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Properties

Label 71.10.g.a.2.15
Level $71$
Weight $10$
Character 71.2
Analytic conductor $36.568$
Analytic rank $0$
Dimension $1272$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [71,10,Mod(2,71)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(71, base_ring=CyclotomicField(70))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("71.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 71 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 71.g (of order \(35\), degree \(24\), 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: \(36.5675443676\)
Analytic rank: \(0\)
Dimension: \(1272\)
Relative dimension: \(53\) over \(\Q(\zeta_{35})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label 2.15
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.07546 + 23.9470i) q^{2} +(111.649 + 97.5446i) q^{3} +(-62.3628 - 5.61275i) q^{4} +(-241.002 - 741.727i) q^{5} +(-2455.97 + 2568.75i) q^{6} +(8147.66 + 2248.61i) q^{7} +(-1446.00 + 10674.8i) q^{8} +(308.388 + 2276.61i) q^{9} +O(q^{10})\) \(q+(-1.07546 + 23.9470i) q^{2} +(111.649 + 97.5446i) q^{3} +(-62.3628 - 5.61275i) q^{4} +(-241.002 - 741.727i) q^{5} +(-2455.97 + 2568.75i) q^{6} +(8147.66 + 2248.61i) q^{7} +(-1446.00 + 10674.8i) q^{8} +(308.388 + 2276.61i) q^{9} +(18021.3 - 4973.57i) q^{10} +(29855.6 - 55481.0i) q^{11} +(-6415.24 - 6709.81i) q^{12} +(25618.1 + 47606.3i) q^{13} +(-62609.9 + 192694. i) q^{14} +(45443.9 - 106321. i) q^{15} +(-285617. - 51831.9i) q^{16} +(148185. + 107663. i) q^{17} +(-54849.7 + 4936.56i) q^{18} +(65646.1 + 153587. i) q^{19} +(10866.4 + 47608.9i) q^{20} +(690336. + 1.04581e6i) q^{21} +(1.29649e6 + 774619. i) q^{22} +(1.63390e6 + 2.04884e6i) q^{23} +(-1.20271e6 + 1.05078e6i) q^{24} +(1.08803e6 - 790503. i) q^{25} +(-1.16758e6 + 562277. i) q^{26} +(1.41997e6 - 2.15116e6i) q^{27} +(-495490. - 185960. i) q^{28} +(-3.15086e6 + 1.88255e6i) q^{29} +(2.49720e6 + 1.20259e6i) q^{30} +(-1.11192e6 + 201784. i) q^{31} +(321095. - 1.40681e6i) q^{32} +(8.74521e6 - 3.28213e6i) q^{33} +(-2.73757e6 + 3.43280e6i) q^{34} +(-295744. - 6.58526e6i) q^{35} +(-6453.88 - 143707. i) q^{36} +(298526. - 374340. i) q^{37} +(-3.74854e6 + 1.40685e6i) q^{38} +(-1.78352e6 + 7.81409e6i) q^{39} +(8.26626e6 - 1.50010e6i) q^{40} +(5.20788e6 + 2.50798e6i) q^{41} +(-2.57865e7 + 1.54067e7i) q^{42} +(-1.01311e7 - 3.80228e6i) q^{43} +(-2.17328e6 + 3.29238e6i) q^{44} +(1.61430e6 - 777407. i) q^{45} +(-5.08208e7 + 3.69234e7i) q^{46} +(-5.51720e6 + 4.82023e6i) q^{47} +(-2.68329e7 - 3.36474e7i) q^{48} +(2.66866e7 + 1.59445e7i) q^{49} +(1.77600e7 + 2.69053e7i) q^{50} +(6.04277e6 + 2.64751e7i) q^{51} +(-1.33041e6 - 3.11265e6i) q^{52} +(8.16912e6 - 735234. i) q^{53} +(4.99866e7 + 3.63174e7i) q^{54} +(-4.83470e7 - 8.77369e6i) q^{55} +(-3.57849e7 + 8.37229e7i) q^{56} +(-7.65225e6 + 2.35512e7i) q^{57} +(-4.16928e7 - 7.74782e7i) q^{58} +(-1.33194e7 - 1.39310e7i) q^{59} +(-3.43077e6 + 6.37543e6i) q^{60} +(-1.56206e8 + 4.31102e7i) q^{61} +(-3.63630e6 - 2.68442e7i) q^{62} +(-2.60657e6 + 1.92425e7i) q^{63} +(-1.09925e8 - 3.03374e7i) q^{64} +(2.91369e7 - 3.04748e7i) q^{65} +(6.91921e7 + 2.12951e8i) q^{66} +(-1.99785e8 - 1.79809e7i) q^{67} +(-8.63696e6 - 7.54589e6i) q^{68} +(-1.74309e7 + 3.88128e8i) q^{69} +1.58015e8 q^{70} +(-2.13458e8 + 1.68530e7i) q^{71} -2.47482e7 q^{72} +(230772. - 5.13855e6i) q^{73} +(8.64326e6 + 7.55139e6i) q^{74} +(1.98587e8 + 1.78732e7i) q^{75} +(-3.23183e6 - 9.94655e6i) q^{76} +(3.68008e8 - 3.84906e8i) q^{77} +(-1.85206e8 - 5.11136e7i) q^{78} +(6.48096e7 - 4.78443e8i) q^{79} +(3.03891e7 + 2.24342e8i) q^{80} +(4.11961e8 - 1.13694e8i) q^{81} +(-6.56595e7 + 1.22016e8i) q^{82} +(2.13401e8 + 2.23200e8i) q^{83} +(-3.71814e7 - 6.90946e7i) q^{84} +(4.41436e7 - 1.35860e8i) q^{85} +(1.01949e8 - 2.38521e8i) q^{86} +(-5.35423e8 - 9.71649e7i) q^{87} +(5.49076e8 + 3.98927e8i) q^{88} +(7.10190e8 - 6.39182e7i) q^{89} +(1.68804e7 + 3.94938e7i) q^{90} +(1.01679e8 + 4.45485e8i) q^{91} +(-9.03947e7 - 1.36942e8i) q^{92} +(-1.43828e8 - 8.59332e7i) q^{93} +(-1.09496e8 - 1.37304e8i) q^{94} +(9.80986e7 - 8.57062e7i) q^{95} +(1.73077e8 - 1.25748e8i) q^{96} +(6.72032e7 - 3.23633e7i) q^{97} +(-4.10522e8 + 6.21915e8i) q^{98} +(1.35516e8 + 5.08599e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15} + 4755334 q^{16} + 2558412 q^{17} - 2619769 q^{18} - 172269 q^{19} + 738120 q^{20} + 1797929 q^{21} + 3015622 q^{22} + 6635088 q^{23} + 4803145 q^{24} - 115100016 q^{25} + 19254293 q^{26} - 17686931 q^{27} + 15761532 q^{28} - 10052927 q^{29} + 62637435 q^{30} - 23748991 q^{31} + 10388192 q^{32} - 15097203 q^{33} + 33217854 q^{34} - 24823174 q^{35} + 27856812 q^{36} - 27156308 q^{37} - 43400577 q^{38} + 251072838 q^{39} - 129856160 q^{40} + 62087988 q^{41} - 91873950 q^{42} - 167299067 q^{43} + 60914131 q^{44} - 31536191 q^{45} - 50201490 q^{46} - 23317743 q^{47} + 10641329 q^{48} + 338745866 q^{49} + 303770229 q^{50} + 448039613 q^{51} - 979580293 q^{52} + 12085215 q^{53} - 182583505 q^{54} - 243892552 q^{55} + 30440435 q^{56} + 714581966 q^{57} - 244549660 q^{58} - 859013315 q^{59} - 1894499000 q^{60} - 876373921 q^{61} + 186553636 q^{62} - 196611021 q^{63} + 5528242635 q^{64} + 867018244 q^{65} + 2727701199 q^{66} - 286780089 q^{67} - 1689988351 q^{68} - 3073308182 q^{69} - 41489396 q^{70} - 2538053548 q^{71} - 6821388000 q^{72} + 128479023 q^{73} + 3282772334 q^{74} + 3407782757 q^{75} + 7133788844 q^{76} + 1087098389 q^{77} + 2715049934 q^{78} + 144243625 q^{79} - 7443877603 q^{80} - 4083269278 q^{81} - 10375744380 q^{82} + 1543773955 q^{83} - 4117054288 q^{84} + 7843382686 q^{85} + 3545751759 q^{86} + 5261609811 q^{87} - 818728797 q^{88} - 1369081479 q^{89} + 10041256259 q^{90} - 7299574322 q^{91} + 602797624 q^{92} - 2146129677 q^{93} - 683447510 q^{94} - 7007204038 q^{95} + 6601829126 q^{96} - 10081488030 q^{97} - 5942379880 q^{98} - 4074592265 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{35}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07546 + 23.9470i −0.0475291 + 1.05832i 0.823571 + 0.567213i \(0.191978\pi\)
−0.871101 + 0.491105i \(0.836593\pi\)
\(3\) 111.649 + 97.5446i 0.795808 + 0.695277i 0.956501 − 0.291728i \(-0.0942301\pi\)
−0.160693 + 0.987004i \(0.551373\pi\)
\(4\) −62.3628 − 5.61275i −0.121802 − 0.0109624i
\(5\) −241.002 − 741.727i −0.172447 − 0.530737i 0.827061 − 0.562112i \(-0.190011\pi\)
−0.999508 + 0.0313756i \(0.990011\pi\)
\(6\) −2455.97 + 2568.75i −0.773647 + 0.809172i
\(7\) 8147.66 + 2248.61i 1.28260 + 0.353975i 0.839923 − 0.542705i \(-0.182600\pi\)
0.442678 + 0.896681i \(0.354029\pi\)
\(8\) −1446.00 + 10674.8i −0.124814 + 0.921412i
\(9\) 308.388 + 2276.61i 0.0156677 + 0.115664i
\(10\) 18021.3 − 4973.57i 0.569884 − 0.157278i
\(11\) 29855.6 − 55481.0i 0.614835 − 1.14255i −0.362725 − 0.931896i \(-0.618153\pi\)
0.977560 − 0.210659i \(-0.0675608\pi\)
\(12\) −6415.24 − 6709.81i −0.0893094 − 0.0934103i
\(13\) 25618.1 + 47606.3i 0.248772 + 0.462296i 0.974103 − 0.226105i \(-0.0725991\pi\)
−0.725331 + 0.688400i \(0.758313\pi\)
\(14\) −62609.9 + 192694.i −0.435579 + 1.34057i
\(15\) 45443.9 − 106321.i 0.231774 − 0.542263i
