Properties

Label 855.2.be.d.64.1
Level $855$
Weight $2$
Character 855.64
Analytic conductor $6.827$
Analytic rank $0$
Dimension $12$
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] = [855,2,Mod(64,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.be (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 64.1
Root \(-0.352587 + 0.203566i\) of defining polynomial
Character \(\chi\) \(=\) 855.64
Dual form 855.2.be.d.334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.12713 + 1.22810i) q^{2} +(2.01647 - 3.49262i) q^{4} +(0.746759 + 2.10769i) q^{5} +4.50527i q^{7} +4.99330i q^{8} +O(q^{10})\) \(q+(-2.12713 + 1.22810i) q^{2} +(2.01647 - 3.49262i) q^{4} +(0.746759 + 2.10769i) q^{5} +4.50527i q^{7} +4.99330i q^{8} +(-4.17691 - 3.56624i) q^{10} -2.19869 q^{11} +(-3.25495 - 1.87925i) q^{13} +(-5.53293 - 9.58332i) q^{14} +(-2.09935 - 3.63617i) q^{16} +(-0.576674 + 0.332943i) q^{17} +(-3.79804 - 2.13891i) q^{19} +(8.86718 + 1.64194i) q^{20} +(4.67691 - 2.70022i) q^{22} +(0.422643 + 0.244013i) q^{23} +(-3.88470 + 3.14787i) q^{25} +9.23163 q^{26} +(15.7352 + 9.08474i) q^{28} +(-1.79804 + 3.11429i) q^{29} +6.83424 q^{31} +(0.282531 + 0.163119i) q^{32} +(0.817776 - 1.41643i) q^{34} +(-9.49572 + 3.36435i) q^{35} -3.01171i q^{37} +(10.7057 - 0.114636i) q^{38} +(-10.5243 + 3.72879i) q^{40} +(0.0362063 + 0.0627112i) q^{41} +(-0.364199 + 0.210271i) q^{43} +(-4.43359 + 7.67920i) q^{44} -1.19869 q^{46} +(4.34986 + 2.51139i) q^{47} -13.2975 q^{49} +(4.39738 - 11.4668i) q^{50} +(-13.1270 + 7.57888i) q^{52} +(-2.26725 - 1.30900i) q^{53} +(-1.64189 - 4.63416i) q^{55} -22.4962 q^{56} -8.83269i q^{58} +(-6.26783 - 10.8562i) q^{59} +(-3.53293 + 6.11922i) q^{61} +(-14.5374 + 8.39315i) q^{62} +7.59607 q^{64} +(1.53020 - 8.26377i) q^{65} +(-4.95944 - 2.86334i) q^{67} +2.68548i q^{68} +(16.0669 - 18.8181i) q^{70} +(3.48626 + 6.03838i) q^{71} +(2.56139 - 1.47882i) q^{73} +(3.69869 + 6.40632i) q^{74} +(-15.1290 + 8.95208i) q^{76} -9.90571i q^{77} +(5.66849 + 9.81811i) q^{79} +(6.09622 - 7.14011i) q^{80} +(-0.154031 - 0.0889301i) q^{82} -15.6999i q^{83} +(-1.13238 - 0.966822i) q^{85} +(0.516467 - 0.894547i) q^{86} -10.9787i q^{88} +(0.668486 - 1.15785i) q^{89} +(8.46652 - 14.6644i) q^{91} +(1.70449 - 0.984089i) q^{92} -12.3370 q^{94} +(1.67193 - 9.60233i) q^{95} +(3.79871 - 2.19319i) q^{97} +(28.2856 - 16.3307i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12713 + 1.22810i −1.50411 + 0.868399i −0.504123 + 0.863632i \(0.668184\pi\)
−0.999989 + 0.00476685i \(0.998483\pi\)
\(3\) 0 0
\(4\) 2.01647 3.49262i 1.00823 1.74631i
\(5\) 0.746759 + 2.10769i 0.333961 + 0.942587i
\(6\) 0 0
\(7\) 4.50527i 1.70283i 0.524490 + 0.851417i \(0.324256\pi\)
−0.524490 + 0.851417i \(0.675744\pi\)
\(8\) 4.99330i 1.76540i
\(9\) 0 0
\(10\) −4.17691 3.56624i −1.32086 1.12774i
\(11\) −2.19869 −0.662930 −0.331465 0.943467i \(-0.607543\pi\)
−0.331465 + 0.943467i \(0.607543\pi\)
\(12\) 0 0
\(13\) −3.25495 1.87925i −0.902761 0.521209i −0.0246661 0.999696i \(-0.507852\pi\)
−0.878095 + 0.478486i \(0.841186\pi\)
\(14\) −5.53293 9.58332i −1.47874 2.56125i
\(15\) 0 0
\(16\) −2.09935 3.63617i −0.524836 0.909043i
\(17\) −0.576674 + 0.332943i −0.139864 + 0.0807506i −0.568299 0.822822i \(-0.692398\pi\)
0.428435 + 0.903573i \(0.359065\pi\)
\(18\) 0 0
\(19\) −3.79804 2.13891i −0.871329 0.490699i
\(20\) 8.86718 + 1.64194i 1.98276 + 0.367149i
\(21\) 0 0
\(22\) 4.67691 2.70022i 0.997121 0.575688i
\(23\) 0.422643 + 0.244013i 0.0881272 + 0.0508802i 0.543416 0.839464i \(-0.317131\pi\)
−0.455289 + 0.890344i \(0.650464\pi\)
\(24\) 0 0
\(25\) −3.88470 + 3.14787i −0.776941 + 0.629574i
\(26\) 9.23163 1.81047
\(27\) 0 0
\(28\) 15.7352 + 9.08474i 2.97368 + 1.71685i
\(29\) −1.79804 + 3.11429i −0.333887 + 0.578309i −0.983270 0.182152i \(-0.941694\pi\)
0.649383 + 0.760461i \(0.275027\pi\)
\(30\) 0 0
\(31\) 6.83424 1.22747 0.613733 0.789514i \(-0.289667\pi\)
0.613733 + 0.789514i \(0.289667\pi\)
\(32\) 0.282531 + 0.163119i 0.0499449 + 0.0288357i
\(33\) 0 0
\(34\) 0.817776 1.41643i 0.140247 0.242916i
\(35\) −9.49572 + 3.36435i −1.60507 + 0.568679i
\(36\) 0 0
\(37\) 3.01171i 0.495123i −0.968872 0.247561i \(-0.920371\pi\)
0.968872 0.247561i \(-0.0796292\pi\)
\(38\) 10.7057 0.114636i 1.73670 0.0185964i
\(39\) 0 0
\(40\) −10.5243 + 3.72879i −1.66404 + 0.589573i
\(41\) 0.0362063 + 0.0627112i 0.00565448 + 0.00979384i 0.868839 0.495095i \(-0.164867\pi\)
−0.863184 + 0.504889i \(0.831533\pi\)
\(42\) 0 0
\(43\) −0.364199 + 0.210271i −0.0555399 + 0.0320660i −0.527513 0.849547i \(-0.676875\pi\)
0.471973 + 0.881613i \(0.343542\pi\)
\(44\) −4.43359 + 7.67920i −0.668389 + 1.15768i
\(45\) 0 0
\(46\) −1.19869 −0.176737
\(47\) 4.34986 + 2.51139i 0.634492 + 0.366324i 0.782490 0.622664i \(-0.213950\pi\)
−0.147998 + 0.988988i \(0.547283\pi\)
\(48\) 0 0
\(49\) −13.2975 −1.89964
\(50\) 4.39738 11.4668i 0.621884 1.62164i
\(51\) 0 0
\(52\) −13.1270 + 7.57888i −1.82039 + 1.05100i
\(53\) −2.26725 1.30900i −0.311430 0.179804i 0.336136 0.941813i \(-0.390880\pi\)
−0.647566 + 0.762009i \(0.724213\pi\)
\(54\) 0 0
\(55\) −1.64189 4.63416i −0.221393 0.624870i
\(56\) −22.4962 −3.00618
\(57\) 0 0
\(58\) 8.83269i 1.15979i
\(59\) −6.26783 10.8562i −0.816002 1.41336i −0.908606 0.417654i \(-0.862852\pi\)
0.0926038 0.995703i \(-0.470481\pi\)
\(60\) 0 0
\(61\) −3.53293 + 6.11922i −0.452346 + 0.783486i −0.998531 0.0541782i \(-0.982746\pi\)
0.546185 + 0.837664i \(0.316079\pi\)
\(62\) −14.5374 + 8.39315i −1.84625 + 1.06593i
\(63\) 0 0
\(64\) 7.59607 0.949509
\(65\) 1.53020 8.26377i 0.189799 1.02499i
\(66\) 0 0
\(67\) −4.95944 2.86334i −0.605892 0.349812i 0.165464 0.986216i \(-0.447088\pi\)
−0.771356 + 0.636404i \(0.780421\pi\)
\(68\) 2.68548i 0.325662i
\(69\) 0 0
\(70\) 16.0669 18.8181i 1.92036 2.24920i
\(71\) 3.48626 + 6.03838i 0.413743 + 0.716624i 0.995296 0.0968847i \(-0.0308878\pi\)
−0.581552 + 0.813509i \(0.697554\pi\)
\(72\) 0 0
\(73\) 2.56139 1.47882i 0.299788 0.173083i −0.342560 0.939496i \(-0.611294\pi\)
0.642348 + 0.766413i \(0.277961\pi\)
\(74\) 3.69869 + 6.40632i 0.429964 + 0.744720i
