Properties

Label 74.4.e.a.11.9
Level $74$
Weight $4$
Character 74.11
Analytic conductor $4.366$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,4,Mod(11,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.11");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.e (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: \(4.36614134042\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 346 x^{18} + 50697 x^{16} + 4104768 x^{14} + 200532432 x^{12} + 6039270720 x^{10} + 109290291168 x^{8} + 1091662316544 x^{6} + \cdots + 1118416232704 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.9
Root \(-5.89146i\) of defining polynomial
Character \(\chi\) \(=\) 74.11
Dual form 74.4.e.a.27.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.73205 - 1.00000i) q^{2} +(2.94573 - 5.10216i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-12.2374 - 7.06527i) q^{5} -11.7829i q^{6} +(0.0476865 - 0.0825955i) q^{7} -8.00000i q^{8} +(-3.85468 - 6.67649i) q^{9} +O(q^{10})\) \(q+(1.73205 - 1.00000i) q^{2} +(2.94573 - 5.10216i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-12.2374 - 7.06527i) q^{5} -11.7829i q^{6} +(0.0476865 - 0.0825955i) q^{7} -8.00000i q^{8} +(-3.85468 - 6.67649i) q^{9} -28.2611 q^{10} +1.95565 q^{11} +(-11.7829 - 20.4086i) q^{12} +(48.4136 + 27.9516i) q^{13} -0.190746i q^{14} +(-72.0963 + 41.6248i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(94.2875 - 54.4369i) q^{17} +(-13.3530 - 7.70935i) q^{18} +(-16.5704 - 9.56693i) q^{19} +(-48.9497 + 28.2611i) q^{20} +(-0.280943 - 0.486608i) q^{21} +(3.38729 - 1.95565i) q^{22} -112.313i q^{23} +(-40.8173 - 23.5659i) q^{24} +(37.3362 + 64.6682i) q^{25} +111.806 q^{26} +113.650 q^{27} +(-0.190746 - 0.330382i) q^{28} +166.296i q^{29} +(-83.2496 + 144.193i) q^{30} +237.659i q^{31} +(-27.7128 - 16.0000i) q^{32} +(5.76083 - 9.97804i) q^{33} +(108.874 - 188.575i) q^{34} +(-1.16712 + 0.673837i) q^{35} -30.8374 q^{36} +(-203.978 + 95.1113i) q^{37} -38.2677 q^{38} +(285.227 - 164.676i) q^{39} +(-56.5222 + 97.8993i) q^{40} +(-79.1501 + 137.092i) q^{41} +(-0.973217 - 0.561887i) q^{42} +72.7216i q^{43} +(3.91130 - 6.77458i) q^{44} +108.937i q^{45} +(-112.313 - 194.532i) q^{46} -0.209175 q^{47} -94.2634 q^{48} +(171.495 + 297.039i) q^{49} +(129.336 + 74.6724i) q^{50} -641.426i q^{51} +(193.654 - 111.806i) q^{52} +(-62.6946 - 108.590i) q^{53} +(196.848 - 113.650i) q^{54} +(-23.9321 - 13.8172i) q^{55} +(-0.660764 - 0.381492i) q^{56} +(-97.6240 + 56.3633i) q^{57} +(166.296 + 288.033i) q^{58} +(-345.801 + 199.648i) q^{59} +332.998i q^{60} +(-421.826 - 243.541i) q^{61} +(237.659 + 411.637i) q^{62} -0.735264 q^{63} -64.0000 q^{64} +(-394.971 - 684.110i) q^{65} -23.0433i q^{66} +(454.388 - 787.022i) q^{67} -435.495i q^{68} +(-573.038 - 330.844i) q^{69} +(-1.34767 + 2.33424i) q^{70} +(53.5520 - 92.7547i) q^{71} +(-53.4119 + 30.8374i) q^{72} -653.673 q^{73} +(-258.188 + 368.715i) q^{74} +439.930 q^{75} +(-66.2817 + 38.2677i) q^{76} +(0.0932582 - 0.161528i) q^{77} +(329.352 - 570.454i) q^{78} +(735.033 + 424.372i) q^{79} +226.089i q^{80} +(438.859 - 760.126i) q^{81} +316.600i q^{82} +(-280.578 - 485.975i) q^{83} -2.24755 q^{84} -1538.45 q^{85} +(72.7216 + 125.957i) q^{86} +(848.469 + 489.864i) q^{87} -15.6452i q^{88} +(109.445 - 63.1878i) q^{89} +(108.937 + 188.685i) q^{90} +(4.61735 - 2.66583i) q^{91} +(-389.063 - 224.626i) q^{92} +(1212.57 + 700.080i) q^{93} +(-0.362301 + 0.209175i) q^{94} +(135.186 + 234.149i) q^{95} +(-163.269 + 94.2634i) q^{96} +1498.15i q^{97} +(594.078 + 342.991i) q^{98} +(-7.53840 - 13.0569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{3} + 40 q^{4} - 18 q^{5} - 2 q^{7} - 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{3} + 40 q^{4} - 18 q^{5} - 2 q^{7} - 76 q^{9} - 16 q^{10} - 16 q^{11} + 8 q^{12} - 150 q^{13} + 198 q^{15} - 160 q^{16} + 90 q^{17} + 162 q^{19} - 72 q^{20} - 30 q^{21} + 532 q^{25} + 528 q^{26} - 644 q^{27} + 8 q^{28} + 312 q^{30} - 596 q^{33} - 488 q^{34} - 342 q^{35} - 608 q^{36} - 112 q^{37} + 144 q^{38} + 1146 q^{39} - 32 q^{40} - 498 q^{41} - 120 q^{42} - 32 q^{44} + 424 q^{47} + 64 q^{48} + 84 q^{49} + 1008 q^{50} - 600 q^{52} - 142 q^{53} + 1080 q^{54} - 540 q^{55} + 138 q^{57} + 224 q^{58} + 1590 q^{59} - 1542 q^{61} + 8 q^{62} + 1864 q^{63} - 1280 q^{64} - 694 q^{65} + 62 q^{67} + 708 q^{69} - 368 q^{70} - 178 q^{71} - 528 q^{73} - 560 q^{74} - 7224 q^{75} + 648 q^{76} + 3468 q^{77} - 1736 q^{78} - 3474 q^{79} + 2414 q^{81} + 938 q^{83} - 240 q^{84} - 1100 q^{85} - 2120 q^{86} + 9420 q^{87} + 510 q^{89} + 2504 q^{90} + 666 q^{91} + 1344 q^{92} + 1728 q^{93} + 264 q^{94} + 4126 q^{95} - 816 q^{98} + 2312 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 1.00000i 0.612372 0.353553i
\(3\) 2.94573 5.10216i 0.566906 0.981911i −0.429963 0.902846i \(-0.641473\pi\)
0.996870 0.0790643i \(-0.0251932\pi\)
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) −12.2374 7.06527i −1.09455 0.631937i −0.159764 0.987155i \(-0.551073\pi\)
−0.934784 + 0.355218i \(0.884407\pi\)
\(6\) 11.7829i 0.801727i
\(7\) 0.0476865 0.0825955i 0.00257483 0.00445974i −0.864735 0.502228i \(-0.832514\pi\)
0.867310 + 0.497768i \(0.165847\pi\)
\(8\) 8.00000i 0.353553i
\(9\) −3.85468 6.67649i −0.142766 0.247278i
\(10\) −28.2611 −0.893694
\(11\) 1.95565 0.0536047 0.0268023 0.999641i \(-0.491468\pi\)
0.0268023 + 0.999641i \(0.491468\pi\)
\(12\) −11.7829 20.4086i −0.283453 0.490955i
\(13\) 48.4136 + 27.9516i 1.03289 + 0.596337i 0.917810 0.397020i \(-0.129956\pi\)
0.115076 + 0.993357i \(0.463289\pi\)
\(14\) 0.190746i 0.00364136i
\(15\) −72.0963 + 41.6248i −1.24101 + 0.716499i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 94.2875 54.4369i 1.34518 0.776640i 0.357618 0.933868i \(-0.383589\pi\)
0.987562 + 0.157228i \(0.0502557\pi\)
\(18\) −13.3530 7.70935i −0.174852 0.100951i
\(19\) −16.5704 9.56693i −0.200080 0.115516i 0.396613 0.917986i \(-0.370186\pi\)
−0.596693 + 0.802470i \(0.703519\pi\)
\(20\) −48.9497 + 28.2611i −0.547274 + 0.315969i
\(21\) −0.280943 0.486608i −0.00291938 0.00505651i
\(22\) 3.38729 1.95565i 0.0328260 0.0189521i
\(23\) 112.313i 1.01821i −0.860704 0.509105i \(-0.829976\pi\)
0.860704 0.509105i \(-0.170024\pi\)
\(24\) −40.8173 23.5659i −0.347158 0.200432i
\(25\) 37.3362 + 64.6682i 0.298690 + 0.517346i
\(26\) 111.806 0.843347
\(27\) 113.650 0.810074
\(28\) −0.190746 0.330382i −0.00128742 0.00222987i
\(29\) 166.296i 1.06484i 0.846480 + 0.532421i \(0.178718\pi\)
−0.846480 + 0.532421i \(0.821282\pi\)
\(30\) −83.2496 + 144.193i −0.506641 + 0.877528i
\(31\) 237.659i 1.37693i 0.725270 + 0.688465i \(0.241715\pi\)
−0.725270 + 0.688465i \(0.758285\pi\)
\(32\) −27.7128 16.0000i −0.153093 0.0883883i
\(33\) 5.76083 9.97804i 0.0303888 0.0526350i
\(34\) 108.874 188.575i 0.549168 0.951186i
\(35\) −1.16712 + 0.673837i −0.00563655 + 0.00325426i
\(36\) −30.8374 −0.142766
\(37\) −203.978 + 95.1113i −0.906316 + 0.422600i
\(38\) −38.2677 −0.163364
\(39\) 285.227 164.676i 1.17110 0.676134i
\(40\) −56.5222 + 97.8993i −0.223424 + 0.386981i
\(41\) −79.1501 + 137.092i −0.301492 + 0.522199i −0.976474 0.215635i \(-0.930818\pi\)
0.674982 + 0.737834i \(0.264151\pi\)
\(42\) −0.973217 0.561887i −0.00357549 0.00206431i
\(43\) 72.7216i 0.257905i 0.991651 + 0.128953i \(0.0411616\pi\)
−0.991651 + 0.128953i \(0.958838\pi\)
\(44\) 3.91130 6.77458i 0.0134012 0.0232115i
\(45\) 108.937i 0.360876i
