Properties

Label 380.2.bh.a.33.2
Level $380$
Weight $2$
Character 380.33
Analytic conductor $3.034$
Analytic rank $0$
Dimension $120$
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] = [380,2,Mod(13,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([0, 27, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.bh (of order \(36\), degree \(12\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(10\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 33.2
Character \(\chi\) \(=\) 380.33
Dual form 380.2.bh.a.357.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41957 - 2.02735i) q^{3} +(0.187939 - 2.22816i) q^{5} +(-3.90736 - 1.04697i) q^{7} +(-1.06893 + 2.93686i) q^{9} +O(q^{10})\) \(q+(-1.41957 - 2.02735i) q^{3} +(0.187939 - 2.22816i) q^{5} +(-3.90736 - 1.04697i) q^{7} +(-1.06893 + 2.93686i) q^{9} +(-1.50482 + 2.60643i) q^{11} +(2.49576 + 1.74755i) q^{13} +(-4.78405 + 2.78200i) q^{15} +(1.54457 - 3.31233i) q^{17} +(-2.24349 + 3.73721i) q^{19} +(3.42418 + 9.40786i) q^{21} +(4.38572 + 0.383700i) q^{23} +(-4.92936 - 0.837516i) q^{25} +(0.299637 - 0.0802874i) q^{27} +(-6.16306 - 2.24317i) q^{29} +(0.0797471 - 0.0460420i) q^{31} +(7.42036 - 0.649197i) q^{33} +(-3.06717 + 8.50944i) q^{35} +(-5.63016 - 5.63016i) q^{37} -7.54055i q^{39} +(-0.252048 - 0.0444428i) q^{41} +(-0.986904 - 11.2804i) q^{43} +(6.34288 + 2.93369i) q^{45} +(-12.1390 + 5.66049i) q^{47} +(8.10914 + 4.68182i) q^{49} +(-8.90788 + 1.57070i) q^{51} +(-0.0341343 + 0.390156i) q^{53} +(5.52472 + 3.84283i) q^{55} +(10.7614 - 0.756885i) q^{57} +(6.11253 - 2.22478i) q^{59} +(-5.92709 + 4.97342i) q^{61} +(7.25151 - 10.3562i) q^{63} +(4.36286 - 5.23251i) q^{65} +(-3.18616 - 6.83274i) q^{67} +(-5.44793 - 9.43609i) q^{69} +(10.3566 - 12.3425i) q^{71} +(4.03907 - 2.82818i) q^{73} +(5.29962 + 11.1825i) q^{75} +(8.60875 - 8.60875i) q^{77} +(1.67176 - 9.48103i) q^{79} +(6.59432 + 5.53329i) q^{81} +(-1.31821 + 4.91963i) q^{83} +(-7.09010 - 4.06405i) q^{85} +(4.20119 + 15.6790i) q^{87} +(1.38111 + 7.83264i) q^{89} +(-7.92219 - 9.44130i) q^{91} +(-0.206550 - 0.0963158i) q^{93} +(7.90545 + 5.70121i) q^{95} +(-4.48907 - 2.09329i) q^{97} +(-6.04617 - 7.20554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.41957 2.02735i −0.819588 1.17049i −0.982940 0.183925i \(-0.941119\pi\)
0.163352 0.986568i \(-0.447769\pi\)
\(4\) 0 0
\(5\) 0.187939 2.22816i 0.0840490 0.996462i
\(6\) 0 0
\(7\) −3.90736 1.04697i −1.47684 0.395719i −0.571572 0.820552i \(-0.693666\pi\)
−0.905272 + 0.424833i \(0.860333\pi\)
\(8\) 0 0
\(9\) −1.06893 + 2.93686i −0.356310 + 0.978953i
\(10\) 0 0
\(11\) −1.50482 + 2.60643i −0.453721 + 0.785868i −0.998614 0.0526377i \(-0.983237\pi\)
0.544892 + 0.838506i \(0.316570\pi\)
\(12\) 0 0
\(13\) 2.49576 + 1.74755i 0.692199 + 0.484683i 0.865965 0.500104i \(-0.166705\pi\)
−0.173766 + 0.984787i \(0.555594\pi\)
\(14\) 0 0
\(15\) −4.78405 + 2.78200i −1.23524 + 0.718309i
\(16\) 0 0
\(17\) 1.54457 3.31233i 0.374612 0.803358i −0.625127 0.780523i \(-0.714953\pi\)
0.999739 0.0228352i \(-0.00726931\pi\)
\(18\) 0 0
\(19\) −2.24349 + 3.73721i −0.514692 + 0.857375i
\(20\) 0 0
\(21\) 3.42418 + 9.40786i 0.747217 + 2.05296i
\(22\) 0 0
\(23\) 4.38572 + 0.383700i 0.914485 + 0.0800071i 0.534675 0.845058i \(-0.320434\pi\)
0.379810 + 0.925065i \(0.375989\pi\)
\(24\) 0 0
\(25\) −4.92936 0.837516i −0.985872 0.167503i
\(26\) 0 0
\(27\) 0.299637 0.0802874i 0.0576651 0.0154513i
\(28\) 0 0
\(29\) −6.16306 2.24317i −1.14445 0.416546i −0.300932 0.953645i \(-0.597298\pi\)
−0.843519 + 0.537099i \(0.819520\pi\)
\(30\) 0 0
\(31\) 0.0797471 0.0460420i 0.0143230 0.00826939i −0.492821 0.870130i \(-0.664034\pi\)
0.507144 + 0.861861i \(0.330701\pi\)
\(32\) 0 0
\(33\) 7.42036 0.649197i 1.29172 0.113011i
\(34\) 0 0
\(35\) −3.06717 + 8.50944i −0.518446 + 1.43836i
\(36\) 0 0
\(37\) −5.63016 5.63016i −0.925592 0.925592i 0.0718248 0.997417i \(-0.477118\pi\)
−0.997417 + 0.0718248i \(0.977118\pi\)
\(38\) 0 0
\(39\) 7.54055i 1.20745i
\(40\) 0 0
\(41\) −0.252048 0.0444428i −0.0393633 0.00694081i 0.153932 0.988081i \(-0.450806\pi\)
−0.193295 + 0.981141i \(0.561917\pi\)
\(42\) 0 0
\(43\) −0.986904 11.2804i −0.150501 1.72024i −0.577842 0.816149i \(-0.696105\pi\)
0.427340 0.904091i \(-0.359451\pi\)
\(44\) 0 0
\(45\) 6.34288 + 2.93369i 0.945541 + 0.437329i
\(46\) 0 0
\(47\) −12.1390 + 5.66049i −1.77065 + 0.825667i −0.794910 + 0.606727i \(0.792482\pi\)
−0.975738 + 0.218940i \(0.929740\pi\)
\(48\) 0 0
\(49\) 8.10914 + 4.68182i 1.15845 + 0.668831i
\(50\) 0 0
\(51\) −8.90788 + 1.57070i −1.24735 + 0.219942i
\(52\) 0 0
\(53\) −0.0341343 + 0.390156i −0.00468870 + 0.0535921i −0.998179 0.0603282i \(-0.980785\pi\)
0.993490 + 0.113920i \(0.0363408\pi\)
\(54\) 0 0
\(55\) 5.52472 + 3.84283i 0.744953 + 0.518167i
\(56\) 0 0
\(57\) 10.7614 0.756885i 1.42539 0.100252i
\(58\) 0 0
\(59\) 6.11253 2.22478i 0.795784 0.289642i 0.0880459 0.996116i \(-0.471938\pi\)
0.707738 + 0.706475i \(0.249716\pi\)
\(60\) 0 0
\(61\) −5.92709 + 4.97342i −0.758886 + 0.636781i −0.937837 0.347077i \(-0.887174\pi\)
0.178951 + 0.983858i \(0.442730\pi\)
\(62\) 0 0
\(63\) 7.25151 10.3562i 0.913604 1.30476i
\(64\) 0 0
\(65\) 4.36286 5.23251i 0.541147 0.649013i
\(66\) 0 0
\(67\) −3.18616 6.83274i −0.389251 0.834752i −0.999107 0.0422399i \(-0.986551\pi\)
0.609856 0.792512i \(-0.291227\pi\)
\(68\) 0 0
\(69\) −5.44793 9.43609i −0.655853 1.13597i
\(70\) 0 0
\(71\) 10.3566 12.3425i 1.22910 1.46479i 0.390002 0.920814i \(-0.372474\pi\)
0.839102 0.543975i \(-0.183081\pi\)
\(72\) 0 0
\(73\) 4.03907 2.82818i 0.472737 0.331014i −0.312810 0.949816i \(-0.601270\pi\)
