Properties

Label 735.2.g.b.734.4
Level $735$
Weight $2$
Character 735.734
Analytic conductor $5.869$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [735,2,Mod(734,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.734");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.g (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 734.4
Character \(\chi\) \(=\) 735.734
Dual form 735.2.g.b.734.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.50798 q^{2} +(1.47954 + 0.900534i) q^{3} +4.28995 q^{4} +(1.94085 + 1.11045i) q^{5} +(-3.71065 - 2.25852i) q^{6} -5.74313 q^{8} +(1.37808 + 2.66475i) q^{9} +O(q^{10})\) \(q-2.50798 q^{2} +(1.47954 + 0.900534i) q^{3} +4.28995 q^{4} +(1.94085 + 1.11045i) q^{5} +(-3.71065 - 2.25852i) q^{6} -5.74313 q^{8} +(1.37808 + 2.66475i) q^{9} +(-4.86760 - 2.78499i) q^{10} -1.71869i q^{11} +(6.34714 + 3.86324i) q^{12} -0.360784 q^{13} +(1.87156 + 3.39076i) q^{15} +5.82374 q^{16} +2.54287i q^{17} +(-3.45618 - 6.68314i) q^{18} +5.69835i q^{19} +(8.32614 + 4.76378i) q^{20} +4.31044i q^{22} +2.50798 q^{23} +(-8.49719 - 5.17188i) q^{24} +(2.53379 + 4.31044i) q^{25} +0.904837 q^{26} +(-0.360784 + 5.18361i) q^{27} -3.76228i q^{29} +(-4.69384 - 8.50394i) q^{30} +2.78499i q^{31} -3.11954 q^{32} +(1.54774 - 2.54287i) q^{33} -6.37747i q^{34} +(5.91187 + 11.4316i) q^{36} +3.30566i q^{37} -14.2913i q^{38} +(-0.533794 - 0.324898i) q^{39} +(-11.1465 - 6.37747i) q^{40} -2.63477 q^{41} -10.0606i q^{43} -7.37310i q^{44} +(-0.284442 + 6.70217i) q^{45} -6.28995 q^{46} -5.82304i q^{47} +(8.61645 + 5.24448i) q^{48} +(-6.35469 - 10.8105i) q^{50} +(-2.28995 + 3.76228i) q^{51} -1.54774 q^{52} -1.45435 q^{53} +(0.904837 - 13.0004i) q^{54} +(1.90853 - 3.33572i) q^{55} +(-5.13156 + 8.43094i) q^{57} +9.43572i q^{58} +6.85856 q^{59} +(8.02891 + 14.5462i) q^{60} +1.60367i q^{61} -6.98468i q^{62} -3.82374 q^{64} +(-0.700227 - 0.400633i) q^{65} +(-3.88170 + 6.37747i) q^{66} +2.49083i q^{67} +10.9088i q^{68} +(3.71065 + 2.25852i) q^{69} +13.1790i q^{71} +(-7.91447 - 15.3040i) q^{72} +11.6437 q^{73} -8.29052i q^{74} +(-0.132851 + 8.65923i) q^{75} +24.4456i q^{76} +(1.33874 + 0.814836i) q^{78} -13.8698 q^{79} +(11.3030 + 6.46698i) q^{80} +(-5.20181 + 7.34446i) q^{81} +6.60793 q^{82} -3.50427i q^{83} +(-2.82374 + 4.93534i) q^{85} +25.2318i q^{86} +(3.38806 - 5.56645i) q^{87} +9.87067i q^{88} +12.2078 q^{89} +(0.713373 - 16.8089i) q^{90} +10.7591 q^{92} +(-2.50798 + 4.12050i) q^{93} +14.6040i q^{94} +(-6.32775 + 11.0596i) q^{95} +(-4.61549 - 2.80926i) q^{96} +8.18747 q^{97} +(4.57989 - 2.36849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{4} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{4} + 12 q^{9} - 24 q^{15} + 24 q^{16} + 24 q^{25} - 36 q^{30} + 84 q^{36} + 24 q^{39} - 72 q^{46} + 24 q^{51} - 24 q^{60} + 24 q^{64} - 96 q^{79} + 12 q^{81} + 48 q^{85} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50798 −1.77341 −0.886704 0.462338i \(-0.847011\pi\)
−0.886704 + 0.462338i \(0.847011\pi\)
\(3\) 1.47954 + 0.900534i 0.854213 + 0.519924i
\(4\) 4.28995 2.14497
\(5\) 1.94085 + 1.11045i 0.867974 + 0.496609i
\(6\) −3.71065 2.25852i −1.51487 0.922036i
\(7\) 0 0
\(8\) −5.74313 −2.03050
\(9\) 1.37808 + 2.66475i 0.459359 + 0.888251i
\(10\) −4.86760 2.78499i −1.53927 0.880690i
\(11\) 1.71869i 0.518205i −0.965850 0.259103i \(-0.916573\pi\)
0.965850 0.259103i \(-0.0834268\pi\)
\(12\) 6.34714 + 3.86324i 1.83226 + 1.11522i
\(13\) −0.360784 −0.100063 −0.0500317 0.998748i \(-0.515932\pi\)
−0.0500317 + 0.998748i \(0.515932\pi\)
\(14\) 0 0
\(15\) 1.87156 + 3.39076i 0.483236 + 0.875490i
\(16\) 5.82374 1.45593
\(17\) 2.54287i 0.616737i 0.951267 + 0.308369i \(0.0997831\pi\)
−0.951267 + 0.308369i \(0.900217\pi\)
\(18\) −3.45618 6.68314i −0.814630 1.57523i
\(19\) 5.69835i 1.30729i 0.756801 + 0.653646i \(0.226761\pi\)
−0.756801 + 0.653646i \(0.773239\pi\)
\(20\) 8.32614 + 4.76378i 1.86178 + 1.06521i
\(21\) 0 0
\(22\) 4.31044i 0.918989i
\(23\) 2.50798 0.522949 0.261475 0.965210i \(-0.415791\pi\)
0.261475 + 0.965210i \(0.415791\pi\)
\(24\) −8.49719 5.17188i −1.73448 1.05571i
\(25\) 2.53379 + 4.31044i 0.506759 + 0.862088i
\(26\) 0.904837 0.177453
\(27\) −0.360784 + 5.18361i −0.0694328 + 0.997587i
\(28\) 0 0
\(29\) 3.76228i 0.698638i −0.937004 0.349319i \(-0.886413\pi\)
0.937004 0.349319i \(-0.113587\pi\)
\(30\) −4.69384 8.50394i −0.856974 1.55260i
\(31\) 2.78499i 0.500198i 0.968220 + 0.250099i \(0.0804632\pi\)
−0.968220 + 0.250099i \(0.919537\pi\)
\(32\) −3.11954 −0.551462
\(33\) 1.54774 2.54287i 0.269427 0.442657i
\(34\) 6.37747i 1.09373i
\(35\) 0 0
\(36\) 5.91187 + 11.4316i 0.985312 + 1.90527i
\(37\) 3.30566i 0.543448i 0.962375 + 0.271724i \(0.0875937\pi\)
−0.962375 + 0.271724i \(0.912406\pi\)
\(38\) 14.2913i 2.31836i
\(39\) −0.533794 0.324898i −0.0854754 0.0520253i
\(40\) −11.1465 6.37747i −1.76242 1.00837i
\(41\) −2.63477 −0.411481 −0.205741 0.978607i \(-0.565960\pi\)
−0.205741 + 0.978607i \(0.565960\pi\)
\(42\) 0 0
\(43\) 10.0606i 1.53423i −0.641510 0.767114i \(-0.721692\pi\)
0.641510 0.767114i \(-0.278308\pi\)
\(44\) 7.37310i 1.11154i
\(45\) −0.284442 + 6.70217i −0.0424021 + 0.999101i
\(46\) −6.28995 −0.927402
\(47\) 5.82304i 0.849378i −0.905339 0.424689i \(-0.860383\pi\)
0.905339 0.424689i \(-0.139617\pi\)
\(48\) 8.61645 + 5.24448i 1.24368 + 0.756975i
\(49\) 0 0
\(50\) −6.35469 10.8105i −0.898689 1.52883i
\(51\) −2.28995 + 3.76228i −0.320656 + 0.526825i
\(52\) −1.54774 −0.214633
\(53\) −1.45435 −0.199770 −0.0998852 0.994999i \(-0.531848\pi\)
−0.0998852 + 0.994999i \(0.531848\pi\)
\(54\) 0.904837 13.0004i 0.123133 1.76913i
\(55\) 1.90853 3.33572i 0.257345 0.449789i
\(56\) 0 0
\(57\) −5.13156 + 8.43094i −0.679692 + 1.11671i
\(58\) 9.43572i 1.23897i
\(59\) 6.85856 0.892909 0.446454 0.894806i \(-0.352687\pi\)
0.446454 + 0.894806i \(0.352687\pi\)
\(60\) 8.02891 + 14.5462i 1.03653 + 1.87790i
\(61\) 1.60367i 0.205329i 0.994716 + 0.102665i \(0.0327368\pi\)
−0.994716 + 0.102665i \(0.967263\pi\)
\(62\) 6.98468i 0.887055i
\(63\) 0 0
\(64\) −3.82374 −0.477967
\(65\) −0.700227 0.400633i −0.0868524 0.0496924i
\(66\) −3.88170 + 6.37747i −0.477804 + 0.785012i
\(67\) 2.49083i 0.304303i 0.988357 + 0.152151i \(0.0486201\pi\)
−0.988357 + 0.152151i \(0.951380\pi\)
\(68\) 10.9088i 1.32288i
\(69\) 3.71065 + 2.25852i 0.446710 + 0.271894i