\(46\) −112.313 194.532i −0.359992 0.623524i
\(47\) −0.209175 −0.000649175 −0.000324588 1.00000i \(-0.500103\pi\)
−0.000324588 1.00000i \(0.500103\pi\)
\(48\) −94.2634 −0.283453
\(49\) 171.495 + 297.039i 0.499987 + 0.866002i
\(50\) 129.336 + 74.6724i 0.365819 + 0.211205i
\(51\) 641.426i 1.76113i
\(52\) 193.654 111.806i 0.516443 0.298168i
\(53\) −62.6946 108.590i −0.162486 0.281434i 0.773274 0.634073i \(-0.218618\pi\)
−0.935760 + 0.352638i \(0.885285\pi\)
\(54\) 196.848 113.650i 0.496067 0.286404i
\(55\) −23.9321 13.8172i −0.0586728 0.0338748i
\(56\) −0.660764 0.381492i −0.00157675 0.000910340i
\(57\) −97.6240 + 56.3633i −0.226853 + 0.130974i
\(58\) 166.296 + 288.033i 0.376479 + 0.652080i
\(59\) −345.801 + 199.648i −0.763041 + 0.440542i −0.830387 0.557188i \(-0.811880\pi\)
0.0673453 + 0.997730i \(0.478547\pi\)
\(60\) 332.998i 0.716499i
\(61\) −421.826 243.541i −0.885398 0.511185i −0.0129634 0.999916i \(-0.504126\pi\)
−0.872434 + 0.488731i \(0.837460\pi\)
\(62\) 237.659 + 411.637i 0.486818 + 0.843194i
\(63\) −0.735264 −0.00147039
\(64\) −64.0000 −0.125000
\(65\) −394.971 684.110i −0.753695 1.30544i
\(66\) 23.0433i 0.0429763i
\(67\) 454.388 787.022i 0.828542 1.43508i −0.0706408 0.997502i \(-0.522504\pi\)
0.899182 0.437574i \(-0.144162\pi\)
\(68\) 435.495i 0.776640i
\(69\) −573.038 330.844i −0.999792 0.577230i
\(70\) −1.34767 + 2.33424i −0.00230111 + 0.00398564i
\(71\) 53.5520 92.7547i 0.0895133 0.155042i −0.817792 0.575514i \(-0.804802\pi\)
0.907306 + 0.420472i \(0.138135\pi\)
\(72\) −53.4119 + 30.8374i −0.0874258 + 0.0504753i
\(73\) −653.673 −1.04804 −0.524018 0.851707i \(-0.675568\pi\)
−0.524018 + 0.851707i \(0.675568\pi\)
\(74\) −258.188 + 368.715i −0.405591 + 0.579220i
\(75\) 439.930 0.677316
\(76\) −66.2817 + 38.2677i −0.100040 + 0.0577580i
\(77\) 0.0932582 0.161528i 0.000138023 0.000239063i
\(78\) 329.352 570.454i 0.478099 0.828092i
\(79\) 735.033 + 424.372i 1.04681 + 0.604374i 0.921754 0.387776i \(-0.126757\pi\)
0.125053 + 0.992150i \(0.460090\pi\)
\(80\) 226.089i 0.315969i
\(81\) 438.859 760.126i 0.602002 1.04270i
\(82\) 316.600i 0.426374i
\(83\) −280.578 485.975i −0.371053 0.642683i 0.618675 0.785647i \(-0.287670\pi\)
−0.989728 + 0.142964i \(0.954337\pi\)
\(84\) −2.24755 −0.00291938
\(85\) −1538.45 −1.96315
\(86\) 72.7216 + 125.957i 0.0911834 + 0.157934i
\(87\) 848.469 + 489.864i 1.04558 + 0.603666i
\(88\) 15.6452i 0.0189521i
\(89\) 109.445 63.1878i 0.130349 0.0752572i −0.433407 0.901198i \(-0.642689\pi\)
0.563757 + 0.825941i \(0.309356\pi\)
\(90\) 108.937 + 188.685i 0.127589 + 0.220991i
\(91\) 4.61735 2.66583i 0.00531901 0.00307093i
\(92\) −389.063 224.626i −0.440898 0.254553i
\(93\) 1212.57 + 700.080i 1.35202 + 0.780590i
\(94\) −0.362301 + 0.209175i −0.000397537 + 0.000229518i
\(95\) 135.186 + 234.149i 0.145998 + 0.252876i
\(96\) −163.269 + 94.2634i −0.173579 + 0.100216i
\(97\) 1498.15i 1.56818i 0.620645 + 0.784092i \(0.286871\pi\)
−0.620645 + 0.784092i \(0.713129\pi\)
\(98\) 594.078 + 342.991i 0.612356 + 0.353544i
\(99\) −7.53840 13.0569i −0.00765291 0.0132552i
\(100\) 298.690 0.298690
\(101\) −96.5966 −0.0951656 −0.0475828 0.998867i \(-0.515152\pi\)
−0.0475828 + 0.998867i \(0.515152\pi\)
\(102\) −641.426 1110.98i −0.622653 1.07847i
\(103\) 1552.28i 1.48496i 0.669868 + 0.742480i \(0.266351\pi\)
−0.669868 + 0.742480i \(0.733649\pi\)
\(104\) 223.613 387.309i 0.210837 0.365180i
\(105\) 7.93977i 0.00737945i
\(106\) −217.181 125.389i −0.199004 0.114895i
\(107\) 767.064 1328.59i 0.693037 1.20037i −0.277802 0.960638i \(-0.589606\pi\)
0.970838 0.239736i \(-0.0770609\pi\)
\(108\) 227.300 393.696i 0.202518 0.350772i
\(109\) −1098.08 + 633.978i −0.964929 + 0.557102i −0.897687 0.440635i \(-0.854753\pi\)
−0.0672424 + 0.997737i \(0.521420\pi\)
\(110\) −55.2689 −0.0479062
\(111\) −115.590 + 1320.90i −0.0988409 + 1.12950i
\(112\) −1.52597 −0.00128742
\(113\) 859.751 496.377i 0.715740 0.413232i −0.0974430 0.995241i \(-0.531066\pi\)
0.813183 + 0.582009i \(0.197733\pi\)
\(114\) −112.727 + 195.248i −0.0926123 + 0.160409i
\(115\) −793.521 + 1374.42i −0.643445 + 1.11448i
\(116\) 576.067 + 332.592i 0.461090 + 0.266211i
\(117\) 430.977i 0.340546i
\(118\) −399.296 + 691.602i −0.311510 + 0.539552i
\(119\) 10.3836i 0.00799887i
\(120\) 332.998 + 576.770i 0.253321 + 0.438764i
\(121\) −1327.18 −0.997127
\(122\) −974.165 −0.722924
\(123\) 466.310 + 807.672i 0.341835 + 0.592076i
\(124\) 823.275 + 475.318i 0.596228 + 0.344232i
\(125\) 711.157i 0.508862i
\(126\) −1.27352 + 0.735264i −0.000900426 + 0.000519861i
\(127\) 404.970 + 701.429i 0.282955 + 0.490093i 0.972111 0.234520i \(-0.0753519\pi\)
−0.689156 + 0.724613i \(0.742019\pi\)
\(128\) −110.851 + 64.0000i −0.0765466 + 0.0441942i
\(129\) 371.037 + 214.218i 0.253240 + 0.146208i
\(130\) −1368.22 789.943i −0.923084 0.532943i
\(131\) 1496.68 864.108i 0.998209 0.576316i 0.0904911 0.995897i \(-0.471156\pi\)
0.907718 + 0.419581i \(0.137823\pi\)
\(132\) −23.0433 39.9122i −0.0151944 0.0263175i
\(133\) −1.58037 + 0.912428i −0.00103034 + 0.000594868i
\(134\) 1817.55i 1.17173i
\(135\) −1390.78 802.970i −0.886664 0.511916i
\(136\) −435.495 754.300i −0.274584 0.475593i
\(137\) 2789.45 1.73955 0.869777 0.493444i \(-0.164262\pi\)
0.869777 + 0.493444i \(0.164262\pi\)
\(138\) −1323.37 −0.816327
\(139\) −750.808 1300.44i −0.458149 0.793538i 0.540714 0.841206i \(-0.318154\pi\)
−0.998863 + 0.0476689i \(0.984821\pi\)
\(140\) 5.39069i 0.00325426i
\(141\) −0.616172 + 1.06724i −0.000368022 + 0.000637432i
\(142\) 214.208i 0.126591i
\(143\) 94.6801 + 54.6636i 0.0553675 + 0.0319664i
\(144\) −61.6748 + 106.824i −0.0356914 + 0.0618194i
\(145\) 1174.93 2035.03i 0.672914 1.16552i
\(146\) −1132.19 + 653.673i −0.641788 + 0.370537i
\(147\) 2020.72 1.13378
\(148\) −78.4798 + 896.822i −0.0435878 + 0.498096i
\(149\) −2968.36 −1.63207 −0.816033 0.578006i \(-0.803831\pi\)
−0.816033 + 0.578006i \(0.803831\pi\)
\(150\) 761.981 439.930i 0.414770 0.239467i
\(151\) 1777.29 3078.36i 0.957841 1.65903i 0.230113 0.973164i \(-0.426090\pi\)
0.727728 0.685866i \(-0.240576\pi\)
\(152\) −76.5355 + 132.563i −0.0408411 + 0.0707389i
\(153\) −726.895 419.673i −0.384091 0.221755i
\(154\) 0.373033i 0.000195194i
\(155\) 1679.13 2908.33i 0.870133 1.50711i
\(156\) 1317.41i 0.676134i
\(157\) −496.502 859.967i −0.252390 0.437152i 0.711794 0.702389i \(-0.247883\pi\)
−0.964183 + 0.265237i \(0.914550\pi\)
\(158\) 1697.49 0.854714
\(159\) −738.726 −0.368458
\(160\) 226.089 + 391.597i 0.111712 + 0.193491i
\(161\) −9.27653 5.35581i −0.00454095 0.00262172i
\(162\) 1755.44i 0.851359i
\(163\) −2444.17 + 1411.14i −1.17449 + 0.678093i −0.954734 0.297461i \(-0.903860\pi\)
−0.219758 + 0.975554i \(0.570527\pi\)
\(164\) 316.600 + 548.368i 0.150746 + 0.261100i
\(165\) −140.995 + 81.4036i −0.0665240 + 0.0384077i
\(166\) −971.950 561.156i −0.454445 0.262374i
\(167\) −1934.58 1116.93i −0.896419 0.517548i −0.0203826 0.999792i \(-0.506488\pi\)
−0.876037 + 0.482244i \(0.839822\pi\)
\(168\) −3.89287 + 2.24755i −0.00178774 + 0.00103216i
\(169\) 464.083 + 803.816i 0.211235 + 0.365870i
\(170\) −2664.67 + 1538.45i −1.20218 + 0.694079i
\(171\) 147.510i 0.0659670i
\(172\) 251.915 + 145.443i 0.111676 + 0.0644764i
\(173\) 907.892 + 1572.52i 0.398993 + 0.691076i 0.993602 0.112939i \(-0.0360265\pi\)
−0.594609 + 0.804015i \(0.702693\pi\)
\(174\) 1959.46 0.853712
\(175\) 7.12173 0.00307630
\(176\) −15.6452 27.0983i −0.00670058 0.0116057i
