Properties

Label 96.3.p.a.5.11
Level $96$
Weight $3$
Character 96.5
Analytic conductor $2.616$
Analytic rank $0$
Dimension $120$
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] = [96,3,Mod(5,96)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(96, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("96.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 96.p (of order \(8\), 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: \(2.61581053786\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(30\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 5.11
Character \(\chi\) \(=\) 96.5
Dual form 96.3.p.a.77.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.896196 - 1.78797i) q^{2} +(2.31396 + 1.90935i) q^{3} +(-2.39366 + 3.20474i) q^{4} +(-0.794982 + 1.91926i) q^{5} +(1.34009 - 5.84843i) q^{6} +(4.69711 + 4.69711i) q^{7} +(7.87517 + 1.40772i) q^{8} +(1.70880 + 8.83629i) q^{9} +O(q^{10})\) \(q+(-0.896196 - 1.78797i) q^{2} +(2.31396 + 1.90935i) q^{3} +(-2.39366 + 3.20474i) q^{4} +(-0.794982 + 1.91926i) q^{5} +(1.34009 - 5.84843i) q^{6} +(4.69711 + 4.69711i) q^{7} +(7.87517 + 1.40772i) q^{8} +(1.70880 + 8.83629i) q^{9} +(4.14403 - 0.298628i) q^{10} +(0.393643 + 0.163052i) q^{11} +(-11.6578 + 2.84530i) q^{12} +(2.31489 - 0.958858i) q^{13} +(4.18875 - 12.6078i) q^{14} +(-5.50408 + 2.92318i) q^{15} +(-4.54074 - 15.3422i) q^{16} +0.432707 q^{17} +(14.2676 - 10.9743i) q^{18} +(23.6610 - 9.80070i) q^{19} +(-4.24780 - 7.14177i) q^{20} +(1.90050 + 19.8373i) q^{21} +(-0.0612491 - 0.849949i) q^{22} +(-31.0794 - 31.0794i) q^{23} +(15.5350 + 18.2938i) q^{24} +(14.6261 + 14.6261i) q^{25} +(-3.78900 - 3.27962i) q^{26} +(-12.9175 + 23.7095i) q^{27} +(-26.2963 + 3.80972i) q^{28} +(-5.18802 + 2.14895i) q^{29} +(10.1593 + 7.22138i) q^{30} -40.7959 q^{31} +(-23.3619 + 21.8683i) q^{32} +(0.599550 + 1.12890i) q^{33} +(-0.387790 - 0.773667i) q^{34} +(-12.7491 + 5.28084i) q^{35} +(-32.4083 - 15.6749i) q^{36} +(-5.92626 - 2.45474i) q^{37} +(-38.7282 - 33.5217i) q^{38} +(7.18734 + 2.20117i) q^{39} +(-8.96240 + 13.9954i) q^{40} +(25.7408 + 25.7408i) q^{41} +(33.7653 - 21.1762i) q^{42} +(29.2668 - 70.6562i) q^{43} +(-1.46479 + 0.871232i) q^{44} +(-18.3176 - 3.74507i) q^{45} +(-27.7157 + 83.4222i) q^{46} -32.4483 q^{47} +(18.7864 - 44.1709i) q^{48} -4.87427i q^{49} +(13.0432 - 39.2589i) q^{50} +(1.00127 + 0.826187i) q^{51} +(-2.46817 + 9.71380i) q^{52} +(69.1389 + 28.6383i) q^{53} +(53.9684 + 1.84765i) q^{54} +(-0.625879 + 0.625879i) q^{55} +(30.3784 + 43.6028i) q^{56} +(73.4634 + 22.4986i) q^{57} +(8.49173 + 7.35013i) q^{58} +(21.9238 - 52.9288i) q^{59} +(3.80688 - 24.6363i) q^{60} +(-32.9968 - 79.6614i) q^{61} +(36.5611 + 72.9417i) q^{62} +(-33.4786 + 49.5315i) q^{63} +(60.0367 + 22.1721i) q^{64} +5.20514i q^{65} +(1.48112 - 2.08369i) q^{66} +(-19.1610 - 46.2587i) q^{67} +(-1.03576 + 1.38671i) q^{68} +(-12.5751 - 131.258i) q^{69} +(20.8677 + 18.0623i) q^{70} +(65.8420 - 65.8420i) q^{71} +(1.01805 + 71.9928i) q^{72} +(-16.0821 + 16.0821i) q^{73} +(0.922099 + 12.7959i) q^{74} +(5.91789 + 61.7705i) q^{75} +(-25.2277 + 99.2869i) q^{76} +(1.08311 + 2.61486i) q^{77} +(-2.50566 - 14.8234i) q^{78} +45.6365i q^{79} +(33.0553 + 3.48189i) q^{80} +(-75.1600 + 30.1988i) q^{81} +(22.9549 - 69.0925i) q^{82} +(-14.7260 - 35.5516i) q^{83} +(-68.1227 - 41.3933i) q^{84} +(-0.343994 + 0.830476i) q^{85} +(-152.560 + 10.9938i) q^{86} +(-16.1079 - 4.93315i) q^{87} +(2.87048 + 1.83820i) q^{88} +(-104.157 + 104.157i) q^{89} +(9.72007 + 36.1076i) q^{90} +(15.3772 + 6.36942i) q^{91} +(173.995 - 25.2078i) q^{92} +(-94.3999 - 77.8934i) q^{93} +(29.0800 + 58.0165i) q^{94} +53.2029i q^{95} +(-95.8125 + 5.99635i) q^{96} +67.7334 q^{97} +(-8.71505 + 4.36831i) q^{98} +(-0.768122 + 3.75697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 32 q^{10} - 4 q^{12} - 8 q^{13} - 40 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 120 q^{22} - 144 q^{24} - 8 q^{25} + 92 q^{27} - 8 q^{28} - 60 q^{30} - 16 q^{31} - 8 q^{33} - 40 q^{34} + 64 q^{36} - 8 q^{37} - 196 q^{39} - 232 q^{40} + 16 q^{42} - 8 q^{43} - 4 q^{45} - 40 q^{46} + 48 q^{48} - 40 q^{51} - 112 q^{52} + 304 q^{54} - 264 q^{55} - 4 q^{57} - 16 q^{58} + 424 q^{60} + 56 q^{61} - 8 q^{63} + 40 q^{64} + 428 q^{66} + 248 q^{67} - 4 q^{69} + 328 q^{70} + 416 q^{72} - 8 q^{73} - 104 q^{75} + 720 q^{76} + 276 q^{78} + 512 q^{82} + 232 q^{84} - 208 q^{85} - 452 q^{87} + 272 q^{88} - 304 q^{90} - 200 q^{91} - 40 q^{93} + 416 q^{94} - 616 q^{96} - 16 q^{97} + 252 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/96\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(65\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.896196 1.78797i −0.448098 0.893984i
\(3\) 2.31396 + 1.90935i 0.771319 + 0.636449i
\(4\) −2.39366 + 3.20474i −0.598416 + 0.801186i
\(5\) −0.794982 + 1.91926i −0.158996 + 0.383851i −0.983223 0.182409i \(-0.941610\pi\)
0.824226 + 0.566261i \(0.191610\pi\)
\(6\) 1.34009 5.84843i 0.223348 0.974739i
\(7\) 4.69711 + 4.69711i 0.671016 + 0.671016i 0.957950 0.286934i \(-0.0926361\pi\)
−0.286934 + 0.957950i \(0.592636\pi\)
\(8\) 7.87517 + 1.40772i 0.984396 + 0.175965i
\(9\) 1.70880 + 8.83629i 0.189866 + 0.981810i
\(10\) 4.14403 0.298628i 0.414403 0.0298628i
\(11\) 0.393643 + 0.163052i 0.0357857 + 0.0148229i 0.400505 0.916295i \(-0.368835\pi\)
−0.364719 + 0.931118i \(0.618835\pi\)
\(12\) −11.6578 + 2.84530i −0.971483 + 0.237109i
\(13\) 2.31489 0.958858i 0.178068 0.0737583i −0.291868 0.956459i \(-0.594277\pi\)
0.469936 + 0.882700i \(0.344277\pi\)
\(14\) 4.18875 12.6078i 0.299197 0.900559i
\(15\) −5.50408 + 2.92318i −0.366939 + 0.194879i
\(16\) −4.54074 15.3422i −0.283796 0.958885i
\(17\) 0.432707 0.0254534 0.0127267 0.999919i \(-0.495949\pi\)
0.0127267 + 0.999919i \(0.495949\pi\)
\(18\) 14.2676 10.9743i 0.792644 0.609685i
\(19\) 23.6610 9.80070i 1.24531 0.515826i 0.339943 0.940446i \(-0.389592\pi\)
0.905372 + 0.424620i \(0.139592\pi\)
\(20\) −4.24780 7.14177i −0.212390 0.357089i
\(21\) 1.90050 + 19.8373i 0.0905002 + 0.944635i
\(22\) −0.0612491 0.849949i −0.00278405 0.0386340i
\(23\) −31.0794 31.0794i −1.35128 1.35128i −0.884235 0.467042i \(-0.845320\pi\)
−0.467042 0.884235i \(-0.654680\pi\)
\(24\) 15.5350 + 18.2938i 0.647291 + 0.762243i
\(25\) 14.6261 + 14.6261i 0.585045 + 0.585045i
\(26\) −3.78900 3.27962i −0.145731 0.126139i
\(27\) −12.9175 + 23.7095i −0.478424 + 0.878129i
\(28\) −26.2963 + 3.80972i −0.939155 + 0.136062i
\(29\) −5.18802 + 2.14895i −0.178897 + 0.0741016i −0.470334 0.882488i \(-0.655867\pi\)
0.291437 + 0.956590i \(0.405867\pi\)
\(30\) 10.1593 + 7.22138i 0.338643 + 0.240713i
\(31\) −40.7959 −1.31600 −0.657998 0.753020i \(-0.728596\pi\)
−0.657998 + 0.753020i \(0.728596\pi\)
\(32\) −23.3619 + 21.8683i −0.730059 + 0.683384i
\(33\) 0.599550 + 1.12890i 0.0181682 + 0.0342090i
\(34\) −0.387790 0.773667i −0.0114056 0.0227549i
\(35\) −12.7491 + 5.28084i −0.364260 + 0.150881i
\(36\) −32.4083 15.6749i −0.900231 0.435413i
\(37\) −5.92626 2.45474i −0.160169 0.0663442i 0.301158 0.953574i \(-0.402627\pi\)
−0.461328 + 0.887230i \(0.652627\pi\)
\(38\) −38.7282 33.5217i −1.01916 0.882151i
\(39\) 7.18734 + 2.20117i 0.184291 + 0.0564401i
\(40\) −8.96240 + 13.9954i −0.224060 + 0.349884i
\(41\) 25.7408 + 25.7408i 0.627824 + 0.627824i 0.947520 0.319696i \(-0.103581\pi\)
−0.319696 + 0.947520i \(0.603581\pi\)
\(42\) 33.7653 21.1762i 0.803936 0.504195i
\(43\) 29.2668 70.6562i 0.680623 1.64317i −0.0822441 0.996612i \(-0.526209\pi\)
0.762867 0.646556i \(-0.223791\pi\)
\(44\) −1.46479 + 0.871232i −0.0332907 + 0.0198007i
\(45\) −18.3176 3.74507i −0.407057 0.0832239i
\(46\) −27.7157 + 83.4222i −0.602516 + 1.81353i
\(47\) −32.4483 −0.690389 −0.345194 0.938531i \(-0.612187\pi\)
−0.345194 + 0.938531i \(0.612187\pi\)
\(48\) 18.7864 44.1709i 0.391383 0.920228i
\(49\) 4.87427i 0.0994750i
\(50\) 13.0432 39.2589i 0.260863 0.785178i
\(51\) 1.00127 + 0.826187i 0.0196327 + 0.0161998i
\(52\) −2.46817 + 9.71380i −0.0474648 + 0.186804i
