Properties

Label 69.7.f.a.10.6
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 10.6
Character \(\chi\) \(=\) 69.10
Dual form 69.7.f.a.7.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.37670 - 6.20505i) q^{2} +(-13.1138 - 8.42776i) q^{3} +(-0.485518 + 3.37685i) q^{4} +(-45.2350 - 20.6582i) q^{5} +(18.2146 + 126.686i) q^{6} +(-13.8057 + 47.0180i) q^{7} +(-418.489 + 268.946i) q^{8} +(100.946 + 221.041i) q^{9} +O(q^{10})\) \(q+(-5.37670 - 6.20505i) q^{2} +(-13.1138 - 8.42776i) q^{3} +(-0.485518 + 3.37685i) q^{4} +(-45.2350 - 20.6582i) q^{5} +(18.2146 + 126.686i) q^{6} +(-13.8057 + 47.0180i) q^{7} +(-418.489 + 268.946i) q^{8} +(100.946 + 221.041i) q^{9} +(115.031 + 391.758i) q^{10} +(464.382 + 402.389i) q^{11} +(34.8263 - 40.1917i) q^{12} +(-2251.53 + 661.110i) q^{13} +(365.978 - 167.137i) q^{14} +(419.103 + 652.138i) q^{15} +(4128.41 + 1212.21i) q^{16} +(-6777.57 + 974.468i) q^{17} +(828.811 - 1814.84i) q^{18} +(12055.0 + 1733.24i) q^{19} +(91.7219 - 142.722i) q^{20} +(577.302 - 500.235i) q^{21} -5045.04i q^{22} +(12163.9 + 272.588i) q^{23} +7754.61 q^{24} +(-8612.75 - 9939.64i) q^{25} +(16208.1 + 10416.3i) q^{26} +(539.088 - 3749.44i) q^{27} +(-152.070 - 69.4479i) q^{28} +(-954.290 - 6637.24i) q^{29} +(1793.15 - 6106.91i) q^{30} +(39322.2 - 25270.8i) q^{31} +(-1449.71 - 3174.43i) q^{32} +(-2698.59 - 9190.56i) q^{33} +(42487.6 + 36815.7i) q^{34} +(1595.81 - 1841.66i) q^{35} +(-795.432 + 233.560i) q^{36} +(63144.5 - 28837.1i) q^{37} +(-54061.1 - 84120.8i) q^{38} +(35097.9 + 10305.7i) q^{39} +(24486.3 - 3520.60i) q^{40} +(-40273.6 + 88186.8i) q^{41} +(-6207.96 - 892.570i) q^{42} +(-56420.3 + 87791.7i) q^{43} +(-1584.27 + 1372.78i) q^{44} -12084.1i q^{45} +(-63710.5 - 76943.5i) q^{46} -54685.7 q^{47} +(-43923.1 - 50690.0i) q^{48} +(96952.5 + 62307.6i) q^{49} +(-15367.7 + 106885. i) q^{50} +(97092.6 + 44340.7i) q^{51} +(-1139.31 - 7924.07i) q^{52} +(-5355.06 + 18237.7i) q^{53} +(-26164.0 + 16814.6i) q^{54} +(-12693.7 - 27795.4i) q^{55} +(-6867.77 - 23389.5i) q^{56} +(-143480. - 124326. i) q^{57} +(-36053.4 + 41607.9i) q^{58} +(-288355. + 84668.7i) q^{59} +(-2405.65 + 1098.62i) q^{60} +(177678. + 276472. i) q^{61} +(-368230. - 108122. i) q^{62} +(-11786.5 + 1694.64i) q^{63} +(102491. - 224425. i) q^{64} +(115506. + 16607.2i) q^{65} +(-42518.3 + 66159.8i) q^{66} +(-51697.0 + 44795.7i) q^{67} -23360.0i q^{68} +(-157219. - 106089. i) q^{69} -20007.8 q^{70} +(69274.3 + 79946.8i) q^{71} +(-101693. - 65354.0i) q^{72} +(-60222.4 + 418856. i) q^{73} +(-518445. - 236766. i) q^{74} +(29177.4 + 202933. i) q^{75} +(-11705.8 + 39866.3i) q^{76} +(-25330.6 + 16279.0i) q^{77} +(-124764. - 273195. i) q^{78} +(-28730.9 - 97848.4i) q^{79} +(-161707. - 140120. i) q^{80} +(-38668.9 + 44626.3i) q^{81} +(763742. - 224255. i) q^{82} +(387283. - 176866. i) q^{83} +(1408.93 + 2192.33i) q^{84} +(326714. + 95932.0i) q^{85} +(848107. - 121939. i) q^{86} +(-43422.6 + 95082.2i) q^{87} +(-302560. - 43501.5i) q^{88} +(409515. - 637218. i) q^{89} +(-74982.6 + 64972.8i) q^{90} -114990. i q^{91} +(-6826.30 + 40943.5i) q^{92} -728641. q^{93} +(294029. + 339327. i) q^{94} +(-509501. - 327437. i) q^{95} +(-7742.00 + 53846.8i) q^{96} +(489734. + 223654. i) q^{97} +(-134663. - 936605. i) q^{98} +(-42066.9 + 143267. 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.37670 6.20505i −0.672088 0.775631i 0.312613 0.949880i \(-0.398796\pi\)
−0.984702 + 0.174249i \(0.944250\pi\)
\(3\) −13.1138 8.42776i −0.485698 0.312139i
\(4\) −0.485518 + 3.37685i −0.00758621 + 0.0527633i
\(5\) −45.2350 20.6582i −0.361880 0.165265i 0.226173 0.974087i \(-0.427378\pi\)
−0.588054 + 0.808822i \(0.700106\pi\)
\(6\) 18.2146 + 126.686i 0.0843270 + 0.586507i
\(7\) −13.8057 + 47.0180i −0.0402499 + 0.137079i −0.977167 0.212474i \(-0.931848\pi\)
0.936917 + 0.349552i \(0.113666\pi\)
\(8\) −418.489 + 268.946i −0.817361 + 0.525286i
\(9\) 100.946 + 221.041i 0.138472 + 0.303211i
\(10\) 115.031 + 391.758i 0.115031 + 0.391758i
\(11\) 464.382 + 402.389i 0.348897 + 0.302321i 0.811624 0.584180i \(-0.198584\pi\)
−0.462727 + 0.886501i \(0.653129\pi\)
\(12\) 34.8263 40.1917i 0.0201541 0.0232591i
\(13\) −2251.53 + 661.110i −1.02482 + 0.300915i −0.750604 0.660753i \(-0.770237\pi\)
−0.274218 + 0.961667i \(0.588419\pi\)
\(14\) 365.978 167.137i 0.133374 0.0609098i
\(15\) 419.103 + 652.138i 0.124179 + 0.193226i
\(16\) 4128.41 + 1212.21i 1.00791 + 0.295950i
\(17\) −6777.57 + 974.468i −1.37952 + 0.198345i −0.791829 0.610743i \(-0.790871\pi\)
−0.587689 + 0.809087i \(0.699962\pi\)
\(18\) 828.811 1814.84i 0.142114 0.311187i
\(19\) 12055.0 + 1733.24i 1.75754 + 0.252696i 0.944266 0.329184i \(-0.106774\pi\)
0.813274 + 0.581880i \(0.197683\pi\)
\(20\) 91.7219 142.722i 0.0114652 0.0178403i
\(21\) 577.302 500.235i 0.0623369 0.0540152i
\(22\) 5045.04i 0.473801i
\(23\) 12163.9 + 272.588i 0.999749 + 0.0224039i
\(24\) 7754.61 0.560953
\(25\) −8612.75 9939.64i −0.551216 0.636137i
\(26\) 16208.1 + 10416.3i 0.922170 + 0.592642i
\(27\) 539.088 3749.44i 0.0273885 0.190491i
\(28\) −152.070 69.4479i −0.00692737 0.00316362i
\(29\) −954.290 6637.24i −0.0391279 0.272141i 0.960860 0.277034i \(-0.0893515\pi\)
−0.999988 + 0.00489344i \(0.998442\pi\)
\(30\) 1793.15 6106.91i 0.0664130 0.226182i
\(31\) 39322.2 25270.8i 1.31993 0.848271i 0.324704 0.945816i \(-0.394735\pi\)
0.995231 + 0.0975453i \(0.0310991\pi\)
\(32\) −1449.71 3174.43i −0.0442417 0.0968759i
\(33\) −2698.59 9190.56i −0.0750923 0.255741i
\(34\) 42487.6 + 36815.7i 1.08100 + 0.936692i
\(35\) 1595.81 1841.66i 0.0372200 0.0429541i
\(36\) −795.432 + 233.560i −0.0170489 + 0.00500600i
\(37\) 63144.5 28837.1i 1.24661 0.569308i 0.320746 0.947165i \(-0.396066\pi\)
0.925864 + 0.377858i \(0.123339\pi\)
\(38\) −54061.1 84120.8i −0.985223 1.53304i
\(39\) 35097.9 + 10305.7i 0.591681 + 0.173733i
\(40\) 24486.3 3520.60i 0.382598 0.0550093i
\(41\) −40273.6 + 88186.8i −0.584344 + 1.27953i 0.354456 + 0.935073i \(0.384666\pi\)
−0.938800 + 0.344462i \(0.888061\pi\)
\(42\) −6207.96 892.570i −0.0837918 0.0120474i
\(43\) −56420.3 + 87791.7i −0.709627 + 1.10420i 0.279925 + 0.960022i \(0.409691\pi\)
−0.989552 + 0.144179i \(0.953946\pi\)
\(44\) −1584.27 + 1372.78i −0.0185982 + 0.0161155i
\(45\) 12084.1i 0.132611i
\(46\) −63710.5 76943.5i −0.654542 0.790494i
\(47\) −54685.7 −0.526721 −0.263360 0.964698i \(-0.584831\pi\)
−0.263360 + 0.964698i \(0.584831\pi\)
\(48\) −43923.1 50690.0i −0.397164 0.458351i
\(49\) 96952.5 + 62307.6i 0.824083 + 0.529606i
\(50\) −15367.7 + 106885.i −0.122942 + 0.855080i
\(51\) 97092.6 + 44340.7i 0.731940 + 0.334266i
\(52\) −1139.31 7924.07i −0.00810274 0.0563558i
\(53\) −5355.06 + 18237.7i −0.0359697 + 0.122502i −0.975521 0.219907i \(-0.929425\pi\)
0.939551 + 0.342409i \(0.111243\pi\)
\(54\) −26164.0 + 16814.6i −0.166158 + 0.106784i
\(55\) −12693.7 27795.4i −0.0762958 0.167064i
\(56\) −6867.77 23389.5i −0.0391068 0.133185i
\(57\) −143480. 124326.i −0.774757 0.671331i
\(58\) −36053.4 + 41607.9i −0.184783 + 0.213251i
\(59\) −288355. + 84668.7i −1.40401 + 0.412256i −0.894061 0.447946i \(-0.852156\pi\)
−0.509954 + 0.860202i \(0.670338\pi\)
\(60\) −2405.65 + 1098.62i −0.0111373 + 0.00508623i
\(61\) 177678. + 276472.i 0.782788 + 1.21804i 0.971739 + 0.236056i \(0.0758549\pi\)
−0.188951 + 0.981986i \(0.560509\pi\)
\(62\) −368230. 108122.i −1.54506 0.453670i
\(63\) −11786.5 + 1694.64i −0.0471372 + 0.00677730i
\(64\) 102491. 224425.i 0.390973 0.856112i
\(65\) 115506. + 16607.2i 0.420594 + 0.0604723i
\(66\) −42518.3 + 66159.8i −0.147892 + 0.230124i
\(67\) −51697.0 + 44795.7i −0.171886 + 0.148940i −0.736556 0.676377i \(-0.763549\pi\)
0.564669 + 0.825317i \(0.309004\pi\)
\(68\) 23360.0i 0.0742926i
\(69\) −157219. 106089.i −0.478583 0.322942i
\(70\) −20007.8 −0.0583317
\(71\) 69274.3 + 79946.8i 0.193552 + 0.223371i 0.844227 0.535985i \(-0.180060\pi\)
−0.650676 + 0.759356i \(0.725514\pi\)
\(72\) −101693. 65354.0i −0.272454 0.175095i
\(73\) −60222.4 + 418856.i −0.154807 + 1.07670i 0.753213 + 0.657776i \(0.228503\pi\)
−0.908020 + 0.418927i \(0.862406\pi\)
\(74\) −518445. 236766.i −1.27940 0.584284i
\(75\) 29177.4 + 202933.i 0.0691612 + 0.481027i
\(76\) −11705.8 + 39866.3i −0.0266661 + 0.0908166i
