Properties

Label 350.2.o.d.157.1
Level $350$
Weight $2$
Character 350.157
Analytic conductor $2.795$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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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: 16.0.478584585616890104119296.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 31x^{12} + 336x^{8} - 19375x^{4} + 390625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 157.1
Root \(1.97578 + 1.04705i\) of defining polynomial
Character \(\chi\) \(=\) 350.157
Dual form 350.2.o.d.243.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 + 0.965926i) q^{2} +(-1.26867 + 0.339939i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.31342i q^{6} +(-2.49342 + 0.884806i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.10411 + 0.637459i) q^{9} +O(q^{10})\) \(q+(-0.258819 + 0.965926i) q^{2} +(-1.26867 + 0.339939i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.31342i q^{6} +(-2.49342 + 0.884806i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.10411 + 0.637459i) q^{9} +(2.63746 - 4.56821i) q^{11} +(1.26867 + 0.339939i) q^{12} +(-0.296014 - 0.296014i) q^{13} +(-0.209313 - 2.63746i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.896575 - 3.34607i) q^{17} +(-0.329973 - 1.23148i) q^{18} +(-2.83616 - 4.91238i) q^{19} +(2.86254 - 1.97014i) q^{21} +(3.72993 + 3.72993i) q^{22} +(-2.89778 - 0.776457i) q^{23} +(-0.656712 + 1.13746i) q^{24} +(0.362541 - 0.209313i) q^{26} +(3.97025 - 3.97025i) q^{27} +(2.60176 + 0.480443i) q^{28} +2.27492i q^{29} +(-3.00000 - 1.73205i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.79315 + 6.69213i) q^{33} +3.46410 q^{34} +1.27492 q^{36} +(1.36525 - 5.09518i) q^{37} +(5.47904 - 1.46811i) q^{38} +(0.476171 + 0.274917i) q^{39} +5.19615i q^{41} +(1.16213 + 3.27491i) q^{42} +(5.85125 - 5.85125i) q^{43} +(-4.56821 + 2.63746i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-12.1712 - 3.26126i) q^{47} +(-0.928731 - 0.928731i) q^{48} +(5.43424 - 4.41238i) q^{49} +(2.27492 + 3.94027i) q^{51} +(0.108349 + 0.404362i) q^{52} +(2.54283 + 9.48998i) q^{53} +(2.80739 + 4.86254i) q^{54} +(-1.13746 + 2.38876i) q^{56} +(5.26806 + 5.26806i) q^{57} +(-2.19740 - 0.588792i) q^{58} +(-5.19615 + 9.00000i) q^{59} +(-12.4124 + 7.16629i) q^{61} +(2.44949 - 2.44949i) q^{62} +(2.18898 - 2.56637i) q^{63} -1.00000i q^{64} +(-6.00000 - 3.46410i) q^{66} +(-3.59815 + 0.964122i) q^{67} +(-0.896575 + 3.34607i) q^{68} +3.94027 q^{69} -6.00000 q^{71} +(-0.329973 + 1.23148i) q^{72} +(-9.22947 + 2.47303i) q^{73} +(4.56821 + 2.63746i) q^{74} +5.67232i q^{76} +(-2.53430 + 13.7241i) q^{77} +(-0.388792 + 0.388792i) q^{78} +(8.66025 - 5.00000i) q^{79} +(-1.77492 + 3.07425i) q^{81} +(-5.01910 - 1.34486i) q^{82} +(-10.1347 - 10.1347i) q^{83} +(-3.46410 + 0.274917i) q^{84} +(4.13746 + 7.16629i) q^{86} +(-0.773333 - 2.88612i) q^{87} +(-1.36525 - 5.09518i) q^{88} +(1.97014 + 3.41238i) q^{89} +(1.00000 + 0.476171i) q^{91} +(2.12132 + 2.12132i) q^{92} +(4.39480 + 1.17758i) q^{93} +(6.30026 - 10.9124i) q^{94} +(1.13746 - 0.656712i) q^{96} +(13.5129 - 13.5129i) q^{97} +(2.85554 + 6.39108i) q^{98} +6.72508i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{11} + 8 q^{16} + 76 q^{21} + 36 q^{26} - 48 q^{31} - 40 q^{36} + 24 q^{46} - 24 q^{51} + 12 q^{56} - 108 q^{61} - 96 q^{66} - 96 q^{71} + 32 q^{81} + 36 q^{86} + 16 q^{91} - 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 + 0.965926i −0.183013 + 0.683013i
\(3\) −1.26867 + 0.339939i −0.732467 + 0.196264i −0.605728 0.795672i \(-0.707118\pi\)
−0.126739 + 0.991936i \(0.540451\pi\)
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) 0 0
\(6\) 1.31342i 0.536203i
\(7\) −2.49342 + 0.884806i −0.942422 + 0.334425i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −1.10411 + 0.637459i −0.368037 + 0.212486i
\(10\) 0 0
\(11\) 2.63746 4.56821i 0.795224 1.37737i −0.127473 0.991842i \(-0.540687\pi\)
0.922697 0.385526i \(-0.125980\pi\)
\(12\) 1.26867 + 0.339939i 0.366234 + 0.0981320i
\(13\) −0.296014 0.296014i −0.0820995 0.0820995i 0.664865 0.746964i \(-0.268489\pi\)
−0.746964 + 0.664865i \(0.768489\pi\)
\(14\) −0.209313 2.63746i −0.0559414 0.704890i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −0.896575 3.34607i −0.217451 0.811540i −0.985289 0.170896i \(-0.945334\pi\)
0.767838 0.640644i \(-0.221333\pi\)
\(18\) −0.329973 1.23148i −0.0777753 0.290262i
\(19\) −2.83616 4.91238i −0.650660 1.12698i −0.982963 0.183804i \(-0.941159\pi\)
0.332303 0.943173i \(-0.392174\pi\)
\(20\) 0 0
\(21\) 2.86254 1.97014i 0.624658 0.429919i
\(22\) 3.72993 + 3.72993i 0.795224 + 0.795224i
\(23\) −2.89778 0.776457i −0.604228 0.161903i −0.0562805 0.998415i \(-0.517924\pi\)
−0.547948 + 0.836512i \(0.684591\pi\)
\(24\) −0.656712 + 1.13746i −0.134051 + 0.232183i
\(25\) 0 0
\(26\) 0.362541 0.209313i 0.0711002 0.0410497i
\(27\) 3.97025 3.97025i 0.764075 0.764075i
\(28\) 2.60176 + 0.480443i 0.491687 + 0.0907953i
\(29\) 2.27492i 0.422442i 0.977438 + 0.211221i \(0.0677439\pi\)
−0.977438 + 0.211221i \(0.932256\pi\)
\(30\) 0 0
\(31\) −3.00000 1.73205i −0.538816 0.311086i 0.205783 0.978598i \(-0.434026\pi\)
−0.744599 + 0.667512i \(0.767359\pi\)
\(32\) −0.965926 + 0.258819i −0.170753 + 0.0457532i
\(33\) −1.79315 + 6.69213i −0.312148 + 1.16495i
\(34\) 3.46410 0.594089
\(35\) 0 0
\(36\) 1.27492 0.212486
\(37\) 1.36525 5.09518i 0.224446 0.837642i −0.758180 0.652045i \(-0.773911\pi\)
0.982626 0.185597i \(-0.0594220\pi\)
\(38\) 5.47904 1.46811i 0.888818 0.238158i
\(39\) 0.476171 + 0.274917i 0.0762483 + 0.0440220i
\(40\) 0 0
\(41\) 5.19615i 0.811503i 0.913984 + 0.405751i \(0.132990\pi\)
−0.913984 + 0.405751i \(0.867010\pi\)
\(42\) 1.16213 + 3.27491i 0.179320 + 0.505330i
\(43\) 5.85125 5.85125i 0.892307 0.892307i −0.102433 0.994740i \(-0.532663\pi\)
0.994740 + 0.102433i \(0.0326626\pi\)
\(44\) −4.56821 + 2.63746i −0.688684 + 0.397612i
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −12.1712 3.26126i −1.77535 0.475703i −0.785625 0.618702i \(-0.787659\pi\)
−0.989723 + 0.142999i \(0.954325\pi\)
\(48\) −0.928731 0.928731i −0.134051 0.134051i
\(49\) 5.43424 4.41238i 0.776320 0.630339i
\(50\) 0 0
\(51\) 2.27492 + 3.94027i 0.318552 + 0.551748i
\(52\) 0.108349 + 0.404362i 0.0150252 + 0.0560750i
\(53\) 2.54283 + 9.48998i 0.349285 + 1.30355i 0.887526 + 0.460758i \(0.152422\pi\)
−0.538241 + 0.842791i \(0.680911\pi\)
\(54\) 2.80739 + 4.86254i 0.382037 + 0.661708i
\(55\) 0 0
\(56\) −1.13746 + 2.38876i −0.151999 + 0.319212i
\(57\) 5.26806 + 5.26806i 0.697772 + 0.697772i
\(58\) −2.19740 0.588792i −0.288533 0.0773122i
\(59\) −5.19615 + 9.00000i −0.676481 + 1.17170i 0.299552 + 0.954080i \(0.403163\pi\)
−0.976034 + 0.217620i \(0.930171\pi\)
\(60\) 0 0
\(61\) −12.4124 + 7.16629i −1.58924 + 0.917549i −0.595810 + 0.803126i \(0.703169\pi\)
