Properties

Label 15.6.e.a.8.4
Level $15$
Weight $6$
Character 15.8
Analytic conductor $2.406$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,6,Mod(2,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.2");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 15.e (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: \(2.40575729719\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 10768x^{12} + 16341006x^{8} + 4217167600x^{4} + 50906640625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{10}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.4
Root \(2.96509 - 2.96509i\) of defining polynomial
Character \(\chi\) \(=\) 15.8
Dual form 15.6.e.a.2.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.879873 - 0.879873i) q^{2} +(-15.5882 + 0.0935382i) q^{3} -30.4516i q^{4} +(-51.8842 - 20.8094i) q^{5} +(13.7979 + 13.6333i) q^{6} +(-11.3356 + 11.3356i) q^{7} +(-54.9495 + 54.9495i) q^{8} +(242.983 - 2.91618i) q^{9} +O(q^{10})\) \(q+(-0.879873 - 0.879873i) q^{2} +(-15.5882 + 0.0935382i) q^{3} -30.4516i q^{4} +(-51.8842 - 20.8094i) q^{5} +(13.7979 + 13.6333i) q^{6} +(-11.3356 + 11.3356i) q^{7} +(-54.9495 + 54.9495i) q^{8} +(242.983 - 2.91618i) q^{9} +(27.3419 + 63.9612i) q^{10} -359.671i q^{11} +(2.84839 + 474.686i) q^{12} +(370.007 + 370.007i) q^{13} +19.9477 q^{14} +(810.726 + 319.527i) q^{15} -877.755 q^{16} +(-1244.30 - 1244.30i) q^{17} +(-216.360 - 211.228i) q^{18} -2005.02i q^{19} +(-633.681 + 1579.96i) q^{20} +(175.640 - 177.761i) q^{21} +(-316.465 + 316.465i) q^{22} +(-245.087 + 245.087i) q^{23} +(851.423 - 861.703i) q^{24} +(2258.94 + 2159.36i) q^{25} -651.119i q^{26} +(-3787.38 + 68.1861i) q^{27} +(345.186 + 345.186i) q^{28} +7056.79 q^{29} +(-432.193 - 994.480i) q^{30} -3032.57 q^{31} +(2530.70 + 2530.70i) q^{32} +(33.6430 + 5606.61i) q^{33} +2189.65i q^{34} +(824.022 - 352.250i) q^{35} +(-88.8025 - 7399.22i) q^{36} +(2362.96 - 2362.96i) q^{37} +(-1764.17 + 1764.17i) q^{38} +(-5802.34 - 5733.13i) q^{39} +(3994.48 - 1707.55i) q^{40} +6435.18i q^{41} +(-310.948 + 1.86587i) q^{42} +(-9718.91 - 9718.91i) q^{43} -10952.6 q^{44} +(-12667.6 - 4905.02i) q^{45} +431.291 q^{46} +(-1492.86 - 1492.86i) q^{47} +(13682.6 - 82.1037i) q^{48} +16550.0i q^{49} +(-87.6175 - 3887.54i) q^{50} +(19512.8 + 19280.0i) q^{51} +(11267.3 - 11267.3i) q^{52} +(18730.5 - 18730.5i) q^{53} +(3392.41 + 3272.42i) q^{54} +(-7484.54 + 18661.2i) q^{55} -1245.77i q^{56} +(187.546 + 31254.6i) q^{57} +(-6209.09 - 6209.09i) q^{58} -21245.6 q^{59} +(9730.14 - 24688.0i) q^{60} -691.744 q^{61} +(2668.28 + 2668.28i) q^{62} +(-2721.29 + 2787.40i) q^{63} +23634.8i q^{64} +(-11497.9 - 26897.1i) q^{65} +(4903.51 - 4962.71i) q^{66} +(40533.4 - 40533.4i) q^{67} +(-37891.0 + 37891.0i) q^{68} +(3797.53 - 3843.38i) q^{69} +(-1034.97 - 415.100i) q^{70} -8449.81i q^{71} +(-13191.5 + 13512.0i) q^{72} +(-11657.9 - 11657.9i) q^{73} -4158.21 q^{74} +(-35414.7 - 33449.2i) q^{75} -61056.2 q^{76} +(4077.07 + 4077.07i) q^{77} +(60.9045 + 10149.8i) q^{78} -29899.1i q^{79} +(45541.6 + 18265.6i) q^{80} +(59032.0 - 1417.16i) q^{81} +(5662.15 - 5662.15i) q^{82} +(30668.9 - 30668.9i) q^{83} +(-5413.11 - 5348.54i) q^{84} +(38666.4 + 90452.7i) q^{85} +17102.8i q^{86} +(-110003. + 660.080i) q^{87} +(19763.8 + 19763.8i) q^{88} +106026. q^{89} +(6830.12 + 15461.7i) q^{90} -8388.47 q^{91} +(7463.29 + 7463.29i) q^{92} +(47272.3 - 283.661i) q^{93} +2627.06i q^{94} +(-41723.3 + 104029. i) q^{95} +(-39685.7 - 39212.3i) q^{96} +(-33142.7 + 33142.7i) q^{97} +(14561.9 - 14561.9i) q^{98} +(-1048.87 - 87393.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 84 q^{6} - 80 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 84 q^{6} - 80 q^{7} + 1060 q^{10} + 420 q^{12} - 2120 q^{13} - 3000 q^{15} - 452 q^{16} + 6000 q^{18} + 1416 q^{21} + 3380 q^{22} + 9160 q^{25} - 12960 q^{27} - 10900 q^{28} - 13380 q^{30} - 21568 q^{31} + 5760 q^{33} + 61932 q^{36} + 55720 q^{37} + 21480 q^{40} - 103020 q^{42} - 23360 q^{43} - 21240 q^{45} - 151168 q^{46} + 74820 q^{48} + 138816 q^{51} + 204160 q^{52} + 89120 q^{55} - 163800 q^{57} - 163500 q^{58} - 217380 q^{60} - 175168 q^{61} + 143040 q^{63} + 263400 q^{66} + 140320 q^{67} + 385260 q^{70} - 328680 q^{72} - 240320 q^{73} - 199920 q^{75} - 271536 q^{76} + 429960 q^{78} + 326016 q^{81} + 431120 q^{82} + 2440 q^{85} - 331680 q^{87} - 401700 q^{88} - 348360 q^{90} - 487168 q^{91} - 22320 q^{93} + 311748 q^{96} + 440800 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.879873 0.879873i −0.155541 0.155541i 0.625046 0.780588i \(-0.285080\pi\)
−0.780588 + 0.625046i \(0.785080\pi\)
\(3\) −15.5882 + 0.0935382i −0.999982 + 0.00600048i
\(4\) 30.4516i 0.951614i
\(5\) −51.8842 20.8094i −0.928133 0.372250i
\(6\) 13.7979 + 13.6333i 0.156472 + 0.154605i
\(7\) −11.3356 + 11.3356i −0.0874375 + 0.0874375i −0.749473 0.662035i \(-0.769693\pi\)
0.662035 + 0.749473i \(0.269693\pi\)
\(8\) −54.9495 + 54.9495i −0.303556 + 0.303556i
\(9\) 242.983 2.91618i 0.999928 0.0120007i
\(10\) 27.3419 + 63.9612i 0.0864626 + 0.202263i
\(11\) 359.671i 0.896238i −0.893974 0.448119i \(-0.852094\pi\)
0.893974 0.448119i \(-0.147906\pi\)
\(12\) 2.84839 + 474.686i 0.00571014 + 0.951597i
\(13\) 370.007 + 370.007i 0.607228 + 0.607228i 0.942221 0.334993i \(-0.108734\pi\)
−0.334993 + 0.942221i \(0.608734\pi\)
\(14\) 19.9477 0.0272003
\(15\) 810.726 + 319.527i 0.930350 + 0.366674i
\(16\) −877.755 −0.857183
\(17\) −1244.30 1244.30i −1.04425 1.04425i −0.998975 0.0452720i \(-0.985585\pi\)
−0.0452720 0.998975i \(-0.514415\pi\)
\(18\) −216.360 211.228i −0.157397 0.153663i
\(19\) 2005.02i 1.27419i −0.770784 0.637096i \(-0.780135\pi\)
0.770784 0.637096i \(-0.219865\pi\)
\(20\) −633.681 + 1579.96i −0.354238 + 0.883224i
\(21\) 175.640 177.761i 0.0869113 0.0879606i
\(22\) −316.465 + 316.465i −0.139402 + 0.139402i
\(23\) −245.087 + 245.087i −0.0966051 + 0.0966051i −0.753758 0.657153i \(-0.771761\pi\)
0.657153 + 0.753758i \(0.271761\pi\)
\(24\) 851.423 861.703i 0.301729 0.305372i
\(25\) 2258.94 + 2159.36i 0.722860 + 0.690995i
\(26\) 651.119i 0.188898i
\(27\) −3787.38 + 68.1861i −0.999838 + 0.0180006i
\(28\) 345.186 + 345.186i 0.0832067 + 0.0832067i
\(29\) 7056.79 1.55816 0.779081 0.626924i \(-0.215686\pi\)
0.779081 + 0.626924i \(0.215686\pi\)
\(30\) −432.193 994.480i −0.0876747 0.201740i
\(31\) −3032.57 −0.566770 −0.283385 0.959006i \(-0.591457\pi\)
−0.283385 + 0.959006i \(0.591457\pi\)
\(32\) 2530.70 + 2530.70i 0.436883 + 0.436883i
\(33\) 33.6430 + 5606.61i 0.00537786 + 0.896222i
\(34\) 2189.65i 0.324847i
\(35\) 824.022 352.250i 0.113702 0.0486050i
\(36\) −88.8025 7399.22i −0.0114201 0.951545i
\(37\) 2362.96 2362.96i 0.283761 0.283761i −0.550846 0.834607i \(-0.685695\pi\)
0.834607 + 0.550846i \(0.185695\pi\)
\(38\) −1764.17 + 1764.17i −0.198189 + 0.198189i
\(39\) −5802.34 5733.13i −0.610860 0.603573i
\(40\) 3994.48 1707.55i 0.394739 0.168742i
\(41\) 6435.18i 0.597862i 0.954275 + 0.298931i \(0.0966301\pi\)
−0.954275 + 0.298931i \(0.903370\pi\)
\(42\) −310.948 + 1.86587i −0.0271998 + 0.000163215i
\(43\) −9718.91 9718.91i −0.801579 0.801579i 0.181763 0.983342i \(-0.441820\pi\)
−0.983342 + 0.181763i \(0.941820\pi\)
\(44\) −10952.6 −0.852873
\(45\) −12667.6 4905.02i −0.932533 0.361085i
\(46\) 431.291 0.0300521
\(47\) −1492.86 1492.86i −0.0985767 0.0985767i 0.656099 0.754675i \(-0.272206\pi\)
−0.754675 + 0.656099i \(0.772206\pi\)
\(48\) 13682.6 82.1037i 0.857168 0.00514351i
\(49\) 16550.0i 0.984709i
\(50\) −87.6175 3887.54i −0.00495639 0.219913i
\(51\) 19512.8 + 19280.0i 1.05049 + 1.03796i
\(52\) 11267.3 11267.3i 0.577846 0.577846i
\(53\) 18730.5 18730.5i 0.915925 0.915925i −0.0808054 0.996730i \(-0.525749\pi\)
0.996730 + 0.0808054i \(0.0257492\pi\)
