Properties

Label 349.2.e.a.227.15
Level $349$
Weight $2$
Character 349.227
Analytic conductor $2.787$
Analytic rank $0$
Dimension $58$
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] = [349,2,Mod(123,349)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(349, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("349.123");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 227.15
Character \(\chi\) \(=\) 349.227
Dual form 349.2.e.a.123.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0377450 - 0.0217921i) q^{2} +(1.71622 + 2.97259i) q^{3} +(-0.999050 - 1.73041i) q^{4} +(1.73771 + 3.00980i) q^{5} -0.149601i q^{6} +(-2.79927 - 1.61616i) q^{7} +0.174254i q^{8} +(-4.39085 + 7.60517i) q^{9} +O(q^{10})\) \(q+(-0.0377450 - 0.0217921i) q^{2} +(1.71622 + 2.97259i) q^{3} +(-0.999050 - 1.73041i) q^{4} +(1.73771 + 3.00980i) q^{5} -0.149601i q^{6} +(-2.79927 - 1.61616i) q^{7} +0.174254i q^{8} +(-4.39085 + 7.60517i) q^{9} -0.151473i q^{10} -0.153470i q^{11} +(3.42919 - 5.93953i) q^{12} +(2.06169 + 1.19032i) q^{13} +(0.0704389 + 0.122004i) q^{14} +(-5.96459 + 10.3310i) q^{15} +(-1.99430 + 3.45423i) q^{16} +5.10067 q^{17} +(0.331465 - 0.191372i) q^{18} +(-2.56067 - 4.43522i) q^{19} +(3.47212 - 6.01388i) q^{20} -11.0947i q^{21} +(-0.00334444 + 0.00579273i) q^{22} +(2.19639 - 3.80426i) q^{23} +(-0.517985 + 0.299059i) q^{24} +(-3.53927 + 6.13019i) q^{25} +(-0.0518790 - 0.0898571i) q^{26} -19.8454 q^{27} +6.45849i q^{28} +(2.29456 + 3.97429i) q^{29} +(0.450268 - 0.259962i) q^{30} +5.19023 q^{31} +(0.452367 - 0.261174i) q^{32} +(0.456203 - 0.263389i) q^{33} +(-0.192525 - 0.111154i) q^{34} -11.2336i q^{35} +17.5467 q^{36} -1.35934 q^{37} +0.223210i q^{38} +8.17140i q^{39} +(-0.524470 + 0.302803i) q^{40} +7.68887 q^{41} +(-0.241778 + 0.418772i) q^{42} +(1.29737 - 0.749037i) q^{43} +(-0.265565 + 0.153324i) q^{44} -30.5201 q^{45} +(-0.165806 + 0.0957280i) q^{46} +2.44212i q^{47} -13.6907 q^{48} +(1.72393 + 2.98593i) q^{49} +(0.267179 - 0.154256i) q^{50} +(8.75388 + 15.1622i) q^{51} -4.75675i q^{52} -6.29968i q^{53} +(0.749063 + 0.432472i) q^{54} +(0.461914 - 0.266686i) q^{55} +(0.281622 - 0.487783i) q^{56} +(8.78937 - 15.2236i) q^{57} -0.200013i q^{58} +(-7.84880 + 4.53151i) q^{59} +23.8357 q^{60} -4.70242i q^{61} +(-0.195905 - 0.113106i) q^{62} +(24.5823 - 14.1926i) q^{63} +7.95445 q^{64} +8.27370i q^{65} -0.0229592 q^{66} +5.98833 q^{67} +(-5.09582 - 8.82622i) q^{68} +15.0780 q^{69} +(-0.244805 + 0.424014i) q^{70} +(8.67606 + 5.00912i) q^{71} +(-1.32523 - 0.765123i) q^{72} +(2.31215 + 4.00477i) q^{73} +(0.0513082 + 0.0296228i) q^{74} -24.2967 q^{75} +(-5.11648 + 8.86201i) q^{76} +(-0.248032 + 0.429604i) q^{77} +(0.178072 - 0.308430i) q^{78} -9.12273i q^{79} -13.8621 q^{80} +(-20.8865 - 36.1765i) q^{81} +(-0.290217 - 0.167557i) q^{82} +(2.69012 - 4.65943i) q^{83} +(-19.1984 + 11.0842i) q^{84} +(8.86347 + 15.3520i) q^{85} -0.0652924 q^{86} +(-7.87594 + 13.6415i) q^{87} +0.0267428 q^{88} +(-0.728326 + 0.420499i) q^{89} +(1.15198 + 0.665096i) q^{90} +(-3.84748 - 6.66403i) q^{91} -8.77722 q^{92} +(8.90759 + 15.4284i) q^{93} +(0.0532188 - 0.0921777i) q^{94} +(8.89941 - 15.4142i) q^{95} +(1.55273 + 0.896467i) q^{96} +(-13.5267 - 7.80965i) q^{97} -0.150272i q^{98} +(1.16717 + 0.673863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0377450 0.0217921i −0.0266898 0.0154093i 0.486596 0.873627i \(-0.338238\pi\)
−0.513286 + 0.858218i \(0.671572\pi\)
\(3\) 1.71622 + 2.97259i 0.990862 + 1.71622i 0.612240 + 0.790672i \(0.290269\pi\)
0.378622 + 0.925551i \(0.376398\pi\)
\(4\) −0.999050 1.73041i −0.499525 0.865203i
\(5\) 1.73771 + 3.00980i 0.777127 + 1.34602i 0.933591 + 0.358340i \(0.116657\pi\)
−0.156464 + 0.987684i \(0.550010\pi\)
\(6\) 0.149601i 0.0610741i
\(7\) −2.79927 1.61616i −1.05802 0.610850i −0.133138 0.991097i \(-0.542505\pi\)
−0.924885 + 0.380248i \(0.875839\pi\)
\(8\) 0.174254i 0.0616081i
\(9\) −4.39085 + 7.60517i −1.46362 + 2.53506i
\(10\) 0.151473i 0.0479001i
\(11\) 0.153470i 0.0462730i −0.999732 0.0231365i \(-0.992635\pi\)
0.999732 0.0231365i \(-0.00736523\pi\)
\(12\) 3.42919 5.93953i 0.989921 1.71459i
\(13\) 2.06169 + 1.19032i 0.571810 + 0.330135i 0.757872 0.652403i \(-0.226239\pi\)
−0.186062 + 0.982538i \(0.559573\pi\)
\(14\) 0.0704389 + 0.122004i 0.0188256 + 0.0326069i
\(15\) −5.96459 + 10.3310i −1.54005 + 2.66745i
\(16\) −1.99430 + 3.45423i −0.498576 + 0.863559i
\(17\) 5.10067 1.23709 0.618547 0.785748i \(-0.287722\pi\)
0.618547 + 0.785748i \(0.287722\pi\)
\(18\) 0.331465 0.191372i 0.0781271 0.0451067i
\(19\) −2.56067 4.43522i −0.587459 1.01751i −0.994564 0.104127i \(-0.966795\pi\)
0.407105 0.913381i \(-0.366538\pi\)
\(20\) 3.47212 6.01388i 0.776389 1.34475i
\(21\) 11.0947i 2.42107i
\(22\) −0.00334444 + 0.00579273i −0.000713036 + 0.00123501i
\(23\) 2.19639 3.80426i 0.457979 0.793244i −0.540875 0.841103i \(-0.681907\pi\)
0.998854 + 0.0478596i \(0.0152400\pi\)
\(24\) −0.517985 + 0.299059i −0.105733 + 0.0610451i
\(25\) −3.53927 + 6.13019i −0.707853 + 1.22604i
\(26\) −0.0518790 0.0898571i −0.0101743 0.0176224i
\(27\) −19.8454 −3.81924
\(28\) 6.45849i 1.22054i
\(29\) 2.29456 + 3.97429i 0.426089 + 0.738007i 0.996521 0.0833373i \(-0.0265579\pi\)
−0.570433 + 0.821344i \(0.693225\pi\)
\(30\) 0.450268 0.259962i 0.0822073 0.0474624i
\(31\) 5.19023 0.932193 0.466096 0.884734i \(-0.345660\pi\)
0.466096 + 0.884734i \(0.345660\pi\)
\(32\) 0.452367 0.261174i 0.0799679 0.0461695i
\(33\) 0.456203 0.263389i 0.0794147 0.0458501i
\(34\) −0.192525 0.111154i −0.0330177 0.0190628i
\(35\) 11.2336i 1.89883i
\(36\) 17.5467 2.92445
\(37\) −1.35934 −0.223474 −0.111737 0.993738i \(-0.535641\pi\)
−0.111737 + 0.993738i \(0.535641\pi\)
\(38\) 0.223210i 0.0362094i
\(39\) 8.17140i 1.30847i
\(40\) −0.524470 + 0.302803i −0.0829260 + 0.0478773i
\(41\) 7.68887 1.20080 0.600400 0.799700i \(-0.295008\pi\)
0.600400 + 0.799700i \(0.295008\pi\)
\(42\) −0.241778 + 0.418772i −0.0373071 + 0.0646179i
\(43\) 1.29737 0.749037i 0.197847 0.114227i −0.397804 0.917471i \(-0.630228\pi\)
0.595651 + 0.803243i \(0.296894\pi\)
\(44\) −0.265565 + 0.153324i −0.0400355 + 0.0231145i
\(45\) −30.5201 −4.54966
\(46\) −0.165806 + 0.0957280i −0.0244467 + 0.0141143i
\(47\) 2.44212i 0.356219i 0.984011 + 0.178110i \(0.0569982\pi\)
−0.984011 + 0.178110i \(0.943002\pi\)
\(48\) −13.6907 −1.97608
\(49\) 1.72393 + 2.98593i 0.246275 + 0.426561i
\(50\) 0.267179 0.154256i 0.0377849 0.0218151i
\(51\) 8.75388 + 15.1622i 1.22579 + 2.12313i
\(52\) 4.75675i 0.659642i
\(53\) 6.29968i 0.865328i −0.901555 0.432664i \(-0.857574\pi\)
0.901555 0.432664i \(-0.142426\pi\)
\(54\) 0.749063 + 0.432472i 0.101935 + 0.0588520i
\(55\) 0.461914 0.266686i 0.0622845 0.0359600i
\(56\) 0.281622 0.487783i 0.0376333 0.0651828i
\(57\) 8.78937 15.2236i 1.16418 2.01642i
\(58\) 0.200013i 0.0262630i
\(59\) −7.84880 + 4.53151i −1.02183 + 0.589952i −0.914633 0.404286i \(-0.867520\pi\)
−0.107195 + 0.994238i \(0.534187\pi\)
\(60\) 23.8357 3.07718
\(61\) 4.70242i 0.602083i −0.953611 0.301041i \(-0.902666\pi\)
0.953611 0.301041i \(-0.0973342\pi\)
\(62\) −0.195905 0.113106i −0.0248800 0.0143645i
\(63\) 24.5823 14.1926i 3.09708 1.78810i
\(64\) 7.95445 0.994306
\(65\) 8.27370i 1.02623i
