Properties

Label 43.6.g.a.24.4
Level $43$
Weight $6$
Character 43.24
Analytic conductor $6.897$
Analytic rank $0$
Dimension $204$
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] = [43,6,Mod(9,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.9");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(17\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 24.4
Character \(\chi\) \(=\) 43.24
Dual form 43.6.g.a.9.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.14921 + 6.45690i) q^{2} +(12.1966 - 1.83835i) q^{3} +(-8.05656 - 35.2981i) q^{4} +(6.56775 - 4.47782i) q^{5} +(-50.9330 + 88.2185i) q^{6} +(-125.151 - 216.768i) q^{7} +(31.2951 + 15.0709i) q^{8} +(-86.8258 + 26.7822i) q^{9} +O(q^{10})\) \(q+(-5.14921 + 6.45690i) q^{2} +(12.1966 - 1.83835i) q^{3} +(-8.05656 - 35.2981i) q^{4} +(6.56775 - 4.47782i) q^{5} +(-50.9330 + 88.2185i) q^{6} +(-125.151 - 216.768i) q^{7} +(31.2951 + 15.0709i) q^{8} +(-86.8258 + 26.7822i) q^{9} +(-4.90589 + 65.4645i) q^{10} +(5.72841 - 25.0978i) q^{11} +(-163.153 - 415.707i) q^{12} +(-50.2681 - 670.781i) q^{13} +(2044.08 + 308.095i) q^{14} +(71.8727 - 66.6881i) q^{15} +(785.395 - 378.226i) q^{16} +(809.365 + 551.816i) q^{17} +(274.154 - 698.532i) q^{18} +(46.5882 + 14.3706i) q^{19} +(-210.972 - 195.753i) q^{20} +(-1924.92 - 2413.77i) q^{21} +(132.557 + 166.222i) q^{22} +(-2661.70 - 2469.70i) q^{23} +(409.400 + 126.283i) q^{24} +(-1118.61 + 2850.16i) q^{25} +(4590.01 + 3129.41i) q^{26} +(-3710.18 + 1786.73i) q^{27} +(-6643.22 + 6164.00i) q^{28} +(3246.12 + 489.275i) q^{29} +(60.5112 + 807.466i) q^{30} +(-1625.48 - 4141.67i) q^{31} +(-1849.33 + 8102.43i) q^{32} +(23.7289 - 316.640i) q^{33} +(-7730.61 + 2384.58i) q^{34} +(-1792.61 - 863.275i) q^{35} +(1644.88 + 2849.01i) q^{36} +(2677.17 - 4636.99i) q^{37} +(-332.682 + 226.818i) q^{38} +(-1846.23 - 8088.87i) q^{39} +(273.023 - 41.1516i) q^{40} +(8109.60 - 10169.1i) q^{41} +25497.3 q^{42} +(-10945.2 + 5216.33i) q^{43} -932.056 q^{44} +(-450.324 + 564.689i) q^{45} +(29652.2 - 4469.35i) q^{46} +(1540.45 + 6749.16i) q^{47} +(8883.87 - 6056.92i) q^{48} +(-22922.1 + 39702.3i) q^{49} +(-12643.3 - 21898.8i) q^{50} +(10886.0 + 5242.40i) q^{51} +(-23272.3 + 7178.56i) q^{52} +(2230.54 - 29764.5i) q^{53} +(7567.76 - 33156.5i) q^{54} +(-74.7606 - 190.487i) q^{55} +(-649.721 - 8669.92i) q^{56} +(594.638 + 89.6272i) q^{57} +(-19874.2 + 18440.5i) q^{58} +(-12046.1 + 5801.11i) q^{59} +(-2933.01 - 1999.69i) q^{60} +(-1891.56 + 4819.61i) q^{61} +(35112.3 + 10830.7i) q^{62} +(16671.9 + 15469.2i) q^{63} +(-25401.7 - 31852.7i) q^{64} +(-3333.78 - 4180.43i) q^{65} +(1922.33 + 1783.66i) q^{66} +(-9985.58 - 3080.14i) q^{67} +(12957.4 - 33014.8i) q^{68} +(-37004.0 - 25228.9i) q^{69} +(14804.6 - 7129.52i) q^{70} +(10771.2 - 9994.21i) q^{71} +(-3120.85 - 470.393i) q^{72} +(-671.483 - 8960.31i) q^{73} +(16155.3 + 41163.0i) q^{74} +(-8403.65 + 36818.8i) q^{75} +(131.913 - 1760.25i) q^{76} +(-6157.32 + 1899.28i) q^{77} +(61735.6 + 29730.3i) q^{78} +(-1004.83 - 1740.42i) q^{79} +(3464.65 - 6000.95i) q^{80} +(-23724.1 + 16174.8i) q^{81} +(23903.0 + 104726. i) q^{82} +(95394.8 - 14378.5i) q^{83} +(-69693.3 + 87392.7i) q^{84} +7786.64 q^{85} +(22677.9 - 97532.3i) q^{86} +40491.3 q^{87} +(557.518 - 699.105i) q^{88} +(9837.97 - 1482.84i) q^{89} +(-1327.33 - 5815.40i) q^{90} +(-139113. + 94845.6i) q^{91} +(-65731.5 + 113850. i) q^{92} +(-27439.3 - 47526.2i) q^{93} +(-51510.8 - 24806.3i) q^{94} +(370.329 - 114.231i) q^{95} +(-7660.49 + 102222. i) q^{96} +(22106.3 - 96853.9i) q^{97} +(-138323. - 352441. i) q^{98} +(174.801 + 2332.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9} + 303 q^{10} - 1340 q^{11} + 858 q^{12} + 814 q^{13} + 1202 q^{14} - 2083 q^{15} - 6248 q^{16} - 214 q^{17} - 174 q^{18} - 246 q^{19} - 17139 q^{20} + 3007 q^{21} + 2118 q^{22} + 3192 q^{23} + 15880 q^{24} + 3652 q^{25} - 1237 q^{26} + 108 q^{27} - 6780 q^{28} - 18827 q^{29} + 98080 q^{30} - 43196 q^{31} - 3930 q^{32} + 28181 q^{33} + 45155 q^{34} + 33275 q^{35} - 49399 q^{36} + 34607 q^{37} - 43374 q^{38} + 15155 q^{39} - 108727 q^{40} + 7156 q^{41} - 48066 q^{42} - 176452 q^{43} + 26068 q^{44} - 96386 q^{45} - 27185 q^{46} + 20402 q^{47} + 198899 q^{48} - 158742 q^{49} + 186243 q^{50} + 98589 q^{51} + 278918 q^{52} + 14102 q^{53} + 270894 q^{54} - 334770 q^{55} + 61999 q^{56} - 202490 q^{57} + 213658 q^{58} - 43753 q^{59} - 389005 q^{60} + 80516 q^{61} + 162349 q^{62} - 75177 q^{63} - 489850 q^{64} + 93726 q^{65} + 246095 q^{66} - 322922 q^{67} + 475089 q^{68} - 397079 q^{69} - 614985 q^{70} - 233345 q^{71} + 379655 q^{72} + 159391 q^{73} + 695938 q^{74} + 344081 q^{75} - 50808 q^{76} + 608177 q^{77} + 605548 q^{78} - 272109 q^{79} + 601054 q^{80} + 193536 q^{81} - 996896 q^{82} + 177813 q^{83} - 919009 q^{84} - 844524 q^{85} - 876752 q^{86} - 188214 q^{87} - 59998 q^{88} - 469041 q^{89} - 453431 q^{90} - 223189 q^{91} - 94922 q^{92} + 569174 q^{93} + 1175168 q^{94} + 435689 q^{95} + 1557688 q^{96} + 643751 q^{97} + 886196 q^{98} + 1422581 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{20}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.14921 + 6.45690i −0.910260 + 1.14143i 0.0792346 + 0.996856i \(0.474752\pi\)
−0.989494 + 0.144573i \(0.953819\pi\)
\(3\) 12.1966 1.83835i 0.782415 0.117930i 0.254325 0.967119i \(-0.418147\pi\)
0.528089 + 0.849189i \(0.322909\pi\)
\(4\) −8.05656 35.2981i −0.251768 1.10307i
\(5\) 6.56775 4.47782i 0.117487 0.0801016i −0.503151 0.864199i \(-0.667826\pi\)
0.620638 + 0.784097i \(0.286874\pi\)
\(6\) −50.9330 + 88.2185i −0.577592 + 1.00042i
\(7\) −125.151 216.768i −0.965361 1.67205i −0.708642 0.705568i \(-0.750692\pi\)
−0.256719 0.966486i \(-0.582641\pi\)
\(8\) 31.2951 + 15.0709i 0.172883 + 0.0832558i
\(9\) −86.8258 + 26.7822i −0.357308 + 0.110215i
\(10\) −4.90589 + 65.4645i −0.0155138 + 0.207017i
\(11\) 5.72841 25.0978i 0.0142742 0.0625394i −0.967289 0.253676i \(-0.918360\pi\)
0.981563 + 0.191137i \(0.0612174\pi\)
\(12\) −163.153 415.707i −0.327071 0.833364i
\(13\) −50.2681 670.781i −0.0824962 1.10084i −0.872786 0.488103i \(-0.837689\pi\)
0.790290 0.612733i \(-0.209930\pi\)
\(14\) 2044.08 + 308.095i 2.78726 + 0.420112i
\(15\) 71.8727 66.6881i 0.0824776 0.0765280i
\(16\) 785.395 378.226i 0.766988 0.369362i
\(17\) 809.365 + 551.816i 0.679238 + 0.463097i 0.853151 0.521664i \(-0.174689\pi\)
−0.173912 + 0.984761i \(0.555641\pi\)
\(18\) 274.154 698.532i 0.199440 0.508165i
\(19\) 46.5882 + 14.3706i 0.0296068 + 0.00913250i 0.309523 0.950892i \(-0.399831\pi\)
−0.279916 + 0.960024i \(0.590307\pi\)
\(20\) −210.972 195.753i −0.117937 0.109429i
\(21\) −1924.92 2413.77i −0.952498 1.19439i
\(22\) 132.557 + 166.222i 0.0583911 + 0.0732201i
\(23\) −2661.70 2469.70i −1.04915 0.973473i −0.0494749 0.998775i \(-0.515755\pi\)
−0.999680 + 0.0253020i \(0.991945\pi\)
\(24\) 409.400 + 126.283i 0.145084 + 0.0447525i
\(25\) −1118.61 + 2850.16i −0.357954 + 0.912052i
\(26\) 4590.01 + 3129.41i 1.33162 + 0.907883i
\(27\) −3710.18 + 1786.73i −0.979459 + 0.471682i
\(28\) −6643.22 + 6164.00i −1.60134 + 1.48583i
\(29\) 3246.12 + 489.275i 0.716754 + 0.108033i 0.497286 0.867586i \(-0.334330\pi\)
0.219468 + 0.975620i \(0.429568\pi\)
\(30\) 60.5112 + 807.466i 0.0122753 + 0.163803i
\(31\) −1625.48 4141.67i −0.303794 0.774053i −0.998500 0.0547596i \(-0.982561\pi\)
0.694706 0.719294i \(-0.255534\pi\)
\(32\) −1849.33 + 8102.43i −0.319256 + 1.39875i
\(33\) 23.7289 316.640i 0.00379308 0.0506151i
\(34\) −7730.61 + 2384.58i −1.14688 + 0.353764i
\(35\) −1792.61 863.275i −0.247352 0.119118i
\(36\) 1644.88 + 2849.01i 0.211533 + 0.366385i
\(37\) 2677.17 4636.99i 0.321493 0.556842i −0.659303 0.751877i \(-0.729149\pi\)
0.980796 + 0.195035i \(0.0624820\pi\)
\(38\) −332.682 + 226.818i −0.0373740 + 0.0254812i
\(39\) −1846.23 8088.87i −0.194368 0.851581i
\(40\) 273.023 41.1516i 0.0269805 0.00406665i
\(41\) 8109.60 10169.1i 0.753424 0.944764i −0.246277 0.969199i \(-0.579207\pi\)
0.999701 + 0.0244354i \(0.00777881\pi\)
\(42\) 25497.3 2.23034
\(43\) −10945.2 + 5216.33i −0.902722 + 0.430224i
\(44\) −932.056 −0.0725789
\(45\) −450.324 + 564.689i −0.0331508 + 0.0415698i
\(46\) 29652.2 4469.35i 2.06615 0.311423i
\(47\) 1540.45 + 6749.16i 0.101719 + 0.445661i 0.999981 + 0.00620004i \(0.00197355\pi\)
−0.898261 + 0.439461i \(0.855169\pi\)
\(48\) 8883.87 6056.92i 0.556543 0.379445i
