Properties

Label 216.2.q.b.121.1
Level $216$
Weight $2$
Character 216.121
Analytic conductor $1.725$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [216,2,Mod(25,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.q (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 121.1
Character \(\chi\) \(=\) 216.121
Dual form 216.2.q.b.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36303 - 1.06872i) q^{3} +(2.18080 + 1.82991i) q^{5} +(0.145059 + 0.0527971i) q^{7} +(0.715688 + 2.91338i) q^{9} +O(q^{10})\) \(q+(-1.36303 - 1.06872i) q^{3} +(2.18080 + 1.82991i) q^{5} +(0.145059 + 0.0527971i) q^{7} +(0.715688 + 2.91338i) q^{9} +(4.10127 - 3.44137i) q^{11} +(0.00459855 - 0.0260797i) q^{13} +(-1.01684 - 4.82488i) q^{15} +(2.88012 - 4.98852i) q^{17} +(3.10159 + 5.37211i) q^{19} +(-0.141294 - 0.226991i) q^{21} +(-3.35846 + 1.22238i) q^{23} +(0.539084 + 3.05730i) q^{25} +(2.13808 - 4.73589i) q^{27} +(0.0327963 + 0.185997i) q^{29} +(-2.56293 + 0.932831i) q^{31} +(-9.26799 + 0.307591i) q^{33} +(0.219731 + 0.380584i) q^{35} +(-4.11754 + 7.13179i) q^{37} +(-0.0341397 + 0.0306327i) q^{39} +(-0.00921569 + 0.0522648i) q^{41} +(-6.21877 + 5.21817i) q^{43} +(-3.77045 + 7.66315i) q^{45} +(-11.8622 - 4.31750i) q^{47} +(-5.34406 - 4.48420i) q^{49} +(-9.25700 + 3.72145i) q^{51} +13.8601 q^{53} +15.2414 q^{55} +(1.51371 - 10.6371i) q^{57} +(3.24676 + 2.72435i) q^{59} +(-4.47554 - 1.62897i) q^{61} +(-0.0500012 + 0.460398i) q^{63} +(0.0577519 - 0.0484596i) q^{65} +(1.03748 - 5.88386i) q^{67} +(5.88406 + 1.92311i) q^{69} +(-1.35870 + 2.35333i) q^{71} +(-7.37683 - 12.7770i) q^{73} +(2.53260 - 4.74331i) q^{75} +(0.776619 - 0.282666i) q^{77} +(0.880151 + 4.99159i) q^{79} +(-7.97558 + 4.17015i) q^{81} +(-0.538876 - 3.05612i) q^{83} +(15.4095 - 5.60860i) q^{85} +(0.154076 - 0.288569i) q^{87} +(2.11862 + 3.66956i) q^{89} +(0.00204399 - 0.00354029i) q^{91} +(4.49028 + 1.46757i) q^{93} +(-3.06653 + 17.3911i) q^{95} +(-9.25397 + 7.76500i) q^{97} +(12.9613 + 9.48561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\)

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 0
\(3\) −1.36303 1.06872i −0.786944 0.617024i
\(4\) 0 0
\(5\) 2.18080 + 1.82991i 0.975284 + 0.818360i 0.983371 0.181607i \(-0.0581298\pi\)
−0.00808726 + 0.999967i \(0.502574\pi\)
\(6\) 0 0
\(7\) 0.145059 + 0.0527971i 0.0548271 + 0.0199554i 0.369288 0.929315i \(-0.379602\pi\)
−0.314461 + 0.949270i \(0.601824\pi\)
\(8\) 0 0
\(9\) 0.715688 + 2.91338i 0.238563 + 0.971127i
\(10\) 0 0
\(11\) 4.10127 3.44137i 1.23658 1.03761i 0.238795 0.971070i \(-0.423248\pi\)
0.997784 0.0665427i \(-0.0211969\pi\)
\(12\) 0 0
\(13\) 0.00459855 0.0260797i 0.00127541 0.00723320i −0.984163 0.177264i \(-0.943275\pi\)
0.985439 + 0.170030i \(0.0543866\pi\)
\(14\) 0 0
\(15\) −1.01684 4.82488i −0.262546 1.24578i
\(16\) 0 0
\(17\) 2.88012 4.98852i 0.698532 1.20989i −0.270443 0.962736i \(-0.587170\pi\)
0.968975 0.247157i \(-0.0794965\pi\)
\(18\) 0 0
\(19\) 3.10159 + 5.37211i 0.711553 + 1.23245i 0.964274 + 0.264907i \(0.0853414\pi\)
−0.252720 + 0.967539i \(0.581325\pi\)
\(20\) 0 0
\(21\) −0.141294 0.226991i −0.0308329 0.0495334i
\(22\) 0 0
\(23\) −3.35846 + 1.22238i −0.700288 + 0.254884i −0.667534 0.744579i \(-0.732650\pi\)
−0.0327542 + 0.999463i \(0.510428\pi\)
\(24\) 0 0
\(25\) 0.539084 + 3.05730i 0.107817 + 0.611460i
\(26\) 0 0
\(27\) 2.13808 4.73589i 0.411473 0.911422i
\(28\) 0 0
\(29\) 0.0327963 + 0.185997i 0.00609012 + 0.0345388i 0.987701 0.156352i \(-0.0499735\pi\)
−0.981611 + 0.190891i \(0.938862\pi\)
\(30\) 0 0
\(31\) −2.56293 + 0.932831i −0.460316 + 0.167541i −0.561761 0.827300i \(-0.689876\pi\)
0.101444 + 0.994841i \(0.467654\pi\)
\(32\) 0 0
\(33\) −9.26799 + 0.307591i −1.61335 + 0.0535447i
\(34\) 0 0
\(35\) 0.219731 + 0.380584i 0.0371412 + 0.0643305i
\(36\) 0 0
\(37\) −4.11754 + 7.13179i −0.676920 + 1.17246i 0.298984 + 0.954258i \(0.403352\pi\)
−0.975904 + 0.218201i \(0.929981\pi\)
\(38\) 0 0
\(39\) −0.0341397 + 0.0306327i −0.00546673 + 0.00490517i
\(40\) 0 0
\(41\) −0.00921569 + 0.0522648i −0.00143925 + 0.00816239i −0.985519 0.169565i \(-0.945764\pi\)
0.984080 + 0.177728i \(0.0568747\pi\)
\(42\) 0 0
\(43\) −6.21877 + 5.21817i −0.948354 + 0.795763i −0.979020 0.203766i \(-0.934682\pi\)
0.0306658 + 0.999530i \(0.490237\pi\)
\(44\) 0 0
\(45\) −3.77045 + 7.66315i −0.562066 + 1.14235i
\(46\) 0 0
\(47\) −11.8622 4.31750i −1.73028 0.629772i −0.731633 0.681699i \(-0.761241\pi\)
−0.998651 + 0.0519270i \(0.983464\pi\)
\(48\) 0 0
\(49\) −5.34406 4.48420i −0.763437 0.640599i
\(50\) 0 0
\(51\) −9.25700 + 3.72145i −1.29624 + 0.521108i
\(52\) 0 0
\(53\) 13.8601 1.90384 0.951919 0.306350i \(-0.0991078\pi\)
0.951919 + 0.306350i \(0.0991078\pi\)
\(54\) 0 0
\(55\) 15.2414 2.05516
\(56\) 0 0
\(57\) 1.51371 10.6371i 0.200496 1.40891i
\(58\) 0 0
\(59\) 3.24676 + 2.72435i 0.422692 + 0.354680i 0.829186 0.558973i \(-0.188804\pi\)
−0.406494 + 0.913653i \(0.633249\pi\)
\(60\) 0 0
\(61\) −4.47554 1.62897i −0.573035 0.208568i 0.0392166 0.999231i \(-0.487514\pi\)
−0.612251 + 0.790663i \(0.709736\pi\)
\(62\) 0 0
\(63\) −0.0500012 + 0.460398i −0.00629956 + 0.0580047i
\(64\) 0 0
\(65\) 0.0577519 0.0484596i 0.00716325 0.00601068i
\(66\) 0 0
\(67\) 1.03748 5.88386i 0.126749 0.718827i −0.853505 0.521084i \(-0.825528\pi\)
0.980254 0.197743i \(-0.0633612\pi\)
\(68\) 0 0
\(69\) 5.88406 + 1.92311i 0.708357 + 0.231515i
\(70\) 0 0
\(71\) −1.35870 + 2.35333i −0.161248 + 0.279289i −0.935316 0.353812i \(-0.884885\pi\)
0.774069 + 0.633101i \(0.218218\pi\)
\(72\) 0 0
\(73\) −7.37683 12.7770i −0.863392 1.49544i −0.868635 0.495453i \(-0.835002\pi\)
