Properties

Label 13.7.f.a.11.4
Level $13$
Weight $7$
Character 13.11
Analytic conductor $2.991$
Analytic rank $0$
Dimension $24$
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] = [13,7,Mod(2,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("13.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 13.f (of order \(12\), degree \(4\), 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: \(2.99070308706\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 11.4
Character \(\chi\) \(=\) 13.11
Dual form 13.7.f.a.6.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.76668 - 6.59335i) q^{2} +(-10.7542 - 18.6268i) q^{3} +(15.0745 + 8.70327i) q^{4} +(-144.857 - 144.857i) q^{5} +(-141.812 + 37.9984i) q^{6} +(49.5658 + 184.982i) q^{7} +(392.922 - 392.922i) q^{8} +(133.195 - 230.701i) q^{9} +O(q^{10})\) \(q+(1.76668 - 6.59335i) q^{2} +(-10.7542 - 18.6268i) q^{3} +(15.0745 + 8.70327i) q^{4} +(-144.857 - 144.857i) q^{5} +(-141.812 + 37.9984i) q^{6} +(49.5658 + 184.982i) q^{7} +(392.922 - 392.922i) q^{8} +(133.195 - 230.701i) q^{9} +(-1211.01 + 699.177i) q^{10} +(1439.16 + 385.622i) q^{11} -374.386i q^{12} +(1708.06 + 1381.79i) q^{13} +1307.22 q^{14} +(-1140.40 + 4256.04i) q^{15} +(-1339.50 - 2320.08i) q^{16} +(-5325.85 - 3074.88i) q^{17} +(-1285.78 - 1285.78i) q^{18} +(2668.98 - 715.152i) q^{19} +(-922.918 - 3444.38i) q^{20} +(2912.58 - 2912.58i) q^{21} +(5085.09 - 8807.63i) q^{22} +(-1100.31 + 635.262i) q^{23} +(-11544.4 - 3093.32i) q^{24} +26342.1i q^{25} +(12128.2 - 8820.62i) q^{26} -21409.2 q^{27} +(-862.768 + 3219.90i) q^{28} +(14334.4 + 24827.9i) q^{29} +(26046.8 + 15038.1i) q^{30} +(-2357.22 - 2357.22i) q^{31} +(16687.9 - 4471.52i) q^{32} +(-8294.10 - 30954.0i) q^{33} +(-29682.9 + 29682.9i) q^{34} +(19616.0 - 33975.9i) q^{35} +(4015.71 - 2318.47i) q^{36} +(37580.6 + 10069.7i) q^{37} -18861.0i q^{38} +(7369.63 - 46675.6i) q^{39} -113835. q^{40} +(-18395.3 + 68652.4i) q^{41} +(-14058.1 - 24349.3i) q^{42} +(-51822.0 - 29919.5i) q^{43} +(18338.5 + 18338.5i) q^{44} +(-52713.0 + 14124.4i) q^{45} +(2244.61 + 8377.01i) q^{46} +(137657. - 137657. i) q^{47} +(-28810.4 + 49901.0i) q^{48} +(70125.5 - 40487.0i) q^{49} +(173683. + 46538.2i) q^{50} +132271. i q^{51} +(13722.0 + 35695.5i) q^{52} -112420. q^{53} +(-37823.3 + 141158. i) q^{54} +(-152613. - 264333. i) q^{55} +(92159.0 + 53208.0i) q^{56} +(-42023.7 - 42023.7i) q^{57} +(189024. - 50648.8i) q^{58} +(90422.1 + 337460. i) q^{59} +(-54232.4 + 54232.4i) q^{60} +(-83261.0 + 144212. i) q^{61} +(-19706.5 + 11377.5i) q^{62} +(49277.5 + 13203.9i) q^{63} -289385. i q^{64} +(-47261.4 - 447586. i) q^{65} -218744. q^{66} +(-42309.5 + 157901. i) q^{67} +(-53523.0 - 92704.6i) q^{68} +(23665.8 + 13663.4i) q^{69} +(-189360. - 189360. i) q^{70} +(312300. - 83680.6i) q^{71} +(-38312.2 - 142983. i) q^{72} +(-413644. + 413644. i) q^{73} +(132786. - 229992. i) q^{74} +(490669. - 283288. i) q^{75} +(46457.8 + 12448.3i) q^{76} +285333. i q^{77} +(-294729. - 131052. i) q^{78} +42458.2 q^{79} +(-142044. + 530115. i) q^{80} +(133139. + 230603. i) q^{81} +(420150. + 242574. i) q^{82} +(-432403. - 432403. i) q^{83} +(69254.6 - 18556.7i) q^{84} +(326069. + 1.21690e6i) q^{85} +(-288823. + 288823. i) q^{86} +(308310. - 534008. i) q^{87} +(716999. - 413959. i) q^{88} +(-112025. - 30017.0i) q^{89} +372509. i q^{90} +(-170946. + 384449. i) q^{91} -22115.4 q^{92} +(-18557.5 + 69257.5i) q^{93} +(-664427. - 1.15082e6i) q^{94} +(-490216. - 283026. i) q^{95} +(-262755. - 262755. i) q^{96} +(966713. - 259030. i) q^{97} +(-143055. - 533890. i) q^{98} +(280653. - 280653. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9} + 4674 q^{10} + 228 q^{11} - 1552 q^{13} - 14616 q^{14} + 7486 q^{15} - 2138 q^{16} + 20898 q^{17} - 5630 q^{18} - 14036 q^{19} - 14634 q^{20} - 314 q^{21} + 37852 q^{22} + 29634 q^{23} + 47154 q^{24} + 510 q^{26} - 107060 q^{27} - 40572 q^{28} + 1026 q^{29} - 247734 q^{30} - 118116 q^{31} + 180876 q^{32} + 306046 q^{33} + 101898 q^{34} + 104862 q^{35} + 105066 q^{36} - 31470 q^{37} + 28510 q^{39} - 275328 q^{40} - 357216 q^{41} - 25636 q^{42} - 480486 q^{43} - 797712 q^{44} + 464248 q^{45} + 1012050 q^{46} + 140028 q^{47} + 676102 q^{48} + 854562 q^{49} + 756714 q^{50} - 771704 q^{52} - 1397076 q^{53} - 1271048 q^{54} - 205490 q^{55} - 1461108 q^{56} - 1483394 q^{57} + 1133806 q^{58} + 1568052 q^{59} + 886808 q^{60} + 768676 q^{61} + 3741966 q^{62} + 1336264 q^{63} - 946968 q^{65} - 5076928 q^{66} - 1489892 q^{67} - 569052 q^{68} - 1475766 q^{69} - 2626556 q^{70} + 2136948 q^{71} + 4787052 q^{72} + 326326 q^{73} + 2159718 q^{74} + 3466008 q^{75} + 1522158 q^{76} - 1573544 q^{78} - 1734344 q^{79} - 5214300 q^{80} - 773072 q^{81} - 3540426 q^{82} - 3642132 q^{83} + 2952364 q^{84} + 3509916 q^{85} - 132324 q^{86} + 531698 q^{87} + 4478052 q^{88} + 632754 q^{89} - 2946788 q^{91} - 1656060 q^{92} - 295514 q^{93} + 1552210 q^{94} - 2753718 q^{95} - 3979208 q^{96} + 2258214 q^{97} + 4984308 q^{98} + 4336480 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.76668 6.59335i 0.220835 0.824169i −0.763195 0.646168i \(-0.776370\pi\)
0.984030 0.178001i \(-0.0569629\pi\)
\(3\) −10.7542 18.6268i −0.398303 0.689881i 0.595214 0.803567i \(-0.297067\pi\)
−0.993517 + 0.113687i \(0.963734\pi\)
\(4\) 15.0745 + 8.70327i 0.235539 + 0.135989i
\(5\) −144.857 144.857i −1.15886 1.15886i −0.984722 0.174134i \(-0.944287\pi\)
−0.174134 0.984722i \(-0.555713\pi\)
\(6\) −141.812 + 37.9984i −0.656538 + 0.175919i
\(7\) 49.5658 + 184.982i 0.144507 + 0.539306i 0.999777 + 0.0211237i \(0.00672440\pi\)
−0.855270 + 0.518182i \(0.826609\pi\)
\(8\) 392.922 392.922i 0.767427 0.767427i
\(9\) 133.195 230.701i 0.182710 0.316463i
\(10\) −1211.01 + 699.177i −1.21101 + 0.699177i
\(11\) 1439.16 + 385.622i 1.08126 + 0.289724i 0.755114 0.655594i \(-0.227582\pi\)
0.326150 + 0.945318i \(0.394248\pi\)
\(12\) 374.386i 0.216659i
\(13\) 1708.06 + 1381.79i 0.777449 + 0.628946i
\(14\) 1307.22 0.476391
\(15\) −1140.40 + 4256.04i −0.337897 + 1.26105i
\(16\) −1339.50 2320.08i −0.327026 0.566425i
\(17\) −5325.85 3074.88i −1.08403 0.625866i −0.152051 0.988373i \(-0.548588\pi\)
−0.931981 + 0.362507i \(0.881921\pi\)
\(18\) −1285.78 1285.78i −0.220470 0.220470i
\(19\) 2668.98 715.152i 0.389121 0.104265i −0.0589537 0.998261i \(-0.518776\pi\)
0.448075 + 0.893996i \(0.352110\pi\)
\(20\) −922.918 3444.38i −0.115365 0.430547i
\(21\) 2912.58 2912.58i 0.314499 0.314499i
\(22\) 5085.09 8807.63i 0.477563 0.827163i
\(23\) −1100.31 + 635.262i −0.0904337 + 0.0522119i −0.544535 0.838738i \(-0.683294\pi\)
0.454101 + 0.890950i \(0.349960\pi\)
\(24\) −11544.4 3093.32i −0.835101 0.223765i
\(25\) 26342.1i 1.68589i
\(26\) 12128.2 8820.62i 0.690046 0.501856i
\(27\) −21409.2 −1.08770
\(28\) −862.768 + 3219.90i −0.0393025 + 0.146679i
\(29\) 14334.4 + 24827.9i 0.587741 + 1.01800i 0.994528 + 0.104474i \(0.0333160\pi\)
−0.406786 + 0.913523i \(0.633351\pi\)
\(30\) 26046.8 + 15038.1i 0.964697 + 0.556968i
\(31\) −2357.22 2357.22i −0.0791253 0.0791253i 0.666436 0.745562i \(-0.267819\pi\)
−0.745562 + 0.666436i \(0.767819\pi\)
\(32\) 16687.9 4471.52i 0.509275 0.136460i
\(33\) −8294.10 30954.0i −0.230796 0.861341i
\(34\) −29682.9 + 29682.9i −0.755212 + 0.755212i
\(35\) 19616.0 33975.9i 0.457516 0.792440i
\(36\) 4015.71 2318.47i 0.0860706 0.0496929i
\(37\) 37580.6 + 10069.7i 0.741923 + 0.198798i 0.609933 0.792453i \(-0.291196\pi\)
0.131991 + 0.991251i \(0.457863\pi\)
\(38\) 18861.0i 0.343727i
\(39\) 7369.63 46675.6i 0.124237 0.786858i
\(40\) −113835. −1.77867
\(41\) −18395.3 + 68652.4i −0.266905 + 0.996102i 0.694169 + 0.719812i \(0.255772\pi\)
−0.961074 + 0.276290i \(0.910895\pi\)
\(42\) −14058.1 24349.3i −0.189748 0.328653i
\(43\) −51822.0 29919.5i −0.651792 0.376312i 0.137351 0.990522i \(-0.456141\pi\)
−0.789142 + 0.614210i \(0.789475\pi\)
\(44\) 18338.5 + 18338.5i 0.215281 + 0.215281i
\(45\) −52713.0 + 14124.4i −0.578469 + 0.155000i
\(46\) 2244.61 + 8377.01i 0.0230605 + 0.0860629i
\(47\) 137657. 137657.i 1.32589 1.32589i 0.416962 0.908924i \(-0.363095\pi\)
0.908924 0.416962i \(-0.136905\pi\)
\(48\) −28810.4 + 49901.0i −0.260510 + 0.451217i
\(49\) 70125.5 40487.0i 0.596057 0.344134i
