Properties

Label 69.6.g.a.5.8
Level $69$
Weight $6$
Character 69.5
Analytic conductor $11.066$
Analytic rank $0$
Dimension $380$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,6,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.0664835671\)
Analytic rank: \(0\)
Dimension: \(380\)
Relative dimension: \(38\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.8
Character \(\chi\) \(=\) 69.5
Dual form 69.6.g.a.14.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.97556 + 6.72815i) q^{2} +(-11.2628 + 10.7772i) q^{3} +(-14.4450 - 9.28323i) q^{4} +(-7.37109 + 51.2671i) q^{5} +(-50.2603 - 97.0690i) q^{6} +(-115.006 + 52.5213i) q^{7} +(-78.5868 + 68.0959i) q^{8} +(10.7027 - 242.764i) q^{9} +O(q^{10})\) \(q+(-1.97556 + 6.72815i) q^{2} +(-11.2628 + 10.7772i) q^{3} +(-14.4450 - 9.28323i) q^{4} +(-7.37109 + 51.2671i) q^{5} +(-50.2603 - 97.0690i) q^{6} +(-115.006 + 52.5213i) q^{7} +(-78.5868 + 68.0959i) q^{8} +(10.7027 - 242.764i) q^{9} +(-330.370 - 150.875i) q^{10} +(298.269 - 87.5798i) q^{11} +(262.739 - 51.1215i) q^{12} +(-505.521 + 1106.94i) q^{13} +(-126.170 - 877.533i) q^{14} +(-469.497 - 656.852i) q^{15} +(-531.162 - 1163.08i) q^{16} +(1360.87 - 874.576i) q^{17} +(1612.21 + 551.605i) q^{18} +(323.799 - 503.841i) q^{19} +(582.399 - 672.124i) q^{20} +(729.254 - 1830.98i) q^{21} +2179.82i q^{22} +(2314.88 + 1038.11i) q^{23} +(151.225 - 1613.90i) q^{24} +(424.438 + 124.626i) q^{25} +(-6448.95 - 5588.05i) q^{26} +(2495.78 + 2849.56i) q^{27} +(2148.82 + 308.954i) q^{28} +(226.976 + 353.181i) q^{29} +(5346.92 - 1861.19i) q^{30} +(-1543.49 - 1781.28i) q^{31} +(5581.07 - 802.437i) q^{32} +(-2415.49 + 4200.91i) q^{33} +(3195.80 + 10883.9i) q^{34} +(-1844.90 - 6283.14i) q^{35} +(-2408.24 + 3407.37i) q^{36} +(-6930.64 + 996.476i) q^{37} +(2750.23 + 3173.93i) q^{38} +(-6236.12 - 17915.4i) q^{39} +(-2911.80 - 4530.85i) q^{40} +(-16312.4 - 2345.37i) q^{41} +(10878.4 + 8523.74i) q^{42} +(-14074.4 - 12195.6i) q^{43} +(-5121.52 - 1503.81i) q^{44} +(12366.9 + 2338.13i) q^{45} +(-11557.7 + 13524.0i) q^{46} +25797.9i q^{47} +(18517.2 + 7375.15i) q^{48} +(-538.447 + 621.401i) q^{49} +(-1677.01 + 2609.47i) q^{50} +(-5901.71 + 24516.6i) q^{51} +(17578.2 - 11296.8i) q^{52} +(-10077.7 - 22067.1i) q^{53} +(-24102.8 + 11162.5i) q^{54} +(2291.39 + 15937.0i) q^{55} +(5461.44 - 11958.9i) q^{56} +(1783.12 + 9164.33i) q^{57} +(-2824.66 + 829.394i) q^{58} +(21342.0 + 9746.58i) q^{59} +(684.175 + 13846.7i) q^{60} +(2620.85 - 2270.98i) q^{61} +(15034.0 - 6865.78i) q^{62} +(11519.4 + 28481.4i) q^{63} +(196.136 - 1364.15i) q^{64} +(-53023.2 - 34075.9i) q^{65} +(-23492.4 - 24550.9i) q^{66} +(8354.29 - 28452.1i) q^{67} -27776.6 q^{68} +(-37260.0 + 13256.0i) q^{69} +45918.6 q^{70} +(-12431.1 + 42336.5i) q^{71} +(15690.1 + 19806.9i) q^{72} +(26734.2 + 17181.0i) q^{73} +(6987.48 - 48599.0i) q^{74} +(-6123.50 + 3170.62i) q^{75} +(-9354.54 + 4272.07i) q^{76} +(-29702.8 + 25737.7i) q^{77} +(132857. - 6564.57i) q^{78} +(40621.6 + 18551.3i) q^{79} +(63543.0 - 18657.9i) q^{80} +(-58819.9 - 5196.47i) q^{81} +(48006.2 - 105119. i) q^{82} +(-10340.6 - 71920.4i) q^{83} +(-27531.5 + 19678.6i) q^{84} +(34805.9 + 76214.2i) q^{85} +(109858. - 70601.7i) q^{86} +(-6362.70 - 1531.65i) q^{87} +(-17476.2 + 27193.5i) q^{88} +(-6573.70 + 7586.46i) q^{89} +(-40162.9 + 78587.3i) q^{90} -153855. i q^{91} +(-23801.4 - 36485.0i) q^{92} +(36581.3 + 3427.73i) q^{93} +(-173572. - 50965.3i) q^{94} +(23443.7 + 20314.1i) q^{95} +(-54210.6 + 69186.2i) q^{96} +(-151689. - 21809.6i) q^{97} +(-3117.14 - 4850.37i) q^{98} +(-18068.9 - 73346.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 380 q - 11 q^{3} + 578 q^{4} + 64 q^{6} - 22 q^{7} + 433 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 380 q - 11 q^{3} + 578 q^{4} + 64 q^{6} - 22 q^{7} + 433 q^{9} - 22 q^{10} + 148 q^{12} - 542 q^{13} + 4620 q^{15} - 11102 q^{16} - 11526 q^{18} - 22 q^{19} + 12496 q^{21} + 15878 q^{24} - 17304 q^{25} - 21014 q^{27} - 22 q^{28} - 33627 q^{30} - 6566 q^{31} + 41250 q^{33} + 75988 q^{34} + 12154 q^{36} - 72138 q^{37} + 45205 q^{39} - 119372 q^{40} - 11 q^{42} + 59334 q^{43} + 119802 q^{46} + 5138 q^{48} + 147060 q^{49} - 11 q^{51} - 246042 q^{52} - 172143 q^{54} - 95048 q^{55} + 92422 q^{57} + 277528 q^{58} + 420629 q^{60} + 125158 q^{61} + 7194 q^{63} - 100196 q^{64} - 312378 q^{66} - 94380 q^{67} - 136956 q^{69} - 395908 q^{70} - 507803 q^{72} + 83336 q^{73} + 577756 q^{75} + 415338 q^{76} - 361512 q^{78} + 342958 q^{79} - 420607 q^{81} + 247868 q^{82} - 978505 q^{84} - 634728 q^{85} + 354721 q^{87} + 22506 q^{88} + 1636316 q^{90} + 1162112 q^{93} + 40940 q^{94} - 102479 q^{96} + 582824 q^{97} - 674663 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97556 + 6.72815i −0.349233 + 1.18938i 0.578358 + 0.815783i \(0.303694\pi\)
−0.927591 + 0.373596i \(0.878125\pi\)
\(3\) −11.2628 + 10.7772i −0.722511 + 0.691359i
\(4\) −14.4450 9.28323i −0.451406 0.290101i
\(5\) −7.37109 + 51.2671i −0.131858 + 0.917093i 0.811272 + 0.584669i \(0.198776\pi\)
−0.943130 + 0.332424i \(0.892134\pi\)
\(6\) −50.2603 97.0690i −0.569964 1.10079i
\(7\) −115.006 + 52.5213i −0.887102 + 0.405126i −0.806233 0.591599i \(-0.798497\pi\)
−0.0808698 + 0.996725i \(0.525770\pi\)
\(8\) −78.5868 + 68.0959i −0.434135 + 0.376180i
\(9\) 10.7027 242.764i 0.0440441 0.999030i
\(10\) −330.370 150.875i −1.04472 0.477109i
\(11\) 298.269 87.5798i 0.743236 0.218234i 0.111875 0.993722i \(-0.464314\pi\)
0.631362 + 0.775488i \(0.282496\pi\)
\(12\) 262.739 51.1215i 0.526710 0.102483i
\(13\) −505.521 + 1106.94i −0.829624 + 1.81662i −0.365815 + 0.930688i \(0.619210\pi\)
−0.463809 + 0.885935i \(0.653518\pi\)
\(14\) −126.170 877.533i −0.172043 1.19658i
\(15\) −469.497 656.852i −0.538772 0.753771i
\(16\) −531.162 1163.08i −0.518713 1.13582i
\(17\) 1360.87 874.576i 1.14207 0.733965i 0.174026 0.984741i \(-0.444322\pi\)
0.968045 + 0.250776i \(0.0806858\pi\)
\(18\) 1612.21 + 551.605i 1.17284 + 0.401280i
\(19\) 323.799 503.841i 0.205774 0.320191i −0.722992 0.690856i \(-0.757234\pi\)
0.928767 + 0.370665i \(0.120870\pi\)
\(20\) 582.399 672.124i 0.325571 0.375729i
\(21\) 729.254 1830.98i 0.360853 0.906015i
\(22\) 2179.82i 0.960205i
\(23\) 2314.88 + 1038.11i 0.912450 + 0.409188i
\(24\) 151.225 1613.90i 0.0535916 0.571937i
\(25\) 424.438 + 124.626i 0.135820 + 0.0398804i
\(26\) −6448.95 5588.05i −1.87092 1.62116i
\(27\) 2495.78 + 2849.56i 0.658866 + 0.752260i
\(28\) 2148.82 + 308.954i 0.517971 + 0.0744729i
\(29\) 226.976 + 353.181i 0.0501169 + 0.0779834i 0.865408 0.501068i \(-0.167059\pi\)
−0.815291 + 0.579051i \(0.803423\pi\)
\(30\) 5346.92 1861.19i 1.08468 0.377562i
\(31\) −1543.49 1781.28i −0.288469 0.332911i 0.592956 0.805235i \(-0.297961\pi\)
−0.881425 + 0.472324i \(0.843415\pi\)
\(32\) 5581.07 802.437i 0.963480 0.138527i
\(33\) −2415.49 + 4200.91i −0.386118 + 0.671520i
\(34\) 3195.80 + 10883.9i 0.474113 + 1.61468i
\(35\) −1844.90 6283.14i −0.254567 0.866975i
\(36\) −2408.24 + 3407.37i −0.309701 + 0.438190i
\(37\) −6930.64 + 996.476i −0.832280 + 0.119664i −0.545266 0.838263i \(-0.683571\pi\)
−0.287013 + 0.957927i \(0.592662\pi\)
\(38\) 2750.23 + 3173.93i 0.308965 + 0.356565i
\(39\) −6236.12 17915.4i −0.656527 1.88610i
\(40\) −2911.80 4530.85i −0.287748 0.447744i
\(41\) −16312.4 2345.37i −1.51551 0.217898i −0.666193 0.745779i \(-0.732077\pi\)
−0.849318 + 0.527882i \(0.822986\pi\)
\(42\) 10878.4 + 8523.74i 0.951573 + 0.745602i
\(43\) −14074.4 12195.6i −1.16081 1.00584i −0.999822 0.0188869i \(-0.993988\pi\)
−0.160984 0.986957i \(-0.551467\pi\)
\(44\) −5121.52 1503.81i −0.398811 0.117101i
\(45\) 12366.9 + 2338.13i 0.910395 + 0.172123i
\(46\) −11557.7 + 13524.0i −0.805338 + 0.942347i
\(47\) 25797.9i 1.70349i 0.523959 + 0.851744i \(0.324455\pi\)
−0.523959 + 0.851744i \(0.675545\pi\)
\(48\) 18517.2 + 7375.15i 1.16004 + 0.462027i
\(49\) −538.447 + 621.401i −0.0320371 + 0.0369728i
\(50\) −1677.01 + 2609.47i −0.0948658 + 0.147614i
\(51\) −5901.71 + 24516.6i −0.317726 + 1.31988i
\(52\) 17578.2 11296.8i 0.901501 0.579359i
\(53\) −10077.7 22067.1i −0.492802 1.07909i −0.978742 0.205094i \(-0.934250\pi\)
0.485940 0.873992i \(-0.338477\pi\)
\(54\) −24102.8 + 11162.5i −1.12482 + 0.520928i
\(55\) 2291.39 + 15937.0i 0.102139 + 0.710393i
\(56\) 5461.44 11958.9i 0.232722 0.509590i
