Properties

Label 69.7.f.a.7.12
Level $69$
Weight $7$
Character 69.7
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 7.12
Character \(\chi\) \(=\) 69.7
Dual form 69.7.f.a.10.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0241383 - 0.0278571i) q^{2} +(13.1138 - 8.42776i) q^{3} +(9.10796 + 63.3472i) q^{4} +(-89.8556 + 41.0357i) q^{5} +(0.0817732 - 0.568745i) q^{6} +(-160.665 - 547.174i) q^{7} +(3.96908 + 2.55077i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})\) \(q+(0.0241383 - 0.0278571i) q^{2} +(13.1138 - 8.42776i) q^{3} +(9.10796 + 63.3472i) q^{4} +(-89.8556 + 41.0357i) q^{5} +(0.0817732 - 0.568745i) q^{6} +(-160.665 - 547.174i) q^{7} +(3.96908 + 2.55077i) q^{8} +(100.946 - 221.041i) q^{9} +(-1.02583 + 3.49365i) q^{10} +(1314.41 - 1138.94i) q^{11} +(653.315 + 753.966i) q^{12} +(1524.28 + 447.568i) q^{13} +(-19.1208 - 8.73219i) q^{14} +(-832.514 + 1295.42i) q^{15} +(-3929.83 + 1153.90i) q^{16} +(7185.39 + 1033.10i) q^{17} +(-3.72088 - 8.14759i) q^{18} +(10098.2 - 1451.91i) q^{19} +(-3417.90 - 5318.35i) q^{20} +(-6718.38 - 5821.51i) q^{21} -64.1078i q^{22} +(-8171.21 - 9014.84i) q^{23} +73.5472 q^{24} +(-3842.09 + 4434.01i) q^{25} +(49.2614 - 31.6584i) q^{26} +(-539.088 - 3749.44i) q^{27} +(33198.6 - 15161.3i) q^{28} +(4730.11 - 32898.6i) q^{29} +(15.9911 + 54.4605i) q^{30} +(34487.9 + 22164.0i) q^{31} +(-188.152 + 411.995i) q^{32} +(7638.25 - 26013.5i) q^{33} +(202.222 - 175.226i) q^{34} +(36890.3 + 42573.6i) q^{35} +(14921.7 + 4381.41i) q^{36} +(-18992.9 - 8673.77i) q^{37} +(203.308 - 316.354i) q^{38} +(23761.1 - 6976.90i) q^{39} +(-461.317 - 66.3273i) q^{40} +(-21125.9 - 46259.2i) q^{41} +(-324.340 + 46.6331i) q^{42} +(-66394.5 - 103312. i) q^{43} +(84120.6 + 72890.9i) q^{44} +24004.1i q^{45} +(-448.366 + 10.0231i) q^{46} -11413.5 q^{47} +(-41810.4 + 48251.8i) q^{48} +(-174613. + 112217. i) q^{49} +(30.7770 + 214.059i) q^{50} +(102935. - 47008.7i) q^{51} +(-14469.2 + 100635. i) q^{52} +(-37971.9 - 129320. i) q^{53} +(-117.461 - 75.4876i) q^{54} +(-71369.9 + 156278. i) q^{55} +(758.024 - 2581.59i) q^{56} +(120190. - 104146. i) q^{57} +(-802.283 - 925.884i) q^{58} +(-123696. - 36320.4i) q^{59} +(-89643.6 - 40938.9i) q^{60} +(-103388. + 160875. i) q^{61} +(1449.90 - 425.730i) q^{62} +(-137166. - 19721.5i) q^{63} +(-108885. - 238424. i) q^{64} +(-155331. + 22333.3i) q^{65} +(-540.285 - 840.700i) q^{66} +(326009. + 282489. i) q^{67} +464584. i q^{68} +(-183131. - 49354.3i) q^{69} +2076.44 q^{70} +(323134. - 372917. i) q^{71} +(964.486 - 619.838i) q^{72} +(70952.4 + 493485. i) q^{73} +(-700.082 + 319.717i) q^{74} +(-13015.8 + 90527.2i) q^{75} +(183949. + 626472. i) q^{76} +(-834380. - 536223. i) q^{77} +(379.197 - 830.326i) q^{78} +(-145534. + 495643. i) q^{79} +(305766. - 264948. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-1798.59 - 528.113i) q^{82} +(793080. + 362188. i) q^{83} +(307586. - 478613. i) q^{84} +(-688042. + 202027. i) q^{85} +(-4480.61 - 644.215i) q^{86} +(-215232. - 471292. i) q^{87} +(8122.19 - 1167.79i) q^{88} +(-306505. - 476930. i) q^{89} +(668.684 + 579.418i) q^{90} -905953. i q^{91} +(496642. - 599730. i) q^{92} +639061. q^{93} +(-275.503 + 317.948i) q^{94} +(-847804. + 544850. i) q^{95} +(1004.80 + 6988.54i) q^{96} +(898080. - 410139. i) q^{97} +(-1088.82 + 7572.94i) q^{98} +(-119068. - 405510. 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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{19}{22}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0241383 0.0278571i 0.00301729 0.00348213i −0.754239 0.656600i \(-0.771994\pi\)
0.757256 + 0.653118i \(0.226539\pi\)
\(3\) 13.1138 8.42776i 0.485698 0.312139i
\(4\) 9.10796 + 63.3472i 0.142312 + 0.989800i
\(5\) −89.8556 + 41.0357i −0.718845 + 0.328286i −0.741033 0.671468i \(-0.765664\pi\)
0.0221883 + 0.999754i \(0.492937\pi\)
\(6\) 0.0817732 0.568745i 0.000378579 0.00263308i
\(7\) −160.665 547.174i −0.468410 1.59526i −0.767510 0.641037i \(-0.778505\pi\)
0.299100 0.954222i \(-0.403314\pi\)
\(8\) 3.96908 + 2.55077i 0.00775211 + 0.00498198i
\(9\) 100.946 221.041i 0.138472 0.303211i
\(10\) −1.02583 + 3.49365i −0.00102583 + 0.00349365i
\(11\) 1314.41 1138.94i 0.987537 0.855706i −0.00199812 0.999998i \(-0.500636\pi\)
0.989535 + 0.144292i \(0.0460906\pi\)
\(12\) 653.315 + 753.966i 0.378076 + 0.436323i
\(13\) 1524.28 + 447.568i 0.693799 + 0.203718i 0.609574 0.792729i \(-0.291340\pi\)
0.0842251 + 0.996447i \(0.473159\pi\)
\(14\) −19.1208 8.73219i −0.00696823 0.00318228i
\(15\) −832.514 + 1295.42i −0.246671 + 0.383827i
\(16\) −3929.83 + 1153.90i −0.959432 + 0.281715i
\(17\) 7185.39 + 1033.10i 1.46253 + 0.210279i 0.827175 0.561945i \(-0.189947\pi\)
0.635350 + 0.772224i \(0.280856\pi\)
\(18\) −3.72088 8.14759i −0.000638011 0.00139705i
\(19\) 10098.2 1451.91i 1.47226 0.211679i 0.640991 0.767548i \(-0.278523\pi\)
0.831270 + 0.555869i \(0.187614\pi\)
\(20\) −3417.90 5318.35i −0.427237 0.664794i
\(21\) −6718.38 5821.51i −0.725448 0.628605i
\(22\) 64.1078i 0.00602064i
\(23\) −8171.21 9014.84i −0.671587 0.740925i
\(24\) 73.5472 0.00532025
\(25\) −3842.09 + 4434.01i −0.245894 + 0.283777i
\(26\) 49.2614 31.6584i 0.00280276 0.00180123i
\(27\) −539.088 3749.44i −0.0273885 0.190491i
\(28\) 33198.6 15161.3i 1.51233 0.690657i
\(29\) 4730.11 32898.6i 0.193944 1.34891i −0.627496 0.778619i \(-0.715920\pi\)
0.821441 0.570294i \(-0.193171\pi\)
\(30\) 15.9911 + 54.4605i 0.000592261 + 0.00201706i
\(31\) 34487.9 + 22164.0i 1.15766 + 0.743983i 0.971150 0.238470i \(-0.0766458\pi\)
0.186511 + 0.982453i \(0.440282\pi\)
\(32\) −188.152 + 411.995i −0.00574194 + 0.0125731i
\(33\) 7638.25 26013.5i 0.212545 0.723863i
\(34\) 202.222 175.226i 0.00514508 0.00445823i
\(35\) 36890.3 + 42573.6i 0.860415 + 0.992971i
\(36\) 14921.7 + 4381.41i 0.319824 + 0.0939089i
\(37\) −18992.9 8673.77i −0.374961 0.171239i 0.219015 0.975721i \(-0.429715\pi\)
−0.593976 + 0.804482i \(0.702443\pi\)
\(38\) 203.308 316.354i 0.00370514 0.00576531i
\(39\) 23761.1 6976.90i 0.400565 0.117617i
\(40\) −461.317 66.3273i −0.00720807 0.00103636i
\(41\) −21125.9 46259.2i −0.306523 0.671192i 0.692200 0.721705i \(-0.256641\pi\)
−0.998723 + 0.0505136i \(0.983914\pi\)
\(42\) −324.340 + 46.6331i −0.00437777 + 0.000629428i
\(43\) −66394.5 103312.i −0.835077 1.29941i −0.951949 0.306258i \(-0.900923\pi\)
0.116872 0.993147i \(-0.462713\pi\)
\(44\) 84120.6 + 72890.9i 0.987516 + 0.855688i
\(45\) 24004.1i 0.263420i
\(46\) −448.366 + 10.0231i −0.00460637 + 0.000102974i
\(47\) −11413.5 −0.109933 −0.0549664 0.998488i \(-0.517505\pi\)
−0.0549664 + 0.998488i \(0.517505\pi\)
\(48\) −41810.4 + 48251.8i −0.378060 + 0.436304i
\(49\) −174613. + 112217.i −1.48419 + 0.953830i
\(50\) 30.7770 + 214.059i 0.000246216 + 0.00171247i
\(51\) 102935. 47008.7i 0.775982 0.354379i
\(52\) −14469.2 + 100635.i −0.102904 + 0.715714i
\(53\) −37971.9 129320.i −0.255055 0.868639i −0.983094 0.183103i \(-0.941386\pi\)
0.728038 0.685536i \(-0.240432\pi\)
\(54\) −117.461 75.4876i −0.000745955 0.000479396i
\(55\) −71369.9 + 156278.i −0.428970 + 0.939314i
\(56\) 758.024 2581.59i 0.00431637 0.0147002i
\(57\) 120190. 104146.i 0.649001 0.562363i
\(58\) −802.283 925.884i −0.00411191 0.00474540i
\(59\) −123696. 36320.4i −0.602282 0.176846i −0.0336440 0.999434i \(-0.510711\pi\)
−0.568638 + 0.822588i \(0.692529\pi\)
\(60\) −89643.6 40938.9i −0.415017 0.189532i
\(61\) −103388. + 160875.i −0.455492 + 0.708759i −0.990715 0.135952i \(-0.956591\pi\)
0.535224 + 0.844710i \(0.320227\pi\)
\(62\) 1449.90 425.730i 0.00608364 0.00178632i
\(63\) −137166. 19721.5i −0.548561 0.0788711i
\(64\) −108885. 238424.i −0.415362 0.909516i
\(65\) −155331. + 22333.3i −0.565612 + 0.0813227i
\(66\) −540.285 840.700i −0.00187928 0.00292421i
\(67\) 326009. + 282489.i 1.08394 + 0.939240i 0.998369 0.0570922i \(-0.0181829\pi\)
0.0855717 + 0.996332i \(0.472728\pi\)
\(68\) 464584.i 1.47753i
\(69\) −183131. 49354.3i −0.557460 0.150237i
\(70\) 2076.44 0.00605377
\(71\) 323134. 372917.i 0.902834 1.04193i −0.0960815 0.995373i \(-0.530631\pi\)
0.998916 0.0465529i \(-0.0148236\pi\)
\(72\) 964.486 619.838i 0.00258404 0.00166066i
\(73\) 70952.4 + 493485.i 0.182389 + 1.26854i 0.851093 + 0.525014i \(0.175940\pi\)
−0.668705 + 0.743528i \(0.733151\pi\)