−0.993432 + 0.114424i \(0.963498\pi\)
\(62\) 2.44949 2.44949i 0.311086 0.311086i
\(63\) 2.18898 2.56637i 0.275785 0.323333i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −6.00000 3.46410i −0.738549 0.426401i
\(67\) −3.59815 + 0.964122i −0.439584 + 0.117786i −0.471822 0.881694i \(-0.656403\pi\)
0.0322373 + 0.999480i \(0.489737\pi\)
\(68\) −0.896575 + 3.34607i −0.108726 + 0.405770i
\(69\) 3.94027 0.474353
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −0.329973 + 1.23148i −0.0388877 + 0.145131i
\(73\) −9.22947 + 2.47303i −1.08023 + 0.289446i −0.754689 0.656083i \(-0.772212\pi\)
−0.325539 + 0.945529i \(0.605546\pi\)
\(74\) 4.56821 + 2.63746i 0.531044 + 0.306598i
\(75\) 0 0
\(76\) 5.67232i 0.650660i
\(77\) −2.53430 + 13.7241i −0.288810 + 1.56400i
\(78\) −0.388792 + 0.388792i −0.0440220 + 0.0440220i
\(79\) 8.66025 5.00000i 0.974355 0.562544i 0.0737937 0.997274i \(-0.476489\pi\)
0.900561 + 0.434730i \(0.143156\pi\)
\(80\) 0 0
\(81\) −1.77492 + 3.07425i −0.197213 + 0.341583i
\(82\) −5.01910 1.34486i −0.554267 0.148515i
\(83\) −10.1347 10.1347i −1.11242 1.11242i −0.992822 0.119602i \(-0.961838\pi\)
−0.119602 0.992822i \(-0.538162\pi\)
\(84\) −3.46410 + 0.274917i −0.377964 + 0.0299959i
\(85\) 0 0
\(86\) 4.13746 + 7.16629i 0.446154 + 0.772761i
\(87\) −0.773333 2.88612i −0.0829100 0.309425i
\(88\) −1.36525 5.09518i −0.145536 0.543148i
\(89\) 1.97014 + 3.41238i 0.208834 + 0.361711i 0.951348 0.308120i \(-0.0996998\pi\)
−0.742513 + 0.669831i \(0.766366\pi\)
\(90\) 0 0
\(91\) 1.00000 + 0.476171i 0.104828 + 0.0499162i
\(92\) 2.12132 + 2.12132i 0.221163 + 0.221163i
\(93\) 4.39480 + 1.17758i 0.455720 + 0.122110i
\(94\) 6.30026 10.9124i 0.649823 1.12553i
\(95\) 0 0
\(96\) 1.13746 0.656712i 0.116091 0.0670254i
\(97\) 13.5129 13.5129i 1.37203 1.37203i 0.514588 0.857438i \(-0.327945\pi\)
0.857438 0.514588i \(-0.172055\pi\)
\(98\) 2.85554 + 6.39108i 0.288453 + 0.645596i
\(99\) 6.72508i 0.675896i
\(100\) 0 0
\(101\) 3.41238 + 1.97014i 0.339544 + 0.196036i 0.660070 0.751204i \(-0.270526\pi\)
−0.320526 + 0.947240i \(0.603860\pi\)
\(102\) −4.39480 + 1.17758i −0.435150 + 0.116598i
\(103\) 1.23651 4.61474i 0.121837 0.454703i −0.877870 0.478899i \(-0.841036\pi\)
0.999707 + 0.0241959i \(0.00770256\pi\)
\(104\) −0.418627 −0.0410497
\(105\) 0 0
\(106\) −9.82475 −0.954264
\(107\) −1.76638 + 6.59220i −0.170762 + 0.637292i 0.826473 + 0.562977i \(0.190344\pi\)
−0.997235 + 0.0743157i \(0.976323\pi\)
\(108\) −5.42346 + 1.45321i −0.521873 + 0.139835i
\(109\) −7.64246 4.41238i −0.732015 0.422629i 0.0871440 0.996196i \(-0.472226\pi\)
−0.819159 + 0.573567i \(0.805559\pi\)
\(110\) 0 0
\(111\) 6.92820i 0.657596i
\(112\) −2.01297 1.71696i −0.190208 0.162237i
\(113\) 4.24264 4.24264i 0.399114 0.399114i −0.478806 0.877920i \(-0.658930\pi\)
0.877920 + 0.478806i \(0.158930\pi\)
\(114\) −6.45203 + 3.72508i −0.604288 + 0.348886i
\(115\) 0 0
\(116\) 1.13746 1.97014i 0.105610 0.182923i
\(117\) 0.515529 + 0.138135i 0.0476606 + 0.0127706i
\(118\) −7.34847 7.34847i −0.676481 0.676481i
\(119\) 5.19615 + 7.54983i 0.476331 + 0.692092i
\(120\) 0 0
\(121\) −8.41238 14.5707i −0.764761 1.32461i
\(122\) −3.70954 13.8442i −0.335846 1.25340i
\(123\) −1.76638 6.59220i −0.159269 0.594399i
\(124\) 1.73205 + 3.00000i 0.155543 + 0.269408i
\(125\) 0 0
\(126\) 1.91238 + 2.77862i 0.170368 + 0.247539i
\(127\) 12.2152 + 12.2152i 1.08392 + 1.08392i 0.996139 + 0.0877853i \(0.0279789\pi\)
0.0877853 + 0.996139i \(0.472021\pi\)
\(128\) 0.965926 + 0.258819i 0.0853766 + 0.0228766i
\(129\) −5.43424 + 9.41238i −0.478458 + 0.828713i
\(130\) 0 0
\(131\) 7.91238 4.56821i 0.691307 0.399127i −0.112794 0.993618i \(-0.535980\pi\)
0.804102 + 0.594492i \(0.202647\pi\)
\(132\) 4.89898 4.89898i 0.426401 0.426401i
\(133\) 11.4182 + 9.73914i 0.990086 + 0.844491i
\(134\) 3.72508i 0.321798i
\(135\) 0 0
\(136\) −3.00000 1.73205i −0.257248 0.148522i
\(137\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(138\) −1.01982 + 3.80601i −0.0868126 + 0.323989i
\(139\) −4.41644 −0.374598 −0.187299 0.982303i \(-0.559973\pi\)
−0.187299 + 0.982303i \(0.559973\pi\)
\(140\) 0 0
\(141\) 16.5498 1.39375
\(142\) 1.55291 5.79555i 0.130318 0.486352i
\(143\) −2.13298 + 0.571530i −0.178369 + 0.0477937i
\(144\) −1.10411 0.637459i −0.0920092 0.0531216i
\(145\) 0 0
\(146\) 9.55505i 0.790782i
\(147\) −5.39432 + 7.44516i −0.444916 + 0.614066i
\(148\) −3.72993 + 3.72993i −0.306598 + 0.306598i
\(149\) 11.1066 6.41238i 0.909885 0.525322i 0.0294908 0.999565i \(-0.490611\pi\)
0.880394 + 0.474243i \(0.157278\pi\)
\(150\) 0 0
\(151\) −1.00000 + 1.73205i −0.0813788 + 0.140952i −0.903842 0.427865i \(-0.859266\pi\)
0.822464 + 0.568818i \(0.192599\pi\)
\(152\) −5.47904 1.46811i −0.444409 0.119079i
\(153\) 3.12290 + 3.12290i 0.252471 + 0.252471i
\(154\) −12.6005 6.00000i −1.01538 0.483494i
\(155\) 0 0
\(156\) −0.274917 0.476171i −0.0220110 0.0381242i
\(157\) 2.58138 + 9.63383i 0.206016 + 0.768864i 0.989137 + 0.146994i \(0.0469599\pi\)
−0.783121 + 0.621869i \(0.786373\pi\)
\(158\) 2.58819 + 9.65926i 0.205905 + 0.768449i
\(159\) −6.45203 11.1752i −0.511679 0.886255i
\(160\) 0 0
\(161\) 7.91238 0.627940i 0.623583 0.0494886i
\(162\) −2.51011 2.51011i −0.197213 0.197213i
\(163\) 11.5911 + 3.10583i 0.907886 + 0.243267i 0.682400 0.730979i \(-0.260936\pi\)
0.225486 + 0.974246i \(0.427603\pi\)
\(164\) 2.59808 4.50000i 0.202876 0.351391i
\(165\) 0 0
\(166\) 12.4124 7.16629i 0.963387 0.556212i
\(167\) 1.22474 1.22474i 0.0947736 0.0947736i −0.658130 0.752904i \(-0.728652\pi\)
0.752904 + 0.658130i \(0.228652\pi\)
\(168\) 0.631026 3.41722i 0.0486847 0.263644i
\(169\) 12.8248i 0.986519i
\(170\) 0 0
\(171\) 6.26287 + 3.61587i 0.478934 + 0.276513i
\(172\) −7.99296 + 2.14171i −0.609457 + 0.163304i
\(173\) −1.22162 + 4.55915i −0.0928781 + 0.346626i −0.996689 0.0813058i \(-0.974091\pi\)
0.903811 + 0.427932i \(0.140758\pi\)
\(174\) 2.98793 0.226514
\(175\) 0 0
\(176\) 5.27492 0.397612
\(177\) 3.53275 13.1844i 0.265538 0.991001i
\(178\) −3.80601 + 1.01982i −0.285273 + 0.0764386i
\(179\) −8.50848 4.91238i −0.635954 0.367168i 0.147100 0.989122i \(-0.453006\pi\)
−0.783054 + 0.621953i \(0.786339\pi\)
\(180\) 0 0
\(181\) 21.2608i 1.58030i −0.612913 0.790151i \(-0.710002\pi\)
0.612913 0.790151i \(-0.289998\pi\)
\(182\) −0.718765 + 0.842684i −0.0532784 + 0.0624639i
\(183\) 13.3111 13.3111i 0.983986 0.983986i
\(184\) −2.59808 + 1.50000i −0.191533 + 0.110581i
\(185\) 0 0
\(186\) −2.27492 + 3.94027i −0.166805 + 0.288915i
\(187\) −17.6502 4.72936i −1.29071 0.345845i
\(188\) 8.90992 + 8.90992i 0.649823 + 0.649823i
\(189\) −6.38658 + 13.4124i −0.464555 + 0.975607i
\(190\) 0 0
\(191\) −4.54983 7.88054i −0.329214 0.570216i 0.653142 0.757236i \(-0.273451\pi\)
−0.982356 + 0.187019i \(0.940117\pi\)
\(192\) 0.339939 + 1.26867i 0.0245330 + 0.0915584i
