Properties

Label 525.2.bf.f.32.12
Level $525$
Weight $2$
Character 525.32
Analytic conductor $4.192$
Analytic rank $0$
Dimension $48$
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(32,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.32");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bf (of order \(12\), degree \(4\), 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: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.12
Character \(\chi\) \(=\) 525.32
Dual form 525.2.bf.f.443.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.35640 + 0.631395i) q^{2} +(-1.72899 + 0.102851i) q^{3} +(3.42191 + 1.97564i) q^{4} +(-4.13914 - 0.849321i) q^{6} +(1.91891 - 1.82148i) q^{7} +(3.36596 + 3.36596i) q^{8} +(2.97884 - 0.355658i) q^{9} +O(q^{10})\) \(q+(2.35640 + 0.631395i) q^{2} +(-1.72899 + 0.102851i) q^{3} +(3.42191 + 1.97564i) q^{4} +(-4.13914 - 0.849321i) q^{6} +(1.91891 - 1.82148i) q^{7} +(3.36596 + 3.36596i) q^{8} +(2.97884 - 0.355658i) q^{9} +(3.08053 + 1.77855i) q^{11} +(-6.11965 - 3.06392i) q^{12} +(-1.28412 + 1.28412i) q^{13} +(5.67179 - 3.08053i) q^{14} +(1.85502 + 3.21299i) q^{16} +(0.792145 + 2.95633i) q^{17} +(7.24390 + 1.04276i) q^{18} +(0.331717 - 0.191517i) q^{19} +(-3.13045 + 3.34668i) q^{21} +(6.13600 + 6.13600i) q^{22} +(-0.658656 + 2.45814i) q^{23} +(-6.16592 - 5.47354i) q^{24} +(-3.83669 + 2.21512i) q^{26} +(-5.11382 + 0.921307i) q^{27} +(10.1649 - 2.44184i) q^{28} -5.51741 q^{29} +(0.323980 - 0.561149i) q^{31} +(-0.121554 - 0.453646i) q^{32} +(-5.50915 - 2.75826i) q^{33} +7.46644i q^{34} +(10.8960 + 4.66809i) q^{36} +(1.34101 - 5.00473i) q^{37} +(0.902580 - 0.241846i) q^{38} +(2.08817 - 2.35231i) q^{39} -10.1075i q^{41} +(-9.48967 + 5.90957i) q^{42} +(0.335236 - 0.335236i) q^{43} +(7.02753 + 12.1720i) q^{44} +(-3.10411 + 5.37648i) q^{46} +(2.80533 + 0.751687i) q^{47} +(-3.53778 - 5.36445i) q^{48} +(0.364449 - 6.99051i) q^{49} +(-1.67368 - 5.03000i) q^{51} +(-6.93111 + 1.85718i) q^{52} +(-3.04243 + 0.815217i) q^{53} +(-12.6319 - 1.05788i) q^{54} +(12.5900 + 0.327966i) q^{56} +(-0.553839 + 0.365249i) q^{57} +(-13.0012 - 3.48367i) q^{58} +(-3.81595 + 6.60942i) q^{59} +(-5.45977 - 9.45659i) q^{61} +(1.11773 - 1.11773i) q^{62} +(5.06832 - 6.10837i) q^{63} -8.56580i q^{64} +(-11.2402 - 9.97802i) q^{66} +(-12.3899 + 3.31987i) q^{67} +(-3.12999 + 11.6813i) q^{68} +(0.885991 - 4.31785i) q^{69} +3.06673i q^{71} +(11.2238 + 8.82954i) q^{72} +(0.849702 + 3.17113i) q^{73} +(6.31993 - 10.9464i) q^{74} +1.51347 q^{76} +(9.15085 - 2.19824i) q^{77} +(6.40579 - 4.22453i) q^{78} +(-3.21262 + 1.85480i) q^{79} +(8.74702 - 2.11890i) q^{81} +(6.38180 - 23.8172i) q^{82} +(-0.973978 - 0.973978i) q^{83} +(-17.3239 + 5.26741i) q^{84} +(1.00162 - 0.578284i) q^{86} +(9.53957 - 0.567471i) q^{87} +(4.38244 + 16.3555i) q^{88} +(-1.51967 - 2.63215i) q^{89} +(-0.125120 + 4.80311i) q^{91} +(-7.11025 + 7.11025i) q^{92} +(-0.502444 + 1.00355i) q^{93} +(6.13587 + 3.54255i) q^{94} +(0.256825 + 0.771850i) q^{96} +(10.3438 + 10.3438i) q^{97} +(5.27256 - 16.2423i) q^{98} +(9.80898 + 4.20240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 2 q^{3} - 24 q^{6} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 2 q^{3} - 24 q^{6} + 12 q^{7} + 10 q^{12} + 16 q^{13} - 8 q^{16} - 14 q^{18} - 28 q^{21} + 8 q^{22} - 40 q^{27} + 60 q^{28} - 24 q^{31} + 4 q^{33} + 8 q^{36} - 4 q^{37} - 14 q^{42} - 16 q^{43} - 32 q^{46} - 44 q^{48} + 8 q^{51} - 36 q^{52} + 88 q^{57} - 56 q^{58} - 8 q^{61} - 44 q^{63} + 76 q^{66} - 12 q^{67} + 34 q^{72} - 52 q^{73} + 64 q^{76} + 120 q^{78} + 20 q^{81} - 104 q^{82} + 46 q^{87} + 72 q^{91} + 44 q^{93} + 12 q^{96} + 120 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.35640 + 0.631395i 1.66623 + 0.446464i 0.964089 0.265578i \(-0.0855629\pi\)
0.702137 + 0.712042i \(0.252230\pi\)
\(3\) −1.72899 + 0.102851i −0.998235 + 0.0593810i
\(4\) 3.42191 + 1.97564i 1.71095 + 0.987819i
\(5\) 0 0
\(6\) −4.13914 0.849321i −1.68980 0.346734i
\(7\) 1.91891 1.82148i 0.725281 0.688453i
\(8\) 3.36596 + 3.36596i 1.19005 + 1.19005i
\(9\) 2.97884 0.355658i 0.992948 0.118553i
\(10\) 0 0
\(11\) 3.08053 + 1.77855i 0.928816 + 0.536252i 0.886437 0.462850i \(-0.153173\pi\)
0.0423788 + 0.999102i \(0.486506\pi\)
\(12\) −6.11965 3.06392i −1.76659 0.884478i
\(13\) −1.28412 + 1.28412i −0.356151 + 0.356151i −0.862392 0.506241i \(-0.831035\pi\)
0.506241 + 0.862392i \(0.331035\pi\)
\(14\) 5.67179 3.08053i 1.51585 0.823307i
\(15\) 0 0
\(16\) 1.85502 + 3.21299i 0.463755 + 0.803247i
\(17\) 0.792145 + 2.95633i 0.192123 + 0.717015i 0.992993 + 0.118175i \(0.0377045\pi\)
−0.800869 + 0.598839i \(0.795629\pi\)
\(18\) 7.24390 + 1.04276i 1.70740 + 0.245780i
\(19\) 0.331717 0.191517i 0.0761011 0.0439370i −0.461467 0.887158i \(-0.652677\pi\)
0.537568 + 0.843221i \(0.319343\pi\)
\(20\) 0 0
\(21\) −3.13045 + 3.34668i −0.683120 + 0.730306i
\(22\) 6.13600 + 6.13600i 1.30820 + 1.30820i
\(23\) −0.658656 + 2.45814i −0.137339 + 0.512557i 0.862638 + 0.505822i \(0.168811\pi\)
−0.999977 + 0.00673550i \(0.997856\pi\)
\(24\) −6.16592 5.47354i −1.25861 1.11728i
\(25\) 0 0
\(26\) −3.83669 + 2.21512i −0.752437 + 0.434420i
\(27\) −5.11382 + 0.921307i −0.984156 + 0.177306i
\(28\) 10.1649 2.44184i 1.92099 0.461465i
\(29\) −5.51741 −1.02456 −0.512279 0.858819i \(-0.671199\pi\)
−0.512279 + 0.858819i \(0.671199\pi\)
\(30\) 0 0
\(31\) 0.323980 0.561149i 0.0581885 0.100785i −0.835464 0.549546i \(-0.814801\pi\)
0.893652 + 0.448760i \(0.148134\pi\)
\(32\) −0.121554 0.453646i −0.0214880 0.0801941i
\(33\) −5.50915 2.75826i −0.959020 0.480152i
\(34\) 7.46644i 1.28048i
\(35\) 0 0
\(36\) 10.8960 + 4.66809i 1.81600 + 0.778015i
\(37\) 1.34101 5.00473i 0.220461 0.822772i −0.763711 0.645558i \(-0.776625\pi\)
0.984172 0.177214i \(-0.0567086\pi\)
\(38\) 0.902580 0.241846i 0.146418 0.0392325i
\(39\) 2.08817 2.35231i 0.334374 0.376671i
\(40\) 0 0
\(41\) 10.1075i 1.57852i −0.614060 0.789259i \(-0.710465\pi\)
0.614060 0.789259i \(-0.289535\pi\)
\(42\) −9.48967 + 5.90957i −1.46429 + 0.911867i
\(43\) 0.335236 0.335236i 0.0511231 0.0511231i −0.681083 0.732206i \(-0.738491\pi\)
0.732206 + 0.681083i \(0.238491\pi\)
\(44\) 7.02753 + 12.1720i 1.05944 + 1.83500i
\(45\) 0 0
\(46\) −3.10411 + 5.37648i −0.457677 + 0.792719i
\(47\) 2.80533 + 0.751687i 0.409200 + 0.109645i 0.457546 0.889186i \(-0.348728\pi\)
−0.0483463 + 0.998831i \(0.515395\pi\)
\(48\) −3.53778 5.36445i −0.510634 0.774291i
\(49\) 0.364449 6.99051i 0.0520641 0.998644i
\(50\) 0 0
\(51\) −1.67368 5.03000i −0.234362 0.704341i
\(52\) −6.93111 + 1.85718i −0.961171 + 0.257545i
\(53\) −3.04243 + 0.815217i −0.417910 + 0.111979i −0.461645 0.887065i \(-0.652741\pi\)
0.0437355 + 0.999043i \(0.486074\pi\)
\(54\) −12.6319 1.05788i −1.71899 0.143959i
\(55\) 0 0
\(56\) 12.5900 + 0.327966i 1.68241 + 0.0438263i
\(57\) −0.553839 + 0.365249i −0.0733578 + 0.0483784i
\(58\) −13.0012 3.48367i −1.70714 0.457428i
\(59\) −3.81595 + 6.60942i −0.496795 + 0.860474i −0.999993 0.00369723i \(-0.998823\pi\)
0.503198 + 0.864171i \(0.332156\pi\)
\(60\) 0 0
\(61\) −5.45977 9.45659i −0.699051 1.21079i −0.968796 0.247860i \(-0.920273\pi\)
0.269744 0.962932i \(-0.413061\pi\)