\(54\) 3392.41 + 3272.42i 0.158316 + 0.152716i
\(55\) −7484.54 + 18661.2i −0.333625 + 0.831828i
\(56\) 1245.77i 0.0530844i
\(57\) 187.546 + 31254.6i 0.00764577 + 1.27417i
\(58\) −6209.09 6209.09i −0.242358 0.242358i
\(59\) −21245.6 −0.794584 −0.397292 0.917692i \(-0.630050\pi\)
−0.397292 + 0.917692i \(0.630050\pi\)
\(60\) 9730.14 24688.0i 0.348932 0.885334i
\(61\) −691.744 −0.0238024 −0.0119012 0.999929i \(-0.503788\pi\)
−0.0119012 + 0.999929i \(0.503788\pi\)
\(62\) 2668.28 + 2668.28i 0.0881560 + 0.0881560i
\(63\) −2721.29 + 2787.40i −0.0863819 + 0.0884805i
\(64\) 23634.8i 0.721276i
\(65\) −11497.9 26897.1i −0.337547 0.789628i
\(66\) 4903.51 4962.71i 0.138563 0.140236i
\(67\) 40533.4 40533.4i 1.10313 1.10313i 0.109098 0.994031i \(-0.465204\pi\)
0.994031 0.109098i \(-0.0347961\pi\)
\(68\) −37891.0 + 37891.0i −0.993720 + 0.993720i
\(69\) 3797.53 3843.38i 0.0960237 0.0971831i
\(70\) −1034.97 415.100i −0.0252454 0.0101253i
\(71\) 8449.81i 0.198930i −0.995041 0.0994652i \(-0.968287\pi\)
0.995041 0.0994652i \(-0.0317132\pi\)
\(72\) −13191.5 + 13512.0i −0.299891 + 0.307177i
\(73\) −11657.9 11657.9i −0.256043 0.256043i 0.567399 0.823443i \(-0.307950\pi\)
−0.823443 + 0.567399i \(0.807950\pi\)
\(74\) −4158.21 −0.0882729
\(75\) −35414.7 33449.2i −0.726993 0.686645i
\(76\) −61056.2 −1.21254
\(77\) 4077.07 + 4077.07i 0.0783649 + 0.0783649i
\(78\) 60.9045 + 10149.8i 0.00113348 + 0.188894i
\(79\) 29899.1i 0.539002i −0.963000 0.269501i \(-0.913141\pi\)
0.963000 0.269501i \(-0.0868588\pi\)
\(80\) 45541.6 + 18265.6i 0.795579 + 0.319086i
\(81\) 59032.0 1417.16i 0.999712 0.0239998i
\(82\) 5662.15 5662.15i 0.0929922 0.0929922i
\(83\) 30668.9 30668.9i 0.488656 0.488656i −0.419226 0.907882i \(-0.637699\pi\)
0.907882 + 0.419226i \(0.137699\pi\)
\(84\) −5413.11 5348.54i −0.0837045 0.0827060i
\(85\) 38666.4 + 90452.7i 0.580479 + 1.35792i
\(86\) 17102.8i 0.249357i
\(87\) −110003. + 660.080i −1.55813 + 0.00934972i
\(88\) 19763.8 + 19763.8i 0.272059 + 0.272059i
\(89\) 106026. 1.41886 0.709428 0.704778i \(-0.248953\pi\)
0.709428 + 0.704778i \(0.248953\pi\)
\(90\) 6830.12 + 15461.7i 0.0888837 + 0.201211i
\(91\) −8388.47 −0.106189
\(92\) 7463.29 + 7463.29i 0.0919308 + 0.0919308i
\(93\) 47272.3 283.661i 0.566760 0.00340089i
\(94\) 2627.06i 0.0306655i
\(95\) −41723.3 + 104029.i −0.474318 + 1.18262i
\(96\) −39685.7 39212.3i −0.439497 0.434254i
\(97\) −33142.7 + 33142.7i −0.357651 + 0.357651i −0.862946 0.505296i \(-0.831383\pi\)
0.505296 + 0.862946i \(0.331383\pi\)
\(98\) 14561.9 14561.9i 0.153163 0.153163i
\(99\) −1048.87 87393.7i −0.0107555 0.896174i
\(100\) 65756.0 68788.4i 0.657560 0.687884i
\(101\) 13738.7i 0.134012i −0.997753 0.0670060i \(-0.978655\pi\)
0.997753 0.0670060i \(-0.0213447\pi\)
\(102\) −204.816 34132.7i −0.00194924 0.324841i
\(103\) −45415.8 45415.8i −0.421807 0.421807i 0.464019 0.885825i \(-0.346407\pi\)
−0.885825 + 0.464019i \(0.846407\pi\)
\(104\) −40663.4 −0.368656
\(105\) −12812.1 + 5568.01i −0.113408 + 0.0492864i
\(106\) −32960.9 −0.284928
\(107\) −47232.9 47232.9i −0.398828 0.398828i 0.478992 0.877819i \(-0.341002\pi\)
−0.877819 + 0.478992i \(0.841002\pi\)
\(108\) 2076.38 + 115332.i 0.0171296 + 0.951460i
\(109\) 57758.8i 0.465642i −0.972520 0.232821i \(-0.925204\pi\)
0.972520 0.232821i \(-0.0747956\pi\)
\(110\) 23005.0 9834.08i 0.181276 0.0774911i
\(111\) −36613.2 + 37055.3i −0.282053 + 0.285458i
\(112\) 9949.85 9949.85i 0.0749499 0.0749499i
\(113\) −136180. + 136180.i −1.00327 + 1.00327i −0.00327423 + 0.999995i \(0.501042\pi\)
−0.999995 + 0.00327423i \(0.998958\pi\)
\(114\) 27335.1 27665.1i 0.196997 0.199375i
\(115\) 17816.2 7616.02i 0.125624 0.0537011i
\(116\) 214891.i 1.48277i
\(117\) 90984.2 + 88826.2i 0.614471 + 0.599897i
\(118\) 18693.5 + 18693.5i 0.123590 + 0.123590i
\(119\) 28209.7 0.182613
\(120\) −62106.9 + 26991.2i −0.393720 + 0.171107i
\(121\) 31687.8 0.196757
\(122\) 608.647 + 608.647i 0.00370225 + 0.00370225i
\(123\) −601.936 100313.i −0.00358746 0.597852i
\(124\) 92346.8i 0.539346i
\(125\) −72268.2 159044.i −0.413687 0.910419i
\(126\) 4846.94 58.1711i 0.0271983 0.000326423i
\(127\) −70532.8 + 70532.8i −0.388044 + 0.388044i −0.873989 0.485945i \(-0.838476\pi\)
0.485945 + 0.873989i \(0.338476\pi\)
\(128\) 101778. 101778.i 0.549072 0.549072i
\(129\) 152409. + 150591.i 0.806375 + 0.796755i
\(130\) −13549.4 + 33782.8i −0.0703172 + 0.175322i
\(131\) 312818.i 1.59263i 0.604884 + 0.796314i \(0.293219\pi\)
−0.604884 + 0.796314i \(0.706781\pi\)
\(132\) 170731. 1024.48i 0.852858 0.00511765i
\(133\) 22728.0 + 22728.0i 0.111412 + 0.111412i
\(134\) −71328.6 −0.343164
\(135\) 197924. + 75275.4i 0.934683 + 0.355483i
\(136\) 136748. 0.633975
\(137\) −44151.7 44151.7i −0.200977 0.200977i 0.599442 0.800418i \(-0.295389\pi\)
−0.800418 + 0.599442i \(0.795389\pi\)
\(138\) −6723.03 + 40.3422i −0.0300516 + 0.000180327i
\(139\) 10378.2i 0.0455600i 0.999741 + 0.0227800i \(0.00725173\pi\)
−0.999741 + 0.0227800i \(0.992748\pi\)
\(140\) −10726.6 25092.8i −0.0462532 0.108201i
\(141\) 23410.6 + 23131.3i 0.0991665 + 0.0979834i
\(142\) −7434.76 + 7434.76i −0.0309419 + 0.0309419i
\(143\) 133081. 133081.i 0.544221 0.544221i
\(144\) −213279. + 2559.69i −0.857121 + 0.0102868i
\(145\) −366136. 146848.i −1.44618 0.580025i
\(146\) 20515.0i 0.0796505i
\(147\) −1548.06 257984.i −0.00590873 0.984692i
\(148\) −71956.1 71956.1i −0.270031 0.270031i
\(149\) −357728. −1.32004 −0.660019 0.751249i \(-0.729452\pi\)
−0.660019 + 0.751249i \(0.729452\pi\)
\(150\) 1729.43 + 60591.5i 0.00627589 + 0.219879i
\(151\) 181033. 0.646124 0.323062 0.946378i \(-0.395288\pi\)
0.323062 + 0.946378i \(0.395288\pi\)
\(152\) 110175. + 110175.i 0.386789 + 0.386789i
\(153\) −305972. 298715.i −1.05670 1.03164i
\(154\) 7174.61i 0.0243779i
\(155\) 157342. + 63106.0i 0.526038 + 0.210980i
\(156\) −174583. + 176691.i −0.574369 + 0.581303i
\(157\) 190153. 190153.i 0.615679 0.615679i −0.328741 0.944420i \(-0.606624\pi\)
0.944420 + 0.328741i \(0.106624\pi\)
\(158\) −26307.4 + 26307.4i −0.0838370 + 0.0838370i
\(159\) −290222. + 293726.i −0.910412 + 0.921404i
\(160\) −78640.9 183966.i −0.242856 0.568116i
\(161\) 5556.39i 0.0168938i
\(162\) −53187.6 50693.8i −0.159229 0.151763i
\(163\) 379306. + 379306.i 1.11820 + 1.11820i 0.992005 + 0.126198i \(0.0402773\pi\)
0.126198 + 0.992005i \(0.459723\pi\)
\(164\) 195962. 0.568934
\(165\) 114925. 291595.i 0.328627 0.833815i
\(166\) −53969.5 −0.152012
\(167\) 212126. + 212126.i 0.588576 + 0.588576i 0.937246 0.348670i \(-0.113367\pi\)
−0.348670 + 0.937246i \(0.613367\pi\)
\(168\) 116.527 + 19419.2i 0.000318532 + 0.0530834i
\(169\) 97482.6i 0.262549i
\(170\) 45565.4 113608.i 0.120924 0.301501i
\(171\) −5847.01 487185.i −0.0152913 1.27410i
\(172\) −295957. + 295957.i −0.762794 + 0.762794i
\(173\) −52714.4 + 52714.4i −0.133910 + 0.133910i −0.770885 0.636974i \(-0.780186\pi\)
0.636974 + 0.770885i \(0.280186\pi\)
\(174\) 97369.1 + 96207.5i 0.243808 + 0.240900i
\(175\) −50083.8 + 1128.79i −0.123624 + 0.00278624i
\(176\) 315703.i 0.768240i
\(177\) 331181. 1987.28i 0.794569 0.00476788i
\(178\) −93289.7 93289.7i −0.220690 0.220690i
\(179\) 524394. 1.22328 0.611639 0.791137i \(-0.290510\pi\)
0.611639 + 0.791137i \(0.290510\pi\)
\(180\) −149366. + 385750.i −0.343613 + 0.887411i
\(181\) 163991. 0.372068 0.186034 0.982543i \(-0.440437\pi\)
0.186034 + 0.982543i \(0.440437\pi\)
\(182\) 7380.79 + 7380.79i 0.0165167 + 0.0165167i
\(183\) 10783.0 64.7045i 0.0238020 0.000142826i
\(184\) 26934.8i 0.0586502i
\(185\) −171772. + 73428.5i −0.368998 + 0.157738i
\(186\) −41843.2 41344.0i −0.0886834 0.0876255i
\(187\) −447539. + 447539.i −0.935894 + 0.935894i
\(188\) −45460.0 + 45460.0i −0.0938070 + 0.0938070i
\(189\) 42159.1 43705.0i 0.0858494 0.0889973i
