Properties

Label 375.2.i.d.274.5
Level $375$
Weight $2$
Character 375.274
Analytic conductor $2.994$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [375,2,Mod(49,375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(375, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("375.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.i (of order \(10\), degree \(4\), not 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: \(2.99439007580\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 274.5
Character \(\chi\) \(=\) 375.274
Dual form 375.2.i.d.349.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.32085 + 0.754089i) q^{2} +(0.587785 - 0.809017i) q^{3} +(3.19965 + 2.32468i) q^{4} +(1.97423 - 1.43436i) q^{6} -3.44028i q^{7} +(2.80415 + 3.85959i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(2.32085 + 0.754089i) q^{2} +(0.587785 - 0.809017i) q^{3} +(3.19965 + 2.32468i) q^{4} +(1.97423 - 1.43436i) q^{6} -3.44028i q^{7} +(2.80415 + 3.85959i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-1.00942 + 3.10669i) q^{11} +(3.76141 - 1.22216i) q^{12} +(-3.07385 + 0.998755i) q^{13} +(2.59428 - 7.98437i) q^{14} +(1.15323 + 3.54927i) q^{16} +(2.97030 + 4.08826i) q^{17} -2.44028i q^{18} +(-2.49274 + 1.81108i) q^{19} +(-2.78325 - 2.02215i) q^{21} +(-4.68544 + 6.44895i) q^{22} +(-1.47190 - 0.478250i) q^{23} +4.77071 q^{24} -7.88709 q^{26} +(-0.951057 - 0.309017i) q^{27} +(7.99756 - 11.0077i) q^{28} +(-2.52590 - 1.83517i) q^{29} +(-6.02080 + 4.37437i) q^{31} -0.434479i q^{32} +(1.92004 + 2.64270i) q^{33} +(3.81069 + 11.7281i) q^{34} +(1.22216 - 3.76141i) q^{36} +(5.47655 - 1.77944i) q^{37} +(-7.15098 + 2.32349i) q^{38} +(-0.998755 + 3.07385i) q^{39} +(1.67476 + 5.15437i) q^{41} +(-4.93461 - 6.79191i) q^{42} -2.53106i q^{43} +(-10.4519 + 7.59371i) q^{44} +(-3.05541 - 2.21989i) q^{46} +(4.15659 - 5.72106i) q^{47} +(3.54927 + 1.15323i) q^{48} -4.83555 q^{49} +5.05337 q^{51} +(-12.1570 - 3.95006i) q^{52} +(5.96693 - 8.21277i) q^{53} +(-1.97423 - 1.43436i) q^{54} +(13.2781 - 9.64708i) q^{56} +3.08119i q^{57} +(-4.47834 - 6.16391i) q^{58} +(-0.534773 - 1.64586i) q^{59} +(2.42149 - 7.45259i) q^{61} +(-17.2720 + 5.61202i) q^{62} +(-3.27190 + 1.06311i) q^{63} +(2.63409 - 8.10689i) q^{64} +(2.46328 + 7.58119i) q^{66} +(1.08687 + 1.49595i) q^{67} +19.9860i q^{68} +(-1.25207 + 0.909685i) q^{69} +(0.577613 + 0.419660i) q^{71} +(2.80415 - 3.85959i) q^{72} +(1.78825 + 0.581036i) q^{73} +14.0521 q^{74} -12.1861 q^{76} +(10.6879 + 3.47270i) q^{77} +(-4.63591 + 6.38079i) q^{78} +(-10.7868 - 7.83708i) q^{79} +(-0.809017 + 0.587785i) q^{81} +13.2254i q^{82} +(2.32614 + 3.20166i) q^{83} +(-4.20457 - 12.9403i) q^{84} +(1.90864 - 5.87419i) q^{86} +(-2.96937 + 0.964807i) q^{87} +(-14.8211 + 4.81567i) q^{88} +(-2.63713 + 8.11624i) q^{89} +(3.43600 + 10.5749i) q^{91} +(-3.59779 - 4.95193i) q^{92} +7.44212i q^{93} +(13.9610 - 10.1433i) q^{94} +(-0.351501 - 0.255380i) q^{96} +(-6.26157 + 8.61831i) q^{97} +(-11.2226 - 3.64643i) q^{98} +3.26656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.32085 + 0.754089i 1.64109 + 0.533221i 0.976781 0.214240i \(-0.0687273\pi\)
0.664306 + 0.747461i \(0.268727\pi\)
\(3\) 0.587785 0.809017i 0.339358 0.467086i
\(4\) 3.19965 + 2.32468i 1.59982 + 1.16234i
\(5\) 0 0
\(6\) 1.97423 1.43436i 0.805976 0.585576i
\(7\) 3.44028i 1.30030i −0.759804 0.650152i \(-0.774705\pi\)
0.759804 0.650152i \(-0.225295\pi\)
\(8\) 2.80415 + 3.85959i 0.991418 + 1.36457i
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) 0 0
\(11\) −1.00942 + 3.10669i −0.304353 + 0.936701i 0.675565 + 0.737300i \(0.263900\pi\)
−0.979918 + 0.199401i \(0.936100\pi\)
\(12\) 3.76141 1.22216i 1.08583 0.352806i
\(13\) −3.07385 + 0.998755i −0.852533 + 0.277005i −0.702506 0.711677i \(-0.747936\pi\)
−0.150026 + 0.988682i \(0.547936\pi\)
\(14\) 2.59428 7.98437i 0.693350 2.13391i
\(15\) 0 0
\(16\) 1.15323 + 3.54927i 0.288307 + 0.887317i
\(17\) 2.97030 + 4.08826i 0.720403 + 0.991550i 0.999510 + 0.0312897i \(0.00996144\pi\)
−0.279107 + 0.960260i \(0.590039\pi\)
\(18\) 2.44028i 0.575180i
\(19\) −2.49274 + 1.81108i −0.571873 + 0.415490i −0.835785 0.549056i \(-0.814987\pi\)
0.263912 + 0.964547i \(0.414987\pi\)
\(20\) 0 0
\(21\) −2.78325 2.02215i −0.607354 0.441269i
\(22\) −4.68544 + 6.44895i −0.998938 + 1.37492i
\(23\) −1.47190 0.478250i −0.306913 0.0997219i 0.151512 0.988455i \(-0.451586\pi\)
−0.458424 + 0.888734i \(0.651586\pi\)
\(24\) 4.77071 0.973817
\(25\) 0 0
\(26\) −7.88709 −1.54679
\(27\) −0.951057 0.309017i −0.183031 0.0594703i
\(28\) 7.99756 11.0077i 1.51140 2.08026i
\(29\) −2.52590 1.83517i −0.469047 0.340783i 0.328022 0.944670i \(-0.393618\pi\)
−0.797070 + 0.603887i \(0.793618\pi\)
\(30\) 0 0
\(31\) −6.02080 + 4.37437i −1.08137 + 0.785659i −0.977921 0.208976i \(-0.932987\pi\)
−0.103446 + 0.994635i \(0.532987\pi\)
\(32\) 0.434479i 0.0768057i
\(33\) 1.92004 + 2.64270i 0.334236 + 0.460036i
\(34\) 3.81069 + 11.7281i 0.653528 + 2.01135i
\(35\) 0 0
\(36\) 1.22216 3.76141i 0.203693 0.626902i
\(37\) 5.47655 1.77944i 0.900339 0.292538i 0.177962 0.984037i \(-0.443050\pi\)
0.722377 + 0.691499i \(0.243050\pi\)
\(38\) −7.15098 + 2.32349i −1.16004 + 0.376921i
\(39\) −0.998755 + 3.07385i −0.159929 + 0.492210i
\(40\) 0 0
\(41\) 1.67476 + 5.15437i 0.261553 + 0.804977i 0.992468 + 0.122508i \(0.0390938\pi\)
−0.730915 + 0.682469i \(0.760906\pi\)
\(42\) −4.93461 6.79191i −0.761427 1.04801i
\(43\) 2.53106i 0.385982i −0.981201 0.192991i \(-0.938181\pi\)
0.981201 0.192991i \(-0.0618189\pi\)
\(44\) −10.4519 + 7.59371i −1.57568 + 1.14480i
\(45\) 0 0
\(46\) −3.05541 2.21989i −0.450496 0.327305i
\(47\) 4.15659 5.72106i 0.606301 0.834502i −0.389966 0.920829i \(-0.627513\pi\)
0.996267 + 0.0863273i \(0.0275131\pi\)
\(48\) 3.54927 + 1.15323i 0.512293 + 0.166454i
\(49\) −4.83555 −0.690793
\(50\) 0 0
\(51\) 5.05337 0.707614
\(52\) −12.1570 3.95006i −1.68588 0.547774i
\(53\) 5.96693 8.21277i 0.819621 1.12811i −0.170147 0.985419i \(-0.554424\pi\)
0.989767 0.142692i \(-0.0455759\pi\)
\(54\) −1.97423 1.43436i −0.268659 0.195192i
\(55\) 0 0
\(56\) 13.2781 9.64708i 1.77436 1.28915i
\(57\) 3.08119i 0.408114i
\(58\) −4.47834 6.16391i −0.588035 0.809361i
\(59\) −0.534773 1.64586i −0.0696215 0.214273i 0.910192 0.414187i \(-0.135934\pi\)
−0.979814 + 0.199913i \(0.935934\pi\)
\(60\) 0 0
\(61\) 2.42149 7.45259i 0.310040 0.954206i −0.667708 0.744424i \(-0.732724\pi\)
0.977748 0.209783i \(-0.0672756\pi\)
\(62\) −17.2720 + 5.61202i −2.19355 + 0.712727i
\(63\) −3.27190 + 1.06311i −0.412221 + 0.133939i
\(64\) 2.63409 8.10689i 0.329261 1.01336i
\(65\) 0 0
\(66\) 2.46328 + 7.58119i 0.303209 + 0.933180i
\(67\) 1.08687 + 1.49595i 0.132783 + 0.182760i 0.870231 0.492644i \(-0.163969\pi\)