\(75\) 0 0
\(76\) −15.1290 + 8.95208i −1.73542 + 1.02687i
\(77\) 9.90571i 1.12886i
\(78\) 0 0
\(79\) 5.66849 + 9.81811i 0.637755 + 1.10462i 0.985924 + 0.167192i \(0.0534699\pi\)
−0.348170 + 0.937431i \(0.613197\pi\)
\(80\) 6.09622 7.14011i 0.681578 0.798289i
\(81\) 0 0
\(82\) −0.154031 0.0889301i −0.0170099 0.00982068i
\(83\) 15.6999i 1.72328i −0.507517 0.861642i \(-0.669436\pi\)
0.507517 0.861642i \(-0.330564\pi\)
\(84\) 0 0
\(85\) −1.13238 0.966822i −0.122824 0.104867i
\(86\) 0.516467 0.894547i 0.0556921 0.0964615i
\(87\) 0 0
\(88\) 10.9787i 1.17034i
\(89\) 0.668486 1.15785i 0.0708594 0.122732i −0.828419 0.560109i \(-0.810759\pi\)
0.899278 + 0.437377i \(0.144092\pi\)
\(90\) 0 0
\(91\) 8.46652 14.6644i 0.887533 1.53725i
\(92\) 1.70449 0.984089i 0.177706 0.102598i
\(93\) 0 0
\(94\) −12.3370 −1.27246
\(95\) 1.67193 9.60233i 0.171536 0.985178i
\(96\) 0 0
\(97\) 3.79871 2.19319i 0.385701 0.222685i −0.294595 0.955622i \(-0.595185\pi\)
0.680296 + 0.732938i \(0.261851\pi\)
\(98\) 28.2856 16.3307i 2.85727 1.64965i
\(99\) 0 0
\(100\) 3.16095 + 19.9154i 0.316095 + 1.99154i
\(101\) −5.28430 + 9.15267i −0.525807 + 0.910725i 0.473741 + 0.880664i \(0.342903\pi\)
−0.999548 + 0.0300608i \(0.990430\pi\)
\(102\) 0 0
\(103\) 5.75615i 0.567171i −0.958947 0.283585i \(-0.908476\pi\)
0.958947 0.283585i \(-0.0915239\pi\)
\(104\) 9.38364 16.2529i 0.920142 1.59373i
\(105\) 0 0
\(106\) 6.43032 0.624568
\(107\) 1.30229i 0.125897i 0.998017 + 0.0629486i \(0.0200504\pi\)
−0.998017 + 0.0629486i \(0.979950\pi\)
\(108\) 0 0
\(109\) −6.01647 10.4208i −0.576273 0.998134i −0.995902 0.0904385i \(-0.971173\pi\)
0.419629 0.907696i \(-0.362160\pi\)
\(110\) 9.18374 + 7.84106i 0.875635 + 0.747616i
\(111\) 0 0
\(112\) 16.3820 9.45813i 1.54795 0.893709i
\(113\) 7.74626i 0.728707i 0.931261 + 0.364353i \(0.118710\pi\)
−0.931261 + 0.364353i \(0.881290\pi\)
\(114\) 0 0
\(115\) −0.198691 + 1.07302i −0.0185281 + 0.100060i
\(116\) 7.25136 + 12.5597i 0.673272 + 1.16614i
\(117\) 0 0
\(118\) 26.6650 + 15.3951i 2.45472 + 1.41723i
\(119\) −1.50000 2.59808i −0.137505 0.238165i
\(120\) 0 0
\(121\) −6.16576 −0.560523
\(122\) 17.3552i 1.57127i
\(123\) 0 0
\(124\) 13.7810 23.8694i 1.23757 2.14354i
\(125\) −9.53566 5.83705i −0.852896 0.522081i
\(126\) 0 0
\(127\) 3.40898 + 1.96818i 0.302498 + 0.174647i 0.643565 0.765392i \(-0.277455\pi\)
−0.341066 + 0.940039i \(0.610788\pi\)
\(128\) −16.7229 + 9.65499i −1.47811 + 0.853389i
\(129\) 0 0
\(130\) 6.89380 + 19.4574i 0.604626 + 1.70653i
\(131\) −8.16248 14.1378i −0.713160 1.23523i −0.963665 0.267114i \(-0.913930\pi\)
0.250505 0.968115i \(-0.419403\pi\)
\(132\) 0 0
\(133\) 9.63635 17.1112i 0.835578 1.48373i
\(134\) 14.0659 1.21511
\(135\) 0 0
\(136\) −1.66248 2.87951i −0.142557 0.246916i
\(137\) −14.2293 8.21529i −1.21569 0.701879i −0.251697 0.967806i \(-0.580989\pi\)
−0.963993 + 0.265927i \(0.914322\pi\)
\(138\) 0 0
\(139\) −1.33424 + 2.31098i −0.113169 + 0.196015i −0.917046 0.398781i \(-0.869433\pi\)
0.803877 + 0.594795i \(0.202767\pi\)
\(140\) −7.39738 + 39.9491i −0.625193 + 3.37631i
\(141\) 0 0
\(142\) −14.8315 8.56297i −1.24463 0.718588i
\(143\) 7.15663 + 4.13188i 0.598468 + 0.345526i
\(144\) 0 0
\(145\) −7.90666 1.46408i −0.656612 0.121585i
\(146\) −3.63228 + 6.29129i −0.300610 + 0.520671i
\(147\) 0 0
\(148\) −10.5188 6.07302i −0.864639 0.499199i
\(149\) 8.98299 + 15.5590i 0.735915 + 1.27464i 0.954321 + 0.298784i \(0.0965812\pi\)
−0.218405 + 0.975858i \(0.570085\pi\)
\(150\) 0 0
\(151\) −12.7344 −1.03631 −0.518154 0.855288i \(-0.673380\pi\)
−0.518154 + 0.855288i \(0.673380\pi\)
\(152\) 10.6802 18.9647i 0.866278 1.53824i
\(153\) 0 0
\(154\) 12.1652 + 21.0708i 0.980301 + 1.69793i
\(155\) 5.10353 + 14.4045i 0.409925 + 1.15699i
\(156\) 0 0
\(157\) −17.3674 + 10.0270i −1.38607 + 0.800245i −0.992869 0.119209i \(-0.961964\pi\)
−0.393197 + 0.919454i \(0.628631\pi\)
\(158\) −24.1153 13.9230i −1.91851 1.10765i
\(159\) 0 0
\(160\) −0.132822 + 0.717298i −0.0105005 + 0.0567074i
\(161\) −1.09935 + 1.90412i −0.0866406 + 0.150066i
\(162\) 0 0
\(163\) 14.2331i 1.11482i 0.830236 + 0.557412i \(0.188206\pi\)
−0.830236 + 0.557412i \(0.811794\pi\)
\(164\) 0.292035 0.0228041
\(165\) 0 0
\(166\) 19.2810 + 33.3957i 1.49650 + 2.59201i
\(167\) 4.86386 + 2.80815i 0.376376 + 0.217301i 0.676241 0.736681i \(-0.263608\pi\)
−0.299864 + 0.953982i \(0.596941\pi\)
\(168\) 0 0
\(169\) 0.563139 + 0.975386i 0.0433184 + 0.0750297i
\(170\) 3.59607 + 0.665886i 0.275806 + 0.0510711i
\(171\) 0 0
\(172\) 1.69601i 0.129320i
\(173\) −9.25824 + 5.34524i −0.703891 + 0.406391i −0.808795 0.588091i \(-0.799880\pi\)
0.104904 + 0.994482i \(0.466546\pi\)
\(174\) 0 0
\(175\) −14.1820 17.5017i −1.07206 1.32300i
\(176\) 4.61581 + 7.99482i 0.347930 + 0.602632i
\(177\) 0 0
\(178\) 3.28388i 0.246137i
\(179\) 7.68942 0.574734 0.287367 0.957821i \(-0.407220\pi\)
0.287367 + 0.957821i \(0.407220\pi\)
\(180\) 0 0
\(181\) 3.06314 5.30551i 0.227681 0.394356i −0.729439 0.684046i \(-0.760219\pi\)
0.957121 + 0.289690i \(0.0935522\pi\)
\(182\) 41.5910i 3.08293i
\(183\) 0 0
\(184\) −1.21843 + 2.11038i −0.0898239 + 0.155580i
\(185\) 6.34776 2.24902i 0.466696 0.165351i
\(186\) 0 0
\(187\) 1.26793 0.732039i 0.0927201 0.0535320i
\(188\) 17.5427 10.1283i 1.27943 0.738680i
\(189\) 0 0
\(190\) 8.23621 + 22.4787i 0.597518 + 1.63078i
\(191\) −5.85517 −0.423666 −0.211833 0.977306i \(-0.567943\pi\)
−0.211833 + 0.977306i \(0.567943\pi\)
\(192\) 0 0
\(193\) −2.24402 + 1.29559i −0.161528 + 0.0932584i −0.578585 0.815622i \(-0.696395\pi\)
0.417057 + 0.908880i \(0.363062\pi\)
\(194\) −5.38692 + 9.33041i −0.386758 + 0.669885i
\(195\) 0 0
\(196\) −26.8140 + 46.4431i −1.91528 + 3.31737i
\(197\) 19.8628i 1.41517i 0.706629 + 0.707584i \(0.250215\pi\)
−0.706629 + 0.707584i \(0.749785\pi\)
\(198\) 0 0
\(199\) −6.38092 + 11.0521i −0.452331 + 0.783460i −0.998530 0.0541948i \(-0.982741\pi\)
0.546199 + 0.837655i \(0.316074\pi\)
\(200\) −15.7183 19.3975i −1.11145 1.37161i
\(201\) 0 0
\(202\) 25.9586i 1.82644i
\(203\) −14.0307 8.10065i −0.984765 0.568554i
