Properties

Label 115.3.i.a.14.10
Level $115$
Weight $3$
Character 115.14
Analytic conductor $3.134$
Analytic rank $0$
Dimension $220$
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] = [115,3,Mod(14,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 21]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("115.14");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 115.i (of order \(22\), 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: \(3.13352304014\)
Analytic rank: \(0\)
Dimension: \(220\)
Relative dimension: \(22\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 14.10
Character \(\chi\) \(=\) 115.14
Dual form 115.3.i.a.74.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.245567 - 0.836325i) q^{2} +(2.37235 - 2.05565i) q^{3} +(2.72588 - 1.75182i) q^{4} +(4.33861 - 2.48524i) q^{5} +(-2.30176 - 1.47925i) q^{6} +(-2.30176 + 5.04015i) q^{7} +(-4.76942 - 4.13272i) q^{8} +(0.121499 - 0.845043i) q^{9} +O(q^{10})\) \(q+(-0.245567 - 0.836325i) q^{2} +(2.37235 - 2.05565i) q^{3} +(2.72588 - 1.75182i) q^{4} +(4.33861 - 2.48524i) q^{5} +(-2.30176 - 1.47925i) q^{6} +(-2.30176 + 5.04015i) q^{7} +(-4.76942 - 4.13272i) q^{8} +(0.121499 - 0.845043i) q^{9} +(-3.14389 - 3.01820i) q^{10} +(-4.65972 + 15.8695i) q^{11} +(2.86561 - 9.75937i) q^{12} +(0.727473 - 0.332226i) q^{13} +(4.78044 + 0.687323i) q^{14} +(5.18391 - 14.8145i) q^{15} +(3.09912 - 6.78612i) q^{16} +(-13.8472 - 8.89908i) q^{17} +(-0.736567 + 0.105902i) q^{18} +(-4.56516 - 7.10352i) q^{19} +(7.47284 - 14.3749i) q^{20} +(4.90021 + 16.6886i) q^{21} +14.4164 q^{22} +(4.85780 + 22.4811i) q^{23} -19.8101 q^{24} +(12.6471 - 21.5650i) q^{25} +(-0.456492 - 0.526820i) q^{26} +(13.8251 + 21.5123i) q^{27} +(2.55509 + 17.7711i) q^{28} +(-20.8719 - 13.4135i) q^{29} +(-13.6628 - 0.697468i) q^{30} +(1.31745 - 1.52042i) q^{31} +(-31.4229 - 4.51793i) q^{32} +(21.5678 + 47.2268i) q^{33} +(-4.04210 + 13.7661i) q^{34} +(2.53955 + 27.5877i) q^{35} +(-1.14917 - 2.51633i) q^{36} +(-0.957842 + 6.66194i) q^{37} +(-4.81980 + 5.56235i) q^{38} +(1.04288 - 2.28359i) q^{39} +(-30.9635 - 6.07713i) q^{40} +(-1.79945 - 12.5154i) q^{41} +(12.7538 - 8.19634i) q^{42} +(40.3379 + 46.5524i) q^{43} +(15.0987 + 51.4214i) q^{44} +(-1.57300 - 3.96827i) q^{45} +(17.6086 - 9.58334i) q^{46} -58.7938i q^{47} +(-6.59771 - 22.4697i) q^{48} +(11.9832 + 13.8293i) q^{49} +(-21.1411 - 5.28146i) q^{50} +(-51.1439 + 7.35338i) q^{51} +(1.40100 - 2.18000i) q^{52} +(-28.8708 + 63.2182i) q^{53} +(14.5963 - 16.8450i) q^{54} +(19.2230 + 80.4324i) q^{55} +(31.8076 - 14.5260i) q^{56} +(-25.4325 - 7.46766i) q^{57} +(-6.09263 + 20.7496i) q^{58} +(-40.0889 - 87.7824i) q^{59} +(-11.8216 - 49.4639i) q^{60} +(-37.9217 - 32.8594i) q^{61} +(-1.59509 - 0.728454i) q^{62} +(3.97948 + 2.55746i) q^{63} +(-0.308870 - 2.14824i) q^{64} +(2.33056 - 3.24935i) q^{65} +(34.2006 - 29.6350i) q^{66} +(106.078 - 31.1474i) q^{67} -53.3354 q^{68} +(57.7378 + 43.3471i) q^{69} +(22.4486 - 8.89852i) q^{70} +(40.2948 - 11.8316i) q^{71} +(-4.07181 + 3.52824i) q^{72} +(9.98549 + 15.5377i) q^{73} +(5.80676 - 0.834886i) q^{74} +(-14.3267 - 77.1578i) q^{75} +(-24.8881 - 11.3660i) q^{76} +(-69.2593 - 60.0135i) q^{77} +(-2.16592 - 0.311412i) q^{78} +(37.3414 - 17.0532i) q^{79} +(-3.41928 - 37.1444i) q^{80} +(84.3920 + 24.7797i) q^{81} +(-10.0251 + 4.57831i) q^{82} +(11.3258 - 78.7729i) q^{83} +(42.5927 + 36.9068i) q^{84} +(-82.1942 - 4.19592i) q^{85} +(29.0273 - 45.1673i) q^{86} +(-77.0889 + 11.0837i) q^{87} +(87.8086 - 56.4311i) q^{88} +(-94.0876 + 81.5274i) q^{89} +(-2.93249 + 2.29002i) q^{90} +4.43127i q^{91} +(52.6246 + 52.7709i) q^{92} -6.31520i q^{93} +(-49.1707 + 14.4378i) q^{94} +(-37.4604 - 19.4739i) q^{95} +(-83.8333 + 53.8764i) q^{96} +(-14.0129 - 97.4619i) q^{97} +(8.62315 - 13.4179i) q^{98} +(12.8443 + 5.86579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30} - 152 q^{31} - 264 q^{34} - 13 q^{35} - 62 q^{36} - 118 q^{39} - 11 q^{40} - 80 q^{41} - 242 q^{44} + 226 q^{46} + 90 q^{49} - 211 q^{50} - 22 q^{51} + 658 q^{54} - 565 q^{55} + 770 q^{56} - 172 q^{59} - 891 q^{60} + 286 q^{61} - 474 q^{64} - 242 q^{65} - 44 q^{66} - 288 q^{69} + 790 q^{70} - 210 q^{71} + 506 q^{74} + 804 q^{75} - 2376 q^{76} + 462 q^{79} + 2398 q^{80} - 2408 q^{81} + 1034 q^{84} + 1197 q^{85} - 1518 q^{86} - 22 q^{89} + 154 q^{90} - 210 q^{94} - 338 q^{95} + 2772 q^{96} + 1628 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(e\left(\frac{21}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.245567 0.836325i −0.122784 0.418163i 0.875044 0.484044i \(-0.160832\pi\)
−0.997827 + 0.0658810i \(0.979014\pi\)
\(3\) 2.37235 2.05565i 0.790783 0.685217i −0.162697 0.986676i \(-0.552019\pi\)
0.953479 + 0.301459i \(0.0974737\pi\)
\(4\) 2.72588 1.75182i 0.681469 0.437954i
\(5\) 4.33861 2.48524i 0.867723 0.497049i
\(6\) −2.30176 1.47925i −0.383627 0.246542i
\(7\) −2.30176 + 5.04015i −0.328822 + 0.720021i −0.999769 0.0214848i \(-0.993161\pi\)
0.670947 + 0.741506i \(0.265888\pi\)
\(8\) −4.76942 4.13272i −0.596177 0.516590i
\(9\) 0.121499 0.845043i 0.0134999 0.0938937i
\(10\) −3.14389 3.01820i −0.314389 0.301820i
\(11\) −4.65972 + 15.8695i −0.423611 + 1.44269i 0.420880 + 0.907116i \(0.361721\pi\)
−0.844491 + 0.535570i \(0.820097\pi\)
\(12\) 2.86561 9.75937i 0.238801 0.813281i
\(13\) 0.727473 0.332226i 0.0559595 0.0255558i −0.387239 0.921979i \(-0.626571\pi\)
0.443198 + 0.896424i \(0.353844\pi\)
\(14\) 4.78044 + 0.687323i 0.341460 + 0.0490945i
\(15\) 5.18391 14.8145i 0.345594 0.987636i
\(16\) 3.09912 6.78612i 0.193695 0.424133i
\(17\) −13.8472 8.89908i −0.814543 0.523475i 0.0657885 0.997834i \(-0.479044\pi\)
−0.880332 + 0.474358i \(0.842680\pi\)
\(18\) −0.736567 + 0.105902i −0.0409204 + 0.00588346i
\(19\) −4.56516 7.10352i −0.240271 0.373870i 0.700086 0.714059i \(-0.253145\pi\)
−0.940357 + 0.340189i \(0.889509\pi\)
\(20\) 7.47284 14.3749i 0.373642 0.718746i
\(21\) 4.90021 + 16.6886i 0.233343 + 0.794695i
\(22\) 14.4164 0.655290
\(23\) 4.85780 + 22.4811i 0.211209 + 0.977441i
\(24\) −19.8101 −0.825423
\(25\) 12.6471 21.5650i 0.505885 0.862601i
\(26\) −0.456492 0.526820i −0.0175574 0.0202623i
\(27\) 13.8251 + 21.5123i 0.512040 + 0.796750i
\(28\) 2.55509 + 17.7711i 0.0912534 + 0.634681i
\(29\) −20.8719 13.4135i −0.719719 0.462536i 0.128820 0.991668i \(-0.458881\pi\)
−0.848539 + 0.529132i \(0.822517\pi\)
\(30\) −13.6628 0.697468i −0.455426 0.0232489i
\(31\) 1.31745 1.52042i 0.0424985 0.0490459i −0.734102 0.679039i \(-0.762397\pi\)
0.776601 + 0.629993i \(0.216942\pi\)
\(32\) −31.4229 4.51793i −0.981965 0.141185i
\(33\) 21.5678 + 47.2268i 0.653569 + 1.43112i
\(34\) −4.04210 + 13.7661i −0.118885 + 0.404886i
\(35\) 2.53955 + 27.5877i 0.0725586 + 0.788219i
\(36\) −1.14917 2.51633i −0.0319213 0.0698980i
\(37\) −0.957842 + 6.66194i −0.0258876 + 0.180052i −0.998663 0.0516988i \(-0.983536\pi\)
0.972775 + 0.231751i \(0.0744455\pi\)
\(38\) −4.81980 + 5.56235i −0.126837 + 0.146378i
\(39\) 1.04288 2.28359i 0.0267405 0.0585535i
\(40\) −30.9635 6.07713i −0.774087 0.151928i
\(41\) −1.79945 12.5154i −0.0438890 0.305255i −0.999928 0.0120146i \(-0.996176\pi\)
0.956039 0.293240i \(-0.0947335\pi\)
\(42\) 12.7538 8.19634i 0.303661 0.195151i
\(43\) 40.3379 + 46.5524i 0.938090 + 1.08261i 0.996439 + 0.0843177i \(0.0268710\pi\)
−0.0583486 + 0.998296i \(0.518583\pi\)
\(44\) 15.0987 + 51.4214i 0.343152 + 1.16867i
\(45\) −1.57300 3.96827i −0.0349556 0.0881838i
\(46\) 17.6086 9.58334i 0.382796 0.208333i
\(47\) 58.7938i 1.25093i −0.780252 0.625466i \(-0.784909\pi\)
0.780252 0.625466i \(-0.215091\pi\)
\(48\) −6.59771 22.4697i −0.137452 0.468120i
\(49\) 11.9832 + 13.8293i 0.244555 + 0.282232i
\(50\) −21.1411 5.28146i −0.422822 0.105629i
\(51\) −51.1439 + 7.35338i −1.00282 + 0.144184i
\(52\) 1.40100 2.18000i 0.0269424 0.0419232i
\(53\) −28.8708 + 63.2182i −0.544732 + 1.19280i 0.414467 + 0.910065i \(0.363968\pi\)
−0.959199 + 0.282733i \(0.908759\pi\)
\(54\) 14.5963 16.8450i 0.270301 0.311944i
\(55\) 19.2230 + 80.4324i 0.349508 + 1.46241i
