Properties

Label 375.2.i.d.199.6
Level $375$
Weight $2$
Character 375.199
Analytic conductor $2.994$
Analytic rank $0$
Dimension $24$
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] = [375,2,Mod(49,375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(375, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("375.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.i (of order \(10\), 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: \(2.99439007580\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 199.6
Character \(\chi\) \(=\) 375.199
Dual form 375.2.i.d.49.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26995 + 1.74793i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.824463 + 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} +3.16056i q^{7} +(-1.37265 + 0.446002i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(1.26995 + 1.74793i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.824463 + 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} +3.16056i q^{7} +(-1.37265 + 0.446002i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.24455 + 0.904220i) q^{11} +(1.56822 - 2.15847i) q^{12} +(-3.08084 + 4.24041i) q^{13} +(-5.52444 + 4.01374i) q^{14} +(1.79417 + 1.30354i) q^{16} +(1.22751 - 0.398843i) q^{17} +2.16056i q^{18} +(-1.68287 - 5.17933i) q^{19} +(0.976667 - 3.00587i) q^{21} +(-3.16103 - 1.02708i) q^{22} +(3.78677 + 5.21204i) q^{23} +1.44329 q^{24} -11.3244 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-8.01972 - 2.60577i) q^{28} +(0.730396 - 2.24793i) q^{29} +(-1.37989 - 4.24687i) q^{31} +7.67809i q^{32} +(1.46306 - 0.475377i) q^{33} +(2.25602 + 1.63910i) q^{34} +(-2.15847 + 1.56822i) q^{36} +(3.50174 - 4.81973i) q^{37} +(6.91596 - 9.51901i) q^{38} +(4.24041 - 3.08084i) q^{39} +(6.90269 + 5.01510i) q^{41} +(6.49436 - 2.11015i) q^{42} -8.48426i q^{43} +(-1.26831 - 3.90347i) q^{44} +(-4.30129 + 13.2380i) q^{46} +(-0.716212 - 0.232712i) q^{47} +(-1.30354 - 1.79417i) q^{48} -2.98914 q^{49} -1.29068 q^{51} +(-8.21974 - 11.3135i) q^{52} +(9.27271 + 3.01289i) q^{53} +(0.667650 - 2.05481i) q^{54} +(-1.40962 - 4.33836i) q^{56} +5.44587i q^{57} +(4.85678 - 1.57806i) q^{58} +(3.32724 + 2.41738i) q^{59} +(8.65159 - 6.28574i) q^{61} +(5.67084 - 7.80525i) q^{62} +(-1.85773 + 2.55695i) q^{63} +(-9.83243 + 7.14368i) q^{64} +(2.68893 + 1.95362i) q^{66} +(-1.80572 + 0.586713i) q^{67} +3.44357i q^{68} +(-1.99082 - 6.12712i) q^{69} +(-0.0219023 + 0.0674084i) q^{71} +(-1.37265 - 0.446002i) q^{72} +(-2.35774 - 3.24515i) q^{73} +12.8716 q^{74} +14.5297 q^{76} +(-2.85784 - 3.93348i) q^{77} +(10.7702 + 3.49944i) q^{78} +(-0.500141 + 1.53928i) q^{79} +(0.309017 + 0.951057i) q^{81} +18.4343i q^{82} +(-12.5053 + 4.06322i) q^{83} +(6.82198 + 4.95646i) q^{84} +(14.8299 - 10.7745i) q^{86} +(-1.38930 + 1.91220i) q^{87} +(1.30506 - 1.79626i) q^{88} +(5.88638 - 4.27671i) q^{89} +(-13.4021 - 9.73718i) q^{91} +(-16.3473 + 5.31155i) q^{92} +4.46542i q^{93} +(-0.502787 - 1.54742i) q^{94} +(2.37266 - 7.30230i) q^{96} +(-9.69499 - 3.15009i) q^{97} +(-3.79604 - 5.22480i) q^{98} -1.53835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26995 + 1.74793i 0.897987 + 1.23597i 0.971106 + 0.238650i \(0.0767048\pi\)
−0.0731189 + 0.997323i \(0.523295\pi\)
\(3\) −0.951057 0.309017i −0.549093 0.178411i
\(4\) −0.824463 + 2.53744i −0.412232 + 1.26872i
\(5\) 0 0
\(6\) −0.667650 2.05481i −0.272567 0.838875i
\(7\) 3.16056i 1.19458i 0.802026 + 0.597290i \(0.203756\pi\)
−0.802026 + 0.597290i \(0.796244\pi\)
\(8\) −1.37265 + 0.446002i −0.485307 + 0.157686i
\(9\) 0.809017 + 0.587785i 0.269672 + 0.195928i
\(10\) 0 0
\(11\) −1.24455 + 0.904220i −0.375247 + 0.272633i −0.759383 0.650644i \(-0.774499\pi\)
0.384137 + 0.923276i \(0.374499\pi\)
\(12\) 1.56822 2.15847i 0.452707 0.623097i
\(13\) −3.08084 + 4.24041i −0.854471 + 1.17608i 0.128389 + 0.991724i \(0.459019\pi\)
−0.982860 + 0.184355i \(0.940981\pi\)
\(14\) −5.52444 + 4.01374i −1.47647 + 1.07272i
\(15\) 0 0
\(16\) 1.79417 + 1.30354i 0.448542 + 0.325885i
\(17\) 1.22751 0.398843i 0.297716 0.0967337i −0.156351 0.987702i \(-0.549973\pi\)
0.454066 + 0.890968i \(0.349973\pi\)
\(18\) 2.16056i 0.509249i
\(19\) −1.68287 5.17933i −0.386076 1.18822i −0.935696 0.352806i \(-0.885228\pi\)
0.549620 0.835415i \(-0.314772\pi\)
\(20\) 0 0
\(21\) 0.976667 3.00587i 0.213126 0.655935i
\(22\) −3.16103 1.02708i −0.673933 0.218974i
\(23\) 3.78677 + 5.21204i 0.789596 + 1.08679i 0.994158 + 0.107932i \(0.0344230\pi\)
−0.204562 + 0.978854i \(0.565577\pi\)
\(24\) 1.44329 0.294611
\(25\) 0 0
\(26\) −11.3244 −2.22090
\(27\) −0.587785 0.809017i −0.113119 0.155695i
\(28\) −8.01972 2.60577i −1.51558 0.492443i
\(29\) 0.730396 2.24793i 0.135631 0.417430i −0.860056 0.510199i \(-0.829572\pi\)
0.995688 + 0.0927690i \(0.0295718\pi\)
\(30\) 0 0
\(31\) −1.37989 4.24687i −0.247836 0.762760i −0.995157 0.0982974i \(-0.968660\pi\)
0.747321 0.664463i \(-0.231340\pi\)
\(32\) 7.67809i 1.35731i
\(33\) 1.46306 0.475377i 0.254686 0.0827525i
\(34\) 2.25602 + 1.63910i 0.386905 + 0.281103i
\(35\) 0 0
\(36\) −2.15847 + 1.56822i −0.359745 + 0.261370i
\(37\) 3.50174 4.81973i 0.575682 0.792358i −0.417532 0.908662i \(-0.637105\pi\)
0.993214 + 0.116304i \(0.0371048\pi\)
\(38\) 6.91596 9.51901i 1.12192 1.54419i
\(39\) 4.24041 3.08084i 0.679009 0.493329i
\(40\) 0 0
\(41\) 6.90269 + 5.01510i 1.07802 + 0.783227i 0.977336 0.211692i \(-0.0678974\pi\)
0.100683 + 0.994919i \(0.467897\pi\)
\(42\) 6.49436 2.11015i 1.00210 0.325603i
\(43\) 8.48426i 1.29384i −0.762559 0.646919i \(-0.776057\pi\)
0.762559 0.646919i \(-0.223943\pi\)
\(44\) −1.26831 3.90347i −0.191206 0.588470i
\(45\) 0 0
\(46\) −4.30129 + 13.2380i −0.634191 + 1.95184i
\(47\) −0.716212 0.232712i −0.104470 0.0339445i 0.256315 0.966593i \(-0.417491\pi\)
−0.360786 + 0.932649i \(0.617491\pi\)
\(48\) −1.30354 1.79417i −0.188150 0.258966i
\(49\) −2.98914 −0.427020
\(50\) 0 0
\(51\) −1.29068 −0.180732
\(52\) −8.21974 11.3135i −1.13987 1.56890i
\(53\) 9.27271 + 3.01289i 1.27371 + 0.413852i 0.866359 0.499422i \(-0.166454\pi\)
0.407346 + 0.913274i \(0.366454\pi\)
\(54\) 0.667650 2.05481i 0.0908556 0.279625i
\(55\) 0 0
\(56\) −1.40962 4.33836i −0.188368 0.579737i
\(57\) 5.44587i 0.721324i
\(58\) 4.85678 1.57806i 0.637727 0.207210i
\(59\) 3.32724 + 2.41738i 0.433170 + 0.314717i 0.782915 0.622128i \(-0.213732\pi\)
−0.349745 + 0.936845i \(0.613732\pi\)
\(60\) 0 0
\(61\) 8.65159 6.28574i 1.10772 0.804807i 0.125419 0.992104i \(-0.459973\pi\)
0.982303 + 0.187297i \(0.0599726\pi\)
\(62\) 5.67084 7.80525i 0.720198 0.991267i
\(63\) −1.85773 + 2.55695i −0.234052 + 0.322145i
\(64\) −9.83243 + 7.14368i −1.22905 + 0.892960i
\(65\) 0 0
\(66\) 2.68893 + 1.95362i 0.330984 + 0.240474i
