Properties

Label 637.2.u.g.361.5
Level $637$
Weight $2$
Character 637.361
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(30,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.30");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.5
Root \(0.874681 + 1.11128i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.g.30.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.16500 + 0.672613i) q^{2} -2.05010 q^{3} +(-0.0951832 - 0.164862i) q^{4} +(3.08979 - 1.78389i) q^{5} +(-2.38837 - 1.37893i) q^{6} -2.94654i q^{8} +1.20292 q^{9} +O(q^{10})\) \(q+(1.16500 + 0.672613i) q^{2} -2.05010 q^{3} +(-0.0951832 - 0.164862i) q^{4} +(3.08979 - 1.78389i) q^{5} +(-2.38837 - 1.37893i) q^{6} -2.94654i q^{8} +1.20292 q^{9} +4.79947 q^{10} +1.27867i q^{11} +(0.195135 + 0.337984i) q^{12} +(-3.57420 + 0.474474i) q^{13} +(-6.33438 + 3.65716i) q^{15} +(1.79151 - 3.10299i) q^{16} +(-3.86960 - 6.70234i) q^{17} +(1.40141 + 0.809103i) q^{18} -0.943878i q^{19} +(-0.588191 - 0.339592i) q^{20} +(-0.860052 + 1.48965i) q^{22} +(0.823637 - 1.42658i) q^{23} +6.04071i q^{24} +(3.86451 - 6.69354i) q^{25} +(-4.48308 - 1.85129i) q^{26} +3.68419 q^{27} +(-2.02242 - 3.50293i) q^{29} -9.83940 q^{30} +(4.46193 + 2.57610i) q^{31} +(-0.929326 + 0.536547i) q^{32} -2.62141i q^{33} -10.4110i q^{34} +(-0.114498 - 0.198317i) q^{36} +(0.914594 + 0.528041i) q^{37} +(0.634865 - 1.09962i) q^{38} +(7.32747 - 0.972721i) q^{39} +(-5.25629 - 9.10417i) q^{40} +(3.63629 - 2.09941i) q^{41} +(1.91532 - 3.31744i) q^{43} +(0.210805 - 0.121708i) q^{44} +(3.71678 - 2.14588i) q^{45} +(1.91908 - 1.10798i) q^{46} +(0.774415 - 0.447109i) q^{47} +(-3.67279 + 6.36146i) q^{48} +(9.00432 - 5.19865i) q^{50} +(7.93308 + 13.7405i) q^{51} +(0.418426 + 0.544088i) q^{52} +(0.0399961 - 0.0692754i) q^{53} +(4.29208 + 2.47804i) q^{54} +(2.28101 + 3.95082i) q^{55} +1.93505i q^{57} -5.44122i q^{58} +(-9.68627 + 5.59237i) q^{59} +(1.20585 + 0.696200i) q^{60} +7.62392 q^{61} +(3.46543 + 6.00231i) q^{62} -8.60961 q^{64} +(-10.1971 + 7.84199i) q^{65} +(1.76319 - 3.05394i) q^{66} -6.32103i q^{67} +(-0.736641 + 1.27590i) q^{68} +(-1.68854 + 2.92464i) q^{69} +(9.89346 + 5.71199i) q^{71} -3.54446i q^{72} +(0.658617 + 0.380253i) q^{73} +(0.710335 + 1.23034i) q^{74} +(-7.92265 + 13.7224i) q^{75} +(-0.155610 + 0.0898413i) q^{76} +(9.19077 + 3.79533i) q^{78} +(1.42765 + 2.47277i) q^{79} -12.7834i q^{80} -11.1617 q^{81} +5.64837 q^{82} -2.32483i q^{83} +(-23.9125 - 13.8059i) q^{85} +(4.46270 - 2.57654i) q^{86} +(4.14617 + 7.18137i) q^{87} +3.76766 q^{88} +(-6.56124 - 3.78813i) q^{89} +5.77339 q^{90} -0.313586 q^{92} +(-9.14742 - 5.28127i) q^{93} +1.20292 q^{94} +(-1.68377 - 2.91638i) q^{95} +(1.90522 - 1.09998i) q^{96} +(0.414443 + 0.239279i) q^{97} +1.53815i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16500 + 0.672613i 0.823779 + 0.475609i 0.851718 0.524000i \(-0.175561\pi\)
−0.0279386 + 0.999610i \(0.508894\pi\)
\(3\) −2.05010 −1.18363 −0.591814 0.806075i \(-0.701588\pi\)
−0.591814 + 0.806075i \(0.701588\pi\)
\(4\) −0.0951832 0.164862i −0.0475916 0.0824311i
\(5\) 3.08979 1.78389i 1.38179 0.797779i 0.389422 0.921059i \(-0.372675\pi\)
0.992372 + 0.123280i \(0.0393415\pi\)
\(6\) −2.38837 1.37893i −0.975048 0.562944i
\(7\) 0 0
\(8\) 2.94654i 1.04176i
\(9\) 1.20292 0.400975
\(10\) 4.79947 1.51772
\(11\) 1.27867i 0.385534i 0.981245 + 0.192767i \(0.0617462\pi\)
−0.981245 + 0.192767i \(0.938254\pi\)
\(12\) 0.195135 + 0.337984i 0.0563307 + 0.0975677i
\(13\) −3.57420 + 0.474474i −0.991304 + 0.131595i
\(14\) 0 0
\(15\) −6.33438 + 3.65716i −1.63553 + 0.944273i
\(16\) 1.79151 3.10299i 0.447878 0.775748i
\(17\) −3.86960 6.70234i −0.938515 1.62556i −0.768242 0.640159i \(-0.778868\pi\)
−0.170273 0.985397i \(-0.554465\pi\)
\(18\) 1.40141 + 0.809103i 0.330315 + 0.190707i
\(19\) 0.943878i 0.216540i −0.994121 0.108270i \(-0.965469\pi\)
0.994121 0.108270i \(-0.0345312\pi\)
\(20\) −0.588191 0.339592i −0.131524 0.0759352i
\(21\) 0 0
\(22\) −0.860052 + 1.48965i −0.183364 + 0.317595i
\(23\) 0.823637 1.42658i 0.171740 0.297463i −0.767288 0.641303i \(-0.778394\pi\)
0.939028 + 0.343840i \(0.111728\pi\)
\(24\) 6.04071i 1.23305i
\(25\) 3.86451 6.69354i 0.772903 1.33871i
\(26\) −4.48308 1.85129i −0.879203 0.363068i
\(27\) 3.68419 0.709023
\(28\) 0 0
\(29\) −2.02242 3.50293i −0.375554 0.650478i 0.614856 0.788639i \(-0.289214\pi\)
−0.990410 + 0.138161i \(0.955881\pi\)
\(30\) −9.83940 −1.79642
\(31\) 4.46193 + 2.57610i 0.801387 + 0.462681i 0.843956 0.536413i \(-0.180221\pi\)
−0.0425691 + 0.999094i \(0.513554\pi\)
\(32\) −0.929326 + 0.536547i −0.164283 + 0.0948490i
\(33\) 2.62141i 0.456329i
\(34\) 10.4110i 1.78547i
\(35\) 0 0
\(36\) −0.114498 0.198317i −0.0190830 0.0330528i
\(37\) 0.914594 + 0.528041i 0.150358 + 0.0868094i 0.573292 0.819351i \(-0.305666\pi\)
−0.422933 + 0.906161i \(0.639000\pi\)
\(38\) 0.634865 1.09962i 0.102989 0.178382i
\(39\) 7.32747 0.972721i 1.17333 0.155760i
\(40\) −5.25629 9.10417i −0.831093 1.43950i
\(41\) 3.63629 2.09941i 0.567893 0.327873i −0.188415 0.982090i \(-0.560335\pi\)
0.756307 + 0.654217i \(0.227002\pi\)
\(42\) 0 0
\(43\) 1.91532 3.31744i 0.292084 0.505904i −0.682218 0.731148i \(-0.738985\pi\)
0.974302 + 0.225244i \(0.0723180\pi\)
\(44\) 0.210805 0.121708i 0.0317800 0.0183482i
\(45\) 3.71678 2.14588i 0.554064 0.319889i
\(46\) 1.91908 1.10798i 0.282952 0.163363i
\(47\) 0.774415 0.447109i 0.112960 0.0652175i −0.442456 0.896790i \(-0.645893\pi\)
0.555416 + 0.831573i \(0.312559\pi\)
\(48\) −3.67279 + 6.36146i −0.530121 + 0.918197i
\(49\) 0 0
\(50\) 9.00432 5.19865i 1.27340 0.735200i
\(51\) 7.93308 + 13.7405i 1.11085 + 1.92405i
\(52\) 0.418426 + 0.544088i 0.0580253 + 0.0754514i
\(53\) 0.0399961 0.0692754i 0.00549389 0.00951570i −0.863265 0.504750i \(-0.831585\pi\)
0.868759 + 0.495235i \(0.164918\pi\)
\(54\) 4.29208 + 2.47804i 0.584079 + 0.337218i
\(55\) 2.28101 + 3.95082i 0.307571 + 0.532729i
\(56\) 0 0
\(57\) 1.93505i 0.256303i
\(58\) 5.44122i 0.714467i
\(59\) −9.68627 + 5.59237i −1.26104 + 0.728064i −0.973277 0.229636i \(-0.926246\pi\)
−0.287768 + 0.957700i \(0.592913\pi\)
\(60\) 1.20585 + 0.696200i 0.155675 + 0.0898790i
\(61\) 7.62392 0.976143 0.488072 0.872804i \(-0.337701\pi\)
0.488072 + 0.872804i \(0.337701\pi\)
\(62\) 3.46543 + 6.00231i 0.440111 + 0.762294i
\(63\) 0 0
\(64\) −8.60961 −1.07620
\(65\) −10.1971 + 7.84199i −1.26479 + 0.972679i
\(66\) 1.76319 3.05394i 0.217034 0.375914i
\(67\) 6.32103i 0.772237i −0.922449 0.386119i \(-0.873816\pi\)
0.922449 0.386119i \(-0.126184\pi\)
\(68\) −0.736641 + 1.27590i −0.0893309 + 0.154726i
\(69\) −1.68854 + 2.92464i −0.203277 + 0.352085i
\(70\) 0 0
\(71\) 9.89346 + 5.71199i 1.17414 + 0.677889i 0.954651 0.297727i \(-0.0962285\pi\)
0.219487 + 0.975616i \(0.429562\pi\)
\(72\) 3.54446i 0.417719i
