Properties

Label 350.2.o.c.257.2
Level $350$
Weight $2$
Character 350.257
Analytic conductor $2.795$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,2,Mod(143,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.o (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: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 257.2
Root \(-0.587308 - 2.01725i\) of defining polynomial
Character \(\chi\) \(=\) 350.257
Dual form 350.2.o.c.143.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.752300 - 2.80762i) q^{3} +(0.866025 - 0.500000i) q^{4} +2.90667i q^{6} +(-2.58583 - 0.559876i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-4.71872 - 2.72435i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.752300 - 2.80762i) q^{3} +(0.866025 - 0.500000i) q^{4} +2.90667i q^{6} +(-2.58583 - 0.559876i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-4.71872 - 2.72435i) q^{9} +(-1.83557 - 3.17930i) q^{11} +(-0.752300 - 2.80762i) q^{12} +(0.830578 + 0.830578i) q^{13} +(2.64263 - 0.128464i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.761471 + 0.204036i) q^{17} +(5.26305 + 1.41023i) q^{18} +(-1.09461 + 1.89593i) q^{19} +(-3.51725 + 6.83885i) q^{21} +(2.59589 + 2.59589i) q^{22} +(-1.21791 - 4.54529i) q^{23} +(1.45333 + 2.51725i) q^{24} +(-1.01725 - 0.587308i) q^{26} +(-5.03288 + 5.03288i) q^{27} +(-2.51934 + 0.808050i) q^{28} +2.62236i q^{29} +(0.0359651 - 0.0207644i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-10.3072 + 2.76180i) q^{33} -0.788333 q^{34} -5.44871 q^{36} +(0.248174 - 0.0664979i) q^{37} +(0.566614 - 2.11463i) q^{38} +(2.95680 - 1.70711i) q^{39} -8.98026i q^{41} +(1.62737 - 7.51616i) q^{42} +(0.474569 - 0.474569i) q^{43} +(-3.17930 - 1.83557i) q^{44} +(2.35282 + 4.07520i) q^{46} +(-1.65648 - 6.18205i) q^{47} +(-2.05532 - 2.05532i) q^{48} +(6.37308 + 2.89549i) q^{49} +(1.14571 - 1.98443i) q^{51} +(1.13459 + 0.304013i) q^{52} +(7.64413 + 2.04824i) q^{53} +(3.55879 - 6.16400i) q^{54} +(2.22435 - 1.43257i) q^{56} +(4.49957 + 4.49957i) q^{57} +(-0.678717 - 2.53301i) q^{58} +(-5.35616 - 9.27713i) q^{59} +(1.72539 + 0.996157i) q^{61} +(-0.0293654 + 0.0293654i) q^{62} +(10.6765 + 9.68662i) q^{63} -1.00000i q^{64} +(9.24117 - 5.33539i) q^{66} +(1.71399 - 6.39671i) q^{67} +(0.761471 - 0.204036i) q^{68} -13.6777 q^{69} +8.11777 q^{71} +(5.26305 - 1.41023i) q^{72} +(-2.55331 + 9.52910i) q^{73} +(-0.222506 + 0.128464i) q^{74} +2.18923i q^{76} +(2.96647 + 9.24884i) q^{77} +(-2.41421 + 2.41421i) q^{78} +(11.6145 + 6.70563i) q^{79} +(2.17114 + 3.76053i) q^{81} +(2.32426 + 8.67427i) q^{82} +(-9.73033 - 9.73033i) q^{83} +(0.373402 + 7.68124i) q^{84} +(-0.335571 + 0.581226i) q^{86} +(7.36260 + 1.97280i) q^{87} +(3.54605 + 0.950161i) q^{88} +(-0.715130 + 1.23864i) q^{89} +(-1.68272 - 2.61276i) q^{91} +(-3.32739 - 3.32739i) q^{92} +(-0.0312422 - 0.116597i) q^{93} +(3.20007 + 5.54268i) q^{94} +(2.51725 + 1.45333i) q^{96} +(-3.16693 + 3.16693i) q^{97} +(-6.90533 - 1.14736i) q^{98} +20.0030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46} - 12 q^{47} - 16 q^{51} + 28 q^{53} - 4 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{61} + 36 q^{63} - 32 q^{67} + 36 q^{68} + 16 q^{71} + 8 q^{72} + 12 q^{73} - 16 q^{77} - 16 q^{78} + 48 q^{82} + 12 q^{86} + 24 q^{87} + 4 q^{88} - 16 q^{91} - 8 q^{92} - 28 q^{93} + 12 q^{96} - 40 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) 0.752300 2.80762i 0.434341 1.62098i −0.308298 0.951290i \(-0.599759\pi\)
0.742639 0.669692i \(-0.233574\pi\)
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 2.90667i 1.18664i
\(7\) −2.58583 0.559876i −0.977353 0.211613i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −4.71872 2.72435i −1.57291 0.908118i
\(10\) 0 0
\(11\) −1.83557 3.17930i −0.553445 0.958596i −0.998023 0.0628551i \(-0.979979\pi\)
0.444577 0.895741i \(-0.353354\pi\)
\(12\) −0.752300 2.80762i −0.217170 0.810491i
\(13\) 0.830578 + 0.830578i 0.230361 + 0.230361i 0.812843 0.582482i \(-0.197918\pi\)
−0.582482 + 0.812843i \(0.697918\pi\)
\(14\) 2.64263 0.128464i 0.706273 0.0343335i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.761471 + 0.204036i 0.184684 + 0.0494859i 0.349976 0.936759i \(-0.386190\pi\)
−0.165292 + 0.986245i \(0.552857\pi\)
\(18\) 5.26305 + 1.41023i 1.24051 + 0.332394i
\(19\) −1.09461 + 1.89593i −0.251122 + 0.434955i −0.963835 0.266500i \(-0.914133\pi\)
0.712713 + 0.701455i \(0.247466\pi\)
\(20\) 0 0
\(21\) −3.51725 + 6.83885i −0.767526 + 1.49236i
\(22\) 2.59589 + 2.59589i 0.553445 + 0.553445i
\(23\) −1.21791 4.54529i −0.253951 0.947759i −0.968671 0.248348i \(-0.920112\pi\)
0.714719 0.699411i \(-0.246554\pi\)
\(24\) 1.45333 + 2.51725i 0.296660 + 0.513831i
\(25\) 0 0
\(26\) −1.01725 0.587308i −0.199498 0.115180i
\(27\) −5.03288 + 5.03288i −0.968579 + 0.968579i
\(28\) −2.51934 + 0.808050i −0.476110 + 0.152707i
\(29\) 2.62236i 0.486960i 0.969906 + 0.243480i \(0.0782891\pi\)
−0.969906 + 0.243480i \(0.921711\pi\)
\(30\) 0 0
\(31\) 0.0359651 0.0207644i 0.00645952 0.00372940i −0.496767 0.867884i \(-0.665480\pi\)
0.503226 + 0.864155i \(0.332146\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) −10.3072 + 2.76180i −1.79425 + 0.480768i
\(34\) −0.788333 −0.135198
\(35\) 0 0
\(36\) −5.44871 −0.908118
\(37\) 0.248174 0.0664979i 0.0407995 0.0109322i −0.238362 0.971176i \(-0.576610\pi\)
0.279161 + 0.960244i \(0.409944\pi\)
\(38\) 0.566614 2.11463i 0.0919169 0.343038i
\(39\) 2.95680 1.70711i 0.473466 0.273356i
\(40\) 0 0
\(41\) 8.98026i 1.40248i −0.712925 0.701241i \(-0.752630\pi\)
0.712925 0.701241i \(-0.247370\pi\)
\(42\) 1.62737 7.51616i 0.251109 1.15977i
\(43\) 0.474569 0.474569i 0.0723711 0.0723711i −0.669995 0.742366i \(-0.733704\pi\)
0.742366 + 0.669995i \(0.233704\pi\)
\(44\) −3.17930 1.83557i −0.479298 0.276723i
\(45\) 0 0
\(46\) 2.35282 + 4.07520i 0.346904 + 0.600855i
\(47\) −1.65648 6.18205i −0.241622 0.901745i −0.975051 0.221980i \(-0.928748\pi\)
0.733429 0.679766i \(-0.237919\pi\)
\(48\) −2.05532 2.05532i −0.296660 0.296660i
\(49\) 6.37308 + 2.89549i 0.910440 + 0.413642i
\(50\) 0 0
\(51\) 1.14571 1.98443i 0.160432 0.277876i
\(52\) 1.13459 + 0.304013i 0.157339 + 0.0421590i
\(53\) 7.64413 + 2.04824i 1.05000 + 0.281347i 0.742252 0.670120i \(-0.233758\pi\)
0.307749 + 0.951468i \(0.400424\pi\)
\(54\) 3.55879 6.16400i 0.484289 0.838814i
\(55\) 0 0
\(56\) 2.22435 1.43257i 0.297242 0.191435i
\(57\) 4.49957 + 4.49957i 0.595982 + 0.595982i
\(58\) −0.678717 2.53301i −0.0891199 0.332600i
\(59\) −5.35616 9.27713i −0.697312 1.20778i −0.969395 0.245506i \(-0.921046\pi\)
0.272083 0.962274i \(-0.412287\pi\)
\(60\) 0 0
\(61\) 1.72539 + 0.996157i 0.220914 + 0.127545i 0.606373 0.795180i \(-0.292624\pi\)
−0.385459 + 0.922725i \(0.625957\pi\)
\(62\) −0.0293654 + 0.0293654i −0.00372940 + 0.00372940i
\(63\) 10.6765 + 9.68662i 1.34512 + 1.22040i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 9.24117 5.33539i 1.13751 0.656741i
\(67\) 1.71399 6.39671i 0.209398 0.781482i −0.778666 0.627438i \(-0.784103\pi\)