\(66\) −0.0229592 −0.00282608
\(67\) 5.98833 0.731590 0.365795 0.930695i \(-0.380797\pi\)
0.365795 + 0.930695i \(0.380797\pi\)
\(68\) −5.09582 8.82622i −0.617959 1.07034i
\(69\) 15.0780 1.81518
\(70\) −0.244805 + 0.424014i −0.0292598 + 0.0506794i
\(71\) 8.67606 + 5.00912i 1.02966 + 0.594474i 0.916887 0.399147i \(-0.130694\pi\)
0.112772 + 0.993621i \(0.464027\pi\)
\(72\) −1.32523 0.765123i −0.156180 0.0901706i
\(73\) 2.31215 + 4.00477i 0.270617 + 0.468723i 0.969020 0.246982i \(-0.0794389\pi\)
−0.698403 + 0.715705i \(0.746106\pi\)
\(74\) 0.0513082 + 0.0296228i 0.00596446 + 0.00344358i
\(75\) −24.2967 −2.80554
\(76\) −5.11648 + 8.86201i −0.586901 + 1.01654i
\(77\) −0.248032 + 0.429604i −0.0282658 + 0.0489579i
\(78\) 0.178072 0.308430i 0.0201627 0.0349228i
\(79\) 9.12273i 1.02639i −0.858273 0.513194i \(-0.828462\pi\)
0.858273 0.513194i \(-0.171538\pi\)
\(80\) −13.8621 −1.54983
\(81\) −20.8865 36.1765i −2.32072 4.01961i
\(82\) −0.290217 0.167557i −0.0320491 0.0185035i
\(83\) 2.69012 4.65943i 0.295279 0.511439i −0.679770 0.733425i \(-0.737921\pi\)
0.975050 + 0.221986i \(0.0712540\pi\)
\(84\) −19.1984 + 11.0842i −2.09472 + 1.20939i
\(85\) 8.86347 + 15.3520i 0.961379 + 1.66516i
\(86\) −0.0652924 −0.00704066
\(87\) −7.87594 + 13.6415i −0.844390 + 1.46253i
\(88\) 0.0267428 0.00285079
\(89\) −0.728326 + 0.420499i −0.0772024 + 0.0445728i −0.538104 0.842878i \(-0.680859\pi\)
0.460902 + 0.887451i \(0.347526\pi\)
\(90\) 1.15198 + 0.665096i 0.121429 + 0.0701073i
\(91\) −3.84748 6.66403i −0.403325 0.698580i
\(92\) −8.77722 −0.915089
\(93\) 8.90759 + 15.4284i 0.923674 + 1.59985i
\(94\) 0.0532188 0.0921777i 0.00548910 0.00950741i
\(95\) 8.89941 15.4142i 0.913060 1.58147i
\(96\) 1.55273 + 0.896467i 0.158474 + 0.0914952i
\(97\) −13.5267 7.80965i −1.37343 0.792950i −0.382071 0.924133i \(-0.624789\pi\)
−0.991358 + 0.131183i \(0.958122\pi\)
\(98\) 0.150272i 0.0151798i
\(99\) 1.16717 + 0.673863i 0.117305 + 0.0677258i
\(100\) 14.1436 1.41436
\(101\) 8.83219i 0.878836i 0.898283 + 0.439418i \(0.144815\pi\)
−0.898283 + 0.439418i \(0.855185\pi\)
\(102\) 0.763062i 0.0755544i
\(103\) 13.9242i 1.37199i −0.727607 0.685994i \(-0.759367\pi\)
0.727607 0.685994i \(-0.240633\pi\)
\(104\) −0.207418 + 0.359258i −0.0203390 + 0.0352281i
\(105\) 33.3930 19.2794i 3.25882 1.88148i
\(106\) −0.137283 + 0.237782i −0.0133341 + 0.0230954i
\(107\) −7.56872 4.36980i −0.731696 0.422445i 0.0873463 0.996178i \(-0.472161\pi\)
−0.819042 + 0.573733i \(0.805495\pi\)
\(108\) 19.8265 + 34.3405i 1.90781 + 3.30442i
\(109\) −2.56617 4.44473i −0.245794 0.425728i 0.716560 0.697525i \(-0.245715\pi\)
−0.962355 + 0.271797i \(0.912382\pi\)
\(110\) −0.0232466 −0.00221648
\(111\) −2.33293 4.04075i −0.221431 0.383531i
\(112\) 11.1652 6.44621i 1.05501 0.609110i
\(113\) −6.95228 4.01390i −0.654015 0.377596i 0.135978 0.990712i \(-0.456583\pi\)
−0.789993 + 0.613116i \(0.789916\pi\)
\(114\) −0.663511 + 0.383078i −0.0621435 + 0.0358785i
\(115\) 15.2668 1.42363
\(116\) 4.58476 7.94103i 0.425684 0.737306i
\(117\) −18.1051 + 10.4530i −1.67382 + 0.966380i
\(118\) 0.395005 0.0363631
\(119\) −14.2781 8.24348i −1.30887 0.755678i
\(120\) −1.80022 1.03935i −0.164336 0.0948797i
\(121\) 10.9764 0.997859
\(122\) −0.102476 + 0.177493i −0.00927770 + 0.0160694i
\(123\) 13.1958 + 22.8558i 1.18983 + 2.06084i
\(124\) −5.18530 8.98120i −0.465654 0.806536i
\(125\) −7.22377 −0.646114
\(126\) −1.23715 −0.110214
\(127\) 7.06750i 0.627139i 0.949565 + 0.313569i \(0.101525\pi\)
−0.949565 + 0.313569i \(0.898475\pi\)
\(128\) −1.20497 0.695693i −0.106506 0.0614911i
\(129\) 4.45316 + 2.57103i 0.392079 + 0.226367i
\(130\) 0.180301 0.312291i 0.0158135 0.0273897i
\(131\) 21.5664i 1.88427i −0.335234 0.942135i \(-0.608816\pi\)
0.335234 0.942135i \(-0.391184\pi\)
\(132\) −0.911539 0.526278i −0.0793393 0.0458066i
\(133\) 16.5538i 1.43540i
\(134\) −0.226030 0.130498i −0.0195260 0.0112733i
\(135\) −34.4854 59.7305i −2.96803 5.14079i
\(136\) 0.888812i 0.0762150i
\(137\) −13.4902 + 7.78856i −1.15254 + 0.665422i −0.949506 0.313749i \(-0.898415\pi\)
−0.203039 + 0.979171i \(0.565082\pi\)
\(138\) −0.569120 0.328581i −0.0484467 0.0279707i
\(139\) 3.54489 0.300674 0.150337 0.988635i \(-0.451964\pi\)
0.150337 + 0.988635i \(0.451964\pi\)
\(140\) −19.4388 + 11.2230i −1.64288 + 0.948514i
\(141\) −7.25940 + 4.19122i −0.611352 + 0.352964i
\(142\) −0.218319 0.378139i −0.0183209 0.0317327i
\(143\) 0.182678 0.316408i 0.0152763 0.0264593i
\(144\) −17.5134 30.3340i −1.45945 2.52784i
\(145\) −7.97454 + 13.8123i −0.662250 + 1.14705i
\(146\) 0.201547i 0.0166801i
\(147\) −5.91729 + 10.2490i −0.488050 + 0.845327i
\(148\) 1.35805 + 2.35220i 0.111631 + 0.193350i
\(149\) −3.56236 2.05673i −0.291840 0.168494i 0.346932 0.937890i \(-0.387224\pi\)
−0.638771 + 0.769397i \(0.720557\pi\)
\(150\) 0.917079 + 0.529476i 0.0748792 + 0.0432315i
\(151\) 10.3680 + 17.9579i 0.843737 + 1.46140i 0.886714 + 0.462319i \(0.152983\pi\)
−0.0429765 + 0.999076i \(0.513684\pi\)
\(152\) 0.772854 0.446208i 0.0626868 0.0361922i
\(153\) −22.3962 + 38.7914i −1.81063 + 3.13610i
\(154\) 0.0187239 0.0108103i 0.00150882 0.000871116i
\(155\) 9.01911 + 15.6216i 0.724432 + 1.25475i
\(156\) 14.1398 8.16364i 1.13209 0.653614i
\(157\) 9.75898 + 16.9031i 0.778852 + 1.34901i 0.932604 + 0.360901i \(0.117531\pi\)
−0.153753 + 0.988109i \(0.549136\pi\)
\(158\) −0.198804 + 0.344338i −0.0158160 + 0.0273941i
\(159\) 18.7264 10.8117i 1.48510 0.857421i
\(160\) 1.57216 + 0.907690i 0.124291 + 0.0717592i
\(161\) −12.2966 + 7.09943i −0.969106 + 0.559513i
\(162\) 1.82064i 0.143043i
\(163\) 8.83252i 0.691817i 0.938268 + 0.345908i \(0.112429\pi\)
−0.938268 + 0.345908i \(0.887571\pi\)
\(164\) −7.68157 13.3049i −0.599830 1.03894i
\(165\) 1.58550 + 0.915387i 0.123431 + 0.0712628i
\(166\) −0.203078 + 0.117247i −0.0157619 + 0.00910012i
\(167\) 3.25894i 0.252184i 0.992019 + 0.126092i \(0.0402435\pi\)
−0.992019 + 0.126092i \(0.959757\pi\)
\(168\) 1.93330 0.149158
\(169\) −3.66629 6.35020i −0.282022 0.488477i
\(170\) 0.772615i 0.0592569i
\(171\) 44.9741 3.43925
\(172\) −2.59228 1.49665i −0.197659 0.114119i
\(173\) −5.29351 3.05621i −0.402458 0.232359i 0.285086 0.958502i \(-0.407978\pi\)
−0.687544 + 0.726143i \(0.741311\pi\)
\(174\) 0.594556 0.343267i 0.0450731 0.0260230i
\(175\) 19.8147 11.4400i 1.49785 0.864784i
\(176\) 0.530122 + 0.306066i 0.0399594 + 0.0230706i
\(177\) −26.9406 15.5542i −2.02498 1.16912i
\(178\) 0.0366542 0.00274735
\(179\) 1.55969i 0.116576i −0.998300 0.0582882i \(-0.981436\pi\)
0.998300 0.0582882i \(-0.0185642\pi\)
\(180\) 30.4911 + 52.8121i 2.27267 + 3.93638i
\(181\) −4.33550 −0.322255 −0.161127 0.986934i \(-0.551513\pi\)
−0.161127 + 0.986934i \(0.551513\pi\)
\(182\) 0.335379i 0.0248599i
\(183\) 13.9783 8.07040i 1.03331 0.596581i
\(184\) 0.662908 + 0.382730i 0.0488702 + 0.0282152i
\(185\) −2.36213 4.09133i −0.173667 0.300801i
\(186\) 0.776461i 0.0569329i
\(187\) 0.782800i 0.0572440i
\(188\) 4.22585 2.43980i 0.308202 0.177940i
\(189\) 55.5524 + 32.0732i 4.04084 + 2.33298i
\(190\) −0.671817 + 0.387874i −0.0487387 + 0.0281393i
\(191\) −7.30153 + 12.6466i −0.528320 + 0.915078i 0.471135 + 0.882061i \(0.343845\pi\)
−0.999455 + 0.0330162i \(0.989489\pi\)
\(192\) 13.6516 + 23.6453i 0.985220 + 1.70645i
