Properties

Label 14.7.d.a.3.1
Level $14$
Weight $7$
Character 14.3
Analytic conductor $3.221$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [14,7,Mod(3,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 14.d (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.22075717068\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 285x^{6} + 282x^{5} + 62091x^{4} + 29260x^{3} + 4838750x^{2} + 2401000x + 294122500 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 3.1
Root \(4.65421 - 8.06134i\) of defining polynomial
Character \(\chi\) \(=\) 14.3
Dual form 14.7.d.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.82843 - 4.89898i) q^{2} +(-12.7609 - 7.36750i) q^{3} +(-16.0000 + 27.7128i) q^{4} +(-106.741 + 61.6269i) q^{5} +83.3537i q^{6} +(-309.691 + 147.446i) q^{7} +181.019 q^{8} +(-255.940 - 443.301i) q^{9} +O(q^{10})\) \(q+(-2.82843 - 4.89898i) q^{2} +(-12.7609 - 7.36750i) q^{3} +(-16.0000 + 27.7128i) q^{4} +(-106.741 + 61.6269i) q^{5} +83.3537i q^{6} +(-309.691 + 147.446i) q^{7} +181.019 q^{8} +(-255.940 - 443.301i) q^{9} +(603.818 + 348.614i) q^{10} +(292.324 - 506.319i) q^{11} +(408.348 - 235.760i) q^{12} -1722.98i q^{13} +(1598.27 + 1100.13i) q^{14} +1816.14 q^{15} +(-512.000 - 886.810i) q^{16} +(1076.36 + 621.438i) q^{17} +(-1447.82 + 2507.69i) q^{18} +(-10061.3 + 5808.88i) q^{19} -3944.12i q^{20} +(5038.24 + 400.105i) q^{21} -3307.26 q^{22} +(-3912.13 - 6776.01i) q^{23} +(-2309.97 - 1333.66i) q^{24} +(-216.757 + 375.434i) q^{25} +(-8440.83 + 4873.31i) q^{26} +18284.4i q^{27} +(868.910 - 10941.6i) q^{28} +40255.0 q^{29} +(-5136.83 - 8897.25i) q^{30} +(8271.32 + 4775.45i) q^{31} +(-2896.31 + 5016.55i) q^{32} +(-7460.61 + 4307.39i) q^{33} -7030.77i q^{34} +(23970.1 - 34823.8i) q^{35} +16380.2 q^{36} +(-41851.5 - 72488.9i) q^{37} +(56915.2 + 32860.0i) q^{38} +(-12694.0 + 21986.7i) q^{39} +(-19322.2 + 11155.7i) q^{40} +66557.3i q^{41} +(-12290.2 - 25813.9i) q^{42} -137672. q^{43} +(9354.36 + 16202.2i) q^{44} +(54638.5 + 31545.6i) q^{45} +(-22130.4 + 38330.9i) q^{46} +(-122613. + 70790.4i) q^{47} +15088.6i q^{48} +(74168.2 - 91325.6i) q^{49} +2452.32 q^{50} +(-9156.89 - 15860.2i) q^{51} +(47748.5 + 27567.6i) q^{52} +(101710. - 176167. i) q^{53} +(89574.7 - 51716.0i) q^{54} +72060.0i q^{55} +(-56060.1 + 26690.6i) q^{56} +171188. q^{57} +(-113858. - 197209. i) q^{58} +(-7927.04 - 4576.68i) q^{59} +(-29058.3 + 50330.4i) q^{60} +(-28024.7 + 16180.0i) q^{61} -54028.0i q^{62} +(144625. + 99549.0i) q^{63} +32768.0 q^{64} +(106182. + 183912. i) q^{65} +(42203.6 + 24366.3i) q^{66} +(17387.6 - 30116.1i) q^{67} +(-34443.6 + 19886.0i) q^{68} +115290. i q^{69} +(-238399. - 18932.1i) q^{70} -76478.5 q^{71} +(-46330.1 - 80246.1i) q^{72} +(-548044. - 316413. i) q^{73} +(-236748. + 410059. i) q^{74} +(5532.01 - 3193.91i) q^{75} -371768. i q^{76} +(-15875.2 + 199905. i) q^{77} +143617. q^{78} +(240692. + 416890. i) q^{79} +(109303. + 63105.9i) q^{80} +(-51870.3 + 89842.0i) q^{81} +(326063. - 188252. i) q^{82} -774360. i q^{83} +(-91699.9 + 133222. i) q^{84} -153189. q^{85} +(389397. + 674455. i) q^{86} +(-513689. - 296579. i) q^{87} +(52916.2 - 91653.6i) q^{88} +(362874. - 209505. i) q^{89} -356897. i q^{90} +(254046. + 533591. i) q^{91} +250376. q^{92} +(-70366.2 - 121878. i) q^{93} +(693601. + 400451. i) q^{94} +(715966. - 1.24009e6i) q^{95} +(73918.9 - 42677.1i) q^{96} +1.26292e6i q^{97} +(-657182. - 105041. i) q^{98} -299269. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 128 q^{4} - 336 q^{5} + 652 q^{7} + 756 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 128 q^{4} - 336 q^{5} + 652 q^{7} + 756 q^{9} - 2016 q^{10} - 1356 q^{11} + 2064 q^{14} + 27144 q^{15} - 4096 q^{16} - 17304 q^{17} - 6816 q^{18} - 32004 q^{19} + 9756 q^{21} + 25248 q^{22} - 4128 q^{23} + 10752 q^{24} + 4664 q^{25} - 4704 q^{26} - 7552 q^{28} - 30312 q^{29} + 9648 q^{30} - 3108 q^{31} + 3276 q^{33} + 98028 q^{35} - 48384 q^{36} - 6124 q^{37} + 155568 q^{38} + 100764 q^{39} + 64512 q^{40} - 315936 q^{42} - 297376 q^{43} - 43392 q^{44} - 172116 q^{45} - 194064 q^{46} + 313908 q^{47} + 32432 q^{49} + 38784 q^{50} + 253692 q^{51} + 255360 q^{52} + 278484 q^{53} + 386064 q^{54} - 125952 q^{56} - 81288 q^{57} - 169824 q^{58} - 835464 q^{59} - 434304 q^{60} - 995316 q^{61} + 1216188 q^{63} + 262144 q^{64} + 8316 q^{65} + 1673280 q^{66} + 648808 q^{67} + 553728 q^{68} - 1572816 q^{70} + 190128 q^{71} - 218112 q^{72} - 1617084 q^{73} - 1158144 q^{74} - 2042208 q^{75} + 1456224 q^{77} + 1122432 q^{78} + 70096 q^{79} + 344064 q^{80} + 1177920 q^{81} + 66528 q^{82} - 1133568 q^{84} + 2190984 q^{85} - 573024 q^{86} - 2057076 q^{87} - 403968 q^{88} + 739116 q^{89} + 2233752 q^{91} + 264192 q^{92} - 23364 q^{93} + 3795120 q^{94} + 725640 q^{95} - 344064 q^{96} - 3532320 q^{98} - 4625928 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82843 4.89898i −0.353553 0.612372i
\(3\) −12.7609 7.36750i −0.472625 0.272870i 0.244713 0.969596i \(-0.421306\pi\)
−0.717338 + 0.696725i \(0.754640\pi\)
\(4\) −16.0000 + 27.7128i −0.250000 + 0.433013i
\(5\) −106.741 + 61.6269i −0.853927 + 0.493015i −0.861974 0.506953i \(-0.830772\pi\)
0.00804690 + 0.999968i \(0.497439\pi\)
\(6\) 83.3537i 0.385897i
\(7\) −309.691 + 147.446i −0.902890 + 0.429872i
\(8\) 181.019 0.353553
\(9\) −255.940 443.301i −0.351084 0.608095i
\(10\) 603.818 + 348.614i 0.603818 + 0.348614i
\(11\) 292.324 506.319i 0.219627 0.380405i −0.735067 0.677995i \(-0.762849\pi\)
0.954694 + 0.297589i \(0.0961826\pi\)
\(12\) 408.348 235.760i 0.236313 0.136435i
\(13\) 1722.98i 0.784241i −0.919914 0.392120i \(-0.871742\pi\)
0.919914 0.392120i \(-0.128258\pi\)
\(14\) 1598.27 + 1100.13i 0.582462 + 0.400922i
\(15\) 1816.14 0.538116
\(16\) −512.000 886.810i −0.125000 0.216506i
\(17\) 1076.36 + 621.438i 0.219085 + 0.126489i 0.605526 0.795825i \(-0.292963\pi\)
−0.386442 + 0.922314i \(0.626296\pi\)
\(18\) −1447.82 + 2507.69i −0.248254 + 0.429988i
\(19\) −10061.3 + 5808.88i −1.46687 + 0.846899i −0.999313 0.0370633i \(-0.988200\pi\)
−0.467559 + 0.883962i \(0.654866\pi\)
\(20\) 3944.12i 0.493015i
\(21\) 5038.24 + 400.105i 0.544028 + 0.0432033i
\(22\) −3307.26 −0.310600
\(23\) −3912.13 6776.01i −0.321536 0.556917i 0.659269 0.751907i \(-0.270866\pi\)
−0.980805 + 0.194990i \(0.937533\pi\)
\(24\) −2309.97 1333.66i −0.167098 0.0964742i
\(25\) −216.757 + 375.434i −0.0138724 + 0.0240278i
\(26\) −8440.83 + 4873.31i −0.480247 + 0.277271i
\(27\) 18284.4i 0.928942i
\(28\) 868.910 10941.6i 0.0395822 0.498431i
\(29\) 40255.0 1.65054 0.825270 0.564738i \(-0.191023\pi\)
0.825270 + 0.564738i \(0.191023\pi\)
\(30\) −5136.83 8897.25i −0.190253 0.329528i
\(31\) 8271.32 + 4775.45i 0.277645 + 0.160298i 0.632357 0.774677i \(-0.282088\pi\)
−0.354712 + 0.934976i \(0.615421\pi\)
\(32\) −2896.31 + 5016.55i −0.0883883 + 0.153093i
\(33\) −7460.61 + 4307.39i −0.207603 + 0.119859i
\(34\) 7030.77i 0.178882i
\(35\) 23970.1 34823.8i 0.559068 0.812218i
\(36\) 16380.2 0.351084
\(37\) −41851.5 72488.9i −0.826238 1.43109i −0.900969 0.433883i \(-0.857143\pi\)
0.0747306 0.997204i \(-0.476190\pi\)
\(38\) 56915.2 + 32860.0i 1.03723 + 0.598848i
\(39\) −12694.0 + 21986.7i −0.213996 + 0.370652i
\(40\) −19322.2 + 11155.7i −0.301909 + 0.174307i
\(41\) 66557.3i 0.965704i 0.875702 + 0.482852i \(0.160399\pi\)
−0.875702 + 0.482852i \(0.839601\pi\)
\(42\) −12290.2 25813.9i −0.165886 0.348422i
\(43\) −137672. −1.73158 −0.865789 0.500410i \(-0.833183\pi\)
−0.865789 + 0.500410i \(0.833183\pi\)
\(44\) 9354.36 + 16202.2i 0.109814 + 0.190203i
\(45\) 54638.5 + 31545.6i 0.599600 + 0.346179i
\(46\) −22130.4 + 38330.9i −0.227360 + 0.393800i
\(47\) −122613. + 70790.4i −1.18098 + 0.681837i −0.956240 0.292582i \(-0.905485\pi\)
−0.224736 + 0.974420i \(0.572152\pi\)
\(48\) 15088.6i 0.136435i
\(49\) 74168.2 91325.6i 0.630420 0.776255i
\(50\) 2452.32 0.0196186
