Properties

Label 35.3.l.a.18.3
Level $35$
Weight $3$
Character 35.18
Analytic conductor $0.954$
Analytic rank $0$
Dimension $24$
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] = [35,3,Mod(2,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.l (of order \(12\), degree \(4\), 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: \(0.953680925261\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 18.3
Character \(\chi\) \(=\) 35.18
Dual form 35.3.l.a.2.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23172 - 0.330037i) q^{2} +(-4.01589 + 1.07605i) q^{3} +(-2.05590 - 1.18698i) q^{4} +(-1.75247 - 4.68282i) q^{5} +5.30157 q^{6} +(-3.92739 + 5.79445i) q^{7} +(5.74725 + 5.74725i) q^{8} +(7.17525 - 4.14263i) q^{9} +O(q^{10})\) \(q+(-1.23172 - 0.330037i) q^{2} +(-4.01589 + 1.07605i) q^{3} +(-2.05590 - 1.18698i) q^{4} +(-1.75247 - 4.68282i) q^{5} +5.30157 q^{6} +(-3.92739 + 5.79445i) q^{7} +(5.74725 + 5.74725i) q^{8} +(7.17525 - 4.14263i) q^{9} +(0.613038 + 6.34629i) q^{10} +(2.98240 - 5.16566i) q^{11} +(9.53353 + 2.55450i) q^{12} +(-15.4106 - 15.4106i) q^{13} +(6.74980 - 5.84093i) q^{14} +(12.0767 + 16.9200i) q^{15} +(-0.434268 - 0.752174i) q^{16} +(-0.226943 - 0.846962i) q^{17} +(-10.2051 + 2.73444i) q^{18} +(-18.0198 + 10.4038i) q^{19} +(-1.95549 + 11.7076i) q^{20} +(9.53681 - 27.4959i) q^{21} +(-5.37832 + 5.37832i) q^{22} +(3.12465 - 11.6614i) q^{23} +(-29.2647 - 16.8960i) q^{24} +(-18.8577 + 16.4130i) q^{25} +(13.8954 + 24.0675i) q^{26} +(2.10122 - 2.10122i) q^{27} +(14.9522 - 7.25111i) q^{28} -7.52964i q^{29} +(-9.29084 - 24.8263i) q^{30} +(-9.90283 + 17.1522i) q^{31} +(-8.12792 - 30.3338i) q^{32} +(-6.41844 + 23.9539i) q^{33} +1.11811i q^{34} +(34.0170 + 8.23666i) q^{35} -19.6688 q^{36} +(13.4154 + 3.59463i) q^{37} +(25.6289 - 6.86725i) q^{38} +(78.4697 + 45.3045i) q^{39} +(16.8415 - 36.9853i) q^{40} +12.0569 q^{41} +(-20.8213 + 30.7197i) q^{42} +(12.3503 + 12.3503i) q^{43} +(-12.2630 + 7.08007i) q^{44} +(-31.9736 - 26.3406i) q^{45} +(-7.69736 + 13.3322i) q^{46} +(-43.9302 - 11.7711i) q^{47} +(2.55335 + 2.55335i) q^{48} +(-18.1513 - 45.5141i) q^{49} +(28.6442 - 13.9924i) q^{50} +(1.82275 + 3.15710i) q^{51} +(13.3907 + 49.9746i) q^{52} +(-9.78248 + 2.62121i) q^{53} +(-3.28158 + 1.89462i) q^{54} +(-29.4164 - 4.91337i) q^{55} +(-55.8739 + 10.7305i) q^{56} +(61.1707 - 61.1707i) q^{57} +(-2.48506 + 9.27437i) q^{58} +(18.2765 + 10.5519i) q^{59} +(-4.74494 - 49.1206i) q^{60} +(-15.1204 - 26.1893i) q^{61} +(17.8583 - 17.8583i) q^{62} +(-4.17570 + 57.8463i) q^{63} +43.5193i q^{64} +(-45.1584 + 99.1715i) q^{65} +(15.8114 - 27.3861i) q^{66} +(-18.6717 - 69.6836i) q^{67} +(-0.538751 + 2.01065i) q^{68} +50.1930i q^{69} +(-39.1809 - 21.3721i) q^{70} -128.667 q^{71} +(65.0467 + 17.4292i) q^{72} +(72.5481 - 19.4392i) q^{73} +(-15.3375 - 8.85513i) q^{74} +(58.0691 - 86.2048i) q^{75} +49.3961 q^{76} +(18.2191 + 37.5689i) q^{77} +(-81.7002 - 81.7002i) q^{78} +(-14.8579 + 8.57820i) q^{79} +(-2.76126 + 3.35176i) q^{80} +(-43.4609 + 75.2765i) q^{81} +(-14.8507 - 3.97924i) q^{82} +(4.42198 + 4.42198i) q^{83} +(-52.2438 + 45.2091i) q^{84} +(-3.56846 + 2.54701i) q^{85} +(-11.1360 - 19.2881i) q^{86} +(8.10230 + 30.2382i) q^{87} +(46.8289 - 12.5478i) q^{88} +(94.1599 - 54.3633i) q^{89} +(30.6890 + 42.9966i) q^{90} +(149.819 - 28.7725i) q^{91} +(-20.2657 + 20.2657i) q^{92} +(21.3120 - 79.5373i) q^{93} +(50.2247 + 28.9972i) q^{94} +(80.2982 + 66.1515i) q^{95} +(65.2816 + 113.071i) q^{96} +(-55.4317 + 55.4317i) q^{97} +(7.33588 + 62.0510i) q^{98} -49.4198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25} + 140 q^{26} + 76 q^{27} + 186 q^{28} + 64 q^{30} + 120 q^{31} + 130 q^{32} + 116 q^{33} - 240 q^{35} - 496 q^{36} + 44 q^{37} + 16 q^{38} - 158 q^{40} + 16 q^{41} - 370 q^{42} - 196 q^{43} - 104 q^{45} - 148 q^{46} - 208 q^{47} - 52 q^{48} + 580 q^{50} - 160 q^{51} - 288 q^{52} - 72 q^{53} + 208 q^{55} + 420 q^{56} + 656 q^{57} - 2 q^{58} + 262 q^{60} + 308 q^{61} + 176 q^{62} + 212 q^{63} + 132 q^{65} + 316 q^{66} + 198 q^{67} + 332 q^{68} - 200 q^{70} - 792 q^{71} + 308 q^{72} + 380 q^{73} - 450 q^{75} - 400 q^{76} - 472 q^{77} - 720 q^{78} - 324 q^{80} - 352 q^{81} - 818 q^{82} - 460 q^{83} + 144 q^{85} - 336 q^{86} - 214 q^{87} - 288 q^{88} + 120 q^{90} + 984 q^{91} + 1372 q^{92} - 68 q^{93} - 88 q^{95} + 816 q^{96} - 72 q^{97} + 482 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23172 0.330037i −0.615858 0.165019i −0.0626137 0.998038i \(-0.519944\pi\)
−0.553244 + 0.833019i \(0.686610\pi\)
\(3\) −4.01589 + 1.07605i −1.33863 + 0.358685i −0.855926 0.517099i \(-0.827012\pi\)
−0.482704 + 0.875784i \(0.660345\pi\)
\(4\) −2.05590 1.18698i −0.513976 0.296744i
\(5\) −1.75247 4.68282i −0.350494 0.936565i
\(6\) 5.30157 0.883595
\(7\) −3.92739 + 5.79445i −0.561055 + 0.827778i
\(8\) 5.74725 + 5.74725i 0.718407 + 0.718407i
\(9\) 7.17525 4.14263i 0.797250 0.460292i
\(10\) 0.613038 + 6.34629i 0.0613038 + 0.634629i
\(11\) 2.98240 5.16566i 0.271127 0.469605i −0.698024 0.716075i \(-0.745937\pi\)
0.969151 + 0.246469i \(0.0792704\pi\)
\(12\) 9.53353 + 2.55450i 0.794461 + 0.212875i
\(13\) −15.4106 15.4106i −1.18543 1.18543i −0.978318 0.207110i \(-0.933594\pi\)
−0.207110 0.978318i \(-0.566406\pi\)
\(14\) 6.74980 5.84093i 0.482129 0.417209i
\(15\) 12.0767 + 16.9200i 0.805113 + 1.12800i
\(16\) −0.434268 0.752174i −0.0271418 0.0470109i
\(17\) −0.226943 0.846962i −0.0133496 0.0498213i 0.958930 0.283644i \(-0.0915433\pi\)
−0.972279 + 0.233822i \(0.924877\pi\)
\(18\) −10.2051 + 2.73444i −0.566949 + 0.151914i
\(19\) −18.0198 + 10.4038i −0.948412 + 0.547566i −0.892587 0.450874i \(-0.851112\pi\)
−0.0558250 + 0.998441i \(0.517779\pi\)
\(20\) −1.95549 + 11.7076i −0.0977747 + 0.585379i
\(21\) 9.53681 27.4959i 0.454134 1.30933i
\(22\) −5.37832 + 5.37832i −0.244469 + 0.244469i
\(23\) 3.12465 11.6614i 0.135854 0.507015i −0.864139 0.503254i \(-0.832136\pi\)
0.999993 0.00376143i \(-0.00119730\pi\)
\(24\) −29.2647 16.8960i −1.21936 0.703999i
\(25\) −18.8577 + 16.4130i −0.754308 + 0.656521i
\(26\) 13.8954 + 24.0675i 0.534437 + 0.925672i
\(27\) 2.10122 2.10122i 0.0778228 0.0778228i
\(28\) 14.9522 7.25111i 0.534007 0.258968i
\(29\) 7.52964i 0.259643i −0.991537 0.129821i \(-0.958560\pi\)
0.991537 0.129821i \(-0.0414404\pi\)
\(30\) −9.29084 24.8263i −0.309695 0.827544i
\(31\) −9.90283 + 17.1522i −0.319446 + 0.553297i −0.980373 0.197154i \(-0.936830\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(32\) −8.12792 30.3338i −0.253997 0.947931i
\(33\) −6.41844 + 23.9539i −0.194498 + 0.725877i
\(34\) 1.11811i 0.0328857i
\(35\) 34.0170 + 8.23666i 0.971915 + 0.235333i
\(36\) −19.6688 −0.546356
\(37\) 13.4154 + 3.59463i 0.362577 + 0.0971523i 0.435508 0.900185i \(-0.356569\pi\)
−0.0729310 + 0.997337i \(0.523235\pi\)
\(38\) 25.6289 6.86725i 0.674446 0.180717i
\(39\) 78.4697 + 45.3045i 2.01204 + 1.16165i
\(40\) 16.8415 36.9853i 0.421037 0.924632i
\(41\) 12.0569 0.294072 0.147036 0.989131i \(-0.453027\pi\)
0.147036 + 0.989131i \(0.453027\pi\)
\(42\) −20.8213 + 30.7197i −0.495746 + 0.731421i
\(43\) 12.3503 + 12.3503i 0.287215 + 0.287215i 0.835978 0.548763i \(-0.184901\pi\)
−0.548763 + 0.835978i \(0.684901\pi\)
\(44\) −12.2630 + 7.08007i −0.278705 + 0.160911i
\(45\) −31.9736 26.3406i −0.710525 0.585346i
\(46\) −7.69736 + 13.3322i −0.167334 + 0.289831i
\(47\) −43.9302 11.7711i −0.934686 0.250448i −0.240834 0.970566i \(-0.577421\pi\)
−0.693852 + 0.720118i \(0.744088\pi\)
\(48\) 2.55335 + 2.55335i 0.0531949 + 0.0531949i
\(49\) −18.1513 45.5141i −0.370434 0.928859i
\(50\) 28.6442 13.9924i 0.572884 0.279849i
\(51\) 1.82275 + 3.15710i 0.0357403 + 0.0619039i
\(52\) 13.3907 + 49.9746i 0.257513 + 0.961050i
\(53\) −9.78248 + 2.62121i −0.184575 + 0.0494567i −0.349923 0.936779i \(-0.613792\pi\)
0.165348 + 0.986235i \(0.447125\pi\)
\(54\) −3.28158 + 1.89462i −0.0607700 + 0.0350856i
\(55\) −29.4164 4.91337i −0.534844 0.0893340i
\(56\) −55.8739 + 10.7305i −0.997747 + 0.191616i
