Properties

Label 76.6.f.a.31.2
Level $76$
Weight $6$
Character 76.31
Analytic conductor $12.189$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,6,Mod(27,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.27");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.f (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Character \(\chi\) \(=\) 76.31
Dual form 76.6.f.a.27.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.64509 - 0.364630i) q^{2} +(2.01363 + 3.48771i) q^{3} +(31.7341 + 4.11673i) q^{4} +(54.6845 + 94.7163i) q^{5} +(-10.0954 - 20.4227i) q^{6} +177.092i q^{7} +(-177.641 - 34.8105i) q^{8} +(113.391 - 196.398i) q^{9} +O(q^{10})\) \(q+(-5.64509 - 0.364630i) q^{2} +(2.01363 + 3.48771i) q^{3} +(31.7341 + 4.11673i) q^{4} +(54.6845 + 94.7163i) q^{5} +(-10.0954 - 20.4227i) q^{6} +177.092i q^{7} +(-177.641 - 34.8105i) q^{8} +(113.391 - 196.398i) q^{9} +(-274.162 - 554.621i) q^{10} -61.3620i q^{11} +(49.5428 + 118.969i) q^{12} +(252.490 + 145.775i) q^{13} +(64.5731 - 999.702i) q^{14} +(-220.229 + 381.447i) q^{15} +(990.105 + 261.282i) q^{16} +(269.971 + 467.603i) q^{17} +(-711.713 + 1067.34i) q^{18} +(-1472.04 - 556.059i) q^{19} +(1345.44 + 3230.86i) q^{20} +(-617.647 + 356.598i) q^{21} +(-22.3744 + 346.394i) q^{22} +(-2540.20 - 1466.59i) q^{23} +(-236.294 - 689.655i) q^{24} +(-4418.28 + 7652.69i) q^{25} +(-1372.18 - 914.980i) q^{26} +1891.93 q^{27} +(-729.042 + 5619.86i) q^{28} +(3743.38 + 2161.24i) q^{29} +(1382.30 - 2073.00i) q^{30} +5976.45 q^{31} +(-5493.96 - 1835.98i) q^{32} +(214.013 - 123.560i) q^{33} +(-1353.51 - 2738.10i) q^{34} +(-16773.5 + 9684.20i) q^{35} +(4406.87 - 5765.72i) q^{36} +2104.57i q^{37} +(8107.03 + 3675.75i) q^{38} +1174.15i q^{39} +(-6417.06 - 18729.1i) q^{40} +(8334.82 - 4812.11i) q^{41} +(3616.70 - 1787.82i) q^{42} +(-16202.5 + 9354.53i) q^{43} +(252.611 - 1947.27i) q^{44} +24802.8 q^{45} +(13804.9 + 9205.25i) q^{46} +(1389.93 + 802.479i) q^{47} +(1082.43 + 3979.32i) q^{48} -14554.7 q^{49} +(27732.0 - 41589.1i) q^{50} +(-1087.24 + 1883.16i) q^{51} +(7412.42 + 5665.48i) q^{52} +(-17327.4 - 10004.0i) q^{53} +(-10680.1 - 689.854i) q^{54} +(5811.98 - 3355.55i) q^{55} +(6164.68 - 31458.8i) q^{56} +(-1024.77 - 6253.74i) q^{57} +(-20343.6 - 13565.3i) q^{58} +(-17573.1 - 30437.5i) q^{59} +(-8559.07 + 11198.3i) q^{60} +(6467.16 - 11201.4i) q^{61} +(-33737.6 - 2179.19i) q^{62} +(34780.6 + 20080.6i) q^{63} +(30344.5 + 12367.5i) q^{64} +31886.6i q^{65} +(-1253.18 + 619.474i) q^{66} +(-2566.32 + 4445.01i) q^{67} +(6642.28 + 15950.4i) q^{68} -11812.7i q^{69} +(98219.2 - 48552.0i) q^{70} +(-19654.5 - 34042.5i) q^{71} +(-26979.5 + 30941.1i) q^{72} +(25575.8 + 44298.5i) q^{73} +(767.390 - 11880.5i) q^{74} -35587.1 q^{75} +(-44424.7 - 23706.0i) q^{76} +10866.7 q^{77} +(428.130 - 6628.18i) q^{78} +(43513.7 + 75368.0i) q^{79} +(29395.7 + 108067. i) q^{80} +(-23744.3 - 41126.3i) q^{81} +(-48805.5 + 24125.7i) q^{82} +32951.6i q^{83} +(-21068.5 + 8773.64i) q^{84} +(-29526.4 + 51141.3i) q^{85} +(94875.6 - 46899.2i) q^{86} +17407.8i q^{87} +(-2136.04 + 10900.4i) q^{88} +(-41492.7 - 23955.8i) q^{89} +(-140014. - 9043.84i) q^{90} +(-25815.7 + 44714.0i) q^{91} +(-74573.5 - 56998.1i) q^{92} +(12034.4 + 20844.1i) q^{93} +(-7553.70 - 5036.88i) q^{94} +(-27829.8 - 169834. i) q^{95} +(-4659.44 - 22858.3i) q^{96} +(77714.5 - 44868.5i) q^{97} +(82162.5 + 5307.07i) q^{98} +(-12051.4 - 6957.88i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.64509 0.364630i −0.997920 0.0644580i
\(3\) 2.01363 + 3.48771i 0.129174 + 0.223737i 0.923357 0.383943i \(-0.125434\pi\)
−0.794183 + 0.607679i \(0.792101\pi\)
\(4\) 31.7341 + 4.11673i 0.991690 + 0.128648i
\(5\) 54.6845 + 94.7163i 0.978225 + 1.69434i 0.668852 + 0.743395i \(0.266786\pi\)
0.309373 + 0.950941i \(0.399881\pi\)
\(6\) −10.0954 20.4227i −0.114484 0.231598i
\(7\) 177.092i 1.36601i 0.730413 + 0.683006i \(0.239328\pi\)
−0.730413 + 0.683006i \(0.760672\pi\)
\(8\) −177.641 34.8105i −0.981336 0.192303i
\(9\) 113.391 196.398i 0.466628 0.808223i
\(10\) −274.162 554.621i −0.866978 1.75387i
\(11\) 61.3620i 0.152904i −0.997073 0.0764518i \(-0.975641\pi\)
0.997073 0.0764518i \(-0.0243591\pi\)
\(12\) 49.5428 + 118.969i 0.0993178 + 0.238496i
\(13\) 252.490 + 145.775i 0.414368 + 0.239235i 0.692665 0.721260i \(-0.256437\pi\)
−0.278297 + 0.960495i \(0.589770\pi\)
\(14\) 64.5731 999.702i 0.0880505 1.36317i
\(15\) −220.229 + 381.447i −0.252723 + 0.437730i
\(16\) 990.105 + 261.282i 0.966899 + 0.255158i
\(17\) 269.971 + 467.603i 0.226566 + 0.392424i 0.956788 0.290786i \(-0.0939168\pi\)
−0.730222 + 0.683210i \(0.760583\pi\)
\(18\) −711.713 + 1067.34i −0.517754 + 0.776465i
\(19\) −1472.04 556.059i −0.935481 0.353376i
\(20\) 1345.44 + 3230.86i 0.752124 + 1.80610i
\(21\) −617.647 + 356.598i −0.305627 + 0.176454i
\(22\) −22.3744 + 346.394i −0.00985587 + 0.152586i
\(23\) −2540.20 1466.59i −1.00126 0.578080i −0.0926422 0.995699i \(-0.529531\pi\)
−0.908622 + 0.417619i \(0.862865\pi\)
\(24\) −236.294 689.655i −0.0837383 0.244401i
\(25\) −4418.28 + 7652.69i −1.41385 + 2.44886i
\(26\) −1372.18 914.980i −0.398085 0.265447i
\(27\) 1891.93 0.499455
\(28\) −729.042 + 5619.86i −0.175735 + 1.35466i
\(29\) 3743.38 + 2161.24i 0.826549 + 0.477208i 0.852670 0.522451i \(-0.174982\pi\)
−0.0261207 + 0.999659i \(0.508315\pi\)
\(30\) 1382.30 2073.00i 0.280413 0.420530i
\(31\) 5976.45 1.11696 0.558482 0.829516i \(-0.311384\pi\)
0.558482 + 0.829516i \(0.311384\pi\)
\(32\) −5493.96 1835.98i −0.948442 0.316952i
\(33\) 214.013 123.560i 0.0342102 0.0197513i
\(34\) −1353.51 2738.10i −0.200800 0.406212i
\(35\) −16773.5 + 9684.20i −2.31448 + 1.33627i
\(36\) 4406.87 5765.72i 0.566727 0.741476i
\(37\) 2104.57i 0.252732i 0.991984 + 0.126366i \(0.0403313\pi\)
−0.991984 + 0.126366i \(0.959669\pi\)
\(38\) 8107.03 + 3675.75i 0.910758 + 0.412940i
\(39\) 1174.15i 0.123612i
\(40\) −6417.06 18729.1i −0.634142 1.85083i
\(41\) 8334.82 4812.11i 0.774349 0.447071i −0.0600749 0.998194i \(-0.519134\pi\)
0.834424 + 0.551123i \(0.185801\pi\)
\(42\) 3616.70 1787.82i 0.316365 0.156387i
\(43\) −16202.5 + 9354.53i −1.33632 + 0.771526i −0.986260 0.165200i \(-0.947173\pi\)
−0.350063 + 0.936726i \(0.613840\pi\)
\(44\) 252.611 1947.27i 0.0196707 0.151633i
\(45\) 24802.8 1.82587
\(46\) 13804.9 + 9205.25i 0.961920 + 0.641418i
\(47\) 1389.93 + 802.479i 0.0917804 + 0.0529894i 0.545188 0.838314i \(-0.316458\pi\)
−0.453407 + 0.891303i \(0.649792\pi\)
\(48\) 1082.43 + 3979.32i 0.0678105 + 0.249291i
\(49\) −14554.7 −0.865989
\(50\) 27732.0 41589.1i 1.56876 2.35263i
\(51\) −1087.24 + 1883.16i −0.0585331 + 0.101382i
\(52\) 7412.42 + 5665.48i 0.380147 + 0.290555i
\(53\) −17327.4 10004.0i −0.847312 0.489196i 0.0124308 0.999923i \(-0.496043\pi\)
−0.859743 + 0.510727i \(0.829376\pi\)
\(54\) −10680.1 689.854i −0.498416 0.0321939i
\(55\) 5811.98 3355.55i 0.259070 0.149574i
\(56\) 6164.68 31458.8i 0.262688 1.34052i
\(57\) −1024.77 6253.74i −0.0417771 0.254949i
\(58\) −20343.6 13565.3i −0.794070 0.529494i
\(59\) −17573.1 30437.5i −0.657230 1.13836i −0.981330 0.192333i \(-0.938395\pi\)
0.324099 0.946023i \(-0.394939\pi\)
\(60\) −8559.07 + 11198.3i −0.306937 + 0.401580i
\(61\) 6467.16 11201.4i 0.222530 0.385433i −0.733045 0.680180i \(-0.761902\pi\)
0.955576 + 0.294746i \(0.0952351\pi\)
\(62\) −33737.6 2179.19i −1.11464 0.0719973i
\(63\) 34780.6 + 20080.6i 1.10404 + 0.637419i
\(64\) 30344.5 + 12367.5i 0.926039 + 0.377427i
\(65\) 31886.6i 0.936104i
\(66\) −1253.18 + 619.474i −0.0354122 + 0.0175051i
\(67\) −2566.32 + 4445.01i −0.0698433 + 0.120972i −0.898832 0.438293i \(-0.855583\pi\)
0.828989 + 0.559265i \(0.188917\pi\)
\(68\) 6642.28 + 15950.4i 0.174199 + 0.418310i
\(69\) 11812.7i 0.298693i
\(70\) 98219.2 48552.0i 2.39580 1.18430i
\(71\) −19654.5 34042.5i −0.462717 0.801449i 0.536378 0.843978i \(-0.319792\pi\)
−0.999095 + 0.0425285i \(0.986459\pi\)
