Properties

Label 315.2.bz.d.73.8
Level $315$
Weight $2$
Character 315.73
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 73.8
Character \(\chi\) \(=\) 315.73
Dual form 315.2.bz.d.82.8

$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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 0.977049 0.213015i \(-0.0683284\pi\)
0.739642 + 0.673001i \(0.234995\pi\)
\(3\) 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 0.0759295 + 0.997113i \(0.475808\pi\)
−0.901490 + 0.432800i \(0.857526\pi\)
\(12\) 0 0
\(13\) −0.579674 + 0.579674i −0.160773 + 0.160773i −0.782909 0.622136i \(-0.786265\pi\)
0.622136 + 0.782909i \(0.286265\pi\)
\(14\) 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 −0.768079 0.640355i \(-0.778787\pi\)
−0.344999 + 0.938603i \(0.612121\pi\)
\(18\) 0 0
\(19\) 0.220281 + 0.381538i 0.0505359 + 0.0875308i 0.890187 0.455596i \(-0.150574\pi\)
−0.839651 + 0.543127i \(0.817240\pi\)
\(20\) 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 −0.901716 0.432328i \(-0.857692\pi\)
0.997073 + 0.0764510i \(0.0243589\pi\)
\(24\) 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 \(0.0252410\pi\)
−0.996858 + 0.0792137i \(0.974759\pi\)
\(30\) 0 0
\(31\) 2.32463 + 1.34213i 0.417516 + 0.241053i 0.694014 0.719962i \(-0.255841\pi\)
−0.276498 + 0.961014i \(0.589174\pi\)
\(32\) 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 0.238245 0.971205i \(-0.423428\pi\)
−0.279276 + 0.960211i \(0.590094\pi\)
\(38\) 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 \(0.00800127\pi\)
−0.999684 + 0.0251341i \(0.991999\pi\)
\(42\) 0 0
\(43\) −0.631635 0.631635i −0.0963234 0.0963234i 0.657303 0.753626i \(-0.271697\pi\)
−0.753626 + 0.657303i \(0.771697\pi\)
\(44\) −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 −0.619774 0.784780i \(-0.712776\pi\)
0.929130 0.369752i \(-0.120557\pi\)
\(48\) 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 0.599340 0.800494i \(-0.295430\pi\)
0.919291 + 0.393579i \(0.128763\pi\)
\(54\) 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 −0.614240 0.789119i \(-0.710537\pi\)
0.990517 + 0.137387i \(0.0438705\pi\)
\(60\) 0 0
\(61\) −5.73145 + 3.30905i −0.733837 + 0.423681i −0.819824 0.572615i \(-0.805929\pi\)
0.0859874 + 0.996296i \(0.472596\pi\)
\(62\) 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 −0.997470 0.0710893i \(-0.977352\pi\)
0.828290 0.560300i \(-0.189314\pi\)
\(68\) −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 0.960530 + 0.278175i \(0.0897296\pi\)
−0.692756 + 0.721172i \(0.743604\pi\)
\(74\) −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 −0.912634 0.408778i \(-0.865955\pi\)
−0.102305 + 0.994753i \(0.532622\pi\)
\(80\) 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 −0.997725 0.0674183i \(-0.978524\pi\)
0.0674183 + 0.997725i \(0.478524\pi\)
\(84\) 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 0.568485 0.822694i \(-0.307530\pi\)
−0.996716 + 0.0809755i \(0.974196\pi\)
\(90\) 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 0.942619 0.333870i \(-0.108355\pi\)
−0.333870 + 0.942619i \(0.608355\pi\)
\(98\) 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 0.335316 0.942106i \(-0.391157\pi\)
−0.648230 + 0.761445i \(0.724490\pi\)
\(102\) 0 0
\(103\) 6.93466 + 1.85814i 0.683293 + 0.183088i 0.583735 0.811944i \(-0.301591\pi\)
0.0995575 + 0.995032i \(0.468257\pi\)
\(104\) −4.77452 −0.468181
\(105\) 0 0
\(106\) 28.7680 2.79420
\(107\) 0.0729848 + 0.0195562i 0.00705571 + 0.00189057i 0.262345 0.964974i \(-0.415504\pi\)
−0.255289 + 0.966865i \(0.582171\pi\)
\(108\) 0 0
\(109\) 3.11046 + 1.79583i 0.297928 + 0.172009i 0.641512 0.767113i \(-0.278308\pi\)
−0.343584 + 0.939122i \(0.611641\pi\)
\(110\) 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 0.969600 + 0.244694i \(0.0786874\pi\)