\(53\) 69.1389 + 28.6383i 1.30451 + 0.540344i 0.923277 0.384136i \(-0.125501\pi\)
0.381230 + 0.924480i \(0.375501\pi\)
\(54\) 53.9684 + 1.84765i 0.999414 + 0.0342158i
\(55\) −0.625879 + 0.625879i −0.0113796 + 0.0113796i
\(56\) 30.3784 + 43.6028i 0.542471 + 0.778621i
\(57\) 73.4634 + 22.4986i 1.28883 + 0.394712i
\(58\) 8.49173 + 7.35013i 0.146409 + 0.126726i
\(59\) 21.9238 52.9288i 0.371590 0.897098i −0.621891 0.783103i \(-0.713635\pi\)
0.993481 0.113994i \(-0.0363645\pi\)
\(60\) 3.80688 24.6363i 0.0634479 0.410605i
\(61\) −32.9968 79.6614i −0.540932 1.30592i −0.924066 0.382232i \(-0.875156\pi\)
0.383135 0.923692i \(-0.374844\pi\)
\(62\) 36.5611 + 72.9417i 0.589695 + 1.17648i
\(63\) −33.4786 + 49.5315i −0.531407 + 0.786214i
\(64\) 60.0367 + 22.1721i 0.938073 + 0.346438i
\(65\) 5.20514i 0.0800791i
\(66\) 1.48112 2.08369i 0.0224412 0.0315711i
\(67\) −19.1610 46.2587i −0.285985 0.690428i 0.713968 0.700179i \(-0.246896\pi\)
−0.999952 + 0.00975034i \(0.996896\pi\)
\(68\) −1.03576 + 1.38671i −0.0152317 + 0.0203929i
\(69\) −12.5751 131.258i −0.182247 1.90228i
\(70\) 20.8677 + 18.0623i 0.298110 + 0.258033i
\(71\) 65.8420 65.8420i 0.927352 0.927352i −0.0701821 0.997534i \(-0.522358\pi\)
0.997534 + 0.0701821i \(0.0223580\pi\)
\(72\) 1.01805 + 71.9928i 0.0141396 + 0.999900i
\(73\) −16.0821 + 16.0821i −0.220303 + 0.220303i −0.808626 0.588323i \(-0.799788\pi\)
0.588323 + 0.808626i \(0.299788\pi\)
\(74\) 0.922099 + 12.7959i 0.0124608 + 0.172917i
\(75\) 5.91789 + 61.7705i 0.0789052 + 0.823607i
\(76\) −25.2277 + 99.2869i −0.331944 + 1.30641i
\(77\) 1.08311 + 2.61486i 0.0140664 + 0.0339592i
\(78\) −2.50566 14.8234i −0.0321238 0.190044i
\(79\) 45.6365i 0.577678i 0.957378 + 0.288839i \(0.0932692\pi\)
−0.957378 + 0.288839i \(0.906731\pi\)
\(80\) 33.0553 + 3.48189i 0.413192 + 0.0435236i
\(81\) −75.1600 + 30.1988i −0.927902 + 0.372825i
\(82\) 22.9549 69.0925i 0.279938 0.842592i
\(83\) −14.7260 35.5516i −0.177421 0.428333i 0.810003 0.586426i \(-0.199465\pi\)
−0.987424 + 0.158093i \(0.949465\pi\)
\(84\) −68.1227 41.3933i −0.810984 0.492777i
\(85\) −0.343994 + 0.830476i −0.00404699 + 0.00977031i
\(86\) −152.560 + 10.9938i −1.77395 + 0.127835i
\(87\) −16.1079 4.93315i −0.185149 0.0567028i
\(88\) 2.87048 + 1.83820i 0.0326190 + 0.0208887i
\(89\) −104.157 + 104.157i −1.17030 + 1.17030i −0.188166 + 0.982137i \(0.560254\pi\)
−0.982137 + 0.188166i \(0.939746\pi\)
\(90\) 9.72007 + 36.1076i 0.108001 + 0.401195i
\(91\) 15.3772 + 6.36942i 0.168980 + 0.0699937i
\(92\) 173.995 25.2078i 1.89125 0.273998i
\(93\) −94.3999 77.8934i −1.01505 0.837564i
\(94\) 29.0800 + 58.0165i 0.309362 + 0.617197i
\(95\) 53.2029i 0.560030i
\(96\) −95.8125 + 5.99635i −0.998047 + 0.0624620i
\(97\) 67.7334 0.698282 0.349141 0.937070i \(-0.386473\pi\)
0.349141 + 0.937070i \(0.386473\pi\)
\(98\) −8.71505 + 4.36831i −0.0889291 + 0.0445746i
\(99\) −0.768122 + 3.75697i −0.00775881 + 0.0379492i
\(100\) −81.8830 + 11.8629i −0.818830 + 0.118629i
\(101\) 11.6999 28.2462i 0.115841 0.279665i −0.855316 0.518107i \(-0.826637\pi\)
0.971157 + 0.238442i \(0.0766368\pi\)
\(102\) 0.579867 2.53066i 0.00568497 0.0248104i
\(103\) 82.0760 + 82.0760i 0.796855 + 0.796855i 0.982598 0.185744i \(-0.0594694\pi\)
−0.185744 + 0.982598i \(0.559469\pi\)
\(104\) 19.5799 4.29246i 0.188269 0.0412737i
\(105\) −39.5838 12.1228i −0.376989 0.115455i
\(106\) −10.7577 149.284i −0.101488 1.40834i
\(107\) 182.577 + 75.6258i 1.70633 + 0.706784i 0.999999 0.00110220i \(-0.000350840\pi\)
0.706327 + 0.707886i \(0.250351\pi\)
\(108\) −45.0627 98.1496i −0.417247 0.908793i
\(109\) 25.7992 10.6864i 0.236690 0.0980403i −0.261186 0.965289i \(-0.584113\pi\)
0.497876 + 0.867248i \(0.334113\pi\)
\(110\) 1.67996 + 0.558141i 0.0152724 + 0.00507401i
\(111\) −9.02617 16.9954i −0.0813168 0.153112i
\(112\) 50.7354 93.3922i 0.452995 0.833859i
\(113\) −115.942 −1.02604 −0.513019 0.858377i \(-0.671473\pi\)
−0.513019 + 0.858377i \(0.671473\pi\)
\(114\) −25.6109 151.513i −0.224657 1.32907i
\(115\) 84.3569 34.9418i 0.733538 0.303841i
\(116\) 5.53155 21.7701i 0.0476858 0.187673i
\(117\) 12.4284 + 18.8165i 0.106226 + 0.160825i
\(118\) −114.283 + 8.23547i −0.968500 + 0.0697922i
\(119\) 2.03247 + 2.03247i 0.0170796 + 0.0170796i
\(120\) −47.4606 + 15.2724i −0.395505 + 0.127270i
\(121\) −85.4316 85.4316i −0.706046 0.706046i
\(122\) −112.860 + 130.390i −0.925086 + 1.06877i
\(123\) 10.4150 + 108.711i 0.0846749 + 0.883831i
\(124\) 97.6516 130.740i 0.787513 1.05436i
\(125\) −87.6802 + 36.3183i −0.701442 + 0.290547i
\(126\) 118.564 + 15.4688i 0.940985 + 0.122769i
\(127\) −106.364 −0.837514 −0.418757 0.908098i \(-0.637534\pi\)
−0.418757 + 0.908098i \(0.637534\pi\)
\(128\) −14.1617 127.214i −0.110638 0.993861i
\(129\) 202.629 107.615i 1.57077 0.834226i
\(130\) 9.30663 4.66483i 0.0715894 0.0358833i
\(131\) −128.050 + 53.0401i −0.977482 + 0.404887i −0.813492 0.581575i \(-0.802436\pi\)
−0.163990 + 0.986462i \(0.552436\pi\)
\(132\) −5.05295 0.780797i −0.0382799 0.00591513i
\(133\) 157.173 + 65.1033i 1.18175 + 0.489498i
\(134\) −65.5371 + 75.7161i −0.489083 + 0.565046i
\(135\) −35.2354 43.6405i −0.261003 0.323263i
\(136\) 3.40764 + 0.609130i 0.0250562 + 0.00447890i
\(137\) 164.125 + 164.125i 1.19799 + 1.19799i 0.974767 + 0.223226i \(0.0716588\pi\)
0.223226 + 0.974767i \(0.428341\pi\)
\(138\) −223.415 + 140.116i −1.61895 + 1.01534i
\(139\) −54.3741 + 131.271i −0.391181 + 0.944394i 0.598502 + 0.801121i \(0.295763\pi\)
−0.989683 + 0.143273i \(0.954237\pi\)
\(140\) 13.5933 53.4981i 0.0970949 0.382129i
\(141\) −75.0839 61.9550i −0.532510 0.439397i
\(142\) −176.731 58.7161i −1.24458 0.413493i
\(143\) 1.06758 0.00746562
\(144\) 127.809 66.3399i 0.887559 0.460694i
\(145\) 11.6655i 0.0804518i
\(146\) 43.1670 + 14.3416i 0.295664 + 0.0982300i
\(147\) 9.30668 11.2789i 0.0633107 0.0767270i
\(148\) 22.0523 13.1163i 0.149002 0.0886237i
\(149\) −148.229 61.3986i −0.994827 0.412071i −0.174930 0.984581i \(-0.555970\pi\)
−0.819898 + 0.572510i \(0.805970\pi\)
\(150\) 105.140 65.9395i 0.700935 0.439597i
\(151\) −122.344 + 122.344i −0.810223 + 0.810223i −0.984667 0.174444i \(-0.944187\pi\)
0.174444 + 0.984667i \(0.444187\pi\)
\(152\) 200.131 43.8742i 1.31665 0.288646i
\(153\) 0.739408 + 3.82352i 0.00483273 + 0.0249904i
\(154\) 3.70461 4.28000i 0.0240559 0.0277922i
\(155\) 32.4320 78.2978i 0.209239 0.505147i
\(156\) −24.2583 + 17.7647i −0.155502 + 0.113876i
\(157\) 72.9368 + 176.085i 0.464566 + 1.12156i 0.966503 + 0.256657i \(0.0826210\pi\)
−0.501937 + 0.864904i \(0.667379\pi\)
\(158\) 81.5967 40.8993i 0.516435 0.258856i
\(159\) 105.304 + 198.278i 0.662290 + 1.24703i
\(160\) −23.3986 62.2224i −0.146241 0.388890i
\(161\) 291.967i 1.81346i
\(162\) 121.353 + 107.320i 0.749091 + 0.662467i
\(163\) −55.2863 133.473i −0.339180 0.818852i −0.997795 0.0663722i \(-0.978858\pi\)
0.658615 0.752480i \(-0.271142\pi\)
\(164\) −144.107 + 20.8778i −0.878704 + 0.127304i
\(165\) −2.64328 + 0.253238i −0.0160199 + 0.00153477i
\(166\) −50.3678 + 58.1908i −0.303421 + 0.350547i
\(167\) 85.7657 85.7657i 0.513567 0.513567i −0.402050 0.915618i \(-0.631702\pi\)
0.915618 + 0.402050i \(0.131702\pi\)
\(168\) −12.9586 + 158.898i −0.0771344 + 0.945820i
\(169\) −115.062 + 115.062i −0.680839 + 0.680839i
\(170\) 1.79315 0.129218i 0.0105480 0.000760108i
\(171\) 127.034 + 192.328i 0.742887 + 1.12472i
\(172\) 156.380 + 262.920i 0.909187 + 1.52860i
\(173\) 75.4770 + 182.218i 0.436283 + 1.05328i 0.977222 + 0.212219i \(0.0680689\pi\)
−0.540939 + 0.841062i \(0.681931\pi\)
\(174\) 5.61556 + 33.2215i 0.0322733 + 0.190928i
\(175\) 137.401i 0.785149i
\(176\) 0.714141 6.77971i 0.00405762 0.0385211i
\(177\) 151.790 80.6148i 0.857571 0.455451i
\(178\) 279.575 + 92.8844i 1.57064 + 0.521822i
\(179\) −39.1321 94.4733i −0.218615 0.527784i 0.776082 0.630632i \(-0.217204\pi\)
−0.994697 + 0.102848i \(0.967204\pi\)
\(180\) 55.8481 49.7387i 0.310267 0.276326i
\(181\) 9.83427 23.7420i 0.0543330 0.131171i −0.894382 0.447304i \(-0.852384\pi\)
0.948715 + 0.316132i \(0.102384\pi\)
\(182\) −2.39261 33.2021i −0.0131462 0.182429i