−0.737448 + 0.675404i \(0.763969\pi\)
\(68\) 19.9860i 2.42366i
\(69\) −1.25207 + 0.909685i −0.150732 + 0.109513i
\(70\) 0 0
\(71\) 0.577613 + 0.419660i 0.0685500 + 0.0498045i 0.621533 0.783388i \(-0.286510\pi\)
−0.552982 + 0.833193i \(0.686510\pi\)
\(72\) 2.80415 3.85959i 0.330473 0.454857i
\(73\) 1.78825 + 0.581036i 0.209298 + 0.0680052i 0.411790 0.911279i \(-0.364904\pi\)
−0.202491 + 0.979284i \(0.564904\pi\)
\(74\) 14.0521 1.63352
\(75\) 0 0
\(76\) −12.1861 −1.39784
\(77\) 10.6879 + 3.47270i 1.21800 + 0.395751i
\(78\) −4.63591 + 6.38079i −0.524914 + 0.722482i
\(79\) −10.7868 7.83708i −1.21361 0.881740i −0.218058 0.975936i \(-0.569972\pi\)
−0.995554 + 0.0941957i \(0.969972\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 13.2254i 1.46050i
\(83\) 2.32614 + 3.20166i 0.255328 + 0.351428i 0.917368 0.398040i \(-0.130309\pi\)
−0.662041 + 0.749468i \(0.730309\pi\)
\(84\) −4.20457 12.9403i −0.458756 1.41190i
\(85\) 0 0
\(86\) 1.90864 5.87419i 0.205814 0.633430i
\(87\) −2.96937 + 0.964807i −0.318350 + 0.103438i
\(88\) −14.8211 + 4.81567i −1.57993 + 0.513352i
\(89\) −2.63713 + 8.11624i −0.279535 + 0.860320i 0.708449 + 0.705762i \(0.249395\pi\)
−0.987984 + 0.154558i \(0.950605\pi\)
\(90\) 0 0
\(91\) 3.43600 + 10.5749i 0.360191 + 1.10855i
\(92\) −3.59779 4.95193i −0.375095 0.516274i
\(93\) 7.44212i 0.771712i
\(94\) 13.9610 10.1433i 1.43997 1.04620i
\(95\) 0 0
\(96\) −0.351501 0.255380i −0.0358749 0.0260646i
\(97\) −6.26157 + 8.61831i −0.635766 + 0.875057i −0.998381 0.0568823i \(-0.981884\pi\)
0.362615 + 0.931939i \(0.381884\pi\)
\(98\) −11.2226 3.64643i −1.13365 0.368345i
\(99\) 3.26656 0.328302
\(100\) 0 0
\(101\) 1.76173 0.175299 0.0876496 0.996151i \(-0.472064\pi\)
0.0876496 + 0.996151i \(0.472064\pi\)
\(102\) 11.7281 + 3.81069i 1.16126 + 0.377315i
\(103\) −9.35416 + 12.8749i −0.921693 + 1.26860i 0.0413198 + 0.999146i \(0.486844\pi\)
−0.963013 + 0.269456i \(0.913156\pi\)
\(104\) −12.4743 9.06313i −1.22321 0.888713i
\(105\) 0 0
\(106\) 20.0415 14.5610i 1.94660 1.41429i
\(107\) 15.7807i 1.52558i −0.646649 0.762788i \(-0.723830\pi\)
0.646649 0.762788i \(-0.276170\pi\)
\(108\) −2.32468 3.19965i −0.223692 0.307886i
\(109\) 3.06539 + 9.43429i 0.293611 + 0.903641i 0.983685 + 0.179902i \(0.0575781\pi\)
−0.690074 + 0.723739i \(0.742422\pi\)
\(110\) 0 0
\(111\) 1.77944 5.47655i 0.168897 0.519811i
\(112\) 12.2105 3.96743i 1.15378 0.374887i
\(113\) 5.24399 1.70388i 0.493313 0.160287i −0.0517868 0.998658i \(-0.516492\pi\)
0.545100 + 0.838371i \(0.316492\pi\)
\(114\) −2.32349 + 7.15098i −0.217615 + 0.669751i
\(115\) 0 0
\(116\) −3.81580 11.7438i −0.354288 1.09039i
\(117\) 1.89974 + 2.61477i 0.175631 + 0.241736i
\(118\) 4.22306i 0.388764i
\(119\) 14.0648 10.2187i 1.28932 0.936743i
\(120\) 0 0
\(121\) 0.266626 + 0.193715i 0.0242387 + 0.0176105i
\(122\) 11.2398 15.4703i 1.01761 1.40061i
\(123\) 5.15437 + 1.67476i 0.464754 + 0.151008i
\(124\) −29.4334 −2.64320
\(125\) 0 0
\(126\) −8.39527 −0.747910
\(127\) −0.943532 0.306572i −0.0837250 0.0272039i 0.266855 0.963737i \(-0.414016\pi\)
−0.350580 + 0.936533i \(0.614016\pi\)
\(128\) 11.7159 16.1255i 1.03555 1.42531i
\(129\) −2.04767 1.48772i −0.180287 0.130986i
\(130\) 0 0
\(131\) 10.2029 7.41286i 0.891434 0.647665i −0.0448175 0.998995i \(-0.514271\pi\)
0.936252 + 0.351330i \(0.114271\pi\)
\(132\) 12.9192i 1.12447i
\(133\) 6.23063 + 8.57573i 0.540264 + 0.743610i
\(134\) 1.39438 + 4.29147i 0.120456 + 0.370727i
\(135\) 0 0
\(136\) −7.44984 + 22.9282i −0.638818 + 1.96608i
\(137\) −7.83732 + 2.54650i −0.669588 + 0.217562i −0.624031 0.781400i \(-0.714506\pi\)
−0.0455566 + 0.998962i \(0.514506\pi\)
\(138\) −3.59186 + 1.16706i −0.305759 + 0.0993471i
\(139\) −2.49182 + 7.66904i −0.211354 + 0.650479i 0.788039 + 0.615626i \(0.211097\pi\)
−0.999392 + 0.0348539i \(0.988903\pi\)
\(140\) 0 0
\(141\) −2.18525 6.72551i −0.184031 0.566390i
\(142\) 1.02409 + 1.40954i 0.0859397 + 0.118286i
\(143\) 10.5577i 0.882875i
\(144\) 3.01919 2.19357i 0.251599 0.182797i
\(145\) 0 0
\(146\) 3.71209 + 2.69699i 0.307215 + 0.223205i
\(147\) −2.84226 + 3.91204i −0.234426 + 0.322660i
\(148\) 21.6597 + 7.03765i 1.78041 + 0.578491i
\(149\) 19.1101 1.56556 0.782781 0.622298i \(-0.213801\pi\)
0.782781 + 0.622298i \(0.213801\pi\)
\(150\) 0 0
\(151\) 1.58550 0.129026 0.0645132 0.997917i \(-0.479451\pi\)
0.0645132 + 0.997917i \(0.479451\pi\)
\(152\) −13.9800 4.54239i −1.13393 0.368437i
\(153\) 2.97030 4.08826i 0.240134 0.330517i
\(154\) 22.1862 + 16.1192i 1.78782 + 1.29892i
\(155\) 0 0
\(156\) −10.3414 + 7.51345i −0.827973 + 0.601558i
\(157\) 21.8510i 1.74390i −0.489599 0.871948i \(-0.662857\pi\)
0.489599 0.871948i \(-0.337143\pi\)
\(158\) −19.1247 26.3229i −1.52148 2.09414i
\(159\) −3.13700 9.65469i −0.248780 0.765667i
\(160\) 0 0
\(161\) −1.64531 + 5.06376i −0.129669 + 0.399080i
\(162\) −2.32085 + 0.754089i −0.182343 + 0.0592468i
\(163\) 9.63786 3.13153i 0.754896 0.245280i 0.0938092 0.995590i \(-0.470096\pi\)
0.661087 + 0.750310i \(0.270096\pi\)
\(164\) −6.62363 + 20.3854i −0.517219 + 1.59184i
\(165\) 0 0
\(166\) 2.98429 + 9.18469i 0.231626 + 0.712870i
\(167\) 0.888195 + 1.22250i 0.0687306 + 0.0945996i 0.841998 0.539480i \(-0.181379\pi\)
−0.773268 + 0.634080i \(0.781379\pi\)
\(168\) 16.4126i 1.26626i
\(169\) −2.06617 + 1.50116i −0.158936 + 0.115474i
\(170\) 0 0
\(171\) 2.49274 + 1.81108i 0.190624 + 0.138497i
\(172\) 5.88389 8.09848i 0.448643 0.617504i
\(173\) 13.1772 + 4.28153i 1.00184 + 0.325518i 0.763602 0.645688i \(-0.223429\pi\)
0.238241 + 0.971206i \(0.423429\pi\)
\(174\) −7.61901 −0.577595
\(175\) 0 0
\(176\) −12.1906 −0.918897
\(177\) −1.64586 0.534773i −0.123711 0.0401960i
\(178\) −12.2407 + 16.8479i −0.917482 + 1.26281i
\(179\) 11.6949 + 8.49685i 0.874119 + 0.635085i 0.931689 0.363257i \(-0.118335\pi\)
−0.0575701 + 0.998341i \(0.518335\pi\)
\(180\) 0 0
\(181\) −13.9068 + 10.1039i −1.03369 + 0.751017i −0.969043 0.246891i \(-0.920591\pi\)
−0.0646435 + 0.997908i \(0.520591\pi\)
\(182\) 27.1338i 2.01129i
\(183\) −4.60595 6.33955i −0.340482 0.468633i
\(184\) −2.28159 7.02201i −0.168201 0.517670i
\(185\) 0 0
\(186\) −5.61202 + 17.2720i −0.411493 + 1.26645i
\(187\) −15.6992 + 5.10099i −1.14804 + 0.373021i
\(188\) 26.5993 8.64262i 1.93995 0.630328i
\(189\) −1.06311 + 3.27190i −0.0773296 + 0.237996i
\(190\) 0 0
\(191\) 3.25778 + 10.0264i 0.235725 + 0.725486i 0.997024 + 0.0770858i \(0.0245615\pi\)
−0.761300 + 0.648400i \(0.775438\pi\)
\(192\) −5.01034 6.89613i −0.361590 0.497686i
\(193\) 0.682908i 0.0491568i 0.999698 + 0.0245784i \(0.00782434\pi\)
−0.999698 + 0.0245784i \(0.992176\pi\)
\(194\) −21.0311 + 15.2800i −1.50995 + 1.09704i
\(195\) 0 0
\(196\) −15.4721 11.2411i −1.10515 0.802936i