\(51\) −9156.89 15860.2i −0.0690299 0.119563i
\(52\) 47748.5 + 27567.6i 0.339586 + 0.196060i
\(53\) 101710. 176167.i 0.683182 1.18331i −0.290823 0.956777i \(-0.593929\pi\)
0.974005 0.226528i \(-0.0727376\pi\)
\(54\) 89574.7 51716.0i 0.568858 0.328430i
\(55\) 72060.0i 0.433118i
\(56\) −56060.1 + 26690.6i −0.319220 + 0.151983i
\(57\) 171188. 0.924374
\(58\) −113858. 197209.i −0.583554 1.01075i
\(59\) −7927.04 4576.68i −0.0385971 0.0222841i 0.480577 0.876952i \(-0.340427\pi\)
−0.519174 + 0.854668i \(0.673760\pi\)
\(60\) −29058.3 + 50330.4i −0.134529 + 0.233011i
\(61\) −28024.7 + 16180.0i −0.123467 + 0.0712837i −0.560462 0.828180i \(-0.689376\pi\)
0.436995 + 0.899464i \(0.356043\pi\)
\(62\) 54028.0i 0.226696i
\(63\) 144625. + 99549.0i 0.578393 + 0.398121i
\(64\) 32768.0 0.125000
\(65\) 106182. + 183912.i 0.386642 + 0.669684i
\(66\) 42203.6 + 24366.3i 0.146797 + 0.0847534i
\(67\) 17387.6 30116.1i 0.0578115 0.100132i −0.835671 0.549230i \(-0.814921\pi\)
0.893483 + 0.449098i \(0.148254\pi\)
\(68\) −34443.6 + 19886.0i −0.109542 + 0.0632443i
\(69\) 115290.i 0.350951i
\(70\) −238399. 18932.1i −0.695040 0.0551957i
\(71\) −76478.5 −0.213680 −0.106840 0.994276i \(-0.534073\pi\)
−0.106840 + 0.994276i \(0.534073\pi\)
\(72\) −46330.1 80246.1i −0.124127 0.214994i
\(73\) −548044. 316413.i −1.40879 0.813366i −0.413520 0.910495i \(-0.635701\pi\)
−0.995272 + 0.0971288i \(0.969034\pi\)
\(74\) −236748. + 410059.i −0.584239 + 1.01193i
\(75\) 5532.01 3193.91i 0.0131129 0.00757075i
\(76\) 371768.i 0.846899i
\(77\) −15875.2 + 199905.i −0.0347733 + 0.437876i
\(78\) 143617. 0.302636
\(79\) 240692. + 416890.i 0.488180 + 0.845553i 0.999908 0.0135952i \(-0.00432761\pi\)
−0.511728 + 0.859148i \(0.670994\pi\)
\(80\) 109303. + 63105.9i 0.213482 + 0.123254i
\(81\) −51870.3 + 89842.0i −0.0976031 + 0.169054i
\(82\) 326063. 188252.i 0.591371 0.341428i
\(83\) 774360.i 1.35428i −0.735854 0.677140i \(-0.763219\pi\)
0.735854 0.677140i \(-0.236781\pi\)
\(84\) −91699.9 + 133222.i −0.154714 + 0.224770i
\(85\) −153189. −0.249443
\(86\) 389397. + 674455.i 0.612205 + 1.06037i
\(87\) −513689. 296579.i −0.780087 0.450383i
\(88\) 52916.2 91653.6i 0.0776499 0.134494i
\(89\) 362874. 209505.i 0.514737 0.297184i −0.220042 0.975490i \(-0.570619\pi\)
0.734779 + 0.678307i \(0.237286\pi\)
\(90\) 356897.i 0.489571i
\(91\) 254046. + 533591.i 0.337123 + 0.708083i
\(92\) 250376. 0.321536
\(93\) −70366.2 121878.i −0.0874813 0.151522i
\(94\) 693601. + 400451.i 0.835077 + 0.482132i
\(95\) 715966. 1.24009e6i 0.835068 1.44638i
\(96\) 73918.9 42677.1i 0.0835491 0.0482371i
\(97\) 1.26292e6i 1.38376i 0.722013 + 0.691880i \(0.243217\pi\)
−0.722013 + 0.691880i \(0.756783\pi\)
\(98\) −657182. 105041.i −0.698244 0.111604i
\(99\) −299269. −0.308430
\(100\) −6936.22 12013.9i −0.00693622 0.0120139i
\(101\) −995828. 574942.i −0.966541 0.558033i −0.0683612 0.997661i \(-0.521777\pi\)
−0.898180 + 0.439628i \(0.855110\pi\)
\(102\) −51799.2 + 89718.8i −0.0488115 + 0.0845441i
\(103\) 902082. 520817.i 0.825533 0.476622i −0.0267879 0.999641i \(-0.508528\pi\)
0.852321 + 0.523020i \(0.175195\pi\)
\(104\) 311892.i 0.277271i
\(105\) −562443. + 267783.i −0.485860 + 0.231321i
\(106\) −1.15072e6 −0.966165
\(107\) 369400. + 639820.i 0.301541 + 0.522284i 0.976485 0.215585i \(-0.0691658\pi\)
−0.674945 + 0.737868i \(0.735832\pi\)
\(108\) −506711. 292550.i −0.402244 0.232235i
\(109\) −36911.1 + 63932.0i −0.0285022 + 0.0493672i −0.879925 0.475113i \(-0.842407\pi\)
0.851422 + 0.524480i \(0.175740\pi\)
\(110\) 353020. 203816.i 0.265229 0.153130i
\(111\) 1.23336e6i 0.901824i
\(112\) 289319. + 199145.i 0.205931 + 0.141747i
\(113\) −828494. −0.574188 −0.287094 0.957902i \(-0.592689\pi\)
−0.287094 + 0.957902i \(0.592689\pi\)
\(114\) −484192. 838644.i −0.326815 0.566061i
\(115\) 835169. + 482185.i 0.549137 + 0.317044i
\(116\) −644080. + 1.11558e6i −0.412635 + 0.714705i
\(117\) −763798. + 440979.i −0.476893 + 0.275334i
\(118\) 51779.2i 0.0315144i
\(119\) −424969. 33748.4i −0.252183 0.0200268i
\(120\) 328757. 0.190253
\(121\) 714874. + 1.23820e6i 0.403528 + 0.698931i
\(122\) 158531. + 91528.2i 0.0873043 + 0.0504052i
\(123\) 490361. 849329.i 0.263512 0.456416i
\(124\) −264682. + 152814.i −0.138822 + 0.0801492i
\(125\) 1.97927e6i 1.01339i
\(126\) 78626.3 990084.i 0.0393057 0.494949i
\(127\) 886054. 0.432563 0.216281 0.976331i \(-0.430607\pi\)
0.216281 + 0.976331i \(0.430607\pi\)
\(128\) −92681.9 160530.i −0.0441942 0.0765466i
\(129\) 1.75682e6 + 1.01430e6i 0.818387 + 0.472496i
\(130\) 600654. 1.04036e6i 0.273398 0.473538i
\(131\) 471848. 272422.i 0.209888 0.121179i −0.391371 0.920233i \(-0.627999\pi\)
0.601259 + 0.799054i \(0.294666\pi\)
\(132\) 275673.i 0.119859i
\(133\) 2.25939e6 3.28245e6i 0.960365 1.39522i
\(134\) −196718. −0.0817578
\(135\) −1.12681e6 1.95169e6i −0.457982 0.793248i
\(136\) 194842. + 112492.i 0.0774581 + 0.0447205i
\(137\) −1.50754e6 + 2.61114e6i −0.586284 + 1.01547i 0.408430 + 0.912790i \(0.366077\pi\)
−0.994714 + 0.102685i \(0.967257\pi\)
\(138\) 564806. 326091.i 0.214913 0.124080i
\(139\) 616326.i 0.229491i 0.993395 + 0.114746i \(0.0366053\pi\)
−0.993395 + 0.114746i \(0.963395\pi\)
\(140\) 581546. + 1.22146e6i 0.211933 + 0.445138i
\(141\) 2.08619e6 0.744212
\(142\) 216314. + 374666.i 0.0755473 + 0.130852i
\(143\) −872377. 503667.i −0.298329 0.172240i
\(144\) −262083. + 453940.i −0.0877709 + 0.152024i
\(145\) −4.29686e6 + 2.48079e6i −1.40944 + 0.813741i
\(146\) 3.57981e6i 1.15027i
\(147\) −1.61929e6 + 618960.i −0.509769 + 0.194855i
\(148\) 2.67849e6 0.826238
\(149\) −2.26864e6 3.92941e6i −0.685816 1.18787i −0.973180 0.230047i \(-0.926112\pi\)
0.287364 0.957822i \(-0.407221\pi\)
\(150\) −31293.8 18067.5i −0.00927224 0.00535333i
\(151\) −1.28825e6 + 2.23132e6i −0.374171 + 0.648083i −0.990203 0.139638i \(-0.955406\pi\)
0.616032 + 0.787721i \(0.288739\pi\)
\(152\) −1.82128e6 + 1.05152e6i −0.518617 + 0.299424i
\(153\) 636204.i 0.177632i
\(154\) 1.02423e6 487644.i 0.280437 0.133518i
\(155\) −1.17718e6 −0.316118
\(156\) −406209. 703574.i −0.106998 0.185326i
\(157\) 1.22590e6 + 707772.i 0.316778 + 0.182892i 0.649955 0.759972i \(-0.274788\pi\)
−0.333178 + 0.942864i \(0.608121\pi\)
\(158\) 1.36156e6 2.35829e6i 0.345195 0.597896i
\(159\) −2.59582e6 + 1.49870e6i −0.645778 + 0.372840i
\(160\) 713962.i 0.174307i
\(161\) 2.21065e6 + 1.52164e6i 0.529715 + 0.364615i
\(162\) 586846. 0.138032
\(163\) −1.72692e6 2.99111e6i −0.398758 0.690669i 0.594815 0.803863i \(-0.297225\pi\)
−0.993573 + 0.113194i \(0.963892\pi\)
\(164\) −1.84449e6 1.06492e6i −0.418162 0.241426i
\(165\) 530902. 919548.i 0.118185 0.204702i
\(166\) −3.79357e6 + 2.19022e6i −0.829324 + 0.478810i
\(167\) 1.70140e6i 0.365306i −0.983177 0.182653i \(-0.941532\pi\)
0.983177 0.182653i \(-0.0584684\pi\)
\(168\) 912019. + 72426.8i 0.192343 + 0.0152747i
\(169\) 1.85816e6 0.384966
\(170\) 433285. + 750471.i 0.0881914 + 0.152752i
\(171\) 5.15016e6 + 2.97345e6i 1.02999 + 0.594665i
\(172\) 2.20276e6 3.81529e6i 0.432894 0.749795i
\(173\) 5.47104e6 3.15871e6i 1.05665 0.610058i 0.132148 0.991230i \(-0.457813\pi\)
0.924504 + 0.381172i \(0.124479\pi\)
\(174\) 3.35541e6i 0.636938i
\(175\) 11771.4 148228.i 0.00219641 0.0276578i
\(176\) −598679. −0.109814
\(177\) 67437.3 + 116805.i 0.0121613 + 0.0210640i
\(178\) −2.05272e6 1.18514e6i −0.363974 0.210141i
\(179\) −1.94905e6 + 3.37586e6i −0.339832 + 0.588607i −0.984401 0.175940i \(-0.943704\pi\)
0.644569 + 0.764546i \(0.277037\pi\)
\(180\) −1.74843e6 + 1.00946e6i −0.299800 + 0.173090i
\(181\) 1.29647e6i 0.218638i −0.994007 0.109319i \(-0.965133\pi\)
0.994007 0.109319i \(-0.0348670\pi\)
\(182\) 1.89550e6 2.75379e6i 0.314419 0.456790i
\(183\) 476826. 0.0778048
\(184\) −708171. 1.22659e6i −0.113680 0.196900i
\(185\) 8.93452e6 + 5.15835e6i 1.41109 + 0.814696i
\(186\) −398051. + 689445.i −0.0618586 + 0.107142i
