Properties

Label 375.2.i.a.199.2
Level $375$
Weight $2$
Character 375.199
Analytic conductor $2.994$
Analytic rank $0$
Dimension $8$
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: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 199.2
Root \(0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 375.199
Dual form 375.2.i.a.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -4.47214i q^{7} +(2.85317 - 0.927051i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -4.47214i q^{7} +(2.85317 - 0.927051i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.61803 + 1.90211i) q^{11} +(0.587785 - 0.809017i) q^{12} +(1.98787 - 2.73607i) q^{13} +(3.61803 - 2.62866i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-2.71441 + 0.881966i) q^{17} +1.00000i q^{18} +(1.00000 + 3.07768i) q^{19} +(1.38197 - 4.25325i) q^{21} +(-3.07768 - 1.00000i) q^{22} +(2.62866 + 3.61803i) q^{23} +3.00000 q^{24} +3.38197 q^{26} +(0.587785 + 0.809017i) q^{27} +(-4.25325 - 1.38197i) q^{28} +(-1.35410 + 4.16750i) q^{29} +(2.23607 + 6.88191i) q^{31} -5.00000i q^{32} +(-3.07768 + 1.00000i) q^{33} +(-2.30902 - 1.67760i) q^{34} +(0.809017 - 0.587785i) q^{36} +(-4.75528 + 6.54508i) q^{37} +(-1.90211 + 2.61803i) q^{38} +(2.73607 - 1.98787i) q^{39} +(1.11803 + 0.812299i) q^{41} +(4.25325 - 1.38197i) q^{42} -5.70820i q^{43} +(1.00000 + 3.07768i) q^{44} +(-1.38197 + 4.25325i) q^{46} +(4.97980 + 1.61803i) q^{47} +(0.587785 + 0.809017i) q^{48} -13.0000 q^{49} -2.85410 q^{51} +(-1.98787 - 2.73607i) q^{52} +(1.31433 + 0.427051i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-4.14590 - 12.7598i) q^{56} +3.23607i q^{57} +(-4.16750 + 1.35410i) q^{58} +(-3.23607 - 2.35114i) q^{59} +(0.500000 - 0.363271i) q^{61} +(-4.25325 + 5.85410i) q^{62} +(2.62866 - 3.61803i) q^{63} +(5.66312 - 4.11450i) q^{64} +(-2.61803 - 1.90211i) q^{66} +(4.97980 - 1.61803i) q^{67} +2.85410i q^{68} +(1.38197 + 4.25325i) q^{69} +(-0.236068 + 0.726543i) q^{71} +(2.85317 + 0.927051i) q^{72} +(-1.81636 - 2.50000i) q^{73} -8.09017 q^{74} +3.23607 q^{76} +(8.50651 + 11.7082i) q^{77} +(3.21644 + 1.04508i) q^{78} +(0.309017 + 0.951057i) q^{81} +1.38197i q^{82} +(-3.35520 + 1.09017i) q^{83} +(-3.61803 - 2.62866i) q^{84} +(4.61803 - 3.35520i) q^{86} +(-2.57565 + 3.54508i) q^{87} +(-5.70634 + 7.85410i) q^{88} +(6.16312 - 4.47777i) q^{89} +(-12.2361 - 8.89002i) q^{91} +(4.25325 - 1.38197i) q^{92} +7.23607i q^{93} +(1.61803 + 4.97980i) q^{94} +(1.54508 - 4.75528i) q^{96} +(-8.42075 - 2.73607i) q^{97} +(-7.64121 - 10.5172i) q^{98} -3.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{4} - 2 q^{6} + 2 q^{9} - 12 q^{11} + 20 q^{14} + 2 q^{16} + 8 q^{19} + 20 q^{21} + 24 q^{24} + 36 q^{26} + 16 q^{29} - 14 q^{34} + 2 q^{36} + 4 q^{39} + 8 q^{44} - 20 q^{46} - 104 q^{49} + 4 q^{51} + 2 q^{54} - 60 q^{56} - 8 q^{59} + 4 q^{61} + 14 q^{64} - 12 q^{66} + 20 q^{69} + 16 q^{71} - 20 q^{74} + 8 q^{76} - 2 q^{81} - 20 q^{84} + 28 q^{86} + 18 q^{89} - 80 q^{91} + 4 q^{94} - 10 q^{96} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.587785 + 0.809017i 0.415627 + 0.572061i 0.964580 0.263792i \(-0.0849733\pi\)
−0.548953 + 0.835853i \(0.684973\pi\)
\(3\) 0.951057 + 0.309017i 0.549093 + 0.178411i
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 0 0
\(6\) 0.309017 + 0.951057i 0.126156 + 0.388267i
\(7\) 4.47214i 1.69031i −0.534522 0.845154i \(-0.679509\pi\)
0.534522 0.845154i \(-0.320491\pi\)
\(8\) 2.85317 0.927051i 1.00875 0.327762i
\(9\) 0.809017 + 0.587785i 0.269672 + 0.195928i
\(10\) 0 0
\(11\) −2.61803 + 1.90211i −0.789367 + 0.573509i −0.907776 0.419456i \(-0.862221\pi\)
0.118409 + 0.992965i \(0.462221\pi\)
\(12\) 0.587785 0.809017i 0.169679 0.233543i
\(13\) 1.98787 2.73607i 0.551336 0.758849i −0.438857 0.898557i \(-0.644616\pi\)
0.990193 + 0.139708i \(0.0446165\pi\)
\(14\) 3.61803 2.62866i 0.966960 0.702538i
\(15\) 0 0
\(16\) 0.809017 + 0.587785i 0.202254 + 0.146946i
\(17\) −2.71441 + 0.881966i −0.658342 + 0.213908i −0.619089 0.785321i \(-0.712498\pi\)
−0.0392530 + 0.999229i \(0.512498\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000 + 3.07768i 0.229416 + 0.706069i 0.997813 + 0.0660962i \(0.0210544\pi\)
−0.768398 + 0.639973i \(0.778946\pi\)
\(20\) 0 0
\(21\) 1.38197 4.25325i 0.301570 0.928136i
\(22\) −3.07768 1.00000i −0.656164 0.213201i
\(23\) 2.62866 + 3.61803i 0.548113 + 0.754412i 0.989755 0.142779i \(-0.0456039\pi\)
−0.441642 + 0.897191i \(0.645604\pi\)
\(24\) 3.00000 0.612372
\(25\) 0 0
\(26\) 3.38197 0.663258
\(27\) 0.587785 + 0.809017i 0.113119 + 0.155695i
\(28\) −4.25325 1.38197i −0.803789 0.261167i
\(29\) −1.35410 + 4.16750i −0.251450 + 0.773885i 0.743058 + 0.669227i \(0.233375\pi\)
−0.994508 + 0.104658i \(0.966625\pi\)
\(30\) 0 0
\(31\) 2.23607 + 6.88191i 0.401610 + 1.23603i 0.923693 + 0.383133i \(0.125155\pi\)
−0.522083 + 0.852894i \(0.674845\pi\)
\(32\) 5.00000i 0.883883i
\(33\) −3.07768 + 1.00000i −0.535756 + 0.174078i
\(34\) −2.30902 1.67760i −0.395993 0.287706i
\(35\) 0 0
\(36\) 0.809017 0.587785i 0.134836 0.0979642i
\(37\) −4.75528 + 6.54508i −0.781764 + 1.07601i 0.213321 + 0.976982i \(0.431572\pi\)
−0.995085 + 0.0990233i \(0.968428\pi\)
\(38\) −1.90211 + 2.61803i −0.308563 + 0.424701i
\(39\) 2.73607 1.98787i 0.438122 0.318314i
\(40\) 0 0
\(41\) 1.11803 + 0.812299i 0.174608 + 0.126860i 0.671657 0.740863i \(-0.265583\pi\)
−0.497049 + 0.867722i \(0.665583\pi\)
\(42\) 4.25325 1.38197i 0.656291 0.213242i
\(43\) 5.70820i 0.870493i −0.900311 0.435246i \(-0.856661\pi\)
0.900311 0.435246i \(-0.143339\pi\)
\(44\) 1.00000 + 3.07768i 0.150756 + 0.463978i
\(45\) 0 0
\(46\) −1.38197 + 4.25325i −0.203760 + 0.627108i
\(47\) 4.97980 + 1.61803i 0.726378 + 0.236015i 0.648786 0.760971i \(-0.275277\pi\)
0.0775917 + 0.996985i \(0.475277\pi\)
\(48\) 0.587785 + 0.809017i 0.0848395 + 0.116772i
\(49\) −13.0000 −1.85714
\(50\) 0 0
\(51\) −2.85410 −0.399654
\(52\) −1.98787 2.73607i −0.275668 0.379424i
\(53\) 1.31433 + 0.427051i 0.180537 + 0.0586600i 0.397890 0.917433i \(-0.369742\pi\)
−0.217354 + 0.976093i \(0.569742\pi\)
\(54\) −0.309017 + 0.951057i −0.0420519 + 0.129422i
\(55\) 0 0
\(56\) −4.14590 12.7598i −0.554019 1.70509i
