Properties

Label 1155.2.c.e.694.20
Level $1155$
Weight $2$
Character 1155.694
Analytic conductor $9.223$
Analytic rank $0$
Dimension $20$
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] = [1155,2,Mod(694,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.694");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.c (of order \(2\), degree \(1\), 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: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + 15624 x^{4} + 2116 x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 694.20
Root \(2.74619i\) of defining polynomial
Character \(\chi\) \(=\) 1155.694
Dual form 1155.2.c.e.694.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.74619i q^{2} -1.00000i q^{3} -5.54154 q^{4} +(2.23561 - 0.0452669i) q^{5} +2.74619 q^{6} +1.00000i q^{7} -9.72574i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+2.74619i q^{2} -1.00000i q^{3} -5.54154 q^{4} +(2.23561 - 0.0452669i) q^{5} +2.74619 q^{6} +1.00000i q^{7} -9.72574i q^{8} -1.00000 q^{9} +(0.124311 + 6.13940i) q^{10} -1.00000 q^{11} +5.54154i q^{12} -0.748249i q^{13} -2.74619 q^{14} +(-0.0452669 - 2.23561i) q^{15} +15.6256 q^{16} +6.15353i q^{17} -2.74619i q^{18} +1.43933 q^{19} +(-12.3887 + 0.250849i) q^{20} +1.00000 q^{21} -2.74619i q^{22} +5.82872i q^{23} -9.72574 q^{24} +(4.99590 - 0.202398i) q^{25} +2.05483 q^{26} +1.00000i q^{27} -5.54154i q^{28} +0.913059 q^{29} +(6.13940 - 0.124311i) q^{30} +2.25971 q^{31} +23.4594i q^{32} +1.00000i q^{33} -16.8987 q^{34} +(0.0452669 + 2.23561i) q^{35} +5.54154 q^{36} +3.26260i q^{37} +3.95267i q^{38} -0.748249 q^{39} +(-0.440254 - 21.7430i) q^{40} -11.5056 q^{41} +2.74619i q^{42} +9.99697i q^{43} +5.54154 q^{44} +(-2.23561 + 0.0452669i) q^{45} -16.0068 q^{46} +8.43122i q^{47} -15.6256i q^{48} -1.00000 q^{49} +(0.555824 + 13.7197i) q^{50} +6.15353 q^{51} +4.14645i q^{52} +5.64500i q^{53} -2.74619 q^{54} +(-2.23561 + 0.0452669i) q^{55} +9.72574 q^{56} -1.43933i q^{57} +2.50743i q^{58} +4.37632 q^{59} +(0.250849 + 12.3887i) q^{60} -9.75318 q^{61} +6.20558i q^{62} -1.00000i q^{63} -33.1726 q^{64} +(-0.0338709 - 1.67279i) q^{65} -2.74619 q^{66} -6.69285i q^{67} -34.1000i q^{68} +5.82872 q^{69} +(-6.13940 + 0.124311i) q^{70} +10.8314 q^{71} +9.72574i q^{72} -3.60606i q^{73} -8.95972 q^{74} +(-0.202398 - 4.99590i) q^{75} -7.97612 q^{76} -1.00000i q^{77} -2.05483i q^{78} +10.6281 q^{79} +(34.9328 - 0.707323i) q^{80} +1.00000 q^{81} -31.5965i q^{82} -13.4443i q^{83} -5.54154 q^{84} +(0.278551 + 13.7569i) q^{85} -27.4535 q^{86} -0.913059i q^{87} +9.72574i q^{88} +5.61820 q^{89} +(-0.124311 - 6.13940i) q^{90} +0.748249 q^{91} -32.3001i q^{92} -2.25971i q^{93} -23.1537 q^{94} +(3.21778 - 0.0651541i) q^{95} +23.4594 q^{96} +14.0142i q^{97} -2.74619i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.74619i 1.94185i 0.239389 + 0.970924i \(0.423053\pi\)
−0.239389 + 0.970924i \(0.576947\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −5.54154 −2.77077
\(5\) 2.23561 0.0452669i 0.999795 0.0202440i
\(6\) 2.74619 1.12113
\(7\) 1.00000i 0.377964i
\(8\) 9.72574i 3.43857i
\(9\) −1.00000 −0.333333
\(10\) 0.124311 + 6.13940i 0.0393107 + 1.94145i
\(11\) −1.00000 −0.301511
\(12\) 5.54154i 1.59971i
\(13\) 0.748249i 0.207527i −0.994602 0.103763i \(-0.966911\pi\)
0.994602 0.103763i \(-0.0330885\pi\)
\(14\) −2.74619 −0.733949
\(15\) −0.0452669 2.23561i −0.0116879 0.577232i
\(16\) 15.6256 3.90640
\(17\) 6.15353i 1.49245i 0.665694 + 0.746225i \(0.268136\pi\)
−0.665694 + 0.746225i \(0.731864\pi\)
\(18\) 2.74619i 0.647282i
\(19\) 1.43933 0.330205 0.165103 0.986276i \(-0.447204\pi\)
0.165103 + 0.986276i \(0.447204\pi\)
\(20\) −12.3887 + 0.250849i −2.77020 + 0.0560914i
\(21\) 1.00000 0.218218
\(22\) 2.74619i 0.585489i
\(23\) 5.82872i 1.21537i 0.794177 + 0.607686i \(0.207902\pi\)
−0.794177 + 0.607686i \(0.792098\pi\)
\(24\) −9.72574 −1.98526
\(25\) 4.99590 0.202398i 0.999180 0.0404797i
\(26\) 2.05483 0.402986
\(27\) 1.00000i 0.192450i
\(28\) 5.54154i 1.04725i
\(29\) 0.913059 0.169551 0.0847754 0.996400i \(-0.472983\pi\)
0.0847754 + 0.996400i \(0.472983\pi\)
\(30\) 6.13940 0.124311i 1.12090 0.0226961i
\(31\) 2.25971 0.405856 0.202928 0.979194i \(-0.434954\pi\)
0.202928 + 0.979194i \(0.434954\pi\)
\(32\) 23.4594i 4.14707i
\(33\) 1.00000i 0.174078i
\(34\) −16.8987 −2.89811
\(35\) 0.0452669 + 2.23561i 0.00765151 + 0.377887i
\(36\) 5.54154 0.923590
\(37\) 3.26260i 0.536369i 0.963368 + 0.268184i \(0.0864236\pi\)
−0.963368 + 0.268184i \(0.913576\pi\)
\(38\) 3.95267i 0.641208i
\(39\) −0.748249 −0.119816
\(40\) −0.440254 21.7430i −0.0696103 3.43786i
\(41\) −11.5056 −1.79687 −0.898437 0.439103i \(-0.855296\pi\)
−0.898437 + 0.439103i \(0.855296\pi\)
\(42\) 2.74619i 0.423746i
\(43\) 9.99697i 1.52452i 0.647269 + 0.762262i \(0.275911\pi\)
−0.647269 + 0.762262i \(0.724089\pi\)
\(44\) 5.54154 0.835419
\(45\) −2.23561 + 0.0452669i −0.333265 + 0.00674799i
\(46\) −16.0068 −2.36007
\(47\) 8.43122i 1.22982i 0.788597 + 0.614910i \(0.210808\pi\)
−0.788597 + 0.614910i \(0.789192\pi\)
\(48\) 15.6256i 2.25536i
\(49\) −1.00000 −0.142857
\(50\) 0.555824 + 13.7197i 0.0786053 + 1.94026i
\(51\) 6.15353 0.861666
\(52\) 4.14645i 0.575010i
\(53\) 5.64500i 0.775400i 0.921786 + 0.387700i \(0.126730\pi\)
−0.921786 + 0.387700i \(0.873270\pi\)
\(54\) −2.74619 −0.373709
\(55\) −2.23561 + 0.0452669i −0.301450 + 0.00610379i
\(56\) 9.72574 1.29966
\(57\) 1.43933i 0.190644i
\(58\) 2.50743i 0.329242i
\(59\) 4.37632 0.569748 0.284874 0.958565i \(-0.408048\pi\)
0.284874 + 0.958565i \(0.408048\pi\)
\(60\) 0.250849 + 12.3887i 0.0323844 + 1.59938i
\(61\) −9.75318 −1.24877 −0.624383 0.781118i \(-0.714650\pi\)
−0.624383 + 0.781118i \(0.714650\pi\)
\(62\) 6.20558i 0.788110i
\(63\) 1.00000i 0.125988i
\(64\) −33.1726 −4.14657
\(65\) −0.0338709 1.67279i −0.00420117 0.207484i
