Properties

Label 75.9.c.h.26.8
Level $75$
Weight $9$
Character 75.26
Analytic conductor $30.553$
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] = [75,9,Mod(26,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.26");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.c (of order \(2\), degree \(1\), 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: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 64 x^{10} + 385774 x^{8} - 323639784 x^{6} - 48708595080 x^{4} + 21531002169600 x^{2} + 82\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{18}\cdot 5^{8} \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 26.8
Root \(17.1763 - 23.2266i\) of defining polynomial
Character \(\chi\) \(=\) 75.26
Dual form 75.9.c.h.26.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.66585i q^{2} +(72.8768 - 35.3550i) q^{3} +223.898 q^{4} +(200.316 + 412.909i) q^{6} +1674.62 q^{7} +2719.03i q^{8} +(4061.05 - 5153.12i) q^{9} +O(q^{10})\) \(q+5.66585i q^{2} +(72.8768 - 35.3550i) q^{3} +223.898 q^{4} +(200.316 + 412.909i) q^{6} +1674.62 q^{7} +2719.03i q^{8} +(4061.05 - 5153.12i) q^{9} +21417.9i q^{11} +(16317.0 - 7915.92i) q^{12} +5980.82 q^{13} +9488.16i q^{14} +41912.3 q^{16} +69210.3i q^{17} +(29196.8 + 23009.3i) q^{18} +18044.8 q^{19} +(122041. - 59206.3i) q^{21} -121351. q^{22} -91800.0i q^{23} +(96131.3 + 198154. i) q^{24} +33886.4i q^{26} +(113768. - 519121. i) q^{27} +374945. q^{28} -1.12754e6i q^{29} -1.27927e6 q^{31} +933541. i q^{32} +(757230. + 1.56087e6i) q^{33} -392135. q^{34} +(909261. - 1.15377e6i) q^{36} +2.19804e6 q^{37} +102239. i q^{38} +(435863. - 211452. i) q^{39} -29007.4i q^{41} +(335454. + 691466. i) q^{42} +6.78169e6 q^{43} +4.79543e6i q^{44} +520125. q^{46} +1.96089e6i q^{47} +(3.05443e6 - 1.48181e6i) q^{48} -2.96044e6 q^{49} +(2.44693e6 + 5.04382e6i) q^{51} +1.33909e6 q^{52} +1.23039e7i q^{53} +(2.94126e6 + 644591. i) q^{54} +4.55335e6i q^{56} +(1.31504e6 - 637973. i) q^{57} +6.38847e6 q^{58} -5.58621e6i q^{59} +312034. q^{61} -7.24817e6i q^{62} +(6.80073e6 - 8.62953e6i) q^{63} +5.44025e6 q^{64} +(-8.84365e6 + 4.29035e6i) q^{66} +853503. q^{67} +1.54961e7i q^{68} +(-3.24559e6 - 6.69009e6i) q^{69} -3.18282e7i q^{71} +(1.40115e7 + 1.10421e7i) q^{72} +2.36800e6 q^{73} +1.24537e7i q^{74} +4.04019e6 q^{76} +3.58669e7i q^{77} +(1.19805e6 + 2.46953e6i) q^{78} -2.92328e7 q^{79} +(-1.00625e7 - 4.18541e7i) q^{81} +164351. q^{82} -6.73076e7i q^{83} +(2.73248e7 - 1.32562e7i) q^{84} +3.84240e7i q^{86} +(-3.98642e7 - 8.21715e7i) q^{87} -5.82360e7 q^{88} -4.90240e7i q^{89} +1.00156e7 q^{91} -2.05539e7i q^{92} +(-9.32293e7 + 4.52287e7i) q^{93} -1.11101e7 q^{94} +(3.30053e7 + 6.80334e7i) q^{96} -7.18400e7 q^{97} -1.67734e7i q^{98} +(1.10369e8 + 8.69792e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9} + 413328 q^{16} - 276192 q^{19} - 604044 q^{21} - 1173336 q^{24} - 279216 q^{31} + 1225344 q^{34} - 10311840 q^{36} - 3780864 q^{39} + 37414536 q^{46} + 6222300 q^{49} + 3931248 q^{51} + 53281692 q^{54} - 91958256 q^{61} - 57497760 q^{64} + 111065040 q^{66} - 8138748 q^{69} - 232646880 q^{76} - 420402672 q^{79} + 98480772 q^{81} + 528357816 q^{84} - 100211328 q^{91} - 543022776 q^{94} + 333306864 q^{96} + 640360080 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.66585i 0.354116i 0.984200 + 0.177058i \(0.0566579\pi\)
−0.984200 + 0.177058i \(0.943342\pi\)
\(3\) 72.8768 35.3550i 0.899713 0.436481i
\(4\) 223.898 0.874602
\(5\) 0 0
\(6\) 200.316 + 412.909i 0.154565 + 0.318602i
\(7\) 1674.62 0.697469 0.348734 0.937222i \(-0.386612\pi\)
0.348734 + 0.937222i \(0.386612\pi\)
\(8\) 2719.03i 0.663826i
\(9\) 4061.05 5153.12i 0.618968 0.785416i
\(10\) 0 0
\(11\) 21417.9i 1.46287i 0.681910 + 0.731436i \(0.261150\pi\)
−0.681910 + 0.731436i \(0.738850\pi\)
\(12\) 16317.0 7915.92i 0.786891 0.381748i
\(13\) 5980.82 0.209405 0.104703 0.994504i \(-0.466611\pi\)
0.104703 + 0.994504i \(0.466611\pi\)
\(14\) 9488.16i 0.246985i
\(15\) 0 0
\(16\) 41912.3 0.639531
\(17\) 69210.3i 0.828657i 0.910127 + 0.414329i \(0.135984\pi\)
−0.910127 + 0.414329i \(0.864016\pi\)
\(18\) 29196.8 + 23009.3i 0.278128 + 0.219186i
\(19\) 18044.8 0.138464 0.0692320 0.997601i \(-0.477945\pi\)
0.0692320 + 0.997601i \(0.477945\pi\)
\(20\) 0 0
\(21\) 122041. 59206.3i 0.627522 0.304432i
\(22\) −121351. −0.518026
\(23\) 91800.0i 0.328043i −0.986457 0.164022i \(-0.947553\pi\)
0.986457 0.164022i \(-0.0524467\pi\)
\(24\) 96131.3 + 198154.i 0.289748 + 0.597253i
\(25\) 0 0
\(26\) 33886.4i 0.0741536i
\(27\) 113768. 519121.i 0.214074 0.976817i
\(28\) 374945. 0.610008
\(29\) 1.12754e6i 1.59419i −0.603854 0.797095i \(-0.706369\pi\)
0.603854 0.797095i \(-0.293631\pi\)
\(30\) 0 0
\(31\) −1.27927e6 −1.38521 −0.692607 0.721316i \(-0.743538\pi\)
−0.692607 + 0.721316i \(0.743538\pi\)
\(32\) 933541.i 0.890294i
\(33\) 757230. + 1.56087e6i 0.638517 + 1.31617i
\(34\) −392135. −0.293440
\(35\) 0 0
\(36\) 909261. 1.15377e6i 0.541351 0.686927i
\(37\) 2.19804e6 1.17281 0.586405 0.810018i \(-0.300543\pi\)
0.586405 + 0.810018i \(0.300543\pi\)
\(38\) 102239.i 0.0490322i
\(39\) 435863. 211452.i 0.188404 0.0914014i
\(40\) 0 0
\(41\) 29007.4i 0.0102653i −0.999987 0.00513267i \(-0.998366\pi\)
0.999987 0.00513267i \(-0.00163379\pi\)
\(42\) 335454. + 691466.i 0.107804 + 0.222215i
\(43\) 6.78169e6 1.98365 0.991823 0.127625i \(-0.0407354\pi\)
0.991823 + 0.127625i \(0.0407354\pi\)
\(44\) 4.79543e6i 1.27943i
\(45\) 0 0
\(46\) 520125. 0.116165
\(47\) 1.96089e6i 0.401847i 0.979607 + 0.200924i \(0.0643943\pi\)
−0.979607 + 0.200924i \(0.935606\pi\)
\(48\) 3.05443e6 1.48181e6i 0.575395 0.279143i
\(49\) −2.96044e6 −0.513537
\(50\) 0 0
\(51\) 2.44693e6 + 5.04382e6i 0.361694 + 0.745554i
\(52\) 1.33909e6 0.183146
\(53\) 1.23039e7i 1.55933i 0.626198 + 0.779664i \(0.284610\pi\)
−0.626198 + 0.779664i \(0.715390\pi\)
\(54\) 2.94126e6 + 644591.i 0.345906 + 0.0758070i
\(55\) 0 0
\(56\) 4.55335e6i 0.462998i
\(57\) 1.31504e6 637973.i 0.124578 0.0604370i
\(58\) 6.38847e6 0.564527
\(59\) 5.58621e6i 0.461009i −0.973071 0.230504i \(-0.925962\pi\)
0.973071 0.230504i \(-0.0740376\pi\)