\(177\) 2352.44i 0.998985i
\(178\) 126.376 218.889i 0.0532149 0.0921709i
\(179\) 1166.29i 0.486996i 0.969901 + 0.243498i \(0.0782949\pi\)
−0.969901 + 0.243498i \(0.921705\pi\)
\(180\) 377.370 + 217.875i 0.156264 + 0.0902190i
\(181\) −1985.15 + 3438.38i −0.815220 + 1.41200i 0.0939501 + 0.995577i \(0.470051\pi\)
−0.909170 + 0.416425i \(0.863283\pi\)
\(182\) 5.33166 9.23470i 0.00217148 0.00376111i
\(183\) −2485.17 + 1434.81i −1.00388 + 0.579588i
\(184\) −898.503 −0.359992
\(185\) 3168.15 + 277.241i 1.25906 + 0.110179i
\(186\) 2800.32 1.10392
\(187\) 184.393 106.460i 0.0721079 0.0416315i
\(188\) −0.418349 + 0.724602i −0.000162294 + 0.000281101i
\(189\) 5.41958 9.38699i 0.00208580 0.00361271i
\(190\) 468.298 + 270.372i 0.178810 + 0.103236i
\(191\) 3362.47i 1.27382i −0.770937 0.636911i \(-0.780212\pi\)
0.770937 0.636911i \(-0.219788\pi\)
\(192\) −188.527 + 326.538i −0.0708633 + 0.122739i
\(193\) 2103.68i 0.784592i 0.919839 + 0.392296i \(0.128319\pi\)
−0.919839 + 0.392296i \(0.871681\pi\)
\(194\) 1498.15 + 2594.87i 0.554437 + 0.960313i
\(195\) −4653.92 −1.70910
\(196\) 1371.96 0.499987
\(197\) 420.773 + 728.801i 0.152177 + 0.263578i 0.932028 0.362388i \(-0.118038\pi\)
−0.779851 + 0.625966i \(0.784705\pi\)
\(198\) −26.1138 15.0768i −0.00937286 0.00541142i
\(199\) 2079.10i 0.740620i 0.928908 + 0.370310i \(0.120749\pi\)
−0.928908 + 0.370310i \(0.879251\pi\)
\(200\) 517.346 298.690i 0.182909 0.105603i
\(201\) −2677.01 4636.71i −0.939411 1.62711i
\(202\) −167.310 + 96.5966i −0.0582768 + 0.0336461i
\(203\) 13.7353 + 7.93009i 0.00474892 + 0.00274179i
\(204\) −2221.96 1282.85i −0.762591 0.440282i
\(205\) 1937.18 1118.43i 0.659994 0.381048i
\(206\) 1552.28 + 2688.63i 0.525013 + 0.909349i
\(207\) −749.856 + 432.930i −0.251781 + 0.145366i
\(208\) 894.451i 0.298168i
\(209\) −32.4060 18.7096i −0.0107252 0.00619220i
\(210\) 7.93977 + 13.7521i 0.00260903 + 0.00451897i
\(211\) 3216.82 1.04955 0.524774 0.851241i \(-0.324150\pi\)
0.524774 + 0.851241i \(0.324150\pi\)
\(212\) −501.557 −0.162486
\(213\) −315.499 546.461i −0.101491 0.175788i
\(214\) 3068.26i 0.980102i
\(215\) 513.798 889.924i 0.162980 0.282290i
\(216\) 909.201i 0.286404i
\(217\) 19.6296 + 11.3331i 0.00614074 + 0.00354536i
\(218\) −1267.96 + 2196.17i −0.393931 + 0.682308i
\(219\) −1925.55 + 3335.14i −0.594138 + 1.02908i
\(220\) −95.7285 + 55.2689i −0.0293364 + 0.0169374i
\(221\) 6086.39 1.85256
\(222\) 1120.69 + 2403.45i 0.338810 + 0.726618i
\(223\) 4008.30 1.20366 0.601829 0.798625i \(-0.294439\pi\)
0.601829 + 0.798625i \(0.294439\pi\)
\(224\) −2.64306 + 1.52597i −0.000788377 + 0.000455170i
\(225\) 287.838 498.550i 0.0852853 0.147718i
\(226\) 992.755 1719.50i 0.292199 0.506104i
\(227\) 74.2758 + 42.8831i 0.0217174 + 0.0125386i 0.510819 0.859688i \(-0.329342\pi\)
−0.489102 + 0.872227i \(0.662675\pi\)
\(228\) 450.906i 0.130974i
\(229\) 1958.26 3391.80i 0.565088 0.978761i −0.431953 0.901896i \(-0.642176\pi\)
0.997041 0.0768654i \(-0.0244912\pi\)
\(230\) 3174.08i 0.909969i
\(231\) −0.549427 0.951636i −0.000156492 0.000271052i
\(232\) 1330.37 0.376479
\(233\) −5722.62 −1.60902 −0.804509 0.593940i \(-0.797572\pi\)
−0.804509 + 0.593940i \(0.797572\pi\)
\(234\) −430.977 746.475i −0.120401 0.208541i
\(235\) 2.55976 + 1.47788i 0.000710553 + 0.000410238i
\(236\) 1597.19i 0.440542i
\(237\) 4330.42 2500.17i 1.18688 0.685247i
\(238\) −10.3836 17.9850i −0.00282803 0.00489829i
\(239\) −6088.49 + 3515.19i −1.64783 + 0.951376i −0.669901 + 0.742451i \(0.733663\pi\)
−0.977932 + 0.208926i \(0.933003\pi\)
\(240\) 1153.54 + 665.997i 0.310253 + 0.179125i
\(241\) 3635.64 + 2099.04i 0.971751 + 0.561041i 0.899770 0.436365i \(-0.143734\pi\)
0.0719814 + 0.997406i \(0.477068\pi\)
\(242\) −2298.74 + 1327.18i −0.610613 + 0.352537i
\(243\) −1051.25 1820.81i −0.277520 0.480679i
\(244\) −1687.30 + 974.165i −0.442699 + 0.255592i
\(245\) 4846.65i 1.26384i
\(246\) 1615.34 + 932.620i 0.418661 + 0.241714i
\(247\) −534.822 926.339i −0.137773 0.238630i
\(248\) 1901.27 0.486818
\(249\) −3306.03 −0.841410
\(250\) 711.157 + 1231.76i 0.179910 + 0.311613i
\(251\) 4729.96i 1.18945i −0.803929 0.594726i \(-0.797261\pi\)
0.803929 0.594726i \(-0.202739\pi\)
\(252\) −1.47053 + 2.54703i −0.000367598 + 0.000636698i
\(253\) 219.645i 0.0545808i
\(254\) 1402.86 + 809.940i 0.346548 + 0.200079i
\(255\) −4531.85 + 7849.39i −1.11292 + 1.92764i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 195.913 113.110i 0.0475515 0.0274538i −0.476036 0.879426i \(-0.657927\pi\)
0.523587 + 0.851972i \(0.324593\pi\)
\(258\) 856.873 0.206770
\(259\) −1.87121 + 21.3831i −0.000448925 + 0.00513006i
\(260\) −3159.77 −0.753695
\(261\) 1110.28 641.018i 0.263312 0.152023i
\(262\) 1728.22 2993.36i 0.407517 0.705840i
\(263\) −3145.20 + 5447.64i −0.737419 + 1.27725i 0.216235 + 0.976341i \(0.430622\pi\)
−0.953654 + 0.300906i \(0.902711\pi\)
\(264\) −79.8243 46.0866i −0.0186093 0.0107441i
\(265\) 1771.82i 0.410724i
\(266\) −1.82486 + 3.16074i −0.000420636 + 0.000728562i
\(267\) 744.538i 0.170655i
\(268\) −1817.55 3148.09i −0.414271 0.717538i
\(269\) −5807.18 −1.31625 −0.658123 0.752911i \(-0.728649\pi\)
−0.658123 + 0.752911i \(0.728649\pi\)
\(270\) −3211.88 −0.723958
\(271\) −147.704 255.830i −0.0331083 0.0573453i 0.848996 0.528399i \(-0.177207\pi\)
−0.882105 + 0.471053i \(0.843874\pi\)
\(272\) −1508.60 870.990i −0.336295 0.194160i
\(273\) 31.4113i 0.00696372i
\(274\) 4831.47 2789.45i 1.06526 0.615026i
\(275\) 73.0166 + 126.468i 0.0160112 + 0.0277321i
\(276\) −2292.15 + 1323.37i −0.499896 + 0.288615i
\(277\) −2356.78 1360.68i −0.511209 0.295147i 0.222121 0.975019i \(-0.428702\pi\)
−0.733330 + 0.679872i \(0.762035\pi\)
\(278\) −2600.88 1501.62i −0.561116 0.323960i
\(279\) 1586.73 916.098i 0.340484 0.196578i
\(280\) 5.39069 + 9.33695i 0.00115056 + 0.00199282i
\(281\) 6481.60 3742.15i 1.37601 0.794442i 0.384336 0.923193i \(-0.374430\pi\)
0.991677 + 0.128751i \(0.0410969\pi\)
\(282\) 2.46469i 0.000520461i
\(283\) −5230.34 3019.74i −1.09863 0.634293i −0.162767 0.986665i \(-0.552042\pi\)
−0.935860 + 0.352372i \(0.885375\pi\)
\(284\) −214.208 371.019i −0.0447567 0.0775208i
\(285\) 1592.89 0.331068
\(286\) 218.654 0.0452073
\(287\) 7.54878 + 13.0749i 0.00155258 + 0.00268915i
\(288\) 246.699i 0.0504753i
\(289\) 3470.25 6010.65i 0.706340 1.22342i
\(290\) 4699.71i 0.951643i
\(291\) 7643.79 + 4413.14i 1.53982 + 0.889014i
\(292\) −1307.35 + 2264.39i −0.262009 + 0.453813i
\(293\) −1353.90 + 2345.03i −0.269951 + 0.467570i −0.968849 0.247652i \(-0.920341\pi\)
0.698898 + 0.715222i \(0.253674\pi\)
\(294\) 3499.99 2020.72i 0.694297 0.400853i
\(295\) 5642.28 1.11358
\(296\) 760.891 + 1631.82i 0.149412 + 0.320431i
\(297\) 222.260 0.0434237
\(298\) −5141.36 + 2968.36i −0.999432 + 0.577022i
\(299\) 3139.32 5437.47i 0.607197 1.05170i
\(300\) 879.860 1523.96i 0.169329 0.293287i
\(301\) 6.00647 + 3.46784i 0.00115019 + 0.000664063i
\(302\) 7109.17i 1.35459i
\(303\) −284.548 + 492.851i −0.0539500 + 0.0934441i
\(304\) 306.142i 0.0577580i
\(305\) 3441.37 + 5960.63i 0.646073 + 1.11903i
\(306\) −1678.69 −0.313609
\(307\) 163.498 0.0303951 0.0151976 0.999885i \(-0.495162\pi\)
0.0151976 + 0.999885i \(0.495162\pi\)
\(308\) −0.373033 0.646112i −6.90114e−5 0.000119531i
\(309\) 7919.99 + 4572.61i 1.45810 + 0.841834i
\(310\) 6716.50i 1.23055i
\(311\) −2834.13 + 1636.29i −0.516749 + 0.298345i −0.735604 0.677412i \(-0.763101\pi\)