\(16\) −285617. − 51831.9i −1.08954 − 0.197723i
\(17\) 148185. + 107663.i 0.430313 + 0.312641i 0.781774 − 0.623562i \(-0.214315\pi\)
−0.351461 + 0.936203i \(0.614315\pi\)
\(18\) −54849.7 + 4936.56i −0.123154 + 0.0110840i
\(19\) 65646.1 + 153587.i 0.115563 + 0.270372i 0.967318 − 0.253568i \(-0.0816042\pi\)
−0.851755 + 0.523941i \(0.824461\pi\)
\(20\) 10866.4 + 47608.9i 0.0151863 + 0.0665354i
\(21\) 690336. + 1.04581e6i 0.774593 + 1.17346i
\(22\) 1.29649e6 + 774619.i 1.17996 + 0.704995i
\(23\) 1.63390e6 + 2.04884e6i 1.21744 + 1.52663i 0.777876 + 0.628418i \(0.216297\pi\)
0.439568 + 0.898209i \(0.355131\pi\)
\(24\) −1.20271e6 + 1.05078e6i −0.739964 + 0.646487i
\(25\) 1.08803e6 − 790503.i 0.557073 − 0.404737i
\(26\) −1.16758e6 + 562277.i −0.501079 + 0.241307i
\(27\) 1.41997e6 − 2.15116e6i 0.514210 − 0.778995i
\(28\) −495490. − 185960.i −0.152343 − 0.0571754i
\(29\) −3.15086e6 + 1.88255e6i −0.827253 + 0.494261i −0.863062 − 0.505098i \(-0.831456\pi\)
0.0358091 + 0.999359i \(0.488599\pi\)
\(30\) 2.49720e6 + 1.20259e6i 0.562870 + 0.271064i
\(31\) −1.11192e6 + 201784.i −0.216246 + 0.0392428i −0.285598 − 0.958349i \(-0.592192\pi\)
0.0693527 + 0.997592i \(0.477907\pi\)
\(32\) 321095. − 1.40681e6i 0.0541326 − 0.237171i
\(33\) 8.74521e6 − 3.28213e6i 1.28368 − 0.481774i
\(34\) −2.73757e6 + 3.43280e6i −0.351326 + 0.440549i
\(35\) −295744. − 6.58526e6i −0.0333127 − 0.741765i
\(36\) −6453.88 − 143707.i −0.000640412 − 0.0142599i
\(37\) 298526. − 374340.i 0.0261863 − 0.0328366i −0.768566 − 0.639771i \(-0.779029\pi\)
0.794752 + 0.606934i \(0.207601\pi\)
\(38\) −3.74854e6 + 1.40685e6i −0.291632 + 0.109451i
\(39\) −1.78352e6 + 7.81409e6i −0.123449 + 0.540864i
\(40\) 8.26626e6 − 1.50010e6i 0.510551 − 0.0926513i
\(41\) 5.20788e6 + 2.50798e6i 0.287828 + 0.138611i 0.572227 − 0.820095i \(-0.306080\pi\)
−0.284399 + 0.958706i \(0.591794\pi\)
\(42\) −2.57865e7 + 1.54067e7i −1.27871 + 0.763992i
\(43\) −1.01311e7 − 3.80228e6i −0.451908 − 0.169604i 0.115034 − 0.993362i \(-0.463302\pi\)
−0.566942 + 0.823758i \(0.691874\pi\)
\(44\) −2.17328e6 + 3.29238e6i −0.0874135 + 0.132426i
\(45\) 1.61430e6 − 777407.i 0.0586852 − 0.0282613i
\(46\) −5.08208e7 + 3.69234e7i −1.67352 + 1.21588i
\(47\) −5.51720e6 + 4.82023e6i −0.164922 + 0.144088i −0.736443 − 0.676499i \(-0.763496\pi\)
0.571522 + 0.820587i \(0.306353\pi\)
\(48\) −2.68329e7 − 3.36474e7i −0.729595 − 0.914884i
\(49\) 2.66866e7 + 1.59445e7i 0.661318 + 0.395119i
\(50\) 1.77600e7 + 2.69053e7i 0.401864 + 0.608797i
\(51\) 6.04277e6 + 2.64751e7i 0.125075 + 0.547989i
\(52\) −1.33041e6 − 3.11265e6i −0.0252331 − 0.0590358i
\(53\) 8.16912e6 − 735234.i 0.142211 − 0.0127992i −0.0183050 − 0.999832i \(-0.505827\pi\)
0.160516 + 0.987033i \(0.448684\pi\)
\(54\) 4.99866e7 + 3.63174e7i 0.799984 + 0.581223i
\(55\) −4.83470e7 − 8.77369e6i −0.712422 − 0.129286i
\(56\) −3.57849e7 + 8.37229e7i −0.486243 + 1.13762i
\(57\) −7.65225e6 + 2.35512e7i −0.0960179 + 0.295513i
\(58\) −4.16928e7 − 7.74782e7i −0.483766 − 0.898988i
\(59\) −1.33194e7 − 1.39310e7i −0.143104 − 0.149675i 0.647358 − 0.762186i \(-0.275874\pi\)
−0.790462 + 0.612511i \(0.790159\pi\)
\(60\) −3.43077e6 + 6.37543e6i −0.0341752 + 0.0635081i
\(61\) −1.56206e8 + 4.31102e7i −1.44449 + 0.398654i −0.898439 − 0.439098i \(-0.855298\pi\)
−0.546051 + 0.837752i \(0.683870\pi\)
\(62\) −3.63630e6 − 2.68442e7i −0.0312534 − 0.230722i
\(63\) −2.60657e6 + 1.92425e7i −0.0208467 + 0.153897i
\(64\) −1.09925e8 − 3.03374e7i −0.819004 − 0.226031i
\(65\) 2.91369e7 − 3.04748e7i 0.202457 − 0.211754i
\(66\) 6.91921e7 + 2.12951e8i 0.448858 + 1.38144i
\(67\) −1.99785e8 − 1.79809e7i −1.21123 − 0.109012i −0.534450 − 0.845200i \(-0.679481\pi\)
−0.676777 + 0.736188i \(0.736624\pi\)
\(68\) −8.63696e6 − 7.54589e6i −0.0489859 − 0.0427977i
\(69\) −1.74309e7 + 3.88128e8i −0.0925759 + 2.06136i
\(70\) 1.58015e8 0.786606
\(71\) −2.13458e8 + 1.68530e7i −0.996898 + 0.0787073i
\(72\) −2.47482e7 −0.108530
\(73\) 230772. − 5.13855e6i 0.000951111 − 0.0211781i −0.998461 − 0.0554514i \(-0.982340\pi\)
0.999412 + 0.0342732i \(0.0109116\pi\)
\(74\) 8.64326e6 + 7.55139e6i 0.0335070 + 0.0292741i
\(75\) 1.98587e8 + 1.78732e7i 0.724728 + 0.0652267i
\(76\) −3.23183e6 − 9.94655e6i −0.0111119 − 0.0341988i
\(77\) 3.68008e8 − 3.84906e8i 1.19302 − 1.24781i
\(78\) −1.85206e8 − 5.11136e7i −0.566538 − 0.156355i
\(79\) 6.48096e7 − 4.78443e8i 0.187205 − 1.38200i −0.616679 − 0.787215i \(-0.711522\pi\)
0.803884 − 0.594787i \(-0.202764\pi\)
\(80\) 3.03891e7 + 2.24342e8i 0.0829494 + 0.612357i
\(81\) 4.11961e8 − 1.13694e8i 1.06334 − 0.293464i
\(82\) −6.56595e7 + 1.22016e8i −0.160375 + 0.298026i
\(83\) 2.13401e8 + 2.23200e8i 0.493565 + 0.516229i 0.921919 − 0.387382i \(-0.126621\pi\)
−0.428354 + 0.903611i \(0.640906\pi\)
\(84\) −3.71814e7 − 6.90946e7i −0.0814833 − 0.151421i
\(85\) 4.41436e7 − 1.35860e8i 0.0917239 − 0.282297i
\(86\) 1.01949e8 − 2.38521e8i 0.200974 − 0.470201i
\(87\) −5.35423e8 − 9.71649e7i −1.00198 − 0.181833i
\(88\) 5.49076e8 + 3.98927e8i 0.976024 + 0.709123i
\(89\) 7.10190e8 − 6.39182e7i 1.19983 − 0.107987i 0.528361 − 0.849020i \(-0.322807\pi\)
0.671468 + 0.741033i \(0.265664\pi\)
\(90\) 1.68804e7 + 3.94938e7i 0.0271202 + 0.0634508i
\(91\) 1.01679e8 + 4.45485e8i 0.155434 + 0.681000i
\(92\) −9.03947e7 − 1.36942e8i −0.131552 − 0.199293i
\(93\) −1.43828e8 − 8.59332e7i −0.199375 − 0.119121i
\(94\) −1.09496e8 − 1.37304e8i −0.144652 − 0.181388i
\(95\) 9.80986e7 − 8.57062e7i 0.123568 − 0.107958i
\(96\) 1.73077e8 − 1.25748e8i 0.207978 − 0.151105i
\(97\) 6.72032e7 − 3.23633e7i 0.0770756 − 0.0371177i −0.394949 − 0.918703i \(-0.629238\pi\)
0.472024 + 0.881585i \(0.343523\pi\)
\(98\) −4.10522e8 + 6.21915e8i −0.449593 + 0.681104i
\(99\) 1.35516e8 + 5.08599e7i 0.141785 + 0.0532129i
\(100\) −7.22897e7 + 4.31911e7i −0.0722897 + 0.0431911i
\(101\) −9.53200e8 − 4.59037e8i −0.911460 − 0.438936i −0.0814457 − 0.996678i \(-0.525954\pi\)
−0.830015 + 0.557742i \(0.811668\pi\)
\(102\) −6.40498e8 + 1.16233e8i −0.585891 + 0.106324i
\(103\) 1.35213e8 − 5.92406e8i 0.118372 − 0.518623i −0.880623 − 0.473817i \(-0.842876\pi\)
0.998996 − 0.0448061i \(-0.0142670\pi\)
\(104\) −5.45231e8 + 2.04628e8i −0.457015 + 0.171521i
\(105\) 6.09337e8 − 7.64084e8i 0.489222 − 0.613464i
\(106\) 8.82108e6 + 1.96417e8i 0.00678649 + 0.151113i
\(107\) 8.53693e7 + 1.90090e9i 0.0629614 + 1.40195i 0.743256 + 0.669007i \(0.233280\pi\)
−0.680295 + 0.732939i \(0.738148\pi\)
\(108\) −1.00627e8 + 1.26182e8i −0.0711717 + 0.0892465i
\(109\) 1.73076e9 − 6.49565e8i 1.17440 − 0.440761i 0.313530 − 0.949578i \(-0.398488\pi\)
0.860875 + 0.508817i \(0.169917\pi\)
\(110\) 2.62099e8 − 1.14833e9i 0.170686 − 0.747824i
\(111\) 6.98449e7 − 1.26750e7i 0.0436698 − 0.00792491i
\(112\) −2.21056e9 − 1.06455e9i −1.32746 − 0.639271i
\(113\) 2.56549e9 − 1.53281e9i 1.48019 − 0.884373i 0.480218 − 0.877149i \(-0.340558\pi\)
0.999974 − 0.00722392i \(-0.00229946\pi\)
\(114\) −5.55750e8 − 2.08577e8i −0.308182 − 0.115663i
\(115\) 1.12591e9 − 1.70568e9i 0.600293 − 0.909404i
\(116\) 2.07063e8 − 9.97162e7i 0.106180 − 0.0511334i
\(117\) −1.00481e8 + 7.30036e7i −0.0495732 + 0.0360170i
\(118\) 3.47930e8 − 3.03978e8i 0.165205 − 0.144335i