\(50\) 173683. + 46538.2i 1.38946 + 0.372305i
\(51\) 132271.i 0.997137i
\(52\) 13722.0 + 35695.5i 0.0975903 + 0.253866i
\(53\) −112420. −0.755122 −0.377561 0.925985i \(-0.623237\pi\)
−0.377561 + 0.925985i \(0.623237\pi\)
\(54\) −37823.3 + 141158.i −0.240203 + 0.896449i
\(55\) −152613. 264333.i −0.917281 1.58878i
\(56\) 92159.0 + 53208.0i 0.524776 + 0.302979i
\(57\) −42023.7 42023.7i −0.226918 0.226918i
\(58\) 189024. 50648.8i 0.968796 0.259588i
\(59\) 90422.1 + 337460.i 0.440269 + 1.64311i 0.728133 + 0.685436i \(0.240388\pi\)
−0.287864 + 0.957671i \(0.592945\pi\)
\(60\) −54232.4 + 54232.4i −0.251076 + 0.251076i
\(61\) −83261.0 + 144212.i −0.366819 + 0.635349i −0.989066 0.147472i \(-0.952887\pi\)
0.622247 + 0.782821i \(0.286220\pi\)
\(62\) −19706.5 + 11377.5i −0.0826863 + 0.0477390i
\(63\) 49277.5 + 13203.9i 0.197073 + 0.0528055i
\(64\) 289385.i 1.10392i
\(65\) −47261.4 447586.i −0.172094 1.62981i
\(66\) −218744. −0.760858
\(67\) −42309.5 + 157901.i −0.140674 + 0.525003i 0.859236 + 0.511580i \(0.170939\pi\)
−0.999910 + 0.0134230i \(0.995727\pi\)
\(68\) −53523.0 92704.6i −0.170221 0.294832i
\(69\) 23665.8 + 13663.4i 0.0720400 + 0.0415923i
\(70\) −189360. 189360.i −0.552069 0.552069i
\(71\) 312300. 83680.6i 0.872564 0.233803i 0.205368 0.978685i \(-0.434161\pi\)
0.667196 + 0.744882i \(0.267494\pi\)
\(72\) −38312.2 142983.i −0.102645 0.383078i
\(73\) −413644. + 413644.i −1.06331 + 1.06331i −0.0654504 + 0.997856i \(0.520848\pi\)
−0.997856 + 0.0654504i \(0.979152\pi\)
\(74\) 132786. 229992.i 0.327686 0.567569i
\(75\) 490669. 283288.i 1.16307 0.671497i
\(76\) 46457.8 + 12448.3i 0.105832 + 0.0283576i
\(77\) 285333.i 0.624999i
\(78\) −294729. 131052.i −0.621068 0.276159i
\(79\) 42458.2 0.0861154 0.0430577 0.999073i \(-0.486290\pi\)
0.0430577 + 0.999073i \(0.486290\pi\)
\(80\) −142044. + 530115.i −0.277429 + 1.03538i
\(81\) 133139. + 230603.i 0.250525 + 0.433921i
\(82\) 420150. + 242574.i 0.762014 + 0.439949i
\(83\) −432403. 432403.i −0.756231 0.756231i 0.219403 0.975634i \(-0.429589\pi\)
−0.975634 + 0.219403i \(0.929589\pi\)
\(84\) 69254.6 18556.7i 0.116845 0.0313086i
\(85\) 326069. + 1.21690e6i 0.530948 + 1.98153i
\(86\) −288823. + 288823.i −0.454084 + 0.454084i
\(87\) 308310. 534008.i 0.468198 0.810943i
\(88\) 716999. 413959.i 1.05213 0.607449i
\(89\) −112025. 30017.0i −0.158908 0.0425791i 0.178488 0.983942i \(-0.442879\pi\)
−0.337396 + 0.941363i \(0.609546\pi\)
\(90\) 372509.i 0.510986i
\(91\) −170946. + 384449.i −0.226848 + 0.510170i
\(92\) −22115.4 −0.0284009
\(93\) −18557.5 + 69257.5i −0.0230712 + 0.0861029i
\(94\) −664427. 1.15082e6i −0.799952 1.38556i
\(95\) −490216. 283026.i −0.571763 0.330108i
\(96\) −262755. 262755.i −0.296987 0.296987i
\(97\) 966713. 259030.i 1.05921 0.283815i 0.313158 0.949701i \(-0.398613\pi\)
0.746053 + 0.665886i \(0.231946\pi\)
\(98\) −143055. 533890.i −0.151994 0.567248i
\(99\) 280653. 280653.i 0.289244 0.289244i
\(100\) −229262. + 397094.i −0.229262 + 0.397094i
\(101\) −989996. + 571574.i −0.960880 + 0.554764i −0.896444 0.443157i \(-0.853858\pi\)
−0.0644364 + 0.997922i \(0.520525\pi\)
\(102\) 872111. + 233681.i 0.821809 + 0.220203i
\(103\) 859775.i 0.786816i −0.919364 0.393408i \(-0.871296\pi\)
0.919364 0.393408i \(-0.128704\pi\)
\(104\) 1.21407e6 128196.i 1.07930 0.113966i
\(105\) −843815. −0.728919
\(106\) −198611. + 741227.i −0.166758 + 0.622348i
\(107\) −246853. 427563.i −0.201506 0.349019i 0.747508 0.664253i \(-0.231250\pi\)
−0.949014 + 0.315234i \(0.897917\pi\)
\(108\) −322733. 186330.i −0.256196 0.147915i
\(109\) 107141. + 107141.i 0.0827324 + 0.0827324i 0.747262 0.664530i \(-0.231368\pi\)
−0.664530 + 0.747262i \(0.731368\pi\)
\(110\) −2.01246e6 + 539236.i −1.51199 + 0.405136i
\(111\) −216583. 808298.i −0.158363 0.591020i
\(112\) 362779. 362779.i 0.258219 0.258219i
\(113\) −716209. + 1.24051e6i −0.496369 + 0.859736i −0.999991 0.00418765i \(-0.998667\pi\)
0.503622 + 0.863924i \(0.332000\pi\)
\(114\) −351319. + 202834.i −0.237131 + 0.136907i
\(115\) 251409. + 67364.9i 0.165306 + 0.0442935i
\(116\) 499025.i 0.319704i
\(117\) 546287. 210002.i 0.341085 0.131119i
\(118\) 2.38474e6 1.45143
\(119\) 304818. 1.13759e6i 0.180884 0.675067i
\(120\) 1.22420e6 + 2.12038e6i 0.708451 + 1.22707i
\(121\) 388267. + 224166.i 0.219166 + 0.126536i
\(122\) 803746. + 803746.i 0.442629 + 0.442629i
\(123\) 1.47660e6 395653.i 0.793501 0.212618i
\(124\) −15018.4 56049.5i −0.00787697 0.0293973i
\(125\) 1.55245e6 1.55245e6i 0.794854 0.794854i
\(126\) 174115. 301577.i 0.0870414 0.150760i
\(127\) −864297. + 499002.i −0.421941 + 0.243608i −0.695908 0.718131i \(-0.744998\pi\)
0.273966 + 0.961739i \(0.411664\pi\)
\(128\) −839988. 225074.i −0.400537 0.107324i
\(129\) 1.28704e6i 0.599545i
\(130\) −3.03459e6 479132.i −1.38124 0.218085i
\(131\) −3.59354e6 −1.59849 −0.799243 0.601008i \(-0.794766\pi\)
−0.799243 + 0.601008i \(0.794766\pi\)
\(132\) 144372. 538802.i 0.0627711 0.234265i
\(133\) 264580. + 458267.i 0.112461 + 0.194788i
\(134\) 966352. + 557923.i 0.401625 + 0.231878i
\(135\) 3.10127e6 + 3.10127e6i 1.26049 + 1.26049i
\(136\) −3.30083e6 + 884456.i −1.31222 + 0.351609i
\(137\) −644543. 2.40547e6i −0.250663 0.935487i −0.970452 0.241294i \(-0.922428\pi\)
0.719789 0.694193i \(-0.244238\pi\)
\(138\) 131898. 131898.i 0.0501880 0.0501880i
\(139\) 1.28864e6 2.23199e6i 0.479830 0.831089i −0.519903 0.854225i \(-0.674032\pi\)
0.999732 + 0.0231362i \(0.00736514\pi\)
\(140\) 591402. 341446.i 0.215526 0.124434i
\(141\) −4.04451e6 1.08372e6i −1.44281 0.386599i
\(142\) 2.20694e6i 0.770772i
\(143\) 1.92532e6 + 2.64729e6i 0.658407 + 0.905302i
\(144\) −713659. −0.239003
\(145\) 1.52006e6 5.67294e6i 0.498605 1.86082i
\(146\) 1.99652e6 + 3.45808e6i 0.641528 + 1.11116i
\(147\) −1.50828e6 870808.i −0.474822 0.274139i
\(148\) 478870. + 478870.i 0.147718 + 0.147718i
\(149\) −1.11954e6 + 299979.i −0.338438 + 0.0906842i −0.424035 0.905646i \(-0.639387\pi\)
0.0855974 + 0.996330i \(0.472720\pi\)
\(150\) −1.00096e6 3.73563e6i −0.296580 1.10685i
\(151\) −1.84569e6 + 1.84569e6i −0.536079 + 0.536079i −0.922375 0.386296i \(-0.873754\pi\)
0.386296 + 0.922375i \(0.373754\pi\)
\(152\) 767704. 1.32970e6i 0.218606 0.378638i
\(153\) −1.41876e6 + 819120.i −0.396126 + 0.228704i
\(154\) 1.88130e6 + 504092.i 0.515105 + 0.138022i
\(155\) 682921.i 0.183390i
\(156\) 517324. 639472.i 0.136266 0.168441i
\(157\) 5.86194e6 1.51475 0.757377 0.652978i \(-0.226480\pi\)
0.757377 + 0.652978i \(0.226480\pi\)
\(158\) 75010.3 279942.i 0.0190173 0.0709736i
\(159\) 1.20899e6 + 2.09403e6i 0.300767 + 0.520944i
\(160\) −3.06510e6 1.76963e6i −0.748314 0.432040i
\(161\) −172050. 172050.i −0.0412264 0.0412264i
\(162\) 1.75566e6 470429.i 0.412949 0.110649i
\(163\) 1.55231e6 + 5.79331e6i 0.358440 + 1.33772i 0.876100 + 0.482130i \(0.160137\pi\)
−0.517660 + 0.855587i \(0.673197\pi\)
\(164\) −874801. + 874801.i −0.198325 + 0.198325i
\(165\) −3.28245e6 + 5.68536e6i −0.730711 + 1.26563i
\(166\) −3.61491e6 + 2.08707e6i −0.790265 + 0.456260i
\(167\) −1.33679e6 358193.i −0.287022 0.0769073i 0.112436 0.993659i \(-0.464135\pi\)
−0.399457 + 0.916752i \(0.630801\pi\)
\(168\) 2.28883e6i 0.482710i
\(169\) 1.00810e6 + 4.72036e6i 0.208855 + 0.977947i
\(170\) 8.59954e6 1.75036
\(171\) 190510. 710993.i 0.0381004 0.142193i
\(172\) −520794. 902042.i −0.102348 0.177273i
\(173\) 2.09107e6 + 1.20728e6i 0.403859 + 0.233168i 0.688148 0.725571i \(-0.258424\pi\)
−0.284289 + 0.958739i \(0.591758\pi\)
\(174\) −2.97622e6 2.97622e6i −0.564959 0.564959i
\(175\) −4.87281e6 + 1.30567e6i −0.909213 + 0.243623i
\(176\) −1.03308e6 3.85551e6i −0.189494 0.707202i
\(177\) 5.31337e6 5.31337e6i 0.958188 0.958188i
\(178\) −395825. + 685589.i −0.0701848 + 0.121564i
\(179\) 990697. 571979.i 0.172736 0.0997289i −0.411140 0.911572i \(-0.634869\pi\)
0.583875 + 0.811843i \(0.301536\pi\)
\(180\) −917551. 245857.i −0.157330 0.0421565i
\(181\) 3.67696e6i 0.620087i 0.950722 + 0.310044i \(0.100344\pi\)
−0.950722 + 0.310044i \(0.899656\pi\)
\(182\) 2.23280e6 + 1.80631e6i 0.370370 + 0.299624i
\(183\) 3.58161e6 0.584420
\(184\) −182726. + 681944.i −0.0293324 + 0.109470i
\(185\) −3.98515e6 6.90249e6i −0.629404 1.09016i