\(66\) −2.74619 −0.338032
\(67\) 6.69285i 0.817661i −0.912610 0.408831i \(-0.865937\pi\)
0.912610 0.408831i \(-0.134063\pi\)
\(68\) 34.1000i 4.13524i
\(69\) 5.82872 0.701696
\(70\) −6.13940 + 0.124311i −0.733799 + 0.0148581i
\(71\) 10.8314 1.28545 0.642726 0.766096i \(-0.277803\pi\)
0.642726 + 0.766096i \(0.277803\pi\)
\(72\) 9.72574i 1.14619i
\(73\) 3.60606i 0.422057i −0.977480 0.211028i \(-0.932319\pi\)
0.977480 0.211028i \(-0.0676813\pi\)
\(74\) −8.95972 −1.04155
\(75\) −0.202398 4.99590i −0.0233709 0.576877i
\(76\) −7.97612 −0.914923
\(77\) 1.00000i 0.113961i
\(78\) 2.05483i 0.232664i
\(79\) 10.6281 1.19575 0.597877 0.801588i \(-0.296011\pi\)
0.597877 + 0.801588i \(0.296011\pi\)
\(80\) 34.9328 0.707323i 3.90560 0.0790811i
\(81\) 1.00000 0.111111
\(82\) 31.5965i 3.48925i
\(83\) 13.4443i 1.47571i −0.674961 0.737854i \(-0.735839\pi\)
0.674961 0.737854i \(-0.264161\pi\)
\(84\) −5.54154 −0.604632
\(85\) 0.278551 + 13.7569i 0.0302131 + 1.49214i
\(86\) −27.4535 −2.96039
\(87\) 0.913059i 0.0978902i
\(88\) 9.72574i 1.03677i
\(89\) 5.61820 0.595528 0.297764 0.954640i \(-0.403759\pi\)
0.297764 + 0.954640i \(0.403759\pi\)
\(90\) −0.124311 6.13940i −0.0131036 0.647150i
\(91\) 0.748249 0.0784378
\(92\) 32.3001i 3.36752i
\(93\) 2.25971i 0.234321i
\(94\) −23.1537 −2.38812
\(95\) 3.21778 0.0651541i 0.330138 0.00668467i
\(96\) 23.4594 2.39431
\(97\) 14.0142i 1.42293i 0.702723 + 0.711464i \(0.251967\pi\)
−0.702723 + 0.711464i \(0.748033\pi\)
\(98\) 2.74619i 0.277407i
\(99\) 1.00000 0.100504
\(100\) −27.6850 + 1.12160i −2.76850 + 0.112160i
\(101\) −2.63227 −0.261921 −0.130960 0.991388i \(-0.541806\pi\)
−0.130960 + 0.991388i \(0.541806\pi\)
\(102\) 16.8987i 1.67322i
\(103\) 0.913885i 0.0900478i −0.998986 0.0450239i \(-0.985664\pi\)
0.998986 0.0450239i \(-0.0143364\pi\)
\(104\) −7.27727 −0.713596
\(105\) 2.23561 0.0452669i 0.218173 0.00441760i
\(106\) −15.5022 −1.50571
\(107\) 12.1001i 1.16976i −0.811121 0.584879i \(-0.801142\pi\)
0.811121 0.584879i \(-0.198858\pi\)
\(108\) 5.54154i 0.533235i
\(109\) −20.2083 −1.93561 −0.967803 0.251707i \(-0.919008\pi\)
−0.967803 + 0.251707i \(0.919008\pi\)
\(110\) −0.124311 6.13940i −0.0118526 0.585369i
\(111\) 3.26260 0.309673
\(112\) 15.6256i 1.47648i
\(113\) 0.0930496i 0.00875337i −0.999990 0.00437669i \(-0.998607\pi\)
0.999990 0.00437669i \(-0.00139315\pi\)
\(114\) 3.95267 0.370202
\(115\) 0.263848 + 13.0307i 0.0246040 + 1.21512i
\(116\) −5.05975 −0.469786
\(117\) 0.748249i 0.0691757i
\(118\) 12.0182i 1.10636i
\(119\) −6.15353 −0.564093
\(120\) −21.7430 + 0.440254i −1.98485 + 0.0401895i
\(121\) 1.00000 0.0909091
\(122\) 26.7840i 2.42491i
\(123\) 11.5056i 1.03743i
\(124\) −12.5223 −1.12453
\(125\) 11.1597 0.678633i 0.998156 0.0606988i
\(126\) 2.74619 0.244650
\(127\) 14.7548i 1.30928i −0.755941 0.654640i \(-0.772820\pi\)
0.755941 0.654640i \(-0.227180\pi\)
\(128\) 44.1794i 3.90494i
\(129\) 9.99697 0.880184
\(130\) 4.59380 0.0930159i 0.402903 0.00815804i
\(131\) 16.5007 1.44168 0.720838 0.693104i \(-0.243757\pi\)
0.720838 + 0.693104i \(0.243757\pi\)
\(132\) 5.54154i 0.482329i
\(133\) 1.43933i 0.124806i
\(134\) 18.3798 1.58777
\(135\) 0.0452669 + 2.23561i 0.00389596 + 0.192411i
\(136\) 59.8476 5.13189
\(137\) 20.1409i 1.72076i 0.509656 + 0.860378i \(0.329773\pi\)
−0.509656 + 0.860378i \(0.670227\pi\)
\(138\) 16.0068i 1.36259i
\(139\) −1.80356 −0.152976 −0.0764881 0.997070i \(-0.524371\pi\)
−0.0764881 + 0.997070i \(0.524371\pi\)
\(140\) −0.250849 12.3887i −0.0212006 1.04704i
\(141\) 8.43122 0.710037
\(142\) 29.7451i 2.49615i
\(143\) 0.748249i 0.0625717i
\(144\) −15.6256 −1.30213
\(145\) 2.04124 0.0413314i 0.169516 0.00343238i
\(146\) 9.90290 0.819570
\(147\) 1.00000i 0.0824786i
\(148\) 18.0799i 1.48616i
\(149\) −6.52258 −0.534350 −0.267175 0.963648i \(-0.586090\pi\)
−0.267175 + 0.963648i \(0.586090\pi\)
\(150\) 13.7197 0.555824i 1.12021 0.0453828i
\(151\) −3.83724 −0.312270 −0.156135 0.987736i \(-0.549903\pi\)
−0.156135 + 0.987736i \(0.549903\pi\)
\(152\) 13.9986i 1.13543i
\(153\) 6.15353i 0.497483i
\(154\) 2.74619 0.221294
\(155\) 5.05183 0.102290i 0.405772 0.00821613i
\(156\) 4.14645 0.331982
\(157\) 20.5461i 1.63976i −0.572538 0.819878i \(-0.694041\pi\)
0.572538 0.819878i \(-0.305959\pi\)
\(158\) 29.1867i 2.32197i
\(159\) 5.64500 0.447678
\(160\) 1.06193 + 52.4460i 0.0839532 + 4.14622i
\(161\) −5.82872 −0.459368
\(162\) 2.74619i 0.215761i
\(163\) 1.68575i 0.132038i 0.997818 + 0.0660189i \(0.0210298\pi\)
−0.997818 + 0.0660189i \(0.978970\pi\)
\(164\) 63.7588 4.97872
\(165\) 0.0452669 + 2.23561i 0.00352403 + 0.174042i
\(166\) 36.9206 2.86560
\(167\) 14.1425i 1.09438i 0.837008 + 0.547190i \(0.184303\pi\)
−0.837008 + 0.547190i \(0.815697\pi\)
\(168\) 9.72574i 0.750357i
\(169\) 12.4401 0.956933
\(170\) −37.7790 + 0.764954i −2.89752 + 0.0586693i
\(171\) −1.43933 −0.110068
\(172\) 55.3986i 4.22411i
\(173\) 13.3765i 1.01700i 0.861063 + 0.508499i \(0.169799\pi\)
−0.861063 + 0.508499i \(0.830201\pi\)
\(174\) 2.50743 0.190088
\(175\) 0.202398 + 4.99590i 0.0152999 + 0.377655i
\(176\) −15.6256 −1.17782
\(177\) 4.37632i 0.328944i
\(178\) 15.4286i 1.15642i
\(179\) 21.2621 1.58920 0.794602 0.607131i \(-0.207680\pi\)
0.794602 + 0.607131i \(0.207680\pi\)
\(180\) 12.3887 0.250849i 0.923401 0.0186971i
\(181\) 10.6061 0.788348 0.394174 0.919036i \(-0.371031\pi\)
0.394174 + 0.919036i \(0.371031\pi\)
\(182\) 2.05483i 0.152314i
\(183\) 9.75318i 0.720976i
\(184\) 56.6886 4.17914
\(185\) 0.147688 + 7.29391i 0.0108582 + 0.536259i
\(186\) 6.20558 0.455015
\(187\) 6.15353i 0.449991i
\(188\) 46.7220i 3.40755i
\(189\) −1.00000 −0.0727393
\(190\) 0.178925 + 8.83664i 0.0129806 + 0.641077i
\(191\) 0.660904 0.0478213 0.0239107 0.999714i \(-0.492388\pi\)
0.0239107 + 0.999714i \(0.492388\pi\)
\(192\) 33.1726i 2.39402i
\(193\) 6.34668i 0.456844i 0.973562 + 0.228422i \(0.0733566\pi\)
