Properties

Label 91.2.ba.a.59.1
Level $91$
Weight $2$
Character 91.59
Analytic conductor $0.727$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,2,Mod(45,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.ba (of order \(12\), degree \(4\), 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: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 59.1
Character \(\chi\) \(=\) 91.59
Dual form 91.2.ba.a.54.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.72056 - 1.72056i) q^{2} +(-1.70689 + 0.985473i) q^{3} +3.92067i q^{4} +(0.227080 + 0.0608458i) q^{5} +(4.63238 + 1.24124i) q^{6} +(1.27342 + 2.31914i) q^{7} +(3.30464 - 3.30464i) q^{8} +(0.442313 - 0.766108i) q^{9} +O(q^{10})\) \(q+(-1.72056 - 1.72056i) q^{2} +(-1.70689 + 0.985473i) q^{3} +3.92067i q^{4} +(0.227080 + 0.0608458i) q^{5} +(4.63238 + 1.24124i) q^{6} +(1.27342 + 2.31914i) q^{7} +(3.30464 - 3.30464i) q^{8} +(0.442313 - 0.766108i) q^{9} +(-0.286016 - 0.495394i) q^{10} +(2.76307 + 0.740362i) q^{11} +(-3.86372 - 6.69215i) q^{12} +(-2.03197 + 2.97844i) q^{13} +(1.79921 - 6.18122i) q^{14} +(-0.447562 + 0.119924i) q^{15} -3.53033 q^{16} -4.03177 q^{17} +(-2.07916 + 0.557110i) q^{18} +(1.42261 + 5.30924i) q^{19} +(-0.238557 + 0.890305i) q^{20} +(-4.45904 - 2.70358i) q^{21} +(-3.48019 - 6.02787i) q^{22} +6.05019i q^{23} +(-2.38402 + 8.89728i) q^{24} +(-4.28226 - 2.47237i) q^{25} +(8.62072 - 1.62847i) q^{26} -4.16929i q^{27} +(-9.09257 + 4.99268i) q^{28} +(3.54072 - 6.13271i) q^{29} +(0.976395 + 0.563722i) q^{30} +(0.595317 + 2.22176i) q^{31} +(-0.535124 - 0.535124i) q^{32} +(-5.44585 + 1.45921i) q^{33} +(6.93691 + 6.93691i) q^{34} +(0.148059 + 0.604111i) q^{35} +(3.00366 + 1.73416i) q^{36} +(7.34878 - 7.34878i) q^{37} +(6.68720 - 11.5826i) q^{38} +(0.533171 - 7.08632i) q^{39} +(0.951490 - 0.549343i) q^{40} +(-0.0713473 - 0.266272i) q^{41} +(3.02037 + 12.3237i) q^{42} +(3.91398 - 2.25974i) q^{43} +(-2.90272 + 10.8331i) q^{44} +(0.147055 - 0.147055i) q^{45} +(10.4097 - 10.4097i) q^{46} +(-0.842735 + 3.14513i) q^{47} +(6.02588 - 3.47904i) q^{48} +(-3.75679 + 5.90648i) q^{49} +(3.11404 + 11.6218i) q^{50} +(6.88178 - 3.97320i) q^{51} +(-11.6775 - 7.96668i) q^{52} +(-3.96785 + 6.87251i) q^{53} +(-7.17352 + 7.17352i) q^{54} +(0.582389 + 0.336242i) q^{55} +(11.8721 + 3.45570i) q^{56} +(-7.66035 - 7.66035i) q^{57} +(-16.6437 + 4.45968i) q^{58} +(-0.514009 - 0.514009i) q^{59} +(-0.470182 - 1.75474i) q^{60} +(1.97520 + 1.14038i) q^{61} +(2.79839 - 4.84695i) q^{62} +(2.33996 + 0.0502034i) q^{63} +8.90209i q^{64} +(-0.642644 + 0.552707i) q^{65} +(11.8806 + 6.85927i) q^{66} +(0.688941 - 2.57116i) q^{67} -15.8072i q^{68} +(-5.96230 - 10.3270i) q^{69} +(0.784667 - 1.29416i) q^{70} +(-0.362587 + 1.35319i) q^{71} +(-1.07003 - 3.99339i) q^{72} +(13.0894 - 3.50729i) q^{73} -25.2881 q^{74} +9.74580 q^{75} +(-20.8158 + 5.57758i) q^{76} +(1.80156 + 7.35072i) q^{77} +(-13.1098 + 11.2751i) q^{78} +(-1.91392 - 3.31501i) q^{79} +(-0.801666 - 0.214806i) q^{80} +(5.43566 + 9.41483i) q^{81} +(-0.335380 + 0.580895i) q^{82} +(4.19588 - 4.19588i) q^{83} +(10.5999 - 17.4824i) q^{84} +(-0.915533 - 0.245316i) q^{85} +(-10.6223 - 2.84623i) q^{86} +13.9571i q^{87} +(11.5776 - 6.68431i) q^{88} +(2.44076 + 2.44076i) q^{89} -0.506034 q^{90} +(-9.49496 - 0.919594i) q^{91} -23.7208 q^{92} +(-3.20562 - 3.20562i) q^{93} +(6.86137 - 3.96141i) q^{94} +1.29218i q^{95} +(1.44075 + 0.386047i) q^{96} +(2.61723 + 0.701285i) q^{97} +(16.6263 - 3.69869i) q^{98} +(1.78934 - 1.78934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 12 q^{6} - 6 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 12 q^{6} - 6 q^{7} - 4 q^{8} + 6 q^{9} - 6 q^{10} + 2 q^{11} - 8 q^{12} - 20 q^{14} + 10 q^{15} + 4 q^{16} - 12 q^{17} + 2 q^{18} + 14 q^{19} + 36 q^{20} - 6 q^{21} - 8 q^{22} - 18 q^{24} + 24 q^{26} + 2 q^{28} - 8 q^{29} - 30 q^{30} - 4 q^{31} + 10 q^{32} - 12 q^{33} - 12 q^{34} - 20 q^{35} + 54 q^{36} - 10 q^{37} - 20 q^{39} + 48 q^{40} - 18 q^{41} - 10 q^{42} + 48 q^{43} - 6 q^{44} - 6 q^{45} + 24 q^{46} - 6 q^{47} - 12 q^{48} - 50 q^{49} + 10 q^{50} - 12 q^{51} - 26 q^{52} + 12 q^{53} - 30 q^{54} + 6 q^{55} + 54 q^{56} + 12 q^{57} - 46 q^{58} + 42 q^{59} + 10 q^{60} + 30 q^{61} + 36 q^{62} + 54 q^{63} + 28 q^{65} + 66 q^{66} - 10 q^{67} - 42 q^{69} - 88 q^{70} - 42 q^{71} + 46 q^{72} + 40 q^{73} + 12 q^{74} - 40 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} + 30 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} + 104 q^{84} - 54 q^{85} - 18 q^{86} - 6 q^{88} + 72 q^{90} + 26 q^{91} - 156 q^{92} + 20 q^{93} - 18 q^{94} - 66 q^{96} - 62 q^{97} - 56 q^{98} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.72056 1.72056i −1.21662 1.21662i −0.968808 0.247814i \(-0.920288\pi\)
−0.247814 0.968808i \(-0.579712\pi\)
\(3\) −1.70689 + 0.985473i −0.985473 + 0.568963i −0.903918 0.427706i \(-0.859322\pi\)
−0.0815547 + 0.996669i \(0.525989\pi\)
\(4\) 3.92067i 1.96034i
\(5\) 0.227080 + 0.0608458i 0.101553 + 0.0272111i 0.309238 0.950985i \(-0.399926\pi\)
−0.207685 + 0.978196i \(0.566593\pi\)
\(6\) 4.63238 + 1.24124i 1.89116 + 0.506735i
\(7\) 1.27342 + 2.31914i 0.481309 + 0.876551i
\(8\) 3.30464 3.30464i 1.16837 1.16837i
\(9\) 0.442313 0.766108i 0.147438 0.255369i
\(10\) −0.286016 0.495394i −0.0904462 0.156657i
\(11\) 2.76307 + 0.740362i 0.833096 + 0.223227i 0.650064 0.759880i \(-0.274742\pi\)
0.183032 + 0.983107i \(0.441409\pi\)
\(12\) −3.86372 6.69215i −1.11536 1.93186i
\(13\) −2.03197 + 2.97844i −0.563566 + 0.826071i
\(14\) 1.79921 6.18122i 0.480860 1.65200i
\(15\) −0.447562 + 0.119924i −0.115560 + 0.0309642i
\(16\) −3.53033 −0.882582
\(17\) −4.03177 −0.977847 −0.488924 0.872327i \(-0.662610\pi\)
−0.488924 + 0.872327i \(0.662610\pi\)
\(18\) −2.07916 + 0.557110i −0.490064 + 0.131312i
\(19\) 1.42261 + 5.30924i 0.326368 + 1.21802i 0.912929 + 0.408118i \(0.133815\pi\)
−0.586561 + 0.809905i \(0.699518\pi\)
\(20\) −0.238557 + 0.890305i −0.0533429 + 0.199078i
\(21\) −4.45904 2.70358i −0.973042 0.589970i
\(22\) −3.48019 6.02787i −0.741979 1.28515i
\(23\) 6.05019i 1.26155i 0.775965 + 0.630776i \(0.217263\pi\)
−0.775965 + 0.630776i \(0.782737\pi\)
\(24\) −2.38402 + 8.89728i −0.486636 + 1.81615i
\(25\) −4.28226 2.47237i −0.856453 0.494473i
\(26\) 8.62072 1.62847i 1.69066 0.319368i
\(27\) 4.16929i 0.802380i
\(28\) −9.09257 + 4.99268i −1.71833 + 0.943527i
\(29\) 3.54072 6.13271i 0.657495 1.13882i −0.323766 0.946137i \(-0.604949\pi\)
0.981262 0.192679i \(-0.0617175\pi\)
\(30\) 0.976395 + 0.563722i 0.178264 + 0.102921i
\(31\) 0.595317 + 2.22176i 0.106922 + 0.399039i 0.998556 0.0537180i \(-0.0171072\pi\)
−0.891634 + 0.452757i \(0.850441\pi\)
\(32\) −0.535124 0.535124i −0.0945975 0.0945975i
\(33\) −5.44585 + 1.45921i −0.948002 + 0.254016i
\(34\) 6.93691 + 6.93691i 1.18967 + 1.18967i
\(35\) 0.148059 + 0.604111i 0.0250265 + 0.102113i
\(36\) 3.00366 + 1.73416i 0.500610 + 0.289027i
\(37\) 7.34878 7.34878i 1.20813 1.20813i 0.236500 0.971632i \(-0.424000\pi\)
0.971632 0.236500i \(-0.0760002\pi\)
\(38\) 6.68720 11.5826i 1.08481 1.87894i
\(39\) 0.533171 7.08632i 0.0853757 1.13472i
\(40\) 0.951490 0.549343i 0.150444 0.0868587i
\(41\) −0.0713473 0.266272i −0.0111426 0.0415847i 0.960131 0.279551i \(-0.0901857\pi\)
−0.971273 + 0.237967i \(0.923519\pi\)
\(42\) 3.02037 + 12.3237i 0.466053 + 1.90159i
\(43\) 3.91398 2.25974i 0.596877 0.344607i −0.170935 0.985282i \(-0.554679\pi\)
0.767812 + 0.640675i \(0.221345\pi\)
\(44\) −2.90272 + 10.8331i −0.437601 + 1.63315i
\(45\) 0.147055 0.147055i 0.0219216 0.0219216i
\(46\) 10.4097 10.4097i 1.53483 1.53483i
\(47\) −0.842735 + 3.14513i −0.122926 + 0.458764i −0.999757 0.0220331i \(-0.992986\pi\)
0.876832 + 0.480797i \(0.159653\pi\)
\(48\) 6.02588 3.47904i 0.869760 0.502156i
\(49\) −3.75679 + 5.90648i −0.536684 + 0.843784i
\(50\) 3.11404 + 11.6218i 0.440392 + 1.64357i
\(51\) 6.88178 3.97320i 0.963642 0.556359i
\(52\) −11.6775 7.96668i −1.61938 1.10478i
