Properties

Label 1080.2.d.g.109.15
Level $1080$
Weight $2$
Character 1080.109
Analytic conductor $8.624$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1080,2,Mod(109,1080)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1080.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.d (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: \(8.62384341830\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} - 3 x^{14} + 36 x^{13} - 78 x^{12} - 96 x^{11} + 1194 x^{10} + 1456 x^{9} + 2243 x^{8} + 23019 x^{7} + 49749 x^{6} + 37798 x^{5} + 78784 x^{4} + 244612 x^{3} + \cdots + 45658 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.15
Root \(-1.59571 + 0.665253i\) of defining polynomial
Character \(\chi\) \(=\) 1080.109
Dual form 1080.2.d.g.109.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.05355 + 0.943417i) q^{2} +(0.219928 + 1.98787i) q^{4} +(0.463409 - 2.18752i) q^{5} -3.14971i q^{7} +(-1.64369 + 2.30180i) q^{8} +O(q^{10})\) \(q+(1.05355 + 0.943417i) q^{2} +(0.219928 + 1.98787i) q^{4} +(0.463409 - 2.18752i) q^{5} -3.14971i q^{7} +(-1.64369 + 2.30180i) q^{8} +(2.55197 - 1.86747i) q^{10} -2.42180i q^{11} -3.12253 q^{13} +(2.97150 - 3.31838i) q^{14} +(-3.90326 + 0.874375i) q^{16} -7.15192i q^{17} -2.34624i q^{19} +(4.45043 + 0.440100i) q^{20} +(2.28477 - 2.55148i) q^{22} +1.28934i q^{23} +(-4.57050 - 2.02743i) q^{25} +(-3.28973 - 2.94585i) q^{26} +(6.26123 - 0.692709i) q^{28} +4.21495i q^{29} +3.05999 q^{31} +(-4.93718 - 2.76121i) q^{32} +(6.74724 - 7.53489i) q^{34} +(-6.89007 - 1.45960i) q^{35} +1.37346 q^{37} +(2.21349 - 2.47188i) q^{38} +(4.27354 + 4.66228i) q^{40} +11.0754 q^{41} -9.70199 q^{43} +(4.81422 - 0.532620i) q^{44} +(-1.21639 + 1.35838i) q^{46} +0.627861i q^{47} -2.92070 q^{49} +(-2.90253 - 6.44789i) q^{50} +(-0.686730 - 6.20718i) q^{52} +9.54695 q^{53} +(-5.29774 - 1.12228i) q^{55} +(7.25002 + 5.17715i) q^{56} +(-3.97646 + 4.44066i) q^{58} -10.1066i q^{59} +12.7235i q^{61} +(3.22385 + 2.88685i) q^{62} +(-2.59658 - 7.56689i) q^{64} +(-1.44701 + 6.83059i) q^{65} -10.5125 q^{67} +(14.2171 - 1.57290i) q^{68} +(-5.88200 - 8.03798i) q^{70} +7.39000 q^{71} -5.73160i q^{73} +(1.44701 + 1.29575i) q^{74} +(4.66403 - 0.516004i) q^{76} -7.62797 q^{77} +11.2071 q^{79} +(0.103909 + 8.94367i) q^{80} +(11.6685 + 10.4488i) q^{82} +3.12640 q^{83} +(-15.6450 - 3.31426i) q^{85} +(-10.2215 - 9.15303i) q^{86} +(5.57450 + 3.98068i) q^{88} +15.9470 q^{89} +9.83507i q^{91} +(-2.56305 + 0.283562i) q^{92} +(-0.592335 + 0.661482i) q^{94} +(-5.13246 - 1.08727i) q^{95} +14.6589i q^{97} +(-3.07710 - 2.75544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8} + 5 q^{10} - 30 q^{16} - q^{20} - 22 q^{25} + 18 q^{32} - 4 q^{34} - 2 q^{35} + 56 q^{38} + 19 q^{40} + 40 q^{46} - 44 q^{49} - 27 q^{50} + 96 q^{53} + 34 q^{55} + 2 q^{62} - 6 q^{64} + 72 q^{68} - 7 q^{70} - 12 q^{77} + 4 q^{79} - 9 q^{80} + 64 q^{83} + 20 q^{92} - 20 q^{94} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).

\(n\) \(217\) \(271\) \(541\) \(1001\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05355 + 0.943417i 0.744971 + 0.667097i
\(3\) 0 0
\(4\) 0.219928 + 1.98787i 0.109964 + 0.993936i
\(5\) 0.463409 2.18752i 0.207243 0.978290i
\(6\) 0 0
\(7\) 3.14971i 1.19048i −0.803548 0.595240i \(-0.797057\pi\)
0.803548 0.595240i \(-0.202943\pi\)
\(8\) −1.64369 + 2.30180i −0.581131 + 0.813810i
\(9\) 0 0
\(10\) 2.55197 1.86747i 0.807004 0.590547i
\(11\) 2.42180i 0.730199i −0.930968 0.365100i \(-0.881035\pi\)
0.930968 0.365100i \(-0.118965\pi\)
\(12\) 0 0
\(13\) −3.12253 −0.866033 −0.433016 0.901386i \(-0.642551\pi\)
−0.433016 + 0.901386i \(0.642551\pi\)
\(14\) 2.97150 3.31838i 0.794166 0.886873i
\(15\) 0 0
\(16\) −3.90326 + 0.874375i −0.975816 + 0.218594i
\(17\) 7.15192i 1.73460i −0.497790 0.867298i \(-0.665855\pi\)
0.497790 0.867298i \(-0.334145\pi\)
\(18\) 0 0
\(19\) 2.34624i 0.538265i −0.963103 0.269133i \(-0.913263\pi\)
0.963103 0.269133i \(-0.0867370\pi\)
\(20\) 4.45043 + 0.440100i 0.995146 + 0.0984094i
\(21\) 0 0
\(22\) 2.28477 2.55148i 0.487114 0.543977i
\(23\) 1.28934i 0.268846i 0.990924 + 0.134423i \(0.0429182\pi\)
−0.990924 + 0.134423i \(0.957082\pi\)
\(24\) 0 0
\(25\) −4.57050 2.02743i −0.914101 0.405487i
\(26\) −3.28973 2.94585i −0.645169 0.577728i
\(27\) 0 0
\(28\) 6.26123 0.692709i 1.18326 0.130910i
\(29\) 4.21495i 0.782697i 0.920242 + 0.391349i \(0.127991\pi\)
−0.920242 + 0.391349i \(0.872009\pi\)
\(30\) 0 0
\(31\) 3.05999 0.549590 0.274795 0.961503i \(-0.411390\pi\)
0.274795 + 0.961503i \(0.411390\pi\)
\(32\) −4.93718 2.76121i −0.872778 0.488118i
\(33\) 0 0
\(34\) 6.74724 7.53489i 1.15714 1.29222i
\(35\) −6.89007 1.45960i −1.16463 0.246718i
\(36\) 0 0
\(37\) 1.37346 0.225795 0.112898 0.993607i \(-0.463987\pi\)
0.112898 + 0.993607i \(0.463987\pi\)
\(38\) 2.21349 2.47188i 0.359075 0.400992i
\(39\) 0 0
\(40\) 4.27354 + 4.66228i 0.675706 + 0.737171i
\(41\) 11.0754 1.72969 0.864847 0.502035i \(-0.167415\pi\)
0.864847 + 0.502035i \(0.167415\pi\)
\(42\) 0 0
\(43\) −9.70199 −1.47954 −0.739770 0.672860i \(-0.765066\pi\)
−0.739770 + 0.672860i \(0.765066\pi\)
\(44\) 4.81422 0.532620i 0.725771 0.0802955i
\(45\) 0 0
\(46\) −1.21639 + 1.35838i −0.179347 + 0.200283i
\(47\) 0.627861i 0.0915829i 0.998951 + 0.0457915i \(0.0145810\pi\)
−0.998951 + 0.0457915i \(0.985419\pi\)
\(48\) 0 0
\(49\) −2.92070 −0.417243
\(50\) −2.90253 6.44789i −0.410480 0.911870i
\(51\) 0 0
\(52\) −0.686730 6.20718i −0.0952323 0.860781i
\(53\) 9.54695 1.31137 0.655687 0.755033i \(-0.272379\pi\)
0.655687 + 0.755033i \(0.272379\pi\)
\(54\) 0 0
\(55\) −5.29774 1.12228i −0.714347 0.151328i
\(56\) 7.25002 + 5.17715i 0.968824 + 0.691825i
\(57\) 0 0
\(58\) −3.97646 + 4.44066i −0.522135 + 0.583087i
\(59\) 10.1066i 1.31577i −0.753117 0.657887i \(-0.771451\pi\)
0.753117 0.657887i \(-0.228549\pi\)
\(60\) 0 0