\(49\) −22922.1 + 39702.3i −1.36384 + 2.36225i
\(50\) −12643.3 21898.8i −0.715212 1.23878i
\(51\) 10886.0 + 5242.40i 0.586059 + 0.282231i
\(52\) −23272.3 + 7178.56i −1.19352 + 0.368154i
\(53\) 2230.54 29764.5i 0.109074 1.45549i −0.627227 0.778837i \(-0.715810\pi\)
0.736301 0.676654i \(-0.236571\pi\)
\(54\) 7567.76 33156.5i 0.353169 1.54734i
\(55\) −74.7606 190.487i −0.00333247 0.00849099i
\(56\) −649.721 8669.92i −0.0276858 0.369441i
\(57\) 594.638 + 89.6272i 0.0242418 + 0.00365387i
\(58\) −19874.2 + 18440.5i −0.775745 + 0.719786i
\(59\) −12046.1 + 5801.11i −0.450523 + 0.216961i −0.645365 0.763874i \(-0.723295\pi\)
0.194842 + 0.980835i \(0.437581\pi\)
\(60\) −2933.01 1999.69i −0.105181 0.0717109i
\(61\) −1891.56 + 4819.61i −0.0650871 + 0.165839i −0.959717 0.280969i \(-0.909344\pi\)
0.894630 + 0.446808i \(0.147439\pi\)
\(62\) 35112.3 + 10830.7i 1.16006 + 0.357831i
\(63\) 16671.9 + 15469.2i 0.529216 + 0.491041i
\(64\) −25401.7 31852.7i −0.775198 0.972068i
\(65\) −3333.78 4180.43i −0.0978710 0.122726i
\(66\) 1922.33 + 1783.66i 0.0543209 + 0.0504024i
\(67\) −9985.58 3080.14i −0.271760 0.0838270i 0.155880 0.987776i \(-0.450179\pi\)
−0.427640 + 0.903949i \(0.640655\pi\)
\(68\) 12957.4 33014.8i 0.339816 0.865838i
\(69\) −37004.0 25228.9i −0.935676 0.637933i
\(70\) 14804.6 7129.52i 0.361120 0.173906i
\(71\) 10771.2 9994.21i 0.253582 0.235290i −0.543130 0.839648i \(-0.682761\pi\)
0.796712 + 0.604359i \(0.206571\pi\)
\(72\) −3120.85 470.393i −0.0709483 0.0106937i
\(73\) −671.483 8960.31i −0.0147478 0.196796i −0.999711 0.0240325i \(-0.992349\pi\)
0.984963 0.172763i \(-0.0552696\pi\)
\(74\) 16155.3 + 41163.0i 0.342954 + 0.873833i
\(75\) −8403.65 + 36818.8i −0.172510 + 0.755816i
\(76\) 131.913 1760.25i 0.00261971 0.0349576i
\(77\) −6157.32 + 1899.28i −0.118349 + 0.0365059i
\(78\) 61735.6 + 29730.3i 1.14895 + 0.553303i
\(79\) −1004.83 1740.42i −0.0181145 0.0313752i 0.856826 0.515606i \(-0.172433\pi\)
−0.874941 + 0.484230i \(0.839100\pi\)
\(80\) 3464.65 6000.95i 0.0605250 0.104832i
\(81\) −23724.1 + 16174.8i −0.401770 + 0.273922i
\(82\) 23903.0 + 104726.i 0.392570 + 1.71996i
\(83\) 95394.8 14378.5i 1.51995 0.229096i 0.664621 0.747180i \(-0.268593\pi\)
0.855329 + 0.518085i \(0.173355\pi\)
\(84\) −69693.3 + 87392.7i −1.07769 + 1.35138i
\(85\) 7786.64 0.116897
\(86\) 22677.9 97532.3i 0.330642 1.42201i
\(87\) 40491.3 0.573539
\(88\) 557.518 699.105i 0.00767454 0.00962357i
\(89\) 9837.97 1482.84i 0.131653 0.0198435i −0.0828852 0.996559i \(-0.526413\pi\)
0.214538 + 0.976716i \(0.431175\pi\)
\(90\) −1327.33 5815.40i −0.0172731 0.0756786i
\(91\) −139113. + 94845.6i −1.76102 + 1.20064i
\(92\) −65731.5 + 113850.i −0.809662 + 1.40238i
\(93\) −27439.3 47526.2i −0.328977 0.569804i
\(94\) −51510.8 24806.3i −0.601282 0.289562i
\(95\) 370.329 114.231i 0.00420996 0.00129860i
\(96\) −7660.49 + 102222.i −0.0848357 + 1.13205i
\(97\) 22106.3 96853.9i 0.238554 1.04517i −0.703759 0.710439i \(-0.748497\pi\)
0.942313 0.334733i \(-0.108646\pi\)
\(98\) −138323. 352441.i −1.45489 3.70699i
\(99\) 174.801 + 2332.56i 0.00179248 + 0.0239190i
\(100\) 109617. + 16522.2i 1.09617 + 0.165222i
\(101\) −80075.1 + 74298.8i −0.781077 + 0.724734i −0.966147 0.257992i \(-0.916939\pi\)
0.185070 + 0.982725i \(0.440749\pi\)
\(102\) −89903.7 + 43295.4i −0.855613 + 0.412041i
\(103\) −74146.5 50552.2i −0.688649 0.469513i 0.167749 0.985830i \(-0.446350\pi\)
−0.856397 + 0.516317i \(0.827303\pi\)
\(104\) 8536.15 21749.7i 0.0773889 0.197184i
\(105\) −23450.8 7233.62i −0.207580 0.0640298i
\(106\) 180701. + 167666.i 1.56205 + 1.44937i
\(107\) 9712.58 + 12179.2i 0.0820115 + 0.102839i 0.821145 0.570720i \(-0.193336\pi\)
−0.739133 + 0.673560i \(0.764765\pi\)
\(108\) 92959.6 + 116568.i 0.766893 + 0.961653i
\(109\) 155555. + 144334.i 1.25406 + 1.16360i 0.979373 + 0.202062i \(0.0647642\pi\)
0.274686 + 0.961534i \(0.411426\pi\)
\(110\) 1614.91 + 498.134i 0.0127253 + 0.00392523i
\(111\) 24128.1 61477.3i 0.185872 0.473595i
\(112\) −180281. 122913.i −1.35801 0.925877i
\(113\) 177088. 85281.1i 1.30465 0.628285i 0.353041 0.935608i \(-0.385147\pi\)
0.951605 + 0.307323i \(0.0994332\pi\)
\(114\) −3640.63 + 3378.01i −0.0262370 + 0.0243444i
\(115\) −28540.2 4301.75i −0.201239 0.0303320i
\(116\) −8882.14 118524.i −0.0612876 0.817826i
\(117\) 22329.6 + 56894.8i 0.150805 + 0.384245i
\(118\) 24570.8 107652.i 0.162448 0.711731i
\(119\) 18323.1 244505.i 0.118613 1.58278i
\(120\) 3254.31 1003.82i 0.0206303 0.00636361i
\(121\) 144505. + 69589.9i 0.897261 + 0.432098i
\(122\) −21379.7 37030.8i −0.130048 0.225249i
\(123\) 80215.4 138937.i 0.478074 0.828049i
\(124\) −133097. + 90744.1i −0.777347 + 0.529986i
\(125\) 10943.3 + 47945.8i 0.0626432 + 0.274458i
\(126\) −185730. + 27994.3i −1.04221 + 0.157088i
\(127\) 198171. 248499.i 1.09026 1.36715i 0.165672 0.986181i \(-0.447021\pi\)
0.924590 0.380964i \(-0.124408\pi\)
\(128\) 70522.7 0.380456
\(129\) −123906. + 83742.9i −0.655567 + 0.443071i
\(130\) 44159.0 0.229172
\(131\) −159728. + 200293.i −0.813211 + 1.01973i 0.186097 + 0.982531i \(0.440416\pi\)
−0.999308 + 0.0372025i \(0.988155\pi\)
\(132\) −11368.0 + 1713.44i −0.0567868 + 0.00855923i
\(133\) −2715.49 11897.3i −0.0133113 0.0583204i
\(134\) 71306.0 48615.6i 0.343055 0.233891i
\(135\) −16366.9 + 28348.3i −0.0772916 + 0.133873i
\(136\) 17012.8 + 29467.0i 0.0788729 + 0.136612i
\(137\) 281512. + 135569.i 1.28143 + 0.617105i 0.945757 0.324874i \(-0.105322\pi\)
0.335673 + 0.941978i \(0.391036\pi\)
\(138\) 353441. 109022.i 1.57986 0.487323i
\(139\) 29858.0 398428.i 0.131076 1.74909i −0.413611 0.910454i \(-0.635733\pi\)
0.544688 0.838639i \(-0.316648\pi\)
\(140\) −16029.7 + 70230.8i −0.0691203 + 0.302836i
\(141\) 31195.6 + 79485.2i 0.132144 + 0.336696i
\(142\) 9068.51 + 121011.i 0.0377411 + 0.503620i
\(143\) −17123.1 2580.89i −0.0700232 0.0105543i
\(144\) −58062.8 + 53874.4i −0.233341 + 0.216509i
\(145\) 23510.6 11322.1i 0.0928633 0.0447206i
\(146\) 61313.4 + 41802.8i 0.238053 + 0.162302i
\(147\) −206586. + 526373.i −0.788511 + 2.00909i
\(148\) −185246. 57140.8i −0.695175 0.214433i
\(149\) −141521. 131312.i −0.522222 0.484551i 0.374450 0.927247i \(-0.377832\pi\)
−0.896672 + 0.442696i \(0.854022\pi\)
\(150\) −194463. 243849.i −0.705682 0.884897i
\(151\) 54392.7 + 68206.3i 0.194133 + 0.243435i 0.869365 0.494170i \(-0.164528\pi\)
−0.675232 + 0.737605i \(0.735957\pi\)
\(152\) 1241.40 + 1151.86i 0.00435817 + 0.00404379i
\(153\) −85052.6 26235.2i −0.293737 0.0906059i
\(154\) 19441.8 49537.0i 0.0660595 0.168317i
\(155\) −29221.4 19922.8i −0.0976949 0.0666072i
\(156\) −270647. + 130337.i −0.890415 + 0.428801i
\(157\) −322671. + 299395.i −1.04475 + 0.969383i −0.999562 0.0295960i \(-0.990578\pi\)
−0.0451841 + 0.998979i \(0.514387\pi\)
\(158\) 16411.8 + 2473.68i 0.0523014 + 0.00788317i
\(159\) −27512.4 367128.i −0.0863050 1.15166i
\(160\) 24135.3 + 61495.7i 0.0745337 + 0.189909i
\(161\) −202237. + 886057.i −0.614887 + 2.69400i
\(162\) 17721.1 236472.i 0.0530522 0.707933i
\(163\) 77605.7 23938.2i 0.228783 0.0705703i −0.178244 0.983986i \(-0.557042\pi\)
0.407027 + 0.913416i \(0.366565\pi\)
\(164\) −424286. 204325.i −1.23182 0.593216i
\(165\) −1262.01 2185.86i −0.00360871 0.00625048i
\(166\) −398367. + 689992.i −1.12205 + 1.94345i
\(167\) 352465. 240306.i 0.977968 0.666767i 0.0349078 0.999391i \(-0.488886\pi\)
0.943060 + 0.332624i \(0.107934\pi\)
\(168\) −23862.7 104549.i −0.0652299 0.285791i
\(169\) −80274.7 + 12099.5i −0.216203 + 0.0325874i
\(170\) −40095.0 + 50277.5i −0.106406 + 0.133429i
\(171\) −4429.93 −0.0115853
\(172\) 272308. + 344321.i 0.701841 + 0.887446i
\(173\) −166882. −0.423930 −0.211965 0.977277i \(-0.567986\pi\)
−0.211965 + 0.977277i \(0.567986\pi\)
\(174\) −208498. + 261448.i −0.522070 + 0.654655i
\(175\) 757819. 114223.i 1.87055 0.281941i
\(176\) −4993.59 21878.3i −0.0121515 0.0532393i
\(177\) −136258. + 92898.9i −0.326910 + 0.222883i
\(178\) −41083.2 + 71158.2i −0.0971884 + 0.168335i
\(179\) −18296.4 31690.3i −0.0426808 0.0739254i 0.843896 0.536507i \(-0.180257\pi\)
−0.886577 + 0.462582i \(0.846923\pi\)
\(180\) 23560.5 + 11346.1i 0.0542005 + 0.0261016i
\(181\) 546388. 168538.i 1.23967 0.382387i 0.395499 0.918466i \(-0.370572\pi\)
0.844167 + 0.536080i \(0.180095\pi\)
\(182\) 103913. 1.38662e6i 0.232536 3.10297i
\(183\) −14210.5 + 62260.4i −0.0313677 + 0.137431i
