Properties

Label 45.3.i.a.41.8
Level $45$
Weight $3$
Character 45.41
Analytic conductor $1.226$
Analytic rank $0$
Dimension $16$
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] = [45,3,Mod(11,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 45.i (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.22616118962\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.8
Root \(-3.09125i\) of defining polynomial
Character \(\chi\) \(=\) 45.41
Dual form 45.3.i.a.11.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.67710 - 1.54563i) q^{2} +(-2.82138 - 1.01971i) q^{3} +(2.77793 - 4.81151i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-9.12922 + 1.63094i) q^{6} +(1.10296 + 1.91037i) q^{7} -4.80953i q^{8} +(6.92040 + 5.75396i) q^{9} +O(q^{10})\) \(q+(2.67710 - 1.54563i) q^{2} +(-2.82138 - 1.01971i) q^{3} +(2.77793 - 4.81151i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-9.12922 + 1.63094i) q^{6} +(1.10296 + 1.91037i) q^{7} -4.80953i q^{8} +(6.92040 + 5.75396i) q^{9} +6.91225 q^{10} +(-15.4454 + 8.91740i) q^{11} +(-12.7439 + 10.7424i) q^{12} +(1.25688 - 2.17697i) q^{13} +(5.90545 + 3.40951i) q^{14} +(-4.32352 - 5.12905i) q^{15} +(3.67796 + 6.37042i) q^{16} -32.6026i q^{17} +(27.4201 + 4.70761i) q^{18} +7.93398 q^{19} +(10.7589 - 6.21163i) q^{20} +(-1.16384 - 6.51459i) q^{21} +(-27.5659 + 47.7456i) q^{22} +(-18.4415 - 10.6472i) q^{23} +(-4.90431 + 13.5695i) q^{24} +(2.50000 + 4.33013i) q^{25} -7.77065i q^{26} +(-13.6577 - 23.2909i) q^{27} +12.2557 q^{28} +(-30.7730 + 17.7668i) q^{29} +(-19.5021 - 7.04847i) q^{30} +(-1.01221 + 1.75321i) q^{31} +(36.3533 + 20.9886i) q^{32} +(52.6705 - 9.40963i) q^{33} +(-50.3914 - 87.2805i) q^{34} +4.93257i q^{35} +(46.9096 - 17.3135i) q^{36} +50.6833 q^{37} +(21.2401 - 12.2630i) q^{38} +(-5.76600 + 4.86043i) q^{39} +(5.37722 - 9.31361i) q^{40} +(4.65056 + 2.68500i) q^{41} +(-13.1848 - 15.6414i) q^{42} +(-7.76798 - 13.4545i) q^{43} +99.0875i q^{44} +(6.96816 + 18.8797i) q^{45} -65.8263 q^{46} +(-1.63440 + 0.943620i) q^{47} +(-3.88098 - 21.7238i) q^{48} +(22.0670 - 38.2211i) q^{49} +(13.3855 + 7.72813i) q^{50} +(-33.2451 + 91.9843i) q^{51} +(-6.98302 - 12.0949i) q^{52} +62.0293i q^{53} +(-72.5622 - 41.2424i) q^{54} -39.8798 q^{55} +(9.18800 - 5.30469i) q^{56} +(-22.3848 - 8.09033i) q^{57} +(-54.9216 + 95.1270i) q^{58} +(31.3202 + 18.0827i) q^{59} +(-36.6889 + 6.55450i) q^{60} +(21.1242 + 36.5883i) q^{61} +6.25802i q^{62} +(-3.35934 + 19.5669i) q^{63} +100.338 q^{64} +(4.86786 - 2.81046i) q^{65} +(126.461 - 106.599i) q^{66} +(7.38738 - 12.7953i) q^{67} +(-156.868 - 90.5675i) q^{68} +(41.1734 + 48.8446i) q^{69} +(7.62391 + 13.2050i) q^{70} -105.070i q^{71} +(27.6738 - 33.2838i) q^{72} -66.9435 q^{73} +(135.684 - 78.3375i) q^{74} +(-2.63800 - 14.7662i) q^{75} +(22.0400 - 38.1744i) q^{76} +(-34.0711 - 19.6710i) q^{77} +(-7.92378 + 21.9240i) q^{78} +(34.5753 + 59.8862i) q^{79} +16.4484i q^{80} +(14.7838 + 79.6394i) q^{81} +16.6001 q^{82} +(-18.3844 + 10.6143i) q^{83} +(-34.5780 - 12.4972i) q^{84} +(36.4508 - 63.1346i) q^{85} +(-41.5914 - 24.0128i) q^{86} +(104.939 - 18.7475i) q^{87} +(42.8885 + 74.2850i) q^{88} -7.16304i q^{89} +(47.8355 + 39.7729i) q^{90} +5.54511 q^{91} +(-102.458 + 59.1541i) q^{92} +(4.64360 - 3.91430i) q^{93} +(-2.91697 + 5.05234i) q^{94} +(15.3641 + 8.87046i) q^{95} +(-81.1643 - 96.2865i) q^{96} +(-55.6703 - 96.4238i) q^{97} -136.429i q^{98} +(-158.199 - 27.1603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} + 16 q^{4} - 22 q^{6} + 2 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} + 16 q^{4} - 22 q^{6} + 2 q^{7} + 8 q^{9} - 18 q^{11} - 22 q^{12} - 10 q^{13} - 54 q^{14} + 10 q^{15} - 32 q^{16} - 8 q^{18} - 52 q^{19} + 72 q^{21} - 24 q^{22} - 54 q^{23} + 108 q^{24} + 40 q^{25} + 34 q^{27} + 32 q^{28} - 54 q^{29} - 100 q^{30} + 32 q^{31} + 216 q^{32} + 62 q^{33} + 54 q^{34} - 86 q^{36} + 44 q^{37} + 252 q^{38} + 160 q^{39} - 30 q^{40} + 144 q^{41} - 270 q^{42} - 124 q^{43} + 140 q^{45} - 108 q^{46} - 216 q^{47} - 172 q^{48} - 54 q^{49} - 106 q^{51} + 62 q^{52} - 316 q^{54} - 18 q^{56} - 236 q^{57} + 90 q^{58} - 486 q^{59} - 10 q^{60} + 62 q^{61} - 132 q^{63} + 256 q^{64} - 90 q^{65} + 208 q^{66} + 14 q^{67} - 288 q^{68} + 90 q^{69} - 60 q^{70} + 804 q^{72} - 268 q^{73} + 540 q^{74} - 20 q^{75} - 106 q^{76} + 702 q^{77} + 290 q^{78} - 40 q^{79} - 112 q^{81} - 204 q^{82} + 522 q^{83} + 714 q^{84} + 30 q^{85} + 54 q^{86} + 106 q^{87} + 144 q^{88} + 250 q^{90} + 136 q^{91} - 1332 q^{92} + 90 q^{93} - 150 q^{94} + 180 q^{95} + 166 q^{96} - 142 q^{97} - 824 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67710 1.54563i 1.33855 0.772813i 0.351959 0.936015i \(-0.385515\pi\)
0.986593 + 0.163202i \(0.0521822\pi\)
\(3\) −2.82138 1.01971i −0.940461 0.339902i
\(4\) 2.77793 4.81151i 0.694481 1.20288i
\(5\) 1.93649 + 1.11803i 0.387298 + 0.223607i
\(6\) −9.12922 + 1.63094i −1.52154 + 0.271824i
\(7\) 1.10296 + 1.91037i 0.157565 + 0.272911i 0.933990 0.357299i \(-0.116302\pi\)
−0.776425 + 0.630210i \(0.782969\pi\)
\(8\) 4.80953i 0.601191i
\(9\) 6.92040 + 5.75396i 0.768933 + 0.639329i
\(10\) 6.91225 0.691225
\(11\) −15.4454 + 8.91740i −1.40413 + 0.810673i −0.994813 0.101721i \(-0.967565\pi\)
−0.409313 + 0.912394i \(0.634232\pi\)
\(12\) −12.7439 + 10.7424i −1.06199 + 0.895203i
\(13\) 1.25688 2.17697i 0.0966828 0.167459i −0.813627 0.581387i \(-0.802510\pi\)
0.910310 + 0.413928i \(0.135843\pi\)
\(14\) 5.90545 + 3.40951i 0.421818 + 0.243537i
\(15\) −4.32352 5.12905i −0.288234 0.341937i
\(16\) 3.67796 + 6.37042i 0.229873 + 0.398151i
\(17\) 32.6026i 1.91780i −0.283746 0.958899i \(-0.591577\pi\)
0.283746 0.958899i \(-0.408423\pi\)
\(18\) 27.4201 + 4.70761i 1.52334 + 0.261534i
\(19\) 7.93398 0.417578 0.208789 0.977961i \(-0.433048\pi\)
0.208789 + 0.977961i \(0.433048\pi\)
\(20\) 10.7589 6.21163i 0.537943 0.310581i
\(21\) −1.16384 6.51459i −0.0554208 0.310218i
\(22\) −27.5659 + 47.7456i −1.25300 + 2.17026i
\(23\) −18.4415 10.6472i −0.801803 0.462921i 0.0422985 0.999105i \(-0.486532\pi\)
−0.844101 + 0.536184i \(0.819865\pi\)
\(24\) −4.90431 + 13.5695i −0.204346 + 0.565397i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) 7.77065i 0.298871i
\(27\) −13.6577 23.2909i −0.505842 0.862626i
\(28\) 12.2557 0.437704
\(29\) −30.7730 + 17.7668i −1.06114 + 0.612647i −0.925746 0.378145i \(-0.876562\pi\)
−0.135390 + 0.990792i \(0.543229\pi\)
\(30\) −19.5021 7.04847i −0.650070 0.234949i
\(31\) −1.01221 + 1.75321i −0.0326521 + 0.0565550i −0.881890 0.471456i \(-0.843729\pi\)
0.849238 + 0.528011i \(0.177062\pi\)
\(32\) 36.3533 + 20.9886i 1.13604 + 0.655893i
\(33\) 52.6705 9.40963i 1.59608 0.285140i
\(34\) −50.3914 87.2805i −1.48210 2.56707i
\(35\) 4.93257i 0.140930i
\(36\) 46.9096 17.3135i 1.30304 0.480929i
\(37\) 50.6833 1.36982 0.684909 0.728628i \(-0.259842\pi\)
0.684909 + 0.728628i \(0.259842\pi\)
\(38\) 21.2401 12.2630i 0.558950 0.322710i
\(39\) −5.76600 + 4.86043i −0.147846 + 0.124626i
\(40\) 5.37722 9.31361i 0.134430 0.232840i
\(41\) 4.65056 + 2.68500i 0.113428 + 0.0654879i 0.555641 0.831422i \(-0.312473\pi\)
−0.442213 + 0.896910i \(0.645806\pi\)
\(42\) −13.1848 15.6414i −0.313925 0.372414i
\(43\) −7.76798 13.4545i −0.180651 0.312896i 0.761452 0.648222i \(-0.224487\pi\)
−0.942102 + 0.335326i \(0.891154\pi\)
\(44\) 99.0875i 2.25199i
\(45\) 6.96816 + 18.8797i 0.154848 + 0.419550i
\(46\) −65.8263 −1.43101
\(47\) −1.63440 + 0.943620i −0.0347744 + 0.0200770i −0.517286 0.855812i \(-0.673058\pi\)
0.482512 + 0.875889i \(0.339724\pi\)
\(48\) −3.88098 21.7238i −0.0808538 0.452580i
\(49\) 22.0670 38.2211i 0.450347 0.780023i
\(50\) 13.3855 + 7.72813i 0.267710 + 0.154563i
\(51\) −33.2451 + 91.9843i −0.651864 + 1.80361i
