Properties

Label 23.4.c.a.2.3
Level $23$
Weight $4$
Character 23.2
Analytic conductor $1.357$
Analytic rank $0$
Dimension $50$
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] = [23,4,Mod(2,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 23.c (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.35704393013\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 2.3
Character \(\chi\) \(=\) 23.2
Dual form 23.4.c.a.12.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.442460 - 0.284352i) q^{2} +(-0.784628 - 5.45721i) q^{3} +(-3.20841 - 7.02543i) q^{4} +(12.7367 + 3.73985i) q^{5} +(-1.20460 + 2.63770i) q^{6} +(-5.26652 + 6.07789i) q^{7} +(-1.17691 + 8.18558i) q^{8} +(-3.25915 + 0.956973i) q^{9} +O(q^{10})\) \(q+(-0.442460 - 0.284352i) q^{2} +(-0.784628 - 5.45721i) q^{3} +(-3.20841 - 7.02543i) q^{4} +(12.7367 + 3.73985i) q^{5} +(-1.20460 + 2.63770i) q^{6} +(-5.26652 + 6.07789i) q^{7} +(-1.17691 + 8.18558i) q^{8} +(-3.25915 + 0.956973i) q^{9} +(-4.57207 - 5.27645i) q^{10} +(-11.1639 + 7.17457i) q^{11} +(-35.8218 + 23.0213i) q^{12} +(47.1024 + 54.3591i) q^{13} +(4.05848 - 1.19168i) q^{14} +(10.4155 - 72.4414i) q^{15} +(-37.6136 + 43.4084i) q^{16} +(47.0046 - 102.926i) q^{17} +(1.71416 + 0.503323i) q^{18} +(8.05364 + 17.6350i) q^{19} +(-14.5906 - 101.480i) q^{20} +(37.3006 + 23.9716i) q^{21} +6.97966 q^{22} +(-99.8811 + 46.8056i) q^{23} +45.5938 q^{24} +(43.0816 + 27.6869i) q^{25} +(-5.38383 - 37.4453i) q^{26} +(-54.0590 - 118.373i) q^{27} +(59.5969 + 17.4992i) q^{28} +(-32.0164 + 70.1062i) q^{29} +(-25.2073 + 29.0908i) q^{30} +(-34.1869 + 237.775i) q^{31} +(92.4639 - 27.1498i) q^{32} +(47.9126 + 55.2941i) q^{33} +(-50.0648 + 32.1747i) q^{34} +(-89.8087 + 57.7166i) q^{35} +(17.1798 + 19.8266i) q^{36} +(-251.254 + 73.7748i) q^{37} +(1.45113 - 10.0928i) q^{38} +(259.691 - 299.699i) q^{39} +(-45.6028 + 99.8562i) q^{40} +(-110.653 - 32.4907i) q^{41} +(-9.68763 - 21.2130i) q^{42} +(-50.2258 - 349.328i) q^{43} +(86.2226 + 55.4119i) q^{44} -45.0899 q^{45} +(57.5026 + 7.69176i) q^{46} +385.301 q^{47} +(266.401 + 171.206i) q^{48} +(39.6095 + 275.490i) q^{49} +(-11.1891 - 24.5006i) q^{50} +(-598.569 - 175.756i) q^{51} +(230.772 - 505.320i) q^{52} +(182.779 - 210.939i) q^{53} +(-9.74053 + 67.7469i) q^{54} +(-169.023 + 49.6296i) q^{55} +(-43.5528 - 50.2627i) q^{56} +(89.9187 - 57.7873i) q^{57} +(34.1008 - 21.9153i) q^{58} +(-329.991 - 380.830i) q^{59} +(-542.349 + 159.248i) q^{60} +(-91.6114 + 637.171i) q^{61} +(82.7380 - 95.4848i) q^{62} +(11.3480 - 24.8487i) q^{63} +(392.255 + 115.177i) q^{64} +(396.637 + 868.514i) q^{65} +(-5.47643 - 38.0894i) q^{66} +(397.284 + 255.319i) q^{67} -873.908 q^{68} +(333.797 + 508.347i) q^{69} +56.1486 q^{70} +(141.871 + 91.1751i) q^{71} +(-3.99765 - 27.8043i) q^{72} +(-277.140 - 606.852i) q^{73} +(132.148 + 38.8021i) q^{74} +(117.290 - 256.829i) q^{75} +(98.0541 - 113.160i) q^{76} +(15.1884 - 105.638i) q^{77} +(-200.123 + 58.7613i) q^{78} +(-541.565 - 625.000i) q^{79} +(-641.415 + 412.212i) q^{80} +(-680.721 + 437.473i) q^{81} +(39.7208 + 45.8402i) q^{82} +(789.153 - 231.716i) q^{83} +(48.7355 - 338.963i) q^{84} +(983.613 - 1135.15i) q^{85} +(-77.1091 + 168.845i) q^{86} +(407.705 + 119.713i) q^{87} +(-45.5892 - 99.8264i) q^{88} +(-80.1047 - 557.140i) q^{89} +(19.9505 + 12.8214i) q^{90} -578.454 q^{91} +(649.288 + 551.536i) q^{92} +1324.41 q^{93} +(-170.480 - 109.561i) q^{94} +(36.6249 + 254.732i) q^{95} +(-220.712 - 483.292i) q^{96} +(-20.4753 - 6.01210i) q^{97} +(60.8104 - 133.156i) q^{98} +(29.5188 - 34.0665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9} + 47 q^{10} - 53 q^{11} + 36 q^{12} - 65 q^{13} + 117 q^{14} - 425 q^{15} - 499 q^{16} - 117 q^{17} + 24 q^{18} + 73 q^{19} + 529 q^{20} + 429 q^{21} + 310 q^{22} + 542 q^{23} + 1606 q^{24} + 246 q^{25} + 324 q^{26} + 65 q^{27} - 677 q^{28} - 497 q^{29} - 1041 q^{30} - 471 q^{31} - 915 q^{32} - 391 q^{33} - 2751 q^{34} - 737 q^{35} - 1865 q^{36} - 1071 q^{37} - 1504 q^{38} + 127 q^{39} + 1479 q^{40} + 569 q^{41} + 3059 q^{42} + 1615 q^{43} + 2518 q^{44} + 2768 q^{45} + 4041 q^{46} + 2904 q^{47} + 2702 q^{48} + 1226 q^{49} + 1322 q^{50} + 589 q^{51} - 2156 q^{52} + 391 q^{53} - 5862 q^{54} - 3323 q^{55} - 7028 q^{56} - 7623 q^{57} - 5639 q^{58} - 2445 q^{59} - 3157 q^{60} - 1059 q^{61} + 1468 q^{62} + 3155 q^{63} + 4570 q^{64} + 2641 q^{65} + 5206 q^{66} + 27 q^{67} + 8350 q^{68} + 4005 q^{69} + 9702 q^{70} + 3465 q^{71} + 5629 q^{72} + 435 q^{73} - 994 q^{74} - 7819 q^{75} - 3598 q^{76} - 5931 q^{77} - 8996 q^{78} - 2559 q^{79} - 14052 q^{80} - 4788 q^{81} - 3822 q^{82} - 3967 q^{83} - 8427 q^{84} + 299 q^{85} + 721 q^{86} + 8363 q^{87} + 5825 q^{88} + 3717 q^{89} + 16742 q^{90} + 7238 q^{91} + 9550 q^{92} + 12750 q^{93} + 6035 q^{94} + 4551 q^{95} + 2493 q^{96} - 2419 q^{97} - 5687 q^{98} - 755 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{1}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.442460 0.284352i −0.156433 0.100533i 0.460082 0.887876i \(-0.347820\pi\)
−0.616516 + 0.787343i \(0.711456\pi\)
\(3\) −0.784628 5.45721i −0.151002 1.05024i −0.914545 0.404484i \(-0.867451\pi\)
0.763544 0.645756i \(-0.223458\pi\)
\(4\) −3.20841 7.02543i −0.401051 0.878178i
\(5\) 12.7367 + 3.73985i 1.13921 + 0.334502i 0.796321 0.604874i \(-0.206777\pi\)
0.342888 + 0.939376i \(0.388595\pi\)
\(6\) −1.20460 + 2.63770i −0.0819626 + 0.179473i
\(7\) −5.26652 + 6.07789i −0.284365 + 0.328175i −0.879904 0.475151i \(-0.842393\pi\)
0.595539 + 0.803327i \(0.296939\pi\)
\(8\) −1.17691 + 8.18558i −0.0520125 + 0.361755i
\(9\) −3.25915 + 0.956973i −0.120709 + 0.0354434i
\(10\) −4.57207 5.27645i −0.144581 0.166856i
\(11\) −11.1639 + 7.17457i −0.306003 + 0.196656i −0.684625 0.728895i \(-0.740034\pi\)
0.378623 + 0.925551i \(0.376398\pi\)
\(12\) −35.8218 + 23.0213i −0.861739 + 0.553806i
\(13\) 47.1024 + 54.3591i 1.00491 + 1.15973i 0.987135 + 0.159888i \(0.0511134\pi\)
0.0177769 + 0.999842i \(0.494341\pi\)
\(14\) 4.05848 1.19168i 0.0774768 0.0227492i
\(15\) 10.4155 72.4414i 0.179285 1.24695i
\(16\) −37.6136 + 43.4084i −0.587712 + 0.678256i
\(17\) 47.0046 102.926i 0.670606 1.46842i −0.201693 0.979449i \(-0.564644\pi\)
0.872299 0.488973i \(-0.162629\pi\)
\(18\) 1.71416 + 0.503323i 0.0224462 + 0.00659079i
\(19\) 8.05364 + 17.6350i 0.0972437 + 0.212934i 0.952002 0.306093i \(-0.0990218\pi\)
−0.854758 + 0.519027i \(0.826294\pi\)
\(20\) −14.5906 101.480i −0.163128 1.13458i
\(21\) 37.3006 + 23.9716i 0.387602 + 0.249097i
\(22\) 6.97966 0.0676395
\(23\) −99.8811 + 46.8056i −0.905507 + 0.424332i
\(24\) 45.5938 0.387783
\(25\) 43.0816 + 27.6869i 0.344653 + 0.221495i
\(26\) −5.38383 37.4453i −0.0406098 0.282448i
\(27\) −54.0590 118.373i −0.385320 0.843734i
\(28\) 59.5969 + 17.4992i 0.402241 + 0.118109i
\(29\) −32.0164 + 70.1062i −0.205010 + 0.448910i −0.984010 0.178114i \(-0.943000\pi\)
0.778999 + 0.627025i \(0.215728\pi\)
\(30\) −25.2073 + 29.0908i −0.153407 + 0.177041i
\(31\) −34.1869 + 237.775i −0.198069 + 1.37760i 0.611810 + 0.791005i \(0.290442\pi\)
−0.809879 + 0.586597i \(0.800467\pi\)
\(32\) 92.4639 27.1498i 0.510796 0.149983i
\(33\) 47.9126 + 55.2941i 0.252743 + 0.291681i
\(34\) −50.0648 + 32.1747i −0.252531 + 0.162292i
\(35\) −89.8087 + 57.7166i −0.433727 + 0.278739i
\(36\) 17.1798 + 19.8266i 0.0795362 + 0.0917896i
\(37\) −251.254 + 73.7748i −1.11638 + 0.327797i −0.787339 0.616520i \(-0.788542\pi\)
−0.329036 + 0.944317i \(0.606724\pi\)
\(38\) 1.45113 10.0928i 0.00619486 0.0430862i
\(39\) 259.691 299.699i 1.06625 1.23052i
\(40\) −45.6028 + 99.8562i −0.180261 + 0.394716i
\(41\) −110.653 32.4907i −0.421490 0.123761i 0.0641076 0.997943i \(-0.479580\pi\)
−0.485598 + 0.874182i \(0.661398\pi\)
\(42\) −9.68763 21.2130i −0.0355913 0.0779340i
\(43\) −50.2258 349.328i −0.178125 1.23888i −0.861097 0.508440i \(-0.830222\pi\)
0.682972 0.730444i \(-0.260687\pi\)
\(44\) 86.2226 + 55.4119i 0.295422 + 0.189856i
\(45\) −45.0899 −0.149369
\(46\) 57.5026 + 7.69176i 0.184311 + 0.0246541i
\(47\) 385.301 1.19579 0.597893 0.801576i \(-0.296005\pi\)