\(67\) −1.80572 + 0.586713i −0.220604 + 0.0716785i −0.417233 0.908799i \(-0.637000\pi\)
0.196630 + 0.980478i \(0.437000\pi\)
\(68\) 3.44357i 0.417594i
\(69\) −1.99082 6.12712i −0.239667 0.737619i
\(70\) 0 0
\(71\) −0.0219023 + 0.0674084i −0.00259933 + 0.00799990i −0.952348 0.305014i \(-0.901339\pi\)
0.949748 + 0.313014i \(0.101339\pi\)
\(72\) −1.37265 0.446002i −0.161769 0.0525619i
\(73\) −2.35774 3.24515i −0.275952 0.379816i 0.648436 0.761270i \(-0.275424\pi\)
−0.924388 + 0.381454i \(0.875424\pi\)
\(74\) 12.8716 1.49629
\(75\) 0 0
\(76\) 14.5297 1.66667
\(77\) −2.85784 3.93348i −0.325681 0.448262i
\(78\) 10.7702 + 3.49944i 1.21948 + 0.396234i
\(79\) −0.500141 + 1.53928i −0.0562703 + 0.173182i −0.975242 0.221143i \(-0.929021\pi\)
0.918971 + 0.394325i \(0.129021\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 18.4343i 2.03573i
\(83\) −12.5053 + 4.06322i −1.37263 + 0.445996i −0.900241 0.435392i \(-0.856610\pi\)
−0.472393 + 0.881388i \(0.656610\pi\)
\(84\) 6.82198 + 4.95646i 0.744339 + 0.540794i
\(85\) 0 0
\(86\) 14.8299 10.7745i 1.59915 1.16185i
\(87\) −1.38930 + 1.91220i −0.148948 + 0.205010i
\(88\) 1.30506 1.79626i 0.139119 0.191481i
\(89\) 5.88638 4.27671i 0.623955 0.453330i −0.230345 0.973109i \(-0.573986\pi\)
0.854301 + 0.519779i \(0.173986\pi\)
\(90\) 0 0
\(91\) −13.4021 9.73718i −1.40492 1.02073i
\(92\) −16.3473 + 5.31155i −1.70432 + 0.553768i
\(93\) 4.46542i 0.463043i
\(94\) −0.502787 1.54742i −0.0518585 0.159604i
\(95\) 0 0
\(96\) 2.37266 7.30230i 0.242159 0.745288i
\(97\) −9.69499 3.15009i −0.984377 0.319843i −0.227771 0.973715i \(-0.573144\pi\)
−0.756606 + 0.653871i \(0.773144\pi\)
\(98\) −3.79604 5.22480i −0.383458 0.527785i
\(99\) −1.53835 −0.154610
\(100\) 0 0
\(101\) 1.08759 0.108219 0.0541096 0.998535i \(-0.482768\pi\)
0.0541096 + 0.998535i \(0.482768\pi\)
\(102\) −1.63910 2.25602i −0.162295 0.223380i
\(103\) −4.69590 1.52579i −0.462701 0.150341i 0.0683845 0.997659i \(-0.478216\pi\)
−0.531085 + 0.847319i \(0.678216\pi\)
\(104\) 2.33769 7.19468i 0.229230 0.705497i
\(105\) 0 0
\(106\) 6.50952 + 20.0343i 0.632261 + 1.94590i
\(107\) 15.3059i 1.47967i −0.672786 0.739837i \(-0.734902\pi\)
0.672786 0.739837i \(-0.265098\pi\)
\(108\) 2.53744 0.824463i 0.244165 0.0793340i
\(109\) 5.38724 + 3.91406i 0.516004 + 0.374899i 0.815097 0.579325i \(-0.196684\pi\)
−0.299092 + 0.954224i \(0.596684\pi\)
\(110\) 0 0
\(111\) −4.81973 + 3.50174i −0.457468 + 0.332370i
\(112\) −4.11991 + 5.67058i −0.389295 + 0.535819i
\(113\) −5.27328 + 7.25804i −0.496068 + 0.682779i −0.981493 0.191499i \(-0.938665\pi\)
0.485425 + 0.874278i \(0.338665\pi\)
\(114\) −9.51901 + 6.91596i −0.891537 + 0.647739i
\(115\) 0 0
\(116\) 5.10179 + 3.70667i 0.473689 + 0.344155i
\(117\) −4.98490 + 1.61969i −0.460854 + 0.149741i
\(118\) 8.88573i 0.817998i
\(119\) 1.26057 + 3.87963i 0.115556 + 0.355645i
\(120\) 0 0
\(121\) −2.66789 + 8.21092i −0.242536 + 0.746448i
\(122\) 21.9741 + 7.13981i 1.98944 + 0.646408i
\(123\) −5.01510 6.90269i −0.452196 0.622395i
\(124\) 11.9138 1.06989
\(125\) 0 0
\(126\) −6.82858 −0.608338
\(127\) 5.88870 + 8.10511i 0.522538 + 0.719212i 0.985970 0.166920i \(-0.0533823\pi\)
−0.463432 + 0.886132i \(0.653382\pi\)
\(128\) −10.3687 3.36899i −0.916471 0.297780i
\(129\) −2.62178 + 8.06901i −0.230835 + 0.710437i
\(130\) 0 0
\(131\) −1.97111 6.06645i −0.172217 0.530029i 0.827279 0.561792i \(-0.189888\pi\)
−0.999495 + 0.0317631i \(0.989888\pi\)
\(132\) 4.10435i 0.357238i
\(133\) 16.3696 5.31880i 1.41942 0.461199i
\(134\) −3.31870 2.41117i −0.286692 0.208294i
\(135\) 0 0
\(136\) −1.50707 + 1.09495i −0.129230 + 0.0938910i
\(137\) 5.39429 7.42461i 0.460866 0.634327i −0.513822 0.857897i \(-0.671771\pi\)
0.974688 + 0.223570i \(0.0717710\pi\)
\(138\) 8.18154 11.2609i 0.696459 0.958594i
\(139\) −7.49586 + 5.44606i −0.635790 + 0.461929i −0.858401 0.512979i \(-0.828542\pi\)
0.222611 + 0.974907i \(0.428542\pi\)
\(140\) 0 0
\(141\) 0.609247 + 0.442644i 0.0513078 + 0.0372773i
\(142\) −0.145640 + 0.0473213i −0.0122218 + 0.00397111i
\(143\) 8.06317i 0.674276i
\(144\) 0.685311 + 2.10917i 0.0571093 + 0.175764i
\(145\) 0 0
\(146\) 2.67809 8.24232i 0.221641 0.682140i
\(147\) 2.84284 + 0.923695i 0.234473 + 0.0761850i
\(148\) 9.34270 + 12.8591i 0.767965 + 1.05701i
\(149\) 10.0817 0.825928 0.412964 0.910747i \(-0.364494\pi\)
0.412964 + 0.910747i \(0.364494\pi\)
\(150\) 0 0
\(151\) 10.7375 0.873804 0.436902 0.899509i \(-0.356076\pi\)
0.436902 + 0.899509i \(0.356076\pi\)
\(152\) 4.61999 + 6.35887i 0.374731 + 0.515773i
\(153\) 1.22751 + 0.398843i 0.0992385 + 0.0322446i
\(154\) 3.24615 9.99061i 0.261582 0.805067i
\(155\) 0 0
\(156\) 4.32137 + 13.2998i 0.345987 + 1.06484i
\(157\) 17.4417i 1.39200i −0.718041 0.696001i \(-0.754961\pi\)
0.718041 0.696001i \(-0.245039\pi\)
\(158\) −3.32570 + 1.08058i −0.264578 + 0.0859667i
\(159\) −7.88784 5.73085i −0.625546 0.454486i
\(160\) 0 0
\(161\) −16.4730 + 11.9683i −1.29825 + 0.943235i
\(162\) −1.26995 + 1.74793i −0.0997763 + 0.137330i
\(163\) −9.55586 + 13.1525i −0.748473 + 1.03018i 0.249613 + 0.968346i \(0.419697\pi\)
−0.998086 + 0.0618392i \(0.980303\pi\)
\(164\) −18.4165 + 13.3804i −1.43809 + 1.04483i
\(165\) 0 0
\(166\) −22.9832 16.6983i −1.78385 1.29604i
\(167\) −10.8331 + 3.51989i −0.838290 + 0.272377i −0.696533 0.717525i \(-0.745275\pi\)
−0.141757 + 0.989902i \(0.545275\pi\)
\(168\) 4.56162i 0.351936i
\(169\) −4.47230 13.7643i −0.344023 1.05879i
\(170\) 0 0
\(171\) 1.68287 5.17933i 0.128692 0.396074i
\(172\) 21.5283 + 6.99496i 1.64152 + 0.533361i
\(173\) −5.55954 7.65205i −0.422684 0.581775i 0.543571 0.839363i \(-0.317072\pi\)
−0.966255 + 0.257589i \(0.917072\pi\)
\(174\) −5.10672 −0.387140
\(175\) 0 0
\(176\) −3.41162 −0.257161
\(177\) −2.41738 3.32724i −0.181702 0.250091i
\(178\) 14.9508 + 4.85780i 1.12061 + 0.364107i
\(179\) −1.26001 + 3.87790i −0.0941773 + 0.289848i −0.987038 0.160484i \(-0.948694\pi\)
0.892861 + 0.450332i \(0.148694\pi\)
\(180\) 0 0
\(181\) −3.43633 10.5759i −0.255421 0.786104i −0.993747 0.111660i \(-0.964383\pi\)
0.738326 0.674444i \(-0.235617\pi\)
\(182\) 35.7916i 2.65305i
\(183\) −10.1705 + 3.30461i −0.751829 + 0.244284i
\(184\) −7.52251 5.46542i −0.554567 0.402916i
\(185\) 0 0
\(186\) −7.80525 + 5.67084i −0.572308 + 0.415806i
\(187\) −1.16706 + 1.60632i −0.0853440 + 0.117466i
\(188\) 1.18098 1.62548i 0.0861319 0.118550i
\(189\) 2.55695 1.85773i 0.185990 0.135130i
\(190\) 0 0
\(191\) −2.92164 2.12270i −0.211403 0.153593i 0.477046 0.878879i \(-0.341708\pi\)
−0.688448 + 0.725286i \(0.741708\pi\)
\(192\) 11.5587 3.75565i 0.834178 0.271041i
\(193\) 17.0562i 1.22774i −0.789409 0.613868i \(-0.789613\pi\)
0.789409 0.613868i \(-0.210387\pi\)
\(194\) −6.80596 20.9466i −0.488640 1.50388i
\(195\) 0 0
\(196\) 2.46443 7.58475i 0.176031 0.541768i