0.785547 + 0.618802i \(0.212382\pi\)
\(74\) 0 0
\(75\) 5.29962 + 11.1825i 0.611947 + 1.29124i
\(76\) 0 0
\(77\) 8.60875 8.60875i 0.981059 0.981059i
\(78\) 0 0
\(79\) 1.67176 9.48103i 0.188088 1.06670i −0.733836 0.679327i \(-0.762272\pi\)
0.921923 0.387372i \(-0.126617\pi\)
\(80\) 0 0
\(81\) 6.59432 + 5.53329i 0.732702 + 0.614810i
\(82\) 0 0
\(83\) −1.31821 + 4.91963i −0.144692 + 0.539999i 0.855077 + 0.518502i \(0.173510\pi\)
−0.999769 + 0.0214974i \(0.993157\pi\)
\(84\) 0 0
\(85\) −7.09010 4.06405i −0.769030 0.440808i
\(86\) 0 0
\(87\) 4.20119 + 15.6790i 0.450414 + 1.68097i
\(88\) 0 0
\(89\) 1.38111 + 7.83264i 0.146397 + 0.830258i 0.966235 + 0.257663i \(0.0829523\pi\)
−0.819838 + 0.572596i \(0.805937\pi\)
\(90\) 0 0
\(91\) −7.92219 9.44130i −0.830472 0.989718i
\(92\) 0 0
\(93\) −0.206550 0.0963158i −0.0214182 0.00998748i
\(94\) 0 0
\(95\) 7.90545 + 5.70121i 0.811082 + 0.584932i
\(96\) 0 0
\(97\) −4.48907 2.09329i −0.455796 0.212541i 0.181141 0.983457i \(-0.442021\pi\)
−0.636937 + 0.770916i \(0.719799\pi\)
\(98\) 0 0
\(99\) −6.04617 7.20554i −0.607663 0.724184i
\(100\) 0 0
\(101\) −1.30683 7.41143i −0.130035 0.737465i −0.978189 0.207716i \(-0.933397\pi\)
0.848154 0.529749i \(-0.177714\pi\)
\(102\) 0 0
\(103\) −0.958897 3.57865i −0.0944830 0.352615i 0.902458 0.430779i \(-0.141761\pi\)
−0.996941 + 0.0781635i \(0.975094\pi\)
\(104\) 0 0
\(105\) 21.6057 5.86150i 2.10850 0.572024i
\(106\) 0 0
\(107\) −0.0632167 + 0.235928i −0.00611139 + 0.0228080i −0.968914 0.247397i \(-0.920425\pi\)
0.962803 + 0.270205i \(0.0870915\pi\)
\(108\) 0 0
\(109\) −1.41305 1.18569i −0.135346 0.113569i 0.572602 0.819834i \(-0.305934\pi\)
−0.707947 + 0.706265i \(0.750379\pi\)
\(110\) 0 0
\(111\) −3.42193 + 19.4067i −0.324795 + 1.84200i
\(112\) 0 0
\(113\) −6.93584 + 6.93584i −0.652469 + 0.652469i −0.953587 0.301118i \(-0.902640\pi\)
0.301118 + 0.953587i \(0.402640\pi\)
\(114\) 0 0
\(115\) 1.67919 9.69995i 0.156586 0.904525i
\(116\) 0 0
\(117\) −7.80009 + 5.46168i −0.721119 + 0.504933i
\(118\) 0 0
\(119\) −9.50310 + 11.3254i −0.871148 + 1.03819i
\(120\) 0 0
\(121\) 0.971015 + 1.68185i 0.0882741 + 0.152895i
\(122\) 0 0
\(123\) 0.267698 + 0.574080i 0.0241375 + 0.0517631i
\(124\) 0 0
\(125\) −2.79254 + 10.8260i −0.249772 + 0.968305i
\(126\) 0 0
\(127\) 10.8104 15.4389i 0.959269 1.36998i 0.0304135 0.999537i \(-0.490318\pi\)
0.928856 0.370441i \(-0.120794\pi\)
\(128\) 0 0
\(129\) −21.4683 + 18.0141i −1.89018 + 1.58605i
\(130\) 0 0
\(131\) 0.819676 0.298338i 0.0716154 0.0260659i −0.305964 0.952043i \(-0.598979\pi\)
0.377579 + 0.925977i \(0.376757\pi\)
\(132\) 0 0
\(133\) 12.6789 12.2538i 1.09940 1.06254i
\(134\) 0 0
\(135\) −0.122579 0.682726i −0.0105499 0.0587597i
\(136\) 0 0
\(137\) −1.38293 + 15.8070i −0.118152 + 1.35048i 0.673355 + 0.739319i \(0.264853\pi\)
−0.791507 + 0.611161i \(0.790703\pi\)
\(138\) 0 0
\(139\) −3.31904 + 0.585237i −0.281518 + 0.0496391i −0.312624 0.949877i \(-0.601208\pi\)
0.0311065 + 0.999516i \(0.490097\pi\)
\(140\) 0 0
\(141\) 28.7079 + 16.5745i 2.41764 + 1.39583i
\(142\) 0 0
\(143\) −8.31054 + 3.87527i −0.694962 + 0.324066i
\(144\) 0 0
\(145\) −6.15642 + 13.3107i −0.511262 + 1.10539i
\(146\) 0 0
\(147\) −2.01979 23.0863i −0.166589 1.90412i
\(148\) 0 0
\(149\) −2.79030 0.492005i −0.228590 0.0403066i 0.0581797 0.998306i \(-0.481470\pi\)
−0.286770 + 0.958000i \(0.592581\pi\)
\(150\) 0 0
\(151\) 16.7953i 1.36678i −0.730054 0.683390i \(-0.760505\pi\)
0.730054 0.683390i \(-0.239495\pi\)
\(152\) 0 0
\(153\) 8.07681 + 8.07681i 0.652972 + 0.652972i
\(154\) 0 0
\(155\) −0.0876011 0.186342i −0.00703629 0.0149674i
\(156\) 0 0
\(157\) −10.6982 + 0.935974i −0.853812 + 0.0746989i −0.505653 0.862737i \(-0.668749\pi\)
−0.348159 + 0.937436i \(0.613193\pi\)
\(158\) 0 0
\(159\) 0.839441 0.484651i 0.0665720 0.0384354i
\(160\) 0 0
\(161\) −16.7349 6.09099i −1.31889 0.480037i
\(162\) 0 0
\(163\) −18.9792 + 5.08547i −1.48657 + 0.398325i −0.908577 0.417718i \(-0.862830\pi\)
−0.577992 + 0.816043i \(0.696163\pi\)
\(164\) 0 0
\(165\) −0.0519356 16.6557i −0.00404318 1.29665i
\(166\) 0 0
\(167\) 19.8346 + 1.73530i 1.53484 + 0.134281i 0.822994 0.568050i \(-0.192302\pi\)
0.711850 + 0.702332i \(0.247858\pi\)
\(168\) 0 0
\(169\) −1.27138 3.49308i −0.0977982 0.268698i
\(170\) 0 0
\(171\) −8.57753 10.5836i −0.655940 0.809350i
\(172\) 0 0
\(173\) 1.92203 4.12181i 0.146129 0.313376i −0.819596 0.572942i \(-0.805802\pi\)
0.965725 + 0.259567i \(0.0835797\pi\)
\(174\) 0 0
\(175\) 18.3839 + 8.43339i 1.38969 + 0.637504i
\(176\) 0 0
\(177\) −13.1876 9.23404i −0.991239 0.694073i
\(178\) 0 0
\(179\) −7.24609 + 12.5506i −0.541598 + 0.938076i 0.457214 + 0.889357i \(0.348847\pi\)
−0.998813 + 0.0487192i \(0.984486\pi\)
\(180\) 0 0
\(181\) 7.37746 20.2694i 0.548362 1.50661i −0.287559 0.957763i \(-0.592844\pi\)
0.835921 0.548849i \(-0.184934\pi\)
\(182\) 0 0
\(183\) 18.4968 + 4.95620i 1.36732 + 0.366373i
\(184\) 0 0
\(185\) −13.6030 + 11.4867i −1.00011 + 0.844522i
\(186\) 0 0
\(187\) 6.30906 + 9.01027i 0.461364 + 0.658896i
\(188\) 0 0
\(189\) −1.25485 −0.0912767
\(190\) 0 0
\(191\) −5.89708 −0.426698 −0.213349 0.976976i \(-0.568437\pi\)
−0.213349 + 0.976976i \(0.568437\pi\)
\(192\) 0 0
\(193\) 0.266322 + 0.380347i 0.0191703 + 0.0273780i 0.828623 0.559807i \(-0.189125\pi\)
−0.809453 + 0.587185i \(0.800236\pi\)
\(194\) 0 0
\(195\) −16.8015 1.41717i −1.20318 0.101485i
\(196\) 0 0
\(197\) 7.73822 + 2.07345i 0.551325 + 0.147727i 0.523718 0.851892i \(-0.324545\pi\)
0.0276072 + 0.999619i \(0.491211\pi\)
\(198\) 0 0