\(53\) −3.96785 + 6.87251i −0.545026 + 0.944012i 0.453580 + 0.891216i \(0.350147\pi\)
−0.998605 + 0.0527963i \(0.983187\pi\)
\(54\) −7.17352 + 7.17352i −0.976193 + 0.976193i
\(55\) 0.582389 + 0.336242i 0.0785293 + 0.0453389i
\(56\) 11.8721 + 3.45570i 1.58648 + 0.461788i
\(57\) −7.66035 7.66035i −1.01464 1.01464i
\(58\) −16.6437 + 4.45968i −2.18543 + 0.585584i
\(59\) −0.514009 0.514009i −0.0669183 0.0669183i 0.672856 0.739774i \(-0.265068\pi\)
−0.739774 + 0.672856i \(0.765068\pi\)
\(60\) −0.470182 1.75474i −0.0607002 0.226536i
\(61\) 1.97520 + 1.14038i 0.252899 + 0.146011i 0.621091 0.783739i \(-0.286690\pi\)
−0.368192 + 0.929750i \(0.620023\pi\)
\(62\) 2.79839 4.84695i 0.355396 0.615563i
\(63\) 2.33996 + 0.0502034i 0.294807 + 0.00632503i
\(64\) 8.90209i 1.11276i
\(65\) −0.642644 + 0.552707i −0.0797102 + 0.0685548i
\(66\) 11.8806 + 6.85927i 1.46240 + 0.844318i
\(67\) 0.688941 2.57116i 0.0841676 0.314118i −0.910988 0.412434i \(-0.864679\pi\)
0.995155 + 0.0983159i \(0.0313456\pi\)
\(68\) 15.8072i 1.91691i
\(69\) −5.96230 10.3270i −0.717776 1.24323i
\(70\) 0.784667 1.29416i 0.0937856 0.154681i
\(71\) −0.362587 + 1.35319i −0.0430312 + 0.160595i −0.984098 0.177626i \(-0.943158\pi\)
0.941067 + 0.338220i \(0.109825\pi\)
\(72\) −1.07003 3.99339i −0.126104 0.470626i
\(73\) 13.0894 3.50729i 1.53200 0.410497i 0.608326 0.793687i \(-0.291841\pi\)
0.923670 + 0.383190i \(0.125174\pi\)
\(74\) −25.2881 −2.93968
\(75\) 9.74580 1.12535
\(76\) −20.8158 + 5.57758i −2.38774 + 0.639792i
\(77\) 1.80156 + 7.35072i 0.205306 + 0.837693i
\(78\) −13.1098 + 11.2751i −1.48439 + 1.27665i
\(79\) −1.91392 3.31501i −0.215333 0.372967i 0.738043 0.674754i \(-0.235750\pi\)
−0.953375 + 0.301787i \(0.902417\pi\)
\(80\) −0.801666 0.214806i −0.0896290 0.0240160i
\(81\) 5.43566 + 9.41483i 0.603962 + 1.04609i
\(82\) −0.335380 + 0.580895i −0.0370365 + 0.0641491i
\(83\) 4.19588 4.19588i 0.460558 0.460558i −0.438280 0.898838i \(-0.644412\pi\)
0.898838 + 0.438280i \(0.144412\pi\)
\(84\) 10.5999 17.4824i 1.15654 1.90749i
\(85\) −0.915533 0.245316i −0.0993035 0.0266083i
\(86\) −10.6223 2.84623i −1.14543 0.306917i
\(87\) 13.9571i 1.49636i
\(88\) 11.5776 6.68431i 1.23417 0.712550i
\(89\) 2.44076 + 2.44076i 0.258720 + 0.258720i 0.824533 0.565813i \(-0.191438\pi\)
−0.565813 + 0.824533i \(0.691438\pi\)
\(90\) −0.506034 −0.0533407
\(91\) −9.49496 0.919594i −0.995343 0.0963996i
\(92\) −23.7208 −2.47307
\(93\) −3.20562 3.20562i −0.332407 0.332407i
\(94\) 6.86137 3.96141i 0.707696 0.408589i
\(95\) 1.29218i 0.132575i
\(96\) 1.44075 + 0.386047i 0.147046 + 0.0394008i
\(97\) 2.61723 + 0.701285i 0.265739 + 0.0712047i 0.389228 0.921141i \(-0.372742\pi\)
−0.123489 + 0.992346i \(0.539408\pi\)
\(98\) 16.6263 3.69869i 1.67951 0.373624i
\(99\) 1.78934 1.78934i 0.179835 0.179835i
\(100\) 9.69334 16.7894i 0.969334 1.67894i
\(101\) −6.89116 11.9358i −0.685697 1.18766i −0.973217 0.229887i \(-0.926164\pi\)
0.287521 0.957774i \(-0.407169\pi\)
\(102\) −18.6767 5.00440i −1.84927 0.495509i
\(103\) −4.01282 6.95040i −0.395395 0.684843i 0.597757 0.801677i \(-0.296059\pi\)
−0.993151 + 0.116834i \(0.962725\pi\)
\(104\) 3.12775 + 16.5576i 0.306701 + 1.62360i
\(105\) −0.848055 0.885243i −0.0827617 0.0863909i
\(106\) 18.6515 4.99766i 1.81160 0.485415i
\(107\) 4.17877 0.403977 0.201988 0.979388i \(-0.435260\pi\)
0.201988 + 0.979388i \(0.435260\pi\)
\(108\) 16.3464 1.57293
\(109\) 13.6069 3.64596i 1.30331 0.349220i 0.460607 0.887604i \(-0.347632\pi\)
0.842699 + 0.538385i \(0.180965\pi\)
\(110\) −0.423510 1.58056i −0.0403801 0.150701i
\(111\) −5.30152 + 19.7856i −0.503198 + 1.87796i
\(112\) −4.49560 8.18731i −0.424795 0.773628i
\(113\) 2.30697 + 3.99579i 0.217022 + 0.375892i 0.953896 0.300137i \(-0.0970325\pi\)
−0.736874 + 0.676030i \(0.763699\pi\)
\(114\) 26.3602i 2.46886i
\(115\) −0.368129 + 1.37388i −0.0343282 + 0.128115i
\(116\) 24.0443 + 13.8820i 2.23246 + 1.28891i
\(117\) 1.38304 + 2.87411i 0.127862 + 0.265712i
\(118\) 1.76877i 0.162828i
\(119\) −5.13415 9.35022i −0.470647 0.857133i
\(120\) −1.08272 + 1.87533i −0.0988388 + 0.171194i
\(121\) −2.43987 1.40866i −0.221807 0.128060i
\(122\) −1.43636 5.36056i −0.130042 0.485322i
\(123\) 0.384185 + 0.384185i 0.0346408 + 0.0346408i
\(124\) −8.71077 + 2.33404i −0.782251 + 0.209603i
\(125\) −1.65315 1.65315i −0.147862 0.147862i
\(126\) −3.93967 4.11243i −0.350974 0.366364i
\(127\) 3.63943 + 2.10123i 0.322947 + 0.186454i 0.652705 0.757612i \(-0.273634\pi\)
−0.329758 + 0.944065i \(0.606967\pi\)
\(128\) 14.2463 14.2463i 1.25921 1.25921i
\(129\) −4.45382 + 7.71425i −0.392137 + 0.679202i
\(130\) 2.05668 + 0.154743i 0.180382 + 0.0135719i
\(131\) −11.9149 + 6.87908i −1.04101 + 0.601028i −0.920119 0.391638i \(-0.871908\pi\)
−0.120891 + 0.992666i \(0.538575\pi\)
\(132\) −5.72109 21.3514i −0.497957 1.85840i
\(133\) −10.5013 + 10.0601i −0.910576 + 0.872324i
\(134\) −5.60922 + 3.23848i −0.484562 + 0.279762i
\(135\) 0.253684 0.946761i 0.0218336 0.0814842i
\(136\) −13.3235 + 13.3235i −1.14248 + 1.14248i
\(137\) −9.75631 + 9.75631i −0.833538 + 0.833538i −0.987999 0.154461i \(-0.950636\pi\)
0.154461 + 0.987999i \(0.450636\pi\)
\(138\) −7.50975 + 28.0268i −0.639272 + 2.38580i
\(139\) 12.9252 7.46236i 1.09630 0.632949i 0.161053 0.986946i \(-0.448511\pi\)
0.935247 + 0.353997i \(0.115178\pi\)
\(140\) −2.36852 + 0.580491i −0.200177 + 0.0490604i
\(141\) −1.66098 6.19888i −0.139880 0.522040i
\(142\) 2.95211 1.70440i 0.247735 0.143030i
\(143\) −7.81959 + 6.72524i −0.653907 + 0.562393i
\(144\) −1.56151 + 2.70461i −0.130126 + 0.225384i
\(145\) 1.17718 1.17718i 0.0977592 0.0977592i
\(146\) −28.5556 16.4866i −2.36328 1.36444i
\(147\) 0.591735 13.7839i 0.0488055 1.13688i
\(148\) 28.8121 + 28.8121i 2.36834 + 2.36834i
\(149\) 10.2136 2.73674i 0.836735 0.224202i 0.185085 0.982723i \(-0.440744\pi\)
0.651650 + 0.758520i \(0.274077\pi\)
\(150\) −16.7683 16.7683i −1.36912 1.36912i
\(151\) −1.16428 4.34514i −0.0947476 0.353603i 0.902233 0.431248i \(-0.141927\pi\)
−0.996981 + 0.0776451i \(0.975260\pi\)
\(152\) 22.2463 + 12.8439i 1.80442 + 1.04178i
\(153\) −1.78330 + 3.08877i −0.144171 + 0.249712i
\(154\) 9.54769 15.7471i 0.769375 1.26893i
\(155\) 0.540738i 0.0434331i
\(156\) 27.7831 + 2.09039i 2.22443 + 0.167365i
\(157\) 11.2646 + 6.50360i 0.899010 + 0.519044i 0.876879 0.480711i \(-0.159622\pi\)
0.0221312 + 0.999755i \(0.492955\pi\)
\(158\) −2.41066 + 8.99670i −0.191782 + 0.715739i
\(159\) 15.6408i 1.24040i
\(160\) −0.0889558 0.154076i −0.00703257 0.0121808i
\(161\) −14.0312 + 7.70446i −1.10581 + 0.607196i
\(162\) 6.84642 25.5512i 0.537906 2.00749i
\(163\) 4.24621 + 15.8471i 0.332589 + 1.24124i 0.906459 + 0.422293i \(0.138775\pi\)
−0.573870 + 0.818946i \(0.694559\pi\)
\(164\) 1.04396 0.279729i 0.0815199 0.0218432i
\(165\) −1.32543 −0.103185
\(166\) −14.4386 −1.12065
\(167\) 9.84852 2.63890i 0.762101 0.204204i 0.143222 0.989691i \(-0.454254\pi\)
0.618879 + 0.785486i \(0.287587\pi\)
\(168\) −23.6699 + 5.80114i −1.82617 + 0.447568i
\(169\) −4.74221 12.1042i −0.364786 0.931091i
\(170\) 1.15315 + 1.99731i 0.0884426 + 0.153187i
\(171\) 4.69669 + 1.25847i 0.359165 + 0.0962380i
\(172\) 8.85970 + 15.3455i 0.675546 + 1.17008i
\(173\) 7.48809 12.9698i 0.569309 0.986072i −0.427325 0.904098i \(-0.640544\pi\)
0.996634 0.0819744i \(-0.0261226\pi\)
\(174\) 24.0141 24.0141i 1.82051 1.82051i
\(175\) 0.280619 13.0795i 0.0212128 0.988719i
\(176\) −9.75453 2.61372i −0.735276 0.197017i
\(177\) 1.38390 + 0.370814i 0.104020 + 0.0278721i
\(178\) 8.39897i 0.629529i
\(179\) 7.95325 4.59181i 0.594454 0.343208i −0.172403 0.985027i \(-0.555153\pi\)
0.766857 + 0.641819i \(0.221820\pi\)
\(180\) 0.576554 + 0.576554i 0.0429738 + 0.0429738i
\(181\) −12.8202 −0.952919 −0.476459 0.879197i \(-0.658080\pi\)
−0.476459 + 0.879197i \(0.658080\pi\)
\(182\) 14.7545 + 17.9189i 1.09367 + 1.32824i
\(183\) −4.49527 −0.332300
\(184\) 19.9937 + 19.9937i 1.47395 + 1.47395i
