0.430722\pi\)
0.215929 + 0.976409i \(0.430722\pi\)
\(114\) −536314. + 570008.i −0.361997 + 0.384739i
\(115\) 1.24203e6 + 1.24203e6i 0.816658 + 0.816658i
\(116\) −7596.39 6723.33i −0.00486668 0.00430735i
\(117\) −7406.80 7406.80i −0.00462459 0.00462459i
\(118\) −2.84310e6 + 86589.6i −1.73040 + 0.0527011i
\(119\) −605101. −0.359077
\(120\) 847896. + 705603.i 0.490680 + 0.408335i
\(121\) 1.65753e6i 0.935635i
\(122\) 2.23085e6 67942.7i 1.22854 0.0374165i
\(123\) 137348. 137348.i 0.0738087 0.0738087i
\(124\) 503226. 30681.0i 0.263936 0.0160918i
\(125\) −3.00311e6 + 3.00311e6i −1.53759 + 1.53759i
\(126\) −745045. + 791853.i −0.372452 + 0.395852i
\(127\) 2.20299e6i 1.07548i 0.843111 + 0.537740i \(0.180722\pi\)
−0.843111 + 0.537740i \(0.819278\pi\)
\(128\) 1.13570e6 1.76302e6i 0.541543 0.840673i
\(129\) −402953. −0.187709
\(130\) 21482.9 + 20213.0i 0.00977827 + 0.00920026i
\(131\) 1.79275e6 + 1.79275e6i 0.797455 + 0.797455i 0.982694 0.185238i \(-0.0593057\pi\)
−0.185238 + 0.982694i \(0.559306\pi\)
\(132\) −69348.8 1.13745e6i −0.0301521 0.494551i
\(133\) 1.53606e6 + 1.53606e6i 0.652909 + 0.652909i
\(134\) −73902.4 2.42652e6i −0.0307145 1.00849i
\(135\) −2.94202e6 −1.19576
\(136\) −928187. + 1.11537e6i −0.368993 + 0.443405i
\(137\) 2.77226e6i 1.07813i −0.842263 0.539066i \(-0.818777\pi\)
0.842263 0.539066i \(-0.181223\pi\)
\(138\) −18357.3 602746.i −0.00698506 0.229349i
\(139\) −550090. + 550090.i −0.204828 + 0.204828i −0.802065 0.597237i \(-0.796265\pi\)
0.597237 + 0.802065i \(0.296265\pi\)
\(140\) 2.02920e6 2.29270e6i 0.739503 0.835531i
\(141\) 541489. 541489.i 0.193167 0.193167i
\(142\) −1.60377e6 1.50897e6i −0.560115 0.527005i
\(143\) 30472.4i 0.0104208i
\(144\) 316748. + 2.58797e6i 0.106078 + 0.866706i
\(145\) −35515.4 −0.0116497
\(146\) −581305. + 617825.i −0.186786 + 0.198521i
\(147\) 489970. + 489970.i 0.154247 + 0.154247i
\(148\) −1.36568e6 + 1.54302e6i −0.421272 + 0.475976i
\(149\) −2.51113e6 2.51113e6i −0.759121 0.759121i 0.217041 0.976162i \(-0.430359\pi\)
−0.976162 + 0.217041i \(0.930359\pi\)
\(150\) 2.65875e6 80974.9i 0.787777 0.0239926i
\(151\) 1.07459e6 0.312112 0.156056 0.987748i \(-0.450122\pi\)
0.156056 + 0.987748i \(0.450122\pi\)
\(152\) 5.18759e6 475156.i 1.47718 0.135302i
\(153\) 1.80403e6i 0.503696i
\(154\) −3.16149e6 + 96286.4i −0.865624 + 0.0263635i
\(155\) 1.24809e6 1.24809e6i 0.335159 0.335159i
\(156\) −616.264 10107.9i −0.000162328 0.00266248i
\(157\) 2.31833e6 2.31833e6i 0.599069 0.599069i −0.340996 0.940065i \(-0.610764\pi\)
0.940065 + 0.340996i \(0.110764\pi\)
\(158\) −3.49505e6 + 3.71463e6i −0.886099 + 0.941769i
\(159\) 2.57025e6i 0.639416i
\(160\) −1.11340e6 7.25721e6i −0.271827 1.77178i
\(161\) −1.67375e6 −0.401063
\(162\) −1.96810e6 1.85176e6i −0.462915 0.435551i
\(163\) −60152.4 60152.4i −0.0138896 0.0138896i 0.700128 0.714017i \(-0.253126\pi\)
−0.714017 + 0.700128i \(0.753126\pi\)
\(164\) −1.29046e6 + 78677.5i −0.292558 + 0.0178369i
\(165\) −2.82108e6 2.82108e6i −0.628005 0.628005i
\(166\) 160876. + 5.28223e6i 0.0351695 + 1.15476i
\(167\) 8.63569e6 1.85416 0.927081 0.374861i \(-0.122309\pi\)
0.927081 + 0.374861i \(0.122309\pi\)
\(168\) −1.04674e6 + 95875.6i −0.220755 + 0.0202200i
\(169\) 4.82654e6i 0.999944i
\(170\) 154650. + 5.07780e6i 0.0314776 + 1.03354i
\(171\) −4.57955e6 + 4.57955e6i −0.915871 + 0.915871i
\(172\) 2.00839e6 + 1.77756e6i 0.394696 + 0.349333i
\(173\) 2.87166e6 2.87166e6i 0.554618 0.554618i −0.373152 0.927770i \(-0.621723\pi\)
0.927770 + 0.373152i \(0.121723\pi\)
\(174\) 8880.08 + 8355.16i 0.00168566 + 0.00158601i
\(175\) 7.38300e6i 1.37759i
\(176\) −4.67204e6 + 5.97518e6i −0.856976 + 1.09601i
\(177\) 3.41879e6 0.616527
\(178\) 1.31732e6 1.40008e6i 0.233578 0.248252i
\(179\) −6.03905e6 6.03905e6i −1.05296 1.05296i −0.998517 0.0544379i \(-0.982663\pi\)
−0.0544379 0.998517i \(-0.517337\pi\)
\(180\) 6.83536e6 + 6.04978e6i 1.17204 + 1.03734i
\(181\) 2.29298e6 + 2.29298e6i 0.386691 + 0.386691i 0.873505 0.486814i \(-0.161841\pi\)
−0.486814 + 0.873505i \(0.661841\pi\)
\(182\) −28094.4 + 855.643i −0.00466021 + 0.000141931i
\(183\) −2.68256e6 −0.437720
\(184\) −2.56742e6 + 3.08517e6i −0.412139 + 0.495251i
\(185\) 7.21407e6i 1.13937i
\(186\) −605684. + 18446.7i −0.0941255 + 0.00286669i
\(187\) 3.71099e6 3.71099e6i 0.567499 0.567499i
\(188\) −5.08757e6 + 310182.i −0.765661 + 0.0466813i
\(189\) 1.98231e6 1.98231e6i 0.293621 0.293621i
\(190\) 1.24975e7 1.32826e7i 1.82206 1.93653i
\(191\) 7.15510e6i 1.02687i 0.858128 + 0.513435i \(0.171627\pi\)
−0.858128 + 0.513435i \(0.828373\pi\)
\(192\) −1.42890e6 + 2.07649e6i −0.201883 + 0.293376i
\(193\) −1.93248e6 −0.268809 −0.134404 0.990927i \(-0.542912\pi\)
−0.134404 + 0.990927i \(0.542912\pi\)
\(194\) 5.06385e6 + 4.76451e6i 0.693546 + 0.652549i
\(195\) −25069.3 25069.3i −0.00338095 0.00338095i
\(196\) −280670. 4.60352e6i −0.0372759 0.611395i
\(197\) 3.89019e6 + 3.89019e6i 0.508830 + 0.508830i 0.914167 0.405338i \(-0.132846\pi\)
−0.405338 + 0.914167i \(0.632846\pi\)
\(198\) −287065. 9.42555e6i −0.0369815 1.21426i
\(199\) −3.70221e6 −0.469788 −0.234894 0.972021i \(-0.575474\pi\)
−0.234894 + 0.972021i \(0.575474\pi\)
\(200\) −1.36089e7 1.13251e7i −1.70111 1.41563i
\(201\) 2.91786e6i 0.359316i
\(202\) 27978.3 + 918644.i 0.00339443 + 0.111453i
\(203\) 23930.0 23930.0i 0.00286059 0.00286059i
\(204\) 1.15591e6 1.30601e6i 0.136155 0.153835i
\(205\) −3.20056e6 + 3.20056e6i −0.371505 + 0.371505i
\(206\) −4.30239e6 4.04807e6i −0.492162 0.463070i
\(207\) 4.99005e6i 0.562593i
\(208\) −41517.8 + 53098.0i −0.00461364 + 0.00590049i
\(209\) −1.88408e7 −2.06377
\(210\) −2.52171e6 + 2.68013e6i −0.272293 + 0.289400i
\(211\) −6.80392e6 6.80392e6i −0.724289 0.724289i 0.245187 0.969476i \(-0.421151\pi\)
−0.969476 + 0.245187i \(0.921151\pi\)
\(212\) 1.13382e7 1.28106e7i 1.18998 1.34450i
\(213\) 1.87151e6 + 1.87151e6i 0.193666 + 0.193666i
\(214\) 5.63387e6 171585.i 0.574865 0.0175081i
\(215\) 9.38983e6 0.944805
\(216\) −613198. 6.69468e6i −0.0608470 0.664307i
\(217\) 1.68191e6i 0.164597i
\(218\) 1.27827e6 38931.0i 0.123382 0.00375774i
\(219\) 720968. 720968.i 0.0686410 0.0686410i
\(220\) 1.61600e6 + 2.65055e7i 0.151766 + 2.48925i
\(221\) 32977.5 32977.5i 0.00305521 0.00305521i
\(222\) 1.69714e6 1.80377e6i 0.155117 0.164862i
\(223\) 1.17213e7i 1.05696i 0.848944 + 0.528482i \(0.177239\pi\)
−0.848944 + 0.528482i \(0.822761\pi\)
\(224\) 5.64006e6 + 4.13965e6i 0.501810 + 0.368315i
\(225\) 2.20114e7 1.93241