\(57\) 1783.12 + 9164.33i 0.0726930 + 0.373606i
\(58\) −2824.66 + 829.394i −0.110254 + 0.0323736i
\(59\) 21342.0 + 9746.58i 0.798189 + 0.364521i 0.772392 0.635146i \(-0.219060\pi\)
0.0257974 + 0.999667i \(0.491788\pi\)
\(60\) 684.175 + 13846.7i 0.0245352 + 0.496555i
\(61\) 2620.85 2270.98i 0.0901814 0.0781426i −0.608603 0.793475i \(-0.708270\pi\)
0.698785 + 0.715332i \(0.253724\pi\)
\(62\) 15034.0 6865.78i 0.496700 0.226835i
\(63\) 11519.4 + 28481.4i 0.365661 + 0.904085i
\(64\) 196.136 1364.15i 0.00598558 0.0416307i
\(65\) −53023.2 34075.9i −1.55662 1.00038i
\(66\) −23492.4 24550.9i −0.663847 0.693758i
\(67\) 8354.29 28452.1i 0.227364 0.774332i −0.764230 0.644944i \(-0.776881\pi\)
0.991594 0.129388i \(-0.0413012\pi\)
\(68\) −27776.6 −0.728461
\(69\) −37260.0 + 13256.0i −0.942151 + 0.335188i
\(70\) 45918.6 1.12006
\(71\) −12431.1 + 42336.5i −0.292661 + 0.996710i 0.673590 + 0.739105i \(0.264751\pi\)
−0.966250 + 0.257605i \(0.917067\pi\)
\(72\) 15690.1 + 19806.9i 0.356694 + 0.450282i
\(73\) 26734.2 + 17181.0i 0.587165 + 0.377348i 0.800233 0.599689i \(-0.204709\pi\)
−0.213068 + 0.977037i \(0.568346\pi\)
\(74\) 6987.48 48599.0i 0.148334 1.03169i
\(75\) −6123.50 + 3170.62i −0.125703 + 0.0650865i
\(76\) −9354.54 + 4272.07i −0.185775 + 0.0848408i
\(77\) −29702.8 + 25737.7i −0.570915 + 0.494700i
\(78\) 132857. 6564.57i 2.47257 0.122172i
\(79\) 40621.6 + 18551.3i 0.732301 + 0.334431i 0.746425 0.665470i \(-0.231769\pi\)
−0.0141240 + 0.999900i \(0.504496\pi\)
\(80\) 63543.0 18657.9i 1.11005 0.325940i
\(81\) −58819.9 5196.47i −0.996120 0.0880027i
\(82\) 48006.2 105119.i 0.788430 1.72642i
\(83\) −10340.6 71920.4i −0.164759 1.14593i −0.889510 0.456916i \(-0.848954\pi\)
0.724751 0.689011i \(-0.241955\pi\)
\(84\) −27531.5 + 19678.6i −0.425727 + 0.304296i
\(85\) 34805.9 + 76214.2i 0.522523 + 1.14416i
\(86\) 109858. 70601.7i 1.60172 1.02936i
\(87\) −6362.70 1531.65i −0.0901246 0.0216951i
\(88\) −17476.2 + 27193.5i −0.240570 + 0.374334i
\(89\) −6573.70 + 7586.46i −0.0879701 + 0.101523i −0.798028 0.602620i \(-0.794123\pi\)
0.710058 + 0.704143i \(0.248669\pi\)
\(90\) −40162.9 + 78587.3i −0.522659 + 1.02269i
\(91\) 153855.i 1.94763i
\(92\) −23801.4 36485.0i −0.293179 0.449413i
\(93\) 36581.3 + 3427.73i 0.438583 + 0.0410960i
\(94\) −173572. 50965.3i −2.02609 0.594915i
\(95\) 23443.7 + 20314.1i 0.266512 + 0.230934i
\(96\) −54210.6 + 69186.2i −0.600352 + 0.766198i
\(97\) −151689. 21809.6i −1.63691 0.235353i −0.738421 0.674340i \(-0.764428\pi\)
−0.898493 + 0.438987i \(0.855337\pi\)
\(98\) −3117.14 4850.37i −0.0327862 0.0510164i
\(99\) −18068.9 73346.5i −0.185287 0.752127i
\(100\) −4974.07 5740.38i −0.0497407 0.0574038i
\(101\) −3020.87 + 434.335i −0.0294665 + 0.00423664i −0.157032 0.987593i \(-0.550193\pi\)
0.127566 + 0.991830i \(0.459284\pi\)
\(102\) −153292. 88141.5i −1.45888 0.838842i
\(103\) 40313.6 + 137296.i 0.374420 + 1.27516i 0.904232 + 0.427042i \(0.140444\pi\)
−0.529812 + 0.848115i \(0.677738\pi\)
\(104\) −35650.5 121415.i −0.323209 1.10075i
\(105\) 88493.5 + 50883.0i 0.783318 + 0.450401i
\(106\) 168380. 24209.4i 1.45555 0.209276i
\(107\) 25821.5 + 29799.6i 0.218033 + 0.251623i 0.854220 0.519911i \(-0.174035\pi\)
−0.636187 + 0.771535i \(0.719490\pi\)
\(108\) −9598.44 64330.7i −0.0791847 0.530712i
\(109\) −43873.5 68268.6i −0.353701 0.550370i 0.618122 0.786082i \(-0.287894\pi\)
−0.971823 + 0.235713i \(0.924258\pi\)
\(110\) −111753. 16067.6i −0.880597 0.126611i
\(111\) 67319.4 85916.3i 0.518600 0.661863i
\(112\) 122173. + 105864.i 0.920303 + 0.797447i
\(113\) −32154.4 9441.39i −0.236889 0.0695568i 0.161133 0.986933i \(-0.448485\pi\)
−0.398022 + 0.917376i \(0.630303\pi\)
\(114\) −65181.6 6107.63i −0.469746 0.0440160i
\(115\) −70284.0 + 111025.i −0.495578 + 0.782847i
\(116\) 7208.76i 0.0497411i
\(117\) 263314. + 134570.i 1.77832 + 0.908830i
\(118\) −107739. + 124337.i −0.712308 + 0.822047i
\(119\) −110573. + 172056.i −0.715786 + 1.11378i
\(120\) 81625.2 + 19649.1i 0.517453 + 0.124563i
\(121\) −54190.3 + 34826.0i −0.336479 + 0.216242i
\(122\) 10101.8 + 22119.9i 0.0614469 + 0.134550i
\(123\) 209001. 149387.i 1.24562 0.890329i
\(124\) 5759.63 + 40059.1i 0.0336388 + 0.233963i
\(125\) −76755.6 + 168071.i −0.439375 + 0.962097i
\(126\) −214384. + 21237.6i −1.20300 + 0.119173i
\(127\) −123371. + 36225.0i −0.678741 + 0.199296i −0.602892 0.797823i \(-0.705985\pi\)
−0.0758491 + 0.997119i \(0.524167\pi\)
\(128\) 172916. + 78968.2i 0.932849 + 0.426018i
\(129\) 289952. 14326.8i 1.53409 0.0758008i
\(130\) 334018. 289429.i 1.73345 1.50205i
\(131\) 84198.5 38452.2i 0.428673 0.195768i −0.189382 0.981904i \(-0.560648\pi\)
0.618055 + 0.786135i \(0.287921\pi\)
\(132\) 73889.8 38258.6i 0.369105 0.191115i
\(133\) −10776.3 + 74950.8i −0.0528251 + 0.367407i
\(134\) 174925. + 112418.i 0.841571 + 0.540845i
\(135\) −164485. + 106947.i −0.776769 + 0.505050i
\(136\) −47391.2 + 161399.i −0.219710 + 0.748264i
\(137\) 8232.86 0.0374757 0.0187378 0.999824i \(-0.494035\pi\)
0.0187378 + 0.999824i \(0.494035\pi\)
\(138\) −15578.5 276879.i −0.0696350 1.23763i
\(139\) 65209.6 0.286269 0.143135 0.989703i \(-0.454282\pi\)
0.143135 + 0.989703i \(0.454282\pi\)
\(140\) −31678.3 + 107886.i −0.136597 + 0.465207i
\(141\) −278029. 290557.i −1.17772 1.23079i
\(142\) −260288. 167277.i −1.08326 0.696169i
\(143\) −53836.2 + 374439.i −0.220158 + 1.53123i
\(144\) −288040. + 116499.i −1.15757 + 0.468183i
\(145\) −19779.6 + 9033.04i −0.0781263 + 0.0356791i
\(146\) −168412. + 145929.i −0.653868 + 0.566580i
\(147\) −632.543 12801.7i −0.00241433 0.0488624i
\(148\) 109364. + 49944.7i 0.410410 + 0.187428i
\(149\) 437741. 128532.i 1.61529 0.474293i 0.655546 0.755156i \(-0.272439\pi\)
0.959748 + 0.280863i \(0.0906206\pi\)
\(150\) −9235.05 47463.5i −0.0335128 0.172239i
\(151\) −56593.1 + 123922.i −0.201986 + 0.442287i −0.983334 0.181808i \(-0.941805\pi\)
0.781348 + 0.624095i \(0.214532\pi\)
\(152\) 8863.15 + 61644.6i 0.0311157 + 0.216414i
\(153\) −197751. 339730.i −0.682951 1.17329i
\(154\) −114487. 250691.i −0.389004 0.851800i
\(155\) 102698. 66000.1i 0.343347 0.220656i
\(156\) −76231.9 + 316679.i −0.250799 + 1.04185i
\(157\) −104989. + 163366.i −0.339934 + 0.528948i −0.968567 0.248755i \(-0.919979\pi\)
0.628632 + 0.777703i \(0.283615\pi\)
\(158\) −205066. + 236659.i −0.653509 + 0.754189i
\(159\) 351326. + 139928.i 1.10209 + 0.438948i
\(160\) 292040.i 0.901866i
\(161\) −320747. + 2192.24i −0.975210 + 0.00666534i
\(162\) 151165. 385483.i 0.452547 1.15403i
\(163\) 111341. + 32692.8i 0.328237 + 0.0963790i 0.441699 0.897163i \(-0.354376\pi\)
−0.113462 + 0.993542i \(0.536194\pi\)
\(164\) 213860. + 185311.i 0.620898 + 0.538011i
\(165\) −197564. 154800.i −0.564933 0.442652i
\(166\) 504319. + 72510.2i 1.42048 + 0.204234i
\(167\) 148226. + 230645.i 0.411277 + 0.639959i 0.983662 0.180026i \(-0.0576182\pi\)
−0.572385 + 0.819985i \(0.693982\pi\)
\(168\) 67372.3 + 193550.i 0.184166 + 0.529078i
\(169\) −726614. 838557.i −1.95698 2.25848i
\(170\) −581541. + 83613.0i −1.54333 + 0.221897i
\(171\) −118849. 83999.2i −0.310817 0.219677i
\(172\) 90090.7 + 306821.i 0.232198 + 0.790794i
\(173\) −95650.3 325755.i −0.242980 0.827515i −0.987187 0.159566i \(-0.948991\pi\)
0.744207 0.667949i \(-0.232828\pi\)
\(174\) 22875.1 39783.3i 0.0572782 0.0996156i
\(175\) −55358.3 + 7959.32i −0.136643 + 0.0196463i
\(176\) −260292. 300393.i −0.633401 0.730984i
\(177\) −345413. + 120234.i −0.828715 + 0.288465i
\(178\) −38056.0 59216.3i −0.0900271 0.140085i
\(179\) 44192.3 + 6353.90i 0.103090 + 0.0148220i 0.193666 0.981067i \(-0.437962\pi\)
−0.0905770 + 0.995889i \(0.528871\pi\)
\(180\) −156934. 148579.i −0.361025 0.341804i
\(181\) 9429.77 + 8170.95i 0.0213946 + 0.0185386i 0.665492 0.746405i \(-0.268222\pi\)
−0.644098 + 0.764943i \(0.722767\pi\)
\(182\) 1.03516e6 + 303949.i 2.31647 + 0.680178i
\(183\) −5043.32 + 53823.1i −0.0111324 + 0.118807i
\(184\) −252610. + 76052.1i −0.550055 + 0.165603i
\(185\) 362659.i 0.779056i
\(186\) −95330.9 + 239353.i −0.202046 + 0.507289i
\(187\) 329310. 380044.i 0.688653 0.794748i
\(188\) 239487. 372650.i 0.494183 0.768964i
\(189\) −436691. 196633.i −0.889242 0.400408i
\(190\) −182990. + 117601.i −0.367743 + 0.236334i
\(191\) −18860.6 41299.0i −0.0374087 0.0819137i 0.890005 0.455951i \(-0.150701\pi\)