\(60\) 0 0
\(61\) 312034. 0.0225363 0.0112681 0.999937i \(-0.496413\pi\)
0.0112681 + 0.999937i \(0.496413\pi\)
\(62\) 7.24817e6i 0.490525i
\(63\) 6.80073e6 8.62953e6i 0.431711 0.547803i
\(64\) 5.44025e6 0.324264
\(65\) 0 0
\(66\) −8.84365e6 + 4.29035e6i −0.466075 + 0.226109i
\(67\) 853503. 0.0423551 0.0211775 0.999776i \(-0.493258\pi\)
0.0211775 + 0.999776i \(0.493258\pi\)
\(68\) 1.54961e7i 0.724746i
\(69\) −3.24559e6 6.69009e6i −0.143185 0.295145i
\(70\) 0 0
\(71\) 3.18282e7i 1.25250i −0.779621 0.626252i \(-0.784588\pi\)
0.779621 0.626252i \(-0.215412\pi\)
\(72\) 1.40115e7 + 1.10421e7i 0.521379 + 0.410887i
\(73\) 2.36800e6 0.0833855 0.0416927 0.999130i \(-0.486725\pi\)
0.0416927 + 0.999130i \(0.486725\pi\)
\(74\) 1.24537e7i 0.415310i
\(75\) 0 0
\(76\) 4.04019e6 0.121101
\(77\) 3.58669e7i 1.02031i
\(78\) 1.19805e6 + 2.46953e6i 0.0323667 + 0.0667170i
\(79\) −2.92328e7 −0.750520 −0.375260 0.926920i \(-0.622447\pi\)
−0.375260 + 0.926920i \(0.622447\pi\)
\(80\) 0 0
\(81\) −1.00625e7 4.18541e7i −0.233757 0.972295i
\(82\) 164351. 0.00363512
\(83\) 6.73076e7i 1.41825i −0.705084 0.709124i \(-0.749091\pi\)
0.705084 0.709124i \(-0.250909\pi\)
\(84\) 2.73248e7 1.32562e7i 0.548832 0.266257i
\(85\) 0 0
\(86\) 3.84240e7i 0.702439i
\(87\) −3.98642e7 8.21715e7i −0.695834 1.43431i
\(88\) −5.82360e7 −0.971093
\(89\) 4.90240e7i 0.781355i −0.920528 0.390678i \(-0.872241\pi\)
0.920528 0.390678i \(-0.127759\pi\)
\(90\) 0 0
\(91\) 1.00156e7 0.146054
\(92\) 2.05539e7i 0.286908i
\(93\) −9.32293e7 + 4.52287e7i −1.24629 + 0.604620i
\(94\) −1.11101e7 −0.142300
\(95\) 0 0
\(96\) 3.30053e7 + 6.80334e7i 0.388597 + 0.801009i
\(97\) −7.18400e7 −0.811483 −0.405741 0.913988i \(-0.632987\pi\)
−0.405741 + 0.913988i \(0.632987\pi\)
\(98\) 1.67734e7i 0.181851i
\(99\) 1.10369e8 + 8.69792e7i 1.14896 + 0.905471i
\(100\) 0 0
\(101\) 1.12197e8i 1.07819i 0.842244 + 0.539097i \(0.181234\pi\)
−0.842244 + 0.539097i \(0.818766\pi\)
\(102\) −2.85775e7 + 1.38639e7i −0.264012 + 0.128081i
\(103\) −1.33889e8 −1.18959 −0.594795 0.803877i \(-0.702767\pi\)
−0.594795 + 0.803877i \(0.702767\pi\)
\(104\) 1.62620e7i 0.139008i
\(105\) 0 0
\(106\) −6.97118e7 −0.552183
\(107\) 3.67153e7i 0.280100i 0.990144 + 0.140050i \(0.0447263\pi\)
−0.990144 + 0.140050i \(0.955274\pi\)
\(108\) 2.54724e7 1.16230e8i 0.187230 0.854327i
\(109\) −1.68006e8 −1.19020 −0.595099 0.803652i \(-0.702887\pi\)
−0.595099 + 0.803652i \(0.702887\pi\)
\(110\) 0 0
\(111\) 1.60186e8 7.77115e7i 1.05519 0.511910i
\(112\) 7.01873e7 0.446053
\(113\) 9.78362e7i 0.600048i −0.953932 0.300024i \(-0.903005\pi\)
0.953932 0.300024i \(-0.0969947\pi\)
\(114\) 3.61466e6 + 7.45084e6i 0.0214017 + 0.0441150i
\(115\) 0 0
\(116\) 2.52454e8i 1.39428i
\(117\) 2.42884e7 3.08198e7i 0.129615 0.164470i
\(118\) 3.16506e7 0.163250
\(119\) 1.15901e8i 0.577963i
\(120\) 0 0
\(121\) −2.44368e8 −1.14000
\(122\) 1.76793e6i 0.00798044i
\(123\) −1.02556e6 2.11397e6i −0.00448063 0.00923586i
\(124\) −2.86427e8 −1.21151
\(125\) 0 0
\(126\) 4.88936e7 + 3.85319e7i 0.193986 + 0.152876i
\(127\) −1.37799e8 −0.529701 −0.264851 0.964289i \(-0.585323\pi\)
−0.264851 + 0.964289i \(0.585323\pi\)
\(128\) 2.69810e8i 1.00512i
\(129\) 4.94228e8 2.39767e8i 1.78471 0.865824i
\(130\) 0 0
\(131\) 7.11572e7i 0.241620i 0.992676 + 0.120810i \(0.0385492\pi\)
−0.992676 + 0.120810i \(0.961451\pi\)
\(132\) 1.69543e8 + 3.49476e8i 0.558448 + 1.15112i
\(133\) 3.02182e7 0.0965743
\(134\) 4.83582e6i 0.0149986i
\(135\) 0 0
\(136\) −1.88185e8 −0.550084
\(137\) 5.04740e8i 1.43280i −0.697689 0.716400i \(-0.745788\pi\)
0.697689 0.716400i \(-0.254212\pi\)
\(138\) 3.79050e7 1.83890e7i 0.104515 0.0507040i
\(139\) −2.09113e8 −0.560171 −0.280086 0.959975i \(-0.590363\pi\)
−0.280086 + 0.959975i \(0.590363\pi\)
\(140\) 0 0
\(141\) 6.93271e7 + 1.42903e8i 0.175399 + 0.361547i
\(142\) 1.80334e8 0.443531
\(143\) 1.28097e8i 0.306333i
\(144\) 1.70208e8 2.15979e8i 0.395849 0.502298i
\(145\) 0 0
\(146\) 1.34167e7i 0.0295281i
\(147\) −2.15747e8 + 1.04666e8i −0.462036 + 0.224149i
\(148\) 4.92136e8 1.02574
\(149\) 2.19726e8i 0.445796i −0.974842 0.222898i \(-0.928448\pi\)
0.974842 0.222898i \(-0.0715517\pi\)
\(150\) 0 0
\(151\) 3.50620e8 0.674418 0.337209 0.941430i \(-0.390517\pi\)
0.337209 + 0.941430i \(0.390517\pi\)
\(152\) 4.90643e7i 0.0919160i
\(153\) 3.56649e8 + 2.81066e8i 0.650841 + 0.512912i
\(154\) −2.03217e8 −0.361307
\(155\) 0 0
\(156\) 9.75889e7 4.73437e7i 0.164779 0.0799399i
\(157\) −7.08761e7 −0.116654 −0.0583272 0.998298i \(-0.518577\pi\)
−0.0583272 + 0.998298i \(0.518577\pi\)
\(158\) 1.65629e8i 0.265771i
\(159\) 4.35003e8 + 8.96665e8i 0.680618 + 1.40295i
\(160\) 0 0
\(161\) 1.53730e8i 0.228800i
\(162\) 2.37139e8 5.70125e7i 0.344305 0.0827771i
\(163\) 7.30934e8 1.03545 0.517724 0.855548i \(-0.326780\pi\)
0.517724 + 0.855548i \(0.326780\pi\)
\(164\) 6.49470e6i 0.00897809i
\(165\) 0 0
\(166\) 3.81355e8 0.502223
\(167\) 1.02725e9i 1.32072i 0.750948 + 0.660361i \(0.229597\pi\)
−0.750948 + 0.660361i \(0.770403\pi\)
\(168\) 1.60984e8 + 3.31833e8i 0.202090 + 0.416565i
\(169\) −7.79961e8 −0.956150
\(170\) 0 0
\(171\) 7.32807e7 9.29868e7i 0.0857048 0.108752i
\(172\) 1.51841e9 1.73490
\(173\) 1.07140e8i 0.119610i 0.998210 + 0.0598050i \(0.0190479\pi\)
−0.998210 + 0.0598050i \(0.980952\pi\)
\(174\) 4.65571e8 2.25864e8i 0.507913 0.246406i
\(175\) 0 0
\(176\) 8.97675e8i 0.935553i
\(177\) −1.97500e8 4.07105e8i −0.201222 0.414776i
\(178\) 2.77763e8 0.276690
\(179\) 1.76590e8i 0.172010i 0.996295 + 0.0860051i \(0.0274101\pi\)
−0.996295 + 0.0860051i \(0.972590\pi\)
\(180\) 0 0
\(181\) −1.03775e9 −0.966896 −0.483448 0.875373i \(-0.660616\pi\)
−0.483448 + 0.875373i \(0.660616\pi\)
\(182\) 5.67469e7i 0.0517198i
\(183\) 2.27400e7 1.10319e7i 0.0202762 0.00983666i
\(184\) 2.49607e8 0.217764
\(185\) 0 0
\(186\) −2.56259e8 5.28223e8i −0.214105 0.441332i
\(187\) −1.48234e9 −1.21222
\(188\) 4.39039e8i 0.351456i
\(189\) 1.90518e8 8.69332e8i 0.149310 0.681300i
\(190\) 0 0
\(191\) 4.41653e8i 0.331854i −0.986138 0.165927i \(-0.946938\pi\)
0.986138 0.165927i \(-0.0530617\pi\)
