Properties

Label 91.10.u.a.30.18
Level $91$
Weight $10$
Character 91.30
Analytic conductor $46.868$
Analytic rank $0$
Dimension $164$
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] = [91,10,Mod(30,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.30");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 91.u (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(46.8682610909\)
Analytic rank: \(0\)
Dimension: \(164\)
Relative dimension: \(82\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 30.18
Character \(\chi\) \(=\) 91.30
Dual form 91.10.u.a.88.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-23.8716 + 13.7823i) q^{2} +180.122 q^{3} +(123.902 - 214.605i) q^{4} +(97.1768 + 56.1050i) q^{5} +(-4299.81 + 2482.50i) q^{6} +(6336.56 - 449.013i) q^{7} -7282.43i q^{8} +12761.0 q^{9} +O(q^{10})\) \(q+(-23.8716 + 13.7823i) q^{2} +180.122 q^{3} +(123.902 - 214.605i) q^{4} +(97.1768 + 56.1050i) q^{5} +(-4299.81 + 2482.50i) q^{6} +(6336.56 - 449.013i) q^{7} -7282.43i q^{8} +12761.0 q^{9} -3093.02 q^{10} -6957.37i q^{11} +(22317.6 - 38655.2i) q^{12} +(-93689.6 - 42740.6i) q^{13} +(-145075. + 98050.9i) q^{14} +(17503.7 + 10105.8i) q^{15} +(163806. + 283721. i) q^{16} +(172213. - 298282. i) q^{17} +(-304626. + 175876. i) q^{18} -549002. i q^{19} +(24080.9 - 13903.1i) q^{20} +(1.14136e6 - 80877.3i) q^{21} +(95888.3 + 166083. i) q^{22} +(-514299. - 890791. i) q^{23} -1.31173e6i q^{24} +(-970267. - 1.68055e6i) q^{25} +(2.82558e6 - 270969. i) q^{26} -1.24680e6 q^{27} +(688754. - 1.41549e6i) q^{28} +(-2.88438e6 + 4.99590e6i) q^{29} -557122. q^{30} +(-411744. + 237720. i) q^{31} +(-4.59158e6 - 2.65095e6i) q^{32} -1.25318e6i q^{33} +9.49396e6i q^{34} +(640958. + 311879. i) q^{35} +(1.58112e6 - 2.73858e6i) q^{36} +(-1.56762e7 + 9.05068e6i) q^{37} +(7.56650e6 + 1.31056e7i) q^{38} +(-1.68756e7 - 7.69853e6i) q^{39} +(408581. - 707683. i) q^{40} +(-1.25179e7 - 7.22720e6i) q^{41} +(-2.61313e7 + 1.76611e7i) q^{42} +(2.18877e6 + 3.79107e6i) q^{43} +(-1.49309e6 - 862034. i) q^{44} +(1.24008e6 + 715958. i) q^{45} +(2.45543e7 + 1.41764e7i) q^{46} +(-3.68808e7 - 2.12932e7i) q^{47} +(2.95052e7 + 5.11045e7i) q^{48} +(3.99504e7 - 5.69040e6i) q^{49} +(4.63237e7 + 2.67450e7i) q^{50} +(3.10194e7 - 5.37272e7i) q^{51} +(-2.07807e7 + 1.48106e7i) q^{52} +(-2.28511e7 - 3.95792e7i) q^{53} +(2.97631e7 - 1.71837e7i) q^{54} +(390343. - 676094. i) q^{55} +(-3.26991e6 - 4.61455e7i) q^{56} -9.88875e7i q^{57} -1.59014e8i q^{58} +(3.69279e7 + 2.13203e7i) q^{59} +(4.33750e6 - 2.50426e6i) q^{60} -3.90134e7 q^{61} +(6.55266e6 - 1.13495e7i) q^{62} +(8.08611e7 - 5.72987e6i) q^{63} -2.15933e7 q^{64} +(-6.70649e6 - 9.40985e6i) q^{65} +(1.72716e7 + 2.99153e7i) q^{66} +4.91502e7i q^{67} +(-4.26752e7 - 7.39156e7i) q^{68} +(-9.26366e7 - 1.60451e8i) q^{69} +(-1.95991e7 + 1.38881e6i) q^{70} +(2.25789e8 - 1.30359e8i) q^{71} -9.29313e7i q^{72} +(1.44684e8 - 8.35334e7i) q^{73} +(2.49478e8 - 4.32108e8i) q^{74} +(-1.74767e8 - 3.02705e8i) q^{75} +(-1.17819e8 - 6.80226e7i) q^{76} +(-3.12395e6 - 4.40858e7i) q^{77} +(5.08951e8 - 4.88076e7i) q^{78} +(2.66269e8 - 4.61191e8i) q^{79} +3.67615e7i q^{80} -4.75752e8 q^{81} +3.98429e8 q^{82} -1.31052e8i q^{83} +(1.24060e8 - 2.54962e8i) q^{84} +(3.34702e7 - 1.93241e7i) q^{85} +(-1.04499e8 - 6.03325e7i) q^{86} +(-5.19542e8 + 8.99873e8i) q^{87} -5.06665e7 q^{88} +(9.55022e8 - 5.51382e8i) q^{89} -3.94702e7 q^{90} +(-6.12861e8 - 2.28761e8i) q^{91} -2.54891e8 q^{92} +(-7.41643e7 + 4.28188e7i) q^{93} +1.17387e9 q^{94} +(3.08018e7 - 5.33503e7i) q^{95} +(-8.27046e8 - 4.77495e8i) q^{96} +(2.90215e8 - 1.67556e8i) q^{97} +(-8.75253e8 + 6.86446e8i) q^{98} -8.87832e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 164 q - 3 q^{2} + 322 q^{3} + 20481 q^{4} - 6 q^{6} + 1023 q^{7} + 1021818 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 164 q - 3 q^{2} + 322 q^{3} + 20481 q^{4} - 6 q^{6} + 1023 q^{7} + 1021818 q^{9} - 82050 q^{10} + 43064 q^{12} - 232462 q^{13} + 82708 q^{14} + 338445 q^{15} - 4712643 q^{16} + 638795 q^{17} - 1176873 q^{18} + 571062 q^{20} + 1367523 q^{21} - 1417332 q^{22} + 1074033 q^{23} + 29660776 q^{25} - 4350684 q^{26} + 7350574 q^{27} - 5807904 q^{28} + 996812 q^{29} + 18354032 q^{30} + 21474090 q^{31} + 786429 q^{32} - 14921172 q^{35} + 131881331 q^{36} + 6476901 q^{37} - 8950274 q^{38} + 27439160 q^{39} - 7901342 q^{40} + 24649770 q^{41} + 107058858 q^{42} + 15892214 q^{43} + 1176612 q^{44} + 20834727 q^{45} + 277543272 q^{46} + 69222114 q^{47} - 15455476 q^{48} - 69917499 q^{49} + 309166224 q^{50} + 52823362 q^{51} - 95118408 q^{52} - 155327528 q^{53} + 82174923 q^{54} - 77925569 q^{55} - 282686919 q^{56} - 216056427 q^{59} + 290928939 q^{60} + 937523074 q^{61} + 238770500 q^{62} - 521903604 q^{63} - 2035250696 q^{64} + 418729590 q^{65} - 154929237 q^{66} - 598026797 q^{68} + 127053056 q^{69} + 1180478502 q^{70} - 269829840 q^{71} + 35353098 q^{73} - 460031457 q^{74} + 803288072 q^{75} + 1140965370 q^{76} - 1032378781 q^{77} - 835494667 q^{78} - 683323974 q^{79} + 3448679004 q^{81} + 649989068 q^{82} + 2491042464 q^{84} - 196261605 q^{85} - 572477022 q^{86} - 1849967933 q^{87} - 74806442 q^{88} - 207815607 q^{89} - 9086462948 q^{90} - 1222123653 q^{91} - 2683122798 q^{92} + 389990277 q^{93} + 5123642528 q^{94} + 198982451 q^{95} - 392112 q^{96} + 6155159124 q^{97} + 1935772011 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −23.8716 + 13.7823i −1.05499 + 0.609096i −0.924041 0.382293i \(-0.875134\pi\)
−0.130945 + 0.991390i \(0.541801\pi\)
\(3\) 180.122 1.28387 0.641936 0.766758i \(-0.278131\pi\)
0.641936 + 0.766758i \(0.278131\pi\)
\(4\) 123.902 214.605i 0.241997 0.419151i
\(5\) 97.1768 + 56.1050i 0.0695341 + 0.0401455i 0.534364 0.845255i \(-0.320551\pi\)
−0.464830 + 0.885400i \(0.653885\pi\)
\(6\) −4299.81 + 2482.50i −1.35447 + 0.782002i
\(7\) 6336.56 449.013i 0.997499 0.0706835i
\(8\) 7282.43i 0.628596i
\(9\) 12761.0 0.648328
\(10\) −3093.02 −0.0978099
\(11\) 6957.37i 0.143277i −0.997431 0.0716387i \(-0.977177\pi\)
0.997431 0.0716387i \(-0.0228229\pi\)
\(12\) 22317.6 38655.2i 0.310693 0.538136i
\(13\) −93689.6 42740.6i −0.909801 0.415045i
\(14\) −145075. + 98050.9i −1.00929 + 0.682143i
\(15\) 17503.7 + 10105.8i 0.0892728 + 0.0515417i
\(16\) 163806. + 283721.i 0.624872 + 1.08231i
\(17\) 172213. 298282.i 0.500088 0.866177i −0.499912 0.866076i \(-0.666634\pi\)
1.00000 0.000101191i \(-3.22101e-5\pi\)
\(18\) −304626. + 175876.i −0.683977 + 0.394894i
\(19\) 549002.i 0.966458i −0.875494 0.483229i \(-0.839464\pi\)
0.875494 0.483229i \(-0.160536\pi\)
\(20\) 24080.9 13903.1i 0.0336540 0.0194302i
\(21\) 1.14136e6 80877.3i 1.28066 0.0907486i
\(22\) 95888.3 + 166083.i 0.0872697 + 0.151156i
\(23\) −514299. 890791.i −0.383213 0.663744i 0.608307 0.793702i \(-0.291849\pi\)
−0.991520 + 0.129958i \(0.958516\pi\)
\(24\) 1.31173e6i 0.807036i
\(25\) −970267. 1.68055e6i −0.496777 0.860442i
\(26\) 2.82558e6 270969.i 1.21263 0.116289i
\(27\) −1.24680e6 −0.451502
\(28\) 688754. 1.41549e6i 0.211764 0.435207i
\(29\) −2.88438e6 + 4.99590e6i −0.757290 + 1.31166i 0.186938 + 0.982372i \(0.440144\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(30\) −557122. −0.125575
\(31\) −411744. + 237720.i −0.0800755 + 0.0462316i −0.539503 0.841984i \(-0.681388\pi\)
0.459428 + 0.888215i \(0.348055\pi\)
\(32\) −4.59158e6 2.65095e6i −0.774082 0.446917i
\(33\) 1.25318e6i 0.183950i
\(34\) 9.49396e6i 1.21841i
\(35\) 640958. + 311879.i 0.0721978 + 0.0351302i
\(36\) 1.58112e6 2.73858e6i 0.156893 0.271747i
\(37\) −1.56762e7 + 9.05068e6i −1.37510 + 0.793914i −0.991565 0.129613i \(-0.958627\pi\)
−0.383535 + 0.923527i \(0.625293\pi\)
\(38\) 7.56650e6 + 1.31056e7i 0.588666 + 1.01960i
\(39\) −1.68756e7 7.69853e6i −1.16807 0.532865i
\(40\) 408581. 707683.i 0.0252353 0.0437088i
\(41\) −1.25179e7 7.22720e6i −0.691836 0.399432i 0.112463 0.993656i \(-0.464126\pi\)
−0.804300 + 0.594224i \(0.797459\pi\)
\(42\) −2.61313e7 + 1.76611e7i −1.29580 + 0.875784i
\(43\) 2.18877e6 + 3.79107e6i 0.0976321 + 0.169104i 0.910704 0.413059i \(-0.135540\pi\)
−0.813072 + 0.582163i \(0.802206\pi\)
\(44\) −1.49309e6 862034.i −0.0600548 0.0346727i