\(185\) 2.11590 1.22162i 0.155564 0.0898150i
\(186\) 11.0309i 0.808828i
\(187\) −11.1400 2.98497i −0.814641 0.218282i
\(188\) −12.3310 3.30409i −0.899332 0.240975i
\(189\) 9.66915 5.30927i 0.703327 0.386192i
\(190\) 2.22328 2.22328i 0.161294 0.161294i
\(191\) 2.69581 4.66928i 0.195062 0.337857i −0.751859 0.659324i \(-0.770843\pi\)
0.946921 + 0.321467i \(0.104176\pi\)
\(192\) −8.77276 15.1949i −0.633120 1.09660i
\(193\) 3.22754 + 0.864817i 0.232323 + 0.0622509i 0.373102 0.927790i \(-0.378294\pi\)
−0.140779 + 0.990041i \(0.544961\pi\)
\(194\) −3.29650 5.70971i −0.236675 0.409933i
\(195\) 0.552245 1.57672i 0.0395471 0.112911i
\(196\) −23.1574 14.7291i −1.65410 1.05208i
\(197\) 3.67856 0.985668i 0.262087 0.0702259i −0.125383 0.992108i \(-0.540016\pi\)
0.387470 + 0.921882i \(0.373349\pi\)
\(198\) −6.15733 −0.437583
\(199\) −22.2669 −1.57846 −0.789229 0.614099i \(-0.789520\pi\)
−0.789229 + 0.614099i \(0.789520\pi\)
\(200\) −22.3216 + 5.98106i −1.57838 + 0.422925i
\(201\) 1.35787 + 5.06762i 0.0957765 + 0.357443i
\(202\) −8.67969 + 32.3931i −0.610701 + 2.27917i
\(203\) 18.7314 + 0.401879i 1.31469 + 0.0282064i
\(204\) 15.5776 + 26.9812i 1.09065 + 1.88906i
\(205\) 0.0648061i 0.00452626i
\(206\) −5.05430 + 18.8629i −0.352150 + 1.31424i
\(207\) 4.63510 + 2.67608i 0.322162 + 0.186000i
\(208\) 7.17351 10.5149i 0.497394 0.729075i
\(209\) 15.7230i 1.08759i
\(210\) −0.0639836 + 2.98225i −0.00441528 + 0.205795i
\(211\) −7.76031 + 13.4412i −0.534242 + 0.925334i 0.464958 + 0.885333i \(0.346069\pi\)
−0.999200 + 0.0400009i \(0.987264\pi\)
\(212\) −26.9449 15.5566i −1.85058 1.06843i
\(213\) −0.714640 2.66707i −0.0489663 0.182745i
\(214\) −7.18983 7.18983i −0.491487 0.491487i
\(215\) 1.02628 0.274992i 0.0699919 0.0187543i
\(216\) −13.7780 13.7780i −0.937473 0.937473i
\(217\) −4.39446 + 4.20986i −0.298315 + 0.285784i
\(218\) −29.6846 17.1384i −2.01050 1.16076i
\(219\) −18.8858 + 18.8858i −1.27618 + 1.27618i
\(220\) −1.31830 + 2.28336i −0.0888795 + 0.153944i
\(221\) 8.19242 12.0084i 0.551082 0.807771i
\(222\) 43.1639 24.9207i 2.89697 1.67257i
\(223\) 1.32002 + 4.92639i 0.0883952 + 0.329895i 0.995935 0.0900697i \(-0.0287090\pi\)
−0.907540 + 0.419965i \(0.862042\pi\)
\(224\) 0.559586 1.92247i 0.0373889 0.128450i
\(225\) −3.78820 + 2.18712i −0.252547 + 0.145808i
\(226\) 2.90572 10.8443i 0.193286 0.721352i
\(227\) −7.63959 + 7.63959i −0.507057 + 0.507057i −0.913622 0.406565i \(-0.866727\pi\)
0.406565 + 0.913622i \(0.366727\pi\)
\(228\) 30.0337 30.0337i 1.98903 1.98903i
\(229\) 3.42227 12.7721i 0.226150 0.844002i −0.755791 0.654813i \(-0.772747\pi\)
0.981941 0.189189i \(-0.0605860\pi\)
\(230\) 2.99723 1.73045i 0.197631 0.114103i
\(231\) −10.3190 10.7715i −0.678940 0.708712i
\(232\) −8.56558 31.9672i −0.562358 2.09875i
\(233\) −10.5909 + 6.11465i −0.693832 + 0.400584i −0.805046 0.593212i \(-0.797859\pi\)
0.111214 + 0.993796i \(0.464526\pi\)
\(234\) 2.56547 7.32470i 0.167710 0.478830i
\(235\) −0.382736 + 0.662918i −0.0249670 + 0.0432440i
\(236\) 2.01526 2.01526i 0.131182 0.131182i
\(237\) 6.53370 + 3.77223i 0.424409 + 0.245033i
\(238\) −7.25401 + 24.9213i −0.470208 + 1.61541i
\(239\) 4.36940 + 4.36940i 0.282633 + 0.282633i 0.834158 0.551525i \(-0.185954\pi\)
−0.551525 + 0.834158i \(0.685954\pi\)
\(240\) 1.58004 0.423370i 0.101991 0.0273284i
\(241\) −8.64343 8.64343i −0.556772 0.556772i 0.371615 0.928387i \(-0.378804\pi\)
−0.928387 + 0.371615i \(0.878804\pi\)
\(242\) 1.77427 + 6.62165i 0.114054 + 0.425656i
\(243\) −7.72400 4.45945i −0.495495 0.286074i
\(244\) −4.47107 + 7.74412i −0.286231 + 0.495767i
\(245\) −1.21248 + 1.11266i −0.0774622 + 0.0710851i
\(246\) 1.32203i 0.0842896i
\(247\) −18.7040 6.55106i −1.19010 0.416834i
\(248\) 9.30940 + 5.37479i 0.591148 + 0.341299i
\(249\) −3.02698 + 11.2968i −0.191827 + 0.715908i
\(250\) 5.68870i 0.359785i
\(251\) 13.4971 + 23.3777i 0.851929 + 1.47558i 0.879465 + 0.475964i \(0.157901\pi\)
−0.0275356 + 0.999621i \(0.508766\pi\)
\(252\) −0.196831 + 9.17422i −0.0123992 + 0.577922i
\(253\) −4.47933 + 16.7171i −0.281613 + 1.05099i
\(254\) −2.64658 9.87716i −0.166061 0.619748i
\(255\) 1.80447 0.483505i 0.113000 0.0302783i
\(256\) −31.2193 −1.95121
\(257\) 19.2922 1.20341 0.601707 0.798717i \(-0.294487\pi\)
0.601707 + 0.798717i \(0.294487\pi\)
\(258\) 20.9359 5.60977i 1.30341 0.349249i
\(259\) 26.4009 + 7.68471i 1.64047 + 0.477505i
\(260\) −2.16698 2.51960i −0.134391 0.156259i
\(261\) −3.13221 5.42515i −0.193879 0.335808i
\(262\) 32.3362 + 8.66447i 1.99774 + 0.535293i
\(263\) 9.95932 + 17.2501i 0.614118 + 1.06368i 0.990539 + 0.137235i \(0.0438215\pi\)
−0.376420 + 0.926449i \(0.622845\pi\)
\(264\) −13.1744 + 22.8187i −0.810829 + 1.40440i
\(265\) −1.31918 + 1.31918i −0.0810367 + 0.0810367i
\(266\) 35.3772 + 0.759011i 2.16911 + 0.0465379i
\(267\) −6.57142 1.76081i −0.402164 0.107760i
\(268\) 10.0807 + 2.70111i 0.615776 + 0.164997i
\(269\) 26.2749i 1.60201i 0.598657 + 0.801006i \(0.295701\pi\)
−0.598657 + 0.801006i \(0.704299\pi\)
\(270\) −2.06544 + 1.19248i −0.125699 + 0.0725722i
\(271\) 3.79858 + 3.79858i 0.230747 + 0.230747i 0.813005 0.582257i \(-0.197830\pi\)
−0.582257 + 0.813005i \(0.697830\pi\)
\(272\) 14.2335 0.863031
\(273\) 17.1131 7.78738i 1.03573 0.471314i
\(274\) 33.5727 2.02820
\(275\) −10.0017 10.0017i −0.603127 0.603127i
\(276\) 40.4888 23.3762i 2.43714 1.40708i
\(277\) 6.51116i 0.391218i −0.980682 0.195609i \(-0.937332\pi\)
0.980682 0.195609i \(-0.0626683\pi\)
\(278\) −35.0780 9.39913i −2.10384 0.563722i
\(279\) 1.96542 + 0.526633i 0.117667 + 0.0315287i
\(280\) 2.48565 + 1.50709i 0.148546 + 0.0900658i
\(281\) −11.1540 + 11.1540i −0.665390 + 0.665390i −0.956645 0.291255i \(-0.905927\pi\)
0.291255 + 0.956645i \(0.405927\pi\)
\(282\) −7.80773 + 13.5234i −0.464944 + 0.805306i
\(283\) 1.18900 + 2.05940i 0.0706784 + 0.122419i 0.899199 0.437540i \(-0.144150\pi\)
−0.828520 + 0.559959i \(0.810817\pi\)
\(284\) −5.30543 1.42159i −0.314819 0.0843556i
\(285\) −1.27341 2.20561i −0.0754303 0.130649i
\(286\) 25.0253 + 1.88289i 1.47978 + 0.111338i
\(287\) 0.526665 0.504541i 0.0310881 0.0297821i
\(288\) −0.646655 + 0.173271i −0.0381045 + 0.0102101i
\(289\) −0.744846 −0.0438145
\(290\) −4.05081 −0.237872
\(291\) −5.15842 + 1.38219i −0.302392 + 0.0810256i
\(292\) 13.7509 + 51.3192i 0.804712 + 3.00323i
\(293\) 8.69014 32.4321i 0.507684 1.89470i 0.0653221 0.997864i \(-0.479193\pi\)
0.442361 0.896837i \(-0.354141\pi\)
\(294\) −24.7342 + 22.6980i −1.44253 + 1.32377i
\(295\) −0.0854457 0.147996i −0.00497484 0.00861668i
\(296\) 48.5701i 2.82308i
\(297\) 3.08678 11.5200i 0.179113 0.668459i
\(298\) −22.2820 12.8645i −1.29076 0.745220i
\(299\) −18.0201 12.2938i −1.04213 0.710968i
\(300\) 38.2101i 2.20606i
\(301\) 10.2248 + 6.19946i 0.589348 + 0.357331i
\(302\) −5.47288 + 9.47931i −0.314929 + 0.545473i
\(303\) 23.5249 + 13.5821i 1.35147 + 0.780272i
\(304\) −5.02227 18.7434i −0.288047 1.07501i
\(305\) 0.379141 + 0.379141i 0.0217095 + 0.0217095i
\(306\) 8.38271 2.24614i 0.479208 0.128403i
\(307\) −19.1548 19.1548i −1.09322 1.09322i −0.995183 0.0980380i \(-0.968743\pi\)
−0.0980380 0.995183i \(-0.531257\pi\)
\(308\) −28.8198 + 7.06331i −1.64216 + 0.402469i
\(309\) 13.6989 + 7.90904i 0.779301 + 0.449930i
\(310\) 0.930374 0.930374i 0.0528417 0.0528417i
\(311\) 16.5705 28.7009i 0.939627 1.62748i 0.173458 0.984841i \(-0.444506\pi\)
0.766168 0.642640i \(-0.222161\pi\)
\(312\) −21.6558 25.1796i −1.22602 1.42552i
\(313\) −1.14049 + 0.658460i −0.0644641 + 0.0372183i −0.531886 0.846816i \(-0.678516\pi\)
0.467422 + 0.884035i \(0.345183\pi\)
\(314\) −8.19154 30.5712i −0.462275 1.72523i
\(315\) 0.528303 + 0.153777i 0.0297665 + 0.00866436i
\(316\) 12.9971 7.50385i 0.731142 0.422125i
\(317\) 2.24279 8.37022i 0.125968 0.470118i −0.873904 0.486098i \(-0.838420\pi\)
0.999872 + 0.0159793i \(0.00508657\pi\)
\(318\) −26.9110 + 26.9110i −1.50909 + 1.50909i
\(319\) 14.3237 14.3237i 0.801972 0.801972i
