Properties

Label 76.7.g.a.7.14
Level $76$
Weight $7$
Character 76.7
Analytic conductor $17.484$
Analytic rank $0$
Dimension $116$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,7,Mod(7,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.7");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 76.g (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: \(17.4841103551\)
Analytic rank: \(0\)
Dimension: \(116\)
Relative dimension: \(58\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 7.14
Character \(\chi\) \(=\) 76.7
Dual form 76.7.g.a.11.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.97766 + 5.31672i) q^{2} +(-4.45729 + 2.57342i) q^{3} +(7.46487 - 63.5632i) q^{4} +(64.1001 + 111.025i) q^{5} +(12.9620 - 39.0812i) q^{6} -508.357i q^{7} +(293.325 + 419.648i) q^{8} +(-351.255 + 608.392i) q^{9} +O(q^{10})\) \(q+(-5.97766 + 5.31672i) q^{2} +(-4.45729 + 2.57342i) q^{3} +(7.46487 - 63.5632i) q^{4} +(64.1001 + 111.025i) q^{5} +(12.9620 - 39.0812i) q^{6} -508.357i q^{7} +(293.325 + 419.648i) q^{8} +(-351.255 + 608.392i) q^{9} +(-973.457 - 322.865i) q^{10} -207.224i q^{11} +(130.301 + 302.530i) q^{12} +(-827.736 + 1433.68i) q^{13} +(2702.79 + 3038.79i) q^{14} +(-571.426 - 329.913i) q^{15} +(-3984.55 - 948.982i) q^{16} +(-1472.03 - 2549.63i) q^{17} +(-1134.97 - 5504.29i) q^{18} +(-6586.99 + 1912.45i) q^{19} +(7535.58 - 3245.62i) q^{20} +(1308.21 + 2265.89i) q^{21} +(1101.75 + 1238.72i) q^{22} +(-3173.03 - 1831.95i) q^{23} +(-2387.37 - 1115.64i) q^{24} +(-405.156 + 701.751i) q^{25} +(-2674.56 - 12970.9i) q^{26} -7367.75i q^{27} +(-32312.8 - 3794.82i) q^{28} +(18351.1 - 31785.1i) q^{29} +(5169.85 - 1066.01i) q^{30} -34971.1i q^{31} +(28863.8 - 15512.1i) q^{32} +(533.274 + 923.658i) q^{33} +(22355.0 + 7414.44i) q^{34} +(56440.2 - 32585.8i) q^{35} +(36049.2 + 26868.4i) q^{36} +11397.6 q^{37} +(29206.8 - 46453.2i) q^{38} -8520.44i q^{39} +(-27789.1 + 59465.8i) q^{40} +(-56264.0 - 97452.2i) q^{41} +(-19867.2 - 6589.33i) q^{42} +(-69432.1 + 40086.6i) q^{43} +(-13171.8 - 1546.90i) q^{44} -90062.0 q^{45} +(28707.3 - 5919.36i) q^{46} +(-74886.2 - 43235.6i) q^{47} +(20202.4 - 6024.03i) q^{48} -140778. q^{49} +(-1309.13 - 6348.93i) q^{50} +(13122.5 + 7576.29i) q^{51} +(84950.3 + 63315.8i) q^{52} +(-29201.4 + 50578.3i) q^{53} +(39172.3 + 44041.9i) q^{54} +(23007.0 - 13283.1i) q^{55} +(213331. - 149114. i) q^{56} +(24438.6 - 25475.4i) q^{57} +(59295.7 + 287568. i) q^{58} +(-48714.4 + 28125.3i) q^{59} +(-25235.9 + 33858.9i) q^{60} +(-17846.4 + 30910.9i) q^{61} +(185931. + 209045. i) q^{62} +(309280. + 178563. i) q^{63} +(-90064.5 + 246187. i) q^{64} -212232. q^{65} +(-8098.57 - 2686.04i) q^{66} +(-61241.0 - 35357.5i) q^{67} +(-173051. + 74534.1i) q^{68} +18857.5 q^{69} +(-164131. + 494863. i) q^{70} +(358000. - 206692. i) q^{71} +(-358342. + 31053.3i) q^{72} +(-305921. - 529870. i) q^{73} +(-68131.0 + 60597.9i) q^{74} -4170.54i q^{75} +(72390.3 + 432966. i) q^{76} -105344. q^{77} +(45300.8 + 50932.3i) q^{78} +(-304769. + 175959. i) q^{79} +(-150050. - 503213. i) q^{80} +(-237105. - 410677. i) q^{81} +(854454. + 283396. i) q^{82} +675982. i q^{83} +(153793. - 66239.7i) q^{84} +(188714. - 326863. i) q^{85} +(201912. - 608776. i) q^{86} +188901. i q^{87} +(86961.1 - 60784.1i) q^{88} +(-569694. + 986739. i) q^{89} +(538360. - 478835. i) q^{90} +(728821. + 420785. i) q^{91} +(-140131. + 188013. i) q^{92} +(89995.1 + 155876. i) q^{93} +(677516. - 139702. i) q^{94} +(-634556. - 608730. i) q^{95} +(-88735.2 + 143420. i) q^{96} +(-325526. - 563827. i) q^{97} +(841522. - 748477. i) q^{98} +(126073. + 72788.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9} - 812 q^{10} - 1462 q^{12} + 2518 q^{13} - 2742 q^{14} + 461 q^{16} + 6838 q^{17} - 13948 q^{18} - 24396 q^{20} + 11176 q^{21} + 22293 q^{22} + 33905 q^{24} - 156252 q^{25} - 78080 q^{26} - 34362 q^{28} - 2 q^{29} + 208344 q^{30} - 10941 q^{32} + 110316 q^{33} + 64648 q^{34} + 78574 q^{36} + 55432 q^{37} + 221994 q^{38} + 242590 q^{40} - 9126 q^{41} + 187550 q^{42} + 138081 q^{44} + 59576 q^{45} - 686052 q^{46} - 141617 q^{48} - 1306636 q^{49} + 167498 q^{50} - 35414 q^{52} + 60758 q^{53} - 348601 q^{54} + 543732 q^{56} - 466566 q^{57} + 1208536 q^{58} - 319142 q^{60} - 839474 q^{61} + 628548 q^{62} - 470026 q^{64} + 151836 q^{65} + 1471119 q^{66} + 341484 q^{68} - 2169836 q^{69} - 68364 q^{70} + 1236042 q^{72} + 207538 q^{73} + 336144 q^{74} - 97437 q^{76} + 1977632 q^{77} - 2740948 q^{78} + 1250050 q^{80} - 3334682 q^{81} - 2244893 q^{82} - 2404612 q^{84} + 788426 q^{85} + 910490 q^{86} + 5123058 q^{88} + 360166 q^{89} + 2446616 q^{90} + 2518692 q^{92} + 2079592 q^{93} - 2221200 q^{94} - 5927450 q^{96} + 3567778 q^{97} + 5270703 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.97766 + 5.31672i −0.747208 + 0.664591i
\(3\) −4.45729 + 2.57342i −0.165085 + 0.0953118i −0.580266 0.814427i \(-0.697051\pi\)
0.415181 + 0.909739i \(0.363718\pi\)
\(4\) 7.46487 63.5632i 0.116639 0.993174i
\(5\) 64.1001 + 111.025i 0.512801 + 0.888198i 0.999890 + 0.0148451i \(0.00472551\pi\)
−0.487089 + 0.873353i \(0.661941\pi\)
\(6\) 12.9620 39.0812i 0.0600094 0.180932i
\(7\) 508.357i 1.48209i −0.671455 0.741045i \(-0.734330\pi\)
0.671455 0.741045i \(-0.265670\pi\)
\(8\) 293.325 + 419.648i 0.572901 + 0.819625i
\(9\) −351.255 + 608.392i −0.481831 + 0.834556i
\(10\) −973.457 322.865i −0.973457 0.322865i
\(11\) 207.224i 0.155691i −0.996965 0.0778453i \(-0.975196\pi\)
0.996965 0.0778453i \(-0.0248040\pi\)
\(12\) 130.301 + 302.530i 0.0754059 + 0.175075i
\(13\) −827.736 + 1433.68i −0.376757 + 0.652563i −0.990588 0.136875i \(-0.956294\pi\)
0.613831 + 0.789437i \(0.289628\pi\)
\(14\) 2702.79 + 3038.79i 0.984983 + 1.10743i
\(15\) −571.426 329.913i −0.169311 0.0977520i
\(16\) −3984.55 948.982i −0.972791 0.231685i
\(17\) −1472.03 2549.63i −0.299619 0.518955i 0.676430 0.736507i \(-0.263526\pi\)
−0.976049 + 0.217552i \(0.930193\pi\)
\(18\) −1134.97 5504.29i −0.194610 0.943807i
\(19\) −6586.99 + 1912.45i −0.960342 + 0.278823i
\(20\) 7535.58 3245.62i 0.941948 0.405703i
\(21\) 1308.21 + 2265.89i 0.141261 + 0.244671i
\(22\) 1101.75 + 1238.72i 0.103470 + 0.116333i
\(23\) −3173.03 1831.95i −0.260790 0.150567i 0.363905 0.931436i \(-0.381443\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(24\) −2387.37 1115.64i −0.172697 0.0807034i
\(25\) −405.156 + 701.751i −0.0259300 + 0.0449121i
\(26\) −2674.56 12970.9i −0.152171 0.737989i
\(27\) 7367.75i 0.374320i
\(28\) −32312.8 3794.82i −1.47197 0.172869i
\(29\) 18351.1 31785.1i 0.752435 1.30326i −0.194205 0.980961i \(-0.562213\pi\)
0.946639 0.322294i \(-0.104454\pi\)
\(30\) 5169.85 1066.01i 0.191476 0.0394817i
\(31\) 34971.1i 1.17388i −0.809631 0.586940i \(-0.800332\pi\)
0.809631 0.586940i \(-0.199668\pi\)
\(32\) 28863.8 15512.1i 0.880853 0.473391i
\(33\) 533.274 + 923.658i 0.0148391 + 0.0257021i
\(34\) 22355.0 + 7414.44i 0.568771 + 0.188643i
\(35\) 56440.2 32585.8i 1.31639 0.760018i
\(36\) 36049.2 + 26868.4i 0.772660 + 0.575884i
\(37\) 11397.6 0.225013 0.112507 0.993651i \(-0.464112\pi\)
0.112507 + 0.993651i \(0.464112\pi\)
\(38\) 29206.8 46453.2i 0.532272 0.846574i
\(39\) 8520.44i 0.143638i
\(40\) −27789.1 + 59465.8i −0.434204 + 0.929154i
\(41\) −56264.0 97452.2i −0.816355 1.41397i −0.908351 0.418210i \(-0.862658\pi\)
0.0919951 0.995759i \(-0.470676\pi\)
\(42\) −19867.2 6589.33i −0.268157 0.0889393i
\(43\) −69432.1 + 40086.6i −0.873283 + 0.504190i −0.868438 0.495798i \(-0.834876\pi\)
−0.00484489 + 0.999988i \(0.501542\pi\)
\(44\) −13171.8 1546.90i −0.154628 0.0181595i
\(45\) −90062.0 −0.988335
\(46\) 28707.3 5919.36i 0.294930 0.0608137i
\(47\) −74886.2 43235.6i −0.721288 0.416436i 0.0939388 0.995578i \(-0.470054\pi\)
−0.815226 + 0.579142i \(0.803388\pi\)
\(48\) 20202.4 6024.03i 0.182675 0.0544707i
\(49\) −140778. −1.19659
\(50\) −1309.13 6348.93i −0.0104730 0.0507915i
\(51\) 13122.5 + 7576.29i 0.0989251 + 0.0571144i
\(52\) 84950.3 + 63315.8i 0.604164 + 0.450300i
\(53\) −29201.4 + 50578.3i −0.196145 + 0.339732i −0.947275 0.320421i \(-0.896176\pi\)
0.751131 + 0.660154i \(0.229509\pi\)
\(54\) 39172.3 + 44041.9i 0.248770 + 0.279695i
