Properties

Label 756.2.be.c.107.7
Level $756$
Weight $2$
Character 756.107
Analytic conductor $6.037$
Analytic rank $0$
Dimension $28$
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] = [756,2,Mod(107,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.be (of order \(6\), degree \(2\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.7
Character \(\chi\) \(=\) 756.107
Dual form 756.2.be.c.431.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.109104 + 1.41000i) q^{2} +(-1.97619 - 0.307674i) q^{4} +(3.44992 + 1.99182i) q^{5} +(0.212727 - 2.63719i) q^{7} +(0.649430 - 2.75286i) q^{8} +O(q^{10})\) \(q+(-0.109104 + 1.41000i) q^{2} +(-1.97619 - 0.307674i) q^{4} +(3.44992 + 1.99182i) q^{5} +(0.212727 - 2.63719i) q^{7} +(0.649430 - 2.75286i) q^{8} +(-3.18486 + 4.64707i) q^{10} +(0.936467 + 1.62201i) q^{11} +1.05785 q^{13} +(3.69522 + 0.587673i) q^{14} +(3.81067 + 1.21604i) q^{16} +(2.30404 - 1.33024i) q^{17} +(0.628053 + 0.362606i) q^{19} +(-6.20489 - 4.99766i) q^{20} +(-2.38920 + 1.14345i) q^{22} +(3.00404 - 5.20316i) q^{23} +(5.43465 + 9.41310i) q^{25} +(-0.115415 + 1.49156i) q^{26} +(-1.23178 + 5.14614i) q^{28} +5.09494i q^{29} +(-3.48051 + 2.00948i) q^{31} +(-2.13038 + 5.24037i) q^{32} +(1.62425 + 3.39382i) q^{34} +(5.98668 - 8.67438i) q^{35} +(4.48131 - 7.76185i) q^{37} +(-0.579798 + 0.845992i) q^{38} +(7.72367 - 8.20362i) q^{40} -6.19225i q^{41} +12.3071i q^{43} +(-1.35159 - 3.49353i) q^{44} +(7.00869 + 4.80339i) q^{46} +(2.03670 - 3.52767i) q^{47} +(-6.90949 - 1.12200i) q^{49} +(-13.8654 + 6.63585i) q^{50} +(-2.09051 - 0.325471i) q^{52} +(-11.2365 + 6.48742i) q^{53} +7.46108i q^{55} +(-7.12165 - 2.29828i) q^{56} +(-7.18386 - 0.555879i) q^{58} +(4.56454 + 7.90602i) q^{59} +(-5.21274 + 9.02873i) q^{61} +(-2.45362 - 5.12676i) q^{62} +(-7.15648 - 3.57558i) q^{64} +(3.64949 + 2.10703i) q^{65} +(-5.00193 + 2.88786i) q^{67} +(-4.96250 + 1.91991i) q^{68} +(11.5777 + 9.38762i) q^{70} +6.24090 q^{71} +(-7.37051 - 12.7661i) q^{73} +(10.4553 + 7.16549i) q^{74} +(-1.12959 - 0.909815i) q^{76} +(4.47675 - 2.12459i) q^{77} +(-4.92434 - 2.84307i) q^{79} +(10.7244 + 11.7854i) q^{80} +(8.73107 + 0.675601i) q^{82} +3.27295 q^{83} +10.5983 q^{85} +(-17.3530 - 1.34275i) q^{86} +(5.07333 - 1.52458i) q^{88} +(8.80546 + 5.08384i) q^{89} +(0.225033 - 2.78973i) q^{91} +(-7.53745 + 9.35818i) q^{92} +(4.75180 + 3.25663i) q^{94} +(1.44449 + 2.50193i) q^{95} -2.03772 q^{97} +(2.33588 - 9.61996i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 4 q^{4} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58} + 6 q^{61} + 8 q^{64} - 24 q^{67} + 128 q^{70} - 22 q^{73} - 48 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} - 16 q^{91} - 12 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.109104 + 1.41000i −0.0771483 + 0.997020i
\(3\) 0 0
\(4\) −1.97619 0.307674i −0.988096 0.153837i
\(5\) 3.44992 + 1.99182i 1.54285 + 0.890767i 0.998657 + 0.0518089i \(0.0164987\pi\)
0.544196 + 0.838958i \(0.316835\pi\)
\(6\) 0 0
\(7\) 0.212727 2.63719i 0.0804033 0.996762i
\(8\) 0.649430 2.75286i 0.229608 0.973283i
\(9\) 0 0
\(10\) −3.18486 + 4.64707i −1.00714 + 1.46953i
\(11\) 0.936467 + 1.62201i 0.282356 + 0.489054i 0.971964 0.235128i \(-0.0755509\pi\)
−0.689609 + 0.724182i \(0.742218\pi\)
\(12\) 0 0
\(13\) 1.05785 0.293394 0.146697 0.989182i \(-0.453136\pi\)
0.146697 + 0.989182i \(0.453136\pi\)
\(14\) 3.69522 + 0.587673i 0.987589 + 0.157062i
\(15\) 0 0
\(16\) 3.81067 + 1.21604i 0.952668 + 0.304011i
\(17\) 2.30404 1.33024i 0.558811 0.322630i −0.193857 0.981030i \(-0.562100\pi\)
0.752668 + 0.658400i \(0.228766\pi\)
\(18\) 0 0
\(19\) 0.628053 + 0.362606i 0.144085 + 0.0831876i 0.570310 0.821430i \(-0.306823\pi\)
−0.426224 + 0.904617i \(0.640157\pi\)
\(20\) −6.20489 4.99766i −1.38745 1.11751i
\(21\) 0 0
\(22\) −2.38920 + 1.14345i −0.509380 + 0.243784i
\(23\) 3.00404 5.20316i 0.626387 1.08493i −0.361884 0.932223i \(-0.617866\pi\)
0.988271 0.152711i \(-0.0488002\pi\)
\(24\) 0 0
\(25\) 5.43465 + 9.41310i 1.08693 + 1.88262i
\(26\) −0.115415 + 1.49156i −0.0226348 + 0.292519i
\(27\) 0 0
\(28\) −1.23178 + 5.14614i −0.232785 + 0.972528i
\(29\) 5.09494i 0.946106i 0.881034 + 0.473053i \(0.156848\pi\)
−0.881034 + 0.473053i \(0.843152\pi\)
\(30\) 0 0
\(31\) −3.48051 + 2.00948i −0.625119 + 0.360912i −0.778859 0.627199i \(-0.784201\pi\)
0.153741 + 0.988111i \(0.450868\pi\)
\(32\) −2.13038 + 5.24037i −0.376602 + 0.926375i
\(33\) 0 0
\(34\) 1.62425 + 3.39382i 0.278557 + 0.582036i
\(35\) 5.98668 8.67438i 1.01193 1.46624i
\(36\) 0 0
\(37\) 4.48131 7.76185i 0.736722 1.27604i −0.217241 0.976118i \(-0.569706\pi\)
0.953963 0.299923i \(-0.0969609\pi\)
\(38\) −0.579798 + 0.845992i −0.0940556 + 0.137238i
\(39\) 0 0
\(40\) 7.72367 8.20362i 1.22122 1.29711i
\(41\) 6.19225i 0.967067i −0.875326 0.483534i \(-0.839353\pi\)
0.875326 0.483534i \(-0.160647\pi\)
\(42\) 0 0
\(43\) 12.3071i 1.87681i 0.345533 + 0.938407i \(0.387698\pi\)
−0.345533 + 0.938407i \(0.612302\pi\)
\(44\) −1.35159 3.49353i −0.203760 0.526669i
\(45\) 0 0
\(46\) 7.00869 + 4.80339i 1.03338 + 0.708221i
\(47\) 2.03670 3.52767i 0.297084 0.514564i −0.678384 0.734708i \(-0.737319\pi\)
0.975467 + 0.220144i \(0.0706526\pi\)
\(48\) 0 0
\(49\) −6.90949 1.12200i −0.987071 0.160286i
\(50\) −13.8654 + 6.63585i −1.96086 + 0.938451i
\(51\) 0 0
\(52\) −2.09051 0.325471i −0.289901 0.0451347i
\(53\) −11.2365 + 6.48742i −1.54346 + 0.891116i −0.544841 + 0.838539i \(0.683410\pi\)
−0.998617 + 0.0525765i \(0.983257\pi\)
\(54\) 0 0
\(55\) 7.46108i 1.00605i
\(56\) −7.12165 2.29828i −0.951671 0.307120i
\(57\) 0 0
\(58\) −7.18386 0.555879i −0.943287 0.0729905i
\(59\) 4.56454 + 7.90602i 0.594253 + 1.02928i 0.993652 + 0.112499i \(0.0358856\pi\)
−0.399399 + 0.916777i \(0.630781\pi\)
\(60\) 0 0
\(61\) −5.21274 + 9.02873i −0.667423 + 1.15601i 0.311199 + 0.950345i \(0.399269\pi\)
−0.978622 + 0.205666i \(0.934064\pi\)
\(62\) −2.45362 5.12676i −0.311610 0.651099i
\(63\) 0 0
\(64\) −7.15648 3.57558i −0.894560 0.446948i
\(65\) 3.64949 + 2.10703i 0.452663 + 0.261345i
\(66\) 0 0
\(67\) −5.00193 + 2.88786i −0.611083 + 0.352809i −0.773389 0.633932i \(-0.781440\pi\)
0.162306 + 0.986740i \(0.448107\pi\)
\(68\) −4.96250 + 1.91991i −0.601792 + 0.232824i
