Properties

Label 27.7.f.a.2.13
Level $27$
Weight $7$
Character 27.2
Analytic conductor $6.211$
Analytic rank $0$
Dimension $102$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,7,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.21146025774\)
Analytic rank: \(0\)
Dimension: \(102\)
Relative dimension: \(17\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 2.13
Character \(\chi\) \(=\) 27.2
Dual form 27.7.f.a.14.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.40620 + 1.30591i) q^{2} +(20.7548 - 17.2696i) q^{3} +(-6.99392 - 2.54558i) q^{4} +(93.4519 + 111.372i) q^{5} +(176.267 - 100.798i) q^{6} +(468.870 - 170.655i) q^{7} +(-465.300 - 268.641i) q^{8} +(132.523 - 716.853i) q^{9} +O(q^{10})\) \(q+(7.40620 + 1.30591i) q^{2} +(20.7548 - 17.2696i) q^{3} +(-6.99392 - 2.54558i) q^{4} +(93.4519 + 111.372i) q^{5} +(176.267 - 100.798i) q^{6} +(468.870 - 170.655i) q^{7} +(-465.300 - 268.641i) q^{8} +(132.523 - 716.853i) q^{9} +(546.682 + 946.881i) q^{10} +(-224.091 + 267.061i) q^{11} +(-189.118 + 67.9491i) q^{12} +(134.825 + 764.633i) q^{13} +(3695.40 - 651.600i) q^{14} +(3862.92 + 697.619i) q^{15} +(-2730.39 - 2291.07i) q^{16} +(-5550.68 + 3204.68i) q^{17} +(1917.64 - 5136.10i) q^{18} +(-1943.92 + 3366.96i) q^{19} +(-370.090 - 1016.81i) q^{20} +(6784.16 - 11639.1i) q^{21} +(-2008.42 + 1685.26i) q^{22} +(-5229.60 + 14368.2i) q^{23} +(-14296.5 + 2459.95i) q^{24} +(-957.130 + 5428.15i) q^{25} +5839.09i q^{26} +(-9629.28 - 17166.8i) q^{27} -3713.65 q^{28} +(-1445.02 - 254.796i) q^{29} +(27698.5 + 10211.3i) q^{30} +(-31916.9 - 11616.8i) q^{31} +(4873.06 + 5807.49i) q^{32} +(-38.9246 + 9412.75i) q^{33} +(-45294.5 + 16485.8i) q^{34} +(62822.9 + 36270.8i) q^{35} +(-2751.66 + 4676.27i) q^{36} +(-45438.5 - 78701.8i) q^{37} +(-18794.0 + 22397.8i) q^{38} +(16003.2 + 13541.4i) q^{39} +(-13564.2 - 76926.2i) q^{40} +(123662. - 21805.0i) q^{41} +(65444.5 - 77341.9i) q^{42} +(103394. + 86758.2i) q^{43} +(2247.10 - 1297.36i) q^{44} +(92221.6 - 52232.0i) q^{45} +(-57495.1 + 99584.5i) q^{46} +(-7944.94 - 21828.6i) q^{47} +(-96234.4 - 397.959i) q^{48} +(100592. - 84406.3i) q^{49} +(-14177.4 + 38952.1i) q^{50} +(-59859.6 + 162370. i) q^{51} +(1003.47 - 5690.99i) q^{52} +92167.3i q^{53} +(-48898.1 - 139715. i) q^{54} -50684.7 q^{55} +(-264010. - 46552.1i) q^{56} +(17800.5 + 103451. i) q^{57} +(-10369.4 - 3774.14i) q^{58} +(-22456.1 - 26762.2i) q^{59} +(-25241.1 - 14712.4i) q^{60} +(-211010. + 76801.5i) q^{61} +(-221213. - 127717. i) q^{62} +(-60198.4 - 358727. i) q^{63} +(142563. + 246927. i) q^{64} +(-72558.7 + 86472.1i) q^{65} +(-12580.5 + 69661.9i) q^{66} +(-1201.29 - 6812.86i) q^{67} +(46978.7 - 8283.62i) q^{68} +(139594. + 388522. i) q^{69} +(417912. + 350670. i) q^{70} +(309301. - 178575. i) q^{71} +(-254239. + 297951. i) q^{72} +(384512. - 665995. i) q^{73} +(-233749. - 642220. i) q^{74} +(73876.9 + 129189. i) q^{75} +(22166.5 - 18599.9i) q^{76} +(-59494.2 + 163459. i) q^{77} +(100839. + 121189. i) q^{78} +(-53075.9 + 301008. i) q^{79} -518192. i q^{80} +(-496316. - 189999. i) q^{81} +944343. q^{82} +(-222841. - 39292.8i) q^{83} +(-77076.1 + 64133.2i) q^{84} +(-875632. - 318704. i) q^{85} +(652461. + 777572. i) q^{86} +(-34391.3 + 19666.7i) q^{87} +(176013. - 64063.5i) q^{88} +(86060.1 + 49686.8i) q^{89} +(751222. - 266407. i) q^{90} +(193704. + 335505. i) q^{91} +(73150.8 - 87177.7i) q^{92} +(-863046. + 310088. i) q^{93} +(-30335.7 - 172042. i) q^{94} +(-556647. + 98151.8i) q^{95} +(201432. + 36377.5i) q^{96} +(-713372. - 598591. i) q^{97} +(855229. - 493766. i) q^{98} +(161746. + 196032. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.40620 + 1.30591i 0.925775 + 0.163239i 0.616158 0.787622i \(-0.288688\pi\)
0.309617 + 0.950861i \(0.399799\pi\)
\(3\) 20.7548 17.2696i 0.768696 0.639614i
\(4\) −6.99392 2.54558i −0.109280 0.0397747i
\(5\) 93.4519 + 111.372i 0.747615 + 0.890973i 0.996998 0.0774321i \(-0.0246721\pi\)
−0.249383 + 0.968405i \(0.580228\pi\)
\(6\) 176.267 100.798i 0.816050 0.466658i
\(7\) 468.870 170.655i 1.36697 0.497535i 0.448766 0.893649i \(-0.351864\pi\)
0.918201 + 0.396114i \(0.129641\pi\)
\(8\) −465.300 268.641i −0.908789 0.524690i
\(9\) 132.523 716.853i 0.181787 0.983338i
\(10\) 546.682 + 946.881i 0.546682 + 0.946881i
\(11\) −224.091 + 267.061i −0.168363 + 0.200647i −0.843628 0.536928i \(-0.819585\pi\)
0.675265 + 0.737575i \(0.264029\pi\)
\(12\) −189.118 + 67.9491i −0.109444 + 0.0393224i
\(13\) 134.825 + 764.633i 0.0613679 + 0.348035i 0.999995 + 0.00310171i \(0.000987307\pi\)
−0.938627 + 0.344933i \(0.887902\pi\)
\(14\) 3695.40 651.600i 1.34672 0.237463i
\(15\) 3862.92 + 697.619i 1.14457 + 0.206702i
\(16\) −2730.39 2291.07i −0.666599 0.559343i
\(17\) −5550.68 + 3204.68i −1.12979 + 0.652287i −0.943883 0.330280i \(-0.892857\pi\)
−0.185911 + 0.982567i \(0.559523\pi\)
\(18\) 1917.64 5136.10i 0.328813 0.880675i
\(19\) −1943.92 + 3366.96i −0.283411 + 0.490882i −0.972223 0.234058i \(-0.924799\pi\)
0.688812 + 0.724940i \(0.258133\pi\)
\(20\) −370.090 1016.81i −0.0462612 0.127102i
\(21\) 6784.16 11639.1i 0.732552 1.25679i
\(22\) −2008.42 + 1685.26i −0.188619 + 0.158271i
\(23\) −5229.60 + 14368.2i −0.429818 + 1.18092i 0.516105 + 0.856526i \(0.327382\pi\)
−0.945923 + 0.324391i \(0.894841\pi\)
\(24\) −14296.5 + 2459.95i −1.03418 + 0.177948i
\(25\) −957.130 + 5428.15i −0.0612563 + 0.347402i
\(26\) 5839.09i 0.332220i
\(27\) −9629.28 17166.8i −0.489218 0.872162i
\(28\) −3713.65 −0.169171
\(29\) −1445.02 254.796i −0.0592489 0.0104472i 0.143945 0.989586i \(-0.454021\pi\)
−0.203194 + 0.979138i \(0.565132\pi\)
\(30\) 27698.5 + 10211.3i 1.02587 + 0.378198i
\(31\) −31916.9 11616.8i −1.07136 0.389944i −0.254676 0.967027i \(-0.581969\pi\)
−0.816685 + 0.577083i \(0.804191\pi\)
\(32\) 4873.06 + 5807.49i 0.148714 + 0.177231i
\(33\) −38.9246 + 9412.75i −0.00108313 + 0.261924i
\(34\) −45294.5 + 16485.8i −1.15241 + 0.419444i
\(35\) 62822.9 + 36270.8i 1.46526 + 0.845966i
\(36\) −2751.66 + 4676.27i −0.0589776 + 0.100229i
\(37\) −45438.5 78701.8i −0.897054 1.55374i −0.831242 0.555911i \(-0.812369\pi\)
−0.0658126 0.997832i \(-0.520964\pi\)
\(38\) −18794.0 + 22397.8i −0.342506 + 0.408183i
\(39\) 16003.2 + 13541.4i 0.269781 + 0.228281i
\(40\) −13564.2 76926.2i −0.211940 1.20197i
\(41\) 123662. 21805.0i 1.79426 0.316376i 0.825505 0.564395i \(-0.190890\pi\)
0.968755 + 0.248018i \(0.0797794\pi\)