\(183\) 75.7479 247.335i 0.413923 1.35156i
\(184\) −201.004 288.506i −1.09242 1.56797i
\(185\) 9.42254 9.42254i 0.0509327 0.0509327i
\(186\) −54.6702 + 238.592i −0.293926 + 1.28275i
\(187\) 0.170332 + 0.0705539i 0.000910867 + 0.000377294i
\(188\) 77.6702 103.988i 0.413140 0.553129i
\(189\) −172.041 + 50.6914i −0.910269 + 0.268208i
\(190\) 95.1251 47.6802i 0.500658 0.250949i
\(191\) 160.835i 0.842071i −0.907044 0.421035i \(-0.861667\pi\)
0.907044 0.421035i \(-0.138333\pi\)
\(192\) 96.5881 + 165.936i 0.503063 + 0.864250i
\(193\) −164.339 −0.851498 −0.425749 0.904841i \(-0.639989\pi\)
−0.425749 + 0.904841i \(0.639989\pi\)
\(194\) −60.7024 121.105i −0.312899 0.624253i
\(195\) −9.93841 + 12.0445i −0.0509662 + 0.0617665i
\(196\) 15.6208 + 11.6674i 0.0796979 + 0.0595274i
\(197\) 14.8274 35.7965i 0.0752659 0.181708i −0.881768 0.471683i \(-0.843647\pi\)
0.957034 + 0.289974i \(0.0936468\pi\)
\(198\) 7.40573 1.99360i 0.0374027 0.0100687i
\(199\) −34.7323 34.7323i −0.174534 0.174534i 0.614434 0.788968i \(-0.289384\pi\)
−0.788968 + 0.614434i \(0.789384\pi\)
\(200\) 94.5937 + 135.773i 0.472969 + 0.678863i
\(201\) 43.9862 143.626i 0.218837 0.714555i
\(202\) −60.9887 + 4.39497i −0.301924 + 0.0217573i
\(203\) −34.4625 14.2748i −0.169766 0.0703195i
\(204\) −5.04441 + 1.23118i −0.0247275 + 0.00603521i
\(205\) −69.8667 + 28.9397i −0.340813 + 0.141169i
\(206\) 73.1931 220.306i 0.355307 1.06944i
\(207\) 221.518 327.735i 1.07014 1.58326i
\(208\) −25.2223 31.1614i −0.121261 0.149815i
\(209\) 10.9120 0.0522106
\(210\) 13.7997 + 81.6390i 0.0657130 + 0.388757i
\(211\) −8.12088 + 3.36378i −0.0384876 + 0.0159421i −0.401844 0.915708i \(-0.631631\pi\)
0.363357 + 0.931650i \(0.381631\pi\)
\(212\) −257.273 + 153.022i −1.21355 + 0.721801i
\(213\) 278.071 26.6404i 1.30550 0.125072i
\(214\) −28.4081 394.217i −0.132748 1.84214i
\(215\) 112.341 + 112.341i 0.522516 + 0.522516i
\(216\) −135.103 + 168.532i −0.625479 + 0.780241i
\(217\) −191.623 191.623i −0.883054 0.883054i
\(218\) −42.2281 36.5511i −0.193707 0.167666i
\(219\) −67.9196 + 6.50700i −0.310135 + 0.0297123i
\(220\) −0.507636 3.50392i −0.00230744 0.0159269i
\(221\) 1.00167 0.414905i 0.00453244 0.00187740i
\(222\) −22.2981 + 31.3697i −0.100442 + 0.141305i
\(223\) 117.273 0.525890 0.262945 0.964811i \(-0.415306\pi\)
0.262945 + 0.964811i \(0.415306\pi\)
\(224\) −212.451 7.01563i −0.948443 0.0313198i
\(225\) −104.248 + 154.234i −0.463323 + 0.685483i
\(226\) 103.907 + 207.301i 0.459766 + 0.917262i
\(227\) −233.716 + 96.8085i −1.02959 + 0.426469i −0.832564 0.553930i \(-0.813128\pi\)
−0.197024 + 0.980399i \(0.563128\pi\)
\(228\) −247.949 + 181.577i −1.08750 + 0.796391i
\(229\) 208.050 + 86.1773i 0.908517 + 0.376320i 0.787489 0.616329i \(-0.211381\pi\)
0.121028 + 0.992649i \(0.461381\pi\)
\(230\) −138.075 119.513i −0.600326 0.519621i
\(231\) −2.48640 + 8.11871i −0.0107636 + 0.0351459i
\(232\) −43.8816 + 9.62006i −0.189145 + 0.0414658i
\(233\) 142.576 + 142.576i 0.611913 + 0.611913i 0.943444 0.331531i \(-0.107565\pi\)
−0.331531 + 0.943444i \(0.607565\pi\)
\(234\) 22.5051 39.0849i 0.0961755 0.167030i
\(235\) 25.7958 62.2766i 0.109769 0.265007i
\(236\) 117.145 + 196.954i 0.496376 + 0.834550i
\(237\) −87.1359 + 105.601i −0.367662 + 0.445574i
\(238\) 1.81250 5.45549i 0.00761556 0.0229222i
\(239\) −380.299 −1.59121 −0.795605 0.605816i \(-0.792847\pi\)
−0.795605 + 0.605816i \(0.792847\pi\)
\(240\) 69.8405 + 71.1710i 0.291002 + 0.296546i
\(241\) 182.069i 0.755473i −0.925913 0.377736i \(-0.876703\pi\)
0.925913 0.377736i \(-0.123297\pi\)
\(242\) −76.1855 + 229.312i −0.314816 + 0.947572i
\(243\) −231.577 73.6277i −0.952992 0.302995i
\(244\) 334.278 + 84.9363i 1.36999 + 0.348100i
\(245\) 9.35499 + 3.87496i 0.0381836 + 0.0158162i
\(246\) 185.038 116.048i 0.752188 0.471741i
\(247\) 45.3750 45.3750i 0.183705 0.183705i
\(248\) −321.274 57.4291i −1.29546 0.231569i
\(249\) 33.8051 110.382i 0.135763 0.443301i
\(250\) 143.515 + 124.221i 0.574059 + 0.496884i
\(251\) 96.8774 233.883i 0.385966 0.931804i −0.604820 0.796362i \(-0.706755\pi\)
0.990785 0.135441i \(-0.0432452\pi\)
\(252\) −78.5989 225.852i −0.311900 0.896238i
\(253\) −7.16662 17.3017i −0.0283266 0.0683864i
\(254\) 95.3233 + 190.176i 0.375289 + 0.748724i
\(255\) −2.38165 + 1.26488i −0.00933982 + 0.00496032i
\(256\) −214.763 + 139.330i −0.838919 + 0.544256i
\(257\) 143.675i 0.559048i −0.960139 0.279524i \(-0.909823\pi\)
0.960139 0.279524i \(-0.0901766\pi\)
\(258\) −374.008 265.850i −1.44964 1.03043i
\(259\) −16.3061 39.3665i −0.0629580 0.151994i
\(260\) −16.6811 12.4594i −0.0641582 0.0479206i
\(261\) −27.8540 42.1707i −0.106720 0.161574i
\(262\) 209.592 + 181.415i 0.799970 + 0.692425i
\(263\) 10.3269 10.3269i 0.0392656 0.0392656i −0.687201 0.726467i \(-0.741161\pi\)
0.726467 + 0.687201i \(0.241161\pi\)
\(264\) 3.13239 + 9.73426i 0.0118651 + 0.0368722i
\(265\) −109.928 + 109.928i −0.414824 + 0.414824i
\(266\) −24.4554 339.366i −0.0919377 1.27581i
\(267\) −439.887 + 42.1431i −1.64752 + 0.157839i
\(268\) 194.112 + 49.3218i 0.724299 + 0.184037i
\(269\) −12.2762 29.6374i −0.0456365 0.110176i 0.899417 0.437091i \(-0.143991\pi\)
−0.945054 + 0.326914i \(0.893991\pi\)
\(270\) −46.4500 + 102.110i −0.172037 + 0.378186i
\(271\) 248.594i 0.917322i −0.888611 0.458661i \(-0.848329\pi\)
0.888611 0.458661i \(-0.151671\pi\)
\(272\) −1.96481 6.63866i −0.00722357 0.0244068i
\(273\) 23.4206 + 44.0989i 0.0857899 + 0.161534i
\(274\) 146.362 440.539i 0.534168 1.60781i
\(275\) 3.37265 + 8.14229i 0.0122642 + 0.0296083i
\(276\) 450.747 + 273.887i 1.63314 + 0.992343i
\(277\) −130.473 + 314.989i −0.471020 + 1.13714i 0.492693 + 0.870203i \(0.336013\pi\)
−0.963713 + 0.266940i \(0.913987\pi\)
\(278\) 283.438 20.4251i 1.01956 0.0734717i
\(279\) −69.7118 360.484i −0.249863 1.29206i
\(280\) −107.835 + 23.6404i −0.385126 + 0.0844301i
\(281\) 45.2477 45.2477i 0.161024 0.161024i −0.621996 0.783020i \(-0.713678\pi\)
0.783020 + 0.621996i \(0.213678\pi\)
\(282\) −43.4836 + 189.771i −0.154197 + 0.672948i
\(283\) −27.7771 11.5057i −0.0981524 0.0406561i 0.333067 0.942903i \(-0.391916\pi\)
−0.431219 + 0.902247i \(0.641916\pi\)
\(284\) 53.4030 + 368.610i 0.188039 + 1.29792i
\(285\) −101.583 + 123.109i −0.356431 + 0.431962i
\(286\) −0.956765 1.90881i −0.00334533 0.00667415i
\(287\) 241.815i 0.842560i
\(288\) −233.155 169.064i −0.809567 0.587028i
\(289\) −288.813 −0.999352
\(290\) −20.8576 + 10.4546i −0.0719226 + 0.0360503i
\(291\) 156.732 + 129.326i 0.538598 + 0.444421i
\(292\) −13.0438 90.0341i −0.0446707 0.308336i
\(293\) −23.9730 + 57.8759i −0.0818191 + 0.197529i −0.959495 0.281726i \(-0.909093\pi\)
0.877676 + 0.479255i \(0.159093\pi\)
\(294\) −28.5069 6.53197i −0.0969621 0.0222176i
\(295\) 84.1549 + 84.1549i 0.285271 + 0.285271i
\(296\) −43.2147 27.6740i −0.145996 0.0934932i
\(297\) −8.95075 + 7.22685i −0.0301372 + 0.0243328i
\(298\) 23.0638 + 320.055i 0.0773953 + 1.07401i
\(299\) −101.746 42.1446i −0.340287 0.140952i
\(300\) −212.124 128.893i −0.707080 0.429642i
\(301\) 469.350 194.411i 1.55930 0.645884i
\(302\) 328.391 + 109.103i 1.08739 + 0.361267i
\(303\) 81.0049 43.0212i 0.267343 0.141984i
\(304\) −257.802 318.508i −0.848034 1.04772i
\(305\) 179.123 0.587287
\(306\) 6.17369 4.74867i 0.0201754 0.0155185i
\(307\) 1.24681 0.516444i 0.00406125 0.00168223i −0.380652 0.924718i \(-0.624300\pi\)
0.384713 + 0.923036i \(0.374300\pi\)
\(308\) −10.9726 2.78801i −0.0356252 0.00905198i
\(309\) 33.2089 + 346.632i 0.107472 + 1.12179i
\(310\) −169.059 + 12.1828i −0.545353 + 0.0392993i
\(311\) 341.758 + 341.758i 1.09890 + 1.09890i 0.994539 + 0.104362i \(0.0332800\pi\)
0.104362 + 0.994539i \(0.466720\pi\)
\(312\) 53.5029 + 27.4523i 0.171484 + 0.0879882i
\(313\) 141.248 + 141.248i 0.451272 + 0.451272i 0.895777 0.444504i \(-0.146620\pi\)
−0.444504 + 0.895777i \(0.646620\pi\)
\(314\) 249.469 288.216i 0.794487 0.917884i
\(315\) −68.4487 103.631i −0.217297 0.328986i
\(316\) −146.253 109.239i −0.462827 0.345692i
\(317\) 400.350 165.831i 1.26293 0.523125i 0.352126 0.935953i \(-0.385459\pi\)
