Properties

Label 74.6.f.a.7.4
Level $74$
Weight $6$
Character 74.7
Analytic conductor $11.868$
Analytic rank $0$
Dimension $48$
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] = [74,6,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.8684026662\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 7.4
Character \(\chi\) \(=\) 74.7
Dual form 74.6.f.a.53.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.75877 + 1.36808i) q^{2} +(-2.35676 - 0.857791i) q^{3} +(12.2567 - 10.2846i) q^{4} +(-1.87431 - 10.6298i) q^{5} +10.0321 q^{6} +(20.8226 + 118.091i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-181.330 - 152.154i) q^{9} +O(q^{10})\) \(q+(-3.75877 + 1.36808i) q^{2} +(-2.35676 - 0.857791i) q^{3} +(12.2567 - 10.2846i) q^{4} +(-1.87431 - 10.6298i) q^{5} +10.0321 q^{6} +(20.8226 + 118.091i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-181.330 - 152.154i) q^{9} +(21.5875 + 37.3906i) q^{10} +(101.156 - 175.208i) q^{11} +(-37.7082 + 13.7247i) q^{12} +(259.129 - 217.435i) q^{13} +(-239.825 - 415.388i) q^{14} +(-4.70080 + 26.6596i) q^{15} +(44.4539 - 252.111i) q^{16} +(789.514 + 662.481i) q^{17} +(889.738 + 323.838i) q^{18} +(1470.71 + 535.296i) q^{19} +(-132.296 - 111.009i) q^{20} +(52.2233 - 296.173i) q^{21} +(-140.525 + 796.955i) q^{22} +(1301.33 + 2253.96i) q^{23} +(122.960 - 103.176i) q^{24} +(2827.06 - 1028.97i) q^{25} +(-676.538 + 1171.80i) q^{26} +(601.560 + 1041.93i) q^{27} +(1469.73 + 1233.25i) q^{28} +(2539.82 - 4399.10i) q^{29} +(-18.8032 - 106.638i) q^{30} +9799.53 q^{31} +(177.816 + 1008.44i) q^{32} +(-388.693 + 326.152i) q^{33} +(-3873.93 - 1409.99i) q^{34} +(1216.25 - 442.678i) q^{35} -3787.36 q^{36} +(-4859.97 + 6762.00i) q^{37} -6260.40 q^{38} +(-797.219 + 290.164i) q^{39} +(649.139 + 236.267i) q^{40} +(3733.80 - 3133.03i) q^{41} +(208.893 + 1184.69i) q^{42} -4327.33 q^{43} +(-562.099 - 3187.82i) q^{44} +(-1277.49 + 2212.68i) q^{45} +(-7974.99 - 6691.81i) q^{46} +(-8005.00 - 13865.1i) q^{47} +(-321.026 + 556.033i) q^{48} +(2281.61 - 830.439i) q^{49} +(-9218.56 + 7735.29i) q^{50} +(-1292.43 - 2238.55i) q^{51} +(939.836 - 5330.08i) q^{52} +(-722.282 + 4096.26i) q^{53} +(-3686.57 - 3093.40i) q^{54} +(-2052.01 - 746.872i) q^{55} +(-7211.57 - 2624.80i) q^{56} +(-3006.95 - 2523.13i) q^{57} +(-3528.29 + 20009.9i) q^{58} +(4984.39 - 28267.9i) q^{59} +(216.567 + 375.105i) q^{60} +(-30397.9 + 25506.8i) q^{61} +(-36834.2 + 13406.5i) q^{62} +(14192.2 - 24581.6i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-2796.97 - 2346.94i) q^{65} +(1014.80 - 1757.69i) q^{66} +(6011.98 + 34095.6i) q^{67} +16490.2 q^{68} +(-1133.49 - 6428.32i) q^{69} +(-3965.97 + 3327.85i) q^{70} +(-23703.9 - 8627.51i) q^{71} +(14235.8 - 5181.41i) q^{72} +26329.4 q^{73} +(9016.57 - 32065.6i) q^{74} -7545.35 q^{75} +(23531.4 - 8564.73i) q^{76} +(22796.7 + 8297.32i) q^{77} +(2599.60 - 2181.32i) q^{78} +(-4.80197 - 27.2333i) q^{79} -2763.20 q^{80} +(9464.36 + 53675.0i) q^{81} +(-9748.27 + 16884.5i) q^{82} +(39504.0 + 33147.8i) q^{83} +(-2405.93 - 4167.20i) q^{84} +(5562.22 - 9634.04i) q^{85} +(16265.5 - 5920.14i) q^{86} +(-9759.27 + 8189.00i) q^{87} +(6474.00 + 11213.3i) q^{88} +(10930.3 - 61988.5i) q^{89} +(1774.67 - 10064.7i) q^{90} +(31072.7 + 26073.1i) q^{91} +(39131.1 + 14242.5i) q^{92} +(-23095.2 - 8405.95i) q^{93} +(49057.5 + 41164.1i) q^{94} +(2933.49 - 16636.6i) q^{95} +(445.964 - 2529.19i) q^{96} +(63744.0 + 110408. i) q^{97} +(-7439.95 + 6242.86i) q^{98} +(-45001.3 + 16379.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.75877 + 1.36808i −0.664463 + 0.241845i
\(3\) −2.35676 0.857791i −0.151186 0.0550273i 0.265319 0.964161i \(-0.414523\pi\)
−0.416505 + 0.909133i \(0.636745\pi\)
\(4\) 12.2567 10.2846i 0.383022 0.321394i
\(5\) −1.87431 10.6298i −0.0335287 0.190151i 0.963443 0.267913i \(-0.0863338\pi\)
−0.996972 + 0.0777616i \(0.975223\pi\)
\(6\) 10.0321 0.113766
\(7\) 20.8226 + 118.091i 0.160616 + 0.910899i 0.953470 + 0.301487i \(0.0974831\pi\)
−0.792854 + 0.609411i \(0.791406\pi\)
\(8\) −32.0000 + 55.4256i −0.176777 + 0.306186i
\(9\) −181.330 152.154i −0.746215 0.626149i
\(10\) 21.5875 + 37.3906i 0.0682656 + 0.118240i
\(11\) 101.156 175.208i 0.252064 0.436588i −0.712030 0.702149i \(-0.752224\pi\)
0.964094 + 0.265561i \(0.0855573\pi\)
\(12\) −37.7082 + 13.7247i −0.0755932 + 0.0275137i
\(13\) 259.129 217.435i 0.425263 0.356838i −0.404898 0.914362i \(-0.632693\pi\)
0.830161 + 0.557524i \(0.188249\pi\)
\(14\) −239.825 415.388i −0.327019 0.566414i
\(15\) −4.70080 + 26.6596i −0.00539441 + 0.0305932i
\(16\) 44.4539 252.111i 0.0434120 0.246202i
\(17\) 789.514 + 662.481i 0.662579 + 0.555970i 0.910858 0.412719i \(-0.135421\pi\)
−0.248280 + 0.968688i \(0.579865\pi\)
\(18\) 889.738 + 323.838i 0.647263 + 0.235585i
\(19\) 1470.71 + 535.296i 0.934639 + 0.340181i 0.764047 0.645161i \(-0.223210\pi\)
0.170592 + 0.985342i \(0.445432\pi\)
\(20\) −132.296 111.009i −0.0739556 0.0620561i
\(21\) 52.2233 296.173i 0.0258414 0.146554i
\(22\) −140.525 + 796.955i −0.0619008 + 0.351057i
\(23\) 1301.33 + 2253.96i 0.512940 + 0.888438i 0.999887 + 0.0150066i \(0.00477692\pi\)
−0.486948 + 0.873431i \(0.661890\pi\)
\(24\) 122.960 103.176i 0.0435748 0.0365636i
\(25\) 2827.06 1028.97i 0.904659 0.329269i
\(26\) −676.538 + 1171.80i −0.196272 + 0.339953i
\(27\) 601.560 + 1041.93i 0.158807 + 0.275062i
\(28\) 1469.73 + 1233.25i 0.354277 + 0.297273i
\(29\) 2539.82 4399.10i 0.560801 0.971335i −0.436626 0.899643i \(-0.643827\pi\)
0.997427 0.0716923i \(-0.0228400\pi\)
\(30\) −18.8032 106.638i −0.00381442 0.0216327i
\(31\) 9799.53 1.83148 0.915738 0.401777i \(-0.131607\pi\)
0.915738 + 0.401777i \(0.131607\pi\)
\(32\) 177.816 + 1008.44i 0.0306970 + 0.174091i
\(33\) −388.693 + 326.152i −0.0621329 + 0.0521357i
\(34\) −3873.93 1409.99i −0.574717 0.209180i
\(35\) 1216.25 442.678i 0.167823 0.0610826i
\(36\) −3787.36 −0.487057
\(37\) −4859.97 + 6762.00i −0.583619 + 0.812027i
\(38\) −6260.40 −0.703304
\(39\) −797.219 + 290.164i −0.0839298 + 0.0305479i
\(40\) 649.139 + 236.267i 0.0641487 + 0.0233482i
\(41\) 3733.80 3133.03i 0.346890 0.291075i −0.452650 0.891688i \(-0.649521\pi\)
0.799540 + 0.600613i \(0.205077\pi\)
\(42\) 208.893 + 1184.69i 0.0182726 + 0.103629i
\(43\) −4327.33 −0.356902 −0.178451 0.983949i \(-0.557109\pi\)
−0.178451 + 0.983949i \(0.557109\pi\)
\(44\) −562.099 3187.82i −0.0437705 0.248235i
\(45\) −1277.49 + 2212.68i −0.0940431 + 0.162887i
\(46\) −7974.99 6691.81i −0.555694 0.466282i
\(47\) −8005.00 13865.1i −0.528588 0.915541i −0.999444 0.0333309i \(-0.989388\pi\)
0.470857 0.882210i \(-0.343945\pi\)
\(48\) −321.026 + 556.033i −0.0201111 + 0.0348335i
\(49\) 2281.61 830.439i 0.135754 0.0494103i
\(50\) −9218.56 + 7735.29i −0.521481 + 0.437574i
\(51\) −1292.43 2238.55i −0.0695793 0.120515i
\(52\) 939.836 5330.08i 0.0481996 0.273354i
\(53\) −722.282 + 4096.26i −0.0353197 + 0.200308i −0.997362 0.0725939i \(-0.976872\pi\)
0.962042 + 0.272902i \(0.0879834\pi\)
\(54\) −3686.57 3093.40i −0.172043 0.144362i
\(55\) −2052.01 746.872i −0.0914690 0.0332920i
\(56\) −7211.57 2624.80i −0.307298 0.111847i
\(57\) −3006.95 2523.13i −0.122585 0.102861i
\(58\) −3528.29 + 20009.9i −0.137719 + 0.781043i
\(59\) 4984.39 28267.9i 0.186415 1.05721i −0.737708 0.675120i \(-0.764092\pi\)
0.924123 0.382095i \(-0.124797\pi\)
\(60\) 216.567 + 375.105i 0.00776629 + 0.0134516i
\(61\) −30397.9 + 25506.8i −1.04597 + 0.877672i −0.992664 0.120907i \(-0.961420\pi\)
−0.0533046 + 0.998578i \(0.516975\pi\)
\(62\) −36834.2 + 13406.5i −1.21695 + 0.442933i
\(63\) 14192.2 24581.6i 0.450504 0.780296i
\(64\) −2048.00 3547.24i −0.0625000 0.108253i
\(65\) −2796.97 2346.94i −0.0821116 0.0688998i
\(66\) 1014.80 1757.69i 0.0286763 0.0496688i
\(67\) 6011.98 + 34095.6i 0.163618 + 0.927923i 0.950478 + 0.310791i \(0.100594\pi\)
−0.786860 + 0.617131i \(0.788295\pi\)
\(68\) 16490.2 0.432468
\(69\) −1133.49 6428.32i −0.0286611 0.162545i
\(70\) −3965.97 + 3327.85i −0.0967397 + 0.0811742i
