Properties

Label 756.2.b.f.55.1
Level $756$
Weight $2$
Character 756.55
Analytic conductor $6.037$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(55,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.b (of order \(2\), degree \(1\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{12} - 4x^{10} - 4x^{8} - 16x^{6} - 16x^{4} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.1
Root \(1.41109 - 0.0939769i\) of defining polynomial
Character \(\chi\) \(=\) 756.55
Dual form 756.2.b.f.55.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41109 - 0.0939769i) q^{2} +(1.98234 + 0.265219i) q^{4} -2.91758i q^{5} +(1.63542 - 2.07976i) q^{7} +(-2.77233 - 0.560541i) q^{8} +O(q^{10})\) \(q+(-1.41109 - 0.0939769i) q^{2} +(1.98234 + 0.265219i) q^{4} -2.91758i q^{5} +(1.63542 - 2.07976i) q^{7} +(-2.77233 - 0.560541i) q^{8} +(-0.274185 + 4.11696i) q^{10} -2.40700i q^{11} -1.28591i q^{13} +(-2.50318 + 2.78103i) q^{14} +(3.85932 + 1.05151i) q^{16} -5.02059i q^{17} -4.84850 q^{19} +(0.773798 - 5.78362i) q^{20} +(-0.226202 + 3.39648i) q^{22} +8.04597i q^{23} -3.51227 q^{25} +(-0.120846 + 1.81454i) q^{26} +(3.79355 - 3.68903i) q^{28} -2.57469 q^{29} +6.34051 q^{31} +(-5.34702 - 1.84646i) q^{32} +(-0.471820 + 7.08450i) q^{34} +(-6.06786 - 4.77148i) q^{35} -6.71864 q^{37} +(6.84165 + 0.455647i) q^{38} +(-1.63542 + 8.08848i) q^{40} +2.30281i q^{41} +9.79488i q^{43} +(0.638382 - 4.77148i) q^{44} +(0.756135 - 11.3536i) q^{46} +1.21071 q^{47} +(-1.65078 - 6.80257i) q^{49} +(4.95612 + 0.330072i) q^{50} +(0.341049 - 2.54912i) q^{52} -5.54465 q^{53} -7.02260 q^{55} +(-5.69972 + 4.84904i) q^{56} +(3.63312 + 0.241961i) q^{58} +12.2309 q^{59} -8.95597i q^{61} +(-8.94701 - 0.595861i) q^{62} +(7.37159 + 3.10801i) q^{64} -3.75176 q^{65} -7.32341i q^{67} +(1.33156 - 9.95251i) q^{68} +(8.11387 + 7.30321i) q^{70} -8.42187i q^{71} -14.7329i q^{73} +(9.48058 + 0.631396i) q^{74} +(-9.61135 - 1.28591i) q^{76} +(-5.00597 - 3.93646i) q^{77} +3.53235i q^{79} +(3.06786 - 11.2599i) q^{80} +(0.216411 - 3.24947i) q^{82} -10.4416 q^{83} -14.6480 q^{85} +(0.920492 - 13.8214i) q^{86} +(-1.34922 + 6.67298i) q^{88} +9.97593i q^{89} +(-2.67439 - 2.10301i) q^{91} +(-2.13394 + 15.9498i) q^{92} +(-1.70842 - 0.113779i) q^{94} +14.1459i q^{95} -11.8187i q^{97} +(1.69011 + 9.75415i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{14} + 4 q^{16} + 26 q^{20} + 10 q^{22} - 20 q^{25} + 6 q^{26} - 11 q^{28} + 6 q^{35} + 8 q^{37} + 20 q^{38} - 6 q^{46} + 8 q^{47} - 14 q^{49} - 21 q^{56} + 14 q^{58} + 44 q^{59} - 48 q^{62} + 24 q^{64} + 2 q^{68} - 27 q^{70} - 54 q^{80} - 4 q^{83} + 8 q^{85} - 34 q^{88} + 47 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41109 0.0939769i −0.997790 0.0664517i
\(3\) 0 0
\(4\) 1.98234 + 0.265219i 0.991168 + 0.132610i
\(5\) 2.91758i 1.30478i −0.757883 0.652391i \(-0.773766\pi\)
0.757883 0.652391i \(-0.226234\pi\)
\(6\) 0 0
\(7\) 1.63542 2.07976i 0.618132 0.786074i
\(8\) −2.77233 0.560541i −0.980165 0.198181i
\(9\) 0 0
\(10\) −0.274185 + 4.11696i −0.0867049 + 1.30190i
\(11\) 2.40700i 0.725737i −0.931840 0.362868i \(-0.881797\pi\)
0.931840 0.362868i \(-0.118203\pi\)
\(12\) 0 0
\(13\) 1.28591i 0.356648i −0.983972 0.178324i \(-0.942932\pi\)
0.983972 0.178324i \(-0.0570676\pi\)
\(14\) −2.50318 + 2.78103i −0.669002 + 0.743261i
\(15\) 0 0
\(16\) 3.85932 + 1.05151i 0.964829 + 0.262877i
\(17\) 5.02059i 1.21767i −0.793296 0.608836i \(-0.791637\pi\)
0.793296 0.608836i \(-0.208363\pi\)
\(18\) 0 0
\(19\) −4.84850 −1.11232 −0.556161 0.831075i \(-0.687726\pi\)
−0.556161 + 0.831075i \(0.687726\pi\)
\(20\) 0.773798 5.78362i 0.173026 1.29326i
\(21\) 0 0
\(22\) −0.226202 + 3.39648i −0.0482264 + 0.724133i
\(23\) 8.04597i 1.67770i 0.544363 + 0.838850i \(0.316772\pi\)
−0.544363 + 0.838850i \(0.683228\pi\)
\(24\) 0 0
\(25\) −3.51227 −0.702454
\(26\) −0.120846 + 1.81454i −0.0236999 + 0.355860i
\(27\) 0 0
\(28\) 3.79355 3.68903i 0.716914 0.697162i
\(29\) −2.57469 −0.478108 −0.239054 0.971006i \(-0.576837\pi\)
−0.239054 + 0.971006i \(0.576837\pi\)
\(30\) 0 0
\(31\) 6.34051 1.13879 0.569394 0.822065i \(-0.307178\pi\)
0.569394 + 0.822065i \(0.307178\pi\)
\(32\) −5.34702 1.84646i −0.945228 0.326410i
\(33\) 0 0
\(34\) −0.471820 + 7.08450i −0.0809164 + 1.21498i
\(35\) −6.06786 4.77148i −1.02565 0.806527i
\(36\) 0 0
\(37\) −6.71864 −1.10454 −0.552268 0.833666i \(-0.686238\pi\)
−0.552268 + 0.833666i \(0.686238\pi\)
\(38\) 6.84165 + 0.455647i 1.10986 + 0.0739156i
\(39\) 0 0
\(40\) −1.63542 + 8.08848i −0.258583 + 1.27890i
\(41\) 2.30281i 0.359639i 0.983700 + 0.179819i \(0.0575513\pi\)
−0.983700 + 0.179819i \(0.942449\pi\)
\(42\) 0 0
\(43\) 9.79488i 1.49370i 0.664990 + 0.746852i \(0.268436\pi\)
−0.664990 + 0.746852i \(0.731564\pi\)
\(44\) 0.638382 4.77148i 0.0962397 0.719327i
\(45\) 0 0
\(46\) 0.756135 11.3536i 0.111486 1.67399i
\(47\) 1.21071 0.176600 0.0883002 0.996094i \(-0.471857\pi\)
0.0883002 + 0.996094i \(0.471857\pi\)
\(48\) 0 0
\(49\) −1.65078 6.80257i −0.235826 0.971795i
\(50\) 4.95612 + 0.330072i 0.700901 + 0.0466792i
\(51\) 0 0
\(52\) 0.341049 2.54912i 0.0472950 0.353499i
\(53\) −5.54465 −0.761617 −0.380808 0.924654i \(-0.624354\pi\)
−0.380808 + 0.924654i \(0.624354\pi\)
\(54\) 0 0
\(55\) −7.02260 −0.946928
\(56\) −5.69972 + 4.84904i −0.761657 + 0.647981i
\(57\) 0 0
\(58\) 3.63312 + 0.241961i 0.477051 + 0.0317711i
\(59\) 12.2309 1.59233 0.796164 0.605081i \(-0.206859\pi\)
0.796164 + 0.605081i \(0.206859\pi\)
\(60\) 0 0
\(61\) 8.95597i 1.14669i −0.819312 0.573347i \(-0.805645\pi\)
0.819312 0.573347i \(-0.194355\pi\)
\(62\) −8.94701 0.595861i −1.13627 0.0756744i
\(63\) 0 0
\(64\) 7.37159 + 3.10801i 0.921448 + 0.388501i
\(65\) −3.75176 −0.465348