\(62\) 1.11773 1.11773i 0.141952 0.141952i
\(63\) 5.06832 6.10837i 0.638548 0.769582i
\(64\) 8.56580i 1.07072i
\(65\) 0 0
\(66\) −11.2402 9.97802i −1.38357 1.22821i
\(67\) −12.3899 + 3.31987i −1.51367 + 0.405586i −0.917652 0.397386i \(-0.869918\pi\)
−0.596017 + 0.802972i \(0.703251\pi\)
\(68\) −3.12999 + 11.6813i −0.379567 + 1.41656i
\(69\) 0.885991 4.31785i 0.106661 0.519808i
\(70\) 0 0
\(71\) 3.06673i 0.363954i 0.983303 + 0.181977i \(0.0582497\pi\)
−0.983303 + 0.181977i \(0.941750\pi\)
\(72\) 11.2238 + 8.82954i 1.32274 + 1.04057i
\(73\) 0.849702 + 3.17113i 0.0994501 + 0.371153i 0.997657 0.0684210i \(-0.0217961\pi\)
−0.898206 + 0.439574i \(0.855129\pi\)
\(74\) 6.31993 10.9464i 0.734676 1.27250i
\(75\) 0 0
\(76\) 1.51347 0.173607
\(77\) 9.15085 2.19824i 1.04284 0.250513i
\(78\) 6.40579 4.22453i 0.725313 0.478334i
\(79\) −3.21262 + 1.85480i −0.361448 + 0.208682i −0.669716 0.742618i \(-0.733584\pi\)
0.308268 + 0.951300i \(0.400251\pi\)
\(80\) 0 0
\(81\) 8.74702 2.11890i 0.971891 0.235433i
\(82\) 6.38180 23.8172i 0.704752 2.63017i
\(83\) −0.973978 0.973978i −0.106908 0.106908i 0.651629 0.758537i \(-0.274086\pi\)
−0.758537 + 0.651629i \(0.774086\pi\)
\(84\) −17.3239 + 5.26741i −1.89020 + 0.574721i
\(85\) 0 0
\(86\) 1.00162 0.578284i 0.108007 0.0623580i
\(87\) 9.53957 0.567471i 1.02275 0.0608393i
\(88\) 4.38244 + 16.3555i 0.467169 + 1.74350i
\(89\) −1.51967 2.63215i −0.161085 0.279007i 0.774173 0.632974i \(-0.218166\pi\)
−0.935258 + 0.353967i \(0.884833\pi\)
\(90\) 0 0
\(91\) −0.125120 + 4.80311i −0.0131161 + 0.503503i
\(92\) −7.11025 + 7.11025i −0.741295 + 0.741295i
\(93\) −0.502444 + 1.00355i −0.0521011 + 0.104063i
\(94\) 6.13587 + 3.54255i 0.632867 + 0.365386i
\(95\) 0 0
\(96\) 0.256825 + 0.771850i 0.0262120 + 0.0787766i
\(97\) 10.3438 + 10.3438i 1.05025 + 1.05025i 0.998669 + 0.0515850i \(0.0164273\pi\)
0.0515850 + 0.998669i \(0.483573\pi\)
\(98\) 5.27256 16.2423i 0.532609 1.64072i
\(99\) 9.80898 + 4.20240i 0.985839 + 0.422357i
\(100\) 0 0
\(101\) 0.158115 + 0.0912877i 0.0157330 + 0.00908347i 0.507846 0.861448i \(-0.330442\pi\)
−0.492113 + 0.870531i \(0.663775\pi\)
\(102\) −0.767931 12.9094i −0.0760365 1.27822i
\(103\) −4.69347 1.25761i −0.462461 0.123916i 0.0200632 0.999799i \(-0.493613\pi\)
−0.482524 + 0.875883i \(0.660280\pi\)
\(104\) −8.64461 −0.847674
\(105\) 0 0
\(106\) −7.68390 −0.746327
\(107\) −10.4080 2.78881i −1.00618 0.269605i −0.282146 0.959371i \(-0.591046\pi\)
−0.724032 + 0.689767i \(0.757713\pi\)
\(108\) −19.3192 6.95044i −1.85899 0.668807i
\(109\) 8.84242 + 5.10517i 0.846950 + 0.488987i 0.859621 0.510933i \(-0.170700\pi\)
−0.0126703 + 0.999920i \(0.504033\pi\)
\(110\) 0 0
\(111\) −1.80386 + 8.79107i −0.171215 + 0.834412i
\(112\) 9.41200 + 2.78657i 0.889350 + 0.263306i
\(113\) −7.98156 7.98156i −0.750842 0.750842i 0.223794 0.974636i \(-0.428156\pi\)
−0.974636 + 0.223794i \(0.928156\pi\)
\(114\) −1.53568 + 0.510981i −0.143830 + 0.0478578i
\(115\) 0 0
\(116\) −18.8801 10.9004i −1.75297 1.01208i
\(117\) −3.36849 + 4.28191i −0.311417 + 0.395862i
\(118\) −13.1651 + 13.1651i −1.21194 + 1.21194i
\(119\) 6.90494 + 4.23006i 0.632974 + 0.387769i
\(120\) 0 0
\(121\) 0.826456 + 1.43146i 0.0751323 + 0.130133i
\(122\) −6.89454 25.7308i −0.624202 2.32955i
\(123\) 1.03956 + 17.4757i 0.0937341 + 1.57573i
\(124\) 2.21726 1.28013i 0.199116 0.114959i
\(125\) 0 0
\(126\) 15.7998 11.1936i 1.40756 0.997209i
\(127\) −2.79324 2.79324i −0.247860 0.247860i 0.572232 0.820092i \(-0.306078\pi\)
−0.820092 + 0.572232i \(0.806078\pi\)
\(128\) 5.16530 19.2771i 0.456552 1.70387i
\(129\) −0.545143 + 0.614101i −0.0479971 + 0.0540686i
\(130\) 0 0
\(131\) −7.64504 + 4.41386i −0.667950 + 0.385641i −0.795299 0.606217i \(-0.792686\pi\)
0.127349 + 0.991858i \(0.459353\pi\)
\(132\) −13.4025 20.3226i −1.16654 1.76886i
\(133\) 0.287692 0.971718i 0.0249461 0.0842587i
\(134\) −31.2917 −2.70319
\(135\) 0 0
\(136\) −7.28455 + 12.6172i −0.624645 + 1.08192i
\(137\) 3.09498 + 11.5506i 0.264422 + 0.986836i 0.962603 + 0.270915i \(0.0873263\pi\)
−0.698181 + 0.715921i \(0.746007\pi\)
\(138\) 4.81402 9.61517i 0.409797 0.818498i
\(139\) 8.03342i 0.681386i 0.940175 + 0.340693i \(0.110662\pi\)
−0.940175 + 0.340693i \(0.889338\pi\)
\(140\) 0 0
\(141\) −4.92772 1.01113i −0.414989 0.0851526i
\(142\) −1.93632 + 7.22644i −0.162492 + 0.606430i
\(143\) −6.23965 + 1.67191i −0.521786 + 0.139812i
\(144\) 6.66853 + 8.91123i 0.555711 + 0.742603i
\(145\) 0 0
\(146\) 8.00895i 0.662826i
\(147\) 0.0888504 + 12.1240i 0.00732825 + 0.999973i
\(148\) 14.4764 14.4764i 1.18995 1.18995i
\(149\) −8.89069 15.3991i −0.728354 1.26155i −0.957579 0.288172i \(-0.906952\pi\)
0.229225 0.973374i \(-0.426381\pi\)
\(150\) 0 0
\(151\) −9.95334 + 17.2397i −0.809991 + 1.40295i 0.102878 + 0.994694i \(0.467195\pi\)
−0.912869 + 0.408252i \(0.866139\pi\)
\(152\) 1.76118 + 0.471908i 0.142851 + 0.0382768i
\(153\) 3.41112 + 8.52470i 0.275772 + 0.689181i
\(154\) 22.9510 + 0.597868i 1.84945 + 0.0481776i
\(155\) 0 0
\(156\) 11.7928 3.92393i 0.944182 0.314166i
\(157\) 9.98465 2.67538i 0.796862 0.213519i 0.162656 0.986683i \(-0.447994\pi\)
0.634206 + 0.773164i \(0.281327\pi\)
\(158\) −8.74132 + 2.34223i −0.695422 + 0.186338i
\(159\) 5.17650 1.72242i 0.410523 0.136597i
\(160\) 0 0
\(161\) 3.21354 + 5.91668i 0.253262 + 0.466300i
\(162\) 21.9493 + 0.529858i 1.72450 + 0.0416296i
\(163\) 19.3203 + 5.17687i 1.51329 + 0.405484i 0.917525 0.397678i \(-0.130184\pi\)
0.595761 + 0.803162i \(0.296851\pi\)
\(164\) 19.9687 34.5868i 1.55929 2.70077i
\(165\) 0 0
\(166\) −1.68012 2.91005i −0.130402 0.225863i
\(167\) 6.08875 6.08875i 0.471162 0.471162i −0.431129 0.902290i \(-0.641884\pi\)
0.902290 + 0.431129i \(0.141884\pi\)
\(168\) −21.8018 + 0.727843i −1.68204 + 0.0561543i
\(169\) 9.70206i 0.746312i
\(170\) 0 0
\(171\) 0.920018 0.688476i 0.0703556 0.0526491i
\(172\) 1.80945 0.484842i 0.137970 0.0369688i
\(173\) 0.435117 1.62388i 0.0330813 0.123461i −0.947411 0.320021i \(-0.896310\pi\)
0.980492 + 0.196559i \(0.0629768\pi\)
\(174\) 22.8373 + 4.68605i 1.73129 + 0.355249i
\(175\) 0 0
\(176\) 13.1969i 0.994758i
\(177\) 5.91797 11.8201i 0.444822 0.888455i
\(178\) −1.91903 7.16190i −0.143837 0.536807i
\(179\) −10.5758 + 18.3178i −0.790470 + 1.36913i 0.135206 + 0.990818i \(0.456830\pi\)
−0.925676 + 0.378317i \(0.876503\pi\)
\(180\) 0 0
\(181\) 22.4232 1.66671 0.833353 0.552740i \(-0.186418\pi\)
0.833353 + 0.552740i \(0.186418\pi\)
\(182\) −3.32750 + 11.2391i −0.246650 + 0.833094i
\(183\) 10.4125 + 15.7889i 0.769716 + 1.16715i
\(184\) −10.4910 + 6.05699i −0.773407 + 0.446527i
\(185\) 0 0
\(186\) −1.81759 + 2.04751i −0.133272 + 0.150131i
\(187\) −2.81773 + 10.5159i −0.206053 + 0.769001i
\(188\) 8.11453 + 8.11453i 0.591813 + 0.591813i
\(189\) −8.13484 + 11.0826i −0.591723 + 0.806142i
\(190\) 0 0
\(191\) 16.3692 9.45078i 1.18444 0.683834i 0.227399 0.973802i \(-0.426978\pi\)
0.957037 + 0.289967i \(0.0936444\pi\)
\(192\) 0.881001 + 14.8102i 0.0635807 + 1.06884i
\(193\) −3.98500 14.8722i −0.286847 1.07053i −0.947479 0.319817i \(-0.896379\pi\)
0.660633 0.750709i \(-0.270288\pi\)
\(194\) 17.8431 + 30.9051i 1.28106 + 2.21886i
\(195\) 0 0
\(196\) 15.0578 23.2008i 1.07556 1.65720i
