Properties

Label 690.3.k.a.553.3
Level $690$
Weight $3$
Character 690.553
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
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] = [690,3,Mod(277,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 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("690.277");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (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: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 553.3
Character \(\chi\) \(=\) 690.553
Dual form 690.3.k.a.277.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(3.78471 + 3.26741i) q^{5} -2.44949 q^{6} +(3.72268 - 3.72268i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(3.78471 + 3.26741i) q^{5} -2.44949 q^{6} +(3.72268 - 3.72268i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(7.05212 - 0.517301i) q^{10} +11.8026 q^{11} +(-2.44949 + 2.44949i) q^{12} +(17.6286 + 17.6286i) q^{13} -7.44536i q^{14} +(-0.633562 - 8.63705i) q^{15} -4.00000 q^{16} +(-20.6341 + 20.6341i) q^{17} +(3.00000 + 3.00000i) q^{18} +6.19835i q^{19} +(6.53482 - 7.56942i) q^{20} -9.11866 q^{21} +(11.8026 - 11.8026i) q^{22} +(-3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(3.64807 + 24.7324i) q^{25} +35.2571 q^{26} +(3.67423 - 3.67423i) q^{27} +(-7.44536 - 7.44536i) q^{28} -0.0875899i q^{29} +(-9.27061 - 8.00349i) q^{30} -0.753876 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-14.4552 - 14.4552i) q^{33} +41.2682i q^{34} +(26.2528 - 1.92575i) q^{35} +6.00000 q^{36} +(28.5265 - 28.5265i) q^{37} +(6.19835 + 6.19835i) q^{38} -43.1810i q^{39} +(-1.03460 - 14.1042i) q^{40} +57.1315 q^{41} +(-9.11866 + 9.11866i) q^{42} +(-1.66664 - 1.66664i) q^{43} -23.6052i q^{44} +(-9.80223 + 11.3541i) q^{45} -6.78233 q^{46} +(40.7708 - 40.7708i) q^{47} +(4.89898 + 4.89898i) q^{48} +21.2833i q^{49} +(28.3805 + 21.0843i) q^{50} +50.5430 q^{51} +(35.2571 - 35.2571i) q^{52} +(7.42708 + 7.42708i) q^{53} -7.34847i q^{54} +(44.6694 + 38.5639i) q^{55} -14.8907 q^{56} +(7.59140 - 7.59140i) q^{57} +(-0.0875899 - 0.0875899i) q^{58} -106.957i q^{59} +(-17.2741 + 1.26712i) q^{60} -91.1049 q^{61} +(-0.753876 + 0.753876i) q^{62} +(11.1680 + 11.1680i) q^{63} +8.00000i q^{64} +(9.11928 + 124.319i) q^{65} -28.9104 q^{66} +(22.3209 - 22.3209i) q^{67} +(41.2682 + 41.2682i) q^{68} +8.30662i q^{69} +(24.3270 - 28.1785i) q^{70} -123.707 q^{71} +(6.00000 - 6.00000i) q^{72} +(14.6619 + 14.6619i) q^{73} -57.0530i q^{74} +(25.8229 - 34.7588i) q^{75} +12.3967 q^{76} +(43.9373 - 43.9373i) q^{77} +(-43.1810 - 43.1810i) q^{78} +22.2431i q^{79} +(-15.1388 - 13.0696i) q^{80} -9.00000 q^{81} +(57.1315 - 57.1315i) q^{82} +(4.59002 + 4.59002i) q^{83} +18.2373i q^{84} +(-145.514 + 10.6741i) q^{85} -3.33329 q^{86} +(-0.107275 + 0.107275i) q^{87} +(-23.6052 - 23.6052i) q^{88} -30.0252i q^{89} +(1.55190 + 21.1564i) q^{90} +131.251 q^{91} +(-6.78233 + 6.78233i) q^{92} +(0.923306 + 0.923306i) q^{93} -81.5417i q^{94} +(-20.2525 + 23.4590i) q^{95} +9.79796 q^{96} +(120.850 - 120.850i) q^{97} +(21.2833 + 21.2833i) q^{98} +35.4078i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 3.78471 + 3.26741i 0.756942 + 0.653482i
\(6\) −2.44949 −0.408248
\(7\) 3.72268 3.72268i 0.531811 0.531811i −0.389300 0.921111i \(-0.627283\pi\)
0.921111 + 0.389300i \(0.127283\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 7.05212 0.517301i 0.705212 0.0517301i
\(11\) 11.8026 1.07296 0.536482 0.843912i \(-0.319753\pi\)
0.536482 + 0.843912i \(0.319753\pi\)
\(12\) −2.44949 + 2.44949i −0.204124 + 0.204124i
\(13\) 17.6286 + 17.6286i 1.35604 + 1.35604i 0.878738 + 0.477305i \(0.158386\pi\)
0.477305 + 0.878738i \(0.341614\pi\)
\(14\) 7.44536i 0.531811i
\(15\) −0.633562 8.63705i −0.0422375 0.575803i
\(16\) −4.00000 −0.250000
\(17\) −20.6341 + 20.6341i −1.21377 + 1.21377i −0.243994 + 0.969777i \(0.578458\pi\)
−0.969777 + 0.243994i \(0.921542\pi\)
\(18\) 3.00000 + 3.00000i 0.166667 + 0.166667i
\(19\) 6.19835i 0.326229i 0.986607 + 0.163114i \(0.0521540\pi\)
−0.986607 + 0.163114i \(0.947846\pi\)
\(20\) 6.53482 7.56942i 0.326741 0.378471i
\(21\) −9.11866 −0.434222
\(22\) 11.8026 11.8026i 0.536482 0.536482i
\(23\) −3.39116 3.39116i −0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 3.64807 + 24.7324i 0.145923 + 0.989296i
\(26\) 35.2571 1.35604
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) −7.44536 7.44536i −0.265906 0.265906i
\(29\) 0.0875899i 0.00302034i −0.999999 0.00151017i \(-0.999519\pi\)
0.999999 0.00151017i \(-0.000480702\pi\)
\(30\) −9.27061 8.00349i −0.309020 0.266783i
\(31\) −0.753876 −0.0243186 −0.0121593 0.999926i \(-0.503871\pi\)
−0.0121593 + 0.999926i \(0.503871\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) −14.4552 14.4552i −0.438036 0.438036i
\(34\) 41.2682i 1.21377i
\(35\) 26.2528 1.92575i 0.750079 0.0550213i
\(36\) 6.00000 0.166667
\(37\) 28.5265 28.5265i 0.770986 0.770986i −0.207293 0.978279i \(-0.566465\pi\)
0.978279 + 0.207293i \(0.0664652\pi\)
\(38\) 6.19835 + 6.19835i 0.163114 + 0.163114i
\(39\) 43.1810i 1.10720i
\(40\) −1.03460 14.1042i −0.0258651 0.352606i
\(41\) 57.1315 1.39345 0.696725 0.717338i \(-0.254640\pi\)
0.696725 + 0.717338i \(0.254640\pi\)
\(42\) −9.11866 + 9.11866i −0.217111 + 0.217111i
\(43\) −1.66664 1.66664i −0.0387592 0.0387592i 0.687462 0.726221i \(-0.258725\pi\)
−0.726221 + 0.687462i \(0.758725\pi\)
\(44\) 23.6052i 0.536482i
\(45\) −9.80223 + 11.3541i −0.217827 + 0.252314i
\(46\) −6.78233 −0.147442
\(47\) 40.7708 40.7708i 0.867464 0.867464i −0.124727 0.992191i \(-0.539805\pi\)
0.992191 + 0.124727i \(0.0398054\pi\)
\(48\) 4.89898 + 4.89898i 0.102062 + 0.102062i
\(49\) 21.2833i 0.434354i
\(50\) 28.3805 + 21.0843i 0.567609 + 0.421687i
\(51\) 50.5430 0.991040
\(52\) 35.2571 35.2571i 0.678021 0.678021i
\(53\) 7.42708 + 7.42708i 0.140134 + 0.140134i 0.773694 0.633560i \(-0.218407\pi\)
−0.633560 + 0.773694i \(0.718407\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 44.6694 + 38.5639i 0.812172 + 0.701162i
\(56\) −14.8907 −0.265906
\(57\) 7.59140 7.59140i 0.133182 0.133182i
\(58\) −0.0875899 0.0875899i −0.00151017 0.00151017i
\(59\) 106.957i 1.81283i −0.422391 0.906413i \(-0.638809\pi\)
0.422391 0.906413i \(-0.361191\pi\)
\(60\) −17.2741 + 1.26712i −0.287902 + 0.0211187i
\(61\) −91.1049 −1.49352 −0.746761 0.665092i \(-0.768392\pi\)
−0.746761 + 0.665092i \(0.768392\pi\)
\(62\) −0.753876 + 0.753876i −0.0121593 + 0.0121593i
\(63\) 11.1680 + 11.1680i 0.177270 + 0.177270i
\(64\) 8.00000i 0.125000i
\(65\) 9.11928 + 124.319i 0.140297 + 1.91260i
\(66\) −28.9104 −0.438036
\(67\) 22.3209 22.3209i 0.333148 0.333148i −0.520633 0.853781i \(-0.674304\pi\)
0.853781 + 0.520633i \(0.174304\pi\)
\(68\) 41.2682 + 41.2682i 0.606885 + 0.606885i
\(69\) 8.30662i 0.120386i
\(70\) 24.3270 28.1785i 0.347529 0.402550i
\(71\) −123.707 −1.74235 −0.871177 0.490969i \(-0.836643\pi\)