\(57\) 61.1707 61.1707i 1.07317 1.07317i
\(58\) −2.48506 + 9.27437i −0.0428459 + 0.159903i
\(59\) 18.2765 + 10.5519i 0.309771 + 0.178847i 0.646824 0.762639i \(-0.276097\pi\)
−0.337053 + 0.941486i \(0.609430\pi\)
\(60\) −4.74494 49.1206i −0.0790824 0.818676i
\(61\) −15.1204 26.1893i −0.247876 0.429333i 0.715061 0.699062i \(-0.246399\pi\)
−0.962936 + 0.269729i \(0.913066\pi\)
\(62\) 17.8583 17.8583i 0.288038 0.288038i
\(63\) −4.17570 + 57.8463i −0.0662810 + 0.918195i
\(64\) 43.5193i 0.679988i
\(65\) −45.1584 + 99.1715i −0.694745 + 1.52572i
\(66\) 15.8114 27.3861i 0.239566 0.414941i
\(67\) −18.6717 69.6836i −0.278682 1.04005i −0.953334 0.301918i \(-0.902373\pi\)
0.674652 0.738136i \(-0.264294\pi\)
\(68\) −0.538751 + 2.01065i −0.00792281 + 0.0295683i
\(69\) 50.1930i 0.727435i
\(70\) −39.1809 21.3721i −0.559727 0.305316i
\(71\) −128.667 −1.81222 −0.906108 0.423047i \(-0.860960\pi\)
−0.906108 + 0.423047i \(0.860960\pi\)
\(72\) 65.0467 + 17.4292i 0.903427 + 0.242072i
\(73\) 72.5481 19.4392i 0.993810 0.266290i 0.274960 0.961456i \(-0.411335\pi\)
0.718850 + 0.695165i \(0.244669\pi\)
\(74\) −15.3375 8.85513i −0.207264 0.119664i
\(75\) 58.0691 86.2048i 0.774255 1.14940i
\(76\) 49.3961 0.649948
\(77\) 18.2191 + 37.5689i 0.236612 + 0.487907i
\(78\) −81.7002 81.7002i −1.04744 1.04744i
\(79\) −14.8579 + 8.57820i −0.188074 + 0.108585i −0.591081 0.806612i \(-0.701299\pi\)
0.403006 + 0.915197i \(0.367965\pi\)
\(80\) −2.76126 + 3.35176i −0.0345157 + 0.0418971i
\(81\) −43.4609 + 75.2765i −0.536554 + 0.929339i
\(82\) −14.8507 3.97924i −0.181106 0.0485273i
\(83\) 4.42198 + 4.42198i 0.0532769 + 0.0532769i 0.733243 0.679966i \(-0.238006\pi\)
−0.679966 + 0.733243i \(0.738006\pi\)
\(84\) −52.2438 + 45.2091i −0.621950 + 0.538203i
\(85\) −3.56846 + 2.54701i −0.0419819 + 0.0299648i
\(86\) −11.1360 19.2881i −0.129488 0.224280i
\(87\) 8.10230 + 30.2382i 0.0931299 + 0.347565i
\(88\) 46.8289 12.5478i 0.532147 0.142588i
\(89\) 94.1599 54.3633i 1.05798 0.610823i 0.133105 0.991102i \(-0.457505\pi\)
0.924872 + 0.380279i \(0.124172\pi\)
\(90\) 30.6890 + 42.9966i 0.340989 + 0.477740i
\(91\) 149.819 28.7725i 1.64636 0.316181i
\(92\) −20.2657 + 20.2657i −0.220280 + 0.220280i
\(93\) 21.3120 79.5373i 0.229161 0.855240i
\(94\) 50.2247 + 28.9972i 0.534305 + 0.308481i
\(95\) 80.2982 + 66.1515i 0.845244 + 0.696331i
\(96\) 65.2816 + 113.071i 0.680017 + 1.17782i
\(97\) −55.4317 + 55.4317i −0.571461 + 0.571461i −0.932537 0.361076i \(-0.882410\pi\)
0.361076 + 0.932537i \(0.382410\pi\)
\(98\) 7.33588 + 62.0510i 0.0748559 + 0.633173i
\(99\) 49.4198i 0.499190i
\(100\) 58.2515 11.3599i 0.582515 0.113599i
\(101\) 80.0618 138.671i 0.792691 1.37298i −0.131605 0.991302i \(-0.542013\pi\)
0.924295 0.381678i \(-0.124654\pi\)
\(102\) −1.20315 4.49023i −0.0117956 0.0440218i
\(103\) −32.1500 + 119.986i −0.312136 + 1.16491i 0.614490 + 0.788925i \(0.289362\pi\)
−0.926626 + 0.375984i \(0.877305\pi\)
\(104\) 177.137i 1.70324i
\(105\) −145.472 + 3.52664i −1.38544 + 0.0335870i
\(106\) 12.9143 0.121833
\(107\) −130.359 34.9296i −1.21831 0.326445i −0.408292 0.912852i \(-0.633875\pi\)
−0.810017 + 0.586407i \(0.800542\pi\)
\(108\) −6.81399 + 1.82580i −0.0630925 + 0.0169056i
\(109\) −113.564 65.5664i −1.04187 0.601527i −0.121511 0.992590i \(-0.538774\pi\)
−0.920364 + 0.391064i \(0.872107\pi\)
\(110\) 34.6111 + 15.7604i 0.314646 + 0.143276i
\(111\) −57.7426 −0.520204
\(112\) 6.06397 + 0.437735i 0.0541426 + 0.00390835i
\(113\) −54.8723 54.8723i −0.485596 0.485596i 0.421317 0.906913i \(-0.361568\pi\)
−0.906913 + 0.421317i \(0.861568\pi\)
\(114\) −95.5334 + 55.1562i −0.838013 + 0.483827i
\(115\) −60.0839 + 5.80398i −0.522469 + 0.0504694i
\(116\) −8.93750 + 15.4802i −0.0770474 + 0.133450i
\(117\) −174.415 46.7343i −1.49072 0.399439i
\(118\) −19.0289 19.0289i −0.161262 0.161262i
\(119\) 5.79897 + 2.01134i 0.0487308 + 0.0169020i
\(120\) −27.8354 + 166.651i −0.231962 + 1.38876i
\(121\) 42.7106 + 73.9770i 0.352980 + 0.611380i
\(122\) 9.98059 + 37.2481i 0.0818081 + 0.305312i
\(123\) −48.4193 + 12.9739i −0.393653 + 0.105479i
\(124\) 40.7185 23.5088i 0.328375 0.189587i
\(125\) 109.907 + 59.5440i 0.879255 + 0.476352i
\(126\) 24.2347 69.8720i 0.192339 0.554540i
\(127\) 119.378 119.378i 0.939985 0.939985i −0.0583136 0.998298i \(-0.518572\pi\)
0.998298 + 0.0583136i \(0.0185723\pi\)
\(128\) −18.1487 + 67.7318i −0.141787 + 0.529155i
\(129\) −62.8868 36.3077i −0.487495 0.281455i
\(130\) 88.3526 107.247i 0.679635 0.824978i
\(131\) −25.8642 44.7981i −0.197437 0.341970i 0.750260 0.661143i \(-0.229928\pi\)
−0.947697 + 0.319173i \(0.896595\pi\)
\(132\) 41.6285 41.6285i 0.315367 0.315367i
\(133\) 10.4868 145.275i 0.0788482 1.09229i
\(134\) 91.9927i 0.686513i
\(135\) −13.5219 6.15731i −0.100163 0.0456097i
\(136\) 3.56341 6.17200i 0.0262015 0.0453824i
\(137\) 50.6274 + 188.944i 0.369543 + 1.37915i 0.861157 + 0.508339i \(0.169740\pi\)
−0.491614 + 0.870813i \(0.663593\pi\)
\(138\) 16.5656 61.8235i 0.120040 0.447996i
\(139\) 127.517i 0.917386i 0.888595 + 0.458693i \(0.151682\pi\)
−0.888595 + 0.458693i \(0.848318\pi\)
\(140\) −60.1590 57.3112i −0.429707 0.409366i
\(141\) 189.085 1.34103
\(142\) 158.481 + 42.4650i 1.11607 + 0.299049i
\(143\) −125.566 + 33.6453i −0.878085 + 0.235282i
\(144\) −6.23196 3.59802i −0.0432775 0.0249863i
\(145\) −35.2600 + 13.1955i −0.243172 + 0.0910032i
\(146\) −95.7743 −0.655988
\(147\) 121.869 + 163.248i 0.829042 + 1.11053i
\(148\) −23.3139 23.3139i −0.157527 0.157527i
\(149\) 192.034 110.871i 1.28882 0.744100i 0.310375 0.950614i \(-0.399545\pi\)
0.978444 + 0.206514i \(0.0662120\pi\)
\(150\) −99.9754 + 87.0148i −0.666503 + 0.580099i
\(151\) 33.2375 57.5691i 0.220116 0.381252i −0.734727 0.678363i \(-0.762690\pi\)
0.954843 + 0.297111i \(0.0960231\pi\)
\(152\) −163.358 43.7715i −1.07472 0.287971i
\(153\) −5.13702 5.13702i −0.0335753 0.0335753i
\(154\) −10.0417 52.2872i −0.0652056 0.339527i
\(155\) 97.6752 + 16.3145i 0.630162 + 0.105255i
\(156\) −107.551 186.283i −0.689428 1.19412i
\(157\) 24.9966 + 93.2888i 0.159214 + 0.594196i 0.998708 + 0.0508258i \(0.0161853\pi\)
−0.839493 + 0.543370i \(0.817148\pi\)
\(158\) 21.1318 5.66225i 0.133746 0.0358370i
\(159\) 36.4648 21.0530i 0.229338 0.132409i
\(160\) −127.804 + 91.2207i −0.798774 + 0.570129i
\(161\) 55.2994 + 63.9043i 0.343475 + 0.396921i
\(162\) 78.3755 78.3755i 0.483799 0.483799i
\(163\) 11.1914 41.7669i 0.0686589 0.256238i −0.923062 0.384651i \(-0.874322\pi\)
0.991721 + 0.128413i \(0.0409883\pi\)
\(164\) −24.7879 14.3113i −0.151146 0.0872641i
\(165\) 123.420 11.9221i 0.748001 0.0722554i
\(166\) −3.98720 6.90604i −0.0240193 0.0416026i
\(167\) 133.439 133.439i 0.799038 0.799038i −0.183906 0.982944i \(-0.558874\pi\)
0.982944 + 0.183906i \(0.0588743\pi\)
\(168\) 212.837 103.216i 1.26688 0.614380i
\(169\) 305.971i 1.81048i
\(170\) 5.23594 1.95946i 0.0307996 0.0115263i
\(171\) −86.1978 + 149.299i −0.504081 + 0.873094i
\(172\) −10.7315 40.0504i −0.0623923 0.232851i
\(173\) −57.9299 + 216.197i −0.334855 + 1.24970i 0.569171 + 0.822219i \(0.307264\pi\)
−0.904026 + 0.427477i \(0.859402\pi\)
\(174\) 39.9189i 0.229419i
\(175\) −21.0430 173.730i −0.120246 0.992744i
\(176\) −5.18064 −0.0294354
\(177\) −84.7509 22.7089i −0.478819 0.128299i
\(178\) −133.920 + 35.8838i −0.752360 + 0.201594i
\(179\) −78.9406 45.5764i −0.441009 0.254617i 0.263016 0.964791i \(-0.415283\pi\)
−0.704026 + 0.710175i \(0.748616\pi\)
\(180\) 34.4690 + 92.1056i 0.191495 + 0.511698i
\(181\) −146.339 −0.808505 −0.404253 0.914647i \(-0.632468\pi\)
−0.404253 + 0.914647i \(0.632468\pi\)
\(182\) −194.030 14.0063i −1.06610 0.0769576i
\(183\) 88.9030 + 88.9030i 0.485809 + 0.485809i
\(184\) 84.9789 49.0626i 0.461842 0.266645i
\(185\) −6.67697 69.1213i −0.0360917 0.373628i
\(186\) −52.5005 + 90.9336i −0.282261 + 0.488890i
\(187\) −5.05195 1.35367i −0.0270158 0.00723885i
\(188\) 76.3443 + 76.3443i 0.406087 + 0.406087i
\(189\) 3.92310 + 20.4277i 0.0207572 + 0.108083i