\(55\) 23007.0 13283.1i 0.138284 0.0798383i
\(56\) 213331. 149114.i 1.21476 0.849091i
\(57\) 24438.6 25475.4i 0.131963 0.137561i
\(58\) 59295.7 + 287568.i 0.303906 + 1.47386i
\(59\) −48714.4 + 28125.3i −0.237193 + 0.136943i −0.613886 0.789395i \(-0.710394\pi\)
0.376693 + 0.926338i \(0.377061\pi\)
\(60\) −25235.9 + 33858.9i −0.116833 + 0.156754i
\(61\) −17846.4 + 30910.9i −0.0786251 + 0.136183i −0.902657 0.430361i \(-0.858386\pi\)
0.824032 + 0.566543i \(0.191720\pi\)
\(62\) 185931. + 209045.i 0.780149 + 0.877132i
\(63\) 309280. + 178563.i 1.23689 + 0.714117i
\(64\) −90064.5 + 246187.i −0.343569 + 0.939128i
\(65\) −212232. −0.772806
\(66\) −8098.57 2686.04i −0.0281693 0.00934289i
\(67\) −61241.0 35357.5i −0.203619 0.117559i 0.394723 0.918800i \(-0.370840\pi\)
−0.598342 + 0.801241i \(0.704174\pi\)
\(68\) −173051. + 74534.1i −0.550360 + 0.237044i
\(69\) 18857.5 0.0574034
\(70\) −164131. + 494863.i −0.478515 + 1.44275i
\(71\) 358000. 206692.i 1.00025 0.577495i 0.0919277 0.995766i \(-0.470697\pi\)
0.908322 + 0.418271i \(0.137364\pi\)
\(72\) −358342. + 31053.3i −0.960065 + 0.0831974i
\(73\) −305921. 529870.i −0.786394 1.36208i −0.928163 0.372175i \(-0.878612\pi\)
0.141768 0.989900i \(-0.454721\pi\)
\(74\) −68131.0 + 60597.9i −0.168132 + 0.149542i
\(75\) 4170.54i 0.00988573i
\(76\) 72390.3 + 432966.i 0.164907 + 0.986309i
\(77\) −105344. −0.230747
\(78\) 45300.8 + 50932.3i 0.0954602 + 0.107327i
\(79\) −304769. + 175959.i −0.618144 + 0.356886i −0.776146 0.630553i \(-0.782828\pi\)
0.158002 + 0.987439i \(0.449495\pi\)
\(80\) −150050. 503213.i −0.293066 0.982839i
\(81\) −237105. 410677.i −0.446154 0.772762i
\(82\) 854454. + 283396.i 1.54970 + 0.513986i
\(83\) 675982.i 1.18223i 0.806589 + 0.591113i \(0.201311\pi\)
−0.806589 + 0.591113i \(0.798689\pi\)
\(84\) 153793. 66239.7i 0.259477 0.111758i
\(85\) 188714. 326863.i 0.307290 0.532242i
\(86\) 201912. 608776.i 0.317444 0.957110i
\(87\) 188901.i 0.286864i
\(88\) 86961.1 60784.1i 0.127608 0.0891953i
\(89\) −569694. + 986739.i −0.808112 + 1.39969i 0.106058 + 0.994360i \(0.466177\pi\)
−0.914170 + 0.405331i \(0.867156\pi\)
\(90\) 538360. 478835.i 0.738491 0.656838i
\(91\) 728821. + 420785.i 0.967157 + 0.558388i
\(92\) −140131. + 188013.i −0.179958 + 0.241448i
\(93\) 89995.1 + 155876.i 0.111885 + 0.193790i
\(94\) 677516. 139702.i 0.815711 0.168197i
\(95\) −634556. 608730.i −0.740115 0.709993i
\(96\) −88735.2 + 143420.i −0.100296 + 0.162105i
\(97\) −325526. 563827.i −0.356673 0.617775i 0.630730 0.776002i \(-0.282756\pi\)
−0.987403 + 0.158227i \(0.949422\pi\)
\(98\) 841522. 748477.i 0.894102 0.795243i
\(99\) 126073. + 72788.5i 0.129933 + 0.0750166i
\(100\) 41581.1 + 30991.5i 0.0415811 + 0.0309915i
\(101\) 238645. 413346.i 0.231627 0.401190i −0.726660 0.686997i \(-0.758928\pi\)
0.958287 + 0.285808i \(0.0922618\pi\)
\(102\) −118723. + 24480.3i −0.111875 + 0.0230684i
\(103\) 1.75153e6i 1.60290i −0.598065 0.801448i \(-0.704063\pi\)
0.598065 0.801448i \(-0.295937\pi\)
\(104\) −844437. + 73177.3i −0.750701 + 0.0650544i
\(105\) −167714. + 290488.i −0.144877 + 0.250935i
\(106\) −94354.9 457596.i −0.0792222 0.384206i
\(107\) 693676.i 0.566246i −0.959084 0.283123i \(-0.908630\pi\)
0.959084 0.283123i \(-0.0913705\pi\)
\(108\) −468317. 54999.3i −0.371765 0.0436602i
\(109\) 768422. + 1.33095e6i 0.593363 + 1.02773i 0.993776 + 0.111400i \(0.0355334\pi\)
−0.400413 + 0.916335i \(0.631133\pi\)
\(110\) −66905.5 + 201724.i −0.0502671 + 0.151558i
\(111\) −50802.4 + 29330.8i −0.0371463 + 0.0214464i
\(112\) −482422. + 2.02557e6i −0.343378 + 1.44176i
\(113\) 1.51427e6 1.04947 0.524734 0.851266i \(-0.324165\pi\)
0.524734 + 0.851266i \(0.324165\pi\)
\(114\) −10639.8 + 282217.i −0.00718158 + 0.190488i
\(115\) 469714.i 0.308844i
\(116\) −1.88337e6 1.40373e6i −1.20660 0.899309i
\(117\) −581493. 1.00717e6i −0.363067 0.628850i
\(118\) 141664. 427125.i 0.0862210 0.259961i
\(119\) −1.29612e6 + 748316.i −0.769139 + 0.444062i
\(120\) −29166.5 336569.i −0.0168788 0.194774i
\(121\) 1.72862e6 0.975760
\(122\) −57664.9 279659.i −0.0317564 0.154010i
\(123\) 501570. + 289582.i 0.269536 + 0.155617i
\(124\) −2.22287e6 261055.i −1.16587 0.136920i
\(125\) 1.89925e6 0.972415
\(126\) −2.79814e6 + 576968.i −1.39881 + 0.288430i
\(127\) −2.44932e6 1.41411e6i −1.19573 0.690357i −0.236132 0.971721i \(-0.575880\pi\)
−0.959601 + 0.281364i \(0.909213\pi\)
\(128\) −770532. 1.95047e6i −0.367418 0.930056i
\(129\) 206319. 357356.i 0.0961105 0.166468i
\(130\) 1.26865e6 1.12838e6i 0.577447 0.513600i
\(131\) −1.70880e6 + 986577.i −0.760112 + 0.438851i −0.829336 0.558750i \(-0.811281\pi\)
0.0692240 + 0.997601i \(0.477948\pi\)
\(132\) 62691.5 27001.6i 0.0272575 0.0117400i
\(133\) 972207. + 3.34854e6i 0.413241 + 1.42331i
\(134\) 554064. 114246.i 0.230274 0.0474819i
\(135\) 818002. 472274.i 0.332470 0.191952i
\(136\) 638162. 1.36560e6i 0.253696 0.542885i
\(137\) −1.94374e6 + 3.36666e6i −0.755923 + 1.30930i 0.188992 + 0.981979i \(0.439478\pi\)
−0.944914 + 0.327318i \(0.893855\pi\)
\(138\) −112724. + 100260.i −0.0428922 + 0.0381497i
\(139\) 1.03636e6 + 598340.i 0.385891 + 0.222794i 0.680378 0.732861i \(-0.261816\pi\)
−0.294487 + 0.955655i \(0.595149\pi\)
\(140\) −1.64993e6 3.83076e6i −0.601288 1.39605i
\(141\) 445053. 0.158765
\(142\) −1.04108e6 + 3.13892e6i −0.363597 + 1.09627i
\(143\) 297093. + 171527.i 0.101598 + 0.0586575i
\(144\) 1.97695e6 2.09083e6i 0.662075 0.700216i
\(145\) 4.70524e6 1.54340
\(146\) 4.64587e6 + 1.54089e6i 1.49282 + 0.495123i
\(147\) 627487. 362280.i 0.197539 0.114049i
\(148\) 85081.7 724468.i 0.0262453 0.223478i
\(149\) −2.31815e6 4.01516e6i −0.700782 1.21379i −0.968192 0.250208i \(-0.919501\pi\)
0.267410 0.963583i \(-0.413832\pi\)
\(150\) 22173.6 + 24930.1i 0.00656997 + 0.00738670i
\(151\) 4.85458e6i 1.41001i 0.709204 + 0.705003i \(0.249054\pi\)
−0.709204 + 0.705003i \(0.750946\pi\)
\(152\) −2.73469e6 2.20324e6i −0.778712 0.627382i
\(153\) 2.06823e6 0.577463
\(154\) 629710. 560084.i 0.172416 0.153353i
\(155\) 3.88265e6 2.24165e6i 1.04264 0.601967i
\(156\) −541586. 63604.0i −0.142657 0.0167537i
\(157\) −408757. 707987.i −0.105625 0.182948i 0.808369 0.588677i \(-0.200351\pi\)
−0.913993 + 0.405729i \(0.867018\pi\)
\(158\) 886284. 2.67219e6i 0.224699 0.677480i
\(159\) 300590.i 0.0747795i
\(160\) 3.57239e6 + 2.21027e6i 0.872167 + 0.539616i
\(161\) −931286. + 1.61303e6i −0.223154 + 0.386515i
\(162\) 3.60079e6 + 1.19427e6i 0.846940 + 0.280904i
\(163\) 5.88436e6i 1.35874i 0.733796 + 0.679370i \(0.237747\pi\)
−0.733796 + 0.679370i \(0.762253\pi\)
\(164\) −6.61437e6 + 2.84885e6i −1.49954 + 0.645860i
\(165\) −68365.9 + 118413.i −0.0152191 + 0.0263602i
\(166\) −3.59401e6 4.04079e6i −0.785696 0.883368i
\(167\) −1.04863e6 605429.i −0.225151 0.129991i 0.383182 0.923673i \(-0.374828\pi\)
−0.608333 + 0.793682i \(0.708162\pi\)
\(168\) −567145. + 1.21363e6i −0.119610 + 0.255953i
\(169\) 1.04311e6 + 1.80672e6i 0.216108 + 0.374310i
\(170\) 609770. + 2.95722e6i 0.124113 + 0.601917i
\(171\) 1.15019e6 4.67923e6i 0.230029 0.935806i
\(172\) 2.02973e6 + 4.71256e6i 0.398890 + 0.926130i
\(173\) −1.73353e6 3.00257e6i −0.334806 0.579902i 0.648641 0.761094i \(-0.275338\pi\)
−0.983448 + 0.181193i \(0.942004\pi\)
\(174\) −1.00433e6 1.12918e6i −0.190647 0.214347i
\(175\) 356740. + 205964.i 0.0665637 + 0.0384306i
\(176\) −196652. + 825695.i −0.0360712 + 0.151454i
\(177\) 144756. 250725.i 0.0261046 0.0452145i
\(178\) −1.84078e6 8.92730e6i −0.326394 1.58292i
\(179\) 2.14219e6i 0.373507i 0.982407 + 0.186753i \(0.0597965\pi\)
−0.982407 + 0.186753i \(0.940204\pi\)
\(180\) −672301. + 5.72462e6i −0.115278 + 0.981589i
\(181\) −4.43673e6 + 7.68465e6i −0.748217 + 1.29595i 0.200459 + 0.979702i \(0.435757\pi\)
−0.948677 + 0.316248i \(0.897577\pi\)
\(182\) −6.59385e6 + 1.35963e6i −1.09377 + 0.225531i
\(183\) 183705.i 0.0299756i
\(184\) −161957. 1.86892e6i −0.0259983 0.300010i
\(185\) 730588. + 1.26542e6i 0.115387 + 0.199856i
\(186\) −1.36671e6 453295.i −0.212392 0.0704438i
\(187\) −528344. + 305040.i −0.0807964 + 0.0466478i
\(188\) −3.30721e6 + 4.43726e6i −0.497723 + 0.667792i
\(189\) −3.74545e6 −0.554777
\(190\) 7.02961e6 + 265023.i 1.02487 + 0.0386387i