\(45\) 1.24008e6 + 715958.i 0.0450809 + 0.0260274i
\(46\) 2.45543e7 + 1.41764e7i 0.808568 + 0.466827i
\(47\) −3.68808e7 2.12932e7i −1.10245 0.636502i −0.165589 0.986195i \(-0.552953\pi\)
−0.936864 + 0.349693i \(0.886286\pi\)
\(48\) 2.95052e7 + 5.11045e7i 0.802256 + 1.38955i
\(49\) 3.99504e7 5.69040e6i 0.990008 0.141013i
\(50\) 4.63237e7 + 2.67450e7i 1.04818 + 0.605170i
\(51\) 3.10194e7 5.37272e7i 0.642049 1.11206i
\(52\) −2.07807e7 + 1.48106e7i −0.394135 + 0.280904i
\(53\) −2.28511e7 3.95792e7i −0.397801 0.689011i 0.595654 0.803241i \(-0.296893\pi\)
−0.993454 + 0.114231i \(0.963560\pi\)
\(54\) 2.97631e7 1.71837e7i 0.476328 0.275008i
\(55\) 390343. 676094.i 0.00575194 0.00996266i
\(56\) −3.26991e6 4.61455e7i −0.0444313 0.627023i
\(57\) 9.88875e7i 1.24081i
\(58\) 1.59014e8i 1.84505i
\(59\) 3.69279e7 + 2.13203e7i 0.396753 + 0.229065i 0.685082 0.728466i \(-0.259766\pi\)
−0.288329 + 0.957531i \(0.593100\pi\)
\(60\) 4.33750e6 2.50426e6i 0.0432075 0.0249458i
\(61\) −3.90134e7 −0.360769 −0.180385 0.983596i \(-0.557734\pi\)
−0.180385 + 0.983596i \(0.557734\pi\)
\(62\) 6.55266e6 1.13495e7i 0.0563190 0.0975474i
\(63\) 8.08611e7 5.72987e6i 0.646706 0.0458261i
\(64\) −2.15933e7 −0.160883
\(65\) −6.70649e6 9.40985e6i −0.0465999 0.0653842i
\(66\) 1.72716e7 + 2.99153e7i 0.112043 + 0.194065i
\(67\) 4.91502e7i 0.297981i 0.988839 + 0.148991i \(0.0476024\pi\)
−0.988839 + 0.148991i \(0.952398\pi\)
\(68\) −4.26752e7 7.39156e7i −0.242039 0.419224i
\(69\) −9.26366e7 1.60451e8i −0.491996 0.852163i
\(70\) −1.95991e7 + 1.38881e6i −0.0975653 + 0.00691355i
\(71\) 2.25789e8 1.30359e8i 1.05449 0.608807i 0.130584 0.991437i \(-0.458315\pi\)
0.923902 + 0.382630i \(0.124982\pi\)
\(72\) 9.29313e7i 0.407536i
\(73\) 1.44684e8 8.35334e7i 0.596304 0.344276i −0.171282 0.985222i \(-0.554791\pi\)
0.767586 + 0.640946i \(0.221458\pi\)
\(74\) 2.49478e8 4.32108e8i 0.967140 1.67514i
\(75\) −1.74767e8 3.02705e8i −0.637798 1.10470i
\(76\) −1.17819e8 6.80226e7i −0.405091 0.233880i
\(77\) −3.12395e6 4.40858e7i −0.0101273 0.142919i
\(78\) 5.08951e8 4.88076e7i 1.55686 0.149301i
\(79\) 2.66269e8 4.61191e8i 0.769127 1.33217i −0.168910 0.985632i \(-0.554025\pi\)
0.938037 0.346536i \(-0.112642\pi\)
\(80\) 3.67615e7i 0.100343i
\(81\) −4.75752e8 −1.22800
\(82\) 3.98429e8 0.973170
\(83\) 1.31052e8i 0.303105i −0.988449 0.151552i \(-0.951573\pi\)
0.988449 0.151552i \(-0.0484272\pi\)
\(84\) 1.24060e8 2.54962e8i 0.271878 0.558751i
\(85\) 3.34702e7 1.93241e7i 0.0695462 0.0401525i
\(86\) −1.04499e8 6.03325e7i −0.206001 0.118935i
\(87\) −5.19542e8 + 8.99873e8i −0.972263 + 1.68401i
\(88\) −5.06665e7 −0.0900635
\(89\) 9.55022e8 5.51382e8i 1.61346 0.931532i 0.624900 0.780704i \(-0.285140\pi\)
0.988560 0.150827i \(-0.0481938\pi\)
\(90\) −3.94702e7 −0.0634129
\(91\) −6.12861e8 2.28761e8i −0.936862 0.349699i
\(92\) −2.54891e8 −0.370945
\(93\) −7.41643e7 + 4.28188e7i −0.102807 + 0.0593555i
\(94\) 1.17387e9 1.55076
\(95\) 3.08018e7 5.33503e7i 0.0387989 0.0672017i
\(96\) −8.27046e8 4.77495e8i −0.993823 0.573784i
\(97\) 2.90215e8 1.67556e8i 0.332849 0.192170i −0.324256 0.945969i \(-0.605114\pi\)
0.657105 + 0.753799i \(0.271781\pi\)
\(98\) −8.75253e8 + 6.86446e8i −0.958553 + 0.751777i
\(99\) 8.87832e7i 0.0928907i
\(100\) −4.80873e8 −0.480873
\(101\) 2.05113e8 0.196131 0.0980656 0.995180i \(-0.468735\pi\)
0.0980656 + 0.995180i \(0.468735\pi\)
\(102\) 1.71007e9i 1.56428i
\(103\) −6.25757e8 + 1.08384e9i −0.547820 + 0.948852i 0.450603 + 0.892724i \(0.351209\pi\)
−0.998424 + 0.0561282i \(0.982124\pi\)
\(104\) −3.11255e8 + 6.82288e8i −0.260896 + 0.571897i
\(105\) 1.15451e8 + 5.61764e7i 0.0926927 + 0.0451027i
\(106\) 1.09098e9 + 6.29880e8i 0.839348 + 0.484598i
\(107\) −2.26116e8 3.91645e8i −0.166765 0.288845i 0.770516 0.637421i \(-0.219999\pi\)
−0.937281 + 0.348576i \(0.886665\pi\)
\(108\) −1.54481e8 + 2.67570e8i −0.109262 + 0.189247i
\(109\) −1.55277e9 + 8.96493e8i −1.05363 + 0.608314i −0.923664 0.383204i \(-0.874820\pi\)
−0.129967 + 0.991518i \(0.541487\pi\)
\(110\) 2.15193e7i 0.0140140i
\(111\) −2.82364e9 + 1.63023e9i −1.76545 + 1.01928i
\(112\) 1.16536e9 + 1.72426e9i 0.699810 + 1.03543i
\(113\) −1.10625e9 1.91608e9i −0.638263 1.10550i −0.985814 0.167843i \(-0.946320\pi\)
0.347551 0.937661i \(-0.387013\pi\)
\(114\) 1.36290e9 + 2.36060e9i 0.755772 + 1.30903i
\(115\) 1.15419e8i 0.0615371i
\(116\) 7.14764e8 + 1.23801e9i 0.366523 + 0.634837i
\(117\) −1.19558e9 5.45414e8i −0.589849 0.269085i
\(118\) −1.17537e9 −0.558092
\(119\) 9.57306e8 1.96741e9i 0.437612 0.899359i
\(120\) 7.35945e7 1.27469e8i 0.0323989 0.0561165i
\(121\) 2.30954e9 0.979472
\(122\) 9.31313e8 5.37694e8i 0.380607 0.219743i
\(123\) −2.25475e9 1.30178e9i −0.888229 0.512819i
\(124\) 1.17816e8i 0.0447516i
\(125\) 4.36908e8i 0.160064i
\(126\) −1.85131e9 + 1.25123e9i −0.654353 + 0.442252i
\(127\) −4.67766e8 + 8.10194e8i −0.159556 + 0.276358i −0.934708 0.355415i \(-0.884339\pi\)
0.775153 + 0.631774i \(0.217673\pi\)
\(128\) 2.86636e9 1.65489e9i 0.943811 0.544910i
\(129\) 3.94247e8 + 6.82855e8i 0.125347 + 0.217108i
\(130\) 2.89784e8 + 1.32198e8i 0.0889875 + 0.0405955i
\(131\) 1.52399e9 2.63963e9i 0.452129 0.783110i −0.546390 0.837531i \(-0.683998\pi\)
0.998518 + 0.0544216i \(0.0173315\pi\)
\(132\) −2.68938e8 1.55271e8i −0.0771027 0.0445153i
\(133\) −2.46509e8 3.47878e9i −0.0683126 0.964040i
\(134\) −6.77402e8 1.17329e9i −0.181499 0.314366i
\(135\) −1.21160e8 6.99518e7i −0.0313948 0.0181258i
\(136\) −2.17222e9 1.25413e9i −0.544475 0.314353i
\(137\) 5.44485e9 + 3.14359e9i 1.32052 + 0.762400i 0.983811 0.179210i \(-0.0573541\pi\)
0.336705 + 0.941610i \(0.390687\pi\)
\(138\) 4.42277e9 + 2.55349e9i 1.03810 + 0.599346i
\(139\) −3.67125e9 6.35880e9i −0.834157 1.44480i −0.894715 0.446638i \(-0.852621\pi\)
0.0605575 0.998165i \(-0.480712\pi\)
\(140\) 1.46347e8 9.89104e7i 0.0321965 0.0217603i
\(141\) −6.64306e9 3.83537e9i −1.41541 0.817187i
\(142\) −3.59330e9 + 6.22378e9i −0.741645 + 1.28457i
\(143\) −2.97362e8 + 6.51833e8i −0.0594666 + 0.130354i
\(144\) 2.09034e9 + 3.62057e9i 0.405122 + 0.701692i
\(145\) −5.60590e8 + 3.23657e8i −0.105315 + 0.0608036i
\(146\) −2.30256e9 + 3.98815e9i −0.419395 + 0.726413i
\(147\) 7.19595e9 1.02497e9i 1.27104 0.181043i
\(148\) 4.48560e9i 0.768498i
\(149\) 8.32325e9i 1.38342i 0.722174 + 0.691711i \(0.243143\pi\)
−0.722174 + 0.691711i \(0.756857\pi\)
\(150\) 8.34392e9 + 4.81737e9i 1.34574 + 0.776961i
\(151\) 2.50330e9 1.44528e9i 0.391847 0.226233i −0.291113 0.956689i \(-0.594026\pi\)
0.682960 + 0.730456i \(0.260692\pi\)
\(152\) −3.99807e9 −0.607511
\(153\) 2.19762e9 3.80639e9i 0.324221 0.561567i
\(154\) 6.82176e8 + 1.00934e9i 0.0977357 + 0.144609i
\(155\) −5.33493e7 −0.00742396
\(156\) −3.74307e9 + 2.66772e9i −0.506019 + 0.360645i
\(157\) −4.99458e9 8.65086e9i −0.656070 1.13635i −0.981624 0.190823i \(-0.938884\pi\)
0.325554 0.945523i \(-0.394449\pi\)
\(158\) 1.46792e10i 1.87389i
\(159\) −4.11599e9 7.12910e9i −0.510725 0.884602i
\(160\) −2.97463e8 5.15221e8i −0.0358834 0.0621518i
\(161\) −3.65886e9 5.41363e9i −0.429170 0.634997i
\(162\) 1.13570e10 6.55694e9i 1.29552 0.747970i
\(163\) 1.70894e10i 1.89620i 0.317976 + 0.948099i \(0.396997\pi\)
−0.317976 + 0.948099i \(0.603003\pi\)
\(164\) −3.10199e9 + 1.79093e9i −0.334844 + 0.193322i
\(165\) 7.03095e7 1.21780e8i 0.00738476 0.0127908i
\(166\) 1.80620e9 + 3.12843e9i 0.184620 + 0.319771i
\(167\) 6.15007e9 + 3.55075e9i 0.611866 + 0.353261i 0.773695 0.633558i \(-0.218406\pi\)
−0.161830 + 0.986819i \(0.551740\pi\)
\(168\) −5.88983e8 8.31184e9i −0.0570441 0.805018i
\(169\) 6.95098e9 + 8.00870e9i 0.655475 + 0.755217i
\(170\) −5.32659e8 + 9.22592e8i −0.0489135 + 0.0847207i
\(171\) 7.00584e9i 0.626581i
\(172\) 1.08478e9 0.0945066
\(173\) 1.10837e10 0.940753 0.470377 0.882466i \(-0.344118\pi\)
0.470377 + 0.882466i \(0.344118\pi\)
\(174\) 2.86419e10i 2.36881i
\(175\) −6.90274e9 1.02133e10i −0.556353 0.823176i
\(176\) 1.97395e9 1.13966e9i 0.155071 0.0895300i
\(177\) 6.65153e9 + 3.84026e9i 0.509380 + 0.294091i
\(178\) −1.51986e10 + 2.63248e10i −1.13479 + 1.96551i
\(179\) −1.16878e10 −0.850933 −0.425467 0.904974i \(-0.639890\pi\)
−0.425467 + 0.904974i \(0.639890\pi\)
\(180\) 3.07297e8 1.77418e8i 0.0218188 0.0125971i