\(226\) 3.63061e6 + 3.41600e6i 0.314524 + 0.295932i
\(227\) −5.78763e6 5.78763e6i −0.494792 0.494792i 0.415020 0.909812i \(-0.363775\pi\)
−0.909812 + 0.415020i \(0.863775\pi\)
\(228\) −6.24960e6 + 381030.i −0.527288 + 0.0321480i
\(229\) −4.21573e6 4.21573e6i −0.351048 0.351048i 0.509451 0.860499i \(-0.329848\pi\)
−0.860499 + 0.509451i \(0.829848\pi\)
\(230\) 427771. + 1.40455e7i 0.0351583 + 1.15439i
\(231\) 3.80164e6 0.308415
\(232\) −7402.39 80816.7i −0.000592799 0.00647198i
\(233\) 1.68651e7i 1.33328i 0.745380 + 0.666640i \(0.232268\pi\)
−0.745380 + 0.666640i \(0.767732\pi\)
\(234\) −2550.98 83759.5i −0.000199095 0.00653712i
\(235\) −1.26181e7 + 1.26181e7i −0.972275 + 0.972275i
\(236\) −1.70398e7 1.50814e7i −1.29637 1.14738i
\(237\) 4.33477e6 4.33477e6i 0.325627 0.325627i
\(238\) −3.52559e6 3.31718e6i −0.261517 0.246059i
\(239\) 8.76368e6i 0.641938i −0.947090 0.320969i \(-0.895992\pi\)
0.947090 0.320969i \(-0.104008\pi\)
\(240\) 1.07208e6 + 8.75934e6i 0.0775518 + 0.633633i
\(241\) 9.78461e6 0.699025 0.349512 0.936932i \(-0.386347\pi\)
0.349512 + 0.936932i \(0.386347\pi\)
\(242\) 9.08665e6 9.65752e6i 0.641147 0.681427i
\(243\) 9.06507e6 + 9.06507e6i 0.631760 + 0.631760i
\(244\) 1.33703e7 + 1.18337e7i 0.920393 + 0.814612i
\(245\) −1.14175e7 1.14175e7i −0.776380 0.776380i
\(246\) 1.55320e6 47304.3i 0.104333 0.00317757i
\(247\) −167428. −0.0111106
\(248\) 3.10021e6 + 2.57994e6i 0.203253 + 0.169143i
\(249\) 6.35180e6i 0.411433i
\(250\) −3.39605e7 + 1.03430e6i −2.17347 + 0.0661955i
\(251\) 1.28892e7 1.28892e7i 0.815089 0.815089i −0.170303 0.985392i \(-0.554475\pi\)
0.985392 + 0.170303i \(0.0544745\pi\)
\(252\) −8.68192e6 + 529325.i −0.542518 + 0.0330766i
\(253\) 1.02648e7 1.02648e7i 0.633855 0.633855i
\(254\) −1.20769e7 + 1.28356e7i −0.736976 + 0.783277i
\(255\) 6.10598e6i 0.368243i
\(256\) 1.62820e7 4.04619e6i 0.970482 0.241172i
\(257\) −2.14023e7 −1.26084 −0.630422 0.776252i \(-0.717118\pi\)
−0.630422 + 0.776252i \(0.717118\pi\)
\(258\) −2.34778e6 2.20900e6i −0.136709 0.128628i
\(259\) −4.86079e6 4.86079e6i −0.279774 0.279774i
\(260\) 14360.5 + 235539.i 0.000817053 + 0.0134012i
\(261\) 71344.1 + 71344.1i 0.00401270 + 0.00401270i
\(262\) 617444. + 2.02733e7i 0.0343316 + 1.12725i
\(263\) −785705. −0.0431909 −0.0215955 0.999767i \(-0.506875\pi\)
−0.0215955 + 0.999767i \(0.506875\pi\)
\(264\) 5.83148e6 7.00746e6i 0.316933 0.380845i
\(265\) 5.98933e7i 3.21840i
\(266\) 529036. + 1.73705e7i 0.0281086 + 0.922925i
\(267\) −1.63382e6 + 1.63382e6i −0.0858360 + 0.0858360i
\(268\) 1.28717e7 1.45431e7i 0.668700 0.755533i
\(269\) −1.24683e7 + 1.24683e7i −0.640546 + 0.640546i −0.950690 0.310143i \(-0.899623\pi\)
0.310143 + 0.950690i \(0.399623\pi\)
\(270\) −1.71415e7 1.61282e7i −0.870879 0.819399i
\(271\) 1.55043e7i 0.779012i 0.921024 + 0.389506i \(0.127354\pi\)
−0.921024 + 0.389506i \(0.872646\pi\)
\(272\) −1.15225e7 + 1.41026e6i −0.572584 + 0.0700799i
\(273\) 33783.1 0.00166039
\(274\) 1.51976e7 1.61524e7i 0.738794 0.785209i
\(275\) 4.52788e7 + 4.52788e7i 2.17719 + 2.17719i
\(276\) 3.19731e6 3.61250e6i 0.152075 0.171823i
\(277\) 1.24335e7 + 1.24335e7i 0.584998 + 0.584998i 0.936272 0.351275i \(-0.114252\pi\)
−0.351275 + 0.936272i \(0.614252\pi\)
\(278\) −6.22068e6 + 189457.i −0.289537 + 0.00881814i
\(279\) −5.01438e6 −0.230890
\(280\) 2.43916e7 2.23414e6i 1.11113 0.101774i
\(281\) 8.37508e6i 0.377459i −0.982029 0.188729i \(-0.939563\pi\)
0.982029 0.188729i \(-0.0604369\pi\)
\(282\) 6.12341e6 186495.i 0.273052 0.00831609i
\(283\) 6.71417e6 6.71417e6i 0.296233 0.296233i −0.543304 0.839536i \(-0.682827\pi\)
0.839536 + 0.543304i \(0.182827\pi\)
\(284\) −1.07206e6 1.75838e7i −0.0468020 0.767641i
\(285\) −1.55001e7 + 1.55001e7i −0.669576 + 0.669576i
\(286\) 167051. 177546.i 0.00714086 0.00758948i
\(287\) 4.31303e6i 0.182447i
\(288\) −1.23418e7 + 1.68151e7i −0.516656 + 0.703917i
\(289\) −1.61055e7 −0.667236
\(290\) −206928. 194696.i −0.00848450 0.00798296i
\(291\) −5.90923e6 5.90923e6i −0.239801 0.239801i
\(292\) −6.77387e6 + 412994.i −0.272075 + 0.0165880i
\(293\) 5.01259e6 + 5.01259e6i 0.199278 + 0.199278i 0.799691 0.600412i \(-0.204997\pi\)
−0.600412 + 0.799691i \(0.704997\pi\)
\(294\) 168751. + 5.54080e6i 0.00664056 + 0.218037i
\(295\) −7.96664e7 −3.10320
\(296\) −1.64159e7 + 1.50361e6i −0.632979 + 0.0579776i
\(297\) 2.43144e7i 0.928099i
\(298\) −864863. 2.83971e7i −0.0326812 1.07306i
\(299\) 91217.8 91217.8i 0.00341245 0.00341245i
\(300\) 1.59349e7 + 1.41035e7i 0.590183 + 0.522353i
\(301\) −6.32680e6 + 6.32680e6i −0.231998 + 0.231998i
\(302\) 6.26101e6 + 5.89091e6i 0.227313 + 0.213876i
\(303\) 1.10466e6i 0.0397099i
\(304\) 3.28300e7 + 2.56700e7i 1.16856 + 0.913704i
\(305\) 6.25104e7 2.20320
\(306\) 9.88973e6 1.05111e7i 0.345160 0.366845i
\(307\) 5.38397e6 + 5.38397e6i 0.186075 + 0.186075i 0.793997 0.607922i \(-0.207997\pi\)
−0.607922 + 0.793997i \(0.707997\pi\)
\(308\) −1.89481e7 1.67704e7i −0.648504 0.573971i
\(309\) 5.02066e6 + 5.02066e6i 0.170171 + 0.170171i
\(310\) 1.41140e7 429856.i 0.473766 0.0144290i
\(311\) 4.70346e7 1.56364 0.781819 0.623506i \(-0.214292\pi\)
0.781819 + 0.623506i \(0.214292\pi\)
\(312\) 51821.1 62271.3i 0.00170625 0.00205033i
\(313\) 1.98492e7i 0.647306i 0.946176 + 0.323653i \(0.104911\pi\)
−0.946176 + 0.323653i \(0.895089\pi\)
\(314\) 2.62168e7 798460.i 0.846819 0.0257908i
\(315\) −2.15327e7 + 2.15327e7i −0.688916 + 0.688916i
\(316\) −4.07274e7 + 2.48310e6i −1.29070 + 0.0786923i
\(317\) −2.53957e7 + 2.53957e7i −0.797229 + 0.797229i −0.982658 0.185429i \(-0.940633\pi\)
0.185429 + 0.982658i \(0.440633\pi\)
\(318\) −1.40902e7 + 1.49754e7i −0.438162 + 0.465690i
\(319\) 293518.i 0.00904197i
\(320\) 3.32970e7 4.83874e7i 1.01615 1.47667i
\(321\) −6.77465e6 −0.204820
\(322\) −9.75199e6 9.17553e6i −0.292096 0.274830i
\(323\) −2.03896e7 2.03896e7i −0.605065 0.605065i
\(324\) −1.31560e6 2.15783e7i −0.0386802 0.634428i
\(325\) 402367. + 402367.i 0.0117212 + 0.0117212i
\(326\) −20717.2 680232.i −0.000597968 0.0196338i
\(327\) −1.53710e6 −0.0439601
\(328\) −7.95009e6 6.61592e6i −0.225294 0.187486i
\(329\) 1.70039e7i 0.477487i
\(330\) −971610. 3.19021e7i −0.0270365 0.887722i
\(331\) 2.88736e7 2.88736e7i 0.796189 0.796189i −0.186303 0.982492i \(-0.559651\pi\)
0.982492 + 0.186303i \(0.0596506\pi\)
\(332\) −2.80200e7 + 3.16585e7i −0.765691 + 0.865119i
\(333\) 1.44918e7 1.44918e7i 0.392454 0.392454i
\(334\) 5.03153e7 + 4.73411e7i 1.35040 + 1.27057i
\(335\) 6.79936e7i 1.80856i
