Properties

Label 72.7.p.b.43.14
Level $72$
Weight $7$
Character 72.43
Analytic conductor $16.564$
Analytic rank $0$
Dimension $136$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [72,7,Mod(43,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.43");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 72.p (of order \(6\), degree \(2\), 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: \(16.5638940206\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(68\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.14
Character \(\chi\) \(=\) 72.43
Dual form 72.7.p.b.67.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.67572 - 4.40849i) q^{2} +(25.5449 - 8.74402i) q^{3} +(25.1304 + 58.8597i) q^{4} +(171.291 - 98.8948i) q^{5} +(-209.079 - 54.2419i) q^{6} +(-265.898 - 153.516i) q^{7} +(91.7187 - 503.718i) q^{8} +(576.084 - 446.730i) q^{9} +O(q^{10})\) \(q+(-6.67572 - 4.40849i) q^{2} +(25.5449 - 8.74402i) q^{3} +(25.1304 + 58.8597i) q^{4} +(171.291 - 98.8948i) q^{5} +(-209.079 - 54.2419i) q^{6} +(-265.898 - 153.516i) q^{7} +(91.7187 - 503.718i) q^{8} +(576.084 - 446.730i) q^{9} +(-1579.47 - 94.9401i) q^{10} +(-476.183 + 824.774i) q^{11} +(1156.62 + 1283.82i) q^{12} +(2219.23 - 1281.27i) q^{13} +(1098.29 + 2197.04i) q^{14} +(3510.87 - 4024.03i) q^{15} +(-2832.92 + 2958.34i) q^{16} +8058.70 q^{17} +(-5815.18 + 442.584i) q^{18} -5597.51 q^{19} +(10125.5 + 7596.85i) q^{20} +(-8134.69 - 1596.54i) q^{21} +(6814.87 - 3406.71i) q^{22} +(-8765.02 + 5060.48i) q^{23} +(-2061.57 - 13669.4i) q^{24} +(11747.9 - 20347.9i) q^{25} +(-20463.4 - 1230.04i) q^{26} +(10809.8 - 16449.0i) q^{27} +(2353.79 - 19508.6i) q^{28} +(-34747.1 - 20061.3i) q^{29} +(-41177.5 + 11385.6i) q^{30} +(24637.7 - 14224.6i) q^{31} +(31953.6 - 7260.11i) q^{32} +(-4952.22 + 25232.5i) q^{33} +(-53797.6 - 35526.7i) q^{34} -60727.9 q^{35} +(40771.6 + 22681.6i) q^{36} +37084.9i q^{37} +(37367.4 + 24676.6i) q^{38} +(45486.5 - 52134.9i) q^{39} +(-34104.5 - 95352.7i) q^{40} +(-25003.7 - 43307.7i) q^{41} +(47266.6 + 46519.8i) q^{42} +(49466.2 - 85678.1i) q^{43} +(-60512.6 - 7301.09i) q^{44} +(54498.6 - 133493. i) q^{45} +(80821.9 + 4858.12i) q^{46} +(-43225.1 - 24956.0i) q^{47} +(-46499.0 + 100342. i) q^{48} +(-11690.0 - 20247.6i) q^{49} +(-168129. + 84046.4i) q^{50} +(205859. - 70465.4i) q^{51} +(131185. + 98424.1i) q^{52} +146625. i q^{53} +(-144678. + 62153.8i) q^{54} +188368. i q^{55} +(-101717. + 119857. i) q^{56} +(-142988. + 48944.8i) q^{57} +(143522. + 287106. i) q^{58} +(174424. + 302111. i) q^{59} +(325083. + 105523. i) q^{60} +(-13556.3 - 7826.75i) q^{61} +(-227184. - 13655.8i) q^{62} +(-221760. + 30346.4i) q^{63} +(-245319. - 92400.7i) q^{64} +(253422. - 438940. i) q^{65} +(144297. - 146613. i) q^{66} +(-164544. - 284999. i) q^{67} +(202518. + 474332. i) q^{68} +(-179653. + 205911. i) q^{69} +(405402. + 267718. i) q^{70} +452950. i q^{71} +(-172188. - 331157. i) q^{72} +351216. q^{73} +(163488. - 247568. i) q^{74} +(122176. - 622508. i) q^{75} +(-140668. - 329468. i) q^{76} +(253232. - 146204. i) q^{77} +(-533491. + 147511. i) q^{78} +(-120521. - 69583.1i) q^{79} +(-192690. + 786897. i) q^{80} +(132305. - 514709. i) q^{81} +(-24003.9 + 399339. i) q^{82} +(-6431.24 + 11139.2i) q^{83} +(-110456. - 518927. i) q^{84} +(1.38038e6 - 796963. i) q^{85} +(-707934. + 353891. i) q^{86} +(-1.06303e6 - 208633. i) q^{87} +(371778. + 315509. i) q^{88} +425243. q^{89} +(-952318. + 650902. i) q^{90} -786784. q^{91} +(-518127. - 388734. i) q^{92} +(504988. - 578799. i) q^{93} +(178540. + 357156. i) q^{94} +(-958802. + 553565. i) q^{95} +(752769. - 464862. i) q^{96} +(-418662. + 725144. i) q^{97} +(-11222.5 + 186702. i) q^{98} +(94129.7 + 687865. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.67572 4.40849i −0.834465 0.551061i
\(3\) 25.5449 8.74402i 0.946108 0.323853i
\(4\) 25.1304 + 58.8597i 0.392663 + 0.919682i
\(5\) 171.291 98.8948i 1.37033 0.791158i 0.379357 0.925250i \(-0.376145\pi\)
0.990969 + 0.134092i \(0.0428118\pi\)
\(6\) −209.079 54.2419i −0.967956 0.251120i
\(7\) −265.898 153.516i −0.775213 0.447570i 0.0595180 0.998227i \(-0.481044\pi\)
−0.834731 + 0.550658i \(0.814377\pi\)
\(8\) 91.7187 503.718i 0.179138 0.983824i
\(9\) 576.084 446.730i 0.790239 0.612799i
\(10\) −1579.47 94.9401i −1.57947 0.0949401i
\(11\) −476.183 + 824.774i −0.357764 + 0.619665i −0.987587 0.157074i \(-0.949794\pi\)
0.629823 + 0.776738i \(0.283127\pi\)
\(12\) 1156.62 + 1283.82i 0.669343 + 0.742954i
\(13\) 2219.23 1281.27i 1.01012 0.583191i 0.0988910 0.995098i \(-0.468470\pi\)
0.911226 + 0.411907i \(0.135137\pi\)
\(14\) 1098.29 + 2197.04i 0.400250 + 0.800671i
\(15\) 3510.87 4024.03i 1.04026 1.19230i
\(16\) −2832.92 + 2958.34i −0.691632 + 0.722250i
\(17\) 8058.70 1.64028 0.820140 0.572163i \(-0.193895\pi\)
0.820140 + 0.572163i \(0.193895\pi\)
\(18\) −5815.18 + 442.584i −0.997116 + 0.0758889i
\(19\) −5597.51 −0.816083 −0.408041 0.912963i \(-0.633788\pi\)
−0.408041 + 0.912963i \(0.633788\pi\)
\(20\) 10125.5 + 7596.85i 1.26569 + 0.949607i
\(21\) −8134.69 1596.54i −0.878382 0.172394i
\(22\) 6814.87 3406.71i 0.640014 0.319939i
\(23\) −8765.02 + 5060.48i −0.720393 + 0.415919i −0.814897 0.579606i \(-0.803207\pi\)
0.0945045 + 0.995524i \(0.469873\pi\)
\(24\) −2061.57 13669.4i −0.149130 0.988818i
\(25\) 11747.9 20347.9i 0.751863 1.30226i
\(26\) −20463.4 1230.04i −1.16428 0.0699838i
\(27\) 10809.8 16449.0i 0.549195 0.835695i
\(28\) 2353.79 19508.6i 0.107224 0.888694i
\(29\) −34747.1 20061.3i −1.42470 0.822554i −0.428008 0.903775i \(-0.640785\pi\)
−0.996696 + 0.0812212i \(0.974118\pi\)
\(30\) −41177.5 + 11385.6i −1.52509 + 0.421690i
\(31\) 24637.7 14224.6i 0.827019 0.477480i −0.0258117 0.999667i \(-0.508217\pi\)
0.852831 + 0.522187i \(0.174884\pi\)
\(32\) 31953.6 7260.11i 0.975147 0.221561i
\(33\) −4952.22 + 25232.5i −0.137803 + 0.702132i
\(34\) −53797.6 35526.7i −1.36876 0.903895i
\(35\) −60727.9 −1.41639
\(36\) 40771.6 + 22681.6i 0.873878 + 0.486146i
\(37\) 37084.9i 0.732135i 0.930588 + 0.366068i \(0.119296\pi\)
−0.930588 + 0.366068i \(0.880704\pi\)
\(38\) 37367.4 + 24676.6i 0.680992 + 0.449712i
\(39\) 45486.5 52134.9i 0.766811 0.878891i
\(40\) −34104.5 95352.7i −0.532883 1.48989i
\(41\) −25003.7 43307.7i −0.362788 0.628367i 0.625630 0.780120i \(-0.284842\pi\)
−0.988419 + 0.151752i \(0.951508\pi\)
\(42\) 47266.6 + 46519.8i 0.637979 + 0.627899i
\(43\) 49466.2 85678.1i 0.622162 1.07762i −0.366920 0.930252i \(-0.619588\pi\)
0.989082 0.147364i \(-0.0470789\pi\)
\(44\) −60512.6 7301.09i −0.710375 0.0857096i
\(45\) 54498.6 133493.i 0.598064 1.46494i
\(46\) 80821.9 + 4858.12i 0.830339 + 0.0499109i
\(47\) −43225.1 24956.0i −0.416334 0.240371i 0.277174 0.960820i \(-0.410602\pi\)
−0.693508 + 0.720449i \(0.743936\pi\)
\(48\) −46499.0 + 100342.i −0.420455 + 0.907313i
\(49\) −11690.0 20247.6i −0.0993630 0.172102i
\(50\) −168129. + 84046.4i −1.34503 + 0.672371i
\(51\) 205859. 70465.4i 1.55188 0.531209i
\(52\) 131185. + 98424.1i 0.932986 + 0.699989i
\(53\) 146625.i 0.984874i 0.870348 + 0.492437i \(0.163894\pi\)
−0.870348 + 0.492437i \(0.836106\pi\)
\(54\) −144678. + 62153.8i −0.918802 + 0.394718i
\(55\) 188368.i 1.13219i
\(56\) −101717. + 119857.i −0.579200 + 0.682496i
\(57\) −142988. + 48944.8i −0.772102 + 0.264291i
\(58\) 143522. + 287106.i 0.735588 + 1.47149i
\(59\) 174424. + 302111.i 0.849278 + 1.47099i 0.881854 + 0.471523i \(0.156295\pi\)
−0.0325763 + 0.999469i \(0.510371\pi\)
\(60\) 325083. + 105523.i 1.50501 + 0.488533i
\(61\) −13556.3 7826.75i −0.0597245 0.0344820i 0.469840 0.882751i \(-0.344311\pi\)
−0.529565 + 0.848269i \(0.677645\pi\)
\(62\) −227184. 13655.8i −0.953239 0.0572983i
\(63\) −221760. + 30346.4i −0.886874 + 0.121363i
\(64\) −245319. 92400.7i −0.935819 0.352481i
\(65\) 253422. 438940.i 0.922793 1.59832i
\(66\) 144297. 146613.i 0.501909 0.509967i
\(67\) −164544. 284999.i −0.547090 0.947588i −0.998472 0.0552572i \(-0.982402\pi\)
0.451382 0.892331i \(-0.350931\pi\)
\(68\) 202518. + 474332.i 0.644077 + 1.50854i
\(69\) −179653. + 205911.i −0.546872 + 0.626805i
\(70\) 405402. + 267718.i 1.18193 + 0.780520i