\(70\) 0 0
\(71\) 13.1790i 1.56406i 0.623243 + 0.782028i \(0.285815\pi\)
−0.623243 + 0.782028i \(0.714185\pi\)
\(72\) −7.91447 15.3040i −0.932729 1.80360i
\(73\) 11.6437 1.36280 0.681398 0.731913i \(-0.261372\pi\)
0.681398 + 0.731913i \(0.261372\pi\)
\(74\) 8.29052i 0.963754i
\(75\) −0.132851 + 8.65923i −0.0153403 + 0.999882i
\(76\) 24.4456i 2.80410i
\(77\) 0 0
\(78\) 1.33874 + 0.814836i 0.151583 + 0.0922621i
\(79\) −13.8698 −1.56048 −0.780239 0.625481i \(-0.784903\pi\)
−0.780239 + 0.625481i \(0.784903\pi\)
\(80\) 11.3030 + 6.46698i 1.26371 + 0.723030i
\(81\) −5.20181 + 7.34446i −0.577979 + 0.816051i
\(82\) 6.60793 0.729724
\(83\) 3.50427i 0.384644i −0.981332 0.192322i \(-0.938398\pi\)
0.981332 0.192322i \(-0.0616018\pi\)
\(84\) 0 0
\(85\) −2.82374 + 4.93534i −0.306277 + 0.535312i
\(86\) 25.2318i 2.72081i
\(87\) 3.38806 5.56645i 0.363239 0.596786i
\(88\) 9.87067i 1.05222i
\(89\) 12.2078 1.29403 0.647014 0.762478i \(-0.276017\pi\)
0.647014 + 0.762478i \(0.276017\pi\)
\(90\) 0.713373 16.8089i 0.0751962 1.77181i
\(91\) 0 0
\(92\) 10.7591 1.12171
\(93\) −2.50798 + 4.12050i −0.260065 + 0.427276i
\(94\) 14.6040i 1.50629i
\(95\) −6.32775 + 11.0596i −0.649213 + 1.13470i
\(96\) −4.61549 2.80926i −0.471066 0.286718i
\(97\) 8.18747 0.831311 0.415656 0.909522i \(-0.363552\pi\)
0.415656 + 0.909522i \(0.363552\pi\)
\(98\) 0 0
\(99\) 4.57989 2.36849i 0.460296 0.238042i
\(100\) 10.8698 + 18.4915i 1.08698 + 1.84915i
\(101\) 1.24693 0.124074 0.0620372 0.998074i \(-0.480240\pi\)
0.0620372 + 0.998074i \(0.480240\pi\)
\(102\) 5.74313 9.43572i 0.568654 0.934275i
\(103\) −4.14604 −0.408521 −0.204261 0.978917i \(-0.565479\pi\)
−0.204261 + 0.978917i \(0.565479\pi\)
\(104\) 2.07203 0.203179
\(105\) 0 0
\(106\) 3.64748 0.354274
\(107\) −1.10752 −0.107068 −0.0535342 0.998566i \(-0.517049\pi\)
−0.0535342 + 0.998566i \(0.517049\pi\)
\(108\) −1.54774 + 22.2374i −0.148931 + 2.13980i
\(109\) −9.11368 −0.872933 −0.436466 0.899721i \(-0.643770\pi\)
−0.436466 + 0.899721i \(0.643770\pi\)
\(110\) −4.78654 + 8.36591i −0.456378 + 0.797659i
\(111\) −2.97686 + 4.89086i −0.282551 + 0.464220i
\(112\) 0 0
\(113\) 3.79282 0.356799 0.178399 0.983958i \(-0.442908\pi\)
0.178399 + 0.983958i \(0.442908\pi\)
\(114\) 12.8698 21.1446i 1.20537 1.98037i
\(115\) 4.86760 + 2.78499i 0.453906 + 0.259701i
\(116\) 16.1400i 1.49856i
\(117\) −0.497187 0.961399i −0.0459650 0.0888814i
\(118\) −17.2011 −1.58349
\(119\) 0 0
\(120\) −10.7486 19.4736i −0.981211 1.77769i
\(121\) 8.04610 0.731463
\(122\) 4.02197i 0.364132i
\(123\) −3.89824 2.37270i −0.351493 0.213939i
\(124\) 11.9474i 1.07291i
\(125\) 0.131176 + 11.1796i 0.0117328 + 0.999931i
\(126\) 0 0
\(127\) 5.98643i 0.531210i −0.964082 0.265605i \(-0.914428\pi\)
0.964082 0.265605i \(-0.0855716\pi\)
\(128\) 15.8289 1.39909
\(129\) 9.05993 14.8851i 0.797682 1.31056i
\(130\) 1.75615 + 1.00478i 0.154025 + 0.0881248i
\(131\) −14.5802 −1.27388 −0.636941 0.770912i \(-0.719801\pi\)
−0.636941 + 0.770912i \(0.719801\pi\)
\(132\) 6.63973 10.9088i 0.577914 0.949488i
\(133\) 0 0
\(134\) 6.24693i 0.539653i
\(135\) −6.45638 + 9.65998i −0.555677 + 0.831399i
\(136\) 14.6040i 1.25229i
\(137\) −15.7133 −1.34248 −0.671240 0.741240i \(-0.734238\pi\)
−0.671240 + 0.741240i \(0.734238\pi\)
\(138\) −9.30622 5.66431i −0.792198 0.482178i
\(139\) 14.7324i 1.24959i −0.780790 0.624794i \(-0.785183\pi\)
0.780790 0.624794i \(-0.214817\pi\)
\(140\) 0 0
\(141\) 5.24385 8.61542i 0.441612 0.725549i
\(142\) 33.0525i 2.77371i
\(143\) 0.620076i 0.0518534i
\(144\) 8.02555 + 15.5188i 0.668796 + 1.29324i
\(145\) 4.17783 7.30202i 0.346950 0.606400i
\(146\) −29.2022 −2.41679
\(147\) 0 0
\(148\) 14.1811i 1.16568i
\(149\) 12.7026i 1.04064i 0.853972 + 0.520319i \(0.174187\pi\)
−0.853972 + 0.520319i \(0.825813\pi\)
\(150\) 0.333186 21.7172i 0.0272046 1.77320i
\(151\) 16.6936 1.35850 0.679252 0.733905i \(-0.262304\pi\)
0.679252 + 0.733905i \(0.262304\pi\)
\(152\) 32.7264i 2.65446i
\(153\) −6.77613 + 3.50427i −0.547818 + 0.283304i
\(154\) 0 0
\(155\) −3.09259 + 5.40524i −0.248403 + 0.434159i
\(156\) −2.28995 1.39379i −0.183342 0.111593i
\(157\) −1.44313 −0.115175 −0.0575873 0.998340i \(-0.518341\pi\)
−0.0575873 + 0.998340i \(0.518341\pi\)
\(158\) 34.7852 2.76736
\(159\) −2.15177 1.30969i −0.170646 0.103865i
\(160\) −6.05456 3.46410i −0.478655 0.273861i
\(161\) 0 0
\(162\) 13.0460 18.4197i 1.02499 1.44719i
\(163\) 16.8619i 1.32072i −0.750947 0.660362i \(-0.770403\pi\)
0.750947 0.660362i \(-0.229597\pi\)
\(164\) −11.3030 −0.882616
\(165\) 5.82767 3.21664i 0.453684 0.250415i
\(166\) 8.78863i 0.682130i
\(167\) 7.20879i 0.557833i 0.960315 + 0.278916i \(0.0899752\pi\)
−0.960315 + 0.278916i \(0.910025\pi\)
\(168\) 0 0
\(169\) −12.8698 −0.989987
\(170\) 7.08187 12.3777i 0.543155 0.949327i
\(171\) −15.1847 + 7.85276i −1.16120 + 0.600516i
\(172\) 43.1595i 3.29088i
\(173\) 8.98599i 0.683192i −0.939847 0.341596i \(-0.889033\pi\)
0.939847 0.341596i \(-0.110967\pi\)
\(174\) −8.49719 + 13.9605i −0.644170 + 1.05834i
\(175\) 0 0
\(176\) 10.0092i 0.754473i
\(177\) 10.1475 + 6.17637i 0.762734 + 0.464244i
\(178\) −30.6170 −2.29484
\(179\) 10.9620i 0.819335i −0.912235 0.409667i \(-0.865645\pi\)
0.912235 0.409667i \(-0.134355\pi\)
\(180\) −1.22024 + 28.7519i −0.0909513 + 2.14304i
\(181\) 5.39306i 0.400863i −0.979708 0.200431i \(-0.935766\pi\)
0.979708 0.200431i \(-0.0642344\pi\)
\(182\) 0 0
\(183\) −1.44416 + 2.37270i −0.106756 + 0.175395i
\(184\) −14.4036 −1.06185
\(185\) −3.67078 + 6.41579i −0.269881 + 0.471698i
\(186\) 6.28995 10.3341i 0.461201 0.757734i
\(187\) 4.37042 0.319597
\(188\) 24.9805i 1.82189i
\(189\) 0 0
\(190\) 15.8698 27.7373i 1.15132 2.01228i
\(191\) 21.3180i 1.54252i −0.636521 0.771259i \(-0.719627\pi\)
0.636521 0.771259i \(-0.280373\pi\)
\(192\) −5.65737 3.44341i −0.408286 0.248507i
\(193\) 13.9361i 1.00314i 0.865116 + 0.501571i \(0.167244\pi\)
−0.865116 + 0.501571i \(0.832756\pi\)
\(194\) −20.5340 −1.47425
\(195\) −0.675229 1.22333i −0.0483542 0.0876045i
\(196\) 0 0
\(197\) −2.01202 −0.143350 −0.0716752 0.997428i \(-0.522835\pi\)
−0.0716752 + 0.997428i \(0.522835\pi\)
\(198\) −11.4863 + 5.94011i −0.816293 + 0.422145i
\(199\) 7.96983i 0.564966i −0.959272 0.282483i \(-0.908842\pi\)
0.959272 0.282483i \(-0.0911581\pi\)
\(200\) −14.5519 24.7554i −1.02897 1.75047i
