Properties

Label 315.2.bz.d.82.8
Level $315$
Weight $2$
Character 315.82
Analytic conductor $2.515$
Analytic rank $0$
Dimension $32$
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] = [315,2,Mod(73,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.73");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bz (of order \(12\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 82.8
Character \(\chi\) \(=\) 315.82
Dual form 315.2.bz.d.73.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.42777 - 0.650518i) q^{2} +(3.73883 - 2.15861i) q^{4} +(-0.780598 + 2.09539i) q^{5} +(1.61838 + 2.09305i) q^{7} +(4.11829 - 4.11829i) q^{8} +O(q^{10})\) \(q+(2.42777 - 0.650518i) q^{2} +(3.73883 - 2.15861i) q^{4} +(-0.780598 + 2.09539i) q^{5} +(1.61838 + 2.09305i) q^{7} +(4.11829 - 4.11829i) q^{8} +(-0.532020 + 5.59492i) q^{10} +(-2.73807 - 4.74248i) q^{11} +(-0.579674 - 0.579674i) q^{13} +(5.29062 + 4.02864i) q^{14} +(3.00199 - 5.19961i) q^{16} +(-4.58934 - 1.22971i) q^{17} +(0.220281 - 0.381538i) q^{19} +(1.60462 + 9.51932i) q^{20} +(-9.73248 - 9.73248i) q^{22} +(0.457316 + 1.70673i) q^{23} +(-3.78133 - 3.27132i) q^{25} +(-1.78440 - 1.03022i) q^{26} +(10.5689 + 4.33208i) q^{28} -0.853158i q^{29} +(2.32463 - 1.34213i) q^{31} +(0.890908 - 3.32491i) q^{32} -11.9418 q^{34} +(-5.64906 + 1.75732i) q^{35} +(-0.249579 + 0.0668745i) q^{37} +(0.286594 - 1.06958i) q^{38} +(5.41470 + 11.8442i) q^{40} -0.321873i q^{41} +(-0.631635 + 0.631635i) q^{43} +(-20.4744 - 11.8209i) q^{44} +(2.22051 + 3.84604i) q^{46} +(2.12084 + 7.91508i) q^{47} +(-1.76168 + 6.77469i) q^{49} +(-11.3082 - 5.48217i) q^{50} +(-3.41859 - 0.916009i) q^{52} +(11.0558 + 2.96239i) q^{53} +(12.0747 - 2.03536i) q^{55} +(15.2847 + 1.95480i) q^{56} +(-0.554995 - 2.07127i) q^{58} +(2.89024 + 5.00605i) q^{59} +(-5.73145 - 3.30905i) q^{61} +(4.77058 - 4.77058i) q^{62} +3.35631i q^{64} +(1.66714 - 0.762151i) q^{65} +(-1.38480 + 5.16814i) q^{67} +(-19.8132 + 5.30893i) q^{68} +(-12.5714 + 7.94117i) q^{70} +8.79651 q^{71} +(2.28786 - 8.53843i) q^{73} +(-0.562417 + 0.324712i) q^{74} -1.90201i q^{76} +(5.49499 - 13.4061i) q^{77} +(-9.02098 - 5.20826i) q^{79} +(8.55186 + 10.3492i) q^{80} +(-0.209384 - 0.781433i) q^{82} +(-8.47550 - 8.47550i) q^{83} +(6.15915 - 8.65655i) q^{85} +(-1.12257 + 1.94435i) q^{86} +(-30.8071 - 8.25473i) q^{88} +(-4.03993 + 6.99736i) q^{89} +(0.275150 - 2.15142i) q^{91} +(5.39399 + 5.39399i) q^{92} +(10.2978 + 17.8363i) q^{94} +(0.627520 + 0.759403i) q^{95} +(5.99549 - 5.99549i) q^{97} +(0.130108 + 17.5934i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8} - 12 q^{10} + 8 q^{11} - 8 q^{22} + 8 q^{23} + 12 q^{25} - 24 q^{26} - 24 q^{28} + 24 q^{31} - 24 q^{32} - 44 q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 40 q^{43} - 40 q^{46} + 60 q^{47} - 72 q^{50} - 108 q^{52} + 24 q^{53} + 48 q^{56} + 4 q^{58} - 24 q^{61} + 4 q^{65} + 8 q^{67} - 132 q^{68} + 4 q^{70} + 16 q^{71} + 36 q^{73} - 60 q^{77} + 12 q^{80} + 12 q^{82} - 72 q^{85} + 16 q^{86} - 32 q^{88} - 24 q^{91} + 56 q^{92} + 12 q^{95} + 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.42777 0.650518i 1.71669 0.459986i 0.739642 0.673001i \(-0.234995\pi\)
0.977049 + 0.213015i \(0.0683284\pi\)
\(3\) 0 0
\(4\) 3.73883 2.15861i 1.86941 1.07931i
\(5\) −0.780598 + 2.09539i −0.349094 + 0.937088i
\(6\) 0 0
\(7\) 1.61838 + 2.09305i 0.611691 + 0.791097i
\(8\) 4.11829 4.11829i 1.45603 1.45603i
\(9\) 0 0
\(10\) −0.532020 + 5.59492i −0.168240 + 1.76927i
\(11\) −2.73807 4.74248i −0.825561 1.42991i −0.901490 0.432800i \(-0.857526\pi\)
0.0759295 0.997113i \(-0.475808\pi\)
\(12\) 0 0
\(13\) −0.579674 0.579674i −0.160773 0.160773i 0.622136 0.782909i \(-0.286265\pi\)
−0.782909 + 0.622136i \(0.786265\pi\)
\(14\) 5.29062 + 4.02864i 1.41398 + 1.07670i
\(15\) 0 0
\(16\) 3.00199 5.19961i 0.750498 1.29990i
\(17\) −4.58934 1.22971i −1.11308 0.298248i −0.344999 0.938603i \(-0.612121\pi\)
−0.768079 + 0.640355i \(0.778787\pi\)
\(18\) 0 0
\(19\) 0.220281 0.381538i 0.0505359 0.0875308i −0.839651 0.543127i \(-0.817240\pi\)
0.890187 + 0.455596i \(0.150574\pi\)
\(20\) 1.60462 + 9.51932i 0.358803 + 2.12858i
\(21\) 0 0
\(22\) −9.73248 9.73248i −2.07497 2.07497i
\(23\) 0.457316 + 1.70673i 0.0953570 + 0.355877i 0.997073 0.0764510i \(-0.0243589\pi\)
−0.901716 + 0.432328i \(0.857692\pi\)
\(24\) 0 0
\(25\) −3.78133 3.27132i −0.756267 0.654264i
\(26\) −1.78440 1.03022i −0.349950 0.202044i
\(27\) 0 0
\(28\) 10.5689 + 4.33208i 1.99734 + 0.818686i
\(29\) 0.853158i 0.158427i −0.996858 0.0792137i \(-0.974759\pi\)
0.996858 0.0792137i \(-0.0252410\pi\)
\(30\) 0 0
\(31\) 2.32463 1.34213i 0.417516 0.241053i −0.276498 0.961014i \(-0.589174\pi\)
0.694014 + 0.719962i \(0.255841\pi\)
\(32\) 0.890908 3.32491i 0.157492 0.587767i
\(33\) 0 0
\(34\) −11.9418 −2.04800
\(35\) −5.64906 + 1.75732i −0.954865 + 0.297041i
\(36\) 0 0
\(37\) −0.249579 + 0.0668745i −0.0410306 + 0.0109941i −0.279276 0.960211i \(-0.590094\pi\)
0.238245 + 0.971205i \(0.423428\pi\)
\(38\) 0.286594 1.06958i 0.0464916 0.173509i
\(39\) 0 0
\(40\) 5.41470 + 11.8442i 0.856139 + 1.87272i
\(41\) 0.321873i 0.0502681i −0.999684 0.0251341i \(-0.991999\pi\)
0.999684 0.0251341i \(-0.00800127\pi\)
\(42\) 0 0
\(43\) −0.631635 + 0.631635i −0.0963234 + 0.0963234i −0.753626 0.657303i \(-0.771697\pi\)
0.657303 + 0.753626i \(0.271697\pi\)
\(44\) −20.4744 11.8209i −3.08663 1.78207i
\(45\) 0 0
\(46\) 2.22051 + 3.84604i 0.327397 + 0.567068i
\(47\) 2.12084 + 7.91508i 0.309356 + 1.15453i 0.929130 + 0.369752i \(0.120557\pi\)
−0.619774 + 0.784780i \(0.712776\pi\)
\(48\) 0 0
\(49\) −1.76168 + 6.77469i −0.251669 + 0.967813i
\(50\) −11.3082 5.48217i −1.59923 0.775296i
\(51\) 0 0
\(52\) −3.41859 0.916009i −0.474073 0.127028i
\(53\) 11.0558 + 2.96239i 1.51863 + 0.406916i 0.919291 0.393579i \(-0.128763\pi\)
0.599340 + 0.800494i \(0.295430\pi\)
\(54\) 0 0
\(55\) 12.0747 2.03536i 1.62815 0.274448i
\(56\) 15.2847 + 1.95480i 2.04251 + 0.261222i
\(57\) 0 0
\(58\) −0.554995 2.07127i −0.0728744 0.271971i
\(59\) 2.89024 + 5.00605i 0.376278 + 0.651732i 0.990517 0.137387i \(-0.0438705\pi\)
−0.614240 + 0.789119i \(0.710537\pi\)
\(60\) 0 0
\(61\) −5.73145 3.30905i −0.733837 0.423681i 0.0859874 0.996296i \(-0.472596\pi\)
−0.819824 + 0.572615i \(0.805929\pi\)
\(62\) 4.77058 4.77058i 0.605864 0.605864i
\(63\) 0 0
\(64\) 3.35631i 0.419539i
\(65\) 1.66714 0.762151i 0.206783 0.0945332i
\(66\) 0 0
