Properties

Label 825.2.bi.h.101.10
Level $825$
Weight $2$
Character 825.101
Analytic conductor $6.588$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(101,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bi (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 101.10
Character \(\chi\) \(=\) 825.101
Dual form 825.2.bi.h.776.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0382790 + 0.117811i) q^{2} +(-0.243783 - 1.71481i) q^{3} +(1.60562 + 1.16655i) q^{4} +(0.211354 + 0.0369209i) q^{6} +(1.86875 - 2.57211i) q^{7} +(-0.399325 + 0.290127i) q^{8} +(-2.88114 + 0.836083i) q^{9} +O(q^{10})\) \(q+(-0.0382790 + 0.117811i) q^{2} +(-0.243783 - 1.71481i) q^{3} +(1.60562 + 1.16655i) q^{4} +(0.211354 + 0.0369209i) q^{6} +(1.86875 - 2.57211i) q^{7} +(-0.399325 + 0.290127i) q^{8} +(-2.88114 + 0.836083i) q^{9} +(2.45933 + 2.22524i) q^{11} +(1.60899 - 3.03772i) q^{12} +(4.24445 + 1.37910i) q^{13} +(0.231488 + 0.318616i) q^{14} +(1.20769 + 3.71689i) q^{16} +(0.436543 + 1.34354i) q^{17} +(0.0117877 - 0.371433i) q^{18} +(-2.96232 - 4.07728i) q^{19} +(-4.86625 - 2.57751i) q^{21} +(-0.356298 + 0.204555i) q^{22} -4.40944i q^{23} +(0.594860 + 0.614038i) q^{24} +(-0.324946 + 0.447250i) q^{26} +(2.13609 + 4.73678i) q^{27} +(6.00100 - 1.94984i) q^{28} +(4.72158 + 3.43043i) q^{29} +(0.721415 - 2.22029i) q^{31} -1.47130 q^{32} +(3.21632 - 4.75976i) q^{33} -0.174994 q^{34} +(-5.60135 - 2.01857i) q^{36} +(-3.86196 - 2.80588i) q^{37} +(0.593742 - 0.192918i) q^{38} +(1.33018 - 7.61462i) q^{39} +(2.66980 - 1.93972i) q^{41} +(0.489933 - 0.474632i) q^{42} +2.97470i q^{43} +(1.35289 + 6.44182i) q^{44} +(0.519478 + 0.168789i) q^{46} +(-3.14996 - 4.33555i) q^{47} +(6.07934 - 2.97707i) q^{48} +(-0.960422 - 2.95587i) q^{49} +(2.19749 - 1.07612i) q^{51} +(5.20617 + 7.16568i) q^{52} +(-0.249485 - 0.0810625i) q^{53} +(-0.639811 + 0.0703354i) q^{54} +1.56928i q^{56} +(-6.26960 + 6.07378i) q^{57} +(-0.584879 + 0.424939i) q^{58} +(5.24873 - 7.22425i) q^{59} +(-14.1273 + 4.59023i) q^{61} +(0.233958 + 0.169981i) q^{62} +(-3.23363 + 8.97305i) q^{63} +(-2.35906 + 7.26044i) q^{64} +(0.437632 + 0.561115i) q^{66} +1.33725 q^{67} +(-0.866386 + 2.66646i) q^{68} +(-7.56134 + 1.07495i) q^{69} +(5.40085 - 1.75484i) q^{71} +(0.907941 - 1.16976i) q^{72} +(3.84559 - 5.29300i) q^{73} +(0.478395 - 0.347574i) q^{74} -10.0023i q^{76} +(10.3194 - 2.16726i) q^{77} +(0.846165 + 0.448189i) q^{78} +(4.98511 + 1.61976i) q^{79} +(7.60193 - 4.81774i) q^{81} +(0.126323 + 0.388781i) q^{82} +(-4.30625 - 13.2533i) q^{83} +(-4.80655 - 9.81523i) q^{84} +(-0.350452 - 0.113869i) q^{86} +(4.73149 - 8.93290i) q^{87} +(-1.62767 - 0.175077i) q^{88} +13.7521i q^{89} +(11.4790 - 8.34000i) q^{91} +(5.14383 - 7.07988i) q^{92} +(-3.98324 - 0.695821i) q^{93} +(0.631351 - 0.205139i) q^{94} +(0.358679 + 2.52300i) q^{96} +(3.27721 - 10.0862i) q^{97} +0.384997 q^{98} +(-8.94616 - 4.35502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0382790 + 0.117811i −0.0270673 + 0.0833047i −0.963678 0.267068i \(-0.913945\pi\)
0.936610 + 0.350373i \(0.113945\pi\)
\(3\) −0.243783 1.71481i −0.140748 0.990045i
\(4\) 1.60562 + 1.16655i 0.802810 + 0.583276i
\(5\) 0 0
\(6\) 0.211354 + 0.0369209i 0.0862851 + 0.0150729i
\(7\) 1.86875 2.57211i 0.706321 0.972167i −0.293548 0.955944i \(-0.594836\pi\)
0.999868 0.0162228i \(-0.00516411\pi\)
\(8\) −0.399325 + 0.290127i −0.141183 + 0.102575i
\(9\) −2.88114 + 0.836083i −0.960380 + 0.278694i
\(10\) 0 0
\(11\) 2.45933 + 2.22524i 0.741516 + 0.670935i
\(12\) 1.60899 3.03772i 0.464475 0.876913i
\(13\) 4.24445 + 1.37910i 1.17720 + 0.382495i 0.831325 0.555786i \(-0.187583\pi\)
0.345873 + 0.938281i \(0.387583\pi\)
\(14\) 0.231488 + 0.318616i 0.0618679 + 0.0851538i
\(15\) 0 0
\(16\) 1.20769 + 3.71689i 0.301923 + 0.929222i
\(17\) 0.436543 + 1.34354i 0.105877 + 0.325856i 0.989935 0.141521i \(-0.0451991\pi\)
−0.884058 + 0.467377i \(0.845199\pi\)
\(18\) 0.0117877 0.371433i 0.00277839 0.0875476i
\(19\) −2.96232 4.07728i −0.679603 0.935393i 0.320326 0.947307i \(-0.396207\pi\)
−0.999929 + 0.0119143i \(0.996207\pi\)
\(20\) 0 0
\(21\) −4.86625 2.57751i −1.06190 0.562459i
\(22\) −0.356298 + 0.204555i −0.0759629 + 0.0436113i
\(23\) 4.40944i 0.919431i −0.888066 0.459716i \(-0.847951\pi\)
0.888066 0.459716i \(-0.152049\pi\)
\(24\) 0.594860 + 0.614038i 0.121425 + 0.125340i
\(25\) 0 0
\(26\) −0.324946 + 0.447250i −0.0637272 + 0.0877130i
\(27\) 2.13609 + 4.73678i 0.411092 + 0.911594i
\(28\) 6.00100 1.94984i 1.13408 0.368486i
\(29\) 4.72158 + 3.43043i 0.876776 + 0.637015i 0.932397 0.361437i \(-0.117714\pi\)
−0.0556204 + 0.998452i \(0.517714\pi\)
\(30\) 0 0
\(31\) 0.721415 2.22029i 0.129570 0.398775i −0.865136 0.501537i \(-0.832768\pi\)
0.994706 + 0.102762i \(0.0327680\pi\)
\(32\) −1.47130 −0.260092
\(33\) 3.21632 4.75976i 0.559889 0.828567i
\(34\) −0.174994 −0.0300112
\(35\) 0 0
\(36\) −5.60135 2.01857i −0.933558 0.336428i
\(37\) −3.86196 2.80588i −0.634903 0.461284i 0.223192 0.974774i \(-0.428352\pi\)
−0.858095 + 0.513490i \(0.828352\pi\)
\(38\) 0.593742 0.192918i 0.0963176 0.0312955i
\(39\) 1.33018 7.61462i 0.212999 1.21932i
\(40\) 0 0
\(41\) 2.66980 1.93972i 0.416953 0.302934i −0.359458 0.933161i \(-0.617038\pi\)
0.776411 + 0.630227i \(0.217038\pi\)
\(42\) 0.489933 0.474632i 0.0755983 0.0732372i
\(43\) 2.97470i 0.453638i 0.973937 + 0.226819i \(0.0728326\pi\)
−0.973937 + 0.226819i \(0.927167\pi\)
\(44\) 1.35289 + 6.44182i 0.203956 + 0.971142i
\(45\) 0 0
\(46\) 0.519478 + 0.168789i 0.0765929 + 0.0248865i
\(47\) −3.14996 4.33555i −0.459469 0.632405i 0.514929 0.857233i \(-0.327818\pi\)
−0.974399 + 0.224827i \(0.927818\pi\)
\(48\) 6.07934 2.97707i 0.877477 0.429703i
\(49\) −0.960422 2.95587i −0.137203 0.422268i
\(50\) 0 0
\(51\) 2.19749 1.07612i 0.307710 0.150687i
\(52\) 5.20617 + 7.16568i 0.721966 + 0.993702i
\(53\) −0.249485 0.0810625i −0.0342694 0.0111348i 0.291832 0.956470i \(-0.405735\pi\)
−0.326102 + 0.945335i \(0.605735\pi\)
\(54\) −0.639811 + 0.0703354i −0.0870672 + 0.00957144i
\(55\) 0 0
\(56\) 1.56928i 0.209704i
\(57\) −6.26960 + 6.07378i −0.830429 + 0.804492i
\(58\) −0.584879 + 0.424939i −0.0767983 + 0.0557973i
\(59\) 5.24873 7.22425i 0.683326 0.940517i −0.316642 0.948545i \(-0.602555\pi\)
0.999968 + 0.00802781i \(0.00255536\pi\)
\(60\) 0 0
\(61\) −14.1273 + 4.59023i −1.80881 + 0.587719i −1.00000 0.000348407i \(-0.999889\pi\)
−0.808812 + 0.588067i \(0.799889\pi\)
\(62\) 0.233958 + 0.169981i 0.0297127 + 0.0215876i
\(63\) −3.23363 + 8.97305i −0.407399 + 1.13050i
\(64\) −2.35906 + 7.26044i −0.294883 + 0.907555i
\(65\) 0 0
\(66\) 0.437632 + 0.561115i 0.0538688 + 0.0690685i
\(67\) 1.33725 0.163371 0.0816854 0.996658i \(-0.473970\pi\)
0.0816854 + 0.996658i \(0.473970\pi\)
\(68\) −0.866386 + 2.66646i −0.105065 + 0.323356i
\(69\) −7.56134 + 1.07495i −0.910279 + 0.129408i
\(70\) 0 0
\(71\) 5.40085 1.75484i 0.640964 0.208262i 0.0295380 0.999564i \(-0.490596\pi\)
0.611426 + 0.791302i \(0.290596\pi\)
\(72\) 0.907941 1.16976i 0.107002 0.137858i