\(197\) −0.582177 + 0.582177i −0.0414784 + 0.0414784i −0.727542 0.686063i \(-0.759337\pi\)
0.686063 + 0.727542i \(0.259337\pi\)
\(198\) 20.4605 + 16.0959i 1.45406 + 1.14388i
\(199\) −4.00381 2.31160i −0.283823 0.163865i 0.351330 0.936252i \(-0.385730\pi\)
−0.635153 + 0.772387i \(0.719063\pi\)
\(200\) 0 0
\(201\) 21.0806 7.01435i 1.48691 0.494754i
\(202\) 0.314943 + 0.314943i 0.0221593 + 0.0221593i
\(203\) −10.5874 + 10.0498i −0.743092 + 0.705360i
\(204\) 4.21030 20.5188i 0.294780 1.43660i
\(205\) 0 0
\(206\) −10.2656 5.92686i −0.715240 0.412944i
\(207\) −1.08778 + 7.55667i −0.0756058 + 0.525225i
\(208\) −6.50794 1.74380i −0.451244 0.120911i
\(209\) 1.36249 0.0942452
\(210\) 0 0
\(211\) 22.8142 1.57060 0.785298 0.619118i \(-0.212510\pi\)
0.785298 + 0.619118i \(0.212510\pi\)
\(212\) −12.0215 3.22115i −0.825639 0.221229i
\(213\) −0.315416 5.30236i −0.0216120 0.363312i
\(214\) −22.7645 13.1431i −1.55615 0.898444i
\(215\) 0 0
\(216\) −20.3140 14.1118i −1.38219 0.960190i
\(217\) −0.400432 1.66692i −0.0271831 0.113158i
\(218\) 17.6129 + 17.6129i 1.19290 + 1.19290i
\(219\) −1.79528 5.39548i −0.121314 0.364593i
\(220\) 0 0
\(221\) −4.81349 2.77907i −0.323791 0.186941i
\(222\) −9.80126 + 19.5763i −0.657818 + 1.31388i
\(223\) 9.51124 9.51124i 0.636920 0.636920i −0.312875 0.949794i \(-0.601292\pi\)
0.949794 + 0.312875i \(0.101292\pi\)
\(224\) −1.05956 0.649100i −0.0707947 0.0433698i
\(225\) 0 0
\(226\) −13.7682 23.8473i −0.915849 1.58630i
\(227\) −0.571878 2.13428i −0.0379569 0.141657i 0.944347 0.328951i \(-0.106695\pi\)
−0.982304 + 0.187294i \(0.940028\pi\)
\(228\) −2.61679 + 0.155662i −0.173301 + 0.0103090i
\(229\) −22.0869 + 12.7519i −1.45954 + 0.842668i −0.998989 0.0449629i \(-0.985683\pi\)
−0.460555 + 0.887631i \(0.652350\pi\)
\(230\) 0 0
\(231\) −15.5957 + 4.74192i −1.02612 + 0.311996i
\(232\) −18.5714 18.5714i −1.21927 1.21927i
\(233\) 6.67968 24.9289i 0.437601 1.63315i −0.297164 0.954826i \(-0.596041\pi\)
0.734765 0.678322i \(-0.237292\pi\)
\(234\) −10.6411 + 7.96303i −0.695629 + 0.520560i
\(235\) 0 0
\(236\) −26.1157 + 15.0779i −1.69998 + 0.981487i
\(237\) 5.36383 3.53737i 0.348418 0.229777i
\(238\) 13.5999 + 14.3274i 0.881554 + 0.928711i
\(239\) 5.35194 0.346188 0.173094 0.984905i \(-0.444624\pi\)
0.173094 + 0.984905i \(0.444624\pi\)
\(240\) 0 0
\(241\) −4.02361 + 6.96910i −0.259184 + 0.448919i −0.966023 0.258454i \(-0.916787\pi\)
0.706840 + 0.707374i \(0.250120\pi\)
\(242\) 1.04364 + 3.89492i 0.0670877 + 0.250375i
\(243\) −14.9056 + 4.56320i −0.956195 + 0.292729i
\(244\) 43.1461i 2.76215i
\(245\) 0 0
\(246\) −8.58447 + 41.8362i −0.547326 + 2.66738i
\(247\) −0.180034 + 0.671896i −0.0114553 + 0.0427517i
\(248\) 2.97931 0.798304i 0.189186 0.0506923i
\(249\) 1.78418 + 1.58383i 0.113068 + 0.100371i
\(250\) 0 0
\(251\) 4.25486i 0.268565i 0.990943 + 0.134282i \(0.0428729\pi\)
−0.990943 + 0.134282i \(0.957127\pi\)
\(252\) 29.4112 10.8891i 1.85273 0.685949i
\(253\) −6.40093 + 6.40093i −0.402423 + 0.402423i
\(254\) −4.81835 8.34562i −0.302330 0.523651i
\(255\) 0 0
\(256\) 15.7772 27.3269i 0.986075 1.70793i
\(257\) 3.49869 + 0.937470i 0.218242 + 0.0584778i 0.366283 0.930503i \(-0.380630\pi\)
−0.148041 + 0.988981i \(0.547297\pi\)
\(258\) −1.67231 + 1.10287i −0.104114 + 0.0686615i
\(259\) −6.54271 12.0463i −0.406544 0.748518i
\(260\) 0 0
\(261\) −16.4355 + 1.96231i −1.01733 + 0.121464i
\(262\) −20.8017 + 5.57379i −1.28513 + 0.344350i
\(263\) 7.44545 1.99500i 0.459106 0.123017i −0.0218510 0.999761i \(-0.506956\pi\)
0.480957 + 0.876744i \(0.340289\pi\)
\(264\) −9.25938 27.8278i −0.569876 1.71268i
\(265\) 0 0
\(266\) 1.29146 2.10811i 0.0791843 0.129256i
\(267\) 2.89822 + 4.39467i 0.177368 + 0.268949i
\(268\) −48.9560 13.1177i −2.99046 0.801292i
\(269\) 9.75238 16.8916i 0.594613 1.02990i −0.398988 0.916956i \(-0.630638\pi\)
0.993601 0.112944i \(-0.0360282\pi\)
\(270\) 0 0
\(271\) 10.1887 + 17.6473i 0.618919 + 1.07200i 0.989683 + 0.143273i \(0.0457626\pi\)
−0.370764 + 0.928727i \(0.620904\pi\)
\(272\) −8.02919 + 8.02919i −0.486841 + 0.486841i
\(273\) −0.277674 8.31743i −0.0168056 0.503394i
\(274\) 29.1720i 1.76235i
\(275\) 0 0
\(276\) 11.5623 13.0249i 0.695968 0.784006i
\(277\) −11.0945 + 2.97277i −0.666605 + 0.178616i −0.576225 0.817291i \(-0.695475\pi\)
−0.0903802 + 0.995907i \(0.528808\pi\)
\(278\) −5.07226 + 18.9299i −0.304214 + 1.13534i
\(279\) 0.765508 1.78680i 0.0458298 0.106973i
\(280\) 0 0
\(281\) 1.16755i 0.0696500i 0.999393 + 0.0348250i \(0.0110874\pi\)
−0.999393 + 0.0348250i \(0.988913\pi\)
\(282\) −10.9732 5.49397i −0.653447 0.327161i
\(283\) 6.31899 + 23.5828i 0.375625 + 1.40185i 0.852430 + 0.522841i \(0.175128\pi\)
−0.476805 + 0.879009i \(0.658205\pi\)
\(284\) −6.05875 + 10.4941i −0.359521 + 0.622708i
\(285\) 0 0
\(286\) −15.7587 −0.931834
\(287\) −18.4105 19.3953i −1.08674 1.14487i
\(288\) −0.523434 1.30811i −0.0308436 0.0770811i
\(289\) 6.61006 3.81632i 0.388827 0.224489i
\(290\) 0 0
\(291\) −18.9482 16.8205i −1.11077 0.986035i
\(292\) −3.35741 + 12.5300i −0.196478 + 0.733264i
\(293\) −17.1201 17.1201i −1.00016 1.00016i −1.00000 0.000164506i \(-0.999948\pi\)
−0.000164506 1.00000i \(-0.500052\pi\)
\(294\) −7.44569 + 28.6252i −0.434241 + 1.66945i
\(295\) 0 0
\(296\) 21.3595 12.3319i 1.24150 0.716779i
\(297\) −17.3919 6.25706i −1.00918 0.363071i
\(298\) −11.2271 41.9000i −0.650367 2.42720i
\(299\) −2.31075 4.00234i −0.133634 0.231462i
\(300\) 0 0
\(301\) 0.0326641 1.25391i 0.00188273 0.0722744i
\(302\) −34.3391 + 34.3391i −1.97599 + 1.97599i
\(303\) −0.282769 0.141574i −0.0162447 0.00813320i
\(304\) 1.23068 + 0.710535i 0.0705845 + 0.0407520i
\(305\) 0 0
\(306\) 2.65550 + 22.2414i 0.151805 + 1.27145i
\(307\) 9.35548 + 9.35548i 0.533946 + 0.533946i 0.921744 0.387799i \(-0.126764\pi\)
−0.387799 + 0.921744i \(0.626764\pi\)
\(308\) 35.6563 + 10.5566i 2.03171 + 0.601518i
\(309\) 8.24432 + 1.69167i 0.469003 + 0.0962359i
\(310\) 0 0
\(311\) −2.36072 1.36296i −0.133864 0.0772864i 0.431572 0.902078i \(-0.357959\pi\)
−0.565436 + 0.824792i \(0.691292\pi\)
\(312\) 14.9465 0.889107i 0.846178 0.0503357i
\(313\) 25.0318 + 6.70726i 1.41488 + 0.379117i 0.883666 0.468118i \(-0.155068\pi\)
0.531218 + 0.847235i \(0.321735\pi\)
\(314\) 25.2171 1.42308
\(315\) 0 0
\(316\) −14.6577 −0.824560
\(317\) 4.55428 + 1.22032i 0.255794 + 0.0685398i 0.384437 0.923151i \(-0.374396\pi\)
−0.128643 + 0.991691i \(0.541062\pi\)
\(318\) 13.2854 0.790297i 0.745010 0.0443177i
\(319\) −16.9966 9.81297i −0.951625 0.549421i
\(320\) 0 0
\(321\) 18.2822 + 3.75137i 1.02041 + 0.209381i
\(322\) 3.83661 + 15.9711i 0.213806 + 0.890033i
\(323\) 0.828954 + 0.828954i 0.0461243 + 0.0461243i
\(324\) 34.1176 + 10.0303i 1.89542 + 0.557238i
\(325\) 0 0
\(326\) 42.2578 + 24.3975i 2.34044 + 1.35125i
\(327\) −15.8136 7.91737i −0.874492 0.437831i
\(328\) 34.0213 34.0213i 1.87851 1.87851i
\(329\) 6.75237 3.66743i 0.372270 0.202192i
\(330\) 0 0
\(331\) −5.05610 8.75743i −0.277909 0.481352i 0.692956 0.720980i \(-0.256308\pi\)
−0.970865 + 0.239628i \(0.922975\pi\)
\(332\) −1.40863 5.25709i −0.0773088 0.288520i
\(333\) 2.21470 15.3852i 0.121365 0.843106i
\(334\) 18.1919 10.5031i 0.995419 0.574705i
\(335\) 0 0
