Properties

Label 675.2.q.a.368.4
Level $675$
Weight $2$
Character 675.368
Analytic conductor $5.390$
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] = [675,2,Mod(143,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.q (of order \(12\), degree \(4\), not 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 368.4
Root \(-0.347596 - 1.29724i\) of defining polynomial
Character \(\chi\) \(=\) 675.368
Dual form 675.2.q.a.332.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.347596 - 1.29724i) q^{2} +(0.170031 + 0.0981673i) q^{4} +(-1.97869 - 0.530190i) q^{7} +(2.08575 - 2.08575i) q^{8} +O(q^{10})\) \(q+(0.347596 - 1.29724i) q^{2} +(0.170031 + 0.0981673i) q^{4} +(-1.97869 - 0.530190i) q^{7} +(2.08575 - 2.08575i) q^{8} +(0.762281 - 0.440103i) q^{11} +(5.36743 - 1.43820i) q^{13} +(-1.37557 + 2.38256i) q^{14} +(-1.78439 - 3.09066i) q^{16} +(-1.13610 - 1.13610i) q^{17} -1.52456i q^{19} +(-0.305956 - 1.14184i) q^{22} +(0.410850 + 1.53331i) q^{23} -7.46278i q^{26} +(-0.284392 - 0.284392i) q^{28} +(-0.796583 - 1.37972i) q^{29} +(3.49518 - 6.05383i) q^{31} +(1.06878 - 0.286379i) q^{32} +(-1.86870 + 1.07889i) q^{34} +(4.25746 - 4.25746i) q^{37} +(-1.97773 - 0.529931i) q^{38} +(-3.11546 - 1.79871i) q^{41} +(-0.497959 + 1.85841i) q^{43} +0.172815 q^{44} +2.13189 q^{46} +(-2.14344 + 7.99942i) q^{47} +(-2.42805 - 1.40183i) q^{49} +(1.05381 + 0.282368i) q^{52} +(4.65601 - 4.65601i) q^{53} +(-5.23290 + 3.02121i) q^{56} +(-2.06672 + 0.553777i) q^{58} +(-3.81780 + 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(-6.63838 - 6.63838i) q^{62} -8.62358i q^{64} +(0.859733 + 3.20857i) q^{67} +(-0.0816439 - 0.304699i) q^{68} +5.89798i q^{71} +(-1.58900 - 1.58900i) q^{73} +(-4.04309 - 7.00284i) q^{74} +(0.149662 - 0.259222i) q^{76} +(-1.74166 + 0.466676i) q^{77} +(-6.69401 + 3.86479i) q^{79} +(-3.41628 + 3.41628i) q^{82} +(-9.59770 - 2.57170i) q^{83} +(2.23772 + 1.29195i) q^{86} +(0.671981 - 2.50787i) q^{88} +4.62765 q^{89} -11.3830 q^{91} +(-0.0806641 + 0.301043i) q^{92} +(9.63215 + 5.56112i) q^{94} +(-3.82988 - 1.02621i) q^{97} +(-2.66250 + 2.66250i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.347596 1.29724i 0.245787 0.917290i −0.727199 0.686427i \(-0.759178\pi\)
0.972986 0.230863i \(-0.0741551\pi\)
\(3\) 0 0
\(4\) 0.170031 + 0.0981673i 0.0850154 + 0.0490837i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.97869 0.530190i −0.747876 0.200393i −0.135300 0.990805i \(-0.543200\pi\)
−0.612576 + 0.790412i \(0.709867\pi\)
\(8\) 2.08575 2.08575i 0.737423 0.737423i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.762281 0.440103i 0.229836 0.132696i −0.380660 0.924715i \(-0.624303\pi\)
0.610497 + 0.792019i \(0.290970\pi\)
\(12\) 0 0
\(13\) 5.36743 1.43820i 1.48866 0.398885i 0.579374 0.815062i \(-0.303297\pi\)
0.909283 + 0.416177i \(0.136630\pi\)
\(14\) −1.37557 + 2.38256i −0.367637 + 0.636766i
\(15\) 0 0
\(16\) −1.78439 3.09066i −0.446098 0.772664i
\(17\) −1.13610 1.13610i −0.275544 0.275544i 0.555783 0.831327i \(-0.312418\pi\)
−0.831327 + 0.555783i \(0.812418\pi\)
\(18\) 0 0
\(19\) 1.52456i 0.349758i −0.984590 0.174879i \(-0.944047\pi\)
0.984590 0.174879i \(-0.0559535\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.305956 1.14184i −0.0652300 0.243442i
\(23\) 0.410850 + 1.53331i 0.0856682 + 0.319718i 0.995440 0.0953909i \(-0.0304101\pi\)
−0.909772 + 0.415109i \(0.863743\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 7.46278i 1.46357i
\(27\) 0 0
\(28\) −0.284392 0.284392i −0.0537450 0.0537450i
\(29\) −0.796583 1.37972i −0.147922 0.256208i 0.782537 0.622603i \(-0.213925\pi\)
−0.930459 + 0.366396i \(0.880592\pi\)
\(30\) 0 0
\(31\) 3.49518 6.05383i 0.627752 1.08730i −0.360249 0.932856i \(-0.617308\pi\)
0.988002 0.154443i \(-0.0493583\pi\)
\(32\) 1.06878 0.286379i 0.188936 0.0506251i
\(33\) 0 0
\(34\) −1.86870 + 1.07889i −0.320479 + 0.185029i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.25746 4.25746i 0.699922 0.699922i −0.264472 0.964393i \(-0.585198\pi\)
0.964393 + 0.264472i \(0.0851975\pi\)
\(38\) −1.97773 0.529931i −0.320830 0.0859661i
\(39\) 0 0
\(40\) 0 0
\(41\) −3.11546 1.79871i −0.486552 0.280911i 0.236591 0.971609i \(-0.423970\pi\)
−0.723143 + 0.690698i \(0.757303\pi\)
\(42\) 0 0
\(43\) −0.497959 + 1.85841i −0.0759380 + 0.283404i −0.993444 0.114317i \(-0.963532\pi\)
0.917506 + 0.397721i \(0.130199\pi\)
\(44\) 0.172815 0.0260528
\(45\) 0 0
\(46\) 2.13189 0.314330
\(47\) −2.14344 + 7.99942i −0.312652 + 1.16683i 0.613503 + 0.789693i \(0.289760\pi\)
−0.926155 + 0.377142i \(0.876907\pi\)
\(48\) 0 0
\(49\) −2.42805 1.40183i −0.346864 0.200262i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.05381 + 0.282368i 0.146137 + 0.0391574i
\(53\) 4.65601 4.65601i 0.639552 0.639552i −0.310893 0.950445i \(-0.600628\pi\)
0.950445 + 0.310893i \(0.100628\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −5.23290 + 3.02121i −0.699275 + 0.403727i
\(57\) 0 0
\(58\) −2.06672 + 0.553777i −0.271374 + 0.0727145i
\(59\) −3.81780 + 6.61262i −0.497035 + 0.860890i −0.999994 0.00342048i \(-0.998911\pi\)
0.502959 + 0.864310i \(0.332245\pi\)
\(60\) 0 0
\(61\) 6.64002 + 11.5008i 0.850167 + 1.47253i 0.881057 + 0.473010i \(0.156833\pi\)
−0.0308900 + 0.999523i \(0.509834\pi\)
\(62\) −6.63838 6.63838i −0.843075 0.843075i
\(63\) 0 0
\(64\) 8.62358i 1.07795i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.859733 + 3.20857i 0.105033 + 0.391989i 0.998349 0.0574406i \(-0.0182940\pi\)
−0.893316 + 0.449429i \(0.851627\pi\)
\(68\) −0.0816439 0.304699i −0.00990078 0.0369502i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.89798i 0.699961i 0.936757 + 0.349980i \(0.113812\pi\)
−0.936757 + 0.349980i \(0.886188\pi\)
\(72\) 0 0
\(73\) −1.58900 1.58900i −0.185979 0.185979i 0.607976 0.793955i \(-0.291982\pi\)
−0.793955 + 0.607976i \(0.791982\pi\)