\(190\) 128244. 54821.1i 0.257722 0.110170i
\(191\) 559164.i 1.10906i −0.832163 0.554531i \(-0.812898\pi\)
0.832163 0.554531i \(-0.187102\pi\)
\(192\) −2210.76 368423.i −0.00432800 0.721263i
\(193\) 150013. + 150013.i 0.289891 + 0.289891i 0.837037 0.547146i \(-0.184286\pi\)
−0.547146 + 0.837037i \(0.684286\pi\)
\(194\) 58322.8 0.111259
\(195\) 181747. + 418202.i 0.342279 + 0.787589i
\(196\) 503975. 0.937063
\(197\) −237011. 237011.i −0.435113 0.435113i 0.455250 0.890363i \(-0.349550\pi\)
−0.890363 + 0.455250i \(0.849550\pi\)
\(198\) −75972.6 + 77818.3i −0.137719 + 0.141065i
\(199\) 602333.i 1.07821i −0.842238 0.539106i \(-0.818762\pi\)
0.842238 0.539106i \(-0.181238\pi\)
\(200\) −242783. + 5471.86i −0.429184 + 0.00967297i
\(201\) −628051. + 635633.i −1.09649 + 1.10973i
\(202\) −12088.4 + 12088.4i −0.0208444 + 0.0208444i
\(203\) −79992.7 + 79992.7i −0.136242 + 0.136242i
\(204\) 587107. 594196.i 0.987739 0.999665i
\(205\) 133912. 333884.i 0.222554 0.554896i
\(206\) 79920.3i 0.131217i
\(207\) −58837.1 + 60266.5i −0.0954388 + 0.0977575i
\(208\) −324776. 324776.i −0.520505 0.520505i
\(209\) −721148. −1.14198
\(210\) 16172.1 + 6373.84i 0.0253057 + 0.00997363i
\(211\) −905177. −1.39968 −0.699838 0.714302i \(-0.746744\pi\)
−0.699838 + 0.714302i \(0.746744\pi\)
\(212\) −570375. 570375.i −0.871607 0.871607i
\(213\) 790.380 + 131717.i 0.00119368 + 0.198927i
\(214\) 83118.0i 0.124068i
\(215\) 302013. + 706502.i 0.445584 + 1.04236i
\(216\) 204368. 211862.i 0.298043 0.308971i
\(217\) 34375.9 34375.9i 0.0495569 0.0495569i
\(218\) −50820.5 + 50820.5i −0.0724265 + 0.0724265i
\(219\) 182816. + 180635.i 0.257575 + 0.254502i
\(220\) 568265. + 227916.i 0.791579 + 0.317482i
\(221\) 920800.i 1.26819i
\(222\) 64819.0 388.952i 0.0882713 0.000529680i
\(223\) 325294. + 325294.i 0.438040 + 0.438040i 0.891352 0.453312i \(-0.149758\pi\)
−0.453312 + 0.891352i \(0.649758\pi\)
\(224\) −57373.8 −0.0764000
\(225\) 555179. + 518099.i 0.731100 + 0.682270i
\(226\) 239642. 0.312099
\(227\) 71799.3 + 71799.3i 0.0924816 + 0.0924816i 0.751834 0.659352i \(-0.229169\pi\)
−0.659352 + 0.751834i \(0.729169\pi\)
\(228\) 951755. 5711.09i 1.21252 0.00727582i
\(229\) 278676.i 0.351165i 0.984465 + 0.175583i \(0.0561809\pi\)
−0.984465 + 0.175583i \(0.943819\pi\)
\(230\) −22377.2 8974.90i −0.0278924 0.0111869i
\(231\) −63935.4 63172.7i −0.0788337 0.0778932i
\(232\) −387768. + 387768.i −0.472990 + 0.472990i
\(233\) −71640.1 + 71640.1i −0.0864503 + 0.0864503i −0.749010 0.662559i \(-0.769470\pi\)
0.662559 + 0.749010i \(0.269470\pi\)
\(234\) −1898.78 158210.i −0.00226691 0.188884i
\(235\) 46390.3 + 108521.i 0.0547971 + 0.128187i
\(236\) 646965.i 0.756137i
\(237\) 2796.71 + 466073.i 0.00323427 + 0.538993i
\(238\) −24821.0 24821.0i −0.0284038 0.0284038i
\(239\) 1.08062e6 1.22371 0.611854 0.790971i \(-0.290424\pi\)
0.611854 + 0.790971i \(0.290424\pi\)
\(240\) −711619. 280467.i −0.797480 0.314307i
\(241\) −342370. −0.379710 −0.189855 0.981812i \(-0.560802\pi\)
−0.189855 + 0.981812i \(0.560802\pi\)
\(242\) −27881.3 27881.3i −0.0306037 0.0306037i
\(243\) −920069. + 27612.7i −0.999550 + 0.0299981i
\(244\) 21064.7i 0.0226507i
\(245\) 344396. 858684.i 0.366558 0.913941i
\(246\) −87732.9 + 88792.2i −0.0924325 + 0.0935485i
\(247\) 741872. 741872.i 0.773725 0.773725i
\(248\) 166638. 166638.i 0.172047 0.172047i
\(249\) −475203. + 480941.i −0.485715 + 0.491579i
\(250\) −76351.4 + 203525.i −0.0772622 + 0.205953i
\(251\) 195789.i 0.196157i 0.995179 + 0.0980787i \(0.0312697\pi\)
−0.995179 + 0.0980787i \(0.968730\pi\)
\(252\) 84880.9 + 82867.6i 0.0841993 + 0.0822022i
\(253\) 88150.6 + 88150.6i 0.0865812 + 0.0865812i
\(254\) 124120. 0.120714
\(255\) −611199. 1.40638e6i −0.588616 1.35441i
\(256\) 577209. 0.550470
\(257\) 614221. + 614221.i 0.580085 + 0.580085i 0.934927 0.354841i \(-0.115465\pi\)
−0.354841 + 0.934927i \(0.615465\pi\)
\(258\) −1599.77 266602.i −0.00149626 0.249353i
\(259\) 53571.0i 0.0496227i
\(260\) −819062. + 350130.i −0.751421 + 0.321215i
\(261\) 1.71468e6 20578.9i 1.55805 0.0186991i
\(262\) 275241. 275241.i 0.247719 0.247719i
\(263\) −398691. + 398691.i −0.355425 + 0.355425i −0.862123 0.506699i \(-0.830866\pi\)
0.506699 + 0.862123i \(0.330866\pi\)
\(264\) −309930. 306232.i −0.273686 0.270421i
\(265\) −1.36159e6 + 582046.i −1.19105 + 0.509147i
\(266\) 39995.6i 0.0346584i
\(267\) −1.65276e6 + 9917.51i −1.41883 + 0.00851382i
\(268\) −1.23431e6 1.23431e6i −1.04975 1.04975i
\(269\) −1.29261e6 −1.08915 −0.544575 0.838712i \(-0.683309\pi\)
−0.544575 + 0.838712i \(0.683309\pi\)
\(270\) −107915. 240381.i −0.0900894 0.200674i
\(271\) −785610. −0.649806 −0.324903 0.945747i \(-0.605332\pi\)
−0.324903 + 0.945747i \(0.605332\pi\)
\(272\) 1.09219e6 + 1.09219e6i 0.895110 + 0.895110i
\(273\) 130761. 784.643i 0.106187 0.000637185i
\(274\) 77695.7i 0.0625203i
\(275\) 776658. 812474.i 0.619296 0.647855i
\(276\) −117037. 115641.i −0.0924808 0.0913775i
\(277\) 1.55247e6 1.55247e6i 1.21569 1.21569i 0.246564 0.969127i \(-0.420699\pi\)
0.969127 0.246564i \(-0.0793014\pi\)
\(278\) 9131.49 9131.49i 0.00708646 0.00708646i
\(279\) −736862. + 8843.53i −0.566729 + 0.00680166i
\(280\) −25923.7 + 64635.6i −0.0197607 + 0.0492694i
\(281\) 1.24917e6i 0.943748i 0.881666 + 0.471874i \(0.156422\pi\)
−0.881666 + 0.471874i \(0.843578\pi\)
\(282\) −245.730 40951.0i −0.000184008 0.0306649i
\(283\) 564054. + 564054.i 0.418654 + 0.418654i 0.884739 0.466086i \(-0.154336\pi\)
−0.466086 + 0.884739i \(0.654336\pi\)
\(284\) −257311. −0.189305
\(285\) 640660. 1.62552e6i 0.467213 1.18544i
\(286\) −234188. −0.169297
\(287\) −72946.4 72946.4i −0.0522756 0.0522756i
\(288\) 622296. + 607536.i 0.442095 + 0.431609i
\(289\) 1.67671e6i 1.18090i
\(290\) 192946. + 451361.i 0.134723 + 0.315158i
\(291\) 513535. 519735.i 0.355498 0.359790i
\(292\) −355002. + 355002.i −0.243654 + 0.243654i
\(293\) 1.97297e6 1.97297e6i 1.34261 1.34261i 0.449165 0.893449i \(-0.351721\pi\)
0.893449 0.449165i \(-0.148279\pi\)
\(294\) −225632. + 228356.i −0.152241 + 0.154079i
\(295\) 1.10231e6 + 442109.i 0.737479 + 0.295784i
\(296\) 259687.i 0.172275i
\(297\) 24524.6 + 1.36221e6i 0.0161328 + 0.896093i
\(298\) 314755. + 314755.i 0.205320 + 0.205320i
\(299\) −181368. −0.117323
\(300\) −1.01858e6 + 1.07844e6i −0.653421 + 0.691817i
\(301\) 220339. 0.140176
\(302\) −159286. 159286.i −0.100499 0.100499i
\(303\) 1285.10 + 214162.i 0.000804136 + 0.134010i
\(304\) 1.75992e6i 1.09222i
\(305\) 35890.6 + 14394.8i 0.0220918 + 0.00886045i
\(306\) 6385.43 + 532048.i 0.00389840 + 0.324823i
\(307\) 712049. 712049.i 0.431185 0.431185i −0.457846 0.889032i \(-0.651379\pi\)
0.889032 + 0.457846i \(0.151379\pi\)
\(308\) 124153. 124153.i 0.0745731 0.0745731i
\(309\) 712197. + 703701.i 0.424330 + 0.419268i
\(310\) −82916.2 193967.i −0.0490044 0.114637i
\(311\) 801658.i 0.469990i −0.971997 0.234995i \(-0.924493\pi\)
0.971997 0.234995i \(-0.0755073\pi\)
\(312\) 633869. 3803.59i 0.368649 0.00221211i
\(313\) −1.36383e6 1.36383e6i −0.786862 0.786862i 0.194116 0.980978i \(-0.437816\pi\)
−0.980978 + 0.194116i \(0.937816\pi\)
\(314\) −334621. −0.191527
\(315\) 199196. 87993.6i 0.113111 0.0499660i
\(316\) −910477. −0.512922
\(317\) −1.44550e6 1.44550e6i −0.807925 0.807925i 0.176394 0.984320i \(-0.443557\pi\)
−0.984320 + 0.176394i \(0.943557\pi\)
\(318\) 513801. 3083.11i 0.284923 0.00170970i
\(319\) 2.53812e6i 1.39648i
\(320\) 491826. 1.22627e6i 0.268495 0.669440i
\(321\) 740693. + 731857.i 0.401214 + 0.396428i
\(322\) −4888.92 + 4888.92i −0.00262768 + 0.00262768i
\(323\) −2.49485e6 + 2.49485e6i −1.33057 + 1.33057i
\(324\) −43154.9 1.79762e6i −0.0228385 0.951340i
\(325\) 36845.2 + 1.63480e6i 0.0193496 + 0.858532i
\(326\) 667482.i 0.347853i