\(181\) −1.36267e10 −0.943707 −0.471853 0.881677i \(-0.656415\pi\)
−0.471853 + 0.881677i \(0.656415\pi\)
\(182\) 1.77828e10 2.98574e9i 1.20138 0.201711i
\(183\) −7.02719e9 −0.463182
\(184\) −6.48712e9 + 3.74534e9i −0.417227 + 0.240886i
\(185\) −2.03116e9 −0.127488
\(186\) 1.18028e9 2.04430e9i 0.0723064 0.125238i
\(187\) −2.07526e9 1.19815e9i −0.124104 0.0716513i
\(188\) −9.13924e9 + 5.27654e9i −0.533580 + 0.308063i
\(189\) −7.90042e9 + 5.59830e8i −0.450373 + 0.0319138i
\(190\) 1.69808e9i 0.0945291i
\(191\) 1.50804e10 0.819905 0.409952 0.912107i \(-0.365545\pi\)
0.409952 + 0.912107i \(0.365545\pi\)
\(192\) −3.88944e9 −0.206553
\(193\) 7.80019e9i 0.404667i 0.979317 + 0.202333i \(0.0648524\pi\)
−0.979317 + 0.202333i \(0.935148\pi\)
\(194\) −4.61860e9 + 7.99964e9i −0.234100 + 0.405474i
\(195\) −1.20799e9 1.69492e9i −0.0598283 0.0839449i
\(196\) 3.72876e9 9.27861e9i 0.180473 0.449087i
\(197\) 9.40448e9 + 5.42968e9i 0.444874 + 0.256848i 0.705663 0.708548i \(-0.250649\pi\)
−0.260789 + 0.965396i \(0.583983\pi\)
\(198\) 1.22363e9 + 2.11940e9i 0.0565794 + 0.0979984i
\(199\) 6.28357e9 1.08835e10i 0.284032 0.491958i −0.688342 0.725387i \(-0.741661\pi\)
0.972374 + 0.233428i \(0.0749944\pi\)
\(200\) −1.22385e10 + 7.06590e9i −0.540870 + 0.312272i
\(201\) 8.85305e9i 0.382570i
\(202\) −4.89637e9 + 2.82692e9i −0.206916 + 0.119463i
\(203\) −1.60338e10 + 3.29519e10i −0.662683 + 1.36191i
\(204\) −7.68675e9 1.33139e10i −0.310747 0.538230i
\(205\) −8.10965e8 1.40463e9i −0.0320708 0.0555482i
\(206\) 3.44974e10i 1.33470i
\(207\) −6.56298e9 1.13674e10i −0.248448 0.430324i
\(208\) −3.22055e9 3.35829e10i −0.119301 1.24404i
\(209\) −3.81961e9 −0.138472
\(210\) −3.53024e9 + 2.50155e8i −0.125261 + 0.00887611i
\(211\) −9.96810e9 + 1.72653e10i −0.346212 + 0.599656i −0.985573 0.169250i \(-0.945865\pi\)
0.639362 + 0.768906i \(0.279199\pi\)
\(212\) −1.13252e10 −0.385066
\(213\) 4.06697e10 2.34806e10i 1.35382 0.781631i
\(214\) 1.07955e10 + 6.23279e9i 0.351869 + 0.203152i
\(215\) 4.91205e8i 0.0156780i
\(216\) 9.07973e9i 0.283812i
\(217\) −2.50230e9 + 1.69121e9i −0.0766074 + 0.0517760i
\(218\) 2.47114e10 4.28015e10i 0.741044 1.28353i
\(219\) 2.60608e10 1.50462e10i 0.765578 0.442007i
\(220\) −9.67289e7 1.67539e8i −0.00278390 0.00482186i
\(221\) −2.88833e10 + 2.05854e10i −0.814483 + 0.580490i
\(222\) 4.49365e10 7.78324e10i 1.24168 2.15066i
\(223\) −4.78673e10 2.76362e10i −1.29619 0.748353i −0.316443 0.948612i \(-0.602488\pi\)
−0.979743 + 0.200259i \(0.935822\pi\)
\(224\) −3.02851e10 1.47362e10i −0.803736 0.391084i
\(225\) −1.23816e10 2.14456e10i −0.322074 0.557849i
\(226\) 5.28159e10 + 3.04932e10i 1.34672 + 0.777527i
\(227\) 2.46225e10 + 1.42158e10i 0.615481 + 0.355348i 0.775108 0.631829i \(-0.217696\pi\)
−0.159626 + 0.987178i \(0.551029\pi\)
\(228\) −2.12218e10 1.22524e10i −0.520085 0.300271i
\(229\) −3.14686e10 1.81684e10i −0.756168 0.436574i 0.0717504 0.997423i \(-0.477142\pi\)
−0.827918 + 0.560849i \(0.810475\pi\)
\(230\) 1.59074e9 + 2.75524e9i 0.0374820 + 0.0649208i
\(231\) −5.62693e8 7.94083e9i −0.0130022 0.183490i
\(232\) 3.63823e10 + 2.10053e10i 0.824506 + 0.476029i
\(233\) 4.36135e10 7.55408e10i 0.969437 1.67911i 0.272246 0.962228i \(-0.412233\pi\)
0.697190 0.716886i \(-0.254433\pi\)
\(234\) 3.60574e10 3.45785e9i 0.786181 0.0753936i
\(235\) −2.38931e9 4.13840e9i −0.0511054 0.0885171i
\(236\) 9.15089e9 5.28327e9i 0.192026 0.110866i
\(237\) 4.79609e10 8.30708e10i 0.987461 1.71033i
\(238\) 4.26291e9 + 6.01590e10i 0.0861212 + 1.21536i
\(239\) 2.43279e10i 0.482296i 0.970488 + 0.241148i \(0.0775239\pi\)
−0.970488 + 0.241148i \(0.922476\pi\)
\(240\) 6.62156e9i 0.128828i
\(241\) 7.52016e10 + 4.34176e10i 1.43599 + 0.829067i 0.997568 0.0697040i \(-0.0222055\pi\)
0.438418 + 0.898771i \(0.355539\pi\)
\(242\) −5.51325e10 + 3.18308e10i −1.03333 + 0.596593i
\(243\) −6.11528e10 −1.12509
\(244\) −4.83385e9 + 8.37248e9i −0.0873050 + 0.151217i
\(245\) 4.20151e9 + 1.68844e9i 0.0745003 + 0.0299391i
\(246\) 7.17659e10 1.24943
\(247\) −2.34647e10 + 5.14358e10i −0.401124 + 0.879284i
\(248\) 1.73118e9 + 2.99850e9i 0.0290610 + 0.0503351i
\(249\) 2.36054e10i 0.389148i
\(250\) 6.02158e9 + 1.04297e10i 0.0974946 + 0.168866i
\(251\) −4.10284e10 7.10632e10i −0.652458 1.13009i −0.982525 0.186133i \(-0.940405\pi\)
0.330067 0.943958i \(-0.392929\pi\)
\(252\) 8.78921e9 1.80631e10i 0.137293 0.282157i
\(253\) −6.19756e9 + 3.57816e9i −0.0950996 + 0.0549058i
\(254\) 2.57875e10i 0.388739i
\(255\) 6.02874e9 3.48069e9i 0.0892885 0.0515507i
\(256\) −4.00884e10 + 6.94352e10i −0.583364 + 1.01042i
\(257\) 1.27287e10 + 2.20467e10i 0.182005 + 0.315242i 0.942563 0.334028i \(-0.108408\pi\)
−0.760558 + 0.649270i \(0.775075\pi\)
\(258\) −1.88226e10 1.08672e10i −0.264479 0.152697i
\(259\) −9.52695e10 + 6.43890e10i −1.31554 + 0.889125i
\(260\) −2.85035e9 + 2.73344e8i −0.0386828 + 0.00370963i
\(261\) −3.68077e10 + 6.37528e10i −0.490972 + 0.850388i
\(262\) 8.40163e10i 1.10156i
\(263\) −8.34471e10 −1.07550 −0.537750 0.843104i \(-0.680726\pi\)
−0.537750 + 0.843104i \(0.680726\pi\)
\(264\) −9.12617e9 −0.115630
\(265\) 5.12824e9i 0.0638796i
\(266\) 5.38301e10 + 7.96467e10i 0.659262 + 0.975440i
\(267\) 1.72021e11 9.93162e10i 2.07148 1.19597i
\(268\) 1.05479e10 + 6.08983e9i 0.124899 + 0.0721105i
\(269\) 5.43242e10 9.40922e10i 0.632569 1.09564i −0.354456 0.935073i \(-0.615334\pi\)
0.987025 0.160569i \(-0.0513329\pi\)
\(270\) 3.85638e9 0.0441614
\(271\) −8.07016e10 + 4.65931e10i −0.908909 + 0.524759i −0.880080 0.474826i \(-0.842511\pi\)
−0.0288290 + 0.999584i \(0.509178\pi\)
\(272\) 1.12838e11 1.24996
\(273\) −1.10390e11 4.12049e10i −1.20281 0.448969i
\(274\) −1.73303e11 −1.85750
\(275\) −1.16922e10 + 6.75050e9i −0.123282 + 0.0711769i
\(276\) −4.59116e10 −0.476246
\(277\) −2.61349e10 + 4.52669e10i −0.266723 + 0.461979i −0.968014 0.250897i \(-0.919274\pi\)
0.701290 + 0.712876i \(0.252608\pi\)
\(278\) 1.75277e11 + 1.01197e11i 1.76005 + 1.01616i
\(279\) −5.25428e9 + 3.03356e9i −0.0519152 + 0.0299732i
\(280\) 2.27124e9 4.66773e9i 0.0220827 0.0453832i
\(281\) 6.29490e10i 0.602297i −0.953577 0.301148i \(-0.902630\pi\)
0.953577 0.301148i \(-0.0973699\pi\)
\(282\) 2.11441e11 1.99098
\(283\) −2.36915e9 −0.0219561 −0.0109780 0.999940i \(-0.503494\pi\)
−0.0109780 + 0.999940i \(0.503494\pi\)
\(284\) 6.46073e10i 0.589318i
\(285\) 5.54809e9 9.60957e9i 0.0498129 0.0862784i
\(286\) −1.88523e9 1.96586e10i −0.0166616 0.173742i
\(287\) −8.25654e10 4.01749e10i −0.718339 0.349531i
\(288\) −5.85933e10 3.38289e10i −0.501859 0.289748i
\(289\) −2.07859e7 3.60022e7i −0.000175278 0.000303591i
\(290\) 8.92146e9 1.54524e10i 0.0740704 0.128294i
\(291\) 5.22742e10 3.01805e10i 0.427335 0.246722i
\(292\) 4.13999e10i 0.333255i
\(293\) 4.73163e10 2.73181e10i 0.375065 0.216544i −0.300604 0.953749i \(-0.597188\pi\)
0.675669 + 0.737205i \(0.263855\pi\)
\(294\) −1.57653e11 + 1.23644e11i −1.23066 + 0.965186i
\(295\) 2.39235e9 + 4.14368e9i 0.0183919 + 0.0318557i
\(296\) 6.59109e10 + 1.14161e11i 0.499051 + 0.864381i
\(297\) 8.67444e9i 0.0646901i
\(298\) −1.14713e11 1.98689e11i −0.842638 1.45949i
\(299\) 1.01115e10 + 1.05439e11i 0.0731634 + 0.762926i
\(300\) −8.66160e10 −0.617380
\(301\) 1.55715e10 + 2.30395e10i 0.109341 + 0.161780i
\(302\) −3.98385e10 + 6.90024e10i −0.275595 + 0.477345i
\(303\) 3.69454e10 0.251807
\(304\) 1.55763e11 8.99301e10i 1.04601 0.603912i
\(305\) −3.79120e9 2.18885e9i −0.0250858 0.0144833i
\(306\) 1.21153e11i 0.789927i
\(307\) 1.08841e11i 0.699313i 0.936878 + 0.349656i \(0.113702\pi\)
−0.936878 + 0.349656i \(0.886298\pi\)
\(308\) −9.84809e9 4.79191e9i −0.0623554 0.0303411i
\(309\) −1.12713e11 + 1.95224e11i −0.703331 + 1.21821i
\(310\) 1.27353e9 7.35274e8i 0.00783218 0.00452191i
\(311\) −9.48539e10 1.64292e11i −0.574954 0.995850i −0.996047 0.0888322i \(-0.971687\pi\)
0.421092 0.907018i \(-0.361647\pi\)
\(312\) −5.60640e10 + 1.22895e11i −0.334957 + 0.734242i
\(313\) −1.13773e11 + 1.97061e11i −0.670024 + 1.16052i 0.307873 + 0.951427i \(0.400383\pi\)
−0.977897 + 0.209088i \(0.932950\pi\)
\(314\) 2.38457e11 + 1.37673e11i 1.38429 + 0.799220i
\(315\) 8.17929e9 + 3.97990e9i 0.0468078 + 0.0227759i
