Properties

Label 525.2.j.c.218.14
Level $525$
Weight $2$
Character 525.218
Analytic conductor $4.192$
Analytic rank $0$
Dimension $32$
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] = [525,2,Mod(218,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.218");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 218.14
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.c.407.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.27211 + 1.27211i) q^{2} +(1.54904 - 0.774907i) q^{3} +1.23654i q^{4} +(2.95632 + 0.984783i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.971203 - 0.971203i) q^{8} +(1.79904 - 2.40072i) q^{9} +O(q^{10})\) \(q+(1.27211 + 1.27211i) q^{2} +(1.54904 - 0.774907i) q^{3} +1.23654i q^{4} +(2.95632 + 0.984783i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.971203 - 0.971203i) q^{8} +(1.79904 - 2.40072i) q^{9} +0.596077i q^{11} +(0.958205 + 1.91545i) q^{12} +(0.651688 + 0.651688i) q^{13} -1.79904 q^{14} +4.94405 q^{16} +(2.63250 + 2.63250i) q^{17} +(5.34257 - 0.765406i) q^{18} -1.16418i q^{19} +(-0.547394 + 1.64328i) q^{21} +(-0.758277 + 0.758277i) q^{22} +(-2.83371 + 2.83371i) q^{23} +(0.751839 - 2.25702i) q^{24} +1.65804i q^{26} +(0.926447 - 5.11290i) q^{27} +(-0.874368 - 0.874368i) q^{28} -9.57511 q^{29} -7.54990 q^{31} +(4.34698 + 4.34698i) q^{32} +(0.461904 + 0.923346i) q^{33} +6.69767i q^{34} +(2.96859 + 2.22459i) q^{36} +(7.81453 - 7.81453i) q^{37} +(1.48096 - 1.48096i) q^{38} +(1.51449 + 0.504492i) q^{39} +8.32646i q^{41} +(-2.78678 + 1.39409i) q^{42} +(-7.71640 - 7.71640i) q^{43} -0.737075 q^{44} -7.20959 q^{46} +(5.33798 + 5.33798i) q^{47} +(7.65852 - 3.83117i) q^{48} -1.00000i q^{49} +(6.11778 + 2.03790i) q^{51} +(-0.805840 + 0.805840i) q^{52} +(-2.54423 + 2.54423i) q^{53} +(7.68273 - 5.32563i) q^{54} +1.37349i q^{56} +(-0.902128 - 1.80335i) q^{57} +(-12.1806 - 12.1806i) q^{58} -4.37549 q^{59} -15.0140 q^{61} +(-9.60433 - 9.60433i) q^{62} +(0.425452 + 2.96968i) q^{63} +1.17161i q^{64} +(-0.587007 + 1.76220i) q^{66} +(1.26066 - 1.26066i) q^{67} +(-3.25520 + 3.25520i) q^{68} +(-2.19366 + 6.58538i) q^{69} -7.16919i q^{71} +(-0.584354 - 4.07882i) q^{72} +(5.66151 + 5.66151i) q^{73} +19.8819 q^{74} +1.43955 q^{76} +(-0.421490 - 0.421490i) q^{77} +(1.28483 + 2.56837i) q^{78} +3.85224i q^{79} +(-2.52691 - 8.63798i) q^{81} +(-10.5922 + 10.5922i) q^{82} +(-4.70691 + 4.70691i) q^{83} +(-2.03198 - 0.676876i) q^{84} -19.6323i q^{86} +(-14.8322 + 7.41982i) q^{87} +(0.578912 + 0.578912i) q^{88} -2.19762 q^{89} -0.921626 q^{91} +(-3.50400 - 3.50400i) q^{92} +(-11.6951 + 5.85047i) q^{93} +13.5810i q^{94} +(10.1021 + 3.36514i) q^{96} +(7.69844 - 7.69844i) q^{97} +(1.27211 - 1.27211i) q^{98} +(1.43101 + 1.07237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 16 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 16 q^{6} - 16 q^{16} - 8 q^{21} + 16 q^{31} + 48 q^{36} + 144 q^{46} - 64 q^{51} - 112 q^{61} - 192 q^{76} - 64 q^{81} + 64 q^{91} + 360 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.27211 + 1.27211i 0.899520 + 0.899520i 0.995394 0.0958737i \(-0.0305645\pi\)
−0.0958737 + 0.995394i \(0.530565\pi\)
\(3\) 1.54904 0.774907i 0.894338 0.447393i
\(4\) 1.23654i 0.618272i
\(5\) 0 0
\(6\) 2.95632 + 0.984783i 1.20691 + 0.402036i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 0.971203 0.971203i 0.343372 0.343372i
\(9\) 1.79904 2.40072i 0.599680 0.800240i
\(10\) 0 0
\(11\) 0.596077i 0.179724i 0.995954 + 0.0898620i \(0.0286426\pi\)
−0.995954 + 0.0898620i \(0.971357\pi\)
\(12\) 0.958205 + 1.91545i 0.276610 + 0.552944i
\(13\) 0.651688 + 0.651688i 0.180746 + 0.180746i 0.791681 0.610935i \(-0.209206\pi\)
−0.610935 + 0.791681i \(0.709206\pi\)
\(14\) −1.79904 −0.480814
\(15\) 0 0
\(16\) 4.94405 1.23601
\(17\) 2.63250 + 2.63250i 0.638474 + 0.638474i 0.950179 0.311705i \(-0.100900\pi\)
−0.311705 + 0.950179i \(0.600900\pi\)
\(18\) 5.34257 0.765406i 1.25926 0.180408i
\(19\) 1.16418i 0.267081i −0.991043 0.133540i \(-0.957365\pi\)
0.991043 0.133540i \(-0.0426345\pi\)
\(20\) 0 0
\(21\) −0.547394 + 1.64328i −0.119451 + 0.358592i
\(22\) −0.758277 + 0.758277i −0.161665 + 0.161665i
\(23\) −2.83371 + 2.83371i −0.590869 + 0.590869i −0.937866 0.346997i \(-0.887201\pi\)
0.346997 + 0.937866i \(0.387201\pi\)
\(24\) 0.751839 2.25702i 0.153469 0.460713i
\(25\) 0 0
\(26\) 1.65804i 0.325169i
\(27\) 0.926447 5.11290i 0.178295 0.983977i
\(28\) −0.874368 0.874368i −0.165240 0.165240i
\(29\) −9.57511 −1.77805 −0.889027 0.457855i \(-0.848618\pi\)
−0.889027 + 0.457855i \(0.848618\pi\)
\(30\) 0 0
\(31\) −7.54990 −1.35600 −0.678001 0.735061i \(-0.737154\pi\)
−0.678001 + 0.735061i \(0.737154\pi\)
\(32\) 4.34698 + 4.34698i 0.768445 + 0.768445i
\(33\) 0.461904 + 0.923346i 0.0804072 + 0.160734i
\(34\) 6.69767i 1.14864i
\(35\) 0 0
\(36\) 2.96859 + 2.22459i 0.494766 + 0.370765i
\(37\) 7.81453 7.81453i 1.28470 1.28470i 0.346740 0.937961i \(-0.387289\pi\)
0.937961 0.346740i \(-0.112711\pi\)
\(38\) 1.48096 1.48096i 0.240244 0.240244i
\(39\) 1.51449 + 0.504492i 0.242512 + 0.0807834i
\(40\) 0 0
\(41\) 8.32646i 1.30037i 0.759774 + 0.650187i \(0.225309\pi\)
−0.759774 + 0.650187i \(0.774691\pi\)
\(42\) −2.78678 + 1.39409i −0.430010 + 0.215112i
\(43\) −7.71640 7.71640i −1.17674 1.17674i −0.980570 0.196171i \(-0.937149\pi\)
−0.196171 0.980570i \(-0.562851\pi\)
\(44\) −0.737075 −0.111118
\(45\) 0 0
\(46\) −7.20959 −1.06300
\(47\) 5.33798 + 5.33798i 0.778624 + 0.778624i 0.979597 0.200972i \(-0.0644102\pi\)
−0.200972 + 0.979597i \(0.564410\pi\)
\(48\) 7.65852 3.83117i 1.10541 0.552982i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 6.11778 + 2.03790i 0.856660 + 0.285363i
\(52\) −0.805840 + 0.805840i −0.111750 + 0.111750i
\(53\) −2.54423 + 2.54423i −0.349476 + 0.349476i −0.859914 0.510438i \(-0.829483\pi\)
0.510438 + 0.859914i \(0.329483\pi\)
\(54\) 7.68273 5.32563i 1.04549 0.724727i
\(55\) 0 0
\(56\) 1.37349i 0.183540i
\(57\) −0.902128 1.80335i −0.119490 0.238860i
\(58\) −12.1806 12.1806i −1.59939 1.59939i
\(59\) −4.37549 −0.569640 −0.284820 0.958581i \(-0.591934\pi\)
−0.284820 + 0.958581i \(0.591934\pi\)
\(60\) 0 0
\(61\) −15.0140 −1.92235 −0.961173 0.275946i \(-0.911009\pi\)
−0.961173 + 0.275946i \(0.911009\pi\)
\(62\) −9.60433 9.60433i −1.21975 1.21975i
\(63\) 0.425452 + 2.96968i 0.0536020 + 0.374144i
\(64\) 1.17161i 0.146451i
\(65\) 0 0
\(66\) −0.587007 + 1.76220i −0.0722555 + 0.216911i