\(57\) 3.23607i 0.428628i
\(58\) −4.16750 + 1.35410i −0.547219 + 0.177802i
\(59\) −3.23607 2.35114i −0.421300 0.306092i 0.356861 0.934158i \(-0.383847\pi\)
−0.778161 + 0.628065i \(0.783847\pi\)
\(60\) 0 0
\(61\) 0.500000 0.363271i 0.0640184 0.0465121i −0.555316 0.831640i \(-0.687403\pi\)
0.619334 + 0.785127i \(0.287403\pi\)
\(62\) −4.25325 + 5.85410i −0.540164 + 0.743472i
\(63\) 2.62866 3.61803i 0.331179 0.455829i
\(64\) 5.66312 4.11450i 0.707890 0.514312i
\(65\) 0 0
\(66\) −2.61803 1.90211i −0.322258 0.234134i
\(67\) 4.97980 1.61803i 0.608379 0.197674i 0.0114051 0.999935i \(-0.496370\pi\)
0.596974 + 0.802261i \(0.296370\pi\)
\(68\) 2.85410i 0.346111i
\(69\) 1.38197 + 4.25325i 0.166369 + 0.512032i
\(70\) 0 0
\(71\) −0.236068 + 0.726543i −0.0280161 + 0.0862247i −0.964087 0.265587i \(-0.914434\pi\)
0.936071 + 0.351812i \(0.114434\pi\)
\(72\) 2.85317 + 0.927051i 0.336249 + 0.109254i
\(73\) −1.81636 2.50000i −0.212588 0.292603i 0.689384 0.724396i \(-0.257881\pi\)
−0.901973 + 0.431793i \(0.857881\pi\)
\(74\) −8.09017 −0.940463
\(75\) 0 0
\(76\) 3.23607 0.371202
\(77\) 8.50651 + 11.7082i 0.969407 + 1.33427i
\(78\) 3.21644 + 1.04508i 0.364190 + 0.118333i
\(79\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 1.38197i 0.152613i
\(83\) −3.35520 + 1.09017i −0.368281 + 0.119662i −0.487310 0.873229i \(-0.662022\pi\)
0.119029 + 0.992891i \(0.462022\pi\)
\(84\) −3.61803 2.62866i −0.394760 0.286810i
\(85\) 0 0
\(86\) 4.61803 3.35520i 0.497975 0.361800i
\(87\) −2.57565 + 3.54508i −0.276139 + 0.380073i
\(88\) −5.70634 + 7.85410i −0.608298 + 0.837250i
\(89\) 6.16312 4.47777i 0.653289 0.474642i −0.211101 0.977464i \(-0.567705\pi\)
0.864390 + 0.502822i \(0.167705\pi\)
\(90\) 0 0
\(91\) −12.2361 8.89002i −1.28269 0.931928i
\(92\) 4.25325 1.38197i 0.443432 0.144080i
\(93\) 7.23607i 0.750345i
\(94\) 1.61803 + 4.97980i 0.166887 + 0.513627i
\(95\) 0 0
\(96\) 1.54508 4.75528i 0.157695 0.485334i
\(97\) −8.42075 2.73607i −0.854998 0.277806i −0.151460 0.988463i \(-0.548397\pi\)
−0.703538 + 0.710658i \(0.748397\pi\)
\(98\) −7.64121 10.5172i −0.771879 1.06240i
\(99\) −3.23607 −0.325237
\(100\) 0 0
\(101\) −16.5623 −1.64801 −0.824006 0.566582i \(-0.808266\pi\)
−0.824006 + 0.566582i \(0.808266\pi\)
\(102\) −1.67760 2.30902i −0.166107 0.228627i
\(103\) −1.17557 0.381966i −0.115832 0.0376362i 0.250527 0.968110i \(-0.419396\pi\)
−0.366360 + 0.930473i \(0.619396\pi\)
\(104\) 3.13525 9.64932i 0.307437 0.946194i
\(105\) 0 0
\(106\) 0.427051 + 1.31433i 0.0414789 + 0.127659i
\(107\) 16.4721i 1.59242i −0.605019 0.796211i \(-0.706835\pi\)
0.605019 0.796211i \(-0.293165\pi\)
\(108\) 0.951057 0.309017i 0.0915155 0.0297352i
\(109\) −15.4443 11.2209i −1.47929 1.07477i −0.977784 0.209617i \(-0.932778\pi\)
−0.501509 0.865152i \(-0.667222\pi\)
\(110\) 0 0
\(111\) −6.54508 + 4.75528i −0.621232 + 0.451351i
\(112\) 2.62866 3.61803i 0.248385 0.341872i
\(113\) 1.57160 2.16312i 0.147843 0.203489i −0.728672 0.684863i \(-0.759862\pi\)
0.876515 + 0.481374i \(0.159862\pi\)
\(114\) −2.61803 + 1.90211i −0.245201 + 0.178149i
\(115\) 0 0
\(116\) 3.54508 + 2.57565i 0.329153 + 0.239144i
\(117\) 3.21644 1.04508i 0.297360 0.0966181i
\(118\) 4.00000i 0.368230i
\(119\) 3.94427 + 12.1392i 0.361571 + 1.11280i
\(120\) 0 0
\(121\) −0.163119 + 0.502029i −0.0148290 + 0.0456390i
\(122\) 0.587785 + 0.190983i 0.0532156 + 0.0172908i
\(123\) 0.812299 + 1.11803i 0.0732426 + 0.100810i
\(124\) 7.23607 0.649818
\(125\) 0 0
\(126\) 4.47214 0.398410
\(127\) 5.70634 + 7.85410i 0.506356 + 0.696939i 0.983299 0.181995i \(-0.0582555\pi\)
−0.476944 + 0.878934i \(0.658255\pi\)
\(128\) −2.85317 0.927051i −0.252187 0.0819405i
\(129\) 1.76393 5.42882i 0.155306 0.477981i
\(130\) 0 0
\(131\) 4.38197 + 13.4863i 0.382854 + 1.17830i 0.938025 + 0.346568i \(0.112653\pi\)
−0.555171 + 0.831736i \(0.687347\pi\)
\(132\) 3.23607i 0.281664i
\(133\) 13.7638 4.47214i 1.19347 0.387783i
\(134\) 4.23607 + 3.07768i 0.365941 + 0.265871i
\(135\) 0 0
\(136\) −6.92705 + 5.03280i −0.593990 + 0.431559i
\(137\) 3.16344 4.35410i 0.270271 0.371996i −0.652210 0.758038i \(-0.726158\pi\)
0.922481 + 0.386042i \(0.126158\pi\)
\(138\) −2.62866 + 3.61803i −0.223766 + 0.307988i
\(139\) −4.09017 + 2.97168i −0.346924 + 0.252055i −0.747577 0.664175i \(-0.768783\pi\)
0.400654 + 0.916230i \(0.368783\pi\)
\(140\) 0 0
\(141\) 4.23607 + 3.07768i 0.356741 + 0.259188i
\(142\) −0.726543 + 0.236068i −0.0609701 + 0.0198104i
\(143\) 10.9443i 0.915206i
\(144\) 0.309017 + 0.951057i 0.0257514 + 0.0792547i
\(145\) 0 0
\(146\) 0.954915 2.93893i 0.0790293 0.243227i
\(147\) −12.3637 4.01722i −1.01974 0.331335i
\(148\) 4.75528 + 6.54508i 0.390882 + 0.538003i
\(149\) 12.1459 0.995031 0.497515 0.867455i \(-0.334246\pi\)
0.497515 + 0.867455i \(0.334246\pi\)
\(150\) 0 0
\(151\) 16.4721 1.34048 0.670242 0.742143i \(-0.266190\pi\)
0.670242 + 0.742143i \(0.266190\pi\)
\(152\) 5.70634 + 7.85410i 0.462845 + 0.637052i
\(153\) −2.71441 0.881966i −0.219447 0.0713027i
\(154\) −4.47214 + 13.7638i −0.360375 + 1.10912i
\(155\) 0 0
\(156\) −1.04508 3.21644i −0.0836738 0.257521i
\(157\) 13.7984i 1.10123i 0.834759 + 0.550615i \(0.185607\pi\)
−0.834759 + 0.550615i \(0.814393\pi\)
\(158\) 0 0
\(159\) 1.11803 + 0.812299i 0.0886659 + 0.0644195i
\(160\) 0 0
\(161\) 16.1803 11.7557i 1.27519 0.926479i
\(162\) −0.587785 + 0.809017i −0.0461808 + 0.0635624i
\(163\) 1.73060 2.38197i 0.135551 0.186570i −0.735845 0.677150i \(-0.763215\pi\)
0.871396 + 0.490580i \(0.163215\pi\)
\(164\) 1.11803 0.812299i 0.0873038 0.0634299i
\(165\) 0 0
\(166\) −2.85410 2.07363i −0.221521 0.160945i
\(167\) −22.2703 + 7.23607i −1.72333 + 0.559944i −0.992460 0.122573i \(-0.960886\pi\)
−0.730870 + 0.682517i \(0.760886\pi\)
\(168\) 13.4164i 1.03510i
\(169\) 0.482779 + 1.48584i 0.0371369 + 0.114295i
\(170\) 0 0
\(171\) −1.00000 + 3.07768i −0.0764719 + 0.235356i
\(172\) −5.42882 1.76393i −0.413944 0.134499i
\(173\) −5.82485 8.01722i −0.442855 0.609538i 0.527988 0.849252i \(-0.322946\pi\)
−0.970844 + 0.239714i \(0.922946\pi\)
\(174\) −4.38197 −0.332196
\(175\) 0 0
\(176\) −3.23607 −0.243928
\(177\) −2.35114 3.23607i −0.176723 0.243238i