0.00524205 0.999986i \(-0.498331\pi\)
\(74\) 0 0
\(75\) 2.53260 4.74331i 0.292439 0.547710i
\(76\) 0 0
\(77\) 0.776619 0.282666i 0.0885040 0.0322128i
\(78\) 0 0
\(79\) 0.880151 + 4.99159i 0.0990247 + 0.561597i 0.993440 + 0.114359i \(0.0364813\pi\)
−0.894415 + 0.447238i \(0.852408\pi\)
\(80\) 0 0
\(81\) −7.97558 + 4.17015i −0.886176 + 0.463349i
\(82\) 0 0
\(83\) −0.538876 3.05612i −0.0591494 0.335453i 0.940845 0.338837i \(-0.110034\pi\)
−0.999994 + 0.00338482i \(0.998923\pi\)
\(84\) 0 0
\(85\) 15.4095 5.60860i 1.67140 0.608338i
\(86\) 0 0
\(87\) 0.154076 0.288569i 0.0165187 0.0309379i
\(88\) 0 0
\(89\) 2.11862 + 3.66956i 0.224574 + 0.388973i 0.956191 0.292742i \(-0.0945677\pi\)
−0.731618 + 0.681715i \(0.761234\pi\)
\(90\) 0 0
\(91\) 0.00204399 0.00354029i 0.000214268 0.000371124i
\(92\) 0 0
\(93\) 4.49028 + 1.46757i 0.465620 + 0.152180i
\(94\) 0 0
\(95\) −3.06653 + 17.3911i −0.314619 + 1.78429i
\(96\) 0 0
\(97\) −9.25397 + 7.76500i −0.939598 + 0.788416i −0.977515 0.210865i \(-0.932372\pi\)
0.0379173 + 0.999281i \(0.487928\pi\)
\(98\) 0 0
\(99\) 12.9613 + 9.48561i 1.30266 + 0.953339i
\(100\) 0 0
\(101\) −8.84886 3.22072i −0.880495 0.320474i −0.138085 0.990420i \(-0.544095\pi\)
−0.742409 + 0.669947i \(0.766317\pi\)
\(102\) 0 0
\(103\) 6.66917 + 5.59610i 0.657133 + 0.551400i 0.909226 0.416303i \(-0.136675\pi\)
−0.252093 + 0.967703i \(0.581119\pi\)
\(104\) 0 0
\(105\) 0.107238 0.753577i 0.0104654 0.0735416i
\(106\) 0 0
\(107\) −0.149779 −0.0144797 −0.00723986 0.999974i \(-0.502305\pi\)
−0.00723986 + 0.999974i \(0.502305\pi\)
\(108\) 0 0
\(109\) 10.0150 0.959265 0.479633 0.877469i \(-0.340770\pi\)
0.479633 + 0.877469i \(0.340770\pi\)
\(110\) 0 0
\(111\) 13.2342 5.32034i 1.25613 0.504985i
\(112\) 0 0
\(113\) −10.6838 8.96477i −1.00505 0.843334i −0.0173710 0.999849i \(-0.505530\pi\)
−0.987676 + 0.156515i \(0.949974\pi\)
\(114\) 0 0
\(115\) −9.56099 3.47991i −0.891567 0.324504i
\(116\) 0 0
\(117\) 0.0792711 0.00526758i 0.00732862 0.000486988i
\(118\) 0 0
\(119\) 0.681166 0.571567i 0.0624424 0.0523954i
\(120\) 0 0
\(121\) 3.06722 17.3951i 0.278838 1.58137i
\(122\) 0 0
\(123\) 0.0684175 0.0613894i 0.00616900 0.00553529i
\(124\) 0 0
\(125\) 2.69814 4.67332i 0.241329 0.417994i
\(126\) 0 0
\(127\) −1.33887 2.31899i −0.118806 0.205777i 0.800489 0.599347i \(-0.204573\pi\)
−0.919295 + 0.393570i \(0.871240\pi\)
\(128\) 0 0
\(129\) 14.0531 0.466402i 1.23731 0.0410644i
\(130\) 0 0
\(131\) 3.77812 1.37512i 0.330096 0.120145i −0.171655 0.985157i \(-0.554912\pi\)
0.501751 + 0.865012i \(0.332689\pi\)
\(132\) 0 0
\(133\) 0.166281 + 0.943027i 0.0144184 + 0.0817708i
\(134\) 0 0
\(135\) 13.3290 6.41554i 1.14717 0.552162i
\(136\) 0 0
\(137\) −0.177470 1.00648i −0.0151623 0.0859894i 0.976288 0.216477i \(-0.0694567\pi\)
−0.991450 + 0.130488i \(0.958346\pi\)
\(138\) 0 0
\(139\) −12.3098 + 4.48042i −1.04411 + 0.380024i −0.806436 0.591322i \(-0.798606\pi\)
−0.237672 + 0.971346i \(0.576384\pi\)
\(140\) 0 0
\(141\) 11.5544 + 18.5622i 0.973053 + 1.56322i
\(142\) 0 0
\(143\) −0.0708899 0.122785i −0.00592811 0.0102678i
\(144\) 0 0
\(145\) −0.268836 + 0.465637i −0.0223256 + 0.0386690i
\(146\) 0 0
\(147\) 2.49176 + 11.8234i 0.205517 + 0.975175i
\(148\) 0 0
\(149\) −1.34138 + 7.60735i −0.109890 + 0.623219i 0.879264 + 0.476336i \(0.158035\pi\)
−0.989154 + 0.146883i \(0.953076\pi\)
\(150\) 0 0
\(151\) 11.4824 9.63488i 0.934425 0.784076i −0.0421814 0.999110i \(-0.513431\pi\)
0.976607 + 0.215034i \(0.0689863\pi\)
\(152\) 0 0
\(153\) 16.5947 + 4.82067i 1.34160 + 0.389728i
\(154\) 0 0
\(155\) −7.29624 2.65562i −0.586048 0.213304i
\(156\) 0 0
\(157\) −18.5483 15.5638i −1.48031 1.24213i −0.905850 0.423598i \(-0.860767\pi\)
−0.574462 0.818532i \(-0.694789\pi\)
\(158\) 0 0
\(159\) −18.8918 14.8126i −1.49821 1.17471i
\(160\) 0 0
\(161\) −0.551713 −0.0434811
\(162\) 0 0
\(163\) 13.3534 1.04592 0.522961 0.852357i \(-0.324827\pi\)
0.522961 + 0.852357i \(0.324827\pi\)
\(164\) 0 0
\(165\) −20.7745 16.2888i −1.61729 1.26808i
\(166\) 0 0
\(167\) 7.07789 + 5.93906i 0.547704 + 0.459578i 0.874163 0.485633i \(-0.161411\pi\)
−0.326459 + 0.945211i \(0.605855\pi\)
\(168\) 0 0
\(169\) 12.2153 + 4.44602i 0.939642 + 0.342002i
\(170\) 0 0
\(171\) −13.4312 + 12.8809i −1.02711 + 0.985025i
\(172\) 0 0
\(173\) −19.7459 + 16.5688i −1.50126 + 1.25970i −0.622319 + 0.782764i \(0.713809\pi\)
−0.878937 + 0.476939i \(0.841746\pi\)
\(174\) 0 0
\(175\) −0.0832176 + 0.471950i −0.00629066 + 0.0356761i
\(176\) 0 0
\(177\) −1.51386 7.18323i −0.113788 0.539925i
\(178\) 0 0
\(179\) 0.113553 0.196679i 0.00848732 0.0147005i −0.861751 0.507332i \(-0.830632\pi\)
0.870238 + 0.492632i \(0.163965\pi\)
\(180\) 0 0
\(181\) 3.80048 + 6.58262i 0.282487 + 0.489282i 0.971997 0.234995i \(-0.0755072\pi\)
−0.689510 + 0.724277i \(0.742174\pi\)
\(182\) 0 0
\(183\) 4.35939 + 7.00341i 0.322255 + 0.517707i
\(184\) 0 0
\(185\) −22.0301 + 8.01829i −1.61968 + 0.589517i
\(186\) 0 0
\(187\) −5.35520 30.3708i −0.391611 2.22093i
\(188\) 0 0
\(189\) 0.560188 0.574098i 0.0407477 0.0417595i
\(190\) 0 0
\(191\) −0.726932 4.12264i −0.0525989 0.298303i 0.947148 0.320797i \(-0.103951\pi\)
−0.999747 + 0.0224933i \(0.992840\pi\)
\(192\) 0 0
\(193\) −0.376522 + 0.137043i −0.0271027 + 0.00986456i −0.355536 0.934663i \(-0.615702\pi\)
0.328433 + 0.944527i \(0.393479\pi\)
\(194\) 0 0
\(195\) −0.130507 + 0.00433134i −0.00934581 + 0.000310173i
\(196\) 0 0
\(197\) 3.55429 + 6.15621i 0.253233 + 0.438612i 0.964414 0.264397i \(-0.0851729\pi\)
−0.711181 + 0.703009i \(0.751840\pi\)
\(198\) 0 0
\(199\) −10.9253 + 18.9232i −0.774474 + 1.34143i 0.160616 + 0.987017i \(0.448652\pi\)