0.218854 + 0.975758i \(0.429768\pi\)
\(312\) −1317.41 2281.82i −0.239050 0.414046i
\(313\) −4363.78 + 2519.43i −0.788037 + 0.454973i −0.839271 0.543714i \(-0.817018\pi\)
0.0512343 + 0.998687i \(0.483684\pi\)
\(314\) −1719.93 993.004i −0.309113 0.178466i
\(315\) 8.99773 + 5.19484i 0.00160941 + 0.000929195i
\(316\) 2940.13 1697.49i 0.523403 0.302187i
\(317\) −3689.08 6389.68i −0.653626 1.13211i −0.982236 0.187648i \(-0.939913\pi\)
0.328610 0.944466i \(-0.393420\pi\)
\(318\) −1279.51 + 738.726i −0.225633 + 0.130270i
\(319\) 325.217i 0.0570805i
\(320\) 783.194 + 452.178i 0.136818 + 0.0789922i
\(321\) −4519.13 7827.37i −0.785774 1.36100i
\(322\) −21.4232 −0.00370767
\(323\) −2083.18 −0.358858
\(324\) −1755.44 3040.51i −0.301001 0.521349i
\(325\) 4174.43i 0.712478i
\(326\) −2822.29 + 4888.34i −0.479484 + 0.830491i
\(327\) 7470.12i 1.26330i
\(328\) 1096.74 + 633.201i 0.184625 + 0.106593i
\(329\) −0.00997481 + 0.0172769i −1.67152e−6 + 2.89515e-6i
\(330\) −162.807 + 281.990i −0.0271583 + 0.0470396i
\(331\) 6893.45 3979.93i 1.14471 0.660897i 0.197115 0.980380i \(-0.436843\pi\)
0.947592 + 0.319483i \(0.103509\pi\)
\(332\) −2244.62 −0.371053
\(333\) 1421.28 + 995.231i 0.233890 + 0.163779i
\(334\) −4467.71 −0.731923
\(335\) −11121.1 + 6420.75i −1.81376 + 1.04717i
\(336\) −4.49509 + 7.78573i −0.000729844 + 0.00126413i
\(337\) 1093.98 1894.83i 0.176833 0.306285i −0.763961 0.645263i \(-0.776748\pi\)
0.940794 + 0.338978i \(0.110081\pi\)
\(338\) 1607.63 + 928.167i 0.258709 + 0.149366i
\(339\) 5848.78i 0.937056i
\(340\) −3076.89 + 5329.33i −0.490788 + 0.850070i
\(341\) 464.778i 0.0738098i
\(342\) 147.510 + 255.494i 0.0233228 + 0.0403963i
\(343\) 65.4250 0.0102992
\(344\) 581.773 0.0911834
\(345\) 4675.00 + 8097.34i 0.729547 + 1.26361i
\(346\) 3145.03 + 1815.78i 0.488664 + 0.282131i
\(347\) 3961.25i 0.612827i −0.951898 0.306414i \(-0.900871\pi\)
0.951898 0.306414i \(-0.0991290\pi\)
\(348\) 3393.88 1959.46i 0.522790 0.301833i
\(349\) 1580.58 + 2737.64i 0.242425 + 0.419892i 0.961404 0.275139i \(-0.0887239\pi\)
−0.718980 + 0.695031i \(0.755391\pi\)
\(350\) 12.3352 7.12173i 0.00188384 0.00108764i
\(351\) 5502.21 + 3176.70i 0.836713 + 0.483077i
\(352\) −54.1966 31.2904i −0.00820650 0.00473803i
\(353\) −10056.1 + 5805.88i −1.51623 + 0.875398i −0.516416 + 0.856338i \(0.672734\pi\)
−0.999818 + 0.0190602i \(0.993933\pi\)
\(354\) 2352.44 + 4074.55i 0.353194 + 0.611751i
\(355\) −1310.67 + 756.718i −0.195953 + 0.113134i
\(356\) 505.503i 0.0752572i
\(357\) −52.9789 30.5874i −0.00785417 0.00453461i
\(358\) 1166.29 + 2020.07i 0.172179 + 0.298223i
\(359\) 4712.85 0.692854 0.346427 0.938077i \(-0.387395\pi\)
0.346427 + 0.938077i \(0.387395\pi\)
\(360\) 871.499 0.127589
\(361\) −3246.45 5623.01i −0.473312 0.819801i
\(362\) 7940.59i 1.15289i
\(363\) −3909.50 + 6771.46i −0.565277 + 0.979089i
\(364\) 21.3266i 0.00307093i
\(365\) 7999.27 + 4618.38i 1.14713 + 0.662293i
\(366\) −2869.63 + 4970.34i −0.409830 + 0.709847i
\(367\) 1086.34 1881.60i 0.154514 0.267626i −0.778368 0.627808i \(-0.783952\pi\)
0.932882 + 0.360182i \(0.117286\pi\)
\(368\) −1556.25 + 898.503i −0.220449 + 0.127276i
\(369\) 1220.39 0.172171
\(370\) 5764.63 2687.95i 0.809970 0.377675i
\(371\) −11.9588 −0.00167350
\(372\) 4850.29 2800.32i 0.676011 0.390295i
\(373\) 3197.15 5537.63i 0.443813 0.768706i −0.554156 0.832413i \(-0.686959\pi\)
0.997969 + 0.0637068i \(0.0202922\pi\)
\(374\) 212.919 368.787i 0.0294379 0.0509880i
\(375\) 3628.43 + 2094.88i 0.499657 + 0.288477i
\(376\) 1.67340i 0.000229518i
\(377\) −4648.24 + 8050.99i −0.635004 + 1.09986i
\(378\) 21.6783i 0.00294977i
\(379\) −3882.27 6724.28i −0.526170 0.911354i −0.999535 0.0304873i \(-0.990294\pi\)
0.473365 0.880867i \(-0.343039\pi\)
\(380\) 1081.49 0.145998
\(381\) 4771.73 0.641636
\(382\) −3362.47 5823.97i −0.450364 0.780053i
\(383\) 8530.01 + 4924.81i 1.13802 + 0.657039i 0.945941 0.324340i \(-0.105142\pi\)
0.192084 + 0.981379i \(0.438475\pi\)
\(384\) 754.107i 0.100216i
\(385\) −2.28248 + 1.31779i −0.000302145 + 0.000174444i
\(386\) 2103.68 + 3643.68i 0.277395 + 0.480462i
\(387\) 485.525 280.318i 0.0637742 0.0368201i
\(388\) 5189.74 + 2996.30i 0.679044 + 0.392046i
\(389\) 6615.30 + 3819.34i 0.862234 + 0.497811i 0.864760 0.502186i \(-0.167471\pi\)
−0.00252586 + 0.999997i \(0.500804\pi\)
\(390\) −8060.82 + 4653.92i −1.04660 + 0.604257i
\(391\) −6113.96 10589.7i −0.790783 1.36968i
\(392\) 2376.31 1371.96i 0.306178 0.176772i
\(393\) 10181.7i 1.30687i
\(394\) 1457.60 + 841.547i 0.186378 + 0.107605i
\(395\) −5996.60 10386.4i −0.763853 1.32303i
\(396\) −60.3072 −0.00765291
\(397\) 3356.13 0.424280 0.212140 0.977239i \(-0.431957\pi\)
0.212140 + 0.977239i \(0.431957\pi\)
\(398\) 2079.10 + 3601.11i 0.261849 + 0.453536i
\(399\) 10.7511i 0.00134894i
\(400\) 597.379 1034.69i 0.0746724 0.129336i
\(401\) 5431.43i 0.676391i 0.941076 + 0.338195i \(0.109817\pi\)
−0.941076 + 0.338195i \(0.890183\pi\)
\(402\) −9273.43 5354.02i −1.15054 0.664264i
\(403\) −6642.95 + 11505.9i −0.821114 + 1.42221i
\(404\) −193.193 + 334.620i −0.0237914 + 0.0412079i
\(405\) −10741.0 + 6201.32i −1.31784 + 0.760855i
\(406\) 31.7203 0.00387747
\(407\) −398.909 + 186.005i −0.0485828 + 0.0226533i
\(408\) −5131.41 −0.622653
\(409\) −7671.52 + 4429.15i −0.927462 + 0.535471i −0.886008 0.463670i \(-0.846532\pi\)
−0.0414543 + 0.999140i \(0.513199\pi\)
\(410\) 2236.87 3874.37i 0.269442 0.466686i
\(411\) 8216.98 14232.2i 0.986165 1.70809i
\(412\) 5377.26 + 3104.56i 0.643007 + 0.371240i
\(413\) 38.0821i 0.00453728i
\(414\) −865.859 + 1499.71i −0.102789 + 0.178036i
\(415\) 7929.44i 0.937929i
\(416\) −894.451 1549.23i −0.105418 0.182590i
\(417\) −8846.72 −1.03891
\(418\) −74.8384 −0.00875709
\(419\) −1730.58 2997.45i −0.201776 0.349487i 0.747324 0.664459i \(-0.231338\pi\)
−0.949101 + 0.314972i \(0.898005\pi\)
\(420\) 27.5042 + 15.8795i 0.00319540 + 0.00184486i
\(421\) 12685.5i 1.46853i −0.678862 0.734266i \(-0.737526\pi\)
0.678862 0.734266i \(-0.262474\pi\)
\(422\) 5571.69 3216.82i 0.642715 0.371072i
\(423\) 0.806300 + 1.39655i 9.26800e−5 + 0.000160527i
\(424\) −868.722 + 501.557i −0.0995021 + 0.0574475i
\(425\) 7040.67 + 4064.93i 0.803583 + 0.463949i
\(426\) −1092.92 630.999i −0.124301 0.0717652i
\(427\) −40.2308 + 23.2273i −0.00455950 + 0.00263243i
\(428\) −3068.26 5314.38i −0.346518 0.600187i
\(429\) 557.804 322.049i 0.0627763 0.0362439i
\(430\) 2055.19i 0.230489i
\(431\) −7515.67 4339.18i −0.839947 0.484944i 0.0172991 0.999850i \(-0.494493\pi\)
−0.857246 + 0.514907i \(0.827827\pi\)
\(432\) −909.201 1574.78i −0.101259 0.175386i
\(433\) 7854.61 0.871752 0.435876 0.900007i \(-0.356439\pi\)
0.435876 + 0.900007i \(0.356439\pi\)
\(434\) 45.3325 0.00501390
\(435\) −6922.05 11989.3i −0.762958 1.32148i
\(436\) 5071.83i 0.557102i
\(437\) −1074.49 + 1861.07i −0.117620 + 0.203723i
\(438\) 7702.18i 0.840238i
\(439\) 3916.95 + 2261.45i 0.425845 + 0.245861i 0.697575 0.716512i \(-0.254262\pi\)
−0.271730 + 0.962373i \(0.587596\pi\)
\(440\) −110.538 + 191.457i −0.0119765 + 0.0207440i
\(441\) 1322.12 2289.98i 0.142762 0.247271i
\(442\) 10541.9 6086.39i 1.13445 0.654978i
\(443\) −116.829 −0.0125299 −0.00626493 0.999980i \(-0.501994\pi\)
−0.00626493 + 0.999980i \(0.501994\pi\)
\(444\) 4344.54 + 3042.21i 0.464376 + 0.325173i
\(445\) −1785.76 −0.190231
\(446\) 6942.58 4008.30i 0.737087 0.425557i