\(336\) −16.5599 3.84993i −0.903416 0.210031i
\(337\) −8.78763 8.78763i −0.478692 0.478692i 0.426021 0.904713i \(-0.359915\pi\)
−0.904713 + 0.426021i \(0.859915\pi\)
\(338\) −6.12584 + 22.8619i −0.333202 + 1.24353i
\(339\) 14.6210 + 12.9792i 0.794103 + 0.704931i
\(340\) 0 0
\(341\) 1.99606 1.15243i 0.108093 0.0624074i
\(342\) 2.60263 1.04143i 0.140734 0.0563141i
\(343\) −12.0337 14.0780i −0.649758 0.760141i
\(344\) 2.25679 0.121678
\(345\) 0 0
\(346\) 2.05062 3.55177i 0.110242 0.190945i
\(347\) 2.85959 + 10.6721i 0.153511 + 0.572911i 0.999228 + 0.0392795i \(0.0125063\pi\)
−0.845717 + 0.533631i \(0.820827\pi\)
\(348\) 33.7647 + 16.9049i 1.80998 + 0.906199i
\(349\) 6.84738i 0.366532i 0.983063 + 0.183266i \(0.0586670\pi\)
−0.983063 + 0.183266i \(0.941333\pi\)
\(350\) 0 0
\(351\) 5.38370 7.74984i 0.287361 0.413656i
\(352\) 0.432380 1.61366i 0.0230459 0.0860085i
\(353\) 21.5279 5.76838i 1.14581 0.307020i 0.364528 0.931192i \(-0.381230\pi\)
0.781287 + 0.624172i \(0.214564\pi\)
\(354\) 21.4083 24.1164i 1.13784 1.28177i
\(355\) 0 0
\(356\) 12.0093i 0.636491i
\(357\) −12.3737 6.60357i −0.654884 0.349498i
\(358\) −36.4865 + 36.4865i −1.92837 + 1.92837i
\(359\) 13.3858 + 23.1849i 0.706476 + 1.22365i 0.966156 + 0.257958i \(0.0830495\pi\)
−0.259680 + 0.965695i \(0.583617\pi\)
\(360\) 0 0
\(361\) −9.42664 + 16.3274i −0.496139 + 0.859338i
\(362\) 52.8381 + 14.1579i 2.77711 + 0.744124i
\(363\) −1.57616 2.38999i −0.0827272 0.125442i
\(364\) −9.91737 + 16.1886i −0.519811 + 0.848514i
\(365\) 0 0
\(366\) 14.5671 + 43.7793i 0.761432 + 2.28838i
\(367\) 16.2394 4.35135i 0.847692 0.227138i 0.191275 0.981536i \(-0.438738\pi\)
0.656417 + 0.754398i \(0.272071\pi\)
\(368\) −9.11979 + 2.44364i −0.475402 + 0.127384i
\(369\) −3.59479 30.1085i −0.187137 1.56739i
\(370\) 0 0
\(371\) −4.35326 + 7.10604i −0.226010 + 0.368927i
\(372\) −3.70196 + 2.44139i −0.191938 + 0.126580i
\(373\) 10.1335 + 2.71527i 0.524694 + 0.140591i 0.511437 0.859321i \(-0.329113\pi\)
0.0132570 + 0.999912i \(0.495780\pi\)
\(374\) −13.2794 + 23.0006i −0.686662 + 1.18933i
\(375\) 0 0
\(376\) 6.91249 + 11.9728i 0.356485 + 0.617450i
\(377\) 7.08503 7.08503i 0.364898 0.364898i
\(378\) −26.1664 + 20.9788i −1.34586 + 1.07903i
\(379\) 22.0750i 1.13391i −0.823747 0.566957i \(-0.808120\pi\)
0.823747 0.566957i \(-0.191880\pi\)
\(380\) 0 0
\(381\) 5.11678 + 4.54221i 0.262141 + 0.232704i
\(382\) 44.5396 11.9344i 2.27885 0.610615i
\(383\) −5.20486 + 19.4248i −0.265956 + 0.992561i 0.695707 + 0.718326i \(0.255091\pi\)
−0.961663 + 0.274235i \(0.911575\pi\)
\(384\) −6.94809 + 33.8613i −0.354568 + 1.72798i
\(385\) 0 0
\(386\) 37.5610i 1.91181i
\(387\) 0.879387 1.11785i 0.0447018 0.0568233i
\(388\) 14.9599 + 55.8311i 0.759474 + 2.83440i
\(389\) −0.689060 + 1.19349i −0.0349368 + 0.0605122i −0.882965 0.469439i \(-0.844456\pi\)
0.848028 + 0.529951i \(0.177790\pi\)
\(390\) 0 0
\(391\) −7.78881 −0.393897
\(392\) 24.7565 22.3031i 1.25039 1.12647i
\(393\) 12.7643 8.41785i 0.643872 0.424624i
\(394\) −1.73943 + 1.00426i −0.0876310 + 0.0505938i
\(395\) 0 0
\(396\) 25.2630 + 33.7592i 1.26951 + 1.69646i
\(397\) −5.76560 + 21.5175i −0.289367 + 1.07993i 0.656222 + 0.754568i \(0.272154\pi\)
−0.945589 + 0.325365i \(0.894513\pi\)
\(398\) −7.97504 7.97504i −0.399753 0.399753i
\(399\) −0.397476 + 1.70969i −0.0198987 + 0.0855913i
\(400\) 0 0
\(401\) −7.51392 + 4.33816i −0.375227 + 0.216638i −0.675740 0.737140i \(-0.736176\pi\)
0.300512 + 0.953778i \(0.402842\pi\)
\(402\) 54.1032 3.21838i 2.69842 0.160518i
\(403\) 0.304555 + 1.13661i 0.0151710 + 0.0566188i
\(404\) 0.360703 + 0.624756i 0.0179457 + 0.0310828i
\(405\) 0 0
\(406\) −31.2936 + 16.9966i −1.55308 + 0.843526i
\(407\) 13.0322 13.0322i 0.645981 0.645981i
\(408\) 11.2973 22.5643i 0.559297 1.11710i
\(409\) 6.78090 + 3.91495i 0.335294 + 0.193582i 0.658189 0.752853i \(-0.271323\pi\)
−0.322895 + 0.946435i \(0.604656\pi\)
\(410\) 0 0
\(411\) −6.53920 19.6526i −0.322555 0.969393i
\(412\) −13.5760 13.5760i −0.668842 0.668842i
\(413\) 4.71643 + 19.6336i 0.232080 + 0.966105i
\(414\) −7.33448 + 17.1197i −0.360470 + 0.841387i
\(415\) 0 0
\(416\) 0.738628 + 0.426447i 0.0362142 + 0.0209083i
\(417\) −0.826245 13.8897i −0.0404614 0.680184i
\(418\) 3.21056 + 0.860268i 0.157034 + 0.0420771i
\(419\) −17.2587 −0.843141 −0.421571 0.906796i \(-0.638521\pi\)
−0.421571 + 0.906796i \(0.638521\pi\)
\(420\) 0 0
\(421\) −30.2371 −1.47366 −0.736832 0.676076i \(-0.763679\pi\)
−0.736832 + 0.676076i \(0.763679\pi\)
\(422\) 53.7594 + 14.4048i 2.61697 + 0.701214i
\(423\) 8.62399 + 1.24142i 0.419313 + 0.0603599i
\(424\) −12.9847 7.49671i −0.630592 0.364073i
\(425\) 0 0
\(426\) 2.60464 12.6936i 0.126195 0.615009i
\(427\) −27.7018 8.20154i −1.34058 0.396900i
\(428\) −30.1055 30.1055i −1.45520 1.45520i
\(429\) 10.6164 3.53248i 0.512563 0.170550i
\(430\) 0 0
\(431\) −17.6840 10.2099i −0.851811 0.491793i 0.00945079 0.999955i \(-0.496992\pi\)
−0.861261 + 0.508162i \(0.830325\pi\)
\(432\) −12.4464 14.7216i −0.598827 0.708294i
\(433\) −14.4338 + 14.4338i −0.693646 + 0.693646i −0.963032 0.269386i \(-0.913179\pi\)
0.269386 + 0.963032i \(0.413179\pi\)
\(434\) 0.108908 4.18076i 0.00522773 0.200683i
\(435\) 0 0
\(436\) 20.1720 + 34.9389i 0.966062 + 1.67327i
\(437\) 0.252288 + 0.941550i 0.0120685 + 0.0450404i
\(438\) −0.823729 13.8474i −0.0393593 0.661656i
\(439\) 12.5945 7.27146i 0.601105 0.347048i −0.168371 0.985724i \(-0.553851\pi\)
0.769476 + 0.638676i \(0.220517\pi\)
\(440\) 0 0
\(441\) −1.40059 20.9532i −0.0666948 0.997773i
\(442\) −9.58782 9.58782i −0.456046 0.456046i
\(443\) −2.65557 + 9.91074i −0.126170 + 0.470873i −0.999879 0.0155764i \(-0.995042\pi\)
0.873709 + 0.486450i \(0.161708\pi\)
\(444\) −23.5406 + 26.5185i −1.11719 + 1.25851i
\(445\) 0 0
\(446\) 28.4176 16.4069i 1.34561 0.776890i
\(447\) 16.9558 + 25.7106i 0.801981 + 1.21607i
\(448\) −15.6024 16.4370i −0.737144 0.776576i
\(449\) −6.70137 −0.316257 −0.158129 0.987419i \(-0.550546\pi\)
−0.158129 + 0.987419i \(0.550546\pi\)
\(450\) 0 0
\(451\) 17.9766 31.1363i 0.846484 1.46615i
\(452\) −11.5435 43.0808i −0.542959 2.02635i
\(453\) 15.4361 30.8310i 0.725253 1.44857i
\(454\) 5.39029i 0.252979i
\(455\) 0 0
\(456\) −3.09361 0.634787i −0.144872 0.0297266i
\(457\) 8.00943 29.8916i 0.374665 1.39827i −0.479168 0.877723i \(-0.659061\pi\)
0.853833 0.520547i \(-0.174272\pi\)
\(458\) −60.0971 + 16.1030i −2.80815 + 0.752442i
\(459\) −6.77458 14.3883i −0.316210 0.671589i
\(460\) 0 0
\(461\) 35.1427i 1.63676i −0.574680 0.818378i \(-0.694873\pi\)
0.574680 0.818378i \(-0.305127\pi\)
\(462\) −39.7437 + 1.32683i −1.84904 + 0.0617295i
\(463\) 3.51567 3.51567i 0.163387 0.163387i −0.620678 0.784065i \(-0.713143\pi\)
0.784065 + 0.620678i \(0.213143\pi\)
\(464\) −10.2349 17.7274i −0.475143 0.822973i
\(465\) 0 0
\(466\) 31.4800 54.5250i 1.45828 2.52582i
\(467\) −29.9748 8.03172i −1.38707 0.371664i −0.513385 0.858159i \(-0.671609\pi\)
−0.873683 + 0.486495i \(0.838275\pi\)
\(468\) −19.9862 + 7.99736i −0.923860 + 0.369678i
\(469\) −17.7281 + 28.9385i −0.818607 + 1.33625i
\(470\) 0 0
\(471\) −16.9882 + 5.65265i −0.782777 + 0.260460i
\(472\) −35.0914 + 9.40271i −1.61521 + 0.432795i