\(61\) 12.7235i 1.62908i 0.580106 + 0.814541i \(0.303011\pi\)
−0.580106 + 0.814541i \(0.696989\pi\)
\(62\) 3.22385 + 2.88685i 0.409429 + 0.366630i
\(63\) 0 0
\(64\) −2.59658 7.56689i −0.324573 0.945861i
\(65\) −1.44701 + 6.83059i −0.179479 + 0.847231i
\(66\) 0 0
\(67\) −10.5125 −1.28431 −0.642155 0.766575i \(-0.721959\pi\)
−0.642155 + 0.766575i \(0.721959\pi\)
\(68\) 14.2171 1.57290i 1.72408 0.190743i
\(69\) 0 0
\(70\) −5.88200 8.03798i −0.703034 0.960722i
\(71\) 7.39000 0.877031 0.438516 0.898724i \(-0.355504\pi\)
0.438516 + 0.898724i \(0.355504\pi\)
\(72\) 0 0
\(73\) 5.73160i 0.670833i −0.942070 0.335417i \(-0.891123\pi\)
0.942070 0.335417i \(-0.108877\pi\)
\(74\) 1.44701 + 1.29575i 0.168211 + 0.150627i
\(75\) 0 0
\(76\) 4.66403 0.516004i 0.535001 0.0591897i
\(77\) −7.62797 −0.869288
\(78\) 0 0
\(79\) 11.2071 1.26090 0.630449 0.776230i \(-0.282871\pi\)
0.630449 + 0.776230i \(0.282871\pi\)
\(80\) 0.103909 + 8.94367i 0.0116174 + 0.999933i
\(81\) 0 0
\(82\) 11.6685 + 10.4488i 1.28857 + 1.15387i
\(83\) 3.12640 0.343167 0.171584 0.985170i \(-0.445112\pi\)
0.171584 + 0.985170i \(0.445112\pi\)
\(84\) 0 0
\(85\) −15.6450 3.31426i −1.69694 0.359482i
\(86\) −10.2215 9.15303i −1.10221 0.986996i
\(87\) 0 0
\(88\) 5.57450 + 3.98068i 0.594243 + 0.424342i
\(89\) 15.9470 1.69038 0.845192 0.534464i \(-0.179486\pi\)
0.845192 + 0.534464i \(0.179486\pi\)
\(90\) 0 0
\(91\) 9.83507i 1.03100i
\(92\) −2.56305 + 0.283562i −0.267216 + 0.0295634i
\(93\) 0 0
\(94\) −0.592335 + 0.661482i −0.0610947 + 0.0682266i
\(95\) −5.13246 1.08727i −0.526579 0.111551i
\(96\) 0 0
\(97\) 14.6589i 1.48839i 0.667963 + 0.744194i \(0.267166\pi\)
−0.667963 + 0.744194i \(0.732834\pi\)
\(98\) −3.07710 2.75544i −0.310834 0.278342i
\(99\) 0 0
\(100\) 3.02510 9.53146i 0.302510 0.953146i
\(101\) 6.22901i 0.619810i 0.950768 + 0.309905i \(0.100297\pi\)
−0.950768 + 0.309905i \(0.899703\pi\)
\(102\) 0 0
\(103\) 10.6041i 1.04485i 0.852686 + 0.522424i \(0.174972\pi\)
−0.852686 + 0.522424i \(0.825028\pi\)
\(104\) 5.13246 7.18744i 0.503279 0.704786i
\(105\) 0 0
\(106\) 10.0582 + 9.00676i 0.976936 + 0.874814i
\(107\) 1.62797 0.157382 0.0786910 0.996899i \(-0.474926\pi\)
0.0786910 + 0.996899i \(0.474926\pi\)
\(108\) 0 0
\(109\) 1.56551i 0.149949i 0.997185 + 0.0749743i \(0.0238875\pi\)
−0.997185 + 0.0749743i \(0.976113\pi\)
\(110\) −4.52264 6.18035i −0.431217 0.589274i
\(111\) 0 0
\(112\) 2.75403 + 12.2942i 0.260232 + 1.16169i
\(113\) 8.57935i 0.807077i 0.914963 + 0.403538i \(0.132220\pi\)
−0.914963 + 0.403538i \(0.867780\pi\)
\(114\) 0 0
\(115\) 2.82046 + 0.597492i 0.263010 + 0.0557164i
\(116\) −8.37879 + 0.926985i −0.777951 + 0.0860684i
\(117\) 0 0
\(118\) 9.53478 10.6478i 0.877748 0.980213i
\(119\) −22.5265 −2.06500
\(120\) 0 0
\(121\) 5.13490 0.466809
\(122\) −12.0036 + 13.4049i −1.08676 + 1.21362i
\(123\) 0 0
\(124\) 0.672976 + 6.08286i 0.0604350 + 0.546257i
\(125\) −6.55307 + 9.05855i −0.586124 + 0.810221i
\(126\) 0 0
\(127\) 10.7524i 0.954124i −0.878870 0.477062i \(-0.841702\pi\)
0.878870 0.477062i \(-0.158298\pi\)
\(128\) 4.40311 10.4217i 0.389183 0.921160i
\(129\) 0 0
\(130\) −7.96859 + 5.83123i −0.698892 + 0.511433i
\(131\) 12.2083i 1.06664i −0.845913 0.533321i \(-0.820944\pi\)
0.845913 0.533321i \(-0.179056\pi\)
\(132\) 0 0
\(133\) −7.39000 −0.640794
\(134\) −11.0754 9.91770i −0.956773 0.856758i
\(135\) 0 0
\(136\) 16.4623 + 11.7555i 1.41163 + 1.00803i
\(137\) 7.44288i 0.635888i −0.948110 0.317944i \(-0.897008\pi\)
0.948110 0.317944i \(-0.102992\pi\)
\(138\) 0 0
\(139\) 10.1260i 0.858878i −0.903096 0.429439i \(-0.858711\pi\)
0.903096 0.429439i \(-0.141289\pi\)
\(140\) 1.38619 14.0176i 0.117154 1.18470i
\(141\) 0 0
\(142\) 7.78572 + 6.97185i 0.653363 + 0.585065i
\(143\) 7.56213i 0.632377i
\(144\) 0 0
\(145\) 9.22031 + 1.95325i 0.765705 + 0.162208i
\(146\) 5.40729 6.03852i 0.447511 0.499751i
\(147\) 0 0
\(148\) 0.302062 + 2.73026i 0.0248293 + 0.224426i
\(149\) 11.6233i 0.952217i 0.879386 + 0.476109i \(0.157953\pi\)
−0.879386 + 0.476109i \(0.842047\pi\)
\(150\) 0 0
\(151\) −10.0529 −0.818094 −0.409047 0.912513i \(-0.634139\pi\)
−0.409047 + 0.912513i \(0.634139\pi\)
\(152\) 5.40059 + 3.85649i 0.438045 + 0.312803i
\(153\) 0 0
\(154\) −8.03644 7.19636i −0.647594 0.579899i
\(155\) 1.41803 6.69379i 0.113899 0.537658i
\(156\) 0 0
\(157\) −13.3874 −1.06843 −0.534217 0.845347i \(-0.679394\pi\)
−0.534217 + 0.845347i \(0.679394\pi\)
\(158\) 11.8072 + 10.5730i 0.939333 + 0.841141i
\(159\) 0 0
\(160\) −8.32814 + 9.52062i −0.658397 + 0.752671i
\(161\) 4.06106 0.320056
\(162\) 0 0
\(163\) 1.37346 0.107578 0.0537888 0.998552i \(-0.482870\pi\)
0.0537888 + 0.998552i \(0.482870\pi\)
\(164\) 2.43580 + 22.0166i 0.190204 + 1.71920i
\(165\) 0 0
\(166\) 3.29382 + 2.94950i 0.255650 + 0.228926i
\(167\) 14.3227i 1.10832i −0.832410 0.554161i \(-0.813039\pi\)
0.832410 0.554161i \(-0.186961\pi\)
\(168\) 0 0
\(169\) −3.24983 −0.249987
\(170\) −13.3560 18.2515i −1.02436 1.39982i
\(171\) 0 0
\(172\) −2.13374 19.2863i −0.162696 1.47057i
\(173\) −3.96953 −0.301798 −0.150899 0.988549i \(-0.548217\pi\)
−0.150899 + 0.988549i \(0.548217\pi\)
\(174\) 0 0
\(175\) −6.38584 + 14.3958i −0.482724 + 1.08822i
\(176\) 2.11756 + 9.45292i 0.159617 + 0.712540i
\(177\) 0 0
\(178\) 16.8010 + 15.0447i 1.25929 + 1.12765i
\(179\) 11.3491i 0.848273i −0.905598 0.424137i \(-0.860578\pi\)
0.905598 0.424137i \(-0.139422\pi\)
\(180\) 0 0
\(181\) 15.5324i 1.15452i −0.816561 0.577259i \(-0.804122\pi\)
0.816561 0.577259i \(-0.195878\pi\)
\(182\) −9.27857 + 10.3617i −0.687774 + 0.768062i
\(183\) 0 0
\(184\) −2.96781 2.11928i −0.218790 0.156235i
\(185\) 0.636473 3.00447i 0.0467944 0.220893i
\(186\) 0 0
\(187\) −17.3205 −1.26660
\(188\) −1.24811 + 0.138084i −0.0910275 + 0.0100708i
\(189\) 0 0
\(190\) −4.38154 5.98754i −0.317871 0.434382i
\(191\) −27.0225 −1.95528 −0.977639 0.210288i \(-0.932560\pi\)