\(320\) −0.541655 + 2.02148i −0.0302794 + 0.113004i
\(321\) −7.13269 + 4.11806i −0.398108 + 0.229848i
\(322\) 37.3976 + 10.8856i 2.08409 + 0.606630i
\(323\) −5.73562 21.4056i −0.319139 1.19104i
\(324\) −36.9125 + 21.3114i −2.05069 + 1.18397i
\(325\) 16.0652 7.73070i 0.891138 0.428822i
\(326\) 19.9600 34.5718i 1.10548 1.91475i
\(327\) −19.6325 + 19.6325i −1.08568 + 1.08568i
\(328\) −1.11571 0.644155i −0.0616047 0.0355675i
\(329\) −8.36714 + 2.05067i −0.461296 + 0.113057i
\(330\) 2.28049 + 2.28049i 0.125537 + 0.125537i
\(331\) −22.5870 + 6.05217i −1.24149 + 0.332657i −0.819045 0.573729i \(-0.805496\pi\)
−0.422449 + 0.906387i \(0.638829\pi\)
\(332\) 16.4507 + 16.4507i 0.902848 + 0.902848i
\(333\) −2.37950 8.88041i −0.130396 0.486644i
\(334\) −21.4854 12.4046i −1.17563 0.678749i
\(335\) 0.312889 0.541940i 0.0170950 0.0296094i
\(336\) 15.7419 + 9.54454i 0.858789 + 0.520697i
\(337\) 5.08165i 0.276815i 0.990375 + 0.138407i \(0.0441984\pi\)
−0.990375 + 0.138407i \(0.955802\pi\)
\(338\) −12.6667 + 28.9853i −0.688980 + 1.57659i
\(339\) −7.87549 4.54691i −0.427738 0.246955i
\(340\) 0.961805 3.58951i 0.0521612 0.194668i
\(341\) 6.57961i 0.356306i
\(342\) −5.91567 10.2462i −0.319883 0.554053i
\(343\) −18.4819 1.19104i −0.997930 0.0643101i
\(344\) 5.46668 20.4019i 0.294744 1.10000i
\(345\) −0.725562 2.70783i −0.0390630 0.145785i
\(346\) −35.1990 + 9.43155i −1.89231 + 0.507043i
\(347\) 0.683981 0.0367180 0.0183590 0.999831i \(-0.494156\pi\)
0.0183590 + 0.999831i \(0.494156\pi\)
\(348\) −54.7214 −2.93337
\(349\) 5.07510 1.35987i 0.271664 0.0727921i −0.120415 0.992724i \(-0.538423\pi\)
0.392079 + 0.919932i \(0.371756\pi\)
\(350\) −22.9870 + 22.0213i −1.22870 + 1.17709i
\(351\) 12.4180 + 8.47186i 0.662822 + 0.452194i
\(352\) −1.08240 1.87477i −0.0576920 0.0999256i
\(353\) 20.9733 + 5.61978i 1.11630 + 0.299111i 0.769384 0.638787i \(-0.220563\pi\)
0.346913 + 0.937897i \(0.387230\pi\)
\(354\) −1.74307 3.01909i −0.0926434 0.160463i
\(355\) −0.164672 + 0.285221i −0.00873991 + 0.0151380i
\(356\) −9.56943 + 9.56943i −0.507179 + 0.507179i
\(357\) 17.9778 + 10.9002i 0.951486 + 0.576901i
\(358\) −21.5846 5.78356i −1.14078 0.305671i
\(359\) 13.7143 + 3.67473i 0.723812 + 0.193945i 0.601872 0.798593i \(-0.294422\pi\)
0.121940 + 0.992537i \(0.461088\pi\)
\(360\) 0.971926i 0.0512250i
\(361\) −9.70976 + 5.60593i −0.511040 + 0.295049i
\(362\) 22.0580 + 22.0580i 1.15934 + 1.15934i
\(363\) 5.55279 0.291446
\(364\) 3.60543 37.2266i 0.188976 1.95121i
\(365\) 3.18574 0.166749
\(366\) 7.73439 + 7.73439i 0.404283 + 0.404283i
\(367\) 2.60256 1.50259i 0.135853 0.0784346i −0.430533 0.902575i \(-0.641674\pi\)
0.566386 + 0.824140i \(0.308341\pi\)
\(368\) 21.3592i 1.11342i
\(369\) −0.235551 0.0631157i −0.0122623 0.00328567i
\(370\) −5.74241 1.53867i −0.298534 0.0799918i
\(371\) −20.9910 0.450359i −1.08980 0.0233815i
\(372\) 12.5682 12.5682i 0.651630 0.651630i
\(373\) 13.0925 22.6769i 0.677906 1.17417i −0.297705 0.954658i \(-0.596221\pi\)
0.975610 0.219509i \(-0.0704456\pi\)
\(374\) 14.0313 + 24.3030i 0.725543 + 1.25668i
\(375\) 4.45088 + 1.19261i 0.229843 + 0.0615861i
\(376\) 7.60858 + 13.1784i 0.392383 + 0.679627i
\(377\) 11.0713 + 23.0073i 0.570200 + 1.18494i
\(378\) −25.7713 7.50144i −1.32553 0.385833i
\(379\) −5.54850 + 1.48672i −0.285007 + 0.0763675i −0.398491 0.917172i \(-0.630466\pi\)
0.113483 + 0.993540i \(0.463799\pi\)
\(380\) −5.06622 −0.259892
\(381\) −8.28280 −0.424341
\(382\) −12.6721 + 3.39548i −0.648361 + 0.173728i
\(383\) −4.20381 15.6888i −0.214804 0.801661i −0.986235 0.165348i \(-0.947125\pi\)
0.771431 0.636313i \(-0.219541\pi\)
\(384\) −10.2775 + 38.3563i −0.524474 + 1.95736i
\(385\) −0.0381642 + 1.77882i −0.00194503 + 0.0906569i
\(386\) −4.06521 7.04116i −0.206914 0.358385i
\(387\) 3.99805i 0.203232i
\(388\) −2.74951 + 10.2613i −0.139585 + 0.520939i
\(389\) −8.04726 4.64609i −0.408012 0.235566i 0.281923 0.959437i \(-0.409028\pi\)
−0.689935 + 0.723871i \(0.742361\pi\)
\(390\) −3.66301 + 1.76267i −0.185484 + 0.0892562i
\(391\) 24.3930i 1.23361i
\(392\) 7.10398 + 31.9336i 0.358805 + 1.61289i
\(393\) 13.5583 23.4836i 0.683925 1.18459i
\(394\) −8.02510 4.63330i −0.404299 0.233422i
\(395\) −0.232908 0.869225i −0.0117189 0.0437355i
\(396\) 7.01540 + 7.01540i 0.352537 + 0.352537i
\(397\) 18.2054 4.87812i 0.913703 0.244826i 0.228811 0.973471i \(-0.426516\pi\)
0.684892 + 0.728645i \(0.259849\pi\)
\(398\) 38.3116 + 38.3116i 1.92039 + 1.92039i
\(399\) 8.01052 27.5202i 0.401028 1.37774i
\(400\) 15.1178 + 8.72826i 0.755890 + 0.436413i
\(401\) −26.4901 + 26.4901i −1.32285 + 1.32285i −0.411393 + 0.911458i \(0.634958\pi\)
−0.911458 + 0.411393i \(0.865042\pi\)
\(402\) 6.38287 11.0555i 0.318349 0.551396i
\(403\) −7.82703 2.74142i −0.389892 0.136560i
\(404\) 46.7965 27.0180i 2.32822 1.34420i
\(405\) 0.661474 + 2.46866i 0.0328689 + 0.122668i
\(406\) −31.5371 32.9201i −1.56516 1.63379i
\(407\) 25.7459 14.8644i 1.27618 0.736801i
\(408\) 9.61181 35.8718i 0.475856 1.77592i
\(409\) 14.4159 14.4159i 0.712820 0.712820i −0.254304 0.967124i \(-0.581846\pi\)
0.967124 + 0.254304i \(0.0818464\pi\)
\(410\) −0.111503 + 0.111503i −0.00550674 + 0.00550674i
\(411\) 7.03836 26.2675i 0.347177 1.29568i
\(412\) 27.2502 15.7329i 1.34252 0.775106i
\(413\) 0.537506 1.84661i 0.0264489 0.0908657i
\(414\) −3.37062 12.5793i −0.165657 0.618241i
\(415\) 1.20810 0.697498i 0.0593034 0.0342388i
\(416\) 2.68119 0.506481i 0.131456 0.0248323i
\(417\) −14.7079 + 25.4748i −0.720249 + 1.24751i
\(418\) 27.0525 27.0525i 1.32318 1.32318i
\(419\) −9.48347 5.47529i −0.463298 0.267485i 0.250132 0.968212i \(-0.419526\pi\)
−0.713430 + 0.700727i \(0.752859\pi\)
\(420\) 3.47075 3.32495i 0.169355 0.162241i
\(421\) −7.99908 7.99908i −0.389852 0.389852i 0.484783 0.874634i \(-0.338899\pi\)
−0.874634 + 0.484783i \(0.838899\pi\)
\(422\) 36.4786 9.77441i 1.77575 0.475811i
\(423\) 2.03676 + 2.03676i 0.0990305 + 0.0990305i
\(424\) 9.59886 + 35.8235i 0.466162 + 1.73974i
\(425\) 17.2651 + 9.96801i 0.837480 + 0.483519i
\(426\) −3.35928 + 5.81845i −0.162758 + 0.281905i
\(427\) −0.129436 + 6.03295i −0.00626384 + 0.291955i
\(428\) 16.3836i 0.791930i
\(429\) 6.71962 19.1852i 0.324426 0.926271i
\(430\) −2.23892 1.29264i −0.107970 0.0623368i
\(431\) −4.52862 + 16.9010i −0.218136 + 0.814095i 0.766903 + 0.641763i \(0.221797\pi\)
−0.985039 + 0.172332i \(0.944870\pi\)
\(432\) 14.7190i 0.708166i
\(433\) −3.05668 5.29433i −0.146895 0.254429i 0.783183 0.621791i \(-0.213595\pi\)
−0.930078 + 0.367361i \(0.880261\pi\)
\(434\) 14.8043 + 0.317623i 0.710628 + 0.0152464i
\(435\) −0.849234 + 3.16938i −0.0407176 + 0.151960i
\(436\) 14.2946 + 53.3482i 0.684588 + 2.55492i
\(437\) −32.1219 + 8.60704i −1.53660 + 0.411731i
\(438\) 64.9883 3.10526
\(439\) −15.7233 −0.750434 −0.375217 0.926937i \(-0.622432\pi\)
−0.375217 + 0.926937i \(0.622432\pi\)
\(440\) 3.03574 0.813425i 0.144723 0.0387785i
\(441\) 2.86333 + 5.49062i 0.136349 + 0.261458i
\(442\) −34.7568 + 6.56560i −1.65321 + 0.312294i
\(443\) 5.63934 + 9.76763i 0.267933 + 0.464074i 0.968328 0.249682i \(-0.0803260\pi\)
−0.700395 + 0.713756i \(0.746993\pi\)
\(444\) −77.5727 20.7855i −3.68144 0.986438i
\(445\) 0.405738 + 0.702758i 0.0192338 + 0.0333139i
\(446\) 6.20498 10.7473i 0.293814 0.508901i
\(447\) −14.7366 + 14.7366i −0.697016 + 0.697016i
\(448\) −20.6451 + 11.3361i −0.975392 + 0.535582i
\(449\) 4.69271 + 1.25741i 0.221463 + 0.0593407i 0.367844 0.929888i \(-0.380096\pi\)
−0.146381 + 0.989228i \(0.546763\pi\)
\(450\) 10.2809 + 2.75476i 0.484647 + 0.129861i
\(451\) 0.788550i 0.0371313i
\(452\) −15.6662 + 9.04488i −0.736876 + 0.425435i
\(453\) 6.26931 + 6.26931i 0.294558 + 0.294558i
\(454\) 26.2888 1.23379
\(455\) −2.10016 0.786550i −0.0984571 0.0368740i
\(456\) −50.6293 −2.37094
\(457\) −6.30355 6.30355i −0.294868 0.294868i 0.544132 0.839000i \(-0.316859\pi\)
−0.839000 + 0.544132i \(0.816859\pi\)
\(458\) −27.8634 + 16.0869i −1.30197 + 0.751693i
