Properties

Label 7.12.c.a.4.3
Level $7$
Weight $12$
Character 7.4
Analytic conductor $5.378$
Analytic rank $0$
Dimension $12$
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] = [7,12,Mod(2,7)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7.2");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 7.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.37840226392\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 1846 x^{10} + 9475 x^{9} + 2735534 x^{8} + 11305015 x^{7} + 1247863105 x^{6} + 8299724444 x^{5} + 456730004116 x^{4} + \cdots + 4089842896896 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{3}\cdot 7^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.3
Root \(-0.427084 - 0.739732i\) of defining polynomial
Character \(\chi\) \(=\) 7.4
Dual form 7.12.c.a.2.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.85417 + 4.94356i) q^{2} +(-366.163 + 634.213i) q^{3} +(1007.71 - 1745.40i) q^{4} +(-4491.11 - 7778.83i) q^{5} -4180.36 q^{6} +(-43014.2 + 11274.1i) q^{7} +23195.3 q^{8} +(-179577. - 311037. i) q^{9} +O(q^{10})\) \(q+(2.85417 + 4.94356i) q^{2} +(-366.163 + 634.213i) q^{3} +(1007.71 - 1745.40i) q^{4} +(-4491.11 - 7778.83i) q^{5} -4180.36 q^{6} +(-43014.2 + 11274.1i) q^{7} +23195.3 q^{8} +(-179577. - 311037. i) q^{9} +(25636.8 - 44404.2i) q^{10} +(-45694.4 + 79145.1i) q^{11} +(737970. + 1.27820e6i) q^{12} -775221. q^{13} +(-178504. - 180465. i) q^{14} +6.57792e6 q^{15} +(-1.99758e6 - 3.45991e6i) q^{16} +(-4.63726e6 + 8.03198e6i) q^{17} +(1.02509e6 - 1.77550e6i) q^{18} +(1.43623e6 + 2.48762e6i) q^{19} -1.81029e7 q^{20} +(8.60003e6 - 3.14083e7i) q^{21} -521678. q^{22} +(-5.26756e6 - 9.12369e6i) q^{23} +(-8.49327e6 + 1.47108e7i) q^{24} +(-1.59261e7 + 2.75848e7i) q^{25} +(-2.21261e6 - 3.83236e6i) q^{26} +1.33289e8 q^{27} +(-2.36679e7 + 8.64380e7i) q^{28} -4.24570e7 q^{29} +(1.87745e7 + 3.25184e7i) q^{30} +(5.29120e7 - 9.16463e7i) q^{31} +(3.51549e7 - 6.08901e7i) q^{32} +(-3.34632e7 - 5.79600e7i) q^{33} -5.29421e7 q^{34} +(2.80881e8 + 2.83967e8i) q^{35} -7.23845e8 q^{36} +(-1.54843e8 - 2.68196e8i) q^{37} +(-8.19848e6 + 1.42002e7i) q^{38} +(2.83857e8 - 4.91655e8i) q^{39} +(-1.04173e8 - 1.80433e8i) q^{40} -1.19606e8 q^{41} +(1.79815e8 - 4.71298e7i) q^{42} +1.16451e9 q^{43} +(9.20932e7 + 1.59510e8i) q^{44} +(-1.61300e9 + 2.79380e9i) q^{45} +(3.00690e7 - 5.20811e7i) q^{46} +(1.25006e8 + 2.16517e8i) q^{47} +2.92576e9 q^{48} +(1.72312e9 - 9.69892e8i) q^{49} -1.81823e8 q^{50} +(-3.39599e9 - 5.88203e9i) q^{51} +(-7.81196e8 + 1.35307e9i) q^{52} +(-1.73284e9 + 3.00136e9i) q^{53} +(3.80428e8 + 6.58921e8i) q^{54} +8.20875e8 q^{55} +(-9.97729e8 + 2.61506e8i) q^{56} -2.10358e9 q^{57} +(-1.21180e8 - 2.09889e8i) q^{58} +(-3.01421e9 + 5.22077e9i) q^{59} +(6.62861e9 - 1.14811e10i) q^{60} +(-5.31834e9 - 9.21163e9i) q^{61} +6.04079e8 q^{62} +(1.12310e10 + 1.13544e10i) q^{63} -7.78074e9 q^{64} +(3.48161e9 + 6.03032e9i) q^{65} +(1.91019e8 - 3.30855e8i) q^{66} +(-1.10439e9 + 1.91285e9i) q^{67} +(9.34601e9 + 1.61878e10i) q^{68} +7.71514e9 q^{69} +(-6.02129e8 + 2.19904e9i) q^{70} -1.34122e10 q^{71} +(-4.16535e9 - 7.21460e9i) q^{72} +(8.02494e9 - 1.38996e10i) q^{73} +(8.83897e8 - 1.53095e9i) q^{74} +(-1.16631e10 - 2.02011e10i) q^{75} +5.78919e9 q^{76} +(1.07322e9 - 3.91953e9i) q^{77} +3.24071e9 q^{78} +(-8.41954e9 - 1.45831e10i) q^{79} +(-1.79427e10 + 3.10777e10i) q^{80} +(-1.69938e10 + 2.94341e10i) q^{81} +(-3.41376e8 - 5.91281e8i) q^{82} -1.25839e10 q^{83} +(-4.61538e10 - 4.66609e10i) q^{84} +8.33059e10 q^{85} +(3.32372e9 + 5.75684e9i) q^{86} +(1.55462e10 - 2.69268e10i) q^{87} +(-1.05990e9 + 1.83580e9i) q^{88} +(3.02118e10 + 5.23283e10i) q^{89} -1.84151e10 q^{90} +(3.33455e10 - 8.73991e9i) q^{91} -2.12326e10 q^{92} +(3.87488e10 + 6.71149e10i) q^{93} +(-7.13578e8 + 1.23595e9i) q^{94} +(1.29005e10 - 2.23444e10i) q^{95} +(2.57448e10 + 4.45914e10i) q^{96} -1.39153e11 q^{97} +(9.71279e9 + 5.75010e9i) q^{98} +3.28227e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 22 q^{2} - 244 q^{3} - 2556 q^{4} - 8782 q^{5} + 38140 q^{6} - 504 q^{7} + 97008 q^{8} - 172348 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 22 q^{2} - 244 q^{3} - 2556 q^{4} - 8782 q^{5} + 38140 q^{6} - 504 q^{7} + 97008 q^{8} - 172348 q^{9} + 111546 q^{10} - 1001572 q^{11} - 173684 q^{12} + 3864504 q^{13} - 1302994 q^{14} - 1286512 q^{15} + 39120 q^{16} - 6704802 q^{17} + 3768052 q^{18} + 4192212 q^{19} - 17646776 q^{20} + 44745358 q^{21} - 8505684 q^{22} - 33871872 q^{23} - 15734760 q^{24} + 13695456 q^{25} + 29350300 q^{26} + 73859384 q^{27} + 181285692 q^{28} - 255125224 q^{29} - 336068498 q^{30} - 331783920 q^{31} + 163252640 q^{32} - 80899438 q^{33} + 1853334396 q^{34} + 1407354844 q^{35} - 2197352048 q^{36} - 833082774 q^{37} - 2086458338 q^{38} + 737605904 q^{39} - 1219023432 q^{40} + 3104076808 q^{41} + 5982095000 q^{42} - 1722177552 q^{43} - 5105122436 q^{44} - 7406493484 q^{45} + 3435559326 q^{46} - 1327587552 q^{47} + 14535793696 q^{48} + 11976558636 q^{49} - 12237094384 q^{50} - 13921261140 q^{51} - 17237001432 q^{52} + 6725755626 q^{53} - 1674595226 q^{54} + 26323921200 q^{55} + 28163516640 q^{56} - 16884487756 q^{57} - 20073189204 q^{58} - 26237179548 q^{59} + 13611677716 q^{60} - 14411013726 q^{61} + 46185665964 q^{62} + 45955779184 q^{63} - 46365999744 q^{64} - 16224702172 q^{65} - 40938633602 q^{66} - 4241860068 q^{67} - 6528332916 q^{68} + 46750854252 q^{69} + 55705143270 q^{70} - 37335334656 q^{71} - 30237166608 q^{72} + 6005568990 q^{73} + 21663581922 q^{74} + 17116276792 q^{75} - 28817353320 q^{76} - 51928077698 q^{77} + 42636498520 q^{78} + 11712395640 q^{79} + 41748525232 q^{80} - 12455008366 q^{81} + 52795921668 q^{82} - 100821781200 q^{83} - 155783007940 q^{84} + 138884613396 q^{85} + 110437384472 q^{86} + 119455310144 q^{87} - 105039956616 q^{88} - 48633519778 q^{89} - 361508123864 q^{90} - 160908361488 q^{91} + 242956324248 q^{92} + 266530114134 q^{93} + 368497095702 q^{94} - 72161225128 q^{95} + 124456168928 q^{96} - 401308415928 q^{97} - 582375436706 q^{98} + 367357472240 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.85417 + 4.94356i 0.0630688 + 0.109238i 0.895836 0.444385i \(-0.146578\pi\)
−0.832767 + 0.553624i \(0.813245\pi\)
\(3\) −366.163 + 634.213i −0.869976 + 1.50684i −0.00795684 + 0.999968i \(0.502533\pi\)
−0.862020 + 0.506875i \(0.830801\pi\)
\(4\) 1007.71 1745.40i 0.492045 0.852246i
\(5\) −4491.11 7778.83i −0.642716 1.11322i −0.984824 0.173556i \(-0.944474\pi\)
0.342108 0.939661i \(-0.388859\pi\)
\(6\) −4180.36 −0.219473
\(7\) −43014.2 + 11274.1i −0.967326 + 0.253538i
\(8\) 23195.3 0.250268
\(9\) −179577. 311037.i −1.01372 1.75581i
\(10\) 25636.8 44404.2i 0.0810706 0.140418i
\(11\) −45694.4 + 79145.1i −0.0855468 + 0.148171i −0.905624 0.424081i \(-0.860597\pi\)
0.820077 + 0.572253i \(0.193930\pi\)
\(12\) 737970. + 1.27820e6i 0.856134 + 1.48287i
\(13\) −775221. −0.579078 −0.289539 0.957166i \(-0.593502\pi\)
−0.289539 + 0.957166i \(0.593502\pi\)
\(14\) −178504. 180465.i −0.0887041 0.0896788i
\(15\) 6.57792e6 2.23659
\(16\) −1.99758e6 3.45991e6i −0.476261 0.824907i
\(17\) −4.63726e6 + 8.03198e6i −0.792123 + 1.37200i 0.132527 + 0.991179i \(0.457691\pi\)
−0.924650 + 0.380818i \(0.875642\pi\)
\(18\) 1.02509e6 1.77550e6i 0.127868 0.221474i
\(19\) 1.43623e6 + 2.48762e6i 0.133070 + 0.230483i 0.924858 0.380312i \(-0.124183\pi\)
−0.791789 + 0.610795i \(0.790850\pi\)
\(20\) −1.81029e7 −1.26498
\(21\) 8.60003e6 3.14083e7i 0.459509 1.67818i
\(22\) −521678. −0.0215813
\(23\) −5.26756e6 9.12369e6i −0.170650 0.295575i 0.767997 0.640453i \(-0.221253\pi\)
−0.938647 + 0.344879i \(0.887920\pi\)
\(24\) −8.49327e6 + 1.47108e7i −0.217728 + 0.377115i
\(25\) −1.59261e7 + 2.75848e7i −0.326167 + 0.564938i
\(26\) −2.21261e6 3.83236e6i −0.0365218 0.0632576i
\(27\) 1.33289e8 1.78769
\(28\) −2.36679e7 + 8.64380e7i −0.259891 + 0.949151i
\(29\) −4.24570e7 −0.384380 −0.192190 0.981358i \(-0.561559\pi\)
−0.192190 + 0.981358i \(0.561559\pi\)
\(30\) 1.87745e7 + 3.25184e7i 0.141059 + 0.244321i
\(31\) 5.29120e7 9.16463e7i 0.331944 0.574944i −0.650949 0.759121i \(-0.725629\pi\)
0.982893 + 0.184178i \(0.0589622\pi\)
\(32\) 3.51549e7 6.08901e7i 0.185209 0.320791i
\(33\) −3.34632e7 5.79600e7i −0.148847 0.257811i
