Properties

Label 76.5.l.a.23.14
Level $76$
Weight $5$
Character 76.23
Analytic conductor $7.856$
Analytic rank $0$
Dimension $228$
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] = [76,5,Mod(23,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.23");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.l (of order \(18\), degree \(6\), 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: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(228\)
Relative dimension: \(38\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 23.14
Character \(\chi\) \(=\) 76.23
Dual form 76.5.l.a.43.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50056 - 3.70787i) q^{2} +(-3.32006 + 0.585416i) q^{3} +(-11.4966 + 11.1278i) q^{4} +(31.7438 - 26.6362i) q^{5} +(7.15261 + 11.4319i) q^{6} +(51.6354 + 29.8117i) q^{7} +(58.5118 + 25.9300i) q^{8} +(-65.4350 + 23.8164i) q^{9} +O(q^{10})\) \(q+(-1.50056 - 3.70787i) q^{2} +(-3.32006 + 0.585416i) q^{3} +(-11.4966 + 11.1278i) q^{4} +(31.7438 - 26.6362i) q^{5} +(7.15261 + 11.4319i) q^{6} +(51.6354 + 29.8117i) q^{7} +(58.5118 + 25.9300i) q^{8} +(-65.4350 + 23.8164i) q^{9} +(-146.397 - 77.7326i) q^{10} +(66.2459 - 38.2471i) q^{11} +(31.6551 - 43.6753i) q^{12} +(47.6602 - 270.294i) q^{13} +(33.0558 - 236.192i) q^{14} +(-89.7981 + 107.017i) q^{15} +(8.34452 - 255.864i) q^{16} +(-219.584 - 79.9221i) q^{17} +(186.497 + 206.887i) q^{18} +(65.3930 - 355.028i) q^{19} +(-68.5442 + 659.465i) q^{20} +(-188.885 - 68.7485i) q^{21} +(-241.221 - 188.239i) q^{22} +(-424.356 + 505.727i) q^{23} +(-209.443 - 51.8355i) q^{24} +(189.651 - 1075.56i) q^{25} +(-1073.73 + 228.876i) q^{26} +(439.794 - 253.915i) q^{27} +(-925.371 + 231.854i) q^{28} +(770.112 - 280.298i) q^{29} +(531.554 + 172.374i) q^{30} +(956.138 + 552.027i) q^{31} +(-961.232 + 353.000i) q^{32} +(-197.550 + 165.764i) q^{33} +(33.1591 + 934.118i) q^{34} +(2433.18 - 429.035i) q^{35} +(487.257 - 1001.96i) q^{36} +1009.86 q^{37} +(-1414.52 + 290.273i) q^{38} +925.294i q^{39} +(2548.07 - 735.416i) q^{40} +(-198.738 - 1127.10i) q^{41} +(28.5233 + 803.523i) q^{42} +(-1941.94 - 2314.31i) q^{43} +(-335.998 + 1176.88i) q^{44} +(-1442.78 + 2498.96i) q^{45} +(2511.94 + 814.580i) q^{46} +(580.185 + 1594.05i) q^{47} +(122.083 + 854.369i) q^{48} +(576.977 + 999.354i) q^{49} +(-4272.64 + 910.751i) q^{50} +(775.821 + 136.798i) q^{51} +(2459.85 + 3637.82i) q^{52} +(990.107 + 830.798i) q^{53} +(-1601.43 - 1249.68i) q^{54} +(1084.14 - 2978.65i) q^{55} +(2248.26 + 3083.25i) q^{56} +(-9.26962 + 1217.00i) q^{57} +(-2194.91 - 2434.87i) q^{58} +(-1220.87 + 3354.30i) q^{59} +(-158.491 - 2229.59i) q^{60} +(-20.3696 - 17.0922i) q^{61} +(612.098 - 4373.59i) q^{62} +(-4088.77 - 720.961i) q^{63} +(2751.27 + 3034.43i) q^{64} +(-5686.70 - 9849.65i) q^{65} +(911.068 + 483.750i) q^{66} +(-746.531 - 2051.08i) q^{67} +(3413.83 - 1524.65i) q^{68} +(1112.83 - 1927.47i) q^{69} +(-5241.94 - 8378.11i) q^{70} +(3890.82 + 4636.90i) q^{71} +(-4446.28 - 303.191i) q^{72} +(1670.93 + 9476.31i) q^{73} +(-1515.36 - 3744.43i) q^{74} +3681.97i q^{75} +(3198.88 + 4809.30i) q^{76} +4560.84 q^{77} +(3430.87 - 1388.46i) q^{78} +(-5574.82 + 982.992i) q^{79} +(-6550.36 - 8344.36i) q^{80} +(3009.29 - 2525.10i) q^{81} +(-3880.93 + 2428.18i) q^{82} +(-3635.44 - 2098.92i) q^{83} +(2936.56 - 1311.50i) q^{84} +(-9099.26 + 3311.86i) q^{85} +(-5667.17 + 10673.2i) q^{86} +(-2392.73 + 1381.44i) q^{87} +(4867.92 - 520.149i) q^{88} +(-47.9543 + 271.962i) q^{89} +(11430.8 + 1599.78i) q^{90} +(10518.9 - 12535.9i) q^{91} +(-748.973 - 10536.3i) q^{92} +(-3497.60 - 1273.02i) q^{93} +(5039.91 - 4543.22i) q^{94} +(-7380.78 - 13011.8i) q^{95} +(2984.70 - 1734.70i) q^{96} +(12941.3 + 4710.26i) q^{97} +(2839.68 - 3638.95i) q^{98} +(-3423.89 + 4080.44i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9} - 453 q^{10} - 3 q^{12} + 516 q^{13} + 81 q^{14} - 720 q^{16} - 12 q^{17} - 12 q^{18} - 1182 q^{20} - 930 q^{21} - 54 q^{22} - 2664 q^{24} - 12 q^{25} - 3099 q^{26} - 4824 q^{28} - 12 q^{29} + 5814 q^{30} + 7419 q^{32} + 1542 q^{33} + 6912 q^{34} + 8547 q^{36} - 24 q^{37} - 1536 q^{38} - 6942 q^{40} + 6396 q^{41} - 18855 q^{42} - 1143 q^{44} - 6 q^{45} - 1488 q^{46} + 6093 q^{48} + 26748 q^{49} + 8070 q^{50} - 12591 q^{52} + 2436 q^{53} - 7365 q^{54} - 14418 q^{56} - 12 q^{57} + 8268 q^{58} + 34632 q^{60} - 31068 q^{61} + 27396 q^{62} + 4575 q^{64} + 3594 q^{65} - 29556 q^{66} - 22782 q^{68} + 29370 q^{69} - 71541 q^{70} - 30174 q^{72} - 6348 q^{73} - 417 q^{74} + 43194 q^{76} - 50436 q^{77} + 45537 q^{78} + 30081 q^{80} - 41994 q^{81} + 72219 q^{82} + 13779 q^{84} - 59244 q^{85} + 19200 q^{86} - 22395 q^{88} + 1860 q^{89} + 45594 q^{90} - 64140 q^{92} + 59118 q^{93} - 55590 q^{94} - 98646 q^{96} - 5556 q^{97} - 52215 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50056 3.70787i −0.375141 0.926968i
\(3\) −3.32006 + 0.585416i −0.368896 + 0.0650463i −0.355023 0.934857i \(-0.615527\pi\)
−0.0138726 + 0.999904i \(0.504416\pi\)
\(4\) −11.4966 + 11.1278i −0.718539 + 0.695487i
\(5\) 31.7438 26.6362i 1.26975 1.06545i 0.275181 0.961392i \(-0.411262\pi\)
0.994571 0.104056i \(-0.0331822\pi\)
\(6\) 7.15261 + 11.4319i 0.198684 + 0.317553i
\(7\) 51.6354 + 29.8117i 1.05378 + 0.608402i 0.923706 0.383101i \(-0.125144\pi\)
0.130078 + 0.991504i \(0.458477\pi\)
\(8\) 58.5118 + 25.9300i 0.914247 + 0.405157i
\(9\) −65.4350 + 23.8164i −0.807840 + 0.294030i
\(10\) −146.397 77.7326i −1.46397 0.777326i
\(11\) 66.2459 38.2471i 0.547487 0.316092i −0.200621 0.979669i \(-0.564296\pi\)
0.748108 + 0.663577i \(0.230963\pi\)
\(12\) 31.6551 43.6753i 0.219827 0.303300i
\(13\) 47.6602 270.294i 0.282013 1.59937i −0.433752 0.901032i \(-0.642811\pi\)
0.715765 0.698341i \(-0.246078\pi\)
\(14\) 33.0558 236.192i 0.168652 1.20506i
\(15\) −89.7981 + 107.017i −0.399103 + 0.475632i
\(16\) 8.34452 255.864i 0.0325958 0.999469i
\(17\) −219.584 79.9221i −0.759807 0.276547i −0.0670806 0.997748i \(-0.521368\pi\)
−0.692727 + 0.721200i \(0.743591\pi\)
\(18\) 186.497 + 206.887i 0.575610 + 0.638539i
\(19\) 65.3930 355.028i 0.181144 0.983457i
\(20\) −68.5442 + 659.465i −0.171361 + 1.64866i
\(21\) −188.885 68.7485i −0.428311 0.155892i
\(22\) −241.221 188.239i −0.498391 0.388924i
\(23\) −424.356 + 505.727i −0.802184 + 0.956006i −0.999705 0.0242926i \(-0.992267\pi\)
0.197521 + 0.980299i \(0.436711\pi\)
\(24\) −209.443 51.8355i −0.363616 0.0899922i
\(25\) 189.651 1075.56i 0.303442 1.72090i
\(26\) −1073.73 + 228.876i −1.58836 + 0.338574i
\(27\) 439.794 253.915i 0.603285 0.348306i
\(28\) −925.371 + 231.854i −1.18032 + 0.295732i
\(29\) 770.112 280.298i 0.915709 0.333291i 0.159179 0.987250i \(-0.449115\pi\)
0.756530 + 0.653959i \(0.226893\pi\)
\(30\) 531.554 + 172.374i 0.590615 + 0.191526i
\(31\) 956.138 + 552.027i 0.994941 + 0.574430i 0.906748 0.421674i \(-0.138557\pi\)
0.0881936 + 0.996103i \(0.471891\pi\)
\(32\) −961.232 + 353.000i −0.938703 + 0.344726i
\(33\) −197.550 + 165.764i −0.181405 + 0.152217i
\(34\) 33.1591 + 934.118i 0.0286843 + 0.808061i
\(35\) 2433.18 429.035i 1.98627 0.350232i
\(36\) 487.257 1001.96i 0.375970 0.773113i
\(37\) 1009.86 0.737662 0.368831 0.929497i \(-0.379758\pi\)
0.368831 + 0.929497i \(0.379758\pi\)
\(38\) −1414.52 + 290.273i −0.979587 + 0.201020i
\(39\) 925.294i 0.608346i
\(40\) 2548.07 735.416i 1.59254 0.459635i
\(41\) −198.738 1127.10i −0.118226 0.670494i −0.985102 0.171970i \(-0.944987\pi\)
0.866876 0.498524i \(-0.166124\pi\)
\(42\) 28.5233 + 803.523i 0.0161696 + 0.455512i
\(43\) −1941.94 2314.31i −1.05026 1.25166i −0.966905 0.255135i \(-0.917880\pi\)
−0.0833580 0.996520i \(-0.526564\pi\)
\(44\) −335.998 + 1176.88i −0.173553 + 0.607894i
\(45\) −1442.78 + 2498.96i −0.712483 + 1.23406i
\(46\) 2511.94 + 814.580i 1.18712 + 0.384962i
\(47\) 580.185 + 1594.05i 0.262646 + 0.721615i 0.998987 + 0.0450035i \(0.0143299\pi\)
−0.736341 + 0.676611i \(0.763448\pi\)
\(48\) 122.083 + 854.369i 0.0529873 + 0.370820i
\(49\) 576.977 + 999.354i 0.240307 + 0.416224i
\(50\) −4272.64 + 910.751i −1.70906 + 0.364301i