\(191\) 9.08149e6i 1.30334i 0.758503 + 0.651669i \(0.225931\pi\)
−0.758503 + 0.651669i \(0.774069\pi\)
\(192\) −232098. 1.32910e6i −0.0327919 0.187782i
\(193\) −145690. 252343.i −0.0202655 0.0351009i 0.855715 0.517448i \(-0.173118\pi\)
−0.875980 + 0.482347i \(0.839784\pi\)
\(194\) 4.94359e6 + 1.63964e6i 0.677076 + 0.224565i
\(195\) 945979. 546161.i 0.127579 0.0736575i
\(196\) −1.05089e6 + 8.94828e6i −0.139569 + 1.18842i
\(197\) 5.22291e6 0.683147 0.341573 0.939855i \(-0.389040\pi\)
0.341573 + 0.939855i \(0.389040\pi\)
\(198\) −1.14062e6 + 235192.i −0.146942 + 0.0302990i
\(199\) 1.13617e7 + 6.55970e6i 1.44174 + 0.832387i 0.997966 0.0637541i \(-0.0203073\pi\)
0.443770 + 0.896141i \(0.353641\pi\)
\(200\) −413331. + 35818.5i −0.0516663 + 0.00447731i
\(201\) 363959. 0.0448192
\(202\) 771105. + 3.73965e6i 0.0935534 + 0.453709i
\(203\) −1.61582e7 9.32893e6i −1.93154 1.11518i
\(204\) 579531. 777553.i 0.0682631 0.0915882i
\(205\) 7.21306e6 1.24934e7i 0.837256 1.45017i
\(206\) 9.31239e6 + 1.04700e7i 1.06527 + 1.19770i
\(207\) 2.22909e6 1.28697e6i 0.251314 0.145096i
\(208\) 4.65869e6 4.92707e6i 0.517695 0.547518i
\(209\) 396306. + 1.36498e6i 0.0434102 + 0.149516i
\(210\) −541912. 2.62813e6i −0.0585155 0.283784i
\(211\) −3.98023e6 + 2.29799e6i −0.423702 + 0.244624i −0.696660 0.717401i \(-0.745331\pi\)
0.272958 + 0.962026i \(0.411998\pi\)
\(212\) 2.99693e6 + 2.23369e6i 0.314535 + 0.234432i
\(213\) −1.06381e6 + 1.84257e6i −0.110084 + 0.190671i
\(214\) 3.68808e6 + 4.14656e6i 0.376322 + 0.423103i
\(215\) −8.90121e6 5.13912e6i −0.895641 0.517098i
\(216\) 3.09186e6 2.16115e6i 0.306802 0.214449i
\(217\) −1.77778e7 −1.73980
\(218\) −1.16696e7 3.87046e6i −1.12639 0.373588i
\(219\) 2.72716e6 + 1.57452e6i 0.259644 + 0.149905i
\(220\) −672571. 1.56155e6i −0.0631641 0.146652i
\(221\) 4.87380e6 0.451535
\(222\) 147736. 445432.i 0.0135029 0.0407120i
\(223\) 5.78619e6 3.34066e6i 0.521768 0.301243i −0.215889 0.976418i \(-0.569265\pi\)
0.737658 + 0.675175i \(0.235932\pi\)
\(224\) −7.88567e6 1.46731e7i −0.701608 1.30550i
\(225\) −284626. 492987.i −0.0249878 0.0432801i
\(226\) −9.05182e6 + 8.05098e6i −0.784171 + 0.697467i
\(227\) 2.12022e7i 1.81261i −0.422626 0.906304i \(-0.638892\pi\)
0.422626 0.906304i \(-0.361108\pi\)
\(228\) −1.43687e6 1.74356e6i −0.121231 0.147107i
\(229\) −1.06404e7 −0.886033 −0.443016 0.896513i \(-0.646092\pi\)
−0.443016 + 0.896513i \(0.646092\pi\)
\(230\) 2.49734e6 + 2.80779e6i 0.205255 + 0.230771i
\(231\) 469548. 271094.i 0.0380929 0.0219929i
\(232\) 1.87214e7 1.62236e6i 1.49925 0.129922i
\(233\) −9.68338e6 1.67721e7i −0.765525 1.32593i −0.939969 0.341260i \(-0.889146\pi\)
0.174444 0.984667i \(-0.444187\pi\)
\(234\) 8.83084e6 + 2.92891e6i 0.689214 + 0.228591i
\(235\) 1.10856e7i 0.854195i
\(236\) 1.42408e6 + 3.30639e6i 0.108343 + 0.251547i
\(237\) 905630. 1.56860e6i 0.0680308 0.117833i
\(238\) 3.76918e6 1.13643e7i 0.279587 0.842969i
\(239\) 1.05286e7i 0.771216i 0.922663 + 0.385608i \(0.126008\pi\)
−0.922663 + 0.385608i \(0.873992\pi\)
\(240\) 1.96379e6 + 1.85683e6i 0.142057 + 0.134319i
\(241\) −4.41990e6 + 7.65550e6i −0.315763 + 0.546918i −0.979599 0.200960i \(-0.935594\pi\)
0.663836 + 0.747878i \(0.268927\pi\)
\(242\) −1.03331e7 + 9.19059e6i −0.729096 + 0.648481i
\(243\) 6.76519e6 + 3.90588e6i 0.471478 + 0.272208i
\(244\) 1.83157e6 + 1.36512e6i 0.126082 + 0.0939726i
\(245\) −9.02387e6 1.56298e7i −0.613613 1.06281i
\(246\) −4.53784e6 + 935690.i −0.304821 + 0.0628531i
\(247\) 2.71044e6 1.10266e7i 0.179866 0.731732i
\(248\) 1.46755e7 1.02579e7i 0.962141 0.672517i
\(249\) −1.73958e6 3.01305e6i −0.112680 0.195168i
\(250\) −1.13531e7 + 1.00978e7i −0.726596 + 0.646258i
\(251\) 1.91100e6 + 1.10332e6i 0.120848 + 0.0697717i 0.559206 0.829029i \(-0.311106\pi\)
−0.438357 + 0.898801i \(0.644440\pi\)
\(252\) 1.36588e7 1.83259e7i 0.853512 1.14515i
\(253\) −379625. + 657529.i −0.0234419 + 0.0406026i
\(254\) 2.21597e7 4.56925e6i 1.35227 0.278833i
\(255\) 1.94256e6i 0.117153i
\(256\) 1.49761e7 + 7.56254e6i 0.892644 + 0.450762i
\(257\) 1.34137e7 2.32332e7i 0.790223 1.36871i −0.135605 0.990763i \(-0.543298\pi\)
0.925829 0.377944i \(-0.123369\pi\)
\(258\) 666654. + 3.23309e6i 0.0388187 + 0.188260i
\(259\) 5.79405e6i 0.333490i
\(260\) −1.58428e6 + 1.34901e7i −0.0901391 + 0.767531i
\(261\) 1.28919e7 + 2.23294e7i 0.725093 + 1.25590i
\(262\) 4.96928e6 1.49826e7i 0.276305 0.833076i
\(263\) 8.82729e6 5.09644e6i 0.485244 0.280156i −0.237355 0.971423i \(-0.576281\pi\)
0.722599 + 0.691267i \(0.242947\pi\)
\(264\) −231188. + 494720.i −0.0125648 + 0.0268873i
\(265\) −7.48726e6 −0.402333
\(266\) −2.36148e7 1.48475e7i −1.25470 0.788875i
\(267\) 5.86424e6i 0.308090i
\(268\) −2.70459e6 + 3.62873e6i −0.140507 + 0.188517i
\(269\) 1.03195e6 + 1.78739e6i 0.0530153 + 0.0918251i 0.891315 0.453384i \(-0.149783\pi\)
−0.838300 + 0.545209i \(0.816450\pi\)
\(270\) −2.37879e6 + 7.17218e6i −0.120855 + 0.364385i
\(271\) −2.58828e7 + 1.49434e7i −1.30048 + 0.750831i −0.980486 0.196589i \(-0.937014\pi\)
−0.319992 + 0.947420i \(0.603680\pi\)
\(272\) 3.44582e6 + 1.15561e7i 0.171232 + 0.574252i
\(273\) −4.33143e6 −0.212884
\(274\) −6.28058e6 3.04591e7i −0.305315 1.48070i
\(275\) 145420. + 83958.1i 0.00699238 + 0.00403705i
\(276\) 140769. 1.19864e6i 0.00669545 0.0570115i
\(277\) −2.91365e7 −1.37087 −0.685437 0.728132i \(-0.740389\pi\)
−0.685437 + 0.728132i \(0.740389\pi\)
\(278\) −9.37620e6 + 1.93334e6i −0.436408 + 0.0899859i
\(279\) 2.12761e7 + 1.22838e7i 0.979669 + 0.565612i
\(280\) 3.02299e7 + 1.41268e7i 1.37709 + 0.643530i
\(281\) 2.52895e6 4.38027e6i 0.113978 0.197416i −0.803393 0.595450i \(-0.796974\pi\)
0.917371 + 0.398034i \(0.130307\pi\)
\(282\) −2.66038e6 + 2.36622e6i −0.118630 + 0.105514i
\(283\) 1.01828e7 5.87907e6i 0.449273 0.259388i −0.258250 0.966078i \(-0.583146\pi\)
0.707523 + 0.706690i \(0.249813\pi\)
\(284\) −1.04655e7 2.42986e7i −0.456885 1.06078i
\(285\) 4.39492e6 + 1.08031e6i 0.189852 + 0.0466674i
\(286\) −2.68788e6 + 554233.i −0.114898 + 0.0236916i
\(287\) −4.95405e7 + 2.86022e7i −2.09563 + 1.20991i
\(288\) −701135. + 2.30092e7i −0.0293511 + 0.963216i
\(289\) 7.73505e6 1.33975e7i 0.320457 0.555048i
\(290\) −2.81263e7 + 2.50165e7i −1.15324 + 1.02573i
\(291\) 2.90193e6 + 1.67543e6i 0.117763 + 0.0679902i
\(292\) −3.59639e7 + 1.54899e7i −1.44450 + 0.622156i
\(293\) 2.72690e7 1.08409 0.542046 0.840349i \(-0.317650\pi\)
0.542046 + 0.840349i \(0.317650\pi\)
\(294\) −1.82476e6 + 5.50177e6i −0.0718067 + 0.216501i
\(295\) −6.24520e6 3.60567e6i −0.243265 0.140449i
\(296\) 3.34321e6 + 4.78298e6i 0.128910 + 0.184426i
\(297\) −1.52678e6 −0.0582781
\(298\) 3.52046e7 + 1.16763e7i 1.33030 + 0.441220i
\(299\) 5.25287e6 3.03275e6i 0.196509 0.113455i
\(300\) −265093. 31132.6i −0.00981826 0.00115306i
\(301\) 2.03783e7 + 3.52963e7i 0.747255 + 1.29428i
\(302\) −2.58105e7 2.90190e7i −0.937077 1.05357i
\(303\) 2.45654e6i 0.0883071i
\(304\) 2.80611e7 1.36932e6i 0.998812 0.0487399i
\(305\) −4.57583e6 −0.161276
\(306\) −1.23632e7 + 1.09962e7i −0.431485 + 0.383777i
\(307\) 4.59065e7 2.65041e7i 1.58657 0.916005i 0.592701 0.805422i \(-0.298062\pi\)
0.993867 0.110583i \(-0.0352718\pi\)
\(308\) −786378. + 6.69599e6i −0.0269141 + 0.229172i
\(309\) 4.50741e6 + 7.80707e6i 0.152775 + 0.264614i
\(310\) −1.12909e7 + 3.40428e7i −0.379005 + 1.14272i
\(311\) 1.64753e7i 0.547711i 0.961771 + 0.273856i \(0.0882991\pi\)
−0.961771 + 0.273856i \(0.911701\pi\)
\(312\) 3.57558e6 2.49926e6i 0.117729 0.0822902i
\(313\) −2.29003e7 + 3.96644e7i −0.746806 + 1.29351i 0.202541 + 0.979274i \(0.435080\pi\)
−0.949346 + 0.314232i \(0.898253\pi\)
\(314\) 6.20758e6 + 2.05886e6i 0.200509 + 0.0665025i
\(315\) 4.57836e7i 1.46480i
\(316\) 8.90942e6 + 2.06856e7i 0.282350 + 0.655552i
\(317\) 1.08379e7 1.87717e7i 0.340224 0.589286i −0.644250 0.764815i \(-0.722830\pi\)
0.984474 + 0.175529i \(0.0561636\pi\)
\(318\) 1.59815e6 + 1.79682e6i 0.0496978 + 0.0558758i
\(319\) −6.58664e6 3.80280e6i −0.202905 0.117147i
\(320\) −3.31059e7 + 5.78122e6i −1.01031 + 0.176429i
\(321\) 1.78512e6 + 3.09191e6i 0.0539699 + 0.0934786i
\(322\) −3.00915e6 1.45936e7i −0.0901314 0.437113i
\(323\) 1.45723e7 + 1.39792e7i 0.432434 + 0.414834i