0.597893 + 0.801576i \(0.296005\pi\)
\(48\) 266.401 + 171.206i 0.801077 + 0.514821i
\(49\) 39.6095 + 275.490i 0.115480 + 0.803178i
\(50\) −11.1891 24.5006i −0.0316475 0.0692983i
\(51\) −598.569 175.756i −1.64346 0.482563i
\(52\) 230.772 505.320i 0.615430 1.34760i
\(53\) 182.779 210.939i 0.473711 0.546692i −0.467729 0.883872i \(-0.654928\pi\)
0.941440 + 0.337180i \(0.109473\pi\)
\(54\) −9.74053 + 67.7469i −0.0245466 + 0.170726i
\(55\) −169.023 + 49.6296i −0.414383 + 0.121674i
\(56\) −43.5528 50.2627i −0.103928 0.119940i
\(57\) 89.9187 57.7873i 0.208948 0.134283i
\(58\) 34.1008 21.9153i 0.0772009 0.0496140i
\(59\) −329.991 380.830i −0.728155 0.840336i 0.264107 0.964493i \(-0.414923\pi\)
−0.992263 + 0.124158i \(0.960377\pi\)
\(60\) −542.349 + 159.248i −1.16695 + 0.342647i
\(61\) −91.6114 + 637.171i −0.192289 + 1.33740i 0.633641 + 0.773627i \(0.281560\pi\)
−0.825930 + 0.563773i \(0.809349\pi\)
\(62\) 82.7380 95.4848i 0.169480 0.195590i
\(63\) 11.3480 24.8487i 0.0226939 0.0496927i
\(64\) 392.255 + 115.177i 0.766124 + 0.224954i
\(65\) 396.637 + 868.514i 0.756873 + 1.65732i
\(66\) −5.47643 38.0894i −0.0102137 0.0710376i
\(67\) 397.284 + 255.319i 0.724417 + 0.465554i 0.850171 0.526507i \(-0.176499\pi\)
−0.125754 + 0.992061i \(0.540135\pi\)
\(68\) −873.908 −1.55848
\(69\) 333.797 + 508.347i 0.582384 + 0.886924i
\(70\) 56.1486 0.0958719
\(71\) 141.871 + 91.1751i 0.237141 + 0.152401i 0.653814 0.756655i \(-0.273168\pi\)
−0.416673 + 0.909056i \(0.636804\pi\)
\(72\) −3.99765 27.8043i −0.00654345 0.0455107i
\(73\) −277.140 606.852i −0.444340 0.972968i −0.990781 0.135471i \(-0.956745\pi\)
0.546442 0.837497i \(-0.315982\pi\)
\(74\) 132.148 + 38.8021i 0.207593 + 0.0609547i
\(75\) 117.290 256.829i 0.180580 0.395414i
\(76\) 98.0541 113.160i 0.147994 0.170795i
\(77\) 15.1884 105.638i 0.0224790 0.156345i
\(78\) −200.123 + 58.7613i −0.290506 + 0.0853001i
\(79\) −541.565 625.000i −0.771277 0.890101i 0.225170 0.974319i \(-0.427706\pi\)
−0.996447 + 0.0842184i \(0.973161\pi\)
\(80\) −641.415 + 412.212i −0.896405 + 0.576084i
\(81\) −680.721 + 437.473i −0.933773 + 0.600100i
\(82\) 39.7208 + 45.8402i 0.0534930 + 0.0617342i
\(83\) 789.153 231.716i 1.04362 0.306435i 0.285385 0.958413i \(-0.407879\pi\)
0.758238 + 0.651977i \(0.226060\pi\)
\(84\) 48.7355 338.963i 0.0633034 0.440285i
\(85\) 983.613 1135.15i 1.25515 1.44852i
\(86\) −77.1091 + 168.845i −0.0966848 + 0.211710i
\(87\) 407.705 + 119.713i 0.502420 + 0.147524i
\(88\) −45.5892 99.8264i −0.0552253 0.120927i
\(89\) −80.1047 557.140i −0.0954054 0.663559i −0.980263 0.197698i \(-0.936654\pi\)
0.884858 0.465861i \(-0.154256\pi\)
\(90\) 19.9505 + 12.8214i 0.0233663 + 0.0150166i
\(91\) −578.454 −0.666357
\(92\) 649.288 + 551.536i 0.735793 + 0.625018i
\(93\) 1324.41 1.47672
\(94\) −170.480 109.561i −0.187061 0.120217i
\(95\) 36.6249 + 254.732i 0.0395541 + 0.275105i
\(96\) −220.712 483.292i −0.234649 0.513810i
\(97\) −20.4753 6.01210i −0.0214325 0.00629316i 0.270999 0.962580i \(-0.412646\pi\)
−0.292431 + 0.956287i \(0.594464\pi\)
\(98\) 60.8104 133.156i 0.0626814 0.137253i
\(99\) 29.5188 34.0665i 0.0299672 0.0345840i
\(100\) 56.2888 391.497i 0.0562888 0.391497i
\(101\) −1466.13 + 430.496i −1.44441 + 0.424118i −0.907690 0.419641i \(-0.862156\pi\)
−0.536723 + 0.843759i \(0.680338\pi\)
\(102\) 214.866 + 247.969i 0.208578 + 0.240711i
\(103\) −894.637 + 574.948i −0.855837 + 0.550013i −0.893390 0.449282i \(-0.851680\pi\)
0.0375532 + 0.999295i \(0.488044\pi\)
\(104\) −500.396 + 321.585i −0.471806 + 0.303211i
\(105\) 385.438 + 444.819i 0.358237 + 0.413427i
\(106\) −140.853 + 41.3583i −0.129065 + 0.0378969i
\(107\) 30.5515 212.491i 0.0276031 0.191984i −0.971354 0.237636i \(-0.923628\pi\)
0.998957 + 0.0456522i \(0.0145366\pi\)
\(108\) −658.175 + 759.575i −0.586416 + 0.676760i
\(109\) 600.455 1314.81i 0.527644 1.15538i −0.438819 0.898575i \(-0.644603\pi\)
0.966463 0.256804i \(-0.0826695\pi\)
\(110\) 88.8981 + 26.1028i 0.0770555 + 0.0226255i
\(111\) 599.745 + 1313.26i 0.512841 + 1.12296i
\(112\) −65.7386 457.222i −0.0554618 0.385745i
\(113\) 455.602 + 292.798i 0.379287 + 0.243753i 0.716368 0.697723i \(-0.245803\pi\)
−0.337081 + 0.941476i \(0.609440\pi\)
\(114\) −56.2173 −0.0461863
\(115\) −1447.21 + 222.611i −1.17350 + 0.180510i
\(116\) 595.248 0.476443
\(117\) −205.534 132.089i −0.162407 0.104373i
\(118\) 37.7181 + 262.335i 0.0294257 + 0.204660i
\(119\) 378.021 + 827.750i 0.291203 + 0.637645i
\(120\) 580.717 + 170.514i 0.441766 + 0.129714i
\(121\) −479.760 + 1050.53i −0.360451 + 0.789278i
\(122\) 221.715 255.873i 0.164534 0.189882i
\(123\) −90.4868 + 629.350i −0.0663327 + 0.461354i
\(124\) 1780.16 522.701i 1.28922 0.378548i
\(125\) −641.440 740.262i −0.458977 0.529688i
\(126\) −12.0868 + 7.76771i −0.00854585 + 0.00549209i
\(127\) 436.222 280.343i 0.304791 0.195877i −0.379300 0.925274i \(-0.623835\pi\)
0.684091 + 0.729396i \(0.260199\pi\)
\(128\) −645.665 745.137i −0.445853 0.514542i
\(129\) −1866.95 + 548.185i −1.27423 + 0.374147i
\(130\) 71.4674 497.067i 0.0482162 0.335351i
\(131\) 559.638 645.856i 0.373250 0.430754i −0.537785 0.843082i \(-0.680739\pi\)
0.911035 + 0.412328i \(0.135284\pi\)
\(132\) 234.742 514.012i 0.154785 0.338932i
\(133\) −149.598 43.9260i −0.0975325 0.0286381i
\(134\) −103.182 225.936i −0.0665190 0.145656i
\(135\) −245.840 1709.85i −0.156730 1.09008i
\(136\) 787.187 + 505.895i 0.496329 + 0.318971i
\(137\) 77.0997 0.0480808 0.0240404 0.999711i \(-0.492347\pi\)
0.0240404 + 0.999711i \(0.492347\pi\)
\(138\) −3.14263 319.839i −0.00193854 0.197293i
\(139\) −396.171 −0.241747 −0.120873 0.992668i \(-0.538570\pi\)
−0.120873 + 0.992668i \(0.538570\pi\)
\(140\) 693.626 + 445.767i 0.418730 + 0.269101i
\(141\) −302.318 2102.67i −0.180566 1.25586i
\(142\) −36.8465 80.6826i −0.0217753 0.0476812i
\(143\) −915.848 268.917i −0.535574 0.157259i
\(144\) 81.0476 177.469i 0.0469025 0.102702i
\(145\) −669.972 + 773.189i −0.383711 + 0.442826i
\(146\) −49.9360 + 347.313i −0.0283064 + 0.196875i
\(147\) 1472.33 432.314i 0.826092 0.242562i
\(148\) 1324.42 + 1528.47i 0.735588 + 0.848914i
\(149\) 2165.16 1391.46i 1.19045 0.765055i 0.213170 0.977015i \(-0.431621\pi\)
0.977278 + 0.211960i \(0.0679848\pi\)
\(150\) −124.926 + 80.2849i −0.0680010 + 0.0437016i
\(151\) 1592.37 + 1837.69i 0.858180 + 0.990392i 1.00000 0.000499681i \(0.000159053\pi\)
−0.141820 + 0.989892i \(0.545295\pi\)
\(152\) −153.831 + 45.1689i −0.0820878 + 0.0241032i
\(153\) −54.6980 + 380.433i −0.0289024 + 0.201021i
\(154\) −36.7585 + 42.4216i −0.0192343 + 0.0221976i
\(155\) −1324.67 + 2900.63i −0.686453 + 1.50312i
\(156\) −2938.71 862.883i −1.50824 0.442858i
\(157\) −1337.01 2927.64i −0.679650 1.48822i −0.863014 0.505180i \(-0.831426\pi\)
0.183365 0.983045i \(-0.441301\pi\)
\(158\) 61.9012 + 430.532i 0.0311683 + 0.216780i
\(159\) −1294.55 831.957i −0.645688 0.414959i
\(160\) 1279.23 0.632073
\(161\) 241.547 853.569i 0.118239 0.417830i
\(162\) 425.587 0.206403
\(163\) 473.856 + 304.529i 0.227701 + 0.146335i 0.649517 0.760347i \(-0.274971\pi\)
−0.421816 + 0.906681i \(0.638607\pi\)
\(164\) 126.759 + 881.628i 0.0603550 + 0.419778i
\(165\) 403.459 + 883.453i 0.190359 + 0.416828i
\(166\) −415.057 121.872i −0.194064 0.0569824i
\(167\) 97.5134 213.525i 0.0451845 0.0989403i −0.885694 0.464270i \(-0.846317\pi\)
0.930878 + 0.365330i \(0.119044\pi\)
\(168\) −240.121 + 277.114i −0.110272 + 0.127261i
\(169\) −423.607 + 2946.25i −0.192811 + 1.34103i
\(170\) −757.991 + 222.566i −0.341972 + 0.100412i
\(171\) −43.1242 49.7680i −0.0192853 0.0222565i
\(172\) −2293.03 + 1473.64i −1.01652 + 0.653281i
\(173\) 1927.54 1238.76i 0.847100 0.544398i −0.0435687 0.999050i \(-0.513873\pi\)
0.890669 + 0.454652i \(0.150236\pi\)
\(174\) −146.353 168.900i −0.0637641 0.0735877i
\(175\) −395.168 + 116.032i −0.170696 + 0.0501210i
\(176\) 108.476 754.466i 0.0464584 0.323125i
\(177\) −1819.35 + 2099.64i −0.772601 + 0.891630i
\(178\) −122.981 + 269.290i −0.0517853 + 0.113394i
\(179\) 2025.63 + 594.777i 0.845823 + 0.248356i 0.675801 0.737084i \(-0.263798\pi\)