\(193\) 2.73050 + 10.1904i 0.196546 + 0.733518i 0.991861 + 0.127323i \(0.0406384\pi\)
−0.795316 + 0.606195i \(0.792695\pi\)
\(194\) 9.55505 + 16.5498i 0.686013 + 1.18821i
\(195\) 0 0
\(196\) −6.91238 + 1.10411i −0.493741 + 0.0788650i
\(197\) 11.1898 + 11.1898i 0.797239 + 0.797239i 0.982659 0.185420i \(-0.0593645\pi\)
−0.185420 + 0.982659i \(0.559365\pi\)
\(198\) −6.49593 1.74058i −0.461646 0.123698i
\(199\) 9.13642 15.8248i 0.647664 1.12179i −0.336015 0.941857i \(-0.609079\pi\)
0.983679 0.179930i \(-0.0575873\pi\)
\(200\) 0 0
\(201\) 4.23713 2.44631i 0.298864 0.172549i
\(202\) −2.78619 + 2.78619i −0.196036 + 0.196036i
\(203\) −2.01286 5.67231i −0.141275 0.398118i
\(204\) 4.54983i 0.318552i
\(205\) 0 0
\(206\) 4.13746 + 2.38876i 0.288270 + 0.166433i
\(207\) 3.69443 0.989919i 0.256780 0.0688041i
\(208\) 0.108349 0.404362i 0.00751262 0.0280375i
\(209\) −29.9210 −2.06968
\(210\) 0 0
\(211\) −5.82475 −0.400992 −0.200496 0.979694i \(-0.564255\pi\)
−0.200496 + 0.979694i \(0.564255\pi\)
\(212\) 2.54283 9.48998i 0.174642 0.651775i
\(213\) 7.61202 2.03963i 0.521567 0.139753i
\(214\) −5.91041 3.41238i −0.404027 0.233265i
\(215\) 0 0
\(216\) 5.61478i 0.382037i
\(217\) 9.01277 + 1.66430i 0.611827 + 0.112980i
\(218\) 6.24004 6.24004i 0.422629 0.422629i
\(219\) 10.8685 6.27492i 0.734424 0.424020i
\(220\) 0 0
\(221\) −0.725083 + 1.25588i −0.0487743 + 0.0844796i
\(222\) −6.69213 1.79315i −0.449146 0.120348i
\(223\) −6.16441 6.16441i −0.412800 0.412800i 0.469913 0.882713i \(-0.344285\pi\)
−0.882713 + 0.469913i \(0.844285\pi\)
\(224\) 2.17945 1.50000i 0.145621 0.100223i
\(225\) 0 0
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) −0.896575 3.34607i −0.0595078 0.222086i 0.929768 0.368146i \(-0.120007\pi\)
−0.989276 + 0.146060i \(0.953341\pi\)
\(228\) −1.92824 7.19631i −0.127701 0.476587i
\(229\) −6.92820 12.0000i −0.457829 0.792982i 0.541017 0.841011i \(-0.318039\pi\)
−0.998846 + 0.0480291i \(0.984706\pi\)
\(230\) 0 0
\(231\) −1.45017 18.2728i −0.0954139 1.20227i
\(232\) 1.60861 + 1.60861i 0.105610 + 0.105610i
\(233\) −24.7755 6.63858i −1.62310 0.434908i −0.671188 0.741287i \(-0.734216\pi\)
−0.951910 + 0.306379i \(0.900883\pi\)
\(234\) −0.266857 + 0.462210i −0.0174450 + 0.0302156i
\(235\) 0 0
\(236\) 9.00000 5.19615i 0.585850 0.338241i
\(237\) −9.28731 + 9.28731i −0.603276 + 0.603276i
\(238\) −8.63744 + 3.06506i −0.559882 + 0.198678i
\(239\) 4.54983i 0.294304i 0.989114 + 0.147152i \(0.0470107\pi\)
−0.989114 + 0.147152i \(0.952989\pi\)
\(240\) 0 0
\(241\) 7.91238 + 4.56821i 0.509681 + 0.294264i 0.732702 0.680549i \(-0.238259\pi\)
−0.223022 + 0.974814i \(0.571592\pi\)
\(242\) 16.2515 4.35457i 1.04468 0.279922i
\(243\) −3.15291 + 11.7668i −0.202259 + 0.754841i
\(244\) 14.3326 0.917549
\(245\) 0 0
\(246\) 6.82475 0.435130
\(247\) −0.614588 + 2.29367i −0.0391053 + 0.145943i
\(248\) −3.34607 + 0.896575i −0.212475 + 0.0569326i
\(249\) 16.3027 + 9.41238i 1.03314 + 0.596485i
\(250\) 0 0
\(251\) 19.5287i 1.23264i 0.787495 + 0.616321i \(0.211378\pi\)
−0.787495 + 0.616321i \(0.788622\pi\)
\(252\) −3.17890 + 1.12805i −0.200252 + 0.0710607i
\(253\) −11.1898 + 11.1898i −0.703496 + 0.703496i
\(254\) −14.9605 + 8.63746i −0.938706 + 0.541962i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 17.6502 + 4.72936i 1.10099 + 0.295009i 0.763168 0.646200i \(-0.223643\pi\)
0.337823 + 0.941210i \(0.390310\pi\)
\(258\) −7.68517 7.68517i −0.478458 0.478458i
\(259\) 1.10411 + 13.9124i 0.0686061 + 0.864473i
\(260\) 0 0
\(261\) −1.45017 2.51176i −0.0897630 0.155474i
\(262\) 2.36468 + 8.82511i 0.146090 + 0.545217i
\(263\) −4.87220 18.1833i −0.300433 1.12123i −0.936806 0.349850i \(-0.886233\pi\)
0.636373 0.771382i \(-0.280434\pi\)
\(264\) 3.46410 + 6.00000i 0.213201 + 0.369274i
\(265\) 0 0
\(266\) −12.3625 + 8.50848i −0.757996 + 0.521689i
\(267\) −3.65945 3.65945i −0.223955 0.223955i
\(268\) 3.59815 + 0.964122i 0.219792 + 0.0588931i
\(269\) −3.22602 + 5.58762i −0.196694 + 0.340683i −0.947454 0.319891i \(-0.896354\pi\)
0.750761 + 0.660574i \(0.229687\pi\)
\(270\) 0 0
\(271\) −6.82475 + 3.94027i −0.414574 + 0.239354i −0.692753 0.721175i \(-0.743602\pi\)
0.278179 + 0.960529i \(0.410269\pi\)
\(272\) 2.44949 2.44949i 0.148522 0.148522i
\(273\) −1.43054 0.264164i −0.0865802 0.0159879i
\(274\) 0 0
\(275\) 0 0
\(276\) −3.41238 1.97014i −0.205401 0.118588i
\(277\) −14.5852 + 3.90808i −0.876337 + 0.234814i −0.668826 0.743419i \(-0.733203\pi\)
−0.207511 + 0.978233i \(0.566536\pi\)
\(278\) 1.14306 4.26596i 0.0685562 0.255855i
\(279\) 4.41644 0.264406
\(280\) 0 0
\(281\) −8.37459 −0.499586 −0.249793 0.968299i \(-0.580363\pi\)
−0.249793 + 0.968299i \(0.580363\pi\)
\(282\) −4.28341 + 15.9859i −0.255073 + 0.951947i
\(283\) 6.80330 1.82294i 0.404414 0.108362i −0.0508774 0.998705i \(-0.516202\pi\)
0.455291 + 0.890343i \(0.349535\pi\)
\(284\) 5.19615 + 3.00000i 0.308335 + 0.178017i
\(285\) 0 0
\(286\) 2.20822i 0.130575i
\(287\) −4.59759 12.9562i −0.271387 0.764778i
\(288\) 0.901503 0.901503i 0.0531216 0.0531216i
\(289\) 4.33013 2.50000i 0.254713 0.147059i
\(290\) 0 0
\(291\) −12.5498 + 21.7370i −0.735684 + 1.27424i
\(292\) 9.22947 + 2.47303i 0.540114 + 0.144723i
\(293\) 3.33753 + 3.33753i 0.194981 + 0.194981i 0.797844 0.602864i \(-0.205974\pi\)
−0.602864 + 0.797844i \(0.705974\pi\)
\(294\) −5.79532 7.13746i −0.337990 0.416265i
\(295\) 0 0
\(296\) −2.63746 4.56821i −0.153299 0.265522i
\(297\) −7.66557 28.6083i −0.444802 1.66002i
\(298\) 3.31929 + 12.3878i 0.192281 + 0.717604i
\(299\) 0.627940 + 1.08762i 0.0363147 + 0.0628989i
\(300\) 0 0
\(301\) −9.41238 + 19.7668i −0.542520 + 1.13934i
\(302\) −1.41421 1.41421i −0.0813788 0.0813788i
\(303\) −4.99891 1.33945i −0.287180 0.0769496i
\(304\) 2.83616 4.91238i 0.162665 0.281744i
\(305\) 0 0
\(306\) −3.82475 + 2.20822i −0.218646 + 0.126236i
\(307\) 2.19417 2.19417i 0.125228 0.125228i −0.641715 0.766943i \(-0.721777\pi\)
0.766943 + 0.641715i \(0.221777\pi\)
\(308\) 9.05681 10.6183i 0.516060 0.605031i
\(309\) 6.27492i 0.356968i
\(310\) 0 0
\(311\) 22.6495 + 13.0767i 1.28434 + 0.741511i 0.977638 0.210296i \(-0.0674426\pi\)
0.306698 + 0.951807i \(0.400776\pi\)
\(312\) 0.531099 0.142308i 0.0300676 0.00805658i
\(313\) 5.16276 19.2677i 0.291816 1.08907i −0.651897 0.758308i \(-0.726026\pi\)
0.943713 0.330765i \(-0.107307\pi\)
\(314\) −9.97368 −0.562847
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −4.65874 + 17.3867i −0.261661 + 0.976532i 0.702601 + 0.711584i \(0.252022\pi\)
−0.964262 + 0.264949i \(0.914645\pi\)
\(318\) 12.4644 3.33982i 0.698967 0.187288i
\(319\) 10.3923 + 6.00000i 0.581857 + 0.335936i
\(320\) 0 0
\(321\) 8.96379i 0.500310i
\(322\) −1.44133 + 7.80529i −0.0803222 + 0.434972i
\(323\) −13.8943 + 13.8943i −0.773099 + 0.773099i
\(324\) 3.07425 1.77492i 0.170791 0.0986065i
\(325\) 0 0
\(326\) −6.00000 + 10.3923i −0.332309 + 0.575577i