\(71\) −23703.9 8627.51i −0.558051 0.203114i 0.0475690 0.998868i \(-0.484853\pi\)
−0.605620 + 0.795754i \(0.707075\pi\)
\(72\) 14235.8 5181.41i 0.323632 0.117792i
\(73\) 26329.4 0.578275 0.289137 0.957288i \(-0.406632\pi\)
0.289137 + 0.957288i \(0.406632\pi\)
\(74\) 9016.57 32065.6i 0.191409 0.680707i
\(75\) −7545.35 −0.154891
\(76\) 23531.4 8564.73i 0.467319 0.170090i
\(77\) 22796.7 + 8297.32i 0.438173 + 0.159482i
\(78\) 2599.60 2181.32i 0.0483804 0.0405960i
\(79\) −4.80197 27.2333i −8.65669e−5 0.000490945i 0.984764 0.173894i \(-0.0556349\pi\)
−0.984851 + 0.173403i \(0.944524\pi\)
\(80\) −2763.20 −0.0482711
\(81\) 9464.36 + 53675.0i 0.160280 + 0.908991i
\(82\) −9748.27 + 16884.5i −0.160101 + 0.277302i
\(83\) 39504.0 + 33147.8i 0.629428 + 0.528153i 0.900751 0.434335i \(-0.143017\pi\)
−0.271323 + 0.962488i \(0.587461\pi\)
\(84\) −2405.93 4167.20i −0.0372036 0.0644386i
\(85\) 5562.22 9634.04i 0.0835027 0.144631i
\(86\) 16265.5 5920.14i 0.237148 0.0863149i
\(87\) −9759.27 + 8189.00i −0.138235 + 0.115993i
\(88\) 6474.00 + 11213.3i 0.0891181 + 0.154357i
\(89\) 10930.3 61988.5i 0.146270 0.829538i −0.820069 0.572265i \(-0.806065\pi\)
0.966339 0.257273i \(-0.0828240\pi\)
\(90\) 1774.67 10064.7i 0.0230947 0.130977i
\(91\) 31072.7 + 26073.1i 0.393347 + 0.330058i
\(92\) 39131.1 + 14242.5i 0.482006 + 0.175436i
\(93\) −23095.2 8405.95i −0.276894 0.100781i
\(94\) 49057.5 + 41164.1i 0.572646 + 0.480507i
\(95\) 2933.49 16636.6i 0.0333484 0.189128i
\(96\) 445.964 2529.19i 0.00493881 0.0280094i
\(97\) 63744.0 + 110408.i 0.687876 + 1.19144i 0.972524 + 0.232804i \(0.0747900\pi\)
−0.284648 + 0.958632i \(0.591877\pi\)
\(98\) −7439.95 + 6242.86i −0.0782537 + 0.0656626i
\(99\) −45001.3 + 16379.1i −0.461463 + 0.167959i
\(100\) 24068.0 41686.9i 0.240680 0.416869i
\(101\) −55859.9 96752.1i −0.544874 0.943750i −0.998615 0.0526161i \(-0.983244\pi\)
0.453740 0.891134i \(-0.350089\pi\)
\(102\) 7920.45 + 6646.04i 0.0753788 + 0.0632503i
\(103\) 65835.1 114030.i 0.611455 1.05907i −0.379541 0.925175i \(-0.623918\pi\)
0.990995 0.133896i \(-0.0427487\pi\)
\(104\) 3759.34 + 21320.3i 0.0340823 + 0.193290i
\(105\) −3246.13 −0.0287338
\(106\) −2889.13 16385.1i −0.0249748 0.141639i
\(107\) 87627.2 73528.0i 0.739911 0.620859i −0.192903 0.981218i \(-0.561790\pi\)
0.932814 + 0.360359i \(0.117346\pi\)
\(108\) 18089.0 + 6583.85i 0.149230 + 0.0543151i
\(109\) −125748. + 45768.7i −1.01376 + 0.368979i −0.794876 0.606771i \(-0.792464\pi\)
−0.218886 + 0.975751i \(0.570242\pi\)
\(110\) 8734.83 0.0688292
\(111\) 17254.2 11767.6i 0.132919 0.0906524i
\(112\) 30697.5 0.231238
\(113\) −178097. + 64821.9i −1.31208 + 0.477557i −0.900912 0.434003i \(-0.857101\pi\)
−0.411167 + 0.911560i \(0.634879\pi\)
\(114\) 14754.3 + 5370.12i 0.106330 + 0.0387009i
\(115\) 21520.0 18057.4i 0.151739 0.127324i
\(116\) −14113.1 80039.6i −0.0973820 0.552281i
\(117\) −80071.6 −0.540771
\(118\) 19937.6 + 113072.i 0.131816 + 0.747564i
\(119\) −61793.0 + 107029.i −0.400011 + 0.692840i
\(120\) −1327.20 1113.65i −0.00841362 0.00705986i
\(121\) 60060.3 + 104028.i 0.372927 + 0.645929i
\(122\) 79363.2 137461.i 0.482747 0.836142i
\(123\) −11487.2 + 4180.99i −0.0684621 + 0.0249182i
\(124\) 120110. 100784.i 0.701496 0.588625i
\(125\) −33101.7 57333.8i −0.189485 0.328198i
\(126\) −19715.6 + 111813.i −0.110633 + 0.627430i
\(127\) 4504.71 25547.5i 0.0247832 0.140553i −0.969905 0.243482i \(-0.921710\pi\)
0.994689 + 0.102929i \(0.0328215\pi\)
\(128\) 12550.9 + 10531.4i 0.0677094 + 0.0568149i
\(129\) 10198.5 + 3711.95i 0.0539588 + 0.0196394i
\(130\) 13724.0 + 4995.12i 0.0712232 + 0.0259231i
\(131\) 24502.1 + 20559.7i 0.124746 + 0.104674i 0.703026 0.711164i \(-0.251832\pi\)
−0.578281 + 0.815838i \(0.696276\pi\)
\(132\) −1409.75 + 7995.10i −0.00704219 + 0.0399383i
\(133\) −32589.4 + 184824.i −0.159752 + 0.906000i
\(134\) −69243.2 119933.i −0.333131 0.577000i
\(135\) 9947.97 8347.34i 0.0469786 0.0394197i
\(136\) −61982.9 + 22559.9i −0.287359 + 0.104590i
\(137\) 22055.9 38201.9i 0.100398 0.173894i −0.811451 0.584421i \(-0.801322\pi\)
0.911849 + 0.410527i \(0.134655\pi\)
\(138\) 13055.0 + 22611.9i 0.0583550 + 0.101074i
\(139\) −109846. 92171.7i −0.482222 0.404632i 0.369007 0.929427i \(-0.379698\pi\)
−0.851229 + 0.524794i \(0.824142\pi\)
\(140\) 10354.4 17934.4i 0.0446484 0.0773333i
\(141\) 6972.55 + 39543.3i 0.0295355 + 0.167504i
\(142\) 100901. 0.419926
\(143\) −11883.8 67396.3i −0.0485976 0.275611i
\(144\) −46420.6 + 38951.5i −0.186554 + 0.156537i
\(145\) −51521.8 18752.4i −0.203503 0.0740691i
\(146\) −98966.3 + 36020.8i −0.384242 + 0.139853i
\(147\) −6089.56 −0.0232430
\(148\) 9977.15 + 132863.i 0.0374414 + 0.498596i
\(149\) −388652. −1.43415 −0.717076 0.696995i \(-0.754520\pi\)
−0.717076 + 0.696995i \(0.754520\pi\)
\(150\) 28361.2 10322.6i 0.102919 0.0374596i
\(151\) 122740. + 44673.6i 0.438069 + 0.159444i 0.551634 0.834087i \(-0.314005\pi\)
−0.113565 + 0.993531i \(0.536227\pi\)
\(152\) −76731.9 + 64385.7i −0.269381 + 0.226038i
\(153\) −42363.6 240256.i −0.146307 0.829746i
\(154\) −97039.0 −0.329719
\(155\) −18367.4 104167.i −0.0614071 0.348257i
\(156\) −6787.06 + 11755.5i −0.0223291 + 0.0386751i
\(157\) 284542. + 238759.i 0.921291 + 0.773055i 0.974233 0.225542i \(-0.0724154\pi\)
−0.0529421 + 0.998598i \(0.516860\pi\)
\(158\) 55.3069 + 95.7944i 0.000176253 + 0.000305279i
\(159\) 5215.99 9034.35i 0.0163623 0.0283403i
\(160\) 10386.2 3780.28i 0.0320743 0.0116741i
\(161\) −239075. + 200608.i −0.726890 + 0.609934i
\(162\) −109006. 188804.i −0.326335 0.565228i
\(163\) 84355.9 478406.i 0.248683 1.41035i −0.563097 0.826391i \(-0.690390\pi\)
0.811781 0.583962i \(-0.198498\pi\)
\(164\) 13542.1 76801.3i 0.0393168 0.222977i
\(165\) 4195.45 + 3520.40i 0.0119969 + 0.0100666i
\(166\) −193835. 70550.3i −0.545963 0.198714i
\(167\) −383222. 139481.i −1.06331 0.387012i −0.249637 0.968339i \(-0.580311\pi\)
−0.813670 + 0.581327i \(0.802534\pi\)
\(168\) 14744.4 + 12372.0i 0.0403046 + 0.0338196i
\(169\) −44604.5 + 252965.i −0.120133 + 0.681308i
\(170\) −7726.95 + 43821.7i −0.0205062 + 0.116297i
\(171\) −185237. 320840.i −0.484438 0.839071i
\(172\) −53038.9 + 44504.9i −0.136701 + 0.114706i
\(173\) 209251. 76161.3i 0.531561 0.193472i −0.0622742 0.998059i \(-0.519835\pi\)
0.593835 + 0.804587i \(0.297613\pi\)
\(174\) 25479.7 44132.1i 0.0638000 0.110505i
\(175\) 180378. + 312423.i 0.445234 + 0.771167i
\(176\) −39675.0 33291.2i −0.0965461 0.0810118i
\(177\) −35995.0 + 62345.1i −0.0863592 + 0.149579i
\(178\) 43721.0 + 247954.i 0.103428 + 0.586572i
\(179\) 175956. 0.410460 0.205230 0.978714i \(-0.434206\pi\)
0.205230 + 0.978714i \(0.434206\pi\)
\(180\) 7098.70 + 40258.7i 0.0163304 + 0.0926144i
\(181\) −101440. + 85118.2i −0.230151 + 0.193119i −0.750569 0.660792i \(-0.770221\pi\)
0.520418 + 0.853912i \(0.325776\pi\)
\(182\) −152465. 55492.9i −0.341187 0.124182i
\(183\) 93520.1 34038.5i 0.206432 0.0751351i
\(184\) −166570. −0.362703
\(185\) 80987.5 + 38986.3i 0.173976 + 0.0837495i
\(186\) 98309.4 0.208359
\(187\) 195936. 71314.9i 0.409742 0.149134i
\(188\) −240712. 87611.9i −0.496710 0.180788i
\(189\) −110516. + 92734.2i −0.225046 + 0.188836i
\(190\) 11734.0 + 66546.6i 0.0235809 + 0.133734i
\(191\) 954517. 1.89322 0.946608 0.322386i \(-0.104485\pi\)
0.946608 + 0.322386i \(0.104485\pi\)
\(192\) 1783.86 + 10116.8i 0.00349226 + 0.0198056i
\(193\) 92996.3 161074.i 0.179710 0.311267i −0.762071 0.647493i \(-0.775817\pi\)
0.941781 + 0.336226i \(0.109151\pi\)
\(194\) −390646. 327791.i −0.745211 0.625306i
\(195\) 4578.61 + 7930.39i 0.00862278 + 0.0149351i
\(196\) 19424.3 33643.9i 0.0361165 0.0625556i
\(197\) 340152. 123805.i 0.624463 0.227286i −0.0103563 0.999946i \(-0.503297\pi\)
0.634820 + 0.772660i \(0.281074\pi\)
\(198\) 146741. 123131.i 0.266005 0.223205i
\(199\) 231117. + 400306.i 0.413713 + 0.716572i 0.995292 0.0969177i \(-0.0308984\pi\)
−0.581579 + 0.813490i \(0.697565\pi\)
\(200\) −33434.9 + 189619.i −0.0591050 + 0.335201i
\(201\) 15078.1 85512.3i 0.0263243 0.149293i