\(34\) −5.29421e7 −0.199833
\(35\) 2.80881e8 + 2.83967e8i 0.903957 + 0.913890i
\(36\) −7.23845e8 −1.99518
\(37\) −1.54843e8 2.68196e8i −0.367099 0.635833i 0.622012 0.783008i \(-0.286315\pi\)
−0.989111 + 0.147174i \(0.952982\pi\)
\(38\) −8.19848e6 + 1.42002e7i −0.0167851 + 0.0290726i
\(39\) 2.83857e8 4.91655e8i 0.503784 0.872580i
\(40\) −1.04173e8 1.80433e8i −0.160851 0.278603i
\(41\) −1.19606e8 −0.161229 −0.0806144 0.996745i \(-0.525688\pi\)
−0.0806144 + 0.996745i \(0.525688\pi\)
\(42\) 1.79815e8 4.71298e7i 0.212302 0.0556448i
\(43\) 1.16451e9 1.20800 0.604001 0.796983i \(-0.293572\pi\)
0.604001 + 0.796983i \(0.293572\pi\)
\(44\) 9.20932e7 + 1.59510e8i 0.0841856 + 0.145814i
\(45\) −1.61300e9 + 2.79380e9i −1.30306 + 2.25697i
\(46\) 3.00690e7 5.20811e7i 0.0215254 0.0372831i
\(47\) 1.25006e8 + 2.16517e8i 0.0795048 + 0.137706i 0.903036 0.429564i \(-0.141333\pi\)
−0.823532 + 0.567270i \(0.807999\pi\)
\(48\) 2.92576e9 1.65734
\(49\) 1.72312e9 9.69892e8i 0.871437 0.490507i
\(50\) −1.81823e8 −0.0822838
\(51\) −3.39599e9 5.88203e9i −1.37826 2.38721i
\(52\) −7.81196e8 + 1.35307e9i −0.284932 + 0.493517i
\(53\) −1.73284e9 + 3.00136e9i −0.569168 + 0.985829i 0.427480 + 0.904025i \(0.359401\pi\)
−0.996648 + 0.0818038i \(0.973932\pi\)
\(54\) 3.80428e8 + 6.58921e8i 0.112747 + 0.195284i
\(55\) 8.20875e8 0.219929
\(56\) −9.97729e8 + 2.61506e8i −0.242091 + 0.0634524i
\(57\) −2.10358e9 −0.463070
\(58\) −1.21180e8 2.09889e8i −0.0242424 0.0419890i
\(59\) −3.01421e9 + 5.22077e9i −0.548893 + 0.950711i 0.449457 + 0.893302i \(0.351617\pi\)
−0.998351 + 0.0574095i \(0.981716\pi\)
\(60\) 6.62861e9 1.14811e10i 1.10050 1.90613i
\(61\) −5.31834e9 9.21163e9i −0.806236 1.39644i −0.915454 0.402423i \(-0.868168\pi\)
0.109218 0.994018i \(-0.465165\pi\)
\(62\) 6.04079e8 0.0837412
\(63\) 1.12310e10 + 1.13544e10i 1.42576 + 1.44143i
\(64\) −7.78074e9 −0.905798
\(65\) 3.48161e9 + 6.03032e9i 0.372183 + 0.644639i
\(66\) 1.91019e8 3.30855e8i 0.0187752 0.0325197i
\(67\) −1.10439e9 + 1.91285e9i −0.0999332 + 0.173089i −0.911657 0.410952i \(-0.865196\pi\)
0.811724 + 0.584042i \(0.198530\pi\)
\(68\) 9.34601e9 + 1.61878e10i 0.779520 + 1.35017i
\(69\) 7.71514e9 0.593846
\(70\) −6.02129e8 + 2.19904e9i −0.0428203 + 0.156385i
\(71\) −1.34122e10 −0.882223 −0.441111 0.897452i \(-0.645416\pi\)
−0.441111 + 0.897452i \(0.645416\pi\)
\(72\) −4.16535e9 7.21460e9i −0.253701 0.439424i
\(73\) 8.02494e9 1.38996e10i 0.453071 0.784742i −0.545504 0.838108i \(-0.683662\pi\)
0.998575 + 0.0533664i \(0.0169951\pi\)
\(74\) 8.83897e8 1.53095e9i 0.0463049 0.0802025i
\(75\) −1.16631e10 2.02011e10i −0.567515 0.982965i
\(76\) 5.78919e9 0.261905
\(77\) 1.07322e9 3.91953e9i 0.0451846 0.165019i
\(78\) 3.24071e9 0.127092
\(79\) −8.41954e9 1.45831e10i −0.307850 0.533212i 0.670042 0.742323i \(-0.266276\pi\)
−0.977892 + 0.209111i \(0.932943\pi\)
\(80\) −1.79427e10 + 3.10777e10i −0.612200 + 1.06036i
\(81\) −1.69938e10 + 2.94341e10i −0.541530 + 0.937958i
\(82\) −3.41376e8 5.91281e8i −0.0101685 0.0176124i
\(83\) −1.25839e10 −0.350659 −0.175329 0.984510i \(-0.556099\pi\)
−0.175329 + 0.984510i \(0.556099\pi\)
\(84\) −4.61538e10 4.66609e10i −1.20412 1.21735i
\(85\) 8.33059e10 2.03644
\(86\) 3.32372e9 + 5.75684e9i 0.0761873 + 0.131960i
\(87\) 1.55462e10 2.69268e10i 0.334402 0.579200i
\(88\) −1.05990e9 + 1.83580e9i −0.0214096 + 0.0370826i
\(89\) 3.02118e10 + 5.23283e10i 0.573497 + 0.993326i 0.996203 + 0.0870594i \(0.0277470\pi\)
−0.422706 + 0.906267i \(0.638920\pi\)
\(90\) −1.84151e10 −0.328731
\(91\) 3.33455e10 8.73991e9i 0.560157 0.146818i
\(92\) −2.12326e10 −0.335870
\(93\) 3.87488e10 + 6.71149e10i 0.577567 + 1.00038i
\(94\) −7.13578e8 + 1.23595e9i −0.0100286 + 0.0173700i
\(95\) 1.29005e10 2.23444e10i 0.171052 0.296270i
\(96\) 2.57448e10 + 4.45914e10i 0.322254 + 0.558160i
\(97\) −1.39153e11 −1.64531 −0.822654 0.568542i \(-0.807508\pi\)
−0.822654 + 0.568542i \(0.807508\pi\)
\(98\) 9.71279e9 + 5.75010e9i 0.108543 + 0.0642587i
\(99\) 3.28227e10 0.346881
\(100\) 3.20977e10 + 5.55949e10i 0.320977 + 0.555949i
\(101\) 7.27138e10 1.25944e11i 0.688413 1.19237i −0.283938 0.958843i \(-0.591641\pi\)
0.972351 0.233524i \(-0.0750258\pi\)
\(102\) 1.93854e10 3.35766e10i 0.173850 0.301117i
\(103\) −9.52360e10 1.64954e11i −0.809462 1.40203i −0.913237 0.407429i \(-0.866425\pi\)
0.103775 0.994601i \(-0.466908\pi\)
\(104\) −1.79815e10 −0.144925
\(105\) −2.82944e11 + 7.41600e10i −2.16351 + 0.567060i
\(106\) −1.97833e10 −0.143587
\(107\) 2.98014e10 + 5.16176e10i 0.205412 + 0.355785i 0.950264 0.311445i \(-0.100813\pi\)
−0.744852 + 0.667230i \(0.767480\pi\)
\(108\) 1.34316e11 2.32642e11i 0.879623 1.52355i
\(109\) −7.38720e10 + 1.27950e11i −0.459869 + 0.796517i −0.998954 0.0457350i \(-0.985437\pi\)
0.539084 + 0.842252i \(0.318770\pi\)
\(110\) 2.34292e9 + 4.05805e9i 0.0138707 + 0.0240247i
\(111\) 2.26791e11 1.27747
\(112\) 1.24932e11 + 1.26304e11i 0.669844 + 0.677204i
\(113\) −2.11327e11 −1.07901 −0.539503 0.841984i \(-0.681388\pi\)
−0.539503 + 0.841984i \(0.681388\pi\)
\(114\) −6.00396e9 1.03992e10i −0.0292052 0.0505850i
\(115\) −4.73144e10 + 8.19510e10i −0.219359 + 0.379941i
\(116\) −4.27843e10 + 7.41046e10i −0.189132 + 0.327586i
\(117\) 1.39212e11 + 2.41122e11i 0.587022 + 1.01675i
\(118\) −3.44123e10 −0.138472
\(119\) 1.08915e11 3.97770e11i 0.418388 1.52800i
\(120\) 1.52577e11 0.559748
\(121\) 1.38480e11 + 2.39854e11i 0.485364 + 0.840674i
\(122\) 3.03589e10 5.25831e10i 0.101697 0.176144i
\(123\) 4.37954e10 7.58558e10i 0.140265 0.242946i
\(124\) −1.06640e11 1.84705e11i −0.326663 0.565796i
\(125\) −1.52481e11 −0.446901
\(126\) −2.40761e10 + 8.79287e10i −0.0675380 + 0.246657i
\(127\) 3.51747e11 0.944735 0.472367 0.881402i \(-0.343400\pi\)
0.472367 + 0.881402i \(0.343400\pi\)
\(128\) −9.42048e10 1.63167e11i −0.242336 0.419738i
\(129\) −4.26401e11 + 7.38549e11i −1.05093 + 1.82027i
\(130\) −1.98742e10 + 3.44231e10i −0.0469462 + 0.0813132i
\(131\) 2.15308e10 + 3.72924e10i 0.0487604 + 0.0844556i 0.889375 0.457177i \(-0.151140\pi\)
−0.840615 + 0.541633i \(0.817806\pi\)
\(132\) −1.34885e11 −0.292958
\(133\) −8.98239e10 9.08109e10i −0.187158 0.189214i
\(134\) −1.26084e10 −0.0252107
\(135\) −5.98614e11 1.03683e12i −1.14898 1.99009i
\(136\) −1.07563e11 + 1.86304e11i −0.198243 + 0.343368i
\(137\) 4.92302e11 8.52692e11i 0.871502 1.50949i 0.0110587 0.999939i \(-0.496480\pi\)
0.860443 0.509547i \(-0.170187\pi\)
\(138\) 2.20203e10 + 3.81403e10i 0.0374532 + 0.0648708i
\(139\) −7.31783e10 −0.119619 −0.0598096 0.998210i \(-0.519049\pi\)
−0.0598096 + 0.998210i \(0.519049\pi\)
\(140\) 7.78682e11 2.04094e11i 1.22365 0.320720i
\(141\) −1.83091e11 −0.276669
\(142\) −3.82806e10 6.63040e10i −0.0556407 0.0963726i
\(143\) 3.54233e10 6.13549e10i 0.0495383 0.0858028i
\(144\) −7.17440e11 + 1.24264e12i −0.965588 + 1.67245i
\(145\) 1.90679e11 + 3.30266e11i 0.247047 + 0.427898i
\(146\) 9.16181e10 0.114299
\(147\) −1.58233e10 + 1.44796e12i −0.0190130 + 1.73985i
\(148\) −6.24147e11 −0.722515
\(149\) 2.21679e11 + 3.83960e11i 0.247287 + 0.428313i 0.962772 0.270314i \(-0.0871277\pi\)
−0.715485 + 0.698628i \(0.753794\pi\)
\(150\) 6.65769e10 1.15315e11i 0.0715850 0.123989i
\(151\) 6.38440e11 1.10581e12i 0.661830 1.14632i −0.318304 0.947989i \(-0.603113\pi\)
0.980134 0.198335i \(-0.0635534\pi\)
\(152\) 3.33138e10 + 5.77012e10i 0.0333031 + 0.0576827i
\(153\) 3.33099e12 3.21196
\(154\) 2.24396e10 5.88145e9i 0.0208762 0.00547168i
\(155\) −9.50535e11 −0.853382
\(156\) −5.72090e11 9.90889e11i −0.495769 0.858697i
\(157\) −4.66854e11 + 8.08615e11i −0.390601 + 0.676541i −0.992529 0.122010i \(-0.961066\pi\)
0.601928 + 0.798550i \(0.294399\pi\)
\(158\) 4.80616e10 8.32451e10i 0.0388315 0.0672581i
\(159\) −1.26900e12 2.19798e12i −0.990326 1.71530i
\(160\) −6.31538e11 −0.476146
\(161\) 3.29441e11 + 3.33061e11i 0.240014 + 0.242651i
\(162\) −1.94013e11 −0.136615
\(163\) 1.23921e12 + 2.14638e12i 0.843556 + 1.46108i 0.886869 + 0.462020i \(0.152875\pi\)
−0.0433132 + 0.999062i \(0.513791\pi\)
\(164\) −1.20528e11 + 2.08761e11i −0.0793317 + 0.137407i
\(165\) −3.00574e11 + 5.20610e11i −0.191333 + 0.331398i
\(166\) −3.59165e10 6.22092e10i −0.0221156 0.0383054i
\(167\) −2.38715e12 −1.42213 −0.711065 0.703126i \(-0.751787\pi\)
−0.711065 + 0.703126i \(0.751787\pi\)