\(201\) −2.24307 + 3.68528i −0.158214 + 0.259939i
\(202\) −3.12728 −0.220035
\(203\) 0 0
\(204\) −9.82374 + 16.1400i −0.687799 + 1.13003i
\(205\) −5.11368 2.92578i −0.357155 0.204345i
\(206\) 10.3982 0.724474
\(207\) 3.45618 + 6.68314i 0.240221 + 0.464510i
\(208\) −2.10111 −0.145686
\(209\) 9.79371 0.677445
\(210\) 0 0
\(211\) −4.95390 −0.341041 −0.170520 0.985354i \(-0.554545\pi\)
−0.170520 + 0.985354i \(0.554545\pi\)
\(212\) −6.23909 −0.428502
\(213\) −11.8681 + 19.4988i −0.813190 + 1.33604i
\(214\) 2.77764 0.189876
\(215\) 11.1718 19.5261i 0.761912 1.33167i
\(216\) 2.07203 29.7701i 0.140984 2.02560i
\(217\) 0 0
\(218\) 22.8569 1.54806
\(219\) 17.2274 + 10.4856i 1.16412 + 0.708550i
\(220\) 8.18747 14.3101i 0.551999 0.964785i
\(221\) 0.917427i 0.0617128i
\(222\) 7.46590 12.2662i 0.501078 0.823251i
\(223\) 15.6534 1.04823 0.524114 0.851648i \(-0.324397\pi\)
0.524114 + 0.851648i \(0.324397\pi\)
\(224\) 0 0
\(225\) −7.99450 + 12.6920i −0.532966 + 0.846136i
\(226\) −9.51230 −0.632749
\(227\) 12.6120i 0.837087i 0.908197 + 0.418544i \(0.137459\pi\)
−0.908197 + 0.418544i \(0.862541\pi\)
\(228\) −22.0141 + 36.1683i −1.45792 + 2.39530i
\(229\) 5.99233i 0.395984i −0.980204 0.197992i \(-0.936558\pi\)
0.980204 0.197992i \(-0.0634421\pi\)
\(230\) −12.2078 6.98468i −0.804961 0.460556i
\(231\) 0 0
\(232\) 21.6073i 1.41859i
\(233\) −21.8033 −1.42838 −0.714190 0.699952i \(-0.753205\pi\)
−0.714190 + 0.699952i \(0.753205\pi\)
\(234\) 1.24693 + 2.41117i 0.0815146 + 0.157623i
\(235\) 6.46621 11.3016i 0.421809 0.737238i
\(236\) 29.4229 1.91526
\(237\) −20.5210 12.4903i −1.33298 0.811330i
\(238\) 0 0
\(239\) 24.9069i 1.61109i −0.592533 0.805546i \(-0.701872\pi\)
0.592533 0.805546i \(-0.298128\pi\)
\(240\) 10.8995 + 19.7469i 0.703560 + 1.27466i
\(241\) 17.0265i 1.09678i −0.836224 0.548388i \(-0.815242\pi\)
0.836224 0.548388i \(-0.184758\pi\)
\(242\) −20.1794 −1.29718
\(243\) −14.3102 + 6.18201i −0.918002 + 0.396576i
\(244\) 6.87967i 0.440426i
\(245\) 0 0
\(246\) 9.77670 + 5.95067i 0.623339 + 0.379401i
\(247\) 2.05587i 0.130812i
\(248\) 15.9945i 1.01565i
\(249\) 3.15572 5.18471i 0.199985 0.328568i
\(250\) −0.328987 28.0381i −0.0208070 1.77328i
\(251\) 27.3925 1.72900 0.864501 0.502631i \(-0.167635\pi\)
0.864501 + 0.502631i \(0.167635\pi\)
\(252\) 0 0
\(253\) 4.31044i 0.270995i
\(254\) 15.0138i 0.942051i
\(255\) −8.62227 + 4.75915i −0.539948 + 0.298030i
\(256\) −32.0511 −2.00319
\(257\) 30.3882i 1.89557i 0.318915 + 0.947783i \(0.396682\pi\)
−0.318915 + 0.947783i \(0.603318\pi\)
\(258\) −22.7221 + 37.3314i −1.41461 + 2.32415i
\(259\) 0 0
\(260\) −3.00393 1.71869i −0.186296 0.106589i
\(261\) 10.0256 5.18471i 0.620566 0.320926i
\(262\) 36.5669 2.25911
\(263\) 19.3366 1.19235 0.596174 0.802855i \(-0.296687\pi\)
0.596174 + 0.802855i \(0.296687\pi\)
\(264\) −8.88888 + 14.6040i −0.547073 + 0.898817i
\(265\) −2.82268 1.61499i −0.173396 0.0992078i
\(266\) 0 0
\(267\) 18.0620 + 10.9936i 1.10538 + 0.672796i
\(268\) 10.6855i 0.652721i
\(269\) 22.0016 1.34146 0.670729 0.741702i \(-0.265981\pi\)
0.670729 + 0.741702i \(0.265981\pi\)
\(270\) 16.1924 24.2270i 0.985441 1.47441i
\(271\) 15.0577i 0.914691i −0.889289 0.457345i \(-0.848800\pi\)
0.889289 0.457345i \(-0.151200\pi\)
\(272\) 14.8090i 0.897929i
\(273\) 0 0
\(274\) 39.4086 2.38076
\(275\) 7.40832 4.35481i 0.446738 0.262605i
\(276\) 15.9185 + 9.68892i 0.958180 + 0.583205i
\(277\) 1.67599i 0.100700i 0.998732 + 0.0503502i \(0.0160338\pi\)
−0.998732 + 0.0503502i \(0.983966\pi\)
\(278\) 36.9486i 2.21603i
\(279\) −7.42130 + 3.83792i −0.444302 + 0.229770i
\(280\) 0 0
\(281\) 2.10086i 0.125327i −0.998035 0.0626633i \(-0.980041\pi\)
0.998035 0.0626633i \(-0.0199594\pi\)
\(282\) −13.1514 + 21.6073i −0.783157 + 1.28669i
\(283\) −5.00401 −0.297457 −0.148729 0.988878i \(-0.547518\pi\)
−0.148729 + 0.988878i \(0.547518\pi\)
\(284\) 56.5371i 3.35486i
\(285\) −19.3217 + 10.6648i −1.14452 + 0.631730i
\(286\) 1.55514i 0.0919571i
\(287\) 0 0
\(288\) −4.29897 8.31281i −0.253319 0.489837i
\(289\) 10.5338 0.619635
\(290\) −10.4779 + 18.3133i −0.615284 + 1.07539i
\(291\) 12.1137 + 7.37310i 0.710117 + 0.432219i
\(292\) 49.9510 2.92316
\(293\) 17.2734i 1.00912i −0.863376 0.504561i \(-0.831654\pi\)
0.863376 0.504561i \(-0.168346\pi\)
\(294\) 0 0
\(295\) 13.3114 + 7.61610i 0.775022 + 0.443427i
\(296\) 18.9848i 1.10347i
\(297\) 8.90903 + 0.620076i 0.516955 + 0.0359805i
\(298\) 31.8578i 1.84547i
\(299\) −0.904837 −0.0523280
\(300\) −0.569922 + 37.1476i −0.0329045 + 2.14472i
\(301\) 0 0
\(302\) −41.8671 −2.40918
\(303\) 1.84489 + 1.12291i 0.105986 + 0.0645093i
\(304\) 33.1857i 1.90333i
\(305\) −1.78080 + 3.11249i −0.101968 + 0.178220i
\(306\) 16.9944 8.78863i 0.971504 0.502413i
\(307\) 10.2324 0.583994 0.291997 0.956419i \(-0.405680\pi\)
0.291997 + 0.956419i \(0.405680\pi\)
\(308\) 0 0
\(309\) −6.13423 3.73365i −0.348964 0.212400i
\(310\) 7.75615 13.5562i 0.440520 0.769941i
\(311\) −10.4779 −0.594148 −0.297074 0.954855i \(-0.596011\pi\)
−0.297074 + 0.954855i \(0.596011\pi\)
\(312\) 3.06564 + 1.86593i 0.173558 + 0.105638i
\(313\) −0.256176 −0.0144799 −0.00723997 0.999974i \(-0.502305\pi\)
−0.00723997 + 0.999974i \(0.502305\pi\)
\(314\) 3.61935 0.204252
\(315\) 0 0
\(316\) −59.5008 −3.34718
\(317\) −30.9385 −1.73768 −0.868840 0.495094i \(-0.835134\pi\)
−0.868840 + 0.495094i \(0.835134\pi\)
\(318\) 5.39659 + 3.28468i 0.302626 + 0.184196i
\(319\) −6.46621 −0.362038
\(320\) −7.42130 4.24608i −0.414863 0.237363i
\(321\) −1.63862 0.997363i −0.0914591 0.0556674i
\(322\) 0 0
\(323\) −14.4902 −0.806256
\(324\) −22.3155 + 31.5073i −1.23975 + 1.75041i
\(325\) −0.914151 1.55514i −0.0507080 0.0862634i
\(326\) 42.2892i 2.34218i
\(327\) −13.4841 8.20719i −0.745670 0.453858i
\(328\) 15.1318 0.835514
\(329\) 0 0
\(330\) −14.6157 + 8.06726i −0.804566 + 0.444088i
\(331\) −8.37902 −0.460553 −0.230276 0.973125i \(-0.573963\pi\)
−0.230276 + 0.973125i \(0.573963\pi\)
\(332\) 15.0331i 0.825051i
\(333\) −8.80877 + 4.55545i −0.482718 + 0.249637i
\(334\) 18.0795i 0.989264i
\(335\) −2.76594 + 4.83432i −0.151120 + 0.264127i
\(336\) 0 0
\(337\) 11.7454i 0.639810i −0.947450 0.319905i \(-0.896349\pi\)
0.947450 0.319905i \(-0.103651\pi\)
\(338\) 32.2772 1.75565
\(339\) 5.61163 + 3.41556i 0.304782 + 0.185508i
