Properties

Label 124.3.n.a.7.12
Level $124$
Weight $3$
Character 124.7
Analytic conductor $3.379$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,3,Mod(7,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 28]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 124.n (of order \(30\), degree \(8\), 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: \(3.37875527807\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(30\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 7.12
Character \(\chi\) \(=\) 124.7
Dual form 124.3.n.a.71.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.673616 - 1.88315i) q^{2} +(-0.736057 - 3.46287i) q^{3} +(-3.09248 + 2.53704i) q^{4} +(3.42633 - 5.93457i) q^{5} +(-6.02528 + 3.71875i) q^{6} +(2.34572 - 5.26857i) q^{7} +(6.86076 + 4.11461i) q^{8} +(-3.22781 + 1.43711i) q^{9} +O(q^{10})\) \(q+(-0.673616 - 1.88315i) q^{2} +(-0.736057 - 3.46287i) q^{3} +(-3.09248 + 2.53704i) q^{4} +(3.42633 - 5.93457i) q^{5} +(-6.02528 + 3.71875i) q^{6} +(2.34572 - 5.26857i) q^{7} +(6.86076 + 4.11461i) q^{8} +(-3.22781 + 1.43711i) q^{9} +(-13.4837 - 2.45465i) q^{10} +(-21.1181 + 2.21960i) q^{11} +(11.0617 + 8.84147i) q^{12} +(11.1195 + 12.3495i) q^{13} +(-11.5016 - 0.868338i) q^{14} +(-23.0726 - 7.49676i) q^{15} +(3.12690 - 15.6915i) q^{16} +(-0.527025 + 5.01431i) q^{17} +(4.88059 + 5.11037i) q^{18} +(15.8066 + 14.2323i) q^{19} +(4.46037 + 27.0453i) q^{20} +(-19.9710 - 4.24496i) q^{21} +(18.4053 + 38.2733i) q^{22} +(4.49597 - 6.18817i) q^{23} +(9.19847 - 26.7865i) q^{24} +(-10.9794 - 19.0169i) q^{25} +(15.7656 - 29.2585i) q^{26} +(-11.3757 - 15.6573i) q^{27} +(6.11245 + 22.2441i) q^{28} +(-15.4208 - 47.4604i) q^{29} +(1.42461 + 48.4991i) q^{30} +(28.2018 - 12.8707i) q^{31} +(-31.6557 + 4.68162i) q^{32} +(23.2303 + 71.4955i) q^{33} +(9.79769 - 2.38525i) q^{34} +(-23.2295 - 31.9727i) q^{35} +(6.33593 - 12.6333i) q^{36} +(-2.79489 - 4.84089i) q^{37} +(16.1540 - 39.3533i) q^{38} +(34.5801 - 47.5955i) q^{39} +(47.9256 - 26.6177i) q^{40} +(7.97361 + 1.69484i) q^{41} +(5.45888 + 40.4677i) q^{42} +(-24.3448 - 21.9201i) q^{43} +(59.6761 - 60.4414i) q^{44} +(-2.53087 + 24.0797i) q^{45} +(-14.6818 - 4.29812i) q^{46} +(72.1870 + 23.4550i) q^{47} +(-56.6392 + 0.721760i) q^{48} +(10.5320 + 11.6970i) q^{49} +(-28.4158 + 33.4860i) q^{50} +(17.7518 - 1.86579i) q^{51} +(-65.7181 - 9.97994i) q^{52} +(-10.4363 + 4.64654i) q^{53} +(-21.8222 + 31.9691i) q^{54} +(-59.1851 + 132.932i) q^{55} +(37.7715 - 26.4946i) q^{56} +(37.6503 - 65.2122i) q^{57} +(-78.9871 + 61.0097i) q^{58} +(-0.326174 - 1.53453i) q^{59} +(90.3713 - 35.3525i) q^{60} -20.6575 q^{61} +(-43.2347 - 44.4383i) q^{62} +20.3770i q^{63} +(30.1400 + 56.4587i) q^{64} +(111.388 - 23.6763i) q^{65} +(118.988 - 91.9066i) q^{66} +(59.0247 + 34.0779i) q^{67} +(-11.0917 - 16.8438i) q^{68} +(-24.7381 - 11.0141i) q^{69} +(-44.5614 + 65.2818i) q^{70} +(14.4569 + 32.4708i) q^{71} +(-28.0583 - 3.42149i) q^{72} +(-11.1730 - 106.304i) q^{73} +(-7.23342 + 8.52408i) q^{74} +(-57.7718 + 52.0179i) q^{75} +(-84.9897 - 3.91132i) q^{76} +(-37.8429 + 116.469i) q^{77} +(-112.923 - 33.0584i) q^{78} +(-51.7623 - 5.44044i) q^{79} +(-82.4084 - 72.3209i) q^{80} +(-67.1241 + 74.5489i) q^{81} +(-2.17951 - 16.1572i) q^{82} +(9.63193 - 45.3147i) q^{83} +(72.5294 - 37.5396i) q^{84} +(27.9520 + 20.3083i) q^{85} +(-24.8798 + 60.6106i) q^{86} +(-152.999 + 88.3338i) q^{87} +(-154.019 - 71.6645i) q^{88} +(19.2011 - 13.9504i) q^{89} +(47.0504 - 11.4544i) q^{90} +(91.1474 - 29.6156i) q^{91} +(1.79590 + 30.5432i) q^{92} +(-65.3279 - 88.1858i) q^{93} +(-4.45716 - 151.738i) q^{94} +(138.622 - 45.0409i) q^{95} +(39.5122 + 106.174i) q^{96} +(-33.1115 + 24.0569i) q^{97} +(14.9326 - 27.7126i) q^{98} +(64.9752 - 37.5135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 6 q^{2} - 10 q^{4} - 8 q^{5} - 5 q^{6} - 27 q^{8} - 96 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 6 q^{2} - 10 q^{4} - 8 q^{5} - 5 q^{6} - 27 q^{8} - 96 q^{9} - 4 q^{10} + 27 q^{12} - 26 q^{13} + 10 q^{14} + 46 q^{16} - 18 q^{17} - 11 q^{18} + 143 q^{20} + 90 q^{21} + 77 q^{22} - 54 q^{24} - 464 q^{25} - 27 q^{26} - 52 q^{28} - 12 q^{29} + 206 q^{30} + 154 q^{32} + 72 q^{33} - 168 q^{34} + 23 q^{36} - 48 q^{37} - 78 q^{38} + 85 q^{40} - 18 q^{41} - 91 q^{42} - 493 q^{44} - 30 q^{45} + 198 q^{46} - 314 q^{48} + 48 q^{49} - 563 q^{50} - 551 q^{52} + 46 q^{53} - 600 q^{54} - 90 q^{56} - 44 q^{57} - 125 q^{58} - 77 q^{60} + 208 q^{61} - 17 q^{62} - 529 q^{64} + 132 q^{65} + 788 q^{66} + 364 q^{68} + 36 q^{69} + 586 q^{70} + 1113 q^{72} + 214 q^{73} + 351 q^{74} + 824 q^{76} + 456 q^{77} + 123 q^{78} + 410 q^{80} + 90 q^{81} - 718 q^{82} - 412 q^{84} + 394 q^{85} + 680 q^{86} - 141 q^{88} + 12 q^{89} + 193 q^{90} - 520 q^{92} + 82 q^{93} - 876 q^{94} + 888 q^{96} - 548 q^{97} + 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{14}{15}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.673616 1.88315i −0.336808 0.941573i
\(3\) −0.736057 3.46287i −0.245352 1.15429i −0.912407 0.409283i \(-0.865779\pi\)
0.667055 0.745008i \(-0.267554\pi\)
\(4\) −3.09248 + 2.53704i −0.773121 + 0.634259i
\(5\) 3.42633 5.93457i 0.685265 1.18691i −0.288088 0.957604i \(-0.593020\pi\)
0.973353 0.229311i \(-0.0736471\pi\)
\(6\) −6.02528 + 3.71875i −1.00421 + 0.619792i
\(7\) 2.34572 5.26857i 0.335102 0.752652i −0.664881 0.746949i \(-0.731518\pi\)
0.999984 0.00570327i \(-0.00181542\pi\)
\(8\) 6.86076 + 4.11461i 0.857595 + 0.514326i
\(9\) −3.22781 + 1.43711i −0.358645 + 0.159679i
\(10\) −13.4837 2.45465i −1.34837 0.245465i
\(11\) −21.1181 + 2.21960i −1.91983 + 0.201782i −0.987248 0.159189i \(-0.949112\pi\)
−0.932577 + 0.360971i \(0.882445\pi\)
\(12\) 11.0617 + 8.84147i 0.921806 + 0.736790i
\(13\) 11.1195 + 12.3495i 0.855349 + 0.949961i 0.999214 0.0396362i \(-0.0126199\pi\)
−0.143865 + 0.989597i \(0.545953\pi\)
\(14\) −11.5016 0.868338i −0.821542 0.0620241i
\(15\) −23.0726 7.49676i −1.53818 0.499784i
\(16\) 3.12690 15.6915i 0.195431 0.980717i
\(17\) −0.527025 + 5.01431i −0.0310015 + 0.294959i 0.968025 + 0.250852i \(0.0807109\pi\)
−0.999027 + 0.0441070i \(0.985956\pi\)
\(18\) 4.88059 + 5.11037i 0.271144 + 0.283909i
\(19\) 15.8066 + 14.2323i 0.831928 + 0.749071i 0.970454 0.241288i \(-0.0775698\pi\)
−0.138526 + 0.990359i \(0.544236\pi\)
\(20\) 4.46037 + 27.0453i 0.223018 + 1.35226i
\(21\) −19.9710 4.24496i −0.950998 0.202141i
\(22\) 18.4053 + 38.2733i 0.836605 + 1.73969i
\(23\) 4.49597 6.18817i 0.195477 0.269051i −0.700016 0.714128i \(-0.746824\pi\)
0.895492 + 0.445077i \(0.146824\pi\)
\(24\) 9.19847 26.7865i 0.383270 1.11610i
\(25\) −10.9794 19.0169i −0.439177 0.760677i
\(26\) 15.7656 29.2585i 0.606370 1.12533i
\(27\) −11.3757 15.6573i −0.421322 0.579901i
\(28\) 6.11245 + 22.2441i 0.218302 + 0.794433i
\(29\) −15.4208 47.4604i −0.531752 1.63656i −0.750564 0.660797i \(-0.770218\pi\)
0.218813 0.975767i \(-0.429782\pi\)
\(30\) 1.42461 + 48.4991i 0.0474871 + 1.61664i
\(31\) 28.2018 12.8707i 0.909737 0.415185i
\(32\) −31.6557 + 4.68162i −0.989240 + 0.146301i
\(33\) 23.2303 + 71.4955i 0.703948 + 2.16653i
\(34\) 9.79769 2.38525i 0.288167 0.0701545i
\(35\) −23.2295 31.9727i −0.663700 0.913504i
\(36\) 6.33593 12.6333i 0.175998 0.350925i
\(37\) −2.79489 4.84089i −0.0755375 0.130835i 0.825782 0.563989i \(-0.190734\pi\)
−0.901320 + 0.433154i \(0.857401\pi\)
\(38\) 16.1540 39.3533i 0.425105 1.03561i
\(39\) 34.5801 47.5955i 0.886670 1.22040i
\(40\) 47.9256 26.6177i 1.19814 0.665441i
\(41\) 7.97361 + 1.69484i 0.194478 + 0.0413377i 0.304121 0.952633i \(-0.401637\pi\)
−0.109643 + 0.993971i \(0.534971\pi\)
\(42\) 5.45888 + 40.4677i 0.129973 + 0.963517i
\(43\) −24.3448 21.9201i −0.566158 0.509771i 0.335605 0.942003i \(-0.391059\pi\)
−0.901762 + 0.432232i \(0.857726\pi\)
\(44\) 59.6761 60.4414i 1.35627 1.37367i
\(45\) −2.53087 + 24.0797i −0.0562416 + 0.535103i
\(46\) −14.6818 4.29812i −0.319169 0.0934373i
\(47\) 72.1870 + 23.4550i 1.53589 + 0.499042i 0.950240 0.311519i \(-0.100838\pi\)
0.585654 + 0.810561i \(0.300838\pi\)
\(48\) −56.6392 + 0.721760i −1.17998 + 0.0150367i