\(71\) 452950.i 1.26554i 0.774341 + 0.632769i \(0.218082\pi\)
−0.774341 + 0.632769i \(0.781918\pi\)
\(72\) −172188. 331157.i −0.461324 0.887232i
\(73\) 351216. 0.902829 0.451414 0.892314i \(-0.350920\pi\)
0.451414 + 0.892314i \(0.350920\pi\)
\(74\) 163488. 247568.i 0.403451 0.610941i
\(75\) 122176. 622508.i 0.289601 1.47557i
\(76\) −140668. 329468.i −0.320445 0.750537i
\(77\) 253232. 146204.i 0.554686 0.320248i
\(78\) −533491. + 147511.i −1.12420 + 0.310843i
\(79\) −120521. 69583.1i −0.244446 0.141131i 0.372772 0.927923i \(-0.378407\pi\)
−0.617219 + 0.786792i \(0.711741\pi\)
\(80\) −192690. + 786897.i −0.376347 + 1.53691i
\(81\) 132305. 514709.i 0.248955 0.968515i
\(82\) −24003.9 + 399339.i −0.0435351 + 0.724269i
\(83\) −6431.24 + 11139.2i −0.0112476 + 0.0194814i −0.871594 0.490228i \(-0.836914\pi\)
0.860347 + 0.509709i \(0.170247\pi\)
\(84\) −110456. 518927.i −0.186360 0.875525i
\(85\) 1.38038e6 796963.i 2.24772 1.29772i
\(86\) −707934. + 353891.i −1.11301 + 0.556383i
\(87\) −1.06303e6 208633.i −1.61431 0.316830i
\(88\) 371778. + 315509.i 0.545552 + 0.462982i
\(89\) 425243. 0.603208 0.301604 0.953433i \(-0.402478\pi\)
0.301604 + 0.953433i \(0.402478\pi\)
\(90\) −952318. + 650902.i −1.30633 + 0.892869i
\(91\) −786784. −1.04407
\(92\) −518127. 388734.i −0.665385 0.499217i
\(93\) 504988. 578799.i 0.627816 0.719580i
\(94\) 178540. + 357156.i 0.214957 + 0.430006i
\(95\) −958802. + 553565.i −1.11830 + 0.645651i
\(96\) 752769. 464862.i 0.850840 0.525424i
\(97\) −418662. + 725144.i −0.458721 + 0.794528i −0.998894 0.0470265i \(-0.985025\pi\)
0.540173 + 0.841554i \(0.318359\pi\)
\(98\) −11222.5 + 186702.i −0.0119237 + 0.198368i
\(99\) 94129.7 + 687865.i 0.0970111 + 0.708920i
\(100\) 1.49290e6 + 180124.i 1.49290 + 0.180124i
\(101\) 597081. + 344725.i 0.579521 + 0.334587i 0.760943 0.648819i \(-0.224737\pi\)
−0.181422 + 0.983405i \(0.558070\pi\)
\(102\) −1.68490e6 437119.i −1.58772 0.411907i
\(103\) −5241.91 + 3026.42i −0.00479709 + 0.00276960i −0.502397 0.864637i \(-0.667548\pi\)
0.497600 + 0.867407i \(0.334215\pi\)
\(104\) −441854. 1.23538e6i −0.392807 1.09825i
\(105\) −1.55129e6 + 531006.i −1.34006 + 0.458703i
\(106\) 646395. 978827.i 0.542726 0.821842i
\(107\) 535932. 0.437480 0.218740 0.975783i \(-0.429805\pi\)
0.218740 + 0.975783i \(0.429805\pi\)
\(108\) 1.23984e6 + 222891.i 0.984222 + 0.176938i
\(109\) 16474.4i 0.0127213i −0.999980 0.00636063i \(-0.997975\pi\)
0.999980 0.00636063i \(-0.00202467\pi\)
\(110\) 830419. 1.25749e6i 0.623906 0.944773i
\(111\) 324271. + 947329.i 0.237104 + 0.692679i
\(112\) 1.20742e6 351716.i 0.859419 0.250345i
\(113\) 489998. + 848702.i 0.339593 + 0.588193i 0.984356 0.176190i \(-0.0563772\pi\)
−0.644763 + 0.764383i \(0.723044\pi\)
\(114\) 1.17032e6 + 303619.i 0.789932 + 0.204934i
\(115\) −1.00091e6 + 1.73363e6i −0.658115 + 1.13989i
\(116\) 307590. 2.54935e6i 0.197060 1.63326i
\(117\) 706079. 1.72952e6i 0.440855 1.07986i
\(118\) 167449. 2.78575e6i 0.101915 1.69550i
\(119\) −2.14279e6 1.23714e6i −1.27157 0.734139i
\(120\) −1.70496e6 2.13757e6i −0.986668 1.23702i
\(121\) 432279. + 748730.i 0.244010 + 0.422639i
\(122\) 55994.1 + 112012.i 0.0308363 + 0.0616858i
\(123\) −1.01740e6 887658.i −0.546735 0.477013i
\(124\) 1.45641e6 + 1.09270e6i 0.763870 + 0.573107i
\(125\) 1.55674e6i 0.797053i
\(126\) 1.61419e6 + 775043.i 0.806943 + 0.387449i
\(127\) 2.71762e6i 1.32671i 0.748304 + 0.663357i \(0.230869\pi\)
−0.748304 + 0.663357i \(0.769131\pi\)
\(128\) 1.23034e6 + 1.69833e6i 0.586669 + 0.809826i
\(129\) 514440. 2.62117e6i 0.239643 1.22103i
\(130\) −3.62684e6 + 1.81303e6i −1.65081 + 0.825230i
\(131\) 2.09088e6 + 3.62151e6i 0.930068 + 1.61092i 0.783201 + 0.621768i \(0.213585\pi\)
0.146867 + 0.989156i \(0.453081\pi\)
\(132\) −1.60963e6 + 342618.i −0.699849 + 0.148966i
\(133\) 1.48837e6 + 859310.i 0.632638 + 0.365254i
\(134\) −157965. + 2.62797e6i −0.0656516 + 1.09221i
\(135\) 224901. 3.88659e6i 0.0914091 1.57967i
\(136\) 739133. 4.05931e6i 0.293837 1.61375i
\(137\) −2.42290e6 + 4.19659e6i −0.942268 + 1.63206i −0.181136 + 0.983458i \(0.557977\pi\)
−0.761132 + 0.648598i \(0.775356\pi\)
\(138\) 2.10707e6 582608.i 0.801754 0.221686i
\(139\) 67664.7 + 117199.i 0.0251952 + 0.0436393i 0.878348 0.478022i \(-0.158646\pi\)
−0.853153 + 0.521661i \(0.825313\pi\)
\(140\) −1.52612e6 3.57442e6i −0.556165 1.30263i
\(141\) −1.32240e6 259538.i −0.471741 0.0925855i
\(142\) 1.99683e6 3.02377e6i 0.697389 1.05605i
\(143\) 2.44048e6i 0.834578i
\(144\) −310424. + 2.96980e6i −0.103960 + 0.994581i
\(145\) −7.93581e6 −2.60308
\(146\) −2.34462e6 1.54833e6i −0.753379 0.497514i
\(147\) −475664. 415006.i −0.149744 0.130648i
\(148\) −2.18280e6 + 931958.i −0.673332 + 0.287482i
\(149\) 1.16829e6 674514.i 0.353177 0.203907i −0.312907 0.949784i \(-0.601303\pi\)
0.666084 + 0.745877i \(0.267969\pi\)
\(150\) −3.55993e6 + 3.61708e6i −1.05479 + 1.07173i
\(151\) 1.40420e6 + 810717.i 0.407849 + 0.235472i 0.689865 0.723938i \(-0.257670\pi\)
−0.282016 + 0.959410i \(0.591003\pi\)
\(152\) −513397. + 2.81957e6i −0.146192 + 0.802882i
\(153\) 4.64249e6 3.60006e6i 1.29621 1.00516i
\(154\) −2.33505e6 140357.i −0.639342 0.0384302i
\(155\) 2.81348e6 4.87309e6i 0.755524 1.30861i
\(156\) 4.21174e6 + 1.36715e6i 1.10940 + 0.360115i
\(157\) −2.35624e6 + 1.36038e6i −0.608865 + 0.351528i −0.772521 0.634989i \(-0.781004\pi\)
0.163656 + 0.986517i \(0.447671\pi\)
\(158\) 497811. + 995835.i 0.126210 + 0.252474i
\(159\) 1.28209e6 + 3.74552e6i 0.318954 + 0.931796i
\(160\) 4.75537e6 4.40363e6i 1.16098 1.07511i
\(161\) 3.10747e6 0.744610
\(162\) −3.15232e6 + 2.85278e6i −0.741456 + 0.671002i
\(163\) 1.71854e6 0.396823 0.198412 0.980119i \(-0.436422\pi\)
0.198412 + 0.980119i \(0.436422\pi\)
\(164\) 1.92072e6 2.56005e6i 0.435445 0.580386i
\(165\) 1.64710e6 + 4.81185e6i 0.366663 + 1.07117i
\(166\) 92040.3 46010.3i 0.0201212 0.0100584i
\(167\) 956468. 552217.i 0.205362 0.118566i −0.393792 0.919200i \(-0.628837\pi\)
0.599154 + 0.800634i \(0.295504\pi\)
\(168\) −1.55031e6 + 3.95116e6i −0.326957 + 0.833290i
\(169\) 869907. 1.50672e6i 0.180224 0.312157i
\(170\) −1.27284e7 765094.i −2.59077 0.155728i
\(171\) −3.22464e6 + 2.50058e6i −0.644900 + 0.500095i
\(172\) 6.28609e6 + 758442.i 1.23536 + 0.149052i
\(173\) 5.20121e6 + 3.00292e6i 1.00454 + 0.579970i 0.909588 0.415512i \(-0.136397\pi\)
0.0949503 + 0.995482i \(0.469731\pi\)
\(174\) 6.17672e6 + 6.07913e6i 1.17249 + 1.15397i
\(175\) −6.24747e6 + 3.60698e6i −1.16571 + 0.673022i
\(176\) −1.09097e6 3.74523e6i −0.200112 0.686975i
\(177\) 7.09730e6 + 6.19223e6i 1.27989 + 1.11668i
\(178\) −2.83880e6 1.87468e6i −0.503356 0.332405i
\(179\) −8.24312e6 −1.43725 −0.718625 0.695398i \(-0.755228\pi\)
−0.718625 + 0.695398i \(0.755228\pi\)
\(180\) 9.22690e6 146952.i 1.58212 0.0251975i
\(181\) 9.69953e6i 1.63574i −0.575401 0.817871i \(-0.695154\pi\)
0.575401 0.817871i \(-0.304846\pi\)
\(182\) 5.25235e6 + 3.46853e6i 0.871243 + 0.575349i
\(183\) −414732. 81396.7i −0.0676729 0.0132817i
\(184\) 1.74514e6 + 4.87924e6i 0.280141 + 0.783246i
\(185\) 3.66750e6 + 6.35229e6i 0.579235 + 1.00326i
\(186\) −5.92279e6 + 1.63766e6i −0.920423 + 0.254499i
\(187\) −3.83742e6 + 6.64660e6i −0.586832 + 1.01642i
\(188\) 382638. 3.17137e6i 0.0575857 0.477280i
\(189\) −5.39949e6 + 2.71427e6i −0.799774 + 0.402039i
\(190\) 8.84108e6 + 531429.i 1.28897 + 0.0774790i
\(191\) 409661. + 236518.i 0.0587928 + 0.0339440i 0.529108 0.848554i \(-0.322527\pi\)
−0.470315 + 0.882498i \(0.655860\pi\)
\(192\) −7.07461e6 215290.i −0.999537 0.0304173i
\(193\) −2.03144e6 3.51855e6i −0.282574 0.489432i 0.689444 0.724339i \(-0.257855\pi\)
−0.972018 + 0.234907i \(0.924521\pi\)
\(194\) 5.99166e6 2.99519e6i 0.820620 0.410222i
\(195\) 2.63554e6 1.34286e7i 0.355440 1.81104i
\(196\) 897994. 1.19690e6i 0.119263 0.158960i
\(197\) 607480.i 0.0794572i −0.999211 0.0397286i \(-0.987351\pi\)
0.999211 0.0397286i \(-0.0126493\pi\)
\(198\) 2.40406e6 5.00696e6i 0.309706 0.645028i
\(199\) 7.48585e6i 0.949909i −0.880010 0.474954i \(-0.842465\pi\)
0.880010 0.474954i \(-0.157535\pi\)
\(200\) −9.17209e6 7.78389e6i −1.14651 0.972986i
\(201\) −6.69531e6 5.84150e6i −0.824485 0.719344i