\(316\) −6.59826e10 1.14285e11i −0.372252 0.644760i
\(317\) 1.86329e11 + 1.07577e11i 1.03637 + 0.598346i 0.918802 0.394719i \(-0.129158\pi\)
0.117564 + 0.993065i \(0.462492\pi\)
\(318\) 1.96511e11 + 1.13455e11i 1.07762 + 0.622161i
\(319\) 3.47583e10 + 2.00677e10i 0.187932 + 0.108503i
\(320\) −2.09837e9 1.21149e9i −0.0111868 0.00645872i
\(321\) −4.07286e10 7.05440e10i −0.214105 0.370840i
\(322\) 1.61955e11 + 7.88045e10i 0.839543 + 0.408507i
\(323\) −1.63757e11 9.45454e10i −0.837124 0.483314i
\(324\) −5.89468e10 + 1.02099e11i −0.297172 + 0.514716i
\(325\) 1.90761e10 + 1.98920e11i 0.0948452 + 0.989016i
\(326\) −2.35531e11 4.07952e11i −1.15497 2.00046i
\(327\) −2.79689e11 + 1.61478e11i −1.35273 + 0.780997i
\(328\) −5.26316e10 + 9.11605e10i −0.251081 + 0.434885i
\(329\) −2.43258e11 1.18365e11i −1.14469 0.556984i
\(330\) 3.87610e9i 0.0179921i
\(331\) 1.70683e11i 0.781564i 0.920483 + 0.390782i \(0.127795\pi\)
−0.920483 + 0.390782i \(0.872205\pi\)
\(332\) −2.81245e10 1.62377e10i −0.127047 0.0733504i
\(333\) −2.00045e11 + 1.15496e11i −0.891515 + 0.514716i
\(334\) −1.95749e11 −0.860679
\(335\) −2.75758e9 + 4.77626e9i −0.0119626 + 0.0207198i
\(336\) 2.09908e11 + 3.10578e11i 0.898467 + 1.32937i
\(337\) 1.79523e11 0.758204 0.379102 0.925355i \(-0.376233\pi\)
0.379102 + 0.925355i \(0.376233\pi\)
\(338\) −2.76309e11 9.53801e10i −1.15152 0.397496i
\(339\) −1.99260e11 3.45128e11i −0.819448 1.41933i
\(340\) 9.57718e9i 0.0388671i
\(341\) 1.65391e9 + 2.86465e9i 0.00662394 + 0.0114730i
\(342\) 9.65564e10 + 1.67241e11i 0.381648 + 0.661034i
\(343\) 2.50593e11 5.39958e10i 0.977564 0.210638i
\(344\) 2.76082e10 1.59396e10i 0.106298 0.0613711i
\(345\) 2.07895e10i 0.0790058i
\(346\) −2.64585e11 + 1.52758e11i −0.992481 + 0.573009i
\(347\) −1.38902e11 + 2.40586e11i −0.514312 + 0.890815i 0.485550 + 0.874209i \(0.338619\pi\)
−0.999862 + 0.0166059i \(0.994714\pi\)
\(348\) 1.28745e11 + 2.22993e11i 0.470569 + 0.815049i
\(349\) −1.30779e11 7.55051e10i −0.471870 0.272434i 0.245152 0.969485i \(-0.421162\pi\)
−0.717022 + 0.697050i \(0.754495\pi\)
\(350\) 3.05541e11 + 1.48671e11i 1.08834 + 0.529567i
\(351\) 1.16812e11 + 5.32890e10i 0.410777 + 0.187394i
\(352\) −1.84436e10 + 3.19453e10i −0.0640331 + 0.110909i
\(353\) 1.38509e11i 0.474778i −0.971415 0.237389i \(-0.923708\pi\)
0.971415 0.237389i \(-0.0762916\pi\)
\(354\) −2.11710e11 −0.716518
\(355\) 2.92553e10 0.0977635
\(356\) 2.73270e11i 0.901710i
\(357\) 1.72432e11 3.54374e11i 0.561838 1.15466i
\(358\) 2.79007e11 1.61085e11i 0.897723 0.518300i
\(359\) 1.36301e11 + 7.86936e10i 0.433087 + 0.250043i 0.700661 0.713494i \(-0.252889\pi\)
−0.267574 + 0.963537i \(0.586222\pi\)
\(360\) 5.21392e9 9.03077e9i 0.0163607 0.0283376i
\(361\) 2.12844e10 0.0659597
\(362\) 3.25291e11 1.87807e11i 0.995597 0.574808i
\(363\) 4.16000e11 1.25752
\(364\) −1.25028e11 + 1.03179e11i −0.373294 + 0.308060i
\(365\) 1.87466e10 0.0552846
\(366\) 1.67750e11 9.68506e10i 0.488650 0.282122i
\(367\) 1.77280e11 0.510109 0.255055 0.966927i \(-0.417907\pi\)
0.255055 + 0.966927i \(0.417907\pi\)
\(368\) 1.68491e11 2.91835e11i 0.478918 0.829510i
\(369\) −1.59741e11 9.22265e10i −0.448537 0.258963i
\(370\) 4.84869e10 2.79939e10i 0.134498 0.0776527i
\(371\) −1.62569e11 2.40536e11i −0.445507 0.659169i
\(372\) 2.12214e10i 0.0574553i
\(373\) 2.08365e11 0.557360 0.278680 0.960384i \(-0.410103\pi\)
0.278680 + 0.960384i \(0.410103\pi\)
\(374\) 6.60529e10 0.174570
\(375\) 7.86968e10i 0.205502i
\(376\) −1.55066e11 + 2.68582e11i −0.400102 + 0.692997i
\(377\) 4.83765e11 3.44783e11i 1.23338 0.879044i
\(378\) 1.80880e11 1.22250e11i 0.455698 0.307989i
\(379\) −5.58249e11 3.22305e11i −1.38980 0.802400i −0.396505 0.918032i \(-0.629777\pi\)
−0.993292 + 0.115633i \(0.963111\pi\)
\(380\) −7.63282e9 1.32204e10i −0.0187784 0.0325252i
\(381\) −8.42551e10 + 1.45934e11i −0.204849 + 0.354809i
\(382\) −3.59994e11 + 2.07843e11i −0.864988 + 0.499401i
\(383\) 2.79351e11i 0.663369i −0.943390 0.331684i \(-0.892383\pi\)
0.943390 0.331684i \(-0.107617\pi\)
\(384\) 5.16294e11 2.98083e11i 1.21173 0.699594i
\(385\) 2.16986e9 4.45938e9i 0.00503336 0.0103443i
\(386\) −1.07504e11 1.86203e11i −0.246481 0.426917i
\(387\) 2.79310e10 + 4.83779e10i 0.0632976 + 0.109635i
\(388\) 8.30421e10i 0.186018i
\(389\) −2.36024e10 4.08805e10i −0.0522615 0.0905196i 0.838711 0.544577i \(-0.183310\pi\)
−0.890973 + 0.454057i \(0.849976\pi\)
\(390\) 5.21965e10 + 2.38117e10i 0.114249 + 0.0521195i
\(391\) −3.54276e11 −0.766560
\(392\) −4.14399e10 2.90936e11i −0.0886404 0.622314i
\(393\) 2.74505e11 4.75457e11i 0.580475 1.00541i
\(394\) −2.99333e11 −0.625781
\(395\) 5.17503e10 2.98780e10i 0.106961 0.0617540i
\(396\) −1.90533e10 1.10004e10i −0.0389352 0.0224792i
\(397\) 3.96248e11i 0.800589i 0.916387 + 0.400294i \(0.131092\pi\)
−0.916387 + 0.400294i \(0.868908\pi\)
\(398\) 3.46408e11i 0.692012i
\(399\) −4.44018e10 6.26607e11i −0.0877046 1.23770i
\(400\) 3.17872e11 5.50570e11i 0.620844 1.07533i
\(401\) 7.24324e11 4.18189e11i 1.39889 0.807649i 0.404612 0.914488i \(-0.367406\pi\)
0.994276 + 0.106840i \(0.0340731\pi\)
\(402\) −1.22015e11 2.11337e11i −0.233022 0.403606i
\(403\) 4.87364e10 4.67375e9i 0.0920410 0.00882659i
\(404\) 2.54139e10 4.40182e10i 0.0474631 0.0822085i
\(405\) −4.62320e10 2.66921e10i −0.0853877 0.0492986i
\(406\) −7.13992e10 1.00760e12i −0.130415 1.84043i
\(407\) 6.29689e10 + 1.09065e11i 0.113750 + 0.197021i
\(408\) −3.91265e11 2.25897e11i −0.699036 0.403589i
\(409\) 1.34955e11 + 7.79161e10i 0.238470 + 0.137681i 0.614473 0.788938i \(-0.289369\pi\)
−0.376003 + 0.926618i \(0.622702\pi\)
\(410\) 3.87180e10 + 2.23539e10i 0.0676684 + 0.0390684i
\(411\) 9.80739e11 + 5.66230e11i 1.69537 + 0.978824i
\(412\) 1.55065e11 + 2.68581e11i 0.265141 + 0.459238i
\(413\) 2.43569e11 + 1.18516e11i 0.411952 + 0.200449i
\(414\) 3.13338e11 + 1.80906e11i 0.524217 + 0.302657i
\(415\) 7.35269e9 1.27352e10i 0.0121683 0.0210761i
\(416\) 3.16880e11 + 4.44613e11i 0.518770 + 0.727884i
\(417\) −6.61275e11 1.14536e12i −1.07095 1.85494i
\(418\) 9.11802e10 5.26429e10i 0.146086 0.0843425i
\(419\) −4.04918e11 + 7.01338e11i −0.641806 + 1.11164i 0.343224 + 0.939254i \(0.388481\pi\)
−0.985029 + 0.172387i \(0.944852\pi\)
\(420\) 2.63604e10 1.78160e10i 0.0413361 0.0279375i
\(421\) 4.08102e11i 0.633140i 0.948569 + 0.316570i \(0.102531\pi\)
−0.948569 + 0.316570i \(0.897469\pi\)
\(422\) 5.49533e11i 0.843505i
\(423\) −4.70637e11 2.71723e11i −0.714751 0.412662i
\(424\) −2.88233e11 + 1.66411e11i −0.433109 + 0.250056i
\(425\) −6.68371e11 −0.993727
\(426\) −6.47233e11 + 1.12104e12i −0.952177 + 1.64922i
\(427\) −2.47211e11 + 1.75175e10i −0.359867 + 0.0255004i
\(428\) −1.12065e11 −0.161426
\(429\) −5.35615e10 + 1.17410e11i −0.0763475 + 0.167358i
\(430\) −6.76992e9 1.17258e10i −0.00954939 0.0165400i
\(431\) 7.17819e11i 1.00200i −0.865448 0.500999i \(-0.832966\pi\)
0.865448 0.500999i \(-0.167034\pi\)
\(432\) −2.04234e11 3.53743e11i −0.282131 0.488665i
\(433\) −3.26978e11 5.66343e11i −0.447016 0.774255i 0.551174 0.834390i \(-0.314180\pi\)
−0.998190 + 0.0601353i \(0.980847\pi\)
\(434\) 3.64252e10 7.48593e10i 0.0492831 0.101284i
\(435\) −1.00975e11 + 5.82978e10i −0.135211 + 0.0780640i
\(436\) 4.44310e11i 0.588840i
\(437\) −4.89046e11 + 2.82351e11i −0.641481 + 0.370359i
\(438\) −4.14742e11 + 7.18355e11i −0.538449 + 0.932622i
\(439\) −1.17874e11 2.04164e11i −0.151471 0.262355i 0.780298 0.625408i \(-0.215068\pi\)
−0.931768 + 0.363053i \(0.881734\pi\)
\(440\) −4.92361e9 2.84265e9i −0.00626248 0.00361565i
\(441\) 5.09808e11 7.26154e10i 0.641849 0.0914229i
\(442\) 4.05777e11 8.89485e11i 0.505694 1.10851i
\(443\) 2.50062e11 4.33120e11i 0.308483 0.534308i −0.669548 0.742769i \(-0.733512\pi\)
0.978031 + 0.208461i \(0.0668455\pi\)
\(444\) 8.07956e11i 0.986653i
\(445\) 1.23741e11 0.149587
\(446\) 1.52356e12 1.82328
\(447\) 1.49920e12i 1.77614i
\(448\) −1.36827e11 + 9.69569e9i −0.160480 + 0.0113718i
\(449\) 1.32277e12 7.63700e11i 1.53594 0.886777i 0.536872 0.843664i \(-0.319606\pi\)
0.999070 0.0431131i \(-0.0137276\pi\)
\(450\) 5.91138e11 + 3.41294e11i 0.679567 + 0.392348i
\(451\) −5.02823e10 + 8.70914e10i −0.0572296 + 0.0991245i
\(452\) −5.48267e11 −0.617830
