Properties

Label 637.2.bb.b.227.2
Level $637$
Weight $2$
Character 637.227
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(227,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.227");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.bb (of order \(12\), degree \(4\), not 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 227.2
Character \(\chi\) \(=\) 637.227
Dual form 637.2.bb.b.362.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.65980 + 1.65980i) q^{2} +(2.39046 - 1.38013i) q^{3} -3.50987i q^{4} +(0.412430 - 1.53921i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} +(2.30952 - 4.00020i) q^{9} +O(q^{10})\) \(q+(-1.65980 + 1.65980i) q^{2} +(2.39046 - 1.38013i) q^{3} -3.50987i q^{4} +(0.412430 - 1.53921i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} +(2.30952 - 4.00020i) q^{9} +(1.87023 + 3.23933i) q^{10} +(0.813080 - 3.03446i) q^{11} +(-4.84407 - 8.39018i) q^{12} +(-1.04831 - 3.44979i) q^{13} +(-1.13841 - 4.24862i) q^{15} -1.29944 q^{16} -0.641590 q^{17} +(2.80620 + 10.4729i) q^{18} +(-7.61472 + 2.04036i) q^{19} +(-5.40242 - 1.44757i) q^{20} +(3.68704 + 6.38614i) q^{22} +0.146149i q^{23} +(9.44938 + 2.53195i) q^{24} +(2.13106 + 1.23037i) q^{25} +(7.46594 + 3.98598i) q^{26} -4.46896i q^{27} +(1.49412 - 2.58790i) q^{29} +(8.94139 + 5.16231i) q^{30} +(-6.46586 + 1.73252i) q^{31} +(-2.85535 + 2.85535i) q^{32} +(-2.24431 - 8.37589i) q^{33} +(1.06491 - 1.06491i) q^{34} +(-14.0402 - 8.10610i) q^{36} +(-2.75050 - 2.75050i) q^{37} +(9.25232 - 16.0255i) q^{38} +(-7.26709 - 6.79977i) q^{39} +(4.89096 - 2.82380i) q^{40} +(5.60356 - 1.50147i) q^{41} +(2.42713 - 1.40130i) q^{43} +(-10.6505 - 2.85380i) q^{44} +(-5.20463 - 5.20463i) q^{45} +(-0.242578 - 0.242578i) q^{46} +(3.04537 + 0.816005i) q^{47} +(-3.10624 + 1.79339i) q^{48} +(-5.57930 + 1.49497i) q^{50} +(-1.53369 + 0.885477i) q^{51} +(-12.1083 + 3.67942i) q^{52} +(3.66059 - 6.34033i) q^{53} +(7.41757 + 7.41757i) q^{54} +(-4.33533 - 2.50300i) q^{55} +(-15.3867 + 15.3867i) q^{57} +(1.81545 + 6.77534i) q^{58} +(2.93283 - 2.93283i) q^{59} +(-14.9121 + 3.99568i) q^{60} +(3.90292 + 2.25335i) q^{61} +(7.85639 - 13.6077i) q^{62} -12.0775i q^{64} +(-5.74230 + 0.190767i) q^{65} +(17.6274 + 10.1772i) q^{66} +(1.36775 + 0.366486i) q^{67} +2.25190i q^{68} +(0.201704 + 0.349362i) q^{69} +(13.8300 + 3.70574i) q^{71} +(15.8126 - 4.23699i) q^{72} +(1.82677 + 6.81760i) q^{73} +9.13055 q^{74} +6.79227 q^{75} +(7.16138 + 26.7267i) q^{76} +(23.3482 - 0.775656i) q^{78} +(0.316458 + 0.548121i) q^{79} +(-0.535926 + 2.00010i) q^{80} +(0.760810 + 1.31776i) q^{81} +(-6.80865 + 11.7929i) q^{82} +(1.07813 + 1.07813i) q^{83} +(-0.264611 + 0.987541i) q^{85} +(-1.70266 + 6.35443i) q^{86} -8.24834i q^{87} +(9.64223 - 5.56694i) q^{88} +(9.60471 - 9.60471i) q^{89} +17.2773 q^{90} +0.512963 q^{92} +(-13.0652 + 13.0652i) q^{93} +(-6.40911 + 3.70030i) q^{94} +12.5621i q^{95} +(-2.88483 + 10.7663i) q^{96} +(0.0487160 - 0.181811i) q^{97} +(-10.2606 - 10.2606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65980 + 1.65980i −1.17366 + 1.17366i −0.192324 + 0.981332i \(0.561602\pi\)
−0.981332 + 0.192324i \(0.938398\pi\)
\(3\) 2.39046 1.38013i 1.38013 0.796818i 0.387956 0.921678i \(-0.373181\pi\)
0.992174 + 0.124860i \(0.0398481\pi\)
\(4\) 3.50987i 1.75493i
\(5\) 0.412430 1.53921i 0.184444 0.688355i −0.810305 0.586009i \(-0.800698\pi\)
0.994749 0.102346i \(-0.0326350\pi\)
\(6\) −1.67694 + 6.25841i −0.684607 + 2.55499i
\(7\) 0 0
\(8\) 2.50608 + 2.50608i 0.886032 + 0.886032i
\(9\) 2.30952 4.00020i 0.769839 1.33340i
\(10\) 1.87023 + 3.23933i 0.591418 + 1.02437i
\(11\) 0.813080 3.03446i 0.245153 0.914923i −0.728154 0.685414i \(-0.759621\pi\)
0.973306 0.229509i \(-0.0737121\pi\)
\(12\) −4.84407 8.39018i −1.39836 2.42204i
\(13\) −1.04831 3.44979i −0.290748 0.956800i
\(14\) 0 0
\(15\) −1.13841 4.24862i −0.293937 1.09699i
\(16\) −1.29944 −0.324859
\(17\) −0.641590 −0.155608 −0.0778042 0.996969i \(-0.524791\pi\)
−0.0778042 + 0.996969i \(0.524791\pi\)
\(18\) 2.80620 + 10.4729i 0.661427 + 2.46848i
\(19\) −7.61472 + 2.04036i −1.74694 + 0.468090i −0.983968 0.178346i \(-0.942925\pi\)
−0.762968 + 0.646436i \(0.776259\pi\)
\(20\) −5.40242 1.44757i −1.20802 0.323687i
\(21\) 0 0
\(22\) 3.68704 + 6.38614i 0.786080 + 1.36153i
\(23\) 0.146149i 0.0304741i 0.999884 + 0.0152371i \(0.00485029\pi\)
−0.999884 + 0.0152371i \(0.995150\pi\)
\(24\) 9.44938 + 2.53195i 1.92885 + 0.516833i
\(25\) 2.13106 + 1.23037i 0.426212 + 0.246074i
\(26\) 7.46594 + 3.98598i 1.46419 + 0.781715i
\(27\) 4.46896i 0.860051i
\(28\) 0 0
\(29\) 1.49412 2.58790i 0.277452 0.480561i −0.693299 0.720650i \(-0.743843\pi\)
0.970751 + 0.240089i \(0.0771768\pi\)
\(30\) 8.94139 + 5.16231i 1.63247 + 0.942505i
\(31\) −6.46586 + 1.73252i −1.16130 + 0.311170i −0.787486 0.616333i \(-0.788618\pi\)
−0.373817 + 0.927503i \(0.621951\pi\)
\(32\) −2.85535 + 2.85535i −0.504760 + 0.504760i
\(33\) −2.24431 8.37589i −0.390685 1.45806i
\(34\) 1.06491 1.06491i 0.182631 0.182631i
\(35\) 0 0
\(36\) −14.0402 8.10610i −2.34003 1.35102i
\(37\) −2.75050 2.75050i −0.452179 0.452179i 0.443898 0.896077i \(-0.353595\pi\)
−0.896077 + 0.443898i \(0.853595\pi\)
\(38\) 9.25232 16.0255i 1.50092 2.59968i
\(39\) −7.26709 6.79977i −1.16367 1.08883i
\(40\) 4.89096 2.82380i 0.773328 0.446481i
\(41\) 5.60356 1.50147i 0.875129 0.234490i 0.206825 0.978378i \(-0.433687\pi\)
0.668305 + 0.743888i \(0.267020\pi\)
\(42\) 0 0
\(43\) 2.42713 1.40130i 0.370133 0.213697i −0.303383 0.952869i \(-0.598116\pi\)
0.673517 + 0.739172i \(0.264783\pi\)
\(44\) −10.6505 2.85380i −1.60563 0.430227i
\(45\) −5.20463 5.20463i −0.775861 0.775861i
\(46\) −0.242578 0.242578i −0.0357661 0.0357661i
\(47\) 3.04537 + 0.816005i 0.444213 + 0.119027i 0.473990 0.880530i \(-0.342813\pi\)
−0.0297773 + 0.999557i \(0.509480\pi\)
\(48\) −3.10624 + 1.79339i −0.448348 + 0.258854i
\(49\) 0 0
\(50\) −5.57930 + 1.49497i −0.789032 + 0.211420i
\(51\) −1.53369 + 0.885477i −0.214760 + 0.123992i
\(52\) −12.1083 + 3.67942i −1.67912 + 0.510243i
\(53\) 3.66059 6.34033i 0.502821 0.870912i −0.497173 0.867651i \(-0.665629\pi\)
0.999995 0.00326078i \(-0.00103794\pi\)
\(54\) 7.41757 + 7.41757i 1.00940 + 1.00940i
\(55\) −4.33533 2.50300i −0.584575 0.337505i
\(56\) 0 0
\(57\) −15.3867 + 15.3867i −2.03802 + 2.03802i
\(58\) 1.81545 + 6.77534i 0.238380 + 0.889646i
\(59\) 2.93283 2.93283i 0.381821 0.381821i −0.489937 0.871758i \(-0.662980\pi\)
0.871758 + 0.489937i \(0.162980\pi\)
\(60\) −14.9121 + 3.99568i −1.92514 + 0.515840i
\(61\) 3.90292 + 2.25335i 0.499718 + 0.288512i 0.728597 0.684942i \(-0.240173\pi\)
−0.228879 + 0.973455i \(0.573506\pi\)
\(62\) 7.85639 13.6077i 0.997763 1.72818i
\(63\) 0 0
\(64\) 12.0775i 1.50969i
\(65\) −5.74230 + 0.190767i −0.712245 + 0.0236617i
\(66\) 17.6274 + 10.1772i 2.16978 + 1.25273i
\(67\) 1.36775 + 0.366486i 0.167097 + 0.0447734i 0.341397 0.939919i \(-0.389100\pi\)
−0.174301 + 0.984692i \(0.555766\pi\)
\(68\) 2.25190i 0.273082i
\(69\) 0.201704 + 0.349362i 0.0242823 + 0.0420582i
\(70\) 0 0