\(324\) −2.78739e7 + 1.20055e7i −0.819526 + 0.352975i
\(325\) −670724. 1.16173e6i −0.0195386 0.0338419i
\(326\) −3.12855e7 3.51747e7i −0.903006 1.01526i
\(327\) −6.85016e6 3.95494e6i −0.195910 0.113109i
\(328\) 2.43919e7 5.21963e7i 0.691233 1.47917i
\(329\) −2.19791e7 + 3.80689e7i −0.617195 + 1.06901i
\(330\) −220902. 1.07132e6i −0.00614693 0.0298110i
\(331\) 4.55446e7i 1.25589i −0.778256 0.627947i \(-0.783895\pi\)
0.778256 0.627947i \(-0.216105\pi\)
\(332\) 4.29675e7 + 5.04612e6i 1.17416 + 0.137893i
\(333\) −4.00347e6 + 6.93421e6i −0.108418 + 0.187786i
\(334\) 9.48727e6 1.95625e6i 0.254626 0.0525030i
\(335\) 9.06569e6i 0.241138i
\(336\) −3.06236e6 1.02700e7i −0.0807305 0.270741i
\(337\) −378346. 655314.i −0.00988551 0.0171222i 0.861040 0.508537i \(-0.169813\pi\)
−0.870926 + 0.491414i \(0.836480\pi\)
\(338\) −1.58412e7 5.25404e6i −0.410240 0.136064i
\(339\) −6.74956e6 + 3.89686e6i −0.173251 + 0.100027i
\(340\) −1.93677e7 1.44353e7i −0.492767 0.367272i
\(341\) −7.24684e6 −0.182762
\(342\) 1.80027e7 + 3.40861e7i 0.450048 + 0.852116i
\(343\) 1.17577e7i 0.291366i
\(344\) −3.71885e7 1.73786e7i −0.913551 0.426913i
\(345\) 1.20877e6 + 2.09365e6i 0.0294365 + 0.0509855i
\(346\) 2.63263e7 + 8.73161e6i 0.635567 + 0.210798i
\(347\) −3.24362e7 + 1.87271e7i −0.776322 + 0.448210i −0.835125 0.550060i \(-0.814605\pi\)
0.0588031 + 0.998270i \(0.481272\pi\)
\(348\) 1.20071e7 + 1.41012e6i 0.284906 + 0.0334594i
\(349\) 3.69240e6 0.0868625 0.0434313 0.999056i \(-0.486171\pi\)
0.0434313 + 0.999056i \(0.486171\pi\)
\(350\) −3.22752e6 + 665506.i −0.0752775 + 0.0155220i
\(351\) 1.05630e7 + 6.09855e6i 0.244268 + 0.141028i
\(352\) −3.21447e6 5.98127e6i −0.0737025 0.137140i
\(353\) 6.63283e7 1.50791 0.753954 0.656927i \(-0.228144\pi\)
0.753954 + 0.656927i \(0.228144\pi\)
\(354\) 467733. + 2.26838e6i 0.0105436 + 0.0511335i
\(355\) 4.58958e7 + 2.64979e7i 1.02586 + 0.592280i
\(356\) 5.84675e7 + 4.35774e7i 1.29588 + 0.965854i
\(357\) 3.85146e6 6.67092e6i 0.0846488 0.146616i
\(358\) −1.13894e7 1.28053e7i −0.248229 0.279087i
\(359\) −2.68967e7 + 1.55288e7i −0.581320 + 0.335625i −0.761658 0.647980i \(-0.775614\pi\)
0.180338 + 0.983605i \(0.442281\pi\)
\(360\) −2.64175e7 3.77943e7i −0.566218 0.810063i
\(361\) 3.97310e7 2.51946e7i 0.844515 0.535532i
\(362\) −1.43359e7 6.95251e7i −0.302203 1.46560i
\(363\) −7.70496e6 + 4.44846e6i −0.161083 + 0.0930015i
\(364\) 3.21870e7 4.31851e7i 0.667385 0.895426i
\(365\) 3.92191e7 6.79295e7i 0.806528 1.39695i
\(366\) 976709. + 1.09813e6i 0.0199215 + 0.0223980i
\(367\) −1.98345e7 1.14515e7i −0.401258 0.231666i 0.285769 0.958299i \(-0.407751\pi\)
−0.687027 + 0.726632i \(0.741084\pi\)
\(368\) 1.09046e7 + 1.03107e7i 0.218810 + 0.206892i
\(369\) 7.90521e7 1.57338
\(370\) −1.10951e7 3.67989e6i −0.219041 0.0726490i
\(371\) 2.57118e7 + 1.48447e7i 0.503514 + 0.290704i
\(372\) 1.05798e7 4.55678e6i 0.205517 0.0885175i
\(373\) −8.57133e7 −1.65166 −0.825832 0.563916i \(-0.809294\pi\)
−0.825832 + 0.563916i \(0.809294\pi\)
\(374\) 1.53645e6 4.63249e6i 0.0293700 0.0885522i
\(375\) −8.46550e6 + 4.88756e6i −0.160531 + 0.0926826i
\(376\) −3.82231e6 4.41079e7i −0.0719056 0.829761i
\(377\) 3.03798e7 + 5.26193e7i 0.566971 + 0.982022i
\(378\) 2.23890e7 1.99135e7i 0.414533 0.368699i
\(379\) 5.17618e7i 0.950806i −0.879768 0.475403i \(-0.842302\pi\)
0.879768 0.475403i \(-0.157698\pi\)
\(380\) −4.34297e7 + 3.57903e7i −0.791473 + 0.652251i
\(381\) 1.45564e7 0.263196
\(382\) −4.82838e7 5.42861e7i −0.866186 0.973864i
\(383\) −6.78918e6 + 3.91973e6i −0.120843 + 0.0697686i −0.559203 0.829031i \(-0.688893\pi\)
0.438360 + 0.898799i \(0.355559\pi\)
\(384\) 8.45385e6 + 6.71091e6i 0.149300 + 0.118519i
\(385\) −6.75255e6 1.16958e7i −0.118328 0.204949i
\(386\) 2.21252e6 + 733824.i 0.0384703 + 0.0127594i
\(387\) 5.63225e7i 0.971738i
\(388\) −3.82686e7 + 1.64825e7i −0.655161 + 0.282182i
\(389\) −4.60315e7 + 7.97288e7i −0.781999 + 1.35446i 0.148777 + 0.988871i \(0.452466\pi\)
−0.930776 + 0.365591i \(0.880867\pi\)
\(390\) −2.75095e6 + 8.29428e6i −0.0463756 + 0.139825i
\(391\) 1.07867e7i 0.180451i
\(392\) −4.12937e7 5.90771e7i −0.685528 0.980756i
\(393\) 5.07775e6 8.79492e6i 0.0836553 0.144895i
\(394\) −3.12208e7 + 2.77688e7i −0.510453 + 0.454013i
\(395\) −3.90715e7 2.25579e7i −0.633970 0.366023i
\(396\) 5.56779e6 7.47027e6i 0.0896597 0.120296i
\(397\) 2.78417e7 + 4.82233e7i 0.444964 + 0.770699i 0.998050 0.0624246i \(-0.0198833\pi\)
−0.553086 + 0.833124i \(0.686550\pi\)
\(398\) −1.02793e8 + 2.11956e7i −1.63047 + 0.336198i
\(399\) −1.29506e7 1.24235e7i −0.203879 0.195581i
\(400\) 2.28031e6 2.41168e6i 0.0356299 0.0376824i
\(401\) 927984. + 1.60732e6i 0.0143915 + 0.0249269i 0.873131 0.487485i \(-0.162086\pi\)
−0.858740 + 0.512412i \(0.828752\pi\)
\(402\) −2.17562e6 + 1.93507e6i −0.0334892 + 0.0297864i
\(403\) 5.01373e7 + 2.89468e7i 0.766030 + 0.442268i
\(404\) −2.44921e7 1.82546e7i −0.371435 0.276840i
\(405\) 3.03969e7 5.26489e7i 0.457577 0.792546i
\(406\) 1.46187e8 3.01434e7i 2.18440 0.450416i
\(407\) 2.36186e6i 0.0350325i
\(408\) 669794. + 7.72915e6i 0.00986191 + 0.113802i
\(409\) −6.81411e6 + 1.18024e7i −0.0995954 + 0.172504i −0.911517 0.411262i \(-0.865088\pi\)
0.811922 + 0.583766i \(0.198422\pi\)
\(410\) 2.33067e7 + 1.13031e8i 0.338165 + 1.64001i
\(411\) 2.00083e7i 0.288193i
\(412\) −1.11333e8 1.30749e7i −1.59195 0.186960i
\(413\) 1.42977e7 + 2.47643e7i 0.202962 + 0.351541i
\(414\) −6.48230e6 + 1.95445e7i −0.0913541 + 0.275438i
\(415\) −7.50506e7 + 4.33305e7i −1.05005 + 0.606247i
\(416\) −1.65223e6 + 5.42213e7i −0.0229504 + 0.753165i
\(417\) −6.15912e6 −0.0849397
\(418\) −9.62622e6 6.05236e6i −0.131803 0.0828697i
\(419\) 9.78093e7i 1.32965i −0.746998 0.664826i \(-0.768506\pi\)
0.746998 0.664826i \(-0.231494\pi\)
\(420\) 1.72124e7 + 1.28289e7i 0.232324 + 0.173157i
\(421\) −3.74276e7 6.48265e7i −0.501586 0.868773i −0.999998 0.00183275i \(-0.999417\pi\)
0.498412 0.866940i \(-0.333917\pi\)
\(422\) 1.15747e7 3.48984e7i 0.154018 0.464374i
\(423\) 5.26083e7 3.03734e7i 0.695078 0.401303i
\(424\) −2.97906e7 + 2.58160e6i −0.390824 + 0.0338681i
\(425\) 2.38560e6 0.0310765
\(426\) −3.43735e6 1.66702e7i −0.0444626 0.215632i
\(427\) 1.57138e7 + 9.07234e6i 0.201835 + 0.116529i
\(428\) −4.40922e7 5.17820e6i −0.562381 0.0660462i
\(429\) −1.76564e6 −0.0223630
\(430\) 8.05317e7 1.66054e7i 1.01289 0.208854i
\(431\) −6.79149e7 3.92107e7i −0.848268 0.489748i 0.0117982 0.999930i \(-0.496244\pi\)
−0.860066 + 0.510183i \(0.829578\pi\)
\(432\) −6.99186e6 + 2.93572e7i −0.0867244 + 0.364135i
\(433\) −8.57089e6 + 1.48452e7i −0.105575 + 0.182862i −0.913973 0.405775i \(-0.867002\pi\)
0.808398 + 0.588637i \(0.200335\pi\)
\(434\) 1.06270e8 9.45195e7i 1.29999 1.15625i
\(435\) −2.09726e7 + 1.21086e7i −0.254792 + 0.147104i
\(436\) 9.03353e7 3.89080e7i 1.08993 0.469439i
\(437\) 2.44043e7 + 5.99878e6i 0.292430 + 0.0718817i
\(438\) −2.46733e7 + 5.08756e6i −0.293633 + 0.0605463i
\(439\) 9.94623e6 5.74246e6i 0.117561 0.0678741i −0.440066 0.897965i \(-0.645045\pi\)
0.557628 + 0.830091i \(0.311712\pi\)
\(440\) 1.23228e7 + 5.75857e6i 0.144660 + 0.0676015i
\(441\) 4.94489e7 8.56480e7i 0.576555 0.998623i
\(442\) −2.91339e7 + 2.59127e7i −0.337390 + 0.300086i
\(443\) 1.65198e7 + 9.53774e6i 0.190018 + 0.109707i 0.591991 0.805945i \(-0.298342\pi\)
−0.401973 + 0.915652i \(0.631675\pi\)
\(444\) 1.48512e6 + 3.44811e6i 0.0169673 + 0.0393942i
\(445\) −1.46070e8 −1.65760
\(446\) −1.68265e7 + 5.07329e7i −0.189666 + 0.571854i
\(447\) 2.06654e7 + 1.19312e7i 0.231377 + 0.133586i
\(448\) 1.25151e8 + 4.57849e7i 1.39187 + 0.509200i
\(449\) −8.89050e7 −0.982171 −0.491085 0.871111i \(-0.663400\pi\)
−0.491085 + 0.871111i \(0.663400\pi\)
\(450\) 4.32248e6 + 1.43363e6i 0.0474346 + 0.0157326i
\(451\) −2.01944e7 + 1.16593e7i −0.220142 + 0.127099i
\(452\) 1.13039e7 9.62521e7i 0.122409 1.04231i
\(453\) −1.24929e7 2.16383e7i −0.134390 0.232771i
\(454\) 1.12726e8 + 1.26740e8i 1.20464 + 1.35439i
\(455\) 1.07890e8i 1.14537i
\(456\) 1.78592e7 + 2.78301e6i 0.188350 + 0.0293509i
\(457\) −1.05563e8 −1.10602 −0.553009 0.833175i \(-0.686521\pi\)
−0.553009 + 0.833175i \(0.686521\pi\)