\(73\) 3.84559 5.29300i 0.450092 0.619499i −0.522325 0.852746i \(-0.674935\pi\)
0.972417 + 0.233248i \(0.0749353\pi\)
\(74\) 0.478395 0.347574i 0.0556122 0.0404047i
\(75\) 0 0
\(76\) 10.0023i 1.14734i
\(77\) 10.3194 2.16726i 1.17601 0.246982i
\(78\) 0.846165 + 0.448189i 0.0958093 + 0.0507474i
\(79\) 4.98511 + 1.61976i 0.560868 + 0.182237i 0.575712 0.817653i \(-0.304725\pi\)
−0.0148435 + 0.999890i \(0.504725\pi\)
\(80\) 0 0
\(81\) 7.60193 4.81774i 0.844659 0.535305i
\(82\) 0.126323 + 0.388781i 0.0139500 + 0.0429337i
\(83\) −4.30625 13.2533i −0.472672 1.45473i −0.849072 0.528277i \(-0.822838\pi\)
0.376400 0.926457i \(-0.377162\pi\)
\(84\) −4.80655 9.81523i −0.524438 1.07093i
\(85\) 0 0
\(86\) −0.350452 0.113869i −0.0377902 0.0122788i
\(87\) 4.73149 8.93290i 0.507269 0.957707i
\(88\) −1.62767 0.175077i −0.173511 0.0186632i
\(89\) 13.7521i 1.45772i 0.684663 + 0.728860i \(0.259949\pi\)
−0.684663 + 0.728860i \(0.740051\pi\)
\(90\) 0 0
\(91\) 11.4790 8.34000i 1.20333 0.874269i
\(92\) 5.14383 7.07988i 0.536282 0.738128i
\(93\) −3.98324 0.695821i −0.413043 0.0721533i
\(94\) 0.631351 0.205139i 0.0651189 0.0211584i
\(95\) 0 0
\(96\) 0.358679 + 2.52300i 0.0366075 + 0.257503i
\(97\) 3.27721 10.0862i 0.332750 1.02410i −0.635070 0.772455i \(-0.719029\pi\)
0.967820 0.251645i \(-0.0809714\pi\)
\(98\) 0.384997 0.0388906
\(99\) −8.94616 4.35502i −0.899123 0.437696i
\(100\) 0 0
\(101\) −0.366757 + 1.12876i −0.0364937 + 0.112316i −0.967644 0.252320i \(-0.918807\pi\)
0.931150 + 0.364636i \(0.118807\pi\)
\(102\) 0.0426605 + 0.300081i 0.00422402 + 0.0297124i
\(103\) −3.79085 2.75421i −0.373524 0.271381i 0.385147 0.922855i \(-0.374151\pi\)
−0.758671 + 0.651474i \(0.774151\pi\)
\(104\) −2.09503 + 0.680716i −0.205434 + 0.0667497i
\(105\) 0 0
\(106\) 0.0191000 0.0262890i 0.00185516 0.00255341i
\(107\) −10.2420 + 7.44124i −0.990130 + 0.719371i −0.959950 0.280173i \(-0.909608\pi\)
−0.0301803 + 0.999544i \(0.509608\pi\)
\(108\) −2.09594 + 10.0973i −0.201682 + 0.971616i
\(109\) 2.33097i 0.223266i 0.993749 + 0.111633i \(0.0356081\pi\)
−0.993749 + 0.111633i \(0.964392\pi\)
\(110\) 0 0
\(111\) −3.87007 + 7.30656i −0.367331 + 0.693508i
\(112\) 11.8171 + 3.83962i 1.11661 + 0.362810i
\(113\) 9.53937 + 13.1298i 0.897388 + 1.23515i 0.971294 + 0.237884i \(0.0764537\pi\)
−0.0739054 + 0.997265i \(0.523546\pi\)
\(114\) −0.475562 0.971123i −0.0445405 0.0909540i
\(115\) 0 0
\(116\) 3.57930 + 11.0159i 0.332329 + 1.02280i
\(117\) −13.3819 0.424685i −1.23716 0.0392621i
\(118\) 0.650177 + 0.894892i 0.0598537 + 0.0823815i
\(119\) 4.27152 + 1.38790i 0.391570 + 0.127229i
\(120\) 0 0
\(121\) 1.09661 + 10.9452i 0.0996921 + 0.995018i
\(122\) 1.84005i 0.166590i
\(123\) −3.97711 4.10533i −0.358604 0.370165i
\(124\) 3.74840 2.72337i 0.336616 0.244566i
\(125\) 0 0
\(126\) −0.933340 0.724435i −0.0831485 0.0645378i
\(127\) −16.8339 + 5.46968i −1.49377 + 0.485355i −0.938194 0.346110i \(-0.887502\pi\)
−0.555576 + 0.831466i \(0.687502\pi\)
\(128\) −3.14567 2.28547i −0.278041 0.202009i
\(129\) 5.10105 0.725182i 0.449122 0.0638487i
\(130\) 0 0
\(131\) −14.7072 −1.28498 −0.642488 0.766296i \(-0.722098\pi\)
−0.642488 + 0.766296i \(0.722098\pi\)
\(132\) 10.7167 3.89036i 0.932768 0.338613i
\(133\) −16.0231 −1.38938
\(134\) −0.0511885 + 0.157542i −0.00442201 + 0.0136096i
\(135\) 0 0
\(136\) −0.564119 0.409856i −0.0483728 0.0351449i
\(137\) −7.48516 + 2.43208i −0.639500 + 0.207786i −0.610779 0.791801i \(-0.709144\pi\)
−0.0287215 + 0.999587i \(0.509144\pi\)
\(138\) 0.162800 0.931954i 0.0138585 0.0793332i
\(139\) 0.816636 1.12400i 0.0692661 0.0953367i −0.772978 0.634432i \(-0.781234\pi\)
0.842245 + 0.539096i \(0.181234\pi\)
\(140\) 0 0
\(141\) −6.66674 + 6.45852i −0.561441 + 0.543906i
\(142\) 0.703452i 0.0590323i
\(143\) 7.36966 + 12.8366i 0.616282 + 1.07345i
\(144\) −6.58715 9.69915i −0.548929 0.808262i
\(145\) 0 0
\(146\) 0.476366 + 0.655662i 0.0394243 + 0.0542630i
\(147\) −4.83462 + 2.36753i −0.398753 + 0.195271i
\(148\) −2.92764 9.01036i −0.240651 0.740647i
\(149\) 3.59655 + 11.0690i 0.294641 + 0.906811i 0.983342 + 0.181766i \(0.0581813\pi\)
−0.688701 + 0.725045i \(0.741819\pi\)
\(150\) 0 0
\(151\) 2.11546 + 2.91168i 0.172154 + 0.236949i 0.886372 0.462974i \(-0.153218\pi\)
−0.714218 + 0.699923i \(0.753218\pi\)
\(152\) 2.36586 + 0.768713i 0.191896 + 0.0623509i
\(153\) −2.38105 3.50594i −0.192496 0.283438i
\(154\) −0.139692 + 1.29870i −0.0112567 + 0.104652i
\(155\) 0 0
\(156\) 11.0186 10.6745i 0.882194 0.854641i
\(157\) −5.49000 + 3.98872i −0.438150 + 0.318335i −0.784899 0.619623i \(-0.787285\pi\)
0.346749 + 0.937958i \(0.387285\pi\)
\(158\) −0.381650 + 0.525296i −0.0303624 + 0.0417903i
\(159\) −0.0781866 + 0.447580i −0.00620060 + 0.0354954i
\(160\) 0 0
\(161\) −11.3416 8.24013i −0.893841 0.649413i
\(162\) 0.276587 + 1.08001i 0.0217307 + 0.0848533i
\(163\) −0.774742 + 2.38441i −0.0606825 + 0.186761i −0.976802 0.214143i \(-0.931304\pi\)
0.916120 + 0.400905i \(0.131304\pi\)
\(164\) 6.54947 0.511428
\(165\) 0 0
\(166\) 1.72621 0.133980
\(167\) −4.07027 + 12.5270i −0.314967 + 0.969368i 0.660801 + 0.750561i \(0.270217\pi\)
−0.975768 + 0.218807i \(0.929783\pi\)
\(168\) 2.69102 0.382564i 0.207617 0.0295155i
\(169\) 5.59619 + 4.06587i 0.430476 + 0.312759i
\(170\) 0 0
\(171\) 11.9438 + 9.27048i 0.913365 + 0.708931i
\(172\) −3.47014 + 4.77624i −0.264596 + 0.364185i
\(173\) −18.3410 + 13.3255i −1.39444 + 1.01312i −0.399077 + 0.916917i \(0.630670\pi\)
−0.995362 + 0.0962022i \(0.969330\pi\)
\(174\) 0.871273 + 0.899362i 0.0660510 + 0.0681805i
\(175\) 0 0
\(176\) −5.30086 + 11.8285i −0.399567 + 0.891604i
\(177\) −13.6678 7.23941i −1.02733 0.544148i
\(178\) −1.62014 0.526416i −0.121435 0.0394566i
\(179\) 1.22646 + 1.68808i 0.0916701 + 0.126173i 0.852389 0.522909i \(-0.175153\pi\)
−0.760718 + 0.649082i \(0.775153\pi\)
\(180\) 0 0
\(181\) 2.57897 + 7.93725i 0.191693 + 0.589971i 0.999999 + 0.00120838i \(0.000384638\pi\)
−0.808306 + 0.588762i \(0.799615\pi\)
\(182\) 0.543135 + 1.67160i 0.0402598 + 0.123907i
\(183\) 11.3154 + 23.1066i 0.836455 + 1.70809i
\(184\) 1.27929 + 1.76080i 0.0943109 + 0.129808i
\(185\) 0 0
\(186\) 0.234449 0.442632i 0.0171907 0.0324554i
\(187\) −1.91610 + 4.27562i −0.140119 + 0.312664i
\(188\) 10.6358i 0.775699i
\(189\) 16.1754 + 3.35758i 1.17658 + 0.244228i
\(190\) 0 0
\(191\) 6.85805 9.43930i 0.496231 0.683004i −0.485291 0.874353i \(-0.661286\pi\)
0.981522 + 0.191349i \(0.0612862\pi\)
\(192\) 13.0254 + 2.27537i 0.940025 + 0.164210i
\(193\) −25.5534 + 8.30282i −1.83938 + 0.597650i −0.840979 + 0.541067i \(0.818020\pi\)
−0.998398 + 0.0565827i \(0.981980\pi\)
\(194\) 1.06281 + 0.772180i 0.0763056 + 0.0554393i
\(195\) 0 0
\(196\) 1.90611 5.86639i 0.136150 0.419028i
\(197\) 2.87880 0.205106 0.102553 0.994728i \(-0.467299\pi\)
0.102553 + 0.994728i \(0.467299\pi\)
\(198\) 0.855518 0.887246i 0.0607990 0.0630539i
\(199\) −4.95263 −0.351083 −0.175541 0.984472i \(-0.556168\pi\)
−0.175541 + 0.984472i \(0.556168\pi\)
\(200\) 0 0