\(67\) 1.26066 1.26066i 0.154015 0.154015i −0.625894 0.779908i \(-0.715266\pi\)
0.779908 + 0.625894i \(0.215266\pi\)
\(68\) −3.25520 + 3.25520i −0.394751 + 0.394751i
\(69\) −2.19366 + 6.58538i −0.264086 + 0.792786i
\(70\) 0 0
\(71\) 7.16919i 0.850826i −0.904999 0.425413i \(-0.860129\pi\)
0.904999 0.425413i \(-0.139871\pi\)
\(72\) −0.584354 4.07882i −0.0688668 0.480694i
\(73\) 5.66151 + 5.66151i 0.662629 + 0.662629i 0.955999 0.293370i \(-0.0947768\pi\)
−0.293370 + 0.955999i \(0.594777\pi\)
\(74\) 19.8819 2.31123
\(75\) 0 0
\(76\) 1.43955 0.165128
\(77\) −0.421490 0.421490i −0.0480333 0.0480333i
\(78\) 1.28483 + 2.56837i 0.145478 + 0.290811i
\(79\) 3.85224i 0.433410i 0.976237 + 0.216705i \(0.0695311\pi\)
−0.976237 + 0.216705i \(0.930469\pi\)
\(80\) 0 0
\(81\) −2.52691 8.63798i −0.280768 0.959776i
\(82\) −10.5922 + 10.5922i −1.16971 + 1.16971i
\(83\) −4.70691 + 4.70691i −0.516651 + 0.516651i −0.916556 0.399905i \(-0.869043\pi\)
0.399905 + 0.916556i \(0.369043\pi\)
\(84\) −2.03198 0.676876i −0.221708 0.0738532i
\(85\) 0 0
\(86\) 19.6323i 2.11700i
\(87\) −14.8322 + 7.41982i −1.59018 + 0.795488i
\(88\) 0.578912 + 0.578912i 0.0617122 + 0.0617122i
\(89\) −2.19762 −0.232947 −0.116474 0.993194i \(-0.537159\pi\)
−0.116474 + 0.993194i \(0.537159\pi\)
\(90\) 0 0
\(91\) −0.921626 −0.0966127
\(92\) −3.50400 3.50400i −0.365317 0.365317i
\(93\) −11.6951 + 5.85047i −1.21272 + 0.606666i
\(94\) 13.5810i 1.40078i
\(95\) 0 0
\(96\) 10.1021 + 3.36514i 1.03105 + 0.343453i
\(97\) 7.69844 7.69844i 0.781658 0.781658i −0.198452 0.980111i \(-0.563591\pi\)
0.980111 + 0.198452i \(0.0635914\pi\)
\(98\) 1.27211 1.27211i 0.128503 0.128503i
\(99\) 1.43101 + 1.07237i 0.143822 + 0.107777i
\(100\) 0 0
\(101\) 12.7638i 1.27005i 0.772493 + 0.635023i \(0.219009\pi\)
−0.772493 + 0.635023i \(0.780991\pi\)
\(102\) 5.19007 + 10.3749i 0.513893 + 1.02727i
\(103\) 6.78916 + 6.78916i 0.668956 + 0.668956i 0.957474 0.288518i \(-0.0931626\pi\)
−0.288518 + 0.957474i \(0.593163\pi\)
\(104\) 1.26584 0.124126
\(105\) 0 0
\(106\) −6.47309 −0.628722
\(107\) −0.176542 0.176542i −0.0170670 0.0170670i 0.698522 0.715589i \(-0.253842\pi\)
−0.715589 + 0.698522i \(0.753842\pi\)
\(108\) 6.32232 + 1.14559i 0.608365 + 0.110235i
\(109\) 11.2027i 1.07303i −0.843892 0.536513i \(-0.819741\pi\)
0.843892 0.536513i \(-0.180259\pi\)
\(110\) 0 0
\(111\) 6.04948 18.1605i 0.574191 1.72372i
\(112\) −3.49597 + 3.49597i −0.330338 + 0.330338i
\(113\) 0.553500 0.553500i 0.0520689 0.0520689i −0.680593 0.732662i \(-0.738278\pi\)
0.732662 + 0.680593i \(0.238278\pi\)
\(114\) 1.14646 3.44168i 0.107376 0.322343i
\(115\) 0 0
\(116\) 11.8400i 1.09932i
\(117\) 2.73693 0.392108i 0.253030 0.0362504i
\(118\) −5.56612 5.56612i −0.512403 0.512403i
\(119\) −3.72291 −0.341279
\(120\) 0 0
\(121\) 10.6447 0.967699
\(122\) −19.0995 19.0995i −1.72919 1.72919i
\(123\) 6.45223 + 12.8980i 0.581778 + 1.16297i
\(124\) 9.33578i 0.838378i
\(125\) 0 0
\(126\) −3.23654 + 4.31899i −0.288334 + 0.384766i
\(127\) −2.62625 + 2.62625i −0.233042 + 0.233042i −0.813961 0.580919i \(-0.802693\pi\)
0.580919 + 0.813961i \(0.302693\pi\)
\(128\) 7.20355 7.20355i 0.636709 0.636709i
\(129\) −17.9325 5.97351i −1.57887 0.525938i
\(130\) 0 0
\(131\) 16.5281i 1.44406i −0.691859 0.722032i \(-0.743208\pi\)
0.691859 0.722032i \(-0.256792\pi\)
\(132\) −1.14176 + 0.571164i −0.0993772 + 0.0497135i
\(133\) 0.823197 + 0.823197i 0.0713803 + 0.0713803i
\(134\) 3.20741 0.277078
\(135\) 0 0
\(136\) 5.11338 0.438469
\(137\) 11.1583 + 11.1583i 0.953316 + 0.953316i 0.998958 0.0456415i \(-0.0145332\pi\)
−0.0456415 + 0.998958i \(0.514533\pi\)
\(138\) −11.1679 + 5.58676i −0.950677 + 0.475576i
\(139\) 2.90366i 0.246285i 0.992389 + 0.123142i \(0.0392972\pi\)
−0.992389 + 0.123142i \(0.960703\pi\)
\(140\) 0 0
\(141\) 12.4052 + 4.13230i 1.04470 + 0.348002i
\(142\) 9.12001 9.12001i 0.765335 0.765335i
\(143\) −0.388456 + 0.388456i −0.0324843 + 0.0324843i
\(144\) 8.89454 11.8693i 0.741211 0.989106i
\(145\) 0 0
\(146\) 14.4041i 1.19210i
\(147\) −0.774907 1.54904i −0.0639132 0.127763i
\(148\) 9.66301 + 9.66301i 0.794294 + 0.794294i
\(149\) 2.77395 0.227251 0.113625 0.993524i \(-0.463754\pi\)
0.113625 + 0.993524i \(0.463754\pi\)
\(150\) 0 0
\(151\) 2.07180 0.168600 0.0843002 0.996440i \(-0.473135\pi\)
0.0843002 + 0.996440i \(0.473135\pi\)
\(152\) −1.13065 1.13065i −0.0917080 0.0917080i
\(153\) 11.0559 1.58392i 0.893813 0.128053i
\(154\) 1.07237i 0.0864137i
\(155\) 0 0
\(156\) −0.623827 + 1.87273i −0.0499461 + 0.149938i
\(157\) −9.28263 + 9.28263i −0.740834 + 0.740834i −0.972739 0.231904i \(-0.925504\pi\)
0.231904 + 0.972739i \(0.425504\pi\)
\(158\) −4.90048 + 4.90048i −0.389861 + 0.389861i
\(159\) −1.96957 + 5.91264i −0.156197 + 0.468903i
\(160\) 0 0
\(161\) 4.00747i 0.315833i
\(162\) 7.77397 14.2030i 0.610781 1.11589i
\(163\) 9.40972 + 9.40972i 0.737026 + 0.737026i 0.972001 0.234975i \(-0.0755009\pi\)
−0.234975 + 0.972001i \(0.575501\pi\)
\(164\) −10.2960 −0.803984
\(165\) 0 0
\(166\) −11.9755 −0.929475
\(167\) −10.4473 10.4473i −0.808437 0.808437i 0.175960 0.984397i \(-0.443697\pi\)
−0.984397 + 0.175960i \(0.943697\pi\)
\(168\) 1.06433 + 2.12759i 0.0821145 + 0.164147i
\(169\) 12.1506i 0.934662i
\(170\) 0 0
\(171\) −2.79486 2.09440i −0.213729 0.160163i
\(172\) 9.54166 9.54166i 0.727545 0.727545i
\(173\) 18.0363 18.0363i 1.37127 1.37127i 0.512707 0.858563i \(-0.328643\pi\)
0.858563 0.512707i \(-0.171357\pi\)
\(174\) −28.3071 9.42941i −2.14596 0.714841i
\(175\) 0 0
\(176\) 2.94703i 0.222141i
\(177\) −6.77780 + 3.39060i −0.509451 + 0.254853i
\(178\) −2.79562 2.79562i −0.209540 0.209540i
\(179\) 18.2401 1.36333 0.681663 0.731666i \(-0.261257\pi\)
0.681663 + 0.731666i \(0.261257\pi\)
\(180\) 0 0
\(181\) 5.06040 0.376137 0.188068 0.982156i \(-0.439777\pi\)
0.188068 + 0.982156i \(0.439777\pi\)
\(182\) −1.17241 1.17241i −0.0869050 0.0869050i
\(183\) −23.2573 + 11.6345i −1.71923 + 0.860043i
\(184\) 5.50421i 0.405776i
\(185\) 0 0
\(186\) −22.3199 7.43502i −1.63658 0.545162i
\(187\) −1.56917 + 1.56917i −0.114749 + 0.114749i
\(188\) −6.60064 + 6.60064i −0.481401 + 0.481401i
\(189\) 2.96027 + 4.27046i 0.215328 + 0.310630i
\(190\) 0 0
\(191\) 4.33413i 0.313607i 0.987630 + 0.156803i \(0.0501189\pi\)
−0.987630 + 0.156803i \(0.949881\pi\)
\(192\) 0.907885 + 1.81486i 0.0655210 + 0.130976i
\(193\) −11.7911 11.7911i −0.848741 0.848741i 0.141235 0.989976i \(-0.454893\pi\)