\(193\) −1.45959 + 0.842697i −0.105064 + 0.0606587i −0.551611 0.834101i \(-0.685987\pi\)
0.446547 + 0.894760i \(0.352653\pi\)
\(194\) 0.340377 + 0.589551i 0.0244377 + 0.0423273i
\(195\) −24.5943 + 14.1995i −1.76123 + 1.01685i
\(196\) 3.44458 5.96619i 0.246041 0.426156i
\(197\) −19.5668 + 11.2969i −1.39407 + 0.804869i −0.993763 0.111511i \(-0.964431\pi\)
−0.400310 + 0.916380i \(0.631098\pi\)
\(198\) −0.0293698 0.0508700i −0.00208722 0.00361517i
\(199\) −14.4447 8.33963i −1.02395 0.591181i −0.108708 0.994074i \(-0.534671\pi\)
−0.915247 + 0.402893i \(0.868005\pi\)
\(200\) −1.06821 0.616732i −0.0755339 0.0436095i
\(201\) 10.2773 + 17.8008i 0.724905 + 1.25557i
\(202\) 0.192472 0.333371i 0.0135423 0.0234559i
\(203\) 14.8335i 1.04110i
\(204\) 17.4911 30.2955i 1.22462 2.12111i
\(205\) 13.3610 + 23.1420i 0.933174 + 1.61630i
\(206\) −0.303437 + 0.525568i −0.0211414 + 0.0366181i
\(207\) 19.2880 + 33.4079i 1.34061 + 2.32201i
\(208\) −8.22327 + 4.74771i −0.570181 + 0.329194i
\(209\) −0.680673 + 0.392987i −0.0470831 + 0.0271835i
\(210\) −1.68056 −0.115970
\(211\) −20.3484 11.7481i −1.40084 0.808775i −0.406360 0.913713i \(-0.633202\pi\)
−0.994479 + 0.104938i \(0.966536\pi\)
\(212\) −10.9010 + 6.29370i −0.748684 + 0.432253i
\(213\) 34.3871i 2.35617i
\(214\) 0.190454 + 0.329877i 0.0130192 + 0.0225499i
\(215\) 4.50891 + 2.60322i 0.307505 + 0.177538i
\(216\) 3.45813i 0.235296i
\(217\) −14.5288 8.38822i −0.986281 0.569430i
\(218\) 0.223689i 0.0151501i
\(219\) −7.93634 + 13.7461i −0.536288 + 0.928879i
\(220\) −0.922951 0.532866i −0.0622254 0.0359258i
\(221\) 10.5160 + 6.07141i 0.707382 + 0.408407i
\(222\) 0.203357i 0.0136485i
\(223\) −12.2642 −0.821273 −0.410637 0.911799i \(-0.634694\pi\)
−0.410637 + 0.911799i \(0.634694\pi\)
\(224\) −1.68839 −0.112811
\(225\) −31.0807 53.8334i −2.07205 3.58890i
\(226\) 0.174943 + 0.303010i 0.0116370 + 0.0201559i
\(227\) −2.56741 + 4.44689i −0.170405 + 0.295150i −0.938562 0.345112i \(-0.887841\pi\)
0.768156 + 0.640262i \(0.221174\pi\)
\(228\) −35.1241 −2.32615
\(229\) −9.63795 5.56447i −0.636894 0.367711i 0.146523 0.989207i \(-0.453192\pi\)
−0.783417 + 0.621496i \(0.786525\pi\)
\(230\) −0.576245 0.332695i −0.0379964 0.0219373i
\(231\) −1.70271 −0.112030
\(232\) −0.692536 + 0.399836i −0.0454672 + 0.0262505i
\(233\) 8.54545 14.8012i 0.559831 0.969656i −0.437679 0.899131i \(-0.644199\pi\)
0.997510 0.0705246i \(-0.0224673\pi\)
\(234\) 0.911171 0.0595651
\(235\) −7.35028 + 4.24369i −0.479479 + 0.276828i
\(236\) 15.6827 + 9.05441i 1.02086 + 0.589392i
\(237\) 27.1181 15.6566i 1.76151 1.01701i
\(238\) 0.359285 + 0.622301i 0.0232890 + 0.0403378i
\(239\) 0.513859 0.0332388 0.0166194 0.999862i \(-0.494710\pi\)
0.0166194 + 0.999862i \(0.494710\pi\)
\(240\) −23.7904 41.2062i −1.53566 2.65985i
\(241\) 1.70481 + 2.95282i 0.109817 + 0.190208i 0.915696 0.401872i \(-0.131640\pi\)
−0.805879 + 0.592080i \(0.798307\pi\)
\(242\) −0.414306 0.239200i −0.0266326 0.0153764i
\(243\) 41.9238 72.6142i 2.68942 4.65820i
\(244\) −8.13709 + 4.69795i −0.520924 + 0.300755i
\(245\) −5.99137 + 10.3774i −0.382774 + 0.662985i
\(246\) 1.15026i 0.0733378i
\(247\) 12.1921i 0.775762i
\(248\) 0.904418i 0.0574306i
\(249\) 18.4674 1.17032
\(250\) 0.272661 + 0.157421i 0.0172446 + 0.00995619i
\(251\) 14.1782i 0.894919i −0.894304 0.447459i \(-0.852329\pi\)
0.894304 0.447459i \(-0.147671\pi\)
\(252\) −49.1179 28.3582i −3.09414 1.78640i
\(253\) −0.583840 0.337080i −0.0367057 0.0211921i
\(254\) 0.154016 0.266763i 0.00966380 0.0167382i
\(255\) −30.4234 + 52.6949i −1.90519 + 3.29988i
\(256\) −7.92412 13.7250i −0.495258 0.857812i
\(257\) 1.16555 0.0727051 0.0363525 0.999339i \(-0.488426\pi\)
0.0363525 + 0.999339i \(0.488426\pi\)
\(258\) −0.112056 0.194087i −0.00697632 0.0120833i
\(259\) 3.80514 + 2.19690i 0.236440 + 0.136509i
\(260\) 14.3169 8.26584i 0.887894 0.512626i
\(261\) −40.3002 −2.49452
\(262\) −0.469978 + 0.814026i −0.0290354 + 0.0502907i
\(263\) 13.8050 0.851252 0.425626 0.904899i \(-0.360054\pi\)
0.425626 + 0.904899i \(0.360054\pi\)
\(264\) 0.0458966 + 0.0794952i 0.00282474 + 0.00489259i
\(265\) 18.9608 10.9470i 1.16475 0.672470i
\(266\) 0.360742 0.624824i 0.0221185 0.0383104i
\(267\) −2.49994 1.44334i −0.152994 0.0883310i
\(268\) −5.98264 10.3622i −0.365448 0.632974i
\(269\) 16.8251 1.02585 0.512923 0.858434i \(-0.328562\pi\)
0.512923 + 0.858434i \(0.328562\pi\)
\(270\) 3.00604i 0.182942i
\(271\) −7.24870 + 12.5551i −0.440327 + 0.762669i −0.997714 0.0675842i \(-0.978471\pi\)
0.557386 + 0.830253i \(0.311804\pi\)
\(272\) −10.1723 + 17.6189i −0.616785 + 1.06830i
\(273\) 13.2063 22.8739i 0.799280 1.38439i
\(274\) 0.678917 0.0410149
\(275\) 0.940801 + 0.543171i 0.0567324 + 0.0327545i
\(276\) −15.0637 26.0911i −0.906727 1.57050i
\(277\) 16.6258 + 9.59892i 0.998949 + 0.576743i 0.907937 0.419107i \(-0.137657\pi\)
0.0910115 + 0.995850i \(0.470990\pi\)
\(278\) −0.133802 0.0772507i −0.00802492 0.00463319i
\(279\) −22.7895 + 39.4726i −1.36437 + 2.36316i
\(280\) 1.95751 0.116983
\(281\) −9.04315 15.6632i −0.539469 0.934388i −0.998933 0.0461911i \(-0.985292\pi\)
0.459464 0.888197i \(-0.348042\pi\)
\(282\) 0.365342 0.0217558
\(283\) −19.8833 −1.18194 −0.590970 0.806693i \(-0.701255\pi\)
−0.590970 + 0.806693i \(0.701255\pi\)
\(284\) 20.0175i 1.18782i
\(285\) 61.0935 3.61887
\(286\) −0.0137904 + 0.00796188i −0.000815442 + 0.000470796i
\(287\) −21.5232 12.4264i −1.27047 0.733508i
\(288\) 4.58710i 0.270298i
\(289\) 9.01679 0.530399
\(290\) 0.601999 0.347564i 0.0353506 0.0204097i
\(291\) 53.6124i 3.14281i
\(292\) 4.61991 8.00193i 0.270360 0.468277i
\(293\) −4.54943 + 7.87984i −0.265780 + 0.460345i −0.967768 0.251844i \(-0.918963\pi\)
0.701987 + 0.712189i \(0.252296\pi\)
\(294\) 0.446697 0.257900i 0.0260519 0.0150411i
\(295\) −27.2779 15.7489i −1.58818 0.916936i
\(296\) 0.236870i 0.0137678i
\(297\) 3.04567i 0.176728i
\(298\) 0.0896409 + 0.155263i 0.00519276 + 0.00899412i
\(299\) 9.05656 5.22881i 0.523754 0.302390i
\(300\) 24.2736 + 42.0431i 1.40144 + 2.42736i
\(301\) −4.84225 −0.279103
\(302\) 0.903764i 0.0520057i
\(303\) −26.2545 + 15.1580i −1.50828 + 0.870805i
\(304\) 20.4270 1.17157
\(305\) 14.1533 8.17143i 0.810418 0.467895i
\(306\) 1.69069 0.976122i 0.0966505 0.0558012i
\(307\) −7.56181 + 13.0974i −0.431575 + 0.747510i −0.997009 0.0772833i \(-0.975375\pi\)
0.565434 + 0.824794i \(0.308709\pi\)
\(308\) 0.991185 0.0564780
\(309\) 41.3908 23.8970i 2.35464 1.35945i
\(310\) 0.786181i 0.0446521i
\(311\) 4.62828i 0.262446i 0.991353 + 0.131223i \(0.0418903\pi\)
−0.991353 + 0.131223i \(0.958110\pi\)
\(312\) −1.42390 −0.0806125
\(313\) −24.2089 −1.36837 −0.684185 0.729309i \(-0.739842\pi\)
−0.684185 + 0.729309i \(0.739842\pi\)
\(314\) 0.850675i 0.0480064i
\(315\) 85.4337 + 49.3252i 4.81365 + 2.77916i
\(316\) −15.7860 + 9.11407i −0.888034 + 0.512706i
\(317\) 2.51279 1.45076i 0.141132 0.0814827i −0.427771 0.903887i \(-0.640701\pi\)
0.568903 + 0.822404i \(0.307368\pi\)
\(318\) −0.942436 −0.0528492
\(319\) 0.609934 0.352146i 0.0341498 0.0197164i
\(320\) 13.8225 + 23.9413i 0.772702 + 1.33836i
\(321\) 29.9982i 1.67434i
\(322\) 0.618846 0.0344869
\(323\) −13.0611 22.6226i −0.726741 1.25875i
\(324\) −41.7334 + 72.2843i −2.31852 + 4.01579i