\(69\) 0 0
\(70\) 11.5777 + 9.38762i 1.38380 + 1.12204i
\(71\) 6.24090 0.740658 0.370329 0.928901i \(-0.379245\pi\)
0.370329 + 0.928901i \(0.379245\pi\)
\(72\) 0 0
\(73\) −7.37051 12.7661i −0.862653 1.49416i −0.869359 0.494181i \(-0.835468\pi\)
0.00670577 0.999978i \(-0.497865\pi\)
\(74\) 10.4553 + 7.16549i 1.21540 + 0.832971i
\(75\) 0 0
\(76\) −1.12959 0.909815i −0.129573 0.104363i
\(77\) 4.47675 2.12459i 0.510173 0.242120i
\(78\) 0 0
\(79\) −4.92434 2.84307i −0.554031 0.319870i 0.196715 0.980461i \(-0.436973\pi\)
−0.750746 + 0.660591i \(0.770306\pi\)
\(80\) 10.7244 + 11.7854i 1.19902 + 1.31765i
\(81\) 0 0
\(82\) 8.73107 + 0.675601i 0.964185 + 0.0746076i
\(83\) 3.27295 0.359253 0.179626 0.983735i \(-0.442511\pi\)
0.179626 + 0.983735i \(0.442511\pi\)
\(84\) 0 0
\(85\) 10.5983 1.14955
\(86\) −17.3530 1.34275i −1.87122 0.144793i
\(87\) 0 0
\(88\) 5.07333 1.52458i 0.540819 0.162521i
\(89\) 8.80546 + 5.08384i 0.933377 + 0.538886i 0.887878 0.460079i \(-0.152179\pi\)
0.0454992 + 0.998964i \(0.485512\pi\)
\(90\) 0 0
\(91\) 0.225033 2.78973i 0.0235898 0.292444i
\(92\) −7.53745 + 9.35818i −0.785833 + 0.975657i
\(93\) 0 0
\(94\) 4.75180 + 3.25663i 0.490111 + 0.335896i
\(95\) 1.44449 + 2.50193i 0.148202 + 0.256693i
\(96\) 0 0
\(97\) −2.03772 −0.206900 −0.103450 0.994635i \(-0.532988\pi\)
−0.103450 + 0.994635i \(0.532988\pi\)
\(98\) 2.33588 9.61996i 0.235959 0.971763i
\(99\) 0 0
\(100\) −7.84376 20.2742i −0.784376 2.02742i
\(101\) −8.70650 + 5.02670i −0.866330 + 0.500176i −0.866127 0.499824i \(-0.833398\pi\)
−0.000202762 1.00000i \(0.500065\pi\)
\(102\) 0 0
\(103\) −8.29973 4.79185i −0.817796 0.472155i 0.0318595 0.999492i \(-0.489857\pi\)
−0.849656 + 0.527337i \(0.823190\pi\)
\(104\) 0.686997 2.91210i 0.0673656 0.285555i
\(105\) 0 0
\(106\) −7.92130 16.5513i −0.769385 1.60761i
\(107\) 2.21486 3.83624i 0.214118 0.370863i −0.738881 0.673836i \(-0.764646\pi\)
0.952999 + 0.302972i \(0.0979789\pi\)
\(108\) 0 0
\(109\) 3.40807 + 5.90294i 0.326433 + 0.565399i 0.981801 0.189910i \(-0.0608198\pi\)
−0.655368 + 0.755310i \(0.727486\pi\)
\(110\) −10.5201 0.814035i −1.00305 0.0776152i
\(111\) 0 0
\(112\) 4.01757 9.79077i 0.379625 0.925141i
\(113\) 11.0586i 1.04030i −0.854074 0.520151i \(-0.825875\pi\)
0.854074 0.520151i \(-0.174125\pi\)
\(114\) 0 0
\(115\) 20.7275 11.9670i 1.93285 1.11593i
\(116\) 1.56758 10.0686i 0.145546 0.934844i
\(117\) 0 0
\(118\) −11.6455 + 5.57342i −1.07205 + 0.513075i
\(119\) −3.01795 6.35915i −0.276655 0.582943i
\(120\) 0 0
\(121\) 3.74606 6.48836i 0.340551 0.589851i
\(122\) −12.1618 8.33503i −1.10107 0.754618i
\(123\) 0 0
\(124\) 7.49643 2.90025i 0.673199 0.260450i
\(125\) 23.3812i 2.09127i
\(126\) 0 0
\(127\) 14.8137i 1.31450i −0.753670 0.657252i \(-0.771719\pi\)
0.753670 0.657252i \(-0.228281\pi\)
\(128\) 5.82237 9.70052i 0.514629 0.857413i
\(129\) 0 0
\(130\) −3.36909 + 4.91589i −0.295489 + 0.431152i
\(131\) 1.22561 2.12281i 0.107082 0.185471i −0.807505 0.589861i \(-0.799183\pi\)
0.914587 + 0.404390i \(0.132516\pi\)
\(132\) 0 0
\(133\) 1.08986 1.57916i 0.0945032 0.136930i
\(134\) −3.52615 7.36779i −0.304613 0.636480i
\(135\) 0 0
\(136\) −2.16564 7.20659i −0.185702 0.617960i
\(137\) 0.536858 0.309955i 0.0458669 0.0264812i −0.476891 0.878962i \(-0.658236\pi\)
0.522758 + 0.852481i \(0.324903\pi\)
\(138\) 0 0
\(139\) 2.00673i 0.170209i 0.996372 + 0.0851044i \(0.0271224\pi\)
−0.996372 + 0.0851044i \(0.972878\pi\)
\(140\) −14.4997 + 15.3003i −1.22545 + 1.29311i
\(141\) 0 0
\(142\) −0.680908 + 8.79966i −0.0571405 + 0.738451i
\(143\) 0.990638 + 1.71583i 0.0828413 + 0.143485i
\(144\) 0 0
\(145\) −10.1482 + 17.5772i −0.842760 + 1.45970i
\(146\) 18.8043 8.99958i 1.55626 0.744810i
\(147\) 0 0
\(148\) −11.2440 + 13.9601i −0.924255 + 1.14752i
\(149\) −6.01927 3.47523i −0.493118 0.284702i 0.232749 0.972537i \(-0.425228\pi\)
−0.725867 + 0.687835i \(0.758561\pi\)
\(150\) 0 0
\(151\) 12.9420 7.47207i 1.05320 0.608068i 0.129660 0.991559i \(-0.458611\pi\)
0.923545 + 0.383490i \(0.125278\pi\)
\(152\) 1.40608 1.49345i 0.114048 0.121135i
\(153\) 0 0
\(154\) 2.50724 + 6.54401i 0.202039 + 0.527332i
\(155\) −16.0100 −1.28596
\(156\) 0 0
\(157\) −7.82313 13.5501i −0.624354 1.08141i −0.988665 0.150135i \(-0.952029\pi\)
0.364312 0.931277i \(-0.381304\pi\)
\(158\) 4.54599 6.63312i 0.361659 0.527702i
\(159\) 0 0
\(160\) −17.7875 + 13.8356i −1.40623 + 1.09380i
\(161\) −13.0827 9.02908i −1.03106 0.711591i
\(162\) 0 0
\(163\) −6.27734 3.62422i −0.491679 0.283871i 0.233592 0.972335i \(-0.424952\pi\)
−0.725271 + 0.688464i \(0.758285\pi\)
\(164\) −1.90519 + 12.2371i −0.148770 + 0.955555i
\(165\) 0 0
\(166\) −0.357092 + 4.61485i −0.0277157 + 0.358182i
\(167\) 18.1132 1.40164 0.700822 0.713337i \(-0.252817\pi\)
0.700822 + 0.713337i \(0.252817\pi\)
\(168\) 0 0
\(169\) −11.8810 −0.913920
\(170\) −1.15632 + 14.9437i −0.0886860 + 1.14613i
\(171\) 0 0
\(172\) 3.78657 24.3212i 0.288723 1.85447i
\(173\) 9.26339 + 5.34822i 0.704283 + 0.406618i 0.808941 0.587890i \(-0.200041\pi\)
−0.104658 + 0.994508i \(0.533375\pi\)
\(174\) 0 0
\(175\) 25.9802 12.3298i 1.96392 0.932043i
\(176\) 1.59614 + 7.31973i 0.120313 + 0.551746i
\(177\) 0 0
\(178\) −8.12892 + 11.8610i −0.609288 + 0.889021i
\(179\) −11.6609 20.1973i −0.871578 1.50962i −0.860364 0.509681i \(-0.829764\pi\)
−0.0112146 0.999937i \(-0.503570\pi\)
\(180\) 0 0
\(181\) −2.90143 −0.215662 −0.107831 0.994169i \(-0.534391\pi\)
−0.107831 + 0.994169i \(0.534391\pi\)
\(182\) 3.90897 + 0.621667i 0.289752 + 0.0460811i
\(183\) 0 0
\(184\) −12.3727 11.6488i −0.912124 0.858761i
\(185\) 30.9204 17.8519i 2.27331 1.31250i
\(186\) 0 0
\(187\) 4.31531 + 2.49145i 0.315567 + 0.182193i
\(188\) −5.11029 + 6.34472i −0.372706 + 0.462736i
\(189\) 0 0
\(190\) −3.68532 + 1.76376i −0.267361 + 0.127956i
\(191\) 4.64881 8.05197i 0.336376 0.582620i −0.647372 0.762174i \(-0.724132\pi\)
0.983748 + 0.179554i \(0.0574654\pi\)
\(192\) 0 0
\(193\) 3.54336 + 6.13728i 0.255056 + 0.441771i 0.964911 0.262578i \(-0.0845726\pi\)
−0.709854 + 0.704348i \(0.751239\pi\)
\(194\) 0.222324 2.87319i 0.0159620 0.206283i
\(195\) 0 0
\(196\) 13.3093 + 4.34316i 0.950663 + 0.310226i
\(197\) 4.03120i 0.287211i −0.989635 0.143606i \(-0.954130\pi\)
