Properties

Label 69.7.f.a.10.1
Level $69$
Weight $7$
Character 69.10
Analytic conductor $15.874$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,7,Mod(7,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.7");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.f (of order \(22\), degree \(10\), 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: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(24\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 10.1
Character \(\chi\) \(=\) 69.10
Dual form 69.7.f.a.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.0393 - 11.5859i) q^{2} +(-13.1138 - 8.42776i) q^{3} +(-24.3387 + 169.280i) q^{4} +(-28.9992 - 13.2435i) q^{5} +(34.0100 + 236.544i) q^{6} +(-177.630 + 604.953i) q^{7} +(1380.21 - 887.009i) q^{8} +(100.946 + 221.041i) q^{9} +O(q^{10})\) \(q+(-10.0393 - 11.5859i) q^{2} +(-13.1138 - 8.42776i) q^{3} +(-24.3387 + 169.280i) q^{4} +(-28.9992 - 13.2435i) q^{5} +(34.0100 + 236.544i) q^{6} +(-177.630 + 604.953i) q^{7} +(1380.21 - 887.009i) q^{8} +(100.946 + 221.041i) q^{9} +(137.692 + 468.937i) q^{10} +(-1091.90 - 946.137i) q^{11} +(1745.82 - 2014.79i) q^{12} +(119.777 - 35.1698i) q^{13} +(8792.21 - 4015.27i) q^{14} +(268.678 + 418.071i) q^{15} +(-13631.2 - 4002.48i) q^{16} +(-708.482 + 101.864i) q^{17} +(1547.54 - 3388.63i) q^{18} +(10569.1 + 1519.60i) q^{19} +(2947.66 - 4586.64i) q^{20} +(7427.81 - 6436.24i) q^{21} +22149.2i q^{22} +(-10036.2 + 6878.26i) q^{23} -25575.4 q^{24} +(-9566.64 - 11040.5i) q^{25} +(-1609.95 - 1034.65i) q^{26} +(539.088 - 3749.44i) q^{27} +(-98082.9 - 44793.0i) q^{28} +(1600.51 + 11131.8i) q^{29} +(2146.41 - 7310.01i) q^{30} +(-29692.1 + 19081.9i) q^{31} +(46855.1 + 102598. i) q^{32} +(6345.20 + 21609.8i) q^{33} +(8292.83 + 7185.78i) q^{34} +(13162.8 - 15190.7i) q^{35} +(-39874.6 + 11708.2i) q^{36} +(36549.2 - 16691.5i) q^{37} +(-88499.6 - 137708. i) q^{38} +(-1867.14 - 548.242i) q^{39} +(-51772.2 + 7443.71i) q^{40} +(6825.48 - 14945.7i) q^{41} +(-149139. - 21443.0i) q^{42} +(60768.4 - 94557.5i) q^{43} +(186737. - 161809. i) q^{44} -7746.88i q^{45} +(180447. + 47226.0i) q^{46} +83870.4 q^{47} +(145025. + 167368. i) q^{48} +(-235443. - 151310. i) q^{49} +(-31872.3 + 221677. i) q^{50} +(10149.4 + 4635.08i) q^{51} +(3038.30 + 21131.8i) q^{52} +(55538.0 - 189145. i) q^{53} +(-48852.8 + 31395.8i) q^{54} +(19134.1 + 41897.8i) q^{55} +(291431. + 992523. i) q^{56} +(-125794. - 109001. i) q^{57} +(112904. - 130298. i) q^{58} +(-96494.9 + 28333.5i) q^{59} +(-77310.2 + 35306.4i) q^{60} +(-5411.12 - 8419.86i) q^{61} +(519169. + 152442. i) q^{62} +(-151650. + 21804.0i) q^{63} +(340600. - 745809. i) q^{64} +(-3939.21 - 566.373i) q^{65} +(186668. - 290461. i) q^{66} +(-3832.67 + 3321.03i) q^{67} -122411. i q^{68} +(189582. - 5617.77i) q^{69} -308143. q^{70} +(-426158. - 491813. i) q^{71} +(335392. + 215543. i) q^{72} +(90950.1 - 632572. i) q^{73} +(-560313. - 255886. i) q^{74} +(32408.8 + 225408. i) q^{75} +(-514476. + 1.75214e6i) q^{76} +(766323. - 492486. i) q^{77} +(12392.8 + 27136.5i) q^{78} +(121586. + 414084. i) q^{79} +(342287. + 296593. i) q^{80} +(-38668.9 + 44626.3i) q^{81} +(-241683. + 70964.4i) q^{82} +(308292. - 140792. i) q^{83} +(908740. + 1.41403e6i) q^{84} +(21894.5 + 6428.79i) q^{85} +(-1.70561e6 + 245229. i) q^{86} +(72827.2 - 159469. i) q^{87} +(-2.34629e6 - 337345. i) q^{88} +(-385386. + 599672. i) q^{89} +(-89754.7 + 77772.9i) q^{90} +78706.8i q^{91} +(-920081. - 1.86633e6i) q^{92} +550195. q^{93} +(-841997. - 971716. i) q^{94} +(-286370. - 184039. i) q^{95} +(250223. - 1.74034e6i) q^{96} +(521758. + 238279. i) q^{97} +(610607. + 4.24686e6i) q^{98} +(98911.9 - 336863. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{3}{22}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.0393 11.5859i −1.25491 1.44824i −0.843804 0.536652i \(-0.819689\pi\)
−0.411104 0.911589i \(-0.634857\pi\)
\(3\) −13.1138 8.42776i −0.485698 0.312139i
\(4\) −24.3387 + 169.280i −0.380293 + 2.64499i
\(5\) −28.9992 13.2435i −0.231994 0.105948i 0.296027 0.955180i \(-0.404338\pi\)
−0.528020 + 0.849232i \(0.677066\pi\)
\(6\) 34.0100 + 236.544i 0.157453 + 1.09511i
\(7\) −177.630 + 604.953i −0.517872 + 1.76371i 0.119161 + 0.992875i \(0.461980\pi\)
−0.637033 + 0.770836i \(0.719839\pi\)
\(8\) 1380.21 887.009i 2.69573 1.73244i
\(9\) 100.946 + 221.041i 0.138472 + 0.303211i
\(10\) 137.692 + 468.937i 0.137692 + 0.468937i
\(11\) −1091.90 946.137i −0.820361 0.710847i 0.139835 0.990175i \(-0.455343\pi\)
−0.960196 + 0.279328i \(0.909888\pi\)
\(12\) 1745.82 2014.79i 1.01031 1.16596i
\(13\) 119.777 35.1698i 0.0545185 0.0160081i −0.254360 0.967110i \(-0.581865\pi\)
0.308878 + 0.951102i \(0.400046\pi\)
\(14\) 8792.21 4015.27i 3.20416 1.46329i
\(15\) 268.678 + 418.071i 0.0796083 + 0.123873i
\(16\) −13631.2 4002.48i −3.32793 0.977167i
\(17\) −708.482 + 101.864i −0.144206 + 0.0207336i −0.214040 0.976825i \(-0.568662\pi\)
0.0698339 + 0.997559i \(0.477753\pi\)
\(18\) 1547.54 3388.63i 0.265353 0.581042i
\(19\) 10569.1 + 1519.60i 1.54091 + 0.221549i 0.859798 0.510635i \(-0.170590\pi\)
0.681108 + 0.732183i \(0.261499\pi\)
\(20\) 2947.66 4586.64i 0.368457 0.573330i
\(21\) 7427.81 6436.24i 0.802053 0.694983i
\(22\) 22149.2i 2.08013i
\(23\) −10036.2 + 6878.26i −0.824871 + 0.565321i
\(24\) −25575.4 −1.85007
\(25\) −9566.64 11040.5i −0.612265 0.706591i
\(26\) −1609.95 1034.65i −0.0915992 0.0588673i
\(27\) 539.088 3749.44i 0.0273885 0.190491i
\(28\) −98082.9 44793.0i −4.46806 2.04050i
\(29\) 1600.51 + 11131.8i 0.0656242 + 0.456427i 0.995966 + 0.0897327i \(0.0286013\pi\)
−0.930342 + 0.366694i \(0.880490\pi\)
\(30\) 2146.41 7310.01i 0.0794968 0.270741i
\(31\) −29692.1 + 19081.9i −0.996680 + 0.640527i −0.933913 0.357501i \(-0.883629\pi\)
−0.0627670 + 0.998028i \(0.519992\pi\)
\(32\) 46855.1 + 102598.i 1.42990 + 3.13105i
\(33\) 6345.20 + 21609.8i 0.176565 + 0.601324i
\(34\) 8292.83 + 7185.78i 0.210992 + 0.182826i
\(35\) 13162.8 15190.7i 0.307005 0.354302i
\(36\) −39874.6 + 11708.2i −0.854650 + 0.250948i
\(37\) 36549.2 16691.5i 0.721560 0.329526i −0.0205634 0.999789i \(-0.506546\pi\)
0.742124 + 0.670263i \(0.233819\pi\)
\(38\) −88499.6 137708.i −1.61284 2.50962i
\(39\) −1867.14 548.242i −0.0314763 0.00924227i
\(40\) −51772.2 + 7443.71i −0.808940 + 0.116308i
\(41\) 6825.48 14945.7i 0.0990334 0.216853i −0.853630 0.520880i \(-0.825604\pi\)
0.952663 + 0.304027i \(0.0983313\pi\)
\(42\) −149139. 21443.0i −2.01300 0.289426i
\(43\) 60768.4 94557.5i 0.764315 1.18930i −0.212905 0.977073i \(-0.568293\pi\)
0.977221 0.212225i \(-0.0680710\pi\)
\(44\) 186737. 161809.i 2.19216 1.89952i
\(45\) 7746.88i 0.0850137i
\(46\) 180447. + 47226.0i 1.85386 + 0.485186i
\(47\) 83870.4 0.807821 0.403910 0.914799i \(-0.367651\pi\)
0.403910 + 0.914799i \(0.367651\pi\)
\(48\) 145025. + 167368.i 1.31135 + 1.51338i
\(49\) −235443. 151310.i −2.00123 1.28611i
\(50\) −31872.3 + 221677.i −0.254978 + 1.77341i
\(51\) 10149.4 + 4635.08i 0.0765122 + 0.0349419i
\(52\) 3038.30 + 21131.8i 0.0216083 + 0.150289i
\(53\) 55538.0 189145.i 0.373047 1.27048i −0.532571 0.846385i \(-0.678774\pi\)
0.905618 0.424095i \(-0.139408\pi\)
\(54\) −48852.8 + 31395.8i −0.310247 + 0.199384i
\(55\) 19134.1 + 41897.8i 0.115006 + 0.251828i
\(56\) 291431. + 992523.i 1.65948 + 5.65167i
\(57\) −125794. 109001.i −0.679261 0.588583i
\(58\) 112904. 130298.i 0.578663 0.667813i
\(59\) −96494.9 + 28333.5i −0.469838 + 0.137957i −0.508077 0.861312i \(-0.669643\pi\)
0.0382388 + 0.999269i \(0.487825\pi\)
\(60\) −77310.2 + 35306.4i −0.357918 + 0.163456i
\(61\) −5411.12 8419.86i −0.0238395 0.0370950i 0.829129 0.559057i \(-0.188837\pi\)
−0.852969 + 0.521962i \(0.825200\pi\)
\(62\) 519169. + 152442.i 2.17838 + 0.639630i
\(63\) −151650. + 21804.0i −0.606487 + 0.0871996i
\(64\) 340600. 745809.i 1.29928 2.84504i
\(65\) −3939.21 566.373i −0.0143440 0.00206235i
\(66\) 186668. 290461.i 0.649289 1.01031i
\(67\) −3832.67 + 3321.03i −0.0127431 + 0.0110420i −0.661209 0.750202i \(-0.729956\pi\)
0.648466 + 0.761244i \(0.275411\pi\)
\(68\) 122411.i 0.389308i
\(69\) 189582. 5617.77i 0.577097 0.0171008i
\(70\) −308143. −0.898377
\(71\) −426158. 491813.i −1.19068 1.37412i −0.910152 0.414274i \(-0.864036\pi\)