0.988064 0.154044i \(-0.0492298\pi\)
\(68\) 0.761471 0.204036i 0.0923420 0.0247430i
\(69\) −13.6777 −1.64660
\(70\) 0 0
\(71\) 8.11777 0.963402 0.481701 0.876336i \(-0.340019\pi\)
0.481701 + 0.876336i \(0.340019\pi\)
\(72\) 5.26305 1.41023i 0.620256 0.166197i
\(73\) −2.55331 + 9.52910i −0.298843 + 1.11530i 0.639274 + 0.768979i \(0.279235\pi\)
−0.938117 + 0.346318i \(0.887432\pi\)
\(74\) −0.222506 + 0.128464i −0.0258658 + 0.0149336i
\(75\) 0 0
\(76\) 2.18923i 0.251122i
\(77\) 2.96647 + 9.24884i 0.338060 + 1.05400i
\(78\) −2.41421 + 2.41421i −0.273356 + 0.273356i
\(79\) 11.6145 + 6.70563i 1.30673 + 0.754443i 0.981550 0.191208i \(-0.0612405\pi\)
0.325184 + 0.945651i \(0.394574\pi\)
\(80\) 0 0
\(81\) 2.17114 + 3.76053i 0.241238 + 0.417836i
\(82\) 2.32426 + 8.67427i 0.256672 + 0.957912i
\(83\) −9.73033 9.73033i −1.06804 1.06804i −0.997509 0.0705331i \(-0.977530\pi\)
−0.0705331 0.997509i \(-0.522470\pi\)
\(84\) 0.373402 + 7.68124i 0.0407415 + 0.838092i
\(85\) 0 0
\(86\) −0.335571 + 0.581226i −0.0361855 + 0.0626752i
\(87\) 7.36260 + 1.97280i 0.789354 + 0.211507i
\(88\) 3.54605 + 0.950161i 0.378010 + 0.101288i
\(89\) −0.715130 + 1.23864i −0.0758036 + 0.131296i −0.901435 0.432914i \(-0.857486\pi\)
0.825632 + 0.564209i \(0.190819\pi\)
\(90\) 0 0
\(91\) −1.68272 2.61276i −0.176397 0.273892i
\(92\) −3.32739 3.32739i −0.346904 0.346904i
\(93\) −0.0312422 0.116597i −0.00323967 0.0120906i
\(94\) 3.20007 + 5.54268i 0.330062 + 0.571684i
\(95\) 0 0
\(96\) 2.51725 + 1.45333i 0.256915 + 0.148330i
\(97\) −3.16693 + 3.16693i −0.321553 + 0.321553i −0.849363 0.527810i \(-0.823013\pi\)
0.527810 + 0.849363i \(0.323013\pi\)
\(98\) −6.90533 1.14736i −0.697544 0.115901i
\(99\) 20.0030i 2.01037i
\(100\) 0 0
\(101\) −0.0622734 + 0.0359536i −0.00619644 + 0.00357751i −0.503095 0.864231i \(-0.667805\pi\)
0.496899 + 0.867809i \(0.334472\pi\)
\(102\) −0.593063 + 2.21334i −0.0587220 + 0.219154i
\(103\) 16.0148 4.29116i 1.57799 0.422820i 0.639685 0.768638i \(-0.279065\pi\)
0.938302 + 0.345817i \(0.112398\pi\)
\(104\) −1.17462 −0.115180
\(105\) 0 0
\(106\) −7.91378 −0.768654
\(107\) 4.41372 1.18265i 0.426690 0.114331i −0.0390819 0.999236i \(-0.512443\pi\)
0.465772 + 0.884905i \(0.345777\pi\)
\(108\) −1.84216 + 6.87505i −0.177262 + 0.661552i
\(109\) 15.6773 9.05131i 1.50162 0.866958i 0.501617 0.865090i \(-0.332739\pi\)
0.999998 0.00186842i \(-0.000594737\pi\)
\(110\) 0 0
\(111\) 0.746804i 0.0708835i
\(112\) −1.77778 + 1.95946i −0.167985 + 0.185152i
\(113\) −1.52064 + 1.52064i −0.143049 + 0.143049i −0.775005 0.631955i \(-0.782253\pi\)
0.631955 + 0.775005i \(0.282253\pi\)
\(114\) −5.51082 3.18168i −0.516136 0.297991i
\(115\) 0 0
\(116\) 1.31118 + 2.27103i 0.121740 + 0.210860i
\(117\) −1.65648 6.18205i −0.153141 0.571531i
\(118\) 7.57475 + 7.57475i 0.697312 + 0.697312i
\(119\) −1.85480 0.953932i −0.170030 0.0874468i
\(120\) 0 0
\(121\) −1.23864 + 2.14539i −0.112604 + 0.195035i
\(122\) −1.92443 0.515649i −0.174229 0.0466846i
\(123\) −25.2132 6.75585i −2.27340 0.609155i
\(124\) 0.0207644 0.0359651i 0.00186470 0.00322976i
\(125\) 0 0
\(126\) −12.8198 6.59327i −1.14208 0.587376i
\(127\) 13.2527 + 13.2527i 1.17599 + 1.17599i 0.980757 + 0.195234i \(0.0625467\pi\)
0.195234 + 0.980757i \(0.437453\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) −0.975392 1.68943i −0.0858785 0.148746i
\(130\) 0 0
\(131\) 12.2929 + 7.09731i 1.07404 + 0.620095i 0.929281 0.369372i \(-0.120427\pi\)
0.144755 + 0.989468i \(0.453761\pi\)
\(132\) −7.54538 + 7.54538i −0.656741 + 0.656741i
\(133\) 3.89197 4.28970i 0.337477 0.371964i
\(134\) 6.62236i 0.572085i
\(135\) 0 0
\(136\) −0.682717 + 0.394167i −0.0585425 + 0.0337995i
\(137\) 4.90887 18.3201i 0.419393 1.56519i −0.356479 0.934303i \(-0.616023\pi\)
0.775871 0.630891i \(-0.217311\pi\)
\(138\) 13.2117 3.54005i 1.12465 0.301349i
\(139\) −8.23706 −0.698658 −0.349329 0.937000i \(-0.613591\pi\)
−0.349329 + 0.937000i \(0.613591\pi\)
\(140\) 0 0
\(141\) −18.6030 −1.56666
\(142\) −7.84116 + 2.10103i −0.658016 + 0.176315i
\(143\) 1.11607 4.16524i 0.0933308 0.348315i
\(144\) −4.71872 + 2.72435i −0.393227 + 0.227029i
\(145\) 0 0
\(146\) 9.86525i 0.816454i
\(147\) 12.9239 15.7149i 1.06595 1.29614i
\(148\) 0.181676 0.181676i 0.0149336 0.0149336i
\(149\) −4.19317 2.42093i −0.343518 0.198330i 0.318309 0.947987i \(-0.396885\pi\)
−0.661826 + 0.749657i \(0.730218\pi\)
\(150\) 0 0
\(151\) −5.02292 8.69995i −0.408759 0.707992i 0.585992 0.810317i \(-0.300705\pi\)
−0.994751 + 0.102325i \(0.967372\pi\)
\(152\) −0.566614 2.11463i −0.0459584 0.171519i
\(153\) −3.03730 3.03730i −0.245551 0.245551i
\(154\) −5.25916 8.16592i −0.423795 0.658028i
\(155\) 0 0
\(156\) 1.70711 2.95680i 0.136678 0.236733i
\(157\) −23.6523 6.33762i −1.88766 0.505797i −0.998872 0.0474774i \(-0.984882\pi\)
−0.888788 0.458320i \(-0.848452\pi\)
\(158\) −12.9543 3.47109i −1.03059 0.276145i
\(159\) 11.5014 19.9209i 0.912117 1.57983i
\(160\) 0 0
\(161\) 0.604505 + 12.4353i 0.0476417 + 0.980035i
\(162\) −3.07046 3.07046i −0.241238 0.241238i
\(163\) 5.68510 + 21.2171i 0.445291 + 1.66185i 0.715166 + 0.698954i \(0.246351\pi\)
−0.269875 + 0.962895i \(0.586982\pi\)
\(164\) −4.49013 7.77713i −0.350620 0.607292i
\(165\) 0 0
\(166\) 11.9172 + 6.88038i 0.924952 + 0.534021i
\(167\) −3.14616 + 3.14616i −0.243457 + 0.243457i −0.818279 0.574821i \(-0.805072\pi\)
0.574821 + 0.818279i \(0.305072\pi\)
\(168\) −2.34873 7.32287i −0.181209 0.564972i
\(169\) 11.6203i 0.893868i
\(170\) 0 0
\(171\) 10.3303 5.96423i 0.789981 0.456096i
\(172\) 0.173704 0.648273i 0.0132448 0.0494304i
\(173\) 5.04844 1.35273i 0.383826 0.102846i −0.0617463 0.998092i \(-0.519667\pi\)
0.445572 + 0.895246i \(0.353000\pi\)
\(174\) −7.62233 −0.577847
\(175\) 0 0
\(176\) −3.67114 −0.276723
\(177\) −30.0761 + 8.05888i −2.26066 + 0.605742i
\(178\) 0.370178 1.38152i 0.0277460 0.103550i
\(179\) −10.8847 + 6.28428i −0.813560 + 0.469709i −0.848191 0.529691i \(-0.822308\pi\)
0.0346308 + 0.999400i \(0.488974\pi\)
\(180\) 0 0
\(181\) 11.6742i 0.867740i 0.900976 + 0.433870i \(0.142852\pi\)
−0.900976 + 0.433870i \(0.857148\pi\)
\(182\) 2.30161 + 2.08821i 0.170607 + 0.154789i
\(183\) 4.09485 4.09485i 0.302700 0.302700i
\(184\) 4.07520 + 2.35282i 0.300428 + 0.173452i
\(185\) 0 0
\(186\) 0.0603553 + 0.104538i 0.00442546 + 0.00766513i
\(187\) −0.749044 2.79547i −0.0547755 0.204425i
\(188\) −4.52558 4.52558i −0.330062 0.330062i
\(189\) 15.8320 10.1964i 1.15161 0.741680i
\(190\) 0 0
\(191\) −7.75170 + 13.4263i −0.560894 + 0.971496i 0.436525 + 0.899692i \(0.356209\pi\)
−0.997419 + 0.0718040i \(0.977124\pi\)
\(192\) −2.80762 0.752300i −0.202623 0.0542926i
\(193\) 8.69132 + 2.32883i 0.625615 + 0.167633i 0.557679 0.830057i \(-0.311692\pi\)
0.0679359 + 0.997690i \(0.478359\pi\)
\(194\) 2.23936 3.87868i 0.160776 0.278473i
\(195\) 0 0
\(196\) 6.96699 0.678966i 0.497642 0.0484976i
\(197\) −12.1951 12.1951i −0.868865 0.868865i 0.123482 0.992347i \(-0.460594\pi\)
−0.992347 + 0.123482i \(0.960594\pi\)