\(51\) 775.821 + 136.798i 0.298278 + 0.0525945i
\(52\) 2459.85 + 3637.82i 0.909706 + 1.34535i
\(53\) 990.107 + 830.798i 0.352477 + 0.295763i 0.801784 0.597614i \(-0.203885\pi\)
−0.449307 + 0.893377i \(0.648329\pi\)
\(54\) −1601.43 1249.68i −0.549186 0.428561i
\(55\) 1084.14 2978.65i 0.358393 0.984677i
\(56\) 2248.26 + 3083.25i 0.716921 + 0.983178i
\(57\) −9.26962 + 1217.00i −0.00285307 + 0.374576i
\(58\) −2194.91 2434.87i −0.652470 0.723802i
\(59\) −1220.87 + 3354.30i −0.350723 + 0.963603i 0.631416 + 0.775444i \(0.282474\pi\)
−0.982139 + 0.188158i \(0.939748\pi\)
\(60\) −158.491 2229.59i −0.0440252 0.619331i
\(61\) −20.3696 17.0922i −0.00547424 0.00459343i 0.640046 0.768336i \(-0.278915\pi\)
−0.645521 + 0.763743i \(0.723360\pi\)
\(62\) 612.098 4373.59i 0.159235 1.13777i
\(63\) −4088.77 720.961i −1.03018 0.181648i
\(64\) 2751.27 + 3034.43i 0.671696 + 0.740827i
\(65\) −5686.70 9849.65i −1.34596 2.33128i
\(66\) 911.068 + 483.750i 0.209152 + 0.111054i
\(67\) −746.531 2051.08i −0.166302 0.456912i 0.828348 0.560214i \(-0.189281\pi\)
−0.994650 + 0.103302i \(0.967059\pi\)
\(68\) 3413.83 1524.65i 0.738286 0.329726i
\(69\) 1112.83 1927.47i 0.233738 0.404846i
\(70\) −5241.94 8378.11i −1.06978 1.70982i
\(71\) 3890.82 + 4636.90i 0.771835 + 0.919837i 0.998534 0.0541279i \(-0.0172379\pi\)
−0.226699 + 0.973965i \(0.572793\pi\)
\(72\) −4446.28 303.191i −0.857693 0.0584859i
\(73\) 1670.93 + 9476.31i 0.313554 + 1.77825i 0.580215 + 0.814463i \(0.302968\pi\)
−0.266661 + 0.963790i \(0.585920\pi\)
\(74\) −1515.36 3744.43i −0.276727 0.683789i
\(75\) 3681.97i 0.654572i
\(76\) 3198.88 + 4809.30i 0.553822 + 0.832635i
\(77\) 4560.84 0.769243
\(78\) 3430.87 1388.46i 0.563917 0.228215i
\(79\) −5574.82 + 982.992i −0.893258 + 0.157506i −0.601392 0.798954i \(-0.705387\pi\)
−0.291866 + 0.956459i \(0.594276\pi\)
\(80\) −6550.36 8344.36i −1.02349 1.30381i
\(81\) 3009.29 2525.10i 0.458664 0.384865i
\(82\) −3880.93 + 2428.18i −0.577175 + 0.361122i
\(83\) −3635.44 2098.92i −0.527716 0.304677i 0.212370 0.977189i \(-0.431882\pi\)
−0.740086 + 0.672512i \(0.765215\pi\)
\(84\) 2936.56 1311.50i 0.416179 0.185870i
\(85\) −9099.26 + 3311.86i −1.25941 + 0.458389i
\(86\) −5667.17 + 10673.2i −0.766247 + 1.44311i
\(87\) −2392.73 + 1381.44i −0.316122 + 0.182513i
\(88\) 4867.92 520.149i 0.628605 0.0671680i
\(89\) −47.9543 + 271.962i −0.00605407 + 0.0343343i −0.987685 0.156455i \(-0.949994\pi\)
0.981631 + 0.190789i \(0.0611046\pi\)
\(90\) 11430.8 + 1599.78i 1.41121 + 0.197504i
\(91\) 10518.9 12535.9i 1.27024 1.51382i
\(92\) −748.973 10536.3i −0.0884893 1.24484i
\(93\) −3497.60 1273.02i −0.404394 0.147187i
\(94\) 5039.91 4543.22i 0.570384 0.514172i
\(95\) −7380.78 13011.8i −0.817814 1.44175i
\(96\) 2984.70 1734.70i 0.323860 0.188227i
\(97\) 12941.3 + 4710.26i 1.37542 + 0.500612i 0.920787 0.390067i \(-0.127548\pi\)
0.454633 + 0.890679i \(0.349770\pi\)
\(98\) 2839.68 3638.95i 0.295677 0.378899i
\(99\) −3423.89 + 4080.44i −0.349341 + 0.416329i
\(100\) 9788.32 + 14475.8i 0.978832 + 1.44758i
\(101\) −604.527 + 3428.44i −0.0592616 + 0.336089i −0.999995 0.00305697i \(-0.999027\pi\)
0.940734 + 0.339146i \(0.110138\pi\)
\(102\) −656.939 3081.92i −0.0631429 0.296224i
\(103\) −2251.42 + 1299.86i −0.212218 + 0.122524i −0.602342 0.798238i \(-0.705766\pi\)
0.390124 + 0.920762i \(0.372432\pi\)
\(104\) 9797.42 14579.6i 0.905826 1.34796i
\(105\) −7827.13 + 2848.84i −0.709944 + 0.258398i
\(106\) 1594.77 4917.85i 0.141934 0.437687i
\(107\) −3448.72 1991.12i −0.301224 0.173912i 0.341768 0.939784i \(-0.388974\pi\)
−0.642993 + 0.765872i \(0.722307\pi\)
\(108\) −2230.63 + 7813.11i −0.191241 + 0.669848i
\(109\) −1891.56 + 1587.20i −0.159209 + 0.133592i −0.718912 0.695101i \(-0.755360\pi\)
0.559703 + 0.828693i \(0.310915\pi\)
\(110\) −12671.3 + 449.801i −1.04721 + 0.0371737i
\(111\) −3352.79 + 591.188i −0.272120 + 0.0479821i
\(112\) 8058.62 12962.9i 0.642428 1.03339i
\(113\) −5364.85 −0.420146 −0.210073 0.977686i \(-0.567370\pi\)
−0.210073 + 0.977686i \(0.567370\pi\)
\(114\) 4526.38 1791.81i 0.348290 0.137874i
\(115\) 27356.9i 2.06858i
\(116\) −5734.59 + 11792.1i −0.426173 + 0.876346i
\(117\) 3318.79 + 18821.8i 0.242442 + 1.37496i
\(118\) 14269.3 506.528i 1.02480 0.0363781i
\(119\) −8955.71 10673.0i −0.632421 0.753689i
\(120\) −8029.21 + 3933.31i −0.557584 + 0.273146i
\(121\) −4394.82 + 7612.05i −0.300172 + 0.519914i
\(122\) −32.8096 + 101.176i −0.00220435 + 0.00679763i
\(123\) 1319.65 + 3625.70i 0.0872263 + 0.239652i
\(124\) −17135.2 + 4293.27i −1.11441 + 0.279219i
\(125\) −9679.17 16764.8i −0.619467 1.07295i
\(126\) 3462.23 + 16242.5i 0.218080 + 1.02308i
\(127\) 25972.7 + 4579.69i 1.61031 + 0.283941i 0.905146 0.425101i \(-0.139762\pi\)
0.705166 + 0.709043i \(0.250873\pi\)
\(128\) 7122.81 14754.7i 0.434742 0.900555i
\(129\) 7802.19 + 6546.81i 0.468853 + 0.393415i
\(130\) −27988.0 + 35865.6i −1.65609 + 2.12222i
\(131\) −9908.05 + 27222.2i −0.577359 + 1.58628i 0.215256 + 0.976558i \(0.430941\pi\)
−0.792615 + 0.609723i \(0.791281\pi\)
\(132\) 426.568 4104.02i 0.0244817 0.235538i
\(133\) 13960.6 16382.5i 0.789224 0.926142i
\(134\) −6484.92 + 5845.82i −0.361156 + 0.325563i
\(135\) 7197.40 19774.7i 0.394919 1.08503i
\(136\) −10775.9 10370.2i −0.582607 0.560673i
\(137\) 5161.54 + 4331.04i 0.275003 + 0.230755i 0.769850 0.638225i \(-0.220331\pi\)
−0.494846 + 0.868981i \(0.664776\pi\)
\(138\) −8816.68 1233.92i −0.462964 0.0647932i
\(139\) 3248.30 + 572.763i 0.168123 + 0.0296446i 0.257076 0.966391i \(-0.417241\pi\)
−0.0889531 + 0.996036i \(0.528352\pi\)
\(140\) −23199.1 + 32008.3i −1.18363 + 1.63308i
\(141\) −2859.43 4952.68i −0.143827 0.249116i
\(142\) 11354.6 21384.6i 0.563112 1.06053i
\(143\) −7180.67 19728.7i −0.351150 0.964778i
\(144\) 5547.73 + 16941.2i 0.267541 + 0.816994i
\(145\) 16980.2 29410.6i 0.807620 1.39884i
\(146\) 32629.6 20415.4i 1.53076 0.957750i
\(147\) −2500.64 2980.14i −0.115722 0.137912i
\(148\) −11610.0 + 11237.5i −0.530038 + 0.513034i
\(149\) 2113.97 + 11988.9i 0.0952195 + 0.540016i 0.994680 + 0.103014i \(0.0328487\pi\)
−0.899460 + 0.437002i \(0.856040\pi\)
\(150\) 13652.3 5525.02i 0.606767 0.245557i
\(151\) 1447.84i 0.0634990i 0.999496 + 0.0317495i \(0.0101079\pi\)
−0.999496 + 0.0317495i \(0.989892\pi\)
\(152\) 13032.1 19077.7i 0.564064 0.825731i
\(153\) 16272.0 0.695115
\(154\) −6843.84 16911.0i −0.288575 0.713064i
\(155\) 45055.4 7944.48i 1.87535 0.330676i
\(156\) −10296.5 10637.8i −0.423097 0.437120i
\(157\) 2870.46 2408.60i 0.116453 0.0977160i −0.582701 0.812686i \(-0.698004\pi\)
0.699155 + 0.714970i \(0.253560\pi\)
\(158\) 12010.2 + 19195.7i 0.481100 + 0.768935i
\(159\) −3773.58 2178.68i −0.149265 0.0861784i
\(160\) −21110.6 + 36809.1i −0.824632 + 1.43786i
\(161\) −36988.4 + 13462.7i −1.42697 + 0.519373i
\(162\) −13878.4 7369.00i −0.528821 0.280788i
\(163\) −3335.65 + 1925.84i −0.125547 + 0.0724845i −0.561458 0.827505i \(-0.689759\pi\)
0.435911 + 0.899990i \(0.356426\pi\)
\(164\) 14827.0 + 10746.3i 0.551270 + 0.399551i
\(165\) −1855.66 + 10524.0i −0.0681601 + 0.386555i
\(166\) −2327.32 + 16629.3i −0.0844579 + 0.603472i
\(167\) 5140.77 6126.53i 0.184330 0.219676i −0.665964 0.745984i \(-0.731980\pi\)
0.850294 + 0.526308i \(0.176424\pi\)
\(168\) −9269.36 8920.40i −0.328421 0.316057i
\(169\) −43948.9 15996.1i −1.53877 0.560067i
\(170\) 25934.0 + 28769.2i 0.897369 + 0.995476i
\(171\) 4176.49 + 24788.7i 0.142830 + 0.847737i
\(172\) 48078.9 + 4997.28i 1.62516 + 0.168918i
\(173\) −2378.42 865.676i −0.0794689 0.0289243i 0.301980 0.953314i \(-0.402352\pi\)
−0.381449 + 0.924390i \(0.624575\pi\)
\(174\) 8712.65 + 6798.98i 0.287774 + 0.224567i
\(175\) 41857.2 49883.4i 1.36676 1.62885i
\(176\) −9233.26 17269.1i −0.298078 0.557499i
\(177\) 2089.69 11851.2i 0.0667014 0.378282i
\(178\) 1080.36 230.288i 0.0340980 0.00726828i
\(179\) −37271.5 + 21518.7i −1.16324 + 0.671599i −0.952079 0.305851i \(-0.901059\pi\)
−0.211164 + 0.977451i \(0.567726\pi\)
\(180\) −11220.9 44784.6i −0.346324 1.38224i
\(181\) 18336.5 6673.93i 0.559705 0.203716i −0.0466484 0.998911i \(-0.514854\pi\)