\(77\) −25330.6 + 16279.0i −0.0554848 + 0.0356579i
\(78\) −124764. 273195.i −0.262909 0.575690i
\(79\) −28730.9 97848.4i −0.0582731 0.198460i 0.925212 0.379452i \(-0.123887\pi\)
−0.983485 + 0.180992i \(0.942069\pi\)
\(80\) −161707. 140120.i −0.315834 0.273671i
\(81\) −38668.9 + 44626.3i −0.0727623 + 0.0839722i
\(82\) 763742. 224255.i 1.38518 0.406725i
\(83\) 387283. 176866.i 0.677320 0.309322i −0.0468910 0.998900i \(-0.514931\pi\)
0.724211 + 0.689578i \(0.242204\pi\)
\(84\) 1408.93 + 2192.33i 0.00237712 + 0.00369887i
\(85\) 326714. + 95932.0i 0.532000 + 0.156209i
\(86\) 848107. 121939.i 1.33338 0.191712i
\(87\) −43422.6 + 95082.2i −0.0659414 + 0.144391i
\(88\) −302560. 43501.5i −0.443980 0.0638346i
\(89\) 409515. 637218.i 0.580898 0.903894i −0.419094 0.907943i \(-0.637652\pi\)
0.999992 + 0.00404833i \(0.00128863\pi\)
\(90\) −74982.6 + 64972.8i −0.102857 + 0.0891260i
\(91\) 114990.i 0.152593i
\(92\) −6826.30 + 40943.5i −0.00876641 + 0.0525801i
\(93\) −728641. −0.905868
\(94\) 294029. + 339327.i 0.354003 + 0.408541i
\(95\) −509501. 327437.i −0.594257 0.381906i
\(96\) −7742.00 + 53846.8i −0.00875063 + 0.0608620i
\(97\) 489734. + 223654.i 0.536594 + 0.245054i 0.665231 0.746638i \(-0.268333\pi\)
−0.128637 + 0.991692i \(0.541060\pi\)
\(98\) −134663. 936605.i −0.143078 0.995126i
\(99\) −42066.9 + 143267.i −0.0433546 + 0.147652i
\(100\) 37746.3 24258.1i 0.0377463 0.0242581i
\(101\) 537878. + 1.17779e6i 0.522059 + 1.14315i 0.968654 + 0.248414i \(0.0799094\pi\)
−0.446595 + 0.894736i \(0.647363\pi\)
\(102\) −246902. 840871.i −0.232661 0.792372i
\(103\) 1.21981e6 + 1.05697e6i 1.11630 + 0.967276i 0.999665 0.0258988i \(-0.00824476\pi\)
0.116632 + 0.993175i \(0.462790\pi\)
\(104\) 764439. 882209.i 0.679583 0.784281i
\(105\) −36448.2 + 10702.2i −0.0314853 + 0.00924493i
\(106\) 141958. 64830.1i 0.119191 0.0544326i
\(107\) 1.19055e6 + 1.85254e6i 0.971847 + 1.51222i 0.854709 + 0.519108i \(0.173736\pi\)
0.117139 + 0.993116i \(0.462628\pi\)
\(108\) 12399.6 + 3640.84i 0.00984316 + 0.00289021i
\(109\) −424147. + 60983.1i −0.327519 + 0.0470901i −0.304113 0.952636i \(-0.598360\pi\)
−0.0234059 + 0.999726i \(0.507451\pi\)
\(110\) −104221. + 228213.i −0.0783029 + 0.171459i
\(111\) −1.07110e6 154001.i −0.783179 0.112604i
\(112\) −113991. + 177374.i −0.0811368 + 0.126251i
\(113\) −673057. + 583207.i −0.466462 + 0.404192i −0.856128 0.516765i \(-0.827136\pi\)
0.389665 + 0.920957i \(0.372591\pi\)
\(114\) 1.55876e6i 1.05212i
\(115\) −544605. 263615.i −0.358087 0.173331i
\(116\) 22876.3 0.0146559
\(117\) −373415. 430944.i −0.233149 0.269069i
\(118\) 2.07577e6 + 1.33402e6i 1.26338 + 0.811925i
\(119\) 47751.8 332121.i 0.0283366 0.197086i
\(120\) −350780. 160196.i −0.202998 0.0927060i
\(121\) −198386. 1.37980e6i −0.111984 0.778864i
\(122\) 760203. 2.58901e6i 0.418649 1.42579i
\(123\) 1.27136e6 817052.i 0.683207 0.439071i
\(124\) 66244.2 + 145054.i 0.0347442 + 0.0760792i
\(125\) 403174. + 1.37308e6i 0.206425 + 0.703019i
\(126\) 73887.9 + 64024.2i 0.0369370 + 0.0320061i
\(127\) −1.23082e6 + 1.42044e6i −0.600875 + 0.693447i −0.971958 0.235153i \(-0.924441\pi\)
0.371084 + 0.928599i \(0.378986\pi\)
\(128\) −2.15793e6 + 633625.i −1.02898 + 0.302136i
\(129\) 1.47977e6 675790.i 0.689329 0.314806i
\(130\) −517991. 806010.i −0.235772 0.366868i
\(131\) −2.27815e6 668926.i −1.01337 0.297553i −0.267440 0.963575i \(-0.586178\pi\)
−0.745932 + 0.666022i \(0.767996\pi\)
\(132\) 32345.4 4650.56i 0.0140634 0.00202201i
\(133\) −247921. + 542871.i −0.105380 + 0.230750i
\(134\) 555919. + 79929.1i 0.231045 + 0.0332193i
\(135\) −101842. + 158469.i −0.0413929 + 0.0644087i
\(136\) 2.57426e6 2.23061e6i 1.02338 0.886760i
\(137\) 1.76869e6i 0.687846i −0.938998 0.343923i \(-0.888244\pi\)
0.938998 0.343923i \(-0.111756\pi\)
\(138\) 187029. + 1.54596e6i 0.0711658 + 0.588249i
\(139\) 120772. 0.0449699 0.0224849 0.999747i \(-0.492842\pi\)
0.0224849 + 0.999747i \(0.492842\pi\)
\(140\) 5444.21 + 6282.96i 0.00198404 + 0.00228971i
\(141\) 717140. + 460878.i 0.255827 + 0.164410i
\(142\) 123606. 859701.i 0.0431693 0.300249i
\(143\) −1.31159e6 598985.i −0.448530 0.204837i
\(144\) 148798. + 1.03491e6i 0.0498322 + 0.346591i
\(145\) −93945.7 + 319950.i −0.0308157 + 0.104949i
\(146\) 2.92282e6 1.87838e6i 0.939168 0.603567i
\(147\) −746307. 1.63418e6i −0.234945 0.514457i
\(148\) 66720.9 + 227230.i 0.0205815 + 0.0700941i
\(149\) 1.31198e6 + 1.13684e6i 0.396614 + 0.343668i 0.830221 0.557434i \(-0.188214\pi\)
−0.433607 + 0.901102i \(0.642759\pi\)
\(150\) 1.10233e6 1.27216e6i 0.326617 0.376936i
\(151\) −604811. + 177588.i −0.175666 + 0.0515803i −0.368383 0.929674i \(-0.620088\pi\)
0.192716 + 0.981254i \(0.438270\pi\)
\(152\) −5.51102e6 + 2.51680e6i −1.56928 + 0.716667i
\(153\) −899565. 1.39975e6i −0.251164 0.390819i
\(154\) 237207. + 69650.4i 0.0649480 + 0.0190705i
\(155\) −2.30079e6 + 330804.i −0.617848 + 0.0888331i
\(156\) −51841.4 + 113517.i −0.0136554 + 0.0299011i
\(157\) −3.09152e6 444494.i −0.798865 0.114860i −0.269220 0.963079i \(-0.586766\pi\)
−0.529645 + 0.848219i \(0.677675\pi\)
\(158\) −452677. + 704379.i −0.114767 + 0.178581i
\(159\) 223928. 194035.i 0.0557080 0.0482712i
\(160\) 173544.i 0.0423691i
\(161\) −180749. + 568161.i −0.0433109 + 0.136142i
\(162\) 484819. 0.114034
\(163\) −4.16579e6 4.80758e6i −0.961911 1.11010i −0.993863 0.110615i \(-0.964718\pi\)
0.0319521 0.999489i \(-0.489828\pi\)
\(164\) −278240. 178814.i −0.0630795 0.0405387i
\(165\) −67789.1 + 471483.i −0.0150907 + 0.104958i
\(166\) −3.17977e6 1.45215e6i −0.695138 0.317459i
\(167\) 1.14385e6 + 7.95566e6i 0.245595 + 1.70815i 0.623098 + 0.782144i \(0.285874\pi\)
−0.377503 + 0.926008i \(0.623217\pi\)
\(168\) −107058. + 364606.i −0.0225783 + 0.0768946i
\(169\) 571769. 367454.i 0.118457 0.0761277i
\(170\) −1.16138e6 2.54308e6i −0.236390 0.517622i
\(171\) 833782. + 2.83960e6i 0.166749 + 0.567896i
\(172\) −269066. 233147.i −0.0528779 0.0458189i
\(173\) 155606. 179579.i 0.0300530 0.0346830i −0.740524 0.672030i \(-0.765423\pi\)
0.770577 + 0.637347i \(0.219968\pi\)
\(174\) 823460. 241790.i 0.156313 0.0458976i
\(175\) 586247. 267730.i 0.109387 0.0499554i
\(176\) 1.42938e6 + 2.22416e6i 0.262186 + 0.407969i
\(177\) 4.49501e6 + 1.31985e6i 0.810608 + 0.238016i
\(178\) −6.15581e6 + 885071.i −1.09150 + 0.156934i
\(179\) −1.47070e6 + 3.22037e6i −0.256427 + 0.561497i −0.993436 0.114386i \(-0.963510\pi\)
0.737010 + 0.675882i \(0.236237\pi\)
\(180\) 40806.3 + 5867.06i 0.00699697 + 0.00100601i
\(181\) 67508.1 105045.i 0.0113847 0.0177149i −0.835515 0.549468i \(-0.814830\pi\)
0.846899 + 0.531753i \(0.178467\pi\)
\(182\) −713516. + 618265.i −0.118356 + 0.102556i
\(183\) 5.12304e6i 0.835940i
\(184\) −5.16379e6 + 3.15737e6i −0.828924 + 0.506842i
\(185\) −3.45207e6 −0.545210
\(186\) 3.91769e6 + 4.52125e6i 0.608823 + 0.702619i
\(187\) −3.53949e6 2.27470e6i −0.541273 0.347855i
\(188\) 26550.9 184665.i 0.00399581 0.0277915i
\(189\) 168848. + 77110.5i 0.0250099 + 0.0114216i
\(190\) 707678. + 4.92201e6i 0.103175 + 0.717599i
\(191\) −1.49164e6 + 5.08007e6i −0.214074 + 0.729070i 0.780510 + 0.625143i \(0.214959\pi\)
−0.994585 + 0.103928i \(0.966859\pi\)
\(192\) −3.23545e6 + 2.07930e6i −0.457121 + 0.293774i
\(193\) 1.05938e6 + 2.31972e6i 0.147360 + 0.322674i 0.968890 0.247492i \(-0.0796063\pi\)
−0.821530 + 0.570165i \(0.806879\pi\)
\(194\) −1.24537e6 4.24135e6i −0.170567 0.580897i
\(195\) −1.37476e6 1.19124e6i −0.185406 0.160655i
\(196\) −257476. + 297143.i −0.0341954 + 0.0394636i
\(197\) 8.70987e6 2.55745e6i 1.13923 0.334509i 0.342904 0.939371i \(-0.388590\pi\)
0.796331 + 0.604861i \(0.206771\pi\)
\(198\) 1.11516e6 509276.i 0.143662 0.0656081i
\(199\) 3.54271e6 + 5.51256e6i 0.449548 + 0.699511i 0.989875 0.141945i \(-0.0453356\pi\)
−0.540326 + 0.841456i \(0.681699\pi\)
\(200\) 6.27757e6 + 1.84326e6i 0.784696 + 0.230408i
\(201\) 1.05547e6 151754.i 0.129975 0.0186876i
\(202\) 4.41623e6 9.67019e6i 0.535793 1.17322i
\(203\) 325244. + 46763.0i 0.0388795 + 0.00559003i
\(204\) −196872. + 306339.i −0.0231896 + 0.0360837i
\(205\) 3.64355e6 3.15716e6i 0.422925 0.366467i
\(206\) 1.32520e7i 1.51593i
\(207\) 1.16765e6 + 2.71624e6i 0.131644 + 0.306237i
\(208\) −1.00967e7 −1.12199