0.170022 + 0.985440i \(0.445616\pi\)
\(180\) 144.667 + 316.776i 0.0599045 + 0.131173i
\(181\) 115.164 + 800.981i 0.0472931 + 0.328931i 0.999709 + 0.0241288i \(0.00768118\pi\)
−0.952416 + 0.304802i \(0.901410\pi\)
\(182\) 255.943 + 164.484i 0.104240 + 0.0669912i
\(183\) 3549.06 1.43363
\(184\) −265.580 872.671i −0.106407 0.349642i
\(185\) −3476.06 −1.38143
\(186\) −585.999 376.598i −0.231008 0.148460i
\(187\) 213.696 + 1486.29i 0.0835668 + 0.581220i
\(188\) −1236.20 2706.91i −0.479571 1.05011i
\(189\) 1004.16 + 294.848i 0.386464 + 0.113476i
\(190\) 56.2284 123.123i 0.0214697 0.0470120i
\(191\) 32.5332 37.5453i 0.0123247 0.0142235i −0.749554 0.661943i \(-0.769732\pi\)
0.761878 + 0.647720i \(0.224277\pi\)
\(192\) 320.768 2230.99i 0.120570 0.838582i
\(193\) −164.227 + 48.2213i −0.0612502 + 0.0179847i −0.312214 0.950012i \(-0.601071\pi\)
0.250964 + 0.967996i \(0.419252\pi\)
\(194\) 7.34996 + 8.48231i 0.00272009 + 0.00313915i
\(195\) 4428.45 2845.99i 1.62630 1.04516i
\(196\) 1808.35 1162.16i 0.659020 0.423527i
\(197\) −1856.72 2142.77i −0.671503 0.774956i 0.313108 0.949718i \(-0.398630\pi\)
−0.984611 + 0.174762i \(0.944084\pi\)
\(198\) −22.7477 + 6.67934i −0.00816471 + 0.00239737i
\(199\) −136.478 + 949.222i −0.0486163 + 0.338134i 0.950968 + 0.309290i \(0.100091\pi\)
−0.999584 + 0.0288433i \(0.990818\pi\)
\(200\) −277.336 + 320.063i −0.0980531 + 0.113159i
\(201\) 1081.61 2368.39i 0.379555 0.831111i
\(202\) 771.117 + 226.420i 0.268592 + 0.0788657i
\(203\) −257.483 563.808i −0.0890234 0.194934i
\(204\) 685.692 + 4769.10i 0.235334 + 1.63678i
\(205\) −1287.85 827.651i −0.438768 0.281979i
\(206\) 559.328 0.189176
\(207\) 280.736 248.130i 0.0942632 0.0833151i
\(208\) −4131.33 −1.37719
\(209\) −216.433 139.093i −0.0716316 0.0460348i
\(210\) −44.0557 306.414i −0.0144768 0.100689i
\(211\) 792.137 + 1734.54i 0.258450 + 0.565926i 0.993726 0.111841i \(-0.0356748\pi\)
−0.735276 + 0.677768i \(0.762948\pi\)
\(212\) −2068.36 607.327i −0.670075 0.196752i
\(213\) 386.245 845.759i 0.124249 0.272068i
\(214\) −73.9399 + 85.3312i −0.0236188 + 0.0272576i
\(215\) 666.720 4637.14i 0.211488 1.47093i
\(216\) 1032.57 303.190i 0.325266 0.0955068i
\(217\) −1265.12 1460.03i −0.395771 0.456744i
\(218\) −639.547 + 411.012i −0.198695 + 0.127694i
\(219\) −3094.26 + 1988.56i −0.954754 + 0.613583i
\(220\) 890.964 + 1028.23i 0.273040 + 0.315105i
\(221\) 7808.98 2292.92i 2.37687 0.697913i
\(222\) 108.064 751.603i 0.0326702 0.227226i
\(223\) −1812.55 + 2091.80i −0.544294 + 0.628149i −0.959544 0.281558i \(-0.909149\pi\)
0.415250 + 0.909707i \(0.363694\pi\)
\(224\) −321.949 + 704.971i −0.0960319 + 0.210281i
\(225\) −166.905 49.0077i −0.0494533 0.0145208i
\(226\) −118.328 259.102i −0.0348277 0.0762621i
\(227\) 661.017 + 4597.48i 0.193274 + 1.34425i 0.823268 + 0.567652i \(0.192148\pi\)
−0.629994 + 0.776600i \(0.716943\pi\)
\(228\) −694.476 446.313i −0.201723 0.129639i
\(229\) −1988.68 −0.573868 −0.286934 0.957950i \(-0.592636\pi\)
−0.286934 + 0.957950i \(0.592636\pi\)
\(230\) 703.630 + 313.019i 0.201722 + 0.0897385i
\(231\) −588.404 −0.167594
\(232\) −536.180 344.582i −0.151732 0.0975125i
\(233\) 57.8677 + 402.479i 0.0162706 + 0.113164i 0.996338 0.0855000i \(-0.0272488\pi\)
−0.980068 + 0.198664i \(0.936340\pi\)
\(234\) 53.3809 + 116.888i 0.0149129 + 0.0326547i
\(235\) 4907.49 + 1440.97i 1.36225 + 0.399993i
\(236\) −1616.75 + 3540.18i −0.445938 + 0.976467i
\(237\) −2985.83 + 3445.83i −0.818355 + 0.944433i
\(238\) 68.1131 473.737i 0.0185509 0.129024i
\(239\) −3412.32 + 1001.95i −0.923534 + 0.271174i −0.708727 0.705482i \(-0.750730\pi\)
−0.214807 + 0.976657i \(0.568912\pi\)
\(240\) 2752.80 + 3176.90i 0.740385 + 0.854450i
\(241\) −4.21781 + 2.71062i −0.00112736 + 0.000724509i −0.541204 0.840891i \(-0.682031\pi\)
0.540077 + 0.841616i \(0.318395\pi\)
\(242\) 510.994 328.396i 0.135735 0.0872318i
\(243\) 620.588 + 716.197i 0.163830 + 0.189070i
\(244\) 4770.33 1400.69i 1.25159 0.367501i
\(245\) −525.794 + 3656.98i −0.137109 + 0.953616i
\(246\) 218.993 252.732i 0.0567582 0.0655024i
\(247\) −579.277 + 1268.44i −0.149225 + 0.326757i
\(248\) −1906.09 559.679i −0.488052 0.143305i
\(249\) −1883.71 4124.76i −0.479420 1.04978i
\(250\) 73.3169 + 509.931i 0.0185479 + 0.129003i
\(251\) −5760.66 3702.15i −1.44864 0.930987i −0.999292 0.0376328i \(-0.988018\pi\)
−0.449353 0.893354i \(-0.648345\pi\)
\(252\) −210.982 −0.0527404
\(253\) 779.248 1239.14i 0.193640 0.307920i
\(254\) −272.727 −0.0673717
\(255\) −6966.52 4477.11i −1.71082 1.09948i
\(256\) −391.644 2723.94i −0.0956162 0.665025i
\(257\) 3258.01 + 7134.05i 0.790774 + 1.73155i 0.674421 + 0.738347i \(0.264393\pi\)
0.116353 + 0.993208i \(0.462880\pi\)
\(258\) 981.926 + 288.320i 0.236946 + 0.0695736i
\(259\) 874.839 1915.63i 0.209884 0.459581i
\(260\) 4829.11 5573.09i 1.15188 1.32934i
\(261\) 37.2566 259.126i 0.00883574 0.0614539i
\(262\) −431.267 + 126.632i −0.101694 + 0.0298600i
\(263\) −836.090 964.900i −0.196029 0.226229i 0.649222 0.760599i \(-0.275095\pi\)
−0.845251 + 0.534370i \(0.820549\pi\)
\(264\) −509.003 + 327.116i −0.118663 + 0.0762599i
\(265\) 3116.89 2003.11i 0.722525 0.464339i
\(266\) 53.7008 + 61.9740i 0.0123782 + 0.0142852i
\(267\) −2977.58 + 874.296i −0.682490 + 0.200397i
\(268\) 519.076 3610.25i 0.118312 0.822878i
\(269\) 135.930 156.871i 0.0308095 0.0355561i −0.740136 0.672458i \(-0.765239\pi\)
0.770945 + 0.636901i \(0.219784\pi\)
\(270\) −377.425 + 826.447i −0.0850718 + 0.186281i
\(271\) 2765.19 + 811.934i 0.619829 + 0.181998i 0.576546 0.817065i \(-0.304400\pi\)
0.0432829 + 0.999063i \(0.486218\pi\)
\(272\) 2699.83 + 5911.80i 0.601843 + 1.31785i
\(273\) 453.871 + 3156.74i 0.100621 + 0.699835i
\(274\) −34.1135 21.9234i −0.00752143 0.00483373i
\(275\) −679.598 −0.149023
\(276\) 2500.40 3976.05i 0.545312 0.867138i
\(277\) 722.581 0.156735 0.0783676 0.996925i \(-0.475029\pi\)
0.0783676 + 0.996925i \(0.475029\pi\)
\(278\) 175.290 + 112.652i 0.0378172 + 0.0243036i
\(279\) −116.124 807.660i −0.0249181 0.173309i
\(280\) −366.747 803.064i −0.0782761 0.171401i
\(281\) 4765.27 + 1399.21i 1.01165 + 0.297046i 0.745226 0.666812i \(-0.232341\pi\)
0.266419 + 0.963857i \(0.414160\pi\)
\(282\) −464.134 + 1016.31i −0.0980098 + 0.214611i
\(283\) 830.070 957.952i 0.174355 0.201217i −0.661845 0.749640i \(-0.730226\pi\)
0.836201 + 0.548424i \(0.184772\pi\)
\(284\) 185.364 1289.23i 0.0387300 0.269373i
\(285\) 1361.39 399.740i 0.282953 0.0830826i
\(286\) 328.759 + 379.408i 0.0679717 + 0.0784435i
\(287\) 780.232 501.424i 0.160473 0.103129i
\(288\) −275.372 + 176.971i −0.0563418 + 0.0362087i
\(289\) −5166.96 5962.99i −1.05169 1.21372i
\(290\) 516.293 151.597i 0.104544 0.0306969i
\(291\) −16.7438 + 116.455i −0.00337298 + 0.0234596i
\(292\) −3374.22 + 3894.05i −0.676237 + 0.780419i
\(293\) 849.042 1859.14i 0.169289 0.370690i −0.805905 0.592045i \(-0.798321\pi\)
0.975193 + 0.221355i \(0.0710479\pi\)
\(294\) −774.375 227.377i −0.153614 0.0451051i
\(295\) −2778.77 6084.65i −0.548427 1.20089i
\(296\) −308.187 2143.49i −0.0605168 0.420904i
\(297\) 1452.78 + 933.645i 0.283834 + 0.182409i
\(298\) −1353.66 −0.263139
\(299\) −7248.95 3224.79i −1.40207 0.623727i
\(300\) −2180.65 −0.419666
\(301\) 2387.69 + 1534.48i 0.457224 + 0.293840i
\(302\) −182.009 1265.90i −0.0346802 0.241206i
\(303\) 3499.67 + 7663.21i 0.663534 + 1.45294i
\(304\) −1068.43 313.720i −0.201575 0.0591878i
\(305\) −3549.75 + 7772.87i −0.666421 + 1.45926i
\(306\) 132.378 152.773i 0.0247306 0.0285406i
\(307\) 489.131 3401.98i 0.0909323 0.632448i −0.892483 0.451081i \(-0.851039\pi\)
0.983415 0.181367i \(-0.0580522\pi\)
\(308\) −790.881 + 232.224i −0.146314 + 0.0429616i
\(309\) 3839.57 + 4431.10i 0.706878 + 0.815781i
\(310\) 1410.91 906.738i 0.258498 0.166127i
\(311\) 744.085 478.194i 0.135669 0.0871894i −0.471046 0.882109i \(-0.656123\pi\)
0.606715 + 0.794919i \(0.292487\pi\)
\(312\) 2147.58 + 2478.44i 0.389688 + 0.449724i
\(313\) −2271.53 + 666.982i −0.410207 + 0.120448i −0.480324 0.877091i \(-0.659481\pi\)