\(473\) 1.62894 0.436473i 0.0748988 0.0200691i
\(474\) 14.8728 4.94876i 0.683130 0.227304i
\(475\) 0 0
\(476\) 15.2710 + 28.1165i 0.699944 + 1.28872i
\(477\) −8.77299 + 3.51047i −0.401687 + 0.160733i
\(478\) 12.6113 + 3.37919i 0.576827 + 0.154560i
\(479\) 7.30399 12.6509i 0.333728 0.578034i −0.649512 0.760352i \(-0.725027\pi\)
0.983240 + 0.182318i \(0.0583600\pi\)
\(480\) 0 0
\(481\) 4.70466 + 8.14871i 0.214514 + 0.371549i
\(482\) −13.8815 + 13.8815i −0.632285 + 0.632285i
\(483\) −6.16472 9.89939i −0.280505 0.450438i
\(484\) 6.53111i 0.296869i
\(485\) 0 0
\(486\) −38.0048 + 1.34139i −1.72393 + 0.0608466i
\(487\) 1.59898 0.428446i 0.0724568 0.0194148i −0.222409 0.974954i \(-0.571392\pi\)
0.294865 + 0.955539i \(0.404725\pi\)
\(488\) 13.4532 50.2079i 0.608996 2.27280i
\(489\) −33.9372 6.96366i −1.53469 0.314908i
\(490\) 0 0
\(491\) 32.6849i 1.47505i 0.675321 + 0.737524i \(0.264005\pi\)
−0.675321 + 0.737524i \(0.735995\pi\)
\(492\) −30.9684 + 61.8541i −1.39617 + 2.78860i
\(493\) −4.37059 16.3113i −0.196842 0.734623i
\(494\) −0.848464 + 1.46958i −0.0381742 + 0.0661196i
\(495\) 0 0
\(496\) 2.40395 0.107941
\(497\) 5.58598 + 5.88479i 0.250565 + 0.263969i
\(498\) 3.20421 + 4.85865i 0.143584 + 0.217721i
\(499\) 17.4676 10.0849i 0.781956 0.451463i −0.0551669 0.998477i \(-0.517569\pi\)
0.837123 + 0.547014i \(0.184236\pi\)
\(500\) 0 0
\(501\) −9.90118 + 11.1537i −0.442352 + 0.498308i
\(502\) −2.68650 + 10.0262i −0.119904 + 0.447489i
\(503\) 9.55454 + 9.55454i 0.426016 + 0.426016i 0.887269 0.461253i \(-0.152600\pi\)
−0.461253 + 0.887269i \(0.652600\pi\)
\(504\) 37.6203 3.50077i 1.67574 0.155937i
\(505\) 0 0
\(506\) −19.1247 + 11.0416i −0.850194 + 0.490860i
\(507\) −0.997867 16.7748i −0.0443168 0.744996i
\(508\) −4.03977 15.0766i −0.179236 0.668917i
\(509\) 2.00475 + 3.47233i 0.0888591 + 0.153908i 0.907029 0.421068i \(-0.138345\pi\)
−0.818170 + 0.574976i \(0.805011\pi\)
\(510\) 0 0
\(511\) 7.40665 + 4.53741i 0.327651 + 0.200723i
\(512\) 26.2078 26.2078i 1.15823 1.15823i
\(513\) −1.51990 + 1.28500i −0.0671050 + 0.0567340i
\(514\) 7.65238 + 4.41811i 0.337532 + 0.194874i
\(515\) 0 0
\(516\) −3.07867 + 1.02439i −0.135531 + 0.0450964i
\(517\) 7.30501 + 7.30501i 0.321274 + 0.321274i
\(518\) −7.81128 32.5168i −0.343208 1.42871i
\(519\) −0.585297 + 2.85243i −0.0256917 + 0.125208i
\(520\) 0 0
\(521\) 0.115369 + 0.0666082i 0.00505440 + 0.00291816i 0.502525 0.864563i \(-0.332404\pi\)
−0.497471 + 0.867481i \(0.665738\pi\)
\(522\) −39.9676 5.75332i −1.74933 0.251816i
\(523\) −27.3590 7.33082i −1.19633 0.320554i −0.394942 0.918706i \(-0.629235\pi\)
−0.801383 + 0.598151i \(0.795902\pi\)
\(524\) −34.8808 −1.52377
\(525\) 0 0
\(526\) 18.8041 0.819897
\(527\) 1.91558 + 0.513278i 0.0834440 + 0.0223587i
\(528\) −1.35732 22.8175i −0.0590697 0.993002i
\(529\) 14.3100 + 8.26186i 0.622173 + 0.359211i
\(530\) 0 0
\(531\) −9.01643 + 21.0456i −0.391280 + 0.913302i
\(532\) 2.90422 2.75675i 0.125914 0.119520i
\(533\) 12.9792 + 12.9792i 0.562192 + 0.562192i
\(534\) 4.05459 + 12.1855i 0.175459 + 0.527319i
\(535\) 0 0
\(536\) −52.8785 30.5294i −2.28400 1.31867i
\(537\) 16.4014 32.7591i 0.707775 1.41366i
\(538\) 33.6458 33.6458i 1.45057 1.45057i
\(539\) 13.5556 20.8863i 0.583883 0.899636i
\(540\) 0 0
\(541\) −7.52532 13.0342i −0.323539 0.560386i 0.657677 0.753300i \(-0.271539\pi\)
−0.981216 + 0.192915i \(0.938206\pi\)
\(542\) 12.8662 + 48.0173i 0.552650 + 2.06252i
\(543\) −38.7697 + 2.30625i −1.66377 + 0.0989708i
\(544\) 1.24484 0.718708i 0.0533720 0.0308143i
\(545\) 0 0
\(546\) 4.59727 19.7745i 0.196745 0.846270i
\(547\) 12.4068 + 12.4068i 0.530476 + 0.530476i 0.920714 0.390238i \(-0.127607\pi\)
−0.390238 + 0.920714i \(0.627607\pi\)
\(548\) −12.2291 + 45.6397i −0.522402 + 1.94963i
\(549\) −19.6271 26.2279i −0.837664 1.11938i
\(550\) 0 0
\(551\) −1.83022 + 1.05668i −0.0779699 + 0.0450160i
\(552\) 17.5159 11.5515i 0.745527 0.491665i
\(553\) −2.78625 + 9.41091i −0.118483 + 0.400193i
\(554\) −28.0201 −1.19046
\(555\) 0 0
\(556\) −15.8711 + 27.4896i −0.673086 + 1.16582i
\(557\) 5.06579 + 18.9058i 0.214645 + 0.801065i 0.986291 + 0.165013i \(0.0527667\pi\)
−0.771647 + 0.636051i \(0.780567\pi\)
\(558\) 2.93202 3.72708i 0.124122 0.157780i
\(559\) 0.860969i 0.0364151i
\(560\) 0 0
\(561\) 3.79027 18.4718i 0.160025 0.779880i
\(562\) −0.737184 + 2.75121i −0.0310962 + 0.116053i
\(563\) 27.3385 7.32534i 1.15218 0.308726i 0.368343 0.929690i \(-0.379925\pi\)
0.783839 + 0.620964i \(0.213259\pi\)
\(564\) −14.8646 13.1954i −0.625911 0.555626i
\(565\) 0 0
\(566\) 59.5602i 2.50350i
\(567\) 12.9252 19.9985i 0.542809 0.839856i
\(568\) −10.3225 + 10.3225i −0.433122 + 0.433122i
\(569\) −3.02998 5.24808i −0.127023 0.220011i 0.795499 0.605955i \(-0.207209\pi\)
−0.922522 + 0.385944i \(0.873876\pi\)
\(570\) 0 0
\(571\) 10.6877 18.5116i 0.447266 0.774687i −0.550941 0.834544i \(-0.685731\pi\)
0.998207 + 0.0598570i \(0.0190645\pi\)
\(572\) −24.6546 6.60618i −1.03086 0.276218i
\(573\) −27.3303 + 18.0239i −1.14174 + 0.752961i
\(574\) −31.1363 57.3274i −1.29961 2.39280i
\(575\) 0 0
\(576\) −3.04649 25.5162i −0.126937 1.06317i
\(577\) −38.1345 + 10.2181i −1.58756 + 0.425386i −0.941256 0.337694i \(-0.890353\pi\)
−0.646305 + 0.763079i \(0.723687\pi\)
\(578\) 17.9855 4.81921i 0.748100 0.200453i
\(579\) 8.41967 + 25.3041i 0.349909 + 1.05160i
\(580\) 0 0
\(581\) −3.64306 0.0949006i −0.151139 0.00393714i
\(582\) −34.0292 51.5996i −1.41056 2.13887i
\(583\) −10.8222 2.89980i −0.448210 0.120098i
\(584\) −7.81384 + 13.5340i −0.323339 + 0.560040i
\(585\) 0 0
\(586\) −29.5322 51.1512i −1.21996 2.11304i
\(587\) −28.9592 + 28.9592i −1.19527 + 1.19527i −0.219708 + 0.975566i \(0.570511\pi\)
−0.975566 + 0.219708i \(0.929489\pi\)
\(588\) −23.6487 + 41.6628i −0.975255 + 1.71815i
\(589\) 0.248190i 0.0102265i
\(590\) 0 0
\(591\) 0.946704 1.06646i 0.0389422 0.0438682i
\(592\) 18.5677 4.97521i 0.763129 0.204480i
\(593\) 8.08560 30.1759i 0.332036 1.23917i −0.575011 0.818146i \(-0.695002\pi\)
0.907047 0.421029i \(-0.138331\pi\)
\(594\) −37.0316 25.7253i −1.51942 1.05552i
\(595\) 0 0
\(596\) 70.2592i 2.87793i
\(597\) 7.16032 + 3.58495i 0.293052 + 0.146722i
\(598\) −2.91800 10.8901i −0.119326 0.445330i
\(599\) −8.18471 + 14.1763i −0.334418 + 0.579229i −0.983373 0.181598i \(-0.941873\pi\)
0.648955 + 0.760827i \(0.275206\pi\)
\(600\) 0 0
\(601\) −0.0942728 −0.00384547 −0.00192273 0.999998i \(-0.500612\pi\)
−0.00192273 + 0.999998i \(0.500612\pi\)
\(602\) 0.868685 2.93410i 0.0354050 0.119585i
\(603\) −35.7269 + 14.2959i −1.45491 + 0.582175i
\(604\) −68.1188 + 39.3284i −2.77171 + 1.60025i
\(605\) 0 0
\(606\) −0.576928 0.512143i −0.0234361 0.0208044i
\(607\) 0.226095 0.843796i 0.00917689 0.0342486i −0.961186 0.275903i \(-0.911023\pi\)
0.970362 + 0.241654i \(0.0776899\pi\)
\(608\) −0.127203 0.127203i −0.00515874 0.00515874i
\(609\) 17.2720 18.4650i 0.699896 0.748241i
\(610\) 0 0
\(611\) −4.56765 + 2.63713i −0.184787 + 0.106687i
\(612\) −5.16921 + 35.9099i −0.208953 + 1.45157i
\(613\) −0.280310 1.04613i −0.0113216 0.0422528i 0.960034 0.279884i \(-0.0902958\pi\)
−0.971356 + 0.237631i \(0.923629\pi\)
\(614\) 16.1382 + 27.9523i 0.651287 + 1.12806i
\(615\) 0 0