−0.927414 + 0.374037i \(0.877973\pi\)
\(192\) 12492.7 + 17478.0i 0.0244571 + 0.0342168i
\(193\) 54056.8 + 375973.i 0.104462 + 0.726547i 0.972980 + 0.230890i \(0.0741637\pi\)
−0.868518 + 0.495657i \(0.834927\pi\)
\(194\) 446410. 977502.i 0.851589 1.86472i
\(195\) 964435. 187651.i 1.81630 0.353399i
\(196\) 13546.5 3977.60i 0.0251876 0.00739574i
\(197\) 233358. + 106571.i 0.428408 + 0.195647i 0.617937 0.786228i \(-0.287969\pi\)
−0.189529 + 0.981875i \(0.560696\pi\)
\(198\) 529182. + 23330.0i 0.959273 + 0.0422913i
\(199\) 3312.52 2870.32i 0.00592961 0.00513804i −0.651891 0.758313i \(-0.726024\pi\)
0.657820 + 0.753175i \(0.271479\pi\)
\(200\) −41841.8 + 19108.5i −0.0739665 + 0.0337794i
\(201\) 212542. + 410487.i 0.371068 + 0.716654i
\(202\) 3045.64 21182.9i 0.00525170 0.0365264i
\(203\) −44653.0 28696.7i −0.0760519 0.0488756i
\(204\) 312843. 299355.i 0.526321 0.503629i
\(205\) 240481. 819002.i 0.399665 1.36113i
\(206\) −1.00339e6 −1.64741
\(207\) 276791. 550860.i 0.448979 0.893542i
\(208\) 1.55597e6 2.49370
\(209\) 52453.0 178639.i 0.0830624 0.282885i
\(210\) −517173. + 494875.i −0.809259 + 0.774367i
\(211\) 553167. + 355499.i 0.855362 + 0.549708i 0.893243 0.449575i \(-0.148424\pi\)
−0.0378809 + 0.999282i \(0.512061\pi\)
\(212\) −59281.7 + 412313.i −0.0905901 + 0.630068i
\(213\) −316260. 610802.i −0.477635 0.922468i
\(214\) −251508. + 114860.i −0.375420 + 0.171449i
\(215\) 728974. 631660.i 1.07551 0.931938i
\(216\) −390179. 53985.2i −0.569022 0.0787300i
\(217\) 271065. + 123791.i 0.390772 + 0.178460i
\(218\) 545996. 160319.i 0.778123 0.228477i
\(219\) −486267. + 94613.6i −0.685116 + 0.133304i
\(220\) 114847. 251480.i 0.159979 0.350306i
\(221\) 280154. + 1.94851e6i 0.385847 + 2.68363i
\(222\) 445063. + 622668.i 0.606093 + 0.847957i
\(223\) −130356. 285440.i −0.175537 0.384373i 0.801329 0.598224i \(-0.204127\pi\)
−0.976866 + 0.213851i \(0.931399\pi\)
\(224\) −599709. + 385410.i −0.798584 + 0.513219i
\(225\) 34797.4 101704.i 0.0458238 0.133932i
\(226\) 127046. 197688.i 0.165459 0.257459i
\(227\) −436282. + 503496.i −0.561956 + 0.648532i −0.963627 0.267252i \(-0.913884\pi\)
0.401670 + 0.915784i \(0.368430\pi\)
\(228\) 59317.5 148932.i 0.0755693 0.189736i
\(229\) 565279.i 0.712319i 0.934425 + 0.356159i \(0.115914\pi\)
−0.934425 + 0.356159i \(0.884086\pi\)
\(230\) −608143. 692218.i −0.758029 0.862826i
\(231\) 57157.5 609993.i 0.0704763 0.752134i
\(232\) −41887.4 12299.3i −0.0510933 0.0150023i
\(233\) −563574. 488339.i −0.680081 0.589294i 0.244789 0.969576i \(-0.421281\pi\)
−0.924870 + 0.380283i \(0.875827\pi\)
\(234\) −1.42560e6 + 1.50577e6i −1.70199 + 1.79770i
\(235\) −1.32258e6 190158.i −1.56226 0.224619i
\(236\) −217806. 338912.i −0.254559 0.396102i
\(237\) −657446. + 228849.i −0.760307 + 0.264653i
\(238\) −939170. 1.08386e6i −1.07474 1.24031i
\(239\) −294691. + 42370.2i −0.333713 + 0.0479806i −0.307135 0.951666i \(-0.599370\pi\)
−0.0265781 + 0.999647i \(0.508461\pi\)
\(240\) −514594. + 894959.i −0.576682 + 1.00294i
\(241\) 104678. + 356499.i 0.116094 + 0.395381i 0.996954 0.0779972i \(-0.0248525\pi\)
−0.880859 + 0.473378i \(0.843034\pi\)
\(242\) −127258. 433401.i −0.139684 0.475720i
\(243\) 718482. 575389.i 0.780549 0.625094i
\(244\) −58940.1 + 8474.30i −0.0633777 + 0.00911233i
\(245\) −27888.5 32185.0i −0.0296831 0.0342561i
\(246\) 592205. + 1.70131e6i 0.623928 + 1.79245i
\(247\) 394033. + 613127.i 0.410951 + 0.639453i
\(248\) 242595. + 34880.0i 0.250469 + 0.0360120i
\(249\) 891567. + 698585.i 0.911288 + 0.714037i
\(250\) −979173. 848458.i −0.990854 0.858579i
\(251\) 847648. + 248892.i 0.849242 + 0.249360i 0.677263 0.735741i \(-0.263166\pi\)
0.171978 + 0.985101i \(0.444984\pi\)
\(252\) 98001.1 518350.i 0.0972142 0.514188i
\(253\) 781375. + 106899.i 0.767465 + 0.104996i
\(254\) 901623.i 0.876881i
\(255\) −1.21339e6 483277.i −1.16856 0.465421i
\(256\) −844036. + 974070.i −0.804936 + 0.928945i
\(257\) −625894. + 973910.i −0.591109 + 0.919784i 0.408865 + 0.912595i \(0.365925\pi\)
−0.999974 + 0.00718899i \(0.997712\pi\)
\(258\) −476426. + 1.97914e6i −0.445601 + 1.85109i
\(259\) 744726. 478607.i 0.689838 0.443332i
\(260\) 449584. + 984453.i 0.412456 + 0.903153i
\(261\) 88168.9 51321.5i 0.0801151 0.0466335i
\(262\) 92372.4 + 642464.i 0.0831360 + 0.578224i
\(263\) 569847. 1.24779e6i 0.508006 1.11238i −0.465777 0.884902i \(-0.654225\pi\)
0.973784 0.227477i \(-0.0730476\pi\)
\(264\) −96239.1 494621.i −0.0849849 0.436780i
\(265\) 1.20560e6 353996.i 1.05460 0.309659i
\(266\) −482991. 220575.i −0.418538 0.191140i
\(267\) −7722.48 156291.i −0.00662947 0.134170i
\(268\) −384805. + 333435.i −0.327268 + 0.283579i
\(269\) −1.14477e6 + 522799.i −0.964578 + 0.440508i −0.834507 0.550997i \(-0.814248\pi\)
−0.130071 + 0.991505i \(0.541520\pi\)
\(270\) −394605. 1.31796e6i −0.329422 1.10025i
\(271\) −80843.3 + 562278.i −0.0668684 + 0.465080i 0.928684 + 0.370872i \(0.120941\pi\)
−0.995553 + 0.0942082i \(0.969968\pi\)
\(272\) −1.74004e6 1.11826e6i −1.42606 0.916473i
\(273\) 1.65813e6 + 1.73284e6i 1.34651 + 1.40719i
\(274\) −16264.5 + 55391.9i −0.0130878 + 0.0445728i
\(275\) 137512. 0.109650
\(276\) 661279. + 154411.i 0.522531 + 0.122013i
\(277\) −1.35075e6 −1.05773 −0.528865 0.848706i \(-0.677382\pi\)
−0.528865 + 0.848706i \(0.677382\pi\)
\(278\) −128826. + 438740.i −0.0999747 + 0.340483i
\(279\) −448950. + 355639.i −0.345293 + 0.273526i
\(280\) 572840. + 368142.i 0.436655 + 0.280621i
\(281\) −178983. + 1.24485e6i −0.135221 + 0.940486i 0.803376 + 0.595472i \(0.203035\pi\)
−0.938598 + 0.345014i \(0.887874\pi\)
\(282\) 2.50417e6 1.29661e6i 1.87517 0.970926i
\(283\) 63677.5 29080.5i 0.0472628 0.0215842i −0.391643 0.920117i \(-0.628093\pi\)
0.438906 + 0.898533i \(0.355366\pi\)
\(284\) 572586. 496149.i 0.421255 0.365020i
\(285\) −482972. + 23864.0i −0.352216 + 0.0174033i
\(286\) −2.41292e6 1.10195e6i −1.74433 0.796609i
\(287\) 1.99920e6 587019.i 1.43269 0.420676i
\(288\) −135070. 1.36347e6i −0.0959574 0.968646i
\(289\) 497245. 1.08882e6i 0.350208 0.766848i
\(290\) −21699.8 150925.i −0.0151517 0.105382i
\(291\) 1.94350e6 1.38915e6i 1.34540 0.961651i
\(292\) −226680. 496360.i −0.155581 0.340674i
\(293\) 2.23652e6 1.43733e6i 1.52196 0.978107i 0.530507 0.847681i \(-0.322002\pi\)
0.991458 0.130427i \(-0.0416348\pi\)
\(294\) 87381.4 + 21034.7i 0.0589591 + 0.0141928i
\(295\) −656993. + 1.02230e6i −0.439547 + 0.683949i
\(296\) 476801. 550258.i 0.316306 0.365037i
\(297\) 993979. + 631356.i 0.653862 + 0.415320i
\(298\) 3.19911e6i 2.08684i
\(299\) −2.31934e6 + 2.03764e6i −1.50033 + 1.31811i
\(300\) 117887. + 11046.3i 0.0756248 + 0.00708618i
\(301\) 2.25916e6 + 663350.i 1.43725 + 0.422014i
\(302\) −721959. 625581.i −0.455507 0.394699i
\(303\) 29342.6 37448.4i 0.0183608 0.0234330i
\(304\) −757998. 108984.i −0.470418 0.0676359i
\(305\) 97107.8 + 151103.i 0.0597729 + 0.0930085i
\(306\) 2.67642e6 659338.i 1.63400 0.402536i
\(307\) 1.15754e6 + 1.33588e6i 0.700958 + 0.808948i 0.988882 0.148705i \(-0.0475105\pi\)
−0.287924 + 0.957653i \(0.592965\pi\)
\(308\) 667986. 96041.8i 0.401227 0.0576878i
\(309\) −1.93371e6 1.11187e6i −1.15211 0.662456i
\(310\) 241172. + 821355.i 0.142535 + 0.485430i
\(311\) −322495. 1.09832e6i −0.189070 0.643912i −0.998399 0.0565574i \(-0.981988\pi\)
0.809330 0.587355i \(-0.199831\pi\)
\(312\) 1.71004e6 + 983258.i 0.994534 + 0.571849i
\(313\) −527309. + 75815.6i −0.304232 + 0.0437419i −0.292740 0.956192i \(-0.594567\pi\)
−0.0114916 + 0.999934i \(0.503658\pi\)
\(314\) −891739. 1.02912e6i −0.510404 0.589037i
\(315\) −1.54507e6 + 380628.i −0.877345 + 0.216135i
\(316\) −414563. 645073.i −0.233546 0.363405i
\(317\) −3.33323e6 479246.i −1.86302 0.267861i −0.883382 0.468653i \(-0.844739\pi\)
−0.979634 + 0.200792i \(0.935649\pi\)
\(318\) −1.63553e6 + 2.08734e6i −0.906963 + 1.15751i
\(319\) 98631.4 + 85464.6i 0.0542673 + 0.0470229i
\(320\) 68490.4 + 20110.6i 0.0373899 + 0.0109787i
\(321\) −611980. 57343.7i −0.331493 0.0310615i
\(322\) 618906. 2.16236e6i 0.332648 1.16222i
\(323\) 968847.i 0.516712i
\(324\) 801413. + 621102.i 0.424125 + 0.328700i
\(325\) −352516. + 406825.i −0.185127 + 0.213648i
\(326\) −439923. + 684534.i −0.229262 + 0.356739i
\(327\) 1.22989e6 + 296062.i 0.636056 + 0.153114i
\(328\) 1.44165e6 926493.i 0.739905 0.475508i