−0.935090 + 0.354411i \(0.884681\pi\)
\(200\) 0 0
\(201\) −7.70229 + 6.91108i −0.543278 + 0.487470i
\(202\) 0 0
\(203\) −0.00506271 + 0.0287121i −0.000355333 + 0.00201519i
\(204\) 0 0
\(205\) −0.115737 + 0.0971152i −0.00808345 + 0.00678282i
\(206\) 0 0
\(207\) −5.96487 8.90964i −0.414587 0.619263i
\(208\) 0 0
\(209\) 31.2079 + 11.3587i 2.15869 + 0.785700i
\(210\) 0 0
\(211\) −7.19890 6.04060i −0.495593 0.415852i 0.360433 0.932785i \(-0.382629\pi\)
−0.856026 + 0.516933i \(0.827073\pi\)
\(212\) 0 0
\(213\) 4.36699 1.75559i 0.299221 0.120291i
\(214\) 0 0
\(215\) −23.1107 −1.57614
\(216\) 0 0
\(217\) −0.421027 −0.0285812
\(218\) 0 0
\(219\) −3.60022 + 25.2992i −0.243280 + 1.70956i
\(220\) 0 0
\(221\) −0.116854 0.0980526i −0.00786048 0.00659573i
\(222\) 0 0
\(223\) −13.0978 4.76722i −0.877095 0.319237i −0.136058 0.990701i \(-0.543443\pi\)
−0.741037 + 0.671464i \(0.765666\pi\)
\(224\) 0 0
\(225\) −8.52126 + 3.75863i −0.568084 + 0.250575i
\(226\) 0 0
\(227\) 13.2560 11.1231i 0.879831 0.738266i −0.0863130 0.996268i \(-0.527509\pi\)
0.966144 + 0.258002i \(0.0830641\pi\)
\(228\) 0 0
\(229\) −1.99437 + 11.3106i −0.131792 + 0.747427i 0.845249 + 0.534373i \(0.179452\pi\)
−0.977040 + 0.213054i \(0.931659\pi\)
\(230\) 0 0
\(231\) −1.36064 0.444704i −0.0895238 0.0292594i
\(232\) 0 0
\(233\) −0.552886 + 0.957626i −0.0362208 + 0.0627362i −0.883568 0.468304i \(-0.844865\pi\)
0.847347 + 0.531040i \(0.178199\pi\)
\(234\) 0 0
\(235\) −17.9685 31.1224i −1.17214 2.03020i
\(236\) 0 0
\(237\) 4.13492 7.74430i 0.268592 0.503046i
\(238\) 0 0
\(239\) 1.17137 0.426344i 0.0757696 0.0275779i −0.303857 0.952718i \(-0.598275\pi\)
0.379627 + 0.925140i \(0.376052\pi\)
\(240\) 0 0
\(241\) 4.62907 + 26.2528i 0.298185 + 1.69109i 0.653969 + 0.756522i \(0.273103\pi\)
−0.355784 + 0.934568i \(0.615786\pi\)
\(242\) 0 0
\(243\) 15.3276 + 2.83962i 0.983269 + 0.182161i
\(244\) 0 0
\(245\) −3.44865 19.5583i −0.220326 1.24953i
\(246\) 0 0
\(247\) 0.154366 0.0561845i 0.00982205 0.00357493i
\(248\) 0 0
\(249\) −2.53162 + 4.74148i −0.160435 + 0.300479i
\(250\) 0 0
\(251\) −8.75536 15.1647i −0.552633 0.957189i −0.998083 0.0618822i \(-0.980290\pi\)
0.445450 0.895307i \(-0.353044\pi\)
\(252\) 0 0
\(253\) −9.56729 + 16.5710i −0.601490 + 1.04181i
\(254\) 0 0
\(255\) −26.9976 8.82373i −1.69066 0.552563i
\(256\) 0 0
\(257\) 1.97148 11.1808i 0.122978 0.697440i −0.859511 0.511117i \(-0.829232\pi\)
0.982489 0.186323i \(-0.0596571\pi\)
\(258\) 0 0
\(259\) −0.973824 + 0.817135i −0.0605105 + 0.0507743i
\(260\) 0 0
\(261\) −0.518408 + 0.228664i −0.0320887 + 0.0141539i
\(262\) 0 0
\(263\) 12.3794 + 4.50573i 0.763346 + 0.277835i 0.694210 0.719772i \(-0.255754\pi\)
0.0691353 + 0.997607i \(0.477976\pi\)
\(264\) 0 0
\(265\) 30.2262 + 25.3628i 1.85678 + 1.55803i
\(266\) 0 0
\(267\) 1.03398 7.26592i 0.0632787 0.444667i
\(268\) 0 0
\(269\) −1.50575 −0.0918074 −0.0459037 0.998946i \(-0.514617\pi\)
−0.0459037 + 0.998946i \(0.514617\pi\)
\(270\) 0 0
\(271\) 25.7002 1.56117 0.780587 0.625047i \(-0.214920\pi\)
0.780587 + 0.625047i \(0.214920\pi\)
\(272\) 0 0
\(273\) −0.00656959 + 0.00264107i −0.000397610 + 0.000159845i
\(274\) 0 0
\(275\) 12.7322 + 10.6836i 0.767782 + 0.644246i
\(276\) 0 0
\(277\) 7.61518 + 2.77170i 0.457552 + 0.166535i 0.560505 0.828151i \(-0.310607\pi\)
−0.102953 + 0.994686i \(0.532829\pi\)
\(278\) 0 0
\(279\) −4.55195 6.79918i −0.272518 0.407056i
\(280\) 0 0
\(281\) −12.0856 + 10.1410i −0.720968 + 0.604964i −0.927653 0.373443i \(-0.878177\pi\)
0.206685 + 0.978408i \(0.433733\pi\)
\(282\) 0 0
\(283\) −2.79183 + 15.8333i −0.165957 + 0.941190i 0.782115 + 0.623134i \(0.214141\pi\)
−0.948072 + 0.318056i \(0.896970\pi\)
\(284\) 0 0
\(285\) 22.7660 20.4273i 1.34854 1.21001i
\(286\) 0 0
\(287\) −0.00409625 + 0.00709491i −0.000241794 + 0.000418799i
\(288\) 0 0
\(289\) −8.09021 14.0127i −0.475895 0.824274i
\(290\) 0 0
\(291\) 20.9120 0.694038i 1.22588 0.0406852i
\(292\) 0 0
\(293\) 11.8571 4.31565i 0.692701 0.252123i 0.0284099 0.999596i \(-0.490956\pi\)
0.664291 + 0.747474i \(0.268733\pi\)
\(294\) 0 0
\(295\) 2.09521 + 11.8825i 0.121988 + 0.691828i
\(296\) 0 0
\(297\) −7.52912 26.7811i −0.436884 1.55399i
\(298\) 0 0
\(299\) 0.0164352 + 0.0932088i 0.000950473 + 0.00539040i
\(300\) 0 0
\(301\) −1.17759 + 0.428608i −0.0678753 + 0.0247046i
\(302\) 0 0
\(303\) 8.61920 + 13.8469i 0.495160 + 0.795481i
\(304\) 0 0
\(305\) −6.77941 11.7423i −0.388188 0.672362i
\(306\) 0 0
\(307\) −4.60942 + 7.98375i −0.263074 + 0.455657i −0.967057 0.254560i \(-0.918070\pi\)
0.703984 + 0.710216i \(0.251403\pi\)
\(308\) 0 0
\(309\) −3.10962 14.7551i −0.176900 0.839388i
\(310\) 0 0
\(311\) 5.17642 29.3569i 0.293528 1.66468i −0.379598 0.925152i \(-0.623938\pi\)
0.673126 0.739528i \(-0.264951\pi\)
\(312\) 0 0
\(313\) 5.64949 4.74048i 0.319328 0.267948i −0.469007 0.883195i \(-0.655388\pi\)
0.788335 + 0.615247i \(0.210944\pi\)
\(314\) 0 0
\(315\) −0.951529 + 0.912539i −0.0536126 + 0.0514157i
\(316\) 0 0
\(317\) 9.63254 + 3.50596i 0.541017 + 0.196914i 0.598051 0.801458i \(-0.295942\pi\)
−0.0570337 + 0.998372i \(0.518164\pi\)
\(318\) 0 0
\(319\) 0.774591 + 0.649959i 0.0433688 + 0.0363907i
\(320\) 0 0
\(321\) 0.204153 + 0.160072i 0.0113947 + 0.00893434i
\(322\) 0 0
\(323\) 35.7318 1.98817
\(324\) 0 0
\(325\) 0.0822123 0.00456032
\(326\) 0 0
\(327\) −13.6508 10.7032i −0.754888 0.591890i
\(328\) 0 0
\(329\) −1.49277 1.25258i −0.0822990 0.0690571i
\(330\) 0 0
\(331\) 23.6982 + 8.62542i 1.30257 + 0.474096i 0.897832 0.440337i \(-0.145141\pi\)
0.404736 + 0.914433i \(0.367363\pi\)
\(332\) 0 0
\(333\) −23.7245 6.89183i −1.30010 0.377670i