\(74\) −4.04309 7.00284i −0.470000 0.814063i
\(75\) 0 0
\(76\) 0.149662 0.259222i 0.0171674 0.0297348i
\(77\) −1.74166 + 0.466676i −0.198480 + 0.0531827i
\(78\) 0 0
\(79\) −6.69401 + 3.86479i −0.753135 + 0.434823i −0.826826 0.562458i \(-0.809856\pi\)
0.0736905 + 0.997281i \(0.476522\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.41628 + 3.41628i −0.377265 + 0.377265i
\(83\) −9.59770 2.57170i −1.05348 0.282280i −0.309794 0.950804i \(-0.600260\pi\)
−0.743691 + 0.668523i \(0.766927\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.23772 + 1.29195i 0.241299 + 0.139314i
\(87\) 0 0
\(88\) 0.671981 2.50787i 0.0716334 0.267340i
\(89\) 4.62765 0.490530 0.245265 0.969456i \(-0.421125\pi\)
0.245265 + 0.969456i \(0.421125\pi\)
\(90\) 0 0
\(91\) −11.3830 −1.19327
\(92\) −0.0806641 + 0.301043i −0.00840982 + 0.0313859i
\(93\) 0 0
\(94\) 9.63215 + 5.56112i 0.993480 + 0.573586i
\(95\) 0 0
\(96\) 0 0
\(97\) −3.82988 1.02621i −0.388865 0.104196i 0.0590888 0.998253i \(-0.481180\pi\)
−0.447954 + 0.894057i \(0.647847\pi\)
\(98\) −2.66250 + 2.66250i −0.268953 + 0.268953i
\(99\) 0 0
\(100\) 0 0
\(101\) 2.23195 1.28862i 0.222087 0.128222i −0.384829 0.922988i \(-0.625740\pi\)
0.606916 + 0.794766i \(0.292406\pi\)
\(102\) 0 0
\(103\) −12.6183 + 3.38106i −1.24332 + 0.333146i −0.819752 0.572719i \(-0.805889\pi\)
−0.423566 + 0.905865i \(0.639222\pi\)
\(104\) 8.19538 14.1948i 0.803623 1.39192i
\(105\) 0 0
\(106\) −4.42157 7.65839i −0.429461 0.743848i
\(107\) 9.23034 + 9.23034i 0.892331 + 0.892331i 0.994742 0.102411i \(-0.0326557\pi\)
−0.102411 + 0.994742i \(0.532656\pi\)
\(108\) 0 0
\(109\) 8.05480i 0.771510i 0.922601 + 0.385755i \(0.126059\pi\)
−0.922601 + 0.385755i \(0.873941\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.89213 + 7.06153i 0.178790 + 0.667252i
\(113\) 3.10662 + 11.5941i 0.292246 + 1.09068i 0.943380 + 0.331714i \(0.107627\pi\)
−0.651134 + 0.758963i \(0.725706\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.312794i 0.0290422i
\(117\) 0 0
\(118\) 7.25113 + 7.25113i 0.667521 + 0.667521i
\(119\) 1.64564 + 2.85034i 0.150856 + 0.261290i
\(120\) 0 0
\(121\) −5.11262 + 8.85532i −0.464784 + 0.805029i
\(122\) 17.2274 4.61608i 1.55970 0.417920i
\(123\) 0 0
\(124\) 1.18858 0.686224i 0.106737 0.0616248i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.90230 + 1.90230i −0.168802 + 0.168802i −0.786452 0.617651i \(-0.788085\pi\)
0.617651 + 0.786452i \(0.288085\pi\)
\(128\) −9.04933 2.42476i −0.799855 0.214321i
\(129\) 0 0
\(130\) 0 0
\(131\) 18.5109 + 10.6873i 1.61731 + 0.933754i 0.987613 + 0.156912i \(0.0501541\pi\)
0.629696 + 0.776841i \(0.283179\pi\)
\(132\) 0 0
\(133\) −0.808307 + 3.01664i −0.0700891 + 0.261576i
\(134\) 4.46113 0.385383
\(135\) 0 0
\(136\) −4.73922 −0.406385
\(137\) 1.77541 6.62594i 0.151684 0.566092i −0.847683 0.530504i \(-0.822003\pi\)
0.999367 0.0355883i \(-0.0113305\pi\)
\(138\) 0 0
\(139\) −1.24863 0.720896i −0.105907 0.0611456i 0.446111 0.894978i \(-0.352809\pi\)
−0.552018 + 0.833832i \(0.686142\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.65111 + 2.05011i 0.642067 + 0.172041i
\(143\) 3.45853 3.45853i 0.289217 0.289217i
\(144\) 0 0
\(145\) 0 0
\(146\) −2.61366 + 1.50900i −0.216308 + 0.124885i
\(147\) 0 0
\(148\) 1.14184 0.305956i 0.0938589 0.0251494i
\(149\) −8.28457 + 14.3493i −0.678699 + 1.17554i 0.296674 + 0.954979i \(0.404122\pi\)
−0.975373 + 0.220562i \(0.929211\pi\)
\(150\) 0 0
\(151\) 0.00283730 + 0.00491435i 0.000230896 + 0.000399924i 0.866141 0.499800i \(-0.166593\pi\)
−0.865910 + 0.500200i \(0.833260\pi\)
\(152\) −3.17985 3.17985i −0.257920 0.257920i
\(153\) 0 0
\(154\) 2.42157i 0.195136i
\(155\) 0 0
\(156\) 0 0
\(157\) −2.18944 8.17112i −0.174737 0.652126i −0.996596 0.0824362i \(-0.973730\pi\)
0.821860 0.569690i \(-0.192937\pi\)
\(158\) 2.68677 + 10.0272i 0.213748 + 0.797717i
\(159\) 0 0
\(160\) 0 0
\(161\) 3.25179i 0.256277i
\(162\) 0 0
\(163\) −4.19302 4.19302i −0.328422 0.328422i 0.523564 0.851986i \(-0.324602\pi\)
−0.851986 + 0.523564i \(0.824602\pi\)
\(164\) −0.353149 0.611672i −0.0275763 0.0477635i
\(165\) 0 0
\(166\) −6.67224 + 11.5567i −0.517866 + 0.896970i
\(167\) −5.76334 + 1.54428i −0.445980 + 0.119500i −0.474818 0.880084i \(-0.657486\pi\)
0.0288375 + 0.999584i \(0.490819\pi\)
\(168\) 0 0
\(169\) 15.4826 8.93886i 1.19097 0.687605i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.267103 + 0.267103i −0.0203664 + 0.0203664i
\(173\) 13.1994 + 3.53677i 1.00353 + 0.268896i 0.722925 0.690927i \(-0.242797\pi\)
0.280608 + 0.959822i \(0.409464\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.72042 1.57063i −0.205059 0.118391i
\(177\) 0 0
\(178\) 1.60855 6.00319i 0.120566 0.449958i
\(179\) 17.2370 1.28836 0.644178 0.764875i \(-0.277199\pi\)
0.644178 + 0.764875i \(0.277199\pi\)
\(180\) 0 0
\(181\) 14.7708 1.09790 0.548952 0.835854i \(-0.315027\pi\)
0.548952 + 0.835854i \(0.315027\pi\)
\(182\) −3.95669 + 14.7666i −0.293289 + 1.09457i
\(183\) 0 0
\(184\) 4.05503 + 2.34117i 0.298941 + 0.172594i
\(185\) 0 0
\(186\) 0 0
\(187\) −1.36603 0.366025i −0.0998937 0.0267664i
\(188\) −1.14973 + 1.14973i −0.0838528 + 0.0838528i
\(189\) 0 0
\(190\) 0 0
\(191\) −4.56792 + 2.63729i −0.330523 + 0.190827i −0.656073 0.754697i \(-0.727784\pi\)
0.325550 + 0.945525i \(0.394450\pi\)
\(192\) 0 0
\(193\) 8.98952 2.40873i 0.647080 0.173384i 0.0796715 0.996821i \(-0.474613\pi\)
0.567408 + 0.823437i \(0.307946\pi\)
\(194\) −2.66250 + 4.61158i −0.191156 + 0.331092i
\(195\) 0 0
\(196\) −0.275228 0.476709i −0.0196592 0.0340507i
\(197\) −9.49539 9.49539i −0.676519 0.676519i 0.282692 0.959211i \(-0.408773\pi\)
−0.959211 + 0.282692i \(0.908773\pi\)
\(198\) 0 0
\(199\) 17.6342i 1.25005i 0.780604 + 0.625026i \(0.214912\pi\)
−0.780604 + 0.625026i \(0.785088\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −0.895835 3.34330i −0.0630307 0.235234i