\(329\) −1.35494e6 2.96690e6i −0.690127 1.51117i
\(330\) 1.43182e6 1.02342e6i 0.723774 0.517331i
\(331\) −277145. 1.92759e6i −0.139039 0.967038i −0.933207 0.359340i \(-0.883002\pi\)
0.794168 0.607699i \(-0.207907\pi\)
\(332\) −518284. + 1.13488e6i −0.258061 + 0.565075i
\(333\) 167732. + 1.69318e6i 0.0828906 + 0.836742i
\(334\) −1.84464e6 + 541635.i −0.904785 + 0.265669i
\(335\) 1.39707e6 + 638022.i 0.680154 + 0.310616i
\(336\) −2.51693e6 + 124364.i −1.21625 + 0.0600959i
\(337\) −2.63189e6 + 2.28055e6i −1.26239 + 1.09387i −0.271047 + 0.962566i \(0.587370\pi\)
−0.991343 + 0.131301i \(0.958085\pi\)
\(338\) 7.07740e6 3.23214e6i 3.36963 1.53886i
\(339\) 463902. 240199.i 0.219244 0.113520i
\(340\) 204744. 1.42402e6i 0.0960535 0.668067i
\(341\) −616379. 396123.i −0.287053 0.184478i
\(342\) 799952. 633688.i 0.369827 0.292961i
\(343\) 627948. 2.13859e6i 0.288196 0.981506i
\(344\) 1.93653e6 0.882325
\(345\) −404947. 2.00792e6i −0.183168 0.908237i
\(346\) 2.38069e6 1.06909
\(347\) 406742. 1.38524e6i 0.181341 0.617590i −0.817775 0.575539i \(-0.804792\pi\)
0.999115 0.0420516i \(-0.0133894\pi\)
\(348\) 77690.4 + 81191.0i 0.0343890 + 0.0359385i
\(349\) −1.99858e6 1.28441e6i −0.878329 0.564468i 0.0219605 0.999759i \(-0.493009\pi\)
−0.900290 + 0.435291i \(0.856646\pi\)
\(350\) 55812.2 388183.i 0.0243534 0.169381i
\(351\) −4.41595e6 + 1.32216e6i −1.91318 + 0.572819i
\(352\) 1.59439e6 728131.i 0.685862 0.313223i
\(353\) −2.40655e6 + 2.08529e6i −1.02792 + 0.890696i −0.994071 0.108731i \(-0.965321\pi\)
−0.0338471 + 0.999427i \(0.510776\pi\)
\(354\) −126567. 2.56152e6i −0.0536798 1.08640i
\(355\) −2.07884e6 949373.i −0.875486 0.399821i
\(356\) 165384. 48561.1i 0.0691621 0.0203078i
\(357\) −608913. 3.12951e6i −0.252862 1.29959i
\(358\) −130055. + 284780.i −0.0536313 + 0.117436i
\(359\) 597561. + 4.15613e6i 0.244707 + 1.70197i 0.627891 + 0.778302i \(0.283919\pi\)
−0.383184 + 0.923672i \(0.625172\pi\)
\(360\) −1.13109e6 + 658389.i −0.459983 + 0.267748i
\(361\) 879599. + 1.92605e6i 0.355236 + 0.777858i
\(362\) −73604.4 + 47302.7i −0.0295211 + 0.0189721i
\(363\) 235009. 976261.i 0.0936089 0.388865i
\(364\) −1.42827e6 + 2.22243e6i −0.565010 + 0.879173i
\(365\) −1.07788e6 + 1.24394e6i −0.423486 + 0.488729i
\(366\) −352166. 140263.i −0.137418 0.0547319i
\(367\) 1.09533e6i 0.424504i 0.977215 + 0.212252i \(0.0680798\pi\)
−0.977215 + 0.212252i \(0.931920\pi\)
\(368\) −22170.7 3.24380e6i −0.00853413 1.24863i
\(369\) −743960. + 3.93497e6i −0.284435 + 1.50444i
\(370\) 2.44002e6 + 716455.i 0.926594 + 0.272072i
\(371\) 2.31799e6 + 2.00855e6i 0.874332 + 0.757613i
\(372\) −496596. 389106.i −0.186057 0.145784i
\(373\) 1.55837e6 + 224059.i 0.579960 + 0.0833856i 0.426051 0.904699i \(-0.359905\pi\)
0.153909 + 0.988085i \(0.450814\pi\)
\(374\) 1.90642e6 + 2.96644e6i 0.704756 + 1.09662i
\(375\) −946858. 2.72017e6i −0.347702 0.998891i
\(376\) −1.75673e6 2.02737e6i −0.640818 0.739543i
\(377\) −505690. + 72707.3i −0.183245 + 0.0263466i
\(378\) 2.18569e6 2.54966e6i 0.786790 0.917810i
\(379\) −688914. 2.34623e6i −0.246358 0.839019i −0.986104 0.166132i \(-0.946872\pi\)
0.739745 0.672887i \(-0.234946\pi\)
\(380\) −150064. 511069.i −0.0533109 0.181560i
\(381\) 999102. 1.73759e6i 0.352612 0.613248i
\(382\) 315126. 45308.3i 0.110491 0.0158862i
\(383\) 2.58564e6 + 2.98399e6i 0.900682 + 1.03944i 0.999019 + 0.0442896i \(0.0141024\pi\)
−0.0983364 + 0.995153i \(0.531352\pi\)
\(384\) −2.79859e6 + 974153.i −0.968525 + 0.337131i
\(385\) −1.10055e6 1.71249e6i −0.378406 0.588812i
\(386\) −2.63640e6 379056.i −0.900621 0.129490i
\(387\) −3.11128e6 + 3.28624e6i −1.05599 + 1.11538i
\(388\) 1.98869e6 + 1.72321e6i 0.670637 + 0.581110i
\(389\) −480344. 141042.i −0.160945 0.0472578i 0.200267 0.979741i \(-0.435819\pi\)
−0.361213 + 0.932483i \(0.617637\pi\)
\(390\) −642755. + 6.85958e6i −0.213985 + 2.28368i
\(391\) 4.05815e6 611812.i 1.34241 0.202384i
\(392\) 85500.0i 0.0281029i
\(393\) −533906. + 1.34051e6i −0.174375 + 0.437812i
\(394\) −1.17804e6 + 1.35953e6i −0.382313 + 0.441213i
\(395\) −1.25049e6 + 1.94581e6i −0.403264 + 0.627491i
\(396\) −419886. + 1.22723e6i −0.134553 + 0.393266i
\(397\) 2.31552e6 1.48809e6i 0.737348 0.473865i −0.117285 0.993098i \(-0.537419\pi\)
0.854632 + 0.519234i \(0.173783\pi\)
\(398\) 12767.8 + 27957.6i 0.00404026 + 0.00884693i
\(399\) −686390. 960297.i −0.215844 0.301977i
\(400\) −80494.7 559853.i −0.0251546 0.174954i
\(401\) −1.95485e6 + 4.28052e6i −0.607088 + 1.32934i 0.317460 + 0.948272i \(0.397170\pi\)
−0.924548 + 0.381066i \(0.875557\pi\)
\(402\) −3.18171e6 + 619069.i −0.981962 + 0.191062i
\(403\) 2.75203e6 808069.i 0.844094 0.247848i
\(404\) 47668.4 + 21769.4i 0.0145304 + 0.00663581i
\(405\) 699975. 2.97722e6i 0.212053 0.901931i
\(406\) 281290. 243739.i 0.0846915 0.0733856i
\(407\) −1.97993e6 + 904203.i −0.592466 + 0.270570i
\(408\) −1.20568e6 2.32856e6i −0.358576 0.692528i
\(409\) 367990. 2.55943e6i 0.108775 0.756545i −0.860302 0.509785i \(-0.829725\pi\)
0.969077 0.246760i \(-0.0793659\pi\)
\(410\) 5.03528e6 + 3.23598e6i 1.47933 + 0.950706i
\(411\) −92725.3 + 88727.4i −0.0270766 + 0.0259092i
\(412\) 692217. 2.35747e6i 0.200909 0.684233i
\(413\) −2.96636e6 −0.855753
\(414\) 3.15945e6 + 2.95055e6i 0.905962 + 0.846061i
\(415\) 3.76337e6 1.07265
\(416\) −1.93310e6 + 6.58355e6i −0.547674 + 1.86520i
\(417\) −734445. + 702779.i −0.206833 + 0.197915i
\(418\) 1.09828e6 + 705823.i 0.307449 + 0.197585i
\(419\) 1.00451e6 6.98649e6i 0.279523 1.94412i −0.0468984 0.998900i \(-0.514934\pi\)
0.326421 0.945224i \(-0.394157\pi\)
\(420\) −805929. 1.55651e6i −0.222933 0.430555i
\(421\) −3.45634e6 + 1.57846e6i −0.950411 + 0.434038i −0.829426 0.558616i \(-0.811332\pi\)
−0.120985 + 0.992654i \(0.538605\pi\)
\(422\) −3.48466e6 + 3.01948e6i −0.952532 + 0.825374i
\(423\) 6.26280e6 + 276107.i 1.70183 + 0.0750286i
\(424\) 2.29466e6 + 1.04793e6i 0.619873 + 0.283087i
\(425\) 686599. 201604.i 0.184387 0.0541409i
\(426\) 4.73435e6 921170.i 1.26397 0.245932i
\(427\) −182137. + 398825.i −0.0483425 + 0.105855i
\(428\) −96354.7 670162.i −0.0254251 0.176836i
\(429\) −3.42907e6 4.79745e6i −0.899565 1.25854i
\(430\) 2.80977e6 + 6.15253e6i 0.732823 + 1.60466i
\(431\) −241288. + 155066.i −0.0625665 + 0.0402091i −0.571550 0.820567i \(-0.693658\pi\)
0.508984 + 0.860776i \(0.330021\pi\)
\(432\) 1.98861e6 4.41638e6i 0.512672 1.13856i
\(433\) −673421. + 1.04786e6i −0.172610 + 0.268587i −0.916771 0.399414i \(-0.869214\pi\)
0.744160 + 0.668001i \(0.232850\pi\)
\(434\) −1.36839e6 + 1.57921e6i −0.348727 + 0.402452i
\(435\) 125423. 314907.i 0.0317800 0.0797919i
\(436\) 1.39343e6i 0.351049i
\(437\) 1.27260e6 830193.i 0.318777 0.207958i
\(438\) 324076. 3.45859e6i 0.0807164 0.861417i
\(439\) 981414. + 288169.i 0.243047 + 0.0713651i 0.400987 0.916084i \(-0.368667\pi\)
−0.157940 + 0.987449i \(0.550485\pi\)
\(440\) −1.26531e6 1.09640e6i −0.311578 0.269984i
\(441\) 145091. + 137366.i 0.0355259 + 0.0336344i
\(442\) −1.36633e7 1.96449e6i −3.32660 0.478293i
\(443\) −602768. 937925.i −0.145929 0.227069i 0.760593 0.649229i \(-0.224908\pi\)
−0.906521 + 0.422160i \(0.861272\pi\)
\(444\) −1.77001e6 + 616118.i −0.426106 + 0.148322i
\(445\) −340480. 392935.i −0.0815064 0.0940634i
\(446\) 2.17801e6 313150.i 0.518469 0.0745445i
\(447\) −3.54498e6 + 6.16527e6i −0.839160 + 1.45943i
\(448\) 49090.4 + 167187.i 0.0115558 + 0.0393556i
\(449\) 1.44905e6 + 4.93502e6i 0.339210 + 1.15524i 0.935751 + 0.352660i \(0.114723\pi\)
−0.596542 + 0.802582i \(0.703459\pi\)
\(450\) 615538. + 435046.i 0.143293 + 0.101275i
\(451\) −5.07091e6 + 729086.i −1.17394 + 0.168786i
\(452\) 376824. + 434878.i 0.0867545 + 0.100120i
\(453\) −698133. 2.00562e6i −0.159843 0.459202i
\(454\) −2.52569e6 3.93006e6i −0.575097 0.894868i
\(455\) 7.88767e6 + 1.13408e6i 1.78616 + 0.256811i
\(456\) −764182. 598772.i −0.172102 0.134850i
\(457\) 1.64555e6 + 1.42588e6i 0.368570 + 0.319368i 0.819378 0.573253i \(-0.194319\pi\)
−0.450808 + 0.892621i \(0.648864\pi\)
\(458\) −3.80328e6 1.11674e6i −0.847217 0.248765i
\(459\) 5.88858e6 + 1.69512e6i 1.30460 + 0.375550i
\(460\) 2.04592e6 951294.i 0.450811 0.209614i
\(461\) 436249.i 0.0956054i 0.998857 + 0.0478027i \(0.0152219\pi\)
−0.998857 + 0.0478027i \(0.984778\pi\)
\(462\) 3.99120e6 + 1.58964e6i 0.869959 + 0.346493i