\(66\) 0 0
\(67\) 7.32341i 0.894696i −0.894360 0.447348i \(-0.852368\pi\)
0.894360 0.447348i \(-0.147632\pi\)
\(68\) 1.33156 9.95251i 0.161475 1.20692i
\(69\) 0 0
\(70\) 8.11387 + 7.30321i 0.969793 + 0.872901i
\(71\) 8.42187i 0.999493i −0.866172 0.499746i \(-0.833427\pi\)
0.866172 0.499746i \(-0.166573\pi\)
\(72\) 0 0
\(73\) 14.7329i 1.72435i −0.506610 0.862175i \(-0.669102\pi\)
0.506610 0.862175i \(-0.330898\pi\)
\(74\) 9.48058 + 0.631396i 1.10210 + 0.0733983i
\(75\) 0 0
\(76\) −9.61135 1.28591i −1.10250 0.147504i
\(77\) −5.00597 3.93646i −0.570483 0.448601i
\(78\) 0 0
\(79\) 3.53235i 0.397420i 0.980058 + 0.198710i \(0.0636752\pi\)
−0.980058 + 0.198710i \(0.936325\pi\)
\(80\) 3.06786 11.2599i 0.342997 1.25889i
\(81\) 0 0
\(82\) 0.216411 3.24947i 0.0238986 0.358844i
\(83\) −10.4416 −1.14612 −0.573058 0.819515i \(-0.694243\pi\)
−0.573058 + 0.819515i \(0.694243\pi\)
\(84\) 0 0
\(85\) −14.6480 −1.58880
\(86\) 0.920492 13.8214i 0.0992592 1.49040i
\(87\) 0 0
\(88\) −1.34922 + 6.67298i −0.143827 + 0.711342i
\(89\) 9.97593i 1.05745i 0.848794 + 0.528723i \(0.177329\pi\)
−0.848794 + 0.528723i \(0.822671\pi\)
\(90\) 0 0
\(91\) −2.67439 2.10301i −0.280352 0.220456i
\(92\) −2.13394 + 15.9498i −0.222479 + 1.66288i
\(93\) 0 0
\(94\) −1.70842 0.113779i −0.176210 0.0117354i
\(95\) 14.1459i 1.45134i
\(96\) 0 0
\(97\) 11.8187i 1.20001i −0.799998 0.600003i \(-0.795166\pi\)
0.799998 0.600003i \(-0.204834\pi\)
\(98\) 1.69011 + 9.75415i 0.170727 + 0.985318i
\(99\) 0 0
\(100\) −6.96250 0.931521i −0.696250 0.0931521i
\(101\) 0.614768i 0.0611717i 0.999532 + 0.0305858i \(0.00973730\pi\)
−0.999532 + 0.0305858i \(0.990263\pi\)
\(102\) 0 0
\(103\) −7.91816 −0.780199 −0.390100 0.920773i \(-0.627559\pi\)
−0.390100 + 0.920773i \(0.627559\pi\)
\(104\) −0.720808 + 3.56497i −0.0706810 + 0.349574i
\(105\) 0 0
\(106\) 7.82399 + 0.521069i 0.759933 + 0.0506107i
\(107\) 7.67670i 0.742135i 0.928606 + 0.371067i \(0.121008\pi\)
−0.928606 + 0.371067i \(0.878992\pi\)
\(108\) 0 0
\(109\) −6.71864 −0.643529 −0.321764 0.946820i \(-0.604276\pi\)
−0.321764 + 0.946820i \(0.604276\pi\)
\(110\) 9.90951 + 0.659962i 0.944835 + 0.0629249i
\(111\) 0 0
\(112\) 8.49850 6.30678i 0.803033 0.595935i
\(113\) 3.25679 0.306373 0.153187 0.988197i \(-0.451046\pi\)
0.153187 + 0.988197i \(0.451046\pi\)
\(114\) 0 0
\(115\) 23.4747 2.18903
\(116\) −5.10391 0.682858i −0.473886 0.0634017i
\(117\) 0 0
\(118\) −17.2589 1.14942i −1.58881 0.105813i
\(119\) −10.4416 8.21080i −0.957181 0.752683i
\(120\) 0 0
\(121\) 5.20637 0.473306
\(122\) −0.841654 + 12.6377i −0.0761998 + 1.14416i
\(123\) 0 0
\(124\) 12.5690 + 1.68162i 1.12873 + 0.151014i
\(125\) 4.34057i 0.388233i
\(126\) 0 0
\(127\) 12.9588i 1.14990i −0.818187 0.574952i \(-0.805021\pi\)
0.818187 0.574952i \(-0.194979\pi\)
\(128\) −10.1099 5.07843i −0.893595 0.448874i
\(129\) 0 0
\(130\) 5.29406 + 0.352578i 0.464320 + 0.0309232i
\(131\) 19.5773 1.71048 0.855240 0.518233i \(-0.173410\pi\)
0.855240 + 0.518233i \(0.173410\pi\)
\(132\) 0 0
\(133\) −7.92935 + 10.0837i −0.687562 + 0.874367i
\(134\) −0.688231 + 10.3340i −0.0594541 + 0.892719i
\(135\) 0 0
\(136\) −2.81425 + 13.9187i −0.241320 + 1.19352i
\(137\) 18.4269 1.57431 0.787156 0.616754i \(-0.211553\pi\)
0.787156 + 0.616754i \(0.211553\pi\)
\(138\) 0 0
\(139\) −10.2935 −0.873079 −0.436540 0.899685i \(-0.643796\pi\)
−0.436540 + 0.899685i \(0.643796\pi\)
\(140\) −10.7630 11.0680i −0.909643 0.935416i
\(141\) 0 0
\(142\) −0.791461 + 11.8840i −0.0664180 + 0.997283i
\(143\) −3.09519 −0.258833
\(144\) 0 0
\(145\) 7.51187i 0.623827i
\(146\) −1.38455 + 20.7894i −0.114586 + 1.72054i
\(147\) 0 0
\(148\) −13.3186 1.78191i −1.09478 0.146472i
\(149\) 14.6452 1.19978 0.599890 0.800082i \(-0.295211\pi\)
0.599890 + 0.800082i \(0.295211\pi\)
\(150\) 0 0
\(151\) 14.0196i 1.14090i 0.821331 + 0.570451i \(0.193232\pi\)
−0.821331 + 0.570451i \(0.806768\pi\)
\(152\) 13.4416 + 2.71778i 1.09026 + 0.220441i
\(153\) 0 0
\(154\) 6.69392 + 6.02513i 0.539412 + 0.485519i
\(155\) 18.4989i 1.48587i
\(156\) 0 0
\(157\) 0.158192i 0.0126251i 0.999980 + 0.00631255i \(0.00200936\pi\)
−0.999980 + 0.00631255i \(0.997991\pi\)
\(158\) 0.331959 4.98445i 0.0264092 0.396542i
\(159\) 0 0
\(160\) −5.38718 + 15.6003i −0.425894 + 1.23332i
\(161\) 16.7337 + 13.1586i 1.31880 + 1.03704i
\(162\) 0 0
\(163\) 6.64972i 0.520847i −0.965495 0.260423i \(-0.916138\pi\)
0.965495 0.260423i \(-0.0838621\pi\)
\(164\) −0.610750 + 4.56495i −0.0476915 + 0.356463i
\(165\) 0 0
\(166\) 14.7340 + 0.981270i 1.14358 + 0.0761613i
\(167\) −4.11552 −0.318468 −0.159234 0.987241i \(-0.550903\pi\)
−0.159234 + 0.987241i \(0.550903\pi\)
\(168\) 0 0
\(169\) 11.3464 0.872802
\(170\) 20.6696 + 1.37657i 1.58528 + 0.105578i
\(171\) 0 0
\(172\) −2.59779 + 19.4167i −0.198080 + 1.48051i
\(173\) 9.82601i 0.747058i −0.927619 0.373529i \(-0.878148\pi\)
0.927619 0.373529i \(-0.121852\pi\)
\(174\) 0 0
\(175\) −5.74405 + 7.30467i −0.434209 + 0.552181i
\(176\) 2.53098 9.28937i 0.190779 0.700212i
\(177\) 0 0
\(178\) 0.937507 14.0769i 0.0702691 1.05511i
\(179\) 2.45324i 0.183364i 0.995788 + 0.0916819i \(0.0292243\pi\)
−0.995788 + 0.0916819i \(0.970776\pi\)
\(180\) 0 0
\(181\) 21.5661i 1.60299i 0.597999 + 0.801497i \(0.295963\pi\)
−0.597999 + 0.801497i \(0.704037\pi\)
\(182\) 3.57616 + 3.21887i 0.265083 + 0.238598i
\(183\) 0 0
\(184\) 4.51010 22.3060i 0.332489 1.64442i
\(185\) 19.6022i 1.44118i
\(186\) 0 0
\(187\) −12.0846 −0.883710
\(188\) 2.40004 + 0.321104i 0.175041 + 0.0234189i
\(189\) 0 0
\(190\) 1.32938 19.9611i 0.0964437 1.44813i
\(191\) 0.329664i 0.0238536i −0.999929 0.0119268i \(-0.996203\pi\)
0.999929 0.0119268i \(-0.00379651\pi\)
\(192\) 0 0