−0.977639 + 0.210288i \(0.932560\pi\)
\(192\) 0 0
\(193\) 8.40105i 0.604721i −0.953194 0.302360i \(-0.902225\pi\)
0.953194 0.302360i \(-0.0977746\pi\)
\(194\) −13.8295 + 15.4439i −0.992899 + 1.10881i
\(195\) 0 0
\(196\) −0.642343 5.80598i −0.0458817 0.414713i
\(197\) 10.4003 0.740989 0.370494 0.928835i \(-0.379188\pi\)
0.370494 + 0.928835i \(0.379188\pi\)
\(198\) 0 0
\(199\) −13.5659 −0.961665 −0.480832 0.876813i \(-0.659665\pi\)
−0.480832 + 0.876813i \(0.659665\pi\)
\(200\) 12.1792 7.18793i 0.861202 0.508263i
\(201\) 0 0
\(202\) −5.87656 + 6.56257i −0.413473 + 0.461741i
\(203\) 13.2759 0.931786
\(204\) 0 0
\(205\) 5.13246 24.2278i 0.358466 1.69214i
\(206\) −10.0041 + 11.1719i −0.697015 + 0.778382i
\(207\) 0 0
\(208\) 12.1880 2.73026i 0.845089 0.189309i
\(209\) −5.68213 −0.393041
\(210\) 0 0
\(211\) 24.5868i 1.69262i 0.532688 + 0.846312i \(0.321182\pi\)
−0.532688 + 0.846312i \(0.678818\pi\)
\(212\) 2.09964 + 18.9781i 0.144204 + 1.30342i
\(213\) 0 0
\(214\) 1.71515 + 1.53586i 0.117245 + 0.104989i
\(215\) −4.49599 + 21.2233i −0.306624 + 1.44742i
\(216\) 0 0
\(217\) 9.63809i 0.654276i
\(218\) −1.47693 + 1.64934i −0.100030 + 0.111707i
\(219\) 0 0
\(220\) 1.06583 10.7780i 0.0718585 0.726655i
\(221\) 22.3321i 1.50222i
\(222\) 0 0
\(223\) 10.6041i 0.710100i −0.934847 0.355050i \(-0.884464\pi\)
0.934847 0.355050i \(-0.115536\pi\)
\(224\) −8.69702 + 15.5507i −0.581094 + 1.03902i
\(225\) 0 0
\(226\) −8.09390 + 9.03875i −0.538398 + 0.601249i
\(227\) −12.5958 −0.836011 −0.418006 0.908444i \(-0.637271\pi\)
−0.418006 + 0.908444i \(0.637271\pi\)
\(228\) 0 0
\(229\) 9.75550i 0.644661i 0.946627 + 0.322331i \(0.104466\pi\)
−0.946627 + 0.322331i \(0.895534\pi\)
\(230\) 2.40781 + 3.29036i 0.158766 + 0.216960i
\(231\) 0 0
\(232\) −9.70199 6.92807i −0.636967 0.454850i
\(233\) 1.25572i 0.0822651i −0.999154 0.0411325i \(-0.986903\pi\)
0.999154 0.0411325i \(-0.0130966\pi\)
\(234\) 0 0
\(235\) 1.37346 + 0.290956i 0.0895946 + 0.0189799i
\(236\) 20.0907 2.22273i 1.30779 0.144687i
\(237\) 0 0
\(238\) −23.7328 21.2519i −1.53837 1.37756i
\(239\) 2.89401 0.187198 0.0935990 0.995610i \(-0.470163\pi\)
0.0935990 + 0.995610i \(0.470163\pi\)
\(240\) 0 0
\(241\) 22.4166 1.44398 0.721990 0.691903i \(-0.243228\pi\)
0.721990 + 0.691903i \(0.243228\pi\)
\(242\) 5.40986 + 4.84435i 0.347759 + 0.311407i
\(243\) 0 0
\(244\) −25.2928 + 2.79826i −1.61920 + 0.179140i
\(245\) −1.35348 + 6.38910i −0.0864706 + 0.408185i
\(246\) 0 0
\(247\) 7.32621i 0.466155i
\(248\) −5.02967 + 7.04349i −0.319384 + 0.447262i
\(249\) 0 0
\(250\) −15.4500 + 3.36134i −0.977141 + 0.212590i
\(251\) 12.2787i 0.775023i 0.921865 + 0.387512i \(0.126665\pi\)
−0.921865 + 0.387512i \(0.873335\pi\)
\(252\) 0 0
\(253\) 3.12253 0.196312
\(254\) 10.1440 11.3282i 0.636493 0.710795i
\(255\) 0 0
\(256\) 14.4709 6.82584i 0.904433 0.426615i
\(257\) 16.1354i 1.00650i −0.864141 0.503250i \(-0.832138\pi\)
0.864141 0.503250i \(-0.167862\pi\)
\(258\) 0 0
\(259\) 4.32600i 0.268805i
\(260\) −13.8966 1.37422i −0.861829 0.0852258i
\(261\) 0 0
\(262\) 11.5175 12.8620i 0.711553 0.794617i
\(263\) 5.20982i 0.321251i 0.987015 + 0.160626i \(0.0513512\pi\)
−0.987015 + 0.160626i \(0.948649\pi\)
\(264\) 0 0
\(265\) 4.42414 20.8842i 0.271773 1.28290i
\(266\) −7.78572 6.97185i −0.477373 0.427472i
\(267\) 0 0
\(268\) −2.31199 20.8975i −0.141227 1.27652i
\(269\) 18.1171i 1.10462i 0.833639 + 0.552310i \(0.186253\pi\)
−0.833639 + 0.552310i \(0.813747\pi\)
\(270\) 0 0
\(271\) 25.1014 1.52480 0.762402 0.647104i \(-0.224020\pi\)
0.762402 + 0.647104i \(0.224020\pi\)
\(272\) 6.25346 + 27.9158i 0.379172 + 1.69265i
\(273\) 0 0
\(274\) 7.02174 7.84143i 0.424199 0.473718i
\(275\) −4.91003 + 11.0688i −0.296086 + 0.667476i
\(276\) 0 0
\(277\) 23.9000 1.43601 0.718005 0.696038i \(-0.245056\pi\)
0.718005 + 0.696038i \(0.245056\pi\)
\(278\) 9.55307 10.6683i 0.572955 0.639839i
\(279\) 0 0
\(280\) 14.6848 13.4604i 0.877587 0.804415i
\(281\) −18.8411 −1.12396 −0.561982 0.827150i \(-0.689961\pi\)
−0.561982 + 0.827150i \(0.689961\pi\)
\(282\) 0 0
\(283\) 30.4794 1.81181 0.905907 0.423477i \(-0.139190\pi\)
0.905907 + 0.423477i \(0.139190\pi\)
\(284\) 1.62526 + 14.6904i 0.0964417 + 0.871713i
\(285\) 0 0
\(286\) −7.13424 + 7.96706i −0.421857 + 0.471102i
\(287\) 34.8845i 2.05917i
\(288\) 0 0
\(289\) −34.1499 −2.00882
\(290\) 7.87131 + 10.7564i 0.462219 + 0.631640i
\(291\) 0 0
\(292\) 11.3937 1.26054i 0.666765 0.0737674i
\(293\) 23.6233 1.38009 0.690043 0.723768i \(-0.257592\pi\)
0.690043 + 0.723768i \(0.257592\pi\)
\(294\) 0 0
\(295\) −22.1085 4.68351i −1.28721 0.272684i
\(296\) −2.25754 + 3.16143i −0.131217 + 0.183754i
\(297\) 0 0
\(298\) −10.9656 + 12.2457i −0.635221 + 0.709374i
\(299\) 4.02601i 0.232830i
\(300\) 0 0
\(301\) 30.5585i 1.76136i
\(302\) −10.5912 9.48409i −0.609457 0.545748i
\(303\) 0 0
\(304\) 2.05150 + 9.15801i 0.117661 + 0.525248i
\(305\) 27.8330 + 5.89620i 1.59371 + 0.337615i
\(306\) 0 0
\(307\) 9.13906 0.521594 0.260797 0.965394i \(-0.416015\pi\)
0.260797 + 0.965394i \(0.416015\pi\)
\(308\) −1.67760 15.1634i −0.0955902 0.864016i
\(309\) 0 0
\(310\) 7.80900 5.71445i 0.443521 0.324559i
\(311\) −29.5409 −1.67511 −0.837555 0.546353i \(-0.816016\pi\)
−0.837555 + 0.546353i \(0.816016\pi\)
\(312\) 0 0
\(313\) 11.6116i 0.656325i 0.944621 + 0.328163i \(0.106429\pi\)
−0.944621 + 0.328163i \(0.893571\pi\)
\(314\) −14.1043 12.6299i −0.795953 0.712749i
\(315\) 0 0
\(316\) 2.46475 + 22.2783i 0.138653 + 1.25325i
\(317\) 23.8869 1.34162 0.670812 0.741628i \(-0.265946\pi\)
0.670812 + 0.741628i \(0.265946\pi\)
\(318\) 0 0
\(319\) 10.2078 0.571525
\(320\) −17.7560 + 2.17352i −0.992591 + 0.121503i
\(321\) 0 0
\(322\) 4.27852 + 3.83127i 0.238433 + 0.213509i
\(323\) −16.7801 −0.933672
\(324\) 0 0
\(325\) 14.2715 + 6.33071i 0.791642 + 0.351165i
\(326\) 1.44701 + 1.29575i 0.0801422 + 0.0717647i
\(327\) 0 0