\(463\) −4.94441e6 + 5.70615e6i −1.07192 + 1.23706i −0.101704 + 0.994815i \(0.532429\pi\)
−0.970215 + 0.242246i \(0.922116\pi\)
\(464\) 290218. 451587.i 0.0625790 0.0973748i
\(465\) −445374. + 1.85015e6i −0.0955195 + 0.396802i
\(466\) 4.39899e6 2.82706e6i 0.938401 0.603074i
\(467\) 1.65486e6 + 3.62363e6i 0.351130 + 0.768868i 0.999968 + 0.00794151i \(0.00252789\pi\)
−0.648838 + 0.760926i \(0.724745\pi\)
\(468\) −2.55433e6 4.38827e6i −0.539091 0.926143i
\(469\) 533551. + 3.71093e6i 0.112007 + 0.779023i
\(470\) 3.89225e6 8.52284e6i 0.812749 1.77967i
\(471\) −578161. 2.97146e6i −0.120087 0.617188i
\(472\) −2.34090e6 + 687351.i −0.483647 + 0.142012i
\(473\) −5.26605e6 2.40493e6i −1.08226 0.494253i
\(474\) −240902. 4.87550e6i −0.0492487 0.996719i
\(475\) 200224. 173495.i 0.0407177 0.0352820i
\(476\) 3.19446e6 1.45886e6i 0.646220 0.295119i
\(477\) −5.46497e6 + 2.21033e6i −1.09974 + 0.444797i
\(478\) 297108. 2.06643e6i 0.0594764 0.413667i
\(479\) 3.66233e6 + 2.35363e6i 0.729320 + 0.468706i 0.851868 0.523757i \(-0.175470\pi\)
−0.122548 + 0.992463i \(0.539106\pi\)
\(480\) −3.14738e6 3.28920e6i −0.623514 0.651608i
\(481\) 2.40055e6 8.17553e6i 0.473095 1.61121i
\(482\) −2.60538e6 −0.510802
\(483\) 3.58889e6 3.48145e6i 0.699991 0.679036i
\(484\) 1.10608e6 0.214621
\(485\) 2.23623e6 7.61591e6i 0.431681 1.47017i
\(486\) 2.45189e6 + 5.97077e6i 0.470880 + 1.14667i
\(487\) −7.74493e6 4.97737e6i −1.47977 0.950993i −0.997172 0.0751525i \(-0.976056\pi\)
−0.482601 0.875840i \(-0.660308\pi\)
\(488\) −51319.9 + 356938.i −0.00975520 + 0.0678489i
\(489\) −1.60636e6 + 831738.i −0.303787 + 0.157295i
\(490\) 271641. 124054.i 0.0511099 0.0233411i
\(491\) 5.38697e6 4.66784e6i 1.00842 0.873800i 0.0163971 0.999866i \(-0.494780\pi\)
0.992022 + 0.126066i \(0.0402350\pi\)
\(492\) −4.40581e6 + 217695.i −0.820565 + 0.0405448i
\(493\) 617767. + 282125.i 0.114474 + 0.0522786i
\(494\) −4.90365e6 + 1.43984e6i −0.904070 + 0.265459i
\(495\) 3.89344e6 385698.i 0.714202 0.0707513i
\(496\) −1.25193e6 + 2.74135e6i −0.228495 + 0.500334i
\(497\) −793919. 5.52183e6i −0.144173 1.00275i
\(498\) −6.46152e6 + 4.61850e6i −1.16751 + 0.834502i
\(499\) 3.99399e6 + 8.74561e6i 0.718051 + 1.57231i 0.816616 + 0.577181i \(0.195847\pi\)
−0.0985653 + 0.995131i \(0.531425\pi\)
\(500\) 2.66898e6 1.71525e6i 0.477441 0.306833i
\(501\) −4.15516e6 1.00024e6i −0.739593 0.178037i
\(502\) −3.34916e6 + 5.21140e6i −0.593167 + 0.922986i
\(503\) −1.23333e6 + 1.42334e6i −0.217350 + 0.250836i −0.853945 0.520362i \(-0.825797\pi\)
0.636595 + 0.771198i \(0.280342\pi\)
\(504\) −2.84474e6 1.45383e6i −0.498845 0.254940i
\(505\) 158073.i 0.0275821i
\(506\) −2.26289e6 + 5.04602e6i −0.392904 + 0.876139i
\(507\) 1.72210e7 + 1.61364e6i 2.97536 + 0.278797i
\(508\) 2.11838e6 + 622012.i 0.364204 + 0.106940i
\(509\) −7.30985e6 6.33402e6i −1.25059 1.08364i −0.993089 0.117361i \(-0.962557\pi\)
−0.257497 0.966279i \(-0.582898\pi\)
\(510\) 5.64869e6 7.20912e6i 0.961661 1.22732i
\(511\) −3.97695e6 571800.i −0.673749 0.0968705i
\(512\) −1.59750e6 2.48576e6i −0.269318 0.419068i
\(513\) 2.24385e6 334793.i 0.376445 0.0561673i
\(514\) −5.31611e6 6.13512e6i −0.887537 1.02427i
\(515\) −7.33590e6 + 1.05474e6i −1.21881 + 0.175238i
\(516\) −4.32135e6 2.48474e6i −0.714489 0.410825i
\(517\) 2.25937e6 + 7.69471e6i 0.371759 + 1.26609i
\(518\) 1.74888e6 + 5.95614e6i 0.286376 + 0.975306i
\(519\) 4.58803e6 + 2.63808e6i 0.747666 + 0.429902i
\(520\) 6.48735e6 932740.i 1.05211 0.151270i
\(521\) 4.90106e6 + 5.65613e6i 0.791036 + 0.912904i 0.997854 0.0654756i \(-0.0208565\pi\)
−0.206819 + 0.978379i \(0.566311\pi\)
\(522\) 171116. + 694602.i 0.0274861 + 0.111573i
\(523\) −4.67980e6 7.28191e6i −0.748123 1.16410i −0.981453 0.191704i \(-0.938599\pi\)
0.233330 0.972398i \(-0.425038\pi\)
\(524\) −1.57321e6 226193.i −0.250298 0.0359874i
\(525\) 537711. 686253.i 0.0851434 0.108664i
\(526\) 7.26955e6 + 6.29911e6i 1.14563 + 0.992692i
\(527\) −3.65834e6 1.07419e6i −0.573797 0.168482i
\(528\) 6.16902e6 + 578049.i 0.963012 + 0.0902359i
\(529\) 4.28100e6 + 4.80620e6i 0.665130 + 0.746728i
\(530\) 8.81080e6i 1.36247i
\(531\) 2.59454e6 5.07677e6i 0.399323 0.781360i
\(532\) 851449. 982625.i 0.130431 0.150525i
\(533\) 1.08425e7 1.68712e7i 1.65314 2.57234i
\(534\) 1.06681e6 + 256805.i 0.161895 + 0.0389718i
\(535\) −1.71807e6 + 1.10414e6i −0.259511 + 0.166778i
\(536\) 1.28093e6 + 2.80485e6i 0.192581 + 0.421694i
\(537\) −566208. + 404708.i −0.0847306 + 0.0605628i
\(538\) −1.25590e6 8.73500e6i −0.187068 1.30109i
\(539\) −106180. + 232502.i −0.0157424 + 0.0344711i
\(540\) 3.36880e6 17896.2i 0.497154 0.00264105i
\(541\) −6.40376e6 + 1.88031e6i −0.940681 + 0.276209i −0.715902 0.698201i \(-0.753984\pi\)
−0.224779 + 0.974410i \(0.572166\pi\)
\(542\) −3.62337e6 1.65474e6i −0.529804 0.241953i
\(543\) −194266. + 9598.84i −0.0282747 + 0.00139707i
\(544\) 6.89330e6 5.97308e6i 0.998688 0.865368i
\(545\) 3.82332e6 1.74605e6i 0.551379 0.251806i
\(546\) −1.49345e7 + 7.73279e6i −2.14393 + 1.11008i
\(547\) −1.20313e6 + 8.36795e6i −0.171927 + 1.19578i 0.702880 + 0.711308i \(0.251897\pi\)
−0.874807 + 0.484471i \(0.839012\pi\)
\(548\) −118924. 76427.5i −0.0169167 0.0108717i
\(549\) −523262. 660553.i −0.0740948 0.0935356i
\(550\) −271663. + 925198.i −0.0382933 + 0.130415i
\(551\) 251441. 0.0352824
\(552\) 2.02547e6 3.57900e6i 0.282930 0.499935i
\(553\) −5.64605e6 −0.785113
\(554\) 2.66849e6 9.08803e6i 0.369395 1.25804i
\(555\) 3.90846e6 + 4.08456e6i 0.538608 + 0.562877i
\(556\) −941951. 605355.i −0.129224 0.0830469i
\(557\) 822059. 5.71754e6i 0.112270 0.780857i −0.853432 0.521205i \(-0.825483\pi\)
0.965702 0.259653i \(-0.0836080\pi\)
\(558\) −1.50586e6 3.72319e6i −0.204738 0.506209i
\(559\) 2.06146e7 9.41439e6i 2.79027 1.27427i
\(560\) −6.32786e6 + 5.48313e6i −0.852682 + 0.738853i
\(561\) 386858. + 7.82941e6i 0.0518972 + 1.05032i
\(562\) −8.02196e6 3.66351e6i −1.07137 0.489279i
\(563\) −6.97252e6 + 2.04732e6i −0.927083 + 0.272216i −0.710215 0.703985i \(-0.751402\pi\)
−0.216868 + 0.976201i \(0.569584\pi\)
\(564\) 1.31882e6 + 6.77810e6i 0.174578 + 0.897243i
\(565\) 721045. 1.57887e6i 0.0950258 0.208077i
\(566\) 69859.2 + 485882.i 0.00916606 + 0.0637514i
\(567\) 7.03754e6 2.49167e6i 0.919313 0.325487i
\(568\) −1.90602e6 4.17360e6i −0.247888 0.542800i
\(569\) 3.03313e6 1.94927e6i 0.392744 0.252401i −0.329333 0.944214i \(-0.606824\pi\)
0.722077 + 0.691813i \(0.243188\pi\)
\(570\) 793580. 3.29665e6i 0.102307 0.424997i
\(571\) −3.10937e6 + 4.83827e6i −0.399100 + 0.621012i −0.981403 0.191960i \(-0.938516\pi\)
0.582302 + 0.812972i \(0.302152\pi\)
\(572\) 4.25367e6 4.90899e6i 0.543592 0.627339i
\(573\) 657513. + 261879.i 0.0836600 + 0.0333207i
\(574\) 1.46106e7i 1.85093i
\(575\) 853148. + 729108.i 0.107610 + 0.0919649i
\(576\) −329068. 62214.8i −0.0413266 0.00781336i
\(577\) 7.55623e6 + 2.21871e6i 0.944856 + 0.277435i 0.717644 0.696410i \(-0.245221\pi\)
0.227212 + 0.973845i \(0.427039\pi\)
\(578\) 6.34337e6 + 5.49656e6i 0.789769 + 0.684339i
\(579\) −4.66078e6 3.65194e6i −0.577780 0.452718i
\(580\) 369572. + 53136.4i 0.0456172 + 0.00655877i
\(581\) 4.96658e6 + 7.72815e6i 0.610403 + 0.949806i
\(582\) 5.50692e6 + 1.58205e7i 0.673909 + 1.93603i
\(583\) −4.93851e6 5.69934e6i −0.601762 0.694470i
\(584\) −3.27091e6 + 470286.i −0.396860 + 0.0570598i
\(585\) −8.83991e6 + 1.25074e7i −1.06797 + 1.51105i
\(586\) 5.25215e6 + 1.78872e7i 0.631820 + 2.15178i
\(587\) 2.83015e6 + 9.63860e6i 0.339011 + 1.15457i 0.935907 + 0.352247i \(0.114582\pi\)
−0.596896 + 0.802319i \(0.703599\pi\)
\(588\) −109704. + 190793.i −0.0130852 + 0.0227572i
\(589\) −1.39726e6 + 200896.i −0.165955 + 0.0238607i
\(590\) −5.58026e6 6.43996e6i −0.659970 0.761646i
\(591\) −3.77682e6 + 1.31466e6i −0.444792 + 0.154827i
\(592\) 4.84028e6 + 7.53162e6i 0.567631 + 0.883251i
\(593\) 5.56068e6 + 799505.i 0.649368 + 0.0933651i 0.459125 0.888372i \(-0.348163\pi\)
0.190244 + 0.981737i \(0.439072\pi\)
\(594\) −6.21152e6 + 5.44035e6i −0.722324 + 0.632646i
\(595\) −8.00574e6 6.93701e6i −0.927062 0.803304i
\(596\) −7.51636e6 2.20700e6i −0.866746 0.254499i
\(597\) −6374.32 + 68027.7i −0.000731978 + 0.00781178i
\(598\) −9.12755e6 1.96304e7i −1.04376 2.24479i
\(599\) 1.28506e7i 1.46337i −0.681642 0.731686i \(-0.738734\pi\)
0.681642 0.731686i \(-0.261266\pi\)