\(209\) 4.90067e6 + 5.65567e6i 0.536805 + 0.619506i
\(210\) 262379. + 168621.i 0.0283316 + 0.0182076i
\(211\) −782957. + 5.44559e6i −0.0833471 + 0.579692i 0.904760 + 0.425922i \(0.140050\pi\)
−0.988107 + 0.153769i \(0.950859\pi\)
\(212\) −58985.9 26937.9i −0.00619071 0.00282720i
\(213\) −234680. 1.63224e6i −0.0242850 0.168906i
\(214\) 5.09383e6 1.73480e7i 0.519761 1.77014i
\(215\) 4.36579e6 2.80572e6i 0.439286 0.282312i
\(216\) 782796. + 1.71408e6i 0.0776761 + 0.170087i
\(217\) 645312. + 2.19773e6i 0.0631525 + 0.215078i
\(218\) 2.65891e6 + 2.30396e6i 0.256646 + 0.222385i
\(219\) 4.31976e6 4.98527e6i 0.411270 0.474631i
\(220\) 100024. 29369.6i 0.00939366 0.00275823i
\(221\) 1.46157e7 6.67477e6i 1.35408 0.618386i
\(222\) 4.80340e6 + 7.47424e6i 0.439026 + 0.683138i
\(223\) −4.06331e6 1.19310e6i −0.366408 0.107587i 0.0933451 0.995634i \(-0.470244\pi\)
−0.459753 + 0.888047i \(0.652062\pi\)
\(224\) 169269. 24337.3i 0.0150603 0.00216535i
\(225\) 1.32764e6 2.90713e6i 0.116556 0.255222i
\(226\) 7.23766e6 + 1.04062e6i 0.627008 + 0.0901501i
\(227\) 1.08564e7 1.68929e7i 0.928129 1.44420i 0.0324618 0.999473i \(-0.489665\pi\)
0.895667 0.444724i \(-0.146698\pi\)
\(228\) 489491. 424147.i 0.0412991 0.0357859i
\(229\) 1.16015e7i 0.966068i −0.875602 0.483034i \(-0.839535\pi\)
0.875602 0.483034i \(-0.160465\pi\)
\(230\) 1.29244e6 + 4.79668e6i 0.106225 + 0.394237i
\(231\) 469378. 0.0380791
\(232\) 2.18442e6 + 2.52096e6i 0.174933 + 0.201884i
\(233\) 1.59307e7 + 1.02381e7i 1.25941 + 0.809375i 0.988204 0.153146i \(-0.0489406\pi\)
0.271208 + 0.962521i \(0.412577\pi\)
\(234\) −666286. + 4.63412e6i −0.0520011 + 0.361676i
\(235\) 2.47371e6 + 1.12971e6i 0.190610 + 0.0870486i
\(236\) −145912. 1.01484e6i −0.0111008 0.0772079i
\(237\) −447870. + 1.52531e6i −0.0336440 + 0.114581i
\(238\) −2.31757e6 + 1.48941e6i −0.171911 + 0.110480i
\(239\) −5.27667e6 1.15543e7i −0.386515 0.846349i −0.998461 0.0554501i \(-0.982341\pi\)
0.611947 0.790899i \(-0.290387\pi\)
\(240\) 939703. + 3.20034e6i 0.0679762 + 0.231506i
\(241\) −1.72467e6 1.49443e6i −0.123212 0.106764i 0.591075 0.806617i \(-0.298704\pi\)
−0.714288 + 0.699852i \(0.753249\pi\)
\(242\) −7.49509e6 + 8.64980e6i −0.528848 + 0.610323i
\(243\) 883197. 259330.i 0.0615515 0.0180732i
\(244\) −1.01987e6 + 465760.i −0.0702063 + 0.0320621i
\(245\) −3.09849e6 4.82135e6i −0.210694 0.327846i
\(246\) −1.19056e7 3.49579e6i −0.799732 0.234823i
\(247\) −2.82880e7 + 4.06721e6i −1.87721 + 0.269901i
\(248\) −9.65939e6 + 2.11511e7i −0.633278 + 1.38669i
\(249\) −6.56935e6 944530.i −0.425524 0.0611812i
\(250\) 6.35231e6 9.88438e6i 0.406548 0.632600i
\(251\) −3.22347e6 + 2.79315e6i −0.203846 + 0.176634i −0.750801 0.660528i \(-0.770332\pi\)
0.546955 + 0.837162i \(0.315787\pi\)
\(252\) 40624.0i 0.00253852i
\(253\) 5.53903e6 + 5.02122e6i 0.342036 + 0.310062i
\(254\) 1.54317e7 0.941700
\(255\) −3.47599e6 4.01151e6i −0.209632 0.241928i
\(256\) 2.25076e6 + 1.44648e6i 0.134156 + 0.0862166i
\(257\) −459102. + 3.19312e6i −0.0270464 + 0.188112i −0.998866 0.0476149i \(-0.984838\pi\)
0.971819 + 0.235727i \(0.0757471\pi\)
\(258\) −1.21496e7 5.54855e6i −0.707463 0.323087i
\(259\) 484108. + 3.36704e6i 0.0278640 + 0.193798i
\(260\) −112160. + 381982.i −0.00638143 + 0.0217331i
\(261\) 1.37077e6 880938.i 0.0770978 0.0495477i
\(262\) 8.09823e6 + 1.77327e7i 0.450284 + 0.985984i
\(263\) −3.07788e6 1.04823e7i −0.169194 0.576222i −0.999812 0.0193795i \(-0.993831\pi\)
0.830618 0.556842i \(-0.187987\pi\)
\(264\) 3.60110e6 + 3.12037e6i 0.195715 + 0.169588i
\(265\) 618993. 714356.i 0.0332620 0.0383864i
\(266\) 4.70154e6 1.38050e6i 0.249802 0.0733484i
\(267\) −1.07406e7 + 4.90508e6i −0.564282 + 0.257699i
\(268\) −126169. 196322.i −0.00655461 0.0101992i
\(269\) 1.50543e7 + 4.42034e6i 0.773400 + 0.227091i 0.644538 0.764572i \(-0.277050\pi\)
0.128861 + 0.991663i \(0.458868\pi\)
\(270\) 1.53089e6 220108.i 0.0777771 0.0111827i
\(271\) −1.61204e7 + 3.52988e7i −0.809970 + 1.77359i −0.202432 + 0.979296i \(0.564884\pi\)
−0.607538 + 0.794290i \(0.707843\pi\)
\(272\) −2.91619e7 4.19284e6i −1.44913 0.208354i
\(273\) −969105. + 1.50796e6i −0.0476302 + 0.0741141i
\(274\) −1.09748e7 + 9.50975e6i −0.533515 + 0.462293i
\(275\) 8.08146e6i 0.388590i
\(276\) 434581. 479396.i 0.0206701 0.0228017i
\(277\) −3.22593e7 −1.51780 −0.758901 0.651206i \(-0.774263\pi\)
−0.758901 + 0.651206i \(0.774263\pi\)
\(278\) −649355. 749396.i −0.0302237 0.0348800i
\(279\) 9.55529e6 + 6.14081e6i 0.439978 + 0.282757i
\(280\) −172520. + 1.19990e6i −0.00785894 + 0.0546602i
\(281\) −1.81282e7 8.27889e6i −0.817027 0.373124i −0.0373475 0.999302i \(-0.511891\pi\)
−0.779680 + 0.626179i \(0.784618\pi\)
\(282\) −996080. 6.92789e6i −0.0444168 0.308925i
\(283\) 1.03782e7 3.53448e7i 0.457891 1.55943i −0.330223 0.943903i \(-0.607124\pi\)
0.788114 0.615530i \(-0.211058\pi\)
\(284\) −303602. + 195113.i −0.0132541 + 0.00851788i
\(285\) 3.92197e6 + 8.58791e6i 0.169422 + 0.370982i
\(286\) 3.33533e6 + 1.13591e7i 0.142574 + 0.485562i
\(287\) −3.59036e6 3.11106e6i −0.151877 0.131602i
\(288\) 555335. 640891.i 0.0232476 0.0268291i
\(289\) 2.18261e7 6.40871e6i 0.904236 0.265508i
\(290\) 2.49042e6 1.13734e6i 0.102112 0.0466332i
\(291\) −4.53740e6 7.06033e6i −0.184131 0.286514i
\(292\) −1.38517e6 406724.i −0.0556360 0.0163362i
\(293\) −3.95830e7 + 5.69118e6i −1.57364 + 0.226256i −0.873167 0.487421i \(-0.837938\pi\)
−0.700475 + 0.713677i \(0.747029\pi\)
\(294\) −6.12752e6 + 1.34174e7i −0.241125 + 0.527991i
\(295\) 1.47929e7 + 2.12689e6i 0.576217 + 0.0828475i
\(296\) −1.86696e7 + 2.90505e7i −0.719881 + 1.12016i
\(297\) 1.75908e6 1.52425e6i 0.0671452 0.0581817i
\(298\) 1.42533e7i 0.538601i
\(299\) −2.75678e7 + 7.42797e6i −1.03131 + 0.277879i
\(300\) −699441. −0.0259052
\(301\) −3.34886e6 3.86480e6i −0.122800 0.141719i
\(302\) 4.35383e6 + 2.79804e6i 0.158071 + 0.101586i
\(303\) 2.87247e6 1.99785e7i 0.103259 0.718181i
\(304\) 4.76668e7 + 2.17687e7i 1.69666 + 0.774840i
\(305\) −2.32587e6 1.61767e7i −0.0819757 0.570153i
\(306\) −3.84882e6 + 1.31079e7i −0.134327 + 0.457476i
\(307\) 1.69562e7 1.08971e7i 0.586022 0.376613i −0.213776 0.976883i \(-0.568576\pi\)
0.799798 + 0.600269i \(0.204940\pi\)
\(308\) −42673.3 93441.5i −0.00146051 0.00319807i
\(309\) −7.08849e6 2.41412e7i −0.240258 0.818244i
\(310\) 1.44233e7 + 1.24979e7i 0.484150 + 0.419518i
\(311\) 3.34731e7 3.86300e7i 1.11279 1.28423i 0.157844 0.987464i \(-0.449546\pi\)
0.954950 0.296768i \(-0.0959087\pi\)
\(312\) −1.74598e7 + 5.12665e6i −0.574877 + 0.168799i
\(313\) −2.06765e7 + 9.44266e6i −0.674287 + 0.307937i −0.722972 0.690877i \(-0.757224\pi\)
0.0486845 + 0.998814i \(0.484497\pi\)
\(314\) 1.38641e7 + 2.15730e7i 0.447819 + 0.696820i
\(315\) 568171. + 166830.i 0.0181781 + 0.00533756i
\(316\) 344369. 49512.8i 0.0109135 0.00156912i
\(317\) 1.36638e7 2.99194e7i 0.428936 0.939238i −0.564563 0.825390i \(-0.690955\pi\)
0.993498 0.113848i \(-0.0363176\pi\)
\(318\) −2.40799e6 346217.i −0.0748813 0.0107663i
\(319\) 2.22760e6 3.46621e6i 0.0686222 0.106778i
\(320\) −9.27239e6 + 8.03457e6i −0.282971 + 0.245196i
\(321\) 3.43276e7i 1.03784i
\(322\) 4.49730e6 1.93328e6i 0.134705 0.0579064i
\(323\) −8.33924e7 −2.47468
\(324\) −131922. 152246.i −0.00387866 0.00447621i
\(325\) 2.59631e7 + 1.66855e7i 0.756321 + 0.486058i
\(326\) −7.43304e6 + 5.16979e7i −0.214543 + 1.49218i
\(327\) 6.07614e6 + 2.77488e6i 0.173774 + 0.0793599i
\(328\) −6.86349e6 4.77366e7i −0.194502 1.35279i
\(329\) 754975. 2.57121e6i 0.0212005 0.0722021i
\(330\) 3.29006e6 2.11439e6i 0.0915508 0.0588361i
\(331\) −961940. 2.10635e6i −0.0265255 0.0580828i 0.895906 0.444245i \(-0.146528\pi\)
−0.922431 + 0.386162i \(0.873801\pi\)
\(332\) 409218. + 1.39367e6i 0.0111825 + 0.0380842i
\(333\) 1.27484e7 + 1.10465e7i 0.345240 + 0.299152i
\(334\) 4.32151e7 4.98729e7i 1.15983 1.33852i
\(335\) 3.26392e6 958372.i 0.0868169 0.0254918i
\(336\) 2.98973e6 1.36536e6i 0.0788160 0.0359940i
\(337\) 2.32655e7 + 3.62018e7i 0.607886 + 0.945890i 0.999666 + 0.0258306i \(0.00822306\pi\)
−0.391780 + 0.920059i \(0.628141\pi\)
\(338\) −5.35430e6 1.57217e6i −0.138661 0.0407144i
\(339\) 1.37415e7 1.97573e6i 0.352724 0.0507141i
\(340\) −482574. + 1.05669e6i −0.0122780 + 0.0268850i