\(119\) 9.65271e8 + 1.21041e9i 0.441253 + 0.553314i
\(120\) 1.06925e9 + 6.38844e8i 0.470719 + 0.281241i
\(121\) −8.87797e8 − 1.34496e9i −0.376513 − 0.570392i
\(122\) −8.64366e8 − 3.78704e9i −0.353247 − 1.54768i
\(123\) 3.36813e8 + 7.88014e8i 0.132683 + 0.310428i
\(124\) 7.04752e7 − 6.34289e6i 0.0267694 − 0.00240929i
\(125\) −2.08088e9 − 1.51185e9i −0.762346 − 0.553877i
\(126\) −4.57997e8 − 8.31141e7i −0.161881 − 0.0293770i
\(127\) −8.54530e8 + 1.99927e9i −0.291481 + 0.681954i −0.999711 − 0.0240274i \(-0.992351\pi\)
0.708230 + 0.705982i \(0.249494\pi\)
\(128\) 1.07301e9 − 3.30239e9i 0.353313 − 1.08739i
\(129\) −7.60237e8 − 1.41276e9i −0.241710 − 0.449173i
\(130\) 6.98445e8 + 7.30516e8i 0.214480 + 0.224329i
\(131\) −8.86453e8 + 1.64731e9i −0.262987 + 0.488713i −0.977507 − 0.210903i \(-0.932360\pi\)
0.714520 + 0.699615i \(0.246645\pi\)
\(132\) −5.63798e8 + 1.55598e8i −0.161637 + 0.0446090i
\(133\) 1.89505e8 + 1.39898e9i 0.0525157 + 0.387686i
\(134\) 6.45450e8 − 4.76490e9i 0.172938 − 1.27668i
\(135\) −1.93779e9 − 5.34795e8i −0.502116 − 0.138575i
\(136\) −1.36355e9 + 1.42616e9i −0.341780 + 0.357474i
\(137\) 4.22093e8 + 1.29907e9i 0.102368 + 0.315057i 0.989104 − 0.147220i \(-0.0470325\pi\)
−0.886735 + 0.462277i \(0.847033\pi\)
\(138\) −9.27576e9 − 8.34833e8i −2.17718 − 0.195949i
\(139\) 5.64838e9 + 4.93484e9i 1.28339 + 1.12126i 0.986043 + 0.166489i \(0.0532432\pi\)
0.297342 + 0.954771i \(0.403900\pi\)
\(140\) −1.85180e7 + 4.12335e8i −0.00407397 + 0.0907139i
\(141\) −1.08618e9 −0.231427
\(142\) −1.74013e8 − 5.12981e9i −0.0359157 − 1.05878i
\(143\) 3.40609e9 0.681152
\(144\) 2.99202e7 − 6.66224e8i 0.00579873 − 0.129119i
\(145\) 2.15570e9 + 1.88338e9i 0.404979 + 0.353820i
\(146\) 1.22805e8 + 1.10526e7i 0.0223680 + 0.00201315i
\(147\) 1.42422e9 + 4.38331e9i 0.251565 + 0.774237i
\(148\) −2.07180e7 + 2.16693e7i −0.00354952 + 0.00371251i
\(149\) −3.96342e9 − 1.09383e9i −0.658767 − 0.181808i −0.0793595 − 0.996846i \(-0.525287\pi\)
−0.579408 + 0.815038i \(0.696716\pi\)
\(150\) −6.41581e8 + 4.73634e9i −0.103476 + 0.763892i
\(151\) −9.87696e7 − 7.29147e8i −0.0154606 − 0.114135i 0.981575 − 0.191078i \(-0.0611983\pi\)
−0.997035 + 0.0769430i \(0.975484\pi\)
\(152\) −1.73443e9 + 4.78672e8i −0.263548 + 0.0727347i
\(153\) −1.99408e8 + 3.70562e8i −0.0294192 + 0.0546701i
\(154\) 8.82157e9 + 9.22664e9i 1.26387 + 1.32191i
\(155\) 4.17645e8 + 7.76114e8i 0.0581185 + 0.108002i
\(156\) 1.55084e8 − 4.77298e8i 0.0209655 − 0.0645252i
\(157\) 4.21589e9 − 9.86355e9i 0.553784 − 1.29564i −0.375687 − 0.926747i \(-0.622593\pi\)
0.929471 − 0.368895i \(-0.120264\pi\)
\(158\) 1.13876e10 + 2.06654e9i 1.45370 + 0.263807i
\(159\) 9.83791e8 + 7.14766e8i 0.122072 + 0.0886904i
\(160\) −1.12085e9 + 1.00879e8i −0.135210 + 0.0121691i
\(161\) 8.70538e9 + 2.03672e10i 1.02111 + 2.38900i
\(162\) 2.27958e9 + 9.98751e9i 0.260039 + 1.13930i
\(163\) 2.42041e9 + 3.66676e9i 0.268562 + 0.406854i 0.943682 − 0.330854i \(-0.107337\pi\)
−0.675120 + 0.737708i \(0.735908\pi\)
\(164\) −3.10701e8 − 1.85635e8i −0.0335387 − 0.0200384i
\(165\) −4.54206e9 − 5.69556e9i −0.477062 − 0.598217i
\(166\) −5.57447e9 + 4.87026e9i −0.569793 + 0.497813i
\(167\) −3.99891e9 + 2.90538e9i −0.397848 + 0.289053i −0.768664 − 0.639653i \(-0.779078\pi\)
0.370816 + 0.928706i \(0.379078\pi\)
\(168\) −1.21621e10 + 5.85694e9i −1.17792 + 0.567256i
\(169\) 4.23191e9 − 6.41107e9i 0.399067 − 0.604561i
\(170\) 3.20596e9 + 1.20322e9i 0.294400 + 0.110490i
\(171\) −3.29413e8 + 1.96815e8i −0.0294617 + 0.0176026i
\(172\) 6.10465e8 + 2.93984e8i 0.0531842 + 0.0256122i
\(173\) −1.81503e10 + 3.29379e9i −1.54055 + 0.279569i −0.881374 − 0.472419i \(-0.843381\pi\)
−0.659177 + 0.751988i \(0.729095\pi\)
\(174\) 2.90263e9 − 1.27173e10i 0.240060 − 1.05177i
\(175\) 1.06425e10 − 3.99418e9i 0.857770 − 0.321926i
\(176\) −1.14030e10 + 1.42989e10i −0.895799 + 1.12330i
\(177\) −1.28201e8 − 2.85462e9i −0.00981775 − 0.218609i
\(178\) 7.66868e8 + 1.70756e10i 0.0572573 + 1.27493i
\(179\) −1.13462e10 + 1.42277e10i −0.826059 + 1.03584i 0.172647 + 0.984984i \(0.444768\pi\)
−0.998706 + 0.0508609i \(0.983803\pi\)
\(180\) −1.05036e8 + 3.94206e7i −0.00745781 + 0.00279896i
\(181\) 2.03555e9 − 8.91831e9i 0.140970 − 0.617631i −0.854241 − 0.519878i \(-0.825977\pi\)
0.995211 − 0.0977528i \(-0.0311655\pi\)
\(182\) −1.07774e10 + 1.95581e9i −0.728101 + 0.132131i
\(183\) −2.16454e10 − 1.04239e10i −1.42671 − 0.687068i
\(184\) −2.42335e10 + 1.44789e10i −1.55861 + 0.931224i
\(185\) −3.49604e8 − 1.31208e8i −0.0219434 − 0.00823548i
\(186\) 2.21252e9 − 3.35183e9i 0.135544 − 0.205340i
\(187\) 1.03974e10 − 5.00713e9i 0.621781 − 0.299434i
\(188\) 3.71123e8 − 2.69636e8i 0.0216674 − 0.0157423i
\(189\) 1.64065e10 − 1.43339e10i 0.935272 − 0.817122i
\(190\) 1.94690e9 + 2.44134e9i 0.108381 + 0.135905i
\(191\) 1.45873e10 + 8.71548e9i 0.793092 + 0.473850i 0.851444 − 0.524446i \(-0.175727\pi\)
−0.0583521 + 0.998296i \(0.518585\pi\)
\(192\) −9.31374e9 − 1.41097e10i −0.494616 − 0.749312i
\(193\) −8.33436e9 − 3.65152e10i −0.432379 − 1.89438i −0.447099 − 0.894485i \(-0.647543\pi\)
0.0147198 − 0.999892i \(-0.495314\pi\)
\(194\) 7.02730e8 + 1.64412e9i 0.0356189 + 0.0833346i
\(195\) 6.22576e9 − 5.60328e8i 0.308345 − 0.0277515i
\(196\) −1.57476e9 − 1.14413e9i −0.0762186 − 0.0553760i
\(197\) 1.05363e10 + 1.91206e9i 0.498415 + 0.0904490i 0.421942 − 0.906623i \(-0.361348\pi\)
0.0764727 + 0.997072i \(0.475634\pi\)
\(198\) −1.36368e9 + 3.19050e9i −0.0630551 + 0.147525i
\(199\) 6.66150e9 − 2.05020e10i 0.301115 − 0.926738i −0.679983 − 0.733228i \(-0.738013\pi\)
0.981098 − 0.193510i \(-0.0619872\pi\)
\(200\) 6.86515e9 + 1.27576e10i 0.303400 + 0.563811i
\(201\) −2.05518e10 − 2.14955e10i −0.888111 − 0.928891i
\(202\) 1.20177e10 − 2.23326e10i 0.507855 − 0.943752i
\(203\) −2.99053e10 + 8.25333e9i −1.23599 + 0.341112i
\(204\) −2.28246e8 − 1.68498e9i −0.00922714 − 0.0681175i
\(205\) 6.05131e8 − 4.46726e9i 0.0239308 − 0.176664i
\(206\) 1.40409e10 + 3.87505e9i 0.543241 + 0.149925i
\(207\) −4.16054e9 + 4.35158e9i −0.157501 + 0.164733i
\(208\) −4.84943e9 − 1.49250e10i −0.179641 − 0.552879i
\(209\) 1.04810e10 + 9.43311e8i 0.379967 + 0.0341977i
\(210\) 1.76422e10 + 1.54135e10i 0.625988 + 0.546909i
\(211\) 9.05872e8 − 2.01708e10i 0.0314627 − 0.700571i −0.919837 − 0.392302i \(-0.871679\pi\)
0.951299 − 0.308269i \(-0.0997497\pi\)
\(212\) −5.13576e8 −0.0174620
\(213\) −2.54763e10 − 1.89401e10i −0.848063 − 0.630484i
\(214\) −4.56125e10 −1.48670
\(215\) −3.78632e8 + 8.43090e9i −0.0120849 + 0.269092i
\(216\) 2.09098e10 + 1.82684e10i 0.653595 + 0.571029i
\(217\) −9.51331e9 − 8.56213e8i −0.291248 − 0.0262128i
\(218\) 1.36938e10 + 4.21451e10i 0.410647 + 1.26384i
\(219\) 5.27003e8 − 5.51202e8i 0.0154816 − 0.0161924i
\(220\) 2.96581e9 + 8.18511e8i 0.0853574 + 0.0235571i
\(221\) −1.32922e9 + 9.81267e9i −0.0374827 + 0.276708i
\(222\) 2.28412e8 + 1.68621e9i 0.00631148 + 0.0465932i
\(223\) 9.26252e8 − 2.55629e8i 0.0250817 − 0.00692211i −0.253473 − 0.967342i \(-0.581573\pi\)
0.278555 + 0.960420i \(0.410144\pi\)
\(224\) 5.77954e9 − 1.07402e10i 0.153383 − 0.285034i
\(225\) 2.13520e9 + 2.23325e9i 0.0555416 + 0.0580919i