\(340\) −12.1137 + 21.1723i −0.656957 + 1.14823i
\(341\) 4.78654 0.259205
\(342\) 38.0829 19.6945i 2.05929 1.06496i
\(343\) 0 0
\(344\) 57.7794i 3.11526i
\(345\) 4.69384 + 8.50394i 0.252708 + 0.457837i
\(346\) 22.5367i 1.21158i
\(347\) −0.442059 −0.0237310 −0.0118655 0.999930i \(-0.503777\pi\)
−0.0118655 + 0.999930i \(0.503777\pi\)
\(348\) 14.5346 23.8798i 0.779137 1.28009i
\(349\) 21.7405i 1.16374i 0.813282 + 0.581870i \(0.197679\pi\)
−0.813282 + 0.581870i \(0.802321\pi\)
\(350\) 0 0
\(351\) 0.130165 1.87016i 0.00694768 0.0998219i
\(352\) 5.36153i 0.285771i
\(353\) 22.7835i 1.21264i −0.795220 0.606321i \(-0.792645\pi\)
0.795220 0.606321i \(-0.207355\pi\)
\(354\) −25.4497 15.4902i −1.35264 0.823294i
\(355\) −14.6346 + 25.5784i −0.776724 + 1.35756i
\(356\) 52.3709 2.77565
\(357\) 0 0
\(358\) 27.4923i 1.45301i
\(359\) 25.0230i 1.32067i −0.750973 0.660333i \(-0.770415\pi\)
0.750973 0.660333i \(-0.229585\pi\)
\(360\) 1.63359 38.4914i 0.0860975 2.02868i
\(361\) −13.4712 −0.709011
\(362\) 13.5257i 0.710893i
\(363\) 11.9045 + 7.24579i 0.624825 + 0.380305i
\(364\) 0 0
\(365\) 22.5987 + 12.9298i 1.18287 + 0.676777i
\(366\) 3.62192 5.95067i 0.189321 0.311046i
\(367\) −21.3471 −1.11431 −0.557156 0.830408i \(-0.688107\pi\)
−0.557156 + 0.830408i \(0.688107\pi\)
\(368\) 14.6058 0.761380
\(369\) −3.63091 7.02100i −0.189017 0.365499i
\(370\) 9.20623 16.0907i 0.478609 0.836513i
\(371\) 0 0
\(372\) −10.7591 + 17.6767i −0.557832 + 0.916495i
\(373\) 14.1348i 0.731872i −0.930640 0.365936i \(-0.880749\pi\)
0.930640 0.365936i \(-0.119251\pi\)
\(374\) −10.9609 −0.566775
\(375\) −9.87351 + 16.6587i −0.509866 + 0.860254i
\(376\) 33.4425i 1.72466i
\(377\) 1.35737i 0.0699081i
\(378\) 0 0
\(379\) −9.53880 −0.489975 −0.244988 0.969526i \(-0.578784\pi\)
−0.244988 + 0.969526i \(0.578784\pi\)
\(380\) −27.1457 + 47.4453i −1.39254 + 2.43389i
\(381\) 5.39099 8.85716i 0.276189 0.453766i
\(382\) 53.4651i 2.73551i
\(383\) 15.7704i 0.805831i −0.915237 0.402916i \(-0.867997\pi\)
0.915237 0.402916i \(-0.132003\pi\)
\(384\) 23.4195 + 14.2545i 1.19512 + 0.727422i
\(385\) 0 0
\(386\) 34.9514i 1.77898i
\(387\) 26.8090 13.8643i 1.36278 0.704761i
\(388\) 35.1238 1.78314
\(389\) 34.1501i 1.73148i −0.500494 0.865740i \(-0.666848\pi\)
0.500494 0.865740i \(-0.333152\pi\)
\(390\) 1.69346 + 3.06808i 0.0857517 + 0.155358i
\(391\) 6.37747i 0.322522i
\(392\) 0 0
\(393\) −21.5721 13.1300i −1.08817 0.662322i
\(394\) 5.04610 0.254219
\(395\) −26.9193 15.4018i −1.35446 0.774948i
\(396\) 19.6475 10.1607i 0.987323 0.510594i
\(397\) 4.28244 0.214930 0.107465 0.994209i \(-0.465727\pi\)
0.107465 + 0.994209i \(0.465727\pi\)
\(398\) 19.9881i 1.00191i
\(399\) 0 0
\(400\) 14.7562 + 25.1029i 0.737808 + 1.25514i
\(401\) 12.5072i 0.624580i −0.949987 0.312290i \(-0.898904\pi\)
0.949987 0.312290i \(-0.101096\pi\)
\(402\) 5.62558 9.24258i 0.280578 0.460978i
\(403\) 1.00478i 0.0500515i
\(404\) 5.34928 0.266136
\(405\) −18.2516 + 8.47813i −0.906930 + 0.421282i
\(406\) 0 0
\(407\) 5.68142 0.281617
\(408\) 13.1514 21.6073i 0.651094 1.06972i
\(409\) 6.45731i 0.319293i −0.987174 0.159647i \(-0.948965\pi\)
0.987174 0.159647i \(-0.0510355\pi\)
\(410\) 12.8250 + 7.33779i 0.633381 + 0.362388i
\(411\) −23.2485 14.1504i −1.14676 0.697987i
\(412\) −17.7863 −0.876267
\(413\) 0 0
\(414\) −8.66802 16.7611i −0.426010 0.823766i
\(415\) 3.89133 6.80127i 0.191018 0.333861i
\(416\) 1.12548 0.0551812
\(417\) 13.2671 21.7972i 0.649691 1.06741i
\(418\) −24.5624 −1.20139
\(419\) −10.0144 −0.489233 −0.244617 0.969620i \(-0.578662\pi\)
−0.244617 + 0.969620i \(0.578662\pi\)
\(420\) 0 0
\(421\) 17.7858 0.866825 0.433413 0.901196i \(-0.357309\pi\)
0.433413 + 0.901196i \(0.357309\pi\)
\(422\) 12.4243 0.604804
\(423\) 15.5170 8.02459i 0.754461 0.390169i
\(424\) 8.35252 0.405634
\(425\) −10.9609 + 6.44312i −0.531682 + 0.312537i
\(426\) 29.7649 48.9025i 1.44212 2.36934i
\(427\) 0 0
\(428\) −4.75121 −0.229659
\(429\) −0.558400 + 0.917427i −0.0269598 + 0.0442938i
\(430\) −28.0187 + 48.9711i −1.35118 + 2.36160i
\(431\) 2.93906i 0.141569i 0.997492 + 0.0707847i \(0.0225503\pi\)
−0.997492 + 0.0707847i \(0.977450\pi\)
\(432\) −2.10111 + 30.1880i −0.101090 + 1.45242i
\(433\) 31.6675 1.52184 0.760922 0.648843i \(-0.224747\pi\)
0.760922 + 0.648843i \(0.224747\pi\)
\(434\) 0 0
\(435\) 12.7570 7.04135i 0.611651 0.337607i
\(436\) −39.0972 −1.87242
\(437\) 14.2913i 0.683647i
\(438\) −43.2058 26.2976i −2.06445 1.25655i
\(439\) 21.4950i 1.02590i −0.858418 0.512951i \(-0.828552\pi\)
0.858418 0.512951i \(-0.171448\pi\)
\(440\) −10.9609 + 19.1575i −0.522541 + 0.913297i
\(441\) 0 0
\(442\) 2.30088i 0.109442i
\(443\) 26.2694 1.24810 0.624048 0.781386i \(-0.285487\pi\)
0.624048 + 0.781386i \(0.285487\pi\)
\(444\) −12.7706 + 20.9815i −0.606065 + 0.995739i
\(445\) 23.6936 + 13.5562i 1.12318 + 0.642626i
\(446\) −39.2583 −1.85893
\(447\) −11.4391 + 18.7940i −0.541052 + 0.888926i
\(448\) 0 0
\(449\) 36.0069i 1.69927i 0.527369 + 0.849636i \(0.323179\pi\)
−0.527369 + 0.849636i \(0.676821\pi\)
\(450\) 20.0500 31.8313i 0.945166 1.50054i
\(451\) 4.52835i 0.213232i
\(452\) 16.2710 0.765323
\(453\) 24.6988 + 15.0331i 1.16045 + 0.706318i
\(454\) 31.6306i 1.48450i
\(455\) 0 0
\(456\) 29.4712 48.4200i 1.38012 2.26747i
\(457\) 18.2465i 0.853537i 0.904361 + 0.426768i \(0.140348\pi\)
−0.904361 + 0.426768i \(0.859652\pi\)
\(458\) 15.0286i 0.702242i
\(459\) −13.1813 0.917427i −0.615249 0.0428218i
\(460\) 20.8818 + 11.9474i 0.973617 + 0.557052i
\(461\) −22.8072 −1.06224 −0.531119 0.847298i \(-0.678228\pi\)
−0.531119 + 0.847298i \(0.678228\pi\)
\(462\) 0 0
\(463\) 23.3718i 1.08618i −0.839674 0.543090i \(-0.817254\pi\)
0.839674 0.543090i \(-0.182746\pi\)
\(464\) 21.9106i 1.01717i
\(465\) −9.44322 + 5.21228i −0.437919 + 0.241714i
\(466\) 54.6821 2.53310
\(467\) 10.8894i 0.503903i −0.967740 0.251951i \(-0.918928\pi\)
0.967740 0.251951i \(-0.0810723\pi\)
\(468\) −2.13291 4.12435i −0.0985936 0.190648i
\(469\) 0 0
\(470\) −16.2171 + 28.3443i −0.748039 + 1.30742i
\(471\) −2.13517 1.29959i −0.0983836 0.0598820i
\(472\) −39.3896 −1.81305
\(473\) −17.2911 −0.795045
\(474\) 51.4661 + 31.3253i 2.36392 + 1.43882i
\(475\) −24.5624 + 14.4384i −1.12700 + 0.662481i
\(476\) 0 0
\(477\) −2.00421 3.87549i −0.0917663 0.177446i
\(478\) 62.4659i 2.85712i