−0.871177 + 0.490969i \(0.836643\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) 14.6619 + 14.6619i 0.200848 + 0.200848i 0.800363 0.599515i \(-0.204640\pi\)
−0.599515 + 0.800363i \(0.704640\pi\)
\(74\) 57.0530i 0.770986i
\(75\) 25.8229 34.7588i 0.344306 0.463451i
\(76\) 12.3967 0.163114
\(77\) 43.9373 43.9373i 0.570614 0.570614i
\(78\) −43.1810 43.1810i −0.553602 0.553602i
\(79\) 22.2431i 0.281558i 0.990041 + 0.140779i \(0.0449607\pi\)
−0.990041 + 0.140779i \(0.955039\pi\)
\(80\) −15.1388 13.0696i −0.189236 0.163370i
\(81\) −9.00000 −0.111111
\(82\) 57.1315 57.1315i 0.696725 0.696725i
\(83\) 4.59002 + 4.59002i 0.0553014 + 0.0553014i 0.734217 0.678915i \(-0.237550\pi\)
−0.678915 + 0.734217i \(0.737550\pi\)
\(84\) 18.2373i 0.217111i
\(85\) −145.514 + 10.6741i −1.71193 + 0.125577i
\(86\) −3.33329 −0.0387592
\(87\) −0.107275 + 0.107275i −0.00123305 + 0.00123305i
\(88\) −23.6052 23.6052i −0.268241 0.268241i
\(89\) 30.0252i 0.337361i −0.985671 0.168681i \(-0.946049\pi\)
0.985671 0.168681i \(-0.0539507\pi\)
\(90\) 1.55190 + 21.1564i 0.0172434 + 0.235071i
\(91\) 131.251 1.44232
\(92\) −6.78233 + 6.78233i −0.0737210 + 0.0737210i
\(93\) 0.923306 + 0.923306i 0.00992802 + 0.00992802i
\(94\) 81.5417i 0.867464i
\(95\) −20.2525 + 23.4590i −0.213185 + 0.246936i
\(96\) 9.79796 0.102062
\(97\) 120.850 120.850i 1.24587 1.24587i 0.288347 0.957526i \(-0.406894\pi\)
0.957526 0.288347i \(-0.0931056\pi\)
\(98\) 21.2833 + 21.2833i 0.217177 + 0.217177i
\(99\) 35.4078i 0.357655i
\(100\) 49.4648 7.29614i 0.494648 0.0729614i
\(101\) −6.35681 −0.0629387 −0.0314693 0.999505i \(-0.510019\pi\)
−0.0314693 + 0.999505i \(0.510019\pi\)
\(102\) 50.5430 50.5430i 0.495520 0.495520i
\(103\) 128.811 + 128.811i 1.25059 + 1.25059i 0.955455 + 0.295136i \(0.0953649\pi\)
0.295136 + 0.955455i \(0.404635\pi\)
\(104\) 70.5142i 0.678021i
\(105\) −34.5115 29.7944i −0.328681 0.283756i
\(106\) 14.8542 0.140134
\(107\) 47.4520 47.4520i 0.443477 0.443477i −0.449702 0.893179i \(-0.648470\pi\)
0.893179 + 0.449702i \(0.148470\pi\)
\(108\) −7.34847 7.34847i −0.0680414 0.0680414i
\(109\) 145.890i 1.33844i −0.743062 0.669222i \(-0.766627\pi\)
0.743062 0.669222i \(-0.233373\pi\)
\(110\) 83.2334 6.10550i 0.756667 0.0555046i
\(111\) −69.8754 −0.629508
\(112\) −14.8907 + 14.8907i −0.132953 + 0.132953i
\(113\) −94.3049 94.3049i −0.834557 0.834557i 0.153580 0.988136i \(-0.450920\pi\)
−0.988136 + 0.153580i \(0.950920\pi\)
\(114\) 15.1828i 0.133182i
\(115\) −1.75425 23.9149i −0.0152544 0.207956i
\(116\) −0.175180 −0.00151017
\(117\) −52.8857 + 52.8857i −0.452014 + 0.452014i
\(118\) −106.957 106.957i −0.906413 0.906413i
\(119\) 153.628i 1.29099i
\(120\) −16.0070 + 18.5412i −0.133391 + 0.154510i
\(121\) 18.3014 0.151252
\(122\) −91.1049 + 91.1049i −0.746761 + 0.746761i
\(123\) −69.9715 69.9715i −0.568874 0.568874i
\(124\) 1.50775i 0.0121593i
\(125\) −67.0040 + 105.525i −0.536032 + 0.844198i
\(126\) 22.3361 0.177270
\(127\) 10.3220 10.3220i 0.0812757 0.0812757i −0.665300 0.746576i \(-0.731696\pi\)
0.746576 + 0.665300i \(0.231696\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 4.08243i 0.0316467i
\(130\) 133.438 + 115.199i 1.02645 + 0.886149i
\(131\) −184.410 −1.40771 −0.703856 0.710343i \(-0.748540\pi\)
−0.703856 + 0.710343i \(0.748540\pi\)
\(132\) −28.9104 + 28.9104i −0.219018 + 0.219018i
\(133\) 23.0745 + 23.0745i 0.173492 + 0.173492i
\(134\) 44.6418i 0.333148i
\(135\) 25.9111 1.90069i 0.191934 0.0140792i
\(136\) 82.5364 0.606885
\(137\) −171.020 + 171.020i −1.24832 + 1.24832i −0.291859 + 0.956461i \(0.594274\pi\)
−0.956461 + 0.291859i \(0.905726\pi\)
\(138\) 8.30662 + 8.30662i 0.0601929 + 0.0601929i
\(139\) 83.8444i 0.603197i −0.953435 0.301599i \(-0.902480\pi\)
0.953435 0.301599i \(-0.0975203\pi\)
\(140\) −3.85149 52.5056i −0.0275107 0.375040i
\(141\) −99.8677 −0.708282
\(142\) −123.707 + 123.707i −0.871177 + 0.871177i
\(143\) 208.063 + 208.063i 1.45498 + 1.45498i
\(144\) 12.0000i 0.0833333i
\(145\) 0.286192 0.331502i 0.00197374 0.00228622i
\(146\) 29.3239 0.200848
\(147\) 26.0666 26.0666i 0.177324 0.177324i
\(148\) −57.0530 57.0530i −0.385493 0.385493i
\(149\) 117.040i 0.785504i 0.919644 + 0.392752i \(0.128477\pi\)
−0.919644 + 0.392752i \(0.871523\pi\)
\(150\) −8.93591 60.5818i −0.0595728 0.403878i
\(151\) 39.9086 0.264295 0.132148 0.991230i \(-0.457813\pi\)
0.132148 + 0.991230i \(0.457813\pi\)
\(152\) 12.3967 12.3967i 0.0815572 0.0815572i
\(153\) −61.9023 61.9023i −0.404590 0.404590i
\(154\) 87.8746i 0.570614i
\(155\) −2.85320 2.46322i −0.0184078 0.0158918i
\(156\) −86.3619 −0.553602
\(157\) −56.3304 + 56.3304i −0.358793 + 0.358793i −0.863368 0.504575i \(-0.831649\pi\)
0.504575 + 0.863368i \(0.331649\pi\)
\(158\) 22.2431 + 22.2431i 0.140779 + 0.140779i
\(159\) 18.1926i 0.114419i
\(160\) −28.2085 + 2.06921i −0.176303 + 0.0129325i
\(161\) −25.2484 −0.156823
\(162\) −9.00000 + 9.00000i −0.0555556 + 0.0555556i
\(163\) 104.950 + 104.950i 0.643867 + 0.643867i 0.951504 0.307637i \(-0.0995382\pi\)
−0.307637 + 0.951504i \(0.599538\pi\)
\(164\) 114.263i 0.696725i
\(165\) −7.47768 101.940i −0.0453193 0.617816i
\(166\) 9.18003 0.0553014
\(167\) −173.661 + 173.661i −1.03989 + 1.03989i −0.0407150 + 0.999171i \(0.512964\pi\)
−0.999171 + 0.0407150i \(0.987036\pi\)
\(168\) 18.2373 + 18.2373i 0.108556 + 0.108556i
\(169\) 452.532i 2.67770i
\(170\) −134.840 + 156.188i −0.793177 + 0.918754i
\(171\) −18.5951 −0.108743
\(172\) −3.33329 + 3.33329i −0.0193796 + 0.0193796i
\(173\) −151.999 151.999i −0.878608 0.878608i 0.114783 0.993391i \(-0.463383\pi\)
−0.993391 + 0.114783i \(0.963383\pi\)
\(174\) 0.214551i 0.00123305i
\(175\) 105.651 + 78.4902i 0.603722 + 0.448515i
\(176\) −47.2104 −0.268241
\(177\) −130.995 + 130.995i −0.740084 + 0.740084i
\(178\) −30.0252 30.0252i −0.168681 0.168681i
\(179\) 133.690i 0.746874i 0.927656 + 0.373437i \(0.121821\pi\)
−0.927656 + 0.373437i \(0.878179\pi\)
\(180\) 22.7083 + 19.6045i 0.126157 + 0.108914i
\(181\) 269.565 1.48931 0.744655 0.667450i \(-0.232614\pi\)
0.744655 + 0.667450i \(0.232614\pi\)
\(182\) 131.251 131.251i 0.721159 0.721159i
\(183\) 111.580 + 111.580i 0.609728 + 0.609728i
\(184\) 13.5647i 0.0737210i
\(185\) 201.172 14.7568i 1.08742 0.0797665i
\(186\) 1.84661 0.00992802
\(187\) −243.536 + 243.536i −1.30233 + 1.30233i
\(188\) −81.5417 81.5417i −0.433732 0.433732i
\(189\) 27.3560i 0.144741i
\(190\) 3.20642 + 43.7115i 0.0168759 + 0.230061i
\(191\) −322.402 −1.68797 −0.843986 0.536366i \(-0.819797\pi\)
−0.843986 + 0.536366i \(0.819797\pi\)
\(192\) 9.79796 9.79796i 0.0510310 0.0510310i
\(193\) −89.8376 89.8376i −0.465480 0.465480i 0.434967 0.900447i \(-0.356760\pi\)
−0.900447 + 0.434967i \(0.856760\pi\)
\(194\) 241.699i 1.24587i
\(195\) 141.090 163.427i 0.723538 0.838090i
\(196\) 42.5666 0.217177
\(197\) −43.4072 + 43.4072i −0.220341 + 0.220341i −0.808642 0.588301i \(-0.799797\pi\)
0.588301 + 0.808642i \(0.299797\pi\)
\(198\) 35.4078 + 35.4078i 0.178827 + 0.178827i