0.0701172 + 0.997539i \(0.477663\pi\)
\(314\) −240.907 + 1675.54i −0.0432967 + 0.301135i
\(315\) 237.467 274.051i 0.0424754 0.0490192i
\(316\) −2653.33 + 5809.98i −0.472346 + 1.03429i
\(317\) 199.581 + 58.6024i 0.0353615 + 0.0103831i 0.299365 0.954139i \(-0.403225\pi\)
−0.264004 + 0.964522i \(0.585043\pi\)
\(318\) 336.218 + 736.215i 0.0592898 + 0.129827i
\(319\) −145.555 1012.36i −0.0255471 0.177684i
\(320\) 4565.31 + 2933.95i 0.797527 + 0.512540i
\(321\) −1183.58 −0.205797
\(322\) −349.588 + 308.986i −0.0605025 + 0.0534755i
\(323\) 2193.66 0.377889
\(324\) 5257.46 + 3378.76i 0.901485 + 0.579349i
\(325\) 524.215 + 3645.99i 0.0894714 + 0.622287i
\(326\) −123.069 269.484i −0.0209085 0.0457832i
\(327\) −7646.35 2245.17i −1.29310 0.379689i
\(328\) 396.184 867.521i 0.0666938 0.146039i
\(329\) −2029.20 + 2341.82i −0.340041 + 0.392428i
\(330\) 72.6967 505.616i 0.0121267 0.0843432i
\(331\) 8247.64 2421.73i 1.36958 0.402145i 0.487451 0.873150i \(-0.337927\pi\)
0.882131 + 0.471005i \(0.156109\pi\)
\(332\) −4159.83 4800.69i −0.687651 0.793591i
\(333\) 748.274 480.886i 0.123139 0.0791364i
\(334\) −103.862 + 66.7479i −0.0170152 + 0.0109350i
\(335\) 4105.25 + 4737.71i 0.669533 + 0.772682i
\(336\) −2443.58 + 717.498i −0.396750 + 0.116496i
\(337\) 199.874 1390.15i 0.0323080 0.224707i −0.967270 0.253749i \(-0.918336\pi\)
0.999578 + 0.0290414i \(0.00924547\pi\)
\(338\) 1025.20 1183.14i 0.164981 0.190398i
\(339\) 1240.38 2716.05i 0.198726 0.435150i
\(340\) −11130.7 3268.28i −1.77544 0.521316i
\(341\) −1324.28 2899.76i −0.210304 0.460501i
\(342\) 4.92912 + 34.2828i 0.000779346 + 0.00542047i
\(343\) −4203.58 2701.48i −0.661726 0.425265i
\(344\) 2918.56 0.457437
\(345\) 2350.35 + 7723.04i 0.366779 + 1.20520i
\(346\) −1205.10 −0.187245
\(347\) −2389.53 1535.66i −0.369673 0.237574i 0.342593 0.939484i \(-0.388695\pi\)
−0.712266 + 0.701909i \(0.752331\pi\)
\(348\) −467.048 3248.39i −0.0719437 0.500379i
\(349\) −3054.69 6688.84i −0.468521 1.02592i −0.985462 0.169896i \(-0.945657\pi\)
0.516941 0.856021i \(-0.327071\pi\)
\(350\) 207.840 + 61.0272i 0.0317414 + 0.00932012i
\(351\) 3888.32 8514.23i 0.591291 1.29475i
\(352\) −837.465 + 966.486i −0.126810 + 0.146346i
\(353\) −1730.05 + 12032.8i −0.260853 + 1.81428i 0.265613 + 0.964080i \(0.414426\pi\)
−0.526466 + 0.850196i \(0.676483\pi\)
\(354\) 1402.02 411.671i 0.210499 0.0618081i
\(355\) 1466.00 + 1691.85i 0.219175 + 0.252941i
\(356\) −3657.14 + 2350.30i −0.544461 + 0.349904i
\(357\) 4220.60 2712.41i 0.625708 0.402118i
\(358\) −727.132 839.155i −0.107347 0.123885i
\(359\) −817.789 + 240.124i −0.120226 + 0.0353016i −0.341292 0.939957i \(-0.610865\pi\)
0.221066 + 0.975259i \(0.429046\pi\)
\(360\) 53.0667 369.087i 0.00776906 0.0540350i
\(361\) 4245.56 4899.63i 0.618976 0.714337i
\(362\) 176.805 387.149i 0.0256703 0.0562102i
\(363\) 6109.38 + 1793.88i 0.883359 + 0.259378i
\(364\) 1855.92 + 4063.89i 0.267243 + 0.585180i
\(365\) −1260.33 8765.78i −0.180736 1.25705i
\(366\) −1570.31 1009.18i −0.224267 0.144127i
\(367\) 13521.3 1.92318 0.961591 0.274485i \(-0.0885074\pi\)
0.961591 + 0.274485i \(0.0885074\pi\)
\(368\) 1725.13 6096.20i 0.244371 0.863550i
\(369\) 391.728 0.0552643
\(370\) 1538.02 + 988.424i 0.216102 + 0.138880i
\(371\) 319.450 + 2221.83i 0.0447036 + 0.310920i
\(372\) −4249.25 9304.55i −0.592240 1.29682i
\(373\) 2122.39 + 623.191i 0.294620 + 0.0865083i 0.425702 0.904863i \(-0.360027\pi\)
−0.131082 + 0.991371i \(0.541845\pi\)
\(374\) 328.076 718.387i 0.0453594 0.0993233i
\(375\) −3536.47 + 4081.30i −0.486993 + 0.562020i
\(376\) −453.465 + 3153.92i −0.0621959 + 0.432582i
\(377\) −5318.96 + 1561.79i −0.726632 + 0.213359i
\(378\) −360.459 415.992i −0.0490477 0.0566041i
\(379\) 801.072 514.818i 0.108571 0.0697742i −0.485229 0.874387i \(-0.661264\pi\)
0.593799 + 0.804613i \(0.297627\pi\)
\(380\) 1672.09 1074.59i 0.225728 0.145066i
\(381\) −1872.16 2160.59i −0.251742 0.290526i
\(382\) −25.0707 + 7.36141i −0.00335792 + 0.000985976i
\(383\) 552.466 3842.48i 0.0737067 0.512641i −0.919204 0.393781i \(-0.871167\pi\)
0.992911 0.118860i \(-0.0379241\pi\)
\(384\) −3559.76 + 4108.18i −0.473068 + 0.545950i
\(385\) 588.520 1288.68i 0.0779059 0.170590i
\(386\) 86.3755 + 25.3621i 0.0113896 + 0.00334430i
\(387\) 497.991 + 1090.45i 0.0654116 + 0.143231i
\(388\) 23.4556 + 163.137i 0.00306901 + 0.0213455i
\(389\) 7420.55 + 4768.90i 0.967189 + 0.621575i 0.925979 0.377576i \(-0.123242\pi\)
0.0412106 + 0.999150i \(0.486879\pi\)
\(390\) −2768.67 −0.359480
\(391\) 122.629 + 12480.4i 0.0158609 + 1.61423i
\(392\) −2301.66 −0.296560
\(393\) −3963.68 2547.30i −0.508756 0.326958i
\(394\) 212.224 + 1476.05i 0.0271363 + 0.188737i
\(395\) −4560.38 9985.84i −0.580905 1.27201i
\(396\) −334.040 98.0830i −0.0423893 0.0124466i
\(397\) −876.282 + 1918.79i −0.110779 + 0.242573i −0.956899 0.290419i \(-0.906205\pi\)
0.846120 + 0.532992i \(0.178932\pi\)
\(398\) 330.299 381.185i 0.0415989 0.0480077i
\(399\) −122.334 + 850.854i −0.0153493 + 0.106757i
\(400\) −2822.29 + 828.700i −0.352787 + 0.103587i
\(401\) −3887.12 4485.98i −0.484074 0.558651i 0.460198 0.887816i \(-0.347778\pi\)
−0.944273 + 0.329165i \(0.893233\pi\)
\(402\) −1152.02 + 740.360i −0.142929 + 0.0918552i
\(403\) −14535.5 + 9341.41i −1.79669 + 1.15466i
\(404\) 7728.36 + 8919.01i 0.951734 + 1.09836i
\(405\) −10306.2 + 3026.19i −1.26450 + 0.371290i
\(406\) −46.3941 + 322.678i −0.00567119 + 0.0394440i
\(407\) 2275.66 2626.25i 0.277151 0.319849i
\(408\) 2143.12 4692.78i 0.260050 0.569430i
\(409\) 7236.21 + 2124.74i 0.874836 + 0.256875i 0.688171 0.725549i \(-0.258414\pi\)
0.186665 + 0.982424i \(0.440232\pi\)
\(410\) 334.478 + 732.404i 0.0402895 + 0.0882217i
\(411\) −60.4946 420.749i −0.00726029 0.0504964i
\(412\) 6909.62 + 4440.54i 0.826244 + 0.530995i
\(413\) 4052.55 0.482840
\(414\) −194.770 + 29.9598i −0.0231218 + 0.00355663i
\(415\) 10917.8 1.29141
\(416\) 5831.11 + 3747.43i 0.687245 + 0.441665i
\(417\) 310.847 + 2161.99i 0.0365042 + 0.253892i
\(418\) 56.2116 + 123.086i 0.00657751 + 0.0144027i
\(419\) −12771.8 3750.15i −1.48913 0.437248i −0.566866 0.823810i \(-0.691844\pi\)
−0.922263 + 0.386563i \(0.873662\pi\)
\(420\) 1888.40 4135.02i 0.219392 0.480401i
\(421\) −8078.67 + 9323.28i −0.935226 + 1.07931i 0.0614718 + 0.998109i \(0.480421\pi\)
−0.996698 + 0.0811996i \(0.974125\pi\)
\(422\) 142.730 992.708i 0.0164644 0.114513i
\(423\) −1255.75 + 368.723i −0.144343 + 0.0423828i
\(424\) 1511.54 + 1744.41i 0.173129 + 0.199802i
\(425\) 4874.73 3132.80i 0.556374 0.357560i
\(426\) −411.391 + 264.385i −0.0467886 + 0.0300692i
\(427\) −3390.18 3912.48i −0.384221 0.443415i
\(428\) −1590.86 + 467.118i −0.179666 + 0.0527547i
\(429\) −748.937 + 5208.97i −0.0842867 + 0.586227i
\(430\) −1613.58 + 1862.16i −0.180962 + 0.208841i
\(431\) 1149.70 2517.50i 0.128490 0.281354i −0.834443 0.551094i \(-0.814210\pi\)
0.962933 + 0.269740i \(0.0869377\pi\)
\(432\) 7171.71 + 2105.80i 0.798725 + 0.234527i
\(433\) 1377.38 + 3016.05i 0.152870 + 0.334739i 0.970537 0.240953i \(-0.0774600\pi\)
−0.817667 + 0.575692i \(0.804733\pi\)
\(434\) 144.604 + 1005.75i 0.0159936 + 0.111238i
\(435\) 4745.13 + 3049.51i 0.523015 + 0.336121i
\(436\) −11163.6 −1.22624
\(437\) −1629.82 1384.45i −0.178410 0.151550i
\(438\) 1934.54 0.211041
\(439\) 5891.81 + 3786.44i 0.640548 + 0.411655i 0.820202 0.572075i \(-0.193861\pi\)
−0.179653 + 0.983730i \(0.557498\pi\)
\(440\) −207.323 1441.96i −0.0224630 0.156234i
\(441\) −392.730 859.958i −0.0424068 0.0928580i
\(442\) −4107.16 1205.97i −0.441985 0.129779i
\(443\) 1843.29 4036.23i 0.197691 0.432883i −0.784661 0.619925i \(-0.787163\pi\)
0.982352 + 0.187042i \(0.0598901\pi\)
\(444\) 7301.98 8426.93i 0.780488 0.900731i
\(445\) 1063.35 7395.74i 0.113275 0.787846i
\(446\) 1396.79 410.134i 0.148296 0.0435435i
\(447\) −9292.35 10723.9i −0.983251 1.13473i
\(448\) −2765.85 + 1777.51i −0.291684 + 0.187454i
\(449\) −3222.49 + 2070.97i −0.338705 + 0.217673i −0.698925 0.715195i \(-0.746338\pi\)
0.360220 + 0.932867i \(0.382702\pi\)