\(71\) 13.8300 + 3.70574i 1.64132 + 0.439791i 0.957165 0.289544i \(-0.0935038\pi\)
0.684157 + 0.729335i \(0.260170\pi\)
\(72\) 15.8126 4.23699i 1.86354 0.499334i
\(73\) 1.82677 + 6.81760i 0.213807 + 0.797940i 0.986583 + 0.163261i \(0.0522011\pi\)
−0.772776 + 0.634679i \(0.781132\pi\)
\(74\) 9.13055 1.06140
\(75\) 6.79227 0.784304
\(76\) 7.16138 + 26.7267i 0.821467 + 3.06576i
\(77\) 0 0
\(78\) 23.3482 0.775656i 2.64366 0.0878258i
\(79\) 0.316458 + 0.548121i 0.0356043 + 0.0616685i 0.883278 0.468849i \(-0.155331\pi\)
−0.847674 + 0.530517i \(0.821998\pi\)
\(80\) −0.535926 + 2.00010i −0.0599184 + 0.223618i
\(81\) 0.760810 + 1.31776i 0.0845344 + 0.146418i
\(82\) −6.80865 + 11.7929i −0.751890 + 1.30231i
\(83\) 1.07813 + 1.07813i 0.118340 + 0.118340i 0.763797 0.645457i \(-0.223333\pi\)
−0.645457 + 0.763797i \(0.723333\pi\)
\(84\) 0 0
\(85\) −0.264611 + 0.987541i −0.0287011 + 0.107114i
\(86\) −1.70266 + 6.35443i −0.183603 + 0.685215i
\(87\) 8.24834i 0.884315i
\(88\) 9.64223 5.56694i 1.02786 0.593438i
\(89\) 9.60471 9.60471i 1.01810 1.01810i 0.0182641 0.999833i \(-0.494186\pi\)
0.999833 0.0182641i \(-0.00581396\pi\)
\(90\) 17.2773 1.82119
\(91\) 0 0
\(92\) 0.512963 0.0534801
\(93\) −13.0652 + 13.0652i −1.35480 + 1.35480i
\(94\) −6.40911 + 3.70030i −0.661049 + 0.381657i
\(95\) 12.5621i 1.28885i
\(96\) −2.88483 + 10.7663i −0.294432 + 1.09884i
\(97\) 0.0487160 0.181811i 0.00494637 0.0184601i −0.963409 0.268037i \(-0.913625\pi\)
0.968355 + 0.249577i \(0.0802916\pi\)
\(98\) 0 0
\(99\) −10.2606 10.2606i −1.03123 1.03123i
\(100\) 4.31843 7.47974i 0.431843 0.747974i
\(101\) −0.596904 1.03387i −0.0593942 0.102874i 0.834799 0.550554i \(-0.185584\pi\)
−0.894194 + 0.447680i \(0.852250\pi\)
\(102\) 1.07591 4.01534i 0.106531 0.397577i
\(103\) −2.39792 4.15331i −0.236274 0.409238i 0.723368 0.690462i \(-0.242593\pi\)
−0.959642 + 0.281224i \(0.909260\pi\)
\(104\) 6.01830 11.2726i 0.590143 1.10537i
\(105\) 0 0
\(106\) 4.44783 + 16.5995i 0.432012 + 1.61229i
\(107\) 15.2964 1.47876 0.739378 0.673290i \(-0.235120\pi\)
0.739378 + 0.673290i \(0.235120\pi\)
\(108\) −15.6855 −1.50933
\(109\) 3.33967 + 12.4638i 0.319883 + 1.19382i 0.919357 + 0.393424i \(0.128710\pi\)
−0.599475 + 0.800394i \(0.704624\pi\)
\(110\) 11.3503 3.04129i 1.08220 0.289976i
\(111\) −10.3710 2.77890i −0.984370 0.263761i
\(112\) 0 0
\(113\) −0.770731 1.33494i −0.0725042 0.125581i 0.827494 0.561475i \(-0.189766\pi\)
−0.899998 + 0.435894i \(0.856432\pi\)
\(114\) 51.0776i 4.78386i
\(115\) 0.224953 + 0.0602761i 0.0209770 + 0.00562078i
\(116\) −9.08318 5.24418i −0.843352 0.486910i
\(117\) −16.2209 3.77391i −1.49963 0.348898i
\(118\) 9.73580i 0.896253i
\(119\) 0 0
\(120\) 7.79441 13.5003i 0.711529 1.23240i
\(121\) 0.979449 + 0.565485i 0.0890408 + 0.0514077i
\(122\) −10.2182 + 2.73796i −0.925111 + 0.247883i
\(123\) 11.3228 11.3228i 1.02095 1.02095i
\(124\) 6.08092 + 22.6943i 0.546083 + 2.03801i
\(125\) 8.40660 8.40660i 0.751910 0.751910i
\(126\) 0 0
\(127\) 2.81842 + 1.62722i 0.250095 + 0.144392i 0.619808 0.784754i \(-0.287211\pi\)
−0.369713 + 0.929146i \(0.620544\pi\)
\(128\) 14.3355 + 14.3355i 1.26709 + 1.26709i
\(129\) 3.86796 6.69950i 0.340555 0.589858i
\(130\) 9.21443 9.84770i 0.808159 0.863701i
\(131\) −14.2615 + 8.23390i −1.24604 + 0.719400i −0.970317 0.241838i \(-0.922250\pi\)
−0.275720 + 0.961238i \(0.588916\pi\)
\(132\) −29.3983 + 7.87724i −2.55879 + 0.685626i
\(133\) 0 0
\(134\) −2.87848 + 1.66189i −0.248663 + 0.143565i
\(135\) −6.87866 1.84313i −0.592021 0.158632i
\(136\) −1.60787 1.60787i −0.137874 0.137874i
\(137\) −0.267239 0.267239i −0.0228318 0.0228318i 0.695599 0.718431i \(-0.255139\pi\)
−0.718431 + 0.695599i \(0.755139\pi\)
\(138\) −0.914659 0.245082i −0.0778610 0.0208628i
\(139\) −8.52132 + 4.91978i −0.722769 + 0.417291i −0.815771 0.578375i \(-0.803687\pi\)
0.0930022 + 0.995666i \(0.470354\pi\)
\(140\) 0 0
\(141\) 8.40602 2.25239i 0.707914 0.189685i
\(142\) −29.1058 + 16.8043i −2.44251 + 1.41018i
\(143\) −11.3206 + 0.376085i −0.946676 + 0.0314498i
\(144\) −3.00107 + 5.19801i −0.250089 + 0.433167i
\(145\) −3.36710 3.36710i −0.279622 0.279622i
\(146\) −14.3479 8.28378i −1.18744 0.685570i
\(147\) 0 0
\(148\) −9.65388 + 9.65388i −0.793544 + 0.793544i
\(149\) 1.43738 + 5.36436i 0.117754 + 0.439465i 0.999478 0.0323006i \(-0.0102834\pi\)
−0.881724 + 0.471766i \(0.843617\pi\)
\(150\) −11.2738 + 11.2738i −0.920503 + 0.920503i
\(151\) −4.58330 + 1.22809i −0.372983 + 0.0999406i −0.440441 0.897782i \(-0.645178\pi\)
0.0674576 + 0.997722i \(0.478511\pi\)
\(152\) −24.1964 13.9698i −1.96258 1.13310i
\(153\) −1.48176 + 2.56649i −0.119793 + 0.207488i
\(154\) 0 0
\(155\) 10.6669i 0.856782i
\(156\) −23.8663 + 25.5065i −1.91083 + 2.04216i
\(157\) −10.9293 6.31006i −0.872257 0.503598i −0.00415919 0.999991i \(-0.501324\pi\)
−0.868098 + 0.496394i \(0.834657\pi\)
\(158\) −1.43503 0.384515i −0.114165 0.0305904i
\(159\) 20.2084i 1.60263i
\(160\) 3.21735 + 5.57262i 0.254354 + 0.440554i
\(161\) 0 0
\(162\) −3.45001 0.924428i −0.271058 0.0726299i
\(163\) 12.6085 3.37843i 0.987571 0.264619i 0.271341 0.962483i \(-0.412533\pi\)
0.716230 + 0.697864i \(0.245866\pi\)
\(164\) −5.26996 19.6678i −0.411515 1.53579i
\(165\) −13.8179 −1.07572
\(166\) −3.57897 −0.277782
\(167\) −4.79697 17.9025i −0.371201 1.38534i −0.858817 0.512282i \(-0.828800\pi\)
0.487616 0.873058i \(-0.337867\pi\)
\(168\) 0 0
\(169\) −10.8021 + 7.23288i −0.830931 + 0.556375i
\(170\) −1.19992 2.07832i −0.0920296 0.159400i
\(171\) −9.42448 + 35.1726i −0.720708 + 2.68972i
\(172\) −4.91839 8.51890i −0.375024 0.649560i
\(173\) −2.79684 + 4.84427i −0.212640 + 0.368303i −0.952540 0.304414i \(-0.901540\pi\)
0.739900 + 0.672717i \(0.234873\pi\)
\(174\) 13.6906 + 13.6906i 1.03788 + 1.03788i
\(175\) 0 0
\(176\) −1.05655 + 3.94308i −0.0796402 + 0.297221i
\(177\) 2.96311 11.0585i 0.222721 0.831205i
\(178\) 31.8838i 2.38979i
\(179\) −8.21928 + 4.74540i −0.614338 + 0.354688i −0.774661 0.632377i \(-0.782080\pi\)
0.160324 + 0.987065i \(0.448746\pi\)
\(180\) −18.2676 + 18.2676i −1.36158 + 1.36158i
\(181\) 6.91516 0.514000 0.257000 0.966411i \(-0.417266\pi\)
0.257000 + 0.966411i \(0.417266\pi\)
\(182\) 0 0
\(183\) 12.4397 0.919568
\(184\) −0.366260 + 0.366260i −0.0270011 + 0.0270011i
\(185\) −5.36798 + 3.09920i −0.394662 + 0.227858i
\(186\) 43.3714i 3.18014i
\(187\) −0.521664 + 1.94688i −0.0381479 + 0.142370i
\(188\) 2.86407 10.6889i 0.208884 0.779565i
\(189\) 0 0
\(190\) −20.8506 20.8506i −1.51266 1.51266i
\(191\) 1.25251 2.16942i 0.0906287 0.156974i −0.817147 0.576429i \(-0.804446\pi\)
0.907776 + 0.419456i \(0.137779\pi\)
\(192\) −16.6685 28.8707i −1.20295 2.08356i
\(193\) −5.83813 + 21.7882i −0.420238 + 1.56835i 0.353870 + 0.935295i \(0.384866\pi\)
−0.774108 + 0.633054i \(0.781801\pi\)
\(194\) 0.220911 + 0.382628i 0.0158605 + 0.0274711i
\(195\) −13.4634 + 8.38114i −0.964136 + 0.600186i
\(196\) 0 0
\(197\) −4.63560 17.3003i −0.330273 1.23259i −0.908904 0.417005i \(-0.863080\pi\)
0.578631 0.815589i \(-0.303587\pi\)
\(198\) 34.0611 2.42062
\(199\) 16.4123 1.16344 0.581720 0.813389i \(-0.302380\pi\)