0.606353 + 0.795196i \(0.292632\pi\)
\(182\) −62265.8 20191.7i −1.87978 0.609580i
\(183\) 77.6345 + 44.8223i 0.00231821 + 0.00133842i
\(184\) −37943.3 + 18587.5i −1.12073 + 0.549016i
\(185\) 32056.8 26898.8i 0.936648 0.785941i
\(186\) 528.168 + 14878.9i 0.0152667 + 0.430076i
\(187\) −17603.3 + 3103.94i −0.503399 + 0.0887627i
\(188\) −24408.4 11870.0i −0.690595 0.335841i
\(189\) 30278.6 0.847642
\(190\) −37170.6 + 46891.9i −1.02966 + 1.29895i
\(191\) 46644.6i 1.27860i 0.768958 + 0.639299i \(0.220776\pi\)
−0.768958 + 0.639299i \(0.779224\pi\)
\(192\) −10910.8 8463.85i −0.295974 0.229597i
\(193\) −12701.6 72034.6i −0.340993 1.93387i −0.357275 0.933999i \(-0.616294\pi\)
0.0162820 0.999867i \(-0.494817\pi\)
\(194\) −1954.25 55052.8i −0.0519250 1.46277i
\(195\) 24646.3 + 29372.4i 0.648161 + 0.772449i
\(196\) −17753.9 5068.71i −0.462148 0.131943i
\(197\) 15759.2 27295.6i 0.406069 0.703333i −0.588376 0.808588i \(-0.700232\pi\)
0.994445 + 0.105255i \(0.0335658\pi\)
\(198\) 20267.5 + 6572.40i 0.516975 + 0.167646i
\(199\) −4842.02 13303.3i −0.122270 0.335935i 0.863424 0.504479i \(-0.168315\pi\)
−0.985694 + 0.168545i \(0.946093\pi\)
\(200\) 38986.3 58015.6i 0.974657 1.45039i
\(201\) 3679.27 + 6372.67i 0.0910687 + 0.157736i
\(202\) 13619.4 2903.09i 0.333775 0.0711471i
\(203\) 48121.2 + 8485.06i 1.16773 + 0.205903i
\(204\) −10441.6 + 7060.46i −0.250903 + 0.169657i
\(205\) −36330.4 30484.8i −0.864495 0.725398i
\(206\) 8198.10 + 6397.45i 0.193187 + 0.150755i
\(207\) 15723.1 43198.9i 0.366942 1.00817i
\(208\) −68760.8 14450.0i −1.58933 0.333996i
\(209\) −9246.76 26020.2i −0.211688 0.595687i
\(210\) 22308.2 + 24747.1i 0.505856 + 0.561159i
\(211\) −6928.60 + 19036.2i −0.155625 + 0.427577i −0.992863 0.119262i \(-0.961947\pi\)
0.837237 + 0.546840i \(0.184169\pi\)
\(212\) −20627.8 + 1466.33i −0.458967 + 0.0326257i
\(213\) −15632.3 13117.0i −0.344559 0.289119i
\(214\) −2207.79 + 15775.2i −0.0482092 + 0.344467i
\(215\) −123289. 21739.2i −2.66715 0.470290i
\(216\) 32317.2 3453.17i 0.692670 0.0740135i
\(217\) 32913.7 + 57008.3i 0.698969 + 1.21065i
\(218\) 8723.55 + 4631.95i 0.183561 + 0.0974655i
\(219\) −11095.2 30483.8i −0.231338 0.635595i
\(220\) 20681.8 + 46308.5i 0.427311 + 0.956786i
\(221\) −32067.9 + 55543.2i −0.656578 + 1.13723i
\(222\) 7223.13 + 11544.6i 0.146561 + 0.234247i
\(223\) 12218.2 + 14561.1i 0.245697 + 0.292810i 0.874772 0.484534i \(-0.161011\pi\)
−0.629076 + 0.777344i \(0.716566\pi\)
\(224\) −60157.1 10428.7i −1.19892 0.207842i
\(225\) 13206.3 + 74896.4i 0.260864 + 1.47944i
\(226\) 8050.29 + 19892.2i 0.157614 + 0.389462i
\(227\) 3600.63i 0.0698758i −0.999389 0.0349379i \(-0.988877\pi\)
0.999389 0.0349379i \(-0.0111233\pi\)
\(228\) −13435.9 14094.5i −0.258462 0.271131i
\(229\) −1792.58 −0.0341828 −0.0170914 0.999854i \(-0.505441\pi\)
−0.0170914 + 0.999854i \(0.505441\pi\)
\(230\) 101436. 41050.8i 1.91750 0.776008i
\(231\) −15142.3 + 2669.99i −0.283771 + 0.0500364i
\(232\) 52328.8 + 3568.29i 0.972220 + 0.0662955i
\(233\) −69462.4 + 58285.9i −1.27949 + 1.07362i −0.286179 + 0.958176i \(0.592385\pi\)
−0.993314 + 0.115446i \(0.963170\pi\)
\(234\) 64808.7 40548.9i 1.18359 0.740539i
\(235\) 60876.7 + 35147.2i 1.10234 + 0.636436i
\(236\) −23290.1 52148.7i −0.418165 0.936309i
\(237\) 17933.3 6527.19i 0.319274 0.116206i
\(238\) −26135.5 + 49222.1i −0.461399 + 0.868973i
\(239\) 1201.15 693.481i 0.0210281 0.0121406i −0.489449 0.872032i \(-0.662802\pi\)
0.510477 + 0.859891i \(0.329469\pi\)
\(240\) 26632.5 + 23869.1i 0.462370 + 0.414394i
\(241\) −9395.14 + 53282.5i −0.161759 + 0.917382i 0.790584 + 0.612354i \(0.209777\pi\)
−0.952343 + 0.305029i \(0.901334\pi\)
\(242\) 34819.2 + 4873.06i 0.594550 + 0.0832092i
\(243\) −34953.4 + 41655.9i −0.591939 + 0.705446i
\(244\) 424.380 30.1671i 0.00712812 0.000506703i
\(245\) 44934.4 + 16354.8i 0.748596 + 0.272467i
\(246\) 11463.4 10333.7i 0.189428 0.170759i
\(247\) −92845.3 34596.0i −1.52183 0.567064i
\(248\) 41631.3 + 57092.8i 0.676888 + 0.928278i
\(249\) 13298.6 + 4840.30i 0.214490 + 0.0780681i
\(250\) −47637.6 + 61045.8i −0.762201 + 0.976733i
\(251\) 28694.3 34196.6i 0.455458 0.542794i −0.488628 0.872492i \(-0.662502\pi\)
0.944086 + 0.329698i \(0.106947\pi\)
\(252\) 55029.7 37210.4i 0.866556 0.585953i
\(253\) −8769.22 + 49732.7i −0.137000 + 0.776964i
\(254\) −21992.8 103176.i −0.340889 1.59922i
\(255\) 28271.3 16322.4i 0.434776 0.251018i
\(256\) −65396.7 4270.12i −0.997875 0.0651569i
\(257\) 30735.8 11186.9i 0.465348 0.169373i −0.0986958 0.995118i \(-0.531467\pi\)
0.564044 + 0.825745i \(0.309245\pi\)
\(258\) 12567.1 38753.4i 0.188797 0.582198i
\(259\) 52144.5 + 30105.6i 0.777336 + 0.448795i
\(260\) 174983. + 49957.3i 2.58850 + 0.739013i
\(261\) −43716.6 + 36682.6i −0.641749 + 0.538491i
\(262\) 115804. 4110.78i 1.68702 0.0598855i
\(263\) −50641.3 + 8929.42i −0.732138 + 0.129096i −0.527275 0.849695i \(-0.676786\pi\)
−0.204863 + 0.978791i \(0.565675\pi\)
\(264\) −15857.3 + 4576.68i −0.227521 + 0.0656664i
\(265\) 53559.1 0.762678
\(266\) −81693.1 27181.0i −1.15457 0.384151i
\(267\) 931.005i 0.0130596i
\(268\) 31406.6 + 15273.2i 0.437271 + 0.212648i
\(269\) 2439.14 + 13833.1i 0.0337080 + 0.191167i 0.997012 0.0772446i \(-0.0246123\pi\)
−0.963304 + 0.268412i \(0.913501\pi\)
\(270\) −84122.2 + 2986.15i −1.15394 + 0.0409623i
\(271\) −14125.1 16833.6i −0.192333 0.229213i 0.661257 0.750160i \(-0.270023\pi\)
−0.853589 + 0.520947i \(0.825579\pi\)
\(272\) −22281.5 + 55516.8i −0.301167 + 0.750389i
\(273\) −27584.6 + 47778.0i −0.370119 + 0.641065i
\(274\) 8313.74 25637.3i 0.110738 0.341485i
\(275\) −28573.6 78505.4i −0.377833 1.03809i
\(276\) 8654.76 + 34542.7i 0.113615 + 0.453459i
\(277\) 1905.29 + 3300.06i 0.0248314 + 0.0430093i 0.878174 0.478341i \(-0.158762\pi\)
−0.853343 + 0.521350i \(0.825428\pi\)
\(278\) −2750.55 12903.7i −0.0355901 0.166965i
\(279\) −75712.2 13350.1i −0.972652 0.171505i
\(280\) 153494. + 37988.7i 1.95784 + 0.484550i
\(281\) 22067.4 + 18516.7i 0.279472 + 0.234504i 0.771739 0.635940i \(-0.219387\pi\)
−0.492267 + 0.870444i \(0.663832\pi\)
\(282\) −14073.2 + 18034.2i −0.176967 + 0.226777i
\(283\) 34620.1 95118.0i 0.432271 1.18765i −0.512145 0.858899i \(-0.671149\pi\)
0.944415 0.328755i \(-0.106629\pi\)
\(284\) −96329.7 10012.4i −1.19433 0.124137i
\(285\) 32121.9 + 38879.0i 0.395468 + 0.478658i
\(286\) −62376.6 + 56229.2i −0.762587 + 0.687433i
\(287\) 23338.9 64123.0i 0.283345 0.778485i
\(288\) 54491.0 45991.6i 0.656962 0.554490i
\(289\) −22151.1 18587.0i −0.265216 0.222543i
\(290\) −134530. 18828.0i −1.59965 0.223876i
\(291\) −45723.5 8062.28i −0.539950 0.0952077i
\(292\) −124660. 90351.8i −1.46205 1.05967i
\(293\) 7825.00 + 13553.3i 0.0911484 + 0.157874i 0.907995 0.418982i \(-0.137613\pi\)
−0.816846 + 0.576856i \(0.804280\pi\)
\(294\) −7297.63 + 13743.9i −0.0844281 + 0.159007i
\(295\) 50591.0 + 138998.i 0.581338 + 1.59721i
\(296\) 59088.7 + 26185.7i 0.674405 + 0.298869i
\(297\) 19423.0 33641.7i 0.220193 0.381386i
\(298\) 41281.2 25828.4i 0.464857 0.290848i
\(299\) 116470. + 138804.i 1.30278 + 1.55260i
\(300\) −40972.2 42330.2i −0.455246 0.470335i
\(301\) −31279.1 177393.i −0.345241 1.95796i
\(302\) 5368.41 2172.58i 0.0588615 0.0238211i
\(303\) 11736.5i 0.127837i
\(304\) −90293.2 19694.2i −0.977029 0.213104i
\(305\) −1101.88 −0.0118450
\(306\) −24417.1 60334.3i −0.260766 0.644350i
\(307\) −154702. + 27278.1i −1.64142 + 0.289426i −0.916686 0.399607i \(-0.869146\pi\)
−0.724730 + 0.689033i \(0.758035\pi\)
\(308\) −52434.3 + 50752.1i −0.552731 + 0.534999i
\(309\) 6713.89 5633.62i 0.0703165 0.0590025i
\(310\) −97065.6 155138.i −1.01005 1.61434i
\(311\) 96272.3 + 55582.8i 0.995361 + 0.574672i 0.906872 0.421405i \(-0.138463\pi\)
0.0884884 + 0.996077i \(0.471796\pi\)
\(312\) −23992.9 + 54140.7i −0.246475 + 0.556179i
\(313\) 66493.3 24201.6i 0.678718 0.247033i 0.0204210 0.999791i \(-0.493499\pi\)
0.658297 + 0.752758i \(0.271277\pi\)
\(314\) −13238.1 7029.03i −0.134266 0.0712913i
\(315\) −148997. + 86023.4i −1.50161 + 0.866952i
\(316\) 53153.1 73336.6i 0.532298 0.734423i