\(334\) 0 0
\(335\) 13.0295 10.9330i 0.711876 0.597335i
\(336\) 0 0
\(337\) −0.600815 + 3.40739i −0.0327285 + 0.185612i −0.996789 0.0800692i \(-0.974486\pi\)
0.964061 + 0.265682i \(0.0855970\pi\)
\(338\) 0 0
\(339\) 4.98151 + 23.6372i 0.270558 + 1.28379i
\(340\) 0 0
\(341\) −7.30105 + 12.6458i −0.395374 + 0.684808i
\(342\) 0 0
\(343\) −1.07874 1.86843i −0.0582465 0.100886i
\(344\) 0 0
\(345\) 9.31284 + 14.9612i 0.501387 + 0.805484i
\(346\) 0 0
\(347\) 21.9683 7.99579i 1.17932 0.429237i 0.323357 0.946277i \(-0.395189\pi\)
0.855961 + 0.517040i \(0.172966\pi\)
\(348\) 0 0
\(349\) −2.94303 16.6908i −0.157537 0.893437i −0.956430 0.291963i \(-0.905692\pi\)
0.798893 0.601474i \(-0.205420\pi\)
\(350\) 0 0
\(351\) −0.113678 0.0775385i −0.00606770 0.00413870i
\(352\) 0 0
\(353\) 1.66836 + 9.46173i 0.0887977 + 0.503597i 0.996472 + 0.0839222i \(0.0267447\pi\)
−0.907675 + 0.419675i \(0.862144\pi\)
\(354\) 0 0
\(355\) −7.26943 + 2.64586i −0.385821 + 0.140427i
\(356\) 0 0
\(357\) −1.53929 + 0.0510868i −0.0814679 + 0.00270380i
\(358\) 0 0
\(359\) 13.3015 + 23.0388i 0.702024 + 1.21594i 0.967755 + 0.251895i \(0.0810536\pi\)
−0.265730 + 0.964047i \(0.585613\pi\)
\(360\) 0 0
\(361\) −9.73971 + 16.8697i −0.512616 + 0.887878i
\(362\) 0 0
\(363\) −22.7711 + 20.4320i −1.19517 + 1.07240i
\(364\) 0 0
\(365\) 7.29343 41.3631i 0.381756 2.16504i
\(366\) 0 0
\(367\) −4.05209 + 3.40011i −0.211518 + 0.177484i −0.742391 0.669967i \(-0.766308\pi\)
0.530874 + 0.847451i \(0.321864\pi\)
\(368\) 0 0
\(369\) −0.158863 + 0.0105565i −0.00827007 + 0.000549548i
\(370\) 0 0
\(371\) 2.01054 + 0.731776i 0.104382 + 0.0379919i
\(372\) 0 0
\(373\) 16.0823 + 13.4947i 0.832711 + 0.698728i 0.955912 0.293654i \(-0.0948714\pi\)
−0.123201 + 0.992382i \(0.539316\pi\)
\(374\) 0 0
\(375\) −8.67209 + 3.48631i −0.447825 + 0.180032i
\(376\) 0 0
\(377\) 0.00500156 0.000257593
\(378\) 0 0
\(379\) −16.5959 −0.852476 −0.426238 0.904611i \(-0.640161\pi\)
−0.426238 + 0.904611i \(0.640161\pi\)
\(380\) 0 0
\(381\) −0.653428 + 4.59172i −0.0334761 + 0.235241i
\(382\) 0 0
\(383\) −9.90918 8.31479i −0.506335 0.424866i 0.353502 0.935434i \(-0.384991\pi\)
−0.859837 + 0.510568i \(0.829435\pi\)
\(384\) 0 0
\(385\) 2.21091 + 0.804704i 0.112678 + 0.0410115i
\(386\) 0 0
\(387\) −19.6532 14.3831i −0.999029 0.731133i
\(388\) 0 0
\(389\) −19.1992 + 16.1100i −0.973438 + 0.816812i −0.983087 0.183142i \(-0.941373\pi\)
0.00964819 + 0.999953i \(0.496929\pi\)
\(390\) 0 0
\(391\) −3.57492 + 20.2744i −0.180791 + 1.02532i
\(392\) 0 0
\(393\) −6.61930 2.16341i −0.333899 0.109130i
\(394\) 0 0
\(395\) −7.21471 + 12.4963i −0.363012 + 0.628755i
\(396\) 0 0
\(397\) −11.8226 20.4773i −0.593359 1.02773i −0.993776 0.111395i \(-0.964468\pi\)
0.400418 0.916333i \(-0.368865\pi\)
\(398\) 0 0
\(399\) 0.781183 1.46308i 0.0391081 0.0732456i
\(400\) 0 0
\(401\) 11.0226 4.01190i 0.550443 0.200345i −0.0518003 0.998657i \(-0.516496\pi\)
0.602243 + 0.798313i \(0.294274\pi\)
\(402\) 0 0
\(403\) 0.0125422 + 0.0711301i 0.000624769 + 0.00354324i
\(404\) 0 0
\(405\) −25.0241 5.50033i −1.24346 0.273314i
\(406\) 0 0
\(407\) 7.65601 + 43.4194i 0.379494 + 2.15222i
\(408\) 0 0
\(409\) 10.3690 3.77401i 0.512715 0.186613i −0.0726893 0.997355i \(-0.523158\pi\)
0.585404 + 0.810742i \(0.300936\pi\)
\(410\) 0 0
\(411\) −0.833747 + 1.56153i −0.0411257 + 0.0770244i
\(412\) 0 0
\(413\) 0.327133 + 0.566611i 0.0160972 + 0.0278811i
\(414\) 0 0
\(415\) 4.41724 7.65088i 0.216834 0.375567i
\(416\) 0 0
\(417\) 21.5670 + 7.04881i 1.05614 + 0.345182i
\(418\) 0 0
\(419\) 0.622392 3.52976i 0.0304058 0.172440i −0.965823 0.259201i \(-0.916541\pi\)
0.996229 + 0.0867614i \(0.0276518\pi\)
\(420\) 0 0
\(421\) 26.6737 22.3819i 1.30000 1.09083i 0.309853 0.950785i \(-0.399720\pi\)
0.990145 0.140043i \(-0.0447241\pi\)
\(422\) 0 0
\(423\) 4.08886 37.6492i 0.198807 1.83057i
\(424\) 0 0
\(425\) 16.8040 + 6.11616i 0.815115 + 0.296677i
\(426\) 0 0
\(427\) −0.563213 0.472592i −0.0272558 0.0228703i
\(428\) 0 0
\(429\) −0.0345974 + 0.243121i −0.00167038 + 0.0117380i
\(430\) 0 0
\(431\) −28.6872 −1.38182 −0.690908 0.722943i \(-0.742789\pi\)
−0.690908 + 0.722943i \(0.742789\pi\)
\(432\) 0 0
\(433\) −14.7618 −0.709407 −0.354703 0.934979i \(-0.615418\pi\)
−0.354703 + 0.934979i \(0.615418\pi\)
\(434\) 0 0
\(435\) 0.864064 0.347367i 0.0414287 0.0166550i
\(436\) 0 0
\(437\) −16.9833 14.2507i −0.812423 0.681704i
\(438\) 0 0
\(439\) −6.35308 2.31233i −0.303216 0.110362i 0.185932 0.982563i \(-0.440470\pi\)
−0.489147 + 0.872201i \(0.662692\pi\)
\(440\) 0 0
\(441\) 9.23949 18.7786i 0.439976 0.894217i
\(442\) 0 0
\(443\) 21.7900 18.2840i 1.03528 0.868700i 0.0438065 0.999040i \(-0.486051\pi\)
0.991469 + 0.130340i \(0.0416070\pi\)
\(444\) 0 0
\(445\) −2.09467 + 11.8795i −0.0992970 + 0.563141i
\(446\) 0 0
\(447\) 9.95845 8.93547i 0.471018 0.422633i
\(448\) 0 0
\(449\) 10.1001 17.4939i 0.476654 0.825589i −0.522988 0.852340i \(-0.675183\pi\)
0.999642 + 0.0267507i \(0.00851603\pi\)
\(450\) 0 0
\(451\) 0.142067 + 0.246067i 0.00668965 + 0.0115868i
\(452\) 0 0
\(453\) −25.9478 + 0.861169i −1.21913 + 0.0404612i
\(454\) 0 0
\(455\) 0.0109360 0.00398036i 0.000512686 0.000186602i
\(456\) 0 0
\(457\) 1.40361 + 7.96027i 0.0656582 + 0.372366i 0.999877 + 0.0156663i \(0.00498693\pi\)
−0.934219 + 0.356700i \(0.883902\pi\)
\(458\) 0 0
\(459\) −17.4671 24.3058i −0.815296 1.13450i
\(460\) 0 0
\(461\) −3.45167 19.5754i −0.160760 0.911717i −0.953329 0.301934i \(-0.902368\pi\)
0.792568 0.609783i \(-0.208743\pi\)
\(462\) 0 0
\(463\) 18.0828 6.58158i 0.840377 0.305872i 0.114266 0.993450i \(-0.463548\pi\)