\(72\) −26979.5 + 30941.1i −0.613342 + 0.703404i
\(73\) 25575.8 + 44298.5i 0.561722 + 0.972931i 0.997346 + 0.0728028i \(0.0231944\pi\)
−0.435624 + 0.900129i \(0.643472\pi\)
\(74\) 767.390 11880.5i 0.0162906 0.252206i
\(75\) −35587.1 −0.730533
\(76\) −44424.7 23706.0i −0.882247 0.470787i
\(77\) 10866.7 0.208868
\(78\) 428.130 6628.18i 0.00796781 0.123355i
\(79\) 43513.7 + 75368.0i 0.784438 + 1.35869i 0.929334 + 0.369240i \(0.120382\pi\)
−0.144896 + 0.989447i \(0.546285\pi\)
\(80\) 29395.7 + 108067.i 0.513522 + 1.88785i
\(81\) −23744.3 41126.3i −0.402111 0.696477i
\(82\) −48805.5 + 24125.7i −0.801556 + 0.396228i
\(83\) 32951.6i 0.525026i 0.964928 + 0.262513i \(0.0845513\pi\)
−0.964928 + 0.262513i \(0.915449\pi\)
\(84\) −21068.5 + 8773.64i −0.325788 + 0.135669i
\(85\) −29526.4 + 51141.3i −0.443265 + 0.767758i
\(86\) 94875.6 46899.2i 1.38327 0.683785i
\(87\) 17407.8i 0.246572i
\(88\) −2136.04 + 10900.4i −0.0294038 + 0.150050i
\(89\) −41492.7 23955.8i −0.555261 0.320580i 0.195980 0.980608i \(-0.437211\pi\)
−0.751241 + 0.660028i \(0.770544\pi\)
\(90\) −140014. 9043.84i −1.82207 0.117692i
\(91\) −25815.7 + 44714.0i −0.326798 + 0.566031i
\(92\) −74573.5 56998.1i −0.918575 0.702087i
\(93\) 12034.4 + 20844.1i 0.144283 + 0.249906i
\(94\) −7553.70 5036.88i −0.0881739 0.0587952i
\(95\) −27829.8 169834.i −0.316374 1.93070i
\(96\) −4659.44 22858.3i −0.0516007 0.253143i
\(97\) 77714.5 44868.5i 0.838635 0.484186i −0.0181653 0.999835i \(-0.505783\pi\)
0.856800 + 0.515649i \(0.172449\pi\)
\(98\) 82162.5 + 5307.07i 0.864188 + 0.0558200i
\(99\) −12051.4 6957.88i −0.123580 0.0713491i
\(100\) −171714. + 224662.i −1.71714 + 2.24662i
\(101\) −16924.1 + 29313.3i −0.165083 + 0.285931i −0.936685 0.350174i \(-0.886122\pi\)
0.771602 + 0.636106i \(0.219456\pi\)
\(102\) 6824.24 10234.2i 0.0649462 0.0973985i
\(103\) 207497. 1.92716 0.963581 0.267417i \(-0.0861700\pi\)
0.963581 + 0.267417i \(0.0861700\pi\)
\(104\) −39778.0 34684.9i −0.360628 0.314454i
\(105\) −67551.4 39000.8i −0.597944 0.345223i
\(106\) 94166.9 + 62791.4i 0.814018 + 0.542795i
\(107\) 23059.0 0.194706 0.0973532 0.995250i \(-0.468962\pi\)
0.0973532 + 0.995250i \(0.468962\pi\)
\(108\) 60038.7 + 7788.58i 0.495304 + 0.0642538i
\(109\) 70405.5 40648.6i 0.567597 0.327702i −0.188592 0.982056i \(-0.560392\pi\)
0.756189 + 0.654353i \(0.227059\pi\)
\(110\) −34032.7 + 16823.2i −0.268173 + 0.132564i
\(111\) −7340.15 + 4237.84i −0.0565454 + 0.0326465i
\(112\) −46271.0 + 175340.i −0.348549 + 1.32080i
\(113\) 64217.9i 0.473107i 0.971618 + 0.236554i \(0.0760179\pi\)
−0.971618 + 0.236554i \(0.923982\pi\)
\(114\) 3504.61 + 35676.6i 0.0252568 + 0.257111i
\(115\) 320798.i 2.26197i
\(116\) 109895. + 83995.5i 0.758289 + 0.579577i
\(117\) 57260.0 33059.1i 0.386711 0.223268i
\(118\) 88103.2 + 178230.i 0.582487 + 1.17835i
\(119\) −82808.9 + 47809.8i −0.536056 + 0.309492i
\(120\) 52400.0 60094.3i 0.332183 0.380961i
\(121\) 157286. 0.976620
\(122\) −40592.1 + 60875.0i −0.246912 + 0.370288i
\(123\) 33566.5 + 19379.6i 0.200052 + 0.115500i
\(124\) 189657. + 24603.5i 1.10768 + 0.143695i
\(125\) −624667. −3.57580
\(126\) −189018. 126039.i −1.06066 0.707258i
\(127\) 10299.4 17839.1i 0.0566636 0.0981442i −0.836302 0.548269i \(-0.815287\pi\)
0.892966 + 0.450125i \(0.148620\pi\)
\(128\) −166788. 80880.3i −0.899785 0.436333i
\(129\) −65251.8 37673.1i −0.345238 0.199323i
\(130\) 11626.8 180002.i 0.0603394 0.934158i
\(131\) 62079.5 35841.6i 0.316060 0.182477i −0.333575 0.942724i \(-0.608255\pi\)
0.649635 + 0.760246i \(0.274922\pi\)
\(132\) 7300.17 3040.04i 0.0364669 0.0151861i
\(133\) 98473.8 260687.i 0.482716 1.27788i
\(134\) 16107.9 24156.7i 0.0774957 0.116219i
\(135\) 103459. + 179197.i 0.488579 + 0.846244i
\(136\) −31680.3 92463.2i −0.146873 0.428669i
\(137\) 164184. 284376.i 0.747361 1.29447i −0.201722 0.979443i \(-0.564654\pi\)
0.949083 0.315025i \(-0.102013\pi\)
\(138\) −4307.24 + 66683.5i −0.0192532 + 0.298072i
\(139\) 288464. + 166545.i 1.26635 + 0.731129i 0.974296 0.225272i \(-0.0723272\pi\)
0.292056 + 0.956401i \(0.405661\pi\)
\(140\) −572160. + 238267.i −2.46716 + 1.02741i
\(141\) 6463.59i 0.0273795i
\(142\) 98538.3 + 199340.i 0.410095 + 0.829608i
\(143\) 8945.06 15493.3i 0.0365800 0.0633583i
\(144\) 163584. 164828.i 0.657407 0.662407i
\(145\) 472745.i 1.86727i
\(146\) −128225. 259395.i −0.497841 1.00712i
\(147\) −29307.8 50762.5i −0.111864 0.193754i
\(148\) −8663.97 + 66786.7i −0.0325134 + 0.250632i
\(149\) −1980.69 3430.66i −0.00730890 0.0126594i 0.862348 0.506316i \(-0.168993\pi\)
−0.869657 + 0.493657i \(0.835660\pi\)
\(150\) 200893. + 12976.1i 0.729014 + 0.0470887i
\(151\) −275213. −0.982260 −0.491130 0.871086i \(-0.663416\pi\)
−0.491130 + 0.871086i \(0.663416\pi\)
\(152\) 242137. + 150021.i 0.850066 + 0.526676i
\(153\) 122449. 0.422888
\(154\) −61343.7 3962.34i −0.208434 0.0134632i
\(155\) 326819. + 566067.i 1.09264 + 1.89251i
\(156\) −4833.66 + 37260.6i −0.0159025 + 0.122585i
\(157\) 206589. + 357822.i 0.668894 + 1.15856i 0.978214 + 0.207600i \(0.0665654\pi\)
−0.309320 + 0.950958i \(0.600101\pi\)
\(158\) −218158. 441326.i −0.695229 1.40642i
\(159\) 80577.2i 0.252767i
\(160\) −126537. 620767.i −0.390767 1.91703i
\(161\) 259721. 449850.i 0.789665 1.36774i
\(162\) 119043. + 240819.i 0.356381 + 0.720948i
\(163\) 58659.1i 0.172928i −0.996255 0.0864642i \(-0.972443\pi\)
0.996255 0.0864642i \(-0.0275568\pi\)
\(164\) 284308. 118396.i 0.825429 0.343737i
\(165\) 23406.4 + 13513.7i 0.0669305 + 0.0386424i
\(166\) 12015.1 186015.i 0.0338422 0.523934i
\(167\) 296161. 512966.i 0.821744 1.42330i −0.0826383 0.996580i \(-0.526335\pi\)
0.904382 0.426723i \(-0.140332\pi\)
\(168\) 122133. 41845.8i 0.333855 0.114388i
\(169\) −143146. 247936.i −0.385533 0.667763i
\(170\) 185327. 277931.i 0.491831 0.737589i
\(171\) −276124. + 226054.i −0.722128 + 0.591183i
\(172\) −552682. + 230156.i −1.42447 + 0.593200i
\(173\) −39293.7 + 22686.2i −0.0998176 + 0.0576297i −0.549078 0.835771i \(-0.685021\pi\)
0.449260 + 0.893401i \(0.351688\pi\)
\(174\) 6347.38 98268.3i 0.0158936 0.246060i
\(175\) −1.35523e6 782444.i −3.34517 1.93134i
\(176\) 16032.8 60754.8i 0.0390146 0.147842i
\(177\) 70771.4 122580.i 0.169795 0.294093i
\(178\) 225495. + 150362.i 0.533442 + 0.355704i
\(179\) 345370. 0.805660 0.402830 0.915275i \(-0.368027\pi\)
0.402830 + 0.915275i \(0.368027\pi\)
\(180\) 787095. + 102107.i 1.81070 + 0.234894i
\(181\) −553203. 319392.i −1.25513 0.724648i −0.283004 0.959119i \(-0.591331\pi\)
−0.972123 + 0.234470i \(0.924664\pi\)
\(182\) 162036. 243002.i 0.362604 0.543789i
\(183\) 52089.9 0.114981
\(184\) 400191. + 348951.i 0.871410 + 0.759837i
\(185\) −199337. + 115088.i −0.428213 + 0.247229i
\(186\) −60334.7 122055.i −0.127875 0.258687i
\(187\) 28693.1 16566.0i 0.0600030 0.0346428i
\(188\) 40804.7 + 31187.9i 0.0842007 + 0.0643565i
\(189\) 335047.i 0.682261i
\(190\) 95175.2 + 968875.i 0.191267 + 1.94708i
\(191\) 571829.i 1.13418i 0.823655 + 0.567091i \(0.191931\pi\)
−0.823655 + 0.567091i \(0.808069\pi\)
\(192\) 17968.1 + 130736.i 0.0351763 + 0.255943i
\(193\) −595146. + 343607.i −1.15009 + 0.664002i −0.948908 0.315553i \(-0.897810\pi\)
−0.201177 + 0.979555i \(0.564477\pi\)
\(194\) −455066. + 224950.i −0.868100 + 0.429122i
\(195\) −111211. + 64207.7i −0.209441 + 0.120921i
\(196\) −461880. 59917.8i −0.858793 0.111408i
\(197\) 833534. 1.53023 0.765117 0.643891i \(-0.222681\pi\)
0.765117 + 0.643891i \(0.222681\pi\)
\(198\) 65494.2 + 43672.1i 0.118724 + 0.0791665i
\(199\) 425483. + 245653.i 0.761640 + 0.439733i 0.829884 0.557936i \(-0.188406\pi\)
−0.0682444 + 0.997669i \(0.521740\pi\)
\(200\) 1.05126e6 1.20563e6i 1.85838 2.13127i
\(201\) −20670.5 −0.0360879
\(202\) 106226. 159305.i 0.183170 0.274696i
\(203\) −382739. + 662923.i −0.651872 + 1.12908i
\(204\) −42255.2 + 55284.5i −0.0710893 + 0.0930096i