0.989635 0.143606i \(-0.0458697\pi\)
\(198\) 0 0
\(199\) −19.5689 + 11.2981i −1.38720 + 0.800900i −0.992999 0.118124i \(-0.962312\pi\)
−0.394201 + 0.919024i \(0.628979\pi\)
\(200\) 29.4424 8.84770i 2.08189 0.625627i
\(201\) 0 0
\(202\) −6.13773 12.8246i −0.431849 0.902335i
\(203\) 13.4363 + 1.08383i 0.943043 + 0.0760701i
\(204\) 0 0
\(205\) 12.3338 21.3628i 0.861431 1.49204i
\(206\) 7.66204 11.1798i 0.533839 0.778933i
\(207\) 0 0
\(208\) 4.03110 + 1.28639i 0.279507 + 0.0891949i
\(209\) 1.35828i 0.0939539i
\(210\) 0 0
\(211\) 3.52953i 0.242983i −0.992592 0.121491i \(-0.961232\pi\)
0.992592 0.121491i \(-0.0387676\pi\)
\(212\) 24.2016 9.36321i 1.66217 0.643068i
\(213\) 0 0
\(214\) 5.16745 + 3.54149i 0.353239 + 0.242091i
\(215\) −24.5134 + 42.4585i −1.67180 + 2.89565i
\(216\) 0 0
\(217\) 4.55896 + 9.60623i 0.309482 + 0.652113i
\(218\) −8.69497 + 4.16133i −0.588898 + 0.281841i
\(219\) 0 0
\(220\) 2.29558 14.7445i 0.154768 0.994076i
\(221\) 2.43732 1.40719i 0.163952 0.0946575i
\(222\) 0 0
\(223\) 5.17037i 0.346234i 0.984901 + 0.173117i \(0.0553839\pi\)
−0.984901 + 0.173117i \(0.944616\pi\)
\(224\) 13.3666 + 6.73298i 0.893096 + 0.449866i
\(225\) 0 0
\(226\) 15.5926 + 1.20654i 1.03720 + 0.0802576i
\(227\) 10.2679 + 17.7846i 0.681507 + 1.18040i 0.974521 + 0.224296i \(0.0720084\pi\)
−0.293014 + 0.956108i \(0.594658\pi\)
\(228\) 0 0
\(229\) 5.10463 8.84148i 0.337323 0.584261i −0.646605 0.762825i \(-0.723812\pi\)
0.983928 + 0.178564i \(0.0571451\pi\)
\(230\) 14.6120 + 30.5313i 0.963487 + 2.01318i
\(231\) 0 0
\(232\) 14.0257 + 3.30881i 0.920829 + 0.217234i
\(233\) 5.42215 + 3.13048i 0.355217 + 0.205085i 0.666981 0.745075i \(-0.267586\pi\)
−0.311764 + 0.950160i \(0.600920\pi\)
\(234\) 0 0
\(235\) 14.0529 8.11347i 0.916713 0.529265i
\(236\) −6.58794 17.0282i −0.428839 1.10844i
\(237\) 0 0
\(238\) 9.29567 3.56149i 0.602549 0.230857i
\(239\) −4.99283 −0.322959 −0.161480 0.986876i \(-0.551627\pi\)
−0.161480 + 0.986876i \(0.551627\pi\)
\(240\) 0 0
\(241\) 3.48576 + 6.03752i 0.224538 + 0.388911i 0.956181 0.292777i \(-0.0945795\pi\)
−0.731643 + 0.681688i \(0.761246\pi\)
\(242\) 8.73987 + 5.98984i 0.561820 + 0.385042i
\(243\) 0 0
\(244\) 13.0793 16.2387i 0.837315 1.03958i
\(245\) −21.6024 17.6333i −1.38013 1.12655i
\(246\) 0 0
\(247\) 0.664383 + 0.383582i 0.0422737 + 0.0244067i
\(248\) 3.27145 + 10.8864i 0.207738 + 0.691286i
\(249\) 0 0
\(250\) −32.9674 2.55098i −2.08504 0.161338i
\(251\) −18.9350 −1.19516 −0.597582 0.801808i \(-0.703872\pi\)
−0.597582 + 0.801808i \(0.703872\pi\)
\(252\) 0 0
\(253\) 11.2528 0.707455
\(254\) 20.8873 + 1.61624i 1.31059 + 0.101412i
\(255\) 0 0
\(256\) 13.0425 + 9.26790i 0.815155 + 0.579244i
\(257\) −0.662857 0.382701i −0.0413479 0.0238722i 0.479184 0.877715i \(-0.340933\pi\)
−0.520531 + 0.853842i \(0.674266\pi\)
\(258\) 0 0
\(259\) −19.5161 13.4692i −1.21267 0.836935i
\(260\) −6.56381 5.28675i −0.407070 0.327871i
\(261\) 0 0
\(262\) 2.85944 + 1.95971i 0.176657 + 0.121071i
\(263\) −7.12695 12.3442i −0.439466 0.761178i 0.558182 0.829719i \(-0.311499\pi\)
−0.997648 + 0.0685403i \(0.978166\pi\)
\(264\) 0 0
\(265\) −51.6870 −3.17511
\(266\) 2.10770 + 1.70900i 0.129231 + 0.104785i
\(267\) 0 0
\(268\) 10.7733 4.16801i 0.658083 0.254602i
\(269\) 8.25667 4.76699i 0.503418 0.290649i −0.226706 0.973963i \(-0.572796\pi\)
0.730124 + 0.683315i \(0.239462\pi\)
\(270\) 0 0
\(271\) 2.98753 + 1.72485i 0.181479 + 0.104777i 0.587988 0.808870i \(-0.299920\pi\)
−0.406508 + 0.913647i \(0.633254\pi\)
\(272\) 10.3976 2.26729i 0.630445 0.137474i
\(273\) 0 0
\(274\) 0.378463 + 0.790786i 0.0228638 + 0.0477731i
\(275\) −10.1788 + 17.6301i −0.613802 + 1.06314i
\(276\) 0 0
\(277\) −7.78023 13.4757i −0.467469 0.809679i 0.531841 0.846844i \(-0.321501\pi\)
−0.999309 + 0.0371652i \(0.988167\pi\)
\(278\) −2.82949 0.218943i −0.169701 0.0131313i
\(279\) 0 0
\(280\) −19.9914 22.1139i −1.19472 1.32156i
\(281\) 7.65968i 0.456938i −0.973551 0.228469i \(-0.926628\pi\)
0.973551 0.228469i \(-0.0733720\pi\)
\(282\) 0 0
\(283\) −27.5108 + 15.8834i −1.63535 + 0.944167i −0.652940 + 0.757410i \(0.726465\pi\)
−0.982406 + 0.186758i \(0.940202\pi\)
\(284\) −12.3332 1.92016i −0.731842 0.113940i
\(285\) 0 0
\(286\) −2.52741 + 1.20959i −0.149449 + 0.0715247i
\(287\) −16.3301 1.31726i −0.963936 0.0777554i
\(288\) 0 0
\(289\) −4.96094 + 8.59260i −0.291820 + 0.505447i
\(290\) −23.6766 16.2267i −1.39034 0.952862i
\(291\) 0 0
\(292\) 10.6378 + 27.4960i 0.622528 + 1.60908i
\(293\) 8.77681i 0.512747i 0.966578 + 0.256373i \(0.0825277\pi\)
−0.966578 + 0.256373i \(0.917472\pi\)
\(294\) 0 0
\(295\) 36.3669i 2.11736i
\(296\) −18.4570 17.3772i −1.07279 1.01003i
\(297\) 0 0
\(298\) 5.55679 8.10800i 0.321896 0.469684i
\(299\) 3.17782 5.50414i 0.183778 0.318313i
\(300\) 0 0
\(301\) 32.4561 + 2.61805i 1.87074 + 0.150902i
\(302\) 9.12358 + 19.0634i 0.525003 + 1.09698i
\(303\) 0 0
\(304\) 1.95236 + 2.14551i 0.111975 + 0.123054i
\(305\) −35.9671 + 20.7656i −2.05947 + 1.18904i
\(306\) 0 0
\(307\) 15.7116i 0.896709i 0.893856 + 0.448355i \(0.147990\pi\)
−0.893856 + 0.448355i \(0.852010\pi\)
\(308\) −9.50060 + 2.82123i −0.541347 + 0.160754i
\(309\) 0 0
\(310\) 1.74676 22.5741i 0.0992093 1.28212i
\(311\) −6.73255 11.6611i −0.381768 0.661241i 0.609547 0.792750i \(-0.291351\pi\)
−0.991315 + 0.131508i \(0.958018\pi\)
\(312\) 0 0
\(313\) −6.18899 + 10.7196i −0.349822 + 0.605910i −0.986218 0.165453i \(-0.947091\pi\)
0.636395 + 0.771363i \(0.280425\pi\)
\(314\) 19.9591 9.55224i 1.12636 0.539064i
\(315\) 0 0
\(316\) 8.85670 + 7.13354i 0.498228 + 0.401293i
\(317\) 15.9748 + 9.22303i 0.897232 + 0.518017i 0.876301 0.481764i \(-0.160004\pi\)
0.0209310 + 0.999781i \(0.493337\pi\)
\(318\) 0 0
\(319\) −8.26404 + 4.77124i −0.462697 + 0.267138i
\(320\) −17.5674 26.5899i −0.982049 1.48642i
\(321\) 0 0
\(322\) 14.1584 17.4614i 0.789014 0.973086i
\(323\) 1.92941 0.107355
\(324\) 0 0
\(325\) 5.74903 + 9.95760i 0.318899 + 0.552348i
\(326\) 5.79503 8.45562i 0.320957 0.468314i
\(327\) 0 0
\(328\) −17.0464 4.02144i −0.941230 0.222047i
\(329\) −8.86987 6.12160i −0.489012 0.337495i
\(330\) 0 0
\(331\) −22.2310 12.8351i −1.22193 0.705480i −0.256599 0.966518i \(-0.582602\pi\)