\(204\) 0 0
\(205\) −0.105138 + 0.123142i −0.00734318 + 0.00860059i
\(206\) 7.06914 + 12.2441i 0.492530 + 0.853088i
\(207\) 0 0
\(208\) 15.7808i 1.09420i
\(209\) 8.35071 + 4.70279i 0.577631 + 0.325299i
\(210\) 0 0
\(211\) −6.92759 11.9989i −0.476915 0.826041i 0.522735 0.852495i \(-0.324912\pi\)
−0.999650 + 0.0264545i \(0.991578\pi\)
\(212\) −9.14366 + 5.27909i −0.627989 + 0.362570i
\(213\) 0 0
\(214\) −1.59935 2.77015i −0.109329 0.189363i
\(215\) −0.715154 0.610597i −0.0487731 0.0416424i
\(216\) 0 0
\(217\) 30.7901i 2.09017i
\(218\) 25.5957 + 14.7777i 1.73356 + 1.00087i
\(219\) 0 0
\(220\) −19.4962 3.61012i −1.31443 0.243394i
\(221\) 2.50273 0.168352
\(222\) 0 0
\(223\) 18.7893 10.8480i 1.25823 0.726437i 0.285496 0.958380i \(-0.407842\pi\)
0.972729 + 0.231943i \(0.0745083\pi\)
\(224\) −0.734898 + 1.27288i −0.0491024 + 0.0850479i
\(225\) 0 0
\(226\) −9.51320 16.4773i −0.632808 1.09606i
\(227\) 8.19628i 0.544006i 0.962296 + 0.272003i \(0.0876861\pi\)
−0.962296 + 0.272003i \(0.912314\pi\)
\(228\) 0 0
\(229\) 16.6619 1.10105 0.550526 0.834818i \(-0.314427\pi\)
0.550526 + 0.834818i \(0.314427\pi\)
\(230\) −0.895133 2.52647i −0.0590233 0.166590i
\(231\) 0 0
\(232\) −15.5506 8.97814i −1.02095 0.589444i
\(233\) −10.5772 + 6.10677i −0.692937 + 0.400068i −0.804711 0.593666i \(-0.797680\pi\)
0.111774 + 0.993734i \(0.464347\pi\)
\(234\) 0 0
\(235\) −2.04494 + 11.0435i −0.133397 + 0.720402i
\(236\) −50.5555 −3.29088
\(237\) 0 0
\(238\) 6.38140 + 3.68430i 0.413645 + 0.238818i
\(239\) 2.03948 0.131923 0.0659614 0.997822i \(-0.478989\pi\)
0.0659614 + 0.997822i \(0.478989\pi\)
\(240\) 0 0
\(241\) −8.76183 + 15.1759i −0.564399 + 0.977568i 0.432706 + 0.901535i \(0.357559\pi\)
−0.997105 + 0.0760330i \(0.975775\pi\)
\(242\) 13.1154 7.57218i 0.843089 0.486758i
\(243\) 0 0
\(244\) 14.2481 + 24.6784i 0.912141 + 1.57987i
\(245\) −9.93002 28.0270i −0.634406 1.79058i
\(246\) 0 0
\(247\) 8.34289 + 14.0995i 0.530846 + 0.897129i
\(248\) 34.1254i 2.16697i
\(249\) 0 0
\(250\) 27.4521 + 0.705418i 1.73622 + 0.0446146i
\(251\) −1.66903 + 2.89084i −0.105348 + 0.182468i −0.913880 0.405984i \(-0.866929\pi\)
0.808532 + 0.588452i \(0.200262\pi\)
\(252\) 0 0
\(253\) −0.929261 0.536509i −0.0584222 0.0337301i
\(254\) −9.66849 −0.606655
\(255\) 0 0
\(256\) 16.1185 27.9181i 1.00741 1.74488i
\(257\) 23.8889 + 13.7922i 1.49015 + 0.860337i 0.999937 0.0112676i \(-0.00358665\pi\)
0.490210 + 0.871604i \(0.336920\pi\)
\(258\) 0 0
\(259\) 13.5686 0.843112
\(260\) −25.7766 22.0080i −1.59860 1.36488i
\(261\) 0 0
\(262\) 34.7254 + 20.0487i 2.14534 + 1.23861i
\(263\) 11.8006 6.81310i 0.727658 0.420114i −0.0899066 0.995950i \(-0.528657\pi\)
0.817565 + 0.575837i \(0.195324\pi\)
\(264\) 0 0
\(265\) 1.06587 5.75615i 0.0654758 0.353598i
\(266\) 0.516467 + 48.2322i 0.0316666 + 2.95731i
\(267\) 0 0
\(268\) −20.0011 + 11.5476i −1.22176 + 0.705385i
\(269\) 1.80404 + 3.12469i 0.109994 + 0.190515i 0.915768 0.401708i \(-0.131583\pi\)
−0.805773 + 0.592224i \(0.798250\pi\)
\(270\) 0 0
\(271\) −5.28157 9.14795i −0.320833 0.555698i 0.659828 0.751417i \(-0.270629\pi\)
−0.980660 + 0.195719i \(0.937296\pi\)
\(272\) 2.42128 + 1.39793i 0.146812 + 0.0847617i
\(273\) 0 0
\(274\) 40.3568 2.43804
\(275\) 8.54126 6.92119i 0.515058 0.417364i
\(276\) 0 0
\(277\) 6.73487i 0.404659i 0.979317 + 0.202330i \(0.0648512\pi\)
−0.979317 + 0.202330i \(0.935149\pi\)
\(278\) 6.55434i 0.393103i
\(279\) 0 0
\(280\) −16.7992 47.4150i −1.00395 2.83359i
\(281\) 11.7152 20.2912i 0.698868 1.21047i −0.269992 0.962863i \(-0.587021\pi\)
0.968859 0.247612i \(-0.0796457\pi\)
\(282\) 0 0
\(283\) −12.7160 + 7.34157i −0.755886 + 0.436411i −0.827817 0.560999i \(-0.810417\pi\)
0.0719306 + 0.997410i \(0.477084\pi\)
\(284\) 28.1197 1.66860
\(285\) 0 0
\(286\) −20.2975 −1.20022
\(287\) −0.282531 + 0.163119i −0.0166773 + 0.00962863i
\(288\) 0 0
\(289\) −8.27830 + 14.3384i −0.486959 + 0.843437i
\(290\) 18.6166 6.59589i 1.09320 0.387324i
\(291\) 0 0
\(292\) 11.9280i 0.698031i
\(293\) 18.1855i 1.06241i 0.847243 + 0.531206i \(0.178261\pi\)
−0.847243 + 0.531206i \(0.821739\pi\)
\(294\) 0 0
\(295\) 18.2009 21.3176i 1.05970 1.24116i
\(296\) 15.0384 0.874089
\(297\) 0 0
\(298\) −38.2161 22.0641i −2.21380 1.27814i
\(299\) −0.917122 1.58850i −0.0530385 0.0918654i
\(300\) 0 0
\(301\) −0.947326 1.64082i −0.0546030 0.0945752i
\(302\) 27.0877 15.6391i 1.55872 0.899928i
\(303\) 0 0
\(304\) 0.195962 + 18.3006i 0.0112392 + 1.04961i
\(305\) −15.5357 2.87674i −0.889570 0.164722i
\(306\) 0 0
\(307\) −25.4439 + 14.6901i −1.45216 + 0.838406i −0.998604 0.0528200i \(-0.983179\pi\)
−0.453559 + 0.891226i \(0.649846\pi\)
\(308\) −34.5969 19.9745i −1.97134 1.13815i
\(309\) 0 0
\(310\) −28.5460 24.3726i −1.62131 1.38427i
\(311\) 0.193232 0.0109572 0.00547859 0.999985i \(-0.498256\pi\)
0.00547859 + 0.999985i \(0.498256\pi\)
\(312\) 0 0
\(313\) 18.4251 + 10.6377i 1.04145 + 0.601281i 0.920243 0.391346i \(-0.127991\pi\)
0.121206 + 0.992627i \(0.461324\pi\)
\(314\) 24.6285 42.6578i 1.38986 2.40732i
\(315\) 0 0
\(316\) 45.7213 2.57202
\(317\) −16.6018 9.58506i −0.932451 0.538351i −0.0448649 0.998993i \(-0.514286\pi\)
−0.887586 + 0.460642i \(0.847619\pi\)
\(318\) 0 0
\(319\) 3.95333 6.84736i 0.221344 0.383379i
\(320\) 5.67243 + 16.0102i 0.317099 + 0.894995i
\(321\) 0 0
\(322\) 5.40043i 0.300954i
\(323\) 2.90236 0.0310783i 0.161492 0.00172924i
\(324\) 0 0
\(325\) 18.5601 2.94584i 1.02953 0.163406i
\(326\) −17.4797 30.2758i −0.968112 1.67682i
\(327\) 0 0
\(328\) −0.313136 + 0.180789i −0.0172900 + 0.00998240i
\(329\) −11.3145 + 19.5973i −0.623789 + 1.08043i
\(330\) 0 0
\(331\) −20.6070 −1.13266 −0.566331 0.824178i \(-0.691638\pi\)
−0.566331 + 0.824178i \(0.691638\pi\)
\(332\) −54.8337 31.6583i −3.00939 1.73747i
\(333\) 0 0
\(334\) −13.7948 −0.754816
\(335\) 2.33151 12.5912i 0.127384 0.687930i
\(336\) 0 0
\(337\) 8.83982 5.10368i 0.481536 0.278015i −0.239520 0.970891i \(-0.576990\pi\)
0.721056 + 0.692876i \(0.243657\pi\)
\(338\) −2.39575 1.38318i −0.130311 0.0752353i
\(339\) 0 0
\(340\) −5.66015 + 2.00540i −0.306965 + 0.108758i