\(42\) 65444.5 77341.9i 0.883335 1.04392i
\(43\) 103394. + 86758.2i 1.30044 + 1.09120i 0.990068 + 0.140587i \(0.0448991\pi\)
0.310375 + 0.950614i \(0.399545\pi\)
\(44\) 2247.10 1297.36i 0.0263793 0.0152301i
\(45\) 92221.6 52232.0i 1.01203 0.573191i
\(46\) −57495.1 + 99584.5i −0.590687 + 1.02310i
\(47\) −7944.94 21828.6i −0.0765239 0.210248i 0.895532 0.444997i \(-0.146795\pi\)
−0.972056 + 0.234749i \(0.924573\pi\)
\(48\) −96234.4 397.959i −0.870175 0.00359844i
\(49\) 100592. 84406.3i 0.855014 0.717442i
\(50\) −14177.4 + 38952.1i −0.113419 + 0.311617i
\(51\) −59859.6 + 162370.i −0.451256 + 1.22404i
\(52\) 1003.47 5690.99i 0.00713668 0.0404741i
\(53\) 92167.3i 0.619084i 0.950886 + 0.309542i \(0.100176\pi\)
−0.950886 + 0.309542i \(0.899824\pi\)
\(54\) −48898.1 139715.i −0.310535 0.887285i
\(55\) −50684.7 −0.304641
\(56\) −264010. 46552.1i −1.50334 0.265079i
\(57\) 17800.5 + 103451.i 0.0961184 + 0.558613i
\(58\) −10369.4 3774.14i −0.0531457 0.0193435i
\(59\) −22456.1 26762.2i −0.109340 0.130306i 0.708599 0.705612i \(-0.249328\pi\)
−0.817939 + 0.575305i \(0.804883\pi\)
\(60\) −25241.1 14712.4i −0.116857 0.0681132i
\(61\) −211010. + 76801.5i −0.929639 + 0.338361i −0.762067 0.647499i \(-0.775815\pi\)
−0.167573 + 0.985860i \(0.553593\pi\)
\(62\) −221213. 127717.i −0.928185 0.535888i
\(63\) −60198.4 358727.i −0.240748 1.43464i
\(64\) 142563. + 246927.i 0.543836 + 0.941952i
\(65\) −72558.7 + 86472.1i −0.264210 + 0.314873i
\(66\) −12580.5 + 69661.9i −0.0437589 + 0.242306i
\(67\) −1201.29 6812.86i −0.00399414 0.0226519i 0.982746 0.184963i \(-0.0592164\pi\)
−0.986740 + 0.162311i \(0.948105\pi\)
\(68\) 46978.7 8283.62i 0.149408 0.0263447i
\(69\) 139594. + 388522.i 0.424931 + 1.18268i
\(70\) 417912. + 350670.i 1.21840 + 1.02236i
\(71\) 309301. 178575.i 0.864185 0.498937i −0.00122661 0.999999i \(-0.500390\pi\)
0.865411 + 0.501062i \(0.167057\pi\)
\(72\) −254239. + 297951.i −0.681153 + 0.798265i
\(73\) 384512. 665995.i 0.988420 1.71199i 0.362797 0.931868i \(-0.381822\pi\)
0.625623 0.780125i \(-0.284845\pi\)
\(74\) −233749. 642220.i −0.576839 1.58485i
\(75\) 73876.9 + 129189.i 0.175116 + 0.306227i
\(76\) 22166.5 18599.9i 0.0504958 0.0423710i
\(77\) −59494.2 + 163459.i −0.130317 + 0.358044i
\(78\) 100839. + 121189.i 0.212492 + 0.255376i
\(79\) −53075.9 + 301008.i −0.107650 + 0.610516i 0.882478 + 0.470353i \(0.155874\pi\)
−0.990129 + 0.140162i \(0.955238\pi\)
\(80\) 518192.i 1.01209i
\(81\) −496316. 189999.i −0.933907 0.357516i
\(82\) 944343. 1.71273
\(83\) −222841. 39292.8i −0.389727 0.0687194i −0.0246485 0.999696i \(-0.507847\pi\)
−0.365078 + 0.930977i \(0.618958\pi\)
\(84\) −77076.1 + 64133.2i −0.130041 + 0.108204i
\(85\) −875632. 318704.i −1.42582 0.518956i
\(86\) 652461. + 777572.i 1.02579 + 1.22249i
\(87\) −34391.3 + 19666.7i −0.0522265 + 0.0298657i
\(88\) 176013. 64063.5i 0.258284 0.0940075i
\(89\) 86060.1 + 49686.8i 0.122076 + 0.0704809i 0.559795 0.828631i \(-0.310880\pi\)
−0.437718 + 0.899112i \(0.644213\pi\)
\(90\) 751222. 266407.i 1.03048 0.365442i
\(91\) 193704. + 335505.i 0.257048 + 0.445220i
\(92\) 73150.8 87177.7i 0.0939411 0.111955i
\(93\) −863046. + 310088.i −1.07296 + 0.385510i
\(94\) −30335.7 172042.i −0.0365233 0.207134i
\(95\) −556647. + 98151.8i −0.649245 + 0.114479i
\(96\) 201432. + 36377.5i 0.227675 + 0.0411168i
\(97\) −713372. 598591.i −0.781630 0.655865i 0.162029 0.986786i \(-0.448196\pi\)
−0.943659 + 0.330921i \(0.892641\pi\)
\(98\) 855229. 493766.i 0.908665 0.524618i
\(99\) 161746. + 196032.i 0.166698 + 0.202032i
\(100\) 20511.9 35527.6i 0.0205119 0.0355276i
\(101\) 247654. + 680425.i 0.240371 + 0.660414i 0.999950 + 0.00999887i \(0.00318279\pi\)
−0.759579 + 0.650415i \(0.774595\pi\)
\(102\) −655374. + 1.12438e6i −0.617573 + 1.05953i
\(103\) 652512. 547522.i 0.597141 0.501060i −0.293385 0.955995i \(-0.594782\pi\)
0.890525 + 0.454934i \(0.150337\pi\)
\(104\) 142677. 392003.i 0.126840 0.348489i
\(105\) 1.93026e6 332132.i 1.66743 0.286908i
\(106\) −120362. + 682610.i −0.101059 + 0.573132i
\(107\) 1.18265e6i 0.965396i −0.875787 0.482698i \(-0.839657\pi\)
0.875787 0.482698i \(-0.160343\pi\)
\(108\) 23647.1 + 144575.i 0.0187718 + 0.114768i
\(109\) −73802.6 −0.0569891 −0.0284946 0.999594i \(-0.509071\pi\)
−0.0284946 + 0.999594i \(0.509071\pi\)
\(110\) −375381. 66189.9i −0.282030 0.0497294i
\(111\) −2.30221e6 848735.i −1.68336 0.620588i
\(112\) −1.67118e6 608259.i −1.18951 0.432947i
\(113\) 814945. + 971214.i 0.564798 + 0.673100i 0.970555 0.240881i \(-0.0774364\pi\)
−0.405757 + 0.913981i \(0.632992\pi\)
\(114\) −3264.52 + 789427.i −0.00220346 + 0.532840i
\(115\) −2.08893e6 + 760307.i −1.37350 + 0.499914i
\(116\) 9457.75 + 5460.44i 0.00605918 + 0.00349827i
\(117\) 565997. + 4681.22i 0.353392 + 0.00292282i
\(118\) −131366. 227532.i −0.0799531 0.138483i
\(119\) −2.05565e6 + 2.44983e6i −1.21986 + 1.45377i
\(120\) −1.61001e6 1.36234e6i −0.931716 0.788391i
\(121\) 286523. + 1.62496e6i 0.161735 + 0.917245i
\(122\) −1.66308e6 + 293246.i −0.915871 + 0.161493i
\(123\) 2.19002e6 2.58815e6i 1.17688 1.39083i
\(124\) 193653. + 162494.i 0.101568 + 0.0852260i
\(125\) 1.27331e6 735149.i 0.651937 0.376396i
\(126\) 22623.9 2.73541e6i 0.0113098 1.36745i
\(127\) 615839. 1.06666e6i 0.300646 0.520735i −0.675636 0.737235i \(-0.736131\pi\)
0.976283 + 0.216500i \(0.0694643\pi\)
\(128\) 567442. + 1.55903e6i 0.270577 + 0.743405i
\(129\) 3.64421e6 + 15069.9i 1.69759 + 0.00702007i
\(130\) −650309. + 545674.i −0.295999 + 0.248372i
\(131\) −1.28721e6 + 3.53658e6i −0.572580 + 1.57315i 0.227832 + 0.973700i \(0.426836\pi\)
−0.800412 + 0.599450i \(0.795386\pi\)
\(132\) 24233.1 65732.9i 0.0105363 0.0285799i
\(133\) −336856. + 1.91041e6i −0.143182 + 0.812027i
\(134\) 52026.2i 0.0216226i
\(135\) 1.01202e6 2.67669e6i 0.411326 1.08792i
\(136\) 3.44364e6 1.36899
\(137\) −155845. 27479.7i −0.0606082 0.0106869i 0.143262 0.989685i \(-0.454241\pi\)
−0.203870 + 0.978998i \(0.565352\pi\)
\(138\) 526483. + 3.05977e6i 0.200331 + 1.16426i
\(139\) −3.24166e6 1.17987e6i −1.20704 0.439328i −0.341367 0.939930i \(-0.610890\pi\)
−0.865678 + 0.500602i \(0.833112\pi\)
\(140\) −347048. 413595.i −0.126475 0.150727i
\(141\) −541866. 315841.i −0.193301 0.112671i
\(142\) 2.52395e6 918643.i 0.881487 0.320835i
\(143\) −234417. 135341.i −0.0801642 0.0462828i
\(144\) −2.00420e6 + 1.65367e6i −0.671202 + 0.553810i
