Properties

Label 735.2.j.g.197.3
Level $735$
Weight $2$
Character 735.197
Analytic conductor $5.869$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [735,2,Mod(197,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.197");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.j (of order \(4\), degree \(2\), 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: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 197.3
Character \(\chi\) \(=\) 735.197
Dual form 735.2.j.g.638.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.06891 + 1.06891i) q^{2} +(1.73199 - 0.0150256i) q^{3} -0.285117i q^{4} +(-2.03205 - 0.933160i) q^{5} +(-1.83527 + 1.86739i) q^{6} +(-1.83305 - 1.83305i) q^{8} +(2.99955 - 0.0520482i) q^{9} +O(q^{10})\) \(q+(-1.06891 + 1.06891i) q^{2} +(1.73199 - 0.0150256i) q^{3} -0.285117i q^{4} +(-2.03205 - 0.933160i) q^{5} +(-1.83527 + 1.86739i) q^{6} +(-1.83305 - 1.83305i) q^{8} +(2.99955 - 0.0520482i) q^{9} +(3.16952 - 1.17461i) q^{10} -0.914115i q^{11} +(-0.00428405 - 0.493818i) q^{12} +(3.07974 - 3.07974i) q^{13} +(-3.53350 - 1.58569i) q^{15} +4.48894 q^{16} +(-0.850861 + 0.850861i) q^{17} +(-3.15060 + 3.26187i) q^{18} -6.87436i q^{19} +(-0.266060 + 0.579371i) q^{20} +(0.977102 + 0.977102i) q^{22} +(1.38222 + 1.38222i) q^{23} +(-3.20235 - 3.14727i) q^{24} +(3.25842 + 3.79245i) q^{25} +6.58390i q^{26} +(5.19439 - 0.135217i) q^{27} +2.72261 q^{29} +(5.47192 - 2.08202i) q^{30} +4.63375 q^{31} +(-1.13216 + 1.13216i) q^{32} +(-0.0137351 - 1.58323i) q^{33} -1.81898i q^{34} +(-0.0148398 - 0.855222i) q^{36} +(0.567326 + 0.567326i) q^{37} +(7.34804 + 7.34804i) q^{38} +(5.28779 - 5.38034i) q^{39} +(2.01431 + 5.43536i) q^{40} +0.922837i q^{41} +(-4.80893 + 4.80893i) q^{43} -0.260630 q^{44} +(-6.14379 - 2.69330i) q^{45} -2.95492 q^{46} +(7.41129 - 7.41129i) q^{47} +(7.77478 - 0.0674490i) q^{48} +(-7.53672 - 0.570823i) q^{50} +(-1.46089 + 1.48646i) q^{51} +(-0.878086 - 0.878086i) q^{52} +(-7.79887 - 7.79887i) q^{53} +(-5.40778 + 5.69685i) q^{54} +(-0.853015 + 1.85752i) q^{55} +(-0.103291 - 11.9063i) q^{57} +(-2.91021 + 2.91021i) q^{58} +9.88045 q^{59} +(-0.452106 + 1.00746i) q^{60} -1.06789 q^{61} +(-4.95304 + 4.95304i) q^{62} +6.55754i q^{64} +(-9.13206 + 3.38428i) q^{65} +(1.70701 + 1.67764i) q^{66} +(-5.00326 - 5.00326i) q^{67} +(0.242595 + 0.242595i) q^{68} +(2.41475 + 2.37321i) q^{69} +0.557759i q^{71} +(-5.59372 - 5.40291i) q^{72} +(-1.54128 + 1.54128i) q^{73} -1.21284 q^{74} +(5.70053 + 6.51951i) q^{75} -1.96000 q^{76} +(0.0989269 + 11.4032i) q^{78} -3.03113i q^{79} +(-9.12174 - 4.18890i) q^{80} +(8.99458 - 0.312242i) q^{81} +(-0.986425 - 0.986425i) q^{82} +(-2.38102 - 2.38102i) q^{83} +(2.52298 - 0.934999i) q^{85} -10.2806i q^{86} +(4.71552 - 0.0409088i) q^{87} +(-1.67562 + 1.67562i) q^{88} +11.2945 q^{89} +(9.44601 - 3.68825i) q^{90} +(0.394093 - 0.394093i) q^{92} +(8.02560 - 0.0696248i) q^{93} +15.8439i q^{94} +(-6.41488 + 13.9690i) q^{95} +(-1.94387 + 1.97789i) q^{96} +(-1.58805 - 1.58805i) q^{97} +(-0.0475780 - 2.74193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 2 q^{3} - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 2 q^{3} - 12 q^{6} + 8 q^{10} + 10 q^{12} - 8 q^{13} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 4 q^{22} - 4 q^{25} + 20 q^{27} - 40 q^{30} + 24 q^{31} + 4 q^{33} + 4 q^{36} - 4 q^{37} + 16 q^{40} + 8 q^{43} - 40 q^{45} + 32 q^{46} + 22 q^{48} - 8 q^{51} - 36 q^{52} - 20 q^{55} - 44 q^{57} - 56 q^{58} + 50 q^{60} + 8 q^{61} - 76 q^{66} - 12 q^{67} + 34 q^{72} - 52 q^{73} - 6 q^{75} + 32 q^{76} - 60 q^{78} - 20 q^{81} - 104 q^{82} - 12 q^{85} + 46 q^{87} - 42 q^{90} + 44 q^{93} - 12 q^{96} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.06891 + 1.06891i −0.755830 + 0.755830i −0.975561 0.219730i \(-0.929482\pi\)
0.219730 + 0.975561i \(0.429482\pi\)
\(3\) 1.73199 0.0150256i 0.999962 0.00867502i
\(4\) 0.285117i 0.142558i
\(5\) −2.03205 0.933160i −0.908759 0.417322i
\(6\) −1.83527 + 1.86739i −0.749245 + 0.762359i
\(7\) 0 0
\(8\) −1.83305 1.83305i −0.648080 0.648080i
\(9\) 2.99955 0.0520482i 0.999849 0.0173494i
\(10\) 3.16952 1.17461i 1.00229 0.371443i
\(11\) 0.914115i 0.275616i −0.990459 0.137808i \(-0.955994\pi\)
0.990459 0.137808i \(-0.0440057\pi\)
\(12\) −0.00428405 0.493818i −0.00123670 0.142553i
\(13\) 3.07974 3.07974i 0.854166 0.854166i −0.136477 0.990643i \(-0.543578\pi\)
0.990643 + 0.136477i \(0.0435781\pi\)
\(14\) 0 0
\(15\) −3.53350 1.58569i −0.912345 0.409423i
\(16\) 4.48894 1.12224
\(17\) −0.850861 + 0.850861i −0.206364 + 0.206364i −0.802720 0.596356i \(-0.796615\pi\)
0.596356 + 0.802720i \(0.296615\pi\)
\(18\) −3.15060 + 3.26187i −0.742603 + 0.768830i
\(19\) 6.87436i 1.57709i −0.614979 0.788543i \(-0.710836\pi\)
0.614979 0.788543i \(-0.289164\pi\)
\(20\) −0.266060 + 0.579371i −0.0594928 + 0.129551i
\(21\) 0 0
\(22\) 0.977102 + 0.977102i 0.208319 + 0.208319i
\(23\) 1.38222 + 1.38222i 0.288212 + 0.288212i 0.836373 0.548161i \(-0.184672\pi\)
−0.548161 + 0.836373i \(0.684672\pi\)
\(24\) −3.20235 3.14727i −0.653678 0.642434i
\(25\) 3.25842 + 3.79245i 0.651685 + 0.758490i
\(26\) 6.58390i 1.29121i
\(27\) 5.19439 0.135217i 0.999661 0.0260225i
\(28\) 0 0
\(29\) 2.72261 0.505576 0.252788 0.967522i \(-0.418652\pi\)
0.252788 + 0.967522i \(0.418652\pi\)
\(30\) 5.47192 2.08202i 0.999032 0.380124i
\(31\) 4.63375 0.832247 0.416123 0.909308i \(-0.363388\pi\)
0.416123 + 0.909308i \(0.363388\pi\)
\(32\) −1.13216 + 1.13216i −0.200139 + 0.200139i
\(33\) −0.0137351 1.58323i −0.00239097 0.275606i
\(34\) 1.81898i 0.311952i
\(35\) 0 0
\(36\) −0.0148398 0.855222i −0.00247330 0.142537i
\(37\) 0.567326 + 0.567326i 0.0932678 + 0.0932678i 0.752201 0.658933i \(-0.228992\pi\)
−0.658933 + 0.752201i \(0.728992\pi\)
\(38\) 7.34804 + 7.34804i 1.19201 + 1.19201i
\(39\) 5.28779 5.38034i 0.846724 0.861544i
\(40\) 2.01431 + 5.43536i 0.318490 + 0.859407i
\(41\) 0.922837i 0.144123i 0.997400 + 0.0720615i \(0.0229578\pi\)
−0.997400 + 0.0720615i \(0.977042\pi\)
\(42\) 0 0
\(43\) −4.80893 + 4.80893i −0.733355 + 0.733355i −0.971283 0.237928i \(-0.923532\pi\)
0.237928 + 0.971283i \(0.423532\pi\)
\(44\) −0.260630 −0.0392914
\(45\) −6.14379 2.69330i −0.915862 0.401493i
\(46\) −2.95492 −0.435679
\(47\) 7.41129 7.41129i 1.08105 1.08105i 0.0846364 0.996412i \(-0.473027\pi\)
0.996412 0.0846364i \(-0.0269729\pi\)
\(48\) 7.77478 0.0674490i 1.12219 0.00973542i
\(49\) 0 0
\(50\) −7.53672 0.570823i −1.06585 0.0807265i
\(51\) −1.46089 + 1.48646i −0.204566 + 0.208147i
\(52\) −0.878086 0.878086i −0.121769 0.121769i
\(53\) −7.79887 7.79887i −1.07126 1.07126i −0.997258 0.0739991i \(-0.976424\pi\)
−0.0739991 0.997258i \(-0.523576\pi\)
\(54\) −5.40778 + 5.69685i −0.735906 + 0.775243i
\(55\) −0.853015 + 1.85752i −0.115021 + 0.250468i
\(56\) 0 0
\(57\) −0.103291 11.9063i −0.0136813 1.57703i
\(58\) −2.91021 + 2.91021i −0.382130 + 0.382130i
\(59\) 9.88045 1.28633 0.643163 0.765730i \(-0.277622\pi\)
0.643163 + 0.765730i \(0.277622\pi\)
\(60\) −0.452106 + 1.00746i −0.0583667 + 0.130062i
\(61\) −1.06789 −0.136729 −0.0683645 0.997660i \(-0.521778\pi\)
