Properties

Label 74.7.d.a.43.9
Level $74$
Weight $7$
Character 74.43
Analytic conductor $17.024$
Analytic rank $0$
Dimension $18$
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] = [74,7,Mod(31,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(4))
 
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("74.31");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 74.d (of order \(4\), 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: \(17.0240021879\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.9
Root \(48.2475i\) of defining polynomial
Character \(\chi\) \(=\) 74.43
Dual form 74.7.d.a.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.00000 - 4.00000i) q^{2} +44.2475i q^{3} -32.0000i q^{4} +(111.595 + 111.595i) q^{5} +(176.990 + 176.990i) q^{6} +600.642 q^{7} +(-128.000 - 128.000i) q^{8} -1228.84 q^{9} +O(q^{10})\) \(q+(4.00000 - 4.00000i) q^{2} +44.2475i q^{3} -32.0000i q^{4} +(111.595 + 111.595i) q^{5} +(176.990 + 176.990i) q^{6} +600.642 q^{7} +(-128.000 - 128.000i) q^{8} -1228.84 q^{9} +892.760 q^{10} +246.334i q^{11} +1415.92 q^{12} +(-1561.93 - 1561.93i) q^{13} +(2402.57 - 2402.57i) q^{14} +(-4937.80 + 4937.80i) q^{15} -1024.00 q^{16} +(4838.50 + 4838.50i) q^{17} +(-4915.37 + 4915.37i) q^{18} +(4177.15 + 4177.15i) q^{19} +(3571.04 - 3571.04i) q^{20} +26576.9i q^{21} +(985.338 + 985.338i) q^{22} +(-11586.6 - 11586.6i) q^{23} +(5663.68 - 5663.68i) q^{24} +9281.87i q^{25} -12495.4 q^{26} -22116.8i q^{27} -19220.6i q^{28} +(-27962.6 + 27962.6i) q^{29} +39502.4i q^{30} +(7332.73 - 7332.73i) q^{31} +(-4096.00 + 4096.00i) q^{32} -10899.7 q^{33} +38708.0 q^{34} +(67028.7 + 67028.7i) q^{35} +39323.0i q^{36} +(6840.45 - 50189.0i) q^{37} +33417.2 q^{38} +(69111.4 - 69111.4i) q^{39} -28568.3i q^{40} +30316.2i q^{41} +(106308. + 106308. i) q^{42} +(-32582.5 - 32582.5i) q^{43} +7882.70 q^{44} +(-137133. - 137133. i) q^{45} -92692.4 q^{46} +40324.0 q^{47} -45309.5i q^{48} +243122. q^{49} +(37127.5 + 37127.5i) q^{50} +(-214092. + 214092. i) q^{51} +(-49981.7 + 49981.7i) q^{52} -42260.0 q^{53} +(-88467.2 - 88467.2i) q^{54} +(-27489.7 + 27489.7i) q^{55} +(-76882.2 - 76882.2i) q^{56} +(-184829. + 184829. i) q^{57} +223701. i q^{58} +(-244670. - 244670. i) q^{59} +(158010. + 158010. i) q^{60} +(178253. - 178253. i) q^{61} -58661.9i q^{62} -738095. q^{63} +32768.0i q^{64} -348607. i q^{65} +(-43598.7 + 43598.7i) q^{66} -237792. i q^{67} +(154832. - 154832. i) q^{68} +(512676. - 512676. i) q^{69} +536229. q^{70} -87512.0 q^{71} +(157292. + 157292. i) q^{72} +4275.04i q^{73} +(-173394. - 228118. i) q^{74} -410700. q^{75} +(133669. - 133669. i) q^{76} +147959. i q^{77} -552892. i q^{78} +(692161. + 692161. i) q^{79} +(-114273. - 114273. i) q^{80} +82786.8 q^{81} +(121265. + 121265. i) q^{82} +1.05044e6 q^{83} +850462. q^{84} +1.07990e6i q^{85} -260660. q^{86} +(-1.23727e6 - 1.23727e6i) q^{87} +(31530.8 - 31530.8i) q^{88} +(767566. - 767566. i) q^{89} -1.09706e6 q^{90} +(-938160. - 938160. i) q^{91} +(-370770. + 370770. i) q^{92} +(324455. + 324455. i) q^{93} +(161296. - 161296. i) q^{94} +932298. i q^{95} +(-181238. - 181238. i) q^{96} +(-375821. - 375821. i) q^{97} +(972489. - 972489. i) q^{98} -302706. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9} + 2352 q^{10} - 2048 q^{12} - 6766 q^{13} - 416 q^{14} - 2136 q^{15} - 18432 q^{16} - 9134 q^{17} - 16168 q^{18} + 7578 q^{19} + 9408 q^{20} + 8928 q^{22} - 50578 q^{23} - 8192 q^{24} - 54128 q^{26} - 42950 q^{29} - 17358 q^{31} - 73728 q^{32} - 11056 q^{33} - 73072 q^{34} + 62152 q^{35} - 238242 q^{37} + 60624 q^{38} + 31572 q^{39} + 229024 q^{42} - 65470 q^{43} + 71424 q^{44} - 482358 q^{45} - 404624 q^{46} + 232192 q^{47} + 791686 q^{49} + 93752 q^{50} - 386848 q^{51} - 216512 q^{52} + 49972 q^{53} - 144560 q^{54} + 160168 q^{55} + 13312 q^{56} + 488476 q^{57} - 181570 q^{59} + 68352 q^{60} + 508802 q^{61} + 404788 q^{63} - 44224 q^{66} - 292288 q^{68} + 604532 q^{69} + 497216 q^{70} - 202632 q^{71} + 517376 q^{72} - 1191224 q^{74} + 2476628 q^{75} + 242496 q^{76} + 1752858 q^{79} - 301056 q^{80} + 2760658 q^{81} - 145808 q^{82} + 2371616 q^{83} + 1832192 q^{84} - 523760 q^{86} - 4188080 q^{87} + 285696 q^{88} + 1148346 q^{89} - 3858864 q^{90} + 433120 q^{91} - 1618496 q^{92} + 1589664 q^{93} + 928768 q^{94} + 262144 q^{96} - 1670270 q^{97} + 3166744 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 4.00000i 0.500000 0.500000i
\(3\) 44.2475i 1.63880i 0.573224 + 0.819398i \(0.305692\pi\)
−0.573224 + 0.819398i \(0.694308\pi\)
\(4\) 32.0000i 0.500000i
\(5\) 111.595 + 111.595i 0.892760 + 0.892760i 0.994782 0.102022i \(-0.0325313\pi\)
−0.102022 + 0.994782i \(0.532531\pi\)
\(6\) 176.990 + 176.990i 0.819398 + 0.819398i
\(7\) 600.642 1.75114 0.875572 0.483088i \(-0.160485\pi\)
0.875572 + 0.483088i \(0.160485\pi\)
\(8\) −128.000 128.000i −0.250000 0.250000i
\(9\) −1228.84 −1.68566
\(10\) 892.760 0.892760
\(11\) 246.334i 0.185075i 0.995709 + 0.0925373i \(0.0294978\pi\)
−0.995709 + 0.0925373i \(0.970502\pi\)
\(12\) 1415.92 0.819398
\(13\) −1561.93 1561.93i −0.710937 0.710937i 0.255794 0.966731i \(-0.417663\pi\)
−0.966731 + 0.255794i \(0.917663\pi\)
\(14\) 2402.57 2402.57i 0.875572 0.875572i
\(15\) −4937.80 + 4937.80i −1.46305 + 1.46305i
\(16\) −1024.00 −0.250000
\(17\) 4838.50 + 4838.50i 0.984836 + 0.984836i 0.999887 0.0150508i \(-0.00479100\pi\)
−0.0150508 + 0.999887i \(0.504791\pi\)
\(18\) −4915.37 + 4915.37i −0.842828 + 0.842828i
\(19\) 4177.15 + 4177.15i 0.609003 + 0.609003i 0.942685 0.333683i \(-0.108291\pi\)
−0.333683 + 0.942685i \(0.608291\pi\)
\(20\) 3571.04 3571.04i 0.446380 0.446380i
\(21\) 26576.9i 2.86977i
\(22\) 985.338 + 985.338i 0.0925373 + 0.0925373i
\(23\) −11586.6 11586.6i −0.952293 0.952293i 0.0466194 0.998913i \(-0.485155\pi\)
−0.998913 + 0.0466194i \(0.985155\pi\)
\(24\) 5663.68 5663.68i 0.409699 0.409699i
\(25\) 9281.87i 0.594040i
\(26\) −12495.4 −0.710937
\(27\) 22116.8i 1.12365i
\(28\) 19220.6i 0.875572i
\(29\) −27962.6 + 27962.6i −1.14652 + 1.14652i −0.159293 + 0.987231i \(0.550921\pi\)
−0.987231 + 0.159293i \(0.949079\pi\)
\(30\) 39502.4i 1.46305i
\(31\) 7332.73 7332.73i 0.246139 0.246139i −0.573245 0.819384i \(-0.694316\pi\)
0.819384 + 0.573245i \(0.194316\pi\)
\(32\) −4096.00 + 4096.00i −0.125000 + 0.125000i
\(33\) −10899.7 −0.303300
\(34\) 38708.0 0.984836
\(35\) 67028.7 + 67028.7i 1.56335 + 1.56335i
\(36\) 39323.0i 0.842828i
\(37\) 6840.45 50189.0i 0.135045 0.990839i
\(38\) 33417.2 0.609003
\(39\) 69111.4 69111.4i 1.16508 1.16508i
\(40\) 28568.3i 0.446380i
\(41\) 30316.2i 0.439869i 0.975515 + 0.219934i \(0.0705844\pi\)
−0.975515 + 0.219934i \(0.929416\pi\)
\(42\) 106308. + 106308.i 1.43488 + 1.43488i
\(43\) −32582.5 32582.5i −0.409807 0.409807i 0.471864 0.881671i \(-0.343581\pi\)
−0.881671 + 0.471864i \(0.843581\pi\)
\(44\) 7882.70 0.0925373
\(45\) −137133. 137133.i −1.50488 1.50488i
\(46\) −92692.4 −0.952293
\(47\) 40324.0 0.388391 0.194196 0.980963i \(-0.437790\pi\)
0.194196 + 0.980963i \(0.437790\pi\)
\(48\) 45309.5i 0.409699i
\(49\) 243122. 2.06650
\(50\) 37127.5 + 37127.5i 0.297020 + 0.297020i