0.581720 + 0.813389i \(0.302380\pi\)
\(200\) 2.25720 + 8.42400i 0.159608 + 0.595667i
\(201\) 3.77533 1.01160i 0.266291 0.0713526i
\(202\) 2.70675 + 0.725273i 0.190447 + 0.0510300i
\(203\) 0 0
\(204\) 3.10791 + 5.38306i 0.217597 + 0.376889i
\(205\) 9.24430i 0.645650i
\(206\) 10.8737 + 2.91361i 0.757609 + 0.203001i
\(207\) 0.584624 + 0.337533i 0.0406342 + 0.0234602i
\(208\) 1.36221 + 4.48278i 0.0944521 + 0.310825i
\(209\) 24.7655i 1.71307i
\(210\) 0 0
\(211\) 4.93176 8.54207i 0.339517 0.588060i −0.644825 0.764330i \(-0.723070\pi\)
0.984342 + 0.176270i \(0.0564032\pi\)
\(212\) −22.2537 12.8482i −1.52839 0.882418i
\(213\) 38.1744 10.2288i 2.61567 0.700867i
\(214\) −25.3889 + 25.3889i −1.73555 + 1.73555i
\(215\) −1.15588 4.31380i −0.0788302 0.294198i
\(216\) 11.1996 11.1996i 0.762033 0.762033i
\(217\) 0 0
\(218\) −26.2306 15.1443i −1.77656 1.02570i
\(219\) 13.7760 + 13.7760i 0.930895 + 0.930895i
\(220\) −8.78520 + 15.2164i −0.592298 + 1.02589i
\(221\) 0.672583 + 2.21335i 0.0452428 + 0.148886i
\(222\) 21.8262 12.6013i 1.46488 0.845747i
\(223\) −8.41926 + 2.25594i −0.563796 + 0.151069i −0.529450 0.848341i \(-0.677602\pi\)
−0.0343461 + 0.999410i \(0.510935\pi\)
\(224\) 0 0
\(225\) 9.84344 5.68312i 0.656230 0.378874i
\(226\) 3.49500 + 0.936482i 0.232484 + 0.0622939i
\(227\) 11.9452 + 11.9452i 0.792834 + 0.792834i 0.981954 0.189120i \(-0.0605636\pi\)
−0.189120 + 0.981954i \(0.560564\pi\)
\(228\) 54.0052 + 54.0052i 3.57658 + 3.57658i
\(229\) −2.36198 0.632892i −0.156084 0.0418227i 0.179931 0.983679i \(-0.442413\pi\)
−0.336015 + 0.941857i \(0.609079\pi\)
\(230\) −0.473424 + 0.273331i −0.0312166 + 0.0180229i
\(231\) 0 0
\(232\) 10.2299 2.74108i 0.671624 0.179961i
\(233\) 4.65474 2.68741i 0.304942 0.176058i −0.339719 0.940527i \(-0.610332\pi\)
0.644661 + 0.764469i \(0.276999\pi\)
\(234\) 33.1874 20.6596i 2.16953 1.35056i
\(235\) 2.51200 4.35092i 0.163865 0.283823i
\(236\) −10.2938 10.2938i −0.670071 0.670071i
\(237\) 1.51296 + 0.873507i 0.0982772 + 0.0567404i
\(238\) 0 0
\(239\) −11.9572 + 11.9572i −0.773448 + 0.773448i −0.978708 0.205260i \(-0.934196\pi\)
0.205260 + 0.978708i \(0.434196\pi\)
\(240\) 1.47930 + 5.52081i 0.0954882 + 0.356367i
\(241\) −9.50881 + 9.50881i −0.612516 + 0.612516i −0.943601 0.331085i \(-0.892585\pi\)
0.331085 + 0.943601i \(0.392585\pi\)
\(242\) −2.56428 + 0.687097i −0.164838 + 0.0441682i
\(243\) 15.2481 + 8.80347i 0.978163 + 0.564743i
\(244\) 7.90898 13.6987i 0.506320 0.876972i
\(245\) 0 0
\(246\) 37.5873i 2.39648i
\(247\) 15.0214 + 24.1303i 0.955786 + 1.53537i
\(248\) −20.5458 11.8621i −1.30466 0.753245i
\(249\) 4.06519 + 1.08926i 0.257621 + 0.0690293i
\(250\) 27.9066i 1.76497i
\(251\) 6.40248 + 11.0894i 0.404121 + 0.699958i 0.994219 0.107374i \(-0.0342441\pi\)
−0.590098 + 0.807332i \(0.700911\pi\)
\(252\) 0 0
\(253\) 0.443482 + 0.118831i 0.0278815 + 0.00747082i
\(254\) −7.37887 + 1.97716i −0.462992 + 0.124058i
\(255\) 0.730395 + 2.72587i 0.0457391 + 0.170701i
\(256\) −23.4332 −1.46457
\(257\) −10.3807 −0.647532 −0.323766 0.946137i \(-0.604949\pi\)
−0.323766 + 0.946137i \(0.604949\pi\)
\(258\) 4.69979 + 17.5399i 0.292596 + 1.09198i
\(259\) 0 0
\(260\) 0.669566 + 20.1547i 0.0415247 + 1.24994i
\(261\) −6.90141 11.9536i −0.427187 0.739909i
\(262\) 10.0047 37.3379i 0.618090 2.30674i
\(263\) 2.18977 + 3.79279i 0.135027 + 0.233873i 0.925608 0.378484i \(-0.123555\pi\)
−0.790581 + 0.612358i \(0.790221\pi\)
\(264\) 15.3662 26.6151i 0.945725 1.63804i
\(265\) −8.24936 8.24936i −0.506754 0.506754i
\(266\) 0 0
\(267\) 9.70388 36.2154i 0.593868 2.21635i
\(268\) 1.28632 4.80061i 0.0785744 0.293244i
\(269\) 11.6847i 0.712427i −0.934405 0.356213i \(-0.884068\pi\)
0.934405 0.356213i \(-0.115932\pi\)
\(270\) 14.4764 8.35797i 0.881007 0.508650i
\(271\) 21.7031 21.7031i 1.31837 1.31837i 0.403303 0.915066i \(-0.367862\pi\)
0.915066 0.403303i \(-0.132138\pi\)
\(272\) 0.833705 0.0505508
\(273\) 0 0
\(274\) 0.887127 0.0535933
\(275\) 5.46622 5.46622i 0.329626 0.329626i
\(276\) 1.22621 0.707955i 0.0738094 0.0426139i
\(277\) 19.0652i 1.14552i −0.819724 0.572758i \(-0.805873\pi\)
0.819724 0.572758i \(-0.194127\pi\)
\(278\) 5.97782 22.3095i 0.358526 1.33804i
\(279\) −8.00258 + 29.8660i −0.479102 + 1.78803i
\(280\) 0 0
\(281\) 11.8671 + 11.8671i 0.707931 + 0.707931i 0.966100 0.258169i \(-0.0831190\pi\)
−0.258169 + 0.966100i \(0.583119\pi\)
\(282\) −10.2138 + 17.6908i −0.608223 + 1.05347i
\(283\) 4.21864 + 7.30690i 0.250772 + 0.434350i 0.963739 0.266848i \(-0.0859821\pi\)
−0.712966 + 0.701198i \(0.752649\pi\)
\(284\) 13.0067 48.5415i 0.771804 2.88041i
\(285\) 17.3374 + 30.0292i 1.02698 + 1.77878i
\(286\) 18.1657 19.4141i 1.07416 1.14798i
\(287\) 0 0
\(288\) 4.82750 + 18.0165i 0.284463 + 1.06163i
\(289\) −16.5884 −0.975786
\(290\) 11.1774 0.656360
\(291\) −0.134469 0.501845i −0.00788271 0.0294187i
\(292\) 23.9289 6.41172i 1.40033 0.375218i
\(293\) −8.00676 2.14541i −0.467760 0.125336i 0.0172376 0.999851i \(-0.494513\pi\)
−0.484998 + 0.874516i \(0.661180\pi\)
\(294\) 0 0
\(295\) −3.30465 5.72382i −0.192404 0.333253i
\(296\) 13.7859i 0.801290i
\(297\) −13.5609 3.63362i −0.786881 0.210844i
\(298\) −11.2895 6.51800i −0.653984 0.377578i
\(299\) 0.504183 0.153209i 0.0291576 0.00886029i
\(300\) 23.8400i 1.37640i
\(301\) 0 0
\(302\) 5.56897 9.64574i 0.320458 0.555050i
\(303\) −2.85375 1.64761i −0.163943 0.0946528i
\(304\) 9.89484 2.65131i 0.567508 0.152063i
\(305\) 5.07807 5.07807i 0.290769 0.290769i
\(306\) −1.80043 6.71929i −0.102924 0.384116i
\(307\) −17.3438 + 17.3438i −0.989863 + 0.989863i −0.999949 0.0100865i \(-0.996789\pi\)
0.0100865 + 0.999949i \(0.496789\pi\)
\(308\) 0 0
\(309\) −11.4642 6.61887i −0.652177 0.376535i
\(310\) −17.7048 17.7048i −1.00557 1.00557i
\(311\) −11.8560 + 20.5353i −0.672294 + 1.16445i 0.304958 + 0.952366i \(0.401358\pi\)
−0.977252 + 0.212082i \(0.931976\pi\)
\(312\) −1.17114 35.2526i −0.0663026 1.99579i
\(313\) −12.1862 + 7.03573i −0.688808 + 0.397683i −0.803165 0.595756i \(-0.796852\pi\)
0.114358 + 0.993440i \(0.463519\pi\)
\(314\) 28.6140 7.66709i 1.61478 0.432679i
\(315\) 0 0
\(316\) 1.92383 1.11073i 0.108224 0.0624832i
\(317\) −16.1695 4.33262i −0.908172 0.243344i −0.225649 0.974209i \(-0.572450\pi\)
−0.682522 + 0.730865i \(0.739117\pi\)
\(318\) 33.5419 + 33.5419i 1.88093 + 1.88093i
\(319\) −6.63803 6.63803i −0.371658 0.371658i
\(320\) −18.5898 4.98112i −1.03920 0.278453i
\(321\) 36.5653 21.1110i 2.04088 1.17830i
\(322\) 0 0
\(323\) 4.88553 1.30907i 0.271838 0.0728388i
\(324\) 4.62517 2.67034i 0.256954 0.148352i
\(325\) 2.01051 8.64152i 0.111523 0.479345i
\(326\) −15.3200 + 26.5350i −0.848497 + 1.46964i
\(327\) 25.1850 + 25.1850i 1.39274 + 1.39274i
\(328\) 17.8058 + 10.2802i 0.983159 + 0.567627i
\(329\) 0 0
\(330\) 22.9349 22.9349i 1.26252 1.26252i
\(331\) −2.50489 9.34837i −0.137681 0.513833i −0.999972 0.00742049i \(-0.997638\pi\)
0.862291 0.506413i \(-0.169029\pi\)
\(332\) 3.78410 3.78410i 0.207680 0.207680i
\(333\) −17.3549 + 4.65022i −0.951041 + 0.254831i
\(334\) 37.6766 + 21.7526i 2.06157 + 1.19025i