\(67\) −1.38480 + 5.16814i −0.169180 + 0.631389i 0.828290 + 0.560300i \(0.189314\pi\)
−0.997470 + 0.0710893i \(0.977352\pi\)
\(68\) −19.8132 + 5.30893i −2.40270 + 0.643803i
\(69\) 0 0
\(70\) −12.5714 + 7.94117i −1.50257 + 0.949151i
\(71\) 8.79651 1.04395 0.521977 0.852960i \(-0.325195\pi\)
0.521977 + 0.852960i \(0.325195\pi\)
\(72\) 0 0
\(73\) 2.28786 8.53843i 0.267774 0.999347i −0.692756 0.721172i \(-0.743604\pi\)
0.960530 0.278175i \(-0.0897296\pi\)
\(74\) −0.562417 + 0.324712i −0.0653796 + 0.0377470i
\(75\) 0 0
\(76\) 1.90201i 0.218175i
\(77\) 5.49499 13.4061i 0.626212 1.52776i
\(78\) 0 0
\(79\) −9.02098 5.20826i −1.01494 0.585975i −0.102305 0.994753i \(-0.532622\pi\)
−0.912634 + 0.408778i \(0.865955\pi\)
\(80\) 8.55186 + 10.3492i 0.956127 + 1.15707i
\(81\) 0 0
\(82\) −0.209384 0.781433i −0.0231226 0.0862948i
\(83\) −8.47550 8.47550i −0.930306 0.930306i 0.0674183 0.997725i \(-0.478524\pi\)
−0.997725 + 0.0674183i \(0.978524\pi\)
\(84\) 0 0
\(85\) 6.15915 8.65655i 0.668054 0.938935i
\(86\) −1.12257 + 1.94435i −0.121050 + 0.209665i
\(87\) 0 0
\(88\) −30.8071 8.25473i −3.28405 0.879958i
\(89\) −4.03993 + 6.99736i −0.428231 + 0.741718i −0.996716 0.0809755i \(-0.974196\pi\)
0.568485 + 0.822694i \(0.307530\pi\)
\(90\) 0 0
\(91\) 0.275150 2.15142i 0.0288436 0.225530i
\(92\) 5.39399 + 5.39399i 0.562362 + 0.562362i
\(93\) 0 0
\(94\) 10.2978 + 17.8363i 1.06214 + 1.83968i
\(95\) 0.627520 + 0.759403i 0.0643822 + 0.0779131i
\(96\) 0 0
\(97\) 5.99549 5.99549i 0.608750 0.608750i −0.333870 0.942619i \(-0.608355\pi\)
0.942619 + 0.333870i \(0.108355\pi\)
\(98\) 0.130108 + 17.5934i 0.0131429 + 1.77720i
\(99\) 0 0
\(100\) −21.1993 4.06846i −2.11993 0.406846i
\(101\) −3.14474 + 1.81562i −0.312914 + 0.180661i −0.648230 0.761445i \(-0.724490\pi\)
0.335316 + 0.942106i \(0.391157\pi\)
\(102\) 0 0
\(103\) 6.93466 1.85814i 0.683293 0.183088i 0.0995575 0.995032i \(-0.468257\pi\)
0.583735 + 0.811944i \(0.301591\pi\)
\(104\) −4.77452 −0.468181
\(105\) 0 0
\(106\) 28.7680 2.79420
\(107\) 0.0729848 0.0195562i 0.00705571 0.00189057i −0.255289 0.966865i \(-0.582171\pi\)
0.262345 + 0.964974i \(0.415504\pi\)
\(108\) 0 0
\(109\) 3.11046 1.79583i 0.297928 0.172009i −0.343584 0.939122i \(-0.611641\pi\)
0.641512 + 0.767113i \(0.278308\pi\)
\(110\) 27.9905 12.7962i 2.66879 1.22007i
\(111\) 0 0
\(112\) 15.7414 2.13164i 1.48742 0.201421i
\(113\) 12.9081 12.9081i 1.21429 1.21429i 0.244694 0.969600i \(-0.421313\pi\)
0.969600 0.244694i \(-0.0786874\pi\)
\(114\) 0 0
\(115\) −3.93324 0.374012i −0.366777 0.0348768i
\(116\) −1.84164 3.18981i −0.170992 0.296166i
\(117\) 0 0
\(118\) 10.2734 + 10.2734i 0.945740 + 0.945740i
\(119\) −4.85346 11.5958i −0.444916 1.06299i
\(120\) 0 0
\(121\) −9.49411 + 16.4443i −0.863101 + 1.49493i
\(122\) −16.0672 4.30520i −1.45466 0.389774i
\(123\) 0 0
\(124\) 5.79426 10.0360i 0.520340 0.901255i
\(125\) 9.80639 5.36979i 0.877111 0.480288i
\(126\) 0 0
\(127\) 13.5294 + 13.5294i 1.20054 + 1.20054i 0.974002 + 0.226539i \(0.0727409\pi\)
0.226539 + 0.974002i \(0.427259\pi\)
\(128\) 3.96516 + 14.7982i 0.350474 + 1.30799i
\(129\) 0 0
\(130\) 3.55162 2.93483i 0.311498 0.257401i
\(131\) −3.87030 2.23452i −0.338149 0.195231i 0.321304 0.946976i \(-0.395879\pi\)
−0.659453 + 0.751745i \(0.729212\pi\)
\(132\) 0 0
\(133\) 1.15507 0.156416i 0.100158 0.0135630i
\(134\) 13.4479i 1.16172i
\(135\) 0 0
\(136\) −23.9645 + 13.8359i −2.05494 + 1.18642i
\(137\) −2.35642 + 8.79428i −0.201323 + 0.751346i 0.789217 + 0.614115i \(0.210487\pi\)
−0.990539 + 0.137231i \(0.956180\pi\)
\(138\) 0 0
\(139\) −11.6277 −0.986251 −0.493126 0.869958i \(-0.664146\pi\)
−0.493126 + 0.869958i \(0.664146\pi\)
\(140\) −17.3275 + 18.7644i −1.46444 + 1.58588i
\(141\) 0 0
\(142\) 21.3559 5.72229i 1.79215 0.480204i
\(143\) −1.16190 + 4.33628i −0.0971632 + 0.362618i
\(144\) 0 0
\(145\) 1.78770 + 0.665974i 0.148460 + 0.0553061i
\(146\) 22.2176i 1.83874i
\(147\) 0 0
\(148\) −0.788777 + 0.788777i −0.0648371 + 0.0648371i
\(149\) −9.66241 5.57860i −0.791576 0.457016i 0.0489412 0.998802i \(-0.484415\pi\)
−0.840517 + 0.541785i \(0.817749\pi\)
\(150\) 0 0
\(151\) −0.805981 1.39600i −0.0655898 0.113605i 0.831366 0.555726i \(-0.187560\pi\)
−0.896955 + 0.442121i \(0.854226\pi\)
\(152\) −0.664102 2.47846i −0.0538658 0.201030i
\(153\) 0 0
\(154\) 4.61966 36.1214i 0.372263 2.91074i
\(155\) 0.997677 + 5.91867i 0.0801353 + 0.475399i
\(156\) 0 0
\(157\) −17.2198 4.61403i −1.37429 0.368240i −0.505247 0.862975i \(-0.668598\pi\)
−0.869044 + 0.494735i \(0.835265\pi\)
\(158\) −25.2889 6.77614i −2.01188 0.539081i
\(159\) 0 0
\(160\) 6.27155 + 4.46222i 0.495810 + 0.352770i
\(161\) −2.83215 + 3.71932i −0.223204 + 0.293123i
\(162\) 0 0
\(163\) 2.15462 + 8.04115i 0.168763 + 0.629832i 0.997530 + 0.0702383i \(0.0223760\pi\)
−0.828767 + 0.559593i \(0.810957\pi\)
\(164\) −0.694800 1.20343i −0.0542547 0.0939719i
\(165\) 0 0
\(166\) −26.0900 15.0631i −2.02498 1.16912i
\(167\) −5.39262 + 5.39262i −0.417293 + 0.417293i −0.884270 0.466976i \(-0.845343\pi\)
0.466976 + 0.884270i \(0.345343\pi\)
\(168\) 0 0
\(169\) 12.3280i 0.948304i
\(170\) 9.32174 25.0227i 0.714945 1.91916i
\(171\) 0 0
\(172\) −0.998119 + 3.72503i −0.0761058 + 0.284031i
\(173\) 17.0601 4.57123i 1.29705 0.347544i 0.456717 0.889612i \(-0.349025\pi\)
0.840335 + 0.542068i \(0.182358\pi\)
\(174\) 0 0
\(175\) 0.727380 13.2087i 0.0549847 0.998487i
\(176\) −32.8787 −2.47833
\(177\) 0 0
\(178\) −5.25609 + 19.6160i −0.393961 + 1.47028i
\(179\) 13.3814 7.72574i 1.00017 0.577449i 0.0918716 0.995771i \(-0.470715\pi\)
0.908299 + 0.418322i \(0.137382\pi\)
\(180\) 0 0
\(181\) 26.5272i 1.97175i −0.167472 0.985877i \(-0.553560\pi\)
0.167472 0.985877i \(-0.446440\pi\)
\(182\) −0.731535 5.40213i −0.0542249 0.400432i
\(183\) 0 0
\(184\) 8.91215 + 5.14543i 0.657012 + 0.379326i
\(185\) 0.0546927 0.575168i 0.00402109 0.0422872i
\(186\) 0 0
\(187\) 6.73407 + 25.1319i 0.492444 + 1.83783i
\(188\) 25.0150 + 25.0150i 1.82441 + 1.82441i
\(189\) 0 0
\(190\) 2.01748 + 1.43544i 0.146363 + 0.104138i
\(191\) −13.2282 + 22.9120i −0.957162 + 1.65785i −0.227822 + 0.973703i \(0.573160\pi\)
−0.729341 + 0.684151i \(0.760173\pi\)
\(192\) 0 0
\(193\) 16.2103 + 4.34354i 1.16684 + 0.312655i 0.789696 0.613499i \(-0.210238\pi\)
0.377147 + 0.926153i \(0.376905\pi\)
\(194\) 10.6555 18.4558i 0.765018 1.32505i
\(195\) 0 0
\(196\) 8.03732 + 29.1322i 0.574094 + 2.08087i