\(51\) −214092. + 214092.i −1.61395 + 1.61395i
\(52\) −49981.7 + 49981.7i −0.355468 + 0.355468i
\(53\) −42260.0 −0.283859 −0.141929 0.989877i \(-0.545331\pi\)
−0.141929 + 0.989877i \(0.545331\pi\)
\(54\) −88467.2 88467.2i −0.561825 0.561825i
\(55\) −27489.7 + 27489.7i −0.165227 + 0.165227i
\(56\) −76882.2 76882.2i −0.437786 0.437786i
\(57\) −184829. + 184829.i −0.998032 + 0.998032i
\(58\) 223701.i 1.14652i
\(59\) −244670. 244670.i −1.19131 1.19131i −0.976700 0.214608i \(-0.931153\pi\)
−0.214608 0.976700i \(-0.568847\pi\)
\(60\) 158010. + 158010.i 0.731526 + 0.731526i
\(61\) 178253. 178253.i 0.785321 0.785321i −0.195402 0.980723i \(-0.562601\pi\)
0.980723 + 0.195402i \(0.0626013\pi\)
\(62\) 58661.9i 0.246139i
\(63\) −738095. −2.95182
\(64\) 32768.0i 0.125000i
\(65\) 348607.i 1.26939i
\(66\) −43598.7 + 43598.7i −0.151650 + 0.151650i
\(67\) 237792.i 0.790629i −0.918546 0.395315i \(-0.870636\pi\)
0.918546 0.395315i \(-0.129364\pi\)
\(68\) 154832. 154832.i 0.492418 0.492418i
\(69\) 512676. 512676.i 1.56062 1.56062i
\(70\) 536229. 1.56335
\(71\) −87512.0 −0.244508 −0.122254 0.992499i \(-0.539012\pi\)
−0.122254 + 0.992499i \(0.539012\pi\)
\(72\) 157292. + 157292.i 0.421414 + 0.421414i
\(73\) 4275.04i 0.0109893i 0.999985 + 0.00549467i \(0.00174902\pi\)
−0.999985 + 0.00549467i \(0.998251\pi\)
\(74\) −173394. 228118.i −0.427897 0.562942i
\(75\) −410700. −0.973510
\(76\) 133669. 133669.i 0.304501 0.304501i
\(77\) 147959.i 0.324092i
\(78\) 552892.i 1.16508i
\(79\) 692161. + 692161.i 1.40387 + 1.40387i 0.787313 + 0.616553i \(0.211472\pi\)
0.616553 + 0.787313i \(0.288528\pi\)
\(80\) −114273. 114273.i −0.223190 0.223190i
\(81\) 82786.8 0.155778
\(82\) 121265. + 121265.i 0.219934 + 0.219934i
\(83\) 1.05044e6 1.83712 0.918562 0.395277i \(-0.129351\pi\)
0.918562 + 0.395277i \(0.129351\pi\)
\(84\) 850462. 1.43488
\(85\) 1.07990e6i 1.75844i
\(86\) −260660. −0.409807
\(87\) −1.23727e6 1.23727e6i −1.87892 1.87892i
\(88\) 31530.8 31530.8i 0.0462687 0.0462687i
\(89\) 767566. 767566.i 1.08879 1.08879i 0.0931410 0.995653i \(-0.470309\pi\)
0.995653 0.0931410i \(-0.0296907\pi\)
\(90\) −1.09706e6 −1.50488
\(91\) −938160. 938160.i −1.24495 1.24495i
\(92\) −370770. + 370770.i −0.476147 + 0.476147i
\(93\) 324455. + 324455.i 0.403372 + 0.403372i
\(94\) 161296. 161296.i 0.194196 0.194196i
\(95\) 932298.i 1.08739i
\(96\) −181238. 181238.i −0.204850 0.204850i
\(97\) −375821. 375821.i −0.411781 0.411781i 0.470578 0.882359i \(-0.344046\pi\)
−0.882359 + 0.470578i \(0.844046\pi\)
\(98\) 972489. 972489.i 1.03325 1.03325i
\(99\) 302706.i 0.311972i
\(100\) 297020. 0.297020
\(101\) 50410.5i 0.0489279i 0.999701 + 0.0244640i \(0.00778790\pi\)
−0.999701 + 0.0244640i \(0.992212\pi\)
\(102\) 1.71273e6i 1.61395i
\(103\) −251781. + 251781.i −0.230416 + 0.230416i −0.812866 0.582450i \(-0.802094\pi\)
0.582450 + 0.812866i \(0.302094\pi\)
\(104\) 399854.i 0.355468i
\(105\) −2.96585e6 + 2.96585e6i −2.56201 + 2.56201i
\(106\) −169040. + 169040.i −0.141929 + 0.141929i
\(107\) −1.95336e6 −1.59452 −0.797262 0.603633i \(-0.793719\pi\)
−0.797262 + 0.603633i \(0.793719\pi\)
\(108\) −707737. −0.561825
\(109\) 586869. + 586869.i 0.453170 + 0.453170i 0.896405 0.443235i \(-0.146169\pi\)
−0.443235 + 0.896405i \(0.646169\pi\)
\(110\) 219917.i 0.165227i
\(111\) 2.22074e6 + 302673.i 1.62378 + 0.221312i
\(112\) −615058. −0.437786
\(113\) 1.17936e6 1.17936e6i 0.817355 0.817355i −0.168369 0.985724i \(-0.553850\pi\)
0.985724 + 0.168369i \(0.0538501\pi\)
\(114\) 1.47863e6i 0.998032i
\(115\) 2.58600e6i 1.70034i
\(116\) 894802. + 894802.i 0.573262 + 0.573262i
\(117\) 1.91936e6 + 1.91936e6i 1.19839 + 1.19839i
\(118\) −1.95736e6 −1.19131
\(119\) 2.90621e6 + 2.90621e6i 1.72459 + 1.72459i
\(120\) 1.26408e6 0.731526
\(121\) 1.71088e6 0.965747
\(122\) 1.42602e6i 0.785321i
\(123\) −1.34142e6 −0.720856
\(124\) −234647. 234647.i −0.123070 0.123070i
\(125\) 707861. 707861.i 0.362425 0.362425i
\(126\) −2.95238e6 + 2.95238e6i −1.47591 + 1.47591i
\(127\) 21725.6 0.0106062 0.00530312 0.999986i \(-0.498312\pi\)
0.00530312 + 0.999986i \(0.498312\pi\)
\(128\) 131072. + 131072.i 0.0625000 + 0.0625000i
\(129\) 1.44170e6 1.44170e6i 0.671590 0.671590i
\(130\) −1.39443e6 1.39443e6i −0.634696 0.634696i
\(131\) −2.29399e6 + 2.29399e6i −1.02042 + 1.02042i −0.0206316 + 0.999787i \(0.506568\pi\)
−0.999787 + 0.0206316i \(0.993432\pi\)
\(132\) 348790.i 0.151650i
\(133\) 2.50897e6 + 2.50897e6i 1.06645 + 1.06645i
\(134\) −951168. 951168.i −0.395315 0.395315i
\(135\) 2.46812e6 2.46812e6i 1.00315 1.00315i
\(136\) 1.23866e6i 0.492418i
\(137\) 3.41062e6 1.32639 0.663196 0.748446i \(-0.269200\pi\)
0.663196 + 0.748446i \(0.269200\pi\)
\(138\) 4.10141e6i 1.56062i
\(139\) 2.10396e6i 0.783417i −0.920089 0.391708i \(-0.871884\pi\)
0.920089 0.391708i \(-0.128116\pi\)
\(140\) 2.14492e6 2.14492e6i 0.781675 0.781675i
\(141\) 1.78424e6i 0.636495i
\(142\) −350048. + 350048.i −0.122254 + 0.122254i
\(143\) 384757. 384757.i 0.131576 0.131576i
\(144\) 1.25833e6 0.421414
\(145\) −6.24097e6 −2.04714
\(146\) 17100.2 + 17100.2i 0.00549467 + 0.00549467i
\(147\) 1.07576e7i 3.38658i
\(148\) −1.60605e6 218894.i −0.495420 0.0675227i
\(149\) −336960. −0.101864 −0.0509318 0.998702i \(-0.516219\pi\)
−0.0509318 + 0.998702i \(0.516219\pi\)
\(150\) −1.64280e6 + 1.64280e6i −0.486755 + 0.486755i
\(151\) 4.04920e6i 1.17608i −0.808830 0.588042i \(-0.799899\pi\)
0.808830 0.588042i \(-0.200101\pi\)
\(152\) 1.06935e6i 0.304501i
\(153\) −5.94575e6 5.94575e6i −1.66009 1.66009i
\(154\) 591835. + 591835.i 0.162046 + 0.162046i
\(155\) 1.63659e6 0.439486
\(156\) −2.21157e6 2.21157e6i −0.582541 0.582541i
\(157\) 98709.9 0.0255071 0.0127536 0.999919i \(-0.495940\pi\)
0.0127536 + 0.999919i \(0.495940\pi\)
\(158\) 5.53729e6 1.40387
\(159\) 1.86990e6i 0.465187i
\(160\) −914186. −0.223190
\(161\) −6.95937e6 6.95937e6i −1.66760 1.66760i
\(162\) 331147. 331147.i 0.0778889 0.0778889i
\(163\) −2.31873e6 + 2.31873e6i −0.535410 + 0.535410i −0.922177 0.386767i \(-0.873592\pi\)
0.386767 + 0.922177i \(0.373592\pi\)
\(164\) 970119. 0.219934
\(165\) −1.21635e6 1.21635e6i −0.270774 0.270774i
\(166\) 4.20177e6 4.20177e6i 0.918562 0.918562i
\(167\) 5.08220e6 + 5.08220e6i 1.09119 + 1.09119i 0.995401 + 0.0957928i \(0.0305386\pi\)
0.0957928 + 0.995401i \(0.469461\pi\)
\(168\) 3.40185e6 3.40185e6i 0.717442 0.717442i
\(169\) 52430.7i 0.0108624i
\(170\) 4.31962e6 + 4.31962e6i 0.879222 + 0.879222i
\(171\) −5.13306e6 5.13306e6i −1.02657 1.02657i
\(172\) −1.04264e6 + 1.04264e6i −0.204903 + 0.204903i
\(173\) 3.50636e6i 0.677203i 0.940930 + 0.338601i \(0.109954\pi\)
−0.940930 + 0.338601i \(0.890046\pi\)
\(174\) −9.89820e6 −1.87892
\(175\) 5.57508e6i 1.04025i
\(176\) 252246.i 0.0462687i
\(177\) 1.08260e7 1.08260e7i 1.95231 1.95231i
\(178\) 6.14053e6i 1.08879i
\(179\) −4.57026e6 + 4.57026e6i −0.796860 + 0.796860i −0.982599 0.185739i \(-0.940532\pi\)
0.185739 + 0.982599i \(0.440532\pi\)
\(180\) −4.38824e6 + 4.38824e6i −0.752442 + 0.752442i
\(181\) 2.39962e6 0.404675 0.202337 0.979316i \(-0.435146\pi\)
0.202337 + 0.979316i \(0.435146\pi\)
\(182\) −7.50528e6 −1.24495