\(199\) 4.99686 13.7288i 0.354218 0.973206i −0.626781 0.779195i \(-0.715628\pi\)
0.980999 0.194011i \(-0.0621497\pi\)
\(200\) 0 0
\(201\) −9.32941 + 16.1590i −0.658046 + 1.13977i
\(202\) 0 0
\(203\) 21.7328 + 15.2174i 1.52534 + 1.06806i
\(204\) 0 0
\(205\) −0.146395 + 0.553250i −0.0102247 + 0.0386406i
\(206\) 0 0
\(207\) −5.81489 + 12.4701i −0.404163 + 0.866730i
\(208\) 0 0
\(209\) −6.36473 11.4713i −0.440258 0.793489i
\(210\) 0 0
\(211\) −2.44195 6.70920i −0.168111 0.461880i 0.826817 0.562471i \(-0.190149\pi\)
−0.994928 + 0.100590i \(0.967927\pi\)
\(212\) 0 0
\(213\) −39.7246 3.47545i −2.72188 0.238134i
\(214\) 0 0
\(215\) −25.3199 + 0.0789521i −1.72680 + 0.00538449i
\(216\) 0 0
\(217\) −0.359805 + 0.0964096i −0.0244252 + 0.00654471i
\(218\) 0 0
\(219\) −11.4675 4.17381i −0.774899 0.282040i
\(220\) 0 0
\(221\) 9.64332 5.56758i 0.648680 0.374516i
\(222\) 0 0
\(223\) 2.79259 0.244320i 0.187006 0.0163609i 0.00673183 0.999977i \(-0.497857\pi\)
0.180274 + 0.983616i \(0.442302\pi\)
\(224\) 0 0
\(225\) 7.72880 13.5816i 0.515253 0.905439i
\(226\) 0 0
\(227\) −0.142147 0.142147i −0.00943464 0.00943464i 0.702374 0.711808i \(-0.252124\pi\)
−0.711808 + 0.702374i \(0.752124\pi\)
\(228\) 0 0
\(229\) 12.4654i 0.823738i 0.911243 + 0.411869i \(0.135124\pi\)
−0.911243 + 0.411869i \(0.864876\pi\)
\(230\) 0 0
\(231\) −29.6737 5.23228i −1.95239 0.344258i
\(232\) 0 0
\(233\) −0.501766 5.73521i −0.0328718 0.375726i −0.994757 0.102271i \(-0.967389\pi\)
0.961885 0.273455i \(-0.0881665\pi\)
\(234\) 0 0
\(235\) 10.3311 + 28.1113i 0.673924 + 1.83378i
\(236\) 0 0
\(237\) −21.5946 + 10.0697i −1.40272 + 0.654099i
\(238\) 0 0
\(239\) 4.96615 + 2.86721i 0.321233 + 0.185464i 0.651942 0.758269i \(-0.273954\pi\)
−0.330709 + 0.943733i \(0.607288\pi\)
\(240\) 0 0
\(241\) 7.31256 1.28940i 0.471044 0.0830577i 0.0669127 0.997759i \(-0.478685\pi\)
0.404131 + 0.914701i \(0.367574\pi\)
\(242\) 0 0
\(243\) 1.93796 22.1510i 0.124320 1.42099i
\(244\) 0 0
\(245\) 11.9558 17.1885i 0.763831 1.09814i
\(246\) 0 0
\(247\) −12.1302 + 5.40658i −0.771824 + 0.344012i
\(248\) 0 0
\(249\) 11.8451 4.31127i 0.750654 0.273216i
\(250\) 0 0
\(251\) −0.758712 + 0.636635i −0.0478895 + 0.0401840i −0.666418 0.745578i \(-0.732173\pi\)
0.618529 + 0.785762i \(0.287729\pi\)
\(252\) 0 0
\(253\) −7.59981 + 10.8537i −0.477796 + 0.682364i
\(254\) 0 0
\(255\) 1.82562 + 20.1433i 0.114325 + 1.26143i
\(256\) 0 0
\(257\) 6.37083 + 13.6623i 0.397402 + 0.852230i 0.998588 + 0.0531217i \(0.0169171\pi\)
−0.601186 + 0.799109i \(0.705305\pi\)
\(258\) 0 0
\(259\) 16.1044 + 27.8937i 1.00068 + 1.73323i
\(260\) 0 0
\(261\) 13.1757 15.7022i 0.815558 0.971944i
\(262\) 0 0
\(263\) −9.13287 + 6.39491i −0.563157 + 0.394327i −0.820203 0.572072i \(-0.806140\pi\)
0.257046 + 0.966399i \(0.417251\pi\)
\(264\) 0 0
\(265\) 0.862914 + 0.149382i 0.0530084 + 0.00917647i
\(266\) 0 0
\(267\) 13.9190 13.9190i 0.851827 0.851827i
\(268\) 0 0
\(269\) 5.10282 28.9395i 0.311124 1.76447i −0.282051 0.959399i \(-0.591015\pi\)
0.593175 0.805074i \(-0.297874\pi\)
\(270\) 0 0
\(271\) 22.0185 + 18.4757i 1.33753 + 1.12232i 0.982253 + 0.187559i \(0.0600576\pi\)
0.355276 + 0.934761i \(0.384387\pi\)
\(272\) 0 0
\(273\) −7.89477 + 29.4637i −0.477813 + 1.78322i
\(274\) 0 0
\(275\) 9.60074 11.5877i 0.578946 0.698765i
\(276\) 0 0
\(277\) −7.48481 27.9337i −0.449719 1.67837i −0.703167 0.711025i \(-0.748231\pi\)
0.253448 0.967349i \(-0.418435\pi\)
\(278\) 0 0
\(279\) 0.0499748 + 0.283421i 0.00299192 + 0.0169680i
\(280\) 0 0
\(281\) 8.34382 + 9.94378i 0.497751 + 0.593196i 0.955171 0.296055i \(-0.0956710\pi\)
−0.457421 + 0.889251i \(0.651227\pi\)
\(282\) 0 0
\(283\) 15.9414 + 7.43361i 0.947619 + 0.441882i 0.834075 0.551651i \(-0.186002\pi\)
0.113544 + 0.993533i \(0.463780\pi\)
\(284\) 0 0
\(285\) 0.336040 24.1204i 0.0199053 1.42877i
\(286\) 0 0
\(287\) 0.938312 + 0.437542i 0.0553868 + 0.0258273i
\(288\) 0 0
\(289\) 2.34154 + 2.79054i 0.137737 + 0.164149i
\(290\) 0 0
\(291\) 2.12871 + 12.0725i 0.124787 + 0.707702i
\(292\) 0 0
\(293\) −4.18365 15.6136i −0.244412 0.912157i −0.973678 0.227927i \(-0.926805\pi\)
0.729267 0.684230i \(-0.239861\pi\)
\(294\) 0 0
\(295\) −3.80837 14.0378i −0.221732 0.817313i
\(296\) 0 0
\(297\) −0.241637 + 0.901800i −0.0140212 + 0.0523277i
\(298\) 0 0
\(299\) 10.2752 + 8.62188i 0.594228 + 0.498616i
\(300\) 0 0
\(301\) −7.95406 + 45.1097i −0.458465 + 2.60008i
\(302\) 0 0
\(303\) −13.1704 + 13.1704i −0.756622 + 0.756622i
\(304\) 0 0
\(305\) 9.96762 + 14.1412i 0.570744 + 0.809722i
\(306\) 0 0
\(307\) −21.1366 + 14.8000i −1.20633 + 0.844682i −0.991261 0.131917i \(-0.957887\pi\)
−0.215070 + 0.976599i \(0.568998\pi\)
\(308\) 0 0
\(309\) −5.89398 + 7.02417i −0.335297 + 0.399591i
\(310\) 0 0
\(311\) 2.85083 + 4.93778i 0.161656 + 0.279996i 0.935463 0.353426i \(-0.114983\pi\)
−0.773807 + 0.633421i \(0.781650\pi\)
\(312\) 0 0
\(313\) −5.49117 11.7759i −0.310379 0.665611i 0.687802 0.725899i \(-0.258576\pi\)
−0.998181 + 0.0602879i \(0.980798\pi\)
\(314\) 0 0
\(315\) −21.7124 18.1038i −1.22336 1.02004i
\(316\) 0 0
\(317\) −10.2972 + 14.7059i −0.578349 + 0.825967i −0.996602 0.0823629i \(-0.973753\pi\)
0.418254 + 0.908330i \(0.362642\pi\)
\(318\) 0 0
\(319\) 15.1210 12.6880i 0.846613 0.710392i
\(320\) 0 0
\(321\) 0.568050 0.206753i 0.0317054 0.0115398i
\(322\) 0 0
\(323\) 8.91367 + 13.2035i 0.495970 + 0.734665i
\(324\) 0 0
\(325\) −10.8389 10.7045i −0.601233 0.593781i
\(326\) 0 0
\(327\) −0.397892 + 4.54793i −0.0220035 + 0.251501i
\(328\) 0 0
\(329\) 53.3577 9.40840i 2.94170 0.518702i
\(330\) 0 0
\(331\) −10.1591 5.86535i −0.558394 0.322389i 0.194107 0.980980i \(-0.437819\pi\)
