Properties

Label 288.2.v.d.109.1
Level $288$
Weight $2$
Character 288.109
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(37,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.v (of order \(8\), degree \(4\), 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: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.1
Character \(\chi\) \(=\) 288.109
Dual form 288.2.v.d.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40823 - 0.129991i) q^{2} +(1.96620 + 0.366115i) q^{4} +(2.51374 - 1.04122i) q^{5} +(2.01027 - 2.01027i) q^{7} +(-2.72127 - 0.771162i) q^{8} +O(q^{10})\) \(q+(-1.40823 - 0.129991i) q^{2} +(1.96620 + 0.366115i) q^{4} +(2.51374 - 1.04122i) q^{5} +(2.01027 - 2.01027i) q^{7} +(-2.72127 - 0.771162i) q^{8} +(-3.67526 + 1.13951i) q^{10} +(1.32741 + 3.20465i) q^{11} +(-5.55375 - 2.30044i) q^{13} +(-3.09223 + 2.56960i) q^{14} +(3.73192 + 1.43971i) q^{16} -4.16447i q^{17} +(4.49866 + 1.86340i) q^{19} +(5.32373 - 1.12694i) q^{20} +(-1.45272 - 4.68542i) q^{22} +(1.94282 + 1.94282i) q^{23} +(1.69919 - 1.69919i) q^{25} +(7.52191 + 3.96148i) q^{26} +(4.68859 - 3.21661i) q^{28} +(1.96103 - 4.73434i) q^{29} -2.87015 q^{31} +(-5.06824 - 2.51256i) q^{32} +(-0.541346 + 5.86452i) q^{34} +(2.96015 - 7.14642i) q^{35} +(6.31049 - 2.61389i) q^{37} +(-6.09290 - 3.20888i) q^{38} +(-7.64351 + 0.894952i) q^{40} +(-0.756366 - 0.756366i) q^{41} +(1.53775 + 3.71245i) q^{43} +(1.43669 + 6.78698i) q^{44} +(-2.48338 - 2.98848i) q^{46} -1.08220i q^{47} -1.08236i q^{49} +(-2.61372 + 2.17196i) q^{50} +(-10.0776 - 6.55645i) q^{52} +(2.90450 + 7.01208i) q^{53} +(6.67351 + 6.67351i) q^{55} +(-7.02073 + 3.92024i) q^{56} +(-3.37700 + 6.41211i) q^{58} +(-10.3425 + 4.28402i) q^{59} +(-2.97711 + 7.18739i) q^{61} +(4.04183 + 0.373095i) q^{62} +(6.81062 + 4.19708i) q^{64} -16.3559 q^{65} +(-3.88805 + 9.38659i) q^{67} +(1.52467 - 8.18820i) q^{68} +(-5.09753 + 9.67899i) q^{70} +(1.88924 - 1.88924i) q^{71} +(-7.00727 - 7.00727i) q^{73} +(-9.22638 + 2.86064i) q^{74} +(8.16306 + 5.31086i) q^{76} +(9.11066 + 3.77376i) q^{77} -11.0255i q^{79} +(10.8801 - 0.266706i) q^{80} +(0.966814 + 1.16346i) q^{82} +(2.30515 + 0.954824i) q^{83} +(-4.33615 - 10.4684i) q^{85} +(-1.68291 - 5.42786i) q^{86} +(-1.14093 - 9.74436i) q^{88} +(-7.65800 + 7.65800i) q^{89} +(-15.7890 + 6.54003i) q^{91} +(3.10868 + 4.53127i) q^{92} +(-0.140676 + 1.52398i) q^{94} +13.2487 q^{95} -11.3029 q^{97} +(-0.140697 + 1.52421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40823 0.129991i −0.995767 0.0919178i
\(3\) 0 0
\(4\) 1.96620 + 0.366115i 0.983102 + 0.183057i
\(5\) 2.51374 1.04122i 1.12418 0.465649i 0.258379 0.966044i \(-0.416812\pi\)
0.865798 + 0.500394i \(0.166812\pi\)
\(6\) 0 0
\(7\) 2.01027 2.01027i 0.759810 0.759810i −0.216477 0.976288i \(-0.569457\pi\)
0.976288 + 0.216477i \(0.0694568\pi\)
\(8\) −2.72127 0.771162i −0.962114 0.272647i
\(9\) 0 0
\(10\) −3.67526 + 1.13951i −1.16222 + 0.360346i
\(11\) 1.32741 + 3.20465i 0.400229 + 0.966238i 0.987610 + 0.156928i \(0.0501590\pi\)
−0.587381 + 0.809310i \(0.699841\pi\)
\(12\) 0 0
\(13\) −5.55375 2.30044i −1.54033 0.638027i −0.558798 0.829304i \(-0.688737\pi\)
−0.981536 + 0.191277i \(0.938737\pi\)
\(14\) −3.09223 + 2.56960i −0.826434 + 0.686753i
\(15\) 0 0
\(16\) 3.73192 + 1.43971i 0.932980 + 0.359928i
\(17\) 4.16447i 1.01003i −0.863110 0.505016i \(-0.831486\pi\)
0.863110 0.505016i \(-0.168514\pi\)
\(18\) 0 0
\(19\) 4.49866 + 1.86340i 1.03206 + 0.427494i 0.833456 0.552585i \(-0.186359\pi\)
0.198606 + 0.980079i \(0.436359\pi\)
\(20\) 5.32373 1.12694i 1.19042 0.251992i
\(21\) 0 0
\(22\) −1.45272 4.68542i −0.309720 0.998936i
\(23\) 1.94282 + 1.94282i 0.405106 + 0.405106i 0.880028 0.474922i \(-0.157524\pi\)
−0.474922 + 0.880028i \(0.657524\pi\)
\(24\) 0 0
\(25\) 1.69919 1.69919i 0.339838 0.339838i
\(26\) 7.52191 + 3.96148i 1.47517 + 0.776910i
\(27\) 0 0
\(28\) 4.68859 3.21661i 0.886060 0.607882i
\(29\) 1.96103 4.73434i 0.364154 0.879145i −0.630530 0.776165i \(-0.717162\pi\)
0.994683 0.102980i \(-0.0328377\pi\)
\(30\) 0 0
\(31\) −2.87015 −0.515495 −0.257747 0.966212i \(-0.582980\pi\)
−0.257747 + 0.966212i \(0.582980\pi\)
\(32\) −5.06824 2.51256i −0.895947 0.444162i
\(33\) 0 0
\(34\) −0.541346 + 5.86452i −0.0928400 + 1.00576i
\(35\) 2.96015 7.14642i 0.500356 1.20797i
\(36\) 0 0
\(37\) 6.31049 2.61389i 1.03744 0.429721i 0.202046 0.979376i \(-0.435241\pi\)
0.835392 + 0.549655i \(0.185241\pi\)
\(38\) −6.09290 3.20888i −0.988399 0.520549i
\(39\) 0 0
\(40\) −7.64351 + 0.894952i −1.20854 + 0.141504i
\(41\) −0.756366 0.756366i −0.118125 0.118125i 0.645574 0.763698i \(-0.276618\pi\)
−0.763698 + 0.645574i \(0.776618\pi\)
\(42\) 0 0
\(43\) 1.53775 + 3.71245i 0.234504 + 0.566143i 0.996697 0.0812067i \(-0.0258774\pi\)
−0.762193 + 0.647350i \(0.775877\pi\)
\(44\) 1.43669 + 6.78698i 0.216589 + 1.02318i
\(45\) 0 0
\(46\) −2.48338 2.98848i −0.366154 0.440627i
\(47\) 1.08220i 0.157855i −0.996880 0.0789273i \(-0.974851\pi\)
0.996880 0.0789273i \(-0.0251495\pi\)
\(48\) 0 0
\(49\) 1.08236i 0.154623i
\(50\) −2.61372 + 2.17196i −0.369636 + 0.307162i
\(51\) 0 0
\(52\) −10.0776 6.55645i −1.39751 0.909215i
\(53\) 2.90450 + 7.01208i 0.398963 + 0.963183i 0.987912 + 0.155013i \(0.0495418\pi\)
−0.588949 + 0.808170i \(0.700458\pi\)
\(54\) 0 0
\(55\) 6.67351 + 6.67351i 0.899856 + 0.899856i
\(56\) −7.02073 + 3.92024i −0.938184 + 0.523864i
\(57\) 0 0
\(58\) −3.37700 + 6.41211i −0.443421 + 0.841951i
\(59\) −10.3425 + 4.28402i −1.34648 + 0.557732i −0.935311 0.353826i \(-0.884880\pi\)
−0.411172 + 0.911558i \(0.634880\pi\)
\(60\) 0 0
\(61\) −2.97711 + 7.18739i −0.381180 + 0.920251i 0.610558 + 0.791972i \(0.290945\pi\)
−0.991738 + 0.128279i \(0.959055\pi\)
\(62\) 4.04183 + 0.373095i 0.513312 + 0.0473831i
\(63\) 0 0
\(64\) 6.81062 + 4.19708i 0.851327 + 0.524635i
\(65\) −16.3559 −2.02870
\(66\) 0 0
\(67\) −3.88805 + 9.38659i −0.475001 + 1.14676i 0.486924 + 0.873444i \(0.338119\pi\)
−0.961926 + 0.273311i \(0.911881\pi\)
\(68\) 1.52467 8.18820i 0.184894 0.992966i
\(69\) 0 0
\(70\) −5.09753 + 9.67899i −0.609271 + 1.15686i
\(71\) 1.88924 1.88924i 0.224211 0.224211i −0.586058 0.810269i \(-0.699321\pi\)
0.810269 + 0.586058i \(0.199321\pi\)
\(72\) 0 0