\(190\) −77.0721 107.981i −0.405643 0.568322i
\(191\) −42.2285 73.1419i −0.221092 0.382942i 0.734048 0.679097i \(-0.237629\pi\)
−0.955140 + 0.296156i \(0.904295\pi\)
\(192\) −46.8291 174.769i −0.243901 0.910253i
\(193\) −104.151 + 27.9071i −0.539641 + 0.144596i −0.518337 0.855177i \(-0.673449\pi\)
−0.0213045 + 0.999773i \(0.506782\pi\)
\(194\) 86.5706 49.9816i 0.446240 0.257637i
\(195\) 74.6372 446.855i 0.382755 2.29156i
\(196\) −16.7069 + 115.118i −0.0852390 + 0.587335i
\(197\) −49.0877 + 49.0877i −0.249176 + 0.249176i −0.820633 0.571456i \(-0.806379\pi\)
0.571456 + 0.820633i \(0.306379\pi\)
\(198\) −16.3104 + 60.8712i −0.0823757 + 0.307430i
\(199\) −180.471 104.195i −0.906891 0.523594i −0.0274617 0.999623i \(-0.508742\pi\)
−0.879430 + 0.476029i \(0.842076\pi\)
\(200\) −202.710 14.0502i −1.01355 0.0702508i
\(201\) 149.967 + 259.750i 0.746103 + 1.29229i
\(202\) −144.380 + 144.380i −0.714752 + 0.714752i
\(203\) 43.6301 + 29.5718i 0.214927 + 0.145674i
\(204\) 8.65426i 0.0424228i
\(205\) −21.1294 56.4605i −0.103070 0.275417i
\(206\) 79.1994 137.177i 0.384463 0.665910i
\(207\) −25.8885 96.6174i −0.125065 0.466751i
\(208\) −4.89911 + 18.2837i −0.0235534 + 0.0879026i
\(209\) 124.112i 0.593839i
\(210\) 180.344 + 43.6672i 0.858779 + 0.207939i
\(211\) −297.303 −1.40902 −0.704509 0.709695i \(-0.748833\pi\)
−0.704509 + 0.709695i \(0.748833\pi\)
\(212\) 23.2231 + 6.22262i 0.109543 + 0.0293520i
\(213\) 516.714 138.453i 2.42589 0.650014i
\(214\) 149.037 + 86.0466i 0.696435 + 0.402087i
\(215\) 36.1907 79.4776i 0.168329 0.369663i
\(216\) 24.1524 0.111817
\(217\) −60.4953 124.745i −0.278780 0.574861i
\(218\) 118.240 + 118.240i 0.542383 + 0.542383i
\(219\) −270.428 + 156.131i −1.23483 + 0.712929i
\(220\) 54.6453 + 45.0180i 0.248388 + 0.204627i
\(221\) −9.55484 + 16.5495i −0.0432346 + 0.0748845i
\(222\) 71.1225 + 19.0572i 0.320372 + 0.0858433i
\(223\) −40.6433 40.6433i −0.182257 0.182257i 0.610082 0.792339i \(-0.291137\pi\)
−0.792339 + 0.610082i \(0.791137\pi\)
\(224\) 207.689 + 72.0357i 0.927183 + 0.321588i
\(225\) −67.3155 + 195.888i −0.299180 + 0.870613i
\(226\) 49.4772 + 85.6970i 0.218926 + 0.379190i
\(227\) 15.6672 + 58.4709i 0.0690186 + 0.257581i 0.991811 0.127718i \(-0.0407651\pi\)
−0.922792 + 0.385299i \(0.874098\pi\)
\(228\) −198.369 + 53.1528i −0.870040 + 0.233126i
\(229\) −12.9816 + 7.49491i −0.0566881 + 0.0327289i −0.528076 0.849197i \(-0.677086\pi\)
0.471388 + 0.881926i \(0.343753\pi\)
\(230\) 75.9218 + 12.6811i 0.330095 + 0.0551351i
\(231\) −113.592 131.268i −0.491741 0.568258i
\(232\) 43.2747 43.2747i 0.186529 0.186529i
\(233\) 59.7065 222.828i 0.256251 0.956341i −0.711139 0.703051i \(-0.751821\pi\)
0.967390 0.253290i \(-0.0815128\pi\)
\(234\) 199.405 + 115.127i 0.852160 + 0.491995i
\(235\) 21.8646 + 226.346i 0.0930407 + 0.963175i
\(236\) −25.0498 43.3876i −0.106143 0.183846i
\(237\) 50.4370 50.4370i 0.212814 0.212814i
\(238\) −6.47886 4.39127i −0.0272221 0.0184507i
\(239\) 382.834i 1.60182i −0.598786 0.800909i \(-0.704350\pi\)
0.598786 0.800909i \(-0.295650\pi\)
\(240\) 7.48223 16.4316i 0.0311760 0.0684649i
\(241\) −140.302 + 243.009i −0.582164 + 1.00834i 0.413058 + 0.910705i \(0.364461\pi\)
−0.995222 + 0.0976334i \(0.968873\pi\)
\(242\) −28.1922 105.215i −0.116497 0.434771i
\(243\) 86.6107 323.236i 0.356423 1.33019i
\(244\) 71.7903i 0.294222i
\(245\) −181.325 + 164.761i −0.740101 + 0.672495i
\(246\) 63.9207 0.259840
\(247\) 438.023 + 117.368i 1.77337 + 0.475174i
\(248\) −155.492 + 41.6640i −0.626984 + 0.168000i
\(249\) −22.5165 12.9999i −0.0904276 0.0522084i
\(250\) −115.722 109.615i −0.462889 0.438458i
\(251\) −20.4968 −0.0816607 −0.0408303 0.999166i \(-0.513000\pi\)
−0.0408303 + 0.999166i \(0.513000\pi\)
\(252\) 77.2470 113.970i 0.306536 0.452262i
\(253\) −50.9196 50.9196i −0.201263 0.201263i
\(254\) −186.439 + 107.641i −0.734012 + 0.423782i
\(255\) 11.5898 14.0684i 0.0454503 0.0551700i
\(256\) 131.747 228.192i 0.514635 0.891374i
\(257\) 359.460 + 96.3170i 1.39868 + 0.374774i 0.877869 0.478900i \(-0.158964\pi\)
0.520807 + 0.853674i \(0.325631\pi\)
\(258\) 65.4758 + 65.4758i 0.253782 + 0.253782i
\(259\) −73.5162 + 63.6171i −0.283846 + 0.245626i
\(260\) 210.556 150.285i 0.809829 0.578019i
\(261\) −31.1925 54.0270i −0.119512 0.207000i
\(262\) 17.0723 + 63.7147i 0.0651614 + 0.243186i
\(263\) 327.017 87.6239i 1.24341 0.333171i 0.423623 0.905839i \(-0.360758\pi\)
0.819788 + 0.572668i \(0.194091\pi\)
\(264\) −174.558 + 100.781i −0.661204 + 0.381746i
\(265\) 29.4182 + 41.2160i 0.111012 + 0.155532i
\(266\) −60.8628 + 175.476i −0.228807 + 0.659684i
\(267\) −319.638 + 319.638i −1.19715 + 1.19715i
\(268\) −44.3256 + 165.426i −0.165394 + 0.617260i
\(269\) −75.2656 43.4546i −0.279798 0.161541i 0.353534 0.935422i \(-0.384980\pi\)
−0.633332 + 0.773880i \(0.718313\pi\)
\(270\) 14.6230 + 12.0468i 0.0541594 + 0.0446177i
\(271\) −99.4914 172.324i −0.367127 0.635882i 0.621988 0.783027i \(-0.286325\pi\)
−0.989115 + 0.147144i \(0.952992\pi\)
\(272\) −0.538509 + 0.538509i −0.00197981 + 0.00197981i
\(273\) −570.695 + 276.760i −2.09046 + 1.01377i
\(274\) 249.434i 0.910343i
\(275\) 28.5430 + 146.363i 0.103793 + 0.532227i
\(276\) 59.5779 103.192i 0.215862 0.373884i
\(277\) −96.5166 360.205i −0.348435 1.30038i −0.888547 0.458785i \(-0.848285\pi\)
0.540112 0.841593i \(-0.318382\pi\)
\(278\) 42.0852 157.064i 0.151386 0.564979i
\(279\) 164.095i 0.588154i
\(280\) 148.166 + 242.843i 0.529165 + 0.867295i
\(281\) 119.086 0.423794 0.211897 0.977292i \(-0.432036\pi\)
0.211897 + 0.977292i \(0.432036\pi\)
\(282\) −232.899 62.4052i −0.825884 0.221295i
\(283\) 9.42015 2.52412i 0.0332868 0.00891916i −0.242137 0.970242i \(-0.577848\pi\)
0.275424 + 0.961323i \(0.411182\pi\)
\(284\) 264.527 + 152.725i 0.931435 + 0.537764i
\(285\) −393.651 179.252i −1.38123 0.628953i
\(286\) 165.766 0.579601
\(287\) −47.3523 + 69.8633i −0.164990 + 0.243426i
\(288\) −183.981 183.981i −0.638825 0.638825i
\(289\) 249.616 144.116i 0.863721 0.498670i
\(290\) 47.7852 4.61596i 0.164777 0.0159171i
\(291\) 162.960 282.255i 0.560000 0.969949i
\(292\) −172.226 46.1478i −0.589814 0.158040i
\(293\) −26.5947 26.5947i −0.0907669 0.0907669i 0.660265 0.751032i \(-0.270444\pi\)
−0.751032 + 0.660265i \(0.770444\pi\)
\(294\) −96.2303 241.296i −0.327314 0.820735i
\(295\) 17.3839 104.078i 0.0589284 0.352806i
\(296\) 56.4422 + 97.7608i 0.190683 + 0.330273i
\(297\) −4.58751 17.1208i −0.0154462 0.0576458i
\(298\) −273.123 + 73.1830i −0.916519 + 0.245581i
\(299\) −227.861 + 131.555i −0.762076 + 0.439985i
\(300\) −221.708 + 108.302i −0.739025 + 0.361007i
\(301\) −120.067 + 23.0587i −0.398894 + 0.0766071i
\(302\) −59.9391 + 59.9391i −0.198474 + 0.198474i
\(303\) −172.302 + 643.038i −0.568652 + 2.12224i
\(304\) 15.6509 + 9.03604i 0.0514832 + 0.0297238i
\(305\) −96.1419 + 116.702i −0.315219 + 0.382630i
\(306\) 4.63194 + 8.02275i 0.0151370 + 0.0262181i
\(307\) −66.6628 + 66.6628i −0.217143 + 0.217143i −0.807293 0.590151i \(-0.799068\pi\)
0.590151 + 0.807293i \(0.299068\pi\)
\(308\) 7.13658 98.8637i 0.0231707 0.320986i
\(309\) 516.444i 1.67134i
\(310\) −114.924 52.3312i −0.370721 0.168810i
\(311\) 108.760 188.377i 0.349710 0.605715i −0.636488 0.771287i \(-0.719614\pi\)
0.986198 + 0.165571i \(0.0529469\pi\)
\(312\) 190.609 + 711.362i 0.610926 + 2.28001i
\(313\) 47.2552 176.359i 0.150975 0.563447i −0.848441 0.529290i \(-0.822459\pi\)
0.999416 0.0341576i \(-0.0108748\pi\)
\(314\) 123.155i 0.392213i
\(315\) 278.202 81.8199i 0.883181 0.259746i
\(316\) 40.7285 0.128888
\(317\) −478.934 128.330i −1.51083 0.404826i −0.594120 0.804376i \(-0.702500\pi\)
−0.916711 + 0.399550i \(0.869166\pi\)
\(318\) −51.8625 + 13.8965i −0.163090 + 0.0436997i
\(319\) −38.8955 22.4564i −0.121930 0.0703961i
\(320\) 203.793 76.2662i 0.636853 0.238332i
\(321\) 561.093 1.74795
\(322\) −47.0224 96.9627i −0.146032 0.301126i
\(323\) 12.9011 + 12.9011i 0.0399413 + 0.0399413i
\(324\) 178.703 103.174i 0.551552 0.318439i
\(325\) 543.542 + 37.6738i 1.67244 + 0.115919i