−0.752501 + 0.658592i \(0.771153\pi\)
\(332\) 0 0
\(333\) 22.5532 10.5167i 1.23591 0.576314i
\(334\) 0 0
\(335\) −15.8232 + 5.81512i −0.864514 + 0.317714i
\(336\) 0 0
\(337\) −2.50771 28.6632i −0.136604 1.56139i −0.687109 0.726555i \(-0.741120\pi\)
0.550505 0.834832i \(-0.314435\pi\)
\(338\) 0 0
\(339\) 23.9073 + 4.21550i 1.29847 + 0.228955i
\(340\) 0 0
\(341\) 0.277140i 0.0150080i
\(342\) 0 0
\(343\) −6.76091 6.76091i −0.365055 0.365055i
\(344\) 0 0
\(345\) −22.0490 + 10.3654i −1.18708 + 0.558055i
\(346\) 0 0
\(347\) 22.4415 1.96338i 1.20472 0.105400i 0.532944 0.846150i \(-0.321086\pi\)
0.671780 + 0.740751i \(0.265530\pi\)
\(348\) 0 0
\(349\) 25.9401 14.9765i 1.38854 0.801674i 0.395389 0.918514i \(-0.370610\pi\)
0.993151 + 0.116840i \(0.0372766\pi\)
\(350\) 0 0
\(351\) 0.888127 + 0.323252i 0.0474047 + 0.0172539i
\(352\) 0 0
\(353\) 27.4121 7.34506i 1.45900 0.390938i 0.559856 0.828590i \(-0.310857\pi\)
0.899144 + 0.437652i \(0.144190\pi\)
\(354\) 0 0
\(355\) −25.5547 25.3958i −1.35630 1.34787i
\(356\) 0 0
\(357\) 36.4508 + 3.18903i 1.92918 + 0.168781i
\(358\) 0 0
\(359\) −5.18695 14.2510i −0.273757 0.752140i −0.998037 0.0626341i \(-0.980050\pi\)
0.724280 0.689506i \(-0.242172\pi\)
\(360\) 0 0
\(361\) −8.93352 16.7688i −0.470185 0.882568i
\(362\) 0 0
\(363\) 2.03128 4.35609i 0.106614 0.228635i
\(364\) 0 0
\(365\) −5.54254 9.53120i −0.290110 0.498886i
\(366\) 0 0
\(367\) 15.5424 + 10.8829i 0.811304 + 0.568081i 0.903960 0.427617i \(-0.140647\pi\)
−0.0926559 + 0.995698i \(0.529536\pi\)
\(368\) 0 0
\(369\) 0.399944 0.692723i 0.0208202 0.0360617i
\(370\) 0 0
\(371\) 0.541859 1.48874i 0.0281319 0.0772918i
\(372\) 0 0
\(373\) −15.2545 4.08743i −0.789848 0.211639i −0.158726 0.987323i \(-0.550739\pi\)
−0.631122 + 0.775683i \(0.717405\pi\)
\(374\) 0 0
\(375\) 25.9123 9.70675i 1.33810 0.501255i
\(376\) 0 0
\(377\) −11.4615 16.3687i −0.590295 0.843029i
\(378\) 0 0
\(379\) 21.5930 1.10916 0.554579 0.832131i \(-0.312879\pi\)
0.554579 + 0.832131i \(0.312879\pi\)
\(380\) 0 0
\(381\) −46.6462 −2.38976
\(382\) 0 0
\(383\) −21.7781 31.1023i −1.11281 1.58925i −0.755348 0.655324i \(-0.772532\pi\)
−0.357459 0.933929i \(-0.616357\pi\)
\(384\) 0 0
\(385\) −17.5637 20.7996i −0.895130 1.06004i
\(386\) 0 0
\(387\) 34.1838 + 9.15951i 1.73766 + 0.465604i
\(388\) 0 0
\(389\) 0.967198 2.65735i 0.0490389 0.134733i −0.912755 0.408507i \(-0.866050\pi\)
0.961794 + 0.273774i \(0.0882719\pi\)
\(390\) 0 0
\(391\) 8.04497 13.9343i 0.406851 0.704687i
\(392\) 0 0
\(393\) −1.76842 1.23826i −0.0892051 0.0624621i
\(394\) 0 0
\(395\) −20.8110 5.50680i −1.04712 0.277077i
\(396\) 0 0
\(397\) −6.06428 + 13.0049i −0.304358 + 0.652697i −0.997691 0.0679201i \(-0.978364\pi\)
0.693333 + 0.720617i \(0.256141\pi\)
\(398\) 0 0
\(399\) −42.8413 8.30953i −2.14475 0.415997i
\(400\) 0 0
\(401\) 3.61702 + 9.93769i 0.180626 + 0.496264i 0.996653 0.0817486i \(-0.0260505\pi\)
−0.816027 + 0.578013i \(0.803828\pi\)
\(402\) 0 0
\(403\) 0.279490 + 0.0244522i 0.0139224 + 0.00121805i
\(404\) 0 0
\(405\) 13.5684 13.6533i 0.674218 0.678435i
\(406\) 0 0
\(407\) 23.1470 6.20222i 1.14735 0.307433i
\(408\) 0 0
\(409\) −3.03263 1.10379i −0.149954 0.0545788i 0.265953 0.963986i \(-0.414313\pi\)
−0.415907 + 0.909407i \(0.636536\pi\)
\(410\) 0 0
\(411\) 34.0095 19.6354i 1.67756 0.968542i
\(412\) 0 0
\(413\) −26.2132 + 2.29336i −1.28987 + 0.112849i
\(414\) 0 0
\(415\) 10.7140 + 3.86177i 0.525927 + 0.189567i
\(416\) 0 0
\(417\) 5.89809 + 5.89809i 0.288831 + 0.288831i
\(418\) 0 0
\(419\) 32.1672i 1.57147i 0.618564 + 0.785735i \(0.287715\pi\)
−0.618564 + 0.785735i \(0.712285\pi\)
\(420\) 0 0
\(421\) 14.6161 + 2.57721i 0.712346 + 0.125606i 0.518066 0.855341i \(-0.326652\pi\)
0.194279 + 0.980946i \(0.437763\pi\)
\(422\) 0 0
\(423\) −3.64837 41.7010i −0.177390 2.02757i
\(424\) 0 0
\(425\) −10.3878 + 15.0341i −0.503884 + 0.729259i
\(426\) 0 0
\(427\) 28.3663 13.2274i 1.37274 0.640120i
\(428\) 0 0
\(429\) 19.6539 + 11.3472i 0.948900 + 0.547848i
\(430\) 0 0
\(431\) 39.8648 7.02923i 1.92022 0.338586i 0.921463 0.388466i \(-0.126995\pi\)
0.998755 + 0.0498802i \(0.0158840\pi\)
\(432\) 0 0
\(433\) −3.28124 + 37.5047i −0.157686 + 1.80236i 0.345746 + 0.938328i \(0.387626\pi\)
−0.503433 + 0.864034i \(0.667930\pi\)
\(434\) 0 0
\(435\) 35.7249 6.41419i 1.71288 0.307537i
\(436\) 0 0
\(437\) −11.2733 + 15.5295i −0.539274 + 0.742878i
\(438\) 0 0
\(439\) −25.5394 + 9.29559i −1.21893 + 0.443654i −0.869793 0.493417i \(-0.835748\pi\)
−0.349137 + 0.937072i \(0.613525\pi\)
\(440\) 0 0
\(441\) −22.4179 + 18.8109i −1.06752 + 0.895756i
\(442\) 0 0
\(443\) 9.52548 13.6038i 0.452569 0.646336i −0.526425 0.850221i \(-0.676468\pi\)
0.978995 + 0.203885i \(0.0653570\pi\)
\(444\) 0 0
\(445\) 17.7119 1.60526i 0.839625 0.0760965i
\(446\) 0 0
\(447\) 2.96355 + 6.35536i 0.140171 + 0.300598i
\(448\) 0 0
\(449\) −19.9824 34.6106i −0.943030 1.63338i −0.759648 0.650334i \(-0.774629\pi\)
−0.183382 0.983042i \(-0.558704\pi\)
\(450\) 0 0
\(451\) 0.495125 0.590067i 0.0233145 0.0277852i
\(452\) 0 0
\(453\) −34.0500 + 23.8420i −1.59981 + 1.12020i
\(454\) 0 0
\(455\) −22.5256 + 15.8775i −1.05602 + 0.744348i
\(456\) 0 0
\(457\) −24.6377 + 24.6377i −1.15250 + 1.15250i −0.166452 + 0.986050i \(0.553231\pi\)
−0.986050 + 0.166452i \(0.946769\pi\)
\(458\) 0 0
\(459\) 0.196870 1.11650i 0.00918910 0.0521140i
\(460\) 0 0
\(461\) 1.32304 + 1.11016i 0.0616202 + 0.0517055i 0.673078 0.739572i \(-0.264972\pi\)
−0.611457 + 0.791277i \(0.709416\pi\)
\(462\) 0 0
\(463\) −0.0346141 + 0.129182i −0.00160865 + 0.00600358i −0.966725 0.255816i \(-0.917656\pi\)