\(192\) 3.96468e8 1.92340e8i 0.291745 0.141535i
\(193\) −1.80470e9 −1.30070 −0.650349 0.759635i \(-0.725377\pi\)
−0.650349 + 0.759635i \(0.725377\pi\)
\(194\) 4.07034e8i 0.287359i
\(195\) 0 0
\(196\) −6.62837e8 −0.449141
\(197\) 1.84458e9i 1.22471i −0.790583 0.612355i \(-0.790222\pi\)
0.790583 0.612355i \(-0.209778\pi\)
\(198\) −4.92811e8 + 6.25334e8i −0.320641 + 0.406866i
\(199\) −1.80610e9 −1.15167 −0.575837 0.817564i \(-0.695324\pi\)
−0.575837 + 0.817564i \(0.695324\pi\)
\(200\) 0 0
\(201\) 6.22005e7 3.01756e7i 0.0381074 0.0184872i
\(202\) −6.35693e8 −0.381805
\(203\) 1.88820e9i 1.11190i
\(204\) 5.47863e8 + 1.12930e9i 0.316338 + 0.652063i
\(205\) 0 0
\(206\) 7.58597e8i 0.421253i
\(207\) −4.73056e8 3.72804e8i −0.257651 0.203048i
\(208\) 2.50670e8 0.133921
\(209\) 3.86481e8i 0.202555i
\(210\) 0 0
\(211\) 2.94285e8 0.148470 0.0742350 0.997241i \(-0.476349\pi\)
0.0742350 + 0.997241i \(0.476349\pi\)
\(212\) 2.75481e9i 1.36379i
\(213\) −1.12529e9 2.31954e9i −0.546695 1.12689i
\(214\) −2.08024e8 −0.0991876
\(215\) 0 0
\(216\) 1.41151e9 + 3.09338e8i 0.648437 + 0.142108i
\(217\) −2.14230e9 −0.966143
\(218\) 9.51897e8i 0.421468i
\(219\) 1.72572e8 8.37207e7i 0.0750230 0.0363962i
\(220\) 0 0
\(221\) 4.13934e8i 0.173525i
\(222\) 4.40302e8 + 9.07588e8i 0.181275 + 0.373660i
\(223\) −3.54930e9 −1.43523 −0.717617 0.696438i \(-0.754767\pi\)
−0.717617 + 0.696438i \(0.754767\pi\)
\(224\) 1.56333e9i 0.620952i
\(225\) 0 0
\(226\) 5.54325e8 0.212486
\(227\) 3.07376e9i 1.15762i −0.815461 0.578811i \(-0.803517\pi\)
0.815461 0.578811i \(-0.196483\pi\)
\(228\) 2.94436e8 1.42841e8i 0.108956 0.0528583i
\(229\) 2.58716e9 0.940767 0.470383 0.882462i \(-0.344116\pi\)
0.470383 + 0.882462i \(0.344116\pi\)
\(230\) 0 0
\(231\) 1.26808e9 + 2.61387e9i 0.445346 + 0.917985i
\(232\) 3.06582e9 1.05826
\(233\) 4.46492e9i 1.51492i 0.652882 + 0.757460i \(0.273560\pi\)
−0.652882 + 0.757460i \(0.726440\pi\)
\(234\) 1.74621e8 + 1.37614e8i 0.0582414 + 0.0458987i
\(235\) 0 0
\(236\) 1.25074e9i 0.403199i
\(237\) −2.13039e9 + 1.03353e9i −0.675253 + 0.327588i
\(238\) −6.56678e8 −0.204666
\(239\) 2.49405e9i 0.764388i −0.924082 0.382194i \(-0.875169\pi\)
0.924082 0.382194i \(-0.124831\pi\)
\(240\) 0 0
\(241\) −1.06935e9 −0.316993 −0.158497 0.987360i \(-0.550665\pi\)
−0.158497 + 0.987360i \(0.550665\pi\)
\(242\) 1.38455e9i 0.403691i
\(243\) −2.21307e9 2.69443e9i −0.634703 0.772756i
\(244\) 6.98637e7 0.0197103
\(245\) 0 0
\(246\) 1.19774e7 5.81065e6i 0.00327056 0.00158666i
\(247\) 1.07922e8 0.0289951
\(248\) 3.47838e9i 0.919540i
\(249\) −2.37966e9 4.90516e9i −0.619039 1.27602i
\(250\) 0 0
\(251\) 2.58790e9i 0.652007i 0.945369 + 0.326003i \(0.105702\pi\)
−0.945369 + 0.326003i \(0.894298\pi\)
\(252\) 1.52267e9 1.93214e9i 0.377575 0.479110i
\(253\) 1.96617e9 0.479886
\(254\) 7.80748e8i 0.187575i
\(255\) 0 0
\(256\) −1.35998e8 −0.0316644
\(257\) 3.99995e9i 0.916900i 0.888720 + 0.458450i \(0.151595\pi\)
−0.888720 + 0.458450i \(0.848405\pi\)
\(258\) 1.35848e9 + 2.80022e9i 0.306602 + 0.631994i
\(259\) 3.68088e9 0.817999
\(260\) 0 0
\(261\) −5.81035e9 4.57900e9i −1.25210 0.986753i
\(262\) −4.03166e8 −0.0855615
\(263\) 2.61772e9i 0.547142i 0.961852 + 0.273571i \(0.0882048\pi\)
−0.961852 + 0.273571i \(0.911795\pi\)
\(264\) −4.24405e9 + 2.05893e9i −0.873705 + 0.423864i
\(265\) 0 0
\(266\) 1.71212e8i 0.0341985i
\(267\) −1.73324e9 3.57271e9i −0.341047 0.702996i
\(268\) 1.91098e8 0.0370439
\(269\) 6.21608e9i 1.18715i 0.804777 + 0.593577i \(0.202285\pi\)
−0.804777 + 0.593577i \(0.797715\pi\)
\(270\) 0 0
\(271\) 5.31021e9 0.984543 0.492271 0.870442i \(-0.336167\pi\)
0.492271 + 0.870442i \(0.336167\pi\)
\(272\) 2.90076e9i 0.529952i
\(273\) 7.29906e8 3.54102e8i 0.131406 0.0637496i
\(274\) 2.85978e9 0.507377
\(275\) 0 0
\(276\) −7.26681e8 1.49790e9i −0.125230 0.258135i
\(277\) −2.24918e9 −0.382037 −0.191018 0.981586i \(-0.561179\pi\)
−0.191018 + 0.981586i \(0.561179\pi\)
\(278\) 1.18480e9i 0.198365i
\(279\) −5.19519e9 + 6.59224e9i −0.857403 + 1.08797i
\(280\) 0 0
\(281\) 7.68684e9i 1.23289i −0.787400 0.616443i \(-0.788573\pi\)
0.787400 0.616443i \(-0.211427\pi\)
\(282\) −8.09667e8 + 3.92797e8i −0.128029 + 0.0621114i
\(283\) 7.20498e9 1.12328 0.561639 0.827382i \(-0.310171\pi\)
0.561639 + 0.827382i \(0.310171\pi\)
\(284\) 7.12628e9i 1.09544i
\(285\) 0 0
\(286\) −7.25776e8 −0.108477
\(287\) 4.85765e7i 0.00715976i
\(288\) 4.81064e9 + 3.79115e9i 0.699251 + 0.551063i
\(289\) 2.18569e9 0.313327
\(290\) 0 0
\(291\) −5.23547e9 + 2.53990e9i −0.730102 + 0.354197i
\(292\) 5.30191e8 0.0729291
\(293\) 3.98677e9i 0.540942i −0.962728 0.270471i \(-0.912821\pi\)
0.962728 0.270471i \(-0.0871794\pi\)
\(294\) −5.93023e8 1.22239e9i −0.0793748 0.163614i
\(295\) 0 0
\(296\) 5.97653e9i 0.778542i
\(297\) 1.11185e10 + 2.43667e9i 1.42896 + 0.313163i
\(298\) 1.24493e9 0.157863
\(299\) 5.49039e8i 0.0686940i
\(300\) 0 0
\(301\) 1.13568e10 1.38353
\(302\) 1.98656e9i 0.238822i
\(303\) 3.96674e9 + 8.17658e9i 0.470612 + 0.970066i
\(304\) 7.56298e8 0.0885520
\(305\) 0 0
\(306\) −1.59248e9 + 2.02072e9i −0.181630 + 0.230473i
\(307\) 9.29130e9 1.04598 0.522990 0.852339i \(-0.324817\pi\)
0.522990 + 0.852339i \(0.324817\pi\)
\(308\) 8.03054e9i 0.892364i
\(309\) −9.75743e9 + 4.73366e9i −1.07029 + 0.519234i
\(310\) 0 0
\(311\) 1.12048e10i 1.19774i 0.800847 + 0.598869i \(0.204383\pi\)
−0.800847 + 0.598869i \(0.795617\pi\)
\(312\) 5.74944e8 + 1.18512e9i 0.0606746 + 0.125068i
\(313\) 9.45147e9 0.984741 0.492371 0.870386i \(-0.336130\pi\)
0.492371 + 0.870386i \(0.336130\pi\)
\(314\) 4.01573e8i 0.0413092i
\(315\) 0 0
\(316\) −6.54518e9 −0.656407
\(317\) 8.48385e8i 0.0840148i −0.999117 0.0420074i \(-0.986625\pi\)
0.999117 0.0420074i \(-0.0133753\pi\)
\(318\) −5.08037e9 + 2.46466e9i −0.496806 + 0.241017i
\(319\) 2.41496e10 2.33210
\(320\) 0 0
\(321\) 1.29807e9 + 2.67570e9i 0.122258 + 0.252009i
\(322\) 8.71013e8 0.0810217
\(323\) 1.24888e9i 0.114739i
\(324\) −2.25297e9 9.37106e9i −0.204445 0.850371i
\(325\) 0 0
\(326\) 4.14136e9i 0.366668i
\(327\) −1.22437e10 + 5.93986e9i −1.07084 + 0.519499i