\(49\) 10.5320 + 11.6970i 0.214939 + 0.238714i
\(50\) −28.4158 + 33.4860i −0.568315 + 0.669720i
\(51\) 17.7518 1.86579i 0.348075 0.0365842i
\(52\) −65.7181 9.97994i −1.26381 0.191922i
\(53\) −10.4363 + 4.64654i −0.196911 + 0.0876705i −0.502823 0.864389i \(-0.667705\pi\)
0.305912 + 0.952060i \(0.401039\pi\)
\(54\) −21.8222 + 31.9691i −0.404114 + 0.592021i
\(55\) −59.1851 + 132.932i −1.07609 + 2.41694i
\(56\) 37.7715 26.4946i 0.674491 0.473119i
\(57\) 37.6503 65.2122i 0.660531 1.14407i
\(58\) −78.9871 + 61.0097i −1.36185 + 1.05189i
\(59\) −0.326174 1.53453i −0.00552838 0.0260090i 0.975297 0.220898i \(-0.0708987\pi\)
−0.980825 + 0.194889i \(0.937565\pi\)
\(60\) 90.3713 35.3525i 1.50619 0.589209i
\(61\) −20.6575 −0.338647 −0.169324 0.985561i \(-0.554158\pi\)
−0.169324 + 0.985561i \(0.554158\pi\)
\(62\) −43.2347 44.4383i −0.697334 0.716747i
\(63\) 20.3770i 0.323444i
\(64\) 30.1400 + 56.4587i 0.470937 + 0.882167i
\(65\) 111.388 23.6763i 1.71366 0.364250i
\(66\) 118.988 91.9066i 1.80285 1.39252i
\(67\) 59.0247 + 34.0779i 0.880966 + 0.508626i 0.870977 0.491324i \(-0.163487\pi\)
0.00998923 + 0.999950i \(0.496820\pi\)
\(68\) −11.0917 16.8438i −0.163113 0.247702i
\(69\) −24.7381 11.0141i −0.358524 0.159625i
\(70\) −44.5614 + 65.2818i −0.636592 + 0.932598i
\(71\) 14.4569 + 32.4708i 0.203619 + 0.457335i 0.986273 0.165121i \(-0.0528015\pi\)
−0.782654 + 0.622456i \(0.786135\pi\)
\(72\) −28.0583 3.42149i −0.389699 0.0475207i
\(73\) −11.1730 106.304i −0.153055 1.45622i −0.753971 0.656908i \(-0.771864\pi\)
0.600916 0.799312i \(-0.294803\pi\)
\(74\) −7.23342 + 8.52408i −0.0977489 + 0.115190i
\(75\) −57.7718 + 52.0179i −0.770290 + 0.693572i
\(76\) −84.9897 3.91132i −1.11829 0.0514647i
\(77\) −37.8429 + 116.469i −0.491467 + 1.51258i
\(78\) −112.923 33.0584i −1.44773 0.423825i
\(79\) −51.7623 5.44044i −0.655219 0.0688663i −0.228915 0.973446i \(-0.573518\pi\)
−0.426304 + 0.904580i \(0.640185\pi\)
\(80\) −82.4084 72.3209i −1.03011 0.904012i
\(81\) −67.1241 + 74.5489i −0.828693 + 0.920357i
\(82\) −2.17951 16.1572i −0.0265795 0.197039i
\(83\) 9.63193 45.3147i 0.116047 0.545960i −0.881260 0.472631i \(-0.843304\pi\)
0.997308 0.0733290i \(-0.0233623\pi\)
\(84\) 72.5294 37.5396i 0.863446 0.446900i
\(85\) 27.9520 + 20.3083i 0.328847 + 0.238922i
\(86\) −24.8798 + 60.6106i −0.289300 + 0.704774i
\(87\) −152.999 + 88.3338i −1.75861 + 1.01533i
\(88\) −154.019 71.6645i −1.75021 0.814370i
\(89\) 19.2011 13.9504i 0.215742 0.156746i −0.474666 0.880166i \(-0.657431\pi\)
0.690408 + 0.723420i \(0.257431\pi\)
\(90\) 47.0504 11.4544i 0.522782 0.127272i
\(91\) 91.1474 29.6156i 1.00162 0.325446i
\(92\) 1.79590 + 30.5432i 0.0195207 + 0.331992i
\(93\) −65.3279 88.1858i −0.702450 0.948235i
\(94\) −4.45716 151.738i −0.0474166 1.61424i
\(95\) 138.622 45.0409i 1.45917 0.474114i
\(96\) 39.5122 + 106.174i 0.411586 + 1.10598i
\(97\) −33.1115 + 24.0569i −0.341356 + 0.248009i −0.745234 0.666804i \(-0.767662\pi\)
0.403878 + 0.914813i \(0.367662\pi\)
\(98\) 14.9326 27.7126i 0.152373 0.282781i
\(99\) 64.9752 37.5135i 0.656315 0.378924i
\(100\) 82.2004 + 30.9543i 0.822004 + 0.309543i
\(101\) −27.4429 19.9385i −0.271712 0.197411i 0.443582 0.896234i \(-0.353707\pi\)
−0.715294 + 0.698823i \(0.753707\pi\)
\(102\) −15.4715 32.1725i −0.151681 0.315417i
\(103\) −21.6739 + 101.968i −0.210426 + 0.989979i 0.738444 + 0.674314i \(0.235561\pi\)
−0.948871 + 0.315664i \(0.897773\pi\)
\(104\) 25.4751 + 130.479i 0.244953 + 1.25461i
\(105\) −93.6190 + 103.974i −0.891610 + 0.990233i
\(106\) 15.7802 + 16.5231i 0.148869 + 0.155878i
\(107\) −60.7723 6.38742i −0.567965 0.0596955i −0.183806 0.982963i \(-0.558842\pi\)
−0.384159 + 0.923267i \(0.625509\pi\)
\(108\) 74.9023 + 19.5594i 0.693540 + 0.181106i
\(109\) −18.3200 + 56.3831i −0.168073 + 0.517276i −0.999250 0.0387326i \(-0.987668\pi\)
0.831176 + 0.556009i \(0.187668\pi\)
\(110\) 290.198 + 21.9091i 2.63817 + 0.199174i
\(111\) −14.7062 + 13.2415i −0.132488 + 0.119293i
\(112\) −75.3368 53.2820i −0.672650 0.475732i
\(113\) −0.758754 7.21906i −0.00671464 0.0638855i 0.990651 0.136417i \(-0.0435588\pi\)
−0.997366 + 0.0725318i \(0.976892\pi\)
\(114\) −148.166 26.9730i −1.29970 0.236605i
\(115\) −21.3195 47.8843i −0.185387 0.416385i
\(116\) 168.097 + 107.647i 1.44911 + 0.927993i
\(117\) −53.6393 23.8818i −0.458455 0.204118i
\(118\) −2.67003 + 1.64792i −0.0226274 + 0.0139654i
\(119\) 25.1820 + 14.5388i 0.211613 + 0.122175i
\(120\) −127.450 146.368i −1.06208 1.21974i
\(121\) 322.691 68.5900i 2.66687 0.566860i
\(122\) 13.9152 + 38.9011i 0.114059 + 0.318861i
\(123\) 28.8591i 0.234627i
\(124\) −54.5602 + 111.352i −0.440002 + 0.897997i
\(125\) 20.8398 0.166719
\(126\) 38.3728 13.7262i 0.304546 0.108938i
\(127\) 18.0978 + 85.1432i 0.142502 + 0.670419i 0.990167 + 0.139888i \(0.0446742\pi\)
−0.847665 + 0.530531i \(0.821992\pi\)
\(128\) 86.0172 94.7894i 0.672009 0.740543i
\(129\) −57.9875 + 100.437i −0.449516 + 0.778584i
\(130\) −119.619 193.811i −0.920144 1.49086i
\(131\) 47.1464 105.893i 0.359897 0.808341i −0.639327 0.768935i \(-0.720787\pi\)
0.999223 0.0394057i \(-0.0125465\pi\)
\(132\) −253.226 162.162i −1.91838 1.22850i
\(133\) 112.062 49.8932i 0.842571 0.375137i
\(134\) 24.4138 134.108i 0.182192 1.00080i
\(135\) −131.896 + 13.8629i −0.977010 + 0.102688i
\(136\) −24.2477 + 32.2335i −0.178292 + 0.237011i
\(137\) 124.964 + 138.786i 0.912144 + 1.01304i 0.999857 + 0.0168927i \(0.00537736\pi\)
−0.0877134 + 0.996146i \(0.527956\pi\)
\(138\) −4.07721 + 54.0048i −0.0295450 + 0.391339i
\(139\) 188.704 + 61.3137i 1.35758 + 0.441106i 0.895236 0.445593i \(-0.147007\pi\)
0.462348 + 0.886699i \(0.347007\pi\)
\(140\) 152.953 + 39.9408i 1.09252 + 0.285292i
\(141\) 28.0879 267.239i 0.199205 1.89531i
\(142\) 51.4089 49.0974i 0.362034 0.345756i
\(143\) −262.234 236.117i −1.83381 1.65117i
\(144\) 12.4574 + 55.1427i 0.0865096 + 0.382936i
\(145\) −334.494 71.0988i −2.30685 0.490337i
\(146\) −192.660 + 92.6486i −1.31959 + 0.634579i
\(147\) 32.7530 45.0806i 0.222809 0.306671i
\(148\) 20.9246 + 7.87963i 0.141383 + 0.0532407i
\(149\) −120.025 207.889i −0.805534 1.39523i −0.915930 0.401339i \(-0.868545\pi\)
0.110395 0.993888i \(-0.464788\pi\)
\(150\) 136.873 + 73.7526i 0.912489 + 0.491684i
\(151\) 116.028 + 159.699i 0.768396 + 1.05761i 0.996469 + 0.0839621i \(0.0267575\pi\)
−0.228073 + 0.973644i \(0.573243\pi\)
\(152\) 49.8848 + 162.683i 0.328190 + 1.07028i
\(153\) −5.50499 16.9426i −0.0359803 0.110736i
\(154\) 244.819 7.19131i 1.58973 0.0466968i
\(155\) 20.2465 211.465i 0.130622 1.36429i
\(156\) 13.8129 + 234.919i 0.0885445 + 1.50589i
\(157\) 56.7323 + 174.604i 0.361353 + 1.11213i 0.952234 + 0.305370i \(0.0987802\pi\)
−0.590881 + 0.806759i \(0.701220\pi\)
\(158\) 24.6228 + 101.141i 0.155840 + 0.640131i
\(159\) 23.7721 + 32.7194i 0.149510 + 0.205783i
\(160\) −80.6793 + 203.904i −0.504246 + 1.27440i
\(161\) −22.0565 38.2030i −0.136997 0.237286i
\(162\) 185.602 + 76.1872i 1.14569 + 0.470292i
\(163\) 57.6825 79.3932i 0.353880 0.487075i −0.594551 0.804058i \(-0.702670\pi\)
0.948431 + 0.316984i \(0.102670\pi\)
\(164\) −28.9581 + 14.9881i −0.176574 + 0.0913907i
\(165\) 503.890 + 107.105i 3.05388 + 0.649122i
\(166\) −91.8224 + 12.3864i −0.553147 + 0.0746166i
\(167\) 146.533 + 131.939i 0.877444 + 0.790054i 0.978805 0.204795i \(-0.0656529\pi\)
−0.101361 + 0.994850i \(0.532320\pi\)
\(168\) −119.550 111.296i −0.711604 0.662478i
\(169\) −11.2006 + 106.567i −0.0662760 + 0.630574i
\(170\) 19.4146 66.3178i 0.114204 0.390105i
\(171\) −71.4742 23.2234i −0.417978 0.135809i
\(172\) 130.898 + 6.02407i 0.761035 + 0.0350237i
\(173\) 15.2146 + 16.8975i 0.0879455 + 0.0976733i 0.785511 0.618848i \(-0.212400\pi\)
−0.697566 + 0.716521i \(0.745733\pi\)
\(174\) 269.408 + 228.616i 1.54832 + 1.31388i
\(175\) −125.947 + 13.2375i −0.719695 + 0.0756430i
\(176\) −31.2053 + 338.314i −0.177303 + 1.92224i
\(177\) −5.07380 + 2.25900i −0.0286655 + 0.0127627i
\(178\) −39.2048 26.7612i −0.220252 0.150344i
\(179\) 73.2462 164.514i 0.409197 0.919071i −0.584954 0.811067i \(-0.698887\pi\)
0.994150 0.108004i \(-0.0344460\pi\)