−0.989976 + 0.141235i \(0.954893\pi\)
\(194\) 19.5866 1.40623
\(195\) 0 0
\(196\) 1.23654 0.0883245
\(197\) −5.36265 5.36265i −0.382073 0.382073i 0.489776 0.871848i \(-0.337079\pi\)
−0.871848 + 0.489776i \(0.837079\pi\)
\(198\) 0.456241 + 3.18458i 0.0324236 + 0.226318i
\(199\) 0.778449i 0.0551828i 0.999619 + 0.0275914i \(0.00878373\pi\)
−0.999619 + 0.0275914i \(0.991216\pi\)
\(200\) 0 0
\(201\) 0.975920 2.92971i 0.0688361 0.206646i
\(202\) −16.2370 + 16.2370i −1.14243 + 1.14243i
\(203\) 6.77063 6.77063i 0.475205 0.475205i
\(204\) −2.51995 + 7.56490i −0.176432 + 0.529649i
\(205\) 0 0
\(206\) 17.2732i 1.20348i
\(207\) 1.70499 + 11.9009i 0.118505 + 0.827169i
\(208\) 3.22198 + 3.22198i 0.223404 + 0.223404i
\(209\) 0.693939 0.0480008
\(210\) 0 0
\(211\) 3.91922 0.269810 0.134905 0.990859i \(-0.456927\pi\)
0.134905 + 0.990859i \(0.456927\pi\)
\(212\) −3.14605 3.14605i −0.216071 0.216071i
\(213\) −5.55545 11.1053i −0.380653 0.760926i
\(214\) 0.449163i 0.0307042i
\(215\) 0 0
\(216\) −4.06589 5.86543i −0.276649 0.399092i
\(217\) 5.33859 5.33859i 0.362407 0.362407i
\(218\) 14.2511 14.2511i 0.965209 0.965209i
\(219\) 13.1570 + 4.38275i 0.889069 + 0.296159i
\(220\) 0 0
\(221\) 3.43113i 0.230803i
\(222\) 30.7979 15.4066i 2.06702 1.03403i
\(223\) −4.95226 4.95226i −0.331628 0.331628i 0.521577 0.853204i \(-0.325344\pi\)
−0.853204 + 0.521577i \(0.825344\pi\)
\(224\) −6.14756 −0.410751
\(225\) 0 0
\(226\) 1.40823 0.0936740
\(227\) 10.4264 + 10.4264i 0.692027 + 0.692027i 0.962678 0.270651i \(-0.0872389\pi\)
−0.270651 + 0.962678i \(0.587239\pi\)
\(228\) 2.22993 1.11552i 0.147680 0.0738772i
\(229\) 18.3432i 1.21215i 0.795406 + 0.606077i \(0.207258\pi\)
−0.795406 + 0.606077i \(0.792742\pi\)
\(230\) 0 0
\(231\) −0.979520 0.326289i −0.0644477 0.0214682i
\(232\) −9.29938 + 9.29938i −0.610534 + 0.610534i
\(233\) 8.53926 8.53926i 0.559426 0.559426i −0.369718 0.929144i \(-0.620546\pi\)
0.929144 + 0.369718i \(0.120546\pi\)
\(234\) 3.98049 + 2.98288i 0.260213 + 0.194997i
\(235\) 0 0
\(236\) 5.41048i 0.352192i
\(237\) 2.98512 + 5.96726i 0.193905 + 0.387615i
\(238\) −4.73597 4.73597i −0.306987 0.306987i
\(239\) −5.98239 −0.386968 −0.193484 0.981103i \(-0.561979\pi\)
−0.193484 + 0.981103i \(0.561979\pi\)
\(240\) 0 0
\(241\) 5.05823 0.325829 0.162914 0.986640i \(-0.447911\pi\)
0.162914 + 0.986640i \(0.447911\pi\)
\(242\) 13.5413 + 13.5413i 0.870465 + 0.870465i
\(243\) −10.6079 11.4224i −0.680498 0.732750i
\(244\) 18.5655i 1.18853i
\(245\) 0 0
\(246\) −8.19975 + 24.6157i −0.522797 + 1.56944i
\(247\) 0.758680 0.758680i 0.0482737 0.0482737i
\(248\) −7.33249 + 7.33249i −0.465614 + 0.465614i
\(249\) −3.64377 + 10.9386i −0.230915 + 0.693206i
\(250\) 0 0
\(251\) 26.3582i 1.66372i 0.554989 + 0.831858i \(0.312723\pi\)
−0.554989 + 0.831858i \(0.687277\pi\)
\(252\) −3.67214 + 0.526090i −0.231323 + 0.0331406i
\(253\) −1.68911 1.68911i −0.106193 0.106193i
\(254\) −6.68178 −0.419252
\(255\) 0 0
\(256\) 20.6707 1.29192
\(257\) 12.5808 + 12.5808i 0.784766 + 0.784766i 0.980631 0.195865i \(-0.0627514\pi\)
−0.195865 + 0.980631i \(0.562751\pi\)
\(258\) −15.2132 30.4111i −0.947131 1.89332i
\(259\) 11.0514i 0.686702i
\(260\) 0 0
\(261\) −17.2260 + 22.9872i −1.06626 + 1.42287i
\(262\) 21.0256 21.0256i 1.29896 1.29896i
\(263\) −7.32034 + 7.32034i −0.451391 + 0.451391i −0.895816 0.444425i \(-0.853408\pi\)
0.444425 + 0.895816i \(0.353408\pi\)
\(264\) 1.34536 + 0.448154i 0.0828012 + 0.0275820i
\(265\) 0 0
\(266\) 2.09440i 0.128416i
\(267\) −3.40419 + 1.70295i −0.208333 + 0.104219i
\(268\) 1.55886 + 1.55886i 0.0952228 + 0.0952228i
\(269\) 7.34074 0.447573 0.223786 0.974638i \(-0.428158\pi\)
0.223786 + 0.974638i \(0.428158\pi\)
\(270\) 0 0
\(271\) −7.40673 −0.449927 −0.224963 0.974367i \(-0.572226\pi\)
−0.224963 + 0.974367i \(0.572226\pi\)
\(272\) 13.0152 + 13.0152i 0.789162 + 0.789162i
\(273\) −1.42763 + 0.714174i −0.0864043 + 0.0432238i
\(274\) 28.3892i 1.71505i
\(275\) 0 0
\(276\) −8.14310 2.71256i −0.490157 0.163277i
\(277\) 11.1225 11.1225i 0.668289 0.668289i −0.289031 0.957320i \(-0.593333\pi\)
0.957320 + 0.289031i \(0.0933331\pi\)
\(278\) −3.69378 + 3.69378i −0.221538 + 0.221538i
\(279\) −13.5826 + 18.1252i −0.813168 + 1.08513i
\(280\) 0 0
\(281\) 17.1123i 1.02084i 0.859927 + 0.510418i \(0.170509\pi\)
−0.859927 + 0.510418i \(0.829491\pi\)
\(282\) 10.5240 + 21.0375i 0.626697 + 1.25277i
\(283\) −10.9094 10.9094i −0.648494 0.648494i 0.304135 0.952629i \(-0.401633\pi\)
−0.952629 + 0.304135i \(0.901633\pi\)
\(284\) 8.86501 0.526041
\(285\) 0 0
\(286\) −0.988321 −0.0584406
\(287\) −5.88769 5.88769i −0.347540 0.347540i
\(288\) 18.2563 2.61549i 1.07576 0.154119i
\(289\) 3.13992i 0.184701i
\(290\) 0 0
\(291\) 5.95961 17.8908i 0.349358 1.04877i
\(292\) −7.00070 + 7.00070i −0.409685 + 0.409685i
\(293\) −15.3592 + 15.3592i −0.897295 + 0.897295i −0.995196 0.0979008i \(-0.968787\pi\)
0.0979008 + 0.995196i \(0.468787\pi\)
\(294\) 0.984783 2.95632i 0.0574337 0.172416i
\(295\) 0 0
\(296\) 15.1790i 0.882262i
\(297\) 3.04768 + 0.552234i 0.176844 + 0.0320439i
\(298\) 3.52878 + 3.52878i 0.204417 + 0.204417i
\(299\) −3.69338 −0.213594
\(300\) 0 0
\(301\) 10.9126 0.628994
\(302\) 2.63556 + 2.63556i 0.151659 + 0.151659i
\(303\) 9.89076 + 19.7716i 0.568209 + 1.13585i
\(304\) 5.75575i 0.330115i
\(305\) 0 0
\(306\) 16.0792 + 12.0494i 0.919188 + 0.688817i
\(307\) −15.5878 + 15.5878i −0.889641 + 0.889641i −0.994488 0.104848i \(-0.966564\pi\)
0.104848 + 0.994488i \(0.466564\pi\)
\(308\) 0.521191 0.521191i 0.0296976 0.0296976i
\(309\) 15.7776 + 5.25571i 0.897558 + 0.298987i
\(310\) 0 0
\(311\) 21.7724i 1.23460i −0.786729 0.617299i \(-0.788227\pi\)
0.786729 0.617299i \(-0.211773\pi\)
\(312\) 1.96084 0.980910i 0.111011 0.0555331i
\(313\) 16.7825 + 16.7825i 0.948603 + 0.948603i 0.998742 0.0501392i \(-0.0159665\pi\)
−0.0501392 + 0.998742i \(0.515966\pi\)
\(314\) −23.6171 −1.33279
\(315\) 0 0
\(316\) −4.76346 −0.267965
\(317\) 19.4564 + 19.4564i 1.09278 + 1.09278i 0.995231 + 0.0975486i \(0.0311002\pi\)
0.0975486 + 0.995231i \(0.468900\pi\)
\(318\) −10.0271 + 5.01604i −0.562290 + 0.281285i
\(319\) 5.70750i 0.319559i
\(320\) 0 0
\(321\) −0.410274 0.136667i −0.0228993 0.00762800i
\(322\) 5.09795 5.09795i 0.284098 0.284098i
\(323\) 3.06469 3.06469i 0.170524 0.170524i
\(324\) 10.6812 3.12464i 0.593402 0.173591i
\(325\) 0 0
\(326\) 23.9405i 1.32594i
\(327\) −8.68107 17.3535i −0.480064 0.959648i