\(183\) 7.88725e6 + 7.88725e6i 1.28698 + 1.28698i
\(184\) 2.96616e6i 0.476147i
\(185\) 6.36420e6 4.83748e6i 1.00514 0.764018i
\(186\) 2.59564e6 0.403372
\(187\) −1.19189e6 + 1.19189e6i −0.182268 + 0.182268i
\(188\) 1.29037e6i 0.194196i
\(189\) 1.32843e7i 1.96767i
\(190\) 3.72919e6 + 3.72919e6i 0.543693 + 0.543693i
\(191\) −7.14407e6 7.14407e6i −1.02529 1.02529i −0.999672 0.0256150i \(-0.991846\pi\)
−0.0256150 0.999672i \(-0.508154\pi\)
\(192\) −1.44990e6 −0.204850
\(193\) −6.02695e6 6.02695e6i −0.838350 0.838350i 0.150291 0.988642i \(-0.451979\pi\)
−0.988642 + 0.150291i \(0.951979\pi\)
\(194\) −3.00657e6 −0.411781
\(195\) 1.54250e7 2.08027
\(196\) 7.77991e6i 1.03325i
\(197\) −8.81944e6 −1.15357 −0.576783 0.816897i \(-0.695692\pi\)
−0.576783 + 0.816897i \(0.695692\pi\)
\(198\) −1.21082e6 1.21082e6i −0.155986 0.155986i
\(199\) 839951. 839951.i 0.106585 0.106585i −0.651803 0.758388i \(-0.725987\pi\)
0.758388 + 0.651803i \(0.225987\pi\)
\(200\) 1.18808e6 1.18808e6i 0.148510 0.148510i
\(201\) 1.05217e7 1.29568
\(202\) 201642. + 201642.i 0.0244640 + 0.0244640i
\(203\) −1.67955e7 + 1.67955e7i −2.00773 + 2.00773i
\(204\) 6.85093e6 + 6.85093e6i 0.806973 + 0.806973i
\(205\) −3.38314e6 + 3.38314e6i −0.392697 + 0.392697i
\(206\) 2.01425e6i 0.230416i
\(207\) 1.42380e7 + 1.42380e7i 1.60524 + 1.60524i
\(208\) 1.59941e6 + 1.59941e6i 0.177734 + 0.177734i
\(209\) −1.02898e6 + 1.02898e6i −0.112711 + 0.112711i
\(210\) 2.37268e7i 2.56201i
\(211\) −5.22570e6 −0.556285 −0.278143 0.960540i \(-0.589719\pi\)
−0.278143 + 0.960540i \(0.589719\pi\)
\(212\) 1.35232e6i 0.141929i
\(213\) 3.87219e6i 0.400699i
\(214\) −7.81345e6 + 7.81345e6i −0.797262 + 0.797262i
\(215\) 7.27209e6i 0.731718i
\(216\) −2.83095e6 + 2.83095e6i −0.280912 + 0.280912i
\(217\) 4.40435e6 4.40435e6i 0.431025 0.431025i
\(218\) 4.69495e6 0.453170
\(219\) −189160. −0.0180093
\(220\) 879670. + 879670.i 0.0826136 + 0.0826136i
\(221\) 1.51148e7i 1.40031i
\(222\) 1.00936e7 7.67226e6i 0.922548 0.701236i
\(223\) −1.24614e7 −1.12370 −0.561852 0.827238i \(-0.689911\pi\)
−0.561852 + 0.827238i \(0.689911\pi\)
\(224\) −2.46023e6 + 2.46023e6i −0.218893 + 0.218893i
\(225\) 1.14060e7i 1.00135i
\(226\) 9.43487e6i 0.817355i
\(227\) 7.73573e6 + 7.73573e6i 0.661339 + 0.661339i 0.955696 0.294357i \(-0.0951055\pi\)
−0.294357 + 0.955696i \(0.595105\pi\)
\(228\) 5.91451e6 + 5.91451e6i 0.499016 + 0.499016i
\(229\) −1.09121e7 −0.908663 −0.454332 0.890833i \(-0.650122\pi\)
−0.454332 + 0.890833i \(0.650122\pi\)
\(230\) −1.03440e7 1.03440e7i −0.850169 0.850169i
\(231\) −6.54681e6 −0.531121
\(232\) 7.15842e6 0.573262
\(233\) 2.31412e6i 0.182944i 0.995808 + 0.0914722i \(0.0291573\pi\)
−0.995808 + 0.0914722i \(0.970843\pi\)
\(234\) 1.53549e7 1.19839
\(235\) 4.49995e6 + 4.49995e6i 0.346740 + 0.346740i
\(236\) −7.82943e6 + 7.82943e6i −0.595654 + 0.595654i
\(237\) −3.06264e7 + 3.06264e7i −2.30065 + 2.30065i
\(238\) 2.32497e7 1.72459
\(239\) −3.56646e6 3.56646e6i −0.261242 0.261242i 0.564316 0.825559i \(-0.309140\pi\)
−0.825559 + 0.564316i \(0.809140\pi\)
\(240\) 5.05631e6 5.05631e6i 0.365763 0.365763i
\(241\) −3.14478e6 3.14478e6i −0.224667 0.224667i 0.585793 0.810460i \(-0.300783\pi\)
−0.810460 + 0.585793i \(0.800783\pi\)
\(242\) 6.84352e6 6.84352e6i 0.482874 0.482874i
\(243\) 1.24600e7i 0.868361i
\(244\) −5.70409e6 5.70409e6i −0.392660 0.392660i
\(245\) 2.71312e7 + 2.71312e7i 1.84489 + 1.84489i
\(246\) −5.36567e6 + 5.36567e6i −0.360428 + 0.360428i
\(247\) 1.30488e7i 0.865925i
\(248\) −1.87718e6 −0.123070
\(249\) 4.64795e7i 3.01067i
\(250\) 5.66289e6i 0.362425i
\(251\) −982226. + 982226.i −0.0621141 + 0.0621141i −0.737481 0.675367i \(-0.763985\pi\)
0.675367 + 0.737481i \(0.263985\pi\)
\(252\) 2.36190e7i 1.47591i
\(253\) 2.85417e6 2.85417e6i 0.176245 0.176245i
\(254\) 86902.5 86902.5i 0.00530312 0.00530312i
\(255\) −4.77831e7 −2.88173
\(256\) 1.04858e6 0.0625000
\(257\) −9.18658e6 9.18658e6i −0.541196 0.541196i 0.382684 0.923879i \(-0.375000\pi\)
−0.923879 + 0.382684i \(0.875000\pi\)
\(258\) 1.15336e7i 0.671590i
\(259\) 4.10866e6 3.01456e7i 0.236484 1.73510i
\(260\) −1.11554e7 −0.634696
\(261\) 3.43616e7 3.43616e7i 1.93264 1.93264i
\(262\) 1.83520e7i 1.02042i
\(263\) 8.68981e6i 0.477687i 0.971058 + 0.238843i \(0.0767682\pi\)
−0.971058 + 0.238843i \(0.923232\pi\)
\(264\) 1.39516e6 + 1.39516e6i 0.0758249 + 0.0758249i
\(265\) −4.71601e6 4.71601e6i −0.253418 0.253418i
\(266\) 2.00718e7 1.06645
\(267\) 3.39629e7 + 3.39629e7i 1.78431 + 1.78431i
\(268\) −7.60934e6 −0.395315
\(269\) −6.14540e6 −0.315714 −0.157857 0.987462i \(-0.550458\pi\)
−0.157857 + 0.987462i \(0.550458\pi\)
\(270\) 1.97450e7i 1.00315i
\(271\) −3.49852e6 −0.175783 −0.0878914 0.996130i \(-0.528013\pi\)
−0.0878914 + 0.996130i \(0.528013\pi\)
\(272\) −4.95462e6 4.95462e6i −0.246209 0.246209i
\(273\) 4.15113e7 4.15113e7i 2.04022 2.04022i
\(274\) 1.36425e7 1.36425e7i 0.663196 0.663196i
\(275\) −2.28644e6 −0.109942
\(276\) −1.64056e7 1.64056e7i −0.780308 0.780308i
\(277\) 9.98601e6 9.98601e6i 0.469843 0.469843i −0.432021 0.901864i \(-0.642199\pi\)
0.901864 + 0.432021i \(0.142199\pi\)
\(278\) −8.41584e6 8.41584e6i −0.391708 0.391708i
\(279\) −9.01077e6 + 9.01077e6i −0.414906 + 0.414906i
\(280\) 1.71593e7i 0.781675i
\(281\) 2.73302e7 + 2.73302e7i 1.23175 + 1.23175i 0.963290 + 0.268461i \(0.0865152\pi\)
0.268461 + 0.963290i \(0.413485\pi\)
\(282\) 7.13694e6 + 7.13694e6i 0.318247 + 0.318247i
\(283\) −2.70268e7 + 2.70268e7i −1.19244 + 1.19244i −0.216054 + 0.976381i \(0.569319\pi\)
−0.976381 + 0.216054i \(0.930681\pi\)
\(284\) 2.80039e6i 0.122254i
\(285\) −4.12519e7 −1.78201
\(286\) 3.07805e6i 0.131576i
\(287\) 1.82092e7i 0.770274i
\(288\) 5.03334e6 5.03334e6i 0.210707 0.210707i
\(289\) 2.26846e7i 0.939804i
\(290\) −2.49639e7 + 2.49639e7i −1.02357 + 1.02357i
\(291\) 1.66292e7 1.66292e7i 0.674826 0.674826i
\(292\) 136801. 0.00549467
\(293\) 5.04915e6 0.200731 0.100366 0.994951i \(-0.467999\pi\)
0.100366 + 0.994951i \(0.467999\pi\)
\(294\) 4.30302e7 + 4.30302e7i 1.69329 + 1.69329i
\(295\) 5.46078e7i 2.12710i
\(296\) −7.29977e6 + 5.54861e6i −0.281471 + 0.213949i
\(297\) 5.44813e6 0.207959
\(298\) −1.34784e6 + 1.34784e6i −0.0509318 + 0.0509318i
\(299\) 3.61947e7i 1.35404i
\(300\) 1.31424e7i 0.486755i
\(301\) −1.95704e7 1.95704e7i −0.717631 0.717631i
\(302\) −1.61968e7 1.61968e7i −0.588042 0.588042i
\(303\) −2.23054e6 −0.0801830
\(304\) −4.27740e6 4.27740e6i −0.152251 0.152251i
\(305\) 3.97842e7 1.40221
\(306\) −4.75660e7 −1.66009
\(307\) 3.08824e7i 1.06732i −0.845698 0.533662i \(-0.820816\pi\)
0.845698 0.533662i \(-0.179184\pi\)
\(308\) 4.73468e6 0.162046
\(309\) −1.11407e7 1.11407e7i −0.377605 0.377605i
\(310\) 6.54637e6 6.54637e6i 0.219743 0.219743i
\(311\) −2.05072e7 + 2.05072e7i −0.681750 + 0.681750i −0.960394 0.278644i \(-0.910115\pi\)
0.278644 + 0.960394i \(0.410115\pi\)
\(312\) −1.76925e7 −0.582541
\(313\) −3.53619e6 3.53619e6i −0.115319 0.115319i 0.647092 0.762412i \(-0.275985\pi\)
−0.762412 + 0.647092i \(0.775985\pi\)
\(314\) 394839. 394839.i 0.0127536 0.0127536i
\(315\) −8.23677e7 8.23677e7i −2.63527 2.63527i
\(316\) 2.21491e7 2.21491e7i 0.701933 0.701933i