\(447\) −8744.00 + 15145.1i −0.925228 + 1.60254i
\(448\) −3.05194 + 5.28611i −0.000321854 + 0.000557467i
\(449\) 4092.73 + 2362.94i 0.430174 + 0.248361i 0.699421 0.714710i \(-0.253441\pi\)
−0.269247 + 0.963071i \(0.586775\pi\)
\(450\) 1151.35i 0.120612i
\(451\) −154.790 + 268.104i −0.0161614 + 0.0279923i
\(452\) 3971.02i 0.413232i
\(453\) −10470.9 18136.1i −1.08601 1.88103i
\(454\) 171.533 0.0177322
\(455\) −75.3392 −0.00776255
\(456\) 450.906 + 780.992i 0.0463062 + 0.0802046i
\(457\) −1581.30 912.964i −0.161860 0.0934500i 0.416882 0.908961i \(-0.363123\pi\)
−0.578742 + 0.815511i \(0.696456\pi\)
\(458\) 7833.02i 0.799155i
\(459\) 10715.8 6186.76i 1.08969 0.629136i
\(460\) 3174.08 + 5497.68i 0.321723 + 0.557240i
\(461\) 420.431 242.736i 0.0424760 0.0245235i −0.478612 0.878027i \(-0.658860\pi\)
0.521088 + 0.853503i \(0.325526\pi\)
\(462\) −1.90327 1.09885i −0.000191663 0.000110657i
\(463\) −251.805 145.380i −0.0252751 0.0145926i 0.487309 0.873229i \(-0.337978\pi\)
−0.512584 + 0.858637i \(0.671312\pi\)
\(464\) 2304.27 1330.37i 0.230545 0.133105i
\(465\) −9892.51 17134.3i −0.986568 1.70879i
\(466\) −9911.87 + 5722.62i −0.985318 + 0.568874i
\(467\) 2296.77i 0.227585i −0.993505 0.113792i \(-0.963700\pi\)
0.993505 0.113792i \(-0.0362998\pi\)
\(468\) −1492.95 861.955i −0.147461 0.0851365i
\(469\) −43.3363 75.0607i −0.00426671 0.00739015i
\(470\) 5.91150 0.000580164
\(471\) −5850.25 −0.572325
\(472\) 1597.19 + 2766.41i 0.155755 + 0.269776i
\(473\) 142.218i 0.0138249i
\(474\) 5000.34 8660.84i 0.484543 0.839252i
\(475\) 1428.77i 0.138014i
\(476\) −35.9699 20.7672i −0.00346361 0.00199972i
\(477\) −483.335 + 837.160i −0.0463949 + 0.0803584i
\(478\) −7030.39 + 12177.0i −0.672725 + 1.16519i
\(479\) 5786.31 3340.73i 0.551948 0.318668i −0.197959 0.980210i \(-0.563431\pi\)
0.749908 + 0.661543i \(0.230098\pi\)
\(480\) 2663.99 0.253321
\(481\) −12533.8 1096.82i −1.18813 0.103972i
\(482\) 8396.15 0.793431
\(483\) −54.6524 + 31.5536i −0.00514859 + 0.00297254i
\(484\) −2654.35 + 4597.47i −0.249282 + 0.431768i
\(485\) 10584.8 18333.5i 0.990994 1.71645i
\(486\) −3641.62 2102.49i −0.339892 0.196237i
\(487\) 4502.78i 0.418974i −0.977811 0.209487i \(-0.932821\pi\)
0.977811 0.209487i \(-0.0671794\pi\)
\(488\) −1948.33 + 3374.61i −0.180731 + 0.313035i
\(489\) 16627.4i 1.53766i
\(490\) −4846.65 8394.64i −0.446835 0.773941i
\(491\) −12253.6 −1.12627 −0.563133 0.826366i \(-0.690404\pi\)
−0.563133 + 0.826366i \(0.690404\pi\)
\(492\) 3730.48 0.341835
\(493\) 9052.65 + 15679.6i 0.826999 + 1.43240i
\(494\) −1852.68 1069.64i −0.168737 0.0974202i
\(495\) 213.044i 0.0193446i
\(496\) 3293.10 1901.27i 0.298114 0.172116i
\(497\) −5.10741 8.84630i −0.000460963 0.000798412i
\(498\) −5726.21 + 3306.03i −0.515256 + 0.297483i
\(499\) 5975.38 + 3449.89i 0.536061 + 0.309495i 0.743481 0.668757i \(-0.233173\pi\)
−0.207420 + 0.978252i \(0.566507\pi\)
\(500\) 2463.52 + 1422.31i 0.220344 + 0.127216i
\(501\) −11397.5 + 6580.34i −1.01637 + 0.586803i
\(502\) −4729.96 8192.53i −0.420535 0.728388i
\(503\) 7161.53 4134.71i 0.634825 0.366516i −0.147794 0.989018i \(-0.547217\pi\)
0.782618 + 0.622502i \(0.213884\pi\)
\(504\) 5.88211i 0.000519861i
\(505\) 1182.09 + 682.481i 0.104163 + 0.0601387i
\(506\) −219.645 380.436i −0.0192972 0.0334238i
\(507\) 5468.26 0.479002
\(508\) 3239.76 0.282955
\(509\) 1485.96 + 2573.75i 0.129399 + 0.224125i 0.923444 0.383734i \(-0.125362\pi\)
−0.794045 + 0.607859i \(0.792029\pi\)
\(510\) 18127.4i 1.57391i
\(511\) −31.1714 + 53.9904i −0.00269851 + 0.00467396i
\(512\) 512.000i 0.0441942i
\(513\) −1883.23 1087.28i −0.162079 0.0935765i
\(514\) 226.221 391.826i 0.0194128 0.0336240i
\(515\) 10967.3 18995.9i 0.938402 1.62536i
\(516\) 1484.15 856.873i 0.126620 0.0731041i
\(517\) −0.409073 −3.47988e−5
\(518\) 18.1421 + 38.9079i 0.00153884 + 0.00330022i
\(519\) 10697.6 0.904766
\(520\) −5472.88 + 3159.77i −0.461542 + 0.266471i
\(521\) −5795.01 + 10037.2i −0.487301 + 0.844030i −0.999893 0.0146018i \(-0.995352\pi\)
0.512592 + 0.858632i \(0.328685\pi\)
\(522\) 1282.04 2220.55i 0.107496 0.186189i
\(523\) 15276.3 + 8819.79i 1.27722 + 0.737404i 0.976337 0.216256i \(-0.0693846\pi\)
0.300885 + 0.953660i \(0.402718\pi\)
\(524\) 6912.86i 0.576316i
\(525\) 20.9787 36.3362i 0.00174397 0.00302065i
\(526\) 12580.8i 1.04287i
\(527\) 12937.4 + 22408.3i 1.06938 + 1.85222i
\(528\) −184.346 −0.0151944
\(529\) −447.177 −0.0367533
\(530\) 1771.82 + 3068.88i 0.145213 + 0.251516i
\(531\) 2665.90 + 1539.16i 0.217872 + 0.125789i
\(532\) 7.29942i 0.000594868i
\(533\) −7663.88 + 4424.74i −0.622813 + 0.359581i
\(534\) −744.538 1289.58i −0.0603357 0.104505i
\(535\) −18773.8 + 10839.0i −1.51712 + 0.875911i
\(536\) −6296.18 3635.10i −0.507376 0.292934i
\(537\) 5950.57 + 3435.57i 0.478187 + 0.276081i
\(538\) −10058.3 + 5807.18i −0.806032 + 0.465363i
\(539\) 335.385 + 580.905i 0.0268016 + 0.0464218i
\(540\) −5563.14 + 3211.88i −0.443332 + 0.255958i
\(541\) 13426.4i 1.06700i 0.845799 + 0.533501i \(0.179124\pi\)
−0.845799 + 0.533501i \(0.820876\pi\)
\(542\) −511.661 295.407i −0.0405493 0.0234111i
\(543\) 11695.4 + 20257.1i 0.924307 + 1.60095i
\(544\) −3483.96 −0.274584
\(545\) 17916.9 1.40821
\(546\) −31.4113 54.4059i −0.00246205 0.00426439i
\(547\) 515.065i 0.0402607i −0.999797 0.0201303i \(-0.993592\pi\)
0.999797 0.0201303i \(-0.00640812\pi\)
\(548\) 5578.91 9662.95i 0.434889 0.753249i
\(549\) 3755.09i 0.291919i
\(550\) 252.937 + 146.033i 0.0196096 + 0.0113216i
\(551\) 1590.94 2755.60i 0.123006 0.213053i
\(552\) −2646.75 + 4584.30i −0.204082 + 0.353480i
\(553\) 70.1023 40.4736i 0.00539070 0.00311232i
\(554\) −5442.74 −0.417400
\(555\) 10747.0 15347.7i 0.821957 1.17383i
\(556\) −6006.47 −0.458149
\(557\) −21533.2 + 12432.2i −1.63804 + 0.945725i −0.656538 + 0.754293i \(0.727980\pi\)
−0.981506 + 0.191432i \(0.938687\pi\)
\(558\) 1832.20 3173.46i 0.139002 0.240758i
\(559\) −2032.68 + 3520.71i −0.153799 + 0.266387i
\(560\) 18.6739 + 10.7814i 0.00140914 + 0.000813566i
\(561\) 1254.41i 0.0944047i
\(562\) 7484.31 12963.2i 0.561755 0.972988i
\(563\) 129.889i 0.00972319i 0.999988 + 0.00486159i \(0.00154750\pi\)
−0.999988 + 0.00486159i \(0.998453\pi\)
\(564\) 2.46469 + 4.26897i 0.000184011 + 0.000318716i
\(565\) −14028.2 −1.04455
\(566\) −12079.0 −0.897025
\(567\) −41.8553 72.4956i −0.00310010 0.00536954i
\(568\) −742.038 428.416i −0.0548155 0.0316477i
\(569\) 20330.5i 1.49789i −0.662633 0.748944i \(-0.730561\pi\)
0.662633 0.748944i \(-0.269439\pi\)
\(570\) 2758.96 1592.89i 0.202737 0.117050i
\(571\) −2585.52 4478.25i −0.189493 0.328212i 0.755588 0.655047i \(-0.227351\pi\)
−0.945081 + 0.326835i \(0.894018\pi\)
\(572\) 378.720 218.654i 0.0276837 0.0159832i
\(573\) −17155.9 9904.94i −1.25078 0.722138i
\(574\) 26.1498 + 15.0976i 0.00190152 + 0.00109784i
\(575\) 7263.07 4193.34i 0.526767 0.304129i
\(576\) 246.699 + 427.296i 0.0178457 + 0.0309097i
\(577\) −9865.78 + 5696.01i −0.711816 + 0.410967i −0.811733 0.584029i \(-0.801476\pi\)
0.0999171 + 0.994996i \(0.468142\pi\)
\(578\) 13881.0i 0.998916i
\(579\) 10733.3 + 6196.88i 0.770399 + 0.444790i
\(580\) −4699.71 8140.14i −0.336457 0.582760i
\(581\) −53.5191 −0.00382160
\(582\) 17652.6 1.25725
\(583\) −122.609 212.365i −0.00871002 0.0150862i
\(584\) 5229.38i 0.370537i
\(585\) −3044.97 + 5274.05i −0.215204 + 0.372744i
\(586\) 5415.61i 0.381769i
\(587\) 19517.4 + 11268.4i 1.37235 + 0.792327i 0.991224 0.132196i \(-0.0422027\pi\)