\(202\) −2.46623e6 4.93352e6i −0.299212 0.598553i
\(203\) 6.15946e6 + 1.06685e7i 0.736300 + 1.27531i
\(204\) 9.32089e6 + 1.03459e7i 1.09791 + 1.21865i
\(205\) −8.56581e6 4.94547e6i −0.994276 0.574046i
\(206\) 48335.4 + 2905.40i 0.00552922 + 0.000332356i
\(207\) −2.78872e6 + 6.83086e6i −0.314408 + 0.770131i
\(208\) −2.49647e6 + 1.01950e7i −0.277419 + 1.13291i
\(209\) 2.66544e6 4.61668e6i 0.291965 0.505698i
\(210\) 1.26969e7 + 3.29399e6i 1.37101 + 0.355684i
\(211\) −516964. 895408.i −0.0550317 0.0953177i 0.837197 0.546901i \(-0.184193\pi\)
−0.892229 + 0.451583i \(0.850859\pi\)
\(212\) −8.63030e6 + 3.68475e6i −0.905771 + 0.386723i
\(213\) 3.96060e6 + 1.15706e7i 0.409848 + 1.19733i
\(214\) −3.57773e6 2.36265e6i −0.365062 0.241079i
\(215\) 1.95678e7i 1.96891i
\(216\) −7.29418e6 6.95377e6i −0.723795 0.690016i
\(217\) −8.73484e6 −0.854822
\(218\) −72627.3 + 109979.i −0.00701020 + 0.0106154i
\(219\) 8.97177e6 3.07104e6i 0.854173 0.292384i
\(220\) −1.10873e7 + 4.73377e6i −1.04126 + 0.444569i
\(221\) 1.78841e7 1.03254e7i 1.65687 0.956597i
\(222\) 2.01155e6 7.75365e6i 0.183854 0.708675i
\(223\) 1.23038e7 + 7.10358e6i 1.10949 + 0.640564i 0.938697 0.344743i \(-0.112034\pi\)
0.170793 + 0.985307i \(0.445367\pi\)
\(224\) −9.61095e6 2.97495e6i −0.855110 0.264689i
\(225\) −2.32226e6 1.69702e7i −0.203875 1.48984i
\(226\) 470404. 7.82584e6i 0.0407517 0.677963i
\(227\) 5.75034e6 9.95989e6i 0.491605 0.851485i −0.508348 0.861152i \(-0.669744\pi\)
0.999953 + 0.00966671i \(0.00307706\pi\)
\(228\) −6.47422e6 7.18622e6i −0.546239 0.606312i
\(229\) −9.35048e6 + 5.39850e6i −0.778624 + 0.449539i −0.835942 0.548817i \(-0.815078\pi\)
0.0573186 + 0.998356i \(0.481745\pi\)
\(230\) 1.43245e7 7.16071e6i 1.17732 0.588535i
\(231\) 5.19039e6 5.94903e6i 0.421079 0.482626i
\(232\) −1.32922e7 + 1.56628e7i −1.06447 + 1.25431i
\(233\) 1.74767e7 1.38163 0.690816 0.723031i \(-0.257251\pi\)
0.690816 + 0.723031i \(0.257251\pi\)
\(234\) −1.23381e7 + 8.43302e6i −0.962946 + 0.658166i
\(235\) −9.87207e6 −0.760685
\(236\) −1.33988e7 + 1.78587e7i −1.01937 + 1.35867i
\(237\) −3.68715e6 723652.i −0.276978 0.0543606i
\(238\) 8.85075e6 + 1.77053e7i 0.656522 + 1.31332i
\(239\) −9.66507e6 + 5.58013e6i −0.707964 + 0.408743i −0.810307 0.586006i \(-0.800700\pi\)
0.102343 + 0.994749i \(0.467366\pi\)
\(240\) 1.95841e6 + 2.17861e7i 0.141667 + 1.57596i
\(241\) −3.06470e6 + 5.30822e6i −0.218946 + 0.379226i −0.954486 0.298255i \(-0.903595\pi\)
0.735540 + 0.677481i \(0.236929\pi\)
\(242\) 414993. 6.90401e6i 0.0292816 0.487142i
\(243\) −1.12090e6 1.43051e7i −0.0781176 0.996944i
\(244\) 120004. 994611.i 0.00826086 0.0684674i
\(245\) −4.00476e6 2.31215e6i −0.272319 0.157224i
\(246\) 2.87865e6 + 1.04110e7i 0.193368 + 0.699335i
\(247\) −1.24222e7 + 7.17193e6i −0.824339 + 0.475932i
\(248\) −4.90544e6 1.37151e7i −0.321605 0.899176i
\(249\) −66883.7 + 340785.i −0.00433234 + 0.0220741i
\(250\) −6.86289e6 + 1.03924e7i −0.439225 + 0.665113i
\(251\) 1.05389e7 0.666462 0.333231 0.942845i \(-0.391861\pi\)
0.333231 + 0.942845i \(0.391861\pi\)
\(252\) −7.35911e6 1.22901e7i −0.459858 0.767988i
\(253\) 9.63887e6i 0.595202i
\(254\) 1.19806e7 1.81420e7i 0.731100 1.10710i
\(255\) 2.82930e7 3.24284e7i 1.70631 1.95571i
\(256\) −726301. 1.67615e7i −0.0432909 0.999063i
\(257\) −1.55955e7 2.70121e7i −0.918753 1.59133i −0.801312 0.598246i \(-0.795864\pi\)
−0.117440 0.993080i \(-0.537469\pi\)
\(258\) −1.49897e7 + 1.52303e7i −0.872836 + 0.886848i
\(259\) 5.69313e6 9.86079e6i 0.327681 0.567561i
\(260\) 3.22045e7 + 3.88560e6i 1.83230 + 0.221074i
\(261\) −2.89792e7 + 3.96562e6i −1.62992 + 0.223043i
\(262\) 2.00727e6 3.33938e7i 0.111609 1.85678i
\(263\) −8.95016e6 5.16738e6i −0.491998 0.284055i 0.233405 0.972380i \(-0.425013\pi\)
−0.725403 + 0.688324i \(0.758347\pi\)
\(264\) 1.22559e7 + 4.80882e6i 0.666089 + 0.261352i
\(265\) 1.45005e7 + 2.51155e7i 0.779191 + 1.34960i
\(266\) −6.14767e6 1.22980e7i −0.326637 0.653414i
\(267\) 1.08628e7 3.71833e6i 0.570700 0.195350i
\(268\) 1.26399e7 1.68472e7i 0.656658 0.875232i
\(269\) 1.65746e7i 0.851502i 0.904840 + 0.425751i \(0.139990\pi\)
−0.904840 + 0.425751i \(0.860010\pi\)
\(270\) −1.86354e7 + 2.49543e7i −0.946775 + 1.26781i
\(271\) 4.92564e6i 0.247488i 0.992314 + 0.123744i \(0.0394902\pi\)
−0.992314 + 0.123744i \(0.960510\pi\)
\(272\) −2.28297e7 + 2.38403e7i −1.13447 + 1.18469i
\(273\) −2.00983e7 + 6.87966e6i −0.987807 + 0.338126i
\(274\) 3.46752e7 1.73339e7i 1.68565 0.842646i
\(275\) 1.11883e7 + 1.93786e7i 0.537978 + 0.931806i
\(276\) −1.66346e7 5.39966e6i −0.791198 0.256826i
\(277\) 1.09746e7 + 6.33621e6i 0.516358 + 0.298120i 0.735443 0.677586i \(-0.236974\pi\)
−0.219085 + 0.975706i \(0.570307\pi\)
\(278\) 64958.9 1.08068e6i 0.00302346 0.0502996i
\(279\) 7.83885e6 1.92010e7i 0.360944 0.884120i
\(280\) −5.56988e6 + 3.05897e7i −0.253730 + 1.39348i
\(281\) −5.56934e6 + 9.64639e6i −0.251007 + 0.434756i −0.963803 0.266615i \(-0.914095\pi\)
0.712797 + 0.701371i \(0.247428\pi\)
\(282\) 7.68377e6 + 7.56237e6i 0.342631 + 0.337218i
\(283\) −9.08529e6 1.57362e7i −0.400848 0.694288i 0.592981 0.805217i \(-0.297951\pi\)
−0.993828 + 0.110928i \(0.964618\pi\)
\(284\) −2.66605e7 + 1.13828e7i −1.16389 + 0.496930i
\(285\) −1.96521e7 + 2.25245e7i −0.848936 + 0.973019i
\(286\) 1.07588e7 1.62920e7i 0.459904 0.696426i
\(287\) 1.53539e7i 0.649492i
\(288\) 1.51647e7 1.84571e7i 0.634827 0.772655i
\(289\) 4.08050e7 1.69052
\(290\) 5.29773e7 + 3.49850e7i 2.17218 + 1.43446i
\(291\) −4.35401e6 + 2.21845e7i −0.176689 + 0.900266i
\(292\) 8.82620e6 + 2.06724e7i 0.354507 + 0.830316i
\(293\) −3.01889e7 + 1.74296e7i −1.20017 + 0.692921i −0.960594 0.277956i \(-0.910343\pi\)
−0.239580 + 0.970877i \(0.577010\pi\)
\(294\) 1.34585e6 + 4.86742e6i 0.0529609 + 0.191539i
\(295\) 5.97544e7 + 3.44992e7i 2.32757 + 1.34383i
\(296\) 1.86803e7 + 3.40138e6i 0.720292 + 0.131153i
\(297\) 8.41924e6 + 1.67484e7i 0.321369 + 0.639298i
\(298\) −1.07728e7 647541.i −0.407079 0.0244691i
\(299\) −1.29677e7 + 2.24607e7i −0.485121 + 0.840253i
\(300\) 3.97110e7 8.45268e6i 1.47078 0.313062i
\(301\) −2.63060e7 + 1.51878e7i −0.964617 + 0.556922i
\(302\) −5.80003e6 1.16025e7i −0.210576 0.421242i
\(303\) 1.82667e7 + 3.58508e6i 0.656646 + 0.128876i
\(304\) 1.58573e7 1.65593e7i 0.564429 0.589416i
\(305\) −3.09610e6 −0.109123
\(306\) −4.68628e7 + 3.56665e6i −1.63555 + 0.124479i
\(307\) −3.26234e7 −1.12749 −0.563747 0.825948i \(-0.690641\pi\)
−0.563747 + 0.825948i \(0.690641\pi\)
\(308\) 1.49694e7 + 1.12310e7i 0.512331 + 0.384386i
\(309\) −107441. + 123145.i −0.00364162 + 0.00417389i
\(310\) −4.02649e7 + 2.01282e7i −1.35158 + 0.675646i
\(311\) 6.87805e6 3.97104e6i 0.228657 0.132015i −0.381295 0.924453i \(-0.624522\pi\)
0.609952 + 0.792438i \(0.291189\pi\)
\(312\) −2.20893e7 2.76941e7i −0.727309 0.911850i
\(313\) −9.81797e6 + 1.70052e7i −0.320176 + 0.554561i −0.980524 0.196398i \(-0.937075\pi\)
0.660348 + 0.750960i \(0.270409\pi\)
\(314\) 2.17268e7 + 1.30598e6i 0.701790 + 0.0421839i
\(315\) −3.49844e7 + 2.71290e7i −1.11929 + 0.867964i
\(316\) 1.06688e6 8.84251e6i 0.0338108 0.280230i
\(317\) 3.07894e7 + 1.77763e7i 0.966549 + 0.558037i 0.898182 0.439623i \(-0.144888\pi\)
0.0683663 + 0.997660i \(0.478221\pi\)
\(318\) 7.95321e6 3.06561e7i 0.247321 0.953314i
\(319\) 3.30920e7 1.91057e7i 1.01941 0.588559i
\(320\) −5.11589e7 + 8.43341e6i −1.56125 + 0.257367i
\(321\) 1.36903e7 4.68620e6i 0.413904 0.141679i
\(322\) −2.07446e7 1.36992e7i −0.621351 0.410326i
\(323\) −4.51087e7 −1.33860
\(324\) 3.36205e7 5.14741e6i 0.988482 0.151340i
\(325\) 6.02088e7i 1.75392i
\(326\) −1.14725e7 7.57618e6i −0.331135 0.218674i
\(327\) −144053. 420837.i −0.00411982 0.0120357i
\(328\) −2.41082e7 + 8.62269e6i −0.683192 + 0.244355i
\(329\) 7.66231e6 + 1.32715e7i 0.215165 + 0.372677i
\(330\) 1.02174e7 3.93837e7i 0.284315 1.09591i
\(331\) 1.27036e7 2.20033e7i 0.350303 0.606742i −0.636000 0.771689i \(-0.719412\pi\)
0.986302 + 0.164947i \(0.0527454\pi\)
\(332\) −817271. 98607.0i −0.0223333 0.00269460i
\(333\) 1.65669e7 + 2.13640e7i 0.448652 + 0.578562i
\(334\) −8.81956e6 530135.i −0.236705 0.0142281i
\(335\) −5.63699e7 3.25452e7i −1.49938 0.865670i