\(479\) 10.2767 0.469555 0.234777 0.972049i \(-0.424564\pi\)
0.234777 + 0.972049i \(0.424564\pi\)
\(480\) −5.83842 10.5776i −0.266486 0.482800i
\(481\) 1.19263i 0.0543792i
\(482\) 42.7021i 1.94503i
\(483\) 0 0
\(484\) 34.5173 1.56897
\(485\) 15.8906 + 9.09179i 0.721557 + 0.412837i
\(486\) 35.8897 15.5043i 1.62799 0.703291i
\(487\) 13.8475i 0.627492i −0.949507 0.313746i \(-0.898416\pi\)
0.949507 0.313746i \(-0.101584\pi\)
\(488\) 9.21010i 0.416921i
\(489\) 15.1847 24.9478i 0.686676 1.12818i
\(490\) 0 0
\(491\) 13.5981i 0.613672i −0.951762 0.306836i \(-0.900730\pi\)
0.951762 0.306836i \(-0.0992704\pi\)
\(492\) −16.7232 10.1787i −0.753942 0.458893i
\(493\) 9.56701 0.430876
\(494\) 5.15608i 0.231983i
\(495\) 11.5190 + 0.488868i 0.517739 + 0.0219730i
\(496\) 16.2190i 0.728256i
\(497\) 0 0
\(498\) −7.91447 + 13.0031i −0.354656 + 0.582684i
\(499\) 36.2109 1.62102 0.810511 0.585723i \(-0.199190\pi\)
0.810511 + 0.585723i \(0.199190\pi\)
\(500\) 0.562740 + 47.9597i 0.0251665 + 2.14482i
\(501\) −6.49176 + 10.6657i −0.290030 + 0.476508i
\(502\) −68.6998 −3.06622
\(503\) 0.513189i 0.0228819i −0.999935 0.0114410i \(-0.996358\pi\)
0.999935 0.0114410i \(-0.00364185\pi\)
\(504\) 0 0
\(505\) 2.42011 + 1.38466i 0.107693 + 0.0616165i
\(506\) 10.8105i 0.480584i
\(507\) −19.0414 11.5897i −0.845660 0.514718i
\(508\) 25.6815i 1.13943i
\(509\) 18.8040 0.833475 0.416737 0.909027i \(-0.363173\pi\)
0.416737 + 0.909027i \(0.363173\pi\)
\(510\) 21.6245 11.9358i 0.957547 0.528528i
\(511\) 0 0
\(512\) 48.7256 2.15339
\(513\) −29.5380 2.05587i −1.30414 0.0907689i
\(514\) 76.2130i 3.36161i
\(515\) −8.04683 4.60397i −0.354586 0.202875i
\(516\) 38.8666 63.8562i 1.71101 2.81111i
\(517\) −10.0080 −0.440152
\(518\) 0 0
\(519\) 8.09219 13.2951i 0.355208 0.583591i
\(520\) 4.02149 + 2.30088i 0.176354 + 0.100900i
\(521\) −30.3694 −1.33051 −0.665254 0.746617i \(-0.731677\pi\)
−0.665254 + 0.746617i \(0.731677\pi\)
\(522\) −25.1438 + 13.0031i −1.10052 + 0.569132i
\(523\) 39.0288 1.70661 0.853305 0.521411i \(-0.174594\pi\)
0.853305 + 0.521411i \(0.174594\pi\)
\(524\) −62.5485 −2.73244
\(525\) 0 0
\(526\) −48.4958 −2.11452
\(527\) −7.08187 −0.308491
\(528\) 9.01364 14.8090i 0.392268 0.644480i
\(529\) −16.7101 −0.726524
\(530\) 7.07920 + 4.05035i 0.307501 + 0.175936i
\(531\) 9.45162 + 18.2764i 0.410165 + 0.793127i
\(532\) 0 0
\(533\) 0.950580 0.0411742
\(534\) −45.2990 27.5716i −1.96028 1.19314i
\(535\) −2.14954 1.22985i −0.0929325 0.0531711i
\(536\) 14.3051i 0.617888i
\(537\) 9.87161 16.2186i 0.425992 0.699886i
\(538\) −55.1794 −2.37895
\(539\) 0 0
\(540\) −27.6975 + 41.4408i −1.19191 + 1.78333i
\(541\) −10.5123 −0.451959 −0.225980 0.974132i \(-0.572558\pi\)
−0.225980 + 0.974132i \(0.572558\pi\)
\(542\) 37.7644i 1.62212i
\(543\) 4.85663 7.97924i 0.208418 0.342422i
\(544\) 7.93260i 0.340108i
\(545\) −17.6883 10.1203i −0.757683 0.433506i
\(546\) 0 0
\(547\) 25.2465i 1.07946i 0.841837 + 0.539731i \(0.181474\pi\)
−0.841837 + 0.539731i \(0.818526\pi\)
\(548\) −67.4093 −2.87958
\(549\) −4.27339 + 2.20998i −0.182384 + 0.0943197i
\(550\) −18.5799 + 10.9218i −0.792249 + 0.465706i
\(551\) 21.4388 0.913324
\(552\) −21.3107 12.9710i −0.907045 0.552081i
\(553\) 0 0
\(554\) 4.20334i 0.178583i
\(555\) −11.2087 + 6.18676i −0.475783 + 0.262613i
\(556\) 63.2013i 2.68033i
\(557\) 20.3489 0.862212 0.431106 0.902301i \(-0.358124\pi\)
0.431106 + 0.902301i \(0.358124\pi\)
\(558\) 18.6124 9.62542i 0.787928 0.407476i
\(559\) 3.62970i 0.153520i
\(560\) 0 0
\(561\) 6.46621 + 3.93571i 0.273003 + 0.166166i
\(562\) 5.26890i 0.222255i
\(563\) 35.6652i 1.50311i −0.659671 0.751555i \(-0.729304\pi\)
0.659671 0.751555i \(-0.270696\pi\)
\(564\) 22.4958 36.9597i 0.947245 1.55628i
\(565\) 7.36129 + 4.21174i 0.309692 + 0.177189i
\(566\) 12.5499 0.527513
\(567\) 0 0
\(568\) 75.6885i 3.17582i
\(569\) 25.1745i 1.05537i 0.849440 + 0.527685i \(0.176940\pi\)
−0.849440 + 0.527685i \(0.823060\pi\)
\(570\) 48.4585 26.7471i 2.02970 1.12031i
\(571\) 4.98040 0.208423 0.104212 0.994555i \(-0.466768\pi\)
0.104212 + 0.994555i \(0.466768\pi\)
\(572\) 2.66009i 0.111224i
\(573\) 19.1976 31.5409i 0.801992 1.31764i
\(574\) 0 0
\(575\) 6.35469 + 10.8105i 0.265009 + 0.450828i
\(576\) −5.26940 10.1893i −0.219558 0.424555i
\(577\) 21.9323 0.913054 0.456527 0.889710i \(-0.349093\pi\)
0.456527 + 0.889710i \(0.349093\pi\)
\(578\) −26.4185 −1.09886
\(579\) −12.5499 + 20.6190i −0.521557 + 0.856897i
\(580\) 17.9227 31.3253i 0.744199 1.30071i
\(581\) 0 0
\(582\) −30.3808 18.4915i −1.25933 0.766499i
\(583\) 2.49958i 0.103522i
\(584\) −66.8715 −2.76716
\(585\) 0.102622 2.41803i 0.00424289 0.0999734i
\(586\) 43.3213i 1.78958i
\(587\) 31.8719i 1.31549i −0.753240 0.657746i \(-0.771510\pi\)
0.753240 0.657746i \(-0.228490\pi\)
\(588\) 0 0
\(589\) −15.8698 −0.653905
\(590\) −33.3848 19.1010i −1.37443 0.786376i
\(591\) −2.97686 1.81189i −0.122452 0.0745313i
\(592\) 19.2513i 0.791224i
\(593\) 32.9073i 1.35134i 0.737205 + 0.675669i \(0.236145\pi\)
−0.737205 + 0.675669i \(0.763855\pi\)
\(594\) −22.3436 1.55514i −0.916771 0.0638080i
\(595\) 0 0
\(596\) 54.4935i 2.23214i
\(597\) 7.17710 11.7917i 0.293739 0.482601i
\(598\) 2.26931 0.0927989
\(599\) 21.8163i 0.891392i −0.895184 0.445696i \(-0.852956\pi\)
0.895184 0.445696i \(-0.147044\pi\)
\(600\) 0.762979 49.7311i 0.0311485 2.03026i
\(601\) 23.9262i 0.975969i −0.872852 0.487985i \(-0.837732\pi\)
0.872852 0.487985i \(-0.162268\pi\)
\(602\) 0 0
\(603\) −6.63744 + 3.43255i −0.270297 + 0.139784i
\(604\) 71.6145 2.91395
\(605\) 15.6163 + 8.93480i 0.634891 + 0.363251i
\(606\) −4.62693 2.81622i −0.187956 0.114401i
\(607\) −44.2982 −1.79801 −0.899005 0.437939i \(-0.855708\pi\)
−0.899005 + 0.437939i \(0.855708\pi\)
\(608\) 17.7763i 0.720922i
\(609\) 0 0
\(610\) 4.46621 7.80604i 0.180831 0.316057i
\(611\) 2.10086i 0.0849916i
\(612\) −29.0692 + 15.0331i −1.17505 + 0.607679i
\(613\) 8.04230i 0.324825i −0.986723 0.162413i \(-0.948072\pi\)
0.986723 0.162413i \(-0.0519276\pi\)
\(614\) −25.6626 −1.03566
\(615\) −4.93113 8.93386i −0.198842 0.360248i
\(616\) 0 0
\(617\) −13.1311 −0.528637 −0.264318 0.964435i \(-0.585147\pi\)
−0.264318 + 0.964435i \(0.585147\pi\)
\(618\) 15.3845 + 9.36390i 0.618855 + 0.376671i
\(619\) 25.1620i 1.01134i 0.862726 + 0.505672i \(0.168755\pi\)
−0.862726 + 0.505672i \(0.831245\pi\)