\(74\) −700.082 + 319.717i −0.00172764 + 0.000788987i
\(75\) −13015.8 + 90527.2i −0.0308524 + 0.214583i
\(76\) 183949. + 626472.i 0.419040 + 1.42712i
\(77\) −834380. 536223.i −1.82764 1.17456i
\(78\) 379.197 830.326i 0.000799063 0.00174970i
\(79\) −145534. + 495643.i −0.295177 + 1.00528i 0.669711 + 0.742622i \(0.266418\pi\)
−0.964889 + 0.262660i \(0.915400\pi\)
\(80\) 305766. 264948.i 0.597200 0.517477i
\(81\) −38668.9 44626.3i −0.0727623 0.0839722i
\(82\) −1798.59 528.113i −0.00326205 0.000957823i
\(83\) 793080. + 362188.i 1.38702 + 0.633431i 0.962324 0.271905i \(-0.0876536\pi\)
0.424696 + 0.905336i \(0.360381\pi\)
\(84\) 307586. 478613.i 0.518953 0.807507i
\(85\) −688042. + 202027.i −1.12036 + 0.328968i
\(86\) −4480.61 644.215i −0.00704437 0.00101283i
\(87\) −215232. 471292.i −0.326850 0.715702i
\(88\) 8122.19 1167.79i 0.0119186 0.00171364i
\(89\) −306505. 476930.i −0.434777 0.676527i 0.552861 0.833273i \(-0.313536\pi\)
−0.987639 + 0.156746i \(0.949899\pi\)
\(90\) 668.684 + 579.418i 0.000917263 + 0.000794812i
\(91\) 905953.i 1.20221i
\(92\) 496642. 599730.i 0.637793 0.770180i
\(93\) 639061. 0.794500
\(94\) −275.503 + 317.948i −0.000331698 + 0.000382800i
\(95\) −847804. + 544850.i −0.988837 + 0.635487i
\(96\) 1004.80 + 6988.54i 0.00113571 + 0.00789901i
\(97\) 898080. 410139.i 0.984011 0.449383i 0.142601 0.989780i \(-0.454453\pi\)
0.841410 + 0.540397i \(0.181726\pi\)
\(98\) −1088.82 + 7572.94i −0.00115686 + 0.00804612i
\(99\) −119068. 405510.i −0.122713 0.417923i
\(100\) −315876. 203001.i −0.315876 0.203001i
\(101\) −274360. + 600765.i −0.266291 + 0.583096i −0.994789 0.101951i \(-0.967491\pi\)
0.728498 + 0.685048i \(0.240219\pi\)
\(102\) 1175.14 4002.17i 0.00110736 0.00377133i
\(103\) −145745. + 126289.i −0.133378 + 0.115572i −0.718995 0.695015i \(-0.755398\pi\)
0.585617 + 0.810588i \(0.300852\pi\)
\(104\) 4908.33 + 5664.52i 0.00436349 + 0.00503574i
\(105\) 842574. + 247402.i 0.727847 + 0.213715i
\(106\) −4519.06 2063.79i −0.00379429 0.00173280i
\(107\) 537337. 836113.i 0.438627 0.682517i −0.549614 0.835419i \(-0.685225\pi\)
0.988241 + 0.152901i \(0.0488617\pi\)
\(108\) 232607. 68299.4i 0.184651 0.0542183i
\(109\) −1.48507e6 213521.i −1.14675 0.164878i −0.457369 0.889277i \(-0.651208\pi\)
−0.689381 + 0.724399i \(0.742117\pi\)
\(110\) 2630.71 + 5760.45i 0.00197649 + 0.00432791i
\(111\) −322170. + 46321.1i −0.235568 + 0.0338696i
\(112\) 1.26277e6 + 1.96491e6i 0.898815 + 1.39858i
\(113\) 1.59816e6 + 1.38482e6i 1.10761 + 0.959747i 0.999409 0.0343827i \(-0.0109465\pi\)
0.108198 + 0.994129i \(0.465492\pi\)
\(114\) 5862.05i 0.00395672i
\(115\) 1.10416e6 + 474723.i 0.726002 + 0.312138i
\(116\) 2.12712e6 1.36276
\(117\) 252800. 291747.i 0.157841 0.182158i
\(118\) −3997.59 + 2569.10i −0.00243306 + 0.00156363i
\(119\) −589151. 4.09764e6i −0.349612 2.43160i
\(120\) −6608.63 + 3018.06i −0.00382444 + 0.00174656i
\(121\) 178365. 1.24055e6i 0.100682 0.700261i
\(122\) 1985.89 + 6763.32i 0.00109364 + 0.00372461i
\(123\) −666903. 428592.i −0.358383 0.230319i
\(124\) −1.08991e6 + 2.38658e6i −0.571646 + 1.25173i
\(125\) 598128. 2.03704e6i 0.306242 1.04296i
\(126\) −3860.33 + 3345.00i −0.00192980 + 0.00167219i
\(127\) 1.26168e6 + 1.45606e6i 0.615942 + 0.710835i 0.974931 0.222507i \(-0.0714240\pi\)
−0.358989 + 0.933342i \(0.616879\pi\)
\(128\) −37083.1 10888.6i −0.0176826 0.00519208i
\(129\) −1.74137e6 795259.i −0.811190 0.370458i
\(130\) −3127.29 + 4866.16i −0.00142344 + 0.00221491i
\(131\) −1.01817e6 + 298961.i −0.452903 + 0.132984i −0.500225 0.865895i \(-0.666749\pi\)
0.0473223 + 0.998880i \(0.484931\pi\)
\(132\) 1.71745e6 + 246932.i 0.746728 + 0.107363i
\(133\) −2.41688e6 5.29222e6i −1.02731 2.24948i
\(134\) 15738.6 2262.87i 0.00654112 0.000940470i
\(135\) 202301. + 314786.i 0.0822236 + 0.127942i
\(136\) 25884.2 + 22428.7i 0.0102900 + 0.00891637i
\(137\) 2.55809e6i 0.994841i 0.867510 + 0.497420i \(0.165719\pi\)
−0.867510 + 0.497420i \(0.834281\pi\)
\(138\) −5795.33 + 3910.16i −0.00220516 + 0.00148784i
\(139\) 98689.5 0.0367474 0.0183737 0.999831i \(-0.494151\pi\)
0.0183737 + 0.999831i \(0.494151\pi\)
\(140\) −2.36093e6 + 2.72466e6i −0.860396 + 0.992950i
\(141\) −149675. + 96190.6i −0.0533941 + 0.0343143i
\(142\) −2588.46 18003.1i −0.000904017 0.00628758i
\(143\) 2.51328e6 1.14778e6i 0.859475 0.392509i
\(144\) −141641. + 985134.i −0.0474353 + 0.329919i
\(145\) 924992. + 3.15023e6i 0.303413 + 1.03333i
\(146\) 15459.7 + 9935.35i 0.00496755 + 0.00319245i
\(147\) −1.34411e6 + 2.94320e6i −0.423139 + 0.926546i
\(148\) 376473. 1.28215e6i 0.116131 0.395506i
\(149\) −3.55225e6 + 3.07805e6i −1.07385 + 0.930500i −0.997780 0.0666022i \(-0.978784\pi\)
−0.0760745 + 0.997102i \(0.524239\pi\)
\(150\) 2207.64 + 2547.75i 0.000654116 + 0.000754890i
\(151\) −2.64844e6 777653.i −0.769237 0.225868i −0.126512 0.991965i \(-0.540378\pi\)
−0.642725 + 0.766097i \(0.722196\pi\)
\(152\) 43784.2 + 19995.6i 0.0124677 + 0.00569381i
\(153\) 953693. 1.48397e6i 0.266277 0.414336i
\(154\) −35078.1 + 10299.9i −0.00960448 + 0.00282013i
\(155\) −4.00844e6 576327.i −1.07642 0.154765i
\(156\) 658383. + 1.44166e6i 0.173422 + 0.379741i
\(157\) −1.74835e6 + 251375.i −0.451784 + 0.0649567i −0.364451 0.931223i \(-0.618743\pi\)
−0.0873325 + 0.996179i \(0.527834\pi\)
\(158\) 10294.2 + 16018.1i 0.00260989 + 0.00406107i
\(159\) −1.58784e6 1.37587e6i −0.395016 0.342283i
\(160\) 44741.0i 0.0109231i
\(161\) −3.61986e6 + 5.91943e6i −0.867389 + 1.41841i
\(162\) −2176.56 −0.000511947
\(163\) −1.56127e6 + 1.80180e6i −0.360508 + 0.416048i −0.906810 0.421540i \(-0.861490\pi\)
0.546302 + 0.837588i \(0.316035\pi\)
\(164\) 2.73798e6 1.75959e6i 0.620724 0.398915i
\(165\) 381142. + 2.65090e6i 0.0848466 + 0.590121i
\(166\) 29233.1 13350.3i 0.00639073 0.00291855i
\(167\) 663192. 4.61260e6i 0.142393 0.990369i −0.785856 0.618410i \(-0.787777\pi\)
0.928249 0.371959i \(-0.121314\pi\)
\(168\) −11816.4 40243.1i −0.00249206 0.00848718i
\(169\) −1.93747e6 1.24513e6i −0.401397 0.257962i
\(170\) −10980.3 + 24043.4i −0.00223494 + 0.00489383i
\(171\) 698445. 2.37869e6i 0.139683 0.475717i
\(172\) 5.93980e6 5.14686e6i 1.16731 1.01148i
\(173\) 2.70114e6 + 3.11728e6i 0.521685 + 0.602057i 0.954052 0.299641i \(-0.0968668\pi\)
−0.432367 + 0.901698i \(0.642321\pi\)
\(174\) −18324.1 5380.45i −0.00347837 0.00102134i
\(175\) 3.04346e6 + 1.38990e6i 0.567876 + 0.259340i
\(176\) −3.85119e6 + 5.99256e6i −0.706410 + 1.09919i
\(177\) −1.92823e6 + 566180.i −0.347728 + 0.102102i
\(178\) −20684.4 2973.96i −0.00366760 0.000527322i
\(179\) 1.27642e6 + 2.79498e6i 0.222554 + 0.487326i 0.987667 0.156571i \(-0.0500440\pi\)
−0.765113 + 0.643897i \(0.777317\pi\)
\(180\) −1.52059e6 + 218629.i −0.260733 + 0.0374877i
\(181\) 1.73093e6 + 2.69339e6i 0.291907 + 0.454216i 0.955972 0.293459i \(-0.0948064\pi\)
−0.664065 + 0.747675i \(0.731170\pi\)
\(182\) −25237.2 21868.1i −0.00418627 0.00362742i
\(183\) 2.98101e6i 0.486419i
\(184\) −9437.36 56623.5i −0.00151495 0.00908956i
\(185\) 2.06255e6 0.325754
\(186\) 15425.8 17802.4i 0.00239723 0.00276655i
\(187\) 1.06212e7 6.82583e6i 1.62424 1.04383i
\(188\) −103954. 723016.i −0.0156447 0.108811i
\(189\) −1.96498e6 + 897377.i −0.291054 + 0.132920i
\(190\) −5286.60 + 36769.1i −0.000770753 + 0.00536071i
\(191\) −1.14668e6 3.90524e6i −0.164567 0.560465i −0.999942 0.0107835i \(-0.996567\pi\)
0.835375 0.549681i \(-0.185251\pi\)
\(192\) −3.43728e6 2.20900e6i −0.485636 0.312099i
\(193\) 2.82900e6 6.19465e6i 0.393515 0.861677i −0.604372 0.796702i \(-0.706576\pi\)
0.997887 0.0649750i \(-0.0206968\pi\)
\(194\) 10252.8 34917.9i 0.00140423 0.00478237i
\(195\) −1.84877e6 + 1.60197e6i −0.249333 + 0.216048i
\(196\) −8.69901e6 1.00392e7i −1.15532 1.33331i
\(197\) −2.19944e6 645812.i −0.287682 0.0844710i 0.134708 0.990885i \(-0.456990\pi\)
−0.422390 + 0.906414i \(0.638809\pi\)
\(198\) −14170.4 6471.42i −0.00182552 0.000833689i
\(199\) −580676. + 903549.i −0.0736842 + 0.114655i −0.876140 0.482057i \(-0.839890\pi\)
0.802456 + 0.596712i \(0.203526\pi\)
\(200\) −26559.7 + 7798.64i −0.00331996 + 0.000974830i
\(201\) 6.65598e6 + 956985.i 0.819641 + 0.117847i
\(202\) 10113.0 + 22144.3i 0.00122694 + 0.00268663i
\(203\) −1.87612e7 + 2.69746e6i −2.24271 + 0.322453i