\(336\) 2.77681e7 1.95423e7i 0.732028 0.515178i
\(337\) −3.21982e7 5.57689e7i −0.841282 1.45714i −0.888811 0.458273i \(-0.848468\pi\)
0.0475296 0.998870i \(-0.484865\pi\)
\(338\) −1.24496e7 + 6.22348e6i −0.322409 + 0.161170i
\(339\) 1.99380e7 + 1.73954e7i 0.511780 + 0.446515i
\(340\) 8.15985e7 + 6.12207e7i 2.07609 + 1.55762i
\(341\) 2.70941e7i 0.683300i
\(342\) 3.25506e7 2.47737e6i 0.813730 0.0619316i
\(343\) 4.33005e7i 1.07303i
\(344\) −3.86206e7 3.27753e7i −0.948732 0.805140i
\(345\) −1.04093e7 + 5.30374e7i −0.253492 + 1.29159i
\(346\) −2.14835e7 4.29762e7i −0.518652 1.03753i
\(347\) −1.88251e7 3.26061e7i −0.450557 0.780387i 0.547864 0.836567i \(-0.315441\pi\)
−0.998421 + 0.0561804i \(0.982108\pi\)
\(348\) −1.44342e7 6.78125e7i −0.342497 1.60906i
\(349\) −4.65328e7 2.68657e7i −1.09467 0.632007i −0.159853 0.987141i \(-0.551102\pi\)
−0.934816 + 0.355134i \(0.884435\pi\)
\(350\) 5.76076e7 + 3.46274e6i 1.34362 + 0.0807636i
\(351\) 2.91379e6 5.03543e7i 0.0673810 1.16443i
\(352\) −9.22783e6 + 2.98116e7i −0.211578 + 0.683530i
\(353\) −6.62146e6 + 1.14687e7i −0.150532 + 0.260730i −0.931423 0.363938i \(-0.881432\pi\)
0.780891 + 0.624667i \(0.214765\pi\)
\(354\) −2.00812e7 7.26260e7i −0.452668 1.63713i
\(355\) 4.47944e7 + 7.75861e7i 1.00124 + 1.73420i
\(356\) 1.06865e7 + 2.50297e7i 0.236857 + 0.554760i
\(357\) −6.55550e7 1.28660e7i −1.44079 0.282775i
\(358\) 5.50287e7 + 3.63397e7i 1.19933 + 0.792013i
\(359\) 2.64953e7i 0.572646i 0.958133 + 0.286323i \(0.0924330\pi\)
−0.958133 + 0.286323i \(0.907567\pi\)
\(360\) −6.22440e7 3.96957e7i −1.33411 0.850816i
\(361\) −1.57137e7 −0.334009
\(362\) −4.27603e7 + 6.47513e7i −0.901394 + 1.36497i
\(363\) 1.75894e7 + 1.53464e7i 0.367733 + 0.320838i
\(364\) −1.97722e7 4.63099e7i −0.409969 0.960217i
\(365\) 6.01600e7 3.47334e7i 1.23717 0.714281i
\(366\) 2.40980e6 + 2.37173e6i 0.0491516 + 0.0483750i
\(367\) −1.68599e7 9.73408e6i −0.341081 0.196923i 0.319669 0.947529i \(-0.396428\pi\)
−0.660750 + 0.750606i \(0.729762\pi\)
\(368\) 9.86001e6 4.02658e7i 0.197849 0.807966i
\(369\) −3.37511e7 1.37790e7i −0.671752 0.274244i
\(370\) 3.52084e6 5.85743e7i 0.0695090 1.15638i
\(371\) 2.25093e7 3.89873e7i 0.440799 0.763487i
\(372\) 4.67585e7 + 1.51780e7i 0.908305 + 0.294839i
\(373\) 7.52432e7 4.34417e7i 1.44991 0.837105i 0.451433 0.892305i \(-0.350913\pi\)
0.998475 + 0.0552001i \(0.0175797\pi\)
\(374\) 5.49190e7 2.74536e7i 1.04980 0.524789i
\(375\) −1.36122e7 3.97669e7i −0.258128 0.754098i
\(376\) −1.65353e7 + 1.94843e7i −0.311064 + 0.366540i
\(377\) −1.02816e8 −1.91882
\(378\) 4.80113e7 + 5.68390e6i 0.888931 + 0.105238i
\(379\) 1.01662e8 1.86742 0.933709 0.358033i \(-0.116552\pi\)
0.933709 + 0.358033i \(0.116552\pi\)
\(380\) −5.66778e7 4.25235e7i −1.03291 0.774958i
\(381\) 2.37629e7 + 6.94212e7i 0.429659 + 1.25521i
\(382\) −1.69209e6 3.38491e6i −0.0303553 0.0607235i
\(383\) −7.69628e7 + 4.44345e7i −1.36989 + 0.790904i −0.990913 0.134503i \(-0.957056\pi\)
−0.378973 + 0.925408i \(0.623723\pi\)
\(384\) 4.62790e7 + 3.26256e7i 0.817317 + 0.576189i
\(385\) 2.89176e7 5.00867e7i 0.506734 0.877689i
\(386\) −1.95020e6 + 3.24444e7i −0.0339092 + 0.564129i
\(387\) −9.77826e6 7.14558e7i −0.168705 1.23283i
\(388\) −5.32029e7 6.41914e6i −0.910836 0.109896i
\(389\) 9.72343e7 + 5.61382e7i 1.65185 + 0.953696i 0.976311 + 0.216371i \(0.0694221\pi\)
0.675539 + 0.737325i \(0.263911\pi\)
\(390\) −7.67940e7 + 7.80268e7i −1.29459 + 1.31538i
\(391\) −7.06346e7 + 4.07809e7i −1.18165 + 0.682223i
\(392\) −1.12713e7 + 4.03136e6i −0.187118 + 0.0669257i
\(393\) 8.50778e7 + 7.42283e7i 1.40165 + 1.22290i
\(394\) −2.67807e6 + 4.05537e6i −0.0437858 + 0.0663043i
\(395\) −2.75256e7 −0.446628
\(396\) −3.81220e7 + 2.28268e7i −0.613889 + 0.367586i
\(397\) 3.22348e7i 0.515174i −0.966255 0.257587i \(-0.917073\pi\)
0.966255 0.257587i \(-0.0829273\pi\)
\(398\) −3.30013e7 + 4.99734e7i −0.523458 + 0.792665i
\(399\) 4.55340e7 + 8.93666e6i 0.716832 + 0.140688i
\(400\) 2.69151e7 + 9.23981e7i 0.420549 + 1.44372i
\(401\) 2.74575e7 + 4.75578e7i 0.425822 + 0.737545i 0.996497 0.0836311i \(-0.0266517\pi\)
−0.570675 + 0.821176i \(0.693318\pi\)
\(402\) 1.89438e7 + 6.85124e7i 0.291601 + 1.05461i
\(403\) 3.64511e7 6.31352e7i 0.556924 0.964621i
\(404\) −5.28550e6 + 4.38071e7i −0.0801571 + 0.664355i
\(405\) −2.82394e7 1.01249e8i −0.425099 1.52414i
\(406\) 5.91316e6 9.83738e7i 0.0883571 1.46995i
\(407\) −3.05866e7 1.76592e7i −0.453678 0.261931i
\(408\) −1.66136e7 1.10158e8i −0.244615 1.62194i
\(409\) −3.00526e6 5.20525e6i −0.0439250 0.0760803i 0.843227 0.537558i \(-0.180653\pi\)
−0.887152 + 0.461477i \(0.847320\pi\)
\(410\) 3.53809e7 + 7.07769e7i 0.513354 + 1.02693i
\(411\) −2.51977e7 + 1.28387e8i −0.362941 + 1.84926i
\(412\) −309865. 232482.i −0.00443079 0.00332428i
\(413\) 1.07108e8i 1.52044i
\(414\) 4.87305e7 3.33069e7i 0.686752 0.469389i
\(415\) 2.54406e6i 0.0355946i
\(416\) 6.16101e7 5.70531e7i 0.855800 0.792499i
\(417\) 2.75327e6 + 2.40217e6i 0.0379701 + 0.0331280i
\(418\) −3.81463e7 + 1.90691e7i −0.522305 + 0.261096i
\(419\) −2.60082e7 4.50475e7i −0.353564 0.612391i 0.633307 0.773901i \(-0.281697\pi\)
−0.986871 + 0.161509i \(0.948364\pi\)
\(420\) −7.02393e7 7.79639e7i −0.948053 1.05231i
\(421\) −7.80909e6 4.50858e6i −0.104654 0.0604218i 0.446760 0.894654i \(-0.352578\pi\)
−0.551413 + 0.834232i \(0.685911\pi\)
\(422\) −496291. + 8.25652e6i −0.00660388 + 0.109865i
\(423\) −3.60499e7 + 4.93319e6i −0.476302 + 0.0651788i
\(424\) 7.38577e7 + 1.34483e7i 0.968942 + 0.176428i
\(425\) 9.46724e7 1.63977e8i 1.23327 2.13608i
\(426\) 2.45688e7 9.47021e7i 0.317801 1.22498i
\(427\) 2.40307e6 + 4.16224e6i 0.0308661 + 0.0534617i
\(428\) 1.34682e7 + 3.15448e7i 0.171782 + 0.402343i
\(429\) 2.13396e7 + 6.23418e7i 0.270280 + 0.789601i
\(430\) −8.62645e7 + 1.30629e8i −1.08499 + 1.64299i
\(431\) 6.23872e6i 0.0779226i −0.999241 0.0389613i \(-0.987595\pi\)
0.999241 0.0389613i \(-0.0124049\pi\)
\(432\) 1.80383e7 + 7.85777e7i 0.223740 + 0.974649i
\(433\) 2.62664e6 0.0323547 0.0161773 0.999869i \(-0.494850\pi\)
0.0161773 + 0.999869i \(0.494850\pi\)
\(434\) 5.83113e7 + 3.85074e7i 0.713319 + 0.471059i
\(435\) −2.02720e8 + 6.93909e7i −2.46279 + 0.843014i
\(436\) 969678. 414009.i 0.0116995 0.00499517i
\(437\) 4.90623e7 2.83261e7i 0.587900 0.339424i
\(438\) −7.34317e7 1.90506e7i −0.873899 0.226718i
\(439\) 7.72216e7 + 4.45839e7i 0.912736 + 0.526968i 0.881310 0.472538i \(-0.156662\pi\)
0.0314254 + 0.999506i \(0.489995\pi\)
\(440\) 9.48844e7 + 1.72769e7i 1.11388 + 0.202819i
\(441\) −1.57796e7 6.44207e6i −0.183984 0.0751120i
\(442\) −1.64908e8 9.91248e6i −1.90975 0.114793i
\(443\) 4.29996e7 7.44775e7i 0.494599 0.856671i −0.505381 0.862896i \(-0.668648\pi\)
0.999981 + 0.00622521i \(0.00198156\pi\)
\(444\) −4.76104e7 + 4.28932e7i −0.543943 + 0.490050i
\(445\) 7.28402e7 4.20543e7i 0.826592 0.477233i
\(446\) −5.08204e7 1.01663e8i −0.572840 1.14593i
\(447\) 2.39459e7 2.74460e7i 0.268108 0.307295i
\(448\) 5.10449e7 + 6.22297e7i 0.567700 + 0.692092i
\(449\) −9.94869e7 −1.09907 −0.549537 0.835469i \(-0.685196\pi\)
−0.549537 + 0.835469i \(0.685196\pi\)
\(450\) −5.93103e7 + 1.23526e8i −0.650867 + 1.35557i
\(451\) 4.76254e7 0.519169
\(452\) −3.76404e7 + 5.01694e7i −0.407605 + 0.543279i
\(453\) 4.29592e7 + 8.43131e6i 0.462127 + 0.0906986i
\(454\) −8.22958e7 + 4.11391e7i −0.879447 + 0.439630i
\(455\) −1.34769e8 + 7.78089e7i −1.43072 + 0.826028i
\(456\) 1.15397e7 + 7.65147e7i 0.121702 + 0.806957i
\(457\) 2.31538e7 4.01035e7i 0.242590 0.420178i −0.718861 0.695154i \(-0.755336\pi\)
0.961451 + 0.274975i \(0.0886696\pi\)
\(458\) 8.62204e7 + 5.18263e6i 0.897457 + 0.0539453i
\(459\) 8.71129e7 1.32557e8i 0.900833 1.37077i
\(460\) −1.27194e8 1.53465e7i −1.30675 0.157665i
\(461\) −2.00556e7 1.15791e7i −0.204707 0.118188i 0.394142 0.919050i \(-0.371042\pi\)
−0.598849 + 0.800862i \(0.704375\pi\)
\(462\) −6.08758e7 + 1.68323e7i −0.617332 + 0.170694i
\(463\) −7.54386e7 + 4.35545e7i −0.760065 + 0.438824i −0.829319 0.558775i \(-0.811271\pi\)
0.0692540 + 0.997599i \(0.477938\pi\)
\(464\) 1.57784e8 4.59617e7i 1.57946 0.460089i
\(465\) 2.92597e7 1.49084e8i 0.291012 1.48276i