\(325\) −14.5937 + 8.42570i −0.809515 + 0.467374i
\(326\) 0.192479 0.333384i 0.0106604 0.0184644i
\(327\) 8.80824 15.2563i 0.487097 0.843676i
\(328\) 1.33982i 0.0739790i
\(329\) 3.94684 6.83613i 0.217596 0.376888i
\(330\) −0.0398964 0.0691026i −0.00219623 0.00380397i
\(331\) −7.88875 + 4.55457i −0.433605 + 0.250342i −0.700881 0.713278i \(-0.747210\pi\)
0.267276 + 0.963620i \(0.413876\pi\)
\(332\) −10.7503 −0.589998
\(333\) 5.96864 10.3380i 0.327079 0.566518i
\(334\) 0.0710191 0.123009i 0.00388599 0.00673073i
\(335\) 10.4060 + 18.0237i 0.568539 + 0.984738i
\(336\) 38.3239 + 22.1263i 2.09074 + 1.20709i
\(337\) 6.47887 11.2217i 0.352927 0.611287i −0.633834 0.773469i \(-0.718520\pi\)
0.986761 + 0.162182i \(0.0518532\pi\)
\(338\) 0.319585i 0.0173831i
\(339\) 27.5550i 1.49658i
\(340\) 17.7101 30.6748i 0.960466 1.66358i
\(341\) 0.796545i 0.0431353i
\(342\) −1.69755 0.980080i −0.0917929 0.0529967i
\(343\) 11.4817i 0.619951i
\(344\) 0.130523 + 0.226072i 0.00703732 + 0.0121890i
\(345\) 26.2012 + 45.3818i 1.41062 + 2.44327i
\(346\) 0.133203 + 0.230714i 0.00716101 + 0.0124032i
\(347\) 31.0899 + 17.9497i 1.66899 + 0.963592i 0.968183 + 0.250242i \(0.0805101\pi\)
0.700807 + 0.713351i \(0.252823\pi\)
\(348\) 31.4739 1.68718
\(349\) 13.4876 12.9261i 0.721975 0.691919i
\(350\) −0.997209 −0.0533030
\(351\) −40.9150 23.6223i −2.18388 1.26086i
\(352\) −0.0400824 0.0694248i −0.00213640 0.00370035i
\(353\) −12.1970 21.1259i −0.649183 1.12442i −0.983318 0.181893i \(-0.941778\pi\)
0.334136 0.942525i \(-0.391556\pi\)
\(354\) 0.677916 + 1.17419i 0.0360308 + 0.0624072i
\(355\) 34.8176i 1.84793i
\(356\) 1.45527 + 0.840199i 0.0771290 + 0.0445305i
\(357\) 56.5906i 2.99509i
\(358\) −0.0339889 + 0.0588704i −0.00179637 + 0.00311140i
\(359\) 37.6526i 1.98723i −0.112826 0.993615i \(-0.535990\pi\)
0.112826 0.993615i \(-0.464010\pi\)
\(360\) 5.31824i 0.280296i
\(361\) −3.61409 + 6.25980i −0.190216 + 0.329463i
\(362\) 0.163644 + 0.0944796i 0.00860091 + 0.00496574i
\(363\) 18.8380 + 32.6284i 0.988740 + 1.71255i
\(364\) −7.68765 + 13.3154i −0.402942 + 0.697917i
\(365\) −8.03570 + 13.9182i −0.420608 + 0.728514i
\(366\) −0.703484 −0.0367717
\(367\) 9.90695 5.71978i 0.517138 0.298570i −0.218625 0.975809i \(-0.570157\pi\)
0.735763 + 0.677239i \(0.236824\pi\)
\(368\) 8.76054 + 15.1737i 0.456675 + 0.790984i
\(369\) −33.7606 + 58.4751i −1.75751 + 3.04409i
\(370\) 0.205903i 0.0107044i
\(371\) −10.1813 + 17.6345i −0.528586 + 0.915537i
\(372\) 17.7983 30.8275i 0.922797 1.59833i
\(373\) −1.76180 + 1.01718i −0.0912227 + 0.0526675i −0.544917 0.838490i \(-0.683439\pi\)
0.453695 + 0.891157i \(0.350106\pi\)
\(374\) −0.0170589 + 0.0295468i −0.000882092 + 0.00152783i
\(375\) −12.3976 21.4733i −0.640210 1.10888i
\(376\) −0.425549 −0.0219460
\(377\) 10.9250i 0.562666i
\(378\) −1.39789 2.42121i −0.0718995 0.124534i
\(379\) −25.8662 + 14.9338i −1.32866 + 0.767100i −0.985092 0.172029i \(-0.944968\pi\)
−0.343564 + 0.939129i \(0.611634\pi\)
\(380\) −35.5638 −1.82439
\(381\) −21.0087 + 12.1294i −1.07631 + 0.621408i
\(382\) 0.551193 0.318231i 0.0282015 0.0162821i
\(383\) 1.70520 + 0.984500i 0.0871319 + 0.0503056i 0.542933 0.839776i \(-0.317314\pi\)
−0.455801 + 0.890082i \(0.650647\pi\)
\(384\) 4.77586i 0.243717i
\(385\) −1.72403 −0.0878646
\(386\) 0.0734566 0.00373884
\(387\) 13.1556i 0.668738i
\(388\) 31.2089i 1.58439i
\(389\) −2.76192 + 1.59459i −0.140035 + 0.0808491i −0.568381 0.822766i \(-0.692430\pi\)
0.428346 + 0.903615i \(0.359097\pi\)
\(390\) 1.23775 0.0626759
\(391\) 11.2031 19.4043i 0.566563 0.981316i
\(392\) −0.520310 + 0.300401i −0.0262796 + 0.0151726i
\(393\) 64.1081 37.0128i 3.23383 1.86705i
\(394\) 0.984730 0.0496100
\(395\) 27.4576 15.8527i 1.38154 0.797634i
\(396\) 2.69289i 0.135323i
\(397\) 11.8828 0.596383 0.298192 0.954506i \(-0.403617\pi\)
0.298192 + 0.954506i \(0.403617\pi\)
\(398\) 0.363476 + 0.629559i 0.0182194 + 0.0315569i
\(399\) −49.2076 + 28.4100i −2.46346 + 1.42228i
\(400\) −14.1167 24.4509i −0.705837 1.22255i
\(401\) 6.23113i 0.311168i −0.987823 0.155584i \(-0.950274\pi\)
0.987823 0.155584i \(-0.0497259\pi\)
\(402\) 0.895857i 0.0446813i
\(403\) 10.7006 + 6.17802i 0.533037 + 0.307749i
\(404\) 15.2833 8.82380i 0.760371 0.439001i
\(405\) 72.5894 125.729i 3.60700 6.24750i
\(406\) −0.323252 + 0.559889i −0.0160427 + 0.0277868i
\(407\) 0.208617i 0.0103408i
\(408\) −2.64207 + 1.52540i −0.130802 + 0.0755185i
\(409\) 17.8181 0.881050 0.440525 0.897740i \(-0.354792\pi\)
0.440525 + 0.897740i \(0.354792\pi\)
\(410\) 1.16466i 0.0575184i
\(411\) −46.3044 26.7338i −2.28403 1.31868i
\(412\) −24.0945 + 13.9109i −1.18705 + 0.685343i
\(413\) 29.2945 1.44149
\(414\) 1.68131i 0.0826318i
\(415\) 18.6986 0.917878
\(416\) 1.24352 0.0609686
\(417\) 6.08383 + 10.5375i 0.297926 + 0.516024i
\(418\) 0.0342560 0.00167552
\(419\) −8.27828 + 14.3384i −0.404420 + 0.700477i −0.994254 0.107048i \(-0.965860\pi\)
0.589833 + 0.807525i \(0.299193\pi\)
\(420\) −66.7225 38.5223i −3.25573 1.87969i
\(421\) 19.1881 + 11.0783i 0.935173 + 0.539923i 0.888444 0.458985i \(-0.151787\pi\)
0.0467292 + 0.998908i \(0.485120\pi\)
\(422\) 0.512033 + 0.886867i 0.0249254 + 0.0431720i
\(423\) −18.5727 10.7230i −0.903036 0.521368i
\(424\) 1.09775 0.0533112
\(425\) −18.0526 + 31.2680i −0.875680 + 1.51672i
\(426\) 0.749367 1.29794i 0.0363070 0.0628855i
\(427\) −7.59984 + 13.1633i −0.367782 + 0.637017i
\(428\) 17.4626i 0.844087i
\(429\) 1.25407 0.0605469
\(430\) −0.113459 0.196517i −0.00547149 0.00947690i
\(431\) 17.7796 + 10.2651i 0.856414 + 0.494451i 0.862810 0.505529i \(-0.168703\pi\)
−0.00639581 + 0.999980i \(0.502036\pi\)
\(432\) 39.5776 68.5505i 1.90418 3.29814i
\(433\) 9.52497 5.49925i 0.457741 0.264277i −0.253353 0.967374i \(-0.581533\pi\)
0.711094 + 0.703097i \(0.248200\pi\)
\(434\) 0.365594 + 0.633228i 0.0175491 + 0.0303959i
\(435\) −54.7444 −2.62479
\(436\) −5.12746 + 8.88102i −0.245561 + 0.425324i
\(437\) −22.4970 −1.07618
\(438\) 0.599115 0.345899i 0.0286268 0.0165277i
\(439\) −0.460783 0.266033i −0.0219920 0.0126971i 0.488964 0.872304i \(-0.337375\pi\)
−0.510956 + 0.859607i \(0.670708\pi\)
\(440\) 0.0464712 + 0.0804904i 0.00221543 + 0.00383723i
\(441\) −30.2780 −1.44181
\(442\) −0.264618 0.458331i −0.0125866 0.0218006i
\(443\) −1.01879 + 1.76459i −0.0484041 + 0.0838383i −0.889212 0.457495i \(-0.848747\pi\)
0.840808 + 0.541333i \(0.182080\pi\)
\(444\) −4.66142 + 8.07381i −0.221221 + 0.383166i
\(445\) −2.53124 1.46141i −0.119992 0.0692775i
\(446\) 0.462914 + 0.267263i 0.0219196 + 0.0126553i
\(447\) 14.1192i 0.667816i
\(448\) −22.2666 12.8556i −1.05200 0.607372i
\(449\) −7.90622 −0.373117 −0.186559 0.982444i \(-0.559733\pi\)
−0.186559 + 0.982444i \(0.559733\pi\)
\(450\) 2.70926i 0.127716i
\(451\) 1.18001i 0.0555646i
\(452\) 16.0404i 0.754475i
\(453\) −35.5877 + 61.6396i −1.67205 + 2.89608i
\(454\) 0.193814 0.111899i 0.00909615 0.00525167i
\(455\) 13.3716 23.1603i 0.626870 1.08577i
\(456\) 2.65278 + 1.53158i 0.124228 + 0.0717230i
\(457\) −6.59094 11.4158i −0.308311 0.534011i 0.669682 0.742648i \(-0.266430\pi\)
−0.977993 + 0.208637i \(0.933097\pi\)
\(458\) 0.242523 + 0.420063i 0.0113324 + 0.0196282i
\(459\) −101.225 −4.72476
\(460\) −15.2523 26.4177i −0.711140 1.23173i