\(458\) 6.36045e7 5.65719e7i 0.662051 0.588849i
\(459\) −1.87850e7 + 1.08455e7i −0.194256 + 0.112154i
\(460\) −2.98565e7 3.50635e6i −0.306736 0.0360232i
\(461\) 2.09161e6 + 3.62278e6i 0.0213490 + 0.0369776i 0.876503 0.481397i \(-0.159871\pi\)
−0.855154 + 0.518375i \(0.826537\pi\)
\(462\) −1.36547e6 + 4.11696e6i −0.0138470 + 0.0417495i
\(463\) 4.33656e6i 0.0436921i 0.999761 + 0.0218460i \(0.00695436\pi\)
−0.999761 + 0.0218460i \(0.993046\pi\)
\(464\) −1.03285e8 + 1.09234e8i −1.03391 + 1.09347i
\(465\) −1.15374e7 + 1.99834e7i −0.114749 + 0.198751i
\(466\) 1.47057e8 + 4.87741e7i 1.45320 + 0.481983i
\(467\) 7.24859e7i 0.711710i −0.934541 0.355855i \(-0.884190\pi\)
0.934541 0.355855i \(-0.115810\pi\)
\(468\) −6.83600e7 + 2.94431e7i −0.666906 + 0.287241i
\(469\) −1.79742e7 + 3.11323e7i −0.174234 + 0.301782i
\(470\) 5.89392e7 + 6.62661e7i 0.567690 + 0.638261i
\(471\) 3.64389e6 + 2.10380e6i 0.0348741 + 0.0201346i
\(472\) −2.60919e7 1.21930e7i −0.248130 0.115954i
\(473\) 8.30692e6 + 1.43880e7i 0.0784976 + 0.135962i
\(474\) 2.92625e6 + 1.41915e7i 0.0274774 + 0.133258i
\(475\) 1.32669e6 5.39727e6i 0.0123791 0.0503608i
\(476\) 3.78899e7 + 8.79716e7i 0.351320 + 0.815684i
\(477\) −2.05143e7 3.55318e7i −0.189017 0.327387i
\(478\) −5.59775e7 6.29362e7i −0.512543 0.576258i
\(479\) 1.43484e8 + 8.28406e7i 1.30556 + 0.753767i 0.981352 0.192219i \(-0.0615683\pi\)
0.324210 + 0.945985i \(0.394902\pi\)
\(480\) −2.16111e7 658534.i −0.195413 0.00595463i
\(481\) −9.43420e6 + 1.63405e7i −0.0847754 + 0.146835i
\(482\) −1.42815e7 6.92614e7i −0.127536 0.618515i
\(483\) 9.58635e6i 0.0850770i
\(484\) 1.29039e7 1.09877e8i 0.113811 0.969100i
\(485\) 4.17325e7 7.22828e7i 0.365804 0.633592i
\(486\) −6.12065e7 + 1.26206e7i −0.533198 + 0.109944i
\(487\) 1.56874e8i 1.35820i 0.734044 + 0.679102i \(0.237630\pi\)
−0.734044 + 0.679102i \(0.762370\pi\)
\(488\) −1.82065e7 + 1.57774e6i −0.156663 + 0.0135761i
\(489\) −1.51429e7 2.62283e7i −0.129504 0.224308i
\(490\) 1.37041e8 + 4.54523e7i 1.16483 + 0.386338i
\(491\) 1.32967e8 7.67683e7i 1.12331 0.648541i 0.181063 0.983472i \(-0.442046\pi\)
0.942243 + 0.334931i \(0.108713\pi\)
\(492\) 2.21509e7 2.97197e7i 0.185993 0.249545i
\(493\) −1.08054e8 −0.901775
\(494\) 4.24235e7 + 8.03242e7i 0.351905 + 0.666294i
\(495\) 1.86630e7i 0.153874i
\(496\) −3.31869e7 + 1.39344e8i −0.271970 + 1.14194i
\(497\) −1.05073e8 1.81992e8i −0.855899 1.48246i
\(498\) 2.64182e7 + 8.76209e6i 0.213902 + 0.0709446i
\(499\) 1.39918e8 8.07816e7i 1.12609 0.650146i 0.183138 0.983087i \(-0.441374\pi\)
0.942948 + 0.332941i \(0.108041\pi\)
\(500\) 1.41776e7 1.20722e8i 0.113421 0.965777i
\(501\) 6.23209e6 0.0495587
\(502\) −1.72893e7 + 3.56501e6i −0.136668 + 0.0281806i
\(503\) −3.37348e7 1.94768e7i −0.265078 0.153043i 0.361571 0.932345i \(-0.382241\pi\)
−0.626649 + 0.779302i \(0.715574\pi\)
\(504\) 1.57862e7 + 1.82166e8i 0.123306 + 1.42290i
\(505\) 6.11888e7 0.475114
\(506\) −1.22663e6 5.94885e6i −0.00946812 0.0459178i
\(507\) −9.29890e6 5.36872e6i −0.0713523 0.0411953i
\(508\) −1.08169e8 + 1.45130e8i −0.825113 + 1.10705i
\(509\) 7.76221e7 1.34445e8i 0.588616 1.01951i −0.405798 0.913963i \(-0.633006\pi\)
0.994414 0.105550i \(-0.0336604\pi\)
\(510\) −1.03281e7 1.16120e7i −0.0778591 0.0875379i
\(511\) −2.69363e8 + 1.55517e8i −2.01872 + 1.16551i
\(512\) −1.29730e8 + 3.44174e7i −0.966563 + 0.256430i
\(513\) 1.40904e7 + 4.85313e7i 0.104369 + 0.359476i
\(514\) 4.33421e7 + 2.10197e8i 0.319169 + 1.54788i
\(515\) 1.94463e8 1.12273e8i 1.42369 0.821967i
\(516\) −2.11745e7 1.57819e7i −0.154122 0.114871i
\(517\) −8.95946e6 + 1.55182e7i −0.0648351 + 0.112298i
\(518\) 3.08054e7 + 3.46349e7i 0.221634 + 0.249186i
\(519\) 1.54537e7 + 8.92221e6i 0.110543 + 0.0638220i
\(520\) −6.22530e7 8.90627e7i −0.442742 0.633411i
\(521\) −4.01950e7 −0.284223 −0.142111 0.989851i \(-0.545389\pi\)
−0.142111 + 0.989851i \(0.545389\pi\)
\(522\) −1.95782e8 6.49348e7i −1.37645 0.456527i
\(523\) −6.74418e7 3.89375e7i −0.471437 0.272184i 0.245404 0.969421i \(-0.421079\pi\)
−0.716841 + 0.697237i \(0.754413\pi\)
\(524\) 4.99539e7 + 1.15981e8i 0.347197 + 0.806111i
\(525\) −2.12012e6 −0.0146515
\(526\) −2.56702e7 + 7.73970e7i −0.176389 + 0.531823i
\(527\) −8.91632e7 + 5.14784e7i −0.609191 + 0.351717i
\(528\) −1.24832e6 4.18643e6i −0.00848058 0.0284408i
\(529\) −6.73058e7 1.16577e8i −0.454659 0.787492i
\(530\) 4.47563e7 3.98077e7i 0.300626 0.267386i
\(531\) 3.95166e7i 0.263934i
\(532\) 2.20101e8 3.68001e7i 1.46180 0.244407i
\(533\) 1.86287e8 1.23027
\(534\) 3.11786e7 + 3.50545e7i 0.204754 + 0.230207i
\(535\) 7.70151e7 4.44647e7i 0.502938 0.290372i
\(536\) −3.12584e6 3.60709e7i −0.0202989 0.234241i
\(537\) −5.51274e6 9.54835e6i −0.0355996 0.0616603i
\(538\) −1.56717e7 5.19781e6i −0.100640 0.0333790i
\(539\) 2.91725e7i 0.186298i
\(540\) −2.39129e7 5.55203e7i −0.151863 0.352590i
\(541\) −1.20395e8 + 2.08530e8i −0.760353 + 1.31697i 0.182316 + 0.983240i \(0.441641\pi\)
−0.942669 + 0.333730i \(0.891693\pi\)
\(542\) 7.52684e7 2.26938e8i 0.472732 1.42531i
\(543\) 4.56703e7i 0.285256i
\(544\) −8.20383e7 5.07577e7i −0.509589 0.315286i
\(545\) −9.85119e7 + 1.70628e8i −0.608554 + 1.05405i
\(546\) 2.58918e7 2.30290e7i 0.159069 0.141481i
\(547\) 6.26460e7 + 3.61687e7i 0.382764 + 0.220989i 0.679020 0.734120i \(-0.262405\pi\)
−0.296256 + 0.955109i \(0.595738\pi\)
\(548\) 1.99486e8 + 1.48682e8i 1.21219 + 0.903478i
\(549\) −1.25373e7 2.17152e7i −0.0757681 0.131234i
\(550\) −1.31565e6 + 271283.i −0.00790775 + 0.00163055i
\(551\) −6.00913e7 + 2.44464e8i −0.359217 + 1.46137i
\(552\) 5.53139e6 + 7.91352e6i 0.0328864 + 0.0470492i
\(553\) 8.94497e7 + 1.54931e8i 0.528937 + 0.916145i
\(554\) 1.74168e8 1.54911e8i 1.02433 0.911070i
\(555\) −6.51289e6 3.76022e6i −0.0380973 0.0219955i
\(556\) 4.57687e7 6.14075e7i 0.266283 0.357271i
\(557\) 1.80867e7 3.13270e7i 0.104663 0.181282i −0.808937 0.587895i \(-0.799957\pi\)
0.913600 + 0.406613i \(0.133290\pi\)
\(558\) −1.92491e8 + 3.96910e7i −1.10792 + 0.228449i
\(559\) 1.32725e8i 0.759829i
\(560\) −2.55812e8 + 7.62789e7i −1.45666 + 0.434350i
\(561\) 1.56999e6 2.71930e6i 0.00889218 0.0154017i
\(562\) 8.17148e6 + 3.96295e7i 0.0460354 + 0.223259i
\(563\) 1.24196e8i 0.695955i −0.937503 0.347978i \(-0.886869\pi\)
0.937503 0.347978i \(-0.113131\pi\)
\(564\) 3.32226e6 2.82890e7i 0.0185181 0.157681i
\(565\) 9.70652e7 + 1.68122e8i 0.538169 + 0.932135i
\(566\) −2.96122e7 + 8.92825e7i −0.163313 + 0.492399i
\(567\) −2.08771e8 + 1.20534e8i −1.14530 + 0.661241i
\(568\) 1.91748e8 + 8.96062e7i 1.04637 + 0.488982i
\(569\) −2.11517e8 −1.14817 −0.574087 0.818794i \(-0.694643\pi\)
−0.574087 + 0.818794i \(0.694643\pi\)
\(570\) −3.20150e7 + 1.69088e7i −0.172874 + 0.0913039i
\(571\) 8.23768e7i 0.442483i −0.975219 0.221242i \(-0.928989\pi\)
0.975219 0.221242i \(-0.0710109\pi\)
\(572\) 1.31206e7 1.76038e7i 0.0701074 0.0940627i
\(573\) −2.33705e7 4.04789e7i −0.124224 0.215161i
\(574\) 1.44066e8 4.34367e8i 0.761774 2.29679i
\(575\) 2.57115e6 1.48445e6i 0.0135246 0.00780842i
\(576\) −1.18142e8 1.41269e8i −0.618213 0.739229i
\(577\) −2.58888e8 −1.34767 −0.673836 0.738881i \(-0.735355\pi\)
−0.673836 + 0.738881i \(0.735355\pi\)
\(578\) 2.49933e7 + 1.21211e8i 0.129432 + 0.627708i
\(579\) 1.29877e6 + 749843.i 0.00669106 + 0.00386309i
\(580\) 3.51240e7 2.99080e8i 0.180020 1.53286i
\(581\) 3.43640e8 1.75217
\(582\) −2.62545e7 + 5.41360e6i −0.133179 + 0.0274611i
\(583\) 1.04810e7 + 6.05124e6i 0.0528931 + 0.0305378i
\(584\) 1.32625e8 2.83803e8i 0.665864 1.42488i
\(585\) 7.45475e7 1.29120e8i 0.372362 0.644950i
\(586\) −1.63005e8 + 1.44982e8i −0.810042 + 0.720477i
\(587\) −1.13023e8 + 6.52538e7i −0.558794 + 0.322620i −0.752661 0.658408i \(-0.771230\pi\)
0.193867 + 0.981028i \(0.437897\pi\)
\(588\) −1.83436e7 4.25895e7i −0.0902301 0.209493i
\(589\) 6.68804e7 + 2.30354e8i 0.327305 + 1.12733i
\(590\) 5.65021e7 1.16506e7i 0.275111 0.0567271i
\(591\) −2.32800e7 + 1.34407e7i −0.112777 + 0.0651119i
\(592\) −4.54143e7 1.08161e7i −0.218891 0.0521322i
\(593\) 7.04042e7 1.21944e8i 0.337625 0.584783i −0.646361 0.763032i \(-0.723710\pi\)
0.983985 + 0.178249i \(0.0570432\pi\)
\(594\) 9.12654e6 8.11744e6i 0.0435459 0.0387311i