\(341\) 2.84292e7 + 4.08750e6i 0.716971 + 0.103085i
\(342\) 1.31369e7 2.04414e7i 0.328408 0.511012i
\(343\) −8.62508e6 + 7.47368e6i −0.213738 + 0.185205i
\(344\) 5.19139e7i 1.27529i
\(345\) 4.92019e6 + 8.04681e6i 0.119819 + 0.195960i
\(346\) −1.95094e6 −0.0470995
\(347\) 1.94867e6 + 2.24889e6i 0.0466392 + 0.0538245i 0.778590 0.627533i \(-0.215935\pi\)
−0.731951 + 0.681358i \(0.761390\pi\)
\(348\) −299996. 192796.i −0.00711832 0.00457467i
\(349\) −9.57140e6 + 6.65706e7i −0.225164 + 1.56605i 0.492907 + 0.870082i \(0.335934\pi\)
−0.718071 + 0.695970i \(0.754975\pi\)
\(350\) −4.81335e6 2.19818e6i −0.112265 0.0512696i
\(351\) 1.26502e6 + 8.79839e6i 0.0292533 + 0.203461i
\(352\) 604135. 2.05749e6i 0.0138518 0.0471749i
\(353\) −2.70961e7 + 1.74136e7i −0.616002 + 0.395880i −0.811103 0.584903i \(-0.801133\pi\)
0.195102 + 0.980783i \(0.437496\pi\)
\(354\) −1.59786e7 3.49882e7i −0.360188 0.788701i
\(355\) −1.48207e6 5.04748e6i −0.0331272 0.112821i
\(356\) 1.95296e6 + 1.69225e6i 0.0432856 + 0.0375072i
\(357\) −3.42524e6 + 3.95294e6i −0.0752812 + 0.0868791i
\(358\) 2.78901e7 8.18926e6i 0.607856 0.178482i
\(359\) 2.77640e6 1.26794e6i 0.0600066 0.0274041i −0.385186 0.922839i \(-0.625863\pi\)
0.445192 + 0.895435i \(0.353135\pi\)
\(360\) 3.24998e6 + 5.05707e6i 0.0696584 + 0.108391i
\(361\) 9.71779e7 + 2.85340e7i 2.06560 + 0.606515i
\(362\) −1.01478e6 + 145903.i −0.0213917 + 0.00307566i
\(363\) −9.02706e6 + 1.97665e7i −0.188724 + 0.413247i
\(364\) 388303. + 55829.5i 0.00805130 + 0.00115760i
\(365\) 1.13770e7 1.77029e7i 0.233963 0.364054i
\(366\) −3.17887e7 + 2.75451e7i −0.648381 + 0.561825i
\(367\) 2.29605e7i 0.464497i −0.972656 0.232249i \(-0.925392\pi\)
0.972656 0.232249i \(-0.0746083\pi\)
\(368\) 4.98873e7 + 1.58706e7i 1.00103 + 0.318457i
\(369\) −2.35583e7 −0.468884
\(370\) 1.85607e7 + 2.14202e7i 0.366429 + 0.422882i
\(371\) −783567. 503568.i −0.0153446 0.00986135i
\(372\) 353768. 2.46051e6i 0.00687211 0.0477966i
\(373\) −8.86191e7 4.04710e7i −1.70766 0.779861i −0.997090 0.0762325i \(-0.975711\pi\)
−0.710568 0.703629i \(-0.751562\pi\)
\(374\) 4.91623e6 + 3.41931e7i 0.0939760 + 0.653618i
\(375\) 6.28486e6 2.14043e7i 0.119180 0.405888i
\(376\) 2.28854e7 1.47075e7i 0.430521 0.276679i
\(377\) 6.53656e6 + 1.43131e7i 0.121990 + 0.267121i
\(378\) −429374. 1.46231e6i −0.00794987 0.0270748i
\(379\) 6.87697e7 + 5.95892e7i 1.26322 + 1.09459i 0.991211 + 0.132293i \(0.0422338\pi\)
0.272010 + 0.962294i \(0.412312\pi\)
\(380\) 1.35308e6 1.56153e6i 0.0246588 0.0284577i
\(381\) 2.81120e7 8.25442e6i 0.508296 0.149249i
\(382\) 3.95422e7 1.80583e7i 0.709367 0.323957i
\(383\) 3.65150e6 + 5.68184e6i 0.0649942 + 0.101133i 0.872230 0.489097i \(-0.162674\pi\)
−0.807235 + 0.590230i \(0.799037\pi\)
\(384\) 3.36388e7 + 9.87724e6i 0.594083 + 0.174438i
\(385\) 1.48213e6 213098.i 0.0259719 0.00373419i
\(386\) 8.69799e6 1.90460e7i 0.151237 0.331162i
\(387\) −2.51009e7 3.60897e6i −0.433069 0.0622659i
\(388\) −993021. + 1.54517e6i −0.0170006 + 0.0264534i
\(389\) 4.38990e7 3.80387e7i 0.745771 0.646214i −0.196715 0.980461i \(-0.563027\pi\)
0.942486 + 0.334247i \(0.108482\pi\)
\(390\) 1.49354e7i 0.251781i
\(391\) −8.27076e7 + 1.00059e7i −1.38362 + 0.167388i
\(392\) −5.73310e7 −0.951768
\(393\) 2.42378e7 + 2.79719e7i 0.399315 + 0.460834i
\(394\) −6.26995e7 4.02945e7i −1.02512 0.658806i
\(395\) −721725. + 5.01971e6i −0.0117106 + 0.0814492i
\(396\) −463366. 211612.i −0.00746171 0.00340765i
\(397\) 9.60529e6 + 6.68062e7i 0.153511 + 1.06769i 0.910275 + 0.414003i \(0.135870\pi\)
−0.756765 + 0.653688i \(0.773221\pi\)
\(398\) 1.51576e7 5.16221e7i 0.240426 0.818816i
\(399\) 7.82638e6 5.02971e6i 0.123209 0.0791816i
\(400\) −2.35080e7 5.14754e7i −0.367313 0.804303i
\(401\) 7.01328e6 + 2.38851e7i 0.108765 + 0.370419i 0.995830 0.0912246i \(-0.0290781\pi\)
−0.887066 + 0.461643i \(0.847260\pi\)
\(402\) −6.61662e6 5.73333e6i −0.101849 0.0882529i
\(403\) −7.18284e7 + 8.28944e7i −1.09744 + 1.26651i
\(404\) −4.23837e6 + 1.24450e6i −0.0642768 + 0.0188734i
\(405\) 2.67108e6 1.21984e6i 0.0402089 0.0183628i
\(406\) −1.45857e6 2.26958e6i −0.0217947 0.0339132i
\(407\) 4.09269e7 + 1.20172e7i 0.607052 + 0.178246i
\(408\) −5.25574e7 + 7.55662e6i −0.773844 + 0.111262i
\(409\) 2.97101e7 6.50561e7i 0.434245 0.950864i −0.558374 0.829589i \(-0.688575\pi\)
0.992619 0.121275i \(-0.0386982\pi\)
\(410\) −3.91806e7 5.63332e6i −0.568486 0.0817359i
\(411\) −1.49061e7 + 2.31944e7i −0.214704 + 0.334085i
\(412\) −4.16146e6 + 3.60593e6i −0.0595051 + 0.0515615i
\(413\) 1.47268e7i 0.209054i
\(414\) 1.05763e7 2.18497e7i 0.149051 0.307925i
\(415\) −2.11725e7 −0.296229
\(416\) 5.36272e6 + 6.18891e6i 0.0744913 + 0.0859675i
\(417\) −1.58378e6 1.01784e6i −0.0218418 0.0140369i
\(418\) 8.74428e6 6.08178e7i 0.119728 0.832725i
\(419\) 2.70036e7 + 1.23321e7i 0.367096 + 0.167647i 0.590418 0.807097i \(-0.298963\pi\)
−0.223322 + 0.974745i \(0.571690\pi\)
\(420\) −18443.3 128276.i −0.000248938 0.00173140i
\(421\) −7.57553e6 + 2.57999e7i −0.101524 + 0.345757i −0.994552 0.104243i \(-0.966758\pi\)
0.893028 + 0.450000i \(0.148576\pi\)
\(422\) 3.79998e7 2.44210e7i 0.505644 0.324957i
\(423\) −5.52029e6 1.20878e7i −0.0729359 0.159707i
\(424\) −2.66392e6 9.07248e6i −0.0349481 0.119022i
\(425\) 6.80594e7 + 5.89738e7i 0.886587 + 0.768232i
\(426\) −8.86630e6 + 1.02323e7i −0.114687 + 0.132356i
\(427\) −1.54521e7 + 4.53716e6i −0.198475 + 0.0582774i
\(428\) −6.83378e6 + 3.12088e6i −0.0871625 + 0.0398058i
\(429\) 1.21519e7 + 1.89088e7i 0.153913 + 0.239493i
\(430\) −4.08832e7 1.20044e7i −0.514209 0.150985i
\(431\) −1.14751e8 + 1.64987e7i −1.43326 + 0.206072i −0.814800 0.579742i \(-0.803153\pi\)
−0.618463 + 0.785814i \(0.712244\pi\)
\(432\) 6.77069e6 1.48257e7i 0.0839811 0.183893i
\(433\) 5.16021e6 + 741926.i 0.0635629 + 0.00913897i 0.174023 0.984742i \(-0.444323\pi\)
−0.110460 + 0.993881i \(0.535232\pi\)
\(434\) 1.01674e7 1.58207e7i 0.124377 0.193534i
\(435\) 3.92845e6 3.40402e6i 0.0477258 0.0413546i
\(436\) 1.46189e6i 0.0176382i
\(437\) 1.46164e8 + 2.43691e7i 1.75144 + 0.292008i
\(438\) −5.41599e7 −0.644549
\(439\) 2.28971e7 + 2.64247e7i 0.270637 + 0.312332i 0.874757 0.484562i \(-0.161021\pi\)
−0.604120 + 0.796893i \(0.706475\pi\)
\(440\) 1.27876e7 + 8.21812e6i 0.150118 + 0.0964749i
\(441\) −3.98555e6 + 2.77201e7i −0.0464700 + 0.323206i
\(442\) −1.20002e8 5.48029e7i −1.38970 0.634653i
\(443\) −1.78122e7 1.23887e8i −0.204884 1.42500i −0.789532 0.613710i \(-0.789677\pi\)
0.584648 0.811287i \(-0.301233\pi\)
\(444\) 1.04008e6 3.54217e6i 0.0118827 0.0404688i
\(445\) −3.16882e7 + 2.03647e7i −0.359598 + 0.231099i
\(446\) 1.44440e7 + 3.16280e7i 0.162811 + 0.356506i
\(447\) −7.62411e6 2.59653e7i −0.0853624 0.290718i
\(448\) 9.13702e6 + 7.91727e6i 0.101618 + 0.0880524i
\(449\) 3.70757e7 4.27876e7i 0.409591 0.472693i −0.513047 0.858361i \(-0.671483\pi\)
0.922638 + 0.385668i \(0.126029\pi\)
\(450\) −2.51772e7 + 7.39271e6i −0.276293 + 0.0811271i
\(451\) −5.41877e7 + 2.47467e7i −0.590706 + 0.269766i
\(452\) −1.64262e6 2.55597e6i −0.0177878 0.0276784i
\(453\) 9.42807e6 + 2.76833e6i 0.101421 + 0.0297799i
\(454\) −1.63193e8 + 2.34636e7i −1.74395 + 0.250742i
\(455\) −2.37547e6 + 5.20156e6i −0.0252183 + 0.0552204i
\(456\) 9.34816e7 + 1.34406e7i 0.985897 + 0.141751i
\(457\) 2.08694e7 3.24734e7i 0.218656 0.340235i −0.714546 0.699589i \(-0.753367\pi\)
0.933201 + 0.359354i \(0.117003\pi\)
\(458\) −7.19879e7 + 6.23779e7i −0.749313 + 0.649283i
\(459\) 2.59374e7i 0.268218i
\(460\) 1.15460e6 1.71106e6i 0.0118620 0.0175789i
\(461\) −1.69673e7 −0.173185 −0.0865927 0.996244i \(-0.527598\pi\)
−0.0865927 + 0.996244i \(0.527598\pi\)
\(462\) −2.52370e6 2.91251e6i −0.0255925 0.0295353i
\(463\) −2.86714e7 1.84260e7i −0.288873 0.185647i 0.388176 0.921585i \(-0.373105\pi\)
−0.677049 + 0.735938i \(0.736742\pi\)
\(464\) 4.10603e6 2.85580e7i 0.0411025 0.285874i
\(465\) 3.29601e7 + 1.50524e7i 0.327816 + 0.149708i
\(466\) −2.21272e7 1.53898e8i −0.218659 1.52081i
\(467\) −8.58162e6 + 2.92263e7i −0.0842595 + 0.286961i −0.990834 0.135084i \(-0.956870\pi\)
0.906575 + 0.422045i \(0.138688\pi\)
\(468\) 1.63653e6 1.05174e6i 0.0159657 0.0102605i
\(469\) −1.39249e6 3.04913e6i −0.0134981 0.0295568i