\(73\) −7.00727 7.00727i −0.820139 0.820139i 0.165989 0.986128i \(-0.446918\pi\)
−0.986128 + 0.165989i \(0.946918\pi\)
\(74\) −9.22638 + 2.86064i −1.07255 + 0.332543i
\(75\) 0 0
\(76\) 8.16306 + 5.31086i 0.936367 + 0.609197i
\(77\) 9.11066 + 3.77376i 1.03826 + 0.430060i
\(78\) 0 0
\(79\) 11.0255i 1.24047i −0.784417 0.620234i \(-0.787038\pi\)
0.784417 0.620234i \(-0.212962\pi\)
\(80\) 10.8801 0.266706i 1.21643 0.0298186i
\(81\) 0 0
\(82\) 0.966814 + 1.16346i 0.106767 + 0.128482i
\(83\) 2.30515 + 0.954824i 0.253023 + 0.104806i 0.505590 0.862774i \(-0.331275\pi\)
−0.252567 + 0.967579i \(0.581275\pi\)
\(84\) 0 0
\(85\) −4.33615 10.4684i −0.470321 1.13546i
\(86\) −1.68291 5.42786i −0.181473 0.585301i
\(87\) 0 0
\(88\) −1.14093 9.74436i −0.121624 1.03875i
\(89\) −7.65800 + 7.65800i −0.811747 + 0.811747i −0.984896 0.173149i \(-0.944606\pi\)
0.173149 + 0.984896i \(0.444606\pi\)
\(90\) 0 0
\(91\) −15.7890 + 6.54003i −1.65514 + 0.685582i
\(92\) 3.10868 + 4.53127i 0.324103 + 0.472418i
\(93\) 0 0
\(94\) −0.140676 + 1.52398i −0.0145096 + 0.157186i
\(95\) 13.2487 1.35928
\(96\) 0 0
\(97\) −11.3029 −1.14764 −0.573819 0.818982i \(-0.694539\pi\)
−0.573819 + 0.818982i \(0.694539\pi\)
\(98\) −0.140697 + 1.52421i −0.0142126 + 0.153968i
\(99\) 0 0
\(100\) 3.96305 2.71885i 0.396305 0.271885i
\(101\) −3.56392 + 1.47622i −0.354623 + 0.146890i −0.552881 0.833260i \(-0.686472\pi\)
0.198258 + 0.980150i \(0.436472\pi\)
\(102\) 0 0
\(103\) −1.94329 + 1.94329i −0.191478 + 0.191478i −0.796335 0.604856i \(-0.793231\pi\)
0.604856 + 0.796335i \(0.293231\pi\)
\(104\) 13.3392 + 10.5430i 1.30802 + 1.03382i
\(105\) 0 0
\(106\) −3.17868 10.2522i −0.308741 0.995777i
\(107\) 5.35190 + 12.9206i 0.517388 + 1.24908i 0.939502 + 0.342542i \(0.111288\pi\)
−0.422114 + 0.906543i \(0.638712\pi\)
\(108\) 0 0
\(109\) 12.1425 + 5.02958i 1.16304 + 0.481747i 0.878886 0.477032i \(-0.158287\pi\)
0.284154 + 0.958779i \(0.408287\pi\)
\(110\) −8.53032 10.2653i −0.813334 0.978760i
\(111\) 0 0
\(112\) 10.3964 4.60795i 0.982365 0.435411i
\(113\) 13.8394i 1.30190i −0.759121 0.650950i \(-0.774371\pi\)
0.759121 0.650950i \(-0.225629\pi\)
\(114\) 0 0
\(115\) 6.90664 + 2.86082i 0.644048 + 0.266773i
\(116\) 5.58909 8.59072i 0.518934 0.797628i
\(117\) 0 0
\(118\) 15.1215 4.68843i 1.39205 0.431605i
\(119\) −8.37171 8.37171i −0.767433 0.767433i
\(120\) 0 0
\(121\) −0.729588 + 0.729588i −0.0663262 + 0.0663262i
\(122\) 5.12675 9.73448i 0.464154 0.881318i
\(123\) 0 0
\(124\) −5.64331 1.05081i −0.506784 0.0943651i
\(125\) −2.70404 + 6.52814i −0.241857 + 0.583894i
\(126\) 0 0
\(127\) −5.47542 −0.485865 −0.242932 0.970043i \(-0.578109\pi\)
−0.242932 + 0.970043i \(0.578109\pi\)
\(128\) −9.04531 6.79576i −0.799500 0.600666i
\(129\) 0 0
\(130\) 23.0329 + 2.12613i 2.02012 + 0.186474i
\(131\) −8.03254 + 19.3923i −0.701806 + 1.69431i 0.0177195 + 0.999843i \(0.494359\pi\)
−0.719525 + 0.694466i \(0.755641\pi\)
\(132\) 0 0
\(133\) 12.7894 5.29756i 1.10899 0.459357i
\(134\) 6.69544 12.7130i 0.578398 1.09824i
\(135\) 0 0
\(136\) −3.21148 + 11.3327i −0.275382 + 0.971767i
\(137\) 3.73965 + 3.73965i 0.319500 + 0.319500i 0.848575 0.529075i \(-0.177461\pi\)
−0.529075 + 0.848575i \(0.677461\pi\)
\(138\) 0 0
\(139\) −4.05949 9.80047i −0.344321 0.831265i −0.997268 0.0738616i \(-0.976468\pi\)
0.652947 0.757403i \(-0.273532\pi\)
\(140\) 8.43666 12.9676i 0.713028 1.09596i
\(141\) 0 0
\(142\) −2.90606 + 2.41489i −0.243871 + 0.202653i
\(143\) 20.8515i 1.74369i
\(144\) 0 0
\(145\) 13.9427i 1.15788i
\(146\) 8.95694 + 10.7787i 0.741282 + 0.892052i
\(147\) 0 0
\(148\) 13.3647 2.82908i 1.09857 0.232549i
\(149\) −4.32999 10.4535i −0.354727 0.856386i −0.996023 0.0890929i \(-0.971603\pi\)
0.641297 0.767293i \(-0.278397\pi\)
\(150\) 0 0
\(151\) 12.1795 + 12.1795i 0.991157 + 0.991157i 0.999961 0.00880460i \(-0.00280263\pi\)
−0.00880460 + 0.999961i \(0.502803\pi\)
\(152\) −10.8051 8.54002i −0.876407 0.692687i
\(153\) 0 0
\(154\) −12.3393 6.49861i −0.994330 0.523673i
\(155\) −7.21481 + 2.98847i −0.579507 + 0.240040i
\(156\) 0 0
\(157\) −5.53996 + 13.3746i −0.442137 + 1.06741i 0.533061 + 0.846077i \(0.321042\pi\)
−0.975198 + 0.221336i \(0.928958\pi\)
\(158\) −1.43322 + 15.5264i −0.114021 + 1.23522i
\(159\) 0 0
\(160\) −15.3563 1.03874i −1.21403 0.0821196i
\(161\) 7.81117 0.615607
\(162\) 0 0
\(163\) 5.79233 13.9839i 0.453690 1.09530i −0.517218 0.855854i \(-0.673032\pi\)
0.970908 0.239451i \(-0.0769675\pi\)
\(164\) −1.21025 1.76409i −0.0945049 0.137752i
\(165\) 0 0
\(166\) −3.12205 1.64426i −0.242318 0.127619i
\(167\) −4.07626 + 4.07626i −0.315430 + 0.315430i −0.847009 0.531579i \(-0.821599\pi\)
0.531579 + 0.847009i \(0.321599\pi\)
\(168\) 0 0
\(169\) 16.3598 + 16.3598i 1.25844 + 1.25844i
\(170\) 4.74548 + 15.3055i 0.363962 + 1.17388i
\(171\) 0 0
\(172\) 1.66434 + 7.86242i 0.126905 + 0.599504i
\(173\) −4.29724 1.77998i −0.326713 0.135329i 0.213297 0.976987i \(-0.431580\pi\)
−0.540010 + 0.841658i \(0.681580\pi\)
\(174\) 0 0
\(175\) 6.83165i 0.516424i
\(176\) 0.340011 + 13.8706i 0.0256293 + 1.04553i
\(177\) 0 0
\(178\) 11.7797 9.78873i 0.882924 0.733696i
\(179\) 0.273384 + 0.113240i 0.0204337 + 0.00846392i 0.392877 0.919591i \(-0.371480\pi\)
−0.372443 + 0.928055i \(0.621480\pi\)
\(180\) 0 0
\(181\) 4.00336 + 9.66497i 0.297567 + 0.718391i 0.999978 + 0.00661937i \(0.00210703\pi\)
−0.702411 + 0.711772i \(0.747893\pi\)
\(182\) 23.0847 7.15741i 1.71115 0.530543i
\(183\) 0 0
\(184\) −3.78871 6.78516i −0.279307 0.500209i
\(185\) 13.1413 13.1413i 0.966165 0.966165i
\(186\) 0 0
\(187\) 13.3457 5.52796i 0.975932 0.404244i
\(188\) 0.396208 2.12782i 0.0288964 0.155187i
\(189\) 0 0
\(190\) −18.6571 1.72221i −1.35353 0.124942i
\(191\) −15.1625 −1.09712 −0.548561 0.836110i \(-0.684824\pi\)
−0.548561 + 0.836110i \(0.684824\pi\)
\(192\) 0 0
\(193\) −18.3549 −1.32122 −0.660608 0.750731i \(-0.729701\pi\)
−0.660608 + 0.750731i \(0.729701\pi\)
\(194\) 15.9171 + 1.46928i 1.14278 + 0.105488i
\(195\) 0 0
\(196\) 0.396268 2.12814i 0.0283048 0.152010i
\(197\) 6.65334 2.75590i 0.474031 0.196350i −0.132861 0.991135i \(-0.542416\pi\)
0.606891 + 0.794785i \(0.292416\pi\)
\(198\) 0 0
\(199\) −0.849057 + 0.849057i −0.0601880 + 0.0601880i −0.736560 0.676372i \(-0.763551\pi\)
0.676372 + 0.736560i \(0.263551\pi\)