\(186\) 423854. + 244712.i 0.0658684 + 0.0380291i
\(187\) −6.47902e6 6.47902e6i −0.990796 0.990796i
\(188\) 3.27319e6 877048.i 0.492604 0.131993i
\(189\) −1.06116e6 3.96032e6i −0.157180 0.586603i
\(190\) −2.73215e6 + 2.73215e6i −0.398330 + 0.398330i
\(191\) 2.20303e6 3.81577e6i 0.316170 0.547623i −0.663515 0.748163i \(-0.730936\pi\)
0.979686 + 0.200540i \(0.0642695\pi\)
\(192\) −5.39031e6 + 3.11209e6i −0.761570 + 0.439693i
\(193\) −4.88717e6 1.30951e6i −0.679807 0.182154i −0.0976386 0.995222i \(-0.531129\pi\)
−0.582168 + 0.813068i \(0.697796\pi\)
\(194\) 6.83151e6i 0.935645i
\(195\) −7.82884e6 + 5.69375e6i −1.05583 + 0.767882i
\(196\) 1.40948e6 0.187193
\(197\) 362631. 1.35336e6i 0.0474314 0.177016i −0.938147 0.346238i \(-0.887459\pi\)
0.985578 + 0.169222i \(0.0541255\pi\)
\(198\) −1.35462e6 2.34627e6i −0.174511 0.302262i
\(199\) 147358. + 85077.1i 0.0186988 + 0.0107958i 0.509320 0.860577i \(-0.329897\pi\)
−0.490621 + 0.871373i \(0.663230\pi\)
\(200\) 1.03504e7 + 1.03504e7i 1.29380 + 1.29380i
\(201\) 3.39620e6 910008.i 0.418220 0.112062i
\(202\) 2.01958e6 + 7.53718e6i 0.245023 + 0.914439i
\(203\) −3.88222e6 + 3.88222e6i −0.464080 + 0.464080i
\(204\) −1.15119e6 + 1.99392e6i −0.135599 + 0.234865i
\(205\) 1.26095e7 7.28008e6i 1.46364 0.845035i
\(206\) −5.66880e6 1.51895e6i −0.648469 0.173757i
\(207\) 338456.i 0.0381585i
\(208\) 917931. 5.81373e6i 0.102005 0.646048i
\(209\) 4.11688e6 0.450951
\(210\) −1.49075e6 + 5.56357e6i −0.160971 + 0.600752i
\(211\) 5.13267e6 + 8.89005e6i 0.546382 + 0.946361i 0.998519 + 0.0544124i \(0.0173286\pi\)
−0.452137 + 0.891949i \(0.649338\pi\)
\(212\) −1.69468e6 978424.i −0.177861 0.102688i
\(213\) −4.91723e6 4.91723e6i −0.508841 0.508841i
\(214\) −3.25518e6 + 872224.i −0.332150 + 0.0889993i
\(215\) 3.17274e6 + 1.18408e7i 0.319241 + 1.19142i
\(216\) −8.41216e6 + 8.41216e6i −0.834730 + 0.834730i
\(217\) 319206. 552881.i 0.0312386 0.0541069i
\(218\) 895701. 517133.i 0.0864557 0.0499152i
\(219\) 1.21533e7 + 3.25646e6i 1.15707 + 0.310037i
\(220\) 5.31292e6i 0.498959i
\(221\) −4.84800e6 1.26113e7i −0.449144 1.16838i
\(222\) −5.71202e6 −0.522073
\(223\) 3.63396e6 1.35621e7i 0.327692 1.22296i −0.583886 0.811835i \(-0.698469\pi\)
0.911578 0.411127i \(-0.134865\pi\)
\(224\) 1.65430e6 + 2.86533e6i 0.147187 + 0.254936i
\(225\) 6.07716e6 + 3.50865e6i 0.533523 + 0.308029i
\(226\) 6.91381e6 + 6.91381e6i 0.598952 + 0.598952i
\(227\) −30129.2 + 8073.09i −0.00257579 + 0.000690180i −0.260107 0.965580i \(-0.583758\pi\)
0.257531 + 0.966270i \(0.417091\pi\)
\(228\) −267743. 999230.i −0.0225898 0.0843065i
\(229\) 5.05317e6 5.05317e6i 0.420783 0.420783i −0.464691 0.885473i \(-0.653834\pi\)
0.885473 + 0.464691i \(0.153834\pi\)
\(230\) 888321. 1.53862e6i 0.0730107 0.126458i
\(231\) 5.31483e6 3.06852e6i 0.431175 0.248939i
\(232\) 1.53878e7 + 4.12314e6i 1.23229 + 0.330190i
\(233\) 1.45683e7i 1.15170i 0.817555 + 0.575850i \(0.195329\pi\)
−0.817555 + 0.575850i \(0.804671\pi\)
\(234\) −419502. 3.97287e6i −0.0327406 0.310068i
\(235\) −3.98813e7 −3.07302
\(236\) −1.57394e6 + 5.87401e6i −0.119743 + 0.446888i
\(237\) −456603. 790860.i −0.0343000 0.0594093i
\(238\) −6.96204e6 4.01954e6i −0.516423 0.298157i
\(239\) −1.22371e7 1.22371e7i −0.896368 0.896368i 0.0987444 0.995113i \(-0.468517\pi\)
−0.995113 + 0.0987444i \(0.968517\pi\)
\(240\) 1.14019e7 3.05513e6i 0.824790 0.221002i
\(241\) −2.56550e6 9.57457e6i −0.183282 0.684019i −0.994992 0.0999575i \(-0.968129\pi\)
0.811709 0.584062i \(-0.198537\pi\)
\(242\) 2.16395e6 2.16395e6i 0.152687 0.152687i
\(243\) −4.94006e6 + 8.55643e6i −0.344281 + 0.596313i
\(244\) −2.51024e6 + 1.44929e6i −0.172801 + 0.0997664i
\(245\) −1.60230e7 4.29335e6i −1.08955 0.291943i
\(246\) 1.04347e7i 0.700932i
\(247\) 5.54696e6 + 2.46646e6i 0.368099 + 0.163676i
\(248\) −1.85241e6 −0.121446
\(249\) −3.40414e6 + 1.27044e7i −0.220500 + 0.822918i
\(250\) −7.49315e6 1.29785e7i −0.479562 0.830625i
\(251\) 1.79413e7 + 1.03584e7i 1.13457 + 0.655046i 0.945081 0.326836i \(-0.105983\pi\)
0.189492 + 0.981882i \(0.439316\pi\)
\(252\) 627917. + 627917.i 0.0392374 + 0.0392374i
\(253\) −1.82849e6 + 489943.i −0.112910 + 0.0302541i
\(254\) 1.76316e6 + 6.58019e6i 0.107594 + 0.401548i
\(255\) 1.91604e7 1.91604e7i 1.15554 1.15554i
\(256\) 6.29233e6 1.08986e7i 0.375052 0.649609i
\(257\) −1.54140e7 + 8.89925e6i −0.908060 + 0.524269i −0.879807 0.475332i \(-0.842328\pi\)
−0.0282538 + 0.999601i \(0.508995\pi\)
\(258\) 8.48588e6 + 2.27379e6i 0.494126 + 0.132401i
\(259\) 7.45085e6i 0.428851i
\(260\) 3.18302e6 7.15847e6i 0.181101 0.407287i
\(261\) 7.63712e6 0.429544
\(262\) −6.34865e6 + 2.36935e7i −0.353002 + 1.31742i
\(263\) −1.49796e7 2.59455e7i −0.823445 1.42625i −0.903102 0.429426i \(-0.858716\pi\)
0.0796577 0.996822i \(-0.474617\pi\)
\(264\) −1.54215e7 8.90358e6i −0.838135 0.483897i
\(265\) 1.62849e7 + 1.62849e7i 0.875078 + 0.875078i
\(266\) 3.48894e6 934859.i 0.185374 0.0496708i
\(267\) 645616. + 2.40947e6i 0.0339188 + 0.126587i
\(268\) −2.01205e6 + 2.01205e6i −0.104529 + 0.104529i
\(269\) 359344. 622402.i 0.0184609 0.0319753i −0.856647 0.515902i \(-0.827457\pi\)
0.875108 + 0.483927i \(0.160790\pi\)
\(270\) 2.59268e7 1.49688e7i 1.31722 0.760495i
\(271\) 3.51219e7 + 9.41089e6i 1.76470 + 0.472850i 0.987661 0.156605i \(-0.0500551\pi\)
0.777037 + 0.629455i \(0.216722\pi\)
\(272\) 1.64752e7i 0.818697i
\(273\) 8.99943e6 950265.i 0.442310 0.0467043i
\(274\) −1.69988e7 −0.826354
\(275\) −1.01581e7 + 3.79106e7i −0.488444 + 1.82290i
\(276\) 237833. + 411939.i 0.0113122 + 0.0195932i
\(277\) 1.55080e7 + 8.95353e6i 0.729652 + 0.421265i 0.818295 0.574799i \(-0.194920\pi\)
−0.0886431 + 0.996063i \(0.528253\pi\)
\(278\) −1.24397e7 1.24397e7i −0.578995 0.578995i
\(279\) −857786. + 229843.i −0.0394972 + 0.0105832i
\(280\) −5.64232e6 2.10574e7i −0.257030 0.959249i
\(281\) −6.31936e6 + 6.31936e6i −0.284809 + 0.284809i −0.835024 0.550214i \(-0.814546\pi\)
0.550214 + 0.835024i \(0.314546\pi\)
\(282\) −1.42907e7 + 2.47523e7i −0.637246 + 1.10374i
\(283\) −1.35802e7 + 7.84053e6i −0.599165 + 0.345928i −0.768713 0.639594i \(-0.779103\pi\)
0.169548 + 0.985522i \(0.445769\pi\)
\(284\) 5.43607e6 + 1.45659e6i 0.237318 + 0.0635891i
\(285\) 1.21749e7i 0.525931i
\(286\) 2.08559e7 8.01738e6i 0.891521 0.342716i
\(287\) −1.36112e7 −0.575773
\(288\) 1.19117e6 4.44551e6i 0.0498651 0.186099i
\(289\) 6.84099e6 + 1.18489e7i 0.283417 + 0.490892i
\(290\) −3.47182e7 2.00446e7i −1.42352 0.821870i
\(291\) −1.52211e7 1.52211e7i −0.617685 0.617685i
\(292\) −9.83554e6 + 2.63542e6i −0.395048 + 0.105853i
\(293\) −298902. 1.11552e6i −0.0118830 0.0443479i 0.959730 0.280925i \(-0.0906411\pi\)
−0.971613 + 0.236577i \(0.923974\pi\)
\(294\) −8.40620e6 + 8.40620e6i −0.330794 + 0.330794i
\(295\) 3.57851e7 6.19817e7i 1.39392 2.41433i
\(296\) 1.87229e7 1.08097e7i 0.721934 0.416809i
\(297\) −3.08113e7 8.25587e6i −1.17609 0.315133i
\(298\) 7.91146e6i 0.298956i
\(299\) −2.75719e6 435333.i −0.103146 0.0162858i
\(300\) 9.86212e6 0.365264
\(301\) 2.96596e6 1.10691e7i 0.108759 0.405895i
\(302\) 8.90855e6 + 1.54301e7i 0.323434 + 0.560205i
\(303\) 2.12932e7 + 1.22936e7i 0.765443 + 0.441928i
\(304\) −5.23430e6 5.23430e6i −0.186311 0.186311i
\(305\) 3.29511e7 8.82922e6i 1.16137 0.311188i
\(306\) 2.89425e6 + 1.08015e7i 0.101012 + 0.376981i
\(307\) 5.46628e6 5.46628e6i 0.188919 0.188919i −0.606309 0.795229i \(-0.707351\pi\)
0.795229 + 0.606309i \(0.207351\pi\)
\(308\) −2.48333e6 + 4.30125e6i −0.0849927 + 0.147212i
\(309\) −1.60148e7 + 9.24617e6i −0.542809 + 0.313391i
\(310\) 4.50274e6 + 1.20650e6i 0.151144 + 0.0404990i
\(311\) 1.86986e7i 0.621623i −0.950472 0.310811i \(-0.899399\pi\)
0.950472 0.310811i \(-0.100601\pi\)
\(312\) −1.54442e7 2.12356e7i −0.508513 0.699199i
\(313\) −4.30155e7 −1.40279 −0.701394 0.712774i \(-0.747439\pi\)
−0.701394 + 0.712774i \(0.747439\pi\)
\(314\) 1.03562e7 3.86498e7i 0.334511 1.24841i
\(315\) −5.22552e6 9.05086e6i −0.167185 0.289573i
\(316\) 640037. + 369526.i 0.0202835 + 0.0117107i
\(317\) −2.47479e7 2.47479e7i −0.776891 0.776891i 0.202410 0.979301i \(-0.435123\pi\)
−0.979301 + 0.202410i \(0.935123\pi\)
\(318\) 1.59426e7 4.27180e6i 0.495766 0.132840i
\(319\) 1.10553e7 + 4.12591e7i 0.340565 + 1.27101i