\(317\) 25845.3 146576.i 0.257195 1.45863i −0.533180 0.846002i \(-0.679003\pi\)
0.790375 0.612624i \(-0.209886\pi\)
\(318\) −2415.76 + 17261.2i −0.0238891 + 0.170693i
\(319\) 40296.2 48023.1i 0.395988 0.471920i
\(320\) 168161. + 23040.9i 1.64220 + 0.225009i
\(321\) 12615.6 + 4591.70i 0.122433 + 0.0445618i
\(322\) 105421. + 116947.i 1.01675 + 1.12791i
\(323\) −42733.9 + 72732.2i −0.409607 + 0.697142i
\(324\) −6497.95 + 62516.9i −0.0618994 + 0.595535i
\(325\) −281680. 102523.i −2.66679 0.970634i
\(326\) 12146.1 + 9478.32i 0.114288 + 0.0891859i
\(327\) 5350.91 6376.97i 0.0500417 0.0596374i
\(328\) 17597.2 71102.0i 0.163567 0.660898i
\(329\) −17563.1 + 99605.6i −0.162260 + 0.920220i
\(330\) 41806.1 8911.33i 0.383894 0.0818304i
\(331\) 105892. 61136.8i 0.966512 0.558016i 0.0683409 0.997662i \(-0.478229\pi\)
0.898171 + 0.439646i \(0.144896\pi\)
\(332\) 65151.6 16323.9i 0.591083 0.148097i
\(333\) −66080.1 + 24051.2i −0.595912 + 0.216894i
\(334\) −30430.4 9868.07i −0.272782 0.0884584i
\(335\) −78330.7 45224.3i −0.697979 0.402978i
\(336\) −19166.4 + 47755.2i −0.169771 + 0.423002i
\(337\) 10521.3 8828.43i 0.0926425 0.0777363i −0.595290 0.803511i \(-0.702963\pi\)
0.687933 + 0.725775i \(0.258518\pi\)
\(338\) 6636.66 + 186960.i 0.0580919 + 1.63650i
\(339\) 17811.6 3140.67i 0.154990 0.0273289i
\(340\) 67757.1 139330.i 0.586134 1.20528i
\(341\) 84453.7 0.726289
\(342\) 85646.1 52682.9i 0.732243 0.450420i
\(343\) 74353.2i 0.631991i
\(344\) −53616.1 185769.i −0.453084 1.56984i
\(345\) −16015.2 90826.7i −0.134553 0.763089i
\(346\) 359.162 + 10117.9i 0.00300012 + 0.0845158i
\(347\) 2917.94 + 3477.46i 0.0242336 + 0.0288804i 0.778025 0.628233i \(-0.216222\pi\)
−0.753792 + 0.657114i \(0.771777\pi\)
\(348\) 12135.9 42507.7i 0.100210 0.351001i
\(349\) −18323.1 + 31736.6i −0.150435 + 0.260561i −0.931387 0.364029i \(-0.881401\pi\)
0.780952 + 0.624591i \(0.214734\pi\)
\(350\) −247771. 80347.7i −2.02262 0.655900i
\(351\) −47671.2 130976.i −0.386938 1.06310i
\(352\) −50176.5 + 60149.1i −0.404962 + 0.485449i
\(353\) −42192.4 73079.3i −0.338598 0.586469i 0.645571 0.763700i \(-0.276619\pi\)
−0.984169 + 0.177231i \(0.943286\pi\)
\(354\) −47078.4 + 10035.2i −0.375678 + 0.0800791i
\(355\) 247019. + 43556.1i 1.96008 + 0.345615i
\(356\) −2475.03 3660.27i −0.0195290 0.0288811i
\(357\) 35981.7 + 30192.2i 0.282322 + 0.236896i
\(358\) 135717. + 105908.i 1.05893 + 0.826345i
\(359\) 48202.5 132435.i 0.374008 1.02758i −0.599789 0.800158i \(-0.704749\pi\)
0.973797 0.227420i \(-0.0730289\pi\)
\(360\) −149218. + 108808.i −1.15137 + 0.839565i
\(361\) −121769. 46432.7i −0.934374 0.356295i
\(362\) −52261.1 57974.7i −0.398806 0.442406i
\(363\) 10134.9 27845.3i 0.0769138 0.211319i
\(364\) 18565.5 + 261173.i 0.140121 + 1.97117i
\(365\) 305455. + 256307.i 2.29277 + 1.92387i
\(366\) 49.6998 355.117i 0.000371016 0.00265100i
\(367\) 76097.3 + 13418.0i 0.564986 + 0.0996222i 0.448843 0.893610i \(-0.351836\pi\)
0.116142 + 0.993233i \(0.462947\pi\)
\(368\) 125856. + 112797.i 0.929350 + 0.832920i
\(369\) 39847.9 + 69018.6i 0.292653 + 0.506890i
\(370\) −147841. 78499.0i −1.07992 0.573404i
\(371\) 26357.0 + 72415.4i 0.191491 + 0.526118i
\(372\) 54376.6 24285.1i 0.392940 0.175491i
\(373\) 88081.7 152562.i 0.633094 1.09655i −0.353822 0.935313i \(-0.615118\pi\)
0.986916 0.161238i \(-0.0515486\pi\)
\(374\) 37924.0 + 60613.3i 0.271126 + 0.433336i
\(375\) 41949.8 + 49993.9i 0.298310 + 0.355512i
\(376\) −7385.96 + 108315.i −0.0522434 + 0.766147i
\(377\) −39059.2 221516.i −0.274815 1.55855i
\(378\) −45435.0 112269.i −0.317985 0.785737i
\(379\) 53659.2i 0.373564i 0.982401 + 0.186782i \(0.0598059\pi\)
−0.982401 + 0.186782i \(0.940194\pi\)
\(380\) 229646. + 67459.5i 1.59035 + 0.467171i
\(381\) −88912.0 −0.612506
\(382\) 172952. 69993.1i 1.18522 0.479655i
\(383\) −139515. + 24600.2i −0.951093 + 0.167703i −0.627607 0.778530i \(-0.715966\pi\)
−0.323485 + 0.946233i \(0.604855\pi\)
\(384\) −15010.5 + 53156.3i −0.101797 + 0.360489i
\(385\) 144779. 121484.i 0.976749 0.819589i
\(386\) −248035. + 155189.i −1.66471 + 1.04156i
\(387\) 182189. + 105187.i 1.21647 + 0.702328i
\(388\) −201196. + 89856.3i −1.33646 + 0.596878i
\(389\) −113800. + 41420.0i −0.752047 + 0.273723i −0.689467 0.724317i \(-0.742155\pi\)
−0.0625800 + 0.998040i \(0.519933\pi\)
\(390\) 71925.6 135461.i 0.472883 0.890602i
\(391\) 133601. 77134.3i 0.873886 0.504538i
\(392\) 7846.71 + 73435.0i 0.0510641 + 0.477894i
\(393\) 16959.1 96179.6i 0.109804 0.622727i
\(394\) −124856. 17474.1i −0.804300 0.112564i
\(395\) −150783. + 179696.i −0.966402 + 1.15171i
\(396\) −6043.05 85011.6i −0.0385359 0.542110i
\(397\) 201707. + 73415.2i 1.27979 + 0.465806i 0.890363 0.455251i \(-0.150450\pi\)
0.389428 + 0.921057i \(0.372673\pi\)
\(398\) −42061.3 + 37916.1i −0.265532 + 0.239363i
\(399\) −36759.4 + 62563.8i −0.230899 + 0.392986i
\(400\) −273616. 57500.0i −1.71010 0.359375i
\(401\) 127737. + 46492.6i 0.794381 + 0.289131i 0.707156 0.707058i \(-0.249978\pi\)
0.0872250 + 0.996189i \(0.472200\pi\)
\(402\) 18108.1 23204.8i 0.112052 0.143591i
\(403\) 194779. 232129.i 1.19931 1.42929i
\(404\) −31201.0 46142.6i −0.191164 0.282709i
\(405\) 28267.4 160312.i 0.172336 0.977365i
\(406\) −40747.4 191160.i −0.247199 1.15970i
\(407\) 66899.0 38624.1i 0.403860 0.233169i
\(408\) 41847.5 + 28121.4i 0.251391 + 0.168934i
\(409\) −201715. + 73418.4i −1.20585 + 0.438893i −0.865261 0.501321i \(-0.832848\pi\)
−0.340586 + 0.940213i \(0.610625\pi\)
\(410\) −58517.8 + 180453.i −0.348113 + 1.07349i
\(411\) −19672.1 11357.7i −0.116457 0.0672367i
\(412\) 11419.2 39997.3i 0.0672728 0.235633i
\(413\) −163037. + 136805.i −0.955844 + 0.802049i
\(414\) −183769. + 6523.40i −1.07219 + 0.0380604i
\(415\) −171310. + 30206.5i −0.994686 + 0.175390i
\(416\) 49601.3 + 276639.i 0.286620 + 1.59855i
\(417\) −11119.9 −0.0639480
\(418\) −82604.3 + 73330.8i −0.472770 + 0.419695i
\(419\) 269807.i 1.53683i 0.639953 + 0.768414i \(0.278954\pi\)
−0.639953 + 0.768414i \(0.721046\pi\)
\(420\) 58284.2 119851.i 0.330409 0.679426i
\(421\) −4461.90 25304.7i −0.0251742 0.142770i 0.969630 0.244576i \(-0.0786489\pi\)
−0.994804 + 0.101806i \(0.967538\pi\)
\(422\) 80980.4 2874.62i 0.454732 0.0161419i
\(423\) −75928.9 90488.5i −0.424352 0.505723i
\(424\) 36390.3 + 74285.0i 0.202420 + 0.413209i
\(425\) −127606. + 221020.i −0.706468 + 1.22364i
\(426\) −25179.1 + 77645.4i −0.138746 + 0.427855i
\(427\) −542.248 1489.81i −0.00297401 0.00817102i
\(428\) 61805.3 15485.5i 0.337395 0.0845351i
\(429\) 35389.8 + 61296.9i 0.192293 + 0.333061i
\(430\) 104397. + 489761.i 0.564612 + 2.64879i
\(431\) −40041.1 7060.32i −0.215551 0.0380075i 0.0648294 0.997896i \(-0.479350\pi\)
−0.280381 + 0.959889i \(0.590461\pi\)
\(432\) −61297.9 114646.i −0.328457 0.614317i
\(433\) 42542.0 + 35697.0i 0.226904 + 0.190395i 0.749151 0.662399i \(-0.230462\pi\)
−0.522247 + 0.852794i \(0.674906\pi\)
\(434\) 161990. 207584.i 0.860021 1.10209i
\(435\) −39157.9 + 107585.i −0.206938 + 0.568558i
\(436\) 4084.43 39296.3i 0.0214861 0.206718i
\(437\) 151797. + 183729.i 0.794880 + 0.962088i
\(438\) −96380.8 + 86882.3i −0.502392 + 0.452880i
\(439\) −5879.45 + 16153.7i −0.0305076 + 0.0838189i −0.954011 0.299770i \(-0.903090\pi\)
0.923504 + 0.383589i \(0.125312\pi\)
\(440\) 140671. 146174.i 0.726608 0.755033i
\(441\) −61555.5 51651.2i −0.316512 0.265585i
\(442\) 254067. + 35557.5i 1.30048 + 0.182006i
\(443\) 35237.7 + 6213.36i 0.179556 + 0.0316606i 0.262703 0.964877i \(-0.415386\pi\)
−0.0831470 + 0.996537i \(0.526497\pi\)
\(444\) 31967.2 44105.9i 0.162158 0.223733i
\(445\) 5721.79 + 9910.44i 0.0288943 + 0.0500464i
\(446\) 35656.6 67153.6i 0.179254 0.337598i
\(447\) −14037.0 38566.4i −0.0702521 0.193016i
\(448\) 51601.3 + 238704.i 0.257102 + 1.18933i
\(449\) 1615.37 2797.90i 0.00801269 0.0138784i −0.861991 0.506923i \(-0.830783\pi\)
0.870004 + 0.493045i \(0.164116\pi\)
\(450\) 257889. 161354.i 1.27353 0.796809i
\(451\) −56273.9 67064.6i −0.276665 0.329716i
\(452\) 61677.6 59698.9i 0.301891 0.292206i