\(461\) 15.8446 9.14790i 0.737958 0.426060i −0.0833684 0.996519i \(-0.526568\pi\)
0.821326 + 0.570459i \(0.193235\pi\)
\(462\) 0.0642689 + 0.0371057i 0.00299006 + 0.00172631i
\(463\) 27.0568 15.6213i 1.25744 0.725982i 0.284863 0.958568i \(-0.408052\pi\)
0.972576 + 0.232586i \(0.0747187\pi\)
\(464\) −18.3042 −0.849750
\(465\) −30.9576 + 53.6201i −1.43562 + 2.48657i
\(466\) −0.645097 + 0.372447i −0.0298835 + 0.0172533i
\(467\) 36.2994 1.67973 0.839867 0.542792i \(-0.182633\pi\)
0.839867 + 0.542792i \(0.182633\pi\)
\(468\) 36.1759 + 20.8861i 1.67223 + 0.965462i
\(469\) −16.7629 9.67807i −0.774040 0.446892i
\(470\) 0.369915 0.0170629
\(471\) −33.4972 + 58.0188i −1.54347 + 2.67337i
\(472\) −0.789634 1.36769i −0.0363458 0.0629529i
\(473\) −0.114955 0.199108i −0.00528563 0.00915498i
\(474\) −1.36477 −0.0626858
\(475\) 36.2516 1.66334
\(476\) 32.9426i 1.50992i
\(477\) 47.9102 + 27.6609i 2.19366 + 1.26651i
\(478\) −0.0193956 0.0111981i −0.000887135 0.000512188i
\(479\) 7.67071 13.2861i 0.350484 0.607056i −0.635850 0.771812i \(-0.719350\pi\)
0.986334 + 0.164756i \(0.0526838\pi\)
\(480\) 6.23119i 0.284414i
\(481\) −2.80253 1.61804i −0.127784 0.0737764i
\(482\) 0.148606i 0.00676880i
\(483\) −42.2073 24.3684i −1.92050 1.10880i
\(484\) −10.9660 18.9937i −0.498456 0.863350i
\(485\) 54.2836i 2.46489i
\(486\) −3.16483 + 1.82722i −0.143560 + 0.0828843i
\(487\) 1.13023 + 0.652541i 0.0512158 + 0.0295695i 0.525389 0.850862i \(-0.323920\pi\)
−0.474173 + 0.880431i \(0.657253\pi\)
\(488\) 0.819415 0.0370932
\(489\) −26.2554 + 15.1586i −1.18731 + 0.685495i
\(490\) 0.452289 0.261129i 0.0204323 0.0117966i
\(491\) −3.83732 6.64643i −0.173176 0.299949i 0.766353 0.642420i \(-0.222070\pi\)
−0.939528 + 0.342471i \(0.888736\pi\)
\(492\) 26.3666 45.6682i 1.18870 2.05888i
\(493\) 11.7038 + 20.2715i 0.527111 + 0.912983i
\(494\) −0.265691 + 0.460190i −0.0119540 + 0.0207049i
\(495\) 4.68391i 0.210526i
\(496\) −10.3509 + 17.9283i −0.464769 + 0.805003i
\(497\) −16.1911 28.0437i −0.726268 1.25793i
\(498\) −0.697053 0.402444i −0.0312357 0.0180339i
\(499\) 37.6940 + 21.7626i 1.68742 + 0.974230i 0.956487 + 0.291776i \(0.0942462\pi\)
0.730929 + 0.682454i \(0.239087\pi\)
\(500\) 7.21691 + 12.5001i 0.322750 + 0.559019i
\(501\) −9.68747 + 5.59306i −0.432804 + 0.249880i
\(502\) −0.308972 + 0.535156i −0.0137901 + 0.0238852i
\(503\) −37.4705 + 21.6336i −1.67073 + 0.964596i −0.703498 + 0.710697i \(0.748380\pi\)
−0.967231 + 0.253899i \(0.918287\pi\)
\(504\) 2.47312 + 4.28356i 0.110161 + 0.190805i
\(505\) −26.5831 + 15.3478i −1.18293 + 0.682967i
\(506\) 0.0146914 + 0.0254462i 0.000653112 + 0.00113122i
\(507\) 12.5843 21.7967i 0.558890 0.968027i
\(508\) 12.2296 7.06078i 0.542602 0.313272i
\(509\) 18.2933 + 10.5617i 0.810838 + 0.468138i 0.847247 0.531199i \(-0.178258\pi\)
−0.0364086 + 0.999337i \(0.511592\pi\)
\(510\) 2.29666 1.32598i 0.101698 0.0587154i
\(511\) 14.9472i 0.661226i
\(512\) 3.47350i 0.153509i
\(513\) 50.8175 + 88.0184i 2.24365 + 3.88611i
\(514\) −0.0439938 0.0253998i −0.00194048 0.00112034i
\(515\) 41.9090 24.1961i 1.84673 1.06621i
\(516\) 10.2744i 0.452303i
\(517\) 0.374792 0.0164833
\(518\) −0.0957502 0.165844i −0.00420702 0.00728678i
\(519\) 20.9806i 0.920944i
\(520\) −1.44173 −0.0632239
\(521\) 12.9141 + 7.45598i 0.565778 + 0.326652i 0.755461 0.655193i \(-0.227413\pi\)
−0.189683 + 0.981845i \(0.560746\pi\)
\(522\) 1.52113 + 0.878226i 0.0665781 + 0.0384389i
\(523\) −24.8498 + 14.3471i −1.08661 + 0.627353i −0.932671 0.360728i \(-0.882528\pi\)
−0.153936 + 0.988081i \(0.549195\pi\)
\(524\) −37.3187 + 21.5460i −1.63028 + 0.941240i
\(525\) 68.0129 + 39.2673i 2.96833 + 1.71376i
\(526\) −0.521070 0.300840i −0.0227197 0.0131172i
\(527\) 26.4736 1.15321
\(528\) 2.10111i 0.0914390i
\(529\) 1.85172 + 3.20728i 0.0805097 + 0.139447i
\(530\) −0.954234 −0.0414493
\(531\) 79.5886i 3.45385i
\(532\) 28.6448 16.5381i 1.24191 0.717017i
\(533\) 15.8521 + 9.15219i 0.686629 + 0.396425i
\(534\) 0.0629069 + 0.108958i 0.00272225 + 0.00471507i
\(535\) 30.3738i 1.31317i
\(536\) 1.04349i 0.0450719i
\(537\) 4.63630 2.67677i 0.200071 0.115511i
\(538\) −0.635066 0.366655i −0.0273796 0.0158076i
\(539\) 0.458251 0.264571i 0.0197383 0.0113959i
\(540\) −68.9054 + 119.348i −2.96522 + 5.13590i
\(541\) 12.8923 + 22.3300i 0.554282 + 0.960044i 0.997959 + 0.0638573i \(0.0203402\pi\)
−0.443677 + 0.896187i \(0.646326\pi\)
\(542\) 0.547205 0.315929i 0.0235045 0.0135703i
\(543\) −7.44068 12.8876i −0.319310 0.553062i
\(544\) 2.30737 1.33216i 0.0989278 0.0571160i
\(545\) 8.91851 15.4473i 0.382027 0.661690i
\(546\) −0.996942 + 0.575585i −0.0426652 + 0.0246328i
\(547\) −2.18920 3.79181i −0.0936035 0.162126i 0.815421 0.578868i \(-0.196505\pi\)
−0.909025 + 0.416742i \(0.863172\pi\)
\(548\) 26.9548 + 15.5623i 1.15145 + 0.664790i
\(549\) 35.7627 + 20.6476i 1.52631 + 0.881217i
\(550\) −0.0236737 0.0410041i −0.00100945 0.00174842i
\(551\) 11.7512 20.3537i 0.500619 0.867097i
\(552\) 2.62740i 0.111830i
\(553\) −14.7438 + 25.5370i −0.626969 + 1.08594i
\(554\) −0.418361 0.724623i −0.0177745 0.0307863i
\(555\) 8.10789 14.0433i 0.344161 0.596104i
\(556\) −3.54153 6.13410i −0.150194 0.260144i
\(557\) −2.49880 + 1.44268i −0.105878 + 0.0611285i −0.552004 0.833842i \(-0.686137\pi\)
0.446126 + 0.894970i \(0.352803\pi\)
\(558\) 1.72038 0.993262i 0.0728295 0.0420481i
\(559\) 3.56637 0.150841
\(560\) 38.8036 + 22.4033i 1.63975 + 0.946712i
\(561\) 2.32694 1.34346i 0.0982434 0.0567209i
\(562\) 0.788277i 0.0332515i
\(563\) 0.704029 + 1.21941i 0.0296713 + 0.0513922i 0.880480 0.474084i \(-0.157221\pi\)
−0.850808 + 0.525476i \(0.823887\pi\)
\(564\) 14.5050 + 8.37447i 0.610771 + 0.352629i
\(565\) 27.9000i 1.17376i
\(566\) 0.750496 + 0.433299i 0.0315457 + 0.0182129i
\(567\) 135.024i 5.67046i
\(568\) −0.872860 + 1.51184i −0.0366244 + 0.0634353i
\(569\) 18.2195 + 10.5190i 0.763801 + 0.440981i 0.830659 0.556782i \(-0.187964\pi\)
−0.0668580 + 0.997763i \(0.521297\pi\)
\(570\) −2.30598 1.33136i −0.0965867 0.0557644i
\(571\) 16.2009i 0.677986i −0.940789 0.338993i \(-0.889914\pi\)
0.940789 0.338993i \(-0.110086\pi\)
\(572\) −0.730018 −0.0305236
\(573\) −50.1242 −2.09397
\(574\) 0.541596 + 0.938071i 0.0226058 + 0.0391543i
\(575\) 15.5472 + 26.9286i 0.648364 + 1.12300i
\(576\) −34.9267 + 60.4949i −1.45528 + 2.52062i
\(577\) −6.87072 −0.286032 −0.143016 0.989720i \(-0.545680\pi\)
−0.143016 + 0.989720i \(0.545680\pi\)
\(578\) −0.340339 0.196495i −0.0141562 0.00817311i
\(579\) −5.00998 2.89251i −0.208208 0.120209i
\(580\) 31.8679 1.32324
\(581\) −15.0607 + 8.69532i −0.624825 + 0.360743i
\(582\) −1.16833 + 2.02360i −0.0484287 + 0.0838810i
\(583\) −0.966813 −0.0400413
\(584\) −0.697847 + 0.402902i −0.0288771 + 0.0166722i
\(585\) −62.9229 36.3285i −2.60154 1.50200i
\(586\) 0.343437 0.198283i 0.0141872 0.00819100i
\(587\) −9.02221 15.6269i −0.372386 0.644992i 0.617546 0.786535i \(-0.288127\pi\)
−0.989932 + 0.141543i \(0.954794\pi\)
\(588\) 23.6467 0.975172
\(589\) −13.2905 23.0198i −0.547625 0.948514i
\(590\) 0.686403 + 1.18888i 0.0282588 + 0.0489456i
\(591\) −67.1618 38.7759i −2.76267 1.59503i
\(592\) 2.71093 4.69547i 0.111418 0.192982i
\(593\) −16.4537 + 9.49956i −0.675674 + 0.390100i −0.798223 0.602362i \(-0.794226\pi\)