\(200\) −5.93430 + 3.31360i −0.419618 + 0.234307i
\(201\) 0 0
\(202\) 5.21070 1.61558i 0.366624 0.113672i
\(203\) −5.57510 13.4595i −0.391295 0.944671i
\(204\) 0 0
\(205\) −2.68885 1.11376i −0.187797 0.0777883i
\(206\) 2.98921 2.48398i 0.208268 0.173067i
\(207\) 0 0
\(208\) −17.4142 16.5809i −1.20746 1.14968i
\(209\) 16.8901i 1.16831i
\(210\) 0 0
\(211\) −7.40729 3.06820i −0.509939 0.211224i 0.112852 0.993612i \(-0.464001\pi\)
−0.622791 + 0.782388i \(0.714001\pi\)
\(212\) 3.14361 + 14.8506i 0.215904 + 1.01994i
\(213\) 0 0
\(214\) −5.85712 18.8909i −0.400384 1.29135i
\(215\) 7.73098 + 7.73098i 0.527248 + 0.527248i
\(216\) 0 0
\(217\) −5.76978 + 5.76978i −0.391678 + 0.391678i
\(218\) −16.4456 8.66121i −1.11384 0.586611i
\(219\) 0 0
\(220\) 10.6782 + 15.5648i 0.719925 + 1.04938i
\(221\) −9.58012 + 23.1285i −0.644429 + 1.55579i
\(222\) 0 0
\(223\) 0.188370 0.0126142 0.00630710 0.999980i \(-0.497992\pi\)
0.00630710 + 0.999980i \(0.497992\pi\)
\(224\) −15.2394 + 5.13760i −1.01823 + 0.343271i
\(225\) 0 0
\(226\) −1.79900 + 19.4890i −0.119668 + 1.29639i
\(227\) 0.106761 0.257744i 0.00708599 0.0171071i −0.920297 0.391221i \(-0.872053\pi\)
0.927383 + 0.374113i \(0.122053\pi\)
\(228\) 0 0
\(229\) 2.03685 0.843689i 0.134599 0.0557526i −0.314367 0.949301i \(-0.601792\pi\)
0.448966 + 0.893549i \(0.351792\pi\)
\(230\) −9.35423 4.92649i −0.616800 0.324843i
\(231\) 0 0
\(232\) −8.98743 + 11.3711i −0.590054 + 0.746552i
\(233\) 4.32675 + 4.32675i 0.283455 + 0.283455i 0.834485 0.551030i \(-0.185765\pi\)
−0.551030 + 0.834485i \(0.685765\pi\)
\(234\) 0 0
\(235\) −1.12681 2.72036i −0.0735049 0.177456i
\(236\) −21.9040 + 4.63670i −1.42583 + 0.301824i
\(237\) 0 0
\(238\) 10.7010 + 12.8775i 0.693644 + 0.834725i
\(239\) 8.26905i 0.534880i −0.963575 0.267440i \(-0.913822\pi\)
0.963575 0.267440i \(-0.0861777\pi\)
\(240\) 0 0
\(241\) 22.7291i 1.46411i 0.681244 + 0.732057i \(0.261439\pi\)
−0.681244 + 0.732057i \(0.738561\pi\)
\(242\) 1.12227 0.932585i 0.0721419 0.0599488i
\(243\) 0 0
\(244\) −8.48503 + 13.0419i −0.543198 + 0.834923i
\(245\) −1.12698 2.72077i −0.0720000 0.173823i
\(246\) 0 0
\(247\) −20.6978 20.6978i −1.31697 1.31697i
\(248\) 7.81046 + 2.21335i 0.495965 + 0.140548i
\(249\) 0 0
\(250\) 4.65651 8.84159i 0.294503 0.559191i
\(251\) 12.3335 5.10871i 0.778485 0.322459i 0.0421812 0.999110i \(-0.486569\pi\)
0.736304 + 0.676651i \(0.236569\pi\)
\(252\) 0 0
\(253\) −3.64714 + 8.80497i −0.229294 + 0.553564i
\(254\) 7.71063 + 0.711757i 0.483808 + 0.0446596i
\(255\) 0 0
\(256\) 11.8545 + 10.7458i 0.740903 + 0.671612i
\(257\) −15.9974 −0.997893 −0.498947 0.866633i \(-0.666280\pi\)
−0.498947 + 0.866633i \(0.666280\pi\)
\(258\) 0 0
\(259\) 7.43116 17.9404i 0.461750 1.11476i
\(260\) −32.1591 5.98815i −1.99442 0.371369i
\(261\) 0 0
\(262\) 13.8325 26.2645i 0.854572 1.62263i
\(263\) 4.44583 4.44583i 0.274141 0.274141i −0.556623 0.830765i \(-0.687903\pi\)
0.830765 + 0.556623i \(0.187903\pi\)
\(264\) 0 0
\(265\) 14.6023 + 14.6023i 0.897011 + 0.897011i
\(266\) −18.6991 + 5.79765i −1.14651 + 0.355477i
\(267\) 0 0
\(268\) −11.0813 + 17.0325i −0.676897 + 1.04042i
\(269\) 11.1204 + 4.60621i 0.678021 + 0.280846i 0.695000 0.719010i \(-0.255405\pi\)
−0.0169781 + 0.999856i \(0.505405\pi\)
\(270\) 0 0
\(271\) 18.7073i 1.13638i −0.822896 0.568192i \(-0.807643\pi\)
0.822896 0.568192i \(-0.192357\pi\)
\(272\) 5.99564 15.5415i 0.363539 0.942341i
\(273\) 0 0
\(274\) −4.78015 5.75240i −0.288780 0.347515i
\(275\) 7.70082 + 3.18978i 0.464377 + 0.192351i
\(276\) 0 0
\(277\) −4.13646 9.98630i −0.248536 0.600019i 0.749544 0.661954i \(-0.230273\pi\)
−0.998080 + 0.0619354i \(0.980273\pi\)
\(278\) 4.44270 + 14.3290i 0.266456 + 0.859395i
\(279\) 0 0
\(280\) −13.5664 + 17.1646i −0.810748 + 1.02578i
\(281\) 13.2105 13.2105i 0.788071 0.788071i −0.193106 0.981178i \(-0.561856\pi\)
0.981178 + 0.193106i \(0.0618563\pi\)
\(282\) 0 0
\(283\) −21.9884 + 9.10789i −1.30707 + 0.541408i −0.924029 0.382321i \(-0.875125\pi\)
−0.383045 + 0.923730i \(0.625125\pi\)
\(284\) 4.40631 3.02295i 0.261466 0.179379i
\(285\) 0 0
\(286\) −2.71051 + 29.3636i −0.160276 + 1.73630i
\(287\) −3.04100 −0.179504
\(288\) 0 0
\(289\) −0.342832 −0.0201666
\(290\) −1.81244 + 19.6345i −0.106430 + 1.15298i
\(291\) 0 0
\(292\) −11.2123 16.3432i −0.656148 0.956413i
\(293\) 18.8878 7.82359i 1.10344 0.457059i 0.244764 0.969583i \(-0.421289\pi\)
0.858673 + 0.512524i \(0.171289\pi\)
\(294\) 0 0
\(295\) −21.5378 + 21.5378i −1.25398 + 1.25398i
\(296\) −19.1883 + 2.24669i −1.11530 + 0.130586i
\(297\) 0 0
\(298\) 4.73874 + 15.2838i 0.274508 + 0.885366i
\(299\) −6.32060 15.2593i −0.365530 0.882466i
\(300\) 0 0
\(301\) 10.5543 + 4.37173i 0.608340 + 0.251983i
\(302\) −15.5683 18.7348i −0.895856 1.07807i
\(303\) 0 0
\(304\) 14.1059 + 13.4308i 0.809026 + 0.770312i
\(305\) 21.1670i 1.21202i
\(306\) 0 0
\(307\) 10.7709 + 4.46145i 0.614728 + 0.254629i 0.668249 0.743938i \(-0.267044\pi\)
−0.0535206 + 0.998567i \(0.517044\pi\)
\(308\) 16.5318 + 10.7555i 0.941986 + 0.612853i
\(309\) 0 0
\(310\) 10.5486 3.27058i 0.599118 0.185757i
\(311\) 6.79085 + 6.79085i 0.385074 + 0.385074i 0.872926 0.487852i \(-0.162220\pi\)
−0.487852 + 0.872926i \(0.662220\pi\)
\(312\) 0 0
\(313\) 12.7080 12.7080i 0.718300 0.718300i −0.249957 0.968257i \(-0.580417\pi\)
0.968257 + 0.249957i \(0.0804166\pi\)
\(314\) 9.54011 18.1144i 0.538379 1.02225i
\(315\) 0 0
\(316\) 4.03661 21.6784i 0.227077 1.21951i
\(317\) 6.89303 16.6412i 0.387151 0.934665i −0.603390 0.797446i \(-0.706184\pi\)
0.990541 0.137219i \(-0.0438163\pi\)
\(318\) 0 0
\(319\) 17.7750 0.995208
\(320\) 21.4902 + 3.45897i 1.20134 + 0.193363i
\(321\) 0 0
\(322\) −10.9999 1.01539i −0.613001 0.0565852i
\(323\) 7.76010 18.7345i 0.431783 1.04242i
\(324\) 0 0
\(325\) −13.3457 + 5.52799i −0.740289 + 0.306638i
\(326\) −9.97470 + 18.9396i −0.552447 + 1.04897i
\(327\) 0 0
\(328\) 1.47500 + 2.64156i 0.0814430 + 0.145856i
\(329\) −2.17550 2.17550i −0.119939 0.119939i
\(330\) 0 0
\(331\) 0.259261 + 0.625913i 0.0142503 + 0.0344033i 0.930845 0.365415i \(-0.119073\pi\)
−0.916594 + 0.399819i \(0.869073\pi\)
\(332\) 4.18282 + 2.72133i 0.229562 + 0.149352i
\(333\) 0 0
\(334\) 6.27017 5.21042i 0.343089 0.285101i