\(198\) −5.17715 19.3214i −0.367924 1.37311i
\(199\) −4.36557 7.56140i −0.309467 0.536013i 0.668779 0.743462i \(-0.266817\pi\)
−0.978246 + 0.207448i \(0.933484\pi\)
\(200\) 0 0
\(201\) −16.6701 9.62450i −1.17582 0.678860i
\(202\) 0.0508460 0.0508460i 0.00357751 0.00357751i
\(203\) 1.46820 6.78099i 0.103047 0.475932i
\(204\) 2.29142i 0.160432i
\(205\) 0 0
\(206\) −14.3585 + 8.28988i −1.00040 + 0.577583i
\(207\) −6.63602 + 24.7660i −0.461235 + 1.72135i
\(208\) 1.13459 0.304013i 0.0786697 0.0210795i
\(209\) 8.03696 0.555928
\(210\) 0 0
\(211\) −11.1745 −0.769288 −0.384644 0.923065i \(-0.625676\pi\)
−0.384644 + 0.923065i \(0.625676\pi\)
\(212\) 7.64413 2.04824i 0.525001 0.140674i
\(213\) 6.10700 22.7916i 0.418445 1.56166i
\(214\) −3.95723 + 2.28471i −0.270511 + 0.156179i
\(215\) 0 0
\(216\) 7.11757i 0.484289i
\(217\) −0.104625 + 0.0335574i −0.00710242 + 0.00227803i
\(218\) −12.8005 + 12.8005i −0.866958 + 0.866958i
\(219\) 24.8333 + 14.3375i 1.67808 + 0.968838i
\(220\) 0 0
\(221\) 0.462994 + 0.801929i 0.0311443 + 0.0539436i
\(222\) 0.193287 + 0.721358i 0.0129726 + 0.0484143i
\(223\) 0.746804 + 0.746804i 0.0500097 + 0.0500097i 0.731669 0.681660i \(-0.238742\pi\)
−0.681660 + 0.731669i \(0.738742\pi\)
\(224\) 1.21006 2.35282i 0.0808507 0.157204i
\(225\) 0 0
\(226\) 1.07525 1.86239i 0.0715247 0.123884i
\(227\) 3.01404 + 0.807609i 0.200049 + 0.0536029i 0.357452 0.933932i \(-0.383646\pi\)
−0.157403 + 0.987534i \(0.550312\pi\)
\(228\) 6.14653 + 1.64696i 0.407064 + 0.109072i
\(229\) −4.21091 + 7.29350i −0.278264 + 0.481968i −0.970954 0.239268i \(-0.923093\pi\)
0.692689 + 0.721236i \(0.256426\pi\)
\(230\) 0 0
\(231\) 28.1989 1.37081i 1.85535 0.0901928i
\(232\) −1.85429 1.85429i −0.121740 0.121740i
\(233\) 5.90027 + 22.0201i 0.386540 + 1.44259i 0.835725 + 0.549148i \(0.185048\pi\)
−0.449186 + 0.893439i \(0.648286\pi\)
\(234\) 3.20007 + 5.54268i 0.209195 + 0.362336i
\(235\) 0 0
\(236\) −9.27713 5.35616i −0.603890 0.348656i
\(237\) 27.5645 27.5645i 1.79051 1.79051i
\(238\) 2.03850 + 0.441369i 0.132136 + 0.0286097i
\(239\) 23.9971i 1.55224i 0.630585 + 0.776120i \(0.282815\pi\)
−0.630585 + 0.776120i \(0.717185\pi\)
\(240\) 0 0
\(241\) −21.4666 + 12.3937i −1.38278 + 0.798350i −0.992488 0.122340i \(-0.960960\pi\)
−0.390295 + 0.920690i \(0.627627\pi\)
\(242\) 0.641168 2.39287i 0.0412158 0.153820i
\(243\) −8.43364 + 2.25979i −0.541018 + 0.144965i
\(244\) 1.99231 0.127545
\(245\) 0 0
\(246\) 26.1026 1.66424
\(247\) −2.48388 + 0.665553i −0.158045 + 0.0423481i
\(248\) −0.0107485 + 0.0401138i −0.000682528 + 0.00254723i
\(249\) −34.6392 + 19.9990i −2.19517 + 1.26738i
\(250\) 0 0
\(251\) 11.1158i 0.701623i −0.936446 0.350811i \(-0.885906\pi\)
0.936446 0.350811i \(-0.114094\pi\)
\(252\) 14.0895 + 3.05060i 0.887552 + 0.192170i
\(253\) −12.2153 + 12.2153i −0.767970 + 0.767970i
\(254\) −16.2312 9.37110i −1.01844 0.587995i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.54637 + 24.4314i 0.408351 + 1.52399i 0.797790 + 0.602935i \(0.206002\pi\)
−0.389439 + 0.921052i \(0.627331\pi\)
\(258\) 1.37941 + 1.37941i 0.0858785 + 0.0858785i
\(259\) −0.678966 + 0.0330060i −0.0421889 + 0.00205090i
\(260\) 0 0
\(261\) 7.14424 12.3742i 0.442217 0.765943i
\(262\) −13.7110 3.67384i −0.847066 0.226971i
\(263\) 10.9595 + 2.93659i 0.675792 + 0.181078i 0.580363 0.814358i \(-0.302911\pi\)
0.0954297 + 0.995436i \(0.469577\pi\)
\(264\) 5.33539 9.24117i 0.328371 0.568755i
\(265\) 0 0
\(266\) −2.64910 + 5.15085i −0.162427 + 0.315819i
\(267\) 2.93964 + 2.93964i 0.179903 + 0.179903i
\(268\) −1.71399 6.39671i −0.104699 0.390741i
\(269\) 4.03346 + 6.98616i 0.245924 + 0.425954i 0.962391 0.271668i \(-0.0875752\pi\)
−0.716467 + 0.697621i \(0.754242\pi\)
\(270\) 0 0
\(271\) 7.27419 + 4.19976i 0.441876 + 0.255117i 0.704393 0.709810i \(-0.251219\pi\)
−0.262517 + 0.964927i \(0.584553\pi\)
\(272\) 0.557436 0.557436i 0.0337995 0.0337995i
\(273\) −8.60155 + 2.75885i −0.520590 + 0.166974i
\(274\) 18.9664i 1.14580i
\(275\) 0 0
\(276\) −11.8452 + 6.83885i −0.713000 + 0.411651i
\(277\) −1.47009 + 5.48646i −0.0883293 + 0.329650i −0.995924 0.0901983i \(-0.971250\pi\)
0.907594 + 0.419848i \(0.137917\pi\)
\(278\) 7.95639 2.13191i 0.477193 0.127863i
\(279\) −0.226279 −0.0135470
\(280\) 0 0
\(281\) 7.27627 0.434066 0.217033 0.976164i \(-0.430362\pi\)
0.217033 + 0.976164i \(0.430362\pi\)
\(282\) 17.9692 4.81482i 1.07005 0.286719i
\(283\) 1.99550 7.44729i 0.118620 0.442696i −0.880912 0.473280i \(-0.843070\pi\)
0.999532 + 0.0305840i \(0.00973671\pi\)
\(284\) 7.03019 4.05888i 0.417165 0.240850i
\(285\) 0 0
\(286\) 4.31218i 0.254984i
\(287\) −5.02784 + 23.2215i −0.296784 + 1.37072i
\(288\) 3.85282 3.85282i 0.227029 0.227029i
\(289\) −14.1842 8.18927i −0.834366 0.481721i
\(290\) 0 0
\(291\) 6.50906 + 11.2740i 0.381568 + 0.660895i
\(292\) 2.55331 + 9.52910i 0.149421 + 0.557648i
\(293\) 3.35198 + 3.35198i 0.195824 + 0.195824i 0.798207 0.602383i \(-0.205782\pi\)
−0.602383 + 0.798207i \(0.705782\pi\)
\(294\) −8.41624 + 18.5244i −0.490845 + 1.08037i
\(295\) 0 0
\(296\) −0.128464 + 0.222506i −0.00746682 + 0.0129329i
\(297\) 25.2393 + 6.76284i 1.46453 + 0.392420i
\(298\) 4.67687 + 1.25316i 0.270924 + 0.0725938i
\(299\) 2.76365 4.78679i 0.159826 0.276827i
\(300\) 0 0
\(301\) −1.49286 + 0.961456i −0.0860468 + 0.0554174i
\(302\) 7.10348 + 7.10348i 0.408759 + 0.408759i
\(303\) 0.0540958 + 0.201888i 0.00310772 + 0.0115982i
\(304\) 1.09461 + 1.89593i 0.0627804 + 0.108739i
\(305\) 0 0
\(306\) 3.71992 + 2.14770i 0.212654 + 0.122776i
\(307\) −1.06546 + 1.06546i −0.0608089 + 0.0608089i −0.736857 0.676048i \(-0.763691\pi\)
0.676048 + 0.736857i \(0.263691\pi\)
\(308\) 7.19345 + 6.52650i 0.409885 + 0.371882i
\(309\) 48.1918i 2.74154i
\(310\) 0 0
\(311\) 11.9584 6.90417i 0.678097 0.391500i −0.121040 0.992648i \(-0.538623\pi\)
0.799138 + 0.601148i \(0.205290\pi\)
\(312\) −0.883663 + 3.29788i −0.0500276 + 0.186706i
\(313\) −22.5515 + 6.04266i −1.27469 + 0.341551i −0.831825 0.555038i \(-0.812704\pi\)
−0.442863 + 0.896590i \(0.646037\pi\)
\(314\) 24.4867 1.38186
\(315\) 0 0
\(316\) 13.4113 0.754443
\(317\) 12.7394 3.41352i 0.715518 0.191722i 0.117347 0.993091i \(-0.462561\pi\)
0.598171 + 0.801369i \(0.295894\pi\)
\(318\) −5.95354 + 22.2189i −0.333858 + 1.24598i
\(319\) 8.33728 4.81353i 0.466798 0.269506i
\(320\) 0 0
\(321\) 13.2818i 0.741316i
\(322\) −3.80239 11.8551i −0.211899 0.660658i
\(323\) −1.22035 + 1.22035i −0.0679023 + 0.0679023i
\(324\) 3.76053 + 2.17114i 0.208918 + 0.120619i
\(325\) 0 0
\(326\) −10.9828 19.0227i −0.608279 1.05357i
\(327\) −13.6186 50.8253i −0.753111 2.81065i
\(328\) 6.35000 + 6.35000i 0.350620 + 0.350620i
\(329\) 0.822187 + 16.9132i 0.0453286 + 0.932454i
\(330\) 0 0
\(331\) 9.54799 16.5376i 0.524805 0.908989i −0.474778 0.880106i \(-0.657472\pi\)
0.999583 0.0288830i \(-0.00919501\pi\)
\(332\) −13.2919 3.56155i −0.729487 0.195465i
\(333\) −1.35222 0.362328i −0.0741015 0.0198554i
\(334\) 2.22467 3.85325i 0.121729 0.210840i
\(335\) 0 0