\(73\) 0.658617 + 0.380253i 0.0770853 + 0.0445052i 0.538047 0.842915i \(-0.319162\pi\)
−0.460962 + 0.887420i \(0.652496\pi\)
\(74\) 0.710335 + 1.23034i 0.0825747 + 0.143024i
\(75\) −7.92265 + 13.7224i −0.914829 + 1.58453i
\(76\) −0.155610 + 0.0898413i −0.0178497 + 0.0103055i
\(77\) 0 0
\(78\) 9.19077 + 3.79533i 1.04065 + 0.429737i
\(79\) 1.42765 + 2.47277i 0.160624 + 0.278208i 0.935093 0.354404i \(-0.115316\pi\)
−0.774469 + 0.632612i \(0.781983\pi\)
\(80\) 12.7834i 1.42923i
\(81\) −11.1617 −1.24019
\(82\) 5.64837 0.623758
\(83\) 2.32483i 0.255183i −0.991827 0.127591i \(-0.959275\pi\)
0.991827 0.127591i \(-0.0407246\pi\)
\(84\) 0 0
\(85\) −23.9125 13.8059i −2.59367 1.49746i
\(86\) 4.46270 2.57654i 0.481226 0.277836i
\(87\) 4.14617 + 7.18137i 0.444516 + 0.769924i
\(88\) 3.76766 0.401634
\(89\) −6.56124 3.78813i −0.695490 0.401541i 0.110176 0.993912i \(-0.464859\pi\)
−0.805665 + 0.592371i \(0.798192\pi\)
\(90\) 5.77339 0.608569
\(91\) 0 0
\(92\) −0.313586 −0.0326936
\(93\) −9.14742 5.28127i −0.948544 0.547642i
\(94\) 1.20292 0.124072
\(95\) −1.68377 2.91638i −0.172751 0.299214i
\(96\) 1.90522 1.09998i 0.194450 0.112266i
\(97\) 0.414443 + 0.239279i 0.0420803 + 0.0242951i 0.520893 0.853622i \(-0.325599\pi\)
−0.478812 + 0.877917i \(0.658933\pi\)
\(98\) 0 0
\(99\) 1.53815i 0.154589i
\(100\) −1.47135 −0.147135
\(101\) 2.87836 0.286407 0.143204 0.989693i \(-0.454260\pi\)
0.143204 + 0.989693i \(0.454260\pi\)
\(102\) 21.3436i 2.11333i
\(103\) 5.66755 + 9.81649i 0.558441 + 0.967248i 0.997627 + 0.0688516i \(0.0219335\pi\)
−0.439186 + 0.898396i \(0.644733\pi\)
\(104\) 1.39806 + 10.5315i 0.137091 + 1.03270i
\(105\) 0 0
\(106\) 0.0931910 0.0538039i 0.00905151 0.00522589i
\(107\) 3.28603 5.69157i 0.317673 0.550225i −0.662329 0.749213i \(-0.730432\pi\)
0.980002 + 0.198988i \(0.0637653\pi\)
\(108\) −0.350673 0.607384i −0.0337435 0.0584455i
\(109\) 5.05684 + 2.91957i 0.484358 + 0.279644i 0.722231 0.691652i \(-0.243117\pi\)
−0.237873 + 0.971296i \(0.576450\pi\)
\(110\) 6.13694i 0.585135i
\(111\) −1.87501 1.08254i −0.177968 0.102750i
\(112\) 0 0
\(113\) −3.26617 + 5.65717i −0.307255 + 0.532181i −0.977761 0.209723i \(-0.932744\pi\)
0.670506 + 0.741904i \(0.266077\pi\)
\(114\) −1.30154 + 2.25433i −0.121900 + 0.211137i
\(115\) 5.87711i 0.548043i
\(116\) −0.385001 + 0.666841i −0.0357464 + 0.0619146i
\(117\) −4.29949 + 0.570756i −0.397488 + 0.0527664i
\(118\) −15.0460 −1.38510
\(119\) 0 0
\(120\) 10.7759 + 18.6645i 0.983705 + 1.70383i
\(121\) 9.36500 0.851363
\(122\) 8.88187 + 5.12795i 0.804127 + 0.464263i
\(123\) −7.45477 + 4.30401i −0.672174 + 0.388080i
\(124\) 0.980805i 0.0880789i
\(125\) 9.73656i 0.870865i
\(126\) 0 0
\(127\) 7.35818 + 12.7447i 0.652932 + 1.13091i 0.982408 + 0.186748i \(0.0597948\pi\)
−0.329475 + 0.944164i \(0.606872\pi\)
\(128\) −8.17154 4.71784i −0.722269 0.417002i
\(129\) −3.92661 + 6.80109i −0.345719 + 0.598802i
\(130\) −17.1542 + 2.27722i −1.50453 + 0.199726i
\(131\) 5.59335 + 9.68796i 0.488693 + 0.846441i 0.999915 0.0130074i \(-0.00414049\pi\)
−0.511222 + 0.859448i \(0.670807\pi\)
\(132\) −0.432171 + 0.249514i −0.0376157 + 0.0217174i
\(133\) 0 0
\(134\) 4.25161 7.36400i 0.367283 0.636153i
\(135\) 11.3834 6.57219i 0.979724 0.565644i
\(136\) −19.7487 + 11.4019i −1.69344 + 0.977706i
\(137\) −15.2687 + 8.81541i −1.30450 + 0.753151i −0.981172 0.193137i \(-0.938134\pi\)
−0.323324 + 0.946288i \(0.604800\pi\)
\(138\) −3.93430 + 2.27147i −0.334910 + 0.193360i
\(139\) −2.92855 + 5.07240i −0.248396 + 0.430235i −0.963081 0.269212i \(-0.913237\pi\)
0.714685 + 0.699447i \(0.246570\pi\)
\(140\) 0 0
\(141\) −1.58763 + 0.916619i −0.133703 + 0.0771932i
\(142\) 7.68392 + 13.3089i 0.644820 + 1.11686i
\(143\) −0.606697 4.57022i −0.0507345 0.382181i
\(144\) 2.15506 3.73267i 0.179588 0.311055i
\(145\) −12.4977 7.21554i −1.03788 0.599218i
\(146\) 0.511526 + 0.885989i 0.0423342 + 0.0733250i
\(147\) 0 0
\(148\) 0.201043i 0.0165256i
\(149\) 10.4790i 0.858470i 0.903193 + 0.429235i \(0.141217\pi\)
−0.903193 + 0.429235i \(0.858783\pi\)
\(150\) −18.4598 + 10.6578i −1.50724 + 0.870203i
\(151\) 4.08249 + 2.35703i 0.332229 + 0.191812i 0.656830 0.754039i \(-0.271897\pi\)
−0.324602 + 0.945851i \(0.605230\pi\)
\(152\) −2.78117 −0.225583
\(153\) −4.65483 8.06241i −0.376321 0.651807i
\(154\) 0 0
\(155\) 18.3819 1.47647
\(156\) −0.857817 1.11544i −0.0686803 0.0893063i
\(157\) 4.50105 7.79604i 0.359223 0.622192i −0.628608 0.777722i \(-0.716375\pi\)
0.987831 + 0.155530i \(0.0497085\pi\)
\(158\) 3.84103i 0.305576i
\(159\) −0.0819962 + 0.142022i −0.00650272 + 0.0112630i
\(160\) −1.91428 + 3.31563i −0.151337 + 0.262123i
\(161\) 0 0
\(162\) −13.0034 7.50754i −1.02165 0.589848i
\(163\) 12.0324i 0.942449i 0.882013 + 0.471224i \(0.156188\pi\)
−0.882013 + 0.471224i \(0.843812\pi\)
\(164\) −0.692227 0.399657i −0.0540538 0.0312080i
\(165\) −4.67630 8.09959i −0.364050 0.630553i
\(166\) 1.56371 2.70842i 0.121367 0.210214i
\(167\) 16.8199 9.71099i 1.30157 0.751459i 0.320893 0.947116i \(-0.396017\pi\)
0.980672 + 0.195657i \(0.0626838\pi\)
\(168\) 0 0
\(169\) 12.5497 3.39173i 0.965365 0.260902i
\(170\) −18.5720 32.1677i −1.42441 2.46715i
\(171\) 1.13541i 0.0868273i
\(172\) −0.729226 −0.0556030
\(173\) 14.3795 1.09325 0.546627 0.837376i \(-0.315912\pi\)
0.546627 + 0.837376i \(0.315912\pi\)
\(174\) 11.1551i 0.845663i
\(175\) 0 0
\(176\) 3.96771 + 2.29076i 0.299077 + 0.172672i
\(177\) 19.8578 11.4649i 1.49261 0.861757i
\(178\) −5.09589 8.82635i −0.381953 0.661563i
\(179\) −5.42606 −0.405563 −0.202781 0.979224i \(-0.564998\pi\)
−0.202781 + 0.979224i \(0.564998\pi\)
\(180\) −0.707550 0.408504i −0.0527376 0.0304481i
\(181\) 15.4902 1.15138 0.575688 0.817669i \(-0.304734\pi\)
0.575688 + 0.817669i \(0.304734\pi\)
\(182\) 0 0
\(183\) −15.6298 −1.15539
\(184\) −4.20348 2.42688i −0.309885 0.178912i
\(185\) 3.76786 0.277019
\(186\) −7.10450 12.3054i −0.520927 0.902272i
\(187\) 8.57010 4.94795i 0.626707 0.361830i
\(188\) −0.147423 0.0851144i −0.0107519 0.00620761i
\(189\) 0 0
\(190\) 4.53011i 0.328649i
\(191\) 4.74622 0.343425 0.171712 0.985147i \(-0.445070\pi\)
0.171712 + 0.985147i \(0.445070\pi\)
\(192\) 17.6506 1.27382
\(193\) 21.0391i 1.51443i −0.653166 0.757215i \(-0.726559\pi\)
0.653166 0.757215i \(-0.273441\pi\)
\(194\) 0.321884 + 0.557519i 0.0231099 + 0.0400276i
\(195\) 20.9051 16.0769i 1.49704 1.15129i
\(196\) 0 0
\(197\) 5.03342 2.90604i 0.358616 0.207047i −0.309857 0.950783i \(-0.600281\pi\)
0.668474 + 0.743736i \(0.266948\pi\)
\(198\) −1.03458 + 1.79194i −0.0735242 + 0.127348i
\(199\) −5.30909 9.19562i −0.376352 0.651860i 0.614177 0.789168i \(-0.289488\pi\)
−0.990528 + 0.137309i \(0.956155\pi\)
\(200\) −19.7228 11.3869i −1.39461 0.805178i
\(201\) 12.9588i 0.914041i
\(202\) 3.35329 + 1.93602i 0.235936 + 0.136218i