\(459\) 16.8096i 0.784605i
\(460\) −5.38652 1.44331i −0.251148 0.0672948i
\(461\) −11.4373 3.06461i −0.532688 0.142733i −0.0175587 0.999846i \(-0.505589\pi\)
−0.515129 + 0.857113i \(0.672256\pi\)
\(462\) −0.778541 + 36.2875i −0.0362210 + 1.68825i
\(463\) −19.6291 + 19.6291i −0.912240 + 0.912240i −0.996448 0.0842083i \(-0.973164\pi\)
0.0842083 + 0.996448i \(0.473164\pi\)
\(464\) −12.4999 + 21.6505i −0.580294 + 1.00510i
\(465\) −0.532883 0.922980i −0.0247118 0.0428022i
\(466\) 28.7429 + 7.70164i 1.33149 + 0.356772i
\(467\) −12.2870 21.2818i −0.568576 0.984803i −0.996707 0.0810863i \(-0.974161\pi\)
0.428131 0.903717i \(-0.359172\pi\)
\(468\) −11.2684 + 5.42246i −0.520884 + 0.250653i
\(469\) 6.84019 1.67643i 0.315851 0.0774104i
\(470\) 1.79911 0.482071i 0.0829870 0.0222363i
\(471\) −25.6365 −1.18127
\(472\) −3.39723 −0.156370
\(473\) 12.4876 3.34605i 0.574182 0.153852i
\(474\) −4.75127 17.7320i −0.218233 0.814458i
\(475\) 7.03441 26.2528i 0.322761 1.20456i
\(476\) 36.6591 20.1293i 1.68027 0.922626i
\(477\) 3.51006 + 6.07960i 0.160715 + 0.278366i
\(478\) 15.0357i 0.687715i
\(479\) 5.47147 20.4198i 0.249998 0.933004i −0.720808 0.693135i \(-0.756229\pi\)
0.970805 0.239869i \(-0.0771045\pi\)
\(480\) 0.303675 + 0.175327i 0.0138608 + 0.00800255i
\(481\) 6.95542 + 36.8204i 0.317140 + 1.67886i
\(482\) 29.7431i 1.35476i
\(483\) 16.3572 26.9780i 0.744278 1.22754i
\(484\) 5.52290 9.56595i 0.251041 0.434816i
\(485\) 0.551650 + 0.318495i 0.0250491 + 0.0144621i
\(486\) 5.61686 + 20.9624i 0.254786 + 0.950873i
\(487\) −10.9256 10.9256i −0.495085 0.495085i 0.414819 0.909904i \(-0.363845\pi\)
−0.909904 + 0.414819i \(0.863845\pi\)
\(488\) 10.2959 2.75877i 0.466073 0.124884i
\(489\) −22.8647 22.8647i −1.03398 1.03398i
\(490\) 4.00054 + 0.171741i 0.180726 + 0.00775845i
\(491\) 19.0691 + 11.0096i 0.860578 + 0.496855i 0.864206 0.503139i \(-0.167822\pi\)
−0.00362809 + 0.999993i \(0.501155\pi\)
\(492\) −1.50627 + 1.50627i −0.0679077 + 0.0679077i
\(493\) −14.2754 + 24.7257i −0.642930 + 1.11359i
\(494\) 20.9098 + 43.4528i 0.940777 + 1.95504i
\(495\) 0.515196 0.297449i 0.0231563 0.0133693i
\(496\) −2.10167 7.84352i −0.0943676 0.352185i
\(497\) −3.59997 + 0.882300i −0.161481 + 0.0395766i
\(498\) 24.6450 14.2288i 1.10437 0.637608i
\(499\) −7.46375 + 27.8551i −0.334123 + 1.24697i 0.570693 + 0.821164i \(0.306675\pi\)
−0.904816 + 0.425802i \(0.859992\pi\)
\(500\) 6.48147 6.48147i 0.289860 0.289860i
\(501\) −14.2098 + 14.2098i −0.634845 + 0.634845i
\(502\) 17.0001 63.4453i 0.758753 2.83170i
\(503\) 7.32350 4.22823i 0.326539 0.188527i −0.327764 0.944759i \(-0.606295\pi\)
0.654303 + 0.756232i \(0.272962\pi\)
\(504\) 7.89863 7.56682i 0.351833 0.337053i
\(505\) −0.838597 3.12969i −0.0373171 0.139269i
\(506\) 36.4698 21.0558i 1.62128 0.936046i
\(507\) 20.0228 + 15.9872i 0.889243 + 0.710016i
\(508\) −8.23822 + 14.2690i −0.365512 + 0.633085i
\(509\) −14.3892 + 14.3892i −0.637789 + 0.637789i −0.950010 0.312221i \(-0.898927\pi\)
0.312221 + 0.950010i \(0.398927\pi\)
\(510\) −3.93660 2.27280i −0.174315 0.100641i
\(511\) 24.8022 + 25.8898i 1.09718 + 1.14530i
\(512\) 25.2221 + 25.2221i 1.11467 + 1.11467i
\(513\) 22.1358 5.93126i 0.977317 0.261871i
\(514\) −33.1934 33.1934i −1.46410 1.46410i
\(515\) −0.488326 1.82246i −0.0215182 0.0803071i
\(516\) −30.2450 17.4620i −1.33146 0.768721i
\(517\) −4.65707 + 8.06628i −0.204818 + 0.354754i
\(518\) −32.2024 58.6465i −1.41489 2.57678i
\(519\) 29.5172i 1.29566i
\(520\) −0.297211 + 3.95020i −0.0130336 + 0.173228i
\(521\) −15.2229 8.78895i −0.666928 0.385051i 0.127984 0.991776i \(-0.459149\pi\)
−0.794911 + 0.606725i \(0.792483\pi\)
\(522\) −3.94515 + 14.7235i −0.172674 + 0.644429i
\(523\) 28.3430i 1.23935i 0.784857 + 0.619677i \(0.212736\pi\)
−0.784857 + 0.619677i \(0.787264\pi\)
\(524\) −26.9706 46.7145i −1.17822 2.04073i
\(525\) 12.4105 + 22.6018i 0.541640 + 0.986425i
\(526\) 12.5442 46.8154i 0.546951 2.04125i
\(527\) −2.40018 8.95760i −0.104554 0.390199i
\(528\) 19.2257 5.15150i 0.836689 0.224190i
\(529\) −13.6048 −0.591514
\(530\) 4.53947 0.197182
\(531\) −0.621139 + 0.166434i −0.0269552 + 0.00722261i
\(532\) −39.4425 41.1721i −1.71005 1.78504i
\(533\) 0.938050 + 0.328552i 0.0406315 + 0.0142312i
\(534\) 8.27696 + 14.3361i 0.358179 + 0.620384i
\(535\) 0.948914 + 0.254261i 0.0410251 + 0.0109926i
\(536\) −6.22006 10.7735i −0.268666 0.465343i
\(537\) −9.05021 + 15.6754i −0.390545 + 0.676444i
\(538\) 45.2077 45.2077i 1.94904 1.94904i
\(539\) −14.7532 + 13.5386i −0.635465 + 0.583150i
\(540\) 3.71194 + 0.994611i 0.159736 + 0.0428012i
\(541\) 12.8053 + 3.43118i 0.550545 + 0.147518i 0.523359 0.852112i \(-0.324679\pi\)
0.0271858 + 0.999630i \(0.491345\pi\)
\(542\) 13.0714i 0.561464i
\(543\) 21.8827 12.6340i 0.939075 0.542175i
\(544\) 2.15750 + 2.15750i 0.0925019 + 0.0925019i
\(545\) 3.31170 0.141857
\(546\) −42.8428 16.0454i −1.83350 0.686682i
\(547\) −28.5769 −1.22186 −0.610930 0.791685i \(-0.709204\pi\)
−0.610930 + 0.791685i \(0.709204\pi\)
\(548\) −38.2513 38.2513i −1.63401 1.63401i
\(549\) 1.74731 1.00881i 0.0745736 0.0430551i
\(550\) 34.4172i 1.46756i
\(551\) 37.5971 + 10.0741i 1.60169 + 0.429172i
\(552\) −53.8302 14.4238i −2.29117 0.613916i
\(553\) 5.25072 8.66005i 0.223283 0.368263i
\(554\) −11.2029 + 11.2029i −0.475964 + 0.475964i
\(555\) −2.40774 + 4.17032i −0.102203 + 0.177020i
\(556\) 29.2575 + 50.6754i 1.24079 + 2.14912i
\(557\) −42.3739 11.3540i −1.79544 0.481086i −0.802187 0.597073i \(-0.796330\pi\)
−0.993251 + 0.115987i \(0.962997\pi\)
\(558\) −2.47553 4.28774i −0.104797 0.181514i
\(559\) −1.22259 + 16.2493i −0.0517100 + 0.687272i
\(560\) −0.522697 2.13271i −0.0220880 0.0901235i
\(561\) 21.9564 5.88321i 0.927001 0.248389i
\(562\) 38.3822 1.61906
\(563\) −6.62349 −0.279147 −0.139573 0.990212i \(-0.544573\pi\)
−0.139573 + 0.990212i \(0.544573\pi\)
\(564\) 24.3038 6.51218i 1.02337 0.274212i
\(565\) 0.280739 + 1.04773i 0.0118108 + 0.0440785i
\(566\) 1.49759 5.58907i 0.0629482 0.234926i
\(567\) −14.9124 + 24.5951i −0.626262 + 1.03290i
\(568\) 3.27360 + 5.67003i 0.137357 + 0.237909i
\(569\) 0.438350i 0.0183766i −0.999958 0.00918829i \(-0.997075\pi\)
0.999958 0.00918829i \(-0.00292477\pi\)
\(570\) −1.60391 + 5.98587i −0.0671804 + 0.250721i
\(571\) −1.04982 0.606116i −0.0439338 0.0253652i 0.477872 0.878429i \(-0.341408\pi\)
−0.521806 + 0.853064i \(0.674742\pi\)
\(572\) −26.3675 30.6580i −1.10248 1.28188i
\(573\) 10.6266i 0.443932i
\(574\) −1.77425 0.0380663i −0.0740560 0.00158886i
\(575\) 14.9583 25.9085i 0.623804 1.08046i
\(576\) 6.81996 + 3.93751i 0.284165 + 0.164063i
\(577\) −0.402507 1.50218i −0.0167566 0.0625365i 0.957041 0.289952i \(-0.0936392\pi\)
−0.973798 + 0.227415i \(0.926973\pi\)
\(578\) 1.28155 + 1.28155i 0.0533057 + 0.0533057i
\(579\) −6.36131 + 1.70451i −0.264367 + 0.0708369i
\(580\) 4.61532 + 4.61532i 0.191641 + 0.191641i
\(581\) 15.0740 + 4.38769i 0.625373 + 0.182032i
\(582\) 11.2535 + 6.49723i 0.466474 + 0.269319i
\(583\) −16.0516 + 16.0516i −0.664788 + 0.664788i
\(584\) 31.6653 54.8460i 1.31032 2.26954i
\(585\) 0.139183 + 0.736805i 0.00575452 + 0.0304631i
\(586\) −70.7533 + 40.8495i −2.92279 + 1.68748i
\(587\) 4.96434 + 18.5272i 0.204900 + 0.764698i 0.989480 + 0.144670i \(0.0462121\pi\)
−0.784580 + 0.620028i \(0.787121\pi\)
\(588\) 54.0422 + 2.32000i 2.22866 + 0.0956752i
\(589\) −10.9489 + 6.32137i −0.451143 + 0.260467i
\(590\) −0.107622 + 0.401652i −0.00443074 + 0.0165357i
\(591\) −5.30755 + 5.30755i −0.218323 + 0.218323i
\(592\) −25.9436 + 25.9436i −1.06627 + 1.06627i
\(593\) −1.95948 + 7.31288i −0.0804662 + 0.300304i −0.994417 0.105521i \(-0.966349\pi\)
0.913951 + 0.405825i \(0.133016\pi\)
\(594\) −25.1319 + 14.5099i −1.03118 + 0.595349i
\(595\) −0.596939 2.43564i −0.0244721 0.0998514i
\(596\) 10.7299 + 40.0444i 0.439512 + 1.64028i
\(597\) 38.0071 21.9434i 1.55553 0.898084i
\(598\) 9.85253 + 52.1570i 0.402900 + 2.13286i
