Properties

Label 460.2.m.b.121.1
Level $460$
Weight $2$
Character 460.121
Analytic conductor $3.673$
Analytic rank $0$
Dimension $50$
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] = [460,2,Mod(41,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), degree \(10\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 121.1
Character \(\chi\) \(=\) 460.121
Dual form 460.2.m.b.441.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.70621 - 0.794614i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(-0.171423 + 1.19227i) q^{7} +(4.16838 + 2.67886i) q^{9} +O(q^{10})\) \(q+(-2.70621 - 0.794614i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(-0.171423 + 1.19227i) q^{7} +(4.16838 + 2.67886i) q^{9} +(2.10463 + 4.60849i) q^{11} +(-0.740487 - 5.15020i) q^{13} +(2.70621 - 0.794614i) q^{15} +(3.58038 - 4.13197i) q^{17} +(-4.35198 - 5.02245i) q^{19} +(1.41130 - 3.09031i) q^{21} +(-2.57265 - 4.04740i) q^{23} +(0.415415 - 0.909632i) q^{25} +(-3.61083 - 4.16711i) q^{27} +(0.744998 - 0.859774i) q^{29} +(0.773413 - 0.227094i) q^{31} +(-2.03358 - 14.1439i) q^{33} +(-0.500380 - 1.09568i) q^{35} +(0.750482 + 0.482306i) q^{37} +(-2.08851 + 14.5259i) q^{39} +(9.50148 - 6.10623i) q^{41} +(5.84422 + 1.71602i) q^{43} -4.95496 q^{45} +3.56689 q^{47} +(5.32433 + 1.56336i) q^{49} +(-12.9726 + 8.33696i) q^{51} +(1.33405 - 9.27851i) q^{53} +(-4.26206 - 2.73906i) q^{55} +(7.78644 + 17.0499i) q^{57} +(-0.929600 - 6.46551i) q^{59} +(-11.9880 + 3.51999i) q^{61} +(-3.90847 + 4.51062i) q^{63} +(3.40734 + 3.93228i) q^{65} +(-0.840823 + 1.84115i) q^{67} +(3.74601 + 12.9974i) q^{69} +(5.44982 - 11.9334i) q^{71} +(1.78926 + 2.06492i) q^{73} +(-1.84700 + 2.13156i) q^{75} +(-5.85534 + 1.71928i) q^{77} +(1.17272 + 8.15647i) q^{79} +(0.285293 + 0.624705i) q^{81} +(-10.6221 - 6.82644i) q^{83} +(-0.778090 + 5.41174i) q^{85} +(-2.69931 + 1.73474i) q^{87} +(6.89031 + 2.02318i) q^{89} +6.26736 q^{91} -2.27347 q^{93} +(6.37646 + 1.87230i) q^{95} +(-9.54090 + 6.13156i) q^{97} +(-3.57259 + 24.8479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.70621 0.794614i −1.56243 0.458770i −0.617643 0.786459i \(-0.711912\pi\)
−0.944786 + 0.327688i \(0.893730\pi\)
\(4\) 0 0
\(5\) −0.841254 + 0.540641i −0.376220 + 0.241782i
\(6\) 0 0
\(7\) −0.171423 + 1.19227i −0.0647916 + 0.450636i 0.931439 + 0.363896i \(0.118554\pi\)
−0.996231 + 0.0867392i \(0.972355\pi\)
\(8\) 0 0
\(9\) 4.16838 + 2.67886i 1.38946 + 0.892952i
\(10\) 0 0
\(11\) 2.10463 + 4.60849i 0.634569 + 1.38951i 0.904434 + 0.426613i \(0.140293\pi\)
−0.269866 + 0.962898i \(0.586979\pi\)
\(12\) 0 0
\(13\) −0.740487 5.15020i −0.205374 1.42841i −0.788004 0.615670i \(-0.788885\pi\)
0.582630 0.812738i \(-0.302024\pi\)
\(14\) 0 0
\(15\) 2.70621 0.794614i 0.698739 0.205168i
\(16\) 0 0
\(17\) 3.58038 4.13197i 0.868369 1.00215i −0.131572 0.991307i \(-0.542003\pi\)
0.999941 0.0108444i \(-0.00345196\pi\)
\(18\) 0 0
\(19\) −4.35198 5.02245i −0.998412 1.15223i −0.988338 0.152279i \(-0.951339\pi\)
−0.0100742 0.999949i \(-0.503207\pi\)
\(20\) 0 0
\(21\) 1.41130 3.09031i 0.307971 0.674362i
\(22\) 0 0
\(23\) −2.57265 4.04740i −0.536435 0.843942i
\(24\) 0 0
\(25\) 0.415415 0.909632i 0.0830830 0.181926i
\(26\) 0 0
\(27\) −3.61083 4.16711i −0.694904 0.801962i
\(28\) 0 0
\(29\) 0.744998 0.859774i 0.138343 0.159656i −0.682350 0.731025i \(-0.739042\pi\)
0.820693 + 0.571369i \(0.193588\pi\)
\(30\) 0 0
\(31\) 0.773413 0.227094i 0.138909 0.0407874i −0.211539 0.977370i \(-0.567848\pi\)
0.350448 + 0.936582i \(0.386029\pi\)
\(32\) 0 0
\(33\) −2.03358 14.1439i −0.354001 2.46213i
\(34\) 0 0
\(35\) −0.500380 1.09568i −0.0845796 0.185204i
\(36\) 0 0
\(37\) 0.750482 + 0.482306i 0.123379 + 0.0792906i 0.600875 0.799343i \(-0.294819\pi\)
−0.477496 + 0.878634i \(0.658455\pi\)
\(38\) 0 0
\(39\) −2.08851 + 14.5259i −0.334429 + 2.32600i
\(40\) 0 0
\(41\) 9.50148 6.10623i 1.48388 0.953633i 0.487110 0.873341i \(-0.338051\pi\)
0.996771 0.0802922i \(-0.0255854\pi\)
\(42\) 0 0
\(43\) 5.84422 + 1.71602i 0.891235 + 0.261690i 0.695123 0.718891i \(-0.255350\pi\)
0.196112 + 0.980581i \(0.437168\pi\)
\(44\) 0 0
\(45\) −4.95496 −0.738642
\(46\) 0 0
\(47\) 3.56689 0.520284 0.260142 0.965570i \(-0.416231\pi\)
0.260142 + 0.965570i \(0.416231\pi\)
\(48\) 0 0
\(49\) 5.32433 + 1.56336i 0.760618 + 0.223338i
\(50\) 0 0
\(51\) −12.9726 + 8.33696i −1.81652 + 1.16741i
\(52\) 0 0
\(53\) 1.33405 9.27851i 0.183246 1.27450i −0.665779 0.746149i \(-0.731901\pi\)
0.849025 0.528353i \(-0.177190\pi\)
\(54\) 0 0
\(55\) −4.26206 2.73906i −0.574696 0.369335i
\(56\) 0 0
\(57\) 7.78644 + 17.0499i 1.03134 + 2.25832i
\(58\) 0 0
\(59\) −0.929600 6.46551i −0.121024 0.841738i −0.956400 0.292060i \(-0.905659\pi\)
0.835376 0.549678i \(-0.185250\pi\)
\(60\) 0 0
\(61\) −11.9880 + 3.51999i −1.53491 + 0.450689i −0.936548 0.350540i \(-0.885998\pi\)
−0.598358 + 0.801229i \(0.704180\pi\)
\(62\) 0 0
\(63\) −3.90847 + 4.51062i −0.492421 + 0.568284i
\(64\) 0 0
\(65\) 3.40734 + 3.93228i 0.422629 + 0.487740i
\(66\) 0 0
\(67\) −0.840823 + 1.84115i −0.102723 + 0.224932i −0.954014 0.299762i \(-0.903093\pi\)
0.851291 + 0.524694i \(0.175820\pi\)
\(68\) 0 0
\(69\) 3.74601 + 12.9974i 0.450966 + 1.56470i
\(70\) 0 0
\(71\) 5.44982 11.9334i 0.646774 1.41624i −0.247575 0.968869i \(-0.579634\pi\)
0.894349 0.447369i \(-0.147639\pi\)
\(72\) 0 0
\(73\) 1.78926 + 2.06492i 0.209417 + 0.241680i 0.850735 0.525595i \(-0.176157\pi\)
−0.641318 + 0.767276i \(0.721612\pi\)