\(328\) −18.2046 + 25.4935i −1.00518 + 1.40764i
\(329\) 1.97758 0.109028
\(330\) 0 0
\(331\) 10.1260i 0.556577i 0.960498 + 0.278288i \(0.0897671\pi\)
−0.960498 + 0.278288i \(0.910233\pi\)
\(332\) 0.687582 + 6.21489i 0.0377360 + 0.341086i
\(333\) 0 0
\(334\) 13.5123 15.0896i 0.739358 0.825668i
\(335\) −4.87159 + 22.9964i −0.266164 + 1.25643i
\(336\) 0 0
\(337\) 1.55511i 0.0847123i 0.999103 + 0.0423561i \(0.0134864\pi\)
−0.999103 + 0.0423561i \(0.986514\pi\)
\(338\) −3.42385 3.06595i −0.186233 0.166765i
\(339\) 0 0
\(340\) 3.14756 31.8291i 0.170700 1.72618i
\(341\) 7.41068i 0.401311i
\(342\) 0 0
\(343\) 12.8486i 0.693760i
\(344\) 15.9470 22.3321i 0.859807 1.20406i
\(345\) 0 0
\(346\) −4.18210 3.74493i −0.224831 0.201329i
\(347\) −15.3552 −0.824310 −0.412155 0.911114i \(-0.635224\pi\)
−0.412155 + 0.911114i \(0.635224\pi\)
\(348\) 0 0
\(349\) 3.28995i 0.176107i 0.996116 + 0.0880536i \(0.0280647\pi\)
−0.996116 + 0.0880536i \(0.971935\pi\)
\(350\) −20.3090 + 9.14215i −1.08556 + 0.488668i
\(351\) 0 0
\(352\) −6.68709 + 11.9568i −0.356423 + 0.637302i
\(353\) 4.75322i 0.252989i −0.991967 0.126494i \(-0.959627\pi\)
0.991967 0.126494i \(-0.0403725\pi\)
\(354\) 0 0
\(355\) 3.42459 16.1658i 0.181758 0.857990i
\(356\) 3.50719 + 31.7007i 0.185881 + 1.68013i
\(357\) 0 0
\(358\) 10.7070 11.9568i 0.565880 0.631939i
\(359\) 7.76560 0.409853 0.204926 0.978777i \(-0.434304\pi\)
0.204926 + 0.978777i \(0.434304\pi\)
\(360\) 0 0
\(361\) 13.4951 0.710271
\(362\) 14.6536 16.3642i 0.770175 0.860082i
\(363\) 0 0
\(364\) −19.5508 + 2.16300i −1.02474 + 0.113372i
\(365\) −12.5380 2.65607i −0.656269 0.139025i
\(366\) 0 0
\(367\) 16.8214i 0.878068i −0.898471 0.439034i \(-0.855321\pi\)
0.898471 0.439034i \(-0.144679\pi\)
\(368\) −1.12737 5.03264i −0.0587682 0.262345i
\(369\) 0 0
\(370\) 3.50503 2.56490i 0.182218 0.133343i
\(371\) 30.0702i 1.56117i
\(372\) 0 0
\(373\) −5.99745 −0.310536 −0.155268 0.987872i \(-0.549624\pi\)
−0.155268 + 0.987872i \(0.549624\pi\)
\(374\) −18.2480 16.3405i −0.943581 0.844945i
\(375\) 0 0
\(376\) −1.44521 1.03201i −0.0745311 0.0532217i
\(377\) 13.1613i 0.677842i
\(378\) 0 0
\(379\) 22.3073i 1.14585i −0.819608 0.572925i \(-0.805808\pi\)
0.819608 0.572925i \(-0.194192\pi\)
\(380\) 1.03258 10.4418i 0.0529703 0.535652i
\(381\) 0 0
\(382\) −28.4695 25.4935i −1.45663 1.30436i
\(383\) 38.3484i 1.95951i 0.200198 + 0.979756i \(0.435842\pi\)
−0.200198 + 0.979756i \(0.564158\pi\)
\(384\) 0 0
\(385\) −3.53487 + 16.6864i −0.180154 + 0.850415i
\(386\) 7.92570 8.85091i 0.403407 0.450499i
\(387\) 0 0
\(388\) −29.1401 + 3.22390i −1.47936 + 0.163669i
\(389\) 17.2044i 0.872298i −0.899874 0.436149i \(-0.856342\pi\)
0.899874 0.436149i \(-0.143658\pi\)
\(390\) 0 0
\(391\) 9.22127 0.466340
\(392\) 4.80072 6.72288i 0.242473 0.339557i
\(393\) 0 0
\(394\) 10.9572 + 9.81180i 0.552015 + 0.494311i
\(395\) 5.19347 24.5158i 0.261312 1.23352i
\(396\) 0 0
\(397\) 12.0140 0.602965 0.301482 0.953472i \(-0.402519\pi\)
0.301482 + 0.953472i \(0.402519\pi\)
\(398\) −14.2924 12.7984i −0.716412 0.641523i
\(399\) 0 0
\(400\) 19.6126 + 3.91727i 0.980631 + 0.195863i
\(401\) 16.7576 0.836833 0.418417 0.908255i \(-0.362585\pi\)
0.418417 + 0.908255i \(0.362585\pi\)
\(402\) 0 0
\(403\) −9.55490 −0.475963
\(404\) −12.3825 + 1.36993i −0.616051 + 0.0681567i
\(405\) 0 0
\(406\) 13.9868 + 12.5247i 0.694154 + 0.621591i
\(407\) 3.32624i 0.164876i
\(408\) 0 0
\(409\) −33.7162 −1.66716 −0.833580 0.552399i \(-0.813712\pi\)
−0.833580 + 0.552399i \(0.813712\pi\)
\(410\) 28.2642 20.6831i 1.39587 1.02147i
\(411\) 0 0
\(412\) −21.0795 + 2.33212i −1.03851 + 0.114896i
\(413\) −31.8331 −1.56640
\(414\) 0 0
\(415\) 1.44880 6.83908i 0.0711189 0.335717i
\(416\) 15.4165 + 8.62195i 0.755854 + 0.422726i
\(417\) 0 0
\(418\) −5.98639 5.36062i −0.292804 0.262196i
\(419\) 25.1125i 1.22683i 0.789762 + 0.613413i \(0.210204\pi\)
−0.789762 + 0.613413i \(0.789796\pi\)
\(420\) 0 0
\(421\) 19.7185i 0.961023i −0.876988 0.480511i \(-0.840451\pi\)
0.876988 0.480511i \(-0.159549\pi\)
\(422\) −23.1956 + 25.9034i −1.12914 + 1.26096i
\(423\) 0 0
\(424\) −15.6922 + 21.9752i −0.762081 + 1.06721i
\(425\) −14.5000 + 32.6879i −0.703355 + 1.58560i
\(426\) 0 0
\(427\) 40.0755 1.93939
\(428\) 0.358036 + 3.23620i 0.0173063 + 0.156428i
\(429\) 0 0
\(430\) −24.7592 + 18.1182i −1.19399 + 0.873737i
\(431\) 21.2536 1.02375 0.511874 0.859061i \(-0.328951\pi\)
0.511874 + 0.859061i \(0.328951\pi\)
\(432\) 0 0
\(433\) 33.7002i 1.61953i 0.586757 + 0.809763i \(0.300404\pi\)
−0.586757 + 0.809763i \(0.699596\pi\)
\(434\) 9.09274 10.1542i 0.436466 0.487417i
\(435\) 0 0
\(436\) −3.11203 + 0.344299i −0.149039 + 0.0164889i
\(437\) 3.02511 0.144711
\(438\) 0 0
\(439\) 25.1313 1.19945 0.599725 0.800206i \(-0.295277\pi\)
0.599725 + 0.800206i \(0.295277\pi\)
\(440\) 11.2911 10.3497i 0.538282 0.493400i
\(441\) 0 0
\(442\) −21.0684 + 23.5279i −1.00212 + 1.11911i
\(443\) −20.5894 −0.978230 −0.489115 0.872219i \(-0.662680\pi\)
−0.489115 + 0.872219i \(0.662680\pi\)
\(444\) 0 0
\(445\) 7.39000 34.8845i 0.350319 1.65368i
\(446\) 10.0041 11.1719i 0.473706 0.529004i
\(447\) 0 0
\(448\) −23.8335 + 8.17849i −1.12603 + 0.386397i
\(449\) 9.09787 0.429355 0.214677 0.976685i \(-0.431130\pi\)
0.214677 + 0.976685i \(0.431130\pi\)
\(450\) 0 0
\(451\) 26.8225i 1.26302i
\(452\) −17.0546 + 1.88683i −0.802182 + 0.0887492i
\(453\) 0 0
\(454\) −13.2703 11.8831i −0.622804 0.557701i
\(455\) 21.5144 + 4.55765i 1.00861 + 0.213666i
\(456\) 0 0
\(457\) 7.10221i 0.332228i −0.986107 0.166114i \(-0.946878\pi\)
0.986107 0.166114i \(-0.0531219\pi\)
\(458\) −9.20351 + 10.2779i −0.430052 + 0.480254i
\(459\) 0 0
\(460\) −0.567440 + 5.73813i −0.0264570 + 0.267541i
\(461\) 2.20090i 0.102506i 0.998686 + 0.0512530i \(0.0163215\pi\)
−0.998686 + 0.0512530i \(0.983679\pi\)
\(462\) 0 0
\(463\) 28.7916i 1.33806i 0.743236 + 0.669029i \(0.233290\pi\)