\(203\) 0.844680 + 3.15239i 0.0592849 + 0.221254i
\(204\) 0 0
\(205\) 0 0
\(206\) 17.5443i 1.22237i
\(207\) 0 0
\(208\) −14.0226 14.0226i −0.972291 0.972291i
\(209\) −0.670964 1.16214i −0.0464116 0.0803872i
\(210\) 0 0
\(211\) 0.0616050 0.106703i 0.00424106 0.00734574i −0.863897 0.503668i \(-0.831983\pi\)
0.868138 + 0.496323i \(0.165317\pi\)
\(212\) 1.24873 0.334597i 0.0857633 0.0229802i
\(213\) 0 0
\(214\) 15.1824 8.76558i 1.03785 0.599203i
\(215\) 0 0
\(216\) 0 0
\(217\) −10.1256 + 10.1256i −0.687368 + 0.687368i
\(218\) 10.4490 + 2.79981i 0.707698 + 0.189627i
\(219\) 0 0
\(220\) 0 0
\(221\) −7.73186 4.46399i −0.520101 0.300281i
\(222\) 0 0
\(223\) −0.648014 + 2.41842i −0.0433942 + 0.161949i −0.984223 0.176933i \(-0.943382\pi\)
0.940829 + 0.338883i \(0.110049\pi\)
\(224\) −2.26663 −0.151445
\(225\) 0 0
\(226\) 16.1202 1.07230
\(227\) 3.94671 14.7293i 0.261952 0.977619i −0.702137 0.712042i \(-0.747771\pi\)
0.964090 0.265577i \(-0.0855626\pi\)
\(228\) 0 0
\(229\) −19.1083 11.0322i −1.26271 0.729029i −0.289116 0.957294i \(-0.593361\pi\)
−0.973599 + 0.228265i \(0.926695\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.53922 1.21628i −0.298014 0.0798527i
\(233\) −4.22173 + 4.22173i −0.276575 + 0.276575i −0.831740 0.555165i \(-0.812655\pi\)
0.555165 + 0.831740i \(0.312655\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.29829 + 0.749566i −0.0845112 + 0.0487926i
\(237\) 0 0
\(238\) 4.26960 1.14404i 0.276757 0.0741569i
\(239\) 6.79199 11.7641i 0.439338 0.760955i −0.558301 0.829639i \(-0.688547\pi\)
0.997639 + 0.0686835i \(0.0218799\pi\)
\(240\) 0 0
\(241\) −2.56728 4.44666i −0.165373 0.286434i 0.771415 0.636333i \(-0.219549\pi\)
−0.936788 + 0.349898i \(0.886216\pi\)
\(242\) 9.71038 + 9.71038i 0.624207 + 0.624207i
\(243\) 0 0
\(244\) 2.60733i 0.166917i
\(245\) 0 0
\(246\) 0 0
\(247\) −2.19262 8.18298i −0.139513 0.520670i
\(248\) −5.33669 19.9168i −0.338880 1.26472i
\(249\) 0 0
\(250\) 0 0
\(251\) 2.60221i 0.164250i −0.996622 0.0821251i \(-0.973829\pi\)
0.996622 0.0821251i \(-0.0261707\pi\)
\(252\) 0 0
\(253\) 0.987999 + 0.987999i 0.0621150 + 0.0621150i
\(254\) 1.80652 + 3.12898i 0.113351 + 0.196329i
\(255\) 0 0
\(256\) 2.33257 4.04013i 0.145786 0.252508i
\(257\) −10.1958 + 2.73197i −0.635999 + 0.170415i −0.562390 0.826872i \(-0.690118\pi\)
−0.0736085 + 0.997287i \(0.523452\pi\)
\(258\) 0 0
\(259\) −10.6815 + 6.16695i −0.663714 + 0.383196i
\(260\) 0 0
\(261\) 0 0
\(262\) 20.2984 20.2984i 1.25404 1.25404i
\(263\) −8.12541 2.17720i −0.501034 0.134252i −0.000554412 1.00000i \(-0.500176\pi\)
−0.500480 + 0.865748i \(0.666843\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 3.63236 + 2.09714i 0.222714 + 0.128584i
\(267\) 0 0
\(268\) −0.168795 + 0.629953i −0.0103108 + 0.0384805i
\(269\) −26.7708 −1.63225 −0.816123 0.577878i \(-0.803881\pi\)
−0.816123 + 0.577878i \(0.803881\pi\)
\(270\) 0 0
\(271\) −18.5850 −1.12896 −0.564480 0.825447i \(-0.690923\pi\)
−0.564480 + 0.825447i \(0.690923\pi\)
\(272\) −1.48405 + 5.53853i −0.0899834 + 0.335823i
\(273\) 0 0
\(274\) −7.97833 4.60629i −0.481989 0.278276i
\(275\) 0 0
\(276\) 0 0
\(277\) 26.3206 + 7.05259i 1.58145 + 0.423749i 0.939375 0.342891i \(-0.111406\pi\)
0.642078 + 0.766640i \(0.278073\pi\)
\(278\) −1.36920 + 1.36920i −0.0821189 + 0.0821189i
\(279\) 0 0
\(280\) 0 0
\(281\) 22.7050 13.1087i 1.35447 0.782002i 0.365595 0.930774i \(-0.380865\pi\)
0.988872 + 0.148772i \(0.0475320\pi\)
\(282\) 0 0
\(283\) −3.44050 + 0.921880i −0.204517 + 0.0548001i −0.359623 0.933098i \(-0.617095\pi\)
0.155106 + 0.987898i \(0.450428\pi\)
\(284\) −0.578988 + 1.00284i −0.0343566 + 0.0595074i
\(285\) 0 0
\(286\) −3.28439 5.68873i −0.194210 0.336382i
\(287\) 5.21088 + 5.21088i 0.307589 + 0.307589i
\(288\) 0 0
\(289\) 14.4186i 0.848151i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.114191 0.426168i −0.00668254 0.0249396i
\(293\) 0.771199 + 2.87816i 0.0450539 + 0.168144i 0.984787 0.173765i \(-0.0555933\pi\)
−0.939733 + 0.341909i \(0.888927\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 17.7600i 1.03228i
\(297\) 0 0
\(298\) 15.7349 + 15.7349i 0.911496 + 0.911496i
\(299\) 4.41042 + 7.63907i 0.255061 + 0.441779i
\(300\) 0 0
\(301\) 1.97062 3.41321i 0.113584 0.196734i
\(302\) 0.00736135 0.00197247i 0.000423598 0.000113503i
\(303\) 0 0
\(304\) −4.71190 + 2.72042i −0.270246 + 0.156027i
\(305\) 0 0
\(306\) 0 0
\(307\) −21.8017 + 21.8017i −1.24429 + 1.24429i −0.286081 + 0.958205i \(0.592353\pi\)
−0.958205 + 0.286081i \(0.907647\pi\)
\(308\) −0.341948 0.0916247i −0.0194843 0.00522080i
\(309\) 0 0
\(310\) 0 0
\(311\) −29.3878 16.9671i −1.66643 0.962114i −0.969539 0.244939i \(-0.921232\pi\)
−0.696892 0.717176i \(-0.745435\pi\)
\(312\) 0 0
\(313\) −6.00279 + 22.4027i −0.339298 + 1.26628i 0.559836 + 0.828603i \(0.310864\pi\)
−0.899134 + 0.437673i \(0.855803\pi\)
\(314\) −11.3610 −0.641137
\(315\) 0 0
\(316\) −1.51758 −0.0853708
\(317\) −1.03536 + 3.86401i −0.0581515 + 0.217024i −0.988887 0.148669i \(-0.952501\pi\)
0.930736 + 0.365693i \(0.119168\pi\)
\(318\) 0 0
\(319\) −1.21444 0.701157i −0.0679956 0.0392573i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.21836 1.13031i −0.235080 0.0629896i
\(323\) −1.73205 + 1.73205i −0.0963739 + 0.0963739i
\(324\) 0 0
\(325\) 0 0
\(326\) −6.89684 + 3.98189i −0.381981 + 0.220537i
\(327\) 0 0
\(328\) −10.2497 + 2.74640i −0.565945 + 0.151645i
\(329\) 8.48242 14.6920i 0.467651 0.809995i
\(330\) 0 0
\(331\) −2.98175 5.16454i −0.163892 0.283869i 0.772369 0.635174i \(-0.219071\pi\)
−0.936261 + 0.351305i \(0.885738\pi\)
\(332\) −1.37945 1.37945i −0.0757071 0.0757071i
\(333\) 0 0
\(334\) 8.01324i 0.438465i
\(335\) 0 0
\(336\) 0 0
\(337\) 2.56397 + 9.56887i 0.139668 + 0.521250i 0.999935 + 0.0114051i \(0.00363044\pi\)
−0.860267 + 0.509845i \(0.829703\pi\)
\(338\) −6.21422 23.1918i −0.338009 1.26147i