\(320\) −4.19194e7 + 4.19194e7i −1.27928 + 1.27928i
\(321\) −5.30941e6 + 9.19617e6i −0.160521 + 0.278030i
\(322\) −1.43834e6 + 830426.i −0.0430818 + 0.0248733i
\(323\) −1.64136e7 4.39801e6i −0.487076 0.130512i
\(324\) 4.63498e6i 0.136274i
\(325\) −3.63994e7 + 4.49938e7i −1.06034 + 1.31070i
\(326\) 4.09398e7 1.18166
\(327\) 843478. 3.14790e6i 0.0241229 0.0900280i
\(328\) 1.97471e7 + 3.42030e7i 0.559605 + 0.969265i
\(329\) 3.22872e7 + 1.86410e7i 0.906657 + 0.523459i
\(330\) 3.16866e7 + 3.16866e7i 0.881725 + 0.881725i
\(331\) −3.75950e6 + 1.00736e6i −0.103668 + 0.0277779i −0.310280 0.950645i \(-0.600423\pi\)
0.206612 + 0.978423i \(0.433756\pi\)
\(332\) −2.75494e6 1.02816e7i −0.0752832 0.280961i
\(333\) 7.32866e6 7.32866e6i 0.198469 0.198469i
\(334\) −4.72338e6 + 8.18114e6i −0.126769 + 0.219571i
\(335\) 2.90020e7 1.67443e7i 0.771423 0.445382i
\(336\) −1.06588e7 2.85602e6i −0.280990 0.0752909i
\(337\) 4.77229e7i 1.24691i −0.781857 0.623457i \(-0.785727\pi\)
0.781857 0.623457i \(-0.214273\pi\)
\(338\) 3.29040e7 + 1.69262e6i 0.852116 + 0.0438337i
\(339\) 3.08090e7 0.790821
\(340\) −5.67573e6 + 2.11821e7i −0.144406 + 0.538930i
\(341\) −2.48343e6 4.30142e6i −0.0626309 0.108480i
\(342\) −4.35125e6 2.51220e6i −0.108777 0.0628023i
\(343\) 2.68968e7 + 2.68968e7i 0.666527 + 0.666527i
\(344\) −3.21180e7 + 8.60601e6i −0.788994 + 0.211410i
\(345\) −1.44891e6 5.40740e6i −0.0352845 0.131683i
\(346\) 1.16543e7 1.16543e7i 0.281356 0.281356i
\(347\) −7.26483e6 + 1.25831e7i −0.173875 + 0.301160i −0.939771 0.341804i \(-0.888962\pi\)
0.765896 + 0.642964i \(0.222296\pi\)
\(348\) 9.29524e6 5.36661e6i 0.220558 0.127339i
\(349\) −6.86790e6 1.84025e6i −0.161565 0.0432912i 0.177130 0.984188i \(-0.443319\pi\)
−0.338695 + 0.940896i \(0.609985\pi\)
\(350\) 3.44349e7i 0.803146i
\(351\) −3.65681e7 2.95831e7i −0.845632 0.684105i
\(352\) 2.57410e7 0.590197
\(353\) 4.25285e6 1.58718e7i 0.0966842 0.360830i −0.900585 0.434680i \(-0.856862\pi\)
0.997269 + 0.0738491i \(0.0235283\pi\)
\(354\) −2.56459e7 4.44200e7i −0.578107 1.00131i
\(355\) −5.73606e7 3.31172e7i −1.28212 0.740233i
\(356\) −1.42747e6 1.42747e6i −0.0316387 0.0316387i
\(357\) −2.44678e7 + 6.55612e6i −0.537762 + 0.144093i
\(358\) −2.02101e6 7.54252e6i −0.0440474 0.164387i
\(359\) 2.44298e7 2.44298e7i 0.528004 0.528004i −0.391973 0.919977i \(-0.628207\pi\)
0.919977 + 0.391973i \(0.128207\pi\)
\(360\) −1.51623e7 + 2.62619e7i −0.324981 + 0.562884i
\(361\) −3.41309e7 + 1.97055e7i −0.725481 + 0.418857i
\(362\) 2.42435e7 + 6.49602e6i 0.511057 + 0.136937i
\(363\) 9.64288e6i 0.201598i
\(364\) −5.92289e6 + 4.30759e6i −0.122809 + 0.0893163i
\(365\) 1.19839e8 2.46444
\(366\) 6.32757e6 2.36148e7i 0.129061 0.481661i
\(367\) −1.05551e7 1.82819e7i −0.213532 0.369848i 0.739286 0.673392i \(-0.235163\pi\)
−0.952817 + 0.303544i \(0.901830\pi\)
\(368\) 2.94771e6 + 1.70186e6i 0.0591482 + 0.0341493i
\(369\) 1.33880e7 + 1.33880e7i 0.266463 + 0.266463i
\(370\) −5.25510e7 + 1.40810e7i −1.03747 + 0.277990i
\(371\) −5.57220e6 2.07957e7i −0.109120 0.407242i
\(372\) −882511. + 882511.i −0.0171432 + 0.0171432i
\(373\) −2.94962e7 + 5.10890e7i −0.568382 + 0.984466i 0.428344 + 0.903616i \(0.359097\pi\)
−0.996726 + 0.0808508i \(0.974236\pi\)
\(374\) −5.41648e7 + 3.12721e7i −1.03539 + 0.597781i
\(375\) −4.56124e7 1.22218e7i −0.864946 0.231762i
\(376\) 1.08177e8i 2.03504i
\(377\) −9.82310e6 + 6.22147e7i −0.183326 + 1.16110i
\(378\) −2.79865e7 −0.518171
\(379\) 1.40945e7 5.26014e7i 0.258900 0.966227i −0.706979 0.707234i \(-0.749943\pi\)
0.965879 0.258993i \(-0.0833907\pi\)
\(380\) −4.92651e6 8.53296e6i −0.0897818 0.155507i
\(381\) 1.85896e7 + 1.07327e7i 0.336121 + 0.194059i
\(382\) −2.12666e7 2.12666e7i −0.381512 0.381512i
\(383\) 3.41117e7 9.14020e6i 0.607165 0.162689i 0.0578788 0.998324i \(-0.481566\pi\)
0.549286 + 0.835634i \(0.314900\pi\)
\(384\) 4.84097e6 + 1.80668e7i 0.0854946 + 0.319070i
\(385\) 4.13324e7 4.13324e7i 0.724284 0.724284i
\(386\) −1.72682e7 + 2.99093e7i −0.300251 + 0.520050i
\(387\) −1.38049e7 + 7.97027e6i −0.238177 + 0.137512i
\(388\) 1.68271e7 + 4.50882e6i 0.288081 + 0.0771911i
\(389\) 2.66394e7i 0.452559i 0.974062 + 0.226280i \(0.0726563\pi\)
−0.974062 + 0.226280i \(0.927344\pi\)
\(390\) 2.37098e7 + 6.16773e7i 0.399700 + 1.03976i
\(391\) 7.81342e6 0.130711
\(392\) 1.16456e7 4.34621e7i 0.193333 0.721527i
\(393\) 3.86456e7 + 6.69361e7i 0.636682 + 1.10276i
\(394\) −8.28250e6 4.78191e6i −0.135417 0.0781830i
\(395\) −6.15037e6 6.15037e6i −0.0997953 0.0997953i
\(396\) 6.67331e6 1.78811e6i 0.107462 0.0287944i
\(397\) 1.01829e7 + 3.80032e7i 0.162742 + 0.607363i 0.998317 + 0.0579865i \(0.0184680\pi\)
−0.835575 + 0.549376i \(0.814865\pi\)
\(398\) 821278. 821278.i 0.0130269 0.0130269i
\(399\) 5.69069e6 9.85656e6i 0.0895872 0.155170i
\(400\) 6.11157e7 3.52852e7i 0.954933 0.551331i
\(401\) −5.23874e6 1.40372e6i −0.0812444 0.0217694i 0.217968 0.975956i \(-0.430057\pi\)
−0.299212 + 0.954187i \(0.596724\pi\)
\(402\) 2.40000e7i 0.369431i
\(403\) −769073. 7.28346e6i −0.0117504 0.111281i
\(404\) −1.98983e7 −0.301767
\(405\) 1.41184e7 5.26907e7i 0.212530 0.793174i
\(406\) 1.87382e7 + 3.24555e7i 0.279995 + 0.484965i
\(407\) 5.02015e7 + 2.89839e7i 0.744619 + 0.429906i
\(408\) 5.19723e7 + 5.19723e7i 0.765229 + 0.765229i
\(409\) −6.44250e7 + 1.72626e7i −0.941639 + 0.252311i −0.696811 0.717255i \(-0.745398\pi\)
−0.244828 + 0.969566i \(0.578732\pi\)
\(410\) −2.57232e7 9.60003e7i −0.373227 1.39290i
\(411\) −3.78746e7 + 3.78746e7i −0.545534 + 0.545534i
\(412\) 7.48285e6 1.29607e7i 0.106998 0.185326i
\(413\) −5.79421e7 + 3.34529e7i −0.822516 + 0.474880i
\(414\) 2.23156e6 + 597945.i 0.0314490 + 0.00842675i
\(415\) 1.25273e8i 1.75273i
\(416\) 3.46826e7 + 1.54217e7i 0.481762 + 0.214216i
\(417\) −5.54330e7 −0.764470
\(418\) 7.27322e6 2.71440e7i 0.0995859 0.371660i
\(419\) 4.01865e7 + 6.96051e7i 0.546309 + 0.946234i 0.998523 + 0.0543253i \(0.0173008\pi\)
−0.452215 + 0.891909i \(0.649366\pi\)
\(420\) −1.27201e7 7.34395e6i −0.171689 0.0991247i
\(421\) 6.54781e6 + 6.54781e6i 0.0877506 + 0.0877506i 0.749620 0.661869i \(-0.230236\pi\)
−0.661869 + 0.749620i \(0.730236\pi\)
\(422\) 6.76830e7 1.81356e7i 0.900622 0.241321i
\(423\) −1.34224e7 5.00931e7i −0.177341 0.661846i
\(424\) −4.41725e7 + 4.41725e7i −0.579501 + 0.579501i
\(425\) 8.09988e7 1.40294e8i 1.05514 1.82756i
\(426\) −4.11082e7 + 2.37339e7i −0.531741 + 0.307001i
\(427\) −3.08035e7 8.25378e6i −0.395655 0.106016i
\(428\) 8.59373e6i 0.109610i
\(429\) 2.86053e7 6.43319e7i 0.362305 0.814807i
\(430\) 8.36759e7 1.05243
\(431\) −2.67316e7 + 9.97636e7i −0.333882 + 1.24606i 0.571195 + 0.820815i \(0.306480\pi\)
−0.905076 + 0.425249i \(0.860186\pi\)
\(432\) 2.86776e7 + 4.96710e7i 0.355706 + 0.616101i
\(433\) −8.93885e7 5.16085e7i −1.10108 0.635708i −0.164574 0.986365i \(-0.552625\pi\)
−0.936504 + 0.350657i \(0.885958\pi\)
\(434\) −3.08140e6 3.08140e6i −0.0376946 0.0376946i
\(435\) −1.22016e8 + 3.26940e7i −1.48234 + 0.397192i
\(436\) 682620. + 2.54757e6i 0.00823606 + 0.0307374i
\(437\) −2.48239e6 + 2.48239e6i −0.0297458 + 0.0297458i
\(438\) 4.29419e7 7.43776e7i 0.511045 0.885156i
\(439\) 8.16466e7 4.71387e7i 0.965038 0.557165i 0.0673180 0.997732i \(-0.478556\pi\)
0.897720 + 0.440567i \(0.145222\pi\)
\(440\) −1.63827e8 4.38974e7i −1.92322 0.515324i
\(441\) 2.15707e7i 0.251506i
\(442\) −9.17156e7 + 9.68440e6i −1.06213 + 0.112152i
\(443\) 4.53236e6 0.0521330 0.0260665 0.999660i \(-0.491702\pi\)
0.0260665 + 0.999660i \(0.491702\pi\)
\(444\) 3.76996e6 1.40697e7i 0.0430712 0.160744i
\(445\) 1.18794e7 + 2.05758e7i 0.134808 + 0.233494i
\(446\) −8.29998e7 4.79199e7i −0.935562 0.540147i
\(447\) 1.76273e7 + 1.76273e7i 0.197362 + 0.197362i
\(448\) 5.35310e7 1.43436e7i 0.595348 0.159523i
\(449\) −2.10984e7 7.87402e7i −0.233083 0.869876i −0.979004 0.203842i \(-0.934657\pi\)
0.745921 0.666034i \(-0.232009\pi\)
\(450\) 3.38702e7 3.38702e7i 0.371689 0.371689i
\(451\) −5.29478e7 + 9.17082e7i −0.577189 + 0.999721i
\(452\) −2.15930e7 + 1.24667e7i −0.233829 + 0.135001i
\(453\) 5.42282e7 + 1.45304e7i 0.583352 + 0.156309i
\(454\) 212915.i 0.00227530i
\(455\) 8.04528e7 3.09275e7i 0.854097 0.328330i
\(456\) −3.30241e7 −0.348286