\(205\) 911570. + 526295.i 1.51498 + 0.874671i
\(206\) −1.17134e6 75659.5i −1.92315 0.124221i
\(207\) −576070. + 332594.i −0.934436 + 0.539497i
\(208\) 211903. + 210304.i 0.339609 + 0.337046i
\(209\) −34120.9 + 90327.3i −0.0540325 + 0.143039i
\(210\) 367113. + 244794.i 0.574449 + 0.383048i
\(211\) 169744. + 294006.i 0.262476 + 0.454621i 0.966899 0.255159i \(-0.0821277\pi\)
−0.704423 + 0.709780i \(0.748794\pi\)
\(212\) −508685. 388799.i −0.777337 0.594136i
\(213\) 79153.7 137098.i 0.119542 0.207054i
\(214\) −130170. 8407.98i −0.194302 0.0125504i
\(215\) −1.77205e6 1.02309e6i −2.61445 1.50945i
\(216\) −336084. 65859.1i −0.490133 0.0960465i
\(217\) 1.05838e6i 1.52579i
\(218\) −412267. + 203793.i −0.587540 + 0.290435i
\(219\) −103000. + 178402.i −0.145120 + 0.251356i
\(220\) 198252. 82558.9i 0.276160 0.115002i
\(221\) 157420.i 0.216810i
\(222\) 42981.0 21246.5i 0.0585321 0.0289338i
\(223\) 75210.3 + 130268.i 0.101278 + 0.175419i 0.912211 0.409720i \(-0.134374\pi\)
−0.810933 + 0.585138i \(0.801040\pi\)
\(224\) 325138. 972938.i 0.432960 1.29558i
\(225\) 1.00198e6 + 1.73549e6i 1.31948 + 2.28541i
\(226\) 23415.7 362516.i 0.0304956 0.472124i
\(227\) 1.30617e6 1.68243 0.841213 0.540703i \(-0.181842\pi\)
0.841213 + 0.540703i \(0.181842\pi\)
\(228\) −6775.10 202676.i −0.00863135 0.258205i
\(229\) −375776. −0.473522 −0.236761 0.971568i \(-0.576086\pi\)
−0.236761 + 0.971568i \(0.576086\pi\)
\(230\) −116972. + 1.81093e6i −0.145802 + 2.25727i
\(231\) 21881.6 + 37900.0i 0.0269805 + 0.0467315i
\(232\) −589742. 514233.i −0.719353 0.627249i
\(233\) −158635. 274764.i −0.191430 0.331566i 0.754295 0.656536i \(-0.227979\pi\)
−0.945724 + 0.324970i \(0.894646\pi\)
\(234\) −335292. + 165743.i −0.400298 + 0.197877i
\(235\) 175533.i 0.207342i
\(236\) −432363. 1.03825e6i −0.505322 1.21345i
\(237\) −175241. + 303527.i −0.202659 + 0.351015i
\(238\) 484897. 239696.i 0.554890 0.274295i
\(239\) 672989.i 0.762102i 0.924554 + 0.381051i \(0.124438\pi\)
−0.924554 + 0.381051i \(0.875562\pi\)
\(240\) −317715. + 320131.i −0.356048 + 0.358756i
\(241\) −1.00505e6 580265.i −1.11466 0.643552i −0.174631 0.984634i \(-0.555873\pi\)
−0.940033 + 0.341082i \(0.889207\pi\)
\(242\) −887892. 57351.0i −0.974590 0.0629510i
\(243\) 325494. 563772.i 0.353612 0.612474i
\(244\) 251343. 328844.i 0.270266 0.353603i
\(245\) −795915. 1.37857e6i −0.847133 1.46728i
\(246\) −182420. 121639.i −0.192191 0.128155i
\(247\) −290615. 354986.i −0.303093 0.370228i
\(248\) −1.06166e6 208044.i −1.09612 0.214795i
\(249\) −114926. + 66352.3i −0.117468 + 0.0678200i
\(250\) 3.52630e6 + 227772.i 3.56837 + 0.230489i
\(251\) −50440.9 29122.1i −0.0505357 0.0291768i 0.474519 0.880245i \(-0.342622\pi\)
−0.525055 + 0.851068i \(0.675955\pi\)
\(252\) 1.02106e6 + 780422.i 1.01287 + 0.774156i
\(253\) −89992.7 + 155872.i −0.0883906 + 0.153097i
\(254\) −64645.9 + 96948.1i −0.0628719 + 0.0942877i
\(255\) −237821. −0.229034
\(256\) 912040. + 517393.i 0.869789 + 0.493424i
\(257\) 220465. + 127285.i 0.208212 + 0.120211i 0.600480 0.799640i \(-0.294976\pi\)
−0.392268 + 0.919851i \(0.628309\pi\)
\(258\) 354615. + 236461.i 0.331672 + 0.221162i
\(259\) −372704. −0.345235
\(260\) −131268. + 1.01189e6i −0.120428 + 0.928325i
\(261\) 848927. 490128.i 0.771382 0.445357i
\(262\) −363513. + 179693.i −0.327165 + 0.161725i
\(263\) 1.47513e6 851669.i 1.31505 0.759244i 0.332122 0.943236i \(-0.392235\pi\)
0.982928 + 0.183992i \(0.0589021\pi\)
\(264\) −42318.6 + 14499.5i −0.0373699 + 0.0128039i
\(265\) 2.18825e6i 1.91418i
\(266\) −650948. + 1.43569e6i −0.564082 + 1.24411i
\(267\) 192953.i 0.165643i
\(268\) −99738.9 + 130493.i −0.0848257 + 0.110982i
\(269\) −322613. + 186261.i −0.271832 + 0.156942i −0.629720 0.776822i \(-0.716830\pi\)
0.357888 + 0.933765i \(0.383497\pi\)
\(270\) −518696. 1.04931e6i −0.433016 0.875977i
\(271\) 312244. 180274.i 0.258268 0.149111i −0.365276 0.930899i \(-0.619025\pi\)
0.623544 + 0.781788i \(0.285692\pi\)
\(272\) 145123. + 533515.i 0.118936 + 0.437244i
\(273\) −207933. −0.168856
\(274\) −1.03053e6 + 1.54546e6i −0.829246 + 1.24360i
\(275\) 469584. + 271115.i 0.374440 + 0.216183i
\(276\) 48629.6 374864.i 0.0384262 0.296211i
\(277\) 1.15217e6 0.902226 0.451113 0.892467i \(-0.351027\pi\)
0.451113 + 0.892467i \(0.351027\pi\)
\(278\) −1.56768e6 1.04534e6i −1.21659 0.811235i
\(279\) 677674. 1.17377e6i 0.521207 0.902757i
\(280\) 3.31677e6 1.13641e6i 2.52825 0.866245i
\(281\) −1.60778e6 928253.i −1.21468 0.701295i −0.250904 0.968012i \(-0.580728\pi\)
−0.963775 + 0.266717i \(0.914061\pi\)
\(282\) 2356.82 36487.5i 0.00176483 0.0273226i
\(283\) −893708. + 515982.i −0.663330 + 0.382974i −0.793544 0.608512i \(-0.791767\pi\)
0.130215 + 0.991486i \(0.458433\pi\)
\(284\) −483572. 1.16122e6i −0.355767 0.854317i
\(285\) 536292. 439045.i 0.391101 0.320182i
\(286\) −56145.0 + 84199.4i −0.0405878 + 0.0608687i
\(287\) 852188. + 1.47603e6i 0.610704 + 1.05777i
\(288\) −983547. + 870821.i −0.698737 + 0.618654i
\(289\) 564160. 977154.i 0.397336 0.688206i
\(290\) 172377. 2.66869e6i 0.120360 1.86339i
\(291\) 312977. + 180697.i 0.216660 + 0.125089i
\(292\) 629259. + 1.51106e6i 0.431889 + 1.03711i
\(293\) 573532.i 0.390291i 0.980774 + 0.195145i \(0.0625179\pi\)
−0.980774 + 0.195145i \(0.937482\pi\)
\(294\) 146935. + 297246.i 0.0991421 + 0.200561i
\(295\) 1.92195e6 3.32891e6i 1.28584 2.22714i
\(296\) 73261.3 373858.i 0.0486010 0.248015i
\(297\) 116093.i 0.0763684i
\(298\) 9930.28 + 20088.6i 0.00647770 + 0.0131042i
\(299\) −427584. 740597.i −0.276594 0.479076i
\(300\) −1.12933e6 146503.i −0.724463 0.0939816i
\(301\) −1.65661e6 2.86934e6i −1.05391 1.82543i
\(302\) 1.55360e6 + 100351.i 0.980217 + 0.0633145i
\(303\) −136315. −0.0852978
\(304\) −1.31218e6 935174.i −0.814350 0.580374i
\(305\) 1.41461e6 0.870738
\(306\) −691234. 44648.4i −0.422009 0.0272585i
\(307\) 392332. + 679539.i 0.237579 + 0.411499i 0.960019 0.279935i \(-0.0903128\pi\)
−0.722440 + 0.691433i \(0.756980\pi\)
\(308\) 344846. + 44735.5i 0.207133 + 0.0268705i
\(309\) 417822. + 723689.i 0.248940 + 0.431177i
\(310\) −1.63852e6 3.31467e6i −0.968383 1.95901i
\(311\) 590840.i 0.346393i −0.984887 0.173196i \(-0.944590\pi\)
0.984887 0.173196i \(-0.0554095\pi\)
\(312\) 40872.8 208577.i 0.0237710 0.121305i
\(313\) 171100. 296353.i 0.0987161 0.170981i −0.812437 0.583048i \(-0.801860\pi\)
0.911153 + 0.412067i \(0.135193\pi\)
\(314\) −1.03574e6 2.09527e6i −0.592825 1.19926i
\(315\) 4.39239e6i 2.49416i
\(316\) 1.07060e6 + 2.57087e6i 0.603128 + 1.44831i
\(317\) 1.40964e6 + 813857.i 0.787881 + 0.454883i 0.839216 0.543798i \(-0.183014\pi\)
−0.0513352 + 0.998681i \(0.516348\pi\)
\(318\) −29380.9 + 454866.i −0.0162928 + 0.252241i
\(319\) 132618. 229701.i 0.0729669 0.126382i
\(320\) 487963. + 3.55043e6i 0.266386 + 1.93823i
\(321\) 46432.2 + 80423.0i 0.0251511 + 0.0435630i
\(322\) −1.63018e6 + 2.44474e6i −0.876184 + 1.31399i
\(323\) −137392. 838450.i −0.0732751 0.447168i
\(324\) −584197. 1.40285e6i −0.309169 0.742420i
\(325\) −2.23114e6 + 1.28815e6i −1.17171 + 0.676486i
\(326\) −21388.8 + 331136.i −0.0111466 + 0.172569i
\(327\) 283541. + 163703.i 0.146638 + 0.0846615i
\(328\) −1.64812e6 + 564687.i −0.845869 + 0.289817i
\(329\) −142113. + 246147.i −0.0723842 + 0.125373i
\(330\) −127204. 84820.6i −0.0643005 0.0428762i
\(331\) 1.63245e6 0.818972 0.409486 0.912316i \(-0.365708\pi\)
0.409486 + 0.912316i \(0.365708\pi\)
\(332\) −135653. + 1.04569e6i −0.0675435 + 0.520663i
\(333\) 413335. + 238639.i 0.204264 + 0.117932i
\(334\) −1.85890e6 + 2.78775e6i −0.911779 + 1.36737i
\(335\) −561352. −0.273290
\(336\) −704708. + 191690.i −0.340534 + 0.0926300i
\(337\) −2.53284e6 + 1.46234e6i −1.21488 + 0.701410i −0.963818 0.266561i \(-0.914113\pi\)
−0.251060 + 0.967971i \(0.580779\pi\)
\(338\) 717666. + 1.45181e6i 0.341689 + 0.691225i
\(339\) −223973. + 129311.i −0.105852 + 0.0611134i