\(56\) 31.8076 14.5260i 0.567992 0.259393i
\(57\) −25.4325 7.46766i −0.446184 0.131012i
\(58\) −6.09263 + 20.7496i −0.105045 + 0.357752i
\(59\) −40.0889 87.7824i −0.679473 1.48784i −0.863201 0.504861i \(-0.831544\pi\)
0.183728 0.982977i \(-0.441184\pi\)
\(60\) −11.8216 49.4639i −0.197027 0.824398i
\(61\) −37.9217 32.8594i −0.621668 0.538678i 0.286074 0.958208i \(-0.407650\pi\)
−0.907742 + 0.419529i \(0.862195\pi\)
\(62\) −1.59509 0.728454i −0.0257273 0.0117493i
\(63\) 3.97948 + 2.55746i 0.0631663 + 0.0405945i
\(64\) −0.308870 2.14824i −0.00482610 0.0335662i
\(65\) 2.33056 3.24935i 0.0358548 0.0499899i
\(66\) 34.2006 29.6350i 0.518192 0.449016i
\(67\) 106.078 31.1474i 1.58326 0.464886i 0.632432 0.774616i \(-0.282057\pi\)
0.950825 + 0.309730i \(0.100239\pi\)
\(68\) −53.3354 −0.784344
\(69\) 57.7378 + 43.3471i 0.836779 + 0.628219i
\(70\) 22.4486 8.89852i 0.320695 0.127122i
\(71\) 40.2948 11.8316i 0.567532 0.166643i 0.0146364 0.999893i \(-0.495341\pi\)
0.552896 + 0.833250i \(0.313523\pi\)
\(72\) −4.07181 + 3.52824i −0.0565529 + 0.0490034i
\(73\) 9.98549 + 15.5377i 0.136787 + 0.212845i 0.902889 0.429875i \(-0.141442\pi\)
−0.766101 + 0.642720i \(0.777806\pi\)
\(74\) 5.80676 0.834886i 0.0784698 0.0112822i
\(75\) −14.3267 77.1578i −0.191023 1.02877i
\(76\) −24.8881 11.3660i −0.327475 0.149553i
\(77\) −69.2593 60.0135i −0.899471 0.779396i
\(78\) −2.16592 0.311412i −0.0277682 0.00399246i
\(79\) 37.3414 17.0532i 0.472676 0.215864i −0.164811 0.986325i \(-0.552701\pi\)
0.637487 + 0.770461i \(0.279974\pi\)
\(80\) −3.41928 37.1444i −0.0427411 0.464305i
\(81\) 84.3920 + 24.7797i 1.04188 + 0.305922i
\(82\) −10.0251 + 4.57831i −0.122257 + 0.0558330i
\(83\) 11.3258 78.7729i 0.136456 0.949071i −0.800428 0.599429i \(-0.795394\pi\)
0.936883 0.349642i \(-0.113697\pi\)
\(84\) 42.5927 + 36.9068i 0.507056 + 0.439366i
\(85\) −82.1942 4.19592i −0.966990 0.0493637i
\(86\) 29.0273 45.1673i 0.337527 0.525201i
\(87\) −77.0889 + 11.0837i −0.886079 + 0.127399i
\(88\) 87.8086 56.4311i 0.997825 0.641263i
\(89\) −94.0876 + 81.5274i −1.05716 + 0.916038i −0.996622 0.0821278i \(-0.973828\pi\)
−0.0605422 + 0.998166i \(0.519283\pi\)
\(90\) −2.93249 + 2.29002i −0.0325832 + 0.0254446i
\(91\) 4.43127i 0.0486953i
\(92\) 52.6246 + 52.7709i 0.572006 + 0.573596i
\(93\) 6.31520i 0.0679054i
\(94\) −49.1707 + 14.4378i −0.523093 + 0.153594i
\(95\) −37.4604 19.4739i −0.394320 0.204989i
\(96\) −83.8333 + 53.8764i −0.873263 + 0.561212i
\(97\) −14.0129 97.4619i −0.144463 1.00476i −0.925085 0.379759i \(-0.876007\pi\)
0.780622 0.625003i \(-0.214902\pi\)
\(98\) 8.62315 13.4179i 0.0879913 0.136917i
\(99\) 12.8443 + 5.86579i 0.129740 + 0.0592505i
\(100\) −3.30338 80.9390i −0.0330338 0.809390i
\(101\) −12.1643 + 84.6043i −0.120438 + 0.837666i 0.836623 + 0.547780i \(0.184527\pi\)
−0.957061 + 0.289887i \(0.906382\pi\)
\(102\) 18.7091 + 40.9671i 0.183422 + 0.401639i
\(103\) 61.5316 + 18.0673i 0.597394 + 0.175411i 0.566430 0.824110i \(-0.308324\pi\)
0.0309638 + 0.999521i \(0.490142\pi\)
\(104\) −4.84262 1.42192i −0.0465636 0.0136723i
\(105\) 62.7353 + 60.2271i 0.597479 + 0.573592i
\(106\) 59.9607 + 8.62105i 0.565667 + 0.0813307i
\(107\) −94.3714 + 108.910i −0.881976 + 1.01785i 0.117716 + 0.993047i \(0.462443\pi\)
−0.999692 + 0.0248073i \(0.992103\pi\)
\(108\) 75.3710 + 34.4208i 0.697880 + 0.318711i
\(109\) 69.1907 107.663i 0.634777 0.987732i −0.363643 0.931538i \(-0.618467\pi\)
0.998420 0.0561940i \(-0.0178965\pi\)
\(110\) 62.5471 35.8282i 0.568610 0.325711i
\(111\) 11.4223 + 17.7734i 0.102903 + 0.160121i
\(112\) 27.0696 + 31.2400i 0.241693 + 0.278929i
\(113\) −97.2995 + 28.5697i −0.861057 + 0.252829i −0.682307 0.731065i \(-0.739023\pi\)
−0.178750 + 0.983895i \(0.557205\pi\)
\(114\) 23.1037i 0.202664i
\(115\) 76.9472 + 85.4642i 0.669106 + 0.743167i
\(116\) −80.3922 −0.693036
\(117\) −0.192358 0.655111i −0.00164408 0.00559924i
\(118\) −63.5701 + 55.0838i −0.538730 + 0.466812i
\(119\) 76.7256 49.3086i 0.644753 0.414358i
\(120\) −85.9486 + 49.2330i −0.716238 + 0.410275i
\(121\) −128.338 82.4777i −1.06064 0.681634i
\(122\) −18.1688 + 39.7841i −0.148924 + 0.326099i
\(123\) −29.9963 25.9919i −0.243872 0.211317i
\(124\) 0.927719 6.45242i 0.00748160 0.0520357i
\(125\) 1.27674 124.993i 0.0102139 0.999948i
\(126\) 1.16164 3.95617i 0.00921933 0.0313981i
\(127\) 0.726279 2.47348i 0.00571873 0.0194762i −0.956584 0.291456i \(-0.905860\pi\)
0.962303 + 0.271980i \(0.0876784\pi\)
\(128\) −117.229 + 53.5369i −0.915855 + 0.418257i
\(129\) 191.391 + 27.5179i 1.48365 + 0.213317i
\(130\) −3.28982 1.15117i −0.0253063 0.00885519i
\(131\) −41.2340 + 90.2900i −0.314764 + 0.689236i −0.999206 0.0398302i \(-0.987318\pi\)
0.684443 + 0.729067i \(0.260046\pi\)
\(132\) 141.524 + 90.9518i 1.07215 + 0.689029i
\(133\) 46.3107 6.65847i 0.348201 0.0500637i
\(134\) −52.0986 81.0671i −0.388796 0.604978i
\(135\) 113.445 + 58.9747i 0.840333 + 0.436849i
\(136\) 29.2658 + 99.6702i 0.215190 + 0.732869i
\(137\) 57.9171 0.422752 0.211376 0.977405i \(-0.432205\pi\)
0.211376 + 0.977405i \(0.432205\pi\)
\(138\) 22.0738 58.9322i 0.159955 0.427045i
\(139\) −235.432 −1.69375 −0.846876 0.531790i \(-0.821519\pi\)
−0.846876 + 0.531790i \(0.821519\pi\)
\(140\) 55.2510 + 70.7518i 0.394650 + 0.505370i
\(141\) −120.859 139.479i −0.857159 0.989214i
\(142\) −19.7902 30.7941i −0.139367 0.216860i
\(143\) 1.88245 + 13.0927i 0.0131640 + 0.0915576i
\(144\) −5.35803 3.44339i −0.0372085 0.0239125i
\(145\) −123.891 6.32448i −0.854420 0.0436171i
\(146\) 10.5425 12.1667i 0.0722087 0.0833333i
\(147\) 56.8566 + 8.17475i 0.386780 + 0.0556105i
\(148\) 9.05953 + 19.8376i 0.0612130 + 0.134038i
\(149\) 54.6824 186.231i 0.366996 1.24987i −0.544568 0.838716i \(-0.683307\pi\)
0.911564 0.411157i \(-0.134875\pi\)
\(150\) −61.0108 + 30.9292i −0.406739 + 0.206195i
\(151\) 94.4704 + 206.861i 0.625632 + 1.36994i 0.911351 + 0.411629i \(0.135040\pi\)
−0.285719 + 0.958313i \(0.592233\pi\)
\(152\) −7.58376 + 52.7462i −0.0498931 + 0.347014i
\(153\) −9.20253 + 10.6203i −0.0601472 + 0.0694136i
\(154\) −33.1830 + 72.6606i −0.215474 + 0.471822i
\(155\) 1.93730 9.87072i 0.0124987 0.0636821i
\(156\) −1.15766 8.05170i −0.00742090 0.0516135i
\(157\) −130.534 + 83.8893i −0.831429 + 0.534327i −0.885732 0.464198i \(-0.846343\pi\)
0.0543030 + 0.998525i \(0.482706\pi\)
\(158\) −23.4319 27.0418i −0.148303 0.171151i
\(159\) 61.4631 + 209.324i 0.386560 + 1.31650i
\(160\) −147.560 + 58.4919i −0.922249 + 0.365575i
\(161\) −124.490 27.2621i −0.773228 0.169330i
\(162\) 76.6642i 0.473236i
\(163\) −48.2178 164.215i −0.295815 1.00745i −0.964539 0.263941i \(-0.914977\pi\)
0.668724 0.743511i \(-0.266841\pi\)
\(164\) −26.8298 30.9633i −0.163596 0.188800i
\(165\) 210.944 + 151.298i 1.27845 + 0.916956i
\(166\) −68.6610 + 9.87197i −0.413621 + 0.0594697i
\(167\) 15.8454 24.6560i 0.0948829 0.147641i −0.790567 0.612376i \(-0.790214\pi\)
0.885450 + 0.464735i \(0.153850\pi\)
\(168\) 45.5982 99.8460i 0.271418 0.594322i
\(169\) −110.253 + 127.238i −0.652382 + 0.752889i
\(170\) 16.6750 + 69.7714i 0.0980885 + 0.410420i
\(171\) −6.55744 + 2.99468i −0.0383476 + 0.0175128i
\(172\) 191.507 + 56.2316i 1.11341 + 0.326928i
\(173\) 90.8078 309.263i 0.524900 1.78765i −0.0864152 0.996259i \(-0.527541\pi\)
0.611315 0.791387i \(-0.290641\pi\)
\(174\) 28.2001 + 61.7496i 0.162069 + 0.354882i
\(175\) 79.5802 + 113.381i 0.454744 + 0.647891i
\(176\) 93.2516 + 80.8030i 0.529839 + 0.459108i
\(177\) −275.555 125.842i −1.55681 0.710970i
\(178\) 91.2882 + 58.6674i 0.512855 + 0.329592i
\(179\) −27.9769 194.584i −0.156296 1.08706i −0.905385 0.424591i \(-0.860418\pi\)
0.749090 0.662468i \(-0.230491\pi\)
\(180\) −11.2395 8.06141i −0.0624416 0.0447856i
\(181\) 105.736 91.6204i 0.584174 0.506190i −0.311888 0.950119i \(-0.600961\pi\)
0.896062 + 0.443929i \(0.146416\pi\)
\(182\) 3.70598 1.08818i 0.0203626 0.00597898i
\(183\) −157.511 −0.860716
\(184\) 69.7394 127.298i 0.379019 0.691836i
\(185\) 12.4008 + 31.2840i 0.0670315 + 0.169103i