\(339\) 0 0
\(340\) 0 0
\(341\) 6.15295i 0.333201i
\(342\) 0 0
\(343\) 14.2007 + 14.2007i 0.766764 + 0.766764i
\(344\) 2.83755 + 4.91478i 0.152990 + 0.264987i
\(345\) 0 0
\(346\) 9.17611 15.8935i 0.493311 0.854440i
\(347\) −10.2471 + 2.74569i −0.550091 + 0.147396i −0.523150 0.852241i \(-0.675243\pi\)
−0.0269407 + 0.999637i \(0.508577\pi\)
\(348\) 0 0
\(349\) −8.08831 + 4.66979i −0.432957 + 0.249968i −0.700606 0.713549i \(-0.747087\pi\)
0.267648 + 0.963517i \(0.413753\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.688675 0.688675i 0.0367065 0.0367065i
\(353\) −18.5470 4.96965i −0.987156 0.264508i −0.271100 0.962551i \(-0.587388\pi\)
−0.716055 + 0.698043i \(0.754054\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.786842 + 0.454284i 0.0417026 + 0.0240770i
\(357\) 0 0
\(358\) 5.99152 22.3606i 0.316662 1.18180i
\(359\) −12.5944 −0.664705 −0.332352 0.943155i \(-0.607842\pi\)
−0.332352 + 0.943155i \(0.607842\pi\)
\(360\) 0 0
\(361\) 16.6757 0.877669
\(362\) 5.13426 19.1613i 0.269851 1.00710i
\(363\) 0 0
\(364\) −1.93546 1.11744i −0.101446 0.0585698i
\(365\) 0 0
\(366\) 0 0
\(367\) −27.3263 7.32206i −1.42642 0.382209i −0.538665 0.842520i \(-0.681071\pi\)
−0.887757 + 0.460312i \(0.847738\pi\)
\(368\) 4.00583 4.00583i 0.208818 0.208818i
\(369\) 0 0
\(370\) 0 0
\(371\) −11.6814 + 6.74425i −0.606467 + 0.350144i
\(372\) 0 0
\(373\) 2.25734 0.604851i 0.116880 0.0313180i −0.199905 0.979815i \(-0.564063\pi\)
0.316785 + 0.948497i \(0.397397\pi\)
\(374\) −0.949649 + 1.64484i −0.0491052 + 0.0850526i
\(375\) 0 0
\(376\) 12.2141 + 21.1554i 0.629894 + 1.09101i
\(377\) −6.25992 6.25992i −0.322402 0.322402i
\(378\) 0 0
\(379\) 18.4618i 0.948320i −0.880439 0.474160i \(-0.842752\pi\)
0.880439 0.474160i \(-0.157248\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.83342 + 6.84241i 0.0938059 + 0.350088i
\(383\) −6.26481 23.3806i −0.320117 1.19469i −0.919131 0.393953i \(-0.871107\pi\)
0.599014 0.800739i \(-0.295559\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.4989i 0.636176i
\(387\) 0 0
\(388\) −0.550457 0.550457i −0.0279452 0.0279452i
\(389\) −13.5444 23.4596i −0.686729 1.18945i −0.972890 0.231268i \(-0.925712\pi\)
0.286161 0.958182i \(-0.407621\pi\)
\(390\) 0 0
\(391\) 1.27523 2.20876i 0.0644911 0.111702i
\(392\) −7.98815 + 2.14042i −0.403463 + 0.108108i
\(393\) 0 0
\(394\) −15.6184 + 9.01729i −0.786844 + 0.454284i
\(395\) 0 0
\(396\) 0 0
\(397\) 18.2252 18.2252i 0.914698 0.914698i −0.0819389 0.996637i \(-0.526111\pi\)
0.996637 + 0.0819389i \(0.0261112\pi\)
\(398\) 22.8758 + 6.12955i 1.14666 + 0.307247i
\(399\) 0 0
\(400\) 0 0
\(401\) 11.1294 + 6.42558i 0.555777 + 0.320878i 0.751449 0.659791i \(-0.229355\pi\)
−0.195672 + 0.980669i \(0.562689\pi\)
\(402\) 0 0
\(403\) 10.0535 37.5202i 0.500801 1.86902i
\(404\) 0.506000 0.0251745
\(405\) 0 0
\(406\) 4.38302 0.217526
\(407\) 1.37166 5.11910i 0.0679906 0.253744i
\(408\) 0 0
\(409\) 22.2450 + 12.8431i 1.09994 + 0.635053i 0.936206 0.351451i \(-0.114312\pi\)
0.163737 + 0.986504i \(0.447645\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.47741 0.663820i −0.122053 0.0327041i
\(413\) 11.0602 11.0602i 0.544237 0.544237i
\(414\) 0 0
\(415\) 0 0
\(416\) 5.32474 3.07424i 0.261067 0.150727i
\(417\) 0 0
\(418\) −1.74081 + 0.466448i −0.0851457 + 0.0228147i
\(419\) −6.13243 + 10.6217i −0.299589 + 0.518903i −0.976042 0.217583i \(-0.930183\pi\)
0.676453 + 0.736486i \(0.263516\pi\)
\(420\) 0 0
\(421\) −7.24056 12.5410i −0.352883 0.611212i 0.633870 0.773439i \(-0.281465\pi\)
−0.986753 + 0.162228i \(0.948132\pi\)
\(422\) −0.117006 0.117006i −0.00569577 0.00569577i
\(423\) 0 0
\(424\) 19.4225i 0.943240i
\(425\) 0 0
\(426\) 0 0
\(427\) −7.04094 26.2771i −0.340735 1.27164i
\(428\) 0.663324 + 2.47556i 0.0320630 + 0.119661i
\(429\) 0 0
\(430\) 0 0
\(431\) 35.9660i 1.73242i 0.499678 + 0.866211i \(0.333452\pi\)
−0.499678 + 0.866211i \(0.666548\pi\)
\(432\) 0 0
\(433\) 0.331545 + 0.331545i 0.0159331 + 0.0159331i 0.715028 0.699095i \(-0.246414\pi\)
−0.699095 + 0.715028i \(0.746414\pi\)
\(434\) 9.61573 + 16.6549i 0.461570 + 0.799462i
\(435\) 0 0
\(436\) −0.790718 + 1.36956i −0.0378685 + 0.0655902i
\(437\) 2.33763 0.626366i 0.111824 0.0299632i
\(438\) 0 0
\(439\) −1.28953 + 0.744511i −0.0615459 + 0.0355336i −0.530457 0.847712i \(-0.677980\pi\)
0.468911 + 0.883245i \(0.344646\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −8.47845 + 8.47845i −0.403279 + 0.403279i
\(443\) 30.9468 + 8.29218i 1.47033 + 0.393973i 0.903044 0.429548i \(-0.141327\pi\)
0.567285 + 0.823522i \(0.307994\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2.91203 + 1.68126i 0.137889 + 0.0796101i
\(447\) 0 0
\(448\) −4.57213 + 17.0634i −0.216013 + 0.806172i
\(449\) 21.8283 1.03014 0.515071 0.857147i \(-0.327766\pi\)
0.515071 + 0.857147i \(0.327766\pi\)
\(450\) 0 0
\(451\) −3.16647 −0.149103
\(452\) −0.609937 + 2.27631i −0.0286890 + 0.107069i
\(453\) 0 0
\(454\) −17.7357 10.2397i −0.832376 0.480572i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.880339 0.235886i −0.0411805 0.0110343i 0.238170 0.971223i \(-0.423452\pi\)
−0.279351 + 0.960189i \(0.590119\pi\)
\(458\) −20.9534 + 20.9534i −0.979090 + 0.979090i
\(459\) 0 0
\(460\) 0 0
\(461\) 18.7320 10.8149i 0.872434 0.503700i 0.00427761 0.999991i \(-0.498638\pi\)
0.868156 + 0.496291i \(0.165305\pi\)
\(462\) 0 0
\(463\) 18.1245 4.85644i 0.842316 0.225698i 0.188236 0.982124i \(-0.439723\pi\)
0.654079 + 0.756426i \(0.273056\pi\)
\(464\) −2.84283 + 4.92393i −0.131975 + 0.228588i
\(465\) 0 0
\(466\) 4.00916 + 6.94407i 0.185721 + 0.321678i
\(467\) 16.8295 + 16.8295i 0.778777 + 0.778777i 0.979623 0.200846i \(-0.0643691\pi\)
−0.200846 + 0.979623i \(0.564369\pi\)
\(468\) 0 0
\(469\) 6.80460i 0.314207i
\(470\) 0 0
\(471\) 0 0
\(472\) 5.82929 + 21.7552i 0.268315 + 1.00136i
\(473\) 0.438306 + 1.63578i 0.0201533 + 0.0752133i