\(616\) 38.2006 + 23.4022i 1.53915 + 0.942902i
\(617\) 19.6770 19.6770i 0.792168 0.792168i −0.189679 0.981846i \(-0.560745\pi\)
0.981846 + 0.189679i \(0.0607446\pi\)
\(618\) 18.3588 + 9.19168i 0.738499 + 0.369744i
\(619\) 16.1891 + 9.34677i 0.650694 + 0.375679i 0.788722 0.614750i \(-0.210743\pi\)
−0.138028 + 0.990428i \(0.544076\pi\)
\(620\) 0 0
\(621\) 1.10355 13.1773i 0.0442840 0.528787i
\(622\) −4.70222 4.70222i −0.188542 0.188542i
\(623\) −7.71051 2.28282i −0.308915 0.0914591i
\(624\) 11.4315 + 2.34567i 0.457628 + 0.0939018i
\(625\) 0 0
\(626\) 54.7501 + 31.6100i 2.18825 + 1.26339i
\(627\) −2.35573 + 0.140133i −0.0940789 + 0.00559638i
\(628\) 39.4521 + 10.5712i 1.57431 + 0.421836i
\(629\) 15.8579 0.632296
\(630\) 0 0
\(631\) −7.63531 −0.303957 −0.151978 0.988384i \(-0.548564\pi\)
−0.151978 + 0.988384i \(0.548564\pi\)
\(632\) −17.0567 4.57034i −0.678481 0.181798i
\(633\) −39.4457 + 2.34647i −1.56782 + 0.0932636i
\(634\) 9.96121 + 5.75111i 0.395610 + 0.228406i
\(635\) 0 0
\(636\) 21.1164 + 4.33292i 0.837319 + 0.171812i
\(637\) 8.50866 + 9.44466i 0.337126 + 0.374211i
\(638\) −33.8548 33.8548i −1.34033 1.34033i
\(639\) 1.09071 + 9.13531i 0.0431477 + 0.361387i
\(640\) 0 0
\(641\) 23.0817 + 13.3263i 0.911674 + 0.526355i 0.880969 0.473173i \(-0.156892\pi\)
0.0307047 + 0.999528i \(0.490225\pi\)
\(642\) 40.7115 + 20.3830i 1.60676 + 0.804453i
\(643\) 21.9767 21.9767i 0.866677 0.866677i −0.125426 0.992103i \(-0.540030\pi\)
0.992103 + 0.125426i \(0.0400298\pi\)
\(644\) −0.692795 + 26.5951i −0.0273000 + 1.04799i
\(645\) 0 0
\(646\) 1.42995 + 2.47675i 0.0562606 + 0.0974462i
\(647\) −6.11969 22.8390i −0.240590 0.897893i −0.975549 0.219782i \(-0.929465\pi\)
0.734959 0.678111i \(-0.237201\pi\)
\(648\) 36.5742 + 22.3100i 1.43677 + 0.876419i
\(649\) −23.5103 + 13.5737i −0.922861 + 0.532814i
\(650\) 0 0
\(651\) 0.863788 + 2.84091i 0.0338545 + 0.111344i
\(652\) 55.8848 + 55.8848i 2.18862 + 2.18862i
\(653\) −7.04229 + 26.2822i −0.275586 + 1.02850i 0.679861 + 0.733341i \(0.262040\pi\)
−0.955448 + 0.295161i \(0.904627\pi\)
\(654\) −32.2641 28.6411i −1.26163 1.11996i
\(655\) 0 0
\(656\) 32.4751 18.7495i 1.26794 0.732046i
\(657\) 3.65897 + 9.14410i 0.142750 + 0.356745i
\(658\) 18.2269 4.37851i 0.710557 0.170692i
\(659\) 43.7515 1.70432 0.852158 0.523285i \(-0.175294\pi\)
0.852158 + 0.523285i \(0.175294\pi\)
\(660\) 0 0
\(661\) −4.32752 + 7.49549i −0.168321 + 0.291541i −0.937830 0.347096i \(-0.887168\pi\)
0.769509 + 0.638636i \(0.220501\pi\)
\(662\) −6.38480 23.8284i −0.248152 0.926117i
\(663\) 8.60834 + 4.30993i 0.334320 + 0.167384i
\(664\) 6.55674i 0.254451i
\(665\) 0 0
\(666\) 14.9329 34.8554i 0.578638 1.35062i
\(667\) 3.63408 13.5626i 0.140712 0.525145i
\(668\) 32.8643 8.80597i 1.27156 0.340713i
\(669\) −15.4666 + 17.4231i −0.597975 + 0.673617i
\(670\) 0 0
\(671\) 38.8418i 1.49947i
\(672\) 1.89873 + 1.01331i 0.0732451 + 0.0390894i
\(673\) −6.15620 + 6.15620i −0.237304 + 0.237304i −0.815733 0.578429i \(-0.803666\pi\)
0.578429 + 0.815733i \(0.303666\pi\)
\(674\) −15.1587 26.2556i −0.583891 1.01133i
\(675\) 0 0
\(676\) −19.1678 + 33.1996i −0.737222 + 1.27691i
\(677\) −5.23005 1.40139i −0.201007 0.0538597i 0.156911 0.987613i \(-0.449847\pi\)
−0.357918 + 0.933753i \(0.616513\pi\)
\(678\) 26.2579 + 39.8157i 1.00843 + 1.52911i
\(679\) 38.6898 + 1.00786i 1.48478 + 0.0386781i
\(680\) 0 0
\(681\) 1.20829 + 3.63134i 0.0463016 + 0.139153i
\(682\) 5.43115 1.45527i 0.207970 0.0557253i
\(683\) −6.89389 + 1.84721i −0.263788 + 0.0706817i −0.388289 0.921538i \(-0.626934\pi\)
0.124501 + 0.992219i \(0.460267\pi\)
\(684\) 4.50840 0.538278i 0.172383 0.0205816i
\(685\) 0 0
\(686\) −19.4674 40.7714i −0.743269 1.55666i
\(687\) 36.8766 24.3196i 1.40693 0.927850i
\(688\) 1.69898 + 0.455240i 0.0647730 + 0.0173559i
\(689\) 2.86001 4.95369i 0.108958 0.188721i
\(690\) 0 0
\(691\) 18.5623 + 32.1509i 0.706144 + 1.22308i 0.966277 + 0.257504i \(0.0829002\pi\)
−0.260133 + 0.965573i \(0.583766\pi\)
\(692\) 4.69713 4.69713i 0.178558 0.178558i
\(693\) 26.4771 9.80279i 1.00578 0.372377i
\(694\) 26.9534i 1.02314i
\(695\) 0 0
\(696\) 34.0199 + 30.1998i 1.28952 + 1.14472i
\(697\) 29.8809 8.00657i 1.13182 0.303271i
\(698\) −4.32340 + 16.1352i −0.163643 + 0.610725i
\(699\) −8.98517 + 43.7890i −0.339850 + 1.65625i
\(700\) 0 0
\(701\) 23.4224i 0.884654i 0.896854 + 0.442327i \(0.145847\pi\)
−0.896854 + 0.442327i \(0.854153\pi\)
\(702\) 17.5794 14.8625i 0.663490 0.560948i
\(703\) −0.513653 1.91698i −0.0193728 0.0723003i
\(704\) 15.2347 26.3872i 0.574178 0.994506i
\(705\) 0 0
\(706\) 54.3705 2.04626
\(707\) 0.469687 0.112830i 0.0176644 0.00424339i
\(708\) 43.6031 28.7556i 1.63870 1.08070i
\(709\) 9.67685 5.58693i 0.363422 0.209822i −0.307159 0.951658i \(-0.599378\pi\)
0.670581 + 0.741837i \(0.266045\pi\)
\(710\) 0 0
\(711\) −8.91020 + 6.66776i −0.334159 + 0.250061i
\(712\) 3.74455 13.9749i 0.140333 0.523730i
\(713\) 1.16599 + 1.16599i 0.0436667 + 0.0436667i
\(714\) −24.9878 23.3733i −0.935146 0.874724i
\(715\) 0 0
\(716\) −72.3786 + 41.7878i −2.70492 + 1.56168i
\(717\) −9.25347 + 0.550452i −0.345577 + 0.0205570i
\(718\) 16.9035 + 63.0846i 0.630832 + 2.35430i
\(719\) −22.9885 39.8173i −0.857328 1.48494i −0.874468 0.485083i \(-0.838789\pi\)
0.0171399 0.999853i \(-0.494544\pi\)
\(720\) 0 0
\(721\) −11.2971 + 6.13579i −0.420724 + 0.228509i
\(722\) −32.5220 + 32.5220i −1.21034 + 1.21034i
\(723\) 6.24002 12.4634i 0.232069 0.463518i
\(724\) 76.7303 + 44.3002i 2.85166 + 1.64641i
\(725\) 0 0
\(726\) −2.20504 6.62695i −0.0818369 0.245949i
\(727\) −35.2560 35.2560i −1.30757 1.30757i −0.923162 0.384411i \(-0.874405\pi\)
−0.384411 0.923162i \(-0.625595\pi\)
\(728\) −16.5882 + 15.7459i −0.614801 + 0.583584i
\(729\) 25.3024 9.42280i 0.937125 0.348993i
\(730\) 0 0
\(731\) 1.25662 + 0.725512i 0.0464779 + 0.0268340i
\(732\) 4.43762 + 74.5994i 0.164019 + 2.75727i
\(733\) −42.1232 11.2869i −1.55586 0.416890i −0.624507 0.781019i \(-0.714700\pi\)
−0.931349 + 0.364129i \(0.881367\pi\)
\(734\) 41.0140 1.51386
\(735\) 0 0
\(736\) 1.19519 0.0440552
\(737\) −44.0721 11.8091i −1.62342 0.434993i
\(738\) 10.5396 73.2174i 0.387968 2.69517i
\(739\) −13.3113 7.68531i −0.489666 0.282709i 0.234770 0.972051i \(-0.424566\pi\)
−0.724436 + 0.689342i \(0.757900\pi\)
\(740\) 0 0
\(741\) 0.242173 1.18022i 0.00889643 0.0433565i
\(742\) −14.7447 + 13.9960i −0.541296 + 0.513811i
\(743\) 34.3837 + 34.3837i 1.26141 + 1.26141i 0.950408 + 0.311007i \(0.100666\pi\)
0.311007 + 0.950408i \(0.399334\pi\)
\(744\) −5.06911 + 1.68669i −0.185842 + 0.0618370i
\(745\) 0 0
\(746\) 22.1642 + 12.7965i 0.811490 + 0.468514i
\(747\) −3.24773 2.55492i −0.118828 0.0934798i
\(748\) −30.4177 + 30.4177i −1.11218 + 1.11218i
\(749\) −25.0518 + 13.6064i −0.915372 + 0.497168i
\(750\) 0 0
\(751\) −10.8814 18.8472i −0.397069 0.687744i 0.596294 0.802766i \(-0.296639\pi\)
−0.993363 + 0.115022i \(0.963306\pi\)
\(752\) 2.78879 + 10.4079i 0.101697 + 0.379537i
\(753\) −0.437617 7.35664i −0.0159477 0.268091i
\(754\) 21.1686 12.2217i 0.770915 0.445088i
\(755\) 0 0
\(756\) −49.7319 + 21.8522i −1.80873 + 0.794756i
\(757\) 20.4109 + 20.4109i 0.741847 + 0.741847i 0.972933 0.231086i \(-0.0742280\pi\)