\(197\) 4.18963 + 1.36129i 0.298498 + 0.0969880i 0.454437 0.890779i \(-0.349840\pi\)
−0.155939 + 0.987767i \(0.549840\pi\)
\(198\) −1.95362 2.68893i −0.138838 0.191094i
\(199\) −16.5956 −1.17643 −0.588214 0.808705i \(-0.700169\pi\)
−0.588214 + 0.808705i \(0.700169\pi\)
\(200\) 0 0
\(201\) 1.89864 0.133920
\(202\) 1.38118 + 1.90103i 0.0971795 + 0.133756i
\(203\) 7.10471 + 2.30846i 0.498653 + 0.162022i
\(204\) 1.06412 3.27503i 0.0745034 0.229298i
\(205\) 0 0
\(206\) −3.29656 10.1458i −0.229682 0.706889i
\(207\) 6.44244i 0.447780i
\(208\) −11.0551 + 3.59202i −0.766532 + 0.249061i
\(209\) 6.77768 + 4.92427i 0.468822 + 0.340619i
\(210\) 0 0
\(211\) −15.0035 + 10.9007i −1.03288 + 0.750434i −0.968884 0.247516i \(-0.920386\pi\)
−0.0640001 + 0.997950i \(0.520386\pi\)
\(212\) −15.2900 + 21.0449i −1.05012 + 1.44537i
\(213\) 0.0416607 0.0573410i 0.00285454 0.00392894i
\(214\) 26.7536 19.4376i 1.82884 1.32873i
\(215\) 0 0
\(216\) 1.16765 + 0.848347i 0.0794485 + 0.0577227i
\(217\) 13.4225 4.36123i 0.911178 0.296060i
\(218\) 14.3872i 0.974422i
\(219\) 1.23954 + 3.81490i 0.0837601 + 0.257787i
\(220\) 0 0
\(221\) −2.09051 + 6.43393i −0.140623 + 0.432793i
\(222\) −12.2416 3.97753i −0.821601 0.266954i
\(223\) 0.453510 + 0.624203i 0.0303693 + 0.0417997i 0.823932 0.566689i \(-0.191776\pi\)
−0.793562 + 0.608489i \(0.791776\pi\)
\(224\) −24.2671 −1.62141
\(225\) 0 0
\(226\) −19.3833 −1.28936
\(227\) 6.71919 + 9.24817i 0.445968 + 0.613823i 0.971525 0.236936i \(-0.0761430\pi\)
−0.525557 + 0.850758i \(0.676143\pi\)
\(228\) −13.8186 4.48992i −0.915157 0.297352i
\(229\) −3.15962 + 9.72432i −0.208794 + 0.642601i 0.790743 + 0.612149i \(0.209695\pi\)
−0.999536 + 0.0304520i \(0.990305\pi\)
\(230\) 0 0
\(231\) 1.50246 + 4.62409i 0.0988544 + 0.304242i
\(232\) 3.41139i 0.223969i
\(233\) 21.4206 6.95997i 1.40331 0.455963i 0.493050 0.870001i \(-0.335882\pi\)
0.910260 + 0.414038i \(0.135882\pi\)
\(234\) −9.16166 6.65634i −0.598917 0.435138i
\(235\) 0 0
\(236\) −8.87715 + 6.44963i −0.577853 + 0.419835i
\(237\) 0.951325 1.30939i 0.0617952 0.0850538i
\(238\) −5.18047 + 7.13030i −0.335800 + 0.462189i
\(239\) −0.476571 + 0.346249i −0.0308268 + 0.0223970i −0.603092 0.797672i \(-0.706065\pi\)
0.572265 + 0.820069i \(0.306065\pi\)
\(240\) 0 0
\(241\) −1.22110 0.887185i −0.0786583 0.0571486i 0.547761 0.836635i \(-0.315480\pi\)
−0.626419 + 0.779486i \(0.715480\pi\)
\(242\) −17.7402 + 5.76414i −1.14038 + 0.370533i
\(243\) 1.00000i 0.0641500i
\(244\) 8.81677 + 27.1352i 0.564436 + 1.73715i
\(245\) 0 0
\(246\) 5.69652 17.5321i 0.363197 1.11780i
\(247\) 27.1472 + 8.82065i 1.72733 + 0.561244i
\(248\) 3.78823 + 5.21405i 0.240553 + 0.331093i
\(249\) 13.1488 0.833274
\(250\) 0 0
\(251\) 11.8953 0.750823 0.375412 0.926858i \(-0.377501\pi\)
0.375412 + 0.926858i \(0.377501\pi\)
\(252\) −4.95646 6.82198i −0.312228 0.429744i
\(253\) −9.42567 3.06258i −0.592587 0.192543i
\(254\) −6.68882 + 20.5861i −0.419694 + 1.29169i
\(255\) 0 0
\(256\) 0.232398 + 0.715248i 0.0145249 + 0.0447030i
\(257\) 18.0492i 1.12588i 0.826498 + 0.562939i \(0.190329\pi\)
−0.826498 + 0.562939i \(0.809671\pi\)
\(258\) −17.4336 + 5.66451i −1.08537 + 0.352657i
\(259\) 15.2330 + 11.0674i 0.946534 + 0.687698i
\(260\) 0 0
\(261\) 1.91220 1.38930i 0.118362 0.0859953i
\(262\) 8.10053 11.1494i 0.500453 0.688814i
\(263\) −11.2306 + 15.4576i −0.692509 + 0.953157i 0.307490 + 0.951551i \(0.400511\pi\)
−0.999999 + 0.00160518i \(0.999489\pi\)
\(264\) −1.79626 + 1.30506i −0.110552 + 0.0803206i
\(265\) 0 0
\(266\) 30.0854 + 21.8583i 1.84465 + 1.34022i
\(267\) −6.91986 + 2.24840i −0.423489 + 0.137600i
\(268\) 5.06562i 0.309432i
\(269\) 6.86791 + 21.1372i 0.418744 + 1.28876i 0.908859 + 0.417103i \(0.136955\pi\)
−0.490115 + 0.871658i \(0.663045\pi\)
\(270\) 0 0
\(271\) 6.24546 19.2216i 0.379385 1.16763i −0.561088 0.827756i \(-0.689617\pi\)
0.940472 0.339870i \(-0.110383\pi\)
\(272\) 2.72227 + 0.884520i 0.165062 + 0.0536319i
\(273\) 9.73718 + 13.4021i 0.589321 + 0.811130i
\(274\) 19.8281 1.19786
\(275\) 0 0
\(276\) 17.1885 1.03463
\(277\) −9.42882 12.9777i −0.566523 0.779752i 0.425615 0.904904i \(-0.360058\pi\)
−0.992137 + 0.125153i \(0.960058\pi\)
\(278\) −19.0387 6.18604i −1.14186 0.371014i
\(279\) 1.37989 4.24687i 0.0826120 0.254253i
\(280\) 0 0
\(281\) 2.58742 + 7.96327i 0.154353 + 0.475049i 0.998095 0.0617001i \(-0.0196522\pi\)
−0.843742 + 0.536749i \(0.819652\pi\)
\(282\) 1.62705i 0.0968896i
\(283\) 1.07465 0.349174i 0.0638811 0.0207562i −0.276902 0.960898i \(-0.589308\pi\)
0.340783 + 0.940142i \(0.389308\pi\)
\(284\) −0.152987 0.111151i −0.00907810 0.00659563i
\(285\) 0 0
\(286\) 14.0939 10.2398i 0.833387 0.605491i
\(287\) −15.8505 + 21.8164i −0.935626 + 1.28778i
\(288\) −4.51307 + 6.21171i −0.265935 + 0.366028i
\(289\) −12.4056 + 9.01318i −0.729740 + 0.530187i
\(290\) 0 0
\(291\) 8.24705 + 5.99183i 0.483451 + 0.351247i
\(292\) 10.1782 3.30711i 0.595636 0.193534i
\(293\) 2.37857i 0.138958i −0.997583 0.0694789i \(-0.977866\pi\)
0.997583 0.0694789i \(-0.0221337\pi\)
\(294\) 1.99570 + 6.14212i 0.116391 + 0.358216i
\(295\) 0 0
\(296\) −2.65706 + 8.17760i −0.154439 + 0.475313i
\(297\) 1.46306 + 0.475377i 0.0848953 + 0.0275842i
\(298\) 12.8032 + 17.6222i 0.741672 + 1.02082i
\(299\) −33.7676 −1.95283
\(300\) 0 0
\(301\) 26.8150 1.54559
\(302\) 13.6360 + 18.7684i 0.784665 + 1.08000i
\(303\) −1.03436 0.336084i −0.0594224 0.0193075i
\(304\) 3.73212 11.4863i 0.214052 0.658783i
\(305\) 0 0
\(306\) 0.861724 + 2.65212i 0.0492615 + 0.151611i
\(307\) 2.89366i 0.165150i −0.996585 0.0825748i \(-0.973686\pi\)
0.996585 0.0825748i \(-0.0263143\pi\)
\(308\) 12.3371 4.00858i 0.702974 0.228410i
\(309\) 3.99457 + 2.90222i 0.227243 + 0.165102i
\(310\) 0 0
\(311\) 5.78079 4.19999i 0.327799 0.238160i −0.411697 0.911321i \(-0.635064\pi\)
0.739496 + 0.673161i \(0.235064\pi\)
\(312\) −4.44656 + 6.12016i −0.251737 + 0.346486i
\(313\) 13.5378 18.6331i 0.765200 1.05321i −0.231563 0.972820i \(-0.574384\pi\)
0.996764 0.0803879i \(-0.0256159\pi\)
\(314\) 30.4869 22.1500i 1.72048 1.25000i
\(315\) 0 0
\(316\) −3.49347 2.53815i −0.196523 0.142782i
\(317\) −19.7582 + 6.41981i −1.10973 + 0.360573i −0.805839 0.592135i \(-0.798285\pi\)
−0.303890 + 0.952707i \(0.598285\pi\)
\(318\) 21.0653i 1.18128i
\(319\) 1.12361 + 3.45810i 0.0629098 + 0.193617i
\(320\) 0 0
\(321\) −4.72978 + 14.5568i −0.263990 + 0.812479i
\(322\) −41.8395 13.5945i −2.33163 0.757591i
\(323\) −4.13148 5.68650i −0.229882 0.316405i
\(324\) −2.66802 −0.148223
\(325\) 0 0
\(326\) −35.1251 −1.94540
\(327\) −3.91406 5.38724i −0.216448 0.297915i
\(328\) −11.7118 3.80538i −0.646673 0.210117i
\(329\) 0.735499 2.26363i 0.0405494 0.124798i
\(330\) 0 0
\(331\) −5.94869 18.3082i −0.326969 1.00631i −0.970544 0.240925i \(-0.922549\pi\)