\(226\) 3.39471e10 + 6.30843e10i 0.865595 + 1.60855i
\(227\) 2.45742e10 − 7.56317e10i 0.614276 − 1.89055i 0.202416 − 0.979300i \(-0.435121\pi\)
0.411860 − 0.911247i \(-0.364879\pi\)
\(228\) 6.09402e8 − 1.42577e9i 0.0149347 − 0.0349415i
\(229\) −4.07813e9 − 7.40071e8i −0.0979944 − 0.0177834i 0.129338 − 0.991601i \(-0.458715\pi\)
−0.227333 + 0.973817i \(0.573000\pi\)
\(230\) 3.96350e10 + 2.87965e10i 0.933907 + 0.678523i
\(231\) 7.86332e10 − 7.07712e9i 1.81699 − 0.163532i
\(232\) −1.55397e10 − 3.63569e10i −0.352165 − 0.823931i
\(233\) 5.90990e9 + 2.58930e10i 0.131365 + 0.575546i 0.997171 + 0.0751670i \(0.0239490\pi\)
−0.865806 + 0.500379i \(0.833194\pi\)
\(234\) −1.64015e9 − 2.48473e9i −0.0357613 − 0.0541760i
\(235\) 4.90495e9 + 2.93057e9i 0.104913 + 0.0626826i
\(236\) 7.52444e8 + 9.43535e8i 0.0157896 + 0.0197995i
\(237\) 5.39055e10 − 4.70958e10i 1.10985 − 0.969649i
\(238\) −3.00238e10 + 2.18136e10i −0.606554 + 0.440687i
\(239\) −3.03476e10 + 1.46146e10i −0.601636 + 0.289733i −0.709803 − 0.704400i \(-0.751216\pi\)
0.108167 + 0.994133i \(0.465502\pi\)
\(240\) −1.84904e10 + 2.80118e10i −0.359746 + 0.544992i
\(241\) −7.25681e10 − 2.72353e10i −1.38570 − 0.520062i −0.456527 − 0.889709i \(-0.650907\pi\)
−0.929172 + 0.369648i \(0.879478\pi\)
\(242\) 3.31624e10 − 1.98136e10i 0.621551 − 0.371360i
\(243\) 1.13755e10 + 5.47816e9i 0.209287 + 0.100787i
\(244\) 9.98344e9 − 1.81173e9i 0.180312 − 0.0327219i
\(245\) 5.39494e9 − 2.36368e10i 0.0956620 − 0.419123i
\(246\) −1.92328e10 + 7.21819e9i −0.334838 + 0.125667i
\(247\) −5.62997e9 + 7.05976e9i −0.0962432 + 0.120685i
\(248\) −5.46165e8 − 1.21613e10i −0.00916836 − 0.204149i
\(249\) 2.05401e9 + 4.57361e10i 0.0338614 + 0.753984i
\(250\) 3.84421e10 − 4.82049e10i 0.622411 − 0.780479i
\(251\) −1.82690e10 + 6.85645e9i −0.290524 + 0.109035i −0.492382 − 0.870379i \(-0.663874\pi\)
0.201858 + 0.979415i \(0.435302\pi\)
\(252\) 2.70557e8 − 1.18539e9i 0.00422625 − 0.0185164i
\(253\) 1.62453e11 − 2.94808e10i 2.49278 − 0.452373i
\(254\) −4.69575e10 − 2.26136e10i −0.707870 − 0.340892i
\(255\) 1.81810e10 − 1.08626e10i 0.269269 − 0.160881i
\(256\) 2.32658e10 + 8.73179e9i 0.338562 + 0.127064i
\(257\) 6.06634e10 − 9.19012e10i 0.867417 − 1.31408i −0.0808892 − 0.996723i \(-0.525776\pi\)
0.948306 − 0.317357i \(-0.102795\pi\)
\(258\) 3.46489e10 − 1.66860e10i 0.486856 − 0.234458i
\(259\) 3.27403e9 − 2.37872e9i 0.0452100 − 0.0328470i
\(260\) −1.98811e9 + 1.73696e9i −0.0269811 + 0.0235727i
\(261\) −5.25753e9 − 6.59273e9i −0.0701293 − 0.0879393i
\(262\) −3.84947e10 − 2.29995e10i −0.504714 − 0.301552i
\(263\) −4.19991e10 − 6.36258e10i −0.541301 − 0.820036i 0.456259 − 0.889847i \(-0.349189\pi\)
−0.997560 + 0.0698112i \(0.977760\pi\)
\(264\) 2.23905e10 + 9.80991e10i 0.283691 + 1.24293i
\(265\) −2.51412e9 − 5.88207e9i −0.0313169 − 0.0732695i
\(266\) −3.37053e10 + 3.03353e9i −0.412791 + 0.0371519i
\(267\) 8.55267e10 + 6.21388e10i 1.02991 + 0.748277i
\(268\) 1.23582e10 + 2.24268e9i 0.146335 + 0.0265559i
\(269\) −4.48409e10 + 1.04910e11i −0.522142 + 1.22161i 0.426277 + 0.904593i \(0.359825\pi\)
−0.948419 + 0.317019i \(0.897318\pi\)
\(270\) 1.48907e10 − 4.58290e10i 0.170522 − 0.524811i
\(271\) −2.03054e10 − 3.77338e10i −0.228691 − 0.424980i 0.740228 − 0.672356i \(-0.234717\pi\)
−0.968920 + 0.247376i \(0.920432\pi\)
\(272\) −3.67439e10 − 3.84311e10i −0.407029 − 0.425719i
\(273\) −3.21023e10 + 5.96561e10i −0.349788 + 0.650015i
\(274\) −3.15627e10 + 8.71076e9i −0.338296 + 0.0933638i
\(275\) −1.13740e10 − 8.39661e10i −0.119927 − 0.885334i
\(276\) 3.26551e9 − 2.41069e10i 0.0338735 − 0.250064i
\(277\) −1.34938e11 − 3.72405e10i −1.37713 − 0.380064i −0.502384 − 0.864644i \(-0.667544\pi\)
−0.874747 + 0.484580i \(0.838972\pi\)
\(278\) −1.24249e11 + 1.29954e11i −1.24765 + 1.30494i
\(279\) −8.02289e8 − 2.46919e9i −0.00792705 − 0.0243970i
\(280\) 7.07238e10 + 6.36526e9i 0.687629 + 0.0618878i
\(281\) 3.78595e10 + 3.30769e10i 0.362240 + 0.316480i 0.819746 − 0.572727i \(-0.194114\pi\)
−0.457506 + 0.889206i \(0.651257\pi\)
\(282\) 1.16814e9 − 2.60106e10i 0.0109995 − 0.244923i
\(283\) −1.23786e11 −1.14718 −0.573590 − 0.819142i \(-0.694450\pi\)
−0.573590 + 0.819142i \(0.694450\pi\)
\(284\) 1.34065e10 + 1.47088e8i 0.122287 + 0.00134167i
\(285\) 1.93128e10 0.173397
\(286\) −3.66311e9 + 8.15656e10i −0.0323745 + 0.720875i
\(287\) 3.67926e10 + 3.21447e10i 0.320104 + 0.279667i
\(288\) 3.30178e9 + 2.97166e8i 0.0282802 + 0.00254526i
\(289\) −2.62781e10 − 8.08757e10i −0.221592 − 0.681989i
\(290\) −4.74197e10 + 4.95971e10i −0.393702 + 0.411780i
\(291\) 1.06600e10 + 2.94198e9i 0.0871444 + 0.0240503i
\(292\) −4.32330e7 + 3.19159e8i −0.000348011 + 0.00256912i
\(293\) −1.57675e9 − 1.16400e10i −0.0124985 − 0.0922677i 0.983626 − 0.180222i \(-0.0576815\pi\)
−0.996125 + 0.0879539i \(0.971967\pi\)
\(294\) −1.06499e11 + 2.93918e10i −0.831346 + 0.229437i
\(295\) −7.12301e9 + 1.32368e10i −0.0547601 + 0.101761i
\(296\) 3.56433e9 + 3.72799e9i 0.0269876 + 0.0282269i
\(297\) −7.69543e10 − 1.43005e11i −0.573891 − 1.06647i
\(298\) 3.04565e10 − 9.37356e10i 0.223721 − 0.688543i
\(299\) −5.56805e10 + 1.30271e11i −0.402887 + 0.942601i
\(300\) −1.22841e10 − 2.22924e9i −0.0875585 − 0.0158895i
\(301\) −7.39952e10 − 5.37606e10i −0.519582 − 0.377498i
\(302\) 1.75671e10 − 1.58107e9i 0.121526 − 0.0109375i
\(303\) −6.16470e10 − 1.44230e11i −0.420166 − 0.983026i
\(304\) −1.07890e10 − 4.72696e10i −0.0724517 − 0.317432i
\(305\) 6.96221e10 + 1.05473e11i 0.460678 + 0.697898i
\(306\) −8.65940e9 − 5.17375e9i −0.0564600 − 0.0337333i
\(307\) 9.47860e10 + 1.18858e11i 0.609006 + 0.763669i 0.986751 − 0.162240i \(-0.0518719\pi\)
−0.377745 + 0.925910i \(0.623300\pi\)
\(308\) −2.51104e10 + 2.19383e10i −0.158992 + 0.138907i
\(309\) 7.28823e10 − 5.29521e10i 0.454788 − 0.330423i
\(310\) −1.90347e10 + 9.16665e9i −0.117063 + 0.0563746i
\(311\) −8.48184e10 + 1.28494e11i −0.514125 + 0.778866i −0.995205 − 0.0978108i \(-0.968816\pi\)
0.481080 + 0.876677i \(0.340245\pi\)
\(312\) −8.08347e10 − 3.03378e10i −0.482950 − 0.181254i
\(313\) 1.19829e11 − 7.15945e10i 0.705687 − 0.421629i −0.114728 − 0.993397i \(-0.536600\pi\)
0.820415 + 0.571768i \(0.193742\pi\)
\(314\) 2.31668e11 + 1.11566e11i 1.34488 + 0.647660i
\(315\) 1.49009e10 − 2.70411e9i 0.0852735 − 0.0154749i
\(316\) −6.72709e9 + 2.94733e10i −0.0379521 + 0.166279i
\(317\) −5.82802e10 + 2.18729e10i −0.324156 + 0.121658i −0.508148 − 0.861270i \(-0.669670\pi\)
0.183991 + 0.982928i \(0.441098\pi\)
\(318\) −1.81745e10 + 2.27901e10i −0.0996646 + 0.124975i
\(319\) 1.03750e10 + 2.31018e11i 0.0560958 + 1.24907i
\(320\) 3.99006e9 + 8.88457e10i 0.0212718 + 0.473654i
\(321\) −1.75891e11 + 2.20560e11i −0.924635 + 1.15946i
\(322\) −4.97096e11 + 1.86563e11i −2.57685 + 0.967108i
\(323\) −6.80780e9 + 2.98269e10i −0.0348013 + 0.152475i
\(324\) −2.63292e10 + 4.77804e9i −0.132735 + 0.0240878i
\(325\) 6.55063e10 + 3.15462e10i 0.325692 + 0.156845i
\(326\) −9.04110e10 + 5.40181e10i −0.443345 + 0.264886i
\(327\) 2.56599e11 + 9.63032e10i 1.24105 + 0.465775i
\(328\) −3.43027e10 + 5.19664e10i −0.163643 + 0.247908i
\(329\) −5.57911e10 + 2.68676e10i −0.262532 + 0.126429i