\(180\) −53.2643 80.8868i −0.295913 0.449371i
\(181\) −138.141 + 239.268i −0.763211 + 1.32192i 0.177976 + 0.984035i \(0.443045\pi\)
−0.941187 + 0.337885i \(0.890288\pi\)
\(182\) −117.169 151.694i −0.643785 0.833486i
\(183\) 15.2051 + 71.5342i 0.0830878 + 0.390898i
\(184\) 56.3076 23.9564i 0.306020 0.130198i
\(185\) −38.3048 −0.207053
\(186\) −122.061 + 182.425i −0.656242 + 0.980782i
\(187\) 107.062i 0.572526i
\(188\) −282.743 + 110.607i −1.50395 + 0.588334i
\(189\) −109.176 + 23.2060i −0.577650 + 0.122783i
\(190\) −178.196 230.704i −0.937875 1.21423i
\(191\) −42.8910 24.7631i −0.224560 0.129650i 0.383500 0.923541i \(-0.374719\pi\)
−0.608060 + 0.793891i \(0.708052\pi\)
\(192\) 173.325 145.928i 0.902732 0.760040i
\(193\) −164.253 73.1300i −0.851050 0.378912i −0.0656070 0.997846i \(-0.520898\pi\)
−0.785443 + 0.618933i \(0.787565\pi\)
\(194\) 67.6071 + 46.1487i 0.348490 + 0.237880i
\(195\) −163.976 368.296i −0.840902 1.88870i
\(196\) −62.2457 9.45262i −0.317580 0.0482277i
\(197\) 21.8790 + 208.164i 0.111061 + 1.05667i 0.898107 + 0.439778i \(0.144943\pi\)
−0.787046 + 0.616895i \(0.788390\pi\)
\(198\) −114.412 97.0882i −0.577837 0.490345i
\(199\) 126.939 114.297i 0.637887 0.574356i −0.285428 0.958400i \(-0.592136\pi\)
0.923315 + 0.384044i \(0.125469\pi\)
\(200\) 2.92006 175.647i 0.0146003 0.878233i
\(201\) 74.5621 229.478i 0.370956 1.14168i
\(202\) −19.0610 + 65.1100i −0.0943616 + 0.322327i
\(203\) −286.221 30.0830i −1.40995 0.148192i
\(204\) −50.1637 + 50.8070i −0.245900 + 0.249054i
\(205\) 37.3784 41.5129i 0.182334 0.202502i
\(206\) 206.620 27.8720i 1.00301 0.135301i
\(207\) −5.61902 + 26.4354i −0.0271450 + 0.127707i
\(208\) 228.551 135.866i 1.09881 0.653203i
\(209\) −365.396 265.475i −1.74830 1.27022i
\(210\) 258.862 + 106.259i 1.23268 + 0.505998i
\(211\) −190.849 + 110.187i −0.904498 + 0.522212i −0.878657 0.477454i \(-0.841560\pi\)
−0.0258415 + 0.999666i \(0.508227\pi\)
\(212\) 20.4856 40.8466i 0.0966303 0.192673i
\(213\) 101.801 73.9629i 0.477940 0.347244i
\(214\) 28.9087 + 118.746i 0.135087 + 0.554887i
\(215\) −213.500 + 69.3703i −0.993023 + 0.322653i
\(216\) −13.6222 154.228i −0.0630657 0.714017i
\(217\) −1.65676 178.774i −0.00763484 0.823845i
\(218\) 118.518 3.48136i 0.543662 0.0159695i
\(219\) −359.894 + 116.937i −1.64335 + 0.533957i
\(220\) −154.224 561.244i −0.701018 2.55111i
\(221\) −67.7845 + 49.2483i −0.306717 + 0.222843i
\(222\) 34.8420 + 18.7742i 0.156946 + 0.0845685i
\(223\) −180.358 + 104.130i −0.808781 + 0.466950i −0.846532 0.532337i \(-0.821314\pi\)
0.0377516 + 0.999287i \(0.487980\pi\)
\(224\) −49.5898 + 177.762i −0.221383 + 0.793580i
\(225\) 62.7689 + 45.6043i 0.278973 + 0.202686i
\(226\) −13.0834 + 6.29172i −0.0578913 + 0.0278395i
\(227\) −60.4654 + 284.467i −0.266367 + 1.25316i 0.617929 + 0.786234i \(0.287972\pi\)
−0.884296 + 0.466926i \(0.845361\pi\)
\(228\) 49.0128 + 297.188i 0.214968 + 1.30345i
\(229\) 57.0135 63.3199i 0.248967 0.276506i −0.605688 0.795702i \(-0.707102\pi\)
0.854655 + 0.519196i \(0.173769\pi\)
\(230\) −75.8121 + 72.4034i −0.329618 + 0.314797i
\(231\) 431.170 + 45.3178i 1.86654 + 0.196181i
\(232\) 89.4825 389.065i 0.385700 1.67700i
\(233\) −87.9802 + 270.775i −0.377597 + 1.16212i 0.564112 + 0.825698i \(0.309218\pi\)
−0.941710 + 0.336427i \(0.890782\pi\)
\(234\) −8.84055 + 117.098i −0.0377801 + 0.500418i
\(235\) 386.532 348.035i 1.64481 1.48100i
\(236\) 4.90185 + 3.91799i 0.0207705 + 0.0166017i
\(237\) 19.2604 + 183.251i 0.0812676 + 0.773210i
\(238\) 10.4157 57.2149i 0.0437636 0.240399i
\(239\) 43.5894 + 97.9034i 0.182382 + 0.409638i 0.981480 0.191563i \(-0.0613558\pi\)
−0.799098 + 0.601201i \(0.794689\pi\)
\(240\) −189.781 + 338.602i −0.790754 + 1.41084i
\(241\) −9.82091 4.37255i −0.0407506 0.0181434i 0.386260 0.922390i \(-0.373767\pi\)
−0.427011 + 0.904247i \(0.640433\pi\)
\(242\) −346.535 561.471i −1.43196 2.32013i
\(243\) 156.715 + 90.4794i 0.644917 + 0.372343i
\(244\) 63.8829 52.4088i 0.261815 0.214790i
\(245\) 105.503 22.4253i 0.430623 0.0915317i
\(246\) −54.3460 + 19.4400i −0.220919 + 0.0790243i
\(247\) 353.461i 1.43102i
\(248\) 246.444 + 27.7366i 0.993726 + 0.111841i
\(249\) −164.009 −0.658669
\(250\) −14.0381 39.2445i −0.0561522 0.156978i
\(251\) 34.6450 + 162.992i 0.138028 + 0.649371i 0.991701 + 0.128562i \(0.0410361\pi\)
−0.853673 + 0.520809i \(0.825631\pi\)
\(252\) −51.6971 63.0154i −0.205147 0.250061i
\(253\) −81.2109 + 140.661i −0.320992 + 0.555974i
\(254\) 148.146 91.4346i 0.583253 0.359979i
\(255\) 49.7509 111.742i 0.195102 0.438206i
\(256\) −236.445 98.1313i −0.923613 0.383325i
\(257\) 300.935 133.985i 1.17095 0.521342i 0.273250 0.961943i \(-0.411902\pi\)
0.897703 + 0.440602i \(0.145235\pi\)
\(258\) 228.200 + 41.5428i 0.884495 + 0.161019i
\(259\) −32.0605 + 3.36970i −0.123786 + 0.0130104i
\(260\) −284.398 + 355.814i −1.09384 + 1.36852i
\(261\) 117.981 + 131.031i 0.452035 + 0.502036i
\(262\) −231.170 17.4527i −0.882328 0.0666133i
\(263\) −259.953 84.4640i −0.988416 0.321156i −0.230189 0.973146i \(-0.573934\pi\)
−0.758227 + 0.651990i \(0.773934\pi\)
\(264\) −134.799 + 586.097i −0.510601 + 2.22006i
\(265\) −8.18294 + 77.8555i −0.0308790 + 0.293794i
\(266\) −169.443 177.420i −0.637003 0.666993i
\(267\) −62.4415 56.2226i −0.233863 0.210572i
\(268\) −268.990 + 44.3624i −1.00369 + 0.165531i
\(269\) 292.579 + 62.1897i 1.08766 + 0.231188i 0.716644 0.697440i \(-0.245677\pi\)
0.371012 + 0.928628i \(0.379011\pi\)
\(270\) 114.953 + 239.042i 0.425753 + 0.885341i
\(271\) 224.488 308.981i 0.828369 1.14015i −0.159856 0.987140i \(-0.551103\pi\)
0.988224 0.153012i \(-0.0488972\pi\)
\(272\) 77.0340 + 23.9490i 0.283213 + 0.0880480i
\(273\) −169.645 293.833i −0.621409 1.07631i
\(274\) 177.177 328.814i 0.646633 1.20005i
\(275\) 274.075 + 377.231i 0.996635 + 1.37175i
\(276\) 104.445 28.7005i 0.378426 0.103987i
\(277\) −32.0678 98.6944i −0.115768 0.356297i 0.876338 0.481696i \(-0.159979\pi\)
−0.992106 + 0.125399i \(0.959979\pi\)
\(278\) −11.6515 396.659i −0.0419118 1.42683i
\(279\) −72.5334 + 82.0734i −0.259976 + 0.294170i
\(280\) −27.8169 314.937i −0.0993460 1.12477i
\(281\) 31.3167 + 96.3830i 0.111447 + 0.343000i 0.991190 0.132451i \(-0.0422848\pi\)
−0.879742 + 0.475451i \(0.842285\pi\)
\(282\) −522.170 + 127.123i −1.85167 + 0.450789i
\(283\) 120.028 + 165.204i 0.424127 + 0.583760i 0.966593 0.256317i \(-0.0825092\pi\)
−0.542466 + 0.840078i \(0.682509\pi\)
\(284\) −127.087 63.7377i −0.447491 0.224428i
\(285\) −258.004 446.876i −0.905278 1.56799i
\(286\) −267.997 + 652.877i −0.937053 + 2.28279i
\(287\) 27.6332 38.0339i 0.0962831 0.132522i
\(288\) 95.4504 60.6041i 0.331425 0.210431i
\(289\) 257.819 + 54.8011i 0.892108 + 0.189623i
\(290\) 91.4308 + 677.794i 0.315279 + 2.33722i
\(291\) 107.678 + 96.9537i 0.370027 + 0.333174i
\(292\) 304.250 + 300.397i 1.04195 + 1.02876i
\(293\) 15.5843 148.275i 0.0531887 0.506057i −0.935201 0.354117i \(-0.884781\pi\)
0.988390 0.151940i \(-0.0485519\pi\)
\(294\) −106.956 31.3116i −0.363797 0.106502i
\(295\) −10.2244 3.32210i −0.0346589 0.0112613i
\(296\) 0.743321 44.7120i 0.00251122 0.151054i
\(297\) 274.986 + 305.403i 0.925879 + 1.02829i
\(298\) −310.634 + 366.061i −1.04240 + 1.22839i
\(299\) 126.414 13.2866i 0.422789 0.0444369i
\(300\) 46.6868 307.434i 0.155623 1.02478i
\(301\) −172.594 + 76.8437i −0.573401 + 0.255295i
\(302\) 222.578 326.073i 0.737012 1.07971i
\(303\) −48.8448 + 109.707i −0.161204 + 0.362070i
\(304\) 272.752 203.526i 0.897212 0.669494i
\(305\) −70.7793 + 122.593i −0.232063 + 0.401945i
\(306\) −28.1972 + 21.7795i −0.0921476 + 0.0711749i
\(307\) −77.0171 362.337i −0.250870 1.18025i −0.905515 0.424314i \(-0.860515\pi\)
0.654645 0.755936i \(-0.272818\pi\)
\(308\) −178.456 456.186i −0.579403 1.48112i
\(309\) 369.055 1.19435
\(310\) −411.858 + 104.319i −1.32858 + 0.336514i
\(311\) 56.5763i 0.181917i −0.995855 0.0909587i \(-0.971007\pi\)
0.995855 0.0909587i \(-0.0289931\pi\)
\(312\) 433.083 184.257i 1.38809 0.590568i
\(313\) −186.346 + 39.6091i −0.595354 + 0.126547i −0.495727 0.868478i \(-0.665098\pi\)
−0.0996273 + 0.995025i \(0.531765\pi\)
\(314\) 290.590 224.452i 0.925444 0.714814i