\(335\) 27.6438i 1.51034i
\(336\) 0 0
\(337\) 24.3244i 1.32504i −0.749046 0.662518i \(-0.769488\pi\)
0.749046 0.662518i \(-0.230512\pi\)
\(338\) −20.9116 25.1649i −1.13744 1.36879i
\(339\) 0 0
\(340\) −4.69312 22.1705i −0.254520 1.20236i
\(341\) −3.80987 9.19783i −0.206316 0.498091i
\(342\) 0 0
\(343\) 11.8960 + 11.8960i 0.642326 + 0.642326i
\(344\) −1.32172 11.2884i −0.0712626 0.608631i
\(345\) 0 0
\(346\) 5.82011 + 3.06521i 0.312891 + 0.164787i
\(347\) −6.95491 + 2.88082i −0.373359 + 0.154650i −0.561469 0.827498i \(-0.689764\pi\)
0.188110 + 0.982148i \(0.439764\pi\)
\(348\) 0 0
\(349\) 11.9159 28.7676i 0.637845 1.53989i −0.191700 0.981454i \(-0.561400\pi\)
0.829545 0.558440i \(-0.188600\pi\)
\(350\) −0.888055 + 9.62051i −0.0474685 + 0.514238i
\(351\) 0 0
\(352\) 1.32424 19.5771i 0.0705824 1.04346i
\(353\) 22.1334 1.17804 0.589021 0.808118i \(-0.299514\pi\)
0.589021 + 0.808118i \(0.299514\pi\)
\(354\) 0 0
\(355\) 2.78193 6.71616i 0.147649 0.356457i
\(356\) −17.8609 + 12.2535i −0.946626 + 0.649434i
\(357\) 0 0
\(358\) −0.370267 0.195005i −0.0195692 0.0103063i
\(359\) 10.1669 10.1669i 0.536586 0.536586i −0.385939 0.922524i \(-0.626122\pi\)
0.922524 + 0.385939i \(0.126122\pi\)
\(360\) 0 0
\(361\) 3.33060 + 3.33060i 0.175295 + 0.175295i
\(362\) −4.38128 14.1309i −0.230275 0.742702i
\(363\) 0 0
\(364\) −33.4389 + 7.07845i −1.75267 + 0.371011i
\(365\) −24.9106 10.3183i −1.30388 0.540084i
\(366\) 0 0
\(367\) 9.77761i 0.510387i 0.966890 + 0.255194i \(0.0821392\pi\)
−0.966890 + 0.255194i \(0.917861\pi\)
\(368\) 4.45334 + 10.0475i 0.232147 + 0.523764i
\(369\) 0 0
\(370\) −20.2141 + 16.7976i −1.05088 + 0.873267i
\(371\) 19.9350 + 8.25734i 1.03497 + 0.428700i
\(372\) 0 0
\(373\) −2.04735 4.94275i −0.106008 0.255926i 0.861971 0.506958i \(-0.169230\pi\)
−0.967979 + 0.251032i \(0.919230\pi\)
\(374\) −19.5123 + 6.04980i −1.00896 + 0.312828i
\(375\) 0 0
\(376\) −0.834549 + 2.94495i −0.0430386 + 0.151874i
\(377\) −21.7821 + 21.7821i −1.12184 + 1.12184i
\(378\) 0 0
\(379\) −29.0333 + 12.0260i −1.49134 + 0.617733i −0.971608 0.236596i \(-0.923968\pi\)
−0.519732 + 0.854329i \(0.673968\pi\)
\(380\) 26.0496 + 4.85053i 1.33631 + 0.248827i
\(381\) 0 0
\(382\) 21.3523 + 1.97100i 1.09248 + 0.100845i
\(383\) −2.47568 −0.126501 −0.0632507 0.997998i \(-0.520147\pi\)
−0.0632507 + 0.997998i \(0.520147\pi\)
\(384\) 0 0
\(385\) 26.8311 1.36744
\(386\) 25.8479 + 2.38598i 1.31562 + 0.121443i
\(387\) 0 0
\(388\) −22.2238 4.13816i −1.12824 0.210083i
\(389\) 9.49742 3.93396i 0.481538 0.199460i −0.128691 0.991685i \(-0.541077\pi\)
0.610229 + 0.792225i \(0.291077\pi\)
\(390\) 0 0
\(391\) 8.09081 8.09081i 0.409170 0.409170i
\(392\) −0.834675 + 2.94539i −0.0421574 + 0.148765i
\(393\) 0 0
\(394\) −9.72766 + 3.01606i −0.490072 + 0.151947i
\(395\) −11.4800 27.7153i −0.577623 1.39451i
\(396\) 0 0
\(397\) −13.8666 5.74373i −0.695944 0.288269i 0.00653022 0.999979i \(-0.497921\pi\)
−0.702474 + 0.711709i \(0.747921\pi\)
\(398\) 1.30603 1.08529i 0.0654656 0.0544009i
\(399\) 0 0
\(400\) 8.78757 3.89489i 0.439379 0.194745i
\(401\) 21.9112i 1.09419i −0.837069 0.547097i \(-0.815733\pi\)
0.837069 0.547097i \(-0.184267\pi\)
\(402\) 0 0
\(403\) 15.9401 + 6.60262i 0.794034 + 0.328900i
\(404\) −7.54786 + 1.59775i −0.375520 + 0.0794913i
\(405\) 0 0
\(406\) 6.10139 + 19.6787i 0.302807 + 0.976639i
\(407\) 16.7532 + 16.7532i 0.830426 + 0.830426i
\(408\) 0 0
\(409\) 13.0005 13.0005i 0.642835 0.642835i −0.308417 0.951251i \(-0.599799\pi\)
0.951251 + 0.308417i \(0.0997991\pi\)
\(410\) 3.64173 + 1.91795i 0.179852 + 0.0947209i
\(411\) 0 0
\(412\) −4.53237 + 3.10944i −0.223294 + 0.153191i
\(413\) −12.1792 + 29.4033i −0.599301 + 1.44684i
\(414\) 0 0
\(415\) 6.78872 0.333245
\(416\) 22.3678 + 25.6133i 1.09667 + 1.25580i
\(417\) 0 0
\(418\) 2.19557 23.7851i 0.107389 1.16337i
\(419\) 7.98199 19.2702i 0.389946 0.941412i −0.600005 0.799997i \(-0.704835\pi\)
0.989950 0.141416i \(-0.0451654\pi\)
\(420\) 0 0
\(421\) −5.11481 + 2.11863i −0.249281 + 0.103255i −0.503825 0.863806i \(-0.668074\pi\)
0.254545 + 0.967061i \(0.418074\pi\)
\(422\) 10.0323 + 5.28361i 0.488365 + 0.257202i
\(423\) 0 0
\(424\) −2.49647 21.3216i −0.121239 1.03547i
\(425\) −7.07622 7.07622i −0.343247 0.343247i
\(426\) 0 0
\(427\) 8.46379 + 20.4334i 0.409591 + 0.988841i
\(428\) 5.79250 + 27.3640i 0.279991 + 1.32269i
\(429\) 0 0
\(430\) −9.88201 11.8919i −0.476553 0.573480i
\(431\) 5.20156i 0.250551i −0.992122 0.125275i \(-0.960019\pi\)
0.992122 0.125275i \(-0.0399814\pi\)
\(432\) 0 0
\(433\) 6.44939i 0.309938i −0.987919 0.154969i \(-0.950472\pi\)
0.987919 0.154969i \(-0.0495278\pi\)
\(434\) 8.87518 7.37514i 0.426022 0.354018i
\(435\) 0 0
\(436\) 22.0332 + 14.3347i 1.05520 + 0.686509i
\(437\) 5.11982 + 12.3603i 0.244914 + 0.591275i
\(438\) 0 0
\(439\) −20.5461 20.5461i −0.980610 0.980610i 0.0192051 0.999816i \(-0.493886\pi\)
−0.999816 + 0.0192051i \(0.993886\pi\)
\(440\) −13.0141 23.3068i −0.620421 1.11111i
\(441\) 0 0
\(442\) 16.4975 31.3248i 0.784705 1.48997i
\(443\) 16.1487 6.68902i 0.767249 0.317805i 0.0354912 0.999370i \(-0.488700\pi\)
0.731757 + 0.681565i \(0.238700\pi\)
\(444\) 0 0
\(445\) −11.2765 + 27.2239i −0.534557 + 1.29054i
\(446\) −0.265268 0.0244865i −0.0125608 0.00115947i
\(447\) 0 0
\(448\) 22.1284 5.25391i 1.04547 0.248224i
\(449\) 0.794308 0.0374857 0.0187428 0.999824i \(-0.494034\pi\)
0.0187428 + 0.999824i \(0.494034\pi\)
\(450\) 0 0
\(451\) 1.41988 3.42790i 0.0668596 0.161413i
\(452\) 5.06680 27.2111i 0.238322 1.27990i
\(453\) 0 0
\(454\) −0.183848 + 0.349084i −0.00862844 + 0.0163833i
\(455\) −32.8798 + 32.8798i −1.54143 + 1.54143i
\(456\) 0 0
\(457\) 21.2796 + 21.2796i 0.995420 + 0.995420i 0.999990 0.00456968i \(-0.00145458\pi\)
−0.00456968 + 0.999990i \(0.501455\pi\)
\(458\) −2.97801 + 0.923333i −0.139153 + 0.0431445i
\(459\) 0 0
\(460\) 12.5325 + 8.15359i 0.584330 + 0.380163i
\(461\) 0.541763 + 0.224405i 0.0252324 + 0.0104516i 0.395264 0.918568i \(-0.370653\pi\)
−0.370032 + 0.929019i \(0.620653\pi\)
\(462\) 0 0
\(463\) 13.0365i 0.605859i 0.953013 + 0.302929i \(0.0979646\pi\)
−0.953013 + 0.302929i \(0.902035\pi\)
\(464\) 14.1345 14.8449i 0.656177 0.689155i
\(465\) 0 0
\(466\) −5.53061 6.65549i −0.256200 0.308310i
