Properties

Label 37.6.c.a.26.2
Level $37$
Weight $6$
Character 37.26
Analytic conductor $5.934$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [37,6,Mod(10,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.10");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 37.c (of order \(3\), 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: \(5.93420133308\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 26.2
Character \(\chi\) \(=\) 37.26
Dual form 37.6.c.a.10.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.15115 - 8.92206i) q^{2} +(13.8137 - 23.9261i) q^{3} +(-37.0688 + 64.2050i) q^{4} +(-33.8746 + 58.6725i) q^{5} -284.626 q^{6} +(-29.2828 + 50.7192i) q^{7} +434.114 q^{8} +(-260.137 - 450.571i) q^{9} +O(q^{10})\) \(q+(-5.15115 - 8.92206i) q^{2} +(13.8137 - 23.9261i) q^{3} +(-37.0688 + 64.2050i) q^{4} +(-33.8746 + 58.6725i) q^{5} -284.626 q^{6} +(-29.2828 + 50.7192i) q^{7} +434.114 q^{8} +(-260.137 - 450.571i) q^{9} +697.972 q^{10} -622.545 q^{11} +(1024.12 + 1773.82i) q^{12} +(5.07443 - 8.78917i) q^{13} +603.360 q^{14} +(935.867 + 1620.97i) q^{15} +(-1049.99 - 1818.63i) q^{16} +(-763.151 - 1321.82i) q^{17} +(-2680.02 + 4641.92i) q^{18} +(909.917 - 1576.02i) q^{19} +(-2511.38 - 4349.83i) q^{20} +(809.008 + 1401.24i) q^{21} +(3206.83 + 5554.39i) q^{22} -2069.18 q^{23} +(5996.73 - 10386.6i) q^{24} +(-732.472 - 1268.68i) q^{25} -104.557 q^{26} -7660.39 q^{27} +(-2170.95 - 3760.20i) q^{28} -297.317 q^{29} +(9641.59 - 16699.7i) q^{30} -2740.49 q^{31} +(-3871.48 + 6705.60i) q^{32} +(-8599.66 + 14895.1i) q^{33} +(-7862.22 + 13617.8i) q^{34} +(-1983.88 - 3436.18i) q^{35} +38571.9 q^{36} +(7295.76 + 4014.46i) q^{37} -18748.5 q^{38} +(-140.194 - 242.822i) q^{39} +(-14705.4 + 25470.6i) q^{40} +(7986.65 - 13833.3i) q^{41} +(8334.65 - 14436.0i) q^{42} -15024.7 q^{43} +(23077.0 - 39970.5i) q^{44} +35248.2 q^{45} +(10658.7 + 18461.4i) q^{46} +757.172 q^{47} -58017.0 q^{48} +(6688.54 + 11584.9i) q^{49} +(-7546.15 + 13070.3i) q^{50} -42167.8 q^{51} +(376.206 + 651.608i) q^{52} +(8184.07 + 14175.2i) q^{53} +(39459.9 + 68346.5i) q^{54} +(21088.4 - 36526.3i) q^{55} +(-12712.1 + 22017.9i) q^{56} +(-25138.7 - 43541.4i) q^{57} +(1531.52 + 2652.68i) q^{58} +(-16896.4 - 29265.4i) q^{59} -138766. q^{60} +(-1207.78 + 2091.94i) q^{61} +(14116.7 + 24450.8i) q^{62} +30470.2 q^{63} +12571.1 q^{64} +(343.788 + 595.459i) q^{65} +177193. q^{66} +(16220.9 - 28095.4i) q^{67} +113156. q^{68} +(-28583.1 + 49507.3i) q^{69} +(-20438.6 + 35400.6i) q^{70} +(6628.21 - 11480.4i) q^{71} +(-112929. - 195599. i) q^{72} +13382.6 q^{73} +(-1764.29 - 85772.3i) q^{74} -40472.6 q^{75} +(67459.0 + 116842. i) q^{76} +(18229.8 - 31575.0i) q^{77} +(-1444.32 + 2501.63i) q^{78} +(-15736.9 + 27257.1i) q^{79} +142272. q^{80} +(-42605.1 + 73794.2i) q^{81} -164562. q^{82} +(-26635.2 - 46133.5i) q^{83} -119956. q^{84} +103406. q^{85} +(77394.4 + 134051. i) q^{86} +(-4107.05 + 7113.62i) q^{87} -270256. q^{88} +(-14441.9 - 25014.2i) q^{89} +(-181569. - 314486. i) q^{90} +(297.187 + 514.743i) q^{91} +(76702.0 - 132852. i) q^{92} +(-37856.4 + 65569.1i) q^{93} +(-3900.31 - 6755.53i) q^{94} +(61646.0 + 106774. i) q^{95} +(106959. + 185259. i) q^{96} +32958.4 q^{97} +(68907.4 - 119351. i) q^{98} +(161947. + 280501. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 4 q^{2} + 16 q^{3} - 230 q^{4} - 51 q^{5} + 60 q^{6} + 50 q^{7} + 24 q^{8} - 1085 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 4 q^{2} + 16 q^{3} - 230 q^{4} - 51 q^{5} + 60 q^{6} + 50 q^{7} + 24 q^{8} - 1085 q^{9} - 44 q^{10} - 1556 q^{11} + 708 q^{12} - 888 q^{13} + 1888 q^{14} + 1020 q^{15} - 4566 q^{16} - 437 q^{17} - 7302 q^{18} + 4358 q^{19} - 1204 q^{20} + 2354 q^{21} + 7958 q^{22} + 2824 q^{23} + 13824 q^{24} - 620 q^{25} - 17604 q^{26} - 32 q^{27} + 11414 q^{28} + 16954 q^{29} + 15994 q^{30} - 4548 q^{31} - 9148 q^{32} - 680 q^{33} - 4576 q^{34} + 11606 q^{35} + 5828 q^{36} + 12449 q^{37} - 84560 q^{38} + 13468 q^{39} - 23018 q^{40} + 32319 q^{41} + 26750 q^{42} - 49916 q^{43} + 12034 q^{44} + 81730 q^{45} + 5300 q^{46} - 57476 q^{47} - 14944 q^{48} - 52069 q^{49} - 19224 q^{50} - 78336 q^{51} + 1316 q^{52} + 65784 q^{53} + 72114 q^{54} - 24742 q^{55} - 81130 q^{56} - 3762 q^{57} - 73868 q^{58} - 49372 q^{59} - 288608 q^{60} + 137725 q^{61} + 118854 q^{62} - 81596 q^{63} + 427612 q^{64} + 35600 q^{65} + 289576 q^{66} + 64042 q^{67} - 60500 q^{68} - 141544 q^{69} + 5200 q^{70} + 136206 q^{71} - 294660 q^{72} - 270556 q^{73} + 133162 q^{74} - 240592 q^{75} + 209502 q^{76} + 152148 q^{77} + 152814 q^{78} - 61886 q^{79} + 264936 q^{80} - 104975 q^{81} - 28160 q^{82} + 202892 q^{83} - 197912 q^{84} + 576930 q^{85} + 154822 q^{86} - 312 q^{87} - 884284 q^{88} - 12065 q^{89} - 312764 q^{90} + 206252 q^{91} - 291924 q^{92} - 60752 q^{93} - 116814 q^{94} + 506 q^{95} + 81968 q^{96} + 132062 q^{97} + 249798 q^{98} + 289874 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.15115 8.92206i −0.910604 1.57721i −0.813213 0.581966i \(-0.802284\pi\)
−0.0973912 0.995246i \(-0.531050\pi\)
\(3\) 13.8137 23.9261i 0.886150 1.53486i 0.0417606 0.999128i \(-0.486703\pi\)
0.844390 0.535730i \(-0.179963\pi\)
\(4\) −37.0688 + 64.2050i −1.15840 + 2.00641i
\(5\) −33.8746 + 58.6725i −0.605967 + 1.04956i 0.385931 + 0.922527i \(0.373880\pi\)
−0.991898 + 0.127037i \(0.959453\pi\)
\(6\) −284.626 −3.22773
\(7\) −29.2828 + 50.7192i −0.225874 + 0.391226i −0.956581 0.291465i \(-0.905857\pi\)
0.730707 + 0.682691i \(0.239191\pi\)
\(8\) 434.114 2.39817
\(9\) −260.137 450.571i −1.07052 1.85420i
\(10\) 697.972 2.20718
\(11\) −622.545 −1.55128 −0.775638 0.631178i \(-0.782572\pi\)
−0.775638 + 0.631178i \(0.782572\pi\)
\(12\) 1024.12 + 1773.82i 2.05303 + 3.55596i
\(13\) 5.07443 8.78917i 0.00832778 0.0144241i −0.861831 0.507195i \(-0.830682\pi\)
0.870159 + 0.492771i \(0.164016\pi\)
\(14\) 603.360 0.822729
\(15\) 935.867 + 1620.97i 1.07395 + 1.86014i
\(16\) −1049.99 1818.63i −1.02538 1.77601i
\(17\) −763.151 1321.82i −0.640455 1.10930i −0.985331 0.170652i \(-0.945413\pi\)
0.344877 0.938648i \(-0.387921\pi\)
\(18\) −2680.02 + 4641.92i −1.94965 + 3.37689i
\(19\) 909.917 1576.02i 0.578253 1.00156i −0.417427 0.908710i \(-0.637068\pi\)
0.995680 0.0928525i \(-0.0295985\pi\)
\(20\) −2511.38 4349.83i −1.40390 2.43163i
\(21\) 809.008 + 1401.24i 0.400317 + 0.693370i
\(22\) 3206.83 + 5554.39i 1.41260 + 2.44669i
\(23\) −2069.18 −0.815603 −0.407801 0.913071i \(-0.633704\pi\)
−0.407801 + 0.913071i \(0.633704\pi\)
\(24\) 5996.73 10386.6i 2.12513 3.68084i
\(25\) −732.472 1268.68i −0.234391 0.405977i
\(26\) −104.557 −0.0303332
\(27\) −7660.39 −2.02228
\(28\) −2170.95 3760.20i −0.523306 0.906392i
\(29\) −297.317 −0.0656484 −0.0328242 0.999461i \(-0.510450\pi\)
−0.0328242 + 0.999461i \(0.510450\pi\)
\(30\) 9641.59 16699.7i 1.95590 3.38771i
\(31\) −2740.49 −0.512182 −0.256091 0.966653i \(-0.582435\pi\)
−0.256091 + 0.966653i \(0.582435\pi\)
\(32\) −3871.48 + 6705.60i −0.668347 + 1.15761i
\(33\) −8599.66 + 14895.1i −1.37466 + 2.38099i
\(34\) −7862.22 + 13617.8i −1.16640 + 2.02027i
\(35\) −1983.88 3436.18i −0.273745 0.474140i
\(36\) 38571.9 4.96038
\(37\) 7295.76 + 4014.46i 0.876125 + 0.482084i
\(38\) −18748.5 −2.10624
\(39\) −140.194 242.822i −0.0147593 0.0255639i
\(40\) −14705.4 + 25470.6i −1.45321 + 2.51703i
\(41\) 7986.65 13833.3i 0.742002 1.28519i −0.209580 0.977791i \(-0.567210\pi\)
0.951582 0.307394i \(-0.0994570\pi\)
\(42\) 8334.65 14436.0i 0.729061 1.26277i