\(186\) −5.28156 + 1.55081i −0.0283955 + 0.00833767i
\(187\) 205.749 178.282i 1.10026 0.953380i
\(188\) −102.996 160.265i −0.547850 0.852471i
\(189\) −140.247 + 20.1645i −0.742047 + 0.106690i
\(190\) −7.08747 + 36.1113i −0.0373025 + 0.190059i
\(191\) 266.195 + 121.567i 1.39369 + 0.636478i 0.963855 0.266428i \(-0.0858435\pi\)
0.429838 + 0.902906i \(0.358571\pi\)
\(192\) −5.14878 4.46144i −0.0268165 0.0232367i
\(193\) −190.167 27.3419i −0.985320 0.141668i −0.369226 0.929340i \(-0.620377\pi\)
−0.616095 + 0.787672i \(0.711286\pi\)
\(194\) −78.0688 + 35.6528i −0.402416 + 0.183777i
\(195\) −1.15062 12.4994i −0.00590060 0.0640995i
\(196\) 56.8912 + 16.7048i 0.290261 + 0.0852284i
\(197\) −101.035 + 46.1410i −0.512866 + 0.234218i −0.655000 0.755629i \(-0.727331\pi\)
0.142133 + 0.989848i \(0.454604\pi\)
\(198\) 1.75157 12.1825i 0.00884633 0.0615276i
\(199\) −20.7031 17.9393i −0.104036 0.0901474i 0.601290 0.799031i \(-0.294654\pi\)
−0.705326 + 0.708884i \(0.749199\pi\)
\(200\) −149.442 + 50.5854i −0.747208 + 0.252927i
\(201\) 187.626 291.952i 0.933464 1.45250i
\(202\) 73.7439 10.6028i 0.365069 0.0524889i
\(203\) 115.648 74.3225i 0.569695 0.366121i
\(204\) −126.530 + 109.639i −0.620246 + 0.537446i
\(205\) −38.9110 49.8276i −0.189810 0.243061i
\(206\) 55.8971i 0.271345i
\(207\) 19.5878 1.37362i 0.0946268 0.00663585i
\(208\) 5.96633i 0.0286843i
\(209\) 134.002 39.3465i 0.641158 0.188261i
\(210\) 34.9637 67.2569i 0.166494 0.320271i
\(211\) 93.6410 60.1794i 0.443796 0.285210i −0.299596 0.954066i \(-0.596852\pi\)
0.743392 + 0.668856i \(0.233216\pi\)
\(212\) 32.0484 + 222.902i 0.151172 + 1.05142i
\(213\) 71.2716 110.901i 0.334608 0.520661i
\(214\) 114.259 + 52.1804i 0.533921 + 0.243834i
\(215\) 290.705 + 101.723i 1.35211 + 0.473132i
\(216\) 22.9666 159.736i 0.106327 0.739519i
\(217\) 4.63069 + 10.1398i 0.0213396 + 0.0467272i
\(218\) −107.032 31.4275i −0.490973 0.144163i
\(219\) 55.6292 + 16.3342i 0.254014 + 0.0745854i
\(220\) 193.302 + 185.574i 0.878646 + 0.843517i
\(221\) −13.0300 1.87343i −0.0589592 0.00847706i
\(222\) 12.0594 13.9173i 0.0543217 0.0626906i
\(223\) 43.4403 + 19.8385i 0.194800 + 0.0889620i 0.510427 0.859921i \(-0.329488\pi\)
−0.315627 + 0.948883i \(0.602215\pi\)
\(224\) 95.0988 147.977i 0.424548 0.660610i
\(225\) −16.6868 13.3075i −0.0741634 0.0591444i
\(226\) 47.7871 + 74.3582i 0.211447 + 0.329019i
\(227\) −155.502 179.458i −0.685029 0.790566i 0.301620 0.953428i \(-0.402473\pi\)
−0.986649 + 0.162863i \(0.947927\pi\)
\(228\) −82.4078 + 24.1971i −0.361438 + 0.106128i
\(229\) 162.397i 0.709159i 0.935026 + 0.354579i \(0.115376\pi\)
−0.935026 + 0.354579i \(0.884624\pi\)
\(230\) 52.5801 85.3401i 0.228609 0.371044i
\(231\) −287.674 −1.24534
\(232\) 44.1122 + 150.232i 0.190139 + 0.647553i
\(233\) 192.707 166.981i 0.827068 0.716658i −0.134593 0.990901i \(-0.542973\pi\)
0.961661 + 0.274243i \(0.0884271\pi\)
\(234\) −0.500649 + 0.321748i −0.00213953 + 0.00137499i
\(235\) −146.117 255.083i −0.621773 1.08546i
\(236\) −263.056 169.056i −1.11464 0.716338i
\(237\) 53.5312 117.217i 0.225870 0.494587i
\(238\) −60.0793 52.0590i −0.252434 0.218735i
\(239\) −61.6369 + 428.694i −0.257895 + 1.79370i 0.289870 + 0.957066i \(0.406388\pi\)
−0.547765 + 0.836632i \(0.684521\pi\)
\(240\) −84.4677 81.0906i −0.351949 0.337878i
\(241\) 89.7462 305.648i 0.372391 1.26825i −0.533884 0.845558i \(-0.679268\pi\)
0.906275 0.422689i \(-0.138914\pi\)
\(242\) −37.4626 + 127.586i −0.154804 + 0.527215i
\(243\) 41.7982 19.0886i 0.172009 0.0785539i
\(244\) −160.934 23.1388i −0.659564 0.0948310i
\(245\) 86.3597 + 30.2190i 0.352489 + 0.123343i
\(246\) −14.3716 + 31.4694i −0.0584212 + 0.127924i
\(247\) −5.68100 3.65096i −0.0230000 0.0147812i
\(248\) −12.5670 + 1.80686i −0.0506733 + 0.00728572i
\(249\) −135.061 210.159i −0.542413 0.844011i
\(250\) −104.849 + 29.6265i −0.419395 + 0.118506i
\(251\) 70.4249 + 239.845i 0.280577 + 0.955559i 0.972367 + 0.233459i \(0.0750045\pi\)
−0.691789 + 0.722099i \(0.743177\pi\)
\(252\) 15.3278 0.0608245
\(253\) −379.401 27.6646i −1.49961 0.109346i
\(254\) −2.24698 −0.00884639
\(255\) −203.618 + 159.008i −0.798504 + 0.623562i
\(256\) 67.8769 + 78.3342i 0.265144 + 0.305993i
\(257\) −77.5981 120.745i −0.301938 0.469825i 0.656820 0.754047i \(-0.271901\pi\)
−0.958758 + 0.284222i \(0.908265\pi\)
\(258\) −23.9855 166.823i −0.0929669 0.646599i
\(259\) −31.3724 20.1618i −0.121129 0.0778449i
\(260\) 0.660574 12.9400i 0.00254067 0.0497694i
\(261\) −13.8709 + 16.0079i −0.0531453 + 0.0613329i
\(262\) 85.6375 + 12.3128i 0.326861 + 0.0469955i
\(263\) 166.656 + 364.925i 0.633671 + 1.38755i 0.905146 + 0.425101i \(0.139762\pi\)
−0.271474 + 0.962446i \(0.587511\pi\)
\(264\) 92.3097 314.378i 0.349658 1.19083i
\(265\) 31.8534 + 346.031i 0.120202 + 1.30578i
\(266\) −16.9410 37.0957i −0.0636881 0.139457i
\(267\) −55.6167 + 386.823i −0.208302 + 1.44877i
\(268\) 234.592 270.733i 0.875342 1.01020i
\(269\) −141.360 + 309.535i −0.525502 + 1.15069i 0.441812 + 0.897108i \(0.354336\pi\)
−0.967314 + 0.253581i \(0.918391\pi\)
\(270\) 21.4636 109.359i 0.0794950 0.405034i
\(271\) 20.2165 + 140.609i 0.0745996 + 0.518852i 0.992520 + 0.122086i \(0.0389584\pi\)
−0.917920 + 0.396766i \(0.870132\pi\)
\(272\) −103.304 + 66.3897i −0.379796 + 0.244080i
\(273\) 9.10915 + 10.5125i 0.0333668 + 0.0385074i
\(274\) −14.2225 48.4375i −0.0519071 0.176779i
\(275\) 283.295 + 301.191i 1.03016 + 1.09524i
\(276\) 233.322 + 17.0131i 0.845371 + 0.0616415i
\(277\) 46.5193i 0.167940i 0.996468 + 0.0839699i \(0.0267600\pi\)
−0.996468 + 0.0839699i \(0.973240\pi\)
\(278\) 57.8143 + 196.897i 0.207965 + 0.708264i
\(279\) −1.12475 1.29804i −0.00403138 0.00465246i
\(280\) 101.900 142.072i 0.363929 0.507401i
\(281\) −332.384 + 47.7896i −1.18286 + 0.170070i −0.705547 0.708663i \(-0.749299\pi\)
−0.477314 + 0.878733i \(0.658389\pi\)
\(282\) −86.9709 + 135.329i −0.308407 + 0.479891i
\(283\) −130.552 + 285.868i −0.461313 + 1.01014i 0.525873 + 0.850563i \(0.323739\pi\)
−0.987186 + 0.159572i \(0.948989\pi\)
\(284\) 89.1119 102.841i 0.313774 0.362115i
\(285\) −128.901 + 30.8067i −0.452283 + 0.108094i
\(286\) 10.4875 4.78949i 0.0366696 0.0167465i
\(287\) 67.2215 + 19.7380i 0.234221 + 0.0687736i
\(288\) −7.63569 + 26.0048i −0.0265128 + 0.0902943i
\(289\) −7.50259 16.4284i −0.0259605 0.0568456i
\(290\) 25.1342 + 105.166i 0.0866697 + 0.362642i
\(291\) −233.591 202.408i −0.802719 0.695560i
\(292\) 54.4384 + 24.8612i 0.186433 + 0.0851411i
\(293\) 481.277 + 309.298i 1.64259 + 1.05563i 0.938366 + 0.345643i \(0.112339\pi\)
0.704219 + 0.709983i \(0.251297\pi\)
\(294\) −7.12537 49.5581i −0.0242360 0.168565i
\(295\) −392.091 281.223i −1.32912 0.953300i
\(296\) 32.1003 27.8151i 0.108447 0.0939698i
\(297\) −405.811 + 119.157i −1.36637 + 0.401201i
\(298\) −169.178 −0.567711
\(299\) 11.0027 + 14.7405i 0.0367984 + 0.0492994i
\(300\) −174.219 185.225i −0.580731 0.617416i
\(301\) −327.479 + 96.1565i −1.08797 + 0.319457i
\(302\) 149.805 129.806i 0.496041 0.429822i
\(303\) 145.059 + 225.716i 0.478743 + 0.744938i
\(304\) −62.3533 + 8.96506i −0.205110 + 0.0294903i
\(305\) −246.191 48.3194i −0.807185 0.158424i
\(306\) 11.1418 + 5.08831i 0.0364113 + 0.0166285i
\(307\) 287.669 + 249.267i 0.937033 + 0.811944i 0.982354 0.187029i \(-0.0598858\pi\)
−0.0453215 + 0.998972i \(0.514431\pi\)
\(308\) −293.925 42.2600i −0.954301 0.137208i
\(309\) 183.114 83.6255i 0.592603 0.270633i
\(310\) −8.73087 + 0.803710i −0.0281641 + 0.00259261i
\(311\) 455.639 + 133.788i 1.46508 + 0.430186i 0.914496 0.404596i \(-0.132588\pi\)
0.550582 + 0.834781i \(0.314406\pi\)
\(312\) −14.4113 + 6.58144i −0.0461902 + 0.0210944i
\(313\) 31.9802 222.427i 0.102173 0.710630i −0.872763 0.488144i \(-0.837674\pi\)
0.974936 0.222485i \(-0.0714170\pi\)
\(314\) 102.214 + 88.5686i 0.325521 + 0.282066i
\(315\) 23.6213 + 1.20584i 0.0749883 + 0.00382807i
\(316\) 71.9139 111.900i 0.227576 0.354115i
\(317\) 304.140 43.7288i 0.959434 0.137946i 0.355233 0.934778i \(-0.384402\pi\)
0.604201 + 0.796832i \(0.293492\pi\)