\(474\) 0 0
\(475\) 0 0
\(476\) 0.646194i 0.0296182i
\(477\) 0 0
\(478\) −12.9000 12.9000i −0.590033 0.590033i
\(479\) 8.91724 + 15.4451i 0.407439 + 0.705705i 0.994602 0.103764i \(-0.0330886\pi\)
−0.587163 + 0.809469i \(0.699755\pi\)
\(480\) 0 0
\(481\) 16.7285 28.9747i 0.762756 1.32113i
\(482\) −6.66078 + 1.78475i −0.303390 + 0.0812931i
\(483\) 0 0
\(484\) −1.73861 + 1.00378i −0.0790275 + 0.0456265i
\(485\) 0 0
\(486\) 0 0
\(487\) 21.8232 21.8232i 0.988904 0.988904i −0.0110354 0.999939i \(-0.503513\pi\)
0.999939 + 0.0110354i \(0.00351274\pi\)
\(488\) 37.8372 + 10.1385i 1.71281 + 0.458946i
\(489\) 0 0
\(490\) 0 0
\(491\) −35.1670 20.3037i −1.58707 0.916292i −0.993787 0.111295i \(-0.964500\pi\)
−0.593278 0.804998i \(-0.702166\pi\)
\(492\) 0 0
\(493\) −0.662503 + 2.47249i −0.0298376 + 0.111356i
\(494\) −11.3775 −0.511896
\(495\) 0 0
\(496\) −24.9471 −1.12016
\(497\) 3.12705 11.6703i 0.140267 0.523484i
\(498\) 0 0
\(499\) 37.3397 + 21.5581i 1.67156 + 0.965073i 0.966768 + 0.255655i \(0.0822910\pi\)
0.704788 + 0.709418i \(0.251042\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −3.37571 0.904518i −0.150665 0.0403706i
\(503\) −28.0936 + 28.0936i −1.25263 + 1.25263i −0.298093 + 0.954537i \(0.596351\pi\)
−0.954537 + 0.298093i \(0.903649\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1.62510 0.938252i 0.0722445 0.0417104i
\(507\) 0 0
\(508\) −0.510193 + 0.136706i −0.0226361 + 0.00606534i
\(509\) −7.39188 + 12.8031i −0.327639 + 0.567488i −0.982043 0.188658i \(-0.939586\pi\)
0.654404 + 0.756145i \(0.272920\pi\)
\(510\) 0 0
\(511\) 2.30168 + 3.98663i 0.101820 + 0.176358i
\(512\) −17.6794 17.6794i −0.781325 0.781325i
\(513\) 0 0
\(514\) 14.1761i 0.625282i
\(515\) 0 0
\(516\) 0 0
\(517\) 1.88667 + 7.04114i 0.0829755 + 0.309669i
\(518\) 4.28721 + 16.0001i 0.188369 + 0.703003i
\(519\) 0 0
\(520\) 0 0
\(521\) 28.4812i 1.24778i −0.781511 0.623892i \(-0.785551\pi\)
0.781511 0.623892i \(-0.214449\pi\)
\(522\) 0 0
\(523\) −15.4076 15.4076i −0.673726 0.673726i 0.284847 0.958573i \(-0.408057\pi\)
−0.958573 + 0.284847i \(0.908057\pi\)
\(524\) 2.09829 + 3.63434i 0.0916641 + 0.158767i
\(525\) 0 0
\(526\) −5.64872 + 9.78386i −0.246296 + 0.426597i
\(527\) −10.8486 + 2.90687i −0.472572 + 0.126625i
\(528\) 0 0
\(529\) 17.7363 10.2401i 0.771145 0.445221i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.433573 + 0.433573i −0.0187978 + 0.0187978i
\(533\) −19.3089 5.17380i −0.836361 0.224102i
\(534\) 0 0
\(535\) 0 0
\(536\) 8.48544 + 4.89907i 0.366515 + 0.211608i
\(537\) 0 0
\(538\) −9.30542 + 34.7283i −0.401185 + 1.49724i
\(539\) −2.46780 −0.106296
\(540\) 0 0
\(541\) −1.11754 −0.0480466 −0.0240233 0.999711i \(-0.507648\pi\)
−0.0240233 + 0.999711i \(0.507648\pi\)
\(542\) −6.46008 + 24.1093i −0.277484 + 1.03558i
\(543\) 0 0
\(544\) −1.53959 0.888885i −0.0660096 0.0381106i
\(545\) 0 0
\(546\) 0 0
\(547\) 31.1213 + 8.33894i 1.33065 + 0.356547i 0.852958 0.521979i \(-0.174806\pi\)
0.477694 + 0.878526i \(0.341473\pi\)
\(548\) 0.952326 0.952326i 0.0406813 0.0406813i
\(549\) 0 0
\(550\) 0 0
\(551\) −2.10347 + 1.21444i −0.0896109 + 0.0517369i
\(552\) 0 0
\(553\) 15.2945 4.09814i 0.650387 0.174271i
\(554\) 18.2979 31.6928i 0.777402 1.34650i
\(555\) 0 0
\(556\) −0.141537 0.245149i −0.00600250 0.0103966i
\(557\) 30.4033 + 30.4033i 1.28823 + 1.28823i 0.935862 + 0.352366i \(0.114623\pi\)
0.352366 + 0.935862i \(0.385377\pi\)
\(558\) 0 0
\(559\) 10.6910i 0.452182i
\(560\) 0 0
\(561\) 0 0
\(562\) −9.11308 34.0105i −0.384412 1.43465i
\(563\) 0.300692 + 1.12220i 0.0126727 + 0.0472950i 0.971973 0.235094i \(-0.0755398\pi\)
−0.959300 + 0.282389i \(0.908873\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 4.78361i 0.201070i
\(567\) 0 0
\(568\) 12.3017 + 12.3017i 0.516167 + 0.516167i
\(569\) 0.145367 + 0.251784i 0.00609412 + 0.0105553i 0.869056 0.494713i \(-0.164727\pi\)
−0.862962 + 0.505268i \(0.831394\pi\)
\(570\) 0 0
\(571\) −13.0283 + 22.5656i −0.545215 + 0.944341i 0.453378 + 0.891318i \(0.350219\pi\)
−0.998593 + 0.0530223i \(0.983115\pi\)
\(572\) 0.927572 0.248542i 0.0387837 0.0103921i
\(573\) 0 0
\(574\) 8.57106 4.94851i 0.357749 0.206547i
\(575\) 0 0
\(576\) 0 0
\(577\) 2.52834 2.52834i 0.105256 0.105256i −0.652517 0.757774i \(-0.726287\pi\)
0.757774 + 0.652517i \(0.226287\pi\)
\(578\) −18.7044 5.01183i −0.778000 0.208465i
\(579\) 0 0
\(580\) 0 0
\(581\) 17.6274 + 10.1772i 0.731309 + 0.422222i
\(582\) 0 0
\(583\) 1.50006 5.59831i 0.0621262 0.231858i
\(584\) −6.62852 −0.274290
\(585\) 0 0
\(586\) 4.00174 0.165310
\(587\) 10.7212 40.0121i 0.442511 1.65147i −0.279914 0.960025i \(-0.590306\pi\)
0.722425 0.691449i \(-0.243027\pi\)
\(588\) 0 0
\(589\) −9.22943 5.32861i −0.380292 0.219562i
\(590\) 0 0
\(591\) 0 0
\(592\) −20.7553 5.56137i −0.853038 0.228571i
\(593\) 26.6583 26.6583i 1.09473 1.09473i 0.0997087 0.995017i \(-0.468209\pi\)
0.995017 0.0997087i \(-0.0317911\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2.81726 + 1.62655i −0.115400 + 0.0666260i
\(597\) 0 0
\(598\) 11.4428 3.06608i 0.467930 0.125382i
\(599\) 13.2427 22.9370i 0.541080 0.937178i −0.457762 0.889075i \(-0.651349\pi\)
0.998842 0.0481037i \(-0.0153178\pi\)
\(600\) 0 0
\(601\) 4.26710 + 7.39084i 0.174059 + 0.301479i 0.939835 0.341628i \(-0.110978\pi\)
−0.765776 + 0.643107i \(0.777645\pi\)
\(602\) −3.74279 3.74279i −0.152545 0.152545i
\(603\) 0 0
\(604\) 0.00111412i 4.53329e-5i
\(605\) 0 0
\(606\) 0 0
\(607\) 11.9000 + 44.4113i 0.483005 + 1.80260i 0.588881 + 0.808220i \(0.299569\pi\)
−0.105876 + 0.994379i \(0.533765\pi\)
\(608\) −0.436602 1.62942i −0.0177066 0.0660818i
\(609\) 0 0
\(610\) 0 0
\(611\) 46.0190i 1.86173i
\(612\) 0 0
\(613\) −17.3219 17.3219i −0.699625 0.699625i 0.264705 0.964330i \(-0.414726\pi\)
−0.964330 + 0.264705i \(0.914726\pi\)
\(614\) 20.7039 + 35.8602i 0.835542 + 1.44720i