−0.231086 + 0.972933i \(0.574228\pi\)
\(758\) 13.9380 52.0174i 0.506252 1.88936i
\(759\) 10.4088 11.7255i 0.377816 0.425609i
\(760\) 0 0
\(761\) −25.7320 + 14.8564i −0.932785 + 0.538544i −0.887691 0.460439i \(-0.847692\pi\)
−0.0450939 + 0.998983i \(0.514359\pi\)
\(762\) 9.18925 + 13.9340i 0.332891 + 0.504774i
\(763\) 26.2668 6.30988i 0.950922 0.228433i
\(764\) 74.6853 2.70202
\(765\) 0 0
\(766\) −24.5295 + 42.4863i −0.886286 + 1.53509i
\(767\) −3.58716 13.3875i −0.129525 0.483393i
\(768\) −24.4681 + 48.8708i −0.882916 + 1.76347i
\(769\) 28.4557i 1.02614i −0.858347 0.513070i \(-0.828508\pi\)
0.858347 0.513070i \(-0.171492\pi\)
\(770\) 0 0
\(771\) −6.14563 1.26104i −0.221329 0.0454151i
\(772\) 15.7458 58.7643i 0.566705 2.11497i
\(773\) 16.9710 4.54737i 0.610406 0.163558i 0.0596432 0.998220i \(-0.481004\pi\)
0.550762 + 0.834662i \(0.314337\pi\)
\(774\) 2.77799 2.07885i 0.0998528 0.0747228i
\(775\) 0 0
\(776\) 69.6336i 2.49970i
\(777\) 12.5513 + 20.1550i 0.450275 + 0.723056i
\(778\) −2.37726 + 2.37726i −0.0852290 + 0.0852290i
\(779\) −1.93575 3.35281i −0.0693553 0.120127i
\(780\) 0 0
\(781\) −5.45433 + 9.44717i −0.195171 + 0.338046i
\(782\) −18.3535 4.91782i −0.656322 0.175861i
\(783\) 28.2151 5.08323i 1.00832 0.181660i
\(784\) 23.1365 11.7966i 0.826302 0.421305i
\(785\) 0 0
\(786\) 35.3927 11.7765i 1.26241 0.420054i
\(787\) 15.5766 4.17374i 0.555246 0.148778i 0.0297245 0.999558i \(-0.490537\pi\)
0.525521 + 0.850780i \(0.323870\pi\)
\(788\) −3.14233 + 0.841984i −0.111941 + 0.0299944i
\(789\) −12.6680 + 4.21512i −0.450991 + 0.150062i
\(790\) 0 0
\(791\) −29.8541 0.777692i −1.06149 0.0276516i
\(792\) 18.8715 + 47.1617i 0.670571 + 1.67582i
\(793\) 19.1544 + 5.13241i 0.680193 + 0.182257i
\(794\) −27.1721 + 47.0635i −0.964302 + 1.67022i
\(795\) 0 0
\(796\) −9.13378 15.8202i −0.323738 0.560731i
\(797\) 7.99994 7.99994i 0.283373 0.283373i −0.551080 0.834452i \(-0.685784\pi\)
0.834452 + 0.551080i \(0.185784\pi\)
\(798\) −2.01610 + 3.77774i −0.0713692 + 0.133730i
\(799\) 8.88893i 0.314468i
\(800\) 0 0
\(801\) −5.46301 7.30027i −0.193026 0.257942i
\(802\) −20.4449 + 5.47819i −0.721934 + 0.193442i
\(803\) −3.02247 + 11.2800i −0.106661 + 0.398063i
\(804\) 85.9938 + 17.6453i 3.03277 + 0.622301i
\(805\) 0 0
\(806\) 2.87061i 0.101113i
\(807\) −15.1245 + 30.2086i −0.532408 + 1.06339i
\(808\) 0.224938 + 0.839480i 0.00791329 + 0.0295328i
\(809\) −16.4490 + 28.4906i −0.578317 + 1.00167i 0.417355 + 0.908743i \(0.362957\pi\)
−0.995673 + 0.0929313i \(0.970376\pi\)
\(810\) 0 0
\(811\) −26.4235 −0.927856 −0.463928 0.885873i \(-0.653560\pi\)
−0.463928 + 0.885873i \(0.653560\pi\)
\(812\) −56.0840 + 13.4727i −1.96816 + 0.472798i
\(813\) −19.4313 29.4642i −0.681484 1.03336i
\(814\) 38.9375 22.4806i 1.36476 0.787943i
\(815\) 0 0
\(816\) 13.0566 14.7082i 0.457073 0.514892i
\(817\) 0.0470002 0.175407i 0.00164433 0.00613671i
\(818\) 13.5066 + 13.5066i 0.472248 + 0.472248i
\(819\) 1.33555 + 14.3522i 0.0466680 + 0.501507i
\(820\) 0 0
\(821\) 19.3688 11.1826i 0.675975 0.390275i −0.122362 0.992486i \(-0.539047\pi\)
0.798337 + 0.602211i \(0.205713\pi\)
\(822\) −3.00037 50.4383i −0.104650 1.75924i
\(823\) 7.07326 + 26.3978i 0.246558 + 0.920168i 0.972594 + 0.232511i \(0.0746942\pi\)
−0.726035 + 0.687657i \(0.758639\pi\)
\(824\) −11.5650 20.0311i −0.402884 0.697816i
\(825\) 0 0
\(826\) −1.28275 + 49.2425i −0.0446327 + 1.71336i
\(827\) −34.1284 + 34.1284i −1.18676 + 1.18676i −0.208804 + 0.977958i \(0.566957\pi\)
−0.977958 + 0.208804i \(0.933043\pi\)
\(828\) −18.6515 + 23.7091i −0.648185 + 0.823950i
\(829\) −11.5297 6.65666i −0.400442 0.231196i 0.286232 0.958160i \(-0.407597\pi\)
−0.686675 + 0.726965i \(0.740930\pi\)
\(830\) 0 0
\(831\) 18.8766 6.28098i 0.654823 0.217885i
\(832\) 10.9995 + 10.9995i 0.381340 + 0.381340i
\(833\) 20.9549 4.46007i 0.726045 0.154532i
\(834\) 6.82295 33.2515i 0.236260 1.15140i
\(835\) 0 0
\(836\) 4.66230 + 2.69178i 0.161249 + 0.0930972i
\(837\) −1.13978 + 3.16810i −0.0393967 + 0.109506i
\(838\) −40.6683 10.8970i −1.40486 0.376432i
\(839\) 25.4141 0.877392 0.438696 0.898636i \(-0.355440\pi\)
0.438696 + 0.898636i \(0.355440\pi\)
\(840\) 0 0
\(841\) 1.44184 0.0497185
\(842\) −71.2506 19.0915i −2.45546 0.657938i
\(843\) −0.120083 2.01868i −0.00413589 0.0695271i
\(844\) 78.0681 + 45.0727i 2.68722 + 1.55146i
\(845\) 0 0
\(846\) 19.5377 + 8.37043i 0.671721 + 0.287781i
\(847\) 4.19327 + 1.24148i 0.144083 + 0.0426579i
\(848\) −8.26305 8.26305i −0.283754 0.283754i
\(849\) −13.3510 40.1246i −0.458205 1.37707i
\(850\) 0 0
\(851\) 11.4191 + 6.59279i 0.391440 + 0.225998i
\(852\) 9.39623 18.7673i 0.321909 0.642958i
\(853\) −33.5959 + 33.5959i −1.15030 + 1.15030i −0.163811 + 0.986492i \(0.552379\pi\)
−0.986492 + 0.163811i \(0.947621\pi\)
\(854\) −60.0980 36.8169i −2.05651 1.25985i
\(855\) 0 0
\(856\) −25.6458 44.4199i −0.876557 1.51824i
\(857\) 1.67126 + 6.23724i 0.0570892 + 0.213060i 0.988578 0.150710i \(-0.0481560\pi\)
−0.931489 + 0.363770i \(0.881489\pi\)
\(858\) 27.2468 1.62080i 0.930190 0.0553333i
\(859\) −20.2860 + 11.7121i −0.692148 + 0.399612i −0.804416 0.594066i \(-0.797522\pi\)
0.112268 + 0.993678i \(0.464189\pi\)
\(860\) 0 0
\(861\) 33.8264 + 31.6409i 1.15280 + 1.07832i
\(862\) −35.2242 35.2242i −1.19974 1.19974i
\(863\) 4.24789 15.8533i 0.144600 0.539654i −0.855173 0.518343i \(-0.826549\pi\)
0.999773 0.0213112i \(-0.00678409\pi\)
\(864\) 1.03955 + 2.20788i 0.0353664 + 0.0751136i
\(865\) 0 0
\(866\) −43.1254 + 24.8984i −1.46546 + 0.846084i
\(867\) −11.0362 + 7.27825i −0.374810 + 0.247182i
\(868\) 1.92299 6.49515i 0.0652705 0.220460i
\(869\) −13.1954 −0.447624
\(870\) 0 0
\(871\) 11.6470 20.1733i 0.394645 0.683545i
\(872\) 12.5794 + 46.9471i 0.425993 + 1.58983i
\(873\) 34.4914 + 27.1337i 1.16736 + 0.918337i
\(874\) 2.37796i 0.0804357i
\(875\) 0 0
\(876\) 4.51622 22.0097i 0.152589 0.743637i
\(877\) −8.78089 + 32.7707i −0.296510 + 1.10659i 0.643501 + 0.765445i \(0.277481\pi\)
−0.940011 + 0.341144i \(0.889186\pi\)
\(878\) 34.2689 9.18234i 1.15652 0.309889i
\(879\) 31.3613 + 27.8397i 1.05779 + 0.939009i
\(880\) 0 0
\(881\) 14.2708i 0.480796i −0.970674 0.240398i \(-0.922722\pi\)
0.970674 0.240398i \(-0.0772780\pi\)
\(882\) 9.92943 50.2585i 0.334341 1.69229i
\(883\) 26.8398 26.8398i 0.903230 0.903230i −0.0924838 0.995714i \(-0.529481\pi\)
0.995714 + 0.0924838i \(0.0294806\pi\)
\(884\) −10.9809 19.0195i −0.369327 0.639693i
\(885\) 0 0
\(886\) −12.5152 + 21.6769i −0.420456 + 0.728251i
\(887\) 38.7423 + 10.3810i 1.30084 + 0.348559i 0.841767 0.539841i \(-0.181516\pi\)
0.459071 + 0.888399i \(0.348182\pi\)
\(888\) −35.6621 + 23.5187i −1.19674 + 0.789235i
\(889\) −10.4478 0.272162i −0.350408 0.00912803i
\(890\) 0 0
\(891\) 30.7140 + 9.02964i 1.02896 + 0.302504i
\(892\) 51.3373 13.7558i 1.71890 0.460578i
\(893\) 1.07454 0.287921i 0.0359580 0.00963492i
\(894\) 23.7210 + 71.2902i 0.793350 + 2.38430i
\(895\) 0 0
\(896\) −25.2011 46.3996i −0.841910 1.55010i
\(897\) 4.40693 + 6.68237i 0.147143 + 0.223118i
\(898\) −15.7911 4.23121i −0.526956 0.141197i
\(899\) −1.78753 + 3.09609i −0.0596175 + 0.103260i
\(900\) 0 0
\(901\) −4.82009 8.34865i −0.160581 0.278134i
\(902\) 62.0193 62.0193i 2.06502 2.06502i