\(341\) −15.0264 −0.813725
\(342\) 0 0
\(343\) 28.3719i 1.53194i
\(344\) −1.04994 1.81856i −0.0566092 0.0980500i
\(345\) 0 0
\(346\) 13.1290 22.7401i 0.705820 1.22252i
\(347\) 4.71213 2.72055i 0.252960 0.146047i −0.368159 0.929763i \(-0.620012\pi\)
0.621119 + 0.783716i \(0.286678\pi\)
\(348\) 0 0
\(349\) 1.55114 0.0830304 0.0415152 0.999138i \(-0.486781\pi\)
0.0415152 + 0.999138i \(0.486781\pi\)
\(350\) 51.6609 + 19.8114i 2.76139 + 1.05896i
\(351\) 0 0
\(352\) −0.621199 0.358649i −0.0331100 0.0191161i
\(353\) 32.9335i 1.75287i 0.481517 + 0.876437i \(0.340086\pi\)
−0.481517 + 0.876437i \(0.659914\pi\)
\(354\) 0 0
\(355\) −10.1236 + 11.8572i −0.537307 + 0.629313i
\(356\) −2.69596 4.66954i −0.142886 0.247485i
\(357\) 0 0
\(358\) −16.3564 + 9.44339i −0.864464 + 0.499098i
\(359\) 1.74864 + 3.02873i 0.0922894 + 0.159850i 0.908474 0.417941i \(-0.137248\pi\)
−0.816185 + 0.577791i \(0.803915\pi\)
\(360\) 0 0
\(361\) 9.85017 + 16.2473i 0.518430 + 0.855120i
\(362\) 15.0474i 0.790873i
\(363\) 0 0
\(364\) −34.1449 59.1408i −1.78968 3.09982i
\(365\) 5.02963 + 4.29429i 0.263263 + 0.224773i
\(366\) 0 0
\(367\) 16.8909 + 9.75196i 0.881697 + 0.509048i 0.871218 0.490897i \(-0.163331\pi\)
0.0104794 + 0.999945i \(0.496664\pi\)
\(368\) 2.04907i 0.106815i
\(369\) 0 0
\(370\) −10.7405 + 12.5797i −0.558372 + 0.653986i
\(371\) 5.89738 10.2146i 0.306177 0.530314i
\(372\) 0 0
\(373\) 23.5158i 1.21760i 0.793322 + 0.608802i \(0.208350\pi\)
−0.793322 + 0.608802i \(0.791650\pi\)
\(374\) −1.79804 + 3.11429i −0.0929743 + 0.161036i
\(375\) 0 0
\(376\) −12.5401 + 21.7201i −0.646708 + 1.12013i
\(377\) 11.7050 6.75791i 0.602841 0.348050i
\(378\) 0 0
\(379\) 7.05148 0.362210 0.181105 0.983464i \(-0.442033\pi\)
0.181105 + 0.983464i \(0.442033\pi\)
\(380\) −30.1659 25.2022i −1.54748 1.29285i
\(381\) 0 0
\(382\) 12.4547 7.19075i 0.637240 0.367911i
\(383\) −2.67090 + 1.54204i −0.136476 + 0.0787947i −0.566684 0.823935i \(-0.691774\pi\)
0.430207 + 0.902730i \(0.358440\pi\)
\(384\) 0 0
\(385\) 20.8781 7.39717i 1.06405 0.376995i
\(386\) 3.18222 5.51177i 0.161971 0.280542i
\(387\) 0 0
\(388\) 17.6900i 0.898072i
\(389\) −4.69542 + 8.13270i −0.238067 + 0.412345i −0.960160 0.279452i \(-0.909847\pi\)
0.722092 + 0.691797i \(0.243181\pi\)
\(390\) 0 0
\(391\) −0.324970 −0.0164344
\(392\) 66.3984i 3.35362i
\(393\) 0 0
\(394\) −24.3936 42.2509i −1.22893 2.12857i
\(395\) −16.4605 + 19.2792i −0.828219 + 0.970040i
\(396\) 0 0
\(397\) 23.1744 13.3797i 1.16309 0.671510i 0.211047 0.977476i \(-0.432313\pi\)
0.952042 + 0.305966i \(0.0989794\pi\)
\(398\) 31.3456i 1.57122i
\(399\) 0 0
\(400\) 19.6015 + 7.51699i 0.980077 + 0.375849i
\(401\) −12.5851 21.7980i −0.628468 1.08854i −0.987859 0.155352i \(-0.950349\pi\)
0.359391 0.933187i \(-0.382984\pi\)
\(402\) 0 0
\(403\) −22.2451 12.8432i −1.10811 0.639767i
\(404\) 21.3112 + 36.9121i 1.06027 + 1.83645i
\(405\) 0 0
\(406\) 39.7937 1.97493
\(407\) 6.62183i 0.328232i
\(408\) 0 0
\(409\) −14.1608 + 24.5271i −0.700204 + 1.21279i 0.268191 + 0.963366i \(0.413574\pi\)
−0.968395 + 0.249423i \(0.919759\pi\)
\(410\) 0.0724126 0.391060i 0.00357621 0.0193131i
\(411\) 0 0
\(412\) −20.1041 11.6071i −0.990457 0.571840i
\(413\) 48.9102 28.2383i 2.40671 1.38952i
\(414\) 0 0
\(415\) 33.0904 11.7240i 1.62435 0.575509i
\(416\) −0.613083 1.06189i −0.0300589 0.0520635i
\(417\) 0 0
\(418\) −23.5386 + 0.252049i −1.15131 + 0.0123281i
\(419\) 13.0449 0.637287 0.318643 0.947875i \(-0.396773\pi\)
0.318643 + 0.947875i \(0.396773\pi\)
\(420\) 0 0
\(421\) −1.66248 2.87951i −0.0810246 0.140339i 0.822666 0.568525i \(-0.192486\pi\)
−0.903690 + 0.428187i \(0.859153\pi\)
\(422\) 29.4718 + 17.0156i 1.43467 + 0.828305i
\(423\) 0 0
\(424\) 6.53621 11.3210i 0.317426 0.549798i
\(425\) 1.19215 3.10868i 0.0578276 0.150793i
\(426\) 0 0
\(427\) −27.5688 15.9168i −1.33415 0.770270i
\(428\) 4.54841 + 2.62603i 0.219856 + 0.126934i
\(429\) 0 0
\(430\) 2.27110 + 0.420541i 0.109522 + 0.0202803i
\(431\) 0.0242034 0.0419216i 0.00116584 0.00201929i −0.865442 0.501009i \(-0.832962\pi\)
0.866608 + 0.498990i \(0.166296\pi\)
\(432\) 0 0
\(433\) 8.28676 + 4.78436i 0.398236 + 0.229922i 0.685723 0.727863i \(-0.259486\pi\)
−0.287486 + 0.957785i \(0.592820\pi\)
\(434\) −37.8134 65.4948i −1.81510 3.14385i
\(435\) 0 0
\(436\) −48.5280 −2.32407
\(437\) −1.08329 1.83076i −0.0518209 0.0875773i
\(438\) 0 0
\(439\) −11.1257 19.2703i −0.531002 0.919723i −0.999345 0.0361764i \(-0.988482\pi\)
0.468343 0.883547i \(-0.344851\pi\)
\(440\) 23.1397 8.19846i 1.10314 0.390846i
\(441\) 0 0
\(442\) −5.32364 + 3.07361i −0.253220 + 0.146197i
\(443\) 17.4207 + 10.0579i 0.827684 + 0.477863i 0.853059 0.521815i \(-0.174745\pi\)
−0.0253753 + 0.999678i \(0.508078\pi\)
\(444\) 0 0
\(445\) 2.93959 + 0.544325i 0.139350 + 0.0258035i
\(446\) −26.6449 + 46.1504i −1.26167 + 2.18528i
\(447\) 0 0
\(448\) 34.2224i 1.61686i
\(449\) −12.4973 −0.589783 −0.294891 0.955531i \(-0.595283\pi\)
−0.294891 + 0.955531i \(0.595283\pi\)
\(450\) 0 0
\(451\) −0.0796065 0.137883i −0.00374852 0.00649263i
\(452\) 27.0548 + 15.6201i 1.27255 + 0.734707i
\(453\) 0 0
\(454\) −10.0659 17.4346i −0.472415 0.818246i
\(455\) 37.2305 + 6.89399i 1.74539 + 0.323195i
\(456\) 0 0
\(457\) 28.3179i 1.32465i 0.749215 + 0.662327i \(0.230431\pi\)
−0.749215 + 0.662327i \(0.769569\pi\)
\(458\) −35.4422 + 20.4626i −1.65610 + 0.956153i
\(459\) 0 0
\(460\) 3.34700 + 2.85766i 0.156054 + 0.133239i
\(461\) 2.65976 + 4.60683i 0.123877 + 0.214562i 0.921293 0.388868i \(-0.127134\pi\)
−0.797416 + 0.603430i \(0.793800\pi\)
\(462\) 0 0
\(463\) 17.9327i 0.833401i −0.909044 0.416701i \(-0.863186\pi\)
0.909044 0.416701i \(-0.136814\pi\)
\(464\) 15.0988 0.700944
\(465\) 0 0
\(466\) 14.9995 25.9798i 0.694836 1.20349i
\(467\) 28.7791i 1.33174i 0.746069 + 0.665868i \(0.231939\pi\)
−0.746069 + 0.665868i \(0.768061\pi\)
\(468\) 0 0
\(469\) 12.9001 22.3436i 0.595672 1.03173i
\(470\) −9.21274 26.0025i −0.424952 1.19941i
\(471\) 0 0
\(472\) 54.2083 31.2972i 2.49514 1.44057i
\(473\) 0.800762 0.462320i 0.0368191 0.0212575i