\(197\) −13.6937 + 18.8478i −0.975639 + 1.34285i −0.0364929 + 0.999334i \(0.511619\pi\)
−0.939146 + 0.343518i \(0.888381\pi\)
\(198\) 7.58119 + 2.46328i 0.538772 + 0.175058i
\(199\) −10.1946 −0.722679 −0.361339 0.932434i \(-0.617680\pi\)
−0.361339 + 0.932434i \(0.617680\pi\)
\(200\) 0 0
\(201\) 1.84910 0.130425
\(202\) 4.08872 + 1.32850i 0.287681 + 0.0934733i
\(203\) −6.31351 + 8.68980i −0.443122 + 0.609905i
\(204\) 16.1690 + 11.7475i 1.13206 + 0.822488i
\(205\) 0 0
\(206\) −31.4184 + 22.8268i −2.18902 + 1.59042i
\(207\) 1.54765i 0.107569i
\(208\) −7.08969 9.75813i −0.491582 0.676604i
\(209\) −3.11023 9.57230i −0.215139 0.662130i
\(210\) 0 0
\(211\) 5.64172 17.3634i 0.388392 1.19535i −0.545598 0.838047i \(-0.683697\pi\)
0.933990 0.357300i \(-0.116303\pi\)
\(212\) 38.1841 12.4068i 2.62250 0.852101i
\(213\) 0.679025 0.220629i 0.0465260 0.0151172i
\(214\) 11.9000 36.6245i 0.813470 2.50360i
\(215\) 0 0
\(216\) −1.47423 4.53722i −0.100309 0.308718i
\(217\) 15.0491 + 20.7133i 1.02160 + 1.40611i
\(218\) 24.2071i 1.63951i
\(219\) 1.52117 1.10520i 0.102791 0.0746823i
\(220\) 0 0
\(221\) −13.2134 9.60011i −0.888831 0.645774i
\(222\) 8.25961 11.3684i 0.554349 0.762996i
\(223\) −16.3813 5.32262i −1.09698 0.356429i −0.296037 0.955176i \(-0.595665\pi\)
−0.800938 + 0.598748i \(0.795665\pi\)
\(224\) −1.49473 −0.0998708
\(225\) 0 0
\(226\) 13.4554 0.895039
\(227\) −4.11692 1.33767i −0.273250 0.0887842i 0.169187 0.985584i \(-0.445886\pi\)
−0.442437 + 0.896800i \(0.645886\pi\)
\(228\) −7.16279 + 9.85874i −0.474367 + 0.652911i
\(229\) 16.4349 + 11.9407i 1.08605 + 0.789062i 0.978728 0.205163i \(-0.0657723\pi\)
0.107322 + 0.994224i \(0.465772\pi\)
\(230\) 0 0
\(231\) 9.09165 6.60547i 0.598187 0.434608i
\(232\) 14.8950i 0.977906i
\(233\) −0.200409 0.275839i −0.0131292 0.0180708i 0.802402 0.596784i \(-0.203555\pi\)
−0.815531 + 0.578713i \(0.803555\pi\)
\(234\) 2.43724 + 7.50107i 0.159328 + 0.490360i
\(235\) 0 0
\(236\) 2.11502 6.50936i 0.137676 0.423723i
\(237\) −12.6807 + 4.12020i −0.823697 + 0.267635i
\(238\) 40.3480 13.1099i 2.61537 0.849786i
\(239\) 2.21407 6.81421i 0.143216 0.440774i −0.853561 0.520993i \(-0.825562\pi\)
0.996777 + 0.0802185i \(0.0255618\pi\)
\(240\) 0 0
\(241\) −3.88194 11.9474i −0.250058 0.769599i −0.994763 0.102206i \(-0.967410\pi\)
0.744705 0.667393i \(-0.232590\pi\)
\(242\) 0.472720 + 0.650643i 0.0303876 + 0.0418249i
\(243\) 1.00000i 0.0641500i
\(244\) 25.0728 18.2165i 1.60512 1.16619i
\(245\) 0 0
\(246\) 10.6996 + 7.77370i 0.682181 + 0.495633i
\(247\) 5.85348 8.05662i 0.372448 0.512631i
\(248\) −33.7665 10.9714i −2.14417 0.696684i
\(249\) 3.95747 0.250795
\(250\) 0 0
\(251\) 17.0160 1.07404 0.537022 0.843568i \(-0.319549\pi\)
0.537022 + 0.843568i \(0.319549\pi\)
\(252\) −12.9403 4.20457i −0.815164 0.264863i
\(253\) 2.97154 4.08998i 0.186819 0.257135i
\(254\) −1.95861 1.42301i −0.122894 0.0892879i
\(255\) 0 0
\(256\) 25.5586 18.5694i 1.59741 1.16059i
\(257\) 4.13200i 0.257747i 0.991661 + 0.128874i \(0.0411361\pi\)
−0.991661 + 0.128874i \(0.958864\pi\)
\(258\) −3.63045 4.99689i −0.226022 0.311093i
\(259\) −6.12177 18.8409i −0.380388 1.17072i
\(260\) 0 0
\(261\) −0.964807 + 2.96937i −0.0597201 + 0.183799i
\(262\) 29.2694 9.51020i 1.80827 0.587542i
\(263\) −0.986940 + 0.320676i −0.0608573 + 0.0197737i −0.339287 0.940683i \(-0.610186\pi\)
0.278430 + 0.960456i \(0.410186\pi\)
\(264\) −4.81567 + 14.8211i −0.296384 + 0.912176i
\(265\) 0 0
\(266\) 7.99348 + 24.6014i 0.490112 + 1.50841i
\(267\) 5.01611 + 6.90408i 0.306981 + 0.422523i
\(268\) 7.31315i 0.446722i
\(269\) −12.7741 + 9.28093i −0.778851 + 0.565869i −0.904634 0.426189i \(-0.859856\pi\)
0.125783 + 0.992058i \(0.459856\pi\)
\(270\) 0 0
\(271\) 11.0838 + 8.05286i 0.673294 + 0.489176i 0.871126 0.491059i \(-0.163390\pi\)
−0.197832 + 0.980236i \(0.563390\pi\)
\(272\) −11.0849 + 15.2571i −0.672122 + 0.925096i
\(273\) 10.5749 + 3.43600i 0.640023 + 0.207956i
\(274\) −20.1095 −1.21486
\(275\) 0 0
\(276\) −6.12092 −0.368436
\(277\) 6.63827 + 2.15691i 0.398855 + 0.129596i 0.501574 0.865114i \(-0.332754\pi\)
−0.102719 + 0.994710i \(0.532754\pi\)
\(278\) −11.5663 + 15.9196i −0.693699 + 0.954795i
\(279\) 6.02080 + 4.37437i 0.360456 + 0.261886i
\(280\) 0 0
\(281\) −6.43834 + 4.67773i −0.384079 + 0.279050i −0.763025 0.646369i \(-0.776287\pi\)
0.378946 + 0.925419i \(0.376287\pi\)
\(282\) 17.2567i 1.02762i
\(283\) −16.3376 22.4868i −0.971169 1.33670i −0.941454 0.337141i \(-0.890540\pi\)
−0.0297149 0.999558i \(-0.509460\pi\)
\(284\) 0.872582 + 2.68553i 0.0517782 + 0.159357i
\(285\) 0 0
\(286\) 7.96141 24.5027i 0.470768 1.44888i
\(287\) 17.7325 5.76163i 1.04672 0.340099i
\(288\) −0.413214 + 0.134261i −0.0243488 + 0.00791142i
\(289\) −2.63794 + 8.11876i −0.155173 + 0.477574i
\(290\) 0 0
\(291\) 3.29190 + 10.1314i 0.192975 + 0.593915i
\(292\) 4.37103 + 6.01621i 0.255795 + 0.352072i
\(293\) 14.2098i 0.830146i 0.909788 + 0.415073i \(0.136244\pi\)
−0.909788 + 0.415073i \(0.863756\pi\)
\(294\) −9.54649 + 6.93593i −0.556763 + 0.404512i
\(295\) 0 0
\(296\) 22.2250 + 16.1474i 1.29180 + 0.938548i
\(297\) 1.92004 2.64270i 0.111412 0.153345i
\(298\) 44.3517 + 14.4107i 2.56922 + 0.834791i
\(299\) 5.00206 0.289276
\(300\) 0 0
\(301\) −8.70755 −0.501895
\(302\) 3.67971 + 1.19561i 0.211744 + 0.0687997i
\(303\) 1.03552 1.42527i 0.0594892 0.0818798i
\(304\) −9.30270 6.75881i −0.533547 0.387644i
\(305\) 0 0
\(306\) 9.97652 7.24837i 0.570320 0.414362i
\(307\) 23.2911i 1.32930i −0.747157 0.664648i \(-0.768582\pi\)
0.747157 0.664648i \(-0.231418\pi\)
\(308\) 26.1245 + 35.9573i 1.48858 + 2.04886i
\(309\) 4.91777 + 15.1354i 0.279762 + 0.861020i
\(310\) 0 0
\(311\) −2.33284 + 7.17976i −0.132283 + 0.407127i −0.995158 0.0982923i \(-0.968662\pi\)
0.862874 + 0.505419i \(0.168662\pi\)
\(312\) −14.6645 + 4.76477i −0.830211 + 0.269752i
\(313\) −30.1072 + 9.78241i −1.70176 + 0.552934i −0.988927 0.148402i \(-0.952587\pi\)
−0.712830 + 0.701337i \(0.752587\pi\)
\(314\) 16.4776 50.7127i 0.929883 2.86188i
\(315\) 0 0
\(316\) −16.2953 50.1518i −0.916682 2.82126i
\(317\) −15.1861 20.9019i −0.852938 1.17397i −0.983208 0.182490i \(-0.941584\pi\)
0.130270 0.991479i \(-0.458416\pi\)
\(318\) 24.7726i 1.38918i
\(319\) 8.25100 5.99471i 0.461968 0.335639i
\(320\) 0 0
\(321\) −12.7668 9.27565i −0.712575 0.517716i
\(322\) −7.63705 + 10.5115i −0.425596 + 0.585783i
\(323\) −14.8083 4.81152i −0.823959 0.267720i
\(324\) −3.95498 −0.219721
\(325\) 0 0
\(326\) 24.7295 1.36964
\(327\) 9.43429 + 3.06539i 0.521717 + 0.169516i
\(328\) −15.1975 + 20.9175i −0.839139 + 1.15498i
\(329\) −19.6821 14.2999i −1.08511 0.788376i
\(330\) 0 0
\(331\) −16.2679 + 11.8193i −0.894166 + 0.649650i −0.936961 0.349434i \(-0.886374\pi\)
0.0427948 + 0.999084i \(0.486374\pi\)