\(318\) 159.970 102.806i 0.503049 0.323290i
\(319\) 310.124 268.724i 0.972174 0.842394i
\(320\) −6.67896 8.55276i −0.0208718 0.0267274i
\(321\) 452.368i 1.40925i
\(322\) 7.77062 + 110.809i 0.0241324 + 0.344126i
\(323\) 138.990i 0.430309i
\(324\) 273.452 80.2926i 0.843986 0.247817i
\(325\) 2.03600 19.8897i 0.00626460 0.0611990i
\(326\) −125.496 + 80.6515i −0.384958 + 0.247397i
\(327\) −57.1728 397.646i −0.174840 1.21604i
\(328\) −43.1405 + 67.1280i −0.131526 + 0.204658i
\(329\) 296.329 + 135.329i 0.900696 + 0.411334i
\(330\) 74.7331 213.572i 0.226464 0.647187i
\(331\) −2.72226 + 18.9337i −0.00822435 + 0.0572016i −0.993520 0.113655i \(-0.963744\pi\)
0.985296 + 0.170856i \(0.0546534\pi\)
\(332\) −107.123 234.566i −0.322659 0.706524i
\(333\) 5.51325 + 1.61884i 0.0165563 + 0.00486137i
\(334\) −24.5115 7.19724i −0.0733878 0.0215486i
\(335\) 382.823 398.766i 1.14276 1.19035i
\(336\) 128.437 + 18.4665i 0.382253 + 0.0549597i
\(337\) −120.797 + 139.407i −0.358448 + 0.413671i −0.906119 0.423023i \(-0.860969\pi\)
0.547671 + 0.836694i \(0.315514\pi\)
\(338\) 133.487 + 60.9615i 0.394932 + 0.180359i
\(339\) −172.099 + 267.791i −0.507666 + 0.789944i
\(340\) −231.402 + 132.551i −0.680593 + 0.389857i
\(341\) 17.9895 + 27.9921i 0.0527550 + 0.0820884i
\(342\) 4.11482 + 4.74876i 0.0120316 + 0.0138853i
\(343\) −357.789 + 105.056i −1.04312 + 0.306287i
\(344\) 388.733i 1.13004i
\(345\) 358.230 + 44.5740i 1.03835 + 0.129200i
\(346\) −280.944 −0.811976
\(347\) −36.1966 123.274i −0.104313 0.355257i 0.890751 0.454491i \(-0.150179\pi\)
−0.995064 + 0.0992340i \(0.968361\pi\)
\(348\) −190.718 + 165.258i −0.548041 + 0.474880i
\(349\) 51.7920 33.2847i 0.148401 0.0953717i −0.464333 0.885661i \(-0.653706\pi\)
0.612734 + 0.790289i \(0.290070\pi\)
\(350\) 75.2810 94.3975i 0.215088 0.269707i
\(351\) 17.2043 + 11.0565i 0.0490151 + 0.0315001i
\(352\) 218.119 477.614i 0.619657 1.35686i
\(353\) 255.530 + 221.418i 0.723881 + 0.627247i 0.936817 0.349820i \(-0.113757\pi\)
−0.212936 + 0.977066i \(0.568303\pi\)
\(354\) −37.5773 + 261.356i −0.106151 + 0.738294i
\(355\) 145.419 151.475i 0.409631 0.426691i
\(356\) −113.650 + 387.058i −0.319243 + 1.08724i
\(357\) 80.6587 274.698i 0.225935 0.769463i
\(358\) −155.865 + 71.1811i −0.435377 + 0.198830i
\(359\) −464.734 66.8186i −1.29452 0.186124i −0.539591 0.841927i \(-0.681421\pi\)
−0.754932 + 0.655803i \(0.772330\pi\)
\(360\) −8.89746 + 25.4271i −0.0247152 + 0.0706309i
\(361\) 120.345 263.520i 0.333367 0.729972i
\(362\) −102.590 65.9303i −0.283397 0.182128i
\(363\) −474.007 + 68.1519i −1.30580 + 0.187746i
\(364\) 7.76277 + 12.0791i 0.0213263 + 0.0331844i
\(365\) 81.9382 + 42.5958i 0.224488 + 0.116701i
\(366\) 38.6795 + 131.730i 0.105682 + 0.359919i
\(367\) −178.376 −0.486037 −0.243019 0.970022i \(-0.578138\pi\)
−0.243019 + 0.970022i \(0.578138\pi\)
\(368\) 167.615 + 36.7061i 0.455475 + 0.0997447i
\(369\) −10.7947 −0.0292540
\(370\) 23.1184 18.0535i 0.0624822 0.0487931i
\(371\) −252.176 291.026i −0.679719 0.784437i
\(372\) −11.0631 17.2145i −0.0297394 0.0462754i
\(373\) 49.7300 + 345.880i 0.133324 + 0.927291i 0.941179 + 0.337909i \(0.109720\pi\)
−0.807854 + 0.589382i \(0.799371\pi\)
\(374\) −199.627 128.292i −0.533762 0.343028i
\(375\) −253.914 299.152i −0.677104 0.797740i
\(376\) −242.978 + 280.412i −0.646219 + 0.745776i
\(377\) −19.6400 2.82381i −0.0520956 0.00749021i
\(378\) 51.3041 + 112.340i 0.135725 + 0.297196i
\(379\) −6.23219 + 21.2249i −0.0164438 + 0.0560023i −0.967306 0.253611i \(-0.918382\pi\)
0.950862 + 0.309614i \(0.100200\pi\)
\(380\) −136.227 + 12.5402i −0.358493 + 0.0330006i
\(381\) −3.36162 7.36093i −0.00882316 0.0193200i
\(382\) 36.3010 252.479i 0.0950287 0.660939i
\(383\) 328.445 379.046i 0.857559 0.989676i −0.142441 0.989803i \(-0.545495\pi\)
1.00000 0.000127612i \(4.06202e-5\pi\)
\(384\) −168.056 + 367.991i −0.437646 + 0.958310i
\(385\) −449.637 88.2493i −1.16789 0.229219i
\(386\) 23.8321 + 165.756i 0.0617411 + 0.429419i
\(387\) 44.2398 28.4312i 0.114315 0.0734656i
\(388\) −208.933 241.121i −0.538487 0.621447i
\(389\) 82.3489 + 280.455i 0.211694 + 0.720963i 0.995049 + 0.0993883i \(0.0316886\pi\)
−0.783355 + 0.621575i \(0.786493\pi\)
\(390\) −10.1710 + 4.03173i −0.0260795 + 0.0103378i
\(391\) 132.794 354.532i 0.339627 0.906731i
\(392\) 115.481i 0.294595i
\(393\) 87.7832 + 298.962i 0.223367 + 0.760717i
\(394\) 63.3997 + 73.1671i 0.160913 + 0.185703i
\(395\) 119.628 166.790i 0.302857 0.422253i
\(396\) 45.2878 6.51140i 0.114363 0.0164429i
\(397\) 303.634 472.464i 0.764821 1.19009i −0.212259 0.977213i \(-0.568082\pi\)
0.977080 0.212872i \(-0.0682816\pi\)
\(398\) −9.91911 + 21.7198i −0.0249224 + 0.0545724i
\(399\) 96.1775 110.995i 0.241046 0.278182i
\(400\) −107.148 152.658i −0.267870 0.381644i
\(401\) −18.5821 + 8.48617i −0.0463395 + 0.0211625i −0.438450 0.898756i \(-0.644472\pi\)
0.392110 + 0.919918i \(0.371745\pi\)
\(402\) −290.242 85.2226i −0.721994 0.211997i
\(403\) 0.453289 1.54376i 0.00112479 0.00383067i
\(404\) 115.053 + 251.931i 0.284784 + 0.623590i
\(405\) 427.728 102.225i 1.05612 0.252407i
\(406\) −90.5572 78.4683i −0.223047 0.193272i
\(407\) −101.259 46.2433i −0.248793 0.113620i
\(408\) 274.316 + 176.292i 0.672343 + 0.432088i
\(409\) −85.7774 596.595i −0.209725 1.45867i −0.774055 0.633118i \(-0.781775\pi\)
0.564331 0.825549i \(-0.309134\pi\)
\(410\) −32.1168 + 44.7783i −0.0783337 + 0.109215i
\(411\) 137.399 119.057i 0.334305 0.289677i
\(412\) 199.378 58.5427i 0.483927 0.142094i
\(413\) 534.711 1.29470
\(414\) −5.95890 16.0444i −0.0143935 0.0387546i
\(415\) −146.631 369.913i −0.353329 0.891356i
\(416\) −24.3603 + 7.15282i −0.0585583 + 0.0171943i
\(417\) −558.525 + 483.965i −1.33939 + 1.16059i
\(418\) −65.8130 102.407i −0.157447 0.244993i
\(419\) 174.698 25.1178i 0.416941 0.0599471i 0.0693479 0.997593i \(-0.477908\pi\)
0.347593 + 0.937645i \(0.386999\pi\)
\(420\) 276.516 + 54.2711i 0.658370 + 0.129217i
\(421\) 195.510 + 89.2865i 0.464395 + 0.212082i 0.633850 0.773456i \(-0.281474\pi\)
−0.169455 + 0.985538i \(0.554201\pi\)
\(422\) −73.3247 63.5362i −0.173755 0.150560i
\(423\) −49.6833 7.14337i −0.117455 0.0168874i
\(424\) 398.960 182.199i 0.940944 0.429715i
\(425\) −367.037 + 186.068i −0.863616 + 0.437807i
\(426\) −110.251 32.3726i −0.258805 0.0759921i
\(427\) 252.903 115.497i 0.592278 0.270484i
\(428\) −66.4540 + 462.198i −0.155266 + 1.07990i
\(429\) 31.3799 + 27.1909i 0.0731467 + 0.0633820i
\(430\) 13.6864 268.103i 0.0318288 0.623496i
\(431\) 125.553 195.364i 0.291307 0.453282i −0.664496 0.747292i \(-0.731354\pi\)
0.955802 + 0.294010i \(0.0949900\pi\)
\(432\) 188.830 27.1497i 0.437107 0.0628465i
\(433\) 65.3272 41.9833i 0.150871 0.0969590i −0.463027 0.886344i \(-0.653237\pi\)
0.613898 + 0.789385i \(0.289600\pi\)
\(434\) 7.34303 6.36277i 0.0169194 0.0146608i
\(435\) −306.913 + 239.672i −0.705547 + 0.550971i
\(436\) 414.685i 0.951112i
\(437\) 137.519 137.137i 0.314688 0.313816i
\(438\) 50.5352i 0.115377i
\(439\) 580.276 170.384i 1.32181 0.388119i 0.456666 0.889638i \(-0.349043\pi\)
0.865147 + 0.501519i \(0.167225\pi\)
\(440\) 240.722 463.059i 0.547096 1.05241i
\(441\) 13.1423 8.44607i 0.0298012 0.0191521i
\(442\) 1.63294 + 11.3574i 0.00369444 + 0.0256954i
\(443\) 352.308 548.202i 0.795278 1.23748i −0.172335 0.985038i \(-0.555131\pi\)
0.967613 0.252439i \(-0.0812326\pi\)
\(444\) 62.2715 + 28.4384i 0.140251 + 0.0640505i
\(445\) −205.594 + 587.546i −0.462010 + 1.32033i
\(446\) 5.92394 41.2019i 0.0132824 0.0923810i
\(447\) −253.101 554.213i −0.566221 1.23985i
\(448\) 11.5384 + 3.38797i 0.0257553 + 0.00756244i
\(449\) −226.655 66.5518i −0.504799 0.148222i 0.0194107 0.999812i \(-0.493821\pi\)
−0.524210 + 0.851589i \(0.675639\pi\)
\(450\) −7.03168 + 17.2234i −0.0156259 + 0.0382743i
\(451\) 206.999 + 29.7620i 0.458978 + 0.0659911i
\(452\) −215.178 + 248.328i −0.476057 + 0.549399i
\(453\) 649.351 + 296.549i 1.43345 + 0.654633i
\(454\) −111.900 + 174.119i −0.246475 + 0.383522i
\(455\) 11.0128 + 19.2256i 0.0242039 + 0.0422540i