0.910809 + 0.412828i \(0.135459\pi\)
\(318\) 260.141 365.976i 0.818054 1.15087i
\(319\) −2.39262 −0.00750037
\(320\) −90.2819 + 97.5994i −0.282131 + 0.304998i
\(321\) 278.079 + 523.597i 0.866291 + 1.63114i
\(322\) −522.027 + 261.659i −1.62120 + 0.812607i
\(323\) 10.2383 4.24083i 0.0316974 0.0131295i
\(324\) 83.1284 313.154i 0.256569 0.966526i
\(325\) 47.8822 + 19.8335i 0.147330 + 0.0610260i
\(326\) −189.098 + 218.468i −0.580055 + 0.670147i
\(327\) 80.1024 + 24.5318i 0.244961 + 0.0750208i
\(328\) 166.477 + 238.949i 0.507553 + 0.728503i
\(329\) −152.413 152.413i −0.463262 0.463262i
\(330\) 2.82167 + 4.49914i 0.00855053 + 0.0136338i
\(331\) −1.03265 + 2.49305i −0.00311980 + 0.00753187i −0.925432 0.378914i \(-0.876298\pi\)
0.922312 + 0.386446i \(0.126298\pi\)
\(332\) 149.183 + 37.9057i 0.449346 + 0.114174i
\(333\) 11.5640 56.5608i 0.0347267 0.169852i
\(334\) −230.209 76.4835i −0.689249 0.228992i
\(335\) 104.015 0.310492
\(336\) 295.718 119.234i 0.880112 0.354863i
\(337\) 140.512i 0.416950i 0.978028 + 0.208475i \(0.0668501\pi\)
−0.978028 + 0.208475i \(0.933150\pi\)
\(338\) 308.845 + 102.609i 0.913742 + 0.303577i
\(339\) −268.285 221.374i −0.791402 0.653020i
\(340\) −1.83805 3.09029i −0.00540604 0.00908910i
\(341\) −16.0590 6.65186i −0.0470939 0.0195069i
\(342\) 230.029 399.496i 0.672600 1.16812i
\(343\) 253.054 253.054i 0.737765 0.737765i
\(344\) 329.945 515.231i 0.959142 1.49776i
\(345\) 261.914 + 80.2127i 0.759171 + 0.232501i
\(346\) 258.157 298.253i 0.746119 0.862003i
\(347\) −148.332 + 358.105i −0.427470 + 1.03200i 0.552617 + 0.833435i \(0.313629\pi\)
−0.980087 + 0.198568i \(0.936371\pi\)
\(348\) 54.3664 39.8135i 0.156225 0.114406i
\(349\) 115.479 + 278.790i 0.330884 + 0.798825i 0.998523 + 0.0543391i \(0.0173052\pi\)
−0.667638 + 0.744486i \(0.732695\pi\)
\(350\) 245.669 123.138i 0.701911 0.351824i
\(351\) −7.16843 + 67.2708i −0.0204229 + 0.191655i
\(352\) −12.7619 + 4.79909i −0.0362555 + 0.0136338i
\(353\) 136.228i 0.385915i −0.981207 0.192958i \(-0.938192\pi\)
0.981207 0.192958i \(-0.0618080\pi\)
\(354\) −280.170 199.149i −0.791442 0.562569i
\(355\) 74.0245 + 178.711i 0.208520 + 0.503411i
\(356\) −84.4794 583.113i −0.237302 1.63796i
\(357\) 0.822362 + 8.58375i 0.00230353 + 0.0240441i
\(358\) −133.845 + 154.634i −0.373870 + 0.431938i
\(359\) −293.915 + 293.915i −0.818705 + 0.818705i −0.985920 0.167215i \(-0.946523\pi\)
0.167215 + 0.985920i \(0.446523\pi\)
\(360\) −138.982 55.2791i −0.386061 0.153553i
\(361\) 208.523 208.523i 0.577625 0.577625i
\(362\) −51.2634 + 3.69415i −0.141612 + 0.0102048i
\(363\) −34.5666 360.803i −0.0952247 0.993949i
\(364\) −57.2201 + 34.0335i −0.157198 + 0.0934987i
\(365\) −18.0807 43.6507i −0.0495362 0.119591i
\(366\) −510.113 + 86.2262i −1.39375 + 0.235591i
\(367\) 316.411i 0.862154i 0.902315 + 0.431077i \(0.141866\pi\)
−0.902315 + 0.431077i \(0.858134\pi\)
\(368\) −335.701 + 617.948i −0.912231 + 1.67921i
\(369\) −183.467 + 271.439i −0.497202 + 0.735607i
\(370\) −25.2917 8.40276i −0.0683558 0.0227102i
\(371\) 190.236 + 459.270i 0.512765 + 1.23792i
\(372\) 475.590 116.077i 1.27847 0.312034i
\(373\) 95.6414 230.899i 0.256411 0.619031i −0.742285 0.670085i \(-0.766258\pi\)
0.998696 + 0.0510533i \(0.0162578\pi\)
\(374\) −0.0265029 0.367779i −7.08634e−5 0.000983366i
\(375\) −272.233 83.3728i −0.725953 0.222327i
\(376\) −255.536 45.6780i −0.679616 0.121484i
\(377\) −9.94914 + 9.94914i −0.0263903 + 0.0263903i
\(378\) 244.817 + 262.174i 0.647664 + 0.693582i
\(379\) −259.429 107.459i −0.684509 0.283533i 0.0132015 0.999913i \(-0.495798\pi\)
−0.697710 + 0.716380i \(0.745798\pi\)
\(380\) −170.502 127.350i −0.448688 0.335131i
\(381\) −246.122 203.086i −0.645991 0.533035i
\(382\) −287.569 + 144.140i −0.752798 + 0.377330i
\(383\) 205.284i 0.535990i −0.963420 0.267995i \(-0.913639\pi\)
0.963420 0.267995i \(-0.0863611\pi\)
\(384\) 210.126 321.408i 0.547204 0.836999i
\(385\) −5.87965 −0.0152718
\(386\) 147.280 + 293.833i 0.381555 + 0.761226i
\(387\) 674.350 + 137.873i 1.74251 + 0.356260i
\(388\) −162.131 + 217.068i −0.417863 + 0.559454i
\(389\) −180.927 + 436.798i −0.465109 + 1.12287i 0.501164 + 0.865353i \(0.332905\pi\)
−0.966273 + 0.257520i \(0.917095\pi\)
\(390\) 30.4419 + 6.97536i 0.0780562 + 0.0178855i
\(391\) −13.4483 13.4483i −0.0343945 0.0343945i
\(392\) 6.86161 38.3857i 0.0175041 0.0979228i
\(393\) −397.575 121.760i −1.01164 0.309821i
\(394\) −77.2913 + 5.56977i −0.196171 + 0.0141365i
\(395\) −87.5882 36.2802i −0.221742 0.0918487i
\(396\) −10.2015 11.4546i −0.0257613 0.0289256i
\(397\) −50.9762 + 21.1150i −0.128404 + 0.0531865i −0.445960 0.895053i \(-0.647138\pi\)
0.317557 + 0.948239i \(0.397138\pi\)
\(398\) −30.9733 + 93.2271i −0.0778223 + 0.234239i
\(399\) 239.387 + 450.744i 0.599969 + 1.12968i
\(400\) 157.983 290.810i 0.394957 0.727024i
\(401\) −380.473 −0.948811 −0.474405 0.880306i \(-0.657337\pi\)
−0.474405 + 0.880306i \(0.657337\pi\)
\(402\) −296.218 + 50.0708i −0.736861 + 0.124554i
\(403\) −94.4379 + 39.1174i −0.234337 + 0.0970656i
\(404\) 62.5159 + 105.107i 0.154742 + 0.260166i
\(405\) 1.79156 168.259i 0.00442360 0.415454i
\(406\) 5.36221 + 74.4110i 0.0132074 + 0.183278i
\(407\) −1.93258 1.93258i −0.00474836 0.00474836i
\(408\) 6.72210 + 7.91587i 0.0164757 + 0.0194016i
\(409\) 27.3084 + 27.3084i 0.0667687 + 0.0667687i 0.739703 0.672934i \(-0.234966\pi\)
−0.672934 + 0.739703i \(0.734966\pi\)
\(410\) 114.358 + 98.9838i 0.278921 + 0.241424i
\(411\) 66.4068 + 693.150i 0.161574 + 1.68650i
\(412\) −459.495 + 66.5701i −1.11528 + 0.161578i
\(413\) 351.591 145.634i 0.851310 0.352624i
\(414\) −784.503 102.353i −1.89493 0.247229i
\(415\) 79.9395 0.192625
\(416\) −33.1116 + 73.0234i −0.0795951 + 0.175537i
\(417\) −376.461 + 199.936i −0.902784 + 0.479463i
\(418\) −9.77930 19.5103i −0.0233955 0.0466754i
\(419\) 110.034 45.5777i 0.262612 0.108777i −0.247493 0.968890i \(-0.579607\pi\)
0.510105 + 0.860112i \(0.329607\pi\)
\(420\) 133.601 97.8380i 0.318097 0.232948i
\(421\) −472.694 195.796i −1.12279 0.465074i −0.257465 0.966288i \(-0.582887\pi\)
−0.865324 + 0.501213i \(0.832887\pi\)
\(422\) 13.2922 + 11.5053i 0.0314982 + 0.0272637i
\(423\) −55.4475 286.722i −0.131081 0.677830i
\(424\) 504.166 + 322.859i 1.18907 + 0.761460i
\(425\) 6.32882 + 6.32882i 0.0148914 + 0.0148914i
\(426\) −296.838 473.307i −0.696803 1.11105i
\(427\) 219.189 529.168i 0.513322 1.23927i
\(428\) −679.389 + 404.089i −1.58736 + 0.944133i
\(429\) 2.47034 + 2.03839i 0.00575838 + 0.00475148i
\(430\) 100.183 301.542i 0.232983 0.701259i
\(431\) 80.7430 0.187339 0.0936694 0.995603i \(-0.470140\pi\)
0.0936694 + 0.995603i \(0.470140\pi\)
\(432\) 422.409 + 90.5229i 0.977799 + 0.209544i
\(433\) 764.221i 1.76494i −0.470365 0.882472i \(-0.655878\pi\)
0.470365 0.882472i \(-0.344122\pi\)
\(434\) −170.884 + 514.347i −0.393742 + 1.18513i
\(435\) 22.2735 26.9935i 0.0512034 0.0620540i
\(436\) −27.5076 + 108.260i −0.0630908 + 0.248302i
\(437\) −1039.97 430.769i −2.37979 0.985741i
\(438\) 72.5036 + 115.607i 0.165533 + 0.263942i
\(439\) −331.477 + 331.477i −0.755072 + 0.755072i −0.975421 0.220349i \(-0.929280\pi\)
0.220349 + 0.975421i \(0.429280\pi\)
\(440\) −5.80996 + 4.04784i −0.0132045 + 0.00919964i
\(441\) 43.0705 8.32914i 0.0976655 0.0188869i
\(442\) −1.63953 1.41912i −0.00370934 0.00321067i
\(443\) 261.149 630.470i 0.589501 1.42318i −0.294479 0.955658i \(-0.595146\pi\)
0.883980 0.467524i \(-0.154854\pi\)
\(444\) 76.0716 + 11.7548i 0.171332 + 0.0264748i
\(445\) −117.101 282.707i −0.263149 0.635297i
\(446\) −105.100 209.681i −0.235650 0.470137i
\(447\) −225.765 425.095i −0.505067 0.950995i
\(448\) 177.854 + 386.144i 0.396996 + 0.861928i
\(449\) 90.5080i 0.201577i −0.994908 0.100788i \(-0.967863\pi\)
0.994908 0.100788i \(-0.0321365\pi\)
\(450\) 369.191 + 48.1677i 0.820425 + 0.107039i
\(451\) 5.93559 + 14.3298i 0.0131610 + 0.0317734i
\(452\) 277.527 371.565i 0.613997 0.822046i
\(453\) −516.695 + 49.5016i −1.14061 + 0.109275i
\(454\) 382.546 + 331.118i 0.842613 + 0.729335i
