Properties

Label 25.7.f.a.2.14
Level $25$
Weight $7$
Character 25.2
Analytic conductor $5.751$
Analytic rank $0$
Dimension $112$
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] = [25,7,Mod(2,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 25.f (of order \(20\), degree \(8\), 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: \(5.75135209050\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 2.14
Character \(\chi\) \(=\) 25.2
Dual form 25.7.f.a.13.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(14.8618 + 2.35387i) q^{2} +(1.72543 + 3.38635i) q^{3} +(154.464 + 50.1883i) q^{4} +(-45.2307 + 116.530i) q^{5} +(17.6719 + 54.3886i) q^{6} +(-314.203 - 314.203i) q^{7} +(1319.42 + 672.277i) q^{8} +(420.005 - 578.088i) q^{9} +O(q^{10})\) \(q+(14.8618 + 2.35387i) q^{2} +(1.72543 + 3.38635i) q^{3} +(154.464 + 50.1883i) q^{4} +(-45.2307 + 116.530i) q^{5} +(17.6719 + 54.3886i) q^{6} +(-314.203 - 314.203i) q^{7} +(1319.42 + 672.277i) q^{8} +(420.005 - 578.088i) q^{9} +(-946.504 + 1625.37i) q^{10} +(1113.60 - 809.077i) q^{11} +(96.5615 + 609.665i) q^{12} +(-3130.66 + 495.848i) q^{13} +(-3930.01 - 5409.20i) q^{14} +(-472.653 + 47.8972i) q^{15} +(9617.18 + 6987.29i) q^{16} +(-534.089 + 1048.21i) q^{17} +(7602.76 - 7602.76i) q^{18} +(-1211.85 + 393.754i) q^{19} +(-12834.9 + 15729.6i) q^{20} +(521.866 - 1606.14i) q^{21} +(18454.5 - 9403.04i) q^{22} +(803.776 - 5074.84i) q^{23} +5627.99i q^{24} +(-11533.4 - 10541.4i) q^{25} -47694.3 q^{26} +(5418.82 + 858.257i) q^{27} +(-32763.6 - 64302.2i) q^{28} +(-13993.0 - 4546.61i) q^{29} +(-7137.21 - 400.729i) q^{30} +(15695.1 + 48304.7i) q^{31} +(59466.9 + 59466.9i) q^{32} +(4661.26 + 2375.03i) q^{33} +(-10404.9 + 14321.1i) q^{34} +(50825.6 - 22402.4i) q^{35} +(93888.8 - 68214.2i) q^{36} +(6723.73 + 42451.9i) q^{37} +(-18937.1 + 2999.34i) q^{38} +(-7080.87 - 9745.98i) q^{39} +(-138019. + 123344. i) q^{40} +(21434.6 + 15573.2i) q^{41} +(11536.5 - 22641.6i) q^{42} +(-9654.08 + 9654.08i) q^{43} +(212617. - 69083.4i) q^{44} +(48367.3 + 75090.4i) q^{45} +(23891.1 - 73529.1i) q^{46} +(2110.83 - 1075.52i) q^{47} +(-7067.63 + 44623.3i) q^{48} +79797.8i q^{49} +(-146593. - 183813. i) q^{50} -4471.14 q^{51} +(-508460. - 80532.1i) q^{52} +(82220.3 + 161367. i) q^{53} +(78513.0 + 25510.4i) q^{54} +(43912.7 + 166363. i) q^{55} +(-203334. - 625797. i) q^{56} +(-3424.36 - 3424.36i) q^{57} +(-197259. - 100508. i) q^{58} +(172654. - 237638. i) q^{59} +(-75411.7 - 16323.3i) q^{60} +(126105. - 91620.4i) q^{61} +(119554. + 754837. i) q^{62} +(-313604. + 49669.9i) q^{63} +(296618. + 408260. i) q^{64} +(83821.0 - 387243. i) q^{65} +(63684.1 + 46269.2i) q^{66} +(-14162.3 + 27795.1i) q^{67} +(-135105. + 135105. i) q^{68} +(18572.1 - 6034.43i) q^{69} +(808090. - 213302. i) q^{70} +(-183249. + 563982. i) q^{71} +(942798. - 480380. i) q^{72} +(73458.6 - 463799. i) q^{73} +646737. i q^{74} +(15797.0 - 57244.6i) q^{75} -206949. q^{76} +(-604110. - 95681.7i) q^{77} +(-82293.4 - 161510. i) q^{78} +(-421357. - 136907. i) q^{79} +(-1.24922e6 + 804647. i) q^{80} +(-154527. - 475585. i) q^{81} +(281899. + 281899. i) q^{82} +(-385321. - 196331. i) q^{83} +(161219. - 221898. i) q^{84} +(-97990.3 - 109648. i) q^{85} +(-166201. + 120752. i) q^{86} +(-8747.60 - 55230.2i) q^{87} +(2.01323e6 - 318864. i) q^{88} +(-335950. - 462396. i) q^{89} +(542070. + 1.22983e6i) q^{90} +(1.13946e6 + 827866. i) q^{91} +(378852. - 743539. i) q^{92} +(-136496. + 136496. i) q^{93} +(33902.3 - 11015.5i) q^{94} +(8928.78 - 159027. i) q^{95} +(-98769.7 + 303982. i) q^{96} +(-562743. + 286732. i) q^{97} +(-187834. + 1.18594e6i) q^{98} -983574. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 40 q^{3} - 10 q^{4} + 60 q^{5} - 6 q^{6} - 560 q^{7} - 1870 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 40 q^{3} - 10 q^{4} + 60 q^{5} - 6 q^{6} - 560 q^{7} - 1870 q^{8} - 10 q^{9} + 4360 q^{10} - 6 q^{11} - 3490 q^{12} - 1970 q^{13} - 10 q^{14} + 80 q^{15} + 22522 q^{16} - 1210 q^{17} - 47740 q^{18} - 19210 q^{19} + 4290 q^{20} - 6 q^{21} + 116790 q^{22} + 68920 q^{23} - 83690 q^{25} + 32544 q^{26} - 147970 q^{27} - 191010 q^{28} - 24810 q^{29} + 128390 q^{30} - 6 q^{31} + 335470 q^{32} + 133250 q^{33} + 32990 q^{34} - 126400 q^{35} - 156358 q^{36} + 64990 q^{37} - 26320 q^{38} - 414810 q^{39} - 609460 q^{40} + 108554 q^{41} - 345630 q^{42} + 228280 q^{43} + 711540 q^{44} + 1026100 q^{45} - 6 q^{46} + 470440 q^{47} + 948520 q^{48} - 453750 q^{50} - 16 q^{51} - 1534020 q^{52} - 922770 q^{53} - 2582460 q^{54} - 1058910 q^{55} - 16390 q^{56} + 283510 q^{57} + 1902200 q^{58} + 2457990 q^{59} + 4557170 q^{60} - 388446 q^{61} - 686820 q^{62} - 2340440 q^{63} - 5040460 q^{64} - 1346350 q^{65} + 186618 q^{66} + 913000 q^{67} + 3094930 q^{68} + 2802790 q^{69} + 3485630 q^{70} - 758886 q^{71} + 3144300 q^{72} + 74290 q^{73} - 890640 q^{75} - 16400 q^{76} - 3146750 q^{77} - 5681900 q^{78} - 2289610 q^{79} - 6528330 q^{80} + 1577702 q^{81} + 1401150 q^{82} + 26480 q^{83} - 1650010 q^{84} - 3408980 q^{85} - 6 q^{86} - 735210 q^{87} + 2183870 q^{88} + 2906240 q^{89} + 3580070 q^{90} - 6 q^{91} + 1367450 q^{92} + 5352610 q^{93} + 14186390 q^{94} + 5887710 q^{95} - 1245186 q^{96} + 7532890 q^{97} + 5872380 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 14.8618 + 2.35387i 1.85772 + 0.294234i 0.982042 0.188661i \(-0.0604147\pi\)
0.875678 + 0.482895i \(0.160415\pi\)
\(3\) 1.72543 + 3.38635i 0.0639049 + 0.125420i 0.920749 0.390154i \(-0.127578\pi\)
−0.856845 + 0.515575i \(0.827578\pi\)
\(4\) 154.464 + 50.1883i 2.41350 + 0.784192i
\(5\) −45.2307 + 116.530i −0.361846 + 0.932238i
\(6\) 17.6719 + 54.3886i 0.0818145 + 0.251799i
\(7\) −314.203 314.203i −0.916043 0.916043i 0.0806957 0.996739i \(-0.474286\pi\)
−0.996739 + 0.0806957i \(0.974286\pi\)
\(8\) 1319.42 + 672.277i 2.57699 + 1.31304i
\(9\) 420.005 578.088i 0.576139 0.792987i
\(10\) −946.504 + 1625.37i −0.946504 + 1.62537i
\(11\) 1113.60 809.077i 0.836663 0.607872i −0.0847731 0.996400i \(-0.527017\pi\)
0.921437 + 0.388529i \(0.127017\pi\)
\(12\) 96.5615 + 609.665i 0.0558805 + 0.352816i
\(13\) −3130.66 + 495.848i −1.42497 + 0.225693i −0.820825 0.571180i \(-0.806486\pi\)
−0.604147 + 0.796873i \(0.706486\pi\)
\(14\) −3930.01 5409.20i −1.43222 1.97128i
\(15\) −472.653 + 47.8972i −0.140045 + 0.0141918i
\(16\) 9617.18 + 6987.29i 2.34794 + 1.70588i
\(17\) −534.089 + 1048.21i −0.108709 + 0.213354i −0.938952 0.344048i \(-0.888202\pi\)
0.830243 + 0.557402i \(0.188202\pi\)
\(18\) 7602.76 7602.76i 1.30363 1.30363i
\(19\) −1211.85 + 393.754i −0.176680 + 0.0574070i −0.396021 0.918241i \(-0.629609\pi\)
0.219341 + 0.975648i \(0.429609\pi\)
\(20\) −12834.9 + 15729.6i −1.60437 + 1.96620i
\(21\) 521.866 1606.14i 0.0563509 0.173430i
\(22\) 18454.5 9403.04i 1.73314 0.883081i
\(23\) 803.776 5074.84i 0.0660620 0.417099i −0.932389 0.361457i \(-0.882279\pi\)
0.998451 0.0556419i \(-0.0177205\pi\)
\(24\) 5627.99i 0.407117i
\(25\) −11533.4 10541.4i −0.738136 0.674652i
\(26\) −47694.3 −2.71361
\(27\) 5418.82 + 858.257i 0.275305 + 0.0436040i
\(28\) −32763.6 64302.2i −1.49251 2.92922i
\(29\) −13993.0 4546.61i −0.573743 0.186420i 0.00775249 0.999970i \(-0.497532\pi\)
−0.581496 + 0.813549i \(0.697532\pi\)
\(30\) −7137.21 400.729i −0.264341 0.0148418i
\(31\) 15695.1 + 48304.7i 0.526842 + 1.62145i 0.760645 + 0.649168i \(0.224883\pi\)
−0.233804 + 0.972284i \(0.575117\pi\)
\(32\) 59466.9 + 59466.9i 1.81478 + 1.81478i
\(33\) 4661.26 + 2375.03i 0.129706 + 0.0660887i
\(34\) −10404.9 + 14321.1i −0.264728 + 0.364366i
\(35\) 50825.6 22402.4i 1.18544 0.522504i
\(36\) 93888.8 68214.2i 2.01236 1.46207i
\(37\) 6723.73 + 42451.9i 0.132741 + 0.838093i 0.960758 + 0.277390i \(0.0894693\pi\)
−0.828017 + 0.560704i \(0.810531\pi\)
\(38\) −18937.1 + 2999.34i −0.345114 + 0.0546607i
\(39\) −7080.87 9745.98i −0.119369 0.164298i
\(40\) −138019. + 123344.i −2.15654 + 1.92725i
\(41\) 21434.6 + 15573.2i 0.311003 + 0.225957i 0.732327 0.680954i \(-0.238434\pi\)
−0.421324 + 0.906910i \(0.638434\pi\)
\(42\) 11536.5 22641.6i 0.155713 0.305605i
\(43\) −9654.08 + 9654.08i −0.121424 + 0.121424i −0.765208 0.643783i \(-0.777364\pi\)
0.643783 + 0.765208i \(0.277364\pi\)
\(44\) 212617. 69083.4i 2.49597 0.810990i
\(45\) 48367.3 + 75090.4i 0.530779 + 0.824037i
\(46\) 23891.1 73529.1i 0.245449 0.755415i
\(47\) 2110.83 1075.52i 0.0203311 0.0103592i −0.443795 0.896128i \(-0.646368\pi\)