\(328\) 8.08668 + 8.08668i 0.446512 + 0.446512i
\(329\) −7.54904 −0.416192
\(330\) 0 0
\(331\) −20.0430 −1.10166 −0.550830 0.834617i \(-0.685689\pi\)
−0.550830 + 0.834617i \(0.685689\pi\)
\(332\) −5.82030 5.82030i −0.319431 0.319431i
\(333\) −4.70185 32.8192i −0.257660 1.79848i
\(334\) 26.5803i 1.45441i
\(335\) 0 0
\(336\) −2.70634 + 8.12444i −0.147643 + 0.443225i
\(337\) −5.35404 + 5.35404i −0.291653 + 0.291653i −0.837733 0.546080i \(-0.816119\pi\)
0.546080 + 0.837733i \(0.316119\pi\)
\(338\) 15.4569 15.4569i 0.840747 0.840747i
\(339\) 0.428482 1.28630i 0.0232720 0.0698624i
\(340\) 0 0
\(341\) 4.50033i 0.243706i
\(342\) −0.891068 6.21970i −0.0481834 0.336323i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −14.9884 −0.808120
\(345\) 0 0
\(346\) 45.8883 2.46697
\(347\) −20.2180 20.2180i −1.08536 1.08536i −0.995999 0.0893604i \(-0.971518\pi\)
−0.0893604 0.995999i \(-0.528482\pi\)
\(348\) −9.17492 18.3407i −0.491828 0.983163i
\(349\) 14.0744i 0.753386i −0.926338 0.376693i \(-0.877061\pi\)
0.926338 0.376693i \(-0.122939\pi\)
\(350\) 0 0
\(351\) 3.93577 2.72826i 0.210076 0.145624i
\(352\) −2.59114 + 2.59114i −0.138108 + 0.138108i
\(353\) 7.05174 7.05174i 0.375326 0.375326i −0.494087 0.869413i \(-0.664497\pi\)
0.869413 + 0.494087i \(0.164497\pi\)
\(354\) −12.9354 4.30891i −0.687506 0.229016i
\(355\) 0 0
\(356\) 2.71745i 0.144025i
\(357\) −5.76694 + 2.88491i −0.305219 + 0.152686i
\(358\) 23.2034 + 23.2034i 1.22634 + 1.22634i
\(359\) 15.8072 0.834270 0.417135 0.908844i \(-0.363034\pi\)
0.417135 + 0.908844i \(0.363034\pi\)
\(360\) 0 0
\(361\) 17.6447 0.928668
\(362\) 6.43741 + 6.43741i 0.338343 + 0.338343i
\(363\) 16.4890 8.24864i 0.865450 0.432941i
\(364\) 1.13963i 0.0597329i
\(365\) 0 0
\(366\) −44.3862 14.7855i −2.32010 0.772853i
\(367\) 13.4893 13.4893i 0.704138 0.704138i −0.261158 0.965296i \(-0.584104\pi\)
0.965296 + 0.261158i \(0.0841043\pi\)
\(368\) −14.0100 + 14.0100i −0.730321 + 0.730321i
\(369\) 19.9895 + 14.9796i 1.04061 + 0.779808i
\(370\) 0 0
\(371\) 3.59808i 0.186803i
\(372\) −7.23436 14.4615i −0.375084 0.749793i
\(373\) 14.7655 + 14.7655i 0.764527 + 0.764527i 0.977137 0.212610i \(-0.0681965\pi\)
−0.212610 + 0.977137i \(0.568197\pi\)
\(374\) −3.99233 −0.206438
\(375\) 0 0
\(376\) 10.3685 0.534716
\(377\) −6.23998 6.23998i −0.321376 0.321376i
\(378\) −1.66672 + 9.19830i −0.0857266 + 0.473110i
\(379\) 31.9071i 1.63896i −0.573109 0.819479i \(-0.694263\pi\)
0.573109 0.819479i \(-0.305737\pi\)
\(380\) 0 0
\(381\) −2.03307 + 6.10327i −0.104157 + 0.312680i
\(382\) −5.51350 + 5.51350i −0.282095 + 0.282095i
\(383\) −10.5821 + 10.5821i −0.540720 + 0.540720i −0.923740 0.383020i \(-0.874884\pi\)
0.383020 + 0.923740i \(0.374884\pi\)
\(384\) 5.57649 16.7406i 0.284574 0.854292i
\(385\) 0 0
\(386\) 29.9992i 1.52692i
\(387\) −32.4070 + 4.64281i −1.64734 + 0.236007i
\(388\) 9.51946 + 9.51946i 0.483277 + 0.483277i
\(389\) −22.7753 −1.15475 −0.577376 0.816478i \(-0.695923\pi\)
−0.577376 + 0.816478i \(0.695923\pi\)
\(390\) 0 0
\(391\) −14.9194 −0.754509
\(392\) −0.971203 0.971203i −0.0490532 0.0490532i
\(393\) −12.8077 25.6026i −0.646064 1.29148i
\(394\) 13.6438i 0.687364i
\(395\) 0 0
\(396\) −1.32603 + 1.76951i −0.0666354 + 0.0889213i
\(397\) 14.8873 14.8873i 0.747172 0.747172i −0.226775 0.973947i \(-0.572818\pi\)
0.973947 + 0.226775i \(0.0728181\pi\)
\(398\) −0.990276 + 0.990276i −0.0496380 + 0.0496380i
\(399\) 1.91307 + 0.637263i 0.0957731 + 0.0319031i
\(400\) 0 0
\(401\) 15.0691i 0.752513i 0.926515 + 0.376257i \(0.122789\pi\)
−0.926515 + 0.376257i \(0.877211\pi\)
\(402\) 4.96841 2.48545i 0.247802 0.123963i
\(403\) −4.92018 4.92018i −0.245092 0.245092i
\(404\) −15.7830 −0.785233
\(405\) 0 0
\(406\) 17.2260 0.854912
\(407\) 4.65806 + 4.65806i 0.230892 + 0.230892i
\(408\) 7.92082 3.96239i 0.392139 0.196168i
\(409\) 25.3358i 1.25277i −0.779512 0.626387i \(-0.784533\pi\)
0.779512 0.626387i \(-0.215467\pi\)
\(410\) 0 0
\(411\) 25.9312 + 8.63798i 1.27909 + 0.426080i
\(412\) −8.39509 + 8.39509i −0.413596 + 0.413596i
\(413\) 3.09394 3.09394i 0.152243 0.152243i
\(414\) −12.9703 + 17.3082i −0.637457 + 0.850652i
\(415\) 0 0
\(416\) 5.66575i 0.277786i
\(417\) 2.25006 + 4.49788i 0.110186 + 0.220262i
\(418\) 0.882769 + 0.882769i 0.0431776 + 0.0431776i
\(419\) 19.4078 0.948133 0.474067 0.880489i \(-0.342786\pi\)
0.474067 + 0.880489i \(0.342786\pi\)
\(420\) 0 0
\(421\) −9.18958 −0.447872 −0.223936 0.974604i \(-0.571891\pi\)
−0.223936 + 0.974604i \(0.571891\pi\)
\(422\) 4.98569 + 4.98569i 0.242700 + 0.242700i
\(423\) 22.4182 3.21176i 1.09001 0.156161i
\(424\) 4.94192i 0.240001i
\(425\) 0 0
\(426\) 7.06009 21.1944i 0.342063 1.02687i
\(427\) 10.6165 10.6165i 0.513769 0.513769i
\(428\) 0.218302 0.218302i 0.0105520 0.0105520i
\(429\) −0.300716 + 0.902751i −0.0145187 + 0.0435852i
\(430\) 0 0
\(431\) 17.0854i 0.822972i −0.911416 0.411486i \(-0.865010\pi\)
0.911416 0.411486i \(-0.134990\pi\)
\(432\) 4.58040 25.2784i 0.220375 1.21621i
\(433\) 20.7996 + 20.7996i 0.999563 + 0.999563i 1.00000 0.000437230i \(-0.000139175\pi\)
−0.000437230 1.00000i \(0.500139\pi\)
\(434\) 13.5826 0.651985
\(435\) 0 0
\(436\) 13.8527 0.663422
\(437\) 3.29894 + 3.29894i 0.157809 + 0.157809i
\(438\) 11.1619 + 22.3126i 0.533335 + 1.06614i
\(439\) 12.3529i 0.589572i −0.955563 0.294786i \(-0.904752\pi\)
0.955563 0.294786i \(-0.0952483\pi\)
\(440\) 0 0
\(441\) −2.40072 1.79904i −0.114320 0.0856685i
\(442\) −4.36479 + 4.36479i −0.207612 + 0.207612i
\(443\) −6.57501 + 6.57501i −0.312388 + 0.312388i −0.845834 0.533446i \(-0.820897\pi\)
0.533446 + 0.845834i \(0.320897\pi\)
\(444\) 22.4563 + 7.48044i 1.06573 + 0.355006i
\(445\) 0 0
\(446\) 12.5997i 0.596611i
\(447\) 4.29696 2.14955i 0.203239 0.101670i
\(448\) −0.828450 0.828450i −0.0391406 0.0391406i
\(449\) −14.2416 −0.672104 −0.336052 0.941843i \(-0.609092\pi\)
−0.336052 + 0.941843i \(0.609092\pi\)
\(450\) 0 0
\(451\) −4.96321 −0.233708
\(452\) 0.684427 + 0.684427i 0.0321927 + 0.0321927i
\(453\) 3.20929 1.60545i 0.150786 0.0754306i
\(454\) 26.5272i 1.24498i
\(455\) 0 0
\(456\) −2.62757 0.875274i −0.123047 0.0409885i
\(457\) −17.6696 + 17.6696i −0.826550 + 0.826550i −0.987038 0.160488i \(-0.948693\pi\)
0.160488 + 0.987038i \(0.448693\pi\)
\(458\) −23.3346 + 23.3346i −1.09036 + 1.09036i
\(459\) 15.8986 11.0208i 0.742081 0.514407i
\(460\) 0 0
\(461\) 21.7105i 1.01116i 0.862780 + 0.505580i \(0.168721\pi\)
−0.862780 + 0.505580i \(0.831279\pi\)