\(199\) 241.437i 1.21325i −0.794989 0.606624i \(-0.792523\pi\)
0.794989 0.606624i \(-0.207477\pi\)
\(200\) 42.1687 56.7609i 0.210843 0.283805i
\(201\) −54.6749 −0.272014
\(202\) −6.35681 + 6.35681i −0.0314693 + 0.0314693i
\(203\) −0.326069 0.326069i −0.00160625 0.00160625i
\(204\) 101.086i 0.495520i
\(205\) 216.226 + 186.672i 1.05476 + 0.910595i
\(206\) 257.622 1.25059
\(207\) 10.1735 10.1735i 0.0491473 0.0491473i
\(208\) −70.5142 70.5142i −0.339011 0.339011i
\(209\) 73.1567i 0.350032i
\(210\) −64.3059 + 4.71710i −0.306219 + 0.0224624i
\(211\) −52.1391 −0.247105 −0.123552 0.992338i \(-0.539429\pi\)
−0.123552 + 0.992338i \(0.539429\pi\)
\(212\) 14.8542 14.8542i 0.0700668 0.0700668i
\(213\) 151.510 + 151.510i 0.711313 + 0.711313i
\(214\) 94.9040i 0.443477i
\(215\) −0.862158 11.7534i −0.00401003 0.0546669i
\(216\) −14.6969 −0.0680414
\(217\) −2.80644 + 2.80644i −0.0129329 + 0.0129329i
\(218\) −145.890 145.890i −0.669222 0.669222i
\(219\) 35.9142i 0.163992i
\(220\) 77.1279 89.3389i 0.350581 0.406086i
\(221\) −727.499 −3.29185
\(222\) −69.8754 + 69.8754i −0.314754 + 0.314754i
\(223\) 280.452 + 280.452i 1.25763 + 1.25763i 0.952221 + 0.305410i \(0.0987935\pi\)
0.305410 + 0.952221i \(0.401206\pi\)
\(224\) 29.7814i 0.132953i
\(225\) −74.1972 + 10.9442i −0.329765 + 0.0486410i
\(226\) −188.610 −0.834557
\(227\) 144.396 144.396i 0.636105 0.636105i −0.313487 0.949592i \(-0.601497\pi\)
0.949592 + 0.313487i \(0.101497\pi\)
\(228\) −15.1828 15.1828i −0.0665912 0.0665912i
\(229\) 362.796i 1.58426i −0.610351 0.792131i \(-0.708972\pi\)
0.610351 0.792131i \(-0.291028\pi\)
\(230\) −25.6692 22.1606i −0.111605 0.0963506i
\(231\) −107.624 −0.465905
\(232\) −0.175180 + 0.175180i −0.000755085 + 0.000755085i
\(233\) −88.1385 88.1385i −0.378277 0.378277i 0.492203 0.870480i \(-0.336192\pi\)
−0.870480 + 0.492203i \(0.836192\pi\)
\(234\) 105.771i 0.452014i
\(235\) 287.521 21.0908i 1.22349 0.0897481i
\(236\) −213.914 −0.906413
\(237\) 27.2421 27.2421i 0.114946 0.114946i
\(238\) 153.628 + 153.628i 0.645497 + 0.645497i
\(239\) 296.594i 1.24098i −0.784214 0.620490i \(-0.786934\pi\)
0.784214 0.620490i \(-0.213066\pi\)
\(240\) 2.53425 + 34.5482i 0.0105594 + 0.143951i
\(241\) −286.041 −1.18689 −0.593445 0.804874i \(-0.702233\pi\)
−0.593445 + 0.804874i \(0.702233\pi\)
\(242\) 18.3014 18.3014i 0.0756258 0.0756258i
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 182.210i 0.746761i
\(245\) −69.5413 + 80.5512i −0.283842 + 0.328780i
\(246\) −139.943 −0.568874
\(247\) −109.268 + 109.268i −0.442380 + 0.442380i
\(248\) 1.50775 + 1.50775i 0.00607965 + 0.00607965i
\(249\) 11.2432i 0.0451534i
\(250\) 38.5207 + 172.529i 0.154083 + 0.690115i
\(251\) 181.698 0.723897 0.361949 0.932198i \(-0.382112\pi\)
0.361949 + 0.932198i \(0.382112\pi\)
\(252\) 22.3361 22.3361i 0.0886352 0.0886352i
\(253\) −40.0246 40.0246i −0.158200 0.158200i
\(254\) 20.6440i 0.0812757i
\(255\) 191.291 + 165.145i 0.750160 + 0.647627i
\(256\) 16.0000 0.0625000
\(257\) 196.253 196.253i 0.763631 0.763631i −0.213346 0.976977i \(-0.568436\pi\)
0.976977 + 0.213346i \(0.0684361\pi\)
\(258\) 4.08243 + 4.08243i 0.0158234 + 0.0158234i
\(259\) 212.390i 0.820039i
\(260\) 248.637 18.2386i 0.956298 0.0701483i
\(261\) 0.262770 0.00100678
\(262\) −184.410 + 184.410i −0.703856 + 0.703856i
\(263\) 231.129 + 231.129i 0.878816 + 0.878816i 0.993412 0.114596i \(-0.0365575\pi\)
−0.114596 + 0.993412i \(0.536557\pi\)
\(264\) 57.8207i 0.219018i
\(265\) 3.84204 + 52.3767i 0.0144983 + 0.197648i
\(266\) 46.1489 0.173492
\(267\) −36.7732 + 36.7732i −0.137727 + 0.137727i
\(268\) −44.6418 44.6418i −0.166574 0.166574i
\(269\) 275.606i 1.02456i 0.858820 + 0.512278i \(0.171198\pi\)
−0.858820 + 0.512278i \(0.828802\pi\)
\(270\) 24.0105 27.8118i 0.0889276 0.103007i
\(271\) −31.3910 −0.115834 −0.0579170 0.998321i \(-0.518446\pi\)
−0.0579170 + 0.998321i \(0.518446\pi\)
\(272\) 82.5364 82.5364i 0.303443 0.303443i
\(273\) −160.749 160.749i −0.588824 0.588824i
\(274\) 342.040i 1.24832i
\(275\) 43.0567 + 291.907i 0.156570 + 1.06148i
\(276\) 16.6132 0.0601929
\(277\) −15.9302 + 15.9302i −0.0575096 + 0.0575096i −0.735277 0.677767i \(-0.762948\pi\)
0.677767 + 0.735277i \(0.262948\pi\)
\(278\) −83.8444 83.8444i −0.301599 0.301599i
\(279\) 2.26163i 0.00810619i
\(280\) −56.3571 48.6541i −0.201275 0.173765i
\(281\) −48.1708 −0.171426 −0.0857131 0.996320i \(-0.527317\pi\)
−0.0857131 + 0.996320i \(0.527317\pi\)
\(282\) −99.8677 + 99.8677i −0.354141 + 0.354141i
\(283\) −136.406 136.406i −0.482000 0.482000i 0.423770 0.905770i \(-0.360706\pi\)
−0.905770 + 0.423770i \(0.860706\pi\)
\(284\) 247.414i 0.871177i
\(285\) 53.5355 3.92704i 0.187844 0.0137791i
\(286\) 416.126 1.45498
\(287\) 212.682 212.682i 0.741053 0.741053i
\(288\) −12.0000 12.0000i −0.0416667 0.0416667i
\(289\) 562.532i 1.94648i
\(290\) −0.0453104 0.617694i −0.000156243 0.00212998i
\(291\) −296.020 −1.01725
\(292\) 29.3239 29.3239i 0.100424 0.100424i
\(293\) 96.8737 + 96.8737i 0.330627 + 0.330627i 0.852825 0.522198i \(-0.174888\pi\)
−0.522198 + 0.852825i \(0.674888\pi\)
\(294\) 52.1333i 0.177324i
\(295\) 349.472 404.801i 1.18465 1.37221i
\(296\) −114.106 −0.385493
\(297\) 43.3655 43.3655i 0.146012 0.146012i
\(298\) 117.040 + 117.040i 0.392752 + 0.392752i
\(299\) 119.563i 0.399875i
\(300\) −69.5177 51.6458i −0.231726 0.172153i
\(301\) −12.4088 −0.0412251
\(302\) 39.9086 39.9086i 0.132148 0.132148i
\(303\) 7.78547 + 7.78547i 0.0256946 + 0.0256946i
\(304\) 24.7934i 0.0815572i
\(305\) −344.806 297.677i −1.13051 0.975990i
\(306\) −123.805 −0.404590
\(307\) 95.1467 95.1467i 0.309924 0.309924i −0.534956 0.844880i \(-0.679672\pi\)
0.844880 + 0.534956i \(0.179672\pi\)
\(308\) −87.8746 87.8746i −0.285307 0.285307i
\(309\) 315.521i 1.02110i
\(310\) −5.31643 + 0.389981i −0.0171498 + 0.00125800i
\(311\) −374.486 −1.20414 −0.602068 0.798445i \(-0.705656\pi\)
−0.602068 + 0.798445i \(0.705656\pi\)
\(312\) −86.3619 + 86.3619i −0.276801 + 0.276801i
\(313\) 276.544 + 276.544i 0.883528 + 0.883528i 0.993891 0.110363i \(-0.0352015\pi\)
−0.110363 + 0.993891i \(0.535201\pi\)
\(314\) 112.661i 0.358793i
\(315\) 5.77724 + 78.7583i 0.0183404 + 0.250026i
\(316\) 44.4862 0.140779
\(317\) 119.954 119.954i 0.378403 0.378403i −0.492123 0.870526i \(-0.663779\pi\)
0.870526 + 0.492123i \(0.163779\pi\)
\(318\) −18.1926 18.1926i −0.0572093 0.0572093i
\(319\) 1.03379i 0.00324072i
\(320\) −26.1393 + 30.2777i −0.0816852 + 0.0946178i
\(321\) −116.233 −0.362097
\(322\) −25.2484 + 25.2484i −0.0784113 + 0.0784113i
\(323\) −127.897 127.897i −0.395967 0.395967i
\(324\) 18.0000i 0.0555556i
\(325\) −371.686 + 500.307i −1.14365 + 1.53941i
\(326\) 209.901 0.643867
\(327\) −178.679 + 178.679i −0.546418 + 0.546418i
\(328\) −114.263 114.263i −0.348363 0.348363i
\(329\) 303.553i 0.922655i
\(330\) −109.417 94.4620i −0.331568 0.286248i
\(331\) −28.1304 −0.0849862 −0.0424931 0.999097i \(-0.513530\pi\)
−0.0424931 + 0.999097i \(0.513530\pi\)