\(204\) 3.91540e6 + 6.09248e6i 0.461196 + 0.717635i
\(205\) 3.79656e6 + 3.28974e6i 0.440685 + 0.381856i
\(206\) 7108.44i 0.000813153i
\(207\) −2.81749e6 + 896157.i −0.317652 + 0.101035i
\(208\) −6.50661e6 −0.723044
\(209\) 1.16196e7 1.34097e7i 1.27278 1.46886i
\(210\) 27230.2 17499.8i 0.00294031 0.00188962i
\(211\) 1.23071e6 + 8.55974e6i 0.131011 + 0.911199i 0.944241 + 0.329257i \(0.106798\pi\)
−0.813230 + 0.581943i \(0.802293\pi\)
\(212\) 7.84624e6 3.58326e6i 0.823482 0.376072i
\(213\) 1.09468e6 7.61367e6i 0.113279 0.787871i
\(214\) −10321.3 35151.0i −0.00105315 0.00358671i
\(215\) 1.02054e7 + 6.55860e6i 1.02687 + 0.659927i
\(216\) 7424.28 16256.9i 0.000736704 0.00161316i
\(217\) 6.58658e6 2.24318e7i 0.644586 2.19526i
\(218\) −41795.2 + 36215.8i −0.00403420 + 0.00349565i
\(219\) 5.08943e6 + 5.87351e6i 0.484548 + 0.559198i
\(220\) −1.05498e7 3.09771e6i −0.990781 0.290919i
\(221\) 1.04901e7 + 4.79069e6i 0.971862 + 0.443834i
\(222\) −6486.27 + 10092.8i −0.000592838 + 0.000922474i
\(223\) 4.44564e6 1.30536e6i 0.400885 0.117710i −0.0750739 0.997178i \(-0.523919\pi\)
0.475959 + 0.879468i \(0.342101\pi\)
\(224\) 255662. + 36758.7i 0.0227469 + 0.00327051i
\(225\) 592253. + 1.29685e6i 0.0519948 + 0.113853i
\(226\) 77153.8 11093.0i 0.00668393 0.000961004i
\(227\) 1.09375e7 + 1.70191e7i 0.935062 + 1.45498i 0.889979 + 0.456001i \(0.150719\pi\)
0.0450827 + 0.998983i \(0.485645\pi\)
\(228\) 7.69203e6 + 6.66518e6i 0.648987 + 0.562351i
\(229\) 5.10081e6i 0.424750i −0.977188 0.212375i \(-0.931880\pi\)
0.977188 0.212375i \(-0.0681198\pi\)
\(230\) 39876.9 19299.6i 0.00327746 0.00158623i
\(231\) −1.54611e7 −1.25431
\(232\) 102691. 118512.i 0.00822373 0.00949069i
\(233\) −1.37716e7 + 8.85050e6i −1.08872 + 0.699681i −0.956557 0.291547i \(-0.905830\pi\)
−0.132168 + 0.991227i \(0.542194\pi\)
\(234\) −2025.05 14084.5i −0.000158048 0.00109925i
\(235\) 1.02557e6 468363.i 0.0790246 0.0360893i
\(236\) 1.17418e6 8.16661e6i 0.0893303 0.621306i
\(237\) 2.26865e6 + 7.72631e6i 0.170421 + 0.580399i
\(238\) −128369. 82497.9i −0.00952204 0.00611944i
\(239\) 4.24713e6 9.29991e6i 0.311101 0.681217i −0.687904 0.725801i \(-0.741469\pi\)
0.999006 + 0.0445847i \(0.0141965\pi\)
\(240\) 1.77686e6 6.05141e6i 0.128534 0.437747i
\(241\) −939625. + 814190.i −0.0671280 + 0.0581667i −0.687779 0.725921i \(-0.741414\pi\)
0.620651 + 0.784087i \(0.286869\pi\)
\(242\) −30252.8 34913.6i −0.00213461 0.00246347i
\(243\) −883197. 259330.i −0.0615515 0.0180732i
\(244\) −1.11326e7 5.08410e6i −0.766352 0.349981i
\(245\) 1.10851e7 1.72487e7i 0.753773 1.17289i
\(246\) −28037.2 + 8232.47i −0.00188334 + 0.000553000i
\(247\) 1.60424e7 + 2.30654e6i 1.06458 + 0.153063i
\(248\) 80349.7 + 175941.i 0.00526780 + 0.0115349i
\(249\) 1.34528e7 1.93422e6i 0.871392 0.125287i
\(250\) −42308.1 65832.7i −0.00270772 0.00421329i
\(251\) −1.01477e7 8.79307e6i −0.641724 0.556057i 0.272049 0.962284i \(-0.412299\pi\)
−0.913772 + 0.406227i \(0.866844\pi\)
\(252\) 8.86871e6i 0.554190i
\(253\) −2.10077e7 2.54266e6i −1.29723 0.157010i
\(254\) 71016.5 0.00433369
\(255\) −7.32023e6 + 8.44800e6i −0.441473 + 0.509487i
\(256\) 1.41109e7 9.06852e6i 0.841075 0.540526i
\(257\) −1.14271e6 7.94770e6i −0.0673187 0.468212i −0.995398 0.0958286i \(-0.969450\pi\)
0.928079 0.372383i \(-0.121459\pi\)
\(258\) −64187.3 + 29313.4i −0.00373758 + 0.00170689i
\(259\) −1.69457e6 + 1.17860e7i −0.0975348 + 0.678370i
\(260\) −2.82950e6 9.63639e6i −0.160987 0.548270i
\(261\) −6.79445e6 4.36653e6i −0.382149 0.245592i
\(262\) −16248.6 + 35579.5i −0.000903468 + 0.00197832i
\(263\) −8.83695e6 + 3.00959e7i −0.485775 + 1.65440i 0.243290 + 0.969954i \(0.421773\pi\)
−0.729065 + 0.684444i \(0.760045\pi\)
\(264\) 96671.3 83766.1i 0.00525395 0.00455257i
\(265\) 8.71874e6 + 1.00620e7i 0.468507 + 0.540686i
\(266\) −205765. 60418.1i −0.0109327 0.00321012i
\(267\) −8.03891e6 3.67125e6i −0.422341 0.192877i
\(268\) −1.49256e7 + 2.32247e7i −0.775402 + 1.20655i
\(269\) −1.99929e7 + 5.87043e6i −1.02711 + 0.301587i −0.751536 0.659692i \(-0.770687\pi\)
−0.275576 + 0.961279i \(0.588869\pi\)
\(270\) 13652.2 + 1962.89i 0.000693605 + 9.97253e-5i
\(271\) 6.38498e6 + 1.39812e7i 0.320813 + 0.702482i 0.999489 0.0319553i \(-0.0101734\pi\)
−0.678676 + 0.734437i \(0.737446\pi\)
\(272\) −2.94295e7 + 4.23132e6i −1.46243 + 0.210266i
\(273\) −7.63515e6 1.18805e7i −0.375258 0.583912i
\(274\) 71260.8 + 61747.8i 0.00346417 + 0.00300172i
\(275\) 1.02040e7i 0.490653i
\(276\) 1.45851e6 1.20503e7i 0.0693716 0.573155i
\(277\) 3.45698e7 1.62652 0.813258 0.581904i \(-0.197692\pi\)
0.813258 + 0.581904i \(0.197692\pi\)
\(278\) 2382.20 2749.20i 0.000110877 0.000127959i
\(279\) 8.38055e6 5.38585e6i 0.385887 0.247994i
\(280\) 37824.7 + 263077.i 0.00172307 + 0.0119842i
\(281\) 1.04163e6 475699.i 0.0469458 0.0214394i −0.391804 0.920049i \(-0.628149\pi\)
0.438750 + 0.898609i \(0.355422\pi\)
\(282\) −933.321 + 6491.39i −4.16183e−5 + 0.000289461i
\(283\) 2.60118e6 + 8.85881e6i 0.114766 + 0.390855i 0.996763 0.0803992i \(-0.0256195\pi\)
−0.881997 + 0.471255i \(0.843801\pi\)
\(284\) 2.65663e7 + 1.70732e7i 1.15978 + 0.745347i
\(285\) −6.52610e6 + 1.42902e7i −0.281916 + 0.617309i
\(286\) 28692.6 97718.1i 0.00122651 0.00417712i
\(287\) −2.19176e7 + 1.89917e7i −0.927146 + 0.803376i
\(288\) 72074.5 + 83178.4i 0.00301720 + 0.00348203i
\(289\) 2.74026e7 + 8.04614e6i 1.13527 + 0.333345i
\(290\) 110084. + 50273.6i 0.00451367 + 0.00206132i
\(291\) 8.32073e6 1.29473e7i 0.337662 0.525413i
\(292\) −3.06147e7 + 8.98927e6i −1.22965 + 0.361057i
\(293\) −7.24799e6 1.04210e6i −0.288147 0.0414293i −0.00327448 0.999995i \(-0.501042\pi\)
−0.284873 + 0.958565i \(0.591951\pi\)
\(294\) 49544.2 + 108487.i 0.00194962 + 0.00426908i
\(295\) 1.26052e7 1.81236e6i 0.491003 0.0705956i
\(296\) −53259.5 82873.4i −0.00205363 0.00319551i
\(297\) −4.97899e6 4.31432e6i −0.190052 0.164681i
\(298\) 173254.i 0.00654689i
\(299\) −8.42043e6 1.73983e7i −0.315007 0.650868i
\(300\) −5.85319e6 −0.216785
\(301\) −4.58622e7 + 5.29279e7i −1.68173 + 1.94082i
\(302\) −85592.0 + 55006.7i −0.00310751 + 0.00199708i
\(303\) 1.46518e6 + 1.01906e7i 0.0526701 + 0.366328i
\(304\) −3.80090e7 + 1.73581e7i −1.35290 + 0.617849i
\(305\) 2.68838e6 1.86981e7i 0.0947526 0.659019i
\(306\) −18318.7 62387.7i −0.000639337 0.00217738i
\(307\) 5.97600e6 + 3.84054e6i 0.206536 + 0.132732i 0.639820 0.768525i \(-0.279009\pi\)
−0.433284 + 0.901257i \(0.642645\pi\)
\(308\) 2.63688e7 5.77395e7i 0.902480 1.97616i
\(309\) −846948. + 2.88444e6i −0.0287066 + 0.0977656i
\(310\) −112812. + 97751.9i −0.00378677 + 0.00328126i
\(311\) −1.85942e7 2.14588e7i −0.618152 0.713386i 0.357203 0.934027i \(-0.383730\pi\)
−0.975355 + 0.220641i \(0.929185\pi\)
\(312\) 112106. + 32917.4i 0.00369119 + 0.00108383i
\(313\) 4.72730e6 + 2.15889e6i 0.154163 + 0.0704039i 0.491002 0.871158i \(-0.336631\pi\)
−0.336839 + 0.941562i \(0.609358\pi\)
\(314\) −35199.7 + 54771.8i −0.00113697 + 0.00176916i
\(315\) 1.31344e7 3.85661e6i 0.420223 0.123388i
\(316\) −3.27231e7 4.70487e6i −1.03704 0.149103i
\(317\) −2.80267e6 6.13699e6i −0.0879821 0.192654i 0.860526 0.509406i \(-0.170135\pi\)
−0.948508 + 0.316752i \(0.897408\pi\)
\(318\) −76655.4 + 11021.4i −0.00238375 + 0.000342732i
\(319\) −3.12524e7 4.86297e7i −0.962745 1.49806i
\(320\) 1.95678e7 + 1.69556e7i 0.597162 + 0.517444i
\(321\) 1.54932e7i 0.468410i
\(322\) 77520.9 + 243724.i 0.00232194 + 0.00730012i
\(323\) 7.40597e7 2.19773
\(324\) 2.47476e6 2.85602e6i 0.0727608 0.0839704i
\(325\) −7.84094e6 + 5.03906e6i −0.228411 + 0.146791i
\(326\) 12506.5 + 86984.6i 0.000360980 + 0.00251067i
\(327\) −2.12745e7 + 9.71575e6i −0.608439 + 0.277865i
\(328\) 34146.4 237494.i 0.000967663 0.00673024i
\(329\) 1.83375e6 + 6.24519e6i 0.0514936 + 0.175371i
\(330\) 83046.3 + 53370.6i 0.00231089 + 0.00148512i
\(331\) −2.20328e7 + 4.82451e7i −0.607555 + 1.33036i 0.316679 + 0.948533i \(0.397432\pi\)
−0.924234 + 0.381827i \(0.875295\pi\)
\(332\) −1.57202e7 + 5.35382e7i −0.429581 + 1.46302i
\(333\) −3.83451e6 + 3.32262e6i −0.103843 + 0.0899804i
\(334\) −112485. 129815.i −0.00301895 0.00348406i
\(335\) −4.08859e7 1.20052e7i −1.08752 0.319326i
\(336\) 3.31196e7 + 1.51252e7i 0.873105 + 0.398734i