\(202\) 342329. + 287248.i 0.590290 + 0.495312i
\(203\) 572378. + 208329.i 0.974862 + 0.354821i
\(204\) −38863.5 14145.1i −0.0653832 0.0237975i
\(205\) −40301.7 33817.1i −0.0669790 0.0562021i
\(206\) −91457.1 + 518679.i −0.150158 + 0.851591i
\(207\) 106980. 606714.i 0.173531 0.984142i
\(208\) −43298.4 74995.0i −0.0693927 0.120192i
\(209\) 242560. 203532.i 0.384108 0.322305i
\(210\) 12201.5 4440.97i 0.0190925 0.00694911i
\(211\) −81792.5 + 141669.i −0.126476 + 0.219063i −0.922309 0.386454i \(-0.873700\pi\)
0.795833 + 0.605516i \(0.207033\pi\)
\(212\) 33275.6 + 57635.1i 0.0508495 + 0.0880739i
\(213\) 48463.8 + 40666.0i 0.0731929 + 0.0614161i
\(214\) −228778. + 396256.i −0.341492 + 0.591482i
\(215\) 8110.78 + 45998.5i 0.0119665 + 0.0678653i
\(216\) −76999.6 −0.112293
\(217\) 204051. + 1.15723e6i 0.294164 + 1.66829i
\(218\) 410044. 344068.i 0.584372 0.490346i
\(219\) −62052.2 22585.1i −0.0874272 0.0318209i
\(220\) −32832.2 + 11950.0i −0.0457345 + 0.0166460i
\(221\) 348632. 0.480161
\(222\) −48755.5 + 67836.7i −0.0663959 + 0.0923810i
\(223\) 1.40603e6 1.89336 0.946680 0.322176i \(-0.104414\pi\)
0.946680 + 0.322176i \(0.104414\pi\)
\(224\) −115385. + 41996.7i −0.153649 + 0.0559236i
\(225\) −669193. 243566.i −0.881242 0.320746i
\(226\) 580743. 487301.i 0.756333 0.634639i
\(227\) −111537. 632559.i −0.143666 0.814772i −0.968428 0.249292i \(-0.919802\pi\)
0.824762 0.565480i \(-0.191309\pi\)
\(228\) −62804.7 −0.0800120
\(229\) 25519.0 + 144725.i 0.0321569 + 0.182371i 0.996656 0.0817168i \(-0.0260403\pi\)
−0.964499 + 0.264088i \(0.914929\pi\)
\(230\) −56184.7 + 97314.7i −0.0700323 + 0.121300i
\(231\) −46609.0 39109.6i −0.0574699 0.0482230i
\(232\) 162549. + 281543.i 0.198273 + 0.343419i
\(233\) −381892. + 661457.i −0.460841 + 0.798200i −0.999003 0.0446412i \(-0.985786\pi\)
0.538162 + 0.842841i \(0.319119\pi\)
\(234\) 300971. 109544.i 0.359323 0.130783i
\(235\) −132379. + 111079.i −0.156368 + 0.131208i
\(236\) −229632. 397734.i −0.268381 0.464850i
\(237\) −12.0434 + 68.3016i −1.39277e−5 + 7.89878e-5i
\(238\) 85842.0 486834.i 0.0982330 0.557107i
\(239\) −369790. 310291.i −0.418756 0.351378i 0.408934 0.912564i \(-0.365901\pi\)
−0.827689 + 0.561186i \(0.810345\pi\)
\(240\) 6512.20 + 2370.25i 0.00729793 + 0.00265623i
\(241\) −132604. 48264.0i −0.147067 0.0535280i 0.267438 0.963575i \(-0.413823\pi\)
−0.414505 + 0.910047i \(0.636045\pi\)
\(242\) −368071. 308848.i −0.404011 0.339006i
\(243\) 74504.2 422534.i 0.0809403 0.459035i
\(244\) −110250. + 625260.i −0.118551 + 0.672336i
\(245\) −13103.8 22696.5i −0.0139471 0.0241570i
\(246\) 37457.7 31430.8i 0.0394642 0.0331144i
\(247\) 497496. 181074.i 0.518857 0.188848i
\(248\) −313585. + 543145.i −0.323762 + 0.560773i
\(249\) −64667.7 112008.i −0.0660981 0.114485i
\(250\) 202859. + 170219.i 0.205279 + 0.172249i
\(251\) −75622.9 + 130983.i −0.0757651 + 0.131229i −0.901419 0.432948i \(-0.857473\pi\)
0.825654 + 0.564177i \(0.190807\pi\)
\(252\) −78862.5 447251.i −0.0782292 0.443660i
\(253\) 526549. 0.517175
\(254\) 18018.8 + 102190.i 0.0175244 + 0.0993857i
\(255\) −21372.8 + 17933.9i −0.0205831 + 0.0172713i
\(256\) −61583.7 22414.6i −0.0587308 0.0213763i
\(257\) −1.37807e6 + 501578.i −1.30149 + 0.473702i −0.897481 0.441054i \(-0.854605\pi\)
−0.404006 + 0.914756i \(0.632383\pi\)
\(258\) −43412.1 −0.0406033
\(259\) −899725. 433115.i −0.833413 0.401194i
\(260\) −58419.0 −0.0535945
\(261\) −1.12989e6 + 411246.i −1.02668 + 0.373680i
\(262\) −120225. 43758.4i −0.108204 0.0393829i
\(263\) −378160. + 317314.i −0.337121 + 0.282878i −0.795594 0.605830i \(-0.792841\pi\)
0.458473 + 0.888708i \(0.348397\pi\)
\(264\) −5639.01 31980.4i −0.00497958 0.0282406i
\(265\) 44896.1 0.0392730
\(266\) −130358. 739294.i −0.112962 0.640639i
\(267\) −78933.2 + 136716.i −0.0677613 + 0.117366i
\(268\) 424347. + 356070.i 0.360898 + 0.302829i
\(269\) 309529. + 536120.i 0.260808 + 0.451733i 0.966457 0.256829i \(-0.0826777\pi\)
−0.705649 + 0.708562i \(0.749344\pi\)
\(270\) −25972.3 + 44985.4i −0.0216821 + 0.0375545i
\(271\) −2.02024e6 + 735306.i −1.67101 + 0.608198i −0.992035 0.125964i \(-0.959798\pi\)
−0.678974 + 0.734162i \(0.737575\pi\)
\(272\) 202116. 169595.i 0.165645 0.138992i
\(273\) −50865.8 88102.1i −0.0413066 0.0715450i
\(274\) −30639.7 + 173767.i −0.0246552 + 0.139827i
\(275\) 105692. 599409.i 0.0842773 0.477960i
\(276\) −80005.5 67132.6i −0.0632189 0.0530470i
\(277\) −1.60028e6 582454.i −1.25313 0.456102i −0.371672 0.928364i \(-0.621215\pi\)
−0.881458 + 0.472262i \(0.843437\pi\)
\(278\) 538984. + 196174.i 0.418277 + 0.152240i
\(279\) −1.77695e6 1.49104e6i −1.36667 1.14678i
\(280\) −14384.2 + 81576.9i −0.0109646 + 0.0621831i
\(281\) 155429. 881480.i 0.117426 0.665958i −0.868094 0.496400i \(-0.834655\pi\)
0.985520 0.169558i \(-0.0542339\pi\)
\(282\) −80306.6 139095.i −0.0601352 0.104157i
\(283\) 720635. 604684.i 0.534871 0.448810i −0.334908 0.942251i \(-0.608705\pi\)
0.869780 + 0.493441i \(0.164261\pi\)
\(284\) −379262. + 138040.i −0.279026 + 0.101557i
\(285\) −21184.3 + 36692.3i −0.0154491 + 0.0267585i
\(286\) 136872. + 237069.i 0.0989463 + 0.171380i
\(287\) 447729. + 375689.i 0.320856 + 0.269230i
\(288\) 121195. 209917.i 0.0861004 0.149130i
\(289\) −62104.2 352211.i −0.0437398 0.248061i
\(290\) 219314. 0.153134
\(291\) −55522.6 314884.i −0.0384359 0.217981i
\(292\) 322712. 270788.i 0.221492 0.185854i
\(293\) −680348. 247626.i −0.462980 0.168511i 0.0999899 0.994988i \(-0.468119\pi\)
−0.562970 + 0.826478i \(0.690341\pi\)
\(294\) 22889.3 8331.01i 0.0154441 0.00562120i
\(295\) −309823. −0.207281
\(296\) −219269. 485751.i −0.145461 0.322244i
\(297\) 243406. 0.160118
\(298\) 1.46085e6 531707.i 0.952941 0.346842i
\(299\) 827301. + 301113.i 0.535163 + 0.194783i
\(300\) −92481.1 + 77600.9i −0.0593267 + 0.0497810i
\(301\) −90106.1 511017.i −0.0573242 0.325102i
\(302\) −522467. −0.329641
\(303\) 48655.3 + 275938.i 0.0304455 + 0.172665i
\(304\) 200333. 346987.i 0.124328 0.215342i
\(305\) 328107. + 275314.i 0.201960 + 0.169465i
\(306\) 487924. + 845109.i 0.297885 + 0.515952i
\(307\) −457041. + 791618.i −0.276764 + 0.479369i −0.970579 0.240785i \(-0.922595\pi\)
0.693815 + 0.720153i \(0.255929\pi\)
\(308\) 364747. 132757.i 0.219086 0.0797409i
\(309\) −252971. + 212268.i −0.150721 + 0.126470i
\(310\) 211547. + 366411.i 0.125027 + 0.216553i
\(311\) −348777. + 1.97801e6i −0.204478 + 1.15965i 0.693781 + 0.720186i \(0.255944\pi\)
−0.898259 + 0.439467i \(0.855167\pi\)
\(312\) 9428.49 53471.6i 0.00548347 0.0310983i
\(313\) 350208. + 293859.i 0.202053 + 0.169543i 0.738200 0.674582i \(-0.235676\pi\)
−0.536147 + 0.844125i \(0.680121\pi\)
\(314\) −1.39617e6 508164.i −0.799123 0.290857i
\(315\) −287898. 104786.i −0.163479 0.0595014i
\(316\) −338.940 284.405i −0.000190944 0.000160221i
\(317\) −476027. + 2.69968e6i −0.266062 + 1.50891i 0.499931 + 0.866065i \(0.333359\pi\)
−0.765993 + 0.642849i \(0.777752\pi\)
\(318\) −7245.97 + 41093.9i −0.00401817 + 0.0227882i
\(319\) −513838. 889993.i −0.282715 0.489677i
\(320\) −33867.7 + 28418.4i −0.0184889 + 0.0155140i
\(321\) −269588. + 98122.1i −0.146029 + 0.0531501i
\(322\) 624180. 1.08111e6i 0.335483 0.581073i
\(323\) 806525. + 1.39694e6i 0.430142 + 0.745027i
\(324\) 668028. + 560542.i 0.353535 + 0.296651i
\(325\) 508840. 881337.i 0.267222 0.462843i
\(326\) 337424. + 1.91362e6i 0.175846 + 0.997270i
\(327\) 335619. 0.173571
\(328\) 54168.6 + 307205.i 0.0278012 + 0.157668i
\(329\) 1.47065e6 1.23402e6i 0.749065 0.628540i
\(330\) −20585.9 7492.66i −0.0104060 0.00378749i
\(331\) 564986. 205638.i 0.283445 0.103165i −0.196386 0.980527i \(-0.562920\pi\)
0.479830 + 0.877361i \(0.340698\pi\)
\(332\) 825101. 0.410830
\(333\) 1.91013e6 486689.i 0.943956 0.240515i
\(334\) 1.63126e6 0.800125
\(335\) 351160. 127812.i 0.170959 0.0622242i
\(336\) −72346.8 26332.1i −0.0349600 0.0127244i
\(337\) −414698. + 347973.i −0.198910 + 0.166905i −0.736802 0.676108i \(-0.763665\pi\)
0.537892 + 0.843014i \(0.319221\pi\)