−0.0683645 + 0.997660i \(0.521778\pi\)
\(62\) −4.95304 + 4.95304i −0.629037 + 0.629037i
\(63\) 0 0
\(64\) 6.55754i 0.819693i
\(65\) −9.13206 + 3.38428i −1.13269 + 0.419768i
\(66\) 1.70701 + 1.67764i 0.210118 + 0.206504i
\(67\) −5.00326 5.00326i −0.611246 0.611246i 0.332025 0.943271i \(-0.392268\pi\)
−0.943271 + 0.332025i \(0.892268\pi\)
\(68\) 0.242595 + 0.242595i 0.0294189 + 0.0294189i
\(69\) 2.41475 + 2.37321i 0.290701 + 0.285701i
\(70\) 0 0
\(71\) 0.557759i 0.0661938i 0.999452 + 0.0330969i \(0.0105370\pi\)
−0.999452 + 0.0330969i \(0.989463\pi\)
\(72\) −5.59372 5.40291i −0.659226 0.636739i
\(73\) −1.54128 + 1.54128i −0.180393 + 0.180393i −0.791527 0.611134i \(-0.790714\pi\)
0.611134 + 0.791527i \(0.290714\pi\)
\(74\) −1.21284 −0.140989
\(75\) 5.70053 + 6.51951i 0.658240 + 0.752808i
\(76\) −1.96000 −0.224827
\(77\) 0 0
\(78\) 0.0989269 + 11.4032i 0.0112013 + 1.29116i
\(79\) 3.03113i 0.341029i −0.985355 0.170514i \(-0.945457\pi\)
0.985355 0.170514i \(-0.0545429\pi\)
\(80\) −9.12174 4.18890i −1.01984 0.468334i
\(81\) 8.99458 0.312242i 0.999398 0.0346936i
\(82\) −0.986425 0.986425i −0.108932 0.108932i
\(83\) −2.38102 2.38102i −0.261351 0.261351i 0.564252 0.825603i \(-0.309165\pi\)
−0.825603 + 0.564252i \(0.809165\pi\)
\(84\) 0 0
\(85\) 2.52298 0.934999i 0.273655 0.101415i
\(86\) 10.2806i 1.10858i
\(87\) 4.71552 0.0409088i 0.505557 0.00438589i
\(88\) −1.67562 + 1.67562i −0.178621 + 0.178621i
\(89\) 11.2945 1.19721 0.598607 0.801043i \(-0.295721\pi\)
0.598607 + 0.801043i \(0.295721\pi\)
\(90\) 9.44601 3.68825i 0.995697 0.388776i
\(91\) 0 0
\(92\) 0.394093 0.394093i 0.0410871 0.0410871i
\(93\) 8.02560 0.0696248i 0.832216 0.00721976i
\(94\) 15.8439i 1.63418i
\(95\) −6.41488 + 13.9690i −0.658153 + 1.43319i
\(96\) −1.94387 + 1.97789i −0.198396 + 0.201868i
\(97\) −1.58805 1.58805i −0.161242 0.161242i 0.621875 0.783117i \(-0.286371\pi\)
−0.783117 + 0.621875i \(0.786371\pi\)
\(98\) 0 0
\(99\) −0.0475780 2.74193i −0.00478177 0.275574i
\(100\) 1.08129 0.929032i 0.108129 0.0929032i
\(101\) 4.64534i 0.462229i −0.972927 0.231114i \(-0.925763\pi\)
0.972927 0.231114i \(-0.0742372\pi\)
\(102\) −0.0273312 3.15045i −0.00270619 0.311941i
\(103\) −7.44634 + 7.44634i −0.733710 + 0.733710i −0.971353 0.237643i \(-0.923625\pi\)
0.237643 + 0.971353i \(0.423625\pi\)
\(104\) −11.2906 −1.10714
\(105\) 0 0
\(106\) 16.6725 1.61938
\(107\) −4.47393 + 4.47393i −0.432511 + 0.432511i −0.889482 0.456971i \(-0.848934\pi\)
0.456971 + 0.889482i \(0.348934\pi\)
\(108\) −0.0385526 1.48101i −0.00370972 0.142510i
\(109\) 8.61909i 0.825559i 0.910831 + 0.412779i \(0.135442\pi\)
−0.910831 + 0.412779i \(0.864558\pi\)
\(110\) −1.07372 2.89731i −0.102376 0.276248i
\(111\) 0.991125 + 0.974076i 0.0940734 + 0.0924552i
\(112\) 0 0
\(113\) 7.44178 + 7.44178i 0.700064 + 0.700064i 0.964424 0.264360i \(-0.0851608\pi\)
−0.264360 + 0.964424i \(0.585161\pi\)
\(114\) 12.8371 + 12.6163i 1.20231 + 1.18162i
\(115\) −1.51890 4.09856i −0.141638 0.382192i
\(116\) 0.776263i 0.0720742i
\(117\) 9.07753 9.39812i 0.839218 0.868857i
\(118\) −10.5613 + 10.5613i −0.972243 + 0.972243i
\(119\) 0 0
\(120\) 3.57043 + 9.38371i 0.325934 + 0.856611i
\(121\) 10.1644 0.924036
\(122\) 1.14147 1.14147i 0.103344 0.103344i
\(123\) 0.0138662 + 1.59834i 0.00125027 + 0.144118i
\(124\) 1.32116i 0.118644i
\(125\) −3.08230 10.7471i −0.275690 0.961247i
\(126\) 0 0
\(127\) −4.42895 4.42895i −0.393006 0.393006i 0.482752 0.875757i \(-0.339637\pi\)
−0.875757 + 0.482752i \(0.839637\pi\)
\(128\) −9.27371 9.27371i −0.819688 0.819688i
\(129\) −8.25674 + 8.40126i −0.726966 + 0.739690i
\(130\) 6.14383 13.3788i 0.538850 1.17340i
\(131\) 8.51315i 0.743797i 0.928273 + 0.371899i \(0.121293\pi\)
−0.928273 + 0.371899i \(0.878707\pi\)
\(132\) −0.451407 + 0.00391611i −0.0392899 + 0.000340854i
\(133\) 0 0
\(134\) 10.6960 0.923996
\(135\) −10.6814 4.57243i −0.919311 0.393532i
\(136\) 3.11934 0.267481
\(137\) 7.30622 7.30622i 0.624212 0.624212i −0.322393 0.946606i \(-0.604487\pi\)
0.946606 + 0.322393i \(0.104487\pi\)
\(138\) −5.11787 + 0.0443993i −0.435662 + 0.00377952i
\(139\) 3.03547i 0.257465i −0.991679 0.128733i \(-0.958909\pi\)
0.991679 0.128733i \(-0.0410909\pi\)
\(140\) 0 0
\(141\) 12.7249 12.9476i 1.07163 1.09039i
\(142\) −0.596191 0.596191i −0.0500313 0.0500313i
\(143\) −2.81523 2.81523i −0.235422 0.235422i
\(144\) 13.4648 0.233641i 1.12207 0.0194701i
\(145\) −5.53247 2.54063i −0.459447 0.210988i
\(146\) 3.29496i 0.272693i
\(147\) 0 0
\(148\) 0.161754 0.161754i 0.0132961 0.0132961i
\(149\) −12.8801 −1.05518 −0.527590 0.849499i \(-0.676904\pi\)
−0.527590 + 0.849499i \(0.676904\pi\)
\(150\) −13.0621 0.875413i −1.06651 0.0714772i
\(151\) 11.8988 0.968309 0.484154 0.874983i \(-0.339127\pi\)
0.484154 + 0.874983i \(0.339127\pi\)
\(152\) −12.6010 + 12.6010i −1.02208 + 1.02208i
\(153\) −2.50791 + 2.59648i −0.202753 + 0.209913i
\(154\) 0 0
\(155\) −9.41600 4.32404i −0.756312 0.347315i
\(156\) −1.53403 1.50764i −0.122820 0.120708i
\(157\) −9.83758 9.83758i −0.785124 0.785124i 0.195566 0.980691i \(-0.437346\pi\)
−0.980691 + 0.195566i \(0.937346\pi\)
\(158\) 3.23999 + 3.23999i 0.257760 + 0.257760i
\(159\) −13.6247 13.3904i −1.08051 1.06192i
\(160\) 3.35709 1.24411i 0.265401 0.0983558i
\(161\) 0 0
\(162\) −9.28060 + 9.94811i −0.729153 + 0.781598i
\(163\) −17.0369 + 17.0369i −1.33443 + 1.33443i −0.433075 + 0.901358i \(0.642571\pi\)
−0.901358 + 0.433075i \(0.857429\pi\)
\(164\) 0.263116 0.0205459
\(165\) −1.44950 + 3.23002i −0.112843 + 0.251457i
\(166\) 5.09016 0.395073
\(167\) 4.98846 4.98846i 0.386018 0.386018i −0.487246 0.873265i \(-0.661999\pi\)
0.873265 + 0.487246i \(0.161999\pi\)
\(168\) 0 0
\(169\) 5.96958i 0.459199i
\(170\) −1.69740 + 3.69625i −0.130185 + 0.283489i
\(171\) −0.357798 20.6200i −0.0273615 1.57685i
\(172\) 1.37111 + 1.37111i 0.104546 + 0.104546i
\(173\) −17.0165 17.0165i −1.29374 1.29374i −0.932454 0.361288i \(-0.882337\pi\)
−0.361288 0.932454i \(-0.617663\pi\)
\(174\) −4.99672 + 5.08418i −0.378800 + 0.385430i
\(175\) 0 0
\(176\) 4.10341i 0.309306i
\(177\) 17.1128 0.148459i 1.28628 0.0111589i
\(178\) −12.0728 + 12.0728i −0.904891 + 0.904891i
\(179\) −5.11855 −0.382578 −0.191289 0.981534i \(-0.561267\pi\)
−0.191289 + 0.981534i \(0.561267\pi\)
\(180\) −0.767904 + 1.75170i −0.0572362 + 0.130564i
\(181\) −1.77024 −0.131581 −0.0657906 0.997833i \(-0.520957\pi\)
−0.0657906 + 0.997833i \(0.520957\pi\)
\(182\) 0 0
\(183\) −1.84957 + 0.0160456i −0.136724 + 0.00118613i
\(184\) 5.06734i 0.373569i
\(185\) −0.623427 1.68224i −0.0458352 0.123681i
\(186\) −8.50418 + 8.65302i −0.623557 + 0.634471i
\(187\) 0.777784 + 0.777784i 0.0568772 + 0.0568772i
\(188\) −2.11309 2.11309i −0.154113 0.154113i
\(189\) 0 0
\(190\) −8.07466 21.7885i −0.585797 1.58070i
\(191\) 9.17909i 0.664176i −0.943248 0.332088i \(-0.892247\pi\)
0.943248 0.332088i \(-0.107753\pi\)
\(192\) 0.0985309 + 11.3576i 0.00711085 + 0.819662i
\(193\) −5.01626 + 5.01626i −0.361079 + 0.361079i −0.864210 0.503131i \(-0.832181\pi\)
0.503131 + 0.864210i \(0.332181\pi\)
\(194\) 3.39495 0.243743
\(195\) −15.7657 + 5.99874i −1.12901 + 0.429579i