\(315\) 120.929 + 69.8181i 0.383900 + 0.221645i
\(316\) 173.877 114.498i 0.550242 0.362337i
\(317\) 11.0316 + 4.91159i 0.0348000 + 0.0154940i 0.424063 0.905633i \(-0.360604\pi\)
−0.389263 + 0.921127i \(0.627270\pi\)
\(318\) 45.6023 66.8066i 0.143403 0.210084i
\(319\) 431.001 + 968.044i 1.35110 + 3.03462i
\(320\) 438.327 + 14.5781i 1.36977 + 0.0455566i
\(321\) 22.6130 + 215.148i 0.0704454 + 0.670243i
\(322\) −57.0842 + 67.2698i −0.177280 + 0.208912i
\(323\) −79.6959 + 71.7585i −0.246737 + 0.222163i
\(324\) 18.4470 400.838i 0.0569351 1.23715i
\(325\) 112.763 347.050i 0.346964 1.06785i
\(326\) −188.365 55.1441i −0.577806 0.169154i
\(327\) 208.732 + 21.9386i 0.638325 + 0.0670906i
\(328\) 47.7314 + 44.4362i 0.145523 + 0.135476i
\(329\) 292.904 325.303i 0.890287 0.988764i
\(330\) −137.734 1021.05i −0.417375 3.09408i
\(331\) 11.8410 55.7073i 0.0357733 0.168300i −0.956635 0.291291i \(-0.905915\pi\)
0.992408 + 0.122991i \(0.0392486\pi\)
\(332\) 85.1784 + 164.571i 0.256561 + 0.495697i
\(333\) 15.9782 + 11.6089i 0.0479827 + 0.0348615i
\(334\) 149.754 364.820i 0.448364 1.09227i
\(335\) 404.476 233.524i 1.20739 0.697088i
\(336\) −129.057 + 300.100i −0.384098 + 0.893156i
\(337\) −154.119 + 111.974i −0.457327 + 0.332268i −0.792482 0.609896i \(-0.791211\pi\)
0.335155 + 0.942163i \(0.391211\pi\)
\(338\) 208.226 50.6928i 0.616054 0.149979i
\(339\) −24.4402 + 7.94111i −0.0720950 + 0.0234251i
\(340\) −137.964 + 8.11211i −0.405777 + 0.0238592i
\(341\) −567.001 + 334.402i −1.66276 + 0.980651i
\(342\) 4.41315 + 150.240i 0.0129039 + 0.439298i
\(343\) 355.091 115.376i 1.03525 0.336374i
\(344\) −76.8308 250.558i −0.223345 0.728366i
\(345\) −150.125 + 109.072i −0.435145 + 0.316151i
\(346\) 21.5717 40.0337i 0.0623459 0.115704i
\(347\) −503.378 + 290.625i −1.45066 + 0.837537i −0.998519 0.0544109i \(-0.982672\pi\)
−0.452138 + 0.891948i \(0.649339\pi\)
\(348\) 249.040 661.334i 0.715631 1.90038i
\(349\) −262.803 190.937i −0.753016 0.547098i 0.143744 0.989615i \(-0.454086\pi\)
−0.896760 + 0.442517i \(0.854086\pi\)
\(350\) 109.768 + 228.259i 0.313622 + 0.652168i
\(351\) 66.8674 314.586i 0.190505 0.896257i
\(352\) 658.116 169.130i 1.86965 0.480483i
\(353\) −370.664 + 411.664i −1.05004 + 1.16619i −0.0642959 + 0.997931i \(0.520480\pi\)
−0.985743 + 0.168256i \(0.946187\pi\)
\(354\) 7.67183 + 8.03301i 0.0216718 + 0.0226921i
\(355\) 242.235 + 25.4599i 0.682351 + 0.0717180i
\(356\) −23.9863 + 91.8552i −0.0673773 + 0.258020i
\(357\) 31.8107 97.9034i 0.0891057 0.274239i
\(358\) −359.143 27.1143i −1.00319 0.0757382i
\(359\) −369.491 + 332.691i −1.02922 + 0.926715i −0.997348 0.0727766i \(-0.976814\pi\)
−0.0318734 + 0.999492i \(0.510147\pi\)
\(360\) −116.442 + 154.791i −0.323450 + 0.429975i
\(361\) 9.55485 + 90.9084i 0.0264677 + 0.251824i
\(362\) 543.630 + 98.9656i 1.50174 + 0.273386i
\(363\) −475.037 1066.95i −1.30864 2.93926i
\(364\) −206.736 + 322.830i −0.567956 + 0.886895i
\(365\) −669.152 297.926i −1.83329 0.816234i
\(366\) 124.467 76.8200i 0.340074 0.209891i
\(367\) −350.358 202.279i −0.954653 0.551169i −0.0601295 0.998191i \(-0.519151\pi\)
−0.894523 + 0.447022i \(0.852485\pi\)
\(368\) −83.0431 89.8981i −0.225661 0.244288i
\(369\) −28.1730 + 5.98835i −0.0763495 + 0.0162286i
\(370\) 25.8027 + 72.1335i 0.0697371 + 0.194955i
\(371\) 65.8838i 0.177584i
\(372\) 425.756 + 106.974i 1.14451 + 0.287565i
\(373\) 244.662 0.655930 0.327965 0.944690i \(-0.393637\pi\)
0.327965 + 0.944690i \(0.393637\pi\)
\(374\) −201.614 + 72.1189i −0.539075 + 0.192831i
\(375\) −15.3393 72.1657i −0.0409048 0.192442i
\(376\) 398.749 + 457.940i 1.06050 + 1.21793i
\(377\) 414.639 718.176i 1.09984 1.90498i
\(378\) 117.243 + 189.962i 0.310166 + 0.502545i
\(379\) −66.2600 + 148.822i −0.174828 + 0.392671i −0.979612 0.200897i \(-0.935614\pi\)
0.804784 + 0.593568i \(0.202281\pi\)
\(380\) −314.414 + 490.976i −0.827407 + 1.29204i
\(381\) 281.519 125.340i 0.738896 0.328978i
\(382\) −17.7405 + 97.4509i −0.0464412 + 0.255107i
\(383\) −110.563 + 11.6206i −0.288675 + 0.0303410i −0.247759 0.968822i \(-0.579694\pi\)
−0.0409158 + 0.999163i \(0.513028\pi\)
\(384\) −391.557 228.096i −1.01968 0.594001i
\(385\) 561.529 + 623.641i 1.45852 + 1.61985i
\(386\) −27.0713 + 358.574i −0.0701329 + 0.928947i
\(387\) 110.082 + 35.7678i 0.284449 + 0.0924232i
\(388\) 41.3635 158.401i 0.106607 0.408249i
\(389\) −19.1964 + 182.642i −0.0493481 + 0.469516i 0.941743 + 0.336333i \(0.109187\pi\)
−0.991091 + 0.133184i \(0.957480\pi\)
\(390\) −583.098 + 556.881i −1.49512 + 1.42790i
\(391\) 28.6599 + 25.8055i 0.0732990 + 0.0659987i
\(392\) 24.1290 + 123.585i 0.0615536 + 0.315268i
\(393\) −401.395 85.3192i −1.02136 0.217097i
\(394\) 377.266 181.424i 0.957528 0.460468i
\(395\) −209.641 + 288.546i −0.530737 + 0.730497i
\(396\) −105.762 + 280.854i −0.267075 + 0.709228i
\(397\) 59.2044 + 102.545i 0.149129 + 0.258300i 0.930906 0.365259i \(-0.119020\pi\)
−0.781777 + 0.623559i \(0.785686\pi\)
\(398\) −300.746 162.053i −0.755643 0.407169i
\(399\) −255.258 351.332i −0.639744 0.880532i
\(400\) −332.735 + 112.820i −0.831839 + 0.282049i
\(401\) 82.4136 + 253.643i 0.205520 + 0.632526i 0.999692 + 0.0248325i \(0.00790525\pi\)
−0.794171 + 0.607694i \(0.792095\pi\)
\(402\) −482.368 + 14.1691i −1.19992 + 0.0352464i
\(403\) 472.538 + 205.162i 1.17255 + 0.509087i
\(404\) 135.451 7.96437i 0.335276 0.0197138i
\(405\) 212.427 + 653.782i 0.524510 + 1.61428i
\(406\) 136.152 + 559.260i 0.335350 + 1.37749i
\(407\) 69.7675 + 96.0267i 0.171419 + 0.235938i
\(408\) 129.468 + 60.2412i 0.317324 + 0.147650i
\(409\) −82.9219 143.625i −0.202743 0.351161i 0.746668 0.665197i \(-0.231652\pi\)
−0.949411 + 0.314035i \(0.898319\pi\)
\(410\) −103.354 42.4252i −0.252082 0.103476i
\(411\) 388.619 534.888i 0.945545 1.30143i
\(412\) −191.670 370.321i −0.465218 0.898838i
\(413\) −8.84989 1.88110i −0.0214283 0.00455473i
\(414\) 53.5668 7.22588i 0.129388 0.0174538i
\(415\) −235.921 212.424i −0.568485 0.511866i
\(416\) −409.812 338.874i −0.985125 0.814601i
\(417\) 73.4246 698.589i 0.176078 1.67527i
\(418\) −253.793 + 866.922i −0.607160 + 2.07398i
\(419\) −485.455 157.734i −1.15860 0.376453i −0.334226 0.942493i \(-0.608475\pi\)
−0.824378 + 0.566040i \(0.808475\pi\)
\(420\) 25.7283 559.054i 0.0612578 1.33108i
\(421\) −518.010 575.309i −1.23043 1.36653i −0.907471 0.420115i \(-0.861990\pi\)
−0.322957 0.946414i \(-0.604677\pi\)
\(422\) 336.057 + 285.173i 0.796344 + 0.675766i
\(423\) −266.713 + 28.0327i −0.630527 + 0.0662711i
\(424\) −90.7195 11.0625i −0.213961 0.0260908i
\(425\) 101.143 45.0319i 0.237984 0.105957i
\(426\) −207.858 141.884i −0.487929 0.333061i
\(427\) −48.4566 + 108.835i −0.113481 + 0.254884i
\(428\) 204.142 134.428i 0.476968 0.314085i
\(429\) −624.623 + 1081.88i −1.45600 + 2.52186i
\(430\) 274.451 + 355.323i 0.638259 + 0.826332i
\(431\) −88.7308 417.445i −0.205872 0.968551i −0.952789 0.303634i \(-0.901800\pi\)
0.746917 0.664917i \(-0.231533\pi\)
\(432\) −281.257 + 129.543i −0.651058 + 0.299868i
\(433\) 690.912 1.59564 0.797819 0.602897i \(-0.205987\pi\)
0.797819 + 0.602897i \(0.205987\pi\)
\(434\) −335.542 + 123.545i −0.773139 + 0.284666i
\(435\) 1210.64i 2.78309i
\(436\) −86.3917 220.842i −0.198146 0.506519i
\(437\) 159.138 33.8259i 0.364161 0.0774047i
\(438\) 462.639 + 598.962i 1.05625 + 1.36749i
\(439\) −233.085 134.572i −0.530946 0.306542i 0.210455 0.977603i \(-0.432505\pi\)
−0.741402 + 0.671062i \(0.765839\pi\)
\(440\) −953.017 + 668.490i −2.16595 + 1.51929i
\(441\) −50.8051 22.6199i −0.115204 0.0512923i
\(442\) 138.402 + 94.4737i 0.313128 + 0.213741i
\(443\) −250.604 562.865i −0.565697 1.27058i −0.939335 0.343002i \(-0.888556\pi\)
0.373638 0.927575i \(-0.378110\pi\)
\(444\) 11.8844 78.2592i 0.0267668 0.176260i
\(445\) −17.0005 161.749i −0.0382033 0.363480i
\(446\) 317.584 + 269.497i 0.712071 + 0.604254i
\(447\) −631.547 + 568.648i −1.41286 + 1.27214i
\(448\) 368.156 26.3583i 0.821777 0.0588355i
\(449\) 258.272 794.879i 0.575216 1.77033i −0.0602266 0.998185i \(-0.519182\pi\)
0.635443 0.772148i \(-0.280818\pi\)
\(450\) 43.5974 148.923i 0.0968831 0.330940i