\(74\) 0 0
\(75\) −1.84700 + 2.13156i −0.213274 + 0.246131i
\(76\) 0 0
\(77\) −5.85534 + 1.71928i −0.667278 + 0.195931i
\(78\) 0 0
\(79\) 1.17272 + 8.15647i 0.131942 + 0.917674i 0.943020 + 0.332737i \(0.107972\pi\)
−0.811078 + 0.584938i \(0.801119\pi\)
\(80\) 0 0
\(81\) 0.285293 + 0.624705i 0.0316992 + 0.0694117i
\(82\) 0 0
\(83\) −10.6221 6.82644i −1.16593 0.749299i −0.193184 0.981163i \(-0.561881\pi\)
−0.972748 + 0.231863i \(0.925518\pi\)
\(84\) 0 0
\(85\) −0.778090 + 5.41174i −0.0843957 + 0.586985i
\(86\) 0 0
\(87\) −2.69931 + 1.73474i −0.289396 + 0.185984i
\(88\) 0 0
\(89\) 6.89031 + 2.02318i 0.730372 + 0.214456i 0.625715 0.780052i \(-0.284807\pi\)
0.104657 + 0.994508i \(0.466626\pi\)
\(90\) 0 0
\(91\) 6.26736 0.656998
\(92\) 0 0
\(93\) −2.27347 −0.235748
\(94\) 0 0
\(95\) 6.37646 + 1.87230i 0.654210 + 0.192094i
\(96\) 0 0
\(97\) −9.54090 + 6.13156i −0.968732 + 0.622566i −0.926401 0.376538i \(-0.877115\pi\)
−0.0423302 + 0.999104i \(0.513478\pi\)
\(98\) 0 0
\(99\) −3.57259 + 24.8479i −0.359059 + 2.49731i
\(100\) 0 0
\(101\) 8.21876 + 5.28188i 0.817797 + 0.525566i 0.881379 0.472410i \(-0.156616\pi\)
−0.0635815 + 0.997977i \(0.520252\pi\)
\(102\) 0 0
\(103\) 2.14524 + 4.69743i 0.211377 + 0.462851i 0.985389 0.170320i \(-0.0544801\pi\)
−0.774012 + 0.633171i \(0.781753\pi\)
\(104\) 0 0
\(105\) 0.483489 + 3.36274i 0.0471837 + 0.328170i
\(106\) 0 0
\(107\) −2.69243 + 0.790567i −0.260287 + 0.0764270i −0.409272 0.912412i \(-0.634217\pi\)
0.148986 + 0.988839i \(0.452399\pi\)
\(108\) 0 0
\(109\) 7.06272 8.15081i 0.676486 0.780706i −0.308891 0.951097i \(-0.599958\pi\)
0.985376 + 0.170392i \(0.0545032\pi\)
\(110\) 0 0
\(111\) −1.64771 1.90156i −0.156394 0.180488i
\(112\) 0 0
\(113\) −5.06204 + 11.0843i −0.476197 + 1.04273i 0.507295 + 0.861773i \(0.330646\pi\)
−0.983492 + 0.180953i \(0.942082\pi\)
\(114\) 0 0
\(115\) 4.35244 + 2.01401i 0.405867 + 0.187807i
\(116\) 0 0
\(117\) 10.7100 23.4516i 0.990140 2.16810i
\(118\) 0 0
\(119\) 4.31267 + 4.97709i 0.395342 + 0.456249i
\(120\) 0 0
\(121\) −9.60524 + 11.0850i −0.873204 + 1.00773i
\(122\) 0 0
\(123\) −30.5651 + 8.97471i −2.75596 + 0.809222i
\(124\) 0 0
\(125\) 0.142315 + 0.989821i 0.0127290 + 0.0885323i
\(126\) 0 0
\(127\) −4.92291 10.7797i −0.436838 0.956541i −0.992168 0.124911i \(-0.960135\pi\)
0.555330 0.831630i \(-0.312592\pi\)
\(128\) 0 0
\(129\) −14.4521 9.28780i −1.27244 0.817745i
\(130\) 0 0
\(131\) 0.842762 5.86154i 0.0736324 0.512125i −0.919311 0.393533i \(-0.871253\pi\)
0.992943 0.118592i \(-0.0378381\pi\)
\(132\) 0 0
\(133\) 6.73414 4.32777i 0.583924 0.375265i
\(134\) 0 0
\(135\) 5.29053 + 1.55344i 0.455336 + 0.133699i
\(136\) 0 0
\(137\) −1.98201 −0.169335 −0.0846673 0.996409i \(-0.526983\pi\)
−0.0846673 + 0.996409i \(0.526983\pi\)
\(138\) 0 0
\(139\) 14.3816 1.21983 0.609916 0.792466i \(-0.291203\pi\)
0.609916 + 0.792466i \(0.291203\pi\)
\(140\) 0 0
\(141\) −9.65274 2.83430i −0.812907 0.238691i
\(142\) 0 0
\(143\) 22.1762 14.2518i 1.85446 1.19179i
\(144\) 0 0
\(145\) −0.161904 + 1.12606i −0.0134454 + 0.0935145i
\(146\) 0 0
\(147\) −13.1665 8.46157i −1.08595 0.697899i
\(148\) 0 0
\(149\) −4.66353 10.2117i −0.382051 0.836575i −0.998779 0.0493990i \(-0.984269\pi\)
0.616728 0.787176i \(-0.288458\pi\)
\(150\) 0 0
\(151\) −2.30772 16.0505i −0.187800 1.30617i −0.837690 0.546146i \(-0.816094\pi\)
0.649890 0.760028i \(-0.274815\pi\)
\(152\) 0 0
\(153\) 25.9933 7.63233i 2.10144 0.617037i
\(154\) 0 0
\(155\) −0.527860 + 0.609183i −0.0423987 + 0.0489307i
\(156\) 0 0
\(157\) −11.3378 13.0845i −0.904856 1.04426i −0.998814 0.0486838i \(-0.984497\pi\)
0.0939579 0.995576i \(-0.470048\pi\)
\(158\) 0 0
\(159\) −10.9830 + 24.0495i −0.871012 + 1.90725i
\(160\) 0 0
\(161\) 5.26661 2.37348i 0.415067 0.187056i
\(162\) 0 0
\(163\) −2.21179 + 4.84315i −0.173241 + 0.379345i −0.976258 0.216612i \(-0.930500\pi\)
0.803017 + 0.595956i \(0.203227\pi\)
\(164\) 0 0
\(165\) 9.35752 + 10.7992i 0.728482 + 0.840713i
\(166\) 0 0
\(167\) 6.45793 7.45285i 0.499730 0.576719i −0.448710 0.893678i \(-0.648116\pi\)
0.948439 + 0.316959i \(0.102662\pi\)
\(168\) 0 0
\(169\) −13.5028 + 3.96478i −1.03868 + 0.304983i
\(170\) 0 0
\(171\) −4.68628 32.5938i −0.358369 2.49251i
\(172\) 0 0
\(173\) 5.30168 + 11.6091i 0.403079 + 0.882620i 0.996949 + 0.0780589i \(0.0248722\pi\)
−0.593870 + 0.804561i \(0.702400\pi\)
\(174\) 0 0
\(175\) 1.01332 + 0.651218i 0.0765994 + 0.0492275i
\(176\) 0 0
\(177\) −2.62189 + 18.2357i −0.197074 + 1.37068i
\(178\) 0 0
\(179\) −5.52160 + 3.54852i −0.412704 + 0.265229i −0.730476 0.682938i \(-0.760702\pi\)
0.317772 + 0.948167i \(0.397065\pi\)
\(180\) 0 0
\(181\) −7.96365 2.33834i −0.591933 0.173807i −0.0279722 0.999609i \(-0.508905\pi\)
−0.563961 + 0.825801i \(0.690723\pi\)
\(182\) 0 0
\(183\) 35.2390 2.60494
\(184\) 0 0
\(185\) −0.892100 −0.0655885
\(186\) 0 0
\(187\) 26.5775 + 7.80386i 1.94354 + 0.570675i
\(188\) 0 0
\(189\) 5.58730 3.59074i 0.406416 0.261188i
\(190\) 0 0
\(191\) −2.39275 + 16.6420i −0.173134 + 1.20417i 0.699079 + 0.715044i \(0.253594\pi\)
−0.872213 + 0.489127i \(0.837316\pi\)
\(192\) 0 0
\(193\) −18.8583 12.1195i −1.35745 0.872380i −0.359303 0.933221i \(-0.616985\pi\)
−0.998147 + 0.0608407i \(0.980622\pi\)
\(194\) 0 0
\(195\) −6.09633 13.3491i −0.436567 0.955948i
\(196\) 0 0
\(197\) 3.27708 + 22.7926i 0.233482 + 1.62390i 0.682851 + 0.730558i \(0.260740\pi\)
−0.449368 + 0.893347i \(0.648351\pi\)
\(198\) 0 0