\(326\) −27.5692 + 47.7513i −0.0845682 + 0.146476i
\(327\) 526.615 + 141.106i 1.61044 + 0.431517i
\(328\) 69.2943 + 69.2943i 0.211263 + 0.211263i
\(329\) 240.738 208.322i 0.731726 0.633197i
\(330\) −155.953 26.0486i −0.472586 0.0789351i
\(331\) 232.008 + 401.849i 0.700930 + 1.21405i 0.968140 + 0.250408i \(0.0805648\pi\)
−0.267210 + 0.963638i \(0.586102\pi\)
\(332\) −3.84238 14.3400i −0.0115734 0.0431926i
\(333\) 111.150 29.7825i 0.333783 0.0894369i
\(334\) −208.399 + 120.319i −0.623949 + 0.360237i
\(335\) −293.595 + 209.555i −0.876402 + 0.625536i
\(336\) −24.8233 + 4.76727i −0.0738788 + 0.0141883i
\(337\) −85.3188 + 85.3188i −0.253171 + 0.253171i −0.822270 0.569098i \(-0.807292\pi\)
0.569098 + 0.822270i \(0.307292\pi\)
\(338\) 100.982 376.869i 0.298762 1.11500i
\(339\) 279.407 + 161.316i 0.824209 + 0.475857i
\(340\) 10.3597 1.00072i 0.0304696 0.00294330i
\(341\) 59.0683 + 102.309i 0.173221 + 0.300027i
\(342\) 155.445 155.445i 0.454519 0.454519i
\(343\) 335.016 + 73.5747i 0.976723 + 0.214503i
\(344\) 141.960i 0.412675i
\(345\) 235.045 87.9617i 0.681290 0.254962i
\(346\) 142.706 247.175i 0.412446 0.714378i
\(347\) −2.74359 10.2392i −0.00790660 0.0295078i 0.961860 0.273543i \(-0.0881955\pi\)
−0.969766 + 0.244035i \(0.921529\pi\)
\(348\) 19.2345 71.7840i 0.0552715 0.206276i
\(349\) 32.0826i 0.0919272i −0.998943 0.0459636i \(-0.985364\pi\)
0.998943 0.0459636i \(-0.0146358\pi\)
\(350\) −31.4185 + 220.931i −0.0897671 + 0.631232i
\(351\) −64.7618 −0.184507
\(352\) −180.935 48.4813i −0.514019 0.137731i
\(353\) −484.555 + 129.836i −1.37268 + 0.367807i −0.868455 0.495768i \(-0.834887\pi\)
−0.504221 + 0.863575i \(0.668220\pi\)
\(354\) 96.8942 + 55.9419i 0.273712 + 0.158028i
\(355\) 225.486 + 602.526i 0.635171 + 1.69726i
\(356\) −258.112 −0.725033
\(357\) −25.4523 1.83730i −0.0712950 0.00514651i
\(358\) 82.1905 + 82.1905i 0.229582 + 0.229582i
\(359\) −361.528 + 208.728i −1.00704 + 0.581415i −0.910324 0.413897i \(-0.864167\pi\)
−0.0967169 + 0.995312i \(0.530834\pi\)
\(360\) −32.3745 335.147i −0.0899291 0.930963i
\(361\) 35.9763 62.3128i 0.0996574 0.172612i
\(362\) 180.249 + 48.2975i 0.497924 + 0.133418i
\(363\) −251.124 251.124i −0.691803 0.691803i
\(364\) −342.166 118.678i −0.940015 0.326039i
\(365\) −218.169 305.663i −0.597723 0.837434i
\(366\) −80.1619 138.844i −0.219022 0.379356i
\(367\) −86.0920 321.300i −0.234583 0.875476i −0.978336 0.207022i \(-0.933623\pi\)
0.743753 0.668454i \(-0.233044\pi\)
\(368\) −10.1283 + 2.71387i −0.0275226 + 0.00737465i
\(369\) 86.5115 49.9475i 0.234449 0.135359i
\(370\) −14.5885 + 87.3414i −0.0394283 + 0.236058i
\(371\) 23.2311 66.9786i 0.0626176 0.180535i
\(372\) −138.224 + 138.224i −0.371571 + 0.371571i
\(373\) 108.916 406.480i 0.292000 1.08976i −0.651571 0.758587i \(-0.725890\pi\)
0.943571 0.331170i \(-0.107443\pi\)
\(374\) 5.77580 + 3.33466i 0.0154433 + 0.00891620i
\(375\) −505.446 120.856i −1.34786 0.322283i
\(376\) −184.827 320.130i −0.491561 0.851408i
\(377\) −116.036 + 116.036i −0.307788 + 0.307788i
\(378\) 1.90974 26.4558i 0.00505223 0.0699890i
\(379\) 513.773i 1.35560i 0.735246 + 0.677801i \(0.237067\pi\)
−0.735246 + 0.677801i \(0.762933\pi\)
\(380\) −86.5651 231.313i −0.227803 0.608719i
\(381\) −350.952 + 607.866i −0.921133 + 1.59545i
\(382\) 27.8739 + 104.027i 0.0729684 + 0.272322i
\(383\) −37.5765 + 140.238i −0.0981111 + 0.366155i −0.997473 0.0710499i \(-0.977365\pi\)
0.899362 + 0.437205i \(0.144032\pi\)
\(384\) 291.533i 0.759199i
\(385\) 144.000 151.155i 0.374026 0.392611i
\(386\) 137.494 0.356203
\(387\) 139.779 + 37.4536i 0.361185 + 0.0967793i
\(388\) 179.758 48.1661i 0.463295 0.124139i
\(389\) −356.579 205.871i −0.916655 0.529231i −0.0340888 0.999419i \(-0.510853\pi\)
−0.882566 + 0.470188i \(0.844186\pi\)
\(390\) −239.410 + 525.765i −0.613873 + 1.34811i
\(391\) −10.5858 −0.0270737
\(392\) 157.261 365.901i 0.401176 0.933421i
\(393\) 152.073 + 152.073i 0.386954 + 0.386954i
\(394\) 76.6629 44.2613i 0.194576 0.112338i
\(395\) 66.2082 + 54.5438i 0.167616 + 0.138086i
\(396\) −58.6602 + 101.602i −0.148132 + 0.256572i
\(397\) 140.406 + 37.6216i 0.353666 + 0.0947646i 0.431278 0.902219i \(-0.358063\pi\)
−0.0776117 + 0.996984i \(0.524729\pi\)
\(398\) 187.901 + 187.901i 0.472113 + 0.472113i
\(399\) 114.209 + 594.691i 0.286239 + 1.49045i
\(400\) 20.5348 + 7.05663i 0.0513369 + 0.0176416i
\(401\) 26.5072 + 45.9119i 0.0661028 + 0.114493i 0.897183 0.441660i \(-0.145610\pi\)
−0.831080 + 0.556153i \(0.812277\pi\)
\(402\) −98.9891 369.432i −0.246242 0.918986i
\(403\) 416.933 111.717i 1.03457 0.277213i
\(404\) −329.198 + 190.063i −0.814848 + 0.470453i
\(405\) 428.671 + 71.6000i 1.05845 + 0.176790i
\(406\) −43.9801 50.8236i −0.108325 0.125181i
\(407\) 58.5786 58.5786i 0.143928 0.143928i
\(408\) −7.66884 + 28.6205i −0.0187962 + 0.0701483i
\(409\) −251.839 145.399i −0.615742 0.355499i 0.159467 0.987203i \(-0.449022\pi\)
−0.775209 + 0.631704i \(0.782356\pi\)
\(410\) 7.39137 + 76.5168i 0.0180277 + 0.186626i
\(411\) −406.628 704.300i −0.989362 1.71363i
\(412\) 208.517 208.517i 0.506110 0.506110i
\(413\) −132.922 + 64.4607i −0.321844 + 0.156079i
\(414\) 127.549i 0.308090i
\(415\) 12.9580 28.4568i 0.0312240 0.0685705i
\(416\) −342.205 + 592.716i −0.822608 + 1.42480i
\(417\) −137.215 512.093i −0.329053 1.22804i
\(418\) 40.9617 152.871i 0.0979945 0.365721i
\(419\) 290.268i 0.692764i −0.938094 0.346382i \(-0.887410\pi\)
0.938094 0.346382i \(-0.112590\pi\)
\(420\) 303.262 + 165.421i 0.722052 + 0.393860i
\(421\) 256.502 0.609268 0.304634 0.952470i \(-0.401466\pi\)
0.304634 + 0.952470i \(0.401466\pi\)
\(422\) 366.193 + 98.1210i 0.867755 + 0.232514i
\(423\) −363.973 + 97.5264i −0.860457 + 0.230559i
\(424\) −71.2871 41.1576i −0.168130 0.0970699i
\(425\) 18.1808 + 12.2469i 0.0427784 + 0.0288163i
\(426\) −682.139 −1.60126
\(427\) 211.136 + 15.2411i 0.494464 + 0.0356935i
\(428\) 226.545 + 226.545i 0.529310 + 0.529310i
\(429\) 468.055 270.232i 1.09104 0.629911i
\(430\) −70.8071 + 85.9495i −0.164668 + 0.199883i
\(431\) −145.835 + 252.594i −0.338364 + 0.586064i −0.984125 0.177475i \(-0.943207\pi\)
0.645761 + 0.763540i \(0.276540\pi\)
\(432\) −2.49297 0.667990i −0.00577077 0.00154627i
\(433\) −122.368 122.368i −0.282605 0.282605i 0.551542 0.834147i \(-0.314040\pi\)
−0.834147 + 0.551542i \(0.814040\pi\)
\(434\) 33.3426 + 173.616i 0.0768263 + 0.400036i
\(435\) 127.401 90.9332i 0.292876 0.209042i
\(436\) 155.652 + 269.596i 0.356999 + 0.618340i
\(437\) 65.0162 + 242.644i 0.148779 + 0.555249i
\(438\) 384.619 103.058i 0.878125 0.235293i
\(439\) 752.706 434.575i 1.71459 0.989921i 0.786485 0.617609i \(-0.211899\pi\)
0.928108 0.372312i \(-0.121435\pi\)
\(440\) −140.825 197.302i −0.320058 0.448414i
\(441\) −318.788 251.381i −0.722875 0.570024i
\(442\) 17.2308 17.2308i 0.0389837 0.0389837i
\(443\) 34.4919 128.725i 0.0778597 0.290576i −0.916007 0.401163i \(-0.868606\pi\)
0.993867 + 0.110586i \(0.0352729\pi\)
\(444\) 118.713 + 68.5391i 0.267372 + 0.154367i
\(445\) −419.586 345.664i −0.942890 0.776774i
\(446\) 36.6472 + 63.4748i 0.0821686 + 0.142320i
\(447\) −651.884 + 651.884i −1.45835 + 1.45835i
\(448\) −252.170 170.917i −0.562880 0.381511i
\(449\) 758.129i 1.68848i 0.535963 + 0.844242i \(0.319949\pi\)
−0.535963 + 0.844242i \(0.680051\pi\)
\(450\) 147.564 219.062i 0.327920 0.486803i
\(451\) 35.9586 62.2821i 0.0797307 0.138098i
\(452\) 47.6801 + 177.944i 0.105487 + 0.393682i
\(453\) −71.5307 + 266.956i −0.157905 + 0.589308i
\(454\) 77.1902i 0.170023i
\(455\) −397.290 651.153i −0.873164 1.43111i
\(456\) 703.127 1.54194
\(457\) −705.542 189.049i −1.54386 0.413675i −0.616347 0.787475i \(-0.711388\pi\)
−0.927509 + 0.373800i \(0.878055\pi\)
\(458\) 18.4632 4.94720i 0.0403126 0.0108017i
\(459\) −2.25650 1.30279i −0.00491613 0.00283833i
\(460\) 130.416 + 59.3858i 0.283513 + 0.129100i
\(461\) 702.980 1.52490 0.762452 0.647045i \(-0.223996\pi\)
0.762452 + 0.647045i \(0.223996\pi\)
\(462\) 96.5900 + 199.174i 0.209069 + 0.431113i