\(335\) 1.12820 1.95410i 0.0616401 0.106764i
\(336\) 0 0
\(337\) 20.0838i 1.09403i 0.837122 + 0.547016i \(0.184236\pi\)
−0.837122 + 0.547016i \(0.815764\pi\)
\(338\) 5.92421 29.9345i 0.322234 1.62822i
\(339\) −3.68479 2.12742i −0.200131 0.115545i
\(340\) 3.46614 + 0.928749i 0.187978 + 0.0503685i
\(341\) 21.0291i 1.13879i
\(342\) −42.7368 74.0223i −2.31094 4.00267i
\(343\) 0 0
\(344\) 9.59434 + 2.57080i 0.517292 + 0.138608i
\(345\) 0.620930 0.166378i 0.0334298 0.00895748i
\(346\) −3.39833 12.6827i −0.182695 0.681827i
\(347\) −22.2015 −1.19184 −0.595920 0.803044i \(-0.703212\pi\)
−0.595920 + 0.803044i \(0.703212\pi\)
\(348\) −28.9506 −1.55191
\(349\) −1.38593 5.17235i −0.0741869 0.276869i 0.918861 0.394582i \(-0.129111\pi\)
−0.993048 + 0.117713i \(0.962444\pi\)
\(350\) 0 0
\(351\) −15.4170 + 4.68484i −0.822897 + 0.250058i
\(352\) 6.34281 + 10.9861i 0.338073 + 0.585560i
\(353\) 6.75514 25.2105i 0.359540 1.34182i −0.515134 0.857110i \(-0.672258\pi\)
0.874674 0.484712i \(-0.161075\pi\)
\(354\) 13.4367 + 23.2730i 0.714151 + 1.23695i
\(355\) 11.4078 19.7589i 0.605465 1.04870i
\(356\) −33.7113 33.7113i −1.78669 1.78669i
\(357\) 0 0
\(358\) 5.76594 21.5188i 0.304739 1.13730i
\(359\) −5.86066 + 21.8723i −0.309314 + 1.15437i 0.619854 + 0.784717i \(0.287192\pi\)
−0.929168 + 0.369658i \(0.879475\pi\)
\(360\) 26.0864i 1.37488i
\(361\) 37.3664 21.5735i 1.96665 1.13545i
\(362\) −11.4778 + 11.4778i −0.603258 + 0.603258i
\(363\) 3.12177 0.163850
\(364\) 0 0
\(365\) 11.2471 0.588702
\(366\) −20.6474 + 20.6474i −1.07926 + 1.07926i
\(367\) −12.2942 + 7.09806i −0.641752 + 0.370516i −0.785289 0.619129i \(-0.787486\pi\)
0.143537 + 0.989645i \(0.454152\pi\)
\(368\) 0.189911i 0.00989980i
\(369\) 6.93534 25.8831i 0.361040 1.34742i
\(370\) 3.76571 14.0538i 0.195770 0.730624i
\(371\) 0 0
\(372\) 45.8573 + 45.8573i 2.37759 + 2.37759i
\(373\) −1.75321 + 3.03665i −0.0907778 + 0.157232i −0.907839 0.419320i \(-0.862269\pi\)
0.817061 + 0.576551i \(0.195602\pi\)
\(374\) −2.36557 4.09728i −0.122321 0.211865i
\(375\) 8.49340 31.6978i 0.438598 1.63687i
\(376\) 5.58697 + 9.67691i 0.288126 + 0.499048i
\(377\) −10.4940 2.44150i −0.540469 0.125744i
\(378\) 0 0
\(379\) 6.94797 + 25.9302i 0.356893 + 1.33194i 0.878085 + 0.478504i \(0.158821\pi\)
−0.521192 + 0.853439i \(0.674513\pi\)
\(380\) 44.0915 2.26184
\(381\) 8.98309 0.460217
\(382\) 1.52188 + 5.67972i 0.0778660 + 0.290600i
\(383\) −32.9891 + 8.83941i −1.68567 + 0.451673i −0.969266 0.246017i \(-0.920878\pi\)
−0.716400 + 0.697690i \(0.754211\pi\)
\(384\) 54.0533 + 14.4835i 2.75839 + 0.739110i
\(385\) 0 0
\(386\) −26.4739 45.8542i −1.34749 2.33392i
\(387\) 12.9453i 0.658048i
\(388\) −0.638132 0.170987i −0.0323962 0.00868054i
\(389\) 23.7849 + 13.7322i 1.20594 + 0.696251i 0.961870 0.273506i \(-0.0881834\pi\)
0.244072 + 0.969757i \(0.421517\pi\)
\(390\) 8.43558 36.2576i 0.427152 1.83598i
\(391\) 0.0937676i 0.00474203i
\(392\) 0 0
\(393\) −22.7277 + 39.3656i −1.14646 + 1.98573i
\(394\) 36.4092 + 21.0208i 1.83427 + 1.05901i
\(395\) 0.974190 0.261034i 0.0490168 0.0131340i
\(396\) −36.0134 + 36.0134i −1.80974 + 1.80974i
\(397\) −9.59343 35.8032i −0.481480 1.79691i −0.595412 0.803420i \(-0.703011\pi\)
0.113932 0.993489i \(-0.463655\pi\)
\(398\) −27.2412 + 27.2412i −1.36548 + 1.36548i
\(399\) 0 0
\(400\) −2.76918 1.59879i −0.138459 0.0799393i
\(401\) 12.2868 + 12.2868i 0.613574 + 0.613574i 0.943876 0.330301i \(-0.107150\pi\)
−0.330301 + 0.943876i \(0.607150\pi\)
\(402\) −4.58725 + 7.94535i −0.228791 + 0.396278i
\(403\) 12.7550 + 20.4896i 0.635374 + 1.02066i
\(404\) −3.62874 + 2.09505i −0.180537 + 0.104233i
\(405\) 2.34209 0.627561i 0.116379 0.0311838i
\(406\) 0 0
\(407\) −10.5826 + 6.10989i −0.524562 + 0.302856i
\(408\) −6.06263 1.62448i −0.300145 0.0804235i
\(409\) 7.97850 + 7.97850i 0.394512 + 0.394512i 0.876292 0.481780i \(-0.160010\pi\)
−0.481780 + 0.876292i \(0.660010\pi\)
\(410\) 15.3437 + 15.3437i 0.757771 + 0.757771i
\(411\) −1.00765 0.269999i −0.0497036 0.0133180i
\(412\) −14.5776 + 8.41637i −0.718186 + 0.414645i
\(413\) 0 0
\(414\) −1.53060 + 0.410122i −0.0752247 + 0.0201564i
\(415\) 2.10413 1.21482i 0.103287 0.0596330i
\(416\) 12.8436 + 6.85708i 0.629712 + 0.336196i
\(417\) −13.5799 + 23.5211i −0.665010 + 1.15183i
\(418\) −41.1058 41.1058i −2.01055 2.01055i
\(419\) 16.1248 + 9.30964i 0.787747 + 0.454806i 0.839169 0.543871i \(-0.183042\pi\)
−0.0514220 + 0.998677i \(0.516375\pi\)
\(420\) 0 0
\(421\) 18.9024 18.9024i 0.921247 0.921247i −0.0758709 0.997118i \(-0.524174\pi\)
0.997118 + 0.0758709i \(0.0241737\pi\)
\(422\) 5.99238 + 22.3639i 0.291704 + 1.08866i
\(423\) 10.2975 10.2975i 0.500683 0.500683i
\(424\) 25.0631 6.71564i 1.21717 0.326140i
\(425\) −1.36727 0.789392i −0.0663222 0.0382911i
\(426\) −46.3841 + 80.3397i −2.24732 + 3.89247i
\(427\) 0 0
\(428\) 53.6883i 2.59512i
\(429\) −26.5423 + 16.5229i −1.28148 + 0.797734i
\(430\) 9.07856 + 5.24151i 0.437807 + 0.252768i
\(431\) 28.5158 + 7.64079i 1.37356 + 0.368044i 0.868777 0.495203i \(-0.164906\pi\)
0.504782 + 0.863247i \(0.331573\pi\)
\(432\) 5.80713i 0.279396i
\(433\) 17.9660 + 31.1180i 0.863390 + 1.49543i 0.868637 + 0.495449i \(0.164996\pi\)
−0.00524758 + 0.999986i \(0.501670\pi\)
\(434\) 0 0
\(435\) −12.6959 3.40186i −0.608723 0.163107i
\(436\) 43.7464 11.7218i 2.09507 0.561373i
\(437\) −0.298196 1.11288i −0.0142646 0.0532363i
\(438\) −45.7308 −2.18510
\(439\) 9.75982 0.465811 0.232906 0.972499i \(-0.425177\pi\)
0.232906 + 0.972499i \(0.425177\pi\)
\(440\) −4.59195 17.1374i −0.218912 0.816992i
\(441\) 0 0
\(442\) −4.79007 2.55737i −0.227840 0.121641i
\(443\) −19.3899 33.5843i −0.921241 1.59564i −0.797497 0.603323i \(-0.793843\pi\)
−0.123744 0.992314i \(-0.539490\pi\)
\(444\) −9.75356 + 36.4008i −0.462884 + 1.72751i
\(445\) −10.8224 18.7449i −0.513030 0.888595i
\(446\) 10.2299 17.7187i 0.484399 0.839004i
\(447\) 10.8395 + 10.8395i 0.512690 + 0.512690i
\(448\) 0 0
\(449\) −2.42216 + 9.03963i −0.114309 + 0.426606i −0.999234 0.0391263i \(-0.987543\pi\)
0.884925 + 0.465733i \(0.154209\pi\)
\(450\) −6.90531 + 25.7710i −0.325520 + 1.21486i
\(451\) 18.2246i 0.858162i
\(452\) −4.68548 + 2.70516i −0.220386 + 0.127240i
\(453\) −9.26124 + 9.26124i −0.435131 + 0.435131i
\(454\) −39.6534 −1.86103
\(455\) 0 0
\(456\) −77.1204 −3.61150
\(457\) 13.5913 13.5913i 0.635775 0.635775i −0.313735 0.949511i \(-0.601580\pi\)
0.949511 + 0.313735i \(0.101580\pi\)
\(458\) 4.97089 2.86995i 0.232275 0.134104i
\(459\) 2.86724i 0.133831i
\(460\) 0.211561 0.789557i 0.00986409 0.0368133i
\(461\) 3.50466 13.0796i 0.163228 0.609175i −0.835031 0.550202i \(-0.814551\pi\)
0.998260 0.0589733i \(-0.0187827\pi\)
\(462\) 0 0
\(463\) −14.6336 14.6336i −0.680081 0.680081i 0.279937 0.960018i \(-0.409686\pi\)
−0.960018 + 0.279937i \(0.909686\pi\)
\(464\) −1.94152 + 3.36281i −0.0901328 + 0.156115i
\(465\) 14.7216 + 25.4986i 0.682700 + 1.18247i
\(466\) −3.26536 + 12.1865i −0.151265 + 0.564529i
\(467\) 15.4866 + 26.8236i 0.716634 + 1.24125i 0.962326 + 0.271899i \(0.0876515\pi\)
−0.245692 + 0.969348i \(0.579015\pi\)