\(184\) −46077.5 117404.i −0.100333 0.255645i
\(185\) −3180.63 42442.5i −0.00683256 0.0911741i
\(186\) 448162. + 67549.6i 0.949846 + 0.143166i
\(187\) 18485.7 17152.3i 0.0386574 0.0358688i
\(188\) 225822. 108750.i 0.465984 0.224406i
\(189\) 851640. + 580638.i 1.73421 + 1.18236i
\(190\) −1169.32 + 2979.37i −0.00234990 + 0.00598744i
\(191\) −562079. 173378.i −1.11484 0.343884i −0.318013 0.948086i \(-0.603016\pi\)
−0.796831 + 0.604202i \(0.793492\pi\)
\(192\) −368372. 341799.i −0.721162 0.669141i
\(193\) −516195. 647288.i −0.997517 1.25085i −0.967913 0.251285i \(-0.919147\pi\)
−0.0296039 0.999562i \(-0.509425\pi\)
\(194\) 511546. + 641458.i 0.975844 + 1.22367i
\(195\) −48346.0 44858.6i −0.0910488 0.0844810i
\(196\) 1.58609e6 + 489244.i 2.94908 + 0.909672i
\(197\) −325737. + 829965.i −0.598001 + 1.52368i 0.235906 + 0.971776i \(0.424194\pi\)
−0.833907 + 0.551905i \(0.813901\pi\)
\(198\) −15961.2 10882.1i −0.0289335 0.0197265i
\(199\) 125558. 60465.6i 0.224756 0.108237i −0.318117 0.948051i \(-0.603051\pi\)
0.542874 + 0.839814i \(0.317336\pi\)
\(200\) −77961.4 + 72337.6i −0.137818 + 0.127876i
\(201\) −127453. 19210.4i −0.222515 0.0335388i
\(202\) −67416.9 899616.i −0.116249 1.55124i
\(203\) −300197. 764890.i −0.511289 1.30274i
\(204\) 97343.5 426490.i 0.163769 0.717519i
\(205\) 7726.39 103101.i 0.0128408 0.171348i
\(206\) 708206. 218453.i 1.16276 0.358665i
\(207\) 297248. + 143147.i 0.482162 + 0.232197i
\(208\) −293188. 507816.i −0.469880 0.813856i
\(209\) 627.546 1086.94i 0.000993756 0.00172124i
\(210\) 167460. 114172.i 0.262037 0.178654i
\(211\) −38940.8 170611.i −0.0602141 0.263815i 0.935856 0.352382i \(-0.114628\pi\)
−0.996070 + 0.0885671i \(0.971771\pi\)
\(212\) −1.06860e6 + 161066.i −1.63296 + 0.246130i
\(213\) 113000. 141697.i 0.170658 0.213999i
\(214\) −128652. −0.192035
\(215\) −48527.8 + 83270.4i −0.0715970 + 0.122855i
\(216\) −143038. −0.208602
\(217\) −694350. + 870688.i −1.00099 + 1.25520i
\(218\) −1.73293e6 + 261198.i −2.46968 + 0.372245i
\(219\) −24662.0 108051.i −0.0347470 0.152237i
\(220\) −6121.51 + 4173.58i −0.00852711 + 0.00581369i
\(221\) 329463. 570646.i 0.453759 0.785934i
\(222\) 272712. + 472352.i 0.371383 + 0.643255i
\(223\) −1.06027e6 510600.i −1.42776 0.687573i −0.449181 0.893441i \(-0.648284\pi\)
−0.978580 + 0.205867i \(0.933998\pi\)
\(224\) 1.98779e6 613153.i 2.64699 0.816487i
\(225\) 20790.2 277426.i 0.0273781 0.365335i
\(226\) −361211. + 1.58257e6i −0.470424 + 2.06106i
\(227\) −81706.1 208184.i −0.105242 0.268153i 0.868546 0.495608i \(-0.165055\pi\)
−0.973789 + 0.227455i \(0.926959\pi\)
\(228\) −1627.06 21711.7i −0.00207285 0.0276603i
\(229\) −1.28550e6 193758.i −1.61988 0.244158i −0.724439 0.689339i \(-0.757901\pi\)
−0.895441 + 0.445181i \(0.853139\pi\)
\(230\) 174735. 162131.i 0.217802 0.202091i
\(231\) −71607.1 + 34484.1i −0.0882929 + 0.0425196i
\(232\) 94213.9 + 64234.0i 0.114920 + 0.0783510i
\(233\) −234599. + 597749.i −0.283098 + 0.721321i 0.716618 + 0.697466i \(0.245689\pi\)
−0.999715 + 0.0238551i \(0.992406\pi\)
\(234\) −482344. 148783.i −0.575860 0.177629i
\(235\) 40338.8 + 37428.9i 0.0476490 + 0.0442118i
\(236\) 301818. + 378468.i 0.352749 + 0.442333i
\(237\) −15455.1 19380.0i −0.0178731 0.0224122i
\(238\) 1.48439e6 + 1.37732e6i 1.69866 + 1.57613i
\(239\) 1.28469e6 + 396275.i 1.45480 + 0.448748i 0.918549 0.395308i \(-0.129362\pi\)
0.536255 + 0.844056i \(0.319838\pi\)
\(240\) 31225.3 79560.7i 0.0349927 0.0891601i
\(241\) −690792. 470974.i −0.766134 0.522342i 0.116051 0.993243i \(-0.462976\pi\)
−0.882186 + 0.470902i \(0.843929\pi\)
\(242\) −1.19342e6 + 574721.i −1.30995 + 0.630839i
\(243\) 473925. 439738.i 0.514866 0.477726i
\(244\) 185363. + 27938.9i 0.199318 + 0.0300424i
\(245\) 27232.7 + 363396.i 0.0289852 + 0.386780i
\(246\) 484058. + 1.23336e6i 0.509987 + 1.29943i
\(247\) 7297.60 31972.9i 0.00761093 0.0333457i
\(248\) 11549.0 154111.i 0.0119239 0.159113i
\(249\) 1.13706e6 350738.i 1.16221 0.358496i
\(250\) −365931. 176223.i −0.370296 0.178325i
\(251\) −714764. 1.23801e6i −0.716108 1.24034i −0.962531 0.271173i \(-0.912589\pi\)
0.246423 0.969162i \(-0.420745\pi\)
\(252\) 411717. 713114.i 0.408411 0.707388i
\(253\) −77231.3 + 52655.4i −0.0758563 + 0.0517180i
\(254\) 584107. + 2.55914e6i 0.568078 + 2.48891i
\(255\) 94970.8 14314.5i 0.0914618 0.0137856i
\(256\) 449718. 563929.i 0.428885 0.537805i
\(257\) 1.20516e6 1.13818 0.569092 0.822274i \(-0.307295\pi\)
0.569092 + 0.822274i \(0.307295\pi\)
\(258\) 97296.5 1.23126e6i 0.0910013 1.15159i
\(259\) −1.34020e6 −1.24143
\(260\) −120703. + 151356.i −0.110735 + 0.138857i
\(261\) −294951. + 44456.7i −0.268009 + 0.0403958i
\(262\) −470797. 2.06270e6i −0.423721 1.85644i
\(263\) 289409. 197316.i 0.258002 0.175903i −0.427411 0.904058i \(-0.640574\pi\)
0.685413 + 0.728155i \(0.259622\pi\)
\(264\) 5514.65 9551.65i 0.00486976 0.00843468i
\(265\) −118630. 205474.i −0.103772 0.179739i
\(266\) 90802.5 + 43728.2i 0.0786853 + 0.0378928i
\(267\) 117264. 36171.2i 0.100667 0.0310517i
\(268\) −28273.8 + 377287.i −0.0240462 + 0.320875i
\(269\) 78156.3 342425.i 0.0658542 0.288526i −0.931268 0.364334i \(-0.881297\pi\)
0.997122 + 0.0758083i \(0.0241537\pi\)
\(270\) −98765.7 251651.i −0.0824512 0.210082i
\(271\) 43659.8 + 582599.i 0.0361126 + 0.481889i 0.985714 + 0.168428i \(0.0538692\pi\)
−0.949601 + 0.313460i \(0.898512\pi\)
\(272\) 844383. + 127270.i 0.692018 + 0.104305i
\(273\) −1.52235e6 + 1.41253e6i −1.23625 + 1.14708i
\(274\) −2.32492e6 + 1.11962e6i −1.87082 + 0.900937i
\(275\) 65125.0 + 44401.5i 0.0519297 + 0.0354051i
\(276\) −592407. + 1.50943e6i −0.468109 + 1.19272i
\(277\) −734808. 226658.i −0.575406 0.177489i −0.00662496 0.999978i \(-0.502109\pi\)
−0.568781 + 0.822489i \(0.692585\pi\)
\(278\) 2.41886e6 + 2.24438e6i 1.87715 + 1.74174i
\(279\) 252057. + 316069.i 0.193860 + 0.243093i
\(280\) −43089.5 54032.5i −0.0328455 0.0411870i
\(281\) 1.81892e6 + 1.68771e6i 1.37420 + 1.27507i 0.924134 + 0.382069i \(0.124789\pi\)
0.450062 + 0.892997i \(0.351402\pi\)
\(282\) −673860. 207858.i −0.504600 0.155648i
\(283\) 681715. 1.73698e6i 0.505984 1.28923i −0.418574 0.908183i \(-0.637470\pi\)
0.924558 0.381043i \(-0.124435\pi\)
\(284\) −439556. 299684.i −0.323384 0.220479i
\(285\) 4306.77 2074.03i 0.00314079 0.00151253i
\(286\) 104835. 97272.6i 0.0757863 0.0703194i
\(287\) −3.21926e6 485226.i −2.30702 0.347728i
\(288\) −56431.7 753029.i −0.0400906 0.534971i
\(289\) −168161. 428466.i −0.118435 0.301767i
\(290\) −47955.2 + 210106.i −0.0334843 + 0.146704i
\(291\) 91571.0 1.22193e6i 0.0633907 0.845890i
\(292\) −310872. + 95891.4i −0.213366 + 0.0658146i
\(293\) 767277. + 369501.i 0.522136 + 0.251447i 0.676337 0.736592i \(-0.263566\pi\)
−0.154202 + 0.988039i \(0.549281\pi\)
\(294\) −2.33498e6 4.04431e6i −1.57549 2.72883i
\(295\) −53139.6 + 92040.5i −0.0355520 + 0.0615778i
\(296\) 153666. 104768.i 0.101941 0.0695021i
\(297\) 23589.6 + 103353.i 0.0155177 + 0.0679877i
\(298\) 1.57659e6 237633.i 1.02844 0.155012i
\(299\) −1.52283e6 + 1.90957e6i −0.985083 + 1.23526i
\(300\) 1.36734e6 0.877148
\(301\) 2.50054e6 + 1.71975e6i 1.59081 + 1.09408i
\(302\) −720481. −0.454574
\(303\) −840060. + 1.05340e6i −0.525658 + 0.659155i
\(304\) 42025.5 6334.32i 0.0260813 0.00393112i
\(305\) 9158.05 + 40124.0i 0.00563707 + 0.0246976i
\(306\) 607352. 414085.i 0.370797 0.252805i
\(307\) 682383. 1.18192e6i 0.413221 0.715720i −0.582019 0.813175i \(-0.697737\pi\)
0.995240 + 0.0974553i \(0.0310703\pi\)
\(308\) 116648. + 202040.i 0.0700648 + 0.121356i
\(309\) −997271. 480260.i −0.594178 0.286141i
\(310\) 279107. 86093.0i 0.164955 0.0508819i
\(311\) 210.375 2807.26i 0.000123337 0.00164581i −0.997142 0.0755530i \(-0.975928\pi\)
0.997265 + 0.0739072i \(0.0235468\pi\)
\(312\) 64128.7 280966.i 0.0372963 0.163406i
\(313\) −376231. 958622.i −0.217067 0.553078i 0.780315 0.625387i \(-0.215059\pi\)
−0.997382 + 0.0723083i \(0.976963\pi\)
\(314\) −271664. 3.62510e6i −0.155492 2.07489i
\(315\) 178765. + 26944.5i 0.101509 + 0.0153001i
\(316\) −53338.0 + 49490.5i −0.0300483 + 0.0278807i
\(317\) 1.42787e6 687625.i 0.798068 0.384329i 0.0100250 0.999950i \(-0.496809\pi\)
0.788043 + 0.615621i \(0.211095\pi\)
\(318\) 2.51217e6 + 1.71277e6i 1.39310 + 0.949799i
\(319\) 30874.8 78667.8i 0.0169874 0.0432833i
\(320\) −309463. 95456.6i −0.168940 0.0521112i
\(321\) 140850. + 130690.i 0.0762949 + 0.0707913i