\(43\) −15024.7 −1.23918 −0.619589 0.784926i \(-0.712701\pi\)
−0.619589 + 0.784926i \(0.712701\pi\)
\(44\) 23077.0 39970.5i 1.79700 3.11249i
\(45\) 35248.2 2.59481
\(46\) 10658.7 + 18461.4i 0.742691 + 1.28638i
\(47\) 757.172 0.0499977 0.0249988 0.999687i \(-0.492042\pi\)
0.0249988 + 0.999687i \(0.492042\pi\)
\(48\) −58017.0 −3.63456
\(49\) 6688.54 + 11584.9i 0.397962 + 0.689290i
\(50\) −7546.15 + 13070.3i −0.426875 + 0.739369i
\(51\) −42167.8 −2.27016
\(52\) 376.206 + 651.608i 0.0192938 + 0.0334178i
\(53\) 8184.07 + 14175.2i 0.400203 + 0.693171i 0.993750 0.111628i \(-0.0356064\pi\)
−0.593548 + 0.804799i \(0.702273\pi\)
\(54\) 39459.9 + 68346.5i 1.84150 + 3.18957i
\(55\) 21088.4 36526.3i 0.940022 1.62817i
\(56\) −12712.1 + 22017.9i −0.541684 + 0.938225i
\(57\) −25138.7 43541.4i −1.02484 1.77507i
\(58\) 1531.52 + 2652.68i 0.0597797 + 0.103542i
\(59\) −16896.4 29265.4i −0.631923 1.09452i −0.987158 0.159745i \(-0.948933\pi\)
0.355236 0.934777i \(-0.384401\pi\)
\(60\) −138766. −4.97628
\(61\) −1207.78 + 2091.94i −0.0415588 + 0.0719820i −0.886057 0.463577i \(-0.846566\pi\)
0.844498 + 0.535559i \(0.179899\pi\)
\(62\) 14116.7 + 24450.8i 0.466395 + 0.807820i
\(63\) 30470.2 0.967216
\(64\) 12571.1 0.383639
\(65\) 343.788 + 595.459i 0.0100927 + 0.0174811i
\(66\) 177193. 5.00710
\(67\) 16220.9 28095.4i 0.441456 0.764624i −0.556342 0.830953i \(-0.687795\pi\)
0.997798 + 0.0663294i \(0.0211288\pi\)
\(68\) 113156. 2.96761
\(69\) −28583.1 + 49507.3i −0.722747 + 1.25183i
\(70\) −20438.6 + 35400.6i −0.498546 + 0.863507i
\(71\) 6628.21 11480.4i 0.156045 0.270278i −0.777394 0.629014i \(-0.783459\pi\)
0.933439 + 0.358736i \(0.116792\pi\)
\(72\) −112929. 195599.i −2.56729 4.44669i
\(73\) 13382.6 0.293922 0.146961 0.989142i \(-0.453051\pi\)
0.146961 + 0.989142i \(0.453051\pi\)
\(74\) −1764.29 85772.3i −0.0374533 1.82082i
\(75\) −40472.6 −0.830822
\(76\) 67459.0 + 116842.i 1.33970 + 2.32042i
\(77\) 18229.8 31575.0i 0.350394 0.606900i
\(78\) −1444.32 + 2501.63i −0.0268798 + 0.0465572i
\(79\) −15736.9 + 27257.1i −0.283695 + 0.491374i −0.972292 0.233770i \(-0.924894\pi\)
0.688597 + 0.725144i \(0.258227\pi\)
\(80\) 142272. 2.48538
\(81\) −42605.1 + 73794.2i −0.721521 + 1.24971i
\(82\) −164562. −2.70268
\(83\) −26635.2 46133.5i −0.424386 0.735058i 0.571977 0.820270i \(-0.306177\pi\)
−0.996363 + 0.0852117i \(0.972843\pi\)
\(84\) −119956. −1.85491
\(85\) 103406. 1.55238
\(86\) 77394.4 + 134051.i 1.12840 + 1.95445i
\(87\) −4107.05 + 7113.62i −0.0581744 + 0.100761i
\(88\) −270256. −3.72022
\(89\) −14441.9 25014.2i −0.193264 0.334743i 0.753066 0.657945i \(-0.228574\pi\)
−0.946330 + 0.323202i \(0.895241\pi\)
\(90\) −181569. 314486.i −2.36284 4.09256i
\(91\) 297.187 + 514.743i 0.00376206 + 0.00651608i
\(92\) 76702.0 132852.i 0.944794 1.63643i
\(93\) −37856.4 + 65569.1i −0.453870 + 0.786126i
\(94\) −3900.31 6755.53i −0.0455281 0.0788569i
\(95\) 61646.0 + 106774.i 0.700803 + 1.21383i
\(96\) 106959. + 185259.i 1.18451 + 2.05163i
\(97\) 32958.4 0.355661 0.177831 0.984061i \(-0.443092\pi\)
0.177831 + 0.984061i \(0.443092\pi\)
\(98\) 68907.4 119351.i 0.724771 1.25534i
\(99\) 161947. + 280501.i 1.66068 + 2.87638i
\(100\) 108607. 1.08607
\(101\) −106657. −1.04036 −0.520182 0.854056i \(-0.674136\pi\)
−0.520182 + 0.854056i \(0.674136\pi\)
\(102\) 217213. + 376224.i 2.06721 + 3.58052i
\(103\) −19481.0 −0.180933 −0.0904664 0.995900i \(-0.528836\pi\)
−0.0904664 + 0.995900i \(0.528836\pi\)
\(104\) 2202.88 3815.51i 0.0199714 0.0345915i
\(105\) −109619. −0.970316
\(106\) 84314.9 146038.i 0.728852 1.26241i
\(107\) −84036.8 + 145556.i −0.709594 + 1.22905i 0.255414 + 0.966832i \(0.417788\pi\)
−0.965008 + 0.262221i \(0.915545\pi\)
\(108\) 283961. 491836.i 2.34261 4.05752i
\(109\) −92438.8 160109.i −0.745226 1.29077i −0.950089 0.311979i \(-0.899008\pi\)
0.204862 0.978791i \(-0.434325\pi\)
\(110\) −434519. −3.42395
\(111\) 196832. 119104.i 1.51631 0.917527i
\(112\) 122986. 0.926428
\(113\) −13837.5 23967.3i −0.101944 0.176572i 0.810541 0.585681i \(-0.199173\pi\)
−0.912486 + 0.409109i \(0.865840\pi\)
\(114\) −258986. + 448577.i −1.86644 + 3.23277i
\(115\) 70092.6 121404.i 0.494228 0.856028i
\(116\) 11021.2 19089.2i 0.0760471 0.131717i
\(117\) −5280.20 −0.0356604
\(118\) −174072. + 301501.i −1.15086 + 1.99335i
\(119\) 89388.7 0.578649
\(120\) 406273. + 703686.i 2.57552 + 4.46093i
\(121\) 226512. 1.40646
\(122\) 24885.8 0.151375
\(123\) −220651. 382178.i −1.31505 2.27773i
\(124\) 101587. 175953.i 0.593311 1.02765i
\(125\) −112467. −0.643801
\(126\) −156957. 271857.i −0.880751 1.52551i
\(127\) 34319.4 + 59443.0i 0.188813 + 0.327033i 0.944855 0.327490i \(-0.106203\pi\)
−0.756042 + 0.654523i \(0.772869\pi\)
\(128\) 59131.7 + 102419.i 0.319004 + 0.552531i
\(129\) −207546. + 359481.i −1.09810 + 1.90196i
\(130\) 3541.81 6134.60i 0.0183809 0.0318367i
\(131\) 50589.2 + 87623.0i 0.257561 + 0.446108i 0.965588 0.260077i \(-0.0837480\pi\)
−0.708027 + 0.706185i \(0.750415\pi\)
\(132\) −637558. 1.10428e6i −3.18482 5.51627i
\(133\) 53289.7 + 92300.5i 0.261225 + 0.452455i
\(134\) −334225. −1.60797
\(135\) 259492. 449454.i 1.22543 2.12252i
\(136\) −331295. 573820.i −1.53592 2.66029i
\(137\) −121328. −0.552282 −0.276141 0.961117i \(-0.589056\pi\)
−0.276141 + 0.961117i \(0.589056\pi\)
\(138\) 588943. 2.63254
\(139\) 16704.8 + 28933.5i 0.0733336 + 0.127018i 0.900360 0.435145i \(-0.143303\pi\)
−0.827027 + 0.562163i \(0.809970\pi\)
\(140\) 294160. 1.26842
\(141\) 10459.4 18116.1i 0.0443054 0.0767393i
\(142\) −136572. −0.568382
\(143\) −3159.06 + 5471.66i −0.0129187 + 0.0223758i
\(144\) −546283. + 946190.i −2.19539 + 3.80252i
\(145\) 10071.5 17444.3i 0.0397808 0.0689023i
\(146\) −68935.6 119400.i −0.267646 0.463577i
\(147\) 369574. 1.41061
\(148\) −528193. + 319613.i −1.98216 + 1.19942i
\(149\) 502499. 1.85425 0.927127 0.374747i \(-0.122271\pi\)
0.927127 + 0.374747i \(0.122271\pi\)
\(150\) 208481. + 361099.i 0.756550 + 1.31038i
\(151\) 142884. 247482.i 0.509965 0.883285i −0.489969 0.871740i \(-0.662992\pi\)
0.999933 0.0115449i \(-0.00367493\pi\)
\(152\) 395008. 684174.i 1.38675 2.40191i
\(153\) −397049. + 687708.i −1.37124 + 2.37507i
\(154\) −375619. −1.27628
\(155\) 92832.9 160791.i 0.310365 0.537568i
\(156\) 20787.2 0.0683888
\(157\) −20802.2 36030.5i −0.0673535 0.116660i 0.830382 0.557194i \(-0.188122\pi\)
−0.897736 + 0.440535i \(0.854789\pi\)
\(158\) 324253. 1.03334
\(159\) 452210. 1.41856
\(160\) −262289. 454299.i −0.809992 1.40295i
\(161\) 60591.3 104947.i 0.184224 0.319085i
\(162\) 877861. 2.62808
\(163\) 186781. + 323515.i 0.550635 + 0.953729i 0.998229 + 0.0594914i \(0.0189479\pi\)
−0.447593 + 0.894237i \(0.647719\pi\)
\(164\) 592111. + 1.02557e6i 1.71907 + 2.97752i
\(165\) −582620. 1.00913e6i −1.66600 2.88560i
\(166\) −274404. + 475282.i −0.772895 + 1.33869i
\(167\) 78686.0 136288.i 0.218326 0.378152i −0.735970 0.677014i \(-0.763274\pi\)
0.954296 + 0.298862i \(0.0966069\pi\)
\(168\) 351202. + 608299.i 0.960027 + 1.66282i
\(169\) 185595. + 321460.i 0.499861 + 0.865785i
\(170\) −532659. 922592.i −1.41360 2.44843i
\(171\) −946813. −2.47613
\(172\) 556946. 964659.i 1.43546 2.48630i
\(173\) −58627.6 101546.i −0.148932 0.257957i 0.781901 0.623402i \(-0.214250\pi\)
−0.930833 + 0.365445i \(0.880917\pi\)
\(174\) 84624.2 0.211895
\(175\) 85795.2 0.211772
\(176\) 653666. + 1.13218e6i 1.59065 + 2.75508i
\(177\) −933608. −2.23991
\(178\) −148785. + 257704.i −0.351973 + 0.609636i
\(179\) 71604.8 0.167036 0.0835179 0.996506i \(-0.473384\pi\)
0.0835179 + 0.996506i \(0.473384\pi\)