−0.973562 + 0.228422i \(0.926643\pi\)
\(194\) −38.4856 −2.76311
\(195\) −1.67279 + 0.0338709i −0.119791 + 0.00242555i
\(196\) 5.54154 0.395824
\(197\) 12.6891i 0.904059i −0.892003 0.452029i \(-0.850700\pi\)
0.892003 0.452029i \(-0.149300\pi\)
\(198\) 2.74619i 0.195163i
\(199\) −7.00407 −0.496505 −0.248253 0.968695i \(-0.579856\pi\)
−0.248253 + 0.968695i \(0.579856\pi\)
\(200\) −1.96847 48.5888i −0.139192 3.43575i
\(201\) −6.69285 −0.472077
\(202\) 7.22871i 0.508610i
\(203\) 0.913059i 0.0640842i
\(204\) −34.1000 −2.38748
\(205\) −25.7220 + 0.520823i −1.79650 + 0.0363759i
\(206\) 2.50970 0.174859
\(207\) 5.82872i 0.405124i
\(208\) 11.6918i 0.810684i
\(209\) −1.43933 −0.0995606
\(210\) 0.124311 + 6.13940i 0.00857830 + 0.423659i
\(211\) −24.9569 −1.71811 −0.859053 0.511887i \(-0.828947\pi\)
−0.859053 + 0.511887i \(0.828947\pi\)
\(212\) 31.2820i 2.14846i
\(213\) 10.8314i 0.742156i
\(214\) 33.2290 2.27149
\(215\) 0.452532 + 22.3493i 0.0308624 + 1.52421i
\(216\) 9.72574 0.661753
\(217\) 2.25971i 0.153399i
\(218\) 55.4958i 3.75865i
\(219\) −3.60606 −0.243675
\(220\) 12.3887 0.250849i 0.835248 0.0169122i
\(221\) 4.60437 0.309724
\(222\) 8.95972i 0.601337i
\(223\) 15.2962i 1.02431i −0.858892 0.512156i \(-0.828847\pi\)
0.858892 0.512156i \(-0.171153\pi\)
\(224\) −23.4594 −1.56744
\(225\) −4.99590 + 0.202398i −0.333060 + 0.0134932i
\(226\) 0.255532 0.0169977
\(227\) 23.0182i 1.52777i 0.645350 + 0.763887i \(0.276711\pi\)
−0.645350 + 0.763887i \(0.723289\pi\)
\(228\) 7.97612i 0.528231i
\(229\) −6.83386 −0.451594 −0.225797 0.974174i \(-0.572499\pi\)
−0.225797 + 0.974174i \(0.572499\pi\)
\(230\) −35.7849 + 0.724577i −2.35958 + 0.0477772i
\(231\) −1.00000 −0.0657952
\(232\) 8.88017i 0.583012i
\(233\) 17.9663i 1.17701i 0.808494 + 0.588504i \(0.200283\pi\)
−0.808494 + 0.588504i \(0.799717\pi\)
\(234\) −2.05483 −0.134329
\(235\) 0.381655 + 18.8489i 0.0248965 + 1.22957i
\(236\) −24.2516 −1.57864
\(237\) 10.6281i 0.690369i
\(238\) 16.8987i 1.09538i
\(239\) 17.8108 1.15208 0.576041 0.817421i \(-0.304597\pi\)
0.576041 + 0.817421i \(0.304597\pi\)
\(240\) −0.707323 34.9328i −0.0456575 2.25490i
\(241\) 10.4906 0.675758 0.337879 0.941190i \(-0.390291\pi\)
0.337879 + 0.941190i \(0.390291\pi\)
\(242\) 2.74619i 0.176532i
\(243\) 1.00000i 0.0641500i
\(244\) 54.0476 3.46005
\(245\) −2.23561 + 0.0452669i −0.142828 + 0.00289200i
\(246\) −31.5965 −2.01452
\(247\) 1.07698i 0.0685265i
\(248\) 21.9773i 1.39556i
\(249\) −13.4443 −0.852000
\(250\) 1.86365 + 30.6467i 0.117868 + 1.93827i
\(251\) −5.13076 −0.323851 −0.161926 0.986803i \(-0.551770\pi\)
−0.161926 + 0.986803i \(0.551770\pi\)
\(252\) 5.54154i 0.349084i
\(253\) 5.82872i 0.366449i
\(254\) 40.5195 2.54242
\(255\) 13.7569 0.278551i 0.861490 0.0174436i
\(256\) 54.9797 3.43623
\(257\) 21.1767i 1.32097i −0.750840 0.660485i \(-0.770351\pi\)
0.750840 0.660485i \(-0.229649\pi\)
\(258\) 27.4535i 1.70918i
\(259\) −3.26260 −0.202728
\(260\) 0.187697 + 9.26985i 0.0116405 + 0.574892i
\(261\) −0.913059 −0.0565169
\(262\) 45.3141i 2.79951i
\(263\) 1.58627i 0.0978133i 0.998803 + 0.0489067i \(0.0155737\pi\)
−0.998803 + 0.0489067i \(0.984426\pi\)
\(264\) 9.72574 0.598578
\(265\) 0.255532 + 12.6200i 0.0156972 + 0.775242i
\(266\) −3.95267 −0.242354
\(267\) 5.61820i 0.343828i
\(268\) 37.0887i 2.26555i
\(269\) 3.62855 0.221237 0.110618 0.993863i \(-0.464717\pi\)
0.110618 + 0.993863i \(0.464717\pi\)
\(270\) −6.13940 + 0.124311i −0.373632 + 0.00756535i
\(271\) 8.16357 0.495902 0.247951 0.968773i \(-0.420243\pi\)
0.247951 + 0.968773i \(0.420243\pi\)
\(272\) 96.1526i 5.83011i
\(273\) 0.748249i 0.0452861i
\(274\) −55.3108 −3.34145
\(275\) −4.99590 + 0.202398i −0.301264 + 0.0122051i
\(276\) −32.3001 −1.94424
\(277\) 8.82549i 0.530272i 0.964211 + 0.265136i \(0.0854169\pi\)
−0.964211 + 0.265136i \(0.914583\pi\)
\(278\) 4.95292i 0.297056i
\(279\) −2.25971 −0.135285
\(280\) 21.7430 0.440254i 1.29939 0.0263102i
\(281\) 16.3437 0.974985 0.487492 0.873127i \(-0.337912\pi\)
0.487492 + 0.873127i \(0.337912\pi\)
\(282\) 23.1537i 1.37878i
\(283\) 11.6256i 0.691073i −0.938405 0.345536i \(-0.887697\pi\)
0.938405 0.345536i \(-0.112303\pi\)
\(284\) −60.0227 −3.56169
\(285\) −0.0651541 3.21778i −0.00385940 0.190605i
\(286\) −2.05483 −0.121505
\(287\) 11.5056i 0.679154i
\(288\) 23.4594i 1.38236i
\(289\) −20.8659 −1.22741
\(290\) 0.113504 + 5.60563i 0.00666516 + 0.329174i
\(291\) 14.0142 0.821527
\(292\) 19.9831i 1.16942i
\(293\) 8.77092i 0.512403i −0.966623 0.256201i \(-0.917529\pi\)
0.966623 0.256201i \(-0.0824710\pi\)
\(294\) −2.74619 −0.160161
\(295\) 9.78375 0.198103i 0.569632 0.0115340i
\(296\) 31.7312 1.84434
\(297\) 1.00000i 0.0580259i
\(298\) 17.9122i 1.03763i
\(299\) 4.36134 0.252223
\(300\) 1.12160 + 27.6850i 0.0647555 + 1.59839i
\(301\) −9.99697 −0.576216
\(302\) 10.5378i 0.606380i
\(303\) 2.63227i 0.151220i
\(304\) 22.4904 1.28991
\(305\) −21.8043 + 0.441496i −1.24851 + 0.0252800i
\(306\) 16.8987 0.966037
\(307\) 28.1213i 1.60497i −0.596675 0.802483i \(-0.703512\pi\)
0.596675 0.802483i \(-0.296488\pi\)
\(308\) 5.54154i 0.315759i
\(309\) −0.913885 −0.0519891
\(310\) 0.280908 + 13.8733i 0.0159545 + 0.787948i
\(311\) −7.52137 −0.426498 −0.213249 0.976998i \(-0.568404\pi\)
−0.213249 + 0.976998i \(0.568404\pi\)
\(312\) 7.27727i 0.411995i
\(313\) 10.1735i 0.575039i 0.957775 + 0.287520i \(0.0928307\pi\)
−0.957775 + 0.287520i \(0.907169\pi\)
\(314\) 56.4234 3.18416
\(315\) −0.0452669 2.23561i −0.00255050 0.125962i
\(316\) −58.8961 −3.31316
\(317\) 1.97131i 0.110720i −0.998466 0.0553599i \(-0.982369\pi\)
0.998466 0.0553599i \(-0.0176306\pi\)
\(318\) 15.5022i 0.869322i
\(319\) −0.913059 −0.0511215
\(320\) −74.1609 + 1.50162i −4.14572 + 0.0839431i
\(321\) −12.1001 −0.675360
\(322\) 16.0068i 0.892022i
\(323\) 8.85697i 0.492815i