\(470\) −6.29053e6 2.14236e7i −0.0605890 0.206347i
\(471\) 3.67957e7 + 3.18836e7i 0.352155 + 0.305144i
\(472\) 9.79020e7 1.12985e8i 0.931034 1.07447i
\(473\) −6.15270e7 + 1.80660e7i −0.581410 + 0.170717i
\(474\) 1.18727e7 5.42206e6i 0.111484 0.0509131i
\(475\) −8.65986e7 1.34750e8i −0.808035 1.25733i
\(476\) 1.09834e6 + 322501.i 0.0101839 + 0.00299027i
\(477\) −4.57184e6 + 657331.i −0.0421246 + 0.00605660i
\(478\) −4.33238e7 + 9.48660e7i −0.396683 + 0.868614i
\(479\) 1.39180e7 + 2.00111e6i 0.126640 + 0.0182081i 0.205343 0.978690i \(-0.434169\pi\)
−0.0787032 + 0.996898i \(0.525078\pi\)
\(480\) 1.46258e6 2.27583e6i 0.0132250 0.0205786i
\(481\) −1.23108e8 + 1.06673e8i −1.10624 + 0.958562i
\(482\) 1.87368e7i 0.167322i
\(483\) 7.15863e6 5.92747e6i 0.0635314 0.0526051i
\(484\) 4.75571e6 0.0419449
\(485\) −1.75329e7 2.02340e7i −0.153684 0.177361i
\(486\) −6.35784e6 4.08594e6i −0.0553861 0.0355945i
\(487\) −3.09096e7 + 2.14981e8i −0.267613 + 1.86129i 0.203314 + 0.979114i \(0.434829\pi\)
−0.470926 + 0.882173i \(0.656080\pi\)
\(488\) −1.48713e8 6.79148e7i −1.27964 0.584393i
\(489\) 1.41124e7 + 9.81542e7i 0.120691 + 0.839426i
\(490\) −1.32570e7 + 4.51493e7i −0.112683 + 0.383762i
\(491\) 1.47090e8 9.45288e7i 1.24262 0.798582i 0.256810 0.966462i \(-0.417328\pi\)
0.985807 + 0.167880i \(0.0536921\pi\)
\(492\) 2.14180e6 + 4.68988e6i 0.0179839 + 0.0393791i
\(493\) 1.29355e7 + 4.40544e7i 0.107955 + 0.367662i
\(494\) 1.77334e8 + 1.53660e8i 1.47099 + 1.27462i
\(495\) 4.86252e6 5.61165e6i 0.0400909 0.0462674i
\(496\) 1.92972e8 5.66616e7i 1.58143 0.464348i
\(497\) −4.71532e6 + 2.15341e6i −0.0384098 + 0.0175412i
\(498\) 2.94606e7 + 4.58416e7i 0.238536 + 0.371169i
\(499\) 4.71548e7 + 1.38459e7i 0.379511 + 0.111434i 0.465924 0.884825i \(-0.345722\pi\)
−0.0864126 + 0.996259i \(0.527540\pi\)
\(500\) −4.83245e6 + 694801.i −0.0386596 + 0.00555841i
\(501\) 5.20480e7 1.13969e8i 0.413896 0.906306i
\(502\) 3.46633e7 + 4.98382e6i 0.274005 + 0.0393960i
\(503\) −9.06661e7 + 1.41079e8i −0.712428 + 1.10856i 0.276622 + 0.960979i \(0.410785\pi\)
−0.989050 + 0.147580i \(0.952851\pi\)
\(504\) 4.47675e6 3.87913e6i 0.0349681 0.0303000i
\(505\) 6.43889e7i 0.499962i
\(506\) 1.37522e6 6.13676e7i 0.0106150 0.473683i
\(507\) −1.05949e7 −0.0812968
\(508\) −4.19904e6 4.84595e6i −0.0320301 0.0369648i
\(509\) −6.83845e7 4.39481e7i −0.518567 0.333263i 0.255038 0.966931i \(-0.417912\pi\)
−0.773605 + 0.633668i \(0.781548\pi\)
\(510\) −6.20222e6 + 4.31374e7i −0.0467559 + 0.325195i
\(511\) −1.88623e7 8.61414e6i −0.141362 0.0645579i
\(512\) 1.73583e7 + 1.20730e8i 0.129329 + 0.899505i
\(513\) 1.29974e7 4.42650e7i 0.0962728 0.327875i
\(514\) 2.22819e7 1.43197e7i 0.164083 0.105450i
\(515\) −3.33430e7 7.30110e7i −0.244109 0.534523i
\(516\) 1.56359e6 + 5.32508e6i 0.0113808 + 0.0387594i
\(517\) −2.53950e7 2.20049e7i −0.183771 0.159239i
\(518\) 1.82898e7 2.11075e7i 0.131589 0.151862i
\(519\) −3.55404e6 + 1.04356e6i −0.0254226 + 0.00746476i
\(520\) −5.28042e7 + 2.41149e7i −0.375542 + 0.171504i
\(521\) 1.16629e8 + 1.81479e8i 0.824699 + 1.28326i 0.956427 + 0.291970i \(0.0943108\pi\)
−0.131729 + 0.991286i \(0.542053\pi\)
\(522\) −1.28365e7 3.76913e6i −0.0902473 0.0264990i
\(523\) −8.62375e7 + 1.23991e7i −0.602825 + 0.0866731i −0.436968 0.899477i \(-0.643948\pi\)
−0.165856 + 0.986150i \(0.553039\pi\)
\(524\) 3.36494e6 7.36820e6i 0.0233875 0.0512115i
\(525\) −9.94431e6 1.42978e6i −0.0687222 0.00988076i
\(526\) −4.84944e7 + 7.54587e7i −0.333222 + 0.518504i
\(527\) −2.41883e8 + 2.09593e8i −1.65262 + 1.43201i
\(528\) 4.12137e7i 0.279988i
\(529\) 1.47887e8 + 6.63149e6i 0.998996 + 0.0447965i
\(530\) −7.76076e6 −0.0521286
\(531\) −4.78235e7 5.51912e7i −0.319417 0.368626i
\(532\) −1.71282e6 1.10077e6i −0.0113757 0.00731072i
\(533\) 3.23761e7 2.25181e8i 0.213817 1.48713i
\(534\) 8.81855e7 + 4.02729e7i 0.579126 + 0.264478i
\(535\) −1.55848e7 1.08394e8i −0.101774 0.707857i
\(536\) 9.58698e6 3.26502e7i 0.0622569 0.212027i
\(537\) 4.64270e7 2.98368e7i 0.299811 0.192677i
\(538\) −5.35141e7 1.17180e8i −0.343654 0.752498i
\(539\) 1.99511e7 + 6.79472e7i 0.127409 + 0.433915i
\(540\) −485681. 420845.i −0.00308440 0.00267264i
\(541\) 7.64340e7 8.82095e7i 0.482719 0.557088i −0.461186 0.887303i \(-0.652576\pi\)
0.943906 + 0.330215i \(0.107121\pi\)
\(542\) 3.05706e8 8.97633e7i 1.92002 0.563769i
\(543\) −1.77058e6 + 808598.i −0.0110590 + 0.00505049i
\(544\) 1.29189e7 + 2.01022e7i 0.0802471 + 0.124867i
\(545\) 2.04461e7 + 6.00351e6i 0.126305 + 0.0370865i
\(546\) 1.45675e7 2.09449e6i 0.0894969 0.0128677i
\(547\) 6.79128e7 1.48708e8i 0.414944 0.908601i −0.580590 0.814196i \(-0.697178\pi\)
0.995534 0.0944048i \(-0.0300948\pi\)
\(548\) 5.97262e6 + 858732.i 0.0362930 + 0.00521815i
\(549\) −4.31758e7 + 6.71828e7i −0.260929 + 0.406014i
\(550\) −5.01459e7 + 4.34516e7i −0.301403 + 0.261167i
\(551\) 8.16657e7i 0.488185i
\(552\) 9.43267e7 + 2.11381e6i 0.560812 + 0.0125675i
\(553\) 4.99728e6 0.0295501
\(554\) 1.73449e8 + 2.00170e8i 1.02010 + 1.17725i
\(555\) 4.52699e7 + 2.90932e7i 0.264808 + 0.170181i
\(556\) −58636.9 + 407829.i −0.000341151 + 0.00237276i
\(557\) 2.63139e8 + 1.20172e8i 1.52272 + 0.695402i 0.988677 0.150057i \(-0.0479456\pi\)
0.534041 + 0.845459i \(0.320673\pi\)
\(558\) −1.32719e7 9.23083e7i −0.0763892 0.531298i
\(559\) 6.89923e7 2.34966e8i 0.394971 1.34515i
\(560\) 8.82063e6 5.66867e6i 0.0502268 0.0322788i
\(561\) 2.72458e7 + 5.96600e7i 0.154316 + 0.337905i
\(562\) 4.60993e7 + 1.57000e8i 0.259708 + 0.884484i
\(563\) −1.02371e8 8.87048e7i −0.573655 0.497075i 0.319037 0.947742i \(-0.396641\pi\)
−0.892692 + 0.450667i \(0.851186\pi\)
\(564\) −1.90450e6 + 2.19791e6i −0.0106156 + 0.0122510i
\(565\) 4.24938e7 1.24773e7i 0.235602 0.0691791i
\(566\) −2.75117e8 + 1.25642e8i −1.51729 + 0.692922i
\(567\) −1.56438e6 2.43423e6i −0.00858211 0.0133540i
\(568\) −5.04919e7 1.48258e7i −0.275535 0.0809044i
\(569\) −8.10551e7 + 1.16540e7i −0.439991 + 0.0632611i −0.358751 0.933433i \(-0.616797\pi\)
−0.0812402 + 0.996695i \(0.525888\pi\)
\(570\) 3.22011e7 7.05106e7i 0.173879 0.380741i
\(571\) −1.12488e8 1.61733e7i −0.604222 0.0868740i −0.166587 0.986027i \(-0.553275\pi\)
−0.437635 + 0.899153i \(0.644184\pi\)
\(572\) 2.65949e6 4.13824e6i 0.0142105 0.0221120i
\(573\) 6.23748e7 5.40480e7i 0.331547 0.287287i
\(574\) 3.90056e7i 0.206249i
\(575\) −1.02056e8 1.23253e8i −0.536826 0.648327i
\(576\) 5.99530e7 0.313721
\(577\) 1.84395e8 + 2.12804e8i 0.959893 + 1.10778i 0.994112 + 0.108361i \(0.0345602\pi\)
−0.0342189 + 0.999414i \(0.510894\pi\)
\(578\) −1.57119e8 1.00974e8i −0.813662 0.522909i
\(579\) 5.65748e6 3.93486e7i 0.0291466 0.202719i
\(580\) −1.03481e6 472581.i −0.00530367 0.00242210i
\(581\) 2.96917e6 + 2.06510e7i 0.0151393 + 0.105296i
\(582\) −1.94134e7 + 6.61161e7i −0.0984767 + 0.335381i
\(583\) −9.82543e6 + 6.31442e6i −0.0495845 + 0.0318660i
\(584\) −8.74474e7 1.91483e8i −0.439044 0.961373i
\(585\) 7.98894e6 + 2.72078e7i 0.0399045 + 0.135902i
\(586\) 2.48140e8 + 2.15015e8i 1.23312 + 1.06850i
\(587\) −4.72359e7 + 5.45132e7i −0.233538 + 0.269518i −0.860407 0.509607i \(-0.829791\pi\)
0.626869 + 0.779125i \(0.284336\pi\)
\(588\) 5.88074e6 1.72674e6i 0.0289268 0.00849367i
\(589\) 5.17828e8 2.36484e8i 2.53419 1.15733i
\(590\) −6.63394e7 1.03226e8i −0.323009 0.502613i
\(591\) −1.35773e8 3.98667e7i −0.657737 0.193129i
\(592\) 2.95643e8 4.25071e7i 1.42496 0.204878i
\(593\) 1.09279e8 2.39287e8i 0.524048 1.14750i −0.443836 0.896108i \(-0.646383\pi\)
0.967884 0.251397i \(-0.0808899\pi\)
\(594\) −1.89161e7 2.71972e6i −0.0902550 0.0129767i
\(595\) −9.02105e6 + 1.40370e7i −0.0428259 + 0.0666384i
\(596\) −4.47591e6 + 3.87840e6i −0.0211419 + 0.0183195i
\(597\) 1.02148e8i 0.480073i
\(598\) 1.94315e8 + 1.31121e8i 0.908661 + 0.613154i
\(599\) −1.78073e8 −0.828546 −0.414273 0.910153i \(-0.635964\pi\)
−0.414273 + 0.910153i \(0.635964\pi\)
\(600\) −6.67885e7 7.70781e7i −0.309206 0.356843i
\(601\) −1.22480e8 7.87129e7i −0.564210 0.362596i 0.227232 0.973841i \(-0.427033\pi\)
−0.791441 + 0.611245i \(0.790669\pi\)
\(602\) −5.97539e6 + 4.15597e7i −0.0273890 + 0.190495i
\(603\) −1.51203e7 6.90520e6i −0.0689617 0.0314937i
\(604\) −306043. 2.12858e6i −0.00138890 0.00966003i