−0.280529 0.959845i \(-0.590510\pi\)
\(72\) 335392. + 215543.i 0.898576 + 0.577480i
\(73\) 90950.1 632572.i 0.233795 1.62608i −0.447651 0.894208i \(-0.647739\pi\)
0.681446 0.731869i \(-0.261352\pi\)
\(74\) −560313. 255886.i −1.38272 0.631469i
\(75\) 32408.8 + 225408.i 0.0768210 + 0.534302i
\(76\) −514476. + 1.75214e6i −1.17199 + 3.99143i
\(77\) 766323. 492486.i 1.67857 1.07875i
\(78\) 12392.8 + 27136.5i 0.0261148 + 0.0571834i
\(79\) 121586. + 414084.i 0.246605 + 0.839861i 0.986022 + 0.166613i \(0.0532830\pi\)
−0.739417 + 0.673248i \(0.764899\pi\)
\(80\) 342287. + 296593.i 0.668529 + 0.579284i
\(81\) −38668.9 + 44626.3i −0.0727623 + 0.0839722i
\(82\) −241683. + 70964.4i −0.438333 + 0.128706i
\(83\) 308292. 140792.i 0.539173 0.246232i −0.127165 0.991882i \(-0.540588\pi\)
0.666339 + 0.745649i \(0.267861\pi\)
\(84\) 908740. + 1.41403e6i 1.53321 + 2.38572i
\(85\) 21894.5 + 6428.79i 0.0356515 + 0.0104682i
\(86\) −1.70561e6 + 245229.i −2.68153 + 0.385546i
\(87\) 72827.2 159469.i 0.110595 0.242169i
\(88\) −2.34629e6 337345.i −3.44297 0.495024i
\(89\) −385386. + 599672.i −0.546671 + 0.850636i −0.999154 0.0411367i \(-0.986902\pi\)
0.452483 + 0.891773i \(0.350538\pi\)
\(90\) −89754.7 + 77772.9i −0.123120 + 0.106684i
\(91\) 78706.8i 0.104445i
\(92\) −920081. 1.86633e6i −1.18158 2.39677i
\(93\) 550195. 0.684019
\(94\) −841997. 971716.i −1.01374 1.16992i
\(95\) −286370. 184039.i −0.334008 0.214654i
\(96\) 250223. 1.74034e6i 0.282823 1.96707i
\(97\) 521758. + 238279.i 0.571681 + 0.261078i 0.680212 0.733015i \(-0.261887\pi\)
−0.108531 + 0.994093i \(0.534615\pi\)
\(98\) 610607. + 4.24686e6i 0.648759 + 4.51222i
\(99\) 98911.9 336863.i 0.101940 0.347174i
\(100\) 2.10177e6 1.35072e6i 2.10177 1.35072i
\(101\) −395477. 865975.i −0.383846 0.840507i −0.998656 0.0518308i \(-0.983494\pi\)
0.614809 0.788676i \(-0.289233\pi\)
\(102\) −48190.9 164123.i −0.0454114 0.154657i
\(103\) 1.10028e6 + 953394.i 1.00691 + 0.872491i 0.991852 0.127396i \(-0.0406619\pi\)
0.0150560 + 0.999887i \(0.495207\pi\)
\(104\) 134122. 154785.i 0.119234 0.137603i
\(105\) −300639. + 88275.5i −0.259703 + 0.0762557i
\(106\) −2.74898e6 + 1.25542e6i −2.30810 + 1.05407i
\(107\) −634150. 986757.i −0.517656 0.805488i 0.479755 0.877402i \(-0.340725\pi\)
−0.997411 + 0.0719145i \(0.977089\pi\)
\(108\) 621583. + 182513.i 0.493432 + 0.144885i
\(109\) 650010. 93457.3i 0.501927 0.0721662i 0.113299 0.993561i \(-0.463858\pi\)
0.388628 + 0.921395i \(0.372949\pi\)
\(110\) 293333. 642309.i 0.220385 0.482576i
\(111\) −619972. 89138.5i −0.453318 0.0651773i
\(112\) 4.84262e6 7.53527e6i 3.44688 5.36345i
\(113\) 725928. 629020.i 0.503105 0.435943i −0.365968 0.930628i \(-0.619262\pi\)
0.869072 + 0.494685i \(0.164717\pi\)
\(114\) 2.55174e6i 1.72235i
\(115\) 382134. 66549.7i 0.251259 0.0437575i
\(116\) −1.92334e6 −1.23220
\(117\) 19865.0 + 22925.4i 0.0124031 + 0.0143139i
\(118\) 1.29701e6 + 833535.i 0.789398 + 0.507315i
\(119\) 64224.7 446693.i 0.0381120 0.265075i
\(120\) 741666. + 338707.i 0.429205 + 0.196011i
\(121\) 44951.8 + 312647.i 0.0253741 + 0.176481i
\(122\) −43228.3 + 147222.i −0.0238061 + 0.0810762i
\(123\) −215467. + 138472.i −0.115789 + 0.0744128i
\(124\) −2.50752e6 5.49070e6i −1.31516 2.87980i
\(125\) 271549. + 924811.i 0.139033 + 0.473503i
\(126\) 1.77508e6 + 1.53811e6i 0.887371 + 0.768911i
\(127\) 968094. 1.11724e6i 0.472614 0.545425i −0.468523 0.883451i \(-0.655214\pi\)
0.941137 + 0.338026i \(0.109759\pi\)
\(128\) −5.13404e6 + 1.50749e6i −2.44810 + 0.718827i
\(129\) −1.59382e6 + 727871.i −0.742453 + 0.339067i
\(130\) 32984.8 + 51325.4i 0.0150136 + 0.0233616i
\(131\) 3.15783e6 + 927222.i 1.40467 + 0.412449i 0.894285 0.447497i \(-0.147684\pi\)
0.510386 + 0.859946i \(0.329503\pi\)
\(132\) −3.81253e6 + 548159.i −1.65764 + 0.238333i
\(133\) −2.79667e6 + 6.12386e6i −1.18874 + 2.60298i
\(134\) 76954.3 + 11064.4i 0.0319829 + 0.00459845i
\(135\) −65288.8 + 101591.i −0.0265361 + 0.0412910i
\(136\) −887502. + 769025.i −0.352819 + 0.305720i
\(137\) 2.81744e6i 1.09570i −0.836575 0.547852i \(-0.815446\pi\)
0.836575 0.547852i \(-0.184554\pi\)
\(138\) −1.96835e6 2.14008e6i −0.748969 0.814315i
\(139\) 1.79486e6 0.668324 0.334162 0.942516i \(-0.391547\pi\)
0.334162 + 0.942516i \(0.391547\pi\)
\(140\) 2.25111e6 + 2.59792e6i 0.820376 + 0.946764i
\(141\) −1.09986e6 706839.i −0.392357 0.252152i
\(142\) −1.41979e6 + 9.87487e6i −0.495861 + 3.44879i
\(143\) −164060. 74923.8i −0.0561042 0.0256219i
\(144\) −491302. 3.41708e6i −0.164536 1.14437i
\(145\) 101010. 344009.i 0.0331330 0.112841i
\(146\) −8.24200e6 + 5.29681e6i −2.64834 + 1.70199i
\(147\) 1.81236e6 + 3.96851e6i 0.570548 + 1.24933i
\(148\) 1.93596e6 + 6.59328e6i 0.597189 + 2.03384i
\(149\) 4.10532e6 + 3.55728e6i 1.24105 + 1.07537i 0.994336 + 0.106283i \(0.0338949\pi\)
0.246710 + 0.969089i \(0.420651\pi\)
\(150\) 2.28620e6 2.63842e6i 0.677394 0.781754i
\(151\) 3.51616e6 1.03244e6i 1.02126 0.299870i 0.272110 0.962266i \(-0.412279\pi\)
0.749154 + 0.662396i \(0.230460\pi\)
\(152\) 1.59355e7 7.27748e6i 4.53768 2.07229i
\(153\) −94034.5 146321.i −0.0262551 0.0408537i
\(154\) −1.33992e7 3.93437e6i −3.66874 1.07724i
\(155\) 1.11376e6 160134.i 0.299086 0.0430021i
\(156\) 138250. 302725.i 0.0364159 0.0797398i
\(157\) −4.96302e6 713574.i −1.28247 0.184391i −0.532821 0.846228i \(-0.678868\pi\)
−0.749648 + 0.661837i \(0.769777\pi\)
\(158\) 3.57691e6 5.56578e6i 0.906853 1.41109i
\(159\) −2.32239e6 + 2.01236e6i −0.577754 + 0.500627i
\(160\) 3.59579e6i 0.877879i
\(161\) −2.37829e6 7.29322e6i −0.569885 1.74760i
\(162\) 905243. 0.212922
\(163\) −2.87854e6 3.32201e6i −0.664676 0.767076i 0.318858 0.947803i \(-0.396701\pi\)
−0.983533 + 0.180726i \(0.942155\pi\)
\(164\) 2.36388e6 + 1.51917e6i 0.535913 + 0.344410i
\(165\) 102183. 710699.i 0.0227472 0.158210i
\(166\) −4.72624e6 2.15840e6i −1.03322 0.471854i
\(167\) 286445. + 1.99227e6i 0.0615023 + 0.427758i 0.997189 + 0.0749262i \(0.0238721\pi\)
−0.935687 + 0.352832i \(0.885219\pi\)
\(168\) 4.54296e6 1.54719e7i 0.958101 3.26299i
\(169\) −4.04746e6 + 2.60114e6i −0.838538 + 0.538895i
\(170\) −145321. 318208.i −0.0295788 0.0647686i
\(171\) 731010. + 2.48959e6i 0.146196 + 0.497897i
\(172\) 1.45276e7 + 1.25883e7i 2.85502 + 2.47389i
\(173\) 2.12917e6 2.45719e6i 0.411217 0.474570i −0.511924 0.859031i \(-0.671067\pi\)
0.923141 + 0.384461i \(0.125613\pi\)
\(174\) −2.57873e6 + 757183.i −0.489506 + 0.143732i
\(175\) 8.37830e6 3.82624e6i 1.56330 0.713934i
\(176\) 1.10970e7 + 1.72673e7i 2.03549 + 3.16728i
\(177\) 1.50421e6 + 441675.i 0.271261 + 0.0796495i
\(178\) 1.08167e7 1.55521e6i 1.91795 0.275759i
\(179\) 1.59348e6 3.48924e6i 0.277836 0.608376i −0.718345 0.695687i \(-0.755100\pi\)
0.996181 + 0.0873109i \(0.0278274\pi\)
\(180\) 1.31139e6 + 188549.i 0.224861 + 0.0323301i
\(181\) −2.71732e6 + 4.22824e6i −0.458253 + 0.713056i −0.991095 0.133159i \(-0.957488\pi\)
0.532842 + 0.846215i \(0.321124\pi\)
\(182\) 911891. 790158.i 0.151262 0.131069i
\(183\) 156020.i 0.0254582i
\(184\) −7.75102e6 + 1.83957e7i −1.24424 + 2.95299i
\(185\) −1.28095e6 −0.202310
\(186\) −5.52355e6 6.37452e6i −0.858380 0.990624i
\(187\) 869970. + 559096.i 0.133039 + 0.0854991i
\(188\) −2.04130e6 + 1.41975e7i −0.307208 + 2.13668i
\(189\) 2.17248e6 + 992136.i 0.321788 + 0.146956i
\(190\) 742682. + 5.16547e6i 0.108279 + 0.753094i
\(191\) 1.79635e6 6.11781e6i 0.257805 0.878003i −0.724271 0.689516i \(-0.757823\pi\)
0.982076 0.188487i \(-0.0603583\pi\)
\(192\) −1.07521e7 + 6.90993e6i −1.51911 + 0.976271i
\(193\) −499598. 1.09397e6i −0.0694943 0.152171i 0.871697 0.490045i \(-0.163020\pi\)
−0.941191 + 0.337874i \(0.890292\pi\)
\(194\) −2.47738e6 8.43719e6i −0.339303 1.15556i
\(195\) 46885.0 + 40626.1i 0.00632310 + 0.00547899i
\(196\) 3.13441e7 3.61730e7i 4.16282 4.80415i
\(197\) −2.14023e6 + 628429.i −0.279938 + 0.0821973i −0.418688 0.908130i \(-0.637510\pi\)
0.138750 + 0.990328i \(0.455692\pi\)
\(198\) −4.89587e6 + 2.23587e6i −0.630717 + 0.288039i
\(199\) −4.56747e6 7.10712e6i −0.579584 0.901850i 0.420401 0.907338i \(-0.361889\pi\)
−0.999985 + 0.00548834i \(0.998253\pi\)
\(200\) −2.29970e7 6.75253e6i −2.87462 0.844066i