\(145\) −106663. 184745.i −0.0349872 0.0605996i
\(146\) 3.71751e6 4.43035e6i 1.19452 1.42357i
\(147\) 630094. 3.48901e6i 0.198360 1.09837i
\(148\) 117452. + 666101.i 0.0362304 + 0.205473i
\(149\) 5.33368e6 940471.i 1.61238 0.284306i 0.706460 0.707753i \(-0.250291\pi\)
0.905921 + 0.423446i \(0.139180\pi\)
\(150\) 378437. + 1.05328e6i 0.112130 + 0.312083i
\(151\) −2.87080e6 2.40888e6i −0.833818 0.699656i 0.122346 0.992488i \(-0.460958\pi\)
−0.956164 + 0.292831i \(0.905403\pi\)
\(152\) 1.80901e6 1.04443e6i 0.515122 0.297406i
\(153\) 1.56170e6 + 4.40371e6i 0.436036 + 1.22955i
\(154\) −654089. + 1.13292e6i −0.179091 + 0.310196i
\(155\) −1.68891e6 4.64025e6i −0.453537 1.24608i
\(156\) −77454.1 135445.i −0.0204019 0.0356770i
\(157\) 2.50682e6 2.10347e6i 0.647776 0.543548i −0.258619 0.965979i \(-0.583268\pi\)
0.906395 + 0.422431i \(0.138823\pi\)
\(158\) −786181. + 2.16001e6i −0.199320 + 0.547628i
\(159\) 1.59169e6 + 1.91291e6i 0.395975 + 0.475887i
\(160\) −191393. + 1.08544e6i −0.0467267 + 0.265001i
\(161\) 7.62928e6i 1.82812i
\(162\) −3.42770e6 2.05532e6i −0.806227 0.483430i
\(163\) −2.41459e6 −0.557546 −0.278773 0.960357i \(-0.589928\pi\)
−0.278773 + 0.960357i \(0.589928\pi\)
\(164\) −920390. 162290.i −0.208660 0.0367925i
\(165\) −1.05195e6 + 875304.i −0.234177 + 0.194853i
\(166\) −1.59909e6 582021.i −0.349582 0.127237i
\(167\) −1.35342e6 1.61294e6i −0.290592 0.346314i 0.600922 0.799308i \(-0.294800\pi\)
−0.891514 + 0.452994i \(0.850356\pi\)
\(168\) −6.28341e6 + 3.59316e6i −1.32516 + 0.757791i
\(169\) 3.96923e6 1.44468e6i 0.822330 0.299304i
\(170\) −6.06891e6 3.50389e6i −1.23528 0.713187i
\(171\) 2.15600e6 + 1.83970e6i 0.431183 + 0.367925i
\(172\) −502282. 869978.i −0.0987103 0.170971i
\(173\) −2.84771e6 + 3.39377e6i −0.549994 + 0.655457i −0.967397 0.253264i \(-0.918496\pi\)
0.417403 + 0.908721i \(0.362940\pi\)
\(174\) −280392. + 100743.i −0.0532253 + 0.0191235i
\(175\) 477570. + 2.70844e6i 0.0891094 + 0.505364i
\(176\) 1.22371e6 215773.i 0.224461 0.0395785i
\(177\) −928244. 167635.i −0.167395 0.0302305i
\(178\) 572492. + 480378.i 0.101510 + 0.0851771i
\(179\) −907387. + 523880.i −0.158210 + 0.0913425i −0.577015 0.816734i \(-0.695782\pi\)
0.418805 + 0.908076i \(0.362449\pi\)
\(180\) −777951. + 130549.i −0.133394 + 0.0223850i
\(181\) −2.36930e6 + 4.10375e6i −0.399563 + 0.692063i −0.993672 0.112321i \(-0.964171\pi\)
0.594109 + 0.804384i \(0.297505\pi\)
\(182\) 996468. + 2.73777e6i 0.165291 + 0.454133i
\(183\) −3.05315e6 + 5.23806e6i −0.498190 + 0.854708i
\(184\) 6.29322e6 5.28064e6i 1.01023 0.847683i
\(185\) 4.51883e6 1.24154e7i 0.713692 1.96085i
\(186\) −6.79684e6 + 1.16951e6i −1.05625 + 0.181746i
\(187\) 388009. 2.20051e6i 0.0593359 0.336510i
\(188\) 172892.i 0.0260196i
\(189\) −7.44446e6 6.40569e6i −1.10268 0.948813i
\(190\) −4.25082e6 −0.619743
\(191\) 620235. + 109364.i 0.0890136 + 0.0156955i 0.217978 0.975954i \(-0.430054\pi\)
−0.128964 + 0.991649i \(0.541165\pi\)
\(192\) 7.22320e6 + 2.66291e6i 1.02053 + 0.376229i
\(193\) 8.25190e6 + 3.00345e6i 1.14784 + 0.417780i 0.844740 0.535177i \(-0.179755\pi\)
0.303103 + 0.952958i \(0.401977\pi\)
\(194\) −4.50167e6 5.36488e6i −0.616551 0.734776i
\(195\) −12603.5 + 3.04777e6i −0.00169975 + 0.411034i
\(196\) −918392. + 334267.i −0.121972 + 0.0443941i
\(197\) −4.60178e6 2.65684e6i −0.601904 0.347510i 0.167886 0.985806i \(-0.446306\pi\)
−0.769790 + 0.638297i \(0.779639\pi\)
\(198\) 941926. + 1.66308e6i 0.121345 + 0.214248i
\(199\) −1.07663e6 1.86477e6i −0.136617 0.236628i 0.789597 0.613626i \(-0.210290\pi\)
−0.926214 + 0.376998i \(0.876956\pi\)
\(200\) 1.90358e6 2.26860e6i 0.237947 0.283574i
\(201\) −142588. 120654.i −0.0175588 0.0148577i
\(202\) 945603. + 5.36278e6i 0.114724 + 0.650633i
\(203\) −721009. + 127133.i −0.0861891 + 0.0151975i
\(204\) 831979. 983228.i 0.0979991 0.115815i
\(205\) 1.39849e7 + 1.17347e7i 1.62330 + 1.36211i
\(206\) 5.54765e6 3.20294e6i 0.634611 0.366393i
\(207\) 9.60686e6 + 5.65297e6i 1.08310 + 0.637332i
\(208\) 1.38370e6 2.39664e6i 0.153763 0.266325i
\(209\) −463571. 1.27365e6i −0.0507782 0.139512i
\(210\) 1.47296e7 + 60911.4i 1.59050 + 0.00657720i
\(211\) 9.37320e6 7.86505e6i 0.997793 0.837248i 0.0111160 0.999938i \(-0.496462\pi\)
0.986677 + 0.162690i \(0.0520172\pi\)
\(212\) 234619. 644611.i 0.0246238 0.0676534i
\(213\) 3.33556e6 9.04780e6i 0.345168 0.936276i
\(214\) 1.54444e6 8.75895e6i 0.157590 0.893740i
\(215\) 1.96229e7i 1.97446i
\(216\) −131193. + 1.05745e7i −0.0130181 + 1.04930i
\(217\) −1.69473e7 −1.65853
\(218\) −546597. 96379.8i −0.0527591 0.00930286i
\(219\) −3.52098e6 2.04629e7i −0.335221 1.94821i
\(220\) 354485. + 129022.i 0.0332912 + 0.0121170i
\(221\) −3.19878e6 3.81216e6i −0.296352 0.353178i
\(222\) −1.59423e7 9.29239e6i −1.45711 0.849315i
\(223\) −9.19176e6 + 3.34553e6i −0.828865 + 0.301682i −0.721393 0.692526i \(-0.756498\pi\)
−0.107472 + 0.994208i \(0.534276\pi\)
\(224\) 3.27591e6 + 1.89135e6i 0.291466 + 0.168278i
\(225\) 3.76435e6 + 1.40548e6i 0.330478 + 0.123389i
\(226\) 4.76733e6 + 8.25725e6i 0.413000 + 0.715336i
\(227\) 3.85892e6 4.59888e6i 0.329904 0.393165i −0.575439 0.817845i \(-0.695169\pi\)
0.905344 + 0.424680i \(0.139613\pi\)
\(228\) 138848. 768842.i 0.0117148 0.0648683i
\(229\) 1.33245e6 + 7.55667e6i 0.110954 + 0.629251i 0.988674 + 0.150078i \(0.0479524\pi\)
−0.877720 + 0.479174i \(0.840936\pi\)
\(230\) −1.64639e7 + 2.90303e6i −1.35316 + 0.238599i
\(231\) 1.58808e6 + 4.42000e6i 0.128836 + 0.358580i
\(232\) 603919. + 506748.i 0.0483632 + 0.0405815i
\(233\) −8.15029e6 + 4.70557e6i −0.644326 + 0.372002i −0.786279 0.617872i \(-0.787995\pi\)
0.141953 + 0.989873i \(0.454662\pi\)
\(234\) 4.18577e6 + 773813.i 0.326684 + 0.0603932i
\(235\) 1.68861e6 2.92476e6i 0.130115 0.225365i
\(236\) 88931.2 + 244336.i 0.00676578 + 0.0185888i
\(237\) 4.09671e6 + 7.16396e6i 0.307744 + 0.538156i
\(238\) −1.84238e7 + 1.54594e7i −1.36662 + 1.14673i
\(239\) 3.04185e6 8.35741e6i 0.222815 0.612178i −0.777036 0.629456i \(-0.783278\pi\)
0.999851 + 0.0172777i \(0.00549994\pi\)
\(240\) −8.94897e6 1.07550e7i −0.647350 0.777993i
\(241\) 3.68622e6 2.09056e7i 0.263348 1.49352i −0.510350 0.859967i \(-0.670484\pi\)
0.773698 0.633555i \(-0.218405\pi\)
\(242\) 1.24089e7i 0.875564i
\(243\) −1.35821e7 + 4.62779e6i −0.946563 + 0.322519i
\(244\) 1.67129e6 0.115049
\(245\) 1.88009e7 + 3.31511e6i 1.27844 + 0.225424i