\(330\) 1.41276e11 − 1.02643e11i 0.655778 − 0.476451i
\(331\) 5.44567e10 − 4.75774e10i 0.249359 − 0.217859i −0.524179 − 0.851608i \(-0.675628\pi\)
0.773538 + 0.633749i \(0.218485\pi\)
\(332\) −1.20555e10 − 1.51171e10i −0.0544583 − 0.0682885i
\(333\) 9.44289e8 + 5.64186e8i 0.00420829 + 0.00251434i
\(334\) −6.52743e10 − 9.88864e10i −0.287001 − 0.434788i
\(335\) 3.48115e10 + 1.52519e11i 0.151015 + 0.661642i
\(336\) −1.42965e11 − 3.34484e11i −0.611933 − 1.43169i
\(337\) 2.26046e11 − 2.03445e10i 0.954691 − 0.0859237i 0.398672 − 0.917094i \(-0.369471\pi\)
0.556019 + 0.831170i \(0.312328\pi\)
\(338\) 1.48975e11 + 1.08236e11i 0.620850 + 0.451074i
\(339\) 4.35952e11 + 7.91136e10i 1.79283 + 0.325351i
\(340\) −3.51547e9 + 8.22484e9i −0.0142668 + 0.0333789i
\(341\) −2.20019e10 + 6.77150e10i −0.0881184 + 0.271200i
\(342\) −4.35886e9 − 8.10011e9i −0.0172288 − 0.0320165i
\(343\) −5.41269e10 − 5.66123e10i −0.211149 − 0.220845i
\(344\) 5.52381e10 − 1.02650e11i 0.212679 − 0.395225i
\(345\) 2.92086e11 − 8.06107e10i 1.11001 − 0.306342i
\(346\) −5.93565e10 − 4.38187e11i −0.222652 − 1.64368i
\(347\) −5.46386e10 + 4.03358e11i −0.202310 + 1.49351i 0.550257 + 0.834995i \(0.314530\pi\)
−0.752567 + 0.658516i \(0.771185\pi\)
\(348\) 3.28451e10 + 9.06467e9i 0.120050 + 0.0331318i
\(349\) −3.23994e11 + 3.38871e11i −1.16902 + 1.22270i −0.198918 + 0.980016i \(0.563743\pi\)
−0.970105 + 0.242686i \(0.921972\pi\)
\(350\) 8.42031e10 + 2.59150e11i 0.299931 + 0.923094i
\(351\) 1.38785e11 + 1.24909e10i 0.488047 + 0.0439250i
\(352\) −6.84648e10 − 5.98159e10i −0.237698 − 0.207670i
\(353\) 1.48852e10 − 3.31445e11i 0.0510234 − 1.13612i −0.796250 − 0.604967i \(-0.793186\pi\)
0.847274 − 0.531156i \(-0.178242\pi\)
\(354\) 6.84974e10 0.231824
\(355\) 6.39442e10 + 1.54266e11i 0.213685 + 0.515517i
\(356\) −4.46482e10 −0.147326
\(357\) −1.02978e10 + 2.29298e11i −0.0335534 + 0.747125i
\(358\) −3.28507e11 − 2.87008e11i −1.05699 − 0.923465i
\(359\) −2.59683e11 − 2.33719e10i −0.825122 − 0.0742623i −0.330974 − 0.943640i \(-0.607377\pi\)
−0.494148 + 0.869378i \(0.664520\pi\)
\(360\) 5.96437e9 + 1.83565e10i 0.0187156 + 0.0576007i
\(361\) 2.03718e11 − 2.13072e11i 0.631316 − 0.660305i
\(362\) 2.11378e11 + 5.83365e10i 0.646949 + 0.178547i
\(363\) 3.20717e10 − 2.36762e11i 0.0969486 − 0.715703i
\(364\) −3.84059e9 − 2.83524e10i −0.0114668 − 0.0846513i
\(365\) −3.86702e9 + 1.06723e9i −0.0114040 + 0.00314731i
\(366\) 2.72900e11 − 5.07132e11i 0.794947 − 1.47726i
\(367\) −2.13364e10 − 2.23161e10i −0.0613937 − 0.0642128i 0.691385 − 0.722487i \(-0.257001\pi\)
−0.752778 + 0.658274i \(0.771287\pi\)
\(368\) −3.60474e11 − 6.69872e11i −1.02461 − 1.90404i
\(369\) −4.10366e9 + 1.26298e10i −0.0115227 + 0.0354631i
\(370\) 3.51803e9 − 8.23084e9i 0.00975870 − 0.0228316i
\(371\) 6.82124e10 + 1.23787e10i 0.186931 + 0.0339230i
\(372\) 8.48719e9 + 6.16630e9i 0.0229784 + 0.0166948i
\(373\) 4.63419e11 − 4.17084e10i 1.23961 − 0.111567i 0.549636 − 0.835404i \(-0.314766\pi\)
0.689970 + 0.723838i \(0.257624\pi\)
\(374\) 1.08724e11 + 2.54371e11i 0.287344 + 0.672274i
\(375\) −8.48552e10 − 3.71775e11i −0.221584 − 0.970821i
\(376\) −4.34770e10 − 6.58649e10i −0.112180 − 0.169945i
\(377\) −1.70340e11 − 1.01774e11i −0.434292 − 0.259477i
\(378\) 3.25610e11 + 4.08302e11i 0.820322 + 1.02865i
\(379\) 1.12979e11 − 9.87067e10i 0.281268 − 0.245737i −0.505730 − 0.862692i \(-0.668777\pi\)
0.786998 + 0.616955i \(0.211634\pi\)
\(380\) −6.59875e9 + 4.79427e9i −0.0162344 + 0.0117950i
\(381\) −2.90426e11 + 1.39862e11i −0.706110 + 0.340045i
\(382\) −2.24397e11 + 3.39948e11i −0.539179 + 0.816821i
\(383\) −5.65838e11 − 2.12363e11i −1.34369 − 0.504294i −0.427126 − 0.904192i \(-0.640474\pi\)
−0.916559 + 0.399898i \(0.869045\pi\)
\(384\) 4.41931e11 − 2.64042e11i 1.03720 − 0.619701i
\(385\) −3.74186e11 − 1.80199e11i −0.867990 − 0.418002i
\(386\) 8.83393e11 − 1.60312e11i 2.02540 − 0.367556i
\(387\) 5.53199e9 − 2.42372e10i 0.0125367 − 0.0549267i
\(388\) −4.37262e9 + 1.64107e9i −0.00979489 + 0.00367608i
\(389\) 5.06062e11 − 6.34581e11i 1.12055 − 1.40512i 0.217245 − 0.976117i \(-0.430293\pi\)
0.903302 − 0.429005i \(-0.141136\pi\)
\(390\) 6.72262e9 + 1.49691e11i 0.0147146 + 0.327645i
\(391\) 2.15352e10 + 4.79518e11i 0.0465965 + 1.03755i
\(392\) −2.08792e11 + 2.61817e11i −0.446609 + 0.560030i
\(393\) −2.59657e11 + 9.74510e10i −0.549078 + 0.206072i
\(394\) −5.71195e10 + 2.50257e11i −0.119413 + 0.523182i
\(395\) −3.70494e11 + 6.72347e10i −0.765762 + 0.138965i
\(396\) −8.16568e9 − 3.93238e9i −0.0166864 − 0.00803577i
\(397\) 1.34539e11 − 8.03830e10i 0.271825 − 0.162408i −0.370518 − 0.928825i \(-0.620820\pi\)
0.642343 + 0.766417i \(0.277963\pi\)
\(398\) 4.83796e11 + 1.81572e11i 0.966471 + 0.362723i
\(399\) −1.15305e11 + 1.74680e11i −0.227757 + 0.345037i
\(400\) −3.51734e11 + 1.69386e11i −0.686981 + 0.330833i
\(401\) 2.83114e11 − 2.05694e11i 0.546779 − 0.397258i −0.279818 − 0.960053i \(-0.590274\pi\)
0.826596 + 0.562795i \(0.190274\pi\)
\(402\) 5.36854e11 − 4.69036e11i 1.02527 − 0.895754i
\(403\) −3.80916e10 − 4.77653e10i −0.0719376 − 0.0902069i
\(404\) 5.68677e10 + 3.39769e10i 0.106206 + 0.0634552i
\(405\) −1.83613e11 − 2.78162e11i −0.339123 − 0.513749i
\(406\) −1.65480e11 − 7.25017e11i −0.302259 − 1.32428i
\(407\) −1.18561e10 − 2.77387e10i −0.0214174 − 0.0501084i
\(408\) −2.91354e11 + 2.62223e10i −0.520535 + 0.0468490i
\(409\) −5.47034e11 − 3.97443e11i −0.966628 − 0.702296i −0.0119470 − 0.999929i \(-0.503803\pi\)
−0.954680 + 0.297633i \(0.903803\pi\)
\(410\) 1.06327e11 + 1.92954e10i 0.185829 + 0.0337231i
\(411\) −7.95909e10 + 1.86212e11i −0.137586 + 0.321899i
\(412\) −1.17573e10 + 3.61852e10i −0.0201034 + 0.0618718i
\(413\) −7.71966e10 − 1.43455e11i −0.130564 − 0.242628i
\(414\) −9.97328e10 − 1.04312e11i −0.166854 − 0.174516i
\(415\) 1.14123e11 − 2.12077e11i 0.188868 − 0.350975i
\(416\) 7.51990e10 − 2.07536e10i 0.123110 − 0.0339761i
\(417\) 1.49268e11 + 1.10194e12i 0.241743 + 1.78462i
\(418\) −3.38614e10 + 2.49975e11i −0.0542515 + 0.400501i
\(419\) −6.53771e10 − 1.80429e10i −0.103625 − 0.0285986i 0.213840 − 0.976869i \(-0.431403\pi\)
−0.317465 + 0.948270i \(0.602831\pi\)
\(420\) −4.22886e10 + 4.42304e10i −0.0663134 + 0.0693584i
\(421\) −3.19346e10 − 9.82845e10i −0.0495441 − 0.152481i 0.923224 − 0.384263i \(-0.125544\pi\)
−0.972768 + 0.231782i \(0.925544\pi\)
\(422\) 4.82056e11 + 4.33858e10i 0.739931 + 0.0665950i
\(423\) −1.26752e10 − 1.10740e10i −0.0192497 − 0.0168180i
\(424\) −3.96406e9 + 8.82667e10i −0.00595654 + 0.132633i
\(425\) 2.46338e11 0.366254
\(426\) 4.80957e11 − 5.89711e11i 0.707560 − 0.867553i
\(427\) −1.36965e12 −1.99382
\(428\) 5.34539e9 − 1.19024e11i 0.00769985 − 0.171450i
\(429\) 3.80286e11 + 3.32246e11i 0.542066 + 0.473589i
\(430\) −2.01487e11 − 1.81342e10i −0.284210 − 0.0255794i
\(431\) −3.36307e11 − 1.03505e12i −0.469449 − 1.44481i −0.853301 − 0.521419i \(-0.825403\pi\)
0.383852 − 0.923395i \(-0.374597\pi\)
\(432\) −5.17065e11 + 5.40808e11i −0.714280 + 0.747078i
\(433\) −8.00523e9 − 2.20930e9i −0.0109440 − 0.00302037i 0.260561 − 0.965458i \(-0.416093\pi\)
−0.271505 + 0.962437i \(0.587521\pi\)
\(434\) 3.07349e10 − 2.26894e11i 0.0415842 − 0.306987i