\(328\) 7.88720e7 0.00681440
\(329\) 3.28374e9i 0.280276i
\(330\) 0 0
\(331\) 4.71539e9 0.392831 0.196415 0.980521i \(-0.437070\pi\)
0.196415 + 0.980521i \(0.437070\pi\)
\(332\) 1.50701e10i 1.24040i
\(333\) 8.92633e9 1.13267e10i 0.725932 0.921144i
\(334\) −5.82026e9 −0.467688
\(335\) 0 0
\(336\) 5.11503e9 2.48147e9i 0.401320 0.194694i
\(337\) 3.45801e8 0.0268106 0.0134053 0.999910i \(-0.495733\pi\)
0.0134053 + 0.999910i \(0.495733\pi\)
\(338\) 4.41914e9i 0.338587i
\(339\) −3.45900e9 7.12999e9i −0.261910 0.539871i
\(340\) 0 0
\(341\) 2.73994e10i 2.02639i
\(342\) 5.26849e8 + 4.15197e8i 0.0385107 + 0.0303494i
\(343\) −1.46115e10 −1.05565
\(344\) 1.84396e10i 1.31679i
\(345\) 0 0
\(346\) −6.07040e8 −0.0423558
\(347\) 3.52962e9i 0.243450i 0.992564 + 0.121725i \(0.0388426\pi\)
−0.992564 + 0.121725i \(0.961157\pi\)
\(348\) −8.92552e9 1.83980e10i −0.608578 1.25445i
\(349\) −8.25013e9 −0.556108 −0.278054 0.960565i \(-0.589689\pi\)
−0.278054 + 0.960565i \(0.589689\pi\)
\(350\) 0 0
\(351\) 6.80424e8 3.10477e9i 0.0448282 0.204550i
\(352\) −1.99945e10 −1.30239
\(353\) 1.08036e10i 0.695776i 0.937536 + 0.347888i \(0.113101\pi\)
−0.937536 + 0.347888i \(0.886899\pi\)
\(354\) 2.30659e9 1.11901e9i 0.146878 0.0712557i
\(355\) 0 0
\(356\) 1.09764e10i 0.683375i
\(357\) 4.09768e9 + 8.44650e9i 0.252270 + 0.520001i
\(358\) −1.00053e9 −0.0609115
\(359\) 1.78116e10i 1.07232i −0.844115 0.536162i \(-0.819874\pi\)
0.844115 0.536162i \(-0.180126\pi\)
\(360\) 0 0
\(361\) −1.66579e10 −0.980828
\(362\) 5.87975e9i 0.342393i
\(363\) −1.78088e10 + 8.63965e9i −1.02567 + 0.497587i
\(364\) 2.24248e9 0.127739
\(365\) 0 0
\(366\) 6.25053e7 + 1.28841e8i 0.00348331 + 0.00718011i
\(367\) 7.25059e9 0.399677 0.199839 0.979829i \(-0.435958\pi\)
0.199839 + 0.979829i \(0.435958\pi\)
\(368\) 3.84755e9i 0.209794i
\(369\) −1.49478e8 1.17800e8i −0.00806256 0.00635392i
\(370\) 0 0
\(371\) 2.06043e10i 1.08758i
\(372\) −2.08739e10 + 1.01266e10i −1.09001 + 0.528802i
\(373\) −1.40594e10 −0.726325 −0.363163 0.931726i \(-0.618303\pi\)
−0.363163 + 0.931726i \(0.618303\pi\)
\(374\) 8.39872e9i 0.429266i
\(375\) 0 0
\(376\) −5.33171e9 −0.266757
\(377\) 6.74361e9i 0.333831i
\(378\) 4.92550e9 + 1.07945e9i 0.241259 + 0.0528730i
\(379\) −9.41156e9 −0.456147 −0.228073 0.973644i \(-0.573243\pi\)
−0.228073 + 0.973644i \(0.573243\pi\)
\(380\) 0 0
\(381\) −1.00423e10 + 4.87188e9i −0.476579 + 0.231205i
\(382\) 2.50234e9 0.117515
\(383\) 2.22515e10i 1.03410i −0.855954 0.517052i \(-0.827029\pi\)
0.855954 0.517052i \(-0.172971\pi\)
\(384\) 9.53913e9 + 1.96629e10i 0.438716 + 0.904320i
\(385\) 0 0
\(386\) 1.02252e10i 0.460598i
\(387\) 2.75408e10 3.49468e10i 1.22781 1.55799i
\(388\) −1.60848e10 −0.709725
\(389\) 1.67518e10i 0.731582i −0.930697 0.365791i \(-0.880798\pi\)
0.930697 0.365791i \(-0.119202\pi\)
\(390\) 0 0
\(391\) 6.35351e9 0.271836
\(392\) 8.04952e9i 0.340899i
\(393\) 2.51576e9 + 5.18570e9i 0.105463 + 0.217389i
\(394\) 1.04511e10 0.433689
\(395\) 0 0
\(396\) 2.47114e10 + 1.94745e10i 1.00489 + 0.791927i
\(397\) 3.88428e9 0.156368 0.0781840 0.996939i \(-0.475088\pi\)
0.0781840 + 0.996939i \(0.475088\pi\)
\(398\) 1.02331e10i 0.407826i
\(399\) 2.20220e9 1.06836e9i 0.0868892 0.0421529i
\(400\) 0 0
\(401\) 3.28950e10i 1.27219i 0.771610 + 0.636096i \(0.219452\pi\)
−0.771610 + 0.636096i \(0.780548\pi\)
\(402\) 1.70970e8 + 3.52419e8i 0.00654661 + 0.0134944i
\(403\) −7.65110e9 −0.290071
\(404\) 2.51208e10i 0.942991i
\(405\) 0 0
\(406\) 1.06983e10 0.393740
\(407\) 4.70774e10i 1.71567i
\(408\) −1.37143e10 + 6.65327e9i −0.494918 + 0.240101i
\(409\) 1.08495e9 0.0387718 0.0193859 0.999812i \(-0.493829\pi\)
0.0193859 + 0.999812i \(0.493829\pi\)
\(410\) 0 0
\(411\) −1.78451e10 3.67838e10i −0.625391 1.28911i
\(412\) −2.99776e10 −1.04042
\(413\) 9.35479e9i 0.321539i
\(414\) 2.11225e9 2.68026e9i 0.0719026 0.0912381i
\(415\) 0 0
\(416\) 5.58334e9i 0.186432i
\(417\) −1.52395e10 + 7.39317e9i −0.503994 + 0.244504i
\(418\) −2.18974e9 −0.0717279
\(419\) 3.39202e10i 1.10053i 0.834990 + 0.550266i \(0.185474\pi\)
−0.834990 + 0.550266i \(0.814526\pi\)
\(420\) 0 0
\(421\) 2.88554e10 0.918542 0.459271 0.888296i \(-0.348111\pi\)
0.459271 + 0.888296i \(0.348111\pi\)
\(422\) 1.66738e9i 0.0525755i
\(423\) 1.01047e10 + 7.96325e9i 0.315617 + 0.248731i
\(424\) −3.34546e10 −1.03512
\(425\) 0 0
\(426\) 1.31422e10 6.37570e9i 0.399051 0.193593i
\(427\) 5.22539e8 0.0157183
\(428\) 8.22050e9i 0.244976i
\(429\) 4.52886e9 + 9.33527e9i 0.133709 + 0.275612i
\(430\) 0 0
\(431\) 7.99799e8i 0.0231778i −0.999933 0.0115889i \(-0.996311\pi\)
0.999933 0.0115889i \(-0.00368894\pi\)
\(432\) 4.76827e9 2.17576e10i 0.136907 0.624705i
\(433\) 2.02420e10 0.575839 0.287920 0.957655i \(-0.407036\pi\)
0.287920 + 0.957655i \(0.407036\pi\)
\(434\) 1.21380e10i 0.342126i
\(435\) 0 0
\(436\) −3.76163e10 −1.04095
\(437\) 1.65651e9i 0.0454222i
\(438\) 4.74349e8 + 9.77768e8i 0.0128885 + 0.0265668i
\(439\) −4.16160e10 −1.12048 −0.560238 0.828332i \(-0.689290\pi\)
−0.560238 + 0.828332i \(0.689290\pi\)
\(440\) 0 0
\(441\) −1.20225e10 + 1.52555e10i −0.317863 + 0.403340i
\(442\) −2.34529e9 −0.0614479
\(443\) 1.00330e10i 0.260504i −0.991481 0.130252i \(-0.958421\pi\)
0.991481 0.130252i \(-0.0415787\pi\)
\(444\) 3.58653e10 1.73995e10i 0.922874 0.447718i
\(445\) 0 0
\(446\) 2.01098e10i 0.508239i
\(447\) −7.76841e9 1.60129e10i −0.194582 0.401088i
\(448\) 9.11037e9 0.226164
\(449\) 2.59211e10i 0.637775i −0.947793 0.318888i \(-0.896691\pi\)
0.947793 0.318888i \(-0.103309\pi\)
\(450\) 0 0
\(451\) 6.21278e8 0.0150169
\(452\) 2.19054e10i 0.524803i
\(453\) 2.55521e10 1.23962e10i 0.606783 0.294371i
\(454\) 1.74155e10 0.409932
\(455\) 0 0
\(456\) 1.73467e9 + 3.57565e9i 0.0401196 + 0.0826980i
\(457\) 5.83258e10 1.33720 0.668599 0.743623i \(-0.266894\pi\)
0.668599 + 0.743623i \(0.266894\pi\)
\(458\) 1.46585e10i 0.333140i
\(459\) 3.59285e10 + 7.87390e9i 0.809447 + 0.177394i
\(460\) 0 0
\(461\) 2.73170e10i 0.604825i −0.953177 0.302412i \(-0.902208\pi\)
0.953177 0.302412i \(-0.0977920\pi\)
\(462\) −1.48098e10 + 7.18472e9i −0.325073 + 0.157704i