\(201\) 78249.8 11250.6i 0.00963596 0.00138544i
\(202\) −6.06282e6 + 1.32757e7i −0.735564 + 1.61066i
\(203\) −7.01851e6 1.00911e6i −0.838990 0.120629i
\(204\) −1.03165e6 + 1.60528e6i −0.121518 + 0.189086i
\(205\) −395867. + 343021.i −0.0459502 + 0.0398161i
\(206\) 2.23191e7i 2.55314i
\(207\) −2.53349e6 1.52408e6i −0.285633 0.171829i
\(208\) −1.77347e6 −0.197076
\(209\) −1.01026e7 1.16590e7i −1.10661 1.27710i
\(210\) 4.04094e6 + 2.59696e6i 0.436340 + 0.280419i
\(211\) −845772. + 5.88247e6i −0.0900339 + 0.626199i 0.893980 + 0.448107i \(0.147902\pi\)
−0.984014 + 0.178092i \(0.943007\pi\)
\(212\) 3.06667e7 + 1.40050e7i 3.21854 + 1.46986i
\(213\) 1.44369e6 + 1.00411e7i 0.149395 + 1.03907i
\(214\) −5.06609e6 + 1.72535e7i −0.516930 + 1.76050i
\(215\) −3.01451e6 + 1.93731e6i −0.303320 + 0.194932i
\(216\) −2.58173e6 5.65320e6i −0.256182 0.560961i
\(217\) −6.26947e6 2.13518e7i −0.613552 2.08957i
\(218\) −7.60840e6 6.59272e6i −0.734385 0.636349i
\(219\) −6.52386e6 + 7.52894e6i −0.621116 + 0.716806i
\(220\) −7.55814e6 + 2.21927e6i −0.709818 + 0.208421i
\(221\) −81277.5 + 37118.2i −0.00752997 + 0.00343882i
\(222\) 5.19131e6 + 8.07783e6i 0.474480 + 0.738305i
\(223\) 1.89304e7 + 5.55848e6i 1.70705 + 0.501235i 0.982227 0.187699i \(-0.0601030\pi\)
0.724824 + 0.688934i \(0.241921\pi\)
\(224\) −7.03900e7 + 1.01206e7i −6.26278 + 0.900452i
\(225\) 1.47468e6 3.22911e6i 0.129465 0.283488i
\(226\) −1.45756e7 2.09565e6i −1.26270 0.181549i
\(227\) −229589. + 357247.i −0.0196279 + 0.0305416i −0.850929 0.525281i \(-0.823960\pi\)
0.831301 + 0.555823i \(0.187597\pi\)
\(228\) 2.15134e7 1.86415e7i 1.81512 1.57281i
\(229\) 5.82275e6i 0.484866i −0.970168 0.242433i \(-0.922055\pi\)
0.970168 0.242433i \(-0.0779455\pi\)
\(230\) −4.60738e6 3.75927e6i −0.378679 0.308972i
\(231\) −1.42000e7 −1.15200
\(232\) 1.20830e7 + 1.39446e7i 0.967636 + 1.11671i
\(233\) 1.00487e7 + 6.45794e6i 0.794409 + 0.510536i 0.873787 0.486309i \(-0.161657\pi\)
−0.0793781 + 0.996845i \(0.525293\pi\)
\(234\) 66182.2 460308.i 0.00516528 0.0359253i
\(235\) −2.43217e6 1.11074e6i −0.187409 0.0855869i
\(236\) −2.44771e6 1.70242e7i −0.186219 1.29518i
\(237\) 1.89534e6 6.45493e6i 0.142378 0.484894i
\(238\) −5.82012e6 + 3.74036e6i −0.431719 + 0.277449i
\(239\) 2.61004e6 + 5.71520e6i 0.191185 + 0.418637i 0.980814 0.194948i \(-0.0624539\pi\)
−0.789628 + 0.613585i \(0.789727\pi\)
\(240\) −1.98908e6 6.77419e6i −0.143886 0.490031i
\(241\) −2.28444e6 1.97948e6i −0.163203 0.141416i 0.569431 0.822039i \(-0.307164\pi\)
−0.732634 + 0.680623i \(0.761709\pi\)
\(242\) 3.17102e6 3.65955e6i 0.223745 0.258215i
\(243\) 883197. 259330.i 0.0615515 0.0180732i
\(244\) 1.55701e6 711063.i 0.107182 0.0489484i
\(245\) 4.82379e6 + 7.50596e6i 0.328012 + 0.510397i
\(246\) 3.76746e6 + 1.10623e6i 0.253071 + 0.0743085i
\(247\) 1.31938e6 189698.i 0.0875544 0.0125884i
\(248\) −2.40555e7 + 5.26743e7i −1.57710 + 3.45337i
\(249\) −5.22946e6 751883.i −0.338734 0.0487026i
\(250\) 7.98863e6 1.24306e7i 0.511273 0.795556i
\(251\) −3.28130e6 + 2.84326e6i −0.207503 + 0.179802i −0.752412 0.658693i \(-0.771110\pi\)
0.544909 + 0.838495i \(0.316564\pi\)
\(252\) 2.62020e7i 1.63732i
\(253\) 1.74663e7 + 1.98525e6i 1.07855 + 0.122590i
\(254\) −2.26632e7 −1.38299
\(255\) −232940. 268827.i −0.0140483 0.0162126i
\(256\) 2.48639e7 + 1.59790e7i 1.48200 + 0.952425i
\(257\) 3.81136e6 2.65086e7i 0.224533 1.56166i −0.496051 0.868294i \(-0.665217\pi\)
0.720584 0.693368i \(-0.243874\pi\)
\(258\) 2.44338e7 + 1.11585e7i 1.42276 + 0.649753i
\(259\) 3.60531e6 + 2.50755e7i 0.207512 + 1.44328i
\(260\) 191751. 653044.i 0.0109098 0.0371554i
\(261\) −2.29901e6 + 1.47749e6i −0.129306 + 0.0831001i
\(262\) −2.09595e7 4.58950e7i −1.16541 2.55189i
\(263\) 3.94177e6 + 1.34244e7i 0.216682 + 0.737952i 0.994052 + 0.108908i \(0.0347354\pi\)
−0.777369 + 0.629044i \(0.783446\pi\)
\(264\) 2.79258e7 + 2.41978e7i 1.51773 + 1.31512i
\(265\) −4.11550e6 + 4.74954e6i −0.221149 + 0.255220i
\(266\) 9.90271e7 2.90770e7i 5.26150 1.54491i
\(267\) 1.01078e7 4.61607e6i 0.531034 0.242515i
\(268\) −468900. 729622.i −0.0243599 0.0379047i
\(269\) −6.08945e6 1.78802e6i −0.312839 0.0918579i 0.121544 0.992586i \(-0.461215\pi\)
−0.434383 + 0.900728i \(0.643034\pi\)
\(270\) 1.83248e6 263471.i 0.0930996 0.0133857i
\(271\) −1.24964e7 + 2.73632e7i −0.627879 + 1.37486i 0.281769 + 0.959482i \(0.409079\pi\)
−0.909648 + 0.415380i \(0.863649\pi\)
\(272\) 1.00652e7 + 1.44715e6i 0.500166 + 0.0719130i
\(273\) 663322. 1.03215e6i 0.0326014 0.0507288i
\(274\) −3.26427e7 + 2.82850e7i −1.58684 + 1.37501i
\(275\) 2.11065e7i 1.01489i
\(276\) −3.66320e6 + 3.22290e7i −0.174234 + 1.53292i
\(277\) 4.87114e6 0.229188 0.114594 0.993412i \(-0.463443\pi\)
0.114594 + 0.993412i \(0.463443\pi\)
\(278\) −1.80191e7 2.07952e7i −0.838685 0.967894i
\(279\) −7.21518e6 4.63691e6i −0.332227 0.213509i
\(280\) 4.69320e6 3.26419e7i 0.213794 1.48697i
\(281\) −2.56383e7 1.17086e7i −1.15550 0.527700i −0.256889 0.966441i \(-0.582697\pi\)
−0.898614 + 0.438741i \(0.855425\pi\)
\(282\) 2.85243e6 + 1.98391e7i 0.127194 + 0.884655i
\(283\) 3.17898e6 1.08266e7i 0.140258 0.477675i −0.859163 0.511702i \(-0.829015\pi\)
0.999421 + 0.0340270i \(0.0108332\pi\)
\(284\) 9.36260e7 6.01698e7i 4.08735 2.62678i
\(285\) 2.20438e6 + 4.82691e6i 0.0952250 + 0.208514i
\(286\) 778982. + 2.65297e6i 0.0332988 + 0.113405i
\(287\) 7.82904e6 + 6.78390e6i 0.331179 + 0.286968i
\(288\) −1.79486e7 + 2.07137e7i −0.751367 + 0.867124i
\(289\) −2.26683e7 + 6.65600e6i −0.939128 + 0.275753i
\(290\) −4.99973e6 + 2.28330e6i −0.205000 + 0.0936201i
\(291\) −4.83410e6 7.52200e6i −0.196172 0.305249i
\(292\) 1.04868e8 + 3.07920e7i 4.21205 + 1.23677i
\(293\) −4.16530e7 + 5.98880e6i −1.65594 + 0.238088i −0.905956 0.423372i \(-0.860846\pi\)
−0.749981 + 0.661460i \(0.769937\pi\)
\(294\) 2.77841e7 6.08388e7i 1.09334 2.39408i
\(295\) 3.17351e6 + 456282.i 0.123616 + 0.0177733i
\(296\) 3.56402e7 5.54572e7i 1.37425 2.13837i
\(297\) −4.13611e6 + 3.58396e6i −0.157879 + 0.136803i
\(298\) 8.32763e7i 3.14683i
\(299\) −960201. + 1.17683e6i −0.0359210 + 0.0440251i
\(300\) −3.89459e7 −1.44244
\(301\) 4.64085e7 + 5.35583e7i 1.70176 + 1.96394i
\(302\) −4.72614e7 3.03731e7i −1.71588 1.10273i
\(303\) −2.11199e6 + 1.46892e7i −0.0759215 + 0.528046i
\(304\) −1.37987e8 6.30165e7i −4.91153 2.24302i
\(305\) 45409.7 + 315831.i 0.00160048 + 0.0111316i
\(306\) −751222. + 2.55843e6i −0.0262183 + 0.0892912i
\(307\) 9.33394e6 5.99856e6i 0.322589 0.207316i −0.369316 0.929304i \(-0.620408\pi\)
0.691905 + 0.721988i \(0.256772\pi\)
\(308\) 6.47165e7 + 1.41709e8i 2.21494 + 4.85005i
\(309\) −6.39387e6 2.17755e7i −0.216715 0.738062i
\(310\) −1.30366e7 1.12963e7i −0.437602 0.379185i
\(311\) −2.88408e7 + 3.32841e7i −0.958796 + 1.10651i 0.0354480 + 0.999372i \(0.488714\pi\)
−0.994244 + 0.107138i \(0.965831\pi\)
\(312\) −3.06335e6 + 899480.i −0.100863 + 0.0296161i
\(313\) 3.46188e6 1.58099e6i 0.112896 0.0515579i −0.358166 0.933658i \(-0.616598\pi\)
0.471062 + 0.882100i \(0.343871\pi\)
\(314\) 4.15576e7 + 6.46649e7i 1.34234 + 2.08872i
\(315\) 4.68650e6 + 1.37608e6i 0.149940 + 0.0440263i
\(316\) −7.30552e7 + 1.05038e7i −2.31521 + 0.332877i
\(317\) 5.93648e6 1.29991e7i 0.186359 0.408070i −0.793274 0.608865i \(-0.791625\pi\)
0.979633 + 0.200795i \(0.0643525\pi\)
\(318\) 4.66301e7 + 6.70440e6i 1.45006 + 0.208487i
\(319\) 8.78460e6 1.36691e7i 0.270614 0.421083i
\(320\) −1.97542e7 + 1.71171e7i −0.602851 + 0.522374i
\(321\) 1.82846e7i 0.552804i
\(322\) −6.06224e7 + 1.00773e8i −1.81579 + 3.01841i
\(323\) −7.64279e6 −0.226801
\(324\) −6.61316e6 7.63200e6i −0.194435 0.224390i
\(325\) −1.53416e6 985942.i −0.0446909 0.0287211i
\(326\) −9.59017e6 + 6.67011e7i −0.276805 + 1.92522i
\(327\) −9.31176e6 4.25254e6i −0.266311 0.121620i
\(328\) −3.83637e6 2.66825e7i −0.108717 0.756145i
\(329\) −1.48979e7 + 5.07376e7i −0.418348 + 1.42476i
\(330\) −9.25994e6 + 5.95100e6i −0.257672 + 0.165595i
\(331\) −1.54471e6 3.38245e6i −0.0425956 0.0932713i 0.887138 0.461504i \(-0.152690\pi\)
−0.929734 + 0.368233i \(0.879963\pi\)
\(332\) 1.63298e7 + 5.56143e7i 0.446239 + 1.51975i
\(333\) 7.37898e6 + 6.39392e6i 0.199831 + 0.173155i
\(334\) 2.02066e7 2.33196e7i 0.542317 0.625867i