\(168\) 1.99481e11 7.28527e11i 0.115001 0.419995i
\(169\) −1.19119e12 −0.664669
\(170\) 2.37769e11 + 4.11828e11i 0.128436 + 0.222457i
\(171\) 5.15828e11 8.93440e11i 0.269790 0.467290i
\(172\) 1.17349e12 2.03254e12i 0.594391 1.02952i
\(173\) −2.71347e11 4.69988e11i −0.133129 0.230586i 0.791752 0.610842i \(-0.209169\pi\)
−0.924881 + 0.380256i \(0.875836\pi\)
\(174\) 1.77486e11 0.0843612
\(175\) 3.74055e11 1.36609e12i 0.172277 0.629174i
\(176\) 3.65113e11 0.162970
\(177\) −2.20739e12 3.82331e12i −0.955049 1.65419i
\(178\) −1.72459e11 + 2.98708e11i −0.0723396 + 0.125296i
\(179\) −1.65743e12 + 2.87075e12i −0.674128 + 1.16762i 0.302594 + 0.953119i \(0.402147\pi\)
−0.976723 + 0.214505i \(0.931186\pi\)
\(180\) 3.25087e12 + 5.63067e12i 1.28233 + 2.22106i
\(181\) −7.57463e11 −0.289821 −0.144910 0.989445i \(-0.546289\pi\)
−0.144910 + 0.989445i \(0.546289\pi\)
\(182\) 1.38380e11 + 1.39901e11i 0.0513666 + 0.0519310i
\(183\) 7.78952e12 2.80562
\(184\) −1.22183e11 2.11627e11i −0.0427083 0.0739730i
\(185\) −1.39084e12 + 2.40900e12i −0.471880 + 0.817320i
\(186\) −2.21191e11 + 3.83115e11i −0.0728529 + 0.126185i
\(187\) −4.23794e11 7.34033e11i −0.135527 0.234740i
\(188\) 5.03879e11 0.156480
\(189\) −5.73330e12 + 1.50271e12i −1.72928 + 0.453247i
\(190\) 1.47281e11 0.0431521
\(191\) 2.41197e12 + 4.17765e12i 0.686575 + 1.18918i 0.972939 + 0.231062i \(0.0742199\pi\)
−0.286364 + 0.958121i \(0.592447\pi\)
\(192\) 2.84902e12 4.93465e12i 0.788022 1.36489i
\(193\) 3.50989e11 6.07931e11i 0.0943471 0.163414i −0.814989 0.579477i \(-0.803257\pi\)
0.909336 + 0.416063i \(0.136590\pi\)
\(194\) −3.97166e11 6.87911e11i −0.103768 0.179731i
\(195\) −5.09934e12 −1.29516
\(196\) 4.35469e10 3.98490e12i 0.0107535 0.984031i
\(197\) 3.47030e12 0.833302 0.416651 0.909066i \(-0.363204\pi\)
0.416651 + 0.909066i \(0.363204\pi\)
\(198\) 9.36815e10 + 1.62261e11i 0.0218774 + 0.0378927i
\(199\) 1.44819e12 2.50834e12i 0.328953 0.569764i −0.653351 0.757055i \(-0.726637\pi\)
0.982304 + 0.187291i \(0.0599708\pi\)
\(200\) −3.69412e11 + 6.39840e11i −0.0816292 + 0.141386i
\(201\) −8.08771e11 1.40083e12i −0.173879 0.301167i
\(202\) 8.30150e11 0.173670
\(203\) 1.82626e12 4.78665e11i 0.371821 0.0974548i
\(204\) −1.36887e13 −2.71266
\(205\) 5.37165e11 + 9.30397e11i 0.103624 + 0.179482i
\(206\) 5.43639e11 9.41611e11i 0.102104 0.176849i
\(207\) −1.89187e12 + 3.27681e12i −0.345982 + 0.599259i
\(208\) 1.54857e12 + 2.68220e12i 0.275792 + 0.477686i
\(209\) −2.62511e11 −0.0455347
\(210\) −1.17418e12 1.18709e12i −0.198395 0.200575i
\(211\) −2.99203e10 −0.00492508 −0.00246254 0.999997i \(-0.500784\pi\)
−0.00246254 + 0.999997i \(0.500784\pi\)
\(212\) 3.49239e12 + 6.04899e12i 0.560113 + 0.970143i
\(213\) 4.91104e12 8.50617e12i 0.767513 1.32937i
\(214\) −1.70117e11 + 2.94651e11i −0.0259102 + 0.0448778i
\(215\) −5.22996e12 9.05855e12i −0.776402 1.34477i
\(216\) 3.09167e12 0.447402
\(217\) −1.24274e12 + 4.53863e12i −0.175328 + 0.640318i
\(218\) −8.43373e11 −0.116014
\(219\) 5.87687e12 + 1.01790e13i 0.788322 + 1.36541i
\(220\) 8.27202e11 1.43276e12i 0.108215 0.187434i
\(221\) 3.59491e12 6.22656e12i 0.458701 0.794494i
\(222\) 6.47301e11 + 1.12116e12i 0.0805684 + 0.139549i
\(223\) −2.52256e12 −0.306312 −0.153156 0.988202i \(-0.548944\pi\)
−0.153156 + 0.988202i \(0.548944\pi\)
\(224\) −8.25680e11 + 3.01548e12i −0.0978245 + 0.357266i
\(225\) 1.14399e13 1.32256
\(226\) −6.03163e11 1.04471e12i −0.0680516 0.117869i
\(227\) −6.08276e12 + 1.05356e13i −0.669820 + 1.16016i 0.308134 + 0.951343i \(0.400296\pi\)
−0.977954 + 0.208820i \(0.933038\pi\)
\(228\) −2.11979e12 + 3.67158e12i −0.227851 + 0.394649i
\(229\) 2.17759e12 + 3.77170e12i 0.228497 + 0.395769i 0.957363 0.288888i \(-0.0932854\pi\)
−0.728866 + 0.684657i \(0.759952\pi\)
\(230\) −5.40173e11 −0.0553388
\(231\) 2.09284e12 + 2.11584e12i 0.209349 + 0.211649i
\(232\) −9.84806e11 −0.0961981
\(233\) −8.54463e12 1.47997e13i −0.815147 1.41188i −0.909222 0.416311i \(-0.863323\pi\)
0.0940755 0.995565i \(-0.470010\pi\)
\(234\) −7.94669e11 + 1.37641e12i −0.0740455 + 0.128251i
\(235\) 1.12283e12 1.94481e12i 0.102198 0.177012i
\(236\) 6.07489e12 + 1.05220e13i 0.540160 + 0.935585i
\(237\) 1.23317e13 1.07129
\(238\) 2.27726e12 5.96875e11i 0.193304 0.0506652i
\(239\) −3.04856e11 −0.0252876 −0.0126438 0.999920i \(-0.504025\pi\)
−0.0126438 + 0.999920i \(0.504025\pi\)
\(240\) −1.31399e13 2.27590e13i −1.06520 1.84498i
\(241\) −8.33995e11 + 1.44452e12i −0.0660800 + 0.114454i −0.897173 0.441680i \(-0.854383\pi\)
0.831093 + 0.556134i \(0.187716\pi\)
\(242\) −7.90490e11 + 1.36917e12i −0.0612226 + 0.106041i
\(243\) −6.39156e11 1.10705e12i −0.0483919 0.0838172i
\(244\) −2.14373e13 −1.58682
\(245\) −1.52833e13 9.04794e12i −1.10613 0.654842i
\(246\) 4.99997e11 0.0353854
\(247\) −1.11339e12 1.92846e12i −0.0770577 0.133468i
\(248\) 1.22731e12 2.12577e12i 0.0830751 0.143890i
\(249\) 4.60775e12 7.98085e12i 0.305065 0.528388i
\(250\) −4.35207e11 7.53801e11i −0.0281855 0.0488187i
\(251\) 1.29045e13 0.817590 0.408795 0.912626i \(-0.365949\pi\)
0.408795 + 0.912626i \(0.365949\pi\)
\(252\) 3.11356e13 8.16069e12i 1.92999 0.505853i
\(253\) 9.62793e11 0.0583943
\(254\) 1.00395e12 + 1.73888e12i 0.0595833 + 0.103201i
\(255\) −3.05035e13 + 5.28337e13i −1.77166 + 3.06860i
\(256\) −7.42973e12 + 1.28687e13i −0.422331 + 0.731499i
\(257\) −1.15462e13 1.99986e13i −0.642402 1.11267i −0.984895 0.173152i \(-0.944605\pi\)
0.342493 0.939520i \(-0.388729\pi\)
\(258\) −4.86809e12 −0.265124
\(259\) 9.68413e12 + 9.79053e12i 0.516311 + 0.521985i
\(260\) 1.40338e13 0.732522
\(261\) 7.62431e12 + 1.32057e13i 0.389653 + 0.674899i
\(262\) −1.22905e11 + 2.12878e11i −0.00615053 + 0.0106530i
\(263\) 1.41565e13 2.45199e13i 0.693746 1.20160i −0.276855 0.960912i \(-0.589292\pi\)
0.970601 0.240692i \(-0.0773744\pi\)
\(264\) −7.76191e11 1.34440e12i −0.0372518 0.0645219i
\(265\) 3.11295e13 1.46325
\(266\) 1.92557e11 7.03240e11i 0.00886564 0.0323783i
\(267\) −4.42497e13 −1.99572
\(268\) 2.22580e12 + 3.85519e12i 0.0983432 + 0.170335i
\(269\) 1.38564e13 2.39999e13i 0.599807 1.03890i −0.393042 0.919521i \(-0.628577\pi\)
0.992849 0.119376i \(-0.0380894\pi\)
\(270\) 3.41709e12 5.91857e12i 0.144929 0.251025i
\(271\) 2.41659e12 + 4.18566e12i 0.100432 + 0.173954i 0.911863 0.410495i \(-0.134644\pi\)
−0.811431 + 0.584449i \(0.801311\pi\)
\(272\) 3.70533e13 1.50903
\(273\) −6.66693e12 + 2.43484e13i −0.266092 + 0.971797i
\(274\) 5.62045e12 0.219858
\(275\) −1.45547e12 2.52095e12i −0.0558050 0.0966572i
\(276\) 7.77461e12 1.34660e13i 0.292199 0.506103i
\(277\) −1.89204e13 + 3.27711e13i −0.697094 + 1.20740i 0.272376 + 0.962191i \(0.412191\pi\)
−0.969470 + 0.245211i \(0.921143\pi\)
\(278\) −2.08863e11 3.61762e11i −0.00754424 0.0130670i
\(279\) −3.80071e13 −1.34599
\(280\) 6.51513e12 + 6.58671e12i 0.226232 + 0.228718i
\(281\) −3.89411e13 −1.32594 −0.662969 0.748647i \(-0.730704\pi\)
−0.662969 + 0.748647i \(0.730704\pi\)
\(282\) −5.22572e11 9.05120e11i −0.0174492 0.0302229i
\(283\) 1.01150e13 1.75197e13i 0.331238 0.573722i −0.651516 0.758634i \(-0.725867\pi\)
0.982755 + 0.184913i \(0.0592002\pi\)
\(284\) −1.35156e13 + 2.34096e13i −0.434093 + 0.751871i
\(285\) 9.44739e12 + 1.63634e13i 0.297622 + 0.515497i
\(286\) 4.04416e11 0.0124973
\(287\) 5.14477e12 1.34845e12i 0.155961 0.0408776i
\(288\) −2.52521e13 −0.750997
\(289\) −2.58725e13 4.48125e13i −0.754919 1.30756i
\(290\) −1.08846e12 + 1.88527e12i −0.0311619 + 0.0539740i
\(291\) 5.09526e13 8.82525e13i 1.43138 2.47922i
\(292\) −1.61736e13 2.80135e13i −0.445862 0.772256i
\(293\) 1.09986e13 0.297554 0.148777 0.988871i \(-0.452466\pi\)
0.148777 + 0.988871i \(0.452466\pi\)
\(294\) −7.20325e12 + 4.05450e12i −0.191257 + 0.107653i
\(295\) 5.41487e13 1.41113
\(296\) −3.59164e12 6.22090e12i −0.0918731 0.159129i
\(297\) −6.09055e12 + 1.05491e13i −0.152931 + 0.264884i
\(298\) −1.26542e12 + 2.19177e12i −0.0311922 + 0.0540264i
\(299\) 4.08353e12 + 7.07287e12i 0.0988197 + 0.171161i
\(300\) −4.70120e13 −1.11697
\(301\) −5.00906e13 + 1.31288e13i −1.16853 + 0.306274i
\(302\) 7.28886e12 0.166963
\(303\) 5.32502e13 + 9.22321e13i 1.19781 + 2.07466i
\(304\) 5.73797e12 9.93845e12i 0.126752 0.219540i
\(305\) −4.77705e13 + 8.27410e13i −1.03636 + 1.79503i