\(336\) −6.62434e6 5.17963e6i −0.174632 0.136546i
\(337\) −5.14079e7 −1.34320 −0.671599 0.740915i \(-0.734392\pi\)
−0.671599 + 0.740915i \(0.734392\pi\)
\(338\) −2.64592e7 + 2.81215e7i −0.685215 + 0.728264i
\(339\) −4.23672e6 4.23672e6i −0.108750 0.108750i
\(340\) −2.69356e7 + 3.04333e7i −0.685314 + 0.774305i
\(341\) −1.03149e7 1.03149e7i −0.260136 0.260136i
\(342\) −5.17877e7 + 1.57725e6i −1.29464 + 0.0394295i
\(343\) 4.05051e7 1.00375
\(344\) 1.95710e6 + 2.13669e7i 0.0480770 + 0.524888i
\(345\) 1.68895e7i 0.411301i
\(346\) 3.24740e7 989030.i 0.783985 0.0238771i
\(347\) 8.11640e6 8.11640e6i 0.194256 0.194256i −0.603276 0.797532i \(-0.706138\pi\)
0.797532 + 0.603276i \(0.206138\pi\)
\(348\) 5936.01 + 97361.7i 0.000140850 + 0.00231020i
\(349\) 2.31407e7 2.31407e7i 0.544378 0.544378i −0.380431 0.924809i \(-0.624224\pi\)
0.924809 + 0.380431i \(0.124224\pi\)
\(350\) 4.04738e7 4.30166e7i 0.943996 1.00330i
\(351\) 216069.i 0.00499655i
\(352\) −5.99774e7 + 9.20175e6i −1.37518 + 0.210980i
\(353\) 7.13339e7 1.62171 0.810853 0.585250i \(-0.199004\pi\)
0.810853 + 0.585250i \(0.199004\pi\)
\(354\) 1.99193e7 + 1.87419e7i 0.449020 + 0.422477i
\(355\) −4.36110e7 4.36110e7i −0.974789 0.974789i
\(356\) 1.53506e7 935903.i 0.340231 0.0207434i
\(357\) 4.11416e6 + 4.11416e6i 0.0904226 + 0.0904226i
\(358\) −2.07992e6 6.82924e7i −0.0453312 1.48841i
\(359\) −7.03447e7 −1.52037 −0.760183 0.649709i \(-0.774891\pi\)
−0.760183 + 0.649709i \(0.774891\pi\)
\(360\) 6.66080e6 + 7.27203e7i 0.142764 + 1.55865i
\(361\) 5.64729e7i 1.20038i
\(362\) 789727. + 2.59301e7i 0.0166476 + 0.546610i
\(363\) −1.12698e7 + 1.12698e7i −0.235611 + 0.235611i
\(364\) −168381. 149029.i −0.00349131 0.00309005i
\(365\) −1.68004e7 + 1.68004e7i −0.345494 + 0.345494i
\(366\) −1.56298e7 1.47059e7i −0.318793 0.299949i
\(367\) 3.10050e7i 0.627239i 0.949549 + 0.313620i \(0.101542\pi\)
−0.949549 + 0.313620i \(0.898458\pi\)
\(368\) −3.18719e7 + 3.90088e6i −0.639536 + 0.0782742i
\(369\) 1.28587e7 0.255928
\(370\) −3.95477e7 + 4.20323e7i −0.780758 + 0.829809i
\(371\) 4.03557e7 + 4.03557e7i 0.790284 + 0.790284i
\(372\) −3.63011e6 3.21290e6i −0.0705164 0.0624120i
\(373\) 6.29288e7 + 6.29288e7i 1.21262 + 1.21262i 0.970163 + 0.242452i \(0.0779517\pi\)
0.242452 + 0.970163i \(0.422048\pi\)
\(374\) 4.19656e7 1.27811e6i 0.802193 0.0244316i
\(375\) 4.08371e7 0.774392
\(376\) −3.13428e7 2.60829e7i −0.589623 0.490674i
\(377\) 2608.33i 4.86787e-5i
\(378\) 2.24169e7 682731.i 0.415050 0.0126408i
\(379\) 5.96910e7 5.96910e7i 1.09646 1.09646i 0.101634 0.994822i \(-0.467593\pi\)
0.994822 0.101634i \(-0.0324072\pi\)
\(380\) 1.45632e8 8.87896e6i 2.65402 0.161812i
\(381\) 1.49784e7 1.49784e7i 0.270827 0.270827i
\(382\) −3.92245e7 + 4.16888e7i −0.703667 + 0.747875i
\(383\) 5.76504e7i 1.02614i 0.858347 + 0.513069i \(0.171492\pi\)
−0.858347 + 0.513069i \(0.828508\pi\)
\(384\) −1.97088e7 + 4.26524e6i −0.348069 + 0.0753268i
\(385\) −8.85879e7 −1.55236
\(386\) −1.12595e7 1.05939e7i −0.195775 0.184202i
\(387\) −1.88625e7 1.88625e7i −0.325436 0.325436i
\(388\) 3.38500e6 + 5.55203e7i 0.0579513 + 0.950509i
\(389\) −6.44525e7 6.44525e7i −1.09494 1.09494i −0.994992 0.0999496i \(-0.968132\pi\)
−0.0999496 0.994992i \(-0.531868\pi\)
\(390\) −8634.16 283496.i −0.000145555 0.00477917i
\(391\) 2.22173e7 0.371674
\(392\) 2.36013e7 2.83608e7i 0.391812 0.470825i
\(393\) 2.43783e7i 0.401630i
\(394\) 1.33983e6 + 4.39921e7i 0.0219058 + 0.719260i
\(395\) −1.01011e8 + 1.01011e8i −1.63900 + 1.63900i
\(396\) 4.99985e7 5.64911e7i 0.805141 0.909692i
\(397\) 3.32033e7 3.32033e7i 0.530652 0.530652i −0.390114 0.920766i \(-0.627565\pi\)
0.920766 + 0.390114i \(0.127565\pi\)
\(398\) −2.15707e7 2.02956e7i −0.342149 0.321924i
\(399\) 2.08877e7i 0.328831i
\(400\) −1.72070e7 1.40589e8i −0.268859 2.19670i
\(401\) −6.57507e7 −1.01969 −0.509844 0.860267i \(-0.670297\pi\)
−0.509844 + 0.860267i \(0.670297\pi\)
\(402\) −1.59958e7 + 1.70007e7i −0.246222 + 0.261691i
\(403\) −91662.4 91662.4i −0.00140048 0.00140048i
\(404\) −4.87302e6 + 5.50580e6i −0.0739016 + 0.0834980i
\(405\) −5.35180e7 5.35180e7i −0.805628 0.805628i
\(406\) 270612. 8241.77i 0.00404361 0.000123152i
\(407\) 5.96209e7 0.884332
\(408\) 1.38944e7 1.27265e6i 0.204578 0.0187383i
\(409\) 3.16009e7i 0.461881i 0.972968 + 0.230940i \(0.0741802\pi\)
−0.972968 + 0.230940i \(0.925820\pi\)
\(410\) −3.61934e7 + 1.10231e6i −0.525144 + 0.0159938i
\(411\) −1.88490e7 + 1.88490e7i −0.271495 + 0.271495i
\(412\) −2.87599e6 4.71717e7i −0.0411241 0.674512i
\(413\) 5.36787e7 5.36787e7i 0.761994 0.761994i
\(414\) 2.73556e7 2.90742e7i 0.385518 0.409739i
\(415\) 1.48013e8i 2.07088i
\(416\) −532986. + 81770.7i −0.00740347 + 0.00113584i
\(417\) 7.48028e6 0.103160
\(418\) −1.09775e8 1.03286e8i −1.50305 1.41420i
\(419\) −3.02706e7 3.02706e7i −0.411509 0.411509i 0.470755 0.882264i \(-0.343982\pi\)
−0.882264 + 0.470755i \(0.843982\pi\)
\(420\) −2.93851e7 + 1.79157e6i −0.396625 + 0.0241817i
\(421\) 1.29835e7 + 1.29835e7i 0.173999 + 0.173999i 0.788734 0.614735i \(-0.210737\pi\)
−0.614735 + 0.788734i \(0.710737\pi\)
\(422\) −2.34335e6 7.69419e7i −0.0311816 1.02382i
\(423\) 5.06949e7 0.669797
\(424\) 1.36289e8 1.24834e7i 1.78799 0.163770i
\(425\) 9.80020e7i 1.27664i
\(426\) 644569. + 2.11639e7i 0.00833760 + 0.273758i
\(427\) −4.21191e7 + 4.21191e7i −0.540998 + 0.540998i
\(428\) 3.37660e7 + 2.98853e7i 0.430674 + 0.381177i
\(429\) −207186. + 207186.i −0.00262415 + 0.00262415i
\(430\) 5.47093e7 + 5.14753e7i 0.688106 + 0.647431i
\(431\) 1.28691e8i 1.60737i −0.595054 0.803686i \(-0.702869\pi\)
0.595054 0.803686i \(-0.297131\pi\)
\(432\) 3.31277e7 4.23677e7i 0.410903 0.525513i
\(433\) 4.42637e7 0.545236 0.272618 0.962122i \(-0.412110\pi\)
0.272618 + 0.962122i \(0.412110\pi\)
\(434\) −9.22026e6 + 9.79953e6i −0.112791 + 0.119877i
\(435\) 241474. + 241474.i 0.00293361 + 0.00293361i
\(436\) 7.66118e6 + 6.78068e6i 0.0924349 + 0.0818114i
\(437\) −5.63990e7 5.63990e7i −0.675814 0.675814i
\(438\) 8.15304e6 248309.i 0.0970281 0.00295509i
\(439\) 2.93985e7 0.347481 0.173741 0.984791i \(-0.444415\pi\)
0.173741 + 0.984791i \(0.444415\pi\)
\(440\) −1.35888e8 + 1.63292e8i −1.59523 + 1.91693i
\(441\) 4.58716e7i 0.534845i
\(442\) 372925. 11357.8i 0.00431871 0.000131531i
\(443\) 7.00084e6 7.00084e6i 0.0805265 0.0805265i −0.665696 0.746223i \(-0.731865\pi\)
0.746223 + 0.665696i \(0.231865\pi\)
\(444\) 1.97766e7 1.20575e6i 0.225945 0.0137756i
\(445\) 3.80721e7 3.80721e7i 0.432043 0.432043i