\(180\) −1.30661e6 + 2.26311e6i −3.00582 + 5.20624i
\(181\) 266097. 460893.i 0.603730 1.04569i −0.388520 0.921440i \(-0.627014\pi\)
0.992251 0.124252i \(-0.0396530\pi\)
\(182\) 3061.71 5303.04i 0.00685150 0.0118671i
\(183\) 33367.9 + 57794.8i 0.0736547 + 0.127574i
\(184\) −898261. −1.95595
\(185\) −482679. + 292072.i −1.03688 + 0.627423i
\(186\) 780016. 1.65318
\(187\) 475096. + 822891.i 0.993522 + 1.72083i
\(188\) −28067.4 + 48614.2i −0.0579173 + 0.100316i
\(189\) 224317. 388529.i 0.456782 0.791169i
\(190\) 635097. 1.10002e6i 1.27631 2.21063i
\(191\) −935329. −1.85516 −0.927579 0.373627i \(-0.878114\pi\)
−0.927579 + 0.373627i \(0.878114\pi\)
\(192\) 173653. 300777.i 0.339962 0.588831i
\(193\) −484455. −0.936181 −0.468091 0.883680i \(-0.655058\pi\)
−0.468091 + 0.883680i \(0.655058\pi\)
\(194\) −169774. 294057.i −0.323867 0.560953i
\(195\) 18996.0 0.0357746
\(196\) −991744. −1.84399
\(197\) 334566. + 579485.i 0.614209 + 1.06384i 0.990523 + 0.137348i \(0.0438580\pi\)
−0.376314 + 0.926492i \(0.622809\pi\)
\(198\) 1.66843e6 2.88981e6i 3.02444 5.23849i
\(199\) −506514. −0.906690 −0.453345 0.891335i \(-0.649769\pi\)
−0.453345 + 0.891335i \(0.649769\pi\)
\(200\) −317976. 550751.i −0.562108 0.973600i
\(201\) −448141. 776203.i −0.782392 1.35514i
\(202\) 549405. + 951598.i 0.947359 + 1.64087i
\(203\) 8706.26 15079.7i 0.0148283 0.0256834i
\(204\) 1.56311e6 2.70739e6i 2.62975 4.55486i
\(205\) 541089. + 937193.i 0.899257 + 1.55756i
\(206\) 100349. + 173810.i 0.164758 + 0.285370i
\(207\) 538271. + 932313.i 0.873123 + 1.51229i
\(208\) −21312.4 −0.0341565
\(209\) −566464. + 981145.i −0.897030 + 1.55370i
\(210\) 564665. + 978028.i 0.883573 + 1.53039i
\(211\) 822328. 1.27157 0.635783 0.771868i \(-0.280677\pi\)
0.635783 + 0.771868i \(0.280677\pi\)
\(212\) −1.21349e6 −1.85438
\(213\) −183121. 317174.i −0.276559 0.479014i
\(214\) 1.73155e6 2.58464
\(215\) 508954. 881534.i 0.750901 1.30060i
\(216\) −3.32549e6 −4.84977
\(217\) 80249.2 138996.i 0.115689 0.200379i
\(218\) −952334. + 1.64949e6i −1.35721 + 2.35076i
\(219\) 184863. 320192.i 0.260459 0.451128i
\(220\) 1.56345e6 + 2.70797e6i 2.17784 + 3.77213i
\(221\) −15490.2 −0.0213343
\(222\) −2.07656e6 1.14262e6i −2.82789 1.55604i
\(223\) −1.39322e6 −1.87610 −0.938050 0.346499i \(-0.887370\pi\)
−0.938050 + 0.346499i \(0.887370\pi\)
\(224\) −226735. 392717.i −0.301925 0.522949i
\(225\) −381087. + 660061.i −0.501842 + 0.869217i
\(226\) −142558. + 246918.i −0.185661 + 0.321575i
\(227\) 601186. 1.04128e6i 0.774362 1.34123i −0.160791 0.986989i \(-0.551404\pi\)
0.935152 0.354246i \(-0.115262\pi\)
\(228\) 3.72744e6 4.74868
\(229\) −388054. + 672128.i −0.488993 + 0.846961i −0.999920 0.0126632i \(-0.995969\pi\)
0.510927 + 0.859624i \(0.329302\pi\)
\(230\) −1.44423e6 −1.80018
\(231\) −503644. 872337.i −0.621003 1.07561i
\(232\) −129069. −0.157436
\(233\) 865545. 1.04448 0.522239 0.852799i \(-0.325097\pi\)
0.522239 + 0.852799i \(0.325097\pi\)
\(234\) 27199.1 + 47110.3i 0.0324725 + 0.0562440i
\(235\) −25648.9 + 44425.1i −0.0302969 + 0.0524758i
\(236\) 2.50531e6 2.92808
\(237\) 434771. + 753045.i 0.502793 + 0.870863i
\(238\) −460455. 797532.i −0.526920 0.912653i
\(239\) −540209. 935670.i −0.611741 1.05957i −0.990947 0.134254i \(-0.957136\pi\)
0.379206 0.925312i \(-0.376197\pi\)
\(240\) 1.96530e6 3.40400e6i 2.20242 3.81471i
\(241\) 512514. 887700.i 0.568411 0.984517i −0.428312 0.903631i \(-0.640892\pi\)
0.996723 0.0808865i \(-0.0257751\pi\)
\(242\) −1.16680e6 2.02095e6i −1.28073 2.21828i
\(243\) 246331. + 426658.i 0.267611 + 0.463516i
\(244\) −89541.9 155091.i −0.0962835 0.166768i
\(245\) −906285. −0.964605
\(246\) −2.27321e6 + 3.93732e6i −2.39498 + 4.14823i
\(247\) −9234.62 15994.8i −0.00963112 0.0166816i
\(248\) −1.18969e6 −1.22830
\(249\) −1.47173e6 −1.50428
\(250\) 579337. + 1.00344e6i 0.586248 + 1.01541i
\(251\) −42030.1 −0.0421091 −0.0210545 0.999778i \(-0.506702\pi\)
−0.0210545 + 0.999778i \(0.506702\pi\)
\(252\) −1.12949e6 + 1.95634e6i −1.12042 + 1.94063i
\(253\) 1.28816e6 1.26523
\(254\) 353570. 612400.i 0.343867 0.595595i
\(255\) 1.42842e6 2.47409e6i 1.37564 2.38268i
\(256\) 810331. 1.40353e6i 0.772792 1.33851i
\(257\) −169959. 294378.i −0.160514 0.278018i 0.774539 0.632526i \(-0.217982\pi\)
−0.935053 + 0.354508i \(0.884648\pi\)
\(258\) 4.27642e6 3.99973
\(259\) −417250. + 252481.i −0.386498 + 0.233872i
\(260\) −50975.3 −0.0467656
\(261\) 77343.2 + 133962.i 0.0702783 + 0.121726i
\(262\) 521185. 902719.i 0.469071 0.812455i
\(263\) 11725.8 20309.6i 0.0104533 0.0181056i −0.860751 0.509025i \(-0.830006\pi\)
0.871205 + 0.490920i \(0.163339\pi\)
\(264\) −3.73324e6 + 6.46616e6i −3.29667 + 5.71000i
\(265\) −1.10893e6 −0.970037
\(266\) 549007. 950909.i 0.475745 0.824014i
\(267\) −797987. −0.685043
\(268\) 1.20258e6 + 2.08292e6i 1.02276 + 1.77148i
\(269\) −273681. −0.230603 −0.115301 0.993331i \(-0.536783\pi\)
−0.115301 + 0.993331i \(0.536783\pi\)
\(270\) −5.34674e6 −4.46354
\(271\) 216147. + 374377.i 0.178783 + 0.309661i 0.941464 0.337114i \(-0.109451\pi\)
−0.762681 + 0.646775i \(0.776117\pi\)
\(272\) −1.60260e6 + 2.77579e6i −1.31342 + 2.27491i
\(273\) 16421.0 0.0133350
\(274\) 624981. + 1.08250e6i 0.502910 + 0.871066i
\(275\) 455997. + 789810.i 0.363605 + 0.629783i
\(276\) −2.11908e6 3.67035e6i −1.67446 2.90025i
\(277\) 1.12776e6 1.95335e6i 0.883119 1.52961i 0.0352640 0.999378i \(-0.488773\pi\)
0.847855 0.530229i \(-0.177894\pi\)
\(278\) 172098. 298082.i 0.133556 0.231325i
\(279\) 712904. + 1.23479e6i 0.548303 + 0.949689i
\(280\) −861231. 1.49170e6i −0.656485 1.13707i
\(281\) 922687. + 1.59814e6i 0.697089 + 1.20739i 0.969471 + 0.245205i \(0.0788553\pi\)
−0.272382 + 0.962189i \(0.587811\pi\)
\(282\) −215511. −0.161379
\(283\) 358728. 621336.i 0.266256 0.461169i −0.701636 0.712536i \(-0.747547\pi\)
0.967892 + 0.251367i \(0.0808800\pi\)
\(284\) 491400. + 851129.i 0.361526 + 0.626181i
\(285\) 3.40624e6 2.48407
\(286\) 65091.3 0.0470552
\(287\) 467743. + 810154.i 0.335199 + 0.580581i
\(288\) 4.02847e6 2.86193
\(289\) −454872. + 787861.i −0.320364 + 0.554888i
\(290\) −207519. −0.144898
\(291\) 455278. 788564.i 0.315169 0.545889i
\(292\) −496075. + 859227.i −0.340479 + 0.589727i
\(293\) −1.40056e6 + 2.42583e6i −0.953084 + 1.65079i −0.214392 + 0.976748i \(0.568777\pi\)
−0.738693 + 0.674043i \(0.764556\pi\)
\(294\) −1.90373e6 3.29736e6i −1.28451 2.22484i
\(295\) 2.28943e6 1.53170
\(296\) 3.16719e6 + 1.74274e6i 2.10109 + 1.15612i
\(297\) 4.76894e6 3.13712
\(298\) −2.58845e6 4.48332e6i −1.68849 2.92455i
\(299\) −10499.9 + 18186.4i −0.00679216 + 0.0117644i
\(300\) 1.50027e6 2.59855e6i 0.962424 1.66697i
\(301\) 439964. 762040.i 0.279899 0.484799i
\(302\) −2.94406e6 −1.85750
\(303\) −1.47333e6 + 2.55188e6i −0.921918 + 1.59681i
\(304\) −3.82161e6 −2.37171
\(305\) −81826.0 141727.i −0.0503665 0.0872374i
\(306\) 8.18103e6 4.99464
\(307\) 309132. 0.187197 0.0935983 0.995610i \(-0.470163\pi\)
0.0935983 + 0.995610i \(0.470163\pi\)
\(308\) 1.35152e6 + 2.34090e6i 0.811792 + 1.40606i
\(309\) −269105. + 466103.i −0.160334 + 0.277706i
\(310\) −1.91279e6 −1.13048
\(311\) −806132. 1.39626e6i −0.472612 0.818589i 0.526896 0.849930i \(-0.323356\pi\)
−0.999509 + 0.0313409i \(0.990022\pi\)
\(312\) −60860.0 105413.i −0.0353953 0.0613065i
\(313\) −1.53468e6 2.65814e6i −0.885434 1.53362i −0.845216 0.534426i \(-0.820528\pi\)
−0.0402183 0.999191i \(-0.512805\pi\)
\(314\) −214311. + 371197.i −0.122665 + 0.212462i
\(315\) −1.03216e6 + 1.78776e6i −0.586101 + 1.01516i