\(336\) 4.16400 + 6.46545i 0.227165 + 0.352719i
\(337\) −0.488226 0.488226i −0.0265953 0.0265953i 0.693684 0.720279i \(-0.255986\pi\)
−0.720279 + 0.693684i \(0.755986\pi\)
\(338\) 3.00755 + 11.2243i 0.163589 + 0.610523i
\(339\) 3.12540 + 5.41335i 0.169748 + 0.294013i
\(340\) 0 0
\(341\) −0.132033 0.0762292i −0.00714998 0.00412804i
\(342\) −8.43469 + 8.43469i −0.456096 + 0.456096i
\(343\) −14.8586 11.0554i −0.802289 0.596936i
\(344\) 0.671142i 0.0361855i
\(345\) 0 0
\(346\) −4.52631 + 2.61327i −0.243336 + 0.140490i
\(347\) −0.986094 + 3.68015i −0.0529363 + 0.197561i −0.987330 0.158682i \(-0.949276\pi\)
0.934393 + 0.356243i \(0.115942\pi\)
\(348\) 7.36260 1.97280i 0.394677 0.105753i
\(349\) 7.91303 0.423575 0.211787 0.977316i \(-0.432072\pi\)
0.211787 + 0.977316i \(0.432072\pi\)
\(350\) 0 0
\(351\) −8.36041 −0.446246
\(352\) 3.54605 0.950161i 0.189005 0.0506438i
\(353\) 6.67203 24.9004i 0.355116 1.32531i −0.525222 0.850965i \(-0.676018\pi\)
0.880338 0.474347i \(-0.157316\pi\)
\(354\) 26.9655 15.5686i 1.43320 0.827459i
\(355\) 0 0
\(356\) 1.43026i 0.0758036i
\(357\) −4.07365 + 4.48995i −0.215601 + 0.237633i
\(358\) 8.88731 8.88731i 0.469709 0.469709i
\(359\) −8.99497 5.19325i −0.474737 0.274089i 0.243484 0.969905i \(-0.421710\pi\)
−0.718220 + 0.695816i \(0.755043\pi\)
\(360\) 0 0
\(361\) 7.10364 + 12.3039i 0.373876 + 0.647572i
\(362\) −3.02152 11.2765i −0.158807 0.592677i
\(363\) 5.09161 + 5.09161i 0.267240 + 0.267240i
\(364\) −2.76365 1.42136i −0.144855 0.0744994i
\(365\) 0 0
\(366\) −2.89549 + 5.01514i −0.151350 + 0.262146i
\(367\) 8.39004 + 2.24811i 0.437957 + 0.117350i 0.471059 0.882102i \(-0.343872\pi\)
−0.0331020 + 0.999452i \(0.510539\pi\)
\(368\) −4.54529 1.21791i −0.236940 0.0634878i
\(369\) −24.4654 + 42.3753i −1.27362 + 2.20597i
\(370\) 0 0
\(371\) −18.6197 9.57617i −0.966686 0.497170i
\(372\) −0.0853553 0.0853553i −0.00442546 0.00442546i
\(373\) −3.44476 12.8560i −0.178363 0.665660i −0.995954 0.0898611i \(-0.971358\pi\)
0.817591 0.575799i \(-0.195309\pi\)
\(374\) 1.44704 + 2.50635i 0.0748247 + 0.129600i
\(375\) 0 0
\(376\) 5.54268 + 3.20007i 0.285842 + 0.165031i
\(377\) −2.17808 + 2.17808i −0.112177 + 0.112177i
\(378\) −12.6535 + 13.9466i −0.650826 + 0.717336i
\(379\) 25.3453i 1.30190i −0.759121 0.650949i \(-0.774371\pi\)
0.759121 0.650949i \(-0.225629\pi\)
\(380\) 0 0
\(381\) 47.1788 27.2387i 2.41704 1.39548i
\(382\) 4.01258 14.9751i 0.205301 0.766195i
\(383\) −17.7739 + 4.76251i −0.908205 + 0.243353i −0.682537 0.730851i \(-0.739123\pi\)
−0.225668 + 0.974204i \(0.572457\pi\)
\(384\) 2.90667 0.148330
\(385\) 0 0
\(386\) −8.99792 −0.457982
\(387\) −3.53225 + 0.946464i −0.179554 + 0.0481114i
\(388\) −1.15918 + 4.32611i −0.0588483 + 0.219625i
\(389\) 19.3621 11.1787i 0.981699 0.566784i 0.0789164 0.996881i \(-0.474854\pi\)
0.902783 + 0.430097i \(0.141521\pi\)
\(390\) 0 0
\(391\) 3.70961i 0.187603i
\(392\) −6.55387 + 2.45902i −0.331020 + 0.124199i
\(393\) 29.1745 29.1745i 1.47166 1.47166i
\(394\) 14.9359 + 8.62324i 0.752459 + 0.434432i
\(395\) 0 0
\(396\) 10.0015 + 17.3231i 0.502594 + 0.870518i
\(397\) 4.08518 + 15.2461i 0.205029 + 0.765181i 0.989441 + 0.144939i \(0.0462987\pi\)
−0.784411 + 0.620241i \(0.787035\pi\)
\(398\) 6.17385 + 6.17385i 0.309467 + 0.309467i
\(399\) −9.11594 14.1543i −0.456368 0.708603i
\(400\) 0 0
\(401\) −6.98528 + 12.0989i −0.348828 + 0.604188i −0.986042 0.166499i \(-0.946754\pi\)
0.637213 + 0.770687i \(0.280087\pi\)
\(402\) 18.5931 + 4.98201i 0.927339 + 0.248480i
\(403\) 0.0471183 + 0.0126253i 0.00234713 + 0.000628911i
\(404\) −0.0359536 + 0.0622734i −0.00178876 + 0.00309822i
\(405\) 0 0
\(406\) 0.336879 + 6.92993i 0.0167190 + 0.343927i
\(407\) −0.666957 0.666957i −0.0330598 0.0330598i
\(408\) 0.593063 + 2.21334i 0.0293610 + 0.109577i
\(409\) 0.156681 + 0.271379i 0.00774737 + 0.0134188i 0.869873 0.493276i \(-0.164201\pi\)
−0.862126 + 0.506694i \(0.830867\pi\)
\(410\) 0 0
\(411\) −47.7431 27.5645i −2.35499 1.35966i
\(412\) 11.7237 11.7237i 0.577583 0.577583i
\(413\) 8.65608 + 26.9879i 0.425938 + 1.32799i
\(414\) 25.6396i 1.26012i
\(415\) 0 0
\(416\) −1.01725 + 0.587308i −0.0498746 + 0.0287951i
\(417\) −6.19675 + 23.1266i −0.303456 + 1.13251i
\(418\) −7.76311 + 2.08012i −0.379706 + 0.101742i
\(419\) −31.6254 −1.54500 −0.772501 0.635014i \(-0.780994\pi\)
−0.772501 + 0.635014i \(0.780994\pi\)
\(420\) 0 0
\(421\) 24.2137 1.18011 0.590053 0.807365i \(-0.299107\pi\)
0.590053 + 0.807365i \(0.299107\pi\)
\(422\) 10.7938 2.89219i 0.525433 0.140789i
\(423\) −9.02565 + 33.6842i −0.438842 + 1.63778i
\(424\) −6.85354 + 3.95689i −0.332837 + 0.192164i
\(425\) 0 0
\(426\) 23.5956i 1.14321i
\(427\) −3.90386 3.54190i −0.188921 0.171405i
\(428\) 3.23107 3.23107i 0.156179 0.156179i
\(429\) −10.8548 6.26703i −0.524075 0.302575i
\(430\) 0 0
\(431\) −0.779037 1.34933i −0.0375249 0.0649950i 0.846653 0.532145i \(-0.178614\pi\)
−0.884178 + 0.467150i \(0.845281\pi\)
\(432\) 1.84216 + 6.87505i 0.0886311 + 0.330776i
\(433\) 6.28166 + 6.28166i 0.301877 + 0.301877i 0.841748 0.539871i \(-0.181527\pi\)
−0.539871 + 0.841748i \(0.681527\pi\)
\(434\) 0.0923749 0.0594930i 0.00443414 0.00285575i
\(435\) 0 0
\(436\) 9.05131 15.6773i 0.433479 0.750808i
\(437\) 9.95068 + 2.66628i 0.476006 + 0.127545i
\(438\) −27.6979 7.42163i −1.32346 0.354619i
\(439\) −11.9571 + 20.7103i −0.570681 + 0.988449i 0.425815 + 0.904810i \(0.359988\pi\)
−0.996496 + 0.0836389i \(0.973346\pi\)
\(440\) 0 0
\(441\) −22.1844 31.0255i −1.05640 1.47741i
\(442\) −0.654772 0.654772i −0.0311443 0.0311443i
\(443\) −3.32895 12.4238i −0.158163 0.590272i −0.998814 0.0486946i \(-0.984494\pi\)
0.840651 0.541578i \(-0.182173\pi\)
\(444\) −0.373402 0.646751i −0.0177209 0.0306935i
\(445\) 0 0
\(446\) −0.914645 0.528070i −0.0433097 0.0250049i
\(447\) −9.95157 + 9.95157i −0.470693 + 0.470693i
\(448\) −0.559876 + 2.58583i −0.0264517 + 0.122169i
\(449\) 17.8932i 0.844435i 0.906495 + 0.422217i \(0.138748\pi\)
−0.906495 + 0.422217i \(0.861252\pi\)
\(450\) 0 0
\(451\) −28.5510 + 16.4839i −1.34441 + 0.776197i
\(452\) −0.556592 + 2.07723i −0.0261799 + 0.0977046i
\(453\) −28.2049 + 7.55749i −1.32518 + 0.355082i
\(454\) −3.12036 −0.146446
\(455\) 0 0
\(456\) −6.36335 −0.297991
\(457\) 33.0454 8.85449i 1.54580 0.414196i 0.617665 0.786442i \(-0.288079\pi\)
0.928134 + 0.372246i \(0.121412\pi\)
\(458\) 2.17973 8.13485i 0.101852 0.380116i
\(459\) −4.85928 + 2.80551i −0.226812 + 0.130950i
\(460\) 0 0
\(461\) 23.3471i 1.08738i 0.839286 + 0.543690i \(0.182973\pi\)
−0.839286 + 0.543690i \(0.817027\pi\)
\(462\) −26.8833 + 8.62252i −1.25072 + 0.401156i
\(463\) −3.98510 + 3.98510i −0.185203 + 0.185203i −0.793619 0.608415i \(-0.791805\pi\)
0.608415 + 0.793619i \(0.291805\pi\)
\(464\) 2.27103 + 1.31118i 0.105430 + 0.0608700i
\(465\) 0 0
\(466\) −11.3985 19.7427i −0.528023 0.914563i
\(467\) 1.26454 + 4.71932i 0.0585159 + 0.218384i 0.988992 0.147968i \(-0.0472732\pi\)
−0.930476 + 0.366352i \(0.880607\pi\)
\(468\) −4.52558 4.52558i −0.209195 0.209195i