\(450\) 59.9133 + 69.1436i 0.00627631 + 0.00724325i
\(451\) 1468.42 431.167i 0.153315 0.0450175i
\(452\) 595.273 4140.21i 0.0619453 0.430839i
\(453\) 8779.24 10131.8i 0.910563 1.05085i
\(454\) 1014.83 2222.16i 0.104908 0.229716i
\(455\) −7367.63 2163.33i −0.759120 0.222898i
\(456\) 367.196 + 804.047i 0.0377095 + 0.0825723i
\(457\) −2134.87 14848.3i −0.218523 1.51986i −0.743495 0.668741i \(-0.766833\pi\)
0.524972 0.851119i \(-0.324076\pi\)
\(458\) 879.911 + 565.485i 0.0897720 + 0.0576929i
\(459\) −14724.6 −1.49736
\(460\) 6207.16 + 9453.02i 0.629153 + 0.958150i
\(461\) 2747.37 0.277566 0.138783 0.990323i \(-0.455681\pi\)
0.138783 + 0.990323i \(0.455681\pi\)
\(462\) 260.345 + 167.314i 0.0262172 + 0.0168488i
\(463\) 686.506 + 4774.75i 0.0689085 + 0.479269i 0.994830 + 0.101553i \(0.0323813\pi\)
−0.925922 + 0.377716i \(0.876710\pi\)
\(464\) −1838.94 4026.73i −0.183989 0.402879i
\(465\) 16868.7 + 4953.09i 1.68229 + 0.493966i
\(466\) 88.8414 194.536i 0.00883154 0.0193384i
\(467\) 8882.43 10250.9i 0.880150 1.01575i −0.119588 0.992824i \(-0.538157\pi\)
0.999737 0.0229232i \(-0.00729733\pi\)
\(468\) −268.543 + 1867.76i −0.0265244 + 0.184481i
\(469\) −3644.10 + 1070.00i −0.358782 + 0.105348i
\(470\) −1761.62 2033.02i −0.172889 0.199524i
\(471\) −14927.7 + 9593.45i −1.46036 + 0.938519i
\(472\) 3505.68 2252.96i 0.341869 0.219706i
\(473\) 3066.99 + 3539.50i 0.298141 + 0.344073i
\(474\) 2300.93 675.615i 0.222965 0.0654684i
\(475\) −141.294 + 982.724i −0.0136485 + 0.0949273i
\(476\) 4602.46 5311.52i 0.443179 0.511456i
\(477\) −393.843 + 862.396i −0.0378047 + 0.0827807i
\(478\) 1794.72 + 526.977i 0.171733 + 0.0504255i
\(479\) 6872.00 + 15047.6i 0.655511 + 1.43537i 0.886647 + 0.462447i \(0.153029\pi\)
−0.231136 + 0.972922i \(0.574244\pi\)
\(480\) −1003.72 6981.00i −0.0954441 0.663828i
\(481\) −15845.0 10183.0i −1.50202 0.965287i
\(482\) 2.63698 0.000249193
\(483\) −4847.63 648.436i −0.456676 0.0610867i
\(484\) 8919.68 0.837686
\(485\) −238.305 153.149i −0.0223111 0.0143385i
\(486\) −70.9335 493.353i −0.00662060 0.0460473i
\(487\) 7988.66 + 17492.7i 0.743328 + 1.62766i 0.778002 + 0.628262i \(0.216234\pi\)
−0.0346736 + 0.999399i \(0.511039\pi\)
\(488\) −5107.80 1499.78i −0.473810 0.139123i
\(489\) 1290.08 2824.87i 0.119303 0.261238i
\(490\) 1272.51 1468.56i 0.117319 0.135393i
\(491\) −2216.23 + 15414.2i −0.203701 + 1.41677i 0.589479 + 0.807784i \(0.299333\pi\)
−0.793180 + 0.608987i \(0.791576\pi\)
\(492\) 4711.77 1383.50i 0.431754 0.126774i
\(493\) 5710.82 + 6590.64i 0.521709 + 0.602084i
\(494\) 616.989 396.515i 0.0561937 0.0361135i
\(495\) 503.377 323.501i 0.0457073 0.0293743i
\(496\) −9035.53 10427.6i −0.817958 0.943974i
\(497\) −1301.32 + 382.102i −0.117449 + 0.0344862i
\(498\) −339.414 + 2360.68i −0.0305412 + 0.212419i
\(499\) 2943.58 3397.07i 0.264074 0.304757i −0.608192 0.793790i \(-0.708105\pi\)
0.872265 + 0.489033i \(0.162650\pi\)
\(500\) −3142.65 + 6881.45i −0.281088 + 0.615496i
\(501\) −1241.76 364.613i −0.110734 0.0325144i
\(502\) 1496.15 + 3276.11i 0.133021 + 0.291275i
\(503\) −565.301 3931.75i −0.0501104 0.348525i −0.999416 0.0341706i \(-0.989121\pi\)
0.949306 0.314355i \(-0.101788\pi\)
\(504\) 190.045 + 122.135i 0.0167962 + 0.0107943i
\(505\) −20283.8 −1.78736
\(506\) −697.136 + 326.687i −0.0612480 + 0.0287016i
\(507\) 16410.7 1.43752
\(508\) −3369.11 2165.19i −0.294252 0.189104i
\(509\) −1780.01 12380.3i −0.155005 1.07809i −0.907671 0.419683i \(-0.862141\pi\)
0.752666 0.658403i \(-0.228768\pi\)
\(510\) 1809.33 + 3961.88i 0.157095 + 0.343990i
\(511\) 5147.94 + 1511.57i 0.445659 + 0.130857i
\(512\) −3877.92 + 8491.46i −0.334730 + 0.732956i
\(513\) 1652.13 1906.66i 0.142190 0.164096i
\(514\) 587.039 4082.95i 0.0503759 0.350372i
\(515\) −13545.0 + 3977.17i −1.15896 + 0.340301i
\(516\) 9841.16 + 11357.3i 0.839598 + 0.968948i
\(517\) −4301.45 + 2764.37i −0.365914 + 0.235159i
\(518\) −931.794 + 598.828i −0.0790360 + 0.0507934i
\(519\) −8272.55 9547.04i −0.699662 0.807454i
\(520\) −7576.09 + 2224.54i −0.638911 + 0.187601i
\(521\) −2255.12 + 15684.7i −0.189633 + 1.31893i 0.643326 + 0.765592i \(0.277554\pi\)
−0.832959 + 0.553334i \(0.813355\pi\)
\(522\) −90.1673 + 104.059i −0.00756038 + 0.00872514i
\(523\) −2550.77 + 5585.41i −0.213265 + 0.466985i −0.985786 0.168004i \(-0.946268\pi\)
0.772522 + 0.634988i \(0.218995\pi\)
\(524\) −6332.96 1859.52i −0.527971 0.155026i
\(525\) 943.269 + 2065.47i 0.0784145 + 0.171704i
\(526\) 95.5655 + 664.673i 0.00792178 + 0.0550972i
\(527\) 22866.2 + 14695.2i 1.89007 + 1.21468i
\(528\) −4202.39 −0.346374
\(529\) 7785.47 9349.99i 0.639884 0.768471i
\(530\) −1948.69 −0.159709
\(531\) 1439.93 + 925.389i 0.117679 + 0.0756280i
\(532\) 171.373 + 1191.92i 0.0139661 + 0.0971362i
\(533\) −3445.86 7545.39i −0.280032 0.613184i
\(534\) 1566.07 + 459.838i 0.126911 + 0.0372643i
\(535\) 1183.81 2592.18i 0.0956646 0.209476i
\(536\) −2557.50 + 2951.51i −0.206095 + 0.237847i
\(537\) 1656.46 11520.9i 0.133113 0.925819i
\(538\) −104.750 + 30.7573i −0.00839421 + 0.00246476i
\(539\) −2418.72 2791.35i −0.193287 0.223065i
\(540\) −11223.7 + 7213.04i −0.894428 + 0.574814i
\(541\) −7266.42 + 4669.84i −0.577463 + 0.371113i −0.796532 0.604596i \(-0.793334\pi\)
0.219069 + 0.975709i \(0.429698\pi\)
\(542\) −992.612 1145.54i −0.0786649 0.0907841i
\(543\) 4280.76 1256.94i 0.338315 0.0993382i
\(544\) 1551.81 10793.1i 0.122304 0.850643i
\(545\) 12565.1 14500.8i 0.987574 1.13972i
\(546\) 696.806 1525.79i 0.0546164 0.119593i
\(547\) 10632.6 + 3122.01i 0.831110 + 0.244036i 0.669494 0.742818i \(-0.266511\pi\)
0.161616 + 0.986854i \(0.448329\pi\)
\(548\) −247.367 541.658i −0.0192828 0.0422235i
\(549\) −311.180 2164.31i −0.0241910 0.168252i
\(550\) 300.695 + 193.245i 0.0233121 + 0.0149818i
\(551\) −1494.17 −0.115524
\(552\) −4553.96 + 2134.05i −0.351140 + 0.164549i
\(553\) 6650.85 0.511434
\(554\) −319.713 205.467i −0.0245186 0.0157571i
\(555\) 2727.42 + 18969.6i 0.208599 + 1.45084i
\(556\) 1271.08 + 2783.27i 0.0969527 + 0.212297i
\(557\) −19394.0 5694.60i −1.47532 0.433192i −0.557493 0.830182i \(-0.688237\pi\)
−0.917823 + 0.396990i \(0.870055\pi\)
\(558\) −178.279 + 390.377i −0.0135254 + 0.0296165i
\(559\) 16623.4 19184.4i 1.25777 1.45155i
\(560\) 872.644 6069.38i 0.0658499 0.457996i
\(561\) 7943.30 2332.36i 0.597801 0.175530i
\(562\) −1710.57 1974.11i −0.128392 0.148172i
\(563\) 19417.5 12478.9i 1.45355 0.934142i 0.454495 0.890749i \(-0.349820\pi\)
0.999058 0.0433924i \(-0.0138166\pi\)
\(564\) −13802.2 + 8870.13i −1.03046 + 0.662234i
\(565\) 4707.87 + 5433.17i 0.350552 + 0.404558i
\(566\) −639.668 + 187.823i −0.0475040 + 0.0139484i
\(567\) 926.120 6441.31i 0.0685950 0.477089i
\(568\) −913.290 + 1053.99i −0.0674662 + 0.0778602i
\(569\) 3050.01 6678.59i 0.224715 0.492058i −0.763371 0.645961i \(-0.776457\pi\)
0.988086 + 0.153903i \(0.0491842\pi\)
\(570\) −716.026 210.244i −0.0526158 0.0154494i
\(571\) −3577.72 7834.11i −0.262212 0.574163i 0.732036 0.681266i \(-0.238570\pi\)
−0.994248 + 0.107102i \(0.965843\pi\)
\(572\) 1049.15 + 7297.02i 0.0766910 + 0.533398i
\(573\) −230.419 148.081i −0.0167991 0.0107961i
\(574\) −487.802 −0.0354712
\(575\) −5598.94 748.934i −0.406073 0.0543178i
\(576\) −1388.64 −0.100451
\(577\) −2255.96 1449.82i −0.162767 0.104604i 0.456721 0.889610i \(-0.349024\pi\)
−0.619489 + 0.785006i \(0.712660\pi\)
\(578\) 590.586 + 4107.61i 0.0425002 + 0.295596i
\(579\) 392.010 + 858.383i 0.0281371 + 0.0616117i
\(580\) 7581.52 + 2226.14i 0.542768 + 0.159371i
\(581\) −2747.74 + 6016.72i −0.196206 + 0.429631i
\(582\) 40.5227 46.7657i 0.00288612 0.00333076i
\(583\) −527.128 + 3666.25i −0.0374466 + 0.260447i
\(584\) 5293.60 1554.34i 0.375087 0.110136i
\(585\) −2123.84 2451.04i −0.150103 0.173228i
\(586\) −904.317 + 581.169i −0.0637491 + 0.0409691i
\(587\) 9418.37 6052.82i 0.662245 0.425599i −0.165877 0.986146i \(-0.553046\pi\)
0.828122 + 0.560547i \(0.189409\pi\)
\(588\) −7761.02 8956.69i −0.544318 0.628176i
\(589\) −4468.49 + 1312.07i −0.312599 + 0.0917874i
\(590\) −500.687 + 3482.36i −0.0349372 + 0.242994i