\(322\) −4.67982e6 5.86831e6i −2.51530 3.15409i
\(323\) 29777.0 + 37339.1i 0.0158809 + 0.0199140i
\(324\) 762076. + 707103.i 0.403307 + 0.374214i
\(325\) 1.96807e6 + 607068.i 1.03355 + 0.318808i
\(326\) −245041. + 624355.i −0.127701 + 0.325377i
\(327\) 2.16258e6 + 1.47442e6i 1.11842 + 0.762523i
\(328\) 407048. 196024.i 0.208911 0.100606i
\(329\) 1.27021e6 1.17859e6i 0.646974 0.600304i
\(330\) 20612.2 + 3106.80i 0.0104193 + 0.00157046i
\(331\) 206399. + 2.75421e6i 0.103547 + 1.38174i 0.770880 + 0.636981i \(0.219817\pi\)
−0.667333 + 0.744760i \(0.732564\pi\)
\(332\) −1.27609e6 3.25142e6i −0.635382 1.61893i
\(333\) −108258. + 474311.i −0.0534996 + 0.234397i
\(334\) −263279. + 3.51322e6i −0.129137 + 1.72321i
\(335\) −79375.1 + 24484.0i −0.0386431 + 0.0119198i
\(336\) −2.42477e6 1.16771e6i −1.17172 0.564270i
\(337\) 513722. + 889792.i 0.246407 + 0.426790i 0.962526 0.271188i \(-0.0874167\pi\)
−0.716119 + 0.697978i \(0.754083\pi\)
\(338\) 335226. 580629.i 0.159605 0.276444i
\(339\) 2.00310e6 1.36569e6i 0.946681 0.645436i
\(340\) −62733.6 274854.i −0.0294308 0.128945i
\(341\) −113258. + 17070.9i −0.0527453 + 0.00795007i
\(342\) 22810.6 28603.6i 0.0105456 0.0132238i
\(343\) 7.26809e6 3.33568
\(344\) −421147. 1709.21i −0.191884 0.000778751i
\(345\) −356003. −0.161030
\(346\) 859310. 1.07754e6i 0.385886 0.483886i
\(347\) 1.52354e6 229637.i 0.679251 0.102381i 0.199650 0.979867i \(-0.436019\pi\)
0.479601 + 0.877487i \(0.340781\pi\)
\(348\) −326220. 1.42926e6i −0.144399 0.632652i
\(349\) −1.27844e6 + 871622.i −0.561843 + 0.383058i −0.810682 0.585487i \(-0.800903\pi\)
0.248839 + 0.968545i \(0.419951\pi\)
\(350\) −3.16464e6 + 5.48132e6i −1.38087 + 2.39175i
\(351\) 1.38501e6 + 2.39891e6i 0.600047 + 1.03931i
\(352\) 192760. + 92828.1i 0.0829200 + 0.0399322i
\(353\) −2.52656e6 + 779341.i −1.07918 + 0.332882i −0.782854 0.622205i \(-0.786237\pi\)
−0.296324 + 0.955088i \(0.595761\pi\)
\(354\) 101780. 1.35816e6i 0.0431672 0.576026i
\(355\) 25990.3 113871.i 0.0109456 0.0479559i
\(356\) −131601. 335315.i −0.0550346 0.140226i
\(357\) −226005. 3.01582e6i −0.0938527 1.25238i
\(358\) 298833. + 45041.8i 0.123231 + 0.0185741i
\(359\) −1.91046e6 + 1.77265e6i −0.782351 + 0.725915i −0.966412 0.257000i \(-0.917266\pi\)
0.184061 + 0.982915i \(0.441076\pi\)
\(360\) −22603.3 + 10885.2i −0.00919212 + 0.00442669i
\(361\) −2.04389e6 1.39350e6i −0.825446 0.562779i
\(362\) −1.72523e6 + 4.39581e6i −0.691951 + 1.76306i
\(363\) 1.89040e6 + 583112.i 0.752988 + 0.232266i
\(364\) 4.46864e6 + 4.14629e6i 1.76775 + 1.64024i
\(365\) −44532.8 55842.3i −0.0174964 0.0219397i
\(366\) −328836. 412347.i −0.128315 0.160902i
\(367\) 403488. + 374382.i 0.156374 + 0.145094i 0.754480 0.656323i \(-0.227889\pi\)
−0.598106 + 0.801417i \(0.704080\pi\)
\(368\) −3.02459e6 932963.i −1.16425 0.359124i
\(369\) −431771. + 1.10013e6i −0.165077 + 0.420610i
\(370\) 290425. + 198008.i 0.110288 + 0.0751932i
\(371\) −6.73116e6 + 3.24156e6i −2.53896 + 1.22270i
\(372\) −1.45652e6 + 1.35145e6i −0.545706 + 0.506341i
\(373\) −1.13621e6 171257.i −0.422852 0.0637346i −0.0658302 0.997831i \(-0.520970\pi\)
−0.357021 + 0.934096i \(0.616208\pi\)
\(374\) 15563.5 + 207681.i 0.00575347 + 0.0767747i
\(375\) 221613. + 564660.i 0.0813798 + 0.207352i
\(376\) −53507.5 + 234432.i −0.0195184 + 0.0855158i
\(377\) 165020. 2.20203e6i 0.0597974 0.797941i
\(378\) −8.13439e6 + 2.50913e6i −2.92817 + 0.903220i
\(379\) −2.61113e6 1.25745e6i −0.933748 0.449669i −0.0957884 0.995402i \(-0.530537\pi\)
−0.837959 + 0.545732i \(0.816252\pi\)
\(380\) −7015.72 12151.6i −0.00249237 0.00431692i
\(381\) 1.96019e6 3.39515e6i 0.691809 1.19825i
\(382\) 4.01375e6 2.73653e6i 1.40732 0.959492i
\(383\) −213696. 936264.i −0.0744389 0.326138i 0.923974 0.382455i \(-0.124921\pi\)
−0.998413 + 0.0563171i \(0.982064\pi\)
\(384\) 860140. 129645.i 0.297674 0.0448671i
\(385\) −31935.1 + 40045.4i −0.0109804 + 0.0137689i
\(386\) 6.83746e6 2.33575
\(387\) 810624. 746050.i 0.275133 0.253216i
\(388\) −3.59686e6 −1.21295
\(389\) −1.52993e6 + 1.91847e6i −0.512623 + 0.642809i −0.969024 0.246965i \(-0.920567\pi\)
0.456402 + 0.889774i \(0.349138\pi\)
\(390\) 538591. 81179.5i 0.179307 0.0270262i
\(391\) −791470. 3.46766e6i −0.261814 1.14708i
\(392\) −1.31570e6 + 897029.i −0.432456 + 0.294843i
\(393\) −1.57994e6 + 2.73653e6i −0.516011 + 0.893757i
\(394\) −3.68171e6 6.37691e6i −1.19484 2.06952i
\(395\) −14392.8 6931.19i −0.00464143 0.00223519i
\(396\) 80926.5 24962.5i 0.0259330 0.00799927i
\(397\) 233856. 3.12060e6i 0.0744686 0.993714i −0.827375 0.561650i \(-0.810167\pi\)
0.901843 0.432064i \(-0.142214\pi\)
\(398\) −256104. + 1.12207e6i −0.0810417 + 0.355067i
\(399\) −54991.3 140115.i −0.0172926 0.0440609i
\(400\) 199459. + 2.66159e6i 0.0623308 + 0.831747i
\(401\) 30117.3 + 4539.45i 0.00935309 + 0.00140975i 0.153717 0.988115i \(-0.450876\pi\)
−0.144364 + 0.989525i \(0.546114\pi\)
\(402\) 780321. 724032.i 0.240829 0.223456i
\(403\) −2.69644e6 + 1.29854e6i −0.827044 + 0.398283i
\(404\) 3.26774e6 + 2.22791e6i 0.996079 + 0.679115i
\(405\) −83386.2 + 212465.i −0.0252614 + 0.0643649i
\(406\) 6.48459e6 + 2.00023e6i 1.95239 + 0.602234i
\(407\) −101042. 93753.7i −0.0302355 0.0280545i
\(408\) 261669. + 328123.i 0.0778220 + 0.0975857i
\(409\) 1.95683e6 + 2.45379e6i 0.578422 + 0.725318i 0.981843 0.189696i \(-0.0607504\pi\)
−0.403421 + 0.915015i \(0.632179\pi\)
\(410\) 625931. + 580779.i 0.183894 + 0.170628i
\(411\) 3.68272e6 + 1.13597e6i 1.07539 + 0.331712i
\(412\) −1.18703e6 + 3.02451e6i −0.344524 + 0.877833i
\(413\) 2.76508e6 + 1.88520e6i 0.797687 + 0.543854i
\(414\) −2.45488e6 + 1.18221e6i −0.703929 + 0.338994i
\(415\) 562145. 521595.i 0.160224 0.148666i
\(416\) 5.52792e6 + 833200.i 1.56613 + 0.236057i
\(417\) −368281. 4.91437e6i −0.103714 1.38397i
\(418\) 3786.91 + 9648.89i 0.00106009 + 0.00270107i
\(419\) 1.57331e6 6.89314e6i 0.437805 1.91815i 0.0437962 0.999040i \(-0.486055\pi\)
0.394008 0.919107i \(-0.371088\pi\)
\(420\) −66400.1 + 886047.i −0.0183673 + 0.245095i
\(421\) 439740. 135642.i 0.120918 0.0372982i −0.233706 0.972307i \(-0.575085\pi\)
0.354624 + 0.935009i \(0.384609\pi\)
\(422\) 1.30213e6 + 627073.i 0.355937 + 0.171410i
\(423\) −314508. 544744.i −0.0854636 0.148027i
\(424\) 518384. 897867.i 0.140035 0.242548i
\(425\) −2.47813e6 + 1.68956e6i −0.665505 + 0.453733i
\(426\) 333065. + 1.45925e6i 0.0889212 + 0.389589i
\(427\) 1.28147e6 193150.i 0.340125 0.0512655i
\(428\) 351652. 440958.i 0.0927906 0.116356i
\(429\) −213589. −0.0560319
\(430\) −287789. 742116.i −0.0750590 0.193553i
\(431\) −119786. −0.0310607 −0.0155304 0.999879i \(-0.504944\pi\)
−0.0155304 + 0.999879i \(0.504944\pi\)
\(432\) −2.23817e6 + 2.80658e6i −0.577011 + 0.723549i
\(433\) −1.62208e6 + 244489.i −0.415770 + 0.0626672i −0.353596 0.935398i \(-0.615041\pi\)
−0.0621734 + 0.998065i \(0.519803\pi\)
\(434\) −2.04659e6 8.96670e6i −0.521563 2.28512i
\(435\) 265937. 181312.i 0.0673837 0.0459414i
\(436\) 3.84148e6 6.65363e6i 0.967792 1.67626i
\(437\) −88512.9 153309.i −0.0221719 0.0384029i
\(438\) 824666. + 397138.i 0.205396 + 0.0989137i
\(439\) −723455. + 223156.i −0.179164 + 0.0552647i −0.383039 0.923732i \(-0.625122\pi\)
0.203875 + 0.978997i \(0.434646\pi\)
\(440\) 531.173 7088.01i 0.000130799 0.00174539i
\(441\) 926916. 4.06108e6i 0.226957 0.994364i
\(442\) 1.98813e6 + 5.06568e6i 0.484049 + 1.23334i
\(443\) −159339. 2.12623e6i −0.0385756 0.514756i −0.982705 0.185180i \(-0.940713\pi\)
0.944129 0.329576i \(-0.106906\pi\)
\(444\) −2.36442e6 356379.i −0.569203 0.0857936i
\(445\) 57973.5 53791.5i 0.0138781 0.0128770i
\(446\) 8.75646e6 4.21689e6i 2.08445 1.00382i
\(447\) −1.96748e6 1.34140e6i −0.465737 0.317534i
\(448\) −3.72560e6 + 9.49268e6i −0.877004 + 2.23457i
\(449\) −6.42171e6 1.98084e6i −1.50326 0.463695i −0.569623 0.821906i \(-0.692911\pi\)
−0.933641 + 0.358211i \(0.883387\pi\)
\(450\) 1.68426e6 + 1.56276e6i 0.392083 + 0.363800i
\(451\) −208767. 261786.i −0.0483305 0.0606045i
\(452\) −4.43698e6 5.56380e6i −1.02151 1.28093i
\(453\) 788795. + 731895.i 0.180600 + 0.167573i
\(454\) 1.76494e6 + 544413.i 0.401875 + 0.123962i
\(455\) −488958. + 1.24584e6i −0.110724 + 0.282121i
\(456\) 17258.5 + 11766.6i 0.00388678 + 0.00264996i
\(457\) 7.33422e6 3.53197e6i 1.64272 0.791092i 0.643039 0.765834i \(-0.277673\pi\)
0.999681 0.0252585i \(-0.00804089\pi\)