\(193\) 15.9539 1.14839 0.574193 0.818720i \(-0.305316\pi\)
0.574193 + 0.818720i \(0.305316\pi\)
\(194\) −1.11068 + 16.6772i −0.0797423 + 1.19735i
\(195\) 0 0
\(196\) −1.46823 13.9228i −0.104873 0.994486i
\(197\) 3.16936 0.225807 0.112904 0.993606i \(-0.463985\pi\)
0.112904 + 0.993606i \(0.463985\pi\)
\(198\) 0 0
\(199\) 27.0253 1.91577 0.957887 0.287146i \(-0.0927064\pi\)
0.957887 + 0.287146i \(0.0927064\pi\)
\(200\) 9.73716 + 1.96877i 0.688521 + 0.139213i
\(201\) 0 0
\(202\) 0.0577740 0.867491i 0.00406496 0.0610365i
\(203\) −4.21071 + 5.35473i −0.295534 + 0.375829i
\(204\) 0 0
\(205\) 6.71864 0.469250
\(206\) 11.1732 + 0.744123i 0.778475 + 0.0518455i
\(207\) 0 0
\(208\) 1.35215 4.96275i 0.0937546 0.344105i
\(209\) 11.6703i 0.807253i
\(210\) 0 0
\(211\) 1.12613i 0.0775260i 0.999248 + 0.0387630i \(0.0123417\pi\)
−0.999248 + 0.0387630i \(0.987658\pi\)
\(212\) −10.9914 1.47055i −0.754890 0.100998i
\(213\) 0 0
\(214\) 0.721432 10.8325i 0.0493161 0.740494i
\(215\) 28.5773 1.94896
\(216\) 0 0
\(217\) 10.3694 13.1867i 0.703922 0.895172i
\(218\) 9.48058 + 0.631396i 0.642106 + 0.0427635i
\(219\) 0 0
\(220\) −13.9212 1.86253i −0.938565 0.125572i
\(221\) −6.45605 −0.434281
\(222\) 0 0
\(223\) −2.78994 −0.186828 −0.0934140 0.995627i \(-0.529778\pi\)
−0.0934140 + 0.995627i \(0.529778\pi\)
\(224\) −12.5848 + 8.10076i −0.840859 + 0.541255i
\(225\) 0 0
\(226\) −4.59562 0.306063i −0.305696 0.0203590i
\(227\) −5.02019 −0.333202 −0.166601 0.986024i \(-0.553279\pi\)
−0.166601 + 0.986024i \(0.553279\pi\)
\(228\) 0 0
\(229\) 1.12772i 0.0745220i 0.999306 + 0.0372610i \(0.0118633\pi\)
−0.999306 + 0.0372610i \(0.988137\pi\)
\(230\) −33.1249 2.20608i −2.18419 0.145465i
\(231\) 0 0
\(232\) 7.13789 + 1.44322i 0.468625 + 0.0947521i
\(233\) −4.15055 −0.271911 −0.135956 0.990715i \(-0.543410\pi\)
−0.135956 + 0.990715i \(0.543410\pi\)
\(234\) 0 0
\(235\) 3.53235i 0.230425i
\(236\) 24.2458 + 3.24387i 1.57827 + 0.211158i
\(237\) 0 0
\(238\) 13.9624 + 12.5674i 0.905049 + 0.814625i
\(239\) 14.8977i 0.963651i 0.876267 + 0.481826i \(0.160026\pi\)
−0.876267 + 0.481826i \(0.839974\pi\)
\(240\) 0 0
\(241\) 24.2961i 1.56505i 0.622620 + 0.782524i \(0.286068\pi\)
−0.622620 + 0.782524i \(0.713932\pi\)
\(242\) −7.34664 0.489278i −0.472260 0.0314520i
\(243\) 0 0
\(244\) 2.37530 17.7538i 0.152063 1.13657i
\(245\) −19.8470 + 4.81628i −1.26798 + 0.307701i
\(246\) 0 0
\(247\) 6.23475i 0.396708i
\(248\) −17.5780 3.55412i −1.11620 0.225687i
\(249\) 0 0
\(250\) −0.407913 + 6.12493i −0.0257987 + 0.387374i
\(251\) −22.5773 −1.42507 −0.712534 0.701637i \(-0.752453\pi\)
−0.712534 + 0.701637i \(0.752453\pi\)
\(252\) 0 0
\(253\) 19.3666 1.21757
\(254\) −1.21782 + 18.2860i −0.0764131 + 1.14736i
\(255\) 0 0
\(256\) 13.7887 + 8.11620i 0.861792 + 0.507263i
\(257\) 8.61820i 0.537588i −0.963198 0.268794i \(-0.913375\pi\)
0.963198 0.268794i \(-0.0866251\pi\)
\(258\) 0 0
\(259\) −10.9878 + 13.9731i −0.682750 + 0.868248i
\(260\) −7.43725 0.995038i −0.461238 0.0617096i
\(261\) 0 0
\(262\) −27.6253 1.83982i −1.70670 0.113664i
\(263\) 24.1043i 1.48634i −0.669104 0.743169i \(-0.733322\pi\)
0.669104 0.743169i \(-0.266678\pi\)
\(264\) 0 0
\(265\) 16.1770i 0.993743i
\(266\) 12.1366 13.4838i 0.744145 0.826745i
\(267\) 0 0
\(268\) 1.94231 14.5175i 0.118645 0.886795i
\(269\) 11.1901i 0.682272i −0.940014 0.341136i \(-0.889188\pi\)
0.940014 0.341136i \(-0.110812\pi\)
\(270\) 0 0
\(271\) −18.4251 −1.11924 −0.559621 0.828748i \(-0.689053\pi\)
−0.559621 + 0.828748i \(0.689053\pi\)
\(272\) 5.27919 19.3761i 0.320098 1.17485i
\(273\) 0 0
\(274\) −26.0019 1.73170i −1.57083 0.104616i
\(275\) 8.45402i 0.509797i
\(276\) 0 0
\(277\) −2.11552 −0.127109 −0.0635546 0.997978i \(-0.520244\pi\)
−0.0635546 + 0.997978i \(0.520244\pi\)
\(278\) 14.5250 + 0.967346i 0.871149 + 0.0580176i
\(279\) 0 0
\(280\) 14.1475 + 16.6294i 0.845473 + 0.993795i
\(281\) 9.03075 0.538729 0.269365 0.963038i \(-0.413186\pi\)
0.269365 + 0.963038i \(0.413186\pi\)
\(282\) 0 0
\(283\) 24.9368 1.48234 0.741171 0.671316i \(-0.234271\pi\)
0.741171 + 0.671316i \(0.234271\pi\)
\(284\) 2.23364 16.6950i 0.132542 0.990665i
\(285\) 0 0
\(286\) 4.36759 + 0.290876i 0.258261 + 0.0171999i
\(287\) 4.78929 + 3.76607i 0.282703 + 0.222304i
\(288\) 0 0
\(289\) −8.20637 −0.482727
\(290\) 0.705942 10.5999i 0.0414543 0.622448i
\(291\) 0 0
\(292\) 3.90744 29.2055i 0.228665 1.70912i
\(293\) 4.95534i 0.289494i −0.989469 0.144747i \(-0.953763\pi\)
0.989469 0.144747i \(-0.0462368\pi\)
\(294\) 0 0
\(295\) 35.6846i 2.07764i
\(296\) 18.6262 + 3.76607i 1.08263 + 0.218899i
\(297\) 0 0
\(298\) −20.6656 1.37631i −1.19713 0.0797274i
\(299\) 10.3464 0.598349
\(300\) 0 0
\(301\) 20.3710 + 16.0188i 1.17416 + 0.923307i
\(302\) 1.31752 19.7829i 0.0758149 1.13838i
\(303\) 0 0
\(304\) −18.7119 5.09823i −1.07320 0.292404i
\(305\) −26.1298 −1.49619
\(306\) 0 0
\(307\) 20.4907 1.16947 0.584734 0.811225i \(-0.301199\pi\)
0.584734 + 0.811225i \(0.301199\pi\)
\(308\) −8.87949 9.13107i −0.505956 0.520291i
\(309\) 0 0
\(310\) −1.73847 + 26.1036i −0.0987385 + 1.48259i
\(311\) −7.69410 −0.436292 −0.218146 0.975916i \(-0.570001\pi\)
−0.218146 + 0.975916i \(0.570001\pi\)
\(312\) 0 0
\(313\) 19.8765i 1.12349i 0.827311 + 0.561744i \(0.189869\pi\)
−0.827311 + 0.561744i \(0.810131\pi\)
\(314\) 0.0148664 0.223223i 0.000838959 0.0125972i
\(315\) 0 0
\(316\) −0.936846 + 7.00230i −0.0527017 + 0.393910i
\(317\) −20.4069 −1.14616 −0.573082 0.819498i \(-0.694252\pi\)
−0.573082 + 0.819498i \(0.694252\pi\)
\(318\) 0 0
\(319\) 6.19727i 0.346981i
\(320\) 9.06786 21.5072i 0.506909 1.20229i
\(321\) 0 0
\(322\) −22.3761 20.1405i −1.24697 1.12238i
\(323\) 24.3423i 1.35444i
\(324\) 0 0
\(325\) 4.51648i 0.250529i