\(306\) 9.50719e12 + 1.64669e13i 0.202574 + 0.350869i
\(307\) −1.77123e13 −0.370692 −0.185346 0.982673i \(-0.559341\pi\)
−0.185346 + 0.982673i \(0.559341\pi\)
\(308\) −5.75965e12 5.82293e12i −0.118404 0.119705i
\(309\) 1.39488e14 2.81685
\(310\) −2.71299e12 4.69903e12i −0.0538218 0.0932221i
\(311\) −7.97859e12 + 1.38193e13i −0.155505 + 0.269342i −0.933243 0.359246i \(-0.883034\pi\)
0.777738 + 0.628589i \(0.216367\pi\)
\(312\) 6.58417e12 1.14041e13i 0.126081 0.218379i
\(313\) 1.52684e13 + 2.64456e13i 0.287276 + 0.497577i 0.973159 0.230136i \(-0.0739169\pi\)
−0.685882 + 0.727712i \(0.740584\pi\)
\(314\) −5.32992e12 −0.0985389
\(315\) 3.78844e13 1.38358e14i 0.688260 2.51360i
\(316\) −3.39377e13 −0.605904
\(317\) −1.70577e13 2.95449e13i −0.299292 0.518390i 0.676682 0.736276i \(-0.263417\pi\)
−0.975974 + 0.217886i \(0.930084\pi\)
\(318\) 7.24389e12 1.25468e13i 0.124917 0.216363i
\(319\) 1.94005e12 3.36027e12i 0.0328825 0.0569541i
\(320\) 3.49442e13 + 6.05251e13i 0.582170 + 1.00835i
\(321\) −4.36487e13 −0.714816
\(322\) −7.06228e11 + 2.57923e12i −0.0113694 + 0.0415224i
\(323\) −2.66407e13 −0.421630
\(324\) 3.42495e13 + 5.93219e13i 0.532914 + 0.923034i
\(325\) 1.23463e13 2.13844e13i 0.188876 0.327143i
\(326\) −7.07384e12 + 1.22523e13i −0.106404 + 0.184297i
\(327\) −5.40984e13 9.37012e13i −0.800151 1.38590i
\(328\) −2.77431e12 −0.0403504
\(329\) −7.81808e12 7.90398e12i −0.111821 0.113049i
\(330\) −3.43156e12 −0.0482686
\(331\) 1.39115e13 + 2.40955e13i 0.192451 + 0.333335i 0.946062 0.323986i \(-0.105023\pi\)
−0.753611 + 0.657321i \(0.771690\pi\)
\(332\) −1.26809e13 + 2.19639e13i −0.172540 + 0.298848i
\(333\) −5.56126e13 + 9.63238e13i −0.744269 + 1.28911i
\(334\) −6.81333e12 1.18010e13i −0.0896920 0.155351i
\(335\) 1.98397e13 0.256914
\(336\) −1.25849e14 + 3.29853e13i −1.60319 + 0.420198i
\(337\) 8.74273e12 0.109568 0.0547839 0.998498i \(-0.482553\pi\)
0.0547839 + 0.998498i \(0.482553\pi\)
\(338\) −3.39986e12 5.88874e12i −0.0419199 0.0726073i
\(339\) 7.73801e13 1.34026e14i 0.938709 1.62589i
\(340\) 8.39480e13 1.45402e14i 1.00202 1.73555i
\(341\) 4.83557e12 + 8.37545e12i 0.0567935 + 0.0983692i
\(342\) 5.88904e12 0.0680614
\(343\) −6.31838e13 + 6.11457e13i −0.718602 + 0.695422i
\(344\) 2.70113e13 0.302325
\(345\) −3.46496e13 6.00148e13i −0.381674 0.661079i
\(346\) 1.54894e12 2.68285e12i 0.0167926 0.0290856i
\(347\) −5.57163e13 + 9.65034e13i −0.594525 + 1.02975i 0.399089 + 0.916912i \(0.369326\pi\)
−0.993614 + 0.112835i \(0.964007\pi\)
\(348\) −3.13320e13 5.42687e13i −0.329081 0.569985i
\(349\) 2.49619e13 0.258070 0.129035 0.991640i \(-0.458812\pi\)
0.129035 + 0.991640i \(0.458812\pi\)
\(350\) 7.82098e12 2.04989e12i 0.0795952 0.0208620i
\(351\) −1.03328e14 −1.03521
\(352\) 3.21277e12 + 5.56467e12i 0.0316880 + 0.0548852i
\(353\) 4.46527e13 7.73407e13i 0.433597 0.751012i −0.563583 0.826060i \(-0.690577\pi\)
0.997180 + 0.0750472i \(0.0239107\pi\)
\(354\) 1.26005e13 2.18247e13i 0.120468 0.208656i
\(355\) 6.02356e13 + 1.04331e14i 0.567019 + 0.982105i
\(356\) 1.21779e14 1.12874
\(357\) 2.12390e14 + 2.14724e14i 1.93847 + 1.95977i
\(358\) −1.89223e13 −0.170066
\(359\) 8.39570e13 + 1.45418e14i 0.743083 + 1.28706i 0.951085 + 0.308929i \(0.0999707\pi\)
−0.208002 + 0.978128i \(0.566696\pi\)
\(360\) −3.74141e13 + 6.48032e13i −0.326116 + 0.564849i
\(361\) 5.41196e13 9.37379e13i 0.464585 0.804685i
\(362\) −2.16193e12 3.74457e12i −0.0182786 0.0316595i
\(363\) −2.02825e14 −1.68902
\(364\) 1.83479e13 6.70086e13i 0.150497 0.549633i
\(365\) −1.44164e14 −1.16478
\(366\) 2.22326e13 + 3.85080e13i 0.176947 + 0.306482i
\(367\) −1.03952e13 + 1.80050e13i −0.0815021 + 0.141166i −0.903895 0.427754i \(-0.859305\pi\)
0.822393 + 0.568919i \(0.192638\pi\)
\(368\) −2.10448e13 + 3.64506e13i −0.162548 + 0.281541i
\(369\) 2.14785e13 + 3.72019e13i 0.163440 + 0.283087i
\(370\) −1.58787e13 −0.119044
\(371\) 4.06990e13 1.48637e14i 0.300627 1.09792i
\(372\) 1.56190e14 1.13675
\(373\) −6.86233e13 1.18859e14i −0.492122 0.852381i 0.507836 0.861454i \(-0.330445\pi\)
−0.999959 + 0.00907250i \(0.997112\pi\)
\(374\) 2.41916e12 4.19011e12i 0.0170951 0.0296095i
\(375\) 5.58330e13 9.67056e13i 0.388793 0.673410i
\(376\) 2.89956e12 + 5.02219e12i 0.0198975 + 0.0344635i
\(377\) 3.29136e13 0.222586
\(378\) −2.37925e13 2.40540e13i −0.158575 0.160318i
\(379\) −5.43469e12 −0.0356992 −0.0178496 0.999841i \(-0.505682\pi\)
−0.0178496 + 0.999841i \(0.505682\pi\)
\(380\) −2.59999e13 4.50332e13i −0.168330 0.291557i
\(381\) −1.28797e14 + 2.23082e14i −0.821897 + 1.42357i
\(382\) −1.37683e13 + 2.38474e13i −0.0866029 + 0.150001i
\(383\) −1.10671e14 1.91687e14i −0.686183 1.18850i −0.973063 0.230537i \(-0.925952\pi\)
0.286881 0.957966i \(-0.407382\pi\)
\(384\) 1.37977e14 0.843307
\(385\) −3.53093e13 + 9.25462e12i −0.212743 + 0.0557603i
\(386\) 4.00713e12 0.0238014
\(387\) −2.09120e14 3.62206e14i −1.22457 2.12102i
\(388\) −1.40225e14 + 2.42877e14i −0.809565 + 1.40221i
\(389\) −5.67324e13 + 9.82634e13i −0.322930 + 0.559331i −0.981091 0.193546i \(-0.938001\pi\)
0.658161 + 0.752877i \(0.271334\pi\)
\(390\) −1.45544e13 2.52089e13i −0.0816842 0.141481i
\(391\) 9.77083e13 0.540704
\(392\) 3.99683e13 2.24970e13i 0.218093 0.122758i
\(393\) −3.15351e13 −0.169682
\(394\) 9.90481e12 + 1.71556e13i 0.0525554 + 0.0910286i
\(395\) −7.56262e13 + 1.30988e14i −0.395720 + 0.685407i
\(396\) 3.30757e13 5.72887e13i 0.170681 0.295628i
\(397\) 6.27094e13 + 1.08616e14i 0.319143 + 0.552771i 0.980309 0.197468i \(-0.0632718\pi\)
−0.661167 + 0.750239i \(0.729938\pi\)
\(398\) 1.65335e13 0.0829868
\(399\) 9.04836e13 2.37159e13i 0.447939 0.117406i
\(400\) 1.27255e14 0.621362
\(401\) 2.01310e13 + 3.48679e13i 0.0969552 + 0.167931i 0.910423 0.413679i \(-0.135756\pi\)
−0.813468 + 0.581610i \(0.802423\pi\)
\(402\) 4.61674e12 7.99642e12i 0.0219327 0.0379885i
\(403\) −4.10185e13 + 7.10461e13i −0.192222 + 0.332937i
\(404\) −1.46548e14 2.53829e14i −0.677460 1.17340i
\(405\) 3.05284e14 1.39220
\(406\) 7.57875e12 + 7.66202e12i 0.0340961 + 0.0344707i
\(407\) 2.83019e13 0.125616
\(408\) −7.87711e13 1.36436e14i −0.344934 0.597443i
\(409\) 9.79564e13 1.69665e14i 0.423209 0.733019i −0.573043 0.819525i \(-0.694237\pi\)
0.996251 + 0.0865068i \(0.0275704\pi\)
\(410\) −3.06632e12 + 5.31102e12i −0.0130709 + 0.0226395i
\(411\) 3.60525e14 + 6.24448e14i 1.51637 + 2.62643i
\(412\) −3.83880e14 −1.59317
\(413\) 7.07945e13 2.58550e14i 0.289918 1.05881i
\(414\) −2.15988e13 −0.0872827
\(415\) 5.65156e13 + 9.78878e13i 0.225374 + 0.390359i
\(416\) −2.72528e13 + 4.72033e13i −0.107250 + 0.185763i
\(417\) 2.67952e13 4.64106e13i 0.104066 0.180247i
\(418\) −7.49250e11 1.29774e12i −0.00287182 0.00497414i
\(419\) 3.11107e14 1.17688 0.588441 0.808541i \(-0.299742\pi\)
0.588441 + 0.808541i \(0.299742\pi\)
\(420\) −1.55686e14 + 5.68582e14i −0.581269 + 2.12286i
\(421\) −3.15409e14 −1.16231 −0.581155 0.813793i \(-0.697399\pi\)
−0.581155 + 0.813793i \(0.697399\pi\)
\(422\) −8.53977e10 1.47913e11i −0.000310619 0.000538008i
\(423\) 4.48965e13 7.77631e13i 0.161191 0.279191i
\(424\) −4.01938e13 + 6.96177e13i −0.142445 + 0.246722i
\(425\) −1.47707e14 2.55836e14i −0.516729 0.895001i
\(426\) 5.60678e13 0.193625
\(427\) 3.32617e14 + 3.36272e14i 1.13394 + 1.14640i
\(428\) 1.20125e14 0.404288
\(429\) 2.59414e13 + 4.49318e13i 0.0861942 + 0.149293i
\(430\) 2.98544e13 5.17093e13i 0.0979335 0.169626i
\(431\) 2.45551e14 4.25307e14i 0.795274 1.37746i −0.127391 0.991853i \(-0.540660\pi\)
0.922665 0.385603i \(-0.126006\pi\)
\(432\) −2.66255e14 4.61167e14i −0.851406 1.47468i
\(433\) −4.66688e14 −1.47348 −0.736739 0.676178i \(-0.763635\pi\)
−0.736739 + 0.676178i \(0.763635\pi\)
\(434\) −2.59840e13 + 6.81044e12i −0.0810050 + 0.0212316i
\(435\) −2.79279e14 −0.859700
\(436\) 1.48883e14 + 2.57873e14i 0.452552 + 0.783844i
\(437\) 1.51309e13 2.62074e13i 0.0454167 0.0786640i
\(438\) −3.35472e13 + 5.81054e13i −0.0994370 + 0.172230i
\(439\) −1.39073e14 2.40882e14i −0.407088 0.705098i 0.587474 0.809243i \(-0.300123\pi\)
−0.994562 + 0.104145i \(0.966789\pi\)
\(440\) 1.90405e13 0.0550412
\(441\) −6.11104e14 3.61782e14i −1.74463 1.03284i
\(442\) 4.10419e13 0.115719
\(443\) 2.19620e14 + 3.80393e14i 0.611578 + 1.05928i 0.990975 + 0.134049i \(0.0427981\pi\)
−0.379397 + 0.925234i \(0.623869\pi\)