\(197\) −0.418962 0.418962i −0.0298498 0.0298498i 0.692024 0.721874i \(-0.256719\pi\)
−0.721874 + 0.692024i \(0.756719\pi\)
\(198\) 0 0
\(199\) 12.2189 + 21.1637i 0.866172 + 1.50025i 0.865878 + 0.500255i \(0.166760\pi\)
0.000294114 1.00000i \(0.499906\pi\)
\(200\) −29.0448 + 2.10039i −2.05378 + 0.148520i
\(201\) 0 0
\(202\) −6.45361 + 6.45361i −0.454074 + 0.454074i
\(203\) 1.78570 1.38074i 0.125332 0.0969086i
\(204\) 0 0
\(205\) 0.674450 + 0.251254i 0.0471057 + 0.0175483i
\(206\) 15.6270 9.02225i 1.08878 0.628610i
\(207\) 0 0
\(208\) −4.75425 + 1.27390i −0.329648 + 0.0883289i
\(209\) −2.41258 −0.166882
\(210\) 0 0
\(211\) −24.7766 −1.70569 −0.852846 0.522162i \(-0.825126\pi\)
−0.852846 + 0.522162i \(0.825126\pi\)
\(212\) 47.7304 12.7893i 3.27814 0.878374i
\(213\) 0 0
\(214\) 0.164469 0.0949559i 0.0112428 0.00649105i
\(215\) −0.830470 1.81658i −0.0566376 0.123889i
\(216\) 0 0
\(217\) 6.57127 + 2.69349i 0.446087 + 0.182846i
\(218\) 6.38326 6.38326i 0.432329 0.432329i
\(219\) 0 0
\(220\) 40.7517 33.6745i 2.74748 2.27033i
\(221\) 1.94749 + 3.37315i 0.131002 + 0.226902i
\(222\) 0 0
\(223\) 8.57407 + 8.57407i 0.574163 + 0.574163i 0.933289 0.359126i \(-0.116925\pi\)
−0.359126 + 0.933289i \(0.616925\pi\)
\(224\) 8.40102 3.51627i 0.561317 0.234940i
\(225\) 0 0
\(226\) 22.9409 39.7349i 1.52601 2.64313i
\(227\) 20.7203 + 5.55199i 1.37525 + 0.368498i 0.869395 0.494117i \(-0.164509\pi\)
0.505860 + 0.862616i \(0.331175\pi\)
\(228\) 0 0
\(229\) 2.85867 4.95136i 0.188906 0.327195i −0.755980 0.654595i \(-0.772839\pi\)
0.944886 + 0.327400i \(0.106173\pi\)
\(230\) −9.79230 + 1.65063i −0.645685 + 0.108839i
\(231\) 0 0
\(232\) −3.51355 3.51355i −0.230676 0.230676i
\(233\) 0.116310 + 0.434077i 0.00761975 + 0.0284373i 0.969631 0.244572i \(-0.0786476\pi\)
−0.962011 + 0.273010i \(0.911981\pi\)
\(234\) 0 0
\(235\) −18.2407 1.73451i −1.18989 0.113147i
\(236\) 21.6122 + 12.4778i 1.40684 + 0.812238i
\(237\) 0 0
\(238\) −19.3264 24.9947i −1.25274 1.62017i
\(239\) 12.3067i 0.796054i 0.917374 + 0.398027i \(0.130305\pi\)
−0.917374 + 0.398027i \(0.869695\pi\)
\(240\) 0 0
\(241\) −2.77345 + 1.60125i −0.178654 + 0.103146i −0.586660 0.809833i \(-0.699557\pi\)
0.408006 + 0.912979i \(0.366224\pi\)
\(242\) −12.3522 + 46.0990i −0.794028 + 2.96335i
\(243\) 0 0
\(244\) −28.5719 −1.82913
\(245\) −12.8205 8.97973i −0.819070 0.573694i
\(246\) 0 0
\(247\) −0.348858 + 0.0934763i −0.0221973 + 0.00594776i
\(248\) 4.04623 15.1007i 0.256936 0.958898i
\(249\) 0 0
\(250\) 20.3145 19.4158i 1.28480 1.22797i
\(251\) 16.6060i 1.04816i −0.851669 0.524081i \(-0.824409\pi\)
0.851669 0.524081i \(-0.175591\pi\)
\(252\) 0 0
\(253\) 6.84196 6.84196i 0.430150 0.430150i
\(254\) 41.6474 + 24.0451i 2.61319 + 1.50873i
\(255\) 0 0
\(256\) 15.8966 + 27.5338i 0.993540 + 1.72086i
\(257\) −0.847796 3.16402i −0.0528841 0.197366i 0.934430 0.356148i \(-0.115910\pi\)
−0.987314 + 0.158782i \(0.949243\pi\)
\(258\) 0 0
\(259\) −0.543886 0.414152i −0.0337954 0.0257342i
\(260\) 4.58794 6.44825i 0.284532 0.399904i
\(261\) 0 0
\(262\) −10.8498 2.90719i −0.670301 0.179607i
\(263\) −15.0506 4.03280i −0.928061 0.248673i −0.237033 0.971502i \(-0.576175\pi\)
−0.691027 + 0.722828i \(0.742842\pi\)
\(264\) 0 0
\(265\) −14.8375 + 20.8538i −0.911461 + 1.28104i
\(266\) 2.70250 1.13114i 0.165701 0.0693545i
\(267\) 0 0
\(268\) 5.97850 + 22.3120i 0.365195 + 1.36293i
\(269\) −4.28256 7.41761i −0.261112 0.452260i 0.705426 0.708784i \(-0.250756\pi\)
−0.966538 + 0.256524i \(0.917423\pi\)
\(270\) 0 0
\(271\) 4.65260 + 2.68618i 0.282625 + 0.163174i 0.634611 0.772832i \(-0.281160\pi\)
−0.351986 + 0.936005i \(0.614494\pi\)
\(272\) −20.1712 + 20.1712i −1.22306 + 1.22306i
\(273\) 0 0
\(274\) 22.8834i 1.38243i
\(275\) −5.16060 + 26.8900i −0.311196 + 1.62153i
\(276\) 0 0
\(277\) 3.28630 12.2646i 0.197454 0.736910i −0.794163 0.607704i \(-0.792091\pi\)
0.991618 0.129206i \(-0.0412427\pi\)
\(278\) −28.2294 + 7.56405i −1.69309 + 0.453662i
\(279\) 0 0
\(280\) −16.0273 + 30.5016i −0.957815 + 1.82282i
\(281\) −17.7795 −1.06064 −0.530318 0.847799i \(-0.677927\pi\)
−0.530318 + 0.847799i \(0.677927\pi\)
\(282\) 0 0
\(283\) 0.560813 2.09298i 0.0333369 0.124415i −0.947252 0.320489i \(-0.896153\pi\)
0.980589 + 0.196074i \(0.0628194\pi\)
\(284\) 32.8886 18.9883i 1.95158 1.12675i
\(285\) 0 0
\(286\) 11.2833i 0.667197i
\(287\) 0.673695 0.520914i 0.0397670 0.0307486i
\(288\) 0 0
\(289\) 4.82740 + 2.78710i 0.283964 + 0.163947i
\(290\) 4.77335 + 0.453897i 0.280301 + 0.0266538i
\(291\) 0 0
\(292\) −9.87723 36.8623i −0.578021 2.15720i
\(293\) −7.48653 7.48653i −0.437368 0.437368i 0.453758 0.891125i \(-0.350083\pi\)
−0.891125 + 0.453758i \(0.850083\pi\)
\(294\) 0 0
\(295\) −12.7458 + 2.14848i −0.742086 + 0.125089i
\(296\) −0.752430 + 1.30325i −0.0437341 + 0.0757497i
\(297\) 0 0
\(298\) −27.0871 7.25796i −1.56911 0.420442i
\(299\) 0.724251 1.25444i 0.0418845 0.0725461i
\(300\) 0 0
\(301\) −2.34427 0.299815i −0.135121 0.0172810i
\(302\) −2.86486 2.86486i −0.164854 0.164854i
\(303\) 0 0
\(304\) −1.32256 2.29075i −0.0758543 0.131383i
\(305\) 11.4077 9.42659i 0.653204 0.539765i
\(306\) 0 0
\(307\) −9.79503 + 9.79503i −0.559032 + 0.559032i −0.929032 0.370000i \(-0.879358\pi\)
0.370000 + 0.929032i \(0.379358\pi\)
\(308\) −8.39370 61.9845i −0.478275 3.53190i
\(309\) 0 0
\(310\) 6.27233 + 13.7201i 0.356244 + 0.779252i
\(311\) −13.4581 + 7.77005i −0.763140 + 0.440599i −0.830422 0.557135i \(-0.811901\pi\)
0.0672821 + 0.997734i \(0.478567\pi\)
\(312\) 0 0
\(313\) 1.29178 0.346130i 0.0730155 0.0195644i −0.222126 0.975018i \(-0.571300\pi\)
0.295142 + 0.955453i \(0.404633\pi\)
\(314\) −44.8072 −2.52862
\(315\) 0 0
\(316\) −44.9705 −2.52979
\(317\) −6.72418 + 1.80174i −0.377668 + 0.101196i −0.442659 0.896690i \(-0.645965\pi\)
0.0649912 + 0.997886i \(0.479298\pi\)
\(318\) 0 0
\(319\) −4.04609 + 2.33601i −0.226538 + 0.130791i
\(320\) −7.03278 2.61993i −0.393145 0.146458i
\(321\) 0 0
\(322\) −4.45631 + 10.8720i −0.248340 + 0.605873i
\(323\) −1.48012 + 1.48012i −0.0823563 + 0.0823563i
\(324\) 0 0
\(325\) 0.295642 + 4.08824i 0.0163993 + 0.226775i
\(326\) 10.4618 + 18.1204i 0.579427 + 1.00360i
\(327\) 0 0
\(328\) −1.32557 1.32557i −0.0731921 0.0731921i
\(329\) −13.1343 + 17.2486i −0.724117 + 0.950947i
\(330\) 0 0
\(331\) −3.07120 + 5.31947i −0.168808 + 0.292385i −0.938001 0.346632i \(-0.887325\pi\)
0.769193 + 0.639017i \(0.220659\pi\)