0.464126 + 0.885769i \(0.346368\pi\)
\(48\) −7067.63 + 44623.3i −0.0639072 + 0.403494i
\(49\) 79797.8i 0.678270i
\(50\) −146593. 183813.i −1.17274 1.47050i
\(51\) −4471.14 −0.0337060
\(52\) −508460. 80532.1i −3.61615 0.572742i
\(53\) 82220.3 + 161367.i 0.552270 + 1.08389i 0.983374 + 0.181589i \(0.0581241\pi\)
−0.431104 + 0.902302i \(0.641876\pi\)
\(54\) 78513.0 + 25510.4i 0.498609 + 0.162008i
\(55\) 43912.7 + 166363.i 0.263938 + 0.999925i
\(56\) −203334. 625797.i −1.15783 3.56344i
\(57\) −3424.36 3424.36i −0.0184908 0.0184908i
\(58\) −197259. 100508.i −1.01100 0.515132i
\(59\) 172654. 237638.i 0.840659 1.15707i −0.145185 0.989405i \(-0.546378\pi\)
0.985844 0.167664i \(-0.0536223\pi\)
\(60\) −75411.7 16323.3i −0.349128 0.0755708i
\(61\) 126105. 91620.4i 0.555574 0.403648i −0.274263 0.961655i \(-0.588434\pi\)
0.829836 + 0.558007i \(0.188434\pi\)
\(62\) 119554. + 754837.i 0.501638 + 3.16722i
\(63\) −313604. + 49669.9i −1.25418 + 0.198642i
\(64\) 296618. + 408260.i 1.13151 + 1.55739i
\(65\) 83821.0 387243.i 0.305220 1.41008i
\(66\) 63684.1 + 46269.2i 0.221513 + 0.160938i
\(67\) −14162.3 + 27795.1i −0.0470879 + 0.0924152i −0.913351 0.407172i \(-0.866515\pi\)
0.866264 + 0.499587i \(0.166515\pi\)
\(68\) −135105. + 135105.i −0.429680 + 0.429680i
\(69\) 18572.1 6034.43i 0.0565344 0.0183691i
\(70\) 808090. 213302.i 2.35595 0.621871i
\(71\) −183249. + 563982.i −0.511995 + 1.57576i 0.276688 + 0.960960i \(0.410763\pi\)
−0.788683 + 0.614800i \(0.789237\pi\)
\(72\) 942798. 480380.i 2.52593 1.28703i
\(73\) 73458.6 463799.i 0.188831 1.19223i −0.693095 0.720846i \(-0.743753\pi\)
0.881926 0.471388i \(-0.156247\pi\)
\(74\) 646737.i 1.59600i
\(75\) 15797.0 57244.6i 0.0374447 0.135691i
\(76\) −206949. −0.471436
\(77\) −604110. 95681.7i −1.32326 0.209583i
\(78\) −82293.4 161510.i −0.173413 0.340342i
\(79\) −421357. 136907.i −0.854612 0.277680i −0.151236 0.988498i \(-0.548325\pi\)
−0.703377 + 0.710817i \(0.748325\pi\)
\(80\) −1.24922e6 + 804647.i −2.43988 + 1.57158i
\(81\) −154527. 475585.i −0.290770 0.894897i
\(82\) 281899. + 281899.i 0.511272 + 0.511272i
\(83\) −385321. 196331.i −0.673890 0.343364i 0.0833320 0.996522i \(-0.473444\pi\)
−0.757222 + 0.653158i \(0.773444\pi\)
\(84\) 161219. 221898.i 0.272005 0.374383i
\(85\) −97990.3 109648.i −0.159561 0.178544i
\(86\) −166201. + 120752.i −0.261300 + 0.189845i
\(87\) −8747.60 55230.2i −0.0132841 0.0838723i
\(88\) 2.01323e6 318864.i 2.95423 0.467905i
\(89\) −335950. 462396.i −0.476546 0.655910i 0.501290 0.865279i \(-0.332859\pi\)
−0.977837 + 0.209370i \(0.932859\pi\)
\(90\) 542070. + 1.22983e6i 0.743580 + 1.68700i
\(91\) 1.13946e6 + 827866.i 1.51208 + 1.09859i
\(92\) 378852. 743539.i 0.486526 0.954861i
\(93\) −136496. + 136496.i −0.169695 + 0.169695i
\(94\) 33902.3 11015.5i 0.0408174 0.0132624i
\(95\) 8928.78 159027.i 0.0104141 0.185481i
\(96\) −98769.7 + 303982.i −0.111637 + 0.343585i
\(97\) −562743. + 286732.i −0.616587 + 0.314167i −0.734242 0.678888i \(-0.762462\pi\)
0.117655 + 0.993055i \(0.462462\pi\)
\(98\) −187834. + 1.18594e6i −0.199570 + 1.26004i
\(99\) 983574.i 1.01368i
\(100\) −1.25243e6 2.20711e6i −1.25243 2.20711i
\(101\) 1.06556e6 1.03422 0.517110 0.855919i \(-0.327008\pi\)
0.517110 + 0.855919i \(0.327008\pi\)
\(102\) −66449.0 10524.5i −0.0626164 0.00991747i
\(103\) −59911.7 117583.i −0.0548277 0.107605i 0.861967 0.506965i \(-0.169233\pi\)
−0.916794 + 0.399359i \(0.869233\pi\)
\(104\) −4.46400e6 1.45044e6i −3.96848 1.28944i
\(105\) 163558. + 133460.i 0.141288 + 0.115287i
\(106\) 842103. + 2.59173e6i 0.707046 + 2.17606i
\(107\) 959629. + 959629.i 0.783343 + 0.783343i 0.980393 0.197051i \(-0.0631363\pi\)
−0.197051 + 0.980393i \(0.563136\pi\)
\(108\) 793937. + 404531.i 0.630253 + 0.321130i
\(109\) 992290. 1.36577e6i 0.766230 1.05462i −0.230440 0.973086i \(-0.574017\pi\)
0.996670 0.0815383i \(-0.0259833\pi\)
\(110\) 261024. + 2.57581e6i 0.196111 + 1.93524i
\(111\) −132156. + 96016.9i −0.0966313 + 0.0702067i
\(112\) −826319. 5.21717e6i −0.588157 3.71348i
\(113\) −2.50711e6 + 397087.i −1.73755 + 0.275201i −0.943193 0.332247i \(-0.892193\pi\)
−0.794360 + 0.607448i \(0.792193\pi\)
\(114\) −42831.5 58952.5i −0.0289101 0.0397913i
\(115\) 555015. + 323202.i 0.364931 + 0.212511i
\(116\) −1.93323e6 1.40457e6i −1.23854 0.899850i
\(117\) −1.02825e6 + 2.01806e6i −0.642010 + 1.26001i
\(118\) 3.12531e6 3.12531e6i 1.90216 1.90216i
\(119\) 497162. 161538.i 0.295024 0.0958591i
\(120\) −655828. 254558.i −0.379530 0.147314i
\(121\) 38054.7 117120.i 0.0214809 0.0661114i
\(122\) 2.08980e6 1.06481e6i 1.15087 0.586396i
\(123\) −15752.2 + 99455.6i −0.00846499 + 0.0534458i
\(124\) 8.24903e6i 4.32651i
\(125\) 1.75005e6 867184.i 0.896028 0.443998i
\(126\) −4.77762e6 −2.38836
\(127\) 281521. + 44588.5i 0.137436 + 0.0217677i 0.224773 0.974411i \(-0.427836\pi\)
−0.0873376 + 0.996179i \(0.527836\pi\)
\(128\) 1.00376e6 + 1.96998e6i 0.478629 + 0.939362i
\(129\) −49349.6 16034.7i −0.0229887 0.00746948i
\(130\) 2.15725e6 5.55781e6i 0.981906 2.52973i
\(131\) 691574. + 2.12844e6i 0.307627 + 0.946779i 0.978684 + 0.205373i \(0.0658407\pi\)
−0.671057 + 0.741406i \(0.734159\pi\)
\(132\) 600797. + 600797.i 0.261220 + 0.261220i
\(133\) 504486. + 257048.i 0.214434 + 0.109260i
\(134\) −275903. + 379748.i −0.114668 + 0.157827i
\(135\) −345110. + 592634.i −0.140267 + 0.240872i
\(136\) −1.40937e6 + 1.02397e6i −0.560286 + 0.407072i
\(137\) −372140. 2.34960e6i −0.144725 0.913760i −0.948028 0.318188i \(-0.896926\pi\)
0.803302 0.595572i \(-0.203074\pi\)
\(138\) 290218. 45966.0i 0.110430 0.0174904i
\(139\) 787465. + 1.08385e6i 0.293215 + 0.403576i 0.930055 0.367420i \(-0.119759\pi\)
−0.636840 + 0.770996i \(0.719759\pi\)
\(140\) 8.97504e6 909502.i 3.27079 0.331451i
\(141\) 7284.20 + 5292.28i 0.00259851 + 0.00188793i
\(142\) −4.05094e6 + 7.95042e6i −1.41479 + 2.77667i
\(143\) −3.08512e6 + 3.08512e6i −1.05503 + 1.05503i
\(144\) 8.07853e6 2.62487e6i 2.70548 0.879065i
\(145\) 1.16273e6 1.42496e6i 0.381395 0.467410i
\(146\) 2.18345e6 6.71996e6i 0.701592 2.15928i
\(147\) −270223. + 137686.i −0.0850690 + 0.0433448i
\(148\) −1.09202e6 + 6.89474e6i −0.336857 + 2.12683i
\(149\) 2.49519e6i 0.754302i −0.926152 0.377151i \(-0.876904\pi\)
0.926152 0.377151i \(-0.123096\pi\)
\(150\) 369518. 813572.i 0.109487 0.241058i
\(151\) 4.13237e6 1.20024 0.600120 0.799910i \(-0.295119\pi\)
0.600120 + 0.799910i \(0.295119\pi\)
\(152\) −1.86365e6 295173.i −0.530682 0.0840517i
\(153\) 381636. + 749003.i 0.106555 + 0.209127i
\(154\) −8.75292e6 2.84400e6i −2.39657 0.778694i
\(155\) −6.33883e6 355903.i −1.70221 0.0955734i
\(156\) −604603. 1.86078e6i −0.159256 0.490140i
\(157\) −4.28440e6 4.28440e6i −1.10711 1.10711i −0.993528 0.113583i \(-0.963767\pi\)
−0.113583 0.993528i \(-0.536233\pi\)
\(158\) −5.93985e6 3.02650e6i −1.50593 0.767308i
\(159\) −404578. + 556854.i −0.100649 + 0.138532i
\(160\) −9.61939e6 + 4.23993e6i −2.34848 + 1.03514i
\(161\) −1.84708e6 + 1.34198e6i −0.442596 + 0.321565i
\(162\) −1.17708e6 7.43177e6i −0.276860 1.74802i
\(163\) 7.40295e6 1.17251e6i 1.70939 0.270741i 0.776297 0.630367i \(-0.217096\pi\)
0.933097 + 0.359626i \(0.117096\pi\)
\(164\) 2.52928e6 + 3.48125e6i 0.573410 + 0.789231i
\(165\) −487594. + 435751.i −0.108544 + 0.0970034i
\(166\) −5.26442e6 3.82482e6i −1.15087 0.836156i
\(167\) −202913. + 398240.i −0.0435673 + 0.0855057i −0.911764 0.410715i \(-0.865279\pi\)
0.868197 + 0.496220i \(0.165279\pi\)
\(168\) 1.76833e6 1.76833e6i 0.372937 0.372937i
\(169\) 4.96461e6 1.61310e6i 1.02855 0.334196i
\(170\) −1.19821e6 1.86023e6i −0.243886 0.378634i
\(171\) −281359. + 865935.i −0.0562695 + 0.173180i
\(172\) −1.97573e6 + 1.00668e6i −0.388277 + 0.197837i
\(173\) −154225. + 973739.i −0.0297863 + 0.188063i −0.998095 0.0616922i \(-0.980350\pi\)
0.968309 + 0.249756i \(0.0803503\pi\)
\(174\) 841409.i 0.159720i
\(175\) 311665. + 6.93597e6i 0.0581533 + 1.29417i
\(176\) 1.63629e7 3.00140
\(177\) 1.10263e6 + 174639.i 0.198842 + 0.0314935i
\(178\) −3.90439e6 7.66280e6i −0.692299 1.35871i
\(179\) 124142. + 40336.1i 0.0216450 + 0.00703290i 0.319820 0.947478i \(-0.396378\pi\)
−0.298174 + 0.954511i \(0.596378\pi\)
\(180\) 3.70233e6 + 1.40262e7i 0.634830 + 2.40504i
\(181\) −1.12023e6 3.44772e6i −0.188917 0.581428i 0.811077 0.584940i \(-0.198882\pi\)
−0.999994 + 0.00351243i \(0.998882\pi\)
\(182\) 1.49857e7 + 1.49857e7i 2.48578 + 2.48578i
\(183\) 527844. + 268950.i 0.0861296 + 0.0438852i