\(469\) −8.01347 + 15.5812i −0.370028 + 0.719473i
\(470\) 0 0
\(471\) −35.5873 + 61.6390i −1.63978 + 2.84017i
\(472\) 10.3473 + 2.77255i 0.476273 + 0.127617i
\(473\) −2.37990 0.637693i −0.109428 0.0293212i
\(474\) −19.4910 + 33.7595i −0.895253 + 1.55062i
\(475\) 0 0
\(476\) −2.08327 + 0.101272i −0.0954867 + 0.00464182i
\(477\) −30.4904 30.4904i −1.39606 1.39606i
\(478\) −6.21090 23.1794i −0.284080 1.06020i
\(479\) 8.55572 + 14.8189i 0.390921 + 0.677094i 0.992571 0.121665i \(-0.0388234\pi\)
−0.601651 + 0.798759i \(0.705490\pi\)
\(480\) 0 0
\(481\) 0.261359 + 0.150896i 0.0119170 + 0.00688026i
\(482\) 17.5274 17.5274i 0.798350 0.798350i
\(483\) 35.3683 + 7.65783i 1.60931 + 0.348443i
\(484\) 2.47728i 0.112604i
\(485\) 0 0
\(486\) 7.56140 4.36557i 0.342992 0.198026i
\(487\) −0.0337240 + 0.125860i −0.00152818 + 0.00570325i −0.966686 0.255966i \(-0.917606\pi\)
0.965158 + 0.261670i \(0.0842731\pi\)
\(488\) −1.92443 + 0.515649i −0.0871147 + 0.0233423i
\(489\) 63.8465 2.88724
\(490\) 0 0
\(491\) 26.9895 1.21802 0.609011 0.793162i \(-0.291567\pi\)
0.609011 + 0.793162i \(0.291567\pi\)
\(492\) −25.2132 + 6.75585i −1.13670 + 0.304577i
\(493\) −0.535055 + 1.99685i −0.0240977 + 0.0899337i
\(494\) 2.22698 1.28575i 0.100197 0.0578486i
\(495\) 0 0
\(496\) 0.0415289i 0.00186470i
\(497\) −20.9912 4.54495i −0.941584 0.203869i
\(498\) 28.2828 28.2828i 1.26738 1.26738i
\(499\) 0.0833977 + 0.0481497i 0.00373339 + 0.00215548i 0.501866 0.864946i \(-0.332647\pi\)
−0.498132 + 0.867101i \(0.665981\pi\)
\(500\) 0 0
\(501\) 6.46638 + 11.2001i 0.288897 + 0.500384i
\(502\) 2.87698 + 10.7370i 0.128406 + 0.479217i
\(503\) −13.6334 13.6334i −0.607883 0.607883i 0.334509 0.942392i \(-0.391429\pi\)
−0.942392 + 0.334509i \(0.891429\pi\)
\(504\) −14.3989 + 0.699963i −0.641379 + 0.0311788i
\(505\) 0 0
\(506\) 8.63753 14.9606i 0.383985 0.665081i
\(507\) −32.6254 8.74194i −1.44894 0.388243i
\(508\) 18.1036 + 4.85084i 0.803217 + 0.215221i
\(509\) 6.16366 10.6758i 0.273199 0.473195i −0.696480 0.717576i \(-0.745251\pi\)
0.969679 + 0.244381i \(0.0785848\pi\)
\(510\) 0 0
\(511\) 11.9376 23.2111i 0.528087 1.02680i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −4.03291 15.0510i −0.178057 0.664520i
\(514\) −12.6466 21.9046i −0.557818 0.966169i
\(515\) 0 0
\(516\) −1.68943 0.975392i −0.0743730 0.0429393i
\(517\) −16.6140 + 16.6140i −0.730684 + 0.730684i
\(518\) 0.647288 0.207611i 0.0284402 0.00912189i
\(519\) 15.1918i 0.666845i
\(520\) 0 0
\(521\) 14.1415 8.16461i 0.619551 0.357698i −0.157143 0.987576i \(-0.550228\pi\)
0.776694 + 0.629878i \(0.216895\pi\)
\(522\) −3.69813 + 13.8016i −0.161863 + 0.604080i
\(523\) 26.4703 7.09270i 1.15747 0.310142i 0.371512 0.928428i \(-0.378839\pi\)
0.785953 + 0.618286i \(0.212173\pi\)
\(524\) 14.1946 0.620095
\(525\) 0 0
\(526\) −11.3461 −0.494714
\(527\) 0.0316231 0.00847337i 0.00137752 0.000369106i
\(528\) −2.76180 + 10.3072i −0.120192 + 0.448563i
\(529\) 0.742186 0.428501i 0.0322689 0.0186305i
\(530\) 0 0
\(531\) 58.3682i 2.53297i
\(532\) 1.22570 5.66098i 0.0531407 0.245435i
\(533\) 7.45881 7.45881i 0.323077 0.323077i
\(534\) −3.60031 2.07864i −0.155801 0.0899517i
\(535\) 0 0
\(536\) 3.31118 + 5.73513i 0.143021 + 0.247720i
\(537\) 9.45533 + 35.2878i 0.408028 + 1.52278i
\(538\) −5.70417 5.70417i −0.245924 0.245924i
\(539\) −2.49258 25.5768i −0.107363 1.10167i
\(540\) 0 0
\(541\) 20.5773 35.6410i 0.884689 1.53233i 0.0386200 0.999254i \(-0.487704\pi\)
0.846069 0.533073i \(-0.178963\pi\)
\(542\) −8.11330 2.17395i −0.348496 0.0933793i
\(543\) 32.7769 + 8.78254i 1.40659 + 0.376895i
\(544\) −0.394167 + 0.682717i −0.0168998 + 0.0292712i
\(545\) 0 0
\(546\) 7.59442 4.89109i 0.325011 0.209320i
\(547\) −8.06541 8.06541i −0.344852 0.344852i 0.513336 0.858188i \(-0.328410\pi\)
−0.858188 + 0.513336i \(0.828410\pi\)
\(548\) −4.90887 18.3201i −0.209696 0.782597i
\(549\) −5.42777 9.40117i −0.231651 0.401232i
\(550\) 0 0
\(551\) −4.97180 2.87047i −0.211806 0.122286i
\(552\) 9.67160 9.67160i 0.411651 0.411651i
\(553\) −26.2788 23.8423i −1.11749 1.01388i
\(554\) 5.68000i 0.241320i
\(555\) 0 0
\(556\) −7.13350 + 4.11853i −0.302528 + 0.174665i
\(557\) 6.64049 24.7826i 0.281367 1.05007i −0.670087 0.742282i \(-0.733743\pi\)
0.951454 0.307792i \(-0.0995901\pi\)
\(558\) 0.218568 0.0585652i 0.00925274 0.00247926i
\(559\) 0.788333 0.0333429
\(560\) 0 0
\(561\) −8.41213 −0.355160
\(562\) −7.02834 + 1.88324i −0.296473 + 0.0794396i
\(563\) 3.31584 12.3749i 0.139746 0.521539i −0.860187 0.509978i \(-0.829653\pi\)
0.999933 0.0115606i \(-0.00367993\pi\)
\(564\) −16.1107 + 9.30152i −0.678383 + 0.391665i
\(565\) 0 0
\(566\) 7.71000i 0.324076i
\(567\) −3.50878 10.9397i −0.147355 0.459423i
\(568\) −5.74013 + 5.74013i −0.240850 + 0.240850i
\(569\) 29.8291 + 17.2218i 1.25050 + 0.721977i 0.971209 0.238229i \(-0.0765669\pi\)
0.279292 + 0.960206i \(0.409900\pi\)
\(570\) 0 0
\(571\) 4.11985 + 7.13579i 0.172410 + 0.298623i 0.939262 0.343201i \(-0.111511\pi\)
−0.766852 + 0.641824i \(0.778178\pi\)
\(572\) −1.11607 4.16524i −0.0466654 0.174158i
\(573\) 31.8645 + 31.8645i 1.33116 + 1.33116i
\(574\) −1.15364 23.7315i −0.0481520 0.990534i
\(575\) 0 0
\(576\) −2.72435 + 4.71872i −0.113515 + 0.196613i
\(577\) 3.39649 + 0.910086i 0.141398 + 0.0378874i 0.328824 0.944391i \(-0.393348\pi\)
−0.187426 + 0.982279i \(0.560015\pi\)
\(578\) 15.8204 + 4.23908i 0.658044 + 0.176322i
\(579\) 13.0770 22.6500i 0.543460 0.941301i
\(580\) 0 0
\(581\) 19.7132 + 30.6088i 0.817843 + 1.26987i
\(582\) −9.20520 9.20520i −0.381568 0.381568i
\(583\) −7.51937 28.0627i −0.311421 1.16224i
\(584\) −4.93262 8.54355i −0.204113 0.353535i
\(585\) 0 0
\(586\) −4.10531 2.37020i −0.169589 0.0979122i
\(587\) −5.37485 + 5.37485i −0.221844 + 0.221844i −0.809275 0.587431i \(-0.800139\pi\)
0.587431 + 0.809275i \(0.300139\pi\)
\(588\) 3.33499 20.0715i 0.137533 0.827734i
\(589\) 0.0909162i 0.00374613i
\(590\) 0 0
\(591\) −43.4136 + 25.0649i −1.78580 + 1.03103i
\(592\) 0.0664979 0.248174i 0.00273305 0.0101999i
\(593\) −0.709668 + 0.190155i −0.0291426 + 0.00780872i −0.273361 0.961912i \(-0.588135\pi\)
0.244218 + 0.969720i \(0.421469\pi\)
\(594\) −26.1296 −1.07211
\(595\) 0 0
\(596\) −4.84185 −0.198330
\(597\) −24.5138 + 6.56845i −1.00328 + 0.268829i
\(598\) −1.43057 + 5.33897i −0.0585005 + 0.218327i
\(599\) −7.23778 + 4.17873i −0.295727 + 0.170738i −0.640522 0.767940i \(-0.721282\pi\)
0.344794 + 0.938678i \(0.387949\pi\)
\(600\) 0 0
\(601\) 39.9236i 1.62852i −0.580501 0.814259i \(-0.697143\pi\)
0.580501 0.814259i \(-0.302857\pi\)
\(602\) 1.19315 1.31508i 0.0486290 0.0535985i
\(603\) −25.5147 + 25.5147i −1.03904 + 1.03904i
\(604\) −8.69995 5.02292i −0.353996 0.204380i
\(605\) 0 0
\(606\) −0.104505 0.181008i −0.00424523 0.00735295i
\(607\) −8.91623 33.2758i −0.361899 1.35062i −0.871577 0.490259i \(-0.836902\pi\)
0.509678 0.860365i \(-0.329765\pi\)
\(608\) −1.54802 1.54802i −0.0627804 0.0627804i
\(609\) −17.9339 9.22349i −0.726720 0.373755i
\(610\) 0 0
\(611\) 3.75885 6.51051i 0.152067 0.263387i