\(317\) 3.88691e7i 1.22019i 0.792330 + 0.610093i \(0.208868\pi\)
−0.792330 + 0.610093i \(0.791132\pi\)
\(318\) −7.47960e6 7.47960e6i −0.232593 0.232593i
\(319\) −6.88814e6 6.88814e6i −0.212193 0.212193i
\(320\) −3.65674e6 + 3.65674e6i −0.111595 + 0.111595i
\(321\) 8.64314e7i 2.61310i
\(322\) −5.56750e7 −1.66760
\(323\) 4.04223e7i 1.19954i
\(324\) 2.64918e6i 0.0778889i
\(325\) 1.44976e7 1.44976e7i 0.422325 0.422325i
\(326\) 1.85498e7i 0.535410i
\(327\) −2.59675e7 + 2.59675e7i −0.742654 + 0.742654i
\(328\) 3.88047e6 3.88047e6i 0.109967 0.109967i
\(329\) 2.42203e7 0.680129
\(330\) −9.73080e6 −0.270774
\(331\) −4.45773e7 4.45773e7i −1.22922 1.22922i −0.964259 0.264961i \(-0.914641\pi\)
−0.264961 0.964259i \(-0.585359\pi\)
\(332\) 3.36142e7i 0.918562i
\(333\) −8.40584e6 + 6.16744e7i −0.227640 + 1.67021i
\(334\) 4.06576e7 1.09119
\(335\) 2.65364e7 2.65364e7i 0.705842 0.705842i
\(336\) 2.72148e7i 0.717442i
\(337\) 4.43359e7i 1.15842i −0.815179 0.579209i \(-0.803361\pi\)
0.815179 0.579209i \(-0.196639\pi\)
\(338\) 209723. + 209723.i 0.00543120 + 0.00543120i
\(339\) 5.21837e7 + 5.21837e7i 1.33948 + 1.33948i
\(340\) 3.45569e7 0.879222
\(341\) 1.80630e6 + 1.80630e6i 0.0455541 + 0.0455541i
\(342\) −4.10645e7 −1.02657
\(343\) 7.53645e7 1.86760
\(344\) 8.34113e6i 0.204903i
\(345\) 1.14424e8 2.78651
\(346\) 1.40255e7 + 1.40255e7i 0.338601 + 0.338601i
\(347\) 2.32138e7 2.32138e7i 0.555594 0.555594i −0.372456 0.928050i \(-0.621484\pi\)
0.928050 + 0.372456i \(0.121484\pi\)
\(348\) −3.95928e7 + 3.95928e7i −0.939460 + 0.939460i
\(349\) 6.82932e7 1.60657 0.803287 0.595592i \(-0.203082\pi\)
0.803287 + 0.595592i \(0.203082\pi\)
\(350\) 2.23003e7 + 2.23003e7i 0.520124 + 0.520124i
\(351\) −3.45448e7 + 3.45448e7i −0.798844 + 0.798844i
\(352\) −1.00899e6 1.00899e6i −0.0231343 0.0231343i
\(353\) 1.97626e7 1.97626e7i 0.449284 0.449284i −0.445832 0.895116i \(-0.647092\pi\)
0.895116 + 0.445832i \(0.147092\pi\)
\(354\) 8.66082e7i 1.95231i
\(355\) −9.76590e6 9.76590e6i −0.218287 0.218287i
\(356\) −2.45621e7 2.45621e7i −0.544397 0.544397i
\(357\) −1.28592e8 + 1.28592e8i −2.82625 + 2.82625i
\(358\) 3.65621e7i 0.796860i
\(359\) 7.16098e7 1.54771 0.773855 0.633363i \(-0.218326\pi\)
0.773855 + 0.633363i \(0.218326\pi\)
\(360\) 3.51060e7i 0.752442i
\(361\) 1.21487e7i 0.258231i
\(362\) 9.59847e6 9.59847e6i 0.202337 0.202337i
\(363\) 7.57022e7i 1.58266i
\(364\) −3.00211e7 + 3.00211e7i −0.622476 + 0.622476i
\(365\) −477073. + 477073.i −0.00981084 + 0.00981084i
\(366\) 6.30980e7 1.28698
\(367\) 1.22255e6 0.0247326 0.0123663 0.999924i \(-0.496064\pi\)
0.0123663 + 0.999924i \(0.496064\pi\)
\(368\) 1.18646e7 + 1.18646e7i 0.238073 + 0.238073i
\(369\) 3.72538e7i 0.741467i
\(370\) 6.10688e6 4.48067e7i 0.120563 0.884581i
\(371\) −2.53832e7 −0.497077
\(372\) 1.03826e7 1.03826e7i 0.201686 0.201686i
\(373\) 7.35725e6i 0.141772i 0.997484 + 0.0708858i \(0.0225826\pi\)
−0.997484 + 0.0708858i \(0.977417\pi\)
\(374\) 9.53511e6i 0.182268i
\(375\) 3.13211e7 + 3.13211e7i 0.593941 + 0.593941i
\(376\) −5.16147e6 5.16147e6i −0.0970979 0.0970979i
\(377\) 8.73511e7 1.63021
\(378\) −5.31371e7 5.31371e7i −0.983836 0.983836i
\(379\) 1.63969e7 0.301193 0.150596 0.988595i \(-0.451881\pi\)
0.150596 + 0.988595i \(0.451881\pi\)
\(380\) 2.98335e7 0.543693
\(381\) 961305.i 0.0173815i
\(382\) −5.71525e7 −1.02529
\(383\) −3.32822e7 3.32822e7i −0.592400 0.592400i 0.345879 0.938279i \(-0.387581\pi\)
−0.938279 + 0.345879i \(0.887581\pi\)
\(384\) −5.79961e6 + 5.79961e6i −0.102425 + 0.102425i
\(385\) −1.65115e7 + 1.65115e7i −0.289337 + 0.289337i
\(386\) −4.82156e7 −0.838350
\(387\) 4.00388e7 + 4.00388e7i 0.690793 + 0.690793i
\(388\) −1.20263e7 + 1.20263e7i −0.205891 + 0.205891i
\(389\) −4.42434e7 4.42434e7i −0.751623 0.751623i 0.223159 0.974782i \(-0.428363\pi\)
−0.974782 + 0.223159i \(0.928363\pi\)
\(390\) 6.16999e7 6.16999e7i 1.04014 1.04014i
\(391\) 1.12123e8i 1.87571i
\(392\) −3.11196e7 3.11196e7i −0.516626 0.516626i
\(393\) −1.01504e8 1.01504e8i −1.67226 1.67226i
\(394\) −3.52778e7 + 3.52778e7i −0.576783 + 0.576783i
\(395\) 1.54483e8i 2.50663i
\(396\) −9.68660e6 −0.155986
\(397\) 8.78508e7i 1.40402i 0.712165 + 0.702012i \(0.247715\pi\)
−0.712165 + 0.702012i \(0.752285\pi\)
\(398\) 6.71961e6i 0.106585i
\(399\) −1.11016e8 + 1.11016e8i −1.74770 + 1.74770i
\(400\) 9.50464e6i 0.148510i
\(401\) 2.12803e7 2.12803e7i 0.330023 0.330023i −0.522572 0.852595i \(-0.675027\pi\)
0.852595 + 0.522572i \(0.175027\pi\)
\(402\) 4.20868e7 4.20868e7i 0.647840 0.647840i
\(403\) −2.29064e7 −0.349979
\(404\) 1.61314e6 0.0244640
\(405\) 9.23858e6 + 9.23858e6i 0.139072 + 0.139072i
\(406\) 1.34364e8i 2.00773i
\(407\) 1.23633e7 + 1.68504e6i 0.183379 + 0.0249935i
\(408\) 5.48074e7 0.806973
\(409\) −8.71985e7 + 8.71985e7i −1.27450 + 1.27450i −0.330796 + 0.943702i \(0.607317\pi\)
−0.943702 + 0.330796i \(0.892683\pi\)
\(410\) 2.70651e7i 0.392697i
\(411\) 1.50911e8i 2.17369i
\(412\) 8.05701e6 + 8.05701e6i 0.115208 + 0.115208i
\(413\) −1.46959e8 1.46959e8i −2.08615 2.08615i
\(414\) 1.13904e8 1.60524
\(415\) 1.17224e8 + 1.17224e8i 1.64011 + 1.64011i
\(416\) 1.27953e7 0.177734
\(417\) 9.30950e7 1.28386
\(418\) 8.23181e6i 0.112711i
\(419\) 1.42045e7 0.193101 0.0965506 0.995328i \(-0.469219\pi\)
0.0965506 + 0.995328i \(0.469219\pi\)
\(420\) 9.49072e7 + 9.49072e7i 1.28101 + 1.28101i
\(421\) −1.01034e8 + 1.01034e8i −1.35401 + 1.35401i −0.472884 + 0.881124i \(0.656787\pi\)
−0.881124 + 0.472884i \(0.843213\pi\)
\(422\) −2.09028e7 + 2.09028e7i −0.278143 + 0.278143i
\(423\) −4.95518e7 −0.654694
\(424\) 5.40928e6 + 5.40928e6i 0.0709647 + 0.0709647i
\(425\) −4.49103e7 + 4.49103e7i −0.585032 + 0.585032i
\(426\) −1.54888e7 1.54888e7i −0.200349 0.200349i
\(427\) 1.07066e8 1.07066e8i 1.37521 1.37521i
\(428\) 6.25076e7i 0.797262i
\(429\) 1.70245e7 + 1.70245e7i 0.215627 + 0.215627i
\(430\) −2.90884e7 2.90884e7i −0.365859 0.365859i
\(431\) −8.31140e7 + 8.31140e7i −1.03811 + 1.03811i −0.0388629 + 0.999245i \(0.512374\pi\)
−0.999245 + 0.0388629i \(0.987626\pi\)
\(432\) 2.26476e7i 0.280912i
\(433\) 1.30194e8 1.60372 0.801859 0.597514i \(-0.203845\pi\)
0.801859 + 0.597514i \(0.203845\pi\)
\(434\) 3.52348e7i 0.431025i
\(435\) 2.76147e8i 3.35485i
\(436\) 1.87798e7 1.87798e7i 0.226585 0.226585i
\(437\) 9.67976e7i 1.15990i
\(438\) −756640. + 756640.i −0.00900465 + 0.00900465i
\(439\) 4819.45 4819.45i 5.69644e−5 5.69644e-5i −0.707078 0.707135i \(-0.749987\pi\)
0.707135 + 0.707078i \(0.249987\pi\)
\(440\) 7.03736e6 0.0826136
\(441\) −2.98759e8 −3.48341
\(442\) −6.04591e7 6.04591e7i −0.700156 0.700156i
\(443\) 4.41724e7i 0.508090i −0.967192 0.254045i \(-0.918239\pi\)
0.967192 0.254045i \(-0.0817611\pi\)
\(444\) 9.68553e6 7.10636e7i 0.110656 0.811892i
\(445\) 1.71313e8 1.94406
\(446\) −4.98456e7 + 4.98456e7i −0.561852 + 0.561852i
\(447\) 1.49096e7i 0.166934i
\(448\) 1.96818e7i 0.218893i
\(449\) −2.61301e7 2.61301e7i −0.288670 0.288670i 0.547884 0.836554i \(-0.315433\pi\)
−0.836554 + 0.547884i \(0.815433\pi\)
\(450\) −4.56238e7 4.56238e7i −0.500673 0.500673i
\(451\) −7.46792e6 −0.0814086
\(452\) −3.77395e7 3.77395e7i −0.408677 0.408677i