\(316\) −1.16670e6 2.02078e6i −0.657265 1.13842i
\(317\) −472314. 818071.i −0.263987 0.457239i 0.703311 0.710882i \(-0.251704\pi\)
−0.967298 + 0.253644i \(0.918371\pi\)
\(318\) −2.32940e6 4.03464e6i −1.29174 2.23737i
\(319\) 185093. 0.101839
\(320\) −425840. + 737577.i −0.232473 + 0.402654i
\(321\) 2.32172e6 + 4.02134e6i 1.25761 + 2.17825i
\(322\) −1.24846e6 −0.671020
\(323\) −2.77762e6 −1.48138
\(324\) −3.15864e6 5.47092e6i −1.67162 2.89533i
\(325\) −14867.5 −0.00780782
\(326\) 1.92428e6 3.33295e6i 1.00282 1.73694i
\(327\) −5.10770e6 −2.64153
\(328\) 3.46712e6 6.00523e6i 1.77944 3.08209i
\(329\) −22172.1 + 38403.2i −0.0112932 + 0.0195604i
\(330\) −6.00233e6 + 1.03963e7i −3.03413 + 5.25528i
\(331\) 65267.1 + 113046.i 0.0327434 + 0.0567133i 0.881933 0.471375i \(-0.156242\pi\)
−0.849189 + 0.528089i \(0.822909\pi\)
\(332\) 3.94934e6 1.96643
\(333\) −89098.0 4.33157e6i −0.0440309 2.14060i
\(334\) −1.62129e6 −0.795236
\(335\) 1.09895e6 + 1.90344e6i 0.535015 + 0.926673i
\(336\) 1.69890e6 2.94258e6i 0.820954 1.42193i
\(337\) −1.29235e6 + 2.23841e6i −0.619876 + 1.07366i 0.369632 + 0.929178i \(0.379484\pi\)
−0.989508 + 0.144479i \(0.953849\pi\)
\(338\) 1.91206e6 3.31178e6i 0.910351 1.57678i
\(339\) −764590. −0.361351
\(340\) −3.83312e6 + 6.63916e6i −1.79827 + 3.11470i
\(341\) 1.70608e6 0.794536
\(342\) 4.87718e6 + 8.44753e6i 2.25478 + 3.90539i
\(343\) −1.76775e6 −0.811306
\(344\) −6.52242e6 −2.97175
\(345\) −1.93648e6 3.35408e6i −0.875921 1.51714i
\(346\) −604000. + 1.04616e6i −0.271236 + 0.469794i
\(347\) 228919. 0.102061 0.0510303 0.998697i \(-0.483750\pi\)
0.0510303 + 0.998697i \(0.483750\pi\)
\(348\) −304487. 527386.i −0.134778 0.233443i
\(349\) −1.13772e6 1.97059e6i −0.500003 0.866031i −1.00000 4.02675e-6i \(-0.999999\pi\)
0.499997 0.866027i \(-0.333335\pi\)
\(350\) −441944. 765470.i −0.192840 0.334009i
\(351\) −38872.1 + 67328.5i −0.0168411 + 0.0291697i
\(352\) 2.41017e6 4.17454e6i 1.03679 1.79578i
\(353\) 1.18083e6 + 2.04527e6i 0.504373 + 0.873600i 0.999987 + 0.00505739i \(0.00160982\pi\)
−0.495614 + 0.868543i \(0.665057\pi\)
\(354\) 4.80916e6 + 8.32971e6i 2.03967 + 3.53282i
\(355\) 449056. + 777787.i 0.189116 + 0.327559i
\(356\) 2.14138e6 0.895506
\(357\) 1.23479e6 2.13872e6i 0.512770 0.888144i
\(358\) −368848. 638863.i −0.152104 0.263451i
\(359\) 2.67447e6 1.09522 0.547611 0.836733i \(-0.315537\pi\)
0.547611 + 0.836733i \(0.315537\pi\)
\(360\) 1.53017e7 6.22278
\(361\) −417847. 723732.i −0.168752 0.292287i
\(362\) −5.48282e6 −2.19904
\(363\) 3.12897e6 5.41953e6i 1.24633 2.15871i
\(364\) −44065.4 −0.0174319
\(365\) −453328. + 785187.i −0.178107 + 0.308490i
\(366\) 343766. 595420.i 0.134141 0.232338i
\(367\) 2.04245e6 3.53763e6i 0.791566 1.37103i −0.133431 0.991058i \(-0.542600\pi\)
0.924997 0.379974i \(-0.124067\pi\)
\(368\) 2.17262e6 + 3.76308e6i 0.836303 + 1.44852i
\(369\) −8.31051e6 −3.17733
\(370\) 5.09224e6 + 2.80198e6i 1.93377 + 1.06405i
\(371\) −958609. −0.361582
\(372\) −2.80658e6 4.86114e6i −1.05153 1.82130i
\(373\) −1.80412e6 + 3.12483e6i −0.671419 + 1.16293i 0.306083 + 0.952005i \(0.400982\pi\)
−0.977502 + 0.210927i \(0.932352\pi\)
\(374\) 4.89459e6 8.47768e6i 1.80941 3.13399i
\(375\) −1.55359e6 + 2.69090e6i −0.570504 + 0.988142i
\(376\) 328699. 0.119903
\(377\) −1508.71 + 2613.17i −0.000546705 + 0.000946922i
\(378\) −4.62198e6 −1.66379
\(379\) −1.65768e6 2.87119e6i −0.592793 1.02675i −0.993854 0.110697i \(-0.964692\pi\)
0.401061 0.916051i \(-0.368641\pi\)
\(380\) −9.14058e6 −3.24724
\(381\) 1.89632e6 0.669265
\(382\) 4.81802e6 + 8.34506e6i 1.68931 + 2.92598i
\(383\) −783022. + 1.35623e6i −0.272758 + 0.472430i −0.969567 0.244826i \(-0.921269\pi\)
0.696809 + 0.717257i \(0.254602\pi\)
\(384\) 3.26732e6 1.13074
\(385\) 1.23506e6 + 2.13918e6i 0.424654 + 0.735522i
\(386\) 2.49550e6 + 4.32233e6i 0.852490 + 1.47656i
\(387\) 3.90848e6 + 6.76968e6i 1.32657 + 2.29769i
\(388\) −1.22173e6 + 2.11609e6i −0.411998 + 0.713601i
\(389\) −1.07043e6 + 1.85404e6i −0.358661 + 0.621219i −0.987737 0.156124i \(-0.950100\pi\)
0.629076 + 0.777343i \(0.283433\pi\)
\(390\) −97851.2 169483.i −0.0325765 0.0564242i
\(391\) 1.57910e6 + 2.73508e6i 0.522357 + 0.904748i
\(392\) 2.90359e6 + 5.02917e6i 0.954378 + 1.65303i
\(393\) 2.79530e6 0.912949
\(394\) 3.44680e6 5.97003e6i 1.11860 1.93747i
\(395\) −1.06616e6 1.84665e6i −0.343820 0.595513i
\(396\) −2.40128e7 −7.69492
\(397\) 271798. 0.0865505 0.0432752 0.999063i \(-0.486221\pi\)
0.0432752 + 0.999063i \(0.486221\pi\)
\(398\) 2.60913e6 + 4.51915e6i 0.825635 + 1.43004i
\(399\) 2.94452e6 0.925938
\(400\) −1.53817e6 + 2.66420e6i −0.480679 + 0.832561i
\(401\) 320744. 0.0996088 0.0498044 0.998759i \(-0.484140\pi\)
0.0498044 + 0.998759i \(0.484140\pi\)
\(402\) −4.61689e6 + 7.99669e6i −1.42490 + 2.46800i
\(403\) −13906.4 + 24086.7i −0.00426534 + 0.00738778i
\(404\) 3.95364e6 6.84790e6i 1.20516 2.08739i
\(405\) −2.88646e6 4.99949e6i −0.874435 1.51457i
\(406\) −179389. −0.0540108
\(407\) −4.54194e6 2.49918e6i −1.35911 0.747846i
\(408\) −1.83057e7 −5.44421
\(409\) −2.92323e6 5.06319e6i −0.864082 1.49663i −0.867956 0.496641i \(-0.834566\pi\)
0.00387378 0.999992i \(-0.498767\pi\)
\(410\) 5.57446e6 9.65525e6i 1.63773 2.83664i
\(411\) −1.67599e6 + 2.90291e6i −0.489405 + 0.847674i
\(412\) 722136. 1.25078e6i 0.209593 0.363025i
\(413\) 1.97909e6 0.570941
\(414\) 5.54544e6 9.60498e6i 1.59014 2.75420i
\(415\) 3.60902e6 1.02865
\(416\) 39291.1 + 68054.2i 0.0111317 + 0.0192807i
\(417\) 923019. 0.259938
\(418\) 1.16718e7 3.26736
\(419\) 918043. + 1.59010e6i 0.255463 + 0.442475i 0.965021 0.262172i \(-0.0844388\pi\)
−0.709558 + 0.704647i \(0.751105\pi\)
\(420\) 4.06345e6 7.03810e6i 1.12401 1.94685i
\(421\) 1.48350e6 0.407927 0.203963 0.978979i \(-0.434618\pi\)
0.203963 + 0.978979i \(0.434618\pi\)
\(422\) −4.23594e6 7.33686e6i −1.15789 2.00553i
\(423\) −196969. 341160.i −0.0535237 0.0927058i
\(424\) 3.55282e6 + 6.15367e6i 0.959752 + 1.66234i
\(425\) −1.11797e6 + 1.93639e6i −0.300234 + 0.520020i
\(426\) −1.88656e6 + 3.26763e6i −0.503672 + 0.872385i
\(427\) −70734.3 122515.i −0.0187741 0.0325178i
\(428\) −6.23028e6 1.07912e7i −1.64399 2.84747i
\(429\) 87276.8 + 151168.i 0.0228958 + 0.0396567i
\(430\) −1.04868e7 −2.73509
\(431\) −2.69018e6 + 4.65953e6i −0.697571 + 1.20823i 0.271735 + 0.962372i \(0.412402\pi\)
−0.969306 + 0.245856i \(0.920931\pi\)
\(432\) 8.04333e6 + 1.39315e7i 2.07361 + 3.59159i
\(433\) −6.39127e6 −1.63820 −0.819100 0.573650i \(-0.805527\pi\)
−0.819100 + 0.573650i \(0.805527\pi\)
\(434\) −1.65350e6 −0.421387
\(435\) −278249. 481941.i −0.0705034 0.122116i
\(436\) 1.37064e7 3.45308
\(437\) −1.88278e6 + 3.26107e6i −0.471624 + 0.816878i
\(438\) −3.80903e6 −0.948700
\(439\) 1.12104e6 1.94169e6i 0.277625 0.480861i −0.693169 0.720775i \(-0.743786\pi\)
0.970794 + 0.239914i \(0.0771194\pi\)
\(440\) 9.15480e6 1.58566e7i 2.25433 3.90461i
\(441\) 3.47988e6 6.02733e6i 0.852055 1.47580i
\(442\) 79792.6 + 138205.i 0.0194271 + 0.0336487i
\(443\) −5.81591e6 −1.40802 −0.704009 0.710191i \(-0.748609\pi\)
−0.704009 + 0.710191i \(0.748609\pi\)
\(444\) 350763. + 1.70526e7i 0.0844416 + 4.10520i
\(445\) 1.95686e6 0.468445
\(446\) 7.17667e6 + 1.24304e7i 1.70838 + 2.95901i
\(447\) 6.94137e6 1.20228e7i 1.64315 2.84601i
\(448\) −368116. + 637596.i −0.0866543 + 0.150090i
\(449\) 2.41736e6 4.18699e6i 0.565881 0.980134i −0.431086 0.902311i \(-0.641870\pi\)
0.996967 0.0778238i \(-0.0247971\pi\)
\(450\) 7.85214e6 1.82792
\(451\) −4.97205e6 + 8.61185e6i −1.15105 + 1.99368i
\(452\) 2.05176e6 0.472368