\(332\) −49.9837 13.3931i −2.74321 0.735042i
\(333\) 0 0
\(334\) −9.58402 + 16.6000i −0.524414 + 0.908312i
\(335\) −9.74831 6.93594i −0.532607 0.378951i
\(336\) 0 0
\(337\) −1.65542 1.65542i −0.0901764 0.0901764i 0.660580 0.750756i \(-0.270311\pi\)
−0.750756 + 0.660580i \(0.770311\pi\)
\(338\) −8.01956 29.9294i −0.436207 1.62795i
\(339\) 0 0
\(340\) 4.34186 45.6606i 0.235470 2.47629i
\(341\) −12.7300 7.34968i −0.689369 0.398007i
\(342\) 0 0
\(343\) −17.0308 + 7.27676i −0.919578 + 0.392908i
\(344\) 5.20251i 0.280500i
\(345\) 0 0
\(346\) 38.4442 22.1957i 2.06677 1.19325i
\(347\) 2.27272 8.48192i 0.122006 0.455334i −0.877709 0.479194i \(-0.840929\pi\)
0.999715 + 0.0238604i \(0.00759572\pi\)
\(348\) 0 0
\(349\) 14.1406 0.756927 0.378463 0.925616i \(-0.376453\pi\)
0.378463 + 0.925616i \(0.376453\pi\)
\(350\) −6.82662 32.5409i −0.364898 1.73939i
\(351\) 0 0
\(352\) −18.2077 + 4.87874i −0.970475 + 0.260038i
\(353\) −6.58802 + 24.5868i −0.350645 + 1.30862i 0.535233 + 0.844705i \(0.320224\pi\)
−0.885877 + 0.463919i \(0.846443\pi\)
\(354\) 0 0
\(355\) −6.86654 + 18.4321i −0.364438 + 0.978276i
\(356\) 34.8825i 1.84877i
\(357\) 0 0
\(358\) 27.4611 27.4611i 1.45136 1.45136i
\(359\) −7.57485 4.37334i −0.399785 0.230816i 0.286606 0.958049i \(-0.407473\pi\)
−0.686391 + 0.727232i \(0.740806\pi\)
\(360\) 0 0
\(361\) 9.40295 + 16.2864i 0.494892 + 0.857179i
\(362\) −17.2564 64.4019i −0.906979 3.38489i
\(363\) 0 0
\(364\) −3.61534 8.63772i −0.189495 0.452739i
\(365\) 16.1054 + 11.4591i 0.842998 + 0.599794i
\(366\) 0 0
\(367\) −32.9994 8.84217i −1.72256 0.461558i −0.744110 0.668057i \(-0.767126\pi\)
−0.978447 + 0.206499i \(0.933793\pi\)
\(368\) 10.2472 + 2.74572i 0.534171 + 0.143131i
\(369\) 0 0
\(370\) −0.241376 1.43195i −0.0125486 0.0744437i
\(371\) 11.6921 + 27.9346i 0.607023 + 1.45029i
\(372\) 0 0
\(373\) −0.481243 1.79602i −0.0249178 0.0929945i 0.952347 0.305016i \(-0.0986619\pi\)
−0.977265 + 0.212022i \(0.931995\pi\)
\(374\) 32.6975 + 56.6337i 1.69075 + 2.92846i
\(375\) 0 0
\(376\) 41.3308 + 23.8623i 2.13147 + 1.23061i
\(377\) −0.494553 + 0.494553i −0.0254708 + 0.0254708i
\(378\) 0 0
\(379\) 5.91800i 0.303987i −0.988381 0.151994i \(-0.951431\pi\)
0.988381 0.151994i \(-0.0485694\pi\)
\(380\) 3.98545 + 1.48470i 0.204449 + 0.0761636i
\(381\) 0 0
\(382\) −17.2104 + 64.2302i −0.880562 + 3.28630i
\(383\) −3.06298 + 0.820722i −0.156511 + 0.0419369i −0.336224 0.941782i \(-0.609150\pi\)
0.179713 + 0.983719i \(0.442483\pi\)
\(384\) 0 0
\(385\) 23.8016 + 21.9789i 1.21304 + 1.12015i
\(386\) 42.1804 2.14692
\(387\) 0 0
\(388\) 9.47416 35.3580i 0.480977 1.79503i
\(389\) −17.8583 + 10.3105i −0.905454 + 0.522764i −0.878966 0.476885i \(-0.841766\pi\)
−0.0264880 + 0.999649i \(0.508432\pi\)
\(390\) 0 0
\(391\) 8.39511i 0.424559i
\(392\) 20.6450 + 35.1552i 1.04273 + 1.77561i
\(393\) 0 0
\(394\) −1.28968 0.744599i −0.0649733 0.0375123i
\(395\) 17.9551 14.8369i 0.903420 0.746526i
\(396\) 0 0
\(397\) −2.66854 9.95911i −0.133930 0.499833i 0.866070 0.499923i \(-0.166638\pi\)
−1.00000 8.92458e-5i \(0.999972\pi\)
\(398\) 43.4319 + 43.4319i 2.17705 + 2.17705i
\(399\) 0 0
\(400\) −28.3611 + 9.84096i −1.41806 + 0.492048i
\(401\) 6.58719 11.4093i 0.328948 0.569755i −0.653355 0.757052i \(-0.726639\pi\)
0.982303 + 0.187296i \(0.0599724\pi\)
\(402\) 0 0
\(403\) −2.12552 0.569532i −0.105880 0.0283704i
\(404\) −7.83843 + 13.5766i −0.389977 + 0.675459i
\(405\) 0 0
\(406\) 3.43707 4.51373i 0.170579 0.224013i
\(407\) 1.00052 + 1.00052i 0.0495938 + 0.0495938i
\(408\) 0 0
\(409\) −9.73831 16.8672i −0.481528 0.834032i 0.518247 0.855231i \(-0.326585\pi\)
−0.999775 + 0.0211993i \(0.993252\pi\)
\(410\) 1.80085 + 0.171243i 0.0889378 + 0.00845709i
\(411\) 0 0
\(412\) 21.9165 21.9165i 1.07975 1.07975i
\(413\) −5.80037 + 14.1511i −0.285418 + 0.696331i
\(414\) 0 0
\(415\) 24.3754 11.1435i 1.19654 0.547014i
\(416\) −2.44380 + 1.41093i −0.119817 + 0.0691765i
\(417\) 0 0
\(418\) −5.85719 + 1.56943i −0.286484 + 0.0767633i
\(419\) 30.3333 1.48188 0.740939 0.671572i \(-0.234381\pi\)
0.740939 + 0.671572i \(0.234381\pi\)
\(420\) 0 0
\(421\) 19.2053 0.936007 0.468004 0.883727i \(-0.344973\pi\)
0.468004 + 0.883727i \(0.344973\pi\)
\(422\) −60.1518 + 16.1176i −2.92815 + 0.784594i
\(423\) 0 0
\(424\) 57.7309 33.3310i 2.80366 1.61870i
\(425\) 13.3310 + 19.6631i 0.646650 + 0.953801i
\(426\) 0 0
\(427\) −2.34967 17.3515i −0.113709 0.839698i
\(428\) 0.230663 0.230663i 0.0111495 0.0111495i
\(429\) 0 0
\(430\) −3.19790 3.86999i −0.154217 0.186627i
\(431\) −1.66744 2.88809i −0.0803177 0.139114i 0.823069 0.567942i \(-0.192260\pi\)
−0.903386 + 0.428828i \(0.858927\pi\)
\(432\) 0 0
\(433\) −12.7765 12.7765i −0.613998 0.613998i 0.329987 0.943985i \(-0.392956\pi\)
−0.943985 + 0.329987i \(0.892956\pi\)
\(434\) 17.7057 + 2.26442i 0.849899 + 0.108696i
\(435\) 0 0
\(436\) 7.75299 13.4286i 0.371301 0.643112i
\(437\) 0.751919 + 0.201476i 0.0359692 + 0.00963791i
\(438\) 0 0
\(439\) −12.1119 + 20.9784i −0.578070 + 1.00125i 0.417631 + 0.908617i \(0.362861\pi\)
−0.995701 + 0.0926297i \(0.970473\pi\)
\(440\) 41.3449 58.1093i 1.97104 2.77025i
\(441\) 0 0
\(442\) 6.92234 + 6.92234i 0.329262 + 0.329262i
\(443\) −5.52124 20.6056i −0.262322 0.979000i −0.963869 0.266376i \(-0.914174\pi\)
0.701547 0.712623i \(-0.252493\pi\)
\(444\) 0 0
\(445\) −11.5086 13.9273i −0.545562 0.660220i
\(446\) 26.3934 + 15.2383i 1.24977 + 0.721553i
\(447\) 0 0
\(448\) −7.02491 + 5.43179i −0.331896 + 0.256628i
\(449\) 10.6514i 0.502669i −0.967900 0.251335i \(-0.919131\pi\)
0.967900 0.251335i \(-0.0808695\pi\)
\(450\) 0 0
\(451\) −1.52648 + 0.881313i −0.0718791 + 0.0414994i
\(452\) 20.3976 76.1249i 0.959423 3.58061i
\(453\) 0 0
\(454\) 53.9157 2.53039
\(455\) 4.29328 + 2.25594i 0.201272 + 0.105760i
\(456\) 0 0
\(457\) −23.3867 + 6.26646i −1.09399 + 0.293133i −0.760313 0.649556i \(-0.774955\pi\)
−0.333672 + 0.942689i \(0.608288\pi\)
\(458\) 3.71923 13.8804i 0.173788 0.648586i
\(459\) 0 0
\(460\) −15.5131 + 7.09198i −0.723300 + 0.330665i
\(461\) 33.1612i 1.54447i −0.635337 0.772235i \(-0.719139\pi\)
0.635337 0.772235i \(-0.280861\pi\)
\(462\) 0 0
\(463\) −17.9439 + 17.9439i −0.833926 + 0.833926i −0.988051 0.154126i \(-0.950744\pi\)
0.154126 + 0.988051i \(0.450744\pi\)
\(464\) −4.43609 2.56118i −0.205940 0.118900i
\(465\) 0 0
\(466\) 0.564750 + 0.978175i 0.0261615 + 0.0453131i
\(467\) 2.50765 + 9.35867i 0.116040 + 0.433067i 0.999363 0.0356983i \(-0.0113655\pi\)