\(615\) 0 0
\(616\) −2.65929 + 4.60603i −0.107146 + 0.185582i
\(617\) 36.3708 9.74553i 1.46423 0.392340i 0.563284 0.826263i \(-0.309538\pi\)
0.900950 + 0.433923i \(0.142871\pi\)
\(618\) 0 0
\(619\) 8.57434 4.95040i 0.344632 0.198973i −0.317687 0.948196i \(-0.602906\pi\)
0.662318 + 0.749223i \(0.269573\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −32.2255 + 32.2255i −1.29213 + 1.29213i
\(623\) −9.15670 2.45353i −0.366855 0.0982986i
\(624\) 0 0
\(625\) 0 0
\(626\) 26.9753 + 15.5742i 1.07815 + 0.622469i
\(627\) 0 0
\(628\) 0.429864 1.60427i 0.0171534 0.0640175i
\(629\) −9.67378 −0.385719
\(630\) 0 0
\(631\) −22.0279 −0.876918 −0.438459 0.898751i \(-0.644476\pi\)
−0.438459 + 0.898751i \(0.644476\pi\)
\(632\) −5.90104 + 22.0230i −0.234731 + 0.876027i
\(633\) 0 0
\(634\) 4.65268 + 2.68622i 0.184781 + 0.106684i
\(635\) 0 0
\(636\) 0 0
\(637\) −15.0485 4.03223i −0.596242 0.159763i
\(638\) −1.33171 + 1.33171i −0.0527227 + 0.0527227i
\(639\) 0 0
\(640\) 0 0
\(641\) −21.8054 + 12.5894i −0.861263 + 0.497251i −0.864435 0.502744i \(-0.832324\pi\)
0.00317173 + 0.999995i \(0.498990\pi\)
\(642\) 0 0
\(643\) −30.0492 + 8.05166i −1.18502 + 0.317526i −0.796918 0.604088i \(-0.793538\pi\)
−0.388107 + 0.921614i \(0.626871\pi\)
\(644\) 0.319219 0.552904i 0.0125790 0.0217875i
\(645\) 0 0
\(646\) 1.64484 + 2.84895i 0.0647154 + 0.112090i
\(647\) −7.86580 7.86580i −0.309237 0.309237i 0.535377 0.844613i \(-0.320170\pi\)
−0.844613 + 0.535377i \(0.820170\pi\)
\(648\) 0 0
\(649\) 6.72090i 0.263818i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.301325 1.12456i −0.0118008 0.0440411i
\(653\) 0.0749391 + 0.279676i 0.00293259 + 0.0109446i 0.967377 0.253343i \(-0.0815300\pi\)
−0.964444 + 0.264287i \(0.914863\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 12.8384i 0.501256i
\(657\) 0 0
\(658\) −16.1106 16.1106i −0.628058 0.628058i
\(659\) −13.4009 23.2111i −0.522026 0.904175i −0.999672 0.0256228i \(-0.991843\pi\)
0.477646 0.878552i \(-0.341490\pi\)
\(660\) 0 0
\(661\) −12.6438 + 21.8997i −0.491787 + 0.851800i −0.999955 0.00945786i \(-0.996989\pi\)
0.508168 + 0.861258i \(0.330323\pi\)
\(662\) −7.73611 + 2.07289i −0.300673 + 0.0805650i
\(663\) 0 0
\(664\) −25.3823 + 14.6545i −0.985024 + 0.568704i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.78827 1.78827i 0.0692421 0.0692421i
\(668\) −1.13154 0.303196i −0.0437807 0.0117310i
\(669\) 0 0
\(670\) 0 0
\(671\) 10.1231 + 5.84458i 0.390799 + 0.225628i
\(672\) 0 0
\(673\) −6.30290 + 23.5227i −0.242959 + 0.906735i 0.731439 + 0.681906i \(0.238849\pi\)
−0.974398 + 0.224829i \(0.927818\pi\)
\(674\) 13.3044 0.512466
\(675\) 0 0
\(676\) 3.51002 0.135001
\(677\) −0.240265 + 0.896681i −0.00923414 + 0.0344623i −0.970389 0.241547i \(-0.922345\pi\)
0.961155 + 0.276009i \(0.0890120\pi\)
\(678\) 0 0
\(679\) 7.03407 + 4.06112i 0.269943 + 0.155852i
\(680\) 0 0
\(681\) 0 0
\(682\) −7.98188 2.13874i −0.305642 0.0818966i
\(683\) −22.2024 + 22.2024i −0.849550 + 0.849550i −0.990077 0.140526i \(-0.955120\pi\)
0.140526 + 0.990077i \(0.455120\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 23.3578 13.4856i 0.891805 0.514884i
\(687\) 0 0
\(688\) 6.63225 1.77711i 0.252852 0.0677515i
\(689\) 18.2945 31.6871i 0.696966 1.20718i
\(690\) 0 0
\(691\) −4.05877 7.02999i −0.154403 0.267433i 0.778439 0.627721i \(-0.216012\pi\)
−0.932841 + 0.360287i \(0.882679\pi\)
\(692\) 1.89711 + 1.89711i 0.0721173 + 0.0721173i
\(693\) 0 0
\(694\) 14.2473i 0.540821i
\(695\) 0 0
\(696\) 0 0
\(697\) 1.49595 + 5.58297i 0.0566633 + 0.211470i
\(698\) 3.24640 + 12.1157i 0.122878 + 0.458586i
\(699\) 0 0
\(700\) 0 0
\(701\) 19.6359i 0.741637i 0.928705 + 0.370819i \(0.120923\pi\)
−0.928705 + 0.370819i \(0.879077\pi\)
\(702\) 0 0
\(703\) −6.49076 6.49076i −0.244804 0.244804i
\(704\) −3.79526 6.57359i −0.143039 0.247752i
\(705\) 0 0
\(706\) −12.8937 + 22.3325i −0.485260 + 0.840496i
\(707\) −5.09956 + 1.36642i −0.191789 + 0.0513896i
\(708\) 0 0
\(709\) −2.68383 + 1.54951i −0.100793 + 0.0581931i −0.549549 0.835461i \(-0.685201\pi\)
0.448756 + 0.893654i \(0.351867\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 9.65210 9.65210i 0.361728 0.361728i
\(713\) 10.7184 + 2.87199i 0.401408 + 0.107557i
\(714\) 0 0
\(715\) 0 0
\(716\) 2.93083 + 1.69211i 0.109530 + 0.0632373i
\(717\) 0 0
\(718\) −4.37774 + 16.3380i −0.163376 + 0.609727i
\(719\) 20.3126 0.757533 0.378767 0.925492i \(-0.376348\pi\)
0.378767 + 0.925492i \(0.376348\pi\)
\(720\) 0 0
\(721\) 26.7604 0.996608
\(722\) 5.79640 21.6325i 0.215720 0.805077i
\(723\) 0 0
\(724\) 2.51149 + 1.45001i 0.0933388 + 0.0538892i
\(725\) 0 0
\(726\) 0 0
\(727\) 17.0647 + 4.57247i 0.632895 + 0.169584i 0.560983 0.827827i \(-0.310423\pi\)
0.0719119 + 0.997411i \(0.477090\pi\)
\(728\) −23.7421 + 23.7421i −0.879941 + 0.879941i
\(729\) 0 0
\(730\) 0 0
\(731\) 2.67706 1.54560i 0.0990147 0.0571662i
\(732\) 0 0
\(733\) −25.4785 + 6.82693i −0.941068 + 0.252158i −0.696568 0.717491i \(-0.745291\pi\)
−0.244500 + 0.969649i \(0.578624\pi\)
\(734\) −18.9970 + 32.9038i −0.701192 + 1.21450i
\(735\) 0 0
\(736\) 0.878218 + 1.52112i 0.0323715 + 0.0560692i
\(737\) 2.06746 + 2.06746i 0.0761558 + 0.0761558i
\(738\) 0 0
\(739\) 6.41459i 0.235965i −0.993016 0.117982i \(-0.962357\pi\)
0.993016 0.117982i \(-0.0376426\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 4.68854 + 17.4979i 0.172122 + 0.642368i
\(743\) −4.95625 18.4970i −0.181827 0.678588i −0.995288 0.0969677i \(-0.969086\pi\)
0.813460 0.581620i \(-0.197581\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.13856i 0.114911i
\(747\) 0 0
\(748\) −0.196335 0.196335i −0.00717870 0.00717870i
\(749\) −13.3702 23.1579i −0.488536 0.846170i
\(750\) 0 0
\(751\) −1.96958 + 3.41141i −0.0718709 + 0.124484i −0.899721 0.436465i \(-0.856230\pi\)
0.827850 + 0.560949i \(0.189564\pi\)
\(752\) 28.5482 7.64946i 1.04105 0.278947i