\(327\) 5402.66 + 900355.i 0.00279408 + 0.465634i
\(328\) −353610. 353610.i −0.181485 0.181485i
\(329\) 33844.8 0.0172386
\(330\) −357686. + 155447.i −0.180808 + 0.0785775i
\(331\) −167596. −0.0840801 −0.0420400 0.999116i \(-0.513386\pi\)
−0.0420400 + 0.999116i \(0.513386\pi\)
\(332\) −933918. 933918.i −0.465011 0.465011i
\(333\) 567267. 581049.i 0.280335 0.287146i
\(334\) 373288.i 0.183095i
\(335\) −2.94652e6 + 1.25957e6i −1.43449 + 0.613210i
\(336\) −154169. + 156031.i −0.0744989 + 0.0753983i
\(337\) −578695. + 578695.i −0.277571 + 0.277571i −0.832139 0.554567i \(-0.812884\pi\)
0.554567 + 0.832139i \(0.312884\pi\)
\(338\) −85772.3 + 85772.3i −0.0408372 + 0.0408372i
\(339\) 2.11006e6 2.13554e6i 0.997231 1.00927i
\(340\) 2.75443e6 1.17745e6i 1.29222 0.552392i
\(341\) 1.09073e6i 0.507961i
\(342\) −423517. + 433806.i −0.195797 + 0.200553i
\(343\) −378120. 378120.i −0.173538 0.173538i
\(344\) 1.06810e6 0.486649
\(345\) −277010. + 120386.i −0.125299 + 0.0544539i
\(346\) 92764.1 0.0416572
\(347\) 55424.5 + 55424.5i 0.0247103 + 0.0247103i 0.719354 0.694644i \(-0.244438\pi\)
−0.694644 + 0.719354i \(0.744438\pi\)
\(348\) 20100.5 + 3.34976e6i 0.00889732 + 1.48274i
\(349\) 1.16783e6i 0.513234i 0.966513 + 0.256617i \(0.0826079\pi\)
−0.966513 + 0.256617i \(0.917392\pi\)
\(350\) 45060.6 + 43074.2i 0.0196620 + 0.0187952i
\(351\) −1.42659e6 1.37613e6i −0.618060 0.596199i
\(352\) 910219. 910219.i 0.391552 0.391552i
\(353\) 227606. 227606.i 0.0972182 0.0972182i −0.656825 0.754043i \(-0.728101\pi\)
0.754043 + 0.656825i \(0.228101\pi\)
\(354\) −293146. 289649.i −0.124330 0.122847i
\(355\) −175836. + 438412.i −0.0740518 + 0.184634i
\(356\) 3.22867e6i 1.35020i
\(357\) −439738. + 2638.68i −0.182609 + 0.00109576i
\(358\) −461401. 461401.i −0.190270 0.190270i
\(359\) 3.03165e6 1.24149 0.620744 0.784014i \(-0.286831\pi\)
0.620744 + 0.784014i \(0.286831\pi\)
\(360\) 965609. 426552.i 0.392686 0.173467i
\(361\) −1.54401e6 −0.623567
\(362\) −144291. 144291.i −0.0578719 0.0578719i
\(363\) −493956. + 2964.02i −0.196753 + 0.00118063i
\(364\) 255443.i 0.101051i
\(365\) 362267. + 847455.i 0.142330 + 0.332954i
\(366\) −9544.63 9430.77i −0.00372440 0.00367997i
\(367\) −3.13626e6 + 3.13626e6i −1.21548 + 1.21548i −0.246277 + 0.969200i \(0.579207\pi\)
−0.969200 + 0.246277i \(0.920793\pi\)
\(368\) 215126. 215126.i 0.0828083 0.0828083i
\(369\) 18766.2 + 1.56364e6i 0.00717479 + 0.597819i
\(370\) 215746. + 86530.0i 0.0819290 + 0.0328596i
\(371\) 424641.i 0.160172i
\(372\) −8637.96 1.43952e6i −0.00323634 0.539336i
\(373\) 3.09998e6 + 3.09998e6i 1.15368 + 1.15368i 0.985808 + 0.167876i \(0.0536907\pi\)
0.167876 + 0.985808i \(0.446309\pi\)
\(374\) 787555. 0.291140
\(375\) 1.14141e6 + 2.47244e6i 0.419143 + 0.907920i
\(376\) 164064. 0.0598472
\(377\) 2.61106e6 + 2.61106e6i 0.946159 + 0.946159i
\(378\) −75549.6 + 1360.16i −0.0271958 + 0.000489620i
\(379\) 3.76652e6i 1.34692i −0.739224 0.673460i \(-0.764807\pi\)
0.739224 0.673460i \(-0.235193\pi\)
\(380\) 3.16785e6 + 1.27054e6i 1.12540 + 0.451368i
\(381\) 1.09288e6 1.10607e6i 0.385709 0.390366i
\(382\) −491993. + 491993.i −0.172505 + 0.172505i
\(383\) 1.03003e6 1.03003e6i 0.358802 0.358802i −0.504569 0.863371i \(-0.668349\pi\)
0.863371 + 0.504569i \(0.168349\pi\)
\(384\) −1.57701e6 + 1.59605e6i −0.545767 + 0.552356i
\(385\) −126694. 296377.i −0.0435617 0.101904i
\(386\) 263984.i 0.0901800i
\(387\) −2.38987e6 2.33318e6i −0.811141 0.791902i
\(388\) 1.00925e6 + 1.00925e6i 0.340345 + 0.340345i
\(389\) −2.93288e6 −0.982698 −0.491349 0.870963i \(-0.663496\pi\)
−0.491349 + 0.870963i \(0.663496\pi\)
\(390\) 208050. 527879.i 0.0692639 0.175741i
\(391\) 609923. 0.201759
\(392\) −909416. 909416.i −0.298915 0.298915i
\(393\) −29260.5 4.87627e6i −0.00955653 1.59260i
\(394\) 417079.i 0.135356i
\(395\) −622183. + 1.55129e6i −0.200644 + 0.500266i
\(396\) −2.66128e6 + 31939.7i −0.852812 + 0.0102351i
\(397\) 2.33959e6 2.33959e6i 0.745013 0.745013i −0.228525 0.973538i \(-0.573390\pi\)
0.973538 + 0.228525i \(0.0733902\pi\)
\(398\) −529977. + 529977.i −0.167706 + 0.167706i
\(399\) −356415. 352163.i −0.112079 0.110742i
\(400\) −1.98279e6 1.89539e6i −0.619623 0.592309i
\(401\) 3.56068e6i 1.10579i 0.833251 + 0.552895i \(0.186477\pi\)
−0.833251 + 0.552895i \(0.813523\pi\)
\(402\) 1.11188e6 6671.95i 0.343158 0.00205915i
\(403\) −1.12207e6 1.12207e6i −0.344158 0.344158i
\(404\) −418367. −0.127528
\(405\) −3.09232e6 1.15489e6i −0.936799 0.349868i
\(406\) 140767. 0.0423824
\(407\) −849888. 849888.i −0.254317 0.254317i
\(408\) −2.13164e6 + 12791.1i −0.633964 + 0.00380416i
\(409\) 2.99031e6i 0.883910i −0.897037 0.441955i \(-0.854285\pi\)
0.897037 0.441955i \(-0.145715\pi\)
\(410\) −411602. + 175950.i −0.120925 + 0.0516927i
\(411\) 692374. + 684114.i 0.202179 + 0.199767i
\(412\) −1.38298e6 + 1.38298e6i −0.401397 + 0.401397i
\(413\) 240831. 240831.i 0.0694764 0.0694764i
\(414\) 104796. 1257.72i 0.0300500 0.000360648i
\(415\) −2.22943e6 + 953029.i −0.635439 + 0.271635i
\(416\) 1.87275e6i 0.530575i
\(417\) −970.757 161777.i −0.000273382 0.0455592i
\(418\) 634519. + 634519.i 0.177625 + 0.177625i
\(419\) 552976. 0.153876 0.0769381 0.997036i \(-0.475486\pi\)
0.0769381 + 0.997036i \(0.475486\pi\)
\(420\) 169555. + 390148.i 0.0469016 + 0.107921i
\(421\) 5.56113e6 1.52918 0.764588 0.644519i \(-0.222942\pi\)
0.764588 + 0.644519i \(0.222942\pi\)
\(422\) 796441. + 796441.i 0.217707 + 0.217707i
\(423\) −367092. 358385.i −0.0997526 0.0973866i
\(424\) 2.05846e6i 0.556069i
\(425\) −123907. 5.49769e6i −0.0332754 1.47641i
\(426\) 115199. 116590.i 0.0307556 0.0311270i
\(427\) 7841.31 7841.31i 0.00208122 0.00208122i
\(428\) −1.43832e6 + 1.43832e6i −0.379530 + 0.379530i
\(429\) −2.06204e6 + 2.08693e6i −0.540945 + 0.547477i
\(430\) 355900. 887366.i 0.0928231 0.231436i
\(431\) 3.18200e6i 0.825100i −0.910935 0.412550i \(-0.864638\pi\)
0.910935 0.412550i \(-0.135362\pi\)
\(432\) 3.32439e6 59850.7i 0.857044 0.0154298i
\(433\) −506874. 506874.i −0.129921 0.129921i 0.639156 0.769077i \(-0.279284\pi\)
−0.769077 + 0.639156i \(0.779284\pi\)
\(434\) −60492.9 −0.0154163
\(435\) 5.72113e6 + 2.25484e6i 1.44963 + 0.571337i
\(436\) −1.75885e6 −0.443111
\(437\) 491404. + 491404.i 0.123094 + 0.123094i
\(438\) −1918.93 319791.i −0.000477941 0.0796491i
\(439\) 4.28320e6i 1.06074i 0.847767 + 0.530368i \(0.177946\pi\)
−0.847767 + 0.530368i \(0.822054\pi\)
\(440\) −614154. 1.43670e6i −0.151233 0.353780i
\(441\) 48262.8 + 4.02136e6i 0.0118172 + 0.984638i
\(442\) −810188. + 810188.i −0.197256 + 0.197256i
\(443\) 1.99417e6 1.99417e6i 0.482784 0.482784i −0.423235 0.906020i \(-0.639106\pi\)
0.906020 + 0.423235i \(0.139106\pi\)
\(444\) 1.12839e6 + 1.11493e6i 0.271646 + 0.268406i
\(445\) −5.50109e6 2.20634e6i −1.31689 0.528169i
\(446\) 572435.i 0.136266i
\(447\) 5.57632e6 33461.2i 1.32002 0.00792087i
\(448\) −267913. 267913.i −0.0630666 0.0630666i
\(449\) −524045. −0.122674 −0.0613370 0.998117i \(-0.519536\pi\)
−0.0613370 + 0.998117i \(0.519536\pi\)
\(450\) −32626.3 944349.i −0.00759515 0.219837i
\(451\) 2.31455e6 0.535827
\(452\) 4.14691e6 + 4.14691e6i 0.954725 + 0.954725i
\(453\) −2.82198e6 + 16933.5i −0.646113 + 0.00387706i
\(454\) 126349.i 0.0287694i
\(455\) 435229. + 174559.i 0.0985574 + 0.0395288i
\(456\) −1.72773e6 1.70712e6i −0.389103 0.384461i
\(457\) −782574. + 782574.i −0.175281 + 0.175281i −0.789295 0.614014i \(-0.789554\pi\)
0.614014 + 0.789295i \(0.289554\pi\)
\(458\) 245200. 245200.i 0.0546206 0.0546206i
\(459\) 4.79749e6 + 4.62780e6i 1.06287 + 1.02528i
\(460\) −231920. 542534.i −0.0511027 0.119545i
\(461\) 1.72240e6i 0.377469i −0.982028 0.188734i \(-0.939562\pi\)
0.982028 0.188734i \(-0.0604385\pi\)
\(462\) 671.100 + 111839.i 0.000146279 + 0.0243775i