\(52\) −6.98302 12.0949i −0.134289 0.232595i
\(53\) 62.0293i 1.17036i 0.810902 + 0.585182i \(0.198977\pi\)
−0.810902 + 0.585182i \(0.801023\pi\)
\(54\) −72.5622 41.2424i −1.34374 0.763749i
\(55\) −39.8798 −0.725088
\(56\) 9.18800 5.30469i 0.164071 0.0947267i
\(57\) −22.3848 8.09033i −0.392716 0.141936i
\(58\) −54.9216 + 95.1270i −0.946924 + 1.64012i
\(59\) 31.3202 + 18.0827i 0.530850 + 0.306487i 0.741363 0.671105i \(-0.234180\pi\)
−0.210512 + 0.977591i \(0.567513\pi\)
\(60\) −36.6889 + 6.55450i −0.611482 + 0.109242i
\(61\) 21.1242 + 36.5883i 0.346299 + 0.599808i 0.985589 0.169158i \(-0.0541049\pi\)
−0.639290 + 0.768966i \(0.720772\pi\)
\(62\) 6.25802i 0.100936i
\(63\) −3.35934 + 19.5669i −0.0533228 + 0.310586i
\(64\) 100.338 1.56779
\(65\) 4.86786 2.81046i 0.0748902 0.0432379i
\(66\) 126.461 106.599i 1.91607 1.61514i
\(67\) 7.38738 12.7953i 0.110259 0.190975i −0.805615 0.592439i \(-0.798165\pi\)
0.915875 + 0.401464i \(0.131498\pi\)
\(68\) −156.868 90.5675i −2.30688 1.33188i
\(69\) 41.1734 + 48.8446i 0.596716 + 0.707893i
\(70\) 7.62391 + 13.2050i 0.108913 + 0.188643i
\(71\) 105.070i 1.47985i −0.672687 0.739927i \(-0.734860\pi\)
0.672687 0.739927i \(-0.265140\pi\)
\(72\) 27.6738 33.2838i 0.384359 0.462276i
\(73\) −66.9435 −0.917034 −0.458517 0.888686i \(-0.651619\pi\)
−0.458517 + 0.888686i \(0.651619\pi\)
\(74\) 135.684 78.3375i 1.83357 1.05861i
\(75\) −2.63800 14.7662i −0.0351733 0.196883i
\(76\) 22.0400 38.1744i 0.290000 0.502295i
\(77\) −34.0711 19.6710i −0.442482 0.255467i
\(78\) −7.92378 + 21.9240i −0.101587 + 0.281076i
\(79\) 34.5753 + 59.8862i 0.437662 + 0.758053i 0.997509 0.0705432i \(-0.0224733\pi\)
−0.559847 + 0.828596i \(0.689140\pi\)
\(80\) 16.4484i 0.205604i
\(81\) 14.7838 + 79.6394i 0.182516 + 0.983203i
\(82\) 16.6001 0.202440
\(83\) −18.3844 + 10.6143i −0.221499 + 0.127883i −0.606644 0.794973i \(-0.707485\pi\)
0.385145 + 0.922856i \(0.374151\pi\)
\(84\) −34.5780 12.4972i −0.411643 0.148777i
\(85\) 36.4508 63.1346i 0.428833 0.742760i
\(86\) −41.5914 24.0128i −0.483621 0.279218i
\(87\) 104.939 18.7475i 1.20620 0.215488i
\(88\) 42.8885 + 74.2850i 0.487369 + 0.844148i
\(89\) 7.16304i 0.0804836i −0.999190 0.0402418i \(-0.987187\pi\)
0.999190 0.0402418i \(-0.0128128\pi\)
\(90\) 47.8355 + 39.7729i 0.531506 + 0.441921i
\(91\) 5.54511 0.0609353
\(92\) −102.458 + 59.1541i −1.11367 + 0.642980i
\(93\) 4.64360 3.91430i 0.0499312 0.0420893i
\(94\) −2.91697 + 5.05234i −0.0310316 + 0.0537483i
\(95\) 15.3641 + 8.87046i 0.161727 + 0.0933733i
\(96\) −81.1643 96.2865i −0.845462 1.00298i
\(97\) −55.6703 96.4238i −0.573921 0.994060i −0.996158 0.0875744i \(-0.972088\pi\)
0.422237 0.906485i \(-0.361245\pi\)
\(98\) 136.429i 1.39214i
\(99\) −158.199 27.1603i −1.59797 0.274346i
\(100\) 27.7793 0.277793
\(101\) 53.8621 31.0973i 0.533288 0.307894i −0.209066 0.977901i \(-0.567042\pi\)
0.742354 + 0.670008i \(0.233709\pi\)
\(102\) 53.1730 + 297.636i 0.521304 + 2.91800i
\(103\) −27.5473 + 47.7133i −0.267449 + 0.463236i −0.968202 0.250168i \(-0.919514\pi\)
0.700753 + 0.713404i \(0.252847\pi\)
\(104\) −10.4702 6.04498i −0.100675 0.0581248i
\(105\) 5.02977 13.9167i 0.0479026 0.132540i
\(106\) 95.8741 + 166.059i 0.904473 + 1.56659i
\(107\) 85.2584i 0.796807i −0.917210 0.398404i \(-0.869564\pi\)
0.917210 0.398404i \(-0.130436\pi\)
\(108\) −150.005 + 1.01389i −1.38893 + 0.00938785i
\(109\) −64.0279 −0.587412 −0.293706 0.955896i \(-0.594889\pi\)
−0.293706 + 0.955896i \(0.594889\pi\)
\(110\) −106.762 + 61.6393i −0.970568 + 0.560358i
\(111\) −142.997 51.6821i −1.28826 0.465604i
\(112\) −8.11326 + 14.0526i −0.0724398 + 0.125469i
\(113\) 131.196 + 75.7460i 1.16103 + 0.670319i 0.951550 0.307495i \(-0.0994908\pi\)
0.209476 + 0.977814i \(0.432824\pi\)
\(114\) −72.4311 + 12.9399i −0.635360 + 0.113508i
\(115\) −23.8078 41.2364i −0.207025 0.358577i
\(116\) 197.419i 1.70189i
\(117\) 21.2243 7.83350i 0.181404 0.0669530i
\(118\) 111.796 0.947428
\(119\) 62.2831 35.9592i 0.523388 0.302178i
\(120\) −24.6683 + 20.7941i −0.205569 + 0.173284i
\(121\) 98.5400 170.676i 0.814380 1.41055i
\(122\) 113.104 + 65.3004i 0.927079 + 0.535249i
\(123\) −10.3831 12.3176i −0.0844155 0.100143i
\(124\) 5.62371 + 9.74055i 0.0453525 + 0.0785528i
\(125\) 11.1803i 0.0894427i
\(126\) 21.2499 + 57.5750i 0.168650 + 0.456944i
\(127\) 42.9132 0.337899 0.168950 0.985625i \(-0.445963\pi\)
0.168950 + 0.985625i \(0.445963\pi\)
\(128\) 123.203 71.1313i 0.962524 0.555713i
\(129\) 8.19676 + 45.8814i 0.0635408 + 0.355670i
\(130\) 8.68785 15.0478i 0.0668296 0.115752i
\(131\) 52.6936 + 30.4227i 0.402241 + 0.232234i 0.687451 0.726231i \(-0.258730\pi\)
−0.285209 + 0.958465i \(0.592063\pi\)
\(132\) 101.040 279.564i 0.765456 2.11791i
\(133\) 8.75083 + 15.1569i 0.0657957 + 0.113961i
\(134\) 45.6726i 0.340840i
\(135\) −0.408060 60.3725i −0.00302267 0.447203i
\(136\) −156.803 −1.15296
\(137\) −180.500 + 104.212i −1.31752 + 0.760670i −0.983329 0.181835i \(-0.941796\pi\)
−0.334191 + 0.942505i \(0.608463\pi\)
\(138\) 185.721 + 67.1235i 1.34581 + 0.486402i
\(139\) −67.2445 + 116.471i −0.483773 + 0.837919i −0.999826 0.0186370i \(-0.994067\pi\)
0.516053 + 0.856556i \(0.327401\pi\)
\(140\) 23.7331 + 13.7023i 0.169522 + 0.0978736i
\(141\) 5.57348 0.995707i 0.0395282 0.00706175i
\(142\) −162.398 281.282i −1.14365 1.98086i
\(143\) 44.8323i 0.313512i
\(144\) −11.2022 + 65.2487i −0.0777931 + 0.453116i
\(145\) −79.4554 −0.547968
\(146\) −179.215 + 103.470i −1.22750 + 0.708696i
\(147\) −101.234 + 85.3346i −0.688665 + 0.580507i
\(148\) 140.794 243.863i 0.951313 1.64772i
\(149\) −105.245 60.7633i −0.706343 0.407807i 0.103363 0.994644i \(-0.467040\pi\)
−0.809705 + 0.586836i \(0.800373\pi\)
\(150\) −29.8852 35.4533i −0.199235 0.236356i
\(151\) 21.0246 + 36.4156i 0.139236 + 0.241163i 0.927208 0.374548i \(-0.122202\pi\)
−0.787972 + 0.615711i \(0.788869\pi\)
\(152\) 38.1587i 0.251044i
\(153\) 187.594 225.623i 1.22611 1.47466i
\(154\) −121.616 −0.789714
\(155\) −3.92029 + 2.26338i −0.0252922 + 0.0146024i
\(156\) 7.36847 + 41.2451i 0.0472338 + 0.264391i
\(157\) −46.7940 + 81.0497i −0.298051 + 0.516240i −0.975690 0.219155i \(-0.929670\pi\)
0.677639 + 0.735395i \(0.263003\pi\)
\(158\) 185.123 + 106.881i 1.17167 + 0.676462i
\(159\) 63.2517 175.008i 0.397809 1.10068i
\(160\) 46.9319 + 81.2884i 0.293324 + 0.508053i
\(161\) 46.9735i 0.291761i
\(162\) 162.671 + 190.353i 1.00414 + 1.17502i
\(163\) −115.792 −0.710377 −0.355189 0.934795i \(-0.615583\pi\)
−0.355189 + 0.934795i \(0.615583\pi\)
\(164\) 25.8378 14.9175i 0.157548 0.0909602i
\(165\) 112.516 + 40.6657i 0.681917 + 0.246459i
\(166\) −32.8114 + 56.8310i −0.197659 + 0.342355i
\(167\) −1.40886 0.813403i −0.00843626 0.00487068i 0.495776 0.868450i \(-0.334884\pi\)
−0.504212 + 0.863580i \(0.668217\pi\)
\(168\) −31.3321 + 5.59751i −0.186501 + 0.0333185i
\(169\) 81.3405 + 140.886i 0.481305 + 0.833645i
\(170\) 225.357i 1.32563i
\(171\) 54.9063 + 45.6518i 0.321090 + 0.266970i
\(172\) −86.3154 −0.501834
\(173\) −104.098 + 60.1013i −0.601725 + 0.347406i −0.769720 0.638382i \(-0.779604\pi\)
0.167995 + 0.985788i \(0.446271\pi\)
\(174\) 251.956 212.386i 1.44803 1.22061i
\(175\) −5.51478 + 9.55187i −0.0315130 + 0.0545821i
\(176\) −113.615 65.5958i −0.645541 0.372703i
\(177\) −69.9271 82.9556i −0.395068 0.468676i
\(178\) −11.0714 19.1762i −0.0621988 0.107732i
\(179\) 157.742i 0.881238i 0.897694 + 0.440619i \(0.145241\pi\)
−0.897694 + 0.440619i \(0.854759\pi\)
\(180\) 110.197 + 18.9191i 0.612206 + 0.105106i
\(181\) −219.069 −1.21033 −0.605164 0.796101i \(-0.706892\pi\)
−0.605164 + 0.796101i \(0.706892\pi\)
\(182\) 14.8448 8.57068i 0.0815651 0.0470916i
\(183\) −22.2903 124.770i −0.121805 0.681803i