\(246\) 1.95996e7 1.63084e7i 1.31657 1.09548i
\(247\) −2.83658e6 1.03243e6i −0.188237 0.0685125i
\(248\) 1.17302e7 + 1.39795e7i 0.769042 + 0.916508i
\(249\) −5.30358e6 + 3.03285e6i −0.343535 + 0.196451i
\(250\) 1.03905e7 3.78182e6i 0.664990 0.242037i
\(251\) −1.36443e7 7.87754e6i −0.862840 0.498161i 0.00212263 0.999998i \(-0.499324\pi\)
−0.864962 + 0.501837i \(0.832658\pi\)
\(252\) −492143. + 2.66214e6i −0.0307532 + 0.166353i
\(253\) −2.66528e6 4.61641e6i −0.164582 0.285064i
\(254\) 5.95400e6 7.09570e6i 0.363335 0.433006i
\(255\) −2.36774e7 + 8.50717e6i −1.42795 + 0.513056i
\(256\) −1.00212e6 5.68333e6i −0.0597313 0.338753i
\(257\) 6.88891e6 1.21470e6i 0.405836 0.0715599i 0.0329962 0.999455i \(-0.489495\pi\)
0.372840 + 0.927896i \(0.378384\pi\)
\(258\) 2.69700e7 + 4.87063e6i 1.57044 + 0.283613i
\(259\) −3.47356e7 2.91466e7i −1.99929 1.67760i
\(260\) 727591. 420075.i 0.0413968 0.0239005i
\(261\) −374150. + 1.00210e6i −0.0210438 + 0.0563625i
\(262\) −1.41518e7 + 2.45117e7i −0.786880 + 1.36292i
\(263\) 9.05082e6 + 2.48669e7i 0.497531 + 1.36696i 0.893653 + 0.448758i \(0.148134\pi\)
−0.396122 + 0.918198i \(0.629644\pi\)
\(264\) 2.54676e6 4.36930e6i 0.138413 0.237465i
\(265\) −1.02648e7 + 8.61321e6i −0.551587 + 0.462836i
\(266\) −4.98965e6 + 1.37089e7i −0.265109 + 0.728382i
\(267\) 2.64423e6 454983.i 0.138920 0.0239035i
\(268\) −8940.93 + 50706.5i −0.000464492 + 0.00263427i
\(269\) 2.07069e6i 0.106379i −0.998584 0.0531897i \(-0.983061\pi\)
0.998584 0.0531897i \(-0.0169388\pi\)
\(270\) 1.09907e7 1.85025e7i 0.558386 0.940026i
\(271\) 387902. 0.0194901 0.00974504 0.999953i \(-0.496898\pi\)
0.00974504 + 0.999953i \(0.496898\pi\)
\(272\) 2.24976e7 + 3.96694e6i 1.11797 + 0.197128i
\(273\) 9.81430e6 + 3.61815e6i 0.482360 + 0.177827i
\(274\) −1.11833e6 407040.i −0.0543651 0.0197873i
\(275\) −1.23516e6 1.47201e6i −0.0593918 0.0707804i
\(276\) 12706.3 3.07264e6i 0.000604355 0.146145i
\(277\) −1.24346e7 + 4.52581e6i −0.585048 + 0.212940i −0.617550 0.786532i \(-0.711875\pi\)
0.0325022 + 0.999472i \(0.489652\pi\)
\(278\) −2.24676e7 1.29717e7i −1.04574 0.603756i
\(279\) −1.25573e7 + 2.13403e7i −0.578206 + 0.982623i
\(280\) −1.94876e7 3.37536e7i −0.887739 1.53761i
\(281\) −1.15069e7 + 1.37134e7i −0.518609 + 0.618055i −0.960251 0.279137i \(-0.909952\pi\)
0.441642 + 0.897191i \(0.354396\pi\)
\(282\) −3.60071e6 3.04681e6i −0.160561 0.135862i
\(283\) 3.00492e6 + 1.70417e7i 0.132579 + 0.751891i 0.976515 + 0.215448i \(0.0691212\pi\)
−0.843937 + 0.536443i \(0.819768\pi\)
\(284\) −2.61780e6 + 461590.i −0.114283 + 0.0201512i
\(285\) −9.85804e6 + 1.16502e7i −0.425850 + 0.503266i
\(286\) −1.55939e6 1.30849e6i −0.0666589 0.0559334i
\(287\) 5.42604e7 3.13272e7i 2.29529 1.32518i
\(288\) 4.80891e6 2.72365e6i 0.201312 0.114018i
\(289\) 8.47122e6 1.46726e7i 0.350956 0.607873i
\(290\) −548705. 1.50755e6i −0.0224981 0.0618129i
\(291\) −2.51433e7 103975.i −1.02034 0.00421940i
\(292\) −4.38459e6 + 3.67911e6i −0.176108 + 0.147773i
\(293\) 6.41469e6 1.76242e7i 0.255019 0.700660i −0.744437 0.667692i \(-0.767282\pi\)
0.999456 0.0329671i \(-0.0104956\pi\)
\(294\) 9.22295e6 2.50175e7i 0.362934 0.984467i
\(295\) 881979. 5.00195e6i 0.0343552 0.194838i
\(296\) 4.88266e7i 1.88270i
\(297\) 6.74240e6 + 1.27531e6i 0.257363 + 0.0486794i
\(298\) 4.07304e7 1.53911
\(299\) −1.16915e7 2.06152e6i −0.437377 0.0771214i
\(300\) −187827. 1.09160e6i −0.00695657 0.0404296i
\(301\) 6.32842e7 + 2.30336e7i 2.32058 + 0.844620i
\(302\) −1.81159e7 2.15897e7i −0.657717 0.783836i
\(303\) 1.68907e7 + 9.84519e6i 0.607182 + 0.353913i
\(304\) 1.30216e7 4.73947e6i 0.463493 0.168698i
\(305\) −2.82728e7 1.63233e7i −0.996483 0.575320i
\(306\) 5.81538e6 + 3.46542e7i 0.202962 + 1.20946i
\(307\) 2.63315e7 + 4.56075e7i 0.910040 + 1.57624i 0.814005 + 0.580857i \(0.197283\pi\)
0.0960344 + 0.995378i \(0.469384\pi\)
\(308\) 832195. 991772.i 0.0284822 0.0339437i
\(309\) 4.08726e6 2.26323e7i 0.138534 0.767103i
\(310\) −6.44867e6 3.65722e7i −0.216464 1.22763i
\(311\) −2.62379e7 + 4.62644e6i −0.872263 + 0.153803i −0.591823 0.806068i \(-0.701591\pi\)
−0.280440 + 0.959872i \(0.590480\pi\)
\(312\) −3.80849e6 1.05999e7i −0.125398 0.349011i
\(313\) 2.52090e7 + 2.11529e7i 0.822096 + 0.689821i 0.953462 0.301513i \(-0.0974918\pi\)
−0.131366 + 0.991334i \(0.541936\pi\)
\(314\) 2.13130e7 1.23051e7i 0.688423 0.397461i
\(315\) 3.43263e7 4.02281e7i 1.09824 1.28706i
\(316\) 1.13745e6 1.97012e6i 0.0360471 0.0624354i
\(317\) −3.45348e6 9.48835e6i −0.108412 0.297860i 0.873610 0.486628i \(-0.161773\pi\)
−0.982022 + 0.188767i \(0.939551\pi\)
\(318\) 9.29029e6 + 1.62460e7i 0.288900 + 0.505203i
\(319\) 391862. 328811.i 0.0120715 0.0101292i
\(320\) −1.41778e7 + 3.89533e7i −0.432674 + 1.18876i
\(321\) −2.04239e7 2.45457e7i −0.617481 0.742096i
\(322\) −9.96317e6 + 5.65040e7i −0.298421 + 1.69243i
\(323\) 2.49186e7i 0.739461i
\(324\) 2.98754e6 + 2.59225e6i 0.0878372 + 0.0762152i
\(325\) −4.27959e6 −0.124667
\(326\) −1.78829e7 3.15325e6i −0.516162 0.0910133i
\(327\) −1.53176e6 + 1.27454e6i −0.0438073 + 0.0364511i
\(328\) −6.33977e7 2.30749e7i −1.79660 0.653910i
\(329\) −7.45029e6 8.87891e6i −0.209211 0.249329i
\(330\) −8.93403e6 + 5.10892e6i −0.248603 + 0.142163i
\(331\) 2.27743e7 8.28916e6i 0.628001 0.228574i −0.00835975 0.999965i \(-0.502661\pi\)
0.636361 + 0.771391i \(0.280439\pi\)
\(332\) 1.45851e6 + 842069.i 0.0398560 + 0.0230109i
\(333\) −6.24393e7 + 2.21430e7i −1.69093 + 0.599657i
\(334\) −7.91734e6 1.37132e7i −0.212491 0.368045i
\(335\) 646496. 770464.i 0.0171962 0.0204936i
\(336\) −4.51893e7 + 1.62363e7i −1.19129 + 0.428024i
\(337\) −8.00076e6 4.53746e7i −0.209046 1.18556i −0.890945 0.454112i \(-0.849957\pi\)
0.681899 0.731447i \(-0.261154\pi\)
\(338\) 3.12836e7 5.51614e6i 0.810151 0.142852i
\(339\) 3.36865e7 + 6.08358e6i 0.864682 + 0.156156i
\(340\) 5.31281e6 + 4.45798e6i 0.135172 + 0.113423i
\(341\) 1.02547e7 5.92055e6i 0.258618 0.149313i
\(342\) 1.35653e7 + 1.64408e7i 0.339119 + 0.411002i
\(343\) 3.40888e6 5.90436e6i 0.0844753 0.146316i
\(344\) −2.48026e7 6.81445e7i −0.609287 1.67400i
\(345\) −3.02251e7 + 5.18549e7i −0.736054 + 1.26279i
\(346\) −2.55227e7 + 2.14161e7i −0.616167 + 0.517025i
\(347\) −8.46370e6 + 2.32538e7i −0.202568 + 0.556552i −0.998828 0.0484031i \(-0.984587\pi\)
0.796259 + 0.604955i \(0.206809\pi\)
\(348\) 290593. 50001.3i 0.00689521 0.00118643i