\(463\) 5.50831e10 1.19866 0.599328 0.800504i \(-0.295435\pi\)
0.599328 + 0.800504i \(0.295435\pi\)
\(464\) 4.72578e10i 1.01953i
\(465\) 0 0
\(466\) −2.52975e10 −0.536456
\(467\) 4.06476e10i 0.854610i 0.904108 + 0.427305i \(0.140537\pi\)
−0.904108 + 0.427305i \(0.859463\pi\)
\(468\) 5.43813e9 6.90051e9i 0.113362 0.143846i
\(469\) 1.42929e9 0.0295414
\(470\) 0 0
\(471\) −5.16522e9 + 2.50582e9i −0.104956 + 0.0509175i
\(472\) 1.51891e10 0.306029
\(473\) 1.45250e11i 2.90182i
\(474\) −5.85580e9 1.20705e10i −0.116004 0.239118i
\(475\) 0 0
\(476\) 2.59501e10i 0.505488i
\(477\) 6.34032e10 + 4.99666e10i 1.22472 + 0.965175i
\(478\) 1.41309e10 0.270682
\(479\) 1.08547e10i 0.206194i 0.994671 + 0.103097i \(0.0328752\pi\)
−0.994671 + 0.103097i \(0.967125\pi\)
\(480\) 0 0
\(481\) 1.31460e10 0.245592
\(482\) 6.05876e9i 0.112252i
\(483\) −5.43514e9 1.12034e10i −0.0998670 0.205855i
\(484\) −5.47137e10 −0.997044
\(485\) 0 0
\(486\) 1.52663e10 1.25389e10i 0.273645 0.224758i
\(487\) 1.77991e10 0.316433 0.158216 0.987404i \(-0.449426\pi\)
0.158216 + 0.987404i \(0.449426\pi\)
\(488\) 8.48429e8i 0.0149602i
\(489\) 5.32681e10 2.58422e10i 0.931606 0.451953i
\(490\) 0 0
\(491\) 7.93615e10i 1.36547i −0.730664 0.682737i \(-0.760789\pi\)
0.730664 0.682737i \(-0.239211\pi\)
\(492\) −2.29620e8 4.73313e8i −0.00391877 0.00807771i
\(493\) 7.80374e10 1.32104
\(494\) 6.11472e8i 0.0102676i
\(495\) 0 0
\(496\) −5.36173e10 −0.885887
\(497\) 5.33003e10i 0.873582i
\(498\) 2.77919e10 1.34828e10i 0.451857 0.219211i
\(499\) −6.54034e10 −1.05487 −0.527434 0.849596i \(-0.676846\pi\)
−0.527434 + 0.849596i \(0.676846\pi\)
\(500\) 0 0
\(501\) 3.63185e10 + 7.48629e10i 0.576471 + 1.18827i
\(502\) −1.46626e10 −0.230886
\(503\) 1.01074e11i 1.57894i −0.613788 0.789471i \(-0.710355\pi\)
0.613788 0.789471i \(-0.289645\pi\)
\(504\) 2.34639e10 + 1.84914e10i 0.363646 + 0.286581i
\(505\) 0 0
\(506\) 1.11400e10i 0.169935i
\(507\) −5.68410e10 + 2.75755e10i −0.860260 + 0.417341i
\(508\) −3.08529e10 −0.463278
\(509\) 1.19907e11i 1.78638i 0.449681 + 0.893189i \(0.351538\pi\)
−0.449681 + 0.893189i \(0.648462\pi\)
\(510\) 0 0
\(511\) 3.96551e9 0.0581588
\(512\) 6.83008e10i 0.993908i
\(513\) 2.05291e9 9.36741e9i 0.0296416 0.135254i
\(514\) −2.26631e10 −0.324689
\(515\) 0 0
\(516\) 1.10657e11 5.36833e10i 1.56091 0.757252i
\(517\) −4.19981e10 −0.587851
\(518\) 2.08553e10i 0.289666i
\(519\) 3.78794e9 + 7.80802e9i 0.0522076 + 0.107615i
\(520\) 0 0
\(521\) 1.21461e11i 1.64849i 0.566230 + 0.824247i \(0.308401\pi\)
−0.566230 + 0.824247i \(0.691599\pi\)
\(522\) 2.59439e10 3.29205e10i 0.349424 0.443389i
\(523\) −8.02894e10 −1.07313 −0.536564 0.843860i \(-0.680278\pi\)
−0.536564 + 0.843860i \(0.680278\pi\)
\(524\) 1.59320e10i 0.211322i
\(525\) 0 0
\(526\) −1.48316e10 −0.193751
\(527\) 8.85389e10i 1.14787i
\(528\) 3.17373e10 + 6.54196e10i 0.408351 + 0.841729i
\(529\) 6.98837e10 0.892387
\(530\) 0 0
\(531\) −2.87864e10 2.26859e10i −0.362084 0.285350i
\(532\) 6.76580e9 0.0844641
\(533\) 1.73488e8i 0.00214961i
\(534\) 2.02424e10 9.82029e9i 0.248942 0.120770i
\(535\) 0 0
\(536\) 2.32070e9i 0.0281164i
\(537\) 6.24334e9 + 1.28693e10i 0.0750793 + 0.154760i
\(538\) −3.52193e10 −0.420390
\(539\) 6.34064e10i 0.751239i
\(540\) 0 0
\(541\) 2.31499e10 0.270246 0.135123 0.990829i \(-0.456857\pi\)
0.135123 + 0.990829i \(0.456857\pi\)
\(542\) 3.00868e10i 0.348642i
\(543\) −7.56281e10 + 3.66897e10i −0.869929 + 0.422032i
\(544\) −6.46106e10 −0.737748
\(545\) 0 0
\(546\) 2.00629e9 + 4.13553e9i 0.0225747 + 0.0465330i
\(547\) −1.06905e11 −1.19412 −0.597061 0.802196i \(-0.703665\pi\)
−0.597061 + 0.802196i \(0.703665\pi\)
\(548\) 1.13010e11i 1.25313i
\(549\) 1.26718e9 1.60794e9i 0.0139492 0.0177003i
\(550\) 0 0
\(551\) 2.03462e10i 0.220738i
\(552\) 1.81906e10 8.82485e9i 0.195925 0.0950498i
\(553\) −4.89540e10 −0.523465
\(554\) 1.27435e10i 0.135285i
\(555\) 0 0
\(556\) −4.68199e10 −0.489927
\(557\) 3.49063e10i 0.362646i −0.983424 0.181323i \(-0.941962\pi\)
0.983424 0.181323i \(-0.0580379\pi\)
\(558\) −3.73507e10 2.94352e10i −0.385267 0.303620i
\(559\) 4.05600e10 0.415385
\(560\) 0 0
\(561\) −1.08028e11 + 5.24081e10i −1.09065 + 0.529112i
\(562\) 4.35525e10 0.436584
\(563\) 1.11294e10i 0.110775i −0.998465 0.0553873i \(-0.982361\pi\)
0.998465 0.0553873i \(-0.0176393\pi\)
\(564\) 1.55222e10 + 3.19957e10i 0.153404 + 0.316210i
\(565\) 0 0
\(566\) 4.08223e10i 0.397770i
\(567\) −1.68509e10 7.00899e10i −0.163038 0.678146i
\(568\) 8.65419e10 0.831444
\(569\) 1.10613e11i 1.05526i −0.849475 0.527629i \(-0.823081\pi\)
0.849475 0.527629i \(-0.176919\pi\)
\(570\) 0 0
\(571\) −3.15777e10 −0.297055 −0.148527 0.988908i \(-0.547453\pi\)
−0.148527 + 0.988908i \(0.547453\pi\)
\(572\) 2.86806e10i 0.267919i
\(573\) −1.56146e10 3.21862e10i −0.144848 0.298574i
\(574\) 2.75227e8 0.00253538
\(575\) 0 0
\(576\) 2.20931e10 2.80343e10i 0.200709 0.254683i
\(577\) 3.66049e10 0.330245 0.165123 0.986273i \(-0.447198\pi\)
0.165123 + 0.986273i \(0.447198\pi\)
\(578\) 1.23838e10i 0.110954i
\(579\) −1.31521e11 + 6.38053e10i −1.17026 + 0.567731i
\(580\) 0 0
\(581\) 1.12715e11i 0.989184i
\(582\) −1.43907e10 2.96634e10i −0.125427 0.258540i
\(583\) −2.63523e11 −2.28110
\(584\) 6.43867e9i 0.0553534i
\(585\) 0 0
\(586\) 2.25884e10 0.191556
\(587\) 5.45783e10i 0.459693i 0.973227 + 0.229846i \(0.0738223\pi\)
−0.973227 + 0.229846i \(0.926178\pi\)
\(588\) −4.83054e10 + 2.34346e10i −0.404098 + 0.196042i
\(589\) −2.30842e10 −0.191802
\(590\) 0 0
\(591\) −6.52152e10 1.34427e11i −0.534563 1.10189i
\(592\) 9.21248e10 0.750049
\(593\) 8.35997e10i 0.676061i −0.941135 0.338031i \(-0.890239\pi\)
0.941135 0.338031i \(-0.109761\pi\)
\(594\) −1.38058e10 + 6.29957e10i −0.110896 + 0.506017i
\(595\) 0 0
\(596\) 4.91962e10i 0.389894i
\(597\) −1.31623e11 + 6.38547e10i −1.03618 + 0.502684i
\(598\) 3.11077e9 0.0243256
\(599\) 1.39529e10i 0.108382i −0.998531 0.0541909i \(-0.982742\pi\)
0.998531 0.0541909i \(-0.0172579\pi\)
\(600\) 0 0
\(601\) 2.42138e11 1.85595 0.927974 0.372645i \(-0.121549\pi\)
0.927974 + 0.372645i \(0.121549\pi\)
\(602\) 6.43457e10i 0.489930i