\(327\) 11.1957 + 2.99988i 0.619124 + 0.165894i
\(328\) 3.67423 + 3.67423i 0.202876 + 0.202876i
\(329\) 33.2334 2.63746i 1.83221 0.145408i
\(330\) 0 0
\(331\) −3.08762 5.34792i −0.169711 0.293948i 0.768607 0.639721i \(-0.220950\pi\)
−0.938318 + 0.345773i \(0.887617\pi\)
\(332\) 3.70954 + 13.8442i 0.203588 + 0.759800i
\(333\) 1.74058 + 6.49593i 0.0953832 + 0.355975i
\(334\) 0.866025 + 1.50000i 0.0473868 + 0.0820763i
\(335\) 0 0
\(336\) 3.13746 + 1.49397i 0.171162 + 0.0815025i
\(337\) −25.5968 25.5968i −1.39435 1.39435i −0.815281 0.579065i \(-0.803418\pi\)
−0.579065 0.815281i \(-0.696582\pi\)
\(338\) 12.3878 + 3.31929i 0.673805 + 0.180546i
\(339\) −3.94027 + 6.82475i −0.214006 + 0.370670i
\(340\) 0 0
\(341\) −15.8248 + 9.13642i −0.856958 + 0.494765i
\(342\) −5.11361 + 5.11361i −0.276513 + 0.276513i
\(343\) −9.64572 + 15.8101i −0.520820 + 0.853667i
\(344\) 8.27492i 0.446154i
\(345\) 0 0
\(346\) −4.08762 2.35999i −0.219752 0.126874i
\(347\) 4.99891 1.33945i 0.268355 0.0719056i −0.122132 0.992514i \(-0.538973\pi\)
0.390487 + 0.920608i \(0.372306\pi\)
\(348\) −0.773333 + 2.88612i −0.0414550 + 0.154712i
\(349\) 3.94027 0.210918 0.105459 0.994424i \(-0.466369\pi\)
0.105459 + 0.994424i \(0.466369\pi\)
\(350\) 0 0
\(351\) −2.35050 −0.125460
\(352\) −1.36525 + 5.09518i −0.0727680 + 0.271574i
\(353\) −0.919891 + 0.246484i −0.0489609 + 0.0131190i −0.283216 0.959056i \(-0.591401\pi\)
0.234255 + 0.972175i \(0.424735\pi\)
\(354\) 11.8208 + 6.82475i 0.628269 + 0.362731i
\(355\) 0 0
\(356\) 3.94027i 0.208834i
\(357\) −9.15869 7.81187i −0.484729 0.413448i
\(358\) 6.94715 6.94715i 0.367168 0.367168i
\(359\) −11.8208 + 6.82475i −0.623879 + 0.360197i −0.778378 0.627796i \(-0.783957\pi\)
0.154499 + 0.987993i \(0.450624\pi\)
\(360\) 0 0
\(361\) −6.58762 + 11.4101i −0.346717 + 0.600532i
\(362\) 20.5363 + 5.50269i 1.07937 + 0.289215i
\(363\) 15.6257 + 15.6257i 0.820135 + 0.820135i
\(364\) −0.627940 0.912376i −0.0329130 0.0478215i
\(365\) 0 0
\(366\) 9.41238 + 16.3027i 0.491993 + 0.852156i
\(367\) 1.56156 + 5.82782i 0.0815128 + 0.304210i 0.994631 0.103485i \(-0.0329994\pi\)
−0.913118 + 0.407695i \(0.866333\pi\)
\(368\) −0.776457 2.89778i −0.0404756 0.151057i
\(369\) −3.31233 5.73713i −0.172433 0.298663i
\(370\) 0 0
\(371\) −14.7371 21.4125i −0.765114 1.11168i
\(372\) −3.21722 3.21722i −0.166805 0.166805i
\(373\) 21.7815 + 5.83633i 1.12780 + 0.302194i 0.774037 0.633141i \(-0.218235\pi\)
0.353765 + 0.935334i \(0.384901\pi\)
\(374\) 9.13642 15.8248i 0.472433 0.818278i
\(375\) 0 0
\(376\) −10.9124 + 6.30026i −0.562763 + 0.324911i
\(377\) 0.673407 0.673407i 0.0346822 0.0346822i
\(378\) −11.3024 9.64034i −0.581332 0.495846i
\(379\) 25.8248i 1.32653i 0.748385 + 0.663264i \(0.230829\pi\)
−0.748385 + 0.663264i \(0.769171\pi\)
\(380\) 0 0
\(381\) −19.6495 11.3446i −1.00667 0.581204i
\(382\) 8.78961 2.35517i 0.449715 0.120501i
\(383\) −5.42413 + 20.2431i −0.277160 + 1.03438i 0.677220 + 0.735781i \(0.263185\pi\)
−0.954380 + 0.298595i \(0.903482\pi\)
\(384\) −1.31342 −0.0670254
\(385\) 0 0
\(386\) −10.5498 −0.536972
\(387\) −2.73050 + 10.1904i −0.138799 + 0.518005i
\(388\) −18.4589 + 4.94606i −0.937111 + 0.251098i
\(389\) 2.68439 + 1.54983i 0.136104 + 0.0785797i 0.566506 0.824058i \(-0.308295\pi\)
−0.430402 + 0.902637i \(0.641628\pi\)
\(390\) 0 0
\(391\) 10.3923i 0.525561i
\(392\) 0.722565 6.96261i 0.0364951 0.351665i
\(393\) −8.48528 + 8.48528i −0.428026 + 0.428026i
\(394\) −13.7046 + 7.91238i −0.690430 + 0.398620i
\(395\) 0 0
\(396\) 3.36254 5.82409i 0.168974 0.292672i
\(397\) −1.61745 0.433394i −0.0811775 0.0217514i 0.218002 0.975948i \(-0.430046\pi\)
−0.299179 + 0.954197i \(0.596713\pi\)
\(398\) 12.9209 + 12.9209i 0.647664 + 0.647664i
\(399\) −17.7967 8.47425i −0.890948 0.424243i
\(400\) 0 0
\(401\) 9.04983 + 15.6748i 0.451927 + 0.782761i 0.998506 0.0546470i \(-0.0174034\pi\)
−0.546579 + 0.837408i \(0.684070\pi\)
\(402\) 1.26630 + 4.72590i 0.0631574 + 0.235707i
\(403\) 0.375330 + 1.40075i 0.0186965 + 0.0697764i
\(404\) −1.97014 3.41238i −0.0980179 0.169772i
\(405\) 0 0
\(406\) 6.00000 0.476171i 0.297775 0.0236319i
\(407\) −19.6751 19.6751i −0.975257 0.975257i
\(408\) 4.39480 + 1.17758i 0.217575 + 0.0582991i
\(409\) −8.89834 + 15.4124i −0.439995 + 0.762093i −0.997688 0.0679538i \(-0.978353\pi\)
0.557694 + 0.830047i \(0.311686\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −3.37822 + 3.37822i −0.166433 + 0.166433i
\(413\) 4.99291 27.0383i 0.245685 1.33047i
\(414\) 3.82475i 0.187976i
\(415\) 0 0
\(416\) 0.362541 + 0.209313i 0.0177751 + 0.0102624i
\(417\) 5.60301 1.50132i 0.274381 0.0735200i
\(418\) 7.74413 28.9015i 0.378778 1.41362i
\(419\) 27.4093 1.33903 0.669515 0.742798i \(-0.266502\pi\)
0.669515 + 0.742798i \(0.266502\pi\)
\(420\) 0 0
\(421\) 34.8248 1.69725 0.848627 0.528991i \(-0.177430\pi\)
0.848627 + 0.528991i \(0.177430\pi\)
\(422\) 1.50756 5.62628i 0.0733867 0.273883i
\(423\) 15.5172 4.15783i 0.754474 0.202161i
\(424\) 8.50848 + 4.91238i 0.413209 + 0.238566i
\(425\) 0 0
\(426\) 7.88054i 0.381814i
\(427\) 24.6084 28.8511i 1.19089 1.39620i
\(428\) 4.82583 4.82583i 0.233265 0.233265i
\(429\) 2.51176 1.45017i 0.121269 0.0700147i
\(430\) 0 0
\(431\) 17.2749 29.9210i 0.832103 1.44125i −0.0642636 0.997933i \(-0.520470\pi\)
0.896367 0.443313i \(-0.146197\pi\)
\(432\) 5.42346 + 1.45321i 0.260936 + 0.0699177i
\(433\) −7.94050 7.94050i −0.381596 0.381596i 0.490081 0.871677i \(-0.336967\pi\)
−0.871677 + 0.490081i \(0.836967\pi\)
\(434\) −3.94027 + 8.27492i −0.189139 + 0.397209i
\(435\) 0 0
\(436\) 4.41238 + 7.64246i 0.211314 + 0.366007i
\(437\) 4.40432 + 16.4371i 0.210687 + 0.786295i
\(438\) 3.24814 + 12.1222i 0.155202 + 0.579222i
\(439\) −10.3923 18.0000i −0.495998 0.859093i 0.503992 0.863708i \(-0.331864\pi\)
−0.999989 + 0.00461537i \(0.998531\pi\)
\(440\) 0 0
\(441\) −3.18729 + 8.33585i −0.151776 + 0.396945i
\(442\) −1.02542 1.02542i −0.0487743 0.0487743i
\(443\) −10.7945 2.89237i −0.512860 0.137421i −0.00689820 0.999976i \(-0.502196\pi\)
−0.505962 + 0.862556i \(0.668862\pi\)
\(444\) 3.46410 6.00000i 0.164399 0.284747i
\(445\) 0 0
\(446\) 7.54983 4.35890i 0.357495 0.206400i
\(447\) −11.9107 + 11.9107i −0.563359 + 0.563359i
\(448\) 0.884806 + 2.49342i 0.0418031 + 0.117803i
\(449\) 22.4502i 1.05949i −0.848157 0.529744i \(-0.822288\pi\)
0.848157 0.529744i \(-0.177712\pi\)
\(450\) 0 0
\(451\) 23.7371 + 13.7046i 1.11774 + 0.645326i
\(452\) −5.79555 + 1.55291i −0.272600 + 0.0730429i
\(453\) 0.679878 2.53734i 0.0319435 0.119215i
\(454\) 3.46410 0.162578
\(455\) 0 0
\(456\) 7.45017 0.348886
\(457\) 8.94216 33.3726i 0.418296 1.56110i −0.359844 0.933013i \(-0.617170\pi\)
0.778140 0.628091i \(-0.216163\pi\)
\(458\) 13.3843 3.58630i 0.625405 0.167577i
\(459\) −16.8443 9.72508i −0.786226 0.453928i
\(460\) 0 0
\(461\) 15.7611i 0.734067i −0.930208 0.367034i \(-0.880373\pi\)