\(456\) 90.4364 + 140.722i 0.198326 + 0.308601i
\(457\) 312.605 + 360.766i 0.684038 + 0.789422i 0.986504 0.163739i \(-0.0523554\pi\)
−0.302466 + 0.953160i \(0.597810\pi\)
\(458\) 135.817 39.8795i 0.296544 0.0870730i
\(459\) 420.916i 0.917028i
\(460\) 359.466 + 98.1675i 0.781448 + 0.213408i
\(461\) 304.880 0.661344 0.330672 0.943746i \(-0.392725\pi\)
0.330672 + 0.943746i \(0.392725\pi\)
\(462\) 70.6433 + 240.589i 0.152908 + 0.520755i
\(463\) −576.176 + 499.260i −1.24444 + 1.07831i −0.250533 + 0.968108i \(0.580606\pi\)
−0.993909 + 0.110207i \(0.964849\pi\)
\(464\) −155.710 + 100.069i −0.335582 + 0.215666i
\(465\) −15.6948 27.3992i −0.0337523 0.0589230i
\(466\) −186.973 120.160i −0.401230 0.257855i
\(467\) −124.008 + 271.540i −0.265542 + 0.581457i −0.994692 0.102898i \(-0.967189\pi\)
0.729149 + 0.684354i \(0.239916\pi\)
\(468\) −1.67198 1.44878i −0.00357260 0.00309568i
\(469\) −87.1790 + 606.343i −0.185883 + 1.29284i
\(470\) −177.451 + 184.841i −0.377556 + 0.393279i
\(471\) −137.226 + 467.347i −0.291349 + 0.992245i
\(472\) −171.580 + 584.347i −0.363517 + 1.23802i
\(473\) −926.729 + 423.223i −1.95926 + 0.894763i
\(474\) −111.177 15.9848i −0.234551 0.0337233i
\(475\) −210.924 + 8.60846i −0.444050 + 0.0181231i
\(476\) 122.765 268.818i 0.257910 0.564744i
\(477\) 49.9144 + 32.0780i 0.104642 + 0.0672495i
\(478\) 373.663 53.7247i 0.781723 0.112395i
\(479\) 32.6871 + 50.8621i 0.0682403 + 0.106184i 0.873697 0.486471i \(-0.161716\pi\)
−0.805456 + 0.592655i \(0.798080\pi\)
\(480\) −229.824 + 442.095i −0.478801 + 0.921031i
\(481\) 1.51646 + 5.16460i 0.00315273 + 0.0107372i
\(482\) −277.660 −0.576057
\(483\) −351.374 + 191.232i −0.727483 + 0.395926i
\(484\) −494.319 −1.02132
\(485\) −303.013 388.024i −0.624769 0.800050i
\(486\) −26.2286 30.2694i −0.0539682 0.0622826i
\(487\) −29.5966 46.0532i −0.0607732 0.0945650i 0.809537 0.587069i \(-0.199718\pi\)
−0.870310 + 0.492504i \(0.836082\pi\)
\(488\) 45.0659 + 313.440i 0.0923481 + 0.642295i
\(489\) −451.957 290.455i −0.924248 0.593978i
\(490\) 4.06582 79.6456i 0.00829759 0.162542i
\(491\) 85.9476 99.1888i 0.175046 0.202014i −0.661446 0.749993i \(-0.730057\pi\)
0.836492 + 0.547979i \(0.184603\pi\)
\(492\) −127.299 18.3029i −0.258738 0.0372010i
\(493\) 169.650 + 371.481i 0.344117 + 0.753511i
\(494\) −1.65832 + 5.64772i −0.00335692 + 0.0114326i
\(495\) 70.3044 6.47178i 0.142029 0.0130743i
\(496\) −6.23483 13.6524i −0.0125702 0.0275250i
\(497\) −33.1158 + 230.325i −0.0666313 + 0.463431i
\(498\) −142.594 + 164.563i −0.286334 + 0.330447i
\(499\) −267.972 + 586.777i −0.537018 + 1.17591i 0.425567 + 0.904927i \(0.360075\pi\)
−0.962585 + 0.270979i \(0.912653\pi\)
\(500\) −215.485 342.954i −0.430971 0.685907i
\(501\) −13.0932 91.0652i −0.0261341 0.181767i
\(502\) 183.295 117.796i 0.365129 0.234654i
\(503\) −353.641 408.123i −0.703063 0.811378i 0.286100 0.958200i \(-0.407641\pi\)
−0.989163 + 0.146821i \(0.953096\pi\)
\(504\) −8.41054 28.6437i −0.0166876 0.0568327i
\(505\) 157.486 + 397.297i 0.311854 + 0.786726i
\(506\) 70.0319 + 324.097i 0.138403 + 0.640507i
\(507\) 528.494i 1.04240i
\(508\) −2.35333 8.01471i −0.00463254 0.0157770i
\(509\) 103.502 + 119.448i 0.203344 + 0.234671i 0.848257 0.529584i \(-0.177652\pi\)
−0.644913 + 0.764256i \(0.723107\pi\)
\(510\) 182.985 + 131.244i 0.358794 + 0.257341i
\(511\) −101.297 + 14.5642i −0.198232 + 0.0285015i
\(512\) −229.857 + 357.665i −0.448940 + 0.698565i
\(513\) 89.6991 196.414i 0.174852 0.382873i
\(514\) −81.9265 + 94.5483i −0.159390 + 0.183946i
\(515\) 311.863 74.5338i 0.605560 0.144726i
\(516\) 569.915 260.271i 1.10449 0.504402i
\(517\) 933.030 + 273.962i 1.80470 + 0.529908i
\(518\) −9.15781 + 31.1886i −0.0176792 + 0.0602097i
\(519\) −420.309 920.348i −0.809844 1.77331i
\(520\) −24.5441 + 5.86592i −0.0472001 + 0.0112806i
\(521\) 1.48862 + 1.28990i 0.00285723 + 0.00247581i 0.656288 0.754510i \(-0.272126\pi\)
−0.653431 + 0.756986i \(0.726671\pi\)
\(522\) 16.7941 + 7.66959i 0.0321725 + 0.0146927i
\(523\) −436.586 280.577i −0.834772 0.536475i 0.0520191 0.998646i \(-0.483434\pi\)
−0.886791 + 0.462171i \(0.847071\pi\)
\(524\) 45.7724 + 318.354i 0.0873519 + 0.607545i
\(525\) 421.863 + 105.390i 0.803549 + 0.200742i
\(526\) 264.271 228.992i 0.502416 0.435346i
\(527\) −31.7735 + 9.32953i −0.0602912 + 0.0177031i
\(528\) 387.328 0.733576
\(529\) −481.803 + 218.418i −0.910782 + 0.412888i
\(530\) 281.572 111.614i 0.531268 0.210592i
\(531\) −79.0507 + 23.2114i −0.148871 + 0.0437126i
\(532\) 114.573 99.2779i 0.215362 0.186613i
\(533\) −5.46700 8.50682i −0.0102570 0.0159603i
\(534\) 337.167 48.4773i 0.631399 0.0907815i
\(535\) −138.772 + 707.056i −0.259387 + 1.32160i
\(536\) −634.654 289.837i −1.18406 0.540741i
\(537\) −466.367 404.109i −0.868467 0.752531i
\(538\) 293.586 + 42.2112i 0.545698 + 0.0784596i
\(539\) −275.304 + 125.727i −0.510768 + 0.233260i
\(540\) 412.550 37.9768i 0.763981 0.0703273i
\(541\) −16.9939 4.98985i −0.0314120 0.00922339i 0.265989 0.963976i \(-0.414302\pi\)
−0.297401 + 0.954753i \(0.596120\pi\)
\(542\) 112.630 51.4365i 0.207805 0.0949013i
\(543\) 62.5020 434.711i 0.115105 0.800572i
\(544\) 394.915 + 342.195i 0.725946 + 0.629036i
\(545\) 32.6234 639.063i 0.0598595 1.17259i
\(546\) 6.55497 10.1997i 0.0120054 0.0186808i
\(547\) 273.215 39.2824i 0.499479 0.0718142i 0.112029 0.993705i \(-0.464265\pi\)
0.387450 + 0.921891i \(0.373356\pi\)
\(548\) 157.875 101.460i 0.288093 0.185146i
\(549\) −32.3750 + 28.0531i −0.0589709 + 0.0510986i
\(550\) 182.326 310.889i 0.331502 0.565253i
\(551\) 209.499i 0.380215i
\(552\) −96.2338 445.355i −0.174337 0.806802i
\(553\) 227.458i 0.411317i
\(554\) 38.9053 11.4236i 0.0702262 0.0206203i
\(555\) 93.7282 + 48.7249i 0.168880 + 0.0877925i
\(556\) −641.758 + 412.433i −1.15424 + 0.741785i
\(557\) −31.9793 222.421i −0.0574135 0.399320i −0.998182 0.0602703i \(-0.980804\pi\)
0.940769 0.339049i \(-0.110105\pi\)
\(558\) −0.809377 + 1.25942i −0.00145050 + 0.00225702i
\(559\) 44.8106 + 20.4643i 0.0801621 + 0.0366088i
\(560\) 195.084 + 68.2638i 0.348364 + 0.121900i
\(561\) 121.621 845.894i 0.216794 1.50783i
\(562\) 121.590 + 266.245i 0.216353 + 0.473746i
\(563\) −387.817 113.873i −0.688840 0.202262i −0.0814643 0.996676i \(-0.525960\pi\)
−0.607376 + 0.794414i \(0.707778\pi\)
\(564\) −573.790 168.480i −1.01736 0.298723i
\(565\) −351.142 + 365.766i −0.621491 + 0.647373i
\(566\) 271.138 + 38.9838i 0.479043 + 0.0688759i
\(567\) −319.143 + 368.311i −0.562863 + 0.649578i
\(568\) −241.079 110.097i −0.424436 0.193833i
\(569\) 178.433 277.646i 0.313590 0.487955i −0.648303 0.761383i \(-0.724521\pi\)
0.961893 + 0.273427i \(0.0881573\pi\)
\(570\) 57.4182 + 100.238i 0.100734 + 0.175856i
\(571\) −6.37000 9.91192i −0.0111559 0.0173589i 0.835631 0.549291i \(-0.185102\pi\)
−0.846787 + 0.531933i \(0.821466\pi\)
\(572\) 28.0674 + 32.3915i 0.0490689 + 0.0566285i
\(573\) 881.408 258.805i 1.53823 0.451666i
\(574\) 61.0661i 0.106387i
\(575\) 546.244 + 179.563i 0.949989 + 0.312284i
\(576\) −1.85288 −0.00321681
\(577\) −232.360 791.345i −0.402703 1.37148i −0.872460 0.488686i \(-0.837476\pi\)
0.469756 0.882796i \(-0.344342\pi\)
\(578\) −11.8971 + 10.3089i −0.0205832 + 0.0178354i
\(579\) −507.347 + 326.052i −0.876247 + 0.563130i
\(580\) −348.791 + 199.794i −0.601363 + 0.344473i
\(581\) 370.958 + 238.400i 0.638481 + 0.410327i
\(582\) −111.917 + 245.063i −0.192296 + 0.421070i
\(583\) −868.715 752.746i −1.49008 1.29116i
\(584\) 16.5881 115.373i 0.0284044 0.197557i
\(585\) −2.46268 2.36422i −0.00420970 0.00404140i
\(586\) 140.488 478.458i 0.239740 0.816481i
\(587\) −27.8951 + 95.0020i −0.0475215 + 0.161843i −0.979835 0.199807i \(-0.935968\pi\)
0.932314 + 0.361650i \(0.117787\pi\)
\(588\) 169.305 77.3189i 0.287933 0.131495i
\(589\) −16.8147 2.41760i −0.0285480 0.00410458i
\(590\) −138.910 + 396.975i −0.235440 + 0.672839i
\(591\) −144.840 + 317.155i −0.245075 + 0.536640i
\(592\) 42.2403 + 27.1462i 0.0713518 + 0.0458550i