\(463\) 4.87630e6 + 4.87630e6i 1.05715 + 1.05715i 0.998265 + 0.0588893i \(0.0187559\pi\)
0.0588893 + 0.998265i \(0.481244\pi\)
\(464\) −6.19414e6 −1.33563
\(465\) −2.45859e6 968990.i −0.527294 0.207820i
\(466\) 126068. 0.0268931
\(467\) −5.35029e6 5.35029e6i −1.13523 1.13523i −0.989294 0.145940i \(-0.953380\pi\)
−0.145940 0.989294i \(-0.546620\pi\)
\(468\) 2.70490e6 2.77062e6i 0.570870 0.584739i
\(469\) 918938.i 0.192910i
\(470\) 54667.5 136303.i 0.0114152 0.0284616i
\(471\) −2.94635e6 + 2.98193e6i −0.611973 + 0.619362i
\(472\) 1.16744e6 1.16744e6i 0.241201 0.241201i
\(473\) −3.49561e6 + 3.49561e6i −0.718406 + 0.718406i
\(474\) 407624. 412546.i 0.0833325 0.0843386i
\(475\) 4.32956e6 4.52922e6i 0.880460 0.921063i
\(476\) 859031.i 0.173777i
\(477\) 4.49656e6 4.60581e6i 0.904867 0.926850i
\(478\) −950808. 950808.i −0.190337 0.190337i
\(479\) −2.68281e6 −0.534257 −0.267129 0.963661i \(-0.586075\pi\)
−0.267129 + 0.963661i \(0.586075\pi\)
\(480\) 1.24308e6 + 2.86033e6i 0.246260 + 0.566648i
\(481\) 1.74862e6 0.344615
\(482\) 301242. + 301242.i 0.0590606 + 0.0590606i
\(483\) 519.735 + 86614.0i 0.000101371 + 0.0168935i
\(484\) 964947.i 0.187236i
\(485\) 2.40926e6 1.02990e6i 0.465082 0.198812i
\(486\) 833840. + 785248.i 0.160137 + 0.150805i
\(487\) −4.62946e6 + 4.62946e6i −0.884521 + 0.884521i −0.993990 0.109469i \(-0.965085\pi\)
0.109469 + 0.993990i \(0.465085\pi\)
\(488\) 38011.0 38011.0i 0.00722537 0.00722537i
\(489\) −5.94817e6 5.87721e6i −1.12489 1.11147i
\(490\) −1.05856e6 + 452508.i −0.199170 + 0.0851405i
\(491\) 5.60483e6i 1.04920i 0.851349 + 0.524600i \(0.175785\pi\)
−0.851349 + 0.524600i \(0.824215\pi\)
\(492\) −3.05469e6 + 18329.9i −0.568924 + 0.00341388i
\(493\) −8.78078e6 8.78078e6i −1.62710 1.62710i
\(494\) −1.30551e6 −0.240692
\(495\) −1.76419e6 + 4.55618e6i −0.323618 + 0.835772i
\(496\) 2.66186e6 0.485826
\(497\) 95783.3 + 95783.3i 0.0173940 + 0.0173940i
\(498\) 841286. 5048.21i 0.152009 0.000912146i
\(499\) 4.52825e6i 0.814103i −0.913405 0.407052i \(-0.866557\pi\)
0.913405 0.407052i \(-0.133443\pi\)
\(500\) −4.84314e6 + 2.20069e6i −0.866367 + 0.393671i
\(501\) −3.32650e6 3.28681e6i −0.592097 0.585033i
\(502\) 172270. 172270.i 0.0305105 0.0305105i
\(503\) 6.67659e6 6.67659e6i 1.17662 1.17662i 0.196015 0.980601i \(-0.437200\pi\)
0.980601 0.196015i \(-0.0628001\pi\)
\(504\) −3632.88 302700.i −0.000637052 0.0530806i
\(505\) −285895. + 712824.i −0.0498859 + 0.124381i
\(506\) 155123.i 0.0269339i
\(507\) 9118.35 + 1.51958e6i 0.00157542 + 0.262544i
\(508\) 2.14784e6 + 2.14784e6i 0.369269 + 0.369269i
\(509\) 5.52619e6 0.945434 0.472717 0.881214i \(-0.343273\pi\)
0.472717 + 0.881214i \(0.343273\pi\)
\(510\) −699655. + 1.77521e6i −0.119113 + 0.302221i
\(511\) 264298. 0.0447756
\(512\) −3.76477e6 3.76477e6i −0.634692 0.634692i
\(513\) 136715. + 7.59378e6i 0.0229362 + 1.27399i
\(514\) 1.08087e6i 0.180454i
\(515\) 1.41129e6 + 3.30144e6i 0.234475 + 0.548510i
\(516\) 4.58574e6 4.64111e6i 0.758203 0.767357i
\(517\) −536938. + 536938.i −0.0883483 + 0.0883483i
\(518\) 47135.7 47135.7i 0.00771836 0.00771836i
\(519\) 816791. 826653.i 0.133104 0.134712i
\(520\) 2.10979e6 + 846182.i 0.342161 + 0.137232i
\(521\) 619733.i 0.100025i 0.998749 + 0.0500127i \(0.0159262\pi\)
−0.998749 + 0.0500127i \(0.984074\pi\)
\(522\) −1.52681e6 1.49059e6i −0.245249 0.239432i
\(523\) 6.44079e6 + 6.44079e6i 1.02964 + 1.02964i 0.999547 + 0.0300909i \(0.00957968\pi\)
0.0300909 + 0.999547i \(0.490420\pi\)
\(524\) 9.52584e6 1.51557
\(525\) 780610. 22280.5i 0.123605 0.00352799i
\(526\) 701596. 0.110566
\(527\) 3.77343e6 + 3.77343e6i 0.591848 + 0.591848i
\(528\) −29530.3 4.92124e6i −0.00460981 0.768227i
\(529\) 6.31621e6i 0.981335i
\(530\) 1.71015e6 + 685897.i 0.264451 + 0.106064i
\(531\) −5.16232e6 + 61956.1i −0.794527 + 0.00953560i
\(532\) 692106. 692106.i 0.106021 0.106021i
\(533\) −2.38106e6 + 2.38106e6i −0.363039 + 0.363039i
\(534\) 1.46294e6 + 1.44549e6i 0.222011 + 0.219362i
\(535\) 1.46775e6 + 3.43353e6i 0.221701 + 0.518629i
\(536\) 4.45459e6i 0.669723i
\(537\) −8.17435e6 + 49050.9i −1.22326 + 0.00734026i
\(538\) 1.13733e6 + 1.13733e6i 0.169408 + 0.169408i
\(539\) 5.95256e6 0.882534
\(540\) 2.29226e6 6.02711e6i 0.338282 0.889457i
\(541\) −8.91778e6 −1.30998 −0.654988 0.755639i \(-0.727326\pi\)
−0.654988 + 0.755639i \(0.727326\pi\)
\(542\) 691237. + 691237.i 0.101072 + 0.101072i
\(543\) −2.55631e6 + 15339.4i −0.372062 + 0.00223259i
\(544\) 6.29790e6i 0.912428i
\(545\) −1.20193e6 + 2.99677e6i −0.173335 + 0.432178i
\(546\) −115743. 114363.i −0.0166156 0.0164173i
\(547\) −4.50080e6 + 4.50080e6i −0.643164 + 0.643164i −0.951332 0.308168i \(-0.900284\pi\)
0.308168 + 0.951332i \(0.400284\pi\)
\(548\) −1.34449e6 + 1.34449e6i −0.191252 + 0.191252i
\(549\) −168082. + 2017.25i −0.0238007 + 0.000285647i
\(550\) −1.39824e6 + 31513.5i −0.197094 + 0.00444211i
\(551\) 1.41490e7i 1.98540i
\(552\) 2519.43 + 419865.i 0.000351929 + 0.0586491i
\(553\) 338923. + 338923.i 0.0471290 + 0.0471290i
\(554\) −2.73195e6 −0.378180
\(555\) 2.67075e6 1.16068e6i 0.368044 0.159949i
\(556\) 316033. 0.0433556
\(557\) 6.79813e6 + 6.79813e6i 0.928435 + 0.928435i 0.997605 0.0691698i \(-0.0220350\pi\)
−0.0691698 + 0.997605i \(0.522035\pi\)
\(558\) 656126. + 640564.i 0.0892076 + 0.0870917i
\(559\) 7.19213e6i 0.973482i
\(560\) −723290. + 309189.i −0.0974636 + 0.0416634i
\(561\) 6.93445e6 7.01818e6i 0.930261 0.941493i
\(562\) 1.09911e6 1.09911e6i 0.146792 0.146792i
\(563\) −9.18684e6 + 9.18684e6i −1.22150 + 1.22150i −0.254408 + 0.967097i \(0.581880\pi\)
−0.967097 + 0.254408i \(0.918120\pi\)
\(564\) 704387. 712891.i 0.0932424 0.0943682i
\(565\) 9.89942e6 4.23177e6i 1.30463 0.557700i
\(566\) 992593.i 0.130236i
\(567\) −653096. + 685225.i −0.0853138 + 0.0895108i
\(568\) 464313. + 464313.i 0.0603866 + 0.0603866i
\(569\) 3.22815e6 0.417996 0.208998 0.977916i \(-0.432980\pi\)
0.208998 + 0.977916i \(0.432980\pi\)
\(570\) −1.99395e6 + 866556.i −0.257056 + 0.111714i
\(571\) −9.43358e6 −1.21084 −0.605420 0.795907i \(-0.706995\pi\)
−0.605420 + 0.795907i \(0.706995\pi\)
\(572\) −4.05253e6 4.05253e6i −0.517888 0.517888i
\(573\) 52303.2 + 8.71634e6i 0.00665490 + 1.10904i
\(574\) 128367.i 0.0162620i
\(575\) −1.08287e6 + 24405.7i −0.136586 + 0.00307837i
\(576\) 68923.3 + 5.74284e6i 0.00865585 + 0.721224i
\(577\) 9.98594e6 9.98594e6i 1.24868 1.24868i 0.292370 0.956305i \(-0.405556\pi\)
0.956305 0.292370i \(-0.0944438\pi\)
\(578\) 1.47529e6 1.47529e6i 0.183679 0.183679i
\(579\) −2.35246e6 2.32439e6i −0.291625 0.288146i
\(580\) −4.47175e6 + 1.11494e7i −0.551960 + 1.37621i
\(581\) 695298.i 0.0854537i
\(582\) −909146. + 5455.41i −0.111257 + 0.000667606i
\(583\) −6.73682e6 6.73682e6i −0.820887 0.820887i
\(584\) 1.28119e6 0.155447
\(585\) −2.87222e6 6.50200e6i −0.346999 0.785521i
\(586\) −3.47193e6 −0.417663
\(587\) −1.08667e7 1.08667e7i −1.30168 1.30168i −0.927260 0.374419i \(-0.877842\pi\)
−0.374419 0.927260i \(-0.622158\pi\)
\(588\) −7.85605e6 + 47140.9i −0.937046 + 0.00562283i
\(589\) 6.08037e6i 0.722174i
\(590\) −580896. 1.35890e6i −0.0687018 0.160715i
\(591\) 3.71673e6 + 3.67239e6i 0.437716 + 0.432494i
\(592\) −2.07410e6 + 2.07410e6i −0.243235 + 0.243235i
\(593\) 6.83953e6 6.83953e6i 0.798710 0.798710i −0.184182 0.982892i \(-0.558964\pi\)
0.982892 + 0.184182i \(0.0589636\pi\)
\(594\) 1.17699e6 1.22015e6i 0.136870 0.141889i
\(595\) −1.46364e6 587027.i −0.169489 0.0679775i
\(596\) 1.08934e7i 1.25617i
\(597\) 56341.2 + 9.38928e6i 0.00646979 + 1.07819i
\(598\) 159581. + 159581.i 0.0182485 + 0.0182485i
\(599\) −1.22951e7 −1.40012 −0.700060 0.714084i \(-0.746844\pi\)
−0.700060 + 0.714084i \(0.746844\pi\)
\(600\) 3.78404e6 108006.i 0.429119 0.0122481i