\(595\) −1.66163e8 9.59343e7i −0.788830 0.455431i
\(596\) −2.72521e8 + 1.17376e8i −1.28724 + 0.554424i
\(597\) −6.75235e7 −0.317345
\(598\) −1.52756e7 + 4.60568e7i −0.0714323 + 0.215372i
\(599\) −1.28755e8 7.43366e7i −0.599077 0.345877i 0.169601 0.985513i \(-0.445752\pi\)
−0.768679 + 0.639635i \(0.779085\pi\)
\(600\) 1.75016e6 1.22333e6i 0.00810259 0.00566355i
\(601\) 2.73158e8 1.25832 0.629158 0.777277i \(-0.283400\pi\)
0.629158 + 0.777277i \(0.283400\pi\)
\(602\) −3.09475e8 1.02643e8i −1.41852 0.470480i
\(603\) 4.30224e7 2.48390e7i 0.196220 0.113288i
\(604\) 3.08573e8 + 3.62388e7i 1.40038 + 0.164461i
\(605\) 1.10805e8 + 1.91919e8i 0.500371 + 0.866668i
\(606\) −1.30607e7 1.46844e7i −0.0586881 0.0659837i
\(607\) 9.41396e7i 0.420926i −0.977602 0.210463i \(-0.932503\pi\)
0.977602 0.210463i \(-0.0674972\pi\)
\(608\) −1.60459e8 + 1.57378e8i −0.713928 + 0.700220i
\(609\) 9.60289e7 0.425158
\(610\) 2.73527e7 2.43284e7i 0.120507 0.107183i
\(611\) 1.23972e8 7.15753e7i 0.543501 0.313790i
\(612\) 1.54391e7 1.31463e8i 0.0673546 0.573522i
\(613\) −1.17549e8 2.03601e8i −0.510314 0.883889i −0.999929 0.0119503i \(-0.996196\pi\)
0.489615 0.871939i \(-0.337137\pi\)
\(614\) −1.33498e8 + 4.02505e8i −0.576727 + 1.73886i
\(615\) 7.42489e7i 0.319201i
\(616\) −3.09000e7 4.42073e7i −0.132195 0.189126i
\(617\) 2.12425e8 3.67931e8i 0.904380 1.56643i 0.0826320 0.996580i \(-0.473667\pi\)
0.821748 0.569851i \(-0.192999\pi\)
\(618\) −6.84518e7 2.27033e7i −0.290014 0.0961887i
\(619\) 4.53433e8i 1.91179i −0.293702 0.955897i \(-0.594887\pi\)
0.293702 0.955897i \(-0.405113\pi\)
\(620\) −1.13503e8 2.63527e8i −0.476246 1.10573i
\(621\) −1.34974e7 + 2.33781e7i −0.0563604 + 0.0976191i
\(622\) −8.75946e7 9.84837e7i −0.364004 0.409254i
\(623\) 5.01615e8 + 2.89608e8i 2.07447 + 1.19769i
\(624\) −8.08575e6 + 3.39501e7i −0.0332787 + 0.139729i
\(625\) 1.28073e8 + 2.21828e8i 0.524585 + 0.908608i
\(626\) −7.39948e7 3.58855e8i −0.301633 1.46284i
\(627\) −5.27912e6 5.06427e6i −0.0214170 0.0205454i
\(628\) −4.80532e7 + 2.06968e7i −0.194019 + 0.0835651i
\(629\) −1.67776e7 2.90596e7i −0.0674183 0.116772i
\(630\) −2.43419e8 2.73679e8i −0.973493 1.09451i
\(631\) −3.08007e7 1.77828e7i −0.122595 0.0707802i 0.437449 0.899243i \(-0.355882\pi\)
−0.560043 + 0.828463i \(0.689216\pi\)
\(632\) −1.63237e8 7.62826e7i −0.646648 0.302186i
\(633\) 1.18274e7 2.04856e7i 0.0466312 0.0807676i
\(634\) 3.50190e7 + 1.69833e8i 0.137416 + 0.666429i
\(635\) 3.62580e8i 1.41606i
\(636\) −1.91064e7 2.24386e6i −0.0742691 0.00872219i
\(637\) 1.16527e8 2.01830e8i 0.450825 0.780851i
\(638\) 5.95911e7 1.22875e7i 0.229467 0.0473153i
\(639\) 2.90406e8i 1.11302i
\(640\) 1.67159e8 2.10573e8i 0.637661 0.803274i
\(641\) 1.76252e8 + 3.05278e8i 0.669207 + 1.15910i 0.978126 + 0.208012i \(0.0666994\pi\)
−0.308919 + 0.951088i \(0.599967\pi\)
\(642\) −2.71097e7 8.99144e6i −0.102452 0.0339801i
\(643\) −2.32741e8 + 1.34373e8i −0.875468 + 0.505452i −0.869161 0.494528i \(-0.835341\pi\)
−0.00630653 + 0.999980i \(0.502007\pi\)
\(644\) 9.55776e7 + 7.12366e7i 0.357848 + 0.266714i
\(645\) 5.29004e7 0.197142
\(646\) −1.61432e8 6.08611e6i −0.598813 0.0225758i
\(647\) 2.34494e7i 0.0865803i −0.999063 0.0432902i \(-0.986216\pi\)
0.999063 0.0432902i \(-0.0137840\pi\)
\(648\) 1.02791e8 2.19962e8i 0.377772 0.808395i
\(649\) 5.82824e6 + 1.00948e7i 0.0213208 + 0.0369287i
\(650\) 1.01860e7 + 3.37836e6i 0.0370904 + 0.0123017i
\(651\) 7.92407e7 4.57497e7i 0.287214 0.165823i
\(652\) 3.74029e8 + 4.39260e7i 1.34947 + 0.158482i
\(653\) 9.44270e7 0.339123 0.169561 0.985520i \(-0.445765\pi\)
0.169561 + 0.985520i \(0.445765\pi\)
\(654\) 6.19753e7 1.27791e7i 0.221557 0.0456844i
\(655\) −2.19069e8 1.26479e8i −0.779573 0.450086i
\(656\) 1.31707e8 + 4.41697e8i 0.466548 + 1.56463i
\(657\) 4.29825e8 1.51564
\(658\) −7.10184e7 3.44420e8i −0.249283 1.20896i
\(659\) 4.17367e8 + 2.40967e8i 1.45835 + 0.841978i 0.998930 0.0462420i \(-0.0147245\pi\)
0.459418 + 0.888220i \(0.348058\pi\)
\(660\) 7.01638e6 + 5.22949e6i 0.0244051 + 0.0181898i
\(661\) 4.64417e7 8.04393e7i 0.160806 0.278525i −0.774352 0.632755i \(-0.781924\pi\)
0.935158 + 0.354231i \(0.115257\pi\)
\(662\) 2.42148e8 + 2.72250e8i 0.834656 + 0.938414i
\(663\) −2.17240e7 + 1.25423e7i −0.0745415 + 0.0430366i
\(664\) −2.83674e8 + 1.98283e8i −0.968982 + 0.677299i
\(665\) −3.09452e8 + 3.22581e8i −1.05227 + 1.09692i
\(666\) −1.29359e7 6.27357e7i −0.0437899 0.212369i
\(667\) −1.16458e8 + 6.72368e7i −0.392455 + 0.226584i
\(668\) −4.63109e7 + 6.21350e7i −0.155365 + 0.208452i
\(669\) −1.71938e7 + 2.97806e7i −0.0574240 + 0.0994614i
\(670\) 4.81998e7 + 5.41916e7i 0.160258 + 0.180180i
\(671\) 6.40548e6 + 3.69820e6i 0.0212023 + 0.0122412i
\(672\) 7.29087e7 + 4.51092e7i 0.240255 + 0.148647i
\(673\) −5.08497e7 −0.166818 −0.0834090 0.996515i \(-0.526581\pi\)
−0.0834090 + 0.996515i \(0.526581\pi\)
\(674\) 5.74574e6 + 1.90568e6i 0.0187658 + 0.00622402i
\(675\) 5.17032e6 + 2.98509e6i 0.0168115 + 0.00970612i
\(676\) 1.22628e8 5.28165e7i 0.396961 0.170974i
\(677\) 1.60871e8 0.518456 0.259228 0.965816i \(-0.416532\pi\)
0.259228 + 0.965816i \(0.416532\pi\)
\(678\) 1.96281e7 5.91797e7i 0.0629779 0.189882i
\(679\) −2.86625e8 + 1.65483e8i −0.915599 + 0.528621i
\(680\) 1.92522e8 1.66836e7i 0.612285 0.0530595i
\(681\) 5.45622e7 + 9.45045e7i 0.172763 + 0.299234i
\(682\) 4.33192e7 3.85295e7i 0.136561 0.121462i
\(683\) 3.60547e8i 1.13162i 0.824536 + 0.565809i \(0.191436\pi\)
−0.824536 + 0.565809i \(0.808564\pi\)
\(684\) −2.88840e8 1.08040e8i −0.902588 0.337610i
\(685\) −4.98377e8 −1.55055
\(686\) −6.25123e7 7.02834e7i −0.193639 0.217711i
\(687\) 4.74272e7 2.73821e7i 0.146271 0.0844494i
\(688\) 3.14697e8 9.38374e7i 0.966335 0.288145i
\(689\) −4.83421e7 8.37310e7i −0.147798 0.255993i
\(690\) −1.83570e7 6.08844e6i −0.0558797 0.0185336i
\(691\) 2.71689e8i 0.823451i 0.911308 + 0.411725i \(0.135074\pi\)
−0.911308 + 0.411725i \(0.864926\pi\)
\(692\) −2.03793e8 + 8.77751e7i −0.614995 + 0.264882i
\(693\) 3.70025e7 6.40903e7i 0.111181 0.192572i
\(694\) 9.43262e7 2.84399e8i 0.282198 0.850842i
\(695\) 1.53415e8i 0.456997i
\(696\) −7.92717e7 + 5.54093e7i −0.235120 + 0.164344i
\(697\) −1.65644e8 + 2.86905e8i −0.489191 + 0.847304i
\(698\) −2.20719e7 + 1.96315e7i −0.0649043 + 0.0577280i
\(699\) 8.63233e7 + 4.98388e7i 0.252753 + 0.145927i
\(700\) 1.57547e7 2.11380e7i 0.0459322 0.0616269i
\(701\) −5.26491e7 9.11909e7i −0.152840 0.264727i 0.779430 0.626489i \(-0.215509\pi\)
−0.932270 + 0.361762i \(0.882175\pi\)
\(702\) −9.55663e7 + 1.97055e7i −0.276244 + 0.0569608i
\(703\) −7.50759e7 + 2.17973e7i −0.216090 + 0.0627390i
\(704\) 5.10158e7 + 1.86635e7i 0.146213 + 0.0534904i
\(705\) 2.85280e7 + 4.94119e7i 0.0814148 + 0.141015i
\(706\) −3.96488e8 + 3.52649e8i −1.12672 + 1.00214i
\(707\) −2.10127e8 1.21317e8i −0.594599 0.343292i
\(708\) −1.48563e7 1.10728e7i −0.0418611 0.0312002i
\(709\) −2.26536e8 + 3.92371e8i −0.635621 + 1.10093i 0.350762 + 0.936464i \(0.385922\pi\)
−0.986383 + 0.164463i \(0.947411\pi\)
\(710\) −4.15231e8 + 8.56195e7i −1.16015 + 0.239220i
\(711\) 2.47225e8i 0.687835i
\(712\) −5.81188e8 + 5.03647e7i −1.61019 + 0.139536i
\(713\) −6.40653e7 + 1.10964e8i −0.176748 + 0.306136i
\(714\) 1.24447e7 + 6.03537e7i 0.0341894 + 0.165809i
\(715\) 4.39796e7i 0.120319i
\(716\) 1.36164e8 + 1.59912e7i 0.370957 + 0.0435653i
\(717\) −2.70944e7 4.69289e7i −0.0735059 0.127316i
\(718\) 7.82168e7 2.35828e8i 0.211313 0.637122i
\(719\) 4.09575e7 2.36468e7i 0.110191 0.0636189i −0.443892 0.896081i \(-0.646402\pi\)
0.554083 + 0.832462i \(0.313069\pi\)
\(720\) 3.58857e8 + 8.54672e7i 0.961443 + 0.228982i
\(721\) −8.90401e8 −2.37564
\(722\) −1.03546e8 + 3.61843e8i −0.275119 + 0.961410i
\(723\) 4.54970e7i 0.120384i
\(724\) 4.55341e8 + 3.39378e8i 1.19983 + 0.894268i
\(725\) 1.48701e7 + 2.57558e7i 0.0390213 + 0.0675868i
\(726\) 2.24064e7 6.75565e7i 0.0585548 0.176546i
\(727\) −3.59271e8 + 2.07425e8i −0.935017 + 0.539832i −0.888395 0.459080i \(-0.848179\pi\)
−0.0466221 + 0.998913i \(0.514846\pi\)
\(728\) 3.72002e7 + 4.29275e8i 0.0964165 + 1.11261i
\(729\) 3.05493e8 0.788530
\(730\) 1.26724e8 + 6.14577e8i 0.325754 + 1.57982i
