Properties

Label 14.7.b.a.13.2
Level $14$
Weight $7$
Character 14.13
Analytic conductor $3.221$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [14,7,Mod(13,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.13");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 14.b (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: \(3.22075717068\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.211968.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 30x^{2} + 207 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 13.2
Root \(3.27984i\) of defining polynomial
Character \(\chi\) \(=\) 14.13
Dual form 14.7.b.a.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.65685 q^{2} +3.84257i q^{3} +32.0000 q^{4} -204.749i q^{5} -21.7369i q^{6} +(-41.7939 - 340.444i) q^{7} -181.019 q^{8} +714.235 q^{9} +O(q^{10})\) \(q-5.65685 q^{2} +3.84257i q^{3} +32.0000 q^{4} -204.749i q^{5} -21.7369i q^{6} +(-41.7939 - 340.444i) q^{7} -181.019 q^{8} +714.235 q^{9} +1158.23i q^{10} -1177.88 q^{11} +122.962i q^{12} +1399.64i q^{13} +(236.422 + 1925.84i) q^{14} +786.762 q^{15} +1024.00 q^{16} -6063.65i q^{17} -4040.32 q^{18} +3134.94i q^{19} -6551.96i q^{20} +(1308.18 - 160.596i) q^{21} +6663.11 q^{22} +8652.59 q^{23} -695.580i q^{24} -26297.0 q^{25} -7917.54i q^{26} +5545.73i q^{27} +(-1337.41 - 10894.2i) q^{28} +32565.6 q^{29} -4450.60 q^{30} +42298.3i q^{31} -5792.62 q^{32} -4526.10i q^{33} +34301.2i q^{34} +(-69705.5 + 8557.26i) q^{35} +22855.5 q^{36} +37578.8 q^{37} -17733.9i q^{38} -5378.21 q^{39} +37063.5i q^{40} -93520.9i q^{41} +(-7400.19 + 908.470i) q^{42} +92007.0 q^{43} -37692.2 q^{44} -146239. i q^{45} -48946.4 q^{46} -24952.4i q^{47} +3934.79i q^{48} +(-114156. + 28457.0i) q^{49} +148758. q^{50} +23300.0 q^{51} +44788.4i q^{52} +109.623 q^{53} -31371.4i q^{54} +241170. i q^{55} +(7565.51 + 61627.0i) q^{56} -12046.2 q^{57} -184219. q^{58} +326590. i q^{59} +25176.4 q^{60} +84599.8i q^{61} -239276. i q^{62} +(-29850.7 - 243157. i) q^{63} +32768.0 q^{64} +286574. q^{65} +25603.5i q^{66} -111002. q^{67} -194037. i q^{68} +33248.2i q^{69} +(394314. - 48407.1i) q^{70} -441825. q^{71} -129290. q^{72} -464201. i q^{73} -212578. q^{74} -101048. i q^{75} +100318. i q^{76} +(49228.3 + 401003. i) q^{77} +30423.7 q^{78} +595011. q^{79} -209663. i q^{80} +499367. q^{81} +529034. i q^{82} -654116. i q^{83} +(41861.8 - 5139.08i) q^{84} -1.24152e6 q^{85} -520470. q^{86} +125136. i q^{87} +213219. q^{88} +298317. i q^{89} +827251. i q^{90} +(476498. - 58496.3i) q^{91} +276883. q^{92} -162534. q^{93} +141152. i q^{94} +641874. q^{95} -22258.6i q^{96} +169894. i q^{97} +(645761. - 160977. i) q^{98} -841284. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 128 q^{4} + 308 q^{7} + 1092 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 128 q^{4} + 308 q^{7} + 1092 q^{9} - 4440 q^{11} + 2688 q^{14} - 4320 q^{15} + 4096 q^{16} - 9984 q^{18} + 19488 q^{21} + 1536 q^{22} + 40584 q^{23} - 40700 q^{25} + 9856 q^{28} - 18264 q^{29} - 42240 q^{30} - 84000 q^{35} + 34944 q^{36} - 23192 q^{37} + 208608 q^{39} + 80640 q^{42} - 44696 q^{43} - 142080 q^{44} + 33792 q^{46} - 310268 q^{49} + 364800 q^{50} + 157824 q^{51} + 248616 q^{53} + 86016 q^{56} - 472992 q^{57} - 840192 q^{58} - 138240 q^{60} - 125580 q^{63} + 131072 q^{64} + 1293600 q^{65} - 434776 q^{67} + 1102080 q^{70} - 451608 q^{71} - 319488 q^{72} - 981504 q^{74} - 309624 q^{77} + 1301760 q^{78} + 2092904 q^{79} - 252828 q^{81} + 623616 q^{84} - 2117760 q^{85} - 2334720 q^{86} + 49152 q^{88} - 1109472 q^{91} + 1298688 q^{92} + 995328 q^{93} - 190560 q^{95} + 827904 q^{98} - 1331928 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.65685 −0.707107
\(3\) 3.84257i 0.142318i 0.997465 + 0.0711588i \(0.0226697\pi\)
−0.997465 + 0.0711588i \(0.977330\pi\)
\(4\) 32.0000 0.500000
\(5\) 204.749i 1.63799i −0.573801 0.818995i \(-0.694532\pi\)
0.573801 0.818995i \(-0.305468\pi\)
\(6\) 21.7369i 0.100634i
\(7\) −41.7939 340.444i −0.121848 0.992549i
\(8\) −181.019 −0.353553
\(9\) 714.235 0.979746
\(10\) 1158.23i 1.15823i
\(11\) −1177.88 −0.884960 −0.442480 0.896778i \(-0.645901\pi\)
−0.442480 + 0.896778i \(0.645901\pi\)
\(12\) 122.962i 0.0711588i
\(13\) 1399.64i 0.637067i 0.947912 + 0.318534i \(0.103190\pi\)
−0.947912 + 0.318534i \(0.896810\pi\)
\(14\) 236.422 + 1925.84i 0.0861597 + 0.701838i
\(15\) 786.762 0.233115
\(16\) 1024.00 0.250000
\(17\) 6063.65i 1.23421i −0.786883 0.617103i \(-0.788306\pi\)
0.786883 0.617103i \(-0.211694\pi\)
\(18\) −4040.32 −0.692785
\(19\) 3134.94i 0.457054i 0.973538 + 0.228527i \(0.0733910\pi\)
−0.973538 + 0.228527i \(0.926609\pi\)
\(20\) 6551.96i 0.818995i
\(21\) 1308.18 160.596i 0.141257 0.0173411i
\(22\) 6663.11 0.625761
\(23\) 8652.59 0.711152 0.355576 0.934647i \(-0.384285\pi\)
0.355576 + 0.934647i \(0.384285\pi\)
\(24\) 695.580i 0.0503168i
\(25\) −26297.0 −1.68301
\(26\) 7917.54i 0.450475i
\(27\) 5545.73i 0.281753i
\(28\) −1337.41 10894.2i −0.0609241 0.496274i
\(29\) 32565.6 1.33526 0.667629 0.744494i \(-0.267309\pi\)
0.667629 + 0.744494i \(0.267309\pi\)
\(30\) −4450.60 −0.164837
\(31\) 42298.3i 1.41984i 0.704284 + 0.709918i \(0.251268\pi\)
−0.704284 + 0.709918i \(0.748732\pi\)
\(32\) −5792.62 −0.176777
\(33\) 4526.10i 0.125945i
\(34\) 34301.2i 0.872715i
\(35\) −69705.5 + 8557.26i −1.62578 + 0.199586i
\(36\) 22855.5 0.489873
\(37\) 37578.8 0.741886 0.370943 0.928656i \(-0.379034\pi\)
0.370943 + 0.928656i \(0.379034\pi\)
\(38\) 17733.9i 0.323186i
\(39\) −5378.21 −0.0906659
\(40\) 37063.5i 0.579117i
\(41\) 93520.9i 1.35693i −0.734634 0.678464i \(-0.762646\pi\)
0.734634 0.678464i \(-0.237354\pi\)
\(42\) −7400.19 + 908.470i −0.0998838 + 0.0122620i
\(43\) 92007.0 1.15722 0.578610 0.815605i \(-0.303596\pi\)
0.578610 + 0.815605i \(0.303596\pi\)
\(44\) −37692.2 −0.442480
\(45\) 146239.i 1.60481i
\(46\) −48946.4 −0.502861
\(47\) 24952.4i 0.240336i −0.992754 0.120168i \(-0.961657\pi\)
0.992754 0.120168i \(-0.0383433\pi\)
\(48\) 3934.79i 0.0355794i
\(49\) −114156. + 28457.0i −0.970306 + 0.241881i
\(50\) 148758. 1.19007
\(51\) 23300.0 0.175649
\(52\) 44788.4i 0.318534i