\(458\) 7.87037e6 7.30263e6i 1.75320 1.62673i
\(459\) −3.98884e6 601221.i −0.883721 0.133199i
\(460\) 78092.6 + 1.04207e6i 0.0172074 + 0.229617i
\(461\) 1.54005e6 + 3.92399e6i 0.337507 + 0.859955i 0.994372 + 0.105946i \(0.0337872\pi\)
−0.656864 + 0.754009i \(0.728118\pi\)
\(462\) 146059. 639926.i 0.0318363 0.139484i
\(463\) 156601. 2.08969e6i 0.0339502 0.453034i −0.954161 0.299293i \(-0.903249\pi\)
0.988111 0.153740i \(-0.0491319\pi\)
\(464\) 2.73455e6 843496.i 0.589645 0.181881i
\(465\) −393028. 189272.i −0.0842929 0.0405933i
\(466\) −2.65160e6 4.59271e6i −0.565645 0.979726i
\(467\) −4.34457e6 + 7.52502e6i −0.921838 + 1.59667i −0.125269 + 0.992123i \(0.539979\pi\)
−0.796569 + 0.604547i \(0.793354\pi\)
\(468\) 1.82838e6 1.24657e6i 0.385879 0.263088i
\(469\) 582030. + 2.55004e6i 0.122184 + 0.535322i
\(470\) −449388. + 67734.3i −0.0938375 + 0.0141437i
\(471\) −3.38511e6 + 4.24479e6i −0.703105 + 0.881666i
\(472\) −464412. −0.0959508
\(473\) 68219.7 + 304583.i 0.0140203 + 0.0625969i
\(474\) 204716. 0.0418511
\(475\) −93072.3 + 116709.i −0.0189272 + 0.0237340i
\(476\) −8.77818e6 + 1.32310e6i −1.77577 + 0.267655i
\(477\) 603491. + 2.64407e6i 0.121444 + 0.532080i
\(478\) −9.17386e6 + 6.25463e6i −1.83646 + 1.25208i
\(479\) 2.89279e6 5.01046e6i 0.576073 0.997788i −0.419851 0.907593i \(-0.637918\pi\)
0.995924 0.0901952i \(-0.0287491\pi\)
\(480\) 407420. + 705672.i 0.0807122 + 0.139798i
\(481\) −3.24499e6 1.56270e6i −0.639514 0.307974i
\(482\) 6.59807e6 2.03523e6i 1.29360 0.399022i
\(483\) −837728. + 1.11787e7i −0.163394 + 2.18034i
\(484\) 1.29218e6 5.66140e6i 0.250732 1.09853i
\(485\) −288505. 735100.i −0.0556929 0.141903i
\(486\) 399008. + 5.32439e6i 0.0766286 + 1.02254i
\(487\) −5.79390e6 873290.i −1.10700 0.166854i −0.429996 0.902831i \(-0.641485\pi\)
−0.677006 + 0.735977i \(0.736723\pi\)
\(488\) −131832. + 122323.i −0.0250595 + 0.0232518i
\(489\) 902522. 434632.i 0.170681 0.0821957i
\(490\) −2.48664e6 1.69536e6i −0.467867 0.318986i
\(491\) 258432. 658473.i 0.0483773 0.123263i −0.904643 0.426171i \(-0.859862\pi\)
0.953020 + 0.302908i \(0.0979574\pi\)
\(492\) −5.55048e6 1.71210e6i −1.03376 0.318871i
\(493\) 2.35731e6 + 2.18726e6i 0.436817 + 0.405307i
\(494\) 168869. + 211755.i 0.0311338 + 0.0390406i
\(495\) 11592.8 + 14536.9i 0.00212655 + 0.00266661i
\(496\) −2.84314e6 2.63804e6i −0.518912 0.481480i
\(497\) −3.51446e6 1.08407e6i −0.638215 0.196863i
\(498\) −3.59030e6 + 9.14792e6i −0.648719 + 1.65291i
\(499\) 2.95878e6 + 2.01726e6i 0.531937 + 0.362669i 0.799305 0.600926i \(-0.205201\pi\)
−0.267367 + 0.963595i \(0.586154\pi\)
\(500\) 1.60423e6 772557.i 0.286974 0.138199i
\(501\) 3.85712e6 3.57888e6i 0.686544 0.637020i
\(502\) 1.16742e7 + 1.75960e6i 2.06760 + 0.311640i
\(503\) −151364. 2.01982e6i −0.0266749 0.355952i −0.994531 0.104446i \(-0.966693\pi\)
0.967856 0.251506i \(-0.0809259\pi\)
\(504\) 288612. + 735371.i 0.0506102 + 0.128953i
\(505\) −193217. + 846538.i −0.0337145 + 0.147713i
\(506\) 57689.1 769808.i 0.0100165 0.133661i
\(507\) −956839. + 295146.i −0.165318 + 0.0509937i
\(508\) −1.03681e7 4.99302e6i −1.78254 0.858428i
\(509\) 296417. + 513409.i 0.0507118 + 0.0878353i 0.890267 0.455439i \(-0.150518\pi\)
−0.839555 + 0.543274i \(0.817184\pi\)
\(510\) −396597. + 686926.i −0.0675186 + 0.116946i
\(511\) −1.85827e6 + 1.26695e6i −0.314816 + 0.214638i
\(512\) 1.82771e6 + 8.00772e6i 0.308129 + 1.35000i
\(513\) −198527. + 29923.2i −0.0333063 + 0.00502012i
\(514\) −6.20563e6 + 7.78161e6i −1.03604 + 1.29916i
\(515\) −713339. −0.118516
\(516\) 3.95422e6 + 3.69896e6i 0.653787 + 0.611582i
\(517\) 178213. 0.0293234
\(518\) 6.90098e6 8.65356e6i 1.13002 1.41700i
\(519\) −2.03540e6 + 306787.i −0.331689 + 0.0499941i
\(520\) −41328.1 181070.i −0.00670250 0.0293656i
\(521\) −5.33008e6 + 3.63399e6i −0.860279 + 0.586529i −0.911103 0.412179i \(-0.864768\pi\)
0.0508235 + 0.998708i \(0.483815\pi\)
\(522\) 1.23171e6 2.13339e6i 0.197848 0.342684i
\(523\) 2.31907e6 + 4.01676e6i 0.370732 + 0.642127i 0.989678 0.143306i \(-0.0457734\pi\)
−0.618946 + 0.785434i \(0.712440\pi\)
\(524\) 8.35681e6 + 4.02443e6i 1.32957 + 0.640289i
\(525\) 9.03286e6 2.78627e6i 1.43030 0.441189i
\(526\) −216179. + 2.88471e6i −0.0340682 + 0.454608i
\(527\) 969827. 4.24909e6i 0.152113 0.666453i
\(528\) −101125. 257662.i −0.0157860 0.0402222i
\(529\) 504257. + 6.72884e6i 0.0783453 + 1.04544i
\(530\) 1.93758e6 + 292043.i 0.299619 + 0.0451603i
\(531\) 890547. 826307.i 0.137063 0.127176i
\(532\) −398076. + 191703.i −0.0609799 + 0.0293664i
\(533\) −7.22890e6 4.92858e6i −1.10218 0.751457i
\(534\) −370263. + 943416.i −0.0561898 + 0.143169i
\(535\) 118326. + 36498.7i 0.0178729 + 0.00551307i
\(536\) −266079. 246885.i −0.0400036 0.0371179i
\(537\) −281412. 352880.i −0.0421121 0.0528069i
\(538\) 1.80856e6 + 2.26786e6i 0.269388 + 0.337801i
\(539\) 865132. + 802726.i 0.128266 + 0.119013i
\(540\) 1.13250e6 + 349331.i 0.167130 + 0.0515529i
\(541\) 1.27385e6 3.24572e6i 0.187122 0.476780i −0.806270 0.591548i \(-0.798517\pi\)
0.993392 + 0.114768i \(0.0366124\pi\)
\(542\) −3.98660e6 2.71802e6i −0.582913 0.397424i
\(543\) 6.35427e6 3.06005e6i 0.924839 0.445379i
\(544\) −5.96783e6 + 5.53734e6i −0.864608 + 0.802239i
\(545\) 1.66795e6 + 251403.i 0.240542 + 0.0362559i
\(546\) −1.28170e6 1.71031e7i −0.183994 2.45524i
\(547\) 3.14472e6 + 8.01261e6i 0.449380 + 1.14500i 0.958699 + 0.284423i \(0.0918021\pi\)
−0.509319 + 0.860578i \(0.670103\pi\)
\(548\) 2.51731e6 1.10291e7i 0.358084 1.56887i
\(549\) 35156.2 469126.i 0.00497818 0.0664292i
\(550\) −622038. + 191873.i −0.0876819 + 0.0270463i
\(551\) 144200. + 69443.1i 0.0202342 + 0.00974428i
\(552\) −777820. 1.34722e6i −0.108650 0.188188i
\(553\) −251512. + 435631.i −0.0349740 + 0.0605767i
\(554\) 5.24719e6 3.57747e6i 0.726361 0.495224i
\(555\) −116817. 511809.i −0.0160981 0.0705302i
\(556\) −1.43043e7 + 2.15603e6i −1.96237 + 0.295779i
\(557\) 5.60917e6 7.03367e6i 0.766056 0.960604i −0.233876 0.972266i \(-0.575141\pi\)
0.999932 + 0.0116628i \(0.00371246\pi\)
\(558\) −3.33872e6 −0.453936
\(559\) 4.04922e6 + 7.07965e6i 0.548077 + 0.958257i
\(560\) −1.73442e6 −0.233714
\(561\) 193932. 243183.i 0.0260161 0.0326232i
\(562\) −2.02634e7 + 3.05422e6i −2.70627 + 0.407905i
\(563\) 1.16640e6 + 5.11032e6i 0.155087 + 0.679481i 0.991360 + 0.131168i \(0.0418727\pi\)
−0.836273 + 0.548313i \(0.815270\pi\)
\(564\) 2.55435e6 1.74152e6i 0.338129 0.230532i
\(565\) 781197. 1.35307e6i 0.102953 0.178320i
\(566\) 7.70522e6 + 1.33458e7i 1.01098 + 1.75107i
\(567\) 6.47529e6 + 3.11834e6i 0.845866 + 0.407348i
\(568\) 487708. 150438.i 0.0634291 0.0195653i
\(569\) 414449. 5.53044e6i 0.0536649 0.716109i −0.903873 0.427801i \(-0.859288\pi\)
0.957538 0.288308i \(-0.0930926\pi\)
\(570\) −8784.63 + 38488.0i −0.00113249 + 0.00496178i
\(571\) 2.52764e6 + 6.44033e6i 0.324433 + 0.826642i 0.996298 + 0.0859684i \(0.0273984\pi\)
−0.671865 + 0.740674i \(0.734506\pi\)
\(572\) 46852.7 + 625206.i 0.00598749 + 0.0798975i
\(573\) −7.17421e6 1.08134e6i −0.912824 0.137586i
\(574\) 1.97097e7 1.82879e7i 2.49690 2.31678i
\(575\) 1.00164e7 4.82366e6i 1.26341 0.608425i
\(576\) 3.05861e6 + 2.08532e6i 0.384121 + 0.261889i
\(577\) −1.96612e6 + 5.00960e6i −0.245851 + 0.626418i −0.999525 0.0308311i \(-0.990185\pi\)
0.753674 + 0.657249i \(0.228280\pi\)
\(578\) 3.63246e6 + 1.12047e6i 0.452253 + 0.139501i
\(579\) −7.48578e6 6.94579e6i −0.927984 0.861044i
\(580\) −589064. 738663.i −0.0727097 0.0911751i
\(581\) −1.50556e7 1.88791e7i −1.85036 2.32028i
\(582\) 7.41837e6 + 6.88324e6i 0.907822 + 0.842336i
\(583\) −734247. 226485.i −0.0894686 0.0275974i
\(584\) 114026. 290534.i 0.0138348 0.0352504i
\(585\) 401420. + 273683.i 0.0484963 + 0.0330642i
\(586\) −6.33670e6 + 3.05159e6i −0.762288 + 0.367099i
\(587\) −8.34286e6 + 7.74104e6i −0.999354 + 0.927265i −0.997351 0.0727325i \(-0.976828\pi\)
−0.00200301 + 0.999998i \(0.500638\pi\)
\(588\) 2.02443e7 + 3.05134e6i 2.41468 + 0.363955i
\(589\) −16210.3 216312.i −0.00192532 0.0256917i
\(590\) −320670. 817053.i −0.0379252 0.0966318i
\(591\) −2.44713e6 + 1.07216e7i −0.288197 + 1.26267i
\(592\) 348803. 4.65445e6i 0.0409049 0.545838i
\(593\) −8.37002e6 + 2.58181e6i −0.977439 + 0.301500i −0.742008 0.670391i \(-0.766126\pi\)
−0.235431 + 0.971891i \(0.575650\pi\)
\(594\) −788805. 379868.i −0.0917283 0.0441740i
\(595\) −974507. 1.68790e6i −0.112848 0.195458i