\(435\) 5.69680e10 + 4.20554e11i 0.0762832 + 0.563145i
\(436\) −1.11581e11 + 3.07944e10i −0.147877 + 0.0408115i
\(437\) −2.07416e11 + 3.85443e11i −0.272067 + 0.505584i
\(438\) 1.26329e10 + 1.32129e10i 0.0164009 + 0.0171540i
\(439\) −2.94348e9 − 5.46991e9i −0.00378243 − 0.00702894i 0.878697 − 0.477379i \(-0.158413\pi\)
−0.882480 + 0.470350i \(0.844128\pi\)
\(440\) 1.63567e11 − 5.03407e11i 0.208045 − 0.640298i
\(441\) −2.80696e10 + 6.56720e10i −0.0353396 + 0.0826812i
\(442\) −2.33554e11 − 4.23839e10i −0.291064 − 0.0528203i
\(443\) 1.22807e12 + 8.92245e11i 1.51498 + 1.10070i 0.963907 + 0.266238i \(0.0857808\pi\)
0.551071 + 0.834458i \(0.314219\pi\)
\(444\) −4.42687e9 + 3.98425e8i −0.00540596 + 0.000486545i
\(445\) −2.18567e11 − 5.11363e11i −0.264219 − 0.618171i
\(446\) 5.12540e9 + 2.24559e10i 0.00613368 + 0.0268734i
\(447\) −3.35813e11 − 5.08736e11i −0.397845 − 0.602710i
\(448\) −8.27414e11 − 4.94357e11i −0.970446 − 0.579815i
\(449\) 5.48778e10 + 6.88146e10i 0.0637219 + 0.0799047i 0.812671 − 0.582723i \(-0.198013\pi\)
−0.748949 + 0.662628i \(0.769441\pi\)
\(450\) −5.57759e10 + 4.87300e10i −0.0641195 + 0.0560196i
\(451\) 2.94630e11 − 2.14061e11i 0.335338 − 0.243637i
\(452\) −1.68595e11 + 8.11909e10i −0.189986 + 0.0914923i
\(453\) 6.00968e10 − 9.10428e10i 0.0670517 − 0.101579i
\(454\) 1.78472e12 + 6.69818e11i 1.97160 + 0.739955i
\(455\) 3.05924e11 − 1.82781e11i 0.334628 − 0.199931i
\(456\) −2.40339e11 − 1.15741e11i −0.260304 − 0.125356i
\(457\) −2.13579e11 + 3.87589e10i −0.229053 + 0.0415670i −0.291870 − 0.956458i \(-0.594277\pi\)
0.0628168 + 0.998025i \(0.479992\pi\)
\(458\) 2.21083e10 − 9.68630e10i 0.0234780 − 0.102864i
\(459\) 4.42018e11 − 1.65892e11i 0.464818 − 0.174449i
\(460\) −7.97884e10 + 1.00051e11i −0.0830863 + 0.104187i
\(461\) 5.29283e10 + 1.17854e12i 0.0545801 + 1.21532i 0.820219 + 0.572049i \(0.193851\pi\)
−0.765639 + 0.643270i \(0.777577\pi\)
\(462\) 8.49087e10 + 1.89064e12i 0.0867089 + 1.93072i
\(463\) 3.27522e11 − 4.10700e11i 0.331227 − 0.415346i −0.588132 − 0.808765i \(-0.700136\pi\)
0.919359 + 0.393419i \(0.128708\pi\)
\(464\) 9.97516e11 − 3.74374e11i 0.999054 − 0.374951i
\(465\) −2.90762e10 + 1.27391e11i −0.0288403 + 0.126357i
\(466\) −6.26415e11 + 1.13678e11i −0.615354 + 0.111670i
\(467\) 9.72845e10 + 4.68497e10i 0.0946493 + 0.0455807i 0.480609 − 0.876935i \(-0.340415\pi\)
−0.385960 + 0.922515i \(0.626130\pi\)
\(468\) 6.67602e9 − 3.98873e9i 0.00643296 − 0.00384352i
\(469\) −1.58734e12 − 5.95741e11i −1.51493 − 0.568564i
\(470\) −7.54535e10 + 1.14307e11i −0.0713245 + 0.108052i
\(471\) 1.43283e12 − 6.90017e11i 1.34154 − 0.646049i
\(472\) 1.67970e11 − 1.22038e11i 0.155773 − 0.113176i
\(473\) −5.13425e11 + 4.48566e11i −0.471631 + 0.412051i
\(474\) 1.06983e12 + 1.34152e12i 0.973446 + 1.22066i
\(475\) 1.92836e11 + 1.15214e11i 0.173807 + 0.103845i
\(476\) −5.34032e10 − 8.09024e10i −0.0476800 − 0.0722321i
\(477\) 4.19310e9 + 1.83712e10i 0.00370854 + 0.0162482i
\(478\) −3.17339e11 − 7.42451e11i −0.278034 − 0.650493i
\(479\) 1.31915e11 − 1.18726e10i 0.114495 − 0.0103047i −0.0322437 − 0.999480i \(-0.510265\pi\)
0.146739 + 0.989175i \(0.453122\pi\)
\(480\) −1.34982e11 − 9.80703e10i −0.116062 − 0.0843242i
\(481\) 2.54686e10 + 4.62187e9i 0.0216946 + 0.00393700i
\(482\) 7.30247e11 − 1.70850e12i 0.616251 − 1.44179i
\(483\) −1.01477e12 + 3.12314e12i −0.848409 + 2.61114i
\(484\) 4.78166e10 + 8.88581e10i 0.0396072 + 0.0736026i
\(485\) −4.02009e10 − 4.20468e10i −0.0329912 − 0.0345060i
\(486\) −1.43419e11 + 2.66518e11i −0.116612 + 0.216702i
\(487\) −1.95062e12 + 5.38337e11i −1.57142 + 0.433684i −0.939837 − 0.341624i \(-0.889023\pi\)
−0.631583 + 0.775308i \(0.717595\pi\)
\(488\) −2.34318e11 − 1.72981e12i −0.187032 − 1.38073i
\(489\) −8.74372e10 + 6.45488e11i −0.0691523 + 0.510503i
\(490\) 5.60228e11 + 1.54613e11i 0.439018 + 0.121161i
\(491\) −1.35991e12 + 1.42235e12i −1.05595 + 1.10443i −0.0616174 + 0.998100i \(0.519626\pi\)
−0.994330 + 0.106335i \(0.966088\pi\)
\(492\) −1.65817e10 − 5.10332e10i −0.0127581 − 0.0392654i
\(493\) −6.69592e11 − 6.02644e10i −0.510504 − 0.0459462i
\(494\) −1.63005e11 − 1.42413e11i −0.123149 − 0.107592i
\(495\) 5.06464e9 − 1.12773e11i 0.00379163 − 0.0844271i
\(496\) 3.28044e11 0.243368
\(497\) −1.77708e12 − 3.42672e11i −1.30648 − 0.251927i
\(498\) −1.09745e12 −0.799563
\(499\) −7.31256e9 + 1.62827e11i −0.00527979 + 0.117564i 0.994622 + 0.103569i \(0.0330262\pi\)
−0.999902 + 0.0139948i \(0.995545\pi\)
\(500\) 1.21284e11 + 1.05963e11i 0.0867837 + 0.0758207i
\(501\) −7.29877e11 − 6.56901e10i −0.517583 − 0.0465833i
\(502\) −1.44544e11 − 4.44860e11i −0.101586 − 0.312649i
\(503\) 1.39452e12 − 1.45856e12i 0.971337 − 1.01594i −0.0285298 − 0.999593i \(-0.509083\pi\)
0.999866 − 0.0163455i \(-0.00520317\pi\)
\(504\) −2.01640e11 − 5.56492e10i −0.139200 − 0.0384168i
\(505\) −1.10757e11 + 8.17643e11i −0.0757811 + 0.559439i
\(506\) 5.31265e11 + 3.92196e12i 0.360275 + 2.65966i
\(507\) 1.09785e12 − 3.02988e11i 0.737918 − 0.203652i
\(508\) 6.45123e10 − 1.19884e11i 0.0429790 − 0.0798683i
\(509\) 1.57009e12 + 1.64218e12i 1.03680 + 1.08440i 0.996362 + 0.0852219i \(0.0271599\pi\)
0.0404345 + 0.999182i \(0.487126\pi\)
\(510\) 2.40574e11 + 4.47062e11i 0.157465 + 0.292619i
\(511\) 1.34348e10 − 4.13482e10i 0.00871643 − 0.0268264i
\(512\) 4.64614e11 − 1.08702e12i 0.298798 − 0.699072i
\(513\) 4.23604e11 + 7.68728e10i 0.270042 + 0.0490055i
\(514\) 2.13551e12 + 1.55154e12i 1.34949 + 0.980459i
\(515\) −4.71990e11 + 4.24799e10i −0.295665 + 0.0266103i
\(516\) 3.94811e10 + 9.23705e10i 0.0245169 + 0.0573601i
\(517\) 1.02712e11 + 4.50010e11i 0.0632286 + 0.277023i
\(518\) 5.34422e10 + 8.09615e10i 0.0326137 + 0.0494077i
\(519\) −2.34775e12 − 1.40271e12i −1.42036 − 0.848626i
\(520\) 2.83180e11 + 3.55097e11i 0.169843 + 0.212976i
\(521\) 1.71409e12 − 1.49756e12i 1.01921 − 0.890459i 0.0251947 − 0.999683i \(-0.491979\pi\)
0.994017 + 0.109224i \(0.0348366\pi\)
\(522\) 1.63530e11 − 1.18812e11i 0.0964009 − 0.0700393i
\(523\) −1.13546e12 + 5.46811e11i −0.663614 + 0.319580i −0.735196 − 0.677855i \(-0.762910\pi\)
0.0715814 + 0.997435i \(0.477195\pi\)
\(524\) 6.45276e10 − 9.77552e10i 0.0373900 − 0.0566434i
\(525\) 1.57783e12 + 5.92169e11i 0.906448 + 0.340196i
\(526\) 1.56882e12 − 9.37324e11i 0.893585 − 0.533892i
\(527\) −1.86495e11 − 8.98115e10i −0.105322 − 0.0507206i
\(528\) −2.66790e12 + 4.84153e11i −1.49389 + 0.271100i
\(529\) −1.12734e12 + 4.93919e12i −0.625898 + 2.74224i
\(530\) 1.43562e11 − 5.38796e10i 0.0790309 − 0.0296608i
\(531\) 2.76080e10 − 3.46193e10i 0.0150699 − 0.0188970i
\(532\) −3.96593e9 − 8.83082e10i −0.00214656 − 0.0477968i
\(533\) 1.40199e10 + 3.12178e11i 0.00752442 + 0.167544i
\(534\) −1.58002e12 + 1.98128e12i −0.840865 + 1.05441i
\(535\) 1.38937e12 − 5.21440e11i 0.733207 − 0.275177i
\(536\) 4.80831e11 − 2.10666e12i 0.251623 − 1.10243i
\(537\) −2.65462e12 + 4.81742e11i −1.37758 + 0.249994i
\(538\) −2.46406e12 − 1.18663e12i −1.26804 − 0.610654i
\(539\) 1.68136e12 − 1.00456e12i 0.858046 − 0.512659i
\(540\) 1.17844e11 + 4.42276e10i 0.0596397 + 0.0223832i
\(541\) −9.50144e11 + 1.43941e12i −0.476872 + 0.722430i −0.990790 − 0.135409i \(-0.956765\pi\)