\(335\) 155126. 45549.2i 0.00412621 0.00121156i
\(336\) −1.27011e8 + 5.80039e7i −3.34829 + 1.52911i
\(337\) −2.44860e7 3.81010e7i −0.639776 0.995512i −0.998082 0.0619072i \(-0.980282\pi\)
0.358305 0.933604i \(-0.383355\pi\)
\(338\) 7.07702e7 + 2.07800e7i 1.83274 + 0.538140i
\(339\) −1.48209e7 + 2.13093e6i −0.380432 + 0.0546978i
\(340\) −1.62115e6 + 3.54982e6i −0.0412464 + 0.0903170i
\(341\) 5.04749e7 + 7.25720e6i 1.27295 + 0.183023i
\(342\) 2.15054e7 3.34631e7i 0.537613 0.836541i
\(343\) 7.72982e7 6.69792e7i 1.91552 1.65981i
\(344\) 1.84412e8i 4.53015i
\(345\) −5.57211e6 2.34781e6i −0.135695 0.0571749i
\(346\) −4.98440e7 −1.20333
\(347\) 5.43822e6 + 6.27605e6i 0.130157 + 0.150210i 0.817087 0.576514i \(-0.195587\pi\)
−0.686930 + 0.726724i \(0.741042\pi\)
\(348\) 2.52224e7 + 1.62094e7i 0.598478 + 0.384618i
\(349\) 3.44099e6 2.39326e7i 0.0809482 0.563007i −0.908474 0.417942i \(-0.862752\pi\)
0.989422 0.145065i \(-0.0463393\pi\)
\(350\) −1.28442e8 5.86577e7i −2.99574 1.36811i
\(351\) −67296.4 468057.i −0.00155622 0.0108237i
\(352\) 4.59110e7 1.56358e8i 1.05266 3.58504i
\(353\) −5.91807e7 + 3.80332e7i −1.34542 + 0.864646i −0.997345 0.0728226i \(-0.976799\pi\)
−0.348070 + 0.937468i \(0.613163\pi\)
\(354\) −9.98391e6 2.18617e7i −0.225056 0.492804i
\(355\) 5.84493e6 + 1.99060e7i 0.130645 + 0.444937i
\(356\) −9.21325e7 7.98333e7i −2.04203 1.76943i
\(357\) −4.60685e6 + 5.31659e6i −0.101251 + 0.116850i
\(358\) −5.64235e7 + 1.65674e7i −1.22973 + 0.361082i
\(359\) 8.10174e6 3.69994e6i 0.175103 0.0799671i −0.325935 0.945392i \(-0.605679\pi\)
0.501038 + 0.865425i \(0.332952\pi\)
\(360\) −6.87155e6 1.06923e7i −0.147281 0.229174i
\(361\) 6.42558e7 + 1.88672e7i 1.36581 + 0.401039i
\(362\) 7.62679e7 1.09657e7i 1.60774 0.231158i
\(363\) 2.04542e6 4.47885e6i 0.0427625 0.0936367i
\(364\) −1.33235e7 1.91562e6i −0.276257 0.0397197i
\(365\) −1.10149e7 + 1.71396e7i −0.226518 + 0.352469i
\(366\) 1.80764e6 1.56633e6i 0.0368696 0.0319477i
\(367\) 1.81997e7i 0.368185i 0.982909 + 0.184093i \(0.0589346\pi\)
−0.982909 + 0.184093i \(0.941065\pi\)
\(368\) 1.64335e8 5.35892e7i 3.29752 1.07531i
\(369\) 3.99261e6 0.0794654
\(370\) 1.28598e7 + 1.48410e7i 0.253880 + 0.292993i
\(371\) 1.04559e8 + 6.71958e7i 2.04757 + 1.31589i
\(372\) −1.33911e7 + 9.31369e7i −0.260127 + 1.80923i
\(373\) −7.15845e6 3.26915e6i −0.137941 0.0629954i 0.345249 0.938511i \(-0.387795\pi\)
−0.483190 + 0.875516i \(0.660522\pi\)
\(374\) −2.25621e6 1.56923e7i −0.0431286 0.299966i
\(375\) 4.23303e6 1.44164e7i 0.0802708 0.273377i
\(376\) 1.15759e8 7.43938e7i 2.17766 1.39950i
\(377\) 583207. + 1.27704e6i 0.0108842 + 0.0238332i
\(378\) −1.03152e7 3.51305e7i −0.190987 0.650442i
\(379\) −3.33280e7 2.88789e7i −0.612198 0.530472i 0.292643 0.956222i \(-0.405465\pi\)
−0.904841 + 0.425749i \(0.860011\pi\)
\(380\) 3.81239e7 4.39973e7i 0.694778 0.801817i
\(381\) −2.21113e7 + 6.49245e6i −0.399796 + 0.117391i
\(382\) −8.89145e7 + 4.06059e7i −1.59508 + 0.728449i
\(383\) 1.25441e7 + 1.95190e7i 0.223277 + 0.347426i 0.934761 0.355276i \(-0.115613\pi\)
−0.711484 + 0.702702i \(0.751977\pi\)
\(384\) 8.00317e7 + 2.34994e7i 1.41341 + 0.415015i
\(385\) −2.87450e7 + 4.13291e6i −0.503709 + 0.0724225i
\(386\) −7.65903e6 + 1.67709e7i −0.133172 + 0.291605i
\(387\) 2.70354e7 + 3.88710e6i 0.466444 + 0.0670645i
\(388\) −5.30347e7 + 8.25236e7i −0.907956 + 1.41281i
\(389\) 3.04586e7 2.63925e7i 0.517441 0.448366i −0.356572 0.934268i \(-0.616054\pi\)
0.874013 + 0.485902i \(0.161509\pi\)
\(390\) 951061.i 0.0160330i
\(391\) 6.40982e6 5.89546e6i 0.107230 0.0986251i
\(392\) −4.59175e8 −7.62289
\(393\) −3.35969e7 3.87729e7i −0.553505 0.638778i
\(394\) 2.87673e7 + 1.84876e7i 0.470338 + 0.302268i
\(395\) 1.95802e6 1.36183e7i 0.0317706 0.220970i
\(396\) 5.46166e7 + 2.49426e7i 0.879507 + 0.401658i
\(397\) −1.47482e7 1.02576e8i −0.235704 1.63936i −0.672716 0.739901i \(-0.734872\pi\)
0.437012 0.899456i \(-0.356037\pi\)
\(398\) −3.64885e7 + 1.24269e8i −0.578772 + 1.97111i
\(399\) 8.82856e7 5.67377e7i 1.38986 0.893209i
\(400\) 8.62153e7 + 1.88785e8i 1.34711 + 2.94977i
\(401\) −1.72510e7 5.87516e7i −0.267536 0.911143i −0.978209 0.207621i \(-0.933428\pi\)
0.710674 0.703522i \(-0.248390\pi\)
\(402\) −915919. 793648.i −0.0140987 0.0122166i
\(403\) −2.88533e6 + 3.32984e6i −0.0440839 + 0.0508755i
\(404\) 1.56217e8 4.58695e7i 2.36911 0.695633i
\(405\) 1.71237e6 782015.i 0.0257771 0.0117720i
\(406\) 5.87692e7 + 9.14466e7i 0.878155 + 1.36644i
\(407\) −5.57005e7 1.63551e7i −0.826182 0.242589i
\(408\) 1.81197e7 2.60522e6i 0.266791 0.0383587i
\(409\) 2.69579e7 5.90296e7i 0.394019 0.862780i −0.603823 0.797118i \(-0.706357\pi\)
0.997842 0.0656621i \(-0.0209160\pi\)
\(410\) 7.94842e6 + 1.14281e6i 0.115327 + 0.0165815i
\(411\) −2.37447e7 + 3.69475e7i −0.342012 + 0.532181i
\(412\) −1.88169e8 + 1.63050e8i −2.69065 + 2.33146i
\(413\) 6.34077e7i 0.900103i
\(414\) 7.77651e6 + 4.46534e7i 0.109593 + 0.629294i
\(415\) −1.08048e7 −0.151173
\(416\) 9.22053e6 + 1.06411e7i 0.128078 + 0.147810i
\(417\) −2.35376e7 1.51267e7i −0.324604 0.208610i
\(418\) −3.36580e7 + 2.34096e8i −0.460850 + 3.20528i
\(419\) 3.96062e7 + 1.80876e7i 0.538420 + 0.245888i 0.666015 0.745938i \(-0.267999\pi\)
−0.127595 + 0.991826i \(0.540726\pi\)
\(420\) −7.62608e6 5.30405e7i −0.102933 0.715913i
\(421\) 1.45743e7 4.96355e7i 0.195318 0.665191i −0.802345 0.596860i \(-0.796415\pi\)
0.997663 0.0683305i \(-0.0217672\pi\)
\(422\) 7.66448e7 4.92566e7i 1.01987 0.655431i
\(423\) 8.46637e6 + 1.85388e7i 0.111860 + 0.244940i
\(424\) −9.11192e7 3.10323e8i −1.19540 4.07115i
\(425\) 7.90243e6 + 6.84749e6i 0.102942 + 0.0892000i
\(426\) 1.01842e8 1.17532e8i 1.31734 1.52029i
\(427\) 6.05480e6 1.77785e6i 0.0777707 0.0228355i
\(428\) 1.82472e8 8.33323e7i 2.32737 1.06287i
\(429\) 1.52002e6 + 2.36520e6i 0.0192521 + 0.0299568i
\(430\) 5.27089e7 + 1.54767e7i 0.662947 + 0.194659i
\(431\) −7.17307e7 + 1.03133e7i −0.895928 + 0.128815i −0.574870 0.818245i \(-0.694947\pi\)
−0.321058 + 0.947060i \(0.604038\pi\)
\(432\) −2.23555e7 + 4.89516e7i −0.277289 + 0.607178i
\(433\) 5.94401e7 + 8.54620e6i 0.732177 + 0.105271i 0.498312 0.866998i \(-0.333954\pi\)
0.233865 + 0.972269i \(0.424863\pi\)
\(434\) −1.84440e8 + 2.86994e8i −2.25624 + 3.51078i
\(435\) −4.22386e6 + 3.65999e6i −0.0513147 + 0.0444644i
\(436\) 1.12308e8i 1.35504i
\(437\) −1.16526e8 + 5.74458e7i −1.39629 + 0.688357i
\(438\) 1.52725e8 1.81755
\(439\) −6.69269e7 7.72378e7i −0.791056 0.912928i 0.206799 0.978383i \(-0.433695\pi\)
−0.997855 + 0.0654557i \(0.979150\pi\)
\(440\) 6.35728e7 + 4.08558e7i 0.746300 + 0.479618i
\(441\) 9.67866e6 6.73166e7i 0.112849 0.784885i
\(442\) 1.24601e6 + 569036.i 0.0144297 + 0.00658981i
\(443\) −2.28941e7 1.59232e8i −0.263337 1.83155i −0.507304 0.861767i \(-0.669358\pi\)
0.243967 0.969784i \(-0.421551\pi\)
\(444\) 3.01787e7 1.02779e8i 0.344787 1.17424i
\(445\) 1.91176e7 1.22862e7i 0.216947 0.139424i
\(446\) −1.25648e8 2.75130e8i −1.41628 3.10122i
\(447\) −2.38566e7 8.12482e7i −0.267108 0.909685i
\(448\) 3.90679e8 + 3.38525e8i 4.34496 + 3.76493i
\(449\) −4.25948e7 + 4.91570e7i −0.470563 + 0.543059i −0.940568 0.339605i \(-0.889707\pi\)
0.470005 + 0.882664i \(0.344252\pi\)
\(450\) −5.22169e7 + 1.53323e7i −0.573025 + 0.168255i
\(451\) −2.15934e7 + 9.86139e6i −0.235392 + 0.107500i
\(452\) 8.88121e7 + 1.38194e8i 0.961739 + 1.49649i
\(453\) −5.48115e7 1.60941e7i −0.589627 0.173130i
\(454\) 6.44395e6 926499.i 0.0688627 0.00990097i
\(455\) 1.04235e6 2.28243e6i 0.0110657 0.0242306i
\(456\) −2.70308e8 3.88644e7i −2.85078 0.409881i
\(457\) 9.30504e7 1.44789e8i 0.974922 1.51701i 0.123622 0.992329i \(-0.460549\pi\)
0.851300 0.524679i \(-0.175815\pi\)
\(458\) −6.74620e7 + 5.84561e7i −0.702203 + 0.608462i
\(459\) 2.71133e6i 0.0280378i
\(460\) 1.96485e6 + 6.63072e7i 0.0201863 + 0.681220i
\(461\) −8.12493e7 −0.829310 −0.414655 0.909979i \(-0.636098\pi\)
−0.414655 + 0.909979i \(0.636098\pi\)
\(462\) 1.42557e8 + 1.64520e8i 1.44565 + 1.66837i
\(463\) 1.09256e8 + 7.02148e7i 1.10079 + 0.707433i 0.959267 0.282502i \(-0.0911644\pi\)
0.141521 + 0.989935i \(0.454801\pi\)
\(464\) 2.27379e7 1.58145e8i 0.227613 1.58308i
\(465\) −1.59552e7 7.28651e6i −0.158688 0.0724704i