−0.965329 + 0.261037i \(0.915935\pi\)
\(332\) −6.46798 1.00700i −0.354976 0.0552663i
\(333\) 0 0
\(334\) −1.97623 + 25.5396i −0.108134 + 1.39747i
\(335\) −23.0084 −1.25708
\(336\) 0 0
\(337\) 1.12521 0.0612942 0.0306471 0.999530i \(-0.490243\pi\)
0.0306471 + 0.999530i \(0.490243\pi\)
\(338\) 1.29626 16.7521i 0.0705074 0.911196i
\(339\) 0 0
\(340\) −20.9444 3.26083i −1.13587 0.176843i
\(341\) −6.51877 3.76362i −0.353011 0.203811i
\(342\) 0 0
\(343\) −4.42877 + 17.9829i −0.239131 + 0.970987i
\(344\) 33.8797 + 7.99259i 1.82667 + 0.430932i
\(345\) 0 0
\(346\) −8.55166 + 12.4779i −0.459740 + 0.670814i
\(347\) 1.10428 + 1.91268i 0.0592811 + 0.102678i 0.894143 0.447782i \(-0.147786\pi\)
−0.834862 + 0.550460i \(0.814453\pi\)
\(348\) 0 0
\(349\) 15.3373 0.820986 0.410493 0.911864i \(-0.365357\pi\)
0.410493 + 0.911864i \(0.365357\pi\)
\(350\) 14.5504 + 37.9773i 0.777752 + 2.02997i
\(351\) 0 0
\(352\) −10.4950 + 1.45194i −0.559383 + 0.0773885i
\(353\) −29.3810 + 16.9631i −1.56379 + 0.902855i −0.566922 + 0.823771i \(0.691866\pi\)
−0.996868 + 0.0790836i \(0.974801\pi\)
\(354\) 0 0
\(355\) 21.5306 + 12.4307i 1.14273 + 0.659754i
\(356\) −15.8371 12.7558i −0.839366 0.676059i
\(357\) 0 0
\(358\) 29.7504 14.2383i 1.57236 0.752516i
\(359\) −3.48440 + 6.03516i −0.183900 + 0.318523i −0.943205 0.332211i \(-0.892205\pi\)
0.759306 + 0.650734i \(0.225539\pi\)
\(360\) 0 0
\(361\) −9.23703 15.9990i −0.486160 0.842053i
\(362\) 0.316559 4.09102i 0.0166379 0.215019i
\(363\) 0 0
\(364\) −1.30304 + 5.44382i −0.0682976 + 0.285334i
\(365\) 58.7228i 3.07369i
\(366\) 0 0
\(367\) 1.65689 0.956605i 0.0864889 0.0499344i −0.456132 0.889912i \(-0.650765\pi\)
0.542621 + 0.839978i \(0.317432\pi\)
\(368\) 17.7747 16.1745i 0.926571 0.843153i
\(369\) 0 0
\(370\) 21.7976 + 45.5454i 1.13320 + 2.36779i
\(371\) 14.7182 + 31.0129i 0.764132 + 1.61011i
\(372\) 0 0
\(373\) −4.08938 + 7.08301i −0.211740 + 0.366745i −0.952259 0.305291i \(-0.901246\pi\)
0.740519 + 0.672035i \(0.234580\pi\)
\(374\) −3.98376 + 5.81276i −0.205995 + 0.300571i
\(375\) 0 0
\(376\) −8.38850 7.89774i −0.432604 0.407295i
\(377\) 5.38966i 0.277582i
\(378\) 0 0
\(379\) 17.1764i 0.882295i −0.897435 0.441147i \(-0.854572\pi\)
0.897435 0.441147i \(-0.145428\pi\)
\(380\) −2.08481 5.38873i −0.106949 0.276436i
\(381\) 0 0
\(382\) 10.8461 + 7.43332i 0.554933 + 0.380322i
\(383\) −11.5136 + 19.9422i −0.588320 + 1.01900i 0.406133 + 0.913814i \(0.366877\pi\)
−0.994453 + 0.105186i \(0.966456\pi\)
\(384\) 0 0
\(385\) 19.6762 + 1.58717i 1.00279 + 0.0808899i
\(386\) −9.04015 + 4.32653i −0.460131 + 0.220214i
\(387\) 0 0
\(388\) 4.02694 + 0.626954i 0.204437 + 0.0318288i
\(389\) −16.4368 + 9.48980i −0.833380 + 0.481152i −0.855009 0.518614i \(-0.826448\pi\)
0.0216286 + 0.999766i \(0.493115\pi\)
\(390\) 0 0
\(391\) 15.9844i 0.808364i
\(392\) −7.57595 + 18.2922i −0.382643 + 0.923896i
\(393\) 0 0
\(394\) 5.68399 + 0.439821i 0.286355 + 0.0221579i
\(395\) −11.3257 19.6167i −0.569859 0.987025i
\(396\) 0 0
\(397\) 17.0876 29.5966i 0.857603 1.48541i −0.0166054 0.999862i \(-0.505286\pi\)
0.874209 0.485550i \(-0.161381\pi\)
\(398\) −13.7952 28.8247i −0.691493 1.44485i
\(399\) 0 0
\(400\) 9.26295 + 42.4790i 0.463148 + 2.12395i
\(401\) −11.4019 6.58287i −0.569382 0.328733i 0.187521 0.982261i \(-0.439955\pi\)
−0.756902 + 0.653528i \(0.773288\pi\)
\(402\) 0 0
\(403\) −3.68184 + 2.12571i −0.183406 + 0.105889i
\(404\) 18.7523 7.25497i 0.932962 0.360948i
\(405\) 0 0
\(406\) −2.99416 + 18.8269i −0.148598 + 0.934364i
\(407\) 16.7864 0.832071
\(408\) 0 0
\(409\) 13.9583 + 24.1765i 0.690193 + 1.19545i 0.971774 + 0.235912i \(0.0758076\pi\)
−0.281582 + 0.959537i \(0.590859\pi\)
\(410\) 28.7759 + 19.7214i 1.42114 + 0.973973i
\(411\) 0 0
\(412\) 14.9275 + 12.0232i 0.735427 + 0.592342i
\(413\) 21.8206 10.3557i 1.07372 0.509572i
\(414\) 0 0
\(415\) 11.2914 + 6.51911i 0.554274 + 0.320010i
\(416\) −2.25361 + 5.54350i −0.110493 + 0.271793i
\(417\) 0 0
\(418\) −1.91517 0.148194i −0.0936739 0.00724839i
\(419\) −32.2539 −1.57571 −0.787854 0.615863i \(-0.788808\pi\)
−0.787854 + 0.615863i \(0.788808\pi\)
\(420\) 0 0
\(421\) −20.3473 −0.991667 −0.495833 0.868418i \(-0.665137\pi\)
−0.495833 + 0.868418i \(0.665137\pi\)
\(422\) 4.97663 + 0.385086i 0.242258 + 0.0187457i
\(423\) 0 0
\(424\) 10.5616 + 35.1458i 0.512917 + 1.70683i
\(425\) 25.0433 + 14.4588i 1.21478 + 0.701353i
\(426\) 0 0
\(427\) 22.7015 + 15.6676i 1.09860 + 0.758209i
\(428\) −5.55729 + 6.89970i −0.268622 + 0.333510i
\(429\) 0 0
\(430\) −57.1920 39.1963i −2.75804 1.89021i
\(431\) 11.8556 + 20.5344i 0.571062 + 0.989108i 0.996457 + 0.0841006i \(0.0268017\pi\)
−0.425395 + 0.905008i \(0.639865\pi\)
\(432\) 0 0
\(433\) 12.4523 0.598417 0.299209 0.954188i \(-0.403277\pi\)
0.299209 + 0.954188i \(0.403277\pi\)
\(434\) −14.0422 + 5.38005i −0.674046 + 0.258250i
\(435\) 0 0
\(436\) −4.91881 12.7139i −0.235568 0.608886i
\(437\) 3.77340 2.17857i 0.180506 0.104215i
\(438\) 0 0
\(439\) 1.32885 + 0.767212i 0.0634225 + 0.0366170i 0.531376 0.847136i \(-0.321675\pi\)
−0.467953 + 0.883753i \(0.655008\pi\)
\(440\) 20.5393 + 4.84545i 0.979173 + 0.230998i
\(441\) 0 0
\(442\) 1.71821 + 3.59014i 0.0817268 + 0.170766i
\(443\) −14.6601 + 25.3921i −0.696523 + 1.20641i 0.273141 + 0.961974i \(0.411937\pi\)
−0.969664 + 0.244440i \(0.921396\pi\)
\(444\) 0 0
\(445\) 20.2521 + 35.0777i 0.960043 + 1.66284i
\(446\) −7.29022 0.564110i −0.345202 0.0267114i
\(447\) 0 0
\(448\) −10.9518 + 18.1123i −0.517426 + 0.855728i
\(449\) 4.29939i 0.202901i 0.994841 + 0.101450i \(0.0323483\pi\)
−0.994841 + 0.101450i \(0.967652\pi\)
\(450\) 0 0
\(451\) 10.0439 5.79884i 0.472948 0.273057i
\(452\) −3.40243 + 21.8539i −0.160037 + 1.02792i
\(453\) 0 0
\(454\) −26.1965 + 12.5374i −1.22946 + 0.588409i
\(455\) 6.33298 9.17615i 0.296895 0.430185i
\(456\) 0 0
\(457\) −2.32454 + 4.02622i −0.108737 + 0.188339i −0.915259 0.402866i \(-0.868014\pi\)
0.806522 + 0.591205i \(0.201347\pi\)
\(458\) 11.9095 + 8.16216i 0.556496 + 0.381393i
\(459\) 0 0
\(460\) −44.6434 + 17.2718i −2.08151 + 0.805302i
\(461\) 24.2351i 1.12874i −0.825521 0.564371i \(-0.809119\pi\)
0.825521 0.564371i \(-0.190881\pi\)
\(462\) 0 0
\(463\) 18.7274i 0.870335i −0.900349 0.435168i \(-0.856689\pi\)