\(187\) 629293. 363322.i 0.0962338 0.0555606i
\(188\) 4.53058e6i 0.681837i
\(189\) −2.69596e6 5.66250e6i −0.399326 0.838732i
\(190\) −8.10023e6 −1.18096
\(191\) 5.04551e6 + 8.73908e6i 0.724111 + 1.25420i 0.959339 + 0.282256i \(0.0910828\pi\)
−0.235228 + 0.971940i \(0.575584\pi\)
\(192\) −418148. 241418.i −0.0590781 0.0341088i
\(193\) −50987.6 + 88313.1i −0.00709239 + 0.0122844i −0.869550 0.493845i \(-0.835591\pi\)
0.862457 + 0.506130i \(0.168924\pi\)
\(194\) 6.18702e6 3.57208e6i 0.847376 0.489233i
\(195\) 3.12917e6i 0.422013i
\(196\) 1.34420e6 + 3.51662e6i 0.178523 + 0.467043i
\(197\) −1.35768e6 −0.177582 −0.0887912 0.996050i \(-0.528300\pi\)
−0.0887912 + 0.996050i \(0.528300\pi\)
\(198\) 846461. + 1.46611e6i 0.109046 + 0.188874i
\(199\) −1.11375e7 6.43022e6i −1.41328 0.815956i −0.417582 0.908639i \(-0.637122\pi\)
−0.995696 + 0.0926828i \(0.970456\pi\)
\(200\) −39237.2 + 67960.8i −0.00490465 + 0.00849510i
\(201\) −443761. + 256206.i −0.0546463 + 0.0315501i
\(202\) 6.50472e6i 0.789178i
\(203\) −1.24666e7 + 5.93545e6i −1.49026 + 0.709522i
\(204\) 586041. 0.0690299
\(205\) −4.10172e6 7.10438e6i −0.476107 0.824641i
\(206\) −5.10295e6 2.94619e6i −0.583740 0.337022i
\(207\) −2.00254e6 + 3.46850e6i −0.225772 + 0.391049i
\(208\) −1.52795e6 + 882164.i −0.169793 + 0.0980301i
\(209\) 6.79229e6i 0.744007i
\(210\) 2.90270e6 + 1.99799e6i 0.313432 + 0.215743i
\(211\) −2.60412e6 −0.277213 −0.138606 0.990348i \(-0.544262\pi\)
−0.138606 + 0.990348i \(0.544262\pi\)
\(212\) 3.25472e6 + 5.63734e6i 0.341591 + 0.591653i
\(213\) 975932. + 563455.i 0.100991 + 0.0583069i
\(214\) 2.08964e6 3.61937e6i 0.213221 0.369310i
\(215\) 1.46953e7 8.48433e6i 1.47864 0.853693i
\(216\) 3.30982e6i 0.328430i
\(217\) −3.26568e6 259340.i −0.319591 0.0253799i
\(218\) 417602. 0.0403082
\(219\) 4.66235e6 + 8.07542e6i 0.443887 + 0.768835i
\(220\) −1.99698e6 1.15296e6i −0.187545 0.108279i
\(221\) 1.07072e6 1.85455e6i 0.0991975 0.171815i
\(222\) 6.04221e6 3.48847e6i 0.552252 0.318843i
\(223\) 2.84513e6i 0.256559i −0.991738 0.128280i \(-0.959054\pi\)
0.991738 0.128280i \(-0.0409455\pi\)
\(224\) 157289. 1.98063e6i 0.0139944 0.176222i
\(225\) 221907. 0.0194815
\(226\) 2.34334e6 + 4.05878e6i 0.203006 + 0.351617i
\(227\) −8.93407e6 5.15809e6i −0.763786 0.440972i 0.0668673 0.997762i \(-0.478700\pi\)
−0.830653 + 0.556790i \(0.812033\pi\)
\(228\) −2.73900e6 + 4.74409e6i −0.231093 + 0.400266i
\(229\) −2.33247e6 + 1.34665e6i −0.194227 + 0.112137i −0.593960 0.804495i \(-0.702436\pi\)
0.399733 + 0.916632i \(0.369103\pi\)
\(230\) 5.45530e6i 0.448368i
\(231\) 1.67538e6 2.43400e6i 0.135918 0.197462i
\(232\) 7.28694e6 0.583554
\(233\) 1.94190e6 + 3.36348e6i 0.153518 + 0.265902i 0.932519 0.361122i \(-0.117606\pi\)
−0.779000 + 0.627024i \(0.784273\pi\)
\(234\) 4.32069e6 + 2.49455e6i 0.337214 + 0.194691i
\(235\) 8.72518e6 1.51125e7i 0.672312 1.16448i
\(236\) 253665. 146454.i 0.0192986 0.0111420i
\(237\) 7.09318e6i 0.532839i
\(238\) 1.03666e6 + 2.17737e6i 0.0768964 + 0.161511i
\(239\) −767.787 −5.62402e−5 −2.81201e−5 1.00000i \(-0.500009\pi\)
−2.81201e−5 1.00000i \(0.500009\pi\)
\(240\) −929865. 1.61057e6i −0.0672646 0.116506i
\(241\) −6.27199e6 3.62114e6i −0.448079 0.258698i 0.258940 0.965893i \(-0.416627\pi\)
−0.707018 + 0.707195i \(0.749960\pi\)
\(242\) 4.04394e6 7.00431e6i 0.285337 0.494219i
\(243\) 1.28673e7 7.42896e6i 0.896746 0.517737i
\(244\) 1.03552e6i 0.0712837i
\(245\) −2.28867e6 + 1.43189e7i −0.155627 + 0.973671i
\(246\) −5.54780e6 −0.372662
\(247\) 1.00086e7 + 1.73353e7i 0.664173 + 1.15038i
\(248\) 1.49727e6 + 864449.i 0.0981623 + 0.0566740i
\(249\) −5.70509e6 + 9.88151e6i −0.369543 + 0.640067i
\(250\) −9.69641e6 + 5.59823e6i −0.620570 + 0.358287i
\(251\) 2.12337e7i 1.34278i −0.741104 0.671390i \(-0.765697\pi\)
0.741104 0.671390i \(-0.234303\pi\)
\(252\) −5.07279e6 + 2.41519e6i −0.316990 + 0.150921i
\(253\) −4.57443e6 −0.282472
\(254\) −2.50614e6 4.34076e6i −0.152934 0.264890i
\(255\) 1.95483e6 + 1.12862e6i 0.117893 + 0.0680656i
\(256\) −524288. + 908093.i −0.0312500 + 0.0541266i
\(257\) −2.35936e7 + 1.36218e7i −1.38993 + 0.802479i −0.993307 0.115500i \(-0.963153\pi\)
−0.396627 + 0.917980i \(0.629819\pi\)
\(258\) 1.14755e7i 0.668210i
\(259\) 2.36492e7 + 1.62783e7i 1.36119 + 0.936937i
\(260\) −6.79563e6 −0.386642
\(261\) −1.03029e7 1.78451e7i −0.579478 1.00368i
\(262\) −2.66918e6 1.54105e6i −0.148413 0.0856865i
\(263\) −9.98954e6 + 1.73024e7i −0.549134 + 0.951128i 0.449200 + 0.893431i \(0.351709\pi\)
−0.998334 + 0.0576966i \(0.981624\pi\)
\(264\) −1.35052e6 + 779720.i −0.0733986 + 0.0423767i
\(265\) 2.50723e7i 1.34728i
\(266\) −2.24712e7 1.78452e6i −1.19394 0.0948150i
\(267\) −6.17412e6 −0.324370
\(268\) 556402. + 963717.i 0.0289058 + 0.0500662i
\(269\) 1.10258e7 + 6.36574e6i 0.566438 + 0.327033i 0.755726 0.654888i \(-0.227284\pi\)
−0.189287 + 0.981922i \(0.560618\pi\)
\(270\) −6.37419e6 + 1.10404e7i −0.323842 + 0.560911i
\(271\) 1.06993e7 6.17726e6i 0.537587 0.310376i −0.206513 0.978444i \(-0.566212\pi\)
0.744101 + 0.668068i \(0.232878\pi\)
\(272\) 1.27271e6i 0.0632443i
\(273\) 689373. 8.68077e6i 0.0338818 0.426649i
\(274\) 1.70559e7 0.829131
\(275\) 126726. + 219496.i 0.00609352 + 0.0105543i
\(276\) −3.19502e6 1.84465e6i −0.151966 0.0877377i
\(277\) 1.10760e7 1.91842e7i 0.521127 0.902619i −0.478571 0.878049i \(-0.658845\pi\)
0.999698 0.0245702i \(-0.00782172\pi\)
\(278\) 3.01937e6 1.74323e6i 0.140534 0.0811374i
\(279\) 4.88891e6i 0.225113i
\(280\) 4.33904e6 6.30379e6i 0.197661 0.287162i
\(281\) 2.38736e7 1.07597 0.537984 0.842955i \(-0.319186\pi\)
0.537984 + 0.842955i \(0.319186\pi\)
\(282\) −5.90064e6 1.02202e7i −0.263119 0.455735i
\(283\) −7.24433e6 4.18252e6i −0.319624 0.184535i 0.331601 0.943420i \(-0.392411\pi\)
−0.651225 + 0.758885i \(0.725745\pi\)
\(284\) 1.22366e6 2.11943e6i 0.0534200 0.0925262i
\(285\) −1.82727e7 + 1.05498e7i −0.789348 + 0.455730i
\(286\) 5.69834e6i 0.243585i
\(287\) −9.81362e6 2.06122e7i −0.415129 0.871924i
\(288\) 2.96513e6 0.124127
\(289\) −1.12964e7 1.95660e7i −0.468001 0.810602i
\(290\) 2.43067e7 + 1.40335e7i 0.996625 + 0.575402i
\(291\) 9.30456e6 1.61160e7i 0.377587 0.653999i
\(292\) 1.75374e7 1.01252e7i 0.704396 0.406683i
\(293\) 1.37943e7i 0.548401i 0.961673 + 0.274201i \(0.0884132\pi\)
−0.961673 + 0.274201i \(0.911587\pi\)
\(294\) 7.61233e6 + 6.18220e6i 0.299554 + 0.243277i
\(295\) 1.12819e6 0.0439455
\(296\) −7.57592e6 1.31219e7i −0.292119 0.505966i
\(297\) 9.25772e6 + 5.34495e6i 0.353374 + 0.204021i
\(298\) −1.28334e7 + 2.22281e7i −0.484945 + 0.839950i
\(299\) −1.16749e7 + 6.74051e6i −0.436757 + 0.252162i
\(300\) 204410.i 0.00757075i
\(301\) 4.26360e7 2.02993e7i 1.56342 0.744357i
\(302\) 1.45749e7 0.529158
\(303\) 8.47176e6 + 1.46735e7i 0.304541 + 0.527481i
\(304\) 1.03027e7 + 5.94829e6i 0.366718 + 0.211725i
\(305\) 1.99425e6 3.45414e6i 0.0702879 0.121742i
\(306\) −3.11675e6 + 1.79946e6i −0.108777 + 0.0628025i
\(307\) 4.52038e7i 1.56228i 0.624353 + 0.781142i \(0.285363\pi\)
−0.624353 + 0.781142i \(0.714637\pi\)
\(308\) −5.28592e6 3.63842e6i −0.180912 0.124526i
\(309\) −1.53485e7 −0.520223
\(310\) 3.32958e6 + 5.76700e6i 0.111765 + 0.193582i
\(311\) −2.86791e7 1.65579e7i −0.953420 0.550457i −0.0592781 0.998242i \(-0.518880\pi\)
−0.894142 + 0.447784i \(0.852213\pi\)
\(312\) −2.29786e6 + 3.98002e6i −0.0756590 + 0.131045i
\(313\) −3.14848e7 + 1.81778e7i −1.02676 + 0.592799i −0.916054 0.401054i \(-0.868644\pi\)
−0.110704 + 0.993853i \(0.535311\pi\)
\(314\) 8.00752e6i 0.258648i
\(315\) −2.15723e7 1.71314e6i −0.690185 0.0548102i
\(316\) −1.54043e7 −0.488180
\(317\) −1.06446e7 1.84369e7i −0.334157 0.578776i 0.649166 0.760647i \(-0.275118\pi\)
−0.983322 + 0.181871i \(0.941785\pi\)
\(318\) 1.46842e7 + 8.47791e6i 0.456634 + 0.263638i
\(319\) 1.17675e7 2.03819e7i 0.362503 0.627874i
\(320\) −3.49769e6 + 2.01939e6i −0.106741 + 0.0616269i