\(444\) 2.28539e14 3.95842e14i 0.628571 1.08872i
\(445\) 2.71369e14 4.70025e14i 0.737191 1.27685i
\(446\) −7.19980e12 1.24704e13i −0.0193187 0.0334611i
\(447\) −3.24683e14 −0.860535
\(448\) 3.34682e14 8.77208e13i 0.876201 0.229654i
\(449\) −8.42239e13 −0.217811 −0.108906 0.994052i \(-0.534735\pi\)
−0.108906 + 0.994052i \(0.534735\pi\)
\(450\) 3.26513e13 + 5.65537e13i 0.0834126 + 0.144475i
\(451\) 5.46534e12 9.46624e12i 0.0137926 0.0238895i
\(452\) −2.12956e14 + 3.68850e14i −0.530919 + 0.919578i
\(453\) 4.67546e14 + 8.09813e14i 1.15155 + 1.99455i
\(454\) −6.94449e13 −0.168979
\(455\) −2.17745e14 2.20137e14i −0.523462 0.529214i
\(456\) −4.87931e13 −0.115892
\(457\) −9.06110e13 1.56943e14i −0.212638 0.368300i 0.739901 0.672716i \(-0.234872\pi\)
−0.952539 + 0.304415i \(0.901539\pi\)
\(458\) −1.24304e13 + 2.15301e13i −0.0288221 + 0.0499214i
\(459\) −6.18094e14 + 1.07057e15i −1.41607 + 2.45271i
\(460\) 9.53582e13 + 1.65165e14i 0.215869 + 0.373896i
\(461\) 2.32317e14 0.519668 0.259834 0.965653i \(-0.416332\pi\)
0.259834 + 0.965653i \(0.416332\pi\)
\(462\) −4.48645e12 + 1.63850e13i −0.00991681 + 0.0362173i
\(463\) 4.85865e14 1.06126 0.530628 0.847605i \(-0.321956\pi\)
0.530628 + 0.847605i \(0.321956\pi\)
\(464\) 8.48114e13 + 1.46898e14i 0.183065 + 0.317078i
\(465\) 3.48051e14 6.02841e14i 0.742423 1.28591i
\(466\) 4.87756e13 8.44819e13i 0.102821 0.178091i
\(467\) −4.71057e13 8.15895e13i −0.0981365 0.169977i 0.812777 0.582575i \(-0.197955\pi\)
−0.910913 + 0.412598i \(0.864622\pi\)
\(468\) 5.61140e14 1.15536
\(469\) 2.59386e13 9.47308e13i 0.0527832 0.192771i
\(470\) 1.28190e13 0.0257820
\(471\) −3.41889e14 5.92170e14i −0.679627 1.17715i
\(472\) −6.99157e13 + 1.21098e14i −0.137371 + 0.237933i
\(473\) −5.32118e13 + 9.21655e13i −0.103341 + 0.178991i
\(474\) 3.51967e13 + 6.09625e13i 0.0675649 + 0.117026i
\(475\) −9.14942e13 −0.173612
\(476\) −5.84514e14 5.90936e14i −1.09637 1.10841i
\(477\) 1.24471e15 2.30790
\(478\) −8.70111e11 1.50708e12i −0.00159486 0.00276237i
\(479\) −3.21363e14 + 5.56617e14i −0.582305 + 1.00858i 0.412900 + 0.910776i \(0.364516\pi\)
−0.995205 + 0.0978061i \(0.968817\pi\)
\(480\) 2.31246e14 4.00530e14i 0.414235 0.717477i
\(481\) 1.20038e14 + 2.07911e14i 0.212579 + 0.368197i
\(482\) −9.52145e12 −0.0166703
\(483\) −3.31861e14 + 8.69813e13i −0.574443 + 0.150562i
\(484\) 5.58189e14 0.955282
\(485\) 6.24951e14 + 1.08245e15i 1.05747 + 1.83158i
\(486\) 3.64852e12 6.31942e12i 0.00610404 0.0105725i
\(487\) −4.11872e14 + 7.13383e14i −0.681323 + 1.18009i 0.293255 + 0.956034i \(0.405262\pi\)
−0.974577 + 0.224051i \(0.928072\pi\)
\(488\) −1.23361e14 2.13667e14i −0.201775 0.349485i
\(489\) −1.81501e15 −2.93550
\(490\) 1.10786e12 1.01379e14i 0.00177177 0.162132i
\(491\) −7.05003e14 −1.11492 −0.557459 0.830204i \(-0.688224\pi\)
−0.557459 + 0.830204i \(0.688224\pi\)
\(492\) −8.82658e13 1.52881e14i −0.138033 0.239081i
\(493\) 1.96885e14 3.41014e14i 0.304476 0.527369i
\(494\) 6.35563e12 1.10083e13i 0.00971987 0.0168353i
\(495\) −1.47410e14 2.55322e14i −0.222946 0.386154i
\(496\) −4.22784e14 −0.632367
\(497\) 5.76914e14 1.51210e14i 0.853397 0.223677i
\(498\) 5.26051e13 0.0769603
\(499\) −4.11492e14 7.12725e14i −0.595399 1.03126i −0.993490 0.113916i \(-0.963661\pi\)
0.398091 0.917346i \(-0.369673\pi\)
\(500\) −1.53657e14 + 2.66141e14i −0.219895 + 0.380870i
\(501\) 8.74086e14 1.51396e15i 1.23722 2.14293i
\(502\) 3.68316e13 + 6.37942e13i 0.0515644 + 0.0893122i
\(503\) 1.18063e15 1.63489 0.817445 0.576007i \(-0.195390\pi\)
0.817445 + 0.576007i \(0.195390\pi\)
\(504\) 2.60507e14 + 2.63370e14i 0.356822 + 0.360743i
\(505\) −1.30626e15 −1.76982
\(506\) 2.74797e12 + 4.75963e12i 0.00368286 + 0.00637889i
\(507\) 4.36171e14 7.55470e14i 0.578246 1.00155i
\(508\) 3.54458e14 6.13939e14i 0.464852 0.805147i
\(509\) −3.07502e14 5.32609e14i −0.398933 0.690972i 0.594661 0.803976i \(-0.297286\pi\)
−0.993595 + 0.113004i \(0.963953\pi\)
\(510\) −3.48249e14 −0.446945
\(511\) −1.88481e14 + 6.88354e14i −0.239305 + 0.873971i
\(512\) −4.70686e14 −0.591216
\(513\) 1.91433e14 + 3.31571e14i 0.237887 + 0.412033i
\(514\) 6.59096e13 1.14159e14i 0.0810310 0.140350i
\(515\) −8.55431e14 + 1.48165e15i −1.04051 + 1.80221i
\(516\) 8.59376e14 + 1.48848e15i 1.03421 + 1.79131i
\(517\) −2.28484e13 −0.0272055
\(518\) −2.07600e13 + 7.58179e13i −0.0244576 + 0.0893220i
\(519\) 3.97430e14 0.463276
\(520\) 8.07570e13 + 1.39875e14i 0.0931455 + 0.161333i
\(521\) −1.98750e14 + 3.44245e14i −0.226830 + 0.392880i −0.956867 0.290527i \(-0.906169\pi\)
0.730037 + 0.683407i \(0.239503\pi\)
\(522\) −4.35221e13 + 7.53826e13i −0.0491499 + 0.0851301i
\(523\) −4.29122e14 7.43262e14i −0.479537 0.830582i 0.520188 0.854052i \(-0.325862\pi\)
−0.999725 + 0.0234698i \(0.992529\pi\)
\(524\) 8.67869e13 0.0959693
\(525\) 7.29428e14 + 7.37443e14i 0.798190 + 0.806961i
\(526\) 1.61621e14 0.175015
\(527\) 4.90734e14 + 8.49976e14i 0.525881 + 0.910853i
\(528\) −1.33691e14 + 2.31560e14i −0.141780 + 0.245571i
\(529\) 4.20910e14 7.29038e14i 0.441757 0.765146i
\(530\) 8.88488e13 + 1.53891e14i 0.0922857 + 0.159843i
\(531\) 2.16514e15 2.22569
\(532\) −2.49018e14 + 6.52679e13i −0.253347 + 0.0664027i
\(533\) 9.27213e13 0.0933640
\(534\) −1.26296e14 2.18751e14i −0.125867 0.218009i
\(535\) 2.67683e14 4.63641e14i 0.264044 0.457337i
\(536\) −2.56166e13 + 4.43693e13i −0.0250101 + 0.0433188i
\(537\) −1.21378e15 2.10232e15i −1.17295 2.03161i
\(538\) 1.58194e14 0.151316
\(539\) −1.97463e12 + 1.80695e14i −0.00186960 + 0.171083i
\(540\) −2.41291e15 −2.26139
\(541\) −3.29697e13 5.71052e13i −0.0305865 0.0529774i 0.850327 0.526255i \(-0.176404\pi\)
−0.880913 + 0.473277i \(0.843071\pi\)
\(542\) −1.37947e13 + 2.38932e13i −0.0126683 + 0.0219421i
\(543\) 2.77355e14 4.80393e14i 0.252137 0.436714i
\(544\) 3.26045e14 + 5.64727e14i 0.293416 + 0.508211i
\(545\) 1.32707e15 1.18226
\(546\) −1.39396e14 + 3.65360e13i −0.122940 + 0.0322227i
\(547\) 1.54397e15 1.34805 0.674027 0.738706i \(-0.264563\pi\)
0.674027 + 0.738706i \(0.264563\pi\)
\(548\) −9.92192e14 1.71853e15i −0.857636 1.48547i
\(549\) −1.91010e15 + 3.30840e15i −1.63459 + 2.83119i
\(550\) 8.30831e12 1.43904e13i 0.00703911 0.0121921i
\(551\) −6.09780e13 1.05617e14i −0.0511493 0.0885932i
\(552\) 1.78955e14 0.148621
\(553\) 5.26571e14 + 5.32356e14i 0.432981 + 0.437738i
\(554\) −2.16008e14 −0.175859
\(555\) −1.01855e15 1.76417e15i −0.821049 1.42210i
\(556\) −7.37423e13 + 1.27725e14i −0.0588580 + 0.101945i
\(557\) −1.07657e15 + 1.86467e15i −0.850822 + 1.47367i 0.0296461 + 0.999560i \(0.490562\pi\)
−0.880468 + 0.474106i \(0.842771\pi\)
\(558\) −1.08479e14 1.87891e14i −0.0848900 0.147034i
\(559\) −9.02755e14 −0.699528
\(560\) 4.21419e14 1.53907e15i 0.323355 1.18093i
\(561\) 6.20711e14 0.471622
\(562\) −1.11144e14 1.92508e14i −0.0836253 0.144843i
\(563\) 7.40273e14 1.28219e15i 0.551564 0.955336i −0.446598 0.894735i \(-0.647365\pi\)
0.998162 0.0606018i \(-0.0193020\pi\)
\(564\) −1.84502e14 + 3.19566e14i −0.136134 + 0.235790i
\(565\) 9.49094e14 + 1.64388e15i 0.693494 + 1.20117i
\(566\) 1.15480e14 0.0835633
\(567\) 3.99131e14 1.45767e15i 0.286028 1.04461i
\(568\) −3.11100e14 −0.220792
\(569\) −7.54590e14 1.30699e15i −0.530388 0.918659i −0.999371 0.0354518i \(-0.988713\pi\)
0.468984 0.883207i \(-0.344620\pi\)
\(570\) −5.39289e13 + 9.34076e13i −0.0375413 + 0.0650235i
\(571\) 1.11735e15 1.93530e15i 0.770352 1.33429i −0.167018 0.985954i \(-0.553414\pi\)
0.937370 0.348335i \(-0.113253\pi\)
\(572\) −7.13926e13 1.23656e14i −0.0487501 0.0844376i
\(573\) −3.53269e15 −2.38922
\(574\) 2.13502e13 + 2.15848e13i 0.0143017 + 0.0144588i
\(575\) 3.35567e14 0.222642
\(576\) 1.39724e15 + 2.42010e15i 0.918223 + 1.59041i
\(577\) −1.10810e15 + 1.91928e15i −0.721293 + 1.24932i 0.239189 + 0.970973i \(0.423119\pi\)
−0.960482 + 0.278343i \(0.910215\pi\)
\(578\) 1.47689e14 2.55805e14i 0.0952237 0.164932i
\(579\) 2.57038e14 + 4.45204e14i 0.164159 + 0.284333i
\(580\) 7.68596e14 0.486233
\(581\) 5.41285e14 1.41872e14i 0.339201 0.0889052i
\(582\) 5.81709e14 0.361102
\(583\) −1.58362e14 2.74291e14i −0.0973810 0.168669i
\(584\) 1.86141e14 3.22406e14i 0.113389 0.196396i
\(585\) 1.25043e15 2.16581e15i 0.754576 1.30696i
\(586\) 3.13919e13 + 5.43724e13i 0.0187664 + 0.0325043i