0.726110 + 0.687578i \(0.241326\pi\)
\(464\) 0 0
\(465\) 7.10688 + 11.4173i 0.329574 + 0.529464i
\(466\) 0 0
\(467\) −1.04526 1.81045i −0.0483690 0.0837776i 0.840827 0.541304i \(-0.182069\pi\)
−0.889196 + 0.457526i \(0.848736\pi\)
\(468\) 0 0
\(469\) 0.461147 0.798729i 0.0212938 0.0368819i
\(470\) 0 0
\(471\) 8.64845 + 41.0368i 0.398500 + 1.89087i
\(472\) 0 0
\(473\) −7.54718 + 42.8022i −0.347020 + 1.96805i
\(474\) 0 0
\(475\) −14.7521 + 12.3785i −0.676874 + 0.567965i
\(476\) 0 0
\(477\) 9.91955 + 40.3799i 0.454185 + 1.84887i
\(478\) 0 0
\(479\) −25.9253 9.43604i −1.18456 0.431143i −0.326748 0.945112i \(-0.605953\pi\)
−0.857809 + 0.513968i \(0.828175\pi\)
\(480\) 0 0
\(481\) 0.167060 + 0.140180i 0.00761728 + 0.00639166i
\(482\) 0 0
\(483\) 0.752000 + 0.589625i 0.0342172 + 0.0268289i
\(484\) 0 0
\(485\) −34.3903 −1.56158
\(486\) 0 0
\(487\) −16.2691 −0.737223 −0.368612 0.929583i \(-0.620167\pi\)
−0.368612 + 0.929583i \(0.620167\pi\)
\(488\) 0 0
\(489\) −18.2011 14.2710i −0.823082 0.645359i
\(490\) 0 0
\(491\) −23.5401 19.7525i −1.06235 0.891418i −0.0680129 0.997684i \(-0.521666\pi\)
−0.994338 + 0.106266i \(0.966110\pi\)
\(492\) 0 0
\(493\) 1.02231 + 0.372089i 0.0460424 + 0.0167581i
\(494\) 0 0
\(495\) 10.9081 + 44.4041i 0.490284 + 1.99582i
\(496\) 0 0
\(497\) −0.321340 + 0.269636i −0.0144141 + 0.0120948i
\(498\) 0 0
\(499\) −0.645667 + 3.66176i −0.0289040 + 0.163923i −0.995843 0.0910844i \(-0.970967\pi\)
0.966939 + 0.255007i \(0.0820778\pi\)
\(500\) 0 0
\(501\) −3.30019 15.6594i −0.147442 0.699609i
\(502\) 0 0
\(503\) −3.24639 + 5.62291i −0.144749 + 0.250713i −0.929279 0.369378i \(-0.879571\pi\)
0.784530 + 0.620091i \(0.212904\pi\)
\(504\) 0 0
\(505\) −13.4040 23.2164i −0.596469 1.03311i
\(506\) 0 0
\(507\) −11.8983 19.1148i −0.528423 0.848918i
\(508\) 0 0
\(509\) 20.6356 7.51076i 0.914659 0.332909i 0.158547 0.987351i \(-0.449319\pi\)
0.756112 + 0.654443i \(0.227097\pi\)
\(510\) 0 0
\(511\) −0.395483 2.24290i −0.0174952 0.0992200i
\(512\) 0 0
\(513\) 32.0731 3.20279i 1.41606 0.141407i
\(514\) 0 0
\(515\) 4.30378 + 24.4079i 0.189647 + 1.07554i
\(516\) 0 0
\(517\) −63.5083 + 23.1151i −2.79309 + 1.01660i
\(518\) 0 0
\(519\) 44.6216 1.48092i 1.95867 0.0650054i
\(520\) 0 0
\(521\) −13.6606 23.6608i −0.598480 1.03660i −0.993046 0.117730i \(-0.962438\pi\)
0.394566 0.918868i \(-0.370895\pi\)
\(522\) 0 0
\(523\) −6.80343 + 11.7839i −0.297493 + 0.515274i −0.975562 0.219725i \(-0.929484\pi\)
0.678069 + 0.734999i \(0.262817\pi\)
\(524\) 0 0
\(525\) 0.617809 0.554345i 0.0269634 0.0241936i
\(526\) 0 0
\(527\) −2.72811 + 15.4719i −0.118839 + 0.673967i
\(528\) 0 0
\(529\) −7.83396 + 6.57347i −0.340607 + 0.285803i
\(530\) 0 0
\(531\) −5.61341 + 11.4088i −0.243601 + 0.495101i
\(532\) 0 0
\(533\) 0.00132067 0.000480684i 5.72045e−5 2.08207e-5i
\(534\) 0 0
\(535\) −0.326639 0.274083i −0.0141218 0.0118496i
\(536\) 0 0
\(537\) −0.364970 + 0.146723i −0.0157496 + 0.00633157i
\(538\) 0 0
\(539\) −37.3492 −1.60874
\(540\) 0 0
\(541\) 19.3887 0.833584 0.416792 0.909002i \(-0.363154\pi\)
0.416792 + 0.909002i \(0.363154\pi\)
\(542\) 0 0
\(543\) 1.85480 13.0339i 0.0795971 0.559339i
\(544\) 0 0
\(545\) 21.8408 + 18.3266i 0.935556 + 0.785025i
\(546\) 0 0
\(547\) 9.85277 + 3.58612i 0.421274 + 0.153331i 0.543954 0.839115i \(-0.316927\pi\)
−0.122680 + 0.992446i \(0.539149\pi\)
\(548\) 0 0
\(549\) 1.54270 14.2048i 0.0658409 0.606246i
\(550\) 0 0
\(551\) −0.897476 + 0.753072i −0.0382338 + 0.0320819i
\(552\) 0 0
\(553\) −0.135868 + 0.770543i −0.00577767 + 0.0327668i
\(554\) 0 0
\(555\) 38.5969 + 12.6148i 1.63835 + 0.535467i
\(556\) 0 0
\(557\) −14.3245 + 24.8107i −0.606947 + 1.05126i 0.384794 + 0.923003i \(0.374273\pi\)
−0.991741 + 0.128260i \(0.959061\pi\)
\(558\) 0 0
\(559\) 0.107491 + 0.186179i 0.00454637 + 0.00787455i
\(560\) 0 0
\(561\) −25.1585 + 47.1195i −1.06219 + 1.98938i
\(562\) 0 0
\(563\) −17.4077 + 6.33587i −0.733646 + 0.267025i −0.681707 0.731625i \(-0.738762\pi\)
−0.0519385 + 0.998650i \(0.516540\pi\)
\(564\) 0 0
\(565\) −6.89452 39.1007i −0.290054 1.64498i
\(566\) 0 0
\(567\) −1.37710 + 0.183829i −0.0578328 + 0.00772009i
\(568\) 0 0
\(569\) 2.20855 + 12.5253i 0.0925873 + 0.525088i 0.995460 + 0.0951806i \(0.0303429\pi\)
−0.902873 + 0.429908i \(0.858546\pi\)
\(570\) 0 0
\(571\) 22.7338 8.27441i 0.951378 0.346273i 0.180729 0.983533i \(-0.442154\pi\)
0.770649 + 0.637260i \(0.219932\pi\)
\(572\) 0 0
\(573\) −3.41510 + 6.39615i −0.142668 + 0.267203i
\(574\) 0 0
\(575\) −5.54768 9.60886i −0.231354 0.400717i
\(576\) 0 0
\(577\) 4.40688 7.63294i 0.183461 0.317764i −0.759596 0.650395i \(-0.774603\pi\)
0.943057 + 0.332632i \(0.107937\pi\)
\(578\) 0 0
\(579\) 0.659670 + 0.215602i 0.0274150 + 0.00896013i
\(580\) 0 0
\(581\) 0.0831855 0.471768i 0.00345111 0.0195722i
\(582\) 0 0
\(583\) 56.8442 47.6979i 2.35425 1.97545i
\(584\) 0 0
\(585\) 0.182514 + 0.133571i 0.00754601 + 0.00552250i
\(586\) 0 0
\(587\) 8.17717 + 2.97625i 0.337508 + 0.122843i 0.505214 0.862994i \(-0.331414\pi\)
−0.167706 + 0.985837i \(0.553636\pi\)
\(588\) 0 0
\(589\) −12.9604 10.8751i −0.534025 0.448101i
\(590\) 0 0
\(591\) 1.73465 12.1896i 0.0713540 0.501414i
\(592\) 0 0
\(593\) 4.83668 0.198619 0.0993094 0.995057i \(-0.468337\pi\)
0.0993094 + 0.995057i \(0.468337\pi\)
\(594\) 0 0
\(595\) 2.53140 0.103777
\(596\) 0 0
\(597\) 35.1150 14.1168i 1.43716 0.577760i
\(598\) 0 0
\(599\) −11.0154 9.24301i −0.450077 0.377659i 0.389388 0.921074i \(-0.372687\pi\)
−0.839464 + 0.543415i \(0.817131\pi\)
\(600\) 0 0
\(601\) −14.2323 5.18014i −0.580548 0.211302i 0.0350189 0.999387i \(-0.488851\pi\)
−0.615567 + 0.788084i \(0.711073\pi\)