\(337\) 3.04691e7 4.74109e7i 0.796105 1.23876i −0.171222 0.985232i \(-0.554772\pi\)
0.967327 0.253531i \(-0.0815920\pi\)
\(338\) −81452.9 + 23916.7i −0.00210939 + 0.000619372i
\(339\) 3.26289e7 + 4.69133e6i 0.837537 + 0.120420i
\(340\) −1.90645e7 4.17455e7i −0.485053 1.06212i
\(341\) 7.05748e7 1.01471e7i 1.77986 0.255906i
\(342\) −49403.9 76874.0i −0.00123505 0.00192177i
\(343\) 3.87516e7 + 3.35784e7i 0.960300 + 0.832104i
\(344\) 579410.i 0.0142335i
\(345\) 1.84806e7 3.08014e6i 0.450048 0.0750090i
\(346\) 152039. 0.00367052
\(347\) 2.20587e7 2.54571e7i 0.527948 0.609284i −0.427655 0.903942i \(-0.640660\pi\)
0.955603 + 0.294658i \(0.0952057\pi\)
\(348\) 2.78947e7 1.79268e7i 0.661888 0.425369i
\(349\) 1.90543e6 + 1.32525e7i 0.0448245 + 0.311761i 0.999882 + 0.0153418i \(0.00488363\pi\)
−0.955058 + 0.296420i \(0.904207\pi\)
\(350\) 112183. 51232.1i 0.00261650 0.00119492i
\(351\) 856410. 5.95646e6i 0.0198043 0.137742i
\(352\) 221930. + 755826.i 0.00508849 + 0.0173298i
\(353\) −1.59594e7 1.02565e7i −0.362821 0.233171i 0.346510 0.938046i \(-0.387367\pi\)
−0.709331 + 0.704875i \(0.751003\pi\)
\(354\) −30772.1 + 67381.5i −0.000693661 + 0.00151890i
\(355\) −1.37325e7 + 4.67687e7i −0.306949 + 1.04537i
\(356\) 2.74206e7 2.37601e7i 0.607753 0.526621i
\(357\) −4.22599e7 4.87706e7i −0.928804 1.07190i
\(358\) 108671. + 31908.6i 0.00236844 + 0.000695437i
\(359\) −1.09891e7 5.01853e6i −0.237507 0.108466i 0.293106 0.956080i \(-0.405311\pi\)
−0.530613 + 0.847614i \(0.678038\pi\)
\(360\) −61229.0 + 95274.2i −0.00131235 + 0.00204206i
\(361\) 5.47263e7 1.60691e7i 1.16325 0.341562i
\(362\) 116812. + 16795.0i 0.00246241 + 0.000354041i
\(363\) −8.11604e6 1.77717e7i −0.169678 0.371542i
\(364\) 5.73896e7 8.25138e6i 1.18995 0.171089i
\(365\) −2.66260e7 4.14308e7i −0.547553 0.852010i
\(366\) 83042.3 + 71956.6i 0.00169378 + 0.00146767i
\(367\) 2.69869e7i 0.545953i −0.962021 0.272976i \(-0.911992\pi\)
0.962021 0.272976i \(-0.0880081\pi\)
\(368\) 4.25137e7 + 2.59980e7i 0.853072 + 0.521671i
\(369\) −1.23577e7 −0.245957
\(370\) 49786.5 57456.7i 0.000982893 0.00113432i
\(371\) −6.46600e7 + 4.15544e7i −1.26623 + 0.813759i
\(372\) 5.82054e6 + 4.04828e7i 0.113067 + 0.786396i
\(373\) 4.36519e6 1.99352e6i 0.0841157 0.0384143i −0.372913 0.927866i \(-0.621641\pi\)
0.457029 + 0.889452i \(0.348914\pi\)
\(374\) 66229.9 460639.i 0.00126602 0.00880534i
\(375\) −9.32389e6 3.17543e7i −0.176809 0.602155i
\(376\) −45301.3 29113.3i −0.000852210 0.000547682i
\(377\) 2.19344e7 4.80296e7i 0.409356 0.896365i
\(378\) −22433.0 + 76399.8i −0.000415348 + 0.00141454i
\(379\) −7.04929e7 + 6.10824e7i −1.29487 + 1.12202i −0.309631 + 0.950857i \(0.600205\pi\)
−0.985244 + 0.171158i \(0.945249\pi\)
\(380\) −4.22365e7 4.87435e7i −0.769728 0.888314i
\(381\) 2.88169e7 + 8.46140e6i 0.521041 + 0.152991i
\(382\) −136468. 62322.7i −0.00244816 0.00111804i
\(383\) −8.75347e6 + 1.36207e7i −0.155806 + 0.242439i −0.910377 0.413779i \(-0.864209\pi\)
0.754571 + 0.656218i \(0.227845\pi\)
\(384\) −578068. + 169736.i −0.0102091 + 0.00299765i
\(385\) 9.69780e7 + 1.39433e7i 1.69938 + 0.244334i
\(386\) −104277. 228336.i −0.00181313 0.00397020i
\(387\) −2.95383e7 + 4.24697e6i −0.509628 + 0.0732734i
\(388\) 3.41609e7 + 5.31554e7i 0.584836 + 0.910022i
\(389\) 5.42241e7 + 4.69855e7i 0.921179 + 0.798206i 0.979780 0.200076i \(-0.0641188\pi\)
−0.0586018 + 0.998281i \(0.518664\pi\)
\(390\) 90170.1i 0.00152009i
\(391\) −4.94000e7 7.32168e7i −0.826412 1.22484i
\(392\) −979294. −0.0162575
\(393\) −1.08325e7 + 1.25014e7i −0.178464 + 0.205959i
\(394\) −71081.0 + 45681.0i −0.00116216 + 0.000746873i
\(395\) −7.26201e6 5.05084e7i −0.117833 0.819544i
\(396\) 2.46035e7 1.12360e7i 0.396197 0.180937i
\(397\) 894719. 6.22291e6i 0.0142993 0.0994539i −0.981422 0.191862i \(-0.938547\pi\)
0.995721 + 0.0924082i \(0.0294565\pi\)
\(398\) 11153.7 + 37986.1i 0.000176917 + 0.000602525i
\(399\) −7.62961e7 4.90325e7i −1.20111 0.771908i
\(400\) 9.98236e6 2.18583e7i 0.155974 0.341536i
\(401\) −1.16771e7 + 3.97684e7i −0.181092 + 0.616744i 0.818042 + 0.575158i \(0.195059\pi\)
−0.999135 + 0.0415865i \(0.986759\pi\)
\(402\) 187323. 162316.i 0.00288345 0.00249852i
\(403\) 4.26492e7 + 4.92198e7i 0.651622 + 0.752011i
\(404\) −4.05556e7 1.19082e7i −0.615045 0.180594i
\(405\) 5.30589e6 + 2.42312e6i 0.0798717 + 0.0364762i
\(406\) −377721. + 587745.i −0.00564407 + 0.00878235i
\(407\) −3.48434e7 + 1.02310e7i −0.516818 + 0.151751i
\(408\) 528465. + 75981.8i 0.00778100 + 0.00111874i
\(409\) −3.05900e7 6.69827e7i −0.447105 0.979023i −0.990239 0.139377i \(-0.955490\pi\)
0.543135 0.839646i \(-0.317237\pi\)
\(410\) 183285. 26352.4i 0.00265935 0.000382356i
\(411\) 2.15589e7 + 3.35463e7i 0.310529 + 0.483192i
\(412\) −9.32750e6 8.08233e6i −0.133375 0.115570i
\(413\) 7.35186e7i 1.04363i
\(414\) −43045.2 + 100119.i −0.000606629 + 0.00141096i
\(415\) −8.61254e7 −1.20500
\(416\) −471192. + 543784.i −0.00654512 + 0.00755347i
\(417\) 1.29420e6 831731.i 0.0178481 0.0114703i
\(418\) −93078.6 647376.i −0.00127445 0.00886396i
\(419\) 1.44512e7 6.59965e6i 0.196455 0.0897178i −0.314759 0.949172i \(-0.601924\pi\)
0.511213 + 0.859454i \(0.329196\pi\)
\(420\) −7.99810e6 + 5.56280e7i −0.107954 + 0.750837i
\(421\) −2.91556e7 9.92949e7i −0.390729 1.33070i −0.886693 0.462358i \(-0.847003\pi\)
0.495964 0.868343i \(-0.334815\pi\)
\(422\) 268156. + 172334.i 0.00356821 + 0.00229315i
\(423\) −1.15215e6 + 2.52286e6i −0.0152226 + 0.0333328i
\(424\) 179153. 610140.i 0.00235032 0.00800446i
\(425\) −3.21877e7 + 2.78908e7i −0.419298 + 0.363324i
\(426\) −185671. 214276.i −0.00240168 0.00277168i
\(427\) 1.04637e8 + 3.07243e7i 1.34401 + 0.394637i
\(428\) 5.78595e7 + 2.64235e7i 0.737978 + 0.337023i
\(429\) 2.32856e7 3.62331e7i 0.294928 0.458917i
\(430\) 429044. 125979.i 0.00539630 0.00158450i
\(431\) 3.23184e7 + 4.64668e6i 0.403662 + 0.0580378i 0.341156 0.940007i \(-0.389182\pi\)
0.0625059 + 0.998045i \(0.480091\pi\)
\(432\) 6.44501e6 + 1.41126e7i 0.0799416 + 0.175048i
\(433\) 7.84418e7 1.12782e7i 0.966238 0.138924i 0.358907 0.933373i \(-0.383149\pi\)
0.607330 + 0.794449i \(0.292240\pi\)
\(434\) −465896. 724948.i −0.00569928 0.00886825i
\(435\) 3.86796e7 + 3.35160e7i 0.469909 + 0.407179i
\(436\) 9.60201e7i 1.15852i
\(437\) −9.56035e7 7.91702e7i −1.14559 0.948675i
\(438\) 286469. 0.00340922
\(439\) −2.77640e7 + 3.20413e7i −0.328162 + 0.378719i −0.895723 0.444612i \(-0.853341\pi\)
0.567561 + 0.823331i \(0.307887\pi\)
\(440\) −681903. + 438233.i −0.00800506 + 0.00514454i
\(441\) 7.17805e6 + 4.99245e7i 0.0836933 + 0.582100i
\(442\) 386668. 176586.i 0.00447787 0.00204498i
\(443\) −2.31251e6 + 1.60838e7i −0.0265994 + 0.185003i −0.998789 0.0491906i \(-0.984336\pi\)
0.972190 + 0.234193i \(0.0752449\pi\)
\(444\) −5.86863e6 1.99867e7i −0.0670483 0.228345i
\(445\) 4.71123e7 + 3.02773e7i 0.534632 + 0.343587i
\(446\) 70946.7 155352.i 0.000799701 0.00175110i
\(447\) −2.06427e7 + 7.03026e7i −0.231123 + 0.787134i
\(448\) −1.12966e8 + 9.78852e7i −1.25635 + 1.08864i
\(449\) 4.48212e7 + 5.17264e7i 0.495159 + 0.571443i 0.947237 0.320535i \(-0.103863\pi\)
−0.452078 + 0.891978i \(0.649317\pi\)
\(450\) 50422.5 + 14805.4i 0.000553333 + 0.000162473i
\(451\) −8.04548e7 3.67425e7i −0.877045 0.400533i
\(452\) −7.31682e7 + 1.13852e8i −0.792332 + 1.23289i
\(453\) −4.12852e7 + 1.21224e7i −0.444119 + 0.130405i
\(454\) 738114. + 106125.i 0.00788780 + 0.00113409i
\(455\) 3.71764e7 + 8.14050e7i 0.394669 + 0.864205i
\(456\) 742697. 106784.i 0.00783280 0.00112619i
\(457\) −1.16300e7 1.80966e7i −0.121851 0.189604i 0.774969 0.631999i \(-0.217765\pi\)
−0.896820 + 0.442395i \(0.854129\pi\)
\(458\) −142094. 123125.i −0.00147903 0.00128159i
\(459\) 2.74981e7i 0.284357i
\(460\) −2.00157e7 + 7.42692e7i −0.205636 + 0.763018i
\(461\) 7.71970e7 0.787948 0.393974 0.919122i \(-0.371100\pi\)
0.393974 + 0.919122i \(0.371100\pi\)
\(462\) −373204. + 430700.i −0.00378460 + 0.00436767i
\(463\) −1.37576e8 + 8.84145e7i −1.38611 + 0.890801i −0.999506 0.0314435i \(-0.989990\pi\)
−0.386608 + 0.922244i \(0.626353\pi\)
\(464\) 1.93733e7 + 1.34744e8i 0.193932 + 1.34883i
\(465\) −5.74233e7 + 2.62243e7i −0.571122 + 0.260823i
\(466\) −85874.9 + 597273.i −0.000848611 + 0.00590222i
\(467\) −3.24099e7 1.10378e8i −0.318220 1.08376i −0.950940 0.309377i \(-0.899880\pi\)