\(201\) −0.325998 2.29312i −0.0229941 0.161745i
\(202\) −0.118941 0.0864157i −0.00836866 0.00608019i
\(203\) 17.6469 5.73383i 1.23857 0.402436i
\(204\) 4.78369 + 0.835649i 0.334925 + 0.0585071i
\(205\) 0 0
\(206\) 0.469586 0.341174i 0.0327176 0.0237707i
\(207\) 3.68665 + 12.7042i 0.256240 + 0.883003i
\(208\) 17.4417i 1.20936i
\(209\) 1.78761 16.6193i 0.123652 1.14958i
\(210\) 0 0
\(211\) −10.7924 3.50665i −0.742976 0.241408i −0.0870200 0.996207i \(-0.527734\pi\)
−0.655956 + 0.754799i \(0.727734\pi\)
\(212\) −0.306014 0.421192i −0.0210171 0.0289276i
\(213\) −4.32586 8.83363i −0.296403 0.605271i
\(214\) −0.484604 1.49146i −0.0331268 0.101954i
\(215\) 0 0
\(216\) −2.22726 1.27178i −0.151546 0.0865335i
\(217\) −4.36269 6.00472i −0.296158 0.407627i
\(218\) −0.274613 0.0892271i −0.0185991 0.00604322i
\(219\) −10.0140 5.30411i −0.676681 0.358418i
\(220\) 0 0
\(221\) 6.30462i 0.424095i
\(222\) −0.712648 0.735623i −0.0478298 0.0493718i
\(223\) 2.06370 1.49937i 0.138196 0.100405i −0.516540 0.856263i \(-0.672780\pi\)
0.654735 + 0.755858i \(0.272780\pi\)
\(224\) −2.74950 + 3.78436i −0.183709 + 0.252853i
\(225\) 0 0
\(226\) −1.91199 + 0.621243i −0.127184 + 0.0413244i
\(227\) 15.8798 + 11.5373i 1.05398 + 0.765759i 0.972965 0.230954i \(-0.0741848\pi\)
0.0810119 + 0.996713i \(0.474185\pi\)
\(228\) −17.1520 + 2.43838i −1.13592 + 0.161486i
\(229\) 2.48950 7.66188i 0.164511 0.506312i −0.834489 0.551024i \(-0.814237\pi\)
0.999000 + 0.0447126i \(0.0142372\pi\)
\(230\) 0 0
\(231\) −6.23214 17.1675i −0.410045 1.12954i
\(232\) −2.88071 −0.189128
\(233\) −3.92966 + 12.0942i −0.257440 + 0.792320i 0.735899 + 0.677092i \(0.236760\pi\)
−0.993339 + 0.115228i \(0.963240\pi\)
\(234\) 0.562278 1.56027i 0.0367572 0.101998i
\(235\) 0 0
\(236\) 16.8549 5.47649i 1.09716 0.356489i
\(237\) 1.56229 8.94338i 0.101482 0.580935i
\(238\) −0.327019 + 0.450103i −0.0211975 + 0.0291759i
\(239\) −11.6028 + 8.42996i −0.750526 + 0.545289i −0.895990 0.444075i \(-0.853532\pi\)
0.145464 + 0.989364i \(0.453532\pi\)
\(240\) 0 0
\(241\) 5.56980i 0.358782i −0.983778 0.179391i \(-0.942587\pi\)
0.983778 0.179391i \(-0.0574128\pi\)
\(242\) −1.33144 0.289779i −0.0855881 0.0186277i
\(243\) −10.1147 11.8614i −0.648860 0.760908i
\(244\) −28.0378 9.11002i −1.79493 0.583210i
\(245\) 0 0
\(246\) 0.635891 0.311398i 0.0405429 0.0198540i
\(247\) −6.95041 21.3912i −0.442244 1.36109i
\(248\) 0.356085 + 1.09592i 0.0226114 + 0.0695909i
\(249\) −21.6770 + 10.6153i −1.37373 + 0.672718i
\(250\) 0 0
\(251\) 22.4384 + 7.29068i 1.41630 + 0.460184i 0.914425 0.404756i \(-0.132644\pi\)
0.501875 + 0.864940i \(0.332644\pi\)
\(252\) −15.6595 + 10.6351i −0.986456 + 0.669949i
\(253\) 9.81205 10.8443i 0.616879 0.681773i
\(254\) 2.19259i 0.137575i
\(255\) 0 0
\(256\) −11.9625 + 8.69129i −0.747658 + 0.543206i
\(257\) 2.60990 3.59223i 0.162801 0.224077i −0.719821 0.694160i \(-0.755776\pi\)
0.882622 + 0.470083i \(0.155776\pi\)
\(258\) −0.109829 + 0.628717i −0.00683764 + 0.0391422i
\(259\) −14.4341 + 4.68992i −0.896891 + 0.291417i
\(260\) 0 0
\(261\) −16.4717 5.93592i −1.01957 0.367424i
\(262\) 0.562978 1.73267i 0.0347809 0.107045i
\(263\) −16.3005 −1.00513 −0.502565 0.864540i \(-0.667610\pi\)
−0.502565 + 0.864540i \(0.667610\pi\)
\(264\) 0.0965758 + 2.83383i 0.00594383 + 0.174410i
\(265\) 0 0
\(266\) 0.613347 1.88769i 0.0376067 0.115742i
\(267\) 23.5822 3.35253i 1.44321 0.205171i
\(268\) 2.14711 + 1.55997i 0.131156 + 0.0952902i
\(269\) −1.84648 + 0.599958i −0.112582 + 0.0365801i −0.364766 0.931099i \(-0.618851\pi\)
0.252184 + 0.967679i \(0.418851\pi\)
\(270\) 0 0
\(271\) 7.23294 9.95529i 0.439370 0.604741i −0.530702 0.847559i \(-0.678072\pi\)
0.970072 + 0.242818i \(0.0780716\pi\)
\(272\) −4.46658 + 3.24516i −0.270826 + 0.196767i
\(273\) −17.0999 17.6512i −1.03493 1.06830i
\(274\) 0.974929i 0.0588976i
\(275\) 0 0
\(276\) −13.3946 7.09474i −0.806261 0.427053i
\(277\) −3.47993 1.13070i −0.209089 0.0679370i 0.202600 0.979262i \(-0.435061\pi\)
−0.411689 + 0.911325i \(0.635061\pi\)
\(278\) 0.101159 + 0.139234i 0.00606714 + 0.00835070i
\(279\) −0.222154 + 7.00012i −0.0133000 + 0.419086i
\(280\) 0 0
\(281\) −5.71578 17.5914i −0.340975 1.04941i −0.963703 0.266975i \(-0.913976\pi\)
0.622729 0.782438i \(-0.286024\pi\)
\(282\) −0.505686 1.03264i −0.0301132 0.0614927i
\(283\) 14.8456 + 20.4332i 0.882480 + 1.21463i 0.975728 + 0.218986i \(0.0702749\pi\)
−0.0932485 + 0.995643i \(0.529725\pi\)
\(284\) 10.7188 + 3.48276i 0.636046 + 0.206664i
\(285\) 0 0
\(286\) −1.79439 + 0.376853i −0.106104 + 0.0222838i
\(287\) 10.4919i 0.619317i
\(288\) 4.23903 1.23013i 0.249787 0.0724862i
\(289\) 12.1388 8.81932i 0.714045 0.518784i
\(290\) 0 0
\(291\) −18.0949 3.16094i −1.06074 0.185298i
\(292\) 12.3491 4.01247i 0.722677 0.234812i
\(293\) −0.689709 0.501103i −0.0402932 0.0292747i 0.567456 0.823403i \(-0.307928\pi\)
−0.607750 + 0.794129i \(0.707928\pi\)
\(294\) −0.0938558 0.660197i −0.00547378 0.0385035i
\(295\) 0 0
\(296\) 2.35624 0.136954
\(297\) −5.28711 + 16.4026i −0.306789 + 0.951777i
\(298\) −1.44172 −0.0835168
\(299\) 6.08107 18.7156i 0.351678 1.08235i
\(300\) 0 0
\(301\) 7.65128 + 5.55898i 0.441012 + 0.320414i
\(302\) −0.424005 + 0.137767i −0.0243987 + 0.00792763i
\(303\) 2.02502 + 0.353745i 0.116334 + 0.0203221i
\(304\) 11.5772 15.9347i 0.664000 0.913918i
\(305\) 0 0
\(306\) 0.504181 0.146309i 0.0288221 0.00836393i
\(307\) 13.3356i 0.761105i 0.924759 + 0.380553i \(0.124266\pi\)
−0.924759 + 0.380553i \(0.875734\pi\)
\(308\) 19.0973 + 8.55836i 1.08817 + 0.487658i
\(309\) −3.79881 + 7.17202i −0.216107 + 0.408002i
\(310\) 0 0
\(311\) −0.449547 0.618749i −0.0254915 0.0350860i 0.796081 0.605190i \(-0.206903\pi\)
−0.821573 + 0.570104i \(0.806903\pi\)
\(312\) 1.67803 + 3.42663i 0.0949998 + 0.193995i
\(313\) −1.30074 4.00328i −0.0735224 0.226279i 0.907542 0.419962i \(-0.137957\pi\)
−0.981064 + 0.193683i \(0.937957\pi\)
\(314\) −0.259762 0.799465i −0.0146592 0.0451164i
\(315\) 0 0
\(316\) 6.11466 + 8.41610i 0.343976 + 0.473443i
\(317\) −21.4920 6.98318i −1.20711 0.392215i −0.364739 0.931110i \(-0.618842\pi\)
−0.842373 + 0.538895i \(0.818842\pi\)
\(318\) −0.0497368 0.0263441i −0.00278910 0.00147731i
\(319\) 3.97840 + 18.9432i 0.222748 + 1.06062i
\(320\) 0 0
\(321\) 15.2571 + 15.7490i 0.851569 + 0.879023i
\(322\) 1.40492 1.02073i 0.0782931 0.0568832i
\(323\) 4.18481 5.75990i 0.232849 0.320489i
\(324\) 17.8260 + 1.13258i 0.990331 + 0.0629212i
\(325\) 0 0
\(326\) −0.251252 0.182546i −0.0139156 0.0101103i
\(327\) 3.99716 0.568250i 0.221044 0.0314243i
\(328\) −0.503353 + 1.54916i −0.0277930 + 0.0855381i
\(329\) −17.0380 −0.939337
\(330\) 0 0
\(331\) −4.29336 −0.235984 −0.117992 0.993015i \(-0.537646\pi\)
−0.117992 + 0.993015i \(0.537646\pi\)
\(332\) 8.54641 26.3032i 0.469045 1.44357i
\(333\) 13.4728 + 4.85522i 0.738305 + 0.266064i
\(334\) −1.32001 0.959041i −0.0722276 0.0524764i
\(335\) 0 0
\(336\) 3.70340 21.2001i 0.202037 1.15656i
\(337\) 8.56709 11.7916i 0.466679 0.642329i −0.509198 0.860650i \(-0.670058\pi\)