−0.743236 + 0.669029i \(0.766710\pi\)
\(464\) −3.68545 16.4521i −0.171093 0.763769i
\(465\) 0 0
\(466\) 1.18467 1.32296i 0.0548788 0.0612851i
\(467\) 37.9504 1.75613 0.878067 0.478538i \(-0.158833\pi\)
0.878067 + 0.478538i \(0.158833\pi\)
\(468\) 0 0
\(469\) 33.1114i 1.52894i
\(470\) 1.17251 + 1.60228i 0.0540840 + 0.0739077i
\(471\) 0 0
\(472\) 23.2635 + 16.6122i 1.07079 + 0.764637i
\(473\) 23.4963i 1.08036i
\(474\) 0 0
\(475\) −4.75685 + 10.7235i −0.218259 + 0.492029i
\(476\) −4.95420 44.7798i −0.227075 2.05248i
\(477\) 0 0
\(478\) 3.04898 + 2.73026i 0.139457 + 0.124879i
\(479\) 4.49599 0.205427 0.102713 0.994711i \(-0.467248\pi\)
0.102713 + 0.994711i \(0.467248\pi\)
\(480\) 0 0
\(481\) −4.28866 −0.195546
\(482\) 23.6170 + 21.1482i 1.07572 + 0.963275i
\(483\) 0 0
\(484\) 1.12931 + 10.2075i 0.0513321 + 0.463978i
\(485\) 32.0667 + 6.79307i 1.45607 + 0.308457i
\(486\) 0 0
\(487\) 38.9154i 1.76342i 0.471789 + 0.881712i \(0.343609\pi\)
−0.471789 + 0.881712i \(0.656391\pi\)
\(488\) −29.2871 20.9135i −1.32576 0.946711i
\(489\) 0 0
\(490\) −7.45355 + 5.45433i −0.336717 + 0.246402i
\(491\) 4.19054i 0.189117i −0.995519 0.0945583i \(-0.969856\pi\)
0.995519 0.0945583i \(-0.0301439\pi\)
\(492\) 0 0
\(493\) 30.1450 1.35766
\(494\) −6.91167 + 7.71851i −0.310971 + 0.347272i
\(495\) 0 0
\(496\) −11.9439 + 2.67558i −0.536299 + 0.120137i
\(497\) 23.2764i 1.04409i
\(498\) 0 0
\(499\) 37.4693i 1.67735i −0.544629 0.838677i \(-0.683330\pi\)
0.544629 0.838677i \(-0.316670\pi\)
\(500\) −19.4484 11.0344i −0.869760 0.493474i
\(501\) 0 0
\(502\) −11.5839 + 12.9362i −0.517016 + 0.577370i
\(503\) 15.8317i 0.705900i −0.935642 0.352950i \(-0.885179\pi\)
0.935642 0.352950i \(-0.114821\pi\)
\(504\) 0 0
\(505\) 13.6261 + 2.88658i 0.606354 + 0.128451i
\(506\) 3.28973 + 2.94585i 0.146246 + 0.130959i
\(507\) 0 0
\(508\) 21.3744 2.36476i 0.948338 0.104919i
\(509\) 15.8382i 0.702018i −0.936372 0.351009i \(-0.885839\pi\)
0.936372 0.351009i \(-0.114161\pi\)
\(510\) 0 0
\(511\) −18.0529 −0.798614
\(512\) 21.6854 + 6.46078i 0.958370 + 0.285529i
\(513\) 0 0
\(514\) 15.2224 16.9994i 0.671432 0.749813i
\(515\) 23.1966 + 4.91401i 1.02216 + 0.216537i
\(516\) 0 0
\(517\) 1.52055 0.0668738
\(518\) 4.08123 4.55765i 0.179319 0.200252i
\(519\) 0 0
\(520\) −13.3442 14.5581i −0.585184 0.638414i
\(521\) 2.08348 0.0912788 0.0456394 0.998958i \(-0.485467\pi\)
0.0456394 + 0.998958i \(0.485467\pi\)
\(522\) 0 0
\(523\) −13.8224 −0.604410 −0.302205 0.953243i \(-0.597723\pi\)
−0.302205 + 0.953243i \(0.597723\pi\)
\(524\) 24.2685 2.68493i 1.06017 0.117292i
\(525\) 0 0
\(526\) −4.91504 + 5.48880i −0.214306 + 0.239323i
\(527\) 21.8848i 0.953317i
\(528\) 0 0
\(529\) 21.3376 0.927722
\(530\) 24.3635 17.8287i 1.05828 0.774428i
\(531\) 0 0
\(532\) −1.62526 14.6904i −0.0704641 0.636908i
\(533\) −34.5834 −1.49797
\(534\) 0 0
\(535\) 0.754416 3.56122i 0.0326163 0.153965i
\(536\) 17.2793 24.1977i 0.746352 1.04518i
\(537\) 0 0
\(538\) −17.0920 + 19.0872i −0.736888 + 0.822909i
\(539\) 7.07335i 0.304671i
\(540\) 0 0
\(541\) 6.68097i 0.287238i −0.989633 0.143619i \(-0.954126\pi\)
0.989633 0.143619i \(-0.0458739\pi\)
\(542\) 26.4456 + 23.6811i 1.13593 + 1.01719i
\(543\) 0 0
\(544\) −19.7480 + 35.3103i −0.846686 + 1.51392i
\(545\) 3.42459 + 0.725471i 0.146693 + 0.0310758i
\(546\) 0 0
\(547\) 18.9416 0.809883 0.404941 0.914343i \(-0.367292\pi\)
0.404941 + 0.914343i \(0.367292\pi\)
\(548\) 14.7955 1.63689i 0.632031 0.0699246i
\(549\) 0 0
\(550\) −15.6155 + 7.02934i −0.665847 + 0.299732i
\(551\) 9.88931 0.421299
\(552\) 0 0
\(553\) 35.2992i 1.50108i
\(554\) 25.1798 + 22.5476i 1.06979 + 0.957957i
\(555\) 0 0
\(556\) 20.1292 2.22699i 0.853669 0.0944455i
\(557\) −33.0653 −1.40102 −0.700511 0.713642i \(-0.747044\pi\)
−0.700511 + 0.713642i \(0.747044\pi\)
\(558\) 0 0
\(559\) 30.2947 1.28133
\(560\) 28.1700 0.327285i 1.19040 0.0138303i
\(561\) 0 0
\(562\) −19.8500 17.7750i −0.837320 0.749792i
\(563\) 2.95023 0.124337 0.0621686 0.998066i \(-0.480198\pi\)
0.0621686 + 0.998066i \(0.480198\pi\)
\(564\) 0 0
\(565\) 18.7675 + 3.97574i 0.789555 + 0.167261i
\(566\) 32.1115 + 28.7548i 1.34975 + 1.20866i
\(567\) 0 0
\(568\) −12.1468 + 17.0103i −0.509670 + 0.713737i
\(569\) 2.78811 0.116884 0.0584419 0.998291i \(-0.481387\pi\)
0.0584419 + 0.998291i \(0.481387\pi\)
\(570\) 0 0
\(571\) 15.0427i 0.629516i 0.949172 + 0.314758i \(0.101923\pi\)
−0.949172 + 0.314758i \(0.898077\pi\)
\(572\) −15.0325 + 1.66312i −0.628542 + 0.0695385i
\(573\) 0 0
\(574\) 32.9106 36.7525i 1.37366 1.53402i
\(575\) 2.61406 5.89295i 0.109014 0.245753i
\(576\) 0 0
\(577\) 23.1614i 0.964220i 0.876111 + 0.482110i \(0.160129\pi\)
−0.876111 + 0.482110i \(0.839871\pi\)
\(578\) −35.9786 32.2177i −1.49651 1.34008i
\(579\) 0 0
\(580\) −1.85500 + 18.7584i −0.0770248 + 0.778898i
\(581\) 9.84728i 0.408534i
\(582\) 0 0
\(583\) 23.1208i 0.957565i
\(584\) 13.1930 + 9.42096i 0.545931 + 0.389842i
\(585\) 0 0
\(586\) 24.8883 + 22.2866i 1.02812 + 0.920651i
\(587\) 14.0705 0.580751 0.290376 0.956913i \(-0.406220\pi\)
0.290376 + 0.956913i \(0.406220\pi\)
\(588\) 0 0
\(589\) 7.17948i 0.295825i
\(590\) −18.8739 25.7918i −0.777025 1.06183i
\(591\) 0 0
\(592\) −5.36097 + 1.20092i −0.220335 + 0.0493575i
\(593\) 1.42743i 0.0586174i −0.999570 0.0293087i \(-0.990669\pi\)
0.999570 0.0293087i \(-0.00933058\pi\)
\(594\) 0 0
\(595\) −10.4390 + 49.2772i −0.427956 + 2.02017i
\(596\) −23.1056 + 2.55628i −0.946443 + 0.104709i
\(597\) 0 0
\(598\) 3.79820 4.24159i 0.155320 0.173452i
\(599\) 26.6469 1.08876 0.544381 0.838838i \(-0.316765\pi\)
0.544381 + 0.838838i \(0.316765\pi\)
\(600\) 0 0
\(601\) −19.8748 −0.810710 −0.405355 0.914159i \(-0.632852\pi\)
−0.405355 + 0.914159i \(0.632852\pi\)
\(602\) −28.8294 + 32.1949i −1.17500 + 1.31216i
\(603\) 0 0
\(604\) −2.21091 19.9839i −0.0899607 0.813133i