0.122549 + 0.992462i \(0.460893\pi\)
\(594\) 0.0663715 0.114959i 0.00272326 0.00471682i
\(595\) 57.2991i 2.34903i
\(596\) 8.21910i 0.336667i
\(597\) 57.2507i 2.34311i
\(598\) −0.455787 −0.0186385
\(599\) 10.2888 + 5.94021i 0.420387 + 0.242711i 0.695243 0.718775i \(-0.255297\pi\)
−0.274856 + 0.961485i \(0.588630\pi\)
\(600\) 4.23380i 0.172844i
\(601\) 38.1423 + 22.0215i 1.55586 + 0.898274i 0.997646 + 0.0685752i \(0.0218453\pi\)
0.558211 + 0.829699i \(0.311488\pi\)
\(602\) 0.182771 + 0.105523i 0.00744918 + 0.00430079i
\(603\) −26.2938 + 45.5422i −1.07077 + 1.85462i
\(604\) 20.7163 35.8817i 0.842936 1.46001i
\(605\) 19.0739 + 33.0369i 0.775463 + 1.34314i
\(606\) 1.32130 0.0536742
\(607\) −0.350397 0.606905i −0.0142222 0.0246335i 0.858827 0.512266i \(-0.171194\pi\)
−0.873049 + 0.487633i \(0.837861\pi\)
\(608\) −2.31673 1.33756i −0.0939557 0.0542454i
\(609\) 44.0937 25.4575i 1.78677 1.03159i
\(610\) −0.712291 −0.0288398
\(611\) −2.90689 + 5.03488i −0.117600 + 0.203690i
\(612\) 89.4999 3.61782
\(613\) 15.2102 + 26.3449i 0.614336 + 1.06406i 0.990501 + 0.137508i \(0.0439092\pi\)
−0.376165 + 0.926553i \(0.622757\pi\)
\(614\) 0.570842 0.329576i 0.0230373 0.0133006i
\(615\) −45.8610 + 79.4336i −1.84929 + 3.20307i
\(616\) −0.0748602 0.0432205i −0.00301620 0.00174141i
\(617\) −12.6704 21.9458i −0.510092 0.883506i −0.999932 0.0116932i \(-0.996278\pi\)
0.489839 0.871813i \(-0.337055\pi\)
\(618\) −2.08306 −0.0837930
\(619\) 33.7826i 1.35784i −0.734214 0.678918i \(-0.762449\pi\)
0.734214 0.678918i \(-0.237551\pi\)
\(620\) 18.0211 31.2134i 0.723744 1.25356i
\(621\) −43.5882 + 75.4969i −1.74913 + 3.02959i
\(622\) 0.100860 0.174695i 0.00404412 0.00700462i
\(623\) 2.71837 0.108909
\(624\) −28.2259 16.2963i −1.12994 0.652372i
\(625\) 5.14352 + 8.90884i 0.205741 + 0.356353i
\(626\) 0.913767 + 0.527564i 0.0365215 + 0.0210857i
\(627\) −2.33637 1.34891i −0.0933058 0.0538701i
\(628\) 19.4994 33.7740i 0.778112 1.34773i
\(629\) −6.93352 −0.276458
\(630\) −2.14980 3.72356i −0.0856501 0.148350i
\(631\) −22.4495 −0.893701 −0.446851 0.894609i \(-0.647454\pi\)
−0.446851 + 0.894609i \(0.647454\pi\)
\(632\) 1.58967 0.0632338
\(633\) 80.6497i 3.20554i
\(634\) −0.126460 −0.00502238
\(635\) −21.2718 + 12.2813i −0.844144 + 0.487367i
\(636\) −37.4171 21.6028i −1.48369 0.856606i
\(637\) 8.20808i 0.325216i
\(638\) −0.0306960 −0.00121527
\(639\) −76.1904 + 43.9886i −3.01405 + 1.74016i
\(640\) 4.83565i 0.191146i
\(641\) 15.2130 26.3497i 0.600878 1.04075i −0.391810 0.920046i \(-0.628151\pi\)
0.992688 0.120705i \(-0.0385156\pi\)
\(642\) −0.653725 + 1.13228i −0.0258005 + 0.0446877i
\(643\) −6.05668 + 3.49683i −0.238852 + 0.137901i −0.614649 0.788801i \(-0.710702\pi\)
0.375797 + 0.926702i \(0.377369\pi\)
\(644\) 24.5698 + 14.1854i 0.968185 + 0.558982i
\(645\) 17.8708i 0.703663i
\(646\) 1.13852i 0.0447944i
\(647\) 0.325177 + 0.563224i 0.0127840 + 0.0221426i 0.872347 0.488888i \(-0.162597\pi\)
−0.859563 + 0.511030i \(0.829264\pi\)
\(648\) 6.30390 3.63956i 0.247641 0.142975i
\(649\) 0.695451 + 1.20456i 0.0272988 + 0.0472830i
\(650\) 0.734455 0.0288077
\(651\) 57.5843i 2.25691i
\(652\) 15.2839 8.82414i 0.598562 0.345580i
\(653\) −8.60111 −0.336587 −0.168294 0.985737i \(-0.553826\pi\)
−0.168294 + 0.985737i \(0.553826\pi\)
\(654\) −0.664934 + 0.383900i −0.0260010 + 0.0150117i
\(655\) 64.9107 37.4762i 2.53627 1.46432i
\(656\) −15.3339 + 26.5592i −0.598690 + 1.03696i
\(657\) −40.6092 −1.58432
\(658\) −0.297947 + 0.172020i −0.0116152 + 0.00670604i
\(659\) 1.04842i 0.0408406i 0.999791 + 0.0204203i \(0.00650043\pi\)
−0.999791 + 0.0204203i \(0.993500\pi\)
\(660\) 3.65807i 0.142390i
\(661\) −6.85802 −0.266746 −0.133373 0.991066i \(-0.542581\pi\)
−0.133373 + 0.991066i \(0.542581\pi\)
\(662\) 0.397015 0.0154304
\(663\) 41.6796i 1.61870i
\(664\) 0.811925 + 0.468765i 0.0315088 + 0.0181916i
\(665\) −49.8236 + 28.7657i −1.93208 + 1.11549i
\(666\) −0.450573 + 0.260138i −0.0174593 + 0.0100802i
\(667\) 20.1590 0.780559
\(668\) 5.63928 3.25584i 0.218190 0.125972i
\(669\) −21.0482 36.4565i −0.813769 1.40949i
\(670\) 0.907072i 0.0350432i
\(671\) −0.721680 −0.0278602
\(672\) −2.89766 5.01890i −0.111780 0.193608i
\(673\) 1.38508 2.39903i 0.0533910 0.0924759i −0.838095 0.545525i \(-0.816330\pi\)
0.891486 + 0.453049i \(0.149664\pi\)
\(674\) −0.489091 + 0.282377i −0.0188391 + 0.0108767i
\(675\) 70.2380 121.656i 2.70346 4.68253i
\(676\) −7.32562 + 12.6883i −0.281754 + 0.488013i
\(677\) 31.0863i 1.19474i −0.801965 0.597371i \(-0.796212\pi\)
0.801965 0.597371i \(-0.203788\pi\)
\(678\) −0.600482 + 1.04006i −0.0230614 + 0.0399434i
\(679\) 25.2432 + 43.7226i 0.968746 + 1.67792i
\(680\) −2.67515 + 1.54450i −0.102587 + 0.0592287i
\(681\) −17.6250 −0.675392
\(682\) −0.0173584 + 0.0300656i −0.000664687 + 0.00115127i
\(683\) −10.7592 + 18.6355i −0.411691 + 0.713069i −0.995075 0.0991272i \(-0.968395\pi\)
0.583384 + 0.812196i \(0.301728\pi\)
\(684\) −44.9314 77.8234i −1.71799 2.97565i
\(685\) −46.8841 27.0685i −1.79135 1.03423i
\(686\) 0.250209 0.433375i 0.00955304 0.0165463i
\(687\) 38.1995i 1.45740i
\(688\) 5.97523i 0.227804i
\(689\) 7.49862 12.9880i 0.285675 0.494803i
\(690\) 2.28392i 0.0869472i
\(691\) −12.7097 7.33796i −0.483501 0.279149i 0.238374 0.971174i \(-0.423386\pi\)
−0.721874 + 0.692024i \(0.756719\pi\)
\(692\) 12.2132i 0.464277i
\(693\) −2.17814 3.77265i −0.0827406 0.143311i
\(694\) −0.782325 1.35503i −0.0296967 0.0514361i
\(695\) 6.15999 + 10.6694i 0.233662 + 0.404714i
\(696\) −2.37709 1.37242i −0.0901035 0.0520213i
\(697\) 39.2183 1.48550
\(698\) −0.790777 + 0.193974i −0.0299314 + 0.00734201i
\(699\) 58.6636 2.21886
\(700\) −39.5918 22.8583i −1.49643 0.863963i
\(701\) −6.99985 12.1241i −0.264381 0.457921i 0.703020 0.711170i \(-0.251834\pi\)
−0.967401 + 0.253249i \(0.918501\pi\)
\(702\) 1.02956 + 1.78325i 0.0388582 + 0.0673043i
\(703\) 3.48082 + 6.02895i 0.131281 + 0.227386i
\(704\) 1.22077i 0.0460095i
\(705\) −25.2294 14.5662i −0.950196 0.548596i
\(706\) 1.06320i 0.0400139i
\(707\) 14.2742 24.7237i 0.536837 0.929829i
\(708\) 62.1576i 2.33602i
\(709\) 46.1829i 1.73444i 0.497929 + 0.867218i \(0.334094\pi\)
−0.497929 + 0.867218i \(0.665906\pi\)
\(710\) 0.758749 1.31419i 0.0284753 0.0493207i
\(711\) 69.3799 + 40.0565i 2.60195 + 1.50224i
\(712\) −0.0732737 0.126914i −0.00274605 0.00475629i
\(713\) 11.3998 19.7450i 0.426925 0.739456i
\(714\) −1.23323 + 2.13601i −0.0461524 + 0.0799383i
\(715\) 1.26977 0.0474865
\(716\) −2.69889 + 1.55821i −0.100862 + 0.0582329i
\(717\) 0.881897 + 1.52749i 0.0329350 + 0.0570452i
\(718\) −0.820530 + 1.42120i −0.0306219 + 0.0530387i
\(719\) 6.76173i 0.252170i 0.992019 + 0.126085i \(0.0402412\pi\)
−0.992019 + 0.126085i \(0.959759\pi\)
\(720\) 60.8662 105.423i 2.26835 3.92890i
\(721\) −22.5036 + 38.9774i −0.838079 + 1.45160i
\(722\) 0.272828 0.157517i 0.0101536 0.00586219i
\(723\) −5.85167 + 10.1354i −0.217626 + 0.376939i
\(724\) 4.33138 + 7.50217i 0.160974 + 0.278816i
\(725\) −32.4842 −1.20643
\(726\) 1.64208i 0.0609434i
\(727\) −19.8092 34.3106i −0.734684 1.27251i −0.954862 0.297050i \(-0.903997\pi\)
0.220178 0.975460i \(-0.429336\pi\)
\(728\) 1.16123 0.670439i 0.0430382 0.0248481i
\(729\) 162.484 6.01791