\(605\) −1.95302e7 + 6.65138e7i −0.0881944 + 0.300363i
\(606\) −1.39412e8 + 8.95944e7i −0.626443 + 0.402590i
\(607\) −4.81025e7 1.05330e8i −0.215081 0.470961i 0.771083 0.636734i \(-0.219715\pi\)
−0.986164 + 0.165773i \(0.946988\pi\)
\(608\) −1.19742e7 4.07803e7i −0.0532764 0.181443i
\(609\) −3.87109e6 3.35432e6i −0.0171388 0.0148509i
\(610\) −8.78720e7 + 1.01410e8i −0.387134 + 0.446776i
\(611\) 1.23127e8 3.61533e7i 0.539795 0.158498i
\(612\) 5.16350e6 2.35809e6i 0.0225263 0.0102874i
\(613\) −1.76808e8 2.75119e8i −0.767575 1.19437i −0.976305 0.216397i \(-0.930569\pi\)
0.208730 0.977973i \(-0.433067\pi\)
\(614\) −1.58786e8 4.66236e7i −0.685971 0.201419i
\(615\) −7.43887e7 + 1.06955e7i −0.319802 + 0.0459807i
\(616\) 6.22240e6 1.36252e7i 0.0266205 0.0582907i
\(617\) 1.21705e8 + 1.74985e7i 0.518145 + 0.0744980i 0.396426 0.918067i \(-0.370250\pi\)
0.121719 + 0.992565i \(0.461159\pi\)
\(618\) −1.11684e8 + 1.73784e8i −0.473181 + 0.736284i
\(619\) −2.20970e8 + 1.91472e8i −0.931670 + 0.807297i −0.981500 0.191461i \(-0.938678\pi\)
0.0498298 + 0.998758i \(0.484132\pi\)
\(620\) 7.93003e6i 0.0332736i
\(621\) 7.57949e6 4.54610e7i 0.0316494 0.189830i
\(622\) −4.19676e8 −1.74399
\(623\) 2.43070e7 + 2.80518e7i 0.100524 + 0.116010i
\(624\) 1.32406e8 + 8.50922e7i 0.544947 + 0.350216i
\(625\) −1.91180e7 + 1.32968e8i −0.0783072 + 0.544639i
\(626\) 1.69764e8 + 7.75286e7i 0.692026 + 0.316038i
\(627\) −1.66020e7 1.15469e8i −0.0673530 0.468451i
\(628\) 3.00198e6 1.02238e7i 0.0121207 0.0412794i
\(629\) −3.99866e8 + 2.56978e8i −1.60680 + 1.03263i
\(630\) −2.01970e6 4.42253e6i −0.00807728 0.0176868i
\(631\) 2.76196e7 + 9.40638e7i 0.109933 + 0.374399i 0.996021 0.0891191i \(-0.0284052\pi\)
−0.886088 + 0.463518i \(0.846587\pi\)
\(632\) 3.83395e7 + 3.32214e7i 0.151878 + 0.131603i
\(633\) 5.61616e7 6.48140e7i 0.221426 0.255539i
\(634\) −2.59118e8 + 7.60838e7i −1.01678 + 0.298555i
\(635\) 8.50200e7 3.88273e7i 0.332047 0.151641i
\(636\) 546505. + 850379.i 0.00212433 + 0.00330553i
\(637\) −2.59484e8 7.61914e7i −1.00390 0.294773i
\(638\) −3.34851e7 + 4.81443e6i −0.128941 + 0.0185389i
\(639\) −1.06785e7 + 2.33827e7i −0.0409269 + 0.0896174i
\(640\) 1.10704e8 + 1.59168e7i 0.422301 + 0.0607177i
\(641\) −1.12474e8 + 1.75013e8i −0.427049 + 0.664502i −0.986387 0.164438i \(-0.947419\pi\)
0.559338 + 0.828940i \(0.311055\pi\)
\(642\) −2.13004e8 + 1.84569e8i −0.804977 + 0.697517i
\(643\) 3.60625e8i 1.35651i 0.734827 + 0.678255i \(0.237264\pi\)
−0.734827 + 0.678255i \(0.762736\pi\)
\(644\) −1.83084e6 886213.i −0.00685475 0.00331803i
\(645\) −8.08983e7 −0.301481
\(646\) 4.48376e8 + 5.17454e8i 1.66320 + 1.91944i
\(647\) 1.99153e8 + 1.27988e8i 0.735315 + 0.472559i 0.853934 0.520381i \(-0.174210\pi\)
−0.118619 + 0.992940i \(0.537847\pi\)
\(648\) 4.18042e6 2.90754e7i 0.0153637 0.106857i
\(649\) −1.67977e8 7.67123e7i −0.614490 0.280628i
\(650\) −3.60618e7 2.50815e8i −0.131313 0.913300i
\(651\) 1.00594e7 3.42592e7i 0.0364611 0.124175i
\(652\) 1.82570e7 1.17331e7i 0.0658700 0.0423321i
\(653\) −8.90224e7 1.94932e8i −0.319713 0.700073i 0.679730 0.733463i \(-0.262097\pi\)
−0.999442 + 0.0333895i \(0.989370\pi\)
\(654\) −1.54514e7 5.26225e7i −0.0552374 0.188121i
\(655\) 8.92335e7 + 7.73213e7i 0.317544 + 0.275154i
\(656\) −2.73167e8 + 3.15251e8i −0.967646 + 1.11672i
\(657\) −9.86633e7 + 2.89702e7i −0.347904 + 0.102154i
\(658\) −2.00138e7 + 9.13998e6i −0.0702508 + 0.0320824i
\(659\) −2.02033e8 3.14369e8i −0.705937 1.09846i −0.990192 0.139711i \(-0.955383\pi\)
0.284255 0.958749i \(-0.408254\pi\)
\(660\) −1.55922e6 457827.i −0.00542343 0.00159246i
\(661\) 1.29884e7 1.86746e6i 0.0449731 0.00646615i −0.119792 0.992799i \(-0.538223\pi\)
0.164765 + 0.986333i \(0.447314\pi\)
\(662\) −7.89796e6 + 1.72941e7i −0.0272233 + 0.0596108i
\(663\) −2.47921e8 3.56457e7i −0.850694 0.122311i
\(664\) −1.14506e8 + 1.78175e8i −0.391133 + 0.608614i
\(665\) 2.24294e7 1.94352e7i 0.0762699 0.0660883i
\(666\) 1.38498e8i 0.468836i
\(667\) −9.79871e6 8.09951e7i −0.0330211 0.272949i
\(668\) −2.74204e7 −0.0919908
\(669\) 4.32305e7 + 4.98907e7i 0.144382 + 0.166625i
\(670\) −2.34959e7 1.50999e7i −0.0781208 0.0502052i
\(671\) −2.87390e7 + 1.99884e8i −0.0951272 + 0.661624i
\(672\) −2.42488e6 1.10741e6i −0.00799066 0.00364921i
\(673\) −2.42695e7 1.68798e8i −0.0796189 0.553762i −0.990117 0.140247i \(-0.955210\pi\)
0.910498 0.413514i \(-0.135699\pi\)
\(674\) 9.95423e7 3.39010e8i 0.325108 1.10722i
\(675\) −4.19111e7 + 2.69346e7i −0.136276 + 0.0875790i
\(676\) 963232. + 2.10918e6i 0.00311811 + 0.00682770i
\(677\) 4.77017e7 + 1.62457e8i 0.153733 + 0.523567i 0.999957 0.00926012i \(-0.00294763\pi\)
−0.846224 + 0.532828i \(0.821129\pi\)
\(678\) −8.61435e7 7.46437e7i −0.276397 0.239499i
\(679\) −1.72769e7 + 1.99386e7i −0.0551895 + 0.0636921i
\(680\) −1.62527e8 + 4.77222e7i −0.516890 + 0.151773i
\(681\) −2.84738e8 + 1.30036e8i −0.901581 + 0.411738i
\(682\) −1.27492e8 1.98382e8i −0.401912 0.625387i
\(683\) 6.71011e7 + 1.97027e7i 0.210605 + 0.0618391i 0.385333 0.922778i \(-0.374087\pi\)
−0.174728 + 0.984617i \(0.555905\pi\)
\(684\) −9.99372e6 + 1.43688e6i −0.0312291 + 0.00449006i
\(685\) −3.65380e7 + 8.00070e7i −0.113677 + 0.248918i
\(686\) 9.27490e7 + 1.33353e7i 0.287301 + 0.0413076i
\(687\) −9.77746e7 + 1.52140e8i −0.301548 + 0.469217i
\(688\) −3.39348e8 + 2.94047e8i −1.04203 + 0.902925i
\(689\) 4.46030e7i 0.136366i
\(690\) 2.34765e7 7.37953e7i 0.0714637 0.224637i
\(691\) 4.31407e8 1.30753 0.653767 0.756696i \(-0.273188\pi\)
0.653767 + 0.756696i \(0.273188\pi\)
\(692\) 530861. + 612647.i 0.00160200 + 0.00184881i
\(693\) −6.15534e6 3.95580e6i −0.0184949 0.0118860i
\(694\) 3.47702e6 2.41832e7i 0.0104023 0.0723495i
\(695\) −5.46312e6 2.49493e6i −0.0162737 0.00743196i
\(696\) −7.40015e6 5.14692e7i −0.0219489 0.152658i
\(697\) 1.87022e8 6.36938e8i 0.552324 1.88104i
\(698\) 4.64536e8 2.98539e8i 1.36601 0.877880i
\(699\) −1.22629e8 2.68520e8i −0.359056 0.786223i
\(700\) 619451. + 2.10965e6i 0.00180598 + 0.00615060i
\(701\) 3.08046e8 + 2.66923e8i 0.894254 + 0.774875i 0.975080 0.221853i \(-0.0712104\pi\)
−0.0808262 + 0.996728i \(0.525756\pi\)
\(702\) 4.77928e7 5.51558e7i 0.138150 0.159434i
\(703\) 8.11187e8 2.38186e8i 2.33483 0.685567i
\(704\) 1.37901e8 6.29773e7i 0.395230 0.180495i
\(705\) −2.29190e7 3.56626e7i −0.0654075 0.101776i
\(706\) 2.53740e8 + 7.45047e7i 0.721065 + 0.211724i
\(707\) −6.28030e7 + 9.02971e6i −0.177714 + 0.0255515i
\(708\) −6.63936e6 + 1.45382e7i −0.0187080 + 0.0409647i
\(709\) −6.91630e7 9.94414e6i −0.194060 0.0279016i 0.0445996 0.999005i \(-0.485799\pi\)
−0.238659 + 0.971103i \(0.576708\pi\)
\(710\) −2.33512e7 + 3.63351e7i −0.0652429 + 0.101520i
\(711\) 1.87282e7 1.62281e7i 0.0521060 0.0451501i
\(712\) 3.76806e8i 1.04395i
\(713\) 4.85201e8 2.96674e8i 1.33861 0.818486i
\(714\) 4.29447e7 0.117982
\(715\) 4.69561e7 + 5.41902e7i 0.128462 + 0.148253i
\(716\) −1.01607e7 6.52986e6i −0.0276811 0.0177896i
\(717\) −2.81793e7 + 1.95992e8i −0.0764493 + 0.531716i
\(718\) −2.27955e7 1.04104e7i −0.0615852 0.0281250i
\(719\) 2.16685e7 + 1.50708e8i 0.0582965 + 0.405461i 0.997986 + 0.0634326i \(0.0202048\pi\)
−0.939690 + 0.342028i \(0.888886\pi\)
\(720\) 1.46485e7 4.98883e7i 0.0392461 0.133660i
\(721\) −6.65368e7 + 4.27606e7i −0.177524 + 0.114088i
\(722\) −3.45442e8 7.56413e8i −0.917833 2.00977i
\(723\) 1.00223e7 + 3.41329e7i 0.0265188 + 0.0903146i
\(724\) 321944. + 278966.i 0.000848329 + 0.000735081i
\(725\) −5.77527e7 + 6.66501e7i −0.151551 + 0.174899i
\(726\) 1.71188e8 5.02653e7i 0.447366 0.131359i
\(727\) −5.55569e7 + 2.53720e7i −0.144589 + 0.0660315i −0.486395 0.873739i \(-0.661689\pi\)
0.341807 + 0.939770i \(0.388961\pi\)
\(728\) 3.09260e7 + 4.81219e7i 0.0801549 + 0.124724i
\(729\) −1.37677e7 4.04255e6i −0.0355368 0.0104345i
\(730\) −1.71018e8 + 2.45886e7i −0.439615 + 0.0632071i
\(731\) 2.96843e8 6.49994e8i 0.759931 1.66402i
\(732\) 1.72997e7 + 2.48733e6i 0.0441069 + 0.00634162i
\(733\) 2.06086e8 3.20676e8i 0.523283 0.814244i −0.474537 0.880235i \(-0.657385\pi\)
0.997820 + 0.0659914i \(0.0210210\pi\)
\(734\) −1.42471e8 + 1.23452e8i −0.360279 + 0.312183i
\(735\) 8.93398e7i 0.225000i
\(736\) −1.67689e7 3.90087e7i −0.0420602 0.0978427i