0.930208 0.367034i \(-0.119627\pi\)
\(462\) 18.0255 + 3.32861i 0.838624 + 0.154861i
\(463\) −22.3091 + 22.3091i −1.03679 + 1.03679i −0.0374951 + 0.999297i \(0.511938\pi\)
−0.999297 + 0.0374951i \(0.988062\pi\)
\(464\) −1.97014 + 1.13746i −0.0914613 + 0.0528052i
\(465\) 0 0
\(466\) 12.8248 22.2131i 0.594095 1.02900i
\(467\) 12.9243 + 3.46306i 0.598066 + 0.160251i 0.545137 0.838347i \(-0.316478\pi\)
0.0529290 + 0.998598i \(0.483144\pi\)
\(468\) −0.377393 0.377393i −0.0174450 0.0174450i
\(469\) 8.11863 5.58762i 0.374883 0.258013i
\(470\) 0 0
\(471\) −6.54983 11.3446i −0.301800 0.522734i
\(472\) 2.68973 + 10.0382i 0.123805 + 0.462045i
\(473\) −11.2973 42.1622i −0.519451 1.93862i
\(474\) −6.56712 11.3746i −0.301638 0.522452i
\(475\) 0 0
\(476\) −0.725083 9.13642i −0.0332341 0.418767i
\(477\) −8.85704 8.85704i −0.405536 0.405536i
\(478\) −4.39480 1.17758i −0.201014 0.0538614i
\(479\) −3.94027 + 6.82475i −0.180036 + 0.311831i −0.941892 0.335915i \(-0.890955\pi\)
0.761857 + 0.647745i \(0.224288\pi\)
\(480\) 0 0
\(481\) −1.91238 + 1.10411i −0.0871968 + 0.0503431i
\(482\) −6.46043 + 6.46043i −0.294264 + 0.294264i
\(483\) −9.82473 + 3.48638i −0.447041 + 0.158636i
\(484\) 16.8248i 0.764761i
\(485\) 0 0
\(486\) −10.5498 6.09095i −0.478550 0.276291i
\(487\) 8.78961 2.35517i 0.398295 0.106723i −0.0541110 0.998535i \(-0.517232\pi\)
0.452406 + 0.891812i \(0.350566\pi\)
\(488\) −3.70954 + 13.8442i −0.167923 + 0.626698i
\(489\) −15.7611 −0.712741
\(490\) 0 0
\(491\) −19.4502 −0.877774 −0.438887 0.898542i \(-0.644627\pi\)
−0.438887 + 0.898542i \(0.644627\pi\)
\(492\) −1.76638 + 6.59220i −0.0796344 + 0.297200i
\(493\) 7.61202 2.03963i 0.342828 0.0918605i
\(494\) −2.05645 1.18729i −0.0925241 0.0534188i
\(495\) 0 0
\(496\) 3.46410i 0.155543i
\(497\) 14.9605 5.30883i 0.671070 0.238134i
\(498\) −13.3111 + 13.3111i −0.596485 + 0.596485i
\(499\) −3.46410 + 2.00000i −0.155074 + 0.0895323i −0.575529 0.817781i \(-0.695204\pi\)
0.420455 + 0.907314i \(0.361871\pi\)
\(500\) 0 0
\(501\) −1.13746 + 1.97014i −0.0508179 + 0.0880192i
\(502\) −18.8633 5.05441i −0.841910 0.225589i
\(503\) 15.0336 + 15.0336i 0.670317 + 0.670317i 0.957789 0.287472i \(-0.0928148\pi\)
−0.287472 + 0.957789i \(0.592815\pi\)
\(504\) −0.266857 3.36254i −0.0118868 0.149779i
\(505\) 0 0
\(506\) −7.91238 13.7046i −0.351748 0.609245i
\(507\) 4.35964 + 16.2704i 0.193618 + 0.722593i
\(508\) −4.47108 16.6863i −0.198372 0.740334i
\(509\) −0.714256 1.23713i −0.0316588 0.0548347i 0.849762 0.527167i \(-0.176746\pi\)
−0.881421 + 0.472332i \(0.843412\pi\)
\(510\) 0 0
\(511\) 20.8248 14.3326i 0.921233 0.634036i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −30.7636 8.24309i −1.35825 0.363941i
\(514\) −9.13642 + 15.8248i −0.402990 + 0.698000i
\(515\) 0 0
\(516\) 9.41238 5.43424i 0.414357 0.239229i
\(517\) −46.9991 + 46.9991i −2.06702 + 2.06702i
\(518\) −13.7241 2.53430i −0.603002 0.111351i
\(519\) 6.19934i 0.272121i
\(520\) 0 0
\(521\) −23.7371 13.7046i −1.03994 0.600411i −0.120125 0.992759i \(-0.538330\pi\)
−0.919817 + 0.392348i \(0.871663\pi\)
\(522\) 2.80150 0.750661i 0.122619 0.0328555i
\(523\) 8.28588 30.9233i 0.362316 1.35218i −0.508707 0.860940i \(-0.669876\pi\)
0.871023 0.491242i \(-0.163457\pi\)
\(524\) −9.13642 −0.399127
\(525\) 0 0
\(526\) 18.8248 0.820798
\(527\) −3.10583 + 11.5911i −0.135292 + 0.504917i
\(528\) −6.69213 + 1.79315i −0.291238 + 0.0780369i
\(529\) −12.1244 7.00000i −0.527146 0.304348i
\(530\) 0 0
\(531\) 13.2493i 0.574972i
\(532\) −5.01890 14.1435i −0.217597 0.613197i
\(533\) 1.53813 1.53813i 0.0666239 0.0666239i
\(534\) 4.48190 2.58762i 0.193951 0.111977i
\(535\) 0 0
\(536\) −1.86254 + 3.22602i −0.0804495 + 0.139343i
\(537\) 12.4644 + 3.33982i 0.537877 + 0.144124i
\(538\) −4.56228 4.56228i −0.196694 0.196694i
\(539\) −5.82409 36.4622i −0.250861 1.57054i
\(540\) 0 0
\(541\) 4.58762 + 7.94600i 0.197237 + 0.341625i 0.947632 0.319365i \(-0.103470\pi\)
−0.750394 + 0.660990i \(0.770136\pi\)
\(542\) −2.03963 7.61202i −0.0876098 0.326964i
\(543\) 7.22737 + 26.9729i 0.310156 + 1.15752i
\(544\) 1.73205 + 3.00000i 0.0742611 + 0.128624i
\(545\) 0 0
\(546\) 0.625414 1.31342i 0.0267652 0.0562094i
\(547\) 9.06847 + 9.06847i 0.387740 + 0.387740i 0.873881 0.486141i \(-0.161596\pi\)
−0.486141 + 0.873881i \(0.661596\pi\)
\(548\) 0 0
\(549\) 9.13642 15.8248i 0.389933 0.675384i
\(550\) 0 0
\(551\) 11.1752 6.45203i 0.476082 0.274866i
\(552\) 2.78619 2.78619i 0.118588 0.118588i
\(553\) −17.1696 + 20.1297i −0.730125 + 0.856003i
\(554\) 15.0997i 0.641523i
\(555\) 0 0
\(556\) 3.82475 + 2.20822i 0.162206 + 0.0936494i
\(557\) −19.4878 + 5.22174i −0.825724 + 0.221252i −0.646848 0.762619i \(-0.723913\pi\)
−0.178877 + 0.983871i \(0.557246\pi\)
\(558\) −1.14306 + 4.26596i −0.0483896 + 0.180592i
\(559\) −3.46410 −0.146516
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 2.16750 8.08923i 0.0914306 0.341224i
\(563\) −6.23218 + 1.66991i −0.262655 + 0.0703783i −0.387743 0.921767i \(-0.626745\pi\)
0.125088 + 0.992146i \(0.460079\pi\)
\(564\) −14.3326 8.27492i −0.603510 0.348437i
\(565\) 0 0
\(566\) 7.04329i 0.296052i
\(567\) 1.70549 9.23583i 0.0716240 0.387868i
\(568\) −4.24264 + 4.24264i −0.178017 + 0.178017i
\(569\) −8.50848 + 4.91238i −0.356694 + 0.205938i −0.667630 0.744494i \(-0.732691\pi\)
0.310935 + 0.950431i \(0.399358\pi\)
\(570\) 0 0
\(571\) 14.8248 25.6772i 0.620397 1.07456i −0.369015 0.929423i \(-0.620305\pi\)
0.989412 0.145135i \(-0.0463617\pi\)
\(572\) 2.13298 + 0.571530i 0.0891843 + 0.0238969i
\(573\) 8.45115 + 8.45115i 0.353052 + 0.353052i
\(574\) 13.7046 1.08762i 0.572020 0.0453966i
\(575\) 0 0
\(576\) 0.637459 + 1.10411i 0.0265608 + 0.0460046i
\(577\) 5.81285 + 21.6938i 0.241992 + 0.903126i 0.974871 + 0.222768i \(0.0715092\pi\)
−0.732880 + 0.680358i \(0.761824\pi\)
\(578\) 1.29410 + 4.82963i 0.0538273 + 0.200886i
\(579\) −6.92820 12.0000i −0.287926 0.498703i
\(580\) 0 0
\(581\) 34.2371 + 16.3027i 1.42040 + 0.676351i
\(582\) −17.7481 17.7481i −0.735684 0.735684i
\(583\) 50.0589 + 13.4132i 2.07323 + 0.555519i
\(584\) −4.77753 + 8.27492i −0.197695 + 0.342419i
\(585\) 0 0
\(586\) −4.08762 + 2.35999i −0.168858 + 0.0974903i
\(587\) −7.34847 + 7.34847i −0.303304 + 0.303304i −0.842305 0.539001i \(-0.818802\pi\)
0.539001 + 0.842305i \(0.318802\pi\)
\(588\) 8.39419 3.75054i 0.346171 0.154670i
\(589\) 19.6495i 0.809644i
\(590\) 0 0
\(591\) −18.0000 10.3923i −0.740421 0.427482i
\(592\) 5.09518 1.36525i 0.209411 0.0561114i
\(593\) 8.56215 31.9544i 0.351605 1.31221i −0.533098 0.846054i \(-0.678972\pi\)
0.884703 0.466155i \(-0.154361\pi\)
\(594\) 29.6175 1.21522
\(595\) 0 0
\(596\) −12.8248 −0.525322
\(597\) −6.21166 + 23.1822i −0.254226 + 0.948785i
\(598\) −1.21309 + 0.325046i −0.0496068 + 0.0132921i
\(599\) 2.51176 + 1.45017i 0.102628 + 0.0592522i 0.550435 0.834878i \(-0.314462\pi\)