\(463\) 618.405 + 618.405i 1.33565 + 1.33565i 0.900227 + 0.435420i \(0.143400\pi\)
0.435420 + 0.900227i \(0.356600\pi\)
\(464\) −5.66360 + 3.26988i −0.0122060 + 0.00704716i
\(465\) −409.808 + 39.5866i −0.881307 + 0.0851325i
\(466\) −147.083 + 254.755i −0.315628 + 0.546684i
\(467\) −120.945 32.4072i −0.258983 0.0693943i 0.126991 0.991904i \(-0.459468\pi\)
−0.385974 + 0.922510i \(0.626135\pi\)
\(468\) 303.108 + 303.108i 0.647666 + 0.647666i
\(469\) 477.109 + 165.482i 1.01729 + 0.352841i
\(470\) 47.7717 286.010i 0.101642 0.608532i
\(471\) −200.768 347.740i −0.426258 0.738301i
\(472\) 44.3950 + 165.684i 0.0940572 + 0.351026i
\(473\) 100.631 26.9639i 0.212750 0.0570061i
\(474\) −78.7701 + 45.4779i −0.166182 + 0.0959450i
\(475\) 169.056 491.951i 0.355906 1.03569i
\(476\) −9.53471 11.0184i −0.0200309 0.0231478i
\(477\) −59.3330 + 59.3330i −0.124388 + 0.124388i
\(478\) −126.350 + 471.543i −0.264330 + 0.986492i
\(479\) 644.603 + 372.161i 1.34573 + 0.776955i 0.987641 0.156734i \(-0.0500966\pi\)
0.358085 + 0.933689i \(0.383430\pi\)
\(480\) 415.088 503.856i 0.864767 1.04970i
\(481\) −151.343 262.134i −0.314642 0.544976i
\(482\) 253.014 253.014i 0.524925 0.524925i
\(483\) −290.841 197.127i −0.602155 0.408131i
\(484\) 202.786i 0.418980i
\(485\) 356.719 + 162.435i 0.735504 + 0.334917i
\(486\) −213.359 + 369.549i −0.439011 + 0.760390i
\(487\) 173.372 + 647.035i 0.356001 + 1.32861i 0.879220 + 0.476416i \(0.158064\pi\)
−0.523219 + 0.852198i \(0.675269\pi\)
\(488\) 63.6158 237.417i 0.130360 0.486511i
\(489\) 179.774i 0.367635i
\(490\) 277.718 143.095i 0.566771 0.292031i
\(491\) −61.5033 −0.125261 −0.0626307 0.998037i \(-0.519949\pi\)
−0.0626307 + 0.998037i \(0.519949\pi\)
\(492\) 114.945 + 30.7995i 0.233629 + 0.0626006i
\(493\) −6.37731 + 1.70880i −0.0129357 + 0.00346612i
\(494\) −500.784 289.128i −1.01373 0.585279i
\(495\) −231.424 + 86.6068i −0.467524 + 0.174963i
\(496\) 17.2019 0.0346813
\(497\) 505.326 745.556i 1.01675 1.50011i
\(498\) 23.4434 + 23.4434i 0.0470752 + 0.0470752i
\(499\) −41.8687 + 24.1729i −0.0839052 + 0.0484427i −0.541366 0.840787i \(-0.682092\pi\)
0.457460 + 0.889230i \(0.348759\pi\)
\(500\) −155.281 252.873i −0.310561 0.505747i
\(501\) −392.289 + 679.465i −0.783013 + 1.35622i
\(502\) 25.2463 + 6.76472i 0.0502914 + 0.0134755i
\(503\) −571.523 571.523i −1.13623 1.13623i −0.989120 0.147108i \(-0.953003\pi\)
−0.147108 0.989120i \(-0.546997\pi\)
\(504\) −356.456 + 308.459i −0.707254 + 0.612021i
\(505\) −789.678 131.898i −1.56372 0.261185i
\(506\) 45.9131 + 79.5239i 0.0907374 + 0.157162i
\(507\) −329.241 1228.74i −0.649391 2.42356i
\(508\) −387.129 + 103.731i −0.762064 + 0.204195i
\(509\) −579.164 + 334.381i −1.13785 + 0.656936i −0.945897 0.324468i \(-0.894815\pi\)
−0.191950 + 0.981405i \(0.561481\pi\)
\(510\) −18.9185 + 13.5031i −0.0370950 + 0.0264767i
\(511\) −172.285 + 496.722i −0.337152 + 0.972058i
\(512\) −39.2534 + 39.2534i −0.0766668 + 0.0766668i
\(513\) −16.0030 + 59.7241i −0.0311950 + 0.116421i
\(514\) −410.964 237.270i −0.799541 0.461615i
\(515\) 618.214 59.7182i 1.20041 0.115958i
\(516\) 86.1929 + 149.290i 0.167040 + 0.289323i
\(517\) −191.823 + 191.823i −0.371030 + 0.371030i
\(518\) 111.547 54.0951i 0.215342 0.104431i
\(519\) 930.561i 1.79299i
\(520\) −829.501 + 310.427i −1.59519 + 0.596975i
\(521\) 478.134 828.153i 0.917724 1.58954i 0.114861 0.993382i \(-0.463358\pi\)
0.802863 0.596163i \(-0.203309\pi\)
\(522\) 20.5894 + 76.8406i 0.0394432 + 0.147204i
\(523\) −232.525 + 867.796i −0.444599 + 1.65927i 0.272394 + 0.962186i \(0.412184\pi\)
−0.716993 + 0.697080i \(0.754482\pi\)
\(524\) 122.801i 0.234353i
\(525\) 271.449 + 675.038i 0.517046 + 1.28579i
\(526\) −431.711 −0.820743
\(527\) 16.7746 + 4.49475i 0.0318304 + 0.00852893i
\(528\) 20.8049 5.57465i 0.0394031 0.0105580i
\(529\) 331.904 + 191.625i 0.627417 + 0.362239i
\(530\) −22.6320 60.4755i −0.0427018 0.114105i
\(531\) 174.851 0.329287
\(532\) −193.997 + 286.223i −0.364657 + 0.538013i
\(533\) −185.804 185.804i −0.348601 0.348601i
\(534\) 499.196 288.211i 0.934823 0.539720i
\(535\) 64.8811 + 671.661i 0.121273 + 1.25544i
\(536\) 293.179 507.800i 0.546975 0.947388i
\(537\) 366.059 + 98.0853i 0.681675 + 0.182654i
\(538\) 78.3641 + 78.3641i 0.145658 + 0.145658i
\(539\) −289.245 41.9776i −0.536632 0.0778805i
\(540\) 20.4912 + 28.7090i 0.0379467 + 0.0531649i
\(541\) −454.145 786.602i −0.839455 1.45398i −0.890351 0.455275i \(-0.849541\pi\)
0.0508961 0.998704i \(-0.483792\pi\)
\(542\) 65.6717 + 245.090i 0.121165 + 0.452196i
\(543\) 587.683 157.469i 1.08229 0.289999i
\(544\) −23.8470 + 13.7681i −0.0438364 + 0.0253089i
\(545\) −108.018 + 646.705i −0.198198 + 1.18661i
\(546\) 794.276 152.539i 1.45472 0.279376i
\(547\) 153.413 153.413i 0.280462 0.280462i −0.552831 0.833293i \(-0.686453\pi\)
0.833293 + 0.552831i \(0.186453\pi\)
\(548\) 120.187 448.544i 0.219319 0.818511i
\(549\) −216.985 125.277i −0.395237 0.228190i
\(550\) 13.1482 189.697i 0.0239059 0.344904i
\(551\) 78.3365 + 135.683i 0.142172 + 0.246248i
\(552\) −288.472 + 288.472i −0.522594 + 0.522594i
\(553\) 8.64668 119.783i 0.0156359 0.216606i
\(554\) 475.524i 0.858346i
\(555\) 101.192 + 270.399i 0.182328 + 0.487205i
\(556\) 151.359 262.162i 0.272229 0.471514i
\(557\) 110.673 + 413.039i 0.198696 + 0.741542i 0.991279 + 0.131779i \(0.0420688\pi\)
−0.792584 + 0.609763i \(0.791265\pi\)
\(558\) 54.1575 202.118i 0.0970564 0.362219i
\(559\) 380.649i 0.680946i
\(560\) −8.57710 29.1636i −0.0153162 0.0520779i
\(561\) 21.7447 0.0387606
\(562\) −146.680 39.3028i −0.260997 0.0699338i
\(563\) −178.196 + 47.7474i −0.316511 + 0.0848088i −0.413577 0.910469i \(-0.635721\pi\)
0.0970662 + 0.995278i \(0.469054\pi\)
\(564\) −388.741 224.440i −0.689257 0.397943i
\(565\) −160.795 + 353.120i −0.284594 + 0.624990i
\(566\) −12.4360 −0.0219717
\(567\) −265.498 547.472i −0.468251 0.965559i
\(568\) −739.484 739.484i −1.30191 1.30191i
\(569\) −211.620 + 122.179i −0.371916 + 0.214726i −0.674295 0.738462i \(-0.735552\pi\)
0.302379 + 0.953188i \(0.402219\pi\)
\(570\) 425.707 + 350.707i 0.746854 + 0.615275i
\(571\) −89.0175 + 154.183i −0.155897 + 0.270022i −0.933385 0.358875i \(-0.883160\pi\)
0.777488 + 0.628898i \(0.216494\pi\)
\(572\) 298.088 + 79.8724i 0.521133 + 0.139637i
\(573\) 248.290 + 248.290i 0.433315 + 0.433315i
\(574\) 81.3820 70.4237i 0.141780 0.122689i
\(575\) 132.474 + 271.191i 0.230390 + 0.471637i
\(576\) 180.284 + 312.261i 0.312993 + 0.542120i
\(577\) 131.070 + 489.160i 0.227158 + 0.847765i 0.981528 + 0.191316i \(0.0612756\pi\)
−0.754370 + 0.656449i \(0.772058\pi\)
\(578\) −355.019 + 95.1270i −0.614219 + 0.164580i
\(579\) 388.228 224.144i 0.670515 0.387122i
\(580\) 88.1538 + 14.7242i 0.151989 + 0.0253865i
\(581\) −42.9898 + 8.25612i −0.0739927 + 0.0142102i
\(582\) −293.875 + 293.875i −0.504940 + 0.504940i
\(583\) −15.6349 + 58.3504i −0.0268181 + 0.100086i
\(584\) 528.674 + 305.230i 0.905264 + 0.522655i
\(585\) 86.8082 + 898.655i 0.148390 + 1.53616i
\(586\) 23.9799 + 41.5343i 0.0409213 + 0.0708777i
\(587\) 178.183 178.183i 0.303548 0.303548i −0.538852 0.842400i \(-0.681142\pi\)
0.842400 + 0.538852i \(0.181142\pi\)
\(588\) −56.7800 480.277i −0.0965646 0.816798i
\(589\) 412.107i 0.699671i
\(590\) −55.7615 + 122.457i −0.0945110 + 0.207554i
\(591\) 144.310 249.952i 0.244179 0.422931i
\(592\) −3.12207 11.6517i −0.00527377 0.0196820i
\(593\) 235.528 879.002i 0.397180 1.48230i −0.420854 0.907128i \(-0.638270\pi\)
0.818034 0.575169i \(-0.195064\pi\)
\(594\) 22.6020i 0.0380505i
\(595\) −0.743777 30.6804i −0.00125005 0.0515636i
\(596\) −526.405 −0.883229
\(597\) 836.873 + 224.239i 1.40180 + 0.375610i
\(598\) 324.078 86.8363i 0.541936 0.145211i
\(599\) −3.19934 1.84714i −0.00534113 0.00308371i 0.497327 0.867563i \(-0.334315\pi\)
−0.502668 + 0.864479i \(0.667648\pi\)
\(600\) 829.179 161.703i 1.38196 0.269505i
\(601\) 77.7927 0.129439 0.0647194 0.997904i \(-0.479385\pi\)
0.0647194 + 0.997904i \(0.479385\pi\)
\(602\) 155.499 + 11.2249i 0.258304 + 0.0186459i