\(340\) −1.14753e6 + 1.50137e6i −0.538352 + 0.704353i
\(341\) 366727.i 0.170788i
\(342\) 1.64117e6 1.17541e6i 0.758733 0.543406i
\(343\) 398868.i 0.183060i
\(344\) 3.20386e6 1.09773e6i 1.45975 0.500148i
\(345\) 1.11885e6 645969.i 0.506086 0.292189i
\(346\) 230088. 113738.i 0.103325 0.0510758i
\(347\) −2.73564e6 + 1.57942e6i −1.21965 + 0.704164i −0.964843 0.262828i \(-0.915345\pi\)
−0.254806 + 0.966992i \(0.582012\pi\)
\(348\) −71663.1 + 552419.i −0.0317210 + 0.244524i
\(349\) −1.02170e6 −0.449016 −0.224508 0.974472i \(-0.572077\pi\)
−0.224508 + 0.974472i \(0.572077\pi\)
\(350\) 7.36510e6 + 4.91112e6i 3.21373 + 2.14294i
\(351\) 477694. + 275797.i 0.206958 + 0.119487i
\(352\) −112659. + 337121.i −0.0484631 + 0.145020i
\(353\) −384733. −0.164332 −0.0821661 0.996619i \(-0.526184\pi\)
−0.0821661 + 0.996619i \(0.526184\pi\)
\(354\) −444207. + 666167.i −0.188398 + 0.282537i
\(355\) 2.14959e6 3.72319e6i 0.905283 1.56800i
\(356\) −1.21811e6 931032.i −0.509405 0.389349i
\(357\) −333493. 192542.i −0.138489 0.0799569i
\(358\) −1.94964e6 125932.i −0.803984 0.0519312i
\(359\) 942762. 544304.i 0.386070 0.222897i −0.294386 0.955687i \(-0.595115\pi\)
0.680456 + 0.732789i \(0.261782\pi\)
\(360\) −4.40599e6 863399.i −1.79179 0.351120i
\(361\) 1.85770e6 + 1.63708e6i 0.750251 + 0.661153i
\(362\) 3.00642e6 + 2.00471e6i 1.20581 + 0.804044i
\(363\) 316715. + 548567.i 0.126154 + 0.218506i
\(364\) −1.00331e6 + 1.31268e6i −0.396902 + 0.519286i
\(365\) −2.79719e6 + 4.84488e6i −1.09898 + 1.90349i
\(366\) −294052. 18993.5i −0.114742 0.00741144i
\(367\) −2.60609e6 1.50463e6i −1.01001 0.583127i −0.0988127 0.995106i \(-0.531504\pi\)
−0.911193 + 0.411979i \(0.864838\pi\)
\(368\) −2.13188e6 2.11578e6i −0.820620 0.814426i
\(369\) 2.18259e6i 0.834462i
\(370\) 1.16724e6 576995.i 0.443258 0.219113i
\(371\) 1.77163e6 3.06855e6i 0.668248 1.15744i
\(372\) 296090. + 711012.i 0.110934 + 0.266391i
\(373\) 1.47256e6i 0.548027i −0.961726 0.274014i \(-0.911649\pi\)
0.961726 0.274014i \(-0.0883514\pi\)
\(374\) −168015. + 83054.0i −0.0621113 + 0.0307030i
\(375\) −1.25785e6 2.17866e6i −0.461903 0.800039i
\(376\) −218974. 190937.i −0.0798773 0.0696500i
\(377\) 630110. + 1.09138e6i 0.228330 + 0.395479i
\(378\) 122168. 1.89137e6i 0.0439772 0.680842i
\(379\) −2.47021e6 −0.883357 −0.441679 0.897173i \(-0.645617\pi\)
−0.441679 + 0.897173i \(0.645617\pi\)
\(380\) −183992. 5.50409e6i −0.0653643 1.95536i
\(381\) 82957.0 0.0292779
\(382\) 208506. 3.22803e6i 0.0731071 1.13182i
\(383\) −1.72934e6 2.99530e6i −0.602396 1.04338i −0.992457 0.122592i \(-0.960879\pi\)
0.390061 0.920789i \(-0.372454\pi\)
\(384\) −53761.4 744570.i −0.0186056 0.257678i
\(385\) 594242. + 1.02926e6i 0.204320 + 0.353893i
\(386\) 3.48494e6 1.72269e6i 1.19049 0.588489i
\(387\) 4.24286e6i 1.44006i
\(388\) 2.65091e6 1.10393e6i 0.893955 0.372274i
\(389\) −777923. + 1.34740e6i −0.260653 + 0.451464i −0.966416 0.256984i \(-0.917271\pi\)
0.705763 + 0.708448i \(0.250604\pi\)
\(390\) 651209. 321908.i 0.216800 0.107169i
\(391\) 1.58374e6i 0.523893i
\(392\) 2.58550e6 + 506656.i 0.849826 + 0.166532i
\(393\) 250010. + 144344.i 0.0816538 + 0.0471429i
\(394\) −4.70538e6 303931.i −1.52705 0.0986359i
\(395\) −4.75905e6 + 8.24292e6i −1.53471 + 2.65820i
\(396\) −353796. 270414.i −0.113374 0.0866546i
\(397\) 958527. + 1.66022e6i 0.305231 + 0.528675i 0.977313 0.211802i \(-0.0679331\pi\)
−0.672082 + 0.740477i \(0.734600\pi\)
\(398\) −2.31232e6 1.54188e6i −0.731712 0.487912i
\(399\) 1.10749e6 181479.i 0.348263 0.0570681i
\(400\) −6.37407e6 + 6.42255e6i −1.99190 + 2.00705i
\(401\) 1.73728e6 1.00302e6i 0.539520 0.311492i −0.205364 0.978686i \(-0.565838\pi\)
0.744885 + 0.667193i \(0.232505\pi\)
\(402\) 116687. + 7537.09i 0.0360128 + 0.00232615i
\(403\) 1.50900e6 + 871219.i 0.462834 + 0.267217i
\(404\) −657745. + 860560.i −0.200495 + 0.262318i
\(405\) 2.59688e6 4.49794e6i 0.786711 1.36262i
\(406\) 2.40232e6 3.60270e6i 0.723295 1.08471i
\(407\) 129141. 0.0386436
\(408\) 258693. 296679.i 0.0769367 0.0882339i
\(409\) 5.69490e6 + 3.28795e6i 1.68336 + 0.971890i 0.959399 + 0.282052i \(0.0910149\pi\)
0.723963 + 0.689838i \(0.242318\pi\)
\(410\) −4.95399e6 3.30337e6i −1.45545 0.970505i
\(411\) 1.32243e6 0.386160
\(412\) 6.58472e6 + 854209.i 1.91115 + 0.247925i
\(413\) 5.39024e6 3.11206e6i 1.55501 0.897785i
\(414\) 3.37324e6 1.66747e6i 0.967267 0.478143i
\(415\) −3.12105e6 + 1.80194e6i −0.889571 + 0.513594i
\(416\) −1.11953e6 1.26445e6i −0.317178 0.358235i
\(417\) 1.34144e6i 0.377773i
\(418\) 225552. 497464.i 0.0631401 0.139258i
\(419\) 5.78950e6i 1.61104i 0.592569 + 0.805520i \(0.298114\pi\)
−0.592569 + 0.805520i \(0.701886\pi\)
\(420\) −1.98312e6 1.51575e6i −0.548563 0.419279i
\(421\) −4.26798e6 + 2.46412e6i −1.17359 + 0.677574i −0.954523 0.298136i \(-0.903635\pi\)
−0.219068 + 0.975709i \(0.570302\pi\)
\(422\) −851019. 1.72158e6i −0.232626 0.470595i
\(423\) 315211. 181987.i 0.0856546 0.0494527i
\(424\) 2.72981e6 + 2.38029e6i 0.737424 + 0.643006i
\(425\) −4.77123e6 −1.28132
\(426\) −496820. + 745070.i −0.132640 + 0.198917i
\(427\) 1.98369e6 + 1.14528e6i 0.526507 + 0.303979i
\(428\) 731755. + 94927.6i 0.193089 + 0.0250486i
\(429\) 72048.2 0.0189008
\(430\) 9.63034e6 + 6.42160e6i 2.51172 + 1.67484i
\(431\) −616672. + 1.06811e6i −0.159905 + 0.276963i −0.934834 0.355085i \(-0.884452\pi\)
0.774930 + 0.632048i \(0.217785\pi\)
\(432\) 1.87321e6 + 494327.i 0.482922 + 0.127440i
\(433\) −3.34659e6 1.93216e6i −0.857794 0.495248i 0.00547864 0.999985i \(-0.498256\pi\)
−0.863273 + 0.504737i \(0.831589\pi\)
\(434\) 385918. 5.97467e6i 0.0983492 1.52261i
\(435\) −1.64880e6 + 951934.i −0.417777 + 0.241203i
\(436\) 2.40159e6 1.00011e6i 0.605039 0.251959i
\(437\) 2.92377e6 + 3.57137e6i 0.732385 + 0.894606i
\(438\) 646497. 969537.i 0.161020 0.241479i
\(439\) −1.84789e6 3.20063e6i −0.457629 0.792637i 0.541206 0.840890i \(-0.317968\pi\)
−0.998835 + 0.0482528i \(0.984635\pi\)
\(440\) −1.14925e6 + 393764.i −0.282998 + 0.0969626i
\(441\) −1.65036e6 + 2.85851e6i −0.404095 + 0.699913i
\(442\) 57400.1 888651.i 0.0139752 0.216359i
\(443\) −479466. 276820.i −0.116078 0.0670174i 0.440837 0.897587i \(-0.354682\pi\)
−0.556915 + 0.830570i \(0.688015\pi\)
\(444\) −250379. + 104266.i −0.0602754 + 0.0251008i
\(445\) 5.24005e6i 1.25440i
\(446\) −377069. 762798.i −0.0897602 0.181582i
\(447\) 7976.77 13816.2i 0.00188825 0.00327054i
\(448\) −2.19020e6 + 5.37377e6i −0.515570 + 1.26498i
\(449\) 6.58290e6i 1.54100i −0.637443 0.770498i \(-0.720008\pi\)
0.637443 0.770498i \(-0.279992\pi\)
\(450\) −5.02347e6 1.01623e7i −1.16943 2.36571i
\(451\) −295281. 511441.i −0.0683587 0.118401i
\(452\) −264368. + 2.03790e6i −0.0608643 + 0.469176i
\(453\) −554177. 959863.i −0.126883 0.219768i
\(454\) −7.37347e6 476270.i −1.67893 0.108446i
\(455\) −5.64686e6 −1.27873
\(456\) −35655.5 + 1.14659e6i −0.00802997 + 0.258224i
\(457\) −2.13565e6 −0.478344 −0.239172 0.970977i \(-0.576876\pi\)
−0.239172 + 0.970977i \(0.576876\pi\)
\(458\) 2.12129e6 + 137019.i 0.472537 + 0.0305223i
\(459\) 510766. + 884673.i 0.113159 + 0.195998i
\(460\) 1.32064e6 1.01802e7i 0.290998 2.24317i
\(461\) −2008.12 3478.17i −0.000440086 0.000762252i 0.865805 0.500381i \(-0.166807\pi\)
−0.866245 + 0.499619i \(0.833473\pi\)
\(462\) −109704. 221928.i −0.0239121 0.0483734i
\(463\) 3.03840e6i 0.658708i −0.944207 0.329354i \(-0.893169\pi\)
0.944207 0.329354i \(-0.106831\pi\)
\(464\) 3.14164e6 + 3.11793e6i 0.677426 + 0.672313i
\(465\) −1.31619e6 + 2.27970e6i −0.282283 + 0.488929i
\(466\) 795322. + 1.60891e6i 0.169659 + 0.343215i
\(467\) 1.68405e6i 0.357325i −0.983910 0.178663i \(-0.942823\pi\)
0.983910 0.178663i \(-0.0571771\pi\)
\(468\) 1.95319e6 813375.i 0.412221 0.171663i
\(469\) −787176. 454476.i −0.165249 0.0954068i
\(470\) 64004.4 990897.i 0.0133649 0.206911i
\(471\) −831987. + 1.44104e6i −0.172808 + 0.299312i