\(338\) −178418. 1.01186e6i −0.0849468 0.481757i
\(339\) 475335. 0.224647
\(340\) −30907.8 175287.i −0.0145001 0.0822341i
\(341\) 991284. 1.71695e6i 0.461649 0.799600i
\(342\) 1.13520e6 + 952546.i 0.524816 + 0.440373i
\(343\) 1.15326e6 + 1.99750e6i 0.529287 + 0.916753i
\(344\) 138475. 239845.i 0.0630920 0.109279i
\(345\) −66207.0 + 24097.4i −0.0299472 + 0.0108999i
\(346\) −682333. + 572546.i −0.306412 + 0.257110i
\(347\) −199976. 346369.i −0.0891568 0.154424i 0.817998 0.575221i \(-0.195084\pi\)
−0.907155 + 0.420797i \(0.861751\pi\)
\(348\) −35396.0 + 200740.i −0.0156677 + 0.0888560i
\(349\) −52989.6 + 300519.i −0.0232877 + 0.132071i −0.994235 0.107222i \(-0.965805\pi\)
0.970947 + 0.239293i \(0.0769157\pi\)
\(350\) −1.10542e6 927557.i −0.482344 0.404735i
\(351\) 382434. + 139195.i 0.165687 + 0.0603051i
\(352\) 194674. + 70855.6i 0.0837436 + 0.0304802i
\(353\) 490860. + 411880.i 0.209663 + 0.175928i 0.741572 0.670874i \(-0.234081\pi\)
−0.531909 + 0.846801i \(0.678525\pi\)
\(354\) 50003.7 283585.i 0.0212077 0.120275i
\(355\) −47279.9 + 268137.i −0.0199116 + 0.112924i
\(356\) −503559. 872189.i −0.210584 0.364742i
\(357\) 237440. 199236.i 0.0986014 0.0827364i
\(358\) −661377. + 240722.i −0.272735 + 0.0992676i
\(359\) 401834. 695997.i 0.164555 0.285017i −0.771942 0.635693i \(-0.780715\pi\)
0.936497 + 0.350675i \(0.114048\pi\)
\(360\) −81759.5 141612.i −0.0332493 0.0575894i
\(361\) −20347.0 17073.2i −0.00821736 0.00689519i
\(362\) 264841. 458718.i 0.106222 0.183982i
\(363\) −52314.0 296687.i −0.0208378 0.118177i
\(364\) 649001. 0.256739
\(365\) −49349.6 279875.i −0.0193888 0.109959i
\(366\) −304953. + 255886.i −0.118995 + 0.0998490i
\(367\) −2.05043e6 746294.i −0.794656 0.289231i −0.0873859 0.996175i \(-0.527851\pi\)
−0.707270 + 0.706943i \(0.750074\pi\)
\(368\) 626097. 227881.i 0.241003 0.0877179i
\(369\) −1.15376e6 −0.441111
\(370\) −357750. 35742.9i −0.135855 0.0135733i
\(371\) −498770. −0.188133
\(372\) −369523. + 134495.i −0.138447 + 0.0503906i
\(373\) 3.41143e6 + 1.24166e6i 1.26959 + 0.462094i 0.886977 0.461813i \(-0.152801\pi\)
0.382616 + 0.923907i \(0.375023\pi\)
\(374\) −638914. + 536112.i −0.236191 + 0.198188i
\(375\) 28832.4 + 163516.i 0.0105877 + 0.0600459i
\(376\) 1.02464e6 0.373768
\(377\) −298377. 1.69218e6i −0.108122 0.613188i
\(378\) 288538. 499762.i 0.103866 0.179901i
\(379\) −709610. 595434.i −0.253759 0.212929i 0.507030 0.861928i \(-0.330743\pi\)
−0.760789 + 0.648999i \(0.775188\pi\)
\(380\) −135146. 234080.i −0.0480115 0.0831583i
\(381\) −32530.9 + 56345.2i −0.0114811 + 0.0198859i
\(382\) −3.58781e6 + 1.30586e6i −1.25797 + 0.457864i
\(383\) 660324. 554078.i 0.230017 0.193007i −0.520494 0.853866i \(-0.674252\pi\)
0.750511 + 0.660858i \(0.229808\pi\)
\(384\) −20545.6 35586.1i −0.00711036 0.0123155i
\(385\) 45470.4 257875.i 0.0156342 0.0886662i
\(386\) −129189. + 732668.i −0.0441324 + 0.250287i
\(387\) 784677. + 658422.i 0.266326 + 0.223474i
\(388\) 1.91679e6 + 697656.i 0.646392 + 0.235267i
\(389\) 382022. + 139045.i 0.128001 + 0.0465887i 0.405227 0.914216i \(-0.367193\pi\)
−0.277225 + 0.960805i \(0.589415\pi\)
\(390\) −28059.4 23544.6i −0.00934149 0.00783844i
\(391\) −465792. + 2.64164e6i −0.154081 + 0.873839i
\(392\) −26984.0 + 153034.i −0.00886933 + 0.0503005i
\(393\) −40109.7 69472.0i −0.0130999 0.0226897i
\(394\) −1.10918e6 + 930710.i −0.359965 + 0.302046i
\(395\) −280.483 + 102.088i −9.04512e−5 + 3.29216e-5i
\(396\) −383115. + 663574.i −0.122770 + 0.212643i
\(397\) −1.90919e6 3.30681e6i −0.607957 1.05301i −0.991577 0.129521i \(-0.958656\pi\)
0.383620 0.923491i \(-0.374677\pi\)
\(398\) −1.41637e6 1.18847e6i −0.448196 0.376081i
\(399\) 235345. 407630.i 0.0740071 0.128184i
\(400\) −133739. 758474.i −0.0417936 0.237023i
\(401\) 4.84120e6 1.50346 0.751731 0.659470i \(-0.229219\pi\)
0.751731 + 0.659470i \(0.229219\pi\)
\(402\) 60312.5 + 342049.i 0.0186141 + 0.105566i
\(403\) 2.53934e6 2.13076e6i 0.778859 0.653540i
\(404\) −1.67971e6 611366.i −0.512014 0.186358i
\(405\) 552814. 201208.i 0.167472 0.0609547i
\(406\) −2.43645e6 −0.733571
\(407\) 693137. + 1.53552e6i 0.207412 + 0.459484i
\(408\) 165431. 0.0492000
\(409\) −1.56959e6 + 571282.i −0.463956 + 0.168866i −0.563412 0.826176i \(-0.690512\pi\)
0.0994566 + 0.995042i \(0.468290\pi\)
\(410\) 197749. + 71974.9i 0.0580973 + 0.0211457i
\(411\) −84749.8 + 71113.5i −0.0247477 + 0.0207658i
\(412\) −365829. 2.07472e6i −0.106178 0.602165i
\(413\) 3.44196e6 0.992957
\(414\) 427920. + 2.42685e6i 0.122705 + 0.695894i
\(415\) 278310. 482048.i 0.0793248 0.137395i
\(416\) 265348. + 222653.i 0.0751766 + 0.0630806i
\(417\) 179817. + 311452.i 0.0506396 + 0.0877103i
\(418\) −633278. + 1.09687e6i −0.177278 + 0.307054i
\(419\) −5.09349e6 + 1.85388e6i −1.41736 + 0.515877i −0.933281 0.359146i \(-0.883068\pi\)
−0.484080 + 0.875024i \(0.660846\pi\)
\(420\) −39786.9 + 33385.1i −0.0110057 + 0.00923485i
\(421\) −3.24775e6 5.62527e6i −0.893053 1.54681i −0.836196 0.548431i \(-0.815225\pi\)
−0.0568576 0.998382i \(-0.518108\pi\)
\(422\) 113625. 644399.i 0.0310594 0.176146i
\(423\) −658079. + 3.73215e6i −0.178825 + 1.01416i
\(424\) −203925. 171113.i −0.0550878 0.0462242i
\(425\) 2.91367e6 + 1.06049e6i 0.782472 + 0.284796i
\(426\) −237799. 86551.7i −0.0634871 0.0231074i
\(427\) −3.64508e6 3.05858e6i −0.967469 0.811803i
\(428\) 317816. 1.80242e6i 0.0838621 0.475606i
\(429\) −29804.7 + 169031.i −0.00781882 + 0.0443428i
\(430\) −93416.3 161802.i −0.0243642 0.0422000i
\(431\) −4.44673e6 + 3.73125e6i −1.15305 + 0.967523i −0.999787 0.0206626i \(-0.993422\pi\)
−0.153262 + 0.988186i \(0.548978\pi\)
\(432\) 289424. 105342.i 0.0746148 0.0271576i
\(433\) 1.10176e6 1.90831e6i 0.282402 0.489135i −0.689574 0.724215i \(-0.742202\pi\)
0.971976 + 0.235081i \(0.0755355\pi\)
\(434\) −2.35017e6 4.07061e6i −0.598928 1.03737i
\(435\) 105339. + 88390.0i 0.0266911 + 0.0223965i
\(436\) −1.07055e6 + 1.85424e6i −0.269706 + 0.467144i
\(437\) 707340. + 4.01152e6i 0.177184 + 1.00486i
\(438\) 264138. 0.0657879
\(439\) 1.00632e6 + 5.70715e6i 0.249217 + 1.41338i 0.810493 + 0.585749i \(0.199200\pi\)
−0.561276 + 0.827629i \(0.689689\pi\)
\(440\) 107060. 89834.3i 0.0263631 0.0221213i
\(441\) −540080. 196573.i −0.132240 0.0481313i
\(442\) −1.31043e6 + 476957.i −0.319049 + 0.116124i
\(443\) 4.78489e6 1.15841 0.579205 0.815182i \(-0.303363\pi\)
0.579205 + 0.815182i \(0.303363\pi\)
\(444\) 90454.7 321684.i 0.0217758 0.0774412i
\(445\) −679410. −0.162642
\(446\) −5.28495e6 + 1.92357e6i −1.25807 + 0.457899i
\(447\) 915960. + 333382.i 0.216824 + 0.0789175i
\(448\) 376251. 315712.i 0.0885692 0.0743184i
\(449\) −738624. 4.18895e6i −0.172905 0.980593i −0.940534 0.339699i \(-0.889675\pi\)
0.767629 0.640894i \(-0.221436\pi\)
\(450\) 2.84856e6 0.663123
\(451\) −171234. 971117.i −0.0396414 0.224817i
\(452\) −1.51621e6 + 2.62616e6i −0.349071 + 0.604609i
\(453\) −250948. 210570.i −0.0574563 0.0482115i
\(454\) 1.28463e6 + 2.22505e6i 0.292509 + 0.506641i
\(455\) 218911. 379165.i 0.0495723 0.0858618i
\(456\) 236068. 85921.9i 0.0531650 0.0193505i
\(457\) 3.38601e6 2.84120e6i 0.758400 0.636373i −0.179310 0.983793i \(-0.557387\pi\)
0.937710 + 0.347420i \(0.112942\pi\)
\(458\) −293916. 509077.i −0.0654725 0.113402i
\(459\) −215320. + 1.22114e6i −0.0477038 + 0.270542i
\(460\) 78051.0 442649.i 0.0171982 0.0975360i
\(461\) −4.73438e6 3.97262e6i −1.03756 0.870612i −0.0458247 0.998949i \(-0.514592\pi\)
−0.991731 + 0.128337i \(0.959036\pi\)
\(462\) 228698. + 83239.2i 0.0498491 + 0.0181436i
\(463\) −1.63975e6 596821.i −0.355489 0.129387i 0.158102 0.987423i \(-0.449463\pi\)
−0.513590 + 0.858036i \(0.671685\pi\)
\(464\) −996156. 835874.i −0.214799 0.180238i
\(465\) −46065.7 + 261251.i −0.00987973 + 0.0560307i
\(466\) 530519. 3.00873e6i 0.113171 0.641827i
\(467\) −2.53715e6 4.39448e6i −0.538337 0.932427i −0.998994 0.0448489i \(-0.985719\pi\)
0.460657 0.887578i \(-0.347614\pi\)
\(468\) −981414. + 823504.i −0.207127 + 0.173801i