\(184\) −51.2079 + 88.6947i −0.278304 + 0.482036i
\(185\) 98.1478 + 56.6656i 0.530528 + 0.306301i
\(186\) 6.38134 17.6563i 0.0343083 0.0949262i
\(187\) 290.730 + 503.560i 1.55471 + 2.69283i
\(188\) 10.4852i 0.0557725i
\(189\) 29.4305 51.7802i 0.155717 0.273969i
\(190\) 54.8417 0.288641
\(191\) 321.773 185.776i 1.68468 0.972648i 0.726196 0.687488i \(-0.241286\pi\)
0.958480 0.285160i \(-0.0920468\pi\)
\(192\) −283.093 102.316i −1.47444 0.532894i
\(193\) 19.7796 34.2593i 0.102485 0.177509i −0.810223 0.586122i \(-0.800654\pi\)
0.912708 + 0.408613i \(0.133987\pi\)
\(194\) −298.070 172.091i −1.53645 0.887067i
\(195\) −16.5999 + 2.96559i −0.0851279 + 0.0152082i
\(196\) −122.601 212.351i −0.625514 1.08342i
\(197\) 104.454i 0.530224i 0.964218 + 0.265112i \(0.0854089\pi\)
−0.964218 + 0.265112i \(0.914591\pi\)
\(198\) −465.494 + 171.805i −2.35098 + 0.867703i
\(199\) 118.036 0.593147 0.296573 0.955010i \(-0.404156\pi\)
0.296573 + 0.955010i \(0.404156\pi\)
\(200\) 20.8259 12.0238i 0.104129 0.0601191i
\(201\) −33.8901 + 28.5675i −0.168608 + 0.142127i
\(202\) 96.1296 166.501i 0.475889 0.824264i
\(203\) −67.8824 39.1919i −0.334396 0.193064i
\(204\) 350.231 + 415.484i 1.71682 + 2.03669i
\(205\) 6.00385 + 10.3990i 0.0292871 + 0.0507267i
\(206\) 170.311i 0.826754i
\(207\) −66.3587 179.794i −0.320574 0.868571i
\(208\) 18.4910 0.0888990
\(209\) −122.543 + 70.7505i −0.586332 + 0.338519i
\(210\) −8.04474 45.0305i −0.0383083 0.214431i
\(211\) −68.1995 + 118.125i −0.323220 + 0.559834i −0.981151 0.193245i \(-0.938099\pi\)
0.657930 + 0.753079i \(0.271432\pi\)
\(212\) 298.454 + 172.313i 1.40780 + 0.812796i
\(213\) −107.140 + 296.442i −0.503005 + 1.39174i
\(214\) −131.778 228.246i −0.615783 1.06657i
\(215\) 34.7395i 0.161579i
\(216\) −112.018 + 65.6872i −0.518603 + 0.304108i
\(217\) −4.46571 −0.0205793
\(218\) −171.409 + 98.9632i −0.786282 + 0.453960i
\(219\) 188.873 + 68.2627i 0.862434 + 0.311702i
\(220\) −110.783 + 191.882i −0.503560 + 0.872191i
\(221\) −70.9749 40.9774i −0.321154 0.185418i
\(222\) −462.699 + 82.6616i −2.08423 + 0.372350i
\(223\) −169.164 293.000i −0.758581 1.31390i −0.943574 0.331162i \(-0.892559\pi\)
0.184993 0.982740i \(-0.440774\pi\)
\(224\) 92.5979i 0.413383i
\(225\) −7.61440 + 44.3511i −0.0338418 + 0.197116i
\(226\) 468.300 2.07212
\(227\) 132.851 76.7018i 0.585248 0.337893i −0.177968 0.984036i \(-0.556952\pi\)
0.763216 + 0.646143i \(0.223619\pi\)
\(228\) −101.110 + 85.2303i −0.443465 + 0.373817i
\(229\) 126.688 219.430i 0.553223 0.958210i −0.444816 0.895622i \(-0.646731\pi\)
0.998039 0.0625886i \(-0.0199356\pi\)
\(230\) −127.472 73.5960i −0.554226 0.319983i
\(231\) 76.0691 + 90.2419i 0.329303 + 0.390658i
\(232\) 85.4498 + 148.003i 0.368318 + 0.637946i
\(233\) 309.268i 1.32733i 0.748030 + 0.663664i \(0.231000\pi\)
−0.748030 + 0.663664i \(0.769000\pi\)
\(234\) 44.7120 53.7760i 0.191077 0.229812i
\(235\) −4.22000 −0.0179574
\(236\) 174.010 100.465i 0.737331 0.425698i
\(237\) −36.4838 204.219i −0.153940 0.861682i
\(238\) 111.159 192.533i 0.467055 0.808962i
\(239\) −62.2034 35.9131i −0.260265 0.150264i 0.364190 0.931325i \(-0.381346\pi\)
−0.624456 + 0.781060i \(0.714679\pi\)
\(240\) 16.7725 46.4071i 0.0698854 0.193363i
\(241\) −151.480 262.370i −0.628546 1.08867i −0.987844 0.155451i \(-0.950317\pi\)
0.359297 0.933223i \(-0.383016\pi\)
\(242\) 609.224i 2.51746i
\(243\) 39.4981 239.768i 0.162544 0.986701i
\(244\) 234.726 0.961993
\(245\) 85.4650 49.3433i 0.348837 0.201401i
\(246\) −46.8351 16.9272i −0.190387 0.0688097i
\(247\) 9.97203 17.2721i 0.0403726 0.0699274i
\(248\) 8.43209 + 4.86827i 0.0340004 + 0.0196301i
\(249\) 62.6930 11.2002i 0.251779 0.0449806i
\(250\) 17.2806 + 29.9309i 0.0691225 + 0.119724i
\(251\) 108.551i 0.432476i 0.976341 + 0.216238i \(0.0693787\pi\)
−0.976341 + 0.216238i \(0.930621\pi\)
\(252\) 84.8144 + 70.5189i 0.336565 + 0.279837i
\(253\) 379.781 1.50111
\(254\) 114.883 66.3278i 0.452296 0.261133i
\(255\) −167.220 + 140.958i −0.655766 + 0.552776i
\(256\) 19.2083 33.2697i 0.0750323 0.129960i
\(257\) −86.8847 50.1629i −0.338073 0.195186i 0.321347 0.946962i \(-0.395865\pi\)
−0.659419 + 0.751775i \(0.729198\pi\)
\(258\) 92.8592 + 110.160i 0.359919 + 0.426978i
\(259\) 55.9014 + 96.8241i 0.215836 + 0.373838i
\(260\) 31.2290i 0.120112i
\(261\) −315.190 54.1133i −1.20763 0.207331i
\(262\) 188.088 0.717895
\(263\) 373.654 215.729i 1.42074 0.820264i 0.424377 0.905486i \(-0.360493\pi\)
0.996362 + 0.0852214i \(0.0271598\pi\)
\(264\) −45.2559 253.320i −0.171424 0.959546i
\(265\) −69.3508 + 120.119i −0.261701 + 0.453280i
\(266\) 46.8538 + 27.0510i 0.176142 + 0.101696i
\(267\) −7.30420 + 20.2097i −0.0273566 + 0.0756917i
\(268\) −41.0432 71.0889i −0.153146 0.265257i
\(269\) 233.075i 0.866448i −0.901286 0.433224i \(-0.857376\pi\)
0.901286 0.433224i \(-0.142624\pi\)
\(270\) −94.4057 160.993i −0.349651 0.596269i
\(271\) 388.155 1.43230 0.716152 0.697944i \(-0.245902\pi\)
0.716152 + 0.697944i \(0.245902\pi\)
\(272\) 207.692 119.911i 0.763574 0.440850i
\(273\) −15.6449 5.65439i −0.0573073 0.0207120i
\(274\) −322.145 + 557.972i −1.17571 + 2.03639i
\(275\) −77.2269 44.5870i −0.280825 0.162135i
\(276\) 349.393 62.4194i 1.26592 0.226157i
\(277\) −17.9546 31.0983i −0.0648182 0.112268i 0.831795 0.555083i \(-0.187313\pi\)
−0.896613 + 0.442814i \(0.853980\pi\)
\(278\) 415.739i 1.49547i
\(279\) −17.0928 + 6.30864i −0.0612645 + 0.0226116i
\(280\) 23.7233 0.0847261
\(281\) −261.015 + 150.697i −0.928879 + 0.536289i −0.886457 0.462811i \(-0.846841\pi\)
−0.0424222 + 0.999100i \(0.513507\pi\)
\(282\) 13.3818 11.2801i 0.0474531 0.0400005i
\(283\) −212.734 + 368.467i −0.751712 + 1.30200i 0.195281 + 0.980747i \(0.437438\pi\)
−0.946993 + 0.321255i \(0.895895\pi\)
\(284\) −505.543 291.875i −1.78008 1.02773i
\(285\) −34.3027 40.6938i −0.120360 0.142785i
\(286\) 69.2940 + 120.021i 0.242287 + 0.419653i
\(287\) 11.8458i 0.0412744i
\(288\) 130.812 + 354.425i 0.454207 + 1.23064i
\(289\) −773.928 −2.67795
\(290\) −212.710 + 122.808i −0.733484 + 0.423477i
\(291\) 58.7432 + 328.816i 0.201867 + 1.12995i
\(292\) −185.964 + 322.099i −0.636863 + 1.10308i
\(293\) −332.917 192.210i −1.13624 0.656006i −0.190740 0.981641i \(-0.561089\pi\)
−0.945496 + 0.325635i \(0.894422\pi\)
\(294\) −139.118 + 384.919i −0.473190 + 1.30925i
\(295\) 40.4342 + 70.0340i 0.137065 + 0.237403i
\(296\) 243.763i 0.823523i
\(297\) 418.643 + 237.946i 1.40957 + 0.801164i
\(298\) −375.669 −1.26064
\(299\) −46.3573 + 26.7644i −0.155041 + 0.0895130i
\(300\) −78.3759 28.3267i −0.261253 0.0944223i
\(301\) 17.1355 29.6795i 0.0569285 0.0986030i
\(302\) 112.570 + 64.9923i 0.372748 + 0.215206i
\(303\) −183.676 + 32.8138i −0.606190 + 0.108296i
\(304\) 29.1809 + 50.5428i 0.0959898 + 0.166259i
\(305\) 94.4705i 0.309739i
\(306\) 153.480 893.966i 0.501569 2.92146i
\(307\) −130.907 −0.426407 −0.213204 0.977008i \(-0.568390\pi\)
−0.213204 + 0.977008i \(0.568390\pi\)
\(308\) −189.294 + 109.289i −0.614592 + 0.354835i
\(309\) 126.375 106.527i 0.408981 0.344749i
\(310\) −6.99668 + 12.1186i −0.0225699 + 0.0390923i
\(311\) 486.453 + 280.854i 1.56416 + 0.903066i 0.996829 + 0.0795736i \(0.0253559\pi\)
0.567327 + 0.823492i \(0.307977\pi\)
\(312\) 23.3764 + 27.7317i 0.0749243 + 0.0888838i
\(313\) −20.2397 35.0562i −0.0646636 0.112001i 0.831881 0.554954i \(-0.187264\pi\)
−0.896545 + 0.442953i \(0.853931\pi\)
\(314\) 289.305i 0.921352i
\(315\) −28.3818 + 34.1353i −0.0901010 + 0.108366i
\(316\) 384.190 1.21579
\(317\) −113.107 + 65.3025i −0.356805 + 0.206001i −0.667678 0.744450i \(-0.732712\pi\)
0.310873 + 0.950451i \(0.399379\pi\)
\(318\) −101.166 566.279i −0.318133 1.78075i
\(319\) 316.867 548.829i 0.993313 1.72047i
\(320\) 194.304 + 112.182i 0.607201 + 0.350568i