\(593\) 315.012 45.2920i 0.531218 0.0763777i 0.128514 0.991708i \(-0.458979\pi\)
0.402704 + 0.915330i \(0.368070\pi\)
\(594\) 199.308 + 310.129i 0.335535 + 0.522102i
\(595\) 210.339 404.613i 0.353511 0.680021i
\(596\) −177.185 603.437i −0.297290 1.01248i
\(597\) −85.9919 −0.144040
\(598\) 9.62597 12.8217i 0.0160969 0.0214409i
\(599\) 800.341 1.33613 0.668064 0.744104i \(-0.267123\pi\)
0.668064 + 0.744104i \(0.267123\pi\)
\(600\) −250.542 + 427.206i −0.417569 + 0.712010i
\(601\) 352.797 + 407.150i 0.587017 + 0.677453i 0.969098 0.246675i \(-0.0793381\pi\)
−0.382081 + 0.924129i \(0.624793\pi\)
\(602\) 160.836 + 250.266i 0.267170 + 0.415724i
\(603\) −13.4325 93.4250i −0.0222761 0.154934i
\(604\) 619.898 + 398.384i 1.02632 + 0.659576i
\(605\) −761.785 38.8883i −1.25915 0.0642781i
\(606\) 153.150 176.745i 0.252724 0.291659i
\(607\) 661.760 + 95.1467i 1.09021 + 0.156749i 0.663897 0.747824i \(-0.268901\pi\)
0.426318 + 0.904573i \(0.359811\pi\)
\(608\) 111.357 + 243.838i 0.183153 + 0.401050i
\(609\) 121.576 414.051i 0.199633 0.679887i
\(610\) 20.0458 + 217.762i 0.0328619 + 0.356986i
\(611\) −19.5328 42.7709i −0.0319686 0.0700014i
\(612\) −6.48019 + 45.0707i −0.0105885 + 0.0736450i
\(613\) 570.824 658.766i 0.931197 1.07466i −0.0658470 0.997830i \(-0.520975\pi\)
0.997044 0.0768292i \(-0.0244796\pi\)
\(614\) 137.826 301.797i 0.224472 0.491525i
\(615\) −194.739 38.2209i −0.316648 0.0621478i
\(616\) 82.3071 + 572.459i 0.133615 + 0.929316i
\(617\) −335.061 + 215.331i −0.543049 + 0.348996i −0.783230 0.621732i \(-0.786429\pi\)
0.240181 + 0.970728i \(0.422793\pi\)
\(618\) −114.905 132.607i −0.185930 0.214575i
\(619\) −190.466 648.668i −0.307700 1.04793i −0.957646 0.287948i \(-0.907027\pi\)
0.649946 0.759980i \(-0.274791\pi\)
\(620\) −12.0108 30.3002i −0.0193723 0.0488713i
\(621\) −416.460 + 415.306i −0.670629 + 0.668770i
\(622\) 413.916i 0.665460i
\(623\) −194.343 661.871i −0.311947 1.06239i
\(624\) −12.2647 14.1542i −0.0196549 0.0226830i
\(625\) −305.100 545.471i −0.488160 0.872754i
\(626\) −193.875 + 27.8750i −0.309704 + 0.0445287i
\(627\) 237.017 368.805i 0.378017 0.588206i
\(628\) −208.862 + 457.344i −0.332583 + 0.728255i
\(629\) 72.5486 83.7255i 0.115340 0.133109i
\(630\) −4.79215 20.0512i −0.00760658 0.0318273i
\(631\) −1022.83 + 467.113i −1.62097 + 0.740274i −0.999082 0.0428290i \(-0.986363\pi\)
−0.621892 + 0.783103i \(0.713636\pi\)
\(632\) −248.573 72.9876i −0.393312 0.115487i
\(633\) 98.4411 335.260i 0.155515 0.529636i
\(634\) −111.258 243.622i −0.175486 0.384262i
\(635\) −2.99615 12.5365i −0.00471835 0.0197424i
\(636\) 534.238 + 462.920i 0.839996 + 0.727861i
\(637\) 13.3119 + 6.07935i 0.0208978 + 0.00954372i
\(638\) −300.897 193.374i −0.471625 0.303095i
\(639\) −5.10246 35.4884i −0.00798507 0.0555373i
\(640\) −375.561 + 523.620i −0.586814 + 0.818156i
\(641\) −520.533 + 451.045i −0.812065 + 0.703658i −0.958354 0.285584i \(-0.907812\pi\)
0.146289 + 0.989242i \(0.453267\pi\)
\(642\) 378.327 111.087i 0.589294 0.173032i
\(643\) −559.378 −0.869950 −0.434975 0.900443i \(-0.643243\pi\)
−0.434975 + 0.900443i \(0.643243\pi\)
\(644\) −387.102 + 143.770i −0.601090 + 0.223245i
\(645\) 898.760 356.264i 1.39343 0.552347i
\(646\) 116.241 34.1313i 0.179939 0.0528349i
\(647\) 32.2143 27.9138i 0.0497902 0.0431435i −0.629610 0.776911i \(-0.716785\pi\)
0.679400 + 0.733768i \(0.262240\pi\)
\(648\) −300.093 466.953i −0.463106 0.720607i
\(649\) 1579.87 227.151i 2.43431 0.350002i
\(650\) −17.1342 + 3.18150i −0.0263603 + 0.00489461i
\(651\) 31.8295 + 14.5361i 0.0488933 + 0.0223288i
\(652\) −419.110 363.160i −0.642806 0.556995i
\(653\) −104.073 14.9635i −0.159377 0.0229150i 0.0621642 0.998066i \(-0.480200\pi\)
−0.221542 + 0.975151i \(0.571109\pi\)
\(654\) −318.521 + 145.464i −0.487036 + 0.222422i
\(655\) 45.4939 + 494.210i 0.0694563 + 0.754519i
\(656\) −90.5080 26.5756i −0.137970 0.0405115i
\(657\) 14.3433 6.55035i 0.0218315 0.00997009i
\(658\) 40.4103 281.060i 0.0614138 0.427143i
\(659\) 150.566 + 130.466i 0.228476 + 0.197976i 0.761574 0.648078i \(-0.224427\pi\)
−0.533098 + 0.846054i \(0.678972\pi\)
\(660\) 840.054 + 42.8838i 1.27281 + 0.0649755i
\(661\) −172.026 + 267.677i −0.260250 + 0.404958i −0.946648 0.322269i \(-0.895555\pi\)
0.686398 + 0.727226i \(0.259191\pi\)
\(662\) 16.5033 2.37281i 0.0249294 0.00358431i
\(663\) −34.7628 + 22.3407i −0.0524326 + 0.0336964i
\(664\) −379.564 + 328.894i −0.571633 + 0.495323i
\(665\) 184.376 143.982i 0.277257 0.216514i
\(666\) 5.00840i 0.00752012i
\(667\) 200.160 534.384i 0.300090 0.801175i
\(668\) 94.9675i 0.142167i
\(669\) 143.837 42.2343i 0.215002 0.0631304i
\(670\) −427.507 222.241i −0.638070 0.331703i
\(671\) 698.168 448.685i 1.04049 0.668682i
\(672\) −78.5809 546.542i −0.116936 0.813307i
\(673\) 40.9681 63.7476i 0.0608739 0.0947216i −0.809482 0.587144i \(-0.800252\pi\)
0.870356 + 0.492423i \(0.163889\pi\)
\(674\) 146.253 + 66.7917i 0.216993 + 0.0990974i
\(675\) 638.760 26.0698i 0.946311 0.0386219i
\(676\) −77.6372 + 539.978i −0.114848 + 0.798784i
\(677\) 136.930 + 299.835i 0.202260 + 0.442887i 0.983396 0.181474i \(-0.0580867\pi\)
−0.781136 + 0.624361i \(0.785359\pi\)
\(678\) 266.222 + 78.1699i 0.392658 + 0.115295i
\(679\) 523.477 + 153.707i 0.770952 + 0.226372i
\(680\) 374.678 + 359.698i 0.550997 + 0.528967i
\(681\) −737.808 106.081i −1.08342 0.155772i
\(682\) 18.9929 21.9190i 0.0278488 0.0321393i
\(683\) −347.263 158.590i −0.508438 0.232196i 0.144643 0.989484i \(-0.453797\pi\)
−0.653081 + 0.757288i \(0.726524\pi\)
\(684\) −12.6287 + 19.6506i −0.0184629 + 0.0287289i
\(685\) 251.280 143.938i 0.366832 0.210128i
\(686\) 175.722 + 273.429i 0.256155 + 0.398585i
\(687\) 333.832 + 385.263i 0.485927 + 0.560790i
\(688\) 440.922 129.466i 0.640875 0.188178i
\(689\) 55.5812i 0.0806694i
\(690\) −50.6912 310.543i −0.0734655 0.450062i
\(691\) 1222.48 1.76914 0.884570 0.466407i \(-0.154452\pi\)
0.884570 + 0.466407i \(0.154452\pi\)
\(692\) −294.240 1002.09i −0.425203 1.44811i
\(693\) −59.1289 + 51.2355i −0.0853231 + 0.0739329i
\(694\) −94.2087 + 60.5442i −0.135747 + 0.0872396i
\(695\) −1021.45 + 585.104i −1.46971 + 0.841877i
\(696\) 413.475 + 265.724i 0.594073 + 0.381787i
\(697\) −86.4585 + 189.318i −0.124044 + 0.271618i
\(698\) −40.5553 35.1414i −0.0581021 0.0503458i
\(699\) 113.912 792.276i 0.162964 1.13344i
\(700\) 415.548 + 169.653i 0.593640 + 0.242361i
\(701\) −142.351 + 484.803i −0.203068 + 0.691588i 0.793482 + 0.608594i \(0.208266\pi\)
−0.996550 + 0.0829935i \(0.973552\pi\)
\(702\) 5.02204 17.1035i 0.00715391 0.0243640i
\(703\) 51.6959 23.6087i 0.0735362 0.0335828i
\(704\) 35.5308 + 5.10856i 0.0504699 + 0.00725648i
\(705\) −871.002 304.781i −1.23546 0.432314i
\(706\) 122.428 268.079i 0.173410 0.379716i
\(707\) −398.419 256.048i −0.563534 0.362162i
\(708\) −971.580 + 139.692i −1.37229 + 0.197305i
\(709\) −595.665 926.873i −0.840149 1.30730i −0.949651 0.313310i \(-0.898562\pi\)
0.109502 0.993987i \(-0.465074\pi\)
\(710\) −162.393 84.4203i −0.228722 0.118902i
\(711\) −9.87379 33.6270i −0.0138872 0.0472954i
\(712\) 785.673 1.10347
\(713\) 40.5808 + 22.2320i 0.0569156 + 0.0311809i
\(714\) −249.544 −0.349502
\(715\) 40.7059 + 52.1260i 0.0569313 + 0.0729035i
\(716\) −417.136 481.401i −0.582592 0.672347i
\(717\) 735.021 + 1143.71i 1.02513 + 1.59514i
\(718\) 58.2413 + 405.077i 0.0811160 + 0.564174i
\(719\) 216.542 + 139.163i 0.301172 + 0.193551i 0.682495 0.730891i \(-0.260895\pi\)
−0.381323 + 0.924442i \(0.624531\pi\)
\(720\) −31.8041 1.62356i −0.0441723 0.00225495i
\(721\) −232.693 + 268.541i −0.322736 + 0.372457i
\(722\) −249.941 35.9361i −0.346179 0.0497730i
\(723\) −415.396 909.589i −0.574544 1.25808i
\(724\) 127.720 434.975i 0.176409 0.600794i
\(725\) −553.232 + 280.459i −0.763079 + 0.386840i
\(726\) 173.398 + 379.688i 0.238840 + 0.522986i
\(727\) −165.743 + 1152.77i −0.227982 + 1.58565i 0.478610 + 0.878027i \(0.341141\pi\)
−0.706592 + 0.707621i \(0.749768\pi\)
\(728\) 18.3132 21.1346i 0.0251555 0.0290310i
\(729\) −268.919 + 588.851i −0.368888 + 0.807751i