\(53\) 109.623 0.000736330 0.000368165 1.00000i \(-0.499883\pi\)
0.000368165 1.00000i \(0.499883\pi\)
\(54\) 31371.4i 0.199229i
\(55\) 241170.i 1.44956i
\(56\) 7565.51 + 61627.0i 0.0430799 + 0.350919i
\(57\) −12046.2 −0.0650468
\(58\) −184219. −0.944170
\(59\) 326590.i 1.59018i 0.606491 + 0.795091i \(0.292577\pi\)
−0.606491 + 0.795091i \(0.707423\pi\)
\(60\) 25176.4 0.116557
\(61\) 84599.8i 0.372717i 0.982482 + 0.186359i \(0.0596687\pi\)
−0.982482 + 0.186359i \(0.940331\pi\)
\(62\) 239276.i 1.00398i
\(63\) −29850.7 243157.i −0.119380 0.972445i
\(64\) 32768.0 0.125000
\(65\) 286574. 1.04351
\(66\) 25603.5i 0.0890568i
\(67\) −111002. −0.369068 −0.184534 0.982826i \(-0.559078\pi\)
−0.184534 + 0.982826i \(0.559078\pi\)
\(68\) 194037.i 0.617103i
\(69\) 33248.2i 0.101209i
\(70\) 394314. 48407.1i 1.14960 0.141129i
\(71\) −441825. −1.23446 −0.617228 0.786784i \(-0.711744\pi\)
−0.617228 + 0.786784i \(0.711744\pi\)
\(72\) −129290. −0.346392
\(73\) 464201.i 1.19327i −0.802514 0.596633i \(-0.796505\pi\)
0.802514 0.596633i \(-0.203495\pi\)
\(74\) −212578. −0.524593
\(75\) 101048.i 0.239522i
\(76\) 100318.i 0.228527i
\(77\) 49228.3 + 401003.i 0.107831 + 0.878366i
\(78\) 30423.7 0.0641104
\(79\) 595011. 1.20682 0.603412 0.797429i \(-0.293807\pi\)
0.603412 + 0.797429i \(0.293807\pi\)
\(80\) 209663.i 0.409497i
\(81\) 499367. 0.939647
\(82\) 529034.i 0.959493i
\(83\) 654116.i 1.14398i −0.820259 0.571992i \(-0.806171\pi\)
0.820259 0.571992i \(-0.193829\pi\)
\(84\) 41861.8 5139.08i 0.0706285 0.00867057i
\(85\) −1.24152e6 −2.02162
\(86\) −520470. −0.818277
\(87\) 125136.i 0.190031i
\(88\) 213219. 0.312881
\(89\) 298317.i 0.423164i 0.977360 + 0.211582i \(0.0678615\pi\)
−0.977360 + 0.211582i \(0.932139\pi\)
\(90\) 827251.i 1.13477i
\(91\) 476498. 58496.3i 0.632320 0.0776255i
\(92\) 276883. 0.355576
\(93\) −162534. −0.202068
\(94\) 141152.i 0.169943i
\(95\) 641874. 0.748650
\(96\) 22258.6i 0.0251584i
\(97\) 169894.i 0.186150i 0.995659 + 0.0930752i \(0.0296697\pi\)
−0.995659 + 0.0930752i \(0.970330\pi\)
\(98\) 645761. 160977.i 0.686110 0.171035i
\(99\) −841284. −0.867036
\(100\) −841505. −0.841505
\(101\) 1.11818e6i 1.08530i 0.839960 + 0.542648i \(0.182578\pi\)
−0.839960 + 0.542648i \(0.817422\pi\)
\(102\) −131805. −0.124203
\(103\) 1.20424e6i 1.10205i −0.834489 0.551025i \(-0.814237\pi\)
0.834489 0.551025i \(-0.185763\pi\)
\(104\) 253361.i 0.225237i
\(105\) −32881.9 267849.i −0.0284046 0.231378i
\(106\) −620.119 −0.000520664
\(107\) −122039. −0.0996204 −0.0498102 0.998759i \(-0.515862\pi\)
−0.0498102 + 0.998759i \(0.515862\pi\)
\(108\) 177464.i 0.140876i
\(109\) 1.10612e6 0.854127 0.427063 0.904222i \(-0.359548\pi\)
0.427063 + 0.904222i \(0.359548\pi\)
\(110\) 1.36426e6i 1.02499i
\(111\) 144399.i 0.105583i
\(112\) −42797.0 348615.i −0.0304621 0.248137i
\(113\) 266739. 0.184864 0.0924318 0.995719i \(-0.470536\pi\)
0.0924318 + 0.995719i \(0.470536\pi\)
\(114\) 68143.7 0.0459951
\(115\) 1.77161e6i 1.16486i
\(116\) 1.04210e6 0.667629
\(117\) 999669.i 0.624164i
\(118\) 1.84747e6i 1.12443i
\(119\) −2.06434e6 + 253424.i −1.22501 + 0.150386i
\(120\) −142419. −0.0824185
\(121\) −384154. −0.216845
\(122\) 478569.i 0.263551i
\(123\) 359361. 0.193115
\(124\) 1.35355e6i 0.709918i
\(125\) 2.18509e6i 1.11876i
\(126\) 168861. + 1.37550e6i 0.0844146 + 0.687623i
\(127\) 1.34435e6 0.656297 0.328149 0.944626i \(-0.393575\pi\)
0.328149 + 0.944626i \(0.393575\pi\)
\(128\) −185364. −0.0883883
\(129\) 353544.i 0.164693i
\(130\) −1.62111e6 −0.737873
\(131\) 3.66483e6i 1.63019i 0.579324 + 0.815097i \(0.303316\pi\)
−0.579324 + 0.815097i \(0.696684\pi\)
\(132\) 144835.i 0.0629727i
\(133\) 1.06727e6 131021.i 0.453649 0.0556913i
\(134\) 627922. 0.260970
\(135\) 1.13548e6 0.461508
\(136\) 1.09764e6i 0.436358i
\(137\) −3.33009e6 −1.29507 −0.647537 0.762034i \(-0.724201\pi\)
−0.647537 + 0.762034i \(0.724201\pi\)
\(138\) 188080.i 0.0715659i
\(139\) 1.18963e6i 0.442962i −0.975165 0.221481i \(-0.928911\pi\)
0.975165 0.221481i \(-0.0710890\pi\)
\(140\) −2.23058e6 + 273832.i −0.812892 + 0.0997931i
\(141\) 95881.3 0.0342040
\(142\) 2.49934e6 0.872892
\(143\) 1.64861e6i 0.563779i
\(144\) 731376. 0.244936
\(145\) 6.66776e6i 2.18714i
\(146\) 2.62592e6i 0.843766i
\(147\) −109348. 438651.i −0.0344238 0.138092i
\(148\) 1.20252e6 0.370943
\(149\) 1.62144e6 0.490166 0.245083 0.969502i \(-0.421185\pi\)
0.245083 + 0.969502i \(0.421185\pi\)
\(150\) 571615.i 0.169368i
\(151\) −4.35030e6 −1.26354 −0.631770 0.775156i \(-0.717671\pi\)
−0.631770 + 0.775156i \(0.717671\pi\)
\(152\) 567484.i 0.161593i
\(153\) 4.33087e6i 1.20921i
\(154\) −278478. 2.26842e6i −0.0762479 0.621099i
\(155\) 8.66053e6 2.32568
\(156\) −172103. −0.0453329
\(157\) 4.64090e6i 1.19923i 0.800288 + 0.599616i \(0.204680\pi\)
−0.800288 + 0.599616i \(0.795320\pi\)
\(158\) −3.36589e6 −0.853354
\(159\) 421.233i 0.000104793i
\(160\) 1.18603e6i 0.289558i
\(161\) −361626. 2.94572e6i −0.0866526 0.705853i
\(162\) −2.82485e6 −0.664431
\(163\) −5.26597e6 −1.21595 −0.607975 0.793956i \(-0.708018\pi\)
−0.607975 + 0.793956i \(0.708018\pi\)
\(164\) 2.99267e6i 0.678464i
\(165\) −926713. −0.206297
\(166\) 3.70024e6i 0.808920i
\(167\) 1.99529e6i 0.428406i 0.976789 + 0.214203i \(0.0687154\pi\)
−0.976789 + 0.214203i \(0.931285\pi\)
\(168\) −236806. + 29071.0i −0.0499419 + 0.00613102i
\(169\) 2.86783e6 0.594145
\(170\) 7.02312e6 1.42950
\(171\) 2.23908e6i 0.447797i
\(172\) 2.94422e6 0.578610
\(173\) 1.97345e6i 0.381142i 0.981673 + 0.190571i \(0.0610340\pi\)
−0.981673 + 0.190571i \(0.938966\pi\)
\(174\) 707874.i 0.134372i
\(175\) 1.09906e6 + 8.95267e6i 0.205072 + 1.67047i
\(176\) −1.20615e6 −0.221240
\(177\) −1.25495e6 −0.226311
\(178\) 1.68754e6i 0.299222i
\(179\) −6.59325e6 −1.14958 −0.574791 0.818300i \(-0.694917\pi\)
−0.574791 + 0.818300i \(0.694917\pi\)
\(180\) 4.67964e6i 0.802407i
\(181\) 2.60968e6i 0.440100i 0.975489 + 0.220050i \(0.0706220\pi\)
−0.975489 + 0.220050i \(0.929378\pi\)
\(182\) −2.69548e6 + 330905.i −0.447118 + 0.0548895i
\(183\) −325081. −0.0530442
\(184\) −1.56629e6 −0.251430
\(185\) 7.69420e6i 1.21520i
\(186\) 919434. 0.142883
\(187\) 7.14227e6i 1.09222i
\(188\) 798475.i 0.120168i