\(196\) 0 0
\(197\) −12.5538 + 12.5538i −0.894420 + 0.894420i −0.994935 0.100516i \(-0.967951\pi\)
0.100516 + 0.994935i \(0.467951\pi\)
\(198\) 2.98172 + 2.88001i 0.211902 + 0.204673i
\(199\) 17.2165i 1.22044i −0.792230 0.610222i \(-0.791080\pi\)
0.792230 0.610222i \(-0.208920\pi\)
\(200\) 0.978894 12.9246i 0.0692183 0.913906i
\(201\) −8.74076 8.59040i −0.616525 0.605920i
\(202\) 4.96543 + 4.96543i 0.349367 + 0.349367i
\(203\) 0 0
\(204\) 0.423816 + 0.416526i 0.0296731 + 0.0291626i
\(205\) 0.861155 1.87525i 0.0601457 0.130973i
\(206\) 15.9189i 1.10912i
\(207\) 4.21797 + 4.07408i 0.293169 + 0.283168i
\(208\) 13.8248 13.8248i 0.958575 0.958575i
\(209\) −6.28395 −0.434670
\(210\) 0 0
\(211\) −9.75343 −0.671454 −0.335727 0.941959i \(-0.608982\pi\)
−0.335727 + 0.941959i \(0.608982\pi\)
\(212\) −2.22359 + 2.22359i −0.152717 + 0.152717i
\(213\) 0.00838065 + 0.966030i 0.000574233 + 0.0661913i
\(214\) 9.56442i 0.653810i
\(215\) 14.2595 5.28447i 0.972488 0.360398i
\(216\) −9.76943 9.27371i −0.664725 0.630996i
\(217\) 0 0
\(218\) −9.21299 9.21299i −0.623982 0.623982i
\(219\) −2.64631 + 2.69263i −0.178821 + 0.181951i
\(220\) 0.529611 + 0.243209i 0.0357064 + 0.0163972i
\(221\) 5.24086i 0.352538i
\(222\) −2.10061 + 0.0182236i −0.140984 + 0.00122308i
\(223\) 9.17286 9.17286i 0.614260 0.614260i −0.329793 0.944053i \(-0.606979\pi\)
0.944053 + 0.329793i \(0.106979\pi\)
\(224\) 0 0
\(225\) 9.97119 + 11.2060i 0.664746 + 0.747069i
\(226\) −15.9091 −1.05826
\(227\) −16.9999 + 16.9999i −1.12832 + 1.12832i −0.137870 + 0.990450i \(0.544026\pi\)
−0.990450 + 0.137870i \(0.955974\pi\)
\(228\) −3.39469 + 0.0294501i −0.224819 + 0.00195038i
\(229\) 3.25690i 0.215222i 0.994193 + 0.107611i \(0.0343201\pi\)
−0.994193 + 0.107611i \(0.965680\pi\)
\(230\) 6.00453 + 2.75741i 0.395927 + 0.181818i
\(231\) 0 0
\(232\) −4.99068 4.99068i −0.327654 0.327654i
\(233\) 11.7937 + 11.7937i 0.772630 + 0.772630i 0.978566 0.205935i \(-0.0660236\pi\)
−0.205935 + 0.978566i \(0.566024\pi\)
\(234\) 0.342680 + 19.7487i 0.0224017 + 1.29101i
\(235\) −21.9760 + 8.14417i −1.43356 + 0.531267i
\(236\) 2.81708i 0.183377i
\(237\) −0.0455445 5.24987i −0.00295843 0.341016i
\(238\) 0 0
\(239\) 15.1824 0.982070 0.491035 0.871140i \(-0.336619\pi\)
0.491035 + 0.871140i \(0.336619\pi\)
\(240\) −15.8617 7.11806i −1.02387 0.459469i
\(241\) 0.118764 0.00765029 0.00382515 0.999993i \(-0.498782\pi\)
0.00382515 + 0.999993i \(0.498782\pi\)
\(242\) −10.8648 + 10.8648i −0.698414 + 0.698414i
\(243\) 15.5738 0.675948i 0.999059 0.0433621i
\(244\) 0.304473i 0.0194919i
\(245\) 0 0
\(246\) −1.72330 1.69365i −0.109873 0.107983i
\(247\) −21.1712 21.1712i −1.34709 1.34709i
\(248\) −8.49389 8.49389i −0.539363 0.539363i
\(249\) −4.15966 4.08811i −0.263608 0.259074i
\(250\) 14.7823 + 8.19290i 0.934914 + 0.518165i
\(251\) 16.8255i 1.06202i 0.847367 + 0.531008i \(0.178187\pi\)
−0.847367 + 0.531008i \(0.821813\pi\)
\(252\) 0 0
\(253\) 1.26350 1.26350i 0.0794358 0.0794358i
\(254\) 9.46825 0.594091
\(255\) 4.35571 1.65731i 0.272765 0.103785i
\(256\) 6.71035 0.419397
\(257\) −9.84080 + 9.84080i −0.613852 + 0.613852i −0.943948 0.330095i \(-0.892919\pi\)
0.330095 + 0.943948i \(0.392919\pi\)
\(258\) −0.154472 17.8058i −0.00961699 1.10854i
\(259\) 0 0
\(260\) 0.964916 + 2.60371i 0.0598416 + 0.161475i
\(261\) 8.16661 0.141707i 0.505500 0.00877144i
\(262\) −9.09975 9.09975i −0.562185 0.562185i
\(263\) 15.2095 + 15.2095i 0.937859 + 0.937859i 0.998179 0.0603201i \(-0.0192121\pi\)
−0.0603201 + 0.998179i \(0.519212\pi\)
\(264\) −2.87696 + 2.92732i −0.177065 + 0.180164i
\(265\) 8.57007 + 23.1253i 0.526455 + 1.42057i
\(266\) 0 0
\(267\) 19.5619 0.169706i 1.19717 0.0103859i
\(268\) −1.42652 + 1.42652i −0.0871383 + 0.0871383i
\(269\) 18.8824 1.15128 0.575639 0.817704i \(-0.304753\pi\)
0.575639 + 0.817704i \(0.304753\pi\)
\(270\) 16.3049 6.52993i 0.992286 0.397399i
\(271\) −3.71182 −0.225477 −0.112739 0.993625i \(-0.535962\pi\)
−0.112739 + 0.993625i \(0.535962\pi\)
\(272\) −3.81947 + 3.81947i −0.231589 + 0.231589i
\(273\) 0 0
\(274\) 15.6193i 0.943597i
\(275\) 3.46673 2.97857i 0.209052 0.179615i
\(276\) 0.676642 0.688485i 0.0407291 0.0414420i
\(277\) 5.34687 + 5.34687i 0.321263 + 0.321263i 0.849251 0.527989i \(-0.177054\pi\)
−0.527989 + 0.849251i \(0.677054\pi\)
\(278\) 3.24463 + 3.24463i 0.194600 + 0.194600i
\(279\) 13.8992 0.241178i 0.832122 0.0144390i
\(280\) 0 0
\(281\) 12.0546i 0.719117i −0.933122 0.359559i \(-0.882927\pi\)
0.933122 0.359559i \(-0.117073\pi\)
\(282\) 0.238064 + 27.4415i 0.0141765 + 1.63412i
\(283\) −16.9801 + 16.9801i −1.00936 + 1.00936i −0.00940506 + 0.999956i \(0.502994\pi\)
−0.999956 + 0.00940506i \(0.997006\pi\)
\(284\) 0.159026 0.00943649
\(285\) −10.9006 + 24.2905i −0.645695 + 1.43885i
\(286\) 6.01844 0.355878
\(287\) 0 0
\(288\) −3.33704 + 3.45489i −0.196637 + 0.203581i
\(289\) 15.5521i 0.914828i
\(290\) 8.62939 3.19799i 0.506735 0.187793i
\(291\) −2.77434 2.72662i −0.162635 0.159837i
\(292\) 0.439445 + 0.439445i 0.0257165 + 0.0257165i
\(293\) −12.2498 12.2498i −0.715644 0.715644i 0.252066 0.967710i \(-0.418890\pi\)
−0.967710 + 0.252066i \(0.918890\pi\)
\(294\) 0 0
\(295\) −20.0775 9.22004i −1.16896 0.536812i
\(296\) 2.07987i 0.120890i
\(297\) −0.123604 4.74827i −0.00717220 0.275523i
\(298\) 13.7676 13.7676i 0.797538 0.797538i
\(299\) 8.51373 0.492362
\(300\) 1.85882 1.62532i 0.107319 0.0938377i
\(301\) 0 0
\(302\) −12.7187 + 12.7187i −0.731877 + 0.731877i
\(303\) −0.0697990 8.04567i −0.00400985 0.462212i
\(304\) 30.8586i 1.76986i
\(305\) 2.17000 + 0.996511i 0.124254 + 0.0570600i
\(306\) −0.0946746 5.45612i −0.00541218 0.311905i
\(307\) −12.5028 12.5028i −0.713571 0.713571i 0.253709 0.967280i \(-0.418349\pi\)
−0.967280 + 0.253709i \(0.918349\pi\)
\(308\) 0 0
\(309\) −12.7851 + 13.0088i −0.727317 + 0.740047i
\(310\) 14.6868 5.44283i 0.834154 0.309132i
\(311\) 23.4396i 1.32914i 0.747227 + 0.664569i \(0.231385\pi\)
−0.747227 + 0.664569i \(0.768615\pi\)
\(312\) −19.5552 + 0.169648i −1.10709 + 0.00960443i
\(313\) −7.49546 + 7.49546i −0.423668 + 0.423668i −0.886465 0.462796i \(-0.846846\pi\)
0.462796 + 0.886465i \(0.346846\pi\)
\(314\) 21.0309 1.18684
\(315\) 0 0
\(316\) −0.864226 −0.0486165
\(317\) 14.5259 14.5259i 0.815858 0.815858i −0.169647 0.985505i \(-0.554263\pi\)
0.985505 + 0.169647i \(0.0542628\pi\)
\(318\) 28.8765 0.250514i 1.61932 0.0140481i
\(319\) 2.48878i 0.139345i
\(320\) 6.11924 13.3252i 0.342076 0.744903i
\(321\) −7.68156 + 7.81601i −0.428743 + 0.436247i
\(322\) 0 0
\(323\) 5.84912 + 5.84912i 0.325454 + 0.325454i
\(324\) −0.0890255 2.56451i −0.00494586 0.142473i
\(325\) 21.7148 + 1.64466i 1.20452 + 0.0912293i
\(326\) 36.4217i 2.01721i
\(327\) 0.129507 + 14.9281i 0.00716174 + 0.825528i
\(328\) 1.69160 1.69160i 0.0934032 0.0934032i
\(329\) 0 0
\(330\) −1.90321 5.00196i −0.104768 0.275349i
\(331\) 31.9317 1.75513 0.877564 0.479460i \(-0.159168\pi\)
0.877564 + 0.479460i \(0.159168\pi\)
\(332\) −0.678868 + 0.678868i −0.0372577 + 0.0372577i
\(333\) 1.73125 + 1.67219i 0.0948719 + 0.0916356i
\(334\) 10.6644i 0.583529i