0.975877 + 0.218320i \(0.0700578\pi\)
\(338\) −0.693219 + 0.503653i −0.0377061 + 0.0273951i
\(339\) 20.1896 19.5590i 1.09655 1.06230i
\(340\) 0 0
\(341\) 6.71487 3.85510i 0.363631 0.208765i
\(342\) −1.54936 + 1.05224i −0.0837796 + 0.0568987i
\(343\) 11.7683 + 3.82374i 0.635427 + 0.206463i
\(344\) −0.863041 1.18787i −0.0465320 0.0640459i
\(345\) 0 0
\(346\) −0.867811 2.67085i −0.0466538 0.143586i
\(347\) −4.24886 13.0766i −0.228091 0.701991i −0.997963 0.0637934i \(-0.979680\pi\)
0.769872 0.638198i \(-0.220320\pi\)
\(348\) 18.0177 8.82331i 0.965848 0.472979i
\(349\) 4.60029 + 6.33176i 0.246248 + 0.338931i 0.914193 0.405279i \(-0.132826\pi\)
−0.667945 + 0.744211i \(0.732826\pi\)
\(350\) 0 0
\(351\) 2.53403 + 23.0509i 0.135256 + 1.23037i
\(352\) −3.61842 3.27400i −0.192863 0.174505i
\(353\) 32.8789i 1.74997i −0.484153 0.874983i \(-0.660872\pi\)
0.484153 0.874983i \(-0.339128\pi\)
\(354\) 1.37607 1.33309i 0.0731372 0.0708529i
\(355\) 0 0
\(356\) −16.0425 + 22.0806i −0.850252 + 1.17027i
\(357\) 1.33866 7.66320i 0.0708495 0.405579i
\(358\) −0.245822 + 0.0798723i −0.0129921 + 0.00422138i
\(359\) 13.9789 + 10.1563i 0.737778 + 0.536027i 0.892014 0.452007i \(-0.149292\pi\)
−0.154237 + 0.988034i \(0.549292\pi\)
\(360\) 0 0
\(361\) −1.97758 + 6.08636i −0.104083 + 0.320335i
\(362\) −1.03381 −0.0543359
\(363\) 18.5016 4.54874i 0.971082 0.238747i
\(364\) 28.1600 1.47598
\(365\) 0 0
\(366\) −3.15534 + 0.448573i −0.164932 + 0.0234473i
\(367\) 18.9024 + 13.7334i 0.986696 + 0.716876i 0.959195 0.282745i \(-0.0912451\pi\)
0.0275007 + 0.999622i \(0.491245\pi\)
\(368\) 16.3894 5.32523i 0.854356 0.277597i
\(369\) −6.07030 + 7.82079i −0.316007 + 0.407134i
\(370\) 0 0
\(371\) −0.674726 + 0.490217i −0.0350301 + 0.0254508i
\(372\) −5.58386 5.76387i −0.289509 0.298843i
\(373\) 26.3240i 1.36301i −0.731815 0.681503i \(-0.761326\pi\)
0.731815 0.681503i \(-0.238674\pi\)
\(374\) −0.430367 0.389403i −0.0222538 0.0201355i
\(375\) 0 0
\(376\) 2.51572 + 0.817406i 0.129738 + 0.0421545i
\(377\) 15.3096 + 21.0718i 0.788484 + 1.08526i
\(378\) −1.01474 + 1.77710i −0.0521923 + 0.0914044i
\(379\) 5.20491 + 16.0191i 0.267358 + 0.822843i 0.991141 + 0.132815i \(0.0424018\pi\)
−0.723783 + 0.690028i \(0.757598\pi\)
\(380\) 0 0
\(381\) 13.4833 + 27.5336i 0.690769 + 1.41059i
\(382\) 0.849530 + 1.16928i 0.0434658 + 0.0598255i
\(383\) −16.9960 5.52233i −0.868454 0.282178i −0.159299 0.987230i \(-0.550923\pi\)
−0.709155 + 0.705053i \(0.750923\pi\)
\(384\) −3.15228 + 5.95139i −0.160864 + 0.303705i
\(385\) 0 0
\(386\) 3.32829i 0.169406i
\(387\) −2.48710 8.57054i −0.126426 0.435665i
\(388\) 17.0280 12.3716i 0.864467 0.628072i
\(389\) −1.15007 + 1.58293i −0.0583106 + 0.0802577i −0.837176 0.546933i \(-0.815795\pi\)
0.778866 + 0.627191i \(0.215795\pi\)
\(390\) 0 0
\(391\) 5.92425 1.92491i 0.299602 0.0973467i
\(392\) 1.24110 + 0.901710i 0.0626849 + 0.0455432i
\(393\) 3.58537 + 25.2201i 0.180858 + 1.27218i
\(394\) −0.110198 + 0.339154i −0.00555168 + 0.0170863i
\(395\) 0 0
\(396\) −9.28377 17.4287i −0.466527 0.875823i
\(397\) 5.31786 0.266896 0.133448 0.991056i \(-0.457395\pi\)
0.133448 + 0.991056i \(0.457395\pi\)
\(398\) 0.189582 0.583472i 0.00950287 0.0292468i
\(399\) 3.90615 + 27.4765i 0.195552 + 1.37555i
\(400\) 0 0
\(401\) −23.8578 + 7.75185i −1.19140 + 0.387109i −0.836590 0.547830i \(-0.815454\pi\)
−0.354809 + 0.934939i \(0.615454\pi\)
\(402\) 0.282633 + 0.0493724i 0.0140965 + 0.00246247i
\(403\) 6.12402 8.42899i 0.305059 0.419878i
\(404\) −1.90563 + 1.38452i −0.0948087 + 0.0688825i
\(405\) 0 0
\(406\) 2.29848i 0.114072i
\(407\) −3.25409 15.4944i −0.161299 0.768028i
\(408\) −0.565303 + 1.06727i −0.0279867 + 0.0528378i
\(409\) −24.4821 7.95473i −1.21056 0.393336i −0.366927 0.930250i \(-0.619590\pi\)
−0.843637 + 0.536914i \(0.819590\pi\)
\(410\) 0 0
\(411\) 5.99530 + 12.2427i 0.295726 + 0.603889i
\(412\) −2.87373 8.84444i −0.141579 0.435734i
\(413\) −8.77304 27.0006i −0.431693 1.32861i
\(414\) −1.63781 0.0519772i −0.0804940 0.00255454i
\(415\) 0 0
\(416\) −6.24487 2.02908i −0.306180 0.0994839i
\(417\) −2.12653 1.12636i −0.104137 0.0551582i
\(418\) 1.88950 + 0.846768i 0.0924183 + 0.0414168i
\(419\) 33.0369i 1.61396i −0.590580 0.806979i \(-0.701101\pi\)
0.590580 0.806979i \(-0.298899\pi\)
\(420\) 0 0
\(421\) 8.07346 5.86571i 0.393476 0.285877i −0.373402 0.927670i \(-0.621809\pi\)
0.766879 + 0.641792i \(0.221809\pi\)
\(422\) 0.826241 1.13722i 0.0402208 0.0553591i
\(423\) 12.7004 + 9.85770i 0.617513 + 0.479298i
\(424\) 0.123144 0.0400119i 0.00598040 0.00194315i
\(425\) 0 0
\(426\) 1.20629 0.171490i 0.0584447 0.00830869i
\(427\) −14.5937 + 44.9149i −0.706241 + 2.17359i
\(428\) −25.1253 −1.21448
\(429\) 20.2157 15.7669i 0.976023 0.761233i
\(430\) 0 0
\(431\) 3.63918 11.2002i 0.175293 0.539496i −0.824354 0.566075i \(-0.808461\pi\)
0.999647 + 0.0265786i \(0.00846124\pi\)
\(432\) −15.0263 + 13.6602i −0.722955 + 0.657226i
\(433\) −8.82447 6.41135i −0.424077 0.308110i 0.355199 0.934791i \(-0.384413\pi\)
−0.779276 + 0.626681i \(0.784413\pi\)
\(434\) 0.874419 0.284116i 0.0419735 0.0136380i
\(435\) 0 0
\(436\) −2.71919 + 3.74265i −0.130226 + 0.179240i
\(437\) −17.9785 + 13.0622i −0.860029 + 0.624848i
\(438\) 1.00820 0.976716i 0.0481739 0.0466693i
\(439\) 4.24090i 0.202407i −0.994866 0.101203i \(-0.967731\pi\)
0.994866 0.101203i \(-0.0322693\pi\)
\(440\) 0 0
\(441\) 5.23846 + 7.71329i 0.249451 + 0.367300i
\(442\) −0.742751 0.241335i −0.0353291 0.0114791i
\(443\) 21.2625 + 29.2653i 1.01021 + 1.39044i 0.918845 + 0.394618i \(0.129123\pi\)
0.0913656 + 0.995817i \(0.470877\pi\)
\(444\) −14.7373 + 7.21692i −0.699403 + 0.342500i
\(445\) 0 0
\(446\) 0.0976450 + 0.300520i 0.00462362 + 0.0142301i
\(447\) 18.1045 8.86584i 0.856314 0.419340i
\(448\) 14.2662 + 19.6357i 0.674014 + 0.927700i
\(449\) −39.3387 12.7819i −1.85651 0.603216i −0.995515 0.0946009i \(-0.969843\pi\)
−0.860994 0.508615i \(-0.830157\pi\)
\(450\) 0 0
\(451\) 10.8823 + 1.17053i 0.512426 + 0.0551179i
\(452\) 32.2097i 1.51501i
\(453\) 4.47727 4.33743i 0.210360 0.203790i
\(454\) −1.96708 + 1.42917i −0.0923196 + 0.0670741i
\(455\) 0 0
\(456\) 0.741441 4.24439i 0.0347212 0.198762i
\(457\) 7.82596 2.54281i 0.366083 0.118948i −0.120198 0.992750i \(-0.538353\pi\)
0.486281 + 0.873802i \(0.338353\pi\)
\(458\) 0.807356 + 0.586578i 0.0377253 + 0.0274090i
\(459\) −5.43156 + 4.93773i −0.253523 + 0.230474i
\(460\) 0 0
\(461\) 20.0965 0.935989 0.467995 0.883731i \(-0.344977\pi\)
0.467995 + 0.883731i \(0.344977\pi\)
\(462\) 2.26108 0.0770566i 0.105195 0.00358500i
\(463\) 36.9595 1.71765 0.858827 0.512266i \(-0.171194\pi\)
0.858827 + 0.512266i \(0.171194\pi\)
\(464\) −7.04832 + 21.6925i −0.327210 + 1.00705i
\(465\) 0 0
\(466\) −1.27441 0.925910i −0.0590357 0.0428920i
\(467\) 13.3870 4.34970i 0.619476 0.201280i 0.0175683 0.999846i \(-0.494408\pi\)
0.601908 + 0.798566i \(0.294408\pi\)
\(468\) −20.9908 16.2925i −0.970301 0.753123i
\(469\) 2.49898 3.43955i 0.115392 0.158824i
\(470\) 0 0