0.632720 0.774381i \(-0.281939\pi\)
\(468\) 2.07839e7 + 1.33570e7i 0.202763 + 0.130308i
\(469\) 1.02192e8 2.23770e8i 0.990602 2.16911i
\(470\) 11708.3 39874.9i 0.000112772 0.000384066i
\(471\) −2.08091e7 + 1.80312e7i −0.199155 + 0.172569i
\(472\) −398314. 459679.i −0.00378791 0.00437148i
\(473\) −2.04936e8 6.01747e7i −1.93658 0.568631i
\(474\) 269994. + 123302.i 0.00253524 + 0.00115780i
\(475\) −3.23606e7 + 5.03541e7i −0.301951 + 0.469844i
\(476\) 2.54208e8 7.46422e7i 2.35705 0.692092i
\(477\) −3.24182e7 4.66103e6i −0.298699 0.0429464i
\(478\) −156550. 342796.i −0.00143341 0.00313872i
\(479\) −1.05130e8 + 1.51155e7i −0.956581 + 0.137536i −0.602888 0.797826i \(-0.705983\pi\)
−0.353693 + 0.935361i \(0.615074\pi\)
\(480\) −377066. 586727.i −0.00340953 0.00530533i
\(481\) −2.50683e7 2.17218e7i −0.225263 0.195192i
\(482\) 45828.3i 0.000409254i
\(483\) 2.41730e6 + 1.08134e8i 0.0214530 + 0.959666i
\(484\) 8.02102e7 0.707446
\(485\) −6.38672e7 + 7.37067e7i −0.559826 + 0.646073i
\(486\) −28543.0 + 18343.5i −0.000248652 + 0.000159799i
\(487\) −1.79173e6 1.24617e7i −0.0155126 0.107893i 0.980594 0.196050i \(-0.0628114\pi\)
−0.996107 + 0.0881570i \(0.971902\pi\)
\(488\) −820710. + 374806.i −0.00706204 + 0.00322512i
\(489\) −5.28910e6 + 3.67865e7i −0.0452330 + 0.314602i
\(490\) −212924. 725152.i −0.00180982 0.00616369i
\(491\) −9.99711e7 6.42475e7i −0.844559 0.542765i 0.0453141 0.998973i \(-0.485571\pi\)
−0.889873 + 0.456207i \(0.849207\pi\)
\(492\) 2.10760e7 4.61500e7i 0.176967 0.387505i
\(493\) 6.79754e7 2.31503e8i 0.567297 1.93204i
\(494\) 451488. 391217.i 0.00374512 0.00324516i
\(495\) 2.73394e7 + 3.15513e7i 0.225410 + 0.260137i
\(496\) −1.61107e8 4.73052e7i −1.32029 0.387671i
\(497\) −2.55967e8 1.16896e8i −2.08504 0.952205i
\(498\) 270845. 421443.i 0.00219297 0.00341233i
\(499\) 5.74635e7 1.68728e7i 0.462477 0.135796i −0.0421899 0.999110i \(-0.513433\pi\)
0.504667 + 0.863314i \(0.331615\pi\)
\(500\) 1.34488e8 + 1.93365e7i 1.07591 + 0.154692i
\(501\) −3.01769e7 6.60782e7i −0.239973 0.525467i
\(502\) −489898. + 70436.7i −0.00387253 + 0.000556785i
\(503\) 1.32682e8 + 2.06457e8i 1.04258 + 1.62228i 0.744353 + 0.667787i \(0.232758\pi\)
0.298225 + 0.954496i \(0.403605\pi\)
\(504\) −494118. 428155.i −0.00385957 0.00334433i
\(505\) 6.52406e7i 0.506575i
\(506\) −577921. + 523838.i −0.00446085 + 0.00404339i
\(507\) −3.59013e7 −0.275478
\(508\) −8.07461e7 + 9.31860e7i −0.615929 + 0.710820i
\(509\) 1.48311e8 9.53139e7i 1.12466 0.722774i 0.160220 0.987081i \(-0.448780\pi\)
0.964439 + 0.264307i \(0.0851432\pi\)
\(510\) 58638.6 + 407840.i 0.000442052 + 0.00307454i
\(511\) 2.58622e8 1.18109e8i 1.93822 0.885156i
\(512\) 440008. 3.06032e6i 0.00327832 0.0228012i
\(513\) −1.08877e7 3.70800e7i −0.0806461 0.274655i
\(514\) −248983. 160011.i −0.00183349 0.00117832i
\(515\) 7.91368e6 1.73285e7i 0.0579371 0.126865i
\(516\) 3.45171e7 1.17554e8i 0.251238 0.855637i
\(517\) −1.50021e7 + 1.29994e7i −0.108563 + 0.0940700i
\(518\) 287419. + 331699.i 0.00206788 + 0.00238646i
\(519\) 6.16940e7 + 1.81150e7i 0.441307 + 0.129579i
\(520\) −673489. 307572.i −0.00478983 0.00218744i
\(521\) −1.16973e7 + 1.82014e7i −0.0827130 + 0.128704i −0.880145 0.474705i \(-0.842555\pi\)
0.797432 + 0.603409i \(0.206191\pi\)
\(522\) −285645. + 83872.9i −0.00200824 + 0.000589672i
\(523\) 7.71237e6 + 1.10887e6i 0.0539117 + 0.00775133i 0.169218 0.985579i \(-0.445876\pi\)
−0.115306 + 0.993330i \(0.536785\pi\)
\(524\) −2.82117e7 6.17751e7i −0.196081 0.429358i
\(525\) 5.16253e7 7.42259e6i 0.356767 0.0512953i
\(526\) 625074. + 972635.i 0.00429511 + 0.00668332i
\(527\) 2.24911e8 + 1.94886e8i 1.53666 + 1.33153i
\(528\) 1.11042e8i 0.754375i
\(529\) −1.44987e7 + 1.47324e8i −0.0979405 + 0.995192i
\(530\) 490752. 0.00329636
\(531\) −2.05149e7 + 2.36755e7i −0.137021 + 0.158130i
\(532\) 3.13235e8 2.01304e8i 2.08034 1.33696i
\(533\) −1.14975e7 7.99671e7i −0.0759317 0.528117i
\(534\) −296316. + 135323.i −0.00194595 + 0.000888684i
\(535\) −1.39723e7 + 9.71795e7i −0.0912445 + 0.634619i
\(536\) 573392. + 1.95279e6i 0.00372355 + 0.0126813i
\(537\) 4.02942e7 + 2.58955e7i 0.260208 + 0.167225i
\(538\) −319060. + 698645.i −0.00204892 + 0.00448652i
\(539\) −1.01705e8 + 3.46374e8i −0.649493 + 2.21197i
\(540\) −1.80983e7 + 1.56823e7i −0.114936 + 0.0995927i
\(541\) 3.27478e7 + 3.77929e7i 0.206819 + 0.238682i 0.849677 0.527304i \(-0.176797\pi\)
−0.642858 + 0.765985i \(0.722252\pi\)
\(542\) 543596. + 159614.i 0.00341412 + 0.00100248i
\(543\) 4.53984e7 + 2.07328e7i 0.283557 + 0.129496i
\(544\) −1.77758e6 + 2.76596e6i −0.0110416 + 0.0171811i
\(545\) 1.42204e8 4.17549e7i 0.878462 0.257940i
\(546\) −515256. 74082.6i −0.00316552 0.000455133i
\(547\) −7.23923e7 1.58517e8i −0.442314 0.968532i −0.991168 0.132614i \(-0.957663\pi\)
0.548854 0.835918i \(-0.315064\pi\)
\(548\) −1.62048e8 + 2.32989e7i −0.984694 + 0.141578i
\(549\) 2.51233e7 + 3.90926e7i 0.151831 + 0.236253i
\(550\) 284255. + 246308.i 0.00170852 + 0.00148044i
\(551\) 3.39086e8i 2.02701i
\(552\) −600969. 663016.i −0.00357301 0.00394191i
\(553\) 2.94585e8 1.74195
\(554\) 834457. 963014.i 0.00490766 0.00566374i
\(555\) 2.70480e7 1.73827e7i 0.158218 0.101681i
\(556\) 898860. + 6.25171e6i 0.00522959 + 0.0363726i
\(557\) 7.13880e7 3.26018e7i 0.413104 0.188658i −0.198011 0.980200i \(-0.563448\pi\)
0.611116 + 0.791541i \(0.290721\pi\)
\(558\) 52258.1 363463.i 0.000300781 0.00209198i
\(559\) −5.49645e7 1.87192e8i −0.314664 1.07165i
\(560\) −1.94098e8 1.24740e8i −1.10524 0.710297i
\(561\) 8.17583e7 1.79026e8i 0.463067 1.01397i
\(562\) 11891.7 40499.4i 6.69939e−5 0.000228160i
\(563\) −4.00547e7 + 3.47076e7i −0.224455 + 0.194491i −0.759827 0.650125i \(-0.774717\pi\)
0.535373 + 0.844616i \(0.320171\pi\)
\(564\) −7.45664e6 8.60542e6i −0.0415629 0.0479662i
\(565\) −2.00431e8 5.88518e7i −1.11127 0.326298i
\(566\) 309569. + 141375.i 0.00170729 + 0.000779694i
\(567\) −1.82056e7 + 2.83284e7i −0.0998747 + 0.155408i
\(568\) 2.23377e6 655894.i 0.0121897 0.00357922i
\(569\) 1.11832e8 + 1.60791e7i 0.607059 + 0.0872820i 0.438988 0.898493i \(-0.355337\pi\)
0.168071 + 0.985775i \(0.446246\pi\)
\(570\) 240553. + 526738.i 0.00129893 + 0.00284427i
\(571\) −4.46443e7 + 6.41888e6i −0.239804 + 0.0344787i −0.261169 0.965293i \(-0.584108\pi\)
0.0213646 + 0.999772i \(0.493199\pi\)
\(572\) 9.55994e7 + 1.48756e8i 0.510819 + 0.794850i
\(573\) −4.79499e7 4.15488e7i −0.254873 0.220849i
\(574\) 1.06899e6i 0.00565246i
\(575\) 7.13664e7 1.59537e6i 0.375397 0.00839188i
\(576\) −6.36929e7 −0.333291
\(577\) −1.84545e8 + 2.12977e8i −0.960673 + 1.10868i 0.0333434 + 0.999444i \(0.489385\pi\)
−0.994016 + 0.109232i \(0.965161\pi\)
\(578\) 885595. 569137.i 0.00458618 0.00294736i
\(579\) −1.51079e7 1.05078e8i −0.0778338 0.541346i
\(580\) −1.91134e8 + 8.72878e7i −0.979610 + 0.447373i
\(581\) 7.07595e7 4.92143e8i 0.360792 2.50936i
\(582\) −159826. 544317.i −0.000810733 0.00276110i
\(583\) −1.97199e8 1.26732e8i −0.995176 0.639561i
\(584\) −977151. + 2.13966e6i −0.00490595 + 0.0107425i
\(585\) −1.07435e7 + 3.65889e7i −0.0536633 + 0.182760i
\(586\) −203984. + 176753.i −0.00101369 + 0.000878363i
\(587\) −3.87312e7 4.46982e7i −0.191490 0.220991i 0.651883 0.758319i \(-0.273979\pi\)
−0.843373 + 0.537328i \(0.819434\pi\)
\(588\) −1.98685e8 5.83393e7i −0.977314 0.286965i
\(589\) 3.80447e8 + 1.73744e8i 1.86187 + 0.850285i
\(590\) 253781. 394892.i 0.00123567 0.00192275i
\(591\) −3.42858e7 + 1.00672e7i −0.166093 + 0.0487694i
\(592\) 8.46476e7 + 1.21705e7i 0.407990 + 0.0586601i
\(593\) 1.12117e8 + 2.45503e8i 0.537662 + 1.17732i 0.962310 + 0.271956i \(0.0876706\pi\)
−0.424648 + 0.905359i \(0.639602\pi\)
\(594\) −240368. + 34559.7i −0.00114688 + 0.000164896i
\(595\) 2.21088e8 + 3.44020e8i 1.04958 + 1.63317i
\(596\) −2.27339e8 1.96991e8i −1.07383 0.930480i
\(597\) 1.67428e7i 0.0786874i
\(598\) −687920. 185396.i −0.00321688 0.000866957i
\(599\) 6.16735e7 0.286958 0.143479 0.989653i \(-0.454171\pi\)
0.143479 + 0.989653i \(0.454171\pi\)
\(600\) −282575. + 326109.i −0.00130822 + 0.00150976i
\(601\) −2.33068e8 + 1.49784e8i −1.07364 + 0.689988i −0.953080 0.302717i \(-0.902106\pi\)
−0.120563 + 0.992706i \(0.538470\pi\)
\(602\) 367379. + 2.55518e6i 0.00168393 + 0.0117120i