\(446\) −6.42563e7 + 6.82933e7i −0.724288 + 0.769792i
\(447\) 3.41471e7i 0.382323i
\(448\) 1.01678e7 + 5.50384e7i 0.113081 + 0.612113i
\(449\) 1.34157e7 0.148209 0.0741043 0.997250i \(-0.476390\pi\)
0.0741043 + 0.997250i \(0.476390\pi\)
\(450\) 1.28248e8 + 1.20667e8i 1.40739 + 1.32419i
\(451\) 2.64511e7 + 2.64511e7i 0.288347 + 0.288347i
\(452\) 2.42693e6 + 3.98062e7i 0.0262810 + 0.431058i
\(453\) −7.30626e6 7.30626e6i −0.0785960 0.0785960i
\(454\) −1.99332e6 6.54492e7i −0.0213015 0.699418i
\(455\) −787231. −0.00835734
\(456\) −3.85017e7 3.20404e7i −0.406056 0.337912i
\(457\) 1.61973e8i 1.69705i −0.529156 0.848524i \(-0.677491\pi\)
0.529156 0.848524i \(-0.322509\pi\)
\(458\) −1.45194e6 4.76734e7i −0.0151131 0.496227i
\(459\) −2.63132e7 + 2.63132e7i −0.272105 + 0.272105i
\(460\) −7.45054e7 + 8.41803e7i −0.765446 + 0.864842i
\(461\) −1.16319e7 + 1.16319e7i −0.118727 + 0.118727i −0.763974 0.645247i \(-0.776754\pi\)
0.645247 + 0.763974i \(0.276754\pi\)
\(462\) 2.21500e7 + 2.08407e7i 0.224620 + 0.211342i
\(463\) 4.02011e7i 0.405037i 0.979278 + 0.202519i \(0.0649127\pi\)
−0.979278 + 0.202519i \(0.935087\pi\)
\(464\) 399910. 511453.i 0.00400321 0.00511979i
\(465\) −1.69718e7 −0.168799
\(466\) −9.24550e7 + 9.82635e7i −0.913634 + 0.971034i
\(467\) −3.28960e7 3.28960e7i −0.322992 0.322992i 0.526922 0.849914i \(-0.323346\pi\)
−0.849914 + 0.526922i \(0.823346\pi\)
\(468\) 444309. 502004.i 0.00433458 0.00489745i
\(469\) 4.58136e7 + 4.58136e7i 0.444095 + 0.444095i
\(470\) −1.42691e8 + 4.34580e6i −1.37437 + 0.0418578i
\(471\) −3.15253e7 −0.301715
\(472\) −1.66047e7 1.81284e8i −0.157908 1.72398i
\(473\) 7.76025e7i 0.733318i
\(474\) 4.90196e7 1.49294e6i 0.460293 0.0140187i
\(475\) 2.48779e8 2.48779e8i 2.32131 2.32131i
\(476\) −2.35673e6 3.86547e7i −0.0218518 0.358411i
\(477\) −1.20315e8 + 1.20315e8i −1.10857 + 1.10857i
\(478\) 4.80427e7 5.10610e7i 0.439890 0.467526i
\(479\) 4.78638e7i 0.435512i 0.976003 + 0.217756i \(0.0698738\pi\)
−0.976003 + 0.217756i \(0.930126\pi\)
\(480\) −4.17726e7 + 5.69129e7i −0.377718 + 0.514620i
\(481\) 529817. 0.00476092
\(482\) 5.70094e7 + 5.36395e7i 0.509103 + 0.479009i
\(483\) 1.13800e7 + 1.13800e7i 0.100996 + 0.100996i
\(484\) 1.05886e8 6.45570e6i 0.933901 0.0569387i
\(485\) 1.37700e8 + 1.37700e8i 1.20700 + 1.20700i
\(486\) 3.12211e6 + 1.02512e8i 0.0271982 + 0.893030i
\(487\) −6.83549e7 −0.591810 −0.295905 0.955217i \(-0.595621\pi\)
−0.295905 + 0.955217i \(0.595621\pi\)
\(488\) 1.30289e7 + 1.42245e8i 0.112111 + 1.22399i
\(489\) 817969.i 0.00699536i
\(490\) −3.93233e6 1.29115e8i −0.0334242 1.09746i
\(491\) −4.09317e7 + 4.09317e7i −0.345793 + 0.345793i −0.858540 0.512747i \(-0.828628\pi\)
0.512747 + 0.858540i \(0.328628\pi\)
\(492\) 9.30893e6 + 8.23906e6i 0.0781636 + 0.0691803i
\(493\) −317647. + 317647.i −0.00265097 + 0.00265097i
\(494\) −975506. 917842.i −0.00809188 0.00761355i
\(495\) 2.64113e8i 2.17758i
\(496\) 3.91989e6 + 3.20273e7i 0.0321240 + 0.262467i
\(497\) 5.87695e7 0.478721
\(498\) 3.48208e7 3.70084e7i 0.281936 0.299648i
\(499\) 3.26564e7 + 3.26564e7i 0.262825 + 0.262825i 0.826201 0.563376i \(-0.190498\pi\)
−0.563376 + 0.826201i \(0.690498\pi\)
\(500\) −2.03539e8 1.80146e8i −1.62831 1.44117i
\(501\) −5.87152e7 5.87152e7i −0.466915 0.466915i
\(502\) 1.45757e8 4.43919e6i 1.15218 0.0350907i
\(503\) −2.43128e8 −1.91043 −0.955216 0.295908i \(-0.904378\pi\)
−0.955216 + 0.295908i \(0.904378\pi\)
\(504\) −5.34864e7 4.45104e7i −0.417784 0.347672i
\(505\) 2.57413e7i 0.199874i
\(506\) 1.16079e8 3.53532e6i 0.895991 0.0272884i
\(507\) 3.28163e7 3.28163e7i 0.251806 0.251806i
\(508\) −1.40730e8 + 8.58013e6i −1.07349 + 0.0654490i
\(509\) −9.12226e6 + 9.12226e6i −0.0691750 + 0.0691750i −0.740848 0.671673i \(-0.765576\pi\)
0.671673 + 0.740848i \(0.265576\pi\)
\(510\) 3.34731e7 3.55761e7i 0.252340 0.268193i
\(511\) 2.26400e7i 0.169673i
\(512\) 1.17047e8 + 6.56834e7i 0.872071 + 0.489380i
\(513\) 1.33593e8 0.989536
\(514\) −1.24699e8 1.17328e8i −0.918279 0.863998i
\(515\) −1.16994e8 1.16994e8i −0.856529 0.856529i
\(516\) −1.56941e6 2.57412e7i −0.0114232 0.187361i
\(517\) 1.04282e8 + 1.04282e8i 0.754639 + 0.754639i
\(518\) −1.67411e6 5.49681e7i −0.0120447 0.395477i
\(519\) −3.90495e7 −0.279328
\(520\) −1.20756e6 + 1.45108e6i −0.00858815 + 0.0103200i
\(521\) 1.20851e8i 0.854548i 0.904122 + 0.427274i \(0.140526\pi\)
−0.904122 + 0.427274i \(0.859474\pi\)
\(522\) 24571.7 + 806793.i 0.000172752 + 0.00567219i
\(523\) −1.56314e8 + 1.56314e8i −1.09268 + 1.09268i −0.0974367 + 0.995242i \(0.531064\pi\)
−0.995242 + 0.0974367i \(0.968936\pi\)
\(524\) −1.07541e8 + 1.21506e8i −0.747448 + 0.844507i
\(525\) −5.01980e7 + 5.01980e7i −0.346903 + 0.346903i
\(526\) −4.57786e6 4.30726e6i −0.0314562 0.0295967i
\(527\) 2.23256e7i 0.152536i
\(528\) 7.23918e7 8.86020e6i 0.491799 0.0601924i
\(529\) −8.65814e7 −0.584867
\(530\) 3.28337e8 3.48965e8i 2.20542 2.34398i
\(531\) 1.60036e8 + 1.60036e8i 1.06889 + 1.06889i
\(532\) −9.21429e7 + 1.04108e8i −0.611966 + 0.691432i
\(533\) 235056. + 235056.i 0.00155235 + 0.00155235i
\(534\) −1.84760e7 + 562705.i −0.121334 + 0.00369536i
\(535\) 1.57866e8 1.03093
\(536\) 1.54722e8 1.41717e7i 1.00475 0.0920297i
\(537\) 8.21207e7i 0.530310i
\(538\) −1.40997e8 + 4.29422e6i −0.905450 + 0.0275764i
\(539\) −9.43605e7 + 9.43605e7i −0.602593 + 0.602593i
\(540\) −1.14585e7 1.87940e8i −0.0727688 1.19354i
\(541\) −1.95480e8 + 1.95480e8i −1.23455 + 1.23455i −0.272359 + 0.962196i \(0.587804\pi\)
−0.962196 + 0.272359i \(0.912196\pi\)
\(542\) −8.49950e7 + 9.03348e7i −0.533821 + 0.567358i
\(543\) 3.11805e7i 0.194753i
\(544\) −7.48662e7 5.49498e7i −0.465038 0.341326i
\(545\) 3.58183e7 0.221267
\(546\) 196835. + 185200.i 0.00120927 + 0.00113779i
\(547\) 1.05737e8 + 1.05737e8i 0.646050 + 0.646050i 0.952036 0.305986i \(-0.0989862\pi\)
−0.305986 + 0.952036i \(0.598986\pi\)
\(548\) 1.77096e8 1.07973e7i 1.07613 0.0656104i
\(549\) −1.25572e8 1.25572e8i −0.758887 0.758887i
\(550\) 1.55945e7 + 5.12033e8i 0.0937311 + 3.07759i
\(551\) 1.61270e6 0.00964051
\(552\) 3.84327e7 3.52024e6i 0.228499 0.0209293i
\(553\) 1.36121e8i 0.804916i
\(554\) 4.28224e6 + 1.40604e8i 0.0251850 + 0.826929i
\(555\) 4.90494e7 4.90494e7i 0.286916 0.286916i
\(556\) −3.72830e7 3.29981e7i −0.216913 0.191984i
\(557\) 9.55244e7 9.55244e7i 0.552776 0.552776i −0.374465 0.927241i \(-0.622174\pi\)
0.927241 + 0.374465i \(0.122174\pi\)
\(558\) −2.92160e7 2.74890e7i −0.168158 0.158218i
\(559\) 689610.i 0.00394792i
\(560\) 1.54364e8 + 1.20698e8i 0.878985 + 0.687286i