\(453\) −3.94751e6 6.83729e6i −0.903811 1.56545i
\(454\) −1.23872e7 −2.82055
\(455\) −40268.3 −0.00911874
\(456\) −1.09131e7 1.89020e7i −2.45773 4.25691i
\(457\) −692319. + 1.19913e6i −0.155066 + 0.268582i −0.933083 0.359661i \(-0.882892\pi\)
0.778017 + 0.628243i \(0.216226\pi\)
\(458\) 7.99569e6 1.78112
\(459\) 5.84604e6 + 1.01256e7i 1.29518 + 2.24332i
\(460\) 5.19649e6 + 9.00059e6i 1.14503 + 1.98325i
\(461\) 1.69242e6 + 2.93136e6i 0.370900 + 0.642417i 0.989704 0.143128i \(-0.0457161\pi\)
−0.618805 + 0.785545i \(0.712383\pi\)
\(462\) −5.18869e6 + 8.98708e6i −1.13098 + 1.95891i
\(463\) −368477. + 638220.i −0.0798836 + 0.138362i −0.903200 0.429221i \(-0.858788\pi\)
0.823316 + 0.567583i \(0.192122\pi\)
\(464\) 312179. + 540710.i 0.0673146 + 0.116592i
\(465\) −2.56474e6 4.44225e6i −0.550060 0.952732i
\(466\) −4.45855e6 7.72244e6i −0.951107 1.64737i
\(467\) 6.97139e6 1.47920 0.739600 0.673047i \(-0.235015\pi\)
0.739600 + 0.673047i \(0.235015\pi\)
\(468\) 195731. 339015.i 0.0413089 0.0715492i
\(469\) 949984. + 1.64542e6i 0.199427 + 0.345418i
\(470\) 528485. 0.110354
\(471\) −1.14942e6 −0.238741
\(472\) −7.33497e6 1.27045e7i −1.51546 2.62485i
\(473\) 9.35354e6 1.92231
\(474\) 4.47914e6 7.75810e6i 0.915691 1.58602i
\(475\) −2.66595e6 −0.542149
\(476\) −3.31353e6 + 5.73921e6i −0.670307 + 1.16101i
\(477\) 4.25797e6 7.37502e6i 0.856853 1.48411i
\(478\) −5.56540e6 + 9.63956e6i −1.11411 + 1.92969i
\(479\) 978758. + 1.69526e6i 0.194911 + 0.337596i 0.946871 0.321613i \(-0.104225\pi\)
−0.751960 + 0.659208i \(0.770892\pi\)
\(480\) −1.44928e7 −2.87110
\(481\) 72305.6 43752.6i 0.0142498 0.00862265i
\(482\) −1.05601e7 −2.07039
\(483\) −1.67398e6 2.89942e6i −0.326500 0.565514i
\(484\) −8.39651e6 + 1.45432e7i −1.62924 + 2.82193i
\(485\) −1.11645e6 + 1.93375e6i −0.215519 + 0.373290i
\(486\) 2.53778e6 4.39556e6i 0.487375 0.844158i
\(487\) −8.85483e6 −1.69183 −0.845917 0.533314i \(-0.820946\pi\)
−0.845917 + 0.533314i \(0.820946\pi\)
\(488\) −524315. + 908140.i −0.0996649 + 0.172625i
\(489\) 1.03206e7 1.95178
\(490\) 4.66842e6 + 8.08593e6i 0.878374 + 1.52139i
\(491\) 5.47395e6 1.02470 0.512350 0.858776i \(-0.328775\pi\)
0.512350 + 0.858776i \(0.328775\pi\)
\(492\) 3.27170e7 6.09342
\(493\) 226898. + 392998.i 0.0420448 + 0.0728238i
\(494\) −95137.9 + 164784.i −0.0175403 + 0.0303806i
\(495\) −2.19436e7 −4.02526
\(496\) 2.87748e6 + 4.98395e6i 0.525181 + 0.909640i
\(497\) 388185. + 672356.i 0.0704933 + 0.122098i
\(498\) 7.58108e6 + 1.31308e7i 1.36980 + 2.37257i
\(499\) 587413. 1.01743e6i 0.105607 0.182917i −0.808379 0.588662i \(-0.799655\pi\)
0.913986 + 0.405746i \(0.132988\pi\)
\(500\) 4.16903e6 7.22097e6i 0.745779 1.29173i
\(501\) −2.17389e6 3.76529e6i −0.386940 0.670200i
\(502\) 216503. + 374995.i 0.0383447 + 0.0664150i
\(503\) 1.29629e6 + 2.24524e6i 0.228445 + 0.395679i 0.957348 0.288939i \(-0.0933024\pi\)
−0.728902 + 0.684618i \(0.759969\pi\)
\(504\) 1.32275e7 2.31954
\(505\) 3.61295e6 6.25781e6i 0.630425 1.09193i
\(506\) −6.63550e6 1.14930e7i −1.15212 1.99553i
\(507\) 1.02550e7 1.77181
\(508\) −5.08872e6 −0.874882
\(509\) 3.22509e6 + 5.58603e6i 0.551757 + 0.955671i 0.998148 + 0.0608332i \(0.0193758\pi\)
−0.446391 + 0.894838i \(0.647291\pi\)
\(510\) −2.94320e7 −5.01065
\(511\) −391878. + 678753.i −0.0663894 + 0.114990i
\(512\) −1.29121e7 −2.17682
\(513\) −6.97032e6 + 1.20729e7i −1.16939 + 2.02544i
\(514\) −1.75097e6 + 3.03277e6i −0.292329 + 0.506329i
\(515\) 659909. 1.14300e6i 0.109639 0.189901i
\(516\) −1.53870e7 2.66511e7i −2.54407 4.40646i
\(517\) −471374. −0.0775602
\(518\) 4.40197e6 + 2.42217e6i 0.720813 + 0.396625i
\(519\) −3.23946e6 −0.527903
\(520\) 149243. + 258497.i 0.0242040 + 0.0419225i
\(521\) −2.48180e6 + 4.29860e6i −0.400564 + 0.693797i −0.993794 0.111236i \(-0.964519\pi\)
0.593230 + 0.805033i \(0.297852\pi\)
\(522\) 796814. 1.38012e6i 0.127991 0.221687i
\(523\) 2.48257e6 4.29994e6i 0.396869 0.687398i −0.596469 0.802636i \(-0.703430\pi\)
0.993338 + 0.115239i \(0.0367633\pi\)
\(524\) −7.50112e6 −1.19343
\(525\) 1.18515e6 2.05274e6i 0.187661 0.325039i
\(526\) −241605. −0.0380752
\(527\) 2.09141e6 + 3.62243e6i 0.328029 + 0.568163i
\(528\) 3.61182e7 5.63821
\(529\) −2.15484e6 −0.334792
\(530\) 5.71226e6 + 9.89392e6i 0.883320 + 1.52996i
\(531\) −8.79077e6 + 1.52261e7i −1.35298 + 2.34343i
\(532\) −7.90154e6 −1.21041
\(533\) −81055.5 140392.i −0.0123585 0.0214055i
\(534\) 4.11055e6 + 7.11969e6i 0.623803 + 1.08046i
\(535\) −5.69342e6 9.86129e6i −0.859980 1.48953i
\(536\) 7.04172e6 1.21966e7i 1.05868 1.83370i
\(537\) 989129. 1.71322e6i 0.148019 0.256376i
\(538\) 1.40977e6 + 2.44180e6i 0.209988 + 0.363709i
\(539\) −4.16392e6 7.21212e6i −0.617348 1.06928i
\(540\) 1.92381e7 + 3.33214e7i 2.83909 + 4.91744i
\(541\) −2.86146e6 −0.420334 −0.210167 0.977665i \(-0.567401\pi\)
−0.210167 + 0.977665i \(0.567401\pi\)
\(542\) 2.22681e6 3.85695e6i 0.325600 0.563956i
\(543\) −7.35157e6 1.27333e7i −1.06999 1.85328i
\(544\) 1.18181e7 1.71218
\(545\) 1.25253e7 1.80633
\(546\) −84587.2 146509.i −0.0121429 0.0210321i
\(547\) 5.10835e6 0.729982 0.364991 0.931011i \(-0.381072\pi\)
0.364991 + 0.931011i \(0.381072\pi\)
\(548\) 4.49749e6 7.78989e6i 0.639763 1.10810i
\(549\) 1.25676e6 0.177959
\(550\) 4.69782e6 8.13686e6i 0.662201 1.14697i
\(551\) −270533. + 468578.i −0.0379614 + 0.0657510i
\(552\) −1.24083e7 + 2.14918e7i −1.73327 + 3.00211i
\(553\) −921641. 1.59633e6i −0.128159 0.221978i
\(554\) −2.32372e7 −3.21669
\(555\) 320538. + 1.55832e7i 0.0441720 + 2.14746i
\(556\) −2.47690e6 −0.339799
\(557\) 1.95324e6 + 3.38310e6i 0.266758 + 0.462038i 0.968023 0.250863i \(-0.0807144\pi\)
−0.701265 + 0.712901i \(0.747381\pi\)
\(558\) 7.34456e6 1.27212e7i 0.998574 1.72958i
\(559\) −76241.7 + 132054.i −0.0103196 + 0.0178741i
\(560\) −4.16611e6 + 7.21591e6i −0.561384 + 0.972346i
\(561\) 2.62514e7 3.52164
\(562\) 9.50580e6 1.64645e7i 1.26954 2.19892i
\(563\) −9.99075e6 −1.32839 −0.664197 0.747557i \(-0.731227\pi\)
−0.664197 + 0.747557i \(0.731227\pi\)
\(564\) 775431. + 1.34309e6i 0.102647 + 0.177790i
\(565\) 1.87496e6 0.247099
\(566\) −7.39146e6 −0.969816
\(567\) −2.49519e6 4.32179e6i −0.325946 0.564555i
\(568\) 2.87740e6 4.98381e6i 0.374222 0.648172i
\(569\) −3.17236e6 −0.410773 −0.205386 0.978681i \(-0.565845\pi\)
−0.205386 + 0.978681i \(0.565845\pi\)
\(570\) −1.75461e7 3.03907e7i −2.26200 3.91790i
\(571\) −1.42508e6 2.46831e6i −0.182915 0.316817i 0.759957 0.649973i \(-0.225220\pi\)
−0.942872 + 0.333156i \(0.891886\pi\)
\(572\) −234205. 405655.i −0.0299300 0.0518403i
\(573\) −1.29204e7 + 2.23787e7i −1.64395 + 2.84740i
\(574\) 4.81883e6 8.34646e6i 0.610466 1.05736i
\(575\) 1.51562e6 + 2.62512e6i 0.191170 + 0.331116i
\(576\) −3.27021e6 5.66417e6i −0.410695 0.711345i
\(577\) 2.25629e6 + 3.90800e6i 0.282134 + 0.488670i 0.971910 0.235353i \(-0.0756245\pi\)
−0.689776 + 0.724022i \(0.742291\pi\)
\(578\) 9.37246e6 1.16690
\(579\) −6.69212e6 + 1.15911e7i −0.829597 + 1.43690i
\(580\) 746675. + 1.29328e6i 0.0921640 + 0.159633i
\(581\) 3.11981e6 0.383432
\(582\) −9.38082e6 −1.14798
\(583\) −5.09496e6 8.82472e6i −0.620825 1.07530i
\(584\) 5.80956e6 0.704873
\(585\) 178864. 309802.i 0.0216090 0.0374279i
\(586\) 2.88579e7 3.47153
\(587\) 7.75988e6 1.34405e7i 0.929522 1.60998i 0.145399 0.989373i \(-0.453554\pi\)
0.784123 0.620605i \(-0.213113\pi\)
\(588\) −1.36997e7 + 2.37285e7i −1.63406 + 2.83027i
\(589\) −2.49362e6 + 4.31907e6i −0.296170 + 0.512982i
\(590\) −1.17932e7 2.04264e7i −1.39477 2.41581i
\(591\) 1.84864e7 2.17712