\(457\) 2.83377e7 1.05758e8i 0.296904 1.10806i −0.642790 0.766043i \(-0.722223\pi\)
0.939693 0.342018i \(-0.111110\pi\)
\(458\) −2.43900e7 4.22447e7i −0.253872 0.439720i
\(459\) 1.14022e8 + 6.58308e7i 1.17910 + 0.680755i
\(460\) 3.20358e6 + 3.20358e6i 0.0329125 + 0.0329125i
\(461\) 3.41485e7 9.15005e6i 0.348553 0.0933944i −0.0802953 0.996771i \(-0.525586\pi\)
0.428848 + 0.903377i \(0.358920\pi\)
\(462\) −1.08422e7 4.04636e7i −0.109949 0.410335i
\(463\) −794093. + 794093.i −0.00800070 + 0.00800070i −0.711096 0.703095i \(-0.751801\pi\)
0.703095 + 0.711096i \(0.251801\pi\)
\(464\) 3.84018e7 6.65139e7i 0.384413 0.665823i
\(465\) 1.27206e7 7.34425e6i 0.126517 0.0730447i
\(466\) 9.60536e7 + 2.57375e7i 0.949196 + 0.254336i
\(467\) 1.15353e8i 1.13260i 0.824198 + 0.566301i \(0.191626\pi\)
−0.824198 + 0.566301i \(0.808374\pi\)
\(468\) 1.00627e7 + 1.58880e6i 0.0981697 + 0.0155000i
\(469\) −3.13060e7 −0.303465
\(470\) −7.04576e7 + 2.62951e8i −0.678632 + 2.53269i
\(471\) −6.30403e7 1.09189e8i −0.603331 1.04500i
\(472\) 1.68124e8 + 9.70666e7i 1.59884 + 0.923090i
\(473\) −6.30427e7 6.30427e7i −0.595732 0.595732i
\(474\) −6.02109e6 + 1.61335e6i −0.0565380 + 0.0151493i
\(475\) 1.88386e7 + 7.03066e7i 0.175779 + 0.656018i
\(476\) 1.44958e7 1.44958e7i 0.134407 0.134407i
\(477\) −1.49739e7 + 2.59355e7i −0.137968 + 0.238968i
\(478\) −1.02303e8 + 5.90647e7i −0.936709 + 0.540809i
\(479\) −2.96536e7 7.94566e6i −0.269818 0.0722975i 0.121373 0.992607i \(-0.461270\pi\)
−0.391191 + 0.920309i \(0.627937\pi\)
\(480\) 7.61238e7i 0.688330i
\(481\) 5.02756e7 + 6.91283e7i 0.451775 + 0.621185i
\(482\) −6.76609e7 −0.604223
\(483\) −1.35448e6 + 5.05498e6i −0.0120207 + 0.0448619i
\(484\) 3.90195e6 + 6.75838e6i 0.0344148 + 0.0596083i
\(485\) −1.77558e8 1.02513e8i −1.55637 0.898573i
\(486\) 4.76881e7 + 4.76881e7i 0.415433 + 0.415433i
\(487\) 1.44522e8 3.87246e7i 1.25126 0.335274i 0.428437 0.903572i \(-0.359064\pi\)
0.822823 + 0.568297i \(0.192398\pi\)
\(488\) 2.39491e7 + 8.93793e7i 0.206077 + 0.769091i
\(489\) 9.12169e7 9.12169e7i 0.780097 0.780097i
\(490\) −5.66151e7 + 9.80602e7i −0.481220 + 0.833498i
\(491\) −9.26070e7 + 5.34667e7i −0.782347 + 0.451688i −0.837261 0.546803i \(-0.815845\pi\)
0.0549143 + 0.998491i \(0.482511\pi\)
\(492\) 2.57025e7 + 6.88696e6i 0.215814 + 0.0578272i
\(493\) 1.76307e8i 1.47139i
\(494\) 2.60620e7 3.22156e7i 0.216186 0.267230i
\(495\) −8.13092e7 −0.670385
\(496\) −2.31145e6 + 8.62643e6i −0.0189426 + 0.0706946i
\(497\) 3.09588e7 + 5.36222e7i 0.252183 + 0.436793i
\(498\) 7.77506e7 + 4.48894e7i 0.629529 + 0.363459i
\(499\) −7.47204e7 7.47204e7i −0.601364 0.601364i 0.339311 0.940674i \(-0.389806\pi\)
−0.940674 + 0.339311i \(0.889806\pi\)
\(500\) 3.69138e7 9.89101e6i 0.295310 0.0791281i
\(501\) 7.70414e6 + 2.87522e7i 0.0612648 + 0.228643i
\(502\) 9.99932e7 9.99932e7i 0.790422 0.790422i
\(503\) −9.89692e6 + 1.71420e7i −0.0777671 + 0.134697i −0.902286 0.431137i \(-0.858112\pi\)
0.824519 + 0.565834i \(0.191446\pi\)
\(504\) 2.45503e7 1.41741e7i 0.191763 0.110715i
\(505\) 2.26204e8 + 6.06113e7i 1.75641 + 0.470630i
\(506\) 1.29215e7i 0.0997378i
\(507\) 7.70838e7 6.95413e7i 0.591479 0.533604i
\(508\) −1.73718e7 −0.132512
\(509\) −7.01657e6 + 2.61862e7i −0.0532073 + 0.198572i −0.987413 0.158162i \(-0.949443\pi\)
0.934206 + 0.356734i \(0.116110\pi\)
\(510\) −9.24810e7 1.60182e8i −0.697175 1.20754i
\(511\) −9.70193e7 5.60141e7i −0.727102 0.419793i
\(512\) −1.00096e8 1.00096e8i −0.745777 0.745777i
\(513\) −5.71408e7 + 1.53108e7i −0.423248 + 0.113409i
\(514\) 3.14443e7 + 1.17352e8i 0.231554 + 0.864172i
\(515\) −1.24544e8 + 1.24544e8i −0.911806 + 0.911806i
\(516\) −1.12014e7 + 1.94014e7i −0.0815312 + 0.141216i
\(517\) 2.51195e8 1.45028e8i 1.81777 1.04949i
\(518\) 4.91261e7 + 1.31633e7i 0.353446 + 0.0947055i
\(519\) 5.19331e7i 0.371486i
\(520\) −1.94437e8 1.57297e8i −1.38283 1.11869i
\(521\) −1.64063e7 −0.116010 −0.0580051 0.998316i \(-0.518474\pi\)
−0.0580051 + 0.998316i \(0.518474\pi\)
\(522\) 1.34924e7 5.03542e7i 0.0948586 0.354017i
\(523\) −1.34607e8 2.33147e8i −0.940943 1.62976i −0.763677 0.645599i \(-0.776608\pi\)
−0.177267 0.984163i \(-0.556725\pi\)
\(524\) −5.41709e7 3.12756e7i −0.376506 0.217376i
\(525\) 7.67235e7 + 7.67235e7i 0.530213 + 0.530213i
\(526\) −1.97532e8 + 5.29286e7i −1.35731 + 0.363691i
\(527\) 5.30603e6 + 1.98024e7i 0.0362525 + 0.135296i
\(528\) −6.07057e7 + 6.07057e7i −0.412409 + 0.412409i
\(529\) −7.32108e7 + 1.26805e8i −0.494548 + 0.856582i
\(530\) 1.36142e8 7.86017e7i 0.914460 0.527964i
\(531\) 8.98962e7 + 2.40876e7i 0.600424 + 0.160883i
\(532\) 9.21086e6i 0.0611737i
\(533\) −1.26284e8 + 9.18435e7i −0.833999 + 0.606550i
\(534\) 1.70271e7 0.111819
\(535\) −2.61770e7 + 9.76939e7i −0.170946 + 0.637979i
\(536\) 4.54186e7 + 7.86673e7i 0.294944 + 0.510858i
\(537\) −2.13083e7 1.23023e7i −0.137602 0.0794446i
\(538\) −3.46887e6 3.46887e6i −0.0222762 0.0222762i
\(539\) 1.16535e8 3.12254e7i 0.744198 0.199407i
\(540\) 1.97590e7 + 7.37414e7i 0.125482 + 0.468307i
\(541\) −2.01236e8 + 2.01236e8i −1.27091 + 1.27091i −0.325292 + 0.945614i \(0.605463\pi\)
−0.945614 + 0.325292i \(0.894537\pi\)
\(542\) 1.24099e8 2.14945e8i 0.779416 1.34999i
\(543\) 6.84899e7 3.95426e7i 0.427786 0.246982i
\(544\) −1.02627e8 2.74988e7i −0.637476 0.170811i
\(545\) 3.10402e7i 0.191750i
\(546\) 9.63371e6 6.10152e7i 0.0591856 0.374852i
\(547\) −1.14810e8 −0.701483 −0.350741 0.936472i \(-0.614070\pi\)
−0.350741 + 0.936472i \(0.614070\pi\)
\(548\) 1.12193e7 4.18708e7i 0.0681746 0.254431i
\(549\) 2.21800e7 + 3.84168e7i 0.134043 + 0.232169i
\(550\) 2.32012e8 + 1.33952e8i 1.39451 + 0.805121i
\(551\) 5.60141e7 + 5.60141e7i 0.334844 + 0.334844i
\(552\) 1.46675e7 3.93014e6i 0.0872044 0.0233663i
\(553\) 2.10448e6 + 7.85401e6i 0.0124442 + 0.0464425i
\(554\) 8.64314e7 8.64314e7i 0.508326 0.508326i
\(555\) −8.57141e7 + 1.48461e8i −0.501387 + 0.868428i
\(556\) 3.88512e7 2.24308e7i 0.226037 0.130503i
\(557\) −6.37551e7 1.70831e7i −0.368935 0.0988558i 0.0695881 0.997576i \(-0.477832\pi\)
−0.438523 + 0.898720i \(0.644498\pi\)
\(558\) 6.06174e6i 0.0348895i
\(559\) −4.71724e7 1.22711e8i −0.270055 0.702505i
\(560\) −1.05102e8 −0.598477
\(561\) −5.10067e7 + 1.90360e8i −0.288894 + 1.07817i
\(562\) 3.05015e7 + 5.28301e7i 0.171835 + 0.297627i
\(563\) 2.53276e8 + 1.46229e8i 1.41928 + 0.819422i 0.996236 0.0866868i \(-0.0276279\pi\)
0.423045 + 0.906109i \(0.360961\pi\)
\(564\) −5.15370e7 5.15370e7i −0.287265 0.287265i
\(565\) 2.83445e8 7.59488e7i 1.57153 0.421090i
\(566\) 2.77035e7 + 1.03391e8i 0.152786 + 0.570207i
\(567\) −3.60583e7 + 3.60583e7i −0.197814 + 0.197814i
\(568\) 8.98298e7 1.55590e8i 0.490202 0.849056i
\(569\) 1.60156e8 9.24658e7i 0.869371 0.501932i 0.00223182 0.999998i \(-0.499290\pi\)
0.867139 + 0.498066i \(0.165956\pi\)
\(570\) 8.02731e7 + 2.15091e7i 0.433456 + 0.116144i
\(571\) 1.19209e8i 0.640325i −0.947363 0.320162i \(-0.896263\pi\)
0.947363 0.320162i \(-0.103737\pi\)
\(572\) 5.98316e6 + 5.66632e7i 0.0319700 + 0.302770i
\(573\) −9.47673e7 −0.503726
\(574\) −2.40467e7 + 8.97436e7i −0.127151 + 0.474534i
\(575\) −1.67341e7 2.89844e7i −0.0880238 0.152462i
\(576\) −6.67614e7 3.85447e7i −0.349348 0.201696i
\(577\) 5.14137e7 + 5.14137e7i 0.267640 + 0.267640i 0.828149 0.560508i \(-0.189394\pi\)
−0.560508 + 0.828149i \(0.689394\pi\)
\(578\) 9.02101e7 2.41717e7i 0.467167 0.125177i
\(579\) 2.81655e7 + 1.05115e8i 0.145105 + 0.541538i
\(580\) 7.22873e7 7.22873e7i 0.370491 0.370491i
\(581\) 5.85544e7 1.01419e8i 0.298560 0.517120i
\(582\) −1.27249e8 + 7.34672e7i −0.645484 + 0.372670i
\(583\) −1.61791e8 4.33518e7i −0.816486 0.218777i
\(584\) 3.25060e8i 1.63202i
\(585\) −1.09554e8 4.87132e7i −0.547217 0.243321i
\(586\) −7.88305e6 −0.0391743
\(587\) 9.28557e6 3.46542e7i 0.0459086 0.171333i −0.939165 0.343466i \(-0.888399\pi\)
0.985074 + 0.172132i \(0.0550657\pi\)
\(588\) −1.51578e7 2.62540e7i −0.0745595 0.129141i
\(589\) −7.97716e6 4.60562e6i −0.0390393 0.0225394i
\(590\) −3.45446e8 3.45446e8i −1.68199 1.68199i
\(591\) −2.91085e7 + 7.79959e6i −0.141012 + 0.0377841i
\(592\) −2.69767e7 1.00678e8i −0.130024 0.485256i
\(593\) −2.24519e8 + 2.24519e8i −1.07669 + 1.07669i −0.0798839 + 0.996804i \(0.525455\pi\)