\(189\) 1.88801e6 231778.i 0.279653 0.0343310i
\(190\) −3.63099e6 −0.529376
\(191\) 1.99290e6 0.286012 0.143006 0.989722i \(-0.454323\pi\)
0.143006 + 0.989722i \(0.454323\pi\)
\(192\) 125913.i 0.0177897i
\(193\) 1.24013e7 1.72503 0.862513 0.506036i \(-0.168890\pi\)
0.862513 + 0.506036i \(0.168890\pi\)
\(194\) 961068.i 0.131628i
\(195\) 1.10118e6i 0.148510i
\(196\) −3.65298e6 + 910624.i −0.485153 + 0.120940i
\(197\) −5.13349e6 −0.671450 −0.335725 0.941960i \(-0.608981\pi\)
−0.335725 + 0.941960i \(0.608981\pi\)
\(198\) 4.75902e6 0.613087
\(199\) 615146.i 0.0780582i 0.999238 + 0.0390291i \(0.0124265\pi\)
−0.999238 + 0.0390291i \(0.987573\pi\)
\(200\) 4.76027e6 0.595034
\(201\) 426533.i 0.0525248i
\(202\) 6.32539e6i 0.767420i
\(203\) −1.36104e6 1.10868e7i −0.162699 1.32531i
\(204\) 745601. 0.0878245
\(205\) −1.91483e7 −2.22263
\(206\) 6.81221e6i 0.779267i
\(207\) 6.17998e6 0.696748
\(208\) 1.43323e6i 0.159267i
\(209\) 3.69258e6i 0.404475i
\(210\) 186008. + 1.51518e6i 0.0200851 + 0.163609i
\(211\) 2.56281e6 0.272815 0.136408 0.990653i \(-0.456444\pi\)
0.136408 + 0.990653i \(0.456444\pi\)
\(212\) 3507.92 0.000368165
\(213\) 1.69775e6i 0.175685i
\(214\) 690358. 0.0704422
\(215\) 1.88383e7i 1.89551i
\(216\) 1.00389e6i 0.0996146i
\(217\) 1.44002e7 1.76781e6i 1.40926 0.173004i
\(218\) −6.25716e6 −0.603959
\(219\) 1.78373e6 0.169823
\(220\) 7.71744e6i 0.724778i
\(221\) 8.48691e6 0.786272
\(222\) 816845.i 0.0746587i
\(223\) 7.82377e6i 0.705507i 0.935716 + 0.352753i \(0.114755\pi\)
−0.935716 + 0.352753i \(0.885245\pi\)
\(224\) 242096. + 1.97206e6i 0.0215399 + 0.175459i
\(225\) −1.87823e7 −1.64892
\(226\) −1.50890e6 −0.130718
\(227\) 8.19085e6i 0.700247i 0.936704 + 0.350124i \(0.113860\pi\)
−0.936704 + 0.350124i \(0.886140\pi\)
\(228\) −385479. −0.0325234
\(229\) 1.30526e7i 1.08690i 0.839442 + 0.543449i \(0.182882\pi\)
−0.839442 + 0.543449i \(0.817118\pi\)
\(230\) 1.00217e7i 0.823681i
\(231\) −1.54088e6 + 189163.i −0.125007 + 0.0153462i
\(232\) −5.89500e6 −0.472085
\(233\) 1.38499e6 0.109491 0.0547456 0.998500i \(-0.482565\pi\)
0.0547456 + 0.998500i \(0.482565\pi\)
\(234\) 5.65498e6i 0.441351i
\(235\) −5.10896e6 −0.393667
\(236\) 1.04509e7i 0.795091i
\(237\) 2.28638e6i 0.171752i
\(238\) 1.16776e7 1.43358e6i 0.866212 0.106339i
\(239\) 4.37563e6 0.320514 0.160257 0.987075i \(-0.448768\pi\)
0.160257 + 0.987075i \(0.448768\pi\)
\(240\) 805644. 0.0582787
\(241\) 8.69878e6i 0.621451i −0.950500 0.310726i \(-0.899428\pi\)
0.950500 0.310726i \(-0.100572\pi\)
\(242\) 2.17311e6 0.153333
\(243\) 5.96170e6i 0.415481i
\(244\) 2.70719e6i 0.186359i
\(245\) 5.82654e6 + 2.33732e7i 0.396198 + 1.58935i
\(246\) −2.03285e6 −0.136553
\(247\) −4.38777e6 −0.291174
\(248\) 7.65682e6i 0.501988i
\(249\) 2.51349e6 0.162809
\(250\) 1.23607e7i 0.791085i
\(251\) 2.65980e7i 1.68201i −0.541031 0.841003i \(-0.681966\pi\)
0.541031 0.841003i \(-0.318034\pi\)
\(252\) −955222. 7.78103e6i −0.0596901 0.486223i
\(253\) −1.01917e7 −0.629342
\(254\) −7.60478e6 −0.464072
\(255\) 4.77065e6i 0.287711i
\(256\) 1.04858e6 0.0625000
\(257\) 7.54668e6i 0.444587i 0.974980 + 0.222293i \(0.0713543\pi\)
−0.974980 + 0.222293i \(0.928646\pi\)
\(258\) 1.99995e6i 0.116455i
\(259\) −1.57056e6 1.27935e7i −0.0903975 0.736358i
\(260\) 9.17036e6 0.521755
\(261\) 2.32595e7 1.30821
\(262\) 2.07314e7i 1.15272i
\(263\) −1.31684e7 −0.723880 −0.361940 0.932201i \(-0.617885\pi\)
−0.361940 + 0.932201i \(0.617885\pi\)
\(264\) 819311.i 0.0445284i
\(265\) 22445.1i 0.00120610i
\(266\) −6.03739e6 + 741168.i −0.320778 + 0.0393797i
\(267\) −1.14631e6 −0.0602236
\(268\) −3.55206e6 −0.184534
\(269\) 1.82863e7i 0.939439i 0.882816 + 0.469719i \(0.155645\pi\)
−0.882816 + 0.469719i \(0.844355\pi\)
\(270\) −6.42326e6 −0.326335
\(271\) 2.78109e7i 1.39736i −0.715435 0.698679i \(-0.753771\pi\)
0.715435 0.698679i \(-0.246229\pi\)
\(272\) 6.20918e6i 0.308551i
\(273\) 224776. + 1.83098e6i 0.0110475 + 0.0899903i
\(274\) 1.88379e7 0.915756
\(275\) 3.09748e7 1.48940
\(276\) 1.06394e6i 0.0506047i
\(277\) −5.25419e6 −0.247210 −0.123605 0.992331i \(-0.539446\pi\)
−0.123605 + 0.992331i \(0.539446\pi\)
\(278\) 6.72954e6i 0.313221i
\(279\) 3.02109e7i 1.39108i
\(280\) 1.26180e7 1.54903e6i 0.574802 0.0705644i
\(281\) −3.12195e7 −1.40704 −0.703522 0.710674i \(-0.748390\pi\)
−0.703522 + 0.710674i \(0.748390\pi\)
\(282\) −542386. −0.0241859
\(283\) 1.81450e7i 0.800569i 0.916391 + 0.400284i \(0.131089\pi\)
−0.916391 + 0.400284i \(0.868911\pi\)
\(284\) −1.41384e7 −0.617228
\(285\) 2.46645e6i 0.106546i
\(286\) 9.32593e6i 0.398652i
\(287\) −3.18386e7 + 3.90860e6i −1.34682 + 0.165339i
\(288\) −4.13729e6 −0.173196
\(289\) −1.26303e7 −0.523263
\(290\) 3.77186e7i 1.54654i
\(291\) −652832. −0.0264925
\(292\) 1.48544e7i 0.596633i
\(293\) 5.83393e6i 0.231931i 0.993253 + 0.115965i \(0.0369962\pi\)
−0.993253 + 0.115965i \(0.963004\pi\)
\(294\) 618567. + 2.48138e6i 0.0243413 + 0.0976455i
\(295\) 6.68689e7 2.60470
\(296\) −6.80248e6 −0.262296
\(297\) 6.53222e6i 0.249340i
\(298\) −9.17227e6 −0.346599
\(299\) 1.21105e7i 0.453052i
\(300\) 3.23354e6i 0.119761i
\(301\) −3.84534e6 3.13233e7i −0.141005 1.14860i
\(302\) 2.46090e7 0.893457
\(303\) −4.29669e6 −0.154457
\(304\) 3.21017e6i 0.114264i
\(305\) 1.73217e7 0.610507
\(306\) 2.44991e7i 0.855039i
\(307\) 2.26871e7i 0.784087i −0.919947 0.392043i \(-0.871768\pi\)
0.919947 0.392043i \(-0.128232\pi\)
\(308\) 1.57531e6 + 1.28321e7i 0.0539154 + 0.439183i
\(309\) 4.62738e6 0.156841
\(310\) −4.89914e7 −1.64450
\(311\) 3.96340e7i 1.31761i −0.752314 0.658805i \(-0.771062\pi\)
0.752314 0.658805i \(-0.228938\pi\)
\(312\) 973560. 0.0320552
\(313\) 1.00856e7i 0.328905i 0.986385 + 0.164452i \(0.0525857\pi\)
−0.986385 + 0.164452i \(0.947414\pi\)
\(314\) 2.62529e7i 0.847986i
\(315\) −4.97861e7 + 6.11189e6i −1.59286 + 0.195544i
\(316\) 1.90404e7 0.603412
\(317\) 2.98372e7 0.936657 0.468329 0.883554i \(-0.344856\pi\)
0.468329 + 0.883554i \(0.344856\pi\)
\(318\) 2382.85i 7.40996e-5i
\(319\) −3.83584e7 −1.18165
\(320\) 6.70921e6i 0.204749i
\(321\) 468945.i 0.0141777i
\(322\) 2.04566e6 + 1.66635e7i 0.0612727 + 0.499114i
\(323\) 1.90092e7 0.564099