\(612\) −4.14903 1.11173i −0.167715 0.0449390i
\(613\) −31.6042 8.46832i −1.27648 0.342032i −0.443971 0.896041i \(-0.646431\pi\)
−0.832510 + 0.554009i \(0.813097\pi\)
\(614\) 0.753393 1.30491i 0.0304044 0.0526620i
\(615\) 0 0
\(616\) −8.63753 4.44231i −0.348016 0.178986i
\(617\) 15.5005 + 15.5005i 0.624025 + 0.624025i 0.946558 0.322533i \(-0.104534\pi\)
−0.322533 + 0.946558i \(0.604534\pi\)
\(618\) 12.4730 + 46.5497i 0.501736 + 1.87250i
\(619\) −4.31138 7.46752i −0.173289 0.300145i 0.766279 0.642508i \(-0.222106\pi\)
−0.939568 + 0.342363i \(0.888773\pi\)
\(620\) 0 0
\(621\) 29.0055 + 16.7463i 1.16395 + 0.672008i
\(622\) −9.76397 + 9.76397i −0.391500 + 0.391500i
\(623\) 2.54269 2.80254i 0.101871 0.112281i
\(624\) 3.41421i 0.136678i
\(625\) 0 0
\(626\) 20.2191 11.6735i 0.808119 0.466568i
\(627\) 6.04621 22.5648i 0.241462 0.901150i
\(628\) −23.6523 + 6.33762i −0.943830 + 0.252898i
\(629\) 0.202545 0.00807600
\(630\) 0 0
\(631\) −4.13675 −0.164682 −0.0823408 0.996604i \(-0.526240\pi\)
−0.0823408 + 0.996604i \(0.526240\pi\)
\(632\) −12.9543 + 3.47109i −0.515294 + 0.138073i
\(633\) −8.40662 + 31.3739i −0.334133 + 1.24700i
\(634\) −11.4219 + 6.59442i −0.453620 + 0.261898i
\(635\) 0 0
\(636\) 23.0027i 0.912117i
\(637\) 2.88840 + 7.69827i 0.114443 + 0.305017i
\(638\) −6.80736 + 6.80736i −0.269506 + 0.269506i
\(639\) −38.3055 22.1157i −1.51534 0.874882i
\(640\) 0 0
\(641\) −5.42807 9.40169i −0.214396 0.371345i 0.738690 0.674046i \(-0.235445\pi\)
−0.953086 + 0.302701i \(0.902112\pi\)
\(642\) 3.43757 + 12.8292i 0.135670 + 0.506328i
\(643\) −8.06230 8.06230i −0.317946 0.317946i 0.530032 0.847978i \(-0.322180\pi\)
−0.847978 + 0.530032i \(0.822180\pi\)
\(644\) 6.74114 + 10.4670i 0.265638 + 0.412457i
\(645\) 0 0
\(646\) 0.862920 1.49462i 0.0339511 0.0588051i
\(647\) 10.0715 + 2.69865i 0.395951 + 0.106095i 0.451300 0.892372i \(-0.350960\pi\)
−0.0553490 + 0.998467i \(0.517627\pi\)
\(648\) −4.19432 1.12387i −0.164769 0.0441496i
\(649\) −19.6632 + 34.0577i −0.771848 + 1.33688i
\(650\) 0 0
\(651\) 0.0155070 + 0.318994i 0.000607766 + 0.0125023i
\(652\) 15.5320 + 15.5320i 0.608279 + 0.608279i
\(653\) 1.72009 + 6.41946i 0.0673123 + 0.251213i 0.991380 0.131015i \(-0.0418236\pi\)
−0.924068 + 0.382228i \(0.875157\pi\)
\(654\) 26.3091 + 45.5687i 1.02877 + 1.78188i
\(655\) 0 0
\(656\) −7.77713 4.49013i −0.303646 0.175310i
\(657\) 38.0090 38.0090i 1.48287 1.48287i
\(658\) −5.17163 16.1241i −0.201611 0.628582i
\(659\) 22.0345i 0.858343i −0.903223 0.429172i \(-0.858806\pi\)
0.903223 0.429172i \(-0.141194\pi\)
\(660\) 0 0
\(661\) −9.94278 + 5.74047i −0.386729 + 0.223278i −0.680742 0.732523i \(-0.738343\pi\)
0.294013 + 0.955802i \(0.405009\pi\)
\(662\) −4.94240 + 18.4453i −0.192092 + 0.716897i
\(663\) 2.59983 0.696621i 0.100969 0.0270545i
\(664\) 13.7608 0.534021
\(665\) 0 0
\(666\) 1.39993 0.0542460
\(667\) 11.9194 3.19379i 0.461521 0.123664i
\(668\) −1.15158 + 4.29774i −0.0445558 + 0.166285i
\(669\) 2.65857 1.53492i 0.102786 0.0593436i
\(670\) 0 0
\(671\) 7.31407i 0.282356i
\(672\) −5.69550 5.16742i −0.219708 0.199338i
\(673\) 15.2073 15.2073i 0.586198 0.586198i −0.350402 0.936600i \(-0.613955\pi\)
0.936600 + 0.350402i \(0.113955\pi\)
\(674\) 0.597952 + 0.345228i 0.0230322 + 0.0132977i
\(675\) 0 0
\(676\) −5.81014 10.0635i −0.223467 0.387056i
\(677\) 1.48523 + 5.54296i 0.0570821 + 0.213033i 0.988576 0.150724i \(-0.0481604\pi\)
−0.931494 + 0.363757i \(0.881494\pi\)
\(678\) −4.41998 4.41998i −0.169748 0.169748i
\(679\) 9.96224 6.41606i 0.382316 0.246226i
\(680\) 0 0
\(681\) 4.53492 7.85472i 0.173779 0.300993i
\(682\) 0.147264 + 0.0394591i 0.00563901 + 0.00151097i
\(683\) 18.7685 + 5.02900i 0.718157 + 0.192430i 0.599349 0.800488i \(-0.295426\pi\)
0.118808 + 0.992917i \(0.462093\pi\)
\(684\) 5.96423 10.3303i 0.228048 0.394991i
\(685\) 0 0
\(686\) 17.2137 + 6.83301i 0.657220 + 0.260886i
\(687\) 17.3095 + 17.3095i 0.660400 + 0.660400i
\(688\) −0.173704 0.648273i −0.00662241 0.0247152i
\(689\) 4.64782 + 8.05027i 0.177068 + 0.306691i
\(690\) 0 0
\(691\) 19.0914 + 11.0224i 0.726270 + 0.419312i 0.817056 0.576558i \(-0.195605\pi\)
−0.0907861 + 0.995870i \(0.528938\pi\)
\(692\) 3.69572 3.69572i 0.140490 0.140490i
\(693\) 11.1992 51.7244i 0.425422 1.96485i
\(694\) 3.80998i 0.144625i
\(695\) 0 0
\(696\) −6.60113 + 3.81116i −0.250215 + 0.144462i
\(697\) 1.83229 6.83821i 0.0694031 0.259016i
\(698\) −7.64340 + 2.04804i −0.289307 + 0.0775196i
\(699\) 66.2630 2.50630
\(700\) 0 0
\(701\) −18.0270 −0.680870 −0.340435 0.940268i \(-0.610574\pi\)
−0.340435 + 0.940268i \(0.610574\pi\)
\(702\) 8.07553 2.16383i 0.304791 0.0816686i
\(703\) −0.145579 + 0.543308i −0.00549062 + 0.0204913i
\(704\) −3.17930 + 1.83557i −0.119824 + 0.0691807i
\(705\) 0 0
\(706\) 25.7787i 0.970196i
\(707\) 0.181158 0.0581046i 0.00681316 0.00218525i
\(708\) −22.0173 + 22.0173i −0.827459 + 0.827459i
\(709\) 37.0614 + 21.3974i 1.39187 + 0.803597i 0.993522 0.113637i \(-0.0362500\pi\)
0.398349 + 0.917234i \(0.369583\pi\)
\(710\) 0 0
\(711\) −36.5370 63.2840i −1.37025 2.37334i
\(712\) −0.370178 1.38152i −0.0138730 0.0517748i
\(713\) −0.138183 0.138183i −0.00517498 0.00517498i
\(714\) 2.77276 5.39130i 0.103768 0.201764i
\(715\) 0 0
\(716\) −6.28428 + 10.8847i −0.234854 + 0.406780i
\(717\) 67.3747 + 18.0530i 2.51615 + 0.674202i
\(718\) 10.0326 + 2.68822i 0.374413 + 0.100324i
\(719\) 2.72691 4.72315i 0.101697 0.176144i −0.810687 0.585480i \(-0.800906\pi\)
0.912384 + 0.409336i \(0.134240\pi\)
\(720\) 0 0
\(721\) −43.8142 + 2.12990i −1.63172 + 0.0793217i
\(722\) −10.0461 10.0461i −0.373876 0.373876i
\(723\) 18.6476 + 69.5938i 0.693512 + 2.58822i
\(724\) 5.83712 + 10.1102i 0.216935 + 0.375742i
\(725\) 0 0
\(726\) −6.23593 3.60031i −0.231437 0.133620i
\(727\) 16.6781 16.6781i 0.618555 0.618555i −0.326606 0.945161i \(-0.605905\pi\)
0.945161 + 0.326606i \(0.105905\pi\)
\(728\) 3.03736 + 0.657639i 0.112572 + 0.0243737i
\(729\) 38.4054i 1.42242i
\(730\) 0 0
\(731\) 0.458200 0.264542i 0.0169471 0.00978443i
\(732\) 1.49882 5.59367i 0.0553979 0.206748i
\(733\) 32.8405 8.79960i 1.21299 0.325021i 0.405057 0.914291i \(-0.367252\pi\)
0.807936 + 0.589271i \(0.200585\pi\)
\(734\) −8.68601 −0.320607
\(735\) 0 0
\(736\) 4.70563 0.173452
\(737\) −23.4832 + 6.29231i −0.865016 + 0.231780i
\(738\) 12.6642 47.2635i 0.466177 1.73979i
\(739\) −25.0733 + 14.4761i −0.922335 + 0.532510i −0.884379 0.466769i \(-0.845418\pi\)
−0.0379557 + 0.999279i \(0.512085\pi\)
\(740\) 0 0
\(741\) 7.47449i 0.274582i
\(742\) 20.4637 + 4.43074i 0.751247 + 0.162658i
\(743\) −34.0351 + 34.0351i −1.24863 + 1.24863i −0.292300 + 0.956327i \(0.594421\pi\)
−0.956327 + 0.292300i \(0.905579\pi\)
\(744\) 0.104538 + 0.0603553i 0.00383257 + 0.00221273i
\(745\) 0 0
\(746\) 6.65477 + 11.5264i 0.243649 + 0.422012i
\(747\) 19.4058 + 72.4235i 0.710022 + 2.64984i
\(748\) −2.04643 2.04643i −0.0748247 0.0748247i
\(749\) −12.0753 + 0.587006i −0.441221 + 0.0214487i
\(750\) 0 0