\(592\) −359625. 1.74834e7i −0.0421741 2.05033i
\(593\) 9.61371e6 1.12268 0.561338 0.827587i \(-0.310287\pi\)
0.561338 + 0.827587i \(0.310287\pi\)
\(594\) −2.45656e7 4.25488e7i −2.85667 4.94790i
\(595\) −3.02800e6 + 5.24466e6i −0.350642 + 0.607330i
\(596\) −1.86270e7 + 3.22629e7i −2.14797 + 3.72039i
\(597\) −6.99684e6 + 1.21189e7i −0.803463 + 1.39164i
\(598\) 216347. 0.0247399
\(599\) 4.37141e6 7.57151e6i 0.497800 0.862214i −0.502197 0.864753i \(-0.667475\pi\)
0.999997 + 0.00253877i \(0.000808116\pi\)
\(600\) −1.75697e7 −1.99245
\(601\) 1.65794e6 + 2.87164e6i 0.187233 + 0.324298i 0.944327 0.329009i \(-0.106715\pi\)
−0.757094 + 0.653306i \(0.773381\pi\)
\(602\) −9.06529e6 −1.01951
\(603\) −1.68786e7 −1.89036
\(604\) 1.05930e7 + 1.83477e7i 1.18149 + 2.04639i
\(605\) −7.67298e6 + 1.32900e7i −0.852267 + 1.47617i
\(606\) 3.03573e7 3.35801
\(607\) −7.99468e6 1.38472e7i −0.880703 1.52542i −0.850561 0.525876i \(-0.823738\pi\)
−0.0301414 0.999546i \(-0.509596\pi\)
\(608\) 7.04545e6 + 1.22031e7i 0.772947 + 1.33878i
\(609\) −240531. 416613.i −0.0262802 0.0455186i
\(610\) −842997. + 1.46011e6i −0.0917279 + 0.158877i
\(611\) 3842.22 6654.91i 0.000416369 0.000721173i
\(612\) −2.94362e7 5.09850e7i −3.17690 5.50255i
\(613\) 1.17552e6 + 2.03606e6i 0.126351 + 0.218846i 0.922260 0.386570i \(-0.126340\pi\)
−0.795909 + 0.605416i \(0.793007\pi\)
\(614\) −1.59239e6 2.75809e6i −0.170462 0.295249i
\(615\) 2.98978e7 3.18751
\(616\) 7.91384e6 1.37072e7i 0.840302 1.45545i
\(617\) −5.22671e6 9.05293e6i −0.552733 0.957362i −0.998076 0.0620018i \(-0.980252\pi\)
0.445343 0.895360i \(-0.353082\pi\)
\(618\) 5.54480e6 0.584002
\(619\) 1.64855e6 0.172932 0.0864658 0.996255i \(-0.472443\pi\)
0.0864658 + 0.996255i \(0.472443\pi\)
\(620\) 6.88241e6 + 1.19207e7i 0.719054 + 1.24544i
\(621\) 1.58507e7 1.64938
\(622\) −8.30502e6 + 1.43847e7i −0.860726 + 1.49082i
\(623\) 1.69160e6 0.174613
\(624\) −294403. + 509921.i −0.0302678 + 0.0524254i
\(625\) 6.09876e6 1.05634e7i 0.624513 1.08169i
\(626\) −1.58107e7 + 2.73850e7i −1.61256 + 2.79303i
\(627\) 1.56500e7 + 2.71065e7i 1.58981 + 2.75362i
\(628\) 3.08445e6 0.312089
\(629\) −261382. 1.27073e7i −0.0263420 1.28064i
\(630\) 2.12673e7 2.13482
\(631\) −1.90948e6 3.30732e6i −0.190916 0.330676i 0.754638 0.656141i \(-0.227812\pi\)
−0.945554 + 0.325465i \(0.894479\pi\)
\(632\) −6.83162e6 + 1.18327e7i −0.680348 + 1.17840i
\(633\) 1.13594e7 1.96751e7i 1.12680 1.95167i
\(634\) −4.86592e6 + 8.42802e6i −0.480775 + 0.832727i
\(635\) −4.65022e6 −0.457657
\(636\) −1.67629e7 + 2.90341e7i −1.64326 + 2.84621i
\(637\) 135762. 0.0132565
\(638\) −953443. 1.65141e6i −0.0927349 0.160622i
\(639\) −6.89699e6 −0.668201
\(640\) −8.01225e6 −0.773222
\(641\) −8.57348e6 1.48497e7i −0.824161 1.42749i −0.902559 0.430567i \(-0.858314\pi\)
0.0783975 0.996922i \(-0.475020\pi\)
\(642\) 2.39191e7 4.14291e7i 2.29038 3.96705i
\(643\) −629612. −0.0600545 −0.0300273 0.999549i \(-0.509559\pi\)
−0.0300273 + 0.999549i \(0.509559\pi\)
\(644\) 4.49209e6 + 7.78053e6i 0.426810 + 0.739256i
\(645\) −1.40611e7 2.43545e7i −1.33082 2.30505i
\(646\) 1.43079e7 + 2.47821e7i 1.34895 + 2.33645i
\(647\) 9.33797e6 1.61738e7i 0.876984 1.51898i 0.0223495 0.999750i \(-0.492885\pi\)
0.854634 0.519230i \(-0.173781\pi\)
\(648\) −1.84955e7 + 3.20351e7i −1.73033 + 2.99701i
\(649\) 1.05188e7 + 1.82190e7i 0.980287 + 1.69791i
\(650\) 76584.8 + 132649.i 0.00710983 + 0.0123146i
\(651\) −2.21708e6 3.84009e6i −0.205035 0.355131i
\(652\) −2.76950e7 −2.55142
\(653\) −6.19483e6 + 1.07298e7i −0.568521 + 0.984707i 0.428191 + 0.903688i \(0.359151\pi\)
−0.996713 + 0.0810193i \(0.974182\pi\)
\(654\) 2.63105e7 + 4.55712e7i 2.40539 + 4.16625i
\(655\) −6.85474e6 −0.624292
\(656\) −3.35436e7 −3.04334
\(657\) −3.48130e6 6.02979e6i −0.314650 0.544991i
\(658\) 456847. 0.0411345
\(659\) −8.99670e6 + 1.55827e7i −0.806993 + 1.39775i 0.107945 + 0.994157i \(0.465573\pi\)
−0.914938 + 0.403595i \(0.867760\pi\)
\(660\) 8.63880e7 7.71958
\(661\) 5.90741e6 1.02319e7i 0.525889 0.910866i −0.473657 0.880710i \(-0.657066\pi\)
0.999545 0.0301561i \(-0.00960044\pi\)
\(662\) 672402. 1.16463e6i 0.0596326 0.103287i
\(663\) −213978. + 370620.i −0.0189054 + 0.0327450i
\(664\) −1.15627e7 2.00272e7i −1.01775 1.76279i
\(665\) −7.22067e6 −0.633174
\(666\) −3.81876e7 + 2.31075e7i −3.33608 + 2.01868i
\(667\) 615202. 0.0535431
\(668\) 5.83359e6 + 1.01041e7i 0.505818 + 0.876103i
\(669\) −1.92455e7 + 3.33342e7i −1.66251 + 2.87955i
\(670\) 1.13217e7 1.96098e7i 0.974374 1.68766i
\(671\) 751898. 1.30233e6i 0.0644692 0.111664i
\(672\) −1.25282e7 −1.07020
\(673\) 2.11460e6 3.66260e6i 0.179966 0.311711i −0.761902 0.647692i \(-0.775734\pi\)
0.941869 + 0.335981i \(0.109068\pi\)
\(674\) 2.66284e7 2.25785
\(675\) 5.61102e6 + 9.71857e6i 0.474004 + 0.821000i
\(676\) −2.75191e7 −2.31616
\(677\) 4.96316e6 0.416185 0.208092 0.978109i \(-0.433274\pi\)
0.208092 + 0.978109i \(0.433274\pi\)
\(678\) 3.93852e6 + 6.82172e6i 0.329048 + 0.569927i
\(679\) −965113. + 1.67162e6i −0.0803348 + 0.139144i
\(680\) 4.48899e7 3.72286
\(681\) −1.66092e7 2.87680e7i −1.37240 2.37707i
\(682\) −8.78828e6 1.52217e7i −0.723507 1.25315i
\(683\) 477051. + 826276.i 0.0391303 + 0.0677756i 0.884927 0.465729i \(-0.154208\pi\)
−0.845797 + 0.533505i \(0.820875\pi\)
\(684\) 3.50972e7 6.07902e7i 2.86835 4.96813i
\(685\) 4.10994e6 7.11863e6i 0.334664 0.579656i
\(686\) 9.10594e6 + 1.57719e7i 0.738779 + 1.27960i
\(687\) 1.07209e7 + 1.85692e7i 0.866643 + 1.50107i
\(688\) 1.57757e7 + 2.73244e7i 1.27063 + 2.20079i
\(689\) 166118. 0.0133312
\(690\) −1.99502e7 + 3.45547e7i −1.59523 + 2.76303i
\(691\) −5.87931e6 1.01833e7i −0.468416 0.811319i 0.530933 0.847414i \(-0.321842\pi\)
−0.999348 + 0.0360944i \(0.988508\pi\)
\(692\) 8.69302e6 0.690089
\(693\) −1.89691e7 −1.50042
\(694\) −1.17920e6 2.04243e6i −0.0929367 0.160971i
\(695\) −2.26346e6 −0.177751
\(696\) −1.78293e6 + 3.08812e6i −0.139512 + 0.241641i
\(697\) −2.43801e7 −1.90088
\(698\) −1.17212e7 + 2.03017e7i −0.910610 + 1.57722i
\(699\) 1.19564e7 2.07091e7i 0.925565 1.60313i
\(700\) −3.18032e6 + 5.50848e6i −0.245316 + 0.424900i
\(701\) −6.71611e6 1.16326e7i −0.516205 0.894094i −0.999823 0.0188145i \(-0.994011\pi\)
0.483618 0.875279i \(-0.339323\pi\)
\(702\) 800946. 0.0613423
\(703\) 1.29654e7 7.84544e6i 0.989459 0.598727i
\(704\) −7.82607e6 −0.595131
\(705\) 708612. + 1.22735e6i 0.0536952 + 0.0930029i
\(706\) 1.21653e7 2.10710e7i 0.918569 1.59101i
\(707\) 3.12320e6 5.40955e6i 0.234991 0.407017i
\(708\) 3.46077e7 5.99423e7i 2.59472 4.49418i
\(709\) 1.65823e7 1.23888 0.619438 0.785045i \(-0.287360\pi\)
0.619438 + 0.785045i \(0.287360\pi\)
\(710\) 4.62631e6 8.01300e6i 0.344420 0.596554i
\(711\) 1.63750e7 1.21481
\(712\) −6.26945e6 1.08590e7i −0.463478 0.802768i
\(713\) 5.67057e6 0.417737
\(714\) −2.54424e7 −1.86772
\(715\) −214024. 370700.i −0.0156566 0.0271180i
\(716\) −2.65430e6 + 4.59739e6i −0.193494 + 0.335142i
\(717\) −2.98492e7 −2.16838
\(718\) −1.37766e7 2.38618e7i −0.997314 1.72740i
\(719\) 4.32789e6 + 7.49613e6i 0.312215 + 0.540773i 0.978842 0.204619i \(-0.0655956\pi\)
−0.666626 + 0.745392i \(0.732262\pi\)
\(720\) −3.70102e7 6.41035e7i −2.66066 4.60840i
\(721\) 570457. 988060.i 0.0408681 0.0707856i
\(722\) −4.30479e6 + 7.45611e6i −0.307333 + 0.532316i
\(723\) −1.41594e7 2.45249e7i −1.00740 1.74486i
\(724\) 1.97278e7 + 3.41695e7i 1.39872 + 2.42266i
\(725\) 217776. + 377199.i 0.0153874 + 0.0266518i
\(726\) −6.44712e7 −4.53967
\(727\) 1.80950e6 3.13415e6i 0.126976 0.219930i −0.795527 0.605918i \(-0.792806\pi\)