0.643574 0.765383i \(-0.277451\pi\)
\(332\) 35.0814i 1.92534i
\(333\) 5.66593 1.84097i 0.310491 0.100885i
\(334\) −19.9099 14.4654i −1.08942 0.791513i
\(335\) 0 0
\(336\) 5.67058 4.11991i 0.309355 0.224760i
\(337\) −12.7587 + 17.5609i −0.695012 + 0.956602i 0.304979 + 0.952359i \(0.401351\pi\)
−0.999991 + 0.00424305i \(0.998649\pi\)
\(338\) 18.3795 25.2972i 0.999712 1.37599i
\(339\) 7.25804 5.27328i 0.394203 0.286405i
\(340\) 0 0
\(341\) 5.55745 + 4.03773i 0.300953 + 0.218655i
\(342\) 11.1903 3.63594i 0.605100 0.196609i
\(343\) 12.6766i 0.684470i
\(344\) 3.78400 + 11.6460i 0.204020 + 0.627908i
\(345\) 0 0
\(346\) 6.31493 19.4354i 0.339493 1.04485i
\(347\) 1.63100 + 0.529944i 0.0875567 + 0.0284489i 0.352468 0.935824i \(-0.385343\pi\)
−0.264911 + 0.964273i \(0.585343\pi\)
\(348\) −3.70667 5.10179i −0.198698 0.273485i
\(349\) 15.5553 0.832654 0.416327 0.909215i \(-0.363317\pi\)
0.416327 + 0.909215i \(0.363317\pi\)
\(350\) 0 0
\(351\) 5.24144 0.279767
\(352\) −6.94268 9.55579i −0.370046 0.509325i
\(353\) 14.7923 + 4.80632i 0.787316 + 0.255814i 0.674961 0.737854i \(-0.264161\pi\)
0.112355 + 0.993668i \(0.464161\pi\)
\(354\) 2.74584 8.45083i 0.145940 0.449157i
\(355\) 0 0
\(356\) 5.99877 + 18.4623i 0.317934 + 0.978501i
\(357\) 4.07928i 0.215899i
\(358\) −8.37844 + 2.72232i −0.442814 + 0.143879i
\(359\) −19.8509 14.4225i −1.04769 0.761191i −0.0759181 0.997114i \(-0.524189\pi\)
−0.971772 + 0.235923i \(0.924189\pi\)
\(360\) 0 0
\(361\) −8.62214 + 6.26435i −0.453797 + 0.329703i
\(362\) 14.1221 19.4373i 0.742239 1.02160i
\(363\) 5.07463 6.98463i 0.266349 0.366598i
\(364\) 35.7570 25.9790i 1.87418 1.36167i
\(365\) 0 0
\(366\) −18.6923 13.5807i −0.977060 0.709876i
\(367\) 26.7311 8.68548i 1.39535 0.453378i 0.487669 0.873029i \(-0.337847\pi\)
0.907686 + 0.419651i \(0.137847\pi\)
\(368\) 14.2875i 0.744786i
\(369\) 2.63659 + 8.11460i 0.137256 + 0.422429i
\(370\) 0 0
\(371\) −9.52241 + 29.3070i −0.494379 + 1.52154i
\(372\) −11.3307 3.68158i −0.587471 0.190881i
\(373\) 5.70637 + 7.85414i 0.295464 + 0.406672i 0.930779 0.365581i \(-0.119130\pi\)
−0.635315 + 0.772253i \(0.719130\pi\)
\(374\) −4.28984 −0.221823
\(375\) 0 0
\(376\) 1.08690 0.0560527
\(377\) 7.28191 + 10.0227i 0.375037 + 0.516195i
\(378\) 6.49436 + 2.11015i 0.334034 + 0.108534i
\(379\) 6.88071 21.1767i 0.353438 1.08777i −0.603471 0.797385i \(-0.706216\pi\)
0.956909 0.290387i \(-0.0937839\pi\)
\(380\) 0 0
\(381\) −3.09587 9.52812i −0.158606 0.488141i
\(382\) 7.80253i 0.399212i
\(383\) 12.9628 4.21189i 0.662371 0.215217i 0.0415099 0.999138i \(-0.486783\pi\)
0.620861 + 0.783921i \(0.286783\pi\)
\(384\) 8.82014 + 6.40820i 0.450101 + 0.327017i
\(385\) 0 0
\(386\) 29.8131 21.6605i 1.51745 1.10249i
\(387\) 4.98692 6.86391i 0.253500 0.348912i
\(388\) 15.9863 22.0033i 0.811582 1.11705i
\(389\) 15.5577 11.3034i 0.788808 0.573103i −0.118801 0.992918i \(-0.537905\pi\)
0.907610 + 0.419815i \(0.137905\pi\)
\(390\) 0 0
\(391\) 6.72710 + 4.88752i 0.340204 + 0.247173i
\(392\) 4.10305 1.33316i 0.207236 0.0673349i
\(393\) 6.37865i 0.321760i
\(394\) 2.94115 + 9.05194i 0.148173 + 0.456030i
\(395\) 0 0
\(396\) 1.26831 3.90347i 0.0637352 0.196157i
\(397\) −21.1402 6.86887i −1.06100 0.344739i −0.274022 0.961723i \(-0.588354\pi\)
−0.786975 + 0.616984i \(0.788354\pi\)
\(398\) −21.0755 29.0079i −1.05642 1.45403i
\(399\) −17.2120 −0.861678
\(400\) 0 0
\(401\) 4.71728 0.235570 0.117785 0.993039i \(-0.462421\pi\)
0.117785 + 0.993039i \(0.462421\pi\)
\(402\) 2.41117 + 3.31870i 0.120258 + 0.165522i
\(403\) 22.2597 + 7.23261i 1.10883 + 0.360282i
\(404\) −0.896678 + 2.75969i −0.0446114 + 0.137300i
\(405\) 0 0
\(406\) 4.98757 + 15.3502i 0.247529 + 0.761815i
\(407\) 9.16474i 0.454279i
\(408\) 1.77166 0.575648i 0.0877104 0.0284988i
\(409\) −10.0971 7.33597i −0.499269 0.362740i 0.309469 0.950910i \(-0.399849\pi\)
−0.808738 + 0.588169i \(0.799849\pi\)
\(410\) 0 0
\(411\) −7.42461 + 5.39429i −0.366229 + 0.266081i
\(412\) 7.74319 10.6576i 0.381480 0.525062i
\(413\) −7.64029 + 10.5160i −0.375954 + 0.517456i
\(414\) −11.2609 + 8.18154i −0.553444 + 0.402101i
\(415\) 0 0
\(416\) −32.5583 23.6550i −1.59630 1.15978i
\(417\) 8.81191 2.86316i 0.431521 0.140210i
\(418\) 18.1005i 0.885322i
\(419\) −10.7996 33.2379i −0.527597 1.62378i −0.759123 0.650947i \(-0.774372\pi\)
0.231527 0.972829i \(-0.425628\pi\)
\(420\) 0 0
\(421\) −12.2247 + 37.6239i −0.595797 + 1.83368i −0.0450804 + 0.998983i \(0.514354\pi\)
−0.550717 + 0.834692i \(0.685646\pi\)
\(422\) −38.1073 12.3818i −1.85503 0.602737i
\(423\) −0.442644 0.609247i −0.0215221 0.0296226i
\(424\) −14.0720 −0.683396
\(425\) 0 0
\(426\) 0.153135 0.00741940
\(427\) 19.8665 + 27.3439i 0.961406 + 1.32326i
\(428\) 38.8377 + 12.6191i 1.87729 + 0.609969i
\(429\) −2.49166 + 7.66853i −0.120298 + 0.370240i
\(430\) 0 0
\(431\) −4.34429 13.3703i −0.209257 0.644027i −0.999512 0.0312481i \(-0.990052\pi\)
0.790255 0.612778i \(-0.209948\pi\)
\(432\) 2.21771i 0.106700i
\(433\) 0.522775 0.169860i 0.0251230 0.00816294i −0.296429 0.955055i \(-0.595796\pi\)
0.321552 + 0.946892i \(0.395796\pi\)
\(434\) 24.6689 + 17.9230i 1.18415 + 0.860333i
\(435\) 0 0
\(436\) −14.3733 + 10.4428i −0.688355 + 0.500119i
\(437\) 20.6223 28.3841i 0.986497 1.35780i
\(438\) −5.09404 + 7.01134i −0.243402 + 0.335015i
\(439\) −2.40583 + 1.74794i −0.114824 + 0.0834245i −0.643715 0.765265i \(-0.722608\pi\)
0.528891 + 0.848690i \(0.322608\pi\)
\(440\) 0 0
\(441\) −2.41826 1.75697i −0.115155 0.0836653i
\(442\) −13.9009 + 4.51667i −0.661198 + 0.214836i
\(443\) 36.6893i 1.74316i −0.490253 0.871580i \(-0.663095\pi\)
0.490253 0.871580i \(-0.336905\pi\)
\(444\) −4.91175 15.1168i −0.233101 0.717412i
\(445\) 0 0
\(446\) −0.515130 + 1.58541i −0.0243921 + 0.0750712i
\(447\) −9.58830 3.11543i −0.453511 0.147355i
\(448\) −22.5780 31.0760i −1.06671 1.46820i
\(449\) 17.8432 0.842071 0.421036 0.907044i \(-0.361667\pi\)
0.421036 + 0.907044i \(0.361667\pi\)
\(450\) 0 0
\(451\) −13.1255 −0.618056
\(452\) −14.0692 19.3646i −0.661759 0.910834i
\(453\) −10.2120 3.31807i −0.479800 0.155896i
\(454\) −7.63215 + 23.4893i −0.358195 + 1.10241i
\(455\) 0 0
\(456\) −2.42887 7.47530i −0.113742 0.350063i
\(457\) 24.1784i 1.13102i 0.824742 + 0.565509i \(0.191320\pi\)
−0.824742 + 0.565509i \(0.808680\pi\)
\(458\) −21.0100 + 6.82655i −0.981731 + 0.318984i
\(459\) −1.04418 0.758645i −0.0487384 0.0354105i
\(460\) 0 0
\(461\) 30.2470 21.9757i 1.40874 1.02351i 0.415240 0.909712i \(-0.363698\pi\)
0.993504 0.113800i \(-0.0363024\pi\)
\(462\) −6.17454 + 8.49852i −0.287266 + 0.395387i
\(463\) 12.0093 16.5294i 0.558120 0.768186i −0.432966 0.901410i \(-0.642533\pi\)
0.991086 + 0.133224i \(0.0425331\pi\)
\(464\) 4.24072 3.08106i 0.196870 0.143035i
\(465\) 0 0