\(178\) 7.24518 + 2.35410i 0.543049 + 0.176447i
\(179\) −1.90983 + 5.87785i −0.142747 + 0.439331i −0.996714 0.0809958i \(-0.974190\pi\)
0.853967 + 0.520327i \(0.174190\pi\)
\(180\) 0 0
\(181\) −3.02786 9.31881i −0.225059 0.692661i −0.998286 0.0585312i \(-0.981358\pi\)
0.773226 0.634130i \(-0.218642\pi\)
\(182\) 15.1246i 1.12111i
\(183\) 0.587785 0.190983i 0.0434503 0.0141179i
\(184\) 10.8541 + 7.88597i 0.800175 + 0.581361i
\(185\) 0 0
\(186\) −5.85410 + 4.25325i −0.429244 + 0.311864i
\(187\) 5.42882 7.47214i 0.396995 0.546417i
\(188\) 3.07768 4.23607i 0.224463 0.308947i
\(189\) 3.61803 2.62866i 0.263173 0.191207i
\(190\) 0 0
\(191\) 19.9443 + 14.4904i 1.44312 + 1.04849i 0.987380 + 0.158371i \(0.0506243\pi\)
0.455737 + 0.890114i \(0.349376\pi\)
\(192\) 6.65740 2.16312i 0.480456 0.156110i
\(193\) 7.67376i 0.552369i 0.961105 + 0.276185i \(0.0890702\pi\)
−0.961105 + 0.276185i \(0.910930\pi\)
\(194\) −2.73607 8.42075i −0.196438 0.604575i
\(195\) 0 0
\(196\) −4.01722 + 12.3637i −0.286944 + 0.883124i
\(197\) −5.11855 1.66312i −0.364682 0.118492i 0.120943 0.992659i \(-0.461408\pi\)
−0.485625 + 0.874167i \(0.661408\pi\)
\(198\) −1.90211 2.61803i −0.135177 0.186056i
\(199\) 18.6525 1.32224 0.661119 0.750281i \(-0.270082\pi\)
0.661119 + 0.750281i \(0.270082\pi\)
\(200\) 0 0
\(201\) 5.23607 0.369324
\(202\) −9.73508 13.3992i −0.684958 0.942764i
\(203\) 18.6376 + 6.05573i 1.30810 + 0.425029i
\(204\) −0.881966 + 2.71441i −0.0617500 + 0.190047i
\(205\) 0 0
\(206\) −0.381966 1.17557i −0.0266128 0.0819059i
\(207\) 4.47214i 0.310835i
\(208\) 3.21644 1.04508i 0.223020 0.0724636i
\(209\) −8.47214 6.15537i −0.586030 0.425776i
\(210\) 0 0
\(211\) 14.4721 10.5146i 0.996303 0.723856i 0.0350106 0.999387i \(-0.488854\pi\)
0.961292 + 0.275530i \(0.0888535\pi\)
\(212\) 0.812299 1.11803i 0.0557889 0.0767869i
\(213\) −0.449028 + 0.618034i −0.0307669 + 0.0423470i
\(214\) 13.3262 9.68208i 0.910963 0.661853i
\(215\) 0 0
\(216\) 2.42705 + 1.76336i 0.165140 + 0.119981i
\(217\) 30.7768 10.0000i 2.08927 0.678844i
\(218\) 19.0902i 1.29295i
\(219\) −0.954915 2.93893i −0.0645272 0.198594i
\(220\) 0 0
\(221\) −2.98278 + 9.18005i −0.200643 + 0.617517i
\(222\) −7.69421 2.50000i −0.516401 0.167789i
\(223\) 8.33499 + 11.4721i 0.558153 + 0.768231i 0.991090 0.133193i \(-0.0425230\pi\)
−0.432938 + 0.901424i \(0.642523\pi\)
\(224\) −22.3607 −1.49404
\(225\) 0 0
\(226\) 2.67376 0.177856
\(227\) −11.7557 16.1803i −0.780254 1.07393i −0.995254 0.0973129i \(-0.968975\pi\)
0.215000 0.976614i \(-0.431025\pi\)
\(228\) 3.07768 + 1.00000i 0.203825 + 0.0662266i
\(229\) 7.71885 23.7562i 0.510076 1.56985i −0.281991 0.959417i \(-0.590995\pi\)
0.792067 0.610435i \(-0.209005\pi\)
\(230\) 0 0
\(231\) 4.47214 + 13.7638i 0.294245 + 0.905593i
\(232\) 13.1459i 0.863070i
\(233\) −13.9026 + 4.51722i −0.910788 + 0.295933i −0.726682 0.686973i \(-0.758939\pi\)
−0.184106 + 0.982906i \(0.558939\pi\)
\(234\) 2.73607 + 1.98787i 0.178862 + 0.129951i
\(235\) 0 0
\(236\) −3.23607 + 2.35114i −0.210650 + 0.153046i
\(237\) 0 0
\(238\) −7.50245 + 10.3262i −0.486312 + 0.669351i
\(239\) −5.70820 + 4.14725i −0.369233 + 0.268263i −0.756893 0.653539i \(-0.773284\pi\)
0.387660 + 0.921803i \(0.373284\pi\)
\(240\) 0 0
\(241\) 0.836881 + 0.608030i 0.0539082 + 0.0391666i 0.614413 0.788985i \(-0.289393\pi\)
−0.560505 + 0.828151i \(0.689393\pi\)
\(242\) −0.502029 + 0.163119i −0.0322716 + 0.0104857i
\(243\) 1.00000i 0.0641500i
\(244\) −0.190983 0.587785i −0.0122264 0.0376291i
\(245\) 0 0
\(246\) −0.427051 + 1.31433i −0.0272278 + 0.0837985i
\(247\) 10.4086 + 3.38197i 0.662285 + 0.215189i
\(248\) 12.7598 + 17.5623i 0.810246 + 1.11521i
\(249\) −3.52786 −0.223569
\(250\) 0 0
\(251\) −26.9443 −1.70071 −0.850354 0.526212i \(-0.823612\pi\)
−0.850354 + 0.526212i \(0.823612\pi\)
\(252\) −2.62866 3.61803i −0.165590 0.227915i
\(253\) −13.7638 4.47214i −0.865324 0.281161i
\(254\) −3.00000 + 9.23305i −0.188237 + 0.579333i
\(255\) 0 0
\(256\) −5.25329 16.1680i −0.328331 1.01050i
\(257\) 12.7984i 0.798341i 0.916877 + 0.399170i \(0.130702\pi\)
−0.916877 + 0.399170i \(0.869298\pi\)
\(258\) 5.42882 1.76393i 0.337984 0.109818i
\(259\) 29.2705 + 21.2663i 1.81878 + 1.32142i
\(260\) 0 0
\(261\) −3.54508 + 2.57565i −0.219435 + 0.159429i
\(262\) −8.33499 + 11.4721i −0.514938 + 0.708751i
\(263\) 6.98791 9.61803i 0.430893 0.593073i −0.537265 0.843414i \(-0.680542\pi\)
0.968158 + 0.250340i \(0.0805425\pi\)
\(264\) −7.85410 + 5.70634i −0.483387 + 0.351201i
\(265\) 0 0
\(266\) 11.7082 + 8.50651i 0.717876 + 0.521567i
\(267\) 7.24518 2.35410i 0.443398 0.144069i
\(268\) 5.23607i 0.319844i
\(269\) 0.0450850 + 0.138757i 0.00274888 + 0.00846018i 0.952422 0.304784i \(-0.0985842\pi\)
−0.949673 + 0.313244i \(0.898584\pi\)
\(270\) 0 0
\(271\) 6.85410 21.0948i 0.416357 1.28142i −0.494674 0.869078i \(-0.664713\pi\)
0.911031 0.412337i \(-0.135287\pi\)
\(272\) −2.71441 0.881966i −0.164585 0.0534770i
\(273\) −8.89002 12.2361i −0.538049 0.740561i
\(274\) 5.38197 0.325136
\(275\) 0 0
\(276\) 4.47214 0.269191
\(277\) −3.40820 4.69098i −0.204779 0.281854i 0.694259 0.719726i \(-0.255732\pi\)
−0.899037 + 0.437872i \(0.855732\pi\)
\(278\) −4.80828 1.56231i −0.288382 0.0937009i
\(279\) −2.23607 + 6.88191i −0.133870 + 0.412009i
\(280\) 0 0
\(281\) −5.37132 16.5312i −0.320426 0.986171i −0.973463 0.228844i \(-0.926505\pi\)
0.653037 0.757326i \(-0.273495\pi\)
\(282\) 5.23607i 0.311803i
\(283\) −0.277515 + 0.0901699i −0.0164965 + 0.00536005i −0.317254 0.948341i \(-0.602761\pi\)
0.300757 + 0.953701i \(0.402761\pi\)
\(284\) 0.618034 + 0.449028i 0.0366736 + 0.0266449i
\(285\) 0 0
\(286\) −8.85410 + 6.43288i −0.523554 + 0.380384i
\(287\) 3.63271 5.00000i 0.214432 0.295141i
\(288\) 2.93893 4.04508i 0.173178 0.238359i
\(289\) −7.16312 + 5.20431i −0.421360 + 0.306136i
\(290\) 0 0
\(291\) −7.16312 5.20431i −0.419909 0.305082i
\(292\) −2.93893 + 0.954915i −0.171988 + 0.0558822i
\(293\) 3.79837i 0.221903i 0.993826 + 0.110952i \(0.0353899\pi\)
−0.993826 + 0.110952i \(0.964610\pi\)
\(294\) −4.01722 12.3637i −0.234289 0.721068i
\(295\) 0 0
\(296\) −7.50000 + 23.0826i −0.435929 + 1.34165i