\(603\) −422.647 422.647i −0.700907 0.700907i
\(604\) −136.666 + 78.9043i −0.226269 + 0.130636i
\(605\) 271.572 329.649i 0.448880 0.544874i
\(606\) 424.453 735.174i 0.700418 1.21316i
\(607\) −663.561 177.801i −1.09318 0.292917i −0.333197 0.942857i \(-0.608127\pi\)
−0.759985 + 0.649940i \(0.774794\pi\)
\(608\) 462.049 + 462.049i 0.759949 + 0.759949i
\(609\) −207.035 71.8087i −0.339958 0.117912i
\(610\) 156.936 112.013i 0.257271 0.183629i
\(611\) 495.591 + 858.388i 0.811114 + 1.40489i
\(612\) 4.46369 + 16.6587i 0.00729362 + 0.0272202i
\(613\) −255.220 + 68.3861i −0.416346 + 0.111560i −0.460910 0.887447i \(-0.652477\pi\)
0.0445637 + 0.999007i \(0.485810\pi\)
\(614\) 104.111 60.1084i 0.169561 0.0978964i
\(615\) 145.608 + 204.003i 0.236761 + 0.331712i
\(616\) −111.208 + 320.628i −0.180532 + 0.520500i
\(617\) 285.496 285.496i 0.462717 0.462717i −0.436828 0.899545i \(-0.643898\pi\)
0.899545 + 0.436828i \(0.143898\pi\)
\(618\) −170.446 + 636.112i −0.275802 + 1.02931i
\(619\) −296.838 171.380i −0.479545 0.276866i 0.240682 0.970604i \(-0.422629\pi\)
−0.720227 + 0.693739i \(0.755962\pi\)
\(620\) −181.446 149.479i −0.292655 0.241095i
\(621\) −17.9375 31.0686i −0.0288848 0.0500299i
\(622\) −196.133 + 196.133i −0.315326 + 0.315326i
\(623\) −54.7972 + 759.110i −0.0879570 + 1.21848i
\(624\) 78.6972i 0.126117i
\(625\) 86.2254 619.024i 0.137961 0.990438i
\(626\) −116.410 + 201.628i −0.185959 + 0.322090i
\(627\) −133.552 498.422i −0.213001 0.794931i
\(628\) 59.3409 221.463i 0.0944918 0.352648i
\(629\) 12.1781i 0.0193610i
\(630\) −369.669 + 8.96181i −0.586776 + 0.0142251i
\(631\) 651.848 1.03304 0.516520 0.856275i \(-0.327227\pi\)
0.516520 + 0.856275i \(0.327227\pi\)
\(632\) −134.693 36.0909i −0.213122 0.0571059i
\(633\) 1193.94 319.914i 1.88615 0.505394i
\(634\) 547.556 + 316.132i 0.863653 + 0.498630i
\(635\) −768.233 349.820i −1.20982 0.550898i
\(636\) −99.9574 −0.157166
\(637\) −421.676 + 981.119i −0.661972 + 1.54022i
\(638\) 40.4968 + 40.4968i 0.0634746 + 0.0634746i
\(639\) −923.219 + 533.021i −1.44479 + 0.834149i
\(640\) 348.981 33.7109i 0.545283 0.0526733i
\(641\) 222.071 384.639i 0.346445 0.600061i −0.639170 0.769065i \(-0.720722\pi\)
0.985615 + 0.169005i \(0.0540553\pi\)
\(642\) −691.107 185.182i −1.07649 0.288445i
\(643\) −251.202 251.202i −0.390672 0.390672i 0.484255 0.874927i \(-0.339091\pi\)
−0.874927 + 0.484255i \(0.839091\pi\)
\(644\) −37.8374 197.020i −0.0587537 0.305932i
\(645\) −59.8155 + 358.116i −0.0927371 + 0.555219i
\(646\) −11.6326 20.1482i −0.0180071 0.0311892i
\(647\) 64.2707 + 239.862i 0.0993365 + 0.370729i 0.997641 0.0686441i \(-0.0218673\pi\)
−0.898305 + 0.439373i \(0.855201\pi\)
\(648\) −682.414 + 182.852i −1.05311 + 0.282179i
\(649\) 109.016 62.9401i 0.167975 0.0969802i
\(650\) −657.055 225.792i −1.01085 0.347373i
\(651\) 377.175 + 435.865i 0.579377 + 0.669531i
\(652\) −72.5847 + 72.5847i −0.111326 + 0.111326i
\(653\) −195.601 + 729.993i −0.299542 + 1.11791i 0.638000 + 0.770036i \(0.279762\pi\)
−0.937543 + 0.347870i \(0.886905\pi\)
\(654\) −602.069 347.605i −0.920595 0.531506i
\(655\) −164.456 + 199.625i −0.251077 + 0.304771i
\(656\) −5.23595 9.06892i −0.00798162 0.0138246i
\(657\) 440.021 440.021i 0.669743 0.669743i
\(658\) −365.274 + 177.141i −0.555128 + 0.269211i
\(659\) 587.795i 0.891950i −0.895045 0.445975i \(-0.852857\pi\)
0.895045 0.445975i \(-0.147143\pi\)
\(660\) −267.891 121.986i −0.405896 0.184827i
\(661\) −87.0160 + 150.716i −0.131643 + 0.228012i −0.924310 0.381642i \(-0.875359\pi\)
0.792667 + 0.609655i \(0.208692\pi\)
\(662\) −153.142 571.535i −0.231333 0.863346i
\(663\) 20.5630 76.7423i 0.0310152 0.115750i
\(664\) 50.8285i 0.0765489i
\(665\) −698.673 + 205.481i −1.05064 + 0.308995i
\(666\) −146.734 −0.220322
\(667\) −87.8058 23.5275i −0.131643 0.0352736i
\(668\) −432.728 + 115.949i −0.647796 + 0.173576i
\(669\) 206.954 + 119.485i 0.309348 + 0.178602i
\(670\) 430.786 161.214i 0.642964 0.240619i
\(671\) −180.380 −0.268823
\(672\) −911.571 65.8027i −1.35650 0.0979207i
\(673\) 280.346 + 280.346i 0.416562 + 0.416562i 0.884017 0.467455i \(-0.154829\pi\)
−0.467455 + 0.884017i \(0.654829\pi\)
\(674\) 133.247 76.9301i 0.197696 0.114140i
\(675\) −5.13679 + 74.1114i −0.00761006 + 0.109795i
\(676\) 363.180 629.046i 0.537249 0.930542i
\(677\) −334.663 89.6728i −0.494333 0.132456i 0.00303575 0.999995i \(-0.499034\pi\)
−0.497369 + 0.867539i \(0.665700\pi\)
\(678\) −290.910 290.910i −0.429070 0.429070i
\(679\) −103.495 538.898i −0.152422 0.793664i
\(680\) −35.1472 5.87056i −0.0516870 0.00863318i
\(681\) −125.836 217.954i −0.184781 0.320050i
\(682\) −38.9895 145.511i −0.0571693 0.213359i
\(683\) −391.865 + 105.000i −0.573741 + 0.153733i −0.534012 0.845477i \(-0.679316\pi\)
−0.0397293 + 0.999210i \(0.512650\pi\)
\(684\) 354.429 204.630i 0.518171 0.299166i
\(685\) 796.068 568.198i 1.16214 0.829486i
\(686\) −388.362 201.191i −0.566125 0.293281i
\(687\) 44.0676 44.0676i 0.0641450 0.0641450i
\(688\) 3.92623 14.6529i 0.00570673 0.0212978i
\(689\) 191.148 + 110.359i 0.277428 + 0.160173i
\(690\) −318.539 + 30.7702i −0.461651 + 0.0445945i
\(691\) 207.562 + 359.508i 0.300380 + 0.520273i 0.976222 0.216773i \(-0.0695533\pi\)
−0.675842 + 0.737046i \(0.736220\pi\)
\(692\) 375.720 375.720i 0.542948 0.542948i
\(693\) 286.361 + 194.091i 0.413219 + 0.280073i
\(694\) 13.5173i 0.0194774i
\(695\) 597.138 223.469i 0.859192 0.321538i
\(696\) −127.221 + 220.353i −0.182788 + 0.316599i
\(697\) −2.73623 10.2118i −0.00392573 0.0146510i
\(698\) −10.5884 + 39.5166i −0.0151697 + 0.0566140i
\(699\) 959.098i 1.37210i
\(700\) −162.951 + 382.150i −0.232788 + 0.545929i
\(701\) −13.0606 −0.0186314 −0.00931568 0.999957i \(-0.502965\pi\)
−0.00931568 + 0.999957i \(0.502965\pi\)
\(702\) 79.7681 + 21.3738i 0.113630 + 0.0304470i
\(703\) −279.140 + 74.7954i −0.397070 + 0.106395i
\(704\) 224.806 + 129.792i 0.319326 + 0.184363i
\(705\) −331.366 885.453i −0.470023 1.25596i
\(706\) 639.684 0.906068
\(707\) 489.089 + 1008.53i 0.691780 + 1.42649i
\(708\) 147.285 + 147.285i 0.208029 + 0.208029i
\(709\) −201.983 + 116.615i −0.284885 + 0.164478i −0.635633 0.771992i \(-0.719261\pi\)
0.350748 + 0.936470i \(0.385927\pi\)
\(710\) −78.8780 816.559i −0.111096 1.15008i
\(711\) −71.0726 + 123.101i −0.0999615 + 0.173138i
\(712\) 853.601 + 228.722i 1.19888 + 0.321238i
\(713\) 169.075 + 169.075i 0.237132 + 0.237132i
\(714\) 30.7436 + 10.6632i 0.0430583 + 0.0149345i
\(715\) 377.606 + 529.042i 0.528120 + 0.739918i
\(716\) 108.196 + 187.401i 0.151112 + 0.261734i
\(717\) 411.951 + 1537.42i 0.574548 + 2.14424i
\(718\) 514.187 137.776i 0.716138 0.191889i
\(719\) 154.548 89.2281i 0.214948 0.124100i −0.388661 0.921381i \(-0.627062\pi\)
0.603609 + 0.797281i \(0.293729\pi\)
\(720\) −5.92759 + 35.4886i −0.00823277 + 0.0492897i
\(721\) −568.985 657.522i −0.789161 0.911958i
\(722\) −64.8781 + 64.8781i −0.0898589 + 0.0898589i
\(723\) 301.944 1126.87i 0.417627 1.55860i
\(724\) 300.860 + 173.701i 0.415552 + 0.239919i
\(725\) 123.584 + 141.992i 0.170461 + 0.195851i
\(726\) 226.433 + 392.194i 0.311892 + 0.540212i
\(727\) 536.560 536.560i 0.738047 0.738047i −0.234153 0.972200i \(-0.575232\pi\)
0.972200 + 0.234153i \(0.0752316\pi\)
\(728\) 1026.41 + 695.685i 1.40990 + 0.955611i
\(729\) 608.980i 0.835363i
\(730\) 167.842 + 448.494i 0.229920 + 0.614376i
\(731\) 7.65740 13.2630i 0.0104752 0.0181436i
\(732\) −77.2502 288.302i −0.105533 0.393855i
\(733\) −68.3024 + 254.908i −0.0931820 + 0.347760i −0.996738 0.0807110i \(-0.974281\pi\)
0.903556 + 0.428471i \(0.140948\pi\)
\(734\) 424.163i 0.577879i
\(735\) 550.888 856.779i 0.749508 1.16569i
\(736\) −379.130 −0.515122
\(737\) −415.648 111.373i −0.563973 0.151116i
\(738\) −123.042 + 32.9690i −0.166724 + 0.0446735i
\(739\) 262.146 + 151.350i 0.354730 + 0.204804i 0.666767 0.745267i \(-0.267678\pi\)
−0.312037 + 0.950070i \(0.601011\pi\)
\(740\) −68.3181 + 150.032i −0.0923218 + 0.202746i
\(741\) −1885.35 −2.54433