\(324\) −5.54154 −0.307863
\(325\) −0.151444 3.73818i −0.00840062 0.207357i
\(326\) −4.62938 −0.256397
\(327\) 20.2083i 1.11752i
\(328\) 111.900i 6.17867i
\(329\) −8.43122 −0.464828
\(330\) −6.13940 + 0.124311i −0.337963 + 0.00684312i
\(331\) −19.5659 −1.07544 −0.537721 0.843123i \(-0.680714\pi\)
−0.537721 + 0.843123i \(0.680714\pi\)
\(332\) 74.5023i 4.08885i
\(333\) 3.26260i 0.178790i
\(334\) −38.8380 −2.12512
\(335\) −0.302965 14.9626i −0.0165527 0.817494i
\(336\) 15.6256 0.852447
\(337\) 28.8041i 1.56906i 0.620093 + 0.784528i \(0.287095\pi\)
−0.620093 + 0.784528i \(0.712905\pi\)
\(338\) 34.1629i 1.85822i
\(339\) −0.0930496 −0.00505376
\(340\) −1.54360 76.2344i −0.0837137 4.13439i
\(341\) −2.25971 −0.122370
\(342\) 3.95267i 0.213736i
\(343\) 1.00000i 0.0539949i
\(344\) 97.2279 5.24218
\(345\) 13.0307 0.263848i 0.701552 0.0142051i
\(346\) −36.7344 −1.97486
\(347\) 21.1332i 1.13449i −0.823549 0.567246i \(-0.808009\pi\)
0.823549 0.567246i \(-0.191991\pi\)
\(348\) 5.05975i 0.271231i
\(349\) 19.1331 1.02417 0.512085 0.858935i \(-0.328873\pi\)
0.512085 + 0.858935i \(0.328873\pi\)
\(350\) −13.7197 + 0.555824i −0.733348 + 0.0297100i
\(351\) 0.748249 0.0399386
\(352\) 23.4594i 1.25039i
\(353\) 30.7309i 1.63564i −0.575475 0.817820i \(-0.695183\pi\)
0.575475 0.817820i \(-0.304817\pi\)
\(354\) 12.0182 0.638760
\(355\) 24.2148 0.490305i 1.28519 0.0260227i
\(356\) −31.1335 −1.65007
\(357\) 6.15353i 0.325679i
\(358\) 58.3897i 3.08599i
\(359\) 16.5201 0.871899 0.435950 0.899971i \(-0.356413\pi\)
0.435950 + 0.899971i \(0.356413\pi\)
\(360\) 0.440254 + 21.7430i 0.0232034 + 1.14595i
\(361\) −16.9283 −0.890964
\(362\) 29.1264i 1.53085i
\(363\) 1.00000i 0.0524864i
\(364\) −4.14645 −0.217333
\(365\) −0.163235 8.06173i −0.00854411 0.421970i
\(366\) −26.7840 −1.40002
\(367\) 22.8531i 1.19292i −0.802641 0.596462i \(-0.796573\pi\)
0.802641 0.596462i \(-0.203427\pi\)
\(368\) 91.0773i 4.74773i
\(369\) 11.5056 0.598958
\(370\) −20.0304 + 0.405579i −1.04133 + 0.0210850i
\(371\) −5.64500 −0.293074
\(372\) 12.5223i 0.649249i
\(373\) 19.1864i 0.993436i −0.867912 0.496718i \(-0.834538\pi\)
0.867912 0.496718i \(-0.165462\pi\)
\(374\) 16.8987 0.873813
\(375\) −0.678633 11.1597i −0.0350444 0.576286i
\(376\) 81.9998 4.22882
\(377\) 0.683195i 0.0351864i
\(378\) 2.74619i 0.141249i
\(379\) 30.4582 1.56453 0.782265 0.622945i \(-0.214064\pi\)
0.782265 + 0.622945i \(0.214064\pi\)
\(380\) −17.8315 + 0.361054i −0.914736 + 0.0185217i
\(381\) −14.7548 −0.755913
\(382\) 1.81497i 0.0928617i
\(383\) 19.3943i 0.991004i 0.868607 + 0.495502i \(0.165016\pi\)
−0.868607 + 0.495502i \(0.834984\pi\)
\(384\) −44.1794 −2.25452
\(385\) −0.0452669 2.23561i −0.00230702 0.113937i
\(386\) −17.4292 −0.887122
\(387\) 9.99697i 0.508175i
\(388\) 77.6603i 3.94261i
\(389\) −30.0679 −1.52450 −0.762251 0.647281i \(-0.775906\pi\)
−0.762251 + 0.647281i \(0.775906\pi\)
\(390\) −0.0930159 4.59380i −0.00471004 0.232616i
\(391\) −35.8672 −1.81388
\(392\) 9.72574i 0.491224i
\(393\) 16.5007i 0.832352i
\(394\) 34.8466 1.75554
\(395\) 23.7603 0.481101i 1.19551 0.0242068i
\(396\) −5.54154 −0.278473
\(397\) 25.3301i 1.27128i −0.771985 0.635640i \(-0.780736\pi\)
0.771985 0.635640i \(-0.219264\pi\)
\(398\) 19.2345i 0.964137i
\(399\) 1.43933 0.0720567
\(400\) 78.0640 3.16260i 3.90320 0.158130i
\(401\) 20.6349 1.03046 0.515228 0.857053i \(-0.327707\pi\)
0.515228 + 0.857053i \(0.327707\pi\)
\(402\) 18.3798i 0.916701i
\(403\) 1.69082i 0.0842260i
\(404\) 14.5868 0.725723
\(405\) 2.23561 0.0452669i 0.111088 0.00224933i
\(406\) −2.50743 −0.124442
\(407\) 3.26260i 0.161721i
\(408\) 59.8476i 2.96290i
\(409\) −26.0758 −1.28937 −0.644683 0.764450i \(-0.723011\pi\)
−0.644683 + 0.764450i \(0.723011\pi\)
\(410\) −1.43028 70.6375i −0.0706364 3.48854i
\(411\) 20.1409 0.993479
\(412\) 5.06433i 0.249502i
\(413\) 4.37632i 0.215345i
\(414\) 16.0068 0.786689
\(415\) −0.608584 30.0563i −0.0298742 1.47540i
\(416\) 17.5534 0.860629
\(417\) 1.80356i 0.0883208i
\(418\) 3.95267i 0.193332i
\(419\) 21.9235 1.07103 0.535517 0.844525i \(-0.320117\pi\)
0.535517 + 0.844525i \(0.320117\pi\)
\(420\) −12.3887 + 0.250849i −0.604508 + 0.0122402i
\(421\) −9.30230 −0.453366 −0.226683 0.973969i \(-0.572788\pi\)
−0.226683 + 0.973969i \(0.572788\pi\)
\(422\) 68.5364i 3.33630i
\(423\) 8.43122i 0.409940i
\(424\) 54.9018 2.66627
\(425\) 1.24546 + 30.7424i 0.0604139 + 1.49123i
\(426\) 29.7451 1.44115
\(427\) 9.75318i 0.471989i
\(428\) 67.0530i 3.24113i
\(429\) 0.748249 0.0361258
\(430\) −61.3754 + 1.24274i −2.95979 + 0.0599301i
\(431\) 28.2950 1.36292 0.681462 0.731854i \(-0.261345\pi\)
0.681462 + 0.731854i \(0.261345\pi\)
\(432\) 15.6256i 0.751787i
\(433\) 11.9658i 0.575042i −0.957774 0.287521i \(-0.907169\pi\)
0.957774 0.287521i \(-0.0928310\pi\)
\(434\) −6.20558 −0.297877
\(435\) −0.0413314 2.04124i −0.00198169 0.0978701i
\(436\) 111.985 5.36312
\(437\) 8.38946i 0.401322i
\(438\) 9.90290i 0.473179i
\(439\) 21.4648 1.02446 0.512229 0.858849i \(-0.328820\pi\)
0.512229 + 0.858849i \(0.328820\pi\)
\(440\) 0.440254 + 21.7430i 0.0209883 + 1.03655i
\(441\) 1.00000 0.0476190
\(442\) 12.6445i 0.601436i
\(443\) 23.8247i 1.13195i −0.824424 0.565973i \(-0.808501\pi\)
0.824424 0.565973i \(-0.191499\pi\)
\(444\) −18.0799 −0.858032
\(445\) 12.5601 0.254319i 0.595406 0.0120559i
\(446\) 42.0064 1.98906
\(447\) 6.52258i 0.308507i
\(448\) 33.1726i 1.56726i
\(449\) 13.3576 0.630383 0.315192 0.949028i \(-0.397931\pi\)
0.315192 + 0.949028i \(0.397931\pi\)
\(450\) −0.555824 13.7197i −0.0262018 0.646752i
\(451\) 11.5056 0.541778
\(452\) 0.515638i 0.0242536i
\(453\) 3.83724i 0.180289i
\(454\) −63.2124 −2.96670
\(455\) 1.67279 0.0338709i 0.0784217 0.00158789i
\(456\) −13.9986 −0.655543
\(457\) 36.4496i 1.70504i −0.522695 0.852520i \(-0.675073\pi\)
0.522695 0.852520i \(-0.324927\pi\)