0.381127 + 0.924523i \(0.375536\pi\)
\(588\) 4041.44 6999.97i 0.283446 0.490942i
\(589\) 2273.67 3938.11i 0.159057 0.275496i
\(590\) 9772.71 5642.28i 0.681926 0.393710i
\(591\) 4957.94 0.345080
\(592\) 2949.72 + 2065.51i 0.204785 + 0.143398i
\(593\) −14939.1 −1.03453 −0.517263 0.855827i \(-0.673049\pi\)
−0.517263 + 0.855827i \(0.673049\pi\)
\(594\) 384.966 222.260i 0.0265915 0.0153526i
\(595\) −73.3631 + 127.069i −0.00505478 + 0.00875514i
\(596\) −5936.73 + 10282.7i −0.408016 + 0.706705i
\(597\) 10607.9 + 6124.47i 0.727223 + 0.419863i
\(598\) 12557.3i 0.858706i
\(599\) 684.642 1185.83i 0.0467007 0.0808880i −0.841730 0.539898i \(-0.818463\pi\)
0.888431 + 0.459010i \(0.151796\pi\)
\(600\) 3519.44i 0.239467i
\(601\) 8280.50 + 14342.2i 0.562011 + 0.973431i 0.997321 + 0.0731508i \(0.0233054\pi\)
−0.435310 + 0.900281i \(0.643361\pi\)
\(602\) 13.8714 0.000939127
\(603\) −7006.07 −0.473149
\(604\) −7109.17 12313.4i −0.478921 0.829515i
\(605\) 16241.2 + 9376.86i 1.09140 + 0.630121i
\(606\) 1138.19i 0.0762968i
\(607\) 8688.32 5016.20i 0.580969 0.335422i −0.180550 0.983566i \(-0.557788\pi\)
0.761518 + 0.648144i \(0.224454\pi\)
\(608\) 306.142 + 530.253i 0.0204205 + 0.0353694i
\(609\) 80.9211 46.7198i 0.00538438 0.00310867i
\(610\) 11921.3 + 6882.74i 0.791275 + 0.456843i
\(611\) −10.1269 5.84676i −0.000670524 0.000387127i
\(612\) −2907.58 + 1678.69i −0.192046 + 0.110878i
\(613\) −5462.70 9461.67i −0.359929 0.623415i 0.628020 0.778197i \(-0.283866\pi\)
−0.987949 + 0.154783i \(0.950532\pi\)
\(614\) 283.186 163.498i 0.0186131 0.0107463i
\(615\) 13178.4i 0.864074i
\(616\) −1.29222 0.746066i −8.45214e−5 4.87985e-5i
\(617\) −9200.76 15936.2i −0.600338 1.03982i −0.992770 0.120035i \(-0.961699\pi\)
0.392432 0.919781i \(-0.371634\pi\)
\(618\) 18290.4 1.19053
\(619\) −15012.6 −0.974811 −0.487405 0.873176i \(-0.662057\pi\)
−0.487405 + 0.873176i \(0.662057\pi\)
\(620\) −6716.50 11633.3i −0.435067 0.753557i
\(621\) 12764.4i 0.824826i
\(622\) −3272.58 + 5668.27i −0.210962 + 0.365397i
\(623\) 12.0528i 0.000775099i
\(624\) −4563.63 2634.81i −0.292775 0.169034i
\(625\) 9691.54 16786.2i 0.620259 1.07432i
\(626\) −5038.86 + 8727.56i −0.321715 + 0.557226i
\(627\) −190.919 + 110.227i −0.0121604 + 0.00702079i
\(628\) −3972.02 −0.252390
\(629\) −14055.0 + 20071.7i −0.890950 + 1.27236i
\(630\) 20.7794 0.00131408
\(631\) 19364.1 11179.9i 1.22167 0.705330i 0.256394 0.966572i \(-0.417466\pi\)
0.965273 + 0.261243i \(0.0841322\pi\)
\(632\) 3394.97 5880.26i 0.213678 0.370102i
\(633\) 9475.88 16412.7i 0.594996 1.03056i
\(634\) −12779.4 7378.17i −0.800526 0.462184i
\(635\) 11444.9i 0.715239i
\(636\) −1477.45 + 2559.02i −0.0921145 + 0.159547i
\(637\) 19174.3i 1.19264i
\(638\) 325.217 + 563.293i 0.0201810 + 0.0349545i
\(639\) −825.702 −0.0511178
\(640\) 1808.71 0.111712
\(641\) 5397.18 + 9348.19i 0.332567 + 0.576024i 0.983015 0.183528i \(-0.0587518\pi\)
−0.650447 + 0.759552i \(0.725418\pi\)
\(642\) −15654.7 9038.26i −0.962372 0.555626i
\(643\) 31503.9i 1.93218i 0.258204 + 0.966090i \(0.416869\pi\)
−0.258204 + 0.966090i \(0.583131\pi\)
\(644\) −37.1061 + 21.4232i −0.00227048 + 0.00131086i
\(645\) −3027.02 5242.96i −0.184789 0.320064i
\(646\) −3608.17 + 2083.18i −0.219755 + 0.126875i
\(647\) −27633.0 15953.9i −1.67908 0.969419i −0.962248 0.272175i \(-0.912257\pi\)
−0.716834 0.697243i \(-0.754410\pi\)
\(648\) −6081.01 3510.87i −0.368649 0.212840i
\(649\) −676.266 + 390.442i −0.0409026 + 0.0236151i
\(650\) 4174.43 + 7230.32i 0.251899 + 0.436302i
\(651\) 115.647 66.7687i 0.00696245 0.00401977i
\(652\) 11289.1i 0.678093i
\(653\) 7212.56 + 4164.17i 0.432234 + 0.249551i 0.700298 0.713851i \(-0.253050\pi\)
−0.268064 + 0.963401i \(0.586384\pi\)
\(654\) 7470.12 + 12938.6i 0.446644 + 0.773609i
\(655\) −24420.6 −1.45678
\(656\) 2532.80 0.150746
\(657\) 2519.70 + 4364.24i 0.149624 + 0.259156i
\(658\) 0.0398992i 2.36388e-6i
\(659\) −14961.2 + 25913.6i −0.884380 + 1.53179i −0.0379570 + 0.999279i \(0.512085\pi\)
−0.846423 + 0.532511i \(0.821248\pi\)
\(660\) 651.229i 0.0384077i
\(661\) −17967.4 10373.5i −1.05726 0.610411i −0.132589 0.991171i \(-0.542329\pi\)
−0.924674 + 0.380760i \(0.875662\pi\)
\(662\) 7959.87 13786.9i 0.467325 0.809430i
\(663\) 17928.9 31053.7i 1.05023 1.81904i
\(664\) −3887.80 + 2244.62i −0.227223 + 0.131187i
\(665\) 25.7862 0.00150368
\(666\) 3456.96 + 302.514i 0.201133 + 0.0176009i
\(667\) 18677.2 1.08423
\(668\) −7738.31 + 4467.71i −0.448210 + 0.258774i
\(669\) 11807.4 20451.0i 0.682361 1.18188i
\(670\) −12841.5 + 22242.1i −0.740463 + 1.28252i
\(671\) −824.944 476.282i −0.0474614 0.0274019i
\(672\) 17.9804i 0.00103216i
\(673\) 10072.6 17446.3i 0.576927 0.999267i −0.418902 0.908031i \(-0.637585\pi\)
0.995829 0.0912356i \(-0.0290816\pi\)
\(674\) 4375.92i 0.250080i
\(675\) 4243.27 + 7349.55i 0.241961 + 0.419088i
\(676\) 3712.67 0.211235
\(677\) 3111.07 0.176615 0.0883074 0.996093i \(-0.471854\pi\)
0.0883074 + 0.996093i \(0.471854\pi\)
\(678\) −5848.78 10130.4i −0.331299 0.573828i
\(679\) 123.740 + 71.4414i 0.00699369 + 0.00403781i
\(680\) 12307.6i 0.694079i
\(681\) 437.593 252.644i 0.0246235 0.0142164i
\(682\) 464.778 + 805.020i 0.0260957 + 0.0451991i
\(683\) −11321.0 + 6536.16i −0.634238 + 0.366177i −0.782391 0.622787i \(-0.786000\pi\)
0.148154 + 0.988964i \(0.452667\pi\)
\(684\) 510.989 + 295.019i 0.0285645 + 0.0164917i
\(685\) −34135.7 19708.2i −1.90403 1.09929i
\(686\) 113.319 65.4250i 0.00630694 0.00364131i
\(687\) −11537.0 19982.7i −0.640704 1.10973i
\(688\) 1007.66 581.773i 0.0558382 0.0322382i
\(689\) 7009.66i 0.387586i
\(690\) 16194.7 + 9350.00i 0.893509 + 0.515867i
\(691\) −13603.7 23562.4i −0.748930 1.29718i −0.948336 0.317267i \(-0.897235\pi\)
0.199407 0.979917i \(-0.436099\pi\)
\(692\) 7263.14 0.398993
\(693\) −1.43792 −7.88198e−5
\(694\) −3961.25 6861.08i −0.216667 0.375278i
\(695\) 21218.7i 1.15809i
\(696\) 3918.91 6787.75i 0.213428 0.369668i
\(697\) 17234.7i 0.936603i
\(698\) 5475.28 + 3161.15i 0.296909 + 0.171420i
\(699\) −16857.3 + 29197.7i −0.912163 + 1.57991i
\(700\) 14.2435 24.6704i 0.000769075 0.00133208i
\(701\) 8163.60 4713.26i 0.439850 0.253948i −0.263684 0.964609i \(-0.584938\pi\)
0.703534 + 0.710662i \(0.251604\pi\)
\(702\) 12706.8 0.683173
\(703\) 4289.92 + 375.405i 0.230153 + 0.0201404i
\(704\) −125.162 −0.00670058
\(705\) 15.0807 8.70685i 0.000805635 0.000465133i
\(706\) −11611.8 + 20112.1i −0.619000 + 1.07214i
\(707\) −4.60636 + 7.97844i −0.000245035 + 0.000424413i
\(708\) 8149.09 + 4704.88i 0.432573 + 0.249746i
\(709\) 3827.30i 0.202733i −0.994849 0.101366i \(-0.967679\pi\)
0.994849 0.101366i \(-0.0323214\pi\)
\(710\) −1513.44 + 2621.35i −0.0799976 + 0.138560i
\(711\) 6543.26i 0.345136i
\(712\) −505.503 875.556i −0.0266075 0.0460855i
\(713\) 26692.2 1.40200
\(714\) −122.349 −0.00641291
\(715\) −772.426 1337.88i −0.0404016 0.0699775i
\(716\) 4040.13 + 2332.57i 0.210875 + 0.121749i
\(717\) 41419.3i 2.15737i
\(718\) 8162.89 4712.85i 0.424285 0.244961i
\(719\) −14868.3 25752.6i −0.771200 1.33576i −0.936905 0.349583i \(-0.886323\pi\)
0.165705 0.986175i \(-0.447010\pi\)
\(720\) 1509.48 871.499i 0.0781320 0.0451095i
\(721\) 128.211 + 74.0229i 0.00662253 + 0.00382352i
\(722\) −11246.0 6492.90i −0.579687 0.334682i
\(723\) 21419.2 12366.4i 1.10178 0.636115i
\(724\) 7940.59 + 13753.5i 0.407610 + 0.706001i
\(725\) −10754.1 + 6208.87i −0.550891 + 0.318057i