\(600\) 265320. 666154.i 0.0300879 0.0755434i
\(601\) 7.35026e6 8.48265e6i 0.830074 0.957956i −0.169546 0.985522i \(-0.554230\pi\)
0.999620 + 0.0275662i \(0.00877570\pi\)
\(602\) −8.92624e6 + 1.38895e7i −1.00387 + 1.56205i
\(603\) −6.81773e6 2.33264e6i −0.763566 0.261248i
\(604\) 1.96788e6 1.26468e6i 0.219486 0.141055i
\(605\) −1.38598e6 3.03488e6i −0.153947 0.337096i
\(606\) 193990. + 271403.i 0.0214585 + 0.0300215i
\(607\) −18315.1 127384.i −0.00201761 0.0140328i 0.988788 0.149328i \(-0.0477109\pi\)
−0.990805 + 0.135295i \(0.956802\pi\)
\(608\) 1.40284e6 3.07180e6i 0.153904 0.337003i
\(609\) 812190. 158029.i 0.0887390 0.0172661i
\(610\) −1.20848e6 + 354843.i −0.131497 + 0.0386110i
\(611\) −2.85566e7 1.30414e7i −3.09459 1.41325i
\(612\) −297285. + 6.74316e6i −0.0320844 + 0.727755i
\(613\) −5.17199e6 + 4.48156e6i −0.555913 + 0.481701i −0.886917 0.461928i \(-0.847158\pi\)
0.331005 + 0.943629i \(0.392612\pi\)
\(614\) −1.12748e7 + 5.14902e6i −1.20694 + 0.551193i
\(615\) 6.11808e6 + 1.18160e7i 0.652270 + 1.25975i
\(616\) 581623. 4.04528e6i 0.0617576 0.429533i
\(617\) 8.42090e6 + 5.41178e6i 0.890524 + 0.572305i 0.903966 0.427605i \(-0.140642\pi\)
−0.0134418 + 0.999910i \(0.504279\pi\)
\(618\) 1.13010e7 1.08137e7i 1.19027 1.13895i
\(619\) −2.23459e6 + 7.61032e6i −0.234407 + 0.798319i 0.755321 + 0.655356i \(0.227481\pi\)
−0.989728 + 0.142963i \(0.954337\pi\)
\(620\) −2.09617e6 −0.219001
\(621\) 2.81929e6 + 9.18728e6i 0.293366 + 0.956000i
\(622\) 8.02674e6 0.831885
\(623\) 357562. 1.21774e6i 0.0369089 0.125700i
\(624\) −1.75247e7 + 1.67691e7i −1.80172 + 1.72404i
\(625\) −6.88783e6 4.42654e6i −0.705314 0.453278i
\(626\) 531633. 3.69759e6i 0.0542221 0.377123i
\(627\) 1.33446e6 + 2.57727e6i 0.135561 + 0.261813i
\(628\) 3.03313e6 1.38518e6i 0.306897 0.140155i
\(629\) −8.56019e6 + 7.41745e6i −0.862694 + 0.747528i
\(630\) 491453. 1.11474e7i 0.0493322 1.11898i
\(631\) −1.55317e7 7.09308e6i −1.55291 0.709188i −0.560044 0.828463i \(-0.689216\pi\)
−0.992861 + 0.119274i \(0.961943\pi\)
\(632\) −4.45559e6 + 1.30828e6i −0.443723 + 0.130289i
\(633\) −1.00615e7 + 1.95768e6i −0.998054 + 0.194193i
\(634\) 9.80943e6 2.14797e7i 0.969216 2.12229i
\(635\) −947770. 6.59189e6i −0.0932758 0.648747i
\(636\) −3.77591e6 5.28271e6i −0.370151 0.517861i
\(637\) −415656. 910159.i −0.0405869 0.0888728i
\(638\) −769870. + 494766.i −0.0748800 + 0.0481225i
\(639\) 1.01447e7 + 3.47094e6i 0.982853 + 0.336276i
\(640\) −5.32305e6 + 8.28283e6i −0.513701 + 0.799335i
\(641\) −869080. + 1.00297e6i −0.0835439 + 0.0964148i −0.795982 0.605320i \(-0.793045\pi\)
0.712439 + 0.701734i \(0.247591\pi\)
\(642\) 1.59482e6 4.00421e6i 0.152712 0.383424i
\(643\) 3.98880e6i 0.380465i −0.981739 0.190233i \(-0.939076\pi\)
0.981739 0.190233i \(-0.0609242\pi\)
\(644\) 4.65354e6 + 2.94590e6i 0.442149 + 0.279900i
\(645\) −1.40277e6 + 1.49706e7i −0.132766 + 1.41690i
\(646\) 6.51854e6 + 1.91402e6i 0.614567 + 0.180453i
\(647\) 273749. + 237205.i 0.0257094 + 0.0222773i 0.667621 0.744502i \(-0.267313\pi\)
−0.641911 + 0.766779i \(0.721858\pi\)
\(648\) 4.97633e6 3.59702e6i 0.465555 0.336515i
\(649\) 7.21928e6 + 1.03798e6i 0.672794 + 0.0967332i
\(650\) −2.04076e6 3.17549e6i −0.189456 0.294800i
\(651\) −4.38708e6 + 1.52709e6i −0.405717 + 0.141225i
\(652\) −1.30483e6 1.50585e6i −0.120208 0.138728i
\(653\) 1.39035e7 1.99903e6i 1.27598 0.183458i 0.529180 0.848510i \(-0.322500\pi\)
0.746797 + 0.665052i \(0.231591\pi\)
\(654\) −4.42167e6 + 7.68996e6i −0.404242 + 0.703040i
\(655\) 1.35069e6 + 4.60004e6i 0.123014 + 0.418947i
\(656\) 5.93668e6 + 2.02185e7i 0.538622 + 1.83438i
\(657\) 4.45707e6 6.30623e6i 0.402843 0.569975i
\(658\) 2.26385e7 3.25492e6i 2.03837 0.293073i
\(659\) 1.04333e7 + 1.20406e7i 0.935851 + 1.08003i 0.996642 + 0.0818787i \(0.0260920\pi\)
−0.0607917 + 0.998150i \(0.519363\pi\)
\(660\) 1.41676e6 + 4.07012e6i 0.126601 + 0.363703i
\(661\) −4.65089e6 7.23693e6i −0.414031 0.644244i 0.570124 0.821559i \(-0.306895\pi\)
−0.984154 + 0.177315i \(0.943259\pi\)
\(662\) 1.35166e7 + 1.94339e6i 1.19873 + 0.172352i
\(663\) −2.41549e7 1.89265e7i −2.13413 1.67219i
\(664\) 5.71012e6 + 4.94784e6i 0.502603 + 0.435508i
\(665\) −3.76307e6 1.10494e6i −0.329981 0.0968911i
\(666\) −1.17233e7 2.21645e6i −1.02415 0.193630i
\(667\) 158781. + 1.05320e6i 0.0138193 + 0.0916632i
\(668\) 4.70768e6i 0.408193i
\(669\) 4.54443e6 + 1.80999e6i 0.392567 + 0.156354i
\(670\) −7.05271e6 + 8.13927e6i −0.606973 + 0.700484i
\(671\) 582827. 906896.i 0.0499727 0.0777591i
\(672\) 2.60078e6 1.08040e7i 0.222167 0.922915i
\(673\) 8.59636e6 5.52454e6i 0.731605 0.470174i −0.121051 0.992646i \(-0.538627\pi\)
0.852656 + 0.522472i \(0.174990\pi\)
\(674\) −1.01444e7 2.22131e7i −0.860154 1.88347i
\(675\) 704175. + 1.52050e6i 0.0594869 + 0.128448i
\(676\) 2.71141e6 + 1.88583e7i 0.228207 + 1.58721i
\(677\) 8.37520e6 1.83391e7i 0.702301 1.53782i −0.134858 0.990865i \(-0.543058\pi\)
0.837159 0.546960i \(-0.184215\pi\)
\(678\) 699625. + 3.59573e6i 0.0584509 + 0.300409i
\(679\) 1.85906e7 5.45869e6i 1.54746 0.454375i
\(680\) −7.92515e6 3.61930e6i −0.657257 0.300159i
\(681\) −512524. 1.03727e7i −0.0423493 0.857085i
\(682\) 3.88287e6 3.36452e6i 0.319662 0.276989i
\(683\) 992680. 453342.i 0.0814250 0.0371855i −0.374286 0.927313i \(-0.622112\pi\)
0.455711 + 0.890128i \(0.349385\pi\)
\(684\) 936988. + 2.31667e6i 0.0765762 + 0.189332i
\(685\) −60685.2 + 422075.i −0.00494147 + 0.0343687i
\(686\) 1.31482e7 + 8.44985e6i 1.06674 + 0.685549i
\(687\) −6.09215e6 6.36665e6i −0.492468 0.514658i
\(688\) −6.70864e6 + 2.28475e7i −0.540335 + 1.84021i
\(689\) 2.95214e7 2.36913
\(690\) 1.43096e7 + 1.24224e6i 1.14421 + 0.0993303i
\(691\) 1.57855e7 1.25766 0.628831 0.777542i \(-0.283534\pi\)
0.628831 + 0.777542i \(0.283534\pi\)
\(692\) −1.64239e6 + 5.59347e6i −0.130380 + 0.444034i
\(693\) 5.93028e6 + 7.48625e6i 0.469075 + 0.592149i
\(694\) 8.51653e6 + 5.47324e6i 0.671219 + 0.431366i
\(695\) −480666. + 3.34310e6i −0.0377469 + 0.262535i
\(696\) 604323. 312906.i 0.0472875 0.0244845i
\(697\) −2.42503e7 + 1.10747e7i −1.89075 + 0.863477i
\(698\) 1.25900e7 1.09093e7i 0.978108 0.847536i
\(699\) 1.16104e7 573678.i 0.898780 0.0444094i
\(700\) 873537. + 398931.i 0.0673808 + 0.0307718i
\(701\) −1.79461e7 + 5.26945e6i −1.37935 + 0.405015i −0.885544 0.464556i \(-0.846214\pi\)
−0.493809 + 0.869570i \(0.664396\pi\)
\(702\) −171712. 3.23232e7i −0.0131510 2.47555i
\(703\) −1.74207e6 + 3.81460e6i −0.132947 + 0.291112i
\(704\) −60971.0 424063.i −0.00463652 0.0322477i
\(705\) 1.69454e7 1.21120e7i 1.28404 0.917791i
\(706\) −9.27584e6 2.03113e7i −0.700392 1.53365i
\(707\) 324605. 208611.i 0.0244234 0.0156960i
\(708\) 6.10564e6 + 1.46977e6i 0.457771 + 0.110196i
\(709\) 3.98461e6 6.20017e6i 0.297694 0.463221i −0.659895 0.751358i \(-0.729399\pi\)
0.957589 + 0.288137i \(0.0930357\pi\)
\(710\) 1.04944e7 1.21112e7i 0.781288 0.901654i
\(711\) 4.93835e6 9.66293e6i 0.366360 0.716861i
\(712\) 1.04384e6i 0.0771672i
\(713\) −1.72383e6 5.72576e6i −0.126990 0.421802i
\(714\) 2.22587e7 + 2.08568e6i 1.63401 + 0.153110i
\(715\) −1.87996e7 5.52005e6i −1.37525 0.403811i
\(716\) −579373. 502030.i −0.0422353 0.0365971i
\(717\) 2.86243e6 3.65316e6i 0.207939 0.265382i
\(718\) −2.91436e7 4.19021e6i −2.10975 0.303337i
\(719\) 6.74984e6 + 1.05030e7i 0.486935 + 0.757686i 0.994590 0.103874i \(-0.0331239\pi\)
−0.507655 + 0.861560i \(0.669488\pi\)
\(720\) −3.84939e6 1.56257e7i −0.276733 1.12333i
\(721\) −1.18472e7 1.36724e7i −0.848748 0.979508i
\(722\) −1.46965e7 + 2.11303e6i −1.04923 + 0.150856i
\(723\) −5.02104e6 2.88706e6i −0.357230 0.205404i
\(724\) −60360.2 205568.i −0.00427961 0.0145750i
\(725\) 52321.4 + 178190.i 0.00369687 + 0.0125904i
\(726\) 6.10415e6 + 3.50984e6i 0.429817 + 0.247141i
\(727\) −1.35955e7 + 1.95474e6i −0.954023 + 0.137168i −0.601710 0.798715i \(-0.705514\pi\)
−0.352313 + 0.935882i \(0.614605\pi\)
\(728\) 1.04769e7 + 1.20909e7i 0.732661 + 0.845535i
\(729\) −1.89105e6 + 1.42237e7i −0.131791 + 0.991278i
\(730\) −6.24000e6 9.70962e6i −0.433388 0.674365i
\(731\) −2.98194e7 4.28738e6i −2.06398 0.296755i
\(732\) 572503. 730655.i 0.0394912 0.0504005i
\(733\) 1.81401e7 + 1.57185e7i 1.24704 + 1.08057i 0.993570 + 0.113223i \(0.0361173\pi\)
0.253470 + 0.967343i \(0.418428\pi\)
\(734\) −7.36957e6 2.16390e6i −0.504896 0.148251i