0.513918 + 0.857840i \(0.328194\pi\)
\(542\) 9.25448e11 − 4.45672e11i 0.460633 − 0.221829i
\(543\) 1.09720e12 − 7.97162e11i 0.541610 − 0.393502i
\(544\) 1.99043e11 − 1.73899e11i 0.0974433 − 0.0851336i
\(545\) −8.98917e11 − 1.12721e12i −0.436451 − 0.547292i
\(546\) −1.39406e12 − 8.32912e11i −0.671297 − 0.401081i
\(547\) −1.88723e12 − 2.85903e12i −0.901324 − 1.36545i −0.930663 − 0.365878i \(-0.880769\pi\)
0.0293388 − 0.999570i \(-0.490660\pi\)
\(548\) −1.90315e10 − 8.33826e10i −0.00901491 − 0.0394969i
\(549\) −1.46317e11 − 3.42327e11i −0.0687418 − 0.160829i
\(550\) 2.02297e12 − 1.82070e11i 0.942664 − 0.0848413i
\(551\) −4.95977e11 − 3.60348e11i −0.229234 − 0.166548i
\(552\) −4.11798e12 − 7.47303e11i −1.88781 − 0.342587i
\(553\) 1.60388e12 − 3.75246e12i 0.729304 − 1.70629i
\(554\) 1.03692e12 − 3.19131e12i 0.467682 − 1.43938i
\(555\) −2.62341e10 − 4.87512e10i −0.0117368 − 0.0218106i
\(556\) −3.24551e11 − 3.39453e11i −0.144028 − 0.150641i
\(557\) −7.09289e11 + 1.31808e12i −0.312230 + 0.580221i −0.987550 − 0.157304i \(-0.949720\pi\)
0.675320 + 0.737525i \(0.264005\pi\)
\(558\) 5.99925e10 − 1.65569e10i 0.0261965 − 0.00722977i
\(559\) −7.85275e10 − 5.79713e11i −0.0340149 − 0.251108i
\(560\) −2.56857e11 + 1.89619e12i −0.110368 + 0.814772i
\(561\) 1.64928e12 + 4.55171e11i 0.703008 + 0.194018i
\(562\) −8.32808e11 + 8.71048e11i −0.352153 + 0.368323i
\(563\) −1.21488e12 − 3.73903e12i −0.509621 − 1.56845i −0.792861 − 0.609403i \(-0.791409\pi\)
0.283240 − 0.959049i \(-0.408591\pi\)
\(564\) 6.77370e10 + 6.09644e9i 0.0281884 + 0.00253700i
\(565\) −1.75522e12 − 1.53349e12i −0.724624 − 0.633085i
\(566\) 1.33127e11 − 2.96430e12i 0.0545244 − 1.21408i
\(567\) 3.61217e12 1.46773
\(568\) 1.28758e11 − 2.30299e12i 0.0519047 − 0.928377i
\(569\) −1.79380e12 −0.717414 −0.358707 − 0.933450i \(-0.616782\pi\)
−0.358707 + 0.933450i \(0.616782\pi\)
\(570\) −2.07701e10 + 4.62483e11i −0.00824142 + 0.183509i
\(571\) −1.63902e12 − 1.43197e12i −0.645242 − 0.563731i 0.271883 − 0.962330i \(-0.412354\pi\)
−0.917125 + 0.398599i \(0.869496\pi\)
\(572\) −2.12413e11 − 1.91175e10i −0.0829659 − 0.00746706i
\(573\) 7.78501e11 + 2.39598e12i 0.301692 + 0.928512i
\(574\) −8.09337e11 + 8.46501e11i −0.311190 + 0.325480i
\(575\) 3.39735e12 + 9.37609e11i 1.29609 + 0.357698i
\(576\) 3.51668e10 − 2.59612e11i 0.0133117 − 0.0982706i
\(577\) 2.97171e11 + 2.19381e12i 0.111613 + 0.823962i 0.957057 + 0.289898i \(0.0936215\pi\)
−0.845444 + 0.534064i \(0.820664\pi\)
\(578\) 1.96499e12 − 5.42303e11i 0.732293 − 0.202100i
\(579\) 2.63134e12 − 4.88985e12i 0.973025 − 1.80818i
\(580\) −1.23865e11 − 1.29552e11i −0.0454487 − 0.0475356i
\(581\) 1.23683e12 + 2.29841e12i 0.450315 + 0.836826i
\(582\) −8.19160e10 + 2.52111e11i −0.0295948 + 0.0910834i
\(583\) 2.03102e11 − 4.75182e11i 0.0728126 − 0.170354i
\(584\) 5.45192e10 + 9.89377e9i 0.0193951 + 0.00351969i
\(585\) 7.83648e10 + 5.69354e10i 0.0276643 + 0.0200993i
\(586\) 2.80439e11 − 2.52400e10i 0.0982426 − 0.00884199i
\(587\) 1.69134e12 + 3.95708e12i 0.587974 + 1.37563i 0.904265 + 0.426972i \(0.140420\pi\)
−0.316291 + 0.948662i \(0.602437\pi\)
\(588\) −6.42161e10 − 2.81349e11i −0.0221537 − 0.0970617i
\(589\) −1.03985e11 − 1.57530e11i −0.0356001 − 0.0539319i
\(590\) −3.09320e11 − 1.84810e11i −0.105093 − 0.0627902i
\(591\) 9.89856e11 + 1.24124e12i 0.333756 + 0.418516i
\(592\) −1.04667e11 + 9.14448e10i −0.0350237 + 0.0305993i
\(593\) −1.79866e12 + 1.30681e12i −0.597316 + 0.433975i −0.844925 − 0.534885i \(-0.820355\pi\)
0.247609 + 0.968860i \(0.420355\pi\)
\(594\) 3.50730e12 − 1.68903e12i 1.15594 − 0.556670i
\(595\) 6.65163e11 − 1.00768e12i 0.217571 − 0.329607i
\(596\) 2.41031e11 + 9.04603e10i 0.0782463 + 0.0293663i
\(597\) 2.74361e12 − 1.63923e12i 0.883969 − 0.528147i
\(598\) −3.05972e12 − 1.47348e12i −0.978422 − 0.471183i
\(599\) 3.77845e12 − 6.85688e11i 1.19920 − 0.217624i 0.458031 − 0.888936i \(-0.348555\pi\)
0.741174 + 0.671313i \(0.234269\pi\)
\(600\) −4.77948e11 + 2.09403e12i −0.150557 + 0.659632i
\(601\) −2.98259e11 + 1.11939e11i −0.0932521 + 0.0349981i −0.397565 − 0.917574i \(-0.630145\pi\)
0.304313 + 0.952572i \(0.401573\pi\)
\(602\) 1.36698e12 − 1.71414e12i 0.424208 − 0.531941i
\(603\) −2.06756e10 − 4.60377e11i −0.00636839 − 0.141803i
\(604\) 2.06703e9 + 4.60260e10i 0.000631947 + 0.0140714i
\(605\) −7.83629e11 + 9.82640e11i −0.237800 + 0.298191i
\(606\) 3.52018e12 − 1.32115e12i 1.06032 − 0.397946i
\(607\) −1.08748e11 + 4.76457e11i −0.0325142 + 0.142454i −0.988580 − 0.150699i \(-0.951847\pi\)
0.956065 + 0.293153i \(0.0947046\pi\)
\(608\) 2.37146e11 − 4.30357e10i 0.0703801 − 0.0127721i
\(609\) −4.14395e12 − 1.99562e12i −1.22078 − 0.587896i
\(610\) −2.60063e12 + 1.55381e12i −0.760493 + 0.454373i
\(611\) −3.70813e11 − 1.39169e11i −0.107639 − 0.0403976i
\(612\) 1.45155e10 − 2.19901e10i 0.00418265 − 0.00633644i
\(613\) −3.87619e12 + 1.86667e12i −1.10875 + 0.533945i −0.896398 − 0.443249i \(-0.853826\pi\)
−0.212349 + 0.977194i \(0.568111\pi\)
\(614\) −2.94823e12 + 2.14201e12i −0.837150 + 0.608225i
\(615\) 5.03319e11 − 4.39736e11i 0.141875 − 0.123952i
\(616\) 3.57665e12 + 4.48498e12i 1.00084 + 1.25501i
\(617\) 7.14002e11 + 4.26596e11i 0.198343 + 0.118504i 0.608637 − 0.793449i \(-0.291717\pi\)
−0.410294 + 0.911953i \(0.634574\pi\)
\(618\) 1.18966e12 + 1.80226e12i 0.328077 + 0.497015i
\(619\) −4.13387e11 − 1.81117e12i −0.113175 − 0.495851i −0.999465 − 0.0327198i \(-0.989583\pi\)
0.886290 − 0.463131i \(-0.153274\pi\)
\(620\) −2.16894e10 − 5.07448e10i −0.00589500 − 0.0137920i
\(621\) 6.72745e12 − 6.05482e11i 1.81526 − 0.163376i
\(622\) −2.98584e12 − 2.16934e12i −0.799851 − 0.581126i
\(623\) 5.93011e12 + 1.07616e12i 1.57713 + 0.286206i
\(624\) 9.14422e11 − 2.13940e12i 0.241444 − 0.564886i
\(625\) 1.91820e11 − 5.90361e11i 0.0502844 − 0.154759i
\(626\) 1.58560e12 + 2.94654e12i 0.412676 + 0.766881i
\(627\) 1.07818e12 + 1.12769e12i 0.278604 + 0.291397i
\(628\) −3.18276e11 + 5.91456e11i −0.0816555 + 0.151741i
\(629\) 8.45397e10 − 2.33315e10i 0.0215344 − 0.00594312i
\(630\) 4.87300e10 + 3.59739e11i 0.0123243 + 0.0909819i
\(631\) 3.95149e10 − 2.91711e11i 0.00992268 − 0.0732521i −0.985311 − 0.170768i \(-0.945375\pi\)
0.995234 + 0.0975155i \(0.0310895\pi\)
\(632\) 5.01356e12 + 1.38365e12i 1.25003 + 0.344986i
\(633\) 2.06869e12 − 2.16368e12i 0.512129 − 0.535645i
\(634\) −4.61112e11 − 1.41916e12i −0.113346 − 0.348842i
\(635\) 1.68886e12 + 1.52000e11i 0.412203 + 0.0370990i
\(636\) −5.73401e10 − 5.00966e10i −0.0138964 − 0.0121409i
\(637\) −7.54002e10 + 1.67892e12i −0.0181445 + 0.404019i
\(638\) −5.54333e12 −1.32458
\(639\) −1.04196e11 − 4.80765e11i −0.0247227 − 0.114072i
\(640\) −2.70807e12 −0.638044
\(641\) −5.89346e10 + 1.31228e12i −0.0137882 + 0.307019i 0.980234 + 0.197842i \(0.0633931\pi\)
−0.994022 + 0.109178i \(0.965178\pi\)
\(642\) −5.09258e12 − 4.44926e12i −1.18312 − 1.03366i
\(643\) 4.72586e12 + 4.25335e11i 1.09026 + 0.0981254i 0.620152 − 0.784482i \(-0.287071\pi\)
0.470111 + 0.882607i \(0.344214\pi\)
\(644\) −4.28575e11 − 1.31902e12i −0.0981840 − 0.302179i
\(645\) −8.64662e11 + 9.04366e11i −0.196711 + 0.205743i