\(730\) 15.5026 78.9871i 0.0212365 0.108201i
\(731\) −144.295 1003.59i −0.197394 1.37290i
\(732\) −429.356 + 275.930i −0.586551 + 0.376954i
\(733\) 105.852 + 122.159i 0.144409 + 0.166657i 0.823346 0.567540i \(-0.192105\pi\)
−0.678937 + 0.734196i \(0.737559\pi\)
\(734\) 43.8032 + 149.180i 0.0596774 + 0.203243i
\(735\) 266.995 105.835i 0.363259 0.143994i
\(736\) −51.0780 728.369i −0.0693995 0.989632i
\(737\) 1828.55i 2.48107i
\(738\) 2.65083 + 9.02790i 0.00359191 + 0.0122329i
\(739\) 793.443 + 915.683i 1.07367 + 1.23908i 0.969647 + 0.244509i \(0.0786266\pi\)
0.104025 + 0.994575i \(0.466828\pi\)
\(740\) 88.6070 + 63.5525i 0.119739 + 0.0858818i
\(741\) −20.9824 + 3.01681i −0.0283163 + 0.00407127i
\(742\) −181.466 + 282.367i −0.244564 + 0.380549i
\(743\) −96.3042 + 210.877i −0.129615 + 0.283818i −0.963302 0.268420i \(-0.913499\pi\)
0.833687 + 0.552238i \(0.186226\pi\)
\(744\) −26.0990 + 30.1198i −0.0350793 + 0.0404836i
\(745\) −225.584 943.884i −0.302797 1.26696i
\(746\) 277.056 126.527i 0.371388 0.169607i
\(747\) −65.1904 19.1416i −0.0872697 0.0256247i
\(748\) 248.528 846.409i 0.332257 1.13156i
\(749\) −331.704 726.331i −0.442863 0.969735i
\(750\) −187.836 + 285.817i −0.250448 + 0.381089i
\(751\) −858.319 743.738i −1.14290 0.990330i −1.00000 0.000593515i \(-0.999811\pi\)
−0.142902 0.989737i \(-0.545643\pi\)
\(752\) −398.982 182.209i −0.530561 0.242299i
\(753\) 660.110 + 424.227i 0.876641 + 0.563383i
\(754\) 2.46132 + 17.1189i 0.00326436 + 0.0227041i
\(755\) 923.971 + 662.710i 1.22380 + 0.877761i
\(756\) −346.971 + 300.652i −0.458957 + 0.397688i
\(757\) 634.061 186.177i 0.837597 0.245941i 0.165319 0.986240i \(-0.447134\pi\)
0.672277 + 0.740300i \(0.265316\pi\)
\(758\) 19.2813 0.0254371
\(759\) −956.941 + 714.287i −1.26079 + 0.941089i
\(760\) 98.1841 + 247.693i 0.129190 + 0.325912i
\(761\) 56.8445 16.6911i 0.0746971 0.0219330i −0.244170 0.969732i \(-0.578516\pi\)
0.318868 + 0.947799i \(0.396697\pi\)
\(762\) −5.33063 + 4.61901i −0.00699557 + 0.00606170i
\(763\) 383.376 + 596.545i 0.502459 + 0.781841i
\(764\) 938.579 134.947i 1.22851 0.176633i
\(765\) −13.5322 + 68.9478i −0.0176892 + 0.0901279i
\(766\) −397.661 181.606i −0.519139 0.237083i
\(767\) −58.3272 50.5408i −0.0760459 0.0658941i
\(768\) 322.055 + 46.3046i 0.419343 + 0.0602924i
\(769\) −1193.06 + 544.851i −1.55144 + 0.708519i −0.992676 0.120807i \(-0.961452\pi\)
−0.558764 + 0.829326i \(0.688724\pi\)
\(770\) 36.6111 + 397.714i 0.0475469 + 0.516512i
\(771\) −432.299 126.935i −0.560699 0.164636i
\(772\) −566.269 + 258.607i −0.733510 + 0.334983i
\(773\) 147.060 1022.82i 0.190246 1.32319i −0.641111 0.767448i \(-0.721526\pi\)
0.831357 0.555739i \(-0.187565\pi\)
\(774\) −34.6416 30.0171i −0.0447565 0.0387818i
\(775\) −16.1259 47.6399i −0.0208077 0.0614709i
\(776\) −335.950 + 522.748i −0.432925 + 0.673644i
\(777\) −115.872 + 16.6599i −0.149127 + 0.0214413i
\(778\) 214.329 137.741i 0.275487 0.177045i
\(779\) −80.6890 + 69.9174i −0.103580 + 0.0897527i
\(780\) −25.0331 32.0562i −0.0320937 0.0410976i
\(781\) 694.592i 0.889362i
\(782\) −329.114 23.9978i −0.420861 0.0306878i
\(783\) 634.444i 0.810273i
\(784\) 130.985 38.4607i 0.167073 0.0490570i
\(785\) −357.853 + 688.373i −0.455863 + 0.876908i
\(786\) 228.473 146.831i 0.290678 0.186807i
\(787\) 201.262 + 1399.80i 0.255733 + 1.77866i 0.562423 + 0.826850i \(0.309869\pi\)
−0.306691 + 0.951809i \(0.599222\pi\)
\(788\) −194.578 + 302.769i −0.246926 + 0.384224i
\(789\) 1145.52 + 523.143i 1.45187 + 0.663045i
\(790\) −168.867 59.0901i −0.213756 0.0747976i
\(791\) 79.9643 556.164i 0.101093 0.703115i
\(792\) −37.0181 81.0583i −0.0467400 0.102346i
\(793\) −38.5038 11.3057i −0.0485546 0.0142569i
\(794\) −469.696 137.915i −0.591557 0.173697i
\(795\) 786.885 + 755.425i 0.989793 + 0.950220i
\(796\) −87.8605 12.6324i −0.110378 0.0158699i
\(797\) 564.469 651.432i 0.708242 0.817355i −0.281599 0.959532i \(-0.590865\pi\)
0.989841 + 0.142177i \(0.0454103\pi\)
\(798\) −116.446 53.1790i −0.145922 0.0666404i
\(799\) −523.210 + 814.131i −0.654831 + 1.01894i
\(800\) −494.839 + 620.496i −0.618548 + 0.775620i
\(801\) 57.4626 + 89.4136i 0.0717386 + 0.111627i
\(802\) 11.6604 + 13.4568i 0.0145391 + 0.0167790i
\(803\) −293.106 + 86.0637i −0.365014 + 0.107178i
\(804\) 1124.51i 1.39865i
\(805\) −607.866 + 191.107i −0.755113 + 0.237401i
\(806\) −1.40240 −0.00173995
\(807\) 300.941 + 1024.91i 0.372914 + 1.27003i
\(808\) 407.663 353.242i 0.504533 0.437180i
\(809\) 235.683 151.464i 0.291327 0.187224i −0.386811 0.922159i \(-0.626424\pi\)
0.678138 + 0.734935i \(0.262787\pi\)
\(810\) −190.529 332.616i −0.235221 0.410637i
\(811\) 798.213 + 512.980i 0.984233 + 0.632528i 0.930602 0.366032i \(-0.119284\pi\)
0.0536312 + 0.998561i \(0.482920\pi\)
\(812\) 185.043 405.188i 0.227886 0.499000i
\(813\) 337.003 + 292.015i 0.414518 + 0.359182i
\(814\) −13.8086 + 96.0410i −0.0169639 + 0.117986i
\(815\) −617.312 592.631i −0.757438 0.727155i
\(816\) −108.600 + 369.857i −0.133088 + 0.453257i
\(817\) 146.537 499.060i 0.179360 0.610845i
\(818\) −477.883 + 218.242i −0.584209 + 0.266799i
\(819\) 3.74462 + 0.538395i 0.00457218 + 0.000657380i
\(820\) −193.355 67.6590i −0.235799 0.0825110i
\(821\) 575.468 1260.10i 0.700935 1.53483i −0.137898 0.990446i \(-0.544035\pi\)
0.838834 0.544388i \(-0.183238\pi\)
\(822\) −133.311 85.6740i −0.162179 0.104226i
\(823\) −485.362 + 69.7845i −0.589747 + 0.0847929i −0.430727 0.902482i \(-0.641743\pi\)
−0.159021 + 0.987275i \(0.550834\pi\)
\(824\) −218.802 340.463i −0.265537 0.413184i
\(825\) 1291.22 + 132.175i 1.56511 + 0.160212i
\(826\) −131.308 447.192i −0.158968 0.541395i
\(827\) −1038.00 −1.25514 −0.627571 0.778560i \(-0.715951\pi\)
−0.627571 + 0.778560i \(0.715951\pi\)
\(828\) 50.9875 38.0584i 0.0615791 0.0459643i
\(829\) −736.301 −0.888180 −0.444090 0.895982i \(-0.646473\pi\)
−0.444090 + 0.895982i \(0.646473\pi\)
\(830\) −273.359 + 213.470i −0.329349 + 0.257193i
\(831\) 95.6275 + 110.360i 0.115075 + 0.132804i
\(832\) −0.938395 1.46017i −0.00112788 0.00175501i
\(833\) −42.8657 298.138i −0.0514594 0.357908i
\(834\) 541.908 + 348.263i 0.649769 + 0.417581i
\(835\) 7.47113 146.353i 0.00894746 0.175272i
\(836\) 296.345 342.001i 0.354480 0.409092i
\(837\) 50.9217 + 7.32143i 0.0608383 + 0.00874723i
\(838\) −63.9068 139.936i −0.0762612 0.166989i
\(839\) −44.1850 + 150.480i −0.0526639 + 0.179357i −0.981625 0.190821i \(-0.938885\pi\)
0.928961 + 0.370178i \(0.120703\pi\)
\(840\) −50.3089 546.516i −0.0598915 0.650614i
\(841\) −93.6522 205.070i −0.111358 0.243840i
\(842\) 26.6617 185.436i 0.0316647 0.220233i
\(843\) −690.291 + 796.639i −0.818851 + 0.945004i
\(844\) 149.831 328.083i 0.177524 0.388724i
\(845\) −162.125 + 826.042i −0.191864 + 0.977565i
\(846\) 6.22640 + 43.3055i 0.00735981 + 0.0511886i
\(847\) 711.102 456.997i 0.839554 0.539548i
\(848\) 339.533 + 391.842i 0.400392 + 0.462077i
\(849\) 277.931 + 946.548i 0.327363 + 1.11490i
\(850\) 245.746 + 261.270i 0.289112 + 0.307376i
\(851\) −154.421 + 10.8290i −0.181458 + 0.0127250i
\(852\) 427.156i 0.501357i
\(853\) 229.570 + 781.844i 0.269133 + 0.916582i 0.977535 + 0.210773i \(0.0675981\pi\)
−0.708402 + 0.705809i \(0.750584\pi\)
\(854\) −158.697 183.147i −0.185828 0.214457i
\(855\) −21.0077 + 29.2896i −0.0245704 + 0.0342569i
\(856\) 900.193 129.428i 1.05163 0.151201i
\(857\) −510.910 + 794.991i −0.596161 + 0.927644i 0.403758 + 0.914866i \(0.367704\pi\)
−0.999918 + 0.0127782i \(0.995932\pi\)
\(858\) 15.0345 32.9210i 0.0175228 0.0383695i
\(859\) −408.729 + 471.698i −0.475819 + 0.549124i −0.942021 0.335554i \(-0.891077\pi\)
0.466202 + 0.884678i \(0.345622\pi\)
\(860\) 970.626 231.975i 1.12863 0.269738i
\(861\) 200.047 91.3586i 0.232343 0.106108i
\(862\) −194.220 57.0281i −0.225313 0.0661579i
\(863\) −95.1123 + 323.923i −0.110211 + 0.375345i −0.996066 0.0886182i \(-0.971755\pi\)
0.885854 + 0.463963i \(0.153573\pi\)
\(864\) −337.233 738.438i −0.390316 0.854673i
\(865\) −374.613 1567.45i −0.433079 1.81208i
\(866\) −51.1539 44.3251i −0.0590691 0.0511837i