\(561\) −5.04630e7 −0.285815
\(562\) 4.59124e7 4.87969e7i 0.258655 0.274905i
\(563\) 7.31393e7 + 7.31393e7i 0.409851 + 0.409851i 0.881686 0.471836i \(-0.156408\pi\)
−0.471836 + 0.881686i \(0.656408\pi\)
\(564\) 3.67000e7 + 3.24821e7i 0.204564 + 0.181053i
\(565\) 9.87264e7 + 9.87264e7i 0.547379 + 0.547379i
\(566\) 7.59270e7 2.31244e6i 0.418742 0.0127532i
\(567\) 7.21201e7 0.395646
\(568\) 9.01487e7 1.08328e8i 0.491942 0.591148i
\(569\) 2.55687e8i 1.38794i −0.720002 0.693972i \(-0.755859\pi\)
0.720002 0.693972i \(-0.244141\pi\)
\(570\) −1.75282e8 + 5.33841e6i −0.946485 + 0.0288262i
\(571\) 1.59086e8 1.59086e8i 0.854524 0.854524i −0.136163 0.990686i \(-0.543477\pi\)
0.990686 + 0.136163i \(0.0434770\pi\)
\(572\) 1.94662e6 118683.i 0.0104014 0.000634162i
\(573\) 4.86485e7 4.86485e7i 0.258586 0.258586i
\(574\) 2.36442e7 2.51296e7i 0.125022 0.132877i
\(575\) 2.71080e8i 1.42591i
\(576\) −1.64089e8 + 3.03138e7i −0.858644 + 0.158625i
\(577\) −1.52809e8 −0.795464 −0.397732 0.917502i \(-0.630203\pi\)
−0.397732 + 0.917502i \(0.630203\pi\)
\(578\) −9.38374e7 8.82905e7i −0.485951 0.457226i
\(579\) 1.31392e7 + 1.31392e7i 0.0676913 + 0.0676913i
\(580\) −138324. 2.26877e6i −0.000708947 0.0116281i
\(581\) −9.97302e7 9.97302e7i −0.508508 0.508508i
\(582\) −2.03520e6 6.68243e7i −0.0103238 0.338973i
\(583\) −4.94990e8 −2.49799
\(584\) −4.17316e7 3.47283e7i −0.209520 0.174359i
\(585\) 2.34702e6i 0.0117233i
\(586\) 1.72639e6 + 5.66847e7i 0.00857920 + 0.281691i
\(587\) 1.42595e8 1.42595e8i 0.705002 0.705002i −0.260478 0.965480i \(-0.583880\pi\)
0.965480 + 0.260478i \(0.0838802\pi\)
\(588\) −2.93916e7 + 3.32083e7i −0.144574 + 0.163348i
\(589\) −5.66739e7 + 5.66739e7i −0.277356 + 0.277356i
\(590\) −4.64171e8 4.36733e8i −2.26007 2.12648i
\(591\) 5.28999e7i 0.256267i
\(592\) −1.03889e8 8.12317e7i −0.500731 0.391526i
\(593\) 3.24485e8 1.55607 0.778037 0.628219i \(-0.216216\pi\)
0.778037 + 0.628219i \(0.216216\pi\)
\(594\) −1.33292e8 + 1.41666e8i −0.635983 + 0.675939i
\(595\) −9.58705e7 9.58705e7i −0.455128 0.455128i
\(596\) 1.50634e8 1.70195e8i 0.711517 0.803911i
\(597\) 2.51718e7 + 2.51718e7i 0.118302 + 0.118302i
\(598\) 1.03153e6 31416.4i 0.00482369 0.000146911i
\(599\) 1.79608e8 0.835689 0.417844 0.908519i \(-0.362786\pi\)
0.417844 + 0.908519i \(0.362786\pi\)
\(600\) 1.55280e7 + 1.69529e8i 0.0718888 + 0.784857i
\(601\) 2.78315e8i 1.28207i −0.767510 0.641037i \(-0.778505\pi\)
0.767510 0.641037i \(-0.221495\pi\)
\(602\) −7.15464e7 + 2.17902e6i −0.327943 + 0.00998785i
\(603\) −1.36587e8 + 1.36587e8i −0.622956 + 0.622956i
\(604\) 4.18526e6 + 6.86461e7i 0.0189938 + 0.311534i
\(605\) 2.62615e8 2.62615e8i 1.18591 1.18591i
\(606\) 6.05575e6 6.43621e6i 0.0272114 0.0289209i
\(607\) 1.38550e8i 0.619499i −0.950818 0.309750i \(-0.899755\pi\)
0.950818 0.309750i \(-0.100245\pi\)
\(608\) 5.05580e7 + 3.29540e8i 0.224947 + 1.46621i
\(609\) −325407. −0.00144070
\(610\) 3.64213e8 + 3.42684e8i 1.60460 + 1.50975i
\(611\) 926698. + 926698.i 0.00406270 + 0.00406270i
\(612\) 1.15244e8 7.02626e6i 0.502763 0.0306528i
\(613\) −6.90262e7 6.90262e7i −0.299663 0.299663i 0.541219 0.840882i \(-0.317963\pi\)
−0.840882 + 0.541219i \(0.817963\pi\)
\(614\) 1.85430e6 + 6.08845e7i 0.00801078 + 0.263028i
\(615\) 4.35221e7 0.187105
\(616\) −1.84642e7 2.01585e8i −0.0789928 0.862415i
\(617\) 1.22553e8i 0.521758i −0.965372 0.260879i \(-0.915988\pi\)
0.965372 0.260879i \(-0.0840124\pi\)
\(618\) 1.72917e6 + 5.67759e7i 0.00732609 + 0.240546i
\(619\) 9.63080e7 9.63080e7i 0.406060 0.406060i −0.474302 0.880362i \(-0.657300\pi\)
0.880362 + 0.474302i \(0.157300\pi\)
\(620\) 8.45907e7 + 7.48686e7i 0.354934 + 0.314141i
\(621\) −7.27840e7 + 7.27840e7i −0.303921 + 0.303921i
\(622\) 2.74044e8 + 2.57845e8i 1.13880 + 1.07149i
\(623\) 5.13054e7i 0.212177i
\(624\) 643305. 78735.6i 0.00264767 0.000324054i
\(625\) −4.11301e8 −1.68469
\(626\) −1.08814e8 + 1.15650e8i −0.443568 + 0.471436i
\(627\) 1.28101e8 + 1.28101e8i 0.519697 + 0.519697i
\(628\) 1.57128e8 + 1.39069e8i 0.634415 + 0.561502i
\(629\) 6.45221e7 + 6.45221e7i 0.259273 + 0.259273i
\(630\) −2.43501e8 + 7.41609e6i −0.973823 + 0.0296588i
\(631\) 4.49697e8 1.78991 0.894957 0.446153i \(-0.147206\pi\)
0.894957 + 0.446153i \(0.147206\pi\)
\(632\) −2.50908e8 2.08801e8i −0.993948 0.827145i
\(633\) 9.25215e7i 0.364780i
\(634\) −2.87187e8 + 8.74658e6i −1.12693 + 0.0343218i
\(635\) −3.49036e8 + 3.49036e8i −1.36317 + 1.36317i
\(636\) −1.64191e8 + 1.00105e7i −0.638231 + 0.0389121i
\(637\) −838529. + 838529.i −0.00324414 + 0.00324414i
\(638\) −1.60907e6 + 1.71017e6i −0.00619604 + 0.00658531i
\(639\) 1.75213e8i 0.671528i
\(640\) 4.59264e8 9.93908e7i 1.75195 0.379146i
\(641\) 1.60286e8 0.608586 0.304293 0.952579i \(-0.401580\pi\)
0.304293 + 0.952579i \(0.401580\pi\)
\(642\) −3.94721e7 3.71388e7i −0.149171 0.140353i
\(643\) −2.80798e8 2.80798e8i −1.05624 1.05624i −0.998322 0.0579139i \(-0.981555\pi\)
−0.0579139 0.998322i \(-0.518445\pi\)
\(644\) −6.51885e6 1.06921e8i −0.0244069 0.400320i
\(645\) −6.38427e7 6.38427e7i −0.237921 0.237921i
\(646\) −7.02242e6 2.30575e8i −0.0260489 0.855294i
\(647\) 2.66079e8 0.982422 0.491211 0.871041i \(-0.336554\pi\)
0.491211 + 0.871041i \(0.336554\pi\)
\(648\) 1.10628e8 1.32937e8i 0.406573 0.488563i
\(649\) 6.58405e8i 2.40857i
\(650\) 138580. + 4.55015e6i 0.000504614 + 0.0165686i
\(651\) 1.14355e7 1.14355e7i 0.0414489 0.0414489i
\(652\) 3.60834e6 4.07690e6i 0.0130186 0.0147091i
\(653\) −4.39341e6 + 4.39341e6i −0.0157784 + 0.0157784i −0.714952 0.699174i \(-0.753551\pi\)
0.699174 + 0.714952i \(0.253551\pi\)
\(654\) −8.95582e6 8.42643e6i −0.0320164 0.0301238i
\(655\) 5.68077e8i 2.02154i
\(656\) −1.00521e7 8.21298e7i −0.0356076 0.290931i
\(657\) 6.74980e7 0.238010
\(658\) 9.32159e7 9.90723e7i 0.327199 0.347756i
\(659\) 9.60616e7 + 9.60616e7i 0.335655 + 0.335655i 0.854729 0.519074i \(-0.173723\pi\)
−0.519074 + 0.854729i \(0.673723\pi\)
\(660\) 1.69227e8 1.91202e8i 0.588623 0.665059i
\(661\) −3.32344e8 3.32344e8i −1.15076 1.15076i −0.986401 0.164354i \(-0.947446\pi\)
−0.164354 0.986401i \(-0.552554\pi\)
\(662\) 3.26516e8 9.94437e6i 1.12546 0.0342771i
\(663\) −448437. −0.00153872
\(664\) −3.36809e8 + 3.08500e7i −1.15048 + 0.105378i
\(665\) 4.86737e8i 1.65512i
\(666\) 1.63880e8 4.99113e6i 0.554757 0.0168957i
\(667\) −878632. + 878632.i −0.00296094 + 0.00296094i
\(668\) 3.36340e7 + 5.51660e8i 0.112836 + 1.85073i
\(669\) 7.96945e7 7.96945e7i 0.266164 0.266164i