\(467\) −36.1793 14.9860i −1.67418 0.693467i −0.675156 0.737675i \(-0.735924\pi\)
−0.999022 + 0.0442081i \(0.985924\pi\)
\(468\) 0 0
\(469\) 11.0535 + 26.6856i 0.510405 + 1.23223i
\(470\) 1.23318 + 3.97735i 0.0568823 + 0.183462i
\(471\) 0 0
\(472\) 31.4485 3.68220i 1.44753 0.169487i
\(473\) −9.85587 + 9.85587i −0.453174 + 0.453174i
\(474\) 0 0
\(475\) 10.8103 4.47779i 0.496012 0.205455i
\(476\) −13.3955 19.5255i −0.613981 0.894950i
\(477\) 0 0
\(478\) −1.07490 + 11.6447i −0.0491650 + 0.532616i
\(479\) −27.6976 −1.26554 −0.632768 0.774341i \(-0.718081\pi\)
−0.632768 + 0.774341i \(0.718081\pi\)
\(480\) 0 0
\(481\) −41.0600 −1.87217
\(482\) 2.95459 32.0078i 0.134578 1.45792i
\(483\) 0 0
\(484\) −1.70163 + 1.16741i −0.0773469 + 0.0530639i
\(485\) −28.4125 + 11.7689i −1.29015 + 0.534396i
\(486\) 0 0
\(487\) 22.8658 22.8658i 1.03615 1.03615i 0.0368273 0.999322i \(-0.488275\pi\)
0.999322 0.0368273i \(-0.0117251\pi\)
\(488\) 13.6442 17.2630i 0.617643 0.781459i
\(489\) 0 0
\(490\) 1.23336 + 3.97795i 0.0557177 + 0.179706i
\(491\) 10.1610 + 24.5308i 0.458559 + 1.10706i 0.968981 + 0.247135i \(0.0794890\pi\)
−0.510423 + 0.859924i \(0.670511\pi\)
\(492\) 0 0
\(493\) −19.7160 8.16665i −0.887965 0.367807i
\(494\) 26.4566 + 31.8377i 1.19034 + 1.43245i
\(495\) 0 0
\(496\) −10.7112 4.13220i −0.480946 0.185541i
\(497\) 7.59575i 0.340716i
\(498\) 0 0
\(499\) −11.6135 4.81046i −0.519890 0.215346i 0.107278 0.994229i \(-0.465786\pi\)
−0.627169 + 0.778883i \(0.715786\pi\)
\(500\) −7.70675 + 11.8457i −0.344656 + 0.529754i
\(501\) 0 0
\(502\) −18.0325 + 5.59097i −0.804829 + 0.249537i
\(503\) −12.9948 12.9948i −0.579412 0.579412i 0.355330 0.934741i \(-0.384369\pi\)
−0.934741 + 0.355330i \(0.884369\pi\)
\(504\) 0 0
\(505\) −7.42167 + 7.42167i −0.330260 + 0.330260i
\(506\) 6.28056 11.9253i 0.279205 0.530144i
\(507\) 0 0
\(508\) −10.7658 2.00463i −0.477655 0.0889411i
\(509\) 13.3636 32.2627i 0.592333 1.43002i −0.288911 0.957356i \(-0.593293\pi\)
0.881244 0.472662i \(-0.156707\pi\)
\(510\) 0 0
\(511\) −28.1730 −1.24630
\(512\) −15.2969 16.6735i −0.676034 0.736871i
\(513\) 0 0
\(514\) 22.5280 + 2.07953i 0.993669 + 0.0917242i
\(515\) −2.86152 + 6.90832i −0.126094 + 0.304417i
\(516\) 0 0
\(517\) 3.46806 1.43652i 0.152525 0.0631780i
\(518\) −12.7969 + 24.2982i −0.562261 + 1.06760i
\(519\) 0 0
\(520\) 44.5089 + 12.6131i 1.95185 + 0.553120i
\(521\) −1.74966 1.74966i −0.0766541 0.0766541i 0.667740 0.744394i \(-0.267262\pi\)
−0.744394 + 0.667740i \(0.767262\pi\)
\(522\) 0 0
\(523\) 7.05117 + 17.0230i 0.308326 + 0.744366i 0.999760 + 0.0219253i \(0.00697960\pi\)
−0.691433 + 0.722440i \(0.743020\pi\)
\(524\) −22.8934 + 35.1883i −1.00010 + 1.53721i
\(525\) 0 0
\(526\) −6.83865 + 5.68281i −0.298179 + 0.247782i
\(527\) 11.9527i 0.520667i
\(528\) 0 0
\(529\) 15.4509i 0.671779i
\(530\) −18.6651 22.4615i −0.810762 0.975665i
\(531\) 0 0
\(532\) 27.0862 5.73369i 1.17434 0.248587i
\(533\) 2.46070 + 5.94064i 0.106585 + 0.257318i
\(534\) 0 0
\(535\) 26.9065 + 26.9065i 1.16327 + 1.16327i
\(536\) 17.8190 22.5451i 0.769665 0.973802i
\(537\) 0 0
\(538\) −15.0612 7.93214i −0.649336 0.341979i
\(539\) 3.46858 1.43673i 0.149402 0.0618845i
\(540\) 0 0
\(541\) 7.86315 18.9833i 0.338063 0.816157i −0.659838 0.751408i \(-0.729375\pi\)
0.997902 0.0647494i \(-0.0206248\pi\)
\(542\) −2.43178 + 26.3441i −0.104454 + 1.13157i
\(543\) 0 0
\(544\) −10.4635 + 21.1065i −0.448618 + 0.904936i
\(545\) 35.7599 1.53179
\(546\) 0 0
\(547\) −0.832145 + 2.00898i −0.0355799 + 0.0858976i −0.940671 0.339321i \(-0.889803\pi\)
0.905091 + 0.425219i \(0.139803\pi\)
\(548\) 5.98377 + 8.72206i 0.255614 + 0.372588i
\(549\) 0 0
\(550\) −10.4299 5.49298i −0.444730 0.234221i
\(551\) 17.6440 17.6440i 0.751659 0.751659i
\(552\) 0 0
\(553\) −22.1643 22.1643i −0.942520 0.942520i
\(554\) 4.52694 + 14.6007i 0.192331 + 0.620324i
\(555\) 0 0
\(556\) −4.39369 20.7560i −0.186334 0.880249i
\(557\) −27.8685 11.5435i −1.18083 0.489115i −0.296070 0.955166i \(-0.595676\pi\)
−0.884758 + 0.466051i \(0.845676\pi\)
\(558\) 0 0
\(559\) 24.1555i 1.02167i
\(560\) 21.3358 22.4081i 0.901603 0.946916i
\(561\) 0 0
\(562\) −20.3206 + 16.8861i −0.857173 + 0.712297i
\(563\) 17.3847 + 7.20096i 0.732676 + 0.303484i 0.717651 0.696403i \(-0.245217\pi\)
0.0150247 + 0.999887i \(0.495217\pi\)
\(564\) 0 0
\(565\) −14.4099 34.7886i −0.606229 1.46357i
\(566\) 32.1486 9.96768i 1.35131 0.418973i
\(567\) 0 0
\(568\) −6.59804 + 3.68422i −0.276847 + 0.154586i
\(569\) 5.37251 5.37251i 0.225227 0.225227i −0.585468 0.810695i \(-0.699089\pi\)
0.810695 + 0.585468i \(0.199089\pi\)
\(570\) 0 0
\(571\) 37.6829 15.6087i 1.57698 0.653206i 0.589047 0.808099i \(-0.299503\pi\)
0.987931 + 0.154893i \(0.0495033\pi\)
\(572\) 7.63402 40.9982i 0.319195 1.71422i
\(573\) 0 0
\(574\) 4.28241 + 0.395303i 0.178745 + 0.0164996i
\(575\) 6.60243 0.275340
\(576\) 0 0
\(577\) 28.6100 1.19105 0.595525 0.803337i \(-0.296944\pi\)
0.595525 + 0.803337i \(0.296944\pi\)
\(578\) 0.482786 + 0.0445653i 0.0200812 + 0.00185367i
\(579\) 0 0
\(580\) 5.10464 27.4143i 0.211959 1.13832i
\(581\) 6.55342 2.71452i 0.271882 0.112617i
\(582\) 0 0
\(583\) −18.6158 + 18.6158i −0.770987 + 0.770987i
\(584\) 13.6649 + 24.4724i 0.565459 + 1.01268i
\(585\) 0 0
\(586\) −27.6153 + 8.56213i −1.14078 + 0.353698i
\(587\) 14.0646 + 33.9550i 0.580509 + 1.40147i 0.892353 + 0.451339i \(0.149053\pi\)
−0.311844 + 0.950133i \(0.600947\pi\)
\(588\) 0 0
\(589\) −12.9118 5.34826i −0.532023 0.220371i
\(590\) 33.1298 27.5303i 1.36393 1.13341i
\(591\) 0 0
\(592\) 27.3135 0.669539i 1.12258 0.0275179i
\(593\) 28.6736i 1.17749i 0.808321 + 0.588743i \(0.200377\pi\)
−0.808321 + 0.588743i \(0.799623\pi\)
\(594\) 0 0
\(595\) −29.7611 12.3274i −1.22009 0.505376i
\(596\) −4.68646 22.1390i −0.191965 0.906850i
\(597\) 0 0
\(598\) 6.91726 + 22.3101i 0.282868 + 0.912329i
\(599\) 28.5413 + 28.5413i 1.16617 + 1.16617i 0.983100 + 0.183067i \(0.0586027\pi\)
0.183067 + 0.983100i \(0.441397\pi\)
\(600\) 0 0
\(601\) −29.9824 + 29.9824i −1.22301 + 1.22301i −0.256448 + 0.966558i \(0.582552\pi\)
−0.966558 + 0.256448i \(0.917448\pi\)
\(602\) −14.2946 7.52836i −0.582603 0.306833i
\(603\) 0 0
\(604\) 19.4884 + 28.4066i 0.792970 + 1.15585i