\(199\) −1.45458 + 0.427102i −0.103112 + 0.0302765i −0.332882 0.942969i \(-0.608021\pi\)
0.229769 + 0.973245i \(0.426203\pi\)
\(200\) 0 0
\(201\) 3.73844 4.31439i 0.263689 0.304314i
\(202\) 0 0
\(203\) 0.897373 + 1.03562i 0.0629832 + 0.0726865i
\(204\) 0 0
\(205\) −4.69188 + 10.2738i −0.327695 + 0.717551i
\(206\) 0 0
\(207\) 0.118607 23.7629i 0.00824377 1.65163i
\(208\) 0 0
\(209\) 13.9866 30.6264i 0.967474 2.11847i
\(210\) 0 0
\(211\) −7.20121 8.31063i −0.495751 0.572128i 0.451642 0.892199i \(-0.350838\pi\)
−0.947393 + 0.320072i \(0.896293\pi\)
\(212\) 0 0
\(213\) −24.2308 + 27.9638i −1.66027 + 1.91605i
\(214\) 0 0
\(215\) −5.84422 + 1.71602i −0.398572 + 0.117031i
\(216\) 0 0
\(217\) 0.138178 + 0.961046i 0.00938010 + 0.0652400i
\(218\) 0 0
\(219\) −3.20130 7.00987i −0.216324 0.473683i
\(220\) 0 0
\(221\) −23.9317 15.3800i −1.60982 1.03457i
\(222\) 0 0
\(223\) 0.113804 0.791521i 0.00762085 0.0530042i −0.985656 0.168766i \(-0.946022\pi\)
0.993277 + 0.115762i \(0.0369309\pi\)
\(224\) 0 0
\(225\) 4.16838 2.67886i 0.277892 0.178590i
\(226\) 0 0
\(227\) 9.30691 + 2.73275i 0.617721 + 0.181379i 0.575598 0.817733i \(-0.304769\pi\)
0.0421236 + 0.999112i \(0.486588\pi\)
\(228\) 0 0
\(229\) −7.95914 −0.525955 −0.262977 0.964802i \(-0.584704\pi\)
−0.262977 + 0.964802i \(0.584704\pi\)
\(230\) 0 0
\(231\) 17.2119 1.13246
\(232\) 0 0
\(233\) 20.2455 + 5.94462i 1.32633 + 0.389445i 0.866772 0.498704i \(-0.166191\pi\)
0.459555 + 0.888149i \(0.348009\pi\)
\(234\) 0 0
\(235\) −3.00066 + 1.92841i −0.195741 + 0.125795i
\(236\) 0 0
\(237\) 3.30761 23.0049i 0.214852 1.49433i
\(238\) 0 0
\(239\) 6.59918 + 4.24104i 0.426866 + 0.274330i 0.736384 0.676563i \(-0.236532\pi\)
−0.309519 + 0.950893i \(0.600168\pi\)
\(240\) 0 0
\(241\) 8.12881 + 17.7996i 0.523623 + 1.14657i 0.968050 + 0.250759i \(0.0806800\pi\)
−0.444427 + 0.895815i \(0.646593\pi\)
\(242\) 0 0
\(243\) 2.07846 + 14.4560i 0.133333 + 0.927353i
\(244\) 0 0
\(245\) −5.32433 + 1.56336i −0.340159 + 0.0998797i
\(246\) 0 0
\(247\) −22.6440 + 26.1326i −1.44080 + 1.66278i
\(248\) 0 0
\(249\) 23.3213 + 26.9143i 1.47793 + 1.70562i
\(250\) 0 0
\(251\) 7.09429 15.5343i 0.447788 0.980518i −0.542315 0.840175i \(-0.682452\pi\)
0.990103 0.140343i \(-0.0448206\pi\)
\(252\) 0 0
\(253\) 13.2379 20.3743i 0.832261 1.28092i
\(254\) 0 0
\(255\) 6.40591 14.0270i 0.401154 0.878404i
\(256\) 0 0
\(257\) 0.737754 + 0.851414i 0.0460199 + 0.0531097i 0.778293 0.627901i \(-0.216086\pi\)
−0.732273 + 0.681011i \(0.761540\pi\)
\(258\) 0 0
\(259\) −0.703688 + 0.812099i −0.0437250 + 0.0504614i
\(260\) 0 0
\(261\) 5.40864 1.58812i 0.334787 0.0983022i
\(262\) 0 0
\(263\) −2.45958 17.1068i −0.151664 1.05485i −0.913430 0.406996i \(-0.866576\pi\)
0.761765 0.647853i \(-0.224333\pi\)
\(264\) 0 0
\(265\) 3.89407 + 8.52682i 0.239211 + 0.523798i
\(266\) 0 0
\(267\) −17.0390 10.9503i −1.04277 0.670146i
\(268\) 0 0
\(269\) 2.22196 15.4541i 0.135475 0.942252i −0.802772 0.596286i \(-0.796642\pi\)
0.938247 0.345966i \(-0.112449\pi\)
\(270\) 0 0
\(271\) −13.6949 + 8.80121i −0.831909 + 0.534635i −0.885884 0.463907i \(-0.846447\pi\)
0.0539751 + 0.998542i \(0.482811\pi\)
\(272\) 0 0
\(273\) −16.9608 4.98013i −1.02651 0.301411i
\(274\) 0 0
\(275\) 5.06632 0.305511
\(276\) 0 0
\(277\) 20.8923 1.25530 0.627649 0.778496i \(-0.284017\pi\)
0.627649 + 0.778496i \(0.284017\pi\)
\(278\) 0 0
\(279\) 3.83223 + 1.12524i 0.229430 + 0.0673666i
\(280\) 0 0
\(281\) −8.96960 + 5.76441i −0.535081 + 0.343876i −0.780112 0.625639i \(-0.784838\pi\)
0.245031 + 0.969515i \(0.421202\pi\)
\(282\) 0 0
\(283\) −3.39119 + 23.5863i −0.201585 + 1.40206i 0.597995 + 0.801500i \(0.295964\pi\)
−0.799581 + 0.600558i \(0.794945\pi\)
\(284\) 0 0
\(285\) −15.7682 10.1336i −0.934030 0.600265i
\(286\) 0 0
\(287\) 5.65151 + 12.3751i 0.333598 + 0.730477i
\(288\) 0 0
\(289\) −1.83477 12.7611i −0.107927 0.750652i
\(290\) 0 0
\(291\) 30.6919 9.01194i 1.79919 0.528290i
\(292\) 0 0
\(293\) 6.40460 7.39130i 0.374161 0.431804i −0.537174 0.843472i \(-0.680508\pi\)
0.911334 + 0.411667i \(0.135053\pi\)
\(294\) 0 0
\(295\) 4.27755 + 4.93655i 0.249048 + 0.287417i
\(296\) 0 0
\(297\) 11.6047 25.4107i 0.673371 1.47448i
\(298\) 0 0
\(299\) −18.9399 + 16.2467i −1.09532 + 0.939572i
\(300\) 0 0
\(301\) −3.04779 + 6.67372i −0.175672 + 0.384667i
\(302\) 0 0
\(303\) −18.0446 20.8246i −1.03664 1.19634i
\(304\) 0 0
\(305\) 8.18189 9.44241i 0.468494 0.540671i
\(306\) 0 0
\(307\) 6.21045 1.82355i 0.354449 0.104076i −0.0996605 0.995022i \(-0.531776\pi\)
0.454110 + 0.890946i \(0.349957\pi\)
\(308\) 0 0
\(309\) −2.07283 14.4169i −0.117919 0.820146i
\(310\) 0 0
\(311\) −6.63313 14.5245i −0.376130 0.823610i −0.999143 0.0413984i \(-0.986819\pi\)
0.623013 0.782212i \(-0.285909\pi\)
\(312\) 0 0
\(313\) −21.9487 14.1056i −1.24062 0.797295i −0.255106 0.966913i \(-0.582110\pi\)
−0.985510 + 0.169618i \(0.945747\pi\)
\(314\) 0 0
\(315\) 0.849392 5.90765i 0.0478578 0.332859i
\(316\) 0 0
\(317\) −5.99536 + 3.85299i −0.336733 + 0.216405i −0.698069 0.716030i \(-0.745957\pi\)
0.361336 + 0.932436i \(0.382321\pi\)
\(318\) 0 0
\(319\) 5.53020 + 1.62381i 0.309632 + 0.0909161i
\(320\) 0 0
\(321\) 7.91445 0.441742
\(322\) 0 0
\(323\) −36.3343 −2.02170
\(324\) 0 0
\(325\) −4.99239 1.46590i −0.276928 0.0813134i
\(326\) 0 0
\(327\) −25.5899 + 16.4456i −1.41513 + 0.909446i
\(328\) 0 0
\(329\) −0.611445 + 4.25269i −0.0337101 + 0.234459i
\(330\) 0 0
\(331\) 27.9802 + 17.9818i 1.53793 + 0.988369i 0.988224 + 0.153012i \(0.0488973\pi\)