\(620\) −13.2671 + 23.1882i −0.532818 + 0.931260i
\(621\) −0.904837 + 13.0004i −0.0363098 + 0.521687i
\(622\) 26.2783 1.05367
\(623\) 0 0
\(624\) −3.10867 1.89212i −0.124447 0.0757455i
\(625\) −12.1598 + 21.8435i −0.486391 + 0.873741i
\(626\) 0.642484 0.0256788
\(627\) 14.4902 + 8.81958i 0.578682 + 0.352220i
\(628\) −6.19097 −0.247046
\(629\) −8.40588 −0.335164
\(630\) 0 0
\(631\) −9.42011 −0.375009 −0.187504 0.982264i \(-0.560040\pi\)
−0.187504 + 0.982264i \(0.560040\pi\)
\(632\) 79.6562 3.16856
\(633\) −7.32950 4.46116i −0.291321 0.177315i
\(634\) 77.5930 3.08161
\(635\) 6.64764 11.6188i 0.263804 0.461076i
\(636\) −9.23097 5.61851i −0.366032 0.222788i
\(637\) 0 0
\(638\) 16.2171 0.642041
\(639\) −35.1187 + 18.1616i −1.38927 + 0.718462i
\(640\) 30.7216 + 17.5773i 1.21438 + 0.694802i
\(641\) 4.91040i 0.193949i 0.995287 + 0.0969747i \(0.0309166\pi\)
−0.995287 + 0.0969747i \(0.969083\pi\)
\(642\) 4.10963 + 2.50136i 0.162194 + 0.0987209i
\(643\) −8.98926 −0.354502 −0.177251 0.984166i \(-0.556720\pi\)
−0.177251 + 0.984166i \(0.556720\pi\)
\(644\) 0 0
\(645\) 34.1131 18.8291i 1.34320 0.741394i
\(646\) 36.3411 1.42982
\(647\) 0.238947i 0.00939397i 0.999989 + 0.00469699i \(0.00149510\pi\)
−0.999989 + 0.00469699i \(0.998505\pi\)
\(648\) 29.8747 42.1802i 1.17359 1.65699i
\(649\) 11.7878i 0.462710i
\(650\) 2.29267 + 3.90024i 0.0899259 + 0.152980i
\(651\) 0 0
\(652\) 72.3365i 2.83292i
\(653\) 1.95812 0.0766272 0.0383136 0.999266i \(-0.487801\pi\)
0.0383136 + 0.999266i \(0.487801\pi\)
\(654\) 33.8177 + 20.5834i 1.32238 + 0.804876i
\(655\) −28.2981 16.1907i −1.10570 0.632622i
\(656\) −15.3442 −0.599090
\(657\) 16.0459 + 31.0277i 0.626012 + 1.21050i
\(658\) 0 0
\(659\) 31.6741i 1.23385i −0.787023 0.616924i \(-0.788379\pi\)
0.787023 0.616924i \(-0.211621\pi\)
\(660\) 25.0004 13.7992i 0.973139 0.537134i
\(661\) 28.7000i 1.11630i 0.829740 + 0.558150i \(0.188489\pi\)
−0.829740 + 0.558150i \(0.811511\pi\)
\(662\) 21.0144 0.816747
\(663\) 0.826174 1.35737i 0.0320860 0.0527159i
\(664\) 20.1255i 0.781020i
\(665\) 0 0
\(666\) 22.0922 11.4250i 0.856055 0.442709i
\(667\) 9.43572i 0.365352i
\(668\) 30.9253i 1.19654i
\(669\) 23.1598 + 14.0964i 0.895409 + 0.544998i
\(670\) 6.93692 12.1244i 0.267996 0.468405i
\(671\) 2.75622 0.106403
\(672\) 0 0
\(673\) 33.9688i 1.30940i 0.755889 + 0.654700i \(0.227205\pi\)
−0.755889 + 0.654700i \(0.772795\pi\)
\(674\) 29.4571i 1.13464i
\(675\) −23.2578 + 11.5791i −0.895193 + 0.445679i
\(676\) −55.2109 −2.12350
\(677\) 7.18943i 0.276312i −0.990410 0.138156i \(-0.955882\pi\)
0.990410 0.138156i \(-0.0441176\pi\)
\(678\) −14.0738 8.56616i −0.540502 0.328981i
\(679\) 0 0
\(680\) 16.2171 28.3443i 0.621897 1.08695i
\(681\) −11.3575 + 18.6599i −0.435222 + 0.715051i
\(682\) −12.0045 −0.459677
\(683\) 8.04026 0.307652 0.153826 0.988098i \(-0.450840\pi\)
0.153826 + 0.988098i \(0.450840\pi\)
\(684\) −65.1415 + 33.6879i −2.49075 + 1.28809i
\(685\) −30.4972 17.4489i −1.16524 0.666688i
\(686\) 0 0
\(687\) 5.39630 8.86589i 0.205882 0.338255i
\(688\) 58.5904i 2.23374i
\(689\) 0.524706 0.0199897
\(690\) −11.7720 21.3277i −0.448154 0.811931i
\(691\) 44.2571i 1.68362i 0.539773 + 0.841810i \(0.318510\pi\)
−0.539773 + 0.841810i \(0.681490\pi\)
\(692\) 38.5494i 1.46543i
\(693\) 0 0
\(694\) 1.10867 0.0420847
\(695\) 16.3597 28.5934i 0.620557 1.08461i
\(696\) −19.4581 + 31.9688i −0.737557 + 1.21177i
\(697\) 6.69988i 0.253776i
\(698\) 54.5246i 2.06379i
\(699\) −32.2588 19.6346i −1.22014 0.742649i
\(700\) 0 0
\(701\) 0.779307i 0.0294340i 0.999892 + 0.0147170i \(0.00468474\pi\)
−0.999892 + 0.0147170i \(0.995315\pi\)
\(702\) −0.326450 + 4.69032i −0.0123211 + 0.177025i
\(703\) −18.8368 −0.710444
\(704\) 6.57183i 0.247685i
\(705\) 19.7445 10.8982i 0.743622 0.410450i
\(706\) 57.1404i 2.15051i
\(707\) 0 0
\(708\) 43.5323 + 26.4963i 1.63604 + 0.995792i
\(709\) −9.26534 −0.347967 −0.173984 0.984749i \(-0.555664\pi\)
−0.173984 + 0.984749i \(0.555664\pi\)
\(710\) 36.7033 64.1500i 1.37745 2.40751i
\(711\) −19.1137 36.9597i −0.716819 1.38610i
\(712\) −70.1112 −2.62753
\(713\) 6.98468i 0.261578i
\(714\) 0 0
\(715\) −0.688564 + 1.20347i −0.0257508 + 0.0450074i
\(716\) 47.0262i 1.75745i
\(717\) 22.4295 36.8507i 0.837645 1.37622i
\(718\) 62.7572i 2.34208i
\(719\) −18.1996 −0.678730 −0.339365 0.940655i \(-0.610212\pi\)
−0.339365 + 0.940655i \(0.610212\pi\)
\(720\) −1.65652 + 39.0317i −0.0617347 + 1.45463i
\(721\) 0 0
\(722\) 33.7855 1.25737
\(723\) 15.3330 25.1914i 0.570239 0.936879i
\(724\) 23.1359i 0.859840i
\(725\) 16.2171 9.53285i 0.602288 0.354041i
\(726\) −29.8563 18.1723i −1.10807 0.674436i
\(727\) −31.6357 −1.17330 −0.586652 0.809839i \(-0.699554\pi\)
−0.586652 + 0.809839i \(0.699554\pi\)
\(728\) 0 0
\(729\) −26.7397 3.74032i −0.990358 0.138531i
\(730\) −56.6771 32.4276i −2.09771 1.20020i
\(731\) 25.5829 0.946216
\(732\) −6.19538 + 10.1787i −0.228988 + 0.376217i
\(733\) −17.0085 −0.628224 −0.314112 0.949386i \(-0.601707\pi\)
−0.314112 + 0.949386i \(0.601707\pi\)
\(734\) 53.5381 1.97613
\(735\) 0 0
\(736\) −7.82374 −0.288387
\(737\) 4.28096 0.157691
\(738\) 9.10623 + 17.6085i 0.335205 + 0.648178i
\(739\) −18.9804 −0.698205 −0.349103 0.937084i \(-0.613514\pi\)
−0.349103 + 0.937084i \(0.613514\pi\)
\(740\) −15.7474 + 27.5234i −0.578887 + 1.01178i
\(741\) 1.85138 3.04174i 0.0680123 0.111741i
\(742\) 0 0
\(743\) 3.80063 0.139432 0.0697159 0.997567i \(-0.477791\pi\)
0.0697159 + 0.997567i \(0.477791\pi\)
\(744\) 14.4036 23.6646i 0.528063 0.867585i
\(745\) −14.1056 + 24.6538i −0.516790 + 0.903247i
\(746\) 35.4497i 1.29791i
\(747\) 9.33802 4.82915i 0.341660 0.176689i
\(748\) 18.7489 0.685526
\(749\) 0 0
\(750\) 24.7625 41.7797i 0.904199 1.52558i
\(751\) −12.6456 −0.461444 −0.230722 0.973020i \(-0.574109\pi\)
−0.230722 + 0.973020i \(0.574109\pi\)
\(752\) 33.9119i 1.23664i
\(753\) 40.5283 + 24.6679i 1.47694 + 0.898949i
\(754\) 3.40425i 0.123976i
\(755\) 32.3997 + 18.5374i 1.17915 + 0.674645i
\(756\) 0 0
\(757\) 6.50118i 0.236289i −0.992996 0.118145i \(-0.962305\pi\)
0.992996 0.118145i \(-0.0376947\pi\)
\(758\) 23.9231 0.868926
\(759\) 3.88170 6.37747i 0.140897 0.231487i
\(760\) 36.3411 63.5169i 1.31823 2.30400i
\(761\) 43.7825 1.58711 0.793556 0.608497i \(-0.208227\pi\)
0.793556 + 0.608497i \(0.208227\pi\)