\(455\) −24.4491 + 24.4491i −0.0537343 + 0.0537343i
\(456\) 546.865 + 280.596i 1.19927 + 0.615342i
\(457\) 393.046 393.046i 0.860057 0.860057i −0.131287 0.991344i \(-0.541911\pi\)
0.991344 + 0.131287i \(0.0419111\pi\)
\(458\) −32.3717 449.220i −0.0706806 0.980829i
\(459\) −5.58947 + 10.2593i −0.0121775 + 0.0223513i
\(460\) −89.9427 + 353.981i −0.195528 + 0.769523i
\(461\) −230.614 556.752i −0.500248 1.20771i −0.949349 0.314224i \(-0.898256\pi\)
0.449101 0.893481i \(-0.351744\pi\)
\(462\) 16.7443 2.83035i 0.0362431 0.00612630i
\(463\) 113.653i 0.245471i 0.992439 + 0.122735i \(0.0391666\pi\)
−0.992439 + 0.122735i \(0.960833\pi\)
\(464\) 56.5269 + 69.8375i 0.121825 + 0.150512i
\(465\) 224.544 119.254i 0.482890 0.256460i
\(466\) 127.145 382.697i 0.272843 0.821238i
\(467\) 341.597 + 824.689i 0.731472 + 1.76593i 0.637632 + 0.770341i \(0.279914\pi\)
0.0938398 + 0.995587i \(0.470086\pi\)
\(468\) −90.0516 5.21057i −0.192418 0.0111337i
\(469\) 127.281 307.284i 0.271388 0.655189i
\(470\) −134.467 + 9.68995i −0.286099 + 0.0206169i
\(471\) −167.435 + 546.715i −0.355488 + 1.16075i
\(472\) 247.163 385.961i 0.523650 0.817713i
\(473\) 23.0413 23.0413i 0.0487132 0.0487132i
\(474\) 266.902 + 61.1571i 0.563085 + 0.129023i
\(475\) 489.414 + 202.722i 1.03035 + 0.426783i
\(476\) −11.3786 + 1.64849i −0.0239046 + 0.00346322i
\(477\) −134.912 + 659.868i −0.282834 + 1.38337i
\(478\) 340.823 + 679.963i 0.713018 + 1.42252i
\(479\) 484.285i 1.01103i −0.862817 0.505516i \(-0.831302\pi\)
0.862817 0.505516i \(-0.168698\pi\)
\(480\) 64.6607 188.656i 0.134710 0.393033i
\(481\) −16.0724 −0.0334145
\(482\) −325.534 + 163.170i −0.675381 + 0.338526i
\(483\) 557.465 675.598i 1.15417 1.39875i
\(484\) 478.281 69.2916i 0.988183 0.143165i
\(485\) −53.8468 + 129.998i −0.111024 + 0.268037i
\(486\) 75.8946 + 480.038i 0.156162 + 0.987732i
\(487\) −413.357 413.357i −0.848783 0.848783i 0.141198 0.989981i \(-0.454905\pi\)
−0.989981 + 0.141198i \(0.954905\pi\)
\(488\) −147.715 673.797i −0.302694 1.38073i
\(489\) 126.916 414.411i 0.259542 0.847467i
\(490\) −1.45559 20.1991i −0.00297060 0.0412228i
\(491\) 409.376 + 169.569i 0.833759 + 0.345354i 0.758390 0.651801i \(-0.225986\pi\)
0.0753695 + 0.997156i \(0.475986\pi\)
\(492\) −373.321 226.841i −0.758783 0.461058i
\(493\) −2.24489 + 0.929864i −0.00455353 + 0.00188613i
\(494\) −121.794 40.4642i −0.246547 0.0819113i
\(495\) −6.59995 4.46095i −0.0133332 0.00901201i
\(496\) 185.244 + 625.897i 0.373475 + 1.26189i
\(497\) 618.535 1.24454
\(498\) −227.655 + 38.4814i −0.457139 + 0.0772718i
\(499\) 144.183 59.7225i 0.288944 0.119684i −0.233504 0.972356i \(-0.575019\pi\)
0.522447 + 0.852671i \(0.325019\pi\)
\(500\) 93.4861 367.926i 0.186972 0.735853i
\(501\) 362.215 34.7018i 0.722983 0.0692650i
\(502\) −504.996 + 36.3911i −1.00597 + 0.0724922i
\(503\) 128.659 + 128.659i 0.255783 + 0.255783i 0.823337 0.567553i \(-0.192110\pi\)
−0.567553 + 0.823337i \(0.692110\pi\)
\(504\) −333.376 + 342.940i −0.661461 + 0.680437i
\(505\) 44.9104 + 44.9104i 0.0889315 + 0.0889315i
\(506\) −24.5123 + 28.3195i −0.0484433 + 0.0559673i
\(507\) −485.941 + 46.5553i −0.958463 + 0.0918250i
\(508\) 254.600 340.870i 0.501182 0.671004i
\(509\) 749.571 310.482i 1.47263 0.609985i 0.505176 0.863016i \(-0.331428\pi\)
0.967458 + 0.253031i \(0.0814275\pi\)
\(510\) 4.39600 + 3.12474i 0.00861961 + 0.00612694i
\(511\) −151.079 −0.295653
\(512\) 441.587 + 259.123i 0.862475 + 0.506100i
\(513\) −73.2701 + 687.589i −0.142827 + 1.34033i
\(514\) −256.887 + 128.761i −0.499780 + 0.250508i
\(515\) −222.774 + 92.2760i −0.432571 + 0.179177i
\(516\) −140.148 + 906.969i −0.271604 + 1.75769i
\(517\) −12.7730 5.29077i −0.0247061 0.0102336i
\(518\) −55.7725 + 64.4349i −0.107669 + 0.124392i
\(519\) −173.266 + 565.755i −0.333846 + 1.09009i
\(520\) −7.32737 + 40.9914i −0.0140911 + 0.0788296i
\(521\) −507.166 507.166i −0.973447 0.973447i 0.0262099 0.999656i \(-0.491656\pi\)
−0.999656 + 0.0262099i \(0.991656\pi\)
\(522\) −50.4373 + 87.5953i −0.0966231 + 0.167807i
\(523\) 134.131 323.820i 0.256464 0.619159i −0.742236 0.670139i \(-0.766235\pi\)
0.998700 + 0.0509803i \(0.0162346\pi\)
\(524\) 136.529 537.328i 0.260552 1.02544i
\(525\) −262.346 + 317.940i −0.499707 + 0.605600i
\(526\) −27.7190 9.20920i −0.0526977 0.0175080i
\(527\) −17.6527 −0.0334965
\(528\) 14.5973 14.3244i 0.0276464 0.0271296i
\(529\) 1402.85i 2.65190i
\(530\) 295.066 + 98.0311i 0.556728 + 0.184964i
\(531\) 505.157 + 103.281i 0.951332 + 0.194502i
\(532\) −584.859 + 347.864i −1.09936 + 0.653880i
\(533\) 84.2688 + 34.9053i 0.158103 + 0.0654883i
\(534\) 469.575 + 748.735i 0.879355 + 1.40213i
\(535\) −290.291 + 290.291i −0.542600 + 0.542600i
\(536\) −85.7768 391.268i −0.160031 0.729978i
\(537\) 89.8322 293.324i 0.167285 0.546227i
\(538\) −41.9889 + 48.5104i −0.0780462 + 0.0901681i
\(539\) 0.794762 1.91872i 0.00147451 0.00355979i
\(540\) 224.198 8.45973i 0.415182 0.0156662i
\(541\) −93.4100 225.512i −0.172662 0.416842i 0.813733 0.581240i \(-0.197432\pi\)
−0.986394 + 0.164397i \(0.947432\pi\)
\(542\) −444.479 + 222.789i −0.820071 + 0.411050i
\(543\) 68.0878 36.1610i 0.125392 0.0665948i
\(544\) −10.1089 + 9.46256i −0.0185825 + 0.0173944i
\(545\) 58.0109i 0.106442i
\(546\) 57.8579 81.3966i 0.105967 0.149078i
\(547\) 54.1278 + 130.676i 0.0989540 + 0.238896i 0.965602 0.260023i \(-0.0837303\pi\)
−0.866648 + 0.498920i \(0.833730\pi\)
\(548\) −918.838 + 133.118i −1.67671 + 0.242916i
\(549\) 647.526 427.695i 1.17946 0.779043i
\(550\) 11.5356 13.3273i 0.0209738 0.0242314i
\(551\) −101.692 + 101.692i −0.184560 + 0.184560i
\(552\) 85.7430 1051.38i 0.155331 1.90467i
\(553\) −214.360 + 214.360i −0.387631 + 0.387631i
\(554\) 680.119 49.0108i 1.22765 0.0884671i
\(555\) 39.7942 3.81247i 0.0717013 0.00686931i
\(556\) −290.536 488.473i −0.522546 0.878549i
\(557\) 15.8639 + 38.2988i 0.0284810 + 0.0687591i 0.937480 0.348039i \(-0.113152\pi\)
−0.908999 + 0.416798i \(0.863152\pi\)
\(558\) −582.059 + 447.707i −1.04312 + 0.802343i
\(559\) 191.624i 0.342798i
\(560\) 138.910 + 171.619i 0.248053 + 0.306463i
\(561\) 0.259430 + 0.488482i 0.000462441 + 0.000870734i
\(562\) −121.452 40.3506i −0.216107 0.0717983i
\(563\) 58.1090 + 140.287i 0.103213 + 0.249178i 0.967047 0.254599i \(-0.0819433\pi\)
−0.863834 + 0.503777i \(0.831943\pi\)
\(564\) 378.275 92.3251i 0.670701 0.163697i
\(565\) 92.1720 222.523i 0.163136 0.393846i
\(566\) 4.32200 + 59.9760i 0.00763604 + 0.105965i
\(567\) −494.882 211.188i −0.872809 0.372465i
\(568\) 611.204 425.830i 1.07606 0.749701i
\(569\) −627.070 + 627.070i −1.10206 + 1.10206i −0.107893 + 0.994162i \(0.534410\pi\)
−0.994162 + 0.107893i \(0.965590\pi\)
\(570\) 311.153 + 71.2967i 0.545883 + 0.125082i
\(571\) −237.127 98.2211i −0.415283 0.172016i 0.165252 0.986251i \(-0.447156\pi\)
−0.580535 + 0.814236i \(0.697156\pi\)
\(572\) −2.55544 + 3.42133i −0.00446755 + 0.00598135i
\(573\) 307.091 372.166i 0.535935 0.649505i
\(574\) 432.357 216.714i 0.753236 0.377550i
\(575\) 909.141i 1.58112i
\(576\) −93.3283 + 568.389i −0.162028 + 0.986786i
\(577\) 1017.18 1.76287 0.881435 0.472305i \(-0.156578\pi\)
0.881435 + 0.472305i \(0.156578\pi\)
\(578\) 258.833 + 516.388i 0.447808 + 0.893405i
\(579\) −380.274 313.780i −0.656777 0.541935i
\(580\) 37.3850 + 27.9233i 0.0644568 + 0.0481436i
\(581\) 97.8204 236.159i 0.168366 0.406470i
\(582\) 90.7689 396.134i 0.155960 0.680643i
\(583\) 22.5465 + 22.5465i 0.0386733 + 0.0386733i
\(584\) −149.288 + 104.010i −0.255631 + 0.178100i
\(585\) −45.9941 + 8.89452i −0.0786224 + 0.0152043i
\(586\) 124.965 9.00523i 0.213251 0.0153673i
\(587\) −578.215 239.505i −0.985035 0.408015i −0.168747 0.985659i \(-0.553972\pi\)
−0.816288 + 0.577645i \(0.803972\pi\)
\(588\) 13.8688 + 56.8233i 0.0235864 + 0.0966383i
\(589\) −965.270 + 399.828i −1.63883 + 0.678825i
\(590\) 75.0470 225.886i 0.127198 0.382857i
\(591\) 102.658 54.5209i 0.173702 0.0922520i
\(592\) −10.7513 + 102.068i −0.0181610 + 0.172412i
\(593\) −99.4042 −0.167629 −0.0838147 0.996481i \(-0.526710\pi\)
−0.0838147 + 0.996481i \(0.526710\pi\)