−0.996804 + 0.0798839i \(0.974545\pi\)
\(594\) −1.08868e8 + 1.88564e8i −0.519445 + 0.899706i
\(595\) −2.08943e8 + 1.20634e8i −0.991923 + 0.572687i
\(596\) −1.94872e7 5.22159e6i −0.0920474 0.0246640i
\(597\) 3.65974e6i 0.0171999i
\(598\) −7.74138e6 + 1.74100e7i −0.0362005 + 0.0814133i
\(599\) 3.80612e8 1.77093 0.885467 0.464702i \(-0.153839\pi\)
0.885467 + 0.464702i \(0.153839\pi\)
\(600\) 8.14846e7 3.04105e8i 0.377244 1.40789i
\(601\) −2.22503e7 3.85386e7i −0.102497 0.177531i 0.810216 0.586132i \(-0.199350\pi\)
−0.912713 + 0.408601i \(0.866017\pi\)
\(602\) −6.77427e7 3.91112e7i −0.310508 0.179272i
\(603\) 3.07926e7 + 3.07926e7i 0.140441 + 0.140441i
\(604\) −4.38865e7 + 1.17593e7i −0.199168 + 0.0533669i
\(605\) −2.37712e7 8.87151e7i −0.107346 0.400619i
\(606\) 1.18674e8 1.18674e8i 0.533261 0.533261i
\(607\) −4.40161e7 + 7.62381e7i −0.196809 + 0.340883i −0.947492 0.319779i \(-0.896391\pi\)
0.750683 + 0.660663i \(0.229725\pi\)
\(608\) 4.13420e7 2.38688e7i 0.183942 0.106199i
\(609\) 1.14063e8 + 3.05632e7i 0.505004 + 0.135315i
\(610\) 2.32857e8i 1.02589i
\(611\) 4.25341e8 4.49125e7i 1.86472 0.196899i
\(612\) −2.85161e7 −0.124404
\(613\) −2.64367e7 + 9.86631e7i −0.114769 + 0.428325i −0.999270 0.0382148i \(-0.987833\pi\)
0.884500 + 0.466540i \(0.154500\pi\)
\(614\) −2.63839e7 4.56983e7i −0.113981 0.197422i
\(615\) −2.71209e8 1.56583e8i −1.16595 0.673159i
\(616\) 1.12114e8 + 1.12114e8i 0.479641 + 0.479641i
\(617\) −9.03845e7 + 2.42184e7i −0.384803 + 0.103108i −0.446034 0.895016i \(-0.647164\pi\)
0.0612312 + 0.998124i \(0.480497\pi\)
\(618\) 3.26701e7 + 1.21926e8i 0.138416 + 0.516574i
\(619\) 6.96140e7 6.96140e7i 0.293511 0.293511i −0.544955 0.838466i \(-0.683453\pi\)
0.838466 + 0.544955i \(0.183453\pi\)
\(620\) −5.94364e6 + 1.02947e7i −0.0249389 + 0.0431955i
\(621\) 2.35567e7 1.36005e7i 0.0983648 0.0567909i
\(622\) −1.23286e8 3.30344e7i −0.512322 0.137276i
\(623\) 2.22104e7i 0.0918527i
\(624\) −1.18163e8 + 4.54238e7i −0.486325 + 0.186952i
\(625\) −3.81706e7 −0.156347
\(626\) −7.59948e7 + 2.83616e8i −0.309785 + 1.15613i
\(627\) −4.42736e7 7.66842e7i −0.179615 0.311102i
\(628\) 8.83658e7 + 5.10180e7i 0.356784 + 0.205989i
\(629\) −1.69186e8 1.69186e8i −0.679848 0.679848i
\(630\) −6.89074e7 + 1.84637e7i −0.275578 + 0.0738408i
\(631\) −8.68249e7 3.24035e8i −0.345586 1.28974i −0.891926 0.452181i \(-0.850646\pi\)
0.546340 0.837563i \(-0.316021\pi\)
\(632\) 1.66828e7 1.66828e7i 0.0660872 0.0660872i
\(633\) 1.10395e8 1.91210e8i 0.435251 0.753876i
\(634\) −2.06893e8 + 1.19450e8i −0.811854 + 0.468724i
\(635\) 1.97483e8 + 5.29155e7i 0.771276 + 0.206663i
\(636\) 4.20886e7i 0.163604i
\(637\) 1.75723e8 + 2.77449e7i 0.679845 + 0.107341i
\(638\) 2.91567e8 1.12273
\(639\) 2.22918e7 8.31940e7i 0.0854362 0.318852i
\(640\) 8.90746e7 + 1.54282e8i 0.339793 + 0.588538i
\(641\) −3.85925e8 2.22814e8i −1.46531 0.845996i −0.466059 0.884754i \(-0.654327\pi\)
−0.999249 + 0.0387576i \(0.987660\pi\)
\(642\) 5.12535e7 + 5.12535e7i 0.193695 + 0.193695i
\(643\) −1.07824e8 + 2.88913e7i −0.405585 + 0.108676i −0.455843 0.890060i \(-0.650662\pi\)
0.0502584 + 0.998736i \(0.483996\pi\)
\(644\) −1.09617e6 4.09096e6i −0.00410412 0.0153168i
\(645\) 1.86436e8 1.86436e8i 0.694786 0.694786i
\(646\) −5.79953e7 + 1.00451e8i −0.215127 + 0.372611i
\(647\) −1.20379e8 + 6.95006e7i −0.444464 + 0.256611i −0.705489 0.708721i \(-0.749273\pi\)
0.261025 + 0.965332i \(0.415939\pi\)
\(648\) 1.42923e8 + 3.82960e7i 0.525262 + 0.140743i
\(649\) 5.20528e8i 1.90419i
\(650\) 2.32354e8 + 3.19484e8i 0.846077 + 1.16334i
\(651\) −1.37312e7 −0.0497697
\(652\) −2.70204e7 + 1.00842e8i −0.0974875 + 0.363828i
\(653\) 1.10440e8 + 1.91288e8i 0.396633 + 0.686988i 0.993308 0.115495i \(-0.0368454\pi\)
−0.596676 + 0.802483i \(0.703512\pi\)
\(654\) −1.92651e7 1.11227e7i −0.0688711 0.0397628i
\(655\) 5.20550e8 + 5.20550e8i 1.85242 + 1.85242i
\(656\) 1.83919e8 4.92810e7i 0.651502 0.174569i
\(657\) 4.03327e7 + 1.50524e8i 0.142220 + 0.530773i
\(658\) 1.79948e8 1.79948e8i 0.631641 0.631641i
\(659\) 2.76369e8 4.78686e8i 0.965681 1.67261i 0.257908 0.966169i \(-0.416967\pi\)
0.707773 0.706440i \(-0.249700\pi\)
\(660\) −9.89625e7 + 5.71360e7i −0.344222 + 0.198737i
\(661\) −1.75380e8 4.69930e7i −0.607263 0.162716i −0.0579319 0.998321i \(-0.518451\pi\)
−0.549331 + 0.835605i \(0.685117\pi\)
\(662\) 2.65674e7i 0.0915747i
\(663\) −1.82772e8 + 2.25927e8i −0.627145 + 0.775223i
\(664\) −3.39802e8 −1.16070
\(665\) 2.80568e7 1.04709e8i 0.0954055 0.356058i
\(666\) −3.53730e7 6.12679e7i −0.119743 0.207401i
\(667\) −3.15445e7 1.82122e7i −0.106303 0.0613742i
\(668\) −1.70341e7 1.70341e7i −0.0571464 0.0571464i
\(669\) −2.91699e8 + 7.81605e7i −0.974219 + 0.261041i
\(670\) −5.91637e7 2.20802e8i −0.196712 0.734139i
\(671\) −1.75437e8 + 1.75437e8i −0.580704 + 0.580704i
\(672\) 3.55813e7 6.16286e7i 0.117250 0.203083i
\(673\) −2.07081e8 + 1.19558e8i −0.679353 + 0.392225i −0.799611 0.600518i \(-0.794961\pi\)
0.120258 + 0.992743i \(0.461628\pi\)
\(674\) −3.14654e8 8.43112e7i −1.02767 0.275363i
\(675\) 5.63964e8i 1.83375i
\(676\) −2.58860e7 + 7.99309e7i −0.0837961 + 0.258747i
\(677\) 9.52489e7 0.306969 0.153484 0.988151i \(-0.450951\pi\)
0.153484 + 0.988151i \(0.450951\pi\)
\(678\) 5.44297e7 2.03134e8i 0.174641 0.651770i
\(679\) 9.58318e7 + 1.65985e8i 0.306126 + 0.530226i
\(680\) 6.06269e8 + 3.50029e8i 1.92814 + 1.11321i
\(681\) 474390. + 474390.i 0.00150208 + 0.00150208i
\(682\) −3.27482e7 + 8.77486e6i −0.103237 + 0.0276622i
\(683\) −6.77910e7 2.52999e8i −0.212770 0.794067i −0.986940 0.161090i \(-0.948499\pi\)
0.774170 0.632978i \(-0.218168\pi\)
\(684\) 9.05980e6 9.05980e6i 0.0283107 0.0283107i
\(685\) −2.55082e8 + 4.41815e8i −0.793612 + 1.37458i
\(686\) 2.24858e8 1.29822e8i 0.696523 0.402138i
\(687\) −1.48467e8 3.97816e7i −0.457889 0.122691i
\(688\) 1.60308e8i 0.492255i
\(689\) −1.92020e8 1.55342e8i −0.587069 0.474931i
\(690\) −3.82126e7 −0.116321
\(691\) 1.59923e8 5.96841e8i 0.484704 1.80894i −0.0966852 0.995315i \(-0.530824\pi\)
0.581389 0.813625i \(-0.302509\pi\)
\(692\) 2.10145e7 + 3.63982e7i 0.0634163 + 0.109840i
\(693\) 6.58266e7 + 3.80050e7i 0.197789 + 0.114193i
\(694\) 7.01299e7 + 7.01299e7i 0.209809 + 0.209809i
\(695\) −5.09988e8 + 1.36651e8i −1.51917 + 0.407059i
\(696\) −8.86820e7 3.30966e8i −0.263031 0.981646i
\(697\) 3.09069e8 3.09069e8i 0.912760 0.912760i
\(698\) −2.42668e7 + 4.20313e7i −0.0713586 + 0.123597i
\(699\) 2.71360e8 1.56670e8i 0.794536 0.458726i
\(700\) −8.48188e7 2.27271e7i −0.247285 0.0662599i
\(701\) 3.52124e8i 1.02221i −0.859517 0.511107i \(-0.829236\pi\)
0.859517 0.511107i \(-0.170764\pi\)
\(702\) −2.59656e8 + 1.88843e8i −0.750563 + 0.545869i
\(703\) 1.07503e8 0.309426
\(704\) 1.11593e8 4.16472e8i 0.319831 1.19362i
\(705\) 4.28891e8 + 7.42860e8i 1.22399 + 2.12002i
\(706\) −9.71352e7 5.60810e7i −0.276034 0.159368i
\(707\) −1.54801e8 1.54801e8i −0.438041 0.438041i
\(708\) 1.26340e8 3.38528e7i 0.355993 0.0953881i
\(709\) −1.12528e8 4.19961e8i −0.315735 1.17834i −0.923303 0.384071i \(-0.874522\pi\)
0.607569 0.794267i \(-0.292145\pi\)
\(710\) −3.19691e8 + 3.19691e8i −0.893214 + 0.893214i
\(711\) 5.65524e6 9.79517e6i 0.0157341 0.0272523i
\(712\) −5.58114e7 + 3.22227e7i −0.154626 + 0.0892735i
\(713\) 4.09112e6 + 1.09621e6i 0.0112869 + 0.00302431i
\(714\) 1.72907e8i 0.475027i
\(715\) 1.04583e8 6.62375e8i 0.286115 1.81211i
\(716\) 1.99124e7 0.0542480
\(717\) −9.63382e7 + 3.59539e8i −0.261361 + 0.975413i
\(718\) −1.17915e8 2.04234e8i −0.318562 0.551766i
\(719\) −2.99046e8 1.72654e8i −0.804546 0.464505i 0.0405122 0.999179i \(-0.487101\pi\)
−0.845058 + 0.534674i \(0.820434\pi\)
\(720\) 1.03379e8 + 1.03379e8i 0.276970 + 0.276970i
\(721\) 1.59043e8 4.26154e7i 0.424334 0.113700i
\(722\) 6.96267e7 + 2.59850e8i 0.184997 + 0.690417i
\(723\) −1.50754e8 + 1.50754e8i −0.398890 + 0.398890i
\(724\) −3.20015e7 + 5.54283e7i −0.0843248 + 0.146055i
\(725\) −6.54020e8 + 3.77599e8i −1.71624 + 0.990870i
\(726\) −6.35789e7 1.70359e7i −0.166151 0.0445200i
\(727\) 3.47043e8i 0.903193i 0.892222 + 0.451596i \(0.149145\pi\)
−0.892222 + 0.451596i \(0.850855\pi\)
\(728\) 8.38903e7 + 2.18227e8i 0.217429 + 0.565607i