\(349\) −5.33348e6 + 3.02476e7i −0.125468 + 0.711566i 0.855560 + 0.517703i \(0.173213\pi\)
−0.981029 + 0.193863i \(0.937898\pi\)
\(350\) 2.06829e7i 0.482400i
\(351\) 1.18280e7 9.67737e6i 0.273520 0.223788i
\(352\) −2.64296e6 −0.0605987
\(353\) −7.67559e7 1.35341e7i −1.74497 0.307685i −0.791947 0.610589i \(-0.790933\pi\)
−0.953021 + 0.302904i \(0.902044\pi\)
\(354\) −6.65585e6 2.45375e6i −0.150035 0.0553121i
\(355\) 4.87930e7 + 1.77592e7i 1.09062 + 0.396952i
\(356\) −475416. 566578.i −0.0105372 0.0125577i
\(357\) −357067. + 8.63459e7i −0.00784774 + 1.89774i
\(358\) −7.40444e6 + 2.69499e6i −0.161377 + 0.0587366i
\(359\) −5.88565e7 3.39808e7i −1.27207 0.734430i −0.296693 0.954973i \(-0.595884\pi\)
−0.975377 + 0.220543i \(0.929217\pi\)
\(360\) −5.69424e7 470956.i −1.22047 0.0100942i
\(361\) 1.59653e7 + 2.76527e7i 0.339356 + 0.587782i
\(362\) −2.29067e7 + 2.72991e7i −0.482877 + 0.575471i
\(363\) 3.40090e7 + 2.87775e7i 0.711008 + 0.601634i
\(364\) −500694. 2.83958e6i −0.0103817 0.0588776i
\(365\) 1.10106e8 1.94147e7i 2.26430 0.399257i
\(366\) −2.94527e7 + 3.48070e7i −0.600733 + 0.709943i
\(367\) 4.51765e6 + 3.79076e6i 0.0913933 + 0.0766881i 0.687340 0.726336i \(-0.258778\pi\)
−0.595946 + 0.803024i \(0.703223\pi\)
\(368\) 4.71974e7 2.72494e7i 0.947053 0.546781i
\(369\) 757083. 9.15373e7i 0.0150683 1.82188i
\(370\) 4.96808e7 8.60496e7i 0.980806 1.69881i
\(371\) 1.57288e7 + 4.32145e7i 0.308016 + 0.846267i
\(372\) 6.82543e6 + 28225.2i 0.132587 + 0.000548288i
\(373\) 1.57238e7 1.31939e7i 0.302993 0.254241i −0.478596 0.878035i \(-0.658854\pi\)
0.781589 + 0.623794i \(0.214410\pi\)
\(374\) 5.74735e6 1.57907e7i 0.109863 0.301847i
\(375\) 1.37317e7 3.72475e7i 0.260393 0.706323i
\(376\) −2.16726e6 + 1.22912e7i −0.0407707 + 0.231222i
\(377\) 1.13926e6i 0.0212618i
\(378\) −4.67699e7 5.71637e7i −0.865947 1.05839i
\(379\) 5.78283e6 0.106224 0.0531120 0.998589i \(-0.483086\pi\)
0.0531120 + 0.998589i \(0.483086\pi\)
\(380\) 4.14299e6 + 730522.i 0.0755029 + 0.0133132i
\(381\) −5.63924e6 3.27737e7i −0.101964 0.592584i
\(382\) 4.45077e6 + 1.61995e6i 0.0798445 + 0.0290610i
\(383\) 4.90584e7 + 5.84656e7i 0.873207 + 1.04065i 0.998820 + 0.0485686i \(0.0154660\pi\)
−0.125612 + 0.992079i \(0.540090\pi\)
\(384\) 3.87010e7 + 2.25579e7i 0.683485 + 0.398388i
\(385\) −2.37645e7 + 8.64959e6i −0.416435 + 0.151570i
\(386\) 5.71930e7 + 3.30204e7i 0.994446 + 0.574144i
\(387\) 7.58950e7 6.26212e7i 1.30942 1.08041i
\(388\) 3.46551e6 + 6.00244e6i 0.0593297 + 0.102762i
\(389\) 3.04941e7 3.63415e7i 0.518044 0.617381i −0.442073 0.896979i \(-0.645757\pi\)
0.960117 + 0.279598i \(0.0902011\pi\)
\(390\) −4.07346e6 + 2.25559e7i −0.0686705 + 0.380248i
\(391\) −1.70178e7 9.65125e7i −0.284690 1.61456i
\(392\) −6.94802e7 + 1.22512e7i −1.15346 + 0.203386i
\(393\) 3.43595e7 + 9.56307e7i 0.566070 + 1.57550i
\(394\) −3.06121e7 2.56866e7i −0.500501 0.419970i
\(395\) −3.84838e7 + 2.22186e7i −0.624434 + 0.360517i
\(396\) −632227. 1.78277e6i −0.0101809 0.0287084i
\(397\) −5.27862e7 + 9.14284e7i −0.843624 + 1.46120i 0.0431860 + 0.999067i \(0.486249\pi\)
−0.886810 + 0.462133i \(0.847084\pi\)
\(398\) −5.53848e6 1.52168e7i −0.0878499 0.241366i
\(399\) 2.60005e7 + 4.54674e7i 0.409321 + 0.715784i
\(400\) 1.50496e7 1.26281e7i 0.235150 0.197314i
\(401\) 8.83539e6 2.42750e7i 0.137023 0.376467i −0.852135 0.523321i \(-0.824693\pi\)
0.989158 + 0.146855i \(0.0469149\pi\)
\(402\) −898471. 1.07979e6i −0.0138301 0.0166212i
\(403\) 4.57938e6 2.59710e7i 0.0699667 0.396801i
\(404\) 5.38926e6i 0.0817307i
\(405\) −2.52212e7 7.30313e7i −0.379666 1.09937i
\(406\) −5.50596e6 −0.0822726
\(407\) 3.12005e7 + 5.50149e6i 0.462784 + 0.0816014i
\(408\) 7.14720e7 5.94702e7i 1.05234 0.875627i
\(409\) −6.59311e7 2.39970e7i −0.963652 0.350741i −0.188189 0.982133i \(-0.560262\pi\)
−0.775464 + 0.631392i \(0.782484\pi\)
\(410\) 8.82506e7 + 1.05173e8i 1.28046 + 1.52599i
\(411\) −3.70910e6 + 2.12104e6i −0.0534248 + 0.0305509i
\(412\) −5.95737e6 + 2.16831e6i −0.0851850 + 0.0310048i
\(413\) −1.50961e7 8.71573e6i −0.214296 0.123724i
\(414\) 6.37680e7 + 5.44128e7i 0.898674 + 0.766831i
\(415\) −1.64488e7 2.84901e7i −0.230139 0.398612i
\(416\) −3.78358e6 + 4.50910e6i −0.0525561 + 0.0626340i
\(417\) −8.76559e7 + 3.14942e7i −1.20885 + 0.434333i
\(418\) −1.77002e6 1.00383e7i −0.0242354 0.137446i
\(419\) −8.25085e6 + 1.45485e6i −0.112165 + 0.0197777i −0.229449 0.973321i \(-0.573692\pi\)
0.117284 + 0.993098i \(0.462581\pi\)
\(420\) −1.43455e7 2.59072e6i −0.193628 0.0349681i
\(421\) 2.18574e7 + 1.83405e7i 0.292922 + 0.245791i 0.777391 0.629018i \(-0.216543\pi\)
−0.484469 + 0.874809i \(0.660987\pi\)
\(422\) 7.96909e7 4.60096e7i 1.06040 0.612224i
\(423\) −1.67008e7 + 2.80258e6i −0.220656 + 0.0370286i
\(424\) 2.47599e7 4.28854e7i 0.324827 0.562616i
\(425\) −1.20828e7 3.31972e7i −0.157399 0.432449i
\(426\) 3.65195e7 6.26538e7i 0.472385 0.810436i
\(427\) −8.58299e7 + 7.20199e7i −1.10244 + 0.925057i
\(428\) −3.01053e6 + 8.27137e6i −0.0383983 + 0.105498i
\(429\) −7.20254e6 + 1.23931e6i −0.0912250 + 0.0156967i
\(430\) −2.56258e7 + 1.45331e8i −0.322309 + 1.82790i
\(431\) 9.56182e7i 1.19429i 0.802134 + 0.597144i \(0.203698\pi\)
−0.802134 + 0.597144i \(0.796302\pi\)
\(432\) −1.30385e7 + 6.89332e7i −0.161725 + 0.855022i
\(433\) −7.37401e6 −0.0908323 −0.0454161 0.998968i \(-0.514461\pi\)
−0.0454161 + 0.998968i \(0.514461\pi\)
\(434\) −1.25515e8 2.21318e7i −1.53542 0.270736i
\(435\) −5.40424e6 1.99233e6i −0.0656549 0.0242044i
\(436\) 516169. + 187870.i 0.00622777 + 0.00226672i
\(437\) −3.82113e7 4.55385e7i −0.457876 0.545675i
\(438\) 645731. 1.56151e8i 0.00768475 1.85833i
\(439\) −5.65628e7 + 2.05872e7i −0.668555 + 0.243334i −0.653926 0.756559i \(-0.726879\pi\)
−0.0146294 + 0.999893i \(0.504657\pi\)
\(440\) 2.35836e7 + 1.36160e7i 0.276855 + 0.159842i
\(441\) −4.71763e7 8.32951e7i −0.550057 0.971189i
\(442\) −1.87125e7 3.24109e7i −0.216702 0.375340i
\(443\) −9.07636e7 + 1.08168e8i −1.04400 + 1.24419i −0.0749862 + 0.997185i \(0.523891\pi\)
−0.969014 + 0.247006i \(0.920553\pi\)
\(444\) 1.39410e7 + 1.17964e7i 0.159274 + 0.134773i
\(445\) 2.50878e6 + 1.42280e7i 0.0284697 + 0.161459i
\(446\) −7.24450e7 + 1.27740e7i −0.816589 + 0.143987i
\(447\) 9.44578e7 1.11630e8i 1.05758 1.24985i
\(448\) 1.08983e8 + 9.14475e7i 1.21206 + 1.01704i
\(449\) 6.86153e6 3.96151e6i 0.0758023 0.0437645i −0.461620 0.887078i \(-0.652732\pi\)