\(469\) −3.90119e6 + 1.41992e6i −0.818964 + 0.298078i
\(470\) 345616. 598624.i 0.0721687 0.125000i
\(471\) −465792. 806775.i −0.0967475 0.167572i
\(472\) 1.40726e6 + 1.18084e6i 0.290751 + 0.243969i
\(473\) −437737. + 758182.i −0.0899622 + 0.155819i
\(474\) −48.1736 273.206i −9.84835e−6 5.58528e-5i
\(475\) 4.70860e6 0.957541
\(476\) 343368. + 1.94734e6i 0.0694612 + 0.393934i
\(477\) 754235. 632878.i 0.151779 0.127357i
\(478\) 1.81446e6 + 660409.i 0.363226 + 0.132204i
\(479\) 1.86765e6 679769.i 0.371926 0.135370i −0.149293 0.988793i \(-0.547700\pi\)
0.521219 + 0.853423i \(0.325477\pi\)
\(480\) −27720.6 −0.00549160
\(481\) 210935. + 2.80896e6i 0.0415705 + 0.553583i
\(482\) 564458. 0.110666
\(483\) 735522. 267708.i 0.143459 0.0522148i
\(484\) 1.80602e6 + 657339.i 0.350437 + 0.127549i
\(485\) 1.05413e6 884523.i 0.203489 0.170748i
\(486\) 298017. + 1.69014e6i 0.0572334 + 0.324587i
\(487\) −7.54640e6 −1.44184 −0.720920 0.693018i \(-0.756281\pi\)
−0.720920 + 0.693018i \(0.756281\pi\)
\(488\) −441001. 2.50104e6i −0.0838281 0.475413i
\(489\) −609180. + 1.05513e6i −0.115205 + 0.199542i
\(490\) 80304.9 + 67383.8i 0.0151096 + 0.0126784i
\(491\) 287775. + 498440.i 0.0538702 + 0.0933060i 0.891703 0.452621i \(-0.149511\pi\)
−0.837833 + 0.545927i \(0.816178\pi\)
\(492\) −97795.1 + 169386.i −0.0182140 + 0.0315475i
\(493\) 4.91955e6 1.79057e6i 0.911608 0.331798i
\(494\) −1.62225e6 + 1.36123e6i −0.299089 + 0.250966i
\(495\) 258453. + 447653.i 0.0474098 + 0.0821162i
\(496\) 435628. 2.47057e6i 0.0795081 0.450913i
\(497\) 525252. 2.97885e6i 0.0953843 0.540951i
\(498\) 396307. + 332541.i 0.0716074 + 0.0600857i
\(499\) −6.88858e6 2.50724e6i −1.23845 0.450759i −0.361966 0.932191i \(-0.617894\pi\)
−0.876483 + 0.481433i \(0.840117\pi\)
\(500\) −995373. 362286.i −0.178058 0.0648077i
\(501\) 783516. + 657448.i 0.139461 + 0.117022i
\(502\) 105054. 595792.i 0.0186061 0.105520i
\(503\) −1.07364e6 + 6.08891e6i −0.189207 + 1.07305i 0.731222 + 0.682140i \(0.238950\pi\)
−0.920429 + 0.390909i \(0.872161\pi\)
\(504\) 908302. + 1.57322e6i 0.159277 + 0.275876i
\(505\) −923753. + 775121.i −0.161186 + 0.135251i
\(506\) −1.97918e6 + 720361.i −0.343643 + 0.125076i
\(507\) 322113. 557917.i 0.0556530 0.0963939i
\(508\) −207533. 359457.i −0.0356802 0.0617999i
\(509\) 6.23301e6 + 5.23012e6i 1.06636 + 0.894782i 0.994718 0.102649i \(-0.0327318\pi\)
0.0716417 + 0.997430i \(0.477176\pi\)
\(510\) 55800.5 96649.2i 0.00949975 0.0164541i
\(511\) 548246. + 3.10926e6i 0.0928802 + 0.526750i
\(512\) 262144. 0.0441942
\(513\) 326980. + 1.85439e6i 0.0548564 + 0.311106i
\(514\) 4.49366e6 3.77063e6i 0.750227 0.629515i
\(515\) −1.33550e6 486084.i −0.221885 0.0807594i
\(516\) 163176. 59391.2i 0.0269794 0.00981969i
\(517\) −3.23902e6 −0.532952
\(518\) 3.97440e6 + 397084.i 0.650799 + 0.0650216i
\(519\) −558486. −0.0910110
\(520\) 219584. 79921.9i 0.0356116 0.0129616i
\(521\) 7.16710e6 + 2.60861e6i 1.15678 + 0.421032i 0.847945 0.530085i \(-0.177840\pi\)
0.308831 + 0.951117i \(0.400062\pi\)
\(522\) 3.68438e6 3.09156e6i 0.591817 0.496594i
\(523\) −1.36543e6 7.74372e6i −0.218280 1.23793i −0.875123 0.483901i \(-0.839220\pi\)
0.656843 0.754028i \(-0.271892\pi\)
\(524\) 511763. 0.0814219
\(525\) −157113. 891034.i −0.0248780 0.141090i
\(526\) 987305. 1.71006e6i 0.155592 0.269493i
\(527\) 7.73687e6 + 6.49200e6i 1.21350 + 1.01824i
\(528\) 64947.5 + 112492.i 0.0101386 + 0.0175606i
\(529\) −168725. + 292240.i −0.0262144 + 0.0454047i
\(530\) −168754. + 61421.5i −0.0260954 + 0.00949796i
\(531\) −5.20490e6 + 4.36743e6i −0.801080 + 0.672186i
\(532\) 1.50140e6 + 2.60050e6i 0.229994 + 0.398361i
\(533\) 286305. 1.62372e6i 0.0436527 0.247567i
\(534\) 109653. 621872.i 0.0166405 0.0943731i
\(535\) −945825. 793642.i −0.142865 0.119878i
\(536\) −2.08216e6 757843.i −0.313041 0.113938i
\(537\) −414686. 150933.i −0.0620559 0.0225865i
\(538\) −1.89690e6 1.59169e6i −0.282546 0.237085i
\(539\) 85299.9 483760.i 0.0126467 0.0717229i
\(540\) 36080.4 204622.i 0.00532459 0.0301973i
\(541\) −5.88780e6 1.01980e7i −0.864888 1.49803i −0.867159 0.498032i \(-0.834056\pi\)
0.00227115 0.999997i \(-0.499277\pi\)
\(542\) 6.58765e6 5.52769e6i 0.963234 0.808250i
\(543\) 312083. 113589.i 0.0454225 0.0165324i
\(544\) −527686. + 913979.i −0.0764502 + 0.132416i
\(545\) 722202. + 1.25089e6i 0.104152 + 0.180396i
\(546\) 311723. + 261567.i 0.0447495 + 0.0375493i
\(547\) −5.63689e6 + 9.76337e6i −0.805510 + 1.39518i 0.110436 + 0.993883i \(0.464775\pi\)
−0.915946 + 0.401301i \(0.868558\pi\)
\(548\) −122559. 695066.i −0.0174339 0.0988723i
\(549\) 9.39303e6 1.33007
\(550\) 422768. + 2.39764e6i 0.0595930 + 0.337969i
\(551\) 6.09017e6 5.11026e6i 0.854576 0.717074i
\(552\) 392565. + 142882.i 0.0548358 + 0.0199586i
\(553\) 3116.01 1134.13i 0.000433297 0.000157707i
\(554\) 6.81192e6 0.942964
\(555\) −157426. 161352.i −0.0216943 0.0222352i
\(556\) −2.29430e6 −0.314748
\(557\) −1.02556e7 + 3.73273e6i −1.40063 + 0.509786i −0.928364 0.371672i \(-0.878785\pi\)
−0.472262 + 0.881458i \(0.656562\pi\)
\(558\) 8.71902e6 + 3.17346e6i 1.18545 + 0.431467i
\(559\) −1.12134e6 + 940914.i −0.151777 + 0.127356i
\(560\) −57536.8 326308.i −0.00775311 0.0439701i
\(561\) −522948. −0.0701538
\(562\) 621715. + 3.52592e6i 0.0830330 + 0.470903i
\(563\) 5.76456e6 9.98451e6i 0.766470 1.32756i −0.172996 0.984923i \(-0.555345\pi\)
0.939466 0.342642i \(-0.111322\pi\)
\(564\) 492148. + 412961.i 0.0651475 + 0.0546652i
\(565\) 1.02285e6 + 1.77163e6i 0.134800 + 0.233481i
\(566\) −1.88144e6 + 3.25876e6i −0.246860 + 0.427574i
\(567\) −6.14144e6 + 2.23530e6i −0.802256 + 0.291997i
\(568\) 1.23671e6 1.03772e6i 0.160841 0.134962i
\(569\) 369142. + 639374.i 0.0477984 + 0.0827893i 0.888935 0.458034i \(-0.151446\pi\)
−0.841136 + 0.540823i \(0.818113\pi\)
\(570\) 29428.9 166900.i 0.00379391 0.0215163i
\(571\) 942489. 5.34512e6i 0.120972 0.686068i −0.862647 0.505807i \(-0.831195\pi\)
0.983619 0.180261i \(-0.0576942\pi\)
\(572\) −838800. 703837.i −0.107193 0.0899460i
\(573\) −2.24957e6 818776.i −0.286228 0.104179i
\(574\) −2.19688e6 799600.i −0.278309 0.101296i
\(575\) 5.99818e6 + 5.03307e6i 0.756571 + 0.634838i
\(576\) −168363. + 954834.i −0.0211442 + 0.119914i
\(577\) 701822. 3.98023e6i 0.0877582 0.497701i −0.908969 0.416864i \(-0.863129\pi\)
0.996727 0.0808379i \(-0.0257596\pi\)
\(578\) 715288. + 1.23891e6i 0.0890556 + 0.154249i
\(579\) −357338. + 299843.i −0.0442979 + 0.0371704i
\(580\) −824350. + 300039.i −0.101752 + 0.0370346i
\(581\) −3.09187e6 + 5.35527e6i −0.379998 + 0.658175i
\(582\) 639484. + 1.10762e6i 0.0782568 + 0.135545i
\(583\) 644634. + 540912.i 0.0785492 + 0.0659106i
\(584\) −842542. + 1.45932e6i −0.102225 + 0.177060i
\(585\) 150079. + 851141.i 0.0181314 + 0.102828i
\(586\) 2.89604e6 0.348386
\(587\) 1.33971e6 + 7.59790e6i 0.160479 + 0.910119i 0.953605 + 0.301062i \(0.0973411\pi\)
−0.793126 + 0.609058i \(0.791548\pi\)
\(588\) −74638.0 + 62628.7i −0.00890259 + 0.00747016i
\(589\) 1.44123e7 + 5.24565e6i 1.71177 + 0.623033i
\(590\) 1.16455e6 423863.i 0.137730 0.0501297i
\(591\) −907855. −0.106917
\(592\) 1.48873e6 + 1.52585e6i 0.174587 + 0.178940i
\(593\) 6.59070e6 0.769653 0.384826 0.922989i \(-0.374261\pi\)
0.384826 + 0.922989i \(0.374261\pi\)
\(594\) −914907. + 332999.i −0.106392 + 0.0387237i
\(595\) 1.25351e6 + 456240.i 0.145156 + 0.0528325i
\(596\) −4.76359e6 + 3.99713e6i −0.549312 + 0.460927i
\(597\) −201308. 1.14168e6i −0.0231167 0.131101i
\(598\) −3.52158e6 −0.402703
\(599\) −333181. 1.88956e6i −0.0379413 0.215176i 0.959943 0.280197i \(-0.0903997\pi\)
−0.997884 + 0.0650208i \(0.979289\pi\)
\(600\) 241451. 418206.i 0.0273811 0.0474255i
\(601\) −1.24634e7 1.04581e7i −1.40751 1.18104i −0.957647 0.287945i \(-0.907028\pi\)
−0.449864 0.893097i \(-0.648527\pi\)
\(602\) 1.03780e6 + 1.79752e6i 0.116714 + 0.202155i
\(603\) 4.09764e6 7.09732e6i 0.458924 0.794879i
\(604\) 1.96383e6 714777.i 0.219035 0.0797221i
\(605\) 993216. 833407.i 0.110320 0.0925697i
\(606\) −560389. 970622.i −0.0619881 0.107366i