\(471\) 8.17826 + 8.44192i 0.376834 + 0.388983i
\(472\) 4.40762i 0.202877i
\(473\) −6.61943 + 7.31578i −0.304362 + 0.336380i
\(474\) 0.993822 + 0.526398i 0.0456477 + 0.0241783i
\(475\) 0 0
\(476\) 5.23939 + 7.21140i 0.240147 + 0.330534i
\(477\) 0.786575 + 0.0249626i 0.0360148 + 0.00114296i
\(478\) −0.548994 1.68963i −0.0251104 0.0772818i
\(479\) 0.417639 + 1.28536i 0.0190824 + 0.0587297i 0.960144 0.279505i \(-0.0901703\pi\)
−0.941062 + 0.338235i \(0.890170\pi\)
\(480\) 0 0
\(481\) −12.5223 17.2355i −0.570968 0.785870i
\(482\) 0.656181 + 0.213206i 0.0298882 + 0.00971128i
\(483\) −11.3654 + 21.4574i −0.517142 + 0.976347i
\(484\) −11.0074 + 18.8531i −0.500336 + 0.856959i
\(485\) 0 0
\(486\) 1.78458 0.737581i 0.0809501 0.0334573i
\(487\) 18.1884 13.2147i 0.824196 0.598814i −0.0937152 0.995599i \(-0.529874\pi\)
0.917911 + 0.396785i \(0.129874\pi\)
\(488\) 4.30963 5.93169i 0.195088 0.268515i
\(489\) 4.27768 + 0.747256i 0.193443 + 0.0337921i
\(490\) 0 0
\(491\) −9.20950 6.69109i −0.415619 0.301965i 0.360254 0.932854i \(-0.382690\pi\)
−0.775873 + 0.630889i \(0.782690\pi\)
\(492\) −1.59665 11.2311i −0.0719825 0.506337i
\(493\) −2.54775 + 7.84117i −0.114745 + 0.353148i
\(494\) 2.78616 0.125355
\(495\) 0 0
\(496\) 9.12381 0.409671
\(497\) 5.57919 17.1710i 0.250261 0.770223i
\(498\) −0.420821 2.96013i −0.0188575 0.132646i
\(499\) −3.16117 2.29673i −0.141513 0.102816i 0.514776 0.857325i \(-0.327875\pi\)
−0.656290 + 0.754509i \(0.727875\pi\)
\(500\) 0 0
\(501\) 22.4737 + 3.92586i 1.00405 + 0.175395i
\(502\) −1.71784 + 2.36440i −0.0766709 + 0.105528i
\(503\) −19.7496 + 14.3489i −0.880593 + 0.639788i −0.933408 0.358816i \(-0.883180\pi\)
0.0528157 + 0.998604i \(0.483180\pi\)
\(504\) −1.31205 4.52132i −0.0584433 0.201396i
\(505\) 0 0
\(506\) 0.901973 + 1.57107i 0.0400976 + 0.0698426i
\(507\) 5.60793 10.5876i 0.249057 0.470211i
\(508\) −33.4096 10.8554i −1.48231 0.481631i
\(509\) −13.5377 18.6330i −0.600047 0.825894i 0.395665 0.918395i \(-0.370514\pi\)
−0.995713 + 0.0925006i \(0.970514\pi\)
\(510\) 0 0
\(511\) −6.42775 19.7826i −0.284347 0.875130i
\(512\) −2.96909 9.13793i −0.131217 0.403843i
\(513\) 12.9854 22.7413i 0.573320 1.00405i
\(514\) 0.323298 + 0.444981i 0.0142601 + 0.0196273i
\(515\) 0 0
\(516\) 9.03631 + 4.78627i 0.397801 + 0.210704i
\(517\) 1.90084 17.6720i 0.0835991 0.777213i
\(518\) 1.88001i 0.0826031i
\(519\) 27.3219 + 28.2028i 1.19930 + 1.23796i
\(520\) 0 0
\(521\) 4.97322 6.84505i 0.217881 0.299887i −0.686060 0.727545i \(-0.740661\pi\)
0.903941 + 0.427658i \(0.140661\pi\)
\(522\) 1.32983 1.71332i 0.0582052 0.0749898i
\(523\) −0.333579 + 0.108386i −0.0145864 + 0.00473941i −0.316301 0.948659i \(-0.602441\pi\)
0.301715 + 0.953398i \(0.402441\pi\)
\(524\) −23.6142 17.1567i −1.03159 0.749495i
\(525\) 0 0
\(526\) 0.623965 1.92037i 0.0272062 0.0837320i
\(527\) 3.29797 0.143662
\(528\) 21.5758 + 6.20638i 0.938966 + 0.270098i
\(529\) 3.55687 0.154646
\(530\) 0 0
\(531\) −9.08224 + 25.2024i −0.394136 + 1.09369i
\(532\) −25.7270 18.6917i −1.11540 0.810389i
\(533\) 14.0069 4.55112i 0.606707 0.197131i
\(534\) −0.507740 + 2.90657i −0.0219721 + 0.125779i
\(535\) 0 0
\(536\) −0.533996 + 0.387971i −0.0230651 + 0.0167578i
\(537\) 2.59575 2.51467i 0.112015 0.108516i
\(538\) 0.240501i 0.0103687i
\(539\) 4.21553 9.40664i 0.181576 0.405173i
\(540\) 0 0
\(541\) −32.0739 10.4214i −1.37896 0.448053i −0.476635 0.879101i \(-0.658144\pi\)
−0.902329 + 0.431048i \(0.858144\pi\)
\(542\) 0.895969 + 1.23320i 0.0384852 + 0.0529703i
\(543\) 12.9822 6.35740i 0.557117 0.272822i
\(544\) −0.642287 1.97675i −0.0275378 0.0847527i
\(545\) 0 0
\(546\) 2.73406 1.33888i 0.117007 0.0572988i
\(547\) 16.6409 + 22.9043i 0.711515 + 0.979316i 0.999763 + 0.0217602i \(0.00692704\pi\)
−0.288249 + 0.957556i \(0.593073\pi\)
\(548\) −14.8555 4.82683i −0.634594 0.206192i
\(549\) 36.8648 25.0367i 1.57335 1.06854i
\(550\) 0 0
\(551\) 29.4133i 1.25305i
\(552\) 2.70756 2.62300i 0.115241 0.111642i
\(553\) 13.4821 9.79533i 0.573318 0.416540i
\(554\) 0.266416 0.366690i 0.0113189 0.0155792i
\(555\) 0 0
\(556\) 2.62241 0.852074i 0.111215 0.0361360i
\(557\) 13.9281 + 10.1194i 0.590153 + 0.428771i 0.842370 0.538899i \(-0.181160\pi\)
−0.252217 + 0.967671i \(0.581160\pi\)
\(558\) −0.816185 0.294130i −0.0345519 0.0124515i
\(559\) −4.10243 + 12.6260i −0.173514 + 0.534022i
\(560\) 0 0
\(561\) 7.79898 + 2.24342i 0.329273 + 0.0947171i
\(562\) 2.29124 0.0966503
\(563\) 9.76130 30.0422i 0.411390 1.26613i −0.504051 0.863674i \(-0.668158\pi\)
0.915441 0.402453i \(-0.131842\pi\)
\(564\) −18.2384 + 2.59284i −0.767977 + 0.109178i
\(565\) 0 0
\(566\) −2.97552 + 0.966807i −0.125071 + 0.0406379i
\(567\) 1.81433 28.5562i 0.0761948 1.19925i
\(568\) −1.64757 + 2.26768i −0.0691305 + 0.0951499i
\(569\) 17.4236 12.6590i 0.730435 0.530692i −0.159266 0.987236i \(-0.550913\pi\)
0.889701 + 0.456543i \(0.150913\pi\)
\(570\) 0 0
\(571\) 31.4210i 1.31493i 0.753485 + 0.657465i \(0.228371\pi\)
−0.753485 + 0.657465i \(0.771629\pi\)
\(572\) −3.14166 + 29.2078i −0.131360 + 1.22124i
\(573\) −17.8585 9.45911i −0.746049 0.395160i
\(574\) 1.23606 + 0.401619i 0.0515920 + 0.0167632i
\(575\) 0 0
\(576\) 0.726454 22.8907i 0.0302689 0.953780i
\(577\) 9.38846 + 28.8947i 0.390847 + 1.20290i 0.932149 + 0.362075i \(0.117931\pi\)
−0.541302 + 0.840828i \(0.682069\pi\)
\(578\) 0.574351 + 1.76767i 0.0238898 + 0.0735253i
\(579\) 20.4672 + 41.7952i 0.850590 + 1.73695i
\(580\) 0 0
\(581\) −42.1362 13.6909i −1.74810 0.567993i
\(582\) 1.06504 2.01077i 0.0441475 0.0833490i
\(583\) −0.433182 0.754523i −0.0179406 0.0312492i
\(584\) 3.22933i 0.133631i
\(585\) 0 0
\(586\) 0.0854366 0.0620733i 0.00352935 0.00256422i
\(587\) −5.46190 + 7.51766i −0.225437 + 0.310287i −0.906720 0.421733i \(-0.861422\pi\)
0.681283 + 0.732020i \(0.261422\pi\)
\(588\) −10.5244 1.83848i −0.434020 0.0758177i
\(589\) −11.1898 + 3.63579i −0.461068 + 0.149810i
\(590\) 0 0
\(591\) −0.701804 4.93660i −0.0288683 0.203065i
\(592\) 5.76509 17.7431i 0.236944 0.729238i
\(593\) 17.5361 0.720120 0.360060 0.932929i \(-0.382756\pi\)
0.360060 + 0.932929i \(0.382756\pi\)
\(594\) −1.73002 1.25075i −0.0709835 0.0513191i
\(595\) 0 0
\(596\) −7.13791 + 21.9682i −0.292380 + 0.899854i
\(597\) 1.20737 + 8.49282i 0.0494142 + 0.347588i
\(598\) 1.97212 + 1.43283i 0.0806460 + 0.0585928i
\(599\) −25.5218 + 8.29252i −1.04279 + 0.338823i −0.779835 0.625985i \(-0.784697\pi\)
−0.262955 + 0.964808i \(0.584697\pi\)
\(600\) 0 0
\(601\) −0.0311549 + 0.0428810i −0.00127083 + 0.00174915i −0.809652 0.586910i \(-0.800344\pi\)
0.808381 + 0.588659i \(0.200344\pi\)
\(602\) −0.947789 + 0.688609i −0.0386290 + 0.0280656i
\(603\) −3.85280 + 1.11805i −0.156898 + 0.0455305i
\(604\) 7.14285i 0.290638i
\(605\) 0 0
\(606\) −0.119191 + 0.225028i −0.00484179 + 0.00914113i
\(607\) −8.80594 2.86122i −0.357422 0.116134i 0.124801 0.992182i \(-0.460171\pi\)
−0.482223 + 0.876048i \(0.660171\pi\)
\(608\) 4.35847 + 5.99892i 0.176759 + 0.243288i
\(609\) −14.1344 28.8633i −0.572757 1.16960i