0.922504 + 0.385988i \(0.126139\pi\)
\(728\) 129013. + 223457.i 0.00902205 + 0.0156266i
\(729\) −7.09507e6 −0.494468
\(730\) 9.34065e6 0.648739
\(731\) 1.14661e7 + 1.98599e7i 0.793638 + 1.37462i
\(732\) −4.94762e6 −0.341286
\(733\) −9.69365e6 + 1.67899e7i −0.666389 + 1.15422i 0.312518 + 0.949912i \(0.398827\pi\)
−0.978907 + 0.204307i \(0.934506\pi\)
\(734\) −4.20840e7 −2.88321
\(735\) −1.25192e7 + 2.16838e7i −0.854785 + 1.48053i
\(736\) 8.01079e6 1.38751e7i 0.545106 0.944151i
\(737\) −1.00982e7 + 1.74906e7i −0.684820 + 1.18614i
\(738\) 4.28087e7 + 7.41469e7i 2.89329 + 5.01132i
\(739\) 1.50944e7 1.01673 0.508363 0.861143i \(-0.330251\pi\)
0.508363 + 0.861143i \(0.330251\pi\)
\(740\) −860156. 4.18172e7i −0.0577428 2.80721i
\(741\) −510258. −0.0341385
\(742\) 4.93794e6 + 8.55277e6i 0.329258 + 0.570292i
\(743\) 1.09683e7 1.89977e7i 0.728899 1.26249i −0.228450 0.973556i \(-0.573366\pi\)
0.957349 0.288935i \(-0.0933011\pi\)
\(744\) −1.64340e7 + 2.84645e7i −1.08846 + 1.88526i
\(745\) −1.70219e7 + 2.94828e7i −1.12362 + 1.94616i
\(746\) 3.71732e7 2.44559
\(747\) −1.38576e7 + 2.40021e7i −0.908631 + 1.57380i
\(748\) −7.04450e7 −4.60358
\(749\) −4.92166e6 8.52456e6i −0.320558 0.555223i
\(750\) 3.20112e7 2.07801
\(751\) 1.46693e7 0.949092 0.474546 0.880231i \(-0.342612\pi\)
0.474546 + 0.880231i \(0.342612\pi\)
\(752\) −795022. 1.37702e6i −0.0512666 0.0887963i
\(753\) −580591. + 1.00561e6i −0.0373150 + 0.0646314i
\(754\) 31086.5 0.00199133
\(755\) 9.68024e6 + 1.67667e7i 0.618043 + 1.07048i
\(756\) 1.66304e7 + 2.88046e7i 1.05827 + 1.83298i
\(757\) 9.97401e6 + 1.72755e7i 0.632601 + 1.09570i 0.987018 + 0.160610i \(0.0513461\pi\)
−0.354417 + 0.935088i \(0.615321\pi\)
\(758\) −1.70780e7 + 2.95799e7i −1.07960 + 1.86992i
\(759\) 1.77943e7 3.08206e7i 1.12118 1.94194i
\(760\) 2.67614e7 + 4.63522e7i 1.68064 + 2.91096i
\(761\) 3.03841e6 + 5.26268e6i 0.190189 + 0.329417i 0.945313 0.326165i \(-0.105757\pi\)
−0.755124 + 0.655582i \(0.772423\pi\)
\(762\) −9.76822e6 1.69191e7i −0.609436 1.05557i
\(763\) 1.08275e7 0.673310
\(764\) 3.46715e7 6.00528e7i 2.14901 3.72220i
\(765\) −2.68997e7 4.65916e7i −1.66186 2.87842i
\(766\) 1.61339e7 0.993498
\(767\) −342958. −0.0210500
\(768\) −2.23874e7 3.87760e7i −1.36962 2.37225i
\(769\) 5.25100e6 0.320204 0.160102 0.987100i \(-0.448818\pi\)
0.160102 + 0.987100i \(0.448818\pi\)
\(770\) 1.27239e7 2.20385e7i 0.773383 1.33954i
\(771\) −9.39108e6 −0.568957
\(772\) 1.79581e7 3.11044e7i 1.08447 1.87836i
\(773\) −1.10307e7 + 1.91057e7i −0.663977 + 1.15004i 0.315585 + 0.948897i \(0.397799\pi\)
−0.979562 + 0.201145i \(0.935534\pi\)
\(774\) 4.02664e7 6.97434e7i 2.41596 4.18457i
\(775\) 2.00733e6 + 3.47680e6i 0.120051 + 0.207934i
\(776\) 1.43077e7 0.852935
\(777\) 277088. + 1.34709e7i 0.0164651 + 0.800465i
\(778\) 2.20558e7 1.30639
\(779\) −1.45344e7 2.51743e7i −0.858129 1.48632i
\(780\) −704158. + 1.21964e6i −0.0414413 + 0.0717784i
\(781\) −4.12636e6 + 7.14707e6i −0.242069 + 0.419276i
\(782\) 1.62684e7 2.81776e7i 0.951320 1.64774i
\(783\) 2.27756e6 0.132760
\(784\) 1.40458e7 2.43280e7i 0.816123 1.41357i
\(785\) 2.81866e6 0.163256
\(786\) −1.43990e7 2.49398e7i −0.831335 1.43991i
\(787\) 1.26169e7 0.726135 0.363068 0.931763i \(-0.381729\pi\)
0.363068 + 0.931763i \(0.381729\pi\)
\(788\) −4.96078e7 −2.84600
\(789\) −323953. 561103.i −0.0185263 0.0320886i
\(790\) −1.09839e7 + 1.90247e7i −0.626167 + 1.08455i
\(791\) 1.62080e6 0.0921062
\(792\) 7.03037e7 + 1.21770e8i 3.98258 + 6.89804i
\(793\) 12257.6 + 21230.8i 0.000692185 + 0.00119890i
\(794\) −1.40007e6 2.42499e6i −0.0788132 0.136508i
\(795\) −1.53184e7 + 2.65323e7i −0.859599 + 1.48887i
\(796\) 1.87759e7 3.25207e7i 1.05031 1.81919i
\(797\) 1.33189e7 + 2.30691e7i 0.742717 + 1.28642i 0.951254 + 0.308409i \(0.0997966\pi\)
−0.208537 + 0.978015i \(0.566870\pi\)
\(798\) −1.51677e7 2.62712e7i −0.843163 1.46040i
\(799\) −577837. 1.00084e6i −0.0320212 0.0554624i
\(800\) 1.13430e7 0.626618
\(801\) −7.51378e6 + 1.30142e7i −0.413787 + 0.716700i
\(802\) −1.65220e6 2.86170e6i −0.0907042 0.157104i
\(803\) −8.33124e6 −0.455954
\(804\) 6.64482e7 3.62529
\(805\) 4.10501e6 + 7.11008e6i 0.223267 + 0.386710i
\(806\) 286537. 0.0155361
\(807\) −3.78055e6 + 6.54811e6i −0.204349 + 0.353942i
\(808\) −4.63012e7 −2.49496
\(809\) −7.55653e6 + 1.30883e7i −0.405930 + 0.703091i −0.994429 0.105406i \(-0.966386\pi\)
0.588499 + 0.808498i \(0.299719\pi\)
\(810\) −2.97372e7 + 5.15063e7i −1.59253 + 2.75834i
\(811\) 1.09636e7 1.89895e7i 0.585331 1.01382i −0.409503 0.912309i \(-0.634298\pi\)
0.994834 0.101514i \(-0.0323686\pi\)
\(812\) 645461. + 1.11797e6i 0.0343542 + 0.0595032i
\(813\) 1.19432e7 0.633713
\(814\) 1.09835e6 + 5.33971e7i 0.0581004 + 2.82460i
\(815\) −2.53085e7 −1.33467
\(816\) 4.42757e7 + 7.66878e7i 2.32777 + 4.03182i
\(817\) −1.36712e7 + 2.36792e7i −0.716558 + 1.24111i
\(818\) −3.01160e7 + 5.21625e7i −1.57367 + 2.72568i
\(819\) 154619. 267808.i 0.00805476 0.0139513i
\(820\) −8.02300e7 −4.16680
\(821\) 1.17227e7 2.03043e7i 0.606973 1.05131i −0.384763 0.923015i \(-0.625717\pi\)
0.991736 0.128293i \(-0.0409499\pi\)
\(822\) 3.45332e7 1.78262
\(823\) −3.99662e6 6.92235e6i −0.205681 0.356249i 0.744669 0.667434i \(-0.232607\pi\)
−0.950349 + 0.311185i \(0.899274\pi\)
\(824\) −8.45697e6 −0.433907
\(825\) 2.51960e7 1.28884
\(826\) −1.01946e7 1.76576e7i −0.519901 0.900495i
\(827\) −1.67372e7 + 2.89896e7i −0.850977 + 1.47394i 0.0293504 + 0.999569i \(0.490656\pi\)
−0.880327 + 0.474366i \(0.842677\pi\)
\(828\) −7.98123e7 −4.04570
\(829\) −3.20542e6 5.55196e6i −0.161994 0.280582i 0.773590 0.633687i \(-0.218459\pi\)
−0.935584 + 0.353105i \(0.885126\pi\)
\(830\) −1.85906e7 3.21999e7i −0.936697 1.62241i
\(831\) −3.11572e7 5.39659e7i −1.56515 2.71092i
\(832\) 63791.1 110489.i 0.00319486 0.00553366i
\(833\) 1.02087e7 1.76821e7i 0.509753 0.882918i
\(834\) −4.75461e6 8.23523e6i −0.236701 0.409978i
\(835\) 5.33091e6 + 9.23340e6i 0.264597 + 0.458295i
\(836\) −4.19963e7 7.27397e7i −2.07824 3.59961i
\(837\) 2.09932e7 1.03578
\(838\) 9.45796e6 1.63817e7i 0.465251 0.805839i
\(839\) −1.59594e7 2.76424e7i −0.782727 1.35572i −0.930347 0.366679i \(-0.880495\pi\)
0.147620 0.989044i \(-0.452839\pi\)
\(840\) −4.75872e7 −2.32698
\(841\) −2.04228e7 −0.995690
\(842\) −7.64174e6 1.32359e7i −0.371460 0.643387i
\(843\) 5.09829e7 2.47090
\(844\) −3.04827e7 + 5.27976e7i −1.47298 + 2.55128i
\(845\) −2.51478e7 −1.21160
\(846\) −2.02923e6 + 3.51473e6i −0.0974778 + 0.168837i
\(847\) −6.63289e6 + 1.14885e7i −0.317683 + 0.550243i
\(848\) 1.71864e7 2.97677e7i 0.820719 1.42153i
\(849\) −9.91074e6 1.71659e7i −0.471886 0.817330i
\(850\) 2.30354e7 1.09358
\(851\) −1.50962e7 8.30665e6i −0.714570 0.393189i
\(852\) 2.71522e7 1.28146
\(853\) 5.64006e6 + 9.76887e6i 0.265406 + 0.459697i 0.967670 0.252220i \(-0.0811606\pi\)
−0.702264 + 0.711917i \(0.747827\pi\)
\(854\) −728726. + 1.26219e6i −0.0341916 + 0.0592216i
\(855\) 3.20729e7 5.55519e7i 1.50045 2.59886i
\(856\) −3.64816e7 + 6.31879e7i −1.70172 + 2.94747i
\(857\) 9.31400e6 0.433196 0.216598 0.976261i \(-0.430504\pi\)
0.216598 + 0.976261i \(0.430504\pi\)
\(858\) 899153. 1.55738e6i 0.0416980 0.0722231i
\(859\) 3.11166e7 1.43883 0.719416 0.694580i \(-0.244410\pi\)
0.719416 + 0.694580i \(0.244410\pi\)
\(860\) 3.77326e7 + 6.53548e7i 1.73969 + 3.01322i
\(861\) 2.58451e7 1.18815
\(862\) 5.54302e7 2.54084
\(863\) 5.90254e6 + 1.02235e7i 0.269782 + 0.467275i 0.968805 0.247823i \(-0.0797152\pi\)
−0.699024 + 0.715098i \(0.746382\pi\)