\(599\) 18.9239 32.7771i 0.773208 1.33924i −0.162588 0.986694i \(-0.551984\pi\)
0.935796 0.352542i \(-0.114683\pi\)
\(600\) 32.2063 32.2063i 1.31482 1.31482i
\(601\) 20.0340 + 11.5666i 0.817205 + 0.471813i 0.849452 0.527667i \(-0.176933\pi\)
−0.0322469 + 0.999480i \(0.510266\pi\)
\(602\) −6.92586 28.2590i −0.282277 1.15175i
\(603\) −1.66506 1.66506i −0.0678066 0.0678066i
\(604\) 17.0359 4.56475i 0.693181 0.185737i
\(605\) −0.468335 0.468335i −0.0190405 0.0190405i
\(606\) −17.1072 63.8449i −0.694933 2.59352i
\(607\) −8.49783 4.90622i −0.344916 0.199137i 0.317528 0.948249i \(-0.397147\pi\)
−0.662444 + 0.749112i \(0.730481\pi\)
\(608\) 2.07983 3.60238i 0.0843483 0.146096i
\(609\) −32.3685 + 17.7733i −1.31164 + 0.720212i
\(610\) 1.30467i 0.0528246i
\(611\) −7.65517 8.90084i −0.309695 0.360089i
\(612\) −12.1101 6.99175i −0.489520 0.282625i
\(613\) 9.62949 35.9377i 0.388931 1.45151i −0.442944 0.896549i \(-0.646066\pi\)
0.831875 0.554962i \(-0.187267\pi\)
\(614\) 65.9140i 2.66007i
\(615\) 0.0638647 + 0.110617i 0.00257527 + 0.00446050i
\(616\) 30.2450 + 18.3380i 1.21860 + 0.738859i
\(617\) −2.10572 + 7.85866i −0.0847732 + 0.316378i −0.995271 0.0971357i \(-0.969032\pi\)
0.910498 + 0.413514i \(0.135699\pi\)
\(618\) −9.96175 37.1778i −0.400720 1.49551i
\(619\) 44.4523 11.9110i 1.78669 0.478742i 0.794912 0.606725i \(-0.207517\pi\)
0.991776 + 0.127984i \(0.0408505\pi\)
\(620\) −2.12006 −0.0851436
\(621\) 25.2250 1.01224
\(622\) −77.8924 + 20.8712i −3.12320 + 0.836859i
\(623\) −2.55234 + 8.76859i −0.102257 + 0.351306i
\(624\) −1.88227 + 25.0170i −0.0753511 + 1.00148i
\(625\) 12.0870 + 20.9353i 0.483481 + 0.837413i
\(626\) 3.09520 + 0.829356i 0.123709 + 0.0331477i
\(627\) −15.4946 26.8375i −0.618796 1.07179i
\(628\) −25.4985 + 44.1647i −1.01750 + 1.76236i
\(629\) −29.6286 + 29.6286i −1.18137 + 1.18137i
\(630\) −0.644396 1.17356i −0.0256733 0.0467558i
\(631\) 5.64724 + 1.51317i 0.224813 + 0.0602384i 0.369467 0.929244i \(-0.379540\pi\)
−0.144654 + 0.989482i \(0.546207\pi\)
\(632\) −17.2797 4.63008i −0.687350 0.184175i
\(633\) 30.5903i 1.21585i
\(634\) −18.2604 + 10.5426i −0.725211 + 0.418701i
\(635\) 0.698590 + 0.698590i 0.0277227 + 0.0277227i
\(636\) 61.3225 2.43160
\(637\) −9.95845 23.1911i −0.394568 0.918867i
\(638\) −49.2896 −1.95139
\(639\) 0.876316 + 0.876316i 0.0346665 + 0.0346665i
\(640\) 4.10189 2.36823i 0.162141 0.0936124i
\(641\) 44.4981i 1.75757i −0.477219 0.878785i \(-0.658355\pi\)
0.477219 0.878785i \(-0.341645\pi\)
\(642\) 19.3576 + 5.18686i 0.763985 + 0.204709i
\(643\) −27.5723 7.38796i −1.08734 0.291353i −0.329743 0.944071i \(-0.606962\pi\)
−0.757601 + 0.652718i \(0.773629\pi\)
\(644\) −30.2066 55.0118i −1.19031 2.16777i
\(645\) −1.48075 + 1.48075i −0.0583046 + 0.0583046i
\(646\) −26.9612 + 46.6982i −1.06078 + 1.83732i
\(647\) −17.6121 30.5051i −0.692404 1.19928i −0.971048 0.238885i \(-0.923218\pi\)
0.278644 0.960395i \(-0.410115\pi\)
\(648\) 49.0755 + 13.1497i 1.92787 + 0.516571i
\(649\) −1.03969 1.80079i −0.0408114 0.0706874i
\(650\) −40.9424 14.3401i −1.60589 0.562463i
\(651\) 3.35216 11.5164i 0.131381 0.451363i
\(652\) −62.1312 + 16.6480i −2.43325 + 0.651987i
\(653\) −15.3961 −0.602498 −0.301249 0.953546i \(-0.597403\pi\)
−0.301249 + 0.953546i \(0.597403\pi\)
\(654\) 67.5579 2.64172
\(655\) −3.12420 + 0.837126i −0.122073 + 0.0327092i
\(656\) 0.251879 + 0.940027i 0.00983424 + 0.0367019i
\(657\) 3.10264 11.5792i 0.121045 0.451748i
\(658\) 17.9245 + 10.8679i 0.698769 + 0.423675i
\(659\) 5.17792 + 8.96841i 0.201703 + 0.349360i 0.949077 0.315043i \(-0.102019\pi\)
−0.747374 + 0.664403i \(0.768686\pi\)
\(660\) 5.19658i 0.202277i
\(661\) 5.27256 19.6775i 0.205079 0.765365i −0.784347 0.620323i \(-0.787002\pi\)
0.989425 0.145042i \(-0.0463318\pi\)
\(662\) 49.2755 + 28.4492i 1.91515 + 1.10571i
\(663\) −2.14962 + 28.5704i −0.0834844 + 1.10958i
\(664\) 27.7317i 1.07620i
\(665\) −2.99674 + 1.64549i −0.116209 + 0.0638095i
\(666\) −11.1852 + 19.3734i −0.433419 + 0.750704i
\(667\) 37.1041 + 21.4220i 1.43668 + 0.829465i
\(668\) 10.3463 + 38.6128i 0.400309 + 1.49397i
\(669\) −7.10795 7.10795i −0.274809 0.274809i
\(670\) −1.47079 + 0.394096i −0.0568215 + 0.0152253i
\(671\) 4.61332 + 4.61332i 0.178095 + 0.178095i
\(672\) 0.939386 + 3.83289i 0.0362376 + 0.147857i
\(673\) −28.0255 16.1805i −1.08030 0.623714i −0.149326 0.988788i \(-0.547710\pi\)
−0.930979 + 0.365074i \(0.881044\pi\)
\(674\) 8.74329 8.74329i 0.336779 0.336779i
\(675\) −10.3080 + 17.8540i −0.396755 + 0.687200i
\(676\) 47.4566 18.5927i 1.82525 0.715103i
\(677\) 11.3616 6.55960i 0.436660 0.252106i −0.265520 0.964105i \(-0.585544\pi\)
0.702180 + 0.712000i \(0.252210\pi\)
\(678\) 5.72702 + 21.3735i 0.219945 + 0.820845i
\(679\) 1.70647 + 6.96274i 0.0654882 + 0.267206i
\(680\) −3.83619 + 2.21482i −0.147111 + 0.0849346i
\(681\) 5.51132 20.5685i 0.211194 0.788188i
\(682\) 11.3206 11.3206i 0.433489 0.433489i
\(683\) −27.1767 + 27.1767i −1.03989 + 1.03989i −0.0407173 + 0.999171i \(0.512964\pi\)
−0.999171 + 0.0407173i \(0.987036\pi\)
\(684\) −4.93407 + 18.4142i −0.188659 + 0.704084i
\(685\) −2.80909 + 1.62183i −0.107330 + 0.0619669i
\(686\) 29.7500 + 33.8486i 1.13586 + 1.29234i
\(687\) 6.74510 + 25.1731i 0.257342 + 0.960412i
\(688\) −13.8177 + 7.97762i −0.526793 + 0.304144i
\(689\) −12.4068 25.7827i −0.472663 0.982243i
\(690\) −3.41062 + 5.90737i −0.129840 + 0.224890i
\(691\) −11.8354 + 11.8354i −0.450240 + 0.450240i −0.895434 0.445194i \(-0.853135\pi\)
0.445194 + 0.895434i \(0.353135\pi\)
\(692\) 50.8502 + 29.3584i 1.93303 + 1.11604i
\(693\) 6.42830 + 1.87113i 0.244191 + 0.0710784i
\(694\) −1.17683 1.17683i −0.0446720 0.0446720i
\(695\) 3.38910 0.908107i 0.128556 0.0344464i
\(696\) 46.1233 + 46.1233i 1.74830 + 1.74830i
\(697\) 0.287656 + 1.07355i 0.0108957 + 0.0406635i
\(698\) −11.0718 6.39229i −0.419072 0.241952i
\(699\) 12.0516 20.8741i 0.455835 0.789529i
\(700\) 51.2805 + 1.10021i 1.93822 + 0.0415842i
\(701\) 22.9034i 0.865051i −0.901622 0.432525i \(-0.857623\pi\)
0.901622 0.432525i \(-0.142377\pi\)
\(702\) −6.78954 35.9423i −0.256255 1.35655i
\(703\) 49.4708 + 28.5620i 1.86583 + 1.07724i
\(704\) −6.59076 + 24.5971i −0.248399 + 0.927037i
\(705\) 1.50870i 0.0568211i
\(706\) −26.4167 45.7551i −0.994206 1.72201i
\(707\) 18.9055 31.1809i 0.711014 1.17268i
\(708\) −1.45384 + 5.42581i −0.0546387 + 0.203914i
\(709\) −1.72913 6.45322i −0.0649390 0.242356i 0.925825 0.377952i \(-0.123372\pi\)
−0.990764 + 0.135596i \(0.956705\pi\)
\(710\) 0.774070 0.207411i 0.0290503 0.00778401i
\(711\) −3.38621 −0.126993
\(712\) 16.1317 0.604560
\(713\) −13.4420 + 3.60178i −0.503408 + 0.134888i
\(714\) −12.1774 49.6865i −0.455729 1.85947i
\(715\) −2.18487 + 1.05138i −0.0817096 + 0.0393193i
\(716\) 18.0030 + 31.1821i 0.672803 + 1.16533i
\(717\) −11.7640 3.15216i −0.439335 0.117719i
\(718\) −17.2737 29.9189i −0.644648 1.11656i
\(719\) −5.57246 + 9.65178i −0.207818 + 0.359951i −0.951027 0.309108i \(-0.899969\pi\)
0.743209 + 0.669059i \(0.233303\pi\)
\(720\) −0.519152 + 0.519152i −0.0193476 + 0.0193476i
\(721\) 11.0089 18.1571i 0.409993 0.676205i
\(722\) 26.3516 + 7.06089i 0.980705 + 0.262779i
\(723\) 23.2712 + 6.23551i 0.865466 + 0.231901i
\(724\) 50.2638i 1.86804i
\(725\) −30.3246 + 17.5079i −1.12623 + 0.650228i
\(726\) −9.55393 9.55393i −0.354580 0.354580i
\(727\) −2.66009 −0.0986574 −0.0493287 0.998783i \(-0.515708\pi\)
−0.0493287 + 0.998783i \(0.515708\pi\)
\(728\) −34.4163 + 28.3385i −1.27555 + 1.05029i
\(729\) −15.0353 −0.556862
\(730\) −5.48126 5.48126i −0.202871 0.202871i
\(731\) −15.7803 + 9.11075i −0.583655 + 0.336973i
\(732\) 17.6245i 0.651419i
\(733\) −18.2289 4.88442i −0.673299 0.180410i −0.0940588 0.995567i \(-0.529984\pi\)
−0.579241 + 0.815157i \(0.696651\pi\)
\(734\) −7.06318 1.89257i −0.260707 0.0698561i
\(735\) 0.973065 3.09405i 0.0358921 0.114126i
\(736\) 3.23760 3.23760i 0.119340 0.119340i
\(737\) 3.80718 6.59423i 0.140239 0.242902i