0.549708 + 0.835357i \(0.314739\pi\)
\(332\) 0 0
\(333\) 1.83627 + 4.02087i 0.100627 + 0.220342i
\(334\) 0 0
\(335\) −0.288053 2.00345i −0.0157380 0.109460i
\(336\) 0 0
\(337\) 21.3861 6.27951i 1.16497 0.342067i 0.358609 0.933488i \(-0.383251\pi\)
0.806363 + 0.591421i \(0.201433\pi\)
\(338\) 0 0
\(339\) 22.5067 25.9741i 1.22240 1.41072i
\(340\) 0 0
\(341\) 2.67431 + 3.08631i 0.144822 + 0.167133i
\(342\) 0 0
\(343\) −6.27932 + 13.7498i −0.339051 + 0.742419i
\(344\) 0 0
\(345\) −10.1782 8.90884i −0.547979 0.479636i
\(346\) 0 0
\(347\) −4.67998 + 10.2477i −0.251235 + 0.550127i −0.992664 0.120904i \(-0.961421\pi\)
0.741430 + 0.671031i \(0.234148\pi\)
\(348\) 0 0
\(349\) −17.8923 20.6488i −0.957753 1.10531i −0.994369 0.105976i \(-0.966203\pi\)
0.0366160 0.999329i \(-0.488342\pi\)
\(350\) 0 0
\(351\) −18.7877 + 21.6822i −1.00281 + 1.15731i
\(352\) 0 0
\(353\) 12.0364 3.53421i 0.640633 0.188107i 0.0547472 0.998500i \(-0.482565\pi\)
0.585886 + 0.810393i \(0.300747\pi\)
\(354\) 0 0
\(355\) 1.86702 + 12.9854i 0.0990913 + 0.689195i
\(356\) 0 0
\(357\) −7.71611 16.8959i −0.408380 0.894228i
\(358\) 0 0
\(359\) −13.7867 8.86018i −0.727635 0.467622i 0.123650 0.992326i \(-0.460540\pi\)
−0.851285 + 0.524703i \(0.824176\pi\)
\(360\) 0 0
\(361\) −3.58131 + 24.9085i −0.188490 + 1.31098i
\(362\) 0 0
\(363\) 34.8021 22.3659i 1.82664 1.17391i
\(364\) 0 0
\(365\) −2.62160 0.769772i −0.137221 0.0402917i
\(366\) 0 0
\(367\) 13.1591 0.686901 0.343451 0.939171i \(-0.388404\pi\)
0.343451 + 0.939171i \(0.388404\pi\)
\(368\) 0 0
\(369\) 55.9635 2.91334
\(370\) 0 0
\(371\) 10.8338 + 3.18109i 0.562463 + 0.165154i
\(372\) 0 0
\(373\) 3.88256 2.49517i 0.201031 0.129195i −0.436252 0.899824i \(-0.643694\pi\)
0.637283 + 0.770630i \(0.280058\pi\)
\(374\) 0 0
\(375\) 0.401393 2.79175i 0.0207278 0.144165i
\(376\) 0 0
\(377\) −4.97967 3.20024i −0.256466 0.164821i
\(378\) 0 0
\(379\) −9.73076 21.3074i −0.499836 1.09449i −0.976523 0.215415i \(-0.930890\pi\)
0.476687 0.879073i \(-0.341838\pi\)
\(380\) 0 0
\(381\) 4.75673 + 33.0838i 0.243695 + 1.69494i
\(382\) 0 0
\(383\) 13.2743 3.89769i 0.678286 0.199163i 0.0755964 0.997138i \(-0.475914\pi\)
0.602690 + 0.797976i \(0.294096\pi\)
\(384\) 0 0
\(385\) 3.99631 4.61199i 0.203671 0.235049i
\(386\) 0 0
\(387\) 19.7640 + 22.8088i 1.00466 + 1.15944i
\(388\) 0 0
\(389\) −3.32424 + 7.27907i −0.168546 + 0.369063i −0.974991 0.222246i \(-0.928661\pi\)
0.806445 + 0.591309i \(0.201389\pi\)
\(390\) 0 0
\(391\) −25.9348 3.86108i −1.31158 0.195263i
\(392\) 0 0
\(393\) −6.93835 + 15.1929i −0.349993 + 0.766378i
\(394\) 0 0
\(395\) −5.39628 6.22764i −0.271516 0.313346i
\(396\) 0 0
\(397\) −22.7904 + 26.3015i −1.14382 + 1.32004i −0.203759 + 0.979021i \(0.565316\pi\)
−0.940058 + 0.341014i \(0.889230\pi\)
\(398\) 0 0
\(399\) −21.6629 + 6.36079i −1.08450 + 0.318438i
\(400\) 0 0
\(401\) −1.55325 10.8031i −0.0775657 0.539482i −0.991141 0.132812i \(-0.957599\pi\)
0.913575 0.406669i \(-0.133310\pi\)
\(402\) 0 0
\(403\) −1.74228 3.81507i −0.0867893 0.190042i
\(404\) 0 0
\(405\) −0.577745 0.371294i −0.0287084 0.0184498i
\(406\) 0 0
\(407\) −0.643215 + 4.47366i −0.0318830 + 0.221751i
\(408\) 0 0
\(409\) −18.5188 + 11.9013i −0.915697 + 0.588483i −0.911406 0.411508i \(-0.865002\pi\)
−0.00429097 + 0.999991i \(0.501366\pi\)
\(410\) 0 0
\(411\) 5.36373 + 1.57493i 0.264573 + 0.0776857i
\(412\) 0 0
\(413\) 7.86799 0.387158
\(414\) 0 0
\(415\) 12.6266 0.619814
\(416\) 0 0
\(417\) −38.9196 11.4278i −1.90590 0.559623i
\(418\) 0 0
\(419\) 17.9113 11.5109i 0.875026 0.562345i −0.0242603 0.999706i \(-0.507723\pi\)
0.899286 + 0.437361i \(0.144087\pi\)
\(420\) 0 0
\(421\) −4.56949 + 31.7815i −0.222703 + 1.54894i 0.505045 + 0.863093i \(0.331476\pi\)
−0.727749 + 0.685844i \(0.759433\pi\)
\(422\) 0 0
\(423\) 14.8681 + 9.55518i 0.722914 + 0.464589i
\(424\) 0 0
\(425\) −2.27123 4.97331i −0.110171 0.241241i
\(426\) 0 0
\(427\) −2.14177 14.8963i −0.103648 0.720884i
\(428\) 0 0
\(429\) −71.3379 + 20.9467i −3.44423 + 1.01132i
\(430\) 0 0
\(431\) −1.41985 + 1.63859i −0.0683915 + 0.0789280i −0.788914 0.614503i \(-0.789356\pi\)
0.720523 + 0.693431i \(0.243902\pi\)
\(432\) 0 0
\(433\) 7.09014 + 8.18246i 0.340730 + 0.393224i 0.900092 0.435700i \(-0.143499\pi\)
−0.559362 + 0.828924i \(0.688954\pi\)
\(434\) 0 0
\(435\) 1.33293 2.91871i 0.0639091 0.139941i
\(436\) 0 0
\(437\) −9.13174 + 30.5352i −0.436830 + 1.46070i
\(438\) 0 0
\(439\) 12.4427 27.2456i 0.593856 1.30036i −0.339228 0.940704i \(-0.610166\pi\)
0.933084 0.359659i \(-0.117107\pi\)
\(440\) 0 0
\(441\) 18.0058 + 20.7798i 0.857419 + 0.989514i
\(442\) 0 0
\(443\) −0.825336 + 0.952489i −0.0392129 + 0.0452541i −0.775017 0.631940i \(-0.782259\pi\)
0.735804 + 0.677194i \(0.236804\pi\)
\(444\) 0 0
\(445\) −6.89031 + 2.02318i −0.326632 + 0.0959078i
\(446\) 0 0
\(447\) 4.50611 + 31.3407i 0.213132 + 1.48236i
\(448\) 0 0
\(449\) 13.4323 + 29.4127i 0.633910 + 1.38807i 0.904957 + 0.425504i \(0.139903\pi\)
−0.271046 + 0.962566i \(0.587370\pi\)
\(450\) 0 0
\(451\) 48.1375 + 30.9361i 2.26671 + 1.45672i
\(452\) 0 0
\(453\) −6.50882 + 45.2698i −0.305811 + 2.12696i
\(454\) 0 0
\(455\) −5.27244 + 3.38839i −0.247176 + 0.158850i
\(456\) 0 0
\(457\) −5.09003 1.49457i −0.238102 0.0699130i 0.160505 0.987035i \(-0.448688\pi\)
−0.398606 + 0.917122i \(0.630506\pi\)
\(458\) 0 0
\(459\) −30.1465 −1.40712
\(460\) 0 0
\(461\) −11.5693 −0.538838 −0.269419 0.963023i \(-0.586832\pi\)