\(203\) 0 0
\(204\) 1.51019 2.61573i 0.105735 0.183138i
\(205\) 7.49023 12.9735i 0.523140 0.906106i
\(206\) 15.2483i 1.06240i
\(207\) 0.990773 1.71607i 0.0688635 0.119275i
\(208\) −4.93093 + 11.9407i −0.341899 + 0.827941i
\(209\) 1.20691 0.0834837
\(210\) 0 0
\(211\) 2.33275 + 4.04043i 0.160593 + 0.278155i 0.935081 0.354433i \(-0.115326\pi\)
−0.774489 + 0.632588i \(0.781993\pi\)
\(212\) −0.0152278 −0.00104585
\(213\) −20.2826 11.7102i −1.38974 0.802368i
\(214\) 7.65645 4.42046i 0.523384 0.302176i
\(215\) 13.6669i 0.932074i
\(216\) 10.8556i 0.738631i
\(217\) 0 0
\(218\) 3.92748 + 6.80260i 0.266003 + 0.460730i
\(219\) −1.35023 0.779558i −0.0912403 0.0526776i
\(220\) 0.434227 0.752104i 0.0292756 0.0507068i
\(221\) 17.0108 + 22.1195i 1.14427 + 1.48792i
\(222\) −1.45626 2.52232i −0.0977377 0.169287i
\(223\) −20.9798 + 12.1127i −1.40491 + 0.811126i −0.994891 0.100950i \(-0.967812\pi\)
−0.410020 + 0.912076i \(0.634478\pi\)
\(224\) 0 0
\(225\) 4.64872 8.05182i 0.309915 0.536788i
\(226\) −7.61017 + 4.39373i −0.506221 + 0.292267i
\(227\) 13.3154 7.68764i 0.883773 0.510247i 0.0118726 0.999930i \(-0.496221\pi\)
0.871901 + 0.489683i \(0.162887\pi\)
\(228\) 0.319016 0.184184i 0.0211274 0.0121979i
\(229\) −14.1608 + 8.17573i −0.935771 + 0.540268i −0.888632 0.458621i \(-0.848344\pi\)
−0.0471389 + 0.998888i \(0.515010\pi\)
\(230\) 3.95302 6.84683i 0.260654 0.451467i
\(231\) 0 0
\(232\) −10.3215 + 5.95913i −0.677641 + 0.391236i
\(233\) −14.5554 25.2106i −0.953554 1.65160i −0.737643 0.675191i \(-0.764061\pi\)
−0.215911 0.976413i \(-0.569272\pi\)
\(234\) −5.39280 2.22696i −0.352538 0.145581i
\(235\) 1.59518 2.76294i 0.104058 0.180234i
\(236\) 1.84394 + 1.06460i 0.120030 + 0.0692995i
\(237\) −2.92684 5.06943i −0.190119 0.329295i
\(238\) 0 0
\(239\) 8.65409i 0.559787i −0.960031 0.279893i \(-0.909701\pi\)
0.960031 0.279893i \(-0.0902991\pi\)
\(240\) 26.2074i 1.69168i
\(241\) −15.7601 + 9.09909i −1.01520 + 0.586124i −0.912709 0.408611i \(-0.866013\pi\)
−0.102487 + 0.994734i \(0.532680\pi\)
\(242\) 10.9102 + 6.29902i 0.701336 + 0.404916i
\(243\) 11.8302 0.758905
\(244\) −0.725669 1.25690i −0.0464562 0.0804645i
\(245\) 0 0
\(246\) −11.5797 −0.738297
\(247\) 0.447846 + 3.37360i 0.0284957 + 0.214657i
\(248\) 7.59057 13.1473i 0.482002 0.834851i
\(249\) 4.76614i 0.302042i
\(250\) 6.54894 11.3431i 0.414191 0.717400i
\(251\) −7.93598 + 13.7455i −0.500915 + 0.867610i 0.499085 + 0.866553i \(0.333670\pi\)
−0.999999 + 0.00105678i \(0.999664\pi\)
\(252\) 0 0
\(253\) 1.82413 + 1.05316i 0.114682 + 0.0662117i
\(254\) 19.7968i 1.24216i
\(255\) 49.0230 + 28.3034i 3.06994 + 1.77243i
\(256\) 2.26304 + 3.91971i 0.141440 + 0.244982i
\(257\) 12.1634 21.0676i 0.758730 1.31416i −0.184769 0.982782i \(-0.559154\pi\)
0.943499 0.331376i \(-0.107513\pi\)
\(258\) −9.14900 + 5.28218i −0.569592 + 0.328854i
\(259\) 0 0
\(260\) 2.26344 + 0.934688i 0.140372 + 0.0579669i
\(261\) −2.43282 4.21376i −0.150588 0.260825i
\(262\) 15.0486i 0.929708i
\(263\) 15.4345 0.951734 0.475867 0.879517i \(-0.342134\pi\)
0.475867 + 0.879517i \(0.342134\pi\)
\(264\) −7.72409 −0.475385
\(265\) 0.285395i 0.0175317i
\(266\) 0 0
\(267\) 13.4512 + 7.76606i 0.823201 + 0.475275i
\(268\) −1.04210 + 0.601656i −0.0636563 + 0.0367520i
\(269\) −6.52035 11.2936i −0.397553 0.688582i 0.595870 0.803081i \(-0.296807\pi\)
−0.993423 + 0.114499i \(0.963474\pi\)
\(270\) 17.6822 1.07610
\(271\) −23.3572 13.4853i −1.41885 0.819174i −0.422654 0.906291i \(-0.638901\pi\)
−0.996198 + 0.0871168i \(0.972235\pi\)
\(272\) −27.7298 −1.68136
\(273\) 0 0
\(274\) −23.7174 −1.43282
\(275\) 8.55884 + 4.94145i 0.516117 + 0.297980i
\(276\) 0.642883 0.0386970
\(277\) 6.35073 + 10.9998i 0.381578 + 0.660913i 0.991288 0.131712i \(-0.0420474\pi\)
−0.609710 + 0.792625i \(0.708714\pi\)
\(278\) −6.82352 + 3.93956i −0.409248 + 0.236279i
\(279\) 5.36737 + 3.09885i 0.321336 + 0.185523i
\(280\) 0 0
\(281\) 26.7216i 1.59408i −0.603930 0.797038i \(-0.706399\pi\)
0.603930 0.797038i \(-0.293601\pi\)
\(282\) −2.46612 −0.146855
\(283\) 14.7423 0.876336 0.438168 0.898893i \(-0.355627\pi\)
0.438168 + 0.898893i \(0.355627\pi\)
\(284\) 2.17474i 0.129047i
\(285\) 3.45191 + 5.97888i 0.204473 + 0.354158i
\(286\) 2.36719 5.73238i 0.139975 0.338963i
\(287\) 0 0
\(288\) −1.11791 + 0.645425i −0.0658734 + 0.0380320i
\(289\) −21.4476 + 37.1483i −1.26162 + 2.18519i
\(290\) −9.70653 16.8122i −0.569987 0.987247i
\(291\) −0.849651 0.490546i −0.0498074 0.0287563i
\(292\) 0.144775i 0.00847230i
\(293\) 10.0312 + 5.79153i 0.586030 + 0.338345i 0.763526 0.645777i \(-0.223466\pi\)
−0.177496 + 0.984121i \(0.556800\pi\)
\(294\) 0 0
\(295\) −19.9523 + 34.5584i −1.16167 + 2.01207i
\(296\) 1.55589 2.69489i 0.0904344 0.156637i
\(297\) 4.71087i 0.273353i
\(298\) −7.04829 + 12.2080i −0.408297 + 0.707190i
\(299\) −2.26697 + 5.48968i −0.131102 + 0.317476i
\(300\) 3.01641 0.174153
\(301\) 0 0
\(302\) 3.17074 + 5.49188i 0.182455 + 0.316022i
\(303\) −5.90093 −0.339000
\(304\) −2.92885 1.69097i −0.167981 0.0969838i
\(305\) 23.5563 13.6002i 1.34883 0.778746i
\(306\) 12.5236i 0.715927i
\(307\) 29.3335i 1.67415i 0.547086 + 0.837076i \(0.315737\pi\)
−0.547086 + 0.837076i \(0.684263\pi\)
\(308\) 0 0
\(309\) −11.6191 20.1248i −0.660986 1.14486i
\(310\) 21.4149 + 12.3639i 1.21628 + 0.702222i
\(311\) 0.0753271 0.130470i 0.00427141 0.00739830i −0.863882 0.503695i \(-0.831974\pi\)
0.868153 + 0.496296i \(0.165307\pi\)
\(312\) −2.86616 21.5907i −0.162264 1.22233i
\(313\) −5.26057 9.11157i −0.297345 0.515016i 0.678183 0.734893i \(-0.262768\pi\)
−0.975528 + 0.219877i \(0.929434\pi\)
\(314\) 10.4874 6.05493i 0.591841 0.341699i
\(315\) 0 0
\(316\) 0.271777 0.470732i 0.0152887 0.0264808i
\(317\) −1.30489 + 0.753380i −0.0732901 + 0.0423140i −0.536197 0.844093i \(-0.680140\pi\)
0.462907 + 0.886407i \(0.346806\pi\)
\(318\) −0.191051 + 0.110303i −0.0107136 + 0.00618551i
\(319\) 4.47910 2.58601i 0.250782 0.144789i
\(320\) −26.6018 + 15.3586i −1.48709 + 0.858571i
\(321\) −6.73671 + 11.6683i −0.376006 + 0.651262i
\(322\) 0 0
\(323\) −6.32619 + 3.65243i −0.351999 + 0.203227i
\(324\) 1.06241 + 1.84015i 0.0590228 + 0.102231i
\(325\) −10.6366 + 25.7576i −0.590014 + 1.42878i
\(326\) −8.09314 + 14.0177i −0.448237 + 0.776370i
\(327\) −10.3671 5.98542i −0.573299 0.330995i
\(328\) −6.18600 10.7145i −0.341565 0.591607i
\(329\) 0 0
\(330\) 12.5814i 0.692582i
\(331\) 25.2509i 1.38791i −0.720017 0.693957i \(-0.755866\pi\)
0.720017 0.693957i \(-0.244134\pi\)
\(332\) −0.383276 + 0.221284i −0.0210350 + 0.0121446i
\(333\) 1.10019 + 0.635193i 0.0602899 + 0.0348084i
\(334\) 26.1270 1.42960
\(335\) −11.2760 19.5306i −0.616075 1.06707i
\(336\) 0 0
\(337\) 32.1811 1.75302 0.876509 0.481386i \(-0.159866\pi\)
0.876509 + 0.481386i \(0.159866\pi\)
\(338\) 16.9018 + 4.48977i 0.919335 + 0.244211i