\(462\) −0.830984 1.66114i −0.0386609 0.0772831i
\(463\) −1.05768 1.05768i −0.0491547 0.0491547i 0.682102 0.731257i \(-0.261066\pi\)
−0.731257 + 0.682102i \(0.761066\pi\)
\(464\) −47.3398 −2.19770
\(465\) 0 0
\(466\) 21.7258 1.00643
\(467\) −26.8566 26.8566i −1.24278 1.24278i −0.958844 0.283932i \(-0.908361\pi\)
−0.283932 0.958844i \(-0.591639\pi\)
\(468\) 0.484858 + 3.38434i 0.0224126 + 0.156441i
\(469\) 1.78285i 0.0823242i
\(470\) 0 0
\(471\) −7.18597 + 21.5723i −0.331112 + 0.994000i
\(472\) −4.24949 + 4.24949i −0.195599 + 0.195599i
\(473\) 4.59957 4.59957i 0.211488 0.211488i
\(474\) −3.79362 + 11.3884i −0.174247 + 0.523089i
\(475\) 0 0
\(476\) 4.60354i 0.211003i
\(477\) 1.53081 + 10.6851i 0.0700910 + 0.489239i
\(478\) −7.61027 7.61027i −0.348086 0.348086i
\(479\) 2.38823 0.109121 0.0545605 0.998510i \(-0.482624\pi\)
0.0545605 + 0.998510i \(0.482624\pi\)
\(480\) 0 0
\(481\) 10.1853 0.464409
\(482\) 6.43463 + 6.43463i 0.293090 + 0.293090i
\(483\) −3.10541 6.20772i −0.141301 0.282461i
\(484\) 13.1626i 0.598301i
\(485\) 0 0
\(486\) 1.03617 28.0251i 0.0470016 1.27124i
\(487\) 15.5114 15.5114i 0.702890 0.702890i −0.262140 0.965030i \(-0.584428\pi\)
0.965030 + 0.262140i \(0.0844281\pi\)
\(488\) −14.5817 + 14.5817i −0.660080 + 0.660080i
\(489\) 21.8677 + 7.28436i 0.988890 + 0.329410i
\(490\) 0 0
\(491\) 33.8566i 1.52793i −0.645259 0.763964i \(-0.723251\pi\)
0.645259 0.763964i \(-0.276749\pi\)
\(492\) −15.9489 + 7.97846i −0.719033 + 0.359697i
\(493\) −25.2065 25.2065i −1.13524 1.13524i
\(494\) 1.93025 0.0868462
\(495\) 0 0
\(496\) −37.3271 −1.67604
\(497\) 5.06938 + 5.06938i 0.227393 + 0.227393i
\(498\) −18.5504 + 9.27986i −0.831265 + 0.415840i
\(499\) 3.55804i 0.159280i 0.996824 + 0.0796398i \(0.0253770\pi\)
−0.996824 + 0.0796398i \(0.974623\pi\)
\(500\) 0 0
\(501\) −24.2790 8.08760i −1.08470 0.361327i
\(502\) −33.5306 + 33.5306i −1.49655 + 1.49655i
\(503\) −8.89336 + 8.89336i −0.396535 + 0.396535i −0.877009 0.480474i \(-0.840465\pi\)
0.480474 + 0.877009i \(0.340465\pi\)
\(504\) 3.29736 + 2.47096i 0.146876 + 0.110065i
\(505\) 0 0
\(506\) 4.29747i 0.191046i
\(507\) −9.41558 18.8218i −0.418161 0.835903i
\(508\) −3.24747 3.24747i −0.144083 0.144083i
\(509\) 24.4919 1.08558 0.542791 0.839868i \(-0.317367\pi\)
0.542791 + 0.839868i \(0.317367\pi\)
\(510\) 0 0
\(511\) −8.00658 −0.354190
\(512\) 11.8883 + 11.8883i 0.525395 + 0.525395i
\(513\) −5.95231 1.07855i −0.262801 0.0476191i
\(514\) 32.0083i 1.41182i
\(515\) 0 0
\(516\) 7.38651 22.1743i 0.325173 0.976169i
\(517\) −3.18185 + 3.18185i −0.139938 + 0.139938i
\(518\) −14.0587 + 14.0587i −0.617702 + 0.617702i
\(519\) 13.9624 41.9153i 0.612883 1.83988i
\(520\) 0 0
\(521\) 28.4652i 1.24708i −0.781790 0.623541i \(-0.785693\pi\)
0.781790 0.623541i \(-0.214307\pi\)
\(522\) −51.1557 + 7.32884i −2.23902 + 0.320775i
\(523\) −7.00886 7.00886i −0.306476 0.306476i 0.537065 0.843541i \(-0.319533\pi\)
−0.843541 + 0.537065i \(0.819533\pi\)
\(524\) 20.4377 0.892824
\(525\) 0 0
\(526\) −18.6246 −0.812071
\(527\) −19.8751 19.8751i −0.865773 0.865773i
\(528\) 2.28368 + 4.56507i 0.0993842 + 0.198669i
\(529\) 6.94022i 0.301749i
\(530\) 0 0
\(531\) −7.87168 + 10.5043i −0.341602 + 0.455849i
\(532\) −1.01792 + 1.01792i −0.0441324 + 0.0441324i
\(533\) −5.42625 + 5.42625i −0.235037 + 0.235037i
\(534\) −6.49686 2.16418i −0.281147 0.0936531i
\(535\) 0 0
\(536\) 2.44872i 0.105769i
\(537\) 28.2546 14.1343i 1.21927 0.609942i
\(538\) 9.33825 + 9.33825i 0.402600 + 0.402600i
\(539\) 0.596077 0.0256749
\(540\) 0 0
\(541\) −5.17756 −0.222601 −0.111300 0.993787i \(-0.535502\pi\)
−0.111300 + 0.993787i \(0.535502\pi\)
\(542\) −9.42220 9.42220i −0.404718 0.404718i
\(543\) 7.83876 3.92134i 0.336393 0.168281i
\(544\) 22.8868i 0.981265i
\(545\) 0 0
\(546\) −2.72462 0.907602i −0.116603 0.0388418i
\(547\) −3.24667 + 3.24667i −0.138818 + 0.138818i −0.773101 0.634283i \(-0.781295\pi\)
0.634283 + 0.773101i \(0.281295\pi\)
\(548\) −13.7977 + 13.7977i −0.589408 + 0.589408i
\(549\) −27.0108 + 36.0444i −1.15279 + 1.53834i
\(550\) 0 0
\(551\) 11.1471i 0.474883i
\(552\) 4.26525 + 8.52623i 0.181541 + 0.362901i
\(553\) −2.72394 2.72394i −0.115834 0.115834i
\(554\) 28.2982 1.20228
\(555\) 0 0
\(556\) −3.59050 −0.152271
\(557\) −9.93063 9.93063i −0.420774 0.420774i 0.464696 0.885470i \(-0.346164\pi\)
−0.885470 + 0.464696i \(0.846164\pi\)
\(558\) −40.3359 + 5.77874i −1.70755 + 0.244634i
\(559\) 10.0574i 0.425382i
\(560\) 0 0
\(561\) −1.21475 + 3.64667i −0.0512866 + 0.153962i
\(562\) −21.7688 + 21.7688i −0.918262 + 0.918262i
\(563\) 11.8553 11.8553i 0.499641 0.499641i −0.411685 0.911326i \(-0.635060\pi\)
0.911326 + 0.411685i \(0.135060\pi\)
\(564\) −5.10977 + 15.3395i −0.215160 + 0.645911i
\(565\) 0 0
\(566\) 27.7559i 1.16667i
\(567\) 7.89477 + 4.32118i 0.331549 + 0.181472i
\(568\) −6.96274 6.96274i −0.292150 0.292150i
\(569\) 19.3729 0.812155 0.406077 0.913839i \(-0.366896\pi\)
0.406077 + 0.913839i \(0.366896\pi\)
\(570\) 0 0
\(571\) −10.8864 −0.455581 −0.227791 0.973710i \(-0.573150\pi\)
−0.227791 + 0.973710i \(0.573150\pi\)
\(572\) −0.480343 0.480343i −0.0200841 0.0200841i
\(573\) 3.35855 + 6.71373i 0.140305 + 0.280470i
\(574\) 14.9796i 0.625237i
\(575\) 0 0
\(576\) 2.81270 + 2.10777i 0.117196 + 0.0878235i
\(577\) 3.36353 3.36353i 0.140025 0.140025i −0.633619 0.773645i \(-0.718431\pi\)
0.773645 + 0.633619i \(0.218431\pi\)
\(578\) 3.99433 3.99433i 0.166142 0.166142i
\(579\) −27.4018 9.12785i −1.13878 0.379341i
\(580\) 0 0
\(581\) 6.65658i 0.276162i
\(582\) 30.3404 15.1778i 1.25765 0.629139i
\(583\) −1.51655 1.51655i −0.0628093 0.0628093i
\(584\) 10.9969 0.455057
\(585\) 0 0
\(586\) −39.0773 −1.61427
\(587\) −11.6266 11.6266i −0.479883 0.479883i 0.425211 0.905094i \(-0.360200\pi\)
−0.905094 + 0.425211i \(0.860200\pi\)
\(588\) 1.91545 0.958205i 0.0789919 0.0395157i
\(589\) 8.78942i 0.362162i
\(590\) 0 0
\(591\) −12.4625 4.15140i −0.512639 0.170766i
\(592\) 38.6354 38.6354i 1.58791 1.58791i
\(593\) 18.7263 18.7263i 0.768999 0.768999i −0.208932 0.977930i \(-0.566999\pi\)
0.977930 + 0.208932i \(0.0669986\pi\)
\(594\) 3.17449 + 4.57950i 0.130251 + 0.187899i
\(595\) 0 0
\(596\) 3.43011i 0.140503i
\(597\) 0.603226 + 1.20585i 0.0246884 + 0.0493521i
\(598\) −4.69840 4.69840i −0.192132 0.192132i
\(599\) −27.9518 −1.14208 −0.571041 0.820922i \(-0.693460\pi\)
−0.571041 + 0.820922i \(0.693460\pi\)
\(600\) 0 0