\(607\) −1.44082e6 + 8.17127e6i −0.158722 + 0.900156i 0.796582 + 0.604530i \(0.206639\pi\)
−0.955304 + 0.295626i \(0.904472\pi\)
\(608\) −278299. + 1.57831e6i −0.0305319 + 0.173155i
\(609\) −1.17026e6 981962.i −0.127861 0.107288i
\(610\) −1.60993e6 585967.i −0.175179 0.0637600i
\(611\) −5.08908e6 1.85227e6i −0.551488 0.200725i
\(612\) −2.99017e6 2.50905e6i −0.322714 0.270789i
\(613\) −1.15259e6 + 6.53666e6i −0.123886 + 0.702595i 0.858077 + 0.513522i \(0.171659\pi\)
−0.981963 + 0.189073i \(0.939452\pi\)
\(614\) 634915. 3.60078e6i 0.0679664 0.385457i
\(615\) 65973.5 + 114269.i 0.00703366 + 0.0121827i
\(616\) −1.18938e6 + 998007.i −0.126290 + 0.105970i
\(617\) −1.58829e7 + 5.78091e6i −1.67965 + 0.611341i −0.993261 0.115898i \(-0.963026\pi\)
−0.686385 + 0.727239i \(0.740803\pi\)
\(618\) 660461. 1.14395e6i 0.0695627 0.120486i
\(619\) −5.27879e6 9.14313e6i −0.553742 0.959110i −0.998000 0.0632107i \(-0.979866\pi\)
0.444258 0.895899i \(-0.353467\pi\)
\(620\) −1.29644e6 1.08784e6i −0.135448 0.113654i
\(621\) −1.56565e6 + 2.71178e6i −0.162917 + 0.282180i
\(622\) −1.39511e6 7.91205e6i −0.144588 0.819999i
\(623\) 7.54786e6 0.779119
\(624\) 37714.0 + 213886.i 0.00387740 + 0.0219898i
\(625\) 6.65460e6 5.58387e6i 0.681431 0.571789i
\(626\) −1.71837e6 625437.i −0.175260 0.0637893i
\(627\) −746243. + 271610.i −0.0758074 + 0.0275916i
\(628\) 5.94309e6 0.601330
\(629\) −8.31671e6 + 2.11905e6i −0.838156 + 0.213557i
\(630\) 1.22550e6 0.123016
\(631\) −7.58685e6 + 2.76139e6i −0.758557 + 0.276092i −0.692202 0.721704i \(-0.743359\pi\)
−0.0663550 + 0.997796i \(0.521137\pi\)
\(632\) 1663.09 + 605.314i 0.000165624 + 6.02821e-5i
\(633\) 314288. 263719.i 0.0311758 0.0261596i
\(634\) −1.90411e6 1.07987e7i −0.188134 1.06696i
\(635\) −280007. −0.0275572
\(636\) −28983.9 164376.i −0.00284128 0.0161137i
\(637\) 410665. 711293.i 0.0400995 0.0694544i
\(638\) 3.14898e6 + 2.64231e6i 0.306280 + 0.256999i
\(639\) 2.98552e6 + 5.17108e6i 0.289247 + 0.500990i
\(640\) 88422.3 153152.i 0.00853320 0.0147799i
\(641\) −1.73913e7 + 6.32990e6i −1.67181 + 0.608488i −0.992151 0.125043i \(-0.960093\pi\)
−0.679656 + 0.733531i \(0.737871\pi\)
\(642\) 879081. 737637.i 0.0841766 0.0706325i
\(643\) −8.34353e6 1.44514e7i −0.795834 1.37843i −0.922308 0.386455i \(-0.873699\pi\)
0.126474 0.991970i \(-0.459634\pi\)
\(644\) −867101. + 4.91758e6i −0.0823863 + 0.467236i
\(645\) 20342.0 115365.i 0.00192528 0.0109188i
\(646\) −4.94267e6 4.14739e6i −0.465994 0.391016i
\(647\) 4.73540e6 + 1.72354e6i 0.444729 + 0.161868i 0.554671 0.832070i \(-0.312844\pi\)
−0.109942 + 0.993938i \(0.535066\pi\)
\(648\) −3.27783e6 1.19303e6i −0.306654 0.111613i
\(649\) −4.44855e6 3.73278e6i −0.414578 0.347873i
\(650\) −706873. + 4.00888e6i −0.0656233 + 0.372168i
\(651\) 511763. 2.90235e6i 0.0473278 0.268410i
\(652\) −3.88629e6 6.73125e6i −0.358027 0.620122i
\(653\) 4.44455e6 3.72942e6i 0.407892 0.342262i −0.415643 0.909528i \(-0.636443\pi\)
0.823535 + 0.567266i \(0.191999\pi\)
\(654\) −1.26151e6 + 459154.i −0.115331 + 0.0419772i
\(655\) 172620. 298987.i 0.0157213 0.0272301i
\(656\) −623889. 1.08061e6i −0.0566041 0.0980411i
\(657\) −4.77432e6 4.00613e6i −0.431517 0.362086i
\(658\) −3.83959e6 + 6.65037e6i −0.345717 + 0.598799i
\(659\) −1.16304e6 6.59591e6i −0.104323 0.591645i −0.991489 0.130194i \(-0.958440\pi\)
0.887166 0.461451i \(-0.152671\pi\)
\(660\) 87628.3 0.00783041
\(661\) 1.42402e6 + 8.07600e6i 0.126768 + 0.718940i 0.980242 + 0.197803i \(0.0633807\pi\)
−0.853473 + 0.521137i \(0.825508\pi\)
\(662\) −1.84232e6 + 1.54589e6i −0.163388 + 0.137099i
\(663\) −821644. 299054.i −0.0725938 0.0264220i
\(664\) −3.10137e6 + 1.12881e6i −0.272981 + 0.0993571i
\(665\) 2.02571e6 0.177633
\(666\) −6.51390e6 + 4.44256e6i −0.569056 + 0.388104i
\(667\) 1.32206e7 1.15063
\(668\) −6.13155e6 + 2.23170e6i −0.531654 + 0.193506i
\(669\) −3.31368e6 1.20608e6i −0.286250 0.104187i
\(670\) −1.14507e6 + 960831.i −0.0985477 + 0.0826913i
\(671\) 1.39406e6 + 7.90612e6i 0.119530 + 0.677886i
\(672\) 307960. 0.0263069
\(673\) −3.29384e6 1.86803e7i −0.280327 1.58981i −0.721515 0.692399i \(-0.756554\pi\)
0.441188 0.897415i \(-0.354557\pi\)
\(674\) 1.08270e6 1.87529e6i 0.0918033 0.159008i
\(675\) 2.77276e6 + 2.32662e6i 0.234235 + 0.196547i
\(676\) 2.05494e6 + 3.55926e6i 0.172955 + 0.299566i
\(677\) −2.69289e6 + 4.66422e6i −0.225812 + 0.391118i −0.956563 0.291527i \(-0.905837\pi\)
0.730751 + 0.682644i \(0.239170\pi\)
\(678\) −1.78668e6 + 650297.i −0.149270 + 0.0543297i
\(679\) −1.17108e7 + 9.82654e6i −0.974794 + 0.817949i
\(680\) 355982. + 616579.i 0.0295227 + 0.0511348i
\(681\) −279737. + 1.58647e6i −0.0231144 + 0.131088i
\(682\) −1.37708e6 + 7.80979e6i −0.113370 + 0.642952i
\(683\) −5.55233e6 4.65896e6i −0.455432 0.382153i 0.386015 0.922492i \(-0.373851\pi\)
−0.841447 + 0.540340i \(0.818296\pi\)
\(684\) −5.57012e6 2.02736e6i −0.455223 0.165688i
\(685\) −447417. 162847.i −0.0364323 0.0132603i
\(686\) −7.06758e6 5.93040e6i −0.573404 0.481143i
\(687\) 64001.9 362973.i 0.00517370 0.0293415i
\(688\) −192367. + 1.09097e6i −0.0154939 + 0.0878700i
\(689\) 703507. + 1.21851e6i 0.0564573 + 0.0977869i
\(690\) 215890. 181153.i 0.0172627 0.0144851i
\(691\) 2.09066e7 7.60940e6i 1.66567 0.606255i 0.674432 0.738337i \(-0.264388\pi\)
0.991239 + 0.132082i \(0.0421662\pi\)
\(692\) 1.78145e6 3.08555e6i 0.141419 0.244945i
\(693\) −2.87126e6 4.97317e6i −0.227112 0.393369i
\(694\) 1.22553e6 + 1.02834e6i 0.0965881 + 0.0810470i
\(695\) −773878. + 1.34040e6i −0.0607729 + 0.105262i
\(696\) −141584. 802962.i −0.0110787 0.0628307i
\(697\) 5.02346e6 0.391671
\(698\) −211959. 1.20208e6i −0.0164669 0.0933886i
\(699\) 1.46742e6 1.23131e6i 0.113596 0.0953181i
\(700\) 5.42399e6 + 1.97417e6i 0.418383 + 0.152279i
\(701\) 4.99004e6 1.81623e6i 0.383539 0.139597i −0.143053 0.989715i \(-0.545692\pi\)
0.526592 + 0.850118i \(0.323470\pi\)
\(702\) −1.62791e6 −0.124677
\(703\) −1.07673e7 + 7.34343e6i −0.821709 + 0.560416i
\(704\) −828672. −0.0630160
\(705\) 407267. 148233.i 0.0308608 0.0112324i
\(706\) −2.40852e6 876628.i −0.181860 0.0661917i
\(707\) 1.02624e7 8.61115e6i 0.772145 0.647907i
\(708\) 200015. + 1.13434e6i 0.0149961 + 0.0850472i
\(709\) 1.41130e7 1.05439 0.527196 0.849743i \(-0.323243\pi\)
0.527196 + 0.849743i \(0.323243\pi\)
\(710\) −189119. 1.07255e6i −0.0140796 0.0798494i
\(711\) −3272.92 + 5668.87i −0.000242807 + 0.000420555i
\(712\) 3.08599e6 + 2.58945e6i 0.228136 + 0.191429i
\(713\) 1.27524e7 + 2.20878e7i 0.939437 + 1.62715i
\(714\) −619911. + 1.07372e6i −0.0455076 + 0.0788215i
\(715\) −694132. + 252644.i −0.0507782 + 0.0184818i
\(716\) 2.15664e6 1.80963e6i 0.157215 0.131919i
\(717\) 605343. + 1.04848e6i 0.0439748 + 0.0761665i
\(718\) −558222. + 3.16583e6i −0.0404106 + 0.229180i
\(719\) −232727. + 1.31986e6i −0.0167890 + 0.0952150i −0.992051 0.125838i \(-0.959838\pi\)
0.975262 + 0.221053i \(0.0709493\pi\)
\(720\) 501051. + 420432.i 0.0360206 + 0.0302249i
\(721\) 1.48367e7 + 5.40011e6i 1.06292 + 0.386870i
\(722\) 99837.2 + 36337.8i 0.00712770 + 0.00259427i
\(723\) 271116. + 227493.i 0.0192890 + 0.0161854i
\(724\) −367913. + 2.08654e6i −0.0260855 + 0.147938i
\(725\) 2.65371e6 1.50499e7i 0.187503 1.06338i
\(726\) 602529. + 1.04361e6i 0.0424264 + 0.0734847i
\(727\) 2.06273e6 1.73084e6i 0.144746 0.121456i −0.567539 0.823346i \(-0.692105\pi\)
0.712286 + 0.701890i \(0.247660\pi\)
\(728\) −2.43945e6 + 887886.i −0.170594 + 0.0620910i
\(729\) 6.08409e6 1.05379e7i 0.424010 0.734408i
\(730\) 568386. + 984473.i 0.0394763 + 0.0683749i
\(731\) −3.41649e6 2.86678e6i −0.236476 0.198427i
\(732\) 796176. 1.37902e6i 0.0549201 0.0951244i
\(733\) 2.79685e6 + 1.58617e7i 0.192269 + 1.09041i 0.916254 + 0.400597i \(0.131197\pi\)
−0.723985 + 0.689816i \(0.757691\pi\)
\(734\) 8.72808e6 0.597969
\(735\) 11413.7 + 64730.6i 0.000779309 + 0.00441968i
\(736\) −2.04160e6 + 1.71310e6i −0.138923 + 0.116571i
\(737\) 6.58197e6 + 2.39564e6i 0.446362 + 0.162462i