\(596\) −3.49490e6 + 6.05334e6i −0.403013 + 0.698039i
\(597\) 1.42023e6 968296.i 0.163088 0.111192i
\(598\) −4.48852e6 1.96655e7i −0.513275 2.24881i
\(599\) −1.21156e7 + 1.82614e6i −1.37968 + 0.207953i −0.796622 0.604477i \(-0.793382\pi\)
−0.583058 + 0.812431i \(0.698144\pi\)
\(600\) −817886. + 1.02560e6i −0.0927501 + 0.116305i
\(601\) −9.99106e6 −1.12830 −0.564151 0.825672i \(-0.690796\pi\)
−0.564151 + 0.825672i \(0.690796\pi\)
\(602\) −2.39801e7 + 7.29042e6i −2.69686 + 0.819901i
\(603\) 949499. 0.106341
\(604\) 1.96934e6 2.46947e6i 0.219648 0.275430i
\(605\) 1.26068e6 190017.i 0.140029 0.0211059i
\(606\) −2.47607e6 1.08484e7i −0.273893 1.20000i
\(607\) −791583. + 539692.i −0.0872016 + 0.0594531i −0.606136 0.795361i \(-0.707281\pi\)
0.518934 + 0.854814i \(0.326329\pi\)
\(608\) −202593. + 350902.i −0.0222263 + 0.0384970i
\(609\) −5.06753e6 8.77722e6i −0.553672 0.958989i
\(610\) −306234. 147474.i −0.0333218 0.0160469i
\(611\) 4.44978e6 1.37257e6i 0.482209 0.148742i
\(612\) −240823. + 3.21356e6i −0.0259908 + 0.346823i
\(613\) 2.39500e6 1.04932e7i 0.257428 1.12786i −0.666563 0.745449i \(-0.732235\pi\)
0.923991 0.382415i \(-0.124908\pi\)
\(614\) 4.11782e6 + 1.04920e7i 0.440805 + 1.12315i
\(615\) −95300.4 1.27169e6i −0.0101603 0.135580i
\(616\) −221318. 33358.3i −0.0234998 0.00354203i
\(617\) 1.17286e7 1.08826e7i 1.24032 1.15085i 0.257505 0.966277i \(-0.417100\pi\)
0.982818 0.184575i \(-0.0590908\pi\)
\(618\) 8.23614e6 3.96632e6i 0.867466 0.417750i
\(619\) 5.73269e6 + 3.90848e6i 0.601356 + 0.409998i 0.825373 0.564587i \(-0.190965\pi\)
−0.224017 + 0.974585i \(0.571917\pi\)
\(620\) −467814. + 1.19197e6i −0.0488758 + 0.124533i
\(621\) 1.42881e7 + 4.40729e6i 1.48677 + 0.458609i
\(622\) 17042.9 + 15813.5i 0.00176631 + 0.00163890i
\(623\) −1.55266e6 1.94698e6i −0.160272 0.200975i
\(624\) −4.50944e6 5.65466e6i −0.463619 0.581360i
\(625\) −6.72740e6 6.24211e6i −0.688886 0.639192i
\(626\) 8.12702e6 + 2.50685e6i 0.828887 + 0.255678i
\(627\) 5655.77 14410.7i 0.000574544 0.00146391i
\(628\) 1.31677e7 + 8.97758e6i 1.33233 + 0.908365i
\(629\) 4.72557e6 2.27572e6i 0.476242 0.229346i
\(630\) −1.09448e6 + 1.01553e6i −0.109864 + 0.101939i
\(631\) 4.01623e6 + 605350.i 0.401555 + 0.0605247i 0.346715 0.937970i \(-0.387297\pi\)
0.0548401 + 0.998495i \(0.482535\pi\)
\(632\) −5216.57 69610.3i −0.000519508 0.00693236i
\(633\) −788588. 2.00929e6i −0.0782242 0.199312i
\(634\) −2.91246e6 + 1.27603e7i −0.287764 + 1.26078i
\(635\) 188807. 2.51945e6i 0.0185816 0.247954i
\(636\) −1.27373e7 + 3.92892e6i −1.24863 + 0.385151i
\(637\) 2.77838e7 + 1.33800e7i 2.71296 + 1.30649i
\(638\) 348969. + 604433.i 0.0339419 + 0.0587890i
\(639\) −667551. + 1.15623e6i −0.0646743 + 0.112019i
\(640\) 463175. 315788.i 0.0446988 0.0304751i
\(641\) 1.37042e6 + 6.00422e6i 0.131738 + 0.577180i 0.997105 + 0.0760415i \(0.0242282\pi\)
−0.865367 + 0.501139i \(0.832915\pi\)
\(642\) −1.56912e6 + 236507.i −0.150251 + 0.0226468i
\(643\) 5.36129e6 6.72285e6i 0.511378 0.641248i −0.457375 0.889274i \(-0.651210\pi\)
0.968753 + 0.248026i \(0.0797818\pi\)
\(644\) 3.29055e7 3.12646
\(645\) −438796. + 1.10483e6i −0.0415302 + 0.104567i
\(646\) −394423. −0.0371861
\(647\) 897546. 1.12549e6i 0.0842939 0.105701i −0.737896 0.674914i \(-0.764181\pi\)
0.822190 + 0.569213i \(0.192752\pi\)
\(648\) −986218. + 148649.i −0.0922647 + 0.0139067i
\(649\) 76589.9 + 335562.i 0.00713772 + 0.0312724i
\(650\) −1.40538e7 + 9.58169e6i −1.30469 + 0.889526i
\(651\) −6.86811e6 + 1.18959e7i −0.635162 + 1.10013i
\(652\) −1.47021e6 2.54647e6i −0.135444 0.234596i
\(653\) 5.76812e6 + 2.77778e6i 0.529360 + 0.254926i 0.679419 0.733751i \(-0.262232\pi\)
−0.150059 + 0.988677i \(0.547946\pi\)
\(654\) −2.06558e7 + 6.37147e6i −1.88842 + 0.582499i
\(655\) −152180. + 2.03071e6i −0.0138597 + 0.184945i
\(656\) 2.52301e6 1.10540e7i 0.228907 1.00291i
\(657\) 298279. + 760002.i 0.0269593 + 0.0686912i
\(658\) 1.06942e6 + 1.42704e7i 0.0962906 + 1.28491i
\(659\) 1.97270e7 + 2.97337e6i 1.76949 + 0.266707i 0.951305 0.308251i \(-0.0997437\pi\)
0.818183 + 0.574958i \(0.194982\pi\)
\(660\) −66989.4 + 62157.1i −0.00598613 + 0.00555432i
\(661\) 1.21075e7 5.83066e6i 1.07783 0.519056i 0.191208 0.981550i \(-0.438760\pi\)
0.886622 + 0.462494i \(0.153045\pi\)
\(662\) −1.88464e7 1.28493e7i −1.67141 1.13955i
\(663\) 2.96929e6 7.56563e6i 0.262343 0.668438i
\(664\) 3.20209e6 + 987712.i 0.281847 + 0.0869381i
\(665\) −71108.7 65979.3i −0.00623546 0.00578567i
\(666\) −2.50513e6 3.14134e6i −0.218849 0.274428i
\(667\) −7.43185e6 9.31925e6i −0.646818 0.811085i
\(668\) −1.13220e7 1.05053e7i −0.981708 0.910892i
\(669\) −1.38704e7 4.27846e6i −1.19819 0.369592i
\(670\) 250628. 638590.i 0.0215696 0.0549586i
\(671\) 110126. + 75082.6i 0.00944242 + 0.00643774i
\(672\) 2.31172e7 1.11327e7i 1.97475 0.950990i
\(673\) −5.88470e6 + 5.46021e6i −0.500826 + 0.464699i −0.889669 0.456605i \(-0.849065\pi\)
0.388843 + 0.921304i \(0.372875\pi\)
\(674\) −8.39056e6 1.26467e6i −0.711444 0.107233i
\(675\) −942237. 1.25733e7i −0.0795977 1.06216i
\(676\) 1.07383e6 + 2.73607e6i 0.0903790 + 0.230282i
\(677\) −2.21809e6 + 9.71810e6i −0.185998 + 0.814910i 0.792701 + 0.609610i \(0.208674\pi\)
−0.978699 + 0.205300i \(0.934183\pi\)
\(678\) −1.49625e6 + 1.99660e7i −0.125006 + 1.66808i
\(679\) −2.37615e7 + 7.32944e6i −1.97787 + 0.610093i
\(680\) 243684. + 117352.i 0.0202094 + 0.00973235i
\(681\) −1.37925e6 2.38894e6i −0.113966 0.197395i
\(682\) 472964. 819198.i 0.0389375 0.0674416i
\(683\) 6.03986e6 4.11790e6i 0.495421 0.337773i −0.289697 0.957118i \(-0.593554\pi\)
0.785118 + 0.619346i \(0.212602\pi\)
\(684\) 35690.0 + 156368.i 0.00291680 + 0.0127793i
\(685\) 2.45595e6 370175.i 0.199983 0.0301426i
\(686\) −3.74249e7 + 4.69293e7i −3.03634 + 3.80745i
\(687\) −1.60349e7 −1.29621
\(688\) −6.62338e6 + 8.23666e6i −0.533469 + 0.663407i
\(689\) −2.00776e7 −1.61125
\(690\) 1.83313e6 2.29868e6i 0.146579 0.183804i
\(691\) 9.06730e6 1.36667e6i 0.722408 0.108886i 0.222461 0.974942i \(-0.428591\pi\)
0.499947 + 0.866056i \(0.333353\pi\)
\(692\) 1.34450e6 + 5.89062e6i 0.106732 + 0.467623i
\(693\) 483747. 329813.i 0.0382636 0.0260876i
\(694\) −6.36228e6 + 1.10198e7i −0.501435 + 0.868510i
\(695\) −1.58799e6 2.75047e6i −0.124705 0.215996i
\(696\) 1.26718e6 + 610240.i 0.0991549 + 0.0477505i
\(697\) 1.21751e7 3.75552e6i 0.949272 0.292812i
\(698\) 954947. 1.27429e7i 0.0741892 0.989987i
\(699\) −1.76245e6 + 7.72180e6i −0.136434 + 0.597758i
\(700\) −1.01373e7 2.58293e7i −0.781944 1.99236i
\(701\) 562284. + 7.50315e6i 0.0432176 + 0.576698i 0.976213 + 0.216811i \(0.0695657\pi\)
−0.932996 + 0.359887i \(0.882815\pi\)
\(702\) −2.26212e7 3.40960e6i −1.73250 0.261132i
\(703\) 191361. 177557.i 0.0146038 0.0135503i
\(704\) −944945. + 455061.i −0.0718579 + 0.0346050i
\(705\) 560805. + 382351.i 0.0424951 + 0.0289727i
\(706\) 7.97765e6 2.03267e7i 0.602370 1.53481i
\(707\) 2.61271e7 + 8.05914e6i 1.96582 + 0.606374i
\(708\) 4.37693e6 + 4.06119e6i 0.328160 + 0.304488i
\(709\) 6.66196e6 + 8.35384e6i 0.497722 + 0.624124i 0.965714 0.259609i \(-0.0835938\pi\)
−0.467992 + 0.883733i \(0.655022\pi\)
\(710\) 601424. + 754162.i 0.0447749 + 0.0561460i
\(711\) 133858. + 124202.i 0.00993045 + 0.00921411i
\(712\) 330228. + 101862.i 0.0244126 + 0.00753028i
\(713\) −5.90211e6 + 1.50383e7i −0.434794 + 1.10784i
\(714\) 2.06366e7 + 1.40698e7i 1.51493 + 1.03286i
\(715\) −124017. + 59723.4i −0.00907227 + 0.00436898i
\(716\) −971201. + 901143.i −0.0707989 + 0.0656918i
\(717\) 1.63974e7 + 2.47151e6i 1.19118 + 0.179542i
\(718\) −1.60846e6 2.14634e7i −0.116439 1.55377i
\(719\) −198211. 505033.i −0.0142990 0.0364333i 0.923546 0.383488i \(-0.125277\pi\)
−0.937845 + 0.347054i \(0.887182\pi\)
\(720\) −140102. + 613828.i −0.0100720 + 0.0441281i
\(721\) −1.67859e6 + 2.23993e7i −0.120256 + 1.60471i
\(722\) 1.95221e7 6.02176e6i 1.39374 0.429913i
\(723\) −9.29116e6 4.47439e6i −0.661035 0.318337i
\(724\) −1.03511e7 1.79286e7i −0.733906 1.27116i
\(725\) −5.02565e6 + 8.70468e6i −0.355097 + 0.615046i
\(726\) −1.34992e7 + 9.20358e6i −0.950530 + 0.648060i
\(727\) 6.19384e6 + 2.71370e7i 0.434635 + 1.90426i 0.426922 + 0.904288i \(0.359598\pi\)
0.00771216 + 0.999970i \(0.497545\pi\)
\(728\) −5.78296e6 + 871641.i −0.404410 + 0.0609550i
\(729\) 9.32222e6 1.16897e7i 0.649681 0.814674i
\(730\) 589877. 0.0409689
\(731\) −1.17372e7 1.81784e6i −0.812399 0.125823i