\(602\) 0 0
\(603\) 17.8844 1.18842i 0.728310 0.0483964i
\(604\) 0 0
\(605\) 38.5204 32.3225i 1.56608 1.31410i
\(606\) 0 0
\(607\) 1.95372 11.0801i 0.0792991 0.449728i −0.919143 0.393925i \(-0.871117\pi\)
0.998442 0.0558030i \(-0.0177719\pi\)
\(608\) 0 0
\(609\) 0.0375857 0.0337247i 0.00152305 0.00136659i
\(610\) 0 0
\(611\) −0.167148 + 0.289509i −0.00676208 + 0.0117123i
\(612\) 0 0
\(613\) 9.66863 + 16.7466i 0.390512 + 0.676387i 0.992517 0.122105i \(-0.0389646\pi\)
−0.602005 + 0.798492i \(0.705631\pi\)
\(614\) 0 0
\(615\) 0.261542 0.00868019i 0.0105464 0.000350019i
\(616\) 0 0
\(617\) −8.79610 + 3.20152i −0.354118 + 0.128888i −0.512953 0.858417i \(-0.671448\pi\)
0.158835 + 0.987305i \(0.449226\pi\)
\(618\) 0 0
\(619\) −1.37563 7.80157i −0.0552911 0.313571i 0.944602 0.328219i \(-0.106448\pi\)
−0.999893 + 0.0146477i \(0.995337\pi\)
\(620\) 0 0
\(621\) −1.39160 + 18.5188i −0.0558429 + 0.743136i
\(622\) 0 0
\(623\) 0.113583 + 0.644160i 0.00455060 + 0.0258077i
\(624\) 0 0
\(625\) 29.0221 10.5632i 1.16088 0.422527i
\(626\) 0 0
\(627\) −30.3979 48.8347i −1.21398 1.95027i
\(628\) 0 0
\(629\) 23.7181 + 41.0809i 0.945701 + 1.63800i
\(630\) 0 0
\(631\) 11.8744 20.5670i 0.472711 0.818759i −0.526801 0.849988i \(-0.676609\pi\)
0.999512 + 0.0312291i \(0.00994216\pi\)
\(632\) 0 0
\(633\) 3.35661 + 15.9271i 0.133413 + 0.633045i
\(634\) 0 0
\(635\) 1.32373 7.50727i 0.0525308 0.297917i
\(636\) 0 0
\(637\) −0.141521 + 0.118750i −0.00560727 + 0.00470506i
\(638\) 0 0
\(639\) −7.82855 2.27415i −0.309693 0.0899639i
\(640\) 0 0
\(641\) 3.44069 + 1.25231i 0.135899 + 0.0494633i 0.409074 0.912501i \(-0.365852\pi\)
−0.273175 + 0.961964i \(0.588074\pi\)
\(642\) 0 0
\(643\) −8.40157 7.04976i −0.331326 0.278015i 0.461914 0.886925i \(-0.347163\pi\)
−0.793240 + 0.608909i \(0.791607\pi\)
\(644\) 0 0
\(645\) 31.5005 + 24.6988i 1.24033 + 0.972513i
\(646\) 0 0
\(647\) 23.9785 0.942691 0.471346 0.881949i \(-0.343768\pi\)
0.471346 + 0.881949i \(0.343768\pi\)
\(648\) 0 0
\(649\) 22.6913 0.890712
\(650\) 0 0
\(651\) 0.573871 + 0.449958i 0.0224918 + 0.0176353i
\(652\) 0 0
\(653\) 20.8792 + 17.5197i 0.817066 + 0.685600i 0.952283 0.305216i \(-0.0987287\pi\)
−0.135217 + 0.990816i \(0.543173\pi\)
\(654\) 0 0
\(655\) 10.7557 + 3.91475i 0.420259 + 0.152962i
\(656\) 0 0
\(657\) 31.9449 30.6359i 1.24629 1.19522i
\(658\) 0 0
\(659\) −24.4799 + 20.5411i −0.953602 + 0.800167i −0.979900 0.199487i \(-0.936072\pi\)
0.0262987 + 0.999654i \(0.491628\pi\)
\(660\) 0 0
\(661\) 5.11913 29.0320i 0.199111 1.12922i −0.707330 0.706884i \(-0.750100\pi\)
0.906441 0.422332i \(-0.138788\pi\)
\(662\) 0 0
\(663\) 0.0544855 + 0.258533i 0.00211604 + 0.0100406i
\(664\) 0 0
\(665\) −1.36303 + 2.36083i −0.0528560 + 0.0915492i
\(666\) 0 0
\(667\) −0.337504 0.584575i −0.0130682 0.0226348i
\(668\) 0 0
\(669\) 12.7579 + 20.4957i 0.493249 + 0.792410i
\(670\) 0 0
\(671\) −23.9613 + 8.72119i −0.925015 + 0.336678i
\(672\) 0 0
\(673\) −4.96715 28.1701i −0.191470 1.08588i −0.917357 0.398065i \(-0.869682\pi\)
0.725887 0.687814i \(-0.241429\pi\)
\(674\) 0 0
\(675\) 15.6316 + 3.98370i 0.601662 + 0.153333i
\(676\) 0 0
\(677\) 3.84630 + 21.8134i 0.147825 + 0.838358i 0.965055 + 0.262047i \(0.0843974\pi\)
−0.817230 + 0.576312i \(0.804491\pi\)
\(678\) 0 0
\(679\) −1.75234 + 0.637799i −0.0672486 + 0.0244765i
\(680\) 0 0
\(681\) −29.9557 + 0.994186i −1.14791 + 0.0380973i
\(682\) 0 0
\(683\) −7.20724 12.4833i −0.275777 0.477660i 0.694554 0.719441i \(-0.255602\pi\)
−0.970331 + 0.241781i \(0.922269\pi\)
\(684\) 0 0
\(685\) 1.45474 2.51969i 0.0555828 0.0962723i
\(686\) 0 0
\(687\) 14.8062 13.2853i 0.564893 0.506865i
\(688\) 0 0
\(689\) 0.0637366 0.361468i 0.00242817 0.0137708i
\(690\) 0 0
\(691\) 2.16578 1.81731i 0.0823903 0.0691337i −0.600662 0.799503i \(-0.705096\pi\)
0.683053 + 0.730369i \(0.260652\pi\)
\(692\) 0 0
\(693\) 1.37933 + 2.06029i 0.0523965 + 0.0782639i
\(694\) 0 0
\(695\) −35.0441 12.7550i −1.32930 0.483825i
\(696\) 0 0
\(697\) 0.234182 + 0.196502i 0.00887026 + 0.00744303i
\(698\) 0 0
\(699\) 1.77703 0.714393i 0.0672135 0.0270208i
\(700\) 0 0
\(701\) −0.0227913 −0.000860816 −0.000430408 1.00000i \(-0.500137\pi\)
−0.000430408 1.00000i \(0.500137\pi\)
\(702\) 0 0
\(703\) −51.0837 −1.92666
\(704\) 0 0
\(705\) −8.76944 + 61.6240i −0.330276 + 2.32089i
\(706\) 0 0
\(707\) −1.11356 0.934388i −0.0418798 0.0351413i
\(708\) 0 0
\(709\) 7.89357 + 2.87303i 0.296449 + 0.107899i 0.485963 0.873979i \(-0.338469\pi\)
−0.189514 + 0.981878i \(0.560691\pi\)
\(710\) 0 0
\(711\) −13.9125 + 6.13663i −0.521759 + 0.230142i
\(712\) 0 0
\(713\) 7.46724 6.26576i 0.279650 0.234654i
\(714\) 0 0
\(715\) 0.0700885 0.397492i 0.00262116 0.0148653i
\(716\) 0 0
\(717\) −2.05225 0.670745i −0.0766427 0.0250494i
\(718\) 0 0
\(719\) 18.8705 32.6847i 0.703753 1.21894i −0.263387 0.964690i \(-0.584840\pi\)
0.967140 0.254245i \(-0.0818269\pi\)
\(720\) 0 0
\(721\) 0.671964 + 1.16388i 0.0250253 + 0.0433450i
\(722\) 0 0
\(723\) 21.7472 40.7304i 0.808788 1.51478i
\(724\) 0 0
\(725\) −0.550969 + 0.200536i −0.0204625 + 0.00744773i
\(726\) 0 0
\(727\) 7.62408 + 43.2383i 0.282761 + 1.60362i 0.713174 + 0.700987i \(0.247257\pi\)
−0.430413 + 0.902632i \(0.641632\pi\)
\(728\) 0 0
\(729\) −17.8573 20.2514i −0.661380 0.750051i
\(730\) 0 0
\(731\) 8.12011 + 46.0514i 0.300333 + 1.70327i
\(732\) 0 0
\(733\) −41.1023 + 14.9600i −1.51815 + 0.552560i −0.960684 0.277642i \(-0.910447\pi\)
−0.557462 + 0.830203i \(0.688225\pi\)
\(734\) 0 0
\(735\) −16.2017 + 30.3441i −0.597607 + 1.11926i
\(736\) 0 0
\(737\) −15.9935 27.7016i −0.589130 1.02040i
\(738\) 0 0