\(753\) 0 0
\(754\) −10.2966 + 5.94472i −0.374979 + 0.216494i
\(755\) 0 0
\(756\) 0 0
\(757\) −17.3710 + 17.3710i −0.631361 + 0.631361i −0.948409 0.317049i \(-0.897308\pi\)
0.317049 + 0.948409i \(0.397308\pi\)
\(758\) −23.9495 6.41725i −0.869885 0.233085i
\(759\) 0 0
\(760\) 0 0
\(761\) −7.11860 4.10993i −0.258049 0.148985i 0.365395 0.930853i \(-0.380934\pi\)
−0.623444 + 0.781868i \(0.714267\pi\)
\(762\) 0 0
\(763\) 4.27057 15.9380i 0.154605 0.576994i
\(764\) −1.03558 −0.0374660
\(765\) 0 0
\(766\) −32.5079 −1.17456
\(767\) −10.9815 + 40.9835i −0.396519 + 1.47983i
\(768\) 0 0
\(769\) −1.91615 1.10629i −0.0690983 0.0398939i 0.465053 0.885283i \(-0.346035\pi\)
−0.534151 + 0.845389i \(0.679369\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.76495 + 0.472918i 0.0635221 + 0.0170207i
\(773\) 8.23173 8.23173i 0.296075 0.296075i −0.543400 0.839474i \(-0.682863\pi\)
0.839474 + 0.543400i \(0.182863\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −10.1286 + 5.84773i −0.363595 + 0.209921i
\(777\) 0 0
\(778\) −35.1408 + 9.41596i −1.25986 + 0.337579i
\(779\) −2.74224 + 4.74970i −0.0982511 + 0.170176i
\(780\) 0 0
\(781\) 2.59572 + 4.49591i 0.0928820 + 0.160876i
\(782\) −2.42204 2.42204i −0.0866119 0.0866119i
\(783\) 0 0
\(784\) 10.0057i 0.357346i
\(785\) 0 0
\(786\) 0 0
\(787\) 9.07119 + 33.8541i 0.323353 + 1.20677i 0.915957 + 0.401276i \(0.131433\pi\)
−0.592604 + 0.805494i \(0.701900\pi\)
\(788\) −0.682372 2.54665i −0.0243085 0.0907205i
\(789\) 0 0
\(790\) 0 0
\(791\) 24.5882i 0.874256i
\(792\) 0 0
\(793\) 52.1803 + 52.1803i 1.85298 + 1.85298i
\(794\) −17.3076 29.9776i −0.614223 1.06387i
\(795\) 0 0
\(796\) −1.73110 + 2.99835i −0.0613571 + 0.106274i
\(797\) −25.2788 + 6.77343i −0.895421 + 0.239927i −0.677049 0.735938i \(-0.736741\pi\)
−0.218372 + 0.975866i \(0.570075\pi\)
\(798\) 0 0
\(799\) 11.5233 6.65297i 0.407664 0.235365i
\(800\) 0 0
\(801\) 0 0
\(802\) 12.2041 12.2041i 0.430941 0.430941i
\(803\) −1.91059 0.511942i −0.0674233 0.0180660i
\(804\) 0 0
\(805\) 0 0
\(806\) −45.1784 26.0837i −1.59134 0.918761i
\(807\) 0 0
\(808\) 1.96755 7.34301i 0.0692183 0.258326i
\(809\) 40.3389 1.41824 0.709120 0.705088i \(-0.249092\pi\)
0.709120 + 0.705088i \(0.249092\pi\)
\(810\) 0 0
\(811\) −4.50040 −0.158030 −0.0790152 0.996873i \(-0.525178\pi\)
−0.0790152 + 0.996873i \(0.525178\pi\)
\(812\) −0.165840 + 0.618923i −0.00581984 + 0.0217199i
\(813\) 0 0
\(814\) −6.16394 3.55875i −0.216046 0.124734i
\(815\) 0 0
\(816\) 0 0
\(817\) 2.83326 + 0.759168i 0.0991231 + 0.0265599i
\(818\) 24.3930 24.3930i 0.852880 0.852880i
\(819\) 0 0
\(820\) 0 0
\(821\) −13.3109 + 7.68503i −0.464552 + 0.268209i −0.713956 0.700190i \(-0.753099\pi\)
0.249404 + 0.968399i \(0.419765\pi\)
\(822\) 0 0
\(823\) 14.0723 3.77065i 0.490528 0.131437i −0.00507263 0.999987i \(-0.501615\pi\)
0.495601 + 0.868551i \(0.334948\pi\)
\(824\) −19.2665 + 33.3706i −0.671182 + 1.16252i
\(825\) 0 0
\(826\) −10.5033 18.1923i −0.365457 0.632989i
\(827\) 3.31824 + 3.31824i 0.115387 + 0.115387i 0.762443 0.647056i \(-0.224000\pi\)
−0.647056 + 0.762443i \(0.724000\pi\)
\(828\) 0 0
\(829\) 33.9539i 1.17927i −0.807671 0.589633i \(-0.799272\pi\)
0.807671 0.589633i \(-0.200728\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −12.4024 46.2865i −0.429977 1.60469i
\(833\) 1.16588 + 4.35112i 0.0403953 + 0.150757i
\(834\) 0 0
\(835\) 0 0
\(836\) 0.263467i 0.00911220i
\(837\) 0 0
\(838\) 11.6473 + 11.6473i 0.402349 + 0.402349i
\(839\) 5.71824 + 9.90428i 0.197416 + 0.341934i 0.947690 0.319193i \(-0.103412\pi\)
−0.750274 + 0.661127i \(0.770079\pi\)
\(840\) 0 0
\(841\) 13.2309 22.9166i 0.456238 0.790228i
\(842\) −18.7855 + 5.03357i −0.647392 + 0.173468i
\(843\) 0 0
\(844\) 0.0209495 0.0120952i 0.000721111 0.000416334i
\(845\) 0 0
\(846\) 0 0
\(847\) 14.8113 14.8113i 0.508923 0.508923i
\(848\) −22.6983 6.08198i −0.779462 0.208856i
\(849\) 0 0
\(850\) 0 0
\(851\) 8.27720 + 4.77884i 0.283739 + 0.163817i
\(852\) 0 0
\(853\) 6.18947 23.0994i 0.211923 0.790909i −0.775304 0.631589i \(-0.782403\pi\)
0.987227 0.159320i \(-0.0509302\pi\)
\(854\) −36.5353 −1.25021
\(855\) 0 0
\(856\) 38.5043 1.31605
\(857\) −3.88189 + 14.4874i −0.132603 + 0.494881i −0.999996 0.00274224i \(-0.999127\pi\)
0.867393 + 0.497623i \(0.165794\pi\)
\(858\) 0 0
\(859\) −37.5983 21.7074i −1.28284 0.740646i −0.305471 0.952201i \(-0.598814\pi\)
−0.977366 + 0.211555i \(0.932147\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 46.6567 + 12.5016i 1.58913 + 0.425807i
\(863\) 2.78648 2.78648i 0.0948527 0.0948527i −0.658088 0.752941i \(-0.728635\pi\)
0.752941 + 0.658088i \(0.228635\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0.545339 0.314852i 0.0185314 0.0106991i
\(867\) 0 0
\(868\) −2.71566 + 0.727658i −0.0921754 + 0.0246983i
\(869\) −3.40181 + 5.89211i −0.115399 + 0.199876i
\(870\) 0 0
\(871\) 9.22911 + 15.9853i 0.312717 + 0.541641i
\(872\) 16.8003 + 16.8003i 0.568929 + 0.568929i
\(873\) 0 0
\(874\) 3.25020i 0.109940i
\(875\) 0 0
\(876\) 0 0
\(877\) −11.1359 41.5598i −0.376033 1.40338i −0.851829 0.523820i \(-0.824507\pi\)
0.475796 0.879556i \(-0.342160\pi\)
\(878\) 0.517577 + 1.93163i 0.0174674 + 0.0651892i
\(879\) 0 0
\(880\) 0 0
\(881\) 47.0487i 1.58511i −0.609801 0.792555i \(-0.708751\pi\)
0.609801 0.792555i \(-0.291249\pi\)
\(882\) 0 0
\(883\) −21.0669 21.0669i −0.708957 0.708957i 0.257359 0.966316i \(-0.417148\pi\)
−0.966316 + 0.257359i \(0.917148\pi\)
\(884\) −0.876436 1.51803i −0.0294777 0.0510569i
\(885\) 0 0
\(886\) 21.5140 37.2633i 0.722776 1.25188i
\(887\) 3.50739 0.939801i 0.117766 0.0315554i −0.199454 0.979907i \(-0.563917\pi\)
0.317221 + 0.948352i \(0.397250\pi\)
\(888\) 0 0
\(889\) 4.77265 2.75549i 0.160069 0.0924161i
\(890\) 0 0
\(891\) 0 0
\(892\) −0.347592 + 0.347592i −0.0116382 + 0.0116382i
\(893\) 12.1956 + 3.26780i 0.408110 + 0.109353i