\(591\) −10236.7 + 11813.8i −0.712491 + 0.822259i
\(592\) 6248.11 13681.5i 0.433777 0.949838i
\(593\) −1521.82 446.846i −0.105385 0.0309440i 0.228615 0.973517i \(-0.426580\pi\)
−0.334000 + 0.942573i \(0.608399\pi\)
\(594\) −377.313 826.200i −0.0260629 0.0570697i
\(595\) 1719.10 + 11956.6i 0.118447 + 0.823819i
\(596\) −16722.3 10746.8i −1.14928 0.738600i
\(597\) 5287.19 0.362463
\(598\) 2290.39 + 3488.09i 0.156624 + 0.238526i
\(599\) −15953.8 −1.08824 −0.544118 0.839009i \(-0.683136\pi\)
−0.544118 + 0.839009i \(0.683136\pi\)
\(600\) 1964.25 + 1262.35i 0.133651 + 0.0858920i
\(601\) −3712.51 25821.1i −0.251974 1.75252i −0.586329 0.810073i \(-0.699427\pi\)
0.334355 0.942447i \(-0.391482\pi\)
\(602\) −620.127 1357.89i −0.0419842 0.0919326i
\(603\) −1539.14 451.932i −0.103945 0.0305209i
\(604\) 7801.60 17083.1i 0.525568 1.15083i
\(605\) −10039.4 + 11586.1i −0.674644 + 0.778581i
\(606\) 630.583 4385.80i 0.0422701 0.293995i
\(607\) −6502.52 + 1909.31i −0.434809 + 0.127671i −0.491810 0.870703i \(-0.663664\pi\)
0.0570008 + 0.998374i \(0.481846\pi\)
\(608\) 1223.46 + 1411.95i 0.0816082 + 0.0941809i
\(609\) −2874.79 + 1847.52i −0.191285 + 0.122931i
\(610\) 3780.85 2429.81i 0.250954 0.161279i
\(611\) 18148.6 + 20944.6i 1.20166 + 1.38679i
\(612\) 2848.20 836.306i 0.188123 0.0552380i
\(613\) −577.035 + 4013.36i −0.0380199 + 0.264434i −0.999961 0.00882233i \(-0.997192\pi\)
0.961941 + 0.273257i \(0.0881008\pi\)
\(614\) −1183.78 + 1366.16i −0.0778070 + 0.0897940i
\(615\) −3506.18 + 7677.46i −0.229891 + 0.503390i
\(616\) 846.831 + 248.652i 0.0553893 + 0.0162638i
\(617\) 10376.6 + 22721.5i 0.677059 + 1.48255i 0.865730 + 0.500512i \(0.166855\pi\)
−0.188671 + 0.982040i \(0.560418\pi\)
\(618\) −438.865 3052.37i −0.0285659 0.198680i
\(619\) −8356.65 5370.49i −0.542621 0.348721i 0.240442 0.970663i \(-0.422707\pi\)
−0.783063 + 0.621942i \(0.786344\pi\)
\(620\) 24628.2 1.59531
\(621\) 10940.0 + 9292.92i 0.706934 + 0.600503i
\(622\) −465.203 −0.0299886
\(623\) 3808.11 + 2447.32i 0.244894 + 0.157384i
\(624\) 3241.55 + 22545.5i 0.207958 + 1.44638i
\(625\) −8060.63 17650.3i −0.515881 1.12962i
\(626\) 1194.72 + 350.801i 0.0762789 + 0.0223975i
\(627\) −589.241 + 1290.26i −0.0375311 + 0.0821817i
\(628\) −16278.3 + 18786.1i −1.03435 + 1.19371i
\(629\) −4216.77 + 29328.3i −0.267303 + 1.85913i
\(630\) −182.997 + 53.7326i −0.0115726 + 0.00339803i
\(631\) −4980.39 5747.68i −0.314210 0.362617i 0.576574 0.817045i \(-0.304389\pi\)
−0.890784 + 0.454428i \(0.849844\pi\)
\(632\) 5753.36 3697.46i 0.362114 0.232717i
\(633\) 8844.20 5683.82i 0.555332 0.356890i
\(634\) −71.6430 82.6805i −0.00448787 0.00517928i
\(635\) 6604.49 1939.25i 0.412742 0.121192i
\(636\) −1691.41 + 11764.0i −0.105454 + 0.733449i
\(637\) −13109.7 + 15129.4i −0.815423 + 0.941048i
\(638\) −223.464 + 489.317i −0.0138668 + 0.0303640i
\(639\) −549.631 161.386i −0.0340267 0.00999115i
\(640\) −5436.97 11905.3i −0.335805 0.735310i
\(641\) −549.425 3821.33i −0.0338549 0.235466i 0.965867 0.259037i \(-0.0834053\pi\)
−0.999722 + 0.0235716i \(0.992496\pi\)
\(642\) 523.685 + 336.552i 0.0321935 + 0.0206895i
\(643\) 10167.9 0.623612 0.311806 0.950146i \(-0.399066\pi\)
0.311806 + 0.950146i \(0.399066\pi\)
\(644\) −6771.67 + 1041.63i −0.414350 + 0.0637358i
\(645\) −25829.0 −1.57677
\(646\) −970.604 623.769i −0.0591144 0.0379905i
\(647\) −1328.49 9239.84i −0.0807238 0.561446i −0.989541 0.144252i \(-0.953922\pi\)
0.908817 0.417194i \(-0.136987\pi\)
\(648\) −2779.82 6086.96i −0.168521 0.369010i
\(649\) 6416.26 + 1883.98i 0.388074 + 0.113949i
\(650\) 804.800 1762.27i 0.0485644 0.106341i
\(651\) −6975.04 + 8049.63i −0.419928 + 0.484623i
\(652\) 619.123 4306.09i 0.0371882 0.258650i
\(653\) −13870.7 + 4072.81i −0.831245 + 0.244075i −0.669551 0.742766i \(-0.733514\pi\)
−0.161693 + 0.986841i \(0.551695\pi\)
\(654\) 2744.78 + 3167.65i 0.164112 + 0.189396i
\(655\) 9543.37 6133.15i 0.569298 0.365866i
\(656\) 5572.42 3581.18i 0.331656 0.213143i
\(657\) 1483.98 + 1712.61i 0.0881212 + 0.101697i
\(658\) 1563.74 459.155i 0.0926457 0.0272032i
\(659\) 2384.81 16586.7i 0.140970 0.980466i −0.789409 0.613867i \(-0.789613\pi\)
0.930379 0.366599i \(-0.119478\pi\)
\(660\) 4912.17 5668.95i 0.289706 0.334339i
\(661\) −3679.60 + 8057.20i −0.216520 + 0.474113i −0.986460 0.164004i \(-0.947559\pi\)
0.769940 + 0.638117i \(0.220286\pi\)
\(662\) −4337.87 1273.71i −0.254677 0.0747799i
\(663\) −18640.1 40816.1i −1.09189 2.39090i
\(664\) 967.970 + 6732.38i 0.0565731 + 0.393474i
\(665\) −1741.12 1118.95i −0.101530 0.0652496i
\(666\) −467.822 −0.0272188
\(667\) −83.5265 8500.84i −0.00484882 0.493484i
\(668\) −1812.96 −0.105009
\(669\) 12837.6 + 8250.20i 0.741897 + 0.476788i
\(670\) −469.232 3263.58i −0.0270567 0.188184i
\(671\) −3548.69 7770.56i −0.204167 0.447063i
\(672\) 4099.78 + 1203.80i 0.235346 + 0.0691038i
\(673\) 1928.85 4223.60i 0.110478 0.241913i −0.846315 0.532683i \(-0.821184\pi\)
0.956793 + 0.290769i \(0.0939112\pi\)
\(674\) −483.728 + 558.252i −0.0276447 + 0.0319036i
\(675\) 948.419 6596.40i 0.0540810 0.376142i
\(676\) 22057.8 6476.74i 1.25499 0.368499i
\(677\) −3310.98 3821.07i −0.187964 0.216921i 0.653945 0.756543i \(-0.273113\pi\)
−0.841908 + 0.539621i \(0.818568\pi\)
\(678\) −1321.13 + 849.040i −0.0748345 + 0.0480932i
\(679\) 144.375 92.7840i 0.00815993 0.00524407i
\(680\) 8134.24 + 9387.41i 0.458726 + 0.529398i
\(681\) 24570.7 7214.62i 1.38260 0.405969i
\(682\) −238.613 + 1659.59i −0.0133973 + 0.0931802i
\(683\) −13635.9 + 15736.6i −0.763926 + 0.881618i −0.995840 0.0911183i \(-0.970956\pi\)
0.231914 + 0.972736i \(0.425501\pi\)
\(684\) −211.282 + 462.642i −0.0118107 + 0.0258619i
\(685\) 982.000 + 288.341i 0.0547741 + 0.0160831i
\(686\) 1091.75 + 2390.59i 0.0607624 + 0.133051i
\(687\) 1560.37 + 10852.6i 0.0866550 + 0.602699i
\(688\) 17052.9 + 10959.3i 0.944966 + 0.607293i
\(689\) 20075.8 1.11005
\(690\) 1156.12 4085.46i 0.0637866 0.225407i
\(691\) −14920.6 −0.821429 −0.410715 0.911764i \(-0.634721\pi\)
−0.410715 + 0.911764i \(0.634721\pi\)
\(692\) −14887.1 9567.38i −0.817809 0.525574i
\(693\) 51.5911 + 358.824i 0.00282797 + 0.0196690i
\(694\) 620.603 + 1358.93i 0.0339449 + 0.0743290i
\(695\) −5045.93 1481.62i −0.275400 0.0808648i
\(696\) −1459.75 + 3196.41i −0.0794997 + 0.174080i
\(697\) −8545.34 + 9861.85i −0.464387 + 0.535931i
\(698\) −550.404 + 3828.15i −0.0298469 + 0.207589i
\(699\) 2151.01 631.592i 0.116393 0.0341760i
\(700\) 2083.03 + 2403.95i 0.112473 + 0.129801i
\(701\) 17144.7 11018.2i 0.923747 0.593656i 0.0100044 0.999950i \(-0.496815\pi\)
0.913742 + 0.406294i \(0.133179\pi\)
\(702\) −4141.46 + 2661.55i −0.222663 + 0.143097i
\(703\) −3324.53 3836.71i −0.178360 0.205838i
\(704\) −5205.42 + 1528.45i −0.278674 + 0.0818262i
\(705\) 4013.11 27911.8i 0.214386 1.49109i
\(706\) 4187.01 4832.07i 0.223202 0.257588i
\(707\) 5104.92 11178.2i 0.271556 0.594625i
\(708\) 20588.1 + 6045.20i 1.09286 + 0.320893i
\(709\) −2626.13 5750.43i −0.139106 0.304601i 0.827238 0.561851i \(-0.189911\pi\)
−0.966345 + 0.257251i \(0.917183\pi\)
\(710\) −167.564 1165.43i −0.00885714 0.0616028i
\(711\) 2363.15 + 1518.70i 0.124648 + 0.0801067i
\(712\) 4654.79 0.245008
\(713\) −7714.58 25349.4i −0.405208 1.33147i
\(714\) −2638.72 −0.138308
\(715\) −10659.2 6850.26i −0.557527 0.358301i
\(716\) −2320.46 16139.2i −0.121117 0.842387i
\(717\) 8145.24 + 17835.6i 0.424253 + 0.928985i
\(718\) 430.118 + 126.294i 0.0223564 + 0.00656442i
\(719\) −12604.0 + 27599.0i −0.653757 + 1.43153i 0.234471 + 0.972123i \(0.424664\pi\)
−0.888227 + 0.459404i \(0.848063\pi\)
\(720\) 1695.99 1957.28i 0.0877859 0.101310i
\(721\) 1217.15 8465.49i 0.0628698 0.437269i
\(722\) −3271.71 + 960.660i −0.168643 + 0.0495181i
\(723\) 18.1018 + 20.8906i 0.000931141 + 0.00107459i
\(724\) 5257.74 3378.95i 0.269893 0.173450i
\(725\) −3320.34 + 2133.85i −0.170089 + 0.109309i
\(726\) −2193.06 2530.93i −0.112111 0.129382i
\(727\) −34798.4 + 10217.7i −1.77524 + 0.521258i −0.994606 0.103729i \(-0.966923\pi\)
−0.780635 + 0.624987i \(0.785104\pi\)