\(732\) 2.31216e6 0.159493
\(733\) 7.53982e6 9.45464e6i 0.518324 0.649958i −0.451928 0.892054i \(-0.649264\pi\)
0.970252 + 0.242097i \(0.0778351\pi\)
\(734\) −4.49499e6 + 677510.i −0.307956 + 0.0464169i
\(735\) 1.00020e6 + 4.38214e6i 0.0682915 + 0.299204i
\(736\) 2.49329e7 1.69990e7i 1.69660 1.15672i
\(737\) −134506. + 232972.i −0.00912166 + 0.0157992i
\(738\) −4.88018e6 8.45271e6i −0.329833 0.571288i
\(739\) −7.99416e6 3.84978e6i −0.538470 0.259313i 0.144823 0.989458i \(-0.453739\pi\)
−0.683293 + 0.730144i \(0.739453\pi\)
\(740\) −1.47251e6 + 454211.i −0.0988508 + 0.0304914i
\(741\) 30228.9 403377.i 0.00202245 0.0269877i
\(742\) 1.37297e7 6.01538e7i 0.915487 4.01101i
\(743\) 510489. + 1.30070e6i 0.0339245 + 0.0864383i 0.946832 0.321728i \(-0.104264\pi\)
−0.912908 + 0.408166i \(0.866168\pi\)
\(744\) −142451. 1.90087e6i −0.00943479 0.125898i
\(745\) −1.51747e6 228721.i −0.100168 0.0150979i
\(746\) 6.95638e6 6.45458e6i 0.457653 0.424640i
\(747\) −7.89764e6 + 3.80330e6i −0.517840 + 0.249379i
\(748\) −754374. 514323.i −0.0492984 0.0336111i
\(749\) 1.42452e6 3.62962e6i 0.0927820 0.236405i
\(750\) −4.78708e6 1.47662e6i −0.310755 0.0958551i
\(751\) 1.61937e6 + 1.50255e6i 0.104772 + 0.0972143i 0.730820 0.682571i \(-0.239138\pi\)
−0.626048 + 0.779785i \(0.715328\pi\)
\(752\) 3.76257e6 + 4.71812e6i 0.242628 + 0.304246i
\(753\) −1.09936e7 1.37855e7i −0.706566 0.886006i
\(754\) 1.33686e7 + 1.24042e7i 0.856362 + 0.794588i
\(755\) 662653. + 204401.i 0.0423077 + 0.0130502i
\(756\) 1.36341e7 3.47392e7i 0.867608 2.21063i
\(757\) −1.25216e7 8.53707e6i −0.794181 0.541463i 0.0969073 0.995293i \(-0.469105\pi\)
−0.891088 + 0.453830i \(0.850057\pi\)
\(758\) 2.15645e7 1.03849e7i 1.36322 0.656491i
\(759\) −845163. + 784197.i −0.0532520 + 0.0494106i
\(760\) 13311.0 + 2006.32i 0.000835945 + 0.000125998i
\(761\) 1.79220e6 + 2.39152e7i 0.112182 + 1.49697i 0.715021 + 0.699103i \(0.246417\pi\)
−0.602838 + 0.797863i \(0.705964\pi\)
\(762\) 1.18287e7 + 3.01391e7i 0.737990 + 1.88037i
\(763\) 1.18191e7 5.17829e7i 0.734977 3.22014i
\(764\) −1.59151e6 + 2.12372e7i −0.0986449 + 1.31633i
\(765\) −676081. + 208543.i −0.0417681 + 0.0128838i
\(766\) 7.14573e6 + 3.44120e6i 0.440022 + 0.211904i
\(767\) 4.49681e6 + 7.78870e6i 0.276004 + 0.478054i
\(768\) 4.44836e6 7.70478e6i 0.272143 0.471365i
\(769\) 1.46761e7 1.00060e7i 0.894942 0.610161i −0.0260850 0.999660i \(-0.508304\pi\)
0.921027 + 0.389499i \(0.127352\pi\)
\(770\) −94128.4 412404.i −0.00572129 0.0250666i
\(771\) 1.46989e7 2.21551e6i 0.890532 0.134226i
\(772\) −1.86893e7 + 2.34356e7i −1.12862 + 1.41525i
\(773\) −6.81698e6 −0.410339 −0.205170 0.978726i \(-0.565775\pi\)
−0.205170 + 0.978726i \(0.565775\pi\)
\(774\) 643099. + 9.07568e6i 0.0385856 + 0.544536i
\(775\) 1.36227e7 0.814721
\(776\) 2.15149e6 2.69789e6i 0.128258 0.160831i
\(777\) −1.63460e7 + 2.46376e6i −0.971311 + 0.146402i
\(778\) −4.50946e6 1.97572e7i −0.267101 1.17025i
\(779\) 523947. 357221.i 0.0309346 0.0210908i
\(780\) −1.19392e6 + 2.06793e6i −0.0702649 + 0.121702i
\(781\) −189131. 327584.i −0.0110952 0.0192174i
\(782\) 2.64657e7 + 1.27452e7i 1.54763 + 0.745299i
\(783\) −1.29179e7 + 3.98465e6i −0.752988 + 0.232266i
\(784\) −2.98647e6 + 3.98517e7i −0.173528 + 2.31556i
\(785\) −778587. + 3.41121e6i −0.0450955 + 0.197576i
\(786\) −9.53409e6 2.42925e7i −0.550456 1.40254i
\(787\) −476017. 6.35200e6i −0.0273959 0.365573i −0.994006 0.109322i \(-0.965132\pi\)
0.966610 0.256250i \(-0.0824871\pi\)
\(788\) 3.19205e7 + 4.81124e6i 1.83128 + 0.276021i
\(789\) 3.16709e6 2.93863e6i 0.181120 0.168055i
\(790\) 118865. 57242.5i 0.00677622 0.00326325i
\(791\) −4.06490e7 2.77140e7i −2.30998 1.57492i
\(792\) −29683.3 + 75631.9i −0.00168151 + 0.00428442i
\(793\) 3.32799e6 + 1.02655e6i 0.187931 + 0.0579691i
\(794\) 1.89452e7 + 1.75786e7i 1.06647 + 0.989538i
\(795\) −1.82463e6 2.28801e6i −0.102390 0.128393i
\(796\) −3.14589e6 3.94482e6i −0.175979 0.220670i
\(797\) 2.45000e6 + 2.27326e6i 0.136622 + 0.126766i 0.745524 0.666479i \(-0.232199\pi\)
−0.608902 + 0.793245i \(0.708390\pi\)
\(798\) 1.18787e6 + 366410.i 0.0660332 + 0.0203686i
\(799\) −2.47751e6 + 6.31258e6i −0.137293 + 0.349816i
\(800\) −2.10246e7 1.43343e7i −1.16145 0.791867i
\(801\) −814475. + 392231.i −0.0448535 + 0.0216003i
\(802\) −184391. + 171090.i −0.0101229 + 0.00939265i
\(803\) −228731. 34475.6i −0.0125180 0.00188679i
\(804\) 348740. + 4.65362e6i 0.0190266 + 0.253893i
\(805\) 2.63936e6 + 6.72498e6i 0.143552 + 0.365764i
\(806\) 5.50001e6 2.40971e7i 0.298212 1.30655i
\(807\) 323748. 4.32011e6i 0.0174994 0.233513i
\(808\) −3.62571e6 + 1.11838e6i −0.195373 + 0.0602646i
\(809\) −7.19638e6 3.46560e6i −0.386583 0.186169i 0.230490 0.973075i \(-0.425967\pi\)
−0.617073 + 0.786906i \(0.711682\pi\)
\(810\) −942490. 1.63244e6i −0.0504736 0.0874228i
\(811\) 7.63217e6 1.32193e7i 0.407470 0.705759i −0.587135 0.809489i \(-0.699744\pi\)
0.994606 + 0.103730i \(0.0330776\pi\)
\(812\) −2.45806e7 + 1.67588e7i −1.30829 + 0.891974i
\(813\) 1.60352e6 + 7.02549e6i 0.0850841 + 0.372778i
\(814\) 1.12565e6 169664.i 0.0595444 0.00897487i
\(815\) 402504. 504724.i 0.0212264 0.0266171i
\(816\) 1.05326e7 0.553745
\(817\) −584881. + 85730.5i −0.0306558 + 0.00449345i
\(818\) −2.59200e7 −1.35441
\(819\) 9.53841e6 1.19608e7i 0.496897 0.623089i
\(820\) −3.70154e6 + 557917.i −0.192242 + 0.0289757i
\(821\) −383332. 1.67949e6i −0.0198480 0.0869598i 0.964034 0.265779i \(-0.0856293\pi\)
−0.983882 + 0.178820i \(0.942772\pi\)
\(822\) −2.62979e7 + 1.79296e7i −1.35751 + 0.925532i
\(823\) −1.66441e7 + 2.88284e7i −0.856565 + 1.48361i 0.0186200 + 0.999827i \(0.494073\pi\)
−0.875185 + 0.483788i \(0.839261\pi\)
\(824\) −1.55855e6 2.69949e6i −0.0799656 0.138505i
\(825\) 875931. + 421826.i 0.0448059 + 0.0215774i
\(826\) −2.64105e7 + 8.14657e6i −1.34687 + 0.415455i
\(827\) −242370. + 3.23421e6i −0.0123230 + 0.164439i 0.987647 + 0.156695i \(0.0500840\pi\)
−0.999970 + 0.00774372i \(0.997535\pi\)
\(828\) 2.65802e6 1.16456e7i 0.134736 0.590316i
\(829\) 5.23845e6 + 1.33474e7i 0.264738 + 0.674542i 0.999995 0.00324692i \(-0.00103353\pi\)
−0.735256 + 0.677789i \(0.762938\pi\)
\(830\) 473282. + 6.31551e6i 0.0238465 + 0.318210i
\(831\) −9.37887e6 1.41364e6i −0.471138 0.0710126i
\(832\) −2.00893e7 + 1.86402e7i −1.00614 + 0.933558i
\(833\) −4.04607e7 + 1.94848e7i −2.02032 + 0.972937i
\(834\) 3.36280e7 + 2.29272e7i 1.67412 + 1.14139i
\(835\) 1.23885e6 3.15654e6i 0.0614898 0.156674i
\(836\) −43422.8 13394.2i −0.00214883 0.000662827i
\(837\) 1.34309e7 + 1.24620e7i 0.662661 + 0.614859i
\(838\) 3.64070e7 + 4.56529e7i 1.79091 + 2.24573i
\(839\) −2.70349e6 3.39007e6i −0.132593 0.166266i 0.711103 0.703088i \(-0.248196\pi\)
−0.843696 + 0.536822i \(0.819625\pi\)
\(840\) −624878. 579802.i −0.0305560 0.0283518i
\(841\) −9.30196e6 2.86927e6i −0.453508 0.139889i
\(842\) −1.38849e6 + 3.53780e6i −0.0674934 + 0.171970i
\(843\) 2.52873e7 + 1.72406e7i 1.22556 + 0.835572i
\(844\) −5.70851e6 + 2.74907e6i −0.275846 + 0.132840i
\(845\) −473045. + 438922.i −0.0227909 + 0.0211468i
\(846\) 5.13683e6 + 774252.i 0.246757 + 0.0371926i
\(847\) −3.00008e6 4.00333e7i −0.143689 1.91740i
\(848\) −9.50588e6 2.42206e7i −0.453944 1.15663i
\(849\) 5.12145e6 2.24385e7i 0.243851 1.06838i
\(850\) 1.85108e6 2.47009e7i 0.0878773 1.17264i
\(851\) −1.85778e7 + 5.73049e6i −0.879367 + 0.271249i
\(852\) −5.91202e6 2.84708e6i −0.279021 0.134370i
\(853\) 2.39635e6 + 4.15060e6i 0.112766 + 0.195316i 0.916885 0.399153i \(-0.130696\pi\)
−0.804119 + 0.594469i \(0.797362\pi\)
\(854\) −5.35139e6 + 9.26888e6i −0.251086 + 0.434893i
\(855\) −29094.7 + 19836.4i −0.00136113 + 0.000928000i
\(856\) 120404. + 527526.i 0.00561640 + 0.0246070i
\(857\) −4.06262e6 + 612342.i −0.188953 + 0.0284801i −0.242837 0.970067i \(-0.578078\pi\)
0.0538838 + 0.998547i \(0.482840\pi\)
\(858\) 1.09981e6 1.37912e6i 0.0510035 0.0639564i
\(859\) −1.31753e7 −0.609227 −0.304613 0.952476i \(-0.598527\pi\)
−0.304613 + 0.952476i \(0.598527\pi\)
\(860\) 3.33025e6 + 1.04207e6i 0.153543 + 0.0480452i
\(861\) −4.01562e7 −1.84606
\(862\) 616801. 773444.i 0.0282733 0.0354536i
\(863\) 2.30718e7 3.47752e6i 1.05452 0.158943i 0.401174 0.916002i \(-0.368602\pi\)
0.653347 + 0.757059i \(0.273364\pi\)
\(864\) −7.61552e6 3.33658e7i −0.347069 1.52061i
\(865\) −1.09604e6 + 747267.i −0.0498065 + 0.0339575i