0.900349 0.435168i \(-0.143311\pi\)
\(464\) −6.19567 + 19.4152i −0.287627 + 0.901326i
\(465\) 0 0
\(466\) −5.00555 + 7.30368i −0.231878 + 0.338336i
\(467\) 9.28665 16.0849i 0.429735 0.744323i −0.567115 0.823639i \(-0.691940\pi\)
0.996850 + 0.0793162i \(0.0252737\pi\)
\(468\) 0 0
\(469\) 6.55179 + 13.8053i 0.302533 + 0.637471i
\(470\) 9.90675 + 20.6999i 0.456964 + 0.954813i
\(471\) 0 0
\(472\) 24.7285 7.43114i 1.13822 0.342046i
\(473\) −19.9622 + 11.5252i −0.917863 + 0.529929i
\(474\) 0 0
\(475\) 7.88256i 0.361677i
\(476\) 4.00751 + 13.4955i 0.183684 + 0.618563i
\(477\) 0 0
\(478\) 0.544739 7.03989i 0.0249158 0.321997i
\(479\) −5.24836 9.09043i −0.239804 0.415352i 0.720854 0.693087i \(-0.243750\pi\)
−0.960658 + 0.277734i \(0.910416\pi\)
\(480\) 0 0
\(481\) 4.74053 8.21084i 0.216150 0.374382i
\(482\) −8.89321 + 4.25620i −0.405074 + 0.193865i
\(483\) 0 0
\(484\) −9.39923 + 11.6697i −0.427238 + 0.530441i
\(485\) −7.03000 4.05877i −0.319216 0.184299i
\(486\) 0 0
\(487\) 23.4523 13.5402i 1.06273 0.613565i 0.136540 0.990635i \(-0.456402\pi\)
0.926185 + 0.377070i \(0.123068\pi\)
\(488\) 21.4695 + 20.2135i 0.971880 + 0.915021i
\(489\) 0 0
\(490\) 27.2198 28.5355i 1.22966 1.28910i
\(491\) 8.39226 0.378737 0.189369 0.981906i \(-0.439356\pi\)
0.189369 + 0.981906i \(0.439356\pi\)
\(492\) 0 0
\(493\) 6.77748 + 11.7389i 0.305242 + 0.528695i
\(494\) −0.613336 + 0.894928i −0.0275953 + 0.0402647i
\(495\) 0 0
\(496\) −15.7067 + 3.42500i −0.705252 + 0.153787i
\(497\) 1.32761 16.4584i 0.0595514 0.738260i
\(498\) 0 0
\(499\) −15.4658 8.92917i −0.692343 0.399724i 0.112146 0.993692i \(-0.464228\pi\)
−0.804489 + 0.593967i \(0.797561\pi\)
\(500\) 7.19376 46.2057i 0.321715 2.06638i
\(501\) 0 0
\(502\) 2.06588 26.6983i 0.0922049 1.19160i
\(503\) 15.3493 0.684392 0.342196 0.939629i \(-0.388829\pi\)
0.342196 + 0.939629i \(0.388829\pi\)
\(504\) 0 0
\(505\) −40.0490 −1.78216
\(506\) −1.22772 + 15.8664i −0.0545790 + 0.705346i
\(507\) 0 0
\(508\) −4.55779 + 29.2748i −0.202219 + 1.29886i
\(509\) 25.2937 + 14.6033i 1.12112 + 0.647281i 0.941687 0.336489i \(-0.109240\pi\)
0.179436 + 0.983770i \(0.442573\pi\)
\(510\) 0 0
\(511\) −35.2345 + 16.7217i −1.55868 + 0.739725i
\(512\) −14.4907 + 17.3787i −0.640405 + 0.768037i
\(513\) 0 0
\(514\) 0.611928 0.892873i 0.0269910 0.0393829i
\(515\) −19.0890 33.0630i −0.841160 1.45693i
\(516\) 0 0
\(517\) 7.62922 0.335533
\(518\) 21.1208 26.0482i 0.927997 1.14449i
\(519\) 0 0
\(520\) 8.17045 8.67816i 0.358298 0.380562i
\(521\) 12.9936 7.50183i 0.569258 0.328661i −0.187595 0.982246i \(-0.560069\pi\)
0.756853 + 0.653585i \(0.226736\pi\)
\(522\) 0 0
\(523\) −10.6638 6.15676i −0.466296 0.269216i 0.248392 0.968660i \(-0.420098\pi\)
−0.714688 + 0.699443i \(0.753431\pi\)
\(524\) −3.07517 + 3.81800i −0.134339 + 0.166790i
\(525\) 0 0
\(526\) 18.1829 8.70218i 0.792814 0.379433i
\(527\) −5.34616 + 9.25981i −0.232882 + 0.403364i
\(528\) 0 0
\(529\) −6.54857 11.3425i −0.284720 0.493150i
\(530\) 5.63927 72.8786i 0.244954 3.16564i
\(531\) 0 0
\(532\) −2.63965 + 2.78539i −0.114443 + 0.120762i
\(533\) 6.55045i 0.283731i
\(534\) 0 0
\(535\) 15.2822 8.82316i 0.660706 0.381459i
\(536\) 4.70148 + 15.6451i 0.203073 + 0.675764i
\(537\) 0 0
\(538\) 5.82061 + 12.1620i 0.250944 + 0.524341i
\(539\) −4.65062 12.2580i −0.200316 0.527989i
\(540\) 0 0
\(541\) 12.1895 21.1128i 0.524066 0.907708i −0.475542 0.879693i \(-0.657748\pi\)
0.999608 0.0280151i \(-0.00891864\pi\)
\(542\) −2.75799 + 4.02422i −0.118466 + 0.172855i
\(543\) 0 0
\(544\) 2.06245 + 14.9079i 0.0884270 + 0.639172i
\(545\) 27.1529i 1.16310i
\(546\) 0 0
\(547\) 26.9284i 1.15138i −0.817669 0.575688i \(-0.804734\pi\)
0.817669 0.575688i \(-0.195266\pi\)
\(548\) −1.15630 + 0.447354i −0.0493947 + 0.0191100i
\(549\) 0 0
\(550\) −23.7479 16.2755i −1.01261 0.693992i
\(551\) −1.84746 + 3.19989i −0.0787043 + 0.136320i
\(552\) 0 0
\(553\) −8.54523 + 12.3816i −0.363380 + 0.526519i
\(554\) 19.8496 9.49985i 0.843331 0.403610i
\(555\) 0 0
\(556\) 0.617418 3.96569i 0.0261844 0.168183i
\(557\) −3.35873 + 1.93917i −0.142314 + 0.0821651i −0.569466 0.822015i \(-0.692850\pi\)
0.427152 + 0.904180i \(0.359517\pi\)
\(558\) 0 0
\(559\) 13.0190i 0.550645i
\(560\) 33.3617 25.7752i 1.40979 1.08920i
\(561\) 0 0
\(562\) 10.8001 + 0.835704i 0.455577 + 0.0352520i
\(563\) 20.6486 + 35.7644i 0.870234 + 1.50729i 0.861755 + 0.507325i \(0.169366\pi\)
0.00847940 + 0.999964i \(0.497301\pi\)
\(564\) 0 0
\(565\) 22.0266 38.1512i 0.926667 1.60503i
\(566\) −19.3940 40.5231i −0.815189 1.70331i
\(567\) 0 0
\(568\) 4.05303 17.1803i 0.170061 0.720870i
\(569\) 8.24961 + 4.76292i 0.345842 + 0.199672i 0.662852 0.748750i \(-0.269346\pi\)
−0.317011 + 0.948422i \(0.602679\pi\)
\(570\) 0 0
\(571\) −22.0822 + 12.7492i −0.924111 + 0.533536i −0.884944 0.465697i \(-0.845804\pi\)
−0.0391670 + 0.999233i \(0.512470\pi\)
\(572\) −1.42977 3.69561i −0.0597819 0.154521i
\(573\) 0 0
\(574\) 3.63902 22.8817i 0.151890 0.955065i
\(575\) 65.3038 2.72336
\(576\) 0 0
\(577\) −2.94249 5.09654i −0.122498 0.212172i 0.798254 0.602320i \(-0.205757\pi\)
−0.920752 + 0.390148i \(0.872424\pi\)
\(578\) −11.5743 7.93241i −0.481427 0.329945i
\(579\) 0 0
\(580\) 25.4628 31.6135i 1.05728 1.31268i
\(581\) 0.696245 8.63137i 0.0288851 0.358090i
\(582\) 0 0
\(583\) −21.0453 12.1505i −0.871608 0.503223i
\(584\) −39.9299 + 11.9993i −1.65231 + 0.496534i
\(585\) 0 0
\(586\) −12.3753 0.957587i −0.511219 0.0395576i
\(587\) −16.1329 −0.665878 −0.332939 0.942948i \(-0.608040\pi\)
−0.332939 + 0.942948i \(0.608040\pi\)
\(588\) 0 0
\(589\) −2.91459 −0.120094
\(590\) −51.2773 3.96778i −2.11105 0.163351i
\(591\) 0 0
\(592\) 26.5156 24.1284i 1.08978 0.991672i
\(593\) 7.56550 + 4.36794i 0.310678 + 0.179370i 0.647230 0.762295i \(-0.275927\pi\)
−0.336552 + 0.941665i \(0.609261\pi\)
\(594\) 0 0
\(595\) 2.25456 27.9498i 0.0924278 1.14583i
\(596\) 10.8260 + 8.71968i 0.443450 + 0.357172i
\(597\) 0 0
\(598\) 7.41411 + 5.08124i 0.303186 + 0.207787i
\(599\) −17.0745 29.5738i −0.697644 1.20835i −0.969281 0.245955i \(-0.920899\pi\)
0.271638 0.962400i \(-0.412435\pi\)
\(600\) 0 0
\(601\) −13.8371 −0.564426 −0.282213 0.959352i \(-0.591068\pi\)
−0.282213 + 0.959352i \(0.591068\pi\)