0.537422 + 0.843313i \(0.319398\pi\)
\(450\) 2.60441e7 + 1.53252e7i 0.285806 + 0.168177i
\(451\) −2.18883e7 + 3.79117e7i −0.238607 + 0.413279i
\(452\) −3.22736e6 8.86710e6i −0.0349488 0.0960210i
\(453\) −1.01183e8 418423.i −1.08846 0.00450113i
\(454\) 3.45857e7 2.90208e7i 0.369597 0.310129i
\(455\) −1.92637e7 + 5.29266e7i −0.204506 + 0.561875i
\(456\) 1.95087e7 5.29178e7i 0.205747 0.558094i
\(457\) 2.45002e7 1.38947e8i 0.256697 1.45580i −0.534982 0.844863i \(-0.679682\pi\)
0.791679 0.610937i \(-0.209207\pi\)
\(458\) 5.77063e7i 0.600657i
\(459\) 1.08463e8 + 6.44283e7i 1.12161 + 0.666252i
\(460\) 1.65452e7 0.169980
\(461\) 6.00137e7 + 1.05820e7i 0.612558 + 0.108011i 0.471316 0.881965i \(-0.343779\pi\)
0.141242 + 0.989975i \(0.454890\pi\)
\(462\) 5.98950e6 + 3.48093e7i 0.0607386 + 0.352996i
\(463\) −7.56770e7 2.75442e7i −0.762467 0.277515i −0.0686251 0.997643i \(-0.521861\pi\)
−0.693842 + 0.720127i \(0.744083\pi\)
\(464\) 3.36171e6 + 4.00633e6i 0.0336517 + 0.0401045i
\(465\) −1.15188e8 6.71406e7i −1.14564 0.667769i
\(466\) −6.65078e7 + 2.42069e7i −0.657226 + 0.239211i
\(467\) −7.67709e7 4.43237e7i −0.753782 0.435196i 0.0732766 0.997312i \(-0.476654\pi\)
−0.827059 + 0.562115i \(0.809988\pi\)
\(468\) −3.94662e6 1.47353e6i −0.0385024 0.0143754i
\(469\) −1.72589e6 2.98934e6i −0.0167300 0.0289772i
\(470\) 1.63257e7 1.94562e7i 0.157245 0.187398i
\(471\) 1.57025e7 8.69490e7i 0.150281 0.832150i
\(472\) 3.25942e6 + 1.84851e7i 0.0309966 + 0.175790i
\(473\) −4.63395e7 + 8.17090e6i −0.437892 + 0.0772123i
\(474\) 2.09855e7 + 5.84077e7i 0.197054 + 0.548447i
\(475\) −1.64158e7 1.37745e7i −0.153173 0.128527i
\(476\) 2.06133e7 1.19011e7i 0.191129 0.110348i
\(477\) 6.60704e7 + 1.22143e7i 0.608768 + 0.112541i
\(478\) 3.34426e7 5.79243e7i 0.306208 0.530368i
\(479\) 6.09968e7 + 1.67587e8i 0.555010 + 1.52488i 0.826786 + 0.562516i \(0.190166\pi\)
−0.271777 + 0.962360i \(0.587611\pi\)
\(480\) 1.47728e7 + 2.58334e7i 0.133579 + 0.233592i
\(481\) 5.40517e7 4.53547e7i 0.485707 0.407556i
\(482\) 5.46018e7 1.50017e8i 0.487602 1.33968i
\(483\) 1.31754e8 + 1.58344e8i 1.16929 + 1.40527i
\(484\) 2.13253e6 1.20942e7i 0.0188087 0.106669i
\(485\) 1.35389e8i 1.18675i
\(486\) −1.06636e8 + 1.65373e7i −0.928952 + 0.144064i
\(487\) −3.83723e6 −0.0332224 −0.0166112 0.999862i \(-0.505288\pi\)
−0.0166112 + 0.999862i \(0.505288\pi\)
\(488\) 1.18815e8 + 2.09503e7i 1.02238 + 0.180273i
\(489\) −5.01143e7 + 4.16990e7i −0.428583 + 0.356614i
\(490\) 1.34914e8 + 4.91048e7i 1.14675 + 0.417384i
\(491\) −3.89588e6 4.64293e6i −0.0329125 0.0392236i 0.749337 0.662189i \(-0.230372\pi\)
−0.782250 + 0.622965i \(0.785928\pi\)
\(492\) −2.19052e7 + 1.25265e7i −0.183929 + 0.105180i
\(493\) 8.83738e6 3.21654e6i 0.0737535 0.0268441i
\(494\) −1.96600e7 1.13507e7i −0.163081 0.0941547i
\(495\) −6.71688e6 + 3.63335e7i −0.0553799 + 0.299566i
\(496\) 6.05307e7 + 1.04842e8i 0.496056 + 0.859194i
\(497\) 1.14547e8 1.36512e8i 0.933074 1.11199i
\(498\) −4.32401e7 + 1.55359e7i −0.350105 + 0.125791i
\(499\) 3.10166e7 + 1.75904e8i 0.249628 + 1.41571i 0.809495 + 0.587126i \(0.199741\pi\)
−0.559868 + 0.828582i \(0.689148\pi\)
\(500\) −1.07768e7 + 1.90025e6i −0.0862147 + 0.0152020i
\(501\) −5.59448e7 1.01033e7i −0.444884 0.0803434i
\(502\) −9.07650e7 7.61609e7i −0.717476 0.602034i
\(503\) −3.54035e7 + 2.04402e7i −0.278191 + 0.160613i −0.632604 0.774475i \(-0.718014\pi\)
0.354413 + 0.935089i \(0.384681\pi\)
\(504\) −6.83583e7 + 1.83087e8i −0.533949 + 1.43010i
\(505\) −5.26363e7 + 9.11687e7i −0.408706 + 0.707899i
\(506\) −1.37110e7 3.76707e7i −0.105832 0.290771i
\(507\) 5.74315e7 9.85311e7i 0.440683 0.756048i
\(508\) −7.02240e6 + 5.89250e6i −0.0535667 + 0.0449478i
\(509\) −3.96572e7 + 1.08957e8i −0.300724 + 0.826233i 0.693650 + 0.720312i \(0.256001\pi\)
−0.994375 + 0.105921i \(0.966221\pi\)
\(510\) −1.86470e8 + 3.20851e7i −1.40572 + 0.241876i
\(511\) 6.66311e7 3.77884e8i 0.499360 2.83201i
\(512\) 1.49582e8i 1.11448i
\(513\) 7.65183e7 + 949324.i 0.566779 + 0.00703173i
\(514\) 5.26069e7 0.387395
\(515\) 1.21957e8 + 2.15043e7i 0.892863 + 0.157436i
\(516\) −2.54489e7 9.38201e6i −0.185234 0.0682884i
\(517\) 7.60995e6 + 2.76979e6i 0.0550693 + 0.0200436i
\(518\) −2.19196e8 2.61227e8i −1.57704 1.87944i
\(519\) −494648. + 1.19616e8i −0.00353830 + 0.855631i
\(520\) 5.69915e7 2.07432e7i 0.405322 0.147525i
\(521\) 5.03955e7 + 2.90958e7i 0.356351 + 0.205739i 0.667479 0.744629i \(-0.267373\pi\)
−0.311128 + 0.950368i \(0.600707\pi\)
\(522\) −4.07968e6 + 6.93316e6i −0.0286824 + 0.0487438i
\(523\) −7.31377e7 1.26678e8i −0.511254 0.885517i −0.999915 0.0130438i \(-0.995848\pi\)
0.488661 0.872474i \(-0.337485\pi\)
\(524\) 1.80053e7 2.14579e7i 0.125143 0.149140i
\(525\) 5.66855e7 + 4.79656e7i 0.391736 + 0.331476i
\(526\) 3.45581e7 + 1.95989e8i 0.237461 + 1.34671i
\(527\) 2.14389e8 3.78025e7i 1.46477 0.258279i
\(528\) 2.16715e7 2.56113e7i 0.147227 0.173992i
\(529\) −6.56947e7 5.51244e7i −0.443775 0.372372i
\(530\) −8.72714e7 + 5.03862e7i −0.586198 + 0.338442i
\(531\) −2.21605e7 + 1.25512e7i −0.148012 + 0.0838301i
\(532\) 7.21903e6 1.25037e7i 0.0479451 0.0830433i
\(533\) 3.33456e7 + 9.16163e7i 0.220220 + 0.605050i
\(534\) 2.01779e7 + 83441.7i 0.132511 + 0.000547973i
\(535\) 1.31714e8 1.10521e8i 0.860142 0.721745i
\(536\) −1.27125e6 + 3.49274e6i −0.00825539 + 0.0226815i
\(537\) −9.78544e6 + 2.65432e7i −0.0631913 + 0.171408i
\(538\) 2.70414e6 1.53359e7i 0.0173653 0.0984834i
\(539\) 4.57788e7i 0.292346i
\(540\) −1.38917e7 + 1.61444e7i −0.0882213 + 0.102528i
\(541\) 1.88227e8 1.18875 0.594373 0.804189i \(-0.297400\pi\)
0.594373 + 0.804189i \(0.297400\pi\)
\(542\) 2.87288e6 + 506566.i 0.0180434 + 0.00318154i
\(543\) 2.16957e7 + 1.26089e8i 0.135511 + 0.787552i
\(544\) −4.56600e7 1.66189e7i −0.283621 0.103230i
\(545\) −6.89699e6 8.21951e6i −0.0426059 0.0507758i
\(546\) 6.79617e7 + 3.96133e7i 0.417529 + 0.243368i
\(547\) 4.38270e6 1.59517e6i 0.0267781 0.00974643i −0.328596 0.944470i \(-0.606576\pi\)
0.355374 + 0.934724i \(0.384353\pi\)
\(548\) 1.02002e6 + 588907.i 0.00619820 + 0.00357853i
\(549\) 2.70917e7 + 1.61442e8i 0.163727 + 0.975659i
\(550\) −7.22556e6 1.25150e7i −0.0434293 0.0752218i
\(551\) 3.66689e6 4.37003e6i 0.0219201 0.0261234i
\(552\) 3.94201e7 2.18280e8i 0.234369 1.29777i
\(553\) 2.64828e7 + 1.50191e8i 0.156599 + 0.888115i
\(554\) −9.80032e7 + 1.72806e7i −0.576383 + 0.101632i