\(321\) −86.9385 + 240.546i −0.270836 + 0.749366i
\(322\) −72.6034 125.753i −0.225477 0.390537i
\(323\) 258.668i 0.800831i
\(324\) 424.254 + 150.100i 1.30943 + 0.463272i
\(325\) 12.5688 0.0386731
\(326\) −309.986 + 178.971i −0.950877 + 0.548989i
\(327\) 180.647 + 65.2897i 0.552438 + 0.199663i
\(328\) 12.9136 22.3670i 0.0393707 0.0681921i
\(329\) −3.60534 2.08154i −0.0109585 0.00632687i
\(330\) 364.072 65.0418i 1.10325 0.197096i
\(331\) −245.341 424.944i −0.741213 1.28382i −0.951943 0.306274i \(-0.900918\pi\)
0.210730 0.977544i \(-0.432416\pi\)
\(332\) 117.943i 0.355249i
\(333\) 350.748 + 291.630i 1.05330 + 0.875765i
\(334\) −5.02887 −0.0150565
\(335\) 28.6112 16.5187i 0.0854066 0.0493095i
\(336\) 37.2201 31.3746i 0.110774 0.0933767i
\(337\) 55.9933 96.9833i 0.166152 0.287784i −0.770912 0.636942i \(-0.780199\pi\)
0.937064 + 0.349158i \(0.113532\pi\)
\(338\) 435.514 + 251.444i 1.28850 + 0.743918i
\(339\) −292.915 347.490i −0.864056 1.02504i
\(340\) −202.515 350.767i −0.595633 1.03167i
\(341\) 36.1053i 0.105881i
\(342\) 217.551 + 37.3501i 0.636113 + 0.109211i
\(343\) 205.445 0.598966
\(344\) −64.7099 + 37.3603i −0.188110 + 0.108606i
\(345\) 25.1220 + 140.621i 0.0728174 + 0.407596i
\(346\) −185.788 + 321.795i −0.536960 + 0.930042i
\(347\) 170.190 + 98.2592i 0.490461 + 0.283168i 0.724766 0.688995i \(-0.241948\pi\)
−0.234305 + 0.972163i \(0.575281\pi\)
\(348\) 201.309 556.995i 0.578476 1.60056i
\(349\) 109.579 + 189.797i 0.313981 + 0.543832i 0.979220 0.202799i \(-0.0650037\pi\)
−0.665239 + 0.746630i \(0.731670\pi\)
\(350\) 34.0951i 0.0974147i
\(351\) −67.8698 + 0.458735i −0.193361 + 0.00130694i
\(352\) −748.654 −2.12686
\(353\) 219.479 126.717i 0.621755 0.358970i −0.155797 0.987789i \(-0.549795\pi\)
0.777552 + 0.628819i \(0.216461\pi\)
\(354\) −315.421 114.000i −0.891019 0.322033i
\(355\) 117.471 203.466i 0.330905 0.573145i
\(356\) −34.4650 19.8984i −0.0968119 0.0558944i
\(357\) −212.392 + 37.9441i −0.594937 + 0.106286i
\(358\) 243.810 + 422.290i 0.681032 + 1.17958i
\(359\) 152.604i 0.425081i −0.977152 0.212540i \(-0.931826\pi\)
0.977152 0.212540i \(-0.0681737\pi\)
\(360\) 90.8026 33.5136i 0.252230 0.0930933i
\(361\) −298.052 −0.825629
\(362\) −586.471 + 338.599i −1.62009 + 0.935357i
\(363\) −452.059 + 381.061i −1.24534 + 1.04976i
\(364\) 15.4039 26.6804i 0.0423184 0.0732977i
\(365\) −129.635 74.8451i −0.355166 0.205055i
\(366\) −252.521 299.570i −0.689949 0.818497i
\(367\) −174.997 303.104i −0.476832 0.825897i 0.522816 0.852446i \(-0.324882\pi\)
−0.999648 + 0.0265489i \(0.991548\pi\)
\(368\) 156.640i 0.425652i
\(369\) 16.7343 + 45.3405i 0.0453505 + 0.122874i
\(370\) 350.336 0.946853
\(371\) −118.499 + 68.4155i −0.319405 + 0.184408i
\(372\) −5.93413 33.2163i −0.0159520 0.0892913i
\(373\) 202.998 351.603i 0.544231 0.942636i −0.454424 0.890786i \(-0.650155\pi\)
0.998655 0.0518506i \(-0.0165119\pi\)
\(374\) 1556.63 + 898.721i 4.16211 + 2.40300i
\(375\) 11.4007 31.5440i 0.0304018 0.0841174i
\(376\) 4.53837 + 7.86068i 0.0120701 + 0.0209061i
\(377\) 89.3225i 0.236930i
\(378\) −1.24441 184.110i −0.00329208 0.487062i
\(379\) 410.698 1.08364 0.541818 0.840496i \(-0.317736\pi\)
0.541818 + 0.840496i \(0.317736\pi\)
\(380\) 85.3606 49.2830i 0.224633 0.129692i
\(381\) −121.074 43.7588i −0.317781 0.114853i
\(382\) 574.280 994.682i 1.50335 2.60388i
\(383\) −421.457 243.328i −1.10041 0.635322i −0.164081 0.986447i \(-0.552466\pi\)
−0.936329 + 0.351125i \(0.885799\pi\)
\(384\) −420.136 + 75.0577i −1.09410 + 0.195463i
\(385\) −43.9857 76.1854i −0.114248 0.197884i
\(386\) 122.288i 0.316807i
\(387\) 23.6594 137.807i 0.0611354 0.356091i
\(388\) −618.592 −1.59431
\(389\) 553.846 319.763i 1.42377 0.822013i 0.427150 0.904181i \(-0.359518\pi\)
0.996619 + 0.0821675i \(0.0261842\pi\)
\(390\) −39.8561 + 33.5965i −0.102195 + 0.0861449i
\(391\) −347.126 + 601.239i −0.887789 + 1.53770i
\(392\) −183.826 106.132i −0.468943 0.270744i
\(393\) −117.647 139.566i −0.299355 0.355130i
\(394\) 161.447 + 279.634i 0.409764 + 0.709732i
\(395\) 154.625i 0.391457i
\(396\) −570.146 + 685.725i −1.43976 + 1.73163i
\(397\) 295.328 0.743899 0.371950 0.928253i \(-0.378689\pi\)
0.371950 + 0.928253i \(0.378689\pi\)
\(398\) 315.995 182.440i 0.793958 0.458392i
\(399\) −9.23386 51.6866i −0.0231425 0.129540i
\(400\) −18.3898 + 31.8521i −0.0459746 + 0.0796303i
\(401\) 35.9199 + 20.7384i 0.0895758 + 0.0517166i 0.544119 0.839008i \(-0.316864\pi\)
−0.454543 + 0.890725i \(0.650197\pi\)
\(402\) −46.5726 + 128.860i −0.115852 + 0.320547i
\(403\) 2.54446 + 4.40713i 0.00631378 + 0.0109358i
\(404\) 345.544i 0.855306i
\(405\) −60.4109 + 170.750i −0.149163 + 0.421605i
\(406\) −242.304 −0.596809
\(407\) −782.823 + 451.963i −1.92340 + 1.11047i
\(408\) 442.401 + 159.893i 1.08432 + 0.391895i
\(409\) −10.4599 + 18.1170i −0.0255742 + 0.0442959i −0.878529 0.477689i \(-0.841475\pi\)
0.852955 + 0.521984i \(0.174808\pi\)
\(410\) 32.1459 + 18.5594i 0.0784046 + 0.0452669i
\(411\) 615.526 109.964i 1.49763 0.267553i
\(412\) 153.049 + 265.088i 0.371477 + 0.643417i
\(413\) 79.7777i 0.193166i
\(414\) −455.544 378.762i −1.10035 0.914884i
\(415\) −47.4684 −0.114382
\(416\) 91.3832 52.7601i 0.219671 0.126827i
\(417\) 308.488 260.039i 0.739780 0.623595i
\(418\) −218.708 + 378.813i −0.523224 + 0.906251i
\(419\) −360.820 208.319i −0.861145 0.497182i 0.00325066 0.999995i \(-0.498965\pi\)
−0.864395 + 0.502813i \(0.832299\pi\)
\(420\) −52.9878 62.8602i −0.126161 0.149667i
\(421\) −167.096 289.420i −0.396904 0.687457i 0.596438 0.802659i \(-0.296582\pi\)
−0.993342 + 0.115201i \(0.963249\pi\)
\(422\) 421.644i 0.999156i
\(423\) −16.7402 2.87404i −0.0395750 0.00679442i
\(424\) 298.332 0.703612
\(425\) 141.173 81.5064i 0.332172 0.191780i
\(426\) 171.363 + 959.204i 0.402260 + 2.25165i
\(427\) −46.5982 + 80.7104i −0.109129 + 0.189017i
\(428\) −410.221 236.841i −0.958461 0.553368i
\(429\) 45.7158 126.489i 0.106564 0.294846i
\(430\) −53.6942 93.0011i −0.124870 0.216282i
\(431\) 389.685i 0.904142i −0.891982 0.452071i \(-0.850685\pi\)
0.891982 0.452071i \(-0.149315\pi\)
\(432\) 98.1402 172.669i 0.227176 0.399696i
\(433\) 742.678 1.71519 0.857596 0.514324i \(-0.171957\pi\)
0.857596 + 0.514324i \(0.171957\pi\)
\(434\) −11.9552 + 6.90232i −0.0275465 + 0.0159040i
\(435\) 224.174 + 81.0212i 0.515343 + 0.186256i
\(436\) −177.865 + 308.071i −0.407947 + 0.706584i
\(437\) −146.314 84.4745i −0.334815 0.193306i
\(438\) 611.142 109.181i 1.39530 0.249272i
\(439\) 110.831 + 191.965i 0.252462 + 0.437277i 0.964203 0.265165i \(-0.0854264\pi\)
−0.711741 + 0.702442i \(0.752093\pi\)
\(440\) 191.803i 0.435916i
\(441\) 372.635 137.533i 0.844978 0.311866i
\(442\) −253.343 −0.573174
\(443\) −151.065 + 87.2171i −0.341003 + 0.196878i −0.660716 0.750636i \(-0.729747\pi\)
0.319712 + 0.947515i \(0.396414\pi\)
\(444\) −645.903 + 544.462i −1.45474 + 1.22627i
\(445\) 8.00853 13.8712i 0.0179967 0.0311712i
\(446\) −905.737 522.928i −2.03080 1.17248i
\(447\) 234.976 + 278.756i 0.525673 + 0.623614i
\(448\) 110.669 + 191.684i 0.247028 + 0.427866i
\(449\) 317.066i 0.706161i 0.935593 + 0.353080i \(0.114866\pi\)
−0.935593 + 0.353080i \(0.885134\pi\)
\(450\) 48.1657 + 130.502i 0.107035 + 0.290003i
\(451\) −95.7730 −0.212357
\(452\) 728.905 420.833i 1.61262 0.931047i
\(453\) −22.1851 124.181i −0.0489738 0.274131i
\(454\) 237.105 410.677i 0.522257 0.904575i
\(455\) 10.7381 + 6.19962i 0.0236001 + 0.0136255i
\(456\) −38.9107 + 107.660i −0.0853304 + 0.236097i
\(457\) 247.622 + 428.893i 0.541842 + 0.938497i 0.998798 + 0.0490082i \(0.0156060\pi\)
−0.456957 + 0.889489i \(0.651061\pi\)
\(458\) 783.250i 1.71015i
\(459\) −759.344 + 445.277i −1.65434 + 0.970103i
\(460\) −264.545 −0.575099