\(603\) 9.53507e7 4.35452e7i 0.434883 0.198604i
\(604\) 2.51403e7 1.74854e8i 0.114093 0.793535i
\(605\) 3.48799e7 + 1.18790e8i 0.157510 + 0.536431i
\(606\) 319246. + 205167.i 0.00143453 + 0.000921913i
\(607\) 3.78166e7 8.28068e7i 0.169089 0.370254i −0.806050 0.591848i \(-0.798399\pi\)
0.975139 + 0.221594i \(0.0711259\pi\)
\(608\) −1.30182e6 + 4.43361e6i −0.00579217 + 0.0197263i
\(609\) −2.23298e8 + 1.93489e8i −0.988630 + 0.856653i
\(610\) −455981. 526230.i −0.00200890 0.00231839i
\(611\) −1.73974e7 5.10834e6i −0.0762713 0.0223953i
\(612\) 1.02692e8 + 4.68978e7i 0.448004 + 0.204597i
\(613\) −5.65805e7 + 8.80410e7i −0.245632 + 0.382211i −0.942076 0.335401i \(-0.891128\pi\)
0.696443 + 0.717612i \(0.254765\pi\)
\(614\) 251237. 73769.7i 0.00108537 0.000318693i
\(615\) 7.75126e7 + 1.11446e7i 0.333232 + 0.0479115i
\(616\) −1.94394e6 4.25662e6i −0.00831648 0.0182106i
\(617\) 1.96601e8 2.82670e7i 0.837010 0.120344i 0.289537 0.957167i \(-0.406499\pi\)
0.547473 + 0.836823i \(0.315590\pi\)
\(618\) 59908.2 + 93218.9i 0.000253817 + 0.000394947i
\(619\) 2.13703e8 + 1.85174e8i 0.901027 + 0.780745i 0.976301 0.216418i \(-0.0694375\pi\)
−0.0752734 + 0.997163i \(0.523983\pi\)
\(620\) 2.59173e8i 1.08746i
\(621\) −2.93956e7 + 3.54972e7i −0.122746 + 0.148224i
\(622\) −1.04661e6 −0.00434925
\(623\) −2.11719e8 + 2.44337e8i −0.875581 + 1.01047i
\(624\) −8.53266e7 + 5.48361e7i −0.351181 + 0.225690i
\(625\) 1.67997e7 + 1.16844e8i 0.0688116 + 0.478595i
\(626\) 174249. 79576.9i 0.000710310 0.000324388i
\(627\) 3.93637e7 2.73780e8i 0.159696 1.11071i
\(628\) −3.18479e7 1.08464e8i −0.128588 0.437931i
\(629\) −1.27510e8 8.19460e7i −0.512382 0.329288i
\(630\) 209608. 458979.i 0.000838276 0.00183557i
\(631\) −1.14584e8 + 3.90236e8i −0.456073 + 1.55324i 0.335424 + 0.942067i \(0.391121\pi\)
−0.791496 + 0.611174i \(0.790698\pi\)
\(632\) −1.84191e6 + 1.59602e6i −0.00729653 + 0.00632248i
\(633\) 8.82787e7 + 1.01879e8i 0.348052 + 0.401674i
\(634\) −238610. 70062.3i −0.000936313 0.000274926i
\(635\) −1.73120e8 7.90613e7i −0.676124 0.308775i
\(636\) 7.26956e7 1.13117e8i 0.282577 0.439698i
\(637\) −3.16384e8 + 9.28987e7i −1.22404 + 0.359411i
\(638\) −2.10906e6 303237.i −0.00812133 0.00116767i
\(639\) −4.98107e7 1.09070e8i −0.190906 0.418026i
\(640\) 3.77895e6 543330.i 0.0144155 0.00207264i
\(641\) 7.74487e7 + 1.20513e8i 0.294063 + 0.457571i 0.956577 0.291478i \(-0.0941471\pi\)
−0.662515 + 0.749049i \(0.730511\pi\)
\(642\) −431595. 373979.i −0.00163107 0.00141333i
\(643\) 3.94027e8i 1.48215i 0.671421 + 0.741076i \(0.265684\pi\)
−0.671421 + 0.741076i \(0.734316\pi\)
\(644\) −4.07949e8 1.75394e8i −1.52738 0.656685i
\(645\) 1.89106e8 0.704736
\(646\) 1.78767e6 2.06309e6i 0.00663118 0.00765279i
\(647\) −1.39975e8 + 8.99568e7i −0.516820 + 0.332140i −0.772913 0.634512i \(-0.781201\pi\)
0.256093 + 0.966652i \(0.417565\pi\)
\(648\) −39648.4 275761.i −0.000145714 0.00101346i
\(649\) −2.03955e8 + 9.31429e7i −0.746104 + 0.340734i
\(650\) −48893.2 + 340060.i −0.000178036 + 0.00123827i
\(651\) −1.02675e8 3.49678e8i −0.372152 1.26743i
\(652\) −1.28359e8 8.24913e7i −0.463109 0.297622i
\(653\) −1.27411e8 + 2.78992e8i −0.457582 + 1.00197i 0.530450 + 0.847716i \(0.322023\pi\)
−0.988032 + 0.154249i \(0.950704\pi\)
\(654\) −242878. + 827168.i −0.000868272 + 0.00295706i
\(655\) 7.92199e7 6.86445e7i 0.281910 0.244276i
\(656\) 1.36400e8 + 1.57414e8i 0.483173 + 0.557611i
\(657\) 1.16242e8 + 3.41319e7i 0.409891 + 0.120355i
\(658\) 218236. + 99665.2i 0.000766036 + 0.000349837i
\(659\) 1.80048e8 2.80160e8i 0.629117 0.978925i −0.369645 0.929173i \(-0.620521\pi\)
0.998762 0.0497517i \(-0.0158430\pi\)
\(660\) −1.64456e8 + 4.82885e7i −0.572028 + 0.167962i
\(661\) −1.18949e8 1.71023e7i −0.411866 0.0592173i −0.0667321 0.997771i \(-0.521257\pi\)
−0.345134 + 0.938554i \(0.612166\pi\)
\(662\) 812133. + 1.77832e6i 0.00279932 + 0.00612966i
\(663\) 1.77941e8 2.55840e7i 0.610569 0.0877866i
\(664\) 2.22394e6 + 3.46052e6i 0.00759659 + 0.0118205i
\(665\) 4.34340e8 + 3.76358e8i 1.47695 + 1.27978i
\(666\) 187021.i 0.000633092i
\(667\) −3.35227e8 + 2.26180e8i −1.12969 + 0.762215i
\(668\) 2.98236e8 1.00053
\(669\) 4.72982e7 5.45850e7i 0.157967 0.182304i
\(670\) −1.32134e6 + 849176.i −0.00439331 + 0.00282341i
\(671\) 4.73331e7 + 3.29209e8i 0.156674 + 1.08969i
\(672\) 3.66251e6 1.67261e6i 0.0120690 0.00551172i
\(673\) −1.52900e7 + 1.06344e8i −0.0501606 + 0.348875i 0.949249 + 0.314525i \(0.101845\pi\)
−0.999410 + 0.0343500i \(0.989064\pi\)
\(674\) −585256. 1.99320e6i −0.00191146 0.00650985i
\(675\) 1.86963e7 + 1.20154e7i 0.0607916 + 0.0390684i
\(676\) 6.12294e7 1.34074e8i 0.198207 0.434014i
\(677\) 1.28782e8 4.38591e8i 0.415039 1.41349i −0.441430 0.897296i \(-0.645529\pi\)
0.856469 0.516198i \(-0.172653\pi\)
\(678\) 918293. 795706.i 0.00294640 0.00255307i
\(679\) −3.68707e8 4.25511e8i −1.17780 1.35926i
\(680\) −3.24622e6 953175.i −0.0103241 0.00303142i
\(681\) 2.86865e8 + 1.31007e8i 0.908315 + 0.414814i
\(682\) 1.42089e6 2.21094e6i 0.00447926 0.00696986i
\(683\) −1.94548e8 + 5.71245e7i −0.610611 + 0.179292i −0.572395 0.819978i \(-0.693986\pi\)
−0.0382159 + 0.999270i \(0.512167\pi\)
\(684\) 1.57045e8 + 2.25796e7i 0.490743 + 0.0705583i
\(685\) −1.04973e8 2.29858e8i −0.326592 0.715136i
\(686\) 1.87079e6 268979.i 0.00579500 0.000833195i
\(687\) −4.29884e7 6.68913e7i −0.132581 0.206300i
\(688\) 3.80131e8 + 3.29385e8i 1.16726 + 1.01144i
\(689\) 2.14115e8i 0.654621i
\(690\) 360287. 589165.i 0.00109673 0.00179345i
\(691\) 1.48086e8 0.448828 0.224414 0.974494i \(-0.427953\pi\)
0.224414 + 0.974494i \(0.427953\pi\)
\(692\) −1.72869e8 + 1.99502e8i −0.521674 + 0.602044i
\(693\) −2.02754e8 + 1.30302e8i −0.609215 + 0.391518i
\(694\) −176701. 1.22898e6i −0.000528639 0.00367677i
\(695\) −8.86781e6 + 4.04979e6i −0.0264157 + 0.0120636i
\(696\) 347886. 2.41960e6i 0.00103183 0.00717656i
\(697\) −1.04007e8 3.54216e8i −0.307160 1.04609i
\(698\) 415170. + 266814.i 0.00122084 + 0.000784588i
\(699\) −1.06009e8 + 2.32128e8i −0.310393 + 0.679667i
\(700\) −6.03268e7 + 2.05454e8i −0.175880 + 0.598992i
\(701\) 9.08598e7 7.87304e7i 0.263765 0.228554i −0.512930 0.858430i \(-0.671440\pi\)
0.776695 + 0.629877i \(0.216895\pi\)
\(702\) −145257. 167636.i −0.000419881 0.000484569i
\(703\) −2.04388e8 6.00138e7i −0.588288 0.172737i
\(704\) −4.14671e8 1.89374e8i −1.18846 0.542753i
\(705\) 9.50193e6 1.47853e7i 0.0271172 0.0421952i
\(706\) −670949. + 197008.i −0.00190667 + 0.000559848i
\(707\) 3.72802e8 + 5.36009e7i 1.05492 + 0.151675i
\(708\) −5.34282e7 1.16991e8i −0.150546 0.329651i
\(709\) −5.21109e7 + 7.49241e6i −0.146214 + 0.0210224i −0.215033 0.976607i \(-0.568986\pi\)
0.0688190 + 0.997629i \(0.478077\pi\)
\(710\) 971359. + 1.51146e6i 0.00271397 + 0.00422302i
\(711\) 9.48662e7 + 8.22020e7i 0.263938 + 0.228704i
\(712\) 2.67480e6i 0.00741056i
\(713\) −8.20025e7 4.92009e8i −0.226234 1.35739i
\(714\) −2.37869e6 −0.00653495
\(715\) −1.78733e8 + 2.06269e8i −0.488974 + 0.564307i
\(716\) −1.65429e8 + 1.06314e8i −0.450683 + 0.289636i
\(717\) −2.26812e7 1.57751e8i −0.0615331 0.427972i
\(718\) −405058. + 184984.i −0.00109432 + 0.000499759i
\(719\) −8.85119e6 + 6.15614e7i −0.0238130 + 0.165623i −0.998258 0.0590042i \(-0.981207\pi\)
0.974445 + 0.224628i \(0.0721165\pi\)
\(720\) −2.76984e7 9.43322e7i −0.0742092 0.252733i
\(721\) 9.25181e7 + 5.94578e7i 0.246843 + 0.158636i
\(722\) 873361. 1.91239e6i 0.00232050 0.00508119i
\(723\) −5.46030e6 + 1.85961e7i −0.0144478 + 0.0492047i
\(724\) −1.54853e8 + 1.34181e8i −0.408042 + 0.353570i
\(725\) 1.27699e8 + 1.47373e8i 0.335100 + 0.386727i
\(726\) −690973. 202888.i −0.00180572 0.000530208i
\(727\) 5.22053e8 + 2.38414e8i 1.35866 + 0.620480i 0.955593 0.294689i \(-0.0952162\pi\)
0.403069 + 0.915170i \(0.367943\pi\)
\(728\) 2.31088e6 3.59580e6i 0.00598940 0.00931968i
\(729\) −1.37677e7 + 4.04255e6i −0.0355368 + 0.0104345i
\(730\) −1.79684e6 258347.i −0.00461894 0.000664103i
\(731\) −3.70338e8 8.10927e8i −0.948083 2.07601i
\(732\) −1.88839e8 + 2.71510e7i −0.481458 + 0.0692232i
\(733\) −1.83901e8 2.86156e8i −0.466952 0.726591i 0.525289 0.850924i \(-0.323957\pi\)
−0.992241 + 0.124333i \(0.960321\pi\)
\(734\) −751777. 651418.i −0.00190108 0.00164730i
\(735\) 3.19619e8i 0.804954i