\(605\) 2.37955 11.2327i 0.0967427 0.456674i
\(606\) 0 0
\(607\) 20.7546i 0.842403i 0.906967 + 0.421202i \(0.138391\pi\)
−0.906967 + 0.421202i \(0.861609\pi\)
\(608\) −6.47847 + 11.5838i −0.262737 + 0.469786i
\(609\) 0 0
\(610\) 23.7609 + 32.4701i 0.962049 + 1.31468i
\(611\) 1.96051i 0.0793138i
\(612\) 0 0
\(613\) 19.4040 0.783719 0.391860 0.920025i \(-0.371832\pi\)
0.391860 + 0.920025i \(0.371832\pi\)
\(614\) 9.62844 + 8.62195i 0.388572 + 0.347954i
\(615\) 0 0
\(616\) 12.5380 17.5581i 0.505171 0.707435i
\(617\) 38.5389i 1.55152i −0.631029 0.775759i \(-0.717367\pi\)
0.631029 0.775759i \(-0.282633\pi\)
\(618\) 0 0
\(619\) 14.4520i 0.580876i −0.956894 0.290438i \(-0.906199\pi\)
0.956894 0.290438i \(-0.0938010\pi\)
\(620\) 13.6183 + 1.34670i 0.546923 + 0.0540849i
\(621\) 0 0
\(622\) −31.1228 27.8694i −1.24791 1.11746i
\(623\) 50.2286i 2.01237i
\(624\) 0 0
\(625\) 16.7790 + 18.5328i 0.671161 + 0.741311i
\(626\) −10.9546 + 12.2334i −0.437832 + 0.488943i
\(627\) 0 0
\(628\) −2.94427 26.6125i −0.117489 1.06195i
\(629\) 9.82287i 0.391663i
\(630\) 0 0
\(631\) −40.5922 −1.61595 −0.807974 0.589218i \(-0.799436\pi\)
−0.807974 + 0.589218i \(0.799436\pi\)
\(632\) −18.4210 + 25.7966i −0.732748 + 1.02613i
\(633\) 0 0
\(634\) 25.1660 + 22.5353i 0.999471 + 0.894993i
\(635\) −23.5212 4.98277i −0.933410 0.197735i
\(636\) 0 0
\(637\) 9.11997 0.361346
\(638\) 10.7544 + 9.63019i 0.425770 + 0.381263i
\(639\) 0 0
\(640\) −20.7573 14.4614i −0.820506 0.571638i
\(641\) 11.8860 0.469468 0.234734 0.972060i \(-0.424578\pi\)
0.234734 + 0.972060i \(0.424578\pi\)
\(642\) 0 0
\(643\) 29.5630 1.16585 0.582925 0.812526i \(-0.301908\pi\)
0.582925 + 0.812526i \(0.301908\pi\)
\(644\) 0.893139 + 8.07287i 0.0351946 + 0.318115i
\(645\) 0 0
\(646\) −17.6787 15.8307i −0.695559 0.622850i
\(647\) 13.5816i 0.533949i −0.963704 0.266974i \(-0.913976\pi\)
0.963704 0.266974i \(-0.0860239\pi\)
\(648\) 0 0
\(649\) −24.4763 −0.960777
\(650\) 9.06323 + 20.1337i 0.355489 + 0.789709i
\(651\) 0 0
\(652\) 0.302062 + 2.73026i 0.0118296 + 0.106925i
\(653\) −2.80243 −0.109667 −0.0548337 0.998496i \(-0.517463\pi\)
−0.0548337 + 0.998496i \(0.517463\pi\)
\(654\) 0 0
\(655\) −26.7058 5.65741i −1.04348 0.221053i
\(656\) −43.2304 + 9.68410i −1.68786 + 0.378101i
\(657\) 0 0
\(658\) 2.08348 + 1.86569i 0.0812224 + 0.0727320i
\(659\) 0.0288607i 0.00112425i −1.00000 0.000562127i \(-0.999821\pi\)
1.00000 0.000562127i \(-0.000178931\pi\)
\(660\) 0 0
\(661\) 2.35497i 0.0915977i 0.998951 + 0.0457989i \(0.0145833\pi\)
−0.998951 + 0.0457989i \(0.985417\pi\)
\(662\) −9.55307 + 10.6683i −0.371290 + 0.414633i
\(663\) 0 0
\(664\) −5.13883 + 7.19636i −0.199425 + 0.279273i
\(665\) −3.42459 + 16.1658i −0.132800 + 0.626882i
\(666\) 0 0
\(667\) −5.43452 −0.210425
\(668\) 28.4716 3.14995i 1.10160 0.121875i
\(669\) 0 0
\(670\) −26.8276 + 19.6318i −1.03644 + 0.758444i
\(671\) 30.8138 1.18956
\(672\) 0 0
\(673\) 39.6306i 1.52765i 0.645425 + 0.763823i \(0.276680\pi\)
−0.645425 + 0.763823i \(0.723320\pi\)
\(674\) −1.46712 + 1.63838i −0.0565113 + 0.0631082i
\(675\) 0 0
\(676\) −0.714727 6.46024i −0.0274895 0.248471i
\(677\) −2.57428 −0.0989377 −0.0494688 0.998776i \(-0.515753\pi\)
−0.0494688 + 0.998776i \(0.515753\pi\)
\(678\) 0 0
\(679\) 46.1714 1.77190
\(680\) 33.3442 30.5640i 1.27869 1.17208i
\(681\) 0 0
\(682\) 6.99136 7.80750i 0.267713 0.298965i
\(683\) −4.26099 −0.163042 −0.0815211 0.996672i \(-0.525978\pi\)
−0.0815211 + 0.996672i \(0.525978\pi\)
\(684\) 0 0
\(685\) −16.2815 3.44909i −0.622082 0.131783i
\(686\) 12.1216 13.5366i 0.462805 0.516831i
\(687\) 0 0
\(688\) 37.8694 8.48318i 1.44376 0.323418i
\(689\) −29.8106 −1.13569
\(690\) 0 0
\(691\) 32.7768i 1.24689i 0.781868 + 0.623443i \(0.214267\pi\)
−0.781868 + 0.623443i \(0.785733\pi\)
\(692\) −0.873010 7.89092i −0.0331869 0.299968i
\(693\) 0 0
\(694\) −16.1774 14.4864i −0.614087 0.549895i
\(695\) −22.1509 4.69249i −0.840231 0.177996i
\(696\) 0 0
\(697\) 79.2107i 3.00032i
\(698\) −3.10380 + 3.46612i −0.117481 + 0.131195i
\(699\) 0 0
\(700\) −30.0214 9.52819i −1.13470 0.360132i
\(701\) 33.0385i 1.24785i −0.781486 0.623923i \(-0.785538\pi\)
0.781486 0.623923i \(-0.214462\pi\)
\(702\) 0 0
\(703\) 3.22247i 0.121538i
\(704\) −18.3255 + 6.28839i −0.690667 + 0.237003i
\(705\) 0 0
\(706\) 4.48427 5.00775i 0.168768 0.188469i
\(707\) 19.6196 0.737872
\(708\) 0 0
\(709\) 26.3511i 0.989637i 0.868996 + 0.494818i \(0.164765\pi\)
−0.868996 + 0.494818i \(0.835235\pi\)
\(710\) 18.8590 13.8006i 0.707767 0.517928i
\(711\) 0 0
\(712\) −26.2120 + 36.7069i −0.982335 + 1.37565i
\(713\) 3.94537i 0.147755i
\(714\) 0 0
\(715\) 16.5423 + 3.50435i 0.618648 + 0.131055i
\(716\) 22.5606 2.49598i 0.843129 0.0932793i
\(717\) 0 0
\(718\) 8.18144 + 7.32621i 0.305329 + 0.273412i
\(719\) −14.7800 −0.551201 −0.275600 0.961272i \(-0.588877\pi\)
−0.275600 + 0.961272i \(0.588877\pi\)
\(720\) 0 0
\(721\) 33.3998 1.24387
\(722\) 14.2178 + 12.7316i 0.529131 + 0.473819i
\(723\) 0 0
\(724\) 30.8765 3.41601i 1.14752 0.126955i
\(725\) 8.54554 19.2645i 0.317373 0.715465i
\(726\) 0 0
\(727\) 10.7322i 0.398035i −0.979996 0.199018i \(-0.936225\pi\)
0.979996 0.199018i \(-0.0637751\pi\)
\(728\) −22.6384 16.1658i −0.839034 0.599144i
\(729\) 0 0
\(730\) −10.7036 14.6269i −0.396158 0.541365i
\(731\) 69.3878i 2.56640i
\(732\) 0 0
\(733\) −20.7774 −0.767432 −0.383716 0.923451i \(-0.625356\pi\)
−0.383716 + 0.923451i \(0.625356\pi\)
\(734\) 15.8696 17.7221i 0.585756 0.654135i
\(735\) 0 0
\(736\) 3.56014 6.36571i 0.131229 0.234643i
\(737\) 25.4592i 0.937802i
\(738\) 0 0
\(739\) 14.7167i 0.541363i 0.962669 + 0.270682i \(0.0872490\pi\)
−0.962669 + 0.270682i \(0.912751\pi\)
\(740\) 6.11248 + 0.604460i 0.224699 + 0.0222204i
\(741\) 0 0
\(742\) 28.3687 31.6804i 1.04145 1.16302i
\(743\) 10.2244i 0.375098i 0.982255 + 0.187549i \(0.0600543\pi\)
−0.982255 + 0.187549i \(0.939946\pi\)