\(587\) 9.98055e14 0.591078 0.295539 0.955331i \(-0.404501\pi\)
0.295539 + 0.955331i \(0.404501\pi\)
\(588\) 2.51133e15 + 1.48674e15i 1.47342 + 0.872287i
\(589\) 3.03975e14 0.176687
\(590\) 1.54549e14 + 2.67688e14i 0.0889983 + 0.154150i
\(591\) −1.27069e15 + 2.20091e15i −0.724953 + 1.25566i
\(592\) −6.18624e14 + 1.07149e15i −0.349669 + 0.605645i
\(593\) 4.92960e13 + 8.53833e13i 0.0276065 + 0.0478159i 0.879499 0.475902i \(-0.157878\pi\)
−0.851892 + 0.523717i \(0.824545\pi\)
\(594\) −6.95338e13 −0.0385807
\(595\) −3.58334e15 + 9.39198e14i −1.96990 + 0.516314i
\(596\) 8.93552e14 0.486705
\(597\) 1.06055e15 + 1.83692e15i 0.572363 + 0.991362i
\(598\) −2.33101e13 + 4.03743e13i −0.0124649 + 0.0215898i
\(599\) −2.95594e14 + 5.11985e14i −0.156621 + 0.271275i −0.933648 0.358192i \(-0.883393\pi\)
0.777027 + 0.629467i \(0.216727\pi\)
\(600\) −2.70530e14 4.68571e14i −0.142031 0.246005i
\(601\) 7.05336e14 0.366932 0.183466 0.983026i \(-0.441268\pi\)
0.183466 + 0.983026i \(0.441268\pi\)
\(602\) −2.07870e14 2.10154e14i −0.107155 0.108332i
\(603\) 7.93290e14 0.405216
\(604\) −1.28672e15 2.22867e15i −0.651300 1.12808i
\(605\) 1.24386e15 2.15442e15i 0.623901 1.08063i
\(606\) −3.03970e14 + 5.26492e14i −0.151089 + 0.261693i
\(607\) 9.23697e13 + 1.59989e14i 0.0454980 + 0.0788048i 0.887878 0.460080i \(-0.152179\pi\)
−0.842380 + 0.538885i \(0.818846\pi\)
\(608\) 2.01962e14 0.0985825
\(609\) −3.65132e14 + 1.33350e15i −0.176626 + 0.645059i
\(610\) −5.45380e14 −0.261448
\(611\) −9.69075e13 1.67849e14i −0.0460395 0.0797428i
\(612\) 3.35666e15 5.81390e15i 1.58043 2.73738i
\(613\) −6.30271e14 + 1.09166e15i −0.294100 + 0.509396i −0.974775 0.223189i \(-0.928353\pi\)
0.680675 + 0.732585i \(0.261687\pi\)
\(614\) −5.05539e13 8.75618e13i −0.0233791 0.0404938i
\(615\) −7.86759e14 −0.360603
\(616\) 2.48937e13 9.09147e13i 0.0113083 0.0412991i
\(617\) −3.07915e15 −1.38632 −0.693159 0.720784i \(-0.743782\pi\)
−0.693159 + 0.720784i \(0.743782\pi\)
\(618\) 3.98121e14 + 6.89566e14i 0.177655 + 0.307708i
\(619\) 1.11640e15 1.93367e15i 0.493768 0.855230i −0.506207 0.862412i \(-0.668953\pi\)
0.999974 + 0.00718174i \(0.00228604\pi\)
\(620\) −9.57861e14 + 1.65906e15i −0.419902 + 0.727292i
\(621\) −7.02106e14 1.21608e15i −0.305069 0.528396i
\(622\) −9.10889e13 −0.0392300
\(623\) −1.88949e15 1.91025e15i −0.806604 0.815467i
\(624\) −2.26811e15 −0.959730
\(625\) 1.46245e15 + 2.53304e15i 0.613397 + 1.06244i
\(626\) −8.71571e13 + 1.50961e14i −0.0362363 + 0.0627631i
\(627\) 9.61217e13 1.66488e14i 0.0396141 0.0686136i
\(628\) 9.40905e14 + 1.62970e15i 0.384386 + 0.665776i
\(629\) 2.87220e15 1.16315
\(630\) 7.92111e14 2.07614e14i 0.317990 0.0833457i
\(631\) −3.18888e15 −1.26905 −0.634523 0.772904i \(-0.718803\pi\)
−0.634523 + 0.772904i \(0.718803\pi\)
\(632\) −1.95294e14 3.38259e14i −0.0770451 0.133446i
\(633\) 1.09557e13 1.89759e13i 0.00428470 0.00742132i
\(634\) 9.73713e13 1.68652e14i 0.0377520 0.0653884i
\(635\) −1.57974e15 2.73618e15i −0.607196 1.05169i
\(636\) −5.11513e15 −1.94914
\(637\) −1.33580e15 + 7.51881e14i −0.504630 + 0.284042i
\(638\) 2.21489e13 0.00829543
\(639\) 2.40852e15 + 4.17168e15i 0.894325 + 1.54902i
\(640\) −8.46168e14 + 1.46561e15i −0.311506 + 0.539545i
\(641\) 5.28395e14 9.15207e14i 0.192859 0.334041i −0.753338 0.657634i \(-0.771557\pi\)
0.946196 + 0.323593i \(0.104891\pi\)
\(642\) −1.24581e14 2.15780e14i −0.0450826 0.0780853i
\(643\) 2.86505e15 1.02795 0.513975 0.857805i \(-0.328172\pi\)
0.513975 + 0.857805i \(0.328172\pi\)
\(644\) 9.13305e14 2.39379e14i 0.324896 0.0851557i
\(645\) 7.66007e15 2.70181
\(646\) −7.60370e13 1.31700e14i −0.0265917 0.0460582i
\(647\) −2.19873e14 + 3.80831e14i −0.0762428 + 0.132056i −0.901626 0.432516i \(-0.857626\pi\)
0.825383 + 0.564573i \(0.190959\pi\)
\(648\) −3.94177e14 + 6.82734e14i −0.135528 + 0.234741i
\(649\) −2.75466e14 4.77120e14i −0.0939121 0.162661i
\(650\) 1.40953e14 0.0476488
\(651\) −2.42341e15 2.45004e15i −0.812328 0.821254i
\(652\) 4.99505e15 1.66027
\(653\) 2.92912e14 + 5.07338e14i 0.0965415 + 0.167215i 0.910251 0.414057i \(-0.135889\pi\)
−0.813709 + 0.581272i \(0.802555\pi\)
\(654\) 3.08812e14 5.34878e14i 0.100929 0.174814i
\(655\) 1.93394e14 3.34969e14i 0.0626782 0.108562i
\(656\) 2.38923e14 + 4.13827e14i 0.0767869 + 0.132999i
\(657\) −5.76438e15 −1.83714
\(658\) 1.67597e13 6.12085e13i 0.00529694 0.0193450i
\(659\) −5.89551e14 −0.184779 −0.0923893 0.995723i \(-0.529450\pi\)
−0.0923893 + 0.995723i \(0.529450\pi\)
\(660\) 6.05782e14 + 1.04924e15i 0.188289 + 0.326126i
\(661\) 2.16762e15 3.75442e15i 0.668151 1.15727i −0.310269 0.950649i \(-0.600419\pi\)
0.978421 0.206623i \(-0.0662474\pi\)
\(662\) −7.94117e13 + 1.37545e14i −0.0242753 + 0.0420461i
\(663\) 2.63264e15 + 4.55987e15i 0.798119 + 1.38238i
\(664\) −2.91887e14 −0.0877588
\(665\) −3.02993e14 + 1.10657e15i −0.0903471 + 0.329958i
\(666\) −6.34911e14 −0.187761
\(667\) 2.23645e14 + 3.87365e14i 0.0655945 + 0.113613i
\(668\) −2.40555e15 + 4.16653e15i −0.699751 + 1.21200i
\(669\) 9.23667e14 1.59984e15i 0.266484 0.461565i
\(670\) 5.66258e13 + 9.80788e13i 0.0162033 + 0.0280649i
\(671\) 9.72074e14 0.275883
\(672\) −1.61012e15 1.62781e15i −0.453239 0.458219i
\(673\) 1.69410e15 0.472994 0.236497 0.971632i \(-0.424001\pi\)
0.236497 + 0.971632i \(0.424001\pi\)
\(674\) 2.49532e13 + 4.32202e13i 0.00691030 + 0.0119690i
\(675\) −2.12277e15 + 3.67674e15i −0.583085 + 1.00993i
\(676\) −1.20037e15 + 2.07911e15i −0.327047 + 0.566461i
\(677\) 2.59774e15 + 4.49941e15i 0.702033 + 1.21596i 0.967752 + 0.251907i \(0.0810576\pi\)
−0.265718 + 0.964051i \(0.585609\pi\)
\(678\) 8.83424e14 0.236813
\(679\) 5.98555e15 1.56882e15i 1.59155 0.417148i
\(680\) 1.93231e15 0.509656
\(681\) −4.45456e15 7.71553e15i −1.16546 2.01863i
\(682\) −2.76030e13 + 4.78099e13i −0.00716379 + 0.0124081i
\(683\) 1.70845e14 2.95913e14i 0.0439834 0.0761815i −0.843196 0.537607i \(-0.819328\pi\)
0.887179 + 0.461425i \(0.152662\pi\)
\(684\) −1.03961e15 1.80065e15i −0.265498 0.459855i
\(685\) −8.84393e15 −2.24051
\(686\) −4.82615e14 1.37833e14i −0.121288 0.0346395i
\(687\) −3.18941e15 −0.795149
\(688\) −2.32621e15 4.02911e15i −0.575324 0.996490i
\(689\) 1.34333e15 2.32672e15i 0.329593 0.570872i
\(690\) 1.97791e14 3.42585e14i 0.0481435 0.0833870i
\(691\) −2.58334e15 4.47447e15i −0.623810 1.08047i −0.988770 0.149447i \(-0.952251\pi\)
0.364960 0.931023i \(-0.381083\pi\)
\(692\) −1.09376e15 −0.262021
\(693\) −1.41184e15 + 3.70046e14i −0.335547 + 0.0879474i
\(694\) −6.36094e14 −0.149984
\(695\) 3.28652e14 + 5.69242e14i 0.0768811 + 0.133162i
\(696\) 3.60599e14 6.24576e14i 0.0836901 0.144956i
\(697\) 5.54646e14 9.60674e14i 0.127713 0.221206i
\(698\) 7.12455e13 + 1.23401e14i 0.0162762 + 0.0281912i
\(699\) 1.25149e16 2.83663
\(700\) −2.00744e15 2.02950e15i −0.451444 0.456404i
\(701\) 3.33033e15 0.743084 0.371542 0.928416i \(-0.378829\pi\)
0.371542 + 0.928416i \(0.378829\pi\)
\(702\) −2.94916e14 5.10809e14i −0.0652896 0.113085i
\(703\) 4.44781e14 7.70382e14i 0.0976993 0.169220i
\(704\) 3.55537e14 6.15807e14i 0.0774880 0.134213i
\(705\) 8.22281e14 + 1.42423e15i 0.177820 + 0.307993i
\(706\) 5.09785e14 0.109386
\(707\) −1.70782e15 + 6.23716e15i −0.363610 + 1.32795i
\(708\) −8.89760e15 −1.87971
\(709\) 7.09927e14 + 1.22963e15i 0.148819 + 0.257763i 0.930791 0.365551i \(-0.119119\pi\)
−0.781972 + 0.623313i \(0.785786\pi\)
\(710\) −3.43845e14 + 5.95557e14i −0.0715224 + 0.123880i
\(711\) −3.02391e15 + 5.23757e15i −0.624146 + 1.08105i
\(712\) 7.00773e14 + 1.21377e15i 0.143528 + 0.248598i
\(713\) −1.11487e15 −0.226585
\(714\) −4.55304e14 + 1.66282e15i −0.0918251 + 0.335356i
\(715\) −6.36360e14 −0.127356
\(716\) 3.34040e15 + 5.78575e15i 0.663403 + 1.14905i
\(717\) 1.11627e14 1.93344e14i 0.0219996 0.0381044i
\(718\) −4.79255e14 + 8.30094e14i −0.0937307 + 0.162346i
\(719\) −4.37317e15 7.57456e15i −0.848765 1.47010i −0.882311 0.470667i \(-0.844013\pi\)
0.0335454 0.999437i \(-0.489320\pi\)
\(720\) 1.28884e16 2.48239
\(721\) 5.95620e15 + 6.02165e15i 1.13848 + 1.15099i
\(722\) 6.17866e14 0.117203
\(723\) −6.10756e14 1.05786e15i −0.114976 0.199144i
\(724\) −7.63301e14 + 1.32208e15i −0.142605 + 0.246999i
\(725\) 6.76176e14 1.17117e15i 0.125372 0.217151i
\(726\) −5.78896e14 1.00268e15i −0.106524 0.184506i