\(332\) 9.18003 9.18003i 0.0276507 0.0276507i
\(333\) 85.5795 + 85.5795i 0.256995 + 0.256995i
\(334\) 347.322i 1.03989i
\(335\) 157.410 11.5466i 0.469880 0.0344676i
\(336\) 36.4747 0.108556
\(337\) −3.26452 + 3.26452i −0.00968699 + 0.00968699i −0.711934 0.702247i \(-0.752180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(338\) 452.532 + 452.532i 1.33885 + 1.33885i
\(339\) 230.999i 0.681413i
\(340\) 21.3481 + 291.028i 0.0627885 + 0.855966i
\(341\) −8.89770 −0.0260930
\(342\) −18.5951 + 18.5951i −0.0543715 + 0.0543715i
\(343\) 261.642 + 261.642i 0.762805 + 0.762805i
\(344\) 6.66658i 0.0193796i
\(345\) −27.1411 + 31.4382i −0.0786700 + 0.0911251i
\(346\) −303.998 −0.878608
\(347\) −298.180 + 298.180i −0.859309 + 0.859309i −0.991257 0.131947i \(-0.957877\pi\)
0.131947 + 0.991257i \(0.457877\pi\)
\(348\) 0.214551 + 0.214551i 0.000616524 + 0.000616524i
\(349\) 330.198i 0.946127i 0.881028 + 0.473063i \(0.156852\pi\)
−0.881028 + 0.473063i \(0.843148\pi\)
\(350\) 184.142 27.1612i 0.526119 0.0776034i
\(351\) 129.543 0.369068
\(352\) −47.2104 + 47.2104i −0.134120 + 0.134120i
\(353\) −121.953 121.953i −0.345476 0.345476i 0.512946 0.858421i \(-0.328554\pi\)
−0.858421 + 0.512946i \(0.828554\pi\)
\(354\) 261.990i 0.740084i
\(355\) −468.196 404.202i −1.31886 1.13860i
\(356\) −60.0503 −0.168681
\(357\) 188.155 188.155i 0.527046 0.527046i
\(358\) 133.690 + 133.690i 0.373437 + 0.373437i
\(359\) 14.1715i 0.0394748i 0.999805 + 0.0197374i \(0.00628302\pi\)
−0.999805 + 0.0197374i \(0.993717\pi\)
\(360\) 42.3127 3.10381i 0.117535 0.00862169i
\(361\) 322.580 0.893575
\(362\) 269.565 269.565i 0.744655 0.744655i
\(363\) −22.4146 22.4146i −0.0617482 0.0617482i
\(364\) 262.502i 0.721159i
\(365\) 7.58464 + 103.398i 0.0207798 + 0.283281i
\(366\) 223.160 0.609728
\(367\) −63.9505 + 63.9505i −0.174252 + 0.174252i −0.788845 0.614593i \(-0.789320\pi\)
0.614593 + 0.788845i \(0.289320\pi\)
\(368\) 13.5647 + 13.5647i 0.0368605 + 0.0368605i
\(369\) 171.394i 0.464483i
\(370\) 186.416 215.929i 0.503826 0.583592i
\(371\) 55.2973 0.149049
\(372\) 1.84661 1.84661i 0.00496401 0.00496401i
\(373\) −160.697 160.697i −0.430824 0.430824i 0.458085 0.888909i \(-0.348536\pi\)
−0.888909 + 0.458085i \(0.848536\pi\)
\(374\) 487.072i 1.30233i
\(375\) 211.304 47.1781i 0.563476 0.125808i
\(376\) −163.083 −0.433732
\(377\) 1.54408 1.54408i 0.00409571 0.00409571i
\(378\) −27.3560 27.3560i −0.0723703 0.0723703i
\(379\) 201.845i 0.532573i 0.963894 + 0.266287i \(0.0857968\pi\)
−0.963894 + 0.266287i \(0.914203\pi\)
\(380\) 46.9179 + 40.5051i 0.123468 + 0.106592i
\(381\) −25.2837 −0.0663613
\(382\) −322.402 + 322.402i −0.843986 + 0.843986i
\(383\) 177.891 + 177.891i 0.464466 + 0.464466i 0.900116 0.435650i \(-0.143481\pi\)
−0.435650 + 0.900116i \(0.643481\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 309.851 22.7288i 0.804808 0.0590359i
\(386\) −179.675 −0.465480
\(387\) 4.99993 4.99993i 0.0129197 0.0129197i
\(388\) −241.699 241.699i −0.622936 0.622936i
\(389\) 501.474i 1.28914i −0.764547 0.644568i \(-0.777037\pi\)
0.764547 0.644568i \(-0.222963\pi\)
\(390\) −22.3376 304.517i −0.0572758 0.780814i
\(391\) 139.947 0.357921
\(392\) 42.5666 42.5666i 0.108588 0.108588i
\(393\) 225.856 + 225.856i 0.574696 + 0.574696i
\(394\) 86.8144i 0.220341i
\(395\) −72.6773 + 84.1836i −0.183993 + 0.213123i
\(396\) 70.8156 0.178827
\(397\) −379.320 + 379.320i −0.955467 + 0.955467i −0.999050 0.0435831i \(-0.986123\pi\)
0.0435831 + 0.999050i \(0.486123\pi\)
\(398\) −241.437 241.437i −0.606624 0.606624i
\(399\) 56.5207i 0.141656i
\(400\) −14.5923 98.9296i −0.0364807 0.247324i
\(401\) 179.175 0.446820 0.223410 0.974725i \(-0.428281\pi\)
0.223410 + 0.974725i \(0.428281\pi\)
\(402\) −54.6749 + 54.6749i −0.136007 + 0.136007i
\(403\) −13.2897 13.2897i −0.0329770 0.0329770i
\(404\) 12.7136i 0.0314693i
\(405\) −34.0624 29.4067i −0.0841047 0.0726091i
\(406\) −0.652138 −0.00160625
\(407\) 336.687 336.687i 0.827241 0.827241i
\(408\) −101.086 101.086i −0.247760 0.247760i
\(409\) 384.881i 0.941029i −0.882392 0.470514i \(-0.844068\pi\)
0.882392 0.470514i \(-0.155932\pi\)
\(410\) 402.898 29.5542i 0.982678 0.0720834i
\(411\) 418.911 1.01925
\(412\) 257.622 257.622i 0.625296 0.625296i
\(413\) −398.166 398.166i −0.964082 0.964082i
\(414\) 20.3470i 0.0491473i
\(415\) 2.37442 + 32.3693i 0.00572150 + 0.0779984i
\(416\) −141.028 −0.339011
\(417\) −102.688 + 102.688i −0.246254 + 0.246254i
\(418\) 73.1567 + 73.1567i 0.175016 + 0.175016i
\(419\) 375.801i 0.896900i −0.893808 0.448450i \(-0.851976\pi\)
0.893808 0.448450i \(-0.148024\pi\)
\(420\) −59.5888 + 69.0230i −0.141878 + 0.164341i
\(421\) 109.575 0.260274 0.130137 0.991496i \(-0.458458\pi\)
0.130137 + 0.991496i \(0.458458\pi\)
\(422\) −52.1391 + 52.1391i −0.123552 + 0.123552i
\(423\) 122.312 + 122.312i 0.289155 + 0.289155i
\(424\) 29.7083i 0.0700668i
\(425\) −585.606 435.056i −1.37790 1.02366i
\(426\) 303.019 0.711313
\(427\) −339.154 + 339.154i −0.794272 + 0.794272i
\(428\) −94.9040 94.9040i −0.221738 0.221738i
\(429\) 509.648i 1.18799i
\(430\) −12.6155 10.8912i −0.0293385 0.0253284i
\(431\) −720.493 −1.67168 −0.835839 0.548975i \(-0.815018\pi\)
−0.835839 + 0.548975i \(0.815018\pi\)
\(432\) −14.6969 + 14.6969i −0.0340207 + 0.0340207i
\(433\) −10.2464 10.2464i −0.0236638 0.0236638i 0.695176 0.718840i \(-0.255326\pi\)
−0.718840 + 0.695176i \(0.755326\pi\)
\(434\) 5.61288i 0.0129329i
\(435\) −0.756518 + 0.0554936i −0.00173912 + 0.000127572i
\(436\) −291.781 −0.669222
\(437\) 21.0196 21.0196i 0.0480998 0.0480998i
\(438\) −35.9142 35.9142i −0.0819960 0.0819960i
\(439\) 627.889i 1.43027i −0.698985 0.715136i \(-0.746365\pi\)
0.698985 0.715136i \(-0.253635\pi\)
\(440\) −12.2110 166.467i −0.0277523 0.378334i
\(441\) −63.8500 −0.144785
\(442\) −727.499 + 727.499i −1.64593 + 1.64593i
\(443\) −253.351 253.351i −0.571898 0.571898i 0.360761 0.932658i \(-0.382517\pi\)
−0.932658 + 0.360761i \(0.882517\pi\)
\(444\) 139.751i 0.314754i
\(445\) 98.1045 113.637i 0.220460 0.255363i
\(446\) 560.903 1.25763
\(447\) 143.344 143.344i 0.320681 0.320681i
\(448\) 29.7814 + 29.7814i 0.0664764 + 0.0664764i
\(449\) 86.2603i 0.192116i −0.995376 0.0960582i \(-0.969377\pi\)
0.995376 0.0960582i \(-0.0306235\pi\)
\(450\) −63.2530 + 85.1414i −0.140562 + 0.189203i
\(451\) 674.300 1.49512
\(452\) −188.610 + 188.610i −0.417278 + 0.417278i
\(453\) −48.8778 48.8778i −0.107898 0.107898i
\(454\) 288.792i 0.636105i
\(455\) 496.747 + 428.850i 1.09175 + 0.942528i
\(456\) −30.3656 −0.0665912
\(457\) 302.229 302.229i 0.661333 0.661333i −0.294361 0.955694i \(-0.595107\pi\)
0.955694 + 0.294361i \(0.0951068\pi\)
\(458\) −362.796 362.796i −0.792131 0.792131i
\(459\) 151.629i 0.330347i
\(460\) −47.8298 + 3.50851i −0.103978 + 0.00762719i
\(461\) −592.540 −1.28534 −0.642668 0.766145i \(-0.722172\pi\)
−0.642668 + 0.766145i \(0.722172\pi\)
\(462\) −107.624 + 107.624i −0.232952 + 0.232952i