\(466\) −1.16670e8 7.70460e7i −1.15292 0.761364i
\(467\) −3.86756e7 −0.379740 −0.189870 0.981809i \(-0.560807\pi\)
−0.189870 + 0.981809i \(0.560807\pi\)
\(468\) 1.19543e8 1.90389e6i 1.16623 0.0185740i
\(469\) 1.01041e8i 0.979444i
\(470\) 6.59032e7 + 4.35209e7i 0.634765 + 0.419184i
\(471\) −4.82948e7 + 5.53537e7i −0.462208 + 0.529766i
\(472\) 1.68177e8 6.01511e7i 1.59934 0.572029i
\(473\) 4.71100e7 + 8.15969e7i 0.445174 + 0.771064i
\(474\) 2.14241e7 + 2.10856e7i 0.201172 + 0.197994i
\(475\) −6.57588e7 + 1.13898e8i −0.613582 + 1.06276i
\(476\) 1.89685e7 1.57214e8i 0.175878 1.45771i
\(477\) 6.55019e7 + 8.44684e7i 0.603529 + 0.778286i
\(478\) 8.91212e7 + 5.35699e6i 0.816014 + 0.0490498i
\(479\) −9.75546e7 5.63232e7i −0.887649 0.512484i −0.0144761 0.999895i \(-0.504608\pi\)
−0.873173 + 0.487411i \(0.837941\pi\)
\(480\) 8.29700e7 1.54071e8i 0.750235 1.39315i
\(481\) 4.75158e7 + 8.22997e7i 0.426975 + 0.739542i
\(482\) 4.38604e7 2.19255e7i 0.391680 0.195798i
\(483\) 7.93800e7 2.71718e7i 0.704482 0.241144i
\(484\) −3.32066e7 + 4.42597e7i −0.292879 + 0.390367i
\(485\) 1.65614e8i 1.45168i
\(486\) −5.55809e7 + 1.00438e8i −0.484191 + 0.874962i
\(487\) 2.12868e8i 1.84299i 0.388392 + 0.921494i \(0.373031\pi\)
−0.388392 + 0.921494i \(0.626969\pi\)
\(488\) −5.18584e6 + 6.11070e6i −0.0446231 + 0.0525814i
\(489\) 4.39000e7 1.50270e7i 0.375438 0.128512i
\(490\) 1.65416e7 + 3.30902e7i 0.140601 + 0.281262i
\(491\) 3.92111e7 + 6.79156e7i 0.331257 + 0.573753i 0.982759 0.184894i \(-0.0591941\pi\)
−0.651502 + 0.758647i \(0.725861\pi\)
\(492\) 2.66796e7 8.21911e7i 0.224018 0.690128i
\(493\) −2.80016e8 1.61668e8i −2.33691 1.34922i
\(494\) 1.14544e8 + 6.88514e6i 0.950150 + 0.0571126i
\(495\) 8.41498e7 + 1.08516e8i 0.693805 + 0.894701i
\(496\) −2.77157e7 + 1.13184e8i −0.227133 + 0.927555i
\(497\) 6.95352e7 1.20439e8i 0.566416 0.981061i
\(498\) 1.94885e6 1.98013e6i 0.0157794 0.0160327i
\(499\) −1.02028e8 1.76717e8i −0.821139 1.42225i −0.904835 0.425763i \(-0.860006\pi\)
0.0836957 0.996491i \(-0.473328\pi\)
\(500\) 9.16295e7 3.91216e7i 0.733036 0.312973i
\(501\) 1.96043e7 2.24697e7i 0.155897 0.178683i
\(502\) −7.03549e7 4.64608e7i −0.556139 0.367261i
\(503\) 1.53051e8i 1.20263i −0.799011 0.601316i \(-0.794643\pi\)
0.799011 0.601316i \(-0.205357\pi\)
\(504\) −5.05353e6 + 1.14488e8i −0.0394733 + 0.894268i
\(505\) 1.36366e8 1.05884
\(506\) −4.24929e7 + 6.43464e7i −0.327993 + 0.496675i
\(507\) 9.04688e6 4.60956e7i 0.0694184 0.353700i
\(508\) −1.59958e8 + 6.82948e7i −1.22015 + 0.520951i
\(509\) 1.77887e8 1.02703e8i 1.34894 0.778808i 0.360836 0.932629i \(-0.382491\pi\)
0.988099 + 0.153821i \(0.0491580\pi\)
\(510\) −3.31837e8 + 9.17534e7i −2.50158 + 0.691691i
\(511\) −9.33876e7 5.39174e7i −0.699885 0.404079i
\(512\) −6.90443e7 + 1.15097e8i −0.514420 + 0.857538i
\(513\) −6.05080e7 + 9.20733e7i −0.448188 + 0.681996i
\(514\) −1.49718e7 + 2.49078e8i −0.110252 + 1.83419i
\(515\) −598594. + 1.03680e6i −0.00438239 + 0.00759051i
\(516\) 1.67209e8 3.55914e7i 1.21706 0.259057i
\(517\) 4.11661e7 2.37673e7i 0.297898 0.171992i
\(518\) −8.14769e7 + 4.07298e7i −0.586200 + 0.293037i
\(519\) 1.59122e8 + 3.12298e7i 1.13823 + 0.223392i
\(520\) −1.97858e8 1.67912e8i −1.40716 1.19419i
\(521\) −2.03967e8 −1.44227 −0.721136 0.692793i \(-0.756380\pi\)
−0.721136 + 0.692793i \(0.756380\pi\)
\(522\) 2.10940e8 + 1.01281e8i 1.48302 + 0.712062i
\(523\) 4.09801e7 0.286463 0.143231 0.989689i \(-0.454251\pi\)
0.143231 + 0.989689i \(0.454251\pi\)
\(524\) −1.60616e8 + 2.14078e8i −1.11634 + 1.48792i
\(525\) −1.28051e8 + 1.46768e8i −0.884925 + 1.01427i
\(526\) 3.69684e7 + 7.39527e7i 0.254023 + 0.508155i
\(527\) 1.98548e8 1.14632e8i 1.35654 0.783201i
\(528\) −6.06170e7 8.61321e7i −0.411806 0.585145i
\(529\) −2.28009e7 + 3.94924e7i −0.154023 + 0.266776i
\(530\) 1.39206e7 2.31589e8i 0.0935041 1.55557i
\(531\) 2.35445e8 + 9.61209e7i 1.57255 + 0.641999i
\(532\) −1.31754e7 + 1.09200e8i −0.0875041 + 0.725248i
\(533\) −1.10978e8 6.40731e7i −0.732917 0.423150i
\(534\) −8.89091e7 2.30660e7i −0.583879 0.151477i
\(535\) 9.18003e7 5.30009e7i 0.599491 0.346116i
\(536\) −1.58651e8 + 5.67442e7i −1.03026 + 0.368491i
\(537\) −2.10570e8 + 7.20780e7i −1.35979 + 0.465457i
\(538\) 7.30689e7 1.10647e8i 0.469230 0.710548i
\(539\) 2.22663e7 0.142194
\(540\) 2.34415e8 8.44341e7i 1.48869 0.536212i
\(541\) 1.71990e8i 1.08620i −0.839667 0.543102i \(-0.817250\pi\)
0.839667 0.543102i \(-0.182750\pi\)
\(542\) 2.17146e7 3.28822e7i 0.136381 0.206520i
\(543\) −8.48129e7 2.47774e8i −0.529739 1.54759i
\(544\) 2.57504e8 5.85070e7i 1.59951 0.363422i
\(545\) −1.62923e6 2.82191e6i −0.0100645 0.0174323i
\(546\) 1.64500e8 + 4.26766e7i 1.01062 + 0.262188i
\(547\) 6.58124e7 1.13990e8i 0.402111 0.696477i −0.591869 0.806034i \(-0.701610\pi\)
0.993981 + 0.109557i \(0.0349432\pi\)
\(548\) −3.07899e8 3.71492e7i −1.87097 0.225740i
\(549\) −1.13060e7 + 1.54716e6i −0.0683271 + 0.00935012i
\(550\) 1.07409e7 1.78690e8i 0.0645582 1.07402i
\(551\) 1.94497e8 + 1.12293e8i 1.16268 + 0.671272i
\(552\) 8.72436e7 + 1.09380e8i 0.518700 + 0.650311i
\(553\) 2.13643e7 + 3.70040e7i 0.126332 + 0.218813i
\(554\) −4.53305e7 9.06804e7i −0.266601 0.533315i
\(555\) 1.49230e8 + 1.30200e8i 0.872928 + 0.761609i
\(556\) −5.19783e6 + 6.92797e6i −0.0302411 + 0.0403071i
\(557\) 1.23660e8i 0.715590i −0.933800 0.357795i \(-0.883529\pi\)
0.933800 0.357795i \(-0.116471\pi\)
\(558\) −1.36977e8 + 9.36229e7i −0.788399 + 0.538865i
\(559\) 2.53519e8i 1.45136i
\(560\) 1.72037e8 1.79653e8i 0.979623 1.02299i
\(561\) −3.99084e7 + 2.03341e8i −0.226035 + 1.15169i
\(562\) 7.97054e7 3.98442e7i 0.449033 0.224469i
\(563\) 2.67443e7 + 4.63224e7i 0.149867 + 0.259577i 0.931178 0.364565i \(-0.118782\pi\)
−0.781311 + 0.624142i \(0.785449\pi\)
\(564\) −1.79560e7 8.43581e7i −0.100086 0.470207i
\(565\) 1.67864e8 + 9.69165e7i 0.930707 + 0.537344i
\(566\) −8.72198e6 + 1.45103e8i −0.0481023 + 0.800251i
\(567\) −1.14196e8 + 1.16549e8i −0.626471 + 0.639381i
\(568\) 2.28159e8 + 4.15440e7i 1.24507 + 0.226706i
\(569\) 3.79964e7 6.58116e7i 0.206255 0.357245i −0.744277 0.667871i \(-0.767206\pi\)
0.950532 + 0.310627i \(0.100539\pi\)
\(570\) 2.30491e8 6.37313e7i 1.24460 0.344134i
\(571\) 1.08931e7 + 1.88675e7i 0.0585119 + 0.101346i 0.893798 0.448471i \(-0.148031\pi\)
−0.835286 + 0.549816i \(0.814698\pi\)
\(572\) −1.43646e8 + 6.13303e7i −0.767547 + 0.327708i
\(573\) 1.25329e7 + 2.45974e6i 0.0666172 + 0.0130745i
\(574\) 6.76876e7 1.02498e8i 0.357910 0.541978i
\(575\) 2.37799e8i 1.25086i
\(576\) −1.82603e8 + 5.63610e7i −0.955520 + 0.294925i
\(577\) −1.33930e8 −0.697189 −0.348595 0.937274i \(-0.613341\pi\)
−0.348595 + 0.937274i \(0.613341\pi\)
\(578\) −2.72403e8 1.79889e8i −1.41068 0.931580i
\(579\) −8.26592e7 7.21182e7i −0.425849 0.371543i
\(580\) −1.99430e8 4.67100e8i −1.02213 2.39401i
\(581\) 3.42011e6 1.97460e6i 0.0174386 0.0100682i
\(582\) 1.26866e8 1.28903e8i 0.643543 0.653874i
\(583\) −1.20932e8 6.98204e7i −0.610291 0.352352i
\(584\) 3.22131e7 1.76914e8i 0.161731 0.888225i
\(585\) −5.00953e7 3.66078e8i −0.250224 1.82854i
\(586\) 2.78371e8 + 1.67326e7i 1.38334 + 0.0831515i
\(587\) −1.74163e8 + 3.01659e8i −0.861075 + 1.49143i 0.00981689 + 0.999952i \(0.496875\pi\)
−0.870892 + 0.491474i \(0.836458\pi\)
\(588\) 1.24735e7 3.84267e7i 0.0613557 0.189017i
\(589\) −1.37910e8 + 7.96224e7i −0.674916 + 0.389663i
\(590\) −2.46814e8 4.93734e8i −1.20175 2.40401i
\(591\) −5.31182e6 1.55180e7i −0.0257324 0.0751751i
\(592\) −1.09709e8 1.05059e8i −0.528785 0.506368i
\(593\) −5.02983e7 −0.241206 −0.120603 0.992701i \(-0.538483\pi\)
−0.120603 + 0.992701i \(0.538483\pi\)
\(594\) 1.76305e7 1.48923e8i 0.0841214 0.710565i
\(595\) −4.89387e8 −2.32328
\(596\) 6.90613e7 + 5.18145e7i 0.326209 + 0.244744i
\(597\) −6.54564e7 1.91225e8i −0.307630 0.898716i
\(598\) 1.85587e8 9.27735e7i 0.867847 0.433831i
\(599\) 6.10638e7 3.52552e7i 0.284121 0.164037i −0.351167 0.936313i \(-0.614215\pi\)
0.635288 + 0.772276i \(0.280882\pi\)
\(600\) −3.02363e8 1.18638e8i −1.39983 0.549248i
\(601\) −5.03593e7 + 8.72248e7i −0.231983 + 0.401806i −0.958392 0.285457i \(-0.907855\pi\)