\(332\) 15.6517i 0.859001i
\(333\) −3.38469 4.65863i −0.185480 0.255291i
\(334\) 1.13949 + 3.50700i 0.0623504 + 0.191895i
\(335\) 0 0
\(336\) 3.96743 12.2105i 0.216441 0.666137i
\(337\) −3.21816 + 1.04564i −0.175304 + 0.0569599i −0.395354 0.918529i \(-0.629378\pi\)
0.220050 + 0.975489i \(0.429378\pi\)
\(338\) −5.92729 + 1.92589i −0.322402 + 0.104755i
\(339\) 1.70388 5.24399i 0.0925419 0.284815i
\(340\) 0 0
\(341\) −7.51225 23.1203i −0.406811 1.25204i
\(342\) 4.41955 + 6.08299i 0.238982 + 0.328930i
\(343\) 7.44633i 0.402064i
\(344\) 9.76882 7.09747i 0.526700 0.382670i
\(345\) 0 0
\(346\) 27.3536 + 19.8735i 1.47054 + 1.06841i
\(347\) −17.1612 + 23.6204i −0.921262 + 1.26801i 0.0419100 + 0.999121i \(0.486656\pi\)
−0.963172 + 0.268887i \(0.913344\pi\)
\(348\) −11.7438 3.81580i −0.629534 0.204548i
\(349\) 20.3979 1.09187 0.545937 0.837826i \(-0.316174\pi\)
0.545937 + 0.837826i \(0.316174\pi\)
\(350\) 0 0
\(351\) 3.23204 0.172513
\(352\) 1.34979 + 0.438573i 0.0719440 + 0.0233760i
\(353\) 1.09532 1.50757i 0.0582978 0.0802400i −0.778873 0.627182i \(-0.784208\pi\)
0.837170 + 0.546942i \(0.184208\pi\)
\(354\) −3.41653 2.48225i −0.181586 0.131930i
\(355\) 0 0
\(356\) −27.3055 + 19.8386i −1.44719 + 1.05145i
\(357\) 17.3850i 0.920113i
\(358\) 20.7347 + 28.5389i 1.09586 + 1.50833i
\(359\) −1.18599 3.65011i −0.0625943 0.192645i 0.914869 0.403751i \(-0.132294\pi\)
−0.977463 + 0.211105i \(0.932294\pi\)
\(360\) 0 0
\(361\) −2.93759 + 9.04097i −0.154610 + 0.475841i
\(362\) −39.8949 + 12.9626i −2.09683 + 0.681301i
\(363\) 0.313438 0.101842i 0.0164512 0.00534532i
\(364\) −13.5893 + 41.8236i −0.712274 + 2.19215i
\(365\) 0 0
\(366\) −5.90913 18.1864i −0.308875 0.950620i
\(367\) −15.0638 20.7335i −0.786324 1.08228i −0.994556 0.104203i \(-0.966771\pi\)
0.208232 0.978079i \(-0.433229\pi\)
\(368\) 5.77570i 0.301079i
\(369\) 4.38457 3.18557i 0.228251 0.165834i
\(370\) 0 0
\(371\) −28.2543 20.5279i −1.46689 1.06576i
\(372\) −17.3005 + 23.8122i −0.896991 + 1.23460i
\(373\) −20.3877 6.62437i −1.05564 0.342997i −0.270758 0.962648i \(-0.587274\pi\)
−0.784878 + 0.619651i \(0.787274\pi\)
\(374\) −40.2821 −2.08294
\(375\) 0 0
\(376\) 33.7366 1.73983
\(377\) 9.59712 + 3.11829i 0.494277 + 0.160600i
\(378\) −4.93461 + 6.79191i −0.253809 + 0.349338i
\(379\) −20.9304 15.2068i −1.07512 0.781120i −0.0982945 0.995157i \(-0.531339\pi\)
−0.976826 + 0.214037i \(0.931339\pi\)
\(380\) 0 0
\(381\) −0.802617 + 0.583135i −0.0411193 + 0.0298749i
\(382\) 25.7264i 1.31628i
\(383\) −8.54263 11.7579i −0.436508 0.600802i 0.532924 0.846163i \(-0.321093\pi\)
−0.969432 + 0.245362i \(0.921093\pi\)
\(384\) −6.15940 18.9567i −0.314321 0.967379i
\(385\) 0 0
\(386\) −0.514974 + 1.58493i −0.0262115 + 0.0806706i
\(387\) −2.40718 + 0.782139i −0.122364 + 0.0397584i
\(388\) −40.0696 + 13.0194i −2.03423 + 0.660960i
\(389\) −7.13973 + 21.9738i −0.361999 + 1.11412i 0.589840 + 0.807520i \(0.299191\pi\)
−0.951839 + 0.306598i \(0.900809\pi\)
\(390\) 0 0
\(391\) −2.41677 7.43806i −0.122221 0.376159i
\(392\) −13.5596 18.6632i −0.684864 0.942635i
\(393\) 12.6115i 0.636167i
\(394\) −45.9940 + 33.4166i −2.31715 + 1.68350i
\(395\) 0 0
\(396\) 10.4519 + 7.59371i 0.525225 + 0.381598i
\(397\) 8.19052 11.2733i 0.411070 0.565790i −0.552409 0.833573i \(-0.686291\pi\)
0.963479 + 0.267784i \(0.0862912\pi\)
\(398\) −23.6602 7.68766i −1.18598 0.385348i
\(399\) 10.6002 0.530673
\(400\) 0 0
\(401\) −27.5822 −1.37739 −0.688694 0.725052i \(-0.741816\pi\)
−0.688694 + 0.725052i \(0.741816\pi\)
\(402\) 4.29147 + 1.39438i 0.214039 + 0.0695456i
\(403\) 14.1381 19.4594i 0.704270 0.969344i
\(404\) 5.63693 + 4.09547i 0.280448 + 0.203757i
\(405\) 0 0
\(406\) −21.2056 + 15.4068i −1.05242 + 0.764625i
\(407\) 18.8101i 0.932383i
\(408\) 14.1704 + 19.5039i 0.701541 + 0.965588i
\(409\) −4.08288 12.5658i −0.201886 0.621340i −0.999827 0.0186048i \(-0.994078\pi\)
0.797941 0.602735i \(-0.205922\pi\)
\(410\) 0 0
\(411\) −2.54650 + 7.83732i −0.125610 + 0.386587i
\(412\) −59.8601 + 19.4497i −2.94909 + 0.958218i
\(413\) −5.66223 + 1.83977i −0.278620 + 0.0905292i
\(414\) −1.16706 + 3.59186i −0.0573581 + 0.176530i
\(415\) 0 0
\(416\) 0.433937 + 1.33552i 0.0212755 + 0.0654794i
\(417\) 4.73973 + 6.52367i 0.232105 + 0.319466i
\(418\) 24.5612i 1.20133i
\(419\) −7.15797 + 5.20057i −0.349690 + 0.254064i −0.748739 0.662865i \(-0.769340\pi\)
0.399049 + 0.916930i \(0.369340\pi\)
\(420\) 0 0
\(421\) 30.3192 + 22.0282i 1.47767 + 1.07359i 0.978299 + 0.207197i \(0.0664341\pi\)
0.499367 + 0.866390i \(0.333566\pi\)
\(422\) 26.1871 36.0435i 1.27477 1.75457i
\(423\) −6.72551 2.18525i −0.327005 0.106250i
\(424\) 48.4301 2.35197
\(425\) 0 0
\(426\) 1.74229 0.0844140
\(427\) −25.6390 8.33062i −1.24076 0.403147i
\(428\) 36.6850 50.4926i 1.77324 2.44065i
\(429\) −8.54132 6.20563i −0.412379 0.299611i
\(430\) 0 0
\(431\) 21.5397 15.6495i 1.03753 0.753809i 0.0677274 0.997704i \(-0.478425\pi\)
0.969802 + 0.243895i \(0.0784252\pi\)
\(432\) 3.73192i 0.179552i
\(433\) 20.5708 + 28.3133i 0.988571 + 1.36065i 0.932082 + 0.362248i \(0.117990\pi\)
0.0564887 + 0.998403i \(0.482010\pi\)
\(434\) 19.3069 + 59.4206i 0.926762 + 2.85228i
\(435\) 0 0
\(436\) −12.1235 + 37.3124i −0.580613 + 1.78694i
\(437\) 4.53521 1.47358i 0.216949 0.0704909i
\(438\) 4.36383 1.41789i 0.208512 0.0677496i
\(439\) −6.19701 + 19.0724i −0.295767 + 0.910277i 0.687196 + 0.726472i \(0.258841\pi\)
−0.982963 + 0.183805i \(0.941159\pi\)
\(440\) 0 0
\(441\) 1.49427 + 4.59888i 0.0711556 + 0.218994i
\(442\) −23.4270 32.2445i −1.11431 1.53371i
\(443\) 4.14871i 0.197111i −0.995132 0.0985556i \(-0.968578\pi\)
0.995132 0.0985556i \(-0.0314222\pi\)
\(444\) 18.4248 13.3864i 0.874402 0.635291i
\(445\) 0 0
\(446\) −34.0048 24.7060i −1.61018 1.16986i
\(447\) 11.2326 15.4604i 0.531286 0.731252i
\(448\) −27.8900 9.06201i −1.31768 0.428140i
\(449\) 8.34804 0.393969 0.196984 0.980407i \(-0.436885\pi\)
0.196984 + 0.980407i \(0.436885\pi\)
\(450\) 0 0
\(451\) −17.7035 −0.833627
\(452\) 20.7399 + 6.73880i 0.975523 + 0.316967i
\(453\) 0.931936 1.28270i 0.0437862 0.0602665i
\(454\) −8.54602 6.20905i −0.401085 0.291405i
\(455\) 0 0
\(456\) −11.8921 + 8.64014i −0.556900 + 0.404612i
\(457\) 20.5774i 0.962571i 0.876564 + 0.481285i \(0.159830\pi\)
−0.876564 + 0.481285i \(0.840170\pi\)
\(458\) 29.1386 + 40.1059i 1.36156 + 1.87402i
\(459\) −1.56158 4.80604i −0.0728882 0.224327i
\(460\) 0 0
\(461\) 8.86541 27.2849i 0.412903 1.27079i −0.501210 0.865326i \(-0.667111\pi\)
0.914113 0.405460i \(-0.132889\pi\)
\(462\) 26.0815 8.47438i 1.21342 0.394264i
\(463\) 38.1181 12.3853i 1.77150 0.575594i 0.773213 0.634146i \(-0.218648\pi\)
0.998284 + 0.0585520i \(0.0186483\pi\)
\(464\) 3.60058 11.0815i 0.167153 0.514444i
\(465\) 0 0