\(605\) −1.07433 + 2.59365i −0.0436776 + 0.105447i
\(606\) 0 0
\(607\) −20.2791 −0.823105 −0.411552 0.911386i \(-0.635013\pi\)
−0.411552 + 0.911386i \(0.635013\pi\)
\(608\) −18.1184 20.7473i −0.734796 0.841415i
\(609\) 0 0
\(610\) 2.75153 29.8080i 0.111406 1.20689i
\(611\) −2.48953 + 6.01025i −0.100715 + 0.243149i
\(612\) 0 0
\(613\) −22.4278 + 9.28988i −0.905849 + 0.375215i −0.786466 0.617633i \(-0.788092\pi\)
−0.119383 + 0.992848i \(0.538092\pi\)
\(614\) −14.5879 7.68286i −0.588721 0.310055i
\(615\) 0 0
\(616\) −21.8824 17.2952i −0.881666 0.696844i
\(617\) 28.6181 + 28.6181i 1.15212 + 1.15212i 0.986127 + 0.165993i \(0.0530829\pi\)
0.165993 + 0.986127i \(0.446917\pi\)
\(618\) 0 0
\(619\) −0.706861 1.70651i −0.0284111 0.0685905i 0.909037 0.416715i \(-0.136819\pi\)
−0.937448 + 0.348124i \(0.886819\pi\)
\(620\) −15.2799 + 3.23450i −0.613656 + 0.129901i
\(621\) 0 0
\(622\) −8.68031 10.4458i −0.348049 0.418839i
\(623\) 30.7893i 1.23355i
\(624\) 0 0
\(625\) 31.2406i 1.24962i
\(626\) −19.5477 + 16.2438i −0.781283 + 0.649234i
\(627\) 0 0
\(628\) −15.7893 + 24.2690i −0.630064 + 0.968440i
\(629\) −10.8855 26.2799i −0.434032 1.04785i
\(630\) 0 0
\(631\) 24.6361 + 24.6361i 0.980748 + 0.980748i 0.999818 0.0190703i \(-0.00607062\pi\)
−0.0190703 + 0.999818i \(0.506071\pi\)
\(632\) −8.50246 + 30.0034i −0.338210 + 1.19347i
\(633\) 0 0
\(634\) −11.8702 + 22.5386i −0.471424 + 0.895122i
\(635\) −13.7638 + 5.70114i −0.546198 + 0.226243i
\(636\) 0 0
\(637\) −2.48990 + 6.01116i −0.0986536 + 0.238171i
\(638\) −25.0312 2.31060i −0.990995 0.0914773i
\(639\) 0 0
\(640\) −29.8134 7.66456i −1.17848 0.302968i
\(641\) −0.278463 −0.0109986 −0.00549931 0.999985i \(-0.501750\pi\)
−0.00549931 + 0.999985i \(0.501750\pi\)
\(642\) 0 0
\(643\) −5.39050 + 13.0138i −0.212581 + 0.513215i −0.993818 0.111019i \(-0.964589\pi\)
0.781238 + 0.624234i \(0.214589\pi\)
\(644\) 15.3584 + 2.85979i 0.605204 + 0.112691i
\(645\) 0 0
\(646\) −13.3633 + 25.3737i −0.525772 + 0.998316i
\(647\) −17.8303 + 17.8303i −0.700980 + 0.700980i −0.964621 0.263641i \(-0.915077\pi\)
0.263641 + 0.964621i \(0.415077\pi\)
\(648\) 0 0
\(649\) −27.4575 27.4575i −1.07780 1.07780i
\(650\) 19.5124 6.04983i 0.765340 0.237294i
\(651\) 0 0
\(652\) 16.5086 25.3746i 0.646527 0.993745i
\(653\) −31.3223 12.9741i −1.22574 0.507716i −0.326507 0.945195i \(-0.605872\pi\)
−0.899229 + 0.437478i \(0.855872\pi\)
\(654\) 0 0
\(655\) 57.1107i 2.23150i
\(656\) −1.73375 3.91165i −0.0676915 0.152724i
\(657\) 0 0
\(658\) 2.78081 + 3.34640i 0.108407 + 0.130456i
\(659\) −38.2358 15.8378i −1.48946 0.616953i −0.518258 0.855224i \(-0.673419\pi\)
−0.971199 + 0.238271i \(0.923419\pi\)
\(660\) 0 0
\(661\) −7.49776 18.1012i −0.291629 0.704055i 0.708369 0.705842i \(-0.249431\pi\)
−0.999998 + 0.00178728i \(0.999431\pi\)
\(662\) −0.283736 0.915129i −0.0110277 0.0355675i
\(663\) 0 0
\(664\) −5.53661 4.37598i −0.214862 0.169821i
\(665\) 26.6334 26.6334i 1.03280 1.03280i
\(666\) 0 0
\(667\) 13.0079 5.38804i 0.503667 0.208626i
\(668\) −9.50714 + 6.52238i −0.367842 + 0.252358i
\(669\) 0 0
\(670\) 3.59345 38.9287i 0.138827 1.50395i
\(671\) −26.9849 −1.04174
\(672\) 0 0
\(673\) 18.3856 0.708711 0.354356 0.935111i \(-0.384700\pi\)
0.354356 + 0.935111i \(0.384700\pi\)
\(674\) −3.16197 + 34.2543i −0.121794 + 1.31943i
\(675\) 0 0
\(676\) 26.1771 + 38.1562i 1.00681 + 1.46755i
\(677\) −34.2111 + 14.1707i −1.31484 + 0.544624i −0.926293 0.376805i \(-0.877023\pi\)
−0.388546 + 0.921429i \(0.627023\pi\)
\(678\) 0 0
\(679\) −22.7219 + 22.7219i −0.871986 + 0.871986i
\(680\) 3.72700 + 31.8312i 0.142924 + 1.22067i
\(681\) 0 0
\(682\) 4.16952 + 13.4479i 0.159659 + 0.514946i
\(683\) −9.51662 22.9752i −0.364143 0.879120i −0.994685 0.102964i \(-0.967167\pi\)
0.630542 0.776155i \(-0.282833\pi\)
\(684\) 0 0
\(685\) 13.2943 + 5.50668i 0.507949 + 0.210399i
\(686\) −15.2059 18.2987i −0.580566 0.698648i
\(687\) 0 0
\(688\) 0.393889 + 16.0685i 0.0150169 + 0.612605i
\(689\) 45.6250i 1.73817i
\(690\) 0 0
\(691\) 18.8902 + 7.82459i 0.718618 + 0.297661i 0.711866 0.702316i \(-0.247851\pi\)
0.00675270 + 0.999977i \(0.497851\pi\)
\(692\) −7.79758 5.07308i −0.296419 0.192849i
\(693\) 0 0
\(694\) 10.1686 3.15276i 0.385993 0.119677i
\(695\) −20.4090 20.4090i −0.774156 0.774156i
\(696\) 0 0
\(697\) −3.14987 + 3.14987i −0.119310 + 0.119310i
\(698\) −20.5199 + 38.9623i −0.776688 + 1.47475i
\(699\) 0 0
\(700\) 2.50117 13.4324i 0.0945352 0.507698i
\(701\) 5.48707 13.2470i 0.207244 0.500331i −0.785743 0.618552i \(-0.787719\pi\)
0.992987 + 0.118222i \(0.0377194\pi\)
\(702\) 0 0
\(703\) 33.2595 1.25440
\(704\) −4.40969 + 27.3969i −0.166197 + 1.03256i
\(705\) 0 0
\(706\) −31.1688 2.87715i −1.17305 0.108283i
\(707\) −4.19683 + 10.1320i −0.157838 + 0.381055i
\(708\) 0 0
\(709\) 3.85647 1.59740i 0.144833 0.0599917i −0.309090 0.951033i \(-0.600024\pi\)
0.453922 + 0.891041i \(0.350024\pi\)
\(710\) −4.79063 + 9.09626i −0.179789 + 0.341376i
\(711\) 0 0
\(712\) 26.7450 14.9339i 1.00231 0.559673i
\(713\) −5.57619 5.57619i −0.208830 0.208830i
\(714\) 0 0
\(715\) −21.7110 52.4151i −0.811946 1.96021i
\(716\) 0.496071 + 0.322742i 0.0185390 + 0.0120614i
\(717\) 0 0
\(718\) −15.6388 + 12.9956i −0.583636 + 0.484993i
\(719\) 8.78550i 0.327644i 0.986490 + 0.163822i \(0.0523823\pi\)
−0.986490 + 0.163822i \(0.947618\pi\)
\(720\) 0 0
\(721\) 7.81307i 0.290974i
\(722\) −4.25729 5.12319i −0.158440 0.190665i
\(723\) 0 0
\(724\) 4.33294 + 20.4690i 0.161032 + 0.760724i
\(725\) −4.71238 11.3767i −0.175013 0.422520i
\(726\) 0 0
\(727\) −10.0533 10.0533i −0.372858 0.372858i 0.495659 0.868517i \(-0.334927\pi\)
−0.868517 + 0.495659i \(0.834927\pi\)
\(728\) 48.0097 5.62129i 1.77936 0.208339i
\(729\) 0 0
\(730\) 33.7384 + 17.7686i 1.24871 + 0.657647i
\(731\) 15.4604 6.40390i 0.571823 0.236857i
\(732\) 0 0
\(733\) 10.3759 25.0496i 0.383242 0.925228i −0.608093 0.793866i \(-0.708065\pi\)
0.991334 0.131362i \(-0.0419350\pi\)
\(734\) 1.27100 13.7691i 0.0469136 0.508226i
\(735\) 0 0
\(736\) −4.96522 14.7281i −0.183021 0.542885i
\(737\) −35.2418 −1.29815
\(738\) 0 0
\(739\) −12.3459 + 29.8057i −0.454153 + 1.09642i 0.516575 + 0.856242i \(0.327207\pi\)
−0.970728 + 0.240180i \(0.922793\pi\)
\(740\) 30.6496 21.0272i 1.12670 0.772975i
\(741\) 0 0