0.244694 + 0.969600i \(0.421313\pi\)
\(114\) 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 0.226539 0.974002i \(-0.427259\pi\)
0.974002 0.226539i \(-0.0727409\pi\)
\(128\) 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 −0.659453 0.751745i \(-0.729212\pi\)
0.321304 + 0.946976i \(0.395879\pi\)
\(132\) 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 −0.990539 0.137231i \(-0.956180\pi\)
0.789217 0.614115i \(-0.210487\pi\)
\(138\) 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 −0.840517 0.541785i \(-0.817749\pi\)
0.0489412 + 0.998802i \(0.484415\pi\)
\(150\) 0 0
\(151\) −0.805981 + 1.39600i −0.0655898 + 0.113605i −0.896955 0.442121i \(-0.854226\pi\)
0.831366 + 0.555726i \(0.187560\pi\)
\(152\) −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 −0.869044 0.494735i \(-0.835265\pi\)
−0.505247 + 0.862975i \(0.668598\pi\)
\(158\) −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 −0.828767 0.559593i \(-0.810957\pi\)
0.997530 0.0702383i \(-0.0223760\pi\)
\(164\) −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 0.466976 0.884270i \(-0.345343\pi\)
−0.884270 + 0.466976i \(0.845343\pi\)
\(168\) 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 0.840335 0.542068i \(-0.182358\pi\)
0.456717 + 0.889612i \(0.349025\pi\)
\(174\) 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 0.908299 0.418322i \(-0.137382\pi\)
0.0918716 + 0.995771i \(0.470715\pi\)
\(180\) 0 0
\(181\) 26.5272i 1.97175i 0.167472 + 0.985877i \(0.446440\pi\)
−0.167472 + 0.985877i \(0.553560\pi\)
\(182\) −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 −0.729341 0.684151i \(-0.760173\pi\)
−0.227822 0.973703i \(-0.573160\pi\)
\(192\) 0 0
\(193\) 16.2103 4.34354i 1.16684 0.312655i 0.377147 0.926153i \(-0.376905\pi\)
0.789696 + 0.613499i \(0.210238\pi\)
\(194\) 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 −0.721874 0.692024i \(-0.756719\pi\)
0.692024 + 0.721874i \(0.256719\pi\)
\(198\) 0 0
\(199\) 12.2189 21.1637i 0.866172 1.50025i 0.000294114 1.00000i \(-0.499906\pi\)
0.865878 0.500255i \(-0.166760\pi\)
\(200\) −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 −0.359126 0.933289i \(-0.616925\pi\)
0.933289 + 0.359126i \(0.116925\pi\)
\(224\) 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 0.505860 0.862616i \(-0.331175\pi\)
0.869395 + 0.494117i \(0.164509\pi\)
\(228\) 0 0
\(229\) 2.85867 + 4.95136i 0.188906 + 0.327195i 0.944886 0.327400i \(-0.106173\pi\)
−0.755980 + 0.654595i \(0.772839\pi\)
\(230\) −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 −0.962011 0.273010i \(-0.911981\pi\)
0.969631 + 0.244572i \(0.0786476\pi\)
\(234\) 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 \(-0.869695\pi\)
0.917374 0.398027i \(-0.130305\pi\)
\(240\) 0 0
\(241\) −2.77345 1.60125i −0.178654 0.103146i 0.408006 0.912979i \(-0.366224\pi\)
−0.586660 + 0.809833i \(0.699557\pi\)
\(242\) −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 \(0.175591\pi\)
−0.851669 + 0.524081i \(0.824409\pi\)
\(252\) 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 −0.987314 0.158782i \(-0.949243\pi\)
0.934430 + 0.356148i \(0.115910\pi\)
\(258\) 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 −0.691027 0.722828i \(-0.742842\pi\)
−0.237033 + 0.971502i \(0.576175\pi\)
\(264\) 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 −0.966538 0.256524i \(-0.917423\pi\)
0.705426 + 0.708784i \(0.250756\pi\)
\(270\) 0 0
\(271\) 4.65260 2.68618i 0.282625 0.163174i −0.351986 0.936005i \(-0.614494\pi\)
0.634611 + 0.772832i \(0.281160\pi\)
\(272\) −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 0.991618 + 0.129206i \(0.0412427\pi\)
−0.794163 + 0.607704i \(0.792091\pi\)