\(453\) −847.590 4806.92i −0.00413037 0.0234245i
\(454\) −13350.7 + 5402.97i −0.0647726 + 0.0262133i
\(455\) 678121.i 3.27555i
\(456\) −32099.1 + 70968.3i −0.154370 + 0.341299i
\(457\) 184239. 0.882162 0.441081 0.897467i \(-0.354595\pi\)
0.441081 + 0.897467i \(0.354595\pi\)
\(458\) 2689.88 + 6646.66i 0.0128234 + 0.0316864i
\(459\) −116865. + 20606.5i −0.554703 + 0.0978091i
\(460\) −304422. 314512.i −1.43867 1.48635i
\(461\) −281594. + 236286.i −1.32502 + 1.11182i −0.339805 + 0.940496i \(0.610361\pi\)
−0.985214 + 0.171327i \(0.945194\pi\)
\(462\) 32622.0 + 52139.2i 0.152836 + 0.244276i
\(463\) 166665. + 96223.8i 0.777466 + 0.448870i 0.835531 0.549443i \(-0.185160\pi\)
−0.0580658 + 0.998313i \(0.518493\pi\)
\(464\) −65291.9 199383.i −0.303266 0.926087i
\(465\) −144936. + 52752.3i −0.670301 + 0.243970i
\(466\) 320349. + 170096.i 1.47520 + 0.783289i
\(467\) −360785. + 208299.i −1.65430 + 0.955112i −0.679029 + 0.734112i \(0.737599\pi\)
−0.975274 + 0.221000i \(0.929068\pi\)
\(468\) −247600. 179456.i −1.13047 0.819345i
\(469\) 22598.7 128164.i 0.102740 0.582665i
\(470\) 38971.9 278463.i 0.176423 1.26059i
\(471\) −8120.07 + 9677.12i −0.0366031 + 0.0436219i
\(472\) −158412. + 164609.i −0.711057 + 0.738874i
\(473\) −217161. 79040.1i −0.970643 0.353285i
\(474\) −51112.0 56699.9i −0.227492 0.252363i
\(475\) −369454. 137666.i −1.63747 0.610153i
\(476\) 221727. + 23046.1i 0.978600 + 0.101715i
\(477\) −84574.3 30782.5i −0.371708 0.135290i
\(478\) −4373.73 3413.08i −0.0191424 0.0149379i
\(479\) 153131. 182494.i 0.667408 0.795386i −0.321021 0.947072i \(-0.604026\pi\)
0.988429 + 0.151686i \(0.0484704\pi\)
\(480\) 48539.8 134567.i 0.210676 0.584059i
\(481\) 48130.0 272959.i 0.208030 1.17980i
\(482\) 211663. 45117.8i 0.911066 0.194202i
\(483\) 114922. 66350.5i 0.492618 0.284413i
\(484\) −34179.8 136418.i −0.145908 0.582344i
\(485\) 536270. 195186.i 2.27982 0.829786i
\(486\) 206904. + 67095.5i 0.875986 + 0.284067i
\(487\) 192225. + 110981.i 0.810499 + 0.467942i 0.847129 0.531387i \(-0.178329\pi\)
−0.0366299 + 0.999329i \(0.511662\pi\)
\(488\) −748.665 1528.28i −0.00314375 0.00641746i
\(489\) 9947.15 8346.65i 0.0415988 0.0349056i
\(490\) −6785.49 191153.i −0.0282611 0.796137i
\(491\) −99879.3 + 17611.4i −0.414298 + 0.0730518i −0.376912 0.926249i \(-0.623014\pi\)
−0.0373855 + 0.999301i \(0.511903\pi\)
\(492\) −55517.5 26998.5i −0.229351 0.111535i
\(493\) −191506. −0.787933
\(494\) 11042.7 + 396172.i 0.0452501 + 1.62342i
\(495\) 220728.i 0.900839i
\(496\) 149222. 240035.i 0.606555 0.975689i
\(497\) 62670.2 + 355420.i 0.253716 + 1.43890i
\(498\) −2008.20 56572.7i −0.00809747 0.228112i
\(499\) 155217. + 184980.i 0.623358 + 0.742889i 0.981644 0.190723i \(-0.0610832\pi\)
−0.358286 + 0.933612i \(0.616639\pi\)
\(500\) 297833. + 85030.9i 1.19133 + 0.340124i
\(501\) −13481.1 + 23350.0i −0.0537094 + 0.0930273i
\(502\) −169854. 55080.8i −0.674014 0.218571i
\(503\) 67597.8 + 185723.i 0.267176 + 0.734059i 0.998638 + 0.0521768i \(0.0166159\pi\)
−0.731462 + 0.681882i \(0.761162\pi\)
\(504\) −220547. 148207.i −0.868240 0.583454i
\(505\) 72130.8 + 124934.i 0.282838 + 0.489890i
\(506\) 197561. 42111.9i 0.771615 0.164477i
\(507\) 155277. + 27379.6i 0.604077 + 0.106515i
\(508\) −349560. + 236368.i −1.35455 + 0.915928i
\(509\) −28947.8 24290.1i −0.111733 0.0937549i 0.585210 0.810882i \(-0.301012\pi\)
−0.696942 + 0.717127i \(0.745457\pi\)
\(510\) −102944. 80333.5i −0.395788 0.308856i
\(511\) −196226. + 539127.i −0.751476 + 2.06466i
\(512\) 82298.9 + 248890.i 0.313945 + 0.949441i
\(513\) −61387.6 172744.i −0.233263 0.656398i
\(514\) −87600.6 97177.6i −0.331574 0.367824i
\(515\) −36845.3 + 101232.i −0.138921 + 0.381682i
\(516\) −162550. + 11554.9i −0.610504 + 0.0433977i
\(517\) 99402.5 + 83408.6i 0.371892 + 0.312054i
\(518\) 33381.7 238520.i 0.124408 0.888927i
\(519\) 8403.30 + 1481.73i 0.0311972 + 0.00550090i
\(520\) −77337.4 723777.i −0.286011 2.67669i
\(521\) 86697.7 + 150165.i 0.319398 + 0.553214i 0.980363 0.197203i \(-0.0631859\pi\)
−0.660964 + 0.750417i \(0.729853\pi\)
\(522\) 201614. + 107051.i 0.739910 + 0.392870i
\(523\) −138211. 379731.i −0.505288 1.38827i −0.886048 0.463593i \(-0.846560\pi\)
0.380761 0.924674i \(-0.375662\pi\)
\(524\) −189013. 423218.i −0.688383 1.54135i
\(525\) −109766. + 190120.i −0.398243 + 0.689777i
\(526\) 109100. + 174372.i 0.394323 + 0.630239i
\(527\) −165834. 197633.i −0.597107 0.711604i
\(528\) 40764.6 + 51929.1i 0.146223 + 0.186270i
\(529\) −27088.5 153627.i −0.0967997 0.548979i
\(530\) −80368.8 198590.i −0.286112 0.706978i
\(531\) 248565.i 0.881559i
\(532\) 21801.9 + 343694.i 0.0770319 + 1.21436i
\(533\) −314121. −1.10571
\(534\) −3452.05 + 1397.03i −0.0121058 + 0.00489918i
\(535\) −162511. + 28655.1i −0.567774 + 0.100114i
\(536\) 9503.60 139370.i 0.0330795 0.485109i
\(537\) 111146. 93262.8i 0.385431 0.323415i
\(538\) 47631.1 29801.4i 0.164561 0.102961i
\(539\) 76444.7 + 44135.4i 0.263130 + 0.151918i
\(540\) 137303. + 307433.i 0.470861 + 1.05430i
\(541\) 1830.93 666.402i 0.00625570 0.00227689i −0.338890 0.940826i \(-0.610052\pi\)
0.345146 + 0.938549i \(0.387829\pi\)
\(542\) −41221.4 + 77634.0i −0.140321 + 0.264273i
\(543\) −56971.2 + 32892.4i −0.193222 + 0.111557i
\(544\) 239284. 689.452i 0.808567 0.00232973i
\(545\) −17768.1 + 100768.i −0.0598202 + 0.339257i
\(546\) 218547. + 30586.4i 0.733094 + 0.102599i
\(547\) 332768. 396578.i 1.11216 1.32542i 0.171843 0.985124i \(-0.445028\pi\)
0.940318 0.340297i \(-0.110528\pi\)
\(548\) −107535. + 7644.15i −0.358088 + 0.0254547i
\(549\) 1739.96 + 633.294i 0.00577291 + 0.00210117i
\(550\) −248211. + 223750.i −0.820533 + 0.739668i
\(551\) −49153.6 291741.i −0.161902 0.960934i
\(552\) 115093. 83924.2i 0.377720 0.275429i
\(553\) −317163. 115438.i −1.03713 0.377484i
\(554\) 9377.18 12016.5i 0.0305529 0.0391524i
\(555\) −90683.4 + 108072.i −0.294403 + 0.350856i
\(556\) −43718.0 + 29561.6i −0.141420 + 0.0956264i
\(557\) 58284.7 330549.i 0.187864 1.06543i −0.734355 0.678765i \(-0.762515\pi\)
0.922220 0.386667i \(-0.126374\pi\)
\(558\) 64110.5 + 300764.i 0.205902 + 0.965956i
\(559\) −718098. + 414594.i −2.29805 + 1.32678i
\(560\) −89470.8 626142.i −0.285302 1.99663i
\(561\) 56627.1 20610.6i 0.179928 0.0654884i
\(562\) 35544.1 109608.i 0.112537 0.347033i
\(563\) −339376. 195939.i −1.07069 0.618164i −0.142321 0.989821i \(-0.545457\pi\)
−0.928370 + 0.371657i \(0.878790\pi\)
\(564\) 87986.2 + 25119.9i 0.276603 + 0.0789697i
\(565\) −170301. + 142899.i −0.533481 + 0.447644i
\(566\) −404635. + 14363.6i −1.26308 + 0.0448365i
\(567\) 230664. 40672.2i 0.717485 0.126512i
\(568\) 107424. + 372202.i 0.332970 + 1.15367i
\(569\) 450807. 1.39241 0.696203 0.717845i \(-0.254871\pi\)
0.696203 + 0.717845i \(0.254871\pi\)
\(570\) 95957.4 177444.i 0.295344 0.546151i
\(571\) 577692.i 1.77184i −0.463841 0.885919i \(-0.653529\pi\)
0.463841 0.885919i \(-0.346471\pi\)
\(572\) 302091. + 146909.i 0.923305 + 0.449010i
\(573\) −27306.5 154863.i −0.0831681 0.471670i
\(574\) −272781. + 9683.13i −0.827925 + 0.0293895i
\(575\) 463463. + 552334.i 1.40178 + 1.67057i
\(576\) −252298. 133032.i −0.760448 0.400971i
\(577\) −318962. + 552458.i −0.958047 + 1.65939i −0.230811 + 0.972998i \(0.574138\pi\)
−0.727236 + 0.686388i \(0.759195\pi\)
\(578\) −35679.0 + 110024.i −0.106796 + 0.329331i
\(579\) 84340.5 + 231724.i 0.251582 + 0.691215i
\(580\) 132060. + 527074.i 0.392568 + 1.56681i
\(581\) −125145. 216757.i −0.370732 0.642127i
\(582\) 38717.1 + 181635.i 0.114303 + 0.536232i
\(583\) 97366.1 + 17168.3i 0.286464 + 0.0505114i
\(584\) −147952. + 597804.i −0.433805 + 1.75280i
\(585\) 606692. + 509075.i 1.77279 + 1.48755i
\(586\) 38512.0 49351.7i 0.112150 0.143717i
\(587\) 142731. 392150.i 0.414230 1.13809i −0.540689 0.841223i \(-0.681836\pi\)
0.954919 0.296866i \(-0.0959414\pi\)
\(588\) 61911.3 + 6435.01i 0.179067 + 0.0186121i
\(589\) 258510. 303357.i 0.745154 0.874427i
\(590\) 439470. 396159.i 1.26248 1.13806i
\(591\) −36342.0 + 99848.9i −0.104048 + 0.285870i
\(592\) 8426.78 258386.i 0.0240446 0.737270i