\(474\) 0 0
\(475\) 21.4872 3.64671i 0.985902 0.167323i
\(476\) −12.0988 −0.554548
\(477\) 0 0
\(478\) −4.33824 + 2.50469i −0.198427 + 0.114562i
\(479\) 4.02574 6.97279i 0.183941 0.318595i −0.759278 0.650766i \(-0.774448\pi\)
0.943219 + 0.332171i \(0.107781\pi\)
\(480\) 0 0
\(481\) −5.65976 + 9.80298i −0.258063 + 0.446978i
\(482\) 43.0417i 1.96049i
\(483\) 0 0
\(484\) −12.4330 + 21.5347i −0.565138 + 0.978849i
\(485\) 7.45928 + 6.36872i 0.338708 + 0.289189i
\(486\) 0 0
\(487\) 1.09761i 0.0497376i −0.999691 0.0248688i \(-0.992083\pi\)
0.999691 0.0248688i \(-0.00791680\pi\)
\(488\) −30.5551 17.6410i −1.38316 0.798571i
\(489\) 0 0
\(490\) 55.5425 + 47.4221i 2.50915 + 2.14231i
\(491\) 6.55267 + 11.3496i 0.295718 + 0.512199i 0.975152 0.221538i \(-0.0711078\pi\)
−0.679434 + 0.733737i \(0.737774\pi\)
\(492\) 0 0
\(493\) 2.39458i 0.107846i
\(494\) −35.0621 19.7456i −1.57752 0.888395i
\(495\) 0 0
\(496\) −14.3474 24.8505i −0.644219 1.11582i
\(497\) −27.2046 + 15.7066i −1.22029 + 0.704536i
\(498\) 0 0
\(499\) 12.0703 + 20.9064i 0.540342 + 0.935900i 0.998884 + 0.0472275i \(0.0150386\pi\)
−0.458542 + 0.888673i \(0.651628\pi\)
\(500\) −39.6150 + 21.5343i −1.77163 + 0.963042i
\(501\) 0 0
\(502\) 8.19895i 0.365937i
\(503\) −16.4214 9.48090i −0.732194 0.422733i 0.0870300 0.996206i \(-0.472262\pi\)
−0.819224 + 0.573473i \(0.805596\pi\)
\(504\) 0 0
\(505\) −23.2371 4.30282i −1.03404 0.191473i
\(506\) 2.63555 0.117165
\(507\) 0 0
\(508\) 13.7482 7.93753i 0.609978 0.352171i
\(509\) −10.9803 + 19.0184i −0.486692 + 0.842974i −0.999883 0.0152997i \(-0.995130\pi\)
0.513191 + 0.858274i \(0.328463\pi\)
\(510\) 0 0
\(511\) 6.66248 + 11.5398i 0.294731 + 0.510489i
\(512\) 40.5609i 1.79255i
\(513\) 0 0
\(514\) −67.7531 −2.98846
\(515\) 12.1322 4.29846i 0.534608 0.189413i
\(516\) 0 0
\(517\) −9.56399 5.52177i −0.420624 0.242847i
\(518\) −28.8622 + 16.6636i −1.26813 + 0.732157i
\(519\) 0 0
\(520\) 41.2635 + 7.64077i 1.80952 + 0.335070i
\(521\) −6.56968 −0.287823 −0.143912 0.989591i \(-0.545968\pi\)
−0.143912 + 0.989591i \(0.545968\pi\)
\(522\) 0 0
\(523\) −3.63538 2.09889i −0.158964 0.0917779i 0.418408 0.908259i \(-0.362588\pi\)
−0.577372 + 0.816481i \(0.695922\pi\)
\(524\) −65.8375 −2.87613
\(525\) 0 0
\(526\) −16.7344 + 28.9848i −0.729653 + 1.26380i
\(527\) −3.94113 + 2.27541i −0.171678 + 0.0991186i
\(528\) 0 0
\(529\) −11.3809 19.7123i −0.494822 0.857058i
\(530\) 4.80189 + 13.5531i 0.208581 + 0.588709i
\(531\) 0 0
\(532\) −40.3316 68.1603i −1.74860 2.95513i
\(533\) 0.272162i 0.0117887i
\(534\) 0 0
\(535\) −2.74482 + 0.972497i −0.118669 + 0.0420447i
\(536\) 14.2975 24.7640i 0.617558 1.06964i
\(537\) 0 0
\(538\) −7.67486 4.43108i −0.330887 0.191038i
\(539\) 29.2371 1.25933
\(540\) 0 0
\(541\) 2.31505 4.00978i 0.0995316 0.172394i −0.811959 0.583714i \(-0.801599\pi\)
0.911491 + 0.411320i \(0.134932\pi\)
\(542\) 22.4692 + 12.9726i 0.965136 + 0.557221i
\(543\) 0 0
\(544\) −0.217238 −0.00931400
\(545\) 17.4710 20.4627i 0.748376 0.876525i
\(546\) 0 0
\(547\) −32.9435 19.0199i −1.40856 0.813233i −0.413312 0.910590i \(-0.635628\pi\)
−0.995250 + 0.0973563i \(0.968961\pi\)
\(548\) −57.3858 + 33.1317i −2.45140 + 1.41532i
\(549\) 0 0
\(550\) −9.66849 + 25.2118i −0.412266 + 1.07504i
\(551\) 13.4902 7.98236i 0.574701 0.340060i
\(552\) 0 0
\(553\) −44.2333 + 25.5381i −1.88099 + 1.08599i
\(554\) −8.27110 14.3260i −0.351406 0.608652i
\(555\) 0 0
\(556\) 5.38092 + 9.32002i 0.228202 + 0.395257i
\(557\) −31.5498 18.2153i −1.33681 0.771807i −0.350476 0.936572i \(-0.613980\pi\)
−0.986333 + 0.164765i \(0.947313\pi\)
\(558\) 0 0
\(559\) 1.58060 0.0668523
\(560\) 32.1682 + 27.4651i 1.35935 + 1.16061i
\(561\) 0 0
\(562\) 57.5496i 2.42758i
\(563\) 20.6856i 0.871795i −0.899996 0.435897i \(-0.856431\pi\)
0.899996 0.435897i \(-0.143569\pi\)
\(564\) 0 0
\(565\) −16.3267 + 5.78459i −0.686870 + 0.243359i
\(566\) 18.0324 31.2330i 0.757958 1.31282i
\(567\) 0 0
\(568\) −30.1515 + 17.4080i −1.26513 + 0.730422i
\(569\) −27.1132 −1.13664 −0.568322 0.822806i \(-0.692407\pi\)
−0.568322 + 0.822806i \(0.692407\pi\)
\(570\) 0 0
\(571\) 46.4687 1.94466 0.972328 0.233622i \(-0.0750578\pi\)
0.972328 + 0.233622i \(0.0750578\pi\)
\(572\) 28.8622 16.6636i 1.20679 0.696741i
\(573\) 0 0
\(574\) 0.400654 0.693954i 0.0167230 0.0289651i
\(575\) −2.40996 + 0.382507i −0.100502 + 0.0159516i
\(576\) 0 0
\(577\) 18.0398i 0.751008i −0.926821 0.375504i \(-0.877470\pi\)
0.926821 0.375504i \(-0.122530\pi\)
\(578\) 40.6664i 1.69150i
\(579\) 0 0
\(580\) −21.0570 + 24.6627i −0.874344 + 1.02406i
\(581\) 70.7322 2.93447
\(582\) 0 0
\(583\) 4.98497 + 2.87808i 0.206457 + 0.119198i
\(584\) 7.38419 + 12.7898i 0.305560 + 0.529245i
\(585\) 0 0
\(586\) −22.3337 38.6831i −0.922597 1.59798i
\(587\) 22.5458 13.0168i 0.930565 0.537262i 0.0435750 0.999050i \(-0.486125\pi\)
0.886990 + 0.461788i \(0.152792\pi\)
\(588\) 0 0
\(589\) −25.9567 14.6178i −1.06953 0.602316i
\(590\) −12.5357 + 67.6980i −0.516085 + 2.78708i
\(591\) 0 0
\(592\) −10.9511 + 6.32263i −0.450088 + 0.259858i
\(593\) −15.7236 9.07803i −0.645691 0.372790i 0.141112 0.989994i \(-0.454932\pi\)
−0.786804 + 0.617203i \(0.788266\pi\)
\(594\) 0 0
\(595\) 4.35580 5.10167i 0.178570 0.209148i
\(596\) 72.4556 2.96790
\(597\) 0 0
\(598\) 3.90168 + 2.25264i 0.159552 + 0.0921172i
\(599\) −20.0357 + 34.7028i −0.818635 + 1.41792i 0.0880531 + 0.996116i \(0.471935\pi\)
−0.906688 + 0.421802i \(0.861398\pi\)
\(600\) 0 0
\(601\) 15.0473 0.613793 0.306897 0.951743i \(-0.400709\pi\)
0.306897 + 0.951743i \(0.400709\pi\)
\(602\) 4.03018 + 2.32683i 0.164258 + 0.0948344i
\(603\) 0 0
\(604\) −25.6784 + 44.4763i −1.04484 + 1.80972i
\(605\) −4.60433 12.9955i −0.187193 0.528342i
\(606\) 0 0
\(607\) 29.3860i 1.19274i 0.802709 + 0.596370i \(0.203391\pi\)
−0.802709 + 0.596370i \(0.796609\pi\)
\(608\) −0.724166 1.22384i −0.0293688 0.0496333i
\(609\) 0 0
\(610\) 36.5794 12.9602i 1.48106 0.524741i
\(611\) −9.43905 16.3489i −0.381863 0.661406i
\(612\) 0 0
\(613\) −30.0578 + 17.3539i −1.21402 + 0.700917i −0.963633 0.267229i \(-0.913892\pi\)