\(602\) −7.23254 + 45.4774i −0.294777 + 1.85352i
\(603\) 0 0
\(604\) −27.8748 + 10.7843i −1.13421 + 0.438808i
\(605\) 25.8472 14.9229i 1.05084 0.606703i
\(606\) 0 0
\(607\) 24.7444 + 14.2862i 1.00434 + 0.579858i 0.909530 0.415638i \(-0.136442\pi\)
0.0948125 + 0.995495i \(0.469775\pi\)
\(608\) −3.23818 + 2.51874i −0.131326 + 0.102148i
\(609\) 0 0
\(610\) −25.3553 52.9792i −1.02661 2.14507i
\(611\) 2.15452 3.73173i 0.0871624 0.150970i
\(612\) 0 0
\(613\) −10.5641 18.2976i −0.426680 0.739032i 0.569895 0.821717i \(-0.306984\pi\)
−0.996576 + 0.0826853i \(0.973650\pi\)
\(614\) −22.1534 1.71420i −0.894037 0.0691796i
\(615\) 0 0
\(616\) −2.94137 13.7036i −0.118511 0.552136i
\(617\) 43.3809i 1.74645i 0.487319 + 0.873224i \(0.337975\pi\)
−0.487319 + 0.873224i \(0.662025\pi\)
\(618\) 0 0
\(619\) −11.8607 + 6.84777i −0.476721 + 0.275235i −0.719049 0.694959i \(-0.755422\pi\)
0.242328 + 0.970194i \(0.422089\pi\)
\(620\) 31.6389 + 4.92586i 1.27065 + 0.197827i
\(621\) 0 0
\(622\) 17.1767 8.22061i 0.688723 0.329616i
\(623\) 15.2802 22.1402i 0.612188 0.887027i
\(624\) 0 0
\(625\) −19.3977 + 33.5978i −0.775907 + 1.34391i
\(626\) −14.4394 9.89602i −0.577116 0.395524i
\(627\) 0 0
\(628\) 11.2910 + 29.1845i 0.450561 + 1.16459i
\(629\) 23.8448i 0.950755i
\(630\) 0 0
\(631\) 28.5175i 1.13526i 0.823283 + 0.567631i \(0.192140\pi\)
−0.823283 + 0.567631i \(0.807860\pi\)
\(632\) −11.0246 + 11.7096i −0.438534 + 0.465784i
\(633\) 0 0
\(634\) −14.7474 + 21.5181i −0.585693 + 0.854594i
\(635\) 29.5062 51.1062i 1.17092 2.02809i
\(636\) 0 0
\(637\) −7.30918 1.18691i −0.289600 0.0470269i
\(638\) −5.82581 12.1728i −0.230646 0.481928i
\(639\) 0 0
\(640\) 39.4084 21.8690i 1.55775 0.864447i
\(641\) −19.9029 + 11.4909i −0.786116 + 0.453864i −0.838593 0.544758i \(-0.816622\pi\)
0.0524773 + 0.998622i \(0.483288\pi\)
\(642\) 0 0
\(643\) 2.79085i 0.110060i −0.998485 0.0550302i \(-0.982474\pi\)
0.998485 0.0550302i \(-0.0175255\pi\)
\(644\) 23.0758 + 21.8684i 0.909315 + 0.861735i
\(645\) 0 0
\(646\) −0.210507 + 2.72046i −0.00828227 + 0.107035i
\(647\) −20.5616 35.6137i −0.808359 1.40012i −0.914000 0.405715i \(-0.867023\pi\)
0.105640 0.994404i \(-0.466311\pi\)
\(648\) 0 0
\(649\) −8.54909 + 14.8075i −0.335581 + 0.581244i
\(650\) −14.6675 + 7.01970i −0.575305 + 0.275335i
\(651\) 0 0
\(652\) 11.2902 + 9.09353i 0.442156 + 0.356130i
\(653\) 20.8186 + 12.0196i 0.814694 + 0.470364i 0.848583 0.529062i \(-0.177456\pi\)
−0.0338892 + 0.999426i \(0.510789\pi\)
\(654\) 0 0
\(655\) 8.45650 4.88236i 0.330423 0.190770i
\(656\) 7.53005 23.5967i 0.293999 0.921294i
\(657\) 0 0
\(658\) 9.59918 11.8386i 0.374215 0.461517i
\(659\) −15.0431 −0.585995 −0.292997 0.956113i \(-0.594653\pi\)
−0.292997 + 0.956113i \(0.594653\pi\)
\(660\) 0 0
\(661\) −10.7083 18.5474i −0.416506 0.721409i 0.579079 0.815271i \(-0.303412\pi\)
−0.995585 + 0.0938618i \(0.970079\pi\)
\(662\) 20.5230 29.9454i 0.797648 1.16386i
\(663\) 0 0
\(664\) 2.12555 9.00997i 0.0824874 0.349655i
\(665\) 6.90533 3.27716i 0.267777 0.127083i
\(666\) 0 0
\(667\) 26.5098 + 15.3054i 1.02646 + 0.592628i
\(668\) −35.7952 5.57296i −1.38496 0.215624i
\(669\) 0 0
\(670\) 2.51031 32.4418i 0.0969817 1.25333i
\(671\) −19.5262 −0.753802
\(672\) 0 0
\(673\) −27.0940 −1.04440 −0.522198 0.852824i \(-0.674888\pi\)
−0.522198 + 0.852824i \(0.674888\pi\)
\(674\) −0.122765 + 1.58655i −0.00472874 + 0.0611115i
\(675\) 0 0
\(676\) 23.4791 + 3.65546i 0.903041 + 0.140595i
\(677\) 40.0846 + 23.1429i 1.54058 + 0.889453i 0.998802 + 0.0489293i \(0.0155809\pi\)
0.541775 + 0.840523i \(0.317752\pi\)
\(678\) 0 0
\(679\) −0.433479 + 5.37386i −0.0166354 + 0.206230i
\(680\) 6.88288 29.1758i 0.263947 1.11884i
\(681\) 0 0
\(682\) 6.01792 8.78084i 0.230438 0.336236i
\(683\) 17.3257 + 30.0090i 0.662949 + 1.14826i 0.979837 + 0.199799i \(0.0640288\pi\)
−0.316888 + 0.948463i \(0.602638\pi\)
\(684\) 0 0
\(685\) 2.46949 0.0943544
\(686\) −24.8727 8.20657i −0.949645 0.313328i
\(687\) 0 0
\(688\) −14.9660 + 46.8983i −0.570572 + 1.78798i
\(689\) −11.8865 + 6.86269i −0.452841 + 0.261448i
\(690\) 0 0
\(691\) 15.5595 + 8.98330i 0.591913 + 0.341741i 0.765853 0.643015i \(-0.222317\pi\)
−0.173941 + 0.984756i \(0.555650\pi\)
\(692\) −16.6607 13.4192i −0.633346 0.510122i
\(693\) 0 0
\(694\) −2.81735 + 1.34836i −0.106945 + 0.0511830i
\(695\) −3.99704 + 6.92307i −0.151616 + 0.262607i
\(696\) 0 0
\(697\) −8.23716 14.2672i −0.312005 0.540408i
\(698\) −1.67336 + 21.6255i −0.0633377 + 0.818539i
\(699\) 0 0
\(700\) −55.1354 + 16.3726i −2.08392 + 0.618826i
\(701\) 2.58336i 0.0975721i −0.998809 0.0487861i \(-0.984465\pi\)
0.998809 0.0487861i \(-0.0155353\pi\)
\(702\) 0 0
\(703\) 5.62899 3.24990i 0.212302 0.122572i
\(704\) −0.902185 14.9563i −0.0340024 0.563686i
\(705\) 0 0
\(706\) −20.7124 43.2779i −0.779520 1.62878i
\(707\) 11.4042 + 24.0300i 0.428900 + 0.903740i
\(708\) 0 0
\(709\) 8.03512 13.9172i 0.301765 0.522673i −0.674771 0.738027i \(-0.735757\pi\)
0.976536 + 0.215355i \(0.0690908\pi\)
\(710\) −19.8764 + 29.0019i −0.745947 + 1.08842i
\(711\) 0 0
\(712\) 19.7136 20.9386i 0.738799 0.784708i
\(713\) 24.1462i 0.904283i
\(714\) 0 0
\(715\) 7.89267i 0.295169i
\(716\) 16.8300 + 43.5015i 0.628968 + 1.62573i
\(717\) 0 0
\(718\) −8.12940 5.57146i −0.303386 0.207925i
\(719\) −12.9613 + 22.4496i −0.483374 + 0.837229i −0.999818 0.0190926i \(-0.993922\pi\)
0.516444 + 0.856321i \(0.327256\pi\)
\(720\) 0 0
\(721\) −14.4026 + 20.8686i −0.536380 + 0.777186i
\(722\) 23.5664 11.2786i 0.877050 0.419748i
\(723\) 0 0
\(724\) 5.73379 + 0.892694i 0.213095 + 0.0331767i
\(725\) −47.9592 + 27.6892i −1.78116 + 1.02835i
\(726\) 0 0
\(727\) 23.7464i 0.880706i −0.897825 0.440353i \(-0.854853\pi\)
0.897825 0.440353i \(-0.145147\pi\)
\(728\) −7.53361 2.43122i −0.279214 0.0901071i
\(729\) 0 0
\(730\) 82.7990 + 6.40690i 3.06453 + 0.237130i
\(731\) 16.3713 + 28.3560i 0.605516 + 1.04878i
\(732\) 0 0
\(733\) 9.21172 15.9552i 0.340243 0.589318i −0.644235 0.764828i \(-0.722824\pi\)
0.984478 + 0.175510i \(0.0561574\pi\)
\(734\) 1.16804 + 2.44058i 0.0431131 + 0.0900835i
\(735\) 0 0
\(736\) 20.8667 + 26.8270i 0.769157 + 0.988857i
\(737\) −9.36828 5.40878i −0.345085 0.199235i
\(738\) 0 0