\(466\) −2.60608e7 1.81257e8i −0.257531 1.79117i
\(467\) −2.97165e7 + 1.01205e8i −0.291774 + 0.993692i 0.674948 + 0.737865i \(0.264166\pi\)
−0.966723 + 0.255827i \(0.917652\pi\)
\(468\) −4.36429e6 + 2.80476e6i −0.0425771 + 0.0273626i
\(469\) −1.32827e6 2.90850e6i −0.0128756 0.0281936i
\(470\) 1.15483e7 + 3.93300e7i 0.111231 + 0.378817i
\(471\) 5.90704e7 + 5.11848e7i 0.565337 + 0.489867i
\(472\) −1.08051e8 + 1.24698e8i −1.02755 + 1.18586i
\(473\) −1.55817e8 + 4.57521e7i −1.47242 + 0.432343i
\(474\) −9.38141e7 + 4.28435e7i −0.880913 + 0.402300i
\(475\) −8.43333e7 1.31225e8i −0.786898 1.22444i
\(476\) 7.40528e7 + 2.17439e7i 0.686627 + 0.201612i
\(477\) 4.74151e7 6.81726e6i 0.436879 0.0628138i
\(478\) 4.00130e7 8.76161e7i 0.366367 0.802233i
\(479\) 8.69842e7 + 1.25064e7i 0.791469 + 0.113796i 0.526181 0.850373i \(-0.323624\pi\)
0.265289 + 0.964169i \(0.414533\pi\)
\(480\) −3.03045e7 + 4.71547e7i −0.274020 + 0.426384i
\(481\) 3.79072e6 3.28468e6i 0.0340633 0.0295160i
\(482\) 4.63398e7i 0.413822i
\(483\) −3.02769e7 + 1.15686e8i −0.268702 + 1.02669i
\(484\) −5.40188e7 −0.476441
\(485\) −1.19749e7 1.38198e7i −0.104966 0.121137i
\(486\) −1.18712e7 7.62917e6i −0.103416 0.0664612i
\(487\) −2.83346e7 + 1.97072e8i −0.245319 + 1.70623i 0.379279 + 0.925282i \(0.376172\pi\)
−0.624598 + 0.780947i \(0.714737\pi\)
\(488\) −1.49370e7 6.82149e6i −0.128530 0.0586976i
\(489\) 9.75162e6 + 6.78240e7i 0.0833970 + 0.580039i
\(490\) 3.85362e7 1.31242e8i 0.327552 1.11554i
\(491\) 5.22470e7 3.35771e7i 0.441385 0.283661i −0.301013 0.953620i \(-0.597325\pi\)
0.742398 + 0.669959i \(0.233688\pi\)
\(492\) −1.81963e7 3.98444e7i −0.152788 0.334559i
\(493\) −2.26787e6 7.72364e6i −0.0189268 0.0644587i
\(494\) −1.54434e7 1.33818e7i −0.128104 0.111003i
\(495\) −7.32961e6 + 8.45882e6i −0.0604317 + 0.0697420i
\(496\) 4.81113e8 1.41268e8i 3.94278 1.15770i
\(497\) 3.73222e8 1.70445e8i 3.04017 1.38840i
\(498\) 4.37887e7 + 6.81365e7i 0.354547 + 0.551686i
\(499\) 1.04897e8 + 3.08004e7i 0.844228 + 0.247888i 0.675118 0.737709i \(-0.264093\pi\)
0.169110 + 0.985597i \(0.445911\pi\)
\(500\) −1.63161e8 + 2.34590e7i −1.30529 + 0.187672i
\(501\) 1.30339e7 2.85404e7i 0.103648 0.226958i
\(502\) 6.58836e7 + 9.47263e6i 0.520794 + 0.0748789i
\(503\) −4.16155e6 + 6.47549e6i −0.0327002 + 0.0508825i −0.857219 0.514952i \(-0.827810\pi\)
0.824519 + 0.565835i \(0.191446\pi\)
\(504\) −1.89969e8 + 1.64609e8i −1.48386 + 1.28577i
\(505\) 3.03501e7i 0.235660i
\(506\) −1.52348e8 2.22294e8i −1.17594 1.71584i
\(507\) 7.49996e7 0.575486
\(508\) 1.65564e8 + 1.91071e8i 1.26291 + 1.45748i
\(509\) −1.02088e7 6.56077e6i −0.0774140 0.0497510i 0.501361 0.865238i \(-0.332833\pi\)
−0.578775 + 0.815487i \(0.696469\pi\)
\(510\) −776066. + 5.39766e6i −0.00585043 + 0.0406907i
\(511\) 3.66521e8 + 1.67384e8i 2.74685 + 1.25445i
\(512\) −1.57472e7 1.09524e8i −0.117326 0.816019i
\(513\) 1.13953e7 3.88089e7i 0.0844062 0.287461i
\(514\) −3.45389e8 + 2.21968e8i −2.54343 + 1.63456i
\(515\) −1.92808e7 4.22192e7i −0.141158 0.309092i
\(516\) −8.44223e7 2.87516e8i −0.614480 2.09273i
\(517\) −9.15781e7 7.93529e7i −0.662705 0.574237i
\(518\) 2.54328e8 2.93510e8i 1.82980 2.11171i
\(519\) −4.86301e7 + 1.42791e7i −0.347859 + 0.102141i
\(520\) −5.93933e6 + 2.71240e6i −0.0422403 + 0.0192905i
\(521\) −2.14481e7 3.33738e7i −0.151661 0.235990i 0.757107 0.653291i \(-0.226612\pi\)
−0.908768 + 0.417302i \(0.862976\pi\)
\(522\) 4.01984e7 + 1.18033e7i 0.282616 + 0.0829837i
\(523\) −4.57953e7 + 6.58437e6i −0.320122 + 0.0460267i −0.300503 0.953781i \(-0.597155\pi\)
−0.0196194 + 0.999808i \(0.506245\pi\)
\(524\) −2.33817e8 + 5.11989e8i −1.62511 + 3.55850i
\(525\) −1.42118e8 2.04335e7i −0.982137 0.141210i
\(526\) 1.15962e8 1.80440e8i 0.796816 1.23987i
\(527\) 1.90926e7 1.65438e7i 0.130446 0.113032i
\(528\) 3.19963e8i 2.17369i
\(529\) 5.34149e7 1.38063e8i 0.360824 0.932634i
\(530\) 9.63444e7 0.647141
\(531\) −1.60036e7 1.84691e7i −0.106889 0.123357i
\(532\) −9.68578e8 6.22467e8i −6.43279 4.13410i
\(533\) 291899. 2.03021e6i 0.00192775 0.0134078i
\(534\) −1.54956e8 7.07661e7i −1.01762 0.464731i
\(535\) 5.32174e6 + 3.70135e7i 0.0347530 + 0.241713i
\(536\) −2.34412e6 + 7.98333e6i −0.0152225 + 0.0518430i
\(537\) −5.03032e7 + 3.23279e7i −0.324842 + 0.208763i
\(538\) 4.04177e7 + 8.85023e7i 0.259552 + 0.568340i
\(539\) 1.13920e8 + 3.87977e8i 0.727503 + 2.47765i
\(540\) −1.56083e7 1.35247e7i −0.0991229 0.0858905i
\(541\) −7.41176e7 + 8.55363e7i −0.468090 + 0.540205i −0.939879 0.341506i \(-0.889063\pi\)
0.471789 + 0.881711i \(0.343608\pi\)
\(542\) 4.42482e8 1.29925e8i 2.77906 0.816006i
\(543\) 7.12691e7 3.25475e7i 0.445145 0.203291i
\(544\) −4.36471e7 6.79162e7i −0.271118 0.421868i
\(545\) −2.00875e7 5.89821e6i −0.124090 0.0364360i
\(546\) −1.86176e7 + 2.67681e6i −0.114379 + 0.0164452i
\(547\) −6.22035e7 + 1.36207e8i −0.380061 + 0.832216i 0.618848 + 0.785511i \(0.287600\pi\)
−0.998909 + 0.0467058i \(0.985128\pi\)
\(548\) 4.76935e8 + 6.85730e7i 2.89813 + 0.416688i
\(549\) 1.31490e6 2.04603e6i 0.00794651 0.0123650i
\(550\) 2.44538e8 2.11893e8i 1.46980 1.27359i
\(551\) 1.20085e8i 0.717849i
\(552\) 2.56680e8 1.75914e8i 1.52607 1.04588i
\(553\) −2.72099e8 −1.60898
\(554\) −4.89027e7 5.64367e7i −0.287609 0.331919i
\(555\) 1.67982e7 + 1.07955e7i 0.0982615 + 0.0631488i
\(556\) −4.36847e7 + 3.03834e8i −0.254159 + 1.76771i
\(557\) −2.49974e8 1.14159e8i −1.44654 0.660612i −0.471341 0.881951i \(-0.656230\pi\)
−0.975197 + 0.221340i \(0.928957\pi\)
\(558\) 1.87121e7 + 1.30146e8i 0.107701 + 0.749078i
\(559\) 3.95311e6 1.34630e7i 0.0226310 0.0770740i
\(560\) −2.40225e8 + 1.54383e8i −1.36790 + 0.879097i
\(561\) −6.69673e6 1.46638e7i −0.0379292 0.0830535i
\(562\) 1.21735e8 + 4.14590e8i 0.685812 + 2.33566i
\(563\) 6.11300e6 + 5.29695e6i 0.0342554 + 0.0296825i 0.671820 0.740714i \(-0.265513\pi\)
−0.637565 + 0.770397i \(0.720058\pi\)
\(564\) 1.46423e8 1.68981e8i 0.816152 0.941890i
\(565\) −2.93818e7 + 8.62726e6i −0.162904 + 0.0478330i
\(566\) −1.57351e8 + 7.18597e7i −0.867800 + 0.396311i
\(567\) −2.01280e7 3.13198e7i −0.110421 0.171819i
\(568\) −1.02443e9 3.00800e8i −5.59033 1.64147i
\(569\) 1.64432e7 2.36418e6i 0.0892587 0.0128335i −0.0975407 0.995232i \(-0.531098\pi\)
0.186799 + 0.982398i \(0.440189\pi\)
\(570\) 3.37939e7 7.39983e7i 0.182479 0.399574i
\(571\) −1.12721e8 1.62069e7i −0.605478 0.0870546i −0.167244 0.985916i \(-0.553487\pi\)
−0.438234 + 0.898861i \(0.644396\pi\)
\(572\) 1.66761e7 2.59485e7i 0.0891058 0.138651i
\(573\) −7.51165e7 + 6.50888e7i −0.399274 + 0.345973i
\(574\) 1.58812e8i 0.839746i
\(575\) 1.71952e8 + 4.50027e7i 0.904490 + 0.236720i
\(576\) 1.99236e8 1.04256
\(577\) 7.34663e7 + 8.47846e7i 0.382438 + 0.441357i 0.914032 0.405643i \(-0.132952\pi\)
−0.531594 + 0.846999i \(0.678407\pi\)
\(578\) 3.04688e8 + 1.95811e8i 1.57787 + 1.01404i
\(579\) −2.66804e6 + 1.85566e7i −0.0137454 + 0.0956011i
\(580\) 5.57753e7 + 2.54717e7i 0.285863 + 0.130549i
\(581\) 3.04107e7 + 2.11511e8i 0.155060 + 1.07846i
\(582\) −3.86186e7 + 1.31523e8i −0.195897 + 0.667163i
\(583\) −2.39599e8 + 1.53981e8i −1.20915 + 0.777073i
\(584\) −4.35566e8 9.53757e8i −2.18683 4.78850i
\(585\) −272456. 927899.i −0.00136091 0.00463482i
\(586\) 4.87551e8 + 4.22466e8i 2.42286 + 2.09942i
\(587\) 1.10928e8 1.28018e8i 0.548437 0.632930i −0.412081 0.911147i \(-0.635198\pi\)
0.960518 + 0.278217i \(0.0897435\pi\)
\(588\) −7.15899e8 + 2.10207e8i −3.52143 + 1.03399i
\(589\) −3.42815e8 + 1.56558e8i −1.67770 + 0.766179i
\(590\) −2.65732e7 4.13488e7i −0.129386 0.201329i
\(591\) 3.33629e7 + 9.79624e6i 0.161623 + 0.0474567i
\(592\) −5.65016e8 + 8.12370e7i −2.72330 + 0.391552i
\(593\) 1.40100e8 3.06776e8i 0.671852 1.47115i −0.199199 0.979959i \(-0.563834\pi\)
0.871051 0.491192i \(-0.163439\pi\)
\(594\) 8.30471e7 + 1.19404e7i 0.396246 + 0.0569716i
\(595\) −7.77824e6 + 1.21032e7i −0.0369258 + 0.0574577i
\(596\) −7.02093e8 + 6.08367e8i −3.31631 + 2.87360i
\(597\) 1.31695e8i 0.618937i
\(598\) 2.32744e7 689678.i 0.108836 0.00322510i
\(599\) 1.92484e8 0.895600 0.447800 0.894134i \(-0.352208\pi\)
0.447800 + 0.894134i \(0.352208\pi\)
\(600\) 2.44670e8 + 2.82365e8i 1.13273 + 1.30724i