\(738\) 0.296686 + 0.513874i 0.0109211 + 0.0189160i
\(739\) 40.8109 + 10.9352i 1.50125 + 0.402259i 0.913519 0.406795i \(-0.133354\pi\)
0.587733 + 0.809055i \(0.300020\pi\)
\(740\) 4.78956 + 8.29575i 0.176068 + 0.304958i
\(741\) 38.3815 7.25031i 1.40998 0.266347i
\(742\) 35.3415 + 36.8913i 1.29743 + 1.35432i
\(743\) 23.2394 6.22698i 0.852571 0.228446i 0.194035 0.980995i \(-0.437842\pi\)
0.658536 + 0.752549i \(0.271176\pi\)
\(744\) −21.1868 −0.776747
\(745\) 2.48583 0.0910738
\(746\) −61.5436 + 16.4906i −2.25327 + 0.603762i
\(747\) −1.35861 5.07039i −0.0497088 0.185516i
\(748\) 11.7031 43.6765i 0.427907 1.59697i
\(749\) 5.32134 + 9.69113i 0.194438 + 0.354106i
\(750\) −5.60606 9.70998i −0.204704 0.354558i
\(751\) 16.7433i 0.610973i −0.952196 0.305486i \(-0.901181\pi\)
0.952196 0.305486i \(-0.0988191\pi\)
\(752\) 2.97513 11.1033i 0.108492 0.404897i
\(753\) −46.0761 26.6020i −1.67911 0.969432i
\(754\) 20.5367 58.6343i 0.747901 2.13534i
\(755\) 1.05754i 0.0384877i
\(756\) 20.8159 + 37.9096i 0.757067 + 1.37876i
\(757\) −13.8538 + 23.9955i −0.503524 + 0.872130i 0.496467 + 0.868055i \(0.334630\pi\)
−0.999992 + 0.00407434i \(0.998703\pi\)
\(758\) 12.1045 + 6.98855i 0.439656 + 0.253836i
\(759\) −8.82851 32.9485i −0.320455 1.19595i
\(760\) 4.27019 + 4.27019i 0.154896 + 0.154896i
\(761\) 21.8743 5.86120i 0.792943 0.212468i 0.160459 0.987042i \(-0.448702\pi\)
0.632483 + 0.774574i \(0.282036\pi\)
\(762\) 14.2511 + 14.2511i 0.516262 + 0.516262i
\(763\) 25.7828 + 26.9134i 0.933401 + 0.974332i
\(764\) 18.3067 + 10.5694i 0.662314 + 0.382387i
\(765\) −0.592891 + 0.592891i −0.0214360 + 0.0214360i
\(766\) −19.7607 + 34.2265i −0.713983 + 1.23665i
\(767\) 2.57540 0.486496i 0.0929921 0.0175663i
\(768\) 53.2879 30.7658i 1.92286 1.11016i
\(769\) 5.25290 + 19.6041i 0.189424 + 0.706941i 0.993640 + 0.112604i \(0.0359191\pi\)
−0.804216 + 0.594338i \(0.797414\pi\)
\(770\) 3.12623 2.99490i 0.112662 0.107929i
\(771\) −32.9296 + 19.0119i −1.18593 + 0.684698i
\(772\) −3.39066 + 12.6541i −0.122033 + 0.455432i
\(773\) 14.4404 14.4404i 0.519384 0.519384i −0.398001 0.917385i \(-0.630296\pi\)
0.917385 + 0.398001i \(0.130296\pi\)
\(774\) −6.87889 + 6.87889i −0.247257 + 0.247257i
\(775\) 2.94369 10.9860i 0.105740 0.394628i
\(776\) 10.9665 6.33150i 0.393674 0.227288i
\(777\) −52.6365 + 12.9004i −1.88832 + 0.462801i
\(778\) 5.85193 + 21.8397i 0.209802 + 0.782991i
\(779\) 1.31220 0.757600i 0.0470145 0.0271438i
\(780\) 6.18179 + 2.16517i 0.221344 + 0.0775256i
\(781\) −2.00371 + 3.47052i −0.0716982 + 0.124185i
\(782\) −41.9696 + 41.9696i −1.50083 + 1.50083i
\(783\) −25.5690 14.7623i −0.913763 0.527561i
\(784\) 13.2627 20.8518i 0.473667 0.744708i
\(785\) 2.16224 + 2.16224i 0.0771736 + 0.0771736i
\(786\) −63.7329 + 17.0772i −2.27328 + 0.609123i
\(787\) 24.9260 + 24.9260i 0.888517 + 0.888517i 0.994381 0.105864i \(-0.0337607\pi\)
−0.105864 + 0.994381i \(0.533761\pi\)
\(788\) 3.86448 + 14.4224i 0.137666 + 0.513778i
\(789\) −33.9989 19.6293i −1.21039 0.698821i
\(790\) −1.09482 + 1.89629i −0.0389521 + 0.0674670i
\(791\) −6.32903 + 10.4385i −0.225035 + 0.371151i
\(792\) 11.8262i 0.420226i
\(793\) −7.41011 + 3.56580i −0.263141 + 0.126625i
\(794\) −39.7167 22.9304i −1.40949 0.813770i
\(795\) 0.951679 3.55171i 0.0337526 0.125966i
\(796\) 87.3012i 3.09431i
\(797\) 10.0235 + 17.3612i 0.355050 + 0.614964i 0.987126 0.159942i \(-0.0511306\pi\)
−0.632077 + 0.774906i \(0.717797\pi\)
\(798\) −61.1329 + 33.5677i −2.16408 + 1.18828i
\(799\) 3.39771 12.6804i 0.120202 0.448602i
\(800\) 0.968520 + 3.61457i 0.0342424 + 0.127794i
\(801\) 2.94947 0.790308i 0.104214 0.0279242i
\(802\) 91.1557 3.21882
\(803\) 38.7635 1.36793
\(804\) −19.8685 + 5.32375i −0.700708 + 0.187754i
\(805\) −3.65499 + 0.895785i −0.128821 + 0.0315723i
\(806\) 8.75012 + 18.1837i 0.308210 + 0.640493i
\(807\) −25.8932 44.8484i −0.911485 1.57874i
\(808\) −62.2165 16.6708i −2.18877 0.586478i
\(809\) −17.2473 29.8731i −0.606381 1.05028i −0.991832 0.127555i \(-0.959287\pi\)
0.385450 0.922729i \(-0.374046\pi\)
\(810\) 3.10937 5.38559i 0.109252 0.189230i
\(811\) 15.8161 15.8161i 0.555379 0.555379i −0.372609 0.927988i \(-0.621537\pi\)
0.927988 + 0.372609i \(0.121537\pi\)
\(812\) −1.57564 + 73.4398i −0.0552940 + 2.57723i
\(813\) −10.2272 2.74036i −0.358682 0.0961085i
\(814\) −69.8726 18.7223i −2.44903 0.656217i
\(815\) 3.85692i 0.135102i
\(816\) −24.2949 + 14.0267i −0.850493 + 0.491032i
\(817\) 17.5656 + 17.5656i 0.614541 + 0.614541i
\(818\) −49.6069 −1.73447
\(819\) −4.90425 + 6.86742i −0.171368 + 0.239967i
\(820\) 0.254084 0.00887298
\(821\) −27.2867 27.2867i −0.952313 0.952313i 0.0466003 0.998914i \(-0.485161\pi\)
−0.998914 + 0.0466003i \(0.985161\pi\)
\(822\) −57.3049 + 33.0850i −1.99874 + 1.15397i
\(823\) 9.45706i 0.329653i −0.986323 0.164826i \(-0.947294\pi\)
0.986323 0.164826i \(-0.0527063\pi\)
\(824\) −36.2295 9.70766i −1.26211 0.338182i
\(825\) 26.9283 + 7.21541i 0.937523 + 0.251208i
\(826\) −4.10202 + 2.25239i −0.142727 + 0.0783708i
\(827\) 12.1614 12.1614i 0.422895 0.422895i −0.463304 0.886199i \(-0.653336\pi\)
0.886199 + 0.463304i \(0.153336\pi\)
\(828\) −10.4920 + 18.1727i −0.364623 + 0.631545i
\(829\) 2.94122 + 5.09434i 0.102153 + 0.176934i 0.912571 0.408918i \(-0.134094\pi\)
−0.810419 + 0.585851i \(0.800760\pi\)
\(830\) −3.27870 0.878526i −0.113805 0.0304941i
\(831\) 6.41657 + 11.1138i 0.222588 + 0.385534i
\(832\) −26.5143 18.0888i −0.919219 0.627115i
\(833\) 15.1465 23.8136i 0.524795 0.825092i
\(834\) 69.1369 18.5252i 2.39401 0.641474i
\(835\) 2.39697 0.0829504
\(836\) −61.6449 −2.13203
\(837\) 9.26314 2.48205i 0.320181 0.0857922i
\(838\) 6.89634 + 25.7375i 0.238230 + 0.889087i
\(839\) −3.66834 + 13.6904i −0.126645 + 0.472646i −0.999893 0.0146305i \(-0.995343\pi\)
0.873248 + 0.487276i \(0.162009\pi\)
\(840\) −5.72792 0.122891i −0.197632 0.00424016i
\(841\) −10.5734 18.3137i −0.364601 0.631507i
\(842\) 27.5259i 0.948604i
\(843\) 8.04666 30.0305i 0.277142 1.03431i
\(844\) −52.6987 30.4256i −1.81397 1.04729i
\(845\) −0.340371 3.03716i −0.0117091 0.104482i
\(846\) 7.00874i 0.240965i
\(847\) 0.159886 7.45223i 0.00549375 0.256061i
\(848\) 14.0078 24.2622i 0.481030 0.833168i
\(849\) −4.05896 2.34344i −0.139303 0.0804268i
\(850\) −12.5551 46.8563i −0.430636 1.60716i
\(851\) 44.4615 + 44.4615i 1.52412 + 1.52412i
\(852\) 10.4567 2.80187i 0.358241 0.0959904i
\(853\) −0.313002 0.313002i −0.0107170 0.0107170i 0.701728 0.712445i \(-0.252412\pi\)
−0.712445 + 0.701728i \(0.752412\pi\)
\(854\) 10.6028 10.1574i 0.362820 0.347578i
\(855\) 0.989951 + 0.571548i 0.0338556 + 0.0195465i
\(856\) 13.8093 13.8093i 0.471993 0.471993i
\(857\) −17.0917 + 29.6037i −0.583842 + 1.01124i 0.411176 + 0.911556i \(0.365118\pi\)
−0.995019 + 0.0996889i \(0.968215\pi\)
\(858\) −44.5709 + 21.4479i −1.52163 + 0.732218i
\(859\) −3.41700 + 1.97280i −0.116586 + 0.0673112i −0.557159 0.830406i \(-0.688109\pi\)
0.440573 + 0.897717i \(0.354775\pi\)
\(860\) 1.07815 + 4.02372i 0.0367647 + 0.137208i
\(861\) −0.401748 + 1.38021i −0.0136915 + 0.0470374i
\(862\) 36.8711 21.2875i 1.25583 0.725056i
\(863\) −9.37524 + 34.9889i −0.319137 + 1.19104i 0.600939 + 0.799295i \(0.294794\pi\)
−0.920076 + 0.391740i \(0.871873\pi\)
\(864\) −2.23109 + 2.23109i −0.0759031 + 0.0759031i
\(865\) 2.48955 2.48955i 0.0846472 0.0846472i
\(866\) −3.85001 + 14.3684i −0.130829 + 0.488260i
\(867\) 1.27137 0.734026i 0.0431780 0.0249288i
\(868\) −16.5055 17.2292i −0.560232 0.584799i
\(869\) −2.83399 10.5766i −0.0961364 0.358786i
\(870\) 6.91428 3.99196i 0.234416 0.135340i
\(871\) 6.25815 + 7.27649i 0.212049 + 0.246555i
\(872\) 32.9173 57.0145i 1.11472 1.93075i
\(873\) 1.69489 1.69489i 0.0573635 0.0573635i
\(874\) 70.0768 + 40.4588i 2.37038 + 1.36854i
\(875\) 1.72872 5.93905i 0.0584415 0.200776i
\(876\) −74.0450 74.0450i −2.50175 2.50175i
\(877\) 38.1725 10.2283i 1.28899 0.345385i 0.451716 0.892162i \(-0.350812\pi\)