\(737\) −4.20325e7 −0.104998
\(738\) 1.26666e8 + 1.46180e8i 0.315131 + 0.363681i
\(739\) −1.21515e8 7.80927e7i −0.301089 0.193498i 0.381369 0.924423i \(-0.375453\pi\)
−0.682458 + 0.730925i \(0.739089\pi\)
\(740\) 1.67604e6 1.16571e7i 0.00413608 0.0287671i
\(741\) 4.05242e8 + 1.85068e8i 0.996002 + 0.454859i
\(742\) 1.08835e6 + 7.56961e6i 0.00266413 + 0.0185294i
\(743\) −3.84244e7 + 1.30861e8i −0.0936786 + 0.319040i −0.992979 0.118292i \(-0.962258\pi\)
0.899300 + 0.437332i \(0.144076\pi\)
\(744\) 3.04928e8 1.95965e8i 0.740421 0.475840i
\(745\) −3.58625e7 7.85279e7i −0.0867305 0.189913i
\(746\) 2.25354e8 + 7.67486e8i 0.542812 + 1.84865i
\(747\) 7.81892e7 + 6.77513e7i 0.187579 + 0.162538i
\(748\) 9.39979e6 1.08479e7i 0.0224602 0.0259204i
\(749\) −1.03539e8 + 3.04018e7i −0.246410 + 0.0723526i
\(750\) −1.66606e8 + 7.60865e7i −0.394919 + 0.180353i
\(751\) 7.84986e7 + 1.22146e8i 0.185328 + 0.288377i 0.921469 0.388452i \(-0.126990\pi\)
−0.736140 + 0.676829i \(0.763354\pi\)
\(752\) −2.25765e8 6.62906e7i −0.530889 0.155883i
\(753\) 6.58120e7 9.46234e6i 0.154142 0.0221622i
\(754\) 5.36681e7 1.17517e8i 0.125199 0.274149i
\(755\) 3.10273e7 + 4.46105e6i 0.0720947 + 0.0103656i
\(756\) −342369. + 532737.i −0.000792373 + 0.00123296i
\(757\) 3.21859e8 2.78892e8i 0.741956 0.642908i −0.199557 0.979886i \(-0.563950\pi\)
0.941513 + 0.336978i \(0.109405\pi\)
\(758\) 7.47113e8i 1.71545i
\(759\) −3.03203e7 1.12529e8i −0.0693439 0.257359i
\(760\) 3.01284e8 0.686333
\(761\) 1.24054e8 + 1.43166e8i 0.281487 + 0.324853i 0.878832 0.477131i \(-0.158323\pi\)
−0.597345 + 0.801984i \(0.703778\pi\)
\(762\) −2.02369e8 1.30055e8i −0.457382 0.293941i
\(763\) 2.98835e6 2.07844e7i 0.00672756 0.0467912i
\(764\) −1.64304e7 7.50352e6i −0.0368441 0.0168261i
\(765\) 1.17756e7 + 8.19011e7i 0.0263026 + 0.182939i
\(766\) 1.56231e7 5.32073e7i 0.0347600 0.118382i
\(767\) 5.93266e8 3.81269e8i 1.31481 0.844978i
\(768\) −1.73256e7 3.79377e7i −0.0382476 0.0837505i
\(769\) 2.44449e8 + 8.32517e8i 0.537538 + 1.83069i 0.556474 + 0.830865i \(0.312154\pi\)
−0.0189358 + 0.999821i \(0.506028\pi\)
\(770\) −9.29124e6 8.05090e6i −0.0203517 0.0176349i
\(771\) 3.29315e7 3.80049e7i 0.0718535 0.0829233i
\(772\) −8.34769e6 + 2.45110e6i −0.0181432 + 0.00532733i
\(773\) −7.68533e8 + 3.50977e8i −1.66389 + 0.759872i −0.663961 + 0.747767i \(0.731126\pi\)
−0.999927 + 0.0121046i \(0.996147\pi\)
\(774\) 1.12566e8 + 1.75157e8i 0.242765 + 0.377750i
\(775\) −5.89855e8 1.73197e8i −1.26719 0.372079i
\(776\) −2.65099e8 + 3.81155e7i −0.567314 + 0.0815674i
\(777\) 2.20281e7 4.82348e7i 0.0469585 0.102825i
\(778\) −4.72063e8 6.78725e7i −1.00245 0.144130i
\(779\) −6.38346e8 + 9.93285e8i −1.35034 + 2.10117i
\(780\) 4.69010e6 4.06399e6i 0.00988321 0.00856385i
\(781\) 6.50010e7i 0.136448i
\(782\) 5.06782e8 + 4.59406e8i 1.05974 + 0.960675i
\(783\) −2.54004e7 −0.0529120
\(784\) 3.24730e8 + 3.74758e8i 0.673867 + 0.777684i
\(785\) 1.30663e8 + 8.39719e7i 0.270111 + 0.173590i
\(786\) 4.32475e7 3.00793e8i 0.0890623 0.619442i
\(787\) 7.13851e8 + 3.26005e8i 1.46448 + 0.668805i 0.978704 0.205278i \(-0.0658099\pi\)
0.485776 + 0.874084i \(0.338537\pi\)
\(788\) 4.40732e6 + 3.06536e7i 0.00900734 + 0.0626474i
\(789\) −4.79795e7 + 1.63403e8i −0.0976842 + 0.332682i
\(790\) 3.50280e7 2.25111e7i 0.0710451 0.0456579i
\(791\) −1.81292e7 3.96974e7i −0.0366310 0.0802107i
\(792\) −2.09265e7 7.12692e7i −0.0421232 0.143459i
\(793\) −5.82827e8 5.05022e8i −1.16875 1.01272i
\(794\) 3.62891e8 4.18799e8i 0.724961 0.836650i
\(795\) −1.41378e7 + 4.15123e6i −0.0281372 + 0.00826182i
\(796\) −2.03351e7 + 9.28675e6i −0.0403188 + 0.0184130i
\(797\) 8.82375e7 + 1.37300e8i 0.174292 + 0.271204i 0.917399 0.397969i \(-0.130285\pi\)
−0.743107 + 0.669173i \(0.766648\pi\)
\(798\) −7.32898e7 2.15198e7i −0.144223 0.0423477i
\(799\) 3.70636e8 5.32894e7i 0.726620 0.104472i
\(800\) −1.90667e7 + 4.17502e7i −0.0372396 + 0.0815433i
\(801\) 1.82190e8 + 2.61949e7i 0.354508 + 0.0509706i
\(802\) 1.10500e8 1.71941e8i 0.214209 0.333315i
\(803\) −1.96509e8 + 1.70276e8i −0.379521 + 0.328857i
\(804\) 3.63786e6i 0.00699967i
\(805\) 1.99133e7 2.19668e7i 0.0381730 0.0421095i
\(806\) 9.00564e8 1.71992
\(807\) −1.60166e8 1.84842e8i −0.304755 0.351706i
\(808\) −5.41858e8 3.48231e8i −1.02719 0.660136i
\(809\) −1.65752e7 + 1.15283e8i −0.0313049 + 0.217731i −0.999469 0.0325862i \(-0.989626\pi\)
0.968164 + 0.250317i \(0.0805348\pi\)
\(810\) −2.19308e7 1.00155e7i −0.0412667 0.0188459i
\(811\) −8.79390e7 6.11629e8i −0.164861 1.14664i −0.889309 0.457307i \(-0.848814\pi\)
0.724448 0.689330i \(-0.242095\pi\)
\(812\) −315823. + 1.07560e6i −0.000589897 + 0.00200900i
\(813\) 5.08891e8 3.27044e8i 0.947007 0.608604i
\(814\) −1.45484e8 3.18566e8i −0.269739 0.590645i
\(815\) 8.91241e7 + 3.03529e8i 0.164635 + 0.560696i
\(816\) 3.47088e8 + 3.00753e8i 0.638806 + 0.553529i
\(817\) −8.32310e8 + 9.60536e8i −1.52623 + 1.76136i
\(818\) −5.63419e8 + 1.65435e8i −1.02937 + 0.302250i
\(819\) 2.54174e7 1.16077e7i 0.0462678 0.0211298i
\(820\) 8.89223e6 + 1.38366e7i 0.0161276 + 0.0250950i
\(821\) −3.61146e8 1.06042e8i −0.652610 0.191624i −0.0613649 0.998115i \(-0.519545\pi\)
−0.591245 + 0.806492i \(0.701364\pi\)
\(822\) 2.24068e8 3.22161e7i 0.403427 0.0580040i
\(823\) 1.89574e8 4.15109e8i 0.340079 0.744669i −0.659899 0.751354i \(-0.729401\pi\)
0.999978 + 0.00668585i \(0.00212819\pi\)
\(824\) −7.94744e8 1.14267e8i −1.42051 0.204239i
\(825\) −6.81086e7 + 1.05979e8i −0.121294 + 0.188738i
\(826\) −9.13804e7 + 7.91816e7i −0.162148 + 0.140502i
\(827\) 9.71096e8i 1.71690i 0.512896 + 0.858451i \(0.328573\pi\)
−0.512896 + 0.858451i \(0.671427\pi\)
\(828\) −9.73925e6 + 2.62418e6i −0.0171567 + 0.00462278i
\(829\) −6.81970e8 −1.19702 −0.598510 0.801115i \(-0.704240\pi\)
−0.598510 + 0.801115i \(0.704240\pi\)
\(830\) 1.13838e8 + 1.31376e8i 0.199092 + 0.229764i
\(831\) 4.23043e8 + 2.71873e8i 0.737193 + 0.473765i
\(832\) −8.23932e7 + 5.73057e8i −0.143061 + 0.995012i
\(833\) −7.17820e8 3.27817e8i −1.24188 0.567148i
\(834\) 2.19982e6 + 1.53001e7i 0.00379218 + 0.0263752i
\(835\) 1.12607e8 3.83504e8i 0.193422 0.658735i
\(836\) −2.14777e7 + 1.38029e7i −0.0367595 + 0.0236239i
\(837\) −7.35533e7 1.61059e8i −0.125437 0.274669i
\(838\) −6.86690e7 2.33865e8i −0.116689 0.397405i
\(839\) −5.86373e8 5.08095e8i −0.992860 0.860318i −0.00266269 0.999996i \(-0.500848\pi\)
−0.990197 + 0.139679i \(0.955393\pi\)
\(840\) 1.23749e7 1.42813e7i 0.0208786 0.0240952i
\(841\) 5.27587e8 1.54913e8i 0.886964 0.260436i
\(842\) 2.00821e8 9.17118e7i 0.336413 0.153635i
\(843\) 1.67958e8 + 2.61348e8i 0.280362 + 0.436252i
\(844\) −1.80088e7 5.28786e6i −0.0299541 0.00879533i
\(845\) −3.34549e7 + 4.81009e6i −0.0554485 + 0.00797230i
\(846\) −4.53241e7 + 9.92460e7i −0.0748546 + 0.163909i
\(847\) 6.76145e7 + 9.72149e6i 0.111273 + 0.0159986i
\(848\) −4.42158e7 + 6.88011e7i −0.0725087 + 0.112826i
\(849\) −4.33976e8 + 3.76042e8i −0.709157 + 0.614488i
\(850\) 7.39396e8i 1.20398i
\(851\) 7.75947e8 3.33561e8i 1.25905 0.541236i
\(852\) 5.62576e6 0.00909625
\(853\) 5.92105e8 + 6.83326e8i 0.954008 + 1.10098i 0.994803 + 0.101816i \(0.0324654\pi\)
−0.0407954 + 0.999168i \(0.512989\pi\)
\(854\) 1.11235e8 + 7.14863e7i 0.178594 + 0.114776i
\(855\) 2.09447e7 1.45674e8i 0.0335102 0.233068i
\(856\) −9.96467e8 4.55071e8i −1.58870 0.725535i
\(857\) 9.34068e7 + 6.49659e8i 0.148401 + 1.03215i 0.918838 + 0.394635i \(0.129129\pi\)
−0.770437 + 0.637516i \(0.779962\pi\)
\(858\) 5.19926e7 1.77070e8i 0.0823151 0.280339i
\(859\) −7.76456e8 + 4.98998e8i −1.22500 + 0.787262i −0.983106 0.183040i \(-0.941406\pi\)
−0.241898 + 0.970302i \(0.577770\pi\)
\(860\) 7.35484e6 + 1.61048e7i 0.0115632 + 0.0253199i
\(861\) 2.08641e7 + 7.10567e7i 0.0326882 + 0.111326i
\(862\) 7.19359e8 + 6.23329e8i 1.12311 + 0.973185i
\(863\) 8.67717e7 1.00140e8i 0.135004 0.155803i −0.684222 0.729274i \(-0.739858\pi\)
0.819226 + 0.573471i \(0.194404\pi\)
\(864\) −1.26838e7 + 3.72431e6i −0.0196657 + 0.00577437i
\(865\) −1.07486e7 + 4.90873e6i −0.0166075 + 0.00758439i
\(866\) −2.31412e7 3.60085e7i −0.0356314 0.0554436i
\(867\) −3.40234e8 9.99019e7i −0.522061 0.153291i
\(868\) −7.73471e6 + 1.11208e6i −0.0118273 + 0.00170051i