\(736\) 5.25150e6 1.67034e6i 0.0131719 0.00418958i
\(737\) 7.50249e8 1.87414
\(738\) −298294. + 344250.i −0.000742123 + 0.000856456i
\(739\) 5.10744e8 3.28235e8i 1.26552 0.813303i 0.276493 0.961016i \(-0.410828\pi\)
0.989030 + 0.147713i \(0.0471913\pi\)
\(740\) 1.87856e7 + 1.30657e8i 0.0463587 + 0.322432i
\(741\) 2.29816e8 1.04953e8i 0.564840 0.257954i
\(742\) −403196. + 2.80429e6i −0.000986971 + 0.00686454i
\(743\) 1.42299e8 + 4.84627e8i 0.346926 + 1.18152i 0.929525 + 0.368760i \(0.120218\pi\)
−0.582599 + 0.812760i \(0.697964\pi\)
\(744\) 2.53648e6 + 1.63010e6i 0.00615905 + 0.00395818i
\(745\) 1.92880e8 4.22349e8i 0.466465 1.02142i
\(746\) 49834.7 169721.i 0.000120037 0.000408809i
\(747\) 1.60116e8 1.38742e8i 0.384126 0.332847i
\(748\) 5.29135e8 + 6.10654e8i 1.26433 + 1.45912i
\(749\) −5.43830e8 1.59683e8i −1.29425 0.380026i
\(750\) −1.10964e6 506757.i −0.00263027 0.00120120i
\(751\) 2.38361e8 3.70896e8i 0.562749 0.875655i −0.436967 0.899477i \(-0.643947\pi\)
0.999716 + 0.0238229i \(0.00758378\pi\)
\(752\) 4.48533e7 1.31701e7i 0.105473 0.0309697i
\(753\) −2.07182e8 2.97882e7i −0.485251 0.0697686i
\(754\) −808506. 1.77038e6i −0.00188612 0.00413002i
\(755\) 2.69889e8 3.88042e7i 0.627111 0.0901650i
\(756\) −7.47433e7 1.16303e8i −0.172984 0.269169i
\(757\) 1.97639e8 + 1.71255e8i 0.455601 + 0.394780i 0.852204 0.523210i \(-0.175266\pi\)
−0.396603 + 0.917990i \(0.629811\pi\)
\(758\) 3.43815e6i 0.00789436i
\(759\) −2.96921e8 + 1.43704e8i −0.679072 + 0.328657i
\(760\) −4.75479e6 −0.0108315
\(761\) −5.17370e8 + 5.97077e8i −1.17394 + 1.35480i −0.251883 + 0.967758i \(0.581050\pi\)
−0.922060 + 0.387046i \(0.873496\pi\)
\(762\) 931300. 598510.i 0.00210487 0.00135272i
\(763\) 1.21766e8 + 8.46899e8i 0.274127 + 1.90659i
\(764\) 2.36942e8 1.08208e8i 0.531328 0.242649i
\(765\) −2.47987e7 + 1.72479e8i −0.0553917 + 0.385258i
\(766\) 168138. + 572626.i 0.000374093 + 0.00127404i
\(767\) −1.72291e8 1.10725e8i −0.381836 0.245391i
\(768\) 1.08621e8 2.37846e8i 0.239789 0.525065i
\(769\) −1.61165e8 + 5.48879e8i −0.354399 + 1.20697i 0.568744 + 0.822515i \(0.307430\pi\)
−0.923143 + 0.384457i \(0.874389\pi\)
\(770\) 2.72930e6 2.36495e6i 0.00597833 0.00518025i
\(771\) −8.19666e7 9.45945e7i −0.178844 0.206397i
\(772\) 4.18180e8 + 1.22789e8i 0.908890 + 0.266874i
\(773\) 3.81470e8 + 1.74212e8i 0.825890 + 0.377171i 0.783087 0.621912i \(-0.213644\pi\)
0.0428029 + 0.999084i \(0.486371\pi\)
\(774\) −594697. + 925366.i −0.00128255 + 0.00199568i
\(775\) −2.30781e8 + 6.77634e7i −0.495787 + 0.145576i
\(776\) 4.61072e6 + 662922.i 0.00986697 + 0.00141866i
\(777\) 7.71071e7 + 1.68841e8i 0.164373 + 0.359927i
\(778\) 2.61776e6 376376.i 0.00555892 0.000799252i
\(779\) −2.80498e8 4.36464e8i −0.593359 0.923285i
\(780\) −1.18319e8 1.02524e8i −0.249327 0.216043i
\(781\) 8.58198e8i 1.80150i
\(782\) −3.23204e6 391188.i −0.00675859 0.000818023i
\(783\) −1.25901e8 −0.262268
\(784\) 5.56713e8 6.42481e8i 1.15527 1.33325i
\(785\) 1.46784e8 9.43324e7i 0.303438 0.195008i
\(786\) 86773.6 + 603524.i 0.000178698 + 0.00124287i
\(787\) 5.28803e8 2.41496e8i 1.08485 0.495434i 0.208950 0.977926i \(-0.432995\pi\)
0.875900 + 0.482492i \(0.160268\pi\)
\(788\) 2.08781e7 1.45210e8i 0.0426689 0.296769i
\(789\) 1.37754e8 + 4.69149e8i 0.280462 + 0.955167i
\(790\) −1.58231e6 1.01689e6i −0.00320930 0.00206249i
\(791\) 5.00966e8 1.09696e9i 1.01223 2.21647i
\(792\) 561771. 1.91322e6i 0.00113080 0.00385114i
\(793\) −2.29594e8 + 1.98945e8i −0.460407 + 0.398945i
\(794\) −151755. 175135.i −0.000303167 0.000349873i
\(795\) 1.99136e8 + 5.84716e7i 0.396322 + 0.116371i
\(796\) −6.25261e7 2.85547e7i −0.123972 0.0566159i
\(797\) −1.79171e7 + 2.78795e7i −0.0353909 + 0.0550694i −0.858498 0.512816i \(-0.828602\pi\)
0.823107 + 0.567886i \(0.192238\pi\)
\(798\) −3.20756e6 + 941824.i −0.00631199 + 0.00185337i
\(799\) −8.20107e7 1.17914e7i −0.160779 0.0231166i
\(800\) −1.10389e6 2.41719e6i −0.00215604 0.00472108i
\(801\) −1.36361e8 + 1.96058e7i −0.265335 + 0.0381493i
\(802\) 825967. + 1.28523e6i 0.00160118 + 0.00249148i
\(803\) 6.55312e8 + 5.67831e8i 1.26561 + 1.09666i
\(804\) 4.30354e8i 0.828052i
\(805\) 8.23565e7 6.80438e8i 0.157874 1.30437i
\(806\) 2.40060e6 0.00458473
\(807\) −2.12709e8 + 2.45479e8i −0.404729 + 0.467082i
\(808\) −2.62137e6 + 1.68465e6i −0.00496929 + 0.00319357i
\(809\) 9.85214e7 + 6.85231e8i 0.186074 + 1.29417i 0.842054 + 0.539393i \(0.181346\pi\)
−0.655980 + 0.754778i \(0.727745\pi\)
\(810\) 195576. 89316.5i 0.000368010 0.000168065i
\(811\) 8.24920e7 5.73745e8i 0.154650 1.07561i −0.753645 0.657282i \(-0.771706\pi\)
0.908295 0.418331i \(-0.137385\pi\)
\(812\) −3.41753e8 1.16390e9i −0.638328 2.17395i
\(813\) 2.01561e8 + 1.29536e8i 0.375090 + 0.241056i
\(814\) −556056. + 1.21759e6i −0.00103097 + 0.00225751i
\(815\) 6.63506e7 2.25969e8i 0.122567 0.417423i
\(816\) −3.50273e8 + 3.03513e8i −0.644668 + 0.558608i
\(817\) −8.20467e8 9.46869e8i −1.50451 1.73630i
\(818\) −2.60433e6 764700.i −0.00475813 0.00139711i
\(819\) −2.00252e8 9.14522e7i −0.364524 0.166472i
\(820\) −1.73817e8 + 2.70464e8i −0.315246 + 0.490533i
\(821\) −3.53756e8 + 1.03872e8i −0.639254 + 0.187702i −0.585268 0.810840i \(-0.699011\pi\)
−0.0539861 + 0.998542i \(0.517193\pi\)
\(822\) 1.45490e6 + 209183.i 0.00261949 + 0.000376626i
\(823\) −1.17547e8 2.57391e8i −0.210868 0.461736i 0.774413 0.632681i \(-0.218045\pi\)
−0.985281 + 0.170945i \(0.945318\pi\)
\(824\) −900609. + 129488.i −0.00160974 + 0.000231445i
\(825\) 8.59972e7 + 1.33814e8i 0.153152 + 0.238309i
\(826\) 2.04801e6 + 1.77461e6i 0.00363406 + 0.00314893i
\(827\) 7.64274e8i 1.35124i 0.737250 + 0.675620i \(0.236124\pi\)
−0.737250 + 0.675620i \(0.763876\pi\)
\(828\) −8.24307e7 1.70318e8i −0.145210 0.300034i
\(829\) −1.95694e8 −0.343490 −0.171745 0.985141i \(-0.554941\pi\)
−0.171745 + 0.985141i \(0.554941\pi\)
\(830\) −2.07892e6 + 2.39920e6i −0.00363583 + 0.00419597i
\(831\) 4.53344e8 2.91346e8i 0.789995 0.507699i
\(832\) −5.92594e7 4.12158e8i −0.102893 0.715639i
\(833\) −1.37060e9 + 6.25930e8i −2.37123 + 1.08291i
\(834\) 8070.15 56129.1i 1.39118e−5 9.67587e-5i
\(835\) 1.29690e8 + 4.41683e8i 0.222765 + 0.758667i
\(836\) 9.55301e8 + 6.13934e8i 1.63501 + 1.05076i
\(837\) 6.45106e7 1.41258e8i 0.110016 0.240901i
\(838\) 164981. 561872.i 0.000280350 0.000954785i
\(839\) −4.72885e8 + 4.09757e8i −0.800699 + 0.693810i −0.955777 0.294092i \(-0.904983\pi\)
0.155078 + 0.987902i \(0.450437\pi\)
\(840\) 2.71317e6 + 3.13117e6i 0.00457762 + 0.00528286i
\(841\) −4.89218e8 1.43647e8i −0.822460 0.241496i
\(842\) −3.46983e6 1.58462e6i −0.00581262 0.00265453i
\(843\) 9.65077e6 1.50169e7i 0.0161094 0.0250667i
\(844\) −5.31027e8 + 1.55924e8i −0.883261 + 0.259349i
\(845\) 2.25187e8 + 3.23770e7i 0.373227 + 0.0536620i
\(846\) 42468.4 + 92992.9i 7.01383e−5 + 0.000153581i
\(847\) −7.07456e8 + 1.01717e8i −1.16426 + 0.167395i
\(848\) 2.98446e8 + 4.64392e8i 0.489417 + 0.761547i
\(849\) 1.08771e8 + 9.42509e7i 0.177743 + 0.154015i
\(850\) 1.56989e6i 0.00255631i
\(851\) 7.70023e7 + 2.42093e8i 0.124944 + 0.392820i
\(852\) 4.92275e8 0.795956
\(853\) −5.69410e8 + 6.57134e8i −0.917441 + 1.05878i 0.0806327 + 0.996744i \(0.474306\pi\)
−0.998074 + 0.0620395i \(0.980240\pi\)
\(854\) 3.38165e6 2.17325e6i 0.00542944 0.00348929i
\(855\) 3.48518e7 + 2.42399e8i 0.0557605 + 0.387823i
\(856\) 4.26547e6 1.94797e6i 0.00680057 0.00310572i
\(857\) 3.60958e7 2.51052e8i 0.0573475 0.398860i −0.940849 0.338826i \(-0.889970\pi\)
0.998196 0.0600339i \(-0.0191209\pi\)
\(858\) −447274. 1.52327e6i −0.000708128 0.00241166i
\(859\) −3.18760e8 2.04855e8i −0.502903 0.323196i 0.264473 0.964393i \(-0.414802\pi\)
−0.767377 + 0.641197i \(0.778438\pi\)
\(860\) −3.22519e8 + 7.06218e8i −0.507061 + 1.11031i
\(861\) −1.27367e8 + 4.33771e8i −0.199548 + 0.679597i
\(862\) 909552. 788132.i 0.00142006 0.00123049i
\(863\) −2.96963e8 3.42714e8i −0.462030 0.533211i 0.476147 0.879366i \(-0.342033\pi\)
−0.938178 + 0.346154i \(0.887487\pi\)
\(864\) 1.64618e6 + 483362.i 0.00255233 + 0.000749431i
\(865\) −3.70632e8 1.69262e8i −0.572658 0.261524i
\(866\) 1.57927e6 2.45740e6i 0.00243166 0.00378374i
\(867\) 4.27165e8 1.25427e8i 0.655448 0.192457i
\(868\) 1.48098e9 + 2.12933e8i 2.26460 + 0.325600i