−0.883323 + 0.468766i \(0.844699\pi\)
\(468\) 0 0
\(469\) −13.0583 + 5.46558i −0.602976 + 0.252377i
\(470\) −45.4125 + 7.65493i −2.09472 + 0.353096i
\(471\) 0 0
\(472\) 32.5192 + 8.71349i 1.49682 + 0.401071i
\(473\) 4.72498 + 1.26606i 0.217255 + 0.0582133i
\(474\) 0 0
\(475\) −2.08109 + 0.722112i −0.0954868 + 0.0331328i
\(476\) −43.1772 32.8781i −1.97902 1.50696i
\(477\) 0 0
\(478\) 8.00572 + 29.8778i 0.366173 + 1.36658i
\(479\) −15.0795 26.1185i −0.689000 1.19338i −0.972162 0.234311i \(-0.924717\pi\)
0.283162 0.959072i \(-0.408617\pi\)
\(480\) 0 0
\(481\) 0.183440 + 0.105909i 0.00836414 + 0.00482904i
\(482\) −5.69165 + 5.69165i −0.259248 + 0.259248i
\(483\) 0 0
\(484\) 81.9764i 3.72620i
\(485\) 7.88283 + 17.2430i 0.357941 + 0.782963i
\(486\) 0 0
\(487\) 9.68429 36.1423i 0.438837 1.63776i −0.292877 0.956150i \(-0.594613\pi\)
0.731714 0.681612i \(-0.238721\pi\)
\(488\) −37.2314 + 9.97612i −1.68539 + 0.451598i
\(489\) 0 0
\(490\) −36.9666 13.4607i −1.66998 0.608094i
\(491\) 13.5014 0.609308 0.304654 0.952463i \(-0.401459\pi\)
0.304654 + 0.952463i \(0.401459\pi\)
\(492\) 0 0
\(493\) −1.04914 + 3.91543i −0.0472507 + 0.176342i
\(494\) −0.786139 + 0.453878i −0.0353701 + 0.0204209i
\(495\) 0 0
\(496\) 16.1162i 0.723639i
\(497\) 14.2361 + 18.4115i 0.638577 + 0.825869i
\(498\) 0 0
\(499\) −18.0515 10.4220i −0.808095 0.466554i 0.0381992 0.999270i \(-0.487838\pi\)
−0.846294 + 0.532717i \(0.821171\pi\)
\(500\) 25.0731 41.2449i 1.12130 1.84453i
\(501\) 0 0
\(502\) −10.8025 40.3155i −0.482139 1.79937i
\(503\) 13.5884 + 13.5884i 0.605878 + 0.605878i 0.941866 0.335988i \(-0.109070\pi\)
−0.335988 + 0.941866i \(0.609070\pi\)
\(504\) 0 0
\(505\) −1.34965 8.00674i −0.0600587 0.356295i
\(506\) 12.1599 21.0615i 0.540572 0.936298i
\(507\) 0 0
\(508\) 79.7889 + 21.3794i 3.54006 + 0.948556i
\(509\) 10.8954 18.8713i 0.482928 0.836456i −0.516880 0.856058i \(-0.672907\pi\)
0.999808 + 0.0196021i \(0.00623993\pi\)
\(510\) 0 0
\(511\) 21.5740 9.02983i 0.954376 0.399456i
\(512\) 34.8385 + 34.8385i 1.53966 + 1.53966i
\(513\) 0 0
\(514\) −4.11650 7.12999i −0.181571 0.314490i
\(515\) −1.51966 + 15.9813i −0.0669642 + 0.704220i
\(516\) 0 0
\(517\) 31.7301 31.7301i 1.39549 1.39549i
\(518\) −1.58984 0.651657i −0.0698536 0.0286322i
\(519\) 0 0
\(520\) 3.72698 10.0045i 0.163439 0.438726i
\(521\) −23.5882 + 13.6187i −1.03342 + 0.596645i −0.917962 0.396668i \(-0.870167\pi\)
−0.115457 + 0.993312i \(0.536833\pi\)
\(522\) 0 0
\(523\) 32.4329 8.69038i 1.41819 0.380004i 0.533351 0.845894i \(-0.320933\pi\)
0.884842 + 0.465891i \(0.154266\pi\)
\(524\) −19.2938 −0.842855
\(525\) 0 0
\(526\) −39.1628 −1.70758
\(527\) −12.3189 + 3.30085i −0.536621 + 0.143787i
\(528\) 0 0
\(529\) 17.2148 9.93897i 0.748470 0.432129i
\(530\) −22.4562 + 60.2802i −0.975437 + 2.61841i
\(531\) 0 0
\(532\) 3.98098 3.07817i 0.172598 0.133456i
\(533\) −0.186581 + 0.186581i −0.00808174 + 0.00808174i
\(534\) 0 0
\(535\) −0.0159939 + 0.168197i −0.000691476 + 0.00727181i
\(536\) 15.5809 + 26.9869i 0.672992 + 1.16566i
\(537\) 0 0
\(538\) −15.2223 15.2223i −0.656282 0.656282i
\(539\) 36.9525 10.1949i 1.59166 0.439124i
\(540\) 0 0
\(541\) −21.7925 + 37.7457i −0.936931 + 1.62281i −0.165778 + 0.986163i \(0.553013\pi\)
−0.771153 + 0.636649i \(0.780320\pi\)
\(542\) 13.0428 + 3.49481i 0.560237 + 0.150115i
\(543\) 0 0
\(544\) −8.17735 + 14.1636i −0.350601 + 0.607259i
\(545\) 1.33494 + 7.91946i 0.0571825 + 0.339232i
\(546\) 0 0
\(547\) 7.79378 + 7.79378i 0.333238 + 0.333238i 0.853815 0.520577i \(-0.174283\pi\)
−0.520577 + 0.853815i \(0.674283\pi\)
\(548\) 10.1732 + 37.9669i 0.434577 + 1.62186i
\(549\) 0 0
\(550\) 4.96371 + 68.6398i 0.211653 + 2.92681i
\(551\) −0.325512 0.187934i −0.0138673 0.00800628i
\(552\) 0 0
\(553\) −3.69825 27.3103i −0.157266 1.16135i
\(554\) 31.9134i 1.35587i
\(555\) 0 0
\(556\) −43.4741 + 25.0998i −1.84371 + 1.06447i
\(557\) 0.180150 0.672329i 0.00763320 0.0284875i −0.962004 0.273035i \(-0.911973\pi\)
0.969637 + 0.244547i \(0.0786393\pi\)
\(558\) 0 0
\(559\) 0.732284 0.0309723
\(560\) −7.82109 + 34.6483i −0.330501 + 1.46416i
\(561\) 0 0
\(562\) −43.1645 + 11.5659i −1.82078 + 0.487877i
\(563\) 9.10686 33.9872i 0.383808 1.43239i −0.456229 0.889863i \(-0.650800\pi\)
0.840037 0.542529i \(-0.182533\pi\)
\(564\) 0 0
\(565\) 16.9715 + 37.1236i 0.713997 + 1.56180i
\(566\) 5.44610i 0.228916i
\(567\) 0 0
\(568\) 36.2266 36.2266i 1.52003 1.52003i
\(569\) −1.66149 0.959261i −0.0696532 0.0402143i 0.464769 0.885432i \(-0.346137\pi\)
−0.534422 + 0.845218i \(0.679471\pi\)
\(570\) 0 0
\(571\) 12.4151 + 21.5037i 0.519558 + 0.899900i 0.999742 + 0.0227326i \(0.00723662\pi\)
−0.480184 + 0.877168i \(0.659430\pi\)
\(572\) 5.01620 + 18.7207i 0.209738 + 0.782752i
\(573\) 0 0
\(574\) 1.29671 1.70291i 0.0541237 0.0710780i
\(575\) 3.85398 7.94973i 0.160722 0.331527i
\(576\) 0 0
\(577\) 30.2968 + 8.11801i 1.26127 + 0.337957i 0.826682 0.562670i \(-0.190226\pi\)
0.434592 + 0.900627i \(0.356892\pi\)
\(578\) 13.5328 + 3.62612i 0.562892 + 0.150827i
\(579\) 0 0
\(580\) 8.12148 1.36899i 0.337226 0.0568443i
\(581\) 4.02302 31.4562i 0.166903 1.30502i
\(582\) 0 0
\(583\) −16.2225 60.5432i −0.671868 2.50744i
\(584\) −25.7416 44.5858i −1.06520 1.84497i
\(585\) 0 0
\(586\) −23.0457 13.3054i −0.952008 0.549642i
\(587\) −5.75225 + 5.75225i −0.237421 + 0.237421i −0.815781 0.578361i \(-0.803693\pi\)
0.578361 + 0.815781i \(0.303693\pi\)
\(588\) 0 0
\(589\) 1.18258i 0.0487273i
\(590\) −29.5461 + 13.5074i −1.21639 + 0.556089i
\(591\) 0 0
\(592\) −0.401514 + 1.49847i −0.0165021 + 0.0615867i
\(593\) 33.8066 9.05846i 1.38827 0.371986i 0.514153 0.857698i \(-0.328106\pi\)
0.874119 + 0.485712i \(0.161440\pi\)
\(594\) 0 0
\(595\) 28.0864 1.11822i 1.15143 0.0458424i
\(596\) −48.1681 −1.97304
\(597\) 0 0
\(598\) 0.942276 3.51662i 0.0385325 0.143805i
\(599\) 16.3670 9.44951i 0.668739 0.386097i −0.126860 0.991921i \(-0.540490\pi\)
0.795599 + 0.605824i \(0.207156\pi\)
\(600\) 0 0
\(601\) 10.3658i 0.422828i 0.977397 + 0.211414i \(0.0678069\pi\)
−0.977397 + 0.211414i \(0.932193\pi\)
\(602\) −5.88637 + 0.797109i −0.239911 + 0.0324877i
\(603\) 0 0
\(604\) −6.02684 3.47960i −0.245229 0.141583i
\(605\) −27.0461 32.7302i −1.09958 1.33067i
\(606\) 0 0
\(607\) 5.77280 + 21.5444i 0.234311 + 0.874459i 0.978458 + 0.206444i \(0.0661892\pi\)
−0.744148 + 0.668015i \(0.767144\pi\)