0.837278 + 0.546777i \(0.184146\pi\)
\(878\) 27.0530 + 27.0530i 0.912994 + 0.912994i
\(879\) 17.1278 + 63.9218i 0.577706 + 2.15603i
\(880\) −2.05602 1.18705i −0.0693085 0.0400153i
\(881\) 3.07636 5.32841i 0.103645 0.179519i −0.809539 0.587067i \(-0.800283\pi\)
0.913184 + 0.407548i \(0.133616\pi\)
\(882\) 4.52041 14.3735i 0.152210 0.483981i
\(883\) 2.86401i 0.0963817i −0.998838 0.0481909i \(-0.984654\pi\)
0.998838 0.0481909i \(-0.0153456\pi\)
\(884\) 47.0809 + 32.1198i 1.58350 + 1.08031i
\(885\) 0.291693 + 0.168409i 0.00980515 + 0.00566100i
\(886\) 7.10297 26.5087i 0.238629 0.890576i
\(887\) 54.0214i 1.81386i −0.421281 0.906930i \(-0.638419\pi\)
0.421281 0.906930i \(-0.361581\pi\)
\(888\) 47.8645 + 82.9037i 1.60623 + 2.78207i
\(889\) −0.238493 + 11.1161i −0.00799881 + 0.372821i
\(890\) 0.511042 1.90724i 0.0171302 0.0639307i
\(891\) 8.04870 + 30.0382i 0.269642 + 1.00632i
\(892\) −19.3148 + 5.17537i −0.646706 + 0.173284i
\(893\) −17.8971 −0.598905
\(894\) 50.7104 1.69601
\(895\) 2.08541 0.558785i 0.0697077 0.0186781i
\(896\) 51.1809 + 14.8976i 1.70983 + 0.497693i
\(897\) 42.8736 + 3.22579i 1.43151 + 0.107706i
\(898\) −5.91065 10.2375i −0.197241 0.341631i
\(899\) 15.7332 + 4.21571i 0.524733 + 0.140602i
\(900\) −8.57498 14.8523i −0.285833 0.495076i
\(901\) 15.9974 27.7084i 0.532952 0.923100i
\(902\) −1.35675 + 1.35675i −0.0451748 + 0.0451748i
\(903\) −23.5620 0.505518i −0.784094 0.0168226i
\(904\) 20.8283 + 5.58094i 0.692741 + 0.185619i
\(905\) −2.91121 0.780056i −0.0967719 0.0259299i
\(906\) 21.5735i 0.716731i
\(907\) −2.95673 + 1.70707i −0.0981766 + 0.0566823i −0.548284 0.836292i \(-0.684719\pi\)
0.450108 + 0.892974i \(0.351386\pi\)
\(908\) −29.9523 29.9523i −0.994003 0.994003i
\(909\) −12.1922 −0.404390
\(910\) 2.26015 + 4.96677i 0.0749232 + 0.164647i
\(911\) 40.6913 1.34816 0.674082 0.738656i \(-0.264539\pi\)
0.674082 + 0.738656i \(0.264539\pi\)
\(912\) 27.0435 + 27.0435i 0.895501 + 0.895501i
\(913\) 14.7000 8.48703i 0.486498 0.280880i
\(914\) 21.6913i 0.717484i
\(915\) −1.02078 0.273518i −0.0337461 0.00904224i
\(916\) 50.0751 + 13.4176i 1.65453 + 0.443330i
\(917\) −31.1262 18.8723i −1.02788 0.623219i
\(918\) 28.9220 28.9220i 0.954567 0.954567i
\(919\) 11.1365 19.2890i 0.367359 0.636285i −0.621793 0.783182i \(-0.713595\pi\)
0.989152 + 0.146897i \(0.0469287\pi\)
\(920\) 3.32363 + 5.75670i 0.109577 + 0.189793i
\(921\) 51.5716 + 13.8186i 1.69934 + 0.455337i
\(922\) 14.4057 + 24.9514i 0.474427 + 0.821732i
\(923\) −3.29364 3.82959i −0.108412 0.126053i
\(924\) 42.2315 40.4574i 1.38931 1.33095i
\(925\) −49.6383 + 13.3005i −1.63210 + 0.437319i
\(926\) 67.5461 2.21970
\(927\) −7.09968 −0.233184
\(928\) −5.17649 + 1.38704i −0.169927 + 0.0455317i
\(929\) 13.8098 + 51.5390i 0.453086 + 1.69094i 0.693654 + 0.720308i \(0.256000\pi\)
−0.240568 + 0.970632i \(0.577334\pi\)
\(930\) −0.671187 + 2.50490i −0.0220091 + 0.0821390i
\(931\) −36.7034 11.5431i −1.20290 0.378309i
\(932\) −23.9735 41.5234i −0.785280 1.36014i
\(933\) 65.3191i 2.13845i
\(934\) −15.4760 + 57.7572i −0.506390 + 1.88987i
\(935\) −2.34806 1.35565i −0.0767897 0.0443345i
\(936\) 14.0683 + 4.92744i 0.459838 + 0.161058i
\(937\) 41.0483i 1.34099i −0.741914 0.670495i \(-0.766082\pi\)
0.741914 0.670495i \(-0.233918\pi\)
\(938\) −14.6534 8.88458i −0.478450 0.290092i
\(939\) 1.29779 2.24784i 0.0423517 0.0733553i
\(940\) −2.59909 1.50058i −0.0847728 0.0489436i
\(941\) −0.900623 3.36117i −0.0293595 0.109571i 0.949691 0.313188i \(-0.101397\pi\)
−0.979051 + 0.203617i \(0.934730\pi\)
\(942\) 44.1092 + 44.1092i 1.43715 + 1.43715i
\(943\) 1.61100 0.431665i 0.0524612 0.0140569i
\(944\) 1.81462 + 1.81462i 0.0590609 + 0.0590609i
\(945\) 2.51871 0.617300i 0.0819338 0.0200808i
\(946\) −27.2428 15.7287i −0.885741 0.511383i
\(947\) 9.62580 9.62580i 0.312796 0.312796i −0.533196 0.845992i \(-0.679009\pi\)
0.845992 + 0.533196i \(0.179009\pi\)
\(948\) −14.7897 + 25.6165i −0.480347 + 0.831985i
\(949\) −16.1509 + 46.1126i −0.524282 + 1.49688i
\(950\) −57.2727 + 33.0664i −1.85817 + 1.07282i
\(951\) 4.42042 + 16.4972i 0.143342 + 0.534960i
\(952\) −47.8656 13.9326i −1.55133 0.451558i
\(953\) −50.4563 + 29.1309i −1.63444 + 0.943643i −0.651737 + 0.758445i \(0.725960\pi\)
−0.982701 + 0.185199i \(0.940707\pi\)
\(954\) 4.42106 16.4996i 0.143137 0.534195i
\(955\) 0.896270 0.896270i 0.0290026 0.0290026i
\(956\) −17.1310 + 17.1310i −0.554056 + 0.554056i
\(957\) −10.3333 + 38.5645i −0.334029 + 1.24661i
\(958\) −44.5475 + 25.7195i −1.43927 + 0.830960i
\(959\) −35.0501 10.2023i −1.13183 0.329449i
\(960\) −1.06757 3.98423i −0.0344557 0.128591i
\(961\) 22.2650 12.8547i 0.718226 0.414668i
\(962\) 51.3845 75.3190i 1.65670 2.42838i
\(963\) 1.84832 3.20139i 0.0595614 0.103163i
\(964\) 33.8880 33.8880i 1.09146 1.09146i
\(965\) 0.680289 + 0.392765i 0.0218993 + 0.0126435i
\(966\) −74.5610 + 18.2738i −2.39896 + 0.587950i
\(967\) 29.7856 + 29.7856i 0.957840 + 0.957840i 0.999147 0.0413063i \(-0.0131520\pi\)
−0.0413063 + 0.999147i \(0.513152\pi\)
\(968\) −12.7180 + 3.40778i −0.408773 + 0.109530i
\(969\) 30.8847 + 30.8847i 0.992161 + 0.992161i
\(970\) −0.401157 1.49714i −0.0128804 0.0480702i
\(971\) −14.2112 8.20486i −0.456060 0.263306i 0.254326 0.967119i \(-0.418146\pi\)
−0.710386 + 0.703812i \(0.751480\pi\)
\(972\) 17.4841 30.2833i 0.560801 0.971336i
\(973\) 33.7654 + 20.4725i 1.08247 + 0.656319i
\(974\) 37.5963i 1.20466i
\(975\) −19.8031 + 29.0273i −0.634208 + 0.929617i
\(976\) −6.97311 4.02593i −0.223204 0.128867i
\(977\) 5.82122 21.7251i 0.186237 0.695047i −0.808125 0.589011i \(-0.799517\pi\)
0.994362 0.106036i \(-0.0338159\pi\)
\(978\) 78.6802i 2.51592i
\(979\) 4.93694 + 8.55104i 0.157785 + 0.273292i
\(980\) −4.36237 4.75372i −0.139351 0.151852i
\(981\) 3.22531 12.0370i 0.102976 0.384313i
\(982\) −13.8670 51.7523i −0.442513 1.65148i
\(983\) −55.3533 + 14.8319i −1.76550 + 0.473063i −0.987820 0.155603i \(-0.950268\pi\)
−0.777675 + 0.628666i \(0.783601\pi\)
\(984\) 2.53919 0.0809463
\(985\) 0.895301 0.0285267
\(986\) 67.1037 17.9804i 2.13702 0.572612i
\(987\) 12.2609 11.7458i 0.390269 0.373874i
\(988\) 25.6846 73.3321i 0.817134 2.33300i
\(989\) 13.6719 + 23.6804i 0.434740 + 0.752991i
\(990\) −1.39821 0.374648i −0.0444379 0.0119071i
\(991\) −8.78106 15.2092i −0.278940 0.483138i 0.692182 0.721723i \(-0.256650\pi\)
−0.971122 + 0.238585i \(0.923316\pi\)
\(992\) 0.870346 1.50748i 0.0276335 0.0478627i
\(993\) 32.5893 32.5893i 1.03419 1.03419i
\(994\) 7.71202 + 4.67592i 0.244611 + 0.148311i
\(995\) −5.05636 1.35485i −0.160297 0.0429516i
\(996\) −44.2912 11.8678i −1.40342 0.376045i
\(997\) 54.1792i 1.71587i 0.513756 + 0.857936i \(0.328254\pi\)
−0.513756 + 0.857936i \(0.671746\pi\)
\(998\) 60.7683 35.0846i 1.92359 1.11058i
\(999\) −30.6392 30.6392i −0.969380 0.969380i
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 91.2.ba.a.59.1 yes 28
3.2 odd 2 819.2.et.b.514.7 28
7.2 even 3 637.2.x.a.215.1 28
7.3 odd 6 637.2.bd.a.293.7 28
7.4 even 3 637.2.bd.b.293.7 28
7.5 odd 6 91.2.w.a.33.1 28
7.6 odd 2 637.2.bb.a.423.1 28
13.2 odd 12 91.2.w.a.80.1 yes 28
21.5 even 6 819.2.gh.b.397.7 28
39.2 even 12 819.2.gh.b.262.7 28
91.2 odd 12 637.2.bb.a.509.1 28
91.41 even 12 637.2.x.a.80.1 28
91.54 even 12 inner 91.2.ba.a.54.1 yes 28
91.67 odd 12 637.2.bd.a.587.7 28
91.80 even 12 637.2.bd.b.587.7 28
273.236 odd 12 819.2.et.b.145.7 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.w.a.33.1 28 7.5 odd 6
91.2.w.a.80.1 yes 28 13.2 odd 12
91.2.ba.a.54.1 yes 28 91.54 even 12 inner
91.2.ba.a.59.1 yes 28 1.1 even 1 trivial
637.2.x.a.80.1 28 91.41 even 12
637.2.x.a.215.1 28 7.2 even 3
637.2.bb.a.423.1 28 7.6 odd 2
637.2.bb.a.509.1 28 91.2 odd 12
637.2.bd.a.293.7 28 7.3 odd 6
637.2.bd.a.587.7 28 91.67 odd 12
637.2.bd.b.293.7 28 7.4 even 3
637.2.bd.b.587.7 28 91.80 even 12
819.2.et.b.145.7 28 273.236 odd 12
819.2.et.b.514.7 28 3.2 odd 2
819.2.gh.b.262.7 28 39.2 even 12
819.2.gh.b.397.7 28 21.5 even 6