\(321\) 1.08862e7i 0.329126i
\(322\) 1.20183e6 1.51338e7i 0.0359978 0.453294i
\(323\) −1.44394e7 −0.428492
\(324\) −1.65985e6 2.87494e6i −0.0488016 0.0845268i
\(325\) 646864. + 373467.i 0.0188435 + 0.0108793i
\(326\) −9.76893e6 + 1.69203e7i −0.281964 + 0.488377i
\(327\) 942037. 543885.i 0.0269417 0.0155548i
\(328\) 1.20482e7i 0.341428i
\(329\) 2.75342e7 4.00019e7i 0.773189 1.12329i
\(330\) −6.00647e6 −0.167139
\(331\) 6.75682e6 + 1.17032e7i 0.186320 + 0.322715i 0.944020 0.329887i \(-0.107011\pi\)
−0.757701 + 0.652602i \(0.773677\pi\)
\(332\) 2.14597e7 + 1.23898e7i 0.586421 + 0.338570i
\(333\) −2.14229e7 + 3.71056e7i −0.580158 + 1.00486i
\(334\) −8.33511e6 + 4.81228e6i −0.223703 + 0.129155i
\(335\) 4.28616e6i 0.114008i
\(336\) −2.22476e6 4.67282e6i −0.0586497 0.123186i
\(337\) −2.15994e7 −0.564354 −0.282177 0.959362i \(-0.591057\pi\)
−0.282177 + 0.959362i \(0.591057\pi\)
\(338\) −5.25567e6 9.10308e6i −0.136106 0.235743i
\(339\) 1.05723e7 + 6.10393e6i 0.271376 + 0.156679i
\(340\) 2.45103e6 4.24530e6i 0.0623608 0.108012i
\(341\) 4.83581e6 2.79195e6i 0.121957 0.0704117i
\(342\) 3.36407e7i 0.840983i
\(343\) −9.50364e6 + 3.92185e7i −0.235509 + 0.971872i
\(344\) −2.49214e7 −0.612205
\(345\) −7.10499e6 1.23062e7i −0.173024 0.299686i
\(346\) −3.09489e7 1.78684e7i −0.747166 0.431376i
\(347\) 3.45994e6 5.99279e6i 0.0828094 0.143430i −0.821646 0.569998i \(-0.806944\pi\)
0.904456 + 0.426568i \(0.140277\pi\)
\(348\) 1.64381e7 9.49052e6i 0.390043 0.225192i
\(349\) 5.59971e7i 1.31731i 0.752443 + 0.658657i \(0.228875\pi\)
−0.752443 + 0.658657i \(0.771125\pi\)
\(350\) −759463. + 361586.i −0.0177134 + 0.00843349i
\(351\) 3.15035e7 0.728514
\(352\) 1.69332e6 + 2.93291e6i 0.0388249 + 0.0672468i
\(353\) 6.67147e7 + 3.85177e7i 1.51669 + 0.875662i 0.999808 + 0.0196071i \(0.00624152\pi\)
0.516884 + 0.856055i \(0.327092\pi\)
\(354\) 381483. 660748.i 0.00859935 0.0148945i
\(355\) 8.16338e6 4.71313e6i 0.182467 0.105347i
\(356\) 1.34083e7i 0.297184i
\(357\) 5.17433e6 + 3.56161e6i 0.113723 + 0.0782785i
\(358\) 2.20510e7 0.480595
\(359\) −2.22864e7 3.86012e7i −0.481678 0.834292i 0.518100 0.855320i \(-0.326639\pi\)
−0.999779 + 0.0210282i \(0.993306\pi\)
\(360\) 9.89063e6 + 5.71036e6i 0.211990 + 0.122393i
\(361\) 4.39632e7 7.61465e7i 0.934475 1.61856i
\(362\) −6.35136e6 + 3.66696e6i −0.133888 + 0.0773002i
\(363\) 2.10673e7i 0.440443i
\(364\) −1.88520e7 1.49711e6i −0.390890 0.0310420i
\(365\) 7.79983e7 1.60401
\(366\) −1.34867e6 2.33596e6i −0.0275082 0.0476455i
\(367\) −5.13587e7 2.96520e7i −1.03900 0.599867i −0.119451 0.992840i \(-0.538113\pi\)
−0.919550 + 0.392973i \(0.871447\pi\)
\(368\) −4.00602e6 + 6.93863e6i −0.0803841 + 0.139229i
\(369\) 2.95049e7 1.70347e7i 0.587240 0.339043i
\(370\) 5.83601e7i 1.15215i
\(371\) −5.52355e6 + 6.95541e7i −0.108167 + 1.36208i
\(372\) 4.50344e6 0.0874813
\(373\) 1.08638e7 + 1.88167e7i 0.209342 + 0.362590i 0.951507 0.307626i \(-0.0995346\pi\)
−0.742166 + 0.670216i \(0.766201\pi\)
\(374\) −3.55982e6 2.05526e6i −0.0680476 0.0392873i
\(375\) −1.45823e7 + 2.52572e7i −0.276523 + 0.478952i
\(376\) −2.21952e7 + 1.28144e7i −0.417538 + 0.241066i
\(377\) 6.93585e7i 1.29442i
\(378\) −2.01152e7 + 2.92234e7i −0.372433 + 0.541073i
\(379\) −5.10745e7 −0.938181 −0.469091 0.883150i \(-0.655418\pi\)
−0.469091 + 0.883150i \(0.655418\pi\)
\(380\) 2.29109e7 + 3.96829e7i 0.417534 + 0.723190i
\(381\) −1.13068e7 6.52800e6i −0.204440 0.118034i
\(382\) 2.85417e7 4.94357e7i 0.512024 0.886851i
\(383\) 2.63520e7 1.52143e7i 0.469048 0.270805i −0.246793 0.969068i \(-0.579377\pi\)
0.715841 + 0.698263i \(0.246043\pi\)
\(384\) 2.73133e6i 0.0482371i
\(385\) −1.06250e7 2.23163e7i −0.186185 0.391058i
\(386\) 576859. 0.0100302
\(387\) 3.52359e7 + 6.10304e7i 0.607928 + 1.05296i
\(388\) −3.49991e7 2.02067e7i −0.599185 0.345940i
\(389\) −5.41261e7 + 9.37492e7i −0.919513 + 1.59264i −0.119357 + 0.992851i \(0.538083\pi\)
−0.800156 + 0.599792i \(0.795250\pi\)
\(390\) −1.53298e7 + 8.85064e6i −0.258429 + 0.149204i
\(391\) 9.72459e6i 0.162683i
\(392\) 1.34259e7 1.65317e7i 0.222887 0.274447i
\(393\) −8.02826e6 −0.132265
\(394\) 3.84011e6 + 6.65126e6i 0.0627849 + 0.108747i
\(395\) −5.13833e7 2.96662e7i −0.833740 0.481360i
\(396\) 4.78831e6 8.29359e6i 0.0771075 0.133554i
\(397\) −3.15471e7 + 1.82137e7i −0.504183 + 0.291090i −0.730439 0.682978i \(-0.760685\pi\)
0.226257 + 0.974068i \(0.427351\pi\)
\(398\) 7.27497e7i 1.15394i
\(399\) −5.30153e7 + 2.52410e7i −0.834608 + 0.397363i
\(400\) 443918. 0.00693622
\(401\) −3.54840e6 6.14602e6i −0.0550300 0.0953148i 0.837198 0.546900i \(-0.184192\pi\)
−0.892228 + 0.451585i \(0.850859\pi\)
\(402\) 2.51029e6 + 1.44932e6i 0.0386408 + 0.0223093i
\(403\) 8.22799e6 1.42513e7i 0.125713 0.217741i
\(404\) 3.18665e7 1.83981e7i 0.483271 0.279016i
\(405\) 1.27864e7i 0.192479i
\(406\) 6.43386e7 + 4.42858e7i 0.961376 + 0.661738i
\(407\) −4.89367e7 −0.725857
\(408\) −1.65757e6 2.87100e6i −0.0244058 0.0422720i
\(409\) −8.67952e7 5.01113e7i −1.26860 0.732429i −0.293880 0.955842i \(-0.594947\pi\)
−0.974724 + 0.223414i \(0.928280\pi\)
\(410\) −2.32028e7 + 4.01885e7i −0.336658 + 0.583109i
\(411\) 3.84752e7 2.22137e7i 0.554185 0.319959i
\(412\) 3.33323e7i 0.476622i
\(413\) 3.12975e6 + 248545.i 0.0444282 + 0.00352821i
\(414\) 2.26562e7 0.319290
\(415\) 4.77214e7 + 8.26559e7i 0.667680 + 1.15646i
\(416\) 8.64341e6 + 4.99027e6i 0.120062 + 0.0693177i
\(417\) 4.54078e6 7.86486e6i 0.0626213 0.108463i
\(418\) 3.32753e7 1.92115e7i 0.455610 0.263046i
\(419\) 1.18946e8i 1.61699i −0.588506 0.808493i \(-0.700284\pi\)
0.588506 0.808493i \(-0.299716\pi\)
\(420\) 1.57806e6 1.98714e7i 0.0212999 0.268214i
\(421\) −4.26074e7 −0.571003 −0.285502 0.958378i \(-0.592160\pi\)
−0.285502 + 0.958378i \(0.592160\pi\)
\(422\) 7.36556e6 + 1.27575e7i 0.0980096 + 0.169758i
\(423\) 6.27629e7 + 3.62362e7i 0.829243 + 0.478764i
\(424\) 1.84115e7 3.18896e7i 0.241541 0.418362i
\(425\) −466618. + 269402.i −0.00607847 + 0.00350941i
\(426\) 6.37476e6i 0.0824585i
\(427\) 6.29330e6 9.14295e6i 0.0808342 0.117436i
\(428\) −2.36416e7 −0.301541
\(429\) 7.42153e6 + 1.28545e7i 0.0939986 + 0.162810i
\(430\) −8.31291e7 4.79946e7i −1.04556 0.603652i
\(431\) 1.59469e7 2.76209e7i 0.199180 0.344990i −0.749083 0.662476i \(-0.769506\pi\)
0.948263 + 0.317487i \(0.102839\pi\)
\(432\) 1.62148e7 9.36159e6i 0.201122 0.116118i
\(433\) 4.34467e7i 0.535172i −0.963534 0.267586i \(-0.913774\pi\)
0.963534 0.267586i \(-0.0862259\pi\)
\(434\) 7.96623e6 + 1.67320e7i 0.0974504 + 0.204682i
\(435\) 7.31089e7 0.888183
\(436\) −1.18116e6 2.04582e6i −0.0142511 0.0246836i
\(437\) 7.87220e7 + 4.54502e7i 0.943305 + 0.544617i
\(438\) 2.63742e7 4.56815e7i 0.313875 0.543648i
\(439\) 9.68525e7 5.59178e7i 1.14477 0.660932i 0.197161 0.980371i \(-0.436828\pi\)
0.947607 + 0.319440i \(0.103495\pi\)
\(440\) 1.30442e7i 0.153130i
\(441\) −5.94673e7 9.50499e6i −0.693366 0.110825i
\(442\) −1.21139e7 −0.140286
\(443\) −2.07530e7 3.59452e7i −0.238709 0.413457i 0.721635 0.692274i \(-0.243391\pi\)
−0.960344 + 0.278817i \(0.910058\pi\)
\(444\) −3.41799e7 1.97338e7i −0.390501 0.225456i
\(445\) −2.58223e7 + 4.47256e7i −0.293032 + 0.507546i
\(446\) −1.39382e7 + 8.04725e6i −0.157110 + 0.0907074i
\(447\) 6.68569e7i 0.748555i
\(448\) −1.01480e7 + 4.83152e6i −0.112861 + 0.0537340i
\(449\) 5.68298e7 0.627823 0.313912 0.949452i \(-0.398360\pi\)
0.313912 + 0.949452i \(0.398360\pi\)
\(450\) −627648. 1.08712e6i −0.00688776 0.0119300i
\(451\) 3.36992e7 + 1.94563e7i 0.367359 + 0.212095i
\(452\) 1.32559e7 2.29599e7i 0.143547 0.248631i
\(453\) 3.28785e7 1.89824e7i 0.353685 0.204200i
\(454\) 5.83571e7i 0.623629i
\(455\) −6.00007e7 4.12999e7i −0.636974 0.438444i
\(456\) 3.09883e7 0.326815
\(457\) 1.15306e7 + 1.99716e7i 0.120810 + 0.209250i 0.920087 0.391713i \(-0.128117\pi\)
−0.799277 + 0.600963i \(0.794784\pi\)
\(458\) 1.31945e7 + 7.61782e6i 0.137339 + 0.0792929i