\(726\) 15638.0i 0.799423i
\(727\) −605.629 349.660i −0.0308962 0.0178379i 0.484472 0.874807i \(-0.339012\pi\)
−0.515369 + 0.856969i \(0.672345\pi\)
\(728\) −21.3266 36.9388i −0.00108574 0.00188055i
\(729\) 11311.6 0.574691
\(730\) 18473.5 0.936624
\(731\) 3958.74 + 6856.73i 0.200300 + 0.346929i
\(732\) 11478.5i 0.579588i
\(733\) 17609.5 30500.5i 0.887342 1.53692i 0.0443357 0.999017i \(-0.485883\pi\)
0.843006 0.537904i \(-0.180784\pi\)
\(734\) 4345.37i 0.218515i
\(735\) −24728.4 14276.9i −1.24098 0.716480i
\(736\) −1797.01 + 3112.51i −0.0899980 + 0.155881i
\(737\) 888.624 1539.14i 0.0444137 0.0769267i
\(738\) 2113.78 1220.39i 0.105433 0.0608716i
\(739\) −1684.77 −0.0838639 −0.0419319 0.999120i \(-0.513351\pi\)
−0.0419319 + 0.999120i \(0.513351\pi\)
\(740\) 7296.68 10420.3i 0.362475 0.517646i
\(741\) −6301.77 −0.312417
\(742\) −20.7132 + 11.9588i −0.00102480 + 0.000591671i
\(743\) 5626.27 9744.98i 0.277803 0.481169i −0.693035 0.720904i \(-0.743727\pi\)
0.970839 + 0.239734i \(0.0770603\pi\)
\(744\) 5600.64 9700.59i 0.275980 0.478012i
\(745\) 36325.1 + 20972.3i 1.78637 + 1.03136i
\(746\) 12788.6i 0.627646i
\(747\) −2163.07 + 3746.55i −0.105947 + 0.183506i
\(748\) 851.677i 0.0416315i
\(749\) −73.1573 126.712i −0.00356890 0.00618152i
\(750\) 8379.51 0.407968
\(751\) 8527.90 0.414364 0.207182 0.978302i \(-0.433571\pi\)
0.207182 + 0.978302i \(0.433571\pi\)
\(752\) 1.67340 + 2.89841i 8.11469e−5 + 0.000140551i
\(753\) −24133.0 13933.2i −1.16794 0.674308i
\(754\) 18593.0i 0.898032i
\(755\) −43498.9 + 25114.1i −2.09681 + 1.21059i
\(756\) −21.6783 37.5480i −0.00104290 0.00180636i
\(757\) 13240.3 7644.26i 0.635700 0.367022i −0.147256 0.989098i \(-0.547044\pi\)
0.782956 + 0.622077i \(0.213711\pi\)
\(758\) −13448.6 7764.53i −0.644424 0.372059i
\(759\) −1120.66 647.015i −0.0535935 0.0309422i
\(760\) 1873.19 1081.49i 0.0894050 0.0516180i
\(761\) 11355.6 + 19668.5i 0.540920 + 0.936900i 0.998852 + 0.0479130i \(0.0152570\pi\)
−0.457932 + 0.888987i \(0.651410\pi\)
\(762\) 8264.89 4771.73i 0.392920 0.226853i
\(763\) 120.929i 0.00573777i
\(764\) −11647.9 6724.95i −0.551581 0.318455i
\(765\) 5930.21 + 10271.4i 0.280271 + 0.485443i
\(766\) 19699.2 0.929193
\(767\) −22321.9 −1.05085
\(768\) 754.107 + 1306.15i 0.0354317 + 0.0613694i
\(769\) 6528.81i 0.306157i −0.988214 0.153079i \(-0.951081\pi\)
0.988214 0.153079i \(-0.0489188\pi\)
\(770\) −2.63558 + 4.56496i −0.000123350 + 0.000213649i
\(771\) 1332.77i 0.0622550i
\(772\) 7287.36 + 4207.36i 0.339738 + 0.196148i
\(773\) 5334.71 9240.00i 0.248223 0.429935i −0.714810 0.699319i \(-0.753487\pi\)
0.963033 + 0.269384i \(0.0868201\pi\)
\(774\) 560.636 971.050i 0.0260357 0.0450952i
\(775\) −15369.0 + 8873.28i −0.712348 + 0.411275i
\(776\) 11985.2 0.554437
\(777\) 103.588 + 72.5363i 0.00478276 + 0.00334907i
\(778\) 15277.4 0.704011
\(779\) 2623.10 1514.45i 0.120645 0.0696543i
\(780\) −9307.84 + 16121.6i −0.427274 + 0.740061i
\(781\) 104.729 181.396i 0.00479833 0.00831095i
\(782\) −21179.4 12227.9i −0.968508 0.559168i
\(783\) 18899.6i 0.862600i
\(784\) 2743.93 4752.62i 0.124997 0.216501i
\(785\) 14031.7i 0.637978i
\(786\) −10181.7 17635.3i −0.462048 0.800291i
\(787\) 6644.21 0.300941 0.150471 0.988614i \(-0.451921\pi\)
0.150471 + 0.988614i \(0.451921\pi\)
\(788\) 3366.19 0.152177
\(789\) 18529.8 + 32094.6i 0.836095 + 1.44816i
\(790\) −20772.8 11993.2i −0.935525 0.540125i
\(791\) 94.6821i 0.00425601i
\(792\) −104.455 + 60.3072i −0.00468643 + 0.00270571i
\(793\) −13614.7 23581.4i −0.609676 1.05599i
\(794\) 5812.99 3356.13i 0.259818 0.150006i
\(795\) 9040.10 + 5219.30i 0.403295 + 0.232842i
\(796\) 7202.21 + 4158.20i 0.320698 + 0.185155i
\(797\) 19132.5 11046.2i 0.850324 0.490935i −0.0104362 0.999946i \(-0.503322\pi\)
0.860760 + 0.509011i \(0.169989\pi\)
\(798\) 10.7511 + 18.6214i 0.000476922 + 0.000826053i
\(799\) −19.7225 + 11.3868i −0.000873258 + 0.000504176i
\(800\) 2389.52i 0.105603i
\(801\) −843.746 487.137i −0.0372189 0.0214883i
\(802\) 5431.43 + 9407.52i 0.239140 + 0.414203i
\(803\) −1278.36 −0.0561796
\(804\) −21416.1 −0.939411
\(805\) 75.6805 + 131.083i 0.00331353 + 0.00573919i
\(806\) 26571.8i 1.16123i
\(807\) −17106.4 + 29629.1i −0.746188 + 1.29244i
\(808\) 772.773i 0.0336461i
\(809\) 6407.11 + 3699.15i 0.278445 + 0.160760i 0.632719 0.774381i \(-0.281939\pi\)
−0.354274 + 0.935142i \(0.615272\pi\)
\(810\) −12402.6 + 21482.0i −0.538005 + 0.931853i
\(811\) −16904.3 + 29279.1i −0.731925 + 1.26773i 0.224135 + 0.974558i \(0.428044\pi\)
−0.956060 + 0.293173i \(0.905289\pi\)
\(812\) 54.9412 31.7203i 0.00237446 0.00137089i
\(813\) −1740.38 −0.0750773
\(814\) −504.926 + 721.078i −0.0217416 + 0.0310489i
\(815\) 39880.4 1.71405
\(816\) −8887.86 + 5131.41i −0.381296 + 0.220141i
\(817\) 695.722 1205.03i 0.0297922 0.0516016i
\(818\) −8858.31 + 15343.0i −0.378635 + 0.655815i
\(819\) −35.5968 20.5518i −0.00151874 0.000876848i
\(820\) 8947.47i 0.381048i
\(821\) −2014.64 + 3489.46i −0.0856413 + 0.148335i −0.905664 0.423995i \(-0.860627\pi\)
0.820023 + 0.572331i \(0.193961\pi\)
\(822\) 32867.9i 1.39465i
\(823\) 16506.0 + 28589.3i 0.699105 + 1.21089i 0.968777 + 0.247933i \(0.0797514\pi\)
−0.269672 + 0.962952i \(0.586915\pi\)
\(824\) 12418.3 0.525013
\(825\) 860.349 0.0363073
\(826\) 38.0821 + 65.9602i 0.00160417 + 0.00277851i
\(827\) −32007.5 18479.5i −1.34584 0.777021i −0.358183 0.933651i \(-0.616604\pi\)
−0.987657 + 0.156630i \(0.949937\pi\)
\(828\) 3463.44i 0.145366i
\(829\) −16530.7 + 9543.99i −0.692562 + 0.399851i −0.804571 0.593856i \(-0.797605\pi\)
0.112009 + 0.993707i \(0.464271\pi\)
\(830\) 7929.44 + 13734.2i 0.331608 + 0.574362i
\(831\) −13884.9 + 8016.43i −0.579615 + 0.334641i
\(832\) −3098.47 1788.90i −0.129111 0.0745421i
\(833\) 32339.7 + 18671.4i 1.34514 + 0.776620i
\(834\) −15323.0 + 8846.72i −0.636200 + 0.367310i
\(835\) 15782.8 + 27336.6i 0.654116 + 1.13296i
\(836\) −129.624 + 74.8384i −0.00536260 + 0.00309610i
\(837\) 27010.0i 1.11541i
\(838\) −5994.90 3461.16i −0.247125 0.142677i
\(839\) −10795.2 18697.9i −0.444210 0.769395i 0.553787 0.832659i \(-0.313182\pi\)
−0.997997 + 0.0632639i \(0.979849\pi\)
\(840\) 63.5182 0.00260903
\(841\) −3265.41 −0.133889
\(842\) −12685.5 21971.9i −0.519205 0.899289i
\(843\) 44093.5i 1.80150i
\(844\) 6433.63 11143.4i 0.262387 0.454468i
\(845\) 13115.5i 0.533949i
\(846\) 2.79311 + 1.61260i 0.000113509 + 6.55347e-5i
\(847\) −63.2884 + 109.619i −0.00256743 + 0.00444692i
\(848\) −1003.11 + 1737.44i −0.0406215 + 0.0703586i
\(849\) −30814.4 + 17790.7i −1.24564 + 0.719169i
\(850\) 16259.7 0.656123
\(851\) 10682.2 + 22909.3i 0.430296 + 0.922821i
\(852\) −2524.00 −0.101491
\(853\) 28079.6 16211.7i 1.12711 0.650738i 0.183904 0.982944i \(-0.441126\pi\)
0.943207 + 0.332206i \(0.107793\pi\)
\(854\) −46.4545 + 80.4616i −0.00186141 + 0.00322405i
\(855\) 1042.20 1805.14i 0.0416870 0.0722040i
\(856\) −10628.8 6136.51i −0.424396 0.245025i
\(857\) 5449.36i 0.217207i −0.994085 0.108604i \(-0.965362\pi\)
0.994085 0.108604i \(-0.0346379\pi\)
\(858\) 644.097 1115.61i 0.0256283 0.0443896i
\(859\) 41508.0i 1.64870i −0.566079 0.824351i \(-0.691540\pi\)
0.566079 0.824351i \(-0.308460\pi\)
\(860\) −2055.19 3559.70i −0.0814900 0.141145i
\(861\) 88.9468 0.00352067
\(862\) −17356.7 −0.685814
\(863\) −14568.5 25233.4i −0.574643 0.995311i −0.996080 0.0884533i \(-0.971808\pi\)
0.421437 0.906858i \(-0.361526\pi\)