\(670\) 3.72742e8 3.96160e8i 1.23932 1.31718i
\(671\) 5.16619e8i 1.71003i
\(672\) −1.02015e7 6.64936e7i −0.0336166 0.219115i
\(673\) −2.59342e8 −0.850801 −0.425400 0.905005i \(-0.639867\pi\)
−0.425400 + 0.905005i \(0.639867\pi\)
\(674\) −2.99525e8 2.81819e8i −0.978257 0.920430i
\(675\) −3.21055e8 3.21055e8i −1.04392 1.04392i
\(676\) −3.08326e8 + 1.87982e7i −0.998091 + 0.0608522i
\(677\) 7.93397e7 + 7.93397e7i 0.255697 + 0.255697i 0.823301 0.567605i \(-0.192130\pi\)
−0.567605 + 0.823301i \(0.692130\pi\)
\(678\) −1.45917e6 4.79108e7i −0.00468186 0.153725i
\(679\) −1.85563e8 −0.592763
\(680\) −3.23774e8 + 2.96560e7i −1.02971 + 0.0943162i
\(681\) 7.87017e7i 0.249197i
\(682\) −3.55256e6 1.16645e8i −0.0111992 0.367717i
\(683\) −9.83571e7 + 9.83571e7i −0.308705 + 0.308705i −0.844407 0.535702i \(-0.820047\pi\)
0.535702 + 0.844407i \(0.320047\pi\)
\(684\) −3.10384e8 2.74712e8i −0.969909 0.858438i
\(685\) 4.39228e8 4.39228e8i 1.36653 1.36653i
\(686\) 2.36000e8 + 2.22050e8i 0.731038 + 0.687825i
\(687\) 5.73266e7i 0.176802i
\(688\) −1.05731e8 + 1.35222e8i −0.324666 + 0.415223i
\(689\) −4.39870e6 −0.0134483
\(690\) 9.25888e7 9.84057e7i 0.281845 0.299553i
\(691\) −2.67048e8 2.67048e8i −0.809386 0.809386i 0.175155 0.984541i \(-0.443957\pi\)
−0.984541 + 0.175155i \(0.943957\pi\)
\(692\) 1.94630e8 + 1.72261e8i 0.587342 + 0.519839i
\(693\) 1.77957e8 + 1.77957e8i 0.534708 + 0.534708i
\(694\) 9.17840e7 2.79538e6i 0.274592 0.00836300i
\(695\) −1.74309e8 −0.519238
\(696\) −499154. + 599813.i −0.00148049 + 0.00177905i
\(697\) 5.72512e7i 0.169078i
\(698\) 2.61686e8 7.96992e6i 0.769510 0.0234362i
\(699\) 1.14668e8 1.14668e8i 0.335746 0.335746i
\(700\) 4.71636e8 2.87550e7i 1.37503 0.0838339i
\(701\) −3.87585e8 + 3.87585e8i −1.12516 + 1.12516i −0.134202 + 0.990954i \(0.542847\pi\)
−0.990954 + 0.134202i \(0.957153\pi\)
\(702\) −1.18449e6 + 1.25891e6i −0.00342390 + 0.00363901i
\(703\) 3.27581e8i 0.942871i
\(704\) −3.99899e8 2.75184e8i −1.14613 0.788689i
\(705\) 1.71584e8 0.489676
\(706\) 4.15623e8 + 3.91054e8i 1.18110 + 1.11128i
\(707\) −1.73443e7 1.73443e7i −0.0490793 0.0490793i
\(708\) 1.33154e7 + 2.18397e8i 0.0375192 + 0.615384i
\(709\) 3.44165e8 + 3.44165e8i 0.965667 + 0.965667i 0.999430 0.0337624i \(-0.0107490\pi\)
−0.0337624 + 0.999430i \(0.510749\pi\)
\(710\) −1.50201e7 4.93173e8i −0.0419660 1.37792i
\(711\) 4.05827e8 1.12910
\(712\) 9.45697e7 + 7.86992e7i 0.262007 + 0.218037i
\(713\) 6.17541e7i 0.170372i
\(714\) 1.41696e6 + 4.65249e7i 0.00389282 + 0.127818i
\(715\) 4.82796e6 4.82796e6i 0.0132083 0.0132083i
\(716\) 3.62262e8 4.09304e8i 0.986925 1.11508i
\(717\) −5.95854e7 + 5.95854e7i −0.161653 + 0.161653i
\(718\) −4.09859e8 3.85632e8i −1.10729 1.04184i
\(719\) 2.26972e8i 0.610641i −0.952250 0.305321i \(-0.901236\pi\)
0.952250 0.305321i \(-0.0987637\pi\)
\(720\) −3.59846e8 + 4.60215e8i −0.964093 + 1.23300i
\(721\) 1.57659e8 0.420644
\(722\) −3.09586e8 + 3.29036e8i −0.822563 + 0.874241i
\(723\) −6.65269e7 6.65269e7i −0.176028 0.176028i
\(724\) −1.37548e8 + 1.55409e8i −0.362442 + 0.409507i
\(725\) −3.87570e6 3.87570e6i −0.0101704 0.0101704i
\(726\) −1.27444e8 + 3.88144e6i −0.333050 + 0.0101434i
\(727\) −1.42830e8 −0.371719 −0.185860 0.982576i \(-0.559507\pi\)
−0.185860 + 0.982576i \(0.559507\pi\)
\(728\) −164081. 1.79137e6i −0.000425268 0.00464293i
\(729\) 1.22978e8i 0.317427i
\(730\) −1.89987e8 + 5.78624e6i −0.488376 + 0.0148740i
\(731\) 8.39820e7 8.39820e7i 0.214998 0.214998i
\(732\) −1.04479e7 1.71366e8i −0.0266377 0.436908i
\(733\) 2.54471e8 2.54471e8i 0.646139 0.646139i −0.305919 0.952058i \(-0.598964\pi\)
0.952058 + 0.305919i \(0.0989636\pi\)
\(734\) −1.69970e8 + 1.80649e8i −0.429818 + 0.456821i
\(735\) 1.55259e8i 0.391015i
\(736\) −2.07084e8 1.51994e8i −0.519414 0.381236i
\(737\) −5.61935e8 −1.40373
\(738\) 7.49205e7 + 7.04918e7i 0.186394 + 0.175376i
\(739\) 2.61656e8 + 2.61656e8i 0.648333 + 0.648333i 0.952590 0.304257i \(-0.0984081\pi\)
−0.304257 + 0.952590i \(0.598408\pi\)
\(740\) −4.60845e8 + 2.80971e7i −1.13726 + 0.0693372i
\(741\) 1.13836e6 + 1.13836e6i 0.00279786 + 0.00279786i
\(742\) 1.38989e7 + 4.56361e8i 0.0340228 + 1.11711i
\(743\) −1.90483e8 −0.464397 −0.232198 0.972668i \(-0.574592\pi\)
−0.232198 + 0.972668i \(0.574592\pi\)
\(744\) −3.53740e6 3.86201e7i −0.00858944 0.0937766i
\(745\) 7.95713e8i 1.92437i
\(746\) 2.16734e7 + 7.11628e8i 0.0522048 + 1.71410i
\(747\) 2.97332e8 2.97332e8i 0.713312 0.713312i
\(748\) 2.51517e8 + 2.22610e8i 0.600982 + 0.531911i
\(749\) −1.06369e8 + 1.06369e8i −0.253146 + 0.253146i
\(750\) 2.37935e8 + 2.23870e8i 0.563993 + 0.530654i
\(751\) 1.15685e8i 0.273122i 0.990632 + 0.136561i \(0.0436050\pi\)
−0.990632 + 0.136561i \(0.956395\pi\)
\(752\) −3.96297e7 3.23793e8i −0.0931896 0.761401i
\(753\) −1.75271e8 −0.410511
\(754\) −14298.9 + 15197.3i −3.33572e−5 + 3.54529e-5i
\(755\) 1.70254e8 + 1.70254e8i 0.395601 + 0.395601i
\(756\) 1.34354e8 + 1.18912e8i 0.310945 + 0.275208i
\(757\) 7.45004e7 + 7.45004e7i 0.171740 + 0.171740i 0.787743 0.616004i \(-0.211249\pi\)
−0.616004 + 0.787743i \(0.711249\pi\)
\(758\) 6.75014e8 2.05583e7i 1.54990 0.0472040i
\(759\) −1.39584e8 −0.319235
\(760\) 8.97188e8 + 7.46623e8i 2.04382 + 1.70083i
\(761\) 2.60939e8i 0.592086i 0.955175 + 0.296043i \(0.0956672\pi\)
−0.955175 + 0.296043i \(0.904333\pi\)
\(762\) 1.69383e8 5.15874e6i 0.382829 0.0116595i
\(763\) −2.41341e7 + 2.41341e7i −0.0543323 + 0.0543323i
\(764\) −4.57078e8 + 2.78674e7i −1.02497 + 0.0624909i
\(765\) 2.85825e8 2.85825e8i 0.638433 0.638433i
\(766\) −3.16041e8 + 3.35897e8i −0.703165 + 0.747342i
\(767\) 5.85088e6i 0.0129669i
\(768\) −1.38214e8 8.31928e7i −0.305118 0.183655i
\(769\) 5.34401e8 1.17514 0.587568 0.809175i \(-0.300085\pi\)
0.587568 + 0.809175i \(0.300085\pi\)
\(770\) −5.16152e8 4.85641e8i −1.13059 1.06376i
\(771\) 1.45517e8 + 1.45517e8i 0.317506 + 0.317506i
\(772\) −7.52655e6 1.23449e8i −0.0163585 0.268310i
\(773\) −3.55344e8 3.55344e8i −0.769325 0.769325i 0.208662 0.977988i \(-0.433089\pi\)
−0.977988 + 0.208662i \(0.933089\pi\)
\(774\) −6.49645e6 2.13306e8i −0.0140105 0.460023i
\(775\) 2.72401e8 0.585199
\(776\) −2.84641e8 + 3.42042e8i −0.609134 + 0.731972i
\(777\) 6.60983e7i 0.140905i
\(778\) −2.21982e7 7.28859e8i −0.0471388 1.54776i
\(779\) 1.45333e8 1.45333e8i 0.307434 0.307434i
\(780\) 1.50382e6 1.69910e6i 0.00316893 0.00358043i
\(781\) −3.60424e8 + 3.60424e8i −0.756590 + 0.756590i
\(782\) 1.29448e8 + 1.21796e8i 0.270692 + 0.254691i
\(783\) 2.08123e6i 0.00433545i