\(326\) −0.624920 + 9.38334i −0.0346111 + 0.519695i
\(327\) 0 0
\(328\) 1.29082 6.38414i 0.0712737 0.352505i
\(329\) 1.98003 2.51799i 0.109162 0.138821i
\(330\) 0 0
\(331\) 18.9813i 1.04331i −0.853157 0.521654i \(-0.825315\pi\)
0.853157 0.521654i \(-0.174685\pi\)
\(332\) −20.6988 2.76932i −1.13599 0.151986i
\(333\) 0 0
\(334\) 5.80736 + 0.386764i 0.317765 + 0.0211628i
\(335\) −21.3666 −1.16738
\(336\) 0 0
\(337\) −25.4865 −1.38834 −0.694169 0.719812i \(-0.744228\pi\)
−0.694169 + 0.719812i \(0.744228\pi\)
\(338\) −16.0108 1.06630i −0.870873 0.0579991i
\(339\) 0 0
\(340\) −29.0372 3.88493i −1.57477 0.210690i
\(341\) 15.2616i 0.826461i
\(342\) 0 0
\(343\) −16.8474 7.69186i −0.909675 0.415321i
\(344\) 5.49043 27.1546i 0.296024 1.46408i
\(345\) 0 0
\(346\) −0.923418 + 13.8654i −0.0496433 + 0.745407i
\(347\) 10.5446i 0.566066i −0.959110 0.283033i \(-0.908659\pi\)
0.959110 0.283033i \(-0.0913405\pi\)
\(348\) 0 0
\(349\) 34.5639i 1.85017i −0.379765 0.925083i \(-0.623995\pi\)
0.379765 0.925083i \(-0.376005\pi\)
\(350\) 8.79183 9.76772i 0.469943 0.522106i
\(351\) 0 0
\(352\) −4.44441 + 12.8703i −0.236888 + 0.685987i
\(353\) 6.44359i 0.342958i 0.985188 + 0.171479i \(0.0548545\pi\)
−0.985188 + 0.171479i \(0.945146\pi\)
\(354\) 0 0
\(355\) −24.5715 −1.30412
\(356\) −2.64581 + 19.7757i −0.140228 + 1.04811i
\(357\) 0 0
\(358\) 0.230548 3.46174i 0.0121848 0.182959i
\(359\) 30.0663i 1.58684i −0.608674 0.793420i \(-0.708298\pi\)
0.608674 0.793420i \(-0.291702\pi\)
\(360\) 0 0
\(361\) 4.50792 0.237259
\(362\) 2.02671 30.4316i 0.106522 1.59945i
\(363\) 0 0
\(364\) −4.74378 4.87818i −0.248642 0.255686i
\(365\) −42.9843 −2.24990
\(366\) 0 0
\(367\) 4.55113 0.237567 0.118784 0.992920i \(-0.462101\pi\)
0.118784 + 0.992920i \(0.462101\pi\)
\(368\) −8.46039 + 31.0519i −0.441028 + 1.61869i
\(369\) 0 0
\(370\) 1.84215 27.6604i 0.0957687 1.43799i
\(371\) −9.06786 + 11.5315i −0.470780 + 0.598687i
\(372\) 0 0
\(373\) 1.81383 0.0939164 0.0469582 0.998897i \(-0.485047\pi\)
0.0469582 + 0.998897i \(0.485047\pi\)
\(374\) 17.0524 + 1.13567i 0.881757 + 0.0587240i
\(375\) 0 0
\(376\) −3.35649 0.678654i −0.173098 0.0349989i
\(377\) 3.31083i 0.170517i
\(378\) 0 0
\(379\) 33.5629i 1.72401i 0.506900 + 0.862005i \(0.330791\pi\)
−0.506900 + 0.862005i \(0.669209\pi\)
\(380\) −3.75176 + 28.0419i −0.192461 + 1.43852i
\(381\) 0 0
\(382\) −0.0309808 + 0.465184i −0.00158511 + 0.0238009i
\(383\) 25.6725 1.31180 0.655902 0.754846i \(-0.272288\pi\)
0.655902 + 0.754846i \(0.272288\pi\)
\(384\) 0 0
\(385\) −11.4849 + 14.6053i −0.585326 + 0.744356i
\(386\) −22.5123 1.49930i −1.14585 0.0763122i
\(387\) 0 0
\(388\) 3.13454 23.4286i 0.159132 1.18941i
\(389\) 14.5542 0.737929 0.368964 0.929443i \(-0.379712\pi\)
0.368964 + 0.929443i \(0.379712\pi\)
\(390\) 0 0
\(391\) 40.3955 2.04289
\(392\) 0.763378 + 19.7843i 0.0385564 + 0.999256i
\(393\) 0 0
\(394\) −4.47224 0.297846i −0.225308 0.0150053i
\(395\) 10.3059 0.518546
\(396\) 0 0
\(397\) 6.27138i 0.314752i 0.987539 + 0.157376i \(0.0503034\pi\)
−0.987539 + 0.157376i \(0.949697\pi\)
\(398\) −38.1351 2.53975i −1.91154 0.127306i
\(399\) 0 0
\(400\) −13.5550 3.69318i −0.677748 0.184659i
\(401\) 22.8730 1.14222 0.571111 0.820873i \(-0.306513\pi\)
0.571111 + 0.820873i \(0.306513\pi\)
\(402\) 0 0
\(403\) 8.15335i 0.406147i
\(404\) −0.163048 + 1.21868i −0.00811195 + 0.0606314i
\(405\) 0 0
\(406\) 6.44490 7.16029i 0.319855 0.355359i
\(407\) 16.1717i 0.801603i
\(408\) 0 0
\(409\) 18.4324i 0.911424i −0.890127 0.455712i \(-0.849385\pi\)
0.890127 0.455712i \(-0.150615\pi\)
\(410\) −9.48058 0.631396i −0.468213 0.0311824i
\(411\) 0 0
\(412\) −15.6965 2.10005i −0.773309 0.103462i
\(413\) 20.0027 25.4373i 0.984269 1.25169i
\(414\) 0 0
\(415\) 30.4642i 1.49543i
\(416\) −2.37438 + 6.87581i −0.116414 + 0.337114i
\(417\) 0 0
\(418\) 1.09674 16.4678i 0.0536433 0.805468i
\(419\) 15.1357 0.739428 0.369714 0.929146i \(-0.379456\pi\)
0.369714 + 0.929146i \(0.379456\pi\)
\(420\) 0 0
\(421\) 32.8126 1.59919 0.799594 0.600541i \(-0.205048\pi\)
0.799594 + 0.600541i \(0.205048\pi\)
\(422\) 0.105830 1.58907i 0.00515174 0.0773547i
\(423\) 0 0
\(424\) 15.3716 + 3.10801i 0.746510 + 0.150938i
\(425\) 17.6337i 0.855359i
\(426\) 0 0
\(427\) −18.6262 14.6468i −0.901387 0.708809i
\(428\) −2.03601 + 15.2178i −0.0984141 + 0.735580i
\(429\) 0 0
\(430\) −40.3251 2.68561i −1.94465 0.129512i
\(431\) 4.81399i 0.231882i 0.993256 + 0.115941i \(0.0369883\pi\)
−0.993256 + 0.115941i \(0.963012\pi\)
\(432\) 0 0
\(433\) 28.8325i 1.38560i 0.721129 + 0.692801i \(0.243623\pi\)
−0.721129 + 0.692801i \(0.756377\pi\)
\(434\) −15.8714 + 17.6331i −0.761851 + 0.846417i
\(435\) 0 0
\(436\) −13.3186 1.78191i −0.637845 0.0853381i
\(437\) 39.0108i 1.86614i
\(438\) 0 0
\(439\) −23.0795 −1.10152 −0.550762 0.834663i \(-0.685663\pi\)
−0.550762 + 0.834663i \(0.685663\pi\)
\(440\) 19.4690 + 3.93646i 0.928146 + 0.187663i
\(441\) 0 0
\(442\) 9.11006 + 0.606720i 0.433321 + 0.0288587i
\(443\) 28.7475i 1.36583i −0.730496 0.682916i \(-0.760711\pi\)
0.730496 0.682916i \(-0.239289\pi\)
\(444\) 0 0
\(445\) 29.1056 1.37974
\(446\) 3.93685 + 0.262190i 0.186415 + 0.0124150i
\(447\) 0 0
\(448\) 18.5196 10.2482i 0.874967 0.484182i
\(449\) 35.0643 1.65479 0.827394 0.561622i \(-0.189822\pi\)
0.827394 + 0.561622i \(0.189822\pi\)
\(450\) 0 0
\(451\) 5.54286 0.261003
\(452\) 6.45605 + 0.863763i 0.303667 + 0.0406280i
\(453\) 0 0
\(454\) 7.08393 + 0.471782i 0.332465 + 0.0221418i
\(455\) −6.13571 + 7.80274i −0.287647 + 0.365798i
\(456\) 0 0
\(457\) 17.1646 0.802926 0.401463 0.915875i \(-0.368502\pi\)
0.401463 + 0.915875i \(0.368502\pi\)
\(458\) 0.105980 1.59132i 0.00495211 0.0743573i
\(459\) 0 0
\(460\) 46.5349 + 6.22595i 2.16970 + 0.290287i