\(864\) −3149.57 1818.40i −0.124017 0.0716011i
\(865\) 25658.0i 1.00855i
\(866\) 13604.6 7854.61i 0.533837 0.308211i
\(867\) −20444.8 35411.5i −0.800857 1.38713i
\(868\) 78.5182 45.3325i 0.00307037 0.00177268i
\(869\) 1437.47 + 829.923i 0.0561137 + 0.0323972i
\(870\) −23978.7 13844.1i −0.934429 0.539493i
\(871\) 43997.1 25401.7i 1.71158 0.988179i
\(872\) 5071.83 + 8784.66i 0.196965 + 0.341154i
\(873\) 10002.4 5774.87i 0.387777 0.223883i
\(874\) 4297.96i 0.166339i
\(875\) 58.7383 + 33.9126i 0.00226939 + 0.00131023i
\(876\) 7702.18 + 13340.6i 0.297069 + 0.514539i
\(877\) −29024.7 −1.11755 −0.558776 0.829319i \(-0.688729\pi\)
−0.558776 + 0.829319i \(0.688729\pi\)
\(878\) 9045.81 0.347701
\(879\) 7976.46 + 13815.6i 0.306074 + 0.530136i
\(880\) 442.151i 0.0169374i
\(881\) 976.779 1691.83i 0.0373536 0.0646984i −0.846744 0.532000i \(-0.821441\pi\)
0.884098 + 0.467302i \(0.154774\pi\)
\(882\) 5288.47i 0.201896i
\(883\) 10460.9 + 6039.58i 0.398681 + 0.230179i 0.685915 0.727682i \(-0.259402\pi\)
−0.287233 + 0.957861i \(0.592736\pi\)
\(884\) 12172.8 21083.9i 0.463139 0.802180i
\(885\) 16620.6 28787.8i 0.631296 1.09344i
\(886\) −202.354 + 116.829i −0.00767294 + 0.00442997i
\(887\) −24942.6 −0.944185 −0.472092 0.881549i \(-0.656501\pi\)
−0.472092 + 0.881549i \(0.656501\pi\)
\(888\) 10567.2 + 924.722i 0.399337 + 0.0349455i
\(889\) 77.2465 0.00291424
\(890\) −3093.02 + 1785.76i −0.116493 + 0.0672570i
\(891\) 858.256 1486.54i 0.0322701 0.0558934i
\(892\) 8016.60 13885.2i 0.300914 0.521199i
\(893\) 3.46611 + 2.00116i 0.000129887 + 7.49902e-5i
\(894\) 34976.0i 1.30847i
\(895\) 8240.13 14272.3i 0.307751 0.533040i
\(896\) 12.2077i 0.000455170i
\(897\) −18495.2 32034.6i −0.688447 1.19243i
\(898\) 9451.76 0.351235
\(899\) −39521.8 −1.46621
\(900\) −1151.35 1994.20i −0.0426426 0.0738592i
\(901\) −11822.6 6825.80i −0.437146 0.252387i
\(902\) 619.160i 0.0228556i
\(903\) 35.3869 20.4306i 0.00130410 0.000752923i
\(904\) −3971.02 6878.01i −0.146100 0.253052i
\(905\) 48586.1 28051.2i 1.78459 1.03034i
\(906\) −36272.1 20941.7i −1.33009 0.767927i
\(907\) 19271.1 + 11126.1i 0.705496 + 0.407318i 0.809391 0.587270i \(-0.199797\pi\)
−0.103895 + 0.994588i \(0.533131\pi\)
\(908\) 297.103 171.533i 0.0108587 0.00626928i
\(909\) 372.349 + 644.927i 0.0135864 + 0.0235323i
\(910\) −130.491 + 75.3392i −0.00475357 + 0.00274447i
\(911\) 1692.67i 0.0615596i 0.999526 + 0.0307798i \(0.00979906\pi\)
−0.999526 + 0.0307798i \(0.990201\pi\)
\(912\) 1561.98 + 901.812i 0.0567132 + 0.0327434i
\(913\) −548.712 950.398i −0.0198902 0.0344508i
\(914\) −3651.86 −0.132158
\(915\) 40549.4 1.46505
\(916\) −7833.02 13567.2i −0.282544 0.489381i
\(917\) 164.825i 0.00593567i
\(918\) 12373.5 21431.6i 0.444866 0.770531i
\(919\) 20238.3i 0.726441i −0.931703 0.363221i \(-0.881677\pi\)
0.931703 0.363221i \(-0.118323\pi\)
\(920\) 10995.4 + 6348.17i 0.394028 + 0.227492i
\(921\) 481.620 834.191i 0.0172312 0.0298453i
\(922\) 485.472 840.862i 0.0173407 0.0300351i
\(923\) 5185.28 2993.73i 0.184914 0.106760i
\(924\) −4.39542 −0.000156492
\(925\) −13766.4 9639.76i −0.489338 0.342652i
\(926\) −581.518 −0.0206370
\(927\) 10363.8 5983.54i 0.367197 0.212001i
\(928\) 2660.74 4608.53i 0.0941196 0.163020i
\(929\) −8516.08 + 14750.3i −0.300757 + 0.520927i −0.976308 0.216387i \(-0.930573\pi\)
0.675550 + 0.737314i \(0.263906\pi\)
\(930\) −34268.7 19785.0i −1.20829 0.697609i
\(931\) 6562.74i 0.231026i
\(932\) −11445.2 + 19823.7i −0.402255 + 0.696725i
\(933\) 19280.3i 0.676535i
\(934\) −2296.77 3978.13i −0.0804633 0.139367i
\(935\) −3008.66 −0.105234
\(936\) −3447.82 −0.120401
\(937\) 13110.5 + 22708.0i 0.457098 + 0.791718i 0.998806 0.0488492i \(-0.0155554\pi\)
−0.541708 + 0.840567i \(0.682222\pi\)
\(938\) −150.121 86.6727i −0.00522563 0.00301702i
\(939\) 29686.3i 1.03171i
\(940\) 10.2390 5.91150i 0.000355277 0.000205119i
\(941\) 21214.3 + 36744.2i 0.734926 + 1.27293i 0.954756 + 0.297392i \(0.0961167\pi\)
−0.219829 + 0.975538i \(0.570550\pi\)
\(942\) −10132.9 + 5850.25i −0.350476 + 0.202348i
\(943\) 15397.2 + 8889.57i 0.531709 + 0.306982i
\(944\) 5532.81 + 3194.37i 0.190760 + 0.110136i
\(945\) −132.643 + 76.5817i −0.00456602 + 0.00263619i
\(946\) 142.218 + 246.329i 0.00488785 + 0.00846601i
\(947\) −22185.0 + 12808.5i −0.761261 + 0.439514i −0.829748 0.558138i \(-0.811516\pi\)
0.0684873 + 0.997652i \(0.478183\pi\)
\(948\) 20001.4i 0.685247i
\(949\) −31646.6 18271.2i −1.08250 0.624982i
\(950\) −1428.77 2474.71i −0.0487952 0.0845158i
\(951\) −43468.2 −1.48218
\(952\) −83.0690 −0.00282803
\(953\) 17693.8 + 30646.5i 0.601424 + 1.04170i 0.992606 + 0.121384i \(0.0387332\pi\)
−0.391181 + 0.920314i \(0.627933\pi\)
\(954\) 1933.34i 0.0656123i
\(955\) −23756.8 + 41148.0i −0.804976 + 1.39426i
\(956\) 28121.5i 0.951376i
\(957\) 1659.31 + 958.003i 0.0560479 + 0.0323593i
\(958\) 6681.46 11572.6i 0.225332 0.390287i
\(959\) 133.019 230.396i 0.00447906 0.00775796i
\(960\) 4614.16 2663.99i 0.155127 0.0895623i
\(961\) −26690.8 −0.895935
\(962\) −22806.0 + 10634.1i −0.764340 + 0.356399i
\(963\) −11827.1 −0.395768
\(964\) 14542.5 8396.15i 0.485876 0.280520i
\(965\) 14863.1 25743.6i 0.495813 0.858773i
\(966\) −63.1071 + 109.305i −0.00210190 + 0.00364060i
\(967\) 44917.8 + 25933.3i 1.49375 + 0.862419i 0.999974 0.00716762i \(-0.00228154\pi\)
0.493780 + 0.869587i \(0.335615\pi\)
\(968\) 10617.4i 0.352537i
\(969\) −6136.48 + 10628.7i −0.203439 + 0.352366i
\(970\) 42339.3i 1.40148i
\(971\) 7240.30 + 12540.6i 0.239292 + 0.414465i 0.960511 0.278241i \(-0.0897515\pi\)
−0.721220 + 0.692707i \(0.756418\pi\)
\(972\) −8409.97 −0.277520
\(973\) −143.214 −0.00471862
\(974\) −4502.78 7799.04i −0.148130 0.256568i
\(975\) 21298.6 + 12296.7i 0.699590 + 0.403909i
\(976\) 7793.32i 0.255592i
\(977\) −37420.2 + 21604.5i −1.22536 + 0.707462i −0.966056 0.258333i \(-0.916827\pi\)
−0.259305 + 0.965796i \(0.583493\pi\)
\(978\) 16627.4 + 28799.5i 0.543646 + 0.941622i
\(979\) 214.035 123.573i 0.00698733 0.00403414i
\(980\) −16789.3 9693.30i −0.547259 0.315960i
\(981\) 8465.51 + 4887.56i 0.275518 + 0.159070i
\(982\) −21223.8 + 12253.6i −0.689694 + 0.398195i
\(983\) 20444.8 + 35411.5i 0.663366 + 1.14898i 0.979726 + 0.200345i \(0.0642061\pi\)
−0.316359 + 0.948639i \(0.602461\pi\)
\(984\) 6461.38 3730.48i 0.209331 0.120857i
\(985\) 11891.5i 0.384665i
\(986\) 31359.3 + 18105.3i 1.01286 + 0.584777i
\(987\) 0.0587662 + 0.101786i 1.89519e−6 + 3.28256e-6i
\(988\) −4278.58 −0.137773
\(989\) 8167.57 0.262602
\(990\) 213.044 + 369.002i 0.00683936 + 0.0118461i
\(991\) 3691.96i 0.118344i −0.998248 0.0591721i \(-0.981154\pi\)
0.998248 0.0591721i \(-0.0188461\pi\)
\(992\) 3802.54 6586.20i 0.121705 0.210798i
\(993\) 46895.3i 1.49867i
\(994\) −17.6926 10.2148i −0.000564562 0.000325950i
\(995\) 14689.4 25442.8i 0.468026 0.810644i
\(996\) −6612.06 + 11452.4i −0.210352 + 0.364341i
\(997\) 43577.3 25159.3i 1.38426 0.799202i 0.391598 0.920137i \(-0.371922\pi\)
0.992660 + 0.120935i \(0.0385891\pi\)
\(998\) 13799.5 0.437692
\(999\) −23182.1 + 10809.4i −0.734183 + 0.342337i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 74.4.e.a.11.9 20
3.2 odd 2 666.4.s.d.307.4 20
37.27 even 6 inner 74.4.e.a.27.9 yes 20
111.101 odd 6 666.4.s.d.397.4 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.4.e.a.11.9 20 1.1 even 1 trivial
74.4.e.a.27.9 yes 20 37.27 even 6 inner
666.4.s.d.307.4 20 3.2 odd 2
666.4.s.d.397.4 20 111.101 odd 6