0.965117 + 0.261820i \(0.0843225\pi\)
\(464\) 0 0
\(465\) −0.253425 + 0.442124i −0.0117523 + 0.0205030i
\(466\) 0 0
\(467\) 3.21248 + 11.9891i 0.148656 + 0.554791i 0.999565 + 0.0294790i \(0.00938481\pi\)
−0.850910 + 0.525312i \(0.823949\pi\)
\(468\) 0 0
\(469\) 5.29577 + 30.0338i 0.244536 + 1.38683i
\(470\) 0 0
\(471\) 17.0844 + 20.3604i 0.787209 + 0.938159i
\(472\) 0 0
\(473\) 30.8866 + 14.4027i 1.42017 + 0.662235i
\(474\) 0 0
\(475\) 14.1889 16.5431i 0.651033 0.759050i
\(476\) 0 0
\(477\) −1.10935 0.517297i −0.0507935 0.0236854i
\(478\) 0 0
\(479\) −4.28350 5.10488i −0.195718 0.233248i 0.659256 0.751919i \(-0.270871\pi\)
−0.854974 + 0.518671i \(0.826427\pi\)
\(480\) 0 0
\(481\) −4.21254 23.8905i −0.192075 1.08931i
\(482\) 0 0
\(483\) 11.4077 + 42.5740i 0.519067 + 1.93719i
\(484\) 0 0
\(485\) −5.50784 + 9.60894i −0.250098 + 0.436319i
\(486\) 0 0
\(487\) −0.882377 + 3.29308i −0.0399843 + 0.149224i −0.983032 0.183434i \(-0.941279\pi\)
0.943048 + 0.332658i \(0.107945\pi\)
\(488\) 0 0
\(489\) 37.2524 + 31.2585i 1.68461 + 1.41356i
\(490\) 0 0
\(491\) 2.71026 15.3706i 0.122312 0.693667i −0.860556 0.509356i \(-0.829884\pi\)
0.982868 0.184311i \(-0.0590052\pi\)
\(492\) 0 0
\(493\) −16.9494 + 16.9494i −0.763361 + 0.763361i
\(494\) 0 0
\(495\) −17.1914 + 12.1176i −0.772695 + 0.544645i
\(496\) 0 0
\(497\) −53.3893 + 37.3836i −2.39484 + 1.67688i
\(498\) 0 0
\(499\) −11.9549 + 14.2473i −0.535174 + 0.637795i −0.964098 0.265545i \(-0.914448\pi\)
0.428925 + 0.903340i \(0.358893\pi\)
\(500\) 0 0
\(501\) −24.6384 42.6750i −1.10076 1.90658i
\(502\) 0 0
\(503\) 3.84939 + 8.25504i 0.171636 + 0.368074i 0.973243 0.229776i \(-0.0737995\pi\)
−0.801608 + 0.597850i \(0.796022\pi\)
\(504\) 0 0
\(505\) −16.7594 + 1.51893i −0.745785 + 0.0675916i
\(506\) 0 0
\(507\) −5.27690 + 7.53620i −0.234355 + 0.334694i
\(508\) 0 0
\(509\) −17.6627 + 14.8208i −0.782887 + 0.656920i −0.943974 0.330020i \(-0.892944\pi\)
0.161087 + 0.986940i \(0.448500\pi\)
\(510\) 0 0
\(511\) −18.7431 + 6.82194i −0.829147 + 0.301785i
\(512\) 0 0
\(513\) −0.372180 + 1.29993i −0.0164322 + 0.0573933i
\(514\) 0 0
\(515\) −8.15401 + 1.46400i −0.359309 + 0.0645117i
\(516\) 0 0
\(517\) 3.51331 40.1574i 0.154515 1.76612i
\(518\) 0 0
\(519\) −11.0848 + 1.95455i −0.486570 + 0.0857954i
\(520\) 0 0
\(521\) −2.69016 1.55316i −0.117858 0.0680453i 0.439912 0.898041i \(-0.355010\pi\)
−0.557770 + 0.829996i \(0.688343\pi\)
\(522\) 0 0
\(523\) −21.1624 + 9.86821i −0.925369 + 0.431507i −0.826080 0.563552i \(-0.809434\pi\)
−0.0992883 + 0.995059i \(0.531657\pi\)
\(524\) 0 0
\(525\) −8.99978 49.2425i −0.392782 2.14912i
\(526\) 0 0
\(527\) −0.0293318 0.335264i −0.00127771 0.0146043i
\(528\) 0 0
\(529\) −3.56330 0.628307i −0.154926 0.0273177i
\(530\) 0 0
\(531\) 20.3298i 0.882237i
\(532\) 0 0
\(533\) −0.551385 0.551385i −0.0238831 0.0238831i
\(534\) 0 0
\(535\) 0.513803 + 0.185197i 0.0222136 + 0.00800675i
\(536\) 0 0
\(537\) 35.7308 3.12604i 1.54190 0.134899i
\(538\) 0 0
\(539\) −24.4057 + 14.0906i −1.05123 + 0.606926i
\(540\) 0 0
\(541\) 3.82579 + 1.39247i 0.164484 + 0.0598671i 0.422950 0.906153i \(-0.360995\pi\)
−0.258466 + 0.966020i \(0.583217\pi\)
\(542\) 0 0
\(543\) −51.5660 + 13.8171i −2.21291 + 0.592948i
\(544\) 0 0
\(545\) −2.90748 + 2.92566i −0.124543 + 0.125322i
\(546\) 0 0
\(547\) 35.8262 + 3.13438i 1.53182 + 0.134017i 0.821640 0.570007i \(-0.193059\pi\)
0.710177 + 0.704023i \(0.248615\pi\)
\(548\) 0 0
\(549\) −8.27059 22.7232i −0.352980 0.969805i
\(550\) 0 0
\(551\) 22.2100 18.0001i 0.946176 0.766832i
\(552\) 0 0
\(553\) −16.4586 + 35.2955i −0.699890 + 1.50092i
\(554\) 0 0
\(555\) 42.5981 + 11.2719i 1.80819 + 0.478465i
\(556\) 0 0
\(557\) −14.4381 10.1097i −0.611762 0.428361i 0.226206 0.974079i \(-0.427368\pi\)
−0.837968 + 0.545719i \(0.816257\pi\)
\(558\) 0 0
\(559\) 17.2499 29.8777i 0.729594 1.26369i
\(560\) 0 0
\(561\) 9.31087 25.5814i 0.393105 1.08005i
\(562\) 0 0
\(563\) −7.71367 2.06687i −0.325092 0.0871083i 0.0925819 0.995705i \(-0.470488\pi\)
−0.417674 + 0.908597i \(0.637155\pi\)
\(564\) 0 0
\(565\) 14.1506 + 16.7576i 0.595321 + 0.704999i
\(566\) 0 0
\(567\) −19.9732 28.5247i −0.838795 1.19792i
\(568\) 0 0
\(569\) 41.8734 1.75542 0.877712 0.479188i \(-0.159069\pi\)
0.877712 + 0.479188i \(0.159069\pi\)
\(570\) 0 0
\(571\) −34.7494 −1.45422 −0.727109 0.686522i \(-0.759137\pi\)
−0.727109 + 0.686522i \(0.759137\pi\)
\(572\) 0 0
\(573\) 8.37131 + 11.9555i 0.349716 + 0.499447i
\(574\) 0 0
\(575\) −21.2974 5.56450i −0.888163 0.232056i
\(576\) 0 0
\(577\) −0.637746 0.170884i −0.0265497 0.00711398i 0.245520 0.969392i \(-0.421041\pi\)
−0.272069 + 0.962278i \(0.587708\pi\)
\(578\) 0 0
\(579\) 0.393036 1.07986i 0.0163340 0.0448773i
\(580\) 0 0
\(581\) 10.3014 17.8426i 0.427376 0.740237i
\(582\) 0 0
\(583\) −0.965549 0.676085i −0.0399890 0.0280006i
\(584\) 0 0
\(585\) 10.7035 + 18.4063i 0.442537 + 0.761006i
\(586\) 0 0
\(587\) 3.28102 7.03616i 0.135422 0.290413i −0.826889 0.562365i \(-0.809891\pi\)
0.962311 + 0.271952i \(0.0876692\pi\)
\(588\) 0 0
\(589\) −0.00684289 + 0.401326i −0.000281956 + 0.0165364i
\(590\) 0 0
\(591\) −6.78132 18.6315i −0.278946 0.766398i
\(592\) 0 0
\(593\) 18.4902 + 1.61768i 0.759301 + 0.0664302i 0.460229 0.887800i \(-0.347767\pi\)
0.299072 + 0.954231i \(0.403323\pi\)
\(594\) 0 0
\(595\) 23.4486 + 23.3029i 0.961301 + 0.955324i
\(596\) 0 0
\(597\) −34.9264 + 9.35851i −1.42944 + 0.383018i
\(598\) 0 0
\(599\) −1.54272 0.561504i −0.0630338 0.0229424i 0.310311 0.950635i \(-0.399567\pi\)
−0.373345 + 0.927693i \(0.621789\pi\)