\(466\) −0.257111 0.791307i −0.0119105 0.0366566i
\(467\) 4.78569 + 6.58694i 0.221456 + 0.304807i 0.905260 0.424858i \(-0.139676\pi\)
−0.683805 + 0.729665i \(0.739676\pi\)
\(468\) 12.7827i 0.590878i
\(469\) 5.14650 3.73915i 0.237643 0.172658i
\(470\) 0 0
\(471\) −17.6778 12.8437i −0.814550 0.591805i
\(472\) 4.85276 6.67925i 0.223366 0.307438i
\(473\) 7.86319 + 2.55491i 0.361550 + 0.117475i
\(474\) −32.5369 −1.49447
\(475\) 0 0
\(476\) 68.7575 3.15149
\(477\) −9.65469 3.13700i −0.442058 0.143633i
\(478\) 10.2770 14.1451i 0.470061 0.646983i
\(479\) −22.7027 16.4945i −1.03731 0.753652i −0.0675535 0.997716i \(-0.521519\pi\)
−0.969759 + 0.244064i \(0.921519\pi\)
\(480\) 0 0
\(481\) −15.0569 + 10.9395i −0.686534 + 0.498796i
\(482\) 30.6554i 1.39631i
\(483\) 3.12957 + 4.30749i 0.142401 + 0.195998i
\(484\) 0.402784 + 1.23964i 0.0183084 + 0.0563473i
\(485\) 0 0
\(486\) −0.754089 + 2.32085i −0.0342062 + 0.105276i
\(487\) 14.4725 4.70239i 0.655810 0.213086i 0.0378360 0.999284i \(-0.487954\pi\)
0.617974 + 0.786198i \(0.287954\pi\)
\(488\) 35.5541 11.5522i 1.60946 0.522945i
\(489\) 3.13153 9.63786i 0.141613 0.435839i
\(490\) 0 0
\(491\) 2.56246 + 7.88645i 0.115642 + 0.355910i 0.992080 0.125604i \(-0.0400869\pi\)
−0.876438 + 0.481514i \(0.840087\pi\)
\(492\) 12.5989 + 17.3409i 0.568002 + 0.781788i
\(493\) 15.7775i 0.710585i
\(494\) 19.6604 14.2842i 0.884565 0.642674i
\(495\) 0 0
\(496\) −22.4691 16.3248i −1.00889 0.733005i
\(497\) 1.44375 1.98715i 0.0647611 0.0891360i
\(498\) 9.18469 + 2.98429i 0.411576 + 0.133729i
\(499\) 24.4006 1.09232 0.546160 0.837681i \(-0.316089\pi\)
0.546160 + 0.837681i \(0.316089\pi\)
\(500\) 0 0
\(501\) 1.51109 0.0675104
\(502\) 39.4916 + 12.8316i 1.76260 + 0.572703i
\(503\) −6.15596 + 8.47295i −0.274481 + 0.377790i −0.923896 0.382644i \(-0.875014\pi\)
0.649415 + 0.760434i \(0.275014\pi\)
\(504\) −13.2781 9.64708i −0.591452 0.429715i
\(505\) 0 0
\(506\) 9.98070 7.25141i 0.443696 0.322364i
\(507\) 2.55393i 0.113424i
\(508\) −2.30629 3.17433i −0.102325 0.140838i
\(509\) 3.41769 + 10.5186i 0.151486 + 0.466227i 0.997788 0.0664770i \(-0.0211759\pi\)
−0.846302 + 0.532704i \(0.821176\pi\)
\(510\) 0 0
\(511\) 1.99893 6.15207i 0.0884274 0.272152i
\(512\) 35.4071 11.5045i 1.56479 0.508431i
\(513\) 2.93039 0.952141i 0.129380 0.0420381i
\(514\) −3.11590 + 9.58974i −0.137436 + 0.422985i
\(515\) 0 0
\(516\) −3.09335 9.52034i −0.136177 0.419110i
\(517\) 13.5778 + 18.6882i 0.597150 + 0.821906i
\(518\) 48.3432i 2.12408i
\(519\) 11.2092 8.14395i 0.492029 0.357480i
\(520\) 0 0
\(521\) 33.5105 + 24.3468i 1.46812 + 1.06665i 0.981153 + 0.193231i \(0.0618968\pi\)
0.486967 + 0.873420i \(0.338103\pi\)
\(522\) −4.47834 + 6.16391i −0.196012 + 0.269787i
\(523\) −12.9748 4.21576i −0.567347 0.184342i 0.0112775 0.999936i \(-0.496410\pi\)
−0.578624 + 0.815594i \(0.696410\pi\)
\(524\) 49.8783 2.17894
\(525\) 0 0
\(526\) −2.53235 −0.110416
\(527\) −35.7671 11.6214i −1.55804 0.506238i
\(528\) −7.16543 + 9.86236i −0.311835 + 0.429204i
\(529\) −16.6696 12.1112i −0.724766 0.526573i
\(530\) 0 0
\(531\) −1.40005 + 1.01720i −0.0607572 + 0.0441427i
\(532\) 41.9235i 1.81762i
\(533\) −10.2959 14.1711i −0.445965 0.613818i
\(534\) 6.43533 + 19.8059i 0.278484 + 0.857086i
\(535\) 0 0
\(536\) −2.72600 + 8.38976i −0.117745 + 0.362382i
\(537\) 13.7482 4.46706i 0.593278 0.192768i
\(538\) −36.6454 + 11.9068i −1.57990 + 0.513339i
\(539\) 4.88112 15.0225i 0.210245 0.647066i
\(540\) 0 0
\(541\) 4.53011 + 13.9423i 0.194765 + 0.599424i 0.999979 + 0.00644072i \(0.00205016\pi\)
−0.805214 + 0.592984i \(0.797950\pi\)
\(542\) 19.6513 + 27.0476i 0.844094 + 1.16180i
\(543\) 17.1898i 0.737685i
\(544\) 1.77626 1.29053i 0.0761566 0.0553310i
\(545\) 0 0
\(546\) 21.9517 + 15.9489i 0.939447 + 0.682548i
\(547\) 15.6423 21.5298i 0.668818 0.920549i −0.330915 0.943661i \(-0.607357\pi\)
0.999733 + 0.0231115i \(0.00735726\pi\)
\(548\) −30.9965 10.0714i −1.32410 0.430227i
\(549\) −7.83611 −0.334437
\(550\) 0 0
\(551\) 9.62005 0.409828
\(552\) −7.02201 2.28159i −0.298877 0.0971109i
\(553\) −26.9618 + 37.1097i −1.14653 + 1.57806i
\(554\) 13.7799 + 10.0117i 0.585453 + 0.425356i
\(555\) 0 0
\(556\) −25.8010 + 18.7455i −1.09421 + 0.794988i
\(557\) 10.3141i 0.437020i −0.975835 0.218510i \(-0.929880\pi\)
0.975835 0.218510i \(-0.0701197\pi\)
\(558\) 10.6747 + 14.6925i 0.451896 + 0.621981i
\(559\) 2.52790 + 7.78008i 0.106919 + 0.329063i
\(560\) 0 0
\(561\) −5.10099 + 15.6992i −0.215364 + 0.662822i
\(562\) −18.4698 + 6.00121i −0.779103 + 0.253146i
\(563\) −32.7193 + 10.6311i −1.37895 + 0.448049i −0.902325 0.431056i \(-0.858141\pi\)
−0.476628 + 0.879105i \(0.658141\pi\)
\(564\) 8.64262 26.5993i 0.363920 1.12003i
\(565\) 0 0
\(566\) −20.9600 64.5083i −0.881016 2.71149i
\(567\) 2.02215 + 2.78325i 0.0849222 + 0.116885i
\(568\) 3.40614i 0.142918i
\(569\) −9.87387 + 7.17378i −0.413934 + 0.300741i −0.775193 0.631725i \(-0.782347\pi\)
0.361259 + 0.932466i \(0.382347\pi\)
\(570\) 0 0
\(571\) −34.0308 24.7248i −1.42415 1.03470i −0.991070 0.133345i \(-0.957428\pi\)
−0.433076 0.901357i \(-0.642572\pi\)
\(572\) 24.5432 33.7808i 1.02620 1.41245i
\(573\) 10.0264 + 3.25778i 0.418859 + 0.136096i
\(574\) 45.4992 1.89910
\(575\) 0 0
\(576\) −8.52409 −0.355170
\(577\) 16.6768 + 5.41863i 0.694266 + 0.225581i 0.634830 0.772652i \(-0.281070\pi\)
0.0594353 + 0.998232i \(0.481070\pi\)
\(578\) −12.2445 + 16.8532i −0.509305 + 0.700999i
\(579\) 0.552485 + 0.401404i 0.0229605 + 0.0166818i
\(580\) 0 0
\(581\) 11.0146 8.00260i 0.456964 0.332004i
\(582\) 25.9959i 1.07756i
\(583\) 19.4913 + 26.8275i 0.807249 + 1.11108i
\(584\) 2.77196 + 8.53120i 0.114704 + 0.353024i
\(585\) 0 0
\(586\) −10.7155 + 32.9788i −0.442651 + 1.36234i
\(587\) 20.8395 6.77115i 0.860137 0.279475i 0.154451 0.988000i \(-0.450639\pi\)
0.705686 + 0.708525i \(0.250639\pi\)
\(588\) −18.1885 + 5.90980i −0.750081 + 0.243716i
\(589\) 7.08595 21.8083i 0.291971 0.898595i
\(590\) 0 0
\(591\) 7.19923 + 22.1569i 0.296137 + 0.911415i
\(592\) 12.6314 + 17.3856i 0.519148 + 0.714545i
\(593\) 38.0061i 1.56072i 0.625330 + 0.780361i \(0.284965\pi\)
−0.625330 + 0.780361i \(0.715035\pi\)
\(594\) 6.44895 4.68544i 0.264604 0.192246i
\(595\) 0 0
\(596\) 61.1456 + 44.4249i 2.50462 + 1.81971i
\(597\) −5.99226 + 8.24764i −0.245247 + 0.337553i
\(598\) 11.6090 + 3.77200i 0.474728 + 0.154248i
\(599\) −16.3154 −0.666629 −0.333314 0.942816i \(-0.608167\pi\)
−0.333314 + 0.942816i \(0.608167\pi\)
\(600\) 0 0
\(601\) 2.31871 0.0945822 0.0472911 0.998881i \(-0.484941\pi\)
0.0472911 + 0.998881i \(0.484941\pi\)
\(602\) −20.2089 6.56626i −0.823653 0.267621i
\(603\) 1.08687 1.49595i 0.0442609 0.0609199i
\(604\) 5.07305 + 3.68579i 0.206420 + 0.149973i
\(605\) 0 0
\(606\) 3.47807 2.52697i 0.141287 0.102651i