\(339\) 6.69598 11.5978i 0.363676 0.629905i
\(340\) 5.25634i 0.285065i
\(341\) −3.29398 + 5.70535i −0.178379 + 0.308962i
\(342\) 0.763694 1.32276i 0.0412959 0.0715265i
\(343\) 0 0
\(344\) −9.77495 5.64357i −0.527030 0.304281i
\(345\) 12.0487i 0.648679i
\(346\) 16.7521 + 9.67185i 0.900600 + 0.519962i
\(347\) −12.3819 21.4461i −0.664695 1.15128i −0.979368 0.202085i \(-0.935228\pi\)
0.314673 0.949200i \(-0.398105\pi\)
\(348\) 0.789291 1.36709i 0.0423104 0.0732838i
\(349\) 10.0075 5.77782i 0.535688 0.309280i −0.207642 0.978205i \(-0.566579\pi\)
0.743330 + 0.668925i \(0.233245\pi\)
\(350\) 0 0
\(351\) −13.1680 + 1.74805i −0.702857 + 0.0933042i
\(352\) −0.686067 1.18830i −0.0365675 0.0633368i
\(353\) 20.0884i 1.06920i −0.845106 0.534599i \(-0.820463\pi\)
0.845106 0.534599i \(-0.179537\pi\)
\(354\) 30.8459 1.63944
\(355\) 40.7582 2.16322
\(356\) 1.44227i 0.0764399i
\(357\) 0 0
\(358\) −6.32136 3.64964i −0.334094 0.192890i
\(359\) −13.0346 + 7.52551i −0.687938 + 0.397181i −0.802839 0.596196i \(-0.796678\pi\)
0.114901 + 0.993377i \(0.463345\pi\)
\(360\) −6.32292 10.9516i −0.333247 0.577201i
\(361\) 18.1091 0.953110
\(362\) 18.0461 + 10.4189i 0.948481 + 0.547606i
\(363\) −19.1992 −1.00770
\(364\) 0 0
\(365\) 2.71331 0.142021
\(366\) −18.2087 10.5128i −0.951787 0.549514i
\(367\) −9.00355 −0.469982 −0.234991 0.971998i \(-0.575506\pi\)
−0.234991 + 0.971998i \(0.575506\pi\)
\(368\) −2.95112 5.11148i −0.153838 0.266454i
\(369\) 4.37418 2.52543i 0.227711 0.131469i
\(370\) 4.38956 + 2.53431i 0.228202 + 0.131753i
\(371\) 0 0
\(372\) 2.01075i 0.104253i
\(373\) −16.1391 −0.835649 −0.417824 0.908528i \(-0.637207\pi\)
−0.417824 + 0.908528i \(0.637207\pi\)
\(374\) 13.3122 0.688358
\(375\) 19.9610i 1.03078i
\(376\) −1.31742 2.28184i −0.0679409 0.117677i
\(377\) 8.89057 + 11.5606i 0.457888 + 0.595400i
\(378\) 0 0
\(379\) −13.5668 + 7.83277i −0.696878 + 0.402342i −0.806183 0.591666i \(-0.798471\pi\)
0.109306 + 0.994008i \(0.465137\pi\)
\(380\) −0.320534 + 0.555181i −0.0164430 + 0.0284802i
\(381\) −15.0850 26.1280i −0.772829 1.33858i
\(382\) 5.52935 + 3.19237i 0.282906 + 0.163336i
\(383\) 24.6328i 1.25868i −0.777131 0.629339i \(-0.783326\pi\)
0.777131 0.629339i \(-0.216674\pi\)
\(384\) 16.7525 + 9.67207i 0.854898 + 0.493576i
\(385\) 0 0
\(386\) 14.1512 24.5106i 0.720277 1.24756i
\(387\) 2.30399 3.99062i 0.117118 0.202855i
\(388\) 0.0911013i 0.00462497i
\(389\) −9.42834 + 16.3304i −0.478036 + 0.827982i −0.999683 0.0251791i \(-0.991984\pi\)
0.521647 + 0.853161i \(0.325318\pi\)
\(390\) 35.1680 4.66854i 1.78080 0.236401i
\(391\) −12.7486 −0.644724
\(392\) 0 0
\(393\) −11.4669 19.8613i −0.578431 1.00187i
\(394\) 7.81857 0.393894
\(395\) 8.82229 + 5.09355i 0.443897 + 0.256284i
\(396\) 0.253582 0.146406i 0.0127430 0.00735716i
\(397\) 14.5030i 0.727884i 0.931422 + 0.363942i \(0.118569\pi\)
−0.931422 + 0.363942i \(0.881431\pi\)
\(398\) 14.2839i 0.715985i
\(399\) 0 0
\(400\) −13.8467 23.9831i −0.692333 1.19916i
\(401\) 18.1770 + 10.4945i 0.907714 + 0.524069i 0.879695 0.475539i \(-0.157747\pi\)
0.0280189 + 0.999607i \(0.491080\pi\)
\(402\) −8.71624 + 15.0970i −0.434727 + 0.752968i
\(403\) −17.1701 7.09041i −0.855304 0.353198i
\(404\) −0.273971 0.474532i −0.0136306 0.0236089i
\(405\) −34.4874 + 19.9113i −1.71369 + 0.989401i
\(406\) 0 0
\(407\) −0.675191 + 1.16947i −0.0334680 + 0.0579683i
\(408\) 40.4869 23.3751i 2.00440 1.15724i
\(409\) 18.5568 10.7138i 0.917576 0.529763i 0.0347148 0.999397i \(-0.488948\pi\)
0.882861 + 0.469635i \(0.155614\pi\)
\(410\) 17.4522 10.0761i 0.861905 0.497621i
\(411\) 31.3025 18.0725i 1.54404 0.891451i
\(412\) 1.07891 1.86873i 0.0531542 0.0920657i
\(413\) 0 0
\(414\) 2.30850 1.33281i 0.113457 0.0655043i
\(415\) −4.14723 7.18321i −0.203580 0.352610i
\(416\) 3.06702 2.35866i 0.150373 0.115643i
\(417\) 6.00383 10.3989i 0.294009 0.509238i
\(418\) 1.40605 + 0.811784i 0.0687722 + 0.0397056i
\(419\) 3.98203 + 6.89708i 0.194535 + 0.336944i 0.946748 0.321976i \(-0.104347\pi\)
−0.752213 + 0.658920i \(0.771014\pi\)
\(420\) 0 0
\(421\) 2.81786i 0.137334i 0.997640 + 0.0686670i \(0.0218746\pi\)
−0.997640 + 0.0686670i \(0.978125\pi\)
\(422\) 6.27614i 0.305518i
\(423\) 0.931562 0.537838i 0.0452941 0.0261506i
\(424\) −0.204122 0.117850i −0.00991306 0.00572331i
\(425\) −59.8165 −2.90152
\(426\) −15.7528 27.2847i −0.763227 1.32195i
\(427\) 0 0
\(428\) −1.25110 −0.0604742
\(429\) 1.24379 + 9.36943i 0.0600508 + 0.452360i
\(430\) 9.19253 15.9219i 0.443303 0.767823i
\(431\) 5.73626i 0.276306i −0.990411 0.138153i \(-0.955883\pi\)
0.990411 0.138153i \(-0.0441166\pi\)
\(432\) 6.60028 11.4320i 0.317556 0.550023i
\(433\) 12.2628 21.2398i 0.589314 1.02072i −0.405009 0.914313i \(-0.632732\pi\)
0.994322 0.106409i \(-0.0339351\pi\)
\(434\) 0 0
\(435\) 25.6215 + 14.7926i 1.22846 + 0.709251i
\(436\) 1.11158i 0.0532349i
\(437\) −1.34652 0.777413i −0.0644128 0.0371887i
\(438\) −1.04868 1.81637i −0.0501079 0.0867895i
\(439\) −18.3211 + 31.7332i −0.874420 + 1.51454i −0.0170416 + 0.999855i \(0.505425\pi\)
−0.857379 + 0.514686i \(0.827909\pi\)
\(440\) 11.6412 6.72108i 0.554975 0.320415i
\(441\) 0 0
\(442\) 4.93973 + 37.2108i 0.234959 + 1.76994i
\(443\) −13.5467 23.4635i −0.643622 1.11479i −0.984618 0.174721i \(-0.944098\pi\)
0.340996 0.940065i \(-0.389236\pi\)
\(444\) 0.412158i 0.0195602i
\(445\) −27.0304 −1.28136
\(446\) −32.5886 −1.54312
\(447\) 21.4830i 1.01611i
\(448\) 0 0
\(449\) 23.7571 + 13.7162i 1.12117 + 0.647307i 0.941699 0.336456i \(-0.109228\pi\)
0.179470 + 0.983764i \(0.442562\pi\)
\(450\) 10.8315 6.25358i 0.510602 0.294796i
\(451\) 2.68446 + 4.64962i 0.126406 + 0.218942i
\(452\) 1.24354 0.0584911
\(453\) −8.36953 4.83215i −0.393235 0.227034i
\(454\) 20.6832 0.970712
\(455\) 0 0
\(456\) 5.70169 0.267006
\(457\) −34.3500 19.8320i −1.60682 0.927700i −0.990075 0.140539i \(-0.955116\pi\)
−0.616748 0.787161i \(-0.711550\pi\)
\(458\) −21.9964 −1.02783
\(459\) −14.2563 24.6927i −0.665429 1.15256i
\(460\) −0.968913 + 0.559402i −0.0451758 + 0.0260823i
\(461\) 4.23988 + 2.44790i 0.197471 + 0.114010i 0.595475 0.803374i \(-0.296964\pi\)
−0.398004 + 0.917384i \(0.630297\pi\)
\(462\) 0 0
\(463\) 4.71193i 0.218982i −0.993988 0.109491i \(-0.965078\pi\)
0.993988 0.109491i \(-0.0349221\pi\)
\(464\) −14.4928 −0.672810
\(465\) −37.6848 −1.74759
\(466\) 39.1605i 1.81408i
\(467\) −16.0081 27.7268i −0.740765 1.28304i −0.952147 0.305639i \(-0.901130\pi\)
0.211383 0.977403i \(-0.432203\pi\)
\(468\) 0.503335 + 0.654496i 0.0232667 + 0.0302541i
\(469\) 0 0
\(470\) 3.71678 2.14588i 0.171442 0.0989822i
\(471\) −9.22761 + 15.9827i −0.425186 + 0.736444i
\(472\) 16.4781 + 28.5410i 0.758467 + 1.31370i
\(473\) 4.24191 + 2.44907i 0.195043 + 0.112608i
\(474\) 7.87452i 0.361689i
\(475\) −6.31788 3.64763i −0.289884 0.167365i