\(453\) 4.50900e11 2.60327e11i 0.503082 0.290454i
\(454\) −7.83703e11 −0.865766
\(455\) −4.67212e10 5.66148e10i −0.0511050 0.0619268i
\(456\) −7.20141e11 −0.779966
\(457\) −6.99688e11 + 4.03965e11i −0.750380 + 0.433232i −0.825831 0.563917i \(-0.809294\pi\)
0.0754512 + 0.997149i \(0.475960\pi\)
\(458\) 1.00161e12 1.06366
\(459\) −2.14715e11 + 3.71898e11i −0.225791 + 0.391081i
\(460\) −2.47695e10 1.43007e10i −0.0257933 0.0148918i
\(461\) −2.66233e11 + 1.53710e11i −0.274541 + 0.158507i −0.630950 0.775824i \(-0.717335\pi\)
0.356408 + 0.934330i \(0.384001\pi\)
\(462\) 1.22875e11 + 1.81805e11i 0.125480 + 0.185660i
\(463\) 1.66768e12i 1.68655i 0.537482 + 0.843275i \(0.319376\pi\)
−0.537482 + 0.843275i \(0.680624\pi\)
\(464\) −1.88992e12 −1.89284
\(465\) −9.60939e9 −0.00953142
\(466\) 2.40437e12i 2.36192i
\(467\) −5.78374e11 + 1.00177e12i −0.562707 + 0.974638i 0.434552 + 0.900647i \(0.356907\pi\)
−0.997259 + 0.0739906i \(0.976427\pi\)
\(468\) −2.65183e11 + 1.88999e11i −0.255529 + 0.182118i
\(469\) 2.20691e10 + 3.11443e11i 0.0210624 + 0.297236i
\(470\) 1.14073e11 + 6.58602e10i 0.107831 + 0.0622562i
\(471\) −8.99635e11 1.55821e12i −0.842310 1.45892i
\(472\) 1.55264e11 2.68925e11i 0.143989 0.249397i
\(473\) 2.63758e10 1.52281e10i 0.0242287 0.0139885i
\(474\) 2.64404e12i 2.40584i
\(475\) −9.22626e11 + 5.32679e11i −0.831581 + 0.480114i
\(476\) −3.03603e11 4.49209e11i −0.271066 0.401067i
\(477\) −2.91603e11 5.05072e11i −0.257905 0.446705i
\(478\) −3.35293e11 5.80745e11i −0.293765 0.508815i
\(479\) 5.19345e11i 0.450761i 0.974271 + 0.225381i \(0.0723625\pi\)
−0.974271 + 0.225381i \(0.927637\pi\)
\(480\) −5.35798e10 9.28029e10i −0.0460697 0.0797950i
\(481\) 1.85553e12 1.77943e11i 1.58058 0.151575i
\(482\) −2.39358e12 −2.01993
\(483\) −6.59042e11 9.75115e11i −0.551000 0.815255i
\(484\) 2.86158e11 4.95640e11i 0.237029 0.410546i
\(485\) 3.76029e10 0.0308591
\(486\) 1.45981e12 8.42824e11i 1.18696 0.685289i
\(487\) 2.16708e10 + 1.25117e10i 0.0174580 + 0.0100794i 0.508704 0.860942i \(-0.330125\pi\)
−0.491246 + 0.871021i \(0.663458\pi\)
\(488\) 2.84112e11i 0.226778i
\(489\) 3.07819e12i 2.43447i
\(490\) −1.23567e11 + 1.76005e10i −0.0968326 + 0.0137925i
\(491\) −1.60501e9 + 2.77995e9i −0.00124626 + 0.00215859i −0.866648 0.498920i \(-0.833730\pi\)
0.865402 + 0.501079i \(0.167063\pi\)
\(492\) −5.58737e11 + 3.22587e11i −0.429897 + 0.248201i
\(493\) 9.93458e11 + 1.72072e12i 0.757422 + 1.31189i
\(494\) −1.48763e11 1.55125e12i −0.112389 1.17195i
\(495\) 4.98118e9 8.62767e9i 0.00372914 0.00645907i
\(496\) −1.34893e11 7.78803e10i −0.100074 0.0577777i
\(497\) 1.37219e12 9.27413e11i 1.00882 0.681819i
\(498\) 3.25336e11 + 5.63499e11i 0.237029 + 0.410546i
\(499\) −1.32611e12 7.65630e11i −0.957474 0.552798i −0.0620795 0.998071i \(-0.519773\pi\)
−0.895395 + 0.445273i \(0.853107\pi\)
\(500\) −9.37626e10 5.41339e10i −0.0670911 0.0387351i
\(501\) 1.10776e12 + 6.39568e11i 0.785557 + 0.453542i
\(502\) 1.95883e12 + 1.13093e12i 1.37667 + 0.794819i
\(503\) −1.22188e12 2.11635e12i −0.851082 1.47412i −0.880233 0.474542i \(-0.842614\pi\)
0.0291511 0.999575i \(-0.490720\pi\)
\(504\) −4.17274e10 5.88865e11i −0.0288061 0.406517i
\(505\) 1.99322e10 + 1.15079e10i 0.0136378 + 0.00787378i
\(506\) 9.86305e10 1.70833e11i 0.0668858 0.115850i
\(507\) 1.25203e12 + 1.44255e12i 0.841546 + 0.969602i
\(508\) 1.15915e11 + 2.00770e11i 0.0772238 + 0.133756i
\(509\) 1.00106e12 5.77965e11i 0.661046 0.381655i −0.131629 0.991299i \(-0.542021\pi\)
0.792676 + 0.609644i \(0.208688\pi\)
\(510\) −9.59437e10 + 1.66179e11i −0.0627987 + 0.108771i
\(511\) 8.79291e11 5.94279e11i 0.570478 0.385564i
\(512\) 5.15432e11i 0.331479i
\(513\) 6.84496e11i 0.436358i
\(514\) −6.07707e11 3.50860e11i −0.384026 0.221717i
\(515\) −1.21618e11 + 7.02162e10i −0.0761843 + 0.0439850i
\(516\) 1.95392e11 0.121334
\(517\) −1.48144e11 + 2.56593e11i −0.0911963 + 0.157957i
\(518\) 1.38681e12 2.85010e12i 0.846317 1.73931i
\(519\) 1.99641e12 1.20781
\(520\) −6.85266e10 + 4.88395e10i −0.0411002 + 0.0292925i
\(521\) −2.47498e10 4.28679e10i −0.0147164 0.0254896i 0.858573 0.512691i \(-0.171351\pi\)
−0.873290 + 0.487201i \(0.838018\pi\)
\(522\) 2.02918e12i 1.19620i
\(523\) −4.10683e11 7.11324e11i −0.240021 0.415728i 0.720699 0.693248i \(-0.243821\pi\)
−0.960720 + 0.277520i \(0.910488\pi\)
\(524\) −3.77652e11 6.54113e11i −0.218827 0.379020i
\(525\) −1.24334e12 1.83963e12i −0.714286 1.05685i
\(526\) 1.99202e12 1.15009e12i 1.13464 0.655083i
\(527\) 1.63754e11i 0.0924794i
\(528\) 3.55553e11 2.05278e11i 0.199091 0.114945i
\(529\) 3.71570e11 6.43578e11i 0.206296 0.357315i
\(530\) 7.06789e10 + 1.22419e11i 0.0389088 + 0.0673921i
\(531\) 4.71238e11 + 2.72069e11i 0.257226 + 0.148509i
\(532\) −7.77108e11 3.78127e11i −0.420609 0.204661i
\(533\) 8.63900e11 + 1.21213e12i 0.463651 + 0.650547i
\(534\) −2.73761e12 + 4.74167e12i −1.45692 + 2.52346i
\(535\) 5.07450e10i 0.0267794i
\(536\) 3.57933e11 0.187310
\(537\) −2.10524e12 −1.09249
\(538\) 2.99484e12i 1.54118i
\(539\) −3.95902e10 2.77949e11i −0.0202040 0.141846i
\(540\) −3.00240e10 + 1.73344e10i −0.0151949 + 0.00877276i
\(541\) −1.18241e11 6.82666e10i −0.0593446 0.0342626i 0.470034 0.882648i \(-0.344242\pi\)
−0.529379 + 0.848386i \(0.677575\pi\)
\(542\) 1.28432e12 2.22450e12i 0.639257 1.10723i
\(543\) −2.45447e12 −1.21160
\(544\) −1.58146e12 + 9.13056e11i −0.774218 + 0.446995i
\(545\) −2.01191e11 −0.0976843
\(546\) 3.20308e12 5.37798e11i 1.54241 0.258972i
\(547\) −3.81914e11 −0.182399 −0.0911996 0.995833i \(-0.529070\pi\)
−0.0911996 + 0.995833i \(0.529070\pi\)
\(548\) 1.34926e12 7.78995e11i 0.639121 0.368997i
\(549\) −4.97852e11 −0.233897
\(550\) 1.86075e11 3.22291e11i 0.0867071 0.150181i
\(551\) 2.74276e12 + 1.58353e12i 1.26767 + 0.731888i
\(552\) −1.16848e12 + 6.74620e11i −0.535666 + 0.309267i
\(553\) 1.48015e12 3.04192e12i 0.673041 1.38320i
\(554\) 1.44079e12i 0.649841i
\(555\) −3.65856e11 −0.163679
\(556\) −1.81951e12 −0.807453
\(557\) 4.59448e11i 0.202250i −0.994874 0.101125i \(-0.967756\pi\)
0.994874 0.101125i \(-0.0322442\pi\)
\(558\) 8.36187e10 1.44832e11i 0.0365132 0.0632427i
\(559\) −4.30328e10 4.48733e11i −0.0186400 0.194372i
\(560\) 1.65064e10 + 2.32941e11i 0.00709261 + 0.100092i
\(561\) −3.73800e11 2.15813e11i −0.159333 0.0919911i
\(562\) 8.67581e11 + 1.50269e12i 0.366857 + 0.635414i
\(563\) −1.54264e11 + 2.67193e11i −0.0647108 + 0.112082i −0.896566 0.442911i \(-0.853946\pi\)
0.831855 + 0.554993i \(0.187279\pi\)
\(564\) −1.64618e12 + 9.50423e11i −0.685049 + 0.395513i
\(565\) 2.48265e11i 0.102494i
\(566\) 5.65555e10 3.26523e10i 0.0231633 0.0133734i
\(567\) −3.01463e12 + 2.13619e11i −1.22493 + 0.0867992i
\(568\) −9.49333e11 1.64429e12i −0.382694 0.662845i
\(569\) 7.38375e10 + 1.27890e11i 0.0295306 + 0.0511484i 0.880413 0.474208i \(-0.157265\pi\)
−0.850882 + 0.525356i \(0.823932\pi\)
\(570\) 3.05861e11i 0.121363i
\(571\) 2.14839e12 + 3.72112e12i 0.845768 + 1.46491i 0.884953 + 0.465681i \(0.154190\pi\)
−0.0391852 + 0.999232i \(0.512476\pi\)
\(572\) 1.03043e11 + 1.44579e11i 0.0402472 + 0.0564707i
\(573\) 2.71632e12 1.05265
\(574\) 2.52467e12 1.78900e11i 0.970736 0.0687870i
\(575\) −9.98014e11 + 1.72861e12i −0.380742 + 0.659465i
\(576\) −2.75553e11 −0.104305
\(577\) −4.28969e12 + 2.47665e12i −1.61115 + 0.930196i −0.622041 + 0.782985i \(0.713696\pi\)
−0.989105 + 0.147211i \(0.952970\pi\)
\(578\) 9.92383e8 + 5.72953e8i 0.000369832 + 0.000213522i
\(579\) 1.40499e12i 0.519540i
\(580\) 1.60407e11i 0.0588570i
\(581\) −5.88442e10 8.30420e11i −0.0214245 0.302347i
\(582\) −8.31912e11 + 1.44091e12i −0.300555 + 0.520577i
\(583\) −2.75367e11 + 1.58983e11i −0.0987197 + 0.0569958i
\(584\) −6.08326e11 1.05365e12i −0.216411 0.374834i
\(585\) −8.55818e10 1.20079e11i −0.0302120 0.0423904i
\(586\) −7.53010e11 + 1.30425e12i −0.263792 + 0.456901i
\(587\) −3.30319e12 1.90710e12i −1.14832 0.662982i −0.199841 0.979828i \(-0.564043\pi\)
−0.948477 + 0.316846i \(0.897376\pi\)
\(588\) 6.71632e11 1.67128e12i 0.231704 0.576570i
\(589\) 1.30509e11 + 2.26048e11i 0.0446809 + 0.0773896i
\(590\) −1.14219e11 6.59442e10i −0.0388064 0.0224049i
\(591\) 1.69396e12 + 9.78006e11i 0.571161 + 0.329760i