−0.269419 + 0.963023i \(0.586832\pi\)
\(462\) 0 0
\(463\) −34.0145 9.98755i −1.58079 0.464161i −0.630669 0.776052i \(-0.717219\pi\)
−0.950118 + 0.311891i \(0.899038\pi\)
\(464\) 0 0
\(465\) 1.91256 1.22913i 0.0886929 0.0569995i
\(466\) 0 0
\(467\) −5.74049 + 39.9260i −0.265638 + 1.84755i 0.222683 + 0.974891i \(0.428519\pi\)
−0.488321 + 0.872664i \(0.662391\pi\)
\(468\) 0 0
\(469\) −2.05101 1.31810i −0.0947067 0.0608643i
\(470\) 0 0
\(471\) 20.2853 + 44.4186i 0.934698 + 2.04670i
\(472\) 0 0
\(473\) 4.39165 + 30.5446i 0.201928 + 1.40444i
\(474\) 0 0
\(475\) −6.37646 + 1.87230i −0.292572 + 0.0859068i
\(476\) 0 0
\(477\) 30.4166 35.1026i 1.39268 1.60724i
\(478\) 0 0
\(479\) −10.2915 11.8771i −0.470233 0.542678i 0.470244 0.882537i \(-0.344166\pi\)
−0.940476 + 0.339859i \(0.889621\pi\)
\(480\) 0 0
\(481\) 1.92825 4.22227i 0.0879205 0.192519i
\(482\) 0 0
\(483\) −16.1385 + 2.23821i −0.734328 + 0.101842i
\(484\) 0 0
\(485\) 4.71134 10.3164i 0.213931 0.468444i
\(486\) 0 0
\(487\) −7.86741 9.07947i −0.356506 0.411430i 0.548960 0.835849i \(-0.315024\pi\)
−0.905466 + 0.424419i \(0.860479\pi\)
\(488\) 0 0
\(489\) 9.83400 11.3490i 0.444709 0.513221i
\(490\) 0 0
\(491\) 31.5084 9.25170i 1.42195 0.417523i 0.521790 0.853074i \(-0.325265\pi\)
0.900164 + 0.435551i \(0.143446\pi\)
\(492\) 0 0
\(493\) −0.885189 6.15663i −0.0398669 0.277281i
\(494\) 0 0
\(495\) −10.4283 22.8349i −0.468719 1.02635i
\(496\) 0 0
\(497\) 13.2937 + 8.54331i 0.596302 + 0.383220i
\(498\) 0 0
\(499\) 2.05589 14.2990i 0.0920344 0.640113i −0.890631 0.454726i \(-0.849737\pi\)
0.982666 0.185387i \(-0.0593538\pi\)
\(500\) 0 0
\(501\) −23.3986 + 15.0374i −1.04537 + 0.671821i
\(502\) 0 0
\(503\) −1.19423 0.350657i −0.0532479 0.0156350i 0.255000 0.966941i \(-0.417924\pi\)
−0.308248 + 0.951306i \(0.599743\pi\)
\(504\) 0 0
\(505\) −9.76966 −0.434744
\(506\) 0 0
\(507\) 39.6918 1.76278
\(508\) 0 0
\(509\) 24.3667 + 7.15471i 1.08004 + 0.317127i 0.772893 0.634536i \(-0.218809\pi\)
0.307143 + 0.951664i \(0.400627\pi\)
\(510\) 0 0
\(511\) −2.76866 + 1.77931i −0.122478 + 0.0787120i
\(512\) 0 0
\(513\) −5.21489 + 36.2704i −0.230243 + 1.60138i
\(514\) 0 0
\(515\) −4.34432 2.79192i −0.191433 0.123027i
\(516\) 0 0
\(517\) 7.50697 + 16.4380i 0.330156 + 0.722941i
\(518\) 0 0
\(519\) −5.12272 35.6293i −0.224862 1.56395i
\(520\) 0 0
\(521\) −5.63827 + 1.65554i −0.247017 + 0.0725307i −0.402897 0.915245i \(-0.631997\pi\)
0.155880 + 0.987776i \(0.450179\pi\)
\(522\) 0 0
\(523\) −9.28134 + 10.7112i −0.405845 + 0.468370i −0.921473 0.388443i \(-0.873013\pi\)
0.515628 + 0.856812i \(0.327559\pi\)
\(524\) 0 0
\(525\) −2.22477 2.56753i −0.0970971 0.112056i
\(526\) 0 0
\(527\) 1.83076 4.00881i 0.0797492 0.174626i
\(528\) 0 0
\(529\) −9.76291 + 20.8251i −0.424475 + 0.905440i
\(530\) 0 0
\(531\) 13.4452 29.4410i 0.583474 1.27763i
\(532\) 0 0
\(533\) −38.4840 44.4129i −1.66693 1.92374i
\(534\) 0 0
\(535\) 1.83760 2.12070i 0.0794463 0.0916860i
\(536\) 0 0
\(537\) 17.7623 5.21548i 0.766500 0.225065i
\(538\) 0 0
\(539\) 4.00098 + 27.8274i 0.172334 + 1.19861i
\(540\) 0 0
\(541\) −3.26843 7.15687i −0.140521 0.307698i 0.826267 0.563279i \(-0.190460\pi\)
−0.966788 + 0.255581i \(0.917733\pi\)
\(542\) 0 0
\(543\) 19.6932 + 12.6560i 0.845116 + 0.543123i
\(544\) 0 0
\(545\) −1.53487 + 10.6753i −0.0657468 + 0.457279i
\(546\) 0 0
\(547\) 21.4552 13.7884i 0.917358 0.589550i 0.00546775 0.999985i \(-0.498260\pi\)
0.911890 + 0.410435i \(0.134623\pi\)
\(548\) 0 0
\(549\) −59.4001 17.4414i −2.53513 0.744383i
\(550\) 0 0
\(551\) −7.56038 −0.322083
\(552\) 0 0
\(553\) −9.92574 −0.422085
\(554\) 0 0
\(555\) 2.41421 + 0.708875i 0.102477 + 0.0300901i
\(556\) 0 0
\(557\) 16.8698 10.8415i 0.714794 0.459370i −0.132028 0.991246i \(-0.542149\pi\)
0.846823 + 0.531876i \(0.178513\pi\)
\(558\) 0 0
\(559\) 4.51026 31.3696i 0.190764 1.32679i
\(560\) 0 0
\(561\) −65.7232 42.2377i −2.77483 1.78328i
\(562\) 0 0
\(563\) 15.9926 + 35.0189i 0.674008 + 1.47587i 0.868870 + 0.495040i \(0.164847\pi\)
−0.194862 + 0.980831i \(0.562426\pi\)
\(564\) 0 0
\(565\) −1.73418 12.0615i −0.0729574 0.507430i
\(566\) 0 0
\(567\) −0.793723 + 0.233058i −0.0333332 + 0.00978752i
\(568\) 0 0
\(569\) 19.7775 22.8245i 0.829118 0.956853i −0.170476 0.985362i \(-0.554530\pi\)
0.999594 + 0.0285090i \(0.00907591\pi\)
\(570\) 0 0
\(571\) −18.5327 21.3879i −0.775570 0.895056i 0.221211 0.975226i \(-0.428999\pi\)
−0.996781 + 0.0801704i \(0.974454\pi\)
\(572\) 0 0
\(573\) 19.6992 43.1353i 0.822947 1.80200i
\(574\) 0 0
\(575\) −4.75036 + 0.658816i −0.198104 + 0.0274745i
\(576\) 0 0
\(577\) 10.9878 24.0599i 0.457427 1.00163i −0.530639 0.847598i \(-0.678048\pi\)
0.988066 0.154028i \(-0.0492246\pi\)
\(578\) 0 0
\(579\) 41.4041 + 47.7829i 1.72070 + 1.98579i
\(580\) 0 0
\(581\) 9.95984 11.4943i 0.413204 0.476862i
\(582\) 0 0
\(583\) 45.5676 13.3798i 1.88722 0.554137i
\(584\) 0 0
\(585\) 3.66908 + 25.5190i 0.151698 + 1.05508i
\(586\) 0 0
\(587\) −8.94537 19.5876i −0.369215 0.808468i −0.999485 0.0320917i \(-0.989783\pi\)
0.630270 0.776376i \(-0.282944\pi\)
\(588\) 0 0
\(589\) −4.50644 2.89612i −0.185685 0.119332i
\(590\) 0 0
\(591\) 9.24285 64.2855i 0.380200 2.64435i
\(592\) 0 0
\(593\) −21.2113 + 13.6316i −0.871042 + 0.559785i −0.898071 0.439850i \(-0.855032\pi\)
0.0270294 + 0.999635i \(0.491395\pi\)
\(594\) 0 0
\(595\) −6.31887 1.85539i −0.259048 0.0760634i
\(596\) 0 0
\(597\) 4.27577 0.174995
\(598\) 0 0
\(599\) −14.2371 −0.581712 −0.290856 0.956767i \(-0.593940\pi\)