\(184\) 4.47222e6 6.15548e6i 0.717909 0.988117i
\(185\) −5.25103e6 1.13662e6i −0.829334 0.179514i
\(186\) −2.34986e6 + 1.70727e6i −0.365177 + 0.265317i
\(187\) 253321. + 1.59940e6i 0.0387388 + 0.244587i
\(188\) 380025. 60190.1i 0.0571925 0.00905840i
\(189\) −1.43294e6 1.97228e6i −0.212248 0.292134i
\(190\) 507026. 2.34240e6i 0.0739212 0.341507i
\(191\) 2.00466e6 + 1.45647e6i 0.287701 + 0.209027i 0.722269 0.691612i \(-0.243099\pi\)
−0.434568 + 0.900639i \(0.643099\pi\)
\(192\) −870718. + 1.70888e6i −0.123020 + 0.241439i
\(193\) −932416. + 932416.i −0.129699 + 0.129699i −0.768976 0.639277i \(-0.779234\pi\)
0.639277 + 0.768976i \(0.279234\pi\)
\(194\) −9.03828e6 + 2.93671e6i −1.23789 + 0.402213i
\(195\) 1.45597e6 384314.i 0.196358 0.0518302i
\(196\) −4.00492e6 + 1.23259e7i −0.531894 + 1.63700i
\(197\) 4.47162e6 2.27841e6i 0.584880 0.298011i −0.136401 0.990654i \(-0.543554\pi\)
0.721281 + 0.692643i \(0.243554\pi\)
\(198\) 2.31521e6 1.46176e7i 0.298260 1.88314i
\(199\) 7.25224e6i 0.920265i 0.887850 + 0.460133i \(0.152198\pi\)
−0.887850 + 0.460133i \(0.847802\pi\)
\(200\) −8.13057e6 2.16622e7i −1.01632 2.70778i
\(201\) −118560. −0.0145999
\(202\) 1.58361e7 + 2.50819e6i 1.92129 + 0.304303i
\(203\) 2.96809e6 + 5.82520e6i 0.354804 + 0.696343i
\(204\) −690629. 224399.i −0.0813494 0.0264320i
\(205\) −2.78424e6 + 1.79338e6i −0.323180 + 0.208167i
\(206\) −613617. 1.88852e6i −0.0701933 0.216033i
\(207\) −2.59611e6 2.59611e6i −0.292693 0.292693i
\(208\) −3.35728e7 1.71062e7i −3.73076 1.90092i
\(209\) −1.03094e6 + 1.41897e6i −0.112926 + 0.155429i
\(210\) 2.11662e6 + 2.36844e6i 0.228552 + 0.255744i
\(211\) 3.09278e6 2.24703e6i 0.329231 0.239201i −0.410873 0.911693i \(-0.634776\pi\)
0.740104 + 0.672492i \(0.234776\pi\)
\(212\) 4.60135e6 + 2.90518e7i 0.482923 + 3.04905i
\(213\) −2.22602e6 + 352568.i −0.230352 + 0.0364841i
\(214\) 1.20029e7 + 1.65206e7i 1.22475 + 1.68572i
\(215\) −688327. 1.56165e6i −0.0692595 0.157133i
\(216\) 6.57271e6 + 4.77535e6i 0.652203 + 0.473853i
\(217\) 1.02460e7 2.01089e7i 1.00271 1.96793i
\(218\) 1.79620e7 1.79620e7i 1.73375 1.73375i
\(219\) 1.69734e6 551498.i 0.161598 0.0525063i
\(220\) −1.56654e6 + 2.79009e7i −0.147120 + 2.62029i
\(221\) 1.15230e6 3.54642e6i 0.106755 0.328559i
\(222\) −2.19008e6 + 1.11590e6i −0.200171 + 0.101992i
\(223\) −1.47586e6 + 9.31818e6i −0.133085 + 0.840266i 0.827335 + 0.561709i \(0.189856\pi\)
−0.960420 + 0.278557i \(0.910144\pi\)
\(224\) 3.73693e7i 3.32484i
\(225\) −1.09380e7 + 2.23983e6i −0.960259 + 0.196638i
\(226\) −3.81948e7 −3.30886
\(227\) −1.31112e7 2.07662e6i −1.12090 0.177533i −0.431638 0.902047i \(-0.642064\pi\)
−0.689260 + 0.724514i \(0.742064\pi\)
\(228\) −357076. 700802.i −0.0301271 0.0591277i
\(229\) 2.74339e6 + 891380.i 0.228444 + 0.0742261i 0.421002 0.907060i \(-0.361678\pi\)
−0.192558 + 0.981286i \(0.561678\pi\)
\(230\) 7.48772e6 + 6.10979e6i 0.615412 + 0.502161i
\(231\) −718340. 2.21082e6i −0.0582766 0.179357i
\(232\) −1.54061e7 1.54061e7i −1.23375 1.23375i
\(233\) 1.69072e7 + 8.61465e6i 1.33661 + 0.681035i 0.968562 0.248772i \(-0.0800271\pi\)
0.368045 + 0.929808i \(0.380027\pi\)
\(234\) −2.00319e7 + 2.75715e7i −1.56341 + 2.15185i
\(235\) 29856.0 + 294621.i 0.00230053 + 0.0227018i
\(236\) 3.85954e7 2.80412e7i 2.93629 2.13334i
\(237\) −263407. 1.66309e6i −0.0197871 0.124931i
\(238\) 7.76895e6 1.23048e6i 0.576277 0.0912734i
\(239\) −4.55403e6 6.26809e6i −0.333582 0.459136i 0.608971 0.793192i \(-0.291582\pi\)
−0.942553 + 0.334056i \(0.891582\pi\)
\(240\) −4.88026e6 2.84193e6i −0.353028 0.205579i
\(241\) 8.74556e6 + 6.35402e6i 0.624794 + 0.453939i 0.854593 0.519299i \(-0.173807\pi\)
−0.229799 + 0.973238i \(0.573807\pi\)
\(242\) 841247. 1.65104e6i 0.0593578 0.116496i
\(243\) 4.17199e6 4.17199e6i 0.290753 0.290753i
\(244\) 2.40769e7 7.82305e6i 1.65741 0.538526i
\(245\) −9.29882e6 3.60931e6i −0.632309 0.245429i
\(246\) −468211. + 1.44101e6i −0.0314512 + 0.0967967i
\(247\) 3.59865e6 1.83361e6i 0.238808 0.121679i
\(248\) −1.17657e7 + 7.42856e7i −0.771369 + 4.87023i
\(249\) 1.64359e6i 0.106462i
\(250\) 2.80501e7 8.76848e6i 1.79521 0.561182i
\(251\) −1.50115e7 −0.949301 −0.474651 0.880174i \(-0.657426\pi\)
−0.474651 + 0.880174i \(0.657426\pi\)
\(252\) −5.09332e7 8.06703e6i −3.18273 0.504094i
\(253\) −3.21085e6 6.30166e6i −0.198271 0.389129i
\(254\) 4.07894e6 + 1.32533e6i 0.248912 + 0.0808765i
\(255\) 202233. 521021.i 0.0121964 0.0314221i
\(256\) 300249. + 924071.i 0.0178962 + 0.0550789i
\(257\) −8.07992e6 8.07992e6i −0.476001 0.476001i 0.427849 0.903850i \(-0.359271\pi\)
−0.903850 + 0.427849i \(0.859271\pi\)
\(258\) −695678. 354466.i −0.0405088 0.0206403i
\(259\) 1.12259e7 1.54511e7i 0.646133 0.889326i
\(260\) 3.23824e7 5.56081e7i 1.84242 3.16387i
\(261\) −8.50548e6 + 6.17959e6i −0.478385 + 0.347567i
\(262\) 5.26792e6 + 3.32603e7i 0.292911 + 1.84936i
\(263\) −1.63977e7 + 2.59714e6i −0.901394 + 0.142767i −0.589895 0.807480i \(-0.700831\pi\)
−0.311499 + 0.950246i \(0.600831\pi\)
\(264\) 4.55348e6 + 6.26732e6i 0.247475 + 0.340620i
\(265\) −2.25229e7 + 2.28240e6i −1.21028 + 0.122646i
\(266\) 6.89249e6 + 5.00769e6i 0.366211 + 0.266068i
\(267\) 986176. 1.93548e6i 0.0518108 0.101685i
\(268\) −3.58255e6 + 3.58255e6i −0.186118 + 0.186118i
\(269\) −2.22907e7 + 7.24269e6i −1.14516 + 0.372086i −0.819319 0.573338i \(-0.805648\pi\)
−0.325843 + 0.945424i \(0.605648\pi\)
\(270\) −6.52392e6 + 7.99525e6i −0.331450 + 0.406201i
\(271\) 9.20466e6 2.83290e7i 0.462487 1.42339i −0.399628 0.916678i \(-0.630861\pi\)
0.862115 0.506712i \(-0.169139\pi\)
\(272\) −1.24606e7 + 6.34898e6i −0.619200 + 0.315498i
\(273\) −837385. + 5.28704e6i −0.0411564 + 0.259851i
\(274\) 3.57951e7i 1.74009i
\(275\) −2.13724e7 2.40756e6i −1.02767 0.115765i
\(276\) 3.17157e6 0.150851
\(277\) 1.16461e7 + 1.84456e6i 0.547950 + 0.0867867i 0.424270 0.905536i \(-0.360531\pi\)
0.123679 + 0.992322i \(0.460531\pi\)
\(278\) 9.15187e6 + 1.79616e7i 0.425966 + 0.836006i
\(279\) 3.45164e7 + 1.12150e7i 1.58932 + 0.516403i
\(280\) 8.21208e7 + 4.61080e6i 3.74093 + 0.210040i
\(281\) −3.15846e6 9.72073e6i −0.142349 0.438107i 0.854311 0.519762i \(-0.173979\pi\)
−0.996661 + 0.0816553i \(0.973979\pi\)
\(282\) 95798.7 + 95798.7i 0.00427181 + 0.00427181i
\(283\) 7.44989e6 + 3.79591e6i 0.328693 + 0.167478i 0.610547 0.791980i \(-0.290949\pi\)
−0.281854 + 0.959457i \(0.590949\pi\)
\(284\) −5.66106e7 + 7.79177e7i −2.47140 + 3.40159i
\(285\) 553926. 244154.i 0.0239286 0.0105470i
\(286\) −5.31124e7 + 3.85884e7i −2.27037 + 1.64952i
\(287\) −1.84168e6 1.16279e7i −0.0779058 0.491878i
\(288\) 5.93534e7 9.40066e6i 2.48467 0.393533i
\(289\) 1.33742e7 + 1.84080e7i 0.554083 + 0.762630i
\(290\) 2.06344e7 1.84405e7i 0.846053 0.756098i
\(291\) −1.94195e6 1.41091e6i −0.0788059 0.0572559i
\(292\) 3.46240e7 6.79534e7i 1.39068 2.72937i
\(293\) 1.77932e7 1.77932e7i 0.707377 0.707377i −0.258606 0.965983i \(-0.583263\pi\)
0.965983 + 0.258606i \(0.0832630\pi\)
\(294\) −4.34009e6 + 1.41018e6i −0.170788 + 0.0554923i
\(295\) 1.98826e7 + 3.08678e7i 0.774474 + 1.20237i
\(296\) −1.96681e7 + 6.05321e7i −0.758380 + 2.33405i
\(297\) 6.72879e6 3.42849e6i 0.256843 0.130868i
\(298\) 5.87336e6 3.70830e7i 0.221941 1.40128i
\(299\) 1.62862e7i 0.609264i
\(300\) 5.31307e6 8.04939e6i 0.196780 0.298126i
\(301\) 6.06668e6 0.222460
\(302\) 6.14143e7 + 9.72707e6i 2.22971 + 0.353151i
\(303\) 1.83855e6 + 3.60836e6i 0.0660918 + 0.129712i
\(304\) −1.44059e7 4.68075e6i −0.512765 0.166608i
\(305\) 4.97270e6 + 1.88390e7i 0.175264 + 0.663985i
\(306\) 3.90873e6 + 1.20298e7i 0.136418 + 0.419851i
\(307\) 4.19973e6 + 4.19973e6i 0.145147 + 0.145147i 0.775946 0.630799i \(-0.217273\pi\)
−0.630799 + 0.775946i \(0.717273\pi\)
\(308\) −8.85110e7 4.50986e7i −3.02932 1.54352i
\(309\) 294805. 405764.i 0.00999216 0.0137530i
\(310\) −9.33685e7 2.02102e7i −3.13412 0.678398i
\(311\) 2.30031e6 1.67127e6i 0.0764725 0.0555605i −0.548892 0.835893i \(-0.684950\pi\)
0.625365 + 0.780333i \(0.284950\pi\)
\(312\) −2.79063e6 1.76193e7i −0.0918836 0.580130i
\(313\) −1.81946e7 + 2.88174e6i −0.593348 + 0.0939771i −0.445885 0.895090i \(-0.647111\pi\)
−0.147463 + 0.989068i \(0.547111\pi\)
\(314\) −5.35889e7 7.37587e7i −1.73095 2.38245i
\(315\) 8.39648e6 3.87907e7i 0.268637 1.24107i
\(316\) −5.82132e7 4.22944e7i −1.84485 1.34036i
\(317\) −2.07121e7 + 4.06497e7i −0.650198 + 1.27609i 0.296828 + 0.954931i \(0.404071\pi\)