\(297\) −3.07768 1.00000i −0.178585 0.0580259i
\(298\) 7.13918 + 9.82624i 0.413562 + 0.569219i
\(299\) 15.1246 0.874679
\(300\) 0 0
\(301\) −25.5279 −1.47140
\(302\) 9.68208 + 13.3262i 0.557141 + 0.766839i
\(303\) −15.7517 5.11803i −0.904911 0.294023i
\(304\) −1.00000 + 3.07768i −0.0573539 + 0.176517i
\(305\) 0 0
\(306\) −0.881966 2.71441i −0.0504186 0.155173i
\(307\) 1.34752i 0.0769073i −0.999260 0.0384536i \(-0.987757\pi\)
0.999260 0.0384536i \(-0.0122432\pi\)
\(308\) 13.7638 4.47214i 0.784266 0.254824i
\(309\) −1.00000 0.726543i −0.0568880 0.0413316i
\(310\) 0 0
\(311\) −3.47214 + 2.52265i −0.196887 + 0.143047i −0.681861 0.731482i \(-0.738829\pi\)
0.484974 + 0.874529i \(0.338829\pi\)
\(312\) 5.96361 8.20820i 0.337623 0.464698i
\(313\) 4.97980 6.85410i 0.281475 0.387417i −0.644747 0.764396i \(-0.723037\pi\)
0.926222 + 0.376979i \(0.123037\pi\)
\(314\) −11.1631 + 8.11048i −0.629971 + 0.457701i
\(315\) 0 0
\(316\) 0 0
\(317\) −23.6174 + 7.67376i −1.32649 + 0.431001i −0.884717 0.466128i \(-0.845649\pi\)
−0.441768 + 0.897129i \(0.645649\pi\)
\(318\) 1.38197i 0.0774968i
\(319\) −4.38197 13.4863i −0.245343 0.755088i
\(320\) 0 0
\(321\) 5.09017 15.6659i 0.284106 0.874387i
\(322\) 19.0211 + 6.18034i 1.06001 + 0.344417i
\(323\) −5.42882 7.47214i −0.302068 0.415761i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 2.94427 0.163068
\(327\) −11.2209 15.4443i −0.620518 0.854070i
\(328\) 3.94298 + 1.28115i 0.217715 + 0.0707398i
\(329\) 7.23607 22.2703i 0.398937 1.22780i
\(330\) 0 0
\(331\) 3.38197 + 10.4086i 0.185890 + 0.572110i 0.999963 0.00865315i \(-0.00275442\pi\)
−0.814073 + 0.580763i \(0.802754\pi\)
\(332\) 3.52786i 0.193617i
\(333\) −7.69421 + 2.50000i −0.421640 + 0.136999i
\(334\) −18.9443 13.7638i −1.03658 0.753123i
\(335\) 0 0
\(336\) 3.61803 2.62866i 0.197380 0.143405i
\(337\) 8.78402 12.0902i 0.478496 0.658594i −0.499719 0.866188i \(-0.666563\pi\)
0.978215 + 0.207594i \(0.0665633\pi\)
\(338\) −0.918300 + 1.26393i −0.0499490 + 0.0687488i
\(339\) 2.16312 1.57160i 0.117484 0.0853575i
\(340\) 0 0
\(341\) −18.9443 13.7638i −1.02589 0.745353i
\(342\) −3.07768 + 1.00000i −0.166422 + 0.0540738i
\(343\) 26.8328i 1.44884i
\(344\) −5.29180 16.2865i −0.285315 0.878108i
\(345\) 0 0
\(346\) 3.06231 9.42481i 0.164631 0.506681i
\(347\) 32.0584 + 10.4164i 1.72099 + 0.559182i 0.992100 0.125453i \(-0.0400385\pi\)
0.728886 + 0.684635i \(0.240038\pi\)
\(348\) 2.57565 + 3.54508i 0.138070 + 0.190037i
\(349\) −25.0344 −1.34006 −0.670031 0.742333i \(-0.733719\pi\)
−0.670031 + 0.742333i \(0.733719\pi\)
\(350\) 0 0
\(351\) 3.38197 0.180516
\(352\) 9.51057 + 13.0902i 0.506915 + 0.697708i
\(353\) −28.8747 9.38197i −1.53685 0.499352i −0.586342 0.810063i \(-0.699433\pi\)
−0.950504 + 0.310712i \(0.899433\pi\)
\(354\) 1.23607 3.80423i 0.0656963 0.202192i
\(355\) 0 0
\(356\) −2.35410 7.24518i −0.124767 0.383994i
\(357\) 12.7639i 0.675539i
\(358\) −5.87785 + 1.90983i −0.310654 + 0.100938i
\(359\) −8.56231 6.22088i −0.451901 0.328325i 0.338445 0.940986i \(-0.390099\pi\)
−0.790346 + 0.612661i \(0.790099\pi\)
\(360\) 0 0
\(361\) 6.89919 5.01255i 0.363115 0.263819i
\(362\) 5.75934 7.92705i 0.302704 0.416637i
\(363\) −0.310271 + 0.427051i −0.0162850 + 0.0224144i
\(364\) −12.2361 + 8.89002i −0.641344 + 0.465964i
\(365\) 0 0
\(366\) 0.500000 + 0.363271i 0.0261354 + 0.0189885i
\(367\) −5.70634 + 1.85410i −0.297868 + 0.0967833i −0.454139 0.890931i \(-0.650053\pi\)
0.156270 + 0.987714i \(0.450053\pi\)
\(368\) 4.47214i 0.233126i
\(369\) 0.427051 + 1.31433i 0.0222314 + 0.0684212i
\(370\) 0 0
\(371\) 1.90983 5.87785i 0.0991534 0.305163i
\(372\) 6.88191 + 2.23607i 0.356810 + 0.115935i
\(373\) −17.2905 23.7984i −0.895270 1.23223i −0.971952 0.235178i \(-0.924433\pi\)
0.0766827 0.997056i \(-0.475567\pi\)
\(374\) 9.23607 0.477586
\(375\) 0 0
\(376\) 15.7082 0.810089
\(377\) 8.71078 + 11.9894i 0.448628 + 0.617483i
\(378\) 4.25325 + 1.38197i 0.218764 + 0.0710807i
\(379\) −7.23607 + 22.2703i −0.371692 + 1.14395i 0.573992 + 0.818861i \(0.305394\pi\)
−0.945684 + 0.325089i \(0.894606\pi\)
\(380\) 0 0
\(381\) 3.00000 + 9.23305i 0.153695 + 0.473024i
\(382\) 24.6525i 1.26133i
\(383\) −19.8132 + 6.43769i −1.01241 + 0.328951i −0.767812 0.640675i \(-0.778655\pi\)
−0.244594 + 0.969626i \(0.578655\pi\)
\(384\) −2.42705 1.76336i −0.123855 0.0899859i
\(385\) 0 0
\(386\) −6.20820 + 4.51052i −0.315989 + 0.229580i
\(387\) 3.35520 4.61803i 0.170554 0.234748i
\(388\) −5.20431 + 7.16312i −0.264209 + 0.363652i
\(389\) −30.0066 + 21.8011i −1.52139 + 1.10536i −0.560603 + 0.828085i \(0.689430\pi\)
−0.960791 + 0.277272i \(0.910570\pi\)
\(390\) 0 0
\(391\) −10.3262 7.50245i −0.522220 0.379415i
\(392\) −37.0912 + 12.0517i −1.87339 + 0.608701i
\(393\) 14.1803i 0.715304i
\(394\) −1.66312 5.11855i −0.0837867 0.257869i
\(395\) 0 0
\(396\) −1.00000 + 3.07768i −0.0502519 + 0.154659i
\(397\) −10.4086 3.38197i −0.522394 0.169736i 0.0359377 0.999354i \(-0.488558\pi\)
−0.558331 + 0.829618i \(0.688558\pi\)
\(398\) 10.9637 + 15.0902i 0.549558 + 0.756402i
\(399\) 14.4721 0.724513
\(400\) 0 0
\(401\) 33.4508 1.67046 0.835228 0.549904i \(-0.185336\pi\)
0.835228 + 0.549904i \(0.185336\pi\)
\(402\) 3.07768 + 4.23607i 0.153501 + 0.211276i
\(403\) 23.2744 + 7.56231i 1.15938 + 0.376705i
\(404\) −5.11803 + 15.7517i −0.254632 + 0.783676i
\(405\) 0 0
\(406\) 6.05573 + 18.6376i 0.300541 + 0.924969i
\(407\) 26.1803i 1.29771i
\(408\) −8.14324 + 2.64590i −0.403150 + 0.130991i
\(409\) 20.8713 + 15.1639i 1.03202 + 0.749807i 0.968712 0.248187i \(-0.0798348\pi\)
0.0633084 + 0.997994i \(0.479835\pi\)
\(410\) 0 0
\(411\) 4.35410 3.16344i 0.214772 0.156041i
\(412\) −0.726543 + 1.00000i −0.0357942 + 0.0492665i
\(413\) −10.5146 + 14.4721i −0.517391 + 0.712127i
\(414\) −3.61803 + 2.62866i −0.177817 + 0.129191i
\(415\) 0 0
\(416\) −13.6803 9.93935i −0.670734 0.487317i
\(417\) −4.80828 + 1.56231i −0.235463 + 0.0765064i
\(418\) 10.4721i 0.512209i
\(419\) −10.1803 31.3319i −0.497342 1.53066i −0.813275 0.581880i \(-0.802317\pi\)
0.315932 0.948782i \(-0.397683\pi\)
\(420\) 0 0
\(421\) 7.15248 22.0131i 0.348590 1.07285i −0.611043 0.791597i \(-0.709250\pi\)