\(453\) 1.79167e8 1.92736
\(454\) 6.18859e7 0.661339
\(455\) 2.09388e8i 2.22289i
\(456\) 4.73161e7 0.499016
\(457\) −6.76262e7 6.76262e7i −0.708543 0.708543i 0.257686 0.966229i \(-0.417040\pi\)
−0.966229 + 0.257686i \(0.917040\pi\)
\(458\) −4.36485e7 + 4.36485e7i −0.454332 + 0.454332i
\(459\) 1.07012e8 1.07012e8i 1.10661 1.10661i
\(460\) −8.27521e7 −0.850169
\(461\) 1.17549e8 + 1.17549e8i 1.19982 + 1.19982i 0.974219 + 0.225605i \(0.0724360\pi\)
0.225605 + 0.974219i \(0.427564\pi\)
\(462\) −2.61872e7 + 2.61872e7i −0.265561 + 0.265561i
\(463\) −8.83216e7 8.83216e7i −0.889865 0.889865i 0.104645 0.994510i \(-0.466629\pi\)
−0.994510 + 0.104645i \(0.966629\pi\)
\(464\) 2.86337e7 2.86337e7i 0.286631 0.286631i
\(465\) 7.24151e7i 0.720229i
\(466\) 9.25650e6 + 9.25650e6i 0.0914722 + 0.0914722i
\(467\) −1.59777e7 1.59777e7i −0.156879 0.156879i 0.624303 0.781182i \(-0.285383\pi\)
−0.781182 + 0.624303i \(0.785383\pi\)
\(468\) 6.14196e7 6.14196e7i 0.599197 0.599197i
\(469\) 1.42828e8i 1.38451i
\(470\) 3.59996e7 0.346740
\(471\) 4.36767e6i 0.0418010i
\(472\) 6.26354e7i 0.595654i
\(473\) 8.02620e6 8.02620e6i 0.0758449 0.0758449i
\(474\) 2.45011e8i 2.30065i
\(475\) −3.87718e7 + 3.87718e7i −0.361772 + 0.361772i
\(476\) 9.29986e7 9.29986e7i 0.862295 0.862295i
\(477\) 5.19309e7 0.478488
\(478\) −2.85317e7 −0.261242
\(479\) 5.97333e7 + 5.97333e7i 0.543513 + 0.543513i 0.924557 0.381044i \(-0.124435\pi\)
−0.381044 + 0.924557i \(0.624435\pi\)
\(480\) 4.04505e7i 0.365763i
\(481\) −8.90759e7 + 6.77073e7i −0.800433 + 0.608416i
\(482\) −2.51583e7 −0.224667
\(483\) 3.07935e8 3.07935e8i 2.73286 2.73286i
\(484\) 5.47482e7i 0.482874i
\(485\) 8.38796e7i 0.735243i
\(486\) −4.98401e7 4.98401e7i −0.434181 0.434181i
\(487\) −4.58606e7 4.58606e7i −0.397057 0.397057i 0.480137 0.877194i \(-0.340587\pi\)
−0.877194 + 0.480137i \(0.840587\pi\)
\(488\) −4.56327e7 −0.392660
\(489\) −1.02598e8 1.02598e8i −0.877429 0.877429i
\(490\) 2.17050e8 1.84489
\(491\) 1.26998e8 1.07288 0.536440 0.843938i \(-0.319769\pi\)
0.536440 + 0.843938i \(0.319769\pi\)
\(492\) 4.29253e7i 0.360428i
\(493\) −2.70594e8 −2.25828
\(494\) −5.21953e7 5.21953e7i −0.432963 0.432963i
\(495\) 3.37805e7 3.37805e7i 0.278516 0.278516i
\(496\) −7.50872e6 + 7.50872e6i −0.0615348 + 0.0615348i
\(497\) −5.25634e7 −0.428168
\(498\) 1.85918e8 + 1.85918e8i 1.50534 + 1.50534i
\(499\) −1.10645e7 + 1.10645e7i −0.0890494 + 0.0890494i −0.750228 0.661179i \(-0.770056\pi\)
0.661179 + 0.750228i \(0.270056\pi\)
\(500\) −2.26516e7 2.26516e7i −0.181212 0.181212i
\(501\) −2.24875e8 + 2.24875e8i −1.78825 + 1.78825i
\(502\) 7.85781e6i 0.0621141i
\(503\) 5.23567e7 + 5.23567e7i 0.411404 + 0.411404i 0.882227 0.470824i \(-0.156043\pi\)
−0.470824 + 0.882227i \(0.656043\pi\)
\(504\) 9.44761e7 + 9.44761e7i 0.737956 + 0.737956i
\(505\) −5.62556e6 + 5.62556e6i −0.0436809 + 0.0436809i
\(506\) 2.28333e7i 0.176245i
\(507\) −2.31993e6 −0.0178013
\(508\) 695220.i 0.00530312i
\(509\) 7.60753e7i 0.576886i 0.957497 + 0.288443i \(0.0931376\pi\)
−0.957497 + 0.288443i \(0.906862\pi\)
\(510\) −1.91132e8 + 1.91132e8i −1.44087 + 1.44087i
\(511\) 2.56777e6i 0.0192439i
\(512\) 4.19430e6 4.19430e6i 0.0312500 0.0312500i
\(513\) 9.23852e7 9.23852e7i 0.684306 0.684306i
\(514\) −7.34926e7 −0.541196
\(515\) −5.61951e7 −0.411412
\(516\) −4.61343e7 4.61343e7i −0.335795 0.335795i
\(517\) 9.93318e6i 0.0718814i
\(518\) −1.04148e8 1.37017e8i −0.749309 0.985793i
\(519\) −1.55148e8 −1.10980
\(520\) −4.46217e7 + 4.46217e7i −0.317348 + 0.317348i
\(521\) 8.45653e7i 0.597969i 0.954258 + 0.298985i \(0.0966479\pi\)
−0.954258 + 0.298985i \(0.903352\pi\)
\(522\) 2.74893e8i 1.93264i
\(523\) −1.78463e8 1.78463e8i −1.24751 1.24751i −0.956816 0.290694i \(-0.906114\pi\)
−0.290694 0.956816i \(-0.593886\pi\)
\(524\) 7.34078e7 + 7.34078e7i 0.510209 + 0.510209i
\(525\) −2.46684e8 −1.70476
\(526\) 3.47592e7 + 3.47592e7i 0.238843 + 0.238843i
\(527\) 7.09588e7 0.484813
\(528\) 1.11613e7 0.0758249
\(529\) 1.20461e8i 0.813725i
\(530\) −3.77280e7 −0.253418
\(531\) 3.00661e8 + 3.00661e8i 2.00813 + 2.00813i
\(532\) 8.02872e7 8.02872e7i 0.533226 0.533226i
\(533\) 4.73517e7 4.73517e7i 0.312719 0.312719i
\(534\) 2.71703e8 1.78431
\(535\) −2.17985e8 2.17985e8i −1.42353 1.42353i
\(536\) −3.04374e7 + 3.04374e7i −0.197657 + 0.197657i
\(537\) −2.02223e8 2.02223e8i −1.30589 1.30589i
\(538\) −2.45816e7 + 2.45816e7i −0.157857 + 0.157857i
\(539\) 5.98893e7i 0.382458i
\(540\) −7.89799e7 7.89799e7i −0.501574 0.501574i
\(541\) 2.92559e7 + 2.92559e7i 0.184766 + 0.184766i 0.793429 0.608663i \(-0.208294\pi\)
−0.608663 + 0.793429i \(0.708294\pi\)
\(542\) −1.39941e7 + 1.39941e7i −0.0878914 + 0.0878914i
\(543\) 1.06177e8i 0.663180i
\(544\) −3.96370e7 −0.246209
\(545\) 1.30983e8i 0.809145i
\(546\) 3.32090e8i 2.04022i
\(547\) −8.91641e7 + 8.91641e7i −0.544789 + 0.544789i −0.924929 0.380140i \(-0.875876\pi\)
0.380140 + 0.924929i \(0.375876\pi\)
\(548\) 1.09140e8i 0.663196i
\(549\) −2.19045e8 + 2.19045e8i −1.32378 + 1.32378i
\(550\) −9.14578e6 + 9.14578e6i −0.0549709 + 0.0549709i
\(551\) −2.33608e8 −1.39647
\(552\) −1.31245e8 −0.780308
\(553\) 4.15741e8 + 4.15741e8i 2.45837 + 2.45837i
\(554\) 7.98881e7i 0.469843i
\(555\) 2.14046e8 + 2.81600e8i 1.25207 + 1.64723i
\(556\) −6.73267e7 −0.391708
\(557\) −1.01266e7 + 1.01266e7i −0.0586002 + 0.0586002i −0.735800 0.677199i \(-0.763193\pi\)
0.677199 + 0.735800i \(0.263193\pi\)
\(558\) 7.20862e7i 0.414906i
\(559\) 1.01783e8i 0.582694i
\(560\) −6.86373e7 6.86373e7i −0.390838 0.390838i
\(561\) −5.27381e7 5.27381e7i −0.298701 0.298701i
\(562\) 2.18641e8 1.23175
\(563\) −5.06100e7 5.06100e7i −0.283603 0.283603i 0.550941 0.834544i \(-0.314269\pi\)
−0.834544 + 0.550941i \(0.814269\pi\)
\(564\) 5.70955e7 0.318247
\(565\) 2.63221e8 1.45940
\(566\) 2.16214e8i 1.19244i
\(567\) 4.97252e7 0.272789
\(568\) 1.12015e7 + 1.12015e7i 0.0611270 + 0.0611270i
\(569\) 5.14258e6 5.14258e6i 0.0279154 0.0279154i −0.693011 0.720927i \(-0.743716\pi\)
0.720927 + 0.693011i \(0.243716\pi\)
\(570\) −1.65007e8 + 1.65007e8i −0.891003 + 0.891003i
\(571\) −2.36499e8 −1.27034 −0.635171 0.772372i \(-0.719070\pi\)
−0.635171 + 0.772372i \(0.719070\pi\)
\(572\) −1.23122e7 1.23122e7i −0.0657882 0.0657882i
\(573\) 3.16107e8 3.16107e8i 1.68024 1.68024i
\(574\) 7.28368e7 + 7.28368e7i 0.385137 + 0.385137i
\(575\) 1.07545e8 1.07545e8i 0.565700 0.565700i
\(576\) 4.02667e7i 0.210707i
\(577\) 8.51919e7 + 8.51919e7i 0.443477 + 0.443477i 0.893179 0.449702i \(-0.148470\pi\)
−0.449702 + 0.893179i \(0.648470\pi\)
\(578\) 9.07383e7 + 9.07383e7i 0.469902 + 0.469902i
\(579\) 2.66677e8 2.66677e8i 1.37389 1.37389i
\(580\) 1.99711e8i 1.02357i
\(581\) 6.30941e8 3.21707
\(582\) 1.33033e8i 0.674826i
\(583\) 1.04101e7i 0.0525350i
\(584\) 547205. 547205.i 0.00274734 0.00274734i
\(585\) 4.28383e8i 2.13976i
\(586\) 2.01966e7 2.01966e7i 0.100366 0.100366i
\(587\) 3.56163e7 3.56163e7i 0.176090 0.176090i −0.613559 0.789649i \(-0.710263\pi\)
0.789649 + 0.613559i \(0.210263\pi\)
\(588\) 3.44242e8 1.69329
\(589\) 6.12599e7 0.299799
\(590\) −2.18431e8 2.18431e8i −1.06355 1.06355i
\(591\) 3.90238e8i 1.89046i