\(727\) −7.92864e14 −0.144797 −0.0723984 0.997376i \(-0.523065\pi\)
−0.0723984 + 0.997376i \(0.523065\pi\)
\(728\) 7.73461e14 2.02725e14i 0.140190 0.0367439i
\(729\) −5.08466e15 −0.914661
\(730\) −4.11467e14 7.12682e14i −0.0734615 0.127239i
\(731\) −5.40015e15 + 9.35334e15i −0.956887 + 1.65738i
\(732\) 7.84955e15 1.35958e16i 1.38049 2.39108i
\(733\) −1.71682e15 2.97363e15i −0.299678 0.519057i 0.676385 0.736549i \(-0.263546\pi\)
−0.976062 + 0.217492i \(0.930212\pi\)
\(734\) −1.18678e14 −0.0205610
\(735\) 1.13345e16 6.37987e15i 1.94905 1.09706i
\(736\) −7.40722e14 −0.126423
\(737\) −1.00929e14 1.74813e14i −0.0170979 0.0296145i
\(738\) −1.22607e14 + 2.12361e14i −0.0206160 + 0.0357079i
\(739\) −1.17677e15 + 2.03823e15i −0.196403 + 0.340180i −0.947359 0.320172i \(-0.896259\pi\)
0.750957 + 0.660351i \(0.229593\pi\)
\(740\) 2.80311e15 + 4.85513e15i 0.464372 + 0.804316i
\(741\) 1.63074e15 0.268154
\(742\) 8.50961e14 2.23038e14i 0.138895 0.0364047i
\(743\) −1.13067e16 −1.83188 −0.915940 0.401316i \(-0.868553\pi\)
−0.915940 + 0.401316i \(0.868553\pi\)
\(744\) 8.98792e14 + 1.55675e15i 0.144547 + 0.250362i
\(745\) 1.99117e15 3.44882e15i 0.317870 0.550567i
\(746\) 3.91725e14 6.78488e14i 0.0620751 0.107517i
\(747\) 2.25977e15 + 3.91404e15i 0.355469 + 0.615690i
\(748\) −1.70824e15 −0.266742
\(749\) −1.86383e15 1.88431e15i −0.288905 0.292080i
\(750\) 6.37427e14 0.0980829
\(751\) 2.89693e15 + 5.01763e15i 0.442505 + 0.766441i 0.997875 0.0651627i \(-0.0207566\pi\)
−0.555370 + 0.831603i \(0.687423\pi\)
\(752\) 4.99420e14 8.65021e14i 0.0757300 0.131168i
\(753\) −4.72515e15 + 8.18420e15i −0.711284 + 1.23198i
\(754\) 9.39410e13 + 1.62711e14i 0.0140382 + 0.0243149i
\(755\) −1.14692e16 −1.70147
\(756\) −3.15466e15 + 1.15212e16i −0.464604 + 1.69679i
\(757\) −3.69592e15 −0.540374 −0.270187 0.962808i \(-0.587086\pi\)
−0.270187 + 0.962808i \(0.587086\pi\)
\(758\) −1.55115e13 2.68667e13i −0.00225151 0.00389973i
\(759\) −3.52539e14 + 6.10616e14i −0.0508016 + 0.0879910i
\(760\) 2.99232e14 5.18285e14i 0.0428088 0.0741471i
\(761\) −7.85569e14 1.36065e15i −0.111575 0.193254i 0.804830 0.593505i \(-0.202256\pi\)
−0.916406 + 0.400251i \(0.868923\pi\)
\(762\) −1.47043e15 −0.207344
\(763\) 1.73503e15 6.33651e15i 0.242896 0.887085i
\(764\) 9.72223e15 1.35130
\(765\) −1.49598e16 2.59112e16i −2.06438 3.57560i
\(766\) 6.31746e14 1.09422e15i 0.0865535 0.149915i
\(767\) 2.33668e15 4.04725e15i 0.317852 0.550536i
\(768\) −5.44098e15 9.42406e15i −0.734836 1.27277i
\(769\) 1.12892e16 1.51380 0.756902 0.653529i \(-0.226712\pi\)
0.756902 + 0.653529i \(0.226712\pi\)
\(770\) −1.46530e14 1.48140e14i −0.0195086 0.0197230i
\(771\) 1.69112e16 2.23550
\(772\) −7.07389e14 1.22523e15i −0.0928460 0.160814i
\(773\) −9.91548e14 + 1.71741e15i −0.129219 + 0.223814i −0.923374 0.383901i \(-0.874580\pi\)
0.794155 + 0.607715i \(0.207914\pi\)
\(774\) 1.19373e15 2.06759e15i 0.154465 0.267541i
\(775\) 1.68537e15 + 2.91914e15i 0.216538 + 0.375055i
\(776\) −3.22770e15 −0.411769
\(777\) −9.75525e15 + 2.55687e15i −1.23573 + 0.323886i
\(778\) −6.47695e14 −0.0814672
\(779\) −1.71782e14 2.97535e14i −0.0214546 0.0371605i
\(780\) −5.13864e15 + 8.90039e15i −0.637277 + 1.10380i
\(781\) 6.12862e14 1.06151e15i 0.0754713 0.130720i
\(782\) 2.78876e14 + 4.83027e14i 0.0341015 + 0.0590656i
\(783\) −5.65904e15 −0.687152
\(784\) −6.79781e15 4.02439e15i −0.819654 0.485246i
\(785\) 8.38678e15 1.00418
\(786\) −9.00065e13 1.55896e14i −0.0107016 0.0185358i
\(787\) −6.95413e15 + 1.20449e16i −0.821073 + 1.42214i 0.0838114 + 0.996482i \(0.473291\pi\)
−0.904884 + 0.425658i \(0.860043\pi\)
\(788\) 3.49705e15 6.05706e15i 0.410022 0.710179i
\(789\) 1.03672e16 + 1.79565e16i 1.20709 + 2.09073i
\(790\) −8.63399e14 −0.0998304
\(791\) 9.09006e15 2.38252e15i 1.04375 0.273568i
\(792\) 7.61334e14 0.0868133
\(793\) 4.12289e15 + 7.14105e15i 0.466873 + 0.808648i
\(794\) −3.57966e14 + 6.20016e14i −0.0402559 + 0.0697252i
\(795\) −1.13985e16 + 1.97427e16i −1.27300 + 2.20489i
\(796\) −2.91871e15 5.05535e15i −0.323719 0.560699i
\(797\) 6.82904e15 0.752210 0.376105 0.926577i \(-0.377263\pi\)
0.376105 + 0.926577i \(0.377263\pi\)
\(798\) 3.75497e14 + 3.79622e14i 0.0410762 + 0.0415275i
\(799\) −2.31875e15 −0.251911
\(800\) 1.11976e15 + 1.93948e15i 0.120818 + 0.209263i
\(801\) 1.08507e16 1.87939e16i 1.16273 2.01391i
\(802\) −1.14914e14 + 1.99038e14i −0.0122297 + 0.0211825i
\(803\) 7.33390e14 + 1.27027e15i 0.0775175 + 0.134264i
\(804\) −3.26002e15 −0.342225
\(805\) 1.11127e15 4.05848e15i 0.115862 0.423142i
\(806\) −4.68295e14 −0.0484927
\(807\) 1.01474e16 + 1.75758e16i 1.04364 + 1.80763i
\(808\) 1.68662e15 2.92131e15i 0.172288 0.298412i
\(809\) 8.33703e15 1.44402e16i 0.845852 1.46506i −0.0390274 0.999238i \(-0.512426\pi\)
0.884879 0.465820i \(-0.154241\pi\)
\(810\) 8.71332e14 + 1.50919e15i 0.0878044 + 0.152082i
\(811\) −5.16144e15 −0.516602 −0.258301 0.966065i \(-0.583163\pi\)
−0.258301 + 0.966065i \(0.583163\pi\)
\(812\) 1.00487e15 3.66990e15i 0.0998969 0.364835i
\(813\) −3.53947e15 −0.349494
\(814\) 8.07784e13 + 1.39912e14i 0.00792247 + 0.0137221i
\(815\) 1.11309e16 1.92793e16i 1.08433 1.87812i
\(816\) −1.35675e16 + 2.34996e16i −1.31282 + 2.27387i
\(817\) 1.67251e15 + 2.89687e15i 0.160748 + 0.278424i
\(818\) 1.11834e15 0.106765
\(819\) −8.70652e15 8.80219e15i −0.825626 0.834698i
\(820\) 2.16522e15 0.203951
\(821\) −5.05873e15 8.76198e15i −0.473319 0.819813i 0.526214 0.850352i \(-0.323611\pi\)
−0.999534 + 0.0305391i \(0.990278\pi\)
\(822\) −2.05800e15 + 3.56456e15i −0.191272 + 0.331292i
\(823\) 3.99868e15 6.92593e15i 0.369163 0.639409i −0.620272 0.784387i \(-0.712978\pi\)
0.989435 + 0.144978i \(0.0463111\pi\)
\(824\) −2.20903e15 3.82616e15i −0.202583 0.350884i
\(825\) 2.13176e15 0.194196
\(826\) 1.48022e15 3.87967e14i 0.133948 0.0351079i
\(827\) −1.50295e16 −1.35102 −0.675512 0.737349i \(-0.736077\pi\)
−0.675512 + 0.737349i \(0.736077\pi\)
\(828\) 3.81290e15 + 6.60413e15i 0.340477 + 0.589724i
\(829\) −6.43760e15 + 1.11502e16i −0.571050 + 0.989087i 0.425409 + 0.905001i \(0.360130\pi\)
−0.996459 + 0.0840857i \(0.973203\pi\)
\(830\) −3.22610e14 + 5.58777e14i −0.0284281 + 0.0492390i
\(831\) −1.38559e16 2.39991e16i −1.21291 2.10082i
\(832\) 6.03180e15 0.524528
\(833\) −2.00394e14 + 1.83377e16i −0.0173116 + 1.58415i
\(834\) 3.05912e14 0.0262532
\(835\) 1.07210e16 + 1.85692e16i 0.914025 + 1.58314i
\(836\) −2.64534e14 + 4.58186e14i −0.0224051 + 0.0388068i
\(837\) 7.05256e15 1.22154e16i 0.593413 1.02782i
\(838\) 8.87952e14 + 1.53798e15i 0.0742245 + 0.128561i
\(839\) −1.90314e16 −1.58045 −0.790225 0.612817i \(-0.790036\pi\)
−0.790225 + 0.612817i \(0.790036\pi\)
\(840\) −6.56298e15 + 1.72017e15i −0.541458 + 0.141917i
\(841\) −1.03979e16 −0.852252
\(842\) −9.00229e14 1.55924e15i −0.0733055 0.126969i
\(843\) 1.42588e16 2.46969e16i 1.15353 1.99798i
\(844\) −3.01510e13 + 5.22230e13i −0.00242336 + 0.00419738i
\(845\) 5.34978e15 + 9.26609e15i 0.427193 + 0.739920i
\(846\) 5.12569e14 0.0406645
\(847\) −8.66074e15 8.75590e15i −0.682647 0.690148i
\(848\) 1.38459e16 1.08429
\(849\) 7.40748e15 + 1.28301e16i 0.576339 + 0.998249i
\(850\) 8.43163e14 1.46040e15i 0.0651789 0.112893i
\(851\) −1.63129e15 + 2.82548e15i −0.125291 + 0.217010i
\(852\) −9.89779e15 1.71435e16i −0.755302 1.30822i
\(853\) −5.80889e15 −0.440427 −0.220213 0.975452i \(-0.570675\pi\)
−0.220213 + 0.975452i \(0.570675\pi\)
\(854\) −7.13036e14 + 2.60409e15i −0.0537147 + 0.196172i
\(855\) −9.26656e15 −0.693593
\(856\) 6.91255e14 + 1.19729e15i 0.0514082 + 0.0890416i
\(857\) 5.44606e15 9.43285e15i 0.402428 0.697025i −0.591591 0.806239i \(-0.701500\pi\)
0.994018 + 0.109213i \(0.0348331\pi\)
\(858\) −1.48082e14 + 2.56486e14i −0.0108723 + 0.0188314i
\(859\) 4.88936e15 + 8.46862e15i 0.356689 + 0.617803i 0.987406 0.158210i \(-0.0505723\pi\)
−0.630717 + 0.776013i \(0.717239\pi\)
\(860\) −2.10811e16 −1.52810
\(861\) −1.02862e15 + 3.75663e15i −0.0740861 + 0.270571i
\(862\) 2.80338e15 0.200628
\(863\) −3.21366e15 5.56622e15i −0.228529 0.395823i 0.728844 0.684680i \(-0.240058\pi\)
−0.957372 + 0.288857i \(0.906725\pi\)
\(864\) 4.68575e15 8.11595e15i 0.331095 0.573474i
\(865\) −2.43730e15 + 4.22153e15i −0.171128 + 0.296402i
\(866\) −1.33201e15 2.30710e15i −0.0929305 0.160960i
\(867\) 3.78942e16 2.62705