\(601\) 5.44748e7 + 3.50089e7i 0.250942 + 0.161270i 0.660065 0.751209i \(-0.270529\pi\)
−0.409123 + 0.912479i \(0.634165\pi\)
\(602\) 1.54615e8 1.07537e9i 0.708700 4.92912i
\(603\) −1.12097e6 511931.i −0.00511262 0.00233485i
\(604\) 8.91918e7 + 6.20343e8i 0.404775 + 2.81528i
\(605\) 2.83697e6 9.66183e6i 0.0128112 0.0436308i
\(606\) 1.91391e8 1.23000e8i 0.860012 0.552696i
\(607\) 3.40102e7 + 7.44719e7i 0.152070 + 0.332986i 0.970300 0.241904i \(-0.0777720\pi\)
−0.818230 + 0.574890i \(0.805045\pi\)
\(608\) 3.39306e8 + 1.15557e9i 1.50967 + 5.14145i
\(609\) 8.35351e7 + 7.23836e7i 0.369843 + 0.320471i
\(610\) 3.20332e6 3.69683e6i 0.0141127 0.0162869i
\(611\) 1.00458e7 2.94970e6i 0.0440412 0.0129317i
\(612\) 2.70578e7 1.23569e7i 0.118042 0.0539081i
\(613\) 4.45775e7 + 6.93639e7i 0.193524 + 0.301129i 0.924432 0.381347i \(-0.124540\pi\)
−0.730908 + 0.682476i \(0.760903\pi\)
\(614\) −1.63205e8 4.79212e7i −0.705063 0.207025i
\(615\) 8.08223e6 1.16205e6i 0.0347461 0.00499573i
\(616\) 6.20849e8 1.35947e9i 2.65610 5.81604i
\(617\) −1.80439e8 2.59431e7i −0.768199 0.110450i −0.252937 0.967483i \(-0.581396\pi\)
−0.515262 + 0.857032i \(0.672306\pi\)
\(618\) −1.88100e8 + 2.92689e8i −0.796935 + 1.24005i
\(619\) 2.72130e8 2.35802e8i 1.14737 0.994203i 0.147384 0.989079i \(-0.452915\pi\)
0.999987 0.00512327i \(-0.00163080\pi\)
\(620\) 1.92434e8i 0.807434i
\(621\) 2.03792e7 + 4.13381e7i 0.0850967 + 0.172614i
\(622\) 6.75167e8 2.80569
\(623\) −2.94317e8 3.39660e8i −1.21717 1.40469i
\(624\) 2.32570e7 + 1.49464e7i 0.0957195 + 0.0615152i
\(625\) −2.81118e7 + 1.95522e8i −0.115146 + 0.800858i
\(626\) −5.30719e7 2.42371e7i −0.216342 0.0988003i
\(627\) 3.42246e7 + 2.38037e8i 0.138847 + 0.965701i
\(628\) 2.41587e8 8.22770e8i 0.975427 3.32200i
\(629\) −2.41942e7 + 1.55487e7i −0.0972208 + 0.0624800i
\(630\) −3.11058e7 6.81122e7i −0.124400 0.272398i
\(631\) −1.64870e7 5.61496e7i −0.0656227 0.223490i 0.920152 0.391561i \(-0.128065\pi\)
−0.985775 + 0.168070i \(0.946246\pi\)
\(632\) 5.35111e8 + 4.63676e8i 2.11979 + 1.83681i
\(633\) 6.06674e7 7.00139e7i 0.239191 0.276041i
\(634\) −2.10204e8 + 6.17215e7i −0.824847 + 0.242197i
\(635\) −4.28701e7 + 1.95781e7i −0.167430 + 0.0764627i
\(636\) −2.84128e8 4.42111e8i −1.10444 1.71854i
\(637\) −3.35222e7 9.84302e6i −0.129692 0.0380811i
\(638\) −2.46560e8 + 3.54500e7i −0.949425 + 0.136507i
\(639\) 6.56916e7 1.43845e8i 0.251772 0.551304i
\(640\) 1.68847e8 + 2.42766e7i 0.644102 + 0.0926078i
\(641\) −1.11897e8 + 1.74115e8i −0.424857 + 0.661091i −0.986022 0.166613i \(-0.946717\pi\)
0.561165 + 0.827704i \(0.310353\pi\)
\(642\) 2.11845e8 1.83564e8i 0.800594 0.693718i
\(643\) 2.05641e8i 0.773530i −0.922178 0.386765i \(-0.873593\pi\)
0.922178 0.386765i \(-0.126407\pi\)
\(644\) 1.29248e9 2.25089e8i 4.83911 0.842744i
\(645\) 5.58589e7 0.208168
\(646\) 7.67280e7 + 8.85488e7i 0.284614 + 0.328462i
\(647\) −1.55227e8 9.97583e7i −0.573132 0.368329i 0.221741 0.975106i \(-0.428826\pi\)
−0.794873 + 0.606776i \(0.792462\pi\)
\(648\) −1.37874e7 + 9.58933e7i −0.0506707 + 0.352422i
\(649\) 1.32170e8 + 6.03601e7i 0.483503 + 0.220809i
\(650\) 3.97874e6 + 2.76727e7i 0.0144879 + 0.100766i
\(651\) −9.77313e7 + 3.32842e8i −0.354234 + 1.20641i
\(652\) 6.32409e8 4.06425e8i 2.28168 1.46635i
\(653\) 1.63582e8 + 3.58196e8i 0.587485 + 1.28641i 0.936950 + 0.349464i \(0.113636\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(654\) 4.42136e7 + 1.50578e8i 0.158060 + 0.538304i
\(655\) −7.92948e7 6.87094e7i −0.282177 0.244507i
\(656\) −1.52859e8 + 1.76409e8i −0.541477 + 0.624898i
\(657\) 1.49005e8 4.37518e7i 0.525418 0.154277i
\(658\) 7.37406e8 3.36762e8i 2.58839 1.18208i
\(659\) 9.04018e7 + 1.40668e8i 0.315879 + 0.491517i 0.962495 0.271298i \(-0.0874529\pi\)
−0.646616 + 0.762815i \(0.723817\pi\)
\(660\) 1.17820e8 + 3.45950e7i 0.409814 + 0.120332i
\(661\) −4.07220e7 + 5.85494e6i −0.141002 + 0.0202730i −0.212454 0.977171i \(-0.568146\pi\)
0.0714525 + 0.997444i \(0.477237\pi\)
\(662\) −2.36811e7 + 5.18543e7i −0.0816257 + 0.178735i
\(663\) 1.37868e6 + 198225.i 0.00473068 + 0.000680170i
\(664\) 3.00625e8 4.67781e8i 1.02688 1.59786i
\(665\) 1.62203e8 1.40549e8i 0.551560 0.477930i
\(666\) 1.49683e8i 0.506697i
\(667\) −9.26304e7 1.00712e8i −0.312159 0.339394i
\(668\) −3.44222e8 −1.15481
\(669\) −2.01405e8 2.32434e8i −0.672656 0.776286i
\(670\) −2.08508e6 1.34000e6i −0.00693264 0.00445534i
\(671\) −2.05794e6 + 1.43133e7i −0.00681186 + 0.0473776i
\(672\) 1.00838e9 + 4.60511e8i 3.32288 + 1.51751i
\(673\) 7.03570e7 + 4.89344e8i 0.230814 + 1.60535i 0.694598 + 0.719398i \(0.255582\pi\)
−0.463784 + 0.885948i \(0.653509\pi\)
\(674\) −1.95614e8 + 6.66199e8i −0.638880 + 2.17582i
\(675\) −4.65529e7 + 2.99177e7i −0.151368 + 0.0972786i
\(676\) −3.41811e8 7.48461e8i −1.10649 2.42286i
\(677\) −9.54586e7 3.25102e8i −0.307644 1.04774i −0.957680 0.287836i \(-0.907064\pi\)
0.650035 0.759904i \(-0.274754\pi\)
\(678\) 1.73480e8 + 1.50321e8i 0.556622 + 0.482316i
\(679\) −2.36828e8 + 2.73314e8i −0.756524 + 0.873075i
\(680\) 3.59214e7 1.05475e7i 0.114242 0.0335445i
\(681\) 6.02159e6 2.74997e6i 0.0190664 0.00870736i
\(682\) −4.22650e8 6.57656e8i −1.33238 2.07322i
\(683\) −2.06318e8 6.05805e7i −0.647553 0.190139i −0.0585688 0.998283i \(-0.518654\pi\)
−0.588984 + 0.808145i \(0.700472\pi\)
\(684\) −4.39229e8 + 6.31516e7i −1.37253 + 0.197340i
\(685\) −3.73128e7 + 8.17035e7i −0.116088 + 0.254196i
\(686\) −1.55203e9 2.23149e8i −4.80760 0.691229i
\(687\) −4.90727e7 + 7.63587e7i −0.151346 + 0.235498i
\(688\) −1.20681e9 + 1.04571e9i −3.70573 + 3.21103i
\(689\) 2.46085e7i 0.0752364i
\(690\) 2.87383e7 + 8.81283e7i 0.0874811 + 0.268268i
\(691\) 2.95689e8 0.896193 0.448097 0.893985i \(-0.352102\pi\)
0.448097 + 0.893985i \(0.352102\pi\)
\(692\) 3.64131e8 + 4.20229e8i 1.09885 + 1.26814i
\(693\) 1.86217e8 + 1.19674e8i 0.559524 + 0.359584i
\(694\) 1.81180e7 1.26014e8i 0.0542042 0.376998i
\(695\) −5.20496e7 2.37703e7i −0.155047 0.0708076i
\(696\) −4.09337e7 2.84700e8i −0.121410 0.844422i
\(697\) −3.31330e6 + 1.12840e7i −0.00978502 + 0.0333247i
\(698\) −3.11826e8 + 2.00399e8i −0.916952 + 0.589289i
\(699\) −7.73518e7 1.69377e8i −0.226485 0.495932i
\(700\) 4.43787e8 + 1.51140e9i 1.29384 + 4.40642i
\(701\) −4.82252e8 4.17874e8i −1.39997 1.21308i −0.946866 0.321628i \(-0.895770\pi\)
−0.453107 0.891456i \(-0.649685\pi\)
\(702\) −4.74726e6 + 5.47863e6i −0.0137225 + 0.0158366i
\(703\) 4.11655e8 1.20873e8i 1.18486 0.347907i
\(704\) −1.07754e9 + 4.92095e8i −3.08827 + 1.41036i
\(705\) 2.25341e7 + 3.50638e7i 0.0643093 + 0.100067i
\(706\) 1.03478e9 + 3.03839e8i 2.94059 + 0.863434i
\(707\) 5.94123e8 8.54220e7i 1.68119 0.241719i
\(708\) −1.11377e8 + 2.43882e8i −0.313831 + 0.687194i
\(709\) −3.44624e8 4.95494e7i −0.966956 0.139027i −0.359295 0.933224i \(-0.616983\pi\)
−0.607661 + 0.794197i \(0.707892\pi\)
\(710\) 1.71951e8 2.67560e8i 0.480428 0.747561i
\(711\) −7.92558e7 + 6.86755e7i −0.220507 + 0.191070i
\(712\) 1.16952e9i 3.24016i
\(713\) 1.66745e8 3.95740e8i 0.460029 1.09180i
\(714\) 1.07847e8 0.296287
\(715\) 3.76536e6 + 4.34546e6i 0.0103012 + 0.0118882i
\(716\) 5.51874e8 + 3.54668e8i 1.50349 + 0.966235i
\(717\) 1.39386e7 9.69451e7i 0.0378148 0.263008i
\(718\) −1.24203e8 5.67214e7i −0.335550 0.153241i
\(719\) 1.36279e7 + 9.47841e7i 0.0366642 + 0.255005i 0.999907 0.0136267i \(-0.00433765\pi\)
−0.963243 + 0.268632i \(0.913429\pi\)
\(720\) −3.10067e7 + 1.05599e8i −0.0830726 + 0.282919i
\(721\) −7.72201e8 + 4.96263e8i −2.06027 + 1.32406i
\(722\) −4.26487e8 9.33876e8i −1.13317 2.48129i
\(723\) 1.32752e7 + 4.52113e7i 0.0351259 + 0.119628i
\(724\) −6.49618e8 5.62897e8i −1.71176 1.48325i
\(725\) 1.07589e8 1.24164e8i 0.282328 0.325823i
\(726\) −7.24261e7 + 2.12662e7i −0.189271 + 0.0555751i
\(727\) −2.66282e7 + 1.21607e7i −0.0693007 + 0.0316486i −0.449764 0.893147i \(-0.648492\pi\)
0.380463 + 0.924796i \(0.375765\pi\)
\(728\) 6.98136e7 + 1.08632e8i 0.180945 + 0.281555i
\(729\) −1.37677e7 4.04255e6i −0.0355368 0.0104345i
\(730\) 3.09160e8 4.44504e7i 0.794720 0.114263i
\(731\) −3.34213e7 + 7.31825e7i −0.0855601 + 0.187351i
\(732\) −2.64111e7 3.79734e6i −0.0673368 0.00968158i
\(733\) −2.01860e8 + 3.14100e8i −0.512552 + 0.797547i −0.997010 0.0772674i \(-0.975380\pi\)