\(461\) 34.9394i 1.62729i −0.581363 0.813644i \(-0.697480\pi\)
0.581363 0.813644i \(-0.302520\pi\)
\(462\) 0 0
\(463\) 12.1288i 0.563674i 0.959462 + 0.281837i \(0.0909438\pi\)
−0.959462 + 0.281837i \(0.909056\pi\)
\(464\) −9.93655 2.70731i −0.461293 0.125684i
\(465\) 0 0
\(466\) 5.85679 + 0.390056i 0.271310 + 0.0180690i
\(467\) −21.7143 −1.00482 −0.502409 0.864630i \(-0.667553\pi\)
−0.502409 + 0.864630i \(0.667553\pi\)
\(468\) 0 0
\(469\) −15.2309 11.9769i −0.703298 0.553041i
\(470\) −0.331959 + 4.98445i −0.0153121 + 0.229916i
\(471\) 0 0
\(472\) −33.9081 6.85593i −1.56074 0.315570i
\(473\) 23.5762 1.08404
\(474\) 0 0
\(475\) 17.0292 0.781355
\(476\) −18.5211 19.0459i −0.848915 0.872967i
\(477\) 0 0
\(478\) 1.40004 21.0219i 0.0640363 0.961521i
\(479\) −13.2107 −0.603613 −0.301806 0.953369i \(-0.597590\pi\)
−0.301806 + 0.953369i \(0.597590\pi\)
\(480\) 0 0
\(481\) 8.63959i 0.393931i
\(482\) 2.28327 34.2839i 0.104000 1.56159i
\(483\) 0 0
\(484\) 10.3208 + 1.38083i 0.469126 + 0.0627649i
\(485\) −34.4819 −1.56574
\(486\) 0 0
\(487\) 13.3925i 0.606871i 0.952852 + 0.303436i \(0.0981337\pi\)
−0.952852 + 0.303436i \(0.901866\pi\)
\(488\) −5.02019 + 24.8289i −0.227253 + 1.12395i
\(489\) 0 0
\(490\) 28.4585 4.93103i 1.28562 0.222761i
\(491\) 17.7604i 0.801515i 0.916184 + 0.400758i \(0.131253\pi\)
−0.916184 + 0.400758i \(0.868747\pi\)
\(492\) 0 0
\(493\) 12.9265i 0.582179i
\(494\) 0.585922 8.79778i 0.0263619 0.395831i
\(495\) 0 0
\(496\) 24.4700 + 6.66709i 1.09874 + 0.299361i
\(497\) −17.5155 13.7733i −0.785675 0.617818i
\(498\) 0 0
\(499\) 26.4052i 1.18206i −0.806651 0.591029i \(-0.798722\pi\)
0.806651 0.591029i \(-0.201278\pi\)
\(500\) 1.15120 8.60448i 0.0514834 0.384804i
\(501\) 0 0
\(502\) 31.8586 + 2.12175i 1.42192 + 0.0946982i
\(503\) −4.30590 −0.191991 −0.0959954 0.995382i \(-0.530603\pi\)
−0.0959954 + 0.995382i \(0.530603\pi\)
\(504\) 0 0
\(505\) 1.79363 0.0798157
\(506\) −27.3280 1.82001i −1.21488 0.0809095i
\(507\) 0 0
\(508\) 3.43691 25.6886i 0.152488 1.13975i
\(509\) 5.30102i 0.234964i 0.993075 + 0.117482i \(0.0374822\pi\)
−0.993075 + 0.117482i \(0.962518\pi\)
\(510\) 0 0
\(511\) −30.6408 24.0945i −1.35547 1.06588i
\(512\) −18.6943 12.7485i −0.826178 0.563409i
\(513\) 0 0
\(514\) −0.809911 + 12.1610i −0.0357236 + 0.536400i
\(515\) 23.1018i 1.01799i
\(516\) 0 0
\(517\) 2.91418i 0.128165i
\(518\) 16.8179 18.6847i 0.738937 0.820959i
\(519\) 0 0
\(520\) 10.4011 + 2.10301i 0.456118 + 0.0922233i
\(521\) 22.7952i 0.998674i 0.866408 + 0.499337i \(0.166423\pi\)
−0.866408 + 0.499337i \(0.833577\pi\)
\(522\) 0 0
\(523\) 5.25087 0.229605 0.114802 0.993388i \(-0.463377\pi\)
0.114802 + 0.993388i \(0.463377\pi\)
\(524\) 38.8089 + 5.19228i 1.69537 + 0.226826i
\(525\) 0 0
\(526\) −2.26525 + 34.0133i −0.0987696 + 1.48305i
\(527\) 31.8331i 1.38667i
\(528\) 0 0
\(529\) −41.7376 −1.81468
\(530\) 1.52026 22.8271i 0.0660359 0.991546i
\(531\) 0 0
\(532\) −18.3930 + 17.8863i −0.797439 + 0.775468i
\(533\) 2.96122 0.128265
\(534\) 0 0
\(535\) 22.3974 0.968323
\(536\) −4.10507 + 20.3029i −0.177312 + 0.876950i
\(537\) 0 0
\(538\) −1.05161 + 15.7902i −0.0453381 + 0.680764i
\(539\) −16.3738 + 3.97342i −0.705268 + 0.171147i
\(540\) 0 0
\(541\) 31.0607 1.33540 0.667702 0.744428i \(-0.267278\pi\)
0.667702 + 0.744428i \(0.267278\pi\)
\(542\) 25.9994 + 1.73153i 1.11677 + 0.0743756i
\(543\) 0 0
\(544\) −9.27030 + 26.8452i −0.397461 + 1.15098i
\(545\) 19.6022i 0.839664i
\(546\) 0 0
\(547\) 25.3068i 1.08204i 0.841009 + 0.541020i \(0.181962\pi\)
−0.841009 + 0.541020i \(0.818038\pi\)
\(548\) 36.5282 + 4.88715i 1.56041 + 0.208769i
\(549\) 0 0
\(550\) 0.794482 11.9294i 0.0338768 0.508670i
\(551\) 12.4834 0.531810
\(552\) 0 0
\(553\) 7.34642 + 5.77688i 0.312402 + 0.245658i
\(554\) 2.98518 + 0.198810i 0.126828 + 0.00844662i
\(555\) 0 0
\(556\) −20.4051 2.73002i −0.865368 0.115779i
\(557\) −36.4584 −1.54479 −0.772397 0.635140i \(-0.780942\pi\)
−0.772397 + 0.635140i \(0.780942\pi\)
\(558\) 0 0
\(559\) 12.5954 0.532727
\(560\) −18.4005 24.7950i −0.777565 1.04778i
\(561\) 0 0
\(562\) −12.7432 0.848681i −0.537538 0.0357995i
\(563\) 13.5989 0.573125 0.286563 0.958061i \(-0.407487\pi\)
0.286563 + 0.958061i \(0.407487\pi\)
\(564\) 0 0
\(565\) 9.50194i 0.399750i
\(566\) −35.1881 2.34349i −1.47907 0.0985041i
\(567\) 0 0
\(568\) −4.72081 + 23.3482i −0.198081 + 0.979668i
\(569\) 15.7437 0.660011 0.330006 0.943979i \(-0.392949\pi\)
0.330006 + 0.943979i \(0.392949\pi\)
\(570\) 0 0
\(571\) 12.8845i 0.539199i −0.962973 0.269599i \(-0.913109\pi\)
0.962973 0.269599i \(-0.0868912\pi\)
\(572\) −6.13571 0.820904i −0.256547 0.0343237i
\(573\) 0 0
\(574\) −6.40418 5.76434i −0.267305 0.240599i
\(575\) 28.2596i 1.17851i
\(576\) 0 0
\(577\) 5.59877i 0.233080i 0.993186 + 0.116540i \(0.0371803\pi\)
−0.993186 + 0.116540i \(0.962820\pi\)
\(578\) 11.5799 + 0.771208i 0.481660 + 0.0320780i
\(579\) 0 0
\(580\) −1.99229 + 14.8911i −0.0827254 + 0.618317i
\(581\) −17.0765 + 21.7160i −0.708451 + 0.900933i
\(582\) 0 0
\(583\) 13.3460i 0.552733i
\(584\) −8.25838 + 40.8443i −0.341734 + 1.69015i
\(585\) 0 0
\(586\) −0.465687 + 6.99242i −0.0192374 + 0.288854i
\(587\) 22.6725 0.935795 0.467898 0.883783i \(-0.345012\pi\)
0.467898 + 0.883783i \(0.345012\pi\)
\(588\) 0 0
\(589\) −30.7419 −1.26670
\(590\) −3.35353 + 50.3541i −0.138063 + 2.07305i
\(591\) 0 0
\(592\) −25.9293 7.06469i −1.06569 0.290357i
\(593\) 0.749311i 0.0307705i −0.999882 0.0153852i \(-0.995103\pi\)
0.999882 0.0153852i \(-0.00489747\pi\)
\(594\) 0 0
\(595\) −23.9557 + 30.4642i −0.982086 + 1.24891i
\(596\) 29.0317 + 3.88418i 1.18918 + 0.159102i
\(597\) 0 0
\(598\) −14.5997 0.972324i −0.597027 0.0397613i