\(728\) 680.788 4734.98i 0.0346589 0.241058i
\(729\) −10885.7 + 12562.8i −0.553051 + 0.638255i
\(730\) −1934.92 + 4236.88i −0.0981022 + 0.214814i
\(731\) −38315.7 11250.5i −1.93866 0.569241i
\(732\) −11386.8 24933.6i −0.574957 1.25898i
\(733\) 4157.00 + 28912.6i 0.209471 + 1.45690i 0.774888 + 0.632099i \(0.217806\pi\)
−0.565417 + 0.824805i \(0.691285\pi\)
\(734\) −5982.65 3844.81i −0.300849 0.193344i
\(735\) 20369.5 1.02223
\(736\) −7964.63 + 7039.58i −0.398886 + 0.352558i
\(737\) −6267.02 −0.313227
\(738\) −173.324 111.388i −0.00864517 0.00555591i
\(739\) 4535.14 + 31542.6i 0.225748 + 1.57011i 0.715728 + 0.698380i \(0.246095\pi\)
−0.489979 + 0.871734i \(0.662996\pi\)
\(740\) 11152.6 + 24420.8i 0.554025 + 1.21315i
\(741\) 7376.65 + 2165.98i 0.365706 + 0.107381i
\(742\) 490.436 1073.91i 0.0242648 0.0531325i
\(743\) 21538.6 24856.9i 1.06349 1.22734i 0.0906476 0.995883i \(-0.471106\pi\)
0.972846 0.231454i \(-0.0743482\pi\)
\(744\) −1558.71 + 10841.1i −0.0768079 + 0.534211i
\(745\) 32781.0 9625.36i 1.61208 0.473350i
\(746\) −761.868 879.242i −0.0373914 0.0431519i
\(747\) −2350.22 + 1510.39i −0.115114 + 0.0739792i
\(748\) 9756.18 6269.92i 0.476900 0.306485i
\(749\) 1130.59 + 1304.78i 0.0551549 + 0.0636522i
\(750\) 2725.27 800.211i 0.132684 0.0389594i
\(751\) −3523.27 + 24504.9i −0.171193 + 1.19067i 0.705176 + 0.709032i \(0.250868\pi\)
−0.876369 + 0.481640i \(0.840041\pi\)
\(752\) −14492.6 + 16725.3i −0.702778 + 0.811049i
\(753\) −15683.4 + 34341.9i −0.759012 + 1.66200i
\(754\) 2797.52 + 821.427i 0.135119 + 0.0396745i
\(755\) 13408.9 + 29361.4i 0.646358 + 1.41533i
\(756\) −1150.32 8000.63i −0.0553395 0.384894i
\(757\) −12562.8 8073.59i −0.603172 0.387635i 0.203119 0.979154i \(-0.434892\pi\)
−0.806291 + 0.591519i \(0.798528\pi\)
\(758\) −500.831 −0.0239987
\(759\) −7373.64 3280.26i −0.352630 0.156872i
\(760\) −2128.23 −0.101578
\(761\) 1643.09 + 1055.95i 0.0782681 + 0.0502999i 0.579190 0.815193i \(-0.303369\pi\)
−0.500921 + 0.865493i \(0.667005\pi\)
\(762\) 213.989 + 1488.33i 0.0101732 + 0.0707564i
\(763\) 4828.98 + 10574.0i 0.229123 + 0.501710i
\(764\) −368.151 108.099i −0.0174336 0.00511896i
\(765\) −2119.43 + 4640.91i −0.100168 + 0.219337i
\(766\) −1337.06 + 1543.05i −0.0630678 + 0.0727841i
\(767\) 5158.19 35876.0i 0.242831 1.68893i
\(768\) −14557.8 + 4274.56i −0.683998 + 0.200840i
\(769\) 23475.2 + 27091.8i 1.10083 + 1.27042i 0.959882 + 0.280406i \(0.0904690\pi\)
0.140946 + 0.990017i \(0.454986\pi\)
\(770\) −626.834 + 402.842i −0.0293371 + 0.0188538i
\(771\) 36375.6 23377.2i 1.69914 1.09197i
\(772\) 865.681 + 999.049i 0.0403582 + 0.0465759i
\(773\) 30693.7 9012.47i 1.42817 0.419348i 0.525908 0.850541i \(-0.323725\pi\)
0.902260 + 0.431193i \(0.141907\pi\)
\(774\) 89.7297 624.084i 0.00416701 0.0289822i
\(775\) −8056.07 + 9297.20i −0.373397 + 0.430923i
\(776\) 73.3101 160.527i 0.00339134 0.00742600i
\(777\) −11140.4 3271.12i −0.514363 0.151031i
\(778\) −1927.25 4220.09i −0.0888114 0.194470i
\(779\) −318.186 2213.04i −0.0146344 0.101785i
\(780\) −34202.5 21980.6i −1.57006 1.00902i
\(781\) −2237.97 −0.102536
\(782\) 3494.57 5556.96i 0.159803 0.254113i
\(783\) 10029.4 0.457756
\(784\) −13448.4 8642.78i −0.612629 0.393713i
\(785\) −6080.22 42288.9i −0.276449 1.92274i
\(786\) 1029.44 + 2254.16i 0.0467161 + 0.102294i
\(787\) −141.788 41.6327i −0.00642210 0.00188570i 0.278520 0.960430i \(-0.410156\pi\)
−0.284942 + 0.958545i \(0.591974\pi\)
\(788\) −9096.78 + 19919.2i −0.411243 + 0.900496i
\(789\) −4609.64 + 5319.81i −0.207994 + 0.240038i
\(790\) −821.705 + 5715.08i −0.0370063 + 0.257384i
\(791\) −4179.03 + 1227.07i −0.187850 + 0.0551577i
\(792\) 244.113 + 281.722i 0.0109523 + 0.0126396i
\(793\) −38951.1 + 25032.4i −1.74426 + 1.12097i
\(794\) 933.330 599.815i 0.0417162 0.0268094i
\(795\) −13377.0 15437.8i −0.596770 0.688709i
\(796\) 7106.57 2086.68i 0.316439 0.0929149i
\(797\) −1283.74 + 8928.63i −0.0570546 + 0.396823i 0.941204 + 0.337838i \(0.109696\pi\)
−0.998259 + 0.0589853i \(0.981213\pi\)
\(798\) 296.070 341.683i 0.0131338 0.0151572i
\(799\) 18111.0 39657.5i 0.801902 1.75592i
\(800\) 4735.18 + 1390.38i 0.209268 + 0.0614465i
\(801\) 794.241 + 1739.15i 0.0350351 + 0.0767162i
\(802\) 444.300 + 3090.18i 0.0195621 + 0.136057i
\(803\) 7447.86 + 4786.45i 0.327309 + 0.210349i
\(804\) −20109.2 −0.882084
\(805\) 6268.74 9968.35i 0.274465 0.436445i
\(806\) 9087.62 0.397144
\(807\) −962.732 618.710i −0.0419947 0.0269884i
\(808\) −1798.35 12507.8i −0.0782992 0.544583i
\(809\) 11307.6 + 24760.1i 0.491413 + 1.07604i 0.979166 + 0.203063i \(0.0650895\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(810\) 5420.60 + 1591.63i 0.235136 + 0.0690423i
\(811\) −2094.12 + 4585.49i −0.0906715 + 0.198543i −0.949535 0.313662i \(-0.898444\pi\)
0.858863 + 0.512205i \(0.171171\pi\)
\(812\) −3134.89 + 3617.85i −0.135484 + 0.156357i
\(813\) 2261.25 15727.3i 0.0975465 0.678451i
\(814\) −1753.67 + 514.923i −0.0755110 + 0.0221720i
\(815\) 4896.50 + 5650.86i 0.210450 + 0.242872i
\(816\) 30143.6 19372.1i 1.29318 0.831077i
\(817\) 5755.90 3699.09i 0.246479 0.158403i
\(818\) −2597.56 2997.74i −0.111029 0.128134i
\(819\) 1885.27 553.565i 0.0804355 0.0236180i
\(820\) −1682.66 + 11703.1i −0.0716597 + 0.498404i
\(821\) 30349.9 35025.7i 1.29016 1.48892i 0.514942 0.857225i \(-0.327813\pi\)
0.775216 0.631697i \(-0.217641\pi\)
\(822\) −92.8742 + 203.366i −0.00394083 + 0.00862921i
\(823\) −17289.7 5076.71i −0.732297 0.215022i −0.105736 0.994394i \(-0.533720\pi\)
−0.626561 + 0.779372i \(0.715538\pi\)
\(824\) −3653.38 7999.78i −0.154456 0.338211i
\(825\) 533.231 + 3708.71i 0.0225027 + 0.156510i
\(826\) −1793.09 1152.35i −0.0755321 0.0485415i
\(827\) −20971.1 −0.881783 −0.440892 0.897560i \(-0.645338\pi\)
−0.440892 + 0.897560i \(0.645338\pi\)
\(828\) −2643.93 1176.19i −0.110970 0.0493664i
\(829\) −21672.6 −0.907987 −0.453993 0.891005i \(-0.650001\pi\)
−0.453993 + 0.891005i \(0.650001\pi\)
\(830\) −4830.69 3104.50i −0.202019 0.129830i
\(831\) −566.957 3943.27i −0.0236673 0.164610i
\(832\) 12215.3 + 26747.7i 0.509001 + 1.11456i
\(833\) 30216.9 + 8872.47i 1.25685 + 0.369043i
\(834\) 477.228 1044.98i 0.0198142 0.0433870i
\(835\) 2040.55 2354.92i 0.0845703 0.0975994i
\(836\) −282.784 + 1966.80i −0.0116989 + 0.0813676i
\(837\) 29994.2 8807.08i 1.23865 0.363700i
\(838\) 4584.66 + 5290.98i 0.188991 + 0.218107i
\(839\) 8628.02 5544.89i 0.355033 0.228166i −0.350951 0.936394i \(-0.614142\pi\)
0.705984 + 0.708228i \(0.250505\pi\)
\(840\) −4094.72 + 2631.52i −0.168192 + 0.108091i
\(841\) 12081.6 + 13942.9i 0.495370 + 0.571687i
\(842\) 6225.57 1827.99i 0.254807 0.0748181i
\(843\) 3896.81 27102.9i 0.159209 1.10732i
\(844\) 9644.37 11130.2i 0.393333 0.453930i
\(845\) −16413.9 + 35941.4i −0.668231 + 1.46322i
\(846\) 660.468 + 193.931i 0.0268408 + 0.00788118i
\(847\) −3858.33 8448.56i −0.156522 0.342734i
\(848\) 2281.52 + 15868.3i 0.0923911 + 0.642594i
\(849\) −5879.04 3778.23i −0.237654 0.152731i
\(850\) −3047.69 −0.122982
\(851\) 21642.4 19128.8i 0.871790 0.770537i
\(852\) −7181.05 −0.288754
\(853\) −26722.7 17173.6i −1.07265 0.689348i −0.119799 0.992798i \(-0.538225\pi\)
−0.952847 + 0.303451i \(0.901861\pi\)
\(854\) 387.500 + 2695.12i 0.0155269 + 0.107992i
\(855\) −363.138 795.160i −0.0145252 0.0318057i
\(856\) 1703.40 + 500.164i 0.0680153 + 0.0199711i
\(857\) −3697.07 + 8095.45i −0.147362 + 0.322678i −0.968891 0.247489i \(-0.920395\pi\)
0.821528 + 0.570168i \(0.193122\pi\)
\(858\) 1812.55 2091.80i 0.0721207 0.0832317i
\(859\) 4599.35 31989.2i 0.182686 1.27061i −0.667691 0.744439i \(-0.732717\pi\)
0.850377 0.526173i \(-0.176374\pi\)
\(860\) −34717.0 + 10193.8i −1.37656 + 0.404194i
\(861\) −3348.57 3864.45i −0.132542 0.152962i
\(862\) −1224.55 + 786.973i −0.0483857 + 0.0310956i
\(863\) −30674.1 + 19713.1i −1.20992 + 0.777567i −0.980645 0.195795i \(-0.937271\pi\)
−0.229273 + 0.973362i \(0.573635\pi\)
\(864\) −8212.30 9477.50i −0.323366 0.373184i
\(865\) 29183.4 8569.02i 1.14713 0.336827i
\(866\) 248.182 1726.14i 0.00973852 0.0677329i