\(607\) 32.2134i 1.30750i 0.756709 + 0.653752i \(0.226806\pi\)
−0.756709 + 0.653752i \(0.773194\pi\)
\(608\) 0.786876 + 1.08304i 0.0319120 + 0.0439231i
\(609\) 3.31921 + 10.2155i 0.134501 + 0.413952i
\(610\) 0 0
\(611\) −7.06281 + 21.7371i −0.285731 + 0.879389i
\(612\) 19.0078 6.17601i 0.768345 0.249651i
\(613\) 24.6782 8.01843i 0.996742 0.323861i 0.235179 0.971952i \(-0.424432\pi\)
0.761563 + 0.648091i \(0.224432\pi\)
\(614\) 17.5636 54.0552i 0.708809 2.18149i
\(615\) 0 0
\(616\) 16.5673 + 50.9888i 0.667514 + 2.05440i
\(617\) −1.11899 1.54016i −0.0450488 0.0620043i 0.785898 0.618356i \(-0.212201\pi\)
−0.830947 + 0.556351i \(0.812201\pi\)
\(618\) 38.8353i 1.56218i
\(619\) −16.0829 + 11.6849i −0.646425 + 0.469655i −0.862052 0.506821i \(-0.830821\pi\)
0.215627 + 0.976476i \(0.430821\pi\)
\(620\) 0 0
\(621\) 1.25207 + 0.909685i 0.0502440 + 0.0365044i
\(622\) −10.8283 + 14.9039i −0.434177 + 0.597594i
\(623\) 27.9222 + 9.07246i 1.11868 + 0.363480i
\(624\) −12.0617 −0.482855
\(625\) 0 0
\(626\) −77.2509 −3.08757
\(627\) −9.57230 3.11023i −0.382281 0.124211i
\(628\) 50.7965 69.9154i 2.02700 2.78993i
\(629\) 23.5418 + 17.1041i 0.938673 + 0.681986i
\(630\) 0 0
\(631\) 26.6152 19.3371i 1.05953 0.769796i 0.0855315 0.996335i \(-0.472741\pi\)
0.974002 + 0.226539i \(0.0727412\pi\)
\(632\) 63.6090i 2.53023i
\(633\) −10.7312 14.7702i −0.426526 0.587063i
\(634\) −19.4828 59.9618i −0.773760 2.38139i
\(635\) 0 0
\(636\) 12.4068 38.1841i 0.491961 1.51410i
\(637\) 14.8638 4.82953i 0.588923 0.191353i
\(638\) 23.6699 7.69080i 0.937099 0.304482i
\(639\) 0.220629 0.679025i 0.00872793 0.0268618i
\(640\) 0 0
\(641\) −12.5963 38.7673i −0.497523 1.53122i −0.812988 0.582280i \(-0.802161\pi\)
0.315465 0.948937i \(-0.397839\pi\)
\(642\) −22.6352 31.1547i −0.893341 1.22958i
\(643\) 24.9947i 0.985695i −0.870116 0.492847i \(-0.835956\pi\)
0.870116 0.492847i \(-0.164044\pi\)
\(644\) −17.0360 + 12.3774i −0.671314 + 0.487738i
\(645\) 0 0
\(646\) −30.7396 22.3336i −1.20943 0.878705i
\(647\) −18.8228 + 25.9073i −0.739999 + 1.01852i 0.258620 + 0.965979i \(0.416732\pi\)
−0.998619 + 0.0525420i \(0.983268\pi\)
\(648\) −4.53722 1.47423i −0.178239 0.0579132i
\(649\) 5.65299 0.221899
\(650\) 0 0
\(651\) 25.6030 1.00346
\(652\) 38.1176 + 12.3852i 1.49280 + 0.485040i
\(653\) 26.2606 36.1446i 1.02766 1.41445i 0.120964 0.992657i \(-0.461401\pi\)
0.906693 0.421791i \(-0.138599\pi\)
\(654\) 19.5840 + 14.2286i 0.765794 + 0.556382i
\(655\) 0 0
\(656\) −16.3629 + 11.8883i −0.638862 + 0.464161i
\(657\) 1.88027i 0.0733564i
\(658\) −34.8957 48.0298i −1.36038 1.87240i
\(659\) 7.42307 + 22.8458i 0.289162 + 0.889948i 0.985120 + 0.171866i \(0.0549796\pi\)
−0.695959 + 0.718082i \(0.745020\pi\)
\(660\) 0 0
\(661\) 11.7095 36.0382i 0.455447 1.40172i −0.415163 0.909747i \(-0.636275\pi\)
0.870610 0.491974i \(-0.163725\pi\)
\(662\) −46.6682 + 15.1634i −1.81381 + 0.589343i
\(663\) −15.5333 + 5.04708i −0.603264 + 0.196012i
\(664\) −5.83423 + 17.9559i −0.226412 + 0.696824i
\(665\) 0 0
\(666\) −4.34233 13.3643i −0.168262 0.517857i
\(667\) 2.84020 + 3.90920i 0.109973 + 0.151365i
\(668\) 5.97633i 0.231231i
\(669\) −13.9348 + 10.1242i −0.538750 + 0.391425i
\(670\) 0 0
\(671\) 20.7085 + 15.0456i 0.799444 + 0.580830i
\(672\) −0.878580 + 1.20926i −0.0338920 + 0.0466483i
\(673\) 17.5249 + 5.69418i 0.675534 + 0.219494i 0.626639 0.779310i \(-0.284430\pi\)
0.0488951 + 0.998804i \(0.484430\pi\)
\(674\) −8.25737 −0.318062
\(675\) 0 0
\(676\) −10.1008 −0.388491
\(677\) −21.6996 7.05064i −0.833985 0.270978i −0.139262 0.990256i \(-0.544473\pi\)
−0.694723 + 0.719277i \(0.744473\pi\)
\(678\) 7.90887 10.8856i 0.303738 0.418060i
\(679\) 29.6494 + 21.5416i 1.13784 + 0.826690i
\(680\) 0 0
\(681\) −3.50206 + 2.54440i −0.134199 + 0.0975015i
\(682\) 59.3236i 2.27162i
\(683\) 18.9304 + 26.0555i 0.724353 + 0.996987i 0.999368 + 0.0355465i \(0.0113172\pi\)
−0.275015 + 0.961440i \(0.588683\pi\)
\(684\) 3.76570 + 11.5896i 0.143985 + 0.443141i
\(685\) 0 0
\(686\) 5.61519 17.2818i 0.214389 0.659822i
\(687\) 19.3204 6.27758i 0.737120 0.239505i
\(688\) 8.98339 2.91888i 0.342489 0.111281i
\(689\) −10.1389 + 31.2043i −0.386261 + 1.18879i
\(690\) 0 0
\(691\) 7.59466 + 23.3740i 0.288915 + 0.889188i 0.985198 + 0.171421i \(0.0548358\pi\)
−0.696283 + 0.717767i \(0.745164\pi\)
\(692\) 32.2092 + 44.3321i 1.22441 + 1.68525i
\(693\) 11.2379i 0.426893i
\(694\) −57.6404 + 41.8782i −2.18800 + 1.58967i
\(695\) 0 0
\(696\) −12.0503 8.75508i −0.456767 0.331860i
\(697\) −16.0979 + 22.1568i −0.609751 + 0.839251i
\(698\) 47.3404 + 15.3818i 1.79186 + 0.582211i
\(699\) −0.340956 −0.0128961
\(700\) 0 0
\(701\) −3.66355 −0.138370 −0.0691852 0.997604i \(-0.522040\pi\)
−0.0691852 + 0.997604i \(0.522040\pi\)
\(702\) 7.50107 + 2.43724i 0.283109 + 0.0919879i
\(703\) −10.4289 + 14.3541i −0.393333 + 0.541377i
\(704\) 22.5267 + 16.3666i 0.849005 + 0.616838i
\(705\) 0 0
\(706\) 3.67890 2.67288i 0.138457 0.100595i
\(707\) 6.06087i 0.227942i
\(708\) −4.02300 5.53719i −0.151194 0.208100i
\(709\) 8.24980 + 25.3903i 0.309828 + 0.953552i 0.977831 + 0.209394i \(0.0671491\pi\)
−0.668003 + 0.744158i \(0.732851\pi\)
\(710\) 0 0
\(711\) −4.12020 + 12.6807i −0.154519 + 0.475562i
\(712\) −38.7202 + 12.5810i −1.45110 + 0.471492i
\(713\) 10.9541 3.55919i 0.410233 0.133293i
\(714\) 13.1099 40.3480i 0.490624 1.50999i
\(715\) 0 0
\(716\) 17.6671 + 54.3739i 0.660252 + 2.03205i
\(717\) −4.21141 5.79651i −0.157278 0.216475i
\(718\) 9.36569i 0.349524i
\(719\) 14.4570 10.5036i 0.539156 0.391720i −0.284616 0.958642i \(-0.591866\pi\)
0.823771 + 0.566922i \(0.191866\pi\)
\(720\) 0 0
\(721\) 44.2933 + 32.1810i 1.64957 + 1.19848i
\(722\) −13.6354 + 18.7675i −0.507457 + 0.698455i
\(723\) −11.9474 3.88194i −0.444328 0.144371i
\(724\) −67.9853 −2.52665
\(725\) 0 0
\(726\) 0.804239 0.0298481
\(727\) −32.4050 10.5290i −1.20184 0.390500i −0.361400 0.932411i \(-0.617701\pi\)
−0.840436 + 0.541910i \(0.817701\pi\)
\(728\) −31.1797 + 42.9152i −1.15560 + 1.59054i
\(729\) 0.809017 + 0.587785i 0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) 10.3476 7.51799i 0.382721 0.278063i
\(732\) 30.9917i 1.14549i
\(733\) −23.6176 32.5068i −0.872335 1.20067i −0.978485 0.206316i \(-0.933853\pi\)
0.106150 0.994350i \(-0.466147\pi\)
\(734\) −19.3258 59.4788i −0.713330 2.19540i
\(735\) 0 0
\(736\) −0.207789 + 0.639509i −0.00765921 + 0.0235726i
\(737\) −5.74457 + 1.86652i −0.211604 + 0.0687542i
\(738\) 12.5781 4.08688i 0.463007 0.150440i
\(739\) −4.78203 + 14.7176i −0.175910 + 0.541395i −0.999674 0.0255381i \(-0.991870\pi\)
0.823764 + 0.566933i \(0.191870\pi\)
\(740\) 0 0
\(741\) −3.07736 9.47113i −0.113050 0.347931i
\(742\) −50.0939 68.9484i −1.83901 2.53118i