\(461\) −185.857 + 107.304i −0.403160 + 0.232764i −0.687846 0.725856i \(-0.741444\pi\)
0.284687 + 0.958621i \(0.408110\pi\)
\(462\) 343.125 + 124.013i 0.742695 + 0.268426i
\(463\) −210.893 + 365.277i −0.455492 + 0.788935i −0.998716 0.0506528i \(-0.983870\pi\)
0.543225 + 0.839587i \(0.317203\pi\)
\(464\) −226.364 130.691i −0.487853 0.281662i
\(465\) 13.3686 2.38832i 0.0287497 0.00513616i
\(466\) 478.012 + 827.942i 1.02578 + 1.77670i
\(467\) 123.800i 0.265097i 0.991177 + 0.132549i \(0.0423160\pi\)
−0.991177 + 0.132549i \(0.957684\pi\)
\(468\) 21.2686 123.882i 0.0454457 0.264705i
\(469\) 32.5918 0.0694922
\(470\) −11.2974 + 6.52254i −0.0240370 + 0.0138777i
\(471\) 214.671 180.956i 0.455777 0.384195i
\(472\) 86.9693 150.635i 0.184257 0.319142i
\(473\) 239.959 + 138.540i 0.507313 + 0.292897i
\(474\) −413.317 490.324i −0.871976 1.03444i
\(475\) 19.8350 + 34.3552i 0.0417578 + 0.0723266i
\(476\) 399.568i 0.839428i
\(477\) −356.914 + 429.267i −0.748248 + 0.899931i
\(478\) −222.033 −0.464505
\(479\) −581.609 + 335.792i −1.21421 + 0.701027i −0.963675 0.267079i \(-0.913941\pi\)
−0.250540 + 0.968106i \(0.580608\pi\)
\(480\) −49.5225 277.202i −0.103172 0.577505i
\(481\) 63.7026 110.336i 0.132438 0.229389i
\(482\) −811.054 468.262i −1.68268 0.971498i
\(483\) −47.8991 + 132.530i −0.0991701 + 0.274389i
\(484\) −547.474 948.252i −1.13114 1.95920i
\(485\) 248.965i 0.513330i
\(486\) −264.852 702.934i −0.544963 1.44637i
\(487\) 134.773 0.276742 0.138371 0.990380i \(-0.455813\pi\)
0.138371 + 0.990380i \(0.455813\pi\)
\(488\) 175.972 101.598i 0.360599 0.208192i
\(489\) 326.692 + 118.073i 0.668082 + 0.241459i
\(490\) 152.533 264.194i 0.311291 0.539172i
\(491\) 411.108 + 237.353i 0.837288 + 0.483408i 0.856341 0.516410i \(-0.172732\pi\)
−0.0190536 + 0.999818i \(0.506065\pi\)
\(492\) −88.1099 + 15.7409i −0.179085 + 0.0319937i
\(493\) 579.243 + 1003.28i 1.17493 + 2.03505i
\(494\) 61.6522i 0.124802i
\(495\) −275.984 229.467i −0.557544 0.463570i
\(496\) −14.8915 −0.0300233
\(497\) 200.722 115.887i 0.403868 0.233173i
\(498\) 150.524 126.884i 0.302258 0.254787i
\(499\) −279.196 + 483.582i −0.559511 + 0.969102i 0.438026 + 0.898962i \(0.355678\pi\)
−0.997537 + 0.0701394i \(0.977656\pi\)
\(500\) 53.7943 + 31.0581i 0.107589 + 0.0621163i
\(501\) 3.14549 + 3.73154i 0.00627842 + 0.00744819i
\(502\) 167.780 + 290.603i 0.334223 + 0.578891i
\(503\) 681.680i 1.35523i −0.735417 0.677614i \(-0.763014\pi\)
0.735417 0.677614i \(-0.236986\pi\)
\(504\) 94.1076 + 16.1568i 0.186721 + 0.0320572i
\(505\) 139.071 0.275389
\(506\) 1016.71 586.999i 2.00931 1.16008i
\(507\) −85.8304 480.437i −0.169291 0.947607i
\(508\) 119.210 206.477i 0.234665 0.406451i
\(509\) 462.890 + 267.250i 0.909412 + 0.525049i 0.880242 0.474525i \(-0.157380\pi\)
0.0291697 + 0.999574i \(0.490714\pi\)
\(510\) −229.798 + 635.819i −0.450585 + 1.24670i
\(511\) −73.8357 127.887i −0.144492 0.250268i
\(512\) 450.295i 0.879483i
\(513\) −108.360 184.790i −0.211228 0.360214i
\(514\) −310.133 −0.603371
\(515\) −106.690 + 61.5976i −0.207165 + 0.119607i
\(516\) 243.529 + 88.0164i 0.471955 + 0.170574i
\(517\) 16.8293 29.1492i 0.0325518 0.0563813i
\(518\) 299.308 + 172.805i 0.577814 + 0.333601i
\(519\) 354.987 63.4188i 0.683983 0.122194i
\(520\) −13.5170 23.4121i −0.0259942 0.0450233i
\(521\) 352.483i 0.676552i 0.941047 + 0.338276i \(0.109844\pi\)
−0.941047 + 0.338276i \(0.890156\pi\)
\(522\) −927.437 + 342.300i −1.77670 + 0.655747i
\(523\) −260.994 −0.499033 −0.249516 0.968371i \(-0.580272\pi\)
−0.249516 + 0.968371i \(0.580272\pi\)
\(524\) 292.758 169.024i 0.558698 0.322564i
\(525\) 25.2994 21.3260i 0.0481893 0.0406210i
\(526\) 666.875 1155.06i 1.26782 2.19593i
\(527\) 57.1590 + 33.0008i 0.108461 + 0.0626201i
\(528\) 253.663 + 300.925i 0.480423 + 0.569933i
\(529\) −37.7751 65.4283i −0.0714084 0.123683i
\(530\) 428.762i 0.808985i
\(531\) 112.701 + 305.355i 0.212242 + 0.575056i
\(532\) 97.2366 0.182776
\(533\) 11.6904 6.74943i 0.0219331 0.0126631i
\(534\) 11.6825 + 65.3930i 0.0218774 + 0.122459i
\(535\) 95.3217 165.102i 0.178171 0.308602i
\(536\) −61.5395 35.5298i −0.114812 0.0662870i
\(537\) 160.850 445.049i 0.299535 0.828769i
\(538\) −360.246 623.965i −0.669603 1.15979i
\(539\) 787.120i 1.46033i
\(540\) −291.616 165.747i −0.540030 0.306938i
\(541\) 492.273 0.909932 0.454966 0.890509i \(-0.349651\pi\)
0.454966 + 0.890509i \(0.349651\pi\)
\(542\) 1039.13 599.942i 1.91721 1.10690i
\(543\) 618.078 + 223.386i 1.13827 + 0.411393i
\(544\) 684.282 1185.21i 1.25787 2.17870i
\(545\) −123.989 71.5854i −0.227504 0.131349i
\(546\) −50.6226 + 9.04377i −0.0927153 + 0.0165637i
\(547\) −429.066 743.164i −0.784399 1.35862i −0.929358 0.369181i \(-0.879638\pi\)
0.144959 0.989438i \(-0.453695\pi\)
\(548\) 1157.97i 2.11309i
\(549\) −64.3394 + 374.753i −0.117194 + 0.682611i
\(550\) −275.659 −0.501199
\(551\) −244.152 + 140.961i −0.443107 + 0.255828i
\(552\) 234.920 198.025i 0.425579 0.358740i
\(553\) −76.2700 + 132.104i −0.137921 + 0.238885i
\(554\) −96.1328 55.5023i −0.173525 0.100185i
\(555\) −219.130 259.957i −0.394829 0.468392i
\(556\) 373.600 + 647.094i 0.671943 + 1.16384i
\(557\) 474.887i 0.852581i −0.904586 0.426290i \(-0.859820\pi\)
0.904586 0.426290i \(-0.140180\pi\)
\(558\) −36.0084 + 43.3080i −0.0645312 + 0.0776129i
\(559\) −39.0535 −0.0698632
\(560\) −31.4225 + 18.1418i −0.0561117 + 0.0323961i
\(561\) −306.778 1717.19i −0.546842 3.06095i
\(562\) −465.843 + 806.864i −0.828902 + 1.43570i
\(563\) −649.150 374.787i −1.15302 0.665696i −0.203398 0.979096i \(-0.565199\pi\)
−0.949621 + 0.313400i \(0.898532\pi\)
\(564\) 10.6919 29.5828i 0.0189572 0.0524518i
\(565\) 169.373 + 293.363i 0.299776 + 0.519226i
\(566\) 1315.23i 2.32373i
\(567\) −135.835 + 116.081i −0.239568 + 0.204729i
\(568\) −505.335 −0.889675
\(569\) −431.712 + 249.249i −0.758720 + 0.438047i −0.828836 0.559492i \(-0.810996\pi\)
0.0701161 + 0.997539i \(0.477663\pi\)
\(570\) −154.729 55.9224i −0.271455 0.0981095i
\(571\) 302.743 524.365i 0.530197 0.918328i −0.469182 0.883101i \(-0.655451\pi\)
0.999379 0.0352270i \(-0.0112154\pi\)
\(572\) 215.711 + 124.541i 0.377117 + 0.217728i
\(573\) −1097.28 + 196.030i −1.91498 + 0.342112i
\(574\) 18.3091 + 31.7123i 0.0318974 + 0.0552480i
\(575\) 106.472i 0.185168i
\(576\) 694.381 + 577.343i 1.20552 + 1.00233i
\(577\) −898.993 −1.55805 −0.779023 0.626995i \(-0.784285\pi\)
−0.779023 + 0.626995i \(0.784285\pi\)
\(578\) −2071.89 + 1196.20i −3.58458 + 2.06956i
\(579\) −90.7403 + 76.4892i −0.156719 + 0.132106i
\(580\) −220.721 + 382.300i −0.380554 + 0.659139i
\(581\) −40.5544 23.4141i −0.0698011 0.0402997i
\(582\) 665.488 + 789.479i 1.14345 + 1.35649i
\(583\) −553.140 958.066i −0.948782 1.64334i
\(584\) 321.966i 0.551312i
\(585\) 49.8588 + 8.55999i 0.0852287 + 0.0146325i
\(586\) −1188.34 −2.02788
\(587\) 730.025 421.480i 1.24365 0.718024i 0.273817 0.961782i \(-0.411714\pi\)
0.969836 + 0.243758i \(0.0783803\pi\)
\(588\) 129.368 + 724.140i 0.220014 + 1.23153i
\(589\) −8.03089 + 13.9099i −0.0136348 + 0.0236161i
\(590\) 216.493 + 124.992i 0.366937 + 0.211851i
\(591\) 106.512 294.705i 0.180224 0.498654i
\(592\) 186.411 + 322.874i 0.314884 + 0.545395i
\(593\) 238.158i 0.401615i 0.979631 + 0.200808i \(0.0643566\pi\)
−0.979631 + 0.200808i \(0.935643\pi\)
\(594\) 1488.53 10.0610i 2.50594 0.0169377i
\(595\) 160.814 0.270276
\(596\) −584.726 + 337.592i −0.981084 + 0.566429i
\(597\) −333.025 120.362i −0.557831 0.201612i
\(598\) −82.7355 + 143.302i −0.138354 + 0.239636i
\(599\) 777.853 + 449.093i 1.29859 + 0.749739i 0.980160 0.198209i \(-0.0635126\pi\)
0.318426 + 0.947948i \(0.396846\pi\)
\(600\) −71.0185 + 12.6875i −0.118364 + 0.0211459i
\(601\) 51.9420 + 89.9663i 0.0864260 + 0.149694i 0.905998 0.423282i \(-0.139122\pi\)