\(600\) 0 0
\(601\) −12.9768 + 7.49216i −0.529335 + 0.305612i −0.740746 0.671786i \(-0.765528\pi\)
0.211411 + 0.977397i \(0.432194\pi\)
\(602\) 0 0
\(603\) 23.4726 2.05358i 0.955876 0.0836284i
\(604\) 0 0
\(605\) 3.92991 1.84749i 0.159774 0.0751110i
\(606\) 0 0
\(607\) −12.1188 12.1188i −0.491888 0.491888i 0.417013 0.908901i \(-0.363077\pi\)
−0.908901 + 0.417013i \(0.863077\pi\)
\(608\) 0 0
\(609\) 65.6622i 2.66077i
\(610\) 0 0
\(611\) −40.1879 7.08621i −1.62583 0.286677i
\(612\) 0 0
\(613\) 0.449626 + 5.13925i 0.0181602 + 0.207572i 0.999854 + 0.0171046i \(0.00544484\pi\)
−0.981693 + 0.190468i \(0.939000\pi\)
\(614\) 0 0
\(615\) 1.32945 0.488580i 0.0536086 0.0197015i
\(616\) 0 0
\(617\) −7.00750 + 3.26765i −0.282111 + 0.131551i −0.558524 0.829488i \(-0.688632\pi\)
0.276413 + 0.961039i \(0.410854\pi\)
\(618\) 0 0
\(619\) −33.9868 19.6223i −1.36605 0.788687i −0.375626 0.926771i \(-0.622572\pi\)
−0.990421 + 0.138084i \(0.955906\pi\)
\(620\) 0 0
\(621\) 1.34493 0.237147i 0.0539701 0.00951638i
\(622\) 0 0
\(623\) 2.80409 32.0509i 0.112344 1.28409i
\(624\) 0 0
\(625\) 23.5971 + 8.25683i 0.943885 + 0.330273i
\(626\) 0 0
\(627\) −14.2213 + 29.1879i −0.567944 + 1.16565i
\(628\) 0 0
\(629\) −27.3451 + 9.95280i −1.09032 + 0.396844i
\(630\) 0 0
\(631\) −5.25882 + 4.41268i −0.209350 + 0.175666i −0.741434 0.671026i \(-0.765854\pi\)
0.532083 + 0.846692i \(0.321409\pi\)
\(632\) 0 0
\(633\) −10.1354 + 14.4749i −0.402846 + 0.575324i
\(634\) 0 0
\(635\) −32.3685 26.9889i −1.28451 1.07102i
\(636\) 0 0
\(637\) 12.0568 + 25.8558i 0.477706 + 1.02444i
\(638\) 0 0
\(639\) 25.1778 + 43.6092i 0.996017 + 1.72515i
\(640\) 0 0
\(641\) 26.5316 31.6191i 1.04793 1.24888i 0.0802335 0.996776i \(-0.474433\pi\)
0.967700 0.252103i \(-0.0811221\pi\)
\(642\) 0 0
\(643\) −18.3224 + 12.8295i −0.722564 + 0.505945i −0.876059 0.482205i \(-0.839836\pi\)
0.153494 + 0.988150i \(0.450947\pi\)
\(644\) 0 0
\(645\) 36.1034 + 51.2203i 1.42157 + 2.01680i
\(646\) 0 0
\(647\) −23.4978 + 23.4978i −0.923793 + 0.923793i −0.997295 0.0735025i \(-0.976582\pi\)
0.0735025 + 0.997295i \(0.476582\pi\)
\(648\) 0 0
\(649\) −3.39955 + 19.2798i −0.133444 + 0.756798i
\(650\) 0 0
\(651\) 0.706225 + 0.592593i 0.0276791 + 0.0232256i
\(652\) 0 0
\(653\) 5.51282 20.5741i 0.215733 0.805128i −0.770174 0.637834i \(-0.779831\pi\)
0.985907 0.167294i \(-0.0535028\pi\)
\(654\) 0 0
\(655\) −0.510693 1.88243i −0.0199544 0.0735528i
\(656\) 0 0
\(657\) 3.98850 + 14.8853i 0.155606 + 0.580731i
\(658\) 0 0
\(659\) −1.14501 6.49368i −0.0446033 0.252958i 0.954350 0.298689i \(-0.0965493\pi\)
−0.998954 + 0.0457312i \(0.985438\pi\)
\(660\) 0 0
\(661\) 5.48023 + 6.53109i 0.213156 + 0.254030i 0.862019 0.506875i \(-0.169200\pi\)
−0.648863 + 0.760905i \(0.724755\pi\)
\(662\) 0 0
\(663\) −24.9768 11.6469i −0.970019 0.452327i
\(664\) 0 0
\(665\) −24.9204 30.5535i −0.966373 1.18481i
\(666\) 0 0
\(667\) −26.1687 12.2027i −1.01326 0.472490i
\(668\) 0 0
\(669\) −4.45960 5.31474i −0.172418 0.205480i
\(670\) 0 0
\(671\) −4.04365 22.9327i −0.156103 0.885305i
\(672\) 0 0
\(673\) 0.688405 + 2.56916i 0.0265361 + 0.0990339i 0.977924 0.208962i \(-0.0670084\pi\)
−0.951388 + 0.307996i \(0.900342\pi\)
\(674\) 0 0
\(675\) −1.54426 + 0.144815i −0.0594385 + 0.00557392i
\(676\) 0 0
\(677\) 10.9891 41.0118i 0.422345 1.57621i −0.347310 0.937751i \(-0.612905\pi\)
0.769654 0.638461i \(-0.220429\pi\)
\(678\) 0 0
\(679\) 15.3488 + 12.8792i 0.589033 + 0.494257i
\(680\) 0 0
\(681\) −0.0863950 + 0.489970i −0.00331066 + 0.0187757i
\(682\) 0 0
\(683\) 0.655986 0.655986i 0.0251006 0.0251006i −0.694445 0.719546i \(-0.744350\pi\)
0.719546 + 0.694445i \(0.244350\pi\)
\(684\) 0 0
\(685\) 34.9605 + 6.05213i 1.33577 + 0.231240i
\(686\) 0 0
\(687\) 25.2718 17.6955i 0.964179 0.675126i
\(688\) 0 0
\(689\) −0.767008 + 0.914085i −0.0292207 + 0.0348239i
\(690\) 0 0
\(691\) 11.1063 + 19.2366i 0.422503 + 0.731796i 0.996184 0.0872827i \(-0.0278183\pi\)
−0.573681 + 0.819079i \(0.694485\pi\)
\(692\) 0 0
\(693\) 16.0805 + 34.4848i 0.610849 + 1.30997i
\(694\) 0 0
\(695\) 0.680220 + 7.50533i 0.0258022 + 0.284694i
\(696\) 0 0
\(697\) −0.536514 + 0.766221i −0.0203219 + 0.0290227i
\(698\) 0 0
\(699\) −10.9150 + 9.15878i −0.412844 + 0.346417i
\(700\) 0 0
\(701\) −17.6498 + 6.42402i −0.666625 + 0.242632i −0.653094 0.757277i \(-0.726529\pi\)
−0.0135312 + 0.999908i \(0.504307\pi\)
\(702\) 0 0
\(703\) 33.6723 8.40991i 1.26997 0.317186i
\(704\) 0 0
\(705\) 42.3259 60.8507i 1.59409 2.29177i
\(706\) 0 0
\(707\) −2.65330 + 30.3274i −0.0997876 + 1.14058i
\(708\) 0 0
\(709\) −29.9735 + 5.28513i −1.12568 + 0.198487i −0.705332 0.708877i \(-0.749202\pi\)
−0.420345 + 0.907364i \(0.638091\pi\)
\(710\) 0 0
\(711\) 26.0574 + 15.0443i 0.977231 + 0.564204i
\(712\) 0 0
\(713\) 0.367414 0.171328i 0.0137598 0.00641629i
\(714\) 0 0
\(715\) 7.07283 + 19.2455i 0.264509 + 0.719741i
\(716\) 0 0
\(717\) −1.23694 14.1383i −0.0461945 0.528006i
\(718\) 0 0
\(719\) −28.1643 4.96612i −1.05035 0.185205i −0.378279 0.925692i \(-0.623484\pi\)
−0.672071 + 0.740487i \(0.734595\pi\)
\(720\) 0 0
\(721\) 14.9870i 0.558146i
\(722\) 0 0
\(723\) −12.9948 12.9948i −0.483280 0.483280i
\(724\) 0 0
\(725\) 28.5012 + 16.2191i 1.05851 + 0.602360i
\(726\) 0 0
\(727\) 34.1776 2.99015i 1.26758 0.110899i 0.566546 0.824030i \(-0.308279\pi\)
0.701030 + 0.713132i \(0.252724\pi\)
\(728\) 0 0
\(729\) −25.2940 + 14.6035i −0.936815 + 0.540870i
\(730\) 0 0
\(731\) −38.8886 14.1543i −1.43835 0.523516i
\(732\) 0 0
\(733\) 42.3237 11.3406i 1.56326 0.418874i 0.629566 0.776947i \(-0.283233\pi\)