\(738\) 4.33670e6 1.57843e6i 0.293102 0.106680i
\(739\) 1.49651e7 1.00802 0.504011 0.863697i \(-0.331857\pi\)
0.504011 + 0.863697i \(0.331857\pi\)
\(740\) 1.39360e6 355081.i 0.0935532 0.0238368i
\(741\) −1.32780e6 −0.0888359
\(742\) 1.87476e6 682357.i 0.125008 0.0454990i
\(743\) 2.17263e7 + 7.90772e6i 1.44382 + 0.525508i 0.940859 0.338800i \(-0.110021\pi\)
0.502963 + 0.864308i \(0.332243\pi\)
\(744\) 1.20495e6 1.01107e6i 0.0798062 0.0669654i
\(745\) 728455. + 4.13128e6i 0.0480853 + 0.272705i
\(746\) −1.45215e7 −0.955353
\(747\) −2.11970e6 1.20214e7i −0.138986 0.788231i
\(748\) 1.66809e6 2.88921e6i 0.109010 0.188810i
\(749\) 1.05076e7 + 8.81691e6i 0.684381 + 0.574264i
\(750\) −332078. 575176.i −0.0215569 0.0373377i
\(751\) 2.16928e6 3.75731e6i 0.140351 0.243095i −0.787278 0.616599i \(-0.788510\pi\)
0.927629 + 0.373503i \(0.121844\pi\)
\(752\) −3.85139e6 + 1.40179e6i −0.248355 + 0.0903938i
\(753\) 290581. 243827.i 0.0186758 0.0156709i
\(754\) 3.43657e6 + 5.95232e6i 0.220139 + 0.381292i
\(755\) 244817. 1.38843e6i 0.0156305 0.0886452i
\(756\) −400832. + 2.27323e6i −0.0255069 + 0.144657i
\(757\) 2.00598e6 + 1.68322e6i 0.127229 + 0.106758i 0.704182 0.710020i \(-0.251314\pi\)
−0.576953 + 0.816777i \(0.695758\pi\)
\(758\) 3.48186e6 + 1.26729e6i 0.220109 + 0.0801133i
\(759\) −1.24095e6 451669.i −0.0781898 0.0284587i
\(760\) 828224. + 694963.i 0.0520133 + 0.0436443i
\(761\) −4.89556e6 + 2.77641e7i −0.306437 + 1.73789i 0.310226 + 0.950663i \(0.399595\pi\)
−0.616663 + 0.787227i \(0.711516\pi\)
\(762\) 45191.5 256294.i 0.00281948 0.0159901i
\(763\) −8.02325e6 1.38967e7i −0.498929 0.864171i
\(764\) 1.16992e7 9.81683e6i 0.725144 0.608468i
\(765\) −2.47446e6 + 900629.i −0.152871 + 0.0556407i
\(766\) −1.72398e6 + 2.98603e6i −0.106160 + 0.183875i
\(767\) −4.85483e6 8.40881e6i −0.297979 0.516114i
\(768\) 125911. + 105652.i 0.00770302 + 0.00646360i
\(769\) −1.53956e7 + 2.66660e7i −0.938817 + 1.62608i −0.171135 + 0.985248i \(0.554743\pi\)
−0.767682 + 0.640831i \(0.778590\pi\)
\(770\) 181882. + 1.03150e6i 0.0110551 + 0.0626965i
\(771\) 3.67804e6 0.222834
\(772\) −516757. 2.93067e6i −0.0312063 0.176980i
\(773\) −5.21608e6 + 4.37681e6i −0.313975 + 0.263456i −0.786133 0.618058i \(-0.787920\pi\)
0.472158 + 0.881514i \(0.343475\pi\)
\(774\) −3.85019e6 1.40136e6i −0.231010 0.0840806i
\(775\) 2.77039e7 1.00834e7i 1.65686 0.603048i
\(776\) −8.15923e6 −0.486402
\(777\) 1.74892e6 + 1.79253e6i 0.103924 + 0.106515i
\(778\) −1.62616e6 −0.0963195
\(779\) 7.16845e6 2.60910e6i 0.423235 0.154045i
\(780\) 137680. + 50111.3i 0.00810276 + 0.00294916i
\(781\) −3.90940e6 + 3.28038e6i −0.229342 + 0.192440i
\(782\) −1.86317e6 1.05666e7i −0.108952 0.617897i
\(783\) 6.11142e6 0.356236
\(784\) −107936. 612135.i −0.00627156 0.0355678i
\(785\) 2.00463e6 3.47212e6i 0.116107 0.201104i
\(786\) 245806. + 206256.i 0.0141918 + 0.0119083i
\(787\) 5.80127e6 + 1.00481e7i 0.333877 + 0.578292i 0.983268 0.182163i \(-0.0583097\pi\)
−0.649392 + 0.760454i \(0.724976\pi\)
\(788\) 2.89585e6 5.01577e6i 0.166135 0.287754i
\(789\) 1.16342e6 423451.i 0.0665341 0.0242164i
\(790\) 914.609 767.448i 5.21396e−5 4.37503e-5i
\(791\) −1.13633e7 1.96818e7i −0.645747 1.11847i
\(792\) 532217. 3.01836e6i 0.0301492 0.170985i
\(793\) −2.33089e6 + 1.32191e7i −0.131625 + 0.746482i
\(794\) 1.17002e7 + 9.81763e6i 0.658631 + 0.552657i
\(795\) −105809. 38511.5i −0.00593754 0.00216109i
\(796\) 6.94973e6 + 2.52949e6i 0.388763 + 0.141498i
\(797\) −2.47223e7 2.07445e7i −1.37862 1.15680i −0.969721 0.244216i \(-0.921469\pi\)
−0.408896 0.912581i \(-0.634086\pi\)
\(798\) −326938. + 1.85416e6i −0.0181743 + 0.103072i
\(799\) 2.86528e6 1.62498e7i 0.158782 0.900496i
\(800\) 1.54035e6 + 2.66796e6i 0.0850931 + 0.147386i
\(801\) −1.14138e7 + 9.57732e6i −0.628563 + 0.527427i
\(802\) −1.81970e7 + 6.62316e6i −0.998995 + 0.363604i
\(803\) 2.66338e6 4.61312e6i 0.145762 0.252468i
\(804\) −694652. 1.20317e6i −0.0378989 0.0656429i
\(805\) 2.58051e6 + 2.16531e6i 0.140351 + 0.117769i
\(806\) −6.62975e6 + 1.14831e7i −0.359467 + 0.622616i
\(807\) −269607. 1.52902e6i −0.0145730 0.0826474i
\(808\) 7.15006e6 0.385284
\(809\) −3.88108e6 2.20107e7i −0.208488 1.18239i −0.891856 0.452320i \(-0.850597\pi\)
0.683368 0.730074i \(-0.260514\pi\)
\(810\) −1.80263e6 + 1.51259e6i −0.0965371 + 0.0810043i
\(811\) −2.14889e6 782133.i −0.114726 0.0417569i 0.284019 0.958819i \(-0.408332\pi\)
−0.398745 + 0.917062i \(0.630554\pi\)
\(812\) 9.15805e6 3.33326e6i 0.487431 0.177410i
\(813\) 5.39195e6 0.286101
\(814\) −4.70606e6 4.82341e6i −0.248941 0.255149i
\(815\) −5.24345e6 −0.276518
\(816\) −621815. + 226322.i −0.0326916 + 0.0118988i
\(817\) −6.36427e6 2.31640e6i −0.333575 0.121411i
\(818\) 5.11815e6 4.29464e6i 0.267442 0.224411i
\(819\) −1.66729e6 9.45569e6i −0.0868565 0.492588i
\(820\) −841762. −0.0437174
\(821\) −6.22137e6 3.52832e7i −0.322128 1.82688i −0.529134 0.848539i \(-0.677483\pi\)
0.207006 0.978340i \(-0.433628\pi\)
\(822\) 221266. 383244.i 0.0114218 0.0197832i
\(823\) 2.71350e7 + 2.27690e7i 1.39647 + 1.17178i 0.962641 + 0.270779i \(0.0872814\pi\)
0.433827 + 0.900996i \(0.357163\pi\)
\(824\) 4.21345e6 + 7.29790e6i 0.216182 + 0.374438i
\(825\) −763259. + 1.32200e6i −0.0390424 + 0.0676235i
\(826\) −1.29375e7 + 4.70888e6i −0.659783 + 0.240141i
\(827\) 766900. 643506.i 0.0389920 0.0327182i −0.623083 0.782155i \(-0.714120\pi\)
0.662075 + 0.749437i \(0.269676\pi\)
\(828\) −4.92859e6 8.53656e6i −0.249831 0.432720i
\(829\) −2.26097e6 + 1.28226e7i −0.114264 + 0.648021i 0.872848 + 0.487991i \(0.162270\pi\)
−0.987112 + 0.160030i \(0.948841\pi\)
\(830\) −386625. + 2.19266e6i −0.0194802 + 0.110478i
\(831\) 3.27185e6 + 2.74541e6i 0.164358 + 0.137913i
\(832\) −1.30199e6 473886.i −0.0652078 0.0237337i
\(833\) 2.35151e6 + 855881.i 0.117418 + 0.0427367i
\(834\) −1.10198e6 924672.i −0.0548604 0.0460333i
\(835\) −764375. + 4.33499e6i −0.0379394 + 0.215165i
\(836\) 879741. 4.98926e6i 0.0435351 0.246900i
\(837\) 5.89500e6 + 1.02104e7i 0.290851 + 0.503768i
\(838\) 1.66090e7 1.39366e7i 0.817022 0.685563i
\(839\) −2.99521e7 + 1.09017e7i −1.46900 + 0.534674i −0.947830 0.318777i \(-0.896728\pi\)
−0.521174 + 0.853450i \(0.674506\pi\)
\(840\) 103876. 179919.i 0.00507946 0.00879788i
\(841\) −2.64583e6 4.58272e6i −0.128995 0.223426i
\(842\) 1.99034e7 + 1.67009e7i 0.967490 + 0.811820i
\(843\) −1.12243e6 + 1.94411e6i −0.0543991 + 0.0942221i
\(844\) 454500. + 2.57760e6i 0.0219623 + 0.124554i
\(845\) 2.77256e6 0.133579
\(846\) −2.63232e6 1.49286e7i −0.126448 0.717123i
\(847\) −1.10341e7 + 9.25868e6i −0.528478 + 0.443446i
\(848\) 1.00060e6 + 364190.i 0.0477829 + 0.0173916i
\(849\) −2.21706e6 + 806943.i −0.105562 + 0.0384214i
\(850\) −1.24027e7 −0.588800
\(851\) −2.15657e7 2.15464e6i −1.02080 0.101988i
\(852\) 1.01224e6 0.0477733
\(853\) −2.86097e7 + 1.04131e7i −1.34630 + 0.490012i −0.911790 0.410657i \(-0.865299\pi\)
−0.434506 + 0.900669i \(0.643077\pi\)
\(854\) 1.78854e7 + 6.50975e6i 0.839178 + 0.305436i
\(855\) −3.06326e6 + 2.57038e6i −0.143308 + 0.120249i
\(856\) 1.27126e6 + 7.20969e6i 0.0592995 + 0.336304i
\(857\) −3.51354e7 −1.63415 −0.817077 0.576529i \(-0.804407\pi\)
−0.817077 + 0.576529i \(0.804407\pi\)
\(858\) −119219. 676123.i −0.00552874 0.0313551i
\(859\) −3.74157e6 + 6.48059e6i −0.173010 + 0.299662i −0.939471 0.342629i \(-0.888683\pi\)
0.766461 + 0.642291i \(0.222016\pi\)
\(860\) 572488. + 480374.i 0.0263949 + 0.0221480i
\(861\) −732928. 1.26947e6i −0.0336940 0.0583598i
\(862\) 1.16096e7 2.01084e7i 0.532168 0.921742i
\(863\) −3.82267e7 + 1.39134e7i −1.74719 + 0.635925i −0.999601 0.0282364i \(-0.991011\pi\)
−0.747589 + 0.664162i \(0.768789\pi\)
\(864\) −943762. + 791910.i −0.0430109 + 0.0360904i
\(865\) −1.20178e6 2.08154e6i −0.0546115 0.0945899i
\(866\) −1.53055e6 + 8.68018e6i −0.0693510 + 0.393309i
\(867\) −155758. + 883349.i −0.00703725 + 0.0399103i
\(868\) 1.44027e7 + 1.20853e7i 0.648849 + 0.544449i
\(869\) −5257.24 1913.48i −0.000236161 8.59556e-5i
\(870\) −516870. 188125.i −0.0231517 0.00842654i