\(594\) 20.9430 + 9.52699i 0.0352576 + 0.0160387i
\(595\) −5.51662 + 2.28506i −0.00927163 + 0.00384043i
\(596\) 551.578 328.069i 0.925466 0.550451i
\(597\) −14.0531 146.685i −0.0235395 0.245703i
\(598\) 15.8312 + 219.688i 0.0264736 + 0.367372i
\(599\) 613.438 + 613.438i 1.02410 + 1.02410i 0.999702 + 0.0244012i \(0.00776792\pi\)
0.0244012 + 0.999702i \(0.492232\pi\)
\(600\) −40.3511 + 494.784i −0.0672518 + 0.824640i
\(601\) 537.631 + 537.631i 0.894561 + 0.894561i 0.994948 0.100388i \(-0.0320083\pi\)
−0.100388 + 0.994948i \(0.532008\pi\)
\(602\) −768.230 664.952i −1.27613 1.10457i
\(603\) 376.013 248.359i 0.623571 0.411872i
\(604\) −99.2303 684.930i −0.164289 1.13399i
\(605\) 231.882 96.0485i 0.383276 0.158758i
\(606\) −149.517 106.279i −0.246727 0.175377i
\(607\) 577.880 0.952026 0.476013 0.879438i \(-0.342081\pi\)
0.476013 + 0.879438i \(0.342081\pi\)
\(608\) −338.441 + 746.388i −0.556646 + 1.22761i
\(609\) −52.4892 98.8323i −0.0861892 0.162286i
\(610\) −160.529 320.266i −0.263162 0.525026i
\(611\) −75.1141 + 31.1133i −0.122936 + 0.0509219i
\(612\) −14.0233 6.78262i −0.0229139 0.0110827i
\(613\) −880.126 364.560i −1.43577 0.594715i −0.477000 0.878903i \(-0.658276\pi\)
−0.958768 + 0.284189i \(0.908276\pi\)
\(614\) −2.04077 1.76641i −0.00332372 0.00287690i
\(615\) −216.924 66.4344i −0.352723 0.108023i
\(616\) 4.84870 + 22.1172i 0.00787126 + 0.0359045i
\(617\) 54.0272 + 54.0272i 0.0875644 + 0.0875644i 0.749532 0.661968i \(-0.230278\pi\)
−0.661968 + 0.749532i \(0.730278\pi\)
\(618\) 590.005 370.027i 0.954701 0.598749i
\(619\) −369.325 + 891.629i −0.596648 + 1.44043i 0.280330 + 0.959904i \(0.409556\pi\)
−0.876978 + 0.480531i \(0.840444\pi\)
\(620\) 173.293 + 291.355i 0.279505 + 0.469927i
\(621\) 1138.34 335.409i 1.83308 0.540112i
\(622\) 304.771 917.336i 0.489985 1.47482i
\(623\) −978.474 −1.57058
\(624\) 1.13474 120.264i 0.00181849 0.192731i
\(625\) 319.958i 0.511933i
\(626\) 125.961 379.134i 0.201216 0.605645i
\(627\) 25.2499 + 20.8348i 0.0402710 + 0.0332293i
\(628\) −738.894 187.745i −1.17658 0.298957i
\(629\) −2.56433 1.06218i −0.00407684 0.00168868i
\(630\) −123.945 + 215.258i −0.196738 + 0.341679i
\(631\) −234.788 + 234.788i −0.372089 + 0.372089i −0.868238 0.496148i \(-0.834747\pi\)
0.496148 + 0.868238i \(0.334747\pi\)
\(632\) −64.2434 + 359.396i −0.101651 + 0.568664i
\(633\) −25.2140 7.72193i −0.0398325 0.0121989i
\(634\) −655.292 567.197i −1.03358 0.894633i
\(635\) 84.5577 204.140i 0.133162 0.321481i
\(636\) −887.491 137.138i −1.39543 0.215626i
\(637\) −4.67374 11.2834i −0.00733711 0.0177133i
\(638\) 2.14426 + 4.27793i 0.00336090 + 0.00670521i
\(639\) 694.310 + 469.288i 1.08656 + 0.734411i
\(640\) 255.415 + 73.9531i 0.399086 + 0.115552i
\(641\) 436.888i 0.681573i 0.940141 + 0.340786i \(0.110693\pi\)
−0.940141 + 0.340786i \(0.889307\pi\)
\(642\) 686.962 966.443i 1.07003 1.50536i
\(643\) −57.5794 139.009i −0.0895480 0.216188i 0.872760 0.488149i \(-0.162328\pi\)
−0.962308 + 0.271961i \(0.912328\pi\)
\(644\) 935.678 + 698.870i 1.45292 + 1.08520i
\(645\) 45.4544 + 474.450i 0.0704719 + 0.735581i
\(646\) −16.7580 14.5051i −0.0259411 0.0224537i
\(647\) −446.411 + 446.411i −0.689970 + 0.689970i −0.962225 0.272255i \(-0.912231\pi\)
0.272255 + 0.962225i \(0.412231\pi\)
\(648\) −634.410 + 132.017i −0.979027 + 0.203730i
\(649\) 17.2603 17.2603i 0.0265953 0.0265953i
\(650\) −7.45025 103.387i −0.0114619 0.159056i
\(651\) −77.5328 809.281i −0.119098 1.24314i
\(652\) 560.083 + 142.311i 0.859023 + 0.218268i
\(653\) 237.310 + 572.918i 0.363416 + 0.877363i 0.994796 + 0.101890i \(0.0324888\pi\)
−0.631380 + 0.775474i \(0.717511\pi\)
\(654\) −27.9253 165.206i −0.0426993 0.252608i
\(655\) 287.927i 0.439584i
\(656\) 278.037 511.802i 0.423837 0.780185i
\(657\) −169.587 114.625i −0.258124 0.174467i
\(658\) −135.918 + 409.102i −0.206562 + 0.621736i
\(659\) −340.627 822.347i −0.516885 1.24787i −0.939807 0.341705i \(-0.888996\pi\)
0.422922 0.906166i \(-0.361004\pi\)
\(660\) 5.51555 9.07718i 0.00835690 0.0137533i
\(661\) 53.7475 129.758i 0.0813123 0.196305i −0.877995 0.478670i \(-0.841119\pi\)
0.959307 + 0.282365i \(0.0911189\pi\)
\(662\) 5.38295 0.387907i 0.00813135 0.000585962i
\(663\) 3.11001 + 0.952460i 0.00469082 + 0.00143659i
\(664\) −65.9228 300.705i −0.0992813 0.452869i
\(665\) −249.900 + 249.900i −0.375789 + 0.375789i
\(666\) −111.493 + 30.0135i −0.167406 + 0.0450653i
\(667\) 228.028 + 94.4524i 0.341871 + 0.141608i
\(668\) 69.5627 + 480.151i 0.104136 + 0.718789i
\(669\) 271.366 + 223.915i 0.405629 + 0.334702i
\(670\) −93.2178 185.976i −0.139131 0.277575i
\(671\) 36.7384i 0.0547517i
\(672\) −478.208 421.877i −0.711619 0.627793i
\(673\) −466.362 −0.692960 −0.346480 0.938057i \(-0.612623\pi\)
−0.346480 + 0.938057i \(0.612623\pi\)
\(674\) 251.232 125.927i 0.372747 0.186835i
\(675\) −535.710 + 157.845i −0.793644 + 0.233845i
\(676\) −93.3240 644.162i −0.138053 0.952903i
\(677\) −259.379 + 626.197i −0.383130 + 0.924958i 0.608226 + 0.793764i \(0.291881\pi\)
−0.991357 + 0.131195i \(0.958119\pi\)
\(678\) −155.373 + 678.080i −0.229164 + 1.00012i
\(679\) 318.151 + 318.151i 0.468559 + 0.468559i
\(680\) −3.87809 + 6.05589i −0.00570308 + 0.00890573i
\(681\) −725.651 222.235i −1.06557 0.326336i
\(682\) 2.49871 + 34.6744i 0.00366380 + 0.0508422i
\(683\) −557.807 231.051i −0.816701 0.338289i −0.0650771 0.997880i \(-0.520729\pi\)
−0.751624 + 0.659591i \(0.770729\pi\)
\(684\) −920.437 53.2584i −1.34567 0.0778632i
\(685\) −445.475 + 184.522i −0.650328 + 0.269375i
\(686\) −679.237 225.666i −0.990142 0.328959i
\(687\) 316.878 + 596.651i 0.461248 + 0.868488i
\(688\) −1216.91 128.183i −1.76877 0.186313i
\(689\) 187.509 0.272146
\(690\) −91.3086 540.180i −0.132331 0.782870i
\(691\) −164.485 + 68.1320i −0.238039 + 0.0985991i −0.498514 0.866882i \(-0.666121\pi\)
0.260475 + 0.965481i \(0.416121\pi\)
\(692\) −764.627 194.283i −1.10495 0.280756i
\(693\) −21.2549 + 14.0389i −0.0306708 + 0.0202582i
\(694\) 773.215 55.7195i 1.11414 0.0802875i
\(695\) −208.716 208.716i −0.300311 0.300311i
\(696\) −119.908 61.5248i −0.172282 0.0883977i
\(697\) 11.1382 + 11.1382i 0.0159802 + 0.0159802i
\(698\) 394.976 456.322i 0.565868 0.653757i
\(699\) 57.6877 + 602.140i 0.0825290 + 0.861431i
\(700\) −440.335 328.892i −0.629050 0.469846i
\(701\) 376.833 156.089i 0.537564 0.222666i −0.0973484 0.995250i \(-0.531036\pi\)
0.634913 + 0.772584i \(0.281036\pi\)
\(702\) 126.702 47.4709i 0.180488 0.0676224i
\(703\) −164.279 −0.233683
\(704\) 20.0178 + 18.5170i 0.0284344 + 0.0263025i
\(705\) 178.598 94.8522i 0.253330 0.134542i
\(706\) −243.572 + 122.087i −0.345002 + 0.172928i
\(707\) 187.631 77.7195i 0.265391 0.109929i
\(708\) −104.985 + 679.413i −0.148284 + 0.959622i
\(709\) 8.80554 + 3.64737i 0.0124197 + 0.00514439i 0.388885 0.921286i \(-0.372860\pi\)
−0.376465 + 0.926431i \(0.622860\pi\)
\(710\) 253.189 292.514i 0.356604 0.411991i
\(711\) −403.258 + 77.9835i −0.567170 + 0.109681i
\(712\) −966.878 + 673.631i −1.35797 + 0.946110i
\(713\) 1267.91 + 1267.91i 1.77828 + 1.77828i
\(714\) 14.6105 9.16308i 0.0204629 0.0128335i
\(715\) −0.848710 + 2.04897i −0.00118701 + 0.00286569i
\(716\) 396.432 + 100.729i 0.553676 + 0.140683i
\(717\) −879.996 726.122i −1.22733 1.01272i
\(718\) 788.917 + 262.105i 1.09877 + 0.365049i
\(719\) 422.265 0.587295 0.293648 0.955914i \(-0.405131\pi\)
0.293648 + 0.955914i \(0.405131\pi\)
\(720\) 25.7179 + 298.036i 0.0357193 + 0.413940i
\(721\) 771.041i 1.06940i
\(722\) −559.709 185.955i −0.775220 0.257555i
\(723\) 347.633 421.300i 0.480820 0.582711i
\(724\) 52.5471 + 88.3467i 0.0725789 + 0.122026i
\(725\) −107.311 44.4498i −0.148016 0.0613101i
\(726\) −614.127 + 385.155i −0.845904 + 0.530516i
\(727\) 884.581 884.581i 1.21676 1.21676i 0.247993 0.968762i \(-0.420229\pi\)
0.968762 0.247993i \(-0.0797711\pi\)
\(728\) 112.131 + 71.8070i 0.154027 + 0.0986360i
\(729\) −395.279 612.532i −0.542221 0.840236i
\(730\) −61.8422 + 71.4473i −0.0847153 + 0.0978730i
\(731\) 12.6639 30.5734i 0.0173241 0.0418241i
\(732\) 611.331 + 834.790i 0.835152 + 1.14042i