−0.447808 + 0.894130i \(0.647795\pi\)
\(600\) 0 0
\(601\) 6.92820i 0.282607i −0.989966 0.141304i \(-0.954871\pi\)
0.989966 0.141304i \(-0.0451294\pi\)
\(602\) −16.6572 14.2077i −0.678896 0.579062i
\(603\) 3.35817 3.35817i 0.136755 0.136755i
\(604\) 1.73205 1.00000i 0.0704761 0.0406894i
\(605\) 0 0
\(606\) 2.58762 4.48190i 0.105115 0.182065i
\(607\) 21.0519 + 5.64083i 0.854469 + 0.228954i 0.659360 0.751827i \(-0.270827\pi\)
0.195109 + 0.980782i \(0.437494\pi\)
\(608\) 4.01094 + 4.01094i 0.162665 + 0.162665i
\(609\) 4.48190 + 6.51204i 0.181616 + 0.263881i
\(610\) 0 0
\(611\) 2.63746 + 4.56821i 0.106700 + 0.184810i
\(612\) −1.14306 4.26596i −0.0462054 0.172441i
\(613\) −3.66882 13.6922i −0.148182 0.553024i −0.999593 0.0285247i \(-0.990919\pi\)
0.851411 0.524500i \(-0.175748\pi\)
\(614\) 1.55151 + 2.68729i 0.0626138 + 0.108450i
\(615\) 0 0
\(616\) 7.91238 + 11.4964i 0.318799 + 0.463204i
\(617\) −22.3796 22.3796i −0.900968 0.900968i 0.0945520 0.995520i \(-0.469858\pi\)
−0.995520 + 0.0945520i \(0.969858\pi\)
\(618\) −6.06110 1.62407i −0.243813 0.0653296i
\(619\) −1.10411 + 1.91238i −0.0443780 + 0.0768649i −0.887361 0.461075i \(-0.847464\pi\)
0.842983 + 0.537940i \(0.180797\pi\)
\(620\) 0 0
\(621\) −14.5876 + 8.42217i −0.585381 + 0.337970i
\(622\) −18.4932 + 18.4932i −0.741511 + 0.741511i
\(623\) −7.93166 6.76528i −0.317775 0.271045i
\(624\) 0.549834i 0.0220110i
\(625\) 0 0
\(626\) 17.2749 + 9.97368i 0.690445 + 0.398628i
\(627\) 37.9599 10.1713i 1.51597 0.406204i
\(628\) 2.58138 9.63383i 0.103008 0.384432i
\(629\) −18.2728 −0.728586
\(630\) 0 0
\(631\) −35.6495 −1.41918 −0.709592 0.704613i \(-0.751121\pi\)
−0.709592 + 0.704613i \(0.751121\pi\)
\(632\) 2.58819 9.65926i 0.102953 0.384225i
\(633\) 7.38969 1.98006i 0.293714 0.0787004i
\(634\) −15.5885 9.00000i −0.619097 0.357436i
\(635\) 0 0
\(636\) 12.9041i 0.511679i
\(637\) −2.91473 0.302485i −0.115486 0.0119849i
\(638\) −8.48528 + 8.48528i −0.335936 + 0.335936i
\(639\) 6.62466 3.82475i 0.262068 0.151305i
\(640\) 0 0
\(641\) 13.5000 23.3827i 0.533218 0.923561i −0.466029 0.884769i \(-0.654316\pi\)
0.999247 0.0387913i \(-0.0123508\pi\)
\(642\) 8.65836 + 2.32000i 0.341718 + 0.0915631i
\(643\) 4.98036 + 4.98036i 0.196406 + 0.196406i 0.798457 0.602051i \(-0.205650\pi\)
−0.602051 + 0.798457i \(0.705650\pi\)
\(644\) −7.16629 3.41238i −0.282391 0.134466i
\(645\) 0 0
\(646\) −9.82475 17.0170i −0.386550 0.669524i
\(647\) −1.34486 5.01910i −0.0528720 0.197321i 0.934438 0.356126i \(-0.115903\pi\)
−0.987310 + 0.158805i \(0.949236\pi\)
\(648\) 0.918765 + 3.42888i 0.0360925 + 0.134699i
\(649\) 27.4093 + 47.4743i 1.07591 + 1.86353i
\(650\) 0 0
\(651\) −12.0000 + 0.952341i −0.470317 + 0.0373252i
\(652\) −8.48528 8.48528i −0.332309 0.332309i
\(653\) 28.4699 + 7.62850i 1.11412 + 0.298526i 0.768500 0.639850i \(-0.221004\pi\)
0.345615 + 0.938376i \(0.387670\pi\)
\(654\) −5.79532 + 10.0378i −0.226615 + 0.392509i
\(655\) 0 0
\(656\) −4.50000 + 2.59808i −0.175695 + 0.101438i
\(657\) 8.61390 8.61390i 0.336060 0.336060i
\(658\) −6.05384 + 32.7836i −0.236003 + 1.27804i
\(659\) 16.5498i 0.644690i −0.946622 0.322345i \(-0.895529\pi\)
0.946622 0.322345i \(-0.104471\pi\)
\(660\) 0 0
\(661\) −8.58762 4.95807i −0.334020 0.192846i 0.323605 0.946192i \(-0.395105\pi\)
−0.657624 + 0.753346i \(0.728439\pi\)
\(662\) 5.96483 1.59827i 0.231830 0.0621186i
\(663\) 0.492968 1.83978i 0.0191453 0.0714512i
\(664\) −14.3326 −0.556212
\(665\) 0 0
\(666\) −6.72508 −0.260592
\(667\) 1.76638 6.59220i 0.0683943 0.255251i
\(668\) −1.67303 + 0.448288i −0.0647316 + 0.0173448i
\(669\) 9.91613 + 5.72508i 0.383380 + 0.221344i
\(670\) 0 0
\(671\) 75.6032i 2.91863i
\(672\) −2.25509 + 2.64389i −0.0869921 + 0.101990i
\(673\) 12.8689 12.8689i 0.496059 0.496059i −0.414150 0.910209i \(-0.635921\pi\)
0.910209 + 0.414150i \(0.135921\pi\)
\(674\) 31.3495 18.0997i 1.20754 0.697173i
\(675\) 0 0
\(676\) −6.41238 + 11.1066i −0.246630 + 0.427175i
\(677\) 29.8214 + 7.99062i 1.14613 + 0.307104i 0.781413 0.624014i \(-0.214499\pi\)
0.364716 + 0.931119i \(0.381166\pi\)
\(678\) −5.57239 5.57239i −0.214006 0.214006i
\(679\) −21.7370 + 45.6495i −0.834188 + 1.75187i
\(680\) 0 0
\(681\) 2.27492 + 3.94027i 0.0871750 + 0.150992i
\(682\) −4.72936 17.6502i −0.181097 0.675862i
\(683\) 7.97803 + 29.7744i 0.305271 + 1.13929i 0.932712 + 0.360622i \(0.117436\pi\)
−0.627441 + 0.778664i \(0.715898\pi\)
\(684\) −3.61587 6.26287i −0.138256 0.239467i
\(685\) 0 0
\(686\) −12.7749 13.4090i −0.487749 0.511958i
\(687\) 12.8689 + 12.8689i 0.490978 + 0.490978i
\(688\) 7.99296 + 2.14171i 0.304729 + 0.0816518i
\(689\) 2.05645 3.56188i 0.0783446 0.135697i
\(690\) 0 0
\(691\) 35.4743 20.4811i 1.34950 0.779137i 0.361325 0.932440i \(-0.382324\pi\)
0.988179 + 0.153303i \(0.0489911\pi\)
\(692\) 3.33753 3.33753i 0.126874 0.126874i
\(693\) −5.95039 16.7684i −0.226037 0.636980i
\(694\) 5.17525i 0.196450i
\(695\) 0 0
\(696\) −2.58762 1.49397i −0.0980836 0.0566286i
\(697\) 17.3867 4.65874i 0.658567 0.176462i
\(698\) −1.01982 + 3.80601i −0.0386007 + 0.144060i
\(699\) 33.6887 1.27422
\(700\) 0 0
\(701\) −8.27492 −0.312539 −0.156270 0.987714i \(-0.549947\pi\)
−0.156270 + 0.987714i \(0.549947\pi\)
\(702\) 0.608353 2.27041i 0.0229608 0.0856909i
\(703\) −28.9015 + 7.74413i −1.09004 + 0.292076i
\(704\) −4.56821 2.63746i −0.172171 0.0994030i
\(705\) 0 0
\(706\) 0.952341i 0.0358418i
\(707\) −10.2517 1.89308i −0.385553 0.0711965i
\(708\) −9.65166 + 9.65166i −0.362731 + 0.362731i
\(709\) −11.4101 + 6.58762i −0.428515 + 0.247403i −0.698714 0.715401i \(-0.746244\pi\)
0.270199 + 0.962805i \(0.412911\pi\)
\(710\) 0 0
\(711\) −6.37459 + 11.0411i −0.239066 + 0.414074i
\(712\) 3.80601 + 1.01982i 0.142636 + 0.0382193i
\(713\) 7.34847 + 7.34847i 0.275202 + 0.275202i
\(714\) 9.91613 6.82475i 0.371102 0.255410i
\(715\) 0 0
\(716\) 4.91238 + 8.50848i 0.183584 + 0.317977i
\(717\) −1.54667 5.77224i −0.0577613 0.215568i
\(718\) −3.53275 13.1844i −0.131841 0.492038i
\(719\) 19.5287 + 33.8248i 0.728299 + 1.26145i 0.957602 + 0.288095i \(0.0930220\pi\)
−0.229303 + 0.973355i \(0.573645\pi\)
\(720\) 0 0
\(721\) 1.00000 + 12.6005i 0.0372419 + 0.469268i
\(722\) −9.31631 9.31631i −0.346717 0.346717i
\(723\) −11.5911 3.10583i −0.431078 0.115507i
\(724\) −10.6304 + 18.4124i −0.395075 + 0.684291i
\(725\) 0 0
\(726\) −19.1375 + 11.0490i −0.710258 + 0.410067i
\(727\) 1.30612 1.30612i 0.0484415 0.0484415i −0.682471 0.730913i \(-0.739095\pi\)
0.730913 + 0.682471i \(0.239095\pi\)
\(728\) 1.04381 0.370403i 0.0386862 0.0137281i
\(729\) 26.6495i 0.987019i
\(730\) 0 0
\(731\) −24.8248 14.3326i −0.918177 0.530110i
\(732\) −18.1833 + 4.87220i −0.672075 + 0.180082i
\(733\) 8.17753 30.5189i 0.302044 1.12724i −0.633416 0.773811i \(-0.718348\pi\)
0.935460 0.353432i \(-0.114985\pi\)