\(729\) 4.06622e8 1.04956
\(730\) 2.11717e8 7.90138e8i 0.544235 2.03111i
\(731\) 1.83997e8 + 3.18693e8i 0.471042 + 0.815869i
\(732\) 5.39910e7 + 3.11717e7i 0.137654 + 0.0794745i
\(733\) 2.91764e8 + 2.91764e8i 0.740831 + 0.740831i 0.972738 0.231907i \(-0.0744965\pi\)
−0.231907 + 0.972738i \(0.574497\pi\)
\(734\) −1.39186e8 + 3.72949e7i −0.351972 + 0.0943107i
\(735\) 9.23428e7 + 3.44628e8i 0.232563 + 0.867938i
\(736\) −1.55213e7 + 1.55213e7i −0.0389308 + 0.0389308i
\(737\) −1.21781e8 + 2.10930e8i −0.304211 + 0.526910i
\(738\) 1.11924e8 6.46195e7i 0.278455 0.160766i
\(739\) 1.70943e8 + 4.58042e7i 0.423564 + 0.113494i 0.464304 0.885676i \(-0.346305\pi\)
−0.0407394 + 0.999170i \(0.512971\pi\)
\(740\) 1.38735e8i 0.342367i
\(741\) −1.37107e7 1.29847e8i −0.0336982 0.319137i
\(742\) −1.46958e8 −0.359734
\(743\) −8.43295e7 + 3.14722e8i −0.205595 + 0.767292i 0.783672 + 0.621175i \(0.213344\pi\)
−0.989267 + 0.146117i \(0.953322\pi\)
\(744\) 1.99212e7 + 3.45045e7i 0.0483722 + 0.0837831i
\(745\) 2.05627e8 + 1.18719e8i 0.497291 + 0.287111i
\(746\) 2.84737e8 + 2.84737e8i 0.685848 + 0.685848i
\(747\) −1.57350e8 + 4.21618e7i −0.377490 + 0.101148i
\(748\) −4.12794e7 1.54057e8i −0.0986343 0.368108i
\(749\) 6.68559e7 6.68559e7i 0.159109 0.159109i
\(750\) −1.61165e8 + 2.79147e8i −0.382022 + 0.661681i
\(751\) 2.88833e8 1.66758e8i 0.681909 0.393701i −0.118665 0.992934i \(-0.537861\pi\)
0.800574 + 0.599234i \(0.204528\pi\)
\(752\) −5.03768e8 1.34984e8i −1.18461 0.317416i
\(753\) 4.45584e8i 1.04363i
\(754\) 3.92849e8 + 1.74681e8i 0.916457 + 0.407504i
\(755\) 5.34723e8 1.24248
\(756\) 1.84712e7 6.89354e7i 0.0427494 0.159543i
\(757\) −2.35132e8 4.07261e8i −0.542032 0.938826i −0.998787 0.0492342i \(-0.984322\pi\)
0.456756 0.889592i \(-0.349011\pi\)
\(758\) −3.21919e8 1.85860e8i −0.739160 0.426754i
\(759\) 2.87900e7 + 2.87900e7i 0.0658439 + 0.0658439i
\(760\) −3.03824e8 + 8.14094e7i −0.692120 + 0.185453i
\(761\) 5.52030e7 + 2.06020e8i 0.125259 + 0.467473i 0.999849 0.0173907i \(-0.00553591\pi\)
−0.874590 + 0.484864i \(0.838869\pi\)
\(762\) 1.03607e8 1.03607e8i 0.234165 0.234165i
\(763\) −1.45086e7 + 2.51296e7i −0.0326627 + 0.0565735i
\(764\) 6.64193e7 3.83472e7i 0.148941 0.0859911i
\(765\) 3.24172e8 + 8.68617e7i 0.724088 + 0.194019i
\(766\) 2.41058e8i 0.536334i
\(767\) −3.11854e8 + 7.01345e8i −0.691138 + 1.55434i
\(768\) −2.70675e8 −0.597537
\(769\) −1.17708e8 + 4.39293e8i −0.258838 + 0.965995i 0.707078 + 0.707136i \(0.250013\pi\)
−0.965915 + 0.258859i \(0.916653\pi\)
\(770\) −1.99498e8 3.45541e8i −0.436985 0.756880i
\(771\) 3.31529e8 + 1.91408e8i 0.723366 + 0.417636i
\(772\) −6.22746e7 6.22746e7i −0.135350 0.135350i
\(773\) 8.33050e8 2.23215e8i 1.80357 0.483265i 0.809042 0.587751i \(-0.199986\pi\)
0.994526 + 0.104486i \(0.0333197\pi\)
\(774\) 2.81619e7 + 1.05102e8i 0.0607350 + 0.226666i
\(775\) 6.20942e7 6.20942e7i 0.133397 0.133397i
\(776\) 2.78065e8 4.81622e8i 0.595060 1.03067i
\(777\) 1.38785e8 8.01278e7i 0.295856 0.170813i
\(778\) 1.75643e8 + 4.70633e7i 0.372985 + 0.0999411i
\(779\) 1.96387e8i 0.415433i
\(780\) −1.67570e8 + 1.76940e7i −0.353112 + 0.0372857i
\(781\) 4.81720e8 1.01121
\(782\) 1.38038e7 5.15166e7i 0.0288655 0.107728i
\(783\) −3.06889e8 5.31547e8i −0.639287 1.10728i
\(784\) −1.87866e8 1.08464e8i −0.389852 0.225081i
\(785\) −8.49143e8 8.49143e8i −1.75538 1.75538i
\(786\) 5.09608e8 1.36549e8i 1.04947 0.281204i
\(787\) 1.39290e8 + 5.19836e8i 0.285755 + 1.06645i 0.948286 + 0.317419i \(0.102816\pi\)
−0.662530 + 0.749035i \(0.730517\pi\)
\(788\) 1.72451e7 1.72451e7i 0.0352442 0.0352442i
\(789\) −3.22188e8 + 5.58045e8i −0.655961 + 1.13616i
\(790\) −5.14173e7 + 2.96858e7i −0.104287 + 0.0602099i
\(791\) −2.64972e8 7.09989e7i −0.535389 0.143457i
\(792\) 2.20550e8i 0.443947i
\(793\) −3.41486e8 + 1.31273e8i −0.684783 + 0.263243i
\(794\) 2.68558e8 0.536509
\(795\) 1.28204e8 4.78465e8i 0.255153 0.952245i
\(796\) 1.48090e6 + 2.56499e6i 0.00293620 + 0.00508565i
\(797\) −2.74469e8 1.58465e8i −0.542148 0.313009i 0.203801 0.979012i \(-0.434670\pi\)
−0.745949 + 0.666003i \(0.768004\pi\)
\(798\) −5.49341e7 5.49341e7i −0.108102 0.108102i
\(799\) −1.15642e9 + 3.09863e8i −2.26713 + 0.607476i
\(800\) 1.17789e8 + 4.39595e8i 0.230057 + 0.858585i
\(801\) −2.18462e7 + 2.18462e7i −0.0425087 + 0.0425087i
\(802\) −1.85104e7 + 3.20609e7i −0.0358833 + 0.0621517i
\(803\) −7.54812e8 + 4.35791e8i −1.45778 + 0.841650i
\(804\) 5.91161e7 + 1.58401e7i 0.113746 + 0.0304782i
\(805\) 4.98452e7i 0.0955510i
\(806\) −4.93812e7 7.79681e6i −0.0943096 0.0148906i
\(807\) −1.54578e7 −0.0294122
\(808\) −1.64407e8 + 6.13576e8i −0.311664 + 1.16315i
\(809\) −2.37410e8 4.11206e8i −0.448387 0.776630i 0.549894 0.835235i \(-0.314668\pi\)
−0.998281 + 0.0586048i \(0.981335\pi\)
\(810\) −3.22465e8 1.86175e8i −0.606775 0.350322i
\(811\) 5.79421e7 + 5.79421e7i 0.108625 + 0.108625i 0.759331 0.650705i \(-0.225527\pi\)
−0.650705 + 0.759331i \(0.725527\pi\)
\(812\) −9.23107e7 + 2.47346e7i −0.172418 + 0.0461994i
\(813\) −2.02413e8 7.55415e8i −0.376675 1.40577i
\(814\) 2.79791e8 2.79791e8i 0.518753 0.518753i
\(815\) 6.14338e8 1.06407e9i 1.13484 1.96560i
\(816\) 3.06879e8 1.77177e8i 0.564803 0.326089i
\(817\) −1.59709e8 4.27939e7i −0.292862 0.0784722i
\(818\) 4.55274e8i 0.831789i
\(819\) 6.59237e7 + 9.06443e7i 0.120002 + 0.165002i
\(820\) 2.53442e8 0.459660
\(821\) −1.51418e8 + 5.65098e8i −0.273619 + 1.02116i 0.683142 + 0.730286i \(0.260613\pi\)
−0.956761 + 0.290875i \(0.906054\pi\)
\(822\) 1.82808e8 + 3.16633e8i 0.329139 + 0.570086i
\(823\) 1.73643e8 + 1.00253e8i 0.311499 + 0.179844i 0.647597 0.761983i \(-0.275774\pi\)
−0.336098 + 0.941827i \(0.609107\pi\)
\(824\) −3.37825e8 3.37825e8i −0.603823 0.603823i
\(825\) 8.15394e8 2.18484e8i 1.45213 0.389097i
\(826\) 1.18201e8 + 4.41133e8i 0.209740 + 0.782762i
\(827\) −2.35925e8 + 2.35925e8i −0.417117 + 0.417117i −0.884209 0.467092i \(-0.845302\pi\)
0.467092 + 0.884209i \(0.345302\pi\)
\(828\) −2.94567e6 + 5.10206e6i −0.00518912 + 0.00898782i
\(829\) 6.24226e8 3.60397e8i 1.09567 0.632583i 0.160587 0.987022i \(-0.448661\pi\)
0.935079 + 0.354438i \(0.115328\pi\)
\(830\) 8.25971e8 + 2.21318e8i 1.44454 + 0.387064i
\(831\) 3.85151e8i 0.671163i
\(832\) 3.99870e8 4.94285e8i 0.694303 0.858238i
\(833\) −4.97970e8 −0.861526
\(834\) −9.79326e7 + 3.65489e8i −0.168822 + 0.630052i
\(835\) 1.41757e8 + 2.45531e8i 0.243493 + 0.421742i
\(836\) 6.20599e7 + 3.58303e7i 0.106217 + 0.0613242i
\(837\) 5.04663e7 + 5.04663e7i 0.0860647 + 0.0860647i
\(838\) 5.29928e8 1.41994e8i 0.900501 0.241289i
\(839\) 1.59597e8 + 5.95624e8i 0.270233 + 1.00852i 0.958969 + 0.283511i \(0.0914994\pi\)
−0.688736 + 0.725012i \(0.741834\pi\)
\(840\) −3.31554e8 + 3.31554e8i −0.559392 + 0.559392i
\(841\) −1.13540e8 + 1.96656e8i −0.190880 + 0.330613i
\(842\) 5.47399e7 3.16041e7i 0.0916997 0.0529429i
\(843\) 1.85669e8 + 4.97498e7i 0.309925 + 0.0830441i
\(844\) 1.78684e8i 0.297207i
\(845\) 5.37747e8 8.29808e8i 0.891267 1.37533i
\(846\) −3.53995e8 −0.584636
\(847\) −2.22219e7 + 8.29333e7i −0.0365705 + 0.136483i
\(848\) 1.50587e8 + 2.60824e8i 0.246944 + 0.427720i
\(849\) 2.92088e8 + 1.68637e8i 0.477298 + 0.275568i
\(850\) −7.81909e8 7.81909e8i −1.27321 1.27321i
\(851\) −4.77471e7 + 1.27938e7i −0.0774745 + 0.0207592i
\(852\) −3.13289e7 1.16921e8i −0.0506554 0.189049i
\(853\) −5.46270e8 + 5.46270e8i −0.880157 + 0.880157i −0.993550 0.113393i \(-0.963828\pi\)
0.113393 + 0.993550i \(0.463828\pi\)
\(854\) −1.08840e8 + 1.88517e8i −0.174749 + 0.302675i
\(855\) −1.30589e8 + 7.53956e7i −0.208934 + 0.120628i
\(856\) −2.64993e8 7.10047e7i −0.422487 0.113205i
\(857\) 2.48438e7i 0.0394708i 0.999805 + 0.0197354i \(0.00628238\pi\)
−0.999805 + 0.0197354i \(0.993718\pi\)
\(858\) −3.73627e8 3.02259e8i −0.591529 0.478539i
\(859\) −9.36388e7 −0.147733 −0.0738663 0.997268i \(-0.523534\pi\)
−0.0738663 + 0.997268i \(0.523534\pi\)
\(860\) −5.52264e7 + 2.06108e8i −0.0868263 + 0.324040i
\(861\) 1.46377e8 + 2.53533e8i 0.229332 + 0.397215i
\(862\) 6.10550e8 + 3.52501e8i 0.953234 + 0.550350i
\(863\) 7.01780e8 + 7.01780e8i 1.09186 + 1.09186i 0.995330 + 0.0965339i \(0.0307756\pi\)
0.0965339 + 0.995330i \(0.469224\pi\)