\(324\) 1.59797e7 0.469824
\(325\) 3.68063e7i 1.07219i
\(326\) 2.97888e7 0.859807
\(327\) 4.25034e6i 0.121557i
\(328\) 1.69291e7i 0.479747i
\(329\) −8.49489e6 + 1.04286e6i −0.238545 + 0.0292845i
\(330\) 5.24228e6 0.145874
\(331\) 1.79016e6 0.0493637 0.0246819 0.999695i \(-0.492143\pi\)
0.0246819 + 0.999695i \(0.492143\pi\)
\(332\) 2.09317e7i 0.571992i
\(333\) 2.68401e7 0.726860
\(334\) 1.12870e7i 0.302929i
\(335\) 2.27275e7i 0.604530i
\(336\) 1.33958e6 164451.i 0.0353143 0.00433528i
\(337\) −1.30113e6 −0.0339964 −0.0169982 0.999856i \(-0.505411\pi\)
−0.0169982 + 0.999856i \(0.505411\pi\)
\(338\) −1.62229e7 −0.420124
\(339\) 1.02496e6i 0.0263093i
\(340\) −3.97288e7 −1.01081
\(341\) 4.98225e7i 1.25650i
\(342\) 1.26661e7i 0.316640i
\(343\) 1.44590e7 + 3.76743e7i 0.358308 + 0.933603i
\(344\) −1.66550e7 −0.409139
\(345\) 6.80753e6 0.165780
\(346\) 1.11635e7i 0.269508i
\(347\) −2.67141e7 −0.639370 −0.319685 0.947524i \(-0.603577\pi\)
−0.319685 + 0.947524i \(0.603577\pi\)
\(348\) 4.00434e6i 0.0950153i
\(349\) 2.39729e7i 0.563956i −0.959421 0.281978i \(-0.909010\pi\)
0.959421 0.281978i \(-0.0909904\pi\)
\(350\) −6.21720e6 5.06440e7i −0.145008 1.18120i
\(351\) −7.76202e6 −0.179495
\(352\) 6.82302e6 0.156440
\(353\) 7.99792e7i 1.81825i 0.416528 + 0.909123i \(0.363247\pi\)
−0.416528 + 0.909123i \(0.636753\pi\)
\(354\) 7.09904e6 0.160026
\(355\) 9.04632e7i 2.02203i
\(356\) 9.54615e6i 0.211582i
\(357\) −973800. 7.93236e6i −0.0214025 0.174340i
\(358\) 3.72970e7 0.812878
\(359\) 4.51314e7 0.975429 0.487714 0.873003i \(-0.337831\pi\)
0.487714 + 0.873003i \(0.337831\pi\)
\(360\) 2.64720e7i 0.567387i
\(361\) 3.72181e7 0.791101
\(362\) 1.47626e7i 0.311197i
\(363\) 1.47614e6i 0.0308609i
\(364\) 1.52479e7 1.87188e6i 0.316160 0.0388128i
\(365\) −9.50445e7 −1.95456
\(366\) 1.83893e6 0.0375079
\(367\) 6.07183e7i 1.22835i 0.789171 + 0.614174i \(0.210511\pi\)
−0.789171 + 0.614174i \(0.789489\pi\)
\(368\) 8.86025e6 0.177788
\(369\) 6.67958e7i 1.32944i
\(370\) 4.35250e7i 0.859277i
\(371\) −4581.56 37320.4i −8.97205e−5 0.000730843i
\(372\) −5.20110e6 −0.101034
\(373\) −9.31710e7 −1.79537 −0.897685 0.440637i \(-0.854753\pi\)
−0.897685 + 0.440637i \(0.854753\pi\)
\(374\) 4.04028e7i 0.772318i
\(375\) −8.39635e6 −0.159220
\(376\) 4.51686e6i 0.0849714i
\(377\) 4.55800e7i 0.850649i
\(378\) −1.06802e7 + 1.31113e6i −0.197745 + 0.0242757i
\(379\) 2.78773e7 0.512075 0.256037 0.966667i \(-0.417583\pi\)
0.256037 + 0.966667i \(0.417583\pi\)
\(380\) 2.05400e7 0.374325
\(381\) 5.16575e6i 0.0934026i
\(382\) −1.12735e7 −0.202241
\(383\) 2.63822e6i 0.0469586i 0.999724 + 0.0234793i \(0.00747438\pi\)
−0.999724 + 0.0234793i \(0.992526\pi\)
\(384\) 712274.i 0.0125792i
\(385\) 8.21049e7 1.00794e7i 1.43875 0.176626i
\(386\) −7.01524e7 −1.21978
\(387\) 6.57146e7 1.13378
\(388\) 5.43662e6i 0.0930752i
\(389\) 3.12589e7 0.531037 0.265519 0.964106i \(-0.414457\pi\)
0.265519 + 0.964106i \(0.414457\pi\)
\(390\) 6.22922e6i 0.105012i
\(391\) 5.24663e7i 0.877708i
\(392\) 2.06644e7 5.15127e6i 0.343055 0.0855177i
\(393\) −1.40824e7 −0.232005
\(394\) 2.90394e7 0.474787
\(395\) 1.21828e8i 1.97677i
\(396\) −2.69211e7 −0.433518
\(397\) 3.33743e7i 0.533385i −0.963782 0.266693i \(-0.914069\pi\)
0.963782 0.266693i \(-0.0859309\pi\)
\(398\) 3.47979e6i 0.0551955i
\(399\) 503459. + 4.10107e6i 0.00792584 + 0.0645622i
\(400\) −2.69282e7 −0.420753
\(401\) −4.06798e6 −0.0630878 −0.0315439 0.999502i \(-0.510042\pi\)
−0.0315439 + 0.999502i \(0.510042\pi\)
\(402\) 2.41284e6i 0.0371407i
\(403\) −5.92023e7 −0.904531
\(404\) 3.57818e7i 0.542648i
\(405\) 1.02245e8i 1.53913i
\(406\) 7.69923e6 + 6.27162e7i 0.115045 + 0.937134i
\(407\) −4.42634e7 −0.656540
\(408\) −4.21775e6 −0.0621013
\(409\) 3.79002e7i 0.553952i −0.960877 0.276976i \(-0.910668\pi\)
0.960877 0.276976i \(-0.0893322\pi\)
\(410\) 1.08319e8 1.57164
\(411\) 1.27961e7i 0.184312i
\(412\) 3.85357e7i 0.551025i
\(413\) 1.11186e8 1.36495e7i 1.57833 0.193761i
\(414\) −3.49592e7 −0.492676
\(415\) −1.33929e8 −1.87384
\(416\) 8.10756e6i 0.112619i
\(417\) 4.57123e6 0.0630412
\(418\) 2.08884e7i 0.286007i
\(419\) 7.34255e7i 0.998171i 0.866553 + 0.499085i \(0.166331\pi\)
−0.866553 + 0.499085i \(0.833669\pi\)
\(420\) −1.05222e6 8.57115e6i −0.0142023 0.115689i
\(421\) 5.94103e6 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(422\) −1.44974e7 −0.192910
\(423\) 1.78218e7i 0.235468i
\(424\) −19843.8 −0.000260332
\(425\) 1.59456e8i 2.07718i
\(426\) 9.60391e6i 0.124228i
\(427\) 2.88015e7 3.53576e6i 0.369940 0.0454149i
\(428\) −3.90526e6 −0.0498102
\(429\) 6.33490e6 0.0802357
\(430\) 1.06566e8i 1.34033i
\(431\) 9.58811e7 1.19757 0.598785 0.800909i \(-0.295650\pi\)
0.598785 + 0.800909i \(0.295650\pi\)
\(432\) 5.67883e6i 0.0704381i
\(433\) 1.23332e8i 1.51919i 0.650396 + 0.759595i \(0.274603\pi\)
−0.650396 + 0.759595i \(0.725397\pi\)
\(434\) −8.14600e7 + 1.00003e7i −0.996495 + 0.122333i
\(435\) 2.56214e7 0.311268
\(436\) 3.53958e7 0.427063
\(437\) 2.71253e7i 0.325035i
\(438\) −1.00903e7 −0.120083
\(439\) 6.41673e7i 0.758438i −0.925307 0.379219i \(-0.876193\pi\)
0.925307 0.379219i \(-0.123807\pi\)
\(440\) 4.36564e7i 0.512495i
\(441\) −8.15338e7 + 2.03250e7i −0.950653 + 0.236981i
\(442\) −4.80092e7 −0.555978
\(443\) −6.58726e7 −0.757693 −0.378847 0.925459i \(-0.623679\pi\)
−0.378847 + 0.925459i \(0.623679\pi\)
\(444\) 4.62077e6i 0.0527917i
\(445\) 6.10801e7 0.693138
\(446\) 4.42579e7i 0.498869i
\(447\) 6.23051e6i 0.0697592i
\(448\) −1.36950e6 1.11557e7i −0.0152310 0.124069i
\(449\) −1.02206e8 −1.12911 −0.564555 0.825395i \(-0.690952\pi\)
−0.564555 + 0.825395i \(0.690952\pi\)
\(450\) 1.06248e8 1.16596
\(451\) 1.10157e8i 1.20083i
\(452\) 8.53565e6 0.0924318
\(453\) 1.67164e7i 0.179824i
\(454\) 4.63344e7i 0.495150i
\(455\) −1.19771e7 9.75624e7i −0.127150 1.03573i
\(456\) 2.18060e6 0.0229975
\(457\) −5.62382e7 −0.589227 −0.294613 0.955617i \(-0.595191\pi\)
−0.294613 + 0.955617i \(0.595191\pi\)
\(458\) 7.38364e7i 0.768553i
\(459\) 3.36274e7 0.347740
\(460\) 5.66914e7i 0.582430i
\(461\) 2.46600e7i 0.251705i 0.992049 + 0.125852i \(0.0401665\pi\)
−0.992049 + 0.125852i \(0.959833\pi\)