−0.290856 + 0.956767i \(0.593940\pi\)
\(600\) 0 0
\(601\) −12.2376 3.59329i −0.499183 0.146573i 0.0224420 0.999748i \(-0.492856\pi\)
−0.521625 + 0.853175i \(0.674674\pi\)
\(602\) 0 0
\(603\) −8.43703 + 5.42215i −0.343583 + 0.220807i
\(604\) 0 0
\(605\) 2.08742 14.5183i 0.0848656 0.590253i
\(606\) 0 0
\(607\) −27.2922 17.5396i −1.10776 0.711911i −0.146953 0.989144i \(-0.546947\pi\)
−0.960803 + 0.277232i \(0.910583\pi\)
\(608\) 0 0
\(609\) −1.60556 3.51568i −0.0650604 0.142462i
\(610\) 0 0
\(611\) −2.64123 18.3702i −0.106853 0.743178i
\(612\) 0 0
\(613\) 24.5343 7.20391i 0.990930 0.290963i 0.254201 0.967151i \(-0.418188\pi\)
0.736729 + 0.676188i \(0.236369\pi\)
\(614\) 0 0
\(615\) 20.8609 24.0747i 0.841191 0.970786i
\(616\) 0 0
\(617\) 11.8450 + 13.6699i 0.476863 + 0.550330i 0.942308 0.334747i \(-0.108651\pi\)
−0.465445 + 0.885077i \(0.654106\pi\)
\(618\) 0 0
\(619\) 19.0204 41.6488i 0.764493 1.67401i 0.0260792 0.999660i \(-0.491698\pi\)
0.738414 0.674347i \(-0.235575\pi\)
\(620\) 0 0
\(621\) −7.57658 + 25.3350i −0.304038 + 1.01666i
\(622\) 0 0
\(623\) −3.59333 + 7.86829i −0.143964 + 0.315236i
\(624\) 0 0
\(625\) −0.654861 0.755750i −0.0261944 0.0302300i
\(626\) 0 0
\(627\) −62.1868 + 71.7674i −2.48350 + 2.86611i
\(628\) 0 0
\(629\) 4.67988 1.37414i 0.186599 0.0547905i
\(630\) 0 0
\(631\) 4.55425 + 31.6755i 0.181302 + 1.26098i 0.853690 + 0.520782i \(0.174360\pi\)
−0.672388 + 0.740199i \(0.734731\pi\)
\(632\) 0 0
\(633\) 12.8842 + 28.2125i 0.512101 + 1.12134i
\(634\) 0 0
\(635\) 9.96934 + 6.40691i 0.395621 + 0.254250i
\(636\) 0 0
\(637\) 4.10904 28.5790i 0.162806 1.13234i
\(638\) 0 0
\(639\) 54.6848 35.1438i 2.16330 1.39027i
\(640\) 0 0
\(641\) 23.1003 + 6.78287i 0.912408 + 0.267907i 0.704054 0.710146i \(-0.251371\pi\)
0.208354 + 0.978053i \(0.433189\pi\)
\(642\) 0 0
\(643\) 5.67481 0.223793 0.111896 0.993720i \(-0.464308\pi\)
0.111896 + 0.993720i \(0.464308\pi\)
\(644\) 0 0
\(645\) 17.1792 0.676432
\(646\) 0 0
\(647\) −47.4863 13.9432i −1.86688 0.548165i −0.998647 0.0520039i \(-0.983439\pi\)
−0.868231 0.496161i \(-0.834743\pi\)
\(648\) 0 0
\(649\) 27.8398 17.8915i 1.09281 0.702304i
\(650\) 0 0
\(651\) 0.389723 2.71059i 0.0152745 0.106236i
\(652\) 0 0
\(653\) 5.03281 + 3.23439i 0.196949 + 0.126571i 0.635399 0.772184i \(-0.280836\pi\)
−0.438450 + 0.898756i \(0.644472\pi\)
\(654\) 0 0
\(655\) 2.46001 + 5.38667i 0.0961205 + 0.210475i
\(656\) 0 0
\(657\) 1.92671 + 13.4005i 0.0751680 + 0.522805i
\(658\) 0 0
\(659\) 32.8569 9.64764i 1.27992 0.375819i 0.430048 0.902806i \(-0.358497\pi\)
0.849873 + 0.526987i \(0.176678\pi\)
\(660\) 0 0
\(661\) −13.8618 + 15.9974i −0.539162 + 0.622226i −0.958323 0.285685i \(-0.907779\pi\)
0.419161 + 0.907912i \(0.362324\pi\)
\(662\) 0 0
\(663\) 52.5430 + 60.6378i 2.04060 + 2.35498i
\(664\) 0 0
\(665\) −3.32535 + 7.28150i −0.128952 + 0.282365i
\(666\) 0 0
\(667\) −5.39647 0.803407i −0.208952 0.0311081i
\(668\) 0 0
\(669\) −0.936929 + 2.05159i −0.0362238 + 0.0793190i
\(670\) 0 0
\(671\) −41.4521 47.8383i −1.60024 1.84678i
\(672\) 0 0
\(673\) 15.0620 17.3825i 0.580597 0.670045i −0.387136 0.922023i \(-0.626536\pi\)
0.967733 + 0.251978i \(0.0810810\pi\)
\(674\) 0 0
\(675\) −5.29053 + 1.55344i −0.203633 + 0.0597919i
\(676\) 0 0
\(677\) −2.29168 15.9390i −0.0880765 0.612585i −0.985277 0.170963i \(-0.945312\pi\)
0.897201 0.441622i \(-0.145597\pi\)
\(678\) 0 0
\(679\) −5.67495 12.4264i −0.217785 0.476882i
\(680\) 0 0
\(681\) −23.0149 14.7908i −0.881934 0.566785i
\(682\) 0 0
\(683\) −2.41816 + 16.8186i −0.0925281 + 0.643547i 0.889796 + 0.456359i \(0.150847\pi\)
−0.982324 + 0.187189i \(0.940062\pi\)
\(684\) 0 0
\(685\) 1.66737 1.07156i 0.0637071 0.0409420i
\(686\) 0 0
\(687\) 21.5391 + 6.32444i 0.821766 + 0.241292i
\(688\) 0 0
\(689\) −48.7740 −1.85814
\(690\) 0 0
\(691\) −15.5830 −0.592805 −0.296403 0.955063i \(-0.595787\pi\)
−0.296403 + 0.955063i \(0.595787\pi\)
\(692\) 0 0
\(693\) −29.0130 8.51898i −1.10211 0.323609i
\(694\) 0 0
\(695\) −12.0986 + 7.77528i −0.458925 + 0.294933i
\(696\) 0 0
\(697\) 8.78808 61.1225i 0.332872 2.31518i
\(698\) 0 0
\(699\) −50.0648 32.1747i −1.89363 1.21696i
\(700\) 0 0
\(701\) 2.58041 + 5.65030i 0.0974606 + 0.213409i 0.952082 0.305843i \(-0.0989381\pi\)
−0.854622 + 0.519251i \(0.826211\pi\)
\(702\) 0 0
\(703\) −0.843725 5.86824i −0.0318217 0.221325i
\(704\) 0 0
\(705\) 9.65274 2.83430i 0.363543 0.106746i
\(706\) 0 0
\(707\) −7.70630 + 8.89355i −0.289825 + 0.334476i
\(708\) 0 0
\(709\) 1.73502 + 2.00232i 0.0651601 + 0.0751988i 0.787394 0.616450i \(-0.211430\pi\)
−0.722234 + 0.691649i \(0.756884\pi\)
\(710\) 0 0
\(711\) −16.9616 + 37.1408i −0.636111 + 1.39289i
\(712\) 0 0
\(713\) −2.90887 2.54608i −0.108938 0.0953513i
\(714\) 0 0
\(715\) −10.9507 + 23.9787i −0.409533 + 0.896752i
\(716\) 0 0
\(717\) −14.4888 16.7209i −0.541093 0.624454i
\(718\) 0 0
\(719\) −3.60585 + 4.16138i −0.134476 + 0.155193i −0.818993 0.573803i \(-0.805467\pi\)
0.684518 + 0.728996i \(0.260013\pi\)
\(720\) 0 0
\(721\) −5.96835 + 1.75246i −0.222273 + 0.0652652i
\(722\) 0 0
\(723\) −7.85442 54.6287i −0.292109 2.03166i
\(724\) 0 0
\(725\) −0.472594 1.03484i −0.0175517 0.0384329i
\(726\) 0 0
\(727\) 32.1763 + 20.6784i 1.19335 + 0.766920i 0.977793 0.209571i \(-0.0672067\pi\)
0.215558 + 0.976491i \(0.430843\pi\)
\(728\) 0 0
\(729\) 6.15541 42.8118i 0.227978 1.58562i
\(730\) 0 0
\(731\) 28.0150 18.0042i 1.03617 0.665909i
\(732\) 0 0