\(468\) −13.2459 + 56.9334i −0.612294 + 2.63175i
\(469\) 0 0
\(470\) 3.05223 + 11.3911i 0.140789 + 0.525431i
\(471\) −34.8348 −1.60510
\(472\) 14.6998 0.676612
\(473\) −2.27874 8.50439i −0.104777 0.391032i
\(474\) −3.96105 + 1.06136i −0.181937 + 0.0487499i
\(475\) −18.7378 5.02078i −0.859750 0.230369i
\(476\) 0 0
\(477\) −16.9084 29.2862i −0.774183 1.34092i
\(478\) 39.6932i 1.81552i
\(479\) 7.09483 + 1.90105i 0.324171 + 0.0868613i 0.417235 0.908799i \(-0.362999\pi\)
−0.0930636 + 0.995660i \(0.529666\pi\)
\(480\) 15.3819 + 8.88072i 0.702083 + 0.405348i
\(481\) −6.60528 + 12.3720i −0.301175 + 0.564115i
\(482\) 31.5654i 1.43777i
\(483\) 0 0
\(484\) 1.98478 3.43773i 0.0902171 0.156261i
\(485\) −0.259753 0.149968i −0.0117948 0.00680971i
\(486\) −39.9207 + 10.6967i −1.81084 + 0.485213i
\(487\) −6.97359 + 6.97359i −0.316004 + 0.316004i −0.847230 0.531226i \(-0.821731\pi\)
0.531226 + 0.847230i \(0.321731\pi\)
\(488\) 4.13395 + 15.4281i 0.187135 + 0.698398i
\(489\) 25.4773 25.4773i 1.15212 1.15212i
\(490\) 0 0
\(491\) 33.1372 + 19.1318i 1.49546 + 0.863404i 0.999986 0.00521946i \(-0.00166141\pi\)
0.495473 + 0.868623i \(0.334995\pi\)
\(492\) −39.7417 39.7417i −1.79169 1.79169i
\(493\) −0.958615 + 1.66037i −0.0431738 + 0.0747793i
\(494\) −64.9838 15.1189i −2.92376 0.680233i
\(495\) −20.0250 + 11.5615i −0.900058 + 0.519649i
\(496\) 8.40197 2.25130i 0.377260 0.101086i
\(497\) 0 0
\(498\) −8.55536 + 4.93944i −0.383375 + 0.221342i
\(499\) −0.00140307 0.000375951i −6.28100e−5 1.68299e-5i 0.258788 0.965934i \(-0.416677\pi\)
−0.258850 + 0.965917i \(0.583344\pi\)
\(500\) −29.5061 29.5061i −1.31955 1.31955i
\(501\) −36.1748 36.1748i −1.61617 1.61617i
\(502\) −29.0331 7.77938i −1.29581 0.347211i
\(503\) −21.6205 + 12.4826i −0.964012 + 0.556573i −0.897406 0.441206i \(-0.854551\pi\)
−0.0666068 + 0.997779i \(0.521217\pi\)
\(504\) 0 0
\(505\) −1.83752 + 0.492362i −0.0817686 + 0.0219098i
\(506\) −0.933326 + 0.538856i −0.0414914 + 0.0239551i
\(507\) −15.8396 + 32.1982i −0.703463 + 1.42997i
\(508\) 5.71132 9.89229i 0.253399 0.438900i
\(509\) −1.85338 1.85338i −0.0821495 0.0821495i 0.664838 0.746988i \(-0.268501\pi\)
−0.746988 + 0.664838i \(0.768501\pi\)
\(510\) −5.73671 3.31209i −0.254026 0.146662i
\(511\) 0 0
\(512\) 10.2233 10.2233i 0.451811 0.451811i
\(513\) 9.11827 + 34.0299i 0.402582 + 1.50245i
\(514\) 17.2299 17.2299i 0.759979 0.759979i
\(515\) −7.38179 + 1.97795i −0.325281 + 0.0871587i
\(516\) −23.5144 13.5760i −1.03516 0.597651i
\(517\) 4.95226 8.57757i 0.217800 0.377241i
\(518\) 0 0
\(519\) 15.4400i 0.677742i
\(520\) −14.8687 13.9126i −0.652037 0.610107i
\(521\) −25.8598 14.9302i −1.13294 0.654102i −0.188266 0.982118i \(-0.560287\pi\)
−0.944672 + 0.328016i \(0.893620\pi\)
\(522\) 31.2955 + 8.38561i 1.36977 + 0.367028i
\(523\) 16.0812i 0.703184i −0.936153 0.351592i \(-0.885640\pi\)
0.936153 0.351592i \(-0.114360\pi\)
\(524\) 28.8999 + 50.0561i 1.26250 + 2.18671i
\(525\) 0 0
\(526\) −9.92985 2.66069i −0.432962 0.116012i
\(527\) 4.14843 1.11157i 0.180708 0.0484207i
\(528\) 2.91634 + 10.8839i 0.126918 + 0.473663i
\(529\) 22.9786 0.999071
\(530\) 27.3846 1.18951
\(531\) −4.95848 18.5053i −0.215180 0.803062i
\(532\) 0 0
\(533\) −11.0540 17.7571i −0.478802 0.769146i
\(534\) 44.0038 + 76.2168i 1.90423 + 3.29822i
\(535\) 6.30868 23.5443i 0.272748 1.01791i
\(536\) 2.50923 + 4.34612i 0.108382 + 0.187724i
\(537\) −13.0985 + 22.6873i −0.565244 + 0.979031i
\(538\) 19.3942 + 19.3942i 0.836143 + 0.836143i
\(539\) 0 0
\(540\) −6.46915 + 24.1432i −0.278388 + 1.03896i
\(541\) 4.55572 17.0022i 0.195866 0.730980i −0.796176 0.605066i \(-0.793147\pi\)
0.992041 0.125915i \(-0.0401865\pi\)
\(542\) 72.0456i 3.09462i
\(543\) 16.5304 9.54381i 0.709386 0.409564i
\(544\) 1.83196 1.83196i 0.0785448 0.0785448i
\(545\) 20.5618 0.880771
\(546\) 0 0
\(547\) −15.8734 −0.678698 −0.339349 0.940661i \(-0.610207\pi\)
−0.339349 + 0.940661i \(0.610207\pi\)
\(548\) −0.937974 + 0.937974i −0.0400683 + 0.0400683i
\(549\) 18.0277 10.4083i 0.769405 0.444216i
\(550\) 18.1457i 0.773734i
\(551\) −6.09709 + 22.7547i −0.259745 + 0.969381i
\(552\) −0.370042 + 1.38101i −0.0157500 + 0.0587799i
\(553\) 0 0
\(554\) 31.6444 + 31.6444i 1.34444 + 1.34444i
\(555\) −8.55461 + 14.8170i −0.363123 + 0.628947i
\(556\) 17.2678 + 29.9087i 0.732318 + 1.26841i
\(557\) 0.655582 2.44666i 0.0277779 0.103668i −0.950645 0.310280i \(-0.899577\pi\)
0.978423 + 0.206612i \(0.0662437\pi\)
\(558\) −36.2889 62.8543i −1.53623 2.66083i
\(559\) −7.37857 6.90409i −0.312080 0.292012i
\(560\) 0 0
\(561\) 1.43993 + 5.37389i 0.0607938 + 0.226886i
\(562\) −39.3940 −1.66173
\(563\) −20.2319 −0.852673 −0.426336 0.904565i \(-0.640196\pi\)
−0.426336 + 0.904565i \(0.640196\pi\)
\(564\) −7.90558 29.5040i −0.332885 1.24234i
\(565\) −2.37263 + 0.635745i −0.0998174 + 0.0267460i
\(566\) −19.1301 5.12589i −0.804098 0.215457i
\(567\) 0 0
\(568\) 25.3722 + 43.9460i 1.06459 + 1.84393i
\(569\) 14.8726i 0.623493i 0.950165 + 0.311747i \(0.100914\pi\)
−0.950165 + 0.311747i \(0.899086\pi\)
\(570\) −78.6191 21.0659i −3.29299 0.882355i
\(571\) −31.9767 18.4617i −1.33818 0.772600i −0.351645 0.936133i \(-0.614378\pi\)
−0.986538 + 0.163533i \(0.947711\pi\)
\(572\) 1.32001 + 39.7338i 0.0551923 + 1.66135i
\(573\) 6.91453i 0.288859i
\(574\) 0 0
\(575\) −0.179817 + 0.311452i −0.00749888 + 0.0129884i
\(576\) −48.3124 27.8932i −2.01302 1.16222i
\(577\) 19.8217 5.31122i 0.825189 0.221109i 0.178575 0.983926i \(-0.442851\pi\)
0.646614 + 0.762817i \(0.276184\pi\)
\(578\) 27.5334 27.5334i 1.14524 1.14524i
\(579\) 16.1148 + 60.1411i 0.669706 + 2.49938i
\(580\) −11.8181 + 11.8181i −0.490718 + 0.490718i
\(581\) 0 0
\(582\) 1.05615 + 0.609771i 0.0437790 + 0.0252758i
\(583\) −16.2631 16.2631i −0.673550 0.673550i
\(584\) −12.5074 + 21.6635i −0.517560 + 0.896441i
\(585\) −12.4988 + 23.4109i −0.516764 + 0.967923i
\(586\) 16.8506 9.72867i 0.696090 0.401888i
\(587\) 19.8321 5.31399i 0.818557 0.219332i 0.174842 0.984597i \(-0.444059\pi\)
0.643715 + 0.765265i \(0.277392\pi\)
\(588\) 0 0
\(589\) 45.7007 26.3853i 1.88307 1.08719i
\(590\) 14.9854 + 4.01534i 0.616941 + 0.165309i
\(591\) −34.9578 34.9578i −1.43797 1.43797i
\(592\) 3.57410 + 3.57410i 0.146894 + 0.146894i
\(593\) 40.1793 + 10.7660i 1.64997 + 0.442107i 0.959603 0.281357i \(-0.0907844\pi\)
0.690362 + 0.723464i \(0.257451\pi\)
\(594\) 28.5394 16.4772i 1.17099 0.676069i
\(595\) 0 0
\(596\) 18.8282 5.04500i 0.771233 0.206651i
\(597\) 39.2330 22.6512i 1.60570 0.927050i
\(598\) −0.582546 + 1.09114i −0.0238221 + 0.0446199i
\(599\) 2.16999 3.75853i 0.0886634 0.153569i −0.818283 0.574816i \(-0.805074\pi\)
0.906946 + 0.421246i \(0.138407\pi\)
\(600\) 17.0220 + 17.0220i 0.694919 + 0.694919i
\(601\) −5.72067 3.30283i −0.233351 0.134725i 0.378766 0.925492i \(-0.376348\pi\)
−0.612117 + 0.790767i \(0.709682\pi\)
\(602\) 0 0
\(603\) 4.62485 4.62485i 0.188339 0.188339i
\(604\) 4.31044 + 16.0868i 0.175389 + 0.654561i
\(605\) 1.27435 1.27435i 0.0518098 0.0518098i
\(606\) 7.47135 2.00194i 0.303503 0.0813233i