\(743\) 17.1140i 0.627853i 0.949447 + 0.313926i \(0.101645\pi\)
−0.949447 + 0.313926i \(0.898355\pi\)
\(744\) −28.7235 + 20.8688i −1.05305 + 0.765089i
\(745\) 0 0
\(746\) −42.3214 30.7483i −1.54950 1.12577i
\(747\) 2.32614 3.20166i 0.0851092 0.117143i
\(748\) −62.0902 20.1743i −2.27024 0.737647i
\(749\) −54.2900 −1.98371
\(750\) 0 0
\(751\) −11.1559 −0.407086 −0.203543 0.979066i \(-0.565246\pi\)
−0.203543 + 0.979066i \(0.565246\pi\)
\(752\) 25.0991 + 8.15518i 0.915268 + 0.297389i
\(753\) 10.0018 13.7663i 0.364485 0.501671i
\(754\) 19.9220 + 14.4742i 0.725516 + 0.527118i
\(755\) 0 0
\(756\) −11.0077 + 7.99756i −0.400346 + 0.290868i
\(757\) 24.6773i 0.896911i 0.893805 + 0.448456i \(0.148026\pi\)
−0.893805 + 0.448456i \(0.851974\pi\)
\(758\) −37.1089 51.0760i −1.34786 1.85516i
\(759\) −1.56223 4.80806i −0.0567054 0.174521i
\(760\) 0 0
\(761\) −12.4372 + 38.2779i −0.450850 + 1.38757i 0.425089 + 0.905151i \(0.360243\pi\)
−0.875939 + 0.482422i \(0.839757\pi\)
\(762\) −2.30249 + 0.748123i −0.0834103 + 0.0271016i
\(763\) 32.4566 10.5458i 1.17501 0.381784i
\(764\) −12.8845 + 39.6543i −0.466143 + 1.43464i
\(765\) 0 0
\(766\) −10.9596 33.7302i −0.395987 1.21872i
\(767\) 3.28763 + 4.52503i 0.118709 + 0.163389i
\(768\) 31.5921i 1.13998i
\(769\) 17.8801 12.9907i 0.644773 0.468455i −0.216714 0.976235i \(-0.569534\pi\)
0.861487 + 0.507780i \(0.169534\pi\)
\(770\) 0 0
\(771\) 3.34286 + 2.42873i 0.120390 + 0.0874685i
\(772\) −1.58754 + 2.18507i −0.0571370 + 0.0786423i
\(773\) −4.66049 1.51429i −0.167626 0.0544651i 0.224002 0.974589i \(-0.428088\pi\)
−0.391628 + 0.920124i \(0.628088\pi\)
\(774\) −6.17649 −0.222009
\(775\) 0 0
\(776\) −50.8215 −1.82439
\(777\) −18.8409 6.12177i −0.675913 0.219617i
\(778\) −33.1405 + 45.6139i −1.18814 + 1.63534i
\(779\) −13.5097 9.81537i −0.484035 0.351672i
\(780\) 0 0
\(781\) −1.88681 + 1.37085i −0.0675153 + 0.0490528i
\(782\) 19.0851i 0.682481i
\(783\) 1.83517 + 2.52590i 0.0655837 + 0.0902682i
\(784\) −5.57648 17.1627i −0.199160 0.612952i
\(785\) 0 0
\(786\) 9.51020 29.2694i 0.339218 1.04400i
\(787\) 3.55198 1.15411i 0.126614 0.0411395i −0.245024 0.969517i \(-0.578796\pi\)
0.371639 + 0.928377i \(0.378796\pi\)
\(788\) −87.6303 + 28.4728i −3.12170 + 1.01430i
\(789\) −0.320676 + 0.986940i −0.0114164 + 0.0351360i
\(790\) 0 0
\(791\) −5.86182 18.0408i −0.208422 0.641458i
\(792\) 9.15994 + 12.6076i 0.325484 + 0.447991i
\(793\) 25.3266i 0.899375i
\(794\) 27.5100 19.9872i 0.976294 0.709319i
\(795\) 0 0
\(796\) −32.6193 23.6993i −1.15616 0.839998i
\(797\) 1.96557 2.70538i 0.0696242 0.0958295i −0.772785 0.634668i \(-0.781137\pi\)
0.842409 + 0.538839i \(0.181137\pi\)
\(798\) 24.6014 + 7.99348i 0.870880 + 0.282966i
\(799\) 35.7355 1.26423
\(800\) 0 0
\(801\) 8.53392 0.301531
\(802\) −64.0140 20.7994i −2.26041 0.734453i
\(803\) −3.61019 + 4.96901i −0.127401 + 0.175352i
\(804\) 5.91646 + 4.29856i 0.208658 + 0.151599i
\(805\) 0 0
\(806\) 47.4866 34.5010i 1.67264 1.21525i
\(807\) 15.7897i 0.555823i
\(808\) 4.94017 + 6.79957i 0.173795 + 0.239208i
\(809\) −10.5954 32.6094i −0.372516 1.14649i −0.945140 0.326667i \(-0.894074\pi\)
0.572624 0.819818i \(-0.305926\pi\)
\(810\) 0 0
\(811\) −1.07152 + 3.29778i −0.0376260 + 0.115801i −0.968105 0.250543i \(-0.919391\pi\)
0.930479 + 0.366344i \(0.119391\pi\)
\(812\) −40.4020 + 13.1274i −1.41783 + 0.460682i
\(813\) 13.0298 4.23364i 0.456975 0.148480i
\(814\) −14.1845 + 43.6554i −0.497167 + 1.53012i
\(815\) 0 0
\(816\) 5.82768 + 17.9358i 0.204010 + 0.627877i
\(817\) 4.58394 + 6.30926i 0.160372 + 0.220733i
\(818\) 32.2422i 1.12732i
\(819\) 8.99556 6.53566i 0.314330 0.228374i
\(820\) 0 0
\(821\) 11.8771 + 8.62922i 0.414514 + 0.301162i 0.775427 0.631438i \(-0.217535\pi\)
−0.360913 + 0.932600i \(0.617535\pi\)
\(822\) −11.8201 + 16.2689i −0.412273 + 0.567445i
\(823\) 19.8483 + 6.44912i 0.691870 + 0.224802i 0.633785 0.773510i \(-0.281501\pi\)
0.0580851 + 0.998312i \(0.481501\pi\)
\(824\) −75.9223 −2.64488
\(825\) 0 0
\(826\) −14.5285 −0.505512
\(827\) 43.0710 + 13.9946i 1.49773 + 0.486641i 0.939354 0.342950i \(-0.111426\pi\)
0.558372 + 0.829590i \(0.311426\pi\)
\(828\) −3.59779 + 4.95193i −0.125032 + 0.172091i
\(829\) −7.81291 5.67641i −0.271354 0.197150i 0.443784 0.896134i \(-0.353636\pi\)
−0.715137 + 0.698984i \(0.753636\pi\)
\(830\) 0 0
\(831\) 5.64685 4.10268i 0.195887 0.142320i
\(832\) 27.5502i 0.955131i
\(833\) −14.3630 19.7690i −0.497649 0.684955i
\(834\) 6.08075 + 18.7146i 0.210559 + 0.648035i
\(835\) 0 0
\(836\) 12.3009 37.8583i 0.425436 1.30936i
\(837\) 7.07787 2.29974i 0.244647 0.0794907i
\(838\) −20.5342 + 6.67198i −0.709344 + 0.230480i
\(839\) 7.77848 23.9397i 0.268543 0.826490i −0.722313 0.691566i \(-0.756921\pi\)
0.990856 0.134924i \(-0.0430789\pi\)
\(840\) 0 0
\(841\) −5.94919 18.3097i −0.205144 0.631370i
\(842\) 53.7550 + 73.9874i 1.85252 + 2.54977i
\(843\) 7.95823i 0.274096i
\(844\) 58.4159 42.4416i 2.01076 1.46090i
\(845\) 0 0
\(846\) −13.9610 10.1433i −0.479989 0.348733i
\(847\) 0.666435 0.917269i 0.0228990 0.0315177i
\(848\) 36.0305 + 11.7070i 1.23729 + 0.402021i
\(849\) −27.7952 −0.953928
\(850\) 0 0
\(851\) −8.91196 −0.305498
\(852\) 2.68553 + 0.872582i 0.0920048 + 0.0298942i
\(853\) 1.88589 2.59571i 0.0645717 0.0888753i −0.775510 0.631336i \(-0.782507\pi\)
0.840081 + 0.542460i \(0.182507\pi\)
\(854\) −53.2222 38.6682i −1.82123 1.32320i
\(855\) 0 0
\(856\) 60.9069 44.2514i 2.08175 1.51248i
\(857\) 19.4569i 0.664634i 0.943168 + 0.332317i \(0.107830\pi\)
−0.943168 + 0.332317i \(0.892170\pi\)
\(858\) −15.1435 20.8432i −0.516991 0.711577i
\(859\) −5.20173 16.0093i −0.177481 0.546230i 0.822257 0.569116i \(-0.192714\pi\)
−0.999738 + 0.0228862i \(0.992714\pi\)
\(860\) 0 0
\(861\) 5.76163 17.7325i 0.196356 0.604322i
\(862\) 61.7914 20.0772i 2.10462 0.683833i
\(863\) 3.62560 1.17803i 0.123417 0.0401006i −0.246657 0.969103i \(-0.579332\pi\)
0.370074 + 0.929002i \(0.379332\pi\)
\(864\) −0.134261 + 0.413214i −0.00456766 + 0.0140578i
\(865\) 0 0
\(866\) 26.3910 + 81.2231i 0.896802 + 2.76007i
\(867\) 5.01767 + 6.90623i 0.170409 + 0.234548i
\(868\) 101.259i 3.43697i
\(869\) 35.2358 25.6003i 1.19529 0.868431i
\(870\) 0 0
\(871\) −4.83497 3.51281i −0.163827 0.119027i
\(872\) −27.8166 + 38.2863i −0.941990 + 1.29654i
\(873\) 10.1314 + 3.29190i 0.342897 + 0.111414i
\(874\) 11.6367 0.393619
\(875\) 0 0
\(876\) 7.43645 0.251254
\(877\) −24.4851 7.95569i −0.826803 0.268644i −0.135105 0.990831i \(-0.543137\pi\)
−0.691698 + 0.722187i \(0.743137\pi\)
\(878\) −28.7646 + 39.5911i −0.970759 + 1.33613i
\(879\) 11.4960 + 8.35231i 0.387749 + 0.281717i
\(880\) 0 0
\(881\) −36.6110 + 26.5995i −1.23346 + 0.896159i −0.997144 0.0755181i \(-0.975939\pi\)
−0.236313 + 0.971677i \(0.575939\pi\)
\(882\) 11.8001i 0.397330i