\(608\) −1.07233 1.07233i −0.0434887 0.0434887i
\(609\) 0 0
\(610\) 21.5631 30.3065i 0.873065 1.22707i
\(611\) 3.35877 5.81755i 0.135881 0.235353i
\(612\) 0 0
\(613\) −17.0896 4.57915i −0.690244 0.184950i −0.103387 0.994641i \(-0.532968\pi\)
−0.586857 + 0.809691i \(0.699635\pi\)
\(614\) −17.4082 + 30.1519i −0.702538 + 1.21683i
\(615\) 0 0
\(616\) −32.5801 77.8400i −1.31269 3.13626i
\(617\) −27.6697 27.6697i −1.11394 1.11394i −0.992612 0.121329i \(-0.961284\pi\)
−0.121329 0.992612i \(-0.538716\pi\)
\(618\) 0 0
\(619\) 10.8012 + 18.7082i 0.434135 + 0.751944i 0.997225 0.0744519i \(-0.0237207\pi\)
−0.563090 + 0.826396i \(0.690387\pi\)
\(620\) 16.5063 + 19.9753i 0.662907 + 0.802227i
\(621\) 0 0
\(622\) −27.6186 + 27.6186i −1.10741 + 1.10741i
\(623\) −21.1839 + 2.86864i −0.848716 + 0.114930i
\(624\) 0 0
\(625\) 3.59696 + 24.7399i 0.143878 + 0.989595i
\(626\) 2.91097 1.68065i 0.116346 0.0671722i
\(627\) 0 0
\(628\) −74.3418 + 19.9198i −2.96656 + 0.794888i
\(629\) 1.22764 0.0489492
\(630\) 0 0
\(631\) 24.2720 0.966253 0.483126 0.875551i \(-0.339501\pi\)
0.483126 + 0.875551i \(0.339501\pi\)
\(632\) −58.6001 + 15.7018i −2.33099 + 0.624586i
\(633\) 0 0
\(634\) −15.1527 + 8.74841i −0.601790 + 0.347444i
\(635\) −38.9104 + 17.7884i −1.54411 + 0.705910i
\(636\) 0 0
\(637\) 4.94831 2.90591i 0.196059 0.115136i
\(638\) −8.30334 + 8.30334i −0.328733 + 0.328733i
\(639\) 0 0
\(640\) −34.1031 3.24287i −1.34804 0.128186i
\(641\) −4.34807 7.53107i −0.171738 0.297460i 0.767289 0.641301i \(-0.221605\pi\)
−0.939028 + 0.343842i \(0.888272\pi\)
\(642\) 0 0
\(643\) 20.2627 + 20.2627i 0.799081 + 0.799081i 0.982951 0.183870i \(-0.0588624\pi\)
−0.183870 + 0.982951i \(0.558862\pi\)
\(644\) −2.56033 + 20.0194i −0.100891 + 0.788875i
\(645\) 0 0
\(646\) −2.63055 + 4.55624i −0.103498 + 0.179263i
\(647\) 42.1899 + 11.3048i 1.65866 + 0.444436i 0.962018 0.272986i \(-0.0880112\pi\)
0.696639 + 0.717422i \(0.254678\pi\)
\(648\) 0 0
\(649\) 15.8274 27.4139i 0.621280 1.07609i
\(650\) 3.37722 + 9.73296i 0.132466 + 0.381758i
\(651\) 0 0
\(652\) 25.4135 + 25.4135i 0.995269 + 0.995269i
\(653\) −1.46486 5.46693i −0.0573243 0.213937i 0.931322 0.364196i \(-0.118656\pi\)
−0.988647 + 0.150258i \(0.951989\pi\)
\(654\) 0 0
\(655\) 7.70333 6.36553i 0.300994 0.248722i
\(656\) −1.67361 0.966261i −0.0653436 0.0377262i
\(657\) 0 0
\(658\) −20.6665 + 50.4197i −0.805662 + 1.96557i
\(659\) 4.78729i 0.186486i −0.995643 0.0932432i \(-0.970277\pi\)
0.995643 0.0932432i \(-0.0297234\pi\)
\(660\) 0 0
\(661\) 27.7652 16.0302i 1.07994 0.623504i 0.149060 0.988828i \(-0.452375\pi\)
0.930880 + 0.365324i \(0.119042\pi\)
\(662\) −3.99574 + 14.9123i −0.155299 + 0.579583i
\(663\) 0 0
\(664\) −69.8090 −2.70912
\(665\) −0.573897 + 2.54243i −0.0222548 + 0.0985913i
\(666\) 0 0
\(667\) 1.45611 0.390163i 0.0563807 0.0151072i
\(668\) −8.52149 + 31.8026i −0.329706 + 1.23048i
\(669\) 0 0
\(670\) −28.1786 10.4974i −1.08863 0.405550i
\(671\) 36.2417i 1.39910i
\(672\) 0 0
\(673\) −15.5097 + 15.5097i −0.597856 + 0.597856i −0.939741 0.341886i \(-0.888934\pi\)
0.341886 + 0.939741i \(0.388934\pi\)
\(674\) −5.09585 2.94209i −0.196285 0.113325i
\(675\) 0 0
\(676\) −26.6113 46.0921i −1.02351 1.77277i
\(677\) 2.82458 + 10.5415i 0.108557 + 0.405142i 0.998724 0.0504927i \(-0.0160792\pi\)
−0.890167 + 0.455634i \(0.849412\pi\)
\(678\) 0 0
\(679\) 22.2518 + 2.84584i 0.853946 + 0.109213i
\(680\) −10.2850 61.0153i −0.394412 2.33983i
\(681\) 0 0
\(682\) −35.6866 9.56220i −1.36651 0.366156i
\(683\) −8.05965 2.15958i −0.308394 0.0826339i 0.101303 0.994856i \(-0.467699\pi\)
−0.409697 + 0.912222i \(0.634366\pi\)
\(684\) 0 0
\(685\) −16.5880 11.8024i −0.633796 0.450947i
\(686\) −36.6132 + 28.7451i −1.39790 + 1.09749i
\(687\) 0 0
\(688\) 1.38809 + 5.18042i 0.0529204 + 0.197502i
\(689\) −4.69154 8.12598i −0.178733 0.309575i
\(690\) 0 0
\(691\) −22.6318 13.0665i −0.860955 0.497073i 0.00337678 0.999994i \(-0.498925\pi\)
−0.864332 + 0.502922i \(0.832258\pi\)
\(692\) 53.9171 53.9171i 2.04962 2.04962i
\(693\) 0 0
\(694\) 22.0706i 0.837788i
\(695\) 9.07658 24.3646i 0.344294 0.924204i
\(696\) 0 0
\(697\) −0.395810 + 1.47718i −0.0149924 + 0.0559523i
\(698\) 34.3300 9.19869i 1.29941 0.348176i
\(699\) 0 0
\(700\) −25.7930 50.9553i −0.974884 1.92593i
\(701\) −22.6216 −0.854408 −0.427204 0.904155i \(-0.640501\pi\)
−0.427204 + 0.904155i \(0.640501\pi\)
\(702\) 0 0
\(703\) −0.0294624 + 0.109955i −0.00111119 + 0.00414703i
\(704\) 15.9172 9.18983i 0.599904 0.346355i
\(705\) 0 0
\(706\) 63.9767i 2.40779i
\(707\) −8.88957 3.64373i −0.334327 0.137037i
\(708\) 0 0
\(709\) −13.1813 7.61025i −0.495035 0.285809i 0.231626 0.972805i \(-0.425596\pi\)
−0.726661 + 0.686996i \(0.758929\pi\)
\(710\) −4.67992 + 49.2158i −0.175634 + 1.84703i
\(711\) 0 0
\(712\) 12.1795 + 45.4547i 0.456448 + 1.70349i
\(713\) 3.35373 + 3.35373i 0.125598 + 0.125598i
\(714\) 0 0
\(715\) −8.17923 5.81954i −0.305886 0.217638i
\(716\) 33.3537 57.7704i 1.24649 2.15898i
\(717\) 0 0
\(718\) −21.2349 5.68987i −0.792479 0.212344i
\(719\) 3.69885 6.40659i 0.137944 0.238925i −0.788774 0.614683i \(-0.789284\pi\)
0.926718 + 0.375757i \(0.122617\pi\)
\(720\) 0 0
\(721\) 15.1121 + 11.5074i 0.562804 + 0.428558i
\(722\) 33.4228 + 33.4228i 1.24387 + 1.24387i
\(723\) 0 0
\(724\) −57.2620 99.1807i −2.12813 3.68602i
\(725\) −2.79095 + 3.22607i −0.103653 + 0.119813i
\(726\) 0 0
\(727\) −7.58690 + 7.58690i −0.281383 + 0.281383i −0.833660 0.552278i \(-0.813759\pi\)
0.552278 + 0.833660i \(0.313759\pi\)
\(728\) −7.72700 9.99330i −0.286382 0.370376i
\(729\) 0 0
\(730\) 46.5546 + 17.3430i 1.72306 + 0.641894i
\(731\) 3.67551 2.12206i 0.135944 0.0784872i
\(732\) 0 0
\(733\) −43.3394 + 11.6127i −1.60078 + 0.428927i −0.945277 0.326270i \(-0.894208\pi\)
−0.655499 + 0.755196i \(0.727542\pi\)
\(734\) −85.8669 −3.16941
\(735\) 0 0
\(736\) 6.08215 0.224191
\(737\) 28.3015 7.58337i 1.04250 0.279337i
\(738\) 0 0
\(739\) 23.6682 13.6649i 0.870650 0.502670i 0.00308556 0.999995i \(-0.499018\pi\)
0.867564 + 0.497325i \(0.165684\pi\)
\(740\) −1.03708 2.26852i −0.0381238 0.0833923i
\(741\) 0 0
\(742\) 46.5576 + 60.2127i 1.70918 + 2.21048i
\(743\) −11.4233 + 11.4233i −0.419081 + 0.419081i −0.884887 0.465806i \(-0.845764\pi\)
0.465806 + 0.884887i \(0.345764\pi\)
\(744\) 0 0
\(745\) 19.2318 15.8919i 0.704599 0.582234i
\(746\) −2.33669 4.04727i −0.0855523 0.148181i
\(747\) 0 0
\(748\) 79.4276 + 79.4276i 2.90416 + 2.90416i