\(742\) −50.7195 + 74.8314i −0.0683552 + 0.100851i
\(743\) −767.699 767.699i −1.03324 1.03324i −0.999428 0.0338136i \(-0.989235\pi\)
−0.0338136 0.999428i \(-0.510765\pi\)
\(744\) 579.607 334.636i 0.779041 0.449780i
\(745\) −855.723 704.964i −1.14862 0.946260i
\(746\) −268.307 + 464.721i −0.359660 + 0.622950i
\(747\) 50.0474 + 13.4102i 0.0669979 + 0.0179520i
\(748\) 8.77955 + 8.77955i 0.0117374 + 0.0117374i
\(749\) 714.368 618.177i 0.953762 0.825336i
\(750\) 582.679 + 315.676i 0.776905 + 0.420902i
\(751\) −519.734 900.206i −0.692056 1.19868i −0.971163 0.238416i \(-0.923372\pi\)
0.279107 0.960260i \(-0.409962\pi\)
\(752\) 10.2236 + 38.1550i 0.0135952 + 0.0507380i
\(753\) 82.3130 22.0557i 0.109313 0.0292904i
\(754\) 181.219 104.627i 0.240344 0.138763i
\(755\) −327.834 54.7574i −0.434217 0.0725263i
\(756\) 16.1816 46.6539i 0.0214043 0.0617116i
\(757\) 612.294 612.294i 0.808843 0.808843i −0.175616 0.984459i \(-0.556192\pi\)
0.984459 + 0.175616i \(0.0561916\pi\)
\(758\) 169.564 632.822i 0.223699 0.834857i
\(759\) 259.280 + 149.695i 0.341607 + 0.197227i
\(760\) 81.3049 + 841.683i 0.106980 + 1.10748i
\(761\) 340.196 + 589.237i 0.447038 + 0.774293i 0.998192 0.0601112i \(-0.0191455\pi\)
−0.551154 + 0.834404i \(0.685812\pi\)
\(762\) 632.891 632.891i 0.830566 0.830566i
\(763\) 825.932 400.538i 1.08248 0.524952i
\(764\) 200.497i 0.262430i
\(765\) −15.0533 + 33.0582i −0.0196775 + 0.0432134i
\(766\) 92.5672 160.331i 0.120845 0.209310i
\(767\) −119.040 444.263i −0.155202 0.579221i
\(768\) −283.533 + 1058.16i −0.369183 + 1.37781i
\(769\) 1288.89i 1.67606i 0.545627 + 0.838028i \(0.316292\pi\)
−0.545627 + 0.838028i \(0.683708\pi\)
\(770\) −227.254 + 138.655i −0.295135 + 0.180071i
\(771\) −1547.19 −2.00674
\(772\) 247.249 + 66.2502i 0.320271 + 0.0858163i
\(773\) −303.870 + 81.4217i −0.393105 + 0.105332i −0.449956 0.893051i \(-0.648560\pi\)
0.0568517 + 0.998383i \(0.481894\pi\)
\(774\) −159.807 92.2644i −0.206468 0.119205i
\(775\) −94.7749 485.986i −0.122290 0.627079i
\(776\) −637.160 −0.821083
\(777\) 226.778 334.587i 0.291863 0.430614i
\(778\) 371.259 + 371.259i 0.477196 + 0.477196i
\(779\) −217.264 + 125.437i −0.278901 + 0.161024i
\(780\) −683.853 + 830.097i −0.876735 + 1.06423i
\(781\) −383.737 + 664.651i −0.491340 + 0.851026i
\(782\) 13.0387 + 3.49372i 0.0166736 + 0.00446767i
\(783\) −15.8214 15.8214i −0.0202061 0.0202061i
\(784\) −26.3520 + 33.4182i −0.0336122 + 0.0426253i
\(785\) 393.049 280.541i 0.500699 0.357377i
\(786\) −137.121 237.500i −0.174454 0.302163i
\(787\) −358.940 1339.58i −0.456086 1.70214i −0.684875 0.728660i \(-0.740143\pi\)
0.228789 0.973476i \(-0.426523\pi\)
\(788\) 159.186 42.6537i 0.202012 0.0541290i
\(789\) −1218.98 + 703.776i −1.54496 + 0.891985i
\(790\) −63.5482 89.0336i −0.0804407 0.112701i
\(791\) 533.460 102.450i 0.674412 0.129520i
\(792\) 284.028 284.028i 0.358622 0.358622i
\(793\) −170.578 + 636.606i −0.215105 + 0.802782i
\(794\) −160.523 92.6781i −0.202170 0.116723i
\(795\) −162.491 133.864i −0.204391 0.168382i
\(796\) 247.354 + 428.431i 0.310747 + 0.538229i
\(797\) −905.526 + 905.526i −1.13617 + 1.13617i −0.147038 + 0.989131i \(0.546974\pi\)
−0.989131 + 0.147038i \(0.953026\pi\)
\(798\) 55.5965 770.183i 0.0696699 0.965142i
\(799\) 39.8786i 0.0499106i
\(800\) 651.143 + 438.622i 0.813929 + 0.548277i
\(801\) 450.414 780.140i 0.562314 0.973957i
\(802\) −17.4967 65.2987i −0.0218164 0.0814198i
\(803\) 115.951 432.734i 0.144397 0.538897i
\(804\) 712.028i 0.885606i
\(805\) 202.342 370.948i 0.251356 0.460805i
\(806\) −550.414 −0.682895
\(807\) 349.018 + 93.5190i 0.432488 + 0.115885i
\(808\) 1257.11 336.842i 1.55583 0.416884i
\(809\) −313.879 181.218i −0.387983 0.224002i 0.293303 0.956020i \(-0.405246\pi\)
−0.681286 + 0.732017i \(0.738579\pi\)
\(810\) −504.369 229.668i −0.622678 0.283541i
\(811\) 668.488 0.824276 0.412138 0.911121i \(-0.364782\pi\)
0.412138 + 0.911121i \(0.364782\pi\)
\(812\) −54.5983 112.585i −0.0672392 0.138651i
\(813\) 584.976 + 584.976i 0.719528 + 0.719528i
\(814\) −91.4852 + 52.8190i −0.112390 + 0.0648882i
\(815\) −215.199 + 20.7878i −0.264048 + 0.0255065i
\(816\) 1.58313 2.74206i 0.00194011 0.00336036i
\(817\) −351.039 94.0606i −0.429668 0.115129i
\(818\) 262.206 + 262.206i 0.320546 + 0.320546i
\(819\) 955.794 827.094i 1.16703 1.00988i
\(820\) −23.5773 + 141.158i −0.0287528 + 0.172143i
\(821\) 360.015 + 623.564i 0.438508 + 0.759518i 0.997575 0.0696047i \(-0.0221738\pi\)
−0.559067 + 0.829123i \(0.688840\pi\)
\(822\) 268.405 + 1001.70i 0.326526 + 1.21861i
\(823\) −706.861 + 189.403i −0.858884 + 0.230137i −0.661275 0.750144i \(-0.729984\pi\)
−0.197609 + 0.980281i \(0.563318\pi\)
\(824\) −874.362 + 504.813i −1.06112 + 0.612637i
\(825\) −272.120 557.062i −0.329842 0.675227i
\(826\) 184.996 35.5282i 0.223966 0.0430123i
\(827\) −709.579 + 709.579i −0.858016 + 0.858016i −0.991104 0.133088i \(-0.957511\pi\)
0.133088 + 0.991104i \(0.457511\pi\)
\(828\) −61.4582 + 229.365i −0.0742249 + 0.277011i
\(829\) −1403.34 810.220i −1.69281 0.977346i −0.952231 0.305379i \(-0.901217\pi\)
−0.740582 0.671966i \(-0.765450\pi\)
\(830\) −25.3523 + 30.7740i −0.0305450 + 0.0370771i
\(831\) 775.200 + 1342.69i 0.932852 + 1.61575i
\(832\) 670.656 670.656i 0.806077 0.806077i
\(833\) −34.4294 + 25.7025i −0.0413318 + 0.0308554i
\(834\) 676.039i 0.810598i
\(835\) −858.721 391.024i −1.02841 0.468293i
\(836\) 147.319 255.163i 0.176218 0.305219i
\(837\) 15.2325 + 56.8484i 0.0181989 + 0.0679193i
\(838\) −95.7992 + 357.527i −0.114319 + 0.426644i
\(839\) 451.819i 0.538521i −0.963067 0.269260i \(-0.913221\pi\)
0.963067 0.269260i \(-0.0867793\pi\)
\(840\) −856.331 815.794i −1.01944 0.971184i
\(841\) 784.305 0.932586
\(842\) −315.937 84.6551i −0.375222 0.100540i
\(843\) −478.236 + 128.143i −0.567303 + 0.152008i
\(844\) 611.226 + 352.892i 0.724202 + 0.418118i
\(845\) 1432.81 536.205i 1.69563 0.634562i
\(846\) 480.499 0.567966
\(847\) −596.397 43.0516i −0.704129 0.0508283i
\(848\) 6.21982 + 6.21982i 0.00733470 + 0.00733470i
\(849\) −35.1142 + 20.2732i −0.0413595 + 0.0238789i
\(850\) −18.3516 21.0851i −0.0215902 0.0248060i
\(851\) 83.8366 145.209i 0.0985154 0.170634i
\(852\) −1226.65 328.681i −1.43973 0.385776i
\(853\) −466.163 466.163i −0.546499 0.546499i 0.378928 0.925426i \(-0.376293\pi\)
−0.925426 + 0.378928i \(0.876293\pi\)
\(854\) −255.030 88.4555i −0.298630 0.103578i
\(855\) 850.200 + 142.007i 0.994386 + 0.166090i
\(856\) −548.457 949.955i −0.640721 1.10976i
\(857\) 40.3902 + 150.738i 0.0471298 + 0.175891i 0.985479 0.169799i \(-0.0543118\pi\)
−0.938349 + 0.345689i \(0.887645\pi\)
\(858\) −665.697 + 178.373i −0.775871 + 0.207894i
\(859\) −14.0348 + 8.10300i −0.0163386 + 0.00943307i −0.508147 0.861270i \(-0.669669\pi\)
0.491808 + 0.870703i \(0.336336\pi\)
\(860\) −168.743 + 120.441i −0.196212 + 0.140047i
\(861\) 114.985 331.517i 0.133548 0.385037i
\(862\) 262.993 262.993i 0.305096 0.305096i
\(863\) 422.849 1578.10i 0.489976 1.82862i −0.0665465 0.997783i \(-0.521198\pi\)
0.556523 0.830832i \(-0.312135\pi\)
\(864\) −80.8163 46.6593i −0.0935374 0.0540038i
\(865\) 1113.94 107.604i 1.28779 0.124398i
\(866\) 110.337 + 191.109i 0.127409 + 0.220680i
\(867\) −847.352 + 847.352i −0.977338 + 0.977338i
\(868\) −23.6965 + 328.270i −0.0273001 + 0.378191i
\(869\) 102.334i 0.117761i
\(870\) −186.933 + 69.9567i −0.214866 + 0.0804100i
\(871\) −786.122 + 1361.60i −0.902552 + 1.56327i
\(872\) −275.856 1029.51i −0.316349 1.18063i
\(873\) −168.103 + 627.369i −0.192558 + 0.718636i
\(874\) 320.326i 0.366506i
\(875\) −776.671 + 402.998i −0.887624 + 0.460569i
\(876\) 741.297 0.846230
\(877\) 662.129 + 177.417i 0.754993 + 0.202300i 0.615732 0.787956i \(-0.288861\pi\)
0.139261 + 0.990256i \(0.455527\pi\)
\(878\) −1070.55 + 286.852i −1.21930 + 0.326711i
\(879\) 135.419 + 78.1840i 0.154060 + 0.0889466i
\(880\) 9.07891 + 24.2600i 0.0103169 + 0.0275682i
\(881\) −974.437 −1.10606 −0.553029 0.833162i \(-0.686528\pi\)
−0.553029 + 0.833162i \(0.686528\pi\)