0.726409 + 0.687263i \(0.241188\pi\)
\(602\) 2.42566e8 + 1.45804e7i 1.11184 + 0.0668314i
\(603\) −2.22109e8 9.06766e7i −1.01301 0.413565i
\(604\) −1.24303e7 + 1.03025e8i −0.0564121 + 0.467552i
\(605\) 1.48091e8 + 8.55004e7i 0.668748 + 0.386102i
\(606\) −1.06138e8 1.04461e8i −0.476930 0.469395i
\(607\) −1.44345e8 + 8.33374e7i −0.645408 + 0.372626i −0.786695 0.617342i \(-0.788209\pi\)
0.141287 + 0.989969i \(0.454876\pi\)
\(608\) −1.78861e8 + 4.06385e7i −0.795800 + 0.180812i
\(609\) 2.50628e8 + 2.18667e8i 1.10963 + 0.968127i
\(610\) 2.06687e7 + 1.36491e7i 0.0910591 + 0.0601333i
\(611\) −1.27902e8 −0.560728
\(612\) 3.28566e8 + 1.82784e8i 1.43340 + 0.797415i
\(613\) 2.84171e8i 1.23367i 0.787093 + 0.616834i \(0.211585\pi\)
−0.787093 + 0.616834i \(0.788415\pi\)
\(614\) 2.17785e8 + 1.43820e8i 0.940854 + 0.621318i
\(615\) −2.62056e8 5.14320e7i −1.12660 0.221110i
\(616\) −5.04193e7 1.40967e8i −0.215702 0.603082i
\(617\) 1.92213e8 + 3.32922e8i 0.818327 + 1.41738i 0.906914 + 0.421316i \(0.138432\pi\)
−0.0885868 + 0.996068i \(0.528235\pi\)
\(618\) 1.26013e6 348428.i 0.00533887 0.00147621i
\(619\) −1.69133e8 + 2.92946e8i −0.713108 + 1.23514i 0.250577 + 0.968097i \(0.419380\pi\)
−0.963685 + 0.267042i \(0.913954\pi\)
\(620\) 3.57532e8 + 4.31377e7i 1.50017 + 0.181001i
\(621\) −1.15083e7 + 1.98878e8i −0.0480546 + 0.830449i
\(622\) −6.34222e7 3.81225e6i −0.263554 0.0158420i
\(623\) −1.13071e8 6.52817e7i −0.467615 0.269977i
\(624\) 2.53729e7 + 2.82259e8i 0.104428 + 1.16170i
\(625\) 2.96063e7 + 5.12797e7i 0.121268 + 0.210042i
\(626\) 1.40509e8 7.02397e7i 0.572773 0.286325i
\(627\) 2.77201e7 1.41239e8i 0.112458 0.572998i
\(628\) −1.39285e8 1.04501e8i −0.562373 0.421930i
\(629\) 2.98856e8i 1.20091i
\(630\) 3.53144e8 2.68772e7i 1.41231 0.107488i
\(631\) 2.29825e8i 0.914766i −0.889270 0.457383i \(-0.848787\pi\)
0.889270 0.457383i \(-0.151213\pi\)
\(632\) −4.61043e7 + 5.43268e7i −0.182638 + 0.215210i
\(633\) −2.10353e7 1.83528e7i −0.0829348 0.0723586i
\(634\) −1.27175e8 2.54404e8i −0.499038 0.998290i
\(635\) 2.68758e8 + 4.65503e8i 1.04964 + 1.81803i
\(636\) −1.88241e8 + 1.69590e8i −0.731716 + 0.659218i
\(637\) −5.18853e7 2.99560e7i −0.200737 0.115895i
\(638\) −3.05140e8 1.83417e7i −1.17500 0.0706280i
\(639\) 2.02346e8 + 2.60937e8i 0.775520 + 1.00008i
\(640\) 3.78701e8 + 1.69234e8i 1.44463 + 0.645578i
\(641\) 2.57748e7 4.46433e7i 0.0978636 0.169505i −0.812937 0.582352i \(-0.802132\pi\)
0.910800 + 0.412848i \(0.135466\pi\)
\(642\) −1.12052e8 2.90700e7i −0.423462 0.109860i
\(643\) 7.87336e6 + 1.36371e7i 0.0296160 + 0.0512965i 0.880454 0.474132i \(-0.157238\pi\)
−0.850838 + 0.525429i \(0.823905\pi\)
\(644\) 7.80920e7 + 1.82905e8i 0.292381 + 0.684805i
\(645\) −1.71101e8 4.99858e8i −0.637638 1.86281i
\(646\) 3.01133e8 + 1.98861e8i 1.11702 + 0.737653i
\(647\) 1.32978e8i 0.490985i −0.969398 0.245492i \(-0.921050\pi\)
0.969398 0.245492i \(-0.0789497\pi\)
\(648\) −2.47133e8 1.13853e8i −0.908251 0.418426i
\(649\) −3.32231e8 −1.21536
\(650\) −2.65430e8 + 4.01937e8i −0.966517 + 1.46358i
\(651\) −2.23131e8 + 7.63776e7i −0.808753 + 0.276836i
\(652\) 4.31877e7 + 1.01153e8i 0.155818 + 0.364952i
\(653\) −4.64214e8 + 2.68014e8i −1.66717 + 0.962539i −0.698012 + 0.716086i \(0.745932\pi\)
−0.969155 + 0.246453i \(0.920735\pi\)
\(654\) −893602. + 3.44444e6i −0.00319456 + 0.0123136i
\(655\) 7.16296e8 + 4.13554e8i 2.54899 + 1.47166i
\(656\) 1.98952e8 + 4.87180e7i 0.704754 + 0.172575i
\(657\) 2.02330e8 1.56899e8i 0.713451 0.553252i
\(658\) 7.35590e6 1.22376e8i 0.0258201 0.429555i
\(659\) 2.37942e8 4.12128e8i 0.831409 1.44004i −0.0655116 0.997852i \(-0.520868\pi\)
0.896921 0.442191i \(-0.145799\pi\)
\(660\) −2.41832e8 + 2.17871e8i −0.841165 + 0.757824i
\(661\) 3.57978e8 2.06679e8i 1.23952 0.715636i 0.270522 0.962714i \(-0.412804\pi\)
0.968995 + 0.247078i \(0.0794705\pi\)
\(662\) −1.81807e8 + 9.08841e7i −0.626667 + 0.313266i
\(663\) 3.66562e8 4.20139e8i 1.25779 1.44163i
\(664\) 5.02116e6 + 4.26121e6i 0.0171514 + 0.0145555i
\(665\) 3.39925e8 1.15589
\(666\) −1.64132e7 2.15655e8i −0.0555609 0.730024i
\(667\) 4.06079e8 1.36846
\(668\) 5.65398e7 + 4.24200e7i 0.189681 + 0.142312i
\(669\) 3.76412e8 + 7.38759e7i 1.25714 + 0.246731i
\(670\) 2.32834e8 + 4.65769e8i 0.774146 + 1.54862i
\(671\) 1.29106e7 7.45393e6i 0.0427345 0.0246728i
\(672\) −2.71524e8 + 8.04347e6i −0.894747 + 0.0265055i
\(673\) −1.07293e8 + 1.85837e8i −0.351987 + 0.609660i −0.986598 0.163173i \(-0.947827\pi\)
0.634610 + 0.772832i \(0.281161\pi\)
\(674\) −3.09106e7 + 5.14243e8i −0.100955 + 1.67953i
\(675\) −2.07710e8 4.13197e8i −0.675376 1.34352i
\(676\) 1.10546e8 + 1.33379e7i 0.357853 + 0.0431764i
\(677\) −4.27718e8 2.46943e8i −1.37845 0.795849i −0.386478 0.922299i \(-0.626308\pi\)
−0.991973 + 0.126450i \(0.959642\pi\)
\(678\) −5.64129e7 2.04024e8i −0.181005 0.654623i
\(679\) 2.22643e8 1.28543e8i 0.711213 0.410619i
\(680\) −2.74838e8 7.68419e8i −0.874077 2.44383i
\(681\) 5.98025e7 3.04706e8i 0.189356 0.964804i
\(682\) 1.19444e8 1.80872e8i 0.376540 0.570189i
\(683\) −2.57573e7 −0.0808424 −0.0404212 0.999183i \(-0.512870\pi\)
−0.0404212 + 0.999183i \(0.512870\pi\)
\(684\) −2.28220e8 1.26961e8i −0.713157 0.396735i
\(685\) 9.58450e8i 2.98193i
\(686\) 1.90890e8 2.89062e8i 0.591303 0.895403i
\(687\) −1.91653e8 + 2.19665e8i −0.591077 + 0.677471i
\(688\) 1.13330e8 + 3.89057e8i 0.348002 + 1.19467i
\(689\) 1.87866e8 + 3.25394e8i 0.574370 + 0.994838i
\(690\) 3.03304e8 3.08173e8i 0.923275 0.938097i
\(691\) 2.74595e6 4.75612e6i 0.00832258 0.0144151i −0.861834 0.507190i \(-0.830684\pi\)
0.870157 + 0.492775i \(0.164017\pi\)
\(692\) −4.60424e7 + 3.81607e8i −0.138944 + 1.15159i
\(693\) 8.05695e7 1.97352e8i 0.242087 0.592984i
\(694\) −1.80723e7 + 3.00659e8i −0.0540675 + 0.899490i
\(695\) 2.31807e7 + 1.33834e7i 0.0690513 + 0.0398668i
\(696\) −2.02592e8 + 5.16331e8i −0.600889 + 1.53144i
\(697\) −2.01497e8 3.49004e8i −0.595074 1.03070i
\(698\) 1.92202e8 + 3.84487e8i 0.565188 + 1.13062i
\(699\) 4.46441e8 1.52817e8i 1.30717 0.447445i
\(700\) −3.69307e8 2.77079e8i −1.07670 0.807810i
\(701\) 4.47882e8i 1.30020i −0.759849 0.650100i \(-0.774727\pi\)
0.759849 0.650100i \(-0.225273\pi\)
\(702\) −2.41438e8 + 3.23306e8i −0.697902 + 0.934549i
\(703\) 2.07583e8i 0.597483i
\(704\) 1.93027e8 1.58333e8i 0.553222 0.453789i
\(705\) −2.52181e8 + 8.63216e7i −0.719689 + 0.246350i
\(706\) 9.47627e7 4.73712e7i 0.269292 0.134617i
\(707\) −1.05842e8 1.83324e8i −0.299502 0.518752i
\(708\) −1.86114e8 + 5.73358e8i −0.524421 + 1.61557i
\(709\) 9.07652e7 + 5.24033e7i 0.254672 + 0.147035i 0.621901 0.783095i \(-0.286360\pi\)
−0.367230 + 0.930130i \(0.619694\pi\)
\(710\) 4.30031e7 7.15419e8i 0.120150 1.99887i
\(711\) −1.00515e8 + 1.37549e7i −0.279656 + 0.0382691i
\(712\) 3.90027e7 2.14202e8i 0.108058 0.593450i
\(713\) −1.43967e8 + 2.49358e8i −0.397186 + 0.687946i
\(714\) 3.80907e8 + 3.74889e8i 1.04646 + 1.02993i
\(715\) 2.41351e8 + 4.18032e8i 0.660284 + 1.14364i
\(716\) −2.07153e8 4.85187e8i −0.564355 1.32181i
\(717\) −1.98101e8 + 2.27055e8i −0.537438 + 0.615991i
\(718\) 1.16804e8 1.76875e8i 0.315563 0.477853i
\(719\) 2.88873e8i 0.777179i 0.921411 + 0.388589i \(0.127038\pi\)
−0.921411 + 0.388589i \(0.872962\pi\)
\(720\) 2.40525e8 + 5.39399e8i 0.644412 + 1.44515i
\(721\) 1.85842e6 0.00495836
\(722\) 1.04900e8 + 6.92739e7i 0.278719 + 0.184059i
\(723\) −3.18724e7 + 1.62396e8i −0.0843333 + 0.429695i
\(724\) 5.70911e8 2.43753e8i 1.50436 0.642295i
\(725\) −8.16408e8 + 4.71354e8i −2.14236 + 1.23689i
\(726\) −4.97678e7 1.79991e8i −0.130059 0.470371i
\(727\) −3.46492e8 2.00047e8i −0.901757 0.520630i −0.0239870 0.999712i \(-0.507636\pi\)
−0.877770 + 0.479083i \(0.840969\pi\)
\(728\) −7.21629e7 + 3.96317e8i −0.187034 + 1.02719i
\(729\) −1.53717e8 3.55620e8i −0.396771 0.917918i
\(730\) −5.54733e8 3.33445e7i −1.42599 0.0857147i
\(731\) 3.98633e8 6.90453e8i 1.02052 1.76759i
\(732\) −5.63141e6 2.64565e7i −0.0143577 0.0674528i
\(733\) −8.75538e7 + 5.05492e7i −0.222312 + 0.128352i −0.607020 0.794686i \(-0.707635\pi\)
0.384708 + 0.923038i \(0.374302\pi\)
\(734\) 6.96395e7 + 1.39309e8i 0.176103 + 0.352282i
\(735\) −1.22519e8 2.40460e7i −0.308561 0.0605592i