\(867\) −51.5698 23.5511i −0.0594807 0.0271639i
\(868\) 30.3858 + 19.5278i 0.0350067 + 0.0224974i
\(869\) 96.6268 + 672.054i 0.111193 + 0.773365i
\(870\) 275.812 + 197.823i 0.317025 + 0.227383i
\(871\) 66.8210 57.9008i 0.0767176 0.0664762i
\(872\) −774.940 + 227.543i −0.888693 + 0.260944i
\(873\) −84.0621 −0.0962911
\(874\) −148.462 81.3338i −0.169865 0.0930593i
\(875\) 627.047 + 294.140i 0.716625 + 0.336160i
\(876\) 180.253 52.9270i 0.205768 0.0604189i
\(877\) 629.736 545.669i 0.718057 0.622200i −0.217218 0.976123i \(-0.569698\pi\)
0.935274 + 0.353924i \(0.115153\pi\)
\(878\) −284.994 443.459i −0.324594 0.505078i
\(879\) 1777.57 255.575i 2.02226 0.290757i
\(880\) 605.398 + 118.820i 0.687952 + 0.135023i
\(881\) −480.494 219.434i −0.545396 0.249074i 0.123610 0.992331i \(-0.460553\pi\)
−0.669006 + 0.743257i \(0.733280\pi\)
\(882\) −10.2910 8.91719i −0.0116678 0.0101102i
\(883\) 77.8107 + 11.1875i 0.0881208 + 0.0126699i 0.186234 0.982505i \(-0.440372\pi\)
−0.0981134 + 0.995175i \(0.531281\pi\)
\(884\) −38.8001 + 17.7194i −0.0438915 + 0.0200446i
\(885\) −1508.27 + 138.842i −1.70426 + 0.156884i
\(886\) −544.991 160.024i −0.615114 0.180614i
\(887\) 1251.71 571.637i 1.41117 0.644461i 0.443408 0.896320i \(-0.353769\pi\)
0.967764 + 0.251859i \(0.0810420\pi\)
\(888\) 18.9750 131.974i 0.0213682 0.148619i
\(889\) 10.7950 + 9.35390i 0.0121428 + 0.0105218i
\(890\) 541.867 + 27.6617i 0.608839 + 0.0310805i
\(891\) −786.485 + 1223.80i −0.882700 + 1.37351i
\(892\) 153.166 22.0220i 0.171711 0.0246884i
\(893\) −417.643 + 268.403i −0.467685 + 0.300563i
\(894\) −401.349 + 347.771i −0.448936 + 0.389005i
\(895\) −604.969 774.694i −0.675942 0.865580i
\(896\) 714.083i 0.796967i
\(897\) 56.4037 + 12.3519i 0.0628804 + 0.0137702i
\(898\) 205.900i 0.229287i
\(899\) −47.8920 + 14.0624i −0.0532725 + 0.0156422i
\(900\) −68.7983 7.04251i −0.0764426 0.00782501i
\(901\) 962.365 618.474i 1.06811 0.686431i
\(902\) −25.9415 180.427i −0.0287600 0.200030i
\(903\) −579.230 + 901.299i −0.641450 + 0.998116i
\(904\) 582.132 + 265.851i 0.643952 + 0.294083i
\(905\) 231.047 660.284i 0.255300 0.729595i
\(906\) 88.5518 615.892i 0.0977393 0.679792i
\(907\) −84.3363 184.671i −0.0929838 0.203606i 0.857425 0.514608i \(-0.172063\pi\)
−0.950409 + 0.311002i \(0.899335\pi\)
\(908\) −738.256 216.772i −0.813058 0.238735i
\(909\) 70.0164 + 20.5587i 0.0770257 + 0.0226168i
\(910\) 13.3745 13.9314i 0.0146972 0.0153093i
\(911\) −407.398 58.5750i −0.447199 0.0642975i −0.0849633 0.996384i \(-0.527077\pi\)
−0.362236 + 0.932087i \(0.617986\pi\)
\(912\) −129.495 + 149.445i −0.141990 + 0.163865i
\(913\) 1197.32 + 546.795i 1.31141 + 0.598900i
\(914\) 224.952 350.032i 0.246118 0.382967i
\(915\) −683.379 + 391.453i −0.746863 + 0.427817i
\(916\) 284.490 + 442.675i 0.310579 + 0.483270i
\(917\) −360.164 415.651i −0.392763 0.453273i
\(918\) −352.022 + 103.363i −0.383467 + 0.112596i
\(919\) 1050.71i 1.14332i −0.820492 0.571659i \(-0.806300\pi\)
0.820492 0.571659i \(-0.193700\pi\)
\(920\) −13.7937 725.616i −0.0149932 0.788713i
\(921\) 1194.86 1.29735
\(922\) −74.8684 254.978i −0.0812022 0.276549i
\(923\) 25.3826 21.9941i 0.0275001 0.0238290i
\(924\) −784.164 + 503.951i −0.848662 + 0.545402i
\(925\) 131.551 + 104.910i 0.142217 + 0.113417i
\(926\) 559.034 + 359.269i 0.603708 + 0.387980i
\(927\) 22.7437 49.8017i 0.0245347 0.0537235i
\(928\) 595.253 + 515.789i 0.641436 + 0.555807i
\(929\) 57.3318 398.752i 0.0617135 0.429227i −0.935418 0.353543i \(-0.884977\pi\)
0.997132 0.0756839i \(-0.0241140\pi\)
\(930\) −19.0605 + 19.8543i −0.0204952 + 0.0213487i
\(931\) 43.5319 148.256i 0.0467582 0.159244i
\(932\) 232.775 792.758i 0.249758 0.850598i
\(933\) 1355.96 619.244i 1.45333 0.663713i
\(934\) 257.548 + 37.0299i 0.275748 + 0.0396465i
\(935\) 449.589 1284.83i 0.480844 1.37415i
\(936\) −1.78996 + 3.91946i −0.00191235 + 0.00418746i
\(937\) −399.568 256.787i −0.426433 0.274052i 0.309771 0.950811i \(-0.399748\pi\)
−0.736205 + 0.676759i \(0.763384\pi\)
\(938\) 528.508 75.9880i 0.563442 0.0810107i
\(939\) −381.364 593.415i −0.406139 0.631964i
\(940\) −845.155 439.357i −0.899102 0.467401i
\(941\) −187.656 639.098i −0.199422 0.679169i −0.997101 0.0760871i \(-0.975757\pi\)
0.797679 0.603082i \(-0.206061\pi\)
\(942\) 424.553 0.450693
\(943\) 272.620 101.251i 0.289099 0.107371i
\(944\) −719.943 −0.762651
\(945\) −558.364 + 436.033i −0.590861 + 0.461411i
\(946\) 581.526 + 671.117i 0.614721 + 0.709426i
\(947\) −929.142 1445.77i −0.981142 1.52669i −0.844144 0.536116i \(-0.819891\pi\)
−0.136998 0.990571i \(-0.543745\pi\)
\(948\) −59.4230 413.296i −0.0626825 0.435966i
\(949\) 12.4262 + 7.98583i 0.0130940 + 0.00841500i
\(950\) 58.9954 + 174.287i 0.0621005 + 0.183460i
\(951\) 631.636 728.946i 0.664181 0.766505i
\(952\) −569.715 81.9127i −0.598440 0.0860427i
\(953\) −60.3216 132.086i −0.0632965 0.138600i 0.875340 0.483508i \(-0.160637\pi\)
−0.938637 + 0.344908i \(0.887910\pi\)
\(954\) 14.5703 49.6220i 0.0152729 0.0520146i
\(955\) 1457.04 134.126i 1.52570 0.140446i
\(956\) 582.978 + 1276.54i 0.609809 + 1.33530i
\(957\) 183.319 1275.01i 0.191556 1.33230i
\(958\) 34.5104 39.8271i 0.0360234 0.0415732i
\(959\) −133.311 + 291.911i −0.139010 + 0.304391i
\(960\) −33.4263 6.56051i −0.0348191 0.00683386i
\(961\) 136.189 + 947.212i 0.141715 + 0.985653i
\(962\) 3.94689 2.53651i 0.00410280 0.00263671i
\(963\) 80.5680 + 92.9804i 0.0836636 + 0.0965529i
\(964\) −290.801 990.377i −0.301661 1.02736i
\(965\) −893.011 + 353.985i −0.925401 + 0.366824i
\(966\) 246.218 + 246.903i 0.254884 + 0.255593i
\(967\) 97.9293i 0.101271i −0.998717 0.0506356i \(-0.983875\pi\)
0.998717 0.0506356i \(-0.0161247\pi\)
\(968\) 271.239 + 923.755i 0.280205 + 0.954292i
\(969\) 285.715 + 329.732i 0.294855 + 0.340281i
\(970\) −250.104 + 348.704i −0.257839 + 0.359488i
\(971\) −1265.45 + 181.944i −1.30325 + 0.187378i −0.758748 0.651384i \(-0.774189\pi\)
−0.544498 + 0.838762i \(0.683280\pi\)
\(972\) 80.4971 125.256i 0.0828160 0.128864i
\(973\) 541.906 1186.61i 0.556944 1.21954i
\(974\) −31.2475 + 36.0615i −0.0320816 + 0.0370241i
\(975\) −36.0561 51.3705i −0.0369806 0.0526877i
\(976\) −340.512 + 155.506i −0.348885 + 0.159330i
\(977\) −23.3317 6.85082i −0.0238810 0.00701210i 0.269770 0.962925i \(-0.413052\pi\)
−0.293651 + 0.955913i \(0.594870\pi\)
\(978\) −131.929 + 449.310i −0.134897 + 0.459417i
\(979\) −855.380 1873.02i −0.873729 1.91320i
\(980\) 288.344 68.9129i 0.294229 0.0703193i
\(981\) −82.5731 71.5500i −0.0841724 0.0729358i
\(982\) −104.060 47.5226i −0.105967 0.0483937i
\(983\) −733.419 471.340i −0.746102 0.479491i 0.111525 0.993762i \(-0.464426\pi\)
−0.857628 + 0.514271i \(0.828063\pi\)
\(984\) 35.6474 + 247.933i 0.0362270 + 0.251964i
\(985\) −323.679 + 451.284i −0.328608 + 0.458156i
\(986\) 269.018 233.106i 0.272838 0.236415i
\(987\) 981.185 288.102i 0.994108 0.291896i
\(988\) −21.8815 −0.0221473
\(989\) −850.598 + 1132.98i −0.860058 + 1.14559i
\(990\) −22.6770 57.2081i −0.0229060 0.0577859i
\(991\) −1532.80 + 450.071i −1.54672 + 0.454158i −0.940119 0.340847i \(-0.889286\pi\)
−0.606602 + 0.795006i \(0.707468\pi\)
\(992\) −48.2674 + 41.8239i −0.0486566 + 0.0421612i
\(993\) 32.4630 + 50.5134i 0.0326919 + 0.0508695i
\(994\) 200.759 28.8648i 0.201971 0.0290390i
\(995\) −134.406 26.3796i −0.135082 0.0265122i
\(996\) −736.318 336.265i −0.739276 0.337616i
\(997\) 290.385 + 251.620i 0.291259 + 0.252377i 0.788217 0.615397i \(-0.211004\pi\)
−0.496958 + 0.867774i \(0.665550\pi\)
\(998\) 556.542 + 80.0186i 0.557657 + 0.0801790i
\(999\) −156.556 + 71.4965i −0.156712 + 0.0715681i
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 115.3.i.a.14.10 220
5.4 even 2 inner 115.3.i.a.14.13 yes 220
23.5 odd 22 inner 115.3.i.a.74.13 yes 220
115.74 odd 22 inner 115.3.i.a.74.10 yes 220
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.3.i.a.14.10 220 1.1 even 1 trivial
115.3.i.a.14.13 yes 220 5.4 even 2 inner
115.3.i.a.74.10 yes 220 115.74 odd 22 inner
115.3.i.a.74.13 yes 220 23.5 odd 22 inner