\(744\) 0 0
\(745\) 25.4262 + 5.38633i 0.931544 + 0.197340i
\(746\) −6.31860 5.65809i −0.231340 0.207158i
\(747\) 0 0
\(748\) −3.80926 34.4309i −0.139280 1.25892i
\(749\) 5.12765i 0.187360i
\(750\) 0 0
\(751\) −45.7533 −1.66956 −0.834780 0.550584i \(-0.814405\pi\)
−0.834780 + 0.550584i \(0.814405\pi\)
\(752\) −0.548986 2.45071i −0.0200195 0.0893681i
\(753\) 0 0
\(754\) 12.4166 13.8661i 0.452186 0.504973i
\(755\) −4.65860 + 21.9910i −0.169544 + 0.800333i
\(756\) 0 0
\(757\) −54.8143 −1.99226 −0.996130 0.0878903i \(-0.971987\pi\)
−0.996130 + 0.0878903i \(0.971987\pi\)
\(758\) 21.0451 23.5019i 0.764393 0.853626i
\(759\) 0 0
\(760\) 10.9388 10.0268i 0.396793 0.363709i
\(761\) −23.3179 −0.845275 −0.422637 0.906299i \(-0.638896\pi\)
−0.422637 + 0.906299i \(0.638896\pi\)
\(762\) 0 0
\(763\) 4.93091 0.178511
\(764\) −5.94299 53.7172i −0.215010 1.94342i
\(765\) 0 0
\(766\) −36.1785 + 40.4019i −1.30718 + 1.45978i
\(767\) 31.5583i 1.13950i
\(768\) 0 0
\(769\) −9.56833 −0.345043 −0.172521 0.985006i \(-0.555191\pi\)
−0.172521 + 0.985006i \(0.555191\pi\)
\(770\) −19.4664 + 14.2450i −0.701519 + 0.513355i
\(771\) 0 0
\(772\) 16.7002 1.84762i 0.601053 0.0664974i
\(773\) 22.8294 0.821117 0.410559 0.911834i \(-0.365334\pi\)
0.410559 + 0.911834i \(0.365334\pi\)
\(774\) 0 0
\(775\) −13.9857 6.20392i −0.502381 0.222852i
\(776\) −33.7419 24.0947i −1.21126 0.864949i
\(777\) 0 0
\(778\) 16.2309 18.1257i 0.581907 0.649837i
\(779\) 25.9857i 0.931034i
\(780\) 0 0
\(781\) 17.8971i 0.640408i
\(782\) 9.71505 + 8.69951i 0.347410 + 0.311094i
\(783\) 0 0
\(784\) 11.4003 2.55379i 0.407153 0.0912068i
\(785\) −6.20386 + 29.2853i −0.221425 + 1.04524i
\(786\) 0 0
\(787\) 23.6303 0.842328 0.421164 0.906985i \(-0.361622\pi\)
0.421164 + 0.906985i \(0.361622\pi\)
\(788\) 2.28731 + 20.6744i 0.0814819 + 0.736495i
\(789\) 0 0
\(790\) 28.6002 20.9290i 1.01755 0.744619i
\(791\) 27.0225 0.960809
\(792\) 0 0
\(793\) 39.7296i 1.41084i
\(794\) 12.6573 + 11.3342i 0.449191 + 0.402236i
\(795\) 0 0
\(796\) −2.98353 26.9674i −0.105748 0.955833i
\(797\) 15.5592 0.551134 0.275567 0.961282i \(-0.411134\pi\)
0.275567 + 0.961282i \(0.411134\pi\)
\(798\) 0 0
\(799\) 4.49041 0.158859
\(800\) 16.9672 + 22.6299i 0.599882 + 0.800088i
\(801\) 0 0
\(802\) 17.6549 + 15.8094i 0.623417 + 0.558249i
\(803\) −13.8808 −0.489842
\(804\) 0 0
\(805\) 1.88193 8.88366i 0.0663293 0.313108i
\(806\) −10.0665 9.01426i −0.354579 0.317514i
\(807\) 0 0
\(808\) −14.3380 10.2386i −0.504407 0.360191i
\(809\) −12.3484 −0.434146 −0.217073 0.976155i \(-0.569651\pi\)
−0.217073 + 0.976155i \(0.569651\pi\)
\(810\) 0 0
\(811\) 36.9485i 1.29744i −0.761028 0.648719i \(-0.775305\pi\)
0.761028 0.648719i \(-0.224695\pi\)
\(812\) 2.91974 + 26.3908i 0.102463 + 0.926135i
\(813\) 0 0
\(814\) 3.13803 3.50435i 0.109988 0.122828i
\(815\) 0.636473 3.00447i 0.0222947 0.105242i
\(816\) 0 0
\(817\) 22.7632i 0.796384i
\(818\) −35.5217 31.8085i −1.24199 1.11216i
\(819\) 0 0
\(820\) 49.2905 + 4.87431i 1.72130 + 0.170218i
\(821\) 10.1482i 0.354175i −0.984195 0.177087i \(-0.943332\pi\)
0.984195 0.177087i \(-0.0566675\pi\)
\(822\) 0 0
\(823\) 21.0044i 0.732166i −0.930582 0.366083i \(-0.880699\pi\)
0.930582 0.366083i \(-0.119301\pi\)
\(824\) −24.4084 17.4298i −0.850308 0.607194i
\(825\) 0 0
\(826\) −33.5377 30.0319i −1.16692 1.04494i
\(827\) −1.54049 −0.0535682 −0.0267841 0.999641i \(-0.508527\pi\)
−0.0267841 + 0.999641i \(0.508527\pi\)
\(828\) 0 0
\(829\) 6.68097i 0.232040i 0.993247 + 0.116020i \(0.0370136\pi\)
−0.993247 + 0.116020i \(0.962986\pi\)
\(830\) 7.97849 5.83847i 0.276937 0.202656i
\(831\) 0 0
\(832\) 8.10789 + 23.6278i 0.281091 + 0.819147i
\(833\) 20.8886i 0.723748i
\(834\) 0 0
\(835\) −31.3312 6.63725i −1.08426 0.229691i
\(836\) −1.24966 11.2953i −0.0432203 0.390657i
\(837\) 0 0
\(838\) −23.6916 + 26.4572i −0.818411 + 0.913950i
\(839\) 33.1670 1.14505 0.572527 0.819886i \(-0.305963\pi\)
0.572527 + 0.819886i \(0.305963\pi\)
\(840\) 0 0
\(841\) 11.2342 0.387385
\(842\) 18.6028 20.7744i 0.641095 0.715934i
\(843\) 0 0
\(844\) −48.8753 + 5.40731i −1.68236 + 0.186127i
\(845\) −1.50600 + 7.10907i −0.0518079 + 0.244560i
\(846\) 0 0
\(847\) 16.1735i 0.555727i
\(848\) −37.2643 + 8.34762i −1.27966 + 0.286658i
\(849\) 0 0
\(850\) −46.1148 + 20.7587i −1.58172 + 0.712017i
\(851\) 1.77086i 0.0607043i
\(852\) 0 0
\(853\) 41.5549 1.42281 0.711406 0.702781i \(-0.248059\pi\)
0.711406 + 0.702781i \(0.248059\pi\)
\(854\) 42.2215 + 37.8079i 1.44479 + 1.29376i
\(855\) 0 0
\(856\) −2.67588 + 3.74727i −0.0914596 + 0.128079i
\(857\) 40.4225i 1.38081i −0.723425 0.690403i \(-0.757433\pi\)
0.723425 0.690403i \(-0.242567\pi\)
\(858\) 0 0
\(859\) 27.9251i 0.952794i −0.879230 0.476397i \(-0.841943\pi\)
0.879230 0.476397i \(-0.158057\pi\)
\(860\) −43.1780 4.26985i −1.47236 0.145601i
\(861\) 0 0
\(862\) 22.3917 + 20.0510i 0.762663 + 0.682939i
\(863\) 38.4008i 1.30718i 0.756849 + 0.653590i \(0.226738\pi\)
−0.756849 + 0.653590i \(0.773262\pi\)
\(864\) 0 0
\(865\) −1.83952 + 8.68344i −0.0625454 + 0.295246i
\(866\) −31.7933 + 35.5047i −1.08038 + 1.20650i
\(867\) 0 0
\(868\) 19.1593 2.11968i 0.650309 0.0719467i
\(869\) 27.1414i 0.920708i
\(870\) 0 0
\(871\) 32.8256 1.11225
\(872\) −3.60349 2.57321i −0.122030 0.0871399i
\(873\) 0 0
\(874\) 3.18710 + 2.85394i 0.107805 + 0.0965360i
\(875\) 28.5318 + 20.6403i 0.964553 + 0.697769i
\(876\) 0 0
\(877\) −21.1530 −0.714288 −0.357144 0.934049i \(-0.616249\pi\)
−0.357144 + 0.934049i \(0.616249\pi\)
\(878\) 26.4770 + 23.7093i 0.893555 + 0.800149i
\(879\) 0 0
\(880\) 21.6598 0.251648i 0.730150 0.00848304i
\(881\) −33.9776 −1.14473 −0.572367 0.819998i \(-0.693975\pi\)
−0.572367 + 0.819998i \(0.693975\pi\)
\(882\) 0 0
\(883\) −14.5736 −0.490440 −0.245220 0.969467i \(-0.578860\pi\)
−0.245220 + 0.969467i \(0.578860\pi\)
\(884\) −44.3932 + 4.91143i −1.49311 + 0.165189i