\(736\) −2.43334e8 + 2.25336e8i −0.610337 + 0.565193i
\(737\) 3.13413e8 0.782916
\(738\) 1.64568e8 + 2.40776e8i 0.409428 + 0.599024i
\(739\) −1.25348e8 −0.310588 −0.155294 0.987868i \(-0.549633\pi\)
−0.155294 + 0.987868i \(0.549633\pi\)
\(740\) −2.81728e8 + 3.75504e8i −0.695241 + 0.926657i
\(741\) −2.54611e8 + 2.91826e8i −0.625782 + 0.717248i
\(742\) −3.22141e8 + 1.61036e8i −0.788560 + 0.394196i
\(743\) 4.97007e8 2.86947e8i 1.21170 0.699577i 0.248573 0.968613i \(-0.420038\pi\)
0.963130 + 0.269036i \(0.0867051\pi\)
\(744\) −2.45234e8 3.07458e8i −0.595474 0.746565i
\(745\) 1.33412e8 2.31076e8i 0.322645 0.558838i
\(746\) −6.93814e8 4.17045e7i −1.67119 0.100454i
\(747\) 1.27130e6 + 9.29016e6i 0.00304990 + 0.0222875i
\(748\) −4.87653e8 5.88372e7i −1.16521 0.140588i
\(749\) −1.42503e8 8.22744e7i −0.339141 0.195803i
\(750\) −8.44407e7 + 3.25482e8i −0.200156 + 0.771512i
\(751\) −1.76012e7 + 1.01620e7i −0.0415549 + 0.0239917i −0.520634 0.853780i \(-0.674304\pi\)
0.479079 + 0.877772i \(0.340971\pi\)
\(752\) 1.96282e8 5.71758e7i 0.461558 0.134449i
\(753\) 2.69216e8 9.21526e7i 0.630545 0.215835i
\(754\) 6.86368e8 + 4.53262e8i 1.60119 + 1.05739i
\(755\) 3.20703e8 0.745181
\(756\) −2.95453e8 2.49602e8i −0.683790 0.577673i
\(757\) 2.30422e8i 0.531173i 0.964087 + 0.265587i \(0.0855657\pi\)
−0.964087 + 0.265587i \(0.914434\pi\)
\(758\) −6.78668e8 4.48177e8i −1.55829 1.02906i
\(759\) −8.42825e7 2.46224e8i −0.192758 0.563126i
\(760\) 1.90900e8 + 5.33738e8i 0.434876 + 1.21587i
\(761\) −2.29064e8 3.96750e8i −0.519759 0.900250i −0.999736 0.0229684i \(-0.992688\pi\)
0.479977 0.877281i \(-0.340645\pi\)
\(762\) 1.47409e8 5.68195e8i 0.333164 1.28420i
\(763\) −2.52909e6 + 4.38051e6i −0.00569365 + 0.00986169i
\(764\) −3.62641e6 + 3.00563e7i −0.00813199 + 0.0673993i
\(765\) 4.39188e8 1.07578e9i 0.980993 2.40291i
\(766\) 7.09671e8 + 4.26576e7i 1.57896 + 0.0949097i
\(767\) 7.74172e8 + 4.46968e8i 1.71574 + 0.990583i
\(768\) −1.65116e8 4.21820e8i −0.364507 0.931201i
\(769\) −2.41434e8 4.18175e8i −0.530907 0.919559i −0.999349 0.0360644i \(-0.988518\pi\)
0.468442 0.883494i \(-0.344815\pi\)
\(770\) −4.13853e8 + 2.06882e8i −0.906512 + 0.453159i
\(771\) −6.34579e8 5.53655e8i −1.38459 1.20803i
\(772\) 1.56050e8 2.07992e8i 0.339166 0.452060i
\(773\) 4.31231e8i 0.933623i 0.884357 + 0.466812i \(0.154597\pi\)
−0.884357 + 0.466812i \(0.845403\pi\)
\(774\) −2.49736e8 + 5.20126e8i −0.538589 + 1.12172i
\(775\) 6.68434e8i 1.43600i
\(776\) 3.26869e8 + 2.77397e8i 0.699501 + 0.593631i
\(777\) 5.92075e7 3.01674e8i 0.126216 0.643094i
\(778\) −4.01624e8 8.03419e8i −0.852865 1.70610i
\(779\) 1.39959e8 + 2.42415e8i 0.296065 + 0.512800i
\(780\) 8.56636e8 1.82339e8i 1.80515 0.384235i
\(781\) −3.73581e8 2.15687e8i −0.784209 0.452763i
\(782\) 6.51319e8 + 3.91502e7i 1.36199 + 0.0818678i
\(783\) −7.05596e8 + 3.54696e8i −1.46984 + 0.738876i
\(784\) 9.30160e7 + 2.27771e7i 0.193023 + 0.0472661i
\(785\) −2.69068e8 + 4.66040e8i −0.556229 + 0.963416i
\(786\) −2.40720e8 8.70592e8i −0.495730 1.79286i
\(787\) −2.32120e8 4.02043e8i −0.476199 0.824800i 0.523430 0.852069i \(-0.324652\pi\)
−0.999628 + 0.0272688i \(0.991319\pi\)
\(788\) 3.57561e7 1.52662e7i 0.0730754 0.0311999i
\(789\) −2.73815e8 5.37398e7i −0.557475 0.109412i
\(790\) 1.83753e8 + 1.21346e8i 0.372695 + 0.246119i
\(791\) 3.00891e8i 0.607966i
\(792\) 3.55123e8 + 1.56753e7i 0.714831 + 0.0315529i
\(793\) −4.01128e7 −0.0804383
\(794\) −1.42107e8 + 2.15190e8i −0.283892 + 0.429894i
\(795\) 5.90023e8 + 5.14781e8i 1.17427 + 1.02452i
\(796\) 4.40615e8 1.88123e8i 0.873614 0.372994i
\(797\) 8.22351e8 4.74784e8i 1.62436 0.937824i 0.638624 0.769519i \(-0.279504\pi\)
0.985735 0.168305i \(-0.0538294\pi\)
\(798\) −2.64575e8 2.60395e8i −0.520644 0.512418i
\(799\) −3.48338e8 2.01113e8i −0.682904 0.394275i
\(800\) 2.27659e8 7.35479e8i 0.444646 1.43648i
\(801\) 2.44976e8 1.89969e8i 0.476678 0.369645i
\(802\) 2.63595e7 4.38528e8i 0.0510992 0.850109i
\(803\) −1.67243e8 + 2.89674e8i −0.322999 + 0.559451i
\(804\) 1.75573e8 5.40883e8i 0.337823 1.04072i
\(805\) 5.32281e8 3.07312e8i 1.02036 0.589105i
\(806\) −5.21669e8 + 2.60779e8i −0.996299 + 0.498043i
\(807\) 1.44928e8 + 4.23396e8i 0.275761 + 0.805612i
\(808\) 2.28408e8 2.69143e8i 0.432989 0.510210i
\(809\) 5.30810e7 0.100252 0.0501261 0.998743i \(-0.484038\pi\)
0.0501261 + 0.998743i \(0.484038\pi\)
\(810\) −2.57838e8 + 8.00403e8i −0.485167 + 1.50610i
\(811\) −4.91860e8 −0.922103 −0.461051 0.887373i \(-0.652528\pi\)
−0.461051 + 0.887373i \(0.652528\pi\)
\(812\) −4.73155e8 + 6.30648e8i −0.883762 + 1.17793i
\(813\) 4.30699e7 + 1.25825e8i 0.0801497 + 0.234151i
\(814\) 1.26337e8 + 2.52729e8i 0.234238 + 0.468577i
\(815\) 2.94370e8 1.69955e8i 0.543778 0.313950i
\(816\) −3.74721e8 + 8.08622e8i −0.689665 + 1.48825i
\(817\) −2.76888e8 + 4.79584e8i −0.507736 + 0.879424i
\(818\) −2.88508e6 + 4.79975e7i −0.00527106 + 0.0876917i
\(819\) −4.53254e8 + 3.51480e8i −0.825068 + 0.639808i
\(820\) 7.58266e7 6.28463e8i 0.137524 1.13982i
\(821\) −2.14262e8 1.23704e8i −0.387183 0.223540i 0.293756 0.955880i \(-0.405095\pi\)
−0.680939 + 0.732340i \(0.738428\pi\)
\(822\) 7.34208e8 7.45994e8i 1.32192 1.34314i
\(823\) 6.18395e7 3.57030e7i 0.110934 0.0640480i −0.443506 0.896271i \(-0.646266\pi\)
0.554441 + 0.832223i \(0.312932\pi\)
\(824\) 1.04368e6 + 2.91802e6i 0.00186546 + 0.00521563i
\(825\) 4.55250e8 + 3.97195e8i 0.810753 + 0.707363i
\(826\) −4.72183e8 + 7.15020e8i −0.837857 + 1.26876i
\(827\) −1.79566e8 −0.317473 −0.158737 0.987321i \(-0.550742\pi\)
−0.158737 + 0.987321i \(0.550742\pi\)
\(828\) −4.72144e8 + 7.51958e6i −0.831732 + 0.0132465i
\(829\) 1.75930e8i 0.308800i 0.988008 + 0.154400i \(0.0493444\pi\)
−0.988008 + 0.154400i \(0.950656\pi\)
\(830\) 1.12155e7 1.69835e7i 0.0196148 0.0297024i
\(831\) 3.35750e8 + 6.58955e7i 0.585077 + 0.114829i
\(832\) −6.62810e8 + 1.09262e8i −1.15085 + 0.189715i
\(833\) −9.42058e7 1.63169e8i −0.162983 0.282295i
\(834\) −7.79016e6 2.81740e7i −0.0134291 0.0485680i
\(835\) 1.09223e8 1.89179e8i 0.187609 0.324948i
\(836\) 3.38720e8 + 4.08679e7i 0.579725 + 0.0699461i
\(837\) 3.23488e7 5.59031e8i 0.0551672 0.953365i
\(838\) −2.49682e7 + 4.15382e8i −0.0424282 + 0.705855i
\(839\) 3.41702e8 + 1.97282e8i 0.578577 + 0.334042i 0.760568 0.649259i \(-0.224921\pi\)
−0.181991 + 0.983300i \(0.558254\pi\)
\(840\) 1.25195e8 + 8.30114e8i 0.211227 + 1.40055i
\(841\) 5.07496e8 + 8.79010e8i 0.853189 + 1.47777i
\(842\) 3.22553e7 + 6.45243e7i 0.0540337 + 0.108090i
\(843\) −5.79202e7 + 2.95114e8i −0.0966823 + 0.492615i
\(844\) 3.97119e7 5.29303e7i 0.0660531 0.0880394i
\(845\) 3.44117e8i 0.570343i
\(846\) 2.62407e8 + 1.25993e8i 0.433375 + 0.208082i
\(847\) 2.65448e8i 0.436847i
\(848\) −4.33766e8 4.15378e8i −0.711325 0.681170i
\(849\) −3.69680e8 3.22537e8i −0.604092 0.527056i
\(850\) −1.35490e9 + 6.77305e8i −2.20623 + 1.10288i
\(851\) −1.87667e8 3.25049e8i −0.304509 0.527425i
\(852\) −5.81508e8 + 5.23893e8i −0.940236 + 0.847079i
\(853\) −2.25261e8 1.30054e8i −0.362943 0.209545i 0.307428 0.951571i \(-0.400532\pi\)
−0.670371 + 0.742026i \(0.733865\pi\)
\(854\) 2.30697e6 3.83798e7i 0.00370398 0.0616211i
\(855\) −3.05057e8 + 7.47226e8i −0.488070 + 1.19551i
\(856\) 4.91550e7 2.69959e8i 0.0783694 0.430404i
\(857\) 1.14395e8 1.98138e8i 0.181746 0.314793i −0.760729 0.649069i \(-0.775159\pi\)
0.942475 + 0.334276i \(0.108492\pi\)
\(858\) 1.32376e8 5.10252e8i 0.209579 0.807835i
\(859\) −2.36395e8 4.09449e8i −0.372958 0.645982i 0.617061 0.786915i \(-0.288323\pi\)
−0.990019 + 0.140933i \(0.954990\pi\)
\(860\) 1.15176e9 4.91747e8i 1.81078 0.773120i
\(861\) 1.34255e8 + 3.92214e8i 0.210340 + 0.614489i
\(862\) −2.75033e7 + 4.16479e7i −0.0429401 + 0.0650237i
\(863\) 3.89747e8i 0.606388i −0.952929 0.303194i \(-0.901947\pi\)
0.952929 0.303194i \(-0.0980530\pi\)
\(864\) 2.25991e8 6.04084e8i 0.350388 0.936605i
\(865\) 1.18789e9 1.83539
\(866\) −1.75347e7 1.15795e7i −0.0269988 0.0178294i
\(867\) 1.04236e9 3.56800e8i 1.59941 0.547479i
\(868\) −2.19510e8 5.14130e8i −0.335657 0.786165i
\(869\) 1.14781e8 6.62686e7i 0.174908 0.100983i
\(870\) 1.65921e9 + 4.30453e8i 2.51967 + 0.653685i