\(472\) 2.06215e6 + 6.01866e6i 0.426054 + 1.24350i
\(473\) 574013. + 994219.i 0.117969 + 0.204329i
\(474\) 1.09993e6 1.64954e6i 0.224863 0.337222i
\(475\) 1.07592e7 8.80822e6i 2.18800 1.79124i
\(476\) −2.82469e6 + 1.17630e6i −0.571417 + 0.237958i
\(477\) −3.92953e6 + 2.26871e6i −0.790759 + 0.456545i
\(478\) 245392. 3.79908e6i 0.0491236 0.760517i
\(479\) 2.91226e6 + 1.68139e6i 0.579951 + 0.334835i 0.761114 0.648618i \(-0.224653\pi\)
−0.181163 + 0.983453i \(0.557986\pi\)
\(480\) 1.91026e6 1.69132e6i 0.378433 0.335060i
\(481\) −306795. + 531384.i −0.0604624 + 0.104724i
\(482\) 5.46200e6 + 3.64212e6i 1.07086 + 0.714062i
\(483\) 2.09193e6 0.408018
\(484\) 4.99132e6 + 647504.i 0.968505 + 0.125640i
\(485\) 8.49955e6 + 4.90722e6i 1.64075 + 0.947286i
\(486\) −2.04301e6 + 3.06386e6i −0.392356 + 0.588408i
\(487\) −6.83855e6 −1.30660 −0.653299 0.757100i \(-0.726615\pi\)
−0.653299 + 0.757100i \(0.726615\pi\)
\(488\) −1.53876e6 + 1.76471e6i −0.292497 + 0.335446i
\(489\) 204586. 118118.i 0.0386904 0.0223379i
\(490\) 3.99035e6 + 8.07234e6i 0.750793 + 1.51883i
\(491\) 126727. 73165.8i 0.0237228 0.0136963i −0.488092 0.872792i \(-0.662307\pi\)
0.511814 + 0.859096i \(0.328974\pi\)
\(492\) 985422. + 753179.i 0.183531 + 0.140277i
\(493\) 2.33389e6i 0.432477i
\(494\) 1.51111e6 + 2.10990e6i 0.278599 + 0.388995i
\(495\) 1.52195e6i 0.279182i
\(496\) 5.91732e6 + 1.56154e6i 1.07999 + 0.285002i
\(497\) 6.02867e6 3.48065e6i 1.09479 0.632077i
\(498\) 672959. 332659.i 0.121595 0.0601072i
\(499\) 7.67261e6 4.42978e6i 1.37940 0.796400i 0.387317 0.921947i \(-0.373402\pi\)
0.992088 + 0.125547i \(0.0400686\pi\)
\(500\) −1.98233e7 2.57159e6i −3.54609 0.460020i
\(501\) 2.38544e6 0.424593
\(502\) 274125. + 182789.i 0.0485500 + 0.0323736i
\(503\) −6.90915e6 3.98900e6i −1.21760 0.702982i −0.253196 0.967415i \(-0.581482\pi\)
−0.964404 + 0.264433i \(0.914815\pi\)
\(504\) −5.47944e6 4.77786e6i −0.960859 0.837833i
\(505\) −3.70193e6 −0.645952
\(506\) 564853. 847097.i 0.0980751 0.147081i
\(507\) 576485. 998501.i 0.0996020 0.172516i
\(508\) 400282. 523709.i 0.0688188 0.0900390i
\(509\) −5.80531e6 3.35170e6i −0.993187 0.573417i −0.0869614 0.996212i \(-0.527716\pi\)
−0.906225 + 0.422795i \(0.861049\pi\)
\(510\) 1.34252e6 + 86716.7i 0.228558 + 0.0147631i
\(511\) −7.84493e6 + 4.52927e6i −1.32904 + 0.767319i
\(512\) −4.95989e6 3.25328e6i −0.836175 0.548463i
\(513\) −2.78500e6 1.05203e6i −0.467230 0.176495i
\(514\) −1.19813e6 798925.i −0.200031 0.133382i
\(515\) 1.13468e7 + 1.96533e7i 1.88520 + 3.26526i
\(516\) −1.91562e6 1.46415e6i −0.316726 0.242081i
\(517\) 49241.7 85289.2i 0.00810228 0.0140336i
\(518\) 2.10395e6 + 135899.i 0.344517 + 0.0222532i
\(519\) −158246. 91363.3i −0.0257878 0.0148886i
\(520\) 1.10999e6 5.66435e6i 0.180015 0.918632i
\(521\) 3.34161e6i 0.539339i −0.962953 0.269670i \(-0.913086\pi\)
0.962953 0.269670i \(-0.0869145\pi\)
\(522\) −4.97099e6 + 2.45728e6i −0.798484 + 0.394709i
\(523\) 3.20091e6 5.54413e6i 0.511704 0.886297i −0.488204 0.872730i \(-0.662348\pi\)
0.999908 0.0135678i \(-0.00431890\pi\)
\(524\) 2.11759e6 881836.i 0.336909 0.140301i
\(525\) 6.30221e6i 0.997917i
\(526\) −8.63781e6 + 4.26987e6i −1.36125 + 0.672900i
\(527\) 1.61347e6 + 2.79461e6i 0.253066 + 0.438323i
\(528\) 244179. 66420.1i 0.0381175 0.0103685i
\(529\) 1.08358e6 + 1.87682e6i 0.168354 + 0.291597i
\(530\) −797900. + 1.23529e7i −0.123384 + 1.91020i
\(531\) −7.97048e6 −1.22673
\(532\) 4.19815e6 7.86726e6i 0.643101 1.20516i
\(533\) 2.80595e6 0.427820
\(534\) −70356.4 + 1.08924e6i −0.0106770 + 0.165299i
\(535\) 1.26097e6 + 2.18406e6i 0.190467 + 0.329898i
\(536\) 610617. 700279.i 0.0918030 0.105283i
\(537\) 695447. + 1.20455e6i 0.104071 + 0.180256i
\(538\) 1.88909e6 933824.i 0.281383 0.139094i
\(539\) 893105.i 0.132413i
\(540\) 2.54548e6 + 6.11256e6i 0.375652 + 0.902067i
\(541\) 2.09132e6 3.62228e6i 0.307205 0.532094i −0.670545 0.741869i \(-0.733940\pi\)
0.977750 + 0.209775i \(0.0672730\pi\)
\(542\) −1.82838e6 + 903811.i −0.267343 + 0.132154i
\(543\) 2.57255e6i 0.374424i
\(544\) −624699. 3.06466e6i −0.0905052 0.444001i
\(545\) 7.70017e6 + 4.44569e6i 1.11048 + 0.641133i
\(546\) 1.17380e6 + 75818.5i 0.168505 + 0.0108841i
\(547\) 239528. 414875.i 0.0342286 0.0592856i −0.848404 0.529350i \(-0.822436\pi\)
0.882632 + 0.470064i \(0.155769\pi\)
\(548\) 6.38094e6 8.34850e6i 0.907681 1.18756i
\(549\) −1.46663e6 2.54028e6i −0.207677 0.359708i
\(550\) −2.55199e6 1.70169e6i −0.359726 0.239869i
\(551\) −4.30862e6 5.26297e6i −0.604587 0.738502i
\(552\) −411205. + 2.09841e6i −0.0574395 + 0.293118i
\(553\) −1.33471e7 + 7.70595e6i −1.85598 + 1.07155i
\(554\) −6.50408e6 420114.i −0.900350 0.0581557i
\(555\) −802784. 463487.i −0.110628 0.0638713i
\(556\) 8.46852e6 + 6.47267e6i 1.16177 + 0.887967i
\(557\) 1.93826e6 3.35717e6i 0.264712 0.458495i −0.702776 0.711411i \(-0.748056\pi\)
0.967488 + 0.252916i \(0.0813897\pi\)
\(558\) −4.25352e6 + 6.37891e6i −0.578313 + 0.867283i
\(559\) −5.45463e6 −0.738305
\(560\) −1.91379e7 + 5.20576e6i −2.57883 + 0.701478i
\(561\) 115555. + 66715.4i 0.0155017 + 0.00894992i
\(562\) 8.73761e6 + 5.82632e6i 1.16695 + 0.778132i
\(563\) 6.98110e6 0.928224 0.464112 0.885777i \(-0.346374\pi\)
0.464112 + 0.885777i \(0.346374\pi\)
\(564\) −26608.9 + 205116.i −0.00352232 + 0.0271520i
\(565\) −6.08248e6 + 3.51172e6i −0.801603 + 0.462806i
\(566\) 5.23320e6 2.58689e6i 0.686636 0.339420i
\(567\) 7.28314e6 4.20493e6i 0.951396 0.549289i
\(568\) 2.30639e6 + 6.73152e6i 0.299960 + 0.875472i
\(569\) 1.45003e6i 0.187757i 0.995584 + 0.0938787i \(0.0299266\pi\)
−0.995584 + 0.0938787i \(0.970073\pi\)
\(570\) −3.18751e6 + 2.28290e6i −0.410926 + 0.294306i
\(571\) 2.09836e6i 0.269334i 0.990891 + 0.134667i \(0.0429964\pi\)
−0.990891 + 0.134667i \(0.957004\pi\)
\(572\) 347645. 454841.i 0.0444269 0.0581259i
\(573\) −1.99437e6 + 1.15145e6i −0.253758 + 0.146507i
\(574\) −4.27247e6 8.64307e6i −0.541252 1.09493i
\(575\) 2.24467e7 1.29596e7i 2.83128 1.63464i
\(576\) 5.86974e6 4.55724e6i 0.737161 0.572328i
\(577\) 9.52681e6 1.19126 0.595632 0.803257i \(-0.296902\pi\)
0.595632 + 0.803257i \(0.296902\pi\)
\(578\) −3.54103e6 + 5.31041e6i −0.440870 + 0.661163i
\(579\) −2.39681e6 1.38380e6i −0.297123 0.171544i
\(580\) −1.94617e6 + 1.50021e7i −0.240220 + 1.85175i
\(581\) −5.83547e6 −0.717192
\(582\) −1.70089e6 1.13417e6i −0.208147 0.138794i
\(583\) −613864. + 1.06324e6i −0.0747999 + 0.129557i
\(584\) −3.00124e6 8.75953e6i −0.364141 1.06279i
\(585\) 6.26246e6 + 3.61563e6i 0.756581 + 0.436812i
\(586\) 209127. 3.23764e6i 0.0251574 0.389479i
\(587\) −6.05280e6 + 3.49458e6i −0.725038 + 0.418601i −0.816604 0.577198i \(-0.804146\pi\)
0.0915661 + 0.995799i \(0.470813\pi\)
\(588\) −721079. 1.73155e6i −0.0860082 0.206535i
\(589\) −8.79757e6 3.32326e6i −1.04490 0.394708i
\(590\) −1.20634e7 + 1.80912e7i −1.42672 + 2.13962i
\(591\) 1.67843e6 + 2.90713e6i 0.197667 + 0.342370i
\(592\) −549887. + 2.08375e6i −0.0644865 + 0.244366i
\(593\) −13576.3 + 23514.8i −0.00158542 + 0.00274602i −0.866817 0.498626i \(-0.833838\pi\)
0.865232 + 0.501372i \(0.167171\pi\)
\(594\) −42330.9 + 655354.i −0.00492256 + 0.0762096i
\(595\) −9.05672e6 5.22890e6i −1.04877 0.605506i
\(596\) −48732.4 117023.i −0.00561956 0.0134945i
\(597\) 1.97862e6i 0.227209i
\(598\) 2.14371e6 + 4.33665e6i 0.245139 + 0.495908i
\(599\) 670686. 1.16166e6i 0.0763752 0.132286i −0.825308 0.564682i \(-0.808999\pi\)
0.901683 + 0.432397i \(0.142332\pi\)
\(600\) 6.32173e6 + 1.23881e6i 0.716898 + 0.140484i
\(601\) 1.09584e6i 0.123754i −0.998084 0.0618771i \(-0.980291\pi\)
0.998084 0.0618771i \(-0.0197087\pi\)
\(602\) 8.30549e6 + 1.68017e7i 0.934059 + 1.88957i
\(603\) 581994. + 1.00804e6i 0.0651816 + 0.112898i
\(604\) −8.73363e6 1.13298e6i −0.974098 0.126366i
\(605\) 8.60108e6 + 1.48975e7i 0.955355 + 1.65472i
\(606\) 769512. + 49704.6i 0.0851204 + 0.00549813i