\(610\) 0 0
\(611\) −7.39068 22.7462i −0.298995 0.920211i
\(612\) 0.266797 8.40682i 0.0107846 0.339826i
\(613\) −9.46428 13.0265i −0.382259 0.526134i 0.573922 0.818910i \(-0.305421\pi\)
−0.956181 + 0.292776i \(0.905421\pi\)
\(614\) −1.57108 0.510475i −0.0634036 0.0206011i
\(615\) 0 0
\(616\) −3.49203 + 3.85938i −0.140698 + 0.155499i
\(617\) 32.5133i 1.30894i −0.756089 0.654469i \(-0.772892\pi\)
0.756089 0.654469i \(-0.227108\pi\)
\(618\) −0.699525 0.722077i −0.0281390 0.0290462i
\(619\) 21.0066 15.2622i 0.844325 0.613438i −0.0792507 0.996855i \(-0.525253\pi\)
0.923575 + 0.383417i \(0.125253\pi\)
\(620\) 0 0
\(621\) 20.8865 9.41897i 0.838148 0.377970i
\(622\) 0.0901034 0.0292764i 0.00361282 0.00117388i
\(623\) 35.3720 + 25.6992i 1.41715 + 1.02962i
\(624\) 29.9091 4.25198i 1.19732 0.170216i
\(625\) 0 0
\(626\) 0.521419 0.0208401
\(627\) −28.9346 + 0.986082i −1.15554 + 0.0393803i
\(628\) −13.4679 −0.537428
\(629\) 2.08390 6.41359i 0.0830906 0.255727i
\(630\) 0 0
\(631\) −22.5141 16.3575i −0.896273 0.651181i 0.0412329 0.999150i \(-0.486871\pi\)
−0.937506 + 0.347969i \(0.886871\pi\)
\(632\) −2.46061 + 0.799502i −0.0978779 + 0.0318025i
\(633\) −3.38224 + 19.3617i −0.134432 + 0.769558i
\(634\) 1.64539 2.26468i 0.0653466 0.0899419i
\(635\) 0 0
\(636\) −0.647663 + 0.627435i −0.0256815 + 0.0248794i
\(637\) 13.8706i 0.549572i
\(638\) −2.38400 0.256429i −0.0943835 0.0101521i
\(639\) −14.0934 + 9.57151i −0.557527 + 0.378643i
\(640\) 0 0
\(641\) 2.50741 + 3.45116i 0.0990369 + 0.136313i 0.855659 0.517539i \(-0.173152\pi\)
−0.756623 + 0.653852i \(0.773152\pi\)
\(642\) −2.43943 + 1.19459i −0.0962764 + 0.0471469i
\(643\) 1.64010 + 5.04772i 0.0646794 + 0.199063i 0.978174 0.207789i \(-0.0666267\pi\)
−0.913494 + 0.406851i \(0.866627\pi\)
\(644\) −8.59771 26.4610i −0.338797 1.04271i
\(645\) 0 0
\(646\) 0.518387 + 0.713499i 0.0203957 + 0.0280722i
\(647\) −19.9531 6.48314i −0.784436 0.254879i −0.110703 0.993854i \(-0.535310\pi\)
−0.673733 + 0.738975i \(0.735310\pi\)
\(648\) −1.63789 + 4.12937i −0.0643423 + 0.162217i
\(649\) 28.9840 6.08715i 1.13772 0.238941i
\(650\) 0 0
\(651\) −9.23340 + 8.94502i −0.361886 + 0.350583i
\(652\) −4.02548 + 2.92468i −0.157650 + 0.114539i
\(653\) −13.2119 + 18.1846i −0.517022 + 0.711620i −0.985084 0.172076i \(-0.944953\pi\)
0.468061 + 0.883696i \(0.344953\pi\)
\(654\) −0.0860615 + 0.492660i −0.00336527 + 0.0192645i
\(655\) 0 0
\(656\) 10.4340 + 7.58077i 0.407380 + 0.295979i
\(657\) −6.65429 + 18.4651i −0.259609 + 0.720392i
\(658\) 0.652198 2.00726i 0.0254253 0.0782511i
\(659\) 9.16132 0.356874 0.178437 0.983951i \(-0.442896\pi\)
0.178437 + 0.983951i \(0.442896\pi\)
\(660\) 0 0
\(661\) 35.3540 1.37511 0.687555 0.726132i \(-0.258684\pi\)
0.687555 + 0.726132i \(0.258684\pi\)
\(662\) 0.164345 0.505803i 0.00638746 0.0196586i
\(663\) 10.8112 1.53696i 0.419873 0.0596906i
\(664\) 5.56471 + 4.04300i 0.215953 + 0.156899i
\(665\) 0 0
\(666\) −1.08772 + 1.40139i −0.0421483 + 0.0543026i
\(667\) 15.1263 20.8195i 0.585692 0.806135i
\(668\) −21.1487 + 15.3654i −0.818267 + 0.594506i
\(669\) −3.07423 3.17334i −0.118856 0.122688i
\(670\) 0 0
\(671\) −44.9580 20.1477i −1.73558 0.777793i
\(672\) 7.15973 + 3.79230i 0.276193 + 0.146291i
\(673\) 3.60658 + 1.17185i 0.139024 + 0.0451715i 0.377702 0.925927i \(-0.376714\pi\)
−0.238679 + 0.971099i \(0.576714\pi\)
\(674\) 1.06124 + 1.46066i 0.0408772 + 0.0562627i
\(675\) 0 0
\(676\) 4.24231 + 13.0565i 0.163166 + 0.502172i
\(677\) 3.41692 + 10.5162i 0.131323 + 0.404171i 0.995000 0.0998751i \(-0.0318443\pi\)
−0.863677 + 0.504046i \(0.831844\pi\)
\(678\) 1.53142 + 3.12725i 0.0588139 + 0.120101i
\(679\) −19.8186 27.2780i −0.760568 1.04683i
\(680\) 0 0
\(681\) 15.9131 30.0434i 0.609791 1.15126i
\(682\) 0.197133 + 0.938652i 0.00754862 + 0.0359429i
\(683\) 1.80834i 0.0691943i −0.999401 0.0345971i \(-0.988985\pi\)
0.999401 0.0345971i \(-0.0110148\pi\)
\(684\) 8.36272 + 28.8179i 0.319757 + 1.10188i
\(685\) 0 0
\(686\) −0.900955 + 1.24006i −0.0343986 + 0.0473456i
\(687\) −13.7456 2.40117i −0.524426 0.0916105i
\(688\) −11.0566 + 3.59252i −0.421531 + 0.136964i
\(689\) −0.947131 0.688131i −0.0360828 0.0262157i
\(690\) 0 0
\(691\) −4.32621 + 13.3147i −0.164577 + 0.506516i −0.999005 0.0446014i \(-0.985798\pi\)
0.834428 + 0.551117i \(0.185798\pi\)
\(692\) −44.9935 −1.71040
\(693\) −27.9197 + 14.8721i −1.06058 + 0.564944i
\(694\) 1.70321 0.0646530
\(695\) 0 0
\(696\) 0.702267 + 4.93986i 0.0266194 + 0.187245i
\(697\) 3.77158 + 2.74021i 0.142859 + 0.103793i
\(698\) −0.922043 + 0.299590i −0.0348998 + 0.0113396i
\(699\) 21.6973 + 3.79024i 0.820667 + 0.143360i
\(700\) 0 0
\(701\) 10.3467 7.51734i 0.390791 0.283926i −0.374989 0.927029i \(-0.622353\pi\)
0.765779 + 0.643103i \(0.222353\pi\)
\(702\) −2.81264 0.583831i −0.106156 0.0220353i
\(703\) 24.0582i 0.907374i
\(704\) −21.9579 + 12.6063i −0.827571 + 0.475120i
\(705\) 0 0
\(706\) 3.87348 + 1.25857i 0.145780 + 0.0473669i
\(707\) 2.21793 + 3.05271i 0.0834137 + 0.114809i
\(708\) −13.5001 27.5679i −0.507364 1.03606i
\(709\) −14.2539 43.8689i −0.535315 1.64753i −0.742967 0.669328i \(-0.766582\pi\)
0.207651 0.978203i \(-0.433418\pi\)
\(710\) 0 0
\(711\) −15.7170 0.498792i −0.589435 0.0187062i
\(712\) −3.98985 5.49156i −0.149526 0.205805i
\(713\) −9.79022 3.18103i −0.366647 0.119131i
\(714\) 0.851563 + 0.451048i 0.0318689 + 0.0168800i
\(715\) 0 0
\(716\) 4.14115i 0.154762i
\(717\) 17.2843 + 17.8416i 0.645496 + 0.666306i
\(718\) −1.73161 + 1.25809i −0.0646232 + 0.0469515i
\(719\) 13.3476 18.3713i 0.497780 0.685135i −0.484019 0.875057i \(-0.660824\pi\)
0.981799 + 0.189922i \(0.0608236\pi\)
\(720\) 0 0
\(721\) −14.1683 + 4.60356i −0.527655 + 0.171446i
\(722\) −0.641338 0.465959i −0.0238681 0.0173412i
\(723\) −9.55114 + 1.35782i −0.355211 + 0.0504980i
\(724\) −5.11836 + 15.7527i −0.190222 + 0.585444i
\(725\) 0 0
\(726\) −0.172333 + 2.35380i −0.00639587 + 0.0873579i
\(727\) −38.1765 −1.41589 −0.707944 0.706268i \(-0.750377\pi\)
−0.707944 + 0.706268i \(0.750377\pi\)
\(728\) −2.16421 + 6.66074i −0.0802108 + 0.246863i
\(729\) −17.8742 + 20.2364i −0.662007 + 0.749497i
\(730\) 0 0
\(731\) −3.99663 + 1.29858i −0.147821 + 0.0480299i
\(732\) −8.78682 + 50.3003i −0.324770 + 1.85915i
\(733\) −12.7538 + 17.5541i −0.471072 + 0.648375i −0.976759 0.214343i \(-0.931239\pi\)
0.505687 + 0.862717i \(0.331239\pi\)
\(734\) −2.34150 + 1.70120i −0.0864264 + 0.0627924i
\(735\) 0 0
\(736\) 6.48762i 0.239137i
\(737\) 3.28873 + 2.97570i 0.121142 + 0.109611i
\(738\) −0.689007 1.01452i −0.0253627 0.0373449i
\(739\) −27.4778 8.92807i −1.01079 0.328425i −0.243619 0.969871i \(-0.578335\pi\)
−0.767168 + 0.641447i \(0.778335\pi\)
\(740\) 0 0
\(741\) −34.9874 + 17.1334i −1.28529 + 0.629412i
\(742\) −0.0319250 0.0982550i −0.00117200 0.00360705i
\(743\) −5.10650 15.7162i −0.187339 0.576571i 0.812641 0.582764i \(-0.198029\pi\)
−0.999981 + 0.00619273i \(0.998029\pi\)
\(744\) 1.79248 0.877784i 0.0657156 0.0321811i
\(745\) 0 0