\(603\) 3.46612e9 4.39820e9i 0.0262164 0.0332664i
\(604\) 7.85032e10 0.589847
\(605\) 0 0
\(606\) −4.63273e10 + 2.24749e10i −0.343515 + 0.166651i
\(607\) −1.24176e11 −0.914712 −0.457356 0.889284i \(-0.651203\pi\)
−0.457356 + 0.889284i \(0.651203\pi\)
\(608\) 1.68455e10i 0.123274i
\(609\) −6.67575e10 1.37606e11i −0.485323 1.00039i
\(610\) 0 0
\(611\) 1.17277e10i 0.0841488i
\(612\) 7.98530e10 + 6.29302e10i 0.569227 + 0.448594i
\(613\) 1.73317e11 1.22743 0.613717 0.789526i \(-0.289673\pi\)
0.613717 + 0.789526i \(0.289673\pi\)
\(614\) 5.26431e10i 0.370397i
\(615\) 0 0
\(616\) −9.75233e10 −0.677307
\(617\) 1.52659e11i 1.05337i −0.850060 0.526687i \(-0.823434\pi\)
0.850060 0.526687i \(-0.176566\pi\)
\(618\) −2.68202e10 5.52841e10i −0.183869 0.379006i
\(619\) 2.41342e11 1.64388 0.821942 0.569571i \(-0.192891\pi\)
0.821942 + 0.569571i \(0.192891\pi\)
\(620\) 0 0
\(621\) −4.76553e10 1.04439e10i −0.320439 0.0702256i
\(622\) −6.34846e10 −0.424137
\(623\) 8.20967e10i 0.544971i
\(624\) 1.82680e10 8.86243e9i 0.120491 0.0584541i
\(625\) 0 0
\(626\) 5.35506e10i 0.348712i
\(627\) 1.36640e10 + 2.81655e10i 0.0884116 + 0.182242i
\(628\) −1.58690e10 −0.102026
\(629\) 1.52127e11i 0.971858i
\(630\) 0 0
\(631\) 1.68033e11 1.05993 0.529966 0.848019i \(-0.322205\pi\)
0.529966 + 0.848019i \(0.322205\pi\)
\(632\) 7.94849e10i 0.498215i
\(633\) 2.14466e10 1.04045e10i 0.133580 0.0648044i
\(634\) 4.80682e9 0.0297510
\(635\) 0 0
\(636\) 9.73963e10 + 2.00762e11i 0.595270 + 1.22702i
\(637\) −1.77058e10 −0.107537
\(638\) 1.36828e11i 0.825832i
\(639\) −1.64015e11 1.29256e11i −0.983737 0.775260i
\(640\) 0 0
\(641\) 1.07087e11i 0.634313i 0.948373 + 0.317156i \(0.102728\pi\)
−0.948373 + 0.317156i \(0.897272\pi\)
\(642\) −1.51601e10 + 7.35467e9i −0.0892404 + 0.0432935i
\(643\) −1.21734e11 −0.712142 −0.356071 0.934459i \(-0.615884\pi\)
−0.356071 + 0.934459i \(0.615884\pi\)
\(644\) 3.44200e10i 0.200109i
\(645\) 0 0
\(646\) −7.07598e9 −0.0406309
\(647\) 1.91646e11i 1.09366i −0.837244 0.546829i \(-0.815835\pi\)
0.837244 0.546829i \(-0.184165\pi\)
\(648\) 1.13803e11 2.73602e10i 0.645434 0.155174i
\(649\) 1.19645e11 0.674397
\(650\) 0 0
\(651\) −1.56124e11 + 7.57410e10i −0.869252 + 0.421704i
\(652\) 1.63655e11 0.905604
\(653\) 1.71426e11i 0.942811i 0.881917 + 0.471406i \(0.156253\pi\)
−0.881917 + 0.471406i \(0.843747\pi\)
\(654\) −3.36543e10 6.93712e10i −0.183963 0.379200i
\(655\) 0 0
\(656\) 1.21577e9i 0.00656500i
\(657\) 9.61657e9 1.22026e10i 0.0516129 0.0654923i
\(658\) −1.86052e10 −0.0992501
\(659\) 6.16692e10i 0.326984i −0.986545 0.163492i \(-0.947724\pi\)
0.986545 0.163492i \(-0.0522758\pi\)
\(660\) 0 0
\(661\) 2.25974e10 0.118373 0.0591864 0.998247i \(-0.481149\pi\)
0.0591864 + 0.998247i \(0.481149\pi\)
\(662\) 2.67167e10i 0.139107i
\(663\) 1.46346e10 + 3.01662e10i 0.0757404 + 0.156123i
\(664\) 1.83012e11 0.941469
\(665\) 0 0
\(666\) 6.41755e10 + 5.05752e10i 0.326192 + 0.257064i
\(667\) −1.03508e11 −0.522964
\(668\) 2.30000e11i 1.15511i
\(669\) −2.58661e11 + 1.25485e11i −1.29130 + 0.626453i
\(670\) 0 0
\(671\) 6.68311e9i 0.0329677i
\(672\) 5.52715e10 + 1.13930e11i 0.271034 + 0.558679i
\(673\) 3.18816e11 1.55410 0.777051 0.629437i \(-0.216715\pi\)
0.777051 + 0.629437i \(0.216715\pi\)
\(674\) 1.95925e9i 0.00949404i
\(675\) 0 0
\(676\) −1.74632e11 −0.836250
\(677\) 3.75454e11i 1.78732i 0.448745 + 0.893660i \(0.351871\pi\)
−0.448745 + 0.893660i \(0.648129\pi\)
\(678\) 4.03974e10 1.95982e10i 0.191177 0.0927463i
\(679\) −1.20305e11 −0.565984
\(680\) 0 0
\(681\) −1.08673e11 2.24006e11i −0.505281 1.04153i
\(682\) 1.55241e11 0.717576
\(683\) 1.83700e11i 0.844162i −0.906558 0.422081i \(-0.861300\pi\)
0.906558 0.422081i \(-0.138700\pi\)
\(684\) 1.64074e10 2.08196e10i 0.0749576 0.0951146i
\(685\) 0 0
\(686\) 8.27865e10i 0.373820i
\(687\) 1.88544e11 9.14692e10i 0.846420 0.410627i
\(688\) 2.84236e11 1.26860
\(689\) 7.35871e10i 0.326531i
\(690\) 0 0
\(691\) 1.46577e11 0.642916 0.321458 0.946924i \(-0.395827\pi\)
0.321458 + 0.946924i \(0.395827\pi\)
\(692\) 2.39885e10i 0.104611i
\(693\) 1.84827e11 + 1.45657e11i 0.801367 + 0.631538i
\(694\) −1.99983e10 −0.0862095
\(695\) 0 0
\(696\) 2.23427e11 1.08392e11i 0.952134 0.461913i
\(697\) 2.00761e9 0.00850645
\(698\) 4.67440e10i 0.196926i
\(699\) 1.57857e11 + 3.25389e11i 0.661234 + 1.36299i
\(700\) 0 0
\(701\) 3.90726e11i 1.61808i −0.587753 0.809041i \(-0.699987\pi\)
0.587753 0.809041i \(-0.300013\pi\)
\(702\) 1.75911e10 + 3.85518e9i 0.0724345 + 0.0158744i
\(703\) 3.96630e10 0.162392
\(704\) 1.16519e11i 0.474358i
\(705\) 0 0
\(706\) −6.12115e10 −0.246385
\(707\) 1.87888e11i 0.752007i
\(708\) −4.42200e10 9.11500e10i −0.175989 0.362764i
\(709\) 3.36760e10 0.133271 0.0666354 0.997777i \(-0.478774\pi\)
0.0666354 + 0.997777i \(0.478774\pi\)
\(710\) 0 0
\(711\) −1.18716e11 + 1.50640e11i −0.464548 + 0.589471i
\(712\) 1.33298e11 0.518684
\(713\) 1.17437e11i 0.454410i
\(714\) −4.78566e10 + 2.32169e10i −0.184140 + 0.0893327i
\(715\) 0 0
\(716\) 3.95382e10i 0.150441i
\(717\) −8.81772e10 1.81758e11i −0.333641 0.687730i
\(718\) 1.00918e11 0.379726
\(719\) 3.34576e11i 1.25193i −0.779852 0.625964i \(-0.784706\pi\)
0.779852 0.625964i \(-0.215294\pi\)
\(720\) 0 0
\(721\) −2.24214e11 −0.829703
\(722\) 9.43814e10i 0.347326i
\(723\) −7.79305e10 + 3.78067e10i −0.285203 + 0.138362i
\(724\) −2.32351e11 −0.845649
\(725\) 0 0
\(726\) −4.89509e10 1.00902e11i −0.176203 0.363206i
\(727\) −7.75537e10 −0.277629 −0.138815 0.990318i \(-0.544329\pi\)
−0.138815 + 0.990318i \(0.544329\pi\)
\(728\) 2.72328e10i 0.0969541i
\(729\) −2.56543e11 1.18118e11i −0.908345 0.418223i
\(730\) 0 0
\(731\) 4.69363e11i 1.64376i
\(732\) 5.09144e9 2.47003e9i 0.0177336 0.00860316i
\(733\) −1.83371e10 −0.0635205 −0.0317603 0.999496i \(-0.510111\pi\)
−0.0317603 + 0.999496i \(0.510111\pi\)
\(734\) 4.10808e10i 0.141532i
\(735\) 0 0
\(736\) 8.56990e10 0.292055
\(737\) 1.82803e10i 0.0619601i
\(738\) 6.67439e8 8.46922e8i 0.00225002 0.00285508i
\(739\) 4.44324e11 1.48978 0.744890 0.667187i \(-0.232502\pi\)
0.744890 + 0.667187i \(0.232502\pi\)
\(740\) 0 0