\(894\) 0 0
\(895\) 0 0
\(896\) 16.6203 + 9.59572i 0.555245 + 0.320571i
\(897\) 0 0
\(898\) 7.58743 28.3167i 0.253196 0.944939i
\(899\) −11.1368 −0.371433
\(900\) 0 0
\(901\) −10.5794 −0.352450
\(902\) −1.10065 + 4.10768i −0.0366477 + 0.136771i
\(903\) 0 0
\(904\) 30.6619 + 17.7026i 1.01980 + 0.588781i
\(905\) 0 0
\(906\) 0 0
\(907\) −10.1363 2.71600i −0.336569 0.0901833i 0.0865764 0.996245i \(-0.472407\pi\)
−0.423145 + 0.906062i \(0.639074\pi\)
\(908\) 2.11700 2.11700i 0.0702551 0.0702551i
\(909\) 0 0
\(910\) 0 0
\(911\) −6.77512 + 3.91162i −0.224470 + 0.129598i −0.608018 0.793923i \(-0.708035\pi\)
0.383548 + 0.923521i \(0.374702\pi\)
\(912\) 0 0
\(913\) −8.44796 + 2.26362i −0.279587 + 0.0749150i
\(914\) −0.612004 + 1.06002i −0.0202433 + 0.0350624i
\(915\) 0 0
\(916\) −2.16600 3.75163i −0.0715668 0.123957i
\(917\) −30.9612 30.9612i −1.02243 1.02243i
\(918\) 0 0
\(919\) 4.61000i 0.152070i 0.997105 + 0.0760349i \(0.0242260\pi\)
−0.997105 + 0.0760349i \(0.975774\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −7.51842 28.0591i −0.247606 0.924078i
\(923\) 8.48246 + 31.6570i 0.279204 + 1.04200i
\(924\) 0 0
\(925\) 0 0
\(926\) 25.1999i 0.828122i
\(927\) 0 0
\(928\) −1.24650 1.24650i −0.0409182 0.0409182i
\(929\) 15.7062 + 27.2039i 0.515302 + 0.892530i 0.999842 + 0.0177609i \(0.00565375\pi\)
−0.484540 + 0.874769i \(0.661013\pi\)
\(930\) 0 0
\(931\) −2.13718 + 3.70170i −0.0700433 + 0.121318i
\(932\) −1.13226 + 0.303388i −0.0370884 + 0.00993782i
\(933\) 0 0
\(934\) 27.6818 15.9821i 0.905778 0.522951i
\(935\) 0 0
\(936\) 0 0
\(937\) 21.3617 21.3617i 0.697856 0.697856i −0.266092 0.963948i \(-0.585732\pi\)
0.963948 + 0.266092i \(0.0857324\pi\)
\(938\) −8.82722 2.36525i −0.288219 0.0772281i
\(939\) 0 0
\(940\) 0 0
\(941\) 5.77035 + 3.33151i 0.188108 + 0.108604i 0.591096 0.806601i \(-0.298695\pi\)
−0.402989 + 0.915205i \(0.632029\pi\)
\(942\) 0 0
\(943\) 1.47800 5.51597i 0.0481303 0.179625i
\(944\) 27.2498 0.886905
\(945\) 0 0
\(946\) 2.27436 0.0739458
\(947\) 0.867814 3.23873i 0.0282002 0.105245i −0.950391 0.311057i \(-0.899317\pi\)
0.978591 + 0.205812i \(0.0659837\pi\)
\(948\) 0 0
\(949\) −10.8142 6.24356i −0.351043 0.202675i
\(950\) 0 0
\(951\) 0 0
\(952\) 9.37748 + 2.51269i 0.303926 + 0.0814367i
\(953\) 30.7161 30.7161i 0.994992 0.994992i −0.00499525 0.999988i \(-0.501590\pi\)
0.999988 + 0.00499525i \(0.00159004\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 2.30970 1.33350i 0.0747009 0.0431286i
\(957\) 0 0
\(958\) 23.1357 6.19919i 0.747480 0.200287i
\(959\) −7.02601 + 12.1694i −0.226882 + 0.392970i
\(960\) 0 0
\(961\) −8.93253 15.4716i −0.288146 0.499084i
\(962\) −31.7725 31.7725i −1.02439 1.02439i
\(963\) 0 0
\(964\) 1.00809i 0.0324684i
\(965\) 0 0
\(966\) 0 0
\(967\) 1.48419 + 5.53906i 0.0477282 + 0.178124i 0.985675 0.168654i \(-0.0539422\pi\)
−0.937947 + 0.346779i \(0.887276\pi\)
\(968\) 7.80632 + 29.1336i 0.250904 + 0.936388i
\(969\) 0 0
\(970\) 0 0
\(971\) 14.2248i 0.456496i −0.973603 0.228248i \(-0.926700\pi\)
0.973603 0.228248i \(-0.0732998\pi\)
\(972\) 0 0
\(973\) 2.08844 + 2.08844i 0.0669524 + 0.0669524i
\(974\) −20.7244 35.8957i −0.664052 1.15017i
\(975\) 0 0
\(976\) 23.6968 41.0440i 0.758516 1.31379i
\(977\) 30.1529 8.07944i 0.964676 0.258484i 0.258097 0.966119i \(-0.416904\pi\)
0.706578 + 0.707635i \(0.250238\pi\)
\(978\) 0 0
\(979\) 3.52757 2.03664i 0.112742 0.0650913i
\(980\) 0 0
\(981\) 0 0
\(982\) −38.5627 + 38.5627i −1.23059 + 1.23059i
\(983\) 9.94750 + 2.66543i 0.317276 + 0.0850139i 0.413943 0.910303i \(-0.364151\pi\)
−0.0966666 + 0.995317i \(0.530818\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 2.97715 + 1.71886i 0.0948116 + 0.0547395i
\(987\) 0 0
\(988\) 0.430488 1.60660i 0.0136956 0.0511128i
\(989\) −3.05411 −0.0971150
\(990\) 0 0
\(991\) 37.9180 1.20450 0.602252 0.798306i \(-0.294270\pi\)
0.602252 + 0.798306i \(0.294270\pi\)
\(992\) 2.00189 7.47116i 0.0635601 0.237210i
\(993\) 0 0
\(994\) −14.0523 8.11308i −0.445711 0.257331i
\(995\) 0 0
\(996\) 0 0
\(997\) −30.1153 8.06937i −0.953761 0.255559i −0.251804 0.967778i \(-0.581024\pi\)
−0.701957 + 0.712219i \(0.747690\pi\)
\(998\) 40.9452 40.9452i 1.29610 1.29610i
\(999\) 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 675.2.q.a.368.4 16
3.2 odd 2 225.2.p.b.68.1 16
5.2 odd 4 inner 675.2.q.a.557.4 16
5.3 odd 4 135.2.m.a.17.1 16
5.4 even 2 135.2.m.a.98.1 16
9.2 odd 6 inner 675.2.q.a.143.4 16
9.7 even 3 225.2.p.b.218.1 16
15.2 even 4 225.2.p.b.32.1 16
15.8 even 4 45.2.l.a.32.4 yes 16
15.14 odd 2 45.2.l.a.23.4 yes 16
45.2 even 12 inner 675.2.q.a.332.4 16
45.4 even 6 405.2.f.a.323.3 16
45.7 odd 12 225.2.p.b.182.1 16
45.13 odd 12 405.2.f.a.242.6 16
45.14 odd 6 405.2.f.a.323.6 16
45.23 even 12 405.2.f.a.242.3 16
45.29 odd 6 135.2.m.a.8.1 16
45.34 even 6 45.2.l.a.38.4 yes 16
45.38 even 12 135.2.m.a.62.1 16
45.43 odd 12 45.2.l.a.2.4 16
60.23 odd 4 720.2.cu.c.257.4 16
60.59 even 2 720.2.cu.c.113.3 16
180.43 even 12 720.2.cu.c.497.3 16
180.79 odd 6 720.2.cu.c.353.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.l.a.2.4 16 45.43 odd 12
45.2.l.a.23.4 yes 16 15.14 odd 2
45.2.l.a.32.4 yes 16 15.8 even 4
45.2.l.a.38.4 yes 16 45.34 even 6
135.2.m.a.8.1 16 45.29 odd 6
135.2.m.a.17.1 16 5.3 odd 4
135.2.m.a.62.1 16 45.38 even 12
135.2.m.a.98.1 16 5.4 even 2
225.2.p.b.32.1 16 15.2 even 4
225.2.p.b.68.1 16 3.2 odd 2
225.2.p.b.182.1 16 45.7 odd 12
225.2.p.b.218.1 16 9.7 even 3
405.2.f.a.242.3 16 45.23 even 12
405.2.f.a.242.6 16 45.13 odd 12
405.2.f.a.323.3 16 45.4 even 6
405.2.f.a.323.6 16 45.14 odd 6
675.2.q.a.143.4 16 9.2 odd 6 inner
675.2.q.a.332.4 16 45.2 even 12 inner
675.2.q.a.368.4 16 1.1 even 1 trivial
675.2.q.a.557.4 16 5.2 odd 4 inner
720.2.cu.c.113.3 16 60.59 even 2
720.2.cu.c.257.4 16 60.23 odd 4
720.2.cu.c.353.4 16 180.79 odd 6
720.2.cu.c.497.3 16 180.43 even 12