−0.250390 + 0.968145i \(0.580559\pi\)
\(614\) 36.0818 62.4955i 1.45614 2.52211i
\(615\) 0 0
\(616\) 49.4622 1.99289
\(617\) −9.29031 5.36376i −0.374014 0.215937i 0.301197 0.953562i \(-0.402614\pi\)
−0.675210 + 0.737625i \(0.735947\pi\)
\(618\) 0 0
\(619\) 36.1437 1.45274 0.726370 0.687304i \(-0.241206\pi\)
0.726370 + 0.687304i \(0.241206\pi\)
\(620\) 60.6004 + 11.2214i 2.43377 + 0.450663i
\(621\) 0 0
\(622\) −0.411031 + 0.237309i −0.0164808 + 0.00951521i
\(623\) 5.21644 + 3.01171i 0.208992 + 0.120662i
\(624\) 0 0
\(625\) 5.18184 24.4571i 0.207274 0.978283i
\(626\) −52.2569 −2.08861
\(627\) 0 0
\(628\) 80.8768i 3.22734i
\(629\) 1.00273 + 1.73678i 0.0399814 + 0.0692499i
\(630\) 0 0
\(631\) 15.7882 27.3460i 0.628519 1.08863i −0.359330 0.933211i \(-0.616995\pi\)
0.987849 0.155417i \(-0.0496720\pi\)
\(632\) −49.0248 + 28.3045i −1.95010 + 1.12589i
\(633\) 0 0
\(634\) 47.0857 1.87001
\(635\) −1.60262 + 8.65483i −0.0635979 + 0.343456i
\(636\) 0 0
\(637\) 43.2827 + 24.9893i 1.71492 + 0.990111i
\(638\) 19.4204i 0.768859i
\(639\) 0 0
\(640\) −32.8377 28.0368i −1.29802 1.10825i
\(641\) 9.91331 + 17.1704i 0.391552 + 0.678188i 0.992654 0.120984i \(-0.0386049\pi\)
−0.601102 + 0.799172i \(0.705272\pi\)
\(642\) 0 0
\(643\) 11.6540 6.72843i 0.459588 0.265343i −0.252283 0.967654i \(-0.581181\pi\)
0.711871 + 0.702310i \(0.247848\pi\)
\(644\) 4.43359 + 7.67920i 0.174708 + 0.302603i
\(645\) 0 0
\(646\) −6.13555 + 3.63051i −0.241400 + 0.142840i
\(647\) 4.19511i 0.164927i 0.996594 + 0.0824634i \(0.0262787\pi\)
−0.996594 + 0.0824634i \(0.973721\pi\)
\(648\) 0 0
\(649\) 13.7810 + 23.8694i 0.540953 + 0.936957i
\(650\) −35.8621 + 29.0600i −1.40663 + 1.13983i
\(651\) 0 0
\(652\) 49.7109 + 28.7006i 1.94683 + 1.12400i
\(653\) 12.1680i 0.476170i 0.971244 + 0.238085i \(0.0765196\pi\)
−0.971244 + 0.238085i \(0.923480\pi\)
\(654\) 0 0
\(655\) 23.7028 27.7615i 0.926143 1.08473i
\(656\) 0.152019 0.263305i 0.00593535 0.0102803i
\(657\) 0 0
\(658\) 55.5814i 2.16679i
\(659\) −4.12236 + 7.14013i −0.160584 + 0.278140i −0.935078 0.354441i \(-0.884671\pi\)
0.774494 + 0.632581i \(0.218004\pi\)
\(660\) 0 0
\(661\) −10.5599 + 18.2902i −0.410731 + 0.711407i −0.994970 0.100175i \(-0.968060\pi\)
0.584239 + 0.811582i \(0.301393\pi\)
\(662\) 43.8338 25.3075i 1.70365 0.983603i
\(663\) 0 0
\(664\) 78.3941 3.04228
\(665\) 43.2611 + 7.53250i 1.67759 + 0.292098i
\(666\) 0 0
\(667\) −1.51986 + 0.877489i −0.0588490 + 0.0339765i
\(668\) 19.6156 11.3251i 0.758951 0.438180i
\(669\) 0 0
\(670\) 10.5038 + 29.6465i 0.405798 + 1.14534i
\(671\) 7.76783 13.4543i 0.299874 0.519397i
\(672\) 0 0
\(673\) 30.2802i 1.16722i −0.812036 0.583608i \(-0.801641\pi\)
0.812036 0.583608i \(-0.198359\pi\)
\(674\) −12.5357 + 21.7124i −0.482856 + 0.836331i
\(675\) 0 0
\(676\) 4.54221 0.174700
\(677\) 49.9003i 1.91783i 0.283701 + 0.958913i \(0.408438\pi\)
−0.283701 + 0.958913i \(0.591562\pi\)
\(678\) 0 0
\(679\) 9.88092 + 17.1142i 0.379195 + 0.656785i
\(680\) 4.82763 5.65430i 0.185131 0.216832i
\(681\) 0 0
\(682\) 31.9632 18.4539i 1.22393 0.706638i
\(683\) 3.11357i 0.119137i −0.998224 0.0595687i \(-0.981027\pi\)
0.998224 0.0595687i \(-0.0189725\pi\)
\(684\) 0 0
\(685\) 6.68942 36.1258i 0.255590 1.38029i
\(686\) 34.8436 + 60.3509i 1.33034 + 2.30421i
\(687\) 0 0
\(688\) 1.52916 + 0.882861i 0.0582987 + 0.0336588i
\(689\) 4.91985 + 8.52143i 0.187431 + 0.324641i
\(690\) 0 0
\(691\) −30.2831 −1.15202 −0.576012 0.817441i \(-0.695392\pi\)
−0.576012 + 0.817441i \(0.695392\pi\)
\(692\) 43.1140i 1.63895i
\(693\) 0 0
\(694\) −6.68222 + 11.5740i −0.253654 + 0.439341i
\(695\) −5.86718 1.08643i −0.222555 0.0412105i
\(696\) 0 0
\(697\) −0.0417585 0.0241093i −0.00158172 0.000913204i
\(698\) −3.29948 + 1.90495i −0.124887 + 0.0721035i
\(699\) 0 0
\(700\) −89.7243 + 14.2409i −3.39126 + 0.538257i
\(701\) 22.2849 + 38.5987i 0.841691 + 1.45785i 0.888464 + 0.458946i \(0.151773\pi\)
−0.0467733 + 0.998906i \(0.514894\pi\)
\(702\) 0 0
\(703\) −6.44177 + 11.4386i −0.242956 + 0.431415i
\(704\) −16.7014 −0.629458
\(705\) 0 0
\(706\) −40.4457 70.0540i −1.52219 2.63652i
\(707\) −41.2353 23.8072i −1.55081 0.895363i
\(708\) 0 0
\(709\) 4.67176 8.09172i 0.175452 0.303891i −0.764866 0.644190i \(-0.777195\pi\)
0.940317 + 0.340299i \(0.110528\pi\)
\(710\) 6.97252 37.6546i 0.261674 1.41315i
\(711\) 0 0
\(712\) 5.78150 + 3.33795i 0.216671 + 0.125095i
\(713\) 2.88844 + 1.66764i 0.108173 + 0.0624538i
\(714\) 0 0
\(715\) −3.36445 + 18.1695i −0.125823 + 0.679500i
\(716\) 15.5055 26.8562i 0.579466 1.00366i
\(717\) 0 0
\(718\) −7.43916 4.29500i −0.277627 0.160288i
\(719\) −12.6987 21.9948i −0.473581 0.820267i 0.525961 0.850508i \(-0.323706\pi\)
−0.999543 + 0.0302417i \(0.990372\pi\)
\(720\) 0 0
\(721\) 25.9330 0.965797
\(722\) −40.9059 22.4631i −1.52236 0.835992i
\(723\) 0 0
\(724\) −12.3534 21.3968i −0.459112 0.795205i
\(725\) −2.81854 17.7581i −0.104678 0.659519i
\(726\) 0 0
\(727\) 27.2259 15.7189i 1.00975 0.582980i 0.0986328 0.995124i \(-0.468553\pi\)
0.911119 + 0.412143i \(0.135220\pi\)
\(728\) 73.2240 + 42.2759i 2.71386 + 1.56685i
\(729\) 0 0
\(730\) −15.9725 2.95764i −0.591170 0.109467i
\(731\) 0.140016 0.242515i 0.00517869 0.00896975i
\(732\) 0 0
\(733\) 25.3946i 0.937971i −0.883206 0.468985i \(-0.844620\pi\)
0.883206 0.468985i \(-0.155380\pi\)
\(734\) −47.9056 −1.76823
\(735\) 0 0
\(736\) 0.0796065 + 0.137883i 0.00293434 + 0.00508242i
\(737\) 10.9043 + 6.29559i 0.401664 + 0.231901i
\(738\) 0 0
\(739\) 17.7541 + 30.7510i 0.653095 + 1.13119i 0.982368 + 0.186959i \(0.0598631\pi\)
−0.329273 + 0.944235i \(0.606804\pi\)
\(740\) 4.94505 26.7054i 0.181784 0.981710i
\(741\) 0 0
\(742\) 28.9703i 1.06353i
\(743\) −14.8176 + 8.55493i −0.543604 + 0.313850i −0.746538 0.665342i \(-0.768286\pi\)
0.202934 + 0.979192i \(0.434952\pi\)
\(744\) 0 0
\(745\) −26.0854 + 30.5522i −0.955695 + 1.11934i
\(746\) −28.8798 50.0213i −1.05737 1.83141i
\(747\) 0 0
\(748\) 5.90453i 0.215891i
\(749\) −5.86718 −0.214382
\(750\) 0 0
\(751\) 3.72562 6.45297i 0.135950 0.235472i −0.790010 0.613094i \(-0.789925\pi\)