\(466\) 39.3685 + 28.6029i 1.82371 + 1.32500i
\(467\) 29.6848 9.64517i 1.37365 0.446325i 0.473072 0.881024i \(-0.343145\pi\)
0.900576 + 0.434699i \(0.143145\pi\)
\(468\) 13.9843i 0.646422i
\(469\) −1.85434 5.70708i −0.0856256 0.263529i
\(470\) 0 0
\(471\) −5.38979 + 16.5881i −0.248348 + 0.764338i
\(472\) −5.64532 1.83427i −0.259847 0.0844293i
\(473\) 7.67164 + 10.5591i 0.352742 + 0.485508i
\(474\) 3.49684 0.160615
\(475\) 0 0
\(476\) −10.8836 −0.498849
\(477\) 5.73085 + 7.88784i 0.262398 + 0.361159i
\(478\) −1.21044 0.393295i −0.0553641 0.0179889i
\(479\) −3.42915 + 10.5538i −0.156682 + 0.482217i −0.998327 0.0578133i \(-0.981587\pi\)
0.841646 + 0.540030i \(0.181587\pi\)
\(480\) 0 0
\(481\) 9.64933 + 29.6976i 0.439972 + 1.35409i
\(482\) 3.26108i 0.148538i
\(483\) 19.3651 6.29211i 0.881144 0.286301i
\(484\) −18.6351 13.5392i −0.847051 0.615418i
\(485\) 0 0
\(486\) 1.74793 1.26995i 0.0792877 0.0576059i
\(487\) −4.19504 + 5.77397i −0.190095 + 0.261644i −0.893417 0.449228i \(-0.851699\pi\)
0.703322 + 0.710871i \(0.251699\pi\)
\(488\) −9.07218 + 12.4868i −0.410678 + 0.565250i
\(489\) 13.1525 9.55586i 0.594777 0.432131i
\(490\) 0 0
\(491\) −5.85201 4.25173i −0.264097 0.191878i 0.447854 0.894107i \(-0.352188\pi\)
−0.711951 + 0.702229i \(0.752188\pi\)
\(492\) 21.6499 7.03448i 0.976053 0.317139i
\(493\) 3.05067i 0.137395i
\(494\) 19.0575 + 58.6531i 0.857439 + 2.63893i
\(495\) 0 0
\(496\) 3.06020 9.41834i 0.137407 0.422896i
\(497\) −0.213048 0.0692236i −0.00955652 0.00310510i
\(498\) 16.6983 + 22.9832i 0.748269 + 1.02990i
\(499\) −16.0169 −0.717014 −0.358507 0.933527i \(-0.616714\pi\)
−0.358507 + 0.933527i \(0.616714\pi\)
\(500\) 0 0
\(501\) 11.3906 0.508894
\(502\) 15.1063 + 20.7921i 0.674229 + 0.927997i
\(503\) −32.1422 10.4436i −1.43315 0.465659i −0.513396 0.858152i \(-0.671613\pi\)
−0.919755 + 0.392492i \(0.871613\pi\)
\(504\) 1.40962 4.33836i 0.0627894 0.193246i
\(505\) 0 0
\(506\) −6.61690 20.3647i −0.294157 0.905322i
\(507\) 14.4727i 0.642753i
\(508\) −25.4212 + 8.25985i −1.12788 + 0.366472i
\(509\) −29.4701 21.4113i −1.30624 0.949038i −0.306243 0.951953i \(-0.599072\pi\)
−0.999996 + 0.00291563i \(0.999072\pi\)
\(510\) 0 0
\(511\) 10.2565 7.45178i 0.453720 0.329647i
\(512\) −13.7715 + 18.9548i −0.608619 + 0.837692i
\(513\) −3.20100 + 4.40581i −0.141328 + 0.194521i
\(514\) −31.5487 + 22.9215i −1.39156 + 1.01102i
\(515\) 0 0
\(516\) −18.3130 13.3052i −0.806187 0.585729i
\(517\) 1.10179 0.357992i 0.0484565 0.0157445i
\(518\) 40.6813i 1.78743i
\(519\) 2.92282 + 8.99552i 0.128298 + 0.394860i
\(520\) 0 0
\(521\) 7.87972 24.2513i 0.345217 1.06247i −0.616251 0.787550i \(-0.711349\pi\)
0.961468 0.274918i \(-0.0886507\pi\)
\(522\) 4.85678 + 1.57806i 0.212576 + 0.0690700i
\(523\) 4.13315 + 5.68880i 0.180730 + 0.248754i 0.889764 0.456420i \(-0.150869\pi\)
−0.709034 + 0.705174i \(0.750869\pi\)
\(524\) 17.0184 0.743450
\(525\) 0 0
\(526\) −41.2811 −1.79994
\(527\) −3.38767 4.66273i −0.147569 0.203112i
\(528\) 3.24465 + 1.05425i 0.141205 + 0.0458803i
\(529\) −5.71836 + 17.5993i −0.248624 + 0.765187i
\(530\) 0 0
\(531\) 1.27089 + 3.91141i 0.0551521 + 0.169741i
\(532\) 45.9220i 1.99097i
\(533\) −42.5322 + 13.8195i −1.84227 + 0.598590i
\(534\) −12.7179 9.24008i −0.550357 0.399858i
\(535\) 0 0
\(536\) 2.21695 1.61071i 0.0957577 0.0695721i
\(537\) 2.39667 3.29874i 0.103424 0.142351i
\(538\) −28.2246 + 38.8478i −1.21685 + 1.67485i
\(539\) 3.72014 2.70284i 0.160238 0.116420i
\(540\) 0 0
\(541\) 21.9629 + 15.9570i 0.944258 + 0.686044i 0.949442 0.313943i \(-0.101650\pi\)
−0.00518365 + 0.999987i \(0.501650\pi\)
\(542\) 41.5293 13.4937i 1.78384 0.579604i
\(543\) 11.1202i 0.477214i
\(544\) 3.06235 + 9.42496i 0.131297 + 0.404092i
\(545\) 0 0
\(546\) −11.0602 + 34.0398i −0.473333 + 1.45677i
\(547\) −41.9196 13.6205i −1.79235 0.582371i −0.792723 0.609582i \(-0.791337\pi\)
−0.999630 + 0.0272113i \(0.991337\pi\)
\(548\) 14.3921 + 19.8090i 0.614799 + 0.846198i
\(549\) 10.6939 0.456407
\(550\) 0 0
\(551\) −12.8719 −0.548363
\(552\) 5.46542 + 7.52251i 0.232624 + 0.320179i
\(553\) −4.86497 1.58073i −0.206880 0.0672193i
\(554\) 10.7099 32.9618i 0.455022 1.40041i
\(555\) 0 0
\(556\) −7.63897 23.5103i −0.323965 0.997061i
\(557\) 9.85667i 0.417641i 0.977954 + 0.208820i \(0.0669624\pi\)
−0.977954 + 0.208820i \(0.933038\pi\)
\(558\) 9.17562 2.98134i 0.388435 0.126210i
\(559\) 35.9768 + 26.1386i 1.52165 + 1.10555i
\(560\) 0 0
\(561\) 1.60632 1.16706i 0.0678190 0.0492734i
\(562\) −10.6334 + 14.6356i −0.448541 + 0.617363i
\(563\) −7.28367 + 10.0251i −0.306970 + 0.422508i −0.934433 0.356138i \(-0.884093\pi\)
0.627463 + 0.778646i \(0.284093\pi\)
\(564\) −1.62548 + 1.18098i −0.0684451 + 0.0497283i
\(565\) 0 0
\(566\) 1.97507 + 1.43497i 0.0830185 + 0.0603165i
\(567\) −3.00587 + 0.976667i −0.126235 + 0.0410161i
\(568\) 0.102297i 0.00429228i
\(569\) 3.62037 + 11.1424i 0.151774 + 0.467112i 0.997820 0.0659983i \(-0.0210232\pi\)
−0.846046 + 0.533110i \(0.821023\pi\)
\(570\) 0 0
\(571\) 8.95523 27.5614i 0.374765 1.15341i −0.568872 0.822426i \(-0.692620\pi\)
0.943637 0.330982i \(-0.107380\pi\)
\(572\) 20.4598 + 6.64779i 0.855467 + 0.277958i
\(573\) 2.12270 + 2.92164i 0.0886769 + 0.122053i
\(574\) −58.2628 −2.43184
\(575\) 0 0
\(576\) −12.1535 −0.506398
\(577\) −19.2808 26.5377i −0.802668 1.10478i −0.992414 0.122945i \(-0.960766\pi\)
0.189745 0.981833i \(-0.439234\pi\)
\(578\) −31.5088 10.2378i −1.31059 0.425838i
\(579\) −5.27067 + 16.2215i −0.219042 + 0.674141i
\(580\) 0 0
\(581\) −12.8420 39.5237i −0.532777 1.63972i
\(582\) 22.0246i 0.912947i
\(583\) −14.2647 + 4.63488i −0.590783 + 0.191957i
\(584\) 4.68371 + 3.40291i 0.193813 + 0.140813i
\(585\) 0 0
\(586\) 4.15758 3.02066i 0.171748 0.124782i
\(587\) −10.9560 + 15.0797i −0.452203 + 0.622405i −0.972869 0.231356i \(-0.925684\pi\)
0.520666 + 0.853761i \(0.325684\pi\)
\(588\) −4.68763 + 6.45197i −0.193315 + 0.266075i
\(589\) −19.6738 + 14.2938i −0.810644 + 0.588967i
\(590\) 0 0
\(591\) −3.56391 2.58933i −0.146600 0.106511i
\(592\) 12.5654 4.08275i 0.516435 0.167800i
\(593\) 1.55882i 0.0640129i 0.999488 + 0.0320064i \(0.0101897\pi\)
−0.999488 + 0.0320064i \(0.989810\pi\)
\(594\) 1.02708 + 3.16103i 0.0421416 + 0.129698i
\(595\) 0 0
\(596\) −8.31202 + 25.5818i −0.340474 + 1.04787i
\(597\) 15.7833 + 5.12831i 0.645969 + 0.209888i
\(598\) −42.8830 59.0234i −1.75362 2.41365i
\(599\) 31.5470 1.28898 0.644489 0.764614i \(-0.277070\pi\)
0.644489 + 0.764614i \(0.277070\pi\)
\(600\) 0 0
\(601\) −32.3999 −1.32162 −0.660809 0.750554i \(-0.729787\pi\)
−0.660809 + 0.750554i \(0.729787\pi\)
\(602\) 34.0536 + 46.8707i 1.38792 + 1.91031i
\(603\) −1.80572 0.586713i −0.0735345 0.0238928i
\(604\) −8.85266 + 27.2457i −0.360210 + 1.10861i
\(605\) 0 0
\(606\) −0.726129 2.23480i −0.0294970 0.0907824i