\(866\) 6.77378e6 1.17325e7i 0.306928 0.531615i
\(867\) −2.83866e6 4.91671e6i −0.128253 0.222140i
\(868\) 3.63277e7 + 1.74945e7i 1.63659 + 0.788138i
\(869\) −49436.8 + 15249.2i −0.00222076 + 0.000685013i
\(870\) −198646. + 2.65074e6i −0.00889776 + 0.118732i
\(871\) −1.56415e6 + 6.85297e6i −0.0698606 + 0.306079i
\(872\) 2.69286e6 + 6.86130e6i 0.119929 + 0.305573i
\(873\) 674567. + 9.00147e6i 0.0299564 + 0.399740i
\(874\) 1.44567e6 + 217900.i 0.0640164 + 0.00964891i
\(875\) 9.02355e6 8.37264e6i 0.398435 0.369694i
\(876\) −3.61531e6 + 1.74104e6i −0.159179 + 0.0766566i
\(877\) 1.11057e7 + 7.57173e6i 0.487581 + 0.332427i 0.782031 0.623240i \(-0.214184\pi\)
−0.294450 + 0.955667i \(0.595136\pi\)
\(878\) 2.28432e6 5.82035e6i 0.100005 0.254808i
\(879\) 1.00375e7 + 3.09615e6i 0.438180 + 0.135161i
\(880\) −130764. 121331.i −0.00569221 0.00528160i
\(881\) 9.19170e6 + 1.15260e7i 0.398985 + 0.500311i 0.940223 0.340558i \(-0.110616\pi\)
−0.541239 + 0.840869i \(0.682045\pi\)
\(882\) 2.14491e7 + 2.68964e7i 0.928407 + 1.16419i
\(883\) −1.76766e7 1.64015e7i −0.762951 0.707915i 0.199342 0.979930i \(-0.436120\pi\)
−0.962293 + 0.272015i \(0.912310\pi\)
\(884\) −2.27971e7 7.03196e6i −0.981179 0.302654i
\(885\) −478922. + 1.22027e6i −0.0205545 + 0.0523720i
\(886\) 1.45493e7 + 9.91956e6i 0.622671 + 0.424530i
\(887\) 2.70286e7 1.30163e7i 1.15349 0.555491i 0.243410 0.969924i \(-0.421734\pi\)
0.910080 + 0.414432i \(0.136020\pi\)
\(888\) 1.68161e6 1.56031e6i 0.0715637 0.0664014i
\(889\) −7.86679e7 1.18573e7i −3.33844 0.503188i
\(890\) 48809.1 + 651312.i 0.00206550 + 0.0275622i
\(891\) 270051. + 688080.i 0.0113960 + 0.0290365i
\(892\) −9.48108e6 + 4.15393e7i −0.398975 + 1.74802i
\(893\) −25222.3 + 336568.i −0.00105842 + 0.0141236i
\(894\) 1.87922e7 5.79664e6i 0.786384 0.242567i
\(895\) −262069. 126206.i −0.0109360 0.00526650i
\(896\) −8.82599e6 1.52871e7i −0.367277 0.636142i
\(897\) −1.50629e7 + 2.60898e7i −0.625070 + 1.08265i
\(898\) 4.58568e7 3.12646e7i 1.89764 1.29379i
\(899\) −3.25011e6 1.42397e7i −0.134122 0.587626i
\(900\) −9.96012e6 + 1.50125e6i −0.409881 + 0.0617797i
\(901\) 1.82299e7 2.28595e7i 0.748121 0.938114i
\(902\) 2.76531e6 0.113169
\(903\) 3.36597e7 + 1.63783e7i 1.37370 + 0.668420i
\(904\) 6.82725e6 0.277859
\(905\) 2.83386e6 3.55355e6i 0.115016 0.144225i
\(906\) −8.78744e6 + 1.32449e6i −0.355666 + 0.0536080i
\(907\) 2.19474e6 + 9.61576e6i 0.0885858 + 0.388120i 0.999712 0.0240084i \(-0.00764283\pi\)
−0.911126 + 0.412128i \(0.864786\pi\)
\(908\) −6.69022e6 + 4.56132e6i −0.269293 + 0.183601i
\(909\) 4.96269e6 8.59564e6i 0.199208 0.345039i
\(910\) −5.52655e6 9.57226e6i −0.221233 0.383187i
\(911\) −2.56596e7 1.23570e7i −1.02436 0.493308i −0.155227 0.987879i \(-0.549611\pi\)
−0.869137 + 0.494571i \(0.835325\pi\)
\(912\) 500925. 154515.i 0.0199428 0.00615153i
\(913\) 185593. 2.47657e6i 0.00736859 0.0983270i
\(914\) −1.49598e7 + 6.55432e7i −0.592326 + 2.59515i
\(915\) 185459. + 472543.i 0.00732312 + 0.0186590i
\(916\) 3.51742e6 + 4.69367e7i 0.138511 + 1.84831i
\(917\) 6.34072e7 + 9.55710e6i 2.49009 + 0.375321i
\(918\) 2.44214e7 2.26597e7i 0.956453 0.887459i
\(919\) 3.91203e7 1.88393e7i 1.52796 0.735829i 0.533995 0.845487i \(-0.320690\pi\)
0.993969 + 0.109658i \(0.0349756\pi\)
\(920\) −828338. 564751.i −0.0322655 0.0219982i
\(921\) 6.15000e6 1.56699e7i 0.238905 0.608721i
\(922\) −3.32669e7 1.02615e7i −1.28880 0.397541i
\(923\) −7.24538e6 6.72273e6i −0.279935 0.259742i
\(924\) 1.79413e6 + 2.24977e6i 0.0691313 + 0.0866879i
\(925\) 1.02215e7 + 1.28173e7i 0.392789 + 0.492542i
\(926\) 1.26866e7 + 1.17714e7i 0.486202 + 0.451130i
\(927\) 7.79173e6 + 2.40343e6i 0.297807 + 0.0918612i
\(928\) −9.96746e6 + 2.53967e7i −0.379940 + 0.968070i
\(929\) 2.63378e7 + 1.79568e7i 1.00125 + 0.682637i 0.948764 0.315985i \(-0.102335\pi\)
0.0524808 + 0.998622i \(0.483287\pi\)
\(930\) 3.24589e6 1.56314e6i 0.123063 0.0592639i
\(931\) −1.63844e6 + 1.52025e6i −0.0619523 + 0.0574833i
\(932\) 2.29895e7 + 3.46510e6i 0.866940 + 0.130670i
\(933\) −2594.85 34625.8i −9.75905e−5 0.00130225i
\(934\) −2.62172e7 6.68003e7i −0.983374 2.50560i
\(935\) 44605.1 195428.i 0.00166861 0.00731066i
\(936\) −158651. + 2.11705e6i −0.00591908 + 0.0789846i
\(937\) −2.63981e7 + 8.14272e6i −0.982252 + 0.302985i −0.743971 0.668212i \(-0.767060\pi\)
−0.238281 + 0.971196i \(0.576584\pi\)
\(938\) −1.94623e7 9.37257e6i −0.722251 0.347818i
\(939\) −6.35104e6 1.10003e7i −0.235061 0.407138i
\(940\) 996179. 1.72543e6i 0.0367720 0.0636910i
\(941\) 2.09236e7 1.42655e7i 0.770306 0.525186i −0.113219 0.993570i \(-0.536116\pi\)
0.883525 + 0.468384i \(0.155164\pi\)
\(942\) −9.97758e6 4.37146e7i −0.366351 1.60509i
\(943\) −4.66999e7 + 7.03888e6i −1.71016 + 0.257765i
\(944\) −7.26684e6 + 9.11232e6i −0.265409 + 0.332812i
\(945\) 8.19335e6 0.298457
\(946\) −2.31794e6 1.12787e6i −0.0842120 0.0409762i
\(947\) 2.61732e7 0.948377 0.474189 0.880423i \(-0.342741\pi\)
0.474189 + 0.880423i \(0.342741\pi\)
\(948\) −559564. + 701671.i −0.0202222 + 0.0253579i
\(949\) −5.97666e6 + 900836.i −0.215423 + 0.0324698i
\(950\) −274330. 1.20192e6i −0.00986197 0.0432081i
\(951\) 1.61511e7 1.10116e7i 0.579096 0.394821i
\(952\) 4.25834e6 7.37566e6i 0.152282 0.263760i
\(953\) 1.67672e6 + 2.90417e6i 0.0598039 + 0.103583i 0.894377 0.447313i \(-0.147619\pi\)
−0.834573 + 0.550897i \(0.814286\pi\)
\(954\) −2.01800e7 9.71816e6i −0.717876 0.345711i
\(955\) −4.46795e6 + 1.37818e6i −0.158526 + 0.0488988i
\(956\) 3.63756e6 4.85398e7i 0.128726 1.71772i
\(957\) 231951. 1.01624e6i 0.00818683 0.0358688i
\(958\) 1.74564e7 + 4.44783e7i 0.614529 + 1.56579i
\(959\) −5.84450e6 7.79894e7i −0.205211 2.73835i
\(960\) −3.94989e6 595350.i −0.138327 0.0208494i
\(961\) 6.47545e6 6.00834e6i 0.226184 0.209868i
\(962\) 2.67993e7 1.29059e7i 0.933654 0.449624i
\(963\) −1.16949e6 797343.i −0.0406378 0.0277063i
\(964\) −1.10591e7 + 2.81781e7i −0.383289 + 0.976606i
\(965\) −6.28867e6 1.93980e6i −0.217391 0.0670561i
\(966\) −6.78661e7 6.29705e7i −2.33997 2.17117i
\(967\) −2.47195e7 3.09973e7i −0.850107 1.06600i −0.997042 0.0768547i \(-0.975512\pi\)
0.146935 0.989146i \(-0.453059\pi\)
\(968\) 3.47351e6 + 4.35564e6i 0.119146 + 0.149405i
\(969\) 431821. + 400672.i 0.0147739 + 0.0137082i
\(970\) 6.23204e6 + 1.92233e6i 0.212667 + 0.0655992i
\(971\) −1.03629e7 + 2.64044e7i −0.352724 + 0.898726i 0.638867 + 0.769317i \(0.279403\pi\)
−0.991591 + 0.129409i \(0.958692\pi\)
\(972\) −1.93401e7 1.31859e7i −0.656590 0.447655i
\(973\) −9.01033e7 + 4.33914e7i −3.05111 + 1.46934i
\(974\) 3.54727e7 3.29139e7i 1.19811 1.11168i
\(975\) 2.51198e7 + 3.78620e6i 0.846261 + 0.127553i
\(976\) 337283. + 4.50074e6i 0.0113337 + 0.151237i
\(977\) 1.27645e7 + 3.25234e7i 0.427826 + 1.09008i 0.968536 + 0.248875i \(0.0800607\pi\)
−0.540709 + 0.841210i \(0.681844\pi\)
\(978\) −1.84090e6 + 8.06550e6i −0.0615435 + 0.269640i
\(979\) 19140.0 255406.i 0.000638242 0.00851675i
\(980\) 1.26078e7 3.88898e6i 0.419347 0.129351i
\(981\) −1.73718e7 8.36580e6i −0.576330 0.277546i
\(982\) 2.92098e6 + 5.05928e6i 0.0966605 + 0.167421i
\(983\) −1.02326e6 + 1.77234e6i −0.0337756 + 0.0585011i −0.882419 0.470464i \(-0.844086\pi\)
0.848643 + 0.528965i \(0.177420\pi\)
\(984\) 4.60426e6 3.13913e6i 0.151591 0.103353i
\(985\) 1.57707e6 + 6.90959e6i 0.0517917 + 0.226914i
\(986\) −2.62612e7 + 3.95824e6i −0.860246 + 0.129661i
\(987\) 1.33257e7 1.67099e7i 0.435408 0.545985i
\(988\) −1.18738e6 −0.0386987
\(989\) 4.20157e7 + 1.31471e7i 1.36591 + 0.427405i
\(990\) −153557. −0.00497946
\(991\) −1.35108e7 + 1.69420e7i −0.437016 + 0.548001i −0.950754 0.309946i \(-0.899689\pi\)
0.513738 + 0.857947i \(0.328260\pi\)
\(992\) 3.65636e7 5.51108e6i 1.17970 0.177811i
\(993\) 7.58056e6 + 3.32126e7i 0.243966 + 1.06888i
\(994\) 2.50964e7 1.71104e7i 0.805647 0.549281i
\(995\) 553880. 959349.i 0.0177361 0.0307198i
\(996\) −2.15412e7 3.73104e7i −0.688052 1.19174i
\(997\) 7.89982e6 + 3.80435e6i 0.251698 + 0.121211i 0.555479 0.831531i \(-0.312535\pi\)
−0.303781 + 0.952742i \(0.598249\pi\)
\(998\) −2.82606e7 + 8.71723e6i −0.898162 + 0.277046i
\(999\) −1.64773e6 + 2.19875e7i −0.0522364 + 0.697047i
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 43.6.g.a.24.4 yes 204
43.9 even 21 inner 43.6.g.a.9.4 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.g.a.9.4 204 43.9 even 21 inner
43.6.g.a.24.4 yes 204 1.1 even 1 trivial