\(335\) 5.49802 + 14.8357i 0.300389 + 0.810561i
\(336\) 0 0
\(337\) 9.40161 + 9.40161i 0.512139 + 0.512139i 0.915181 0.403043i \(-0.132047\pi\)
−0.403043 + 0.915181i \(0.632047\pi\)
\(338\) 6.38092 + 6.38092i 0.347076 + 0.347076i
\(339\) 13.0009 + 12.7772i 0.706111 + 0.693964i
\(340\) −0.266584 0.719344i −0.0144576 0.0390119i
\(341\) 4.23578i 0.229380i
\(342\) 22.4233 + 21.6584i 1.21251 + 1.17115i
\(343\) 0 0
\(344\) 17.6300 0.950546
\(345\) −2.69229 7.07582i −0.144948 0.380949i
\(346\) 36.3781 1.95570
\(347\) 11.3727 11.3727i 0.610520 0.610520i −0.332561 0.943082i \(-0.607913\pi\)
0.943082 + 0.332561i \(0.107913\pi\)
\(348\) −0.0116638 1.34448i −0.000625245 0.0720715i
\(349\) 9.21013i 0.493007i −0.969142 0.246503i \(-0.920718\pi\)
0.969142 0.246503i \(-0.0792817\pi\)
\(350\) 0 0
\(351\) 15.5809 16.4138i 0.831649 0.876104i
\(352\) 1.03492 + 1.03492i 0.0551616 + 0.0551616i
\(353\) 7.38772 + 7.38772i 0.393209 + 0.393209i 0.875829 0.482621i \(-0.160315\pi\)
−0.482621 + 0.875829i \(0.660315\pi\)
\(354\) −18.1333 + 18.4506i −0.963772 + 0.980641i
\(355\) 0.520478 1.13339i 0.0276241 0.0601542i
\(356\) 3.22025i 0.170673i
\(357\) 0 0
\(358\) 5.47124 5.47124i 0.289164 0.289164i
\(359\) −1.54177 −0.0813713 −0.0406857 0.999172i \(-0.512954\pi\)
−0.0406857 + 0.999172i \(0.512954\pi\)
\(360\) 6.32492 + 16.1988i 0.333353 + 0.853752i
\(361\) −28.2568 −1.48720
\(362\) 1.89222 1.89222i 0.0994530 0.0994530i
\(363\) 17.6046 0.152726i 0.924001 0.00801603i
\(364\) 0 0
\(365\) 4.57021 1.69369i 0.239216 0.0886517i
\(366\) 1.95986 1.99416i 0.102444 0.104237i
\(367\) 11.3381 + 11.3381i 0.591844 + 0.591844i 0.938129 0.346285i \(-0.112557\pi\)
−0.346285 + 0.938129i \(0.612557\pi\)
\(368\) 6.20469 + 6.20469i 0.323442 + 0.323442i
\(369\) 0.0480320 + 2.76809i 0.00250045 + 0.144101i
\(370\) 2.46454 + 1.13177i 0.128125 + 0.0588379i
\(371\) 0 0
\(372\) −0.0198512 2.28823i −0.00102924 0.118639i
\(373\) 19.8427 19.8427i 1.02742 1.02742i 0.0278035 0.999613i \(-0.491149\pi\)
0.999613 0.0278035i \(-0.00885126\pi\)
\(374\) −1.66276 −0.0859790
\(375\) −5.49999 18.5674i −0.284018 0.958819i
\(376\) −27.1705 −1.40121
\(377\) 8.38493 8.38493i 0.431846 0.431846i
\(378\) 0 0
\(379\) 18.6208i 0.956485i 0.878228 + 0.478243i \(0.158726\pi\)
−0.878228 + 0.478243i \(0.841274\pi\)
\(380\) 3.98280 + 1.82899i 0.204314 + 0.0938253i
\(381\) −7.73742 7.60433i −0.396400 0.389582i
\(382\) 9.81158 + 9.81158i 0.502004 + 0.502004i
\(383\) 11.4679 + 11.4679i 0.585984 + 0.585984i 0.936541 0.350557i \(-0.114008\pi\)
−0.350557 + 0.936541i \(0.614008\pi\)
\(384\) −16.2013 15.9226i −0.826768 0.812546i
\(385\) 0 0
\(386\) 10.7238i 0.545828i
\(387\) −14.1743 + 14.6749i −0.720522 + 0.745968i
\(388\) −0.452781 + 0.452781i −0.0229864 + 0.0229864i
\(389\) −33.4890 −1.69796 −0.848980 0.528426i \(-0.822783\pi\)
−0.848980 + 0.528426i \(0.822783\pi\)
\(390\) 10.4400 23.2642i 0.528650 1.17803i
\(391\) −2.35215 −0.118953
\(392\) 0 0
\(393\) 0.127915 + 14.7447i 0.00645246 + 0.743769i
\(394\) 26.8376i 1.35206i
\(395\) −2.82853 + 6.15939i −0.142319 + 0.309913i
\(396\) −0.781771 + 0.0135653i −0.0392855 + 0.000681682i
\(397\) 7.51668 + 7.51668i 0.377251 + 0.377251i 0.870110 0.492858i \(-0.164048\pi\)
−0.492858 + 0.870110i \(0.664048\pi\)
\(398\) 18.4028 + 18.4028i 0.922449 + 0.922449i
\(399\) 0 0
\(400\) 14.6269 + 17.0241i 0.731344 + 0.851204i
\(401\) 38.4777i 1.92148i 0.277446 + 0.960741i \(0.410512\pi\)
−0.277446 + 0.960741i \(0.589488\pi\)
\(402\) 18.5254 0.160714i 0.923961 0.00801569i
\(403\) 14.2708 14.2708i 0.710877 0.710877i
\(404\) −1.32447 −0.0658947
\(405\) −18.5688 7.75890i −0.922690 0.385543i
\(406\) 0 0
\(407\) 0.518601 0.518601i 0.0257061 0.0257061i
\(408\) 5.40265 0.0468698i 0.267471 0.00232040i
\(409\) 0.968600i 0.0478942i 0.999713 + 0.0239471i \(0.00762333\pi\)
−0.999713 + 0.0239471i \(0.992377\pi\)
\(410\) 1.08397 + 2.92496i 0.0535334 + 0.144453i
\(411\) 12.5445 12.7640i 0.618774 0.629604i
\(412\) 2.12308 + 2.12308i 0.104597 + 0.104597i
\(413\) 0 0
\(414\) −8.86342 + 0.153798i −0.435613 + 0.00755876i
\(415\) 2.61647 + 7.06021i 0.128437 + 0.346572i
\(416\) 6.97351i 0.341904i
\(417\) −0.0456097 5.25739i −0.00223352 0.257456i
\(418\) 6.71695 6.71695i 0.328537 0.328537i
\(419\) 24.3482 1.18949 0.594743 0.803916i \(-0.297254\pi\)
0.594743 + 0.803916i \(0.297254\pi\)
\(420\) 0 0
\(421\) 1.75923 0.0857395 0.0428698 0.999081i \(-0.486350\pi\)
0.0428698 + 0.999081i \(0.486350\pi\)
\(422\) 10.4255 10.4255i 0.507505 0.507505i
\(423\) 21.8448 22.6163i 1.06213 1.09964i
\(424\) 28.5914i 1.38852i
\(425\) −5.99931 0.454382i −0.291009 0.0220407i
\(426\) −1.04155 1.02364i −0.0504634 0.0495954i
\(427\) 0 0
\(428\) 1.27559 + 1.27559i 0.0616581 + 0.0616581i
\(429\) −4.91825 4.83364i −0.237455 0.233371i
\(430\) −9.59343 + 20.8906i −0.462636 + 1.00744i
\(431\) 21.4413i 1.03279i 0.856351 + 0.516395i \(0.172726\pi\)
−0.856351 + 0.516395i \(0.827274\pi\)
\(432\) 23.3173 0.606980i 1.12186 0.0292033i
\(433\) −26.8036 + 26.8036i −1.28810 + 1.28810i −0.352161 + 0.935940i \(0.614553\pi\)
−0.935940 + 0.352161i \(0.885447\pi\)
\(434\) 0 0
\(435\) −9.62034 4.31721i −0.461260 0.206994i
\(436\) 2.45745 0.117690
\(437\) 9.50185 9.50185i 0.454535 0.454535i
\(438\) −0.0495087 5.70682i −0.00236562 0.272683i
\(439\) 2.37243i 0.113230i −0.998396 0.0566149i \(-0.981969\pi\)
0.998396 0.0566149i \(-0.0180307\pi\)
\(440\) 4.96855 1.84131i 0.236866 0.0877810i
\(441\) 0 0
\(442\) −5.60198 5.60198i −0.266459 0.266459i
\(443\) 15.3844 + 15.3844i 0.730933 + 0.730933i 0.970805 0.239871i \(-0.0771053\pi\)
−0.239871 + 0.970805i \(0.577105\pi\)
\(444\) 0.277726 0.282587i 0.0131803 0.0134110i
\(445\) −22.9509 10.5396i −1.08798 0.499624i
\(446\) 19.6098i 0.928552i
\(447\) −22.3082 + 0.193531i −1.05514 + 0.00915372i
\(448\) 0 0
\(449\) −28.8886 −1.36334 −0.681669 0.731661i \(-0.738746\pi\)
−0.681669 + 0.731661i \(0.738746\pi\)
\(450\) −22.6365 1.31994i −1.06709 0.0622225i
\(451\) 0.843579 0.0397226
\(452\) 2.12178 2.12178i 0.0998000 0.0998000i
\(453\) 20.6085 0.178786i 0.968272 0.00840010i
\(454\) 36.3425i 1.70564i
\(455\) 0 0
\(456\) −21.6355 + 22.0141i −1.01317 + 1.03091i
\(457\) −1.39005 1.39005i −0.0650239 0.0650239i 0.673847 0.738871i \(-0.264641\pi\)
−0.738871 + 0.673847i \(0.764641\pi\)
\(458\) −3.48132 3.48132i −0.162671 0.162671i
\(459\) −4.30466 + 4.53476i −0.200924 + 0.211664i
\(460\) −1.16857 + 0.433064i −0.0544848 + 0.0201917i
\(461\) 17.4281i 0.811709i 0.913938 + 0.405854i \(0.133026\pi\)
−0.913938 + 0.405854i \(0.866974\pi\)
\(462\) 0 0
\(463\) 14.8405 14.8405i 0.689698 0.689698i −0.272467 0.962165i \(-0.587840\pi\)
0.962165 + 0.272467i \(0.0878395\pi\)
\(464\) 12.2216 0.567376
\(465\) −16.3734 7.34769i −0.759296 0.340741i
\(466\) −25.2127 −1.16795
\(467\) −8.91392 + 8.91392i −0.412487 + 0.412487i −0.882604 0.470117i \(-0.844212\pi\)
0.470117 + 0.882604i \(0.344212\pi\)
\(468\) −2.67956 2.58816i −0.123863 0.119638i
\(469\) 0 0
\(470\) 14.7849 32.1956i 0.681978 1.48507i
\(471\) −17.1864 16.8907i −0.791906 0.778284i
\(472\) −18.1113 18.1113i −0.833642 0.833642i