0.933694 + 0.358073i \(0.116566\pi\)
\(734\) 0 0
\(735\) −51.8194 + 0.161582i −1.91139 + 0.00596006i
\(736\) 0 0
\(737\) 22.6037 + 1.97756i 0.832617 + 0.0728445i
\(738\) 0 0
\(739\) −11.7587 32.3067i −0.432550 1.18842i −0.944242 0.329252i \(-0.893203\pi\)
0.511692 0.859169i \(-0.329019\pi\)
\(740\) 0 0
\(741\) 28.1807 + 16.9171i 1.03524 + 0.621467i
\(742\) 0 0
\(743\) 4.85465 10.4108i 0.178100 0.381936i −0.796910 0.604098i \(-0.793534\pi\)
0.975010 + 0.222162i \(0.0713113\pi\)
\(744\) 0 0
\(745\) −1.62067 + 6.12475i −0.0593768 + 0.224394i
\(746\) 0 0
\(747\) −13.0392 9.13013i −0.477078 0.334054i
\(748\) 0 0
\(749\) 0.494021 0.855669i 0.0180511 0.0312655i
\(750\) 0 0
\(751\) −15.9735 + 43.8868i −0.582880 + 1.60145i 0.200354 + 0.979724i \(0.435791\pi\)
−0.783234 + 0.621727i \(0.786431\pi\)
\(752\) 0 0
\(753\) 2.36773 + 0.634431i 0.0862848 + 0.0231199i
\(754\) 0 0
\(755\) −37.4225 3.15649i −1.36194 0.114877i
\(756\) 0 0
\(757\) −3.37238 4.81626i −0.122571 0.175050i 0.753177 0.657818i \(-0.228520\pi\)
−0.875748 + 0.482768i \(0.839631\pi\)
\(758\) 0 0
\(759\) 32.7927 1.19030
\(760\) 0 0
\(761\) 25.4796 0.923636 0.461818 0.886975i \(-0.347197\pi\)
0.461818 + 0.886975i \(0.347197\pi\)
\(762\) 0 0
\(763\) 4.27992 + 6.11236i 0.154944 + 0.221282i
\(764\) 0 0
\(765\) 19.5144 16.4784i 0.705543 0.595780i
\(766\) 0 0
\(767\) 19.1433 + 5.12944i 0.691226 + 0.185213i
\(768\) 0 0
\(769\) 9.48778 26.0675i 0.342138 0.940017i −0.642635 0.766172i \(-0.722159\pi\)
0.984773 0.173844i \(-0.0556189\pi\)
\(770\) 0 0
\(771\) 18.6545 32.3105i 0.671824 1.16363i
\(772\) 0 0
\(773\) −3.27286 2.29168i −0.117716 0.0824260i 0.513236 0.858248i \(-0.328447\pi\)
−0.630952 + 0.775822i \(0.717336\pi\)
\(774\) 0 0
\(775\) −0.431663 + 0.160168i −0.0155058 + 0.00575340i
\(776\) 0 0
\(777\) 33.6891 72.2464i 1.20859 2.59183i
\(778\) 0 0
\(779\) 0.731559 0.842250i 0.0262108 0.0301767i
\(780\) 0 0
\(781\) 16.5851 + 45.5671i 0.593461 + 1.63052i
\(782\) 0 0
\(783\) −2.02678 0.177320i −0.0724311 0.00633690i
\(784\) 0 0
\(785\) 0.0748778 + 24.0132i 0.00267250 + 0.857070i
\(786\) 0 0
\(787\) 10.5341 2.82261i 0.375502 0.100615i −0.0661320 0.997811i \(-0.521066\pi\)
0.441633 + 0.897196i \(0.354399\pi\)
\(788\) 0 0
\(789\) 25.9295 + 9.43756i 0.923114 + 0.335986i
\(790\) 0 0
\(791\) 34.3625 19.8392i 1.22179 0.705400i
\(792\) 0 0
\(793\) −23.4839 + 2.05457i −0.833937 + 0.0729600i
\(794\) 0 0
\(795\) −0.922115 1.96149i −0.0327040 0.0695669i
\(796\) 0 0
\(797\) 11.3553 + 11.3553i 0.402224 + 0.402224i 0.879016 0.476792i \(-0.158201\pi\)
−0.476792 + 0.879016i \(0.658201\pi\)
\(798\) 0 0
\(799\) 48.9512i 1.73177i
\(800\) 0 0
\(801\) −24.4797 4.31642i −0.864946 0.152513i
\(802\) 0 0
\(803\) 1.29339 + 14.7835i 0.0456426 + 0.521697i
\(804\) 0 0
\(805\) −16.7168 + 36.1431i −0.589190 + 1.27388i
\(806\) 0 0
\(807\) −65.9144 + 30.7364i −2.32030 + 1.08197i
\(808\) 0 0
\(809\) −9.09647 5.25185i −0.319815 0.184645i 0.331495 0.943457i \(-0.392447\pi\)
−0.651310 + 0.758812i \(0.725780\pi\)
\(810\) 0 0
\(811\) 23.8159 4.19939i 0.836291 0.147461i 0.260927 0.965358i \(-0.415972\pi\)
0.575364 + 0.817898i \(0.304861\pi\)
\(812\) 0 0
\(813\) 6.20005 70.8669i 0.217445 2.48541i
\(814\) 0 0
\(815\) 7.76428 + 43.2445i 0.271971 + 1.51479i
\(816\) 0 0
\(817\) 44.3712 + 21.6191i 1.55235 + 0.756357i
\(818\) 0 0
\(819\) 36.1960 13.1743i 1.26479 0.460347i
\(820\) 0 0
\(821\) −5.56040 + 4.66573i −0.194059 + 0.162835i −0.734640 0.678457i \(-0.762649\pi\)
0.540581 + 0.841292i \(0.318205\pi\)
\(822\) 0 0
\(823\) −0.410000 + 0.585541i −0.0142917 + 0.0204107i −0.826234 0.563327i \(-0.809521\pi\)
0.811943 + 0.583737i \(0.198410\pi\)
\(824\) 0 0
\(825\) −37.1213 3.01454i −1.29240 0.104953i
\(826\) 0 0
\(827\) −0.891565 1.91197i −0.0310028 0.0664857i 0.890197 0.455577i \(-0.150567\pi\)
−0.921199 + 0.389091i \(0.872789\pi\)
\(828\) 0 0
\(829\) 1.80848 + 3.13238i 0.0628110 + 0.108792i 0.895721 0.444617i \(-0.146660\pi\)
−0.832910 + 0.553409i \(0.813327\pi\)
\(830\) 0 0
\(831\) −46.0063 + 54.8282i −1.59594 + 1.90197i
\(832\) 0 0
\(833\) 28.0328 19.6288i 0.971280 0.680097i
\(834\) 0 0
\(835\) 7.59421 43.8684i 0.262808 1.51813i
\(836\) 0 0
\(837\) 0.0201985 0.0201985i 0.000698164 0.000698164i
\(838\) 0 0
\(839\) 2.15677 12.2317i 0.0744600 0.422284i −0.924677 0.380752i \(-0.875665\pi\)
0.999137 0.0415318i \(-0.0132238\pi\)
\(840\) 0 0
\(841\) 10.7362 + 9.00875i 0.370214 + 0.310647i
\(842\) 0 0
\(843\) 8.31493 31.0317i 0.286381 1.06879i
\(844\) 0 0
\(845\) −8.02207 + 2.17634i −0.275967 + 0.0748683i
\(846\) 0 0
\(847\) −2.03326 7.58821i −0.0698635 0.260734i
\(848\) 0 0
\(849\) −7.55939 42.8714i −0.259438 1.47134i
\(850\) 0 0
\(851\) −22.5320 26.8526i −0.772386 0.920494i
\(852\) 0 0
\(853\) −23.4572 10.9383i −0.803159 0.374519i −0.0227126 0.999742i \(-0.507230\pi\)
−0.780446 + 0.625223i \(0.785008\pi\)
\(854\) 0 0
\(855\) −25.1940 + 17.1230i −0.861617 + 0.585594i
\(856\) 0 0
\(857\) 17.0219 + 7.93745i 0.581458 + 0.271138i 0.691013 0.722843i \(-0.257165\pi\)
−0.109555 + 0.993981i \(0.534943\pi\)
\(858\) 0 0
\(859\) −10.0782 12.0107i −0.343863 0.409799i 0.566202 0.824267i \(-0.308412\pi\)
−0.910064 + 0.414467i \(0.863968\pi\)
\(860\) 0 0
\(861\) −0.444946 2.52341i −0.0151637 0.0859976i
\(862\) 0 0
\(863\) 6.52037 + 24.3344i 0.221956 + 0.828351i 0.983601 + 0.180357i \(0.0577252\pi\)
−0.761645 + 0.647994i \(0.775608\pi\)
\(864\) 0 0
\(865\) −8.82281 5.05724i −0.299985 0.171951i
\(866\) 0 0
\(867\) 2.33343 8.70848i 0.0792475 0.295756i
\(868\) 0 0
\(869\) 22.1959 + 18.6246i 0.752946 + 0.631796i
\(870\) 0 0