\(868\) 6.66940e15 + 6.74268e15i 0.459440 + 0.464488i
\(869\) 1.53890e15 0.105342
\(870\) −7.97109e14 1.38063e15i −0.0542203 0.0939123i
\(871\) 8.56144e14 1.48288e15i 0.0578691 0.100232i
\(872\) −1.71349e15 + 2.96785e15i −0.115091 + 0.199343i
\(873\) 2.49887e16 + 4.32816e16i 1.66788 + 2.88885i
\(874\) 1.72744e14 0.0114575
\(875\) 6.55886e15 1.71909e15i 0.432299 0.113306i
\(876\) 2.36887e16 1.55156
\(877\) −1.22064e16 2.11421e16i −0.794491 1.37610i −0.923162 0.384412i \(-0.874404\pi\)
0.128670 0.991687i \(-0.458929\pi\)
\(878\) 7.93877e14 1.37504e15i 0.0513492 0.0889394i
\(879\) −4.02729e15 + 6.97546e15i −0.258865 + 0.448368i
\(880\) −1.63977e15 2.84016e15i −0.104743 0.181421i
\(881\) −2.26230e16 −1.43609 −0.718045 0.695996i \(-0.754963\pi\)
−0.718045 + 0.695996i \(0.754963\pi\)
\(882\) 4.42979e13 4.05362e15i 0.00279451 0.255721i
\(883\) 2.40396e14 0.0150711 0.00753554 0.999972i \(-0.497601\pi\)
0.00753554 + 0.999972i \(0.497601\pi\)
\(884\) −7.24523e15 1.25491e16i −0.451403 0.781853i
\(885\) −1.98272e16 + 3.43418e16i −1.22765 + 2.12635i
\(886\) −1.25367e15 + 2.17141e15i −0.0771429 + 0.133615i
\(887\) 7.90944e15 + 1.36996e16i 0.483689 + 0.837773i 0.999825 0.0187334i \(-0.00596339\pi\)
−0.516136 + 0.856507i \(0.672630\pi\)
\(888\) 5.26050e15 0.319710
\(889\) −1.51301e16 + 3.96563e15i −0.913866 + 0.239526i
\(890\) 3.09813e15 0.185975
\(891\) −1.55304e15 2.68995e15i −0.0926523 0.160478i
\(892\) −2.54200e15 + 4.40287e15i −0.150719 + 0.261054i
\(893\) −3.59075e14 + 6.21937e14i −0.0211594 + 0.0366491i
\(894\) −9.26701e14 1.60509e15i −0.0542729 0.0940034i
\(895\) 2.97748e16 1.73309
\(896\) 5.89171e15 + 5.95644e15i 0.340837 + 0.344582i
\(897\) −5.98094e15 −0.343883
\(898\) −2.40389e14 4.16366e14i −0.0137371 0.0237934i
\(899\) −2.24649e15 + 3.89103e15i −0.127593 + 0.220997i
\(900\) 1.15280e16 1.99671e16i 0.650761 1.12715i
\(901\) −1.60713e16 2.78362e16i −0.901703 1.56180i
\(902\) 6.23960e13 0.00347953
\(903\) 1.00148e16 3.65754e16i 0.555088 2.02724i
\(904\) −4.90180e15 −0.270041
\(905\) 3.40185e15 + 5.89218e15i 0.186272 + 0.322633i
\(906\) −2.66891e15 + 4.62269e15i −0.145254 + 0.251588i
\(907\) −2.57501e15 + 4.46004e15i −0.139296 + 0.241267i −0.927230 0.374492i \(-0.877817\pi\)
0.787934 + 0.615759i \(0.211151\pi\)
\(908\) 1.22593e16 + 2.12337e16i 0.659163 + 1.14170i
\(909\) −5.22309e16 −2.79143
\(910\) 4.66783e14 1.70474e15i 0.0247963 0.0905590i
\(911\) 2.54507e16 1.34384 0.671922 0.740622i \(-0.265469\pi\)
0.671922 + 0.740622i \(0.265469\pi\)
\(912\) 4.20206e15 + 7.27819e15i 0.220542 + 0.381990i
\(913\) 5.75013e14 9.95951e14i 0.0299977 0.0519576i
\(914\) 5.17238e14 8.95882e14i 0.0268217 0.0464565i
\(915\) −3.49836e16 6.05934e16i −1.80322 3.12327i
\(916\) 8.77750e15 0.449724
\(917\) −1.34657e15 1.36136e15i −0.0685799 0.0693334i
\(918\) −7.05658e15 −0.357240
\(919\) −3.49711e15 6.05718e15i −0.175984 0.304814i 0.764517 0.644604i \(-0.222978\pi\)
−0.940502 + 0.339789i \(0.889644\pi\)
\(920\) −1.09747e15 + 1.90088e15i −0.0548986 + 0.0950872i
\(921\) 6.48558e15 1.12334e16i 0.322494 0.558575i
\(922\) 6.63072e14 + 1.14848e15i 0.0327749 + 0.0567677i
\(923\) 1.03974e16 0.510876
\(924\) 5.80195e15 1.52070e15i 0.283386 0.0742759i
\(925\) 9.86420e15 0.478942
\(926\) 1.38674e15 + 2.40191e15i 0.0669322 + 0.115930i
\(927\) −3.42044e16 + 5.92438e16i −1.64113 + 2.84253i
\(928\) −1.49257e15 + 2.58521e15i −0.0711904 + 0.123305i
\(929\) 6.32951e15 + 1.09630e16i 0.300112 + 0.519810i 0.976161 0.217047i \(-0.0696425\pi\)
−0.676049 + 0.736857i \(0.736309\pi\)
\(930\) 3.97358e15 0.187295
\(931\) 4.88751e15 + 2.89347e15i 0.229015 + 0.135580i
\(932\) −3.44420e16 −1.60435
\(933\) −5.84292e15 1.01202e16i −0.270571 0.468643i
\(934\) 2.68895e14 4.65740e14i 0.0123787 0.0214405i
\(935\) −3.80662e15 + 6.59325e15i −0.174211 + 0.301742i
\(936\) 3.22907e15 + 5.59291e15i 0.146913 + 0.254461i
\(937\) 2.80207e16 1.26739 0.633697 0.773582i \(-0.281537\pi\)
0.633697 + 0.773582i \(0.281537\pi\)
\(938\) 5.42341e14 1.42148e14i 0.0243869 0.00639185i
\(939\) −2.23629e16 −0.999694
\(940\) −2.26298e15 3.91959e15i −0.100572 0.174196i
\(941\) 2.38780e15 4.13578e15i 0.105500 0.182732i −0.808442 0.588576i \(-0.799689\pi\)
0.913943 + 0.405844i \(0.133022\pi\)
\(942\) 1.95162e15 3.38031e15i 0.0857266 0.148483i
\(943\) 6.30033e14 + 1.09125e15i 0.0275137 + 0.0476551i
\(944\) 2.40846e16 1.04567
\(945\) 3.74382e16 + 3.78496e16i 1.61600 + 1.63375i
\(946\) −6.07501e14 −0.0260703
\(947\) −1.48624e16 2.57425e16i −0.634110 1.09831i −0.986703 0.162534i \(-0.948033\pi\)
0.352593 0.935777i \(-0.385300\pi\)
\(948\) 1.24267e16 2.15237e16i 0.527122 0.913002i
\(949\) −6.22110e15 + 1.07753e16i −0.262363 + 0.454427i
\(950\) −2.61140e14 4.52307e14i −0.0109495 0.0189650i
\(951\) 2.49837e16 1.04151
\(952\) 2.52632e15 9.22641e15i 0.104709 0.382410i
\(953\) 4.28873e15 0.176733 0.0883665 0.996088i \(-0.471835\pi\)
0.0883665 + 0.996088i \(0.471835\pi\)
\(954\) 3.55262e15 + 6.15332e15i 0.145557 + 0.252112i
\(955\) 2.16648e16 3.75246e16i 0.882545 1.52861i
\(956\) −3.07206e14 + 5.32096e14i −0.0124426 + 0.0215512i
\(957\) 1.42075e15 + 2.46081e15i 0.0572139 + 0.0990974i
\(958\) −3.66890e15 −0.146901
\(959\) −1.15626e16 + 4.22281e16i −0.460315 + 1.68112i
\(960\) −5.11811e16 −2.02590
\(961\) 7.10488e15 + 1.23060e16i 0.279626 + 0.484327i
\(962\) −6.85216e14 + 1.18683e15i −0.0268142 + 0.0464435i
\(963\) 1.07033e16 1.85387e16i 0.416460 0.721331i
\(964\) 1.68085e15 + 2.91131e15i 0.0650286 + 0.112633i
\(965\) −6.30533e15 −0.242553
\(966\) −1.37718e15 1.39232e15i −0.0526766 0.0532554i
\(967\) 8.30400e15 0.315822 0.157911 0.987453i \(-0.449524\pi\)
0.157911 + 0.987453i \(0.449524\pi\)
\(968\) 3.21209e15 + 5.56350e15i 0.121471 + 0.210394i
\(969\) 9.75483e15 1.68959e16i 0.366808 0.635331i
\(970\) −3.56743e15 + 6.17897e15i −0.133386 + 0.231032i
\(971\) 1.68239e16 + 2.91399e16i 0.625491 + 1.08338i 0.988446 + 0.151576i \(0.0484348\pi\)
−0.362954 + 0.931807i \(0.618232\pi\)
\(972\) −2.57633e15 −0.0952439
\(973\) 3.14771e15 8.25019e14i 0.115711 0.0303280i
\(974\) −4.70221e15 −0.171881
\(975\) 9.04149e15 + 1.56603e16i 0.328636 + 0.569213i
\(976\) −2.12476e16 + 3.68020e16i −0.767956 + 1.33014i
\(977\) 1.98072e16 3.43071e16i 0.711875 1.23300i −0.252277 0.967655i \(-0.581180\pi\)
0.964152 0.265349i \(-0.0854871\pi\)
\(978\) −5.18036e15 8.97264e15i −0.185138 0.320669i
\(979\) −5.52204e15 −0.196243
\(980\) −3.11934e16 + 1.75579e16i −1.10235 + 0.620481i
\(981\) 5.30629e16 1.86471
\(982\) −2.01220e15 3.48523e15i −0.0703166 0.121792i
\(983\) −1.53479e16 + 2.65834e16i −0.533342 + 0.923775i 0.465900 + 0.884838i \(0.345731\pi\)
−0.999242 + 0.0389378i \(0.987603\pi\)
\(984\) 1.01585e15 1.75950e15i 0.0351039 0.0608018i
\(985\) −1.55855e16 2.69949e16i −0.535576 0.927646i
\(986\) 2.24777e15 0.0768118
\(987\) 7.87550e15 2.06418e15i 0.267629 0.0701461i
\(988\) −4.48791e15 −0.151663
\(989\) −6.13414e15 1.06246e16i −0.206146 0.357055i
\(990\) 8.41468e14 1.45747e15i 0.0281219 0.0487085i
\(991\) −7.01280e15 + 1.21465e16i −0.233070 + 0.403689i −0.958710 0.284385i \(-0.908211\pi\)
0.725640 + 0.688075i \(0.241544\pi\)
\(992\) −3.72023e15 6.44363e15i −0.122958 0.212969i
\(993\) −2.03755e16 −0.669712
\(994\) 2.39413e15 + 2.42043e15i 0.0782568 + 0.0791167i
\(995\) −2.60160e16 −0.845694
\(996\) −9.28652e15 1.60847e16i −0.300211 0.519981i
\(997\) 1.01222e16 1.75321e16i 0.325424 0.563651i −0.656174 0.754610i \(-0.727826\pi\)
0.981598 + 0.190959i \(0.0611596\pi\)
\(998\) 2.34893e15 4.06847e15i 0.0751023 0.130081i
\(999\) −2.06388e16 3.57475e16i −0.656258 1.13667i
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 7.12.c.a.4.3 yes 12
3.2 odd 2 63.12.e.b.46.4 12
4.3 odd 2 112.12.i.c.81.6 12
7.2 even 3 inner 7.12.c.a.2.3 12
7.3 odd 6 49.12.a.f.1.4 6
7.4 even 3 49.12.a.g.1.4 6
7.5 odd 6 49.12.c.i.30.3 12
7.6 odd 2 49.12.c.i.18.3 12
21.2 odd 6 63.12.e.b.37.4 12
28.23 odd 6 112.12.i.c.65.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.12.c.a.2.3 12 7.2 even 3 inner
7.12.c.a.4.3 yes 12 1.1 even 1 trivial
49.12.a.f.1.4 6 7.3 odd 6
49.12.a.g.1.4 6 7.4 even 3
49.12.c.i.18.3 12 7.6 odd 2
49.12.c.i.30.3 12 7.5 odd 6
63.12.e.b.37.4 12 21.2 odd 6
63.12.e.b.46.4 12 3.2 odd 2
112.12.i.c.65.6 12 28.23 odd 6
112.12.i.c.81.6 12 4.3 odd 2