\(473\) 4.39591 + 4.39591i 0.202124 + 0.202124i
\(474\) 5.66030 + 5.56293i 0.259986 + 0.255514i
\(475\) 26.0707 22.3996i 1.19620 1.02776i
\(476\) 0 0
\(477\) −23.7990 22.9872i −1.08968 1.05251i
\(478\) −16.2286 + 16.2286i −0.742278 + 0.742278i
\(479\) −10.2879 −0.470065 −0.235032 0.971988i \(-0.575520\pi\)
−0.235032 + 0.971988i \(0.575520\pi\)
\(480\) 5.79573 2.20523i 0.264538 0.100654i
\(481\) 3.49443 0.159332
\(482\) −0.126948 + 0.126948i −0.00578232 + 0.00578232i
\(483\) 0 0
\(484\) 2.89804i 0.131729i
\(485\) 1.74509 + 4.70890i 0.0792404 + 0.213820i
\(486\) −15.9244 + 17.3694i −0.722345 + 0.787894i
\(487\) 13.1841 + 13.1841i 0.597430 + 0.597430i 0.939628 0.342198i \(-0.111171\pi\)
−0.342198 + 0.939628i \(0.611171\pi\)
\(488\) 1.95749 + 1.95749i 0.0886114 + 0.0886114i
\(489\) −29.2517 + 29.7637i −1.32281 + 1.34596i
\(490\) 0 0
\(491\) 24.6940i 1.11442i 0.830370 + 0.557212i \(0.188129\pi\)
−0.830370 + 0.557212i \(0.811871\pi\)
\(492\) 0.455714 0.00395348i 0.0205452 0.000178237i
\(493\) −2.31656 + 2.31656i −0.104333 + 0.104333i
\(494\) 45.2601 2.03635
\(495\) −2.46198 + 5.61613i −0.110658 + 0.252426i
\(496\) 20.8007 0.933977
\(497\) 0 0
\(498\) 8.81609 0.0764827i 0.395058 0.00342727i
\(499\) 12.8777i 0.576483i 0.957558 + 0.288242i \(0.0930707\pi\)
−0.957558 + 0.288242i \(0.906929\pi\)
\(500\) −3.06417 + 0.878817i −0.137034 + 0.0393019i
\(501\) 8.56498 8.71489i 0.382655 0.389352i
\(502\) −17.9849 17.9849i −0.802704 0.802704i
\(503\) −2.81929 2.81929i −0.125706 0.125706i 0.641455 0.767161i \(-0.278331\pi\)
−0.767161 + 0.641455i \(0.778331\pi\)
\(504\) 0 0
\(505\) −4.33485 + 9.43955i −0.192898 + 0.420055i
\(506\) 2.70113i 0.120080i
\(507\) −0.0896964 10.3392i −0.00398356 0.459181i
\(508\) −1.26277 + 1.26277i −0.0560263 + 0.0560263i
\(509\) −40.5589 −1.79774 −0.898871 0.438213i \(-0.855611\pi\)
−0.898871 + 0.438213i \(0.855611\pi\)
\(510\) −2.88433 + 6.42736i −0.127720 + 0.284608i
\(511\) 0 0
\(512\) 11.3747 11.3747i 0.502695 0.502695i
\(513\) −0.929528 35.7081i −0.0410397 1.57655i
\(514\) 21.0378i 0.927936i
\(515\) 22.0799 8.18268i 0.972958 0.360572i
\(516\) 2.39534 + 2.35414i 0.105449 + 0.103635i
\(517\) −6.77477 6.77477i −0.297954 0.297954i
\(518\) 0 0
\(519\) −29.7281 29.2167i −1.30492 1.28247i
\(520\) 22.9431 + 10.5360i 1.00612 + 0.462032i
\(521\) 15.8396i 0.693945i 0.937875 + 0.346973i \(0.112790\pi\)
−0.937875 + 0.346973i \(0.887210\pi\)
\(522\) −8.57786 + 8.88080i −0.375443 + 0.388702i
\(523\) 9.52401 9.52401i 0.416456 0.416456i −0.467524 0.883980i \(-0.654854\pi\)
0.883980 + 0.467524i \(0.154854\pi\)
\(524\) 2.42724 0.106035
\(525\) 0 0
\(526\) −32.5151 −1.41772
\(527\) −3.94268 + 3.94268i −0.171746 + 0.171746i
\(528\) −0.0616561 7.10704i −0.00268324 0.309294i
\(529\) 19.1790i 0.833868i
\(530\) −33.8793 15.5581i −1.47162 0.675802i
\(531\) 29.6369 0.514259i 1.28613 0.0223170i
\(532\) 0 0
\(533\) 2.84210 + 2.84210i 0.123105 + 0.123105i
\(534\) −20.7284 + 21.0912i −0.897007 + 0.912707i
\(535\) 13.2661 4.91634i 0.573545 0.212552i
\(536\) 18.3424i 0.792273i
\(537\) −8.86525 + 0.0769091i −0.382564 + 0.00331887i
\(538\) −20.1835 + 20.1835i −0.870171 + 0.870171i
\(539\) 0 0
\(540\) −1.30368 + 3.04546i −0.0561014 + 0.131056i
\(541\) −31.9532 −1.37377 −0.686887 0.726764i \(-0.741023\pi\)
−0.686887 + 0.726764i \(0.741023\pi\)
\(542\) 3.96759 3.96759i 0.170422 0.170422i
\(543\) −3.06604 + 0.0265989i −0.131576 + 0.00114147i
\(544\) 1.92662i 0.0826031i
\(545\) 8.04299 17.5144i 0.344524 0.750234i
\(546\) 0 0
\(547\) 24.7307 + 24.7307i 1.05741 + 1.05741i 0.998249 + 0.0591593i \(0.0188420\pi\)
0.0591593 + 0.998249i \(0.481158\pi\)
\(548\) −2.08313 2.08313i −0.0889868 0.0889868i
\(549\) −3.20318 + 0.0555816i −0.136708 + 0.00237217i
\(550\) −0.521797 + 6.88942i −0.0222495 + 0.293766i
\(551\) 18.7162i 0.797338i
\(552\) −0.0761397 8.77655i −0.00324072 0.373555i
\(553\) 0 0
\(554\) −11.4306 −0.485640
\(555\) −1.10504 2.90425i −0.0469064 0.123278i
\(556\) −0.865465 −0.0367039
\(557\) 2.73832 2.73832i 0.116026 0.116026i −0.646710 0.762736i \(-0.723856\pi\)
0.762736 + 0.646710i \(0.223856\pi\)
\(558\) −14.5991 + 15.1147i −0.618029 + 0.639856i
\(559\) 29.6205i 1.25281i
\(560\) 0 0
\(561\) 1.35880 + 1.33542i 0.0573685 + 0.0563817i
\(562\) 12.8852 + 12.8852i 0.543531 + 0.543531i
\(563\) −25.8490 25.8490i −1.08941 1.08941i −0.995589 0.0938172i \(-0.970093\pi\)
−0.0938172 0.995589i \(-0.529907\pi\)
\(564\) −3.69158 3.62808i −0.155444 0.152770i
\(565\) −8.17767 22.0664i −0.344037 0.928341i
\(566\) 36.3002i 1.52581i
\(567\) 0 0
\(568\) 1.02240 1.02240i 0.0428989 0.0428989i
\(569\) 16.2393 0.680787 0.340393 0.940283i \(-0.389440\pi\)
0.340393 + 0.940283i \(0.389440\pi\)
\(570\) −14.3126 37.6160i −0.599488 1.57556i
\(571\) 40.2805 1.68569 0.842843 0.538159i \(-0.180880\pi\)
0.842843 + 0.538159i \(0.180880\pi\)
\(572\) −0.802671 + 0.802671i −0.0335614 + 0.0335614i
\(573\) −0.137921 15.8980i −0.00576174 0.664151i
\(574\) 0 0
\(575\) −0.738139 + 9.74583i −0.0307825 + 0.406429i
\(576\) 0.341308 + 19.6697i 0.0142212 + 0.819570i
\(577\) 12.2206 + 12.2206i 0.508750 + 0.508750i 0.914143 0.405393i \(-0.132865\pi\)
−0.405393 + 0.914143i \(0.632865\pi\)
\(578\) −16.6237 16.6237i −0.691454 0.691454i
\(579\) −8.61273 + 8.76347i −0.357933 + 0.364197i
\(580\) −0.724378 + 1.57740i −0.0300781 + 0.0654980i
\(581\) 0 0
\(582\) 5.88001 0.0510111i 0.243734 0.00211448i
\(583\) −7.12906 + 7.12906i −0.295256 + 0.295256i
\(584\) 5.65047 0.233818
\(585\) −27.2159 + 10.6266i −1.12524 + 0.439357i
\(586\) 26.1878 1.08181
\(587\) −0.596922 + 0.596922i −0.0246376 + 0.0246376i −0.719318 0.694681i \(-0.755546\pi\)
0.694681 + 0.719318i \(0.255546\pi\)
\(588\) 0 0
\(589\) 31.8541i 1.31253i
\(590\) 31.3163 11.6056i 1.28927 0.477796i
\(591\) −21.5543 + 21.9316i −0.886627 + 0.902145i
\(592\) 2.54669 + 2.54669i 0.104668 + 0.104668i
\(593\) −6.63562 6.63562i −0.272492 0.272492i 0.557610 0.830103i \(-0.311718\pi\)
−0.830103 + 0.557610i \(0.811718\pi\)
\(594\) 5.20757 + 4.94333i 0.213669 + 0.202827i
\(595\) 0 0
\(596\) 3.67234i 0.150425i
\(597\) −0.258688 29.8187i −0.0105874 1.22040i
\(598\) −9.10037 + 9.10037i −0.372142 + 0.372142i
\(599\) 6.28684 0.256873 0.128437 0.991718i \(-0.459004\pi\)
0.128437 + 0.991718i \(0.459004\pi\)
\(600\) 1.50123 22.3999i 0.0612875 0.914472i
\(601\) 9.39584 0.383264 0.191632 0.981467i \(-0.438622\pi\)
0.191632 + 0.981467i \(0.438622\pi\)
\(602\) 0 0
\(603\) −15.2679 14.7471i −0.621759 0.600549i
\(604\) 3.39254i 0.138041i
\(605\) −20.6545 9.48501i −0.839726 0.385620i
\(606\) 8.67467 + 8.52545i 0.352384 + 0.346323i
\(607\) 10.0128 + 10.0128i 0.406408 + 0.406408i 0.880484 0.474076i \(-0.157218\pi\)
−0.474076 + 0.880484i \(0.657218\pi\)
\(608\) 7.78287 + 7.78287i 0.315637 + 0.315637i
\(609\) 0 0
\(610\) −3.38470 + 1.25435i −0.137042 + 0.0507870i
\(611\) 45.6497i 1.84679i
\(612\) 0.740302 + 0.715048i 0.0299249 + 0.0289041i
\(613\) −3.06941 + 3.06941i −0.123972 + 0.123972i −0.766371 0.642399i \(-0.777939\pi\)
0.642399 + 0.766371i \(0.277939\pi\)
\(614\) 26.7286 1.07868
\(615\) 1.46333 3.26084i 0.0590072 0.131490i