\(592\) −5.13574e12 2.96512e12i −1.71852 0.992189i
\(593\) 3.12009e12 + 1.80138e12i 1.03614 + 0.598218i 0.918739 0.394866i \(-0.129209\pi\)
0.117406 + 0.993084i \(0.462542\pi\)
\(594\) −1.19554e11 2.07073e11i −0.0394025 0.0682471i
\(595\) 2.03409e11 1.37477e11i 0.0665342 0.0449679i
\(596\) 1.78621e12 + 1.03127e12i 0.579862 + 0.334784i
\(597\) 1.13181e12 1.96035e12i 0.364661 0.631612i
\(598\) −1.69457e12 2.37765e12i −0.541882 0.760312i
\(599\) 1.58550e12 + 2.74617e12i 0.503206 + 0.871579i 0.999993 + 0.00370646i \(0.00117981\pi\)
−0.496787 + 0.867873i \(0.665487\pi\)
\(600\) −2.20443e12 + 1.27273e12i −0.694408 + 0.400917i
\(601\) 1.64733e12 2.85326e12i 0.515045 0.892084i −0.484803 0.874624i \(-0.661109\pi\)
0.999848 0.0174602i \(-0.00555805\pi\)
\(602\) −6.89254e11 3.35379e11i −0.213892 0.104076i
\(603\) 6.27208e11i 0.193189i
\(604\) 7.16295e11i 0.218991i
\(605\) 2.24434e11 + 1.29577e11i 0.0681066 + 0.0393214i
\(606\) −8.81946e11 + 5.09191e11i −0.265653 + 0.153375i
\(607\) 5.68934e12 1.70103 0.850516 0.525949i \(-0.176290\pi\)
0.850516 + 0.525949i \(0.176290\pi\)
\(608\) −1.45538e12 + 2.52079e12i −0.431926 + 0.748118i
\(609\) −2.88805e12 + 5.93538e12i −0.850800 + 1.74852i
\(610\) 1.20669e11 0.0352868
\(611\) 2.54527e12 + 3.57126e12i 0.738836 + 1.03666i
\(612\) −5.44580e11 9.43240e11i −0.156921 0.271795i
\(613\) 1.89118e12i 0.540953i −0.962727 0.270477i \(-0.912819\pi\)
0.962727 0.270477i \(-0.0871813\pi\)
\(614\) −1.50008e12 2.59822e12i −0.425949 0.737765i
\(615\) −1.46073e11 2.53005e11i −0.0411748 0.0713168i
\(616\) −3.21051e11 + 2.27499e10i −0.0898383 + 0.00636601i
\(617\) −3.25286e12 + 1.87804e12i −0.903612 + 0.521700i −0.878370 0.477981i \(-0.841369\pi\)
−0.0252414 + 0.999681i \(0.508035\pi\)
\(618\) 6.21375e12i 1.71359i
\(619\) 2.98606e10 1.72400e10i 0.00817505 0.00471987i −0.495907 0.868376i \(-0.665164\pi\)
0.504082 + 0.863656i \(0.331831\pi\)
\(620\) −6.61010e9 + 1.14490e10i −0.00179657 + 0.00311176i
\(621\) 6.41228e11 + 1.11064e12i 0.173021 + 0.299682i
\(622\) 4.52863e12 + 2.61460e12i 1.21314 + 0.700405i
\(623\) 5.80398e12 3.92268e12i 1.54358 1.04325i
\(624\) −5.80093e11 6.04903e12i −0.153168 1.59718i
\(625\) −1.87054e12 + 3.23987e12i −0.490351 + 0.849313i
\(626\) 6.27221e12i 1.63244i
\(627\) −6.87997e11 −0.177780
\(628\) −2.47536e12 −0.635067
\(629\) 6.23458e12i 1.58811i
\(630\) −2.50105e11 + 1.77226e10i −0.0632543 + 0.00448224i
\(631\) 6.46324e12 3.73156e12i 1.62300 0.937039i 0.636888 0.770957i \(-0.280222\pi\)
0.986112 0.166082i \(-0.0531118\pi\)
\(632\) −3.35859e12 1.93908e12i −0.837394 0.483470i
\(633\) −1.79548e12 + 3.10986e12i −0.444491 + 0.769882i
\(634\) −5.93062e12 −1.45780
\(635\) −9.09120e10 + 5.24881e10i −0.0221891 + 0.0128109i
\(636\) −2.03992e12 −0.494375
\(637\) −3.98615e12 1.17437e12i −0.959237 0.282604i
\(638\) −1.10632e12 −0.264354
\(639\) 2.88130e12 1.66352e12i 0.683652 0.394707i
\(640\) 3.71391e11 0.0875027
\(641\) 7.21213e11 1.24918e12i 0.168734 0.292256i −0.769241 0.638959i \(-0.779365\pi\)
0.937975 + 0.346703i \(0.112699\pi\)
\(642\) 1.94451e12 + 1.12266e12i 0.451755 + 0.260821i
\(643\) 4.79064e12 2.76588e12i 1.10521 0.638092i 0.167624 0.985851i \(-0.446390\pi\)
0.937584 + 0.347759i \(0.113057\pi\)
\(644\) −1.61513e12 + 1.14449e11i −0.370017 + 0.0262197i
\(645\) 8.84769e10i 0.0201285i
\(646\) 5.21220e12 1.17754
\(647\) 1.93927e11 0.0435081 0.0217540 0.999763i \(-0.493075\pi\)
0.0217540 + 0.999763i \(0.493075\pi\)
\(648\) 3.46463e12i 0.771915i
\(649\) 1.48333e11 2.56921e11i 0.0328199 0.0568457i
\(650\) −3.19695e12 4.48563e12i −0.702466 0.985628i
\(651\) −4.50720e11 + 3.04624e11i −0.0983541 + 0.0664737i
\(652\) 3.66748e12 + 2.11742e12i 0.794792 + 0.458873i
\(653\) −1.24614e12 2.15837e12i −0.268198 0.464533i 0.700198 0.713948i \(-0.253095\pi\)
−0.968397 + 0.249415i \(0.919762\pi\)
\(654\) 4.45108e12 7.70950e12i 0.951405 1.64788i
\(655\) 2.96193e11 1.71007e11i 0.0628767 0.0363019i
\(656\) 4.73545e12i 0.998375i
\(657\) 1.84632e12 1.06597e12i 0.386600 0.223204i
\(658\) 7.43831e12 5.27084e11i 1.54688 0.109613i
\(659\) −1.11732e12 1.93525e12i −0.230777 0.399718i 0.727260 0.686362i \(-0.240794\pi\)
−0.958037 + 0.286644i \(0.907460\pi\)
\(660\) −1.74230e10 3.01776e10i −0.00357417 0.00619065i
\(661\) 2.02720e11i 0.0413038i −0.999787 0.0206519i \(-0.993426\pi\)
0.999787 0.0206519i \(-0.00657417\pi\)
\(662\) −2.35240e12 4.07448e12i −0.476048 0.824539i
\(663\) −5.20253e12 + 3.70789e12i −1.04569 + 0.745274i
\(664\) −9.54378e11 −0.190530
\(665\) 1.71222e11 3.51888e11i 0.0339518 0.0697761i
\(666\) 3.18360e12 5.51415e12i 0.627024 1.08604i
\(667\) 5.93374e12 1.16081
\(668\) 1.52402e12 8.79891e11i 0.296139 0.170976i
\(669\) −8.62197e12 4.97790e12i −1.66414 0.960790i
\(670\) 1.52023e11i 0.0291455i
\(671\) 2.71431e11i 0.0516901i
\(672\) −5.45503e12 2.65432e12i −1.03189 0.502102i
\(673\) −1.30813e12 + 2.26574e12i −0.245800 + 0.425738i −0.962356 0.271791i \(-0.912384\pi\)
0.716556 + 0.697529i \(0.245717\pi\)
\(674\) −4.28551e12 + 2.47424e12i −0.799895 + 0.461819i
\(675\) 1.20973e12 + 2.09531e12i 0.224296 + 0.388492i
\(676\) 2.57995e12 4.99420e11i 0.475172 0.0919825i
\(677\) −3.69464e12 + 6.39930e12i −0.675963 + 1.17080i 0.300224 + 0.953869i \(0.402939\pi\)
−0.976186 + 0.216933i \(0.930395\pi\)
\(678\) 9.51331e12 + 5.49251e12i 1.72901 + 0.998246i
\(679\) 1.76373e12 1.19204e12i 0.318433 0.215217i
\(680\) −1.40726e11 2.43745e11i −0.0252397 0.0437165i
\(681\) 4.43505e12 + 2.56058e12i 0.790200 + 0.456222i
\(682\) −7.89629e10 4.55892e10i −0.0139763 0.00806924i
\(683\) −4.24353e12 2.45000e12i −0.746163 0.430798i 0.0781426 0.996942i \(-0.475101\pi\)
−0.824306 + 0.566145i \(0.808434\pi\)
\(684\) −1.50349e12 8.68039e11i −0.262632 0.151631i
\(685\) 3.52742e11 + 6.10967e11i 0.0612139 + 0.106026i
\(686\) −5.23787e12 + 4.74271e12i −0.903018 + 0.817651i
\(687\) −5.66820e12 3.27254e12i −0.970823 0.560505i
\(688\) −7.17070e11 + 1.24200e12i −0.122015 + 0.211336i
\(689\) 4.49268e11 + 4.68483e12i 0.0759485 + 0.791968i
\(690\) 2.86527e11 + 4.96279e11i 0.0481221 + 0.0833500i
\(691\) 5.12641e12 2.95974e12i 0.855386 0.493857i −0.00707832 0.999975i \(-0.502253\pi\)
0.862465 + 0.506117i \(0.168920\pi\)
\(692\) 1.37329e12 2.37861e12i 0.227659 0.394317i
\(693\) −3.98648e10 5.62580e11i −0.00656584 0.0926584i
\(694\) 7.65756e12i 1.25306i
\(695\) 8.23904e11i 0.133951i
\(696\) 6.55326e12 + 3.78353e12i 1.05856 + 0.611160i
\(697\) −4.31148e12 + 2.48924e12i −0.691957 + 0.399502i
\(698\) 4.16253e12 0.663755
\(699\) 7.85577e12 1.36066e13i 1.24463 2.15577i
\(700\) −3.04708e12 + 2.15918e11i −0.479670 + 0.0339898i
\(701\) −5.59634e12 −0.875332 −0.437666 0.899138i \(-0.644195\pi\)
−0.437666 + 0.899138i \(0.644195\pi\)
\(702\) −3.52294e12 + 3.37844e11i −0.547505 + 0.0525049i
\(703\) 4.96884e12 + 8.60629e12i 0.767284 + 1.32898i
\(704\) 1.50233e11i 0.0230509i
\(705\) −4.30367e11 7.45418e11i −0.0656128 0.113645i
\(706\) 1.90897e12 + 3.30642e12i 0.289186 + 0.500884i
\(707\) 1.29971e12 9.20984e10i 0.195641 0.0138632i
\(708\) 1.64828e12 9.51635e11i 0.246537 0.142338i
\(709\) 1.05831e13i 1.57291i −0.617646 0.786456i \(-0.711913\pi\)
0.617646 0.786456i \(-0.288087\pi\)
\(710\) −6.98371e11 + 4.03205e11i −0.103139 + 0.0595474i
\(711\) 3.39786e12 5.88527e12i 0.498647 0.863681i
\(712\) −4.01540e12 6.95488e12i −0.585557 1.01421i
\(713\) 4.23519e11 + 2.44519e11i 0.0613719 + 0.0354331i
\(714\) 7.67845e11 + 1.08360e13i 0.110569 + 1.56037i
\(715\) −6.54678e10 + 4.66595e10i −0.00936808 + 0.00667672i
\(716\) −1.44815e12 + 2.50827e12i −0.205923 + 0.356669i
\(717\) 4.38199e12i 0.619206i
\(718\) −4.33831e12 −0.609201
\(719\) 4.41211e12 0.615696 0.307848 0.951436i \(-0.400391\pi\)
0.307848 + 0.951436i \(0.400391\pi\)
\(720\) 4.69114e11i 0.0650553i
\(721\) −3.47849e12 + 7.14881e12i −0.479382 + 0.985201i
\(722\) −5.08092e11 + 2.93347e11i −0.0695865 + 0.0401758i
\(723\) 1.35455e13 + 7.82049e12i 1.84362 + 1.06442i
\(724\) −1.68838e12 + 2.92436e12i −0.228374 + 0.395555i
\(725\) 1.11945e13 1.50482
\(726\) −9.93059e12 + 5.73343e12i −1.32666 + 0.765949i
\(727\) −3.24655e12 −0.431040 −0.215520 0.976499i \(-0.569145\pi\)
−0.215520 + 0.976499i \(0.569145\pi\)
\(728\) −1.66593e12 + 4.46312e12i −0.219819 + 0.588907i