\(739\) −12.1438 + 7.01125i −0.446718 + 0.257913i −0.706443 0.707770i \(-0.749701\pi\)
0.259725 + 0.965683i \(0.416368\pi\)
\(740\) −66.5971 + 25.7654i −2.44816 + 0.947154i
\(741\) 0 0
\(742\) −45.3340 + 17.3690i −1.66426 + 0.637637i
\(743\) 49.8064 1.82722 0.913610 0.406592i \(-0.133283\pi\)
0.913610 + 0.406592i \(0.133283\pi\)
\(744\) 0 0
\(745\) −13.8440 23.9785i −0.507205 0.878506i
\(746\) −9.54087 6.53881i −0.349316 0.239403i
\(747\) 0 0
\(748\) −7.76134 6.25129i −0.283783 0.228570i
\(749\) −9.64572 6.65706i −0.352447 0.243244i
\(750\) 0 0
\(751\) −1.68526 0.972983i −0.0614959 0.0355047i 0.468937 0.883232i \(-0.344637\pi\)
−0.530433 + 0.847727i \(0.677971\pi\)
\(752\) 12.0510 10.9661i 0.439455 0.399892i
\(753\) 0 0
\(754\) −7.59941 0.588034i −0.276754 0.0214149i
\(755\) 59.5319 2.16659
\(756\) 0 0
\(757\) 6.74999 0.245333 0.122666 0.992448i \(-0.460855\pi\)
0.122666 + 0.992448i \(0.460855\pi\)
\(758\) 24.2188 + 1.87402i 0.879665 + 0.0680675i
\(759\) 0 0
\(760\) 7.82556 2.35165i 0.283863 0.0853033i
\(761\) 29.0741 + 16.7859i 1.05393 + 0.608489i 0.923748 0.383000i \(-0.125109\pi\)
0.130186 + 0.991490i \(0.458443\pi\)
\(762\) 0 0
\(763\) 16.2921 7.73198i 0.589815 0.279917i
\(764\) −11.6643 + 14.4819i −0.422000 + 0.523938i
\(765\) 0 0
\(766\) −26.8623 18.4100i −0.970575 0.665180i
\(767\) 4.82858 + 8.36335i 0.174350 + 0.301983i
\(768\) 0 0
\(769\) 9.09355 0.327922 0.163961 0.986467i \(-0.447573\pi\)
0.163961 + 0.986467i \(0.447573\pi\)
\(770\) −4.38468 + 27.5703i −0.158013 + 0.993565i
\(771\) 0 0
\(772\) −5.11408 13.2186i −0.184060 0.475749i
\(773\) 9.08272 5.24391i 0.326683 0.188610i −0.327685 0.944787i \(-0.606268\pi\)
0.654367 + 0.756177i \(0.272935\pi\)
\(774\) 0 0
\(775\) −37.8308 21.8416i −1.35892 0.784574i
\(776\) −1.32336 + 5.60957i −0.0475058 + 0.201372i
\(777\) 0 0
\(778\) −11.5873 24.2113i −0.415424 0.868016i
\(779\) 2.24535 3.88906i 0.0804480 0.139340i
\(780\) 0 0
\(781\) 5.84440 + 10.1228i 0.209129 + 0.362222i
\(782\) 22.5379 + 1.74396i 0.805955 + 0.0623639i
\(783\) 0 0
\(784\) −24.9654 12.6778i −0.891622 0.452780i
\(785\) 62.3289i 2.22461i
\(786\) 0 0
\(787\) −7.11401 + 4.10728i −0.253587 + 0.146409i −0.621406 0.783489i \(-0.713438\pi\)
0.367819 + 0.929898i \(0.380105\pi\)
\(788\) −1.24029 + 7.96643i −0.0441836 + 0.283792i
\(789\) 0 0
\(790\) 28.8953 13.8290i 1.02805 0.492013i
\(791\) −29.1635 2.35246i −1.03693 0.0836438i
\(792\) 0 0
\(793\) −5.51427 + 9.55100i −0.195818 + 0.339166i
\(794\) 39.8669 + 27.3226i 1.41482 + 0.969644i
\(795\) 0 0
\(796\) 42.1480 16.3064i 1.49390 0.577964i
\(797\) 27.6583i 0.979709i 0.871804 + 0.489854i \(0.162950\pi\)
−0.871804 + 0.489854i \(0.837050\pi\)
\(798\) 0 0
\(799\) 10.8372i 0.383392i
\(800\) −60.9060 + 8.42611i −2.15335 + 0.297908i
\(801\) 0 0
\(802\) 10.5258 15.3584i 0.371680 0.542323i
\(803\) 13.8045 23.9101i 0.487150 0.843768i
\(804\) 0 0
\(805\) −27.1499 57.2079i −0.956909 2.01631i
\(806\) −2.59555 5.42332i −0.0914243 0.191028i
\(807\) 0 0
\(808\) 8.18354 + 27.2323i 0.287896 + 0.958028i
\(809\) 30.5781 17.6543i 1.07507 0.620691i 0.145507 0.989357i \(-0.453519\pi\)
0.929562 + 0.368666i \(0.120185\pi\)
\(810\) 0 0
\(811\) 3.31379i 0.116363i 0.998306 + 0.0581815i \(0.0185302\pi\)
−0.998306 + 0.0581815i \(0.981470\pi\)
\(812\) −26.2192 6.27586i −0.920115 0.220239i
\(813\) 0 0
\(814\) −1.83147 + 23.6688i −0.0641928 + 0.829591i
\(815\) −14.4376 25.0066i −0.505726 0.875943i
\(816\) 0 0
\(817\) −4.46263 + 7.72950i −0.156128 + 0.270421i
\(818\) −35.6117 + 17.0434i −1.24513 + 0.595909i
\(819\) 0 0
\(820\) −30.9468 + 38.4222i −1.08071 + 1.34176i
\(821\) −9.83140 5.67616i −0.343118 0.198099i 0.318532 0.947912i \(-0.396810\pi\)
−0.661650 + 0.749813i \(0.730144\pi\)
\(822\) 0 0
\(823\) 33.0277 19.0685i 1.15127 0.664687i 0.202075 0.979370i \(-0.435231\pi\)
0.949197 + 0.314682i \(0.101898\pi\)
\(824\) −18.5814 + 19.7360i −0.647313 + 0.687537i
\(825\) 0 0
\(826\) 12.2208 + 31.8969i 0.425217 + 1.10984i
\(827\) 9.51543 0.330884 0.165442 0.986220i \(-0.447095\pi\)
0.165442 + 0.986220i \(0.447095\pi\)
\(828\) 0 0
\(829\) 14.5375 + 25.1798i 0.504910 + 0.874529i 0.999984 + 0.00567849i \(0.00180753\pi\)
−0.495074 + 0.868851i \(0.664859\pi\)
\(830\) −10.4239 + 15.2096i −0.361818 + 0.527934i
\(831\) 0 0
\(832\) −7.57045 3.78241i −0.262458 0.131132i
\(833\) −17.4123 + 6.60613i −0.603299 + 0.228889i
\(834\) 0 0
\(835\) 62.4893 + 36.0782i 2.16253 + 1.24854i
\(836\) 0.417906 2.68422i 0.0144536 0.0928355i
\(837\) 0 0
\(838\) 3.51904 45.4780i 0.121563 1.57101i
\(839\) 1.01793 0.0351429 0.0175715 0.999846i \(-0.494407\pi\)
0.0175715 + 0.999846i \(0.494407\pi\)
\(840\) 0 0
\(841\) 3.04159 0.104883
\(842\) 2.21998 28.6897i 0.0765054 0.988711i
\(843\) 0 0
\(844\) −1.08594 + 6.97502i −0.0373797 + 0.240090i
\(845\) −40.9884 23.6647i −1.41004 0.814090i
\(846\) 0 0
\(847\) −16.3141 11.2593i −0.560560 0.386874i
\(848\) −50.7078 + 11.0573i −1.74131 + 0.379710i
\(849\) 0 0
\(850\) −23.1192 + 33.7335i −0.792981 + 1.15705i
\(851\) −26.9241 46.6339i −0.922946 1.59859i
\(852\) 0 0
\(853\) 13.2563 0.453887 0.226944 0.973908i \(-0.427127\pi\)
0.226944 + 0.973908i \(0.427127\pi\)
\(854\) −24.5682 + 30.2997i −0.840705 + 1.03684i
\(855\) 0 0
\(856\) −9.12224 8.58856i −0.311792 0.293551i
\(857\) −20.4031 + 11.7797i −0.696956 + 0.402388i −0.806213 0.591626i \(-0.798486\pi\)
0.109257 + 0.994014i \(0.465153\pi\)
\(858\) 0 0
\(859\) 0.285175 + 0.164646i 0.00973004 + 0.00561764i 0.504857 0.863203i \(-0.331545\pi\)
−0.495127 + 0.868821i \(0.664879\pi\)
\(860\) 61.5067 76.3641i 2.09736 2.60399i
\(861\) 0 0
\(862\) −30.2470 + 14.4759i −1.03022 + 0.493052i
\(863\) 25.0532 43.3934i 0.852820 1.47713i −0.0258325 0.999666i \(-0.508224\pi\)
0.878653 0.477462i \(-0.158443\pi\)
\(864\) 0 0
\(865\) 21.3053 + 36.9019i 0.724403 + 1.25470i
\(866\) −1.35859 + 17.5577i −0.0461669 + 0.596634i
\(867\) 0 0
\(868\) −6.05380 20.3864i −0.205479 0.691960i
\(869\) 10.6498i 0.361268i
\(870\) 0 0
\(871\) −5.29127 + 3.05491i −0.179288 + 0.103512i
\(872\) 18.4633 5.54838i 0.625245 0.187892i
\(873\) 0 0
\(874\) 2.66009 + 5.55818i 0.0899789 + 0.188008i
\(875\) 61.6605 + 4.97381i 2.08450 + 0.168145i
\(876\) 0 0