\(607\) 24.8410i 1.00827i −0.863626 0.504133i \(-0.831812\pi\)
0.863626 0.504133i \(-0.168188\pi\)
\(608\) 39.7674 12.9212i 1.61278 0.524024i
\(609\) −6.04363 4.39095i −0.244900 0.177930i
\(610\) 0 0
\(611\) 3.19333 2.32009i 0.129188 0.0938607i
\(612\) −2.02408 + 2.78590i −0.0818185 + 0.112614i
\(613\) −2.31915 + 3.19204i −0.0936697 + 0.128925i −0.853280 0.521454i \(-0.825390\pi\)
0.759610 + 0.650379i \(0.225390\pi\)
\(614\) 5.05791 3.67478i 0.204120 0.148302i
\(615\) 0 0
\(616\) 5.67717 + 4.12471i 0.228740 + 0.166189i
\(617\) −16.6264 + 5.40225i −0.669354 + 0.217486i −0.623929 0.781481i \(-0.714464\pi\)
−0.0454257 + 0.998968i \(0.514464\pi\)
\(618\) 10.6679i 0.429126i
\(619\) 4.44581 + 13.6828i 0.178692 + 0.549958i 0.999783 0.0208398i \(-0.00663400\pi\)
−0.821091 + 0.570798i \(0.806634\pi\)
\(620\) 0 0
\(621\) 1.99082 6.12712i 0.0798890 0.245873i
\(622\) 14.6826 + 4.77066i 0.588718 + 0.191286i
\(623\) 13.5168 + 18.6043i 0.541539 + 0.745364i
\(624\) 11.6240 0.465333
\(625\) 0 0
\(626\) 49.7617 1.98888
\(627\) −4.92427 6.77768i −0.196656 0.270674i
\(628\) 44.2573 + 14.3801i 1.76606 + 0.573827i
\(629\) 2.37611 7.31292i 0.0947418 0.291585i
\(630\) 0 0
\(631\) −5.46214 16.8107i −0.217444 0.669225i −0.998971 0.0453529i \(-0.985559\pi\)
0.781527 0.623872i \(-0.214441\pi\)
\(632\) 2.33596i 0.0929194i
\(633\) 17.6377 5.73083i 0.701035 0.227780i
\(634\) −36.3132 26.3831i −1.44218 1.04781i
\(635\) 0 0
\(636\) 21.0449 15.2900i 0.834485 0.606289i
\(637\) 9.20905 12.6752i 0.364876 0.502209i
\(638\) −4.61760 + 6.35559i −0.182813 + 0.251620i
\(639\) −0.0573410 + 0.0416607i −0.00226837 + 0.00164807i
\(640\) 0 0
\(641\) 2.21774 + 1.61128i 0.0875954 + 0.0636417i 0.630721 0.776010i \(-0.282759\pi\)
−0.543126 + 0.839651i \(0.682759\pi\)
\(642\) −31.4507 + 10.2190i −1.24126 + 0.403310i
\(643\) 20.9276i 0.825303i 0.910889 + 0.412651i \(0.135397\pi\)
−0.910889 + 0.412651i \(0.864603\pi\)
\(644\) −16.7875 51.6665i −0.661519 2.03595i
\(645\) 0 0
\(646\) 4.69284 14.4431i 0.184637 0.568256i
\(647\) 1.75629 + 0.570653i 0.0690469 + 0.0224347i 0.343337 0.939212i \(-0.388443\pi\)
−0.274290 + 0.961647i \(0.588443\pi\)
\(648\) −0.848347 1.16765i −0.0333262 0.0458696i
\(649\) −6.32678 −0.248348
\(650\) 0 0
\(651\) −14.1132 −0.553141
\(652\) −25.4952 35.0912i −0.998470 1.37428i
\(653\) −17.5121 5.69002i −0.685300 0.222667i −0.0543858 0.998520i \(-0.517320\pi\)
−0.630914 + 0.775853i \(0.717320\pi\)
\(654\) 4.44588 13.6830i 0.173848 0.535048i
\(655\) 0 0
\(656\) 5.84721 + 17.9959i 0.228295 + 0.702620i
\(657\) 4.01123i 0.156493i
\(658\) 4.89071 1.58909i 0.190660 0.0619491i
\(659\) −10.8246 7.86455i −0.421668 0.306360i 0.356641 0.934242i \(-0.383922\pi\)
−0.778308 + 0.627882i \(0.783922\pi\)
\(660\) 0 0
\(661\) −31.7001 + 23.0315i −1.23299 + 0.895820i −0.997111 0.0759628i \(-0.975797\pi\)
−0.235879 + 0.971782i \(0.575797\pi\)
\(662\) 24.4469 33.6483i 0.950155 1.30778i
\(663\) 3.97639 5.47303i 0.154430 0.212555i
\(664\) 15.3532 11.1548i 0.595821 0.432890i
\(665\) 0 0
\(666\) 10.4133 + 7.56571i 0.403507 + 0.293165i
\(667\) 14.4821 4.70553i 0.560751 0.182199i
\(668\) 30.3903i 1.17584i
\(669\) −0.238424 0.733794i −0.00921801 0.0283701i
\(670\) 0 0
\(671\) −5.08365 + 15.6459i −0.196252 + 0.604002i
\(672\) 23.0794 + 7.49894i 0.890305 + 0.289278i
\(673\) −11.3978 15.6877i −0.439353 0.604718i 0.530715 0.847550i \(-0.321923\pi\)
−0.970068 + 0.242832i \(0.921923\pi\)
\(674\) −46.8981 −1.80645
\(675\) 0 0
\(676\) 38.6133 1.48513
\(677\) −26.8522 36.9588i −1.03201 1.42044i −0.903425 0.428746i \(-0.858956\pi\)
−0.128587 0.991698i \(-0.541044\pi\)
\(678\) 18.4346 + 5.98977i 0.707978 + 0.230036i
\(679\) 9.95606 30.6416i 0.382078 1.17592i
\(680\) 0 0
\(681\) −3.53249 10.8719i −0.135365 0.416611i
\(682\) 14.8417i 0.568319i
\(683\) −11.0220 + 3.58128i −0.421747 + 0.137034i −0.512199 0.858867i \(-0.671169\pi\)
0.0904520 + 0.995901i \(0.471169\pi\)
\(684\) 11.7548 + 8.54034i 0.449455 + 0.326548i
\(685\) 0 0
\(686\) −22.1577 + 16.0985i −0.845987 + 0.614645i
\(687\) 6.00996 8.27200i 0.229294 0.315596i
\(688\) 11.0596 15.2222i 0.421642 0.580340i
\(689\) −41.3436 + 30.0379i −1.57507 + 1.14435i
\(690\) 0 0
\(691\) 17.5091 + 12.7211i 0.666077 + 0.483934i 0.868710 0.495321i \(-0.164950\pi\)
−0.202632 + 0.979255i \(0.564950\pi\)
\(692\) 24.0002 7.79815i 0.912352 0.296441i
\(693\) 4.86205i 0.184694i
\(694\) 1.14498 + 3.52388i 0.0434627 + 0.133764i
\(695\) 0 0
\(696\) 1.05418 3.24442i 0.0399585 0.122980i
\(697\) 10.4734 + 3.40301i 0.396707 + 0.128898i
\(698\) 19.7543 + 27.1895i 0.747713 + 1.02914i
\(699\) −22.5229 −0.851896
\(700\) 0 0
\(701\) −8.61904 −0.325537 −0.162768 0.986664i \(-0.552042\pi\)
−0.162768 + 0.986664i \(0.552042\pi\)
\(702\) 6.65634 + 9.16166i 0.251227 + 0.345785i
\(703\) −30.8559 10.0257i −1.16375 0.378126i
\(704\) 5.77751 17.7814i 0.217748 0.670160i
\(705\) 0 0
\(706\) 10.3843 + 31.9597i 0.390820 + 1.20282i
\(707\) 3.43739i 0.129276i
\(708\) 10.4357 3.39077i 0.392198 0.127433i
\(709\) 12.9443 + 9.40460i 0.486134 + 0.353197i 0.803696 0.595041i \(-0.202864\pi\)
−0.317562 + 0.948238i \(0.602864\pi\)
\(710\) 0 0
\(711\) −1.30939 + 0.951325i −0.0491058 + 0.0356775i
\(712\) −6.17255 + 8.49579i −0.231326 + 0.318393i
\(713\) 16.9095 23.2740i 0.633267 0.871617i
\(714\) 7.13030 5.18047i 0.266845 0.193874i
\(715\) 0 0
\(716\) −8.80110 6.39437i −0.328913 0.238969i
\(717\) 0.560243 0.182034i 0.0209226 0.00679818i
\(718\) 53.0138i 1.97846i
\(719\) 15.0132 + 46.2060i 0.559899 + 1.72319i 0.682642 + 0.730753i \(0.260831\pi\)
−0.122743 + 0.992438i \(0.539169\pi\)
\(720\) 0 0
\(721\) 4.82235 14.8417i 0.179594 0.552733i
\(722\) −21.8993 7.11551i −0.815007 0.264812i
\(723\) 0.887185 + 1.22110i 0.0329948 + 0.0454134i
\(724\) 29.6689 1.10264
\(725\) 0 0
\(726\) 18.6531 0.692283
\(727\) 14.9490 + 20.5756i 0.554429 + 0.763106i 0.990605 0.136755i \(-0.0436675\pi\)
−0.436176 + 0.899861i \(0.643667\pi\)
\(728\) 22.7392 + 7.38842i 0.842772 + 0.273833i
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) −3.38389 10.4145i −0.125158 0.385196i
\(732\) 28.5317i 1.05456i
\(733\) 17.7077 5.75358i 0.654049 0.212513i 0.0368505 0.999321i \(-0.488267\pi\)
0.617199 + 0.786807i \(0.288267\pi\)
\(734\) 49.1287 + 35.6941i 1.81337 + 1.31749i
\(735\) 0 0
\(736\) −40.0185 + 29.0752i −1.47510 + 1.07172i
\(737\) 1.71679 2.36296i 0.0632389 0.0870408i
\(738\) −10.8354 + 14.9137i −0.398857 + 0.548980i
\(739\) 37.9326 27.5596i 1.39537 1.01380i 0.400121 0.916462i \(-0.368968\pi\)
0.995252 0.0973351i \(-0.0310319\pi\)
\(740\) 0 0
\(741\) −23.0927 16.7779i −0.848333 0.616350i
\(742\) −63.3194 + 20.5737i −2.32453 + 0.755286i
\(743\) 42.7061i 1.56674i −0.621558 0.783368i \(-0.713500\pi\)
0.621558 0.783368i \(-0.286500\pi\)