\(739\) −5.73565 + 9.93444i −0.210989 + 0.365444i −0.952024 0.306022i \(-0.901002\pi\)
0.741035 + 0.671466i \(0.234335\pi\)
\(740\) 0 0
\(741\) −0.270450 0.0883921i −0.00993523 0.00324717i
\(742\) 0 0
\(743\) −1.09070 + 6.18567i −0.0400139 + 0.226930i −0.998256 0.0590266i \(-0.981200\pi\)
0.958242 + 0.285957i \(0.0923114\pi\)
\(744\) 0 0
\(745\) −16.8461 + 14.1355i −0.617192 + 0.517885i
\(746\) 0 0
\(747\) 8.51797 3.75718i 0.311656 0.137468i
\(748\) 0 0
\(749\) −0.0217268 0.00790792i −0.000793881 0.000288949i
\(750\) 0 0
\(751\) −6.91154 5.79947i −0.252206 0.211626i 0.507916 0.861407i \(-0.330416\pi\)
−0.760121 + 0.649781i \(0.774861\pi\)
\(752\) 0 0
\(753\) −4.27300 + 30.0269i −0.155717 + 1.09424i
\(754\) 0 0
\(755\) 42.6718 1.55299
\(756\) 0 0
\(757\) 37.3499 1.35751 0.678753 0.734367i \(-0.262521\pi\)
0.678753 + 0.734367i \(0.262521\pi\)
\(758\) 0 0
\(759\) 30.7502 12.3620i 1.11616 0.448714i
\(760\) 0 0
\(761\) −18.8028 15.7774i −0.681601 0.571931i 0.234872 0.972026i \(-0.424533\pi\)
−0.916474 + 0.400095i \(0.868977\pi\)
\(762\) 0 0
\(763\) 1.45277 + 0.528764i 0.0525937 + 0.0191425i
\(764\) 0 0
\(765\) 27.3684 + 40.8798i 0.989507 + 1.47801i
\(766\) 0 0
\(767\) 0.0859805 0.0721462i 0.00310458 0.00260505i
\(768\) 0 0
\(769\) 2.87291 16.2931i 0.103600 0.587543i −0.888171 0.459514i \(-0.848024\pi\)
0.991770 0.128030i \(-0.0408652\pi\)
\(770\) 0 0
\(771\) −14.6363 + 13.1328i −0.527114 + 0.472967i
\(772\) 0 0
\(773\) −9.29539 + 16.1001i −0.334332 + 0.579080i −0.983356 0.181688i \(-0.941844\pi\)
0.649024 + 0.760768i \(0.275177\pi\)
\(774\) 0 0
\(775\) −4.23358 7.33278i −0.152075 0.263401i
\(776\) 0 0
\(777\) 2.20064 0.0730358i 0.0789474 0.00262014i
\(778\) 0 0
\(779\) −0.309356 + 0.112596i −0.0110838 + 0.00403418i
\(780\) 0 0
\(781\) 2.52631 + 14.3274i 0.0903985 + 0.512675i
\(782\) 0 0
\(783\) 0.950982 + 0.242356i 0.0339853 + 0.00866111i
\(784\) 0 0
\(785\) −11.9697 67.8833i −0.427215 2.42286i
\(786\) 0 0
\(787\) 21.2388 7.73030i 0.757082 0.275555i 0.0654995 0.997853i \(-0.479136\pi\)
0.691583 + 0.722297i \(0.256914\pi\)
\(788\) 0 0
\(789\) −12.0581 19.3715i −0.429280 0.689643i
\(790\) 0 0
\(791\) −1.07646 1.86449i −0.0382747 0.0662937i
\(792\) 0 0
\(793\) −0.0630639 + 0.109230i −0.00223946 + 0.00387886i
\(794\) 0 0
\(795\) −14.0935 66.8735i −0.499845 2.37176i
\(796\) 0 0
\(797\) 2.87762 16.3198i 0.101930 0.578076i −0.890472 0.455039i \(-0.849625\pi\)
0.992402 0.123037i \(-0.0392635\pi\)
\(798\) 0 0
\(799\) −55.7026 + 46.7400i −1.97062 + 1.65354i
\(800\) 0 0
\(801\) −9.17456 + 8.79862i −0.324167 + 0.310884i
\(802\) 0 0
\(803\) −74.2249 27.0157i −2.61934 0.953362i
\(804\) 0 0
\(805\) −1.20318 1.00958i −0.0424064 0.0355832i
\(806\) 0 0
\(807\) 2.05238 + 1.60922i 0.0722473 + 0.0566474i
\(808\) 0 0
\(809\) 9.21641 0.324032 0.162016 0.986788i \(-0.448200\pi\)
0.162016 + 0.986788i \(0.448200\pi\)
\(810\) 0 0
\(811\) 33.0857 1.16180 0.580898 0.813976i \(-0.302701\pi\)
0.580898 + 0.813976i \(0.302701\pi\)
\(812\) 0 0
\(813\) −35.0301 27.4662i −1.22856 0.963282i
\(814\) 0 0
\(815\) 29.1212 + 24.4356i 1.02007 + 0.855941i
\(816\) 0 0
\(817\) −47.3207 17.2233i −1.65554 0.602567i
\(818\) 0 0
\(819\) 0.0117771 + 0.00342118i 0.000411525 + 0.000119546i
\(820\) 0 0
\(821\) −21.7195 + 18.2249i −0.758017 + 0.636052i −0.937610 0.347689i \(-0.886966\pi\)
0.179593 + 0.983741i \(0.442522\pi\)
\(822\) 0 0
\(823\) −0.223793 + 1.26919i −0.00780092 + 0.0442412i −0.988460 0.151484i \(-0.951595\pi\)
0.980659 + 0.195725i \(0.0627060\pi\)
\(824\) 0 0
\(825\) −5.93663 28.1692i −0.206687 0.980726i
\(826\) 0 0
\(827\) −21.3919 + 37.0519i −0.743870 + 1.28842i 0.206850 + 0.978373i \(0.433679\pi\)
−0.950721 + 0.310049i \(0.899655\pi\)
\(828\) 0 0
\(829\) 14.1816 + 24.5632i 0.492547 + 0.853116i 0.999963 0.00858516i \(-0.00273277\pi\)
−0.507417 + 0.861701i \(0.669399\pi\)
\(830\) 0 0
\(831\) −7.41754 11.9164i −0.257312 0.413375i
\(832\) 0 0
\(833\) −37.7610 + 13.7439i −1.30834 + 0.476198i
\(834\) 0 0
\(835\) 4.56754 + 25.9038i 0.158066 + 0.896438i
\(836\) 0 0
\(837\) −1.06196 + 14.1322i −0.0367069 + 0.488481i
\(838\) 0 0
\(839\) 0.381436 + 2.16323i 0.0131686 + 0.0746830i 0.990684 0.136182i \(-0.0434831\pi\)
−0.977515 + 0.210865i \(0.932372\pi\)
\(840\) 0 0
\(841\) 27.2176 9.90638i 0.938537 0.341599i
\(842\) 0 0
\(843\) 27.3110 0.906410i 0.940639 0.0312184i
\(844\) 0 0
\(845\) 18.5034 + 32.0489i 0.636537 + 1.10251i
\(846\) 0 0
\(847\) 1.36334 2.36137i 0.0468448 0.0811376i
\(848\) 0 0
\(849\) 20.7266 18.5975i 0.711336 0.638264i
\(850\) 0 0
\(851\) 5.11085 28.9851i 0.175198 0.993595i
\(852\) 0 0
\(853\) −3.50247 + 2.93892i −0.119922 + 0.100627i −0.700777 0.713381i \(-0.747163\pi\)
0.580854 + 0.814008i \(0.302719\pi\)
\(854\) 0 0
\(855\) −52.8617 + 3.51267i −1.80783 + 0.120131i
\(856\) 0 0
\(857\) 21.1746 + 7.70694i 0.723312 + 0.263264i 0.677331 0.735678i \(-0.263136\pi\)
0.0459809 + 0.998942i \(0.485359\pi\)
\(858\) 0 0
\(859\) 35.7935 + 30.0343i 1.22126 + 1.02476i 0.998758 + 0.0498252i \(0.0158664\pi\)
0.222501 + 0.974933i \(0.428578\pi\)
\(860\) 0 0
\(861\) 0.0131657 0.00529283i 0.000448687 0.000180379i
\(862\) 0 0
\(863\) 7.31841 0.249122 0.124561 0.992212i \(-0.460248\pi\)
0.124561 + 0.992212i \(0.460248\pi\)
\(864\) 0 0
\(865\) −73.3814 −2.49504
\(866\) 0 0
\(867\) −3.94838 + 27.7458i −0.134094 + 0.942296i
\(868\) 0 0
\(869\) 20.7876 + 17.4429i 0.705172 + 0.591710i
\(870\) 0 0
\(871\) −0.148678 0.0541144i −0.00503776 0.00183360i
\(872\) 0 0
\(873\) −29.2454 21.4030i −0.989805 0.724382i
\(874\) 0 0
\(875\) 0.638127 0.535452i 0.0215726 0.0181016i
\(876\) 0 0