\(867\) −28487.1 + 32875.9i −1.11589 + 1.28780i
\(868\) −6198.31 + 13572.4i −0.242378 + 0.530735i
\(869\) 10530.1 + 3091.91i 0.411056 + 0.120697i
\(870\) −1232.40 2698.57i −0.0480254 0.105161i
\(871\) 4834.13 + 33622.1i 0.188058 + 1.30797i
\(872\) 10055.8 + 6462.49i 0.390520 + 0.250972i
\(873\) 72.4856 0.00281016
\(874\) 327.461 + 1076.01i 0.0126734 + 0.0416435i
\(875\) 7877.39 0.304348
\(876\) 23898.2 + 15358.4i 0.921740 + 0.592366i
\(877\) 4841.01 + 33670.0i 0.186396 + 1.29641i 0.841245 + 0.540654i \(0.181823\pi\)
−0.654849 + 0.755760i \(0.727268\pi\)
\(878\) −1530.21 3350.69i −0.0588178 0.128793i
\(879\) −10811.9 3174.66i −0.414877 0.121819i
\(880\) 4203.22 9203.76i 0.161012 0.352567i
\(881\) 10055.6 11604.8i 0.384544 0.443787i −0.530169 0.847892i \(-0.677871\pi\)
0.914713 + 0.404105i \(0.132417\pi\)
\(882\) −70.7634 + 492.170i −0.00270150 + 0.0187894i
\(883\) −8783.03 + 2578.93i −0.334737 + 0.0982876i −0.444782 0.895639i \(-0.646719\pi\)
0.110045 + 0.993927i \(0.464901\pi\)
\(884\) −41163.2 47504.8i −1.56614 1.80742i
\(885\) −31024.9 + 19938.5i −1.17841 + 0.757316i
\(886\) −1963.29 + 1261.73i −0.0744447 + 0.0478427i
\(887\) −15467.2 17850.1i −0.585500 0.675703i 0.383278 0.923633i \(-0.374795\pi\)
−0.968778 + 0.247930i \(0.920250\pi\)
\(888\) −11455.6 + 3363.68i −0.432912 + 0.127114i
\(889\) −593.480 + 4127.75i −0.0223900 + 0.155726i
\(890\) −2573.48 + 2969.95i −0.0969249 + 0.111857i
\(891\) 4460.79 9767.76i 0.167724 0.367264i
\(892\) 20511.2 + 6022.63i 0.769917 + 0.226068i
\(893\) 3103.08 + 6794.79i 0.116283 + 0.254624i
\(894\) 1062.12 + 7387.21i 0.0397345 + 0.276359i
\(895\) 23575.5 + 15151.1i 0.880494 + 0.565859i
\(896\) 7929.27 0.295645
\(897\) −11910.6 + 42089.3i −0.443348 + 1.56669i
\(898\) 2014.70 0.0748681
\(899\) −15575.0 10009.4i −0.577813 0.371338i
\(900\) 191.198 + 1329.81i 0.00708143 + 0.0492524i
\(901\) −13119.6 28727.8i −0.485101 1.06222i
\(902\) −772.321 226.774i −0.0285094 0.00837111i
\(903\) 6500.51 14234.1i 0.239561 0.524565i
\(904\) −2932.92 + 3384.77i −0.107907 + 0.124531i
\(905\) −1528.74 + 10632.6i −0.0561513 + 0.390541i
\(906\) −6765.45 + 1986.52i −0.248087 + 0.0728450i
\(907\) 13032.7 + 15040.5i 0.477115 + 0.550620i 0.942377 0.334553i \(-0.108585\pi\)
−0.465262 + 0.885173i \(0.654040\pi\)
\(908\) 30178.4 19394.5i 1.10298 0.708843i
\(909\) 4366.37 2806.10i 0.159322 0.102390i
\(910\) 2644.73 + 3052.18i 0.0963429 + 0.111186i
\(911\) 14904.9 4376.48i 0.542066 0.159165i 0.000774332 1.00000i \(-0.499754\pi\)
0.541292 + 0.840835i \(0.317935\pi\)
\(912\) −873.713 + 6076.81i −0.0317232 + 0.220640i
\(913\) −7147.52 + 8248.68i −0.259089 + 0.299005i
\(914\) −3277.56 + 7176.85i −0.118613 + 0.259725i
\(915\) 45203.4 + 13272.9i 1.63320 + 0.479551i
\(916\) 6380.50 + 13971.3i 0.230150 + 0.503959i
\(917\) 978.100 + 6802.83i 0.0352232 + 0.244983i
\(918\) 6515.05 + 4186.97i 0.234236 + 0.150534i
\(919\) −5021.93 −0.180259 −0.0901296 0.995930i \(-0.528728\pi\)
−0.0901296 + 0.995930i \(0.528728\pi\)
\(920\) −118.971 12108.2i −0.00426345 0.433909i
\(921\) −18949.1 −0.677953
\(922\) −1215.60 781.219i −0.0434205 0.0279046i
\(923\) 1726.28 + 12006.6i 0.0615615 + 0.428169i
\(924\) 1887.84 + 4133.79i 0.0672136 + 0.147177i
\(925\) −12867.0 3778.10i −0.457367 0.134295i
\(926\) 1053.96 2307.85i 0.0374030 0.0819012i
\(927\) 2365.55 2729.99i 0.0838131 0.0967255i
\(928\) −1056.99 + 7351.54i −0.0373895 + 0.260050i
\(929\) −31688.1 + 9304.46i −1.11911 + 0.328600i −0.788418 0.615139i \(-0.789100\pi\)
−0.330690 + 0.943739i \(0.607282\pi\)
\(930\) −6055.30 6988.18i −0.213506 0.246400i
\(931\) −4539.27 + 2917.21i −0.159794 + 0.102694i
\(932\) 2641.92 1697.86i 0.0928531 0.0596731i
\(933\) −3193.44 3685.42i −0.112056 0.129320i
\(934\) −6844.97 + 2009.86i −0.239801 + 0.0704120i
\(935\) −2836.70 + 19729.7i −0.0992191 + 0.690084i
\(936\) 1323.12 1526.96i 0.0462045 0.0533228i
\(937\) 8003.25 17524.7i 0.279034 0.610999i −0.717279 0.696786i \(-0.754613\pi\)
0.996314 + 0.0857862i \(0.0273402\pi\)
\(938\) 1916.63 + 562.772i 0.0667165 + 0.0195897i
\(939\) 5422.17 + 11872.9i 0.188441 + 0.412627i
\(940\) −5621.79 39100.4i −0.195067 1.35672i
\(941\) −43184.4 27752.9i −1.49604 0.961445i −0.995402 0.0957878i \(-0.969463\pi\)
−0.500637 0.865658i \(-0.666901\pi\)
\(942\) 9332.82 0.322802
\(943\) 12572.9 1933.98i 0.434178 0.0667858i
\(944\) 28943.3 0.997908
\(945\) 11687.0 + 7510.80i 0.402306 + 0.258546i
\(946\) −350.559 2438.19i −0.0120483 0.0837975i
\(947\) −16533.4 36203.0i −0.567331 1.24228i −0.948206 0.317655i \(-0.897105\pi\)
0.380876 0.924626i \(-0.375623\pi\)
\(948\) 33788.1 + 9921.10i 1.15758 + 0.339897i
\(949\) 19934.0 43649.3i 0.681858 1.49306i
\(950\) 341.956 394.638i 0.0116784 0.0134776i
\(951\) 163.208 1135.14i 0.00556508 0.0387060i
\(952\) −7220.51 + 2120.13i −0.245817 + 0.0721785i
\(953\) 9932.68 + 11462.9i 0.337619 + 0.389633i 0.899018 0.437912i \(-0.144282\pi\)
−0.561399 + 0.827546i \(0.689737\pi\)
\(954\) 419.483 269.585i 0.0142361 0.00914901i
\(955\) 554.780 356.536i 0.0187982 0.0120809i
\(956\) 17987.2 + 20758.4i 0.608523 + 0.702273i
\(957\) −5410.45 + 1588.65i −0.182753 + 0.0536613i
\(958\) 1238.22 8612.02i 0.0417590 0.290440i
\(959\) −406.047 + 468.604i −0.0136725 + 0.0157789i
\(960\) 12429.1 27215.9i 0.417862 0.914990i
\(961\) −26783.9 7864.47i −0.899061 0.263988i
\(962\) 4115.23 + 9011.10i 0.137921 + 0.302006i
\(963\) 103.776 + 721.776i 0.00347261 + 0.0241525i
\(964\) 32.5757 + 20.9352i 0.00108838 + 0.000699457i
\(965\) −2272.05 −0.0757928
\(966\) 1960.50 + 1665.34i 0.0652981 + 0.0554672i
\(967\) −14243.5 −0.473673 −0.236836 0.971550i \(-0.576110\pi\)
−0.236836 + 0.971550i \(0.576110\pi\)
\(968\) −8034.55 5163.49i −0.266777 0.171447i
\(969\) −1721.20 11971.2i −0.0570619 0.396874i
\(970\) 61.8921 + 135.525i 0.00204870 + 0.00448602i
\(971\) −51147.6 15018.3i −1.69043 0.496354i −0.711867 0.702314i \(-0.752150\pi\)
−0.978560 + 0.205960i \(0.933968\pi\)
\(972\) 3040.49 6657.75i 0.100333 0.219699i
\(973\) 2086.44 2407.89i 0.0687444 0.0793353i
\(974\) 1439.42 10011.4i 0.0473533 0.329349i
\(975\) 19485.6 5721.49i 0.640040 0.187933i
\(976\) −24212.7 27943.0i −0.794088 0.916427i
\(977\) −2009.21 + 1291.24i −0.0657936 + 0.0422830i −0.573124 0.819469i \(-0.694269\pi\)
0.507330 + 0.861752i \(0.330632\pi\)
\(978\) −1374.06 + 883.057i −0.0449261 + 0.0288722i
\(979\) 4891.52 + 5645.12i 0.159687 + 0.184289i
\(980\) 27378.8 8039.15i 0.892433 0.262042i
\(981\) −698.733 + 4859.80i −0.0227409 + 0.158166i
\(982\) 5363.65 6189.99i 0.174298 0.201151i
\(983\) 4208.98 9216.38i 0.136567 0.299041i −0.828976 0.559285i \(-0.811076\pi\)
0.965543 + 0.260244i \(0.0838031\pi\)
\(984\) −5045.10 1481.37i −0.163447 0.0479924i
\(985\) −15635.0 34235.8i −0.505758 1.10746i
\(986\) −652.749 4539.97i −0.0210829 0.146635i
\(987\) 14372.0 + 9236.30i 0.463490 + 0.297867i
\(988\) 10769.9 0.346797
\(989\) 21367.1 + 32540.4i 0.686992 + 1.04623i
\(990\) −314.712 −0.0101032
\(991\) 46499.0 + 29883.1i 1.49050 + 0.957889i 0.996060 + 0.0886801i \(0.0282649\pi\)
0.494445 + 0.869209i \(0.335371\pi\)
\(992\) 3294.50 + 22913.8i 0.105444 + 0.733380i
\(993\) −19687.2 43108.9i −0.629158 1.37766i
\(994\) 684.433 + 200.968i 0.0218399 + 0.00641278i
\(995\) −5288.23 + 11579.6i −0.168490 + 0.368943i
\(996\) −22934.5 + 26467.8i −0.729625 + 0.842032i
\(997\) −1590.62 + 11063.0i −0.0505271 + 0.351424i 0.948837 + 0.315766i \(0.102262\pi\)
−0.999364 + 0.0356574i \(0.988648\pi\)
\(998\) −2268.38 + 666.056i −0.0719481 + 0.0211259i
\(999\) 22315.4 + 25753.4i 0.706736 + 0.815617i
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 23.4.c.a.2.3 50
3.2 odd 2 207.4.i.a.163.3 50
23.9 even 11 529.4.a.n.1.12 25
23.12 even 11 inner 23.4.c.a.12.3 yes 50
23.14 odd 22 529.4.a.m.1.12 25
69.35 odd 22 207.4.i.a.127.3 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.4.c.a.2.3 50 1.1 even 1 trivial
23.4.c.a.12.3 yes 50 23.12 even 11 inner
207.4.i.a.127.3 50 69.35 odd 22
207.4.i.a.163.3 50 3.2 odd 2
529.4.a.m.1.12 25 23.14 odd 22
529.4.a.n.1.12 25 23.9 even 11