\(601\) 5.35161e6 0.604364 0.302182 0.953250i \(-0.402285\pi\)
0.302182 + 0.953250i \(0.402285\pi\)
\(602\) −193870. 193870.i −0.0218032 0.0218032i
\(603\) 9.73071e6 9.96711e6i 1.08981 1.11629i
\(604\) 5.51276e6i 0.614861i
\(605\) −1.64410e6 659405.i −0.182616 0.0732426i
\(606\) 187305. 189566.i 0.0207189 0.0209691i
\(607\) 1.03013e7 1.03013e7i 1.13480 1.13480i 0.145433 0.989368i \(-0.453542\pi\)
0.989368 0.145433i \(-0.0464576\pi\)
\(608\) 5.07411e6 5.07411e6i 0.556674 0.556674i
\(609\) 1.23946e6 1.25442e6i 0.135422 0.137057i
\(610\) −18913.6 44244.8i −0.00205802 0.00481435i
\(611\) 1.10474e6i 0.119717i
\(612\) −9.09636e6 + 9.31735e6i −0.981723 + 1.00557i
\(613\) 4.89015e6 + 4.89015e6i 0.525619 + 0.525619i 0.919263 0.393644i \(-0.128786\pi\)
−0.393644 + 0.919263i \(0.628786\pi\)
\(614\) −1.25303e6 −0.134134
\(615\) −2.05622e6 + 5.21717e6i −0.219221 + 0.556221i
\(616\) −448066. −0.0475763
\(617\) 833237. + 833237.i 0.0881162 + 0.0881162i 0.749791 0.661675i \(-0.230154\pi\)
−0.661675 + 0.749791i \(0.730154\pi\)
\(618\) −7475.60 1.24581e6i −0.000787363 0.131214i
\(619\) 1.53788e7i 1.61323i 0.591076 + 0.806616i \(0.298703\pi\)
−0.591076 + 0.806616i \(0.701297\pi\)
\(620\) 1.92168e6 4.79134e6i 0.200772 0.500585i
\(621\) 911525. 944948.i 0.0948505 0.0983284i
\(622\) −705358. + 705358.i −0.0731027 + 0.0731027i
\(623\) −1.20187e6 + 1.20187e6i −0.124061 + 0.124061i
\(624\) 5.09304e6 + 5.03228e6i 0.523619 + 0.517373i
\(625\) 439972. + 9.75571e6i 0.0450532 + 0.998985i
\(626\) 2.39999e6i 0.244779i
\(627\) 1.12414e7 67454.9i 1.14196 0.00685243i
\(628\) −5.79047e6 5.79047e6i −0.585888 0.585888i
\(629\) −5.88047e6 −0.592632
\(630\) −252690. 97843.9i −0.0253651 0.00982160i
\(631\) 6.50224e6 0.650114 0.325057 0.945694i \(-0.394617\pi\)
0.325057 + 0.945694i \(0.394617\pi\)
\(632\) 1.64294e6 + 1.64294e6i 0.163618 + 0.163618i
\(633\) 1.41101e7 84668.6i 1.39965 0.00839872i
\(634\) 2.54372e6i 0.251331i
\(635\) 5.12728e6 2.19179e6i 0.504606 0.215707i
\(636\) 8.94445e6 + 8.83775e6i 0.876821 + 0.866361i
\(637\) −6.12362e6 + 6.12362e6i −0.597943 + 0.597943i
\(638\) −2.23323e6 + 2.23323e6i −0.217211 + 0.217211i
\(639\) −24641.2 2.05316e6i −0.00238731 0.198916i
\(640\) −7.39861e6 + 3.16273e6i −0.714003 + 0.305219i
\(641\) 3.82299e6i 0.367501i −0.982973 0.183750i \(-0.941176\pi\)
0.982973 0.183750i \(-0.0588238\pi\)
\(642\) −7774.71 1.29566e6i −0.000744469 0.124066i
\(643\) −7.11939e6 7.11939e6i −0.679071 0.679071i 0.280719 0.959790i \(-0.409427\pi\)
−0.959790 + 0.280719i \(0.909427\pi\)
\(644\) −169201. −0.0160764
\(645\) −4.77392e6 1.09848e7i −0.451831 1.03967i
\(646\) 4.39031e6 0.413917
\(647\) 6.21104e6 + 6.21104e6i 0.583316 + 0.583316i 0.935813 0.352497i \(-0.114667\pi\)
−0.352497 + 0.935813i \(0.614667\pi\)
\(648\) −3.16591e6 + 3.32165e6i −0.296184 + 0.310754i
\(649\) 7.64144e6i 0.712137i
\(650\) 1.40600e6 1.47084e6i 0.130527 0.136547i
\(651\) −532642. + 539073.i −0.0492587 + 0.0498534i
\(652\) 1.15505e7 1.15505e7i 1.06410 1.06410i
\(653\) −752240. + 752240.i −0.0690356 + 0.0690356i −0.740782 0.671746i \(-0.765545\pi\)
0.671746 + 0.740782i \(0.265545\pi\)
\(654\) 787445. 796952.i 0.0719906 0.0728598i
\(655\) 6.50957e6 1.62303e7i 0.592855 1.47817i
\(656\) 5.64852e6i 0.512478i
\(657\) −2.86666e6 2.79867e6i −0.259097 0.252952i
\(658\) −29779.1 29779.1i −0.00268131 0.00268131i
\(659\) −1.49063e7 −1.33707 −0.668536 0.743679i \(-0.733079\pi\)
−0.668536 + 0.743679i \(0.733079\pi\)
\(660\) −8.87954e6 3.49965e6i −0.793470 0.312726i
\(661\) −1.55144e7 −1.38112 −0.690558 0.723277i \(-0.742635\pi\)
−0.690558 + 0.723277i \(0.742635\pi\)
\(662\) 147463. + 147463.i 0.0130779 + 0.0130779i
\(663\) 86130.0 + 1.43536e7i 0.00760976 + 1.26817i
\(664\) 3.37048e6i 0.296669i
\(665\) −706269. 1.65218e6i −0.0619321 0.144878i
\(666\) −1.01037e6 + 12126.1i −0.0882666 + 0.00105934i
\(667\) −1.72953e6 + 1.72953e6i −0.150526 + 0.150526i
\(668\) 6.45958e6 6.45958e6i 0.560097 0.560097i
\(669\) −5.10116e6 5.04031e6i −0.440660 0.435403i
\(670\) 3.70082e6 + 1.48430e6i 0.318501 + 0.127743i
\(671\) 248800.i 0.0213326i
\(672\) 894352. 5366.64i 0.0763986 0.000458437i
\(673\) −9.88243e6 9.88243e6i −0.841058 0.841058i 0.147938 0.988997i \(-0.452736\pi\)
−0.988997 + 0.147938i \(0.952736\pi\)
\(674\) 1.01836e6 0.0863475
\(675\) −8.70270e6 8.02428e6i −0.735181 0.677871i
\(676\) −2.96851e6 −0.249845
\(677\) 9.07764e6 + 9.07764e6i 0.761204 + 0.761204i 0.976540 0.215336i \(-0.0690847\pi\)
−0.215336 + 0.976540i \(0.569085\pi\)
\(678\) −3.73559e6 + 22415.7i −0.312094 + 0.00187274i
\(679\) 751382.i 0.0625441i
\(680\) −7.09503e6 2.84563e6i −0.588413 0.235997i
\(681\) −1.12594e6 1.11250e6i −0.0930349 0.0919250i
\(682\) 959702. 959702.i 0.0790088 0.0790088i
\(683\) −1.17688e7 + 1.17688e7i −0.965341 + 0.965341i −0.999419 0.0340786i \(-0.989150\pi\)
0.0340786 + 0.999419i \(0.489150\pi\)
\(684\) −1.48356e7 + 178051.i −1.21245 + 0.0145514i
\(685\) 1.37200e6 + 3.20954e6i 0.111719 + 0.261347i
\(686\) 665396.i 0.0539846i
\(687\) −26066.9 4.34405e6i −0.00210716 0.351159i
\(688\) 8.53083e6 + 8.53083e6i 0.687100 + 0.687100i
\(689\) 1.38608e7 1.11235
\(690\) 349659. + 137809.i 0.0279590 + 0.0110193i
\(691\) 1.13832e7 0.906920 0.453460 0.891277i \(-0.350189\pi\)
0.453460 + 0.891277i \(0.350189\pi\)
\(692\) 1.60524e6 + 1.60524e6i 0.127431 + 0.127431i
\(693\) 1.00255e6 + 978767.i 0.0792996 + 0.0774188i
\(694\) 97533.0i 0.00768693i
\(695\) 215964. 538463.i 0.0169597 0.0422858i
\(696\) 6.00832e6 6.08086e6i 0.470143 0.475819i
\(697\) 8.00730e6 8.00730e6i 0.624316 0.624316i
\(698\) 1.02754e6 1.02754e6i 0.0798290 0.0798290i
\(699\) 1.11004e6 1.12344e6i 0.0859300 0.0869674i
\(700\) 34373.5 + 1.52514e6i 0.00265142 + 0.117642i
\(701\) 1.43910e7i 1.10611i 0.833146 + 0.553053i \(0.186537\pi\)
−0.833146 + 0.553053i \(0.813463\pi\)
\(702\) 44397.2 + 2.46604e6i 0.00340027 + 0.188867i
\(703\) −4.73779e6 4.73779e6i −0.361566 0.361566i
\(704\) 8.50074e6 0.646436
\(705\) −733291. 1.68731e6i −0.0555653 0.127856i
\(706\) −400530. −0.0302429
\(707\) 155736. + 155736.i 0.0117177 + 0.0117177i
\(708\) −60515.9 1.00850e7i −0.00453719 0.756123i
\(709\) 3.32746e6i 0.248598i 0.992245 + 0.124299i \(0.0396681\pi\)
−0.992245 + 0.124299i \(0.960332\pi\)
\(710\) 540460. 231034.i 0.0402362 0.0172000i
\(711\) −87191.2 7.26496e6i −0.00646843 0.538963i
\(712\) −5.82609e6 + 5.82609e6i −0.430703 + 0.430703i
\(713\) 743243. 743243.i 0.0547529 0.0547529i
\(714\) 389235. + 384592.i 0.0285737 + 0.0282328i
\(715\) −9.67412e6 + 4.13546e6i −0.707695 + 0.302523i
\(716\) 1.59687e7i 1.16409i
\(717\) −1.68449e7 + 101079.i −1.22369 + 0.00734283i
\(718\) −2.66746e6 2.66746e6i −0.193102 0.193102i
\(719\) 4.31981e6 0.311632 0.155816 0.987786i \(-0.450199\pi\)
0.155816 + 0.987786i \(0.450199\pi\)
\(720\) 1.11191e7 + 4.30540e6i 0.799351 + 0.309516i
\(721\) 1.02963e6 0.0737635
\(722\) 1.35854e6 + 1.35854e6i 0.0969903 + 0.0969903i
\(723\) 5.33692e6 32024.6i 0.379704 0.00227845i
\(724\) 4.99378e6i 0.354065i
\(725\) 1.59409e7 + 1.52381e7i 1.12633 + 1.07668i
\(726\) 437226. + 432011.i 0.0307868 + 0.0304195i
\(727\) −1.03718e7 + 1.03718e7i −0.727811 + 0.727811i −0.970183 0.242373i \(-0.922074\pi\)
0.242373 + 0.970183i \(0.422074\pi\)
\(728\) 460943. 460943.i 0.0322343 0.0322343i
\(729\) 1.43396e7 516494.i 0.999352 0.0359953i
\(730\) 426904. 1.06440e6i 0.0296499 0.0739262i
\(731\) 2.41865e7i 1.67409i
\(732\) −1970.36 328361.i −0.000135915 0.0226503i
\(733\) 6.93586e6 + 6.93586e6i 0.476804 + 0.476804i 0.904108 0.427304i \(-0.140537\pi\)
−0.427304 + 0.904108i \(0.640537\pi\)
\(734\) 5.51902e6 0.378113
\(735\) −5.28818e6 + 1.34175e7i −0.361067 + 0.916124i
\(736\) −1.24048e6 −0.0844104
\(737\) −1.45787e7 1.45787e7i −0.988666 0.988666i