\(462\) 8.71656e6 1.07007e6i 0.0883932 0.0108514i
\(463\) 1.91959e8 1.93404 0.967018 0.254707i \(-0.0819791\pi\)
0.967018 + 0.254707i \(0.0819791\pi\)
\(464\) 3.33472e7 0.333814
\(465\) 3.32787e7i 0.330985i
\(466\) −7.83469e6 −0.0774219
\(467\) 1.50925e8i 1.48187i −0.671578 0.740934i \(-0.734383\pi\)
0.671578 0.740934i \(-0.265617\pi\)
\(468\) 3.19894e7i 0.312082i
\(469\) 4.63921e6 + 3.77900e7i 0.0449703 + 0.366318i
\(470\) 2.89007e7 0.278365
\(471\) −1.78330e7 −0.170672
\(472\) 5.91191e7i 0.562214i
\(473\) −1.08373e8 −1.02409
\(474\) 1.29337e7i 0.121447i
\(475\) 8.24395e7i 0.769227i
\(476\) −6.60587e7 + 8.10956e6i −0.612505 + 0.0751929i
\(477\) 78296.3 0.000721416
\(478\) −2.47523e7 −0.226638
\(479\) 4.70415e7i 0.428031i 0.976830 + 0.214015i \(0.0686542\pi\)
−0.976830 + 0.214015i \(0.931346\pi\)
\(480\) −4.55741e6 −0.0412092
\(481\) 5.25966e7i 0.472631i
\(482\) 4.92077e7i 0.439432i
\(483\) 1.13192e7 1.38957e6i 0.100455 0.0123322i
\(484\) −1.22929e7 −0.108423
\(485\) 3.47857e7 0.304912
\(486\) 3.37244e7i 0.293789i
\(487\) −4.36014e7 −0.377497 −0.188748 0.982025i \(-0.560443\pi\)
−0.188748 + 0.982025i \(0.560443\pi\)
\(488\) 1.53142e7i 0.131775i
\(489\) 2.02349e7i 0.173051i
\(490\) −3.29599e7 1.32219e8i −0.280154 1.12384i
\(491\) 7.78280e7 0.657494 0.328747 0.944418i \(-0.393374\pi\)
0.328747 + 0.944418i \(0.393374\pi\)
\(492\) 1.14995e7 0.0965573
\(493\) 1.97466e8i 1.64798i
\(494\) 2.48210e7 0.205891
\(495\) 1.72252e8i 1.42020i
\(496\) 4.33135e7i 0.354959i
\(497\) 1.84656e7 + 1.50417e8i 0.150416 + 1.22526i
\(498\) −1.42184e7 −0.115123
\(499\) −6.33741e7 −0.510047 −0.255024 0.966935i \(-0.582083\pi\)
−0.255024 + 0.966935i \(0.582083\pi\)
\(500\) 6.99227e7i 0.559382i
\(501\) −7.66703e6 −0.0609697
\(502\) 1.50461e8i 1.18936i
\(503\) 1.88800e8i 1.48354i −0.670657 0.741768i \(-0.733988\pi\)
0.670657 0.741768i \(-0.266012\pi\)
\(504\) 5.40355e6 + 4.40161e7i 0.0422073 + 0.343811i
\(505\) 2.28946e8 1.77770
\(506\) 5.76531e7 0.445012
\(507\) 1.10198e7i 0.0845573i
\(508\) 4.30191e7 0.328149
\(509\) 5.84845e7i 0.443493i 0.975104 + 0.221747i \(0.0711758\pi\)
−0.975104 + 0.221747i \(0.928824\pi\)
\(510\) 2.69869e7i 0.203443i
\(511\) −1.58034e8 + 1.94008e7i −1.18437 + 0.145397i
\(512\) −5.93164e6 −0.0441942
\(513\) −1.73855e7 −0.128776
\(514\) 4.26905e7i 0.314370i
\(515\) −2.46566e8 −1.80515
\(516\) 1.13134e7i 0.0823463i
\(517\) 2.93909e7i 0.212687i
\(518\) 8.88445e6 + 7.23708e7i 0.0639207 + 0.520684i
\(519\) −7.58311e6 −0.0542432
\(520\) −5.18754e7 −0.368936
\(521\) 1.51011e7i 0.106781i 0.998574 + 0.0533907i \(0.0170029\pi\)
−0.998574 + 0.0533907i \(0.982997\pi\)
\(522\) −1.31575e8 −0.925046
\(523\) 2.31852e8i 1.62071i −0.585939 0.810355i \(-0.699274\pi\)
0.585939 0.810355i \(-0.300726\pi\)
\(524\) 1.17274e8i 0.815097i
\(525\) −3.44013e7 + 4.22321e6i −0.237737 + 0.0291853i
\(526\) 7.44918e7 0.511860
\(527\) 2.56482e8 1.75237
\(528\) 4.63473e6i 0.0314863i
\(529\) −7.31686e7 −0.494262
\(530\) 126969.i 0.000852842i
\(531\) 2.33262e8i 1.55797i
\(532\) 3.41527e7 4.19268e6i 0.226824 0.0278456i
\(533\) 1.30895e8 0.864455
\(534\) 6.48448e6 0.0425845
\(535\) 2.49874e7i 0.163177i
\(536\) 2.00935e7 0.130485
\(537\) 2.53350e7i 0.163606i
\(538\) 1.03443e8i 0.664284i
\(539\) 1.34462e8 3.35190e7i 0.858682 0.214055i
\(540\) 3.63354e7 0.230754
\(541\) −1.16913e7 −0.0738363 −0.0369181 0.999318i \(-0.511754\pi\)
−0.0369181 + 0.999318i \(0.511754\pi\)
\(542\) 1.57322e8i 0.988082i
\(543\) −1.00279e7 −0.0626339
\(544\) 3.51244e7i 0.218179i
\(545\) 2.26476e8i 1.39905i
\(546\) −1.27153e6 1.03576e7i −0.00781174 0.0636327i
\(547\) −1.11900e8 −0.683704 −0.341852 0.939754i \(-0.611054\pi\)
−0.341852 + 0.939754i \(0.611054\pi\)
\(548\) −1.06563e8 −0.647537
\(549\) 6.04241e7i 0.365168i
\(550\) −1.75220e8 −1.05316
\(551\) 1.02091e8i 0.610285i
\(552\) 6.01857e6i 0.0357829i
\(553\) −2.48679e7 2.02568e8i −0.147049 1.19783i
\(554\) 2.97222e7 0.174804
\(555\) 2.95655e7 0.172945
\(556\) 3.80680e7i 0.221481i
\(557\) −1.37837e8 −0.797629 −0.398815 0.917032i \(-0.630578\pi\)
−0.398815 + 0.917032i \(0.630578\pi\)
\(558\) 1.70899e8i 0.983641i
\(559\) 1.28776e8i 0.737227i
\(560\) −7.13784e7 + 8.76263e6i −0.406446 + 0.0498965i
\(561\) −2.74447e7 −0.155442
\(562\) 1.76604e8 0.994930
\(563\) 3.73228e7i 0.209146i 0.994517 + 0.104573i \(0.0333476\pi\)
−0.994517 + 0.104573i \(0.966652\pi\)
\(564\) 3.06820e6 0.0171020
\(565\) 5.46145e7i 0.302805i
\(566\) 1.02644e8i 0.566088i
\(567\) −2.08705e7 1.70007e8i −0.114494 0.932646i
\(568\) 7.99789e7 0.436446
\(569\) 1.41857e8 0.770042 0.385021 0.922908i \(-0.374194\pi\)
0.385021 + 0.922908i \(0.374194\pi\)
\(570\) 1.39523e7i 0.0753394i
\(571\) 2.47829e8 1.33120 0.665600 0.746308i \(-0.268176\pi\)
0.665600 + 0.746308i \(0.268176\pi\)
\(572\) 5.27554e7i 0.281890i
\(573\) 7.65786e6i 0.0407046i
\(574\) 1.80107e8 2.21104e7i 0.952344 0.116913i
\(575\) −2.27537e8 −1.19688
\(576\) 2.34040e7 0.122468
\(577\) 1.43601e8i 0.747531i −0.927523 0.373766i \(-0.878066\pi\)
0.927523 0.373766i \(-0.121934\pi\)
\(578\) 7.14478e7 0.370003
\(579\) 4.76529e7i 0.245501i
\(580\) 2.13368e8i 1.09357i
\(581\) −2.22690e8 + 2.73381e7i −1.13546 + 0.139393i
\(582\) 3.69297e6 0.0187330
\(583\) −129123. −0.000651623
\(584\) 8.40293e7i 0.421883i
\(585\) 2.04681e8 1.02237
\(586\) 3.30017e7i 0.164000i
\(587\) 1.55774e8i 0.770160i 0.922883 + 0.385080i \(0.125826\pi\)
−0.922883 + 0.385080i \(0.874174\pi\)
\(588\) −3.49914e6 1.40368e7i −0.0172119 0.0690458i
\(589\) −1.32603e8 −0.648942
\(590\) −3.78267e8 −1.84180
\(591\) 1.97258e7i 0.0955591i
\(592\) 3.84806e7 0.185472
\(593\) 6.85593e7i 0.328777i −0.986396 0.164389i \(-0.947435\pi\)
0.986396 0.164389i \(-0.0525651\pi\)
\(594\) 3.69518e7i 0.176310i
\(595\) 5.18882e7 + 4.22670e8i 0.246330 + 2.00655i
\(596\) 5.18862e7 0.245083
\(597\) −2.36374e6 −0.0111091
\(598\) 6.85073e7i 0.320356i
\(599\) 6.44816e7 0.300024 0.150012 0.988684i \(-0.452069\pi\)
0.150012 + 0.988684i \(0.452069\pi\)
\(600\) 1.82917e7i 0.0846838i
\(601\) 2.18773e8i 1.00779i 0.863765 + 0.503895i \(0.168100\pi\)
−0.863765 + 0.503895i \(0.831900\pi\)
\(602\) 2.17525e7 + 1.77191e8i 0.0997057 + 0.812180i