0.484458 + 0.874815i \(0.339017\pi\)
\(734\) 2.10860e8 1.82712e8i 0.533221 0.462038i
\(735\) 1.39086e8i 0.350284i
\(736\) −1.17595e9 7.07416e8i −2.94954 1.77436i
\(737\) 7.32704e6 0.0183032
\(738\) −4.00829e7 4.62581e7i −0.0997217 0.115085i
\(739\) −5.35839e8 3.44363e8i −1.32770 0.853263i −0.331771 0.943360i \(-0.607646\pi\)
−0.995933 + 0.0900966i \(0.971282\pi\)
\(740\) 3.11767e7 2.16839e8i 0.0769370 0.535108i
\(741\) −1.89008e7 8.63172e6i −0.0464544 0.0212150i
\(742\) −2.71167e8 1.88601e9i −0.663781 4.61670i
\(743\) 1.89319e8 6.44763e8i 0.461560 1.57193i −0.319570 0.947563i \(-0.603538\pi\)
0.781130 0.624368i \(-0.214643\pi\)
\(744\) 7.59387e8 4.88028e8i 1.84393 1.18502i
\(745\) −7.19401e7 1.57527e8i −0.173981 0.380966i
\(746\) 3.39894e7 + 1.15757e8i 0.0818703 + 0.278825i
\(747\) 6.22416e7 + 5.39327e7i 0.149320 + 0.129387i
\(748\) −1.15818e8 + 1.33661e8i −0.276738 + 0.319373i
\(749\) 7.09586e8 2.08353e8i 1.68873 0.495855i
\(750\) −2.09523e8 + 9.56861e7i −0.496648 + 0.226812i
\(751\) −2.80990e8 4.37229e8i −0.663393 1.03226i −0.996014 0.0891985i \(-0.971569\pi\)
0.332621 0.943060i \(-0.392067\pi\)
\(752\) −1.14325e9 3.35689e8i −2.68837 0.789376i
\(753\) 6.69928e7 9.63210e6i 0.156907 0.0225599i
\(754\) 8.94078e6 1.95776e7i 0.0208575 0.0456714i
\(755\) −1.15639e8 1.66264e7i −0.268697 0.0386328i
\(756\) −2.20824e8 + 3.43609e8i −0.511070 + 0.795241i
\(757\) 2.73697e8 2.37160e8i 0.630931 0.546705i −0.279615 0.960112i \(-0.590207\pi\)
0.910546 + 0.413407i \(0.135661\pi\)
\(758\) 6.76058e8i 1.55230i
\(759\) −2.12319e8 1.73236e8i −0.485584 0.396199i
\(760\) −5.58495e8 −1.27227
\(761\) −1.99020e8 2.29682e8i −0.451589 0.521161i 0.483610 0.875283i \(-0.339325\pi\)
−0.935199 + 0.354122i \(0.884780\pi\)
\(762\) 2.97202e8 + 1.91000e8i 0.671717 + 0.431686i
\(763\) −5.89241e7 + 4.09826e8i −0.132654 + 0.922627i
\(764\) 9.91899e8 + 4.52985e8i 2.22427 + 1.01579i
\(765\) 789131. + 5.48853e6i 0.00176264 + 0.0122595i
\(766\) 1.00212e8 3.41292e8i 0.222964 0.759346i
\(767\) −1.05614e7 + 6.78740e6i −0.0234065 + 0.0150424i
\(768\) −1.91393e8 4.19093e8i −0.422516 0.925181i
\(769\) −9.84248e7 3.35204e8i −0.216434 0.737106i −0.994104 0.108433i \(-0.965417\pi\)
0.777670 0.628673i \(-0.216402\pi\)
\(770\) 3.36462e8 + 2.91546e8i 0.736994 + 0.638609i
\(771\) −2.73389e8 + 3.15508e8i −0.596511 + 0.688410i
\(772\) 1.97346e8 5.79460e7i 0.428920 0.125942i
\(773\) 2.79839e8 1.27798e8i 0.605855 0.276685i −0.0887750 0.996052i \(-0.528295\pi\)
0.694630 + 0.719367i \(0.255568\pi\)
\(774\) −2.26379e8 3.52253e8i −0.488218 0.759683i
\(775\) 4.94727e8 + 1.45265e8i 1.06282 + 0.312073i
\(776\) 9.31492e8 1.33928e8i 1.99340 0.286607i
\(777\) 1.64050e8 3.59220e8i 0.349715 0.765769i
\(778\) −6.11564e8 8.79296e7i −1.29868 0.186722i
\(779\) 9.48505e7 1.47590e8i 0.200644 0.312209i
\(780\) −8.01828e6 + 6.94788e6i −0.0168965 + 0.0146409i
\(781\) 9.40214e8i 1.97367i
\(782\) −1.32654e8 1.50777e7i −0.277396 0.0315293i
\(783\) 4.26008e7 0.0887426
\(784\) 2.60375e9 + 3.00489e9i 5.40321 + 6.23563i
\(785\) 1.34473e8 + 8.64208e7i 0.277989 + 0.178653i
\(786\) −1.11932e8 + 7.78501e8i −0.230508 + 1.60322i
\(787\) −3.84329e8 1.75517e8i −0.788459 0.360077i −0.0198555 0.999803i \(-0.506321\pi\)
−0.768603 + 0.639726i \(0.779048\pi\)
\(788\) −5.42897e7 3.77593e8i −0.110953 0.771694i
\(789\) 6.14460e7 2.09266e8i 0.125102 0.426057i
\(790\) −1.77438e8 + 1.14032e8i −0.359886 + 0.231285i
\(791\) 2.51581e8 + 5.50885e8i 0.508333 + 1.11309i
\(792\) −1.62281e8 5.52678e8i −0.326657 1.11249i
\(793\) −944253. 818200.i −0.00189352 0.00164074i
\(794\) −1.04037e9 + 1.20066e9i −2.07840 + 2.39860i
\(795\) 9.39980e7 2.76003e7i 0.187076 0.0549304i
\(796\) 1.31426e9 6.00201e8i 2.60580 1.19003i
\(797\) 6.74195e7 + 1.04907e8i 0.133171 + 0.207218i 0.901434 0.432916i \(-0.142515\pi\)
−0.768263 + 0.640134i \(0.778879\pi\)
\(798\) −1.54368e9 4.53265e8i −3.03773 0.891957i
\(799\) −5.94207e7 + 8.54341e6i −0.116492 + 0.0167491i
\(800\) 6.84490e8 1.49882e9i 1.33689 2.92739i
\(801\) −1.71455e8 2.46515e7i −0.333620 0.0479674i
\(802\) −5.07504e8 + 7.89691e8i −0.983821 + 1.53086i
\(803\) −6.97808e8 + 6.04654e8i −1.34769 + 1.16778i
\(804\) 1.35199e7i 0.0260139i
\(805\) −2.76191e7 + 2.42994e8i −0.0529447 + 0.465810i
\(806\) 6.75459e7 0.129001
\(807\) 6.47871e7 + 7.47683e7i 0.123273 + 0.142265i
\(808\) −1.31397e9 8.44437e8i −2.49087 1.60079i
\(809\) −6.04166e7 + 4.20207e8i −0.114107 + 0.793629i 0.849746 + 0.527192i \(0.176755\pi\)
−0.963853 + 0.266436i \(0.914154\pi\)
\(810\) −2.62513e7 1.19886e7i −0.0493965 0.0225586i
\(811\) −1.14370e8 7.95463e8i −0.214413 1.49127i −0.758184 0.652040i \(-0.773913\pi\)
0.543772 0.839233i \(-0.316996\pi\)
\(812\) 3.41643e8 1.16353e9i 0.638123 2.17325i
\(813\) 3.94486e8 2.53521e8i 0.734108 0.471782i
\(814\) 3.69702e8 + 8.09535e8i 0.685455 + 1.50094i
\(815\) 3.94803e7 + 1.34458e8i 0.0729303 + 0.248378i
\(816\) −1.19797e8 1.03805e8i −0.220483 0.191049i
\(817\) 7.85956e8 9.07041e8i 1.44123 1.66326i
\(818\) −9.54551e8 + 2.80281e8i −1.74397 + 0.512076i
\(819\) −1.73974e7 + 7.94512e6i −0.0316689 + 0.0144627i
\(820\) −4.84315e7 7.53609e7i −0.0878388 0.136680i
\(821\) −1.50300e8 4.41321e7i −0.271600 0.0797489i 0.143097 0.989709i \(-0.454294\pi\)
−0.414696 + 0.909960i \(0.636112\pi\)
\(822\) 6.66450e8 9.58211e7i 1.19992 0.172522i
\(823\) −2.90964e7 + 6.37122e7i −0.0521963 + 0.114294i −0.933933 0.357447i \(-0.883647\pi\)
0.881737 + 0.471741i \(0.156374\pi\)
\(824\) 2.36428e9 + 3.39933e8i 4.22589 + 0.607591i
\(825\) 1.77880e8 2.76787e8i 0.316786 0.492928i
\(826\) −7.34637e8 + 6.36567e8i −1.30357 + 1.12955i
\(827\) 2.30121e8i 0.406855i 0.979090 + 0.203428i \(0.0652081\pi\)
−0.979090 + 0.203428i \(0.934792\pi\)
\(828\) 3.19657e8 3.91774e8i 0.563110 0.690151i
\(829\) 3.79895e8 0.666807 0.333403 0.942784i \(-0.391803\pi\)
0.333403 + 0.942784i \(0.391803\pi\)
\(830\) 1.08472e8 + 1.25184e8i 0.189708 + 0.218934i
\(831\) −6.38794e7 4.10528e7i −0.111316 0.0715385i
\(832\) 1.45661e7 1.01310e8i 0.0252915 0.175906i
\(833\) 1.82220e8 + 8.32172e7i 0.315255 + 0.143972i
\(834\) 6.10433e7 + 4.24565e8i 0.105230 + 0.731891i
\(835\) 1.80779e7 6.15677e7i 0.0310519 0.105753i
\(836\) 2.21952e9 1.42640e9i 3.79875 2.44131i
\(837\) 5.55399e7 + 1.21616e8i 0.0947172 + 0.207402i
\(838\) −1.88056e8 6.40460e8i −0.319562 1.08833i
\(839\) −1.26377e8 1.09506e8i −0.213984 0.185418i 0.541273 0.840847i \(-0.317942\pi\)
−0.755257 + 0.655429i \(0.772488\pi\)
\(840\) −3.36644e8 + 3.88508e8i −0.567981 + 0.655484i
\(841\) 4.49374e8 1.31948e8i 0.755474 0.221827i
\(842\) −7.21389e8 + 3.29447e8i −1.20846 + 0.551886i
\(843\) 2.37540e8 + 3.69619e8i 0.396509 + 0.616980i
\(844\) −9.75198e8 2.86344e8i −1.62205 0.476278i
\(845\) 1.51821e8 2.18286e7i 0.251630 0.0361790i
\(846\) 1.29793e8 2.84206e8i 0.214358 0.469377i
\(847\) −1.97121e8 2.83418e7i −0.324402 0.0466420i
\(848\) −1.51410e9 + 2.35598e9i −2.48294 + 3.86353i
\(849\) −1.32933e8 + 1.15187e8i −0.217224 + 0.188226i
\(850\) 1.60301e8i 0.261023i
\(851\) −2.52007e8 + 4.18914e8i −0.408906 + 0.679729i
\(852\) −1.73489e9 −2.80514
\(853\) 7.18104e7 + 8.28736e7i 0.115702 + 0.133527i 0.810646 0.585537i \(-0.199116\pi\)
−0.694944 + 0.719064i \(0.744571\pi\)
\(854\) −8.13837e7 5.23022e7i −0.130666 0.0839742i
\(855\) 1.17722e7 8.18773e7i 0.0188347 0.130998i
\(856\) −1.75052e9 7.99438e8i −2.79092 1.27457i
\(857\) 7.90725e7 + 5.49961e8i 0.125627 + 0.873755i 0.951005 + 0.309175i \(0.100053\pi\)
−0.825378 + 0.564580i \(0.809038\pi\)
\(858\) 1.21431e7 4.13557e7i 0.0192251 0.0654747i
\(859\) 2.78877e8 1.79223e8i 0.439980 0.282758i −0.301838 0.953359i \(-0.597600\pi\)
0.741818 + 0.670601i \(0.233964\pi\)
\(860\) −2.54577e8 5.57446e8i −0.400243 0.876411i
\(861\) −4.54958e7 1.54944e8i −0.0712790 0.242754i
\(862\) 8.39612e8 + 7.27528e8i 1.31086 + 1.13587i
\(863\) 6.09941e8 7.03910e8i 0.948977 1.09518i −0.0463801 0.998924i \(-0.514769\pi\)
0.995357 0.0962537i \(-0.0306860\pi\)
\(864\) 4.09945e8 1.20371e8i 0.635601 0.186629i
\(865\) −9.42858e7 + 4.30589e7i −0.145679 + 0.0665296i
\(866\) −4.97719e8 7.74466e8i −0.766356 1.19247i
\(867\) 3.53363e8 + 1.03757e8i 0.542206 + 0.159206i