\(877\) −6.19410 + 35.1285i −0.209160 + 1.18621i 0.681598 + 0.731727i \(0.261285\pi\)
−0.890758 + 0.454478i \(0.849826\pi\)
\(878\) 0 0
\(879\) −20.7738 6.78958i −0.700683 0.229007i
\(880\) 0 0
\(881\) 4.44794 7.70406i 0.149855 0.259556i −0.781319 0.624132i \(-0.785453\pi\)
0.931174 + 0.364576i \(0.118786\pi\)
\(882\) 0 0
\(883\) 20.3831 + 35.3046i 0.685947 + 1.18809i 0.973138 + 0.230221i \(0.0739451\pi\)
−0.287192 + 0.957873i \(0.592722\pi\)
\(884\) 0 0
\(885\) 9.84324 18.4354i 0.330877 0.619700i
\(886\) 0 0
\(887\) 17.3762 6.32442i 0.583436 0.212353i −0.0334041 0.999442i \(-0.510635\pi\)
0.616840 + 0.787089i \(0.288413\pi\)
\(888\) 0 0
\(889\) −0.0717789 0.407079i −0.00240739 0.0136530i
\(890\) 0 0
\(891\) −18.3590 + 44.5498i −0.615049 + 1.49248i
\(892\) 0 0
\(893\) −13.5977 77.1163i −0.455029 2.58060i
\(894\) 0 0
\(895\) 0.607540 0.221127i 0.0203078 0.00739145i
\(896\) 0 0
\(897\) 0.0772121 0.144611i 0.00257804 0.00482841i
\(898\) 0 0
\(899\) −0.257559 0.446104i −0.00859006 0.0148784i
\(900\) 0 0
\(901\) 39.9189 69.1416i 1.32989 2.30344i
\(902\) 0 0
\(903\) 2.06315 + 0.674307i 0.0686574 + 0.0224395i
\(904\) 0 0
\(905\) −3.75751 + 21.3099i −0.124904 + 0.708365i
\(906\) 0 0
\(907\) −21.3031 + 17.8754i −0.707357 + 0.593543i −0.923856 0.382740i \(-0.874981\pi\)
0.216499 + 0.976283i \(0.430536\pi\)
\(908\) 0 0
\(909\) 3.05017 28.0851i 0.101168 0.931525i
\(910\) 0 0
\(911\) 27.4572 + 9.99359i 0.909696 + 0.331102i 0.754132 0.656723i \(-0.228058\pi\)
0.155565 + 0.987826i \(0.450280\pi\)
\(912\) 0 0
\(913\) −12.7273 10.6795i −0.421213 0.353439i
\(914\) 0 0
\(915\) −3.30866 + 23.2503i −0.109381 + 0.768633i
\(916\) 0 0
\(917\) 0.620652 0.0204957
\(918\) 0 0
\(919\) −34.4464 −1.13628 −0.568140 0.822932i \(-0.692337\pi\)
−0.568140 + 0.822932i \(0.692337\pi\)
\(920\) 0 0
\(921\) 14.8151 5.95591i 0.488175 0.196254i
\(922\) 0 0
\(923\) 0.0551260 + 0.0462562i 0.00181450 + 0.00152254i
\(924\) 0 0
\(925\) −24.0237 8.74392i −0.789895 0.287498i
\(926\) 0 0
\(927\) −11.5305 + 23.4349i −0.378712 + 0.769703i
\(928\) 0 0
\(929\) 7.95774 6.67733i 0.261085 0.219076i −0.502843 0.864378i \(-0.667713\pi\)
0.763928 + 0.645301i \(0.223268\pi\)
\(930\) 0 0
\(931\) 7.51453 42.6170i 0.246279 1.39672i
\(932\) 0 0
\(933\) −38.4299 + 34.4822i −1.25814 + 1.12890i
\(934\) 0 0
\(935\) 43.8972 76.0322i 1.43559 2.48652i
\(936\) 0 0
\(937\) 24.9638 + 43.2386i 0.815533 + 1.41254i 0.908945 + 0.416917i \(0.136889\pi\)
−0.0934120 + 0.995628i \(0.529777\pi\)
\(938\) 0 0
\(939\) −12.7666 + 0.423706i −0.416624 + 0.0138271i
\(940\) 0 0
\(941\) 40.0988 14.5948i 1.30718 0.475776i 0.407853 0.913047i \(-0.366277\pi\)
0.899329 + 0.437272i \(0.144055\pi\)
\(942\) 0 0
\(943\) −0.0329369 0.186794i −0.00107257 0.00608286i
\(944\) 0 0
\(945\) 2.27221 0.226900i 0.0739149 0.00738106i
\(946\) 0 0
\(947\) 0.101817 + 0.577431i 0.00330860 + 0.0187640i 0.986417 0.164258i \(-0.0525231\pi\)
−0.983109 + 0.183022i \(0.941412\pi\)
\(948\) 0 0
\(949\) −0.367144 + 0.133629i −0.0119180 + 0.00433779i
\(950\) 0 0
\(951\) −9.38254 15.0732i −0.304250 0.488781i
\(952\) 0 0
\(953\) 1.20182 + 2.08161i 0.0389307 + 0.0674299i 0.884834 0.465906i \(-0.154272\pi\)
−0.845904 + 0.533336i \(0.820938\pi\)
\(954\) 0 0
\(955\) 5.95876 10.3209i 0.192821 0.333975i
\(956\) 0 0
\(957\) −0.361167 1.71373i −0.0116749 0.0553971i
\(958\) 0 0
\(959\) 0.0273957 0.155369i 0.000884653 0.00501712i
\(960\) 0 0
\(961\) −18.0489 + 15.1449i −0.582224 + 0.488544i
\(962\) 0 0
\(963\) −0.107195 0.436365i −0.00345432 0.0140617i
\(964\) 0 0
\(965\) −1.07190 0.390138i −0.0345056 0.0125590i
\(966\) 0 0
\(967\) −14.5185 12.1825i −0.466885 0.391763i 0.378772 0.925490i \(-0.376346\pi\)
−0.845657 + 0.533727i \(0.820791\pi\)
\(968\) 0 0
\(969\) −48.7035 38.1872i −1.56458 1.22675i
\(970\) 0 0
\(971\) 41.3490 1.32695 0.663476 0.748197i \(-0.269080\pi\)
0.663476 + 0.748197i \(0.269080\pi\)
\(972\) 0 0
\(973\) −2.02220 −0.0648289
\(974\) 0 0
\(975\) −0.112058 0.0878617i −0.00358872 0.00281383i
\(976\) 0 0
\(977\) 27.1804 + 22.8070i 0.869577 + 0.729662i 0.964009 0.265869i \(-0.0856590\pi\)
−0.0944318 + 0.995531i \(0.530103\pi\)
\(978\) 0 0
\(979\) 21.3174 + 7.75889i 0.681306 + 0.247975i
\(980\) 0 0
\(981\) 7.16763 + 29.1776i 0.228845 + 0.931569i
\(982\) 0 0
\(983\) 2.64290 2.21765i 0.0842954 0.0707322i −0.599666 0.800250i \(-0.704700\pi\)
0.683962 + 0.729518i \(0.260256\pi\)
\(984\) 0 0
\(985\) −3.51411 + 19.9295i −0.111969 + 0.635006i
\(986\) 0 0
\(987\) 0.696030 + 3.30265i 0.0221549 + 0.105125i
\(988\) 0 0
\(989\) 14.5069 25.1267i 0.461293 0.798984i
\(990\) 0 0
\(991\) 11.1010 + 19.2275i 0.352636 + 0.610783i 0.986710 0.162489i \(-0.0519522\pi\)
−0.634075 + 0.773272i \(0.718619\pi\)
\(992\) 0 0
\(993\) −23.0831 37.0833i −0.732520 1.17680i
\(994\) 0 0
\(995\) −58.4536 + 21.2754i −1.85310 + 0.674475i
\(996\) 0 0
\(997\) 7.06268 + 40.0545i 0.223677 + 1.26854i 0.865197 + 0.501431i \(0.167193\pi\)
−0.641520 + 0.767106i \(0.721696\pi\)
\(998\) 0 0
\(999\) 24.9717 + 34.7485i 0.790071 + 1.09940i
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 216.2.q.b.121.1 yes 30
3.2 odd 2 648.2.q.b.577.1 30
4.3 odd 2 432.2.u.f.337.5 30
27.2 odd 18 648.2.q.b.73.1 30
27.5 odd 18 5832.2.a.l.1.4 15
27.22 even 9 5832.2.a.k.1.12 15
27.25 even 9 inner 216.2.q.b.25.1 30
108.79 odd 18 432.2.u.f.241.5 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.q.b.25.1 30 27.25 even 9 inner
216.2.q.b.121.1 yes 30 1.1 even 1 trivial
432.2.u.f.241.5 30 108.79 odd 18
432.2.u.f.337.5 30 4.3 odd 2
648.2.q.b.73.1 30 27.2 odd 18
648.2.q.b.577.1 30 3.2 odd 2
5832.2.a.k.1.12 15 27.22 even 9
5832.2.a.l.1.4 15 27.5 odd 18