\(459\) −1.13626e7 + 1.96806e7i −0.117500 + 0.203517i
\(460\) −2.67254e7 + 1.54299e7i −0.274568 + 0.158522i
\(461\) 9.79606e7i 0.999882i 0.866059 + 0.499941i \(0.166645\pi\)
−0.866059 + 0.499941i \(0.833355\pi\)
\(462\) −1.66628e7 1.32325e6i −0.168975 0.0134189i
\(463\) −6.08861e7 −0.613444 −0.306722 0.951799i \(-0.599232\pi\)
−0.306722 + 0.951799i \(0.599232\pi\)
\(464\) −2.06106e7 3.56986e7i −0.206318 0.357352i
\(465\) 1.50219e7 + 8.67290e6i 0.149405 + 0.0862592i
\(466\) 1.09851e7 1.90267e7i 0.108554 0.188021i
\(467\) −1.20792e7 + 6.97395e6i −0.118601 + 0.0684744i −0.558127 0.829756i \(-0.688480\pi\)
0.439526 + 0.898230i \(0.355146\pi\)
\(468\) 2.82226e7i 0.275334i
\(469\) −944264. + 1.18904e7i −0.00915324 + 0.115260i
\(470\) −9.87141e7 −0.950793
\(471\) −1.04290e7 1.80636e7i −0.0998114 0.172878i
\(472\) −1.43495e6 828467.i −0.0136461 0.00787861i
\(473\) −4.02449e7 + 6.97063e7i −0.380301 + 0.658701i
\(474\) −3.47494e7 + 2.00626e7i −0.326296 + 0.188387i
\(475\) 5.03645e6i 0.0469942i
\(476\) 7.73476e6 1.12371e7i 0.0717177 0.104192i
\(477\) −1.04127e8 −0.959416
\(478\) 2171.63 + 3761.37i 1.98839e−5 + 3.44400e-5i
\(479\) 1.36558e8 + 7.88418e7i 1.24254 + 0.717381i 0.969611 0.244653i \(-0.0786742\pi\)
0.272929 + 0.962034i \(0.412007\pi\)
\(480\) −5.26011e6 + 9.11078e6i −0.0475632 + 0.0823819i
\(481\) −1.24897e8 + 7.21091e7i −1.12232 + 0.647970i
\(482\) 4.09685e7i 0.365855i
\(483\) −1.69991e7 3.57044e7i −0.150864 0.316870i
\(484\) −4.57520e7 −0.403528
\(485\) −7.78298e7 1.34805e8i −0.682214 1.18163i
\(486\) −7.27886e7 4.20245e7i −0.634095 0.366095i
\(487\) 3.45352e7 5.98168e7i 0.299003 0.517888i −0.676905 0.736070i \(-0.736679\pi\)
0.975908 + 0.218182i \(0.0700126\pi\)
\(488\) −5.07301e6 + 2.92890e6i −0.0436522 + 0.0252026i
\(489\) 5.08923e7i 0.435237i
\(490\) 7.66215e7 2.92879e7i 0.651272 0.248943i
\(491\) 4.51500e7 0.381429 0.190714 0.981646i \(-0.438920\pi\)
0.190714 + 0.981646i \(0.438920\pi\)
\(492\) 1.56915e7 + 2.71785e7i 0.131756 + 0.228208i
\(493\) 4.33290e7 + 2.50160e7i 0.361608 + 0.208774i
\(494\) 5.66170e7 9.80635e7i 0.469641 0.813442i
\(495\) 3.19443e7 1.84430e7i 0.263377 0.152061i
\(496\) 9.78012e6i 0.0801492i
\(497\) 2.36847e7 1.12765e7i 0.192930 0.0918552i
\(498\) 6.45458e7 0.522612
\(499\) 2.55111e6 + 4.41865e6i 0.0205318 + 0.0355622i 0.876109 0.482114i \(-0.160131\pi\)
−0.855577 + 0.517676i \(0.826797\pi\)
\(500\) 5.48512e7 + 3.16684e7i 0.438810 + 0.253347i
\(501\) −1.25350e7 + 2.17113e7i −0.0996810 + 0.172653i
\(502\) −1.04024e8 + 6.00580e7i −0.822282 + 0.474745i
\(503\) 1.69533e8i 1.33214i −0.745889 0.666071i \(-0.767975\pi\)
0.745889 0.666071i \(-0.232025\pi\)
\(504\) 2.61800e7 + 1.80203e7i 0.204493 + 0.140757i
\(505\) 1.41727e8 1.10047
\(506\) 1.29385e7 + 2.24101e7i 0.0998690 + 0.172978i
\(507\) −2.37117e7 1.36900e7i −0.181945 0.105046i
\(508\) −1.41769e7 + 2.45551e7i −0.108141 + 0.187305i
\(509\) −5.33060e7 + 3.07762e7i −0.404225 + 0.233379i −0.688305 0.725421i \(-0.741645\pi\)
0.284081 + 0.958800i \(0.408312\pi\)
\(510\) 1.27689e7i 0.0962593i
\(511\) 2.16378e8 + 1.71834e7i 1.62163 + 0.128779i
\(512\) 5.93164e6 0.0441942
\(513\) −1.06212e8 1.83964e8i −0.786719 1.36264i
\(514\) 1.33465e8 + 7.70563e7i 0.982832 + 0.567439i
\(515\) −6.41927e7 + 1.11185e8i −0.469963 + 0.814000i
\(516\) −5.62183e7 + 3.24577e7i −0.409193 + 0.236248i
\(517\) 8.27748e7i 0.599000i
\(518\) 1.28570e7 1.61899e8i 0.0925019 1.16481i
\(519\) −9.30871e7 −0.665867
\(520\) 1.92209e7 + 3.32916e7i 0.136699 + 0.236769i
\(521\) −5.95417e7 3.43764e7i −0.421025 0.243079i 0.274491 0.961590i \(-0.411491\pi\)
−0.695516 + 0.718511i \(0.744824\pi\)
\(522\) −5.82818e7 + 1.00947e8i −0.409753 + 0.709712i
\(523\) −2.80297e7 + 1.61830e7i −0.195936 + 0.113124i −0.594758 0.803905i \(-0.702752\pi\)
0.398823 + 0.917028i \(0.369419\pi\)
\(524\) 1.74350e7i 0.121179i
\(525\) −1.24229e6 + 1.80480e6i −0.00858507 + 0.0124724i
\(526\) 1.13019e8 0.776592
\(527\) 5.93530e6 + 1.02802e7i 0.0405518 + 0.0702378i
\(528\) 7.63967e6 + 4.41076e6i 0.0519006 + 0.0299648i
\(529\) 4.34084e7 7.51856e7i 0.293229 0.507887i
\(530\) 1.22829e8 7.09151e7i 0.825034 0.476334i
\(531\) 4.68542e6i 0.0312943i
\(532\) 5.48158e7 + 1.15133e8i 0.364058 + 0.764656i
\(533\) 1.14677e8 0.757345
\(534\) 1.74630e7 + 3.02469e7i 0.114682 + 0.198635i
\(535\) −7.88602e7 4.55300e7i −0.514987 0.297328i
\(536\) 3.14749e6 5.45160e6i 0.0204395 0.0354022i
\(537\) 4.97432e7 2.87193e7i 0.321226 0.185460i
\(538\) 7.20201e7i 0.462495i
\(539\) −2.45588e7 6.42494e7i −0.156834 0.410301i
\(540\) 7.21157e7 0.457982
\(541\) −9.64842e6 1.67116e7i −0.0609347 0.105542i 0.833949 0.551842i \(-0.186075\pi\)
−0.894883 + 0.446300i \(0.852741\pi\)
\(542\) −6.05246e7 3.49439e7i −0.380132 0.219469i
\(543\) −9.55171e6 + 1.65440e7i −0.0596598 + 0.103334i
\(544\) −6.23496e6 + 3.59976e6i −0.0387291 + 0.0223602i
\(545\) 9.09887e6i 0.0562080i
\(546\) −4.44768e7 + 2.11757e7i −0.273247 + 0.130095i
\(547\) 1.69343e8 1.03468 0.517340 0.855780i \(-0.326922\pi\)
0.517340 + 0.855780i \(0.326922\pi\)
\(548\) −4.82414e7 8.35566e7i −0.293142 0.507737i
\(549\) 1.43453e7 + 8.28224e6i 0.0866945 + 0.0500531i
\(550\) 716872. 1.24166e6i 0.00430877 0.00746301i
\(551\) −4.05017e8 + 2.33837e8i −2.42113 + 1.39784i
\(552\) 2.08698e7i 0.124080i
\(553\) −1.36009e8 9.36182e7i −0.804252 0.553586i
\(554\) −1.25311e8 −0.736986
\(555\) −7.60082e7 1.31650e8i −0.444613 0.770091i
\(556\) −1.70801e7 9.86122e6i −0.0993727 0.0573728i
\(557\) 7.09397e7 1.22871e8i 0.410510 0.711025i −0.584435 0.811440i \(-0.698684\pi\)
0.994946 + 0.100416i \(0.0320173\pi\)
\(558\) −2.39507e7 + 1.38279e7i −0.137853 + 0.0795893i
\(559\) 2.37207e8i 1.35797i
\(560\) −4.31548e7 3.42708e6i −0.245734 0.0195146i
\(561\) −1.07071e7 −0.0606434
\(562\) −6.75248e7 1.16956e8i −0.380412 0.658893i
\(563\) −3.21231e7 1.85463e7i −0.180008 0.103928i 0.407288 0.913300i \(-0.366474\pi\)
−0.587297 + 0.809372i \(0.699808\pi\)
\(564\) −3.33791e7 + 5.78142e7i −0.186053 + 0.322253i
\(565\) 8.84342e7 5.10575e7i 0.490315 0.283083i
\(566\) 4.73198e7i 0.260972i
\(567\) 2.81691e6 3.54714e7i 0.0154534 0.194594i
\(568\) −1.38441e7 −0.0755473
\(569\) 1.78272e8 + 3.08775e8i 0.967710 + 1.67612i 0.702151 + 0.712028i \(0.252223\pi\)
0.265559 + 0.964094i \(0.414443\pi\)
\(570\) 1.03366e8 + 5.96784e7i 0.558153 + 0.322250i
\(571\) −1.18161e8 + 2.04662e8i −0.634699 + 1.09933i 0.351880 + 0.936045i \(0.385542\pi\)
−0.986579 + 0.163285i \(0.947791\pi\)
\(572\) 2.79161e7 1.61173e7i 0.149165 0.0861202i
\(573\) 1.48691e8i 0.790353i
\(574\) −7.32217e7 + 1.06377e8i −0.387172 + 0.562486i
\(575\) 3.39192e6 0.0178420
\(576\) −8.38664e6 1.45261e7i −0.0438855 0.0760118i
\(577\) 1.18513e8 + 6.84236e7i 0.616935 + 0.356188i 0.775675 0.631133i \(-0.217410\pi\)
−0.158740 + 0.987320i \(0.550743\pi\)
\(578\) −6.39022e7 + 1.10682e8i −0.330927 + 0.573182i
\(579\) 1.30129e6 751302.i 0.00670408 0.00387060i
\(580\) 1.58771e8i 0.813741i
\(581\) 1.14176e8 + 2.39812e8i 0.582168 + 1.22277i
\(582\) −1.05269e8 −0.533988
\(583\) −5.94645e7 1.02996e8i −0.300090 0.519772i
\(584\) −9.92065e7 5.72769e7i −0.498083 0.287568i
\(585\) 5.43523e7 9.41409e7i 0.271488 0.470231i
\(586\) 6.75782e7 3.90163e7i 0.335826 0.193889i
\(587\) 6.41884e7i 0.317353i 0.987331 + 0.158676i \(0.0507227\pi\)
−0.987331 + 0.158676i \(0.949277\pi\)
\(588\) 8.75555e6 5.47785e7i 0.0430677 0.269450i
\(589\) −1.10960e8 −0.543026
\(590\) −3.19099e6 5.52696e6i −0.0155371 0.0269110i
\(591\) 1.73252e7 + 1.00027e7i 0.0839299 + 0.0484569i
\(592\) −4.28559e7 + 7.42286e7i −0.206560 + 0.357772i
\(593\) 1.30545e8 7.53701e7i 0.626030 0.361439i −0.153183 0.988198i \(-0.548952\pi\)
0.779213 + 0.626759i \(0.215619\pi\)
\(594\) 6.04712e7i 0.288529i
\(595\) 4.74413e7 2.25872e7i 0.225220 0.107229i
\(596\) 1.45193e8 0.685816
\(597\) 9.47493e7 + 1.64111e8i 0.445300 + 0.771283i