\(734\) −6.03341 −0.222697
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −5.08567 + 18.9800i −0.187333 + 0.699136i
\(738\) 6.39893 1.71459i 0.235548 0.0631149i
\(739\) −3.61587 2.08762i −0.133012 0.0767945i 0.432017 0.901865i \(-0.357802\pi\)
−0.565029 + 0.825071i \(0.691135\pi\)
\(740\) 0 0
\(741\) 3.11884i 0.114573i
\(742\) 24.4972 8.69300i 0.899320 0.319130i
\(743\) −10.6066 + 10.6066i −0.389118 + 0.389118i −0.874373 0.485254i \(-0.838727\pi\)
0.485254 + 0.874373i \(0.338727\pi\)
\(744\) 3.94027 2.27492i 0.144457 0.0834025i
\(745\) 0 0
\(746\) −11.2749 + 19.5287i −0.412804 + 0.714998i
\(747\) 17.6502 + 4.72936i 0.645788 + 0.173038i
\(748\) 12.9209 + 12.9209i 0.472433 + 0.472433i
\(749\) −1.42851 18.0000i −0.0521967 0.657706i
\(750\) 0 0
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) −3.26126 12.1712i −0.118926 0.443837i
\(753\) −6.63858 24.7755i −0.241923 0.902870i
\(754\) 0.476171 + 0.824752i 0.0173411 + 0.0300357i
\(755\) 0 0
\(756\) 12.2371 8.42217i 0.445060 0.306311i
\(757\) 4.24264 + 4.24264i 0.154201 + 0.154201i 0.779992 0.625790i \(-0.215223\pi\)
−0.625790 + 0.779992i \(0.715223\pi\)
\(758\) −24.9448 6.68394i −0.906036 0.242772i
\(759\) 10.3923 18.0000i 0.377217 0.653359i
\(760\) 0 0
\(761\) −43.9124 + 25.3528i −1.59182 + 0.919039i −0.598828 + 0.800878i \(0.704367\pi\)
−0.992994 + 0.118161i \(0.962300\pi\)
\(762\) 16.0438 16.0438i 0.581204 0.581204i
\(763\) 22.9599 + 4.23979i 0.831205 + 0.153491i
\(764\) 9.09967i 0.329214i
\(765\) 0 0
\(766\) −18.1495 10.4786i −0.655768 0.378608i
\(767\) 4.20226 1.12599i 0.151735 0.0406572i
\(768\) 0.339939 1.26867i 0.0122665 0.0457792i
\(769\) 17.9693 0.647990 0.323995 0.946059i \(-0.394974\pi\)
0.323995 + 0.946059i \(0.394974\pi\)
\(770\) 0 0
\(771\) −24.0000 −0.864339
\(772\) 2.73050 10.1904i 0.0982728 0.366759i
\(773\) 32.2476 8.64071i 1.15986 0.310785i 0.372953 0.927850i \(-0.378345\pi\)
0.786912 + 0.617066i \(0.211679\pi\)
\(774\) −9.13642 5.27492i −0.328402 0.189603i
\(775\) 0 0
\(776\) 19.1101i 0.686013i
\(777\) −6.13011 17.2749i −0.219917 0.619733i
\(778\) −2.19180 + 2.19180i −0.0785797 + 0.0785797i
\(779\) 25.5255 14.7371i 0.914544 0.528012i
\(780\) 0 0
\(781\) −15.8248 + 27.4093i −0.566254 + 0.980781i
\(782\) −10.0382 2.68973i −0.358965 0.0961844i
\(783\) 9.03199 + 9.03199i 0.322777 + 0.322777i
\(784\) 6.53835 + 2.50000i 0.233512 + 0.0892857i
\(785\) 0 0
\(786\) −6.00000 10.3923i −0.214013 0.370681i
\(787\) 8.22221 + 30.6857i 0.293090 + 1.09383i 0.942722 + 0.333578i \(0.108256\pi\)
−0.649632 + 0.760249i \(0.725077\pi\)
\(788\) −4.09575 15.2855i −0.145905 0.544525i
\(789\) 12.3624 + 21.4124i 0.440115 + 0.762301i
\(790\) 0 0
\(791\) −6.82475 + 14.3326i −0.242660 + 0.509608i
\(792\) 4.75535 + 4.75535i 0.168974 + 0.168974i
\(793\) 5.79555 + 1.55291i 0.205806 + 0.0551456i
\(794\) 0.837253 1.45017i 0.0297130 0.0514645i
\(795\) 0 0
\(796\) −15.8248 + 9.13642i −0.560893 + 0.323832i
\(797\) −9.79796 + 9.79796i −0.347062 + 0.347062i −0.859014 0.511952i \(-0.828922\pi\)
0.511952 + 0.859014i \(0.328922\pi\)
\(798\) 12.7916 14.9970i 0.452818 0.530887i
\(799\) 43.6495i 1.54421i
\(800\) 0 0
\(801\) −4.35050 2.51176i −0.153717 0.0887487i
\(802\) −17.4829 + 4.68454i −0.617344 + 0.165417i
\(803\) −13.0450 + 48.6847i −0.460349 + 1.71805i
\(804\) −4.89261 −0.172549
\(805\) 0 0
\(806\) −1.45017 −0.0510799
\(807\) 2.19330 8.18550i 0.0772078 0.288143i
\(808\) 3.80601 1.01982i 0.133895 0.0358771i
\(809\) −5.28247 3.04983i −0.185722 0.107226i 0.404256 0.914646i \(-0.367530\pi\)
−0.589978 + 0.807419i \(0.700864\pi\)
\(810\) 0 0
\(811\) 17.0170i 0.597547i 0.954324 + 0.298773i \(0.0965774\pi\)
−0.954324 + 0.298773i \(0.903423\pi\)
\(812\) −1.09297 + 5.91880i −0.0383557 + 0.207709i
\(813\) 7.31891 7.31891i 0.256685 0.256685i
\(814\) 24.0969 13.9124i 0.844597 0.487629i
\(815\) 0 0
\(816\) −2.27492 + 3.94027i −0.0796380 + 0.137937i
\(817\) −45.3386 12.1484i −1.58620 0.425020i
\(818\) −12.5842 12.5842i −0.439995 0.439995i
\(819\) −1.40765 + 0.111714i −0.0491873 + 0.00390359i
\(820\) 0 0
\(821\) −24.0997 41.7419i −0.841084 1.45680i −0.888979 0.457948i \(-0.848584\pi\)
0.0478946 0.998852i \(-0.484749\pi\)
\(822\) 0 0
\(823\) −4.87220 18.1833i −0.169834 0.633830i −0.997374 0.0724232i \(-0.976927\pi\)
0.827540 0.561407i \(-0.189740\pi\)
\(824\) −2.38876 4.13746i −0.0832165 0.144135i
\(825\) 0 0
\(826\) 24.8248 + 11.8208i 0.863764 + 0.411299i
\(827\) −18.7201 18.7201i −0.650963 0.650963i 0.302262 0.953225i \(-0.402258\pi\)
−0.953225 + 0.302262i \(0.902258\pi\)
\(828\) −3.69443 0.989919i −0.128390 0.0344020i
\(829\) −5.67232 + 9.82475i −0.197008 + 0.341228i −0.947557 0.319587i \(-0.896456\pi\)
0.750549 + 0.660815i \(0.229789\pi\)
\(830\) 0 0
\(831\) 17.1752 9.91613i 0.595803 0.343987i
\(832\) −0.296014 + 0.296014i −0.0102624 + 0.0102624i
\(833\) −19.6363 14.2273i −0.680358 0.492946i
\(834\) 5.80066i 0.200861i
\(835\) 0 0
\(836\) 25.9124 + 14.9605i 0.896198 + 0.517420i
\(837\) −18.7874 + 5.03407i −0.649388 + 0.174003i
\(838\) −7.09404 + 26.4753i −0.245060 + 0.914575i
\(839\) 2.51176 0.0867156 0.0433578 0.999060i \(-0.486194\pi\)
0.0433578 + 0.999060i \(0.486194\pi\)
\(840\) 0 0
\(841\) 23.8248 0.821543
\(842\) −9.01331 + 33.6381i −0.310619 + 1.15925i
\(843\) 10.6246 2.84685i 0.365930 0.0980507i
\(844\) 5.04438 + 2.91238i 0.173635 + 0.100248i
\(845\) 0 0
\(846\) 16.0646i 0.552313i
\(847\) 33.8678 + 28.8874i 1.16371 + 0.992583i
\(848\) −6.94715 + 6.94715i −0.238566 + 0.238566i
\(849\) −8.01145 + 4.62541i −0.274952 + 0.158744i
\(850\) 0 0
\(851\) −7.91238 + 13.7046i −0.271233 + 0.469789i
\(852\) −7.61202 2.03963i −0.260784 0.0698767i
\(853\) −24.3616 24.3616i −0.834127 0.834127i 0.153952 0.988078i \(-0.450800\pi\)
−0.988078 + 0.153952i \(0.950800\pi\)
\(854\) 21.4989 + 31.2371i 0.735676 + 1.06891i
\(855\) 0 0
\(856\) 3.41238 + 5.91041i 0.116633 + 0.202014i
\(857\) 4.07927 + 15.2240i 0.139345 + 0.520043i 0.999942 + 0.0107567i \(0.00342404\pi\)
−0.860597 + 0.509287i \(0.829909\pi\)
\(858\) 0.750661 + 2.80150i 0.0256271 + 0.0956418i
\(859\) −1.25588 2.17525i −0.0428501 0.0742185i 0.843805 0.536650i \(-0.180310\pi\)
−0.886655 + 0.462431i \(0.846977\pi\)
\(860\) 0 0
\(861\) 10.2371 + 14.8742i 0.348880 + 0.506911i
\(862\) 24.4304 + 24.4304i 0.832103 + 0.832103i
\(863\) −37.6711 10.0939i −1.28234 0.343602i −0.447593 0.894237i \(-0.647719\pi\)
−0.834746 + 0.550635i \(0.814385\pi\)
\(864\) −2.80739 + 4.86254i −0.0955093 + 0.165427i
\(865\) 0 0
\(866\) 9.72508 5.61478i 0.330472 0.190798i
\(867\) −4.64366 + 4.64366i −0.157707 + 0.157707i
\(868\) −6.97314 5.94772i −0.236684 0.201879i
\(869\) 52.7492i 1.78939i
\(870\) 0 0
\(871\) 1.35050 + 0.779710i 0.0457598 + 0.0264195i
\(872\) −8.52406 + 2.28401i −0.288661 + 0.0773465i
\(873\) −6.30582 + 23.5336i −0.213420 + 0.796492i
\(874\) −17.0170 −0.575608