\(877\) −7.33001 + 12.6959i −0.247517 + 0.428712i −0.962836 0.270086i \(-0.912948\pi\)
0.715319 + 0.698798i \(0.246281\pi\)
\(878\) −1.22675 + 1.78997i −0.0414008 + 0.0604086i
\(879\) 0 0
\(880\) −9.07300 + 28.4317i −0.305851 + 0.958434i
\(881\) 37.4296i 1.26104i 0.776174 + 0.630518i \(0.217158\pi\)
−0.776174 + 0.630518i \(0.782842\pi\)
\(882\) 0 0
\(883\) 33.1664i 1.11614i −0.829794 0.558070i \(-0.811542\pi\)
0.829794 0.558070i \(-0.188458\pi\)
\(884\) −5.24956 + 2.03097i −0.176562 + 0.0683089i
\(885\) 0 0
\(886\) −34.2033 23.4411i −1.14908 0.787520i
\(887\) −10.7263 + 18.5785i −0.360154 + 0.623804i −0.987986 0.154544i \(-0.950609\pi\)
0.627832 + 0.778349i \(0.283942\pi\)
\(888\) 0 0
\(889\) −39.0665 3.15128i −1.31025 0.105691i
\(890\) −51.6691 + 24.7283i −1.73195 + 0.828896i
\(891\) 0 0
\(892\) 1.59079 10.2177i 0.0532635 0.342112i
\(893\) 2.55831 1.47704i 0.0856107 0.0494274i
\(894\) 0 0
\(895\) 92.9056i 3.10549i
\(896\) −24.3435 17.4182i −0.813259 0.581902i
\(897\) 0 0
\(898\) −6.06213 0.469081i −0.202296 0.0156535i
\(899\) −10.2382 17.7330i −0.341462 0.591429i
\(900\) 0 0
\(901\) −17.2596 + 29.8945i −0.575001 + 0.995931i
\(902\) 7.08053 + 14.7945i 0.235756 + 0.492604i
\(903\) 0 0
\(904\) −30.4427 7.18177i −1.01251 0.238862i
\(905\) −10.0097 5.77912i −0.332735 0.192104i
\(906\) 0 0
\(907\) 4.53272 2.61697i 0.150507 0.0868951i −0.422855 0.906197i \(-0.638972\pi\)
0.573362 + 0.819302i \(0.305639\pi\)
\(908\) −14.8196 38.3049i −0.491805 1.27119i
\(909\) 0 0
\(910\) 12.2474 + 9.93065i 0.405998 + 0.329198i
\(911\) 43.4199 1.43857 0.719283 0.694717i \(-0.244471\pi\)
0.719283 + 0.694717i \(0.244471\pi\)
\(912\) 0 0
\(913\) 3.06501 + 5.30875i 0.101437 + 0.175694i
\(914\) −5.42334 3.71687i −0.179388 0.122943i
\(915\) 0 0
\(916\) −12.8080 + 15.9019i −0.423189 + 0.525414i
\(917\) −5.33753 3.68373i −0.176261 0.121648i
\(918\) 0 0
\(919\) −14.3771 8.30065i −0.474258 0.273813i 0.243762 0.969835i \(-0.421618\pi\)
−0.718021 + 0.696022i \(0.754952\pi\)
\(920\) −19.4825 64.8315i −0.642317 2.13743i
\(921\) 0 0
\(922\) 34.1715 + 2.64415i 1.12538 + 0.0870806i
\(923\) 6.60190 0.217304
\(924\) 0 0
\(925\) 97.4174 3.20307
\(926\) 26.4056 + 2.04324i 0.867741 + 0.0671449i
\(927\) 0 0
\(928\) −26.6994 10.8542i −0.876450 0.356305i
\(929\) −19.1671 11.0661i −0.628851 0.363067i 0.151456 0.988464i \(-0.451604\pi\)
−0.780307 + 0.625397i \(0.784937\pi\)
\(930\) 0 0
\(931\) −3.93268 3.21010i −0.128888 0.105207i
\(932\) −9.75205 7.85469i −0.319439 0.257289i
\(933\) 0 0
\(934\) 21.6665 + 14.8491i 0.708951 + 0.485877i
\(935\) 9.92500 + 17.1906i 0.324582 + 0.562193i
\(936\) 0 0
\(937\) 23.3303 0.762167 0.381083 0.924541i \(-0.375551\pi\)
0.381083 + 0.924541i \(0.375551\pi\)
\(938\) −20.1803 + 7.73179i −0.658911 + 0.252452i
\(939\) 0 0
\(940\) −30.2676 + 11.7101i −0.987221 + 0.381940i
\(941\) −37.7784 + 21.8114i −1.23154 + 0.711030i −0.967351 0.253441i \(-0.918438\pi\)
−0.264190 + 0.964471i \(0.585104\pi\)
\(942\) 0 0
\(943\) −32.2193 18.6018i −1.04920 0.605758i
\(944\) 7.77992 + 35.6780i 0.253215 + 1.16122i
\(945\) 0 0
\(946\) −14.0725 29.4041i −0.457538 0.956011i
\(947\) 12.6981 21.9938i 0.412634 0.714702i −0.582543 0.812800i \(-0.697942\pi\)
0.995177 + 0.0980973i \(0.0312756\pi\)
\(948\) 0 0
\(949\) −7.79686 13.5046i −0.253097 0.438377i
\(950\) −11.1144 0.860021i −0.360599 0.0279028i
\(951\) 0 0
\(952\) −19.4658 + 4.17817i −0.630890 + 0.135415i
\(953\) 1.61704i 0.0523809i −0.999657 0.0261905i \(-0.991662\pi\)
0.999657 0.0261905i \(-0.00833763\pi\)
\(954\) 0 0
\(955\) 32.0761 18.5191i 1.03796 0.599265i
\(956\) 9.86680 + 1.53616i 0.319115 + 0.0496830i
\(957\) 0 0
\(958\) 13.3901 6.40838i 0.432615 0.207045i
\(959\) −0.703204 1.48173i −0.0227077 0.0478475i
\(960\) 0 0
\(961\) −7.42402 + 12.8588i −0.239485 + 0.414799i
\(962\) 11.0601 + 7.57998i 0.356591 + 0.244388i
\(963\) 0 0
\(964\) −5.03095 13.0038i −0.162036 0.418823i
\(965\) 28.2309i 0.908783i
\(966\) 0 0
\(967\) 27.8714i 0.896282i 0.893963 + 0.448141i \(0.147914\pi\)
−0.893963 + 0.448141i \(0.852086\pi\)
\(968\) −15.4288 14.5261i −0.495899 0.466887i
\(969\) 0 0
\(970\) 6.48986 9.46946i 0.208377 0.304046i
\(971\) −14.9960 + 25.9738i −0.481243 + 0.833538i −0.999768 0.0215245i \(-0.993148\pi\)
0.518525 + 0.855062i \(0.326481\pi\)
\(972\) 0 0
\(973\) 5.29212 + 0.426886i 0.169658 + 0.0136853i
\(974\) 16.5329 + 34.5450i 0.529748 + 1.10689i
\(975\) 0 0
\(976\) −30.8434 + 28.0666i −0.987273 + 0.898391i
\(977\) 2.90454 1.67694i 0.0929246 0.0536500i −0.452818 0.891603i \(-0.649581\pi\)
0.545742 + 0.837953i \(0.316248\pi\)
\(978\) 0 0
\(979\) 19.0434i 0.608629i
\(980\) 37.2652 + 41.4932i 1.19039 + 1.32545i
\(981\) 0 0
\(982\) −0.915631 + 11.8331i −0.0292190 + 0.377609i
\(983\) 13.4540 + 23.3029i 0.429115 + 0.743249i 0.996795 0.0800007i \(-0.0254923\pi\)
−0.567680 + 0.823249i \(0.692159\pi\)
\(984\) 0 0
\(985\) 8.02941 13.9073i 0.255838 0.443125i
\(986\) −17.2913 + 8.27547i −0.550668 + 0.263545i
\(987\) 0 0
\(988\) −1.19493 0.962444i −0.0380158 0.0306194i
\(989\) 64.0357 + 36.9710i 2.03622 + 1.17561i
\(990\) 0 0
\(991\) −35.8246 + 20.6834i −1.13801 + 0.657029i −0.945936 0.324352i \(-0.894854\pi\)
−0.192071 + 0.981381i \(0.561520\pi\)
\(992\) −3.11557 22.5201i −0.0989195 0.715015i
\(993\) 0 0
\(994\) 23.0615 + 3.66761i 0.731466 + 0.116329i
\(995\) −90.0148 −2.85366
\(996\) 0 0
\(997\) −7.74005 13.4062i −0.245130 0.424577i 0.717038 0.697034i \(-0.245497\pi\)
−0.962168 + 0.272457i \(0.912164\pi\)
\(998\) 14.2775 20.8325i 0.451946 0.659441i
\(999\) 0 0
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 756.2.be.c.107.7 28
3.2 odd 2 inner 756.2.be.c.107.8 yes 28
4.3 odd 2 756.2.be.d.107.12 yes 28
7.4 even 3 756.2.be.d.431.3 yes 28
12.11 even 2 756.2.be.d.107.3 yes 28
21.11 odd 6 756.2.be.d.431.12 yes 28
28.11 odd 6 inner 756.2.be.c.431.8 yes 28
84.11 even 6 inner 756.2.be.c.431.7 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.be.c.107.7 28 1.1 even 1 trivial
756.2.be.c.107.8 yes 28 3.2 odd 2 inner
756.2.be.c.431.7 yes 28 84.11 even 6 inner
756.2.be.c.431.8 yes 28 28.11 odd 6 inner
756.2.be.d.107.3 yes 28 12.11 even 2
756.2.be.d.107.12 yes 28 4.3 odd 2
756.2.be.d.431.3 yes 28 7.4 even 3
756.2.be.d.431.12 yes 28 21.11 odd 6