\(741\) 7.86504e9 3.81560e9i 0.0260872 0.0126558i
\(742\) −1.16741e11 −0.385130
\(743\) 5.92783e10i 0.194509i −0.995260 0.0972547i \(-0.968994\pi\)
0.995260 0.0972547i \(-0.0310061\pi\)
\(744\) −1.22978e11 2.53493e11i −0.401362 0.827323i
\(745\) 0 0
\(746\) 7.96584e10i 0.257203i
\(747\) −3.46844e11 2.73340e11i −1.11391 0.877850i
\(748\) −3.31893e11 −1.06021
\(749\) 6.14843e10i 0.195361i
\(750\) 0 0
\(751\) −1.35059e11 −0.424585 −0.212292 0.977206i \(-0.568093\pi\)
−0.212292 + 0.977206i \(0.568093\pi\)
\(752\) 8.21853e10i 0.256994i
\(753\) 9.14950e10 + 1.88598e11i 0.284589 + 0.586619i
\(754\) 3.82083e10 0.118215
\(755\) 0 0
\(756\) 4.26567e10 1.94642e11i 0.130587 0.595866i
\(757\) 3.52798e11 1.07434 0.537171 0.843473i \(-0.319493\pi\)
0.537171 + 0.843473i \(0.319493\pi\)
\(758\) 5.33245e10i 0.161529i
\(759\) 1.43288e11 6.95138e10i 0.431760 0.209461i
\(760\) 0 0
\(761\) 4.67185e11i 1.39300i 0.717558 + 0.696499i \(0.245260\pi\)
−0.717558 + 0.696499i \(0.754740\pi\)
\(762\) −2.76033e10 5.68984e10i −0.0818732 0.168764i
\(763\) −2.81347e11 −0.830126
\(764\) 9.88853e10i 0.290241i
\(765\) 0 0
\(766\) 1.26074e11 0.366193
\(767\) 3.34101e10i 0.0965375i
\(768\) −9.91106e9 + 4.80819e9i −0.0284889 + 0.0138209i
\(769\) 1.44792e11 0.414038 0.207019 0.978337i \(-0.433624\pi\)
0.207019 + 0.978337i \(0.433624\pi\)
\(770\) 0 0
\(771\) 1.41418e11 + 2.91503e11i 0.400210 + 0.824947i
\(772\) −4.04070e11 −1.13759
\(773\) 1.13132e11i 0.316860i −0.987370 0.158430i \(-0.949357\pi\)
0.987370 0.158430i \(-0.0506433\pi\)
\(774\) 1.98003e11 + 1.56042e11i 0.551707 + 0.434788i
\(775\) 0 0
\(776\) 1.95335e11i 0.538683i
\(777\) 2.68251e11 1.30138e11i 0.735964 0.357041i
\(778\) 9.49132e10 0.259065
\(779\) 5.23432e8i 0.00142138i
\(780\) 0 0
\(781\) 6.81694e11 1.83225
\(782\) 3.59980e10i 0.0962612i
\(783\) −5.85330e11 1.28278e11i −1.55723 0.341275i
\(784\) −1.24079e11 −0.328423
\(785\) 0 0
\(786\) −2.93814e10 + 1.42539e10i −0.0769808 + 0.0373460i
\(787\) −4.10788e10 −0.107083 −0.0535413 0.998566i \(-0.517051\pi\)
−0.0535413 + 0.998566i \(0.517051\pi\)
\(788\) 4.12999e11i 1.07113i
\(789\) 9.25494e10 + 1.90771e11i 0.238817 + 0.492271i
\(790\) 0 0
\(791\) 1.63839e11i 0.418515i
\(792\) −2.36499e11 + 3.00097e11i −0.601075 + 0.762712i
\(793\) 1.86622e9 0.00471921
\(794\) 2.20077e10i 0.0553723i
\(795\) 0 0
\(796\) −4.04383e11 −1.00726
\(797\) 1.01477e11i 0.251498i 0.992062 + 0.125749i \(0.0401334\pi\)
−0.992062 + 0.125749i \(0.959867\pi\)
\(798\) 6.05319e9 + 1.24774e10i 0.0149270 + 0.0307688i
\(799\) −1.35713e11 −0.332994
\(800\) 0 0
\(801\) −2.52626e11 1.99089e11i −0.613689 0.483634i
\(802\) −1.86378e11 −0.450503
\(803\) 5.07177e10i 0.121982i
\(804\) 1.39266e10 6.75626e9i 0.0333288 0.0161690i
\(805\) 0 0
\(806\) 4.33500e10i 0.102719i
\(807\) 2.19769e11 + 4.53008e11i 0.518171 + 1.06810i
\(808\) −3.05068e11 −0.715733
\(809\) 2.81290e11i 0.656689i 0.944558 + 0.328344i \(0.106491\pi\)
−0.944558 + 0.328344i \(0.893509\pi\)
\(810\) 0 0
\(811\) 3.06605e11 0.708754 0.354377 0.935103i \(-0.384693\pi\)
0.354377 + 0.935103i \(0.384693\pi\)
\(812\) 4.22766e11i 0.972468i
\(813\) 3.86991e11 1.87742e11i 0.885806 0.429735i
\(814\) −2.66733e11 −0.607546
\(815\) 0 0
\(816\) 1.02556e11 + 2.11398e11i 0.231314 + 0.476805i
\(817\) 1.22374e11 0.274663
\(818\) 6.14716e9i 0.0137297i
\(819\) 4.06739e10 5.16116e10i 0.0904024 0.114713i
\(820\) 0 0
\(821\) 5.33533e11i 1.17433i −0.809469 0.587163i \(-0.800245\pi\)
0.809469 0.587163i \(-0.199755\pi\)
\(822\) 2.08412e11 1.01108e11i 0.456494 0.221461i
\(823\) −5.45096e11 −1.18816 −0.594078 0.804407i \(-0.702483\pi\)
−0.594078 + 0.804407i \(0.702483\pi\)
\(824\) 3.64050e11i 0.789681i
\(825\) 0 0
\(826\) 5.30028e10 0.113862
\(827\) 7.10494e11i 1.51893i −0.650547 0.759466i \(-0.725460\pi\)
0.650547 0.759466i \(-0.274540\pi\)
\(828\) −1.05916e11 8.34702e10i −0.225342 0.177587i
\(829\) −3.64341e11 −0.771419 −0.385710 0.922620i \(-0.626043\pi\)
−0.385710 + 0.922620i \(0.626043\pi\)
\(830\) 0 0
\(831\) −1.63913e11 + 7.95198e10i −0.343724 + 0.166752i
\(832\) 3.25372e10 0.0679026
\(833\) 2.04893e11i 0.425546i
\(834\) −4.18886e10 8.63444e10i −0.0865828 0.178472i
\(835\) 0 0
\(836\) 8.65325e10i 0.177155i
\(837\) −1.45540e11 + 6.64098e11i −0.296538 + 1.35310i
\(838\) −1.92187e11 −0.389715
\(839\) 3.80877e11i 0.768665i 0.923195 + 0.384333i \(0.125568\pi\)
−0.923195 + 0.384333i \(0.874432\pi\)
\(840\) 0 0
\(841\) −7.71101e11 −1.54144
\(842\) 1.63490e11i 0.325270i
\(843\) −2.71768e11 5.60192e11i −0.538132 1.10924i
\(844\) 6.58899e10 0.129852
\(845\) 0 0
\(846\) −4.51186e10 + 5.72515e10i −0.0880793 + 0.111765i
\(847\) −4.09225e11 −0.795112
\(848\) 5.15683e11i 0.997240i
\(849\) 5.25076e11 2.54732e11i 1.01063 0.490290i
\(850\) 0 0
\(851\) 2.01780e11i 0.384733i
\(852\) −2.51950e11 5.19340e11i −0.478140 0.985584i
\(853\) 8.33398e11 1.57419 0.787093 0.616834i \(-0.211585\pi\)
0.787093 + 0.616834i \(0.211585\pi\)
\(854\) 2.96062e9i 0.00556611i
\(855\) 0 0
\(856\) −9.98301e10 −0.185937
\(857\) 2.81549e11i 0.521952i 0.965345 + 0.260976i \(0.0840444\pi\)
−0.965345 + 0.260976i \(0.915956\pi\)
\(858\) −5.28922e10 + 2.56598e10i −0.0975984 + 0.0473483i
\(859\) −6.11769e11 −1.12361 −0.561804 0.827271i \(-0.689892\pi\)
−0.561804 + 0.827271i \(0.689892\pi\)
\(860\) 0 0
\(861\) −1.71742e9 3.54010e9i −0.00312510 0.00644173i
\(862\) 4.53154e9 0.00820761
\(863\) 4.91320e11i 0.885771i 0.896578 + 0.442886i \(0.146045\pi\)
−0.896578 + 0.442886i \(0.853955\pi\)
\(864\) 4.84620e11 + 1.06207e11i 0.869654 + 0.190589i
\(865\) 0 0
\(866\) 1.14688e11i 0.203914i
\(867\) 1.59286e11 7.72752e10i 0.281904 0.136761i
\(868\) −4.79657e11 −0.844991
\(869\) 6.26106e11i 1.09792i
\(870\) 0 0
\(871\) 5.10464e9 0.00886937
\(872\) 4.56814e11i 0.790084i
\(873\) −2.91746e11 + 3.70200e11i −0.502282 + 0.637352i
\(874\) 9.38553e9 0.0160847
\(875\) 0 0
\(876\) 3.86386e10 1.87449e10i 0.0656153 0.0318322i
\(877\) 2.91940e11 0.493509 0.246755 0.969078i \(-0.420636\pi\)
0.246755 + 0.969078i \(0.420636\pi\)
\(878\) 2.35790e11i 0.396778i
\(879\) −1.40952e11 2.90543e11i −0.236111 0.486693i