\(742\) −26.9996 14.2196i −0.991186 0.522017i
\(743\) −16.0222 + 16.0222i −0.587799 + 0.587799i −0.937035 0.349236i \(-0.886441\pi\)
0.349236 + 0.937035i \(0.386441\pi\)
\(744\) 0 0
\(745\) −21.7689 21.7689i −0.797551 0.797551i
\(746\) 2.24062 + 7.22665i 0.0820351 + 0.264586i
\(747\) 0 0
\(748\) 28.2642 5.98305i 1.03344 0.218762i
\(749\) 36.7327 + 15.2152i 1.34218 + 0.555951i
\(750\) 0 0
\(751\) 26.5917i 0.970346i 0.874418 + 0.485173i \(0.161243\pi\)
−0.874418 + 0.485173i \(0.838757\pi\)
\(752\) 1.55805 4.03867i 0.0568163 0.147275i
\(753\) 0 0
\(754\) 33.5057 27.8427i 1.22020 1.01397i
\(755\) 43.2978 + 17.9345i 1.57577 + 0.652704i
\(756\) 0 0
\(757\) 5.33084 + 12.8698i 0.193753 + 0.467760i 0.990662 0.136338i \(-0.0435334\pi\)
−0.796910 + 0.604098i \(0.793533\pi\)
\(758\) 42.4487 13.1612i 1.54181 0.478037i
\(759\) 0 0
\(760\) −36.0532 10.2169i −1.30779 0.370604i
\(761\) −11.8263 + 11.8263i −0.428704 + 0.428704i −0.888187 0.459483i \(-0.848035\pi\)
0.459483 + 0.888187i \(0.348035\pi\)
\(762\) 0 0
\(763\) 34.5205 14.2989i 1.24973 0.517653i
\(764\) −29.8126 5.55122i −1.07858 0.200836i
\(765\) 0 0
\(766\) 3.48632 + 0.321817i 0.125966 + 0.0116277i
\(767\) 67.2950 2.42988
\(768\) 0 0
\(769\) 39.2000 1.41359 0.706795 0.707419i \(-0.250140\pi\)
0.706795 + 0.707419i \(0.250140\pi\)
\(770\) −37.7843 3.48781i −1.36165 0.125692i
\(771\) 0 0
\(772\) −36.0895 6.72001i −1.29889 0.241858i
\(773\) −39.7946 + 16.4834i −1.43131 + 0.592868i −0.957675 0.287852i \(-0.907059\pi\)
−0.473636 + 0.880721i \(0.657059\pi\)
\(774\) 0 0
\(775\) −4.87693 + 4.87693i −0.175184 + 0.175184i
\(776\) 30.7583 + 8.71638i 1.10416 + 0.312900i
\(777\) 0 0
\(778\) −13.8859 + 4.30532i −0.497833 + 0.154353i
\(779\) −1.99321 4.81205i −0.0714143 0.172409i
\(780\) 0 0
\(781\) 8.56214 + 3.54655i 0.306377 + 0.126906i
\(782\) −12.4454 + 10.3420i −0.445048 + 0.369828i
\(783\) 0 0
\(784\) 1.55829 4.03928i 0.0556531 0.144260i
\(785\) 39.3887i 1.40584i
\(786\) 0 0
\(787\) 3.18736 + 1.32025i 0.113617 + 0.0470618i 0.438768 0.898600i \(-0.355415\pi\)
−0.325151 + 0.945662i \(0.605415\pi\)
\(788\) 14.0908 2.98279i 0.501964 0.106257i
\(789\) 0 0
\(790\) 12.5637 + 40.5217i 0.446998 + 1.44170i
\(791\) −27.8209 27.8209i −0.989197 0.989197i
\(792\) 0 0
\(793\) 33.0683 33.0683i 1.17429 1.17429i
\(794\) 18.7807 + 9.89101i 0.666501 + 0.351019i
\(795\) 0 0
\(796\) −1.98027 + 1.35857i −0.0701888 + 0.0481531i
\(797\) 9.15542 22.1031i 0.324302 0.782934i −0.674693 0.738099i \(-0.735724\pi\)
0.998994 0.0448349i \(-0.0142762\pi\)
\(798\) 0 0
\(799\) −4.50678 −0.159438
\(800\) −12.8812 + 4.34258i −0.455419 + 0.153533i
\(801\) 0 0
\(802\) −2.84827 + 30.8560i −0.100576 + 1.08956i
\(803\) 13.1543 31.7574i 0.464206 1.12069i
\(804\) 0 0
\(805\) 19.6352 8.13318i 0.692051 0.286657i
\(806\) −21.5890 11.3701i −0.760441 0.400493i
\(807\) 0 0
\(808\) 10.8368 1.26884i 0.381237 0.0446378i
\(809\) 1.21564 + 1.21564i 0.0427396 + 0.0427396i 0.728154 0.685414i \(-0.240379\pi\)
−0.685414 + 0.728154i \(0.740379\pi\)
\(810\) 0 0
\(811\) −6.74157 16.2756i −0.236728 0.571513i 0.760212 0.649675i \(-0.225095\pi\)
−0.996941 + 0.0781619i \(0.975095\pi\)
\(812\) −6.03408 28.5052i −0.211755 1.00034i
\(813\) 0 0
\(814\) −21.4145 25.7701i −0.750579 0.903241i
\(815\) 41.1830i 1.44258i
\(816\) 0 0
\(817\) 19.5665i 0.684544i
\(818\) −19.9976 + 16.6177i −0.699201 + 0.581026i
\(819\) 0 0
\(820\) −4.87907 3.17430i −0.170384 0.110852i
\(821\) −2.00047 4.82956i −0.0698169 0.168553i 0.885119 0.465364i \(-0.154077\pi\)
−0.954936 + 0.296811i \(0.904077\pi\)
\(822\) 0 0
\(823\) −13.5268 13.5268i −0.471516 0.471516i 0.430889 0.902405i \(-0.358200\pi\)
−0.902405 + 0.430889i \(0.858200\pi\)
\(824\) 6.78681 3.78963i 0.236430 0.132018i
\(825\) 0 0
\(826\) 20.9733 39.8233i 0.729755 1.38563i
\(827\) 22.3808 9.27041i 0.778255 0.322364i 0.0420440 0.999116i \(-0.486613\pi\)
0.736211 + 0.676752i \(0.236613\pi\)
\(828\) 0 0
\(829\) 1.75314 4.23245i 0.0608890 0.146999i −0.890507 0.454970i \(-0.849650\pi\)
0.951396 + 0.307971i \(0.0996500\pi\)
\(830\) −9.56006 0.882475i −0.331835 0.0306312i
\(831\) 0 0
\(832\) −28.1694 38.9770i −0.976597 1.35128i
\(833\) −4.50746 −0.156174
\(834\) 0 0
\(835\) −6.00234 + 14.4909i −0.207720 + 0.501479i
\(836\) −6.18372 + 33.2094i −0.213868 + 1.14857i
\(837\) 0 0
\(838\) −13.7454 + 26.0993i −0.474827 + 0.901584i
\(839\) 23.6794 23.6794i 0.817503 0.817503i −0.168242 0.985746i \(-0.553809\pi\)
0.985746 + 0.168242i \(0.0538091\pi\)
\(840\) 0 0
\(841\) 1.93775 + 1.93775i 0.0668190 + 0.0668190i
\(842\) 7.47822 2.31862i 0.257716 0.0799050i
\(843\) 0 0
\(844\) −13.4409 8.74463i −0.462656 0.301003i
\(845\) 58.1583 + 24.0900i 2.00071 + 0.828720i
\(846\) 0 0
\(847\) 2.93333i 0.100791i
\(848\) 0.743977 + 30.3501i 0.0255483 + 1.04223i
\(849\) 0 0
\(850\) 9.04507 + 10.8848i 0.310243 + 0.373344i
\(851\) 17.3385 + 7.18182i 0.594354 + 0.246190i
\(852\) 0 0
\(853\) 1.47996 + 3.57295i 0.0506730 + 0.122335i 0.947189 0.320676i \(-0.103910\pi\)
−0.896516 + 0.443011i \(0.853910\pi\)
\(854\) −9.26276 29.8751i −0.316965 1.02230i
\(855\) 0 0
\(856\) −4.60007 39.2877i −0.157227 1.34283i
\(857\) 1.99585 1.99585i 0.0681769 0.0681769i −0.672196 0.740373i \(-0.734649\pi\)
0.740373 + 0.672196i \(0.234649\pi\)
\(858\) 0 0
\(859\) 28.4574 11.7874i 0.970953 0.402182i 0.159886 0.987135i \(-0.448887\pi\)
0.811067 + 0.584954i \(0.198887\pi\)
\(860\) 12.3703 + 18.0311i 0.421822 + 0.614855i
\(861\) 0 0
\(862\) −0.676158 + 7.32498i −0.0230300 + 0.249490i
\(863\) 56.7230 1.93087 0.965436 0.260639i \(-0.0839333\pi\)
0.965436 + 0.260639i \(0.0839333\pi\)
\(864\) 0 0
\(865\) −12.6555 −0.430299
\(866\) −0.838365 + 9.08220i −0.0284888 + 0.308626i
\(867\) 0 0
\(868\) −13.4570 + 9.23216i −0.456759 + 0.313360i
\(869\) 35.3329 14.6354i 1.19859 0.496471i
\(870\) 0 0
\(871\) 43.1866 43.1866i 1.46332 1.46332i
\(872\) −29.1644 23.0507i −0.987630 0.780595i
\(873\) 0 0
\(874\) −5.60312 18.0717i −0.189529 0.611283i
\(875\) 7.68746 + 18.5592i 0.259883 + 0.627414i
\(876\) 0 0
\(877\) 35.4309 + 14.6760i 1.19642 + 0.495572i 0.889839 0.456274i \(-0.150816\pi\)
0.306577 + 0.951846i \(0.400816\pi\)
\(878\) 26.2627 + 31.6043i 0.886324 + 1.06659i
\(879\) 0 0
\(880\) 15.2971 + 34.5130i 0.515664 + 1.16343i