\(746\) 3.10125 + 1.00766i 0.113545 + 0.0368929i
\(747\) 23.4877 + 34.5841i 0.859371 + 1.26537i
\(748\) −8.06425 + 4.62980i −0.294858 + 0.169282i
\(749\) 40.2493i 1.47068i
\(750\) 0 0
\(751\) 18.6456 13.5468i 0.680386 0.494330i −0.193099 0.981179i \(-0.561854\pi\)
0.873486 + 0.486850i \(0.161854\pi\)
\(752\) 12.3106 16.9441i 0.448921 0.617887i
\(753\) 7.03202 40.2549i 0.256261 1.46697i
\(754\) −3.06852 + 0.997024i −0.111749 + 0.0363095i
\(755\) 0 0
\(756\) 22.0547 + 24.2604i 0.802122 + 0.882342i
\(757\) −0.547305 + 1.68443i −0.0198921 + 0.0612217i −0.960510 0.278246i \(-0.910247\pi\)
0.940618 + 0.339468i \(0.110247\pi\)
\(758\) −2.08645 −0.0757834
\(759\) −20.9878 14.1822i −0.761811 0.514780i
\(760\) 0 0
\(761\) −9.11640 + 28.0574i −0.330469 + 1.01708i 0.638441 + 0.769670i \(0.279579\pi\)
−0.968911 + 0.247410i \(0.920421\pi\)
\(762\) −3.75987 + 0.534516i −0.136206 + 0.0193635i
\(763\) 5.99551 + 4.35600i 0.217052 + 0.157698i
\(764\) 22.0229 7.15566i 0.796759 0.258883i
\(765\) 0 0
\(766\) 1.30118 1.79092i 0.0470134 0.0647085i
\(767\) 32.2409 23.4244i 1.16415 0.845807i
\(768\) 17.8202 + 18.3947i 0.643030 + 0.663761i
\(769\) 49.6159i 1.78919i 0.446873 + 0.894597i \(0.352538\pi\)
−0.446873 + 0.894597i \(0.647462\pi\)
\(770\) 0 0
\(771\) −6.79623 3.59976i −0.244760 0.129642i
\(772\) −50.7148 16.4782i −1.82526 0.593065i
\(773\) −2.78805 3.83742i −0.100279 0.138023i 0.755929 0.654654i \(-0.227186\pi\)
−0.856208 + 0.516632i \(0.827186\pi\)
\(774\) 1.10490 + 0.0350650i 0.0397150 + 0.00126038i
\(775\) 0 0
\(776\) 1.61761 + 4.97848i 0.0580687 + 0.178717i
\(777\) 11.5611 + 23.6084i 0.414752 + 0.846946i
\(778\) −0.142462 0.196083i −0.00510753 0.00702991i
\(779\) −15.8176 5.13945i −0.566725 0.184140i
\(780\) 0 0
\(781\) 17.1874 + 7.70246i 0.615015 + 0.275616i
\(782\) 0.771623i 0.0275932i
\(783\) −6.16345 + 29.6928i −0.220264 + 1.06114i
\(784\) 9.82676 7.13956i 0.350956 0.254984i
\(785\) 0 0
\(786\) −3.10844 0.543004i −0.110874 0.0193683i
\(787\) −15.8758 + 5.15836i −0.565911 + 0.183876i −0.577979 0.816051i \(-0.696159\pi\)
0.0120680 + 0.999927i \(0.496159\pi\)
\(788\) 4.62227 + 3.35827i 0.164661 + 0.119634i
\(789\) 3.97378 + 27.9522i 0.141470 + 0.995124i
\(790\) 0 0
\(791\) 51.5981 1.83462
\(792\) 4.83593 0.856449i 0.171837 0.0304326i
\(793\) −66.2929 −2.35413
\(794\) −0.203562 + 0.626500i −0.00722415 + 0.0222337i
\(795\) 0 0
\(796\) −7.95204 5.77750i −0.281853 0.204778i
\(797\) 23.7656 7.72191i 0.841821 0.273524i 0.143804 0.989606i \(-0.454066\pi\)
0.698016 + 0.716082i \(0.254066\pi\)
\(798\) −3.38655 0.591586i −0.119882 0.0209419i
\(799\) 4.44989 6.12475i 0.157426 0.216678i
\(800\) 0 0
\(801\) −11.4979 39.6217i −0.406258 1.39996i
\(802\) 3.10743i 0.109727i
\(803\) 21.2358 4.45988i 0.749394 0.157386i
\(804\) 2.15162 4.06218i 0.0758817 0.143262i
\(805\) 0 0
\(806\) 0.758603 + 1.04413i 0.0267206 + 0.0367778i
\(807\) 1.47895 + 3.02010i 0.0520617 + 0.106313i
\(808\) −0.181029 0.557149i −0.00636856 0.0196004i
\(809\) −3.70400 11.3997i −0.130226 0.400794i 0.864591 0.502476i \(-0.167577\pi\)
−0.994817 + 0.101682i \(0.967577\pi\)
\(810\) 0 0
\(811\) 17.3957 + 23.9431i 0.610845 + 0.840757i 0.996647 0.0818253i \(-0.0260750\pi\)
−0.385801 + 0.922582i \(0.626075\pi\)
\(812\) 35.0230 + 11.3797i 1.22907 + 0.399348i
\(813\) −18.8347 9.97619i −0.660562 0.349880i
\(814\) 1.94997 + 0.209743i 0.0683463 + 0.00735150i
\(815\) 0 0
\(816\) 6.65370 + 6.86821i 0.232926 + 0.240436i
\(817\) 12.1287 8.81203i 0.424330 0.308294i
\(818\) 1.87430 2.57976i 0.0655335 0.0901991i
\(819\) −26.0997 + 33.6261i −0.911999 + 1.17499i
\(820\) 0 0
\(821\) 30.9352 + 22.4757i 1.07964 + 0.784408i 0.977621 0.210374i \(-0.0674683\pi\)
0.102024 + 0.994782i \(0.467468\pi\)
\(822\) −1.67182 + 0.237671i −0.0583113 + 0.00828973i
\(823\) −13.6460 + 41.9982i −0.475671 + 1.46396i 0.369380 + 0.929278i \(0.379570\pi\)
−0.845051 + 0.534686i \(0.820430\pi\)
\(824\) 2.31285 0.0805720
\(825\) 0 0
\(826\) 3.51678 0.122365
\(827\) −7.12866 + 21.9398i −0.247888 + 0.762920i 0.747260 + 0.664532i \(0.231369\pi\)
−0.995148 + 0.0983889i \(0.968631\pi\)
\(828\) −8.90074 + 24.6988i −0.309322 + 0.858342i
\(829\) 10.7964 + 7.84404i 0.374974 + 0.272435i 0.759271 0.650775i \(-0.225556\pi\)
−0.384296 + 0.923210i \(0.625556\pi\)
\(830\) 0 0
\(831\) −1.09058 + 6.24306i −0.0378319 + 0.216569i
\(832\) −20.0258 + 27.5632i −0.694270 + 0.955581i
\(833\) 3.55207 2.58073i 0.123072 0.0894170i
\(834\) 0.214099 0.207412i 0.00741364 0.00718209i
\(835\) 0 0
\(836\) 22.2574 24.5989i 0.769790 0.850770i
\(837\) 12.0580 1.32556i 0.416786 0.0458180i
\(838\) 3.89210 + 1.26462i 0.134450 + 0.0436855i
\(839\) −9.03502 12.4356i −0.311923 0.429326i 0.624056 0.781379i \(-0.285484\pi\)
−0.935980 + 0.352053i \(0.885484\pi\)
\(840\) 0 0
\(841\) 1.56400 + 4.81351i 0.0539312 + 0.165983i
\(842\) 0.381999 + 1.17567i 0.0131646 + 0.0405164i
\(843\) −28.7724 + 14.0899i −0.990975 + 0.485284i
\(844\) −13.2377 18.2202i −0.455662 0.627164i
\(845\) 0 0
\(846\) −1.64750 + 1.11889i −0.0566422 + 0.0384684i
\(847\) 30.2016 + 17.6332i 1.03774 + 0.605885i
\(848\) 1.02521i 0.0352057i
\(849\) 31.4200 30.4386i 1.07833 1.04465i
\(850\) 0 0
\(851\) −12.3724 + 17.0291i −0.424119 + 0.583750i
\(852\) 3.35920 19.2298i 0.115084 0.658802i
\(853\) 22.2057 7.21506i 0.760307 0.247039i 0.0968968 0.995294i \(-0.469108\pi\)
0.663411 + 0.748256i \(0.269108\pi\)
\(854\) −4.73282 3.43860i −0.161954 0.117666i
\(855\) 0 0
\(856\) 1.93098 5.94294i 0.0659995 0.203126i
\(857\) 16.1869 0.552933 0.276467 0.961023i \(-0.410836\pi\)
0.276467 + 0.961023i \(0.410836\pi\)
\(858\) 1.08367 + 2.98516i 0.0369959 + 0.101912i
\(859\) 10.3515 0.353187 0.176594 0.984284i \(-0.443492\pi\)
0.176594 + 0.984284i \(0.443492\pi\)
\(860\) 0 0
\(861\) −17.9916 + 2.55774i −0.613151 + 0.0871677i
\(862\) 1.18020 + 0.857467i 0.0401979 + 0.0292055i
\(863\) −33.3949 + 10.8507i −1.13678 + 0.369361i −0.816147 0.577844i \(-0.803894\pi\)
−0.320628 + 0.947205i \(0.603894\pi\)
\(864\) −3.14284 6.96924i −0.106922 0.237098i
\(865\) 0 0
\(866\) 1.09312 0.794196i 0.0371456 0.0269879i
\(867\) −18.0827 18.6657i −0.614120 0.633919i
\(868\) 14.7306i 0.499989i
\(869\) 8.65567 + 15.0766i 0.293624 + 0.511438i
\(870\) 0 0
\(871\) 5.67588 + 1.84421i 0.192320 + 0.0624885i
\(872\) −0.676276 0.930814i −0.0229016 0.0315213i
\(873\) −1.00919 + 31.7998i −0.0341559 + 1.07626i
\(874\) −0.850661 2.61807i −0.0287741 0.0885574i
\(875\) 0 0
\(876\) −9.89112 20.1982i −0.334190 0.682434i
\(877\) −23.6165 32.5053i −0.797472 1.09763i −0.993137 0.116956i \(-0.962686\pi\)
0.195665 0.980671i \(-0.437314\pi\)
\(878\) 0.499622 + 0.162337i 0.0168614 + 0.00547861i
\(879\) −0.691156 + 1.30488i −0.0233121 + 0.0440125i
\(880\) 0 0
\(881\) 12.1990i 0.410996i −0.978658 0.205498i \(-0.934119\pi\)
0.978658 0.205498i \(-0.0658813\pi\)
\(882\) −1.10923 + 0.321889i −0.0373497 + 0.0108386i
\(883\) −38.3546 + 27.8662i −1.29073 + 0.937773i −0.999820 0.0189757i \(-0.993959\pi\)
−0.290914 + 0.956749i \(0.593959\pi\)