−0.819572 + 0.572976i \(0.805789\pi\)
\(602\) 105.940i 0.175980i
\(603\) 124.747 46.0420i 0.206878 0.0763549i
\(604\) 233.619 0.386786
\(605\) 381.644 220.342i 0.630816 0.364202i
\(606\) −441.001 + 371.740i −0.727724 + 0.613432i
\(607\) −539.314 + 934.118i −0.888490 + 1.53891i −0.0468297 + 0.998903i \(0.514912\pi\)
−0.841660 + 0.540007i \(0.818422\pi\)
\(608\) 288.426 + 166.523i 0.474385 + 0.273887i
\(609\) 151.558 + 179.795i 0.248864 + 0.295231i
\(610\) 146.016 + 252.907i 0.239371 + 0.414602i
\(611\) 4.74405i 0.00776441i
\(612\) −564.464 1529.37i −0.922326 2.49898i
\(613\) −387.302 −0.631814 −0.315907 0.948790i \(-0.602309\pi\)
−0.315907 + 0.948790i \(0.602309\pi\)
\(614\) −350.452 + 202.333i −0.570768 + 0.329533i
\(615\) −6.33526 35.4617i −0.0103012 0.0576612i
\(616\) −94.6082 + 163.866i −0.153585 + 0.266016i
\(617\) 459.415 + 265.244i 0.744596 + 0.429892i 0.823738 0.566971i \(-0.191885\pi\)
−0.0791422 + 0.996863i \(0.525218\pi\)
\(618\) 173.668 480.513i 0.281015 0.777530i
\(619\) −321.146 556.241i −0.518814 0.898613i −0.999761 0.0218628i \(-0.993040\pi\)
0.480947 0.876750i \(-0.340293\pi\)
\(620\) 25.1500i 0.0405645i
\(621\) 3.88601 + 574.935i 0.00625766 + 0.925821i
\(622\) 1736.38 2.79161
\(623\) 13.6841 7.90052i 0.0219648 0.0126814i
\(624\) −52.1701 18.8554i −0.0836060 0.0302170i
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) −108.368 62.5661i −0.173111 0.0999459i
\(627\) 417.887 74.6558i 0.666486 0.119068i
\(628\) 259.981 + 450.300i 0.413982 + 0.717038i
\(629\) 1652.41i 2.62704i
\(630\) −23.2206 + 135.251i −0.0368581 + 0.214685i
\(631\) −88.5117 −0.140272 −0.0701361 0.997537i \(-0.522343\pi\)
−0.0701361 + 0.997537i \(0.522343\pi\)
\(632\) 288.024 166.291i 0.455735 0.263119i
\(633\) 312.870 263.732i 0.494265 0.416639i
\(634\) −201.867 + 349.643i −0.318401 + 0.551487i
\(635\) 83.1010 + 47.9784i 0.130868 + 0.0755565i
\(636\) −666.346 790.496i −1.04771 1.24292i
\(637\) −55.4709 96.0785i −0.0870815 0.150830i
\(638\) 1959.03i 3.07058i
\(639\) 604.567 727.123i 0.946114 1.13791i
\(640\) 318.109 0.497045
\(641\) 285.641 164.915i 0.445618 0.257278i −0.260360 0.965512i \(-0.583841\pi\)
0.705978 + 0.708234i \(0.250508\pi\)
\(642\) 139.052 + 778.342i 0.216591 + 1.21237i
\(643\) 39.2339 67.9551i 0.0610170 0.105684i −0.833903 0.551911i \(-0.813899\pi\)
0.894920 + 0.446226i \(0.147232\pi\)
\(644\) −226.013 130.489i −0.350952 0.202622i
\(645\) −35.4240 + 98.0133i −0.0549210 + 0.151959i
\(646\) −399.805 692.482i −0.618893 1.07195i
\(647\) 68.7558i 0.106269i −0.998587 0.0531343i \(-0.983079\pi\)
0.998587 0.0531343i \(-0.0169212\pi\)
\(648\) 383.028 71.1031i 0.591093 0.109727i
\(649\) −645.003 −0.993841
\(650\) 33.6479 19.4266i 0.0517660 0.0298871i
\(651\) 12.5995 + 4.55371i 0.0193540 + 0.00699495i
\(652\) −321.660 + 557.132i −0.493344 + 0.854497i
\(653\) 832.196 + 480.468i 1.27442 + 0.735786i 0.975816 0.218591i \(-0.0701462\pi\)
0.298603 + 0.954378i \(0.403479\pi\)
\(654\) 584.525 104.426i 0.893769 0.159673i
\(655\) 68.0272 + 117.826i 0.103858 + 0.179888i
\(656\) 39.5014i 0.0602155i
\(657\) −463.275 385.190i −0.705138 0.586287i
\(658\) −12.8691 −0.0195580
\(659\) −105.512 + 60.9172i −0.160109 + 0.0924389i −0.577914 0.816098i \(-0.696133\pi\)
0.417805 + 0.908537i \(0.362800\pi\)
\(660\) 508.225 428.406i 0.770038 0.649101i
\(661\) −418.001 + 723.999i −0.632377 + 1.09531i 0.354688 + 0.934985i \(0.384587\pi\)
−0.987064 + 0.160324i \(0.948746\pi\)
\(662\) −1313.61 758.413i −1.98430 1.14564i
\(663\) 158.463 + 187.987i 0.239008 + 0.283539i
\(664\) 51.0496 + 88.4205i 0.0768819 + 0.133163i
\(665\) 39.1349i 0.0588495i
\(666\) 1389.74 + 238.597i 2.08670 + 0.358254i
\(667\) 756.664 1.13443
\(668\) −7.82739 + 4.51915i −0.0117177 + 0.00676519i
\(669\) 178.501 + 999.162i 0.266818 + 1.49352i
\(670\) 51.0635 88.4445i 0.0762141 0.132007i
\(671\) −652.544 376.747i −0.972495 0.561470i
\(672\) 94.4226 261.254i 0.140510 0.388771i
\(673\) −171.808 297.580i −0.255287 0.442169i 0.709687 0.704517i \(-0.248837\pi\)
−0.964973 + 0.262348i \(0.915503\pi\)
\(674\) 346.179i 0.513619i
\(675\) 66.7083 117.367i 0.0988270 0.173877i
\(676\) 903.832 1.33703
\(677\) 334.217 192.960i 0.493674 0.285023i −0.232424 0.972615i \(-0.574666\pi\)
0.726097 + 0.687592i \(0.241332\pi\)
\(678\) −1321.25 477.529i −1.94875 0.704320i
\(679\) 122.804 212.702i 0.180860 0.313258i
\(680\) −303.648 175.311i −0.446541 0.257810i
\(681\) −453.038 + 80.9356i −0.665254 + 0.118848i
\(682\) −55.8053 96.6576i −0.0818259 0.141727i
\(683\) 699.925i 1.02478i 0.858753 + 0.512390i \(0.171240\pi\)
−0.858753 + 0.512390i \(0.828760\pi\)
\(684\) 372.180 137.365i 0.544123 0.200826i
\(685\) −466.050 −0.680364
\(686\) 549.998 317.542i 0.801747 0.462889i
\(687\) −581.190 + 489.912i −0.845982 + 0.713118i
\(688\) 57.1407 98.9706i 0.0830533 0.143853i
\(689\) 135.036 + 77.9631i 0.195989 + 0.113154i
\(690\) 284.601 + 337.627i 0.412465 + 0.489314i
\(691\) 257.065 + 445.249i 0.372019 + 0.644355i 0.989876 0.141935i \(-0.0453324\pi\)
−0.617857 + 0.786290i \(0.711999\pi\)
\(692\) 667.827i 0.965068i
\(693\) −122.600 332.175i −0.176912 0.479329i
\(694\) 607.488 0.875344
\(695\) −260.437 + 150.363i −0.374729 + 0.216350i
\(696\) −90.1665 504.708i −0.129550 0.725155i
\(697\) 87.5380 151.620i 0.125593 0.217533i
\(698\) 586.712 + 338.738i 0.840561 + 0.485298i
\(699\) 315.362 872.562i 0.451162 1.24830i
\(700\) 30.6393 + 53.0688i 0.0437704 + 0.0758125i
\(701\) 842.009i 1.20115i −0.799567 0.600577i \(-0.794938\pi\)
0.799567 0.600577i \(-0.205062\pi\)
\(702\) −180.985 + 106.129i −0.257814 + 0.151181i
\(703\) 402.120 0.572006
\(704\) −1549.76 + 894.757i −2.20137 + 1.27096i
\(705\) 11.9062 + 4.30316i 0.0168883 + 0.00610377i
\(706\) 391.713 678.467i 0.554834 0.961001i
\(707\) 118.815 + 68.5978i 0.168055 + 0.0970267i
\(708\) −593.394 + 106.010i −0.838127 + 0.149732i
\(709\) 84.2898 + 145.994i 0.118885 + 0.205916i 0.919326 0.393496i \(-0.128735\pi\)
−0.800441 + 0.599412i \(0.795401\pi\)
\(710\) 726.268i 1.02291i
\(711\) −105.308 + 613.381i −0.148113 + 0.862702i
\(712\) −34.4509 −0.0483860
\(713\) 37.3334 21.5545i 0.0523610 0.0302306i
\(714\) −509.949 + 429.860i −0.714215 + 0.602044i
\(715\) −50.1240 + 86.8173i −0.0701035 + 0.121423i
\(716\) 758.974 + 438.194i 1.06002 + 0.612003i
\(717\) 138.879 + 164.754i 0.193694 + 0.229782i
\(718\) −235.869 408.537i −0.328508 0.568993i
\(719\) 1132.23i 1.57472i 0.616490 + 0.787362i \(0.288554\pi\)
−0.616490 + 0.787362i \(0.711446\pi\)
\(720\) −94.6433 + 113.829i −0.131449 + 0.158096i
\(721\) −121.534 −0.168563
\(722\) −797.916 + 460.677i −1.10515 + 0.638057i
\(723\) 159.841 + 894.712i 0.221080 + 1.23750i
\(724\) −608.558 + 1054.05i −0.840550 + 1.45587i
\(725\) −153.865 88.8339i −0.212227 0.122529i
\(726\) −621.230 + 1718.86i −0.855689 + 2.36757i
\(727\) −476.178 824.764i −0.654990 1.13448i −0.981896 0.189420i \(-0.939339\pi\)
0.326906 0.945057i \(-0.393994\pi\)
\(728\) 26.6694i 0.0366338i
\(729\) −355.933 + 636.202i −0.488248 + 0.872705i
\(730\) −462.730 −0.633877
\(731\) −438.652 + 253.256i −0.600072 + 0.346452i
\(732\) −662.253 239.352i −0.904717 0.326984i
\(733\) −69.0917 + 119.670i −0.0942588 + 0.163261i −0.909299 0.416143i \(-0.863381\pi\)
0.815040 + 0.579404i \(0.196715\pi\)
\(734\) −936.972 540.961i −1.27653 0.737004i
\(735\) −291.445 + 52.0670i −0.396524 + 0.0708394i
\(736\) −446.938 774.120i −0.607253 1.05179i
\(737\) 263.505i 0.357537i
\(738\) 114.879 + 95.5161i 0.155663 + 0.129426i
\(739\) 529.373 0.716337 0.358168 0.933657i \(-0.383401\pi\)
0.358168 + 0.933657i \(0.383401\pi\)
\(740\) 545.294 314.826i 0.736884 0.425440i
\(741\) −45.7474 + 38.5626i −0.0617373 + 0.0520412i