\(729\) −1.65075e12 −0.216475
\(730\) −4.47511e11 + 2.58370e11i −0.0583244 + 0.0336736i
\(731\) 1.50774e12 0.195298
\(732\) −8.70684e11 + 1.50807e12i −0.112088 + 0.194143i
\(733\) −1.36014e12 7.85278e11i −0.174027 0.100474i 0.410456 0.911880i \(-0.365369\pi\)
−0.584483 + 0.811406i \(0.698703\pi\)
\(734\) −4.23196e12 + 2.44333e12i −0.538158 + 0.310706i
\(735\) 7.56786e11 + 3.04126e11i 0.0956489 + 0.0384380i
\(736\) 5.45352e12i 0.685057i
\(737\) 3.41956e11 0.0426940
\(738\) 5.08437e12 0.630933
\(739\) 1.00804e13i 1.24331i 0.783293 + 0.621653i \(0.213538\pi\)
−0.783293 + 0.621653i \(0.786462\pi\)
\(740\) −2.51665e11 + 4.35896e11i −0.0308517 + 0.0534368i
\(741\) −4.22651e12 + 9.26473e12i −0.514992 + 1.12889i
\(742\) 7.19591e12 + 3.50141e12i 0.871501 + 0.424058i
\(743\) 3.90160e11 + 2.25259e11i 0.0469671 + 0.0271165i 0.523300 0.852149i \(-0.324701\pi\)
−0.476333 + 0.879265i \(0.658034\pi\)
\(744\) 3.11825e11 + 5.40096e11i 0.0373106 + 0.0646238i
\(745\) −4.66977e11 + 8.08827e11i −0.0555382 + 0.0961950i
\(746\) −4.97402e12 + 2.87175e12i −0.588007 + 0.339486i
\(747\) 1.67236e12i 0.196511i
\(748\) −5.14258e11 + 2.96907e11i −0.0600653 + 0.0346787i
\(749\) −1.60865e12 2.38015e12i −0.186764 0.276335i
\(750\) 1.08462e12 + 1.87862e12i 0.125171 + 0.216802i
\(751\) 4.33485e11 + 7.50818e11i 0.0497272 + 0.0861301i 0.889818 0.456316i \(-0.150831\pi\)
−0.840090 + 0.542446i \(0.817498\pi\)
\(752\) 1.39518e13i 1.59093i
\(753\) −7.39012e12 1.28001e13i −0.837673 1.45089i
\(754\) −6.79633e12 + 1.48979e13i −0.765779 + 1.67863i
\(755\) 3.24350e11 0.0363290
\(756\) −8.58738e11 + 1.76484e12i −0.0956121 + 0.196497i
\(757\) −9.20406e11 + 1.59419e12i −0.101870 + 0.176445i −0.912455 0.409176i \(-0.865816\pi\)
0.810585 + 0.585621i \(0.199149\pi\)
\(758\) 1.77684e13 1.95496
\(759\) −1.11632e12 + 6.44507e11i −0.122096 + 0.0704920i
\(760\) −3.88519e11 2.24312e11i −0.0422427 0.0243888i
\(761\) 3.70938e12i 0.400932i −0.979701 0.200466i \(-0.935754\pi\)
0.979701 0.200466i \(-0.0642456\pi\)
\(762\) 4.64491e12i 0.499091i
\(763\) −9.43669e12 + 6.37790e12i −1.00800 + 0.681267i
\(764\) 1.86850e12 3.23634e12i 0.198414 0.343664i
\(765\) 4.27115e11 2.46595e11i 0.0450888 0.0260320i
\(766\) 3.85009e12 + 6.66855e12i 0.404056 + 0.699845i
\(767\) −2.54851e12 3.57581e12i −0.265894 0.373074i
\(768\) −7.22082e12 + 1.25068e13i −0.748964 + 1.29724i
\(769\) −1.22728e13 7.08572e12i −1.26554 0.730660i −0.291399 0.956602i \(-0.594121\pi\)
−0.974141 + 0.225942i \(0.927454\pi\)
\(770\) 9.66244e9 + 1.36358e11i 0.000990555 + 0.0139789i
\(771\) 2.29272e12 + 3.97110e12i 0.233671 + 0.404731i
\(772\) 1.67396e12 + 9.66462e11i 0.169616 + 0.0979280i
\(773\) 4.76580e10 + 2.75153e10i 0.00480096 + 0.00277183i 0.502399 0.864636i \(-0.332451\pi\)
−0.497598 + 0.867408i \(0.665784\pi\)
\(774\) −1.33352e12 7.69906e11i −0.133556 0.0771087i
\(775\) 7.99003e11 + 4.61305e11i 0.0795593 + 0.0459336i
\(776\) −1.22021e12 2.11347e12i −0.120797 0.209227i
\(777\) −1.71602e13 + 1.15979e13i −1.68899 + 1.14152i
\(778\) 1.12685e12 + 6.50588e11i 0.110270 + 0.0636646i
\(779\) −3.96775e12 + 6.87234e12i −0.386034 + 0.668630i
\(780\) −5.13412e11 + 4.92354e10i −0.0496638 + 0.00476269i
\(781\) −9.06958e11 1.57090e12i −0.0872284 0.151084i
\(782\) 8.45713e12 4.88273e12i 0.808710 0.466909i
\(783\) 3.59625e12 6.22889e12i 0.341918 0.592219i
\(784\) 8.15861e12 + 1.04026e13i 0.771248 + 0.983380i
\(785\) 1.12088e12i 0.105353i
\(786\) 1.51332e13i 1.41426i
\(787\) 3.47084e12 + 2.00389e12i 0.322514 + 0.186203i 0.652512 0.757778i \(-0.273715\pi\)
−0.329999 + 0.943981i \(0.607048\pi\)
\(788\) 2.33047e12 1.34550e12i 0.215316 0.124313i
\(789\) −1.50307e13 −1.38081
\(790\) −8.23575e11 + 1.42647e12i −0.0752283 + 0.130299i
\(791\) −7.87016e12 1.16446e13i −0.714808 1.05762i
\(792\) −6.46557e11 −0.0583907
\(793\) 3.65515e12 + 1.66746e12i 0.328228 + 0.149736i
\(794\) −5.46120e12 9.45907e12i −0.487636 0.844610i
\(795\) 9.23711e11i 0.0820133i
\(796\) −1.55710e12 2.69697e12i −0.137470 0.238105i
\(797\) −1.90260e12 3.29540e12i −0.167026 0.289298i 0.770347 0.637625i \(-0.220083\pi\)
−0.937373 + 0.348327i \(0.886750\pi\)
\(798\) 9.69601e12 + 1.43461e13i 0.846408 + 1.25234i
\(799\) −1.27027e13 + 7.33392e12i −1.10265 + 0.636613i
\(800\) 1.02885e13i 0.888071i
\(801\) 1.21871e13 7.03621e12i 1.04605 0.603938i
\(802\) −1.15272e13 + 1.99657e13i −0.983872 + 1.70412i
\(803\) −5.81172e11 1.00662e12i −0.0493270 0.0854369i
\(804\) 1.89991e12 + 1.09691e12i 0.160354 + 0.0925806i
\(805\) −5.18247e10 7.31359e11i −0.00434966 0.0613832i
\(806\) −1.09900e12 + 7.83269e11i −0.0917257 + 0.0653737i
\(807\) 9.78500e12 1.69481e13i 0.812138 1.40666i
\(808\) 1.49372e12i 0.123287i
\(809\) −8.63807e12 −0.709003 −0.354502 0.935055i \(-0.615350\pi\)
−0.354502 + 0.935055i \(0.615350\pi\)
\(810\) 1.47151e12 0.120110
\(811\) 1.21629e13i 0.987288i −0.869664 0.493644i \(-0.835665\pi\)
0.869664 0.493644i \(-0.164335\pi\)
\(812\) 5.08502e12 + 7.52377e12i 0.410479 + 0.607342i
\(813\) −1.45362e13 + 8.39245e12i −1.16692 + 0.673723i
\(814\) −3.00634e12 1.73571e12i −0.240009 0.138569i
\(815\) −9.58804e11 + 1.66070e12i −0.0761238 + 0.131850i
\(816\) 2.03247e13 1.60479
\(817\) 2.08130e12 1.20164e12i 0.163432 0.0943573i
\(818\) −4.29545e12 −0.335443
\(819\) −7.82074e12 2.91922e12i −0.607394 0.226720i
\(820\) −4.01921e11 −0.0310441
\(821\) 1.62400e12 9.37615e11i 0.124750 0.0720245i −0.436326 0.899788i \(-0.643721\pi\)
0.561077 + 0.827764i \(0.310387\pi\)
\(822\) −3.12158e13 −2.38479
\(823\) 5.25147e12 9.09582e12i 0.399008 0.691103i −0.594596 0.804025i \(-0.702688\pi\)
0.993604 + 0.112922i \(0.0360211\pi\)
\(824\) 7.89301e12 + 4.55703e12i 0.596444 + 0.344357i
\(825\) −2.10603e12 + 1.21592e12i −0.158278 + 0.0913820i
\(826\) −7.44780e12 + 5.27757e11i −0.556696 + 0.0394479i
\(827\) 1.05828e13i 0.786730i −0.919382 0.393365i \(-0.871311\pi\)
0.919382 0.393365i \(-0.128689\pi\)
\(828\) −3.25267e12 −0.240494
\(829\) −7.66841e12 −0.563910 −0.281955 0.959428i \(-0.590983\pi\)
−0.281955 + 0.959428i \(0.590983\pi\)
\(830\) 4.05347e11i 0.0296467i
\(831\) −4.70747e12 + 8.15358e12i −0.342439 + 0.593121i
\(832\) 2.02307e12 + 9.22912e11i 0.146371 + 0.0667736i
\(833\) 5.18264e12 1.28964e13i 0.372948 0.928041i
\(834\) 3.15714e13 + 1.82277e13i 2.25968 + 1.30463i
\(835\) 3.98429e11 + 6.90100e11i 0.0283637 + 0.0491273i
\(836\) −4.73258e11 + 8.19707e11i −0.0335097 + 0.0580404i
\(837\) 5.13362e11 2.96390e11i 0.0361543 0.0208737i
\(838\) 2.23227e13i 1.56369i
\(839\) 3.62059e12 2.09035e12i 0.252261 0.145643i −0.368538 0.929613i \(-0.620142\pi\)
0.620799 + 0.783970i \(0.286808\pi\)
\(840\) 4.09101e11 8.40763e11i 0.0283513 0.0582662i
\(841\) −9.38577e12 1.62566e13i −0.646976 1.12059i
\(842\) −5.62458e12 9.74205e12i −0.385643 0.667953i
\(843\) 1.13385e13i 0.773272i
\(844\) 2.47014e12 + 4.27841e12i 0.167564 + 0.290230i
\(845\) 2.26146e11 + 1.16824e12i 0.0152592 + 0.0788277i
\(846\) 1.49798e13 1.00540
\(847\) 1.46346e13 1.03702e12i 0.977022 0.0692325i
\(848\) 7.48631e12 1.29667e13i 0.497149 0.861087i
\(849\) −4.26737e11 −0.0281888
\(850\) 1.59551e13 9.21167e12i 1.04837 0.605276i
\(851\) 1.61245e13 + 9.30950e12i 1.05391 + 0.608476i
\(852\) 1.16372e13i 0.756608i
\(853\) 1.84410e13i 1.19265i −0.802743 0.596325i \(-0.796627\pi\)
0.802743 0.596325i \(-0.203373\pi\)
\(854\) 5.65989e12 3.82530e12i 0.364122 0.246096i
\(855\) 3.93063e11 6.80805e11i 0.0251544 0.0435687i
\(856\) −2.85213e12 + 1.64668e12i −0.181567 + 0.104828i
\(857\) −8.80749e11 1.52550e12i −0.0557748 0.0966049i 0.836790 0.547524i \(-0.184430\pi\)
−0.892565 + 0.450919i \(0.851096\pi\)
\(858\) −3.39572e11 3.54096e12i −0.0213914 0.223063i
\(859\) 1.31521e13 2.27801e13i 0.824188 1.42754i −0.0783498 0.996926i \(-0.524965\pi\)
0.902538 0.430610i \(-0.141702\pi\)
\(860\) 1.05415e11 + 6.08614e10i 0.00657142 + 0.00379401i
\(861\) −1.48719e13 7.23639e12i −0.922255 0.448754i
\(862\) 9.89318e12 + 1.71355e13i 0.610314 + 1.05709i
\(863\) −6.07485e12 3.50732e12i −0.372810 0.215242i 0.301876 0.953347i \(-0.402387\pi\)
−0.674685 + 0.738106i \(0.735721\pi\)
\(864\) 5.72478e12 + 3.30520e12i 0.349500 + 0.201784i
\(865\) 1.07707e12 + 6.21849e11i 0.0654144 + 0.0377670i