\(744\) −1.99159 6.12948i −0.0730152 0.224718i
\(745\) 0 0
\(746\) −6.48171 + 19.9487i −0.237312 + 0.730372i
\(747\) −12.5053 4.06322i −0.457545 0.148665i
\(748\) −3.11374 4.28570i −0.113850 0.156701i
\(749\) 48.3751 1.76759
\(750\) 0 0
\(751\) −2.64893 −0.0966608 −0.0483304 0.998831i \(-0.515390\pi\)
−0.0483304 + 0.998831i \(0.515390\pi\)
\(752\) −0.981657 1.35113i −0.0357973 0.0492708i
\(753\) −11.3131 3.67584i −0.412272 0.133955i
\(754\) −8.27133 + 25.4565i −0.301224 + 0.927072i
\(755\) 0 0
\(756\) 2.60577 + 8.01972i 0.0947708 + 0.291674i
\(757\) 52.9153i 1.92324i −0.274383 0.961620i \(-0.588474\pi\)
0.274383 0.961620i \(-0.411526\pi\)
\(758\) 45.7534 14.8662i 1.66184 0.539964i
\(759\) 8.01795 + 5.82538i 0.291033 + 0.211448i
\(760\) 0 0
\(761\) −41.0808 + 29.8470i −1.48918 + 1.08195i −0.514728 + 0.857354i \(0.672107\pi\)
−0.974451 + 0.224598i \(0.927893\pi\)
\(762\) 12.7229 17.5116i 0.460902 0.634377i
\(763\) −12.3706 + 17.0267i −0.447847 + 0.616408i
\(764\) 7.79499 5.66339i 0.282013 0.204894i
\(765\) 0 0
\(766\) 23.8242 + 17.3093i 0.860803 + 0.625410i
\(767\) −20.5014 + 6.66131i −0.740263 + 0.240526i
\(768\) 0.752056i 0.0271375i
\(769\) −7.59580 23.3775i −0.273912 0.843013i −0.989505 0.144496i \(-0.953844\pi\)
0.715594 0.698517i \(-0.246156\pi\)
\(770\) 0 0
\(771\) 5.57751 17.1658i 0.200869 0.618212i
\(772\) 43.2791 + 14.0622i 1.55765 + 0.506111i
\(773\) 11.7623 + 16.1894i 0.423061 + 0.582293i 0.966343 0.257257i \(-0.0828186\pi\)
−0.543282 + 0.839550i \(0.682819\pi\)
\(774\) 18.3308 0.658885
\(775\) 0 0
\(776\) 14.7128 0.528159
\(777\) −11.0674 15.2330i −0.397042 0.546482i
\(778\) 39.5149 + 12.8392i 1.41668 + 0.460307i
\(779\) 14.3586 44.1911i 0.514449 1.58331i
\(780\) 0 0
\(781\) −0.0336934 0.103698i −0.00120565 0.00371060i
\(782\) 17.9654i 0.642441i
\(783\) −2.24793 + 0.730396i −0.0803344 + 0.0261022i
\(784\) −5.36302 3.89646i −0.191536 0.139159i
\(785\) 0 0
\(786\) −11.1494 + 8.10053i −0.397687 + 0.288936i
\(787\) −5.28579 + 7.27526i −0.188418 + 0.259335i −0.892767 0.450519i \(-0.851239\pi\)
0.704349 + 0.709854i \(0.251239\pi\)
\(788\) −6.90838 + 9.50857i −0.246101 + 0.338729i
\(789\) 15.4576 11.2306i 0.550305 0.399820i
\(790\) 0 0
\(791\) −22.9395 16.6665i −0.815634 0.592593i
\(792\) 2.11162 0.686108i 0.0750333 0.0243798i
\(793\) 56.0517i 1.99045i
\(794\) −14.8406 45.6747i −0.526674 1.62093i
\(795\) 0 0
\(796\) 13.6824 42.1102i 0.484961 1.49256i
\(797\) 35.9084 + 11.6674i 1.27194 + 0.413279i 0.865735 0.500502i \(-0.166851\pi\)
0.406207 + 0.913781i \(0.366851\pi\)
\(798\) −21.8583 30.0854i −0.773776 1.06501i
\(799\) −0.971976 −0.0343860
\(800\) 0 0
\(801\) 7.27597 0.257084
\(802\) 5.99069 + 8.24547i 0.211538 + 0.291158i
\(803\) 5.86866 + 1.90684i 0.207100 + 0.0672910i
\(804\) −1.56536 + 4.81769i −0.0552061 + 0.169907i
\(805\) 0 0
\(806\) 15.6265 + 48.0934i 0.550420 + 1.69402i
\(807\) 22.2250i 0.782358i
\(808\) −1.49289 + 0.485068i −0.0525195 + 0.0170646i
\(809\) −39.5610 28.7428i −1.39089 1.01054i −0.995767 0.0919140i \(-0.970702\pi\)
−0.395124 0.918628i \(-0.629298\pi\)
\(810\) 0 0
\(811\) 14.6069 10.6125i 0.512916 0.372655i −0.301013 0.953620i \(-0.597325\pi\)
0.813929 + 0.580965i \(0.197325\pi\)
\(812\) −11.7151 + 16.1245i −0.411121 + 0.565860i
\(813\) −11.8796 + 16.3508i −0.416635 + 0.573449i
\(814\) −16.0193 + 11.6387i −0.561477 + 0.407937i
\(815\) 0 0
\(816\) −2.31570 1.68246i −0.0810658 0.0588978i
\(817\) −43.9428 + 14.2779i −1.53736 + 0.499520i
\(818\) 26.9653i 0.942819i
\(819\) −5.11914 15.7551i −0.178877 0.550527i
\(820\) 0 0
\(821\) 15.6393 48.1327i 0.545814 1.67984i −0.173232 0.984881i \(-0.555421\pi\)
0.719046 0.694962i \(-0.244579\pi\)
\(822\) −18.8577 6.12723i −0.657737 0.213712i
\(823\) 15.7568 + 21.6873i 0.549246 + 0.755972i 0.989910 0.141700i \(-0.0452568\pi\)
−0.440664 + 0.897672i \(0.645257\pi\)
\(824\) 7.12635 0.248258
\(825\) 0 0
\(826\) −28.0839 −0.977163
\(827\) −12.5580 17.2845i −0.436683 0.601042i 0.532788 0.846249i \(-0.321144\pi\)
−0.969471 + 0.245206i \(0.921144\pi\)
\(828\) −16.3473 5.31155i −0.568107 0.184589i
\(829\) 14.8675 45.7575i 0.516370 1.58922i −0.264405 0.964412i \(-0.585176\pi\)
0.780775 0.624812i \(-0.214824\pi\)
\(830\) 0 0
\(831\) 4.95702 + 15.2561i 0.171957 + 0.529230i
\(832\) 63.7021i 2.20847i
\(833\) −3.66921 + 1.19220i −0.127130 + 0.0413072i
\(834\) 16.1953 + 11.7665i 0.560796 + 0.407442i
\(835\) 0 0
\(836\) −18.0830 + 13.1380i −0.625412 + 0.454389i
\(837\) −2.62471 + 3.61260i −0.0907232 + 0.124870i
\(838\) 44.3825 61.0873i 1.53317 2.11022i
\(839\) −33.8606 + 24.6012i −1.16900 + 0.849327i −0.990889 0.134684i \(-0.956998\pi\)
−0.178110 + 0.984011i \(0.556998\pi\)
\(840\) 0 0
\(841\) 18.9418 + 13.7620i 0.653165 + 0.474552i
\(842\) −81.2886 + 26.4123i −2.80139 + 0.910227i
\(843\) 8.37308i 0.288384i
\(844\) −15.2900 47.0577i −0.526302 1.61979i
\(845\) 0 0
\(846\) 0.502787 1.54742i 0.0172862 0.0532014i
\(847\) −25.9511 8.43203i −0.891691 0.289728i
\(848\) 12.7094 + 17.4930i 0.436442 + 0.600711i
\(849\) −1.12995 −0.0387798
\(850\) 0 0
\(851\) 38.3809 1.31568
\(852\) 0.111151 + 0.152987i 0.00380799 + 0.00524124i
\(853\) −55.3537 17.9855i −1.89527 0.615812i −0.973819 0.227327i \(-0.927002\pi\)
−0.921455 0.388485i \(-0.872998\pi\)
\(854\) −22.5658 + 69.4504i −0.772186 + 2.37654i
\(855\) 0 0
\(856\) 6.82646 + 21.0097i 0.233324 + 0.718096i
\(857\) 3.22045i 0.110008i 0.998486 + 0.0550042i \(0.0175172\pi\)
−0.998486 + 0.0550042i \(0.982483\pi\)
\(858\) −16.5683 + 5.38337i −0.565633 + 0.183785i
\(859\) 40.0003 + 29.0619i 1.36479 + 0.991580i 0.998124 + 0.0612288i \(0.0195019\pi\)
0.366669 + 0.930351i \(0.380498\pi\)
\(860\) 0 0
\(861\) 21.8164 15.8505i 0.743500 0.540184i
\(862\) 17.8534 24.5731i 0.608089 0.836963i
\(863\) 12.6329 17.3878i 0.430030 0.591886i −0.537930 0.842990i \(-0.680793\pi\)
0.967960 + 0.251104i \(0.0807935\pi\)
\(864\) 6.21171 4.51307i 0.211327 0.153538i
\(865\) 0 0
\(866\) 0.960798 + 0.698061i 0.0326493 + 0.0237211i
\(867\) 14.5836 4.73851i 0.495286 0.160928i
\(868\) 37.6544i 1.27807i
\(869\) −0.769392 2.36795i −0.0260999 0.0803271i
\(870\) 0 0
\(871\) 3.07522 9.46456i 0.104200 0.320694i
\(872\) −9.14051 2.96993i −0.309537 0.100575i
\(873\) −5.99183 8.24705i −0.202793 0.279120i
\(874\) 75.8026 2.56406
\(875\) 0 0
\(876\) −10.7020 −0.361588
\(877\) 9.03971 + 12.4421i 0.305249 + 0.420140i 0.933892 0.357554i \(-0.116389\pi\)
−0.628643 + 0.777694i \(0.716389\pi\)
\(878\) −6.11054 1.98544i −0.206221 0.0670052i
\(879\) −0.735020 + 2.26216i −0.0247916 + 0.0763007i
\(880\) 0 0
\(881\) 5.84891 + 18.0011i 0.197055 + 0.606472i 0.999946 + 0.0103472i \(0.00329367\pi\)
−0.802892 + 0.596125i \(0.796706\pi\)
\(882\) 6.45821i 0.217459i