\(607\) 7.00239e6 0.771391 0.385695 0.922626i \(-0.373962\pi\)
0.385695 + 0.922626i \(0.373962\pi\)
\(608\) 7.06641e6 + 5.75760e6i 0.775246 + 0.631659i
\(609\) −3.08278e6 −0.336821
\(610\) −7.98561e6 515809.i −0.868928 0.0561261i
\(611\) 233963. + 405236.i 0.0253539 + 0.0439142i
\(612\) 3.88580e6 + 504089.i 0.419374 + 0.0544037i
\(613\) 1.08004e6 + 1.87068e6i 0.116088 + 0.201071i 0.918214 0.396084i \(-0.129631\pi\)
−0.802126 + 0.597155i \(0.796298\pi\)
\(614\) −1.96697e6 3.97912e6i −0.210560 0.425957i
\(615\) 4.23906e6i 0.451941i
\(616\) −1.93038e6 378277.i −0.204970 0.0401660i
\(617\) 930657. 1.61195e6i 0.0984185 0.170466i −0.812612 0.582806i \(-0.801955\pi\)
0.911030 + 0.412340i \(0.135288\pi\)
\(618\) −2.09476e6 4.23764e6i −0.220630 0.446326i
\(619\) 6.22804e6i 0.653318i −0.945142 0.326659i \(-0.894077\pi\)
0.945142 0.326659i \(-0.105923\pi\)
\(620\) 8.04096e6 + 1.93091e7i 0.840096 + 2.01735i
\(621\) −4.80589e6 2.77468e6i −0.500086 0.288725i
\(622\) −215438. + 3.33534e6i −0.0223278 + 0.345672i
\(623\) 4.24240e6 7.34805e6i 0.437916 0.758493i
\(624\) −306784. + 1.16253e6i −0.0315407 + 0.119521i
\(625\) −2.03525e7 3.52515e7i −2.08409 3.60976i
\(626\) −1.07393e6 + 1.61055e6i −0.109532 + 0.164263i
\(627\) −383742. + 62881.9i −0.0389826 + 0.00638788i
\(628\) 5.08284e6 + 1.22056e7i 0.514290 + 1.23498i
\(629\) −984106. + 568174.i −0.0991780 + 0.0572604i
\(630\) 1.60159e6 2.47954e7i 0.160769 2.48897i
\(631\) 3.43366e6 + 1.98242e6i 0.343308 + 0.198209i 0.661734 0.749739i \(-0.269821\pi\)
−0.318426 + 0.947948i \(0.603154\pi\)
\(632\) −5.10621e6 1.49032e7i −0.508518 1.48418i
\(633\) −683605. + 1.18404e6i −0.0678103 + 0.117451i
\(634\) −7.66080e6 5.10829e6i −0.756921 0.504722i
\(635\) 2.25288e6 0.221719
\(636\) 331715. 2.55705e6i 0.0325179 0.250666i
\(637\) −3.67491e6 2.12171e6i −0.358838 0.207175i
\(638\) −832397. + 1.24833e6i −0.0809615 + 0.121416i
\(639\) −8.91452e6 −0.863666
\(640\) −1.46001e6 2.02204e7i −0.140898 1.95137i
\(641\) 2.02946e6 1.17171e6i 0.195090 0.112636i −0.399273 0.916832i \(-0.630737\pi\)
0.594363 + 0.804197i \(0.297404\pi\)
\(642\) −232790. 470926.i −0.0222908 0.0450936i
\(643\) 3.81707e6 2.20379e6i 0.364085 0.210205i −0.306786 0.951778i \(-0.599254\pi\)
0.670871 + 0.741574i \(0.265920\pi\)
\(644\) 1.00939e7 1.32064e7i 0.959060 1.25479i
\(645\) 8.24054e6i 0.779931i
\(646\) 469869. + 4.78322e6i 0.0442992 + 0.450961i
\(647\) 2.24473e6i 0.210816i −0.994429 0.105408i \(-0.966385\pi\)
0.994429 0.105408i \(-0.0336149\pi\)
\(648\) 2.78632e6 + 8.13225e6i 0.260671 + 0.760805i
\(649\) −1.86770e6 + 1.07832e6i −0.174059 + 0.100493i
\(650\) 1.30647e7 6.45819e6i 1.21288 0.599553i
\(651\) −3.69134e6 + 2.13119e6i −0.341375 + 0.197093i
\(652\) 241484. 1.86149e6i 0.0222469 0.171491i
\(653\) −5.15559e6 −0.473146 −0.236573 0.971614i \(-0.576024\pi\)
−0.236573 + 0.971614i \(0.576024\pi\)
\(654\) −1.54092e6 1.02750e6i −0.140876 0.0939375i
\(655\) 6.78957e6 + 3.91996e6i 0.618356 + 0.357008i
\(656\) 9.50966e6 2.58676e6i 0.862791 0.234691i
\(657\) 1.16002e7 1.04846
\(658\) 891993. 1.33770e6i 0.0803150 0.120447i
\(659\) −9.66959e6 + 1.67482e7i −0.867351 + 1.50230i −0.00265631 + 0.999996i \(0.500846\pi\)
−0.864694 + 0.502299i \(0.832488\pi\)
\(660\) 687148. + 525202.i 0.0614031 + 0.0469317i
\(661\) −5.15993e6 2.97909e6i −0.459347 0.265204i 0.252423 0.967617i \(-0.418773\pi\)
−0.711769 + 0.702413i \(0.752106\pi\)
\(662\) −9.21531e6 595239.i −0.817269 0.0527893i
\(663\) −549036. + 316986.i −0.0485084 + 0.0280064i
\(664\) 1.14706e6 5.85354e6i 0.100964 0.515227i
\(665\) 3.00763e7 4.92844e6i 2.63736 0.432171i
\(666\) −2.24630e6 1.49785e6i −0.196237 0.130853i
\(667\) −6.33929e6 1.09800e7i −0.551729 0.955623i
\(668\) 1.15101e7 1.50593e7i 0.998021 1.30576i
\(669\) −302891. + 524623.i −0.0261651 + 0.0453192i
\(670\) 3.16888e6 + 204686.i 0.272722 + 0.0176157i
\(671\) −687343. 396838.i −0.0589342 0.0340257i
\(672\) 4.04803e6 825151.i 0.345797 0.0704872i
\(673\) 7.93595e6i 0.675400i 0.941254 + 0.337700i \(0.109649\pi\)
−0.941254 + 0.337700i \(0.890351\pi\)
\(674\) 1.48313e7 7.33147e6i 1.25756 0.621643i
\(675\) −8.35908e6 + 1.44784e7i −0.706154 + 1.22309i
\(676\) −3.52191e6 8.45730e6i −0.296423 0.711812i
\(677\) 1.37549e6i 0.115341i 0.998336 + 0.0576707i \(0.0183673\pi\)
−0.998336 + 0.0576707i \(0.981633\pi\)
\(678\) 1.31150e6 648305.i 0.109571 0.0541633i
\(679\) 7.94586e6 + 1.37626e7i 0.661404 + 1.14559i
\(680\) 7.02535e6 8.05694e6i 0.582634 0.668187i
\(681\) 2.63015e6 + 4.55555e6i 0.217327 + 0.376421i
\(682\) −133720. + 2.07021e6i −0.0110087 + 0.170433i
\(683\) −1.35393e7 −1.11057 −0.555285 0.831660i \(-0.687391\pi\)
−0.555285 + 0.831660i \(0.687391\pi\)
\(684\) −9.69316e6 + 6.03688e6i −0.792182 + 0.493370i
\(685\) 3.59133e7 2.92435
\(686\) 145439. 2.25165e6i 0.0117997 0.182679i
\(687\) −756674. 1.31060e6i −0.0611669 0.105944i
\(688\) −1.84864e7 + 5.02854e6i −1.48895 + 0.405015i
\(689\) −2.91666e6 5.05181e6i −0.234066 0.405414i
\(690\) −6.55155e6 + 3.23859e6i −0.523868 + 0.258960i
\(691\) 2.13347e7i 1.69977i −0.526966 0.849887i \(-0.676670\pi\)
0.526966 0.849887i \(-0.323330\pi\)
\(692\) −1.34034e6 + 558164.i −0.106402 + 0.0443095i
\(693\) 1.23219e6 2.13421e6i 0.0974638 0.168812i
\(694\) 1.60188e7 7.91848e6i 1.26250 0.624084i
\(695\) 3.64296e7i 2.86083i
\(696\) 605973. 3.09233e6i 0.0474166 0.241970i
\(697\) 4.50032e6 + 2.59826e6i 0.350882 + 0.202582i
\(698\) 5.76761e6 + 372544.i 0.448082 + 0.0289427i
\(699\) 638864. 1.10655e6i 0.0494556 0.0856597i
\(700\) −3.97859e7 3.04093e7i −3.06891 2.34564i
\(701\) 7.00091e6 + 1.21259e7i 0.538096 + 0.932010i 0.999007 + 0.0445630i \(0.0141895\pi\)
−0.460911 + 0.887447i \(0.652477\pi\)
\(702\) −2.59606e6 1.73108e6i −0.198826 0.132579i
\(703\) 1.17027e6 3.09801e6i 0.0893093 0.236426i
\(704\) 758897. 1.86200e6i 0.0577100 0.141595i
\(705\) −612207. + 353458.i −0.0463901 + 0.0267833i
\(706\) 2.17185e6 + 140285.i 0.163991 + 0.0105925i
\(707\) −5.19117e6 2.99712e6i −0.390586 0.225505i
\(708\) 2.75049e6 3.59860e6i 0.206218 0.269806i
\(709\) 7.01897e6 1.21572e7i 0.524394 0.908277i −0.475203 0.879876i \(-0.657625\pi\)
0.999597 0.0284008i \(-0.00904146\pi\)
\(710\) −1.34922e7 + 2.02340e7i −1.00447 + 1.50638i
\(711\) 1.97362e7 1.46416
\(712\) 6.53689e6 + 5.69992e6i 0.483249 + 0.421375i
\(713\) −1.51814e7 8.76499e6i −1.11838 0.645695i
\(714\) 1.81239e6 + 1.20852e6i 0.133048 + 0.0887174i
\(715\) 1.95662e6 0.143134
\(716\) 1.09600e7 + 1.42180e6i 0.798965 + 0.103646i
\(717\) −2.34719e6 + 1.35515e6i −0.170510 + 0.0984441i
\(718\) −5.52044e6 + 2.72888e6i −0.399634 + 0.197549i
\(719\) 1.11491e7 6.43693e6i 0.804299 0.464362i −0.0406733 0.999172i \(-0.512950\pi\)
0.844972 + 0.534810i \(0.179617\pi\)
\(720\) 2.45574e7 + 6.48052e6i 1.76543 + 0.465885i
\(721\) 3.67461e7i 2.63253i
\(722\) −9.88993e6 9.91884e6i −0.706074 0.708138i
\(723\) 4.67375e6i 0.332522i
\(724\) −1.62405e7 1.24130e7i −1.15147 0.880096i
\(725\) −3.30786e7 + 1.90979e7i −2.33723 + 1.34940i
\(726\) −1.58786e6 3.21219e6i −0.111808 0.226183i
\(727\) −1.92785e7 + 1.11305e7i −1.35281 + 0.781046i −0.988642 0.150287i \(-0.951980\pi\)
−0.364169 + 0.931333i \(0.618647\pi\)
\(728\) 6.14243e6 7.04438e6i 0.429548 0.492622i
\(729\) −8.91801e6 −0.621512
\(730\) 1.75570e7 2.63299e7i 1.21939 1.82870i
\(731\) −8.74842e6 5.05090e6i −0.605530 0.349603i
\(732\) 1.65302e6 + 214440.i 0.114025 + 0.0147920i
\(733\) −2.32106e7 −1.59561 −0.797804 0.602917i \(-0.794005\pi\)
−0.797804 + 0.602917i \(0.794005\pi\)
\(734\) 1.41630e7 + 9.44401e6i 0.970319 + 0.647018i
\(735\) 3.20536e6 5.55184e6i 0.218856 0.379069i
\(736\) 1.12632e7 + 1.27211e7i 0.766417 + 0.865628i
\(737\) 272754. + 157475.i 0.0184971 + 0.0106793i
\(738\) −795838. + 1.23209e7i −0.0537878 + 0.832727i
\(739\) −1.66903e7 + 9.63613e6i −1.12422 + 0.649070i −0.942475 0.334275i \(-0.891508\pi\)