\(738\) 1.35929e6 1.39231e6i 0.0918695 0.0941015i
\(739\) 5.27869e6i 0.355562i −0.984070 0.177781i \(-0.943108\pi\)
0.984070 0.177781i \(-0.0568919\pi\)
\(740\) 2.23602e6 + 5.23074e6i 0.150105 + 0.351143i
\(741\) −1.14950e7 + 1.16338e7i −0.769068 + 0.778354i
\(742\) 373631. 373631.i 0.0249134 0.0249134i
\(743\) 1.42934e7 1.42934e7i 0.949871 0.949871i −0.0489311 0.998802i \(-0.515581\pi\)
0.998802 + 0.0489311i \(0.0155815\pi\)
\(744\) −2.58200e6 + 2.61318e6i −0.171011 + 0.173076i
\(745\) 1.85604e7 + 7.44410e6i 1.22517 + 0.491384i
\(746\) 5.45518e6i 0.358891i
\(747\) 7.36257e6 7.54144e6i 0.482756 0.494485i
\(748\) 1.36283e7 + 1.36283e7i 0.890610 + 0.890610i
\(749\) 1.07082e6 0.0697450
\(750\) 1.17114e6 3.17973e6i 0.0760250 0.206413i
\(751\) −4.87198e6 −0.315214 −0.157607 0.987502i \(-0.550378\pi\)
−0.157607 + 0.987502i \(0.550378\pi\)
\(752\) 1.31037e6 + 1.31037e6i 0.0844983 + 0.0844983i
\(753\) −18313.8 3.05200e6i −0.00117704 0.196154i
\(754\) 4.59481e6i 0.294333i
\(755\) −9.39277e6 3.76719e6i −0.599689 0.240520i
\(756\) −1.33089e6 1.28382e6i −0.0846910 0.0816955i
\(757\) −4.56529e6 + 4.56529e6i −0.289554 + 0.289554i −0.836904 0.547350i \(-0.815637\pi\)
0.547350 + 0.836904i \(0.315637\pi\)
\(758\) −3.31406e6 + 3.31406e6i −0.209501 + 0.209501i
\(759\) −1.38235e6 1.36586e6i −0.0870992 0.0860601i
\(760\) −3.42367e6 8.00902e6i −0.215009 0.502974i
\(761\) 2.03979e7i 1.27680i −0.769703 0.638402i \(-0.779596\pi\)
0.769703 0.638402i \(-0.220404\pi\)
\(762\) −1.93480e6 + 11609.9i −0.120712 + 0.000724341i
\(763\) 654729. + 654729.i 0.0407146 + 0.0407146i
\(764\) −1.70275e7 −1.05540
\(765\) 9.65903e6 + 2.18657e7i 0.596733 + 1.35086i
\(766\) −1.81260e6 −0.111617
\(767\) −7.86103e6 7.86103e6i −0.482493 0.482493i
\(768\) −8.99764e6 + 53991.2i −0.550460 + 0.00330308i
\(769\) 2.14987e7i 1.31098i −0.755203 0.655490i \(-0.772462\pi\)
0.755203 0.655490i \(-0.227538\pi\)
\(770\) −149299. + 372249.i −0.00907468 + 0.0226259i
\(771\) −9.63204e6 9.51713e6i −0.583555 0.576594i
\(772\) 4.56813e6 4.56813e6i 0.275864 0.275864i
\(773\) −1.03836e7 + 1.03836e7i −0.625029 + 0.625029i −0.946813 0.321784i \(-0.895718\pi\)
0.321784 + 0.946813i \(0.395718\pi\)
\(774\) 49874.9 + 4.15569e6i 0.00299247 + 0.249339i
\(775\) −6.85039e6 6.54841e6i −0.409695 0.391635i
\(776\) 3.64236e6i 0.217134i
\(777\) −5010.93 835074.i −0.000297760 0.0496218i
\(778\) 2.58056e6 + 2.58056e6i 0.152850 + 0.152850i
\(779\) 1.29027e7 0.761792
\(780\) 1.27349e7 5.53450e6i 0.749480 0.325718i
\(781\) −3.03915e6 −0.178289
\(782\) −536655. 536655.i −0.0313818 0.0313818i
\(783\) −2.67268e7 + 481175.i −1.55791 + 0.0280478i
\(784\) 1.45269e7i 0.844076i
\(785\) −1.38229e7 + 5.90896e6i −0.800618 + 0.342245i
\(786\) −4.26475e6 + 4.31625e6i −0.246228 + 0.249201i
\(787\) −6.79785e6 + 6.79785e6i −0.391232 + 0.391232i −0.875126 0.483894i \(-0.839222\pi\)
0.483894 + 0.875126i \(0.339222\pi\)
\(788\) −7.21736e6 + 7.21736e6i −0.414060 + 0.414060i
\(789\) 6.17758e6 6.25216e6i 0.353285 0.357551i
\(790\) 1.91238e6 817498.i 0.109020 0.0466035i
\(791\) 3.08735e6i 0.175447i
\(792\) 4.85988e6 + 4.74461e6i 0.275304 + 0.268774i
\(793\) −255950. 255950.i −0.0144535 0.0144535i
\(794\) −4.11709e6 −0.231760
\(795\) 2.11702e7 9.20040e6i 1.18798 0.516284i
\(796\) −1.83420e7 −1.02604
\(797\) −1.32048e7 1.32048e7i −0.736354 0.736354i 0.235516 0.971870i \(-0.424322\pi\)
−0.971870 + 0.235516i \(0.924322\pi\)
\(798\) 3741.12 + 623458.i 0.000207967 + 0.0346577i
\(799\) 3.71513e6i 0.205877i
\(800\) 252006. + 1.11814e7i 0.0139215 + 0.617690i
\(801\) 2.57625e7 309192.i 1.41875 0.0170273i
\(802\) 3.13295e6 3.13295e6i 0.171996 0.171996i
\(803\) −4.19301e6 + 4.19301e6i −0.229476 + 0.229476i
\(804\) 1.93561e7 + 1.91252e7i 1.05603 + 1.04343i
\(805\) −115625. + 288289.i −0.00628872 + 0.0156797i
\(806\) 1.97456e6i 0.107062i
\(807\) 2.01495e7 120909.i 1.08913 0.00653542i
\(808\) 754938. + 754938.i 0.0406802 + 0.0406802i
\(809\) −9.33642e6 −0.501544 −0.250772 0.968046i \(-0.580684\pi\)
−0.250772 + 0.968046i \(0.580684\pi\)
\(810\) 1.70469e6 + 3.73701e6i 0.0912920 + 0.200130i
\(811\) 2.41694e7 1.29037 0.645184 0.764028i \(-0.276781\pi\)
0.645184 + 0.764028i \(0.276781\pi\)
\(812\) 2.43591e6 + 2.43591e6i 0.129650 + 0.129650i
\(813\) 1.22462e7 73484.6i 0.649794 0.00389915i
\(814\) 1.49559e6i 0.0791136i
\(815\) −1.17868e7 2.75731e7i −0.621589 1.45409i
\(816\) −1.71274e7 1.69231e7i −0.900465 0.889723i
\(817\) −1.94866e7 + 1.94866e7i −1.02137 + 1.02137i
\(818\) −2.63109e6 + 2.63109e6i −0.137484 + 0.137484i
\(819\) −2.03825e6 + 24462.3i −0.106181 + 0.00127435i
\(820\) −1.01673e7 4.07785e6i −0.528046 0.211786i
\(821\) 2.01715e7i 1.04443i −0.852813 0.522217i \(-0.825105\pi\)
0.852813 0.522217i \(-0.174895\pi\)
\(822\) −7267.52 1.21114e6i −0.000375152 0.0625191i
\(823\) 1.86980e7 + 1.86980e7i 0.962269 + 0.962269i 0.999314 0.0370443i \(-0.0117943\pi\)
−0.0370443 + 0.999314i \(0.511794\pi\)
\(824\) 4.99115e6 0.256084
\(825\) −1.20307e7 + 1.27376e7i −0.615397 + 0.651559i
\(826\) −423802. −0.0216129
\(827\) 2.18328e7 + 2.18328e7i 1.11006 + 1.11006i 0.993142 + 0.116916i \(0.0373008\pi\)
0.116916 + 0.993142i \(0.462699\pi\)
\(828\) 1.83521e6 + 1.79169e6i 0.0930274 + 0.0908209i
\(829\) 1.09016e7i 0.550941i −0.961310 0.275470i \(-0.911166\pi\)
0.961310 0.275470i \(-0.0888336\pi\)
\(830\) 2.80016e6 + 1.12307e6i 0.141087 + 0.0565865i
\(831\) −2.40549e7 + 2.43453e7i −1.20837 + 1.22296i
\(832\) −8.74504e6 + 8.74504e6i −0.437979 + 0.437979i
\(833\) 2.05932e7 2.05932e7i 1.02828 1.02828i
\(834\) −141489. + 143197.i −0.00704381 + 0.00712886i
\(835\) −6.59176e6 1.54202e7i −0.327179 0.765373i
\(836\) 2.19601e7i 1.08672i
\(837\) 1.14855e7 206779.i 0.566678 0.0102022i
\(838\) −486549. 486549.i −0.0239341 0.0239341i
\(839\) 2.66932e7 1.30917 0.654585 0.755989i \(-0.272844\pi\)
0.654585 + 0.755989i \(0.272844\pi\)
\(840\) 398057. 1.00998e6i 0.0194647 0.0493870i
\(841\) 2.92872e7 1.42787
\(842\) −4.89309e6 4.89309e6i −0.237850 0.237850i
\(843\) −116845. 1.94723e7i −0.00566294 0.943731i
\(844\) 2.75641e7i 1.33195i
\(845\) −2.02855e6 + 5.05780e6i −0.0977338 + 0.243680i
\(846\) 7660.97 + 638329.i 0.000368008 + 0.0306633i
\(847\) −359199. + 359199.i −0.0172039 + 0.0172039i
\(848\) −1.64408e7 + 1.64408e7i −0.785115 + 0.785115i
\(849\) −8.84534e6 8.73982e6i −0.421158 0.416134i
\(850\) −4.72825e6 + 4.94629e6i −0.224467 + 0.234819i
\(851\) 1.15826e6i 0.0548255i
\(852\) 4.01100e6 24068.4i 0.189302 0.00113592i
\(853\) −1.62298e7 1.62298e7i −0.763729 0.763729i 0.213265 0.976994i \(-0.431590\pi\)
−0.976994 + 0.213265i \(0.931590\pi\)
\(854\) −13798.7 −0.000647432
\(855\) −9.83467e6 + 2.53989e7i −0.460092 + 1.18823i
\(856\) 5.19086e6 0.242133
\(857\) −1.20256e7 1.20256e7i −0.559313 0.559313i 0.369799 0.929112i \(-0.379427\pi\)
−0.929112 + 0.369799i \(0.879427\pi\)
\(858\) 3.65057e6 21905.6i 0.169294 0.00101587i
\(859\) 8.22165e6i 0.380169i 0.981768 + 0.190084i \(0.0608761\pi\)
−0.981768 + 0.190084i \(0.939124\pi\)
\(860\) 2.15142e7 9.19679e6i 0.991924 0.424024i
\(861\) 1.14392e6 + 1.13028e6i 0.0525883 + 0.0519610i
\(862\) −2.79975e6 + 2.79975e6i −0.128337 + 0.128337i
\(863\) 1.99274e7 1.99274e7i 0.910803 0.910803i −0.0855327 0.996335i \(-0.527259\pi\)
0.996335 + 0.0855327i \(0.0272592\pi\)
\(864\) −9.75728e6 9.41216e6i −0.444677 0.428948i
\(865\) 3.83200e6 1.63809e6i 0.174135 0.0744385i
\(866\) 891970.i 0.0404162i
\(867\) −156837. 2.61369e7i −0.00708598 1.18088i
\(868\) −1.04680e6 1.04680e6i −0.0471591 0.0471591i
\(869\) −1.07538e7 −0.483075
\(870\) −3.04990e6 7.01784e6i −0.136611 0.314344i
\(871\) 2.99953e7 1.33970
\(872\) 3.17382e6 + 3.17382e6i 0.141349 + 0.141349i
\(873\) −7.95645e6 + 8.14975e6i −0.353333 + 0.361917i