−0.947027 + 0.321155i \(0.895929\pi\)
\(318\) −7.32351e6 + 7.32351e6i −0.227739 + 0.227739i
\(319\) −1.92612e7 + 6.25834e6i −0.593350 + 0.192791i
\(320\) −6.09907e7 + 1.60990e7i −1.86129 + 0.491302i
\(321\) −1.59387e6 + 4.90542e6i −0.0481878 + 0.148307i
\(322\) −3.06097e7 + 1.55964e7i −0.916835 + 0.467151i
\(323\) 234500. 1.48057e6i 0.00695881 0.0439362i
\(324\) 8.12160e7i 2.38785i
\(325\) 4.13340e7 + 2.72829e7i 1.20409 + 0.794768i
\(326\) 1.12781e8 3.25524
\(327\) 6.33711e6 + 1.00370e6i 0.181237 + 0.0287052i
\(328\) 1.78117e7 + 3.49575e7i 0.504760 + 0.990647i
\(329\) −1.00116e6 325297.i −0.0281136 0.00913466i
\(330\) −8.27221e6 + 5.32830e6i −0.230186 + 0.148268i
\(331\) 1.90206e7 + 5.85393e7i 0.524493 + 1.61422i 0.765316 + 0.643655i \(0.222583\pi\)
−0.240823 + 0.970569i \(0.577417\pi\)
\(332\) −4.96646e7 4.96646e7i −1.35717 1.35717i
\(333\) 2.73649e7 + 1.39431e7i 0.741074 + 0.377596i
\(334\) −3.95305e6 + 5.44091e6i −0.106095 + 0.146027i
\(335\) −2.59838e6 2.90752e6i −0.0691144 0.0773372i
\(336\) 1.62414e7 1.18001e7i 0.428160 0.311077i
\(337\) 498494. + 3.14737e6i 0.0130248 + 0.0822352i 0.993344 0.115181i \(-0.0367449\pi\)
−0.980320 + 0.197416i \(0.936745\pi\)
\(338\) 7.75800e7 1.22875e7i 2.00909 0.318209i
\(339\) −5.67053e6 7.80481e6i −0.145554 0.200338i
\(340\) −9.63287e6 2.18547e7i −0.245086 0.556042i
\(341\) 5.65603e7 + 4.10935e7i 1.42642 + 1.03636i
\(342\) −6.21980e6 + 1.22070e7i −0.155488 + 0.305163i
\(343\) −1.18930e7 + 1.18930e7i −0.294719 + 0.294719i
\(344\) −1.92280e7 + 6.24755e6i −0.472344 + 0.153474i
\(345\) −136837. + 2.43714e6i −0.00333231 + 0.0593503i
\(346\) −4.58412e6 + 1.41085e7i −0.110669 + 0.340605i
\(347\) −1.13754e7 + 5.79607e6i −0.272257 + 0.138722i −0.584789 0.811185i \(-0.698823\pi\)
0.312532 + 0.949907i \(0.398823\pi\)
\(348\) 1.42072e6 8.97009e6i 0.0337110 0.212843i
\(349\) 6.90705e7i 1.62486i −0.583057 0.812431i \(-0.698144\pi\)
0.583057 0.812431i \(-0.301856\pi\)
\(350\) −1.16945e7 + 1.03814e8i −0.272758 + 2.42133i
\(351\) −1.73901e7 −0.402142
\(352\) 1.14336e8 + 1.81090e7i 2.62152 + 0.415208i
\(353\) −1.04162e7 2.04429e7i −0.236801 0.464749i 0.741771 0.670654i \(-0.233986\pi\)
−0.978572 + 0.205905i \(0.933986\pi\)
\(354\) 1.59759e7 + 5.19089e6i 0.360127 + 0.117012i
\(355\) −5.74322e7 4.68632e7i −1.28372 1.04748i
\(356\) −2.86853e7 8.82842e7i −0.635783 1.95674i
\(357\) 1.40484e6 + 1.40484e6i 0.0308762 + 0.0308762i
\(358\) 1.75002e6 + 891678.i 0.0381411 + 0.0194339i
\(359\) 1.52212e7 2.09502e7i 0.328976 0.452797i −0.612205 0.790699i \(-0.709717\pi\)
0.941181 + 0.337902i \(0.109717\pi\)
\(360\) 1.33351e7 + 1.31592e8i 0.285818 + 2.82047i
\(361\) −3.67474e7 + 2.66985e7i −0.781097 + 0.567500i
\(362\) −8.53312e6 5.38760e7i −0.179880 1.13572i
\(363\) 462272. 73216.7i 0.00966446 0.00153070i
\(364\) 1.34456e8 + 1.85063e8i 2.78789 + 3.83720i
\(365\) 5.07238e7 + 2.95381e7i 1.04312 + 0.607440i
\(366\) 7.21162e6 + 5.23955e6i 0.147092 + 0.106869i
\(367\) −5.24664e6 + 1.02971e7i −0.106141 + 0.208314i −0.937968 0.346721i \(-0.887295\pi\)
0.831827 + 0.555035i \(0.187295\pi\)
\(368\) 4.31894e7 4.31894e7i 0.866631 0.866631i
\(369\) 1.80053e7 5.85027e6i 0.358361 0.116439i
\(370\) −7.53642e7 2.92524e7i −1.48785 0.577505i
\(371\) 2.48679e7 7.65357e7i 0.486988 1.49879i
\(372\) −2.79341e7 + 1.42331e7i −0.542633 + 0.276485i
\(373\) −5.96415e6 + 3.76561e7i −0.114927 + 0.725620i 0.861175 + 0.508308i \(0.169729\pi\)
−0.976102 + 0.217312i \(0.930271\pi\)
\(374\) 2.43662e7i 0.465772i
\(375\) 5.95619e6 + 4.43003e6i 0.112947 + 0.0840066i
\(376\) 3.50812e6 0.0659950
\(377\) 4.60619e7 + 7.29548e6i 0.859642 + 0.136154i
\(378\) −1.66536e7 3.26845e7i −0.308341 0.605154i
\(379\) −6.87967e7 2.23534e7i −1.26372 0.410607i −0.400900 0.916122i \(-0.631303\pi\)
−0.862818 + 0.505515i \(0.831303\pi\)
\(380\) 9.36044e6 2.41157e7i 0.170587 0.439490i
\(381\) 334753. + 1.03026e6i 0.00605270 + 0.0186283i
\(382\) 2.63645e7 + 2.63645e7i 0.472965 + 0.472965i
\(383\) −6.02266e7 3.06870e7i −1.07199 0.546208i −0.173337 0.984863i \(-0.555455\pi\)
−0.898656 + 0.438655i \(0.855455\pi\)
\(384\) −4.93915e6 + 6.79815e6i −0.0872285 + 0.120060i
\(385\) 3.84741e7 6.60691e7i 0.674196 1.15775i
\(386\) −1.60521e7 + 1.16626e7i −0.279107 + 0.202783i
\(387\) 1.52614e6 + 9.63567e6i 0.0263306 + 0.166245i
\(388\) −1.01314e8 + 1.60465e7i −1.73450 + 0.274717i
\(389\) −2.31310e7 3.18371e7i −0.392958 0.540860i 0.566001 0.824404i \(-0.308490\pi\)
−0.958959 + 0.283544i \(0.908490\pi\)
\(390\) 2.25429e7 2.28442e6i 0.380028 0.0385108i
\(391\) 4.89021e6 + 3.55294e6i 0.0818082 + 0.0594371i
\(392\) −5.36463e7 + 1.05287e8i −0.890597 + 1.74790i
\(393\) −6.01440e6 + 6.01440e6i −0.0990866 + 0.0990866i
\(394\) 7.18193e7 2.33355e7i 1.17423 0.381530i
\(395\) 3.50120e7 4.29082e7i 0.568102 0.696225i
\(396\) 4.93639e7 1.51927e8i 0.794921 2.44652i
\(397\) −9.82853e7 + 5.00789e7i −1.57079 + 0.800355i −0.999788 0.0205960i \(-0.993444\pi\)
−0.570998 + 0.820951i \(0.693444\pi\)
\(398\) −1.70708e7 + 1.07781e8i −0.270773 + 1.70960i
\(399\) 2.15189e6i 0.0338767i
\(400\) −3.72623e7 1.81966e8i −0.582224 2.84322i
\(401\) −1.04939e8 −1.62744 −0.813718 0.581260i \(-0.802560\pi\)
−0.813718 + 0.581260i \(0.802560\pi\)
\(402\) −1.76201e6 279075.i −0.0271225 0.00429579i
\(403\) −7.30880e7 1.43443e8i −1.11669 2.19162i
\(404\) 1.64590e8 + 5.34786e7i 2.49609 + 0.811027i
\(405\) 6.24091e7 + 3.50405e6i 0.939471 + 0.0527480i
\(406\) 3.03993e7 + 9.35593e7i 0.454240 + 1.39801i
\(407\) 4.18344e7 + 4.18344e7i 0.620513 + 0.620513i
\(408\) −5.89931e6 3.00585e6i −0.0868601 0.0442575i
\(409\) −5.18020e7 + 7.12994e7i −0.757141 + 1.04212i 0.240305 + 0.970697i \(0.422753\pi\)
−0.997446 + 0.0714182i \(0.977247\pi\)
\(410\) −4.56001e7 + 2.00991e7i −0.661628 + 0.291625i
\(411\) 7.31447e6 5.31427e6i 0.105356 0.0765453i
\(412\) −3.35288e6 2.11692e7i −0.0479431 0.302701i
\(413\) −1.28915e8 + 2.04181e7i −1.83000 + 0.289844i
\(414\) −3.24719e7 4.46937e7i −0.457622 0.629862i
\(415\) 4.03068e7 3.60212e7i 0.563941 0.503981i
\(416\) −2.15657e8 1.56684e8i −2.99560 2.17643i
\(417\) −2.31159e6 + 4.53675e6i −0.0318788 + 0.0625657i
\(418\) −1.86616e7 + 1.86616e7i −0.255518 + 0.255518i
\(419\) 4.82860e7 1.56891e7i 0.656415 0.213282i 0.0381747 0.999271i \(-0.487846\pi\)
0.618241 + 0.785989i \(0.287846\pi\)
\(420\) 1.85657e7 + 2.88234e7i 0.250590 + 0.389043i
\(421\) 1.70260e7 5.24005e7i 0.228174 0.702246i −0.769780 0.638309i \(-0.779634\pi\)
0.997954 0.0639371i \(-0.0203657\pi\)
\(422\) 5.12533e7 2.61149e7i 0.682001 0.347497i
\(423\) 264814. 1.67197e6i 0.00349881 0.0220906i
\(424\) 2.68185e8i 3.51833i
\(425\) 1.72095e7 6.45931e6i 0.224182 0.0841432i
\(426\) −3.39125e7 −0.438664
\(427\) −6.84098e7 1.08350e7i −0.878688 0.139171i
\(428\) 1.00066e8 + 1.96390e8i 1.27630 + 2.50489i
\(429\) −1.57705e7 5.12414e6i −0.199744 0.0649007i
\(430\) −6.55383e6 2.48291e7i −0.0824308 0.312288i
\(431\) 9.85616e6 + 3.03341e7i 0.123105 + 0.378878i 0.993551 0.113385i \(-0.0361695\pi\)
−0.870446 + 0.492264i \(0.836169\pi\)
\(432\) 4.61169e7 + 4.61169e7i 0.572017 + 0.572017i
\(433\) 1.14222e8 + 5.81991e7i 1.40698 + 0.716890i 0.982100 0.188362i \(-0.0603177\pi\)
0.424876 + 0.905252i \(0.360318\pi\)
\(434\) 1.99608e8 2.74736e8i 2.44179 3.36083i
\(435\) 6.83162e6 + 1.47874e6i 0.0829958 + 0.0179649i
\(436\) 2.21818e8 1.61161e8i 2.67632 1.94446i
\(437\) 1.02418e6 + 6.46644e6i 0.0122725 + 0.0774856i
\(438\) 2.65236e7 4.20092e6i 0.315653 0.0499945i
\(439\) 8.08799e6 + 1.11322e7i 0.0955976 + 0.131579i 0.854136 0.520049i \(-0.174086\pi\)
−0.758539 + 0.651628i \(0.774086\pi\)
\(440\) −5.39026e7 + 2.49023e8i −0.632778 + 2.92336i
\(441\) 4.61301e7 + 3.35155e7i 0.537859 + 0.390778i
\(442\) 2.54730e7 4.99936e7i 0.294994 0.578959i
\(443\) 1.06518e8 1.06518e8i 1.22522 1.22522i 0.259462 0.965753i \(-0.416455\pi\)
0.965753 0.259462i \(-0.0835452\pi\)
\(444\) −2.52322e7 + 8.19844e6i −0.288275 + 0.0936661i
\(445\) 6.90781e7 1.82337e7i 0.783900 0.206917i
\(446\) −4.38676e7 + 1.35011e8i −0.494469 + 1.52182i
\(447\) 8.44960e6 4.30529e6i 0.0946049 0.0482036i
\(448\) 3.50782e7 2.21475e8i 0.390124 2.46315i
\(449\) 3.76443e7i 0.415872i 0.978142 + 0.207936i \(0.0666746\pi\)
−0.978142 + 0.207936i \(0.933325\pi\)
\(450\) −1.67830e8 + 7.54136e6i −1.84175 + 0.0827584i
\(451\) 3.64694e7 0.397557
\(452\) −4.07186e8 6.44920e7i −4.40938 0.698378i
\(453\) 7.13012e6 + 1.39937e7i 0.0767013 + 0.150535i