\(599\) 17.9701i 0.734237i 0.930174 + 0.367118i \(0.119656\pi\)
−0.930174 + 0.367118i \(0.880344\pi\)
\(600\) 0 0
\(601\) 8.11913i 0.331186i 0.986194 + 0.165593i \(0.0529538\pi\)
−0.986194 + 0.165593i \(0.947046\pi\)
\(602\) −27.2398 24.5183i −1.11021 0.999291i
\(603\) 0 0
\(604\) −3.71828 + 27.7917i −0.151295 + 1.13083i
\(605\) 15.1900i 0.617561i
\(606\) 0 0
\(607\) 15.4587 0.627449 0.313724 0.949514i \(-0.398423\pi\)
0.313724 + 0.949514i \(0.398423\pi\)
\(608\) 25.9250 + 8.95253i 1.05140 + 0.363073i
\(609\) 0 0
\(610\) 36.8714 + 2.45559i 1.49288 + 0.0994241i
\(611\) 1.55687i 0.0629843i
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) −28.9142 1.92565i −1.16688 0.0777131i
\(615\) 0 0
\(616\) 11.6716 + 13.7192i 0.470263 + 0.552762i
\(617\) −9.96087 −0.401009 −0.200505 0.979693i \(-0.564258\pi\)
−0.200505 + 0.979693i \(0.564258\pi\)
\(618\) 0 0
\(619\) 16.1653 0.649739 0.324869 0.945759i \(-0.394680\pi\)
0.324869 + 0.945759i \(0.394680\pi\)
\(620\) 4.90627 36.6711i 0.197041 1.47275i
\(621\) 0 0
\(622\) 10.8570 + 0.723067i 0.435328 + 0.0289923i
\(623\) 20.7475 + 16.3149i 0.831232 + 0.653642i
\(624\) 0 0
\(625\) −30.2253 −1.20901
\(626\) 1.86793 28.0475i 0.0746576 1.12100i
\(627\) 0 0
\(628\) −0.0419556 + 0.313590i −0.00167421 + 0.0125136i
\(629\) 33.7315i 1.34496i
\(630\) 0 0
\(631\) 10.7815i 0.429203i −0.976702 0.214602i \(-0.931155\pi\)
0.976702 0.214602i \(-0.0688453\pi\)
\(632\) 1.98003 9.79282i 0.0787612 0.389537i
\(633\) 0 0
\(634\) 28.7959 + 1.91777i 1.14363 + 0.0761646i
\(635\) −37.8082 −1.50037
\(636\) 0 0
\(637\) −8.74752 + 2.12276i −0.346589 + 0.0841068i
\(638\) 0.582400 8.74490i 0.0230575 0.346214i
\(639\) 0 0
\(640\) −14.8167 + 29.4964i −0.585682 + 1.16595i
\(641\) 8.70174 0.343698 0.171849 0.985123i \(-0.445026\pi\)
0.171849 + 0.985123i \(0.445026\pi\)
\(642\) 0 0
\(643\) −5.75116 −0.226803 −0.113402 0.993549i \(-0.536175\pi\)
−0.113402 + 0.993549i \(0.536175\pi\)
\(644\) 29.6818 + 30.5228i 1.16963 + 1.20277i
\(645\) 0 0
\(646\) 2.28762 34.3492i 0.0900051 1.35145i
\(647\) 9.55700 0.375724 0.187862 0.982195i \(-0.439844\pi\)
0.187862 + 0.982195i \(0.439844\pi\)
\(648\) 0 0
\(649\) 29.4397i 1.15561i
\(650\) 0.424444 6.37315i 0.0166481 0.249975i
\(651\) 0 0
\(652\) 1.76363 13.1820i 0.0690692 0.516247i
\(653\) 21.4789 0.840533 0.420267 0.907401i \(-0.361937\pi\)
0.420267 + 0.907401i \(0.361937\pi\)
\(654\) 0 0
\(655\) 57.1184i 2.23180i
\(656\) −2.42142 + 8.88728i −0.0945407 + 0.346990i
\(657\) 0 0
\(658\) −3.03062 + 3.36702i −0.118146 + 0.131260i
\(659\) 1.35908i 0.0529421i −0.999650 0.0264710i \(-0.991573\pi\)
0.999650 0.0264710i \(-0.00842698\pi\)
\(660\) 0 0
\(661\) 1.78646i 0.0694851i 0.999396 + 0.0347426i \(0.0110611\pi\)
−0.999396 + 0.0347426i \(0.988939\pi\)
\(662\) −1.78381 + 26.7843i −0.0693296 + 1.04100i
\(663\) 0 0
\(664\) 28.9476 + 5.85296i 1.12338 + 0.227139i
\(665\) 29.4200 + 23.1345i 1.14086 + 0.897117i
\(666\) 0 0
\(667\) 20.7159i 0.802122i
\(668\) −8.15835 1.09151i −0.315656 0.0422320i
\(669\) 0 0
\(670\) 30.1502 + 2.00797i 1.16480 + 0.0775746i
\(671\) −21.5570 −0.832199
\(672\) 0 0
\(673\) 17.1646 0.661647 0.330823 0.943693i \(-0.392674\pi\)
0.330823 + 0.943693i \(0.392674\pi\)
\(674\) 35.9637 + 2.39514i 1.38527 + 0.0922573i
\(675\) 0 0
\(676\) 22.4924 + 3.00929i 0.865094 + 0.115742i
\(677\) 4.28166i 0.164557i −0.996609 0.0822787i \(-0.973780\pi\)
0.996609 0.0822787i \(-0.0262198\pi\)
\(678\) 0 0
\(679\) −24.5800 19.3285i −0.943293 0.741762i
\(680\) 40.6090 + 8.21080i 1.55728 + 0.314870i
\(681\) 0 0
\(682\) −1.43424 + 21.5354i −0.0549197 + 0.824634i
\(683\) 22.0539i 0.843870i −0.906626 0.421935i \(-0.861351\pi\)
0.906626 0.421935i \(-0.138649\pi\)
\(684\) 0 0
\(685\) 53.7618i 2.05413i
\(686\) 23.0503 + 12.4372i 0.880065 + 0.474853i
\(687\) 0 0
\(688\) −10.2994 + 37.8015i −0.392660 + 1.44117i
\(689\) 7.12995i 0.271629i
\(690\) 0 0
\(691\) −7.60142 −0.289172 −0.144586 0.989492i \(-0.546185\pi\)
−0.144586 + 0.989492i \(0.546185\pi\)
\(692\) 2.60605 19.4785i 0.0990671 0.740460i
\(693\) 0 0
\(694\) −0.990952 + 14.8794i −0.0376160 + 0.564814i
\(695\) 30.0320i 1.13918i
\(696\) 0 0
\(697\) 11.5615 0.437922
\(698\) −3.24821 + 48.7728i −0.122947 + 1.84608i
\(699\) 0 0
\(700\) −13.3240 + 12.9569i −0.503599 + 0.489724i
\(701\) 5.13174 0.193823 0.0969116 0.995293i \(-0.469104\pi\)
0.0969116 + 0.995293i \(0.469104\pi\)
\(702\) 0 0
\(703\) 32.5753 1.22860
\(704\) 7.48096 17.7434i 0.281949 0.668729i
\(705\) 0 0
\(706\) 0.605548 9.09247i 0.0227901 0.342199i
\(707\) 1.27857 + 1.00541i 0.0480855 + 0.0378122i
\(708\) 0 0
\(709\) −28.2756 −1.06191 −0.530957 0.847399i \(-0.678167\pi\)
−0.530957 + 0.847399i \(0.678167\pi\)
\(710\) 34.6725 + 2.30915i 1.30124 + 0.0866609i
\(711\) 0 0
\(712\) 5.59192 27.6565i 0.209566 1.03647i
\(713\) 51.0155i 1.91055i
\(714\) 0 0
\(715\) 9.03047i 0.337720i
\(716\) −0.650646 + 4.86315i −0.0243158 + 0.181744i
\(717\) 0 0
\(718\) −2.82554 + 42.4262i −0.105448 + 1.58333i
\(719\) −19.6725 −0.733661 −0.366831 0.930288i \(-0.619557\pi\)
−0.366831 + 0.930288i \(0.619557\pi\)
\(720\) 0 0
\(721\) −12.9495 + 16.4678i −0.482266 + 0.613294i
\(722\) −6.36108 0.423640i −0.236735 0.0157663i
\(723\) 0 0
\(724\) −5.71974 + 42.7512i −0.212572 + 1.58884i
\(725\) 9.04301 0.335849
\(726\) 0 0
\(727\) 0.895551 0.0332142 0.0166071 0.999862i \(-0.494714\pi\)
0.0166071 + 0.999862i \(0.494714\pi\)
\(728\) 6.23545 + 7.32935i 0.231101 + 0.271644i
\(729\) 0 0
\(730\) 60.6546 + 4.03953i 2.24493 + 0.149510i
\(731\) 49.1761 1.81884
\(732\) 0 0
\(733\) 6.22595i 0.229961i −0.993368 0.114980i \(-0.963319\pi\)
0.993368 0.114980i \(-0.0366805\pi\)
\(734\) −6.42205 0.427701i −0.237042 0.0157867i
\(735\) 0 0