\(874\) 864747.i 0.0382922i
\(875\) 2.62205e6 + 983648.i 0.115777 + 0.0434330i
\(876\) 5.50063e6 5.56704e6i 0.242188 0.245112i
\(877\) 6.32074e6 6.32074e6i 0.277504 0.277504i −0.554608 0.832112i \(-0.687132\pi\)
0.832112 + 0.554608i \(0.187132\pi\)
\(878\) 3.76868e6 3.76868e6i 0.164988 0.164988i
\(879\) −3.05704e7 + 3.09395e7i −1.33453 + 1.35065i
\(880\) 6.56959e6 1.63800e7i 0.285977 0.713029i
\(881\) 3.32918e7i 1.44510i 0.691319 + 0.722550i \(0.257030\pi\)
−0.691319 + 0.722550i \(0.742970\pi\)
\(882\) 3.49583e6 3.58076e6i 0.151314 0.154990i
\(883\) −5.57402e6 5.57402e6i −0.240584 0.240584i 0.576508 0.817092i \(-0.304415\pi\)
−0.817092 + 0.576508i \(0.804415\pi\)
\(884\) −2.80399e7 −1.20683
\(885\) −1.72244e7 6.78856e6i −0.739241 0.291353i
\(886\) −3.50924e6 −0.150186
\(887\) 2.79973e7 + 2.79973e7i 1.19483 + 1.19483i 0.975693 + 0.219141i \(0.0703256\pi\)
0.219141 + 0.975693i \(0.429674\pi\)
\(888\) −24290.7 4.04805e6i −0.00103373 0.172272i
\(889\) 1.59906e6i 0.0678593i
\(890\) 2.89896e6 + 6.78156e6i 0.122678 + 0.286982i
\(891\) −509712. 2.12321e7i −0.0215095 0.895980i
\(892\) 9.90573e6 9.90573e6i 0.416845 0.416845i
\(893\) −2.99322e6 + 2.99322e6i −0.125606 + 0.125606i
\(894\) −4.93590e6 4.87701e6i −0.206549 0.204085i
\(895\) −2.72078e7 1.09123e7i −1.13536 0.455365i
\(896\) 2.30742e6i 0.0960189i
\(897\) 2.82719e6 16964.8i 0.117321 0.000703992i
\(898\) 461093. + 461093.i 0.0190809 + 0.0190809i
\(899\) −2.14002e7 −0.883119
\(900\) 1.57770e7 1.69061e7i 0.649258 0.695725i
\(901\) −4.66128e7 −1.91290
\(902\) −2.03651e6 2.03651e6i −0.0833432 0.0833432i
\(903\) −3.43468e6 + 20610.1i −0.140174 + 0.000841124i
\(904\) 1.49661e7i 0.609097i
\(905\) −8.50852e6 3.41255e6i −0.345329 0.138502i
\(906\) 2.49788e6 + 2.46809e6i 0.101100 + 0.0998941i
\(907\) −4.07896e6 + 4.07896e6i −0.164638 + 0.164638i −0.784618 0.619980i \(-0.787141\pi\)
0.619980 + 0.784618i \(0.287141\pi\)
\(908\) 2.18641e6 2.18641e6i 0.0880068 0.0880068i
\(909\) −40064.7 3.33827e6i −0.00160824 0.134002i
\(910\) −229357. 536536.i −0.00918137 0.0214781i
\(911\) 1.63280e7i 0.651833i 0.945399 + 0.325917i \(0.105673\pi\)
−0.945399 + 0.325917i \(0.894327\pi\)
\(912\) −164620. 2.74339e7i −0.00655382 1.09220i
\(913\) −1.10307e7 1.10307e7i −0.437952 0.437952i
\(914\) 1.37713e6 0.0545268
\(915\) −560815. 221031.i −0.0221446 0.00872772i
\(916\) 8.48615e6 0.334174
\(917\) −3.54597e6 3.54597e6i −0.139255 0.139255i
\(918\) −149304. 8.29306e6i −0.00584743 0.324794i
\(919\) 3.57465e7i 1.39619i 0.716005 + 0.698095i \(0.245969\pi\)
−0.716005 + 0.698095i \(0.754031\pi\)
\(920\) −560497. + 1.39749e6i −0.0218325 + 0.0544351i
\(921\) −1.10329e7 + 1.11662e7i −0.428590 + 0.433765i
\(922\) −1.51549e6 + 1.51549e6i −0.0587119 + 0.0587119i
\(923\) 3.12649e6 3.12649e6i 0.120796 0.120796i
\(924\) −1.92371e6 + 1.94694e6i −0.0741243 + 0.0750192i
\(925\) 1.04403e7 235303.i 0.401196 0.00904218i
\(926\) 8.58106e6i 0.328862i
\(927\) −1.11677e7 1.09028e7i −0.426838 0.416714i
\(928\) 1.78586e7 + 1.78586e7i 0.680735 + 0.680735i
\(929\) 6.93935e6 0.263803 0.131901 0.991263i \(-0.457892\pi\)
0.131901 + 0.991263i \(0.457892\pi\)
\(930\) 1.31066e6 + 3.01583e6i 0.0496914 + 0.114340i
\(931\) 3.31831e7 1.25471
\(932\) 2.18156e6 + 2.18156e6i 0.0822673 + 0.0822673i
\(933\) 74985.7 + 1.24964e7i 0.00282016 + 0.469981i
\(934\) 9.41515e6i 0.353151i
\(935\) 3.25332e7 1.39072e7i 1.21702 0.520247i
\(936\) −9.88050e6 + 118582.i −0.368629 + 0.00442414i
\(937\) 1.00667e7 1.00667e7i 0.374575 0.374575i −0.494565 0.869141i \(-0.664673\pi\)
0.869141 + 0.494565i \(0.164673\pi\)
\(938\) 808549. 808549.i 0.0300054 0.0300054i
\(939\) 2.13872e7 + 2.11320e7i 0.791569 + 0.782126i
\(940\) 3.30465e6 1.41266e6i 0.121985 0.0521457i
\(941\) 1.13958e7i 0.419536i −0.977751 0.209768i \(-0.932729\pi\)
0.977751 0.209768i \(-0.0672709\pi\)
\(942\) 5.21613e6 31299.9i 0.191523 0.00114925i
\(943\) −1.57718e6 1.57718e6i −0.0577566 0.0577566i
\(944\) 1.86485e7 0.681104
\(945\) −3.09687e6 + 1.39029e6i −0.112809 + 0.0506438i
\(946\) 6.15139e6 0.223483
\(947\) 2.70855e7 + 2.70855e7i 0.981436 + 0.981436i 0.999831 0.0183949i \(-0.00585562\pi\)
−0.0183949 + 0.999831i \(0.505856\pi\)
\(948\) 1.41927e7 85164.4i 0.512913 0.00307778i
\(949\) 8.62701e6i 0.310953i
\(950\) −7.79460e6 + 175675.i −0.280211 + 0.00631540i
\(951\) 2.26680e7 + 2.23976e7i 0.812759 + 0.803063i
\(952\) −1.55011e6 + 1.55011e6i −0.0554332 + 0.0554332i
\(953\) −1.31117e7 + 1.31117e7i −0.467656 + 0.467656i −0.901154 0.433498i \(-0.857279\pi\)
0.433498 + 0.901154i \(0.357279\pi\)
\(954\) −8.00893e6 + 96120.1i −0.284907 + 0.00341935i
\(955\) −1.16359e7 + 2.90118e7i −0.412848 + 1.02936i
\(956\) 3.29066e7i 1.16450i
\(957\) 237412. + 3.95647e7i 0.00837958 + 1.39646i
\(958\) 2.36053e6 + 2.36053e6i 0.0830990 + 0.0830990i
\(959\) 1.00097e6 0.0351458
\(960\) −7.55196e6 + 1.91613e7i −0.264473 + 0.671039i
\(961\) −1.94327e7 −0.678772
\(962\) −1.53857e6 1.53857e6i −0.0536018 0.0536018i
\(963\) −1.16145e7 1.13390e7i −0.403585 0.394013i
\(964\) 1.04257e7i 0.361338i
\(965\) −4.66161e6 1.09050e7i −0.161145 0.376969i
\(966\) 75752.0 76666.6i 0.00261187 0.00264340i
\(967\) −1.94460e7 + 1.94460e7i −0.668751 + 0.668751i −0.957427 0.288676i \(-0.906785\pi\)
0.288676 + 0.957427i \(0.406785\pi\)
\(968\) −1.74123e6 + 1.74123e6i −0.0597267 + 0.0597267i
\(969\) 3.86568e7 3.91235e7i 1.32256 1.33853i
\(970\) −3.02603e6 1.21366e6i −0.103263 0.0414161i
\(971\) 1.06222e7i 0.361548i −0.983525 0.180774i \(-0.942140\pi\)
0.983525 0.180774i \(-0.0578603\pi\)
\(972\) 840853. + 2.80176e7i 0.0285466 + 0.951186i
\(973\) −117642. 117642.i −0.00398366 0.00398366i
\(974\) 8.14668e6 0.275159
\(975\) −727265. 2.54801e7i −0.0245009 0.858400i
\(976\) 607182. 0.0204030
\(977\) −3.25074e7 3.25074e7i −1.08955 1.08955i −0.995575 0.0939726i \(-0.970043\pi\)
−0.0939726 0.995575i \(-0.529957\pi\)
\(978\) 62435.1 + 1.04048e7i 0.00208729 + 0.347847i
\(979\) 3.81346e7i 1.27163i
\(980\) −2.61483e7 1.04874e7i −0.869719 0.348822i
\(981\) −168435. 1.40344e7i −0.00558805 0.465609i
\(982\) 4.93154e6 4.93154e6i 0.163194 0.163194i
\(983\) −342472. + 342472.i −0.0113042 + 0.0113042i −0.712736 0.701432i \(-0.752544\pi\)
0.701432 + 0.712736i \(0.252544\pi\)
\(984\) 5.54522e6 + 5.47907e6i 0.182571 + 0.180393i
\(985\) 7.36505e6 + 1.72291e7i 0.241872 + 0.565813i
\(986\) 1.54519e7i 0.506163i
\(987\) −527579. + 3165.78i −0.0172383 + 0.000103440i
\(988\) −2.25912e7 2.25912e7i −0.736288 0.736288i
\(989\) 4.76395e6 0.154873
\(990\) 5.56113e6 2.45660e6i 0.180333 0.0796610i
\(991\) −2.24558e7 −0.726346 −0.363173 0.931722i \(-0.618307\pi\)
−0.363173 + 0.931722i \(0.618307\pi\)
\(992\) −7.67453e6 7.67453e6i −0.247612 0.247612i
\(993\) 2.61251e6 15676.6i 0.0840786 0.000504521i
\(994\) 168554.i 0.00541096i
\(995\) −1.25342e7 + 3.12516e7i −0.401364 + 1.00072i
\(996\) 1.46454e7 + 1.44707e7i 0.467793 + 0.462213i
\(997\) 2.66705e7 2.66705e7i 0.849755 0.849755i −0.140347 0.990102i \(-0.544822\pi\)
0.990102 + 0.140347i \(0.0448220\pi\)
\(998\) −3.98429e6 + 3.98429e6i −0.126627 + 0.126627i
\(999\) −8.78832e6 + 9.11056e6i −0.278607 + 0.288823i
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 15.6.e.a.8.4 yes 16
3.2 odd 2 inner 15.6.e.a.8.5 yes 16
5.2 odd 4 inner 15.6.e.a.2.5 yes 16
5.3 odd 4 75.6.e.e.32.4 16
5.4 even 2 75.6.e.e.68.5 16
15.2 even 4 inner 15.6.e.a.2.4 16
15.8 even 4 75.6.e.e.32.5 16
15.14 odd 2 75.6.e.e.68.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.6.e.a.2.4 16 15.2 even 4 inner
15.6.e.a.2.5 yes 16 5.2 odd 4 inner
15.6.e.a.8.4 yes 16 1.1 even 1 trivial
15.6.e.a.8.5 yes 16 3.2 odd 2 inner
75.6.e.e.32.4 16 5.3 odd 4
75.6.e.e.32.5 16 15.8 even 4
75.6.e.e.68.4 16 15.14 odd 2
75.6.e.e.68.5 16 5.4 even 2