\(784\) 2.92986e8 3.58592e7i 0.607993 0.0744137i
\(785\) 7.34619e8 1.51864
\(786\) 1.33643e8 1.42039e8i 0.275218 0.292509i
\(787\) −3.27339e8 3.27339e8i −0.671542 0.671542i 0.286529 0.958071i \(-0.407498\pi\)
−0.958071 + 0.286529i \(0.907498\pi\)
\(788\) −2.33359e8 + 2.63662e8i −0.476921 + 0.538852i
\(789\) 5.34212e6 + 5.34212e6i 0.0108763 + 0.0108763i
\(790\) −1.14228e9 + 3.47894e7i −2.31682 + 0.0705611i
\(791\) −1.33042e8 −0.268819
\(792\) 6.00999e8 5.50484e7i 1.20976 0.110807i
\(793\) 4.59090e6i 0.00920616i
\(794\) 3.75478e8 1.14356e7i 0.750108 0.0228453i
\(795\) −4.07223e8 + 4.07223e8i −0.810458 + 0.810458i
\(796\) −1.44192e7 2.36502e8i −0.0285893 0.468917i
\(797\) −2.74877e8 + 2.74877e8i −0.542955 + 0.542955i −0.924394 0.381439i \(-0.875429\pi\)
0.381439 + 0.924394i \(0.375429\pi\)
\(798\) 1.14507e8 1.21701e8i 0.225332 0.239489i
\(799\) 2.25710e8i 0.442497i
\(800\) 6.70457e8 9.13462e8i 1.30949 1.78410i
\(801\) −1.52960e8 −0.297633
\(802\) −3.83093e8 3.60447e8i −0.742644 0.698745i
\(803\) 1.38847e8 + 1.38847e8i 0.268158 + 0.268158i
\(804\) −1.86397e8 + 1.13644e7i −0.358650 + 0.0218664i
\(805\) −2.65184e8 2.65184e8i −0.508346 0.508346i
\(806\) −31569.6 1.03656e6i −6.02925e−5 0.00197966i
\(807\) 1.69547e8 0.322604
\(808\) −5.85753e7 + 5.36519e6i −0.111040 + 0.0101707i
\(809\) 7.49473e8i 1.41550i −0.706462 0.707751i \(-0.749710\pi\)
0.706462 0.707751i \(-0.250290\pi\)
\(810\) −1.84322e7 6.05206e8i −0.0346834 1.13880i
\(811\) −5.97328e8 + 5.97328e8i −1.11983 + 1.11983i −0.128058 + 0.991767i \(0.540875\pi\)
−0.991767 + 0.128058i \(0.959125\pi\)
\(812\) 1.62189e6 + 1.43548e6i 0.00302937 + 0.00268120i
\(813\) 1.05416e8 1.05416e8i 0.196171 0.196171i
\(814\) 3.47377e8 + 3.26843e8i 0.644063 + 0.605991i
\(815\) 1.90607e7i 0.0352101i
\(816\) 8.79315e7 + 6.87544e7i 0.161836 + 0.126541i
\(817\) −4.26379e8 −0.781861
\(818\) −1.73237e8 + 1.84121e8i −0.316505 + 0.336390i
\(819\) 1.58141e6 + 1.58141e6i 0.00287867 + 0.00287867i
\(820\) −2.16922e8 1.91991e8i −0.393425 0.348208i
\(821\) −3.66612e8 3.66612e8i −0.662488 0.662488i 0.293478 0.955966i \(-0.405187\pi\)
−0.955966 + 0.293478i \(0.905187\pi\)
\(822\) −2.13153e8 + 6.49179e6i −0.383774 + 0.0116882i
\(823\) −5.77764e8 −1.03646 −0.518228 0.855243i \(-0.673408\pi\)
−0.518228 + 0.855243i \(0.673408\pi\)
\(824\) 2.41840e8 2.90609e8i 0.432261 0.519431i
\(825\) 6.15713e8i 1.09652i
\(826\) 6.07023e8 1.84875e7i 1.07712 0.0328049i
\(827\) 3.54236e8 3.54236e8i 0.626290 0.626290i −0.320842 0.947133i \(-0.603966\pi\)
0.947133 + 0.320842i \(0.103966\pi\)
\(828\) 3.18771e8 1.94351e7i 0.561550 0.0342369i
\(829\) −8.00560e7 + 8.00560e7i −0.140517 + 0.140517i −0.773866 0.633349i \(-0.781680\pi\)
0.633349 + 0.773866i \(0.281680\pi\)
\(830\) −8.11412e8 + 8.62389e8i −1.41908 + 1.50824i
\(831\) 1.69074e8i 0.294628i
\(832\) −3.55368e6 2.44541e6i −0.00617032 0.00424602i
\(833\) −2.04235e8 −0.353342
\(834\) 4.35834e7 + 4.10071e7i 0.0751316 + 0.0706904i
\(835\) 1.36821e9 + 1.36821e9i 2.35014 + 2.35014i
\(836\) −7.33804e7 1.20358e9i −0.125592 2.05994i
\(837\) 7.31388e7 + 7.31388e7i 0.124730 + 0.124730i
\(838\) −1.04255e7 3.42314e8i −0.0177160 0.581691i
\(839\) 6.76738e8 1.14587 0.572934 0.819602i \(-0.305805\pi\)
0.572934 + 0.819602i \(0.305805\pi\)
\(840\) −1.81032e8 1.50652e8i −0.305434 0.254177i
\(841\) 5.94798e8i 0.999958i
\(842\) 4.47167e6 + 1.46824e8i 0.00749089 + 0.245957i
\(843\) −5.69433e7 + 5.69433e7i −0.0950516 + 0.0950516i
\(844\) 4.08144e8 4.61143e8i 0.678869 0.767023i
\(845\) −7.64702e8 + 7.64702e8i −1.26743 + 1.26743i
\(846\) 2.95371e8 + 2.77911e8i 0.487816 + 0.458980i
\(847\) 3.53896e8i 0.582405i
\(848\) 8.62517e8 + 6.74409e8i 1.41442 + 1.10595i
\(849\) −9.13011e7 −0.149195
\(850\) −5.37249e8 + 5.71002e8i −0.874821 + 0.929782i
\(851\) 1.78472e8 + 1.78472e8i 0.289589 + 0.289589i
\(852\) −1.12266e8 + 1.26844e8i −0.181521 + 0.205093i
\(853\) 3.99632e8 + 3.99632e8i 0.643892 + 0.643892i 0.951510 0.307618i \(-0.0995317\pi\)
−0.307618 + 0.951510i \(0.599532\pi\)
\(854\) −4.76302e8 + 1.45063e7i −0.764731 + 0.0232907i
\(855\) −1.45114e9 −2.32173
\(856\) 3.29037e7 + 3.59231e8i 0.0524594 + 0.572734i
\(857\) 4.22100e8i 0.670615i −0.942109 0.335307i \(-0.891160\pi\)
0.942109 0.335307i \(-0.108840\pi\)
\(858\) −2.34296e6 + 71357.2i −0.00370939 + 0.000112973i
\(859\) 3.35359e8 3.35359e8i 0.529090 0.529090i −0.391211 0.920301i \(-0.627944\pi\)
0.920301 + 0.391211i \(0.127944\pi\)
\(860\) 3.65711e7 + 5.99835e8i 0.0574967 + 0.943054i
\(861\) −2.93249e7 + 2.93249e7i −0.0459438 + 0.0459438i
\(862\) 7.05487e8 7.49810e8i 1.10146 1.17066i
\(863\) 7.06487e8i 1.09919i 0.835432 + 0.549593i \(0.185217\pi\)
−0.835432 + 0.549593i \(0.814783\pi\)
\(864\) 4.25277e8 6.52461e7i 0.659373 0.101161i
\(865\) 9.09953e8 1.40595
\(866\) 2.57900e8 + 2.42655e8i 0.397098 + 0.373625i
\(867\) 1.09503e8 + 1.09503e8i 0.168023 + 0.168023i
\(868\) −1.07443e8 + 6.55063e6i −0.164292 + 0.0100167i
\(869\) 8.34809e8 + 8.34809e8i 1.27212 + 1.27212i
\(870\) 83166.3 + 2.73070e6i 0.000126296 + 0.00414683i
\(871\) −4.99360e6 −0.00755717
\(872\) 7.46552e6 + 8.15060e7i 0.0112593 + 0.122925i
\(873\) 5.53230e8i 0.831501i
\(874\) −1.94244e7 6.37786e8i −0.0290947 0.955302i
\(875\) 6.41186e8 6.41186e8i 0.957106 0.957106i
\(876\) 4.88644e7 + 4.32484e7i 0.0726910 + 0.0643366i
\(877\) 1.18842e8 1.18842e8i 0.176185 0.176185i −0.613505 0.789691i \(-0.710241\pi\)
0.789691 + 0.613505i \(0.210241\pi\)
\(878\) 1.71288e8 + 1.61163e8i 0.253072 + 0.238113i
\(879\) 6.81626e7i 0.100364i
\(880\) −1.68691e9 + 2.06465e8i −2.47540 + 0.302969i
\(881\) −8.18267e8 −1.19665 −0.598326 0.801253i \(-0.704167\pi\)
−0.598326 + 0.801253i \(0.704167\pi\)
\(882\) −2.51469e8 + 2.67268e8i −0.366504 + 0.389530i
\(883\) −8.74250e8 8.74250e8i −1.26985 1.26985i −0.946163 0.323690i \(-0.895076\pi\)
−0.323690 0.946163i \(-0.604924\pi\)
\(884\) 2.23509e6 + 1.97821e6i 0.00323547 + 0.00286362i
\(885\) 5.41662e8 + 5.41662e8i 0.781446 + 0.781446i
\(886\) 7.91687e7 2.41117e6i 0.113829 0.00346678i
\(887\) −9.08568e8 −1.30193 −0.650963 0.759109i \(-0.725635\pi\)
−0.650963 + 0.759109i \(0.725635\pi\)
\(888\) 1.21837e8 + 1.01391e8i 0.173997 + 0.144797i
\(889\) 4.70356e8i 0.669454i
\(890\) 4.30537e8 1.31124e7i 0.610717 0.0186000i
\(891\) −4.42301e8 + 4.42301e8i −0.625294 + 0.625294i
\(892\) −7.48771e8 + 4.56516e7i −1.05501 + 0.0643222i
\(893\) 5.72968e8 5.72968e8i 0.804593 0.804593i
\(894\) −1.87195e8 + 1.98956e8i −0.261988 + 0.278448i