\(592\) −7.00462e6 + 5.13935e7i −0.0337613 + 0.247710i
\(593\) −1.38971e7 −0.0666441 −0.0333220 0.999445i \(-0.510609\pi\)
−0.0333220 + 0.999445i \(0.510609\pi\)
\(594\) 2.17925e7 2.17925e7i 0.103980 0.103980i
\(595\) 6.48636e8i 3.07929i
\(596\) 1.07827e7i 0.0509318i
\(597\) 3.71657e7 + 3.71657e7i 0.174671 + 0.174671i
\(598\) 1.44779e8 + 1.44779e8i 0.677020 + 0.677020i
\(599\) −1.49063e8 −0.693567 −0.346783 0.937945i \(-0.612726\pi\)
−0.346783 + 0.937945i \(0.612726\pi\)
\(600\) 5.25696e7 + 5.25696e7i 0.243378 + 0.243378i
\(601\) 4.67270e7 0.215251 0.107625 0.994192i \(-0.465675\pi\)
0.107625 + 0.994192i \(0.465675\pi\)
\(602\) −1.56564e8 −0.717631
\(603\) 2.92209e8i 1.33273i
\(604\) −1.29574e8 −0.588042
\(605\) 1.90926e8 + 1.90926e8i 0.862180 + 0.862180i
\(606\) −8.92216e6 + 8.92216e6i −0.0400915 + 0.0400915i
\(607\) −2.92860e7 + 2.92860e7i −0.130947 + 0.130947i −0.769542 0.638596i \(-0.779516\pi\)
0.638596 + 0.769542i \(0.279516\pi\)
\(608\) −3.42192e7 −0.152251
\(609\) −7.43159e8 7.43159e8i −3.29026 3.29026i
\(610\) 1.59137e8 1.59137e8i 0.701103 0.701103i
\(611\) −6.29831e7 6.29831e7i −0.276122 0.276122i
\(612\) −1.90264e8 + 1.90264e8i −0.830047 + 0.830047i
\(613\) 2.00531e8i 0.870563i 0.900294 + 0.435282i \(0.143351\pi\)
−0.900294 + 0.435282i \(0.856649\pi\)
\(614\) −1.23530e8 1.23530e8i −0.533662 0.533662i
\(615\) −1.49695e8 1.49695e8i −0.643551 0.643551i
\(616\) 1.89387e7 1.89387e7i 0.0810231 0.0810231i
\(617\) 1.10584e8i 0.470802i 0.971898 + 0.235401i \(0.0756404\pi\)
−0.971898 + 0.235401i \(0.924360\pi\)
\(618\) −8.91256e7 −0.377605
\(619\) 2.02631e8i 0.854348i −0.904169 0.427174i \(-0.859509\pi\)
0.904169 0.427174i \(-0.140491\pi\)
\(620\) 5.23709e7i 0.219743i
\(621\) −2.56257e8 + 2.56257e8i −1.07004 + 1.07004i
\(622\) 1.64058e8i 0.681750i
\(623\) 4.61033e8 4.61033e8i 1.90663 1.90663i
\(624\) −7.07701e7 + 7.07701e7i −0.291270 + 0.291270i
\(625\) 3.03017e8 1.24116
\(626\) −2.82895e7 −0.115319
\(627\) −4.55296e7 4.55296e7i −0.184710 0.184710i
\(628\) 3.15872e6i 0.0127536i
\(629\) 2.75937e8 2.09742e8i 1.10881 0.842817i
\(630\) −6.58941e8 −2.63527
\(631\) −1.22295e8 + 1.22295e8i −0.486768 + 0.486768i −0.907285 0.420517i \(-0.861849\pi\)
0.420517 + 0.907285i \(0.361849\pi\)
\(632\) 1.77193e8i 0.701933i
\(633\) 2.31224e8i 0.911638i
\(634\) 1.55476e8 + 1.55476e8i 0.610093 + 0.610093i
\(635\) 2.42447e6 + 2.42447e6i 0.00946882 + 0.00946882i
\(636\) −5.98368e7 −0.232593
\(637\) −3.79739e8 3.79739e8i −1.46915 1.46915i
\(638\) −5.51052e7 −0.212193
\(639\) 1.07539e8 0.412156
\(640\) 2.92539e7i 0.111595i
\(641\) 6.86101e7 0.260504 0.130252 0.991481i \(-0.458421\pi\)
0.130252 + 0.991481i \(0.458421\pi\)
\(642\) −3.45726e8 3.45726e8i −1.30655 1.30655i
\(643\) −1.49047e8 + 1.49047e8i −0.560648 + 0.560648i −0.929492 0.368843i \(-0.879754\pi\)
0.368843 + 0.929492i \(0.379754\pi\)
\(644\) −2.22700e8 + 2.22700e8i −0.833801 + 0.833801i
\(645\) 3.21772e8 1.19914
\(646\) 1.61689e8 + 1.61689e8i 0.599768 + 0.599768i
\(647\) −1.49330e8 + 1.49330e8i −0.551358 + 0.551358i −0.926833 0.375474i \(-0.877480\pi\)
0.375474 + 0.926833i \(0.377480\pi\)
\(648\) −1.05967e7 1.05967e7i −0.0389445 0.0389445i
\(649\) 6.02706e7 6.02706e7i 0.220481 0.220481i
\(650\) 1.15981e8i 0.422325i
\(651\) 1.94881e8 + 1.94881e8i 0.706362 + 0.706362i
\(652\) 7.41992e7 + 7.41992e7i 0.267705 + 0.267705i
\(653\) −1.47226e8 + 1.47226e8i −0.528743 + 0.528743i −0.920197 0.391455i \(-0.871972\pi\)
0.391455 + 0.920197i \(0.371972\pi\)
\(654\) 2.07740e8i 0.742654i
\(655\) −5.11996e8 −1.82198
\(656\) 3.10438e7i 0.109967i
\(657\) 5.25335e6i 0.0185242i
\(658\) 9.68811e7 9.68811e7i 0.340065 0.340065i
\(659\) 8.98408e7i 0.313919i −0.987605 0.156959i \(-0.949831\pi\)
0.987605 0.156959i \(-0.0501692\pi\)
\(660\) −3.89232e7 + 3.89232e7i −0.135387 + 0.135387i
\(661\) −3.52940e8 + 3.52940e8i −1.22207 + 1.22207i −0.255175 + 0.966895i \(0.582133\pi\)
−0.966895 + 0.255175i \(0.917867\pi\)
\(662\) −3.56618e8 −1.22922
\(663\) 6.68791e8 2.29483
\(664\) −1.34457e8 1.34457e8i −0.459281 0.459281i
\(665\) 5.59978e8i 1.90417i
\(666\) 2.13074e8 + 2.80321e8i 0.721287 + 0.948927i
\(667\) 6.47980e8 2.18365
\(668\) 1.62630e8 1.62630e8i 0.545597 0.545597i
\(669\) 5.51385e8i 1.84152i
\(670\) 2.12291e8i 0.705842i
\(671\) 4.39098e7 + 4.39098e7i 0.145343 + 0.145343i
\(672\) −1.08859e8 1.08859e8i −0.358721 0.358721i
\(673\) −1.07584e8 −0.352941 −0.176470 0.984306i \(-0.556468\pi\)
−0.176470 + 0.984306i \(0.556468\pi\)
\(674\) −1.77343e8 1.77343e8i −0.579209 0.579209i
\(675\) 2.05285e8 0.667492
\(676\) 1.67778e6 0.00543120
\(677\) 1.88022e8i 0.605959i 0.952997 + 0.302980i \(0.0979814\pi\)
−0.952997 + 0.302980i \(0.902019\pi\)
\(678\) 4.17469e8 1.33948
\(679\) −2.25734e8 2.25734e8i −0.721088 0.721088i
\(680\) 1.38228e8 1.38228e8i 0.439611 0.439611i
\(681\) −3.42287e8 + 3.42287e8i −1.08380 + 1.08380i
\(682\) 1.44504e7 0.0455541
\(683\) −2.35728e8 2.35728e8i −0.739860 0.739860i 0.232691 0.972551i \(-0.425247\pi\)
−0.972551 + 0.232691i \(0.925247\pi\)
\(684\) −1.64258e8 + 1.64258e8i −0.513284 + 0.513284i
\(685\) 3.80608e8 + 3.80608e8i 1.18415 + 1.18415i
\(686\) 3.01458e8 3.01458e8i 0.933801 0.933801i
\(687\) 4.82834e8i 1.48911i
\(688\) 3.33645e7 + 3.33645e7i 0.102452 + 0.102452i
\(689\) 6.60071e7 + 6.60071e7i 0.201806 + 0.201806i
\(690\) 4.57697e8 4.57697e8i 1.39325 1.39325i
\(691\) 1.69059e7i 0.0512395i −0.999672 0.0256197i \(-0.991844\pi\)
0.999672 0.0256197i \(-0.00815591\pi\)
\(692\) 1.12204e8 0.338601
\(693\) 1.81818e8i 0.546308i
\(694\) 1.85710e8i 0.555594i
\(695\) 2.34791e8 2.34791e8i 0.699403 0.699403i
\(696\) 3.16742e8i 0.939460i
\(697\) −1.46685e8 + 1.46685e8i −0.433199 + 0.433199i
\(698\) 2.73173e8 2.73173e8i 0.803287 0.803287i
\(699\) −1.02394e8 −0.299809
\(700\) 1.78403e8 0.520124
\(701\) −1.08170e8 1.08170e8i −0.314017 0.314017i 0.532447 0.846464i \(-0.321273\pi\)
−0.846464 + 0.532447i \(0.821273\pi\)
\(702\) 2.76359e8i 0.798844i
\(703\) 2.38221e8 1.81073e8i 0.685667 0.521181i
\(704\) −8.07189e6 −0.0231343
\(705\) −1.99112e8 + 1.99112e8i −0.568237 + 0.568237i
\(706\) 1.58101e8i 0.449284i
\(707\) 3.02787e7i 0.0856799i
\(708\) −3.46433e8 3.46433e8i −0.976156 0.976156i
\(709\) 2.12594e7 + 2.12594e7i 0.0596501 + 0.0596501i 0.736303 0.676652i \(-0.236570\pi\)
−0.676652 + 0.736303i \(0.736570\pi\)
\(710\) −7.81272e7 −0.218287
\(711\) −8.50557e8 8.50557e8i −2.36643 2.36643i
\(712\) −1.96497e8 −0.544397
\(713\) −1.69922e8 −0.468793
\(714\) 1.02874e9i 2.82625i
\(715\) 8.58738e7 0.234932
\(716\) 1.46248e8 + 1.46248e8i 0.398430 + 0.398430i
\(717\) 1.57807e8 1.57807e8i 0.428123 0.428123i
\(718\) 2.86439e8 2.86439e8i 0.773855 0.773855i
\(719\) −9.23207e7 −0.248378 −0.124189 0.992259i \(-0.539633\pi\)
−0.124189 + 0.992259i \(0.539633\pi\)
\(720\) 1.40424e8 + 1.40424e8i 0.376221 + 0.376221i
\(721\) −1.51231e8 + 1.51231e8i −0.403491 + 0.403491i
\(722\) −4.85948e7 4.85948e7i −0.129115 0.129115i
\(723\) 1.39149e8 1.39149e8i 0.368184 0.368184i
\(724\) 7.67877e7i 0.202337i
\(725\) −2.59545e8 2.59545e8i −0.681081 0.681081i
\(726\) 3.02809e8 + 3.02809e8i 0.791332 + 0.791332i