\(476\) 0 0
\(477\) 0.0481123 0.0833330i 0.00220291 0.00381556i
\(478\) 5.82086 10.0820i 0.266240 0.461141i
\(479\) 18.0245i 0.823560i 0.911283 + 0.411780i \(0.135093\pi\)
−0.911283 + 0.411780i \(0.864907\pi\)
\(480\) 3.92447 6.79738i 0.179127 0.310257i
\(481\) −3.51948 1.45337i −0.160474 0.0662680i
\(482\) −24.4807 −1.11506
\(483\) 0 0
\(484\) −0.891390 1.54393i −0.0405177 0.0701788i
\(485\) 1.70739 0.0775284
\(486\) 13.7821 + 7.95712i 0.625170 + 0.360942i
\(487\) −15.2424 + 8.80020i −0.690699 + 0.398775i −0.803874 0.594800i \(-0.797231\pi\)
0.113175 + 0.993575i \(0.463898\pi\)
\(488\) 22.4642i 1.01691i
\(489\) 24.6676i 1.11551i
\(490\) 0 0
\(491\) 1.93180 + 3.34598i 0.0871810 + 0.151002i 0.906318 0.422595i \(-0.138881\pi\)
−0.819138 + 0.573597i \(0.805547\pi\)
\(492\) 1.41914 + 0.819339i 0.0639796 + 0.0369387i
\(493\) −15.6519 + 27.1099i −0.704926 + 1.22097i
\(494\) −1.74739 + 4.23148i −0.0786188 + 0.190383i
\(495\) 2.74388 + 4.75254i 0.123328 + 0.213611i
\(496\) 15.9872 9.23023i 0.717848 0.414450i
\(497\) 0 0
\(498\) −3.20576 + 5.55255i −0.143654 + 0.248816i
\(499\) 10.9528 6.32363i 0.490317 0.283084i −0.234389 0.972143i \(-0.575309\pi\)
0.724706 + 0.689058i \(0.241976\pi\)
\(500\) −1.60519 + 0.926757i −0.0717863 + 0.0414458i
\(501\) −34.4826 + 19.9085i −1.54057 + 0.889448i
\(502\) −18.4908 + 10.6757i −0.825287 + 0.476480i
\(503\) 11.0180 19.0837i 0.491268 0.850902i −0.508681 0.860955i \(-0.669867\pi\)
0.999949 + 0.0100533i \(0.00320011\pi\)
\(504\) 0 0
\(505\) 8.89351 5.13467i 0.395756 0.228490i
\(506\) 1.41674 + 2.45387i 0.0629818 + 0.109088i
\(507\) −25.7283 + 6.95339i −1.14263 + 0.308811i
\(508\) 1.40075 2.42617i 0.0621482 0.107644i
\(509\) 13.5708 + 7.83509i 0.601514 + 0.347284i 0.769637 0.638482i \(-0.220437\pi\)
−0.168123 + 0.985766i \(0.553771\pi\)
\(510\) 38.0745 + 65.9470i 1.68597 + 2.92018i
\(511\) 0 0
\(512\) 24.9600i 1.10309i
\(513\) 3.47743i 0.153532i
\(514\) 28.3406 16.3625i 1.25005 0.721718i
\(515\) 35.0230 + 20.2206i 1.54330 + 0.891025i
\(516\) 1.49499 0.0658132
\(517\) 0.571705 + 0.990222i 0.0251436 + 0.0435499i
\(518\) 0 0
\(519\) −29.4795 −1.29401
\(520\) 23.1067 + 30.0461i 1.01330 + 1.31761i
\(521\) −12.6207 + 21.8598i −0.552925 + 0.957694i 0.445137 + 0.895463i \(0.353155\pi\)
−0.998062 + 0.0622317i \(0.980178\pi\)
\(522\) 6.54538i 0.286483i
\(523\) −6.62383 + 11.4728i −0.289640 + 0.501671i −0.973724 0.227733i \(-0.926869\pi\)
0.684084 + 0.729403i \(0.260202\pi\)
\(524\) 1.06479 1.84426i 0.0465154 0.0805670i
\(525\) 0 0
\(526\) 17.9812 + 10.3815i 0.784019 + 0.452654i
\(527\) 39.8738i 1.73693i
\(528\) −8.13422 4.69629i −0.353996 0.204380i
\(529\) 10.1432 + 17.5686i 0.441011 + 0.763853i
\(530\) 0.191960 0.332485i 0.00833822 0.0144422i
\(531\) −11.6518 + 6.72720i −0.505647 + 0.291935i
\(532\) 0 0
\(533\) −12.0007 + 9.22903i −0.519807 + 0.399754i
\(534\) 10.4471 + 18.0949i 0.452091 + 0.783044i
\(535\) 23.4477i 1.01373i
\(536\) −18.6252 −0.804485
\(537\) 11.1240 0.480036
\(538\) 17.5427i 0.756320i
\(539\) 0 0
\(540\) −2.16701 1.25112i −0.0932532 0.0538398i
\(541\) 12.4737 7.20170i 0.536287 0.309625i −0.207286 0.978280i \(-0.566463\pi\)
0.743573 + 0.668655i \(0.233130\pi\)
\(542\) −18.1408 31.4208i −0.779214 1.34964i
\(543\) −31.7565 −1.36280
\(544\) 7.19224 + 4.15244i 0.308365 + 0.178034i
\(545\) 20.8328 0.892377
\(546\) 0 0
\(547\) 2.00679 0.0858042 0.0429021 0.999079i \(-0.486340\pi\)
0.0429021 + 0.999079i \(0.486340\pi\)
\(548\) 2.90665 + 1.67816i 0.124166 + 0.0716873i
\(549\) 9.17100 0.391409
\(550\) 6.64736 + 11.5136i 0.283445 + 0.490940i
\(551\) −3.30634 + 1.90892i −0.140855 + 0.0813226i
\(552\) 8.61757 + 4.97535i 0.366788 + 0.211765i
\(553\) 0 0
\(554\) 17.0863i 0.725928i
\(555\) −7.72451 −0.327887
\(556\) 1.11499 0.0472863
\(557\) 8.57916i 0.363511i 0.983344 + 0.181755i \(0.0581779\pi\)
−0.983344 + 0.181755i \(0.941822\pi\)
\(558\) 4.16865 + 7.22032i 0.176473 + 0.305661i
\(559\) −5.27170 + 12.7659i −0.222969 + 0.539942i
\(560\) 0 0
\(561\) −17.5696 + 10.1438i −0.741788 + 0.428272i
\(562\) 17.9733 31.1306i 0.758157 1.31317i
\(563\) 6.38718 + 11.0629i 0.269188 + 0.466247i 0.968652 0.248421i \(-0.0799115\pi\)
−0.699465 + 0.714667i \(0.746578\pi\)
\(564\) 0.302231 + 0.174493i 0.0127262 + 0.00734750i
\(565\) 23.3059i 0.980487i
\(566\) 17.1747 + 9.91583i 0.721908 + 0.416794i
\(567\) 0 0
\(568\) 16.8306 29.1515i 0.706196 1.22317i
\(569\) −2.89558 + 5.01530i −0.121389 + 0.210252i −0.920316 0.391176i \(-0.872068\pi\)
0.798927 + 0.601429i \(0.205402\pi\)
\(570\) 9.28720i 0.388998i
\(571\) −22.0666 + 38.2204i −0.923458 + 1.59948i −0.129435 + 0.991588i \(0.541316\pi\)
−0.794023 + 0.607888i \(0.792017\pi\)
\(572\) −0.695710 + 0.535030i −0.0290891 + 0.0223707i
\(573\) −9.73025 −0.406487
\(574\) 0 0
\(575\) −6.36592 11.0261i −0.265477 0.459820i
\(576\) −10.3567 −0.431529
\(577\) 10.3343 + 5.96649i 0.430221 + 0.248388i 0.699441 0.714691i \(-0.253432\pi\)
−0.269220 + 0.963079i \(0.586766\pi\)
\(578\) −49.9729 + 28.8518i −2.07860 + 1.20008i
\(579\) 43.1324i 1.79252i
\(580\) 2.74719i 0.114071i
\(581\) 0 0
\(582\) −0.659895 1.14297i −0.0273535 0.0473777i
\(583\) 0.0885805 + 0.0511420i 0.00366863 + 0.00211808i
\(584\) 1.12043 1.94064i 0.0463637 0.0803043i
\(585\) −12.2663 + 9.43332i −0.507150 + 0.390020i
\(586\) 7.79091 + 13.4943i 0.321840 + 0.557443i
\(587\) −17.6250 + 10.1758i −0.727462 + 0.420000i −0.817493 0.575939i \(-0.804637\pi\)
0.0900312 + 0.995939i \(0.471303\pi\)
\(588\) 0 0
\(589\) 2.43152 4.21152i 0.100189 0.173533i
\(590\) −46.4889 + 26.8404i −1.91392 + 1.10500i
\(591\) −10.3190 + 5.95769i −0.424468 + 0.245067i
\(592\) 3.27701 1.89199i 0.134684 0.0777601i
\(593\) 15.7443 9.09000i 0.646543 0.373282i −0.140588 0.990068i \(-0.544899\pi\)
0.787130 + 0.616787i \(0.211566\pi\)
\(594\) −3.16859 + 5.48817i −0.130009 + 0.225182i
\(595\) 0 0
\(596\) 1.72759 0.997422i 0.0707646 0.0408560i
\(597\) 10.8842 + 18.8520i 0.445460 + 0.771560i
\(598\) −6.33344 + 4.87068i −0.258994 + 0.199177i
\(599\) 19.1341 33.1412i 0.781797 1.35411i −0.149096 0.988823i \(-0.547636\pi\)
0.930894 0.365290i \(-0.119030\pi\)
\(600\) 40.4337 + 23.3444i 1.65070 + 0.953031i
\(601\) −13.4360 23.2718i −0.548064 0.949275i −0.998407 0.0564195i \(-0.982032\pi\)
0.450343 0.892856i \(-0.351302\pi\)
\(602\) 0 0
\(603\) 7.60372i 0.309648i
\(604\) 0.897398i 0.0365146i
\(605\) 28.9358 16.7061i 1.17641 0.679200i
\(606\) −6.87459 3.96904i −0.279261 0.161231i
\(607\) 9.40209 0.381619 0.190810 0.981627i \(-0.438889\pi\)
0.190810 + 0.981627i \(0.438889\pi\)
\(608\) 0.506435 + 0.877171i 0.0205386 + 0.0355740i
\(609\) 0 0
\(610\) 36.5908 1.48152
\(611\) −2.55577 + 1.96549i −0.103395 + 0.0795153i
\(612\) −0.886124 + 1.53481i −0.0358194 + 0.0620411i
\(613\) 13.2894i 0.536753i −0.963314 0.268376i \(-0.913513\pi\)