0.959634 0.281253i \(-0.0907502\pi\)
\(422\) 17.0130 + 5.52786i 0.828181 + 0.269092i
\(423\) 3.07768 + 4.23607i 0.149642 + 0.205965i
\(424\) 4.14590 0.201343
\(425\) 0 0
\(426\) −0.763932 −0.0370126
\(427\) −1.62460 2.23607i −0.0786198 0.108211i
\(428\) −15.6659 5.09017i −0.757241 0.246043i
\(429\) −3.38197 + 10.4086i −0.163283 + 0.502533i
\(430\) 0 0
\(431\) −3.29180 10.1311i −0.158560 0.487998i 0.839944 0.542673i \(-0.182588\pi\)
−0.998504 + 0.0546749i \(0.982588\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −23.7562 + 7.71885i −1.14165 + 0.370944i −0.817991 0.575230i \(-0.804912\pi\)
−0.323657 + 0.946174i \(0.604912\pi\)
\(434\) 26.1803 + 19.0211i 1.25670 + 0.913043i
\(435\) 0 0
\(436\) −15.4443 + 11.2209i −0.739646 + 0.537385i
\(437\) −8.50651 + 11.7082i −0.406921 + 0.560079i
\(438\) 1.81636 2.50000i 0.0867889 0.119455i
\(439\) −5.00000 + 3.63271i −0.238637 + 0.173380i −0.700676 0.713480i \(-0.747118\pi\)
0.462039 + 0.886860i \(0.347118\pi\)
\(440\) 0 0
\(441\) −10.5172 7.64121i −0.500820 0.363867i
\(442\) −9.18005 + 2.98278i −0.436650 + 0.141876i
\(443\) 30.7639i 1.46164i −0.682571 0.730819i \(-0.739138\pi\)
0.682571 0.730819i \(-0.260862\pi\)
\(444\) 2.50000 + 7.69421i 0.118645 + 0.365151i
\(445\) 0 0
\(446\) −4.38197 + 13.4863i −0.207492 + 0.638595i
\(447\) 11.5514 + 3.75329i 0.546364 + 0.177524i
\(448\) −18.4006 25.3262i −0.869346 1.19655i
\(449\) 7.79837 0.368028 0.184014 0.982924i \(-0.441091\pi\)
0.184014 + 0.982924i \(0.441091\pi\)
\(450\) 0 0
\(451\) −4.47214 −0.210585
\(452\) −1.57160 2.16312i −0.0739217 0.101745i
\(453\) 15.6659 + 5.09017i 0.736050 + 0.239157i
\(454\) 6.18034 19.0211i 0.290058 0.892706i
\(455\) 0 0
\(456\) 3.00000 + 9.23305i 0.140488 + 0.432377i
\(457\) 22.3607i 1.04599i −0.852336 0.522994i \(-0.824815\pi\)
0.852336 0.522994i \(-0.175185\pi\)
\(458\) 23.7562 7.71885i 1.11005 0.360678i
\(459\) −2.30902 1.67760i −0.107776 0.0783036i
\(460\) 0 0
\(461\) 6.63525 4.82079i 0.309035 0.224527i −0.422448 0.906387i \(-0.638829\pi\)
0.731482 + 0.681861i \(0.238829\pi\)
\(462\) −8.50651 + 11.7082i −0.395759 + 0.544715i
\(463\) 13.6578 18.7984i 0.634733 0.873635i −0.363588 0.931560i \(-0.618448\pi\)
0.998321 + 0.0579252i \(0.0184485\pi\)
\(464\) −3.54508 + 2.57565i −0.164576 + 0.119572i
\(465\) 0 0
\(466\) −11.8262 8.59226i −0.547840 0.398029i
\(467\) 5.53483 1.79837i 0.256121 0.0832188i −0.178142 0.984005i \(-0.557009\pi\)
0.434263 + 0.900786i \(0.357009\pi\)
\(468\) 3.38197i 0.156331i
\(469\) −7.23607 22.2703i −0.334131 1.02835i
\(470\) 0 0
\(471\) −4.26393 + 13.1230i −0.196472 + 0.604677i
\(472\) −11.4127 3.70820i −0.525311 0.170684i
\(473\) 10.8576 + 14.9443i 0.499235 + 0.687138i
\(474\) 0 0
\(475\) 0 0
\(476\) 12.7639 0.585034
\(477\) 0.812299 + 1.11803i 0.0371926 + 0.0511913i
\(478\) −6.71040 2.18034i −0.306926 0.0997264i
\(479\) −0.326238 + 1.00406i −0.0149062 + 0.0458765i −0.958233 0.285989i \(-0.907678\pi\)
0.943327 + 0.331865i \(0.107678\pi\)
\(480\) 0 0
\(481\) 8.45492 + 26.0216i 0.385511 + 1.18648i
\(482\) 1.03444i 0.0471175i
\(483\) 19.0211 6.18034i 0.865491 0.281215i
\(484\) 0.427051 + 0.310271i 0.0194114 + 0.0141032i
\(485\) 0 0
\(486\) −0.809017 + 0.587785i −0.0366978 + 0.0266625i
\(487\) 2.17963 3.00000i 0.0987684 0.135943i −0.756772 0.653679i \(-0.773225\pi\)
0.855541 + 0.517736i \(0.173225\pi\)
\(488\) 1.08981 1.50000i 0.0493336 0.0679018i
\(489\) 2.38197 1.73060i 0.107716 0.0782604i
\(490\) 0 0
\(491\) 24.1803 + 17.5680i 1.09124 + 0.792835i 0.979609 0.200915i \(-0.0643914\pi\)
0.111635 + 0.993749i \(0.464391\pi\)
\(492\) 1.31433 0.427051i 0.0592545 0.0192529i
\(493\) 12.5066i 0.563268i
\(494\) 3.38197 + 10.4086i 0.152162 + 0.468306i
\(495\) 0 0
\(496\) −2.23607 + 6.88191i −0.100402 + 0.309007i
\(497\) 3.24920 + 1.05573i 0.145746 + 0.0473559i
\(498\) −2.07363 2.85410i −0.0929214 0.127895i
\(499\) 6.00000 0.268597 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(500\) 0 0
\(501\) −23.4164 −1.04617
\(502\) −15.8374 21.7984i −0.706860 0.972909i
\(503\) 33.6830 + 10.9443i 1.50185 + 0.487981i 0.940557 0.339636i \(-0.110304\pi\)
0.561294 + 0.827617i \(0.310304\pi\)
\(504\) 4.14590 12.7598i 0.184673 0.568365i
\(505\) 0 0
\(506\) −4.47214 13.7638i −0.198811 0.611876i
\(507\) 1.56231i 0.0693844i
\(508\) 9.23305 3.00000i 0.409650 0.133103i
\(509\) 21.7254 + 15.7844i 0.962963 + 0.699633i 0.953837 0.300325i \(-0.0970952\pi\)
0.00912564 + 0.999958i \(0.497095\pi\)
\(510\) 0 0
\(511\) −11.1803 + 8.12299i −0.494589 + 0.359340i
\(512\) 6.46564 8.89919i 0.285744 0.393292i
\(513\) −1.90211 + 2.61803i −0.0839803 + 0.115589i
\(514\) −10.3541 + 7.52270i −0.456700 + 0.331812i
\(515\) 0 0
\(516\) −4.61803 3.35520i −0.203298 0.147704i
\(517\) −16.1150 + 5.23607i −0.708735 + 0.230282i
\(518\) 36.1803i 1.58967i
\(519\) −3.06231 9.42481i −0.134420 0.413703i
\(520\) 0 0
\(521\) 0.628677 1.93487i 0.0275428 0.0847682i −0.936340 0.351094i \(-0.885810\pi\)
0.963883 + 0.266326i \(0.0858097\pi\)
\(522\) −4.16750 1.35410i −0.182406 0.0592674i
\(523\) 7.22494 + 9.94427i 0.315924 + 0.434833i 0.937217 0.348746i \(-0.113392\pi\)
−0.621293 + 0.783578i \(0.713392\pi\)
\(524\) 14.1803 0.619471
\(525\) 0 0
\(526\) 11.8885 0.518365
\(527\) −12.1392 16.7082i −0.528793 0.727821i
\(528\) −3.07768 1.00000i −0.133939 0.0435194i
\(529\) 0.927051 2.85317i 0.0403066 0.124051i
\(530\) 0 0
\(531\) −1.23607 3.80423i −0.0536408 0.165089i
\(532\) 14.4721i 0.627447i
\(533\) 4.44501 1.44427i 0.192535 0.0625584i
\(534\) 6.16312 + 4.47777i 0.266704 + 0.193772i
\(535\) 0 0
\(536\) 12.7082 9.23305i 0.548911 0.398807i
\(537\) −3.63271 + 5.00000i −0.156763 + 0.215766i
\(538\) −0.0857567 + 0.118034i −0.00369723 + 0.00508881i
\(539\) 34.0344 24.7275i 1.46597 1.06509i
\(540\) 0 0
\(541\) 28.5795 + 20.7642i 1.22873 + 0.892724i 0.996794 0.0800067i \(-0.0254942\pi\)
0.231936 + 0.972731i \(0.425494\pi\)
\(542\) 21.0948 6.85410i 0.906097 0.294409i
\(543\) 9.79837i 0.420488i
\(544\) 4.40983 + 13.5721i 0.189070 + 0.581897i
\(545\) 0 0
\(546\) 4.67376 14.3844i 0.200019 0.615594i
\(547\) 2.24514 + 0.729490i 0.0959952 + 0.0311907i 0.356621 0.934249i \(-0.383929\pi\)