\(603\) −7.92815e7 −0.361593
\(604\) −1.39210e8 −0.631770
\(605\) 7.86551e7i 0.355190i
\(606\) 2.43058e7 0.109217
\(607\) 3.55798e8i 1.59088i 0.606032 + 0.795441i \(0.292760\pi\)
−0.606032 + 0.795441i \(0.707240\pi\)
\(608\) 1.81595e7i 0.0807965i
\(609\) 4.26017e7 5.22991e6i 0.188615 0.0231549i
\(610\) −9.79863e7 −0.431694
\(611\) 3.49242e7 0.153110
\(612\) 1.38588e8i 0.604604i
\(613\) 1.50352e7 0.0652719 0.0326360 0.999467i \(-0.489610\pi\)
0.0326360 + 0.999467i \(0.489610\pi\)
\(614\) 1.28338e8i 0.554433i
\(615\) 7.35786e7i 0.316320i
\(616\) −8.91128e6 7.25893e7i −0.0381240 0.310549i
\(617\) 4.45354e7 0.189605 0.0948025 0.995496i \(-0.469778\pi\)
0.0948025 + 0.995496i \(0.469778\pi\)
\(618\) −2.61764e7 −0.110903
\(619\) 3.58045e7i 0.150962i −0.997147 0.0754808i \(-0.975951\pi\)
0.997147 0.0754808i \(-0.0240491\pi\)
\(620\) 2.77137e8 1.16284
\(621\) 4.79850e7i 0.200369i
\(622\) 2.24204e8i 0.931691i
\(623\) 1.01560e8 1.24679e7i 0.420011 0.0515617i
\(624\) −5.50728e6 −0.0226665
\(625\) 3.65022e7 0.149513
\(626\) 5.70530e7i 0.232571i
\(627\) 1.41890e7 0.0575639
\(628\) 1.48509e8i 0.599616i
\(629\) 2.27864e8i 0.915640i
\(630\) 2.81633e8 3.45741e7i 1.12632 0.138270i
\(631\) −4.30383e8 −1.71304 −0.856520 0.516115i \(-0.827378\pi\)
−0.856520 + 0.516115i \(0.827378\pi\)
\(632\) −1.07709e8 −0.426677
\(633\) 9.84778e6i 0.0388264i
\(634\) −1.68785e8 −0.662317
\(635\) 2.75253e8i 1.07501i
\(636\) 13479.5i 5.23963e-5i
\(637\) −3.98295e7 1.59776e8i −0.154094 0.618150i
\(638\) 2.16988e8 0.835553
\(639\) −3.15567e8 −1.20945
\(640\) 3.79530e7i 0.144779i
\(641\) 1.87109e8 0.710429 0.355215 0.934785i \(-0.384408\pi\)
0.355215 + 0.934785i \(0.384408\pi\)
\(642\) 2.65275e6i 0.0100252i
\(643\) 2.52905e8i 0.951314i −0.879631 0.475657i \(-0.842210\pi\)
0.879631 0.475657i \(-0.157790\pi\)
\(644\) −1.15720e7 9.42632e7i −0.0433263 0.352927i
\(645\) 7.23876e7 0.269765
\(646\) −1.07532e8 −0.398878
\(647\) 1.95969e8i 0.723560i −0.932263 0.361780i \(-0.882169\pi\)
0.932263 0.361780i \(-0.117831\pi\)
\(648\) −9.03951e7 −0.332216
\(649\) 3.84684e8i 1.40725i
\(650\) 2.08208e8i 0.758153i
\(651\) 6.79295e6 + 5.53339e7i 0.0246216 + 0.200562i
\(652\) −1.68511e8 −0.607975
\(653\) 1.11109e8 0.399033 0.199516 0.979894i \(-0.436063\pi\)
0.199516 + 0.979894i \(0.436063\pi\)
\(654\) 2.40436e7i 0.0859539i
\(655\) 7.50368e8 2.67024
\(656\) 9.57654e7i 0.339232i
\(657\) 3.31548e8i 1.16910i
\(658\) 4.80543e7 5.89929e6i 0.168677 0.0207072i
\(659\) −2.24885e8 −0.785786 −0.392893 0.919584i \(-0.628526\pi\)
−0.392893 + 0.919584i \(0.628526\pi\)
\(660\) −2.96548e7 −0.103149
\(661\) 5.19969e8i 1.80042i 0.435458 + 0.900209i \(0.356586\pi\)
−0.435458 + 0.900209i \(0.643414\pi\)
\(662\) −1.01267e7 −0.0349054
\(663\) 3.26116e7i 0.111900i
\(664\) 1.18408e8i 0.404460i
\(665\) −2.68264e7 2.18522e8i −0.0912217 0.743072i
\(666\) −1.51830e8 −0.513967
\(667\) 2.81777e8 0.949571
\(668\) 6.38491e7i 0.214203i
\(669\) −3.00634e7 −0.100406
\(670\) 1.28566e8i 0.427467i
\(671\) 9.96486e7i 0.329840i
\(672\) −7.57780e6 + 930273.i −0.0249710 + 0.00306551i
\(673\) −3.68354e8 −1.20842 −0.604212 0.796823i \(-0.706512\pi\)
−0.604212 + 0.796823i \(0.706512\pi\)
\(674\) 7.36033e6 0.0240391
\(675\) 1.45836e8i 0.474192i
\(676\) 9.17704e7 0.297073
\(677\) 1.91687e7i 0.0617770i −0.999523 0.0308885i \(-0.990166\pi\)
0.999523 0.0308885i \(-0.00983367\pi\)
\(678\) 5.79808e6i 0.0186035i
\(679\) 5.78396e7 7.10056e6i 0.184763 0.0226821i
\(680\) 2.24740e8 0.714749
\(681\) −3.14739e7 −0.0996574
\(682\) 2.81838e8i 0.888479i
\(683\) −3.28267e8 −1.03030 −0.515152 0.857099i \(-0.672264\pi\)
−0.515152 + 0.857099i \(0.672264\pi\)
\(684\) 7.16505e7i 0.223898i
\(685\) 6.81833e8i 2.12132i
\(686\) −8.17926e7 2.13118e8i −0.253362 0.660157i
\(687\) −5.01554e7 −0.154685
\(688\) 9.42152e7 0.289305
\(689\) 153432.i 0.000469092i
\(690\) −3.85092e7 −0.117224
\(691\) 1.96349e8i 0.595107i 0.954705 + 0.297554i \(0.0961707\pi\)
−0.954705 + 0.297554i \(0.903829\pi\)
\(692\) 6.31503e7i 0.190571i
\(693\) 3.51606e7 + 2.86410e8i 0.105647 + 0.860576i
\(694\) 1.51118e8 0.452103
\(695\) −2.43574e8 −0.725567
\(696\) 2.26520e7i 0.0671859i
\(697\) −5.67078e8 −1.67473
\(698\) 1.35611e8i 0.398777i
\(699\) 5.32193e6i 0.0155825i
\(700\) 3.51698e7 + 2.86486e8i 0.102536 + 0.835235i
\(701\) 4.19696e8 1.21837 0.609187 0.793026i \(-0.291496\pi\)
0.609187 + 0.793026i \(0.291496\pi\)
\(702\) 4.39086e7 0.126922
\(703\) 1.17807e8i 0.339082i
\(704\) −3.85968e7 −0.110620
\(705\) 1.96316e7i 0.0560257i
\(706\) 4.52430e8i 1.28569i
\(707\) 3.80678e8 4.67332e7i 1.07721 0.132241i
\(708\) −4.01583e7 −0.113155
\(709\) 6.46327e8 1.81348 0.906742 0.421686i \(-0.138562\pi\)
0.906742 + 0.421686i \(0.138562\pi\)
\(710\) 5.11737e8i 1.42979i
\(711\) 4.24978e8 1.18238
\(712\) 5.40012e7i 0.149611i
\(713\) 3.65990e8i 1.00972i
\(714\) 5.50864e6 + 4.48722e7i 0.0151339 + 0.123277i
\(715\) −3.37550e8 −0.923465
\(716\) −2.10984e8 −0.574791
\(717\) 1.68137e7i 0.0456148i
\(718\) −2.55302e8 −0.689732
\(719\) 3.24953e8i 0.874246i 0.899402 + 0.437123i \(0.144002\pi\)
−0.899402 + 0.437123i \(0.855998\pi\)
\(720\) 1.49748e8i 0.401203i
\(721\) −4.09976e8 + 5.03299e7i −1.09384 + 0.134283i
\(722\) −2.10537e8 −0.559393
\(723\) 3.34257e7 0.0884434
\(724\) 8.35097e7i 0.220050i
\(725\) −8.56378e8 −2.24725
\(726\) 8.35032e6i 0.0218219i
\(727\) 5.08659e8i 1.32380i −0.749591 0.661902i \(-0.769750\pi\)
0.749591 0.661902i \(-0.230250\pi\)
\(728\) −8.62554e7 + 1.05890e7i −0.223559 + 0.0274448i
\(729\) 3.41130e8 0.880517
\(730\) 5.37653e8 1.38208
\(731\) 5.57899e8i 1.42825i
\(732\) −1.04026e7 −0.0265221
\(733\) 7.52837e8i 1.91156i 0.294075 + 0.955782i \(0.404989\pi\)
−0.294075 + 0.955782i \(0.595011\pi\)
\(734\) 3.43475e8i 0.868573i
\(735\) −8.98132e7 + 2.23889e7i −0.226193 + 0.0563859i
\(736\) −5.01212e7 −0.125715
\(737\) 1.30747e8 0.326611
\(738\) 3.77854e8i 0.940059i
\(739\) −1.58548e8 −0.392850 −0.196425 0.980519i \(-0.562933\pi\)
−0.196425 + 0.980519i \(0.562933\pi\)
\(740\) 2.46214e8i 0.607601i
\(741\) 1.68603e7i 0.0414392i
\(742\) 25917.2 + 211116.i 6.34420e−5 + 0.000516784i
\(743\) 5.89089e8 1.43620 0.718099 0.695941i \(-0.245013\pi\)