\(458\) 18.7670i 0.876927i
\(459\) −6.15353 −0.287222
\(460\) −1.46213 72.2104i −0.0681720 3.36683i
\(461\) 25.8103 1.20211 0.601053 0.799209i \(-0.294748\pi\)
0.601053 + 0.799209i \(0.294748\pi\)
\(462\) 2.74619i 0.127764i
\(463\) 12.5698i 0.584170i 0.956392 + 0.292085i \(0.0943489\pi\)
−0.956392 + 0.292085i \(0.905651\pi\)
\(464\) 14.2671 0.662333
\(465\) −0.102290 5.05183i −0.00474359 0.234273i
\(466\) −49.3387 −2.28557
\(467\) 26.1670i 1.21087i −0.795896 0.605433i \(-0.793000\pi\)
0.795896 0.605433i \(-0.207000\pi\)
\(468\) 4.14645i 0.191670i
\(469\) 6.69285 0.309047
\(470\) −51.7627 + 1.04810i −2.38763 + 0.0483451i
\(471\) −20.5461 −0.946714
\(472\) 42.5629i 1.95912i
\(473\) 9.99697i 0.459661i
\(474\) 29.1867 1.34059
\(475\) 7.19076 0.291318i 0.329935 0.0133666i
\(476\) 34.1000 1.56297
\(477\) 5.64500i 0.258467i
\(478\) 48.9117i 2.23717i
\(479\) −39.7023 −1.81404 −0.907022 0.421082i \(-0.861650\pi\)
−0.907022 + 0.421082i \(0.861650\pi\)
\(480\) 52.4460 1.06193i 2.39382 0.0484704i
\(481\) 2.44124 0.111311
\(482\) 28.8091i 1.31222i
\(483\) 5.82872i 0.265216i
\(484\) −5.54154 −0.251888
\(485\) 0.634380 + 31.3303i 0.0288057 + 1.42264i
\(486\) 2.74619 0.124570
\(487\) 13.3271i 0.603909i 0.953322 + 0.301954i \(0.0976391\pi\)
−0.953322 + 0.301954i \(0.902361\pi\)
\(488\) 94.8568i 4.29397i
\(489\) 1.68575 0.0762321
\(490\) −0.124311 6.13940i −0.00561582 0.277350i
\(491\) 22.1471 0.999487 0.499743 0.866173i \(-0.333428\pi\)
0.499743 + 0.866173i \(0.333428\pi\)
\(492\) 63.7588i 2.87447i
\(493\) 5.61853i 0.253046i
\(494\) 2.95758 0.133068
\(495\) 2.23561 0.0452669i 0.100483 0.00203460i
\(496\) 35.3093 1.58543
\(497\) 10.8314i 0.485855i
\(498\) 36.9206i 1.65445i
\(499\) −15.4018 −0.689479 −0.344739 0.938698i \(-0.612033\pi\)
−0.344739 + 0.938698i \(0.612033\pi\)
\(500\) −61.8421 + 3.76067i −2.76566 + 0.168182i
\(501\) 14.1425 0.631841
\(502\) 14.0900i 0.628869i
\(503\) 13.1271i 0.585308i 0.956218 + 0.292654i \(0.0945384\pi\)
−0.956218 + 0.292654i \(0.905462\pi\)
\(504\) −9.72574 −0.433219
\(505\) −5.88473 + 0.119155i −0.261867 + 0.00530232i
\(506\) 16.0068 0.711587
\(507\) 12.4401i 0.552485i
\(508\) 81.7646i 3.62772i
\(509\) −28.6739 −1.27095 −0.635475 0.772121i \(-0.719196\pi\)
−0.635475 + 0.772121i \(0.719196\pi\)
\(510\) 0.764954 + 37.7790i 0.0338727 + 1.67288i
\(511\) 3.60606 0.159523
\(512\) 62.6257i 2.76769i
\(513\) 1.43933i 0.0635480i
\(514\) 58.1553 2.56512
\(515\) −0.0413688 2.04309i −0.00182293 0.0900293i
\(516\) −55.3986 −2.43879
\(517\) 8.43122i 0.370805i
\(518\) 8.95972i 0.393667i
\(519\) 13.3765 0.587164
\(520\) −16.2691 + 0.329420i −0.713449 + 0.0144460i
\(521\) 24.7030 1.08226 0.541128 0.840940i \(-0.317997\pi\)
0.541128 + 0.840940i \(0.317997\pi\)
\(522\) 2.50743i 0.109747i
\(523\) 4.81571i 0.210576i −0.994442 0.105288i \(-0.966423\pi\)
0.994442 0.105288i \(-0.0335765\pi\)
\(524\) −91.4395 −3.99455
\(525\) 4.99590 0.202398i 0.218039 0.00883339i
\(526\) −4.35618 −0.189939
\(527\) 13.9052i 0.605719i
\(528\) 15.6256i 0.680017i
\(529\) −10.9740 −0.477130
\(530\) −34.6569 + 0.701738i −1.50540 + 0.0304816i
\(531\) −4.37632 −0.189916
\(532\) 7.97612i 0.345809i
\(533\) 8.60906i 0.372900i
\(534\) 15.4286 0.667662
\(535\) −0.547733 27.0510i −0.0236805 1.16952i
\(536\) −65.0929 −2.81158
\(537\) 21.2621i 0.917527i
\(538\) 9.96467i 0.429608i
\(539\) 1.00000 0.0430730
\(540\) −0.250849 12.3887i −0.0107948 0.533126i
\(541\) −21.8196 −0.938096 −0.469048 0.883173i \(-0.655403\pi\)
−0.469048 + 0.883173i \(0.655403\pi\)
\(542\) 22.4187i 0.962966i
\(543\) 10.6061i 0.455153i
\(544\) −144.358 −6.18929
\(545\) −45.1779 + 0.914769i −1.93521 + 0.0391844i
\(546\) 2.05483 0.0879387
\(547\) 6.70571i 0.286715i 0.989671 + 0.143358i \(0.0457899\pi\)
−0.989671 + 0.143358i \(0.954210\pi\)
\(548\) 111.612i 4.76782i
\(549\) 9.75318 0.416255
\(550\) −0.555824 13.7197i −0.0237004 0.585009i
\(551\) 1.31419 0.0559866
\(552\) 56.6886i 2.41283i
\(553\) 10.6281i 0.451953i
\(554\) −24.2364 −1.02971
\(555\) 7.29391 0.147688i 0.309609 0.00626901i
\(556\) 9.99452 0.423862
\(557\) 17.9230i 0.759421i −0.925105 0.379710i \(-0.876024\pi\)
0.925105 0.379710i \(-0.123976\pi\)
\(558\) 6.20558i 0.262703i
\(559\) 7.48022 0.316380
\(560\) 0.707323 + 34.9328i 0.0298899 + 1.47618i
\(561\) −6.15353 −0.259802
\(562\) 44.8829i 1.89327i
\(563\) 8.34113i 0.351537i −0.984432 0.175768i \(-0.943759\pi\)
0.984432 0.175768i \(-0.0562409\pi\)
\(564\) −46.7220 −1.96735
\(565\) −0.00421207 0.208023i −0.000177203 0.00875158i
\(566\) 31.9262 1.34196
\(567\) 1.00000i 0.0419961i
\(568\) 105.343i 4.42011i
\(569\) −33.2594 −1.39431 −0.697154 0.716922i \(-0.745550\pi\)
−0.697154 + 0.716922i \(0.745550\pi\)
\(570\) 8.83664 0.178925i 0.370126 0.00749436i
\(571\) −37.7037 −1.57785 −0.788926 0.614489i \(-0.789362\pi\)
−0.788926 + 0.614489i \(0.789362\pi\)
\(572\) 4.14645i 0.173372i
\(573\) 0.660904i 0.0276097i
\(574\) 31.5965 1.31881
\(575\) 1.17972 + 29.1197i 0.0491979 + 1.21438i
\(576\) 33.1726 1.38219
\(577\) 17.4572i 0.726752i −0.931643 0.363376i \(-0.881624\pi\)
0.931643 0.363376i \(-0.118376\pi\)
\(578\) 57.3017i 2.38344i
\(579\) 6.34668 0.263759
\(580\) −11.3116 + 0.229039i −0.469690 + 0.00951035i
\(581\) 13.4443 0.557765
\(582\) 38.4856i 1.59528i
\(583\) 5.64500i 0.233792i
\(584\) −35.0716 −1.45127
\(585\) 0.0338709 + 1.67279i 0.00140039 + 0.0691615i
\(586\) 24.0866 0.995008
\(587\) 14.2485i 0.588100i −0.955790 0.294050i \(-0.904997\pi\)
0.955790 0.294050i \(-0.0950032\pi\)
\(588\) 5.54154i 0.228529i
\(589\) 3.25247 0.134016
\(590\) 0.544027 + 26.8680i 0.0223972 + 1.10614i
\(591\) −12.6891 −0.521959
\(592\) 50.9802i 2.09527i
\(593\) 32.3418i 1.32812i 0.747680 + 0.664059i \(0.231168\pi\)
−0.747680 + 0.664059i \(0.768832\pi\)
\(594\) 2.74619 0.112677
\(595\) −13.7569 + 0.278551i −0.563977 + 0.0114195i