\(733\) 375.129 + 905.641i 0.511772 + 1.23553i 0.942852 + 0.333213i \(0.108133\pi\)
−0.431080 + 0.902314i \(0.641867\pi\)
\(734\) 565.732 283.566i 0.770752 0.386330i
\(735\) 14.2484 + 26.8284i 0.0193856 + 0.0365012i
\(736\) 1405.73 + 46.4203i 1.90995 + 0.0630710i
\(737\) 21.3337i 0.0289466i
\(738\) 649.747 + 84.7713i 0.880416 + 0.114866i
\(739\) 307.653 + 742.740i 0.416310 + 1.00506i 0.983408 + 0.181410i \(0.0580662\pi\)
−0.567098 + 0.823651i \(0.691934\pi\)
\(740\) 7.64241 + 52.7512i 0.0103276 + 0.0712854i
\(741\) 191.633 18.3593i 0.258613 0.0247763i
\(742\) 650.672 751.732i 0.876916 1.01312i
\(743\) 424.903 424.903i 0.571875 0.571875i −0.360777 0.932652i \(-0.617488\pi\)
0.932652 + 0.360777i \(0.117488\pi\)
\(744\) −633.763 746.313i −0.851833 1.00311i
\(745\) 235.679 235.679i 0.316348 0.316348i
\(746\) −498.553 + 35.9268i −0.668302 + 0.0481592i
\(747\) 288.981 190.873i 0.386855 0.255520i
\(748\) −0.633825 + 0.376988i −0.000847360 + 0.000503995i
\(749\) 502.361 + 1212.81i 0.670709 + 1.61924i
\(750\) 94.9059 + 561.462i 0.126541 + 0.748616i
\(751\) 252.843i 0.336675i 0.985729 + 0.168337i \(0.0538398\pi\)
−0.985729 + 0.168337i \(0.946160\pi\)
\(752\) 147.339 + 497.826i 0.195930 + 0.662003i
\(753\) 670.733 356.222i 0.890748 0.473071i
\(754\) 26.7051 + 8.87237i 0.0354179 + 0.0117671i
\(755\) −137.548 332.070i −0.182183 0.439828i
\(756\) 249.355 672.685i 0.329835 0.889794i
\(757\) −87.6710 + 211.657i −0.115814 + 0.279599i −0.971148 0.238477i \(-0.923352\pi\)
0.855334 + 0.518076i \(0.173352\pi\)
\(758\) 40.3659 + 560.155i 0.0532532 + 0.738991i
\(759\) 16.4518 53.7191i 0.0216756 0.0707761i
\(760\) −74.8947 + 418.982i −0.0985456 + 0.551292i
\(761\) 596.240 596.240i 0.783496 0.783496i −0.196923 0.980419i \(-0.563095\pi\)
0.980419 + 0.196923i \(0.0630949\pi\)
\(762\) −142.538 + 622.064i −0.187057 + 0.816357i
\(763\) 171.377 + 70.9867i 0.224610 + 0.0930364i
\(764\) 515.436 + 384.986i 0.674655 + 0.503909i
\(765\) −7.92614 1.62052i −0.0103610 0.00211833i
\(766\) −367.042 + 183.975i −0.479167 + 0.240176i
\(767\) 143.546i 0.187152i
\(768\) −762.981 87.6548i −0.993465 0.114134i
\(769\) 386.407 0.502480 0.251240 0.967925i \(-0.419162\pi\)
0.251240 + 0.967925i \(0.419162\pi\)
\(770\) 5.26932 + 10.5126i 0.00684327 + 0.0136528i
\(771\) 274.326 332.459i 0.355805 0.431204i
\(772\) 393.373 526.665i 0.509550 0.682208i
\(773\) −27.3769 + 66.0938i −0.0354165 + 0.0855029i −0.940598 0.339522i \(-0.889735\pi\)
0.905182 + 0.425025i \(0.139735\pi\)
\(774\) −357.838 1329.28i −0.462323 1.71741i
\(775\) −596.685 596.685i −0.769916 0.769916i
\(776\) 533.412 + 95.3495i 0.687387 + 0.122873i
\(777\) 37.4325 122.226i 0.0481757 0.157305i
\(778\) 943.127 67.9637i 1.21225 0.0873570i
\(779\) 861.330 + 356.775i 1.10569 + 0.457991i
\(780\) −14.8102 60.6805i −0.0189874 0.0777955i
\(781\) 36.6539 15.1826i 0.0469321 0.0194399i
\(782\) −11.9928 + 36.0974i −0.0153360 + 0.0461603i
\(783\) 16.0655 150.764i 0.0205179 0.192547i
\(784\) −74.7819 + 22.1328i −0.0953850 + 0.0282306i
\(785\) −395.936 −0.504377
\(786\) 138.603 + 819.972i 0.176339 + 1.04322i
\(787\) −980.553 + 406.158i −1.24594 + 0.516084i −0.905565 0.424207i \(-0.860553\pi\)
−0.340372 + 0.940291i \(0.610553\pi\)
\(788\) 79.2267 + 133.203i 0.100542 + 0.169039i
\(789\) 43.6134 4.17836i 0.0552768 0.00529577i
\(790\) 13.6283 + 189.119i 0.0172511 + 0.239391i
\(791\) −544.594 544.594i −0.688488 0.688488i
\(792\) −11.3378 + 28.5055i −0.0143155 + 0.0359918i
\(793\) −152.768 152.768i −0.192646 0.192646i
\(794\) 83.4377 + 72.2206i 0.105085 + 0.0909580i
\(795\) −464.261 + 44.4783i −0.583976 + 0.0559475i
\(796\) 194.445 28.1706i 0.244278 0.0353902i
\(797\) −612.225 + 253.592i −0.768162 + 0.318183i −0.732128 0.681167i \(-0.761473\pi\)
−0.0360343 + 0.999351i \(0.511473\pi\)
\(798\) 591.379 831.973i 0.741076 1.04257i
\(799\) −14.0406 −0.0175727
\(800\) −661.542 21.8456i −0.826927 0.0273070i
\(801\) −1098.34 742.378i −1.37122 0.926815i
\(802\) 340.979 + 680.274i 0.425160 + 0.848222i
\(803\) −8.95283 + 3.70839i −0.0111492 + 0.00461816i
\(804\) 354.995 + 484.756i 0.441536 + 0.602930i
\(805\) 560.359 + 232.108i 0.696098 + 0.288333i
\(806\) 154.576 + 133.795i 0.191781 + 0.165999i
\(807\) 28.1814 92.0192i 0.0349212 0.114026i
\(808\) 131.902 205.973i 0.163245 0.254917i
\(809\) −313.261 313.261i −0.387220 0.387220i 0.486475 0.873695i \(-0.338283\pi\)
−0.873695 + 0.486475i \(0.838283\pi\)
\(810\) −302.447 + 147.590i −0.373392 + 0.182210i
\(811\) −142.266 + 343.461i −0.175421 + 0.423503i −0.986996 0.160745i \(-0.948610\pi\)
0.811575 + 0.584248i \(0.198610\pi\)
\(812\) 128.239 76.2743i 0.157930 0.0939339i
\(813\) 474.652 575.236i 0.583828 0.707548i
\(814\) −1.72342 + 5.18737i −0.00211723 + 0.00637268i
\(815\) 300.120 0.368246
\(816\) 8.12900 19.1131i 0.00996201 0.0234229i
\(817\) 1958.63i 2.39734i
\(818\) 24.3529 73.3003i 0.0297713 0.0896091i
\(819\) −30.0057 + 146.761i −0.0366369 + 0.179195i
\(820\) 74.4930 293.177i 0.0908451 0.357533i
\(821\) 683.281 + 283.024i 0.832255 + 0.344731i 0.757795 0.652493i \(-0.226277\pi\)
0.0744599 + 0.997224i \(0.476277\pi\)
\(822\) 1179.82 739.932i 1.43530 0.900160i
\(823\) 441.372 441.372i 0.536296 0.536296i −0.386143 0.922439i \(-0.626193\pi\)
0.922439 + 0.386143i \(0.126193\pi\)
\(824\) 530.823 + 761.903i 0.644203 + 0.924639i
\(825\) −7.74229 + 25.2805i −0.00938460 + 0.0306430i
\(826\) −575.483 498.117i −0.696711 0.603047i
\(827\) 10.7367 25.9207i 0.0129827 0.0313430i −0.917255 0.398300i \(-0.869600\pi\)
0.930238 + 0.366957i \(0.119600\pi\)
\(828\) 520.065 + 1494.39i 0.628098 + 1.80482i
\(829\) −387.431 935.342i −0.467348 1.12828i −0.965317 0.261082i \(-0.915921\pi\)
0.497969 0.867195i \(-0.334079\pi\)
\(830\) −71.6415 142.929i −0.0863151 0.172204i
\(831\) −903.330 + 479.753i −1.08704 + 0.577320i
\(832\) 160.238 6.24081i 0.192594 0.00750097i
\(833\) 2.10913i 0.00253197i
\(834\) 694.862 + 493.918i 0.833168 + 0.592228i
\(835\) 96.4242 + 232.789i 0.115478 + 0.278789i
\(836\) −26.1197 + 34.9702i −0.0312436 + 0.0418304i
\(837\) 526.979 967.249i 0.629604 1.15561i
\(838\) −180.104 155.891i −0.214921 0.186028i
\(839\) 701.963 701.963i 0.836666 0.836666i −0.151753 0.988419i \(-0.548492\pi\)
0.988419 + 0.151753i \(0.0484917\pi\)
\(840\) −294.664 151.192i −0.350790 0.179990i
\(841\) −572.379 + 572.379i −0.680594 + 0.680594i
\(842\) 73.5490 + 1020.63i 0.0873504 + 1.21215i
\(843\) 191.095 18.3077i 0.226684 0.0217174i
\(844\) 8.65862 34.0771i 0.0102590 0.0403757i
\(845\) −129.361 312.305i −0.153090 0.369592i
\(846\) −462.959 + 356.098i −0.547232 + 0.420919i
\(847\) 802.563i 0.947536i
\(848\) 125.431 1190.78i 0.147914 1.40422i
\(849\) −42.3068 79.6598i −0.0498313 0.0938278i
\(850\) 5.64387 16.9876i 0.00663985 0.0199854i
\(851\) 107.893 + 260.476i 0.126783 + 0.306082i
\(852\) −580.232 + 954.913i −0.681024 + 1.12079i
\(853\) −493.096 + 1190.44i −0.578073 + 1.39559i 0.316467 + 0.948604i \(0.397503\pi\)
−0.894540 + 0.446988i \(0.852497\pi\)
\(854\) −1142.57 + 82.3362i −1.33791 + 0.0964124i
\(855\) −470.116 + 90.9129i −0.549843 + 0.106331i
\(856\) 1331.36 + 852.583i 1.55533 + 0.996009i
\(857\) 485.381 485.381i 0.566372 0.566372i −0.364738 0.931110i \(-0.618842\pi\)
0.931110 + 0.364738i \(0.118842\pi\)
\(858\) 1.43066 6.24369i 0.00166743 0.00727703i
\(859\) −1010.06 418.380i −1.17585 0.487055i −0.292731 0.956195i \(-0.594564\pi\)
−0.883124 + 0.469140i \(0.844564\pi\)
\(860\) −628.930 + 91.1172i −0.731314 + 0.105950i
\(861\) −461.708 + 559.549i −0.536246 + 0.649883i
\(862\) −72.3616 144.366i −0.0839462 0.167478i
\(863\) 341.486i 0.395696i 0.980233 + 0.197848i \(0.0633953\pi\)
−0.980233 + 0.197848i \(0.936605\pi\)
\(864\) −216.710 836.381i −0.250821 0.968033i
\(865\) −409.725 −0.473671
\(866\) −1366.40 + 684.892i −1.57783 + 0.790868i
\(867\) −668.300 551.443i −0.770819 0.636036i
\(868\) 1072.78 155.421i 1.23592 0.179056i
\(869\) −7.44114 + 17.9645i −0.00856288 + 0.0206726i
\(870\) −68.2249 15.6328i −0.0784195 0.0179688i
\(871\) −88.7110 88.7110i −0.101850 0.101850i