\(601\) 19.9760 0.814837 0.407418 0.913242i \(-0.366429\pi\)
0.407418 + 0.913242i \(0.366429\pi\)
\(602\) 13.8821 + 13.8821i 0.565793 + 0.565793i
\(603\) −0.758517 5.29448i −0.0308892 0.215608i
\(604\) 2.56187i 0.104241i
\(605\) 0 0
\(606\) −12.5696 + 37.7339i −0.510604 + 1.53283i
\(607\) −23.8478 + 23.8478i −0.967953 + 0.967953i −0.999502 0.0315491i \(-0.989956\pi\)
0.0315491 + 0.999502i \(0.489956\pi\)
\(608\) 5.06065 5.06065i 0.205237 0.205237i
\(609\) 5.24136 15.7346i 0.212390 0.637597i
\(610\) 0 0
\(611\) 6.95740i 0.281466i
\(612\) 1.95859 + 13.6710i 0.0791712 + 0.552619i
\(613\) −11.8807 11.8807i −0.479858 0.479858i 0.425228 0.905086i \(-0.360194\pi\)
−0.905086 + 0.425228i \(0.860194\pi\)
\(614\) −39.6588 −1.60050
\(615\) 0 0
\(616\) −0.818705 −0.0329866
\(617\) −7.72276 7.72276i −0.310906 0.310906i 0.534354 0.845261i \(-0.320555\pi\)
−0.845261 + 0.534354i \(0.820555\pi\)
\(618\) 13.3851 + 26.7568i 0.538427 + 1.07632i
\(619\) 7.02322i 0.282287i −0.989989 0.141144i \(-0.954922\pi\)
0.989989 0.141144i \(-0.0450779\pi\)
\(620\) 0 0
\(621\) 11.8632 + 17.1137i 0.476052 + 0.686750i
\(622\) 27.6969 27.6969i 1.11054 1.11054i
\(623\) 1.55395 1.55395i 0.0622577 0.0622577i
\(624\) 7.48770 + 2.49423i 0.299748 + 0.0998493i
\(625\) 0 0
\(626\) 42.6985i 1.70657i
\(627\) 1.07494 0.537738i 0.0429289 0.0214752i
\(628\) −11.4784 11.4784i −0.458037 0.458037i
\(629\) 41.1435 1.64050
\(630\) 0 0
\(631\) −23.6907 −0.943111 −0.471555 0.881836i \(-0.656307\pi\)
−0.471555 + 0.881836i \(0.656307\pi\)
\(632\) 3.74131 + 3.74131i 0.148821 + 0.148821i
\(633\) 6.07102 3.03703i 0.241301 0.120711i
\(634\) 49.5014i 1.96595i
\(635\) 0 0
\(636\) −7.31124 2.43545i −0.289909 0.0965720i
\(637\) 0.651688 0.651688i 0.0258208 0.0258208i
\(638\) 7.26059 7.26059i 0.287450 0.287450i
\(639\) −17.2112 12.8976i −0.680865 0.510223i
\(640\) 0 0
\(641\) 0.574461i 0.0226898i −0.999936 0.0113449i \(-0.996389\pi\)
0.999936 0.0113449i \(-0.00361128\pi\)
\(642\) −0.348059 0.695771i −0.0137368 0.0274599i
\(643\) 4.70272 + 4.70272i 0.185457 + 0.185457i 0.793729 0.608272i \(-0.208137\pi\)
−0.608272 + 0.793729i \(0.708137\pi\)
\(644\) 4.95540 0.195270
\(645\) 0 0
\(646\) 7.79727 0.306779
\(647\) 4.55125 + 4.55125i 0.178928 + 0.178928i 0.790888 0.611960i \(-0.209619\pi\)
−0.611960 + 0.790888i \(0.709619\pi\)
\(648\) −10.8434 5.93509i −0.425968 0.233152i
\(649\) 2.60813i 0.102378i
\(650\) 0 0
\(651\) 4.13277 12.4066i 0.161976 0.486252i
\(652\) −11.6355 + 11.6355i −0.455682 + 0.455682i
\(653\) −18.2705 + 18.2705i −0.714980 + 0.714980i −0.967573 0.252593i \(-0.918717\pi\)
0.252593 + 0.967573i \(0.418717\pi\)
\(654\) 11.0323 33.1189i 0.431395 1.29505i
\(655\) 0 0
\(656\) 41.1664i 1.60728i
\(657\) 23.7770 3.40642i 0.927628 0.132897i
\(658\) −9.60324 9.60324i −0.374373 0.374373i
\(659\) 23.1110 0.900276 0.450138 0.892959i \(-0.351375\pi\)
0.450138 + 0.892959i \(0.351375\pi\)
\(660\) 0 0
\(661\) 16.9566 0.659537 0.329768 0.944062i \(-0.393029\pi\)
0.329768 + 0.944062i \(0.393029\pi\)
\(662\) −25.4969 25.4969i −0.990965 0.990965i
\(663\) 2.65881 + 5.31496i 0.103260 + 0.206416i
\(664\) 9.14274i 0.354807i
\(665\) 0 0
\(666\) 35.7684 47.7310i 1.38600 1.84954i
\(667\) 27.1331 27.1331i 1.05060 1.05060i
\(668\) 12.9186 12.9186i 0.499834 0.499834i
\(669\) −11.5088 3.83370i −0.444955 0.148219i
\(670\) 0 0
\(671\) 8.94951i 0.345492i
\(672\) −9.52280 + 4.76378i −0.367350 + 0.183767i
\(673\) 20.0108 + 20.0108i 0.771359 + 0.771359i 0.978344 0.206985i \(-0.0663653\pi\)
−0.206985 + 0.978344i \(0.566365\pi\)
\(674\) −13.6219 −0.524696
\(675\) 0 0
\(676\) 15.0247 0.577875
\(677\) −9.33392 9.33392i −0.358732 0.358732i 0.504614 0.863345i \(-0.331635\pi\)
−0.863345 + 0.504614i \(0.831635\pi\)
\(678\) 2.18140 1.09125i 0.0837762 0.0419091i
\(679\) 10.8872i 0.417814i
\(680\) 0 0
\(681\) 24.2305 + 8.07143i 0.928513 + 0.309298i
\(682\) 5.72492 5.72492i 0.219219 0.219219i
\(683\) 34.9400 34.9400i 1.33694 1.33694i 0.437939 0.899005i \(-0.355709\pi\)
0.899005 0.437939i \(-0.144291\pi\)
\(684\) 2.58982 3.45597i 0.0990241 0.132142i
\(685\) 0 0
\(686\) 1.79904i 0.0686876i
\(687\) 14.2143 + 28.4143i 0.542308 + 1.08407i
\(688\) −38.1503 38.1503i −1.45447 1.45447i
\(689\) −3.31608 −0.126333
\(690\) 0 0
\(691\) −35.0437 −1.33313 −0.666563 0.745449i \(-0.732235\pi\)
−0.666563 + 0.745449i \(0.732235\pi\)
\(692\) 22.3026 + 22.3026i 0.847818 + 0.847818i
\(693\) −1.77016 + 0.253602i −0.0672427 + 0.00963356i
\(694\) 51.4392i 1.95261i
\(695\) 0 0
\(696\) −7.19895 + 21.6112i −0.272875 + 0.819172i
\(697\) −21.9194 + 21.9194i −0.830255 + 0.830255i
\(698\) 17.9042 17.9042i 0.677686 0.677686i
\(699\) 6.61051 19.8448i 0.250033 0.750598i
\(700\) 0 0
\(701\) 52.2978i 1.97526i 0.156805 + 0.987630i \(0.449881\pi\)
−0.156805 + 0.987630i \(0.550119\pi\)
\(702\) 8.47739 + 1.53609i 0.319959 + 0.0579759i
\(703\) −9.09750 9.09750i −0.343119 0.343119i
\(704\) −0.698367 −0.0263207
\(705\) 0 0
\(706\) 17.9412 0.675227
\(707\) −9.02537 9.02537i −0.339434 0.339434i
\(708\) −4.19262 8.38105i −0.157568 0.314979i
\(709\) 22.2416i 0.835302i −0.908608 0.417651i \(-0.862854\pi\)
0.908608 0.417651i \(-0.137146\pi\)
\(710\) 0 0
\(711\) 9.24814 + 6.93033i 0.346832 + 0.259908i
\(712\) −2.13433 + 2.13433i −0.0799875 + 0.0799875i
\(713\) 21.3942 21.3942i 0.801219 0.801219i
\(714\) −11.0061 3.66626i −0.411894 0.137206i
\(715\) 0 0
\(716\) 22.5546i 0.842906i
\(717\) −9.26695 + 4.63579i −0.346080 + 0.173127i
\(718\) 20.1085 + 20.1085i 0.750443 + 0.750443i
\(719\) −40.5531 −1.51238 −0.756188 0.654354i \(-0.772941\pi\)
−0.756188 + 0.654354i \(0.772941\pi\)
\(720\) 0 0
\(721\) −9.60132 −0.357572
\(722\) 22.4460 + 22.4460i 0.835355 + 0.835355i
\(723\) 7.83539 3.91965i 0.291401 0.145773i
\(724\) 6.25741i 0.232555i
\(725\) 0 0
\(726\) 31.4691 + 10.4827i 1.16793 + 0.389050i
\(727\) 25.9411 25.9411i 0.962103 0.962103i −0.0372050 0.999308i \(-0.511845\pi\)
0.999308 + 0.0372050i \(0.0118454\pi\)
\(728\) −0.895086 + 0.895086i −0.0331741 + 0.0331741i
\(729\) −25.2834 9.47366i −0.936422 0.350876i
\(730\) 0 0
\(731\) 40.6268i 1.50264i
\(732\) −14.3865 28.7586i −0.531740 1.06295i
\(733\) 20.5005 + 20.5005i 0.757205 + 0.757205i 0.975813 0.218608i \(-0.0701515\pi\)
−0.218608 + 0.975813i \(0.570152\pi\)
\(734\) 34.3199 1.26677
\(735\) 0 0
\(736\) −24.6361 −0.908100
\(737\) 0.751453 + 0.751453i 0.0276801 + 0.0276801i
\(738\) 6.37312 + 44.4847i 0.234598 + 1.63750i