\(883\) −6.00790 + 1.95208i −0.202182 + 0.0656928i −0.408357 0.912822i \(-0.633898\pi\)
0.206175 + 0.978515i \(0.433898\pi\)
\(884\) −14.6021 10.6091i −0.491123 0.356822i
\(885\) 0 0
\(886\) 64.1303 46.5934i 2.15450 1.56534i
\(887\) −0.0424138 + 0.0583776i −0.00142412 + 0.00196013i −0.809728 0.586805i \(-0.800386\pi\)
0.808304 + 0.588765i \(0.200386\pi\)
\(888\) 5.05404 6.95628i 0.169602 0.233438i
\(889\) −25.6167 + 18.6116i −0.859156 + 0.624213i
\(890\) 0 0
\(891\) −1.24455 0.904220i −0.0416941 0.0302925i
\(892\) −1.95778 + 0.636120i −0.0655512 + 0.0212989i
\(893\) 4.10113i 0.137239i
\(894\) −6.73107 20.7161i −0.225121 0.692850i
\(895\) 0 0
\(896\) 10.6479 32.7709i 0.355721 1.09480i
\(897\) 32.1149 + 10.4348i 1.07229 + 0.348407i
\(898\) 22.6599 + 31.1886i 0.756169 + 1.04078i
\(899\) −10.5545 −0.352013
\(900\) 0 0
\(901\) 12.5840 0.419235
\(902\) −16.6687 22.9425i −0.555006 0.763901i
\(903\) −25.5026 8.28629i −0.848673 0.275751i
\(904\) 4.00128 12.3147i 0.133081 0.409580i
\(905\) 0 0
\(906\) −7.16888 22.0635i −0.238170 0.733012i
\(907\) 25.4951i 0.846550i 0.906001 + 0.423275i \(0.139120\pi\)
−0.906001 + 0.423275i \(0.860880\pi\)
\(908\) −29.0064 + 9.42474i −0.962610 + 0.312771i
\(909\) 0.879879 + 0.639269i 0.0291837 + 0.0212032i
\(910\) 0 0
\(911\) −2.87851 + 2.09136i −0.0953692 + 0.0692898i −0.634448 0.772966i \(-0.718773\pi\)
0.539079 + 0.842255i \(0.318773\pi\)
\(912\) −7.09891 + 9.77081i −0.235068 + 0.323544i
\(913\) 11.8894 16.3644i 0.393483 0.541583i
\(914\) −42.2621 + 30.7052i −1.39791 + 1.01564i
\(915\) 0 0
\(916\) −22.0698 16.0347i −0.729208 0.529801i
\(917\) 19.1734 6.22981i 0.633161 0.205727i
\(918\) 2.78860i 0.0920375i
\(919\) −2.46277 7.57962i −0.0812392 0.250029i 0.902185 0.431350i \(-0.141963\pi\)
−0.983424 + 0.181321i \(0.941963\pi\)
\(920\) 0 0
\(921\) −0.894189 + 2.75203i −0.0294645 + 0.0906825i
\(922\) 76.8241 + 24.9617i 2.53007 + 0.822068i
\(923\) −0.218362 0.300549i −0.00718747 0.00989270i
\(924\) −12.9720 −0.426749
\(925\) 0 0
\(926\) 44.1434 1.45064
\(927\) −2.90222 3.99457i −0.0953216 0.131199i
\(928\) 17.2598 + 5.60805i 0.566581 + 0.184093i
\(929\) −15.0004 + 46.1666i −0.492149 + 1.51468i 0.329205 + 0.944258i \(0.393219\pi\)
−0.821354 + 0.570419i \(0.806781\pi\)
\(930\) 0 0
\(931\) 5.03032 + 15.4817i 0.164862 + 0.507394i
\(932\) 60.0916i 1.96837i
\(933\) −6.79573 + 2.20807i −0.222482 + 0.0722888i
\(934\) 54.5571 + 39.6381i 1.78516 + 1.29700i
\(935\) 0 0
\(936\) 6.12016 4.44656i 0.200044 0.145340i
\(937\) −18.6502 + 25.6698i −0.609274 + 0.838594i −0.996518 0.0833833i \(-0.973427\pi\)
0.387243 + 0.921978i \(0.373427\pi\)
\(938\) 7.62066 10.4889i 0.248823 0.342476i
\(939\) −18.6331 + 13.5378i −0.608070 + 0.441789i
\(940\) 0 0
\(941\) −33.1752 24.1032i −1.08148 0.785742i −0.103541 0.994625i \(-0.533017\pi\)
−0.977941 + 0.208883i \(0.933017\pi\)
\(942\) −35.8395 + 11.6450i −1.16771 + 0.379414i
\(943\) 54.9681i 1.79001i
\(944\) 2.81848 + 8.67439i 0.0917337 + 0.282327i
\(945\) 0 0
\(946\) −8.71401 + 26.8190i −0.283317 + 0.871960i
\(947\) 9.33737 + 3.03389i 0.303424 + 0.0985883i 0.456772 0.889584i \(-0.349006\pi\)
−0.153348 + 0.988172i \(0.549006\pi\)
\(948\) 2.53815 + 3.49347i 0.0824353 + 0.113463i
\(949\) 21.0246 0.682487
\(950\) 0 0
\(951\) 20.7750 0.673674
\(952\) −3.46065 4.76317i −0.112160 0.154375i
\(953\) 50.5123 + 16.4125i 1.63626 + 0.531652i 0.975697 0.219123i \(-0.0703197\pi\)
0.660558 + 0.750775i \(0.270320\pi\)
\(954\) −6.50952 + 20.0343i −0.210754 + 0.648633i
\(955\) 0 0
\(956\) −0.485670 1.49474i −0.0157077 0.0483433i
\(957\) 3.63606i 0.117537i
\(958\) −22.8022 + 7.40888i −0.736705 + 0.239370i
\(959\) 23.4659 + 17.0490i 0.757754 + 0.550540i
\(960\) 0 0
\(961\) 8.94773 6.50090i 0.288636 0.209707i
\(962\) −39.6552 + 54.5807i −1.27853 + 1.75975i
\(963\) 8.99657 12.3827i 0.289910 0.399027i
\(964\) 3.25793 2.36703i 0.104931 0.0762368i
\(965\) 0 0
\(966\) 35.5908 + 25.8583i 1.14512 + 0.831976i
\(967\) −2.32754 + 0.756262i −0.0748485 + 0.0243198i −0.346202 0.938160i \(-0.612529\pi\)
0.271353 + 0.962480i \(0.412529\pi\)
\(968\) 12.4606i 0.400500i
\(969\) 2.17205 + 6.68488i 0.0697763 + 0.214749i
\(970\) 0 0
\(971\) −14.8230 + 45.6205i −0.475693 + 1.46403i 0.369328 + 0.929299i \(0.379588\pi\)
−0.845021 + 0.534734i \(0.820412\pi\)
\(972\) 2.53744 + 0.824463i 0.0813883 + 0.0264447i
\(973\) −17.2126 23.6911i −0.551811 0.759502i
\(974\) −15.4200 −0.494088
\(975\) 0 0
\(976\) 23.7161 0.759134
\(977\) 13.9276 + 19.1696i 0.445582 + 0.613291i 0.971441 0.237280i \(-0.0762560\pi\)
−0.525859 + 0.850572i \(0.676256\pi\)
\(978\) 33.4060 + 10.8543i 1.06820 + 0.347081i
\(979\) −3.45883 + 10.6452i −0.110545 + 0.340221i
\(980\) 0 0
\(981\) 2.05774 + 6.33308i 0.0656987 + 0.202200i
\(982\) 15.6284i 0.498721i
\(983\) −12.3167 + 4.00193i −0.392841 + 0.127642i −0.498775 0.866731i \(-0.666217\pi\)
0.105934 + 0.994373i \(0.466217\pi\)
\(984\) 9.96261 + 7.23826i 0.317597 + 0.230747i
\(985\) 0 0
\(986\) 5.33236 3.87419i 0.169817 0.123379i
\(987\) −1.39900 + 1.92556i −0.0445307 + 0.0612913i
\(988\) −44.7637 + 61.6119i −1.42412 + 1.96014i
\(989\) 44.2203 32.1279i 1.40612 1.02161i
\(990\) 0 0
\(991\) −35.9986 26.1545i −1.14353 0.830826i −0.155926 0.987769i \(-0.549836\pi\)
−0.987608 + 0.156943i \(0.949836\pi\)
\(992\) 32.6079 10.5949i 1.03530 0.336389i
\(993\) 19.2504i 0.610891i
\(994\) −0.149562 0.460303i −0.00474381 0.0145999i
\(995\) 0 0
\(996\) −10.8407 + 33.3644i −0.343502 + 1.05719i
\(997\) 52.8324 + 17.1663i 1.67322 + 0.543662i 0.983577 0.180488i \(-0.0577678\pi\)
0.689642 + 0.724150i \(0.257768\pi\)
\(998\) −20.3406 27.9964i −0.643869 0.886209i
\(999\) −5.95751 −0.188487
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 375.2.i.d.199.6 24
5.2 odd 4 75.2.g.c.61.1 yes 12
5.3 odd 4 375.2.g.c.301.3 12
5.4 even 2 inner 375.2.i.d.199.1 24
15.2 even 4 225.2.h.d.136.3 12
25.3 odd 20 1875.2.a.k.1.2 6
25.4 even 10 1875.2.b.f.1249.10 12
25.9 even 10 inner 375.2.i.d.49.6 24
25.12 odd 20 75.2.g.c.16.1 12
25.13 odd 20 375.2.g.c.76.3 12
25.16 even 5 inner 375.2.i.d.49.1 24
25.21 even 5 1875.2.b.f.1249.3 12
25.22 odd 20 1875.2.a.j.1.5 6
75.47 even 20 5625.2.a.p.1.2 6
75.53 even 20 5625.2.a.q.1.5 6
75.62 even 20 225.2.h.d.91.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.c.16.1 12 25.12 odd 20
75.2.g.c.61.1 yes 12 5.2 odd 4
225.2.h.d.91.3 12 75.62 even 20
225.2.h.d.136.3 12 15.2 even 4
375.2.g.c.76.3 12 25.13 odd 20
375.2.g.c.301.3 12 5.3 odd 4
375.2.i.d.49.1 24 25.16 even 5 inner
375.2.i.d.49.6 24 25.9 even 10 inner
375.2.i.d.199.1 24 5.4 even 2 inner
375.2.i.d.199.6 24 1.1 even 1 trivial
1875.2.a.j.1.5 6 25.22 odd 20
1875.2.a.k.1.2 6 25.3 odd 20
1875.2.b.f.1249.3 12 25.21 even 5
1875.2.b.f.1249.10 12 25.4 even 10
5625.2.a.p.1.2 6 75.47 even 20
5625.2.a.q.1.5 6 75.53 even 20