\(646\) −7.06944e11 − 1.95104e11i −0.159712 − 0.0440778i
\(647\) 7.90309e11 − 5.83429e12i 0.177308 − 1.30894i −0.655424 − 0.755261i \(-0.727510\pi\)
0.832732 − 0.553677i \(-0.186776\pi\)
\(648\) 6.17964e11 + 4.56200e12i 0.137682 + 1.01641i
\(649\) −1.17057e12 + 3.23055e11i −0.258997 + 0.0714786i
\(650\) −8.25885e11 + 1.53475e12i −0.181472 + 0.337231i
\(651\) −9.78630e11 − 1.02357e12i −0.213552 − 0.223358i
\(652\) −1.30363e11 − 2.42255e11i −0.0282514 − 0.0524999i
\(653\) −9.75809e11 + 3.00323e12i −0.210017 + 0.646367i 0.789452 + 0.613812i \(0.210365\pi\)
−0.999470 + 0.0325556i \(0.989635\pi\)
\(654\) −2.58213e12 + 6.04120e12i −0.551923 + 1.29129i
\(655\) 1.43549e12 + 2.60503e11i 0.304729 + 0.0553002i
\(656\) −1.35747e12 − 9.86258e11i −0.286195 − 0.207933i
\(657\) 1.17696e10 − 1.05929e9i 0.00246445 − 0.000221804i
\(658\) −5.83396e11 − 1.36492e12i −0.121324 − 0.283852i
\(659\) −4.51033e11 − 1.97611e12i −0.0931589 − 0.408156i 0.906750 − 0.421669i \(-0.138556\pi\)
−0.999909 + 0.0135132i \(0.995698\pi\)
\(660\) 2.51288e11 + 3.80685e11i 0.0515494 + 0.0780940i
\(661\) −4.66712e12 − 2.78847e12i −0.950916 − 0.568146i −0.0484120 − 0.998827i \(-0.515416\pi\)
−0.902504 + 0.430682i \(0.858273\pi\)
\(662\) 1.08077e12 + 1.35524e12i 0.218712 + 0.274256i
\(663\) −1.10558e12 + 9.65915e11i −0.222218 + 0.194146i
\(664\) −2.69118e12 + 1.95526e12i −0.537263 + 0.390345i
\(665\) 9.91993e11 − 4.77719e11i 0.196703 − 0.0947273i
\(666\) −1.45261e10 + 2.20061e10i −0.00286098 + 0.00433420i
\(667\) −9.00523e12 − 3.37972e12i −1.76169 − 0.661172i
\(668\) 2.65690e11 − 1.58742e11i 0.0516275 − 0.0308460i
\(669\) 1.28350e11 + 6.18102e10i 0.0247730 + 0.0119301i
\(670\) −3.68981e12 + 6.69602e11i −0.707405 + 0.128375i
\(671\) −2.27184e12 + 9.95357e12i −0.432639 + 1.89552i
\(672\) 1.69293e12 − 6.35366e11i 0.320241 − 0.120188i
\(673\) 3.09390e12 − 3.87963e12i 0.581352 − 0.728992i −0.400991 − 0.916082i \(-0.631334\pi\)
0.982343 + 0.187090i \(0.0599056\pi\)
\(674\) 2.44086e11 + 5.43501e12i 0.0455590 + 1.01445i
\(675\) −1.55524e11 − 3.46302e12i −0.0288358 − 0.642078i
\(676\) −2.99897e11 + 3.76059e11i −0.0552348 + 0.0692622i
\(677\) −6.92057e12 + 2.59733e12i −1.26617 + 0.475202i −0.891949 − 0.452136i \(-0.850662\pi\)
−0.374223 + 0.927339i \(0.622091\pi\)
\(678\) −2.36338e12 + 1.03546e13i −0.429536 + 1.88192i
\(679\) 6.20321e11 − 1.12572e11i 0.111996 − 0.0203243i
\(680\) 1.38644e12 + 6.67676e11i 0.248664 + 0.119750i
\(681\) 1.01211e13 − 6.04710e12i 1.80330 − 1.07742i
\(682\) −1.59791e12 − 5.99705e11i −0.282828 − 0.106147i
\(683\) −1.50840e10 + 2.28514e10i −0.00265231 + 0.00401808i −0.835897 − 0.548886i \(-0.815052\pi\)
0.833245 + 0.552904i \(0.186481\pi\)
\(684\) 2.16478e10 − 1.04250e10i 0.00378147 − 0.00182106i
\(685\) 8.61829e11 − 6.26156e11i 0.149559 − 0.108661i
\(686\) 1.41391e12 − 1.23529e12i 0.243760 − 0.212966i
\(687\) −3.83128e11 − 4.80428e11i −0.0656204 − 0.0822854i
\(688\) 2.69655e12 + 1.61111e12i 0.458839 + 0.274143i
\(689\) 2.44279e11 + 3.70067e11i 0.0412952 + 0.0625595i
\(690\) 1.61626e12 + 7.08128e12i 0.271450 + 1.18930i
\(691\) −7.03022e10 − 1.64480e11i −0.0117305 − 0.0274450i 0.913560 − 0.406704i \(-0.133322\pi\)
−0.925291 + 0.379259i \(0.876179\pi\)
\(692\) 1.15039e12 − 1.03537e11i 0.190707 − 0.0171640i
\(693\) 9.89772e11 + 7.19111e11i 0.163018 + 0.118440i
\(694\) −9.60046e12 − 1.74223e12i −1.57099 − 0.285093i
\(695\) 2.29904e12 − 5.37886e12i 0.373778 − 0.874498i
\(696\) 1.81143e12 − 5.57502e12i 0.292604 − 0.900543i
\(697\) 5.01715e11 + 9.32342e11i 0.0805210 + 0.149633i
\(698\) −7.76651e12 − 8.12313e12i −1.23844 − 1.29531i
\(699\) −1.86589e12 + 3.46740e12i −0.295623 + 0.549359i
\(700\) −6.86112e11 + 1.89355e11i −0.108007 + 0.0298082i
\(701\) −4.54384e11 − 3.35440e12i −0.0710709 − 0.524666i −0.991131 − 0.132889i \(-0.957575\pi\)
0.920060 − 0.391777i \(-0.128140\pi\)
\(702\) −4.48378e11 + 3.31006e12i −0.0696831 + 0.514421i
\(703\) 7.70907e10 + 2.12757e10i 0.0119043 + 0.00328537i
\(704\) −4.96502e12 + 5.19300e12i −0.761805 + 0.796786i
\(705\) 2.61770e11 + 8.05646e11i 0.0399089 + 0.122827i
\(706\) 7.92111e12 + 7.12912e11i 1.19995 + 0.107998i
\(707\) −6.73415e12 − 5.88345e12i −1.01367 − 0.885614i
\(708\) −8.02729e9 + 1.78741e11i −0.00120066 + 0.0267347i
\(709\) 8.90156e12 1.32299 0.661497 − 0.749948i \(-0.269921\pi\)
0.661497 + 0.749948i \(0.269921\pi\)
\(710\) −3.76298e12 + 1.36536e12i −0.555737 + 0.201644i
\(711\) 1.10922e12 0.162781
\(712\) −3.44619e11 + 7.67354e12i −0.0502550 + 1.11902i
\(713\) −2.23019e12 − 1.94846e12i −0.323176 − 0.282351i
\(714\) −5.47992e12 − 4.93202e11i −0.789100 − 0.0710203i
\(715\) −8.20873e11 − 2.52639e12i −0.117462 − 0.361512i
\(716\) 7.87435e11 − 8.23593e11i 0.111971 − 0.117113i
\(717\) −4.81385e12 − 1.32854e12i −0.680231 − 0.187732i
\(718\) 8.38965e11 − 6.19349e12i 0.117810 − 0.869711i
\(719\) −1.02947e12 − 7.59987e12i −0.143660 − 1.06054i −0.908966 − 0.416871i \(-0.863127\pi\)
0.765306 − 0.643667i \(-0.222588\pi\)
\(720\) −5.01367e11 + 1.38369e11i −0.0695280 + 0.0191885i
\(721\) 2.43376e12 − 4.52268e12i 0.335404 − 0.623285i
\(722\) 4.88335e12 + 5.10758e12i 0.668806 + 0.699517i
\(723\) −5.44549e12 − 1.01194e13i −0.741164 − 1.37731i
\(724\) −1.76999e11 + 5.44746e11i −0.0239412 + 0.0736835i
\(725\) −1.94008e12 + 4.53905e12i −0.260795 + 0.610160i
\(726\) 5.63526e12 + 1.02265e12i 0.752833 + 0.136619i
\(727\) −1.37737e12 − 1.00072e12i −0.182872 − 0.132864i 0.492583 − 0.870265i \(-0.336053\pi\)
−0.675455 + 0.737401i \(0.736053\pi\)
\(728\) −4.90248e12 + 4.41231e11i −0.646882 + 0.0582204i
\(729\) −2.57034e12 − 6.01361e12i −0.337067 − 0.788608i
\(730\) −2.13981e10 − 9.37512e10i −0.00278883 − 0.0122187i
\(731\) −1.09192e12 − 1.65419e12i −0.141437 − 0.214268i
\(732\) 1.29136e12 + 7.71553e11i 0.166245 + 0.0993267i
\(733\) 9.25646e12 + 1.16072e13i 1.18434 + 1.48512i 0.836848 + 0.547436i \(0.184396\pi\)
0.347494 + 0.937682i \(0.387033\pi\)
\(734\) 5.57351e11 − 4.86943e11i 0.0708755 − 0.0619221i
\(735\) 2.90798e12 − 2.11277e12i 0.367535 − 0.267030i
\(736\) 3.40697e12 − 1.64071e12i 0.427974 − 0.206102i
\(737\) −6.96229e12 + 1.05474e13i −0.869258 + 1.31687i
\(738\) −2.98031e11 − 1.11853e11i −0.0369835 − 0.0138801i
\(739\) −8.56426e12 + 5.11691e12i −1.05631 + 0.631114i −0.932492 − 0.361191i \(-0.882370\pi\)
−0.123815 + 0.992305i \(0.539513\pi\)
\(740\) 2.10658e10 + 1.01448e10i 0.00258247 + 0.00124365i
\(741\) −1.31722e12 + 2.39040e11i −0.160501 + 0.0291266i
\(742\) −3.69793e11 + 1.62017e12i −0.0447859 + 0.196220i
\(743\) −1.24290e13 + 4.66468e12i −1.49619 + 0.561529i −0.959365 − 0.282167i \(-0.908947\pi\)
−0.536822 + 0.843695i \(0.680375\pi\)
\(744\) 1.12529e12 − 1.41107e12i 0.134644 − 0.168838i
\(745\) 1.43865e11 + 3.20339e12i 0.0171100 + 0.380984i
\(746\) 5.00403e11 + 1.11423e13i 0.0591555 + 1.31720i
\(747\) −4.42329e11 + 5.54663e11i −0.0519760 + 0.0651758i
\(748\) −6.76515e11 + 2.53900e11i −0.0790169 + 0.0296555i
\(749\) −3.57881e12 + 1.56798e13i −0.415500 + 1.82042i
\(750\) 8.99415e12 − 1.63220e12i 1.03797 − 0.188364i
\(751\) −7.11943e12 − 3.42854e12i −0.816706 − 0.393305i −0.0215934 − 0.999767i \(-0.506874\pi\)
−0.795112 + 0.606462i \(0.792588\pi\)
\(752\) 1