\(871\) 8.97146e6 + 7.52795e6i 0.400699 + 0.336226i
\(872\) 1.48719e6 8.43428e6i 0.0662332 0.375627i
\(873\) 5.24030e6 2.97192e7i 0.232713 1.31978i
\(874\) −8.14682e6 1.41107e7i −0.360753 0.624842i
\(875\) 6.08132e6 5.10283e6i 0.268521 0.225316i
\(876\) −992835. + 361362.i −0.0437136 + 0.0159105i
\(877\) −1.40646e7 + 2.43607e7i −0.617490 + 1.06952i 0.372453 + 0.928051i \(0.378517\pi\)
−0.989942 + 0.141472i \(0.954816\pi\)
\(878\) −1.15904e7 2.00751e7i −0.507413 0.878865i
\(879\) 1.39101e6 + 1.16719e6i 0.0607235 + 0.0509531i
\(880\) −279515. + 484134.i −0.0121674 + 0.0210746i
\(881\) −4.27661e6 2.42538e7i −0.185635 1.05279i −0.925137 0.379633i \(-0.876050\pi\)
0.739502 0.673154i \(-0.235061\pi\)
\(882\) 2.29896e6 0.0995086
\(883\) 2.88096e6 + 1.63387e7i 0.124347 + 0.705206i 0.981694 + 0.190467i \(0.0610002\pi\)
−0.857347 + 0.514739i \(0.827889\pi\)
\(884\) 4.27309e6 3.58555e6i 0.183912 0.154321i
\(885\) 730179. + 265764.i 0.0313380 + 0.0114061i
\(886\) −1.79853e7 + 6.54611e6i −0.769721 + 0.280155i
\(887\) 1.71827e7 0.733300 0.366650 0.930359i \(-0.380505\pi\)
0.366650 + 0.930359i \(0.380505\pi\)
\(888\) 100091. + 1.33289e6i 0.00425955 + 0.0567232i
\(889\) 3.11072e6 0.132010
\(890\) 2.55375e6 929488.i 0.108069 0.0393340i
\(891\) 1.03617e7 + 3.77134e6i 0.437255 + 0.159148i
\(892\) 1.72333e7 1.44605e7i 0.725199 0.608514i
\(893\) −4.35115e6 2.46766e7i −0.182589 1.03552i
\(894\) −3.89898e6 −0.163157
\(895\) −329796. 1.87037e6i −0.0137622 0.0780493i
\(896\) −982322. + 1.70143e6i −0.0408774 + 0.0708018i
\(897\) −1.69146e6 1.41930e6i −0.0701909 0.0588971i
\(898\) 8.50713e6 + 1.47348e7i 0.352040 + 0.609752i
\(899\) 2.48891e7 4.31092e7i 1.02709 1.77898i
\(900\) −1.07071e7 + 3.89706e6i −0.440621 + 0.160373i
\(901\) −3.28395e6 + 2.75556e6i −0.134767 + 0.113083i
\(902\) 1.97220e6 + 3.41594e6i 0.0807112 + 0.139796i
\(903\) −225987. + 1.28164e6i −0.00922285 + 0.0523054i
\(904\) 2.10630e6 1.19454e7i 0.0857234 0.486161i
\(905\) 1.09492e6 + 918744.i 0.0444385 + 0.0372883i
\(906\) 1.23133e6 + 448168.i 0.0498373 + 0.0181393i
\(907\) −3.80381e7 1.38447e7i −1.53533 0.558813i −0.570408 0.821362i \(-0.693215\pi\)
−0.964919 + 0.262549i \(0.915437\pi\)
\(908\) −7.87270e6 6.60598e6i −0.316890 0.265902i
\(909\) −4.59215e6 + 2.60434e7i −0.184335 + 1.04541i
\(910\) −304108. + 1.72468e6i −0.0121738 + 0.0690408i
\(911\) 2.73081e6 + 4.72991e6i 0.109017 + 0.188824i 0.915372 0.402608i \(-0.131896\pi\)
−0.806355 + 0.591432i \(0.798563\pi\)
\(912\) −769779. + 645921.i −0.0306464 + 0.0257153i
\(913\) 9.80383e6 3.56830e6i 0.389241 0.141672i
\(914\) −8.84025e6 + 1.53118e7i −0.350025 + 0.606261i
\(915\) −537107. 930297.i −0.0212084 0.0367341i
\(916\) 1.80122e6 + 1.51140e6i 0.0709297 + 0.0595171i
\(917\) −1.91771e6 + 3.32157e6i −0.0753112 + 0.130443i
\(918\) −861281. 4.88456e6i −0.0337317 0.191302i
\(919\) 2.72417e7 1.06401 0.532005 0.846741i \(-0.321439\pi\)
0.532005 + 0.846741i \(0.321439\pi\)
\(920\) 312204. + 1.77060e6i 0.0121610 + 0.0689684i
\(921\) 1.75618e6 1.47361e6i 0.0682213 0.0572445i
\(922\) 2.32303e7 + 8.45515e6i 0.899970 + 0.327562i
\(923\) −8.01829e6 + 2.91842e6i −0.309797 + 0.112757i
\(924\) −973501. −0.0375108
\(925\) −6.78158e6 + 2.41173e7i −0.260601 + 0.926776i
\(926\) 6.97995e6 0.267501
\(927\) −2.92880e7 + 1.06600e7i −1.11941 + 0.407433i
\(928\) 4.88787e6 + 1.77904e6i 0.186316 + 0.0678134i
\(929\) −3.04790e7 + 2.55749e7i −1.15867 + 0.972242i −0.999886 0.0150710i \(-0.995203\pi\)
−0.158786 + 0.987313i \(0.550758\pi\)
\(930\) −184263. 1.04501e6i −0.00698603 0.0396197i
\(931\) 3.80013e6 0.143689
\(932\) 2.12208e6 + 1.20349e7i 0.0800242 + 0.453840i
\(933\) 2.51871e6 4.36253e6i 0.0947269 0.164072i
\(934\) 1.55486e7 + 1.30468e7i 0.583208 + 0.489369i
\(935\) −1.12531e6 1.94909e6i −0.0420961 0.0729125i
\(936\) 2.56229e6 4.43802e6i 0.0955958 0.165577i
\(937\) −7.02420e6 + 2.55660e6i −0.261365 + 0.0951292i −0.469379 0.882997i \(-0.655522\pi\)
0.208014 + 0.978126i \(0.433300\pi\)
\(938\) 1.27211e7 1.06743e7i 0.472082 0.396124i
\(939\) −573287. 992962.i −0.0212182 0.0367509i
\(940\) −480124. + 2.72292e6i −0.0177229 + 0.100511i
\(941\) −3.20984e6 + 1.82039e7i −0.118171 + 0.670178i 0.866961 + 0.498376i \(0.166070\pi\)
−0.985131 + 0.171802i \(0.945041\pi\)
\(942\) 2.85454e6 + 2.39524e6i 0.104811 + 0.0879473i
\(943\) 1.19206e7 + 4.33875e6i 0.436536 + 0.158886i
\(944\) −6.90506e6 2.51324e6i −0.252196 0.0917917i
\(945\) 1.19288e6 + 1.00095e6i 0.0434529 + 0.0364613i
\(946\) 608097. 3.44869e6i 0.0220925 0.125293i
\(947\) 7.51455e6 4.26171e7i 0.272288 1.54422i −0.475160 0.879899i \(-0.657610\pi\)
0.747448 0.664321i \(-0.231279\pi\)
\(948\) 554.842 + 961.014i 2.00516e−5 + 3.47303e-5i
\(949\) 6.82271e6 5.72494e6i 0.245919 0.206350i
\(950\) −1.76985e7 + 6.44174e6i −0.636251 + 0.231576i
\(951\) 3.43765e6 5.95418e6i 0.123257 0.213487i
\(952\) −3.95475e6 6.84984e6i −0.141425 0.244956i
\(953\) −1.69799e6 1.42478e6i −0.0605622 0.0508177i 0.612004 0.790855i \(-0.290364\pi\)
−0.672566 + 0.740037i \(0.734808\pi\)
\(954\) −1.96917e6 + 3.41070e6i −0.0700506 + 0.121331i
\(955\) −1.78906e6 1.01463e7i −0.0634772 0.359997i
\(956\) −7.72363e6 −0.273323
\(957\) 447565. + 2.53827e6i 0.0157971 + 0.0895896i
\(958\) −6.09009e6 + 5.11019e6i −0.214393 + 0.179897i
\(959\) 4.97055e6 + 1.80913e6i 0.174525 + 0.0635219i
\(960\) 104195. 37924.0i 0.00364896 0.00132811i
\(961\) 6.74017e7 2.35430
\(962\) −4.63574e6 1.02697e7i −0.161503 0.357782i
\(963\) −2.70771e7 −0.940883
\(964\) −2.12167e6 + 772224.i −0.0735334 + 0.0267640i
\(965\) −1.88649e6 686625.i −0.0652132 0.0237357i
\(966\) −2.39841e6 + 2.01251e6i −0.0826953 + 0.0693896i
\(967\) 6.35528e6 + 3.60426e7i 0.218559 + 1.23951i 0.874623 + 0.484804i \(0.161109\pi\)
−0.656064 + 0.754705i \(0.727780\pi\)
\(968\) −7.68772e6 −0.263700
\(969\) −702503. 3.98409e6i −0.0240347 0.136308i
\(970\) −2.75215e6 + 4.76686e6i −0.0939165 + 0.162668i
\(971\) 803228. + 673989.i 0.0273395 + 0.0229406i 0.656355 0.754452i \(-0.272097\pi\)
−0.629015 + 0.777393i \(0.716542\pi\)
\(972\) −3.43242e6 5.94512e6i −0.116529 0.201834i
\(973\) 8.59734e6 1.48910e7i 0.291127 0.504246i
\(974\) 2.83652e7 1.03241e7i 0.958050 0.348702i
\(975\) −1.95522e6 + 1.64062e6i −0.0658694 + 0.0552710i
\(976\) 5.07925e6 + 8.79751e6i 0.170677 + 0.295621i
\(977\) 222005. 1.25905e6i 0.00744090 0.0421995i −0.980861 0.194708i \(-0.937624\pi\)
0.988302 + 0.152509i \(0.0487352\pi\)
\(978\) 846263. 4.79940e6i 0.0282917 0.160450i
\(979\) −9.75521e6 8.18559e6i −0.325297 0.272956i
\(980\) −394034. 143417.i −0.0131060 0.00477018i
\(981\) 2.97659e7 + 1.08339e7i 0.987520 + 0.359428i
\(982\) −1.76359e6 1.47982e6i −0.0583603 0.0489701i
\(983\) 165775. 940154.i 0.00547185 0.0310324i −0.981950 0.189143i \(-0.939429\pi\)
0.987421 + 0.158110i \(0.0505402\pi\)
\(984\) 135856. 770475.i 0.00447291 0.0253671i
\(985\) −1.95357e6 3.38368e6i −0.0641561 0.111122i
\(986\) −1.60418e7 + 1.34607e7i −0.525486 + 0.440935i
\(987\) −4.52450e6 + 1.64679e6i −0.147835 + 0.0538077i
\(988\) 4.23540e6 7.33592e6i 0.138039 0.239090i
\(989\) −5.63127e6 9.75365e6i −0.183069 0.317085i
\(990\) −1.58389e6 1.32904e6i −0.0513614 0.0430973i
\(991\) −1.02075e7 + 1.76799e7i −0.330169 + 0.571869i −0.982545 0.186026i \(-0.940439\pi\)
0.652376 + 0.757896i \(0.273772\pi\)
\(992\) 1.74251e6 + 9.88227e6i 0.0562207 + 0.318843i
\(993\) −1.50793e6 −0.0485299
\(994\) 2.10101e6 + 1.19154e7i 0.0674469 + 0.382510i
\(995\) 3.82198e6 3.20702e6i 0.122386 0.102694i
\(996\) −1.94457e6 707765.i −0.0621119 0.0226069i
\(997\) 1.03464e7 3.76577e6i 0.329648 0.119982i −0.171894 0.985115i \(-0.554989\pi\)
0.501542 + 0.865133i \(0.332766\pi\)
\(998\) 2.93227e7 0.931917
\(999\) −9.96910e6 996017.i −0.316040 0.0315757i
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 74.6.f.a.7.4 48
37.16 even 9 inner 74.6.f.a.53.4 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.6.f.a.7.4 48 1.1 even 1 trivial
74.6.f.a.53.4 yes 48 37.16 even 9 inner