\(864\) 2.96571e7 5.13675e7i 1.35159 2.34102i
\(865\) 7.94394e6 0.360990
\(866\) 3.29224e7 + 5.70233e7i 1.49175 + 2.58379i
\(867\) 1.25669e7 + 2.17666e7i 0.567782 + 0.983428i
\(868\) 5.94948e6 + 1.03048e7i 0.268028 + 0.464237i
\(869\) 9.79694e6 1.69688e7i 0.440090 0.762258i
\(870\) −2.86661e6 + 4.96511e6i −0.128401 + 0.222398i
\(871\) −164623. 285136.i −0.00735269 0.0127352i
\(872\) −4.01290e7 6.95055e7i −1.78718 3.09548i
\(873\) −8.57371e6 1.48501e7i −0.380744 0.659468i
\(874\) 3.87940e7 1.71785
\(875\) 3.29336e6 5.70426e6i 0.145418 0.251872i
\(876\) 1.37053e7 + 2.37382e7i 0.603431 + 1.04517i
\(877\) 1.64532e7 0.722358 0.361179 0.932497i \(-0.382374\pi\)
0.361179 + 0.932497i \(0.382374\pi\)
\(878\) −2.30985e7 −1.01123
\(879\) 3.86938e7 + 6.70195e7i 1.68915 + 2.92570i
\(880\) −8.85705e7 −3.85552
\(881\) 7.06547e6 1.22378e7i 0.306691 0.531205i −0.670945 0.741507i \(-0.734111\pi\)
0.977636 + 0.210302i \(0.0674447\pi\)
\(882\) −7.17016e7 −3.10354
\(883\) −1.34256e7 + 2.32539e7i −0.579472 + 1.00368i 0.416068 + 0.909334i \(0.363408\pi\)
−0.995540 + 0.0943418i \(0.969925\pi\)
\(884\) 574204. 994551.i 0.0247136 0.0428052i
\(885\) 3.16256e7 5.47771e7i 1.35731 2.35093i
\(886\) 2.99586e7 + 5.18899e7i 1.28215 + 2.22074i
\(887\) 6.60614e6 0.281928 0.140964 0.990015i \(-0.454980\pi\)
0.140964 + 0.990015i \(0.454980\pi\)
\(888\) 8.54475e7 5.17048e7i 3.63636 2.20038i
\(889\) −4.01987e6 −0.170592
\(890\) −1.00801e7 1.74592e7i −0.426568 0.738838i
\(891\) 2.65236e7 4.59402e7i 1.11928 1.93865i
\(892\) 5.16448e7 8.94514e7i 2.17327 3.76422i
\(893\) 688963. 1.19332e6i 0.0289113 0.0500758i
\(894\) −1.43024e8 −5.98503
\(895\) −2.42558e6 + 4.20123e6i −0.101218 + 0.175315i
\(896\) −6.92616e6 −0.288219
\(897\) 290086. + 502443.i 0.0120377 + 0.0208500i
\(898\) −4.98087e7 −2.06117
\(899\) 814794. 0.0336239
\(900\) −2.82528e7 4.89354e7i −1.16267 2.01380i
\(901\) 1.24914e7 2.16357e7i 0.512623 0.887889i
\(902\) 1.02447e8 4.19261
\(903\) −1.21551e7 2.10532e7i −0.496064 0.859209i
\(904\) −6.00706e6 1.04045e7i −0.244479 0.423450i
\(905\) 1.80278e7 + 3.12251e7i 0.731681 + 1.26731i
\(906\) −4.06685e7 + 7.04398e7i −1.64603 + 2.85100i
\(907\) −1.27218e7 + 2.20347e7i −0.513486 + 0.889384i 0.486391 + 0.873741i \(0.338313\pi\)
−0.999878 + 0.0156431i \(0.995020\pi\)
\(908\) 4.45704e7 + 7.71983e7i 1.79404 + 3.10737i
\(909\) 2.77454e7 + 4.80565e7i 1.11373 + 1.92904i
\(910\) 207428. + 359276.i 0.00830356 + 0.0143822i
\(911\) −3.35547e7 −1.33955 −0.669773 0.742566i \(-0.733609\pi\)
−0.669773 + 0.742566i \(0.733609\pi\)
\(912\) −5.27906e7 + 9.14360e7i −2.10169 + 3.64024i
\(913\) 1.65816e7 + 2.87202e7i 0.658340 + 1.14028i
\(914\) 1.42650e7 0.564814
\(915\) −4.52129e6 −0.178529
\(916\) −2.87693e7 4.98300e7i −1.13290 1.96224i
\(917\) −5.92556e6 −0.232705
\(918\) 6.02277e7 1.04317e8i 2.35879 4.08555i
\(919\) 1.85292e6 0.0723715 0.0361857 0.999345i \(-0.488479\pi\)
0.0361857 + 0.999345i \(0.488479\pi\)
\(920\) 3.04282e7 5.27032e7i 1.18524 2.05290i
\(921\) 4.27026e6 7.39631e6i 0.165884 0.287320i
\(922\) 1.74359e7 3.01998e7i 0.675485 1.16997i
\(923\) −67268.8 116513.i −0.00259902 0.00450164i
\(924\) 7.46779e7 2.87748
\(925\) −250874. 1.21964e7i −0.00964054 0.468683i
\(926\) 7.59232e6 0.290969
\(927\) 5.06773e6 + 8.77757e6i 0.193693 + 0.335486i
\(928\) 1.15106e6 1.99369e6i 0.0438759 0.0759954i
\(929\) 6.43982e6 1.11541e7i 0.244813 0.424029i −0.717266 0.696800i \(-0.754607\pi\)
0.962079 + 0.272771i \(0.0879401\pi\)
\(930\) −2.64227e7 + 4.57655e7i −1.00177 + 1.73512i
\(931\) 2.43440e7 0.920489
\(932\) −3.20847e7 + 5.55723e7i −1.20992 + 2.09565i
\(933\) −4.45427e7 −1.67522
\(934\) −3.59107e7 6.21991e7i −1.34697 2.33301i
\(935\) −6.43747e7 −2.40817
\(936\) −2.29221e6 −0.0855194
\(937\) −5.82182e6 1.00837e7i −0.216625 0.375206i 0.737149 0.675731i \(-0.236172\pi\)
−0.953774 + 0.300524i \(0.902838\pi\)
\(938\) 9.78703e6 1.69516e7i 0.363198 0.629078i
\(939\) −8.47984e7 −3.13851
\(940\) −1.90154e6 3.29357e6i −0.0701919 0.121576i
\(941\) 2.03437e6 + 3.52362e6i 0.0748953 + 0.129723i 0.901041 0.433734i \(-0.142804\pi\)
−0.826145 + 0.563457i \(0.809471\pi\)
\(942\) 5.92086e6 + 1.02552e7i 0.217399 + 0.376546i
\(943\) −1.65258e7 + 2.86236e7i −0.605179 + 1.04820i
\(944\) −3.54820e7 + 6.14567e7i −1.29592 + 2.24460i
\(945\) 1.51973e7 + 2.63225e7i 0.553589 + 0.958844i
\(946\) −4.81815e7 8.34528e7i −1.75046 3.03189i
\(947\) −1.13362e7 1.96348e7i −0.410763 0.711462i 0.584211 0.811602i \(-0.301404\pi\)
−0.994973 + 0.100140i \(0.968071\pi\)
\(948\) −6.44657e7 −2.32974
\(949\) 67908.8 117622.i 0.00244771 0.00423957i
\(950\) 1.37327e7 + 2.37858e7i 0.493683 + 0.855084i
\(951\) −2.60976e7 −0.935728
\(952\) 3.88049e7 1.38770
\(953\) −9.24432e6 1.60116e7i −0.329718 0.571089i 0.652738 0.757584i \(-0.273620\pi\)
−0.982456 + 0.186495i \(0.940287\pi\)
\(954\) −8.77338e7 −3.12102
\(955\) 3.16839e7 5.48781e7i 1.12416 1.94711i
\(956\) 8.00996e7 2.83456
\(957\) 2.55682e6 4.42855e6i 0.0902445 0.156308i
\(958\) 1.00835e7 1.74651e7i 0.354974 0.614832i
\(959\) 3.55283e6 6.15368e6i 0.124746 0.216067i
\(960\) 1.17649e7 + 2.03774e7i 0.412011 + 0.713624i
\(961\) −2.11189e7 −0.737670
\(962\) −762820. 419739.i −0.0265757 0.0146232i
\(963\) 8.74444e7 3.03855
\(964\) 3.79965e7 + 6.58119e7i 1.31690 + 2.28093i
\(965\) 1.64107e7 2.84242e7i 0.567295 0.982583i
\(966\) −1.72459e7 + 2.98708e7i −0.594624 + 1.02992i
\(967\) 2.09259e6 3.62447e6i 0.0719644 0.124646i −0.827798 0.561027i \(-0.810407\pi\)
0.899762 + 0.436381i \(0.143740\pi\)
\(968\) 9.83319e7 3.37292
\(969\) −3.83692e7 + 6.64574e7i −1.31272 + 2.27370i
\(970\) 2.30040e7 0.785009
\(971\) 2.15145e7 + 3.72641e7i 0.732289 + 1.26836i 0.955903 + 0.293684i \(0.0948812\pi\)
−0.223614 + 0.974678i \(0.571785\pi\)
\(972\) −3.65248e7 −1.24000
\(973\) −1.95665e6 −0.0662567
\(974\) 4.56126e7 + 7.90034e7i 1.54059 + 2.66838i
\(975\) −205376. + 355721.i −0.00691890 + 0.0119839i
\(976\) 5.07262e6 0.170454
\(977\) 2.36821e6 + 4.10186e6i 0.0793750 + 0.137482i 0.902980 0.429682i \(-0.141374\pi\)
−0.823605 + 0.567163i \(0.808041\pi\)
\(978\) −5.31629e7 9.20808e7i −1.77730 3.07838i
\(979\) 8.99076e6 + 1.55724e7i 0.299805 + 0.519278i
\(980\) 3.35949e7 5.81881e7i 1.11740 1.93539i
\(981\) −4.80936e7 + 8.33006e7i −1.59557 + 2.76360i
\(982\) −2.81972e7 4.88389e7i −0.933097 1.61617i
\(983\) −1.22973e7 2.12995e7i −0.405906 0.703051i 0.588520 0.808483i \(-0.299711\pi\)
−0.994427 + 0.105432i \(0.966377\pi\)
\(984\) −9.57876e7 1.65909e8i −3.15371 5.46239i
\(985\) −4.53331e7 −1.48876
\(986\) 2.33757e6 4.04879e6i 0.0765724 0.132627i
\(987\) 612558. + 1.06098e6i 0.0200149 + 0.0346669i
\(988\) 1.36926e6 0.0446267
\(989\) 3.10887e7 1.01068
\(990\) 1.13035e8 + 1.95782e8i 3.66542 + 6.34870i
\(991\) −9.08498e6 −0.293860 −0.146930 0.989147i \(-0.546939\pi\)
−0.146930 + 0.989147i \(0.546939\pi\)
\(992\) 1.06098e7 1.83766e7i 0.342315 0.592907i
\(993\) 3.60632e6 0.116062
\(994\) 3.99920e6 6.92682e6i 0.128383 0.222366i
\(995\) 1.71579e7 2.97184e7i 0.549424 0.951630i
\(996\) 5.45551e7 9.44921e7i 1.74256 3.01820i
\(997\) −4.72014e6 8.17552e6i −0.150389 0.260482i 0.780981 0.624554i \(-0.214719\pi\)
−0.931371 + 0.364073i \(0.881386\pi\)
\(998\) −1.21034e7 −0.384664
\(999\) −5.58884e7 3.07524e7i −1.77177 0.974910i
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 37.6.c.a.26.2 yes 30
37.10 even 3 inner 37.6.c.a.10.2 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.6.c.a.10.2 30 37.10 even 3 inner
37.6.c.a.26.2 yes 30 1.1 even 1 trivial