\(278\) −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 0.980589 0.196074i \(-0.0628194\pi\)
−0.947252 + 0.320489i \(0.896153\pi\)
\(284\) 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 −0.891125 0.453758i \(-0.850083\pi\)
0.453758 + 0.891125i \(0.350083\pi\)
\(294\) 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 0.370000 0.929032i \(-0.379358\pi\)
−0.929032 + 0.370000i \(0.879358\pi\)
\(308\) −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 0.0672821 0.997734i \(-0.478567\pi\)
−0.830422 + 0.557135i \(0.811901\pi\)
\(312\) 0 0
\(313\) 1.29178 + 0.346130i 0.0730155 + 0.0195644i 0.295142 0.955453i \(-0.404633\pi\)
−0.222126 + 0.975018i \(0.571300\pi\)
\(314\) −44.8072 −2.52862
\(315\) 0 0
\(316\) −44.9705 −2.52979
\(317\) −6.72418 1.80174i −0.377668 0.101196i 0.0649912 0.997886i \(-0.479298\pi\)
−0.442659 + 0.896690i \(0.645965\pi\)
\(318\) 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 0.769193 0.639017i \(-0.220659\pi\)
−0.938001 + 0.346632i \(0.887325\pi\)
\(332\) −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 −0.750756 0.660580i \(-0.770311\pi\)
0.660580 + 0.750756i \(0.270311\pi\)
\(338\) −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 0.999715 0.0238604i \(-0.00759572\pi\)
−0.877709 + 0.479194i \(0.840929\pi\)
\(348\) 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 −0.885877 0.463919i \(-0.846443\pi\)
0.535233 0.844705i \(-0.320224\pi\)
\(354\) 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 −0.686391 0.727232i \(-0.740806\pi\)
0.286606 + 0.958049i \(0.407473\pi\)
\(360\) 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 −0.978447 0.206499i \(-0.933793\pi\)
−0.744110 + 0.668057i \(0.767126\pi\)
\(368\) 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 −0.977265 0.212022i \(-0.931995\pi\)
0.952347 + 0.305016i \(0.0986619\pi\)
\(374\) 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 \(0.0485694\pi\)
−0.988381 + 0.151994i \(0.951431\pi\)
\(380\) 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 0.179713 0.983719i \(-0.442483\pi\)
−0.336224 + 0.941782i \(0.609150\pi\)
\(384\) 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 −0.0264880 0.999649i \(-0.508432\pi\)
−0.878966 + 0.476885i \(0.841766\pi\)
\(390\) 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 −1.00000 8.92458e-5i \(-0.999972\pi\)
0.866070 + 0.499923i \(0.166638\pi\)
\(398\) 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 0.982303 0.187296i \(-0.0599724\pi\)
−0.653355 + 0.757052i \(0.726639\pi\)
\(402\) 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 −0.999775 0.0211993i \(-0.993252\pi\)
0.518247 + 0.855231i \(0.326585\pi\)
\(410\) 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 −0.903386 0.428828i \(-0.858927\pi\)
0.823069 + 0.567942i \(0.192260\pi\)
\(432\) 0 0
\(433\) −12.7765 + 12.7765i −0.613998 + 0.613998i −0.943985 0.329987i \(-0.892956\pi\)
0.329987 + 0.943985i \(0.392956\pi\)
\(434\) 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 −0.995701 0.0926297i \(-0.970473\pi\)
0.417631 0.908617i \(-0.362861\pi\)
\(440\) 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 0.701547 + 0.712623i \(0.252493\pi\)
−0.963869 + 0.266376i \(0.914174\pi\)
\(444\) 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 \(0.0808695\pi\)
−0.967900 + 0.251335i \(0.919131\pi\)
\(450\) 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 −0.333672 0.942689i \(-0.608288\pi\)
−0.760313 + 0.649556i \(0.774955\pi\)
\(458\) 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 \(0.280861\pi\)
−0.635337 + 0.772235i \(0.719139\pi\)
\(462\) 0 0
\(463\) −17.9439 17.9439i −0.833926 0.833926i 0.154126 0.988051i \(-0.450744\pi\)
−0.988051 + 0.154126i \(0.950744\pi\)