0.925960 + 0.377622i \(0.123258\pi\)
\(752\) 21.0891i 0.769041i
\(753\) 0 0
\(754\) −16.5988 + 28.7500i −0.604493 + 1.04701i
\(755\) −9.50949 26.8401i −0.346086 0.976810i
\(756\) 0 0
\(757\) −46.5640 + 26.8838i −1.69240 + 0.977107i −0.739824 + 0.672801i \(0.765091\pi\)
−0.952574 + 0.304306i \(0.901575\pi\)
\(758\) −14.9994 + 8.65994i −0.544804 + 0.314543i
\(759\) 0 0
\(760\) 47.9473 + 8.34845i 1.73923 + 0.302830i
\(761\) −23.3939 −0.848029 −0.424014 0.905655i \(-0.639379\pi\)
−0.424014 + 0.905655i \(0.639379\pi\)
\(762\) 0 0
\(763\) 46.9487 27.1058i 1.69966 0.981297i
\(764\) −11.8068 + 20.4499i −0.427154 + 0.739852i
\(765\) 0 0
\(766\) 3.78757 6.56027i 0.136851 0.237032i
\(767\) 47.1152i 1.70123i
\(768\) 0 0
\(769\) −6.62236 + 11.4703i −0.238808 + 0.413628i −0.960373 0.278719i \(-0.910090\pi\)
0.721564 + 0.692347i \(0.243423\pi\)
\(770\) −35.3261 + 41.3753i −1.27307 + 1.49106i
\(771\) 0 0
\(772\) 10.4500i 0.376105i
\(773\) −15.4198 8.90262i −0.554611 0.320205i 0.196369 0.980530i \(-0.437085\pi\)
−0.750980 + 0.660325i \(0.770418\pi\)
\(774\) 0 0
\(775\) −26.5490 + 21.5133i −0.953668 + 0.772781i
\(776\) 10.9512 + 18.9681i 0.393127 + 0.680916i
\(777\) 0 0
\(778\) 23.0658i 0.826949i
\(779\) −0.00337965 0.315621i −0.000121088 0.0113083i
\(780\) 0 0
\(781\) −7.66521 13.2765i −0.274283 0.475072i
\(782\) 0.691255 0.399096i 0.0247192 0.0142716i
\(783\) 0 0
\(784\) 27.9160 + 48.3520i 0.997001 + 1.72686i
\(785\) −34.1031 29.1172i −1.21719 1.03924i
\(786\) 0 0
\(787\) 43.5779i 1.55339i 0.629880 + 0.776693i \(0.283104\pi\)
−0.629880 + 0.776693i \(0.716896\pi\)
\(788\) 69.3734 + 40.0527i 2.47132 + 1.42682i
\(789\) 0 0
\(790\) 11.3370 61.2246i 0.403351 2.17827i
\(791\) −34.8990 −1.24087
\(792\) 0 0
\(793\) 22.9991 13.2785i 0.816721 0.471534i
\(794\) −32.8634 + 56.9210i −1.16628 + 2.02005i
\(795\) 0 0
\(796\) 25.7338 + 44.5723i 0.912111 + 1.57982i
\(797\) 16.1311i 0.571395i −0.958320 0.285697i \(-0.907775\pi\)
0.958320 0.285697i \(-0.0922252\pi\)
\(798\) 0 0
\(799\) −3.34460 −0.118323
\(800\) −1.61103 + 0.255700i −0.0569584 + 0.00904038i
\(801\) 0 0
\(802\) 53.5403 + 30.9115i 1.89057 + 1.09152i
\(803\) −5.63170 + 3.25147i −0.198739 + 0.114742i
\(804\) 0 0
\(805\) −4.83424 0.895159i −0.170385 0.0315502i
\(806\) 63.0912 2.22229
\(807\) 0 0
\(808\) −45.7021 26.3861i −1.60779 0.928259i
\(809\) 28.7134 1.00951 0.504755 0.863263i \(-0.331583\pi\)
0.504755 + 0.863263i \(0.331583\pi\)
\(810\) 0 0
\(811\) −10.7711 + 18.6561i −0.378225 + 0.655104i −0.990804 0.135305i \(-0.956799\pi\)
0.612579 + 0.790409i \(0.290132\pi\)
\(812\) −56.5850 + 32.6694i −1.98575 + 1.14647i
\(813\) 0 0
\(814\) −8.13228 14.0855i −0.285036 0.493697i
\(815\) −29.9990 + 10.6287i −1.05082 + 0.372307i
\(816\) 0 0
\(817\) 1.83299 0.0196275i 0.0641282 0.000686680i
\(818\) 69.5634i 2.43223i
\(819\) 0 0
\(820\) 0.218080 + 0.615520i 0.00761568 + 0.0214949i
\(821\) 16.6602 28.8563i 0.581445 1.00709i −0.413863 0.910339i \(-0.635821\pi\)
0.995308 0.0967536i \(-0.0308459\pi\)
\(822\) 0 0
\(823\) −32.2499 18.6195i −1.12416 0.649035i −0.181701 0.983354i \(-0.558160\pi\)
−0.942460 + 0.334319i \(0.891494\pi\)
\(824\) 28.7422 1.00128
\(825\) 0 0
\(826\) −69.3590 + 120.133i −2.41331 + 4.17997i
\(827\) −25.1591 14.5256i −0.874868 0.505105i −0.00590503 0.999983i \(-0.501880\pi\)
−0.868963 + 0.494877i \(0.835213\pi\)
\(828\) 0 0
\(829\) −34.5380 −1.19956 −0.599778 0.800166i \(-0.704744\pi\)
−0.599778 + 0.800166i \(0.704744\pi\)
\(830\) −55.9895 + 65.5769i −1.94342 + 2.27621i
\(831\) 0 0
\(832\) −24.7249 14.2749i −0.857180 0.494893i
\(833\) 7.66832 4.42731i 0.265692 0.153397i
\(834\) 0 0
\(835\) −2.28658 + 12.3485i −0.0791302 + 0.427338i
\(836\) 33.2640 19.6829i 1.15046 0.680746i
\(837\) 0 0
\(838\) −27.7483 + 16.0205i −0.958550 + 0.553419i
\(839\) 22.3622 + 38.7324i 0.772028 + 1.33719i 0.936450 + 0.350801i \(0.114091\pi\)
−0.164422 + 0.986390i \(0.552576\pi\)
\(840\) 0 0
\(841\) 8.03413 + 13.9155i 0.277039 + 0.479845i
\(842\) 7.07266 + 4.08340i 0.243740 + 0.140723i
\(843\) 0 0
\(844\) −55.8770 −1.92337
\(845\) −1.63528 + 1.91530i −0.0562554 + 0.0658883i
\(846\) 0 0
\(847\) 27.7784i 0.954478i
\(848\) 10.9921i 0.377471i
\(849\) 0 0
\(850\) 1.28192 + 8.07666i 0.0439694 + 0.277027i
\(851\) 0.734898 1.27288i 0.0251920 0.0436338i
\(852\) 0 0
\(853\) 14.0818 8.13013i 0.482152 0.278370i −0.239161 0.970980i \(-0.576872\pi\)
0.721313 + 0.692610i \(0.243539\pi\)
\(854\) 78.1900 2.67561
\(855\) 0 0
\(856\) −6.50273 −0.222259
\(857\) 14.4089 8.31896i 0.492197 0.284170i −0.233288 0.972408i \(-0.574949\pi\)
0.725485 + 0.688237i \(0.241615\pi\)
\(858\) 0 0
\(859\) 20.1362 34.8769i 0.687038 1.18999i −0.285753 0.958303i \(-0.592244\pi\)
0.972792 0.231682i \(-0.0744229\pi\)
\(860\) −3.57467 + 1.26651i −0.121895 + 0.0431878i
\(861\) 0 0
\(862\) 0.118897i 0.00404965i
\(863\) 32.9634i 1.12209i −0.827786 0.561044i \(-0.810400\pi\)
0.827786 0.561044i \(-0.189600\pi\)
\(864\) 0 0
\(865\) −18.1798 15.5219i −0.618131 0.527759i
\(866\) −23.5027 −0.798655
\(867\) 0 0
\(868\) 107.538 + 62.0873i 3.65009 + 2.10738i
\(869\) −12.4633 21.5870i −0.422787 0.732288i
\(870\) 0 0
\(871\) 10.7618 + 18.6400i 0.364651 + 0.631594i
\(872\) 52.0343 30.0420i 1.76210 1.01735i
\(873\) 0 0
\(874\) 4.55267 + 2.56389i 0.153996 + 0.0867248i
\(875\) 26.2975 42.9608i 0.889018 1.45234i
\(876\) 0 0
\(877\) 0.184636 0.106600i 0.00623472 0.00359962i −0.496879 0.867820i \(-0.665521\pi\)
0.503114 + 0.864220i \(0.332188\pi\)
\(878\) 47.3319 + 27.3271i 1.59737 + 0.922244i
\(879\) 0 0
\(880\) −13.4037 + 15.6989i −0.451839 + 0.529210i
\(881\) −51.8661 −1.74741 −0.873707 0.486453i \(-0.838290\pi\)
−0.873707 + 0.486453i \(0.838290\pi\)
\(882\) 0 0
\(883\) 36.0657 + 20.8225i 1.21371 + 0.700734i 0.963565 0.267475i \(-0.0861892\pi\)
0.250142 + 0.968209i \(0.419523\pi\)
\(884\) 5.04667 8.74109i 0.169738 0.293995i
\(885\) 0 0
\(886\) −49.4083 −1.65990
\(887\) 3.54486 + 2.04663i 0.119025 + 0.0687190i 0.558330 0.829619i \(-0.311442\pi\)
−0.439306 + 0.898338i \(0.644775\pi\)
\(888\) 0 0
\(889\) −8.86718 + 15.3584i −0.297396 + 0.515104i