\(598\) 6.60433e7 + 3.81301e7i 0.308834 + 0.178305i
\(599\) 1.31513e8 2.27788e8i 0.611912 1.05986i −0.379005 0.925395i \(-0.623734\pi\)
0.990918 0.134469i \(-0.0429329\pi\)
\(600\) 1.00140e6 578159.i 0.00463612 0.00267666i
\(601\) 1.39021e8i 0.640409i −0.947348 0.320204i \(-0.896248\pi\)
0.947348 0.320204i \(-0.103752\pi\)
\(602\) −2.20038e8 1.51458e8i −1.00858 0.694227i
\(603\) −1.78007e7 −0.0811867
\(604\) −4.12241e7 7.14022e7i −0.187085 0.324042i
\(605\) −1.52613e8 8.81109e7i −0.689167 0.397891i
\(606\) 4.79235e7 8.30060e7i 0.215343 0.372985i
\(607\) 2.70399e8 1.56115e8i 1.20903 0.698036i 0.246486 0.969146i \(-0.420724\pi\)
0.962548 + 0.271110i \(0.0873907\pi\)
\(608\) 6.72972e7i 0.299424i
\(609\) 2.02814e8 + 1.61063e7i 0.897940 + 0.0713087i
\(610\) −2.25624e7 −0.0994021
\(611\) 1.21970e8 + 2.11259e8i 0.534725 + 0.926170i
\(612\) 1.76310e7 + 1.01793e7i 0.0769170 + 0.0444081i
\(613\) 1.21906e8 2.11147e8i 0.529227 0.916649i −0.470192 0.882564i \(-0.655815\pi\)
0.999419 0.0340844i \(-0.0108515\pi\)
\(614\) 2.21453e8 1.27856e8i 0.956700 0.552351i
\(615\) 1.20878e8i 0.519661i
\(616\) −2.87371e6 + 3.61866e7i −0.0122942 + 0.154812i
\(617\) −3.32787e8 −1.41681 −0.708405 0.705807i \(-0.750585\pi\)
−0.708405 + 0.705807i \(0.750585\pi\)
\(618\) 4.34120e7 + 7.51919e7i 0.183927 + 0.318570i
\(619\) −2.10926e8 1.21778e8i −0.889320 0.513449i −0.0155997 0.999878i \(-0.504966\pi\)
−0.873720 + 0.486429i \(0.838299\pi\)
\(620\) 1.88349e7 3.26231e7i 0.0790295 0.136883i
\(621\) 1.23895e8 7.15308e7i 0.517343 0.298688i
\(622\) 1.87331e8i 0.778464i
\(623\) −8.14880e7 + 1.18386e8i −0.337000 + 0.489595i
\(624\) 2.59974e7 0.106998
\(625\) 1.18590e8 + 2.05403e8i 0.485743 + 0.841331i
\(626\) 1.78105e8 + 1.02829e8i 0.726028 + 0.419172i
\(627\) 5.00422e7 8.66756e7i 0.203018 0.351637i
\(628\) −3.92287e7 + 2.26487e7i −0.158389 + 0.0914459i
\(629\) 1.04032e8i 0.418039i
\(630\) 5.26232e7 + 1.10528e8i 0.210453 + 0.442029i
\(631\) −3.10369e8 −1.23535 −0.617676 0.786433i \(-0.711926\pi\)
−0.617676 + 0.786433i \(0.711926\pi\)
\(632\) 4.35699e7 + 7.54652e7i 0.172598 + 0.298948i
\(633\) 3.32308e7 + 1.91858e7i 0.131018 + 0.0756432i
\(634\) −6.02147e7 + 1.04295e8i −0.236284 + 0.409257i
\(635\) −9.45782e7 + 5.46048e7i −0.369377 + 0.213260i
\(636\) 9.59166e7i 0.372840i
\(637\) −1.57352e8 1.27790e8i −0.608771 0.494401i
\(638\) −1.33134e8 −0.512657
\(639\) 1.95739e7 + 3.39030e7i 0.0750196 + 0.129938i
\(640\) 1.97859e7 + 1.14234e7i 0.0754772 + 0.0435768i
\(641\) −2.39978e7 + 4.15653e7i −0.0911164 + 0.157818i −0.907981 0.419011i \(-0.862377\pi\)
0.816865 + 0.576829i \(0.195710\pi\)
\(642\) −5.33314e7 + 3.07909e7i −0.201548 + 0.116364i
\(643\) 1.09004e8i 0.410023i 0.978760 + 0.205011i \(0.0657232\pi\)
−0.978760 + 0.205011i \(0.934277\pi\)
\(644\) −7.75394e7 + 3.69171e7i −0.290312 + 0.138220i
\(645\) −2.50033e8 −0.931790
\(646\) 4.08409e7 + 7.07385e7i 0.151495 + 0.262397i
\(647\) −1.68753e8 9.74296e7i −0.623073 0.359731i 0.154992 0.987916i \(-0.450465\pi\)
−0.778064 + 0.628185i \(0.783798\pi\)
\(648\) −9.38953e6 + 1.62631e7i −0.0345079 + 0.0597695i
\(649\) −4.63452e6 + 2.67574e6i −0.0169539 + 0.00978837i
\(650\) 4.22530e6i 0.0153857i
\(651\) 3.97622e7 + 2.73693e7i 0.144121 + 0.0992019i
\(652\) 1.10523e8 0.398758
\(653\) −2.05641e7 3.56181e7i −0.0738535 0.127918i 0.826734 0.562594i \(-0.190196\pi\)
−0.900587 + 0.434676i \(0.856863\pi\)
\(654\) −5.32897e6 3.07668e6i −0.0190506 0.0109989i
\(655\) −3.35770e7 + 5.81570e7i −0.119486 + 0.206956i
\(656\) 5.90237e7 3.40773e7i 0.209081 0.120713i
\(657\) 3.23931e8i 1.14224i
\(658\) −2.73847e8 2.17472e7i −0.961237 0.0763354i
\(659\) 4.47299e8 1.56294 0.781468 0.623945i \(-0.214471\pi\)
0.781468 + 0.623945i \(0.214471\pi\)
\(660\) 1.69888e7 + 2.94255e7i 0.0590925 + 0.102351i
\(661\) −4.20493e8 2.42772e8i −1.45598 0.840608i −0.457166 0.889381i \(-0.651135\pi\)
−0.998810 + 0.0487734i \(0.984469\pi\)
\(662\) 3.82224e7 6.62031e7i 0.131748 0.228194i
\(663\) −2.73268e7 + 1.57771e7i −0.0937665 + 0.0541361i
\(664\) 1.40174e8i 0.478810i
\(665\) −3.88819e7 + 4.89611e8i −0.132215 + 1.66489i
\(666\) 2.42373e8 0.820467
\(667\) −1.57483e8 2.72768e8i −0.530708 0.919214i
\(668\) 4.71505e7 + 2.72224e7i 0.158182 + 0.0913264i
\(669\) −2.09615e7 + 3.63064e7i −0.0700074 + 0.121256i
\(670\) 2.09978e7 1.21231e7i 0.0698152 0.0403078i
\(671\) 1.89192e7i 0.0626233i
\(672\) −1.65995e7 + 2.41158e7i −0.0546998 + 0.0794682i
\(673\) −2.07406e7 −0.0680418 −0.0340209 0.999421i \(-0.510831\pi\)
−0.0340209 + 0.999421i \(0.510831\pi\)
\(674\) 6.10923e7 + 1.05815e8i 0.199529 + 0.345595i
\(675\) −6.86457e6 3.96326e6i −0.0223204 0.0128867i
\(676\) −2.97305e7 + 5.14948e7i −0.0962416 + 0.166695i
\(677\) 4.25988e8 2.45944e8i 1.37288 0.792630i 0.381586 0.924333i \(-0.375378\pi\)
0.991289 + 0.131703i \(0.0420446\pi\)
\(678\) 6.90581e7i 0.221577i
\(679\) −1.86213e8 3.91115e8i −0.594840 1.24938i
\(680\) −2.77302e7 −0.0881914
\(681\) 7.60044e7 + 1.31643e8i 0.240656 + 0.416829i
\(682\) −2.73554e7 1.57937e7i −0.0862364 0.0497886i
\(683\) −3.67239e7 + 6.36076e7i −0.115262 + 0.199640i −0.917884 0.396848i \(-0.870104\pi\)
0.802622 + 0.596487i \(0.203437\pi\)
\(684\) −1.64805e8 + 9.51504e7i −0.514995 + 0.297332i
\(685\) 3.71621e8i 1.15619i
\(686\) 2.19011e8 6.43687e7i 0.678413 0.199389i
\(687\) 3.96859e7 0.122396
\(688\) 7.04883e7 + 1.22089e8i 0.216447 + 0.374897i
\(689\) −3.03532e8 1.75244e8i −0.927996 0.535779i
\(690\) −4.01919e7 + 6.96144e7i −0.122346 + 0.211910i
\(691\) −2.33029e8 + 1.34539e8i −0.706278 + 0.407770i −0.809681 0.586870i \(-0.800360\pi\)
0.103404 + 0.994639i \(0.467027\pi\)
\(692\) 2.02157e8i 0.610058i
\(693\) 9.26810e7 4.41261e7i 0.278478 0.132585i
\(694\) −3.91447e7 −0.117110
\(695\) −3.79823e7 6.57872e7i −0.113143 0.195969i
\(696\) −9.29877e7 5.36865e7i −0.275802 0.159235i
\(697\) −4.13613e7 + 7.16398e7i −0.122151 + 0.211571i
\(698\) 2.74329e8 1.58384e8i 0.806687 0.465741i
\(699\) 5.72279e7i 0.167562i
\(700\) 3.91949e6 + 2.69787e6i 0.0114271 + 0.00786552i
\(701\) 5.35900e8 1.55571 0.777857 0.628441i \(-0.216307\pi\)
0.777857 + 0.628441i \(0.216307\pi\)
\(702\) −8.91054e7 1.54335e8i −0.257569 0.446122i
\(703\) 8.42158e8 + 4.86220e8i 2.42397 + 1.39948i
\(704\) 9.57886e6 1.65911e7i 0.0274534 0.0475507i
\(705\) −2.22682e8 + 1.28565e8i −0.635503 + 0.366908i
\(706\) 4.35779e8i 1.23837i
\(707\) 3.93172e8 + 3.12233e7i 1.11256 + 0.0883528i
\(708\) −4.31599e6 −0.0121613
\(709\) 8.56791e7 + 1.48400e8i 0.240401 + 0.416386i 0.960829 0.277144i \(-0.0893878\pi\)
−0.720428 + 0.693530i \(0.756054\pi\)
\(710\) −4.61790e7 2.66615e7i −0.129024 0.0744919i
\(711\) 1.23205e8 2.13398e8i 0.342784 0.593719i
\(712\) 6.56872e7 3.79245e7i 0.181987 0.105070i
\(713\) 7.47288e7i 0.206167i
\(714\) 2.81305e6 3.54227e7i 0.00772828 0.0973167i
\(715\) 1.24158e8 0.339669
\(716\) −6.23697e7 1.08027e8i −0.169916 0.294303i
\(717\) 9797.63 + 5656.67i 2.65805e−5 + 1.53463e-5i
\(718\) −1.26071e8 + 2.18362e8i −0.340598 + 0.589933i
\(719\) 1.34498e8 7.76524e7i 0.361850 0.208914i −0.308042 0.951373i \(-0.599674\pi\)
0.669892 + 0.742458i \(0.266340\pi\)
\(720\) 6.46053e7i 0.173090i
\(721\) −2.02574e8 + 2.94301e8i −0.540479 + 0.785210i
\(722\) −4.97387e8 −1.32155
\(723\) 5.33574e7 + 9.24178e7i 0.141182 + 0.244535i
\(724\) 3.59287e7 + 2.07435e7i 0.0946730 + 0.0546595i
\(725\) −8.72555e6 + 1.51131e7i −0.0228970 + 0.0396588i
\(726\) −1.03208e8 + 5.95874e7i −0.269715 + 0.155720i
\(727\) 2.49335e8i 0.648902i 0.945902 + 0.324451i \(0.105180\pi\)
−0.945902 + 0.324451i \(0.894820\pi\)
\(728\) 4.59873e7 + 9.65902e7i 0.119191 + 0.250345i
\(729\) −1.43304e8 −0.369894
\(730\) −2.20612e8 3.82112e8i −0.567102 0.982250i
\(731\) −1.48186e8 8.55550e7i −0.379362 0.219025i
\(732\) −7.62921e6 + 1.32142e7i −0.0194512 + 0.0336905i
\(733\) −2.32809e8 + 1.34412e8i −0.591136 + 0.341293i −0.765547 0.643380i \(-0.777531\pi\)