\(555\) −1.20621e8 3.35717e8i −0.705577 1.96379i
\(556\) 1.96685e7 + 1.65038e7i 0.114432 + 0.0960196i
\(557\) −1.68576e8 + 9.73273e7i −0.975506 + 0.563209i −0.900910 0.434005i \(-0.857100\pi\)
−0.0745956 + 0.997214i \(0.523767\pi\)
\(558\) −1.20870e8 + 1.41652e8i −0.695691 + 0.815302i
\(559\) −5.23979e7 + 9.07559e7i −0.299971 + 0.519564i
\(560\) −8.84319e7 2.42965e8i −0.503553 1.38350i
\(561\) −2.99488e7 5.23719e7i −0.169626 0.296626i
\(562\) −1.03131e8 + 8.65373e7i −0.581006 + 0.487522i
\(563\) −1.48600e7 + 4.08274e7i −0.0832708 + 0.228785i −0.974339 0.225084i \(-0.927734\pi\)
0.891069 + 0.453869i \(0.149957\pi\)
\(564\) 2.98577e6 + 3.58833e6i 0.0166425 + 0.0200012i
\(565\) −3.20075e7 + 1.81524e8i −0.177462 + 1.00644i
\(566\) 1.30139e8i 0.717724i
\(567\) −2.65132e8 4.38598e6i −1.45450 0.0240612i
\(568\) −1.91890e8 −1.04715
\(569\) 4.85439e7 + 8.55960e6i 0.263511 + 0.0464640i 0.303842 0.952722i \(-0.401730\pi\)
−0.0403318 + 0.999186i \(0.512841\pi\)
\(570\) −8.82248e7 + 7.34098e7i −0.476394 + 0.396396i
\(571\) −9.17986e7 3.34120e7i −0.493092 0.179471i 0.0834924 0.996508i \(-0.473393\pi\)
−0.576584 + 0.817038i \(0.695615\pi\)
\(572\) 1.29497e6 + 1.54329e6i 0.00691946 + 0.00824629i
\(573\) 1.47615e7 8.44138e6i 0.0784635 0.0448693i
\(574\) 4.42774e8 1.61156e8i 2.34124 0.852142i
\(575\) −7.29875e7 4.21393e7i −0.383923 0.221658i
\(576\) 1.95903e8 6.94736e7i 1.02512 0.363540i
\(577\) 9.04646e7 + 1.56689e8i 0.470925 + 0.815665i 0.999447 0.0332541i \(-0.0105871\pi\)
−0.528522 + 0.848919i \(0.677254\pi\)
\(578\) 8.19007e7 9.76054e7i 0.424135 0.505464i
\(579\) 2.23135e8 8.01710e7i 1.14956 0.413030i
\(580\) 275707. + 1.56361e6i 0.00141307 + 0.00801393i
\(581\) −1.11189e8 + 1.96056e7i −0.566934 + 0.0999658i
\(582\) −1.86081e8 3.36050e7i −0.943914 0.170465i
\(583\) −2.46143e7 2.06538e7i −0.124217 0.104231i
\(584\) −3.57827e8 + 2.06592e8i −1.79653 + 1.03723i
\(585\) 5.23721e7 + 6.34735e7i 0.261597 + 0.317048i
\(586\) 7.05242e7 1.22151e8i 0.350466 0.607024i
\(587\) −1.75536e7 4.82280e7i −0.0867863 0.238443i 0.888706 0.458478i \(-0.151605\pi\)
−0.975492 + 0.220035i \(0.929383\pi\)
\(588\) −1.32884e7 + 2.27979e7i −0.0653642 + 0.112141i
\(589\) 1.01157e8 8.48809e7i 0.495052 0.415398i
\(590\) 1.30642e7 3.58937e7i 0.0636103 0.174768i
\(591\) −1.41392e8 + 2.43287e7i −0.684954 + 0.117857i
\(592\) −5.62464e7 + 3.18989e8i −0.271100 + 1.53748i
\(593\) 2.89171e8i 1.38672i −0.720589 0.693362i \(-0.756129\pi\)
0.720589 0.693362i \(-0.243871\pi\)
\(594\) 4.82702e7 + 1.82502e7i 0.230314 + 0.0870779i
\(595\) −4.64946e8 −2.20725
\(596\) −3.96973e7 6.99971e6i −0.187509 0.0330629i
\(597\) −5.45490e7 2.01100e7i −0.256368 0.0945127i
\(598\) −8.38973e7 3.05361e7i −0.392324 0.142794i
\(599\) −1.31785e8 1.57055e8i −0.613175 0.730754i 0.366706 0.930337i \(-0.380486\pi\)
−0.979881 + 0.199583i \(0.936041\pi\)
\(600\) 330652. 7.99582e7i 0.00153080 0.370177i
\(601\) 1.69067e7 6.15352e6i 0.0778815 0.0283466i −0.302786 0.953059i \(-0.597917\pi\)
0.380667 + 0.924712i \(0.375694\pi\)
\(602\) 4.38616e8 + 2.53235e8i 2.01046 + 1.16074i
\(603\) −5.04302e6 41709.6i −0.0230006 0.000190232i
\(604\) 1.39461e7 + 2.41554e7i 0.0632910 + 0.109623i
\(605\) −1.54198e8 + 1.83766e8i −0.696325 + 0.829848i
\(606\) 1.12239e8 + 9.49732e7i 0.504342 + 0.426760i
\(607\) 5.33230e6 + 3.02410e7i 0.0238423 + 0.135216i 0.994405 0.105630i \(-0.0336860\pi\)
−0.970563 + 0.240847i \(0.922575\pi\)
\(608\) −2.90264e7 + 5.11814e6i −0.129147 + 0.0227720i
\(609\) −1.27688e7 + 1.50901e7i −0.0565327 + 0.0668100i
\(610\) −1.88077e8 1.57816e8i −0.828605 0.695282i
\(611\) 1.56196e7 9.01801e6i 0.0684774 0.0395355i
\(612\) 287613. 3.47746e7i 0.00125474 0.151708i
\(613\) −4.37849e6 + 7.58376e6i −0.0190083 + 0.0329233i −0.875373 0.483448i \(-0.839384\pi\)
0.856365 + 0.516371i \(0.172718\pi\)
\(614\) 1.35457e8 + 3.72165e8i 0.585189 + 1.60779i
\(615\) 4.92908e8 + 2.03833e6i 2.11905 + 0.00876291i
\(616\) 7.15944e7 6.00749e7i 0.306293 0.257010i
\(617\) 9.24068e7 2.53886e8i 0.393413 1.08089i −0.572020 0.820240i \(-0.693840\pi\)
0.965433 0.260653i \(-0.0839378\pi\)
\(618\) 5.98269e7 1.62282e8i 0.253473 0.687551i
\(619\) 2.10547e6 1.19407e7i 0.00887724 0.0503453i −0.980047 0.198764i \(-0.936307\pi\)
0.988925 + 0.148419i \(0.0474183\pi\)
\(620\) 3.67528e7i 0.154211i
\(621\) 2.97013e8 4.85802e7i 1.24022 0.202854i
\(622\) −2.00365e8 −0.832626
\(623\) 4.88303e7 + 8.61010e6i 0.201941 + 0.0356077i
\(624\) −1.26705e7 7.36376e7i −0.0521485 0.303072i
\(625\) 2.81798e8 + 1.02566e8i 1.15424 + 0.420110i
\(626\) 1.59079e8 + 1.89583e8i 0.648471 + 0.772817i
\(627\) −3.16167e7 1.84287e7i −0.128267 0.0747638i
\(628\) −2.28871e7 + 8.33021e6i −0.0924084 + 0.0336339i
\(629\) 5.04429e8 + 2.91232e8i 2.02697 + 1.17027i
\(630\) 3.06762e8 2.53110e8i 1.22682 1.01225i
\(631\) −1.17821e8 2.04072e8i −0.468959 0.812261i 0.530411 0.847741i \(-0.322038\pi\)
−0.999370 + 0.0354793i \(0.988704\pi\)
\(632\) 1.05559e8 1.25801e8i 0.418163 0.498347i
\(633\) 5.87127e7 3.25109e8i 0.231484 1.28179i
\(634\) −1.31862e7 7.47826e7i −0.0517430 0.293449i
\(635\) 1.76347e8 3.10948e7i 0.688728 0.121441i
\(636\) −6.26269e6 1.74305e7i −0.0243439 0.0677547i
\(637\) 7.81021e7 + 6.55355e7i 0.302165 + 0.253547i
\(638\) 3.33161e6 1.92350e6i 0.0128290 0.00740681i
\(639\) −8.70227e7 2.45389e8i −0.333526 0.940486i
\(640\) −1.20604e8 + 2.08892e8i −0.460066 + 0.796858i
\(641\) −1.25610e7 3.45111e7i −0.0476926 0.131034i 0.913560 0.406705i \(-0.133322\pi\)
−0.961252 + 0.275671i \(0.911100\pi\)
\(642\) −1.19209e8 2.08462e8i −0.450509 0.787811i
\(643\) 3.51780e8 2.95178e8i 1.32324 1.11033i 0.337629 0.941279i \(-0.390375\pi\)
0.985608 0.169049i \(-0.0540695\pi\)
\(644\) 1.94209e7 5.33585e7i 0.0727130 0.199777i
\(645\) 3.38880e8 + 4.07269e8i 1.26289 + 1.51776i
\(646\) 3.25415e7 1.84552e8i 0.120709 0.684575i
\(647\) 3.08588e8i 1.13937i 0.821862 + 0.569687i \(0.192936\pi\)
−0.821862 + 0.569687i \(0.807064\pi\)
\(648\) 1.79895e8 + 2.21737e8i 0.661139 + 0.814918i
\(649\) 1.21793e7 0.0445543
\(650\) −3.16955e7 5.58877e6i −0.115414 0.0203506i
\(651\) −3.51739e8 + 2.92674e8i −1.27490 + 1.06082i
\(652\) 1.68874e7 + 6.14653e6i 0.0609286 + 0.0221762i
\(653\) −4.26290e7 5.08033e7i −0.153097 0.182454i 0.684045 0.729440i \(-0.260219\pi\)
−0.837141 + 0.546987i \(0.815775\pi\)
\(654\) −1.30089e7 + 7.43916e6i −0.0465060 + 0.0265944i