\(751\) 9.30569 16.1179i 0.339569 0.588151i −0.644782 0.764366i \(-0.723052\pi\)
0.984352 + 0.176215i \(0.0563853\pi\)
\(752\) −6.18205 1.65648i −0.225436 0.0604055i
\(753\) −31.2090 8.36242i −1.13732 0.304743i
\(754\) 1.54013 2.66759i 0.0560883 0.0971478i
\(755\) 0 0
\(756\) 8.61270 16.7463i 0.313241 0.609059i
\(757\) −29.7422 29.7422i −1.08100 1.08100i −0.996416 0.0845825i \(-0.973044\pi\)
−0.0845825 0.996416i \(-0.526956\pi\)
\(758\) 6.55984 + 24.4816i 0.238264 + 0.889213i
\(759\) 25.1064 + 43.4856i 0.911305 + 1.57843i
\(760\) 0 0
\(761\) 17.6474 + 10.1887i 0.639718 + 0.369341i 0.784506 0.620122i \(-0.212917\pi\)
−0.144788 + 0.989463i \(0.546250\pi\)
\(762\) −38.5213 + 38.5213i −1.39548 + 1.39548i
\(763\) −45.6066 + 14.6278i −1.65107 + 0.529563i
\(764\) 15.5034i 0.560894i
\(765\) 0 0
\(766\) 15.9357 9.20046i 0.575779 0.332426i
\(767\) 3.25668 12.1541i 0.117592 0.438859i
\(768\) −2.80762 + 0.752300i −0.101311 + 0.0271463i
\(769\) −40.9728 −1.47752 −0.738759 0.673970i \(-0.764588\pi\)
−0.738759 + 0.673970i \(0.764588\pi\)
\(770\) 0 0
\(771\) 73.5189 2.64772
\(772\) 8.69132 2.32883i 0.312808 0.0838165i
\(773\) −6.39265 + 23.8577i −0.229928 + 0.858101i 0.750443 + 0.660936i \(0.229840\pi\)
−0.980370 + 0.197166i \(0.936826\pi\)
\(774\) 3.16693 1.82843i 0.113833 0.0657215i
\(775\) 0 0
\(776\) 4.47871i 0.160776i
\(777\) −0.418118 + 1.93111i −0.0149999 + 0.0692783i
\(778\) −15.8091 + 15.8091i −0.566784 + 0.566784i
\(779\) 17.0259 + 9.82991i 0.610017 + 0.352193i
\(780\) 0 0
\(781\) −14.9007 25.8088i −0.533190 0.923513i
\(782\) 0.960117 + 3.58321i 0.0343337 + 0.128135i
\(783\) −13.1980 13.1980i −0.471659 0.471659i
\(784\) 5.69411 4.07150i 0.203361 0.145411i
\(785\) 0 0
\(786\) −20.6295 + 35.7314i −0.735831 + 1.27450i
\(787\) −7.92843 2.12442i −0.282618 0.0757273i 0.114725 0.993397i \(-0.463401\pi\)
−0.397343 + 0.917670i \(0.630068\pi\)
\(788\) −16.6588 4.46372i −0.593446 0.159013i
\(789\) 16.4897 28.5610i 0.587048 1.01680i
\(790\) 0 0
\(791\) 4.78348 3.08075i 0.170081 0.109539i
\(792\) −14.1442 14.1442i −0.502594 0.502594i
\(793\) 0.605689 + 2.26046i 0.0215086 + 0.0802713i
\(794\) −7.89197 13.6693i −0.280076 0.485105i
\(795\) 0 0
\(796\) −7.56140 4.36557i −0.268007 0.154734i
\(797\) 11.7928 11.7928i 0.417722 0.417722i −0.466696 0.884418i \(-0.654556\pi\)
0.884418 + 0.466696i \(0.154556\pi\)
\(798\) 12.4687 + 11.3127i 0.441388 + 0.400464i
\(799\) 5.04544i 0.178495i
\(800\) 0 0
\(801\) 6.74899 3.89653i 0.238464 0.137677i
\(802\) 3.61585 13.4945i 0.127680 0.476508i
\(803\) 34.9827 9.37358i 1.23451 0.330786i
\(804\) −19.2490 −0.678860
\(805\) 0 0
\(806\) −0.0487805 −0.00171822
\(807\) 22.6489 6.06875i 0.797278 0.213630i
\(808\) 0.0186109 0.0694570i 0.000654730 0.00244349i
\(809\) 28.8498 16.6564i 1.01430 0.585609i 0.101855 0.994799i \(-0.467522\pi\)
0.912449 + 0.409191i \(0.134189\pi\)
\(810\) 0 0
\(811\) 55.2368i 1.93963i 0.243850 + 0.969813i \(0.421590\pi\)
−0.243850 + 0.969813i \(0.578410\pi\)
\(812\) −2.11900 6.60661i −0.0743623 0.231847i
\(813\) 17.2637 17.2637i 0.605465 0.605465i
\(814\) 0.816852 + 0.471610i 0.0286307 + 0.0165299i
\(815\) 0 0
\(816\) −1.14571 1.98443i −0.0401079 0.0694689i
\(817\) 0.380278 + 1.41922i 0.0133042 + 0.0496521i
\(818\) −0.221580 0.221580i −0.00774737 0.00774737i
\(819\) 0.822187 + 16.9132i 0.0287295 + 0.590995i
\(820\) 0 0
\(821\) −9.31457 + 16.1333i −0.325081 + 0.563056i −0.981529 0.191315i \(-0.938725\pi\)
0.656448 + 0.754371i \(0.272058\pi\)
\(822\) 53.2505 + 14.2684i 1.85732 + 0.497669i
\(823\) −16.3139 4.37130i −0.568668 0.152374i −0.0369821 0.999316i \(-0.511774\pi\)
−0.531685 + 0.846942i \(0.678441\pi\)
\(824\) −8.28988 + 14.3585i −0.288792 + 0.500202i
\(825\) 0 0
\(826\) −15.3461 23.8280i −0.533960 0.829081i
\(827\) 5.62716 + 5.62716i 0.195675 + 0.195675i 0.798143 0.602468i \(-0.205816\pi\)
−0.602468 + 0.798143i \(0.705816\pi\)
\(828\) 6.63602 + 24.7660i 0.230618 + 0.860677i
\(829\) −3.29757 5.71155i −0.114529 0.198370i 0.803062 0.595895i \(-0.203203\pi\)
−0.917591 + 0.397525i \(0.869869\pi\)
\(830\) 0 0
\(831\) 14.2980 + 8.25494i 0.495991 + 0.286361i
\(832\) 0.830578 0.830578i 0.0287951 0.0287951i
\(833\) 4.26213 + 3.50517i 0.147674 + 0.121447i
\(834\) 23.9424i 0.829057i
\(835\) 0 0
\(836\) 6.96021 4.01848i 0.240724 0.138982i
\(837\) −0.0765030 + 0.285513i −0.00264433 + 0.00986877i
\(838\) 30.5478 8.18525i 1.05526 0.282755i
\(839\) −46.0930 −1.59131 −0.795654 0.605752i \(-0.792872\pi\)
−0.795654 + 0.605752i \(0.792872\pi\)
\(840\) 0 0
\(841\) 22.1232 0.762870
\(842\) −23.3887 + 6.26698i −0.806027 + 0.215974i
\(843\) 5.47394 20.4290i 0.188533 0.703613i
\(844\) −9.67744 + 5.58727i −0.333111 + 0.192322i
\(845\) 0 0
\(846\) 34.8724i 1.19894i
\(847\) 4.40407 4.85413i 0.151326 0.166790i
\(848\) 5.59589 5.59589i 0.192164 0.192164i
\(849\) −19.4080 11.2052i −0.666080 0.384562i
\(850\) 0 0
\(851\) −0.604505 1.04703i −0.0207222 0.0358918i
\(852\) −6.10700 22.7916i −0.209222 0.780828i
\(853\) 14.9594 + 14.9594i 0.512200 + 0.512200i 0.915200 0.403000i \(-0.132032\pi\)
−0.403000 + 0.915200i \(0.632032\pi\)
\(854\) 4.68755 + 2.41082i 0.160405 + 0.0824967i
\(855\) 0 0
\(856\) −2.28471 + 3.95723i −0.0780897 + 0.135255i
\(857\) −11.6491 3.12136i −0.397924 0.106623i 0.0543068 0.998524i \(-0.482705\pi\)
−0.452231 + 0.891901i \(0.649372\pi\)
\(858\) 12.1070 + 3.24405i 0.413325 + 0.110750i
\(859\) 2.90061 5.02401i 0.0989677 0.171417i −0.812290 0.583254i \(-0.801779\pi\)
0.911258 + 0.411837i \(0.135113\pi\)
\(860\) 0 0
\(861\) 61.4147 + 31.5858i 2.09301 + 1.07644i
\(862\) 1.10172 + 1.10172i 0.0375249 + 0.0375249i
\(863\) 0.778623 + 2.90586i 0.0265046 + 0.0989167i 0.977911 0.209021i \(-0.0670278\pi\)
−0.951406 + 0.307938i \(0.900361\pi\)
\(864\) −3.55879 6.16400i −0.121072 0.209703i
\(865\) 0 0
\(866\) −7.69343 4.44180i −0.261433 0.150939i
\(867\) −33.6632 + 33.6632i −1.14326 + 1.14326i
\(868\) −0.0738294 + 0.0813742i −0.00250593 + 0.00276202i
\(869\) 49.2347i 1.67017i
\(870\) 0 0
\(871\) 6.73657 3.88936i 0.228260 0.131786i
\(872\) −4.68530 + 17.4858i −0.158664 + 0.592143i
\(873\) 23.5717 6.31601i 0.797780 0.213765i
\(874\) −10.3017 −0.348460
\(875\) 0 0
\(876\) 28.6750 0.968838
\(877\) 33.8582 9.07228i 1.14331 0.306349i 0.363030 0.931778i \(-0.381742\pi\)
0.780282 + 0.625428i \(0.215076\pi\)
\(878\) 6.18945 23.0994i 0.208884 0.779565i
\(879\) 11.9328 6.88939i 0.402483 0.232373i
\(880\) 0 0
\(881\) 23.7116i 0.798864i −0.916763 0.399432i \(-0.869207\pi\)
0.916763 0.399432i \(-0.130793\pi\)
\(882\) 29.4585 + 24.2266i 0.991919 + 0.815753i
\(883\) 7.95370 7.95370i 0.267663 0.267663i −0.560495 0.828158i \(-0.689389\pi\)
0.828158 + 0.560495i \(0.189389\pi\)
\(884\) 0.801929 + 0.462994i 0.0269718 + 0.0155722i
\(885\) 0 0
\(886\) 6.43103 + 11.1389i 0.216055 + 0.374218i
\(887\) 5.27738 + 19.6954i 0.177197 + 0.661308i 0.996167 + 0.0874718i \(0.0278788\pi\)
−0.818970 + 0.573836i \(0.805455\pi\)
\(888\) 0.528070 + 0.528070i 0.0177209 + 0.0177209i
\(889\) −26.8495 41.6893i −0.900503 1.39821i
\(890\) 0 0