\(463\) −210.922 210.922i −0.455554 0.455554i 0.441639 0.897193i \(-0.354397\pi\)
−0.897193 + 0.441639i \(0.854397\pi\)
\(464\) 0.350360i 0.000755085i
\(465\) 0.477627 + 6.51126i 0.00102716 + 0.0140027i
\(466\) −176.277 −0.378277
\(467\) −75.0504 + 75.0504i −0.160707 + 0.160707i −0.782880 0.622173i \(-0.786250\pi\)
0.622173 + 0.782880i \(0.286250\pi\)
\(468\) 105.771 + 105.771i 0.226007 + 0.226007i
\(469\) 166.187i 0.354344i
\(470\) 266.430 308.612i 0.566872 0.656620i
\(471\) 137.981 0.292953
\(472\) −213.914 + 213.914i −0.453207 + 0.453207i
\(473\) −19.6707 19.6707i −0.0415872 0.0415872i
\(474\) 54.4842i 0.114946i
\(475\) −153.300 + 22.6120i −0.322737 + 0.0476043i
\(476\) 307.257 0.645497
\(477\) −22.2813 + 22.2813i −0.0467112 + 0.0467112i
\(478\) −296.594 296.594i −0.620490 0.620490i
\(479\) 582.683i 1.21646i −0.793762 0.608229i \(-0.791880\pi\)
0.793762 0.608229i \(-0.208120\pi\)
\(480\) 37.0824 + 32.0139i 0.0772551 + 0.0666957i
\(481\) 1005.76 2.09098
\(482\) −286.041 + 286.041i −0.593445 + 0.593445i
\(483\) 30.9229 + 30.9229i 0.0640226 + 0.0640226i
\(484\) 36.6029i 0.0756258i
\(485\) 852.246 62.5157i 1.75721 0.128898i
\(486\) 22.0454 0.0453609
\(487\) 324.456 324.456i 0.666234 0.666234i −0.290608 0.956842i \(-0.593858\pi\)
0.956842 + 0.290608i \(0.0938575\pi\)
\(488\) 182.210 + 182.210i 0.373381 + 0.373381i
\(489\) 257.075i 0.525715i
\(490\) 11.0099 + 150.093i 0.0224692 + 0.306311i
\(491\) 371.828 0.757288 0.378644 0.925542i \(-0.376390\pi\)
0.378644 + 0.925542i \(0.376390\pi\)
\(492\) −139.943 + 139.943i −0.284437 + 0.284437i
\(493\) 1.80734 + 1.80734i 0.00366600 + 0.00366600i
\(494\) 218.536i 0.442380i
\(495\) −115.692 + 134.008i −0.233721 + 0.270724i
\(496\) 3.01550 0.00607965
\(497\) −460.522 + 460.522i −0.926604 + 0.926604i
\(498\) −11.2432 11.2432i −0.0225767 0.0225767i
\(499\) 116.928i 0.234325i 0.993113 + 0.117163i \(0.0373799\pi\)
−0.993113 + 0.117163i \(0.962620\pi\)
\(500\) 211.049 + 134.008i 0.422099 + 0.268016i
\(501\) 425.381 0.849063
\(502\) 181.698 181.698i 0.361949 0.361949i
\(503\) −97.5611 97.5611i −0.193959 0.193959i 0.603446 0.797404i \(-0.293794\pi\)
−0.797404 + 0.603446i \(0.793794\pi\)
\(504\) 44.6721i 0.0886352i
\(505\) −24.0587 20.7703i −0.0476410 0.0411293i
\(506\) −80.0491 −0.158200
\(507\) 554.236 554.236i 1.09317 1.09317i
\(508\) −20.6440 20.6440i −0.0406379 0.0406379i
\(509\) 442.972i 0.870278i 0.900363 + 0.435139i \(0.143301\pi\)
−0.900363 + 0.435139i \(0.856699\pi\)
\(510\) 356.435 26.1460i 0.698893 0.0512666i
\(511\) 109.163 0.213627
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 22.7742 + 22.7742i 0.0443941 + 0.0443941i
\(514\) 392.506i 0.763631i
\(515\) 66.6340 + 908.390i 0.129386 + 1.76386i
\(516\) 8.16486 0.0158234
\(517\) 481.202 481.202i 0.930758 0.930758i
\(518\) −212.390 212.390i −0.410019 0.410019i
\(519\) 372.320i 0.717380i
\(520\) 230.399 266.876i 0.443075 0.513223i
\(521\) −666.249 −1.27879 −0.639394 0.768879i \(-0.720815\pi\)
−0.639394 + 0.768879i \(0.720815\pi\)
\(522\) 0.262770 0.262770i 0.000503390 0.000503390i
\(523\) −57.5211 57.5211i −0.109983 0.109983i 0.649974 0.759957i \(-0.274780\pi\)
−0.759957 + 0.649974i \(0.774780\pi\)
\(524\) 368.821i 0.703856i
\(525\) −33.2655 225.526i −0.0633629 0.429574i
\(526\) 462.257 0.878816
\(527\) 15.5556 15.5556i 0.0295172 0.0295172i
\(528\) 57.8207 + 57.8207i 0.109509 + 0.109509i
\(529\) 23.0000i 0.0434783i
\(530\) 56.2187 + 48.5346i 0.106073 + 0.0915748i
\(531\) 320.870 0.604276
\(532\) 46.1489 46.1489i 0.0867461 0.0867461i
\(533\) 1007.15 + 1007.15i 1.88958 + 1.88958i
\(534\) 73.5464i 0.137727i
\(535\) 334.637 24.5470i 0.625490 0.0458822i
\(536\) −89.2837 −0.166574
\(537\) 163.737 163.737i 0.304910 0.304910i
\(538\) 275.606 + 275.606i 0.512278 + 0.512278i
\(539\) 251.199i 0.466046i
\(540\) −3.80137 51.8223i −0.00703958 0.0959672i
\(541\) 487.704 0.901487 0.450743 0.892654i \(-0.351159\pi\)
0.450743 + 0.892654i \(0.351159\pi\)
\(542\) −31.3910 + 31.3910i −0.0579170 + 0.0579170i
\(543\) −330.148 330.148i −0.608008 0.608008i
\(544\) 165.073i 0.303443i
\(545\) 476.684 552.153i 0.874650 1.01313i
\(546\) −321.498 −0.588824
\(547\) −151.290 + 151.290i −0.276582 + 0.276582i −0.831743 0.555161i \(-0.812657\pi\)
0.555161 + 0.831743i \(0.312657\pi\)
\(548\) 342.040 + 342.040i 0.624160 + 0.624160i
\(549\) 273.315i 0.497841i
\(550\) 334.963 + 248.850i 0.609024 + 0.452454i
\(551\) 0.542913 0.000985323
\(552\) 16.6132 16.6132i 0.0300965 0.0300965i
\(553\) 82.8039 + 82.8039i 0.149736 + 0.149736i
\(554\) 31.8603i 0.0575096i
\(555\) −264.458 228.311i −0.476501 0.411372i
\(556\) −167.689 −0.301599
\(557\) −54.8204 + 54.8204i −0.0984208 + 0.0984208i −0.754603 0.656182i \(-0.772170\pi\)
0.656182 + 0.754603i \(0.272170\pi\)
\(558\) −2.26163 2.26163i −0.00405310 0.00405310i
\(559\) 58.7611i 0.105118i
\(560\) −105.011 + 7.70299i −0.187520 + 0.0137553i
\(561\) 596.539 1.06335
\(562\) −48.1708 + 48.1708i −0.0857131 + 0.0857131i
\(563\) 393.961 + 393.961i 0.699753 + 0.699753i 0.964357 0.264604i \(-0.0852412\pi\)
−0.264604 + 0.964357i \(0.585241\pi\)
\(564\) 199.735i 0.354141i
\(565\) −48.7841 665.050i −0.0863435 1.17708i
\(566\) −272.812 −0.482000
\(567\) −33.5041 + 33.5041i −0.0590901 + 0.0590901i
\(568\) 247.414 + 247.414i 0.435589 + 0.435589i
\(569\) 928.406i 1.63165i −0.578302 0.815823i \(-0.696284\pi\)
0.578302 0.815823i \(-0.303716\pi\)
\(570\) 49.6084 57.4625i 0.0870323 0.100811i
\(571\) −817.767 −1.43217 −0.716083 0.698015i \(-0.754067\pi\)
−0.716083 + 0.698015i \(0.754067\pi\)
\(572\) 416.126 416.126i 0.727492 0.727492i
\(573\) 394.861 + 394.861i 0.689111 + 0.689111i
\(574\) 425.364i 0.741053i
\(575\) 71.5004 96.2429i 0.124349 0.167379i
\(576\) −24.0000 −0.0416667
\(577\) 259.934 259.934i 0.450491 0.450491i −0.445026 0.895518i \(-0.646806\pi\)
0.895518 + 0.445026i \(0.146806\pi\)
\(578\) −562.532 562.532i −0.973240 0.973240i
\(579\) 220.056i 0.380063i
\(580\) −0.663005 0.572384i −0.00114311 0.000986869i
\(581\) 34.1743 0.0588198
\(582\) −296.020 + 296.020i −0.508625 + 0.508625i
\(583\) 87.6589 + 87.6589i 0.150358 + 0.150358i
\(584\) 58.6477i 0.100424i
\(585\) −372.956 + 27.3578i −0.637532 + 0.0467655i
\(586\) 193.747 0.330627
\(587\) 331.058 331.058i 0.563984 0.563984i −0.366453 0.930437i \(-0.619428\pi\)
0.930437 + 0.366453i \(0.119428\pi\)
\(588\) −52.1333 52.1333i −0.0886620 0.0886620i
\(589\) 4.67279i 0.00793343i
\(590\) −55.3289 754.272i −0.0937778 1.27843i
\(591\) 106.325 0.179908
\(592\) −114.106 + 114.106i −0.192747 + 0.192747i
\(593\) 614.053 + 614.053i 1.03550 + 1.03550i 0.999346 + 0.0361568i \(0.0115116\pi\)
0.0361568 + 0.999346i \(0.488488\pi\)
\(594\) 86.7311i 0.146012i
\(595\) −501.967 + 581.439i −0.843641 + 0.977208i
\(596\) 234.080 0.392752
\(597\) −295.698 + 295.698i −0.495307 + 0.495307i
\(598\) −119.563 119.563i −0.199938 0.199938i
\(599\) 536.579i 0.895791i 0.894086 + 0.447895i \(0.147826\pi\)