\(869\) 2.60310e7 5.70000e7i 0.0396673 0.0868592i
\(870\) −4.22442e7 6.07380e6i −0.0641518 0.00922364i
\(871\) 8.67827e7 1.35037e8i 0.131335 0.204360i
\(872\) 1.61099e8 1.39593e8i 0.242965 0.210531i
\(873\) 1.30828e8i 0.196634i
\(874\) −6.34667e8 1.03798e9i −0.950630 1.55472i
\(875\) −7.01257e7 −0.104677
\(876\) 1.47372e7 + 1.70076e7i 0.0219231 + 0.0253006i
\(877\) −9.01681e8 5.79475e8i −1.33676 0.859085i −0.340074 0.940399i \(-0.610452\pi\)
−0.996689 + 0.0813135i \(0.974089\pi\)
\(878\) 4.08553e7 2.84155e8i 0.0603622 0.419829i
\(879\) 5.67049e8 + 2.58963e8i 0.834938 + 0.381303i
\(880\) −1.87110e7 1.30138e8i −0.0274568 0.190966i
\(881\) 1.48546e8 5.05903e8i 0.217237 0.739843i −0.776698 0.629874i \(-0.783107\pi\)
0.993935 0.109969i \(-0.0350751\pi\)
\(882\) 1.93434e8 1.24312e8i 0.281921 0.181179i
\(883\) −3.86950e7 8.47303e7i −0.0562047 0.123071i 0.879446 0.475999i \(-0.157913\pi\)
−0.935651 + 0.352928i \(0.885186\pi\)
\(884\) 1.54435e7 + 5.25957e7i 0.0223557 + 0.0761366i
\(885\) −1.76066e8 1.52562e8i −0.254007 0.220099i
\(886\) −6.72952e8 + 7.76628e8i −0.967572 + 1.11664i
\(887\) 6.31416e8 1.85401e8i 0.904784 0.265668i 0.203940 0.978983i \(-0.434625\pi\)
0.700844 + 0.713315i \(0.252807\pi\)
\(888\) 4.89661e8 2.23621e8i 0.699289 0.319355i
\(889\) −4.97940e7 7.74810e7i −0.0708715 0.110278i
\(890\) 2.96742e8 + 8.71313e7i 0.420929 + 0.123596i
\(891\) −3.59142e7 + 5.16369e6i −0.0507731 + 0.00730007i
\(892\) 6.00171e6 1.31419e7i 0.00845630 0.0185167i
\(893\) −6.59234e8 9.47836e7i −0.925732 0.133100i
\(894\) −1.20124e8 + 1.86916e8i −0.168119 + 0.261598i
\(895\) 1.33054e8 1.15292e8i 0.185592 0.160816i
\(896\) 1.10209e8i 0.153212i
\(897\) 4.24120e8 + 1.34925e8i 0.587641 + 0.186946i
\(898\) −4.64844e8 −0.641916
\(899\) −2.05253e8 2.36875e8i −0.282495 0.326017i
\(900\) 9.17235e6 + 5.89471e6i 0.0125821 + 0.00808603i
\(901\) 1.85223e7 1.28825e8i 0.0253233 0.176128i
\(902\) 4.44906e8 + 2.03182e8i 0.606245 + 0.276863i
\(903\) 1.13449e7 + 7.89057e7i 0.0154077 + 0.107163i
\(904\) 1.24815e8 4.25082e8i 0.168952 0.575397i
\(905\) −5.22376e6 + 3.35711e6i −0.00704754 + 0.00452918i
\(906\) −3.35143e7 7.33861e7i −0.0450657 0.0986800i
\(907\) −7.05027e7 2.40110e8i −0.0944896 0.321802i 0.898661 0.438644i \(-0.144541\pi\)
−0.993151 + 0.116842i \(0.962723\pi\)
\(908\) 5.17738e7 + 4.48622e7i 0.0691596 + 0.0599271i
\(909\) −2.06043e8 + 2.37786e8i −0.274325 + 0.316588i
\(910\) 4.50482e7 1.32273e7i 0.0597796 0.0175529i
\(911\) 5.15921e7 2.35613e7i 0.0682382 0.0311634i −0.381004 0.924574i \(-0.624421\pi\)
0.449242 + 0.893410i \(0.351694\pi\)
\(912\) −4.41634e8 6.87196e8i −0.582208 0.905933i
\(913\) 2.51016e8 + 7.37050e7i 0.329829 + 0.0968466i
\(914\) −3.13707e8 + 4.51043e7i −0.410853 + 0.0590717i
\(915\) −1.05833e8 + 2.31741e8i −0.138152 + 0.302510i
\(916\) 3.91765e7 + 5.63273e6i 0.0509729 + 0.00732880i
\(917\) 6.29030e7 9.78791e7i 0.0815762 0.126935i
\(918\) 1.60943e8 1.39458e8i 0.208039 0.180266i
\(919\) 7.73088e8i 0.996052i 0.867162 + 0.498026i \(0.165942\pi\)
−0.867162 + 0.498026i \(0.834058\pi\)
\(920\) 2.98810e8 3.61497e7i 0.383735 0.0464238i
\(921\) −3.14199e8 −0.402185
\(922\) 9.12284e7 + 1.05283e8i 0.116396 + 0.134328i
\(923\) −2.08827e8 1.34205e8i −0.265572 0.170673i
\(924\) −227891. + 1.58502e6i −0.000288876 + 0.00200918i
\(925\) −8.30479e8 3.79267e8i −1.04931 0.479203i
\(926\) 3.98236e7 + 2.76979e8i 0.0501542 + 0.348830i
\(927\) −1.10499e8 + 3.76324e8i −0.138713 + 0.472413i
\(928\) −1.96860e7 + 1.26514e7i −0.0246328 + 0.0158305i
\(929\) −4.54782e7 9.95834e7i −0.0567226 0.124205i 0.879148 0.476548i \(-0.158112\pi\)
−0.935871 + 0.352343i \(0.885385\pi\)
\(930\) −8.38161e7 2.85451e8i −0.104203 0.354881i
\(931\) 1.06077e9 + 9.19159e8i 1.31453 + 1.13905i
\(932\) −4.23070e7 + 4.88249e7i −0.0522594 + 0.0603106i
\(933\) −7.64525e8 + 2.24485e8i −0.941340 + 0.276402i
\(934\) 2.27492e8 1.03892e8i 0.279206 0.127509i
\(935\) 1.13118e8 + 1.76015e8i 0.138388 + 0.215336i
\(936\) 2.72171e8 + 7.99166e7i 0.331905 + 0.0974562i
\(937\) −1.20405e9 + 1.73116e8i −1.46361 + 0.210435i −0.827631 0.561272i \(-0.810312\pi\)
−0.635977 + 0.771708i \(0.719403\pi\)
\(938\) −1.14330e7 + 2.50347e7i −0.0138532 + 0.0303343i
\(939\) 3.50730e8 + 5.04273e7i 0.423619 + 0.0609072i
\(940\) −5.01588e6 + 7.80485e6i −0.00603897 + 0.00939683i
\(941\) 5.42415e8 4.70005e8i 0.650973 0.564071i −0.265528 0.964103i \(-0.585546\pi\)
0.916501 + 0.400032i \(0.131001\pi\)
\(942\) 3.99748e8i 0.478226i
\(943\) −5.13924e8 + 1.06172e9i −0.612864 + 1.26612i
\(944\) −1.29309e9 −1.53713
\(945\) −6.04491e6 6.97619e6i −0.00716299 0.00826653i
\(946\) 4.42913e8 + 2.84643e8i 0.523172 + 0.336222i
\(947\) 4.74487e7 3.30013e8i 0.0558695 0.388581i −0.942631 0.333837i \(-0.891657\pi\)
0.998500 0.0547441i \(-0.0174343\pi\)
\(948\) −4.93328e6 2.25295e6i −0.00579043 0.00264440i
\(949\) −1.41317e8 9.82882e8i −0.165347 1.15001i
\(950\) −3.70515e8 + 1.26186e9i −0.432151 + 1.47177i
\(951\) −4.31338e8 + 2.77204e8i −0.501506 + 0.322298i
\(952\) 6.93391e7 + 1.51831e8i 0.0803651 + 0.175975i
\(953\) 4.69179e7 + 1.59788e8i 0.0542076 + 0.184614i 0.982146 0.188119i \(-0.0602390\pi\)
−0.927939 + 0.372733i \(0.878421\pi\)
\(954\) 2.86602e7 + 2.48342e7i 0.0330091 + 0.0286026i
\(955\) 1.72419e8 1.98983e8i 0.197959 0.228457i
\(956\) 4.15790e7 1.22087e7i 0.0475883 0.0139732i
\(957\) −5.84247e7 + 2.66817e7i −0.0666593 + 0.0304423i
\(958\) −6.24162e7 9.71216e7i −0.0709906 0.110464i
\(959\) 8.31604e7 + 2.44181e7i 0.0942889 + 0.0276857i
\(960\) 1.89310e8 2.72187e7i 0.213974 0.0307648i
\(961\) 5.38936e8 1.18011e9i 0.607250 1.32969i
\(962\) 1.32383e9 + 1.90337e8i 1.48698 + 0.213796i
\(963\) −2.89305e8 + 4.50167e8i −0.323949 + 0.504075i
\(964\) 5.88384e6 5.09837e6i 0.00656795 0.00569116i
\(965\) 1.26817e8i 0.141123i
\(966\) −7.52700e7 1.25494e7i −0.0835008 0.0139217i
\(967\) 8.81022e6 0.00974333 0.00487166 0.999988i \(-0.498449\pi\)
0.00487166 + 0.999988i \(0.498449\pi\)
\(968\) 4.54116e8 + 5.24078e8i 0.500657 + 0.577789i
\(969\) 1.09359e9 + 7.02811e8i 1.20195 + 0.772444i
\(970\) −3.12840e7 + 2.17585e8i −0.0342773 + 0.238404i
\(971\) 2.68488e8 + 1.22615e8i 0.293270 + 0.133932i 0.556617 0.830769i \(-0.312099\pi\)
−0.263347 + 0.964701i \(0.584826\pi\)
\(972\) 446911. + 3.10833e6i 0.000486656 + 0.00338477i
\(973\) −1.66734e6 + 5.67845e6i −0.00181003 + 0.00616441i
\(974\) 1.50016e9 9.64094e8i 1.62353 1.04338i
\(975\) −1.99855e8 4.37621e8i −0.215626 0.472155i
\(976\) 3.98385e8 + 1.35678e9i 0.428503 + 1.45935i
\(977\) 3.46386e8 + 3.00145e8i 0.371429 + 0.321845i 0.820495 0.571653i \(-0.193698\pi\)
−0.449066 + 0.893499i \(0.648243\pi\)
\(978\) 5.33173e8 6.15314e8i 0.569969 0.657780i
\(979\) 4.46581e8 1.31128e8i 0.475940 0.139748i
\(980\) 1.77853e7 8.12229e6i 0.0188966 0.00862979i
\(981\) −5.62956e7 8.75976e7i −0.0596303 0.0927866i
\(982\) −1.37741e9 4.04445e8i −1.45455 0.427095i
\(983\) −2.03641e8 + 2.92792e7i −0.214390 + 0.0308247i −0.248673 0.968588i \(-0.579994\pi\)
0.0342827 + 0.999412i \(0.489085\pi\)
\(984\) −3.12306e8 + 6.83854e8i −0.327789 + 0.717758i
\(985\) −4.46824e8 6.42435e7i −0.467549 0.0672235i
\(986\) 2.03809e8 3.17133e8i 0.212615 0.330835i
\(987\) −3.15702e7 + 2.73557e7i −0.0328341 + 0.0284509i
\(988\) 9.74991e7i 0.101095i
\(989\) −7.10225e8 + 1.05251e9i −0.734187 + 1.08803i
\(990\) −6.09649e7 −0.0628311
\(991\) 5.35994e8 + 6.18570e8i 0.550730 + 0.635576i 0.961053 0.276364i \(-0.0891296\pi\)
−0.410323 + 0.911940i \(0.634584\pi\)
\(992\) −1.37226e8 8.81900e7i −0.140573 0.0903409i
\(993\) −5.13711e6 + 3.57294e7i −0.00524652 + 0.0364903i
\(994\) 3.87149e7 + 1.76805e7i 0.0394202 + 0.0180026i
\(995\) −4.63752e7 3.22547e8i −0.0470779 0.327434i
\(996\) 6.37907e6 2.17251e7i 0.00645624 0.0219879i
\(997\) 1.19728e7 7.69446e6i 0.0120812 0.00776412i −0.534586 0.845114i \(-0.679533\pi\)
0.546667 + 0.837350i \(0.315896\pi\)
\(998\) −1.67623e8 3.67043e8i −0.168633 0.369254i
\(999\) −7.40826e7 2.52302e8i −0.0743053 0.253061i
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.10.6 yes 240
23.7 odd 22 inner 69.7.f.a.7.6 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.7.f.a.7.6 240 23.7 odd 22 inner
69.7.f.a.10.6 yes 240 1.1 even 1 trivial