\(464\) −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 −0.883323 0.468766i \(-0.844699\pi\)
0.999363 + 0.0356983i \(0.0113655\pi\)
\(468\) 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 0.283162 + 0.959072i \(0.408617\pi\)
−0.972162 + 0.234311i \(0.924717\pi\)
\(480\) 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 0.731714 + 0.681612i \(0.238721\pi\)
−0.292877 + 0.956150i \(0.594613\pi\)
\(488\) −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 −0.846294 0.532717i \(-0.821171\pi\)
0.0381992 + 0.999270i \(0.487838\pi\)
\(500\) 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 −0.335988 0.941866i \(-0.609070\pi\)
0.941866 + 0.335988i \(0.109070\pi\)
\(504\) 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 0.999808 0.0196021i \(-0.00623993\pi\)
−0.516880 + 0.856058i \(0.672907\pi\)
\(510\) 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 −0.115457 0.993312i \(-0.536833\pi\)
−0.917962 + 0.396668i \(0.870167\pi\)
\(522\) 0 0
\(523\) 32.4329 + 8.69038i 1.41819 + 0.380004i 0.884842 0.465891i \(-0.154266\pi\)
0.533351 + 0.845894i \(0.320933\pi\)
\(524\) −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 −0.771153 0.636649i \(-0.780320\pi\)
−0.165778 0.986163i \(-0.553013\pi\)
\(542\) 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 −0.520577 0.853815i \(-0.674283\pi\)
0.853815 + 0.520577i \(0.174283\pi\)
\(548\) 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 0.969637 0.244547i \(-0.0786393\pi\)
−0.962004 + 0.273035i \(0.911973\pi\)
\(558\) 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 0.840037 + 0.542529i \(0.182533\pi\)
−0.456229 + 0.889863i \(0.650800\pi\)
\(564\) 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 −0.534422 0.845218i \(-0.679471\pi\)
0.464769 + 0.885432i \(0.346137\pi\)
\(570\) 0 0
\(571\) 12.4151 21.5037i 0.519558 0.899900i −0.480184 0.877168i \(-0.659430\pi\)
0.999742 0.0227326i \(-0.00723662\pi\)
\(572\) 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 0.434592 0.900627i \(-0.356892\pi\)
0.826682 + 0.562670i \(0.190226\pi\)
\(578\) 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 0.578361 0.815781i \(-0.303693\pi\)
−0.815781 + 0.578361i \(0.803693\pi\)
\(588\) 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 0.874119 0.485712i \(-0.161440\pi\)
0.514153 + 0.857698i \(0.328106\pi\)
\(594\) 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 0.795599 0.605824i \(-0.207156\pi\)
−0.126860 + 0.991921i \(0.540490\pi\)
\(600\) 0 0
\(601\) 10.3658i 0.422828i −0.977397 0.211414i \(-0.932193\pi\)
0.977397 0.211414i \(-0.0678069\pi\)
\(602\) −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 −0.744148 0.668015i \(-0.767144\pi\)
0.978458 0.206444i \(-0.0661892\pi\)
\(608\) −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 −0.586857 0.809691i \(-0.699635\pi\)
−0.103387 + 0.994641i \(0.532968\pi\)
\(614\) −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 −0.121329 + 0.992612i \(0.538716\pi\)
−0.992612 + 0.121329i \(0.961284\pi\)
\(618\) 0 0
\(619\) 10.8012 18.7082i 0.434135 0.751944i −0.563090 0.826396i \(-0.690387\pi\)
0.997225 + 0.0744519i \(0.0237207\pi\)
\(620\) 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 −0.939028 0.343842i \(-0.888272\pi\)
0.767289 + 0.641301i \(0.221605\pi\)
\(642\) 0 0
\(643\) 20.2627 20.2627i 0.799081 0.799081i −0.183870 0.982951i \(-0.558862\pi\)
0.982951 + 0.183870i \(0.0588624\pi\)
\(644\) −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 0.696639 0.717422i \(-0.254678\pi\)
0.962018 + 0.272986i \(0.0880112\pi\)
\(648\) 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 −0.988647 0.150258i \(-0.951989\pi\)
0.931322 + 0.364196i \(0.118656\pi\)
\(654\) 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 \(0.0297234\pi\)