\(868\) 3.76702e9 5.41616e8i 5.76022 0.828195i
\(869\) 2.59020e8 5.67176e8i 0.394707 0.864288i
\(870\) 8.48088e7 + 1.21937e7i 0.128790 + 0.0185173i
\(871\) −342266. + 532577.i −0.000517976 + 0.000805987i
\(872\) 8.14254e8 7.05555e8i 1.22803 1.06410i
\(873\) 1.39383e8i 0.209492i
\(874\) 1.83539e9 + 7.73343e8i 2.74913 + 1.15835i
\(875\) −6.07702e8 −0.907124
\(876\) −1.11571e9 1.28760e9i −1.65974 1.91544i
\(877\) 3.32699e8 + 2.13812e8i 0.493233 + 0.316982i 0.763504 0.645803i \(-0.223477\pi\)
−0.270271 + 0.962784i \(0.587113\pi\)
\(878\) −2.22974e8 + 1.55082e9i −0.329436 + 2.29128i
\(879\) 5.96704e8 + 2.72505e8i 0.878602 + 0.401244i
\(880\) −9.31253e7 6.47701e8i −0.136653 0.950443i
\(881\) 6.45107e7 2.19703e8i 0.0943418 0.321299i −0.898778 0.438405i \(-0.855544\pi\)
0.993119 + 0.117106i \(0.0373618\pi\)
\(882\) −8.77091e8 + 5.63672e8i −1.27832 + 0.821525i
\(883\) −2.51878e8 5.51537e8i −0.365855 0.801111i −0.999619 0.0275845i \(-0.991218\pi\)
0.633765 0.773526i \(-0.281509\pi\)
\(884\) −4.30516e6 1.46620e7i −0.00623207 0.0212245i
\(885\) −3.77715e7 3.27292e7i −0.0544922 0.0472177i
\(886\) −1.61501e9 + 1.86382e9i −2.32206 + 2.67980i
\(887\) −1.06091e9 + 3.11512e8i −1.52023 + 0.446379i −0.932043 0.362347i \(-0.881976\pi\)
−0.588185 + 0.808726i \(0.700157\pi\)
\(888\) −9.34760e8 + 4.26890e8i −1.33494 + 0.609646i
\(889\) 5.03915e8 + 7.84107e8i 0.717219 + 1.11601i
\(890\) −3.34274e8 9.81516e7i −0.474168 0.139228i
\(891\) 8.44451e7 1.21414e7i 0.119383 0.0171646i
\(892\) −1.40168e9 + 3.06925e9i −1.97494 + 4.32452i
\(893\) 8.86432e8 + 1.27450e8i 1.24478 + 0.178972i
\(894\) −7.01832e8 + 1.09207e9i −0.982247 + 1.52841i
\(895\) −9.24195e7 + 8.00820e7i −0.128912 + 0.111703i
\(896\) 3.37363e9i 4.69000i
\(897\) 2.25100e7 7.34042e6i 0.0311887 0.0101705i
\(898\) 9.97150e8 1.37699
\(899\) −2.59939e8 2.99985e8i −0.357760 0.412877i
\(900\) 5.10730e8 + 3.28226e8i 0.700590 + 0.450242i
\(901\) −2.00806e7 + 1.39663e8i −0.0274537 + 0.190945i
\(902\) 3.31035e8 + 1.51179e8i 0.451081 + 0.206002i
\(903\) −1.57218e8 1.09348e9i −0.213520 1.48507i
\(904\) 4.43989e8 1.51209e9i 0.600989 2.04678i
\(905\) 1.34797e8 8.66286e7i 0.181859 0.116873i
\(906\) 3.63802e8 + 7.96615e8i 0.489193 + 1.07118i
\(907\) 1.23467e8 + 4.20488e8i 0.165473 + 0.563550i 0.999922 + 0.0124647i \(0.00396775\pi\)
−0.834449 + 0.551085i \(0.814214\pi\)
\(908\) −5.48868e7 4.75597e7i −0.0733180 0.0635304i
\(909\) 1.51494e8 1.74833e8i 0.201699 0.232773i
\(910\) −3.69085e7 + 1.08373e7i −0.0489782 + 0.0143813i
\(911\) −2.29705e8 + 1.04903e8i −0.303819 + 0.138749i −0.561491 0.827483i \(-0.689772\pi\)
0.257672 + 0.966232i \(0.417045\pi\)
\(912\) 1.27845e9 + 1.98931e9i 1.68539 + 2.62251i
\(913\) −4.69833e8 1.37956e8i −0.617350 0.181270i
\(914\) −2.61168e9 + 3.75502e8i −3.42043 + 0.491783i
\(915\) 2.06625e6 4.52447e6i 0.00269725 0.00590614i
\(916\) 9.85673e8 + 1.41718e8i 1.28247 + 0.184391i
\(917\) −1.12185e9 + 1.74564e9i −1.45488 + 2.26384i
\(918\) 3.14132e7 2.72197e7i 0.0406054 0.0351848i
\(919\) 2.32737e8i 0.299861i 0.988697 + 0.149930i \(0.0479050\pi\)
−0.988697 + 0.149930i \(0.952095\pi\)
\(920\) 4.68396e8 4.30809e8i 0.601520 0.553250i
\(921\) −1.72958e8 −0.221392
\(922\) 8.15683e8 + 9.41348e8i 1.04071 + 1.20104i
\(923\) −6.83409e7 4.39200e7i −0.0869112 0.0558544i
\(924\) 3.45610e8 2.40377e9i 0.438097 3.04703i
\(925\) −5.33935e8 2.43840e8i −0.674626 0.308091i
\(926\) −2.83350e8 1.97074e9i −0.356853 2.48197i
\(927\) −9.96705e7 + 3.39447e8i −0.125120 + 0.426120i
\(928\) −1.06711e9 + 6.85790e8i −1.33526 + 0.858119i
\(929\) 2.84343e8 + 6.22625e8i 0.354647 + 0.776568i 0.999920 + 0.0126165i \(0.00401607\pi\)
−0.645274 + 0.763951i \(0.723257\pi\)
\(930\) 7.57577e7 + 2.58007e8i 0.0941842 + 0.320762i
\(931\) −2.25848e9 1.95699e9i −2.79877 2.42515i
\(932\) −1.33777e9 + 1.54387e9i −1.65247 + 1.90705i
\(933\) 6.58724e8 1.93419e8i 0.811070 0.238152i
\(934\) 1.47089e9 6.71731e8i 1.80525 0.824432i
\(935\) −1.78241e7 2.77348e7i −0.0218058 0.0339305i
\(936\) 4.77529e7 + 1.40215e7i 0.0582334 + 0.0170989i
\(937\) −6.63762e8 + 9.54345e7i −0.806851 + 0.116008i −0.533384 0.845874i \(-0.679080\pi\)
−0.273468 + 0.961881i \(0.588171\pi\)
\(938\) −2.03628e7 + 4.45884e7i −0.0246734 + 0.0540273i
\(939\) −5.87227e7 8.44305e6i −0.0709267 0.0101977i
\(940\) 2.47221e8 3.84684e8i 0.297647 0.463148i
\(941\) 7.86447e8 6.81460e8i 0.943845 0.817846i −0.0395702 0.999217i \(-0.512599\pi\)
0.983415 + 0.181371i \(0.0580534\pi\)
\(942\) 1.19824e9i 1.43348i
\(943\) 3.42986e7 + 1.96946e8i 0.0409017 + 0.234861i
\(944\) 1.42874e9 1.69839
\(945\) −4.98607e7 5.75423e7i −0.0590831 0.0681855i
\(946\) 2.09437e9 + 1.34597e9i 2.47389 + 1.58987i
\(947\) −7.93518e7 + 5.51904e8i −0.0934344 + 0.649850i 0.888253 + 0.459354i \(0.151919\pi\)
−0.981688 + 0.190497i \(0.938990\pi\)
\(948\) 1.04656e9 + 4.77947e8i 1.22840 + 0.560990i
\(949\) −1.13536e7 7.89663e7i −0.0132842 0.0923939i
\(950\) −6.73721e8 + 2.29448e9i −0.785795 + 2.67617i
\(951\) −1.87403e8 + 1.20437e8i −0.217889 + 0.140029i
\(952\) −3.07577e8 6.73499e8i −0.356486 0.780595i
\(953\) 1.58063e7 + 5.38312e7i 0.0182621 + 0.0621950i 0.968120 0.250487i \(-0.0805908\pi\)
−0.949858 + 0.312682i \(0.898773\pi\)
\(954\) −5.54997e8 4.80907e8i −0.639213 0.553881i
\(955\) −1.33114e8 + 1.53622e8i −0.152832 + 0.176377i
\(956\) −1.03099e9 + 3.02727e8i −1.18000 + 0.346479i
\(957\) −2.30400e8 + 1.05220e8i −0.262873 + 0.120050i
\(958\) −7.28359e8 1.13335e9i −0.828417 1.28904i
\(959\) 1.70442e9 + 5.00463e8i 1.93251 + 0.567435i
\(960\) 4.03313e8 5.79877e7i 0.455857 0.0655423i
\(961\) 1.48817e8 3.25864e8i 0.167680 0.367169i
\(962\) −7.61121e7 1.09433e7i −0.0854926 0.0122920i
\(963\) 1.54099e8 2.39782e8i 0.172552 0.268496i
\(964\) 3.90686e8 3.38531e8i 0.436110 0.377892i
\(965\) 3.83406e7i 0.0426655i
\(966\) 1.64428e9 8.10614e8i 1.82409 0.899254i
\(967\) 4.61731e8 0.510634 0.255317 0.966857i \(-0.417820\pi\)
0.255317 + 0.966857i \(0.417820\pi\)
\(968\) 3.39364e8 + 3.91647e8i 0.374144 + 0.431786i
\(969\) 1.00226e8 + 6.44116e7i 0.110157 + 0.0707934i
\(970\) −3.98957e7 + 2.77481e8i −0.0437131 + 0.304031i
\(971\) 1.50541e9 + 6.87496e8i 1.64436 + 0.750952i 0.999906 0.0136940i \(-0.00435907\pi\)
0.644450 + 0.764646i \(0.277086\pi\)
\(972\) 2.24034e7 + 1.55819e8i 0.0243958 + 0.169676i
\(973\) −3.18822e8 + 1.08581e9i −0.346107 + 1.17873i
\(974\) 2.56772e9 1.65017e9i 2.77888 1.78588i
\(975\) 1.18094e7 + 2.58590e7i 0.0127413 + 0.0278996i
\(976\) 4.00596e7 + 1.36431e8i 0.0430881 + 0.146745i
\(977\) −5.95654e8 5.16138e8i −0.638720 0.553454i 0.274159 0.961684i \(-0.411601\pi\)
−0.912879 + 0.408230i \(0.866146\pi\)
\(978\) 6.87905e8 7.93885e8i 0.735380 0.848674i
\(979\) 9.88176e8 2.90155e8i 1.05314 0.309230i
\(980\) −1.38801e9 + 6.33883e8i −1.47474 + 0.673490i
\(981\) 8.62736e7 + 1.34244e8i 0.0913842 + 0.142197i
\(982\) −9.13544e8 2.68241e8i −0.964706 0.283263i
\(983\) −9.37760e8 + 1.34830e8i −0.987259 + 0.141946i −0.616984 0.786976i \(-0.711646\pi\)
−0.370275 + 0.928922i \(0.620737\pi\)
\(984\) −1.74564e8 + 3.82242e8i −0.183219 + 0.401193i
\(985\) 7.03877e7 + 1.01202e7i 0.0736526 + 0.0105896i
\(986\) −6.67178e7 + 1.03815e8i −0.0696003 + 0.108300i
\(987\) 6.22973e8 5.39809e8i 0.647915 0.561422i
\(988\) 2.27961e8i 0.236368i
\(989\) 4.05070e7 + 1.36698e9i 0.0418737 + 1.41310i
\(990\) 1.71587e8 0.176839
\(991\) −1.96786e8 2.27103e8i −0.202196 0.233346i 0.645591 0.763683i \(-0.276611\pi\)
−0.847787 + 0.530337i \(0.822066\pi\)
\(992\) −3.34900e9 2.15227e9i −3.43068 2.20476i
\(993\) −8.24934e6 + 5.73755e7i −0.00842503 + 0.0585974i
\(994\) −5.72163e9 2.61298e9i −5.82587 2.66059i
\(995\) 3.83299e7 + 2.66590e8i 0.0389106 + 0.270629i
\(996\) 2.54557e8 8.66941e8i 0.257636 0.877428i
\(997\) 1.28514e9 8.25909e8i 1.29678 0.833387i 0.303919 0.952698i \(-0.401705\pi\)
0.992857 + 0.119311i \(0.0380686\pi\)
\(998\) −6.96233e8 1.52454e9i −0.700427 1.53372i
\(999\) −4.28804e7 1.46037e8i −0.0430093 0.146476i
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 69.7.f.a.10.1 yes 240
23.7 odd 22 inner 69.7.f.a.7.1 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.7.f.a.7.1 240 23.7 odd 22 inner
69.7.f.a.10.1 yes 240 1.1 even 1 trivial