\(451\) −172.149 18.0936i −0.381706 0.0401189i
\(452\) 20.6615 + 20.3998i 0.0457112 + 0.0451324i
\(453\) 467.613 519.337i 1.03226 1.14644i
\(454\) 576.424 77.7566i 1.26966 0.171270i
\(455\) 136.545 642.394i 0.300099 1.41185i
\(456\) 526.632 292.489i 1.15489 0.641422i
\(457\) 305.947 + 222.284i 0.669469 + 0.486398i 0.869848 0.493321i \(-0.164217\pi\)
−0.200378 + 0.979719i \(0.564217\pi\)
\(458\) −157.646 64.7115i −0.344205 0.141292i
\(459\) 84.5059 48.7895i 0.184109 0.106295i
\(460\) 187.414 + 93.9932i 0.407423 + 0.204333i
\(461\) −321.660 + 233.699i −0.697743 + 0.506940i −0.879196 0.476459i \(-0.841920\pi\)
0.181453 + 0.983400i \(0.441920\pi\)
\(462\) −205.103 842.484i −0.443946 1.82356i
\(463\) −262.579 + 85.3171i −0.567125 + 0.184270i −0.578525 0.815665i \(-0.696371\pi\)
0.0113994 + 0.999935i \(0.496371\pi\)
\(464\) −792.943 + 93.5715i −1.70893 + 0.201663i
\(465\) −747.180 + 85.5395i −1.60684 + 0.183956i
\(466\) 569.174 16.7189i 1.22140 0.0358775i
\(467\) 61.9549 20.1304i 0.132666 0.0431057i −0.241932 0.970293i \(-0.577781\pi\)
0.374597 + 0.927188i \(0.377781\pi\)
\(468\) 226.467 62.2309i 0.483905 0.132972i
\(469\) 317.997 231.038i 0.678032 0.492619i
\(470\) −915.774 493.454i −1.94846 1.04990i
\(471\) 562.874 324.975i 1.19506 0.689969i
\(472\) 4.07619 11.8701i 0.00863600 0.0251486i
\(473\) 562.769 + 408.876i 1.18979 + 0.864430i
\(474\) 332.114 159.711i 0.700662 0.336943i
\(475\) 97.1079 456.857i 0.204438 0.961803i
\(476\) −114.760 + 18.9265i −0.241093 + 0.0397616i
\(477\) 27.0087 29.9962i 0.0566221 0.0628852i
\(478\) 155.004 148.035i 0.324276 0.309696i
\(479\) −715.594 75.2120i −1.49393 0.157019i −0.677956 0.735103i \(-0.737134\pi\)
−0.815977 + 0.578084i \(0.803801\pi\)
\(480\) 765.477 + 129.298i 1.59474 + 0.269370i
\(481\) 28.7047 88.3438i 0.0596770 0.183667i
\(482\) −1.61863 + 21.4396i −0.00335816 + 0.0444806i
\(483\) −116.057 + 104.498i −0.240284 + 0.216353i
\(484\) −823.900 + 1030.79i −1.70227 + 2.12973i
\(485\) 29.3167 + 278.929i 0.0604467 + 0.575112i
\(486\) 64.8203 356.066i 0.133375 0.732645i
\(487\) 269.684 + 605.720i 0.553766 + 1.24378i 0.946076 + 0.323945i \(0.105009\pi\)
−0.392310 + 0.919833i \(0.628324\pi\)
\(488\) −141.726 84.9975i −0.290422 0.174175i
\(489\) −317.386 141.309i −0.649051 0.288976i
\(490\) −113.298 183.571i −0.231221 0.374634i
\(491\) 575.489 + 332.259i 1.17208 + 0.676698i 0.954168 0.299272i \(-0.0967436\pi\)
0.217907 + 0.975969i \(0.430077\pi\)
\(492\) 73.2166 + 89.2463i 0.148814 + 0.181395i
\(493\) 246.108 52.3119i 0.499205 0.106109i
\(494\) 665.619 238.097i 1.34741 0.481978i
\(495\) 514.134i 1.03865i
\(496\) −113.777 482.774i −0.229388 0.973335i
\(497\) 204.986 0.412448
\(498\) 110.479 + 308.852i 0.221845 + 0.620186i
\(499\) −97.0842 456.745i −0.194557 0.915321i −0.961755 0.273910i \(-0.911683\pi\)
0.767198 0.641411i \(-0.221650\pi\)
\(500\) −64.4469 + 52.8714i −0.128894 + 0.105743i
\(501\) 349.032 604.540i 0.696670 1.20667i
\(502\) 283.600 175.036i 0.564941 0.348677i
\(503\) 171.535 385.273i 0.341023 0.765951i −0.658883 0.752246i \(-0.728971\pi\)
0.999906 0.0137051i \(-0.00436262\pi\)
\(504\) −83.8432 + 139.801i −0.166356 + 0.277384i
\(505\) −212.355 + 94.5464i −0.420504 + 0.187221i
\(506\) 319.591 + 58.1803i 0.631603 + 0.114981i
\(507\) 377.273 39.6529i 0.744127 0.0782109i
\(508\) −271.978 217.389i −0.535391 0.427932i
\(509\) 139.926 + 155.404i 0.274905 + 0.305312i 0.864749 0.502205i \(-0.167478\pi\)
−0.589844 + 0.807517i \(0.700811\pi\)
\(510\) −243.940 18.4168i −0.478314 0.0361114i
\(511\) −586.279 190.494i −1.14732 0.372786i
\(512\) −25.5225 + 511.363i −0.0498487 + 0.998757i
\(513\) 43.0289 409.392i 0.0838769 0.798036i
\(514\) −455.027 476.450i −0.885267 0.926945i
\(515\) 530.873 + 478.000i 1.03082 + 0.928156i
\(516\) −75.4877 457.717i −0.146294 0.887049i
\(517\) −1576.51 335.098i −3.04934 0.648158i
\(518\) 27.9421 + 58.1048i 0.0539423 + 0.112171i
\(519\) 47.3151 65.1236i 0.0911658 0.125479i
\(520\) 861.625 + 295.882i 1.65697 + 0.569003i
\(521\) 282.580 + 489.443i 0.542380 + 0.939430i 0.998767 + 0.0496487i \(0.0158102\pi\)
−0.456386 + 0.889782i \(0.650856\pi\)
\(522\) 167.277 310.441i 0.320455 0.594714i
\(523\) −28.3790 39.0604i −0.0542620 0.0746853i 0.781024 0.624501i \(-0.214698\pi\)
−0.835286 + 0.549816i \(0.814698\pi\)
\(524\) 122.854 + 447.083i 0.234454 + 0.853213i
\(525\) 138.544 + 426.394i 0.263893 + 0.812178i
\(526\) 16.0507 + 546.427i 0.0305147 + 1.03883i
\(527\) 49.6748 + 148.196i 0.0942595 + 0.281207i
\(528\) 1194.51 140.958i 2.26233 0.266967i
\(529\) 145.390 + 447.465i 0.274840 + 0.845870i
\(530\) 152.125 37.0350i 0.287029 0.0698774i
\(531\) 3.25812 + 4.48442i 0.00613582 + 0.00844523i
\(532\) −219.969 + 438.599i −0.413475 + 0.824434i
\(533\) 67.7324 + 117.316i 0.127078 + 0.220105i
\(534\) −63.8138 + 155.459i −0.119501 + 0.291122i
\(535\) −246.132 + 338.772i −0.460060 + 0.633219i
\(536\) 264.737 + 476.664i 0.493912 + 0.889299i
\(537\) −623.603 132.551i −1.16127 0.246836i
\(538\) −79.9739 592.862i −0.148650 1.10197i
\(539\) −248.378 223.641i −0.460813 0.414918i
\(540\) 372.717 377.496i 0.690216 0.699068i
\(541\) −43.9345 + 418.009i −0.0812098 + 0.772659i 0.875814 + 0.482649i \(0.160325\pi\)
−0.957024 + 0.290010i \(0.906341\pi\)
\(542\) −733.076 214.609i −1.35254 0.395958i
\(543\) 930.233 + 302.251i 1.71314 + 0.556632i
\(544\) −6.79177 161.199i −0.0124849 0.296321i
\(545\) 271.839 + 301.908i 0.498788 + 0.553960i
\(546\) −439.056 + 517.397i −0.804131 + 0.947613i
\(547\) −133.717 + 14.0542i −0.244455 + 0.0256933i −0.225964 0.974136i \(-0.572553\pi\)
−0.0184917 + 0.999829i \(0.505886\pi\)
\(548\) −738.554 112.157i −1.34773 0.204666i
\(549\) 66.6783 29.6871i 0.121454 0.0540749i
\(550\) 525.761 770.231i 0.955928 1.40042i
\(551\) 431.721 969.662i 0.783524 1.75982i
\(552\) −124.403 177.353i −0.225369 0.321292i
\(553\) −150.083 + 259.951i −0.271398 + 0.470075i
\(554\) −164.255 + 126.870i −0.296489 + 0.229008i
\(555\) 28.1945 + 132.645i 0.0508009 + 0.238999i
\(556\) −739.119 + 289.138i −1.32935 + 0.520032i
\(557\) 354.890 0.637145 0.318573 0.947898i \(-0.396797\pi\)
0.318573 + 0.947898i \(0.396797\pi\)
\(558\) 203.416 + 81.3050i 0.364545 + 0.145708i
\(559\) 544.388i 0.973860i
\(560\) −574.334 + 264.530i −1.02560 + 0.472375i
\(561\) −370.744 + 78.8040i −0.660862 + 0.140471i
\(562\) 160.408 123.899i 0.285423 0.220461i
\(563\) 691.410 + 399.186i 1.22808 + 0.709033i 0.966628 0.256183i \(-0.0824651\pi\)
0.261453 + 0.965216i \(0.415798\pi\)
\(564\) 591.133 + 897.691i 1.04811 + 1.59165i
\(565\) −45.4418 20.2320i −0.0804279 0.0358088i
\(566\) 230.251 337.314i 0.406804 0.595962i
\(567\) 235.312 + 528.518i 0.415012 + 0.932131i
\(568\) −34.4192 + 282.259i −0.0605972 + 0.496935i
\(569\) −52.1278 495.963i −0.0916130 0.871640i −0.939750 0.341863i \(-0.888942\pi\)
0.848137 0.529777i \(-0.177724\pi\)
\(570\) −667.738 + 786.883i −1.17147 + 1.38050i
\(571\) 162.676 146.474i 0.284897 0.256523i −0.514274 0.857626i \(-0.671939\pi\)
0.799171 + 0.601103i \(0.205272\pi\)
\(572\) 1409.99 + 64.8893i 2.46502 + 0.113443i
\(573\) −54.1814 + 166.753i −0.0945574 + 0.291018i
\(574\) −90.2376 26.4172i −0.157208 0.0460230i
\(575\) −167.043 17.5569i −0.290510 0.0305338i
\(576\) −178.423 138.923i −0.309763 0.241186i
\(577\) −185.455 + 205.968i −0.321412 + 0.356964i −0.882099 0.471063i \(-0.843870\pi\)
0.560687 + 0.828028i \(0.310537\pi\)
\(578\) −70.4725 522.426i −0.121925 0.903851i
\(579\) −132.341 + 622.614i −0.228568 + 1.07533i
\(580\) 1214.80 628.751i 2.09448 1.08405i
\(581\) −216.150 157.042i −0.372030 0.270296i
\(582\) 110.044 268.083i 0.189080 0.460624i
\(583\) 210.081 121.290i 0.360345 0.208045i
\(584\) 360.745 775.299i 0.617713 1.32757i
\(585\) −325.514 + 236.500i −0.556434 + 0.404273i
\(586\) −289.721 + 70.5327i −0.494404 + 0.120363i
\(587\) −175.325 + 56.9667i −0.298680 + 0.0970472i −0.454524 0.890735i \(-0.650191\pi\)
0.155843 + 0.987782i \(0.450191\pi\)
\(588\) 13.0831 + 222.507i 0.0222502 + 0.378412i
\(589\) 628.957 + 197.936i 1.06784 + 0.336054i
\(590\) 0.631300 + 21.4918i 0.00107000 + 0.0364268i