−0.995643 + 0.0932432i \(0.970277\pi\)
\(660\) 0 0
\(661\) 27.7652 + 16.0302i 1.07994 + 0.623504i 0.930880 0.365324i \(-0.119042\pi\)
0.149060 + 0.988828i \(0.452375\pi\)
\(662\) −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 0.341886 0.939741i \(-0.388934\pi\)
−0.939741 + 0.341886i \(0.888934\pi\)
\(674\) −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 −0.890167 0.455634i \(-0.849412\pi\)
0.998724 + 0.0504927i \(0.0160792\pi\)
\(678\) 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 −0.409697 0.912222i \(-0.634366\pi\)
0.101303 + 0.994856i \(0.467699\pi\)
\(684\) 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 −0.864332 0.502922i \(-0.832258\pi\)
0.00337678 + 0.999994i \(0.498925\pi\)
\(692\) 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 −0.726661 0.686996i \(-0.758929\pi\)
0.231626 + 0.972805i \(0.425596\pi\)
\(710\) −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 0.926718 0.375757i \(-0.122617\pi\)
−0.788774 + 0.614683i \(0.789284\pi\)
\(720\) 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 0.552278 0.833660i \(-0.313759\pi\)
−0.833660 + 0.552278i \(0.813759\pi\)
\(728\) −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 −0.655499 0.755196i \(-0.727542\pi\)
−0.945277 + 0.326270i \(0.894208\pi\)
\(734\) −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 0.867564 0.497325i \(-0.165684\pi\)
0.00308556 + 0.999995i \(0.499018\pi\)
\(740\) −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 0.465806 0.884887i \(-0.345764\pi\)
−0.884887 + 0.465806i \(0.845764\pi\)
\(744\) 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 0.901619 0.432531i \(-0.142379\pi\)
−0.825392 + 0.564559i \(0.809046\pi\)
\(752\) 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 −0.972029 0.234862i \(-0.924536\pi\)
0.234862 + 0.972029i \(0.424536\pi\)
\(758\) −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 −0.0103614 0.999946i \(-0.503298\pi\)
0.860798 + 0.508946i \(0.169965\pi\)
\(762\) 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 −0.911555 0.411178i \(-0.865117\pi\)
0.583841 0.811868i \(-0.301549\pi\)
\(774\) 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 0.338304 0.941037i \(-0.390147\pi\)
0.763498 + 0.645810i \(0.223480\pi\)
\(788\) −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 0.461774 0.886998i \(-0.347213\pi\)
−0.886998 + 0.461774i \(0.847213\pi\)
\(798\) 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 0.0123895 0.999923i \(-0.496056\pi\)
−0.859764 + 0.510691i \(0.829390\pi\)
\(810\) 0 0
\(811\) 9.68692i 0.340154i −0.985431 0.170077i \(-0.945598\pi\)
0.985431 0.170077i \(-0.0544016\pi\)
\(812\) 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 0.971183 0.238334i \(-0.0766014\pi\)
−0.691995 + 0.721902i \(0.743268\pi\)
\(822\) 0 0
\(823\) 3.54651 0.950285i 0.123624 0.0331248i −0.196477 0.980508i \(-0.562950\pi\)
0.320100 + 0.947384i \(0.396283\pi\)
\(824\) 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 −0.997882 0.0650544i \(-0.979278\pi\)
0.0650544 + 0.997882i \(0.479278\pi\)
\(828\) 0 0
\(829\) 20.5625 35.6154i 0.714167 1.23697i −0.249113 0.968474i \(-0.580139\pi\)
0.963280 0.268499i \(-0.0865275\pi\)
\(830\) 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 −0.981497 0.191475i \(-0.938673\pi\)
0.191475 + 0.981497i \(0.438673\pi\)
\(854\) −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 −0.103189 0.994662i \(-0.532905\pi\)
0.407966 + 0.912997i \(0.366238\pi\)
\(858\) 0 0
\(859\) 25.5426 + 44.2411i 0.871503 + 1.50949i 0.860442 + 0.509549i \(0.170188\pi\)
0.0110616 + 0.999939i \(0.496479\pi\)
\(860\) −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 0.802106 + 0.597181i \(0.203713\pi\)
−0.993235 + 0.116121i \(0.962954\pi\)