\(593\) 51386.5 + 43118.4i 0.146130 + 0.122618i 0.712922 0.701243i \(-0.247371\pi\)
−0.566792 + 0.823861i \(0.691816\pi\)
\(594\) −153885. 21536.7i −0.436136 0.0610387i
\(595\) −568577. 100255.i −1.60603 0.283187i
\(596\) −157714. 114308.i −0.443993 0.321799i
\(597\) 23863.8 + 41333.3i 0.0669562 + 0.115972i
\(598\) 339896. 640141.i 0.950481 1.79008i
\(599\) 71146.6 + 195474.i 0.198290 + 0.544797i 0.998490 0.0549365i \(-0.0174956\pi\)
−0.800200 + 0.599733i \(0.795273\pi\)
\(600\) −95473.5 + 215439.i −0.265204 + 0.598441i
\(601\) 255493. 442527.i 0.707344 1.22516i −0.258495 0.966013i \(-0.583227\pi\)
0.965839 0.259143i \(-0.0834400\pi\)
\(602\) −610813. + 382168.i −1.68545 + 1.05454i
\(603\) 97698.6 + 116433.i 0.268691 + 0.320214i
\(604\) −16111.3 16645.3i −0.0441627 0.0456265i
\(605\) 63248.0 + 358697.i 0.172797 + 0.979980i
\(606\) −43517.6 + 17611.4i −0.118500 + 0.0479567i
\(607\) 469911.i 1.27538i 0.770295 + 0.637688i \(0.220109\pi\)
−0.770295 + 0.637688i \(0.779891\pi\)
\(608\) 62466.9 + 364348.i 0.168983 + 0.985619i
\(609\) −164733. −0.444166
\(610\) 1653.44 + 4085.63i 0.00444354 + 0.0109799i
\(611\) 458513. 80848.2i 1.22820 0.216565i
\(612\) −187072. + 181071.i −0.499467 + 0.483444i
\(613\) −437186. + 366843.i −1.16344 + 0.976246i −0.999947 0.0102977i \(-0.996722\pi\)
−0.163498 + 0.986544i \(0.552278\pi\)
\(614\) 333284. + 532682.i 0.884051 + 1.41296i
\(615\) 138466. + 79943.1i 0.366093 + 0.211364i
\(616\) 266863. + 118263.i 0.703279 + 0.311664i
\(617\) −462494. + 168334.i −1.21489 + 0.442182i −0.868396 0.495871i \(-0.834849\pi\)
−0.346490 + 0.938054i \(0.612626\pi\)
\(618\) −30963.4 16440.6i −0.0810720 0.0430469i
\(619\) 57654.1 33286.6i 0.150470 0.0868736i −0.422875 0.906188i \(-0.638979\pi\)
0.573344 + 0.819314i \(0.305646\pi\)
\(620\) −429580. + 592702.i −1.11753 + 1.54189i
\(621\) −58217.3 + 330166.i −0.150962 + 0.856150i
\(622\) 61631.3 440371.i 0.159302 1.13825i
\(623\) −10583.8 + 12613.3i −0.0272688 + 0.0324977i
\(624\) 236749. + 7721.13i 0.608023 + 0.0198295i
\(625\) −112372. 40900.2i −0.287673 0.104705i
\(626\) −189514. 210233.i −0.483607 0.536477i
\(627\) 45932.5 + 80975.5i 0.116838 + 0.205977i
\(628\) −6198.16 + 59632.6i −0.0157161 + 0.151205i
\(629\) −221749. 80710.1i −0.560481 0.203998i
\(630\) 542543. + 423378.i 1.36695 + 1.06671i
\(631\) 332245. 395954.i 0.834448 0.994457i −0.165518 0.986207i \(-0.552929\pi\)
0.999966 0.00824991i \(-0.00262606\pi\)
\(632\) −351682. 87038.7i −0.880473 0.217911i
\(633\) 11859.3 67257.3i 0.0295972 0.167854i
\(634\) −582267. + 124115.i −1.44858 + 0.308778i
\(635\) 946458. 546438.i 2.34722 1.35517i
\(636\) 67627.3 16944.2i 0.167189 0.0418896i
\(637\) 297618. 108324.i 0.733467 0.266960i
\(638\) −238530. 77351.3i −0.586006 0.190032i
\(639\) −365030. 210750.i −0.893978 0.516138i
\(640\) −166904. 658095.i −0.407481 1.60668i
\(641\) 395902. 332201.i 0.963544 0.808510i −0.0179817 0.999838i \(-0.505724\pi\)
0.981526 + 0.191329i \(0.0612796\pi\)
\(642\) −1905.06 53667.1i −0.00462209 0.130208i
\(643\) 417196. 73562.9i 1.00906 0.177925i 0.355403 0.934713i \(-0.384344\pi\)
0.653660 + 0.756788i \(0.273233\pi\)
\(644\) 275431. 566374.i 0.664113 1.36563i
\(645\) 422053. 1.01449
\(646\) 333806. + 49312.4i 0.799889 + 0.118166i
\(647\) 406880.i 0.971981i 0.873964 + 0.485991i \(0.161541\pi\)
−0.873964 + 0.485991i \(0.838459\pi\)
\(648\) 241555. 69717.0i 0.575263 0.166031i
\(649\) 47414.9 + 268903.i 0.112571 + 0.638420i
\(650\) 42536.1 + 1.19828e6i 0.100677 + 2.83616i
\(651\) −142649. 170003.i −0.336595 0.401138i
\(652\) 16918.4 59259.1i 0.0397982 0.139399i
\(653\) 325842. 564374.i 0.764153 1.32355i −0.176540 0.984293i \(-0.556491\pi\)
0.940693 0.339258i \(-0.110176\pi\)
\(654\) −31674.3 10271.4i −0.0740546 0.0240146i
\(655\) 410576. + 1.12805e6i 0.956998 + 2.62933i
\(656\) −290043. + 41444.9i −0.673992 + 0.0963081i
\(657\) −335029. 580287.i −0.776161 1.34435i
\(658\) 395679. 84342.6i 0.913885 0.194803i
\(659\) −469564. 82796.7i −1.08124 0.190652i −0.395478 0.918475i \(-0.629421\pi\)
−0.685765 + 0.727823i \(0.740532\pi\)
\(660\) −95774.7 141639.i −0.219868 0.325159i
\(661\) −33682.3 28262.8i −0.0770901 0.0646863i 0.603428 0.797417i \(-0.293801\pi\)
−0.680518 + 0.732731i \(0.738245\pi\)
\(662\) −385585. 300894.i −0.879841 0.686591i
\(663\) 73951.5 203180.i 0.168236 0.462226i
\(664\) −158291. 217079.i −0.359021 0.492358i
\(665\) 6793.43 891901.i 0.0153619 2.01685i
\(666\) 188336. + 208926.i 0.424605 + 0.471026i
\(667\) −185047. + 508412.i −0.415940 + 1.14278i
\(668\) 9073.29 + 127640.i 0.0203335 + 0.286044i
\(669\) −49089.7 41191.1i −0.109683 0.0920347i
\(670\) −50145.5 + 358302.i −0.111708 + 0.798178i
\(671\) −2003.13 353.206i −0.00444902 0.000784482i
\(672\) 205831. 593.063i 0.455797 0.00131329i
\(673\) 267915. + 464043.i 0.591517 + 1.02454i 0.994028 + 0.109123i \(0.0348042\pi\)
−0.402511 + 0.915415i \(0.631862\pi\)
\(674\) −48522.6 25764.1i −0.106813 0.0567145i
\(675\) −189695. 521183.i −0.416340 1.14389i
\(676\) 683265. 305153.i 1.49519 0.667766i
\(677\) 307740. 533021.i 0.671438 1.16296i −0.306058 0.952013i \(-0.599010\pi\)
0.977496 0.210952i \(-0.0676564\pi\)
\(678\) −38372.7 61330.4i −0.0834762 0.133419i
\(679\) 527810. + 629019.i 1.14482 + 1.36435i
\(680\) −618291. 42161.1i −1.33713 0.0911789i
\(681\) 2107.87 + 11954.3i 0.00454516 + 0.0257769i
\(682\) −126728. 313143.i −0.272461 0.673247i
\(683\) 18652.0i 0.0399838i −0.999800 0.0199919i \(-0.993636\pi\)
0.999800 0.0199919i \(-0.00636405\pi\)
\(684\) −323859. 238511.i −0.692219 0.509795i
\(685\) 279210. 0.595044
\(686\) −275692. + 111572.i −0.585836 + 0.237086i
\(687\) 5951.48 1049.41i 0.0126099 0.00222346i
\(688\) −608353. + 477560.i −1.28522 + 1.00891i
\(689\) 271749. 228024.i 0.572438 0.480333i
\(690\) −312742. + 195674.i −0.656883 + 0.410993i
\(691\) −406712. 234815.i −0.851787 0.491779i 0.00946644 0.999955i \(-0.496987\pi\)
−0.861253 + 0.508176i \(0.830320\pi\)
\(692\) 36976.9 16514.3i 0.0772180 0.0344863i
\(693\) −298439. + 108623.i −0.621425 + 0.226180i
\(694\) 8515.43 16037.5i 0.0176802 0.0332979i
\(695\) 118370. 68340.7i 0.245059 0.141485i
\(696\) −175824. + 18787.2i −0.362960 + 0.0387832i
\(697\) −46440.5 + 263377.i −0.0955942 + 0.542141i
\(698\) 145170. + 20317.1i 0.297966 + 0.0417013i
\(699\) 196498. 234177.i 0.402164 0.479281i
\(700\) 73876.5 + 1.03927e6i 0.150768 + 2.12096i
\(701\) −789547. 287372.i −1.60673 0.584801i −0.625938 0.779873i \(-0.715284\pi\)
−0.980789 + 0.195072i \(0.937506\pi\)
\(702\) −414107. + 373296.i −0.840307 + 0.757493i
\(703\) 66037.7 358528.i 0.133623 0.725458i
\(704\) 298318. + 95790.3i 0.601914 + 0.193275i
\(705\) −222690. 81052.5i −0.448046 0.163075i
\(706\) −207656. + 266104.i −0.416616 + 0.533878i
\(707\) −133423. + 159007.i −0.266926 + 0.318110i
\(708\) 107853. + 159502.i 0.215163 + 0.318200i
\(709\) −133037. + 754488.i −0.264654 + 1.50093i 0.505364 + 0.862906i \(0.331358\pi\)
−0.770018 + 0.638022i \(0.779753\pi\)
\(710\) −209167. 981273.i −0.414932 1.94658i
\(711\) 341377. 197094.i 0.675298 0.389883i
\(712\) −9857.88 + 14669.6i −0.0194457 + 0.0289372i
\(713\) −684918. + 249290.i −1.34728 + 0.490371i
\(714\) 57956.0 178721.i 0.113685 0.350573i
\(715\) −753441. 434999.i −1.47379 0.850896i
\(716\) 189040. 662142.i 0.368747 1.29159i
\(717\) −3581.90 + 3005.57i −0.00696747 + 0.00584640i
\(718\) −563384. + 19998.9i −1.09284 + 0.0387932i
\(719\) −505235. + 89086.5i −0.977317 + 0.172327i −0.639422 0.768856i \(-0.720826\pi\)
−0.337895 + 0.941184i \(0.609715\pi\)
\(720\) 627356. + 390007.i 1.21018 + 0.752329i
\(721\) −155004. −0.298176
\(722\) 10555.0 + 521177.i 0.0202482 + 0.999795i
\(723\) 182401.i 0.348940i
\(724\) −136541. + 280772.i −0.260488 + 0.535645i
\(725\) −155426. 881464.i −0.295697 1.67698i
\(726\) −118455. + 4204.88i −0.224739 + 0.00797774i
\(727\) −655488. 781180.i −1.24021 1.47803i −0.821808 0.569765i \(-0.807034\pi\)
−0.418404 0.908261i \(-0.637410\pi\)
\(728\) 940536. 460744.i 1.77465 0.869355i
\(729\) −67436.8 + 116804.i −0.126894 + 0.219787i