\(731\) 2.04412e8 + 1.18017e8i 0.523304 + 0.302130i
\(732\) −1.16769e7 1.37133e6i −0.0297710 0.00349631i
\(733\) 1.85084e8 0.469956 0.234978 0.972001i \(-0.424498\pi\)
0.234978 + 0.972001i \(0.424498\pi\)
\(734\) 1.79448e8 3.70017e7i 0.453786 0.0935693i
\(735\) 8.04441e7 + 4.64444e7i 0.202597 + 0.116969i
\(736\) −1.20003e8 3.65673e6i −0.300995 0.00917191i
\(737\) −7.32693e6 + 1.26906e7i −0.0183029 + 0.0317015i
\(738\) −4.72547e8 + 4.20298e8i −1.17564 + 1.04566i
\(739\) 4.93518e8 2.84933e8i 1.22284 0.706007i 0.257318 0.966327i \(-0.417161\pi\)
0.965523 + 0.260319i \(0.0838278\pi\)
\(740\) 8.58875e7 3.69923e7i 0.211951 0.0912885i
\(741\) 1.62949e7 + 5.61240e7i 0.0400495 + 0.137941i
\(742\) −2.32622e8 + 4.79660e7i −0.569428 + 0.117414i
\(743\) 4.82920e8 2.78814e8i 1.17736 0.679748i 0.221956 0.975057i \(-0.428756\pi\)
0.955402 + 0.295309i \(0.0954225\pi\)
\(744\) −3.90152e7 + 8.34887e7i −0.0947360 + 0.202726i
\(745\) 2.97188e8 5.14744e8i 0.718724 1.24487i
\(746\) 5.12365e8 4.55714e8i 1.23414 1.09768i
\(747\) −4.11261e8 2.37442e8i −0.986634 0.569634i
\(748\) 1.54453e7 + 3.58603e7i 0.0369055 + 0.0856859i
\(749\) −3.52635e8 −0.839228
\(750\) 2.46181e7 7.42249e7i 0.0583540 0.175940i
\(751\) 3.17598e8 + 1.83365e8i 0.749821 + 0.432909i 0.825629 0.564213i \(-0.190820\pi\)
−0.0758081 + 0.997122i \(0.524154\pi\)
\(752\) 2.57358e8 + 2.43340e8i 0.605180 + 0.572216i
\(753\) −1.13572e7 −0.0266002
\(754\) −4.61363e8 1.53020e8i −1.07629 0.356971i
\(755\) −5.38978e8 + 3.11179e8i −1.25236 + 0.723053i
\(756\) −2.79593e7 + 2.38072e8i −0.0647084 + 0.550990i
\(757\) −3.52587e8 6.10698e8i −0.812790 1.40779i −0.910904 0.412618i \(-0.864614\pi\)
0.0981143 0.995175i \(-0.468719\pi\)
\(758\) 2.75203e8 + 3.09415e8i 0.631897 + 0.710449i
\(759\) 3.90773e6i 0.00893716i
\(760\) 6.93208e7 4.44846e8i 0.157915 1.01337i
\(761\) 3.91113e8 0.887458 0.443729 0.896161i \(-0.353655\pi\)
0.443729 + 0.896161i \(0.353655\pi\)
\(762\) −8.70134e7 + 7.73926e7i −0.196662 + 0.174918i
\(763\) 6.76596e8 3.90633e8i 1.52320 0.879417i
\(764\) 5.77248e8 + 6.77922e7i 1.29444 + 0.152020i
\(765\) 1.32574e8 + 2.29625e8i 0.296124 + 0.512902i
\(766\) 1.97433e7 5.95270e7i 0.0439271 0.132443i
\(767\) 9.31212e7i 0.206378i
\(768\) −8.62143e7 + 4.83130e6i −0.190325 + 0.0106655i
\(769\) −1.60875e8 + 2.78644e8i −0.353761 + 0.612733i −0.986905 0.161301i \(-0.948431\pi\)
0.633144 + 0.774034i \(0.281764\pi\)
\(770\) 1.02548e8 + 3.40119e7i 0.224623 + 0.0745003i
\(771\) 1.38076e8i 0.301270i
\(772\) −1.71272e7 + 7.37681e6i −0.0372251 + 0.0160331i
\(773\) 3.33246e8 5.77199e8i 0.721484 1.24965i −0.238921 0.971039i \(-0.576794\pi\)
0.960405 0.278608i \(-0.0898730\pi\)
\(774\) 2.99451e8 + 3.36677e8i 0.645808 + 0.726090i
\(775\) 2.45410e7 + 1.41687e7i 0.0527214 + 0.0304387i
\(776\) 1.41124e8 3.01991e8i 0.302006 0.646262i
\(777\) 1.49105e7 + 2.58258e7i 0.0317855 + 0.0550542i
\(778\) −1.48736e8 7.21329e8i −0.315847 1.53177i
\(779\) 5.56983e8 + 5.34314e8i 1.17823 + 1.13028i
\(780\) −2.76541e7 6.42065e7i −0.0582742 0.135299i
\(781\) −4.28315e7 7.41863e7i −0.0899104 0.155729i
\(782\) −5.73501e7 6.44795e7i −0.119926 0.134835i
\(783\) −2.34185e8 1.35207e8i −0.487835 0.281652i
\(784\) 5.60936e8 + 1.33596e8i 1.16403 + 0.277232i
\(785\) 5.24027e7 9.07642e7i 0.108329 0.187631i
\(786\) 1.64071e7 + 7.95700e7i 0.0337881 + 0.163863i
\(787\) 4.33947e7i 0.0890251i 0.999009 + 0.0445126i \(0.0141735\pi\)
−0.999009 + 0.0445126i \(0.985827\pi\)
\(788\) 3.89884e7 3.31985e8i 0.0796813 0.678484i
\(789\) −2.62305e7 + 4.54326e7i −0.0534043 + 0.0924989i
\(790\) 3.53490e8 7.28887e7i 0.716962 0.147835i
\(791\) 7.69792e8i 1.55541i
\(792\) 6.43499e6 + 7.42571e7i 0.0129531 + 0.149473i
\(793\) −2.95442e7 5.11721e7i −0.0592451 0.102616i
\(794\) −4.22818e8 1.40236e8i −0.844680 0.280154i
\(795\) 3.33729e7 1.92678e7i 0.0664190 0.0383470i
\(796\) 5.01770e8 6.73221e8i 0.994867 1.33481i
\(797\) −4.74346e8 −0.936959 −0.468480 0.883474i \(-0.655198\pi\)
−0.468480 + 0.883474i \(0.655198\pi\)
\(798\) 1.43467e8 + 5.40883e6i 0.282321 + 0.0106437i
\(799\) 2.54576e8i 0.499088i
\(800\) −808726. + 2.65400e7i −0.00157954 + 0.0518359i
\(801\) −4.00216e8 6.93194e8i −0.778747 1.34883i
\(802\) −1.40928e7 4.67415e6i −0.0273196 0.00906108i
\(803\) −1.09802e8 + 6.33942e7i −0.212062 + 0.122434i
\(804\) 2.71691e6 2.31344e7i 0.00522765 0.0445133i
\(805\) −2.38782e8 −0.457735
\(806\) −4.53606e8 + 9.35322e7i −0.866311 + 0.178631i
\(807\) −9.19938e6 5.31127e6i −0.0175040 0.0101060i
\(808\) 2.43460e8 2.10978e7i 0.461524 0.0399948i
\(809\) −1.46868e8 −0.277385 −0.138692 0.990336i \(-0.544290\pi\)
−0.138692 + 0.990336i \(0.544290\pi\)
\(810\) 9.82177e7 + 4.76329e8i 0.184814 + 0.896298i
\(811\) −9.89525e7 5.71303e7i −0.185509 0.107104i 0.404370 0.914596i \(-0.367491\pi\)
−0.589878 + 0.807492i \(0.700824\pi\)
\(812\) −7.13595e8 + 9.57425e8i −1.33286 + 1.78829i
\(813\) 7.69114e7 1.33214e8i 0.143126 0.247902i
\(814\) 1.25573e7 + 1.41184e7i 0.0232822 + 0.0261765i
\(815\) −6.53310e8 + 3.77188e8i −1.20683 + 0.696764i
\(816\) −4.50976e7 4.26411e7i −0.0830009 0.0784799i
\(817\) 3.80685e8 3.96836e8i 0.698070 0.727687i
\(818\) −2.20176e7 1.06779e8i −0.0402263 0.195087i
\(819\) −5.12004e8 + 2.95606e8i −0.932013 + 0.538098i
\(820\) −7.40275e8 5.51747e8i −1.34262 1.00069i
\(821\) 1.31524e8 2.27806e8i 0.237670 0.411657i −0.722375 0.691502i \(-0.756950\pi\)
0.960045 + 0.279844i \(0.0902829\pi\)
\(822\) 1.06378e8 + 1.19603e8i 0.191531 + 0.215340i
\(823\) −6.81538e8 3.93486e8i −1.22262 0.705879i −0.257142 0.966374i \(-0.582781\pi\)
−0.965475 + 0.260495i \(0.916114\pi\)
\(824\) 7.35024e8 5.13767e8i 1.31377 0.918301i
\(825\) −864237. −0.00153912
\(826\) −2.17132e8 7.20158e7i −0.385286 0.127787i
\(827\) −5.14130e8 2.96833e8i −0.908984 0.524802i −0.0288800 0.999583i \(-0.509194\pi\)
−0.880104 + 0.474781i \(0.842527\pi\)
\(828\) −6.51637e7 1.51295e8i −0.114793 0.266522i
\(829\) −6.56933e8 −1.15307 −0.576537 0.817071i \(-0.695596\pi\)
−0.576537 + 0.817071i \(0.695596\pi\)
\(830\) 2.18251e8 6.58039e8i 0.381700 1.15085i
\(831\) 1.29870e8 7.49803e7i 0.226311 0.130660i
\(832\) −2.78403e8 3.32901e8i −0.483398 0.578023i
\(833\) 2.07229e8 + 3.58931e8i 0.358522 + 0.620978i
\(834\) 3.68171e7 3.27463e7i 0.0634676 0.0564501i
\(835\) 1.55232e8i 0.266638i
\(836\) 8.97210e7 1.50010e7i 0.153559 0.0256745i
\(837\) −2.57658e8 −0.439407
\(838\) 5.20025e8 + 5.84671e8i 0.883674 + 0.993526i
\(839\) 6.63925e8 3.83317e8i 1.12417 0.649042i 0.181710 0.983352i \(-0.441837\pi\)
0.942463 + 0.334310i \(0.108503\pi\)
\(840\) −1.71097e8 + 1.48270e7i −0.288673 + 0.0250158i
\(841\) −3.76117e8 6.51453e8i −0.632317 1.09520i
\(842\) 5.68394e8 + 1.88519e8i 0.952168 + 0.315804i
\(843\) 2.60322e7i 0.0434538i
\(844\) 1.16355e8 + 2.70150e8i 0.193535 + 0.449343i
\(845\) −1.33727e8 + 2.31622e8i −0.221641 + 0.383893i
\(846\) −1.52988e8 + 4.61266e8i −0.252665 + 0.761799i
\(847\) 8.78756e8i 1.44616i
\(848\) 1.64352e8 1.73820e8i 0.269518 0.285045i
\(849\) −3.02586e7 + 5.24094e7i −0.0494454 + 0.0856419i
\(850\) −1.42603e7 + 1.26836e7i −0.0232206 + 0.0206531i
\(851\) −3.61650e7 2.08799e7i −0.0586813 0.0338797i
\(852\) 1.09178e8 + 8.13736e7i 0.176530 + 0.131572i
\(853\) −552301. 956613.i −0.000889874 0.00154131i 0.865580 0.500770i \(-0.166950\pi\)
−0.866470 + 0.499229i \(0.833617\pi\)
\(854\) −1.42167e8 + 2.93143e7i −0.228257 + 0.0470659i
\(855\) 5.93237e8 1.72239e8i 0.949140 0.275571i
\(856\) 2.91099e8 2.03473e8i 0.464109 0.324403i
\(857\) 1.38697e8 + 2.40230e8i 0.220356 + 0.381667i 0.954916 0.296876i \(-0.0959449\pi\)
−0.734560 + 0.678543i \(0.762612\pi\)
\(858\) 1.05544e7 9.38743e6i 0.0167098 0.0148623i
\(859\) 8.89123e8 + 5.13335e8i 1.40276 + 0.809882i 0.994675 0.103064i \(-0.0328645\pi\)
0.408082 + 0.912945i \(0.366198\pi\)
\(860\) −3.93105e8 + 5.27426e8i −0.618035 + 0.829214i
\(861\) 1.47211e8 2.54977e8i 0.230638 0.399476i
\(862\) 6.14444e8 1.26697e8i 0.959314 0.197808i
\(863\) 1.96458e8i 0.305659i −0.988253 0.152830i \(-0.951161\pi\)
0.988253 0.152830i \(-0.0488386\pi\)
\(864\) −1.14289e8 2.12661e8i −0.177200 0.329721i
\(865\) 2.22239e8 3.84930e8i 0.343378 0.594749i
\(866\) −2.76941e7 1.34309e8i −0.0426416 0.206800i