−0.894086 + 0.447895i \(0.852174\pi\)
\(600\) −121.164 + 17.8718i −0.201939 + 0.0297864i
\(601\) −764.010 −1.27123 −0.635616 0.772006i \(-0.719254\pi\)
−0.635616 + 0.772006i \(0.719254\pi\)
\(602\) −12.4088 + 12.4088i −0.0206126 + 0.0206126i
\(603\) 66.9628 + 66.9628i 0.111049 + 0.111049i
\(604\) 79.8172i 0.132148i
\(605\) 69.2657 + 59.7983i 0.114489 + 0.0988402i
\(606\) 15.5709 0.0256946
\(607\) −375.415 + 375.415i −0.618476 + 0.618476i −0.945140 0.326665i \(-0.894075\pi\)
0.326665 + 0.945140i \(0.394075\pi\)
\(608\) −24.7934 24.7934i −0.0407786 0.0407786i
\(609\) 0.798703i 0.00131150i
\(610\) −642.483 + 47.1287i −1.05325 + 0.0772601i
\(611\) 1437.46 2.35264
\(612\) −123.805 + 123.805i −0.202295 + 0.202295i
\(613\) −195.776 195.776i −0.319374 0.319374i 0.529153 0.848527i \(-0.322510\pi\)
−0.848527 + 0.529153i \(0.822510\pi\)
\(614\) 190.293i 0.309924i
\(615\) −36.1963 493.447i −0.0588558 0.802353i
\(616\) −175.749 −0.285307
\(617\) −124.149 + 124.149i −0.201214 + 0.201214i −0.800520 0.599306i \(-0.795443\pi\)
0.599306 + 0.800520i \(0.295443\pi\)
\(618\) −315.521 315.521i −0.510552 0.510552i
\(619\) 144.829i 0.233972i 0.993134 + 0.116986i \(0.0373232\pi\)
−0.993134 + 0.116986i \(0.962677\pi\)
\(620\) −4.92644 + 5.70641i −0.00794588 + 0.00920388i
\(621\) −24.9199 −0.0401286
\(622\) −374.486 + 374.486i −0.602068 + 0.602068i
\(623\) −111.774 111.774i −0.179413 0.179413i
\(624\) 172.724i 0.276801i
\(625\) −598.383 + 180.451i −0.957413 + 0.288722i
\(626\) 553.088 0.883528
\(627\) 89.5983 89.5983i 0.142900 0.142900i
\(628\) 112.661 + 112.661i 0.179396 + 0.179396i
\(629\) 1177.24i 1.87160i
\(630\) 84.5356 + 72.9811i 0.134183 + 0.115843i
\(631\) 990.046 1.56901 0.784506 0.620122i \(-0.212917\pi\)
0.784506 + 0.620122i \(0.212917\pi\)
\(632\) 44.4862 44.4862i 0.0703895 0.0703895i
\(633\) 63.8570 + 63.8570i 0.100880 + 0.100880i
\(634\) 239.907i 0.378403i
\(635\) 72.7921 5.33959i 0.114633 0.00840881i
\(636\) −36.3851 −0.0572093
\(637\) −375.194 + 375.194i −0.589002 + 0.589002i
\(638\) −1.03379 1.03379i −0.00162036 0.00162036i
\(639\) 371.121i 0.580785i
\(640\) 4.13841 + 56.4170i 0.00646627 + 0.0881515i
\(641\) −1189.18 −1.85519 −0.927595 0.373587i \(-0.878128\pi\)
−0.927595 + 0.373587i \(0.878128\pi\)
\(642\) −116.233 + 116.233i −0.181049 + 0.181049i
\(643\) 44.5224 + 44.5224i 0.0692416 + 0.0692416i 0.740880 0.671638i \(-0.234409\pi\)
−0.671638 + 0.740880i \(0.734409\pi\)
\(644\) 50.4969i 0.0784113i
\(645\) −13.3390 + 15.4508i −0.0206806 + 0.0239547i
\(646\) −255.795 −0.395967
\(647\) 360.032 360.032i 0.556464 0.556464i −0.371835 0.928299i \(-0.621271\pi\)
0.928299 + 0.371835i \(0.121271\pi\)
\(648\) 18.0000 + 18.0000i 0.0277778 + 0.0277778i
\(649\) 1262.37i 1.94510i
\(650\) 128.620 + 871.993i 0.197878 + 1.34153i
\(651\) 6.87434 0.0105597
\(652\) 209.901 209.901i 0.321934 0.321934i
\(653\) 712.901 + 712.901i 1.09173 + 1.09173i 0.995344 + 0.0963890i \(0.0307293\pi\)
0.0963890 + 0.995344i \(0.469271\pi\)
\(654\) 357.357i 0.546418i
\(655\) −697.940 602.544i −1.06556 0.919914i
\(656\) −228.526 −0.348363
\(657\) −43.9858 + 43.9858i −0.0669495 + 0.0669495i
\(658\) −303.553 303.553i −0.461327 0.461327i
\(659\) 1012.88i 1.53699i −0.639854 0.768497i \(-0.721005\pi\)
0.639854 0.768497i \(-0.278995\pi\)
\(660\) −203.879 + 14.9554i −0.308908 + 0.0226596i
\(661\) −913.639 −1.38221 −0.691104 0.722756i \(-0.742875\pi\)
−0.691104 + 0.722756i \(0.742875\pi\)
\(662\) −28.1304 + 28.1304i −0.0424931 + 0.0424931i
\(663\) 891.001 + 891.001i 1.34389 + 1.34389i
\(664\) 18.3601i 0.0276507i
\(665\) 11.9365 + 162.724i 0.0179496 + 0.244698i
\(666\) 171.159 0.256995
\(667\) −0.297032 + 0.297032i −0.000445325 + 0.000445325i
\(668\) 347.322 + 347.322i 0.519943 + 0.519943i
\(669\) 686.964i 1.02685i
\(670\) 145.863 168.956i 0.217706 0.252174i
\(671\) −1075.27 −1.60250
\(672\) 36.4747 36.4747i 0.0542778 0.0542778i
\(673\) −493.188 493.188i −0.732820 0.732820i 0.238357 0.971178i \(-0.423391\pi\)
−0.971178 + 0.238357i \(0.923391\pi\)
\(674\) 6.52903i 0.00968699i
\(675\) 104.277 + 77.4688i 0.154484 + 0.114769i
\(676\) 905.064 1.33885
\(677\) −415.571 + 415.571i −0.613842 + 0.613842i −0.943945 0.330103i \(-0.892917\pi\)
0.330103 + 0.943945i \(0.392917\pi\)
\(678\) 230.999 + 230.999i 0.340706 + 0.340706i
\(679\) 899.769i 1.32514i
\(680\) 312.376 + 269.680i 0.459377 + 0.396589i
\(681\) −353.696 −0.519378
\(682\) −8.89770 + 8.89770i −0.0130465 + 0.0130465i
\(683\) 236.634 + 236.634i 0.346463 + 0.346463i 0.858790 0.512327i \(-0.171217\pi\)
−0.512327 + 0.858790i \(0.671217\pi\)
\(684\) 37.1901i 0.0543715i
\(685\) −1206.05 + 88.4688i −1.76066 + 0.129152i
\(686\) 523.284 0.762805
\(687\) −444.333 + 444.333i −0.646772 + 0.646772i
\(688\) 6.66658 + 6.66658i 0.00968979 + 0.00968979i
\(689\) 261.858i 0.380054i
\(690\) 4.29703 + 58.5793i 0.00622758 + 0.0848976i
\(691\) −81.6305 −0.118134 −0.0590670 0.998254i \(-0.518813\pi\)
−0.0590670 + 0.998254i \(0.518813\pi\)
\(692\) −303.998 + 303.998i −0.439304 + 0.439304i
\(693\) 131.812 + 131.812i 0.190205 + 0.190205i
\(694\) 596.361i 0.859309i
\(695\) 273.954 317.327i 0.394179 0.456586i
\(696\) 0.429101 0.000616524
\(697\) −1178.86 + 1178.86i −1.69133 + 1.69133i
\(698\) 330.198 + 330.198i 0.473063 + 0.473063i
\(699\) 215.894i 0.308862i
\(700\) 156.980 211.303i 0.224258 0.301861i
\(701\) 1277.39 1.82224 0.911122 0.412137i \(-0.135218\pi\)
0.911122 + 0.412137i \(0.135218\pi\)
\(702\) 129.543 129.543i 0.184534 0.184534i
\(703\) 176.817 + 176.817i 0.251518 + 0.251518i
\(704\) 94.4208i 0.134120i
\(705\) −377.970 326.309i −0.536128 0.462849i
\(706\) −243.906 −0.345476
\(707\) −23.6644 + 23.6644i −0.0334715 + 0.0334715i
\(708\) 261.990 + 261.990i 0.370042 + 0.370042i
\(709\) 1056.16i 1.48965i 0.667260 + 0.744825i \(0.267467\pi\)
−0.667260 + 0.744825i \(0.732533\pi\)
\(710\) −872.398 + 63.9939i −1.22873 + 0.0901322i
\(711\) −66.7293 −0.0938527
\(712\) −60.0503 + 60.0503i −0.0843404 + 0.0843404i
\(713\) 2.55652 + 2.55652i 0.00358558 + 0.00358558i
\(714\) 376.311i 0.527046i
\(715\) 107.631 + 1467.28i 0.150533 + 2.05215i
\(716\) 267.381 0.373437
\(717\) −363.252 + 363.252i −0.506628 + 0.506628i
\(718\) 14.1715 + 14.1715i 0.0197374 + 0.0197374i
\(719\) 532.010i 0.739931i −0.929046 0.369965i \(-0.879370\pi\)
0.929046 0.369965i \(-0.120630\pi\)
\(720\) 39.2089 45.4165i 0.0544568 0.0630785i
\(721\) 959.043 1.33016
\(722\) 322.580 322.580i 0.446787 0.446787i
\(723\) 350.327 + 350.327i 0.484546 + 0.484546i
\(724\) 539.130i 0.744655i
\(725\) 2.16631 0.319534i 0.00298801 0.000440737i
\(726\) −44.8292 −0.0617482
\(727\) 310.493 310.493i 0.427087 0.427087i −0.460548 0.887635i \(-0.652347\pi\)
0.887635 + 0.460548i \(0.152347\pi\)
\(728\) −262.502 262.502i −0.360579 0.360579i
\(729\) 27.0000i 0.0370370i
\(730\) 110.982 + 95.8131i 0.152031 + 0.131251i
\(731\) 68.7794 0.0940895
\(732\) 223.160 223.160i 0.304864 0.304864i