\(871\) −7.30323e8 4.21652e8i −1.10525 0.638116i
\(872\) −8.29845e6 1.51101e6i −0.0125155 0.00227886i
\(873\) 8.27592e7 + 6.04773e8i 0.124387 + 0.908970i
\(874\) −4.52401e8 2.71934e7i −0.677625 0.0407314i
\(875\) −2.38986e8 + 4.13935e8i −0.356737 + 0.617886i
\(876\) 4.06225e8 + 4.50899e8i 0.604302 + 0.670760i
\(877\) 1.08030e8 6.23709e7i 0.160156 0.0924663i −0.417780 0.908548i \(-0.637192\pi\)
0.577936 + 0.816082i \(0.303858\pi\)
\(878\) −3.18962e8 6.38060e8i −0.471254 0.942710i
\(879\) −6.18768e8 + 7.09209e8i −0.911090 + 1.04426i
\(880\) −5.57257e8 5.33633e8i −0.817725 0.783059i
\(881\) −2.68274e8 −0.392330 −0.196165 0.980571i \(-0.562849\pi\)
−0.196165 + 0.980571i \(0.562849\pi\)
\(882\) 7.69405e7 + 1.12570e8i 0.112137 + 0.164065i
\(883\) 3.81495e8 0.554124 0.277062 0.960852i \(-0.410639\pi\)
0.277062 + 0.960852i \(0.410639\pi\)
\(884\) 1.05718e9 + 7.93170e8i 1.53036 + 1.14818i
\(885\) 1.82808e9 + 3.58785e8i 2.63734 + 0.517613i
\(886\) −6.15387e8 + 3.07627e8i −0.884804 + 0.442307i
\(887\) −1.06726e9 + 6.16182e8i −1.52932 + 0.882954i −0.529930 + 0.848041i \(0.677782\pi\)
−0.999390 + 0.0349124i \(0.988885\pi\)
\(888\) 5.06928e8 7.64531e7i 0.723948 0.109183i
\(889\) 4.17199e8 7.22609e8i 0.593796 1.02849i
\(890\) −6.71656e8 4.03726e7i −0.952746 0.0572686i
\(891\) 3.61517e8 + 3.54217e8i 0.511087 + 0.500768i
\(892\) −1.08916e8 + 9.02711e8i −0.153460 + 1.27190i
\(893\) 2.41953e8 + 1.39691e8i 0.339763 + 0.196162i
\(894\) −2.80852e8 + 7.76560e7i −0.393065 + 0.108683i
\(895\) −1.41197e9 + 8.15201e8i −1.96950 + 1.13709i
\(896\) −6.64225e7 6.40459e8i −0.0923402 0.890364i
\(897\) −1.34862e8 + 6.87147e8i −0.186858 + 0.952078i
\(898\) 6.64146e8 + 4.38587e8i 0.917138 + 0.605657i
\(899\) −1.14145e9 −1.57101
\(900\) 9.40502e8 5.63156e8i 1.29013 0.772505i
\(901\) 1.18161e9i 1.61547i
\(902\) −3.17934e8 2.09956e8i −0.433229 0.286094i
\(903\) −5.39181e8 + 6.17990e8i −0.732271 + 0.839301i
\(904\) 4.72448e8 1.68979e8i 0.639512 0.228732i
\(905\) −9.59233e8 1.66144e9i −1.29413 2.24150i
\(906\) −2.49614e8 2.45670e8i −0.335648 0.330345i
\(907\) 2.03038e8 3.51672e8i 0.272117 0.471320i −0.697287 0.716792i \(-0.745610\pi\)
0.969404 + 0.245472i \(0.0789429\pi\)
\(908\) 7.30744e8 + 8.81672e7i 0.976131 + 0.117774i
\(909\) 4.97968e8 6.81437e7i 0.662995 0.0907264i
\(910\) 1.24270e9 + 7.46974e7i 1.64908 + 0.0991246i
\(911\) −5.04498e8 2.91272e8i −0.667274 0.385251i 0.127769 0.991804i \(-0.459218\pi\)
−0.795043 + 0.606553i \(0.792552\pi\)
\(912\) 2.60279e8 5.61663e8i 0.343126 0.740443i
\(913\) −6.12490e6 1.06086e7i −0.00804797 0.0139395i
\(914\) −3.31364e8 + 1.65647e8i −0.433977 + 0.216942i
\(915\) −7.90895e7 + 2.70723e7i −0.103242 + 0.0353397i
\(916\) −5.52736e8 4.14700e8i −0.719169 0.539569i
\(917\) 1.28394e9i 1.66508i
\(918\) −1.16592e9 + 5.00879e8i −1.50709 + 0.647448i
\(919\) 2.58453e8i 0.332992i −0.986042 0.166496i \(-0.946755\pi\)
0.986042 0.166496i \(-0.0532454\pi\)
\(920\) 7.81458e8 + 6.63183e8i 1.00356 + 0.851667i
\(921\) −8.33362e8 + 2.85260e8i −1.06673 + 0.365142i
\(922\) 8.28392e7 + 1.65714e8i 0.105692 + 0.211430i
\(923\) 5.80352e8 + 1.00520e9i 0.738050 + 1.27834i
\(924\) 4.80595e8 + 1.56003e8i 0.609205 + 0.197750i
\(925\) 7.54598e8 + 4.35667e8i 0.953434 + 0.550465i
\(926\) 6.95617e8 + 4.18128e7i 0.876066 + 0.0526595i
\(927\) −1.66779e6 + 4.08519e6i −0.00209364 + 0.00512830i
\(928\) −1.25594e9 3.88762e8i −1.57154 0.486451i
\(929\) −2.67285e8 + 4.62952e8i −0.333371 + 0.577416i −0.983171 0.182690i \(-0.941520\pi\)
0.649799 + 0.760106i \(0.274853\pi\)
\(930\) −8.52563e8 + 8.66249e8i −1.05993 + 1.07695i
\(931\) 6.54347e7 + 1.13336e8i 0.0810885 + 0.140449i
\(932\) 4.39198e8 + 1.02867e9i 0.542516 + 1.27066i
\(933\) 1.40976e8 1.61582e8i 0.173580 0.198952i
\(934\) 2.58187e8 + 1.70501e8i 0.316880 + 0.209260i
\(935\) 1.51800e9i 1.85711i
\(936\) −8.06427e8 5.14294e8i −0.983417 0.627167i
\(937\) −4.53409e8 −0.551152 −0.275576 0.961279i \(-0.588869\pi\)
−0.275576 + 0.961279i \(0.588869\pi\)
\(938\) 4.45439e8 6.74522e8i 0.539733 0.817311i
\(939\) −1.02105e8 + 5.20245e8i −0.123325 + 0.628364i
\(940\) −2.48089e8 5.81067e8i −0.298693 0.699588i
\(941\) −7.67813e8 + 4.43297e8i −0.921481 + 0.532017i −0.884107 0.467284i \(-0.845233\pi\)
−0.0373737 + 0.999301i \(0.511899\pi\)
\(942\) 5.66429e8 1.56619e8i 0.677630 0.187366i
\(943\) 4.38316e8 + 2.53062e8i 0.522700 + 0.301781i
\(944\) −1.38788e9 3.39853e8i −1.64981 0.403994i
\(945\) −6.56456e8 + 9.98911e8i −0.777876 + 1.18367i
\(946\) 4.52262e7 7.52402e8i 0.0534215 0.888744i
\(947\) −1.30828e7 + 2.26601e7i −0.0154047 + 0.0266816i −0.873625 0.486600i \(-0.838237\pi\)
0.858220 + 0.513281i \(0.171570\pi\)
\(948\) −5.00656e7 2.35210e8i −0.0587645 0.276077i
\(949\) 7.79428e8 4.50003e8i 0.911963 0.526522i
\(950\) 9.41103e8 4.70451e8i 1.09766 0.548711i
\(951\) 9.41949e8 + 1.84870e8i 1.09518 + 0.214944i
\(952\) −8.19705e8 + 9.65894e8i −0.950050 + 1.11949i
\(953\) 6.67253e8 0.770925 0.385462 0.922724i \(-0.374042\pi\)
0.385462 + 0.922724i \(0.374042\pi\)
\(954\) −6.48939e7 8.52651e8i −0.0747409 0.982034i
\(955\) 9.35614e7 0.107420
\(956\) −5.71332e8 4.28652e8i −0.653905 0.490604i
\(957\) 6.78271e8 7.77410e8i 0.773869 0.886981i
\(958\) 4.02947e8 + 8.06066e8i 0.458301 + 0.916799i
\(959\) 1.28849e9 7.43910e8i 1.46092 0.843461i
\(960\) −1.23311e9 + 6.62765e8i −1.39376 + 0.749111i
\(961\) −3.90732e7 + 6.76768e7i −0.0440260 + 0.0762552i
\(962\) 4.56157e7 7.58882e8i 0.0512376 0.852411i
\(963\) 3.08742e8 2.39417e8i 0.345714 0.268087i
\(964\) −3.89458e8 4.69896e7i −0.434740 0.0524531i
\(965\) −6.95933e8 4.01797e8i −0.774436 0.447121i
\(966\) −6.49705e8 1.68555e8i −0.720750 0.186986i
\(967\) −1.20372e9 + 6.94967e8i −1.33121 + 0.768572i −0.985485 0.169765i \(-0.945699\pi\)
−0.345721 + 0.938337i \(0.612366\pi\)
\(968\) 4.16797e8 1.49074e8i 0.459513 0.164353i
\(969\) −1.15230e9 + 3.94431e8i −1.26646 + 0.433511i
\(970\) 7.30108e8 1.10559e9i 0.799966 1.21138i
\(971\) −1.34516e8 −0.146932 −0.0734659 0.997298i \(-0.523406\pi\)
−0.0734659 + 0.997298i \(0.523406\pi\)
\(972\) 8.13822e8 4.25468e8i 0.886198 0.463306i
\(973\) 4.15505e7i 0.0451064i
\(974\) 9.38425e8 1.42104e9i 1.01560 1.53791i
\(975\) −5.26467e8 1.53803e9i −0.568011 1.65940i
\(976\) 6.15582e7 1.79316e7i 0.0662120 0.0192872i
\(977\) 2.57064e8 + 4.45248e8i 0.275650 + 0.477439i 0.970299 0.241909i \(-0.0777737\pi\)
−0.694649 + 0.719349i \(0.744440\pi\)
\(978\) −3.59310e8 9.32169e7i −0.384108 0.0996502i
\(979\) −2.02494e8 + 3.50729e8i −0.215806 + 0.373787i
\(980\) 3.54511e7 2.93825e8i 0.0376662 0.312183i
\(981\) −7.35962e6 9.49065e6i −0.00779558 0.0100528i
\(982\) 3.76431e7 6.26247e8i 0.0397513 0.661320i
\(983\) 1.07148e8 + 6.18618e7i 0.112804 + 0.0651272i 0.555340 0.831623i \(-0.312588\pi\)
−0.442537 + 0.896750i \(0.645921\pi\)
\(984\) −5.40444e8 + 4.31068e8i −0.567238 + 0.452440i
\(985\) −6.00766e7 1.04056e8i −0.0628633 0.108882i
\(986\) 1.15660e9 + 2.31370e9i 1.20657 + 2.41366i
\(987\) 3.11779e8 + 2.72020e8i 0.324262 + 0.282911i
\(988\) −7.34311e8 5.50930e8i −0.761394 0.571249i
\(989\) 1.00129e9i 1.03508i
\(990\) −8.33687e7 1.09540e9i −0.0859206 1.12893i
\(991\) 1.43046e9i 1.46979i −0.678183 0.734893i \(-0.737232\pi\)
0.678183 0.734893i \(-0.262768\pi\)
\(992\) 6.83992e8 6.33400e8i 0.700674 0.648848i
\(993\) 1.32115e8 6.73153e8i 0.134929 0.687489i
\(994\) −9.95149e8 + 4.97468e8i −1.01328 + 0.506531i
\(995\) −7.40311e8 1.28226e9i −0.751528 1.30168i
\(996\) −2.17393e7 + 4.62733e6i −0.0220023 + 0.00468330i
\(997\) −4.98265e8 2.87674e8i −0.502777 0.290278i 0.227083 0.973875i \(-0.427081\pi\)
−0.729860 + 0.683597i \(0.760415\pi\)
\(998\) −9.79478e7 + 1.62950e9i −0.0985379 + 1.63932i
\(999\) 6.10008e8 + 4.00880e8i 0.611841 + 0.402085i
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 72.7.p.b.43.14 136
8.3 odd 2 inner 72.7.p.b.43.60 yes 136
9.4 even 3 inner 72.7.p.b.67.60 yes 136
72.67 odd 6 inner 72.7.p.b.67.14 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.7.p.b.43.14 136 1.1 even 1 trivial
72.7.p.b.43.60 yes 136 8.3 odd 2 inner
72.7.p.b.67.14 yes 136 72.67 odd 6 inner
72.7.p.b.67.60 yes 136 9.4 even 3 inner