\(730\) 0.606616 0.350230i 0.0224518 0.0129626i
\(731\) 6.61745 3.82059i 0.244755 0.141310i
\(732\) −27.9301 16.1255i −1.03233 0.596014i
\(733\) 28.2153i 1.04215i 0.853510 + 0.521077i \(0.174470\pi\)
−0.853510 + 0.521077i \(0.825530\pi\)
\(734\) −0.498584 −0.0184031
\(735\) −41.1301 −1.51711
\(736\) 2.29456i 0.0845787i
\(737\) 0.919029i 0.0338529i
\(738\) 2.54859 1.47143i 0.0938150 0.0541641i
\(739\) 10.3735 0.381594 0.190797 0.981629i \(-0.438893\pi\)
0.190797 + 0.981629i \(0.438893\pi\)
\(740\) −4.71978 + 8.17489i −0.173502 + 0.300515i
\(741\) 36.2419 20.9243i 1.33138 0.768673i
\(742\) 0.768585 0.443743i 0.0282157 0.0162903i
\(743\) 17.1978 0.630926 0.315463 0.948938i \(-0.397840\pi\)
0.315463 + 0.948938i \(0.397840\pi\)
\(744\) −2.68846 + 1.55218i −0.0985638 + 0.0569058i
\(745\) 14.2960i 0.523764i
\(746\) 0.0886658 0.00324629
\(747\) 23.6238 + 40.9177i 0.864351 + 1.49710i
\(748\) −1.35456 + 0.782056i −0.0495276 + 0.0285948i
\(749\) 14.1246 + 24.4645i 0.516101 + 0.893913i
\(750\) 1.08068i 0.0394608i
\(751\) 20.9053i 0.762846i 0.924401 + 0.381423i \(0.124566\pi\)
−0.924401 + 0.381423i \(0.875434\pi\)
\(752\) −8.43564 4.87032i −0.307616 0.177602i
\(753\) 42.1459 24.3329i 1.53588 0.886741i
\(754\) 0.238079 0.412365i 0.00867032 0.0150174i
\(755\) −36.0332 + 62.4113i −1.31138 + 2.27138i
\(756\) 128.171i 4.66153i
\(757\) −18.7721 + 10.8381i −0.682283 + 0.393916i −0.800715 0.599046i \(-0.795547\pi\)
0.118432 + 0.992962i \(0.462213\pi\)
\(758\) 1.30176 0.0472820
\(759\) 2.31402i 0.0839937i
\(760\) 2.68599 + 1.55076i 0.0974312 + 0.0562519i
\(761\) 7.19378 4.15333i 0.260774 0.150558i −0.363913 0.931433i \(-0.618560\pi\)
0.624688 + 0.780875i \(0.285226\pi\)
\(762\) 1.05730 0.0383020
\(763\) 16.5893i 0.600574i
\(764\) 29.1784 1.05564
\(765\) −155.673 −5.62835
\(766\) −0.0429087 0.0743200i −0.00155035 0.00268529i
\(767\) −21.5757 −0.779055
\(768\) 27.1991 47.1103i 0.981464 1.69995i
\(769\) −41.8215 24.1457i −1.50812 0.870715i −0.999955 0.00945575i \(-0.996990\pi\)
−0.508167 0.861259i \(-0.669677\pi\)
\(770\) 0.0650735 + 0.0375702i 0.00234509 + 0.00135394i
\(771\) 2.00035 + 3.46470i 0.0720407 + 0.124778i
\(772\) 2.91642 + 1.68379i 0.104964 + 0.0606010i
\(773\) −32.0059 −1.15117 −0.575586 0.817741i \(-0.695226\pi\)
−0.575586 + 0.817741i \(0.695226\pi\)
\(774\) 0.286689 0.496560i 0.0103048 0.0178485i
\(775\) −18.3696 + 31.8171i −0.659856 + 1.14290i
\(776\) 1.36086 2.35708i 0.0488521 0.0846144i
\(777\) 15.0815i 0.541046i
\(778\) 0.138998 0.00498333
\(779\) −19.6887 34.1018i −0.705420 1.22182i
\(780\) 49.1419 + 28.3721i 1.75956 + 1.01588i
\(781\) 0.768750 1.33151i 0.0275081 0.0476453i
\(782\) −0.845720 + 0.488277i −0.0302429 + 0.0174607i
\(783\) −45.5363 78.8712i −1.62733 2.81863i
\(784\) −13.7521 −0.491148
\(785\) −33.9165 + 58.7452i −1.21053 + 2.09671i
\(786\) −3.22635 −0.115080
\(787\) −24.1844 + 13.9629i −0.862081 + 0.497723i −0.864709 0.502274i \(-0.832497\pi\)
0.00262765 + 0.999997i \(0.499164\pi\)
\(788\) 39.0963 + 22.5723i 1.39275 + 0.804104i
\(789\) 23.6924 + 41.0365i 0.843473 + 1.46094i
\(790\) −1.38185 −0.0491641
\(791\) 12.9742 + 22.4720i 0.461309 + 0.799011i
\(792\) −0.117423 + 0.203383i −0.00417246 + 0.00722691i
\(793\) 5.59737 9.69492i 0.198768 0.344277i
\(794\) −0.448519 0.258952i −0.0159173 0.00918987i
\(795\) 65.0819 + 37.5751i 2.30822 + 1.33265i
\(796\) 33.3268i 1.18124i
\(797\) 36.6442 + 21.1565i 1.29800 + 0.749402i 0.980059 0.198707i \(-0.0636743\pi\)
0.317944 + 0.948110i \(0.397008\pi\)
\(798\) 2.47646 0.0876656
\(799\) 12.4564i 0.440676i
\(800\) 3.69746i 0.130725i
\(801\) 7.38539i 0.260950i
\(802\) −0.135789 + 0.235194i −0.00479489 + 0.00830499i
\(803\) 0.614612 0.354846i 0.0216892 0.0125223i
\(804\) 20.5351 35.5678i 0.724217 1.25438i
\(805\) −42.7357 24.6735i −1.50624 0.869626i
\(806\) −0.269264 0.466379i −0.00948442 0.0164275i
\(807\) 28.8757 + 50.0142i 1.01647 + 1.76058i
\(808\) −1.53905 −0.0541434
\(809\) −20.1639 34.9248i −0.708923 1.22789i −0.965257 0.261303i \(-0.915848\pi\)
0.256333 0.966588i \(-0.417486\pi\)
\(810\) −5.47978 + 3.16375i −0.192540 + 0.111163i
\(811\) −29.3237 16.9301i −1.02970 0.594495i −0.112798 0.993618i \(-0.535981\pi\)
−0.916897 + 0.399123i \(0.869315\pi\)
\(812\) −25.6679 + 14.8194i −0.900767 + 0.520058i
\(813\) −49.7616 −1.74521
\(814\) 0.00454621 0.00787427i 0.000159345 0.000275993i
\(815\) −26.5841 + 15.3484i −0.931202 + 0.537630i
\(816\) −69.8316 −2.44459
\(817\) −6.64429 3.83608i −0.232454 0.134207i
\(818\) −0.672546 0.388295i −0.0235150 0.0135764i
\(819\) 67.5748 2.36125
\(820\) 26.6967 46.2400i 0.932288 1.61477i
\(821\) −12.8795 22.3080i −0.449499 0.778555i 0.548854 0.835918i \(-0.315064\pi\)
−0.998353 + 0.0573629i \(0.981731\pi\)
\(822\) 1.16517 + 2.01814i 0.0406401 + 0.0703907i
\(823\) 26.3297 0.917794 0.458897 0.888489i \(-0.348245\pi\)
0.458897 + 0.888489i \(0.348245\pi\)
\(824\) 2.42634 0.0845256
\(825\) 3.72881i 0.129821i
\(826\) −1.10572 0.638389i −0.0384730 0.0222124i
\(827\) 38.2686 + 22.0944i 1.33073 + 0.768297i 0.985412 0.170189i \(-0.0544377\pi\)
0.345318 + 0.938486i \(0.387771\pi\)
\(828\) 38.5394 66.7523i 1.33934 2.31980i
\(829\) 37.7758i 1.31201i 0.754758 + 0.656004i \(0.227755\pi\)
−0.754758 + 0.656004i \(0.772245\pi\)
\(830\) −0.705780 0.407482i −0.0244980 0.0141439i
\(831\) 65.8956i 2.28589i
\(832\) 16.3996 + 9.46831i 0.568554 + 0.328255i
\(833\) 8.79318 + 15.2302i 0.304665 + 0.527696i
\(834\) 0.530318i 0.0183634i
\(835\) −9.80875 + 5.66308i −0.339446 + 0.195979i
\(836\) 1.36005 + 0.785227i 0.0470384 + 0.0271576i
\(837\) −103.002 −3.56027
\(838\) 0.624928 0.360802i 0.0215878 0.0124637i
\(839\) 37.3588 21.5691i 1.28977 0.744649i 0.311157 0.950359i \(-0.399284\pi\)
0.978613 + 0.205710i \(0.0659502\pi\)
\(840\) 3.35952 + 5.81886i 0.115914 + 0.200770i
\(841\) 3.97002 6.87627i 0.136897 0.237113i
\(842\) −0.482838 0.836300i −0.0166397 0.0288208i
\(843\) 31.0401 53.7631i 1.06908 1.85170i
\(844\) 46.9479i 1.61601i
\(845\) 12.7419 22.0696i 0.438334 0.759217i
\(846\) 0.467351 + 0.809476i 0.0160679 + 0.0278304i
\(847\) −30.7260 17.7397i −1.05576 0.609542i
\(848\) 21.7606 + 12.5635i 0.747262 + 0.431432i
\(849\) −34.1242 59.1049i −1.17114 2.02847i
\(850\) 1.36279 0.786809i 0.0467434 0.0269873i
\(851\) −2.98564 + 5.17127i −0.102346 + 0.177269i
\(852\) 59.5036 34.3544i 2.03856 1.17696i
\(853\) −6.59669 11.4258i −0.225866 0.391212i 0.730713 0.682685i \(-0.239188\pi\)
−0.956579 + 0.291473i \(0.905855\pi\)
\(854\) 0.573713 0.331233i 0.0196320 0.0113346i
\(855\) 78.1519 + 135.363i 2.67274 + 4.62932i
\(856\) 0.761456 1.31888i 0.0260260 0.0450784i
\(857\) 10.2273 5.90473i 0.349358 0.201702i −0.315045 0.949077i \(-0.602019\pi\)
0.664402 + 0.747375i \(0.268686\pi\)
\(858\) −0.0473347 0.0273287i −0.00161598 0.000932987i
\(859\) 9.96916 5.75570i 0.340143 0.196382i −0.320192 0.947353i \(-0.603747\pi\)
0.660335 + 0.750971i \(0.270414\pi\)
\(860\) 10.4030i 0.354739i
\(861\) 85.3060i 2.90722i
\(862\) −0.447395 0.774911i −0.0152383 0.0263936i
\(863\) −15.6693 9.04665i −0.533388 0.307952i 0.209007 0.977914i \(-0.432977\pi\)
−0.742395 + 0.669963i \(0.766310\pi\)
\(864\) −8.97738 + 5.18309i −0.305417 + 0.176332i
\(865\) 21.2432i 0.722291i