\(616\) 0 0
\(617\) −3.80377 + 3.80377i −0.153134 + 0.153134i −0.779516 0.626382i \(-0.784535\pi\)
0.626382 + 0.779516i \(0.284535\pi\)
\(618\) −0.239190 27.5712i −0.00962164 1.10908i
\(619\) 21.8072i 0.876505i 0.898852 + 0.438252i \(0.144402\pi\)
−0.898852 + 0.438252i \(0.855598\pi\)
\(620\) −1.23286 + 2.68466i −0.0495127 + 0.107819i
\(621\) 7.36667 + 6.99288i 0.295614 + 0.280614i
\(622\) −25.0547 25.0547i −1.00460 1.00460i
\(623\) 0 0
\(624\) 23.7366 24.1520i 0.950224 0.966855i
\(625\) −3.76535 + 24.7148i −0.150614 + 0.988593i
\(626\) 16.0239i 0.640443i
\(627\) −10.8837 + 0.0944200i −0.434654 + 0.00377077i
\(628\) −2.80486 + 2.80486i −0.111926 + 0.111926i
\(629\) −0.965431 −0.0384943
\(630\) 0 0
\(631\) 8.91815 0.355026 0.177513 0.984118i \(-0.443195\pi\)
0.177513 + 0.984118i \(0.443195\pi\)
\(632\) −5.55620 + 5.55620i −0.221014 + 0.221014i
\(633\) −16.8928 + 0.146551i −0.671429 + 0.00582488i
\(634\) 31.0537i 1.23330i
\(635\) 4.86691 + 13.1327i 0.193137 + 0.521157i
\(636\) −3.81782 + 3.88464i −0.151386 + 0.154036i
\(637\) 0 0
\(638\) 2.66027 + 2.66027i 0.105321 + 0.105321i
\(639\) 0.0290303 + 1.67302i 0.00114842 + 0.0661838i
\(640\) 10.1908 + 27.4985i 0.402825 + 1.08697i
\(641\) 39.0775i 1.54347i −0.635944 0.771735i \(-0.719389\pi\)
0.635944 0.771735i \(-0.280611\pi\)
\(642\) −0.143711 16.5654i −0.00567182 0.653785i
\(643\) 10.9666 10.9666i 0.432481 0.432481i −0.456991 0.889471i \(-0.651073\pi\)
0.889471 + 0.456991i \(0.151073\pi\)
\(644\) 0 0
\(645\) 24.6178 9.36688i 0.969325 0.368821i
\(646\) −12.5043 −0.491976
\(647\) −10.2096 + 10.2096i −0.401380 + 0.401380i −0.878719 0.477339i \(-0.841601\pi\)
0.477339 + 0.878719i \(0.341601\pi\)
\(648\) −17.0599 15.9151i −0.670174 0.625206i
\(649\) 9.03186i 0.354532i
\(650\) −24.9691 + 21.4531i −0.979369 + 0.841461i
\(651\) 0 0
\(652\) 4.85751 + 4.85751i 0.190235 + 0.190235i
\(653\) −12.3763 12.3763i −0.484323 0.484323i 0.422186 0.906509i \(-0.361263\pi\)
−0.906509 + 0.422186i \(0.861263\pi\)
\(654\) −16.0952 15.8183i −0.629372 0.618546i
\(655\) 7.94413 17.2991i 0.310403 0.675932i
\(656\) 4.14256i 0.161740i
\(657\) −4.54292 + 4.70336i −0.177236 + 0.183496i
\(658\) 0 0
\(659\) −7.49888 −0.292115 −0.146057 0.989276i \(-0.546658\pi\)
−0.146057 + 0.989276i \(0.546658\pi\)
\(660\) 0.920934 + 0.413277i 0.0358473 + 0.0160868i
\(661\) −25.7103 −1.00002 −0.500008 0.866021i \(-0.666669\pi\)
−0.500008 + 0.866021i \(0.666669\pi\)
\(662\) −34.1320 + 34.1320i −1.32658 + 1.32658i
\(663\) 0.0787469 + 9.07709i 0.00305828 + 0.352525i
\(664\) 8.72904i 0.338752i
\(665\) 0 0
\(666\) −3.63796 + 0.0631259i −0.140968 + 0.00244608i
\(667\) 3.76324 + 3.76324i 0.145713 + 0.145713i
\(668\) −1.42229 1.42229i −0.0550302 0.0550302i
\(669\) 15.7494 16.0251i 0.608908 0.619566i
\(670\) −21.7348 9.98111i −0.839689 0.385604i
\(671\) 0.976172i 0.0376847i
\(672\) 0 0
\(673\) 9.04384 9.04384i 0.348614 0.348614i −0.510979 0.859593i \(-0.670717\pi\)
0.859593 + 0.510979i \(0.170717\pi\)
\(674\) −20.0989 −0.774179
\(675\) 17.4383 + 19.2589i 0.671202 + 0.741275i
\(676\) −1.70203 −0.0654627
\(677\) 24.1492 24.1492i 0.928131 0.928131i −0.0694543 0.997585i \(-0.522126\pi\)
0.997585 + 0.0694543i \(0.0221258\pi\)
\(678\) −27.5544 + 0.239044i −1.05822 + 0.00918042i
\(679\) 0 0
\(680\) −6.33864 2.91084i −0.243076 0.111626i
\(681\) −29.1881 + 29.6990i −1.11849 + 1.13807i
\(682\) 4.52765 + 4.52765i 0.173373 + 0.173373i
\(683\) 16.8972 + 16.8972i 0.646552 + 0.646552i 0.952158 0.305606i \(-0.0988590\pi\)
−0.305606 + 0.952158i \(0.598859\pi\)
\(684\) −5.87911 + 0.102014i −0.224793 + 0.00390061i
\(685\) −21.6644 + 8.02870i −0.827756 + 0.306761i
\(686\) 0 0
\(687\) 0.0489368 + 5.64091i 0.00186706 + 0.215214i
\(688\) −21.5870 + 21.5870i −0.822997 + 0.822997i
\(689\) −48.0370 −1.83006
\(690\) 10.4412 + 4.68557i 0.397489 + 0.178377i
\(691\) 20.1951 0.768259 0.384129 0.923279i \(-0.374502\pi\)
0.384129 + 0.923279i \(0.374502\pi\)
\(692\) −4.85170 + 4.85170i −0.184434 + 0.184434i
\(693\) 0 0
\(694\) 24.3128i 0.922899i
\(695\) −2.83258 + 6.16822i −0.107446 + 0.233974i
\(696\) −8.71877 8.56879i −0.330484 0.324799i
\(697\) −0.785206 0.785206i −0.0297418 0.0297418i
\(698\) 9.84475 + 9.84475i 0.372629 + 0.372629i
\(699\) 20.6037 + 20.2493i 0.779304 + 0.765899i
\(700\) 0 0
\(701\) 49.4540i 1.86785i 0.357467 + 0.933926i \(0.383640\pi\)
−0.357467 + 0.933926i \(0.616360\pi\)
\(702\) 0.890253 + 34.1994i 0.0336004 + 1.29077i
\(703\) 3.90000 3.90000i 0.147091 0.147091i
\(704\) 5.99435 0.225920
\(705\) −37.9398 + 14.4358i −1.42889 + 0.543683i
\(706\) −15.7936 −0.594398
\(707\) 0 0
\(708\) −0.0423283 4.87915i −0.00159080 0.183370i
\(709\) 39.2209i 1.47297i −0.676453 0.736486i \(-0.736484\pi\)
0.676453 0.736486i \(-0.263516\pi\)
\(710\) 0.655146 + 1.76783i 0.0245872 + 0.0663455i
\(711\) −0.157765 9.09202i −0.00591664 0.340977i
\(712\) −20.7034 20.7034i −0.775891 0.775891i
\(713\) 6.40485 + 6.40485i 0.239864 + 0.239864i
\(714\) 0 0
\(715\) 3.09362 + 8.34775i 0.115695 + 0.312188i
\(716\) 1.45938i 0.0545397i
\(717\) 26.2958 0.228125i 0.982033 0.00851948i
\(718\) 1.64800 1.64800i 0.0615029 0.0615029i
\(719\) −1.93192 −0.0720484 −0.0360242 0.999351i \(-0.511469\pi\)
−0.0360242 + 0.999351i \(0.511469\pi\)
\(720\) −27.5791 12.0900i −1.02781 0.450569i
\(721\) 0 0
\(722\) 30.2039 30.2039i 1.12407 1.12407i
\(723\) 0.205698 0.00178450i 0.00765000 6.63664e-5i
\(724\) 0.504726i 0.0187580i
\(725\) 8.87142 + 10.3254i 0.329476 + 0.383475i
\(726\) −18.6544 + 18.9809i −0.692329 + 0.704447i
\(727\) 15.8726 + 15.8726i 0.588684 + 0.588684i 0.937275 0.348591i \(-0.113340\pi\)
−0.348591 + 0.937275i \(0.613340\pi\)
\(728\) 0 0
\(729\) 26.9634 1.40474i 0.998646 0.0520273i
\(730\) −3.07473 + 6.69551i −0.113801 + 0.247812i
\(731\) 8.18346i 0.302676i
\(732\) 0.00457488 + 0.527343i 0.000169093 + 0.0194912i
\(733\) −30.7539 + 30.7539i −1.13592 + 1.13592i −0.146746 + 0.989174i \(0.546880\pi\)
−0.989174 + 0.146746i \(0.953120\pi\)
\(734\) −24.2387 −0.894668
\(735\) 0 0
\(736\) −3.12978 −0.115365
\(737\) −4.57356 + 4.57356i −0.168469 + 0.168469i
\(738\) −3.01017 2.90749i −0.110806 0.107026i
\(739\) 27.0647i 0.995592i −0.867294 0.497796i \(-0.834143\pi\)
0.867294 0.497796i \(-0.165857\pi\)
\(740\) −0.479635 + 0.177749i −0.0176317 + 0.00653420i
\(741\) −36.9864 36.3502i −1.35873 1.33536i
\(742\) 0 0
\(743\) 2.20467 + 2.20467i 0.0808816 + 0.0808816i 0.746390 0.665509i \(-0.231785\pi\)
−0.665509 + 0.746390i \(0.731785\pi\)
\(744\) −14.8389 14.5837i −0.544021 0.534663i
\(745\) 26.1730 + 12.0192i 0.958905 + 0.440350i
\(746\) 42.4200i 1.55311i
\(747\) −7.26590 7.01805i −0.265846 0.256777i
\(748\) 0.221760 0.221760i 0.00810833 0.00810833i
\(749\) 0 0
\(750\) 25.7258 + 13.9679i 0.939374 + 0.510035i
\(751\) 23.9281 0.873148 0.436574 0.899668i \(-0.356192\pi\)
0.436574 + 0.899668i \(0.356192\pi\)
\(752\) 33.2689 33.2689i 1.21319 1.21319i
\(753\) 0.252813 + 29.1415i 0.00921302 + 1.06198i
\(754\) 17.9254i 0.652804i
\(755\) −24.1789 11.1035i −0.879959 0.404096i
\(756\) 0 0
\(757\) 34.0440 + 34.0440i 1.23735 + 1.23735i 0.961081 + 0.276268i \(0.0890977\pi\)