\(454\) −1.89968e8 6.17243e7i −2.03008 0.659613i
\(455\) −1.48010e8 + 9.53360e7i −1.57129 + 1.01210i
\(456\) −2.21604e6 6.82028e6i −0.0233714 0.0719297i
\(457\) −5.49553e7 5.49553e7i −0.575786 0.575786i 0.357953 0.933740i \(-0.383475\pi\)
−0.933740 + 0.357953i \(0.883475\pi\)
\(458\) 3.86734e7 + 1.97051e7i 0.402546 + 0.205107i
\(459\) −3.79377e6 + 5.22167e6i −0.0392313 + 0.0539972i
\(460\) 6.95086e7 + 7.77783e7i 0.714110 + 0.799070i
\(461\) −1.29105e8 + 9.38003e7i −1.31777 + 0.957418i −0.317816 + 0.948153i \(0.602949\pi\)
−0.999957 + 0.00926543i \(0.997051\pi\)
\(462\) −5.47180e6 3.45476e7i −0.0554887 0.350342i
\(463\) 6.10394e7 9.66768e6i 0.614988 0.0974046i 0.158834 0.987305i \(-0.449227\pi\)
0.456154 + 0.889901i \(0.349227\pi\)
\(464\) −1.02805e8 1.41499e8i −1.02911 1.41644i
\(465\) −9.73202e6 2.20796e7i −0.0967930 0.219600i
\(466\) 2.30993e8 + 1.67826e8i 2.28266 + 1.65845i
\(467\) −7.56598e6 + 1.48491e7i −0.0742873 + 0.145797i −0.925163 0.379570i \(-0.876072\pi\)
0.850876 + 0.525367i \(0.176072\pi\)
\(468\) −2.60110e8 + 2.60110e8i −2.53758 + 2.53758i
\(469\) 1.31831e7 4.28346e6i 0.127791 0.0415218i
\(470\) −249788. + 4.44887e6i −0.00240591 + 0.0428505i
\(471\) 7.11605e6 2.19010e7i 0.0681046 0.209604i
\(472\) 3.87561e8 1.97472e8i 3.68565 1.87793i
\(473\) −2.93988e6 + 1.85617e7i −0.0277809 + 0.175402i
\(474\) 2.53365e7i 0.237909i
\(475\) 1.81275e7 + 8.23335e6i 0.169144 + 0.0768238i
\(476\) 8.49009e7 0.787211
\(477\) 1.27817e8 + 2.02442e7i 1.17770 + 0.186529i
\(478\) −5.29267e7 1.03874e8i −0.484609 0.951098i
\(479\) −6.56180e7 2.13206e7i −0.597058 0.193996i −0.00512998 0.999987i \(-0.501633\pi\)
−0.591928 + 0.805991i \(0.701633\pi\)
\(480\) −3.09555e7 2.52589e7i −0.279907 0.228397i
\(481\) −4.20994e7 1.29569e8i −0.378304 1.16430i
\(482\) 1.15018e8 + 1.15018e8i 1.02713 + 1.02713i
\(483\) −7.73143e6 3.93936e6i −0.0686149 0.0349610i
\(484\) 1.17562e7 1.61810e7i 0.103688 0.142714i
\(485\) −7.95953e6 7.85453e7i −0.0697690 0.688486i
\(486\) 7.18235e7 5.21828e7i 0.625688 0.454589i
\(487\) 3.24782e7 + 2.05060e8i 0.281194 + 1.77539i 0.573642 + 0.819106i \(0.305530\pi\)
−0.292448 + 0.956281i \(0.594470\pi\)
\(488\) 2.27979e8 3.61084e7i 1.96171 0.310705i
\(489\) 1.67438e7 + 2.30459e7i 0.143195 + 0.197091i
\(490\) −1.29701e8 7.55289e7i −1.10244 0.641985i
\(491\) 7.92753e7 + 5.75969e7i 0.669720 + 0.486580i 0.869932 0.493173i \(-0.164163\pi\)
−0.200211 + 0.979753i \(0.564163\pi\)
\(492\) −7.42465e6 + 1.45717e7i −0.0623420 + 0.122353i
\(493\) 1.22393e7 1.22393e7i 0.102145 0.102145i
\(494\) 5.77984e7 1.87799e7i 0.479441 0.155780i
\(495\) 1.14616e8 + 4.44878e7i 0.944993 + 0.366796i
\(496\) −1.86576e8 + 5.74221e8i −1.52901 + 4.70581i
\(497\) 2.34782e8 1.19627e8i 1.91247 0.974454i
\(498\) 3.86880e6 2.44267e7i 0.0313248 0.197777i
\(499\) 1.36446e8i 1.09814i 0.835776 + 0.549070i \(0.185018\pi\)
−0.835776 + 0.549070i \(0.814982\pi\)
\(500\) 3.13842e8 4.61162e7i 2.51074 0.368929i
\(501\) −1.69869e6 −0.0135083
\(502\) −2.23098e8 3.53353e7i −1.76354 0.279317i
\(503\) −3.92632e7 7.70583e7i −0.308519 0.605502i 0.683735 0.729730i \(-0.260354\pi\)
−0.992254 + 0.124229i \(0.960354\pi\)
\(504\) −4.47166e8 1.45293e8i −3.49283 1.13489i
\(505\) −4.81959e7 + 1.24169e8i −0.374228 + 0.964140i
\(506\) −3.28857e7 1.01212e8i −0.253837 0.781230i
\(507\) 1.40286e7 + 1.40286e7i 0.107644 + 0.107644i
\(508\) 4.12469e7 + 2.10164e7i 0.314630 + 0.160312i
\(509\) −3.24086e7 + 4.46066e7i −0.245757 + 0.338256i −0.914020 0.405670i \(-0.867038\pi\)
0.668262 + 0.743926i \(0.267038\pi\)
\(510\) 4.23195e6 7.26726e6i 0.0319029 0.0547848i
\(511\) −1.68808e8 + 1.22646e8i −1.26512 + 0.919160i
\(512\) −1.98487e7 1.25320e8i −0.147884 0.933703i
\(513\) −6.90475e6 + 1.09360e6i −0.0511441 + 0.00810043i
\(514\) −1.01063e8 1.39101e8i −0.744221 1.02433i
\(515\) 1.64118e7 1.66312e6i 0.120153 0.0121759i
\(516\) −6.81797e6 4.95354e6i −0.0496256 0.0360551i
\(517\) 1.48044e6 2.90553e6i 0.0107132 0.0210258i
\(518\) 2.03207e8 2.03207e8i 1.46200 1.46200i
\(519\) −3.56353e6 + 1.15786e6i −0.0254905 + 0.00828236i
\(520\) 3.70930e8 4.54585e8i 2.63804 3.23299i
\(521\) 2.50072e7 7.69644e7i 0.176829 0.544223i −0.822884 0.568210i \(-0.807636\pi\)
0.999712 + 0.0239873i \(0.00763614\pi\)
\(522\) −1.40952e8 + 7.18188e7i −0.990971 + 0.504925i
\(523\) 5.16844e6 3.26323e7i 0.0361289 0.228109i −0.963017 0.269442i \(-0.913161\pi\)
0.999145 + 0.0413335i \(0.0131606\pi\)
\(524\) 3.63476e8i 2.52628i
\(525\) −2.29499e7 + 1.30230e7i −0.158600 + 0.0899978i
\(526\) −2.49812e8 −1.71655
\(527\) −5.90160e7 9.34721e6i −0.403216 0.0638631i
\(528\) 2.82332e7 + 5.54107e7i 0.191804 + 0.376436i
\(529\) 1.15683e8 + 3.75875e7i 0.781449 + 0.253908i
\(530\) −3.40102e8 1.90955e7i −2.28445 0.128264i
\(531\) −6.48598e7 1.99618e8i −0.433204 1.33326i
\(532\) 6.50239e7 + 6.50239e7i 0.431855 + 0.431855i
\(533\) −7.48264e7 3.81260e7i −0.494167 0.251790i
\(534\) 1.92122e7 2.64433e7i 0.126169 0.173657i
\(535\) −1.55230e8 + 6.84206e7i −1.01371 + 0.446813i
\(536\) −3.73720e7 + 2.71523e7i −0.242690 + 0.176325i
\(537\) 77605.9 + 489984.i 0.000501155 + 0.00316417i
\(538\) −3.48328e8 + 5.51697e7i −2.23687 + 0.354286i
\(539\) 6.45626e7 + 8.88627e7i 0.412301 + 0.567484i
\(540\) −8.30502e7 + 7.42200e7i −0.527423 + 0.471346i
\(541\) −7.12105e7 5.17374e7i −0.449730 0.326748i 0.339759 0.940512i \(-0.389654\pi\)
−0.789489 + 0.613764i \(0.789654\pi\)
\(542\) 2.03480e8 3.99353e8i 1.27798 2.50818i
\(543\) 9.74230e6 9.74230e6i 0.0608502 0.0608502i
\(544\) −9.40943e7 + 3.05731e7i −0.584476 + 0.189908i
\(545\) 1.14271e8 + 1.77406e8i 0.705904 + 1.09592i
\(546\) −2.48900e7 + 7.66037e7i −0.152914 + 0.470621i
\(547\) 1.22625e8 6.24807e7i 0.749236 0.381755i −0.0372964 0.999304i \(-0.511875\pi\)
0.786532 + 0.617550i \(0.211875\pi\)
\(548\) 6.04403e7 3.81605e8i 0.367269 2.31885i
\(549\) 1.11381e8i 0.673120i
\(550\) −3.11964e8 8.60884e7i −1.87507 0.517436i
\(551\) 1.87477e7 0.112071
\(552\) 2.85611e7 + 4.52364e6i 0.169808 + 0.0268950i
\(553\) 8.93749e7 + 1.75408e8i 0.528494 + 1.03723i
\(554\) 1.68740e8 + 5.48268e7i 0.992402 + 0.322451i
\(555\) −5.21132e6 1.97430e7i −0.0304838 0.115487i
\(556\) 6.72380e7 + 2.06937e8i 0.391193 + 1.20397i
\(557\) −1.13426e8 1.13426e8i −0.656366 0.656366i 0.298152 0.954518i \(-0.403630\pi\)
−0.954518 + 0.298152i \(0.903630\pi\)
\(558\) 4.86575e8 + 2.47922e8i 2.80058 + 1.42697i
\(559\) 2.54367e7 3.50106e7i 0.145621 0.200431i
\(560\) 6.45330e8 + 1.39686e8i 3.67467 + 0.795403i
\(561\) −4.97906e6 + 3.61750e6i −0.0282006 + 0.0204889i
\(562\) −2.40589e7 1.51902e8i −0.135540 0.855764i
\(563\) −6.80026e7 + 1.07705e7i −0.381066 + 0.0603549i −0.344029 0.938959i \(-0.611792\pi\)
−0.0370368 + 0.999314i \(0.511792\pi\)
\(564\) 859533. + 1.18305e6i 0.00479099 + 0.00659424i
\(565\) 6.71258e7 3.10113e8i 0.372173 1.71939i
\(566\) 1.01783e8 + 7.39500e7i 0.561342 + 0.407839i
\(567\) −1.00877e8 + 1.97983e8i −0.553407 + 1.08612i
\(568\) −6.20934e8 + 6.20934e8i −3.38844 + 3.38844i
\(569\) −3.21728e8 + 1.04536e8i −1.74643 + 0.567450i −0.995656 0.0931079i \(-0.970320\pi\)
−0.750775 + 0.660558i \(0.770320\pi\)
\(570\) 8.80702e6 2.32468e6i 0.0475559 0.0125528i
\(571\) 1.12155e8 3.45177e8i 0.602435 1.85410i 0.0888903 0.996041i \(-0.471668\pi\)
0.513545 0.858063i \(-0.328332\pi\)
\(572\) −6.31377e8 + 3.21703e8i −3.37365 + 1.71896i
\(573\) −1.47322e6 + 9.30155e6i −0.00783076 + 0.0494415i
\(574\) 1.77147e8i 0.936694i
\(575\) −6.27664e7 + 5.00571e7i −0.330159 + 0.263307i
\(576\) 3.60592e8 1.88690
\(577\) −2.44937e7 3.87942e6i −0.127505 0.0201948i 0.0923558 0.995726i \(-0.470560\pi\)
−0.219861 + 0.975531i \(0.570560\pi\)
\(578\) 1.55434e8 + 3.05057e8i 0.804940 + 1.57978i
\(579\) −4.76631e6 1.54867e6i −0.0245554 0.00797852i
\(580\) 2.51116e8 1.61749e8i 1.28703 0.829005i
\(581\) 5.93813e7 + 1.82757e8i 0.302776 + 0.931848i
\(582\) −2.55397e7 2.55397e7i −0.129553 0.129553i
\(583\) 2.22118e8 + 1.13175e8i 1.12093 + 0.571143i
\(584\) 4.08725e8 5.62561e8i 2.05207 2.82443i
\(585\) −1.88655e8 2.11100e8i −0.942325 1.05444i
\(586\) 3.06321e8 2.22555e8i 1.52224 1.10598i
\(587\) −3.77871e7 2.38578e8i −0.186823 1.17955i −0.885682 0.464292i \(-0.846309\pi\)
0.698859 0.715259i \(-0.253691\pi\)
\(588\) −4.86499e7 + 7.70539e6i −0.239304 + 0.0379021i
\(589\) −3.80403e7 5.23580e7i −0.186165 0.256234i
\(590\) 2.22832e8 + 5.05551e8i 1.08498 + 2.46155i
\(591\) 1.54310e7 + 1.12113e7i 0.0747534 + 0.0543115i