\(739\) 11.5622i 0.425323i 0.977126 + 0.212661i \(0.0682131\pi\)
−0.977126 + 0.212661i \(0.931787\pi\)
\(740\) 0 0
\(741\) 0.587318 1.76313i 0.0215757 0.0647702i
\(742\) 4.57716 4.57716i 0.168033 0.168033i
\(743\) −24.6182 + 24.6182i −0.903153 + 0.903153i −0.995708 0.0925542i \(-0.970497\pi\)
0.0925542 + 0.995708i \(0.470497\pi\)
\(744\) −5.67632 + 17.0403i −0.208104 + 0.624728i
\(745\) 0 0
\(746\) 37.5667i 1.37541i
\(747\) 2.83206 + 19.7679i 0.103620 + 0.723270i
\(748\) −1.94035 1.94035i −0.0709461 0.0709461i
\(749\) 0.249668 0.00912268
\(750\) 0 0
\(751\) 40.1876 1.46647 0.733233 0.679977i \(-0.238010\pi\)
0.733233 + 0.679977i \(0.238010\pi\)
\(752\) 26.3912 + 26.3912i 0.962389 + 0.962389i
\(753\) 20.4252 + 40.8299i 0.744334 + 1.48792i
\(754\) 15.8759i 0.578167i
\(755\) 0 0
\(756\) −5.28061 + 3.66050i −0.192054 + 0.133131i
\(757\) 4.46261 4.46261i 0.162196 0.162196i −0.621343 0.783539i \(-0.713412\pi\)
0.783539 + 0.621343i \(0.213412\pi\)
\(758\) 40.5895 40.5895i 1.47428 1.47428i
\(759\) −3.92539 1.30759i −0.142483 0.0474626i
\(760\) 0 0
\(761\) 27.3558i 0.991646i −0.868424 0.495823i \(-0.834867\pi\)
0.868424 0.495823i \(-0.165133\pi\)
\(762\) −10.3503 + 5.17775i −0.374953 + 0.187570i
\(763\) 7.92153 + 7.92153i 0.286779 + 0.286779i
\(764\) −5.35934 −0.193894
\(765\) 0 0
\(766\) −26.9232 −0.972776
\(767\) −2.85145 2.85145i −0.102960 0.102960i
\(768\) 32.0196 16.0178i 1.15541 0.577994i
\(769\) 10.3542i 0.373382i 0.982419 + 0.186691i \(0.0597762\pi\)
−0.982419 + 0.186691i \(0.940224\pi\)
\(770\) 0 0
\(771\) 29.2370 + 9.73916i 1.05294 + 0.350747i
\(772\) 14.5802 14.5802i 0.524752 0.524752i
\(773\) −1.59901 + 1.59901i −0.0575125 + 0.0575125i −0.735278 0.677766i \(-0.762948\pi\)
0.677766 + 0.735278i \(0.262948\pi\)
\(774\) −47.1316 35.3192i −1.69411 1.26952i
\(775\) 0 0
\(776\) 14.9535i 0.536800i
\(777\) 8.56382 + 17.1191i 0.307225 + 0.614143i
\(778\) −28.9727 28.9727i −1.03872 1.03872i
\(779\) 9.69347 0.347305
\(780\) 0 0
\(781\) 4.27339 0.152914
\(782\) −18.9792 18.9792i −0.678696 0.678696i
\(783\) −8.87084 + 48.9565i −0.317018 + 1.74956i
\(784\) 4.94405i 0.176573i
\(785\) 0 0
\(786\) 16.2766 48.8623i 0.580566 1.74286i
\(787\) −6.16607 + 6.16607i −0.219797 + 0.219797i −0.808413 0.588616i \(-0.799673\pi\)
0.588616 + 0.808413i \(0.299673\pi\)
\(788\) 6.63114 6.63114i 0.236225 0.236225i
\(789\) −5.66691 + 17.0121i −0.201747 + 0.605646i
\(790\) 0 0
\(791\) 0.782768i 0.0278320i
\(792\) 2.43129 0.348320i 0.0863922 0.0123770i
\(793\) −9.78445 9.78445i −0.347456 0.347456i
\(794\) 37.8767 1.34419
\(795\) 0 0
\(796\) −0.962586 −0.0341180
\(797\) 24.9323 + 24.9323i 0.883148 + 0.883148i 0.993853 0.110705i \(-0.0353109\pi\)
−0.110705 + 0.993853i \(0.535311\pi\)
\(798\) 1.62296 + 3.24431i 0.0574523 + 0.114847i
\(799\) 28.1044i 0.994263i
\(800\) 0 0
\(801\) −3.95360 + 5.27587i −0.139694 + 0.186414i
\(802\) −19.1696 + 19.1696i −0.676901 + 0.676901i
\(803\) −3.37469 + 3.37469i −0.119090 + 0.119090i
\(804\) 3.62272 + 1.20677i 0.127763 + 0.0425594i
\(805\) 0 0
\(806\) 12.5181i 0.440930i
\(807\) 11.3711 5.68839i 0.400281 0.200241i
\(808\) 12.3962 + 12.3962i 0.436099 + 0.436099i
\(809\) −21.2421 −0.746831 −0.373416 0.927664i \(-0.621813\pi\)
−0.373416 + 0.927664i \(0.621813\pi\)
\(810\) 0 0
\(811\) −20.9414 −0.735351 −0.367675 0.929954i \(-0.619846\pi\)
−0.367675 + 0.929954i \(0.619846\pi\)
\(812\) 8.37217 + 8.37217i 0.293806 + 0.293806i
\(813\) −11.4733 + 5.73952i −0.402386 + 0.201294i
\(814\) 11.8512i 0.415383i
\(815\) 0 0
\(816\) 30.2466 + 10.0755i 1.05884 + 0.352712i
\(817\) −8.98326 + 8.98326i −0.314284 + 0.314284i
\(818\) 32.2300 32.2300i 1.12689 1.12689i
\(819\) −1.65804 + 2.21257i −0.0579367 + 0.0773133i
\(820\) 0 0
\(821\) 13.9737i 0.487684i −0.969815 0.243842i \(-0.921592\pi\)
0.969815 0.243842i \(-0.0784078\pi\)
\(822\) 21.9990 + 43.9759i 0.767302 + 1.53384i
\(823\) 9.64020 + 9.64020i 0.336036 + 0.336036i 0.854873 0.518837i \(-0.173635\pi\)
−0.518837 + 0.854873i \(0.673635\pi\)
\(824\) 13.1873 0.459402
\(825\) 0 0
\(826\) 7.87168 0.273891
\(827\) −11.2829 11.2829i −0.392345 0.392345i 0.483178 0.875522i \(-0.339482\pi\)
−0.875522 + 0.483178i \(0.839482\pi\)
\(828\) −14.7160 + 2.10829i −0.511415 + 0.0732681i
\(829\) 18.8442i 0.654485i −0.944940 0.327242i \(-0.893881\pi\)
0.944940 0.327242i \(-0.106119\pi\)
\(830\) 0 0
\(831\) 8.61031 25.8482i 0.298688 0.896663i
\(832\) −0.763521 + 0.763521i −0.0264703 + 0.0264703i
\(833\) 2.63250 2.63250i 0.0912106 0.0912106i
\(834\) −2.85947 + 8.58414i −0.0990154 + 0.297244i
\(835\) 0 0
\(836\) 0.858086i 0.0296775i
\(837\) −6.99459 + 38.6019i −0.241768 + 1.33428i
\(838\) 24.6889 + 24.6889i 0.852865 + 0.852865i
\(839\) −46.9582 −1.62118 −0.810588 0.585617i \(-0.800852\pi\)
−0.810588 + 0.585617i \(0.800852\pi\)
\(840\) 0 0
\(841\) 62.6827 2.16147
\(842\) −11.6902 11.6902i −0.402870 0.402870i
\(843\) 13.2605 + 26.5076i 0.456714 + 0.912972i
\(844\) 4.84628i 0.166816i
\(845\) 0 0
\(846\) 32.6042 + 24.4328i 1.12096 + 0.840017i
\(847\) −7.52693 + 7.52693i −0.258629 + 0.258629i
\(848\) −12.5788 + 12.5788i −0.431957 + 0.431957i
\(849\) −25.3527 8.44528i −0.870104 0.289841i
\(850\) 0 0
\(851\) 44.2882i 1.51818i
\(852\) 13.7322 6.86955i 0.470459 0.235347i
\(853\) −26.8180 26.8180i −0.918232 0.918232i 0.0786690 0.996901i \(-0.474933\pi\)
−0.996901 + 0.0786690i \(0.974933\pi\)
\(854\) 27.0108 0.924290
\(855\) 0 0
\(856\) −0.342917 −0.0117207
\(857\) 24.3943 + 24.3943i 0.833293 + 0.833293i 0.987966 0.154673i \(-0.0494324\pi\)
−0.154673 + 0.987966i \(0.549432\pi\)
\(858\) −1.53095 + 0.765856i −0.0522657 + 0.0261459i
\(859\) 1.97722i 0.0674617i 0.999431 + 0.0337309i \(0.0107389\pi\)
−0.999431 + 0.0337309i \(0.989261\pi\)
\(860\) 0 0
\(861\) −13.6827 4.55785i −0.466304 0.155331i
\(862\) 21.7345 21.7345i 0.740280 0.740280i
\(863\) −17.7690 + 17.7690i −0.604863 + 0.604863i −0.941599 0.336736i \(-0.890677\pi\)
0.336736 + 0.941599i \(0.390677\pi\)
\(864\) 26.2529 18.1984i 0.893142 0.619122i
\(865\) 0 0
\(866\) 52.9188i 1.79825i
\(867\) −2.43314 4.86385i −0.0826339 0.165185i
\(868\) 6.60140 + 6.60140i 0.224066 + 0.224066i
\(869\) −2.29623 −0.0778943
\(870\) 0 0
\(871\) 1.64312 0.0556749
\(872\) −10.8801 10.8801i −0.368448 0.368448i
\(873\) −4.63200 32.3316i −0.156770 1.09426i
\(874\) 8.39324i 0.283905i
\(875\) 0 0
\(876\) −5.41946 + 16.2692i −0.183107 + 0.549686i
\(877\) 30.0684 30.0684i 1.01534 1.01534i 0.0154576 0.999881i \(-0.495079\pi\)