\(881\) 16.0453i 0.540579i −0.962779 0.270290i \(-0.912881\pi\)
0.962779 0.270290i \(-0.0871194\pi\)
\(882\) 0 0
\(883\) −3.76841 1.56093i −0.126817 0.0525294i 0.318373 0.947966i \(-0.396864\pi\)
−0.445190 + 0.895436i \(0.646864\pi\)
\(884\) −27.3041 + 41.9678i −0.918338 + 1.41153i
\(885\) 0 0
\(886\) −23.6106 + 7.32046i −0.793212 + 0.245936i
\(887\) −41.9135 41.9135i −1.40732 1.40732i −0.773396 0.633923i \(-0.781444\pi\)
−0.633923 0.773396i \(-0.718556\pi\)
\(888\) 0 0
\(889\) −11.0071 + 11.0071i −0.369165 + 0.369165i
\(890\) 19.4187 36.8715i 0.650918 1.23594i
\(891\) 0 0
\(892\) 0.370374 + 0.0689650i 0.0124010 + 0.00230912i
\(893\) 2.01657 4.86843i 0.0674819 0.162916i
\(894\) 0 0
\(895\) 0.805124 0.0269123
\(896\) −31.8448 + 4.52220i −1.06386 + 0.151076i
\(897\) 0 0
\(898\) −1.11857 0.103253i −0.0373270 0.00344560i
\(899\) −5.62845 + 13.5883i −0.187719 + 0.453195i
\(900\) 0 0
\(901\) 29.2016 12.0957i 0.972846 0.402966i
\(902\) −2.44511 + 4.64268i −0.0814133 + 0.154584i
\(903\) 0 0
\(904\) −10.6724 + 37.6607i −0.354959 + 1.25258i
\(905\) 20.1268 + 20.1268i 0.669037 + 0.669037i
\(906\) 0 0
\(907\) −8.10967 19.5785i −0.269277 0.650093i 0.730173 0.683263i \(-0.239440\pi\)
−0.999450 + 0.0331702i \(0.989440\pi\)
\(908\) 0.304278 0.467691i 0.0100978 0.0155209i
\(909\) 0 0
\(910\) 50.5764 42.0282i 1.67659 1.39322i
\(911\) 32.2546i 1.06864i −0.845282 0.534321i \(-0.820567\pi\)
0.845282 0.534321i \(-0.179433\pi\)
\(912\) 0 0
\(913\) 8.65464i 0.286427i
\(914\) −27.2004 32.7327i −0.899709 1.08270i
\(915\) 0 0
\(916\) 4.31374 0.913146i 0.142530 0.0301712i
\(917\) 22.8361 + 55.1312i 0.754114 + 1.82059i
\(918\) 0 0
\(919\) −31.0572 31.0572i −1.02448 1.02448i −0.999693 0.0247905i \(-0.992108\pi\)
−0.0247905 0.999693i \(-0.507892\pi\)
\(920\) −16.5887 13.1112i −0.546912 0.432264i
\(921\) 0 0
\(922\) −0.733754 0.386438i −0.0241649 0.0127267i
\(923\) −14.8384 + 6.14628i −0.488413 + 0.202307i
\(924\) 0 0
\(925\) 6.28122 15.1642i 0.206525 0.498596i
\(926\) 1.69464 18.3584i 0.0556892 0.603294i
\(927\) 0 0
\(928\) −21.8343 + 19.0676i −0.716745 + 0.625924i
\(929\) 32.4744 1.06545 0.532725 0.846288i \(-0.321168\pi\)
0.532725 + 0.846288i \(0.321168\pi\)
\(930\) 0 0
\(931\) 2.01687 4.86916i 0.0661004 0.159580i
\(932\) 6.92319 + 10.0914i 0.226777 + 0.330554i
\(933\) 0 0
\(934\) 49.0006 + 25.8066i 1.60335 + 0.844418i
\(935\) 27.7917 27.7917i 0.908884 0.908884i
\(936\) 0 0
\(937\) −29.6117 29.6117i −0.967373 0.967373i 0.0321113 0.999484i \(-0.489777\pi\)
−0.999484 + 0.0321113i \(0.989777\pi\)
\(938\) −12.0970 39.0163i −0.394981 1.27393i
\(939\) 0 0
\(940\) −1.21957 5.76132i −0.0397781 0.187913i
\(941\) −7.86542 3.25796i −0.256405 0.106207i 0.250778 0.968045i \(-0.419313\pi\)
−0.507184 + 0.861838i \(0.669313\pi\)
\(942\) 0 0
\(943\) 2.93896i 0.0957058i
\(944\) −44.7653 + 1.09734i −1.45699 + 0.0357153i
\(945\) 0 0
\(946\) 15.1605 12.5981i 0.492910 0.409600i
\(947\) −48.5504 20.1102i −1.57767 0.653494i −0.589631 0.807672i \(-0.700727\pi\)
−0.988043 + 0.154178i \(0.950727\pi\)
\(948\) 0 0
\(949\) 22.7968 + 55.0364i 0.740017 + 1.78656i
\(950\) −15.8055 + 4.90049i −0.512797 + 0.158993i
\(951\) 0 0
\(952\) 16.3257 + 29.2376i 0.529120 + 0.947597i
\(953\) 17.0094 17.0094i 0.550988 0.550988i −0.375738 0.926726i \(-0.622611\pi\)
0.926726 + 0.375738i \(0.122611\pi\)
\(954\) 0 0
\(955\) −38.1146 + 15.7876i −1.23336 + 0.510874i
\(956\) 3.02742 16.2586i 0.0979137 0.525842i
\(957\) 0 0
\(958\) 39.0045 + 3.60045i 1.26018 + 0.116325i
\(959\) 15.0354 0.485518
\(960\) 0 0
\(961\) −22.7622 −0.734265
\(962\) 57.8218 + 5.33745i 1.86425 + 0.172086i
\(963\) 0 0
\(964\) −8.32147 + 44.6902i −0.268017 + 1.43937i
\(965\) −46.1394 + 19.1116i −1.48528 + 0.615223i
\(966\) 0 0
\(967\) 28.7386 28.7386i 0.924170 0.924170i −0.0731512 0.997321i \(-0.523306\pi\)
0.997321 + 0.0731512i \(0.0233056\pi\)
\(968\) 2.54804 1.42277i 0.0818970 0.0457297i
\(969\) 0 0
\(970\) 41.5412 12.8798i 1.33381 0.413547i
\(971\) 12.3179 + 29.7379i 0.395299 + 0.954336i 0.988765 + 0.149477i \(0.0477591\pi\)
−0.593466 + 0.804859i \(0.702241\pi\)
\(972\) 0 0
\(973\) −27.8622 11.5409i −0.893222 0.369985i
\(974\) −35.1726 + 29.2279i −1.12700 + 0.936522i
\(975\) 0 0
\(976\) −21.4581 + 22.5366i −0.686858 + 0.721378i
\(977\) 13.3790i 0.428032i 0.976830 + 0.214016i \(0.0686545\pi\)
−0.976830 + 0.214016i \(0.931345\pi\)
\(978\) 0 0
\(979\) −34.7065 14.3759i −1.10922 0.459456i
\(980\) −1.21976 5.76219i −0.0389637 0.184066i
\(981\) 0 0
\(982\) −11.1202 35.8657i −0.354859 1.14452i
\(983\) 13.7710 + 13.7710i 0.439227 + 0.439227i 0.891752 0.452525i \(-0.149477\pi\)
−0.452525 + 0.891752i \(0.649477\pi\)
\(984\) 0 0
\(985\) 13.8552 13.8552i 0.441464 0.441464i
\(986\) 26.7030 + 14.0634i 0.850398 + 0.447870i
\(987\) 0 0
\(988\) −33.1183 48.2738i −1.05363 1.53579i
\(989\) −4.22505 + 10.2002i −0.134349 + 0.324347i
\(990\) 0 0
\(991\) 8.30842 0.263926 0.131963 0.991255i \(-0.457872\pi\)
0.131963 + 0.991255i \(0.457872\pi\)
\(992\) 14.5466 + 7.21143i 0.461856 + 0.228963i
\(993\) 0 0
\(994\) −0.987382 + 10.6965i −0.0313179 + 0.339274i
\(995\) −1.25025 + 3.01836i −0.0396355 + 0.0956885i
\(996\) 0 0
\(997\) −25.3066 + 10.4823i −0.801468 + 0.331979i −0.745544 0.666456i \(-0.767810\pi\)
−0.0559236 + 0.998435i \(0.517810\pi\)
\(998\) 15.7291 + 8.28386i 0.497895 + 0.262221i
\(999\) 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 288.2.v.d.109.1 32
3.2 odd 2 96.2.n.a.13.8 32
4.3 odd 2 1152.2.v.c.145.7 32
12.11 even 2 384.2.n.a.145.6 32
24.5 odd 2 768.2.n.a.289.7 32
24.11 even 2 768.2.n.b.289.3 32
32.5 even 8 inner 288.2.v.d.37.1 32
32.27 odd 8 1152.2.v.c.1009.7 32
96.5 odd 8 96.2.n.a.37.8 yes 32
96.11 even 8 768.2.n.b.481.3 32
96.53 odd 8 768.2.n.a.481.7 32
96.59 even 8 384.2.n.a.241.6 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.2.n.a.13.8 32 3.2 odd 2
96.2.n.a.37.8 yes 32 96.5 odd 8
288.2.v.d.37.1 32 32.5 even 8 inner
288.2.v.d.109.1 32 1.1 even 1 trivial
384.2.n.a.145.6 32 12.11 even 2
384.2.n.a.241.6 32 96.59 even 8
768.2.n.a.289.7 32 24.5 odd 2
768.2.n.a.481.7 32 96.53 odd 8
768.2.n.b.289.3 32 24.11 even 2
768.2.n.b.481.3 32 96.11 even 8
1152.2.v.c.145.7 32 4.3 odd 2
1152.2.v.c.1009.7 32 32.27 odd 8