\(596\) 36.1451 1.48056
\(597\) 7.00407i 0.286657i
\(598\) 11.9770i 0.489778i
\(599\) −16.0797 −0.656998 −0.328499 0.944504i \(-0.606543\pi\)
−0.328499 + 0.944504i \(0.606543\pi\)
\(600\) −48.5888 + 1.96847i −1.98363 + 0.0803626i
\(601\) 43.1542 1.76030 0.880149 0.474698i \(-0.157443\pi\)
0.880149 + 0.474698i \(0.157443\pi\)
\(602\) 27.4535i 1.11892i
\(603\) 6.69285i 0.272554i
\(604\) 21.2642 0.865228
\(605\) 2.23561 0.0452669i 0.0908905 0.00184036i
\(606\) −7.22871 −0.293646
\(607\) 2.85844i 0.116020i 0.998316 + 0.0580102i \(0.0184756\pi\)
−0.998316 + 0.0580102i \(0.981524\pi\)
\(608\) 33.7658i 1.36938i
\(609\) 0.913059 0.0369990
\(610\) −1.21243 59.8787i −0.0490899 2.42442i
\(611\) 6.30865 0.255221
\(612\) 34.1000i 1.37841i
\(613\) 36.8928i 1.49009i 0.667016 + 0.745043i \(0.267571\pi\)
−0.667016 + 0.745043i \(0.732429\pi\)
\(614\) 77.2263 3.11660
\(615\) 0.520823 + 25.7220i 0.0210016 + 1.03721i
\(616\) −9.72574 −0.391861
\(617\) 12.9981i 0.523285i −0.965165 0.261642i \(-0.915736\pi\)
0.965165 0.261642i \(-0.0842641\pi\)
\(618\) 2.50970i 0.100955i
\(619\) −13.3094 −0.534951 −0.267475 0.963565i \(-0.586189\pi\)
−0.267475 + 0.963565i \(0.586189\pi\)
\(620\) −27.9949 + 0.566845i −1.12430 + 0.0227650i
\(621\) −5.82872 −0.233899
\(622\) 20.6551i 0.828193i
\(623\) 5.61820i 0.225088i
\(624\) −11.6918 −0.468048
\(625\) 24.9181 2.02232i 0.996723 0.0808930i
\(626\) −27.9383 −1.11664
\(627\) 1.43933i 0.0574814i
\(628\) 113.857i 4.54339i
\(629\) −20.0765 −0.800503
\(630\) 6.13940 0.124311i 0.244600 0.00495269i
\(631\) 33.2052 1.32188 0.660939 0.750440i \(-0.270158\pi\)
0.660939 + 0.750440i \(0.270158\pi\)
\(632\) 103.366i 4.11168i
\(633\) 24.9569i 0.991949i
\(634\) 5.41358 0.215001
\(635\) −0.667906 32.9861i −0.0265050 1.30901i
\(636\) −31.2820 −1.24041
\(637\) 0.748249i 0.0296467i
\(638\) 2.50743i 0.0992701i
\(639\) −10.8314 −0.428484
\(640\) −1.99986 98.7679i −0.0790516 3.90414i
\(641\) 18.8363 0.743991 0.371996 0.928235i \(-0.378674\pi\)
0.371996 + 0.928235i \(0.378674\pi\)
\(642\) 33.2290i 1.31145i
\(643\) 24.9394i 0.983512i −0.870733 0.491756i \(-0.836355\pi\)
0.870733 0.491756i \(-0.163645\pi\)
\(644\) 32.3001 1.27280
\(645\) 22.3493 0.452532i 0.880004 0.0178184i
\(646\) −24.3229 −0.956971
\(647\) 8.94306i 0.351588i −0.984427 0.175794i \(-0.943751\pi\)
0.984427 0.175794i \(-0.0562493\pi\)
\(648\) 9.72574i 0.382063i
\(649\) −4.37632 −0.171786
\(650\) 10.2657 0.415895i 0.402655 0.0163127i
\(651\) 2.25971 0.0885649
\(652\) 9.34164i 0.365847i
\(653\) 1.77376i 0.0694126i 0.999398 + 0.0347063i \(0.0110496\pi\)
−0.999398 + 0.0347063i \(0.988950\pi\)
\(654\) −55.4958 −2.17006
\(655\) 36.8892 0.746937i 1.44138 0.0291853i
\(656\) −179.782 −7.01931
\(657\) 3.60606i 0.140686i
\(658\) 23.1537i 0.902626i
\(659\) 5.71183 0.222501 0.111251 0.993792i \(-0.464514\pi\)
0.111251 + 0.993792i \(0.464514\pi\)
\(660\) −0.250849 12.3887i −0.00976427 0.482231i
\(661\) −2.38412 −0.0927315 −0.0463657 0.998925i \(-0.514764\pi\)
−0.0463657 + 0.998925i \(0.514764\pi\)
\(662\) 53.7317i 2.08834i
\(663\) 4.60437i 0.178819i
\(664\) −130.756 −5.07432
\(665\) 0.0651541 + 3.21778i 0.00252657 + 0.124780i
\(666\) 8.95972 0.347182
\(667\) 5.32197i 0.206067i
\(668\) 78.3713i 3.03228i
\(669\) −15.2962 −0.591387
\(670\) 41.0901 0.831997i 1.58745 0.0321429i
\(671\) 9.75318 0.376517
\(672\) 23.4594i 0.904965i
\(673\) 11.8632i 0.457292i 0.973510 + 0.228646i \(0.0734298\pi\)
−0.973510 + 0.228646i \(0.926570\pi\)
\(674\) −79.1013 −3.04687
\(675\) 0.202398 + 4.99590i 0.00779032 + 0.192292i
\(676\) −68.9375 −2.65144
\(677\) 7.00471i 0.269213i 0.990899 + 0.134606i \(0.0429770\pi\)
−0.990899 + 0.134606i \(0.957023\pi\)
\(678\) 0.255532i 0.00981363i
\(679\) −14.0142 −0.537816
\(680\) 133.796 2.70912i 5.13084 0.103890i
\(681\) 23.0182 0.882061
\(682\) 6.20558i 0.237624i
\(683\) 13.4790i 0.515759i −0.966177 0.257879i \(-0.916976\pi\)
0.966177 0.257879i \(-0.0830237\pi\)
\(684\) 7.97612 0.304974
\(685\) 0.911718 + 45.0273i 0.0348350 + 1.72040i
\(686\) 2.74619 0.104850
\(687\) 6.83386i 0.260728i
\(688\) 156.209i 5.95540i
\(689\) 4.22387 0.160917
\(690\) 0.724577 + 35.7849i 0.0275842 + 1.36231i
\(691\) 43.3563 1.64935 0.824676 0.565605i \(-0.191357\pi\)
0.824676 + 0.565605i \(0.191357\pi\)
\(692\) 74.1266i 2.81787i
\(693\) 1.00000i 0.0379869i
\(694\) 58.0358 2.20301
\(695\) −4.03206 + 0.0816417i −0.152945 + 0.00309685i
\(696\) −8.88017 −0.336602
\(697\) 70.8000i 2.68174i
\(698\) 52.5430i 1.98878i
\(699\) 17.9663 0.679546
\(700\) −1.12160 27.6850i −0.0423925 1.04639i
\(701\) −49.3615 −1.86436 −0.932178 0.361999i \(-0.882094\pi\)
−0.932178 + 0.361999i \(0.882094\pi\)
\(702\) 2.05483i 0.0775546i
\(703\) 4.69597i 0.177112i
\(704\) 33.1726 1.25024
\(705\) 18.8489 0.381655i 0.709891 0.0143740i
\(706\) 84.3927 3.17616
\(707\) 2.63227i 0.0989968i
\(708\) 24.2516i 0.911430i
\(709\) −39.2337 −1.47345 −0.736727 0.676190i \(-0.763630\pi\)
−0.736727 + 0.676190i \(0.763630\pi\)
\(710\) 1.34647 + 66.4984i 0.0505321 + 2.49564i
\(711\) −10.6281 −0.398585
\(712\) 54.6411i 2.04776i
\(713\) 13.1712i 0.493266i
\(714\) −16.8987 −0.632419
\(715\) 0.0338709 + 1.67279i 0.00126670 + 0.0625589i
\(716\) −117.825 −4.40332
\(717\) 17.8108i 0.665155i
\(718\) 45.3674i 1.69310i
\(719\) 18.6722 0.696357 0.348178 0.937428i \(-0.386800\pi\)
0.348178 + 0.937428i \(0.386800\pi\)
\(720\) −34.9328 + 0.707323i −1.30187 + 0.0263604i
\(721\) 0.913885 0.0340349
\(722\) 46.4883i 1.73012i
\(723\) 10.4906i 0.390149i
\(724\) −58.7743 −2.18433
\(725\) 4.56155 0.184802i 0.169412 0.00686336i
\(726\) 2.74619 0.101921
\(727\) 12.7687i 0.473566i −0.971563 0.236783i \(-0.923907\pi\)
0.971563 0.236783i \(-0.0760931\pi\)
\(728\) 7.27727i 0.269714i
\(729\) −1.00000 −0.0370370
\(730\) 22.1390 0.448274i 0.819402 0.0165914i
\(731\) −61.5166 −2.27527
\(732\) 54.0476i 1.99766i