\(866\) 1.56110e13 + 9.01301e12i 0.943192 + 0.544552i
\(867\) −3.74400e9 6.48479e9i −0.000225035 0.000389771i
\(868\) 5.29011e10 + 7.46551e11i 0.00316320 + 0.0446396i
\(869\) −3.20867e12 1.85253e12i −0.190870 0.110199i
\(870\) 1.60695e12 2.78333e12i 0.0950970 0.164713i
\(871\) 2.10071e12 4.60486e12i 0.123676 0.271104i
\(872\) 6.52865e12 + 1.13079e13i 0.382383 + 0.662307i
\(873\) 3.70344e12 2.13818e12i 0.215795 0.124589i
\(874\) 7.78288e12 1.34803e13i 0.451169 0.781447i
\(875\) −1.96177e11 2.76849e12i −0.0113139 0.159664i
\(876\) 7.45704e12i 0.427857i
\(877\) 1.60112e13i 0.913956i 0.889478 + 0.456978i \(0.151068\pi\)
−0.889478 + 0.456978i \(0.848932\pi\)
\(878\) 5.62770e12 + 3.24915e12i 0.319599 + 0.184521i
\(879\) 8.52272e12 4.92059e12i 0.481535 0.278014i
\(880\) 2.55763e11 0.0143769
\(881\) 1.68502e13 2.91854e13i 0.942352 1.63220i 0.181384 0.983412i \(-0.441942\pi\)
0.760968 0.648789i \(-0.224724\pi\)
\(882\) −1.11691e13 + 8.75976e12i −0.621457 + 0.487398i
\(883\) −1.84093e13 −1.01910 −0.509548 0.860442i \(-0.670187\pi\)
−0.509548 + 0.860442i \(0.670187\pi\)
\(884\) 8.39024e11 + 8.74909e12i 0.0462104 + 0.481867i
\(885\) 4.30916e11 + 7.46369e11i 0.0236128 + 0.0408986i
\(886\) 1.37857e13i 0.751583i
\(887\) −1.39914e13 2.42338e13i −0.758936 1.31452i −0.943394 0.331675i \(-0.892386\pi\)
0.184458 0.982840i \(-0.440947\pi\)
\(888\) 1.18720e13 + 2.05630e13i 0.640717 + 1.10976i
\(889\) −2.60024e12 + 5.34388e12i −0.139622 + 0.286945i
\(890\) −2.95390e12 + 1.70544e12i −0.157812 + 0.0911131i
\(891\) 3.30998e12i 0.175945i
\(892\) −1.18617e13 + 6.84838e12i −0.627345 + 0.362198i
\(893\) −1.16900e13 + 2.02476e13i −0.615152 + 1.06547i
\(894\) −2.06624e13 3.57884e13i −1.08184 1.87380i
\(895\) −1.13579e12 6.55747e11i −0.0591688 0.0341611i
\(896\) 1.74198e13 1.17733e13i 0.902934 0.610259i
\(897\) 1.82130e12 + 1.89920e13i 0.0939325 + 0.979499i
\(898\) −2.10511e13 + 3.64615e13i −1.08026 + 1.87107i
\(899\) 2.74271e12i 0.140043i
\(900\) −6.13644e12 −0.311763
\(901\) −1.57410e13 −0.795740
\(902\) 2.77202e12i 0.139433i
\(903\) 2.80478e12 + 4.14993e12i 0.140380 + 0.207705i
\(904\) −1.39537e13 + 8.05618e12i −0.694915 + 0.401209i
\(905\) −1.32420e12 7.64527e11i −0.0656198 0.0378856i
\(906\) −7.17581e12 + 1.24289e13i −0.353829 + 0.612850i
\(907\) 3.28247e13 1.61053 0.805264 0.592917i \(-0.202024\pi\)
0.805264 + 0.592917i \(0.202024\pi\)
\(908\) 6.10156e12 3.52274e12i 0.297889 0.171986i
\(909\) 2.61745e12 0.127157
\(910\) 1.89559e12 + 7.07561e11i 0.0916344 + 0.0342041i
\(911\) 9.98172e12 0.480146 0.240073 0.970755i \(-0.422829\pi\)
0.240073 + 0.970755i \(0.422829\pi\)
\(912\) 2.80565e13 1.61984e13i 1.34294 0.775346i
\(913\) −9.11778e11 −0.0434281
\(914\) 1.11351e13 1.92866e13i 0.527760 0.914107i
\(915\) −6.82879e11 3.94261e11i −0.0322069 0.0185947i
\(916\) −7.79807e12 + 4.50222e12i −0.365980 + 0.211299i
\(917\) 8.47164e12 1.74105e13i 0.395645 0.813109i
\(918\) 1.18371e13i 0.550113i
\(919\) −3.56352e13 −1.64801 −0.824004 0.566583i \(-0.808265\pi\)
−0.824004 + 0.566583i \(0.808265\pi\)
\(920\) −8.40531e11 −0.0386819
\(921\) 1.96048e13i 0.897828i
\(922\) 4.23694e12 7.33860e12i 0.193092 0.334444i
\(923\) −2.67257e13 + 2.56296e12i −1.21205 + 0.116234i
\(924\) −1.77386e12 8.63130e11i −0.0800563 0.0389540i
\(925\) 3.04203e13 + 1.75631e13i 1.36623 + 0.788796i
\(926\) −2.29845e13 3.98103e13i −1.02727 1.77929i
\(927\) −7.98530e12 + 1.38310e13i −0.355167 + 0.615167i
\(928\) 2.64877e13 1.52927e13i 1.17241 0.676891i
\(929\) 8.31459e11i 0.0366244i 0.999832 + 0.0183122i \(0.00582928\pi\)
−0.999832 + 0.0183122i \(0.994171\pi\)
\(930\) 2.29392e11 1.32439e11i 0.0100555 0.00580555i
\(931\) −3.12404e12 2.19328e13i −0.136283 0.956800i
\(932\) −1.08076e13 1.87194e13i −0.469201 0.812680i
\(933\) −1.70853e13 2.95926e13i −0.738168 1.27854i
\(934\) 3.18852e13i 1.37097i
\(935\) −1.34444e11 2.32865e11i −0.00575295 0.00996440i
\(936\) −3.97194e12 + 8.70670e12i −0.169146 + 0.370776i
\(937\) −1.72923e13 −0.732864 −0.366432 0.930445i \(-0.619421\pi\)
−0.366432 + 0.930445i \(0.619421\pi\)
\(938\) −4.81922e12 7.13049e12i −0.203266 0.300751i
\(939\) −2.04931e13 + 3.54951e13i −0.860225 + 1.48995i
\(940\) −1.18416e12 −0.0494693
\(941\) 1.82667e13 1.05463e13i 0.759461 0.438475i −0.0696410 0.997572i \(-0.522185\pi\)
0.829102 + 0.559097i \(0.188852\pi\)
\(942\) 4.29514e13 + 2.47980e13i 1.77725 + 1.02610i
\(943\) 1.48678e13i 0.612270i
\(944\) 1.39696e13i 0.572546i
\(945\) −7.99147e11 3.88851e11i −0.0325974 0.0158614i
\(946\) −4.19756e11 + 7.27038e11i −0.0170407 + 0.0295153i
\(947\) 2.52196e13 1.45605e13i 1.01897 0.588305i 0.105168 0.994454i \(-0.466462\pi\)
0.913807 + 0.406149i \(0.133129\pi\)
\(948\) −1.18849e13 2.05853e13i −0.477925 0.827790i
\(949\) −1.71257e13 + 1.64232e12i −0.685408 + 0.0657296i
\(950\) 1.46830e13 2.54318e13i 0.584871 1.01303i
\(951\) 3.35619e13 + 1.93770e13i 1.33056 + 0.768200i
\(952\) −1.43275e13 6.97151e12i −0.565333 0.275081i
\(953\) 2.12878e13 + 3.68715e13i 0.836012 + 1.44802i 0.893204 + 0.449652i \(0.148452\pi\)
−0.0571915 + 0.998363i \(0.518215\pi\)
\(954\) 1.39221e13 + 8.03792e12i 0.544172 + 0.314178i
\(955\) 1.46547e12 + 8.46088e11i 0.0570113 + 0.0329155i
\(956\) 5.22088e12 + 3.01428e12i 0.202155 + 0.116714i
\(957\) 6.26074e12 + 3.61464e12i 0.241280 + 0.139303i
\(958\) −7.15776e12 1.23976e13i −0.274557 0.475547i
\(959\) 3.59132e13 + 1.74747e13i 1.37110 + 0.667155i
\(960\) −3.77963e11 2.18217e11i −0.0143625 0.00829217i
\(961\) −1.31068e13 + 2.27016e13i −0.495725 + 0.858621i
\(962\) −4.18421e13 + 2.98212e13i −1.57516 + 1.12263i
\(963\) −2.88548e12 4.99779e12i −0.108118 0.187266i
\(964\) 1.86353e13 1.07591e13i 0.695008 0.401263i
\(965\) −4.37630e11 + 7.57997e11i −0.0162455 + 0.0281381i
\(966\) 2.91717e13 + 1.41944e13i 1.07787 + 0.524471i
\(967\) 1.04997e13i 0.386153i −0.981184 0.193076i \(-0.938153\pi\)
0.981184 0.193076i \(-0.0618465\pi\)
\(968\) 1.68191e13i 0.615691i
\(969\) −2.94964e13 1.70297e13i −1.07476 0.620513i
\(970\) −8.97641e11 + 5.18253e11i −0.0325559 + 0.0187962i
\(971\) 4.64721e13 1.67767 0.838833 0.544389i \(-0.183239\pi\)
0.838833 + 0.544389i \(0.183239\pi\)
\(972\) −7.57697e12 + 1.31237e13i −0.272268 + 0.471583i
\(973\) −2.61183e13 3.86445e13i −0.934195 1.38223i
\(974\) −6.89757e11 −0.0245573
\(975\) 3.43604e12 + 3.58299e13i 0.121769 + 1.26977i
\(976\) −6.39065e12 1.10689e13i −0.225435 0.390464i
\(977\) 2.13900e13i 0.751078i −0.926807 0.375539i \(-0.877458\pi\)
0.926807 0.375539i \(-0.122542\pi\)
\(978\) −4.24244e13 7.34813e13i −1.48283 2.56834i
\(979\) −3.83617e12 6.64444e12i −0.133467 0.231172i
\(980\) 8.82925e11 6.92463e11i 0.0305778 0.0239817i
\(981\) −1.98150e13 + 1.14402e13i −0.683098 + 0.394387i
\(982\) 8.84825e10i 0.00303638i
\(983\) −1.53024e12 + 8.83484e11i −0.0522719 + 0.0301792i −0.525908 0.850541i \(-0.676274\pi\)
0.473636 + 0.880721i \(0.342941\pi\)
\(984\) −9.48012e12 + 1.64200e13i −0.322356 + 0.558337i
\(985\) 6.09265e11 + 1.05528e12i 0.0206226 + 0.0357194i
\(986\) −4.74308e13 2.73842e13i −1.59814 0.922686i
\(987\) −4.38163e13 2.13202e13i −1.46963 0.715097i
\(988\) 8.13105e12 + 1.14087e13i 0.271482 + 0.380915i
\(989\) 2.25137e12 3.89948e12i 0.0748278 0.129605i
\(990\) 2.74608e11i 0.00908563i
\(991\) 5.29730e13 1.74471 0.872356 0.488872i \(-0.162592\pi\)
0.872356 + 0.488872i \(0.162592\pi\)
\(992\) 2.52074e12 0.0826467
\(993\) 3.07438e13i 1.00343i
\(994\) −1.99746e13 + 4.10508e13i −0.648992 + 1.33378i
\(995\) 1.22123e12 7.05080e11i 0.0394998 0.0228052i
\(996\) −5.06584e12 2.92477e12i −0.163112 0.0941725i
\(997\) −1.80816e13 + 3.13183e13i −0.579574 + 1.00385i 0.415954 + 0.909386i \(0.363448\pi\)
−0.995528 + 0.0944664i \(0.969885\pi\)
\(998\) 4.22085e13 1.34683
\(999\) 1.95451e13 1.12844e13i 0.620860 0.358454i
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 91.10.u.a.30.18 yes 164
7.4 even 3 91.10.k.a.4.18 164
13.10 even 6 91.10.k.a.23.65 yes 164
91.88 even 6 inner 91.10.u.a.88.18 yes 164
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.10.k.a.4.18 164 7.4 even 3
91.10.k.a.23.65 yes 164 13.10 even 6
91.10.u.a.30.18 yes 164 1.1 even 1 trivial
91.10.u.a.88.18 yes 164 91.88 even 6 inner