\(749\) 0.159049 + 0.121111i 0.00581154 + 0.00442531i
\(750\) 0 0
\(751\) 2.08894 3.61815i 0.0762265 0.132028i −0.825392 0.564559i \(-0.809046\pi\)
0.901619 + 0.432531i \(0.142379\pi\)
\(752\) 47.5220 + 12.7335i 1.73295 + 0.464342i
\(753\) 0 0
\(754\) −0.878944 + 1.52238i −0.0320093 + 0.0554417i
\(755\) 3.55431 0.599130i 0.129355 0.0218046i
\(756\) 0 0
\(757\) −20.2821 20.2821i −0.737166 0.737166i 0.234862 0.972029i \(-0.424536\pi\)
−0.972029 + 0.234862i \(0.924536\pi\)
\(758\) −3.84977 14.3675i −0.139830 0.521852i
\(759\) 0 0
\(760\) 5.71175 + 0.543130i 0.207187 + 0.0197014i
\(761\) 23.4603 + 13.5448i 0.850437 + 0.491000i 0.860798 0.508946i \(-0.169965\pi\)
−0.0103614 + 0.999946i \(0.503298\pi\)
\(762\) 0 0
\(763\) 8.79266 + 3.60401i 0.318316 + 0.130474i
\(764\) 114.219i 4.13229i
\(765\) 0 0
\(766\) −6.90230 + 3.98504i −0.249390 + 0.143985i
\(767\) 1.22648 4.57727i 0.0442855 0.165276i
\(768\) 0 0
\(769\) −42.3447 −1.52699 −0.763494 0.645815i \(-0.776518\pi\)
−0.763494 + 0.645815i \(0.776518\pi\)
\(770\) 72.0824 + 37.8763i 2.59767 + 1.36497i
\(771\) 0 0
\(772\) 69.9835 18.7520i 2.51876 0.674900i
\(773\) −9.11140 + 34.0042i −0.327714 + 1.22305i 0.583841 + 0.811868i \(0.301549\pi\)
−0.911555 + 0.411178i \(0.865117\pi\)
\(774\) 0 0
\(775\) −13.1807 2.52958i −0.473465 0.0908652i
\(776\) 49.3823i 1.77272i
\(777\) 0 0
\(778\) −36.6487 + 36.6487i −1.31392 + 1.31392i
\(779\) −0.122807 0.0709025i −0.00440001 0.00254035i
\(780\) 0 0
\(781\) −24.0855 41.7173i −0.861847 1.49276i
\(782\) −5.46117 20.3814i −0.195291 0.728836i
\(783\) 0 0
\(784\) 29.9372 + 29.4976i 1.06918 + 1.05349i
\(785\) 23.1100 32.4805i 0.824830 1.15928i
\(786\) 0 0
\(787\) 30.9094 + 8.28215i 1.10180 + 0.295227i 0.763498 0.645810i \(-0.223480\pi\)
0.338304 + 0.941037i \(0.390147\pi\)
\(788\) −2.47080 0.662049i −0.0880186 0.0235845i
\(789\) 0 0
\(790\) 33.9391 47.7007i 1.20750 1.69711i
\(791\) 47.9076 + 6.12703i 1.70340 + 0.217852i
\(792\) 0 0
\(793\) 1.40420 + 5.24054i 0.0498646 + 0.186097i
\(794\) −12.9572 22.4425i −0.459833 0.796453i
\(795\) 0 0
\(796\) 91.3685 + 52.7516i 3.23847 + 1.86973i
\(797\) −12.0046 + 12.0046i −0.425224 + 0.425224i −0.886998 0.461774i \(-0.847213\pi\)
0.461774 + 0.886998i \(0.347213\pi\)
\(798\) 0 0
\(799\) 38.9330i 1.37735i
\(800\) −14.2457 + 9.65816i −0.503660 + 0.341468i
\(801\) 0 0
\(802\) 8.57017 31.9843i 0.302623 1.12941i
\(803\) −46.7577 + 12.5287i −1.65004 + 0.442128i
\(804\) 0 0
\(805\) −5.58266 8.83775i −0.196763 0.311490i
\(806\) −5.53076 −0.194813
\(807\) 0 0
\(808\) −5.47372 + 20.4282i −0.192565 + 0.718661i
\(809\) −24.1018 + 13.9152i −0.847375 + 0.489232i −0.859764 0.510691i \(-0.829390\pi\)
0.0123895 + 0.999923i \(0.496056\pi\)
\(810\) 0 0
\(811\) 9.68692i 0.340154i 0.985431 + 0.170077i \(0.0544016\pi\)
−0.985431 + 0.170077i \(0.945598\pi\)
\(812\) 3.69595 9.01696i 0.129702 0.316433i
\(813\) 0 0
\(814\) 3.07988 + 1.77817i 0.107950 + 0.0623248i
\(815\) −18.5313 1.76214i −0.649121 0.0617249i
\(816\) 0 0
\(817\) 0.101855 + 0.380130i 0.00356347 + 0.0132991i
\(818\) −34.6148 34.6148i −1.21028 1.21028i
\(819\) 0 0
\(820\) 3.06401 0.516483i 0.107000 0.0180364i
\(821\) 7.99960 13.8557i 0.279188 0.483568i −0.691995 0.721902i \(-0.743268\pi\)
0.971183 + 0.238334i \(0.0766014\pi\)
\(822\) 0 0
\(823\) 3.54651 + 0.950285i 0.123624 + 0.0331248i 0.320100 0.947384i \(-0.396283\pi\)
−0.196477 + 0.980508i \(0.562950\pi\)
\(824\) 20.9066 36.2113i 0.728315 1.26148i
\(825\) 0 0
\(826\) −4.87640 + 38.1288i −0.169672 + 1.32667i
\(827\) −26.8259 26.8259i −0.932827 0.932827i 0.0650544 0.997882i \(-0.479278\pi\)
−0.997882 + 0.0650544i \(0.979278\pi\)
\(828\) 0 0
\(829\) 20.5625 + 35.6154i 0.714167 + 1.23697i 0.963280 + 0.268499i \(0.0865275\pi\)
−0.249113 + 0.968474i \(0.580139\pi\)
\(830\) 51.9288 42.9105i 1.80248 1.48945i
\(831\) 0 0
\(832\) 1.94556 1.94556i 0.0674503 0.0674503i
\(833\) 16.4159 28.9250i 0.568776 1.00219i
\(834\) 0 0
\(835\) −7.09018 15.5091i −0.245366 0.536715i
\(836\) −9.02023 + 5.20783i −0.311971 + 0.180117i
\(837\) 0 0
\(838\) 73.6422 19.7324i 2.54393 0.681643i
\(839\) 14.6665 0.506345 0.253172 0.967421i \(-0.418526\pi\)
0.253172 + 0.967421i \(0.418526\pi\)
\(840\) 0 0
\(841\) 28.2721 0.974901
\(842\) 46.6259 12.4934i 1.60683 0.430550i
\(843\) 0 0
\(844\) −92.6355 + 53.4831i −3.18864 + 1.84097i
\(845\) 25.8319 + 9.62318i 0.888644 + 0.331048i
\(846\) 0 0
\(847\) −49.7837 + 6.74151i −1.71059 + 0.231641i
\(848\) 48.5927 48.5927i 1.66868 1.66868i
\(849\) 0 0
\(850\) 45.1559 + 39.0654i 1.54883 + 1.33993i
\(851\) −0.228273 0.395381i −0.00782510 0.0135535i
\(852\) 0 0
\(853\) −23.0735 23.0735i −0.790022 0.790022i 0.191475 0.981497i \(-0.438673\pi\)
−0.981497 + 0.191475i \(0.938673\pi\)
\(854\) −16.9919 40.5969i −0.581451 1.38920i
\(855\) 0 0
\(856\) 0.220034 0.381111i 0.00752062 0.0130261i
\(857\) 8.92222 + 2.39070i 0.304777 + 0.0816648i 0.407966 0.912997i \(-0.366238\pi\)
−0.103189 + 0.994662i \(0.532905\pi\)
\(858\) 0 0
\(859\) 25.5426 44.2411i 0.871503 1.50949i 0.0110616 0.999939i \(-0.496479\pi\)
0.860442 0.509549i \(-0.170188\pi\)
\(860\) −7.02627 4.99920i −0.239594 0.170471i
\(861\) 0 0
\(862\) −5.92690 5.92690i −0.201871 0.201871i
\(863\) −5.61477 20.9546i −0.191129 0.713303i −0.993235 0.116121i \(-0.962954\pi\)
0.802106 0.597181i \(-0.203713\pi\)
\(864\) 0 0
\(865\) −3.73854 + 39.3158i −0.127114 + 1.33678i
\(866\) −39.3296 22.7070i −1.33647 0.771614i
\(867\) 0 0
\(868\) 30.3830 4.11435i 1.03127 0.139650i
\(869\) 57.0425i 1.93503i
\(870\) 0 0
\(871\) 3.79857 2.19310i 0.128710 0.0743105i
\(872\) 5.41405 20.2055i 0.183343 0.684245i
\(873\) 0 0
\(874\) 1.95655 0.0661812
\(875\) 27.1097 + 11.8349i 0.916475 + 0.400092i
\(876\) 0 0
\(877\) 35.3523 9.47262i 1.19376 0.319868i 0.393391 0.919371i \(-0.371302\pi\)
0.800372 + 0.599504i \(0.204635\pi\)
\(878\) −15.7580 + 58.8098i −0.531808 + 1.98473i
\(879\) 0 0
\(880\) 25.6651 68.8938i 0.865170 2.32241i
\(881\) 57.6727i 1.94304i 0.236949 + 0.971522i \(0.423852\pi\)
−0.236949 + 0.971522i \(0.576148\pi\)
\(882\) 0 0
\(883\) −27.2669 + 27.2669i −0.917604 + 0.917604i −0.996855 0.0792504i \(-0.974747\pi\)
0.0792504 + 0.996855i \(0.474747\pi\)
\(884\) 14.5626 + 8.40774i 0.489795 + 0.282783i
\(885\) 0 0
\(886\) −26.8086 46.4338i −0.900652 1.55997i
\(887\) −1.03798 3.87380i −0.0348520 0.130070i 0.946308 0.323266i \(-0.104781\pi\)