\(607\) −39.8777 23.0234i −1.61859 0.934492i −0.987286 0.158954i \(-0.949188\pi\)
−0.631301 0.775538i \(-0.717479\pi\)
\(608\) 15.9168 27.5686i 0.645510 1.11806i
\(609\) 0 0
\(610\) 16.8571i 0.682526i
\(611\) −0.377438 11.3613i −0.0152695 0.459630i
\(612\) 9.00804 + 5.20079i 0.364128 + 0.210230i
\(613\) −27.7207 7.42773i −1.11963 0.300003i −0.348895 0.937162i \(-0.613443\pi\)
−0.770733 + 0.637159i \(0.780110\pi\)
\(614\) 57.5744i 2.32352i
\(615\) −12.7583 22.0981i −0.514466 0.891081i
\(616\) 0 0
\(617\) 0.0947548 + 0.0253895i 0.00381469 + 0.00102214i 0.260726 0.965413i \(-0.416038\pi\)
−0.256911 + 0.966435i \(0.582705\pi\)
\(618\) 30.0143 8.04231i 1.20735 0.323509i
\(619\) 10.9468 + 40.8542i 0.439991 + 1.64207i 0.728834 + 0.684691i \(0.240063\pi\)
−0.288843 + 0.957376i \(0.593271\pi\)
\(620\) 37.4392 1.50360
\(621\) 0.653133 0.0262093
\(622\) −14.4058 53.7630i −0.577619 2.15570i
\(623\) 0 0
\(624\) 9.44312 + 8.83587i 0.378027 + 0.353718i
\(625\) −3.32054 5.75135i −0.132822 0.230054i
\(626\) 8.54882 31.9046i 0.341680 1.27517i
\(627\) 34.1796 + 59.2008i 1.36500 + 2.36425i
\(628\) −22.1475 + 38.3606i −0.883781 + 1.53075i
\(629\) 1.76469 + 1.76469i 0.0703629 + 0.0703629i
\(630\) 0 0
\(631\) 2.02584 7.56053i 0.0806473 0.300980i −0.913807 0.406148i \(-0.866872\pi\)
0.994454 + 0.105169i \(0.0335383\pi\)
\(632\) −0.580566 + 2.16670i −0.0230937 + 0.0861868i
\(633\) 27.2259i 1.08213i
\(634\) 34.0295 19.6469i 1.35148 0.780279i
\(635\) 3.66703 3.66703i 0.145522 0.145522i
\(636\) −70.9288 −2.81251
\(637\) 0 0
\(638\) 22.0356 0.872397
\(639\) 46.7644 46.7644i 1.84997 1.84997i
\(640\) 27.9777 16.1530i 1.10592 0.638502i
\(641\) 33.4026i 1.31932i −0.751563 0.659661i \(-0.770700\pi\)
0.751563 0.659661i \(-0.229300\pi\)
\(642\) −25.6511 + 95.7311i −1.01237 + 3.77820i
\(643\) 4.94009 18.4367i 0.194818 0.727071i −0.797496 0.603324i \(-0.793842\pi\)
0.992314 0.123746i \(-0.0394909\pi\)
\(644\) 0 0
\(645\) −8.71667 8.71667i −0.343219 0.343219i
\(646\) −5.93619 + 10.2818i −0.233556 + 0.404532i
\(647\) −16.4522 28.4961i −0.646804 1.12030i −0.983882 0.178821i \(-0.942772\pi\)
0.337078 0.941477i \(-0.390561\pi\)
\(648\) −1.39576 + 5.20906i −0.0548308 + 0.204631i
\(649\) −6.51491 11.2842i −0.255733 0.442942i
\(650\) 11.0061 + 17.6802i 0.431696 + 0.693475i
\(651\) 0 0
\(652\) −11.8578 44.2541i −0.464389 1.73312i
\(653\) 27.9965 1.09559 0.547793 0.836614i \(-0.315468\pi\)
0.547793 + 0.836614i \(0.315468\pi\)
\(654\) −83.6042 −3.26918
\(655\) 6.79182 + 25.3474i 0.265378 + 0.990405i
\(656\) −7.28147 + 1.95106i −0.284294 + 0.0761763i
\(657\) 31.4907 + 8.43792i 1.22857 + 0.329195i
\(658\) 0 0
\(659\) −5.35203 9.27000i −0.208486 0.361108i 0.742752 0.669567i \(-0.233520\pi\)
−0.951238 + 0.308459i \(0.900187\pi\)
\(660\) 48.4989i 1.88782i
\(661\) 23.2066 + 6.21818i 0.902631 + 0.241859i 0.680146 0.733077i \(-0.261916\pi\)
0.222485 + 0.974936i \(0.428583\pi\)
\(662\) 19.6740 + 11.3588i 0.764653 + 0.441473i
\(663\) 4.66249 + 4.36266i 0.181076 + 0.169432i
\(664\) 5.40377i 0.209707i
\(665\) 0 0
\(666\) 21.0872 36.5240i 0.817111 1.41528i
\(667\) 0.378218 + 0.218364i 0.0146447 + 0.00845510i
\(668\) −62.8356 + 16.8367i −2.43118 + 0.651433i
\(669\) −17.0124 + 17.0124i −0.657737 + 0.657737i
\(670\) 1.37083 + 5.11599i 0.0529596 + 0.197648i
\(671\) 10.0111 10.0111i 0.386474 0.386474i
\(672\) 0 0
\(673\) 4.79792 + 2.77008i 0.184946 + 0.106779i 0.589615 0.807685i \(-0.299280\pi\)
−0.404668 + 0.914464i \(0.632613\pi\)
\(674\) −33.3350 33.3350i −1.28402 1.28402i
\(675\) 5.49846 9.52362i 0.211636 0.366564i
\(676\) 25.3864 + 37.9140i 0.976402 + 1.45823i
\(677\) 38.1640 22.0340i 1.46676 0.846835i 0.467454 0.884018i \(-0.345172\pi\)
0.999309 + 0.0371822i \(0.0118382\pi\)
\(678\) 9.64710 2.58493i 0.370495 0.0992738i
\(679\) 0 0
\(680\) −3.13799 + 1.81172i −0.120336 + 0.0694763i
\(681\) 45.0406 + 12.0686i 1.72596 + 0.462469i
\(682\) −34.9040 34.9040i −1.33654 1.33654i
\(683\) 3.64259 + 3.64259i 0.139380 + 0.139380i 0.773354 0.633974i \(-0.218578\pi\)
−0.633974 + 0.773354i \(0.718578\pi\)
\(684\) 123.451 + 33.0787i 4.72028 + 1.26480i
\(685\) −0.521554 + 0.301120i −0.0199276 + 0.0115052i
\(686\) 0 0
\(687\) −6.51969 + 1.74695i −0.248742 + 0.0666501i
\(688\) −3.15390 + 1.82090i −0.120241 + 0.0694213i
\(689\) −25.7103 5.98167i −0.979483 0.227883i
\(690\) −0.754466 + 1.30677i −0.0287220 + 0.0497480i
\(691\) 2.16091 + 2.16091i 0.0822048 + 0.0822048i 0.747014 0.664809i \(-0.231487\pi\)
−0.664809 + 0.747014i \(0.731487\pi\)
\(692\) 17.0028 + 9.81655i 0.646348 + 0.373169i
\(693\) 0 0
\(694\) 36.8501 36.8501i 1.39881 1.39881i
\(695\) 4.05813 + 15.1452i 0.153934 + 0.574489i
\(696\) 20.6710 20.6710i 0.783532 0.783532i
\(697\) −3.59519 + 0.963328i −0.136177 + 0.0364886i
\(698\) 10.8854 + 6.28470i 0.412019 + 0.237879i
\(699\) 7.41796 12.8483i 0.280573 0.485967i
\(700\) 0 0
\(701\) 11.0158i 0.416061i −0.978122 0.208031i \(-0.933295\pi\)
0.978122 0.208031i \(-0.0667054\pi\)
\(702\) 17.8132 33.3650i 0.672315 1.25928i
\(703\) 26.5563 + 15.3323i 1.00159 + 0.578267i
\(704\) −36.6486 9.81997i −1.38125 0.370104i
\(705\) 13.8676i 0.522283i
\(706\) 30.6322 + 53.0566i 1.15286 + 1.99681i
\(707\) 0 0
\(708\) −38.8138 10.4001i −1.45871 0.390860i
\(709\) −27.2109 + 7.29113i −1.02192 + 0.273824i −0.730604 0.682801i \(-0.760761\pi\)
−0.291321 + 0.956625i \(0.594095\pi\)
\(710\) 13.8612 + 51.7306i 0.520200 + 1.94141i
\(711\) 2.92346 0.109638
\(712\) 48.1403 1.80413
\(713\) −0.253206 0.944977i −0.00948263 0.0353897i
\(714\) 0 0
\(715\) −4.09008 + 17.5799i −0.152960 + 0.657450i
\(716\) 16.6557 + 28.8486i 0.622454 + 1.07812i
\(717\) −12.0807 + 45.0857i −0.451161 + 1.68376i
\(718\) −26.5761 46.0311i −0.991811 1.71787i
\(719\) −21.0559 + 36.4699i −0.785252 + 1.36010i 0.143596 + 0.989636i \(0.454133\pi\)
−0.928848 + 0.370460i \(0.879200\pi\)
\(720\) 6.76309 + 6.76309i 0.252045 + 0.252045i
\(721\) 0 0
\(722\) −26.2130 + 97.8284i −0.975548 + 3.64079i
\(723\) −9.60699 + 35.8538i −0.357288 + 1.33342i
\(724\) 24.2713i 0.902035i
\(725\) 6.36814 3.67665i 0.236507 0.136547i
\(726\) −5.18151 + 5.18151i −0.192304 + 0.192304i
\(727\) −10.0901 −0.374223 −0.187111 0.982339i \(-0.559913\pi\)
−0.187111 + 0.982339i \(0.559913\pi\)
\(728\) 0 0
\(729\) 44.0349 1.63092
\(730\) −18.6680 + 18.6680i −0.690933 + 0.690933i
\(731\) −1.55722 + 0.899062i −0.0575959 + 0.0332530i
\(732\) 43.6617i 1.61378i
\(733\) 6.87790 25.6687i 0.254041 0.948093i −0.714581 0.699553i \(-0.753382\pi\)
0.968622 0.248540i \(-0.0799509\pi\)
\(734\) 8.62455 32.1873i 0.318338 1.18805i
\(735\) 0 0
\(736\) −0.417306 0.417306i −0.0153821 0.0153821i
\(737\) 2.22417 3.85238i 0.0819285 0.141904i
\(738\) 31.4494 + 54.4719i 1.15767 + 2.00514i
\(739\) 6.51146 24.3011i 0.239528 0.893930i −0.736528 0.676407i \(-0.763536\pi\)
0.976055 0.217522i \(-0.0697975\pi\)
\(740\) 10.8778 + 18.8409i 0.399876 + 0.692605i
\(741\) 69.2108 + 36.9509i 2.54252 + 1.35742i
\(742\) 0 0
\(743\) −2.81817 10.5175i −0.103388 0.385851i 0.894769 0.446530i \(-0.147340\pi\)
−0.998157 + 0.0606785i \(0.980674\pi\)
\(744\) −65.4850 −2.40080