\(736\) 14.8565 43.0219i 0.547619 1.58581i
\(737\) −17.6274 −0.649314
\(738\) 0 0
\(739\) 2.85866i 0.105158i 0.998617 + 0.0525788i \(0.0167441\pi\)
−0.998617 + 0.0525788i \(0.983256\pi\)
\(740\) −5.19887 + 38.8581i −0.191114 + 1.42845i
\(741\) 0 0
\(742\) 13.8792 15.4198i 0.509523 0.566080i
\(743\) 15.8280i 0.580672i −0.956925 0.290336i \(-0.906233\pi\)
0.956925 0.290336i \(-0.0937671\pi\)
\(744\) 0 0
\(745\) 42.7285i 1.56545i
\(746\) −2.55947 0.170458i −0.0937088 0.00624090i
\(747\) 0 0
\(748\) −23.9557 3.20506i −0.875906 0.117188i
\(749\) 15.9657 + 12.5547i 0.583373 + 0.458737i
\(750\) 0 0
\(751\) 50.6346i 1.84768i 0.382773 + 0.923842i \(0.374969\pi\)
−0.382773 + 0.923842i \(0.625031\pi\)
\(752\) 4.67252 + 1.27307i 0.170389 + 0.0464242i
\(753\) 0 0
\(754\) 0.311142 4.67188i 0.0113311 0.170140i
\(755\) 40.9034 1.48863
\(756\) 0 0
\(757\) −37.1804 −1.35135 −0.675673 0.737201i \(-0.736147\pi\)
−0.675673 + 0.737201i \(0.736147\pi\)
\(758\) 3.15413 47.3602i 0.114563 1.72020i
\(759\) 0 0
\(760\) 7.92935 39.2170i 0.287628 1.42255i
\(761\) 34.3898i 1.24663i 0.781970 + 0.623315i \(0.214215\pi\)
−0.781970 + 0.623315i \(0.785785\pi\)
\(762\) 0 0
\(763\) −10.9878 + 13.9731i −0.397786 + 0.505861i
\(764\) 0.0874331 0.653504i 0.00316322 0.0236430i
\(765\) 0 0
\(766\) −36.2262 2.41262i −1.30890 0.0871716i
\(767\) 15.7279i 0.567901i
\(768\) 0 0
\(769\) 32.6448i 1.17720i −0.808424 0.588601i \(-0.799679\pi\)
0.808424 0.588601i \(-0.200321\pi\)
\(770\) 17.5788 19.5301i 0.633496 0.703814i
\(771\) 0 0
\(772\) 31.6260 + 4.23128i 1.13824 + 0.152287i
\(773\) 39.6845i 1.42735i 0.700475 + 0.713677i \(0.252971\pi\)
−0.700475 + 0.713677i \(0.747029\pi\)
\(774\) 0 0
\(775\) −22.2696 −0.799946
\(776\) −6.62486 + 32.7652i −0.237819 + 1.17620i
\(777\) 0 0
\(778\) −20.5373 1.36776i −0.736298 0.0490366i
\(779\) 11.1652i 0.400034i
\(780\) 0 0
\(781\) −20.2714 −0.725369
\(782\) −57.0016 3.79625i −2.03837 0.135753i
\(783\) 0 0
\(784\) 0.782071 27.9891i 0.0279311 0.999610i
\(785\) 0.461538 0.0164730
\(786\) 0 0
\(787\) −22.0860 −0.787282 −0.393641 0.919264i \(-0.628785\pi\)
−0.393641 + 0.919264i \(0.628785\pi\)
\(788\) 6.28273 + 0.840574i 0.223813 + 0.0299442i
\(789\) 0 0
\(790\) −14.5425 0.968516i −0.517400 0.0344583i
\(791\) 5.32623 6.77333i 0.189379 0.240832i
\(792\) 0 0
\(793\) −11.5166 −0.408967
\(794\) 0.589365 8.84947i 0.0209158 0.314056i
\(795\) 0 0
\(796\) 53.5733 + 7.16763i 1.89885 + 0.254050i
\(797\) 35.9370i 1.27295i −0.771296 0.636477i \(-0.780391\pi\)
0.771296 0.636477i \(-0.219609\pi\)
\(798\) 0 0
\(799\) 6.07849i 0.215042i
\(800\) 18.7802 + 6.48525i 0.663979 + 0.229288i
\(801\) 0 0
\(802\) −32.2758 2.14953i −1.13970 0.0759026i
\(803\) −35.4619 −1.25142
\(804\) 0 0
\(805\) 38.3912 48.8218i 1.35311 1.72074i
\(806\) −0.766226 + 11.5051i −0.0269892 + 0.405249i
\(807\) 0 0
\(808\) 0.344603 1.70434i 0.0121231 0.0599584i
\(809\) 32.2780 1.13483 0.567417 0.823431i \(-0.307943\pi\)
0.567417 + 0.823431i \(0.307943\pi\)
\(810\) 0 0
\(811\) 33.7682 1.18576 0.592881 0.805290i \(-0.297990\pi\)
0.592881 + 0.805290i \(0.297990\pi\)
\(812\) −9.76723 + 9.49812i −0.342762 + 0.333319i
\(813\) 0 0
\(814\) 1.51977 22.8197i 0.0532679 0.799831i
\(815\) −19.4011 −0.679591
\(816\) 0 0
\(817\) 47.4904i 1.66148i
\(818\) −1.73222 + 26.0097i −0.0605656 + 0.909409i
\(819\) 0 0
\(820\) 13.3186 + 1.78191i 0.465106 + 0.0622270i
\(821\) 4.46728 0.155909 0.0779547 0.996957i \(-0.475161\pi\)
0.0779547 + 0.996957i \(0.475161\pi\)
\(822\) 0 0
\(823\) 52.2387i 1.82093i 0.413590 + 0.910463i \(0.364275\pi\)
−0.413590 + 0.910463i \(0.635725\pi\)
\(824\) 21.9517 + 4.43845i 0.764724 + 0.154621i
\(825\) 0 0
\(826\) −30.6161 + 34.0145i −1.06527 + 1.18352i
\(827\) 9.64827i 0.335503i 0.985829 + 0.167752i \(0.0536506\pi\)
−0.985829 + 0.167752i \(0.946349\pi\)
\(828\) 0 0
\(829\) 36.3958i 1.26408i −0.774936 0.632040i \(-0.782218\pi\)
0.774936 0.632040i \(-0.217782\pi\)
\(830\) 2.86293 42.9877i 0.0993739 1.49213i
\(831\) 0 0
\(832\) 3.99663 9.47923i 0.138558 0.328633i
\(833\) −34.1529 + 8.28789i −1.18333 + 0.287158i
\(834\) 0 0
\(835\) 12.0074i 0.415532i
\(836\) −3.09519 + 23.1345i −0.107049 + 0.800123i
\(837\) 0 0
\(838\) −21.3578 1.42241i −0.737794 0.0491362i
\(839\) 31.9439 1.10283 0.551414 0.834232i \(-0.314089\pi\)
0.551414 + 0.834232i \(0.314089\pi\)
\(840\) 0 0
\(841\) −22.3710 −0.771413
\(842\) −46.3014 3.08362i −1.59565 0.106269i
\(843\) 0 0
\(844\) −0.298671 + 2.23237i −0.0102807 + 0.0768414i
\(845\) 33.1041i 1.13882i
\(846\) 0 0
\(847\) 8.51461 10.8280i 0.292566 0.372054i
\(848\) −21.3986 5.83024i −0.734830 0.200211i
\(849\) 0 0
\(850\) 1.65716 24.8827i 0.0568400 0.853468i
\(851\) 54.0579i 1.85308i
\(852\) 0 0
\(853\) 25.8116i 0.883772i 0.897071 + 0.441886i \(0.145690\pi\)
−0.897071 + 0.441886i \(0.854310\pi\)
\(854\) 24.9068 + 22.4184i 0.852293 + 0.767141i
\(855\) 0 0
\(856\) 4.30311 21.2823i 0.147077 0.727415i
\(857\) 11.8918i 0.406217i −0.979156 0.203109i \(-0.934896\pi\)
0.979156 0.203109i \(-0.0651045\pi\)
\(858\) 0 0
\(859\) −30.2839 −1.03327 −0.516637 0.856205i \(-0.672816\pi\)
−0.516637 + 0.856205i \(0.672816\pi\)
\(860\) 56.6499 + 7.57926i 1.93175 + 0.258450i
\(861\) 0 0
\(862\) 0.452404 6.79297i 0.0154089 0.231369i
\(863\) 56.2350i 1.91426i 0.289658 + 0.957130i \(0.406459\pi\)
−0.289658 + 0.957130i \(0.593541\pi\)
\(864\) 0 0
\(865\) −28.6682 −0.974747
\(866\) 2.70959 40.6852i 0.0920755 1.38254i
\(867\) 0 0
\(868\) 24.0530 23.3903i 0.816413 0.793920i
\(869\) 8.50235 0.288422
\(870\) 0 0
\(871\) −9.41727 −0.319092
\(872\) 18.6262 + 3.76607i 0.630764 + 0.127535i
\(873\) 0 0
\(874\) −3.66612 + 55.0477i −0.124008 + 1.86202i
\(875\) −9.02734 7.09867i −0.305180 0.239979i