\(762\) −13.5205 + 22.2135i −0.489795 + 0.804712i
\(763\) 0 0
\(764\) 91.4531i 3.30866i
\(765\) −17.0428 0.723300i −0.616183 0.0261510i
\(766\) 39.5519i 1.42907i
\(767\) −2.47446 −0.0893474
\(768\) −47.4209 28.8631i −1.71115 1.04151i
\(769\) 33.3141i 1.20134i 0.799498 + 0.600668i \(0.205099\pi\)
−0.799498 + 0.600668i \(0.794901\pi\)
\(770\) 0 0
\(771\) −27.3657 + 44.9606i −0.985550 + 1.61922i
\(772\) 59.7851i 2.15171i
\(773\) 42.3324i 1.52259i 0.648405 + 0.761296i \(0.275437\pi\)
−0.648405 + 0.761296i \(0.724563\pi\)
\(774\) −67.2364 + 34.7713i −2.41676 + 1.24983i
\(775\) −12.0045 + 7.05658i −0.431215 + 0.253480i
\(776\) −47.0217 −1.68798
\(777\) 0 0
\(778\) 85.6477i 3.07062i
\(779\) 15.0138i 0.537926i
\(780\) −2.89670 5.24802i −0.103718 0.187909i
\(781\) 22.6506 0.810502
\(782\) 15.9945i 0.571963i
\(783\) 19.5022 + 1.35737i 0.696952 + 0.0485084i
\(784\) 0 0
\(785\) −2.80091 1.60253i −0.0999686 0.0571968i
\(786\) 54.1022 + 32.9298i 1.92976 + 1.17457i
\(787\) −25.9101 −0.923597 −0.461799 0.886985i \(-0.652796\pi\)
−0.461799 + 0.886985i \(0.652796\pi\)
\(788\) −8.63145 −0.307483
\(789\) 28.6093 + 17.4133i 1.01852 + 0.619930i
\(790\) 67.5129 + 38.6273i 2.40200 + 1.37430i
\(791\) 0 0
\(792\) −26.3029 + 13.6025i −0.934633 + 0.483345i
\(793\) 0.578579i 0.0205459i
\(794\) −10.7403 −0.381158
\(795\) −2.72191 4.93135i −0.0965362 0.174897i
\(796\) 34.1901i 1.21184i
\(797\) 27.5780i 0.976865i −0.872602 0.488432i \(-0.837569\pi\)
0.872602 0.488432i \(-0.162431\pi\)
\(798\) 0 0
\(799\) 14.8073 0.523843
\(800\) −7.90428 13.4466i −0.279458 0.475409i
\(801\) 16.8233 + 32.5309i 0.594423 + 1.14942i
\(802\) 31.3678i 1.10764i
\(803\) 20.0120i 0.706208i
\(804\) −9.62267 + 15.8096i −0.339365 + 0.557563i
\(805\) 0 0
\(806\) 2.51996i 0.0887617i
\(807\) 32.5522 + 19.8132i 1.14589 + 0.697456i
\(808\) −7.16130 −0.251934
\(809\) 31.1891i 1.09655i 0.836298 + 0.548275i \(0.184715\pi\)
−0.836298 + 0.548275i \(0.815285\pi\)
\(810\) 45.7746 21.2630i 1.60836 0.747104i
\(811\) 17.5174i 0.615120i 0.951529 + 0.307560i \(0.0995124\pi\)
−0.951529 + 0.307560i \(0.900488\pi\)
\(812\) 0 0
\(813\) 13.5600 22.2785i 0.475569 0.781341i
\(814\) −14.2489 −0.499422
\(815\) 18.7243 32.7264i 0.655884 1.14635i
\(816\) −13.3360 + 21.9106i −0.466855 + 0.767023i
\(817\) 57.3289 2.00568
\(818\) 16.1948i 0.566237i
\(819\) 0 0
\(820\) −21.9374 12.5514i −0.766088 0.438315i
\(821\) 35.4867i 1.23849i 0.785197 + 0.619247i \(0.212562\pi\)
−0.785197 + 0.619247i \(0.787438\pi\)
\(822\) 58.3066 + 35.4888i 2.03368 + 1.23782i
\(823\) 30.0470i 1.04737i 0.851912 + 0.523686i \(0.175443\pi\)
−0.851912 + 0.523686i \(0.824557\pi\)
\(824\) 23.8112 0.829503
\(825\) 14.8826 + 0.228329i 0.518144 + 0.00794941i
\(826\) 0 0
\(827\) 21.6751 0.753717 0.376859 0.926271i \(-0.377004\pi\)
0.376859 + 0.926271i \(0.377004\pi\)
\(828\) 14.8268 + 28.6703i 0.515268 + 0.996361i
\(829\) 9.16245i 0.318225i 0.987260 + 0.159113i \(0.0508633\pi\)
−0.987260 + 0.159113i \(0.949137\pi\)
\(830\) −9.75935 + 17.0574i −0.338752 + 0.592071i
\(831\) −1.50929 + 2.47969i −0.0523566 + 0.0860196i
\(832\) 1.37954 0.0478270
\(833\) 0 0
\(834\) −33.2735 + 54.6669i −1.15217 + 1.89296i
\(835\) −8.00501 + 13.9912i −0.277025 + 0.484184i
\(836\) 42.0145 1.45310
\(837\) −14.4363 1.00478i −0.498991 0.0347302i
\(838\) 25.1158 0.867610
\(839\) 31.7155 1.09494 0.547471 0.836825i \(-0.315591\pi\)
0.547471 + 0.836825i \(0.315591\pi\)
\(840\) 0 0
\(841\) 14.8452 0.511904
\(842\) −44.6063 −1.53723
\(843\) 1.89189 3.10830i 0.0651603 0.107056i
\(844\) −21.2520 −0.731523
\(845\) −24.9784 14.2913i −0.859284 0.491637i
\(846\) −38.9162 + 20.1255i −1.33797 + 0.691928i
\(847\) 0 0
\(848\) −8.46976 −0.290853
\(849\) −7.40363 4.50628i −0.254092 0.154655i
\(850\) 27.4897 16.1592i 0.942888 0.554255i
\(851\) 8.29052i 0.284195i
\(852\) −50.9136 + 83.6488i −1.74427 + 2.86576i
\(853\) −10.2006 −0.349262 −0.174631 0.984634i \(-0.555873\pi\)
−0.174631 + 0.984634i \(0.555873\pi\)
\(854\) 0 0
\(855\) −38.1913 1.62085i −1.30612 0.0554319i
\(856\) 6.36065 0.217402
\(857\) 1.80558i 0.0616774i 0.999524 + 0.0308387i \(0.00981783\pi\)
−0.999524 + 0.0308387i \(0.990182\pi\)
\(858\) 1.40045 2.30088i 0.0478107 0.0785509i
\(859\) 7.71307i 0.263166i 0.991305 + 0.131583i \(0.0420061\pi\)
−0.991305 + 0.131583i \(0.957994\pi\)
\(860\) 47.9265 83.7660i 1.63428 2.85640i
\(861\) 0 0
\(862\) 7.37109i 0.251060i
\(863\) −22.3531 −0.760909 −0.380455 0.924800i \(-0.624233\pi\)
−0.380455 + 0.924800i \(0.624233\pi\)
\(864\) 1.12548 16.1705i 0.0382896 0.550132i
\(865\) 9.97851 17.4405i 0.339280 0.592993i
\(866\) −79.4214 −2.69885
\(867\) 15.5852 + 9.48604i 0.529300 + 0.322163i
\(868\) 0 0
\(869\) 23.8380i 0.808648i
\(870\) −31.9942 + 17.6595i −1.08471 + 0.598715i
\(871\) 0.898649i 0.0304496i
\(872\) 52.3411 1.77249
\(873\) 11.2830 + 21.8176i 0.381870 + 0.738413i
\(874\) 35.8423i 1.21238i
\(875\) 0 0
\(876\) 73.9045 + 44.9826i 2.49700 + 1.51982i
\(877\) 51.7428i 1.74723i 0.486618 + 0.873615i \(0.338230\pi\)
−0.486618 + 0.873615i \(0.661770\pi\)
\(878\) 53.9090i 1.81934i
\(879\) 15.5553 25.5567i 0.524667 0.862005i
\(880\) 11.1148 19.4264i 0.374678 0.654863i
\(881\) −40.9882 −1.38093 −0.690464 0.723367i \(-0.742594\pi\)
−0.690464 + 0.723367i \(0.742594\pi\)
\(882\) 0 0
\(883\) 10.6943i 0.359891i −0.983677 0.179945i \(-0.942408\pi\)
0.983677 0.179945i \(-0.0575921\pi\)
\(884\) 3.93571i 0.132372i
\(885\) 12.8362 + 23.2557i 0.431485 + 0.781733i
\(886\) −65.8830 −2.21338
\(887\) 47.0848i 1.58095i 0.612493 + 0.790476i \(0.290167\pi\)
−0.612493 + 0.790476i \(0.709833\pi\)
\(888\) 17.0965 28.0888i 0.573721 0.942599i
\(889\) 0 0
\(890\) −59.4229 33.9987i −1.99186 1.13964i
\(891\) 12.6229 + 8.94032i 0.422882 + 0.299512i
\(892\) 67.1521 2.24842
\(893\) 33.1817 1.11038
\(894\) 28.6891 47.1349i 0.959506 1.57643i
\(895\) 12.1727 21.2755i 0.406889 0.711161i
\(896\) 0 0
\(897\) −1.33874 0.814836i −0.0446993 0.0272066i
\(898\) 90.3046i 3.01350i
\(899\) 10.4779 0.349458
\(900\) −34.2960 + 54.4482i −1.14320 + 1.81494i
\(901\) 3.69823i 0.123206i
\(902\) 11.3570i 0.378147i
\(903\) 0 0
\(904\) −21.7827 −0.724480
\(905\) 5.98873 10.4671i 0.199072 0.347939i
\(906\) −61.9440 37.7028i −2.05795 1.25259i
\(907\) 8.71819i 0.289483i 0.989470 + 0.144741i \(0.0462350\pi\)
−0.989470 + 0.144741i \(0.953765\pi\)