0.963314 0.268376i \(-0.0864871\pi\)
\(614\) −19.7301 + 34.1735i −0.796242 + 1.37913i
\(615\) −15.3557 + 26.5969i −0.619204 + 1.07249i
\(616\) 0 0
\(617\) −9.72211 5.61306i −0.391397 0.225973i 0.291368 0.956611i \(-0.405890\pi\)
−0.682765 + 0.730638i \(0.739223\pi\)
\(618\) 31.2606i 1.25748i
\(619\) −8.04109 4.64253i −0.323199 0.186599i 0.329619 0.944114i \(-0.393080\pi\)
−0.652817 + 0.757515i \(0.726413\pi\)
\(620\) −1.74965 3.03048i −0.0702675 0.121707i
\(621\) 3.03444 5.25580i 0.121768 0.210908i
\(622\) 0.175512 0.101332i 0.00703740 0.00406304i
\(623\) 0 0
\(624\) 10.1089 24.4797i 0.404681 0.979974i
\(625\) 1.95363 + 3.38379i 0.0781452 + 0.135351i
\(626\) 14.1533i 0.565680i
\(627\) −2.47429 −0.0988137
\(628\) −1.71370 −0.0683839
\(629\) 8.17322i 0.325888i
\(630\) 0 0
\(631\) 9.00894 + 5.20132i 0.358640 + 0.207061i 0.668484 0.743726i \(-0.266943\pi\)
−0.309844 + 0.950787i \(0.600277\pi\)
\(632\) 7.28611 4.20664i 0.289826 0.167331i
\(633\) −4.78237 8.28331i −0.190082 0.329232i
\(634\) −2.02693 −0.0804998
\(635\) 45.4704 + 26.2523i 1.80444 + 1.04179i
\(636\) 0.0312187 0.00123790
\(637\) 0 0
\(638\) 6.95754 0.275452
\(639\) 11.9011 + 6.87109i 0.470800 + 0.271816i
\(640\) −33.6644 −1.33070
\(641\) 7.42955 + 12.8684i 0.293449 + 0.508269i 0.974623 0.223853i \(-0.0718634\pi\)
−0.681174 + 0.732122i \(0.738530\pi\)
\(642\) −15.6965 + 9.06239i −0.619492 + 0.357664i
\(643\) −1.98945 1.14861i −0.0784563 0.0452968i 0.460259 0.887785i \(-0.347757\pi\)
−0.538715 + 0.842488i \(0.681090\pi\)
\(644\) 0 0
\(645\) 28.0185i 1.10323i
\(646\) −9.82669 −0.386626
\(647\) 7.99865 0.314459 0.157230 0.987562i \(-0.449744\pi\)
0.157230 + 0.987562i \(0.449744\pi\)
\(648\) 32.8885i 1.29198i
\(649\) −7.15081 12.3856i −0.280694 0.486176i
\(650\) −29.7166 + 22.8533i −1.16558 + 0.896380i
\(651\) 0 0
\(652\) 1.98368 1.14528i 0.0776871 0.0448526i
\(653\) −1.99222 + 3.45062i −0.0779615 + 0.135033i −0.902370 0.430962i \(-0.858174\pi\)
0.824409 + 0.565995i \(0.191508\pi\)
\(654\) −8.05175 13.9460i −0.314848 0.545333i
\(655\) 34.5645 + 19.9558i 1.35055 + 0.779738i
\(656\) 15.0445i 0.587389i
\(657\) 0.792267 + 0.457415i 0.0309093 + 0.0178455i
\(658\) 0 0
\(659\) 13.7501 23.8159i 0.535629 0.927737i −0.463504 0.886095i \(-0.653408\pi\)
0.999133 0.0416417i \(-0.0132588\pi\)
\(660\) −0.890211 + 1.54189i −0.0346514 + 0.0600180i
\(661\) 6.98621i 0.271732i 0.990727 + 0.135866i \(0.0433817\pi\)
−0.990727 + 0.135866i \(0.956618\pi\)
\(662\) 16.9841 29.4173i 0.660105 1.14333i
\(663\) −34.8739 45.3472i −1.35439 1.76114i
\(664\) −6.85019 −0.265839
\(665\) 0 0
\(666\) 0.854479 + 1.48000i 0.0331104 + 0.0573488i
\(667\) −6.66296 −0.257991
\(668\) −3.20195 1.84865i −0.123887 0.0715263i
\(669\) 43.0108 24.8323i 1.66289 0.960071i
\(670\) 30.3376i 1.17204i
\(671\) 9.74849i 0.376336i
\(672\) 0 0
\(673\) 2.72783 + 4.72474i 0.105150 + 0.182125i 0.913800 0.406166i \(-0.133134\pi\)
−0.808649 + 0.588291i \(0.799801\pi\)
\(674\) 37.4910 + 21.6455i 1.44410 + 0.833752i
\(675\) 14.2376 24.6603i 0.548006 0.949174i
\(676\) −1.75369 1.74614i −0.0674497 0.0671594i
\(677\) 16.8961 + 29.2649i 0.649371 + 1.12474i 0.983273 + 0.182135i \(0.0583009\pi\)
−0.333903 + 0.942607i \(0.608366\pi\)
\(678\) 15.6016 9.00761i 0.599177 0.345935i
\(679\) 0 0
\(680\) −40.6795 + 70.4590i −1.55999 + 2.70198i
\(681\) −27.2979 + 15.7605i −1.04606 + 0.603942i
\(682\) −7.67498 + 4.43115i −0.293890 + 0.169678i
\(683\) −10.6511 + 6.14942i −0.407553 + 0.235301i −0.689738 0.724059i \(-0.742274\pi\)
0.282185 + 0.959360i \(0.408941\pi\)
\(684\) −0.187187 + 0.108072i −0.00715726 + 0.00413225i
\(685\) −31.4514 + 54.4754i −1.20170 + 2.08140i
\(686\) 0 0
\(687\) 29.0311 16.7611i 1.10760 0.639476i
\(688\) −6.86265 11.8865i −0.261636 0.453167i
\(689\) −0.110085 + 0.266581i −0.00419389 + 0.0101559i
\(690\) −8.10410 + 14.0367i −0.308518 + 0.534369i
\(691\) −9.60393 5.54483i −0.365351 0.210935i 0.306075 0.952008i \(-0.400984\pi\)
−0.671425 + 0.741072i \(0.734318\pi\)
\(692\) −1.36869 2.37064i −0.0520297 0.0901181i
\(693\) 0 0
\(694\) 33.3129i 1.26454i
\(695\) 20.8968i 0.792662i
\(696\) 21.1602 12.2168i 0.802075 0.463078i
\(697\) −28.1419 16.2478i −1.06595 0.615428i
\(698\) 15.5449 0.588385
\(699\) 29.8400 + 51.6844i 1.12865 + 1.95488i
\(700\) 0 0
\(701\) 10.6470 0.402133 0.201066 0.979578i \(-0.435559\pi\)
0.201066 + 0.979578i \(0.435559\pi\)
\(702\) −16.5165 6.82050i −0.623375 0.257423i
\(703\) 0.498406 0.863265i 0.0187977 0.0325587i
\(704\) 11.0089i 0.414912i
\(705\) −3.27029 + 5.66431i −0.123166 + 0.213330i
\(706\) 13.5117 23.4030i 0.508521 0.880784i
\(707\) 0 0
\(708\) −3.78027 2.18254i −0.142071 0.0820248i
\(709\) 40.7069i 1.52878i 0.644754 + 0.764391i \(0.276960\pi\)
−0.644754 + 0.764391i \(0.723040\pi\)
\(710\) 47.4833 + 27.4145i 1.78202 + 1.02885i
\(711\) 1.71736 + 2.97455i 0.0644060 + 0.111554i
\(712\) −11.1619 + 19.3329i −0.418309 + 0.724532i
\(713\) 7.35003 4.24354i 0.275261 0.158922i
\(714\) 0 0
\(715\) −10.0273 13.0387i −0.375001 0.487621i
\(716\) 0.516470 + 0.894552i 0.0193014 + 0.0334310i
\(717\) 17.7418i 0.662579i
\(718\) −20.2470 −0.755612
\(719\) −9.77537 −0.364560 −0.182280 0.983247i \(-0.558348\pi\)
−0.182280 + 0.983247i \(0.558348\pi\)
\(720\) 15.3775i 0.573086i
\(721\) 0 0
\(722\) 21.0971 + 12.1804i 0.785153 + 0.453308i
\(723\) 32.3098 18.6541i 1.20161 0.693752i
\(724\) −1.47441 2.55375i −0.0547959 0.0949092i
\(725\) −31.2627 −1.16107
\(726\) −22.3671 12.9136i −0.830120 0.479270i
\(727\) 12.2091 0.452811 0.226406 0.974033i \(-0.427303\pi\)
0.226406 + 0.974033i \(0.427303\pi\)
\(728\) 0 0
\(729\) 9.23219 0.341933
\(730\) 3.16101 + 1.82501i 0.116994 + 0.0675467i
\(731\) −29.6461 −1.09650
\(732\) 1.48770 + 2.57677i 0.0549869 + 0.0952400i
\(733\) −19.3256 + 11.1577i −0.713809 + 0.412118i −0.812470 0.583003i \(-0.801877\pi\)
0.0986608 + 0.995121i \(0.468544\pi\)
\(734\) −10.4891 6.05591i −0.387161 0.223528i
\(735\) 0 0
\(736\) 1.76768i 0.0651576i
\(737\) 8.08253 0.297724
\(738\) 6.79456 0.250111
\(739\) 42.3729i 1.55871i 0.626580 + 0.779357i \(0.284454\pi\)
−0.626580 + 0.779357i \(0.715546\pi\)
\(740\) −0.358637 0.621178i −0.0131838 0.0228350i
\(741\) −0.918130 6.91624i −0.0337283 0.254074i
\(742\) 0 0
\(743\) −26.8296 + 15.4901i −0.984282 + 0.568276i −0.903560 0.428461i \(-0.859056\pi\)
−0.0807220 + 0.996737i \(0.525723\pi\)
\(744\) −15.5615 + 26.9532i −0.570511 + 0.988153i
\(745\) 18.6933 + 32.3778i 0.684870 + 1.18623i
\(746\) −18.8020 10.8553i −0.688390 0.397442i
\(747\) 2.79659i 0.102322i
\(748\) −1.63146 0.941923i −0.0596520 0.0344401i
\(749\) 0 0
\(750\) −13.4260 + 23.2545i −0.490248 + 0.849135i
\(751\) 11.2830 19.5427i 0.411722 0.713123i −0.583356 0.812216i \(-0.698261\pi\)
0.995078 + 0.0990930i \(0.0315941\pi\)