−0.181747 + 0.983345i \(0.558175\pi\)
\(740\) −6.79958e6 + 2.83158e6i −0.456460 + 0.190086i
\(741\) 652897. 1.72839e6i 0.0436816 0.115637i
\(742\) −1.11199e7 + 1.66762e7i −0.741464 + 1.11196i
\(743\) −8.35960e6 1.44792e7i −0.555538 0.962219i −0.997861 0.0653639i \(-0.979179\pi\)
0.442324 0.896855i \(-0.354154\pi\)
\(744\) −1.41220e6 4.12169e6i −0.0935327 0.272988i
\(745\) 216626. 375208.i 0.0142995 0.0247675i
\(746\) −536941. + 8.31276e6i −0.0353248 + 0.546888i
\(747\) 6.47163e6 + 3.73640e6i 0.424338 + 0.244992i
\(748\) 978746. 407584.i 0.0639611 0.0266356i
\(749\) 4.08356e6i 0.265971i
\(750\) 6.30627e6 + 1.27574e7i 0.409373 + 0.828148i
\(751\) 1.00966e7 1.74878e7i 0.653242 1.13145i −0.329090 0.944299i \(-0.606742\pi\)
0.982332 0.187149i \(-0.0599248\pi\)
\(752\) 1.16651e6 + 1.15770e6i 0.0752217 + 0.0746539i
\(753\) 234564.i 0.0150756i
\(754\) −3.15908e6 6.39071e6i −0.202363 0.409375i
\(755\) −1.50499e7 2.60671e7i −0.960871 1.66428i
\(756\) −1.37930e6 + 1.06324e7i −0.0877715 + 0.676592i
\(757\) 6.17824e6 + 1.07010e7i 0.391855 + 0.678713i 0.992694 0.120657i \(-0.0385002\pi\)
−0.600839 + 0.799370i \(0.705167\pi\)
\(758\) 1.39446e7 + 900713.i 0.881520 + 0.0569395i
\(759\) −724848. −0.0456712
\(760\) −968301. + 3.11382e7i −0.0608102 + 1.95551i
\(761\) 9.76295e6 0.611110 0.305555 0.952174i \(-0.401158\pi\)
0.305555 + 0.952174i \(0.401158\pi\)
\(762\) −468300. 30248.6i −0.0292171 0.00188720i
\(763\) 7.19856e6 + 1.24683e7i 0.447645 + 0.775344i
\(764\) −2.35407e6 + 1.81465e7i −0.145910 + 1.12476i
\(765\) 6.69604e6 + 1.15979e7i 0.413680 + 0.716514i
\(766\) 8.67008e6 + 1.75393e7i 0.533889 + 1.08004i
\(767\) 1.02469e7i 0.628931i
\(768\) 31995.7 + 4.22277e6i 0.00195744 + 0.258342i
\(769\) 9.21316e6 1.59577e7i 0.561814 0.973091i −0.435524 0.900177i \(-0.643437\pi\)
0.997338 0.0729135i \(-0.0232297\pi\)
\(770\) −2.97925e6 6.02693e6i −0.181084 0.366327i
\(771\) 1.02522e6i 0.0621129i
\(772\) −2.03009e7 + 8.45401e6i −1.22595 + 0.510528i
\(773\) −7.40351e6 4.27442e6i −0.445645 0.257293i 0.260344 0.965516i \(-0.416164\pi\)
−0.705989 + 0.708223i \(0.749497\pi\)
\(774\) 1.54707e6 2.39513e7i 0.0928236 1.43707i
\(775\) −2.64057e7 + 4.57359e7i −1.57922 + 2.73529i
\(776\) −1.53672e7 + 5.26519e6i −0.916092 + 0.313877i
\(777\) −750488. 1.29988e6i −0.0445955 0.0772417i
\(778\) 4.88275e6 7.32255e6i 0.289211 0.433724i
\(779\) −1.49450e7 + 2.44896e6i −0.882373 + 0.144590i
\(780\) −3.79351e6 + 1.57975e6i −0.223257 + 0.0929718i
\(781\) −2.08892e6 + 1.20604e6i −0.122545 + 0.0707511i
\(782\) −577480. + 8.94037e6i −0.0337691 + 0.522804i
\(783\) 7.08221e6 + 4.08892e6i 0.412824 + 0.238344i
\(784\) −1.44107e7 3.80287e6i −0.837325 0.220964i
\(785\) −2.25944e7 + 3.91346e7i −1.30866 + 2.26666i
\(786\) −1.35870e6 905994.i −0.0784453 0.0523081i
\(787\) −2.21755e7 −1.27625 −0.638126 0.769932i \(-0.720290\pi\)
−0.638126 + 0.769932i \(0.720290\pi\)
\(788\) 2.64515e7 + 3.43144e6i 1.51752 + 0.196862i
\(789\) 5.94075e6 + 3.42989e6i 0.339742 + 0.196150i
\(790\) 2.98709e7 4.47967e7i 1.70287 2.55375i
\(791\) −1.13725e7 −0.646270
\(792\) 1.89861e6 + 1.65552e6i 0.107553 + 0.0937823i
\(793\) 3.26579e6 1.88550e6i 0.184419 0.106474i
\(794\) −4.80561e6 9.72159e6i −0.270519 0.547250i
\(795\) 7.63198e6 4.40632e6i 0.428271 0.247263i
\(796\) 1.24910e7 + 9.54717e6i 0.698740 + 0.534062i
\(797\) 1.80645e7i 1.00735i −0.863894 0.503674i \(-0.831981\pi\)
0.863894 0.503674i \(-0.168019\pi\)
\(798\) −6.31805e6 + 620640.i −0.351217 + 0.0345010i
\(799\) 866584.i 0.0480224i
\(800\) 3.83240e7 3.39317e7i 2.11712 1.87448i
\(801\) −9.40977e6 + 5.43274e6i −0.518201 + 0.299183i
\(802\) −1.01728e7 + 5.02866e6i −0.558477 + 0.276068i
\(803\) 2.71825e6 1.56938e6i 0.148765 0.0858894i
\(804\) −655960. 85095.1i −0.0357880 0.00464263i
\(805\) 5.68109e7 3.08988
\(806\) −8.20074e6 5.46833e6i −0.444647 0.296495i
\(807\) −1.29925e6 750120.i −0.0702276 0.0405459i
\(808\) 4.02681e6 4.61811e6i 0.216987 0.248849i
\(809\) −2.67213e7 −1.43544 −0.717721 0.696331i \(-0.754815\pi\)
−0.717721 + 0.696331i \(0.754815\pi\)
\(810\) −1.62997e7 + 2.44444e7i −0.872907 + 1.30908i
\(811\) 1.18737e7 2.05658e7i 0.633918 1.09798i −0.352825 0.935689i \(-0.614779\pi\)
0.986743 0.162290i \(-0.0518879\pi\)
\(812\) −1.48749e7 + 1.94616e7i −0.791709 + 1.03583i
\(813\) 1.25749e6 + 726012.i 0.0667233 + 0.0385227i
\(814\) −729012. 47088.6i −0.0385633 0.00249089i
\(815\) 5.55597e6 3.20774e6i 0.292999 0.169163i
\(816\) −1.56852e6 + 1.58045e6i −0.0824641 + 0.0830913i
\(817\) 2.90524e7 4.76067e6i 1.52274 0.249524i
\(818\) −3.09493e7 2.06373e7i −1.61722 1.07838i
\(819\) 5.85451e6 + 1.01403e7i 0.304986 + 0.528252i
\(820\) 2.67612e7 + 2.04542e7i 1.38986 + 1.06230i
\(821\) 4.68020e6 8.10634e6i 0.242330 0.419727i −0.719048 0.694961i \(-0.755422\pi\)
0.961377 + 0.275233i \(0.0887551\pi\)
\(822\) −7.46522e6 482196.i −0.385357 0.0248911i
\(823\) 3.96039e6 + 2.28653e6i 0.203816 + 0.117673i 0.598434 0.801172i \(-0.295790\pi\)
−0.394618 + 0.918845i \(0.629123\pi\)
\(824\) −3.68599e7 7.22307e6i −1.89119 0.370599i
\(825\) 2.18370e6i 0.111701i
\(826\) −3.15631e7 + 1.56024e7i −1.60964 + 0.795685i
\(827\) −7.49273e6 + 1.29778e7i −0.380957 + 0.659838i −0.991199 0.132377i \(-0.957739\pi\)
0.610242 + 0.792215i \(0.291072\pi\)
\(828\) −1.96503e7 + 8.18305e6i −0.996076 + 0.414800i
\(829\) 5.06167e6i 0.255804i 0.991787 + 0.127902i \(0.0408243\pi\)
−0.991787 + 0.127902i \(0.959176\pi\)
\(830\) 1.82757e7 9.03408e6i 0.920826 0.455186i
\(831\) 2.32004e6 + 4.01842e6i 0.116545 + 0.201861i
\(832\) 5.85879e6 + 7.54615e6i 0.293427 + 0.377935i
\(833\) −3.92934e6 6.80582e6i −0.196204 0.339835i
\(834\) 489128. 7.57254e6i 0.0243505 0.376987i
\(835\) 6.47816e7 3.21540
\(836\) −1.45465e6 + 2.72599e6i −0.0719851 + 0.134899i
\(837\) 1.13070e7 0.557873
\(838\) 2.11102e6 3.26823e7i 0.103844 1.60769i
\(839\) 1.30260e7 + 2.25616e7i 0.638859 + 1.10654i 0.985683 + 0.168607i \(0.0539268\pi\)
−0.346824 + 0.937930i \(0.612740\pi\)
\(840\) 1.06422e7 + 9.27963e6i 0.520397 + 0.453766i
\(841\) −913661. 1.58251e6i −0.0445446 0.0771535i
\(842\) 2.49916e7 1.23539e7i 1.21483 0.600517i
\(843\) 7.47664e6i 0.362358i
\(844\) 4.17634e6 + 1.00288e7i 0.201809 + 0.484611i
\(845\) 1.56557e7 2.71164e7i 0.754276 1.30644i
\(846\) −1.84575e6 + 912399.i −0.0886641 + 0.0438287i
\(847\) 2.78541e7i 1.33408i
\(848\) −1.45421e7 1.44323e7i −0.694444 0.689202i
\(849\) −3.59919e6 2.07800e6i −0.171371 0.0989408i
\(850\) 2.69340e7 + 1.73973e6i 1.27866 + 0.0825914i
\(851\) 3.08654e6 5.34605e6i 0.146099 0.253051i
\(852\) 3.07627e6 4.02483e6i 0.145186 0.189954i
\(853\) −1.77268e7 3.07038e7i −0.834178 1.44484i −0.894698 0.446671i \(-0.852609\pi\)
0.0605207 0.998167i \(-0.480724\pi\)
\(854\) −1.07805e7 7.18854e6i −0.505818 0.337284i
\(855\) −3.65107e7 1.37918e7i −1.70807 0.645218i
\(856\) −4.09621e6 802695.i −0.191072 0.0374426i
\(857\) −2.63286e7 + 1.52008e7i −1.22455 + 0.706993i −0.965884 0.258975i \(-0.916615\pi\)
−0.258663 + 0.965968i \(0.583282\pi\)
\(858\) −406719. 26270.9i −0.0188615 0.00121831i
\(859\) 1.69942e7 + 9.81163e6i 0.785812 + 0.453689i 0.838486 0.544923i \(-0.183441\pi\)
−0.0526738 + 0.998612i \(0.516774\pi\)
\(860\) −5.20226e7 3.97620e7i −2.39854 1.83325i
\(861\) −3.43198e6 + 5.94437e6i −0.157775 + 0.273274i
\(862\) 3.87063e6 5.80470e6i 0.177424 0.266080i
\(863\) −3.16833e6 −0.144812 −0.0724059 0.997375i \(-0.523068\pi\)
−0.0724059 + 0.997375i \(0.523068\pi\)
\(864\) −1.03942e7 3.47355e6i −0.473704 0.158303i
\(865\) −4.29750e6 2.48117e6i −0.195288 0.112750i
\(866\) 1.81873e7 + 1.21275e7i 0.824088 + 0.549510i
\(867\) 4.54404e6 0.205303
\(868\) −4.35709e6 + 3.35869e7i −0.196289 + 1.51311i
\(869\) 4.62473e6 2.67009e6i 0.207748 0.119943i
\(870\) 9.65471e6 4.77255e6i 0.432455 0.213773i
\(871\) −1.29594e6 + 748213.i −0.0578816 + 0.0334180i
\(872\) −1.39219e7 + 4.77000e6i −0.620021 + 0.212435i