\(733\) 13.7757i 0.508818i −0.967097 0.254409i \(-0.918119\pi\)
0.967097 0.254409i \(-0.0818810\pi\)
\(734\) 62.7590 2.31648
\(735\) 0.0452669 + 2.23561i 0.00166970 + 0.0824617i
\(736\) −136.738 −5.04023
\(737\) 6.69285i 0.246534i
\(738\) 31.5965i 1.16308i
\(739\) −23.4848 −0.863901 −0.431951 0.901897i \(-0.642175\pi\)
−0.431951 + 0.901897i \(0.642175\pi\)
\(740\) −0.818419 40.4195i −0.0300857 1.48585i
\(741\) −1.07698 −0.0395638
\(742\) 15.5022i 0.569105i
\(743\) 15.1428i 0.555536i −0.960648 0.277768i \(-0.910405\pi\)
0.960648 0.277768i \(-0.0895946\pi\)
\(744\) −21.9773 −0.805728
\(745\) −14.5819 + 0.295257i −0.534241 + 0.0108174i
\(746\) 52.6896 1.92910
\(747\) 13.4443i 0.491902i
\(748\) 34.1000i 1.24682i
\(749\) 12.1001 0.442127
\(750\) 30.6467 1.86365i 1.11906 0.0680510i
\(751\) 22.7886 0.831569 0.415784 0.909463i \(-0.363507\pi\)
0.415784 + 0.909463i \(0.363507\pi\)
\(752\) 131.743i 4.80417i
\(753\) 5.13076i 0.186975i
\(754\) 1.87618 0.0683265
\(755\) −8.57856 + 0.173700i −0.312206 + 0.00632159i
\(756\) 5.54154 0.201544
\(757\) 15.8664i 0.576675i 0.957529 + 0.288338i \(0.0931026\pi\)
−0.957529 + 0.288338i \(0.906897\pi\)
\(758\) 83.6438i 3.03808i
\(759\) −5.82872 −0.211569
\(760\) −0.633672 31.2953i −0.0229857 1.13520i
\(761\) 36.6802 1.32966 0.664829 0.746996i \(-0.268504\pi\)
0.664829 + 0.746996i \(0.268504\pi\)
\(762\) 40.5195i 1.46787i
\(763\) 20.2083i 0.731591i
\(764\) −3.66243 −0.132502
\(765\) −0.278551 13.7569i −0.0100710 0.497381i
\(766\) −53.2605 −1.92438
\(767\) 3.27458i 0.118238i
\(768\) 54.9797i 1.98391i
\(769\) −18.1791 −0.655555 −0.327778 0.944755i \(-0.606300\pi\)
−0.327778 + 0.944755i \(0.606300\pi\)
\(770\) 6.13940 0.124311i 0.221249 0.00447987i
\(771\) −21.1767 −0.762662
\(772\) 35.1704i 1.26581i
\(773\) 49.4475i 1.77850i 0.457418 + 0.889252i \(0.348774\pi\)
−0.457418 + 0.889252i \(0.651226\pi\)
\(774\) 27.4535 0.986797
\(775\) 11.2893 0.457361i 0.405523 0.0164289i
\(776\) 136.298 4.89283
\(777\) 3.26260i 0.117045i
\(778\) 82.5720i 2.96035i
\(779\) −16.5604 −0.593337
\(780\) 9.26985 0.187697i 0.331914 0.00672064i
\(781\) −10.8314 −0.387578
\(782\) 98.4980i 3.52228i
\(783\) 0.913059i 0.0326301i
\(784\) −15.6256 −0.558057
\(785\) −0.930058 45.9330i −0.0331952 1.63942i
\(786\) 45.3141 1.61630
\(787\) 5.07894i 0.181045i 0.995894 + 0.0905224i \(0.0288537\pi\)
−0.995894 + 0.0905224i \(0.971146\pi\)
\(788\) 70.3170i 2.50494i
\(789\) 1.58627 0.0564726
\(790\) 1.32119 + 65.2502i 0.0470060 + 2.32150i
\(791\) 0.0930496 0.00330846
\(792\) 9.72574i 0.345589i
\(793\) 7.29781i 0.259153i
\(794\) 69.5612 2.46863
\(795\) 12.6200 0.255532i 0.447586 0.00906278i
\(796\) 38.8133 1.37570
\(797\) 21.0140i 0.744354i 0.928162 + 0.372177i \(0.121389\pi\)
−0.928162 + 0.372177i \(0.878611\pi\)
\(798\) 3.95267i 0.139923i
\(799\) −51.8818 −1.83544
\(800\) 4.74814 + 117.201i 0.167872 + 4.14367i
\(801\) −5.61820 −0.198509
\(802\) 56.6672i 2.00099i
\(803\) 3.60606i 0.127255i
\(804\) 37.0887 1.30802
\(805\) −13.0307 + 0.263848i −0.459273 + 0.00929943i
\(806\) 4.64332 0.163554
\(807\) 3.62855i 0.127731i
\(808\) 25.6008i 0.900633i
\(809\) −42.3417 −1.48866 −0.744328 0.667814i \(-0.767230\pi\)
−0.744328 + 0.667814i \(0.767230\pi\)
\(810\) 0.124311 + 6.13940i 0.00436786 + 0.215717i
\(811\) 8.26639 0.290272 0.145136 0.989412i \(-0.453638\pi\)
0.145136 + 0.989412i \(0.453638\pi\)
\(812\) 5.05975i 0.177563i
\(813\) 8.16357i 0.286309i
\(814\) 8.95972 0.314038
\(815\) 0.0763086 + 3.76867i 0.00267297 + 0.132011i
\(816\) 96.1526 3.36601
\(817\) 14.3890i 0.503406i
\(818\) 71.6090i 2.50375i
\(819\) −0.748249 −0.0261459
\(820\) 142.540 2.88616i 4.97770 0.100789i
\(821\) 12.6391 0.441107 0.220553 0.975375i \(-0.429214\pi\)
0.220553 + 0.975375i \(0.429214\pi\)
\(822\) 55.3108i 1.92918i
\(823\) 26.7117i 0.931111i 0.885019 + 0.465555i \(0.154145\pi\)
−0.885019 + 0.465555i \(0.845855\pi\)
\(824\) −8.88821 −0.309635
\(825\) 0.202398 + 4.99590i 0.00704661 + 0.173935i
\(826\) −12.0182 −0.418166
\(827\) 54.8572i 1.90757i 0.300486 + 0.953786i \(0.402851\pi\)
−0.300486 + 0.953786i \(0.597149\pi\)
\(828\) 32.3001i 1.12251i
\(829\) 22.6349 0.786144 0.393072 0.919508i \(-0.371412\pi\)
0.393072 + 0.919508i \(0.371412\pi\)
\(830\) 82.5402 1.67128i 2.86501 0.0580111i
\(831\) 8.82549 0.306153
\(832\) 24.8214i 0.860526i
\(833\) 6.15353i 0.213207i
\(834\) −4.95292 −0.171506
\(835\) 0.640188 + 31.6171i 0.0221546 + 1.09416i
\(836\) 7.97612 0.275860
\(837\) 2.25971i 0.0781069i
\(838\) 60.2061i 2.07978i
\(839\) 8.57558 0.296062 0.148031 0.988983i \(-0.452706\pi\)
0.148031 + 0.988983i \(0.452706\pi\)
\(840\) −0.440254 21.7430i −0.0151902 0.750203i
\(841\) −28.1663 −0.971253
\(842\) 25.5459i 0.880369i
\(843\) 16.3437i 0.562908i
\(844\) 138.300 4.76048
\(845\) 27.8113 0.563126i 0.956736 0.0193721i
\(846\) 23.1537 0.796041
\(847\) 1.00000i 0.0343604i
\(848\) 88.2066i 3.02903i
\(849\) −11.6256 −0.398991
\(850\) −84.4244 + 3.42028i −2.89573 + 0.117315i
\(851\) −19.0168 −0.651888
\(852\) 60.0227i 2.05635i
\(853\) 36.0856i 1.23555i −0.786356 0.617774i \(-0.788035\pi\)
0.786356 0.617774i \(-0.211965\pi\)
\(854\) 26.7840 0.916531
\(855\) −3.21778 + 0.0651541i −0.110046 + 0.00222822i
\(856\) −117.682 −4.02229
\(857\) 35.6459i 1.21764i −0.793308 0.608820i \(-0.791643\pi\)
0.793308 0.608820i \(-0.208357\pi\)
\(858\) 2.05483i 0.0701508i
\(859\) −25.2433 −0.861289 −0.430644 0.902522i \(-0.641714\pi\)
−0.430644 + 0.902522i \(0.641714\pi\)
\(860\) −2.50773 123.850i −0.0855127 4.22324i
\(861\) −11.5056 −0.392110
\(862\) 77.7034i 2.64659i
\(863\) 10.9658i 0.373281i −0.982428 0.186641i \(-0.940240\pi\)
0.982428 0.186641i \(-0.0597600\pi\)
\(864\) −23.4594 −0.798104
\(865\) 0.605514 + 29.9047i 0.0205881 + 1.01679i
\(866\) 32.8604 1.11664
\(867\) 20.8659i 0.708643i
\(868\) 12.5223i 0.425033i