−0.981160 + 0.193197i \(0.938114\pi\)
\(888\) 0 0
\(889\) −6.42193 + 50.2134i −0.215385 + 1.68410i
\(890\) −37.0003 26.3258i −1.24025 0.882442i
\(891\) 0 0
\(892\) 50.5651 + 13.5489i 1.69304 + 0.453650i
\(893\) 3.48708 + 0.934361i 0.116691 + 0.0312672i
\(894\) 0 0
\(895\) 5.74297 + 34.0699i 0.191966 + 1.13883i
\(896\) −24.5561 + 32.2483i −0.820362 + 1.07734i
\(897\) 0 0
\(898\) −6.92891 25.8590i −0.231221 0.862927i
\(899\) −1.14505 1.98328i −0.0381894 0.0661460i
\(900\) 0 0
\(901\) −47.0959 27.1908i −1.56899 0.905858i
\(902\) −3.13262 + 3.13262i −0.104305 + 0.104305i
\(903\) 0 0
\(904\) 106.319i 3.53611i
\(905\) 55.5849 + 20.7071i 1.84771 + 0.688328i
\(906\) 0 0
\(907\) 6.43290 24.0079i 0.213601 0.797169i −0.773054 0.634341i \(-0.781272\pi\)
0.986654 0.162828i \(-0.0520617\pi\)
\(908\) 89.4542 23.9692i 2.96864 0.795445i
\(909\) 0 0
\(910\) 11.8906 + 2.68404i 0.394170 + 0.0889751i
\(911\) −19.0430 −0.630921 −0.315461 0.948939i \(-0.602159\pi\)
−0.315461 + 0.948939i \(0.602159\pi\)
\(912\) 0 0
\(913\) −16.9884 + 63.4014i −0.562233 + 2.09828i
\(914\) −52.7011 + 30.4270i −1.74320 + 1.00644i
\(915\) 0 0
\(916\) 24.6830i 0.815550i
\(917\) −1.58667 11.7170i −0.0523965 0.386930i
\(918\) 0 0
\(919\) −0.948190 0.547437i −0.0312779 0.0180583i 0.484280 0.874913i \(-0.339082\pi\)
−0.515557 + 0.856855i \(0.672415\pi\)
\(920\) −17.7385 + 14.6579i −0.584821 + 0.483258i
\(921\) 0 0
\(922\) −21.5719 80.5076i −0.710434 2.65138i
\(923\) −5.09911 5.09911i −0.167839 0.167839i
\(924\) 0 0
\(925\) 1.16251 + 0.563578i 0.0382231 + 0.0185303i
\(926\) −31.8908 + 55.2366i −1.04800 + 1.81519i
\(927\) 0 0
\(928\) −2.83668 0.760085i −0.0931185 0.0249510i
\(929\) −17.5714 + 30.4346i −0.576499 + 0.998526i 0.419378 + 0.907812i \(0.362248\pi\)
−0.995877 + 0.0907143i \(0.971085\pi\)
\(930\) 0 0
\(931\) 2.19674 + 2.16448i 0.0719951 + 0.0709381i
\(932\) 1.37187 + 1.37187i 0.0449370 + 0.0449370i
\(933\) 0 0
\(934\) 12.1760 + 21.0894i 0.398410 + 0.690066i
\(935\) −57.9178 5.50740i −1.89411 0.180111i
\(936\) 0 0
\(937\) −25.8188 + 25.8188i −0.843465 + 0.843465i −0.989308 0.145843i \(-0.953411\pi\)
0.145843 + 0.989308i \(0.453411\pi\)
\(938\) −28.1470 + 21.7638i −0.919034 + 0.710614i
\(939\) 0 0
\(940\) −71.9430 + 32.8896i −2.34652 + 1.07274i
\(941\) 43.6393 25.1952i 1.42260 0.821339i 0.426081 0.904685i \(-0.359894\pi\)
0.996521 + 0.0833460i \(0.0265607\pi\)
\(942\) 0 0
\(943\) 0.549350 0.147198i 0.0178893 0.00479342i
\(944\) 34.7060 1.12958
\(945\) 0 0
\(946\) 12.2947 0.399737
\(947\) −2.33947 + 0.626858i −0.0760225 + 0.0203702i −0.296630 0.954993i \(-0.595863\pi\)
0.220607 + 0.975363i \(0.429196\pi\)
\(948\) 0 0
\(949\) −6.27572 + 3.62329i −0.203718 + 0.117617i
\(950\) −4.58265 + 3.10691i −0.148681 + 0.100801i
\(951\) 0 0
\(952\) −67.7429 27.7670i −2.19556 0.899934i
\(953\) −9.85550 + 9.85550i −0.319251 + 0.319251i −0.848479 0.529228i \(-0.822481\pi\)
0.529228 + 0.848479i \(0.322481\pi\)
\(954\) 0 0
\(955\) −37.6837 45.6034i −1.21941 1.47569i
\(956\) 26.5654 + 46.0126i 0.859186 + 1.48815i
\(957\) 0 0
\(958\) −53.6000 53.6000i −1.73174 1.73174i
\(959\) −22.2204 + 9.30040i −0.717535 + 0.300326i
\(960\) 0 0
\(961\) −11.8974 + 20.6069i −0.383787 + 0.664739i
\(962\) 0.514245 + 0.137792i 0.0165799 + 0.00444258i
\(963\) 0 0
\(964\) −6.91297 + 11.9736i −0.222652 + 0.385644i
\(965\) −21.7551 + 30.5764i −0.700323 + 0.984288i
\(966\) 0 0
\(967\) −9.44361 9.44361i −0.303686 0.303686i 0.538768 0.842454i \(-0.318890\pi\)
−0.842454 + 0.538768i \(0.818890\pi\)
\(968\) 28.6228 + 106.822i 0.919971 + 3.43338i
\(969\) 0 0
\(970\) 30.3545 + 36.7340i 0.974625 + 1.17946i
\(971\) −27.7635 16.0293i −0.890974 0.514404i −0.0167131 0.999860i \(-0.505320\pi\)
−0.874261 + 0.485456i \(0.838654\pi\)
\(972\) 0 0
\(973\) −18.8181 24.3374i −0.603281 0.780220i
\(974\) 94.0448i 3.01339i
\(975\) 0 0
\(976\) −34.4115 + 19.8675i −1.10149 + 0.635944i
\(977\) 10.9872 41.0047i 0.351510 1.31185i −0.533309 0.845921i \(-0.679052\pi\)
0.884819 0.465934i \(-0.154282\pi\)
\(978\) 0 0
\(979\) 44.2465 1.41412
\(980\) −67.3173 5.89922i −2.15037 0.188444i
\(981\) 0 0
\(982\) 32.7782 8.78289i 1.04599 0.280273i
\(983\) −11.2295 + 41.9091i −0.358166 + 1.33669i 0.518287 + 0.855207i \(0.326570\pi\)
−0.876453 + 0.481487i \(0.840097\pi\)
\(984\) 0 0
\(985\) 1.20493 0.550848i 0.0383922 0.0175515i
\(986\) 10.1882i 0.324459i
\(987\) 0 0
\(988\) −1.10254 + 1.10254i −0.0350765 + 0.0350765i
\(989\) −1.36689 0.789172i −0.0434644 0.0250942i
\(990\) 0 0
\(991\) −2.15480 3.73222i −0.0684495 0.118558i 0.829769 0.558106i \(-0.188472\pi\)
−0.898219 + 0.439548i \(0.855139\pi\)
\(992\) −2.39142 8.92490i −0.0759277 0.283366i
\(993\) 0 0
\(994\) 46.5390 + 35.4380i 1.47613 + 1.12402i
\(995\) −53.8843 + 9.08297i −1.70825 + 0.287949i
\(996\) 0 0
\(997\) 7.21115 + 1.93222i 0.228379 + 0.0611940i 0.371194 0.928555i \(-0.378949\pi\)
−0.142814 + 0.989749i \(0.545615\pi\)
\(998\) −50.6045 13.5594i −1.60186 0.429216i
\(999\) 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 315.2.bz.d.82.8 32
3.2 odd 2 105.2.u.a.82.1 yes 32
5.3 odd 4 inner 315.2.bz.d.208.1 32
7.3 odd 6 inner 315.2.bz.d.262.1 32
15.2 even 4 525.2.bc.e.418.1 32
15.8 even 4 105.2.u.a.103.8 yes 32
15.14 odd 2 525.2.bc.e.82.8 32
21.2 odd 6 735.2.m.c.97.15 32
21.5 even 6 735.2.m.c.97.16 32
21.11 odd 6 735.2.v.b.472.8 32
21.17 even 6 105.2.u.a.52.8 32
21.20 even 2 735.2.v.b.607.1 32
35.3 even 12 inner 315.2.bz.d.73.8 32
105.17 odd 12 525.2.bc.e.493.8 32
105.23 even 12 735.2.m.c.538.16 32
105.38 odd 12 105.2.u.a.73.1 yes 32
105.53 even 12 735.2.v.b.178.1 32
105.59 even 6 525.2.bc.e.157.1 32
105.68 odd 12 735.2.m.c.538.15 32
105.83 odd 4 735.2.v.b.313.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.u.a.52.8 32 21.17 even 6
105.2.u.a.73.1 yes 32 105.38 odd 12
105.2.u.a.82.1 yes 32 3.2 odd 2
105.2.u.a.103.8 yes 32 15.8 even 4
315.2.bz.d.73.8 32 35.3 even 12 inner
315.2.bz.d.82.8 32 1.1 even 1 trivial
315.2.bz.d.208.1 32 5.3 odd 4 inner
315.2.bz.d.262.1 32 7.3 odd 6 inner
525.2.bc.e.82.8 32 15.14 odd 2
525.2.bc.e.157.1 32 105.59 even 6
525.2.bc.e.418.1 32 15.2 even 4
525.2.bc.e.493.8 32 105.17 odd 12
735.2.m.c.97.15 32 21.2 odd 6
735.2.m.c.97.16 32 21.5 even 6
735.2.m.c.538.15 32 105.68 odd 12
735.2.m.c.538.16 32 105.23 even 12
735.2.v.b.178.1 32 105.53 even 12
735.2.v.b.313.8 32 105.83 odd 4
735.2.v.b.472.8 32 21.11 odd 6
735.2.v.b.607.1 32 21.20 even 2