\(872\) 218.217 47.8391i 0.250249 0.0548614i
\(873\) 115.743 + 598.512i 0.132580 + 0.685580i
\(874\) 161.814 + 2245.48i 0.185142 + 2.56920i
\(875\) −582.435 241.253i −0.665640 0.275717i
\(876\) 141.723 233.240i 0.161785 0.266256i
\(877\) 1520.59 629.849i 1.73385 0.718186i 0.734645 0.678452i \(-0.237349\pi\)
0.999210 0.0397340i \(-0.0126510\pi\)
\(878\) 889.738 + 295.602i 1.01337 + 0.336676i
\(879\) −165.978 + 88.1497i −0.188825 + 0.100284i
\(880\) 12.4443 + 6.76037i 0.0141412 + 0.00768224i
\(881\) −203.840 −0.231374 −0.115687 0.993286i \(-0.536907\pi\)
−0.115687 + 0.993286i \(0.536907\pi\)
\(882\) −53.4919 69.5442i −0.0606484 0.0788483i
\(883\) −319.448 + 132.320i −0.361776 + 0.149852i −0.556165 0.831072i \(-0.687728\pi\)
0.194389 + 0.980925i \(0.437728\pi\)
\(884\) −1.06800 + 4.20323i −0.00120814 + 0.00475479i
\(885\) 34.0500 + 355.411i 0.0384746 + 0.401595i
\(886\) −1361.30 + 98.0982i −1.53646 + 0.110720i
\(887\) 295.914 + 295.914i 0.333612 + 0.333612i 0.853957 0.520344i \(-0.174196\pi\)
−0.520344 + 0.853957i \(0.674196\pi\)
\(888\) −47.1578 146.548i −0.0531057 0.165032i
\(889\) −499.605 499.605i −0.561985 0.561985i
\(890\) −400.526 + 462.734i −0.450029 + 0.519926i
\(891\) −34.5102 0.367452i −0.0387320 0.000412404i
\(892\) −280.713 + 375.831i −0.314701 + 0.421335i
\(893\) −767.758 + 318.016i −0.859751 + 0.356120i
\(894\) −557.726 + 784.629i −0.623855 + 0.877661i
\(895\) 212.428 0.237350
\(896\) 531.020 664.058i 0.592656 0.741137i
\(897\) −154.967 291.789i −0.172762 0.325294i
\(898\) −161.825 + 81.1129i −0.180206 + 0.0903262i
\(899\) 211.650 87.6681i 0.235428 0.0975174i
\(900\) −244.745 703.270i −0.271939 0.781411i
\(901\) 29.9169 + 12.3920i 0.0332041 + 0.0137536i
\(902\) 20.3018 23.4550i 0.0225075 0.0260033i
\(903\) 1457.25 + 446.292i 1.61379 + 0.494233i
\(904\) −913.065 163.214i −1.01003 0.180547i
\(905\) 37.7490 + 37.7490i 0.0417116 + 0.0417116i
\(906\) 551.567 + 879.470i 0.608794 + 0.970718i
\(907\) −339.651 + 819.990i −0.374477 + 0.904068i 0.618502 + 0.785783i \(0.287740\pi\)
−0.992980 + 0.118285i \(0.962260\pi\)
\(908\) 249.192 980.728i 0.274441 1.08010i
\(909\) 269.584 + 55.1172i 0.296572 + 0.0606349i
\(910\) 65.6255 + 21.8031i 0.0721159 + 0.0239594i
\(911\) −1069.12 −1.17357 −0.586786 0.809742i \(-0.699607\pi\)
−0.586786 + 0.809742i \(0.699607\pi\)
\(912\) 11.5984 1229.25i 0.0127175 1.34786i
\(913\) 16.3957i 0.0179581i
\(914\) −1055.00 350.508i −1.15427 0.383487i
\(915\) 414.482 + 342.007i 0.452986 + 0.373778i
\(916\) −774.179 + 460.468i −0.845174 + 0.502695i
\(917\) −850.602 352.331i −0.927592 0.384221i
\(918\) 23.3525 + 0.799491i 0.0254385 + 0.000870906i
\(919\) 563.193 563.193i 0.612833 0.612833i −0.330851 0.943683i \(-0.607336\pi\)
0.943683 + 0.330851i \(0.107336\pi\)
\(920\) 713.513 156.422i 0.775557 0.170023i
\(921\) 3.87112 + 1.18555i 0.00420317 + 0.00128725i
\(922\) −788.780 + 911.291i −0.855510 + 0.988385i
\(923\) 89.2837 215.550i 0.0967321 0.233532i
\(924\) −20.0668 27.4017i −0.0217173 0.0296556i
\(925\) −50.7749 122.581i −0.0548918 0.132520i
\(926\) 203.208 101.855i 0.219447 0.109995i
\(927\) −584.996 + 865.499i −0.631064 + 0.933656i
\(928\) 74.2081 163.656i 0.0799656 0.176354i
\(929\) 1001.53i 1.07808i −0.842282 0.539038i \(-0.818788\pi\)
0.842282 0.539038i \(-0.181212\pi\)
\(930\) −414.457 294.602i −0.445653 0.316777i
\(931\) −47.7713 115.330i −0.0513118 0.123878i
\(932\) −798.197 + 115.640i −0.856434 + 0.124077i
\(933\) 138.279 + 1443.35i 0.148209 + 1.54700i
\(934\) 1168.38 1349.85i 1.25094 1.44523i
\(935\) −0.270822 + 0.270822i −0.000289649 + 0.000289649i
\(936\) 71.3875 + 165.679i 0.0762687 + 0.177008i
\(937\) 665.490 665.490i 0.710235 0.710235i −0.256349 0.966584i \(-0.582520\pi\)
0.966584 + 0.256349i \(0.0825197\pi\)
\(938\) −663.482 + 47.8119i −0.707337 + 0.0509722i
\(939\) 57.1507 + 596.534i 0.0608633 + 0.635287i
\(940\) 137.834 + 231.738i 0.146632 + 0.246530i
\(941\) −347.922 839.958i −0.369737 0.892623i −0.993793 0.111244i \(-0.964516\pi\)
0.624056 0.781379i \(-0.285484\pi\)
\(942\) 1127.56 190.596i 1.19699 0.202331i
\(943\) 1600.02i 1.69673i
\(944\) −911.592 96.0226i −0.965669 0.101719i
\(945\) 39.4796 370.489i 0.0417774 0.392052i
\(946\) −61.8467 20.5476i −0.0653771 0.0217205i
\(947\) −246.808 595.848i −0.260621 0.629195i 0.738356 0.674411i \(-0.235602\pi\)
−0.998977 + 0.0452158i \(0.985602\pi\)
\(948\) −129.850 532.022i −0.136972 0.561204i
\(949\) −21.8078 + 52.6487i −0.0229798 + 0.0554781i
\(950\) −76.1507 1056.74i −0.0801586 1.11235i
\(951\) 1243.02 + 380.682i 1.30707 + 0.400297i
\(952\) 13.1449 + 18.8672i 0.0138077 + 0.0198185i
\(953\) 9.75518 9.75518i 0.0102363 0.0102363i −0.701970 0.712206i \(-0.747696\pi\)
0.712206 + 0.701970i \(0.247696\pi\)
\(954\) 1300.73 350.153i 1.36345 0.367037i
\(955\) 308.685 + 127.861i 0.323230 + 0.133886i
\(956\) 910.308 1218.76i 0.952205 1.27485i
\(957\) −5.53642 4.56833i −0.00578518 0.00477360i
\(958\) −865.886 + 434.014i −0.903847 + 0.453042i
\(959\) 1541.83i 1.60774i
\(960\) −395.260 + 53.4613i −0.411729 + 0.0556889i
\(961\) 703.303 0.731845
\(962\) 14.4040 + 28.7369i 0.0149730 + 0.0298720i
\(963\) −356.265 + 1742.53i −0.369953 + 1.80948i
\(964\) 583.484 + 435.812i 0.605274 + 0.452087i
\(965\) 130.647 315.409i 0.135385 0.326849i
\(966\) −1707.55 391.262i −1.76765 0.405033i
\(967\) 797.727 + 797.727i 0.824950 + 0.824950i 0.986813 0.161863i \(-0.0517502\pi\)
−0.161863 + 0.986813i \(0.551750\pi\)
\(968\) −552.525 793.052i −0.570790 0.819268i
\(969\) 31.7881 + 9.73530i 0.0328051 + 0.0100467i
\(970\) 280.689 20.2271i 0.289370 0.0208526i
\(971\) 1064.95 + 441.118i 1.09676 + 0.454292i 0.856358 0.516382i \(-0.172721\pi\)
0.240400 + 0.970674i \(0.422721\pi\)
\(972\) 790.276 565.905i 0.813041 0.582207i
\(973\) −871.995 + 361.192i −0.896192 + 0.371215i
\(974\) −368.621 + 1109.52i −0.378461 + 1.13914i
\(975\) 72.9284 + 137.317i 0.0747984 + 0.140838i
\(976\) −1072.35 + 867.964i −1.09872 + 0.889308i
\(977\) −757.558 −0.775392 −0.387696 0.921787i \(-0.626729\pi\)
−0.387696 + 0.921787i \(0.626729\pi\)
\(978\) −854.696 + 144.472i −0.873922 + 0.147722i
\(979\) −57.9837 + 24.0177i −0.0592275 + 0.0245328i
\(980\) −34.8109 + 20.7050i −0.0355214 + 0.0211275i
\(981\) 138.514 + 209.709i 0.141196 + 0.213770i
\(982\) −63.6970 883.918i −0.0648646 0.900121i
\(983\) −515.745 515.745i −0.524664 0.524664i 0.394312 0.918977i \(-0.370983\pi\)
−0.918977 + 0.394312i \(0.870983\pi\)
\(984\) −71.0147 + 870.781i −0.0721694 + 0.884940i
\(985\) 56.9152 + 56.9152i 0.0577819 + 0.0577819i
\(986\) 3.67443 + 3.18045i 0.00372660 + 0.00322561i
\(987\) −61.6681 643.687i −0.0624803 0.652165i
\(988\) 36.8027 + 254.028i 0.0372497 + 0.257113i
\(989\) −3105.54 + 1286.36i −3.14008 + 1.30067i
\(990\) −2.06119 + 15.7984i −0.00208201 + 0.0159580i
\(991\) −945.010 −0.953592 −0.476796 0.879014i \(-0.658202\pi\)
−0.476796 + 0.879014i \(0.658202\pi\)
\(992\) 953.069 892.136i 0.960755 0.899331i
\(993\) −7.14961 + 3.79711i −0.00720001 + 0.00382388i
\(994\) −554.328 1105.92i −0.557674 1.11260i
\(995\) 94.2717 39.0486i 0.0947454 0.0392448i
\(996\) 272.827 + 372.554i 0.273923 + 0.374050i
\(997\) 728.420 + 301.722i 0.730612 + 0.302629i 0.716804 0.697275i \(-0.245604\pi\)
0.0138087 + 0.999905i \(0.495604\pi\)
\(998\) −235.998 204.271i −0.236471 0.204681i
\(999\) 134.753 108.800i 0.134888 0.108908i
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 96.3.p.a.5.11 120
3.2 odd 2 inner 96.3.p.a.5.20 yes 120
4.3 odd 2 384.3.p.a.113.7 120
12.11 even 2 384.3.p.a.113.15 120
32.13 even 8 inner 96.3.p.a.77.20 yes 120
32.19 odd 8 384.3.p.a.17.15 120
96.77 odd 8 inner 96.3.p.a.77.11 yes 120
96.83 even 8 384.3.p.a.17.7 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.3.p.a.5.11 120 1.1 even 1 trivial
96.3.p.a.5.20 yes 120 3.2 odd 2 inner
96.3.p.a.77.11 yes 120 96.77 odd 8 inner
96.3.p.a.77.20 yes 120 32.13 even 8 inner
384.3.p.a.17.7 120 96.83 even 8
384.3.p.a.17.15 120 32.19 odd 8
384.3.p.a.113.7 120 4.3 odd 2
384.3.p.a.113.15 120 12.11 even 2