\(733\) −737.954 737.954i −1.00676 1.00676i −0.999977 0.00678219i \(-0.997841\pi\)
−0.00678219 0.999977i \(-0.502159\pi\)
\(734\) 127.901i 0.174252i
\(735\) 183.825 13.4843i 0.250102 0.0183460i
\(736\) 27.1293 0.0368605
\(737\) 263.445 263.445i 0.357456 0.357456i
\(738\) 171.394 + 171.394i 0.232242 + 0.232242i
\(739\) 258.876i 0.350306i −0.984541 0.175153i \(-0.943958\pi\)
0.984541 0.175153i \(-0.0560421\pi\)
\(740\) −29.5136 402.345i −0.0398832 0.543709i
\(741\) 267.651 0.361202
\(742\) 55.2973 55.2973i 0.0745247 0.0745247i
\(743\) −570.017 570.017i −0.767183 0.767183i 0.210427 0.977610i \(-0.432515\pi\)
−0.977610 + 0.210427i \(0.932515\pi\)
\(744\) 3.69322i 0.00496401i
\(745\) −382.418 + 442.963i −0.513313 + 0.594581i
\(746\) −321.395 −0.430824
\(747\) −13.7700 + 13.7700i −0.0184338 + 0.0184338i
\(748\) 487.072 + 487.072i 0.651166 + 0.651166i
\(749\) 353.297i 0.471692i
\(750\) 164.126 258.482i 0.218834 0.344642i
\(751\) −739.550 −0.984754 −0.492377 0.870382i \(-0.663872\pi\)
−0.492377 + 0.870382i \(0.663872\pi\)
\(752\) −163.083 + 163.083i −0.216866 + 0.216866i
\(753\) −222.534 222.534i −0.295530 0.295530i
\(754\) 3.08817i 0.00409571i
\(755\) 151.042 + 130.398i 0.200056 + 0.172712i
\(756\) −54.7120 −0.0723703
\(757\) −383.596 + 383.596i −0.506732 + 0.506732i −0.913522 0.406789i \(-0.866648\pi\)
0.406789 + 0.913522i \(0.366648\pi\)
\(758\) 201.845 + 201.845i 0.266287 + 0.266287i
\(759\) 98.0398i 0.129170i
\(760\) 87.4230 6.41283i 0.115030 0.00843793i
\(761\) −619.693 −0.814314 −0.407157 0.913358i \(-0.633480\pi\)
−0.407157 + 0.913358i \(0.633480\pi\)
\(762\) −25.2837 + 25.2837i −0.0331807 + 0.0331807i
\(763\) −543.103 543.103i −0.711800 0.711800i
\(764\) 644.805i 0.843986i
\(765\) −32.0222 436.543i −0.0418590 0.570644i
\(766\) 355.781 0.464466
\(767\) 1885.49 1885.49i 2.45827 2.45827i
\(768\) −19.5959 19.5959i −0.0255155 0.0255155i
\(769\) 587.333i 0.763762i −0.924211 0.381881i \(-0.875276\pi\)
0.924211 0.381881i \(-0.124724\pi\)
\(770\) 287.122 332.580i 0.372886 0.431922i
\(771\) −480.720 −0.623502
\(772\) −179.675 + 179.675i −0.232740 + 0.232740i
\(773\) 541.479 + 541.479i 0.700490 + 0.700490i 0.964516 0.264026i \(-0.0850504\pi\)
−0.264026 + 0.964516i \(0.585050\pi\)
\(774\) 9.99987i 0.0129197i
\(775\) −2.75019 18.6452i −0.00354864 0.0240583i
\(776\) −483.399 −0.622936
\(777\) −260.124 + 260.124i −0.334779 + 0.334779i
\(778\) −501.474 501.474i −0.644568 0.644568i
\(779\) 354.121i 0.454584i
\(780\) −326.855 282.180i −0.419045 0.361769i
\(781\) −1460.07 −1.86948
\(782\) 139.947 139.947i 0.178961 0.178961i
\(783\) −0.321826 0.321826i −0.000411016 0.000411016i
\(784\) 85.1333i 0.108588i
\(785\) −397.249 + 29.1398i −0.506050 + 0.0371208i
\(786\) 451.711 0.574696
\(787\) 748.081 748.081i 0.950548 0.950548i −0.0482856 0.998834i \(-0.515376\pi\)
0.998834 + 0.0482856i \(0.0153758\pi\)
\(788\) 86.8144 + 86.8144i 0.110171 + 0.110171i
\(789\) 566.147i 0.717550i
\(790\) 11.5064 + 156.861i 0.0145650 + 0.198558i
\(791\) −702.134 −0.887653
\(792\) 70.8156 70.8156i 0.0894137 0.0894137i
\(793\) −1606.05 1606.05i −2.02528 2.02528i
\(794\) 758.641i 0.955467i
\(795\) 59.4426 68.8536i 0.0747705 0.0866083i
\(796\) −482.873 −0.606624
\(797\) 521.090 521.090i 0.653814 0.653814i −0.300095 0.953909i \(-0.597018\pi\)
0.953909 + 0.300095i \(0.0970184\pi\)
\(798\) −56.5207 56.5207i −0.0708279 0.0708279i
\(799\) 1682.54i 2.10581i
\(800\) −113.522 84.3373i −0.141902 0.105422i
\(801\) 90.0755 0.112454
\(802\) 179.175 179.175i 0.223410 0.223410i
\(803\) 173.049 + 173.049i 0.215503 + 0.215503i
\(804\) 109.350i 0.136007i
\(805\) −95.5580 82.4970i −0.118706 0.102481i
\(806\) −26.5795 −0.0329770
\(807\) 337.547 337.547i 0.418273 0.418273i
\(808\) 12.7136 + 12.7136i 0.0157347 + 0.0157347i
\(809\) 1423.19i 1.75920i 0.475718 + 0.879598i \(0.342188\pi\)
−0.475718 + 0.879598i \(0.657812\pi\)
\(810\) −63.4691 + 4.65571i −0.0783569 + 0.00574779i
\(811\) 619.095 0.763372 0.381686 0.924292i \(-0.375344\pi\)
0.381686 + 0.924292i \(0.375344\pi\)
\(812\) −0.652138 + 0.652138i −0.000803126 + 0.000803126i
\(813\) 38.4460 + 38.4460i 0.0472890 + 0.0472890i
\(814\) 673.374i 0.827241i
\(815\) 54.2909 + 740.122i 0.0666147 + 0.908126i
\(816\) −202.172 −0.247760
\(817\) 10.3304 10.3304i 0.0126444 0.0126444i
\(818\) −384.881 384.881i −0.470514 0.470514i
\(819\) 393.753i 0.480773i
\(820\) 373.344 432.452i 0.455297 0.527381i
\(821\) −1268.52 −1.54510 −0.772548 0.634957i \(-0.781018\pi\)
−0.772548 + 0.634957i \(0.781018\pi\)
\(822\) 418.911 418.911i 0.509625 0.509625i
\(823\) 908.627 + 908.627i 1.10404 + 1.10404i 0.993918 + 0.110125i \(0.0351250\pi\)
0.110125 + 0.993918i \(0.464875\pi\)
\(824\) 515.244i 0.625296i
\(825\) 304.778 410.245i 0.369428 0.497266i
\(826\) −796.332 −0.964082
\(827\) −692.885 + 692.885i −0.837829 + 0.837829i −0.988573 0.150744i \(-0.951833\pi\)
0.150744 + 0.988573i \(0.451833\pi\)
\(828\) −20.3470 20.3470i −0.0245737 0.0245737i
\(829\) 513.279i 0.619155i −0.950874 0.309577i \(-0.899812\pi\)
0.950874 0.309577i \(-0.100188\pi\)
\(830\) 34.7438 + 29.9949i 0.0418600 + 0.0361385i
\(831\) 39.0208 0.0469564
\(832\) −141.028 + 141.028i −0.169505 + 0.169505i
\(833\) −439.162 439.162i −0.527206 0.527206i
\(834\) 205.376i 0.246254i
\(835\) −1224.68 + 89.8350i −1.46668 + 0.107587i
\(836\) 146.313 0.175016
\(837\) −2.76992 + 2.76992i −0.00330934 + 0.00330934i
\(838\) −375.801 375.801i −0.448450 0.448450i
\(839\) 888.628i 1.05915i 0.848263 + 0.529575i \(0.177649\pi\)
−0.848263 + 0.529575i \(0.822351\pi\)
\(840\) 9.43419 + 128.612i 0.0112312 + 0.153109i
\(841\) 840.992 0.999991
\(842\) 109.575 109.575i 0.130137 0.130137i
\(843\) 58.9969 + 58.9969i 0.0699844 + 0.0699844i
\(844\) 104.278i 0.123552i
\(845\) −1478.61 + 1712.70i −1.74983 + 2.02687i
\(846\) 244.625 0.289155
\(847\) 68.1304 68.1304i 0.0804373 0.0804373i
\(848\) −29.7083 29.7083i −0.0350334 0.0350334i
\(849\) 334.125i 0.393551i
\(850\) −1020.66 + 150.549i −1.20078 + 0.177117i
\(851\) −193.476 −0.227352
\(852\) 303.019 303.019i 0.355657 0.355657i
\(853\) −34.9834 34.9834i −0.0410122 0.0410122i 0.686303 0.727315i \(-0.259232\pi\)
−0.727315 + 0.686303i \(0.759232\pi\)
\(854\) 678.308i 0.794272i
\(855\) −70.3769 60.7576i −0.0823122 0.0710616i
\(856\) −189.808 −0.221738
\(857\) 58.3631 58.3631i 0.0681016 0.0681016i −0.672236 0.740337i \(-0.734666\pi\)
0.740337 + 0.672236i \(0.234666\pi\)
\(858\) −509.648 509.648i −0.593995 0.593995i
\(859\) 1424.70i 1.65856i 0.558834 + 0.829280i \(0.311249\pi\)
−0.558834 + 0.829280i \(0.688751\pi\)
\(860\) −23.5068 + 1.72432i −0.0273334 + 0.00200502i
\(861\) −520.963 −0.605067
\(862\) −720.493 + 720.493i −0.835839 + 0.835839i
\(863\) −683.671 683.671i −0.792203 0.792203i 0.189649 0.981852i \(-0.439265\pi\)
−0.981852 + 0.189649i \(0.939265\pi\)
\(864\) 29.3939i 0.0340207i
\(865\) −78.6293 1071.92i −0.0909010 1.23921i
\(866\) −20.4928 −0.0236638