\(742\) −211.490 + 366.311i −0.285027 + 0.493681i
\(743\) 537.511 + 310.332i 0.723434 + 0.417675i 0.816015 0.578030i \(-0.196178\pi\)
−0.0925813 + 0.995705i \(0.529512\pi\)
\(744\) −18.8260 22.3335i −0.0253037 0.0300182i
\(745\) −135.871 235.335i −0.182377 0.315886i
\(746\) 1255.04i 1.68236i
\(747\) −188.302 32.3285i −0.252077 0.0432778i
\(748\) 3230.51 4.31886
\(749\) 162.875 94.0362i 0.217457 0.125549i
\(750\) −18.2345 102.068i −0.0243127 0.136090i
\(751\) 49.6464 85.9901i 0.0661070 0.114501i −0.831077 0.556157i \(-0.812275\pi\)
0.897185 + 0.441656i \(0.145609\pi\)
\(752\) −12.0225 6.94120i −0.0159874 0.00923032i
\(753\) 110.691 306.265i 0.146999 0.406726i
\(754\) 138.059 + 239.126i 0.183103 + 0.317143i
\(755\) 94.0248i 0.124536i
\(756\) −167.385 285.447i −0.221409 0.377575i
\(757\) 395.640 0.522642 0.261321 0.965252i \(-0.415842\pi\)
0.261321 + 0.965252i \(0.415842\pi\)
\(758\) 1099.48 634.786i 1.45050 0.837449i
\(759\) −1071.51 387.265i −1.41173 0.510230i
\(760\) 42.6627 73.8940i 0.0561352 0.0972290i
\(761\) 1219.62 + 704.146i 1.60265 + 0.925291i 0.990955 + 0.134198i \(0.0428458\pi\)
0.611696 + 0.791093i \(0.290487\pi\)
\(762\) −391.764 + 69.9890i −0.514126 + 0.0918491i
\(763\) −70.6199 122.317i −0.0925556 0.160311i
\(764\) 2064.28i 2.70194i
\(765\) 615.528 227.180i 0.804612 0.296968i
\(766\) −1504.38 −1.96394
\(767\) 78.7311 45.4554i 0.102648 0.0592639i
\(768\) −88.1192 + 74.2797i −0.114739 + 0.0967184i
\(769\) −382.059 + 661.746i −0.496826 + 0.860528i −0.999993 0.00366110i \(-0.998835\pi\)
0.503167 + 0.864189i \(0.332168\pi\)
\(770\) −235.508 135.971i −0.305855 0.176586i
\(771\) 193.984 + 230.126i 0.251600 + 0.298477i
\(772\) −109.893 190.340i −0.142348 0.246554i
\(773\) 477.095i 0.617199i 0.951192 + 0.308600i \(0.0998603\pi\)
−0.951192 + 0.308600i \(0.900140\pi\)
\(774\) −149.660 405.493i −0.193359 0.523893i
\(775\) −10.1221 −0.0130608
\(776\) −463.753 + 267.748i −0.597620 + 0.345036i
\(777\) −58.9871 330.181i −0.0759165 0.424943i
\(778\) 988.469 1712.08i 1.27053 2.20062i
\(779\) 36.8975 + 21.3028i 0.0473652 + 0.0273463i
\(780\) −31.8444 + 88.1089i −0.0408262 + 0.112960i
\(781\) 936.948 + 1622.84i 1.19968 + 2.07790i
\(782\) 2146.11i 2.74438i
\(783\) 834.093 + 474.076i 1.06525 + 0.605461i
\(784\) 324.646 0.414090
\(785\) −181.233 + 104.635i −0.230870 + 0.133293i
\(786\) −530.669 191.795i −0.675152 0.244014i
\(787\) 615.120 1065.42i 0.781600 1.35377i −0.149409 0.988776i \(-0.547737\pi\)
0.931009 0.364996i \(-0.118930\pi\)
\(788\) 502.581 + 290.165i 0.637794 + 0.368230i
\(789\) −1274.20 + 227.638i −1.61496 + 0.288514i
\(790\) 238.993 + 413.949i 0.302523 + 0.523986i
\(791\) 334.178i 0.422475i
\(792\) −130.628 + 760.861i −0.164934 + 0.960683i
\(793\) 106.202 0.133925
\(794\) 790.624 456.467i 0.995748 0.574895i
\(795\) 318.152 268.185i 0.400191 0.337339i
\(796\) 327.896 567.932i 0.411929 0.713483i
\(797\) 82.5422 + 47.6557i 0.103566 + 0.0597939i 0.550888 0.834579i \(-0.314289\pi\)
−0.447322 + 0.894373i \(0.647622\pi\)
\(798\) −104.608 124.098i −0.131088 0.155512i
\(799\) 30.7644 + 53.2856i 0.0385037 + 0.0666903i
\(800\) 209.886i 0.262357i
\(801\) 41.2159 49.5711i 0.0514556 0.0618865i
\(802\) 128.215 0.159869
\(803\) 1033.97 596.962i 1.28763 0.743414i
\(804\) 43.3087 + 242.421i 0.0538666 + 0.301519i
\(805\) 52.5179 90.9637i 0.0652397 0.112998i
\(806\) 13.6235 + 7.86556i 0.0169027 + 0.00975876i
\(807\) −237.668 + 657.593i −0.294508 + 0.814861i
\(808\) −149.563 259.051i −0.185103 0.320608i
\(809\) 1184.24i 1.46383i −0.681395 0.731916i \(-0.738626\pi\)
0.681395 0.731916i \(-0.261374\pi\)
\(810\) 102.189 + 550.488i 0.126160 + 0.679615i
\(811\) −991.880 −1.22303 −0.611517 0.791232i \(-0.709440\pi\)
−0.611517 + 0.791232i \(0.709440\pi\)
\(812\) −377.144 + 217.744i −0.464464 + 0.268158i
\(813\) −1095.13 395.804i −1.34703 0.486844i
\(814\) −1397.13 + 2419.90i −1.71638 + 2.97286i
\(815\) −224.229 129.459i −0.275128 0.158845i
\(816\) −708.253 + 126.530i −0.867957 + 0.155061i
\(817\) −61.6310 106.748i −0.0754357 0.130659i
\(818\) 64.6682i 0.0790565i
\(819\) 38.3744 + 31.9064i 0.0468552 + 0.0389577i
\(820\) 66.7130 0.0813573
\(821\) −986.241 + 569.407i −1.20127 + 0.693553i −0.960837 0.277114i \(-0.910622\pi\)
−0.240431 + 0.970666i \(0.577289\pi\)
\(822\) 1477.86 1245.76i 1.79789 1.51552i
\(823\) −381.236 + 660.320i −0.463227 + 0.802333i −0.999120 0.0419536i \(-0.986642\pi\)
0.535893 + 0.844286i \(0.319975\pi\)
\(824\) 229.478 + 132.489i 0.278493 + 0.160788i
\(825\) 172.421 + 204.546i 0.208995 + 0.247934i
\(826\) 123.307 + 213.573i 0.149282 + 0.258563i
\(827\) 1111.94i 1.34455i −0.740301 0.672275i \(-0.765317\pi\)
0.740301 0.672275i \(-0.234683\pi\)
\(828\) −1049.42 180.169i −1.26742 0.217596i
\(829\) −128.075 −0.154493 −0.0772465 0.997012i \(-0.524613\pi\)
−0.0772465 + 0.997012i \(0.524613\pi\)
\(830\) −127.078 + 73.3685i −0.153106 + 0.0883958i
\(831\) 18.9457 + 106.049i 0.0227987 + 0.127616i
\(832\) 126.113 218.434i 0.151578 0.262541i
\(833\) −1246.11 719.440i −1.49593 0.863674i
\(834\) 423.932 1172.96i 0.508312 1.40643i
\(835\) −1.81883 3.15030i −0.00217823 0.00377281i
\(836\) 786.158i 0.940381i
\(837\) 54.6583 0.369438i 0.0653026 0.000441383i
\(838\) −1287.94 −1.53692
\(839\) 597.707 345.086i 0.712404 0.411307i −0.0995467 0.995033i \(-0.531739\pi\)
0.811950 + 0.583726i \(0.198406\pi\)
\(840\) −66.9325 24.1908i −0.0796816 0.0287986i
\(841\) 210.816 365.145i 0.250674 0.434179i
\(842\) −894.669 516.538i −1.06255 0.613465i
\(843\) 890.090 159.015i 1.05586 0.188630i
\(844\) 378.906 + 656.285i 0.448941 + 0.777589i
\(845\) 363.766i 0.430492i
\(846\) −49.2576 + 18.1801i −0.0582241 + 0.0214894i
\(847\) 434.741 0.513272
\(848\) −395.153 + 228.142i −0.465982 + 0.269035i
\(849\) 975.933 822.659i 1.14951 0.968974i
\(850\) 251.957 436.403i 0.296420 0.513415i
\(851\) −934.674 539.634i −1.09832 0.634118i
\(852\) 1128.70 + 1339.00i 1.32477 + 1.57159i
\(853\) 21.2098 + 36.7364i 0.0248649 + 0.0430673i 0.878190 0.478312i \(-0.158751\pi\)
−0.853325 + 0.521379i \(0.825418\pi\)
\(854\) 288.094i 0.337346i
\(855\) 55.2853 + 149.792i 0.0646612 + 0.175195i
\(856\) −410.052 −0.479033
\(857\) −129.055 + 74.5099i −0.150589 + 0.0869427i −0.573401 0.819275i \(-0.694376\pi\)
0.422812 + 0.906217i \(0.361043\pi\)
\(858\) −73.1189 409.284i −0.0852202 0.477021i
\(859\) 101.735 176.211i 0.118435 0.205135i −0.800713 0.599048i \(-0.795546\pi\)
0.919148 + 0.393913i \(0.128879\pi\)
\(860\) −167.149 96.5036i −0.194359 0.112213i
\(861\) 12.0792 33.4214i 0.0140293 0.0388170i
\(862\) −602.308 1043.23i −0.698733 1.21024i
\(863\) 923.552i 1.07016i 0.844800 + 0.535082i \(0.179719\pi\)
−0.844800 + 0.535082i \(0.820281\pi\)
\(864\) −7.66041 1133.36i −0.00886622 1.31176i
\(865\) −268.781 −0.310729
\(866\) 1988.23 1147.90i 2.29587 1.32552i
\(867\) 2183.55 + 789.180i 2.51851 + 0.910242i
\(868\) −12.4054 + 21.4868i −0.0142919 + 0.0247544i
\(869\) −1068.06 616.644i −1.22907 0.709601i
\(870\) 725.366 129.587i 0.833754 0.148951i
\(871\) −18.5701 32.1643i −0.0213204 0.0369280i
\(872\) 307.944i 0.353147i
\(873\) 169.558 987.616i 0.194225 1.13129i
\(874\) −522.265 −0.597557
\(875\) −21.3586 + 12.3314i −0.0244099 + 0.0140930i
\(876\) 853.122 719.136i 0.973883 0.820931i
\(877\) 333.571 577.762i 0.380355 0.658794i −0.610758 0.791817i \(-0.709135\pi\)
0.991113 + 0.133023i \(0.0424686\pi\)
\(878\) 593.412 + 342.606i 0.675867 + 0.390212i
\(879\) 743.289 + 881.775i 0.845607 + 1.00316i
\(880\) −146.677 254.051i −0.166678 0.288695i
\(881\) 837.220i 0.950307i 0.879903 + 0.475153i \(0.157607\pi\)
−0.879903 + 0.475153i \(0.842393\pi\)
\(882\) 785.009 944.145i 0.890033 1.07046i
\(883\) −790.539 −0.895287 −0.447644 0.894212i \(-0.647737\pi\)