\(655\) −5.14168e8 + 1.87142e8i −1.82970 + 0.665958i
\(656\) −3.87602e8 2.23782e8i −1.37301 0.792710i
\(657\) −4.26464e8 3.63898e8i −1.50379 1.28317i
\(658\) −4.35833e7 7.54884e7i −0.152983 0.264974i
\(659\) −2.56591e8 + 3.05793e8i −0.896573 + 1.06849i 0.100717 + 0.994915i \(0.467886\pi\)
−0.997289 + 0.0735785i \(0.976558\pi\)
\(660\) 9.58541e6 3.44398e6i 0.0333410 0.0119792i
\(661\) 1.52381e7 + 8.64194e7i 0.0527625 + 0.299231i 0.999758 0.0220169i \(-0.00700877\pi\)
−0.946995 + 0.321248i \(0.895898\pi\)
\(662\) 1.79496e8 3.16500e7i 0.618700 0.109094i
\(663\) −1.32224e8 2.38789e7i −0.453702 0.0819359i
\(664\) 9.31321e7 + 7.81471e7i 0.318123 + 0.266937i
\(665\) −2.44245e8 + 1.41015e8i −0.830540 + 0.479512i
\(666\) −4.91354e8 + 8.24549e7i −1.66331 + 0.279122i
\(667\) 1.12178e7 1.94299e7i 0.0378035 0.0654776i
\(668\) 5.35984e6 + 1.47260e7i 0.0179813 + 0.0494033i
\(669\) −1.32997e8 + 2.28174e8i −0.444185 + 0.762056i
\(670\) 5.79424e6 4.86194e6i 0.0192651 0.0161654i
\(671\) 2.67748e7 7.35632e7i 0.0886255 0.243497i
\(672\) 1.00654e8 1.73191e7i 0.331682 0.0570712i
\(673\) 2.82148e6 1.60014e7i 0.00925618 0.0524944i −0.979830 0.199834i \(-0.935960\pi\)
0.989086 + 0.147339i \(0.0470709\pi\)
\(674\) 3.46502e8i 1.13169i
\(675\) 1.02400e8 3.58384e7i 0.332958 0.116530i
\(676\) −3.14380e7 −0.101769
\(677\) 8.29921e7 + 1.46337e7i 0.267467 + 0.0471617i 0.305773 0.952104i \(-0.401085\pi\)
−0.0383060 + 0.999266i \(0.512196\pi\)
\(678\) 2.41544e8 + 8.90478e7i 0.775011 + 0.285716i
\(679\) −4.36631e8 1.58921e8i −1.39478 0.507658i
\(680\) 3.21815e8 + 3.83524e8i 1.02348 + 1.21973i
\(681\) 670295. 1.62091e8i 0.00212239 0.513236i
\(682\) 8.36800e7 3.04570e7i 0.263796 0.0960139i
\(683\) −2.94407e7 1.69976e7i −0.0924031 0.0533489i 0.453086 0.891467i \(-0.350323\pi\)
−0.545489 + 0.838118i \(0.683656\pi\)
\(684\) −1.03958e7 1.83550e7i −0.0324856 0.0573570i
\(685\) −1.15036e7 1.99247e7i −0.0357899 0.0619899i
\(686\) 3.29575e7 3.92772e7i 0.102090 0.121666i
\(687\) 1.58155e8 + 1.33826e8i 0.487768 + 0.412735i
\(688\) −8.35379e7 4.73767e8i −0.256518 1.45479i
\(689\) −7.04741e7 + 1.24265e7i −0.215463 + 0.0379919i
\(690\) −2.91571e8 + 3.44577e8i −0.887558 + 1.04891i
\(691\) 2.23677e8 + 1.87687e8i 0.677934 + 0.568854i 0.915402 0.402541i \(-0.131873\pi\)
−0.237468 + 0.971395i \(0.576317\pi\)
\(692\) 2.85558e7 1.64867e7i 0.0861739 0.0497525i
\(693\) 1.09292e8 + 6.43107e7i 0.328388 + 0.193234i
\(694\) −9.30513e7 + 1.61170e8i −0.278384 + 0.482175i
\(695\) −1.71536e8 4.71290e8i −0.510975 1.40389i
\(696\) 2.12856e7 + 88022.3i 0.0631331 + 0.000261075i
\(697\) −6.16531e8 + 5.17331e8i −1.82078 + 1.52781i
\(698\) −7.90016e7 + 2.17055e8i −0.232311 + 0.638269i
\(699\) −8.78943e7 + 2.38415e8i −0.257353 + 0.698076i
\(700\) 3.55445e6 2.01583e7i 0.0103628 0.0587705i
\(701\) 2.39283e8i 0.694638i −0.937747 0.347319i \(-0.887092\pi\)
0.937747 0.347319i \(-0.112908\pi\)
\(702\) 1.00238e8 5.62263e7i 0.289749 0.162528i
\(703\) 3.53314e8 1.01694
\(704\) −9.78917e7 1.72610e7i −0.280561 0.0494706i
\(705\) −1.54626e7 8.98644e7i −0.0441282 0.256460i
\(706\) −5.50795e8 2.00473e8i −1.56522 0.569694i
\(707\) 2.32235e8 + 2.76767e8i 0.657159 + 0.783171i
\(708\) 6.06533e6 + 3.53535e6i 0.0170905 + 0.00996167i
\(709\) 1.85616e8 6.75588e7i 0.520808 0.189558i −0.0682216 0.997670i \(-0.521733\pi\)
0.589029 + 0.808112i \(0.299510\pi\)
\(710\) 3.38179e8 + 1.95248e8i 0.944868 + 0.545520i
\(711\) 2.08745e8 + 7.79380e7i 0.580774 + 0.216841i
\(712\) −2.66958e7 4.62386e7i −0.0739612 0.128105i
\(713\) 3.33825e8 3.97838e8i 0.920981 1.09758i
\(714\) −1.15405e8 + 6.39029e8i −0.317051 + 1.75560i
\(715\) −6.83359e6 3.87552e7i −0.0186952 0.106026i
\(716\) 7.67977e6 1.35415e6i 0.0209223 0.00368916i
\(717\) −8.11961e7 2.25988e8i −0.220281 0.613095i
\(718\) −3.91527e8 3.28530e8i −1.05776 0.887569i
\(719\) −9.46559e7 + 5.46496e7i −0.254660 + 0.147028i −0.621896 0.783100i \(-0.713637\pi\)
0.367236 + 0.930128i \(0.380304\pi\)
\(720\) −3.71468e8 6.86723e7i −0.995231 0.183986i
\(721\) 2.12506e8 3.68071e8i 0.566976 0.982032i
\(722\) 8.21303e7 + 2.25651e8i 0.218219 + 0.599551i
\(723\) −2.84524e8 4.97551e8i −0.752843 1.31651i
\(724\) 2.70171e7 2.26701e7i 0.0711908 0.0597362i
\(725\) 2.76615e6 7.59992e6i 0.00725874 0.0199432i
\(726\) 2.14297e8 + 2.57545e8i 0.560023 + 0.673043i
\(727\) −6.00966e7 + 3.40825e8i −0.156404 + 0.887009i 0.801088 + 0.598547i \(0.204255\pi\)
−0.957491 + 0.288462i \(0.906856\pi\)
\(728\) 2.08147e8i 0.539481i
\(729\) −2.01974e8 + 3.30607e8i −0.521331 + 0.853354i
\(730\) 8.40823e8 2.16140
\(731\) −8.51941e8 1.50220e8i −2.18101 0.384571i
\(732\) 3.46874e7 2.88626e7i 0.0884378 0.0735871i
\(733\) 5.91331e8 + 2.15227e8i 1.50148 + 0.546493i 0.956442 0.291921i \(-0.0942946\pi\)
0.545034 + 0.838414i \(0.316517\pi\)
\(734\) 2.85082e7 + 3.39748e7i 0.0720912 + 0.0859149i
\(735\) 4.47460e8 2.55880e8i 1.12692 0.644428i
\(736\) −1.08927e8 + 3.96463e7i −0.273215 + 0.0994420i
\(737\) 2.08865e6 + 1.20588e6i 0.00521750 + 0.00301233i
\(738\) 1.25147e8 6.76955e8i 0.311352 1.68419i
\(739\) 5.36635e7 + 9.29479e7i 0.132967 + 0.230306i 0.924819 0.380407i \(-0.124216\pi\)
−0.791852 + 0.610713i \(0.790883\pi\)
\(740\) −6.32087e7 + 7.53292e7i −0.155985 + 0.185895i
\(741\) −7.67022e7 + 2.75587e7i −0.188518 + 0.0677335i
\(742\) 6.00562e7 + 3.40595e8i 0.147010 + 0.833733i
\(743\) −6.67182e8 + 1.17642e8i −1.62659 + 0.286811i −0.911215 0.411931i \(-0.864854\pi\)
−0.715373 + 0.698742i \(0.753743\pi\)
\(744\) 4.84878e8 + 8.75660e7i 1.17737 + 0.212626i
\(745\) 6.03184e8 + 5.06131e8i 1.45875 + 1.22404i
\(746\) 1.33684e8 7.71825e7i 0.322005 0.185910i
\(747\) −5.76987e7 + 1.54537e8i −0.138422 + 0.370741i
\(748\) −8.31527e6 + 1.44025e7i −0.0198688 + 0.0344138i
\(749\) −2.01825e8 5.54510e8i −0.480319 1.31966i
\(750\) 1.50342e8 2.57930e8i 0.356365 0.611390i
\(751\) 1.15180e8 9.66475e7i 0.271930 0.228176i −0.496617 0.867970i \(-0.665425\pi\)
0.768547 + 0.639793i \(0.220980\pi\)
\(752\) −2.83179e7 + 7.78028e7i −0.0665898 + 0.182954i
\(753\) −4.19226e8 + 7.21347e7i −0.981892 + 0.168950i
\(754\) 1.48778e6 8.43761e6i 0.00347076 0.0196836i
\(755\) 5.44840e8i 1.26598i
\(756\) 3.57598e7 + 6.37514e7i 0.0827617 + 0.147545i
\(757\) 7.40692e8 1.70746 0.853729 0.520717i \(-0.174335\pi\)
0.853729 + 0.520717i \(0.174335\pi\)
\(758\) 4.28288e7 + 7.55187e6i 0.0983395 + 0.0173399i
\(759\) −1.35041e8 4.97842e7i −0.308844