\(730\) 491999. 1.51719e6i 0.923249 2.84705i
\(731\) 241454. + 663390.i 0.451856 + 1.24146i
\(732\) −1391.31 + 348.596i −0.00259658 + 0.000650579i
\(733\) −115246. 199613.i −0.214496 0.371518i 0.738621 0.674121i \(-0.235478\pi\)
−0.953117 + 0.302603i \(0.902144\pi\)
\(734\) −64436.6 302294.i −0.119603 0.561096i
\(735\) −158760. 27993.6i −0.293877 0.0518184i
\(736\) 229383. 635919.i 0.423453 1.17394i
\(737\) −127902. 107323.i −0.235474 0.197586i
\(738\) 196118. 251318.i 0.360084 0.461435i
\(739\) −258871. + 711243.i −0.474018 + 1.30235i 0.440480 + 0.897762i \(0.354808\pi\)
−0.914498 + 0.404591i \(0.867414\pi\)
\(740\) −69220.0 + 665966.i −0.126406 + 1.21615i
\(741\) 328505. + 60507.8i 0.598282 + 0.110198i
\(742\) 228957. 206392.i 0.415858 0.374874i
\(743\) −101615. + 279185.i −0.184069 + 0.505726i −0.997066 0.0765419i \(-0.975612\pi\)
0.812997 + 0.582267i \(0.197834\pi\)
\(744\) −171642. 165180.i −0.310082 0.298409i
\(745\) 386444. + 324265.i 0.696265 + 0.584236i
\(746\) −697852. 97666.7i −1.25397 0.175497i
\(747\) 287873. + 50759.9i 0.515894 + 0.0909660i
\(748\) 167839. 231571.i 0.299978 0.413887i
\(749\) −118717. 205624.i −0.211617 0.366531i
\(750\) 122422. 230564.i 0.217640 0.409891i
\(751\) 117557. + 322984.i 0.208433 + 0.572666i 0.999223 0.0394225i \(-0.0125518\pi\)
−0.790789 + 0.612089i \(0.790330\pi\)
\(752\) 412700. 135147.i 0.729792 0.238985i
\(753\) −75247.7 + 130333.i −0.132710 + 0.229860i
\(754\) −762741. + 477225.i −1.34163 + 0.839422i
\(755\) 38565.0 + 45960.0i 0.0676549 + 0.0806280i
\(756\) −348102. + 336934.i −0.609064 + 0.589524i
\(757\) 64616.6 + 366459.i 0.112759 + 0.639490i 0.987835 + 0.155504i \(0.0497002\pi\)
−0.875076 + 0.483986i \(0.839189\pi\)
\(758\) 198961. 80519.0i 0.346282 0.140139i
\(759\) 170249.i 0.295530i
\(760\) −94467.4 952725.i −0.163552 1.64946i
\(761\) −507063. −0.875574 −0.437787 0.899079i \(-0.644238\pi\)
−0.437787 + 0.899079i \(0.644238\pi\)
\(762\) 133418. + 329674.i 0.229776 + 0.567774i
\(763\) −144989. + 25565.4i −0.249049 + 0.0439141i
\(764\) −519051. 536255.i −0.889249 0.918723i
\(765\) 516534. 433423.i 0.882624 0.740610i
\(766\) 300565. + 480389.i 0.512249 + 0.818720i
\(767\) 848461. + 489859.i 1.44225 + 0.832685i
\(768\) 219621. 24107.3i 0.372350 0.0408720i
\(769\) 987248. 359329.i 1.66945 0.607631i 0.677646 0.735389i \(-0.263000\pi\)
0.991805 + 0.127758i \(0.0407781\pi\)
\(770\) −667695. 354526.i −1.12615 0.597953i
\(771\) −95495.7 + 55134.5i −0.160648 + 0.0927501i
\(772\) 947612. + 686813.i 1.59000 + 1.15240i
\(773\) −21922.6 + 124329.i −0.0366888 + 0.208073i −0.997641 0.0686402i \(-0.978134\pi\)
0.960953 + 0.276713i \(0.0892450\pi\)
\(774\) 116633. 833374.i 0.194689 1.39110i
\(775\) 775073. 923697.i 1.29044 1.53789i
\(776\) 635083. + 611175.i 1.05465 + 1.01494i
\(777\) −190747. 69426.3i −0.315948 0.114996i
\(778\) 324345. + 359804.i 0.535856 + 0.594439i
\(779\) −413148. 3146.87i −0.680818 0.00518565i
\(780\) −610199. 63423.6i −1.00296 0.104246i
\(781\) 435099. + 158363.i 0.713322 + 0.259628i
\(782\) −486480. 379629.i −0.795521 0.620791i
\(783\) 267519. 318817.i 0.436346 0.520017i
\(784\) 260513. 139289.i 0.423836 0.226612i
\(785\) 26963.3 152916.i 0.0437556 0.248150i
\(786\) −382070. + 81441.6i −0.618440 + 0.131826i
\(787\) 243297. 140468.i 0.392814 0.226792i −0.290564 0.956855i \(-0.593843\pi\)
0.683379 + 0.730064i \(0.260510\pi\)
\(788\) 122563. + 489172.i 0.197382 + 0.787788i
\(789\) 162905. 59292.5i 0.261685 0.0952457i
\(790\) 892549. + 289438.i 1.43014 + 0.463769i
\(791\) −277016. 159935.i −0.442743 0.255618i
\(792\) −306144. + 149972.i −0.488062 + 0.239089i
\(793\) −5590.73 + 4691.18i −0.00889042 + 0.00745995i
\(794\) −30459.4 858067.i −0.0483149 1.36107i
\(795\) −177819. + 31354.4i −0.281349 + 0.0496094i
\(796\) 203704. + 99062.5i 0.321494 + 0.156345i
\(797\) 835261. 1.31494 0.657469 0.753482i \(-0.271627\pi\)
0.657469 + 0.753482i \(0.271627\pi\)
\(798\) 287138. + 42418.2i 0.450905 + 0.0666111i
\(799\) 396397.i 0.620922i
\(800\) 197375. + 1.10081e6i 0.308399 + 1.72002i
\(801\) −3339.27 18938.0i −0.00520459 0.0295167i
\(802\) −19289.4 543398.i −0.0299896 0.844830i
\(803\) 473134. + 563859.i 0.733758 + 0.874458i
\(804\) −113213. 32322.1i −0.175139 0.0500020i
\(805\) −815557. + 1.41259e6i −1.25853 + 2.17983i
\(806\) −1.15298e6 373892.i −1.77481 0.575541i
\(807\) −16196.2 44498.7i −0.0248695 0.0683283i
\(808\) −124272. + 184929.i −0.190348 + 0.283258i
\(809\) 367353. + 636275.i 0.561290 + 0.972182i 0.997384 + 0.0722814i \(0.0230280\pi\)
−0.436095 + 0.899901i \(0.643639\pi\)
\(810\) −636835. + 135747.i −0.970637 + 0.206900i
\(811\) −1.03782e6 182996.i −1.57791 0.278228i −0.685026 0.728519i \(-0.740209\pi\)
−0.892882 + 0.450291i \(0.851320\pi\)
\(812\) −647651. + 437933.i −0.982266 + 0.664195i
\(813\) 56750.9 + 47619.7i 0.0858602 + 0.0720453i
\(814\) −243600. 190095.i −0.367644 0.286894i
\(815\) −54589.2 + 149983.i −0.0821848 + 0.225801i
\(816\) 41475.6 197363.i 0.0622891 0.296405i
\(817\) −948634. + 538102.i −1.42120 + 0.806159i
\(818\) 574913. + 637766.i 0.859202 + 0.953135i
\(819\) −389743. + 1.07081e6i −0.581046 + 1.59641i
\(820\) 756906. 53804.7i 1.12568 0.0800189i
\(821\) 500490. + 419961.i 0.742522 + 0.623050i 0.933514 0.358542i \(-0.116726\pi\)
−0.190992 + 0.981592i \(0.561170\pi\)
\(822\) −12593.6 + 89984.5i −0.0186383 + 0.133175i
\(823\) −330313. 58243.1i −0.487670 0.0859894i −0.0755937 0.997139i \(-0.524085\pi\)
−0.412076 + 0.911149i \(0.635196\pi\)
\(824\) −165440. + 17677.7i −0.243661 + 0.0260358i
\(825\) 140824. + 243915.i 0.206905 + 0.358369i
\(826\) 751902. + 399238.i 1.10205 + 0.585156i
\(827\) −359439. 987549.i −0.525550 1.44394i −0.864260 0.503045i \(-0.832213\pi\)
0.338711 0.940891i \(-0.390009\pi\)
\(828\) 299946. + 671605.i 0.437504 + 0.979609i
\(829\) −311982. + 540368.i −0.453963 + 0.786286i −0.998628 0.0523672i \(-0.983323\pi\)
0.544665 + 0.838654i \(0.316657\pi\)
\(830\) 369063. + 589868.i 0.535728 + 0.856246i
\(831\) −8257.58 9841.01i −0.0119578 0.0142507i
\(832\) 951314. 599030.i 1.37429 0.865370i
\(833\) −46824.6 265556.i −0.0674814 0.382706i
\(834\) 16686.1 + 41231.0i 0.0239895 + 0.0592778i
\(835\) 331410.i 0.475327i
\(836\) 395854. + 196249.i 0.566399 + 0.280798i
\(837\) 560673. 0.800310
\(838\) 1.00041e6 404863.i 1.42459 0.576527i
\(839\) −9843.90 + 1735.75i −0.0139844 + 0.00246582i −0.180636 0.983550i \(-0.557816\pi\)
0.166652 + 0.986016i \(0.446704\pi\)
\(840\) −531850. 36266.8i −0.753756 0.0513985i
\(841\) −27303.7 + 22910.5i −0.0386038 + 0.0323924i
\(842\) −87131.2 + 54515.5i −0.122899 + 0.0768946i
\(843\) −84105.0 48558.0i −0.118350 0.0683291i
\(844\) −132175. 295951.i −0.185551 0.415466i
\(845\) −1.82118e6 + 662855.i −2.55058 + 0.928336i
\(846\) −221584. + 417318.i −0.309597 + 0.583078i
\(847\) −453857. + 262034.i −0.632633 + 0.365251i
\(848\) 220833. 246400.i 0.307095 0.342649i
\(849\) −59257.3 + 336065.i −0.0822104 + 0.466238i
\(850\) 1.01099e6 + 141492.i 1.39930 + 0.195836i
\(851\) −428539. + 510713.i −0.591741 + 0.705209i
\(852\) 325682. 23151.1i 0.448657 0.0318928i
\(853\) 955679. + 347839.i 1.31345 + 0.478057i 0.901354 0.433082i \(-0.142574\pi\)
0.412098 + 0.911140i \(0.364796\pi\)
\(854\) −4710.36 + 4246.15i −0.00645860 + 0.00582210i
\(855\) 792854. + 675641.i 1.08458 + 0.924238i
\(856\) −150161. 205929.i −0.204932 0.281041i
\(857\) 124345. + 45257.9i 0.169304 + 0.0616216i 0.425281 0.905061i \(-0.360175\pi\)
−0.255978 + 0.966683i \(0.582397\pi\)
\(858\) 174177. 223201.i 0.236600 0.303194i
\(859\) 183890. 219152.i 0.249214 0.297002i −0.626906 0.779095i \(-0.715679\pi\)
0.876120 + 0.482093i \(0.160123\pi\)
\(860\) 1.65931e6 1.12201e6i 2.24353 1.51705i
\(861\) −39947.8 + 226555.i −0.0538874 + 0.305610i
\(862\) 33905.4 + 159062.i 0.0456304 + 0.214067i
\(863\) −106304. + 61374.7i −0.142734 + 0.0824077i −0.569666 0.821876i \(-0.692928\pi\)
0.426932 + 0.904284i \(0.359594\pi\)
\(864\) −333112. + 399319.i −0.446235 + 0.534924i
\(865\) −98558.6 + 35872.4i −0.131723 + 0.0479433i