−0.447644 + 0.894212i \(0.647737\pi\)
\(884\) −394.326 + 227.664i −0.446070 + 0.257539i
\(885\) −42.6661 238.824i −0.0482103 0.269857i
\(886\) −269.610 + 466.979i −0.304301 + 0.527064i
\(887\) −336.825 194.466i −0.379735 0.219240i 0.297968 0.954576i \(-0.403691\pi\)
−0.677703 + 0.735336i \(0.737025\pi\)
\(888\) −248.566 + 687.748i −0.279917 + 0.774491i
\(889\) 47.3313 + 81.9803i 0.0532411 + 0.0922163i
\(890\) 49.5128i 0.0556323i
\(891\) −938.518 1098.23i −1.05333 1.23258i
\(892\) −1879.70 −2.10728
\(893\) −12.9673 + 7.48666i −0.0145210 + 0.00838372i
\(894\) 1059.91 + 383.073i 1.18558 + 0.428493i
\(895\) −176.360 + 305.465i −0.197051 + 0.341302i
\(896\) 271.775 + 156.909i 0.303320 + 0.175122i
\(897\) 158.083 28.2417i 0.176236 0.0314847i
\(898\) 490.066 + 848.819i 0.545730 + 0.945233i
\(899\) 71.9351i 0.0800168i
\(900\) 192.243 + 159.841i 0.213604 + 0.177601i
\(901\) 2022.31 2.24452
\(902\) −256.394 + 148.029i −0.284251 + 0.164112i
\(903\) −78.6101 + 66.2641i −0.0870543 + 0.0733821i
\(904\) 364.302 630.990i 0.402989 0.697998i
\(905\) −424.226 244.927i −0.468758 0.270637i
\(906\) −251.330 298.156i −0.277406 0.329091i
\(907\) −36.6233 63.4335i −0.0403785 0.0699377i 0.845130 0.534561i \(-0.179523\pi\)
−0.885508 + 0.464623i \(0.846190\pi\)
\(908\) 852.287i 0.938642i
\(909\) 551.680 + 94.7149i 0.606908 + 0.104197i
\(910\) 38.3292 0.0421200
\(911\) −830.528 + 479.506i −0.911667 + 0.526351i −0.880967 0.473178i \(-0.843107\pi\)
−0.0306997 + 0.999529i \(0.509774\pi\)
\(912\) −30.7917 172.357i −0.0337628 0.188987i
\(913\) 189.303 327.883i 0.207342 0.359127i
\(914\) 1325.82 + 765.461i 1.45057 + 0.837485i
\(915\) 96.3322 266.537i 0.105281 0.291298i
\(916\) −703.860 1219.12i −0.768406 1.33092i
\(917\) 134.219i 0.146368i
\(918\) −1344.61 + 2365.72i −1.46472 + 2.57703i
\(919\) 1280.94 1.39384 0.696919 0.717149i \(-0.254554\pi\)
0.696919 + 0.717149i \(0.254554\pi\)
\(920\) −198.327 + 114.504i −0.215573 + 0.124461i
\(921\) 369.339 + 133.487i 0.401019 + 0.144937i
\(922\) −331.705 + 574.530i −0.359767 + 0.623135i
\(923\) −228.734 132.059i −0.247816 0.143076i
\(924\) 645.514 115.322i 0.698608 0.124807i
\(925\) 126.708 + 219.465i 0.136982 + 0.237260i
\(926\) 1303.85i 1.40804i
\(927\) −465.179 + 171.689i −0.501811 + 0.185209i
\(928\) −1491.60 −1.60732
\(929\) 1468.25 847.697i 1.58047 0.912483i 0.585676 0.810545i \(-0.300829\pi\)
0.994791 0.101938i \(-0.0325042\pi\)
\(930\) 32.0977 27.0567i 0.0345137 0.0290932i
\(931\) 175.079 303.246i 0.188055 0.325720i
\(932\) 1488.04 + 859.122i 1.59661 + 0.921805i
\(933\) −1086.08 1288.43i −1.16407 1.38096i
\(934\) 191.349 + 331.426i 0.204871 + 0.354846i
\(935\) 1300.19i 1.39057i
\(936\) −37.6754 102.079i −0.0402515 0.109059i
\(937\) −1690.96 −1.80465 −0.902326 0.431054i \(-0.858142\pi\)
−0.902326 + 0.431054i \(0.858142\pi\)
\(938\) 87.2517 50.3748i 0.0930189 0.0537045i
\(939\) 21.3569 + 119.546i 0.0227443 + 0.127312i
\(940\) −11.7228 + 20.3045i −0.0124711 + 0.0216006i
\(941\) −1049.49 605.926i −1.11530 0.643917i −0.175100 0.984551i \(-0.556025\pi\)
−0.940196 + 0.340634i \(0.889358\pi\)
\(942\) 295.006 816.239i 0.313170 0.866496i
\(943\) −57.1754 99.0308i −0.0606314 0.105017i
\(944\) 266.030i 0.281812i
\(945\) 114.884 67.3677i 0.121570 0.0712885i
\(946\) 856.527 0.905419
\(947\) −510.822 + 294.923i −0.539411 + 0.311429i −0.744840 0.667243i \(-0.767474\pi\)
0.205429 + 0.978672i \(0.434141\pi\)
\(948\) −1083.95 391.762i −1.14341 0.413251i
\(949\) −84.1397 + 145.734i −0.0886614 + 0.153566i
\(950\) 106.200 + 61.3149i 0.111790 + 0.0645420i
\(951\) 385.708 68.9071i 0.405582 0.0724575i
\(952\) −172.947 299.553i −0.181667 0.314656i
\(953\) 1597.56i 1.67635i 0.545402 + 0.838174i \(0.316377\pi\)
−0.545402 + 0.838174i \(0.683623\pi\)
\(954\) −292.010 + 1700.85i −0.306090 + 1.78286i
\(955\) 830.815 0.869963
\(956\) −345.593 + 199.528i −0.361499 + 0.208711i
\(957\) −1453.65 + 1225.35i −1.51896 + 1.28040i
\(958\) −1038.02 + 1797.90i −1.08353 + 1.87672i
\(959\) −398.167 229.882i −0.415190 0.239710i
\(960\) −433.814 514.641i −0.451890 0.536084i
\(961\) 478.451 + 828.701i 0.497868 + 0.862332i
\(962\) 393.842i 0.409399i
\(963\) 490.574 590.022i 0.509422 0.612691i
\(964\) −1683.20 −1.74605
\(965\) 76.6061 44.2286i 0.0793846 0.0458327i
\(966\) 76.6111 + 428.831i 0.0793075 + 0.443925i
\(967\) −313.476 + 542.957i −0.324174 + 0.561486i −0.981345 0.192256i \(-0.938420\pi\)
0.657171 + 0.753742i \(0.271753\pi\)
\(968\) −820.873 473.931i −0.848009 0.489598i
\(969\) −263.766 + 729.802i −0.272204 + 0.753150i
\(970\) −384.807 666.506i −0.396708 0.687119i
\(971\) 1907.25i 1.96421i −0.188328 0.982106i \(-0.560307\pi\)
0.188328 0.982106i \(-0.439693\pi\)
\(972\) −1043.92 856.104i −1.07400 0.880766i
\(973\) −296.671 −0.304903
\(974\) 360.802 208.309i 0.370434 0.213870i
\(975\) −35.4613 12.8164i −0.0363705 0.0131451i
\(976\) −155.388 + 269.141i −0.159209 + 0.275759i
\(977\) −764.149 441.181i −0.782138 0.451568i 0.0550495 0.998484i \(-0.482468\pi\)
−0.837187 + 0.546916i \(0.815802\pi\)
\(978\) 1057.09 188.849i 1.08087 0.193098i
\(979\) 63.8757 + 110.636i 0.0652459 + 0.113009i
\(980\) 548.288i 0.559477i
\(981\) −443.099 368.414i −0.451680 0.375550i
\(982\) 1467.44 1.49434
\(983\) 838.049 483.848i 0.852543 0.492216i −0.00896527 0.999960i \(-0.502854\pi\)
0.861508 + 0.507744i \(0.169520\pi\)
\(984\) −59.2420 + 49.9378i −0.0602053 + 0.0507498i
\(985\) −116.783 + 202.274i −0.118562 + 0.205355i
\(986\) 3101.39 + 1790.59i 3.14542 + 1.81601i
\(987\) 8.04947 + 9.54921i 0.00815549 + 0.00967498i
\(988\) −55.4031 95.9610i −0.0560760 0.0971265i
\(989\) 330.828i 0.334508i
\(990\) −1093.51 187.739i −1.10455 0.189635i
\(991\) 416.462 0.420245 0.210122 0.977675i \(-0.432614\pi\)
0.210122 + 0.977675i \(0.432614\pi\)
\(992\) −73.5946 + 42.4899i −0.0741881 + 0.0428325i
\(993\) 258.884 + 1449.11i 0.260709 + 1.45932i
\(994\) 358.236 620.484i 0.360399 0.624229i
\(995\) 228.576 + 131.969i 0.229725 + 0.132632i
\(996\) 120.267 332.761i 0.120750 0.334097i
\(997\) 438.591 + 759.663i 0.439911 + 0.761948i 0.997682 0.0680464i \(-0.0216766\pi\)
−0.557771 + 0.829995i \(0.688343\pi\)
\(998\) 1726.13i 1.72959i
\(999\) −692.219 1180.46i −0.692912 1.18164i
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 45.3.i.a.41.8 yes 16
3.2 odd 2 135.3.i.a.71.1 16
4.3 odd 2 720.3.bs.c.401.8 16
5.2 odd 4 225.3.i.b.149.14 32
5.3 odd 4 225.3.i.b.149.3 32
5.4 even 2 225.3.j.b.176.1 16
9.2 odd 6 inner 45.3.i.a.11.8 16
9.4 even 3 405.3.c.a.161.14 16
9.5 odd 6 405.3.c.a.161.3 16
9.7 even 3 135.3.i.a.116.1 16
12.11 even 2 2160.3.bs.c.881.3 16
15.2 even 4 675.3.i.c.449.3 32
15.8 even 4 675.3.i.c.449.14 32
15.14 odd 2 675.3.j.b.476.8 16
36.7 odd 6 2160.3.bs.c.1601.3 16
36.11 even 6 720.3.bs.c.641.8 16
45.2 even 12 225.3.i.b.74.3 32
45.7 odd 12 675.3.i.c.224.14 32
45.29 odd 6 225.3.j.b.101.1 16
45.34 even 6 675.3.j.b.251.8 16
45.38 even 12 225.3.i.b.74.14 32
45.43 odd 12 675.3.i.c.224.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.3.i.a.11.8 16 9.2 odd 6 inner
45.3.i.a.41.8 yes 16 1.1 even 1 trivial
135.3.i.a.71.1 16 3.2 odd 2
135.3.i.a.116.1 16 9.7 even 3
225.3.i.b.74.3 32 45.2 even 12
225.3.i.b.74.14 32 45.38 even 12
225.3.i.b.149.3 32 5.3 odd 4
225.3.i.b.149.14 32 5.2 odd 4
225.3.j.b.101.1 16 45.29 odd 6
225.3.j.b.176.1 16 5.4 even 2
405.3.c.a.161.3 16 9.5 odd 6
405.3.c.a.161.14 16 9.4 even 3
675.3.i.c.224.3 32 45.43 odd 12
675.3.i.c.224.14 32 45.7 odd 12
675.3.i.c.449.3 32 15.2 even 4
675.3.i.c.449.14 32 15.8 even 4
675.3.j.b.251.8 16 45.34 even 6
675.3.j.b.476.8 16 15.14 odd 2
720.3.bs.c.401.8 16 4.3 odd 2
720.3.bs.c.641.8 16 36.11 even 6
2160.3.bs.c.881.3 16 12.11 even 2
2160.3.bs.c.1601.3 16 36.7 odd 6