\(745\) 8.84969 0.324227
\(746\) −2.13025 7.95021i −0.0779941 0.291078i
\(747\) 6.80271 1.82278i 0.248898 0.0666921i
\(748\) 6.83328 + 1.83097i 0.249850 + 0.0669470i
\(749\) 0 0
\(750\) 38.5147 + 66.7094i 1.40636 + 2.43588i
\(751\) 32.2340i 1.17623i 0.808776 + 0.588117i \(0.200131\pi\)
−0.808776 + 0.588117i \(0.799869\pi\)
\(752\) −3.95727 1.06035i −0.144307 0.0386669i
\(753\) 30.6097 + 17.6725i 1.11548 + 0.644022i
\(754\) 21.4704 13.3655i 0.781904 0.486744i
\(755\) 7.56115i 0.275179i
\(756\) 0 0
\(757\) −16.9609 + 29.3771i −0.616453 + 1.06773i 0.373675 + 0.927560i \(0.378098\pi\)
−0.990128 + 0.140168i \(0.955236\pi\)
\(758\) −54.5711 31.5066i −1.98211 1.14437i
\(759\) 1.22413 0.328004i 0.0444330 0.0119058i
\(760\) −31.4817 + 31.4817i −1.14196 + 1.14196i
\(761\) 2.50812 + 9.36045i 0.0909194 + 0.339316i 0.996369 0.0851375i \(-0.0271329\pi\)
−0.905450 + 0.424453i \(0.860466\pi\)
\(762\) −14.9101 + 14.9101i −0.540137 + 0.540137i
\(763\) 0 0
\(764\) −7.61437 4.39616i −0.275478 0.159047i
\(765\) 3.33924 + 3.33924i 0.120730 + 0.120730i
\(766\) 40.0837 69.4270i 1.44828 2.50850i
\(767\) −13.1921 7.04313i −0.476340 0.254313i
\(768\) −56.0159 + 32.3408i −2.02130 + 1.16700i
\(769\) 14.6001 3.91210i 0.526495 0.141074i 0.0142256 0.999899i \(-0.495472\pi\)
0.512269 + 0.858825i \(0.328805\pi\)
\(770\) 0 0
\(771\) −24.8147 + 14.3268i −0.893678 + 0.515965i
\(772\) 76.4737 + 20.4911i 2.75235 + 0.737490i
\(773\) −27.6552 27.6552i −0.994687 0.994687i 0.00529914 0.999986i \(-0.498313\pi\)
−0.999986 + 0.00529914i \(0.998313\pi\)
\(774\) 21.4867 + 21.4867i 0.772322 + 0.772322i
\(775\) −15.9108 4.26328i −0.571532 0.153142i
\(776\) 0.577718 0.333546i 0.0207389 0.0119736i
\(777\) 0 0
\(778\) −62.2709 + 16.6854i −2.23252 + 0.598202i
\(779\) −39.6060 + 22.8665i −1.41903 + 0.819279i
\(780\) 29.4167 + 47.2549i 1.05329 + 1.69200i
\(781\) 22.4898 38.9535i 0.804750 1.39387i
\(782\) 0.155635 + 0.155635i 0.00556551 + 0.00556551i
\(783\) −11.5652 6.67718i −0.413307 0.238623i
\(784\) 0 0
\(785\) −14.2201 + 14.2201i −0.507537 + 0.507537i
\(786\) −27.6155 103.062i −0.985012 3.67611i
\(787\) 1.23354 1.23354i 0.0439711 0.0439711i −0.684779 0.728750i \(-0.740101\pi\)
0.728750 + 0.684779i \(0.240101\pi\)
\(788\) −60.7217 + 16.2703i −2.16312 + 0.579607i
\(789\) 10.4691 + 6.04433i 0.372709 + 0.215184i
\(790\) −1.18370 + 2.05022i −0.0421141 + 0.0729437i
\(791\) 0 0
\(792\) 51.4278i 1.82741i
\(793\) 3.68214 15.8265i 0.130757 0.562015i
\(794\) 75.3492 + 43.5029i 2.67404 + 1.54386i
\(795\) −31.1049 8.33454i −1.10318 0.295596i
\(796\) 57.6051i 2.04176i
\(797\) −12.2921 21.2905i −0.435407 0.754148i 0.561921 0.827191i \(-0.310062\pi\)
−0.997329 + 0.0730430i \(0.976729\pi\)
\(798\) 0 0
\(799\) −1.95388 0.523540i −0.0691233 0.0185215i
\(800\) −9.59806 + 2.57179i −0.339343 + 0.0909266i
\(801\) −16.2385 60.6030i −0.573760 2.14130i
\(802\) −40.7873 −1.44025
\(803\) 22.1730 0.782469
\(804\) −3.55057 13.2509i −0.125219 0.467324i
\(805\) 0 0
\(806\) −55.1795 12.8379i −1.94362 0.452195i
\(807\) −16.1264 27.9317i −0.567675 0.983241i
\(808\) 1.09507 4.08684i 0.0385243 0.143775i
\(809\) 1.41467 + 2.45029i 0.0497373 + 0.0861475i 0.889822 0.456307i \(-0.150828\pi\)
−0.840085 + 0.542455i \(0.817495\pi\)
\(810\) −2.84577 + 4.92903i −0.0999903 + 0.173188i
\(811\) −6.39483 6.39483i −0.224553 0.224553i 0.585860 0.810412i \(-0.300757\pi\)
−0.810412 + 0.585860i \(0.800757\pi\)
\(812\) 0 0
\(813\) 21.9272 81.8334i 0.769020 2.87002i
\(814\) 7.42387 27.7063i 0.260207 0.971104i
\(815\) 20.8004i 0.728607i
\(816\) 1.99294 1.15062i 0.0697667 0.0402798i
\(817\) −15.6227 + 15.6227i −0.546570 + 0.546570i
\(818\) −26.4854 −0.926041
\(819\) 0 0
\(820\) −32.4463 −1.13307
\(821\) 26.3858 26.3858i 0.920872 0.920872i −0.0762190 0.997091i \(-0.524285\pi\)
0.997091 + 0.0762190i \(0.0242848\pi\)
\(822\) 2.12064 1.22435i 0.0739657 0.0427041i
\(823\) 39.4868i 1.37642i 0.725510 + 0.688212i \(0.241604\pi\)
−0.725510 + 0.688212i \(0.758396\pi\)
\(824\) 4.39916 16.4179i 0.153252 0.571944i
\(825\) 5.52266 20.6109i 0.192274 0.717578i
\(826\) 0 0
\(827\) −24.4804 24.4804i −0.851267 0.851267i 0.139022 0.990289i \(-0.455604\pi\)
−0.990289 + 0.139022i \(0.955604\pi\)
\(828\) 1.18470 2.05195i 0.0411711 0.0713104i
\(829\) −6.73903 11.6723i −0.234056 0.405397i 0.724942 0.688810i \(-0.241867\pi\)
−0.958998 + 0.283413i \(0.908533\pi\)
\(830\) −1.47607 + 5.50878i −0.0512352 + 0.191212i
\(831\) −26.3125 45.5745i −0.912769 1.58096i
\(832\) −41.6648 + 12.6609i −1.44447 + 0.438938i
\(833\) 0 0
\(834\) −16.5003 61.5801i −0.571360 2.13234i
\(835\) −29.5342 −1.02207
\(836\) 86.9237 3.00632
\(837\) 7.74257 + 28.8957i 0.267622 + 0.998780i
\(838\) −42.2160 + 11.3118i −1.45833 + 0.390758i
\(839\) 48.1190 + 12.8935i 1.66125 + 0.445132i 0.962732 0.270457i \(-0.0871749\pi\)
0.698522 + 0.715589i \(0.253842\pi\)
\(840\) 0 0
\(841\) 10.0352 + 17.3815i 0.346041 + 0.599360i
\(842\) 62.7484i 2.16245i
\(843\) 44.7459 + 11.9896i 1.54113 + 0.412944i
\(844\) −29.9815 17.3098i −1.03201 0.595829i
\(845\) 6.67780 + 19.6098i 0.229723 + 0.674596i
\(846\) 34.1836i 1.17526i
\(847\) 0 0
\(848\) −4.75671 + 8.23886i −0.163346 + 0.282924i
\(849\) 20.1690 + 11.6445i 0.692197 + 0.399640i
\(850\) 3.57962 0.959157i 0.122780 0.0328988i
\(851\) 0.401982 0.401982i 0.0137798 0.0137798i
\(852\) −35.9018 133.987i −1.22997 4.59033i
\(853\) −15.4604 + 15.4604i −0.529355 + 0.529355i −0.920380 0.391025i \(-0.872121\pi\)
0.391025 + 0.920380i \(0.372121\pi\)
\(854\) 0 0
\(855\) 50.2511 + 29.0125i 1.71855 + 0.992207i
\(856\) 38.3339 + 38.3339i 1.31023 + 1.31023i
\(857\) −12.5050 + 21.6594i −0.427164 + 0.739869i −0.996620 0.0821525i \(-0.973821\pi\)
0.569456 + 0.822022i \(0.307154\pi\)
\(858\) 16.6302 71.4797i 0.567747 2.44028i
\(859\) 30.9754 17.8837i 1.05687 0.610183i 0.132304 0.991209i \(-0.457762\pi\)
0.924564 + 0.381026i \(0.124429\pi\)
\(860\) −15.1409 + 4.05698i −0.516299 + 0.138342i
\(861\) 0 0
\(862\) −60.0127 + 34.6484i −2.04404 + 1.18013i
\(863\) −39.9815 10.7130i −1.36099 0.364675i −0.496807 0.867861i \(-0.665494\pi\)
−0.864178 + 0.503186i \(0.832161\pi\)
\(864\) 12.7604 + 12.7604i 0.434119 + 0.434119i
\(865\) 6.30285 + 6.30285i 0.214303 + 0.214303i
\(866\) −81.4695 21.8297i −2.76845 0.741803i
\(867\) −39.6537 + 22.8941i −1.34671 + 0.777524i
\(868\) 0 0
\(869\) 1.92056 0.514612i 0.0651504 0.0174570i
\(870\) 26.7191 15.4263i 0.905862 0.523000i
\(871\) −0.169516 5.10263i −0.00574382 0.172896i
\(872\) −22.8658 + 39.6048i −0.774335 + 1.34119i
\(873\) −0.614769 0.614769i −0.0208068 0.0208068i
\(874\) 2.34210 + 1.35221i 0.0792229 + 0.0457393i
\(875\) 0 0
\(876\) 48.3519 48.3519i 1.63366 1.63366i
\(877\) 6.49432 + 24.2371i 0.219298 + 0.818430i 0.984609 + 0.174770i \(0.0559183\pi\)
−0.765312 + 0.643660i \(0.777415\pi\)
\(878\) −16.1994 + 16.1994i −0.546702 + 0.546702i
\(879\) −22.1007 + 5.92188i −0.745440 + 0.199740i
\(880\) 5.63348 + 3.25249i 0.189905 + 0.109641i
\(881\) −18.7477 + 32.4719i −0.631624 + 1.09401i 0.355595 + 0.934640i \(0.384278\pi\)
−0.987220 + 0.159365i \(0.949055\pi\)