\(869\) 3.73218e8 + 8.17234e8i 0.568727 + 1.24534i
\(870\) 1.86732e6 268480.i 0.00283570 0.000407712i
\(871\) 3.70496e8 + 5.76502e8i 0.560697 + 0.872462i
\(872\) −5.34973e6 4.63557e6i −0.00806831 0.00699123i
\(873\) 2.39914e8i 0.360589i
\(874\) −4.51315e6 + 752201.i −0.00675999 + 0.00112668i
\(875\) −1.21071e9 −1.80724
\(876\) −3.25716e8 + 3.75897e8i −0.484537 + 0.559186i
\(877\) −4.51925e8 + 2.90434e8i −0.669989 + 0.430576i −0.830921 0.556390i \(-0.812186\pi\)
0.160933 + 0.986965i \(0.448550\pi\)
\(878\) 222403. + 1.54685e6i 0.000328592 + 0.00228541i
\(879\) −1.03832e8 + 4.74183e7i −0.152884 + 0.0698199i
\(880\) 1.00142e8 6.96502e8i 0.146949 1.02205i
\(881\) −8.19986e6 2.79262e7i −0.0119916 0.0408398i 0.953280 0.302089i \(-0.0976839\pi\)
−0.965271 + 0.261249i \(0.915866\pi\)
\(882\) 1.56401e6 + 1.00513e6i 0.00227948 + 0.00146493i
\(883\) 3.72362e7 8.15359e7i 0.0540858 0.118431i −0.880660 0.473750i \(-0.842900\pi\)
0.934745 + 0.355318i \(0.115627\pi\)
\(884\) −2.07933e8 + 7.08155e8i −0.301000 + 1.02511i
\(885\) 1.50029e8 1.30001e8i 0.216444 0.187550i
\(886\) 392228. + 452656.i 0.000563946 + 0.000650829i
\(887\) 1.00862e8 + 2.96159e7i 0.144530 + 0.0424379i 0.353197 0.935549i \(-0.385094\pi\)
−0.208667 + 0.977987i \(0.566913\pi\)
\(888\) −1.39687e6 637931.i −0.00199489 0.000911034i
\(889\) 5.94011e8 9.24298e8i 0.845452 1.31555i
\(890\) 1.98065e6 581570.i 0.00280955 0.000824959i
\(891\) −1.01654e8 1.46156e7i −0.143711 0.0206625i
\(892\) 1.23182e8 + 2.69730e8i 0.173561 + 0.380045i
\(893\) −1.15257e8 + 1.65714e7i −0.161850 + 0.0232705i
\(894\) 1.46014e6 + 2.27203e6i 0.00204354 + 0.00317981i
\(895\) −2.29388e8 1.98766e8i −0.319964 0.277250i
\(896\) 2.20403e7i 0.0306403i
\(897\) −2.57053e8 1.57193e8i −0.356160 0.217799i
\(898\) 2.52285e6 0.00348388
\(899\) 8.92297e8 1.02977e9i 1.22809 1.41729i
\(900\) −7.67579e7 + 4.93293e7i −0.105292 + 0.0676670i
\(901\) −1.39242e8 9.68446e8i −0.190368 1.32404i
\(902\) −2.96558e6 + 1.35433e6i −0.00404101 + 0.00184547i
\(903\) −1.55367e8 + 1.08060e9i −0.211007 + 1.46758i
\(904\) 2.81088e6 + 9.57299e6i 0.00380485 + 0.0129581i
\(905\) −2.66059e8 1.70986e8i −0.358949 0.230682i
\(906\) −658858. + 1.44270e6i −0.000885946 + 0.00193995i
\(907\) −2.56864e7 + 8.74800e7i −0.0344256 + 0.117243i −0.974913 0.222585i \(-0.928551\pi\)
0.940488 + 0.339828i \(0.110369\pi\)
\(908\) −9.78493e8 + 8.47869e8i −1.30707 + 1.13259i
\(909\) 1.05098e8 + 1.21289e8i 0.139927 + 0.161485i
\(910\) 3.16508e6 + 929351.i 0.00420011 + 0.00123326i
\(911\) −7.09532e8 3.24032e8i −0.938462 0.428581i −0.113353 0.993555i \(-0.536159\pi\)
−0.825109 + 0.564974i \(0.808886\pi\)
\(912\) −3.52154e8 + 5.47963e8i −0.464247 + 0.722382i
\(913\) 1.45495e9 4.27211e8i 1.91176 0.561345i
\(914\) −784845. 112844.i −0.00102789 0.000147788i
\(915\) −1.22328e8 2.67861e8i −0.159684 0.349660i
\(916\) 3.23122e8 4.64580e7i 0.420417 0.0604469i
\(917\) 3.27167e8 + 5.09081e8i 0.424288 + 0.660206i
\(918\) −766016. 663757.i −0.000990170 0.000857988i
\(919\) 6.78222e8i 0.873826i −0.899504 0.436913i \(-0.856072\pi\)
0.899504 0.436913i \(-0.143928\pi\)
\(920\) 3.17158e6 + 4.70067e6i 0.00407298 + 0.00603665i
\(921\) 1.10735e8 0.141745
\(922\) 1.86340e6 2.15048e6i 0.00237747 0.00274374i
\(923\) 6.59452e8 4.23804e8i 0.838645 0.538964i
\(924\) −1.40819e8 9.79417e8i −0.178503 1.24151i
\(925\) 1.11432e8 5.08893e7i 0.140794 0.0642986i
\(926\) −857872. + 5.96663e6i −0.00108041 + 0.00751443i
\(927\) 1.32026e7 + 4.49640e7i 0.0165737 + 0.0564450i
\(928\) 1.26641e7 + 8.13872e6i 0.0158464 + 0.0101839i
\(929\) 3.39166e8 7.42670e8i 0.423024 0.926294i −0.571383 0.820683i \(-0.693593\pi\)
0.994408 0.105611i \(-0.0336798\pi\)
\(930\) −655566. + 2.23265e6i −0.000815019 + 0.00277570i
\(931\) −1.60036e9 + 1.38672e9i −1.98321 + 1.71846i
\(932\) −6.86086e8 7.91785e8i −0.847482 0.978047i
\(933\) −4.24691e8 1.24700e8i −0.522911 0.153540i
\(934\) −3.85713e6 1.76149e6i −0.00473395 0.00216192i
\(935\) −6.74272e8 + 1.04919e9i −0.824898 + 1.28357i
\(936\) 1.74756e6 513131.i 0.00213111 0.000625750i
\(937\) 1.06152e9 + 1.52624e8i 1.29036 + 0.185525i 0.753107 0.657898i \(-0.228554\pi\)
0.537249 + 0.843424i \(0.319463\pi\)
\(938\) −3.76682e6 8.24819e6i −0.00456422 0.00999424i
\(939\) 8.01877e7 1.15292e7i 0.0968525 0.0139253i
\(940\) 3.90103e7 + 6.07013e7i 0.0469674 + 0.0730826i
\(941\) 3.91459e7 + 3.39201e7i 0.0469804 + 0.0407088i 0.678035 0.735030i \(-0.262832\pi\)
−0.631054 + 0.775739i \(0.717377\pi\)
\(942\) 1.01492e6i 0.00121417i
\(943\) −2.44395e8 + 5.68440e8i −0.291446 + 0.677875i
\(944\) 5.28015e8 0.627669
\(945\) 1.39740e8 1.61269e8i 0.165587 0.191097i
\(946\) −6.62309e6 + 4.25640e6i −0.00782325 + 0.00502770i
\(947\) −1.16963e8 8.13497e8i −0.137721 0.957869i −0.935098 0.354388i \(-0.884689\pi\)
0.797377 0.603481i \(-0.206220\pi\)
\(948\) −4.68777e8 + 2.14083e8i −0.550227 + 0.251280i
\(949\) −1.12717e8 + 7.83963e8i −0.131884 + 0.917270i
\(950\) 621587. + 2.11693e6i 0.000724989 + 0.00246909i
\(951\) −8.84748e7 5.68593e7i −0.102868 0.0661089i
\(952\) 8.11375e6 1.77666e7i 0.00940396 0.0205918i
\(953\) 3.67354e8 1.25109e9i 0.424430 1.44548i −0.418877 0.908043i \(-0.637576\pi\)
0.843307 0.537432i \(-0.180606\pi\)
\(954\) −912361. + 790566.i −0.00105080 + 0.000910527i
\(955\) 2.63290e8 + 3.03853e8i 0.302291 + 0.348862i
\(956\) 6.27806e8 + 1.84341e8i 0.718542 + 0.210983i
\(957\) −8.19678e8 3.74335e8i −0.935207 0.427095i
\(958\) −2.11660e6 + 3.29349e6i −0.00240736 + 0.00374593i
\(959\) 1.39972e9 4.10994e8i 1.58703 0.465993i
\(960\) 3.99507e8 + 5.74404e7i 0.451555 + 0.0649238i
\(961\) 3.29487e8 + 7.21477e8i 0.371252 + 0.812928i
\(962\) −1.21021e6 + 174002.i −0.00135937 + 0.000195448i
\(963\) −1.30573e8 2.03175e8i −0.146209 0.227506i
\(964\) −6.01347e7 5.21070e7i −0.0671265 0.0581655i
\(965\) 6.72714e8i 0.748598i
\(966\) 3.07064e6 + 2.54283e6i 0.00340641 + 0.00282088i
\(967\) 1.74729e8 0.193235 0.0966175 0.995322i \(-0.469198\pi\)
0.0966175 + 0.995322i \(0.469198\pi\)
\(968\) 3.87231e6 4.46889e6i 0.00426918 0.00492690i
\(969\) 9.71208e8 6.24157e8i 1.06743 0.685998i
\(970\) 511607. + 3.55831e6i 0.000560559 + 0.00389877i
\(971\) 3.82383e8 1.74629e8i 0.417678 0.190747i −0.195480 0.980708i \(-0.562626\pi\)
0.613157 + 0.789961i \(0.289899\pi\)
\(972\) 8.38372e6 5.83100e7i 0.00912931 0.0634957i
\(973\) −1.58559e7 5.40003e7i −0.0172129 0.0586216i
\(974\) −390396. 250893.i −0.000422502 0.000271526i
\(975\) −6.03568e7 + 1.32163e8i −0.0651197 + 0.142592i
\(976\) 2.20663e8 7.51511e8i 0.237345 0.808324i
\(977\) −1.67187e8 + 1.44868e8i −0.179274 + 0.155342i −0.739875 0.672744i \(-0.765116\pi\)
0.560601 + 0.828086i \(0.310570\pi\)
\(978\) 897094. + 1.03530e6i 0.000959006 + 0.00110675i
\(979\) −9.46070e8 2.77791e8i −1.00827 0.296054i
\(980\) 1.19362e9 + 5.45108e8i 1.26820 + 0.579168i
\(981\) −1.97109e8 + 3.06707e8i −0.208785 + 0.324876i
\(982\) −4.20288e6 + 1.23408e6i −0.00443826 + 0.00130319i
\(983\) −1.58774e9 2.28283e8i −1.67155 0.240333i −0.759529 0.650473i \(-0.774571\pi\)
−0.912023 + 0.410140i \(0.865480\pi\)
\(984\) −1.55375e6 3.40223e6i −0.00163078 0.00357091i
\(985\) 2.24133e8 3.22255e7i 0.234529 0.0337202i
\(986\) −4.80818e6 7.48167e6i −0.00501591 0.00780491i
\(987\) 7.66805e7 + 6.64440e7i 0.0797505 + 0.0691042i
\(988\) 1.03725e9i 1.07550i
\(989\) −3.88816e8 + 1.44272e9i −0.401935 + 1.49139i
\(990\) 1.53885e6 0.00158596
\(991\) 9.57910e8 1.10549e9i 0.984247 1.13588i −0.00647574 0.999979i \(-0.502061\pi\)
0.990722 0.135902i \(-0.0433932\pi\)
\(992\) −1.56204e7 + 1.00386e7i −0.0160014 + 0.0102835i
\(993\) 1.17663e8 + 8.18366e8i 0.120169 + 0.835795i
\(994\) −9.43497e6 + 4.30881e6i −0.00960686 + 0.00438731i
\(995\) 1.50992e7 1.05017e8i 0.0153280 0.106609i
\(996\) 2.45054e8 + 8.34578e8i 0.248019 + 0.844674i
\(997\) 3.43958e7 + 2.21048e7i 0.0347072 + 0.0223050i 0.557879 0.829922i \(-0.311615\pi\)
−0.523172 + 0.852227i \(0.675252\pi\)
\(998\) 917043. 2.00804e6i 0.000922567 0.00202014i
\(999\) −2.22829e7 + 7.58886e7i −0.0223499 + 0.0761168i
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.7.12 240
23.10 odd 22 inner 69.7.f.a.10.12 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.7.f.a.7.12 240 1.1 even 1 trivial
69.7.f.a.10.12 yes 240 23.10 odd 22 inner