\(883\) 26.0964 + 35.9186i 0.878212 + 1.20876i 0.976913 + 0.213639i \(0.0685315\pi\)
−0.0987003 + 0.995117i \(0.531469\pi\)
\(884\) −19.9611 61.4340i −0.671365 2.06625i
\(885\) 0 0
\(886\) 3.12850 9.62853i 0.105104 0.323477i
\(887\) 37.0844 12.0495i 1.24517 0.404581i 0.388984 0.921245i \(-0.372826\pi\)
0.856189 + 0.516664i \(0.172826\pi\)
\(888\) 26.1270 8.48919i 0.876766 0.284878i
\(889\) −1.05470 + 3.24602i −0.0353734 + 0.108868i
\(890\) 0 0
\(891\) −1.00942 3.10669i −0.0338170 0.104078i
\(892\) −40.0411 55.1119i −1.34068 1.84528i
\(893\) 21.7890i 0.729142i
\(894\) 37.7278 27.4108i 1.26181 0.916755i
\(895\) 0 0
\(896\) −55.4764 40.3059i −1.85334 1.34653i
\(897\) 2.94014 4.04675i 0.0981683 0.135117i
\(898\) 19.3745 + 6.29517i 0.646537 + 0.210072i
\(899\) 23.2356 0.774952
\(900\) 0 0
\(901\) 51.2995 1.70903
\(902\) −41.0872 13.3500i −1.36805 0.444508i
\(903\) −5.11817 + 7.04455i −0.170322 + 0.234428i
\(904\) 21.2812 + 15.4617i 0.707803 + 0.514249i
\(905\) 0 0
\(906\) 3.13015 2.27419i 0.103992 0.0755548i
\(907\) 11.0201i 0.365915i 0.983121 + 0.182958i \(0.0585671\pi\)
−0.983121 + 0.182958i \(0.941433\pi\)
\(908\) −10.0630 13.8506i −0.333954 0.459648i
\(909\) −0.544406 1.67551i −0.0180568 0.0555731i
\(910\) 0 0
\(911\) −16.3540 + 50.3325i −0.541833 + 1.66759i 0.186571 + 0.982441i \(0.440263\pi\)
−0.728404 + 0.685148i \(0.759737\pi\)
\(912\) −10.9360 + 3.55332i −0.362127 + 0.117662i
\(913\) −12.2946 + 3.99477i −0.406893 + 0.132207i
\(914\) −15.5172 + 47.7570i −0.513263 + 1.57966i
\(915\) 0 0
\(916\) 24.8277 + 76.4119i 0.820331 + 2.52472i
\(917\) −25.5023 35.1010i −0.842162 1.15914i
\(918\) 12.3317i 0.407005i
\(919\) −38.5129 + 27.9812i −1.27042 + 0.923016i −0.999219 0.0395064i \(-0.987421\pi\)
−0.271203 + 0.962522i \(0.587421\pi\)
\(920\) 0 0
\(921\) −18.8429 13.6902i −0.620896 0.451107i
\(922\) 41.1505 56.6388i 1.35522 1.86530i
\(923\) −2.19463 0.713080i −0.0722372 0.0234713i
\(924\) 44.4457 1.46216
\(925\) 0 0
\(926\) 97.8059 3.21410
\(927\) 15.1354 + 4.91777i 0.497110 + 0.161521i
\(928\) −0.797343 + 1.09745i −0.0261741 + 0.0360255i
\(929\) 17.5465 + 12.7483i 0.575682 + 0.418258i 0.837165 0.546951i \(-0.184211\pi\)
−0.261483 + 0.965208i \(0.584211\pi\)
\(930\) 0 0
\(931\) 12.0538 8.75757i 0.395046 0.287018i
\(932\) 1.34848i 0.0441708i
\(933\) 4.43733 + 6.10746i 0.145272 + 0.199949i
\(934\) 6.13972 + 18.8961i 0.200898 + 0.618300i
\(935\) 0 0
\(936\) −4.76477 + 14.6645i −0.155741 + 0.479323i
\(937\) −2.09317 + 0.680112i −0.0683809 + 0.0222183i −0.343008 0.939333i \(-0.611446\pi\)
0.274627 + 0.961551i \(0.411446\pi\)
\(938\) 14.7639 4.79708i 0.482058 0.156630i
\(939\) −9.78241 + 30.1072i −0.319237 + 0.982510i
\(940\) 0 0
\(941\) −5.18833 15.9680i −0.169135 0.520543i 0.830183 0.557492i \(-0.188236\pi\)
−0.999317 + 0.0369489i \(0.988236\pi\)
\(942\) −31.3422 43.1388i −1.02118 1.40554i
\(943\) 8.38767i 0.273140i
\(944\) 5.22489 3.79611i 0.170056 0.123553i
\(945\) 0 0
\(946\) 16.3226 + 11.8591i 0.530695 + 0.385572i
\(947\) 21.5207 29.6207i 0.699329 0.962544i −0.300632 0.953740i \(-0.597198\pi\)
0.999961 0.00880418i \(-0.00280249\pi\)
\(948\) −50.1518 16.2953i −1.62885 0.529247i
\(949\) −6.07711 −0.197271
\(950\) 0 0
\(951\) −25.8362 −0.837796
\(952\) 78.8796 + 25.6295i 2.55650 + 0.830658i
\(953\) −25.8201 + 35.5383i −0.836394 + 1.15120i 0.150305 + 0.988640i \(0.451974\pi\)
−0.986699 + 0.162558i \(0.948026\pi\)
\(954\) −20.0415 14.5610i −0.648867 0.471430i
\(955\) 0 0
\(956\) 22.9251 16.6561i 0.741450 0.538695i
\(957\) 10.1988i 0.329680i
\(958\) −40.2512 55.4010i −1.30046 1.78993i
\(959\) 8.76068 + 26.9626i 0.282897 + 0.870668i
\(960\) 0 0
\(961\) 7.53541 23.1916i 0.243078 0.748116i
\(962\) −43.1940 + 14.0346i −1.39263 + 0.452493i
\(963\) −15.0083 + 4.87650i −0.483636 + 0.157143i
\(964\) 15.3530 47.2517i 0.494487 1.52188i
\(965\) 0 0
\(966\) 4.01503 + 12.3570i 0.129182 + 0.397580i
\(967\) −14.3899 19.8059i −0.462747 0.636916i 0.512329 0.858789i \(-0.328783\pi\)
−0.975076 + 0.221873i \(0.928783\pi\)
\(968\) 1.57227i 0.0505348i
\(969\) −12.5967 + 9.15206i −0.404665 + 0.294007i
\(970\) 0 0
\(971\) 15.8773 + 11.5355i 0.509526 + 0.370192i 0.812644 0.582761i \(-0.198028\pi\)
−0.303118 + 0.952953i \(0.598028\pi\)
\(972\) −2.32468 + 3.19965i −0.0745642 + 0.102629i
\(973\) 26.3837 + 8.57257i 0.845822 + 0.274824i
\(974\) 37.1344 1.18986
\(975\) 0 0
\(976\) 29.2438 0.936070
\(977\) 29.0298 + 9.43236i 0.928746 + 0.301768i 0.734050 0.679096i \(-0.237628\pi\)
0.194696 + 0.980864i \(0.437628\pi\)
\(978\) 14.5356 20.0066i 0.464798 0.639739i
\(979\) −22.5526 16.3854i −0.720785 0.523681i
\(980\) 0 0
\(981\) 8.02529 5.83071i 0.256228 0.186160i
\(982\) 20.2356i 0.645743i
\(983\) 6.09271 + 8.38590i 0.194327 + 0.267469i 0.895051 0.445964i \(-0.147139\pi\)
−0.700723 + 0.713433i \(0.747139\pi\)
\(984\) 7.98977 + 24.5900i 0.254705 + 0.783901i
\(985\) 0 0
\(986\) 11.8977 36.6173i 0.378899 1.16613i
\(987\) −23.1376 + 7.51788i −0.736479 + 0.239297i
\(988\) 37.4582 12.1709i 1.19170 0.387208i
\(989\) −1.21048 + 3.72546i −0.0384909 + 0.118463i
\(990\) 0 0
\(991\) −3.12376 9.61395i −0.0992295 0.305397i 0.889103 0.457707i \(-0.151329\pi\)
−0.988333 + 0.152309i \(0.951329\pi\)
\(992\) 1.90057 + 2.61591i 0.0603431 + 0.0830552i
\(993\) 20.1083i 0.638116i
\(994\) 4.84921 3.52316i 0.153808 0.111748i
\(995\) 0 0
\(996\) 12.6625 + 9.19986i 0.401227 + 0.291509i
\(997\) 12.5574 17.2838i 0.397697 0.547382i −0.562467 0.826819i \(-0.690148\pi\)
0.960164 + 0.279437i \(0.0901478\pi\)
\(998\) 56.6300 + 18.4002i 1.79259 + 0.582448i
\(999\) −5.75838 −0.182187
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 375.2.i.d.274.5 24
5.2 odd 4 375.2.g.c.226.1 12
5.3 odd 4 75.2.g.c.46.3 yes 12
5.4 even 2 inner 375.2.i.d.274.2 24
15.8 even 4 225.2.h.d.46.1 12
25.6 even 5 inner 375.2.i.d.349.2 24
25.8 odd 20 75.2.g.c.31.3 12
25.9 even 10 1875.2.b.f.1249.2 12
25.12 odd 20 1875.2.a.k.1.1 6
25.13 odd 20 1875.2.a.j.1.6 6
25.16 even 5 1875.2.b.f.1249.11 12
25.17 odd 20 375.2.g.c.151.1 12
25.19 even 10 inner 375.2.i.d.349.5 24
75.8 even 20 225.2.h.d.181.1 12
75.38 even 20 5625.2.a.p.1.1 6
75.62 even 20 5625.2.a.q.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.c.31.3 12 25.8 odd 20
75.2.g.c.46.3 yes 12 5.3 odd 4
225.2.h.d.46.1 12 15.8 even 4
225.2.h.d.181.1 12 75.8 even 20
375.2.g.c.151.1 12 25.17 odd 20
375.2.g.c.226.1 12 5.2 odd 4
375.2.i.d.274.2 24 5.4 even 2 inner
375.2.i.d.274.5 24 1.1 even 1 trivial
375.2.i.d.349.2 24 25.6 even 5 inner
375.2.i.d.349.5 24 25.19 even 10 inner
1875.2.a.j.1.6 6 25.13 odd 20
1875.2.a.k.1.1 6 25.12 odd 20
1875.2.b.f.1249.2 12 25.9 even 10
1875.2.b.f.1249.11 12 25.16 even 5
5625.2.a.p.1.1 6 75.38 even 20
5625.2.a.q.1.6 6 75.62 even 20