\(876\) 0 0
\(877\) −47.5932 −1.60711 −0.803554 0.595232i \(-0.797060\pi\)
−0.803554 + 0.595232i \(0.797060\pi\)
\(878\) 32.5672 + 2.16894i 1.09909 + 0.0731981i
\(879\) 0 0
\(880\) −27.1025 7.38432i −0.913624 0.248925i
\(881\) 54.1981i 1.82598i −0.407980 0.912991i \(-0.633767\pi\)
0.407980 0.912991i \(-0.366233\pi\)
\(882\) 0 0
\(883\) 45.0923i 1.51748i −0.651395 0.758739i \(-0.725816\pi\)
0.651395 0.758739i \(-0.274184\pi\)
\(884\) −12.7981 1.71227i −0.430446 0.0575899i
\(885\) 0 0
\(886\) −2.70160 + 40.5652i −0.0907619 + 1.36281i
\(887\) −44.4058 −1.49100 −0.745500 0.666506i \(-0.767789\pi\)
−0.745500 + 0.666506i \(0.767789\pi\)
\(888\) 0 0
\(889\) −26.9511 21.1931i −0.903911 0.710793i
\(890\) −41.0705 2.73525i −1.37669 0.0916858i
\(891\) 0 0
\(892\) −5.53060 0.739945i −0.185178 0.0247752i
\(893\) −5.87013 −0.196436
\(894\) 0 0
\(895\) 7.15752 0.239250
\(896\) −27.0958 + 12.7207i −0.905208 + 0.424969i
\(897\) 0 0
\(898\) −49.4788 3.29524i −1.65113 0.109963i
\(899\) −16.3248 −0.544464
\(900\) 0 0
\(901\) 27.8375i 0.927400i
\(902\) −7.82146 0.520901i −0.260426 0.0173441i
\(903\) 0 0
\(904\) −9.02888 1.82557i −0.300296 0.0607174i
\(905\) 62.9207 2.09156
\(906\) 0 0
\(907\) 47.2418i 1.56864i 0.620357 + 0.784320i \(0.286988\pi\)
−0.620357 + 0.784320i \(0.713012\pi\)
\(908\) −9.95171 1.33145i −0.330259 0.0441858i
\(909\) 0 0
\(910\) 9.39131 10.4337i 0.311319 0.345875i
\(911\) 40.2417i 1.33327i 0.745386 + 0.666634i \(0.232265\pi\)
−0.745386 + 0.666634i \(0.767735\pi\)
\(912\) 0 0
\(913\) 25.1329i 0.831779i
\(914\) −24.2208 1.61307i −0.801151 0.0533558i
\(915\) 0 0
\(916\) −0.299094 + 2.23553i −0.00988233 + 0.0738638i
\(917\) 32.0172 40.7161i 1.05730 1.34456i
\(918\) 0 0
\(919\) 22.6252i 0.746335i −0.927764 0.373168i \(-0.878272\pi\)
0.927764 0.373168i \(-0.121728\pi\)
\(920\) −65.0797 13.1586i −2.14561 0.433825i
\(921\) 0 0
\(922\) −3.28349 + 49.3025i −0.108136 + 1.62369i
\(923\) −10.8298 −0.356468
\(924\) 0 0
\(925\) 23.5977 0.775886
\(926\) 1.13983 17.1148i 0.0374571 0.562428i
\(927\) 0 0
\(928\) 13.7669 + 4.75405i 0.451921 + 0.156059i
\(929\) 16.7562i 0.549752i 0.961480 + 0.274876i \(0.0886368\pi\)
−0.961480 + 0.274876i \(0.911363\pi\)
\(930\) 0 0
\(931\) 8.00380 + 32.9822i 0.262314 + 1.08095i
\(932\) −8.22778 1.10081i −0.269510 0.0360581i
\(933\) 0 0
\(934\) 30.6408 + 2.04064i 1.00260 + 0.0667718i
\(935\) 35.2576i 1.15305i
\(936\) 0 0
\(937\) 8.34871i 0.272741i −0.990658 0.136370i \(-0.956456\pi\)
0.990658 0.136370i \(-0.0435437\pi\)
\(938\) 20.3666 + 18.3318i 0.664993 + 0.598553i
\(939\) 0 0
\(940\) 0.936846 7.00230i 0.0305566 0.228390i
\(941\) 17.7578i 0.578889i −0.957195 0.289445i \(-0.906529\pi\)
0.957195 0.289445i \(-0.0934706\pi\)
\(942\) 0 0
\(943\) −18.5283 −0.603366
\(944\) 47.2029 + 12.8609i 1.53632 + 0.418586i
\(945\) 0 0
\(946\) −33.2681 2.21562i −1.08164 0.0720360i
\(947\) 30.1863i 0.980924i 0.871463 + 0.490462i \(0.163172\pi\)
−0.871463 + 0.490462i \(0.836828\pi\)
\(948\) 0 0
\(949\) −18.9452 −0.614987
\(950\) −24.0297 1.60035i −0.779627 0.0519223i
\(951\) 0 0
\(952\) 24.3451 + 28.6160i 0.789028 + 0.927449i
\(953\) 32.3987 1.04950 0.524748 0.851257i \(-0.324159\pi\)
0.524748 + 0.851257i \(0.324159\pi\)
\(954\) 0 0
\(955\) −0.961820 −0.0311238
\(956\) −3.95115 + 29.5322i −0.127789 + 0.955141i
\(957\) 0 0
\(958\) 18.6415 + 1.24150i 0.602279 + 0.0401111i
\(959\) 30.1357 38.3234i 0.973133 1.23753i
\(960\) 0 0
\(961\) 9.20202 0.296839
\(962\) 0.811921 12.1912i 0.0261774 0.393061i
\(963\) 0 0
\(964\) −6.44379 + 48.1630i −0.207540 + 1.55123i
\(965\) 46.5467i 1.49839i
\(966\) 0 0
\(967\) 8.90900i 0.286494i −0.989687 0.143247i \(-0.954246\pi\)
0.989687 0.143247i \(-0.0457543\pi\)
\(968\) −14.4337 2.91838i −0.463918 0.0938004i
\(969\) 0 0
\(970\) 48.6570 + 3.24050i 1.56228 + 0.104046i
\(971\) 13.5238 0.433998 0.216999 0.976172i \(-0.430373\pi\)
0.216999 + 0.976172i \(0.430373\pi\)
\(972\) 0 0
\(973\) −16.8342 + 21.4079i −0.539678 + 0.686305i
\(974\) 1.25858 18.8980i 0.0403276 0.605530i
\(975\) 0 0
\(976\) 9.41727 34.5639i 0.301440 1.10636i
\(977\) −26.8330 −0.858465 −0.429232 0.903194i \(-0.641216\pi\)
−0.429232 + 0.903194i \(0.641216\pi\)
\(978\) 0 0
\(979\) 24.0120 0.767428
\(980\) −40.6209 + 4.28367i −1.29759 + 0.136837i
\(981\) 0 0
\(982\) 1.66907 25.0615i 0.0532620 0.799744i
\(983\) −20.3679 −0.649634 −0.324817 0.945777i \(-0.605303\pi\)
−0.324817 + 0.945777i \(0.605303\pi\)
\(984\) 0 0
\(985\) 9.24685i 0.294629i
\(986\) 1.21479 18.2404i 0.0386868 0.580893i
\(987\) 0 0
\(988\) −1.65358 + 12.3594i −0.0526073 + 0.393204i
\(989\) −78.8092 −2.50599
\(990\) 0 0
\(991\) 15.9105i 0.505413i −0.967543 0.252706i \(-0.918679\pi\)
0.967543 0.252706i \(-0.0813206\pi\)
\(992\) −33.9028 11.7075i −1.07642 0.371712i
\(993\) 0 0
\(994\) 23.4215 + 21.0814i 0.742884 + 0.668662i
\(995\) 78.8485i 2.49967i
\(996\) 0 0
\(997\) 5.88360i 0.186336i −0.995650 0.0931678i \(-0.970301\pi\)
0.995650 0.0931678i \(-0.0296993\pi\)
\(998\) −2.48147 + 37.2600i −0.0785497 + 1.17944i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 756.2.b.f.55.1 yes 16
3.2 odd 2 756.2.b.e.55.16 yes 16
4.3 odd 2 756.2.b.e.55.2 yes 16
7.6 odd 2 756.2.b.e.55.1 16
12.11 even 2 inner 756.2.b.f.55.15 yes 16
21.20 even 2 inner 756.2.b.f.55.16 yes 16
28.27 even 2 inner 756.2.b.f.55.2 yes 16
84.83 odd 2 756.2.b.e.55.15 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.b.e.55.1 16 7.6 odd 2
756.2.b.e.55.2 yes 16 4.3 odd 2
756.2.b.e.55.15 yes 16 84.83 odd 2
756.2.b.e.55.16 yes 16 3.2 odd 2
756.2.b.f.55.1 yes 16 1.1 even 1 trivial
756.2.b.f.55.2 yes 16 28.27 even 2 inner
756.2.b.f.55.15 yes 16 12.11 even 2 inner
756.2.b.f.55.16 yes 16 21.20 even 2 inner