\(735\) 660968. + 61933.9i 0.0451297 + 0.00422873i
\(736\) 1.37525e7 + 3.93621e6i 0.935811 + 0.267845i
\(737\) 9.21805e6i 0.625130i
\(738\) −2.50053e7 1.27793e7i −1.69002 0.863703i
\(739\) 2.39380e6 2.76259e6i 0.161241 0.186082i −0.669380 0.742920i \(-0.733440\pi\)
0.830621 + 0.556838i \(0.187986\pi\)
\(740\) −3.36664e6 + 5.23860e6i −0.226005 + 0.351671i
\(741\) −1.10457e7 2.65897e6i −0.739008 0.177896i
\(742\) −1.80931e7 + 1.16278e7i −1.20644 + 0.775329i
\(743\) 889041. + 1.94673e6i 0.0590812 + 0.129370i 0.936870 0.349678i \(-0.113709\pi\)
−0.877789 + 0.479048i \(0.840982\pi\)
\(744\) −3.10822e6 + 2.22166e6i −0.205864 + 0.147145i
\(745\) 3.36285e6 + 2.33891e7i 0.221981 + 1.54391i
\(746\) −4.58616e6 + 1.00423e7i −0.301718 + 0.660671i
\(747\) −1.75704e7 + 1.74058e6i −1.15207 + 0.114128i
\(748\) −8.28491e6 + 2.43267e6i −0.541419 + 0.158975i
\(749\) −4.53473e6 2.07094e6i −0.295357 0.134885i
\(750\) 2.01723e7 996729.i 1.30949 0.0647029i
\(751\) −3.65247e6 + 3.16489e6i −0.236313 + 0.204766i −0.764964 0.644073i \(-0.777243\pi\)
0.528651 + 0.848839i \(0.322698\pi\)
\(752\) 3.00050e7 1.37028e7i 1.93486 0.883621i
\(753\) −1.22293e7 + 6.33207e6i −0.785984 + 0.406966i
\(754\) 509837. 3.54599e6i 0.0326590 0.227148i
\(755\) −5.93594e6 3.81480e6i −0.378985 0.243559i
\(756\) 4.48261e6 + 6.89427e6i 0.285250 + 0.438716i
\(757\) 3.78507e6 1.28908e7i 0.240068 0.817597i −0.748016 0.663681i \(-0.768993\pi\)
0.988084 0.153916i \(-0.0491885\pi\)
\(758\) 1.71467e7 1.08395
\(759\) −9.95258e6 + 7.21707e6i −0.627092 + 0.454733i
\(760\) −3.22567e6 −0.202575
\(761\) −3.26322e6 + 1.11135e7i −0.204260 + 0.695647i 0.792099 + 0.610393i \(0.208988\pi\)
−0.996359 + 0.0852541i \(0.972830\pi\)
\(762\) 9.71700e6 + 1.01548e7i 0.606240 + 0.633556i
\(763\) 8.63126e6 + 5.54697e6i 0.536738 + 0.344941i
\(764\) −110947. + 771651.i −0.00687672 + 0.0478286i
\(765\) 1.88746e7 7.63392e6i 1.16607 0.471622i
\(766\) −2.51848e7 + 1.15015e7i −1.55084 + 0.708245i
\(767\) −2.15777e7 + 1.86972e7i −1.32439 + 1.14759i
\(768\) −991534. 2.00672e7i −0.0606603 1.22767i
\(769\) −5.79720e6 2.64749e6i −0.353511 0.161443i 0.230742 0.973015i \(-0.425885\pi\)
−0.584252 + 0.811572i \(0.698612\pi\)
\(770\) 1.36961e7 4.02154e6i 0.832473 0.244436i
\(771\) −3.44671e6 1.77144e7i −0.208818 1.07322i
\(772\) 2.70940e6 5.93275e6i 0.163617 0.358272i
\(773\) 1.38345e6 + 9.62209e6i 0.0832748 + 0.579189i 0.988148 + 0.153507i \(0.0490568\pi\)
−0.904873 + 0.425682i \(0.860034\pi\)
\(774\) −1.59638e7 2.74253e7i −0.957819 1.64550i
\(775\) −433120. 948401.i −0.0259033 0.0567202i
\(776\) 1.34059e7 8.61547e6i 0.799177 0.513600i
\(777\) −3.22968e6 + 1.34166e7i −0.191914 + 0.797239i
\(778\) 1.89790e6 2.95319e6i 0.112415 0.174921i
\(779\) −6.46364e6 + 7.45944e6i −0.381622 + 0.440415i
\(780\) −1.56733e7 6.24245e6i −0.922408 0.367383i
\(781\) 1.37164e7i 0.804660i
\(782\) −3.90077e6 + 2.85125e7i −0.228104 + 1.66732i
\(783\) −439928. + 1.52824e6i −0.0256435 + 0.0890816i
\(784\) 1.00874e6 + 296194.i 0.0586126 + 0.0172102i
\(785\) −7.60142e6 6.58667e6i −0.440272 0.381497i
\(786\) −7.96436e6 6.24045e6i −0.459827 0.360296i
\(787\) 2.52354e7 + 3.62830e6i 1.45236 + 0.208817i 0.822886 0.568207i \(-0.192363\pi\)
0.629471 + 0.777024i \(0.283272\pi\)
\(788\) −2.38153e6 3.70574e6i −0.136628 0.212598i
\(789\) 7.02964e6 + 2.01950e7i 0.402013 + 1.15492i
\(790\) −1.06212e7 1.22576e7i −0.605491 0.698774i
\(791\) 4.19381e6 602979.i 0.238324 0.0342658i
\(792\) 6.41457e6 + 4.53364e6i 0.363375 + 0.256823i
\(793\) 1.18894e6 + 4.04914e6i 0.0671390 + 0.228655i
\(794\) 5.43766e6 + 1.85190e7i 0.306098 + 1.04248i
\(795\) −9.76338e6 + 1.69800e7i −0.547876 + 0.952842i
\(796\) −74495.1 + 10710.8i −0.00416721 + 0.000599154i
\(797\) 8.70409e6 + 1.00451e7i 0.485375 + 0.560153i 0.944624 0.328155i \(-0.106427\pi\)
−0.459249 + 0.888308i \(0.651881\pi\)
\(798\) 7.81703e6 2.72101e6i 0.434545 0.151260i
\(799\) 2.25622e7 + 3.51074e7i 1.25030 + 1.94550i
\(800\) 2.46882e6 + 354963.i 0.136384 + 0.0196091i
\(801\) 1.77136e6 + 1.67706e6i 0.0975498 + 0.0923562i
\(802\) −2.49380e7 2.16089e7i −1.36907 1.18631i
\(803\) 9.47871e6 + 2.78320e6i 0.518753 + 0.152320i
\(804\) 740483. 7.90255e6i 0.0403994 0.431149i
\(805\) 2.25187e6 1.64599e7i 0.122476 0.895237i
\(806\) 2.01125e7i 1.09050i
\(807\) 7.25903e6 1.82256e7i 0.392369 0.985142i
\(808\) 207824. 239842.i 0.0111987 0.0129240i
\(809\) −1.21997e6 + 1.89831e6i −0.0655358 + 0.101976i −0.872475 0.488659i \(-0.837486\pi\)
0.806939 + 0.590635i \(0.201123\pi\)
\(810\) 1.86483e7 + 1.05912e7i 0.998682 + 0.567196i
\(811\) 6.24004e6 4.01023e6i 0.333146 0.214100i −0.363363 0.931647i \(-0.618372\pi\)
0.696510 + 0.717547i \(0.254735\pi\)
\(812\) 378613. + 829047.i 0.0201514 + 0.0441255i
\(813\) −5.14927e6 7.20410e6i −0.273224 0.382255i
\(814\) −2.17214e6 1.51075e7i −0.114902 0.799159i
\(815\) −2.49677e6 + 5.46716e6i −0.131669 + 0.288315i
\(816\) 3.16495e7 6.15810e6i 1.66396 0.323758i
\(817\) −1.07019e7 + 3.14236e6i −0.560926 + 0.164703i
\(818\) 1.64932e7 + 7.53220e6i 0.861831 + 0.393585i
\(819\) −3.73504e7 1.64666e6i −1.94574 0.0857817i
\(820\) −1.10767e7 + 9.59804e6i −0.575277 + 0.498480i
\(821\) −7.38030e6 + 3.37047e6i −0.382134 + 0.174515i −0.597215 0.802081i \(-0.703726\pi\)
0.215080 + 0.976596i \(0.430999\pi\)
\(822\) −413786. 799156.i −0.0213598 0.0412527i
\(823\) 1.03241e6 7.18054e6i 0.0531313 0.369537i −0.945858 0.324582i \(-0.894776\pi\)
0.998989 0.0449549i \(-0.0143144\pi\)
\(824\) −1.25174e7 8.04443e6i −0.642237 0.412741i
\(825\) −1.54877e6 + 1.48199e6i −0.0792231 + 0.0758074i
\(826\) 5.86022e6 1.99581e7i 0.298857 1.01781i
\(827\) −2.98197e7 −1.51614 −0.758072 0.652171i \(-0.773858\pi\)
−0.758072 + 0.652171i \(0.773858\pi\)
\(828\) −9.11200e6 + 5.38764e6i −0.461889 + 0.273101i
\(829\) 1.03159e6 0.0521340 0.0260670 0.999660i \(-0.491702\pi\)
0.0260670 + 0.999660i \(0.491702\pi\)
\(830\) −7.43477e6 + 2.53205e7i −0.374604 + 1.27578i
\(831\) 1.52133e7 1.45573e7i 0.764222 0.731272i
\(832\) 1.41088e6 + 906719.i 0.0706614 + 0.0454113i
\(833\) −189292. + 1.31656e6i −0.00945193 + 0.0657396i
\(834\) −3.27746e6 6.32983e6i −0.163163 0.315121i
\(835\) −1.29171e7 + 5.89902e6i −0.641132 + 0.292795i
\(836\) −2.41602e6 + 2.09350e6i −0.119560 + 0.103599i
\(837\) 1.22365e6 8.84394e6i 0.0603731 0.436347i
\(838\) 4.50217e7 + 2.05607e7i 2.21468 + 1.01141i
\(839\) −1.58104e7 + 4.64236e6i −0.775422 + 0.227685i −0.645419 0.763829i \(-0.723317\pi\)
−0.130004 + 0.991514i \(0.541499\pi\)
\(840\) −1.04193e7 + 2.02731e6i −0.509498 + 0.0991337i
\(841\) 8.44742e6 1.84973e7i 0.411845 0.901815i
\(842\) −3.79188e6 2.63731e7i −0.184321 1.28198i
\(843\) −1.14002e7 1.59495e7i −0.552515 0.772998i
\(844\) −4.69031e6 1.02703e7i −0.226645 0.496282i
\(845\) 4.83463e7 3.10703e7i 2.32928 1.49694i
\(846\) −1.42302e7 + 4.15915e7i −0.683575 + 1.99792i
\(847\) 4.40308e6 6.85133e6i 0.210886 0.328145i
\(848\) −2.03130e7 + 2.34424e7i −0.970028 + 1.11947i
\(849\) −403781. + 1.01380e6i −0.0192255 + 0.0482704i
\(850\) 5.01782e6i 0.238214i
\(851\) −1.70781e7 4.88804e6i −0.808379 0.231372i
\(852\) −1.10183e6 + 1.17589e7i −0.0520016 + 0.554969i
\(853\) 2.08710e7 + 6.12827e6i 0.982133 + 0.288380i 0.733105 0.680116i \(-0.238071\pi\)
0.249029 + 0.968496i \(0.419889\pi\)
\(854\) −2.32353e6 2.01335e6i −0.109019 0.0944658i
\(855\) 5.18244e6 5.47387e6i 0.242448 0.256082i
\(856\) −4.05846e6 583518.i −0.189311 0.0272189i
\(857\) 9.04739e6 + 1.40780e7i 0.420796 + 0.654771i 0.985334 0.170636i \(-0.0545822\pi\)
−0.564538 + 0.825407i \(0.690946\pi\)
\(858\) 3.90523e7 1.35936e7i 1.81104 0.630400i
\(859\) 1.08792e7 + 1.25553e7i 0.503054 + 0.580555i 0.949306 0.314352i \(-0.101787\pi\)
−0.446253 + 0.894907i \(0.647242\pi\)
\(860\) −1.63939e7 + 2.35708e6i −0.755849 + 0.108675i
\(861\) −1.61902e7 + 2.81574e7i −0.744296 + 1.29445i
\(862\) −566629. 1.92976e6i −0.0259735 0.0884577i
\(863\) −1.55238e6 5.28692e6i −0.0709531 0.241644i 0.916379 0.400312i \(-0.131098\pi\)
−0.987332 + 0.158668i \(0.949280\pi\)
\(864\) 1.62157e7 + 1.39009e7i 0.739013 + 0.633516i
\(865\) 1.74056e7 2.50254e6i 0.790947 0.113721i
\(866\) −5.71979e6 6.60099e6i −0.259171 0.299099i
\(867\) 6.13402e6 + 1.76221e7i 0.277139 + 0.796176i
\(868\) −2.76634e6 4.30452e6i −0.124626 0.193921i
\(869\) 1.37409e7 + 1.97564e6i 0.617257 + 0.0887481i