\(727\) 1.14944e8 1.14944e8i 0.299146 0.299146i −0.541534 0.840679i \(-0.682156\pi\)
0.840679 + 0.541534i \(0.182156\pi\)
\(728\) 2.40169e8i 0.622476i
\(729\) 6.11677e8 1.57885
\(730\) 3.81658e6i 0.00981084i
\(731\) 3.15301e8i 0.807185i
\(732\) 2.52392e8 2.52392e8i 0.643491 0.643491i
\(733\) 2.63841e8i 0.669931i −0.942230 0.334965i \(-0.891275\pi\)
0.942230 0.334965i \(-0.108725\pi\)
\(734\) 4.89022e6 4.89022e6i 0.0123663 0.0123663i
\(735\) −1.20049e9 + 1.20049e9i −3.02340 + 3.02340i
\(736\) 9.49170e7 0.238073
\(737\) 5.85763e7 0.146325
\(738\) −1.49015e8 1.49015e8i −0.370734 0.370734i
\(739\) 9.46158e7i 0.234439i −0.993106 0.117220i \(-0.962602\pi\)
0.993106 0.117220i \(-0.0373981\pi\)
\(740\) −1.54799e8 2.03654e8i −0.382009 0.502572i
\(741\) 5.77378e8 1.41908
\(742\) −1.01533e8 + 1.01533e8i −0.248539 + 0.248539i
\(743\) 7.09886e8i 1.73070i 0.501166 + 0.865351i \(0.332904\pi\)
−0.501166 + 0.865351i \(0.667096\pi\)
\(744\) 8.30605e7i 0.201686i
\(745\) −3.76030e7 3.76030e7i −0.0909397 0.0909397i
\(746\) 2.94290e7 + 2.94290e7i 0.0708858 + 0.0708858i
\(747\) −1.29083e9 −3.09676
\(748\) 3.81404e7 + 3.81404e7i 0.0911341 + 0.0911341i
\(749\) −1.17327e9 −2.79224
\(750\) 2.50569e8 0.593941
\(751\) 4.67753e7i 0.110432i −0.998474 0.0552162i \(-0.982415\pi\)
0.998474 0.0552162i \(-0.0175848\pi\)
\(752\) −4.12917e7 −0.0970979
\(753\) −4.34611e7 4.34611e7i −0.101792 0.101792i
\(754\) 3.49404e8 3.49404e8i 0.815106 0.815106i
\(755\) 4.51870e8 4.51870e8i 1.04996 1.04996i
\(756\) −4.25097e8 −0.983836
\(757\) 3.67066e8 + 3.67066e8i 0.846168 + 0.846168i 0.989653 0.143485i \(-0.0458309\pi\)
−0.143485 + 0.989653i \(0.545831\pi\)
\(758\) 6.55877e7 6.55877e7i 0.150596 0.150596i
\(759\) 1.26290e8 + 1.26290e8i 0.288830 + 0.288830i
\(760\) 1.19334e8 1.19334e8i 0.271847 0.271847i
\(761\) 4.61005e8i 1.04605i 0.852318 + 0.523025i \(0.175196\pi\)
−0.852318 + 0.523025i \(0.824804\pi\)
\(762\) 3.84522e6 + 3.84522e6i 0.00869073 + 0.00869073i
\(763\) 3.52498e8 + 3.52498e8i 0.793567 + 0.793567i
\(764\) −2.28610e8 + 2.28610e8i −0.512643 + 0.512643i
\(765\) 1.32703e9i 2.96413i
\(766\) −2.66257e8 −0.592400
\(767\) 7.64313e8i 1.69389i
\(768\) 4.63969e7i 0.102425i
\(769\) 1.61970e8 1.61970e8i 0.356168 0.356168i −0.506230 0.862398i \(-0.668961\pi\)
0.862398 + 0.506230i \(0.168961\pi\)
\(770\) 1.32092e8i 0.289337i
\(771\) 4.06483e8 4.06483e8i 0.886910 0.886910i
\(772\) −1.92862e8 + 1.92862e8i −0.419175 + 0.419175i
\(773\) −3.85167e8 −0.833893 −0.416947 0.908931i \(-0.636900\pi\)
−0.416947 + 0.908931i \(0.636900\pi\)
\(774\) 3.20310e8 0.690793
\(775\) 6.80615e7 + 6.80615e7i 0.146216 + 0.146216i
\(776\) 9.62103e7i 0.205891i
\(777\) 1.33387e9 + 1.81798e8i 2.84348 + 0.387549i
\(778\) −3.53948e8 −0.751623
\(779\) −1.26635e8 + 1.26635e8i −0.267881 + 0.267881i
\(780\) 4.93599e8i 1.04014i
\(781\) 2.15572e7i 0.0452522i
\(782\) −4.48492e8 4.48492e8i −0.937853 0.937853i
\(783\) 6.18442e8 + 6.18442e8i 1.28829 + 1.28829i
\(784\) −2.48957e8 −0.516626
\(785\) 1.10155e7 + 1.10155e7i 0.0227717 + 0.0227717i
\(786\) −8.12028e8 −1.67226
\(787\) −4.83332e7 −0.0991566 −0.0495783 0.998770i \(-0.515788\pi\)
−0.0495783 + 0.998770i \(0.515788\pi\)
\(788\) 2.82222e8i 0.576783i
\(789\) −3.84503e8 −0.782831
\(790\) 6.17933e8 + 6.17933e8i 1.25332 + 1.25332i
\(791\) 7.08373e8 7.08373e8i 1.43131 1.43131i
\(792\) −3.87464e7 + 3.87464e7i −0.0779930 + 0.0779930i
\(793\) −5.56836e8 −1.11663
\(794\) 3.51403e8 + 3.51403e8i 0.702012 + 0.702012i
\(795\) 2.08672e8 2.08672e8i 0.415300 0.415300i
\(796\) −2.68784e7 2.68784e7i −0.0532923 0.0532923i
\(797\) 3.86346e8 3.86346e8i 0.763134 0.763134i −0.213753 0.976888i \(-0.568569\pi\)
0.976888 + 0.213753i \(0.0685689\pi\)
\(798\) 8.88127e8i 1.74770i
\(799\) 1.95107e8 + 1.95107e8i 0.382502 + 0.382502i
\(800\) −3.80185e7 3.80185e7i −0.0742550 0.0742550i
\(801\) −9.43218e8 + 9.43218e8i −1.83533 + 1.83533i
\(802\) 1.70242e8i 0.330023i
\(803\) −1.05309e6 −0.00203385
\(804\) 3.36695e8i 0.647840i
\(805\) 1.55326e9i 2.97754i
\(806\) −9.16256e7 + 9.16256e7i −0.174989 + 0.174989i
\(807\) 2.71919e8i 0.517391i
\(808\) 6.45255e6 6.45255e6i 0.0122320 0.0122320i
\(809\) −2.96742e6 + 2.96742e6i −0.00560445 + 0.00560445i −0.709903 0.704299i \(-0.751261\pi\)
0.704299 + 0.709903i \(0.251261\pi\)
\(810\) 7.39087e7 0.139072
\(811\) −1.01026e9 −1.89396 −0.946979 0.321296i \(-0.895882\pi\)
−0.946979 + 0.321296i \(0.895882\pi\)
\(812\) 5.37456e8 + 5.37456e8i 1.00386 + 1.00386i
\(813\) 1.54801e8i 0.288072i
\(814\) 5.61932e7 4.27129e7i 0.104186 0.0791929i
\(815\) −5.17516e8 −0.955985
\(816\) 2.19230e8 2.19230e8i 0.403486 0.403486i
\(817\) 2.72204e8i 0.499147i
\(818\) 6.97588e8i 1.27450i
\(819\) 1.15285e9 + 1.15285e9i 2.09856 + 2.09856i
\(820\) 1.08260e8 + 1.08260e8i 0.196349 + 0.196349i
\(821\) −6.31182e8 −1.14058 −0.570290 0.821444i \(-0.693169\pi\)
−0.570290 + 0.821444i \(0.693169\pi\)
\(822\) 6.03646e8 + 6.03646e8i 1.08684 + 1.08684i
\(823\) 2.23279e8 0.400542 0.200271 0.979741i \(-0.435818\pi\)
0.200271 + 0.979741i \(0.435818\pi\)
\(824\) 6.44561e7 0.115208
\(825\) 1.01169e8i 0.180172i
\(826\) −1.17567e9 −2.08615
\(827\) −6.52598e7 6.52598e7i −0.115380 0.115380i 0.647060 0.762439i \(-0.275998\pi\)
−0.762439 + 0.647060i \(0.775998\pi\)
\(828\) 4.55618e8 4.55618e8i 0.802619 0.802619i
\(829\) 4.57143e8 4.57143e8i 0.802395 0.802395i −0.181074 0.983469i \(-0.557957\pi\)
0.983469 + 0.181074i \(0.0579575\pi\)
\(830\) 9.37794e8 1.64011
\(831\) 4.41856e8 + 4.41856e8i 0.769977 + 0.769977i
\(832\) 5.11813e7 5.11813e7i 0.0888671 0.0888671i
\(833\) 1.17635e9 + 1.17635e9i 2.03517 + 2.03517i
\(834\) 3.72380e8 3.72380e8i 0.641931 0.641931i
\(835\) 1.13429e9i 1.94835i
\(836\) 3.29272e7 + 3.29272e7i 0.0563555 + 0.0563555i
\(837\) −1.62176e8 1.62176e8i −0.276574 0.276574i
\(838\) 5.68182e7 5.68182e7i 0.0965506 0.0965506i
\(839\) 3.29453e8i 0.557837i −0.960315 0.278918i \(-0.910024\pi\)
0.960315 0.278918i \(-0.0899759\pi\)
\(840\) 7.59258e8 1.28101
\(841\) 9.68988e8i 1.62904i
\(842\) 8.08272e8i 1.35401i
\(843\) −1.20929e9 + 1.20929e9i −2.01859 + 2.01859i
\(844\) 1.67223e8i 0.278143i
\(845\) −5.85100e6 + 5.85100e6i −0.00969751 + 0.00969751i
\(846\) −1.98207e8 + 1.98207e8i −0.327347 + 0.327347i
\(847\) 1.02763e9 1.69116
\(848\) 4.32743e7 0.0709647
\(849\) −1.19587e9 1.19587e9i −1.95416 1.95416i
\(850\) 3.59283e8i 0.585032i
\(851\) −6.60775e8 + 5.02260e8i −1.07217 + 0.814967i
\(852\) −1.23910e8 −0.200349
\(853\) −3.32297e7 + 3.32297e7i −0.0535402 + 0.0535402i −0.733370 0.679830i \(-0.762054\pi\)
0.679830 + 0.733370i \(0.262054\pi\)
\(854\) 8.56530e8i 1.37521i
\(855\) 1.14565e9i 1.83296i
\(856\) 2.50030e8 + 2.50030e8i 0.398631 + 0.398631i
\(857\) 3.81758e8 + 3.81758e8i 0.606520 + 0.606520i 0.942035 0.335515i \(-0.108910\pi\)
−0.335515 + 0.942035i \(0.608910\pi\)
\(858\) 1.36196e8 0.215627
\(859\) 4.91969e8 + 4.91969e8i 0.776172 + 0.776172i 0.979178 0.203005i \(-0.0650709\pi\)
−0.203005 + 0.979178i \(0.565071\pi\)
\(860\) −2.32707e8 −0.365859
\(861\) −8.05712e8 −1.26232
\(862\) 6.64912e8i 1.03811i
\(863\) −5.75659e8 −0.895639 −0.447819 0.894124i \(-0.647799\pi\)
−0.447819 + 0.894124i \(0.647799\pi\)