0.174410 + 0.984673i \(0.444198\pi\)
\(734\) 3.35474e8i 0.848340i
\(735\) 1.34700e8 1.65860e8i 0.339239 0.417715i
\(736\) 4.53230e7 0.113680
\(737\) −1.01656e7 1.76073e7i −0.0253939 0.0439836i
\(738\) −1.66905e8 9.63627e7i −0.415241 0.239740i
\(739\) −8.13582e7 + 1.40917e8i −0.201590 + 0.349163i −0.949041 0.315153i \(-0.897944\pi\)
0.747451 + 0.664317i \(0.231277\pi\)
\(740\) −2.85905e8 + 1.65067e8i −0.705547 + 0.407348i
\(741\) 2.94952e8i 0.724932i
\(742\) 3.56367e8 1.69669e8i 0.872340 0.415328i
\(743\) 1.49147e8 0.363621 0.181810 0.983334i \(-0.441804\pi\)
0.181810 + 0.983334i \(0.441804\pi\)
\(744\) −1.27376e7 2.20623e7i −0.0309293 0.0535712i
\(745\) 4.84314e8 + 2.79619e8i 1.17127 + 0.676235i
\(746\) 6.14550e7 1.06443e8i 0.148027 0.256390i
\(747\) −3.43275e8 + 1.98190e8i −0.823531 + 0.475466i
\(748\) 2.32526e7i 0.0555606i
\(749\) −2.08739e8 1.43680e8i −0.496773 0.341941i
\(750\) 1.64980e8 0.391063
\(751\) −3.48848e8 6.04223e8i −0.823601 1.42652i −0.902984 0.429675i \(-0.858628\pi\)
0.0793828 0.996844i \(-0.474705\pi\)
\(752\) 1.25555e8 + 7.24893e7i 0.295244 + 0.170459i
\(753\) −1.56439e8 + 2.70961e8i −0.366405 + 0.634632i
\(754\) −3.39786e8 + 1.96175e8i −0.792668 + 0.457647i
\(755\) 3.17564e8i 0.737888i
\(756\) 2.00059e8 + 1.58875e7i 0.463013 + 0.0367696i
\(757\) −2.80318e8 −0.646195 −0.323098 0.946366i \(-0.604724\pi\)
−0.323098 + 0.946366i \(0.604724\pi\)
\(758\) 1.44461e8 + 2.50213e8i 0.331697 + 0.574516i
\(759\) 5.83738e7 + 3.37021e7i 0.133503 + 0.0770783i
\(760\) 1.29604e8 2.24480e8i 0.295241 0.511372i
\(761\) −4.19441e8 + 2.42165e8i −0.951737 + 0.549486i −0.893620 0.448824i \(-0.851843\pi\)
−0.0581172 + 0.998310i \(0.518510\pi\)
\(762\) 7.38559e7i 0.166925i
\(763\) 2.00453e6 2.52416e7i 0.00451272 0.0568254i
\(764\) −3.22913e8 −0.724111
\(765\) 3.92072e7 + 6.79089e7i 0.0875754 + 0.151685i
\(766\) −1.49069e8 8.60653e7i −0.331667 0.191488i
\(767\) −7.88551e6 + 1.36581e7i −0.0174761 + 0.0302694i
\(768\) 1.33808e7 7.72538e6i 0.0295391 0.0170544i
\(769\) 5.15227e8i 1.13297i 0.824071 + 0.566486i \(0.191698\pi\)
−0.824071 + 0.566486i \(0.808302\pi\)
\(770\) −7.92753e7 + 1.15172e8i −0.173646 + 0.252274i
\(771\) 4.01433e8 0.875891
\(772\) −1.63160e6 2.82602e6i −0.00354620 0.00614219i
\(773\) −2.90012e8 1.67439e8i −0.627882 0.362508i 0.152050 0.988373i \(-0.451413\pi\)
−0.779931 + 0.625865i \(0.784746\pi\)
\(774\) 1.99324e8 3.45240e8i 0.429870 0.744557i
\(775\) −3.58573e6 + 2.07022e6i −0.00770322 + 0.00444746i
\(776\) 2.28613e8i 0.489233i
\(777\) −1.81855e8 3.81961e8i −0.387669 0.814247i
\(778\) 6.12367e8 1.30039
\(779\) −3.86623e8 6.69651e8i −0.817854 1.41656i
\(780\) 8.67182e7 + 5.00668e7i 0.182737 + 0.105503i
\(781\) −2.23565e7 + 3.87225e7i −0.0469299 + 0.0812850i
\(782\) −4.76406e7 + 2.75053e7i −0.0996224 + 0.0575170i
\(783\) 7.36037e8i 1.53326i
\(784\) −1.18963e8 1.90144e7i −0.246866 0.0394580i
\(785\) −1.74471e8 −0.360674
\(786\) 2.27073e7 + 3.93303e7i 0.0467626 + 0.0809952i
\(787\) 8.27918e8 + 4.77998e8i 1.69849 + 0.980624i 0.947196 + 0.320656i \(0.103903\pi\)
0.751294 + 0.659968i \(0.229430\pi\)
\(788\) 2.17229e7 3.76252e7i 0.0443956 0.0768954i
\(789\) 2.54951e8 1.47196e8i 0.519069 0.299685i
\(790\) 3.35634e8i 0.680746i
\(791\) 2.56577e8 1.22158e8i 0.518428 0.246828i
\(792\) −5.41735e7 −0.109046
\(793\) 2.78778e7 + 4.82858e7i 0.0559036 + 0.0968278i
\(794\) 1.78457e8 + 1.03032e8i 0.356511 + 0.205832i
\(795\) 1.84720e8 3.19944e8i 0.367631 0.636756i
\(796\) 3.56399e8 2.05767e8i 0.706639 0.407978i
\(797\) 1.22214e7i 0.0241404i 0.999927 + 0.0120702i \(0.00384216\pi\)
−0.999927 + 0.0120702i \(0.996158\pi\)
\(798\) 2.73605e8 + 1.88329e8i 0.538412 + 0.370602i
\(799\) −1.75967e8 −0.344978
\(800\) −1.25559e6 2.17474e6i −0.00245232 0.00424755i
\(801\) −1.85748e8 1.07242e8i −0.361432 0.208673i
\(802\) −2.00728e7 + 3.47671e7i −0.0389121 + 0.0673978i
\(803\) −3.20412e8 + 1.84990e8i −0.618818 + 0.357274i
\(804\) 1.63972e7i 0.0315501i
\(805\) −3.29741e8 2.61859e7i −0.632099 0.0501973i
\(806\) −9.30891e7 −0.177784
\(807\) −9.37991e7 1.62465e8i −0.178475 0.309128i
\(808\) −1.80264e8 1.04076e8i −0.341724 0.197294i
\(809\) 1.04438e7 1.80893e7i 0.0197249 0.0341645i −0.855994 0.516985i \(-0.827054\pi\)
0.875719 + 0.482820i \(0.160388\pi\)
\(810\) −6.26404e7 + 3.61655e7i −0.117869 + 0.0680517i
\(811\) 9.93784e8i 1.86307i −0.363650 0.931536i \(-0.618470\pi\)
0.363650 0.931536i \(-0.381530\pi\)
\(812\) 3.49780e7 4.40452e8i 0.0653321 0.822680i
\(813\) −1.82044e8 −0.338770
\(814\) 1.38414e8 + 2.39740e8i 0.256629 + 0.444495i
\(815\) 3.68666e8 + 2.12849e8i 0.681020 + 0.393187i
\(816\) −9.37665e6 + 1.62408e7i −0.0172575 + 0.0298908i
\(817\) 1.38516e9 7.99723e8i 2.54000 1.46647i
\(818\) 5.66944e8i 1.03581i
\(819\) 1.71521e8 2.49186e8i 0.312223 0.453599i
\(820\) 2.62510e8 0.476107
\(821\) −2.09416e8 3.62720e8i −0.378426 0.655453i 0.612407 0.790542i \(-0.290201\pi\)
−0.990833 + 0.135089i \(0.956868\pi\)
\(822\) −2.17648e8 1.25659e8i −0.391868 0.226245i
\(823\) −4.60456e8 + 7.97534e8i −0.826017 + 1.43070i 0.0751227 + 0.997174i \(0.476065\pi\)
−0.901140 + 0.433529i \(0.857268\pi\)
\(824\) 1.63294e8 9.42780e7i 0.291870 0.168511i
\(825\) 3.73462e6i 0.00665097i
\(826\) −7.63465e6 1.60356e7i −0.0135472 0.0284540i
\(827\) −5.88771e8 −1.04095 −0.520475 0.853877i \(-0.674245\pi\)
−0.520475 + 0.853877i \(0.674245\pi\)
\(828\) −6.40813e7 1.10992e8i −0.112886 0.195525i
\(829\) 7.07004e8 + 4.08189e8i 1.24096 + 0.716469i 0.969290 0.245921i \(-0.0790905\pi\)
0.271671 + 0.962390i \(0.412424\pi\)
\(830\) 2.69953e8 4.67572e8i 0.472121 0.817738i
\(831\) −2.82679e8 + 1.63205e8i −0.492596 + 0.284400i
\(832\) 5.64585e7i 0.0980301i
\(833\) 1.36585e8 5.22085e7i 0.236303 0.0903246i
\(834\) −5.13731e7 −0.0885600
\(835\) 1.04852e8 + 1.81609e8i 0.180101 + 0.311944i
\(836\) −1.88233e8 1.08677e8i −0.322165 0.186002i
\(837\) −8.73160e7 + 1.51236e8i −0.148908 + 0.257916i
\(838\) −5.82712e8 + 3.36429e8i −0.990197 + 0.571691i
\(839\) 2.04755e8i 0.346697i −0.984861 0.173348i \(-0.944541\pi\)
0.984861 0.173348i \(-0.0554586\pi\)
\(840\) −1.01813e8 + 4.84740e7i −0.171777 + 0.0817845i
\(841\) 1.02564e9 1.72428
\(842\) 1.20512e8 + 2.08733e8i 0.201880 + 0.349667i
\(843\) −3.04648e8 1.75889e8i −0.508529 0.293600i
\(844\) 4.16659e7 7.21675e7i 0.0693032 0.120037i
\(845\) −1.98342e8 + 1.14513e8i −0.328733 + 0.189794i
\(846\) 4.09966e8i 0.677074i
\(847\) −4.03958e8 2.78054e8i −0.664792 0.457592i
\(848\) −2.08302e8 −0.341591
\(849\) 6.16294e7 + 1.06745e8i 0.100708 + 0.174432i
\(850\) 2.63959e6 + 1.52397e6i 0.00429813 + 0.00248153i
\(851\) −3.27457e8 + 5.67172e8i −0.531331 + 0.920293i
\(852\) −3.12298e7 + 1.80306e7i −0.0504953 + 0.0291535i
\(853\) 1.61333e8i 0.259942i 0.991518 + 0.129971i \(0.0414884\pi\)
−0.991518 + 0.129971i \(0.958512\pi\)
\(854\) −6.25913e7 4.97061e6i −0.100494 0.00798060i
\(855\) −7.32977e8 −1.17271
\(856\) 6.68686e7 + 1.15820e8i 0.106611 + 0.184655i
\(857\) −7.34234e8 4.23910e8i −1.16652 0.673490i −0.213661 0.976908i \(-0.568539\pi\)
−0.952858 + 0.303418i \(0.901872\pi\)
\(858\) 4.19825e7 7.27158e7i 0.0664671 0.115124i
\(859\) −3.89328e8 + 2.24778e8i −0.614237 + 0.354630i −0.774622 0.632425i \(-0.782060\pi\)
0.160385 + 0.987055i \(0.448726\pi\)
\(860\) 5.42997e8i 0.853693i
\(861\) −2.66299e7 + 3.35332e8i −0.0417216 + 0.525370i
\(862\) −1.80419e8 −0.281683
\(863\) 5.39411e8 + 9.34288e8i 0.839243 + 1.45361i 0.890528 + 0.454928i \(0.150335\pi\)
−0.0512854 + 0.998684i \(0.516332\pi\)
\(864\) −9.17245e7 5.29572e7i −0.142215 0.0821076i
\(865\) −3.89323e8 + 6.74327e8i −0.601536 + 1.04189i
\(866\) −2.12845e8 + 1.22886e8i −0.327724 + 0.189212i
\(867\) 3.32905e8i 0.510814i
\(868\) 5.94379e7 8.63517e7i 0.0908875 0.132042i
\(869\) 2.81440e8 0.428870
\(870\) −2.06783e8 3.58159e8i −0.314020 0.543899i
\(871\) −5.18894e7 2.99584e7i −0.0785280 0.0453381i