\(733\) 22.7810 + 6.68911i 0.841437 + 0.247068i 0.673923 0.738802i \(-0.264608\pi\)
0.167514 + 0.985870i \(0.446426\pi\)
\(734\) 0 0
\(735\) 15.6510 0.577296
\(736\) 0 0
\(737\) −10.2545 −0.377730
\(738\) 0 0
\(739\) 37.0259 + 10.8718i 1.36202 + 0.399925i 0.879474 0.475946i \(-0.157894\pi\)
0.482545 + 0.875871i \(0.339712\pi\)
\(740\) 0 0
\(741\) 82.0447 52.7269i 3.01399 1.93697i
\(742\) 0 0
\(743\) −0.720350 + 5.01014i −0.0264271 + 0.183804i −0.998759 0.0497979i \(-0.984142\pi\)
0.972332 + 0.233602i \(0.0750514\pi\)
\(744\) 0 0
\(745\) 9.44407 + 6.06934i 0.346004 + 0.222363i
\(746\) 0 0
\(747\) −25.9901 56.9104i −0.950928 2.08224i
\(748\) 0 0
\(749\) −0.481027 3.34562i −0.0175764 0.122246i
\(750\) 0 0
\(751\) 28.8878 8.48222i 1.05413 0.309520i 0.291645 0.956527i \(-0.405797\pi\)
0.762485 + 0.647006i \(0.223979\pi\)
\(752\) 0 0
\(753\) −31.5424 + 36.4019i −1.14947 + 1.32656i
\(754\) 0 0
\(755\) 10.6190 + 12.2549i 0.386463 + 0.446002i
\(756\) 0 0
\(757\) −13.6934 + 29.9845i −0.497697 + 1.08980i 0.479514 + 0.877534i \(0.340813\pi\)
−0.977211 + 0.212270i \(0.931914\pi\)
\(758\) 0 0
\(759\) −52.0143 + 44.6180i −1.88800 + 1.61953i
\(760\) 0 0
\(761\) −17.9251 + 39.2504i −0.649783 + 1.42283i 0.241961 + 0.970286i \(0.422209\pi\)
−0.891744 + 0.452540i \(0.850518\pi\)
\(762\) 0 0
\(763\) 8.50726 + 9.81790i 0.307983 + 0.355432i
\(764\) 0 0
\(765\) −17.7406 + 20.4738i −0.641414 + 0.740231i
\(766\) 0 0
\(767\) −32.6103 + 9.57525i −1.17749 + 0.345742i
\(768\) 0 0
\(769\) 5.50569 + 38.2929i 0.198540 + 1.38088i 0.808523 + 0.588464i \(0.200267\pi\)
−0.609983 + 0.792414i \(0.708824\pi\)
\(770\) 0 0
\(771\) −1.31997 2.89033i −0.0475376 0.104093i
\(772\) 0 0
\(773\) 15.4203 + 9.91000i 0.554628 + 0.356438i 0.787736 0.616013i \(-0.211253\pi\)
−0.233108 + 0.972451i \(0.574889\pi\)
\(774\) 0 0
\(775\) 0.114715 0.797860i 0.00412068 0.0286600i
\(776\) 0 0
\(777\) 2.54963 1.63855i 0.0914675 0.0587826i
\(778\) 0 0
\(779\) −72.0184 21.1465i −2.58033 0.757653i
\(780\) 0 0
\(781\) 66.4649 2.37830
\(782\) 0 0
\(783\) −6.27283 −0.224173
\(784\) 0 0
\(785\) 16.6120 + 4.87773i 0.592908 + 0.174094i
\(786\) 0 0
\(787\) 17.4175 11.1936i 0.620869 0.399008i −0.192050 0.981385i \(-0.561514\pi\)
0.812919 + 0.582377i \(0.197877\pi\)
\(788\) 0 0
\(789\) −6.93714 + 48.2489i −0.246969 + 1.71771i
\(790\) 0 0
\(791\) −12.3478 7.93542i −0.439036 0.282151i
\(792\) 0 0
\(793\) 27.0056 + 59.1341i 0.958998 + 2.09991i
\(794\) 0 0
\(795\) −3.76262 26.1696i −0.133446 0.928141i
\(796\) 0 0
\(797\) 16.6326 4.88378i 0.589158 0.172992i 0.0264529 0.999650i \(-0.491579\pi\)
0.562705 + 0.826658i \(0.309761\pi\)
\(798\) 0 0
\(799\) 12.7708 14.7383i 0.451799 0.521403i
\(800\) 0 0
\(801\) 23.3016 + 26.8915i 0.823323 + 0.950165i
\(802\) 0 0
\(803\) −5.75042 + 12.5917i −0.202928 + 0.444351i
\(804\) 0 0
\(805\) −3.14735 + 4.84404i −0.110930 + 0.170730i
\(806\) 0 0
\(807\) −18.2931 + 40.0563i −0.643948 + 1.41005i
\(808\) 0 0
\(809\) 16.0828 + 18.5605i 0.565439 + 0.652552i 0.964410 0.264412i \(-0.0851778\pi\)
−0.398970 + 0.916964i \(0.630632\pi\)
\(810\) 0 0
\(811\) −10.9663 + 12.6558i −0.385079 + 0.444405i −0.914885 0.403714i \(-0.867719\pi\)
0.529806 + 0.848119i \(0.322265\pi\)
\(812\) 0 0
\(813\) 44.0549 12.9357i 1.54507 0.453674i
\(814\) 0 0
\(815\) −0.757726 5.27010i −0.0265420 0.184604i
\(816\) 0 0
\(817\) −16.8153 36.8204i −0.588293 1.28818i
\(818\) 0 0
\(819\) 26.1247 + 16.7894i 0.912872 + 0.586667i
\(820\) 0 0
\(821\) −3.34047 + 23.2335i −0.116583 + 0.810854i 0.844690 + 0.535256i \(0.179785\pi\)
−0.961273 + 0.275598i \(0.911124\pi\)
\(822\) 0 0
\(823\) 5.60227 3.60036i 0.195283 0.125501i −0.439345 0.898318i \(-0.644790\pi\)
0.634628 + 0.772818i \(0.281153\pi\)
\(824\) 0 0
\(825\) −13.7105 4.02577i −0.477339 0.140159i
\(826\) 0 0
\(827\) 40.7873 1.41831 0.709156 0.705051i \(-0.249076\pi\)
0.709156 + 0.705051i \(0.249076\pi\)
\(828\) 0 0
\(829\) 17.9533 0.623545 0.311772 0.950157i \(-0.399077\pi\)
0.311772 + 0.950157i \(0.399077\pi\)
\(830\) 0 0
\(831\) −56.5389 16.6013i −1.96131 0.575894i
\(832\) 0 0
\(833\) 25.5229 16.4026i 0.884315 0.568315i
\(834\) 0 0
\(835\) −1.40344 + 9.76115i −0.0485681 + 0.337799i
\(836\) 0 0
\(837\) −3.73899 2.40290i −0.129238 0.0830564i
\(838\) 0 0
\(839\) −5.44458 11.9220i −0.187968 0.411592i 0.792063 0.610440i \(-0.209007\pi\)
−0.980030 + 0.198848i \(0.936280\pi\)
\(840\) 0 0
\(841\) 3.94294 + 27.4238i 0.135964 + 0.945647i
\(842\) 0 0
\(843\) 28.8541 8.47231i 0.993786 0.291802i
\(844\) 0 0
\(845\) 9.21576 10.6356i 0.317032 0.365874i
\(846\) 0 0
\(847\) −11.5698 13.3523i −0.397543 0.458789i
\(848\) 0 0
\(849\) 27.9192 61.1346i 0.958186 2.09813i
\(850\) 0 0
\(851\) 0.0213542 4.27831i 0.000732014 0.146658i
\(852\) 0 0
\(853\) −9.46367 + 20.7226i −0.324030 + 0.709527i −0.999615 0.0277557i \(-0.991164\pi\)
0.675585 + 0.737282i \(0.263891\pi\)
\(854\) 0 0
\(855\) 21.5639 + 24.8860i 0.737469 + 0.851085i
\(856\) 0 0
\(857\) 22.7300 26.2318i 0.776441 0.896060i −0.220406 0.975408i \(-0.570738\pi\)
0.996847 + 0.0793479i \(0.0252838\pi\)
\(858\) 0 0
\(859\) −44.4697 + 13.0575i −1.51729 + 0.445516i −0.931132 0.364683i \(-0.881177\pi\)
−0.586155 + 0.810199i \(0.699359\pi\)
\(860\) 0 0
\(861\) −5.46074 37.9803i −0.186101 1.29436i
\(862\) 0 0
\(863\) −3.04819 6.67461i −0.103762 0.227206i 0.850629 0.525766i \(-0.176221\pi\)
−0.954391 + 0.298559i \(0.903494\pi\)
\(864\) 0 0
\(865\) −10.7364 6.89986i −0.365048 0.234602i
\(866\) 0 0