\(864\) −3.57276e8 + 9.57317e7i −0.553939 + 0.148428i
\(865\) −1.28023e8 4.77788e8i −0.197806 0.738222i
\(866\) −4.98194e8 + 4.98194e8i −0.767087 + 0.767087i
\(867\) 1.47138e8 2.54851e8i 0.225771 0.391048i
\(868\) 9.62375e6 5.55627e6i 0.0147158 0.00849619i
\(869\) 6.11043e7 + 1.63728e7i 0.0931135 + 0.0249497i
\(870\) 8.62252e8i 1.30941i
\(871\) −2.90454e8 + 2.11241e8i −0.439565 + 0.319687i
\(872\) 8.41961e7 0.126982
\(873\) 6.90032e7 2.57524e8i 0.103711 0.387056i
\(874\) 1.19817e7 + 2.07529e7i 0.0179466 + 0.0310845i
\(875\) 3.64123e8 + 2.10227e8i 0.543531 + 0.313808i
\(876\) 1.54863e8 + 1.54863e8i 0.230374 + 0.230374i
\(877\) 7.88387e8 2.11248e8i 1.16880 0.313179i 0.378325 0.925673i \(-0.376500\pi\)
0.790476 + 0.612493i \(0.209833\pi\)
\(878\) −1.66558e8 6.21604e8i −0.246083 0.918396i
\(879\) −1.75640e7 + 1.75640e7i −0.0258617 + 0.0258617i
\(880\) −4.08848e8 + 7.08146e8i −0.599949 + 1.03914i
\(881\) 9.79118e8 5.65294e8i 1.43188 0.826698i 0.434618 0.900615i \(-0.356883\pi\)
0.997264 + 0.0739169i \(0.0235500\pi\)
\(882\) −1.42223e8 3.81086e7i −0.207284 0.0555415i
\(883\) 3.21234e8i 0.466594i −0.972405 0.233297i \(-0.925049\pi\)
0.972405 0.233297i \(-0.0749515\pi\)
\(884\) 3.66783e7 2.32302e8i 0.0530949 0.336277i
\(885\) −1.53936e9 −2.22080
\(886\) 8.00724e6 2.98834e7i 0.0115128 0.0429664i
\(887\) −5.59665e8 9.69369e8i −0.801969 1.38905i −0.918318 0.395843i \(-0.870452\pi\)
0.116349 0.993208i \(-0.462881\pi\)
\(888\) −4.02698e8 2.32498e8i −0.575097 0.332032i
\(889\) −1.35146e8 1.35146e8i −0.192352 0.192352i
\(890\) 1.56650e8 4.19743e7i 0.222209 0.0595407i
\(891\) 1.02683e8 + 3.83217e8i 0.145166 + 0.541766i
\(892\) 1.72815e8 1.72815e8i 0.243493 0.243493i
\(893\) 2.68959e8 4.65851e8i 0.377687 0.654174i
\(894\) 1.47365e8 8.50812e7i 0.206244 0.119075i
\(895\) −2.26365e8 6.06542e7i −0.315747 0.0846042i
\(896\) 1.66539e8i 0.231521i
\(897\) 2.15424e7 + 5.60391e7i 0.0298481 + 0.0776451i
\(898\) −5.56436e8 −0.768398
\(899\) 2.47356e7 9.23144e7i 0.0340442 0.127055i
\(900\) 6.10734e7 + 1.05782e8i 0.0837770 + 0.145106i
\(901\) 5.98733e8 + 3.45679e8i 0.818576 + 0.472605i
\(902\) 5.11123e8 + 5.11123e8i 0.696475 + 0.696475i
\(903\) −2.38078e8 + 6.37929e7i −0.323338 + 0.0866382i
\(904\) 2.06010e8 + 7.68839e8i 0.278858 + 1.04071i
\(905\) 5.32633e8 5.32633e8i 0.718592 0.718592i
\(906\) 1.91608e8 3.31875e8i 0.257650 0.446262i
\(907\) −9.91511e7 + 5.72449e7i −0.132885 + 0.0767211i −0.564969 0.825112i \(-0.691112\pi\)
0.432084 + 0.901833i \(0.357778\pi\)
\(908\) −524445. 140525.i −0.000700555 0.000187713i
\(909\) 3.04524e8i 0.405444i
\(910\) −6.17809e7 5.85093e8i −0.0819842 0.776427i
\(911\) −1.32550e9 −1.75317 −0.876585 0.481247i \(-0.840184\pi\)
−0.876585 + 0.481247i \(0.840184\pi\)
\(912\) −4.12076e7 + 1.53789e8i −0.0543241 + 0.202740i
\(913\) −4.55554e8 7.89043e8i −0.598587 1.03678i
\(914\) −6.47234e8 3.73681e8i −0.847662 0.489398i
\(915\) −5.18822e8 5.18822e8i −0.677259 0.677259i
\(916\) 1.20153e8 3.21950e7i 0.156332 0.0418891i
\(917\) −1.78117e8 6.64740e8i −0.230992 0.862073i
\(918\) 6.35487e8 6.35487e8i 0.821445 0.821445i
\(919\) 3.95474e8 6.84982e8i 0.509533 0.882536i −0.490407 0.871494i \(-0.663152\pi\)
0.999939 0.0110424i \(-0.00351498\pi\)
\(920\) 1.25254e8 7.23151e7i 0.160852 0.0928679i
\(921\) −1.60604e8 4.30338e7i −0.205579 0.0550847i
\(922\) 2.41318e8i 0.307891i
\(923\) 6.49056e8 + 2.88603e8i 0.825424 + 0.367026i
\(924\) 1.06825e8 0.135411
\(925\) −2.65257e8 + 9.89953e8i −0.335152 + 1.25080i
\(926\) 3.83282e6 + 6.63864e6i 0.00482709 + 0.00836077i
\(927\) −1.98351e8 1.14518e8i −0.248998 0.143759i
\(928\) 3.50231e8 + 3.50231e8i 0.438238 + 0.438238i
\(929\) 3.43440e8 9.20245e7i 0.428355 0.114777i −0.0381989 0.999270i \(-0.512162\pi\)
0.466554 + 0.884493i \(0.345495\pi\)
\(930\) −2.59499e7 9.68464e7i −0.0322617 0.120402i
\(931\) 1.58209e8 1.58209e8i 0.196057 0.196057i
\(932\) −1.26791e8 + 2.19609e8i −0.156618 + 0.271271i
\(933\) −3.48294e8 + 2.01088e8i −0.428846 + 0.247594i
\(934\) 7.60562e8 + 2.03792e8i 0.933456 + 0.250119i
\(935\) 1.87706e9i 2.29638i
\(936\) 1.32134e8 2.97163e8i 0.161134 0.362382i
\(937\) −4.59905e8 −0.559048 −0.279524 0.960139i \(-0.590177\pi\)
−0.279524 + 0.960139i \(0.590177\pi\)
\(938\) −5.53078e7 + 2.06411e8i −0.0670159 + 0.250107i
\(939\) 4.62596e8 + 8.01240e8i 0.558734 + 0.967756i
\(940\) −6.01191e8 3.47098e8i −0.723817 0.417896i
\(941\) 5.05371e7 + 5.05371e7i 0.0606515 + 0.0606515i 0.736782 0.676130i \(-0.236344\pi\)
−0.676130 + 0.736782i \(0.736344\pi\)
\(942\) −8.31294e8 + 2.22744e8i −0.994493 + 0.266474i
\(943\) −2.33717e7 8.72245e7i −0.0278712 0.104017i
\(944\) 6.61812e8 6.61812e8i 0.786718 0.786718i
\(945\) −4.19963e8 + 7.27397e8i −0.497640 + 0.861938i
\(946\) −5.27039e8 + 3.04286e8i −0.622543 + 0.359425i
\(947\) 1.53870e9 + 4.12294e8i 1.81178 + 0.485464i 0.995713 0.0924986i \(-0.0294854\pi\)
0.816063 + 0.577963i \(0.196152\pi\)
\(948\) 1.58958e7i 0.0186576i
\(949\) −1.27810e9 + 1.34957e8i −1.49543 + 0.157905i
\(950\) 4.96838e8 0.579488
\(951\) −1.94830e8 + 7.27116e8i −0.226524 + 0.845399i
\(952\) −3.27217e8 5.66756e8i −0.379249 0.656879i
\(953\) 5.59920e8 + 3.23270e8i 0.646915 + 0.373497i 0.787273 0.616604i \(-0.211492\pi\)
−0.140358 + 0.990101i \(0.544825\pi\)
\(954\) 1.44548e8 + 1.44548e8i 0.166482 + 0.166482i
\(955\) −8.71866e8 + 2.33616e8i −1.00101 + 0.268220i
\(956\) −7.79658e7 2.90972e8i −0.0892340 0.333026i
\(957\) 6.49633e8 6.49633e8i 0.741195 0.741195i
\(958\) −1.04777e8 + 1.81479e8i −0.119171 + 0.206410i
\(959\) 4.13021e8 2.38458e8i 0.468291 0.270368i
\(960\) 1.23163e9 + 3.30015e8i 1.39209 + 0.373009i
\(961\) 8.76391e8i 0.987478i
\(962\) 5.44608e8 2.09357e8i 0.611729 0.235159i
\(963\) −1.31519e8 −0.147268
\(964\) 4.46565e7 1.66660e8i 0.0498486 0.186038i
\(965\) 5.18249e8 + 8.97633e8i 0.576709 + 0.998888i
\(966\) 3.09363e7 + 1.78611e7i 0.0343192 + 0.0198142i
\(967\) 1.18037e8 + 1.18037e8i 0.130539 + 0.130539i 0.769358 0.638818i \(-0.220577\pi\)
−0.638818 + 0.769358i \(0.720577\pi\)
\(968\) 2.40638e8 6.44789e7i 0.265301 0.0710872i
\(969\) 9.45940e7 + 3.53030e8i 0.103966 + 0.388007i
\(970\) −9.89591e8 + 9.89591e8i −1.08428 + 1.08428i
\(971\) −5.93531e8 + 1.02803e9i −0.648314 + 1.12291i 0.335211 + 0.942143i \(0.391192\pi\)
−0.983525 + 0.180770i \(0.942141\pi\)
\(972\) −1.48938e8 + 8.59893e7i −0.162183 + 0.0936366i
\(973\) 4.76750e8 + 1.27745e8i 0.517550 + 0.138677i
\(974\) 1.02130e9i 1.10529i
\(975\) 1.22953e9 + 1.94132e8i 1.32656 + 0.209451i
\(976\) 4.46111e8 0.479837
\(977\) −1.38766e7 + 5.17882e7i −0.0148799 + 0.0555324i −0.972967 0.230946i \(-0.925818\pi\)
0.958087 + 0.286478i \(0.0924846\pi\)
\(978\) −4.40274e8 7.62576e8i −0.470659 0.815205i
\(979\) −1.49647e8 8.63986e7i −0.159485 0.0920786i
\(980\) −2.04172e8 2.04172e8i −0.216930 0.216930i
\(981\) 3.89882e7 1.04469e7i 0.0412977 0.0110657i
\(982\) 1.88917e8 + 7.05050e8i 0.199498 + 0.744535i
\(983\) −7.12926e7 + 7.12926e7i −0.0750557 + 0.0750557i −0.743638 0.668582i \(-0.766901\pi\)
0.668582 + 0.743638i \(0.266901\pi\)
\(984\) 4.24728e8 7.35650e8i 0.445785 0.772122i
\(985\) −2.48573e8 + 1.43514e8i −0.260103 + 0.150170i
\(986\) −1.16245e9 3.11478e8i −1.21267 0.324935i
\(987\) 8.01876e8i 0.833981i
\(988\) 6.21514e7 + 8.54575e7i 0.0644437 + 0.0886093i
\(989\) 7.60268e7 0.0785919
\(990\) −1.43648e8 + 5.36100e8i −0.148045 + 0.552510i
\(991\) −4.04022e8 6.99786e8i −0.415130 0.719026i 0.580312 0.814394i \(-0.302930\pi\)
−0.995442 + 0.0953684i \(0.969597\pi\)
\(992\) −4.98776e7 2.87968e7i −0.0510940 0.0294992i
\(993\) 5.91942e7 + 5.91942e7i 0.0604549 + 0.0604549i
\(994\) 4.08245e8 1.09389e8i 0.415682 0.111382i
\(995\) −9.02181e6 3.36698e7i −0.00915850 0.0341800i
\(996\) −1.61886e8 + 1.61886e8i −0.163844 + 0.163844i
\(997\) −4.19444e7 + 7.26499e7i −0.0423242 + 0.0733077i −0.886411 0.462898i \(-0.846810\pi\)
0.844087 + 0.536206i \(0.180143\pi\)
\(998\) −6.24665e8 + 3.60650e8i −0.628428 + 0.362823i
\(999\) −8.04572e8 2.15584e8i −0.806991 0.216232i
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 13.7.f.a.11.4 yes 24
13.6 odd 12 inner 13.7.f.a.6.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.7.f.a.6.4 24 13.6 odd 12 inner
13.7.f.a.11.4 yes 24 1.1 even 1 trivial