\(867\) 7.96221e7i 0.122173i
\(868\) −1.32709e8 + 1.13001e9i −0.202927 + 1.72792i
\(869\) 3.64629e7 + 6.31555e7i 0.0555637 + 0.0962392i
\(870\) 6.09894e7 1.83887e8i 0.0926183 0.279249i
\(871\) 1.01383e8 5.85334e7i 0.153430 0.0885827i
\(872\) −3.33131e8 + 7.12867e8i −0.502418 + 1.07512i
\(873\) 4.57370e8 0.687425
\(874\) −1.77774e8 + 9.38921e7i −0.266278 + 0.140635i
\(875\) 9.65495e8i 1.44121i
\(876\) 1.20440e8 1.61593e8i 0.179167 0.240387i
\(877\) 5.71631e8 + 9.90093e8i 0.847455 + 1.46784i 0.883472 + 0.468484i \(0.155200\pi\)
−0.0360167 + 0.999351i \(0.511467\pi\)
\(878\) −2.89241e7 + 8.72078e7i −0.0427343 + 0.128846i
\(879\) −1.21546e8 + 7.01745e7i −0.178967 + 0.103327i
\(880\) −1.04278e8 + 3.10939e7i −0.153019 + 0.0456276i
\(881\) −5.53156e8 −0.808947 −0.404474 0.914550i \(-0.632545\pi\)
−0.404474 + 0.914550i \(0.632545\pi\)
\(882\) 1.59778e8 + 7.74881e8i 0.232869 + 1.12935i
\(883\) 7.50721e8 + 4.33429e8i 1.09043 + 0.629558i 0.933690 0.358082i \(-0.116569\pi\)
0.156737 + 0.987640i \(0.449903\pi\)
\(884\) 3.63823e7 3.09794e8i 0.0526664 0.448453i
\(885\) 3.71156e7 0.0535459
\(886\) −1.49460e8 + 3.08181e7i −0.214893 + 0.0443103i
\(887\) −8.70971e8 5.02855e8i −1.24805 0.720564i −0.277332 0.960774i \(-0.589450\pi\)
−0.970721 + 0.240211i \(0.922783\pi\)
\(888\) −2.72102e7 1.27157e7i −0.0388592 0.0181593i
\(889\) −7.18875e8 + 1.24513e9i −1.02317 + 1.77218i
\(890\) 8.73156e8 7.76613e8i 1.23857 1.10163i
\(891\) −8.51022e7 + 4.91338e7i −0.120312 + 0.0694620i
\(892\) −1.69150e8 3.92726e8i −0.238329 0.553344i
\(893\) 5.75961e8 + 1.41576e8i 0.808795 + 0.198809i
\(894\) −1.86965e8 + 3.85516e7i −0.261667 + 0.0539548i
\(895\) −2.37836e8 + 1.37314e8i −0.331748 + 0.191535i
\(896\) −9.91534e8 + 3.91705e8i −1.37843 + 0.544547i
\(897\) −1.56090e7 + 2.70357e7i −0.0216271 + 0.0374593i
\(898\) 5.31444e8 4.72683e8i 0.733886 0.652742i
\(899\) −1.11156e9 6.41758e8i −1.52987 0.883268i
\(900\) −3.34605e7 + 1.44117e7i −0.0458992 + 0.0197691i
\(901\) 1.71941e8 0.235075
\(902\) 5.87264e7 1.77063e8i 0.0800228 0.241273i
\(903\) −1.81664e8 1.04884e8i −0.246721 0.142444i
\(904\) 4.44175e8 + 6.35462e8i 0.601242 + 0.860170i
\(905\) −1.13758e9 −1.53475
\(906\) 1.89723e8 + 6.29252e7i 0.255115 + 0.0846135i
\(907\) −3.46279e8 + 1.99924e8i −0.464092 + 0.267944i −0.713763 0.700387i \(-0.753011\pi\)
0.249671 + 0.968331i \(0.419677\pi\)
\(908\) −1.34768e9 1.58272e8i −1.80024 0.211420i
\(909\) 1.67651e8 + 2.90380e8i 0.223210 + 0.386611i
\(910\) −5.73619e8 6.44927e8i −0.761201 0.855828i
\(911\) 1.07845e9i 1.42642i 0.700951 + 0.713209i \(0.252759\pi\)
−0.700951 + 0.713209i \(0.747241\pi\)
\(912\) −1.21553e8 + 7.83163e7i −0.160243 + 0.103245i
\(913\) 1.40080e8 0.184061
\(914\) 6.31019e8 5.61248e8i 0.826425 0.735049i
\(915\) 2.03958e7 1.17755e7i 0.0266242 0.0153715i
\(916\) −7.94290e7 + 6.76335e8i −0.103346 + 0.879985i
\(917\) 5.01533e8 + 8.68681e8i 0.650417 + 1.12655i
\(918\) 5.46277e7 1.64706e8i 0.0706131 0.212902i
\(919\) 2.91285e8i 0.375293i 0.982237 + 0.187647i \(0.0600860\pi\)
−0.982237 + 0.187647i \(0.939914\pi\)
\(920\) 1.97114e8 1.37779e8i 0.253136 0.176937i
\(921\) −1.36412e8 + 2.36273e8i −0.174612 + 0.302437i
\(922\) −3.17642e7 1.05352e7i −0.0405271 0.0134416i
\(923\) 6.84344e8i 0.870301i
\(924\) −1.37265e7 3.18696e7i −0.0173997 0.0403981i
\(925\) −4.61781e6 + 7.99828e6i −0.00583459 + 0.0101058i
\(926\) −2.30563e7 2.59225e7i −0.0290373 0.0326470i
\(927\) 1.06561e9 + 6.15233e8i 1.33771 + 0.772325i
\(928\) 3.66304e7 1.20210e9i 0.0458351 1.50417i
\(929\) 2.32249e7 + 4.02267e7i 0.0289672 + 0.0501727i 0.880146 0.474704i \(-0.157445\pi\)
−0.851178 + 0.524877i \(0.824111\pi\)
\(930\) −3.72794e7 1.80795e8i −0.0463468 0.224770i
\(931\) 9.27302e8 2.69230e8i 1.14914 0.333638i
\(932\) −1.13837e9 + 4.90304e8i −1.40617 + 0.605645i
\(933\) −4.23978e7 7.34351e7i −0.0522033 0.0904189i
\(934\) 3.85388e8 + 4.33296e8i 0.472996 + 0.531795i
\(935\) −6.77339e7 3.91062e7i −0.0828650 0.0478421i
\(936\) 2.52092e8 5.39452e8i 0.307420 0.657848i
\(937\) 7.97410e8 1.38115e9i 0.969311 1.67890i 0.271752 0.962367i \(-0.412397\pi\)
0.697558 0.716528i \(-0.254270\pi\)
\(938\) −5.80779e7 2.81662e8i −0.0703724 0.341288i
\(939\) 2.35728e8i 0.284718i
\(940\) −7.04638e8 8.27528e7i −0.848364 0.0996321i
\(941\) 4.89377e8 8.47626e8i 0.587320 1.01727i −0.407262 0.913311i \(-0.633516\pi\)
0.994582 0.103957i \(-0.0331503\pi\)
\(942\) −3.29673e7 + 6.79776e6i −0.0394395 + 0.00813229i
\(943\) 4.12292e8i 0.491666i
\(944\) 2.20795e8 6.58375e7i 0.262467 0.0782632i
\(945\) −2.40084e8 4.15837e8i −0.284490 0.492751i
\(946\) −1.26153e8 4.18410e7i −0.149013 0.0494230i
\(947\) −1.38377e9 + 7.98920e8i −1.62935 + 0.940705i −0.645062 + 0.764130i \(0.723168\pi\)
−0.984287 + 0.176575i \(0.943498\pi\)
\(948\) −9.29446e7 6.92741e7i −0.109094 0.0813103i
\(949\) 1.01289e9 1.18512
\(950\) 2.07652e7 + 3.93167e7i 0.0242196 + 0.0458571i
\(951\) 1.11561e8i 0.129710i
\(952\) −6.94214e8 3.24414e8i −0.804605 0.376001i
\(953\) 1.28036e8 + 2.21764e8i 0.147929 + 0.256220i 0.930462 0.366389i \(-0.119406\pi\)
−0.782533 + 0.622609i \(0.786073\pi\)
\(954\) 3.11540e8 + 1.03328e8i 0.358814 + 0.119007i
\(955\) −1.00827e9 + 5.82125e8i −1.15762 + 0.668353i
\(956\) 6.69229e8 + 7.85945e7i 0.765952 + 0.0899536i
\(957\) 3.91448e7 0.0446620
\(958\) −1.29814e9 + 2.67673e8i −1.47647 + 0.304444i
\(959\) 1.71147e9 + 9.88116e8i 1.94050 + 1.12035i
\(960\) 1.32685e8 1.10964e8i 0.149972 0.125420i
\(961\) −3.35471e8 −0.377994
\(962\) −3.04836e7 1.47837e8i −0.0342405 0.166057i
\(963\) 4.22026e8 + 2.43657e8i 0.472564 + 0.272835i
\(964\) 4.53614e8 + 3.38090e8i 0.506355 + 0.377400i
\(965\) 1.86775e7 3.23504e7i 0.0207844 0.0359996i
\(966\) 5.09680e7 + 5.73040e7i 0.0565413 + 0.0635702i
\(967\) −1.04930e9 + 6.05815e8i −1.16044 + 0.669978i −0.951408 0.307932i \(-0.900363\pi\)
−0.209027 + 0.977910i \(0.567030\pi\)
\(968\) 5.07048e8 + 7.25411e8i 0.559014 + 0.799757i
\(969\) −1.00927e8 2.48088e7i −0.110927 0.0272668i
\(970\) 1.34845e8 + 6.53962e8i 0.147747 + 0.716535i
\(971\) 1.02434e8 5.91404e7i 0.111889 0.0645992i −0.443011 0.896516i \(-0.646090\pi\)
0.554900 + 0.831917i \(0.312756\pi\)
\(972\) 2.98772e8 4.00860e8i 0.325342 0.436509i
\(973\) 3.04171e8 5.26839e8i 0.330201 0.571925i
\(974\) −8.34057e8 9.37741e8i −0.902649 1.01486i
\(975\) 5.97923e6 + 3.45211e6i 0.00645106 + 0.00372452i
\(976\) 1.00444e8 1.06230e8i 0.108037 0.114261i
\(977\) 1.53178e9 1.64253 0.821266 0.570546i \(-0.193268\pi\)
0.821266 + 0.570546i \(0.193268\pi\)
\(978\) 2.29968e8 + 7.62732e7i 0.245839 + 0.0815372i
\(979\) 2.04476e8 + 1.18054e8i 0.217919 + 0.125815i
\(980\) −1.06084e9 + 4.56911e8i −1.12713 + 0.485460i
\(981\) −1.07965e9 −1.14360
\(982\) −3.86673e8 + 1.16584e9i −0.408328 + 1.23113i
\(983\) 1.52906e9 8.82801e8i 1.60977 0.929399i 0.620346 0.784329i \(-0.286992\pi\)
0.989421 0.145071i \(-0.0463410\pi\)
\(984\) 2.56010e7 + 2.95425e8i 0.0268702 + 0.310071i
\(985\) 3.34789e8 + 5.79872e8i 0.350318 + 0.606769i
\(986\) 6.45908e8 5.74491e8i 0.673813 0.599311i
\(987\) 2.26246e8i 0.235304i
\(988\) −6.80655e8 2.54597e8i −0.705759 0.263987i
\(989\) 2.93747e8 0.303658
\(990\) −9.92261e7 1.11561e8i −0.102263 0.114976i
\(991\) 7.85228e8 4.53352e8i 0.806817 0.465816i −0.0390326 0.999238i \(-0.512428\pi\)
0.845849 + 0.533422i \(0.179094\pi\)
\(992\) −5.42473e8 1.00940e9i −0.555704 1.03401i
\(993\) 1.17205e8 + 2.03006e8i 0.119702 + 0.207329i
\(994\) 1.59569e9 + 5.29242e8i 1.62476 + 0.538884i
\(995\) 1.68191e9i 1.70740i
\(996\) −2.04505e8 + 8.80814e7i −0.206978 + 0.0891469i
\(997\) −5.05028e8 + 8.74734e8i −0.509600 + 0.882654i 0.490338 + 0.871532i \(0.336873\pi\)
−0.999938 + 0.0111212i \(0.996460\pi\)
\(998\) −4.06888e8 + 1.22679e9i −0.409339 + 1.23418i
\(999\) 8.39747e7i 0.0842271i
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 76.7.g.a.7.14 116
4.3 odd 2 inner 76.7.g.a.7.52 yes 116
19.11 even 3 inner 76.7.g.a.11.52 yes 116
76.11 odd 6 inner 76.7.g.a.11.14 yes 116
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.7.g.a.7.14 116 1.1 even 1 trivial
76.7.g.a.7.52 yes 116 4.3 odd 2 inner
76.7.g.a.11.14 yes 116 76.11 odd 6 inner
76.7.g.a.11.52 yes 116 19.11 even 3 inner