\(866\) 68522.9 211306.i 0.0913692 0.281758i
\(867\) 84424.1 + 48742.3i 0.112313 + 0.0648437i
\(868\) −1.01277e6 289145.i −1.34423 0.383775i
\(869\) −331713. + 278340.i −0.439261 + 0.368584i
\(870\) 457672. 16246.3i 0.604666 0.0214643i
\(871\) −589974. + 104028.i −0.777673 + 0.137125i
\(872\) −151835. + 43822.1i −0.199682 + 0.0576316i
\(873\) −958997. −1.25831
\(874\) 453462. 838542.i 0.593633 1.09775i
\(875\) 1.15421e6i 1.50754i
\(876\) 466774. + 226995.i 0.608273 + 0.295807i
\(877\) −226320. 1.28352e6i −0.294255 1.66880i −0.670217 0.742165i \(-0.733799\pi\)
0.375962 0.926635i \(-0.377312\pi\)
\(878\) 68718.2 2439.34i 0.0891420 0.00316434i
\(879\) −33913.8 40416.9i −0.0438934 0.0523101i
\(880\) −753082. 302247.i −0.972472 0.390299i
\(881\) −205177. + 355376.i −0.264348 + 0.457864i −0.967393 0.253281i \(-0.918490\pi\)
0.703045 + 0.711146i \(0.251823\pi\)
\(882\) −99148.1 + 305746.i −0.127452 + 0.393028i
\(883\) −115459. 317220.i −0.148083 0.406855i 0.843368 0.537337i \(-0.180570\pi\)
−0.991451 + 0.130482i \(0.958347\pi\)
\(884\) −249401. 995404.i −0.319149 1.27378i
\(885\) −249337. 431864.i −0.318346 0.551392i
\(886\) −29838.1 139981.i −0.0380105 0.178320i
\(887\) −781269. 137759.i −0.993009 0.175094i −0.346541 0.938035i \(-0.612644\pi\)
−0.646469 + 0.762941i \(0.723755\pi\)
\(888\) −211508. 52346.6i −0.268225 0.0663838i
\(889\) 1.20458e6 + 1.01077e6i 1.52417 + 1.27893i
\(890\) 28160.7 36086.9i 0.0355520 0.0455585i
\(891\) 102776. 282374.i 0.129460 0.355688i
\(892\) −302502. 31441.8i −0.380188 0.0395164i
\(893\) 603871. 101743.i 0.757253 0.127585i
\(894\) −121936. + 109919.i −0.152565 + 0.137530i
\(895\) −609962. + 1.67586e6i −0.761477 + 2.09214i
\(896\) 807652. 549521.i 1.00602 0.684492i
\(897\) −467947. 392654.i −0.581583 0.488006i
\(898\) −12798.2 1791.15i −0.0158707 0.00222116i
\(899\) 891065. + 157119.i 1.10253 + 0.194406i
\(900\) −985259. 714099.i −1.21637 0.881604i
\(901\) −151013. 261562.i −0.186022 0.322199i
\(902\) −164224. + 309291.i −0.201848 + 0.380149i
\(903\) 207697. + 570644.i 0.254716 + 0.699825i
\(904\) −313907. 139111.i −0.384117 0.170225i
\(905\) 404301. 700271.i 0.493638 0.855005i
\(906\) −16551.6 + 10355.8i −0.0201643 + 0.0126162i
\(907\) −818198. 975090.i −0.994589 1.18531i −0.982668 0.185376i \(-0.940650\pi\)
−0.0119214 0.999929i \(-0.503795\pi\)
\(908\) 40067.1 + 41395.1i 0.0485977 + 0.0502085i
\(909\) −42095.9 238738.i −0.0509463 0.288931i
\(910\) −2.51439e6 + 1.01756e6i −3.03633 + 1.22879i
\(911\) 939285.i 1.13178i −0.824482 0.565888i \(-0.808533\pi\)
0.824482 0.565888i \(-0.191467\pi\)
\(912\) 311308. + 12527.0i 0.374284 + 0.0150611i
\(913\) −321110. −0.385223
\(914\) −276462. 683134.i −0.330935 0.817736i
\(915\) 3658.31 645.059i 0.00436957 0.000770473i
\(916\) 20608.6 19947.5i 0.0245617 0.0237737i
\(917\) −1.32315e6 + 1.11025e6i −1.57351 + 1.32033i
\(918\) 251770. + 402400.i 0.298758 + 0.477500i
\(919\) 486006. + 280596.i 0.575454 + 0.332239i 0.759325 0.650712i \(-0.225529\pi\)
−0.183871 + 0.982950i \(0.558863\pi\)
\(920\) −709366. + 1.60070e6i −0.838098 + 1.89119i
\(921\) 497651. 181130.i 0.586685 0.213536i
\(922\) 1.29867e6 + 689554.i 1.52769 + 0.811160i
\(923\) 1.43876e6 830670.i 1.68883 0.975047i
\(924\) 144374. 199196.i 0.169101 0.233312i
\(925\) 191521. 1.08617e6i 0.223837 1.26944i
\(926\) 106695. 762360.i 0.124429 0.889075i
\(927\) 116364. 138677.i 0.135412 0.161378i
\(928\) −641311. + 541280.i −0.744685 + 0.628530i
\(929\) 1.19192e6 + 433824.i 1.38107 + 0.502669i 0.922503 0.385990i \(-0.126140\pi\)
0.458569 + 0.888659i \(0.348362\pi\)
\(930\) 413084. + 458245.i 0.477609 + 0.529824i
\(931\) 392529. 139492.i 0.452868 0.160935i
\(932\) 149990. 1.44305e6i 0.172675 1.66131i
\(933\) −352169. 128179.i −0.404565 0.147249i
\(934\) 1.31373e6 + 1.02518e6i 1.50595 + 1.17518i
\(935\) −476120. + 567417.i −0.544619 + 0.649052i
\(936\) −293861. + 1.18735e6i −0.335421 + 1.35528i
\(937\) 140484. 796724.i 0.160010 0.907463i −0.794051 0.607851i \(-0.792032\pi\)
0.954061 0.299612i \(-0.0968571\pi\)
\(938\) −509125. + 108525.i −0.578654 + 0.123345i
\(939\) −206594. + 119277.i −0.234308 + 0.135278i
\(940\) −1.09099e6 + 273349.i −1.23471 + 0.309359i
\(941\) −1.06239e6 + 386677.i −1.19978 + 0.436685i −0.863149 0.504950i \(-0.831511\pi\)
−0.336634 + 0.941635i \(0.609289\pi\)
\(942\) 48066.2 + 15587.0i 0.0541674 + 0.0175655i
\(943\) 654341. + 377784.i 0.735836 + 0.424835i
\(944\) 848057. + 340366.i 0.951659 + 0.381946i
\(945\) 961159. 806508.i 1.07630 0.903119i
\(946\) 32793.2 + 923809.i 0.0366438 + 1.03229i
\(947\) −1.12230e6 + 197892.i −1.25144 + 0.220662i −0.759810 0.650145i \(-0.774708\pi\)
−0.491626 + 0.870807i \(0.663597\pi\)
\(948\) −133539. + 274599.i −0.148591 + 0.305550i
\(949\) 2.64103e6 2.93252
\(950\) 43941.4 + 1.57646e6i 0.0486885 + 1.74677i
\(951\) 501771.i 0.554810i
\(952\) −247264. 856718.i −0.272826 0.945288i
\(953\) −98829.4 560489.i −0.108818 0.617137i −0.989626 0.143664i \(-0.954111\pi\)
0.880809 0.473472i \(-0.157000\pi\)
\(954\) 12771.4 + 359782.i 0.0140328 + 0.395314i
\(955\) 1.24243e6 + 1.48068e6i 1.36228 + 1.62350i
\(956\) −6092.19 + 21338.8i −0.00666588 + 0.0233482i
\(957\) −105672. + 183030.i −0.115382 + 0.199847i
\(958\) −906447. 293945.i −0.987669 0.320284i
\(959\) 137402. + 377510.i 0.149402 + 0.410479i
\(960\) −571795. + 21947.2i −0.620437 + 0.0238142i
\(961\) 147707. + 255835.i 0.159939 + 0.277022i
\(962\) −1.08432e6 + 231132.i −1.17167 + 0.249753i
\(963\) 273088. + 48152.8i 0.294476 + 0.0519241i
\(964\) −484904. 717115.i −0.521797 0.771676i
\(965\) −2.32193e6 1.94833e6i −2.49341 2.09222i
\(966\) −418467. 326554.i −0.448443 0.349946i
\(967\) 106407. 292351.i 0.113793 0.312645i −0.869702 0.493577i \(-0.835689\pi\)
0.983496 + 0.180932i \(0.0579114\pi\)
\(968\) −454530. + 331437.i −0.485078 + 0.353713i
\(969\) 99300.4 266492.i 0.105756 0.283816i
\(970\) −1.52843e6 1.69553e6i −1.62444 1.80203i
\(971\) 102816. 282485.i 0.109049 0.299610i −0.873150 0.487451i \(-0.837927\pi\)
0.982199 + 0.187841i \(0.0601490\pi\)
\(972\) −61691.6 867856.i −0.0652970 0.918576i
\(973\) 150652. + 126412.i 0.159129 + 0.133525i
\(974\) 123058. 879281.i 0.129716 0.926851i
\(975\) 995214. + 175483.i 1.04691 + 0.184598i
\(976\) −4543.24 + 5069.23i −0.00476943 + 0.00532160i
\(977\) 336990. + 583684.i 0.353044 + 0.611489i 0.986781 0.162059i \(-0.0518134\pi\)
−0.633738 + 0.773548i \(0.718480\pi\)
\(978\) −45874.6 24358.1i −0.0479617 0.0254663i
\(979\) 7224.99 + 19850.5i 0.00753827 + 0.0207112i
\(980\) −698587. + 311996.i −0.727392 + 0.324861i
\(981\) 85972.5 148909.i 0.0893350 0.154733i
\(982\) 215176. + 343912.i 0.223137 + 0.356636i
\(983\) −878154. 1.04654e6i −0.908791 1.08305i −0.996218 0.0868836i \(-0.972309\pi\)
0.0874278 0.996171i \(-0.472135\pi\)
\(984\) −16799.6 + 246365.i −0.0173503 + 0.254442i
\(985\) −226797. 1.28623e6i −0.233758 1.32570i
\(986\) 287367. + 710081.i 0.295586 + 0.730389i
\(987\) 340978.i 0.350020i
\(988\) 1.45238e6 635426.i 1.48788 0.650955i
\(989\) 1.99448e6 2.03909
\(990\) 818431. 331216.i 0.835049 0.337942i
\(991\) −187692. + 33095.2i −0.191117 + 0.0336991i −0.268387 0.963311i \(-0.586491\pi\)
0.0772703 + 0.997010i \(0.475380\pi\)
\(992\) −1.11394e6 193109.i −1.13198 0.196237i
\(993\) −315778. + 264969.i −0.320245 + 0.268718i
\(994\) 1.22381e6 765703.i 1.23863 0.774975i
\(995\) −508055. 293326.i −0.513174 0.296281i
\(996\) −206751. + 92337.1i −0.208415 + 0.0930803i
\(997\) 365729. 133115.i 0.367934 0.133917i −0.151435 0.988467i \(-0.548389\pi\)
0.519369 + 0.854550i \(0.326167\pi\)
\(998\) 452970. 853098.i 0.454787 0.856521i
\(999\) 444130. 256419.i 0.445020 0.256932i
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 76.5.l.a.23.14 yes 228
4.3 odd 2 inner 76.5.l.a.23.7 228
19.5 even 9 inner 76.5.l.a.43.7 yes 228
76.43 odd 18 inner 76.5.l.a.43.14 yes 228
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.5.l.a.23.7 228 4.3 odd 2 inner
76.5.l.a.23.14 yes 228 1.1 even 1 trivial
76.5.l.a.43.7 yes 228 19.5 even 9 inner
76.5.l.a.43.14 yes 228 76.43 odd 18 inner