\(591\) 704.743 228.985i 1.19246 0.387453i
\(592\) −84.7000 + 28.7189i −0.143074 + 0.0485117i
\(593\) −592.466 + 430.452i −0.999099 + 0.725888i −0.961895 0.273420i \(-0.911845\pi\)
−0.0372043 + 0.999308i \(0.511845\pi\)
\(594\) 389.883 723.563i 0.656369 1.21812i
\(595\) 172.563 99.6295i 0.290022 0.167445i
\(596\) 898.595 + 338.386i 1.50771 + 0.567761i
\(597\) −489.230 355.446i −0.819481 0.595388i
\(598\) −110.175 229.106i −0.184239 0.383120i
\(599\) −221.009 + 1039.76i −0.368963 + 1.73583i 0.266622 + 0.963801i \(0.414092\pi\)
−0.635585 + 0.772031i \(0.719241\pi\)
\(600\) −610.391 + 119.174i −1.01732 + 0.198623i
\(601\) 693.605 770.326i 1.15408 1.28174i 0.200811 0.979630i \(-0.435642\pi\)
0.953273 0.302110i \(-0.0976911\pi\)
\(602\) 260.970 + 273.256i 0.433505 + 0.453914i
\(603\) −239.494 25.1718i −0.397171 0.0417444i
\(604\) −763.975 199.498i −1.26486 0.330295i
\(605\) 698.591 2150.04i 1.15470 3.55379i
\(606\) 239.498 + 18.0814i 0.395211 + 0.0298373i
\(607\) 47.7306 42.9768i 0.0786335 0.0708020i −0.628877 0.777505i \(-0.716485\pi\)
0.707510 + 0.706703i \(0.249818\pi\)
\(608\) −567.000 376.534i −0.932566 0.619299i
\(609\) 106.501 + 1013.29i 0.174879 + 1.66386i
\(610\) 278.539 + 50.7069i 0.456622 + 0.0831261i
\(611\) 513.029 + 1152.28i 0.839654 + 1.88589i
\(612\) 60.0081 + 38.4284i 0.0980524 + 0.0627915i
\(613\) −511.719 227.832i −0.834778 0.371667i −0.0555874 0.998454i \(-0.517703\pi\)
−0.779191 + 0.626787i \(0.784370\pi\)
\(614\) −630.454 + 389.110i −1.02680 + 0.633730i
\(615\) −171.267 98.8808i −0.278482 0.160782i
\(616\) −738.854 + 643.353i −1.19944 + 1.04440i
\(617\) −1106.89 + 235.276i −1.79398 + 0.381322i −0.979909 0.199444i \(-0.936087\pi\)
−0.814071 + 0.580766i \(0.802753\pi\)
\(618\) −248.601 694.984i −0.402267 1.12457i
\(619\) 62.7835i 0.101427i −0.998713 0.0507136i \(-0.983850\pi\)
0.998713 0.0507136i \(-0.0161496\pi\)
\(620\) 473.883 + 705.319i 0.764328 + 1.13761i
\(621\) −148.035 −0.238381
\(622\) −106.542 + 38.1107i −0.171289 + 0.0612713i
\(623\) −28.4583 133.886i −0.0456795 0.214905i
\(624\) −638.715 691.440i −1.02358 1.10808i
\(625\) 345.890 599.099i 0.553424 0.958558i
\(626\) 200.115 + 324.235i 0.319673 + 0.517948i
\(627\) −650.356 + 1460.72i −1.03725 + 2.32970i
\(628\) −618.421 396.028i −0.984747 0.630619i
\(629\) 25.7467 11.4632i 0.0409327 0.0182244i
\(630\) 50.0184 274.757i 0.0793942 0.436122i
\(631\) −294.165 + 30.9180i −0.466189 + 0.0489984i −0.334711 0.942321i \(-0.608639\pi\)
−0.131477 + 0.991319i \(0.541972\pi\)
\(632\) −332.743 250.307i −0.526492 0.396056i
\(633\) 522.039 + 579.783i 0.824706 + 0.915929i
\(634\) 1.81817 24.0827i 0.00286778 0.0379853i
\(635\) 567.298 + 184.326i 0.893382 + 0.290277i
\(636\) −156.525 40.8737i −0.246109 0.0642669i
\(637\) −27.3407 + 260.130i −0.0429211 + 0.408367i
\(638\) 1532.64 1463.73i 2.40226 2.29424i
\(639\) −93.3283 84.0332i −0.146054 0.131507i
\(640\) −267.812 835.255i −0.418456 1.30509i
\(641\) 570.528 + 121.269i 0.890059 + 0.189188i 0.630176 0.776452i \(-0.282983\pi\)
0.259883 + 0.965640i \(0.416316\pi\)
\(642\) 389.923 187.511i 0.607357 0.292073i
\(643\) −473.581 + 651.829i −0.736519 + 1.01373i 0.262293 + 0.964988i \(0.415521\pi\)
−0.998811 + 0.0487425i \(0.984479\pi\)
\(644\) 165.132 + 62.1839i 0.256416 + 0.0965589i
\(645\) 397.369 + 688.263i 0.616075 + 1.06707i
\(646\) 188.816 + 101.741i 0.292285 + 0.157494i
\(647\) 168.537 + 231.971i 0.260490 + 0.358534i 0.919151 0.393906i \(-0.128877\pi\)
−0.658660 + 0.752440i \(0.728877\pi\)
\(648\) −767.262 + 235.272i −1.18405 + 0.363074i
\(649\) 10.2942 + 31.6824i 0.0158617 + 0.0488172i
\(650\) −729.505 + 21.4285i −1.12232 + 0.0329669i
\(651\) −617.854 + 137.325i −0.949084 + 0.210945i
\(652\) 23.0411 + 391.865i 0.0353392 + 0.601019i
\(653\) −107.373 330.461i −0.164431 0.506066i 0.834563 0.550912i \(-0.185720\pi\)
−0.998994 + 0.0448464i \(0.985720\pi\)
\(654\) −99.2917 407.851i −0.151822 0.623626i
\(655\) −466.888 642.617i −0.712807 0.981094i
\(656\) 51.5273 119.818i 0.0785477 0.182650i
\(657\) 188.835 + 327.072i 0.287420 + 0.497827i
\(658\) −809.899 332.452i −1.23085 0.505247i
\(659\) −419.662 + 577.616i −0.636817 + 0.876504i −0.998441 0.0558206i \(-0.982223\pi\)
0.361624 + 0.932324i \(0.382223\pi\)
\(660\) −1830.00 + 947.166i −2.77273 + 1.43510i
\(661\) −367.407 78.0947i −0.555835 0.118146i −0.0785744 0.996908i \(-0.525037\pi\)
−0.477260 + 0.878762i \(0.658370\pi\)
\(662\) −112.881 + 15.2271i −0.170516 + 0.0230016i
\(663\) 220.434 + 198.480i 0.332479 + 0.299366i
\(664\) 252.535 271.261i 0.380323 0.408526i
\(665\) 87.8661 835.990i 0.132129 1.25713i
\(666\) 11.0980 37.9093i 0.0166637 0.0569209i
\(667\) −363.024 117.954i −0.544264 0.176842i
\(668\) −787.885 36.2594i −1.17947 0.0542805i
\(669\) 493.342 + 547.912i 0.737432 + 0.819001i
\(670\) −712.222 604.382i −1.06302 0.902063i
\(671\) 436.246 45.8513i 0.650144 0.0683328i
\(672\) 652.068 + 40.8805i 0.970339 + 0.0608341i
\(673\) 595.289 265.040i 0.884531 0.393819i 0.0863702 0.996263i \(-0.472473\pi\)
0.798161 + 0.602445i \(0.205807\pi\)
\(674\) 314.681 + 214.802i 0.466886 + 0.318697i
\(675\) −172.855 + 388.240i −0.256082 + 0.575170i
\(676\) −235.727 357.973i −0.348708 0.529546i
\(677\) −539.394 + 934.258i −0.796742 + 1.38000i 0.124985 + 0.992159i \(0.460112\pi\)
−0.921727 + 0.387839i \(0.873222\pi\)
\(678\) 31.4176 + 40.6752i 0.0463386 + 0.0599930i
\(679\) 49.0752 + 230.881i 0.0722757 + 0.340031i
\(680\) 108.211 + 254.342i 0.159134 + 0.374033i
\(681\) 1029.58 1.51187
\(682\) 1011.67 + 842.487i 1.48339 + 1.23532i
\(683\) 1034.00i 1.51391i −0.653467 0.756955i \(-0.726686\pi\)
0.653467 0.756955i \(-0.273314\pi\)
\(684\) 279.951 109.515i 0.409285 0.160109i
\(685\) 1251.80 266.079i 1.82745 0.388437i
\(686\) −456.466 590.970i −0.665402 0.861472i
\(687\) −261.234 150.824i −0.380253 0.219539i
\(688\) −420.083 + 313.464i −0.610586 + 0.455616i
\(689\) −173.429 77.2156i −0.251711 0.112069i
\(690\) 306.526 + 209.235i 0.444240 + 0.303239i
\(691\) −442.302 993.427i −0.640090 1.43767i −0.883822 0.467823i \(-0.845038\pi\)
0.243732 0.969843i \(-0.421628\pi\)
\(692\) −89.9203 13.6553i −0.129943 0.0197331i
\(693\) −45.2287 430.322i −0.0652651 0.620956i
\(694\) 886.374 + 752.164i 1.27720 + 1.08381i
\(695\) 1010.43 909.797i 1.45386 1.30906i
\(696\) −1413.15 23.4930i −2.03038 0.0337544i
\(697\) −12.7008 + 39.0890i −0.0182221 + 0.0560817i
\(698\) −182.535 + 623.514i −0.261511 + 0.893287i
\(699\) 1002.42 + 105.358i 1.43407 + 0.150727i
\(700\) 355.904 360.468i 0.508434 0.514954i
\(701\) 151.228 167.956i 0.215732 0.239595i −0.625559 0.780177i \(-0.715129\pi\)
0.841291 + 0.540582i \(0.181796\pi\)
\(702\) −637.455 + 85.9893i −0.908056 + 0.122492i
\(703\) 24.7195 116.296i 0.0351628 0.165428i
\(704\) −761.814 1125.40i −1.08212 1.59858i
\(705\) −1489.71 1082.34i −2.11306 1.53523i
\(706\) 1024.91 + 420.711i 1.45171 + 0.595908i
\(707\) −169.420 + 97.8150i −0.239633 + 0.138352i
\(708\) 9.95947 19.8583i 0.0140671 0.0280485i
\(709\) −399.359 + 290.151i −0.563270 + 0.409240i −0.832654 0.553793i \(-0.813180\pi\)
0.269384 + 0.963033i \(0.413180\pi\)
\(710\) −115.228 473.313i −0.162294 0.666639i
\(711\) 174.897 56.8275i 0.245988 0.0799262i
\(712\) 189.134 16.7053i 0.265638 0.0234626i
\(713\) 47.1483 232.384i 0.0661267 0.325924i
\(714\) −205.795 + 6.04501i −0.288228 + 0.00846640i
\(715\) −2299.75 + 747.235i −3.21644 + 1.04508i
\(716\) 190.864 + 694.584i 0.266570 + 0.970089i
\(717\) 306.943 223.007i 0.428093 0.311028i
\(718\) 875.400 + 471.699i 1.21922 + 0.656962i
\(719\) 325.051 187.668i 0.452087 0.261013i −0.256624 0.966511i \(-0.582610\pi\)
0.708711 + 0.705499i \(0.249277\pi\)
\(720\) 369.932 + 115.008i 0.513794 + 0.159733i
\(721\) 486.383 + 353.378i 0.674595 + 0.490122i
\(722\) 164.757 79.2305i 0.228196 0.109738i
\(723\) −7.91284 + 37.2270i −0.0109445 + 0.0514896i
\(724\) −179.831 1090.40i −0.248386 1.50608i
\(725\) −733.239 + 814.344i −1.01136 + 1.12323i
\(726\) −1689.23 + 1613.28i −2.32677 + 2.22215i
\(727\) 436.548 + 45.8830i 0.600478 + 0.0631128i 0.399891 0.916563i \(-0.369048\pi\)
0.200588 + 0.979676i \(0.435715\pi\)