\(592\) −2.31961e8 + 4.55248e8i −1.11802 + 2.19424i
\(593\) 2.31243e8 2.31243e8i 1.10893 1.10893i 0.115639 0.993291i \(-0.463108\pi\)
0.993291 0.115639i \(-0.0368916\pi\)
\(594\) 1.08072e8 3.51147e7i 0.515648 0.167544i
\(595\) −3.66304e6 + 6.52407e7i −0.0173896 + 0.309719i
\(596\) 1.25229e8 3.85417e8i 0.591518 1.82050i
\(597\) −2.45587e7 + 1.25133e7i −0.115420 + 0.0588095i
\(598\) −3.83356e7 + 2.42041e8i −0.179266 + 1.13184i
\(599\) 3.78075e8i 1.75913i 0.475779 + 0.879565i \(0.342166\pi\)
−0.475779 + 0.879565i \(0.657834\pi\)
\(600\) 5.93271e7 6.49097e7i 0.274663 0.300508i
\(601\) −3.08731e8 −1.42219 −0.711093 0.703098i \(-0.751799\pi\)
−0.711093 + 0.703098i \(0.751799\pi\)
\(602\) 9.01615e7 + 1.42802e7i 0.413268 + 0.0654552i
\(603\) 1.01197e7 + 1.98611e7i 0.0461549 + 0.0905841i
\(604\) 6.38301e8 + 2.07397e8i 2.89677 + 0.941219i
\(605\) 1.19268e7 + 9.73195e6i 0.0538588 + 0.0439474i
\(606\) 1.88305e7 + 5.79543e7i 0.0846142 + 0.260416i
\(607\) 2.05854e8 + 2.05854e8i 0.920437 + 0.920437i 0.997060 0.0766232i \(-0.0244138\pi\)
−0.0766232 + 0.997060i \(0.524414\pi\)
\(608\) −9.54803e7 4.86496e7i −0.424818 0.216456i
\(609\) −1.46050e7 + 2.01020e7i −0.0646619 + 0.0889995i
\(610\) 2.95585e7 + 2.91686e8i 0.130225 + 1.28507i
\(611\) −6.07500e6 + 4.41375e6i −0.0266332 + 0.0193501i
\(612\) 2.13577e7 + 1.34848e8i 0.0931754 + 0.588286i
\(613\) 6.28413e7 9.95308e6i 0.272812 0.0432092i −0.0185294 0.999828i \(-0.505898\pi\)
0.291341 + 0.956619i \(0.405898\pi\)
\(614\) 5.25298e7 + 7.23011e7i 0.226935 + 0.312349i
\(615\) −1.08770e7 6.33405e6i −0.0467612 0.0272305i
\(616\) −7.32750e8 5.32374e8i −3.13483 2.27759i
\(617\) 7.30826e7 1.43433e8i 0.311142 0.610650i −0.681489 0.731828i \(-0.738667\pi\)
0.992631 + 0.121178i \(0.0386672\pi\)
\(618\) 5.33644e6 5.33644e6i 0.0226093 0.0226093i
\(619\) 1.61701e8 5.25399e7i 0.681776 0.221522i 0.0524032 0.998626i \(-0.483312\pi\)
0.629373 + 0.777104i \(0.283312\pi\)
\(620\) −9.61257e8 3.73109e8i −4.03334 1.56553i
\(621\) 8.71103e6 2.68098e7i 0.0363743 0.111949i
\(622\) 3.81207e7 1.94234e7i 0.158412 0.0807151i
\(623\) −3.97296e7 + 2.50843e8i −0.164305 + 1.03738i
\(624\) 1.43205e8i 0.589392i
\(625\) 2.18965e7 + 2.43157e8i 0.0896882 + 0.995970i
\(626\) −2.77187e8 −1.12993
\(627\) −6.58393e6 1.04279e6i −0.0267106 0.00423054i
\(628\) −4.46758e8 8.76812e8i −1.80382 3.54020i
\(629\) −4.80896e7 1.56252e7i −0.193241 0.0627878i
\(630\) 2.16095e8 5.56735e8i 0.864218 2.22652i
\(631\) 2.02453e7 + 6.23085e7i 0.0805815 + 0.248004i 0.983229 0.182377i \(-0.0583791\pi\)
−0.902647 + 0.430381i \(0.858379\pi\)
\(632\) −4.63907e8 4.63907e8i −1.83772 1.83772i
\(633\) 1.29456e7 + 6.59613e6i 0.0510402 + 0.0260063i
\(634\) −4.03502e8 + 5.55373e8i −1.58335 + 2.17930i
\(635\) −1.79293e7 + 3.07888e7i −0.0700231 + 0.120246i
\(636\) −9.04402e7 + 6.57087e7i −0.351553 + 0.255418i
\(637\) −3.95676e7 2.49820e8i −0.153081 0.966516i
\(638\) −3.00986e8 + 4.76716e7i −1.15900 + 0.183568i
\(639\) 2.49065e8 + 3.42809e8i 0.954576 + 1.31386i
\(640\) −2.74962e8 + 2.78638e7i −1.04890 + 0.106292i
\(641\) 1.14206e8 + 8.29754e7i 0.433625 + 0.315047i 0.783097 0.621900i \(-0.213639\pi\)
−0.349472 + 0.936947i \(0.613639\pi\)
\(642\) −3.52344e7 + 6.91514e7i −0.133156 + 0.261334i
\(643\) 8.03397e7 8.03397e7i 0.302202 0.302202i −0.539673 0.841875i \(-0.681452\pi\)
0.841875 + 0.539673i \(0.181452\pi\)
\(644\) −3.52658e8 + 1.14586e8i −1.32037 + 0.429015i
\(645\) 4.10063e6 5.02544e6i 0.0152817 0.0187281i
\(646\) 6.97016e6 2.14519e7i 0.0258550 0.0795736i
\(647\) 1.43297e7 7.30133e6i 0.0529082 0.0269581i −0.427336 0.904093i \(-0.640548\pi\)
0.480244 + 0.877135i \(0.340548\pi\)
\(648\) 1.15839e8 7.31381e8i 0.425727 2.68793i
\(649\) 4.04323e8i 1.47909i
\(650\) 5.50076e8 + 5.02767e8i 2.00301 + 1.83074i
\(651\) 8.57747e7 0.310897
\(652\) 1.20233e9 + 1.90431e8i 4.33793 + 0.687060i
\(653\) −1.24034e8 2.43430e8i −0.445451 0.874247i −0.999138 0.0415220i \(-0.986779\pi\)
0.553686 0.832725i \(-0.313221\pi\)
\(654\) 9.18180e7 + 2.98335e7i 0.328242 + 0.106652i
\(655\) −2.79308e8 1.56821e7i −0.993937 0.0558061i
\(656\) 9.73263e7 + 2.99540e8i 0.344761 + 1.06107i
\(657\) −2.37264e8 2.37264e8i −0.836633 0.836633i
\(658\) −1.41133e7 7.19109e6i −0.0495395 0.0252416i
\(659\) 4.92680e7 6.78116e7i 0.172151 0.236945i −0.714220 0.699921i \(-0.753218\pi\)
0.886371 + 0.462976i \(0.153218\pi\)
\(660\) −9.71852e7 + 4.28363e7i −0.338040 + 0.148998i
\(661\) −2.17813e8 + 1.58250e8i −0.754188 + 0.547950i −0.897122 0.441783i \(-0.854346\pi\)
0.142934 + 0.989732i \(0.454346\pi\)
\(662\) 1.44885e8 + 9.14770e8i 0.499402 + 3.15310i
\(663\) 1.39976e7 2.21701e6i 0.0480302 0.00760723i
\(664\) −3.76411e8 5.18086e8i −1.28576 1.76969i
\(665\) −5.27720e7 + 4.71611e7i −0.179448 + 0.160369i
\(666\) 3.73871e8 + 2.71633e8i 1.26561 + 0.919517i
\(667\) −3.43206e7 + 6.73579e7i −0.115658 + 0.226992i
\(668\) −5.13297e7 + 5.13297e7i −0.172202 + 0.172202i
\(669\) −3.41011e7 + 1.10801e7i −0.113891 + 0.0370055i
\(670\) −3.17726e7 4.93271e7i −0.105640 0.164007i
\(671\) 6.63021e7 2.04057e8i 0.219462 0.675435i
\(672\) 1.26546e8 6.44782e7i 0.417003 0.212474i
\(673\) −3.46141e7 + 2.18545e8i −0.113556 + 0.716961i 0.863559 + 0.504248i \(0.168230\pi\)
−0.977115 + 0.212714i \(0.931770\pi\)
\(674\) 4.79488e7i 0.156602i
\(675\) −5.34500e7 6.70208e7i −0.173795 0.217921i
\(676\) 8.47812e8 2.74447
\(677\) 5.19375e8 + 8.22608e7i 1.67384 + 0.265111i 0.919993 0.391936i \(-0.128194\pi\)
0.753850 + 0.657046i \(0.228194\pi\)
\(678\) −6.59025e7 1.29341e8i −0.211452 0.414999i
\(679\) 2.66907e8 + 8.67234e7i 0.852611 + 0.277030i
\(680\) −5.55760e7 2.10549e8i −0.176751 0.669617i
\(681\) −1.55904e7 4.79823e7i −0.0493647 0.151929i
\(682\) 7.43857e8 + 7.43857e8i 2.34496 + 2.34496i
\(683\) −1.96502e8 1.00123e8i −0.616743 0.314246i 0.117562 0.993066i \(-0.462492\pi\)
−0.734306 + 0.678819i \(0.762492\pi\)
\(684\) −8.69196e7 + 1.19635e8i −0.271612 + 0.373842i
\(685\) 2.90630e8 + 6.29086e7i 0.904210 + 0.195721i
\(686\) −2.04745e8 + 1.48756e8i −0.634221 + 0.460788i
\(687\) 1.71500e6 + 1.08281e7i 0.00528925 + 0.0333950i
\(688\) −1.60301e8 + 2.53892e7i −0.492233 + 0.0779620i
\(689\) −3.37417e8 4.64415e8i −1.03160 1.41987i
\(690\) −7.77035e6 + 3.58981e7i −0.0236534 + 0.109276i
\(691\) 7.81141e7 + 5.67532e7i 0.236753 + 0.172011i 0.699835 0.714304i \(-0.253257\pi\)
−0.463083 + 0.886315i \(0.653257\pi\)
\(692\) −7.26925e7 + 1.42667e8i −0.219367 + 0.430532i
\(693\) −3.09042e8 + 3.09042e8i −0.928576 + 0.928576i
\(694\) −1.82702e8 + 5.93635e7i −0.546595 + 0.177599i
\(695\) −1.61919e8 + 4.27397e7i −0.482328 + 0.127314i
\(696\) 2.55883e7 7.87526e7i 0.0758950 0.233581i
\(697\) −2.77719e7 + 1.41505e7i −0.0820177 + 0.0417901i
\(698\) 1.62583e8 1.02651e9i 0.478090 3.01854i
\(699\) 7.21177e7i 0.211159i
\(700\) −2.99963e8 + 1.08700e9i −0.874529 + 3.16909i
\(701\) 7.08218e7 0.205595 0.102798 0.994702i \(-0.467221\pi\)
0.102798 + 0.994702i \(0.467221\pi\)
\(702\) −2.58447e8 4.09340e7i −0.747068 0.118324i
\(703\) −2.48638e7 4.87979e7i −0.0715651 0.140454i
\(704\) 6.60628e8 + 2.14651e8i 1.89339 + 0.615198i
\(705\) −946177. + 609452.i −0.00270026 + 0.00173929i
\(706\) −1.06683e8 3.28336e8i −0.303166 0.933049i
\(707\) −3.34801e8 3.34801e8i −0.947390 0.947390i
\(708\) 1.61551e8 + 8.23144e7i 0.455208 + 0.231940i
\(709\) 8.29170e6 1.14125e7i 0.0232651 0.0320217i −0.797226 0.603681i \(-0.793700\pi\)
0.820491 + 0.571659i \(0.193700\pi\)
\(710\) −7.43233e8 8.31658e8i −2.07659 2.32364i
\(711\) −2.56117e8 + 1.86080e8i −0.712572 + 0.517714i
\(712\) −1.32401e8 8.35946e8i −0.366818 2.31600i
\(713\) 2.57754e8 4.08242e7i 0.711110 0.112629i
\(714\) 1.75716e7 + 2.41853e7i 0.0482745 + 0.0664442i
\(715\) −2.19966e8 4.99051e8i −0.601781 1.36530i
\(716\) 1.71510e7 + 1.24609e7i 0.0467250 + 0.0339477i
\(717\) 1.33683e7 2.62367e7i 0.0362676 0.0711791i
\(718\) 2.75528e8 2.75528e8i 0.744375 0.744375i
\(719\) 1.91581e8 6.22485e7i 0.515426 0.167472i −0.0397427 0.999210i \(-0.512654\pi\)
0.555168 + 0.831738i \(0.312654\pi\)
\(720\) −5.95217e7 + 1.06011e9i −0.159470 + 2.84024i
\(721\) −1.81206e7 + 5.57694e7i −0.0483467 + 0.148796i
\(722\) −6.08976e8 + 3.10289e8i −1.61804 + 0.824431i
\(723\) −6.42708e6 + 4.05790e7i −0.0170059 + 0.107371i
\(724\) 5.88769e8i 1.55142i
\(725\) 1.13459e8 + 1.99944e8i 0.297731 + 0.524681i
\(726\) 7.04252e6 0.0184043
\(727\) −2.79649e8 4.42921e7i −0.727797 0.115272i −0.218469 0.975844i \(-0.570106\pi\)