0.718099 + 0.695941i \(0.245013\pi\)
\(744\) 2.94219e7 0.0714417
\(745\) 3.31988e8i 0.802886i
\(746\) 5.27055e8 1.26952
\(747\) 4.67192e8i 1.12081i
\(748\) 2.28553e8i 0.546111i
\(749\) 5.10050e6 + 4.15475e7i 0.0121386 + 0.0988781i
\(750\) 4.74969e7 0.112585
\(751\) −3.67603e8 −0.867879 −0.433939 0.900942i \(-0.642877\pi\)
−0.433939 + 0.900942i \(0.642877\pi\)
\(752\) 2.55512e7i 0.0600839i
\(753\) 1.02205e8 0.239379
\(754\) 2.57839e8i 0.601500i
\(755\) 8.90719e8i 2.06966i
\(756\) 6.04164e7 7.41690e6i 0.139827 0.0171655i
\(757\) 6.54505e8 1.50878 0.754389 0.656427i \(-0.227933\pi\)
0.754389 + 0.656427i \(0.227933\pi\)
\(758\) −1.57698e8 −0.362092
\(759\) 3.91625e7i 0.0895663i
\(760\) −1.16192e8 −0.264688
\(761\) 6.48428e7i 0.147132i −0.997290 0.0735661i \(-0.976562\pi\)
0.997290 0.0735661i \(-0.0234380\pi\)
\(762\) 2.92219e7i 0.0660456i
\(763\) −4.62291e7 3.76572e8i −0.104074 0.847763i
\(764\) 6.37727e7 0.143006
\(765\) −8.86740e8 −1.98067
\(766\) 1.49240e7i 0.0332047i
\(767\) −4.57107e8 −1.01305
\(768\) 4.02923e6i 0.00889485i
\(769\) 7.56321e8i 1.66313i −0.555425 0.831566i \(-0.687444\pi\)
0.555425 0.831566i \(-0.312556\pi\)
\(770\) −4.64455e8 + 5.70179e7i −1.01735 + 0.124893i
\(771\) −2.89987e7 −0.0632725
\(772\) 3.96842e8 0.862513
\(773\) 2.42896e8i 0.525875i 0.964813 + 0.262937i \(0.0846913\pi\)
−0.964813 + 0.262937i \(0.915309\pi\)
\(774\) −3.71738e8 −0.801704
\(775\) 1.11232e9i 2.38960i
\(776\) 3.07542e7i 0.0658141i
\(777\) 4.91598e7 6.03501e6i 0.104797 0.0128651i
\(778\) −1.76827e8 −0.375500
\(779\) 2.93182e8 0.620190
\(780\) 3.52378e7i 0.0742549i
\(781\) 5.20418e8 1.09244
\(782\) 2.96794e8i 0.620633i
\(783\) 1.80600e8i 0.376212i
\(784\) −1.16895e8 + 2.91400e7i −0.242577 + 0.0604701i
\(785\) 9.50219e8 1.96433
\(786\) 7.96619e7 0.164052
\(787\) 4.68172e8i 0.960465i 0.877141 + 0.480232i \(0.159448\pi\)
−0.877141 + 0.480232i \(0.840552\pi\)
\(788\) −1.64272e8 −0.335725
\(789\) 5.06006e7i 0.103021i
\(790\) 6.89162e8i 1.39778i
\(791\) −1.11481e7 9.08098e7i −0.0225253 0.183486i
\(792\) 1.52289e8 0.306544
\(793\) −1.18409e8 −0.237446
\(794\) 1.88794e8i 0.377160i
\(795\) 86246.9 0.000171649
\(796\) 1.96847e7i 0.0390291i
\(797\) 1.00075e8i 0.197674i 0.995104 + 0.0988370i \(0.0315122\pi\)
−0.995104 + 0.0988370i \(0.968488\pi\)
\(798\) −2.84799e6 2.31991e7i −0.00560442 0.0456523i
\(799\) −1.51302e8 −0.296623
\(800\) 1.52329e8 0.297517
\(801\) 2.13068e8i 0.414593i
\(802\) 2.30119e7 0.0446098
\(803\) 5.46774e8i 1.05599i
\(804\) 1.36491e7i 0.0262624i
\(805\) −6.03133e8 + 7.40424e7i −1.15618 + 0.141936i
\(806\) 3.34899e8 0.639600
\(807\) −7.02664e7 −0.133699
\(808\) 2.02412e8i 0.383710i
\(809\) −5.87217e8 −1.10906 −0.554528 0.832165i \(-0.687101\pi\)
−0.554528 + 0.832165i \(0.687101\pi\)
\(810\) 5.78384e8i 1.08833i
\(811\) 8.86023e8i 1.66105i −0.556983 0.830524i \(-0.688041\pi\)
0.556983 0.830524i \(-0.311959\pi\)
\(812\) −4.35534e7 3.54777e8i −0.0813494 0.662654i
\(813\) 1.06866e8 0.198869
\(814\) 2.50391e8 0.464244
\(815\) 1.07820e9i 1.99171i
\(816\) 2.38592e7 0.0439123
\(817\) 2.88436e8i 0.528912i
\(818\) 2.14396e8i 0.391703i
\(819\) 3.40332e8 4.17801e7i 0.619513 0.0760533i
\(820\) −6.12745e8 −1.11132
\(821\) −5.51065e8 −0.995803 −0.497902 0.867233i \(-0.665896\pi\)
−0.497902 + 0.867233i \(0.665896\pi\)
\(822\) 7.23858e7i 0.130328i
\(823\) 5.33974e8 0.957901 0.478951 0.877842i \(-0.341017\pi\)
0.478951 + 0.877842i \(0.341017\pi\)
\(824\) 2.17991e8i 0.389633i
\(825\) 1.19023e8i 0.211967i
\(826\) −6.28961e8 + 7.72131e7i −1.11605 + 0.137010i
\(827\) −5.33590e8 −0.943390 −0.471695 0.881762i \(-0.656358\pi\)
−0.471695 + 0.881762i \(0.656358\pi\)
\(828\) 1.97759e8 0.348374
\(829\) 1.11584e9i 1.95857i −0.202476 0.979287i \(-0.564899\pi\)
0.202476 0.979287i \(-0.435101\pi\)
\(830\) 7.57619e8 1.32500
\(831\) 2.01896e7i 0.0351823i
\(832\) 4.58633e7i 0.0796334i
\(833\) 1.72553e8 + 6.92199e8i 0.298530 + 1.19756i
\(834\) −2.58588e7 −0.0445769
\(835\) 4.08532e8 0.701725
\(836\) 1.18163e8i 0.202237i
\(837\) −2.34575e8 −0.400042
\(838\) 4.15357e8i 0.705813i
\(839\) 2.23881e8i 0.379081i 0.981873 + 0.189540i \(0.0606998\pi\)
−0.981873 + 0.189540i \(0.939300\pi\)
\(840\) 5.95226e6 + 4.84858e7i 0.0100425 + 0.0818043i
\(841\) 4.65694e8 0.782912
\(842\) −3.36075e7 −0.0562989
\(843\) 1.19963e8i 0.200247i
\(844\) 8.20098e7 0.136408
\(845\) 5.87184e8i 0.973204i
\(846\) 1.00816e8i 0.166501i
\(847\) 1.60553e7 + 1.30783e8i 0.0264222 + 0.215229i
\(848\) 112254. 0.000184082
\(849\) −6.97237e7 −0.113935
\(850\) 9.02020e8i 1.46879i
\(851\) 3.25154e8 0.527594
\(852\) 5.43279e7i 0.0878424i
\(853\) 2.97785e8i 0.479795i −0.970798 0.239898i \(-0.922886\pi\)
0.970798 0.239898i \(-0.0771139\pi\)
\(854\) −1.62926e8 + 2.00013e7i −0.261587 + 0.0321132i
\(855\) 4.58449e8 0.733487
\(856\) 2.20915e7 0.0352211
\(857\) 7.86923e8i 1.25023i −0.780533 0.625115i \(-0.785052\pi\)
0.780533 0.625115i \(-0.214948\pi\)
\(858\) −3.58356e7 −0.0567352
\(859\) 7.66256e8i 1.20891i 0.796639 + 0.604456i \(0.206609\pi\)
−0.796639 + 0.604456i \(0.793391\pi\)
\(860\) 6.02826e8i 0.947757i
\(861\) −1.50191e7 1.22342e8i −0.0235307 0.191676i
\(862\) −5.42385e8 −0.846811
\(863\) −1.16650e9 −1.81490 −0.907452 0.420157i \(-0.861975\pi\)
−0.907452 + 0.420157i \(0.861975\pi\)
\(864\) 3.21243e7i 0.0498073i
\(865\) 4.04061e8 0.624307
\(866\) 6.97671e8i 1.07423i
\(867\) 4.85329e7i 0.0744695i
\(868\) 4.60807e8 5.65700e7i 0.704628 0.0865022i
\(869\) −7.00853e8 −1.06799
\(870\) −1.44936e8 −0.220100
\(871\) 1.55363e8i 0.235121i
\(872\) −2.00229e8 −0.301979
\(873\) 1.21344e8i 0.182380i
\(874\) 1.53444e8i 0.229835i
\(875\) 7.43900e8 9.13233e7i 1.11043 0.136319i
\(876\) 5.70792e7 0.0849113
\(877\) 7.56442e8 1.12144 0.560721 0.828005i \(-0.310524\pi\)
0.560721 + 0.828005i \(0.310524\pi\)
\(878\) 3.62985e8i 0.536297i
\(879\) −2.24173e7 −0.0330078
\(880\) 2.46958e8i 0.362389i
\(881\) 3.69412e8i 0.540235i −0.962827 0.270118i \(-0.912937\pi\)
0.962827 0.270118i \(-0.0870626\pi\)
\(882\) 4.61225e8 1.14975e8i 0.672213 0.167571i
\(883\) −5.87419e8 −0.853230 −0.426615 0.904433i \(-0.640294\pi\)
−0.426615 + 0.904433i \(0.640294\pi\)