\(882\) 0 0
\(883\) 19.9652i 0.671881i 0.941883 + 0.335941i \(0.109054\pi\)
−0.941883 + 0.335941i \(0.890946\pi\)
\(884\) 7.76857 2.36068i 0.261285 0.0793982i
\(885\) −15.7992 9.12168i −0.531085 0.306622i
\(886\) 87.9265 + 23.5598i 2.95395 + 0.791508i
\(887\) 51.4854i 1.72871i 0.502882 + 0.864355i \(0.332273\pi\)
−0.502882 + 0.864355i \(0.667727\pi\)
\(888\) −19.0264 32.9546i −0.638483 1.10588i
\(889\) 0 0
\(890\) 49.0758 + 13.1498i 1.64502 + 0.440783i
\(891\) 4.61729 1.23720i 0.154685 0.0414477i
\(892\) 7.91803 + 29.5505i 0.265115 + 0.989424i
\(893\) −24.8546 −0.831727
\(894\) −35.9828 −1.20344
\(895\) 3.91429 + 14.6083i 0.130840 + 0.488303i
\(896\) 0 0
\(897\) 0.993778 1.06208i 0.0331813 0.0354617i
\(898\) −10.9837 19.0243i −0.366530 0.634848i
\(899\) −5.17720 + 19.3216i −0.172669 + 0.644411i
\(900\) −19.9470 34.5492i −0.664899 1.15164i
\(901\) −2.34860 + 4.06789i −0.0782432 + 0.135521i
\(902\) 30.2492 + 30.2492i 1.00719 + 1.00719i
\(903\) 0 0
\(904\) 1.41396 5.27699i 0.0470277 0.175510i
\(905\) 2.85202 10.6439i 0.0948042 0.353814i
\(906\) 30.7436i 1.02139i
\(907\) −25.0770 + 14.4782i −0.832669 + 0.480742i −0.854766 0.519014i \(-0.826299\pi\)
0.0220968 + 0.999756i \(0.492966\pi\)
\(908\) 41.9262 41.9262i 1.39137 1.39137i
\(909\) −5.51424 −0.182896
\(910\) 0 0
\(911\) 3.65299 0.121029 0.0605144 0.998167i \(-0.480726\pi\)
0.0605144 + 0.998167i \(0.480726\pi\)
\(912\) 19.9940 19.9940i 0.662068 0.662068i
\(913\) 4.14815 2.39494i 0.137284 0.0792609i
\(914\) 45.1178i 1.49236i
\(915\) 5.13050 19.1473i 0.169609 0.632990i
\(916\) −2.22137 + 8.29025i −0.0733960 + 0.273918i
\(917\) 0 0
\(918\) −4.75904 4.75904i −0.157072 0.157072i
\(919\) −21.3670 + 37.0087i −0.704831 + 1.22080i 0.261922 + 0.965089i \(0.415644\pi\)
−0.966753 + 0.255714i \(0.917690\pi\)
\(920\) 0.412694 + 0.714807i 0.0136061 + 0.0235665i
\(921\) −17.5229 + 65.3963i −0.577398 + 2.15488i
\(922\) 15.8924 + 27.5265i 0.523389 + 0.906536i
\(923\) −1.71407 51.5954i −0.0564192 1.69828i
\(924\) 0 0
\(925\) −2.47735 9.24560i −0.0814548 0.303994i
\(926\) 48.5777 1.59636
\(927\) −22.1521 −0.727571
\(928\) 3.12311 + 11.6556i 0.102521 + 0.382614i
\(929\) 16.3504 4.38107i 0.536438 0.143738i 0.0195786 0.999808i \(-0.493768\pi\)
0.516860 + 0.856070i \(0.327101\pi\)
\(930\) −66.7576 17.8876i −2.18907 0.586559i
\(931\) 0 0
\(932\) −9.43247 16.3375i −0.308971 0.535153i
\(933\) 65.4515i 2.14279i
\(934\) −70.2264 18.8171i −2.29788 0.615714i
\(935\) 2.78150 + 1.60590i 0.0909648 + 0.0525186i
\(936\) −31.1932 50.1087i −1.01958 1.63785i
\(937\) 46.5686i 1.52133i −0.649145 0.760665i \(-0.724873\pi\)
0.649145 0.760665i \(-0.275127\pi\)
\(938\) 0 0
\(939\) −19.4205 + 33.6372i −0.633763 + 1.09771i
\(940\) −15.2712 8.81680i −0.498090 0.287572i
\(941\) −11.4955 + 3.08022i −0.374744 + 0.100412i −0.441275 0.897372i \(-0.645474\pi\)
0.0665310 + 0.997784i \(0.478807\pi\)
\(942\) 57.8188 57.8188i 1.88384 1.88384i
\(943\) 0.219438 + 0.818954i 0.00714588 + 0.0266688i
\(944\) −3.81102 + 3.81102i −0.124038 + 0.124038i
\(945\) 0 0
\(946\) 17.8978 + 10.3333i 0.581909 + 0.335965i
\(947\) 30.5491 + 30.5491i 0.992714 + 0.992714i 0.999974 0.00726000i \(-0.00231095\pi\)
−0.00726000 + 0.999974i \(0.502311\pi\)
\(948\) 3.06589 5.31028i 0.0995756 0.172470i
\(949\) 21.6043 13.4489i 0.701305 0.436570i
\(950\) 39.4345 22.7675i 1.27942 0.738676i
\(951\) −44.6321 + 11.9591i −1.44730 + 0.387802i
\(952\) 0 0
\(953\) −50.8066 + 29.3332i −1.64579 + 0.950195i −0.667066 + 0.744999i \(0.732450\pi\)
−0.978721 + 0.205196i \(0.934217\pi\)
\(954\) 76.6738 + 20.5447i 2.48241 + 0.665159i
\(955\) −2.82261 2.82261i −0.0913376 0.0913376i
\(956\) 41.9682 + 41.9682i 1.35735 + 1.35735i
\(957\) −25.0292 6.70657i −0.809080 0.216792i
\(958\) −14.9314 + 8.62062i −0.482410 + 0.278520i
\(959\) 0 0
\(960\) −51.3127 + 13.7492i −1.65611 + 0.443753i
\(961\) 11.9589 6.90448i 0.385771 0.222725i
\(962\) −9.57161 31.4985i −0.308601 1.01555i
\(963\) 35.3273 61.1886i 1.13840 1.97178i
\(964\) 33.3747 + 33.3747i 1.07493 + 1.07493i
\(965\) 31.1288 + 17.9722i 1.00207 + 0.578546i
\(966\) 0 0
\(967\) −7.53769 + 7.53769i −0.242396 + 0.242396i −0.817841 0.575445i \(-0.804829\pi\)
0.575445 + 0.817841i \(0.304829\pi\)
\(968\) 1.03743 + 3.87172i 0.0333441 + 0.124442i
\(969\) 9.87194 9.87194i 0.317132 0.317132i
\(970\) 0.680055 0.182220i 0.0218353 0.00585074i
\(971\) −27.3314 15.7798i −0.877107 0.506398i −0.00740334 0.999973i \(-0.502357\pi\)
−0.869703 + 0.493575i \(0.835690\pi\)
\(972\) 30.8990 53.5187i 0.991086 1.71661i
\(973\) 0 0
\(974\) 23.1495i 0.741759i
\(975\) −7.12039 23.4319i −0.228035 0.750422i
\(976\) −5.07160 2.92809i −0.162338 0.0937259i
\(977\) 1.10312 + 0.295580i 0.0352919 + 0.00945644i 0.276422 0.961036i \(-0.410851\pi\)
−0.241130 + 0.970493i \(0.577518\pi\)
\(978\) 84.5744i 2.70439i
\(979\) −21.3357 36.9545i −0.681891 1.18107i
\(980\) 0 0
\(981\) 57.5708 + 15.4261i 1.83810 + 0.492516i
\(982\) −86.7559 + 23.2462i −2.76849 + 0.741815i
\(983\) 7.63569 + 28.4968i 0.243541 + 0.908907i 0.974111 + 0.226069i \(0.0725876\pi\)
−0.730570 + 0.682837i \(0.760746\pi\)
\(984\) 56.7518 1.80918
\(985\) −28.5406 −0.909380
\(986\) −1.16477 4.34699i −0.0370939 0.138436i
\(987\) 0 0
\(988\) 84.6940 52.7230i 2.69448 1.67734i
\(989\) 0.204799 + 0.354722i 0.00651222 + 0.0112795i
\(990\) 14.0478 52.4272i 0.446469 1.66625i
\(991\) 22.8046 + 39.4987i 0.724412 + 1.25472i 0.959216 + 0.282675i \(0.0912219\pi\)
−0.234804 + 0.972043i \(0.575445\pi\)
\(992\) 13.5153 23.4093i 0.429113 0.743245i
\(993\) −18.8898 18.8898i −0.599450 0.599450i
\(994\) 0 0
\(995\) 6.76894 25.2620i 0.214590 0.800860i
\(996\) 3.82317 14.2683i 0.121142 0.452108i
\(997\) 26.0713i 0.825686i 0.910802 + 0.412843i \(0.135464\pi\)
−0.910802 + 0.412843i \(0.864536\pi\)
\(998\) 0.00295282 0.00170481i 9.34698e−5 5.39648e-5i
\(999\) −12.2919 + 12.2919i −0.388897 + 0.388897i
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 637.2.bb.b.227.2 32
7.2 even 3 637.2.x.b.19.8 32
7.3 odd 6 91.2.bc.a.6.2 yes 32
7.4 even 3 91.2.bc.a.6.1 32
7.5 odd 6 637.2.x.b.19.7 32
7.6 odd 2 inner 637.2.bb.b.227.1 32
13.11 odd 12 637.2.x.b.570.8 32
21.11 odd 6 819.2.fm.g.370.7 32
21.17 even 6 819.2.fm.g.370.8 32
91.11 odd 12 91.2.bc.a.76.2 yes 32
91.24 even 12 91.2.bc.a.76.1 yes 32
91.37 odd 12 inner 637.2.bb.b.362.1 32
91.76 even 12 637.2.x.b.570.7 32
91.89 even 12 inner 637.2.bb.b.362.2 32
273.11 even 12 819.2.fm.g.622.8 32
273.206 odd 12 819.2.fm.g.622.7 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bc.a.6.1 32 7.4 even 3
91.2.bc.a.6.2 yes 32 7.3 odd 6
91.2.bc.a.76.1 yes 32 91.24 even 12
91.2.bc.a.76.2 yes 32 91.11 odd 12
637.2.x.b.19.7 32 7.5 odd 6
637.2.x.b.19.8 32 7.2 even 3
637.2.x.b.570.7 32 91.76 even 12
637.2.x.b.570.8 32 13.11 odd 12
637.2.bb.b.227.1 32 7.6 odd 2 inner
637.2.bb.b.227.2 32 1.1 even 1 trivial
637.2.bb.b.362.1 32 91.37 odd 12 inner
637.2.bb.b.362.2 32 91.89 even 12 inner
819.2.fm.g.370.7 32 21.11 odd 6
819.2.fm.g.370.8 32 21.17 even 6
819.2.fm.g.622.7 32 273.206 odd 12
819.2.fm.g.622.8 32 273.11 even 12