\(728\) 747.197 + 171.851i 1.02637 + 0.236059i
\(729\) −81.0249 + 249.369i −0.111145 + 0.342070i
\(730\) −110.286 + 1460.80i −0.151077 + 2.00109i
\(731\) 122.745 110.520i 0.167913 0.151190i
\(732\) −228.506 182.643i −0.312167 0.249512i
\(733\) 38.3991 + 365.343i 0.0523863 + 0.498422i 0.988985 + 0.148018i \(0.0472892\pi\)
−0.936598 + 0.350405i \(0.886044\pi\)
\(734\) −144.915 + 796.033i −0.197431 + 1.08451i
\(735\) −155.312 348.836i −0.211309 0.474607i
\(736\) −113.352 + 216.939i −0.154011 + 0.294754i
\(737\) −1322.13 588.649i −1.79393 0.798710i
\(738\) 30.2547 + 49.0200i 0.0409955 + 0.0664227i
\(739\) −209.215 120.790i −0.283106 0.163451i 0.351723 0.936104i \(-0.385596\pi\)
−0.634829 + 0.772653i \(0.718929\pi\)
\(740\) 118.457 97.1806i 0.160077 0.131325i
\(741\) 1223.99 260.167i 1.65181 0.351103i
\(742\) 124.069 44.3804i 0.167209 0.0598118i
\(743\) 28.2234i 0.0379857i −0.999820 0.0189929i \(-0.993954\pi\)
0.999820 0.0189929i \(-0.00604598\pi\)
\(744\) −85.3482 873.820i −0.114715 1.17449i
\(745\) −1644.97 −2.20802
\(746\) −164.808 460.734i −0.220922 0.617606i
\(747\) 34.0322 + 160.109i 0.0455586 + 0.214336i
\(748\) 271.621 + 331.089i 0.363130 + 0.442632i
\(749\) −176.207 + 305.200i −0.235256 + 0.407476i
\(750\) −125.566 + 77.4982i −0.167421 + 0.103331i
\(751\) 382.794 859.770i 0.509713 1.14483i −0.457116 0.889407i \(-0.651117\pi\)
0.966828 0.255427i \(-0.0822159\pi\)
\(752\) 593.765 1059.38i 0.789581 1.40875i
\(753\) 538.920 239.943i 0.715697 0.318649i
\(754\) −1631.74 297.051i −2.16411 0.393967i
\(755\) 1345.29 141.396i 1.78184 0.187279i
\(756\) 278.750 348.747i 0.368717 0.461306i
\(757\) 831.247 + 923.193i 1.09808 + 1.21954i 0.973827 + 0.227291i \(0.0729869\pi\)
0.124253 + 0.992251i \(0.460346\pi\)
\(758\) 324.888 + 24.5281i 0.428612 + 0.0323590i
\(759\) 546.869 + 177.688i 0.720512 + 0.234109i
\(760\) 1136.37 + 261.359i 1.49523 + 0.343894i
\(761\) −32.3289 + 307.589i −0.0424821 + 0.404190i 0.952531 + 0.304443i \(0.0984702\pi\)
−0.995013 + 0.0997477i \(0.968196\pi\)
\(762\) −425.670 445.711i −0.558623 0.584922i
\(763\) 254.085 + 228.779i 0.333007 + 0.299841i
\(764\) 195.465 32.2365i 0.255844 0.0421943i
\(765\) −119.409 25.3812i −0.156090 0.0331780i
\(766\) 96.3600 + 200.378i 0.125796 + 0.261590i
\(767\) 15.3238 21.0914i 0.0199788 0.0274985i
\(768\) −165.779 + 891.009i −0.215859 + 1.16017i
\(769\) −472.061 817.633i −0.613863 1.06324i −0.990583 0.136915i \(-0.956281\pi\)
0.376720 0.926327i \(-0.377052\pi\)
\(770\) 796.152 1477.54i 1.03396 1.91888i
\(771\) −685.477 943.479i −0.889076 1.22371i
\(772\) 693.482 190.562i 0.898293 0.246842i
\(773\) 247.286 + 761.070i 0.319905 + 0.984566i 0.973688 + 0.227884i \(0.0731808\pi\)
−0.653783 + 0.756682i \(0.726819\pi\)
\(774\) −6.79697 231.394i −0.00878161 0.298959i
\(775\) −554.402 394.999i −0.715358 0.509677i
\(776\) −326.155 + 28.8077i −0.420302 + 0.0371233i
\(777\) 35.2672 + 108.541i 0.0453889 + 0.139693i
\(778\) 356.872 86.8808i 0.458705 0.111672i
\(779\) 101.914 + 140.273i 0.130827 + 0.180068i
\(780\) 1441.47 + 722.936i 1.84804 + 0.926841i
\(781\) −377.375 653.633i −0.483195 0.836917i
\(782\) 29.2898 71.3538i 0.0374549 0.0912453i
\(783\) −567.679 + 781.344i −0.725005 + 0.997884i
\(784\) 216.475 128.687i 0.276116 0.164142i
\(785\) 1230.58 + 261.569i 1.56762 + 0.333209i
\(786\) 109.718 + 813.359i 0.139590 + 1.03481i
\(787\) −160.113 144.166i −0.203447 0.183185i 0.561109 0.827742i \(-0.310375\pi\)
−0.764556 + 0.644558i \(0.777042\pi\)
\(788\) −595.781 588.237i −0.756067 0.746494i
\(789\) −101.148 + 962.356i −0.128197 + 1.21972i
\(790\) 684.593 + 200.416i 0.866573 + 0.253691i
\(791\) −39.8139 12.9363i −0.0503337 0.0163544i
\(792\) 600.133 + 9.97699i 0.757743 + 0.0125972i
\(793\) −229.702 255.109i −0.289662 0.321702i
\(794\) 153.226 180.566i 0.192980 0.227414i
\(795\) 275.627 28.9695i 0.346700 0.0364397i
\(796\) −102.583 + 675.511i −0.128873 + 0.848632i
\(797\) −430.979 + 191.884i −0.540752 + 0.240758i −0.658891 0.752239i \(-0.728974\pi\)
0.118139 + 0.992997i \(0.462307\pi\)
\(798\) −489.664 + 717.351i −0.613614 + 0.898936i
\(799\) −155.655 + 349.607i −0.194812 + 0.437555i
\(800\) 436.592 + 550.593i 0.545740 + 0.688241i
\(801\) −41.9290 + 72.6232i −0.0523459 + 0.0906657i
\(802\) 422.132 326.055i 0.526349 0.406552i
\(803\) 471.905 + 2220.14i 0.587678 + 2.76481i
\(804\) 351.613 + 898.825i 0.437330 + 1.11794i
\(805\) −302.291 −0.375517
\(806\) 68.0406 1028.06i 0.0844176 1.27551i
\(807\) 1058.94i 1.31219i
\(808\) −106.240 249.710i −0.131486 0.309047i
\(809\) −608.102 + 129.256i −0.751671 + 0.159773i −0.567787 0.823175i \(-0.692200\pi\)
−0.183884 + 0.982948i \(0.558867\pi\)
\(810\) 1088.07 840.428i 1.34330 1.03757i
\(811\) −1375.96 794.413i −1.69663 0.979548i −0.948919 0.315520i \(-0.897821\pi\)
−0.747708 0.664028i \(-0.768846\pi\)
\(812\) 961.455 633.121i 1.18406 0.779706i
\(813\) −1235.20 549.946i −1.51931 0.676440i
\(814\) 133.836 196.068i 0.164417 0.240869i
\(815\) −273.525 614.348i −0.335614 0.753801i
\(816\) 26.2311 284.387i 0.0321460 0.348513i
\(817\) −72.8338 692.967i −0.0891478 0.848185i
\(818\) −214.609 + 252.902i −0.262359 + 0.309171i
\(819\) −251.645 + 226.582i −0.307259 + 0.276657i
\(820\) −10.2723 + 223.208i −0.0125272 + 0.272205i
\(821\) 338.985 1043.29i 0.412893 1.27075i −0.501229 0.865314i \(-0.667119\pi\)
0.914122 0.405439i \(-0.132881\pi\)
\(822\) −1269.05 371.517i −1.54386 0.451967i
\(823\) 22.7701 + 2.39323i 0.0276672 + 0.00290794i 0.118352 0.992972i \(-0.462239\pi\)
−0.0906848 + 0.995880i \(0.528906\pi\)
\(824\) −568.257 + 610.396i −0.689633 + 0.740772i
\(825\) 1104.57 1226.75i 1.33887 1.48697i
\(826\) 2.41904 + 17.9328i 0.00292862 + 0.0217104i
\(827\) −237.061 + 1115.28i −0.286652 + 1.34859i 0.565263 + 0.824910i \(0.308775\pi\)
−0.851915 + 0.523680i \(0.824559\pi\)
\(828\) −49.6908 96.0067i −0.0600131 0.115950i
\(829\) −2.96676 2.15547i −0.00357872 0.00260009i 0.585994 0.810315i \(-0.300704\pi\)
−0.589573 + 0.807715i \(0.700704\pi\)
\(830\) −241.106 + 587.367i −0.290489 + 0.707671i
\(831\) −318.163 + 183.691i −0.382867 + 0.221048i
\(832\) −362.094 + 1000.01i −0.435209 + 1.20193i
\(833\) −64.2029 + 46.6461i −0.0770743 + 0.0559977i
\(834\) −1365.00 + 332.311i −1.63670 + 0.398455i
\(835\) 1285.07 417.545i 1.53901 0.500054i
\(836\) 1803.50 106.044i 2.15730 0.126846i
\(837\) −522.337 295.152i −0.624059 0.352630i
\(838\) 29.9743 + 1020.44i 0.0357688 + 1.21770i
\(839\) 517.510 168.149i 0.616818 0.200416i 0.0160911 0.999871i \(-0.494878\pi\)
0.600727 + 0.799454i \(0.294878\pi\)
\(840\) −1070.11 + 328.138i −1.27394 + 0.390640i
\(841\) −1334.30 + 969.427i −1.58657 + 1.15271i
\(842\) −734.451 + 1363.03i −0.872269 + 1.61880i
\(843\) 310.711 179.389i 0.368578 0.212799i
\(844\) 310.650 824.942i 0.368069 0.977420i
\(845\) 594.053 + 431.605i 0.703021 + 0.510775i
\(846\) 232.452 + 483.376i 0.274766 + 0.571367i
\(847\) 395.570 1861.01i 0.467025 2.19718i
\(848\) 40.2778 + 178.290i 0.0474974 + 0.210248i
\(849\) 483.734 537.241i 0.569769 0.632793i
\(850\) −152.933 160.133i −0.179922 0.188392i
\(851\) −42.5219 4.46924i −0.0499670 0.00525175i
\(852\) −127.172 + 487.002i −0.149263 + 0.571599i
\(853\) −294.219 + 905.514i −0.344923 + 1.06156i 0.616702 + 0.787197i \(0.288468\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(854\) 237.594 + 17.9377i 0.278213 + 0.0210043i
\(855\) −382.715 + 344.598i −0.447619 + 0.403038i
\(856\) −390.662 293.877i −0.456381 0.343314i
\(857\) 15.7780 + 150.118i 0.0184108 + 0.175167i 0.999863 0.0165389i \(-0.00526474\pi\)
−0.981452 + 0.191706i \(0.938598\pi\)
\(858\) 2458.09 + 447.486i 2.86491 + 0.521545i
\(859\) 116.044 + 260.640i 0.135092 + 0.303422i 0.968406 0.249378i \(-0.0802260\pi\)
−0.833314 + 0.552800i \(0.813559\pi\)
\(860\) 484.250 756.183i 0.563081 0.879283i
\(861\) −152.046 67.6953i −0.176593 0.0786241i
\(862\) −726.341 + 448.291i −0.842622 + 0.520059i
\(863\) −805.231 464.900i −0.933060 0.538703i −0.0452820 0.998974i \(-0.514419\pi\)
−0.887778 + 0.460272i \(0.847752\pi\)
\(864\) 433.407 + 442.386i 0.501629 + 0.512021i