\(864\) 9.05904e7 + 9.05904e7i 0.140456 + 0.140456i
\(865\) −3.91292e8 + 3.91292e8i −0.604579 + 0.604579i
\(866\) 5.20777e8 5.20777e8i 0.801859 0.801859i
\(867\) −1.00374e9 −1.54015
\(868\) −1.40939e8 1.40939e8i −0.215513 0.215513i
\(869\) −1.70503e8 + 1.70503e8i −0.259820 + 0.259820i
\(870\) −1.10459e9 1.10459e9i −1.67742 1.67742i
\(871\) −3.71414e8 + 3.71414e8i −0.562087 + 0.562087i
\(872\) 1.50238e8i 0.226585i
\(873\) 4.61825e8 + 4.61825e8i 0.694121 + 0.694121i
\(874\) −3.87190e8 3.87190e8i −0.579949 0.579949i
\(875\) 4.25171e8 4.25171e8i 0.634658 0.634658i
\(876\) 6.05312e6i 0.00900465i
\(877\) 8.64610e8 1.28180 0.640902 0.767623i \(-0.278561\pi\)
0.640902 + 0.767623i \(0.278561\pi\)
\(878\) 38555.6i 5.69644e-5i
\(879\) 2.23412e8i 0.328958i
\(880\) 2.81494e7 2.81494e7i 0.0413068 0.0413068i
\(881\) 8.04062e8i 1.17588i −0.808906 0.587938i \(-0.799940\pi\)
0.808906 0.587938i \(-0.200060\pi\)
\(882\) −1.19504e9 + 1.19504e9i −1.74171 + 1.74171i
\(883\) 6.47858e8 6.47858e8i 0.941017 0.941017i −0.0573378 0.998355i \(-0.518261\pi\)
0.998355 + 0.0573378i \(0.0182612\pi\)
\(884\) −4.83673e8 −0.700156
\(885\) 2.41626e9 3.48589
\(886\) −1.76690e8 1.76690e8i −0.254045 0.254045i
\(887\) 4.90984e8i 0.703552i −0.936084 0.351776i \(-0.885578\pi\)
0.936084 0.351776i \(-0.114422\pi\)
\(888\) −2.45512e8 3.22997e8i −0.350618 0.461274i
\(889\) 1.30493e7 0.0185730
\(890\) 6.85252e8 6.85252e8i 0.972031 0.972031i
\(891\) 2.03932e7i 0.0288305i
\(892\) 3.98764e8i 0.561852i
\(893\) 1.68439e8 + 1.68439e8i 0.236532 + 0.236532i
\(894\) −5.96385e7 5.96385e7i −0.0834669 0.0834669i
\(895\) −1.02004e9 −1.42281
\(896\) 7.87274e7 + 7.87274e7i 0.109446 + 0.109446i
\(897\) −1.60153e9 −2.21900
\(898\) −2.09041e8 −0.288670
\(899\) 4.10084e8i 0.564409i
\(900\) −3.64991e8 −0.500673
\(901\) −2.04475e8 2.04475e8i −0.279554 0.279554i
\(902\) −2.98717e7 + 2.98717e7i −0.0407043 + 0.0407043i
\(903\) 8.65943e8 8.65943e8i 1.17605 1.17605i
\(904\) −3.01916e8 −0.408677
\(905\) 2.67785e8 + 2.67785e8i 0.361277 + 0.361277i
\(906\) 7.16668e8 7.16668e8i 0.963681 0.963681i
\(907\) −1.46791e8 1.46791e8i −0.196733 0.196733i 0.601865 0.798598i \(-0.294425\pi\)
−0.798598 + 0.601865i \(0.794425\pi\)
\(908\) 2.47543e8 2.47543e8i 0.330669 0.330669i
\(909\) 6.19466e7i 0.0824756i
\(910\) −8.37552e8 8.37552e8i −1.11144 1.11144i
\(911\) −5.58937e8 5.58937e8i −0.739277 0.739277i 0.233161 0.972438i \(-0.425093\pi\)
−0.972438 + 0.233161i \(0.925093\pi\)
\(912\) 1.89264e8 1.89264e8i 0.249508 0.249508i
\(913\) 2.58760e8i 0.340005i
\(914\) −5.41009e8 −0.708543
\(915\) 1.76035e9i 2.29793i
\(916\) 3.49188e8i 0.454332i
\(917\) −1.37787e9 + 1.37787e9i −1.78690 + 1.78690i
\(918\) 8.56096e8i 1.10661i
\(919\) −8.40968e8 + 8.40968e8i −1.08351 + 1.08351i −0.0873309 + 0.996179i \(0.527834\pi\)
−0.996179 + 0.0873309i \(0.972166\pi\)
\(920\) −3.31008e8 + 3.31008e8i −0.425085 + 0.425085i
\(921\) 1.36647e9 1.74913
\(922\) 9.40395e8 1.19982
\(923\) 1.36688e8 + 1.36688e8i 0.173830 + 0.173830i
\(924\) 2.09498e8i 0.265561i
\(925\) 4.65848e8 + 6.34922e7i 0.588598 + 0.0802223i
\(926\) −7.06573e8 −0.889865
\(927\) 3.09400e8 3.09400e8i 0.388401 0.388401i
\(928\) 2.29069e8i 0.286631i
\(929\) 2.82257e8i 0.352044i 0.984386 + 0.176022i \(0.0563230\pi\)
−0.984386 + 0.176022i \(0.943677\pi\)
\(930\) 2.89660e8 + 2.89660e8i 0.360114 + 0.360114i
\(931\) 1.01556e9 + 1.01556e9i 1.25851 + 1.25851i
\(932\) 7.40520e7 0.0914722
\(933\) −9.07392e8 9.07392e8i −1.11725 1.11725i
\(934\) −1.27822e8 −0.156879
\(935\) −2.66018e8 −0.325443
\(936\) 4.91357e8i 0.599197i
\(937\) −8.83005e8 −1.07336 −0.536678 0.843787i \(-0.680321\pi\)
−0.536678 + 0.843787i \(0.680321\pi\)
\(938\) −5.71312e8 5.71312e8i −0.692253 0.692253i
\(939\) 1.56468e8 1.56468e8i 0.188985 0.188985i
\(940\) 1.43998e8 1.43998e8i 0.173370 0.173370i
\(941\) 3.11294e8 0.373595 0.186798 0.982398i \(-0.440189\pi\)
0.186798 + 0.982398i \(0.440189\pi\)
\(942\) 1.74707e7 + 1.74707e7i 0.0209005 + 0.0209005i
\(943\) 3.51260e8 3.51260e8i 0.418884 0.418884i
\(944\) 2.50542e8 + 2.50542e8i 0.297827 + 0.297827i
\(945\) 1.48246e9 1.48246e9i 1.75666 1.75666i
\(946\) 6.42096e7i 0.0758449i
\(947\) −6.02686e8 6.02686e8i −0.709645 0.709645i 0.256816 0.966460i \(-0.417327\pi\)
−0.966460 + 0.256816i \(0.917327\pi\)
\(948\) 9.80045e8 + 9.80045e8i 1.15033 + 1.15033i
\(949\) 6.67731e6 6.67731e6i 0.00781273 0.00781273i
\(950\) 3.10174e8i 0.361772i
\(951\) −1.71986e9 −1.99964
\(952\) 7.43989e8i 0.862295i
\(953\) 2.53838e7i 0.0293277i −0.999892 0.0146638i \(-0.995332\pi\)
0.999892 0.0146638i \(-0.00466781\pi\)
\(954\) 2.07724e8 2.07724e8i 0.239244 0.239244i
\(955\) 1.59448e9i 1.83067i
\(956\) −1.14127e8 + 1.14127e8i −0.130621 + 0.130621i
\(957\) 3.04783e8 3.04783e8i 0.347741 0.347741i
\(958\) 4.77866e8 0.543513
\(959\) 2.04856e9 2.32270
\(960\) −1.61802e8 1.61802e8i −0.182881 0.182881i
\(961\) 7.79966e8i 0.878831i
\(962\) −8.54743e7 + 6.27133e8i −0.0960087 + 0.704424i
\(963\) 2.40037e9 2.68782
\(964\) −1.00633e8 + 1.00633e8i −0.112334 + 0.112334i
\(965\) 1.34515e9i 1.49689i
\(966\) 2.46348e9i 2.73286i
\(967\) −8.11671e8 8.11671e8i −0.897637 0.897637i 0.0975900 0.995227i \(-0.468887\pi\)
−0.995227 + 0.0975900i \(0.968887\pi\)
\(968\) −2.18993e8 2.18993e8i −0.241437 0.241437i
\(969\) −1.78859e9 −1.96580
\(970\) −3.35518e8 3.35518e8i −0.367622 0.367622i
\(971\) 5.17035e8 0.564758 0.282379 0.959303i \(-0.408876\pi\)
0.282379 + 0.959303i \(0.408876\pi\)
\(972\) −3.98721e8 −0.434181
\(973\) 1.26373e9i 1.37188i
\(974\) −3.66885e8 −0.397057
\(975\) 6.41483e8 + 6.41483e8i 0.692104 + 0.692104i
\(976\) −1.82531e8 + 1.82531e8i −0.196330 + 0.196330i
\(977\) −8.57304e7 + 8.57304e7i −0.0919287 + 0.0919287i −0.751576 0.659647i \(-0.770706\pi\)
0.659647 + 0.751576i \(0.270706\pi\)
\(978\) −8.20783e8 −0.877429
\(979\) 1.89078e8 + 1.89078e8i 0.201508 + 0.201508i
\(980\) 8.68199e8 8.68199e8i 0.922446 0.922446i
\(981\) −7.21169e8 7.21169e8i −0.763889 0.763889i
\(982\) 5.07990e8 5.07990e8i 0.536440 0.536440i
\(983\) 9.48208e8i 0.998259i 0.866527 + 0.499130i \(0.166347\pi\)
−0.866527 + 0.499130i \(0.833653\pi\)
\(984\) 1.71701e8 + 1.71701e8i 0.180214 + 0.180214i
\(985\) −9.84206e8 9.84206e8i −1.02986 1.02986i
\(986\) −1.08238e9 + 1.08238e9i −1.12914 + 1.12914i
\(987\) 1.07169e9i 1.11459i
\(988\) −4.17562e8 −0.432963
\(989\) 7.55038e8i 0.780513i
\(990\) 2.70244e8i 0.278516i
\(991\) −1.07229e9 + 1.07229e9i −1.10177 + 1.10177i −0.107577 + 0.994197i \(0.534309\pi\)
−0.994197 + 0.107577i \(0.965691\pi\)
\(992\) 6.00697e7i 0.0615348i
\(993\) 1.97243e9 1.97243e9i 2.01444 2.01444i
\(994\) −2.10254e8 + 2.10254e8i −0.214084 + 0.214084i
\(995\) 1.87469e8 0.190309
\(996\) 1.48734e9 1.50534
\(997\) 1.01415e9 + 1.01415e9i 1.02334 + 1.02334i 0.999721 + 0.0236141i \(0.00751729\pi\)
0.0236141 + 0.999721i \(0.492483\pi\)
\(998\) 8.85162e7i 0.0890494i
\(999\) −1.11002e9 1.51289e8i −1.11336 0.151744i
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 74.7.d.a.43.9 yes 18
37.31 odd 4 inner 74.7.d.a.31.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.7.d.a.31.1 18 37.31 odd 4 inner
74.7.d.a.43.9 yes 18 1.1 even 1 trivial