\(864\) 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 0.800372 0.599504i \(-0.204635\pi\)
0.393391 + 0.919371i \(0.371302\pi\)
\(878\) −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 \(-0.576148\pi\)
0.236949 0.971522i \(-0.423852\pi\)
\(882\) 0 0
\(883\) −27.2669 27.2669i −0.917604 0.917604i 0.0792504 0.996855i \(-0.474747\pi\)
−0.996855 + 0.0792504i \(0.974747\pi\)
\(884\) 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 −0.981160 0.193197i \(-0.938114\pi\)
0.946308 + 0.323266i \(0.104781\pi\)
\(888\) 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 0.986654 + 0.162828i \(0.0520617\pi\)
−0.773054 + 0.634341i \(0.781272\pi\)
\(908\) 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 −0.515557 0.856855i \(-0.672415\pi\)
0.484280 + 0.874913i \(0.339082\pi\)
\(920\) −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 −0.995877 0.0907143i \(-0.971085\pi\)
0.419378 0.907812i \(-0.362248\pi\)
\(930\) 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 0.145843 0.989308i \(-0.453411\pi\)
−0.989308 + 0.145843i \(0.953411\pi\)
\(938\) −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 0.996521 0.0833460i \(-0.0265607\pi\)
0.426081 + 0.904685i \(0.359894\pi\)
\(942\) 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 0.220607 0.975363i \(-0.429196\pi\)
−0.296630 + 0.954993i \(0.595863\pi\)
\(948\) 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 0.529228 0.848479i \(-0.322481\pi\)
−0.848479 + 0.529228i \(0.822481\pi\)
\(954\) 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 −0.842454 0.538768i \(-0.818890\pi\)
0.538768 + 0.842454i \(0.318890\pi\)
\(968\) 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 −0.874261 0.485456i \(-0.838654\pi\)
−0.0167131 + 0.999860i \(0.505320\pi\)
\(972\) 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 0.884819 + 0.465934i \(0.154282\pi\)
−0.533309 + 0.845921i \(0.679052\pi\)
\(978\) 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 −0.876453 0.481487i \(-0.840097\pi\)
0.518287 0.855207i \(-0.326570\pi\)
\(984\) 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 −0.898219 0.439548i \(-0.855139\pi\)
0.829769 + 0.558106i \(0.188472\pi\)
\(992\) −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 −0.142814 0.989749i \(-0.545615\pi\)
0.371194 + 0.928555i \(0.378949\pi\)
\(998\) −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.73.8 32
3.2 odd 2 105.2.u.a.73.1 yes 32
5.2 odd 4 inner 315.2.bz.d.262.1 32
7.5 odd 6 inner 315.2.bz.d.208.1 32
15.2 even 4 105.2.u.a.52.8 32
15.8 even 4 525.2.bc.e.157.1 32
15.14 odd 2 525.2.bc.e.493.8 32
21.2 odd 6 735.2.v.b.313.8 32
21.5 even 6 105.2.u.a.103.8 yes 32
21.11 odd 6 735.2.m.c.538.15 32
21.17 even 6 735.2.m.c.538.16 32
21.20 even 2 735.2.v.b.178.1 32
35.12 even 12 inner 315.2.bz.d.82.8 32
105.2 even 12 735.2.v.b.607.1 32
105.17 odd 12 735.2.m.c.97.15 32
105.32 even 12 735.2.m.c.97.16 32
105.47 odd 12 105.2.u.a.82.1 yes 32
105.62 odd 4 735.2.v.b.472.8 32
105.68 odd 12 525.2.bc.e.82.8 32
105.89 even 6 525.2.bc.e.418.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.u.a.52.8 32 15.2 even 4
105.2.u.a.73.1 yes 32 3.2 odd 2
105.2.u.a.82.1 yes 32 105.47 odd 12
105.2.u.a.103.8 yes 32 21.5 even 6
315.2.bz.d.73.8 32 1.1 even 1 trivial
315.2.bz.d.82.8 32 35.12 even 12 inner
315.2.bz.d.208.1 32 7.5 odd 6 inner
315.2.bz.d.262.1 32 5.2 odd 4 inner
525.2.bc.e.82.8 32 105.68 odd 12
525.2.bc.e.157.1 32 15.8 even 4
525.2.bc.e.418.1 32 105.89 even 6
525.2.bc.e.493.8 32 15.14 odd 2
735.2.m.c.97.15 32 105.17 odd 12
735.2.m.c.97.16 32 105.32 even 12
735.2.m.c.538.15 32 21.11 odd 6
735.2.m.c.538.16 32 21.17 even 6
735.2.v.b.178.1 32 21.20 even 2
735.2.v.b.313.8 32 21.2 odd 6
735.2.v.b.472.8 32 105.62 odd 4
735.2.v.b.607.1 32 105.2 even 12