\(867\) −688.959 + 688.959i −0.794647 + 0.794647i
\(868\) 5.61288 + 5.61288i 0.00646645 + 0.00646645i
\(869\) 262.526i 0.302102i
\(870\) −0.701024 + 0.812012i −0.000805775 + 0.000933347i
\(871\) 786.971 0.903526
\(872\) −291.781 + 291.781i −0.334611 + 0.334611i
\(873\) 362.549 + 362.549i 0.415291 + 0.415291i
\(874\) 42.0393i 0.0480998i
\(875\) 143.400 + 642.269i 0.163886 + 0.734022i
\(876\) −71.8285 −0.0819960
\(877\) 621.453 621.453i 0.708612 0.708612i −0.257631 0.966243i \(-0.582942\pi\)
0.966243 + 0.257631i \(0.0829420\pi\)
\(878\) −627.889 627.889i −0.715136 0.715136i
\(879\) 237.291i 0.269956i
\(880\) −178.678 154.256i −0.203043 0.175291i
\(881\) 1514.77 1.71938 0.859689 0.510818i \(-0.170657\pi\)
0.859689 + 0.510818i \(0.170657\pi\)
\(882\) −63.8500 + 63.8500i −0.0723923 + 0.0723923i
\(883\) 725.056 + 725.056i 0.821128 + 0.821128i 0.986270 0.165142i \(-0.0528081\pi\)
−0.165142 + 0.986270i \(0.552808\pi\)
\(884\) 1455.00i 1.64593i
\(885\) −923.791 + 67.7638i −1.04383 + 0.0765692i
\(886\) −506.701 −0.571898
\(887\) 13.7391 13.7391i 0.0154894 0.0154894i −0.699320 0.714809i \(-0.746514\pi\)
0.714809 + 0.699320i \(0.246514\pi\)
\(888\) 139.751 + 139.751i 0.157377 + 0.157377i
\(889\) 76.8511i 0.0864467i
\(890\) −15.5321 211.741i −0.0174518 0.237911i
\(891\) −106.223 −0.119218
\(892\) 560.903 560.903i 0.628815 0.628815i
\(893\) 252.712 + 252.712i 0.282992 + 0.282992i
\(894\) 286.688i 0.320681i
\(895\) −436.822 + 505.980i −0.488069 + 0.565341i
\(896\) 59.5629 0.0664764
\(897\) −146.434 + 146.434i −0.163248 + 0.163248i
\(898\) −86.2603 86.2603i −0.0960582 0.0960582i
\(899\) 0.0660319i 7.34504e-5i
\(900\) 21.8884 + 148.394i 0.0243205 + 0.164883i
\(901\) −306.502 −0.340180
\(902\) 674.300 674.300i 0.747561 0.747561i
\(903\) 15.1976 + 15.1976i 0.0168301 + 0.0168301i
\(904\) 377.220i 0.417278i
\(905\) 1020.23 + 880.779i 1.12732 + 0.973237i
\(906\) −97.7557 −0.107898
\(907\) 16.3128 16.3128i 0.0179854 0.0179854i −0.698057 0.716042i \(-0.745952\pi\)
0.716042 + 0.698057i \(0.245952\pi\)
\(908\) −288.792 288.792i −0.318053 0.318053i
\(909\) 19.0704i 0.0209796i
\(910\) 925.597 67.8963i 1.01714 0.0746113i
\(911\) 1548.82 1.70013 0.850065 0.526678i \(-0.176563\pi\)
0.850065 + 0.526678i \(0.176563\pi\)
\(912\) −30.3656 + 30.3656i −0.0332956 + 0.0332956i
\(913\) 54.1741 + 54.1741i 0.0593364 + 0.0593364i
\(914\) 604.459i 0.661333i
\(915\) 57.7206 + 786.877i 0.0630826 + 0.859975i
\(916\) −725.592 −0.792131
\(917\) −686.500 + 686.500i −0.748637 + 0.748637i
\(918\) 151.629 + 151.629i 0.165173 + 0.165173i
\(919\) 222.682i 0.242310i 0.992634 + 0.121155i \(0.0386597\pi\)
−0.992634 + 0.121155i \(0.961340\pi\)
\(920\) −44.3213 + 51.3383i −0.0481753 + 0.0558025i
\(921\) −233.061 −0.253052
\(922\) −592.540 + 592.540i −0.642668 + 0.642668i
\(923\) −2180.78 2180.78i −2.36271 2.36271i
\(924\) 215.248i 0.232952i
\(925\) 809.595 + 601.462i 0.875238 + 0.650229i
\(926\) −421.843 −0.455554
\(927\) −386.433 + 386.433i −0.416864 + 0.416864i
\(928\) 0.350360 + 0.350360i 0.000377543 + 0.000377543i
\(929\) 461.755i 0.497045i 0.968626 + 0.248522i \(0.0799450\pi\)
−0.968626 + 0.248522i \(0.920055\pi\)
\(930\) 6.98889 + 6.03364i 0.00751494 + 0.00648778i
\(931\) −131.921 −0.141699
\(932\) −176.277 + 176.277i −0.189138 + 0.189138i
\(933\) 458.650 + 458.650i 0.491587 + 0.491587i
\(934\) 150.101i 0.160707i
\(935\) −1717.45 + 125.982i −1.83684 + 0.134740i
\(936\) 211.543 0.226007
\(937\) 316.509 316.509i 0.337789 0.337789i −0.517745 0.855535i \(-0.673229\pi\)
0.855535 + 0.517745i \(0.173229\pi\)
\(938\) −166.187 166.187i −0.177172 0.177172i
\(939\) 677.392i 0.721397i
\(940\) −42.1816 575.042i −0.0448741 0.611746i
\(941\) 595.796 0.633152 0.316576 0.948567i \(-0.397467\pi\)
0.316576 + 0.948567i \(0.397467\pi\)
\(942\) 137.981 137.981i 0.146476 0.146476i
\(943\) −193.742 193.742i −0.205453 0.205453i
\(944\) 427.827i 0.453207i
\(945\) 89.3832 103.535i 0.0945854 0.109560i
\(946\) −39.3415 −0.0415872
\(947\) −72.4252 + 72.4252i −0.0764786 + 0.0764786i −0.744311 0.667833i \(-0.767222\pi\)
0.667833 + 0.744311i \(0.267222\pi\)
\(948\) −54.4842 54.4842i −0.0574728 0.0574728i
\(949\) 516.937i 0.544718i
\(950\) −130.688 + 175.912i −0.137566 + 0.185171i
\(951\) −293.825 −0.308965
\(952\) 307.257 307.257i 0.322749 0.322749i
\(953\) −241.669 241.669i −0.253587 0.253587i 0.568852 0.822440i \(-0.307388\pi\)
−0.822440 + 0.568852i \(0.807388\pi\)
\(954\) 44.5625i 0.0467112i
\(955\) −1220.20 1053.42i −1.27770 1.10306i
\(956\) −593.189 −0.620490
\(957\) −1.26613 + 1.26613i −0.00132302 + 0.00132302i
\(958\) −582.683 582.683i −0.608229 0.608229i
\(959\) 1273.30i 1.32774i
\(960\) 69.0964 5.06850i 0.0719754 0.00527968i
\(961\) −960.432 −0.999409
\(962\) 1005.76 1005.76i 1.04549 1.04549i
\(963\) 142.356 + 142.356i 0.147826 + 0.147826i
\(964\) 572.081i 0.593445i
\(965\) −46.4731 633.546i −0.0481587 0.656524i
\(966\) 61.8458 0.0640226
\(967\) −855.265 + 855.265i −0.884452 + 0.884452i −0.993983 0.109532i \(-0.965065\pi\)
0.109532 + 0.993983i \(0.465065\pi\)
\(968\) −36.6029 36.6029i −0.0378129 0.0378129i
\(969\) 313.283i 0.323306i
\(970\) 789.731 914.762i 0.814155 0.943054i
\(971\) −1220.33 −1.25678 −0.628390 0.777899i \(-0.716286\pi\)
−0.628390 + 0.777899i \(0.716286\pi\)
\(972\) 22.0454 22.0454i 0.0226805 0.0226805i
\(973\) −312.126 312.126i −0.320787 0.320787i
\(974\) 648.912i 0.666234i
\(975\) 1067.97 157.527i 1.09535 0.161566i
\(976\) 364.420 0.373381
\(977\) −319.958 + 319.958i −0.327490 + 0.327490i −0.851631 0.524141i \(-0.824386\pi\)
0.524141 + 0.851631i \(0.324386\pi\)
\(978\) −257.075 257.075i −0.262858 0.262858i
\(979\) 354.375i 0.361977i
\(980\) 161.102 + 139.083i 0.164390 + 0.141921i
\(981\) 437.671 0.446148
\(982\) 371.828 371.828i 0.378644 0.378644i
\(983\) −749.299 749.299i −0.762258 0.762258i 0.214472 0.976730i \(-0.431197\pi\)
−0.976730 + 0.214472i \(0.931197\pi\)
\(984\) 279.886i 0.284437i
\(985\) −306.113 + 22.4546i −0.310774 + 0.0227965i
\(986\) 3.61468 0.00366600
\(987\) −371.776 + 371.776i −0.376672 + 0.376672i
\(988\) 218.536 + 218.536i 0.221190 + 0.221190i
\(989\) 11.3037i 0.0114295i
\(990\) 18.3165 + 249.700i 0.0185015 + 0.252222i
\(991\) −1463.17 −1.47646 −0.738230 0.674549i \(-0.764338\pi\)
−0.738230 + 0.674549i \(0.764338\pi\)
\(992\) 3.01550 3.01550i 0.00303982 0.00303982i
\(993\) 34.4526 + 34.4526i 0.0346955 + 0.0346955i
\(994\) 921.044i 0.926604i
\(995\) 788.872 913.767i 0.792836 0.918359i
\(996\) −22.4864 −0.0225767
\(997\) 174.886 174.886i 0.175413 0.175413i −0.613940 0.789353i \(-0.710416\pi\)
0.789353 + 0.613940i \(0.210416\pi\)
\(998\) 116.928 + 116.928i 0.117163 + 0.117163i
\(999\) 209.626i 0.209836i
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 690.3.k.a.553.3 yes 40
5.2 odd 4 inner 690.3.k.a.277.3 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.3.k.a.277.3 40 5.2 odd 4 inner
690.3.k.a.553.3 yes 40 1.1 even 1 trivial