\(903\) 0.0724902 + 2.17137i 0.00241232 + 0.0722587i
\(904\) 53.7313i 1.78707i
\(905\) 0 0
\(906\) 55.8403 62.9039i 1.85517 2.08984i
\(907\) −5.50258 + 1.47441i −0.182710 + 0.0489570i −0.349014 0.937118i \(-0.613483\pi\)
0.166304 + 0.986075i \(0.446817\pi\)
\(908\) 2.25965 8.43312i 0.0749891 0.279863i
\(909\) 0.503467 + 0.215697i 0.0166989 + 0.00715422i
\(910\) 0 0
\(911\) 11.4287i 0.378651i 0.981914 + 0.189326i \(0.0606301\pi\)
−0.981914 + 0.189326i \(0.939370\pi\)
\(912\) −2.20092 1.10193i −0.0728798 0.0364887i
\(913\) −1.26811 4.73264i −0.0419682 0.156627i
\(914\) 37.7468 65.3794i 1.24855 2.16256i
\(915\) 0 0
\(916\) −100.772 −3.32962
\(917\) −6.63041 + 22.3951i −0.218955 + 0.739550i
\(918\) −6.87889 38.1821i −0.227037 1.26020i
\(919\) −32.2477 + 18.6182i −1.06375 + 0.614158i −0.926468 0.376374i \(-0.877171\pi\)
−0.137285 + 0.990532i \(0.543838\pi\)
\(920\) 0 0
\(921\) −17.1378 15.2134i −0.564710 0.501297i
\(922\) 22.1889 82.8101i 0.730753 2.72721i
\(923\) −3.93806 3.93806i −0.129623 0.129623i
\(924\) −62.7353 14.5850i −2.06384 0.479812i
\(925\) 0 0
\(926\) 10.5041 6.06454i 0.345186 0.199293i
\(927\) −14.4284 2.07696i −0.473890 0.0682162i
\(928\) 0.670665 + 2.50295i 0.0220156 + 0.0821635i
\(929\) 1.75415 + 3.03828i 0.0575519 + 0.0996828i 0.893366 0.449330i \(-0.148337\pi\)
−0.835814 + 0.549013i \(0.815004\pi\)
\(930\) 0 0
\(931\) −1.21791 2.38867i −0.0399153 0.0782854i
\(932\) 72.1078 72.1078i 2.36197 2.36197i
\(933\) 4.22185 + 2.11375i 0.138217 + 0.0692010i
\(934\) −65.5614 37.8519i −2.14523 1.23855i
\(935\) 0 0
\(936\) −25.7509 + 3.07452i −0.841696 + 0.100494i
\(937\) 8.69968 + 8.69968i 0.284206 + 0.284206i 0.834784 0.550578i \(-0.185593\pi\)
−0.550578 + 0.834784i \(0.685593\pi\)
\(938\) −60.0461 + 56.9971i −1.96057 + 1.86102i
\(939\) −43.9698 9.02227i −1.43490 0.294431i
\(940\) 0 0
\(941\) 36.0321 + 20.8032i 1.17461 + 0.678164i 0.954762 0.297370i \(-0.0961094\pi\)
0.219851 + 0.975533i \(0.429443\pi\)
\(942\) −43.6001 + 2.59360i −1.42057 + 0.0845040i
\(943\) 24.8455 + 6.65734i 0.809081 + 0.216793i
\(944\) −28.3147 −0.921564
\(945\) 0 0
\(946\) 4.11402 0.133758
\(947\) 53.1753 + 14.2483i 1.72796 + 0.463007i 0.979712 0.200408i \(-0.0642269\pi\)
0.748252 + 0.663415i \(0.230894\pi\)
\(948\) 25.3431 1.50756i 0.823105 0.0489632i
\(949\) −5.16324 2.98100i −0.167606 0.0967673i
\(950\) 0 0
\(951\) −7.99984 1.64151i −0.259413 0.0532295i
\(952\) 9.00354 + 37.4800i 0.291806 + 1.21473i
\(953\) −19.2607 19.2607i −0.623916 0.623916i 0.322614 0.946531i \(-0.395438\pi\)
−0.946531 + 0.322614i \(0.895438\pi\)
\(954\) −22.8891 + 2.73284i −0.741064 + 0.0884789i
\(955\) 0 0
\(956\) 18.3138 + 10.5735i 0.592311 + 0.341971i
\(957\) 30.3962 + 15.2185i 0.982571 + 0.491943i
\(958\) 25.1988 25.1988i 0.814137 0.814137i
\(959\) 26.9782 + 16.5272i 0.871171 + 0.533691i
\(960\) 0 0
\(961\) 15.2901 + 26.4832i 0.493228 + 0.854296i
\(962\) 5.94100 + 22.1721i 0.191545 + 0.714857i
\(963\) −31.9956 4.60575i −1.03104 0.148418i
\(964\) −27.5368 + 15.8984i −0.886902 + 0.512053i
\(965\) 0 0
\(966\) −8.27612 27.2193i −0.266280 0.875766i
\(967\) −30.3993 30.3993i −0.977576 0.977576i 0.0221785 0.999754i \(-0.492940\pi\)
−0.999754 + 0.0221785i \(0.992940\pi\)
\(968\) −2.03643 + 7.60007i −0.0654534 + 0.244275i
\(969\) −1.51852 1.34800i −0.0487818 0.0433040i
\(970\) 0 0
\(971\) 3.05677 1.76483i 0.0980965 0.0566360i −0.450149 0.892953i \(-0.648629\pi\)
0.548246 + 0.836317i \(0.315296\pi\)
\(972\) −60.0208 13.8333i −1.92517 0.443702i
\(973\) 14.6327 + 15.4154i 0.469102 + 0.494196i
\(974\) 4.03836 0.129397
\(975\) 0 0
\(976\) 20.2559 35.0843i 0.648377 1.12302i
\(977\) 10.3641 + 38.6793i 0.331577 + 1.23746i 0.907533 + 0.419980i \(0.137963\pi\)
−0.575957 + 0.817480i \(0.695370\pi\)
\(978\) −75.5728 37.8370i −2.41655 1.20989i
\(979\) 10.8112i 0.345528i
\(980\) 0 0
\(981\) 28.1559 + 12.0626i 0.898948 + 0.385131i
\(982\) −20.6371 + 77.0186i −0.658556 + 2.45776i
\(983\) −35.7125 + 9.56912i −1.13905 + 0.305208i −0.778569 0.627559i \(-0.784054\pi\)
−0.360481 + 0.932766i \(0.617388\pi\)
\(984\) −55.3235 + 62.3217i −1.76365 + 1.98674i
\(985\) 0 0
\(986\) 41.1954i 1.31193i
\(987\) −11.2976 + 7.03545i −0.359607 + 0.223941i
\(988\) −1.94348 + 1.94348i −0.0618304 + 0.0618304i
\(989\) 0.603252 + 1.04486i 0.0191823 + 0.0332247i
\(990\) 0 0
\(991\) 20.0560 34.7381i 0.637101 1.10349i −0.348964 0.937136i \(-0.613467\pi\)
0.986066 0.166356i \(-0.0532001\pi\)
\(992\) −0.293945 0.0787622i −0.00933275 0.00250070i
\(993\) 9.64268 + 14.6215i 0.306001 + 0.464000i
\(994\) 9.44717 + 17.3939i 0.299646 + 0.551700i
\(995\) 0 0
\(996\) 2.97621 + 8.94460i 0.0943050 + 0.283420i
\(997\) 35.4747 9.50542i 1.12350 0.301040i 0.351198 0.936301i \(-0.385774\pi\)
0.772297 + 0.635261i \(0.219108\pi\)
\(998\) 47.5282 12.7351i 1.50448 0.403124i
\(999\) −2.24681 + 26.8288i −0.0710860 + 0.848825i
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.bf.f.32.12 48
3.2 odd 2 inner 525.2.bf.f.32.1 48
5.2 odd 4 105.2.x.a.53.1 yes 48
5.3 odd 4 inner 525.2.bf.f.368.12 48
5.4 even 2 105.2.x.a.32.1 yes 48
7.2 even 3 inner 525.2.bf.f.107.1 48
15.2 even 4 105.2.x.a.53.12 yes 48
15.8 even 4 inner 525.2.bf.f.368.1 48
15.14 odd 2 105.2.x.a.32.12 yes 48
21.2 odd 6 inner 525.2.bf.f.107.12 48
35.2 odd 12 105.2.x.a.23.12 yes 48
35.4 even 6 735.2.j.g.197.12 24
35.9 even 6 105.2.x.a.2.12 yes 48
35.12 even 12 735.2.y.i.128.12 48
35.17 even 12 735.2.j.e.638.1 24
35.19 odd 6 735.2.y.i.422.12 48
35.23 odd 12 inner 525.2.bf.f.443.1 48
35.24 odd 6 735.2.j.e.197.12 24
35.27 even 4 735.2.y.i.263.1 48
35.32 odd 12 735.2.j.g.638.1 24
35.34 odd 2 735.2.y.i.557.1 48
105.2 even 12 105.2.x.a.23.1 yes 48
105.17 odd 12 735.2.j.e.638.12 24
105.23 even 12 inner 525.2.bf.f.443.12 48
105.32 even 12 735.2.j.g.638.12 24
105.44 odd 6 105.2.x.a.2.1 48
105.47 odd 12 735.2.y.i.128.1 48
105.59 even 6 735.2.j.e.197.1 24
105.62 odd 4 735.2.y.i.263.12 48
105.74 odd 6 735.2.j.g.197.1 24
105.89 even 6 735.2.y.i.422.1 48
105.104 even 2 735.2.y.i.557.12 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.x.a.2.1 48 105.44 odd 6
105.2.x.a.2.12 yes 48 35.9 even 6
105.2.x.a.23.1 yes 48 105.2 even 12
105.2.x.a.23.12 yes 48 35.2 odd 12
105.2.x.a.32.1 yes 48 5.4 even 2
105.2.x.a.32.12 yes 48 15.14 odd 2
105.2.x.a.53.1 yes 48 5.2 odd 4
105.2.x.a.53.12 yes 48 15.2 even 4
525.2.bf.f.32.1 48 3.2 odd 2 inner
525.2.bf.f.32.12 48 1.1 even 1 trivial
525.2.bf.f.107.1 48 7.2 even 3 inner
525.2.bf.f.107.12 48 21.2 odd 6 inner
525.2.bf.f.368.1 48 15.8 even 4 inner
525.2.bf.f.368.12 48 5.3 odd 4 inner
525.2.bf.f.443.1 48 35.23 odd 12 inner
525.2.bf.f.443.12 48 105.23 even 12 inner
735.2.j.e.197.1 24 105.59 even 6
735.2.j.e.197.12 24 35.24 odd 6
735.2.j.e.638.1 24 35.17 even 12
735.2.j.e.638.12 24 105.17 odd 12
735.2.j.g.197.1 24 105.74 odd 6
735.2.j.g.197.12 24 35.4 even 6
735.2.j.g.638.1 24 35.32 odd 12
735.2.j.g.638.12 24 105.32 even 12
735.2.y.i.128.1 48 105.47 odd 12
735.2.y.i.128.12 48 35.12 even 12
735.2.y.i.263.1 48 35.27 even 4
735.2.y.i.263.12 48 105.62 odd 4
735.2.y.i.422.1 48 105.89 even 6
735.2.y.i.422.12 48 35.19 odd 6
735.2.y.i.557.1 48 35.34 odd 2
735.2.y.i.557.12 48 105.104 even 2