−0.260626 + 0.965440i \(0.583929\pi\)
\(548\) −3.16344 4.35410i −0.135135 0.185998i
\(549\) 0.618034 0.0263770
\(550\) 0 0
\(551\) −14.1803 −0.604103
\(552\) 7.88597 + 10.8541i 0.335649 + 0.461981i
\(553\) 0 0
\(554\) 1.79180 5.51458i 0.0761261 0.234292i
\(555\) 0 0
\(556\) 1.56231 + 4.80828i 0.0662565 + 0.203917i
\(557\) 22.2705i 0.943632i −0.881697 0.471816i \(-0.843599\pi\)
0.881697 0.471816i \(-0.156401\pi\)
\(558\) −6.88191 + 2.23607i −0.291334 + 0.0946603i
\(559\) −15.6180 11.3472i −0.660572 0.479934i
\(560\) 0 0
\(561\) 7.47214 5.42882i 0.315474 0.229205i
\(562\) 10.2169 14.0623i 0.430972 0.593183i
\(563\) −10.3026 + 14.1803i −0.434204 + 0.597630i −0.968912 0.247407i \(-0.920422\pi\)
0.534708 + 0.845037i \(0.320422\pi\)
\(564\) 4.23607 3.07768i 0.178371 0.129594i
\(565\) 0 0
\(566\) −0.236068 0.171513i −0.00992268 0.00720925i
\(567\) 4.25325 1.38197i 0.178620 0.0580371i
\(568\) 2.29180i 0.0961616i
\(569\) 9.35410 + 28.7890i 0.392144 + 1.20690i 0.931163 + 0.364603i \(0.118795\pi\)
−0.539019 + 0.842294i \(0.681205\pi\)
\(570\) 0 0
\(571\) −6.56231 + 20.1967i −0.274624 + 0.845206i 0.714695 + 0.699437i \(0.246566\pi\)
−0.989319 + 0.145769i \(0.953434\pi\)
\(572\) 10.4086 + 3.38197i 0.435206 + 0.141407i
\(573\) 14.4904 + 19.9443i 0.605344 + 0.833184i
\(574\) 6.18034 0.257962
\(575\) 0 0
\(576\) 7.00000 0.291667
\(577\) −18.1886 25.0344i −0.757201 1.04220i −0.997442 0.0714842i \(-0.977226\pi\)
0.240241 0.970713i \(-0.422774\pi\)
\(578\) −8.42075 2.73607i −0.350257 0.113805i
\(579\) −2.37132 + 7.29818i −0.0985488 + 0.303302i
\(580\) 0 0
\(581\) 4.87539 + 15.0049i 0.202265 + 0.622508i
\(582\) 8.85410i 0.367014i
\(583\) −4.25325 + 1.38197i −0.176152 + 0.0572352i
\(584\) −7.50000 5.44907i −0.310352 0.225484i
\(585\) 0 0
\(586\) −3.07295 + 2.23263i −0.126942 + 0.0922290i
\(587\) 8.57202 11.7984i 0.353805 0.486971i −0.594605 0.804018i \(-0.702691\pi\)
0.948410 + 0.317047i \(0.102691\pi\)
\(588\) −7.64121 + 10.5172i −0.315118 + 0.433723i
\(589\) −18.9443 + 13.7638i −0.780585 + 0.567128i
\(590\) 0 0
\(591\) −4.35410 3.16344i −0.179104 0.130127i
\(592\) −7.69421 + 2.50000i −0.316230 + 0.102749i
\(593\) 32.7426i 1.34458i −0.740288 0.672290i \(-0.765311\pi\)
0.740288 0.672290i \(-0.234689\pi\)
\(594\) −1.00000 3.07768i −0.0410305 0.126279i
\(595\) 0 0
\(596\) 3.75329 11.5514i 0.153741 0.473165i
\(597\) 17.7396 + 5.76393i 0.726032 + 0.235902i
\(598\) 8.89002 + 12.2361i 0.363540 + 0.500370i
\(599\) 12.4721 0.509598 0.254799 0.966994i \(-0.417991\pi\)
0.254799 + 0.966994i \(0.417991\pi\)
\(600\) 0 0
\(601\) −24.3262 −0.992288 −0.496144 0.868240i \(-0.665251\pi\)
−0.496144 + 0.868240i \(0.665251\pi\)
\(602\) −15.0049 20.6525i −0.611554 0.841732i
\(603\) 4.97980 + 1.61803i 0.202793 + 0.0658914i
\(604\) 5.09017 15.6659i 0.207116 0.637438i
\(605\) 0 0
\(606\) −5.11803 15.7517i −0.207906 0.639869i
\(607\) 39.2361i 1.59254i 0.604940 + 0.796271i \(0.293197\pi\)
−0.604940 + 0.796271i \(0.706803\pi\)
\(608\) 15.3884 5.00000i 0.624083 0.202777i
\(609\) 15.8541 + 11.5187i 0.642441 + 0.466760i
\(610\) 0 0
\(611\) 14.3262 10.4086i 0.579578 0.421088i
\(612\) −1.67760 + 2.30902i −0.0678129 + 0.0933365i
\(613\) 23.2214 31.9615i 0.937903 1.29091i −0.0187931 0.999823i \(-0.505982\pi\)
0.956696 0.291089i \(-0.0940176\pi\)
\(614\) 1.09017 0.792055i 0.0439957 0.0319647i
\(615\) 0 0
\(616\) 35.1246 + 25.5195i 1.41521 + 1.02821i
\(617\) 25.6583 8.33688i 1.03296 0.335630i 0.257002 0.966411i \(-0.417265\pi\)
0.775961 + 0.630781i \(0.217265\pi\)
\(618\) 1.23607i 0.0497219i
\(619\) −8.76393 26.9726i −0.352252 1.08412i −0.957586 0.288149i \(-0.906960\pi\)
0.605333 0.795972i \(-0.293040\pi\)
\(620\) 0 0
\(621\) −1.38197 + 4.25325i −0.0554564 + 0.170677i
\(622\) −4.08174 1.32624i −0.163663 0.0531773i
\(623\) −20.0252 27.5623i −0.802292 1.10426i
\(624\) 3.38197 0.135387
\(625\) 0 0
\(626\) 8.47214 0.338615
\(627\) −6.15537 8.47214i −0.245822 0.338345i
\(628\) 13.1230 + 4.26393i 0.523666 + 0.170149i
\(629\) 7.13525 21.9601i 0.284501 0.875605i
\(630\) 0 0
\(631\) 3.18034 + 9.78808i 0.126607 + 0.389657i 0.994190 0.107635i \(-0.0343277\pi\)
−0.867583 + 0.497292i \(0.834328\pi\)
\(632\) 0 0
\(633\) 17.0130 5.52786i 0.676207 0.219713i
\(634\) −20.0902 14.5964i −0.797883 0.579696i
\(635\) 0 0
\(636\) 1.11803 0.812299i 0.0443329 0.0322098i
\(637\) −25.8423 + 35.5689i −1.02391 + 1.40929i
\(638\) 8.33499 11.4721i 0.329986 0.454186i
\(639\) −0.618034 + 0.449028i −0.0244490 + 0.0177633i
\(640\) 0 0
\(641\) −31.5066 22.8909i −1.24444 0.904135i −0.246549 0.969130i \(-0.579297\pi\)
−0.997886 + 0.0649953i \(0.979297\pi\)
\(642\) 15.6659 5.09017i 0.618285 0.200893i
\(643\) 13.8885i 0.547711i 0.961771 + 0.273855i \(0.0882990\pi\)
−0.961771 + 0.273855i \(0.911701\pi\)
\(644\) −6.18034 19.0211i −0.243540 0.749538i
\(645\) 0 0
\(646\) 2.85410 8.78402i 0.112293 0.345603i
\(647\) −9.85359 3.20163i −0.387385 0.125869i 0.108848 0.994058i \(-0.465284\pi\)
−0.496233 + 0.868189i \(0.665284\pi\)
\(648\) 1.76336 + 2.42705i 0.0692712 + 0.0953436i
\(649\) 12.9443 0.508107
\(650\) 0 0
\(651\) 32.3607 1.26832
\(652\) −1.73060 2.38197i −0.0677755 0.0932850i
\(653\) 42.8958 + 13.9377i 1.67864 + 0.545424i 0.984647 0.174555i \(-0.0558488\pi\)
0.693995 + 0.719979i \(0.255849\pi\)
\(654\) 5.89919 18.1558i 0.230676 0.709949i
\(655\) 0 0
\(656\) 0.427051 + 1.31433i 0.0166735 + 0.0513159i
\(657\) 3.09017i 0.120559i
\(658\) 22.2703 7.23607i 0.868188 0.282091i
\(659\) −5.32624 3.86974i −0.207481 0.150744i 0.479192 0.877710i \(-0.340930\pi\)
−0.686673 + 0.726966i \(0.740930\pi\)
\(660\) 0 0
\(661\) −20.5623 + 14.9394i −0.799781 + 0.581075i −0.910850 0.412738i \(-0.864573\pi\)
0.111069 + 0.993813i \(0.464573\pi\)
\(662\) −6.43288 + 8.85410i −0.250021 + 0.344124i
\(663\) −5.67358 + 7.80902i −0.220344 + 0.303277i
\(664\) −8.56231 + 6.22088i −0.332282 + 0.241417i
\(665\) 0 0
\(666\) −6.54508 4.75528i −0.253617 0.184263i
\(667\) −18.6376 + 6.05573i −0.721651 + 0.234479i
\(668\) 23.4164i 0.906008i
\(669\) 4.38197 + 13.4863i 0.169417 + 0.521411i
\(670\) 0 0
\(671\) −0.618034 + 1.90211i −0.0238589 + 0.0734303i