\(885\) 0 0
\(886\) −21.6919 19.4244i −0.728753 0.652574i
\(887\) 24.3962i 0.819146i −0.912277 0.409573i \(-0.865678\pi\)
0.912277 0.409573i \(-0.134322\pi\)
\(888\) 0 0
\(889\) −33.8671 −1.13587
\(890\) 40.6964 29.7807i 1.36415 0.998250i
\(891\) 0 0
\(892\) 21.0795 2.33212i 0.705794 0.0780853i
\(893\) 1.47311 0.0492959
\(894\) 0 0
\(895\) −24.8264 5.25928i −0.829857 0.175798i
\(896\) −32.8255 13.8685i −1.09662 0.463315i
\(897\) 0 0
\(898\) 9.58504 + 8.58309i 0.319857 + 0.286421i
\(899\) 12.8977i 0.430163i
\(900\) 0 0
\(901\) 68.2790i 2.27470i
\(902\) 25.3048 28.2588i 0.842558 0.940915i
\(903\) 0 0
\(904\) −19.7480 14.1018i −0.656807 0.469018i
\(905\) −33.9776 7.19787i −1.12945 0.239265i
\(906\) 0 0
\(907\) −24.7326 −0.821233 −0.410616 0.911808i \(-0.634686\pi\)
−0.410616 + 0.911808i \(0.634686\pi\)
\(908\) −2.77016 25.0388i −0.0919310 0.830942i
\(909\) 0 0
\(910\) 18.3667 + 25.0988i 0.608851 + 0.832017i
\(911\) 29.3757 0.973260 0.486630 0.873608i \(-0.338226\pi\)
0.486630 + 0.873608i \(0.338226\pi\)
\(912\) 0 0
\(913\) 7.57152i 0.250581i
\(914\) 6.70035 7.48252i 0.221628 0.247500i
\(915\) 0 0
\(916\) −19.3927 + 2.14550i −0.640752 + 0.0708894i
\(917\) −38.4526 −1.26982
\(918\) 0 0
\(919\) 18.4626 0.609026 0.304513 0.952508i \(-0.401506\pi\)
0.304513 + 0.952508i \(0.401506\pi\)
\(920\) −6.01127 + 5.51006i −0.198186 + 0.181661i
\(921\) 0 0
\(922\) −2.07636 + 2.31875i −0.0683814 + 0.0763640i
\(923\) −23.0755 −0.759538
\(924\) 0 0
\(925\) −6.27740 2.78460i −0.206400 0.0915570i
\(926\) −27.1625 + 30.3333i −0.892614 + 0.996814i
\(927\) 0 0
\(928\) 11.6384 20.8100i 0.382048 0.683121i
\(929\) −45.4688 −1.49178 −0.745892 0.666067i \(-0.767977\pi\)
−0.745892 + 0.666067i \(0.767977\pi\)
\(930\) 0 0
\(931\) 6.85268i 0.224588i
\(932\) 2.49621 0.276168i 0.0817662 0.00904618i
\(933\) 0 0
\(934\) 39.9825 + 35.8030i 1.30827 + 1.17151i
\(935\) −8.02647 + 37.8890i −0.262494 + 1.23910i
\(936\) 0 0
\(937\) 5.96656i 0.194919i −0.995239 0.0974595i \(-0.968928\pi\)
0.995239 0.0974595i \(-0.0310716\pi\)
\(938\) −31.2379 + 34.8845i −1.01995 + 1.13902i
\(939\) 0 0
\(940\) −0.276322 + 2.79425i −0.00901262 + 0.0911384i
\(941\) 11.2275i 0.366006i −0.983112 0.183003i \(-0.941418\pi\)
0.983112 0.183003i \(-0.0585818\pi\)
\(942\) 0 0
\(943\) 14.2800i 0.465022i
\(944\) 8.83700 + 39.4489i 0.287620 + 1.28395i
\(945\) 0 0
\(946\) −22.1668 + 24.7544i −0.720704 + 0.804836i
\(947\) −33.1571 −1.07746 −0.538731 0.842478i \(-0.681096\pi\)
−0.538731 + 0.842478i \(0.681096\pi\)
\(948\) 0 0
\(949\) 17.8971i 0.580964i
\(950\) −15.1283 + 6.81005i −0.490828 + 0.220947i
\(951\) 0 0
\(952\) 37.0265 51.8515i 1.20004 1.68052i
\(953\) 9.07923i 0.294105i −0.989129 0.147053i \(-0.953021\pi\)
0.989129 0.147053i \(-0.0469786\pi\)
\(954\) 0 0
\(955\) −12.5225 + 59.1123i −0.405217 + 1.91283i
\(956\) 0.636473 + 5.75292i 0.0205850 + 0.186063i
\(957\) 0 0
\(958\) 4.73674 + 4.24159i 0.153037 + 0.137040i
\(959\) −23.4429 −0.757012
\(960\) 0 0
\(961\) −21.6365 −0.697950
\(962\) −4.51831 4.04600i −0.145676 0.130448i
\(963\) 0 0
\(964\) 4.93003 + 44.5613i 0.158786 + 1.43522i
\(965\) −18.3775 3.89312i −0.591592 0.125324i
\(966\) 0 0
\(967\) 41.4918i 1.33429i 0.744929 + 0.667144i \(0.232483\pi\)
−0.744929 + 0.667144i \(0.767517\pi\)
\(968\) −8.44017 + 11.8195i −0.271277 + 0.379893i
\(969\) 0 0
\(970\) 27.3751 + 37.4091i 0.878962 + 1.20113i
\(971\) 50.8245i 1.63104i 0.578731 + 0.815519i \(0.303548\pi\)
−0.578731 + 0.815519i \(0.696452\pi\)
\(972\) 0 0
\(973\) −31.8941 −1.02248
\(974\) −36.7134 + 40.9992i −1.17637 + 1.31370i
\(975\) 0 0
\(976\) −11.1252 49.6633i −0.356107 1.58968i
\(977\) 8.25072i 0.263964i −0.991252 0.131982i \(-0.957866\pi\)
0.991252 0.131982i \(-0.0421341\pi\)
\(978\) 0 0
\(979\) 38.6205i 1.23432i
\(980\) −12.9984 1.28540i −0.415218 0.0410607i
\(981\) 0 0
\(982\) 3.95343 4.41494i 0.126159 0.140886i
\(983\) 16.5792i 0.528796i 0.964414 + 0.264398i \(0.0851732\pi\)
−0.964414 + 0.264398i \(0.914827\pi\)
\(984\) 0 0
\(985\) 4.81958 22.7508i 0.153564 0.724902i
\(986\) 31.7592 + 28.4393i 1.01142 + 0.905693i
\(987\) 0 0
\(988\) −14.5636 + 1.61123i −0.463328 + 0.0512602i
\(989\) 12.5092i 0.397769i
\(990\) 0 0
\(991\) −15.3390 −0.487260 −0.243630 0.969868i \(-0.578338\pi\)
−0.243630 + 0.969868i \(0.578338\pi\)
\(992\) −15.1077 8.44927i −0.479670 0.268265i
\(993\) 0 0
\(994\) 21.9593 24.5228i 0.696508 0.777816i
\(995\) −6.28658 + 29.6758i −0.199298 + 0.940786i
\(996\) 0 0
\(997\) −40.0534 −1.26850 −0.634252 0.773126i \(-0.718692\pi\)
−0.634252 + 0.773126i \(0.718692\pi\)
\(998\) 35.3491 39.4757i 1.11896 1.24958i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1080.2.d.g.109.15 yes 16
3.2 odd 2 1080.2.d.h.109.2 yes 16
4.3 odd 2 4320.2.d.g.3889.9 16
5.4 even 2 1080.2.d.h.109.1 yes 16
8.3 odd 2 4320.2.d.h.3889.8 16
8.5 even 2 1080.2.d.h.109.4 yes 16
12.11 even 2 4320.2.d.h.3889.7 16
15.14 odd 2 inner 1080.2.d.g.109.16 yes 16
20.19 odd 2 4320.2.d.h.3889.6 16
24.5 odd 2 inner 1080.2.d.g.109.13 16
24.11 even 2 4320.2.d.g.3889.10 16
40.19 odd 2 4320.2.d.g.3889.11 16
40.29 even 2 inner 1080.2.d.g.109.14 yes 16
60.59 even 2 4320.2.d.g.3889.12 16
120.29 odd 2 1080.2.d.h.109.3 yes 16
120.59 even 2 4320.2.d.h.3889.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.2.d.g.109.13 16 24.5 odd 2 inner
1080.2.d.g.109.14 yes 16 40.29 even 2 inner
1080.2.d.g.109.15 yes 16 1.1 even 1 trivial
1080.2.d.g.109.16 yes 16 15.14 odd 2 inner
1080.2.d.h.109.1 yes 16 5.4 even 2
1080.2.d.h.109.2 yes 16 3.2 odd 2
1080.2.d.h.109.3 yes 16 120.29 odd 2
1080.2.d.h.109.4 yes 16 8.5 even 2
4320.2.d.g.3889.9 16 4.3 odd 2
4320.2.d.g.3889.10 16 24.11 even 2
4320.2.d.g.3889.11 16 40.19 odd 2
4320.2.d.g.3889.12 16 60.59 even 2
4320.2.d.h.3889.5 16 120.59 even 2
4320.2.d.h.3889.6 16 20.19 odd 2
4320.2.d.h.3889.7 16 12.11 even 2
4320.2.d.h.3889.8 16 8.3 odd 2