\(884\) −7.35466 + 10.1228i −0.247364 + 0.340468i
\(885\) 0 0
\(886\) −4.26167 + 1.38470i −0.143173 + 0.0465199i
\(887\) −22.7959 16.5622i −0.765410 0.556103i 0.135155 0.990824i \(-0.456847\pi\)
−0.900565 + 0.434721i \(0.856847\pi\)
\(888\) −0.574411 4.04050i −0.0192760 0.135590i
\(889\) −17.3898 + 53.5202i −0.583234 + 1.79501i
\(890\) 0 0
\(891\) 29.4163 + 5.06771i 0.985483 + 0.169775i
\(892\) 5.06261 0.169509
\(893\) −8.34608 + 25.6866i −0.279291 + 0.859569i
\(894\) 0.351467 + 2.47228i 0.0117548 + 0.0826854i
\(895\) 0 0
\(896\) −11.7570 + 3.82007i −0.392772 + 0.127619i
\(897\) −33.5762 5.86533i −1.12108 0.195838i
\(898\) 3.01169 4.14524i 0.100501 0.138328i
\(899\) 11.0228 8.00851i 0.367630 0.267099i
\(900\) 0 0
\(901\) 0.370580i 0.0123458i
\(902\) −0.554463 + 1.23724i −0.0184616 + 0.0411956i
\(903\) 7.66733 14.4757i 0.255153 0.481720i
\(904\) −7.61861 2.47544i −0.253391 0.0823318i
\(905\) 0 0
\(906\) 0.339610 + 0.693502i 0.0112828 + 0.0230400i
\(907\) 7.61902 + 23.4489i 0.252986 + 0.778610i 0.994220 + 0.107363i \(0.0342407\pi\)
−0.741234 + 0.671246i \(0.765759\pi\)
\(908\) 12.0380 + 37.0491i 0.399494 + 1.22952i
\(909\) 0.112940 3.55876i 0.00374598 0.118037i
\(910\) 0 0
\(911\) 10.6875 + 3.47258i 0.354092 + 0.115052i 0.480662 0.876906i \(-0.340397\pi\)
−0.126569 + 0.991958i \(0.540397\pi\)
\(912\) −30.1473 15.9681i −0.998277 0.528758i
\(913\) 18.9012 42.1766i 0.625539 1.39584i
\(914\) 1.01932i 0.0337160i
\(915\) 0 0
\(916\) 12.9352 9.39795i 0.427390 0.310517i
\(917\) −27.4841 + 37.8286i −0.907605 + 1.24921i
\(918\) −0.373803 0.828907i −0.0123373 0.0273580i
\(919\) 47.3177 15.3745i 1.56087 0.507157i 0.603828 0.797115i \(-0.293641\pi\)
0.957039 + 0.289958i \(0.0936413\pi\)
\(920\) 0 0
\(921\) 22.8681 3.25100i 0.753529 0.107124i
\(922\) −0.769275 + 2.36759i −0.0253347 + 0.0779723i
\(923\) 25.3438 0.834200
\(924\) 10.0204 34.8346i 0.329645 1.14598i
\(925\) 0 0
\(926\) −1.41477 + 4.35422i −0.0464923 + 0.143089i
\(927\) 13.2247 + 4.76581i 0.434357 + 0.156530i
\(928\) −6.94688 5.04721i −0.228043 0.165683i
\(929\) 7.97273 2.59050i 0.261577 0.0849915i −0.175293 0.984516i \(-0.556087\pi\)
0.436869 + 0.899525i \(0.356087\pi\)
\(930\) 0 0
\(931\) −9.20686 + 12.6722i −0.301743 + 0.415313i
\(932\) −20.4181 + 14.8346i −0.668816 + 0.485924i
\(933\) −0.951444 + 0.921729i −0.0311489 + 0.0301760i
\(934\) 1.74363i 0.0570534i
\(935\) 0 0
\(936\) 5.46694 3.71286i 0.178692 0.121358i
\(937\) 35.4510 + 11.5187i 1.15813 + 0.376300i 0.824201 0.566297i \(-0.191625\pi\)
0.333931 + 0.942597i \(0.391625\pi\)
\(938\) 0.309557 + 0.426069i 0.0101074 + 0.0139116i
\(939\) −6.54775 + 3.20646i −0.213678 + 0.104639i
\(940\) 0 0
\(941\) 9.62434 + 29.6207i 0.313744 + 0.965606i 0.976268 + 0.216565i \(0.0694854\pi\)
−0.662524 + 0.749041i \(0.730515\pi\)
\(942\) −1.30760 + 0.640338i −0.0426040 + 0.0208633i
\(943\) −8.55309 11.7723i −0.278527 0.383359i
\(944\) 33.1906 + 10.7843i 1.08026 + 0.350998i
\(945\) 0 0
\(946\) −0.608491 1.05988i −0.0197838 0.0344597i
\(947\) 4.34152i 0.141080i 0.997509 + 0.0705402i \(0.0224723\pi\)
−0.997509 + 0.0705402i \(0.977528\pi\)
\(948\) 12.9414 12.5372i 0.420316 0.407188i
\(949\) 23.6220 17.1624i 0.766803 0.557115i
\(950\) 0 0
\(951\) −6.73543 + 38.5571i −0.218411 + 1.25030i
\(952\) −2.10839 + 0.685059i −0.0683334 + 0.0222029i
\(953\) −12.6364 9.18085i −0.409332 0.297397i 0.363999 0.931399i \(-0.381411\pi\)
−0.773331 + 0.634002i \(0.781411\pi\)
\(954\) −0.0330502 + 0.0917114i −0.00107004 + 0.00296927i
\(955\) 0 0
\(956\) −28.4637 −0.920583
\(957\) 31.5141 11.4402i 1.01871 0.369810i
\(958\) −0.167416 −0.00540897
\(959\) −7.73231 + 23.7976i −0.249689 + 0.768465i
\(960\) 0 0
\(961\) 20.6703 + 15.0178i 0.666784 + 0.484447i
\(962\) 2.50986 0.815504i 0.0809212 0.0262929i
\(963\) 23.2871 30.0024i 0.750416 0.966813i
\(964\) 6.49746 8.94298i 0.209269 0.288034i
\(965\) 0 0
\(966\) −2.09286 2.16033i −0.0673366 0.0695075i
\(967\) 40.2132i 1.29317i −0.762843 0.646584i \(-0.776197\pi\)
0.762843 0.646584i \(-0.223803\pi\)
\(968\) −3.61340 4.05254i −0.116139 0.130253i
\(969\) −10.8973 5.77199i −0.350072 0.185423i
\(970\) 0 0
\(971\) −20.4169 28.1014i −0.655209 0.901818i 0.344102 0.938932i \(-0.388183\pi\)
−0.999311 + 0.0371145i \(0.988183\pi\)
\(972\) −2.40350 30.8442i −0.0770924 0.989329i
\(973\) −1.36497 4.20096i −0.0437591 0.134677i
\(974\) 0.860593 + 2.64863i 0.0275752 + 0.0848677i
\(975\) 0 0
\(976\) −34.1227 46.9659i −1.09224 1.50334i
\(977\) −8.56456 2.78279i −0.274004 0.0890294i 0.168792 0.985652i \(-0.446013\pi\)
−0.442796 + 0.896622i \(0.646013\pi\)
\(978\) −0.251780 + 0.475351i −0.00805103 + 0.0152001i
\(979\) −30.6017 + 33.8210i −0.978035 + 1.08092i
\(980\) 0 0
\(981\) −1.94888 6.71584i −0.0622230 0.214420i
\(982\) 1.14081 0.828849i 0.0364048 0.0264496i
\(983\) 22.2883 30.6772i 0.710885 0.978450i −0.288892 0.957362i \(-0.593287\pi\)
0.999778 0.0210882i \(-0.00671308\pi\)
\(984\) 2.77922 + 0.485495i 0.0885984 + 0.0154770i
\(985\) 0 0
\(986\) −0.826247 0.600304i −0.0263131 0.0191176i
\(987\) 4.15358 + 29.2170i 0.132210 + 0.929986i
\(988\) 13.7942 42.4541i 0.438851 1.35064i
\(989\) 13.1168 0.417089
\(990\) 0 0
\(991\) −34.7931 −1.10524 −0.552620 0.833433i \(-0.686372\pi\)
−0.552620 + 0.833433i \(0.686372\pi\)
\(992\) −1.06142 + 3.26672i −0.0337001 + 0.103718i
\(993\) 1.04665 + 7.36229i 0.0332144 + 0.233635i
\(994\) 1.80936 + 1.31457i 0.0573893 + 0.0416958i
\(995\) 0 0
\(996\) −47.1884 8.24321i −1.49522 0.261196i
\(997\) −26.1445 + 35.9848i −0.828004 + 1.13965i 0.160288 + 0.987070i \(0.448758\pi\)
−0.988291 + 0.152579i \(0.951242\pi\)
\(998\) 0.391585 0.284503i 0.0123954 0.00900579i
\(999\) 5.04133 24.2869i 0.159500 0.768404i
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 825.2.bi.h.101.10 80
3.2 odd 2 inner 825.2.bi.h.101.12 80
5.2 odd 4 165.2.r.a.134.9 80
5.3 odd 4 165.2.r.a.134.12 yes 80
5.4 even 2 inner 825.2.bi.h.101.11 80
11.6 odd 10 inner 825.2.bi.h.776.12 80
15.2 even 4 165.2.r.a.134.11 yes 80
15.8 even 4 165.2.r.a.134.10 yes 80
15.14 odd 2 inner 825.2.bi.h.101.9 80
33.17 even 10 inner 825.2.bi.h.776.10 80
55.17 even 20 165.2.r.a.149.10 yes 80
55.28 even 20 165.2.r.a.149.11 yes 80
55.39 odd 10 inner 825.2.bi.h.776.9 80
165.17 odd 20 165.2.r.a.149.12 yes 80
165.83 odd 20 165.2.r.a.149.9 yes 80
165.149 even 10 inner 825.2.bi.h.776.11 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.r.a.134.9 80 5.2 odd 4
165.2.r.a.134.10 yes 80 15.8 even 4
165.2.r.a.134.11 yes 80 15.2 even 4
165.2.r.a.134.12 yes 80 5.3 odd 4
165.2.r.a.149.9 yes 80 165.83 odd 20
165.2.r.a.149.10 yes 80 55.17 even 20
165.2.r.a.149.11 yes 80 55.28 even 20
165.2.r.a.149.12 yes 80 165.17 odd 20
825.2.bi.h.101.9 80 15.14 odd 2 inner
825.2.bi.h.101.10 80 1.1 even 1 trivial
825.2.bi.h.101.11 80 5.4 even 2 inner
825.2.bi.h.101.12 80 3.2 odd 2 inner
825.2.bi.h.776.9 80 55.39 odd 10 inner
825.2.bi.h.776.10 80 33.17 even 10 inner
825.2.bi.h.776.11 80 165.149 even 10 inner
825.2.bi.h.776.12 80 11.6 odd 10 inner