\(908\) 54.1048i 1.79553i
\(909\) 1.71837 + 3.32277i 0.0569947 + 0.110209i
\(910\) 0 0
\(911\) 4.85314i 0.160792i −0.996763 0.0803958i \(-0.974382\pi\)
0.996763 0.0803958i \(-0.0256184\pi\)
\(912\) −29.8849 + 49.0996i −0.989587 + 1.62585i
\(913\) −6.02277 −0.199324
\(914\) 45.7619i 1.51367i
\(915\) −5.43767 + 3.00138i −0.179764 + 0.0992224i
\(916\) 25.7068i 0.849376i
\(917\) 0 0
\(918\) 33.0583 + 2.30088i 1.09109 + 0.0759405i
\(919\) −35.8584 −1.18286 −0.591429 0.806357i \(-0.701436\pi\)
−0.591429 + 0.806357i \(0.701436\pi\)
\(920\) −27.9553 15.9945i −0.921658 0.527324i
\(921\) 15.1392 + 9.21462i 0.498855 + 0.303632i
\(922\) 57.1999 1.88378
\(923\) 4.75475i 0.156505i
\(924\) 0 0
\(925\) −14.2489 + 8.37587i −0.468500 + 0.275397i
\(926\) 58.6160i 1.92624i
\(927\) −5.71355 11.0482i −0.187658 0.362869i
\(928\) 11.7366i 0.385273i
\(929\) 25.4003 0.833355 0.416678 0.909054i \(-0.363194\pi\)
0.416678 + 0.909054i \(0.363194\pi\)
\(930\) 23.6834 13.0723i 0.776608 0.428657i
\(931\) 0 0
\(932\) −93.5349 −3.06384
\(933\) −15.5025 9.43572i −0.507528 0.308911i
\(934\) 27.3104i 0.893625i
\(935\) 8.48232 + 4.85314i 0.277402 + 0.158715i
\(936\) 2.85541 + 5.52144i 0.0933320 + 0.180474i
\(937\) −40.3037 −1.31667 −0.658333 0.752727i \(-0.728738\pi\)
−0.658333 + 0.752727i \(0.728738\pi\)
\(938\) 0 0
\(939\) −0.379023 0.230695i −0.0123689 0.00752846i
\(940\) 27.7397 48.4834i 0.904768 1.58136i
\(941\) 18.2413 0.594650 0.297325 0.954776i \(-0.403906\pi\)
0.297325 + 0.954776i \(0.403906\pi\)
\(942\) 5.35497 + 3.25935i 0.174474 + 0.106195i
\(943\) −6.60793 −0.215184
\(944\) 39.9425 1.30002
\(945\) 0 0
\(946\) 43.3657 1.40994
\(947\) −18.8485 −0.612494 −0.306247 0.951952i \(-0.599073\pi\)
−0.306247 + 0.951952i \(0.599073\pi\)
\(948\) −88.0338 53.5825i −2.85921 1.74028i
\(949\) −4.20087 −0.136366
\(950\) 61.6019 36.2113i 1.99863 1.17485i
\(951\) −45.7747 27.8612i −1.48435 0.903461i
\(952\) 0 0
\(953\) −25.3110 −0.819903 −0.409952 0.912107i \(-0.634454\pi\)
−0.409952 + 0.912107i \(0.634454\pi\)
\(954\) 5.02650 + 9.71963i 0.162739 + 0.314684i
\(955\) 23.6726 41.3751i 0.766029 1.33887i
\(956\) 106.849i 3.45575i
\(957\) −9.56701 5.82304i −0.309257 0.188232i
\(958\) −25.7737 −0.832712
\(959\) 0 0
\(960\) −7.15637 12.9654i −0.230971 0.418456i
\(961\) 23.2438 0.749802
\(962\) 2.99108i 0.0964364i
\(963\) −1.52625 2.95128i −0.0491827 0.0951035i
\(964\) 73.0429i 2.35255i
\(965\) −15.4754 + 27.0479i −0.498170 + 0.870702i
\(966\) 0 0
\(967\) 32.2840i 1.03818i 0.854718 + 0.519092i \(0.173730\pi\)
−0.854718 + 0.519092i \(0.826270\pi\)
\(968\) −46.2098 −1.48524
\(969\) −21.4388 13.0489i −0.688714 0.419191i
\(970\) −39.8534 22.8020i −1.27961 0.732128i
\(971\) −1.38783 −0.0445377 −0.0222688 0.999752i \(-0.507089\pi\)
−0.0222688 + 0.999752i \(0.507089\pi\)
\(972\) −61.3901 + 26.5205i −1.96909 + 0.850645i
\(973\) 0 0
\(974\) 34.7293i 1.11280i
\(975\) 0.0479303 3.12411i 0.00153500 0.100052i
\(976\) 9.33937i 0.298946i
\(977\) −57.8116 −1.84956 −0.924779 0.380505i \(-0.875750\pi\)
−0.924779 + 0.380505i \(0.875750\pi\)
\(978\) −38.0829 + 62.5685i −1.21776 + 2.00072i
\(979\) 20.9815i 0.670572i
\(980\) 0 0
\(981\) −12.5593 24.2857i −0.400989 0.775383i
\(982\) 34.1036i 1.08829i
\(983\) 26.0114i 0.829635i −0.909905 0.414818i \(-0.863845\pi\)
0.909905 0.414818i \(-0.136155\pi\)
\(984\) 22.3881 + 13.6267i 0.713706 + 0.434403i
\(985\) −3.90503 2.23425i −0.124424 0.0711891i
\(986\) −23.9938 −0.764119
\(987\) 0 0
\(988\) 8.81958i 0.280588i
\(989\) 25.2318i 0.802324i
\(990\) −28.8893 1.22607i −0.918162 0.0389670i
\(991\) −36.2324 −1.15096 −0.575480 0.817816i \(-0.695185\pi\)
−0.575480 + 0.817816i \(0.695185\pi\)
\(992\) 8.68788i 0.275841i
\(993\) −12.3971 7.54560i −0.393410 0.239452i
\(994\) 0 0
\(995\) 8.85011 15.4682i 0.280567 0.490376i
\(996\) 13.5379 22.2421i 0.428963 0.704769i
\(997\) 34.5948 1.09563 0.547814 0.836600i \(-0.315460\pi\)
0.547814 + 0.836600i \(0.315460\pi\)
\(998\) −90.8160 −2.87473
\(999\) −17.1353 1.19263i −0.542136 0.0377331i
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 735.2.g.b.734.4 24
3.2 odd 2 inner 735.2.g.b.734.23 24
5.4 even 2 inner 735.2.g.b.734.21 24
7.2 even 3 105.2.p.a.59.11 yes 24
7.3 odd 6 105.2.p.a.89.12 yes 24
7.4 even 3 735.2.p.f.509.11 24
7.5 odd 6 735.2.p.f.374.12 24
7.6 odd 2 inner 735.2.g.b.734.1 24
15.14 odd 2 inner 735.2.g.b.734.2 24
21.2 odd 6 105.2.p.a.59.1 24
21.5 even 6 735.2.p.f.374.2 24
21.11 odd 6 735.2.p.f.509.1 24
21.17 even 6 105.2.p.a.89.2 yes 24
21.20 even 2 inner 735.2.g.b.734.22 24
35.2 odd 12 525.2.t.j.101.2 24
35.3 even 12 525.2.t.j.26.1 24
35.4 even 6 735.2.p.f.509.2 24
35.9 even 6 105.2.p.a.59.2 yes 24
35.17 even 12 525.2.t.j.26.12 24
35.19 odd 6 735.2.p.f.374.1 24
35.23 odd 12 525.2.t.j.101.11 24
35.24 odd 6 105.2.p.a.89.1 yes 24
35.34 odd 2 inner 735.2.g.b.734.24 24
105.2 even 12 525.2.t.j.101.12 24
105.17 odd 12 525.2.t.j.26.2 24
105.23 even 12 525.2.t.j.101.1 24
105.38 odd 12 525.2.t.j.26.11 24
105.44 odd 6 105.2.p.a.59.12 yes 24
105.59 even 6 105.2.p.a.89.11 yes 24
105.74 odd 6 735.2.p.f.509.12 24
105.89 even 6 735.2.p.f.374.11 24
105.104 even 2 inner 735.2.g.b.734.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.p.a.59.1 24 21.2 odd 6
105.2.p.a.59.2 yes 24 35.9 even 6
105.2.p.a.59.11 yes 24 7.2 even 3
105.2.p.a.59.12 yes 24 105.44 odd 6
105.2.p.a.89.1 yes 24 35.24 odd 6
105.2.p.a.89.2 yes 24 21.17 even 6
105.2.p.a.89.11 yes 24 105.59 even 6
105.2.p.a.89.12 yes 24 7.3 odd 6
525.2.t.j.26.1 24 35.3 even 12
525.2.t.j.26.2 24 105.17 odd 12
525.2.t.j.26.11 24 105.38 odd 12
525.2.t.j.26.12 24 35.17 even 12
525.2.t.j.101.1 24 105.23 even 12
525.2.t.j.101.2 24 35.2 odd 12
525.2.t.j.101.11 24 35.23 odd 12
525.2.t.j.101.12 24 105.2 even 12
735.2.g.b.734.1 24 7.6 odd 2 inner
735.2.g.b.734.2 24 15.14 odd 2 inner
735.2.g.b.734.3 24 105.104 even 2 inner
735.2.g.b.734.4 24 1.1 even 1 trivial
735.2.g.b.734.21 24 5.4 even 2 inner
735.2.g.b.734.22 24 21.20 even 2 inner
735.2.g.b.734.23 24 3.2 odd 2 inner
735.2.g.b.734.24 24 35.34 odd 2 inner
735.2.p.f.374.1 24 35.19 odd 6
735.2.p.f.374.2 24 21.5 even 6
735.2.p.f.374.11 24 105.89 even 6
735.2.p.f.374.12 24 7.5 odd 6
735.2.p.f.509.1 24 21.11 odd 6
735.2.p.f.509.2 24 35.4 even 6
735.2.p.f.509.11 24 7.4 even 3
735.2.p.f.509.12 24 105.74 odd 6