\(752\) 3.20400i 0.116838i
\(753\) 16.2696 28.1798i 0.592897 1.02693i
\(754\) 2.58172 + 19.4480i 0.0940206 + 0.708254i
\(755\) 16.8187 0.612095
\(756\) 0 0
\(757\) −16.1404 27.9560i −0.586633 1.01608i −0.994670 0.103112i \(-0.967120\pi\)
0.408037 0.912965i \(-0.366213\pi\)
\(758\) −21.0737 −0.765431
\(759\) −3.73966 2.15909i −0.135741 0.0783701i
\(760\) −8.59323 + 4.96130i −0.311709 + 0.179965i
\(761\) 29.7517i 1.07850i 0.842147 + 0.539249i \(0.181292\pi\)
−0.842147 + 0.539249i \(0.818708\pi\)
\(762\) 40.5855i 1.47026i
\(763\) 0 0
\(764\) −0.451761 0.782473i −0.0163441 0.0283089i
\(765\) −28.7649 16.6074i −1.04000 0.600442i
\(766\) 16.5684 28.6972i 0.598639 1.03687i
\(767\) 31.9672 24.5841i 1.15427 0.887680i
\(768\) −4.63947 8.03581i −0.167413 0.289967i
\(769\) 36.2090 20.9053i 1.30573 0.753863i 0.324349 0.945938i \(-0.394855\pi\)
0.981380 + 0.192075i \(0.0615215\pi\)
\(770\) 0 0
\(771\) −24.9361 + 43.1907i −0.898053 + 1.55547i
\(772\) −3.46856 + 2.00257i −0.124836 + 0.0720742i
\(773\) −35.8826 + 20.7168i −1.29061 + 0.745132i −0.978762 0.205001i \(-0.934280\pi\)
−0.311845 + 0.950133i \(0.600947\pi\)
\(774\) 5.36829 3.09938i 0.192959 0.111405i
\(775\) 34.4864 19.9107i 1.23879 0.715215i
\(776\) 0.705044 1.22117i 0.0253096 0.0438375i
\(777\) 0 0
\(778\) −21.9680 + 12.6832i −0.787592 + 0.454716i
\(779\) −1.98159 3.43221i −0.0709978 0.122972i
\(780\) −4.64028 1.91621i −0.166149 0.0686112i
\(781\) −7.30376 + 12.6505i −0.261349 + 0.452670i
\(782\) −14.8521 8.57486i −0.531110 0.306637i
\(783\) −7.45098 12.9055i −0.266276 0.461204i
\(784\) 0 0
\(785\) 32.1175i 1.14632i
\(786\) 30.8513i 1.10043i
\(787\) −20.6657 + 11.9313i −0.736651 + 0.425306i −0.820851 0.571143i \(-0.806500\pi\)
0.0841992 + 0.996449i \(0.473167\pi\)
\(788\) −0.958193 0.553213i −0.0341342 0.0197074i
\(789\) −31.6424 −1.12650
\(790\) 6.85198 + 11.8680i 0.243782 + 0.422243i
\(791\) 0 0
\(792\) 4.53221 0.161045
\(793\) −27.2494 + 3.61735i −0.967654 + 0.128456i
\(794\) −9.75490 + 16.8960i −0.346188 + 0.599616i
\(795\) 0.585088i 0.0207509i
\(796\) −1.01067 + 1.75054i −0.0358223 + 0.0620461i
\(797\) −25.4115 + 44.0141i −0.900123 + 1.55906i −0.0727899 + 0.997347i \(0.523190\pi\)
−0.827333 + 0.561712i \(0.810143\pi\)
\(798\) 0 0
\(799\) −5.99335 3.46026i −0.212029 0.122415i
\(800\) 8.29397i 0.293236i
\(801\) −7.89267 4.55683i −0.278874 0.161008i
\(802\) 14.1174 + 24.4521i 0.498504 + 0.863434i
\(803\) −0.486219 + 0.842156i −0.0171583 + 0.0297190i
\(804\) 2.13641 1.23346i 0.0753454 0.0435007i
\(805\) 0 0
\(806\) −15.2341 19.8092i −0.536598 0.697748i
\(807\) 13.3674 + 23.1530i 0.470555 + 0.815025i
\(808\) 8.48119i 0.298367i
\(809\) 4.41176 0.155109 0.0775547 0.996988i \(-0.475289\pi\)
0.0775547 + 0.996988i \(0.475289\pi\)
\(810\) −53.5704 −1.88227
\(811\) 17.6493i 0.619750i 0.950777 + 0.309875i \(0.100287\pi\)
−0.950777 + 0.309875i \(0.899713\pi\)
\(812\) 0 0
\(813\) 47.8848 + 27.6463i 1.67939 + 0.969598i
\(814\) −1.57320 + 0.908285i −0.0551405 + 0.0318354i
\(815\) 21.4644 + 37.1775i 0.751866 + 1.30227i
\(816\) 56.8489 1.99011
\(817\) −3.13126 1.80783i −0.109549 0.0632480i
\(818\) 28.8249 1.00784
\(819\) 0 0
\(820\) −2.85178 −0.0995884
\(821\) 3.08342 + 1.78022i 0.107612 + 0.0621299i 0.552840 0.833287i \(-0.313544\pi\)
−0.445228 + 0.895417i \(0.646877\pi\)
\(822\) 48.6232 1.69593
\(823\) 10.9332 + 18.9369i 0.381109 + 0.660100i 0.991221 0.132215i \(-0.0422091\pi\)
−0.610112 + 0.792315i \(0.708876\pi\)
\(824\) 28.9247 16.6997i 1.00764 0.581760i
\(825\) −17.5465 10.1305i −0.610891 0.352698i
\(826\) 0 0
\(827\) 18.1361i 0.630653i −0.948983 0.315327i \(-0.897886\pi\)
0.948983 0.315327i \(-0.102114\pi\)
\(828\) −0.377220 −0.0131093
\(829\) 30.8994 1.07318 0.536590 0.843843i \(-0.319712\pi\)
0.536590 + 0.843843i \(0.319712\pi\)
\(830\) 11.1579i 0.387297i
\(831\) −13.0196 22.5507i −0.451646 0.782275i
\(832\) 30.7724 4.08504i 1.06684 0.141623i
\(833\) 0 0
\(834\) 13.9889 8.07651i 0.484397 0.279667i
\(835\) 34.6466 60.0097i 1.19900 2.07672i
\(836\) −0.114878 0.198974i −0.00397313 0.00688165i
\(837\) 16.4386 + 9.49084i 0.568202 + 0.328051i
\(838\) 10.7135i 0.370090i
\(839\) 13.3333 + 7.69796i 0.460315 + 0.265763i 0.712177 0.702000i \(-0.247709\pi\)
−0.251862 + 0.967763i \(0.581043\pi\)
\(840\) 0 0
\(841\) 6.31965 10.9459i 0.217919 0.377446i
\(842\) −1.89533 + 3.28280i −0.0653173 + 0.113133i
\(843\) 54.7820i 1.88679i
\(844\) 0.444076 0.769163i 0.0152857 0.0264757i
\(845\) 32.7256 32.8671i 1.12579 1.13066i
\(846\) 1.44703 0.0497498
\(847\) 0 0
\(848\) −0.143307 0.248216i −0.00492119 0.00852376i
\(849\) −30.2231 −1.03726
\(850\) −69.6862 40.2333i −2.39022 1.37999i
\(851\) 1.50659 0.869829i 0.0516451 0.0298173i
\(852\) 4.45845i 0.152744i
\(853\) 23.7772i 0.814116i −0.913402 0.407058i \(-0.866555\pi\)
0.913402 0.407058i \(-0.133445\pi\)
\(854\) 0 0
\(855\) −2.02545 3.50818i −0.0692690 0.119977i
\(856\) −16.7704 9.68242i −0.573202 0.330938i
\(857\) 15.0525 26.0717i 0.514184 0.890592i −0.485681 0.874136i \(-0.661428\pi\)
0.999865 0.0164561i \(-0.00523837\pi\)
\(858\) −4.85299 + 11.7520i −0.165678 + 0.401206i
\(859\) −7.56717 13.1067i −0.258188 0.447195i 0.707568 0.706645i \(-0.249792\pi\)
−0.965757 + 0.259450i \(0.916459\pi\)
\(860\) −2.25315 + 1.30086i −0.0768318 + 0.0443589i
\(861\) 0 0
\(862\) 3.85828 6.68274i 0.131414 0.227615i
\(863\) −15.8186 + 9.13287i −0.538471 + 0.310886i −0.744459 0.667668i \(-0.767293\pi\)
0.205988 + 0.978555i \(0.433959\pi\)
\(864\) −3.42382 + 1.97674i −0.116481 + 0.0672501i
\(865\) 44.4296 25.6514i 1.51065 0.872175i
\(866\) 28.5724 16.4963i 0.970929 0.560566i
\(867\) 43.9697 76.1578i 1.49329 2.58646i
\(868\) 0 0
\(869\) −3.16186 + 1.82550i −0.107259 + 0.0619259i
\(870\) 19.8994 + 34.4668i 0.674653 + 1.16853i
\(871\) 2.99917 + 22.5926i 0.101623 + 0.765521i
\(872\) 8.60263 14.9002i 0.291322 0.504584i
\(873\) 0.498543 + 0.287834i 0.0168731 + 0.00974171i
\(874\) −1.04580 1.81137i −0.0353746 0.0612706i
\(875\) 0 0
\(876\) 0.296803i 0.0100281i
\(877\) 6.99639i 0.236251i −0.992999 0.118126i \(-0.962311\pi\)
0.992999 0.118126i \(-0.0376886\pi\)
\(878\) −42.6883 + 24.6461i −1.44066 + 0.831765i
\(879\) −20.5650 11.8732i −0.693641 0.400474i
\(880\) 16.3458 0.551018
\(881\) −12.8873 22.3215i −0.434184 0.752029i 0.563045 0.826427i \(-0.309630\pi\)
−0.997229 + 0.0743977i \(0.976297\pi\)
\(882\) 0 0
\(883\) −16.4526 −0.553674 −0.276837 0.960917i \(-0.589286\pi\)
−0.276837 + 0.960917i \(0.589286\pi\)
\(884\) 2.02752 4.90983i 0.0681928 0.165136i
\(885\) 40.9043 70.8484i 1.37498 2.38154i
\(886\) 36.4467i 1.22445i
\(887\) 27.6227 47.8440i 0.927481 1.60644i 0.139958 0.990157i \(-0.455303\pi\)
0.787522 0.616286i \(-0.211364\pi\)
\(888\) −3.18974 + 5.52479i −0.107041 + 0.185400i
\(889\) 0 0
\(890\) −31.4904 18.1810i −1.05556 0.609429i