0.999881 0.0154576i \(-0.00492051\pi\)
\(878\) 15.7143 15.7143i 0.530331 0.530331i
\(879\) −11.8901 + 35.6940i −0.401042 + 1.20393i
\(880\) 0 0
\(881\) 34.7319i 1.17015i −0.810980 0.585074i \(-0.801066\pi\)
0.810980 0.585074i \(-0.198934\pi\)
\(882\) −0.765406 5.34257i −0.0257726 0.179894i
\(883\) −0.424655 0.424655i −0.0142908 0.0142908i 0.699925 0.714216i \(-0.253217\pi\)
−0.714216 + 0.699925i \(0.753217\pi\)
\(884\) −4.24274 −0.142699
\(885\) 0 0
\(886\) −16.7283 −0.561999
\(887\) 39.8779 + 39.8779i 1.33897 + 1.33897i 0.897059 + 0.441912i \(0.145700\pi\)
0.441912 + 0.897059i \(0.354300\pi\)
\(888\) −11.7623 23.5129i −0.394717 0.789040i
\(889\) 3.71408i 0.124566i
\(890\) 0 0
\(891\) 5.14890 1.50624i 0.172495 0.0504608i
\(892\) 6.12368 6.12368i 0.205036 0.205036i
\(893\) 6.21435 6.21435i 0.207955 0.207955i
\(894\) 8.20069 + 2.73174i 0.274272 + 0.0913630i
\(895\) 0 0
\(896\) 10.1874i 0.340336i
\(897\) −5.72119 + 2.86203i −0.191025 + 0.0955603i
\(898\) −18.1170 18.1170i −0.604571 0.604571i
\(899\) 72.2912 2.41105
\(900\) 0 0
\(901\) −13.3953 −0.446263
\(902\) −6.31376 6.31376i −0.210225 0.210225i
\(903\) 16.9041 8.45628i 0.562533 0.281407i
\(904\) 1.07512i 0.0357580i
\(905\) 0 0
\(906\) 6.12490 + 2.04027i 0.203486 + 0.0677834i
\(907\) −12.8493 + 12.8493i −0.426653 + 0.426653i −0.887487 0.460834i \(-0.847550\pi\)
0.460834 + 0.887487i \(0.347550\pi\)
\(908\) −12.8927 + 12.8927i −0.427860 + 0.427860i
\(909\) 30.6423 + 22.9626i 1.01634 + 0.761621i
\(910\) 0 0
\(911\) 15.5488i 0.515156i 0.966258 + 0.257578i \(0.0829244\pi\)
−0.966258 + 0.257578i \(0.917076\pi\)
\(912\) −4.46017 8.91587i −0.147691 0.295234i
\(913\) −2.80568 2.80568i −0.0928546 0.0928546i
\(914\) −44.9555 −1.48700
\(915\) 0 0
\(916\) −22.6822 −0.749440
\(917\) 11.6871 + 11.6871i 0.385943 + 0.385943i
\(918\) 34.2445 + 6.20504i 1.13024 + 0.204797i
\(919\) 53.8863i 1.77755i 0.458348 + 0.888773i \(0.348441\pi\)
−0.458348 + 0.888773i \(0.651559\pi\)
\(920\) 0 0
\(921\) −12.0670 + 36.2251i −0.397621 + 1.19366i
\(922\) −27.6182 + 27.6182i −0.909558 + 0.909558i
\(923\) 4.67207 4.67207i 0.153783 0.153783i
\(924\) 0.403470 1.21122i 0.0132732 0.0398462i
\(925\) 0 0
\(926\) 2.69098i 0.0884313i
\(927\) 28.5128 4.08491i 0.936485 0.134166i
\(928\) −41.6228 41.6228i −1.36634 1.36634i
\(929\) 14.9417 0.490220 0.245110 0.969495i \(-0.421176\pi\)
0.245110 + 0.969495i \(0.421176\pi\)
\(930\) 0 0
\(931\) −1.16418 −0.0381544
\(932\) 10.5592 + 10.5592i 0.345877 + 0.345877i
\(933\) −16.8715 33.7262i −0.552350 1.10415i
\(934\) 68.3293i 2.23580i
\(935\) 0 0
\(936\) 2.27730 3.03894i 0.0744359 0.0993307i
\(937\) −13.0089 + 13.0089i −0.424981 + 0.424981i −0.886915 0.461933i \(-0.847156\pi\)
0.461933 + 0.886915i \(0.347156\pi\)
\(938\) −2.26798 + 2.26798i −0.0740523 + 0.0740523i
\(939\) 39.0016 + 12.9919i 1.27277 + 0.423974i
\(940\) 0 0
\(941\) 3.15194i 0.102750i −0.998679 0.0513751i \(-0.983640\pi\)
0.998679 0.0513751i \(-0.0163604\pi\)
\(942\) −36.5838 + 18.3010i −1.19196 + 0.596280i
\(943\) −23.5947 23.5947i −0.768350 0.768350i
\(944\) −21.6326 −0.704082
\(945\) 0 0
\(946\) 11.7023 0.380476
\(947\) −14.6574 14.6574i −0.476302 0.476302i 0.427645 0.903947i \(-0.359343\pi\)
−0.903947 + 0.427645i \(0.859343\pi\)
\(948\) −7.37878 + 3.69123i −0.239652 + 0.119886i
\(949\) 7.37907i 0.239535i
\(950\) 0 0
\(951\) 45.2156 + 15.0618i 1.46622 + 0.488412i
\(952\) −3.61571 + 3.61571i −0.117186 + 0.117186i
\(953\) 9.88130 9.88130i 0.320087 0.320087i −0.528714 0.848800i \(-0.677325\pi\)
0.848800 + 0.528714i \(0.177325\pi\)
\(954\) −11.6453 + 15.5401i −0.377032 + 0.503128i
\(955\) 0 0
\(956\) 7.39748i 0.239252i
\(957\) −4.42278 8.84114i −0.142968 0.285794i
\(958\) 3.03810 + 3.03810i 0.0981565 + 0.0981565i
\(959\) −15.7802 −0.509569
\(960\) 0 0
\(961\) 26.0011 0.838744
\(962\) 12.9568 + 12.9568i 0.417745 + 0.417745i
\(963\) −0.741435 + 0.106222i −0.0238924 + 0.00342296i
\(964\) 6.25471i 0.201451i
\(965\) 0 0
\(966\) 3.94648 11.8474i 0.126976 0.381182i
\(967\) −1.97663 + 1.97663i −0.0635642 + 0.0635642i −0.738174 0.674610i \(-0.764312\pi\)
0.674610 + 0.738174i \(0.264312\pi\)
\(968\) 10.3382 10.3382i 0.332281 0.332281i
\(969\) 2.37248 7.12218i 0.0762149 0.228797i
\(970\) 0 0
\(971\) 3.57758i 0.114810i 0.998351 + 0.0574051i \(0.0182827\pi\)
−0.998351 + 0.0574051i \(0.981717\pi\)
\(972\) 14.1243 13.1171i 0.453038 0.420733i
\(973\) −2.05320 2.05320i −0.0658224 0.0658224i
\(974\) 39.4646 1.26453
\(975\) 0 0
\(976\) −74.2300 −2.37604
\(977\) −23.9909 23.9909i −0.767537 0.767537i 0.210135 0.977672i \(-0.432610\pi\)
−0.977672 + 0.210135i \(0.932610\pi\)
\(978\) 18.5516 + 37.0847i 0.593215 + 1.18584i
\(979\) 1.30995i 0.0418662i
\(980\) 0 0
\(981\) −26.8946 20.1542i −0.858679 0.643473i
\(982\) 43.0694 43.0694i 1.37440 1.37440i
\(983\) −24.6787 + 24.6787i −0.787127 + 0.787127i −0.981022 0.193895i \(-0.937888\pi\)
0.193895 + 0.981022i \(0.437888\pi\)
\(984\) 18.7930 + 6.26016i 0.599099 + 0.199567i
\(985\) 0 0
\(986\) 64.1309i 2.04234i
\(987\) −11.6938 + 5.84980i −0.372216 + 0.186201i
\(988\) 0.938141 + 0.938141i 0.0298462 + 0.0298462i
\(989\) 43.7320 1.39060
\(990\) 0 0
\(991\) −25.6595 −0.815102 −0.407551 0.913182i \(-0.633617\pi\)
−0.407551 + 0.913182i \(0.633617\pi\)
\(992\) −32.8193 32.8193i −1.04201 1.04201i
\(993\) −31.0473 + 15.5314i −0.985256 + 0.492875i
\(994\) 12.8976i 0.409089i
\(995\) 0 0
\(996\) −13.5261 4.50568i −0.428590 0.142768i
\(997\) −17.2215 + 17.2215i −0.545409 + 0.545409i −0.925109 0.379701i \(-0.876027\pi\)
0.379701 + 0.925109i \(0.376027\pi\)
\(998\) −4.52623 + 4.52623i −0.143275 + 0.143275i
\(999\) −32.7151 47.1946i −1.03506 1.49317i
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 525.2.j.c.218.14 yes 32
3.2 odd 2 inner 525.2.j.c.218.4 yes 32
5.2 odd 4 inner 525.2.j.c.407.4 yes 32
5.3 odd 4 inner 525.2.j.c.407.13 yes 32
5.4 even 2 inner 525.2.j.c.218.3 32
15.2 even 4 inner 525.2.j.c.407.14 yes 32
15.8 even 4 inner 525.2.j.c.407.3 yes 32
15.14 odd 2 inner 525.2.j.c.218.13 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.j.c.218.3 32 5.4 even 2 inner
525.2.j.c.218.4 yes 32 3.2 odd 2 inner
525.2.j.c.218.13 yes 32 15.14 odd 2 inner
525.2.j.c.218.14 yes 32 1.1 even 1 trivial
525.2.j.c.407.3 yes 32 15.8 even 4 inner
525.2.j.c.407.4 yes 32 5.2 odd 4 inner
525.2.j.c.407.13 yes 32 5.3 odd 4 inner
525.2.j.c.407.14 yes 32 15.2 even 4 inner