\(867\) −5.17488 + 35.9920i −0.175748 + 1.22235i
\(868\) 0 0
\(869\) −35.1208 + 22.5708i −1.19139 + 0.765662i
\(870\) 0 0
\(871\) 10.1049 + 2.96706i 0.342391 + 0.100535i
\(872\) 0 0
\(873\) −56.1957 −1.90193
\(874\) 0 0
\(875\) −1.20453 −0.0407206
\(876\) 0 0
\(877\) −39.9113 11.7190i −1.34771 0.395723i −0.473294 0.880905i \(-0.656935\pi\)
−0.874413 + 0.485182i \(0.838753\pi\)
\(878\) 0 0
\(879\) −23.2054 + 14.9132i −0.782699 + 0.503010i
\(880\) 0 0
\(881\) 3.13801 21.8253i 0.105722 0.735314i −0.866146 0.499791i \(-0.833410\pi\)
0.971869 0.235524i \(-0.0756806\pi\)
\(882\) 0 0
\(883\) 15.1537 + 9.73871i 0.509963 + 0.327734i 0.770191 0.637814i \(-0.220161\pi\)
−0.260227 + 0.965547i \(0.583797\pi\)
\(884\) 0 0
\(885\) −7.65327 16.7583i −0.257262 0.563325i
\(886\) 0 0
\(887\) 1.07087 + 7.44808i 0.0359564 + 0.250082i 0.999870 0.0161336i \(-0.00513572\pi\)
−0.963913 + 0.266216i \(0.914227\pi\)
\(888\) 0 0
\(889\) 13.6962 4.02156i 0.459355 0.134879i
\(890\) 0 0
\(891\) −2.27851 + 2.62954i −0.0763329 + 0.0880929i
\(892\) 0 0
\(893\) −15.5230 17.9145i −0.519458 0.599486i
\(894\) 0 0
\(895\) 2.72659 5.97041i 0.0911400 0.199569i
\(896\) 0 0
\(897\) 64.1651 28.9171i 2.14241 0.965512i
\(898\) 0 0
\(899\) 0.380941 0.834145i 0.0127051 0.0278203i
\(900\) 0 0
\(901\) −33.5622 38.7328i −1.11812 1.29038i
\(902\) 0 0
\(903\) 13.5510 15.6387i 0.450948 0.520422i
\(904\) 0 0
\(905\) 7.96365 2.33834i 0.264721 0.0777290i
\(906\) 0 0
\(907\) 2.02183 + 14.0622i 0.0671339 + 0.466927i 0.995462 + 0.0951638i \(0.0303375\pi\)
−0.928328 + 0.371763i \(0.878753\pi\)
\(908\) 0 0
\(909\) 20.1095 + 44.0337i 0.666991 + 1.46051i
\(910\) 0 0
\(911\) −28.6925 18.4396i −0.950626 0.610930i −0.0292371 0.999573i \(-0.509308\pi\)
−0.921389 + 0.388642i \(0.872944\pi\)
\(912\) 0 0
\(913\) 9.10392 63.3191i 0.301296 2.09556i
\(914\) 0 0
\(915\) −29.6450 + 19.0517i −0.980032 + 0.629828i
\(916\) 0 0
\(917\) 6.84407 + 2.00960i 0.226011 + 0.0663628i
\(918\) 0 0
\(919\) 1.02662 0.0338652 0.0169326 0.999857i \(-0.494610\pi\)
0.0169326 + 0.999857i \(0.494610\pi\)
\(920\) 0 0
\(921\) −18.2558 −0.601548
\(922\) 0 0
\(923\) −65.4950 19.2311i −2.15580 0.632999i
\(924\) 0 0
\(925\) 0.750482 0.482306i 0.0246757 0.0158581i
\(926\) 0 0
\(927\) −3.64154 + 25.3275i −0.119604 + 0.831863i
\(928\) 0 0
\(929\) −44.7473 28.7573i −1.46811 0.943498i −0.998149 0.0608107i \(-0.980631\pi\)
−0.469962 0.882687i \(-0.655732\pi\)
\(930\) 0 0
\(931\) −15.3194 33.5449i −0.502074 1.09939i
\(932\) 0 0
\(933\) 6.40922 + 44.5771i 0.209829 + 1.45939i
\(934\) 0 0
\(935\) −26.5775 + 7.80386i −0.869177 + 0.255213i
\(936\) 0 0
\(937\) 16.1964 18.6916i 0.529112 0.610628i −0.426776 0.904357i \(-0.640351\pi\)
0.955889 + 0.293729i \(0.0948963\pi\)
\(938\) 0 0
\(939\) 48.1893 + 55.6134i 1.57260 + 1.81488i
\(940\) 0 0
\(941\) −4.69474 + 10.2800i −0.153044 + 0.335120i −0.970588 0.240746i \(-0.922608\pi\)
0.817544 + 0.575866i \(0.195335\pi\)
\(942\) 0 0
\(943\) −49.1584 22.7471i −1.60082 0.740747i
\(944\) 0 0
\(945\) −2.75904 + 6.04145i −0.0897515 + 0.196528i
\(946\) 0 0
\(947\) 32.8498 + 37.9107i 1.06747 + 1.23193i 0.971623 + 0.236536i \(0.0760121\pi\)
0.0958521 + 0.995396i \(0.469442\pi\)
\(948\) 0 0
\(949\) 9.30981 10.7441i 0.302209 0.348768i
\(950\) 0 0
\(951\) 19.2863 5.66298i 0.625402 0.183635i
\(952\) 0 0
\(953\) 1.14376 + 7.95501i 0.0370499 + 0.257688i 0.999925 0.0122600i \(-0.00390258\pi\)
−0.962875 + 0.269948i \(0.912993\pi\)
\(954\) 0 0
\(955\) −6.98442 15.2937i −0.226010 0.494894i
\(956\) 0 0
\(957\) −13.6756 8.78874i −0.442068 0.284100i
\(958\) 0 0
\(959\) 0.339761 2.36309i 0.0109715 0.0763082i
\(960\) 0 0
\(961\) −25.5323 + 16.4086i −0.823621 + 0.529309i
\(962\) 0 0
\(963\) −13.3409 3.91723i −0.429903 0.126231i
\(964\) 0 0
\(965\) 22.4169 0.721626
\(966\) 0 0
\(967\) 6.97557 0.224319 0.112160 0.993690i \(-0.464223\pi\)
0.112160 + 0.993690i \(0.464223\pi\)
\(968\) 0 0
\(969\) 98.3282 + 28.8718i 3.15876 + 0.927495i
\(970\) 0 0
\(971\) 2.54343 1.63457i 0.0816227 0.0524557i −0.499193 0.866491i \(-0.666370\pi\)
0.580816 + 0.814035i \(0.302734\pi\)
\(972\) 0 0
\(973\) −2.46533 + 17.1467i −0.0790349 + 0.549700i
\(974\) 0 0
\(975\) 12.3456 + 7.93405i 0.395376 + 0.254093i
\(976\) 0 0
\(977\) 2.34135 + 5.12683i 0.0749063 + 0.164022i 0.943381 0.331712i \(-0.107626\pi\)
−0.868474 + 0.495734i \(0.834899\pi\)
\(978\) 0 0
\(979\) 5.17774 + 36.0119i 0.165481 + 1.15095i
\(980\) 0 0
\(981\) 51.2749 15.0557i 1.63708 0.480691i
\(982\) 0 0
\(983\) −26.2948 + 30.3458i −0.838673 + 0.967880i −0.999819 0.0190508i \(-0.993936\pi\)
0.161146 + 0.986931i \(0.448481\pi\)
\(984\) 0 0
\(985\) −15.0795 17.4026i −0.480471 0.554494i
\(986\) 0 0
\(987\) 5.03395 11.0228i 0.160232 0.350860i
\(988\) 0 0
\(989\) −8.08974 28.0686i −0.257239 0.892530i
\(990\) 0 0
\(991\) −13.5805 + 29.7372i −0.431399 + 0.944633i 0.561698 + 0.827342i \(0.310148\pi\)
−0.993098 + 0.117291i \(0.962579\pi\)
\(992\) 0 0
\(993\) −61.4317 70.8959i −1.94947 2.24981i
\(994\) 0 0
\(995\) 0.992759 1.14571i 0.0314726 0.0363213i
\(996\) 0 0
\(997\) 29.1902 8.57102i 0.924463 0.271447i 0.215346 0.976538i \(-0.430912\pi\)
0.709117 + 0.705091i \(0.249094\pi\)
\(998\) 0 0
\(999\) −0.700037 4.86887i −0.0221482 0.154044i
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 460.2.m.b.121.1 50
23.4 even 11 inner 460.2.m.b.441.1 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.m.b.121.1 50 1.1 even 1 trivial
460.2.m.b.441.1 yes 50 23.4 even 11 inner