\(870\) 1.87096e6 + 1.46598e6i 0.0838042 + 0.0656645i
\(871\) 2.72714e7 + 2.36308e7i 1.21804 + 1.05544i
\(872\) 8.09669e6 + 2.37740e6i 0.360592 + 0.105879i
\(873\) −6.91809e6 + 3.65913e7i −0.307221 + 1.62496i
\(874\) 3.07157e6 + 1.02023e7i 0.136013 + 0.451773i
\(875\) 2.33604e7i 1.03148i
\(876\) 7.90244e6 + 3.14743e6i 0.347937 + 0.138579i
\(877\) 5.45847e6 6.29941e6i 0.239647 0.276567i −0.623167 0.782089i \(-0.714154\pi\)
0.862814 + 0.505521i \(0.168700\pi\)
\(878\) −3.87769e6 + 6.03380e6i −0.169760 + 0.264152i
\(879\) −9.69920e6 + 4.02919e7i −0.423412 + 1.75892i
\(880\) 1.73189e7 1.11302e7i 0.753899 0.484502i
\(881\) −945544. 2.07045e6i −0.0410433 0.0898722i 0.888000 0.459844i \(-0.152095\pi\)
−0.929043 + 0.369972i \(0.879367\pi\)
\(882\) −1.21086e6 + 704819.i −0.0524109 + 0.0305074i
\(883\) −248658. 1.72945e6i −0.0107325 0.0746461i 0.983751 0.179537i \(-0.0574599\pi\)
−0.994484 + 0.104891i \(0.966551\pi\)
\(884\) 1.40417e7 3.07469e7i 0.604349 1.32334i
\(885\) −3.61797e6 1.85946e7i −0.155277 0.798045i
\(886\) 7.50130e6 2.20258e6i 0.321035 0.0942643i
\(887\) 2.09983e7 + 9.58962e6i 0.896140 + 0.409253i 0.809591 0.586994i \(-0.199689\pi\)
0.0865488 + 0.996248i \(0.472416\pi\)
\(888\) 560124. + 1.13361e7i 0.0238370 + 0.482425i
\(889\) 1.22858e7 1.06457e7i 0.521373 0.451772i
\(890\) 3.31636e6 1.51453e6i 0.140342 0.0640919i
\(891\) −1.79993e7 + 3.60149e6i −0.759558 + 0.151980i
\(892\) −766813. + 5.33330e6i −0.0322684 + 0.224432i
\(893\) 1.29980e7 + 8.35331e6i 0.545442 + 0.350534i
\(894\) −3.44775e7 3.60310e7i −1.44275 1.50776i
\(895\) −651491. + 2.21878e6i −0.0271864 + 0.0925882i
\(896\) −2.40339e7 −1.00012
\(897\) 4.16224e6 4.79457e7i 0.172721 1.98961i
\(898\) −3.60662e7 −1.49248
\(899\) 278780. 949437.i 0.0115044 0.0391802i
\(900\) −1.44679e6 + 1.14609e6i −0.0595389 + 0.0471641i
\(901\) −3.30138e7 2.12167e7i −1.35483 0.870694i
\(902\) 5.11249e6 3.55581e7i 0.209226 1.45520i
\(903\) −3.25937e7 + 1.68763e7i −1.33019 + 0.688745i
\(904\) 3.16983e6 1.44761e6i 0.129008 0.0589158i
\(905\) −488408. + 423208.i −0.0198226 + 0.0171764i
\(906\) 1.48733e7 734904.i 0.601988 0.0297447i
\(907\) 8.89764e6 + 4.06342e6i 0.359134 + 0.164011i 0.586807 0.809727i \(-0.300385\pi\)
−0.227673 + 0.973738i \(0.573112\pi\)
\(908\) 1.09762e7 3.22289e6i 0.441810 0.129727i
\(909\) 73109.6 + 738007.i 0.00293471 + 0.0296245i
\(910\) −2.32128e7 + 5.08290e7i −0.929232 + 2.03474i
\(911\) 5.03960e6 + 3.50512e7i 0.201187 + 1.39929i 0.800769 + 0.598974i \(0.204425\pi\)
−0.599582 + 0.800314i \(0.704666\pi\)
\(912\) 9.71174e6 6.94165e6i 0.386643 0.276360i
\(913\) −9.38306e6 2.05460e7i −0.372535 0.815739i
\(914\) −1.28444e7 + 8.25458e6i −0.508566 + 0.326836i
\(915\) −2.72218e6 655291.i −0.107489 0.0258751i
\(916\) 5.24762e6 8.16545e6i 0.206644 0.321545i
\(917\) −7.66374e6 + 8.84443e6i −0.300966 + 0.347333i
\(918\) −2.30383e7 + 3.62704e7i −0.902283 + 1.42052i
\(919\) 3.23815e7i 1.26476i −0.774658 0.632381i \(-0.782078\pi\)
0.774658 0.632381i \(-0.217922\pi\)
\(920\) −2.03696e6 1.35112e7i −0.0793437 0.526287i
\(921\) −2.74343e7 2.57064e6i −1.06572 0.0998602i
\(922\) −2.93515e6 861837.i −0.113711 0.0333886i
\(923\) −4.05797e7 3.51625e7i −1.56785 1.35855i
\(924\) −6.48834e6 + 8.28074e6i −0.250008 + 0.319072i
\(925\) −3.06582e6 440798.i −0.117813 0.0169389i
\(926\) −2.86238e7 4.45396e7i −1.09698 1.70694i
\(927\) 3.37619e7 8.31727e6i 1.29041 0.317893i
\(928\) 1.55017e6 + 1.78899e6i 0.0590894 + 0.0681928i
\(929\) 4.31709e7 6.20704e6i 1.64116 0.235964i 0.740997 0.671508i \(-0.234353\pi\)
0.900167 + 0.435545i \(0.143444\pi\)
\(930\) −1.15682e7 6.65162e6i −0.438590 0.252186i
\(931\) 138739. + 472501.i 0.00524594 + 0.0178660i
\(932\) 3.60745e6 + 1.22858e7i 0.136038 + 0.463303i
\(933\) 1.54690e7 + 8.89455e6i 0.581779 + 0.334518i
\(934\) −2.76496e7 + 3.97541e6i −1.03710 + 0.149113i
\(935\) 1.70563e7 + 1.96841e7i 0.638053 + 0.736353i
\(936\) −2.98567e7 + 7.35521e6i −1.11391 + 0.274413i
\(937\) −1.43458e7 2.23225e7i −0.533797 0.830605i 0.464697 0.885470i \(-0.346163\pi\)
−0.998494 + 0.0548653i \(0.982527\pi\)
\(938\) −2.60217e7 3.74136e6i −0.965670 0.138842i
\(939\) 5.12191e6 6.53683e6i 0.189569 0.241937i
\(940\) 1.73394e7 + 1.50246e7i 0.640049 + 0.554606i
\(941\) 2.83019e7 + 8.31018e6i 1.04194 + 0.305940i 0.757555 0.652771i \(-0.226394\pi\)
0.284381 + 0.958711i \(0.408212\pi\)
\(942\) 2.11346e7 + 1.98035e6i 0.776009 + 0.0727134i
\(943\) −3.53266e7 2.23633e7i −1.29367 0.818950i
\(944\) 2.99996e7i 1.09568i
\(945\) 1.32997e7 2.09385e7i 0.484465 0.762721i
\(946\) 2.65841e7 3.06797e7i 0.965816 1.11461i
\(947\) −1.29642e7 + 2.01726e7i −0.469753 + 0.730950i −0.992594 0.121480i \(-0.961236\pi\)
0.522841 + 0.852430i \(0.324872\pi\)
\(948\) 1.16212e7 + 2.79750e6i 0.419983 + 0.101100i
\(949\) −3.25331e7 + 2.09077e7i −1.17263 + 0.753601i
\(950\) 771746. + 1.68989e6i 0.0277438 + 0.0607504i
\(951\) 4.27065e7 3.05253e7i 1.53124 1.09448i
\(952\) −3.02666e6 2.10509e7i −0.108236 0.752797i
\(953\) 1.06875e7 2.34024e7i 0.381193 0.834697i −0.617642 0.786459i \(-0.711912\pi\)
0.998836 0.0482381i \(-0.0153606\pi\)
\(954\) −4.07505e6 4.11357e7i −0.144965 1.46335i
\(955\) 2.25630e6 662510.i 0.0800551 0.0235063i
\(956\) 4.65014e6 + 2.12365e6i 0.164559 + 0.0751516i
\(957\) −2.03194e6 + 100400.i −0.0717184 + 0.00354367i
\(958\) −2.30707e7 + 1.99909e7i −0.812172 + 0.703751i
\(959\) −946825. + 432400.i −0.0332448 + 0.0151824i
\(960\) −988132. + 511634.i −0.0346048 + 0.0179177i
\(961\) 3.28375e6 2.28390e7i 0.114700 0.797753i
\(962\) 5.02637e7 + 3.23025e7i 1.75112 + 1.12538i
\(963\) 7.51064e6 5.94960e6i 0.260982 0.206739i
\(964\) 1.79740e6 6.12137e6i 0.0622947 0.212156i
\(965\) −1.96735e7 −0.680085
\(966\) 1.63337e7 + 3.10244e7i 0.563171 + 1.06970i
\(967\) −2.44682e7 −0.841466 −0.420733 0.907185i \(-0.638227\pi\)
−0.420733 + 0.907185i \(0.638227\pi\)
\(968\) 1.88714e6 6.42700e6i 0.0647314 0.220455i
\(969\) 1.04415e7 + 1.09120e7i 0.357234 + 0.373330i
\(970\) 4.68231e7 + 3.00914e7i 1.59783 + 1.02686i
\(971\) 4.00266e6 2.78391e7i 0.136239 0.947561i −0.800948 0.598734i \(-0.795671\pi\)
0.937187 0.348828i \(-0.113420\pi\)
\(972\) −1.57199e7 + 1.64164e6i −0.533685 + 0.0557331i
\(973\) −7.49947e6 + 3.42489e6i −0.253950 + 0.115975i
\(974\) 4.87890e7 4.22759e7i 1.64788 1.42789i
\(975\) −414119. 8.38115e6i −0.0139513 0.282353i
\(976\) −4.03343e6 1.84200e6i −0.135534 0.0618965i
\(977\) 2.23357e7 6.55836e6i 0.748624 0.219816i 0.114902 0.993377i \(-0.463345\pi\)
0.633722 + 0.773561i \(0.281526\pi\)
\(978\) −2.42260e6 1.24509e7i −0.0809905 0.416251i
\(979\) −1.29631e6 + 2.83853e6i −0.0432268 + 0.0946536i
\(980\) 104068. + 723807.i 0.00346139 + 0.0240745i
\(981\) −1.70427e7 + 9.92027e6i −0.565414 + 0.329117i
\(982\) 2.07636e7 + 4.54659e7i 0.687106 + 1.50455i
\(983\) −7.64069e6 + 4.91038e6i −0.252202 + 0.162081i −0.660634 0.750708i \(-0.729712\pi\)
0.408431 + 0.912789i \(0.366076\pi\)
\(984\) −6.25205e6 + 2.59720e7i −0.205842 + 0.855100i
\(985\) −7.18369e6 + 1.11780e7i −0.235916 + 0.367092i
\(986\) −3.11861e6 + 3.59907e6i −0.102157 + 0.117896i
\(987\) 4.72353e7 + 1.88132e7i 1.54338 + 0.614709i
\(988\) 1.25145e7i 0.407870i
\(989\) −1.99203e7 4.28420e7i −0.647598 1.39277i
\(990\) −5.09671e6 + 2.69576e7i −0.165273 + 0.874166i
\(991\) 2.44473e6 + 717839.i 0.0790765 + 0.0232190i 0.321032 0.947069i \(-0.395970\pi\)
−0.241955 + 0.970287i \(0.577789\pi\)
\(992\) −1.00437e7 8.70289e6i −0.324051 0.280792i
\(993\) 2.38955e7 + 1.87232e7i 0.769028 + 0.602570i
\(994\) 3.87201e7 + 5.56711e6i 1.24300 + 0.178716i
\(995\) 122736. + 190981.i 0.00393019 + 0.00611549i
\(996\) −6.39355e6 1.83677e7i −0.204218 0.586686i
\(997\) 3.67120e7 + 4.23679e7i 1.16969 + 1.34989i 0.924852 + 0.380328i \(0.124189\pi\)
0.244837 + 0.969564i \(0.421266\pi\)
\(998\) −6.67321e7 + 9.59463e6i −2.12084 + 0.304931i
\(999\) −2.01369e7 1.72623e7i −0.638379 0.547248i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 69.6.g.a.5.8 380
3.2 odd 2 inner 69.6.g.a.5.31 yes 380
23.14 odd 22 inner 69.6.g.a.14.31 yes 380
69.14 even 22 inner 69.6.g.a.14.8 yes 380
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.g.a.5.8 380 1.1 even 1 trivial
69.6.g.a.5.31 yes 380 3.2 odd 2 inner
69.6.g.a.14.8 yes 380 69.14 even 22 inner
69.6.g.a.14.31 yes 380 23.14 odd 22 inner