−0.509328 + 0.860572i \(0.670106\pi\)
\(728\) 9.46869e8 + 1.85834e9i 2.45412 + 4.81648i
\(729\) −3.25375e8 1.05721e8i −0.839850 0.272884i
\(730\) 6.84317e8 + 5.58385e8i 1.75909 + 1.43538i
\(731\) −4.96335e6 1.52756e7i −0.0127064 0.0391063i
\(732\) 6.80346e7 + 6.80346e7i 0.173459 + 0.173459i
\(733\) 2.37860e8 + 1.21196e8i 0.603962 + 0.307734i 0.729102 0.684405i \(-0.239938\pi\)
−0.125140 + 0.992139i \(0.539938\pi\)
\(734\) −1.02212e8 + 1.40683e8i −0.258473 + 0.355758i
\(735\) −3.82209e6 3.77167e7i −0.00962584 0.0949886i
\(736\) 3.49583e8 2.53987e8i 0.876833 0.637056i
\(737\) 6.71724e6 + 4.24110e7i 0.0167799 + 0.105944i
\(738\) 2.81361e8 4.45632e7i 0.699995 0.110868i
\(739\) −6.58988e7 9.07019e7i −0.163284 0.224741i 0.719533 0.694458i \(-0.244356\pi\)
−0.882817 + 0.469717i \(0.844356\pi\)
\(740\) −7.54049e8 4.39106e8i −1.86082 1.08361i
\(741\) 1.24185e7 + 9.02255e6i 0.0305221 + 0.0221756i
\(742\) 5.49737e8 1.07892e9i 1.34568 2.64105i
\(743\) 1.64252e8 1.64252e8i 0.400447 0.400447i −0.477944 0.878391i \(-0.658618\pi\)
0.878391 + 0.477944i \(0.158618\pi\)
\(744\) −2.71858e8 + 8.83320e7i −0.660121 + 0.214486i
\(745\) 2.90764e8 + 1.12859e8i 0.703189 + 0.272941i
\(746\) −1.77275e8 + 5.45598e8i −0.427004 + 1.31418i
\(747\) −2.75334e8 + 1.40289e8i −0.660537 + 0.336561i
\(748\) −4.11425e7 + 2.59764e8i −0.0983073 + 0.620688i
\(749\) 6.03036e8i 1.43515i
\(750\) 7.80918e7 + 7.98582e7i 0.185106 + 0.189294i
\(751\) 8.04661e8 1.89974 0.949868 0.312651i \(-0.101217\pi\)
0.949868 + 0.312651i \(0.101217\pi\)
\(752\) 2.78152e7 + 4.40550e6i 0.0654077 + 0.0103596i
\(753\) −2.59014e7 5.08344e7i −0.0606650 0.119062i
\(754\) 6.67388e8 + 2.16847e8i 1.55691 + 0.505872i
\(755\) −1.86910e8 + 4.81544e8i −0.434302 + 1.11891i
\(756\) −1.22352e8 3.76562e8i −0.283170 0.871507i
\(757\) −3.51612e8 3.51612e8i −0.810543 0.810543i 0.174172 0.984715i \(-0.444275\pi\)
−0.984715 + 0.174172i \(0.944275\pi\)
\(758\) −9.69824e8 4.94150e8i −2.22682 1.13462i
\(759\) 1.57995e7 2.17462e7i 0.0361342 0.0497345i
\(760\) 1.18691e8 2.03820e8i 0.270381 0.464308i
\(761\) 1.95134e8 1.41773e8i 0.442771 0.321692i −0.343964 0.938983i \(-0.611770\pi\)
0.786735 + 0.617291i \(0.211770\pi\)
\(762\) 2.54991e6 + 1.60995e7i 0.00576315 + 0.0363871i
\(763\) −7.40909e8 + 1.17348e8i −1.66798 + 0.264182i
\(764\) 2.36550e8 + 3.25583e8i 0.530448 + 0.730099i
\(765\) −1.04543e8 + 1.05940e7i −0.233512 + 0.0236634i
\(766\) −8.22840e8 5.97828e8i −1.83075 1.33012i
\(767\) −4.22689e8 + 8.29573e8i −0.936773 + 1.83852i
\(768\) −2.61117e6 + 2.61117e6i −0.00576437 + 0.00576437i
\(769\) 3.17184e8 1.03059e8i 0.697481 0.226625i 0.0612485 0.998123i \(-0.480492\pi\)
0.636233 + 0.771497i \(0.280492\pi\)
\(770\) 7.27311e8 8.91340e8i 1.59312 1.95241i
\(771\) 1.34201e7 4.13028e7i 0.0292815 0.0901191i
\(772\) −1.90821e8 + 9.72280e7i −0.414738 + 0.211319i
\(773\) −1.25750e8 + 7.93951e8i −0.272250 + 1.71892i 0.350556 + 0.936542i \(0.385993\pi\)
−0.622806 + 0.782377i \(0.714007\pi\)
\(774\) 1.46795e8i 0.316584i
\(775\) 3.28183e8 7.22565e8i 0.705036 1.55229i
\(776\) −9.35256e8 −2.00145
\(777\) 7.16925e7 + 1.13550e7i 0.152831 + 0.0242060i
\(778\) −2.68827e8 5.27603e8i −0.570867 1.12039i
\(779\) −3.21075e7 1.04324e7i −0.0679195 0.0220684i
\(780\) 2.44182e8 + 1.37100e7i 0.514554 + 0.0288904i
\(781\) 2.52239e8 + 7.76312e8i 0.529492 + 1.62961i
\(782\) 6.43139e7 + 6.43139e7i 0.134488 + 0.134488i
\(783\) −7.19235e7 3.66469e7i −0.149825 0.0763399i
\(784\) −5.57570e8 + 7.67430e8i −1.15705 + 1.59254i
\(785\) 6.93047e8 3.05474e8i 1.43270 0.631488i
\(786\) −1.03542e8 + 7.52275e7i −0.213230 + 0.154921i
\(787\) 1.21573e8 + 7.67580e8i 0.249409 + 1.57471i 0.721029 + 0.692905i \(0.243669\pi\)
−0.471620 + 0.881802i \(0.656331\pi\)
\(788\) 8.05053e8 1.27508e8i 1.64530 0.260590i
\(789\) −3.70879e7 5.10471e7i −0.0755094 0.103930i
\(790\) 6.21341e8 5.55278e8i 1.26023 1.12624i
\(791\) 9.12506e8 + 6.62975e8i 1.84377 + 1.33958i
\(792\) 6.61235e8 1.29775e9i 1.33101 2.61225i
\(793\) −3.49361e8 + 3.49361e8i −0.700576 + 0.700576i
\(794\) −1.57857e9 + 5.12909e8i −3.15357 + 1.02466i
\(795\) −4.65907e7 7.23323e7i −0.0927253 0.143956i
\(796\) −3.63978e8 + 1.12021e9i −0.721665 + 2.22106i
\(797\) 4.03733e8 2.05712e8i 0.797480 0.406336i −0.00725280 0.999974i \(-0.502309\pi\)
0.804733 + 0.593637i \(0.202309\pi\)
\(798\) −5.06527e6 + 3.19808e7i −0.00996767 + 0.0629334i
\(799\) 2.78702e6i 0.00546386i
\(800\) −5.89866e7 1.31272e9i −0.115208 2.56391i
\(801\) −4.08406e8 −0.794684
\(802\) −1.55958e9 2.47013e8i −3.02332 0.478847i
\(803\) −2.93446e8 5.75920e8i −0.566737 1.11228i
\(804\) −1.83132e7 5.95033e6i −0.0352368 0.0114491i
\(805\) −7.28361e7 2.75938e8i −0.139624 0.528962i
\(806\) −7.48569e8 2.30386e9i −1.42964 4.39998i
\(807\) −6.29874e7 6.29874e7i −0.119849 0.119849i
\(808\) 1.40592e9 + 7.16351e8i 2.66518 + 1.35797i
\(809\) −1.71333e8 + 2.35820e8i −0.323591 + 0.445384i −0.939559 0.342386i \(-0.888765\pi\)
0.615969 + 0.787771i \(0.288765\pi\)
\(810\) 9.19262e8 + 1.98980e8i 1.72975 + 0.374415i
\(811\) 2.92670e8 2.12637e8i 0.548675 0.398636i −0.278621 0.960401i \(-0.589877\pi\)
0.827297 + 0.561765i \(0.189877\pi\)
\(812\) 1.66105e8 + 1.04875e9i 0.310252 + 1.95885i
\(813\) 1.11814e8 1.77096e7i 0.208077 0.0329562i
\(814\) 5.23260e8 + 7.20206e8i 0.970163 + 1.33531i
\(815\) −1.98208e8 + 9.15698e8i −0.366141 + 1.69153i
\(816\) −4.29998e7 3.12412e7i −0.0791399 0.0574985i
\(817\) 7.89797e6 1.55006e7i 0.0144827 0.0284239i
\(818\) −9.37699e8 + 9.37699e8i −1.71318 + 1.71318i
\(819\) 9.57158e8 3.11000e8i 1.74234 0.566119i
\(820\) −5.20071e8 + 1.37277e8i −0.943237 + 0.248975i
\(821\) 5.68763e7 1.75047e8i 0.102778 0.316319i −0.886424 0.462874i \(-0.846818\pi\)
0.989203 + 0.146554i \(0.0468183\pi\)
\(822\) 1.21215e8 6.17621e7i 0.218243 0.111201i
\(823\) 9.38721e7 5.92685e8i 0.168398 1.06322i −0.748218 0.663453i \(-0.769090\pi\)
0.916616 0.399770i \(-0.130910\pi\)
\(824\) 1.95419e8i 0.349289i
\(825\) −2.87238e7 7.65285e7i −0.0511540 0.136289i
\(826\) −1.96396e9 −3.48492
\(827\) 4.40069e8 + 6.97002e7i 0.778045 + 0.123230i 0.532812 0.846234i \(-0.321135\pi\)
0.245233 + 0.969464i \(0.421135\pi\)
\(828\) −2.70711e8 5.31300e8i −0.476886 0.935941i
\(829\) 3.01082e8 + 9.78274e7i 0.528471 + 0.171711i 0.561086 0.827757i \(-0.310384\pi\)
−0.0326153 + 0.999468i \(0.510384\pi\)
\(830\) 6.83819e8 4.40462e8i 1.19593 0.770325i
\(831\) 1.38482e7 + 4.26204e7i 0.0241319 + 0.0742702i
\(832\) −1.13105e9 1.13105e9i −1.96386 1.96386i
\(833\) −8.36448e7 4.26191e7i −0.144712 0.0737343i
\(834\) −4.50332e7 + 6.19829e7i −0.0776309 + 0.106850i
\(835\) −3.72289e7 4.16581e7i −0.0639470 0.0715550i
\(836\) −2.30458e8 + 1.67438e8i −0.394433 + 0.286572i
\(837\) 4.35913e7 + 2.75225e8i 0.0743402 + 0.469365i
\(838\) 7.54545e8 1.19508e8i 1.28219 0.203079i
\(839\) −5.41031e7 7.44666e7i −0.0916087 0.126088i 0.760753 0.649042i \(-0.224830\pi\)
−0.852361 + 0.522954i \(0.824830\pi\)
\(840\) 1.26080e8 + 2.86046e8i 0.212720 + 0.482612i
\(841\) −3.06089e8 2.22387e8i −0.514588 0.373870i
\(842\) 3.76380e8 7.38687e8i 0.630507 1.23744i
\(843\) 2.74681e7 2.74681e7i 0.0458507 0.0458507i
\(844\) 5.90496e8 1.91864e8i 0.982177 0.319129i
\(845\) −3.65787e7 + 6.51487e8i −0.0606259 + 1.07978i
\(846\) 7.87121e6 2.42251e7i 0.0129996 0.0400087i
\(847\) −4.87565e7 + 2.48427e7i −0.0802384 + 0.0408835i
\(848\) −3.36787e8 + 2.12639e9i −0.552290 + 3.48702i
\(849\) 3.17776e7i 0.0519275i
\(850\) 2.70968e8 5.54878e7i 0.441226 0.0903526i
\(851\) 2.20841e8 0.358337
\(852\) −3.61535e8 5.72615e7i −0.584563 0.0925857i
\(853\) 3.90663e8 + 7.66720e8i 0.629442 + 1.23535i 0.956882 + 0.290477i \(0.0938140\pi\)
−0.327440 + 0.944872i \(0.606186\pi\)
\(854\) −9.91186e8 3.22056e8i −1.59141 0.517080i
\(855\) −8.81811e7 7.19536e7i −0.141084 0.115121i
\(856\) 6.21015e8 + 1.91129e9i 0.990105 + 3.04723i
\(857\) 2.08452e8 + 2.08452e8i 0.331180 + 0.331180i 0.853035 0.521854i \(-0.174760\pi\)
−0.521854 + 0.853035i \(0.674760\pi\)
\(858\) −2.22316e8 1.13276e8i −0.351972 0.179339i
\(859\) 3.29298e8 4.53240e8i 0.519530 0.715071i −0.465960 0.884806i \(-0.654291\pi\)
0.985490 + 0.169735i \(0.0542910\pi\)
\(860\) −2.79450e7 2.75764e8i −0.0439349 0.433553i
\(861\) 3.61986e7 2.62998e7i 0.0567130 0.0412044i
\(862\) 7.50772e7 + 4.74019e8i 0.117216 + 0.740072i
\(863\) −5.58222e8 + 8.84136e7i −0.868509 + 0.137558i −0.574758 0.818324i \(-0.694904\pi\)