\(872\) −6.68163e6 + 1.15729e7i −0.0100770 + 0.0174539i
\(873\) 5.59854e8 3.23232e8i 0.841457 0.485815i
\(874\) 5.14210e8i 0.770205i
\(875\) 2.91836e8 + 6.12963e8i 0.435627 + 0.914977i
\(876\) −2.98390e8 −0.443887
\(877\) 3.05654e8 + 5.29409e8i 0.453139 + 0.784860i 0.998579 0.0532899i \(-0.0169707\pi\)
−0.545440 + 0.838150i \(0.683637\pi\)
\(878\) −5.47880e8 3.16319e8i −0.809473 0.467349i
\(879\) 1.01630e8 1.76028e8i 0.149642 0.259188i
\(880\) 6.39035e7 3.68947e7i 0.0937727 0.0541397i
\(881\) 9.76241e8i 1.42768i −0.700311 0.713838i \(-0.746955\pi\)
0.700311 0.713838i \(-0.253045\pi\)
\(882\) 1.21634e8 + 3.18213e8i 0.177276 + 0.463781i
\(883\) −2.98921e8 −0.434185 −0.217092 0.976151i \(-0.569657\pi\)
−0.217092 + 0.976151i \(0.569657\pi\)
\(884\) 3.42632e7 + 5.93455e7i 0.0495987 + 0.0859076i
\(885\) −1.43966e7 8.31190e6i −0.0207697 0.0119914i
\(886\) −1.17397e8 + 2.03337e8i −0.168793 + 0.292358i
\(887\) 4.19997e8 2.42485e8i 0.601832 0.347468i −0.167930 0.985799i \(-0.553708\pi\)
0.769762 + 0.638331i \(0.220375\pi\)
\(888\) 2.23262e8i 0.318843i
\(889\) −2.74403e8 + 1.30645e8i −0.390556 + 0.185947i
\(890\) 2.92146e8 0.414410
\(891\) 3.03258e7 + 5.25259e7i 0.0428726 + 0.0742575i
\(892\) 7.88466e7 + 4.55221e7i 0.111093 + 0.0641399i
\(893\) 8.22425e8 1.42448e9i 1.15489 2.00034i
\(894\) 3.27531e8 1.89100e8i 0.458395 0.264654i
\(895\) 4.80456e8i 0.670169i
\(896\) 5.23723e7 + 3.60491e7i 0.0728077 + 0.0501152i
\(897\) 1.98643e8 0.275230
\(898\) −1.60739e8 2.78408e8i −0.221969 0.384462i
\(899\) 3.32962e8 + 1.92236e8i 0.458264 + 0.264579i
\(900\) −3.55051e6 + 6.14966e6i −0.00487038 + 0.00843575i
\(901\) 2.18954e8 1.26413e8i 0.299349 0.172829i
\(902\) 2.20123e8i 0.299947i
\(903\) −6.93627e8 5.50835e7i −0.942026 0.0748098i
\(904\) −1.49973e8 −0.203006
\(905\) 7.98971e7 + 1.38386e8i 0.107792 + 0.186701i
\(906\) −1.85989e8 1.07381e8i −0.250093 0.144391i
\(907\) 3.22657e8 5.58858e8i 0.432433 0.748996i −0.564649 0.825331i \(-0.690989\pi\)
0.997082 + 0.0763351i \(0.0243219\pi\)
\(908\) 2.85890e8 1.65059e8i 0.381893 0.220486i
\(909\) 5.88602e8i 0.783665i
\(910\) −3.26196e7 + 4.10756e8i −0.0432868 + 0.545079i
\(911\) 9.00820e8 1.19147 0.595735 0.803181i \(-0.296861\pi\)
0.595735 + 0.803181i \(0.296861\pi\)
\(912\) −8.76480e7 1.51811e8i −0.115547 0.200133i
\(913\) −3.92073e8 2.26364e8i −0.515175 0.297437i
\(914\) 6.52270e7 1.12977e8i 0.0854258 0.147962i
\(915\) −5.08968e7 + 2.93853e7i −0.0664396 + 0.0383589i
\(916\) 8.61858e7i 0.112137i
\(917\) −1.05960e8 + 1.53939e8i −0.137414 + 0.199636i
\(918\) 1.28553e8 0.166171
\(919\) −1.12912e8 1.95569e8i −0.145476 0.251972i 0.784074 0.620667i \(-0.213138\pi\)
−0.929551 + 0.368695i \(0.879805\pi\)
\(920\) 1.51182e8 + 8.72848e7i 0.194149 + 0.112092i
\(921\) 3.33039e8 5.76841e8i 0.426301 0.738375i
\(922\) 4.79907e8 2.77074e8i 0.612300 0.353512i
\(923\) 1.31771e8i 0.167577i
\(924\) 4.06469e7 + 8.53734e7i 0.0515242 + 0.108220i
\(925\) 3.62863e7 0.0458478
\(926\) 1.72212e8 + 2.98280e8i 0.216885 + 0.375656i
\(927\) −4.61758e8 2.66596e8i −0.579662 0.334668i
\(928\) −1.16591e8 + 2.01942e8i −0.145889 + 0.252686i
\(929\) −3.59609e8 + 2.07621e8i −0.448522 + 0.258954i −0.707206 0.707008i \(-0.750045\pi\)
0.258684 + 0.965962i \(0.416711\pi\)
\(930\) 9.81227e7i 0.121989i
\(931\) −2.15728e8 + 1.34969e9i −0.267336 + 1.67257i
\(932\) −1.24282e8 −0.153518
\(933\) 2.43980e8 + 4.22586e8i 0.300407 + 0.520320i
\(934\) 6.83305e7 + 3.94506e7i 0.0838637 + 0.0484187i
\(935\) −4.47808e7 + 7.75627e7i −0.0547844 + 0.0948894i
\(936\) −1.38262e8 + 7.98257e7i −0.168607 + 0.0973453i
\(937\) 7.39751e8i 0.899221i −0.893225 0.449611i \(-0.851563\pi\)
0.893225 0.449611i \(-0.148437\pi\)
\(938\) 6.09218e7 2.90053e7i 0.0738183 0.0351454i
\(939\) 5.35699e8 0.647029
\(940\) 2.79206e8 + 4.83599e8i 0.336156 + 0.582239i
\(941\) −3.00928e8 1.73741e8i −0.361155 0.208513i 0.308432 0.951246i \(-0.400196\pi\)
−0.669587 + 0.742733i \(0.733529\pi\)
\(942\) −5.89954e7 + 1.02183e8i −0.0705773 + 0.122244i
\(943\) 4.50993e8 2.60381e8i 0.537817 0.310509i
\(944\) 9.37304e6i 0.0111420i
\(945\) 6.36731e8 + 4.38277e8i 0.754503 + 0.519342i
\(946\) 4.55319e8 0.537827
\(947\) −1.54081e8 2.66875e8i −0.181425 0.314238i 0.760941 0.648821i \(-0.224738\pi\)
−0.942366 + 0.334583i \(0.891404\pi\)
\(948\) 1.96572e8 + 1.13491e8i 0.230726 + 0.133210i
\(949\) −5.45173e8 + 9.44267e8i −0.637875 + 1.10483i
\(950\) −2.46735e7 + 1.42452e7i −0.0287779 + 0.0166150i
\(951\) 3.13695e8i 0.364726i
\(952\) −7.69276e7 6.10910e6i −0.0891602 0.00708055i
\(953\) −7.95730e8 −0.919363 −0.459681 0.888084i \(-0.652036\pi\)
−0.459681 + 0.888084i \(0.652036\pi\)
\(954\) 2.94515e8 + 5.10114e8i 0.339205 + 0.587520i
\(955\) −1.07712e9 6.21878e8i −1.23668 0.713995i
\(956\) 12284.6 21277.5i 1.40601e−5 2.43527e-5i
\(957\) −3.00327e8 + 1.73394e8i −0.342656 + 0.197833i
\(958\) 8.91993e8i 1.01453i
\(959\) 8.18700e7 1.03093e9i 0.0928258 1.16889i
\(960\) 5.95114e7 0.0672646
\(961\) −3.98142e8 6.89602e8i −0.448609 0.777013i
\(962\) 7.06522e8 + 4.07911e8i 0.793598 + 0.458184i
\(963\) 1.89089e8 3.27511e8i 0.211732 0.366731i
\(964\) 2.00704e8 1.15876e8i 0.224039 0.129349i
\(965\) 1.25688e7i 0.0139866i
\(966\) −1.26834e8 + 1.84266e8i −0.140704 + 0.204415i
\(967\) −1.75844e9 −1.94468 −0.972341 0.233564i \(-0.924961\pi\)
−0.972341 + 0.233564i \(0.924961\pi\)
\(968\) 1.29406e8 + 2.24138e8i 0.142669 + 0.247109i
\(969\) 1.84260e8 + 1.06383e8i 0.202516 + 0.116923i
\(970\) −4.40272e8 + 7.62573e8i −0.482398 + 0.835538i
\(971\) −7.22413e8 + 4.17085e8i −0.789092 + 0.455583i −0.839643 0.543139i \(-0.817236\pi\)
0.0505508 + 0.998721i \(0.483902\pi\)
\(972\) 4.75453e8i 0.517737i
\(973\) −9.08750e7 1.90871e8i −0.0986520 0.207205i
\(974\) −3.90721e8 −0.422854
\(975\) −5.50303e6 9.53153e6i −0.00593729 0.0102837i
\(976\) 2.86973e7 + 1.65684e7i 0.0308667 + 0.0178209i
\(977\) −2.04042e8 + 3.53411e8i −0.218794 + 0.378963i −0.954440 0.298404i \(-0.903546\pi\)
0.735645 + 0.677367i \(0.236879\pi\)
\(978\) 2.49320e8 1.43945e8i 0.266527 0.153879i
\(979\) 2.44973e8i 0.261078i
\(980\) −3.60199e8 2.92528e8i −0.382705 0.310806i
\(981\) 3.77881e7 0.0400266
\(982\) −1.27704e8 2.21189e8i −0.134855 0.233576i
\(983\) 3.90839e7 + 2.25651e7i 0.0411469 + 0.0237562i 0.520432 0.853903i \(-0.325771\pi\)
−0.479285 + 0.877659i \(0.659104\pi\)
\(984\) 8.87647e7 1.53745e8i 0.0931655 0.161367i
\(985\) 1.44920e8 8.36698e7i 0.151642 0.0875508i
\(986\) 2.83024e8i 0.295252i
\(987\) −6.46075e8 + 3.07601e8i −0.671942 + 0.319916i
\(988\) −6.40548e8 −0.664173
\(989\) 5.38593e8 + 9.32870e8i 0.556765 + 0.964345i
\(990\) −1.80704e8 1.04330e8i −0.186235 0.107523i
\(991\) 1.33166e8 2.30650e8i 0.136827 0.236991i −0.789467 0.613793i \(-0.789643\pi\)
0.926294 + 0.376802i \(0.122976\pi\)
\(992\) −4.79126e7 + 2.76624e7i −0.0490812 + 0.0283370i
\(993\) 1.99123e8i 0.203364i
\(994\) −1.22234e8 8.41362e7i −0.124460 0.0856690i
\(995\) 1.58510e9 1.60911
\(996\) −1.82563e8 3.16208e8i −0.184771 0.320033i
\(997\) 2.78483e8 + 1.60782e8i 0.281005 + 0.162238i 0.633878 0.773433i \(-0.281462\pi\)
−0.352873 + 0.935671i \(0.614795\pi\)
\(998\) 1.44313e7 2.49957e7i 0.0145182 0.0251463i
\(999\) 1.32541e9 7.65227e8i 1.32940 0.767527i
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 14.7.d.a.3.1 8
3.2 odd 2 126.7.n.c.73.4 8
4.3 odd 2 112.7.s.c.17.3 8
7.2 even 3 98.7.d.c.19.2 8
7.3 odd 6 98.7.b.c.97.6 8
7.4 even 3 98.7.b.c.97.7 8
7.5 odd 6 inner 14.7.d.a.5.1 yes 8
7.6 odd 2 98.7.d.c.31.2 8
21.5 even 6 126.7.n.c.19.4 8
28.19 even 6 112.7.s.c.33.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.7.d.a.3.1 8 1.1 even 1 trivial
14.7.d.a.5.1 yes 8 7.5 odd 6 inner
98.7.b.c.97.6 8 7.3 odd 6
98.7.b.c.97.7 8 7.4 even 3
98.7.d.c.19.2 8 7.2 even 3
98.7.d.c.31.2 8 7.6 odd 2
112.7.s.c.17.3 8 4.3 odd 2
112.7.s.c.33.3 8 28.19 even 6
126.7.n.c.19.4 8 21.5 even 6
126.7.n.c.73.4 8 3.2 odd 2