\(873\) 2.03507e7i 0.903739i
\(874\) −1.52027e7 2.12268e7i −0.673197 0.939954i
\(875\) 1.10624e8i 4.88459i
\(876\) −4.00305e6 + 5.23739e6i −0.176251 + 0.230598i
\(877\) −2.54127e7 + 1.46721e7i −1.11571 + 0.644157i −0.940303 0.340338i \(-0.889458\pi\)
−0.175410 + 0.984495i \(0.556125\pi\)
\(878\) 9.26444e6 + 1.87417e7i 0.405586 + 0.820487i
\(879\) −2.00031e6 + 1.15488e6i −0.0873224 + 0.0504156i
\(880\) 6.63122e6 1.80378e6i 0.288660 0.0785195i
\(881\) −1.98402e7 −0.861206 −0.430603 0.902541i \(-0.641699\pi\)
−0.430603 + 0.902541i \(0.641699\pi\)
\(882\) 1.03588e7 1.55348e7i 0.448369 0.672410i
\(883\) −1.22889e7 7.09503e6i −0.530411 0.306233i 0.210773 0.977535i \(-0.432402\pi\)
−0.741184 + 0.671302i \(0.765735\pi\)
\(884\) −648057. + 4.99559e6i −0.0278922 + 0.215009i
\(885\) 1.54804e7 0.664390
\(886\) 2.60569e6 + 1.73750e6i 0.111516 + 0.0743602i
\(887\) −3.89916e6 + 6.75355e6i −0.166404 + 0.288219i −0.937153 0.348919i \(-0.886549\pi\)
0.770749 + 0.637139i \(0.219882\pi\)
\(888\) 1.45143e6 497298.i 0.0617680 0.0211633i
\(889\) 3.15917e6 + 1.82395e6i 0.134066 + 0.0774031i
\(890\) −1.91068e6 + 2.95806e7i −0.0808560 + 1.25179i
\(891\) −2.52359e6 + 1.45700e6i −0.106494 + 0.0614843i
\(892\) 1.85045e6 + 4.44356e6i 0.0778691 + 0.186990i
\(893\) −1.59981e6 1.95417e6i −0.0671336 0.0820036i
\(894\) −50067.4 + 75085.0i −0.00209513 + 0.00314202i
\(895\) 1.88864e7 + 3.27121e7i 0.788117 + 1.36506i
\(896\) 1.43233e7 2.95368e7i 0.596036 1.22912i
\(897\) 1.72199e6 2.98258e6i 0.0714579 0.123769i
\(898\) −2.40032e6 + 3.71611e7i −0.0993295 + 1.53779i
\(899\) 2.23721e7 + 1.29166e7i 0.923226 + 0.533025i
\(900\) 2.46525e7 + 5.91989e7i 1.01451 + 2.43617i
\(901\) 1.08031e7i 0.443341i
\(902\) 1.48040e6 + 2.99480e6i 0.0605847 + 0.122561i
\(903\) 6.67162e6 1.15556e7i 0.272278 0.471599i
\(904\) 2.23546e6 1.14077e7i 0.0909799 0.464277i
\(905\) 6.98631e7i 2.83548i
\(906\) 2.77839e6 + 5.62058e6i 0.112453 + 0.227489i
\(907\) −2.02692e6 3.51073e6i −0.0818123 0.141703i 0.822216 0.569175i \(-0.192737\pi\)
−0.904028 + 0.427472i \(0.859404\pi\)
\(908\) 4.14502e7 + 5.37717e6i 1.66845 + 0.216441i
\(909\) 3.83806e6 + 6.64771e6i 0.154064 + 0.266847i
\(910\) 3.18771e7 + 2.05901e6i 1.27607 + 0.0824244i
\(911\) 1.57962e7 0.630603 0.315301 0.948992i \(-0.397894\pi\)
0.315301 + 0.948992i \(0.397894\pi\)
\(912\) 619360. 6.45961e6i 0.0246579 0.257170i
\(913\) 2.02198e6 0.0802784
\(914\) 1.20560e7 + 778722.i 0.477349 + 0.0308331i
\(915\) 2.84851e6 + 4.93376e6i 0.112477 + 0.194816i
\(916\) −1.19249e7 1.54697e6i −0.469587 0.0609176i
\(917\) 6.34727e6 + 1.09938e7i 0.249266 + 0.431742i
\(918\) −2.56074e6 5.18030e6i −0.100290 0.202884i
\(919\) 1.25713e7i 0.491012i −0.969395 0.245506i \(-0.921046\pi\)
0.969395 0.245506i \(-0.0789542\pi\)
\(920\) −1.11671e7 + 5.69868e7i −0.434983 + 2.21975i
\(921\) −1.58002e6 + 2.73668e6i −0.0613783 + 0.106310i
\(922\) 10067.8 + 20366.8i 0.000390038 + 0.000789034i
\(923\) 1.14605e7i 0.442793i
\(924\) 538368. + 1.29280e6i 0.0207443 + 0.0498142i
\(925\) −1.61056e7 9.29860e6i −0.618905 0.357325i
\(926\) −1.10789e6 + 1.71521e7i −0.0424590 + 0.657338i
\(927\) 2.35282e7 4.07520e7i 0.899268 1.55758i
\(928\) −1.65980e7 1.87465e7i −0.632681 0.714580i
\(929\) 6.00665e6 + 1.04038e7i 0.228346 + 0.395507i 0.957318 0.289037i \(-0.0933350\pi\)
−0.728972 + 0.684543i \(0.760002\pi\)
\(930\) 8.26124e6 1.23892e7i 0.313212 0.469717i
\(931\) 2.14251e7 + 8.09326e6i 0.810117 + 0.306020i
\(932\) −3.90301e6 9.37244e6i −0.147184 0.353438i
\(933\) 2.06068e6 1.18973e6i 0.0775008 0.0447451i
\(934\) −614056. + 9.50664e6i −0.0230325 + 0.356582i
\(935\) 3.13813e6 + 1.81180e6i 0.117393 + 0.0677769i
\(936\) −1.13225e7 + 3.87939e6i −0.422428 + 0.144735i
\(937\) −324149. + 561442.i −0.0120613 + 0.0208908i −0.871993 0.489518i \(-0.837173\pi\)
0.859932 + 0.510409i \(0.170506\pi\)
\(938\) 4.27797e6 + 2.85259e6i 0.158756 + 0.105860i
\(939\) 1.37813e6 0.0510064
\(940\) −722621. + 5.57037e6i −0.0266742 + 0.205619i
\(941\) −1.47141e7 8.49518e6i −0.541700 0.312751i 0.204067 0.978957i \(-0.434584\pi\)
−0.745768 + 0.666206i \(0.767917\pi\)
\(942\) 5.22209e6 7.83145e6i 0.191742 0.287551i
\(943\) −2.82295e7 −1.03377
\(944\) −9.44644e6 3.47278e7i −0.345015 1.26837i
\(945\) −3.17344e7 + 1.83218e7i −1.15598 + 0.667405i
\(946\) −2.87783e6 5.82176e6i −0.104553 0.211508i
\(947\) 2.79671e7 1.61468e7i 1.01338 0.585074i 0.101200 0.994866i \(-0.467732\pi\)
0.912179 + 0.409792i \(0.134399\pi\)
\(948\) −6.81066e6 + 8.91072e6i −0.246132 + 0.322027i
\(949\) 1.49133e7i 0.537535i
\(950\) −6.39485e7 + 4.58001e7i −2.29891 + 1.64648i
\(951\) 6.55523e6i 0.235037i
\(952\) 1.63745e7 5.61034e6i 0.585567 0.200630i
\(953\) 3.91360e7 2.25952e7i 1.39587 0.805905i 0.401911 0.915679i \(-0.368346\pi\)
0.993957 + 0.109774i \(0.0350127\pi\)
\(954\) 2.30098e7 1.13743e7i 0.818543 0.404625i
\(955\) −5.41615e7 + 3.12702e7i −1.92169 + 1.10949i
\(956\) −2.77052e6 + 2.13567e7i −0.0980428 + 0.755769i
\(957\) 1.06817e6 0.0377018
\(958\) −1.58269e7 1.05535e7i −0.557162 0.371521i
\(959\) 5.03608e7 + 2.90758e7i 1.76826 + 1.02090i
\(960\) −1.14003e7 + 8.85112e6i −0.399243 + 0.309970i
\(961\) 7.08886e6 0.247610
\(962\) 1.92564e6 2.88784e6i 0.0670869 0.100609i
\(963\) 2.61467e6 4.52874e6i 0.0908555 0.157366i
\(964\) −2.95055e7 2.25517e7i −1.02261 0.781603i
\(965\) −6.50904e7 3.75800e7i −2.25008 1.29909i
\(966\) −1.18091e7 762780.i −0.407170 0.0263000i
\(967\) 1.29473e7 7.47511e6i 0.445258 0.257070i −0.260567 0.965456i \(-0.583910\pi\)
0.705825 + 0.708386i \(0.250576\pi\)
\(968\) −2.79403e7 5.47520e6i −0.958392 0.187807i
\(969\) 2.64761e6 2.16751e6i 0.0905826 0.0741570i
\(970\) −4.61914e7 3.08009e7i −1.57628 1.05108i
\(971\) 1.61857e6 + 2.80345e6i 0.0550915 + 0.0954213i 0.892256 0.451530i \(-0.149122\pi\)
−0.837164 + 0.546951i \(0.815788\pi\)
\(972\) 1.26502e7 1.65508e7i 0.429467 0.561893i
\(973\) −2.94938e7 + 5.10847e7i −0.998731 + 1.72985i
\(974\) 3.86042e7 + 2.49354e6i 1.30388 + 0.0842207i
\(975\) −8.98540e6 5.18772e6i −0.302709 0.174769i
\(976\) 9.32989e6 9.40085e6i 0.313511 0.315895i
\(977\) 4.57877e7i 1.53466i −0.641253 0.767330i \(-0.721585\pi\)
0.641253 0.767330i \(-0.278415\pi\)
\(978\) −1.19798e6 + 592187.i −0.0400498 + 0.0197976i
\(979\) −1.46998e6 + 2.54608e6i −0.0490179 + 0.0849014i
\(980\) −1.95825e7 4.70241e7i −0.651331 1.56407i
\(981\) 1.84367e7i 0.611660i
\(982\) −742064. + 366819.i −0.0245563 + 0.0121387i
\(983\) −1.20067e7 2.07963e7i −0.396316 0.686439i 0.596952 0.802277i \(-0.296378\pi\)
−0.993268 + 0.115837i \(0.963045\pi\)
\(984\) −5.28816e6 4.61108e6i −0.174107 0.151815i
\(985\) 4.55814e7 + 7.89493e7i 1.49691 + 2.59273i
\(986\) 851004. 1.31750e7i 0.0278766 0.431577i
\(987\) −1.14465e6 −0.0374008
\(988\) −7.76103e6 1.24615e7i −0.252946 0.406144i
\(989\) 5.48769e7 1.78402
\(990\) −554948. + 8.59155e6i −0.0179955 + 0.278602i
\(991\) 8.51586e6 + 1.47499e7i 0.275451 + 0.477095i 0.970249 0.242110i \(-0.0778395\pi\)
−0.694798 + 0.719205i \(0.744506\pi\)
\(992\) −3.28344e7 1.09727e7i −1.05938 0.354024i
\(993\) 3.28715e6 + 5.69350e6i 0.105790 + 0.183234i
\(994\) −3.53015e7 + 1.74504e7i −1.13325 + 0.560194i
\(995\) 5.37336e7i 1.72063i
\(996\) −3.92021e6 + 1.63251e6i −0.125216 + 0.0521444i
\(997\) −1.97560e7 + 3.42184e7i −0.629450 + 1.09024i 0.358212 + 0.933640i \(0.383387\pi\)
−0.987662 + 0.156600i \(0.949947\pi\)
\(998\) −4.49278e7 + 2.22089e7i −1.42787 + 0.705830i
\(999\) 3.98171e6i 0.126228i
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 76.6.f.a.31.2 yes 96
4.3 odd 2 inner 76.6.f.a.31.18 yes 96
19.8 odd 6 inner 76.6.f.a.27.18 yes 96
76.27 even 6 inner 76.6.f.a.27.2 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.6.f.a.27.2 96 76.27 even 6 inner
76.6.f.a.27.18 yes 96 19.8 odd 6 inner
76.6.f.a.31.2 yes 96 1.1 even 1 trivial
76.6.f.a.31.18 yes 96 4.3 odd 2 inner