\(890\) −6.92139 + 2.45226i −0.232006 + 0.0822000i
\(891\) 0 0
\(892\) 87.4987i 2.92967i
\(893\) −11.1493 18.8423i −0.373097 0.630533i
\(894\) 0 0
\(895\) 5.74214 + 16.2069i 0.191939 + 0.541737i
\(896\) −43.4984 75.3414i −1.45318 2.51698i
\(897\) 0 0
\(898\) 26.5834 15.3479i 0.887099 0.512167i
\(899\) −12.2882 + 21.2838i −0.409835 + 0.709855i
\(900\) 0 0
\(901\) 1.74328 0.0580772
\(902\) 0.338668 + 0.195530i 0.0112764 + 0.00651043i
\(903\) 0 0
\(904\) −38.6794 −1.28646
\(905\) 13.4698 + 2.49421i 0.447751 + 0.0829102i
\(906\) 0 0
\(907\) 7.28090 4.20363i 0.241758 0.139579i −0.374226 0.927337i \(-0.622092\pi\)
0.615985 + 0.787758i \(0.288758\pi\)
\(908\) 28.6265 + 16.5275i 0.950005 + 0.548486i
\(909\) 0 0
\(910\) −87.6609 + 31.0584i −2.90593 + 1.02958i
\(911\) −8.87918 −0.294180 −0.147090 0.989123i \(-0.546991\pi\)
−0.147090 + 0.989123i \(0.546991\pi\)
\(912\) 0 0
\(913\) 34.5192i 1.14242i
\(914\) −34.7772 60.2359i −1.15033 1.99243i
\(915\) 0 0
\(916\) 33.5983 58.1939i 1.11012 1.92278i
\(917\) 63.6948 36.7742i 2.10339 1.21439i
\(918\) 0 0
\(919\) 45.9834 1.51685 0.758427 0.651758i \(-0.225968\pi\)
0.758427 + 0.651758i \(0.225968\pi\)
\(920\) −5.35790 0.992125i −0.176645 0.0327094i
\(921\) 0 0
\(922\) −11.3153 6.53290i −0.372650 0.215150i
\(923\) 26.2062i 0.862587i
\(924\) 0 0
\(925\) 9.48048 + 11.6996i 0.311716 + 0.384681i
\(926\) 22.0231 + 38.1452i 0.723725 + 1.25353i
\(927\) 0 0
\(928\) −1.01600 + 0.586589i −0.0333519 + 0.0192557i
\(929\) 11.0889 + 19.2065i 0.363814 + 0.630145i 0.988585 0.150663i \(-0.0481409\pi\)
−0.624771 + 0.780808i \(0.714808\pi\)
\(930\) 0 0
\(931\) 50.5044 + 28.4421i 1.65521 + 0.932152i
\(932\) 49.2564i 1.61345i
\(933\) 0 0
\(934\) −35.3436 61.2170i −1.15648 2.00308i
\(935\) 2.48975 + 2.12574i 0.0814234 + 0.0695192i
\(936\) 0 0
\(937\) −29.7284 17.1637i −0.971186 0.560714i −0.0715882 0.997434i \(-0.522807\pi\)
−0.899598 + 0.436720i \(0.856140\pi\)
\(938\) 63.3706i 2.06912i
\(939\) 0 0
\(940\) 34.4474 + 29.4111i 1.12355 + 0.959286i
\(941\) 16.8606 29.2035i 0.549641 0.952006i −0.448658 0.893704i \(-0.648098\pi\)
0.998299 0.0583025i \(-0.0185688\pi\)
\(942\) 0 0
\(943\) 0.0353393i 0.00115080i
\(944\) −26.3167 + 45.5818i −0.856535 + 1.48356i
\(945\) 0 0
\(946\) −1.13555 + 1.96683i −0.0369200 + 0.0639473i
\(947\) 19.1794 11.0732i 0.623248 0.359832i −0.154885 0.987933i \(-0.549501\pi\)
0.778132 + 0.628100i \(0.216167\pi\)
\(948\) 0 0
\(949\) −11.1163 −0.360849
\(950\) −41.2277 + 34.1456i −1.33760 + 1.10783i
\(951\) 0 0
\(952\) 12.9730 7.48995i 0.420457 0.242751i
\(953\) −32.2999 + 18.6484i −1.04630 + 0.604079i −0.921610 0.388117i \(-0.873126\pi\)
−0.124686 + 0.992196i \(0.539792\pi\)
\(954\) 0 0
\(955\) −4.37240 12.3409i −0.141488 0.399342i
\(956\) 4.11254 7.12313i 0.133009 0.230378i
\(957\) 0 0
\(958\) 19.7761i 0.638936i
\(959\) 37.0121 64.1069i 1.19518 2.07012i
\(960\) 0 0
\(961\) 15.7069 0.506674
\(962\) 27.8030i 0.896405i
\(963\) 0 0
\(964\) 35.3359 + 61.2036i 1.13809 + 1.97123i
\(965\) −4.40644 3.76221i −0.141848 0.121110i
\(966\) 0 0
\(967\) −16.1718 + 9.33679i −0.520050 + 0.300251i −0.736955 0.675942i \(-0.763737\pi\)
0.216905 + 0.976193i \(0.430404\pi\)
\(968\) 30.7875i 0.989547i
\(969\) 0 0
\(970\) −23.6883 4.38638i −0.760587 0.140838i
\(971\) 14.2903 + 24.7515i 0.458598 + 0.794314i 0.998887 0.0471649i \(-0.0150186\pi\)
−0.540290 + 0.841479i \(0.681685\pi\)
\(972\) 0 0
\(973\) −10.4116 6.01113i −0.333780 0.192708i
\(974\) 1.34798 + 2.33477i 0.0431921 + 0.0748109i
\(975\) 0 0
\(976\) 29.6674 0.949630
\(977\) 58.1909i 1.86169i −0.365411 0.930846i \(-0.619072\pi\)
0.365411 0.930846i \(-0.380928\pi\)
\(978\) 0 0
\(979\) −1.46980 + 2.54576i −0.0469749 + 0.0813628i
\(980\) −117.911 21.8337i −3.76654 0.697451i
\(981\) 0 0
\(982\) −27.8768 16.0947i −0.889586 0.513602i
\(983\) 41.6320 24.0363i 1.32786 0.766638i 0.342888 0.939376i \(-0.388595\pi\)
0.984968 + 0.172738i \(0.0552615\pi\)
\(984\) 0 0
\(985\) −41.8647 + 14.8327i −1.33392 + 0.472610i
\(986\) 2.94078 + 5.09359i 0.0936536 + 0.162213i
\(987\) 0 0
\(988\) 66.0674 0.707444i 2.10188 0.0225068i
\(989\) −0.205235 −0.00652609
\(990\) 0 0
\(991\) −19.1976 33.2512i −0.609832 1.05626i −0.991268 0.131865i \(-0.957904\pi\)
0.381436 0.924395i \(-0.375430\pi\)
\(992\) 1.93089 + 1.11480i 0.0613057 + 0.0353949i
\(993\) 0 0
\(994\) 38.5785 66.8200i 1.22364 2.11940i
\(995\) −28.0593 5.19576i −0.889540 0.164717i
\(996\) 0 0
\(997\) −32.7546 18.9109i −1.03735 0.598914i −0.118268 0.992982i \(-0.537734\pi\)
−0.919081 + 0.394068i \(0.871067\pi\)
\(998\) −51.3504 29.6472i −1.62547 0.938465i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 855.2.be.d.64.1 12
3.2 odd 2 95.2.i.b.64.6 yes 12
5.4 even 2 inner 855.2.be.d.64.6 12
15.2 even 4 475.2.e.g.26.6 12
15.8 even 4 475.2.e.g.26.1 12
15.14 odd 2 95.2.i.b.64.1 yes 12
19.11 even 3 inner 855.2.be.d.334.6 12
57.11 odd 6 95.2.i.b.49.1 12
57.26 odd 6 1805.2.b.f.1084.6 6
57.50 even 6 1805.2.b.g.1084.1 6
95.49 even 6 inner 855.2.be.d.334.1 12
285.68 even 12 475.2.e.g.201.1 12
285.83 even 12 9025.2.a.bu.1.6 6
285.107 odd 12 9025.2.a.bt.1.6 6
285.164 even 6 1805.2.b.g.1084.6 6
285.182 even 12 475.2.e.g.201.6 12
285.197 even 12 9025.2.a.bu.1.1 6
285.239 odd 6 95.2.i.b.49.6 yes 12
285.254 odd 6 1805.2.b.f.1084.1 6
285.278 odd 12 9025.2.a.bt.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.i.b.49.1 12 57.11 odd 6
95.2.i.b.49.6 yes 12 285.239 odd 6
95.2.i.b.64.1 yes 12 15.14 odd 2
95.2.i.b.64.6 yes 12 3.2 odd 2
475.2.e.g.26.1 12 15.8 even 4
475.2.e.g.26.6 12 15.2 even 4
475.2.e.g.201.1 12 285.68 even 12
475.2.e.g.201.6 12 285.182 even 12
855.2.be.d.64.1 12 1.1 even 1 trivial
855.2.be.d.64.6 12 5.4 even 2 inner
855.2.be.d.334.1 12 95.49 even 6 inner
855.2.be.d.334.6 12 19.11 even 3 inner
1805.2.b.f.1084.1 6 285.254 odd 6
1805.2.b.f.1084.6 6 57.26 odd 6
1805.2.b.g.1084.1 6 57.50 even 6
1805.2.b.g.1084.6 6 285.164 even 6
9025.2.a.bt.1.1 6 285.278 odd 12
9025.2.a.bt.1.6 6 285.107 odd 12
9025.2.a.bu.1.1 6 285.197 even 12
9025.2.a.bu.1.6 6 285.83 even 12