\(865\) 152.409 32.3956i 0.176196 0.0374516i
\(866\) −465.409 1301.09i −0.537424 1.50241i
\(867\) 933.132i 1.07628i
\(868\) 458.681 + 548.653i 0.528434 + 0.632089i
\(869\) 1105.20 1.27180
\(870\) 2279.82 815.508i 2.62048 0.937365i
\(871\) 235.482 + 1107.86i 0.270358 + 1.27194i
\(872\) −357.683 + 311.451i −0.410187 + 0.357169i
\(873\) 72.3050 125.236i 0.0828236 0.143455i
\(874\) −170.897 276.895i −0.195534 0.316813i
\(875\) 48.8844 109.796i 0.0558678 0.125481i
\(876\) 816.293 1274.69i 0.931841 1.45512i
\(877\) 694.713 309.306i 0.792147 0.352687i 0.0295524 0.999563i \(-0.490592\pi\)
0.762595 + 0.646877i \(0.223925\pi\)
\(878\) −96.4086 + 529.584i −0.109805 + 0.603171i
\(879\) −524.927 + 55.1721i −0.597187 + 0.0627669i
\(880\) 1900.83 + 1344.37i 2.16004 + 1.52769i
\(881\) 275.301 + 305.753i 0.312487 + 0.347052i 0.878845 0.477108i \(-0.158315\pi\)
−0.566358 + 0.824159i \(0.691648\pi\)
\(882\) −8.37343 + 110.911i −0.00949369 + 0.125749i
\(883\) 653.037 + 212.185i 0.739567 + 0.240300i 0.654486 0.756074i \(-0.272885\pi\)
0.0850809 + 0.996374i \(0.472885\pi\)
\(884\) 84.6776 324.271i 0.0957891 0.366823i
\(885\) −3.97829 + 37.8509i −0.00449525 + 0.0427694i
\(886\) −891.147 + 851.079i −1.00581 + 0.960585i
\(887\) −198.250 178.505i −0.223506 0.201246i 0.549768 0.835317i \(-0.314716\pi\)
−0.773275 + 0.634071i \(0.781383\pi\)
\(888\) −155.379 + 30.3365i −0.174977 + 0.0341628i
\(889\) 491.035 + 104.373i 0.552345 + 0.117405i
\(890\) −293.145 + 140.971i −0.329376 + 0.158394i
\(891\) 1252.06 1723.32i 1.40523 1.93414i
\(892\) 293.573 779.595i 0.329118 0.873985i
\(893\) 807.213 + 1398.13i 0.903934 + 1.56566i
\(894\) 1496.27 + 806.246i 1.67368 + 0.901841i
\(895\) −725.353 998.362i −0.810450 1.11549i
\(896\) −297.632 675.537i −0.332179 0.753947i
\(897\) −139.058 427.975i −0.155025 0.477119i
\(898\) −1670.85 + 49.0796i −1.86064 + 0.0546543i
\(899\) −1045.74 1139.99i −1.16323 1.26807i
\(900\) −309.812 + 18.2165i −0.344235 + 0.0202406i
\(901\) −17.7990 54.7797i −0.0197547 0.0607987i
\(902\) 81.8896 + 336.371i 0.0907867 + 0.372916i
\(903\) 393.139 + 541.109i 0.435369 + 0.599235i
\(904\) 24.4980 52.6502i 0.0270996 0.0582414i
\(905\) 946.634 + 1639.62i 1.04600 + 1.81173i
\(906\) −1292.98 530.750i −1.42713 0.585817i
\(907\) −231.928 + 319.222i −0.255709 + 0.351953i −0.917501 0.397735i \(-0.869796\pi\)
0.661791 + 0.749688i \(0.269796\pi\)
\(908\) −534.716 1033.11i −0.588894 1.13779i
\(909\) 117.234 + 24.9189i 0.128971 + 0.0274135i
\(910\) −1301.70 + 175.592i −1.43044 + 0.192959i
\(911\) −58.4898 52.6644i −0.0642039 0.0578095i 0.636404 0.771356i \(-0.280421\pi\)
−0.700608 + 0.713546i \(0.747088\pi\)
\(912\) −905.547 794.700i −0.992924 0.871382i
\(913\) −102.827 + 978.338i −0.112626 + 1.07156i
\(914\) 212.502 725.878i 0.232497 0.794177i
\(915\) 476.623 + 154.864i 0.520899 + 0.169250i
\(916\) −15.6684 + 340.461i −0.0171052 + 0.371683i
\(917\) −447.310 496.788i −0.487797 0.541754i
\(918\) −148.802 126.272i −0.162094 0.137551i
\(919\) 997.023 104.791i 1.08490 0.114028i 0.454839 0.890573i \(-0.349697\pi\)
0.630061 + 0.776546i \(0.283030\pi\)
\(920\) 50.7576 416.244i 0.0551713 0.452439i
\(921\) −1198.04 + 533.401i −1.30080 + 0.579154i
\(922\) 656.765 + 448.309i 0.712327 + 0.486235i
\(923\) −240.244 + 539.596i −0.260286 + 0.584611i
\(924\) −1448.36 + 953.750i −1.56749 + 1.03220i
\(925\) −61.3725 + 106.300i −0.0663487 + 0.114919i
\(926\) 337.542 + 437.004i 0.364516 + 0.471926i
\(927\) −76.5799 360.280i −0.0826104 0.388652i
\(928\) 710.348 + 1430.20i 0.765461 + 1.54116i
\(929\) −423.542 −0.455911 −0.227956 0.973672i \(-0.573204\pi\)
−0.227956 + 0.973672i \(0.573204\pi\)
\(930\) 664.396 + 1349.43i 0.714404 + 1.45100i
\(931\) 334.785i 0.359597i
\(932\) −414.889 1060.58i −0.445160 1.13796i
\(933\) −195.917 + 41.6434i −0.209986 + 0.0446338i
\(934\) −79.6422 103.110i −0.0852700 0.110396i
\(935\) −635.369 366.831i −0.679540 0.392332i
\(936\) −269.742 384.552i −0.288186 0.410846i
\(937\) −1413.32 629.252i −1.50835 0.671560i −0.524639 0.851325i \(-0.675800\pi\)
−0.983710 + 0.179765i \(0.942466\pi\)
\(938\) −649.287 443.204i −0.692204 0.472499i
\(939\) 274.322 + 616.138i 0.292143 + 0.656164i
\(940\) −312.366 + 2056.94i −0.332304 + 2.18823i
\(941\) −161.748 1538.93i −0.171890 1.63542i −0.652004 0.758216i \(-0.726071\pi\)
0.480114 0.877206i \(-0.340595\pi\)
\(942\) −991.138 841.066i −1.05216 0.892851i
\(943\) 46.3371 41.7221i 0.0491379 0.0442440i
\(944\) −25.0990 + 0.319839i −0.0265879 + 0.000338813i
\(945\) −236.354 + 727.423i −0.250110 + 0.769760i
\(946\) 390.882 1335.20i 0.413195 1.41142i
\(947\) 667.254 + 70.1313i 0.704598 + 0.0740562i 0.450049 0.893004i \(-0.351406\pi\)
0.254549 + 0.967060i \(0.418073\pi\)
\(948\) −524.476 517.835i −0.553245 0.546240i
\(949\) 1188.56 1320.03i 1.25244 1.39097i
\(950\) −925.742 + 124.878i −0.974465 + 0.131450i
\(951\) 8.88833 41.8163i 0.00934629 0.0439709i
\(952\) 112.946 + 203.361i 0.118641 + 0.213615i
\(953\) −467.136 339.394i −0.490174 0.356132i 0.315077 0.949066i \(-0.397970\pi\)
−0.805251 + 0.592934i \(0.797970\pi\)
\(954\) −74.6808 30.6555i −0.0782818 0.0321336i
\(955\) −293.917 + 169.693i −0.307767 + 0.177689i
\(956\) −383.184 192.177i −0.400820 0.201022i
\(957\) 3034.97 2205.04i 3.17134 2.30411i
\(958\) 340.401 + 1398.23i 0.355324 + 1.45953i
\(959\) 1024.33 332.826i 1.06813 0.347056i
\(960\) −272.152 1528.60i −0.283491 1.59229i
\(961\) 629.688 725.957i 0.655243 0.755418i
\(962\) −185.700 + 5.45476i −0.193036 + 0.00567023i
\(963\) 205.340 66.7191i 0.213230 0.0692826i
\(964\) 41.4643 11.3940i 0.0430128 0.0118195i
\(965\) −996.779 + 724.202i −1.03293 + 0.750469i
\(966\) 274.964 + 148.161i 0.284642 + 0.153376i
\(967\) −1010.78 + 583.573i −1.04527 + 0.603488i −0.921322 0.388800i \(-0.872890\pi\)
−0.123950 + 0.992288i \(0.539556\pi\)
\(968\) 2496.12 + 857.167i 2.57864 + 0.885503i
\(969\) 307.151 + 223.159i 0.316978 + 0.230298i
\(970\) 505.517 243.099i 0.521151 0.250617i
\(971\) 284.492 1338.43i 0.292988 1.37840i −0.547606 0.836736i \(-0.684461\pi\)
0.840594 0.541665i \(-0.182206\pi\)
\(972\) −714.188 + 117.785i −0.734761 + 0.121178i
\(973\) 765.681 850.375i 0.786928 0.873973i
\(974\) 958.996 915.877i 0.984595 0.940325i
\(975\) −1284.79 135.037i −1.31773 0.138499i
\(976\) −64.5939 + 324.146i −0.0661822 + 0.332117i
\(977\) 171.709 528.465i 0.175751 0.540906i −0.823916 0.566712i \(-0.808215\pi\)
0.999667 + 0.0258061i \(0.00821524\pi\)
\(978\) −52.3099 + 692.873i −0.0534866 + 0.708459i
\(979\) −374.525 + 337.224i −0.382559 + 0.344458i
\(980\) −269.371 + 337.014i −0.274869 + 0.343891i
\(981\) −21.8955 208.322i −0.0223195 0.212356i
\(982\) 238.033 1307.54i 0.242396 1.33151i
\(983\) 348.949 + 783.752i 0.354983 + 0.797306i 0.999466 + 0.0326866i \(0.0104063\pi\)
−0.644482 + 0.764619i \(0.722927\pi\)
\(984\) 118.744 197.995i 0.120675 0.201215i
\(985\) 1310.33 + 583.397i 1.33029 + 0.592281i
\(986\) −264.293 428.220i −0.268046 0.434300i
\(987\) −1342.08 774.849i −1.35975 0.785055i
\(988\) −896.743 1093.07i −0.907635 1.10635i
\(989\) −245.099 + 52.0974i −0.247825 + 0.0526768i
\(990\) −968.189 + 346.329i −0.977969 + 0.349827i
\(991\) 913.664i 0.921962i 0.887410 + 0.460981i \(0.152502\pi\)
−0.887410 + 0.460981i \(0.847498\pi\)
\(992\) −832.493 + 539.462i −0.839207 + 0.543813i
\(993\) −201.623 −0.203044
\(994\) −138.082 386.020i −0.138916 0.388350i
\(995\) −243.367 1144.95i −0.244589 1.15070i
\(996\) 507.194 416.096i 0.509231 0.417767i
\(997\) −660.034 + 1143.21i −0.662020 + 1.14665i 0.318064 + 0.948069i \(0.396967\pi\)
−0.980084 + 0.198583i \(0.936366\pi\)
\(998\) −794.721 + 490.495i −0.796313 + 0.491478i
\(999\) −44.0015 + 98.8289i −0.0440455 + 0.0989279i
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 124.3.n.a.7.12 240
4.3 odd 2 inner 124.3.n.a.7.13 yes 240
31.9 even 15 inner 124.3.n.a.71.13 yes 240
124.71 odd 30 inner 124.3.n.a.71.12 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.3.n.a.7.12 240 1.1 even 1 trivial
124.3.n.a.7.13 yes 240 4.3 odd 2 inner
124.3.n.a.71.12 yes 240 124.71 odd 30 inner
124.3.n.a.71.13 yes 240 31.9 even 15 inner