\(880\) 0 0
\(881\) 3.04364e11i 0.505230i 0.967567 + 0.252615i \(0.0812906\pi\)
−0.967567 + 0.252615i \(0.918709\pi\)
\(882\) −8.64353e10 6.81176e10i −0.142829 0.112560i
\(883\) −4.35514e11 −0.716407 −0.358203 0.933644i \(-0.616611\pi\)
−0.358203 + 0.933644i \(0.616611\pi\)
\(884\) 9.26791e10i 0.151765i
\(885\) 0 0
\(886\) 5.68453e10 0.0922486
\(887\) 1.80753e11i 0.292006i 0.989284 + 0.146003i \(0.0466409\pi\)
−0.989284 + 0.146003i \(0.953359\pi\)
\(888\) 2.11300e11 + 4.35550e11i 0.339819 + 0.700464i
\(889\) −2.30761e11 −0.369450
\(890\) 0 0
\(891\) 8.96428e11 2.15518e11i 1.42234 0.341957i
\(892\) −7.94681e11 −1.25526
\(893\) 3.53837e10i 0.0556414i
\(894\) 9.07267e10 4.40146e10i 0.142032 0.0689044i
\(895\) 0 0
\(896\) 4.51830e11i 0.701040i
\(897\) −1.94113e10 4.00122e10i −0.0299836 0.0618049i
\(898\) 1.46865e11 0.225846
\(899\) 1.44243e12i 2.20829i
\(900\) 0 0
\(901\) −8.51553e11 −1.29215
\(902\) 3.52007e9i 0.00531771i
\(903\) 8.27645e11 4.01519e11i 1.24478 0.603885i
\(904\) 2.66020e11 0.398327
\(905\) 0 0
\(906\) 7.02348e10 + 1.44774e11i 0.104241 + 0.214871i
\(907\) 1.24264e12 1.83618 0.918089 0.396374i \(-0.129732\pi\)
0.918089 + 0.396374i \(0.129732\pi\)
\(908\) 6.88210e11i 1.01246i
\(909\) 5.78166e11 + 4.55639e11i 0.846832 + 0.667368i
\(910\) 0 0
\(911\) 3.34146e10i 0.0485135i −0.999706 0.0242568i \(-0.992278\pi\)
0.999706 0.0242568i \(-0.00772193\pi\)
\(912\) 5.51166e10 2.67389e10i 0.0796715 0.0386513i
\(913\) 1.44159e12 2.07472
\(914\) 3.30465e11i 0.473523i
\(915\) 0 0
\(916\) 5.79261e11 0.822797
\(917\) 1.19161e11i 0.168523i
\(918\) −4.46123e10 + 2.03565e11i −0.0628180 + 0.286638i
\(919\) −1.22601e12 −1.71882 −0.859412 0.511283i \(-0.829170\pi\)
−0.859412 + 0.511283i \(0.829170\pi\)
\(920\) 0 0
\(921\) 6.77120e11 3.28494e11i 0.941081 0.456550i
\(922\) 1.54774e11 0.214178
\(923\) 1.90359e11i 0.262281i
\(924\) 2.83920e11 + 5.85240e11i 0.389500 + 0.802872i
\(925\) 0 0
\(926\) 3.12093e11i 0.424463i
\(927\) −5.43732e11 + 6.89948e11i −0.736319 + 0.934324i
\(928\) 1.05260e12 1.41930
\(929\) 1.46087e12i 1.96133i −0.195701 0.980664i \(-0.562698\pi\)
0.195701 0.980664i \(-0.437302\pi\)
\(930\) 0 0
\(931\) −5.34204e10 −0.0711064
\(932\) 9.99686e11i 1.32495i
\(933\) 3.96145e11 + 8.16568e11i 0.522790 + 1.07762i
\(934\) −2.30303e11 −0.302631
\(935\) 0 0
\(936\) 8.38001e10 + 6.60409e10i 0.109179 + 0.0860418i
\(937\) 1.02495e12 1.32968 0.664838 0.746987i \(-0.268500\pi\)
0.664838 + 0.746987i \(0.268500\pi\)
\(938\) 8.09817e9i 0.0104611i
\(939\) 6.88793e11 3.34157e11i 0.885985 0.429821i
\(940\) 0 0
\(941\) 1.83735e11i 0.234333i −0.993112 0.117166i \(-0.962619\pi\)
0.993112 0.117166i \(-0.0373811\pi\)
\(942\) −1.41976e10 2.92654e10i −0.0180307 0.0371664i
\(943\) −2.66288e9 −0.00336748
\(944\) 2.34131e11i 0.294829i
\(945\) 0 0
\(946\) −8.22962e11 −1.02758
\(947\) 2.26053e11i 0.281067i 0.990076 + 0.140533i \(0.0448817\pi\)
−0.990076 + 0.140533i \(0.955118\pi\)
\(948\) −4.76991e11 + 2.31405e11i −0.590578 + 0.286509i
\(949\) 1.41626e10 0.0174613
\(950\) 0 0
\(951\) −2.99946e10 6.18276e10i −0.0366709 0.0755893i
\(952\) −3.15139e11 −0.383667
\(953\) 1.49255e12i 1.80949i 0.425953 + 0.904745i \(0.359939\pi\)
−0.425953 + 0.904745i \(0.640061\pi\)
\(954\) −2.83103e11 + 3.59233e11i −0.341783 + 0.433693i
\(955\) 0 0
\(956\) 5.58414e11i 0.668535i
\(957\) 1.75994e12 8.53808e11i 2.09822 1.01792i
\(958\) −6.15012e10 −0.0730166
\(959\) 8.45250e11i 0.999334i
\(960\) 0 0
\(961\) 7.83650e11 0.918816
\(962\) 7.44835e10i 0.0869681i
\(963\) 1.89198e11 + 1.49103e11i 0.219995 + 0.173373i
\(964\) −2.39425e11 −0.277243
\(965\) 0 0
\(966\) 6.34766e10 3.07947e10i 0.0728963 0.0353645i
\(967\) −7.94256e11 −0.908352 −0.454176 0.890912i \(-0.650066\pi\)
−0.454176 + 0.890912i \(0.650066\pi\)
\(968\) 6.64445e11i 0.756759i
\(969\) 4.41543e10 + 9.10146e10i 0.0500815 + 0.103232i
\(970\) 0 0
\(971\) 7.55855e10i 0.0850279i 0.999096 + 0.0425139i \(0.0135367\pi\)
−0.999096 + 0.0425139i \(0.986463\pi\)
\(972\) −4.95503e11 6.03279e11i −0.555113 0.675854i
\(973\) −3.50185e11 −0.390702
\(974\) 1.00847e11i 0.112054i
\(975\) 0 0
\(976\) 1.30780e10 0.0144126
\(977\) 1.31247e11i 0.144049i 0.997403 + 0.0720244i \(0.0229460\pi\)
−0.997403 + 0.0720244i \(0.977054\pi\)
\(978\) 1.46418e11 + 3.01809e11i 0.160044 + 0.329896i
\(979\) 1.04999e12 1.14302
\(980\) 0 0
\(981\) −6.82281e11 + 8.65755e11i −0.736694 + 0.934801i
\(982\) 4.49650e11 0.483536
\(983\) 2.55150e11i 0.273264i −0.990622 0.136632i \(-0.956372\pi\)
0.990622 0.136632i \(-0.0436277\pi\)
\(984\) 5.74794e9 2.78852e9i 0.00613100 0.00297436i
\(985\) 0 0
\(986\) 4.42148e11i 0.467800i
\(987\) 1.16097e11 + 2.39309e11i 0.122335 + 0.252168i
\(988\) 2.41636e10 0.0253591
\(989\) 6.22559e11i 0.650722i
\(990\) 0 0
\(991\) −1.00441e12 −1.04139 −0.520697 0.853742i \(-0.674328\pi\)
−0.520697 + 0.853742i \(0.674328\pi\)
\(992\) 1.19425e12i 1.23325i
\(993\) 3.43642e11 1.66713e11i 0.353435 0.171463i
\(994\) 3.01991e11 0.309349
\(995\) 0 0
\(996\) −5.32802e11 1.09826e12i −0.541413 1.11601i
\(997\) −1.22258e12 −1.23737 −0.618683 0.785641i \(-0.712333\pi\)
−0.618683 + 0.785641i \(0.712333\pi\)
\(998\) 3.70566e11i 0.373545i
\(999\) 2.50066e11 1.14105e12i 0.251068 1.14562i
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 75.9.c.h.26.8 12
3.2 odd 2 inner 75.9.c.h.26.6 12
5.2 odd 4 15.9.d.c.14.5 12
5.3 odd 4 15.9.d.c.14.8 yes 12
5.4 even 2 inner 75.9.c.h.26.5 12
15.2 even 4 15.9.d.c.14.7 yes 12
15.8 even 4 15.9.d.c.14.6 yes 12
15.14 odd 2 inner 75.9.c.h.26.7 12
20.3 even 4 240.9.c.c.209.3 12
20.7 even 4 240.9.c.c.209.10 12
60.23 odd 4 240.9.c.c.209.9 12
60.47 odd 4 240.9.c.c.209.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.9.d.c.14.5 12 5.2 odd 4
15.9.d.c.14.6 yes 12 15.8 even 4
15.9.d.c.14.7 yes 12 15.2 even 4
15.9.d.c.14.8 yes 12 5.3 odd 4
75.9.c.h.26.5 12 5.4 even 2 inner
75.9.c.h.26.6 12 3.2 odd 2 inner
75.9.c.h.26.7 12 15.14 odd 2 inner
75.9.c.h.26.8 12 1.1 even 1 trivial
240.9.c.c.209.3 12 20.3 even 4
240.9.c.c.209.4 12 60.47 odd 4
240.9.c.c.209.9 12 60.23 odd 4
240.9.c.c.209.10 12 20.7 even 4