\(866\) −0.479361 −0.0162893
\(867\) 15.4748 + 26.8032i 0.525553 + 0.910284i
\(868\) 33.5210i 1.13778i
\(869\) −1.40007 −0.0474940
\(870\) 2.06633 + 1.19300i 0.0700551 + 0.0404464i
\(871\) 12.3461 + 7.12801i 0.418331 + 0.241523i
\(872\) 0.774513 0.447165i 0.0262283 0.0151429i
\(873\) 118.787 68.5819i 4.02034 2.32115i
\(874\) 0.849149 + 0.490256i 0.0287229 + 0.0165832i
\(875\) 20.2213 + 11.6747i 0.683603 + 0.394678i
\(876\) 31.7152 1.07156
\(877\) 9.53162i 0.321860i 0.986966 + 0.160930i \(0.0514493\pi\)
−0.986966 + 0.160930i \(0.948551\pi\)
\(878\) 0.0115948 + 0.0200829i 0.000391307 + 0.000677763i
\(879\) −31.2313 −1.05341
\(880\) 2.12741i 0.0717151i
\(881\) 1.81420 1.04743i 0.0611221 0.0352888i −0.469128 0.883130i \(-0.655432\pi\)
0.530250 + 0.847842i \(0.322098\pi\)
\(882\) 1.14284 + 0.659821i 0.0384816 + 0.0222173i
\(883\) −20.0918 34.8001i −0.676144 1.17112i −0.976133 0.217174i \(-0.930316\pi\)
0.299989 0.953943i \(-0.403017\pi\)
\(884\) 24.2626i 0.816039i
\(885\) 108.114i 3.63423i
\(886\) 0.0769083 0.0444031i 0.00258379 0.00149175i
\(887\) −27.2470 15.7311i −0.914864 0.528197i −0.0328711 0.999460i \(-0.510465\pi\)
−0.881993 + 0.471263i \(0.843798\pi\)
\(888\) 0.704116 0.406522i 0.0236286 0.0136420i
\(889\) 11.4222 19.7838i 0.383088 0.663527i
\(890\) 0.0636944 + 0.110322i 0.00213504 + 0.00369800i
\(891\) −5.55201 + 3.20546i −0.185999 + 0.107387i
\(892\) 12.2526 + 21.2221i 0.410247 + 0.710568i
\(893\) 10.8313 6.25346i 0.362456 0.209264i
\(894\) −0.307688 + 0.532930i −0.0102906 + 0.0178239i
\(895\) 4.69435 2.71028i 0.156915 0.0905947i
\(896\) 2.24870 + 3.89486i 0.0751237 + 0.130118i
\(897\) 31.0862 + 17.9476i 1.03794 + 0.599253i
\(898\) 0.298420 + 0.172293i 0.00995842 + 0.00574950i
\(899\) 11.9093 + 20.6275i 0.397197 + 0.687965i
\(900\) −62.1025 + 107.565i −2.07008 + 3.58549i
\(901\) 32.1326i 1.07049i
\(902\) −0.0257149 + 0.0445396i −0.000856213 + 0.00148301i
\(903\) −8.31038 14.3940i −0.276552 0.479002i
\(904\) 0.699438 1.21146i 0.0232630 0.0402927i
\(905\) −7.53383 13.0490i −0.250433 0.433763i
\(906\) 2.68651 1.55106i 0.0892535 0.0515305i
\(907\) −40.5522 + 23.4128i −1.34651 + 0.777410i −0.987754 0.156020i \(-0.950134\pi\)
−0.358760 + 0.933430i \(0.616800\pi\)
\(908\) 10.2599 0.340487
\(909\) −67.1703 38.7808i −2.22790 1.28628i
\(910\) −1.00942 + 0.582791i −0.0334620 + 0.0193193i
\(911\) 35.4798i 1.17550i 0.809043 + 0.587750i \(0.199986\pi\)
−0.809043 + 0.587750i \(0.800014\pi\)
\(912\) 35.0574 + 60.7211i 1.16087 + 2.01068i
\(913\) −0.715083 0.412853i −0.0236658 0.0136635i
\(914\) 0.574522i 0.0190035i
\(915\) 48.5806 + 28.0480i 1.60602 + 0.927238i
\(916\) 22.2368i 0.734723i
\(917\) −34.8548 + 60.3702i −1.15101 + 1.99360i
\(918\) 3.82072 + 2.20590i 0.126103 + 0.0728054i
\(919\) −48.1720 27.8121i −1.58905 0.917438i −0.993464 0.114145i \(-0.963587\pi\)
−0.595585 0.803293i \(-0.703080\pi\)
\(920\) 2.66030i 0.0877073i
\(921\) −51.9110 −1.71053
\(922\) −0.797408 −0.0262612
\(923\) 11.9249 + 20.6545i 0.392513 + 0.679852i
\(924\) 1.70109 + 2.94638i 0.0559619 + 0.0969288i
\(925\) 4.81105 8.33299i 0.158186 0.273987i
\(926\) −1.36168 −0.0447477
\(927\) 105.896 + 61.1389i 3.47807 + 2.00806i
\(928\) 2.07596 + 1.19856i 0.0681468 + 0.0393446i
\(929\) −17.2028 −0.564404 −0.282202 0.959355i \(-0.591065\pi\)
−0.282202 + 0.959355i \(0.591065\pi\)
\(930\) 2.33699 1.34926i 0.0766330 0.0442441i
\(931\) 8.82883 15.2920i 0.289353 0.501174i
\(932\) −34.1493 −1.11860
\(933\) −13.7580 + 7.94316i −0.450416 + 0.260048i
\(934\) −1.37012 0.791040i −0.0448317 0.0258836i
\(935\) 2.35607 1.36028i 0.0770517 0.0444858i
\(936\) −1.82148 3.15489i −0.0595369 0.103121i
\(937\) 3.17941 0.103867 0.0519334 0.998651i \(-0.483462\pi\)
0.0519334 + 0.998651i \(0.483462\pi\)
\(938\) 0.421811 + 0.730599i 0.0137726 + 0.0238549i
\(939\) −41.5479 71.9631i −1.35587 2.34843i
\(940\) 14.6866 + 8.47931i 0.479024 + 0.276565i
\(941\) −11.7882 + 20.4178i −0.384286 + 0.665603i −0.991670 0.128806i \(-0.958886\pi\)
0.607384 + 0.794408i \(0.292219\pi\)
\(942\) 2.52871 1.45995i 0.0823897 0.0475677i
\(943\) 16.8878 29.2505i 0.549941 0.952527i
\(944\) 36.1488i 1.17654i
\(945\) 222.936i 7.25210i
\(946\) 0.0100204i 0.000325792i
\(947\) −35.8512 −1.16501 −0.582503 0.812828i \(-0.697927\pi\)
−0.582503 + 0.812828i \(0.697927\pi\)
\(948\) −54.1847 31.2836i −1.75984 1.01604i
\(949\) 11.0088i 0.357360i
\(950\) −1.36832 0.789999i −0.0443941 0.0256310i
\(951\) 8.62501 + 4.97965i 0.279685 + 0.161476i
\(952\) 1.43646 2.48802i 0.0465559 0.0806372i
\(953\) 8.51296 14.7449i 0.275762 0.477634i −0.694565 0.719430i \(-0.744403\pi\)
0.970327 + 0.241796i \(0.0777365\pi\)
\(954\) −1.20558 2.08813i −0.0390321 0.0676056i
\(955\) −50.7518 −1.64229
\(956\) −0.513371 0.889184i −0.0166036 0.0287583i
\(957\) 2.09357 + 1.20872i 0.0676754 + 0.0390724i
\(958\) −0.579063 + 0.334322i −0.0187087 + 0.0108015i
\(959\) 50.3502 1.62589
\(960\) −47.4450 + 82.1772i −1.53128 + 2.65226i
\(961\) −4.06153 −0.131017
\(962\) 0.0705211 + 0.122146i 0.00227369 + 0.00393815i
\(963\) 66.4662 38.3743i 2.14184 1.23659i
\(964\) 3.40638 5.90003i 0.109712 0.190027i
\(965\) −5.07270 2.92872i −0.163296 0.0942790i
\(966\) 1.06208 + 1.83957i 0.0341718 + 0.0591873i
\(967\) −18.6195 −0.598762 −0.299381 0.954134i \(-0.596780\pi\)
−0.299381 + 0.954134i \(0.596780\pi\)
\(968\) 1.91269i 0.0614762i
\(969\) 44.8317 77.6507i 1.44020 2.49450i
\(970\) −1.18295 + 2.04894i −0.0379824 + 0.0657874i
\(971\) 0.808954 1.40115i 0.0259606 0.0449650i −0.852753 0.522314i \(-0.825069\pi\)
0.878714 + 0.477349i \(0.158402\pi\)
\(972\) −167.536 −5.37372
\(973\) −9.92310 5.72911i −0.318120 0.183667i
\(974\) −0.0284405 0.0492604i −0.000911293 0.00157840i
\(975\) −50.0922 28.9208i −1.60424 0.926206i
\(976\) 16.2432 + 9.37804i 0.519934 + 0.300184i
\(977\) 6.42665 11.1313i 0.205607 0.356122i −0.744719 0.667378i \(-0.767417\pi\)
0.950326 + 0.311257i \(0.100750\pi\)
\(978\) 1.32135 0.0422521
\(979\) 0.0645340 + 0.111776i 0.00206252 + 0.00357238i
\(980\) 23.9427 0.764822
\(981\) 45.0706 1.43899
\(982\) 0.334493i 0.0106741i
\(983\) −20.3939 −0.650463 −0.325231 0.945634i \(-0.605442\pi\)
−0.325231 + 0.945634i \(0.605442\pi\)
\(984\) −3.98272 + 2.29942i −0.126964 + 0.0733030i
\(985\) −68.0026 39.2613i −2.16674 1.25097i
\(986\) 1.02020i 0.0324898i
\(987\) 27.0947 0.862432
\(988\) −21.0972 + 12.1805i −0.671191 + 0.387512i
\(989\) 6.58072i 0.209255i
\(990\) 0.102072 0.176795i 0.00324407 0.00561890i
\(991\) −1.83244 + 3.17387i −0.0582093 + 0.100821i −0.893662 0.448741i \(-0.851872\pi\)
0.835452 + 0.549563i \(0.185206\pi\)
\(992\) 2.34789 1.35555i 0.0745455 0.0430389i
\(993\) −27.0777 15.6333i −0.859285 0.496109i
\(994\) 1.41135i 0.0447653i
\(995\) 57.9674i 1.83769i
\(996\) −18.4499 31.9561i −0.584606 1.01257i
\(997\) 23.3751 13.4956i 0.740297 0.427411i −0.0818800 0.996642i \(-0.526092\pi\)
0.822177 + 0.569231i \(0.192759\pi\)
\(998\) −0.948508 1.64286i −0.0300245 0.0520039i
\(999\) 26.9765 0.853499
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 349.2.e.a.227.15 yes 58
349.123 even 6 inner 349.2.e.a.123.15 58
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
349.2.e.a.123.15 58 349.123 even 6 inner
349.2.e.a.227.15 yes 58 1.1 even 1 trivial