0.276268 + 0.961081i \(0.410902\pi\)
\(758\) −19.9038 19.9038i −0.722940 0.722940i
\(759\) 2.16939 2.20736i 0.0787437 0.0801219i
\(760\) 37.3647 13.8471i 1.35536 0.502287i
\(761\) 6.63770i 0.240616i 0.992737 + 0.120308i \(0.0383883\pi\)
−0.992737 + 0.120308i \(0.961612\pi\)
\(762\) 16.3989 0.142266i 0.594069 0.00515375i
\(763\) 0 0
\(764\) −2.61711 −0.0946838
\(765\) 7.51913 2.93589i 0.271855 0.106147i
\(766\) −24.5163 −0.885809
\(767\) 30.4292 30.4292i 1.09873 1.09873i
\(768\) 11.6222 0.100827i 0.419381 0.00363828i
\(769\) 22.0730i 0.795972i −0.917391 0.397986i \(-0.869709\pi\)
0.917391 0.397986i \(-0.130291\pi\)
\(770\) 0 0
\(771\) −16.8963 + 17.1920i −0.608504 + 0.619155i
\(772\) 1.43022 + 1.43022i 0.0514748 + 0.0514748i
\(773\) 23.1387 + 23.1387i 0.832240 + 0.832240i 0.987823 0.155583i \(-0.0497256\pi\)
−0.155583 + 0.987823i \(0.549726\pi\)
\(774\) −0.535086 30.8371i −0.0192333 1.10842i
\(775\) 15.0987 + 17.5733i 0.542363 + 0.631251i
\(776\) 5.82195i 0.208996i
\(777\) 0 0
\(778\) 35.7966 35.7966i 1.28337 1.28337i
\(779\) 6.34391 0.227294
\(780\) 1.71034 + 4.49508i 0.0612401 + 0.160950i
\(781\) 0.509855 0.0182441
\(782\) 2.51422 2.51422i 0.0899084 0.0899084i
\(783\) 14.1423 0.368142i 0.505405 0.0131563i
\(784\) 0 0
\(785\) 10.8104 + 29.1705i 0.385839 + 1.04114i
\(786\) −15.8974 15.6239i −0.567040 0.557286i
\(787\) −8.67333 8.67333i −0.309171 0.309171i 0.535417 0.844588i \(-0.320154\pi\)
−0.844588 + 0.535417i \(0.820154\pi\)
\(788\) 3.57930 + 3.57930i 0.127507 + 0.127507i
\(789\) 26.5712 + 26.1141i 0.945960 + 0.929688i
\(790\) −3.56038 9.60724i −0.126673 0.341810i
\(791\) 0 0
\(792\) −4.93888 + 5.11330i −0.175495 + 0.181693i
\(793\) −3.28882 + 3.28882i −0.116789 + 0.116789i
\(794\) −16.0692 −0.570276
\(795\) 15.1907 + 39.9239i 0.538759 + 1.41595i
\(796\) −4.90871 −0.173985
\(797\) 27.2098 27.2098i 0.963820 0.963820i −0.0355479 0.999368i \(-0.511318\pi\)
0.999368 + 0.0355479i \(0.0113176\pi\)
\(798\) 0 0
\(799\) 12.6120i 0.446179i
\(800\) −7.98271 0.604602i −0.282231 0.0213759i
\(801\) 33.8784 0.587858i 1.19703 0.0207709i
\(802\) −41.1290 41.1290i −1.45231 1.45231i
\(803\) 1.40890 + 1.40890i 0.0497192 + 0.0497192i
\(804\) −2.44927 + 2.49214i −0.0863791 + 0.0878909i
\(805\) 0 0
\(806\) 30.5082i 1.07460i
\(807\) 32.7040 0.283719i 1.15124 0.00998737i
\(808\) −8.51513 + 8.51513i −0.299561 + 0.299561i
\(809\) −38.3573 −1.34857 −0.674285 0.738471i \(-0.735548\pi\)
−0.674285 + 0.738471i \(0.735548\pi\)
\(810\) 28.1418 11.5547i 0.988802 0.405992i
\(811\) 3.87781 0.136168 0.0680841 0.997680i \(-0.478311\pi\)
0.0680841 + 0.997680i \(0.478311\pi\)
\(812\) 0 0
\(813\) −6.42883 + 0.0557723i −0.225469 + 0.00195602i
\(814\) 1.10867i 0.0388589i
\(815\) 50.5179 18.7216i 1.76957 0.655789i
\(816\) −6.55787 + 6.67265i −0.229571 + 0.233589i
\(817\) 33.0583 + 33.0583i 1.15656 + 1.15656i
\(818\) −1.03534 1.03534i −0.0361999 0.0361999i
\(819\) 0 0
\(820\) −0.534665 0.245530i −0.0186713 0.00857427i
\(821\) 8.04772i 0.280867i 0.990090 + 0.140434i \(0.0448497\pi\)
−0.990090 + 0.140434i \(0.955150\pi\)
\(822\) 0.234689 + 27.0524i 0.00818573 + 0.943562i
\(823\) 1.27909 1.27909i 0.0445862 0.0445862i −0.684462 0.729048i \(-0.739963\pi\)
0.729048 + 0.684462i \(0.239963\pi\)
\(824\) 27.2990 0.951005
\(825\) 5.95958 5.21094i 0.207486 0.181421i
\(826\) 0 0
\(827\) 27.7405 27.7405i 0.964633 0.964633i −0.0347627 0.999396i \(-0.511068\pi\)
0.999396 + 0.0347627i \(0.0110676\pi\)
\(828\) 1.16159 1.20261i 0.0403680 0.0417937i
\(829\) 9.32952i 0.324028i 0.986788 + 0.162014i \(0.0517989\pi\)
−0.986788 + 0.162014i \(0.948201\pi\)
\(830\) −10.3434 4.74994i −0.359026 0.164873i
\(831\) 9.34105 + 9.18037i 0.324037 + 0.318464i
\(832\) 20.1955 + 20.1955i 0.700154 + 0.700154i
\(833\) 0 0
\(834\) 5.66841 + 5.57090i 0.196281 + 0.192905i
\(835\) −14.7918 + 5.48174i −0.511891 + 0.189704i
\(836\) 1.79166i 0.0619659i
\(837\) 24.0695 0.626561i 0.831965 0.0216571i
\(838\) −26.0259 + 26.0259i −0.899050 + 0.899050i
\(839\) −3.18996 −0.110130 −0.0550649 0.998483i \(-0.517537\pi\)
−0.0550649 + 0.998483i \(0.517537\pi\)
\(840\) 0 0
\(841\) −21.5874 −0.744393
\(842\) −1.88045 + 1.88045i −0.0648045 + 0.0648045i
\(843\) −0.181127 20.8784i −0.00623836 0.719090i
\(844\) 2.78087i 0.0957215i
\(845\) −5.57058 + 12.1305i −0.191634 + 0.417301i
\(846\) 0.824648 + 47.5247i 0.0283520 + 1.63393i
\(847\) 0 0
\(848\) −35.0087 35.0087i −1.20220 1.20220i
\(849\) −29.1541 + 29.6644i −1.00057 + 1.01808i
\(850\) 6.89839 5.92701i 0.236613 0.203295i
\(851\) 1.56833i 0.0537618i
\(852\) 0.275432 0.00238946i 0.00943613 8.18617e-5i
\(853\) −5.14974 + 5.14974i −0.176324 + 0.176324i −0.789751 0.613427i \(-0.789790\pi\)
0.613427 + 0.789751i \(0.289790\pi\)
\(854\) 0 0
\(855\) −18.5147 + 42.2346i −0.633189 + 1.44439i
\(856\) 16.4019 0.560604
\(857\) −8.17961 + 8.17961i −0.279410 + 0.279410i −0.832873 0.553463i \(-0.813306\pi\)
0.553463 + 0.832873i \(0.313306\pi\)
\(858\) 10.4238 0.0904305i 0.355864 0.00308725i
\(859\) 27.8219i 0.949270i −0.880183 0.474635i \(-0.842580\pi\)
0.880183 0.474635i \(-0.157420\pi\)
\(860\) −1.50669 4.06562i −0.0513778 0.138636i
\(861\) 0 0
\(862\) −22.9187 22.9187i −0.780613 0.780613i
\(863\) −5.52270 5.52270i −0.187995 0.187995i 0.606834 0.794829i \(-0.292439\pi\)
−0.794829 + 0.606834i \(0.792439\pi\)
\(864\) −5.72779 + 6.03397i −0.194863 + 0.205280i
\(865\) 18.6992 + 50.4575i 0.635793 + 1.71561i
\(866\) 57.3011i 1.94717i
\(867\) 0.233679 + 26.9360i 0.00793615 + 0.914793i
\(868\) 0 0
\(869\) −2.77080 −0.0939929
\(870\) 14.8979 5.66854i 0.505087 0.192182i
\(871\) −30.8175 −1.04421
\(872\) 15.7992 15.7992i 0.535028 0.535028i
\(873\) −4.84609 4.68078i −0.164015 0.158421i
\(874\) 20.3132i 0.687103i
\(875\) 0 0
\(876\) 0.767715 + 0.754509i 0.0259387 + 0.0254925i
\(877\) −11.0212 11.0212i −0.372160 0.372160i 0.496103 0.868263i \(-0.334764\pi\)
−0.868263 + 0.496103i \(0.834764\pi\)
\(878\) 2.53590 + 2.53590i 0.0855825 + 0.0855825i
\(879\) −21.4006 21.0325i −0.721825 0.709408i
\(880\) −3.82914 + 8.33831i −0.129080 + 0.281085i
\(881\) 8.59639i 0.289620i −0.989459 0.144810i \(-0.953743\pi\)
0.989459 0.144810i \(-0.0462571\pi\)
\(882\) 0 0
\(883\) −31.4000 + 31.4000i −1.05670 + 1.05670i −0.0584026 + 0.998293i \(0.518601\pi\)
−0.998293 + 0.0584026i \(0.981399\pi\)
\(884\) 1.49426 0.0502573
\(885\) −34.9125 15.6673i −1.17357 0.526651i
\(886\) −32.8889 −1.10492
\(887\) 1.41909 1.41909i 0.0476485 0.0476485i −0.682881 0.730530i \(-0.739273\pi\)
0.730530 + 0.682881i \(0.239273\pi\)
\(888\) −0.0312513 3.60231i −0.00104872 0.120885i
\(889\) 0 0
\(890\) 35.7982 13.2666i 1.19996 0.444697i
\(891\) −0.285425 8.22208i −0.00956210 0.275450i
\(892\) −2.61534 2.61534i −0.0875680 0.0875680i
\(893\) −50.9479 50.9479i −1.70491 1.70491i
\(894\) 23.6385 24.0522i 0.790589 0.804426i
\(895\) 10.4011 + 4.77642i 0.347671 + 0.159658i
\(896\) 0 0
\(897\) 14.7457 0.127924i 0.492343 0.00427125i
\(898\) 30.8792 30.8792i 1.03045 1.03045i
\(899\) 12.6159 0.420764
\(900\) 3.19503 2.84296i 0.106501 0.0947652i
\(901\) 13.2715 0.442138