\(882\) 309.691 + 414.841i 0.351124 + 0.470342i
\(883\) 191.886 + 191.886i 0.217311 + 0.217311i 0.807365 0.590053i \(-0.200893\pi\)
−0.590053 + 0.807365i \(0.700893\pi\)
\(884\) 39.2876 22.6827i 0.0444430 0.0256592i
\(885\) 42.1815 + 436.670i 0.0476627 + 0.493413i
\(886\) −84.9683 + 147.169i −0.0959010 + 0.166105i
\(887\) −948.556 254.165i −1.06940 0.286544i −0.319152 0.947703i \(-0.603398\pi\)
−0.750246 + 0.661159i \(0.770065\pi\)
\(888\) −331.862 331.862i −0.373718 0.373718i
\(889\) 222.886 + 1160.57i 0.250716 + 1.30548i
\(890\) 402.729 + 564.239i 0.452504 + 0.633977i
\(891\) 259.235 + 449.008i 0.290949 + 0.503938i
\(892\) 35.3161 + 131.801i 0.0395920 + 0.147759i
\(893\) 914.079 244.927i 1.02360 0.274274i
\(894\) 1018.08 587.790i 1.13879 0.657483i
\(895\) −75.0852 + 449.536i −0.0838940 + 0.502275i
\(896\) −321.192 371.171i −0.358473 0.414253i
\(897\) 773.502 773.502i 0.862321 0.862321i
\(898\) 250.211 933.799i 0.278631 1.03987i
\(899\) 129.150 + 74.5647i 0.143659 + 0.0829418i
\(900\) 370.909 322.825i 0.412121 0.358694i
\(901\) 4.44012 + 7.69052i 0.00492799 + 0.00853554i
\(902\) −64.8461 + 64.8461i −0.0718915 + 0.0718915i
\(903\) 457.364 221.800i 0.506494 0.245626i
\(904\) 630.730i 0.697711i
\(905\) 256.456 + 685.282i 0.283376 + 0.757218i
\(906\) 176.211 305.206i 0.194493 0.336872i
\(907\) 231.530 + 864.080i 0.255270 + 0.952680i 0.967940 + 0.251181i \(0.0808188\pi\)
−0.712670 + 0.701499i \(0.752515\pi\)
\(908\) 37.1932 138.807i 0.0409617 0.152871i
\(909\) 1326.67i 1.45948i
\(910\) 274.443 + 933.155i 0.301586 + 1.02545i
\(911\) 670.054 0.735515 0.367757 0.929922i \(-0.380126\pi\)
0.367757 + 0.929922i \(0.380126\pi\)
\(912\) −72.5755 19.4465i −0.0795784 0.0213230i
\(913\) 36.0305 9.65436i 0.0394639 0.0105743i
\(914\) 806.634 + 465.710i 0.882532 + 0.509530i
\(915\) 260.517 572.117i 0.284718 0.625265i
\(916\) 35.5851 0.0388484
\(917\) 361.159 + 26.0707i 0.393849 + 0.0284304i
\(918\) 2.34940 + 2.34940i 0.00255926 + 0.00255926i
\(919\) −224.983 + 129.894i −0.244813 + 0.141343i −0.617387 0.786660i \(-0.711809\pi\)
0.372574 + 0.928003i \(0.378475\pi\)
\(920\) −378.675 311.961i −0.411603 0.339088i
\(921\) 195.978 339.443i 0.212788 0.368559i
\(922\) −865.872 232.010i −0.939123 0.251637i
\(923\) 1982.83 + 1982.83i 2.14825 + 2.14825i
\(924\) 77.7229 + 404.705i 0.0841157 + 0.437992i
\(925\) −311.982 + 152.400i −0.337277 + 0.164757i
\(926\) −557.602 965.795i −0.602162 1.04298i
\(927\) 266.372 + 994.112i 0.287348 + 1.07240i
\(928\) −228.402 + 61.2003i −0.246123 + 0.0659486i
\(929\) 1154.31 666.442i 1.24253 0.717376i 0.272922 0.962036i \(-0.412010\pi\)
0.969609 + 0.244660i \(0.0786764\pi\)
\(930\) 517.832 + 86.4924i 0.556808 + 0.0930026i
\(931\) 800.600 + 631.315i 0.859936 + 0.678104i
\(932\) −387.242 + 387.242i −0.415495 + 0.415495i
\(933\) −234.063 + 873.534i −0.250871 + 0.936264i
\(934\) 138.274 + 79.8328i 0.148045 + 0.0854741i
\(935\) 2.51441 + 26.0296i 0.00268921 + 0.0278392i
\(936\) −733.812 1271.00i −0.783988 1.35791i
\(937\) 343.232 343.232i 0.366310 0.366310i −0.499820 0.866129i \(-0.666600\pi\)
0.866129 + 0.499820i \(0.166600\pi\)
\(938\) −533.047 361.291i −0.568280 0.385171i
\(939\) 759.087i 0.808400i
\(940\) 223.716 491.298i 0.237996 0.522658i
\(941\) 556.358 963.640i 0.591241 1.02406i −0.402824 0.915277i \(-0.631971\pi\)
0.994066 0.108783i \(-0.0346952\pi\)
\(942\) 132.521 + 494.577i 0.140681 + 0.525029i
\(943\) 37.6737 140.600i 0.0399509 0.149099i
\(944\) 18.3295i 0.0194168i
\(945\) 88.7841 54.1701i 0.0939514 0.0573228i
\(946\) −132.847 −0.140431
\(947\) 1636.49 + 438.497i 1.72808 + 0.463038i 0.979739 0.200277i \(-0.0641841\pi\)
0.748341 + 0.663314i \(0.230851\pi\)
\(948\) −163.561 + 43.8261i −0.172533 + 0.0462300i
\(949\) −1417.58 818.438i −1.49376 0.862421i
\(950\) −370.590 + 550.149i −0.390095 + 0.579104i
\(951\) 2061.43 2.16765
\(952\) 21.7685 + 44.8878i 0.0228660 + 0.0471511i
\(953\) −892.480 892.480i −0.936495 0.936495i 0.0616058 0.998101i \(-0.480378\pi\)
−0.998101 + 0.0616058i \(0.980378\pi\)
\(954\) 92.6634 53.4993i 0.0971315 0.0560789i
\(955\) −268.506 + 325.928i −0.281159 + 0.341285i
\(956\) −454.416 + 787.071i −0.475330 + 0.823296i
\(957\) 180.364 + 48.3285i 0.188469 + 0.0505000i
\(958\) −671.140 671.140i −0.700563 0.700563i
\(959\) −1293.66 448.698i −1.34897 0.467881i
\(960\) −736.344 + 525.569i −0.767025 + 0.547468i
\(961\) 284.368 + 492.540i 0.295908 + 0.512528i
\(962\) 99.8975 + 372.823i 0.103844 + 0.387550i
\(963\) −1080.06 + 289.401i −1.12156 + 0.300520i
\(964\) 576.893 333.069i 0.598437 0.345508i
\(965\) 313.205 + 438.813i 0.324565 + 0.454729i
\(966\) 293.174 + 338.793i 0.303492 + 0.350717i
\(967\) 456.890 456.890i 0.472482 0.472482i −0.430235 0.902717i \(-0.641569\pi\)
0.902717 + 0.430235i \(0.141569\pi\)
\(968\) −179.696 + 670.634i −0.185636 + 0.692803i
\(969\) −65.6914 37.9270i −0.0677930 0.0391403i
\(970\) −385.767 317.804i −0.397698 0.327633i
\(971\) −659.395 1142.11i −0.679089 1.17622i −0.975256 0.221080i \(-0.929042\pi\)
0.296167 0.955136i \(-0.404291\pi\)
\(972\) −561.736 + 561.736i −0.577918 + 0.577918i
\(973\) −738.889 500.807i −0.759393 0.514704i
\(974\) 854.182i 0.876984i
\(975\) −2223.34 + 433.586i −2.28035 + 0.444704i
\(976\) −13.1326 + 22.7464i −0.0134556 + 0.0233057i
\(977\) −178.032 664.423i −0.182223 0.680065i −0.995208 0.0977804i \(-0.968826\pi\)
0.812985 0.582284i \(-0.197841\pi\)
\(978\) 59.3320 221.430i 0.0606666 0.226411i
\(979\) 648.531i 0.662442i
\(980\) 568.354 123.505i 0.579953 0.126026i
\(981\) −1086.47 −1.10751
\(982\) 75.7546 + 20.2984i 0.0771432 + 0.0206704i
\(983\) 385.752 103.362i 0.392423 0.105149i −0.0572115 0.998362i \(-0.518221\pi\)
0.449634 + 0.893213i \(0.351554\pi\)
\(984\) −352.843 203.714i −0.358580 0.207026i
\(985\) 315.894 + 143.844i 0.320705 + 0.146035i
\(986\) 8.41900 0.00853854
\(987\) −742.611 + 1095.64i −0.752392 + 1.11008i
\(988\) −761.221 761.221i −0.770466 0.770466i
\(989\) 182.611 105.431i 0.184642 0.106603i
\(990\) 313.633 30.2963i 0.316801 0.0306023i
\(991\) 352.050 609.769i 0.355248 0.615307i −0.631913 0.775040i \(-0.717730\pi\)
0.987160 + 0.159733i \(0.0510632\pi\)
\(992\) 600.781 + 160.979i 0.605626 + 0.162277i
\(993\) −1364.13 1364.13i −1.37375 1.37375i
\(994\) −868.479 + 751.536i −0.873721 + 0.756073i
\(995\) −171.657 + 1027.71i −0.172520 + 1.03288i
\(996\) 30.8611 + 53.4531i 0.0309851 + 0.0536677i
\(997\) −190.370 710.472i −0.190943 0.712610i −0.993280 0.115738i \(-0.963077\pi\)
0.802336 0.596872i \(-0.203590\pi\)
\(998\) 59.5483 15.9559i 0.0596676 0.0159879i
\(999\) 35.7417 20.6355i 0.0357774 0.0206561i
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 35.3.l.a.18.3 yes 24
3.2 odd 2 315.3.ca.a.298.4 24
5.2 odd 4 inner 35.3.l.a.32.4 yes 24
5.3 odd 4 175.3.p.c.32.3 24
5.4 even 2 175.3.p.c.18.4 24
7.2 even 3 inner 35.3.l.a.23.4 yes 24
7.3 odd 6 245.3.g.b.148.4 12
7.4 even 3 245.3.g.c.148.4 12
7.5 odd 6 245.3.m.b.128.4 24
7.6 odd 2 245.3.m.b.18.3 24
15.2 even 4 315.3.ca.a.172.3 24
21.2 odd 6 315.3.ca.a.163.3 24
35.2 odd 12 inner 35.3.l.a.2.3 24
35.9 even 6 175.3.p.c.93.3 24
35.12 even 12 245.3.m.b.177.3 24
35.17 even 12 245.3.g.b.197.4 12
35.23 odd 12 175.3.p.c.107.4 24
35.27 even 4 245.3.m.b.67.4 24
35.32 odd 12 245.3.g.c.197.4 12
105.2 even 12 315.3.ca.a.37.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.3.l.a.2.3 24 35.2 odd 12 inner
35.3.l.a.18.3 yes 24 1.1 even 1 trivial
35.3.l.a.23.4 yes 24 7.2 even 3 inner
35.3.l.a.32.4 yes 24 5.2 odd 4 inner
175.3.p.c.18.4 24 5.4 even 2
175.3.p.c.32.3 24 5.3 odd 4
175.3.p.c.93.3 24 35.9 even 6
175.3.p.c.107.4 24 35.23 odd 12
245.3.g.b.148.4 12 7.3 odd 6
245.3.g.b.197.4 12 35.17 even 12
245.3.g.c.148.4 12 7.4 even 3
245.3.g.c.197.4 12 35.32 odd 12
245.3.m.b.18.3 24 7.6 odd 2
245.3.m.b.67.4 24 35.27 even 4
245.3.m.b.128.4 24 7.5 odd 6
245.3.m.b.177.3 24 35.12 even 12
315.3.ca.a.37.4 24 105.2 even 12
315.3.ca.a.163.3 24 21.2 odd 6
315.3.ca.a.172.3 24 15.2 even 4
315.3.ca.a.298.4 24 3.2 odd 2