\(672\) −21.2663 6.90983i −0.820364 0.266552i
\(673\) −17.5150 24.1074i −0.675155 0.929272i 0.324708 0.945814i \(-0.394734\pi\)
−0.999863 + 0.0165428i \(0.994734\pi\)
\(674\) 14.9443 0.575632
\(675\) 0 0
\(676\) 1.56231 0.0600887
\(677\) 21.9928 + 30.2705i 0.845252 + 1.16339i 0.984889 + 0.173187i \(0.0554066\pi\)
−0.139636 + 0.990203i \(0.544593\pi\)
\(678\) 2.54290 + 0.826238i 0.0976594 + 0.0317315i
\(679\) −12.2361 + 37.6587i −0.469577 + 1.44521i
\(680\) 0 0
\(681\) −6.18034 19.0211i −0.236831 0.728891i
\(682\) 23.4164i 0.896661i
\(683\) −7.05342 + 2.29180i −0.269892 + 0.0876931i −0.440836 0.897588i \(-0.645318\pi\)
0.170945 + 0.985281i \(0.445318\pi\)
\(684\) 2.61803 + 1.90211i 0.100103 + 0.0727291i
\(685\) 0 0
\(686\) −21.7082 + 15.7719i −0.828823 + 0.602175i
\(687\) 14.6821 20.2082i 0.560158 0.770991i
\(688\) 3.35520 4.61803i 0.127916 0.176061i
\(689\) 3.78115 2.74717i 0.144050 0.104659i
\(690\) 0 0
\(691\) 17.1803 + 12.4822i 0.653571 + 0.474847i 0.864486 0.502657i \(-0.167644\pi\)
−0.210915 + 0.977504i \(0.567644\pi\)
\(692\) −9.42481 + 3.06231i −0.358277 + 0.116411i
\(693\) 14.4721i 0.549751i
\(694\) 10.4164 + 32.0584i 0.395401 + 1.21692i
\(695\) 0 0
\(696\) −4.06231 + 12.5025i −0.153981 + 0.473906i
\(697\) −3.75123 1.21885i −0.142088 0.0461671i
\(698\) −14.7149 20.2533i −0.556966 0.766598i
\(699\) −14.6180 −0.552905
\(700\) 0 0
\(701\) 0.437694 0.0165315 0.00826574 0.999966i \(-0.497369\pi\)
0.00826574 + 0.999966i \(0.497369\pi\)
\(702\) 1.98787 + 2.73607i 0.0750273 + 0.103266i
\(703\) −24.8990 8.09017i −0.939083 0.305127i
\(704\) −7.00000 + 21.5438i −0.263822 + 0.811962i
\(705\) 0 0
\(706\) −9.38197 28.8747i −0.353095 1.08671i
\(707\) 74.0689i 2.78565i
\(708\) −3.80423 + 1.23607i −0.142972 + 0.0464543i
\(709\) −5.44427 3.95550i −0.204464 0.148552i 0.480841 0.876808i \(-0.340331\pi\)
−0.685305 + 0.728256i \(0.740331\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 13.4333 18.4894i 0.503434 0.692918i
\(713\) −19.0211 + 26.1803i −0.712347 + 0.980461i
\(714\) −10.3262 + 7.50245i −0.386450 + 0.280772i
\(715\) 0 0
\(716\) 5.00000 + 3.63271i 0.186859 + 0.135761i
\(717\) −6.71040 + 2.18034i −0.250604 + 0.0814263i
\(718\) 10.5836i 0.394976i
\(719\) 11.0902 + 34.1320i 0.413594 + 1.27291i 0.913503 + 0.406832i \(0.133367\pi\)
−0.499909 + 0.866078i \(0.666633\pi\)
\(720\) 0 0
\(721\) −1.70820 + 5.25731i −0.0636168 + 0.195792i
\(722\) 8.11048 + 2.63525i 0.301841 + 0.0980740i
\(723\) 0.608030 + 0.836881i 0.0226129 + 0.0311239i
\(724\) −9.79837 −0.364154
\(725\) 0 0
\(726\) −0.527864 −0.0195909
\(727\) 9.02105 + 12.4164i 0.334572 + 0.460499i 0.942846 0.333228i \(-0.108138\pi\)
−0.608274 + 0.793727i \(0.708138\pi\)
\(728\) −43.1531 14.0213i −1.59936 0.519663i
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) 5.03444 + 15.4944i 0.186206 + 0.573082i
\(732\) 0.618034i 0.0228432i
\(733\) −2.45714 + 0.798374i −0.0907566 + 0.0294886i −0.354043 0.935229i \(-0.615193\pi\)
0.263287 + 0.964718i \(0.415193\pi\)
\(734\) −4.85410 3.52671i −0.179168 0.130173i
\(735\) 0 0
\(736\) 18.0902 13.1433i 0.666813 0.484468i
\(737\) −9.95959 + 13.7082i −0.366866 + 0.504948i
\(738\) −0.812299 + 1.11803i −0.0299011 + 0.0411554i
\(739\) 14.3262 10.4086i 0.526999 0.382887i −0.292235 0.956347i \(-0.594399\pi\)
0.819234 + 0.573459i \(0.194399\pi\)
\(740\) 0 0
\(741\) 8.85410 + 6.43288i 0.325264 + 0.236318i
\(742\) 5.87785 1.90983i 0.215783 0.0701121i
\(743\) 0.875388i 0.0321149i 0.999871 + 0.0160574i \(0.00511146\pi\)
−0.999871 + 0.0160574i \(0.994889\pi\)
\(744\) 6.70820 + 20.6457i 0.245935 + 0.756909i
\(745\) 0 0
\(746\) 9.09017 27.9767i 0.332815 1.02430i
\(747\) −3.35520 1.09017i −0.122760 0.0398872i
\(748\) −5.42882 7.47214i −0.198497 0.273208i
\(749\) −73.6656 −2.69168
\(750\) 0 0
\(751\) 5.34752 0.195134 0.0975670 0.995229i \(-0.468894\pi\)
0.0975670 + 0.995229i \(0.468894\pi\)
\(752\) 3.07768 + 4.23607i 0.112232 + 0.154474i
\(753\) −25.6255 8.32624i −0.933846 0.303425i
\(754\) −4.57953 + 14.0943i −0.166777 + 0.513285i
\(755\) 0 0
\(756\) −1.38197 4.25325i −0.0502616 0.154689i
\(757\) 27.3820i 0.995214i −0.867402 0.497607i \(-0.834212\pi\)
0.867402 0.497607i \(-0.165788\pi\)
\(758\) −22.2703 + 7.23607i −0.808895 + 0.262826i
\(759\) −11.7082 8.50651i −0.424981 0.308767i
\(760\) 0 0
\(761\) 7.88197 5.72658i 0.285721 0.207588i −0.435688 0.900098i \(-0.643495\pi\)
0.721409 + 0.692509i \(0.243495\pi\)
\(762\) −5.70634 + 7.85410i −0.206719 + 0.284524i
\(763\) −50.1815 + 69.0689i −1.81669 + 2.50046i
\(764\) 19.9443 14.4904i 0.721558 0.524243i
\(765\) 0 0
\(766\) −16.8541 12.2452i −0.608963 0.442438i
\(767\) −12.8658 + 4.18034i −0.464556 + 0.150943i
\(768\) 17.0000i 0.613435i
\(769\) 1.74265 + 5.36331i 0.0628414 + 0.193406i 0.977548 0.210712i \(-0.0675784\pi\)
−0.914707 + 0.404118i \(0.867578\pi\)
\(770\) 0 0
\(771\) −3.95492 + 12.1720i −0.142433 + 0.438363i
\(772\) 7.29818 + 2.37132i 0.262667 + 0.0853458i
\(773\) 21.1150 + 29.0623i 0.759454 + 1.04530i 0.997259 + 0.0739857i \(0.0235719\pi\)
−0.237805 + 0.971313i \(0.576428\pi\)
\(774\) 5.70820 0.205177
\(775\) 0 0
\(776\) −26.5623 −0.953531
\(777\) 21.2663 + 29.2705i 0.762923 + 1.05007i
\(778\) −35.2748 11.4615i −1.26466 0.410914i
\(779\) −1.38197 + 4.25325i −0.0495141 + 0.152389i
\(780\) 0 0
\(781\) −0.763932 2.35114i −0.0273356 0.0841304i
\(782\) 12.7639i 0.456437i
\(783\) −4.16750 + 1.35410i −0.148934 + 0.0483917i
\(784\) −10.5172 7.64121i −0.375615 0.272900i
\(785\) 0 0
\(786\) −11.4721 + 8.33499i −0.409198 + 0.297299i
\(787\) −4.80828 + 6.61803i −0.171397 + 0.235907i −0.886070 0.463551i \(-0.846575\pi\)
0.714674 + 0.699458i \(0.246575\pi\)
\(788\) −3.16344 + 4.35410i −0.112693 + 0.155108i
\(789\) 9.61803 6.98791i 0.342411 0.248776i
\(790\) 0 0
\(791\) −9.67376 7.02840i −0.343959 0.249901i
\(792\) −9.23305 + 3.00000i −0.328082 + 0.106600i
\(793\) 2.09017i 0.0742241i
\(794\) −3.38197 10.4086i −0.120021 0.369388i
\(795\) 0 0
\(796\) 5.76393 17.7396i 0.204297 0.628762i
\(797\) −36.2384 11.7746i −1.28363 0.417077i −0.413773 0.910380i \(-0.635789\pi\)
−0.869857 + 0.493303i \(0.835789\pi\)
\(798\) 8.50651 + 11.7082i 0.301127 + 0.414466i