\(895\) 1.91362e9i 2.66923i
\(896\) −2.42480e8 + 3.76418e8i −0.337095 + 0.523294i
\(897\) −1.24040e6 −0.00171864
\(898\) 7.81656e7 + 7.35451e7i 0.107941 + 0.101560i
\(899\) 882915. + 882915.i 0.00121518 + 0.00121518i
\(900\) 8.57292e7 + 1.40612e9i 0.117598 + 1.92883i
\(901\) −5.35681e8 5.35681e8i −0.732373 0.732373i
\(902\) 9.11007e6 + 2.99122e8i 0.0124137 + 0.407595i
\(903\) 8.60335e7 0.116843
\(904\) −2.04078e8 + 2.45233e8i −0.276243 + 0.331951i
\(905\) 7.26585e8i 0.980259i
\(906\) −2.51636e6 8.26226e7i −0.00338367 0.111100i
\(907\) 4.33430e8 4.33430e8i 0.580895 0.580895i −0.354254 0.935149i \(-0.615265\pi\)
0.935149 + 0.354254i \(0.115265\pi\)
\(908\) 3.47180e8 3.92263e8i 0.463764 0.523986i
\(909\) 5.17097e7 5.17097e7i 0.0688462 0.0688462i
\(910\) −4.58675e6 4.31562e6i −0.00608669 0.00572690i
\(911\) 8.08779e8i 1.06973i −0.844937 0.534865i \(-0.820362\pi\)
0.844937 0.534865i \(-0.179638\pi\)
\(912\) −4.86814e7 3.97749e8i −0.0641769 0.524354i
\(913\) 1.22326e9 1.60733
\(914\) 8.87941e8 9.43726e8i 1.16291 1.23597i
\(915\) −4.25017e8 4.25017e8i −0.554808 0.554808i
\(916\) 2.52887e8 2.85726e8i 0.329034 0.371760i
\(917\) −3.82766e8 3.82766e8i −0.496393 0.496393i
\(918\) −2.97562e8 + 9.06257e6i −0.384636 + 0.0117145i
\(919\) 9.98417e8 1.28637 0.643184 0.765711i \(-0.277613\pi\)
0.643184 + 0.765711i \(0.277613\pi\)
\(920\) −8.95580e8 + 8.20305e7i −1.15011 + 0.105344i
\(921\) 7.32127e7i 0.0937146i
\(922\) −1.31539e8 + 4.00617e6i −0.167827 + 0.00511136i
\(923\) −3.20288e6 + 3.20288e6i −0.00407320 + 0.00407320i
\(924\) 1.48065e7 + 2.42854e8i 0.0187688 + 0.307843i
\(925\) −7.87251e8 + 7.87251e8i −0.994691 + 0.994691i
\(926\) −2.20384e8 + 2.34229e8i −0.277553 + 0.294991i
\(927\) 4.70040e8i 0.590060i
\(928\) 5.13385e6 787636.i 0.00642391 0.000985557i
\(929\) −1.15058e9 −1.43506 −0.717531 0.696527i \(-0.754728\pi\)
−0.717531 + 0.696527i \(0.754728\pi\)
\(930\) −9.88854e7 9.30401e7i −0.122937 0.115670i
\(931\) 5.18454e8 + 5.18454e8i 0.642482 + 0.642482i
\(932\) −1.07737e9 + 6.56856e7i −1.33081 + 0.0811376i
\(933\) −3.19794e8 3.19794e8i −0.393755 0.393755i
\(934\) −1.13297e7 3.72003e8i −0.0139053 0.456568i
\(935\) 1.17592e9 1.43861
\(936\) 5.34074e6 489184.i 0.00651289 0.000596547i
\(937\) 1.04563e9i 1.27104i 0.772086 + 0.635518i \(0.219213\pi\)
−0.772086 + 0.635518i \(0.780787\pi\)
\(938\) 1.57787e7 + 5.18081e8i 0.0191189 + 0.627754i
\(939\) 1.34957e8 1.34957e8i 0.163004 0.163004i
\(940\) −8.55203e8 7.56915e8i −1.02964 0.911304i
\(941\) 9.38599e8 9.38599e8i 1.12645 1.12645i 0.135698 0.990750i \(-0.456672\pi\)
0.990750 0.135698i \(-0.0433278\pi\)
\(942\) −1.83680e8 1.72823e8i −0.219740 0.206751i
\(943\) 1.58360e8i 0.188848i
\(944\) 8.97057e8 1.14727e9i 1.06636 1.36379i
\(945\) 6.28144e8 0.744326
\(946\) 4.25419e8 4.52146e8i 0.502509 0.534079i
\(947\) −8.73243e8 8.73243e8i −1.02822 1.02822i −0.999590 0.0286279i \(-0.990886\pi\)
−0.0286279 0.999590i \(-0.509114\pi\)
\(948\) 2.93794e8 + 2.60028e8i 0.344840 + 0.305208i
\(949\) 1.23386e6 + 1.23386e6i 0.00144366 + 0.00144366i
\(950\) 2.81331e9 8.56824e7i 3.28131 0.0999357i
\(951\) 3.45338e8 0.401516
\(952\) 1.98175e8 2.38139e8i 0.229688 0.276007i
\(953\) 1.04703e9i 1.20970i 0.796338 + 0.604852i \(0.206768\pi\)
−0.796338 + 0.604852i \(0.793232\pi\)
\(954\) −1.36058e9 + 4.14378e7i −1.56703 + 0.0477256i
\(955\) −1.13363e9 + 1.13363e9i −1.30156 + 1.30156i
\(956\) 5.59836e8 3.41325e7i 0.640748 0.0390655i
\(957\) 1.99567e6 1.99567e6i 0.00227695 0.00227695i
\(958\) −2.62391e8 + 2.78875e8i −0.298436 + 0.317186i
\(959\) 5.91898e8i 0.671106i
\(960\) −5.55383e8 + 1.02601e8i −0.627739 + 0.115968i
\(961\) 8.25449e8 0.930079
\(962\) 3.08695e6 + 2.90447e6i 0.00346740 + 0.00326244i
\(963\) −3.17126e8 3.17126e8i −0.355102 0.355102i
\(964\) 3.81087e7 + 6.25055e8i 0.0425396 + 0.697729i
\(965\) −3.06176e8 3.06176e8i −0.340714 0.340714i
\(966\) 3.91941e6 + 1.28691e8i 0.00434800 + 0.142763i
\(967\) −2.11963e8 −0.234412 −0.117206 0.993108i \(-0.537394\pi\)
−0.117206 + 0.993108i \(0.537394\pi\)
\(968\) 6.52326e8 + 5.42854e8i 0.719182 + 0.598490i
\(969\) 2.77264e8i 0.304735i
\(970\) 4.74254e7 + 1.55718e9i 0.0519632 + 1.70617i
\(971\) 4.03408e8 4.03408e8i 0.440643 0.440643i −0.451585 0.892228i \(-0.649141\pi\)
0.892228 + 0.451585i \(0.149141\pi\)
\(972\) −5.43783e8 + 6.14395e8i −0.592143 + 0.669035i
\(973\) 1.17448e8 1.17448e8i 0.127500 0.127500i
\(974\) −3.98265e8 3.74723e8i −0.431018 0.405540i
\(975\) 5.47149e6i 0.00590326i
\(976\) −7.03878e8 + 9.00206e8i −0.757091 + 0.968261i
\(977\) −1.56036e9 −1.67317 −0.836586 0.547836i \(-0.815452\pi\)
−0.836586 + 0.547836i \(0.815452\pi\)
\(978\) −4.48413e6 + 4.76584e6i −0.00479359 + 0.00509475i
\(979\) −3.14648e8 3.14648e8i −0.335333 0.335333i
\(980\) 6.84899e8 7.73836e8i 0.727693 0.822188i
\(981\) −7.19527e7 7.19527e7i −0.0762149 0.0762149i
\(982\) −4.62875e8 + 1.40973e7i −0.488798 + 0.0148869i
\(983\) 3.49167e7 0.0367598 0.0183799 0.999831i \(-0.494149\pi\)
0.0183799 + 0.999831i \(0.494149\pi\)
\(984\) 9.07120e6 + 9.90362e7i 0.00952093 + 0.103946i
\(985\) 1.23270e9i 1.28988i
\(986\) −3.59210e6 + 109401.i −0.00374730 + 0.000114128i
\(987\) −1.15612e8 + 1.15612e8i −0.120241 + 0.120241i
\(988\) −652090. 1.06955e7i −0.000676141 0.0110900i
\(989\) 2.32299e8 2.32299e8i 0.240137 0.240137i
\(990\) 1.44787e9 1.53884e9i 1.49219 1.58594i
\(991\) 1.02328e9i 1.05142i −0.850664 0.525709i \(-0.823800\pi\)
0.850664 0.525709i \(-0.176200\pi\)
\(992\) −1.52735e8 + 2.08094e8i −0.156461 + 0.213169i
\(993\) −3.92630e8 −0.400992
\(994\) 3.42417e8 + 3.22176e8i 0.348655 + 0.328045i
\(995\) −5.86568e8 5.86568e8i −0.595455 0.595455i
\(996\) 4.05762e8 2.47388e7i 0.410670 0.0250380i
\(997\) 9.21368e8 + 9.21368e8i 0.929711 + 0.929711i 0.997687 0.0679761i \(-0.0216542\pi\)
−0.0679761 + 0.997687i \(0.521654\pi\)
\(998\) 1.12472e7 + 3.69294e8i 0.0113150 + 0.371519i
\(999\) −4.22749e8 −0.424020
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 16.7.f.a.11.8 yes 22
4.3 odd 2 64.7.f.a.15.6 22
8.3 odd 2 128.7.f.a.31.6 22
8.5 even 2 128.7.f.b.31.6 22
16.3 odd 4 inner 16.7.f.a.3.8 22
16.5 even 4 128.7.f.a.95.6 22
16.11 odd 4 128.7.f.b.95.6 22
16.13 even 4 64.7.f.a.47.6 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.7.f.a.3.8 22 16.3 odd 4 inner
16.7.f.a.11.8 yes 22 1.1 even 1 trivial
64.7.f.a.15.6 22 4.3 odd 2
64.7.f.a.47.6 22 16.13 even 4
128.7.f.a.31.6 22 8.3 odd 2
128.7.f.a.95.6 22 16.5 even 4
128.7.f.b.31.6 22 8.5 even 2
128.7.f.b.95.6 22 16.11 odd 4