\(891\) 7.97057 13.8054i 0.267024 0.462499i
\(892\) 1.02015 + 0.273349i 0.0341573 + 0.00915241i
\(893\) 13.5339 + 3.62640i 0.452895 + 0.121353i
\(894\) 7.03682 12.1881i 0.235347 0.407632i
\(895\) 0 0
\(896\) −0.128464 2.64263i −0.00429168 0.0882841i
\(897\) −11.3604 11.3604i −0.379313 0.379313i
\(898\) −4.63111 17.2836i −0.154542 0.576760i
\(899\) 0.0544519 + 0.0943134i 0.00181607 + 0.00314553i
\(900\) 0 0
\(901\) 5.40287 + 3.11935i 0.179996 + 0.103921i
\(902\) 23.3118 23.3118i 0.776197 0.776197i
\(903\) 1.57633 + 4.91468i 0.0524570 + 0.163550i
\(904\) 2.15051i 0.0715247i
\(905\) 0 0
\(906\) 25.2878 14.5999i 0.840132 0.485051i
\(907\) 1.68614 6.29276i 0.0559874 0.208948i −0.932266 0.361775i \(-0.882171\pi\)
0.988253 + 0.152827i \(0.0488377\pi\)
\(908\) 3.01404 0.807609i 0.100024 0.0268014i
\(909\) 0.391801 0.0129952
\(910\) 0 0
\(911\) −24.2528 −0.803531 −0.401765 0.915743i \(-0.631603\pi\)
−0.401765 + 0.915743i \(0.631603\pi\)
\(912\) 6.14653 1.64696i 0.203532 0.0545362i
\(913\) −13.0749 + 48.7964i −0.432718 + 1.61492i
\(914\) −29.6277 + 17.1056i −0.979997 + 0.565802i
\(915\) 0 0
\(916\) 8.42181i 0.278264i
\(917\) −27.8138 25.2350i −0.918493 0.833333i
\(918\) 3.96759 3.96759i 0.130950 0.130950i
\(919\) 31.2542 + 18.0446i 1.03098 + 0.595236i 0.917265 0.398277i \(-0.130392\pi\)
0.113714 + 0.993513i \(0.463725\pi\)
\(920\) 0 0
\(921\) 2.18986 + 3.79295i 0.0721583 + 0.124982i
\(922\) −6.04266 22.5515i −0.199004 0.742695i
\(923\) 6.74244 + 6.74244i 0.221930 + 0.221930i
\(924\) 23.7356 15.2866i 0.780844 0.502893i
\(925\) 0 0
\(926\) 2.81789 4.88073i 0.0926017 0.160391i
\(927\) −87.2600 23.3813i −2.86600 0.767941i
\(928\) −2.53301 0.678717i −0.0831500 0.0222800i
\(929\) 21.2041 36.7266i 0.695685 1.20496i −0.274264 0.961654i \(-0.588434\pi\)
0.969949 0.243307i \(-0.0782323\pi\)
\(930\) 0 0
\(931\) −12.4657 + 8.91344i −0.408547 + 0.292126i
\(932\) 16.1198 + 16.1198i 0.528023 + 0.528023i
\(933\) −10.3880 38.7686i −0.340089 1.26923i
\(934\) −2.44290 4.23123i −0.0799342 0.138450i
\(935\) 0 0
\(936\) 5.54268 + 3.20007i 0.181168 + 0.104597i
\(937\) 4.06709 4.06709i 0.132866 0.132866i −0.637546 0.770412i \(-0.720050\pi\)
0.770412 + 0.637546i \(0.220050\pi\)
\(938\) 3.70770 17.1243i 0.121061 0.559129i
\(939\) 67.8621i 2.21460i
\(940\) 0 0
\(941\) −17.4071 + 10.0500i −0.567455 + 0.327621i −0.756132 0.654419i \(-0.772913\pi\)
0.188677 + 0.982039i \(0.439580\pi\)
\(942\) 18.4213 68.7494i 0.600200 2.23998i
\(943\) −40.8179 + 10.9371i −1.32921 + 0.356162i
\(944\) −10.7123 −0.348656
\(945\) 0 0
\(946\) 2.46386 0.0801069
\(947\) −56.9449 + 15.2583i −1.85046 + 0.495830i −0.999565 0.0295030i \(-0.990608\pi\)
−0.850897 + 0.525333i \(0.823941\pi\)
\(948\) 10.0893 37.6538i 0.327685 1.22294i
\(949\) −10.0354 + 5.79393i −0.325762 + 0.188079i
\(950\) 0 0
\(951\) 38.3355i 1.24311i
\(952\) 1.98608 0.637013i 0.0643691 0.0206457i
\(953\) 31.1044 31.1044i 1.00757 1.00757i 0.00759828 0.999971i \(-0.497581\pi\)
0.999971 0.00759828i \(-0.00241863\pi\)
\(954\) 37.3429 + 21.5599i 1.20902 + 0.698029i
\(955\) 0 0
\(956\) 11.9985 + 20.7821i 0.388060 + 0.672140i
\(957\) −7.24244 27.0292i −0.234115 0.873729i
\(958\) −12.0996 12.0996i −0.390921 0.390921i
\(959\) −22.9505 + 44.6245i −0.741111 + 1.44100i
\(960\) 0 0
\(961\) −15.4991 + 26.8453i −0.499972 + 0.865977i
\(962\) −0.291508 0.0781094i −0.00939861 0.00251835i
\(963\) −24.0491 6.44392i −0.774970 0.207653i
\(964\) −12.3937 + 21.4666i −0.399175 + 0.691391i
\(965\) 0 0
\(966\) −36.1451 + 1.75709i −1.16295 + 0.0565336i
\(967\) 21.5036 + 21.5036i 0.691510 + 0.691510i 0.962564 0.271054i \(-0.0873721\pi\)
−0.271054 + 0.962564i \(0.587372\pi\)
\(968\) −0.641168 2.39287i −0.0206079 0.0769098i
\(969\) 2.50822 + 4.34437i 0.0805756 + 0.139561i
\(970\) 0 0
\(971\) −45.3034 26.1559i −1.45385 0.839384i −0.455158 0.890411i \(-0.650417\pi\)
−0.998697 + 0.0510273i \(0.983750\pi\)
\(972\) −6.17385 + 6.17385i −0.198026 + 0.198026i
\(973\) 21.2997 + 4.61174i 0.682836 + 0.147845i
\(974\) 0.130300i 0.00417507i
\(975\) 0 0
\(976\) 1.72539 0.996157i 0.0552285 0.0318862i
\(977\) −14.6477 + 54.6658i −0.468620 + 1.74891i 0.175979 + 0.984394i \(0.443691\pi\)
−0.644599 + 0.764520i \(0.722976\pi\)
\(978\) −61.6710 + 16.5247i −1.97202 + 0.528401i
\(979\) 5.25068 0.167813
\(980\) 0 0
\(981\) −98.6358 −3.14920
\(982\) −26.0699 + 6.98541i −0.831924 + 0.222913i
\(983\) −4.00621 + 14.9514i −0.127778 + 0.476875i −0.999923 0.0123723i \(-0.996062\pi\)
0.872145 + 0.489247i \(0.162728\pi\)
\(984\) 22.6055 13.0513i 0.720638 0.416061i
\(985\) 0 0
\(986\) 2.06729i 0.0658361i
\(987\) 48.1044 + 10.4154i 1.53118 + 0.331526i
\(988\) −1.81832 + 1.81832i −0.0578486 + 0.0578486i
\(989\) −2.73504 1.57907i −0.0869691 0.0502116i
\(990\) 0 0
\(991\) 26.8648 + 46.5311i 0.853388 + 1.47811i 0.878133 + 0.478417i \(0.158789\pi\)
−0.0247453 + 0.999694i \(0.507877\pi\)
\(992\) 0.0107485 + 0.0401138i 0.000341264 + 0.00127362i
\(993\) −39.2484 39.2484i −1.24551 1.24551i
\(994\) 21.4523 1.04284i 0.680424 0.0330769i
\(995\) 0 0
\(996\) −19.9990 + 34.6392i −0.633692 + 1.09759i
\(997\) −37.2167 9.97217i −1.17866 0.315822i −0.384267 0.923222i \(-0.625546\pi\)
−0.794396 + 0.607400i \(0.792213\pi\)
\(998\) −0.0930180 0.0249241i −0.00294443 0.000788959i
\(999\) −0.914352 + 1.58370i −0.0289288 + 0.0501062i
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 350.2.o.c.257.2 16
5.2 odd 4 70.2.k.a.33.1 yes 16
5.3 odd 4 inner 350.2.o.c.243.4 16
5.4 even 2 70.2.k.a.47.3 yes 16
7.3 odd 6 inner 350.2.o.c.157.4 16
15.2 even 4 630.2.bv.c.523.4 16
15.14 odd 2 630.2.bv.c.397.1 16
20.7 even 4 560.2.ci.c.33.4 16
20.19 odd 2 560.2.ci.c.257.4 16
35.2 odd 12 490.2.g.c.293.4 16
35.3 even 12 inner 350.2.o.c.143.2 16
35.4 even 6 490.2.l.c.227.2 16
35.9 even 6 490.2.g.c.97.1 16
35.12 even 12 490.2.g.c.293.1 16
35.17 even 12 70.2.k.a.3.3 16
35.19 odd 6 490.2.g.c.97.4 16
35.24 odd 6 70.2.k.a.17.1 yes 16
35.27 even 4 490.2.l.c.313.2 16
35.32 odd 12 490.2.l.c.423.4 16
35.34 odd 2 490.2.l.c.117.4 16
105.17 odd 12 630.2.bv.c.73.1 16
105.59 even 6 630.2.bv.c.577.4 16
140.59 even 6 560.2.ci.c.17.4 16
140.87 odd 12 560.2.ci.c.353.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.k.a.3.3 16 35.17 even 12
70.2.k.a.17.1 yes 16 35.24 odd 6
70.2.k.a.33.1 yes 16 5.2 odd 4
70.2.k.a.47.3 yes 16 5.4 even 2
350.2.o.c.143.2 16 35.3 even 12 inner
350.2.o.c.157.4 16 7.3 odd 6 inner
350.2.o.c.243.4 16 5.3 odd 4 inner
350.2.o.c.257.2 16 1.1 even 1 trivial
490.2.g.c.97.1 16 35.9 even 6
490.2.g.c.97.4 16 35.19 odd 6
490.2.g.c.293.1 16 35.12 even 12
490.2.g.c.293.4 16 35.2 odd 12
490.2.l.c.117.4 16 35.34 odd 2
490.2.l.c.227.2 16 35.4 even 6
490.2.l.c.313.2 16 35.27 even 4
490.2.l.c.423.4 16 35.32 odd 12
560.2.ci.c.17.4 16 140.59 even 6
560.2.ci.c.33.4 16 20.7 even 4
560.2.ci.c.257.4 16 20.19 odd 2
560.2.ci.c.353.4 16 140.87 odd 12
630.2.bv.c.73.1 16 105.17 odd 12
630.2.bv.c.397.1 16 15.14 odd 2
630.2.bv.c.523.4 16 15.2 even 4
630.2.bv.c.577.4 16 105.59 even 6