−0.293751 + 0.955882i \(0.594904\pi\)
\(864\) 2.71202e8 + 3.73278e8i 0.420487 + 0.578750i
\(865\) −1.06494e8 6.20147e7i −0.164542 0.0958179i
\(866\) 1.56055e9 + 1.13381e9i 2.40283 + 1.74576i
\(867\) −3.92598e7 + 7.70516e7i −0.0602408 + 0.118229i
\(868\) 2.59187e9 2.59187e9i 3.96327 3.96327i
\(869\) −5.79991e8 + 1.88451e8i −0.883817 + 0.287169i
\(870\) 9.80492e7 + 3.80575e7i 0.148897 + 0.0577940i
\(871\) 3.05552e7 9.40393e7i 0.0462414 0.142316i
\(872\) 2.22742e9 1.13493e9i 3.35933 1.71167i
\(873\) −7.05988e7 + 4.45743e8i −0.106110 + 0.669949i
\(874\) 9.85135e7i 0.147558i
\(875\) −8.22343e8 2.77400e8i −1.22752 0.414079i
\(876\) 2.89856e8 0.431191
\(877\) −1.14636e9 1.81565e8i −1.69950 0.269175i −0.770015 0.638026i \(-0.779751\pi\)
−0.929488 + 0.368852i \(0.879751\pi\)
\(878\) 9.39981e7 + 1.84482e8i 0.138879 + 0.272565i
\(879\) 9.09550e7 + 2.95531e7i 0.133925 + 0.0435147i
\(880\) −7.40107e8 + 1.90677e9i −1.08604 + 2.79802i
\(881\) 4.21503e8 + 1.29725e9i 0.616415 + 1.89713i 0.377000 + 0.926213i \(0.376956\pi\)
0.239415 + 0.970917i \(0.423044\pi\)
\(882\) 6.06684e8 + 6.06684e8i 0.884212 + 0.884212i
\(883\) 4.59887e8 + 2.34324e8i 0.667988 + 0.340357i 0.754882 0.655861i \(-0.227694\pi\)
−0.0868937 + 0.996218i \(0.527694\pi\)
\(884\) 3.55977e8 4.89961e8i 0.515306 0.709258i
\(885\) −7.02232e7 + 1.20590e8i −0.101310 + 0.173973i
\(886\) 1.83378e9 1.33232e9i 2.63661 1.91561i
\(887\) −1.16341e8 7.34549e8i −0.166710 1.05257i −0.919150 0.393907i \(-0.871123\pi\)
0.752440 0.658661i \(-0.228877\pi\)
\(888\) −2.38919e8 + 3.78410e7i −0.341202 + 0.0540411i
\(889\) −7.44448e7 1.02464e8i −0.105957 0.145837i
\(890\) 1.06954e9 1.08384e8i 1.51715 0.153743i
\(891\) −5.56866e8 4.04587e8i −0.787259 0.571977i
\(892\) −6.95630e8 + 1.36525e9i −0.980130 + 1.92361i
\(893\) −2.13452e6 + 2.13452e6i −0.00299741 + 0.00299741i
\(894\) 1.35710e8 4.40949e7i 0.189933 0.0617129i
\(895\) −1.03154e7 + 1.26418e7i −0.0143885 + 0.0176335i
\(896\) 3.03591e8 9.34358e8i 0.422051 1.29894i
\(897\) −5.51507e7 + 2.81007e7i −0.0764141 + 0.0389350i
\(898\) −8.86098e7 + 5.59460e8i −0.122364 + 0.772574i
\(899\) 7.47288e8i 1.02851i
\(900\) −1.80193e9 2.02984e8i −2.47178 0.278442i
\(901\) −2.13059e8 −0.291290
\(902\) 5.42000e8 + 8.58444e7i 0.738550 + 0.116975i
\(903\) 1.04676e7 + 2.05439e7i 0.0142163 + 0.0279010i
\(904\) −3.57488e9 1.16155e9i −4.83901 1.57229i
\(905\) 4.52430e8 + 2.54024e7i 0.610388 + 0.0342711i
\(906\) 7.30269e7 + 2.24754e8i 0.0981971 + 0.302220i
\(907\) −4.15273e8 4.15273e8i −0.556560 0.556560i 0.371766 0.928326i \(-0.378752\pi\)
−0.928326 + 0.371766i \(0.878752\pi\)
\(908\) −1.92099e9 9.78792e8i −2.56606 1.30747i
\(909\) 4.47540e8 6.15986e8i 0.595854 0.820123i
\(910\) −2.42409e9 + 1.06847e9i −3.21681 + 1.41787i
\(911\) 6.84469e8 4.97296e8i 0.905313 0.657748i −0.0345124 0.999404i \(-0.510988\pi\)
0.939825 + 0.341656i \(0.110988\pi\)
\(912\) −9.00569e6 5.68597e7i −0.0118722 0.0749583i
\(913\) −5.87941e8 + 9.31206e7i −0.772540 + 0.122358i
\(914\) −6.87375e8 9.46091e8i −0.900234 1.23907i
\(915\) −5.52154e7 + 4.93447e7i −0.0720771 + 0.0644136i
\(916\) 3.79017e8 + 2.75372e8i 0.493142 + 0.358289i
\(917\) 4.51469e8 8.86058e8i 0.585490 1.14909i
\(918\) −6.86732e7 + 6.86732e7i −0.0887686 + 0.0887686i
\(919\) −1.22899e9 + 3.99324e8i −1.58344 + 0.514492i −0.962941 0.269713i \(-0.913071\pi\)
−0.620502 + 0.784205i \(0.713071\pi\)
\(920\) 5.15015e8 + 7.99563e8i 0.661388 + 1.02681i
\(921\) −6.97542e6 + 2.14681e7i −0.00892877 + 0.0274799i
\(922\) −2.13952e9 + 1.09014e9i −2.72976 + 1.39088i
\(923\) 2.94041e8 1.85650e9i 0.373940 2.36097i
\(924\) 3.77544e8i 0.478577i
\(925\) 3.69957e8 5.60492e8i 0.467441 0.708180i
\(926\) 9.29909e8 1.17114
\(927\) −9.31367e7 1.47514e7i −0.116918 0.0185180i
\(928\) −5.61749e8 1.10249e9i −0.702907 1.37953i
\(929\) 2.38900e8 + 7.76233e7i 0.297968 + 0.0968156i 0.454186 0.890907i \(-0.349930\pi\)
−0.156218 + 0.987723i \(0.549930\pi\)
\(930\) −9.26624e7 3.51050e8i −0.115201 0.436435i
\(931\) −3.14207e7 9.67030e7i −0.0389374 0.119837i
\(932\) 2.17919e9 + 2.17919e9i 2.69183 + 2.69183i
\(933\) 9.62856e6 + 4.90600e6i 0.0118554 + 0.00604063i
\(934\) −1.47397e8 + 2.02874e8i −0.180904 + 0.248992i
\(935\) −1.97836e8 4.28228e7i −0.242031 0.0523890i
\(936\) −2.71339e9 + 1.97139e9i −3.30890 + 2.40406i
\(937\) −1.22237e8 7.71777e8i −0.148589 0.938152i −0.943487 0.331409i \(-0.892476\pi\)
0.794899 0.606742i \(-0.207524\pi\)
\(938\) 2.06007e8 3.26283e7i 0.249617 0.0395354i
\(939\) −4.11521e7 5.66411e7i −0.0497045 0.0684124i
\(940\) −1.01749e7 + 4.70067e7i −0.0122503 + 0.0565948i
\(941\) −9.39694e8 6.82728e8i −1.12776 0.819367i −0.142395 0.989810i \(-0.545480\pi\)
−0.985368 + 0.170443i \(0.945480\pi\)
\(942\) 1.57309e8 3.08737e8i 0.188192 0.369348i
\(943\) 9.62599e7 9.62599e7i 0.114792 0.114792i
\(944\) 3.32088e9 1.07902e9i 3.94764 1.28267i
\(945\) 2.94642e8 7.77730e7i 0.349139 0.0921581i
\(946\) −8.73836e7 + 2.68939e8i −0.103218 + 0.317673i
\(947\) 1.00642e9 5.12799e8i 1.18503 0.603805i 0.253457 0.967347i \(-0.418432\pi\)
0.931578 + 0.363541i \(0.118432\pi\)
\(948\) 4.27807e7 2.70107e8i 0.0502138 0.317037i
\(949\) 1.48842e9i 1.74152i
\(950\) 2.50026e8 + 1.65032e8i 0.291618 + 0.192485i
\(951\) −1.73392e8 −0.201598
\(952\) 7.64564e8 + 1.21095e8i 0.886141 + 0.140351i
\(953\) 3.48955e8 + 6.84862e8i 0.403172 + 0.791270i 0.999938 0.0111457i \(-0.00354787\pi\)
−0.596766 + 0.802415i \(0.703548\pi\)
\(954\) 1.85193e9 + 6.01729e8i 2.13295 + 0.693037i
\(955\) −2.60395e8 + 1.67726e8i −0.298966 + 0.192570i
\(956\) −3.88848e8 1.19675e9i −0.445048 1.36972i
\(957\) −5.44268e7 5.44268e7i −0.0620979 0.0620979i
\(958\) −9.25013e8 4.71318e8i −1.05209 0.536065i
\(959\) −6.21323e8 + 8.55178e8i −0.704469 + 0.969618i
\(960\) −1.59752e8 1.78758e8i −0.180565 0.202047i
\(961\) −1.36900e9 + 9.94635e8i −1.54253 + 1.12071i
\(962\) −3.20684e8 2.02472e9i −0.360207 2.27425i
\(963\) 9.57798e8 1.51700e8i 1.07249 0.169866i
\(964\) 1.03197e9 + 1.42039e9i 1.15196 + 1.58554i
\(965\) −6.64804e7 1.50828e8i −0.0739795 0.167842i
\(966\) −1.05630e8 7.67446e7i −0.117181 0.0851367i
\(967\) −5.20685e8 + 1.02190e9i −0.575832 + 1.13013i 0.400990 + 0.916082i \(0.368666\pi\)
−0.976822 + 0.214052i \(0.931334\pi\)
\(968\) 1.28948e8 1.28948e8i 0.142163 0.142163i
\(969\) 5.41836e6 1.76053e6i 0.00595520 0.00193496i
\(970\) 6.65930e7 1.18606e9i 0.0729648 1.29954i
\(971\) 8.52093e7 2.62247e8i 0.0930742 0.286453i −0.893673 0.448719i \(-0.851880\pi\)
0.986747 + 0.162266i \(0.0518804\pi\)
\(972\) 8.53806e8 4.35036e8i 0.929738 0.473725i
\(973\) 9.31258e7 5.87973e8i 0.101095 0.638291i
\(974\) 3.12400e9i 3.38091i
\(975\) −2.10704e7 + 1.87046e8i −0.0227331 + 0.201807i
\(976\) 1.85295e9 1.99303
\(977\) 9.20157e8 + 1.45739e8i 0.986684 + 0.156275i 0.628864 0.777515i \(-0.283520\pi\)
0.357820 + 0.933791i \(0.383520\pi\)
\(978\) 1.94596e8 + 3.81916e8i 0.208026 + 0.408273i
\(979\) −7.48228e8 2.43114e8i −0.797418 0.259097i
\(980\) −1.25518e9 1.02420e9i −1.33361 1.08819i
\(981\) −3.72768e8 1.14726e9i −0.394849 1.21522i
\(982\) 1.04259e9 + 1.04259e9i 1.10098 + 1.10098i
\(983\) −5.87073e8 2.99129e8i −0.618061 0.314918i 0.116779 0.993158i \(-0.462743\pi\)
−0.734841 + 0.678240i \(0.762743\pi\)
\(984\) −8.76455e7 + 1.20634e8i −0.0919908 + 0.126614i
\(985\) 6.32474e7 + 6.24131e8i 0.0661811 + 0.653081i
\(986\) 2.10708e8 1.53088e8i 0.219811 0.159702i
\(987\) −625866. 3.95156e6i −0.000650924 0.00410977i
\(988\) 6.47887e8 1.02615e8i 0.671782 0.106400i
\(989\) 4.12332e7 + 5.67526e7i 0.0426244 + 0.0586674i
\(990\) 1.59867e9 + 9.30957e8i 1.64761 + 0.959454i
\(991\) −1.50197e9 1.09125e9i −1.54327 1.12125i −0.948245 0.317541i \(-0.897143\pi\)
−0.595023 0.803709i \(-0.702857\pi\)
\(992\) −1.93919e9 + 3.80587e9i −1.98648 + 3.89869i
\(993\) −1.65416e8 + 1.65416e8i −0.168939 + 0.168939i
\(994\) 3.77086e9 1.22523e9i 3.83956 1.24755i
\(995\) −8.45102e8 3.28024e8i −0.857906 0.332994i
\(996\) 8.24890e7 2.53875e8i 0.0834868 0.256946i
\(997\) 8.41268e8 4.28647e8i 0.848885 0.432528i 0.0252719 0.999681i \(-0.491955\pi\)
0.823613 + 0.567152i \(0.191955\pi\)
\(998\) −3.21175e8 + 2.02782e9i −0.323110 + 2.04004i
\(999\) 2.35810e8i 0.236519i
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 25.7.f.a.2.14 112
25.13 odd 20 inner 25.7.f.a.13.14 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.7.f.a.2.14 112 1.1 even 1 trivial
25.7.f.a.13.14 yes 112 25.13 odd 20 inner