\(875\) 0 0
\(876\) −12.5498 −0.424020
\(877\) 3.66882 13.6922i 0.123887 0.462354i −0.875910 0.482474i \(-0.839738\pi\)
0.999798 + 0.0201202i \(0.00640488\pi\)
\(878\) 20.0764 5.37945i 0.677545 0.181548i
\(879\) −5.36878 3.09967i −0.181085 0.104549i
\(880\) 0 0
\(881\) 31.3495i 1.05619i −0.849184 0.528097i \(-0.822906\pi\)
0.849184 0.528097i \(-0.177094\pi\)
\(882\) −7.22688 5.23617i −0.243342 0.176311i
\(883\) −6.43444 + 6.43444i −0.216536 + 0.216536i −0.807037 0.590501i \(-0.798930\pi\)
0.590501 + 0.807037i \(0.298930\pi\)
\(884\) 1.25588 0.725083i 0.0422398 0.0243872i
\(885\) 0 0
\(886\) 5.58762 9.67805i 0.187720 0.325140i
\(887\) −21.4562 5.74918i −0.720430 0.193039i −0.120066 0.992766i \(-0.538311\pi\)
−0.600363 + 0.799727i \(0.704977\pi\)
\(888\) 4.89898 + 4.89898i 0.164399 + 0.164399i
\(889\) −41.2657 19.6495i −1.38401 0.659023i
\(890\) 0 0
\(891\) 9.36254 + 16.2164i 0.313657 + 0.543270i
\(892\) 2.25633 + 8.42075i 0.0755476 + 0.281947i
\(893\) 18.4989 + 69.0388i 0.619042 + 2.31030i
\(894\) −8.42217 14.5876i −0.281679 0.487883i
\(895\) 0 0
\(896\) −2.63746 + 0.209313i −0.0881113 + 0.00699267i
\(897\) −1.16637 1.16637i −0.0389441 0.0389441i
\(898\) 21.6852 + 5.81053i 0.723644 + 0.193900i
\(899\) 3.94027 6.82475i 0.131415 0.227618i
\(900\) 0 0
\(901\) 29.4743 17.0170i 0.981930 0.566917i
\(902\) −19.3813 + 19.3813i −0.645326 + 0.645326i
\(903\) 5.22169 28.2772i 0.173767 0.941006i
\(904\) 6.00000i 0.199557i
\(905\) 0 0
\(906\) 2.27492 + 1.31342i 0.0755791 + 0.0436356i
\(907\) −26.9729 + 7.22737i −0.895621 + 0.239981i −0.677135 0.735859i \(-0.736779\pi\)
−0.218486 + 0.975840i \(0.570112\pi\)
\(908\) −0.896575 + 3.34607i −0.0297539 + 0.111043i
\(909\) −5.02352 −0.166620
\(910\) 0 0
\(911\) −19.6495 −0.651017 −0.325509 0.945539i \(-0.605535\pi\)
−0.325509 + 0.945539i \(0.605535\pi\)
\(912\) −1.92824 + 7.19631i −0.0638506 + 0.238294i
\(913\) −73.0270 + 19.5675i −2.41684 + 0.647591i
\(914\) 29.9210 + 17.2749i 0.989700 + 0.571403i
\(915\) 0 0
\(916\) 13.8564i 0.457829i
\(917\) −15.6869 + 18.3914i −0.518026 + 0.607336i
\(918\) 13.7533 13.7533i 0.453928 0.453928i
\(919\) −29.1413 + 16.8248i −0.961284 + 0.554997i −0.896568 0.442906i \(-0.853947\pi\)
−0.0647157 + 0.997904i \(0.520614\pi\)
\(920\) 0 0
\(921\) −2.03779 + 3.52956i −0.0671475 + 0.116303i
\(922\) 15.2240 + 4.07927i 0.501377 + 0.134344i
\(923\) 1.77608 + 1.77608i 0.0584605 + 0.0584605i
\(924\) −7.88054 + 16.5498i −0.259251 + 0.544450i
\(925\) 0 0
\(926\) −15.7749 27.3230i −0.518396 0.897888i
\(927\) 1.57645 + 5.88341i 0.0517775 + 0.193236i
\(928\) −0.588792 2.19740i −0.0193280 0.0721332i
\(929\) 6.53835 + 11.3248i 0.214516 + 0.371553i 0.953123 0.302584i \(-0.0978492\pi\)
−0.738607 + 0.674137i \(0.764516\pi\)
\(930\) 0 0
\(931\) −37.0876 14.1808i −1.21550 0.464757i
\(932\) 18.1369 + 18.1369i 0.594095 + 0.594095i
\(933\) −33.1800 8.89056i −1.08627 0.291064i
\(934\) −6.69012 + 11.5876i −0.218907 + 0.379159i
\(935\) 0 0
\(936\) 0.462210 0.266857i 0.0151078 0.00872250i
\(937\) 37.5785 37.5785i 1.22764 1.22764i 0.262781 0.964856i \(-0.415360\pi\)
0.964856 0.262781i \(-0.0846397\pi\)
\(938\) 3.29597 + 9.28818i 0.107617 + 0.303270i
\(939\) 26.1993i 0.854983i
\(940\) 0 0
\(941\) −4.35050 2.51176i −0.141822 0.0818811i 0.427410 0.904058i \(-0.359426\pi\)
−0.569232 + 0.822177i \(0.692759\pi\)
\(942\) 12.6533 3.39044i 0.412267 0.110467i
\(943\) 4.03459 15.0573i 0.131384 0.490333i
\(944\) −10.3923 −0.338241
\(945\) 0 0
\(946\) 43.6495 1.41917
\(947\) 4.87220 18.1833i 0.158325 0.590878i −0.840472 0.541855i \(-0.817722\pi\)
0.998798 0.0490237i \(-0.0156110\pi\)
\(948\) 12.6867 3.39939i 0.412045 0.110407i
\(949\) 3.46410 + 2.00000i 0.112449 + 0.0649227i
\(950\) 0 0
\(951\) 23.6416i 0.766632i
\(952\) 9.01277 + 1.66430i 0.292106 + 0.0539404i
\(953\) 27.7886 27.7886i 0.900161 0.900161i −0.0952888 0.995450i \(-0.530377\pi\)
0.995450 + 0.0952888i \(0.0303775\pi\)
\(954\) 10.8476 6.26287i 0.351204 0.202768i
\(955\) 0 0
\(956\) 2.27492 3.94027i 0.0735761 0.127438i
\(957\) −15.2240 4.07927i −0.492123 0.131864i
\(958\) −5.57239 5.57239i −0.180036 0.180036i
\(959\) 0 0
\(960\) 0 0
\(961\) −9.50000 16.4545i −0.306452 0.530790i
\(962\) −0.571530 2.13298i −0.0184269 0.0687700i
\(963\) −2.25198 8.40451i −0.0725691 0.270832i
\(964\) −4.56821 7.91238i −0.147132 0.254840i
\(965\) 0 0
\(966\) −0.824752 10.3923i −0.0265359 0.334367i
\(967\) −19.7455 19.7455i −0.634974 0.634974i 0.314337 0.949311i \(-0.398218\pi\)
−0.949311 + 0.314337i \(0.898218\pi\)
\(968\) −16.2515 4.35457i −0.522342 0.139961i
\(969\) 12.9041 22.3505i 0.414538 0.718001i
\(970\) 0 0
\(971\) 41.7371 24.0969i 1.33941 0.773308i 0.352689 0.935741i \(-0.385267\pi\)
0.986720 + 0.162433i \(0.0519342\pi\)
\(972\) 8.61390 8.61390i 0.276291 0.276291i
\(973\) 11.0120 3.90769i 0.353029 0.125275i
\(974\) 9.09967i 0.291572i
\(975\) 0 0
\(976\) −12.4124 7.16629i −0.397310 0.229387i
\(977\) 18.9800 5.08567i 0.607223 0.162705i 0.0579102 0.998322i \(-0.481556\pi\)
0.549313 + 0.835617i \(0.314890\pi\)
\(978\) 4.07927 15.2240i 0.130441 0.486811i
\(979\) 20.7846 0.664279
\(980\) 0 0
\(981\) 11.2508 0.359211
\(982\) 5.03407 18.7874i 0.160644 0.599531i
\(983\) 33.6274 9.01044i 1.07255 0.287388i 0.321008 0.947076i \(-0.395978\pi\)
0.751539 + 0.659688i \(0.229312\pi\)
\(984\) −5.91041 3.41238i −0.188417 0.108783i
\(985\) 0 0
\(986\) 7.88054i 0.250968i
\(987\) −41.2656 + 14.6434i −1.31350 + 0.466104i
\(988\) 1.67909 1.67909i 0.0534188 0.0534188i
\(989\) −21.4989 + 12.4124i −0.683624 + 0.394691i
\(990\) 0 0
\(991\) 10.8248 18.7490i 0.343860 0.595582i −0.641286 0.767302i \(-0.721599\pi\)
0.985146 + 0.171719i \(0.0549322\pi\)
\(992\) 3.34607 + 0.896575i 0.106238 + 0.0284663i
\(993\) 5.73514 + 5.73514i 0.181999 + 0.181999i
\(994\) 1.25588 + 15.8248i 0.0398341 + 0.501931i
\(995\) 0 0
\(996\) −9.41238 16.3027i −0.298243 0.516571i
\(997\) −7.85248 29.3059i −0.248691 0.928126i −0.971492 0.237071i \(-0.923813\pi\)
0.722802 0.691055i \(-0.242854\pi\)
\(998\) −1.03528 3.86370i −0.0327711 0.122303i
\(999\) −14.8087 25.6495i −0.468528 0.811514i
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.d.157.1 yes 16
5.2 odd 4 inner 350.2.o.d.143.2 16
5.3 odd 4 inner 350.2.o.d.143.3 yes 16
5.4 even 2 inner 350.2.o.d.157.4 yes 16
7.5 odd 6 inner 350.2.o.d.257.3 yes 16
35.12 even 12 inner 350.2.o.d.243.4 yes 16
35.19 odd 6 inner 350.2.o.d.257.2 yes 16
35.33 even 12 inner 350.2.o.d.243.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.o.d.143.2 16 5.2 odd 4 inner
350.2.o.d.143.3 yes 16 5.3 odd 4 inner
350.2.o.d.157.1 yes 16 1.1 even 1 trivial
350.2.o.d.157.4 yes 16 5.4 even 2 inner
350.2.o.d.243.1 yes 16 35.33 even 12 inner
350.2.o.d.243.4 yes 16 35.12 even 12 inner
350.2.o.d.257.2 yes 16 35.19 odd 6 inner
350.2.o.d.257.3 yes 16 7.5 odd 6 inner