\(871\) 3.98866 22.6208i 0.135151 0.766478i
\(872\) 0 0
\(873\) 10.9462 10.9462i 0.370472 0.370472i
\(874\) 0 0
\(875\) 22.2460 39.3773i 0.752051 1.33120i
\(876\) 0 0
\(877\) 0.0424860 0.0297490i 0.00143465 0.00100455i −0.572859 0.819654i \(-0.694166\pi\)
0.574294 + 0.818649i \(0.305277\pi\)
\(878\) 0 0
\(879\) −25.7153 + 30.6463i −0.867357 + 1.03368i
\(880\) 0 0
\(881\) 7.53797 + 13.0562i 0.253961 + 0.439873i 0.964613 0.263671i \(-0.0849332\pi\)
−0.710652 + 0.703544i \(0.751600\pi\)
\(882\) 0 0
\(883\) −15.1663 32.5243i −0.510388 1.09453i −0.977617 0.210393i \(-0.932525\pi\)
0.467229 0.884136i \(-0.345252\pi\)
\(884\) 0 0
\(885\) −23.0534 + 27.6485i −0.774930 + 0.929396i
\(886\) 0 0
\(887\) −9.09887 + 12.9945i −0.305510 + 0.436314i −0.942323 0.334705i \(-0.891363\pi\)
0.636813 + 0.771018i \(0.280252\pi\)
\(888\) 0 0
\(889\) −58.4043 + 49.0070i −1.95882 + 1.64364i
\(890\) 0 0
\(891\) −24.3454 + 8.86101i −0.815602 + 0.296855i
\(892\) 0 0
\(893\) 6.07916 58.0651i 0.203431 1.94307i
\(894\) 0 0
\(895\) 26.6029 + 18.5042i 0.889236 + 0.618526i
\(896\) 0 0
\(897\) 2.89331 33.0707i 0.0966049 1.10420i
\(898\) 0 0
\(899\) −0.594766 + 0.104873i −0.0198366 + 0.00349772i
\(900\) 0 0
\(901\) 1.23960 + 0.715686i 0.0412972 + 0.0238429i
\(902\) 0 0
\(903\) 102.745 47.9107i 3.41913 1.59437i
\(904\) 0 0
\(905\) −43.7769 20.2475i −1.45519 0.673051i
\(906\) 0 0
\(907\) −0.132267 1.51181i −0.00439184 0.0501990i 0.993683 0.112228i \(-0.0357986\pi\)
−0.998074 + 0.0620286i \(0.980243\pi\)
\(908\) 0 0
\(909\) 23.1632 + 4.08430i 0.768276 + 0.135468i
\(910\) 0 0
\(911\) 18.3158i 0.606830i 0.952859 + 0.303415i \(0.0981268\pi\)
−0.952859 + 0.303415i \(0.901873\pi\)
\(912\) 0 0
\(913\) −10.8390 10.8390i −0.358718 0.358718i
\(914\) 0 0
\(915\) 14.5195 40.2823i 0.479999 1.33169i
\(916\) 0 0
\(917\) −3.51512 + 0.307533i −0.116080 + 0.0101556i
\(918\) 0 0
\(919\) 43.4759 25.1008i 1.43414 0.827999i 0.436704 0.899605i \(-0.356146\pi\)
0.997433 + 0.0716060i \(0.0228124\pi\)
\(920\) 0 0
\(921\) 60.0098 + 21.8418i 1.97739 + 0.719711i
\(922\) 0 0
\(923\) 47.4168 12.7053i 1.56074 0.418200i
\(924\) 0 0
\(925\) 23.0377 + 32.4684i 0.757476 + 1.06755i
\(926\) 0 0
\(927\) 11.5350 + 1.00918i 0.378859 + 0.0331459i
\(928\) 0 0
\(929\) 9.87325 + 27.1265i 0.323931 + 0.889993i 0.989613 + 0.143757i \(0.0459185\pi\)
−0.665682 + 0.746235i \(0.731859\pi\)
\(930\) 0 0
\(931\) −35.6897 + 19.8020i −1.16968 + 0.648984i
\(932\) 0 0
\(933\) 5.96368 12.7892i 0.195242 0.418698i
\(934\) 0 0
\(935\) 21.2620 12.3642i 0.695342 0.404352i
\(936\) 0 0
\(937\) −17.8425 12.4935i −0.582889 0.408143i 0.244601 0.969624i \(-0.421343\pi\)
−0.827490 + 0.561481i \(0.810232\pi\)
\(938\) 0 0
\(939\) −16.0787 + 27.8492i −0.524710 + 0.908824i
\(940\) 0 0
\(941\) −11.1837 + 30.7270i −0.364579 + 1.00167i 0.612812 + 0.790229i \(0.290038\pi\)
−0.977390 + 0.211443i \(0.932184\pi\)
\(942\) 0 0
\(943\) −1.08836 0.291625i −0.0354418 0.00949660i
\(944\) 0 0
\(945\) −0.235835 + 2.79600i −0.00767172 + 0.0909537i
\(946\) 0 0
\(947\) 23.7297 + 33.8895i 0.771110 + 1.10126i 0.992034 + 0.125968i \(0.0402038\pi\)
−0.220924 + 0.975291i \(0.570907\pi\)
\(948\) 0 0
\(949\) 15.0229 0.487665
\(950\) 0 0
\(951\) 44.4317 1.44080
\(952\) 0 0
\(953\) 13.7455 + 19.6306i 0.445260 + 0.635897i 0.977560 0.210659i \(-0.0675610\pi\)
−0.532300 + 0.846556i \(0.678672\pi\)
\(954\) 0 0
\(955\) −1.10829 + 13.1396i −0.0358635 + 0.425188i
\(956\) 0 0
\(957\) −47.1884 12.6441i −1.52538 0.408725i
\(958\) 0 0
\(959\) 21.9531 60.3156i 0.708902 1.94769i
\(960\) 0 0
\(961\) −15.4958 + 26.8394i −0.499863 + 0.865789i
\(962\) 0 0
\(963\) −0.625312 0.437848i −0.0201504 0.0141095i
\(964\) 0 0
\(965\) 0.897525 0.521924i 0.0288923 0.0168013i
\(966\) 0 0
\(967\) 4.21350 9.03588i 0.135497 0.290574i −0.826838 0.562440i \(-0.809863\pi\)
0.962335 + 0.271865i \(0.0876406\pi\)
\(968\) 0 0
\(969\) 14.1147 36.8145i 0.453429 1.18265i
\(970\) 0 0
\(971\) 13.2089 + 36.2912i 0.423895 + 1.16464i 0.949460 + 0.313888i \(0.101632\pi\)
−0.525565 + 0.850753i \(0.676146\pi\)
\(972\) 0 0
\(973\) 13.5814 + 1.18822i 0.435401 + 0.0380926i
\(974\) 0 0
\(975\) −6.31534 + 37.1701i −0.202253 + 1.19040i
\(976\) 0 0
\(977\) −19.1294 + 5.12571i −0.612004 + 0.163986i −0.551490 0.834181i \(-0.685941\pi\)
−0.0605139 + 0.998167i \(0.519274\pi\)
\(978\) 0 0
\(979\) −22.4935 8.18698i −0.718897 0.261657i
\(980\) 0 0
\(981\) 4.99266 2.88252i 0.159403 0.0920316i
\(982\) 0 0
\(983\) −47.2352 + 4.13254i −1.50657 + 0.131808i −0.810317 0.585991i \(-0.800705\pi\)
−0.696251 + 0.717799i \(0.745150\pi\)
\(984\) 0 0
\(985\) 6.07428 16.8523i 0.193543 0.536958i
\(986\) 0 0
\(987\) −94.8190 94.8190i −3.01812 3.01812i
\(988\) 0 0
\(989\) 49.8512i 1.58517i
\(990\) 0 0
\(991\) 11.6050 + 2.04627i 0.368645 + 0.0650020i 0.354902 0.934904i \(-0.384514\pi\)
0.0137428 + 0.999906i \(0.495625\pi\)
\(992\) 0 0
\(993\) 2.53038 + 28.9223i 0.0802990 + 0.917822i
\(994\) 0 0
\(995\) −29.6507 13.7140i −0.939991 0.434762i
\(996\) 0 0
\(997\) −8.67341 + 4.04448i −0.274689 + 0.128090i −0.555082 0.831796i \(-0.687313\pi\)
0.280393 + 0.959885i \(0.409535\pi\)
\(998\) 0 0
\(999\) −2.13903 1.23497i −0.0676760 0.0390727i
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 380.2.bh.a.33.2 120
5.2 odd 4 inner 380.2.bh.a.337.2 yes 120
19.15 odd 18 inner 380.2.bh.a.53.2 yes 120
95.72 even 36 inner 380.2.bh.a.357.2 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.bh.a.33.2 120 1.1 even 1 trivial
380.2.bh.a.53.2 yes 120 19.15 odd 18 inner
380.2.bh.a.337.2 yes 120 5.2 odd 4 inner
380.2.bh.a.357.2 yes 120 95.72 even 36 inner