\(869\) −10.6281 −0.360534
\(870\) 5.60563 0.113504i 0.190049 0.00384813i
\(871\) −5.00792 −0.169687
\(872\) 196.541i 6.65571i
\(873\) 14.0142i 0.474309i
\(874\) −23.0390 −0.779307
\(875\) 0.678633 + 11.1597i 0.0229420 + 0.377268i
\(876\) 19.9831 0.675167
\(877\) 11.8214i 0.399179i −0.979880 0.199589i \(-0.936039\pi\)
0.979880 0.199589i \(-0.0639608\pi\)
\(878\) 58.9463i 1.98934i
\(879\) −8.77092 −0.295836
\(880\) −34.9328 + 0.707323i −1.17758 + 0.0238439i
\(881\) 0.829270 0.0279388 0.0139694 0.999902i \(-0.495553\pi\)
0.0139694 + 0.999902i \(0.495553\pi\)
\(882\) 2.74619i 0.0924689i
\(883\) 19.6106i 0.659950i 0.943990 + 0.329975i \(0.107040\pi\)
−0.943990 + 0.329975i \(0.892960\pi\)
\(884\) −25.5153 −0.858173
\(885\) −0.198103 9.78375i −0.00665915 0.328877i
\(886\) 65.4271 2.19807
\(887\) 28.2995i 0.950205i −0.879930 0.475103i \(-0.842411\pi\)
0.879930 0.475103i \(-0.157589\pi\)
\(888\) 31.7312i 1.06483i
\(889\) 14.7548 0.494861
\(890\) 0.698406 + 34.4924i 0.0234106 + 1.15619i
\(891\) −1.00000 −0.0335013
\(892\) 84.7648i 2.83814i
\(893\) 12.1353i 0.406093i
\(894\) −17.9122 −0.599074
\(895\) 47.5338 0.962470i 1.58888 0.0321718i
\(896\) 44.1794 1.47593
\(897\) 4.36134i 0.145621i
\(898\) 36.6824i 1.22411i
\(899\) 2.06325 0.0688131
\(900\) 27.6850 1.12160i 0.922833 0.0373866i
\(901\) −34.7367 −1.15725
\(902\) 31.5965i 1.05205i
\(903\) 9.99697i 0.332678i
\(904\) −0.904976 −0.0300991
\(905\) 23.7112 0.480107i 0.788186 0.0159593i
\(906\) −10.5378 −0.350094
\(907\) 0.464498i 0.0154234i −0.999970 0.00771170i \(-0.997545\pi\)
0.999970 0.00771170i \(-0.00245473\pi\)
\(908\) 127.557i 4.23311i
\(909\) 2.63227 0.0873070
\(910\) 0.0930159 + 4.59380i 0.00308345 + 0.152283i
\(911\) 3.65543 0.121110 0.0605549 0.998165i \(-0.480713\pi\)
0.0605549 + 0.998165i \(0.480713\pi\)
\(912\) 22.4904i 0.744733i
\(913\) 13.4443i 0.444942i
\(914\) 100.097 3.31093
\(915\) 0.441496 + 21.8043i 0.0145954 + 0.720828i
\(916\) 37.8701 1.25126
\(917\) 16.5007i 0.544902i
\(918\) 16.8987i 0.557741i
\(919\) −4.13390 −0.136365 −0.0681823 0.997673i \(-0.521720\pi\)
−0.0681823 + 0.997673i \(0.521720\pi\)
\(920\) 126.734 2.56612i 4.17828 0.0846024i
\(921\) −28.1213 −0.926628
\(922\) 70.8799i 2.33431i
\(923\) 8.10460i 0.266766i
\(924\) 5.54154 0.182303
\(925\) 0.660346 + 16.2996i 0.0217120 + 0.535929i
\(926\) −34.5191 −1.13437
\(927\) 0.913885i 0.0300159i
\(928\) 21.4198i 0.703139i
\(929\) 11.8017 0.387202 0.193601 0.981080i \(-0.437983\pi\)
0.193601 + 0.981080i \(0.437983\pi\)
\(930\) 13.8733 0.280908i 0.454922 0.00921132i
\(931\) −1.43933 −0.0471722
\(932\) 99.5608i 3.26122i
\(933\) 7.52137i 0.246239i
\(934\) 71.8596 2.35132
\(935\) −0.278551 13.7569i −0.00910960 0.449898i
\(936\) 7.27727 0.237865
\(937\) 17.1766i 0.561136i −0.959834 0.280568i \(-0.909477\pi\)
0.959834 0.280568i \(-0.0905229\pi\)
\(938\) 18.3798i 0.600122i
\(939\) 10.1735 0.331999
\(940\) −2.11496 104.452i −0.0689824 3.40685i
\(941\) −9.65994 −0.314905 −0.157453 0.987527i \(-0.550328\pi\)
−0.157453 + 0.987527i \(0.550328\pi\)
\(942\) 56.4234i 1.83837i
\(943\) 67.0630i 2.18387i
\(944\) 68.3827 2.22567
\(945\) −2.23561 + 0.0452669i −0.0727244 + 0.00147253i
\(946\) 27.4535 0.892592
\(947\) 22.0118i 0.715287i 0.933858 + 0.357643i \(0.116420\pi\)
−0.933858 + 0.357643i \(0.883580\pi\)
\(948\) 58.8961i 1.91285i
\(949\) −2.69823 −0.0875882
\(950\) 0.800015 + 19.7472i 0.0259559 + 0.640683i
\(951\) −1.97131 −0.0639241
\(952\) 59.8476i 1.93967i
\(953\) 16.2420i 0.526131i 0.964778 + 0.263065i \(0.0847335\pi\)
−0.964778 + 0.263065i \(0.915267\pi\)
\(954\) 15.5022 0.501903
\(955\) 1.47752 0.0299171i 0.0478115 0.000968094i
\(956\) −98.6990 −3.19215
\(957\) 0.913059i 0.0295150i
\(958\) 109.030i 3.52260i
\(959\) −20.1409 −0.650385
\(960\) 1.50162 + 74.1609i 0.0484646 + 2.39353i
\(961\) −25.8937 −0.835281
\(962\) 6.70410i 0.216149i
\(963\) 12.1001i 0.389919i
\(964\) −58.1340 −1.87237
\(965\) 0.287295 + 14.1887i 0.00924835 + 0.456751i
\(966\) −16.0068 −0.515009
\(967\) 28.7859i 0.925691i 0.886439 + 0.462846i \(0.153172\pi\)
−0.886439 + 0.462846i \(0.846828\pi\)
\(968\) 9.72574i 0.312597i
\(969\) 8.85697 0.284527
\(970\) −86.0389 + 1.74213i −2.76254 + 0.0559363i
\(971\) 28.6005 0.917833 0.458916 0.888479i \(-0.348238\pi\)
0.458916 + 0.888479i \(0.348238\pi\)
\(972\) 5.54154i 0.177745i
\(973\) 1.80356i 0.0578196i
\(974\) −36.5987 −1.17270
\(975\) −3.73818 + 0.151444i −0.119718 + 0.00485010i
\(976\) −152.399 −4.87818
\(977\) 61.8504i 1.97877i 0.145322 + 0.989384i \(0.453578\pi\)
−0.145322 + 0.989384i \(0.546422\pi\)
\(978\) 4.62938i 0.148031i
\(979\) −5.61820 −0.179558
\(980\) 12.3887 0.250849i 0.395743 0.00801306i
\(981\) 20.2083 0.645202
\(982\) 60.8202i 1.94085i
\(983\) 7.66340i 0.244425i −0.992504 0.122212i \(-0.961001\pi\)
0.992504 0.122212i \(-0.0389989\pi\)
\(984\) 111.900 3.56726
\(985\) −0.574395 28.3678i −0.0183018 0.903874i
\(986\) −15.4295 −0.491377
\(987\) 8.43122i 0.268369i
\(988\) 5.96812i 0.189871i
\(989\) −58.2696 −1.85286
\(990\) 0.124311 + 6.13940i 0.00395088 + 0.195123i
\(991\) 1.79343 0.0569703 0.0284851 0.999594i \(-0.490932\pi\)
0.0284851 + 0.999594i \(0.490932\pi\)
\(992\) 53.0113i 1.68311i
\(993\) 19.5659i 0.620906i
\(994\) −29.7451 −0.943457
\(995\) −15.6584 + 0.317052i −0.496403 + 0.0100512i
\(996\) 74.5023 2.36070
\(997\) 24.0260i 0.760911i −0.924799 0.380456i \(-0.875767\pi\)
0.924799 0.380456i \(-0.124233\pi\)
\(998\) 42.2962i 1.33886i
\(999\) −3.26260 −0.103224
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 1155.2.c.e.694.20 yes 20
5.2 odd 4 5775.2.a.cm.1.1 10
5.3 odd 4 5775.2.a.cp.1.10 10
5.4 even 2 inner 1155.2.c.e.694.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.c.e.694.1 20 5.4 even 2 inner
1155.2.c.e.694.20 yes 20 1.1 even 1 trivial
5775.2.a.cm.1.1 10 5.2 odd 4
5775.2.a.cp.1.10 10 5.3 odd 4