\(884\) 2.71581e8 0.393136
\(885\) 2.56948e8i 0.370695i
\(886\) 3.72632e8 0.535770
\(887\) 2.15522e7i 0.0308831i 0.999881 + 0.0154416i \(0.00491540\pi\)
−0.999881 + 0.0154416i \(0.995085\pi\)
\(888\) 2.61390e7i 0.0373294i
\(889\) −5.61856e7 4.57675e8i −0.0799686 0.651407i
\(890\) −3.45521e8 −0.490122
\(891\) −5.88196e8 −0.831551
\(892\) 2.50361e8i 0.352753i
\(893\) 7.82240e7 0.109846
\(894\) 3.52451e7i 0.0493272i
\(895\) 1.34996e9i 1.88300i
\(896\) 7.74708e6 + 6.31060e7i 0.0107700 + 0.0877297i
\(897\) −4.65354e7 −0.0644772
\(898\) 5.78163e8 0.798402
\(899\) 1.37747e9i 1.89585i
\(900\) −6.01032e8 −0.824461
\(901\) 664713.i 0.000908782i
\(902\) 6.23140e8i 0.849113i
\(903\) 1.20362e8 1.47760e7i 0.163465 0.0200675i
\(904\) −4.82849e7 −0.0653591
\(905\) 5.34328e8 0.720879
\(906\) 9.45620e7i 0.127155i
\(907\) −1.14115e9 −1.52939 −0.764697 0.644390i \(-0.777111\pi\)
−0.764697 + 0.644390i \(0.777111\pi\)
\(908\) 2.62107e8i 0.350124i
\(909\) 7.98644e8i 1.06331i
\(910\) 6.77524e7 + 5.51896e8i 0.0899085 + 0.732375i
\(911\) −3.29876e8 −0.436310 −0.218155 0.975914i \(-0.570004\pi\)
−0.218155 + 0.975914i \(0.570004\pi\)
\(912\) −1.23353e7 −0.0162617
\(913\) 7.70471e8i 1.01238i
\(914\) 3.18131e8 0.416646
\(915\) 6.65599e7i 0.0868859i
\(916\) 4.17682e8i 0.543449i
\(917\) 1.24767e9 1.53167e8i 1.61805 0.198636i
\(918\) −1.90225e8 −0.245890
\(919\) −1.10236e8 −0.142029 −0.0710144 0.997475i \(-0.522624\pi\)
−0.0710144 + 0.997475i \(0.522624\pi\)
\(920\) 3.20695e8i 0.411840i
\(921\) 8.71769e7 0.111589
\(922\) 1.39498e8i 0.177982i
\(923\) 6.18395e8i 0.786432i
\(924\) −4.93083e7 + 6.05323e6i −0.0625035 + 0.00767311i
\(925\) −9.88210e8 −1.24860
\(926\) −1.08588e9 −1.36757
\(927\) 8.60109e8i 1.07973i
\(928\) −1.88640e8 −0.236042
\(929\) 4.58674e8i 0.572081i −0.958218 0.286040i \(-0.907661\pi\)
0.958218 0.286040i \(-0.0923391\pi\)
\(930\) 1.88253e8i 0.234041i
\(931\) −8.92109e7 3.57870e8i −0.110553 0.443483i
\(932\) 4.43197e7 0.0547456
\(933\) 1.52297e8 0.187519
\(934\) 8.53759e8i 1.04784i
\(935\) 1.46237e9 1.78905
\(936\) 1.80959e8i 0.220675i
\(937\) 9.98325e8i 1.21354i 0.794878 + 0.606769i \(0.207535\pi\)
−0.794878 + 0.606769i \(0.792465\pi\)
\(938\) −2.62433e7 2.13772e8i −0.0317988 0.259026i
\(939\) −3.87548e7 −0.0468089
\(940\) −1.63487e8 −0.196834
\(941\) 1.08263e9i 1.29930i −0.760231 0.649652i \(-0.774915\pi\)
0.760231 0.649652i \(-0.225085\pi\)
\(942\) 1.00879e8 0.120683
\(943\) 8.09198e8i 0.964983i
\(944\) 3.34428e8i 0.397545i
\(945\) −4.74563e7 3.86568e8i −0.0562339 0.458069i
\(946\) 6.13053e8 0.724143
\(947\) 7.97542e8 0.939082 0.469541 0.882911i \(-0.344419\pi\)
0.469541 + 0.882911i \(0.344419\pi\)
\(948\) 7.31640e7i 0.0858761i
\(949\) 6.49713e8 0.760191
\(950\) 4.66348e8i 0.543926i
\(951\) 1.14652e8i 0.133303i
\(952\) 3.73685e8 4.58746e7i 0.433106 0.0531694i
\(953\) −1.15116e9 −1.33002 −0.665009 0.746836i \(-0.731572\pi\)
−0.665009 + 0.746836i \(0.731572\pi\)
\(954\) −442910. −0.000510118
\(955\) 4.08043e8i 0.468485i
\(956\) 1.40020e8 0.160257
\(957\) 1.47395e8i 0.168169i
\(958\) 2.66107e8i 0.302663i
\(959\) 1.39178e8 + 1.13371e9i 0.157803 + 1.28542i
\(960\) 2.57806e7 0.0291393
\(961\) −9.01645e8 −1.01593
\(962\) 2.97531e8i 0.334201i
\(963\) −8.71646e7 −0.0976026
\(964\) 2.78361e8i 0.310726i
\(965\) 2.53915e9i 2.82557i
\(966\) −6.40308e7 + 7.86062e6i −0.0710326 + 0.00872018i
\(967\) −6.50101e8 −0.718954 −0.359477 0.933154i \(-0.617045\pi\)
−0.359477 + 0.933154i \(0.617045\pi\)
\(968\) 6.95394e7 0.0766663
\(969\) 7.30441e7i 0.0802812i
\(970\) −1.96777e8 −0.215606
\(971\) 4.14091e8i 0.452312i 0.974091 + 0.226156i \(0.0726159\pi\)
−0.974091 + 0.226156i \(0.927384\pi\)
\(972\) 1.90774e8i 0.207740i
\(973\) −4.05001e8 + 4.97192e7i −0.439661 + 0.0539741i
\(974\) 2.46647e8 0.266931
\(975\) 1.41431e8 0.152592
\(976\) 8.66302e7i 0.0931793i
\(977\) −1.24398e9 −1.33392 −0.666962 0.745091i \(-0.732406\pi\)
−0.666962 + 0.745091i \(0.732406\pi\)
\(978\) 1.14466e8i 0.122366i
\(979\) 3.51383e8i 0.374483i
\(980\) 1.86449e8 + 7.47942e8i 0.198099 + 0.794676i
\(981\) 7.90029e8 0.836827
\(982\) −4.40262e8 −0.464918
\(983\) 1.65067e9i 1.73780i −0.494986 0.868901i \(-0.664827\pi\)
0.494986 0.868901i \(-0.335173\pi\)
\(984\) −6.50512e7 −0.0682763
\(985\) 1.05107e9i 1.09983i
\(986\) 1.11704e9i 1.16530i
\(987\) −4.00726e6 3.26422e7i −0.00416769 0.0339491i
\(988\) −1.40409e8 −0.145587
\(989\) 7.96099e8 0.822959
\(990\) 9.74404e8i 1.00423i
\(991\) 1.85734e9 1.90841 0.954203 0.299159i \(-0.0967060\pi\)
0.954203 + 0.299159i \(0.0967060\pi\)
\(992\) 2.45018e8i 0.250994i
\(993\) 6.87882e6i 0.00702532i
\(994\) −1.04457e8 8.50887e8i −0.106360 0.866388i
\(995\) 1.25950e8 0.127859
\(996\) 8.04316e7 0.0814046
\(997\) 1.40620e9i 1.41893i 0.704740 + 0.709466i \(0.251064\pi\)
−0.704740 + 0.709466i \(0.748936\pi\)
\(998\) 3.58498e8 0.360658
\(999\) 2.08402e8i 0.209028i
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 14.7.b.a.13.2 yes 4
3.2 odd 2 126.7.c.a.55.4 4
4.3 odd 2 112.7.c.c.97.2 4
5.2 odd 4 350.7.d.a.349.3 8
5.3 odd 4 350.7.d.a.349.6 8
5.4 even 2 350.7.b.a.251.3 4
7.2 even 3 98.7.d.b.31.3 8
7.3 odd 6 98.7.d.b.19.3 8
7.4 even 3 98.7.d.b.19.4 8
7.5 odd 6 98.7.d.b.31.4 8
7.6 odd 2 inner 14.7.b.a.13.1 4
8.3 odd 2 448.7.c.e.321.3 4
8.5 even 2 448.7.c.h.321.2 4
21.20 even 2 126.7.c.a.55.3 4
28.27 even 2 112.7.c.c.97.3 4
35.13 even 4 350.7.d.a.349.7 8
35.27 even 4 350.7.d.a.349.2 8
35.34 odd 2 350.7.b.a.251.4 4
56.13 odd 2 448.7.c.h.321.3 4
56.27 even 2 448.7.c.e.321.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.7.b.a.13.1 4 7.6 odd 2 inner
14.7.b.a.13.2 yes 4 1.1 even 1 trivial
98.7.d.b.19.3 8 7.3 odd 6
98.7.d.b.19.4 8 7.4 even 3
98.7.d.b.31.3 8 7.2 even 3
98.7.d.b.31.4 8 7.5 odd 6
112.7.c.c.97.2 4 4.3 odd 2
112.7.c.c.97.3 4 28.27 even 2
126.7.c.a.55.3 4 21.20 even 2
126.7.c.a.55.4 4 3.2 odd 2
350.7.b.a.251.3 4 5.4 even 2
350.7.b.a.251.4 4 35.34 odd 2
350.7.d.a.349.2 8 35.27 even 4
350.7.d.a.349.3 8 5.2 odd 4
350.7.d.a.349.6 8 5.3 odd 4
350.7.d.a.349.7 8 35.13 even 4
448.7.c.e.321.2 4 56.27 even 2
448.7.c.e.321.3 4 8.3 odd 2
448.7.c.h.321.2 4 8.5 even 2
448.7.c.h.321.3 4 56.13 odd 2