\(891\) 14.2722i 0.478137i
\(892\) 3.99385 + 2.30585i 0.133724 + 0.0772056i
\(893\) −0.422016 0.730953i −0.0141222 0.0244604i
\(894\) 14.4497 25.0277i 0.483271 0.837050i
\(895\) −16.7654 + 9.67949i −0.560404 + 0.323550i
\(896\) 0 0
\(897\) 4.64751 11.2544i 0.155176 0.375774i
\(898\) 18.4514 + 31.9587i 0.615731 + 1.06648i
\(899\) 20.8398i 0.695046i
\(900\) −1.76992 −0.0589973
\(901\) −0.619076 −0.0206244
\(902\) 7.22241i 0.240480i
\(903\) 0 0
\(904\) 16.6691 + 9.62388i 0.554405 + 0.320086i
\(905\) 47.8614 27.6328i 1.59097 0.918544i
\(906\) −6.50034 11.2589i −0.215959 0.374052i
\(907\) −47.8424 −1.58858 −0.794290 0.607538i \(-0.792157\pi\)
−0.794290 + 0.607538i \(0.792157\pi\)
\(908\) −2.53480 1.46347i −0.0841204 0.0485669i
\(909\) 3.46245 0.114842
\(910\) 0 0
\(911\) −23.0711 −0.764380 −0.382190 0.924084i \(-0.624830\pi\)
−0.382190 + 0.924084i \(0.624830\pi\)
\(912\) 6.00444 + 3.46666i 0.198827 + 0.114793i
\(913\) 2.97269 0.0983817
\(914\) −26.6785 46.2085i −0.882445 1.52844i
\(915\) −48.2928 + 27.8819i −1.59651 + 0.921746i
\(916\) 2.69574 + 1.55638i 0.0890697 + 0.0514244i
\(917\) 0 0
\(918\) 38.3560i 1.26594i
\(919\) −43.4368 −1.43285 −0.716424 0.697665i \(-0.754222\pi\)
−0.716424 + 0.697665i \(0.754222\pi\)
\(920\) −17.3171 −0.570929
\(921\) 60.1367i 1.98157i
\(922\) 3.29298 + 5.70360i 0.108448 + 0.187838i
\(923\) −38.0714 15.7216i −1.25313 0.517482i
\(924\) 0 0
\(925\) 7.06892 4.08124i 0.232425 0.134190i
\(926\) 3.16931 5.48940i 0.104150 0.180393i
\(927\) 6.81764 + 11.8085i 0.223921 + 0.387842i
\(928\) 3.75897 + 2.17024i 0.123394 + 0.0712418i
\(929\) 12.7819i 0.419361i −0.977770 0.209680i \(-0.932758\pi\)
0.977770 0.209680i \(-0.0672424\pi\)
\(930\) −43.9027 25.3473i −1.43963 0.831169i
\(931\) 0 0
\(932\) −2.77085 + 4.79926i −0.0907623 + 0.157205i
\(933\) −0.154428 + 0.267478i −0.00505576 + 0.00875683i
\(934\) 43.0689i 1.40926i
\(935\) 17.6532 30.5762i 0.577320 0.999948i
\(936\) 1.68175 + 12.6686i 0.0549699 + 0.414086i
\(937\) −16.2533 −0.530971 −0.265486 0.964115i \(-0.585532\pi\)
−0.265486 + 0.964115i \(0.585532\pi\)
\(938\) 0 0
\(939\) 10.7847 + 18.6797i 0.351946 + 0.609588i
\(940\) −0.607339 −0.0198092
\(941\) 39.1000 + 22.5744i 1.27462 + 0.735905i 0.975855 0.218420i \(-0.0700904\pi\)
0.298770 + 0.954325i \(0.403424\pi\)
\(942\) −21.5003 + 12.4132i −0.700519 + 0.404445i
\(943\) 6.91662i 0.225236i
\(944\) 40.0752i 1.30434i
\(945\) 0 0
\(946\) 3.29455 + 5.70633i 0.107115 + 0.185529i
\(947\) 17.1956 + 9.92787i 0.558781 + 0.322612i 0.752656 0.658414i \(-0.228772\pi\)
−0.193875 + 0.981026i \(0.562106\pi\)
\(948\) −0.557172 + 0.965050i −0.0180961 + 0.0313434i
\(949\) −2.53445 1.04660i −0.0822716 0.0339741i
\(950\) −4.90689 8.49898i −0.159200 0.275743i
\(951\) 2.67516 1.54451i 0.0867482 0.0500841i
\(952\) 0 0
\(953\) 7.86433 13.6214i 0.254751 0.441241i −0.710077 0.704124i \(-0.751340\pi\)
0.964828 + 0.262883i \(0.0846733\pi\)
\(954\) 0.112102 0.0647220i 0.00362943 0.00209545i
\(955\) 14.6648 8.46673i 0.474542 0.273977i
\(956\) −1.42673 + 0.823724i −0.0461438 + 0.0266412i
\(957\) −9.18262 + 5.30159i −0.296832 + 0.171376i
\(958\) −12.1235 + 20.9985i −0.391693 + 0.678432i
\(959\) 0 0
\(960\) 54.5365 31.4867i 1.76016 1.01623i
\(961\) −2.22744 3.85804i −0.0718529 0.124453i
\(962\) −3.12264 4.06042i −0.100678 0.130913i
\(963\) 3.95285 6.84653i 0.127379 0.220626i
\(964\) 3.00019 + 1.73216i 0.0966296 + 0.0557891i
\(965\) −37.5315 65.0064i −1.20818 2.09263i
\(966\) 0 0
\(967\) 52.1912i 1.67835i 0.543858 + 0.839177i \(0.316963\pi\)
−0.543858 + 0.839177i \(0.683037\pi\)
\(968\) 27.5943i 0.886915i
\(969\) 12.9693 7.48786i 0.416635 0.240545i
\(970\) 1.98910 + 1.14841i 0.0638663 + 0.0368732i
\(971\) 22.4584 0.720724 0.360362 0.932813i \(-0.382653\pi\)
0.360362 + 0.932813i \(0.382653\pi\)
\(972\) −1.12603 1.95035i −0.0361175 0.0625574i
\(973\) 0 0
\(974\) −23.6765 −0.758645
\(975\) 21.8062 52.8058i 0.698357 1.69114i
\(976\) 13.6584 23.6570i 0.437193 0.757241i
\(977\) 41.0345i 1.31281i 0.754409 + 0.656405i \(0.227924\pi\)
−0.754409 + 0.656405i \(0.772076\pi\)
\(978\) 16.5918 28.7378i 0.530546 0.918933i
\(979\) 4.84378 8.38967i 0.154808 0.268135i
\(980\) 0 0
\(981\) 6.08300 + 3.51202i 0.194215 + 0.112130i
\(982\) 5.19742i 0.165856i
\(983\) −23.2379 13.4164i −0.741173 0.427916i 0.0813229 0.996688i \(-0.474085\pi\)
−0.822496 + 0.568772i \(0.807419\pi\)
\(984\) 12.6819 + 21.9658i 0.404285 + 0.700243i
\(985\) 10.3681 17.9581i 0.330356 0.572193i
\(986\) −36.4689 + 21.0553i −1.16141 + 0.670539i
\(987\) 0 0
\(988\) 0.513552 0.394943i 0.0163383 0.0125648i
\(989\) −3.15506 5.46473i −0.100325 0.173768i
\(990\) 7.38228i 0.234624i
\(991\) 10.3751 0.329576 0.164788 0.986329i \(-0.447306\pi\)
0.164788 + 0.986329i \(0.447306\pi\)
\(992\) −5.52879 −0.175539
\(993\) 51.7669i 1.64277i
\(994\) 0 0
\(995\) −32.8079 18.9417i −1.04008 0.600491i
\(996\) 0.785755 0.453656i 0.0248976 0.0143746i
\(997\) −26.9549 46.6872i −0.853669 1.47860i −0.877874 0.478891i \(-0.841039\pi\)
0.0242056 0.999707i \(-0.492294\pi\)
\(998\) 17.0134 0.538550
\(999\) 3.36954 + 1.94540i 0.106607 + 0.0615499i
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 637.2.u.g.361.5 12
7.2 even 3 637.2.k.i.569.2 12
7.3 odd 6 637.2.q.g.491.2 12
7.4 even 3 637.2.q.i.491.2 12
7.5 odd 6 91.2.k.b.23.2 yes 12
7.6 odd 2 91.2.u.b.88.5 yes 12
13.4 even 6 637.2.k.i.459.5 12
21.5 even 6 819.2.bm.f.478.5 12
21.20 even 2 819.2.do.e.361.2 12
91.4 even 6 637.2.q.i.589.2 12
91.11 odd 12 8281.2.a.co.1.9 12
91.17 odd 6 637.2.q.g.589.2 12
91.24 even 12 8281.2.a.cp.1.9 12
91.30 even 6 inner 637.2.u.g.30.5 12
91.41 even 12 1183.2.e.j.508.9 24
91.54 even 12 1183.2.e.j.170.9 24
91.67 odd 12 8281.2.a.co.1.4 12
91.69 odd 6 91.2.k.b.4.5 12
91.76 even 12 1183.2.e.j.508.4 24
91.80 even 12 8281.2.a.cp.1.4 12
91.82 odd 6 91.2.u.b.30.5 yes 12
91.89 even 12 1183.2.e.j.170.4 24
273.173 even 6 819.2.do.e.667.2 12
273.251 even 6 819.2.bm.f.550.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.k.b.4.5 12 91.69 odd 6
91.2.k.b.23.2 yes 12 7.5 odd 6
91.2.u.b.30.5 yes 12 91.82 odd 6
91.2.u.b.88.5 yes 12 7.6 odd 2
637.2.k.i.459.5 12 13.4 even 6
637.2.k.i.569.2 12 7.2 even 3
637.2.q.g.491.2 12 7.3 odd 6
637.2.q.g.589.2 12 91.17 odd 6
637.2.q.i.491.2 12 7.4 even 3
637.2.q.i.589.2 12 91.4 even 6
637.2.u.g.30.5 12 91.30 even 6 inner
637.2.u.g.361.5 12 1.1 even 1 trivial
819.2.bm.f.478.5 12 21.5 even 6
819.2.bm.f.550.2 12 273.251 even 6
819.2.do.e.361.2 12 21.20 even 2
819.2.do.e.667.2 12 273.173 even 6
1183.2.e.j.170.4 24 91.89 even 12
1183.2.e.j.170.9 24 91.54 even 12
1183.2.e.j.508.4 24 91.76 even 12
1183.2.e.j.508.9 24 91.41 even 12
8281.2.a.co.1.4 12 91.67 odd 12
8281.2.a.co.1.9 12 91.11 odd 12
8281.2.a.cp.1.4 12 91.80 even 12
8281.2.a.cp.1.9 12 91.24 even 12