\(902\) −0.901706 + 0.901706i −0.0300235 + 0.0300235i
\(903\) 0 0
\(904\) 27.2823i 0.907395i
\(905\) 3.59722 + 1.65192i 0.119576 + 0.0549117i
\(906\) −21.8374 + 22.2197i −0.725500 + 0.738198i
\(907\) 6.51113 + 6.51113i 0.216198 + 0.216198i 0.806894 0.590696i \(-0.201147\pi\)
−0.590696 + 0.806894i \(0.701147\pi\)
\(908\) 4.84695 + 4.84695i 0.160852 + 0.160852i
\(909\) −0.241782 13.9339i −0.00801939 0.462159i
\(910\) 0 0
\(911\) 32.1044i 1.06367i −0.846849 0.531834i \(-0.821503\pi\)
0.846849 0.531834i \(-0.178497\pi\)
\(912\) −0.463668 53.4467i −0.0153536 1.76980i
\(913\) −2.17652 + 2.17652i −0.0720324 + 0.0720324i
\(914\) 2.97167 0.0982940
\(915\) 3.77338 + 1.69334i 0.124744 + 0.0559800i
\(916\) 0.928598 0.0306817
\(917\) 0 0
\(918\) −0.245956 9.44849i −0.00811777 0.311847i
\(919\) 35.3855i 1.16726i −0.812020 0.583630i \(-0.801632\pi\)
0.812020 0.583630i \(-0.198368\pi\)
\(920\) −4.72864 + 10.2971i −0.155899 + 0.339484i
\(921\) −21.8425 21.4668i −0.719734 0.707354i
\(922\) −18.6290 18.6290i −0.613514 0.613514i
\(923\) 1.71775 + 1.71775i 0.0565405 + 0.0565405i
\(924\) 0 0
\(925\) −0.302967 + 4.00014i −0.00996148 + 0.131524i
\(926\) 31.7263i 1.04259i
\(927\) −21.9481 + 22.7232i −0.720870 + 0.746329i
\(928\) −3.08243 + 3.08243i −0.101186 + 0.101186i
\(929\) −45.3102 −1.48658 −0.743290 0.668969i \(-0.766736\pi\)
−0.743290 + 0.668969i \(0.766736\pi\)
\(930\) 25.3555 9.64758i 0.831441 0.316357i
\(931\) 0 0
\(932\) 3.36258 3.36258i 0.110145 0.110145i
\(933\) 0.352194 + 40.5971i 0.0115303 + 1.32909i
\(934\) 19.0563i 0.623540i
\(935\) −0.854696 2.30629i −0.0279516 0.0754238i
\(936\) −33.8667 + 0.587656i −1.10697 + 0.0192081i
\(937\) −2.63830 2.63830i −0.0861894 0.0861894i 0.662698 0.748887i \(-0.269411\pi\)
−0.748887 + 0.662698i \(0.769411\pi\)
\(938\) 0 0
\(939\) −12.8694 + 13.0947i −0.419977 + 0.427328i
\(940\) 2.32204 + 6.26574i 0.0757366 + 0.204366i
\(941\) 27.0062i 0.880376i 0.897906 + 0.440188i \(0.145088\pi\)
−0.897906 + 0.440188i \(0.854912\pi\)
\(942\) 36.4252 0.316001i 1.18680 0.0102959i
\(943\) −1.27556 + 1.27556i −0.0415380 + 0.0415380i
\(944\) 44.3528 1.44356
\(945\) 0 0
\(946\) −9.39763 −0.305543
\(947\) −9.83573 + 9.83573i −0.319618 + 0.319618i −0.848620 0.529002i \(-0.822566\pi\)
0.529002 + 0.848620i \(0.322566\pi\)
\(948\) −1.49683 + 0.0129855i −0.0486147 + 0.000421749i
\(949\) 9.49347i 0.308171i
\(950\) −3.92404 + 51.8101i −0.127313 + 1.68094i
\(951\) 24.9405 25.3770i 0.808750 0.822905i
\(952\) 0 0
\(953\) −20.8791 20.8791i −0.676342 0.676342i 0.282829 0.959170i \(-0.408727\pi\)
−0.959170 + 0.282829i \(0.908727\pi\)
\(954\) 50.0100 0.867774i 1.61913 0.0280952i
\(955\) −8.56556 + 18.6523i −0.277175 + 0.603575i
\(956\) 4.32877i 0.140002i
\(957\) −0.0373953 4.31053i −0.00120882 0.139340i
\(958\) 10.9968 10.9968i 0.355289 0.355289i
\(959\) 0 0
\(960\) 10.3982 23.1711i 0.335601 0.747843i
\(961\) −9.52832 −0.307365
\(962\) −3.73522 + 3.73522i −0.120428 + 0.120428i
\(963\) −13.1869 + 13.6526i −0.424942 + 0.439950i
\(964\) 0.0338618i 0.00109061i
\(965\) 14.8743 5.51230i 0.478819 0.177447i
\(966\) 0 0
\(967\) −38.5871 38.5871i −1.24088 1.24088i −0.959638 0.281238i \(-0.909255\pi\)
−0.281238 0.959638i \(-0.590745\pi\)
\(968\) −18.6318 18.6318i −0.598849 0.598849i
\(969\) 10.2185 + 10.0427i 0.328265 + 0.322618i
\(970\) −6.89870 3.16804i −0.221504 0.101720i
\(971\) 21.4943i 0.689786i 0.938642 + 0.344893i \(0.112085\pi\)
−0.938642 + 0.344893i \(0.887915\pi\)
\(972\) −0.192724 4.44035i −0.00618163 0.142424i
\(973\) 0 0
\(974\) −28.1852 −0.903112
\(975\) 37.6345 + 2.52225i 1.20527 + 0.0807766i
\(976\) −4.79369 −0.153442
\(977\) −31.5962 + 31.5962i −1.01085 + 1.01085i −0.0109125 + 0.999940i \(0.503474\pi\)
−0.999940 + 0.0109125i \(0.996526\pi\)
\(978\) −0.547257 63.0818i −0.0174993 2.01713i
\(979\) 10.3245i 0.329971i
\(980\) 0 0
\(981\) 0.448608 + 25.8534i 0.0143229 + 0.825435i
\(982\) −26.3955 26.3955i −0.842315 0.842315i
\(983\) 9.20130 + 9.20130i 0.293476 + 0.293476i 0.838452 0.544976i \(-0.183461\pi\)
−0.544976 + 0.838452i \(0.683461\pi\)
\(984\) 2.90442 2.95525i 0.0925894 0.0942100i
\(985\) 37.2245 13.7952i 1.18607 0.439551i
\(986\) 4.95237i 0.157716i
\(987\) 0 0
\(988\) −6.03628 + 6.03628i −0.192040 + 0.192040i
\(989\) −13.2940 −0.422724
\(990\) −3.37149 8.63473i −0.107153 0.274430i
\(991\) 13.4625 0.427652 0.213826 0.976872i \(-0.431407\pi\)
0.213826 + 0.976872i \(0.431407\pi\)
\(992\) −5.24615 + 5.24615i −0.166565 + 0.166565i
\(993\) 55.3053 0.479793i 1.75506 0.0152258i
\(994\) 0 0
\(995\) −16.0657 + 34.9847i −0.509318 + 1.10909i
\(996\) −1.16559 + 1.18599i −0.0369331 + 0.0375796i
\(997\) −26.8715 26.8715i −0.851029 0.851029i 0.139231 0.990260i \(-0.455537\pi\)
−0.990260 + 0.139231i \(0.955537\pi\)
\(998\) −13.7650 13.7650i −0.435724 0.435724i
\(999\) 3.02363 + 2.87020i 0.0956633 + 0.0908092i
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 735.2.j.g.197.3 24
3.2 odd 2 inner 735.2.j.g.197.10 24
5.3 odd 4 inner 735.2.j.g.638.10 24
7.2 even 3 105.2.x.a.32.10 yes 48
7.3 odd 6 735.2.y.i.422.3 48
7.4 even 3 105.2.x.a.2.3 48
7.5 odd 6 735.2.y.i.557.10 48
7.6 odd 2 735.2.j.e.197.3 24
15.8 even 4 inner 735.2.j.g.638.3 24
21.2 odd 6 105.2.x.a.32.3 yes 48
21.5 even 6 735.2.y.i.557.3 48
21.11 odd 6 105.2.x.a.2.10 yes 48
21.17 even 6 735.2.y.i.422.10 48
21.20 even 2 735.2.j.e.197.10 24
35.2 odd 12 525.2.bf.f.368.3 48
35.3 even 12 735.2.y.i.128.3 48
35.4 even 6 525.2.bf.f.107.10 48
35.9 even 6 525.2.bf.f.32.3 48
35.13 even 4 735.2.j.e.638.10 24
35.18 odd 12 105.2.x.a.23.3 yes 48
35.23 odd 12 105.2.x.a.53.10 yes 48
35.32 odd 12 525.2.bf.f.443.10 48
35.33 even 12 735.2.y.i.263.10 48
105.2 even 12 525.2.bf.f.368.10 48
105.23 even 12 105.2.x.a.53.3 yes 48
105.32 even 12 525.2.bf.f.443.3 48
105.38 odd 12 735.2.y.i.128.10 48
105.44 odd 6 525.2.bf.f.32.10 48
105.53 even 12 105.2.x.a.23.10 yes 48
105.68 odd 12 735.2.y.i.263.3 48
105.74 odd 6 525.2.bf.f.107.3 48
105.83 odd 4 735.2.j.e.638.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.x.a.2.3 48 7.4 even 3
105.2.x.a.2.10 yes 48 21.11 odd 6
105.2.x.a.23.3 yes 48 35.18 odd 12
105.2.x.a.23.10 yes 48 105.53 even 12
105.2.x.a.32.3 yes 48 21.2 odd 6
105.2.x.a.32.10 yes 48 7.2 even 3
105.2.x.a.53.3 yes 48 105.23 even 12
105.2.x.a.53.10 yes 48 35.23 odd 12
525.2.bf.f.32.3 48 35.9 even 6
525.2.bf.f.32.10 48 105.44 odd 6
525.2.bf.f.107.3 48 105.74 odd 6
525.2.bf.f.107.10 48 35.4 even 6
525.2.bf.f.368.3 48 35.2 odd 12
525.2.bf.f.368.10 48 105.2 even 12
525.2.bf.f.443.3 48 105.32 even 12
525.2.bf.f.443.10 48 35.32 odd 12
735.2.j.e.197.3 24 7.6 odd 2
735.2.j.e.197.10 24 21.20 even 2
735.2.j.e.638.3 24 105.83 odd 4
735.2.j.e.638.10 24 35.13 even 4
735.2.j.g.197.3 24 1.1 even 1 trivial
735.2.j.g.197.10 24 3.2 odd 2 inner
735.2.j.g.638.3 24 15.8 even 4 inner
735.2.j.g.638.10 24 5.3 odd 4 inner
735.2.y.i.128.3 48 35.3 even 12
735.2.y.i.128.10 48 105.38 odd 12
735.2.y.i.263.3 48 105.68 odd 12
735.2.y.i.263.10 48 35.33 even 12
735.2.y.i.422.3 48 7.3 odd 6
735.2.y.i.422.10 48 21.17 even 6
735.2.y.i.557.3 48 21.5 even 6
735.2.y.i.557.10 48 7.5 odd 6