\(799\) −14.9443 −0.528690
\(800\) 0 0
\(801\) 7.61803 0.269170
\(802\) 19.6619 + 27.0623i 0.694286 + 0.955603i
\(803\) 9.51057 + 3.09017i 0.335621 + 0.109050i
\(804\) 1.61803 4.97980i 0.0570637 0.175624i
\(805\) 0 0
\(806\) 7.56231 + 23.2744i 0.266371 + 0.819805i
\(807\) 0.145898i 0.00513585i
\(808\) −47.2551 + 15.3541i −1.66243 + 0.540155i
\(809\) −18.7812 13.6453i −0.660310 0.479743i 0.206457 0.978456i \(-0.433806\pi\)
−0.866768 + 0.498712i \(0.833806\pi\)
\(810\) 0 0
\(811\) −7.47214 + 5.42882i −0.262382 + 0.190632i −0.711197 0.702993i \(-0.751846\pi\)
0.448814 + 0.893625i \(0.351846\pi\)
\(812\) 11.5187 15.8541i 0.404226 0.556370i
\(813\) 13.0373 17.9443i 0.457237 0.629333i
\(814\) 21.1803 15.3884i 0.742371 0.539364i
\(815\) 0 0
\(816\) −2.30902 1.67760i −0.0808318 0.0587277i
\(817\) 17.5680 5.70820i 0.614628 0.199705i
\(818\) 25.7984i 0.902019i
\(819\) −4.67376 14.3844i −0.163314 0.502630i
\(820\) 0 0
\(821\) 1.56231 4.80828i 0.0545249 0.167810i −0.920086 0.391717i \(-0.871881\pi\)
0.974611 + 0.223907i \(0.0718812\pi\)
\(822\) 5.11855 + 1.66312i 0.178530 + 0.0580079i
\(823\) 8.67802 + 11.9443i 0.302497 + 0.416351i 0.933023 0.359817i \(-0.117161\pi\)
−0.630526 + 0.776168i \(0.717161\pi\)
\(824\) −3.70820 −0.129181
\(825\) 0 0
\(826\) −17.8885 −0.622422
\(827\) 12.9718 + 17.8541i 0.451072 + 0.620848i 0.972628 0.232370i \(-0.0746479\pi\)
−0.521555 + 0.853218i \(0.674648\pi\)
\(828\) 4.25325 + 1.38197i 0.147811 + 0.0480266i
\(829\) 8.19098 25.2093i 0.284485 0.875554i −0.702068 0.712110i \(-0.747740\pi\)
0.986553 0.163444i \(-0.0522602\pi\)
\(830\) 0 0
\(831\) −1.79180 5.51458i −0.0621567 0.191299i
\(832\) 23.6738i 0.820740i
\(833\) 35.2874 11.4656i 1.22263 0.397258i
\(834\) −4.09017 2.97168i −0.141631 0.102901i
\(835\) 0 0
\(836\) −8.47214 + 6.15537i −0.293015 + 0.212888i
\(837\) −4.25325 + 5.85410i −0.147014 + 0.202347i
\(838\) 19.3642 26.6525i 0.668924 0.920695i
\(839\) −35.6525 + 25.9030i −1.23086 + 0.894272i −0.996954 0.0779870i \(-0.975151\pi\)
−0.233906 + 0.972259i \(0.575151\pi\)
\(840\) 0 0
\(841\) 7.92705 + 5.75934i 0.273347 + 0.198598i
\(842\) 22.0131 7.15248i 0.758620 0.246491i
\(843\) 17.3820i 0.598667i
\(844\) −5.52786 17.0130i −0.190277 0.585612i
\(845\) 0 0
\(846\) −1.61803 + 4.97980i −0.0556292 + 0.171209i
\(847\) 2.24514 + 0.729490i 0.0771439 + 0.0250656i
\(848\) 0.812299 + 1.11803i 0.0278945 + 0.0383934i
\(849\) −0.291796 −0.0100144
\(850\) 0 0
\(851\) −36.1803 −1.24025
\(852\) 0.449028 + 0.618034i 0.0153834 + 0.0211735i
\(853\) 28.3929 + 9.22542i 0.972156 + 0.315873i 0.751686 0.659521i \(-0.229241\pi\)
0.220470 + 0.975394i \(0.429241\pi\)
\(854\) 0.854102 2.62866i 0.0292268 0.0899507i
\(855\) 0 0
\(856\) −15.2705 46.9978i −0.521935 1.60635i
\(857\) 3.52786i 0.120510i 0.998183 + 0.0602548i \(0.0191913\pi\)
−0.998183 + 0.0602548i \(0.980809\pi\)
\(858\) −10.4086 + 3.38197i −0.355344 + 0.115458i
\(859\) 2.76393 + 2.00811i 0.0943041 + 0.0685160i 0.633938 0.773384i \(-0.281437\pi\)
−0.539634 + 0.841900i \(0.681437\pi\)
\(860\) 0 0
\(861\) 5.00000 3.63271i 0.170400 0.123803i
\(862\) 6.26137 8.61803i 0.213263 0.293531i
\(863\) 30.0503 41.3607i 1.02292 1.40793i 0.112790 0.993619i \(-0.464021\pi\)
0.910134 0.414315i \(-0.135979\pi\)
\(864\) 4.04508 2.93893i 0.137617 0.0999843i
\(865\) 0 0
\(866\) −20.2082 14.6821i −0.686703 0.498919i
\(867\) −8.42075 + 2.73607i −0.285984 + 0.0929217i
\(868\) 32.3607i 1.09839i
\(869\) 0 0
\(870\) 0 0
\(871\) 5.47214 16.8415i 0.185416 0.570653i
\(872\) −54.4675 17.6976i −1.84450 0.599315i
\(873\) −5.20431 7.16312i −0.176139 0.242435i
\(874\) −14.4721 −0.489527
\(875\) 0 0
\(876\) −3.09017 −0.104407
\(877\) 10.7064 + 14.7361i 0.361529 + 0.497602i 0.950574 0.310499i \(-0.100496\pi\)
−0.589045 + 0.808100i \(0.700496\pi\)
\(878\) −5.87785 1.90983i −0.198368 0.0644536i
\(879\) −1.17376 + 3.61247i −0.0395900 + 0.121846i
\(880\) 0 0
\(881\) 7.74265 + 23.8294i 0.260856 + 0.802833i 0.992619 + 0.121274i \(0.0386979\pi\)
−0.731763 + 0.681559i \(0.761302\pi\)
\(882\) 13.0000i 0.437733i
\(883\) 0.171513 0.0557281i 0.00577189 0.00187540i −0.306130 0.951990i \(-0.599034\pi\)
0.311902 + 0.950114i \(0.399034\pi\)
\(884\) 7.80902 + 5.67358i 0.262646 + 0.190823i
\(885\) 0 0
\(886\) 24.8885 18.0826i 0.836147 0.607496i
\(887\) −10.0656 + 13.8541i −0.337970 + 0.465175i −0.943847 0.330383i \(-0.892822\pi\)
0.605877 + 0.795558i \(0.292822\pi\)
\(888\) −14.2658 + 19.6353i −0.478731 + 0.658916i
\(889\) 35.1246 25.5195i 1.17804 0.855897i
\(890\) 0 0
\(891\) −2.61803 1.90211i −0.0877074 0.0637232i
\(892\) 13.4863 4.38197i 0.451555 0.146719i
\(893\) 16.9443i 0.567018i
\(894\) 3.75329 + 11.5514i 0.125529 + 0.386338i
\(895\) 0 0
\(896\) −4.14590 + 12.7598i −0.138505 + 0.426274i
\(897\) 14.3844 + 4.67376i 0.480280 + 0.156052i
\(898\) 4.58377 + 6.30902i 0.152962 + 0.210535i
\(899\) −31.7082 −1.05753
\(900\) 0 0
\(901\) −3.94427 −0.131403
\(902\) −2.62866 3.61803i −0.0875247 0.120467i
\(903\) −24.2784 7.88854i −0.807936 0.262514i
\(904\) 2.47871 7.62870i 0.0824408 0.253727i
\(905\) 0 0
\(906\) 5.09017 + 15.6659i 0.169110 + 0.520466i
\(907\) 33.1246i 1.09988i 0.835203 + 0.549942i \(0.185350\pi\)
−0.835203 + 0.549942i \(0.814650\pi\)
\(908\) −19.0211 + 6.18034i −0.631238 + 0.205102i
\(909\) −13.3992 9.73508i −0.444423 0.322892i
\(910\) 0 0
\(911\) 3.38197 2.45714i 0.112050 0.0814088i −0.530349 0.847779i \(-0.677939\pi\)
0.642399 + 0.766370i \(0.277939\pi\)
\(912\) −1.90211 + 2.61803i −0.0629853 + 0.0866918i
\(913\) 6.71040 9.23607i 0.222082 0.305669i
\(914\) 18.0902 13.1433i 0.598370 0.434741i
\(915\) 0 0
\(916\) −20.2082 14.6821i −0.667698 0.485111i
\(917\) 60.3126 19.5967i 1.99170 0.647142i
\(918\) 2.85410i 0.0941994i
\(919\) 15.2016 + 46.7858i 0.501455 + 1.54332i 0.806649 + 0.591031i \(0.201279\pi\)
−0.305194 + 0.952290i \(0.598721\pi\)
\(920\) 0 0
\(921\) 0.416408 1.28157i 0.0137211 0.0422292i
\(922\) 7.80021 + 2.53444i 0.256886 + 0.0834674i
\(923\) 1.51860 + 2.09017i 0.0499852 + 0.0687988i
\(924\) 14.4721 0.476098
\(925\) 0 0
\(926\) 23.2361 0.763585
\(927\) −0.726543 1.00000i −0.0238628 0.0328443i
\(928\) 20.8375 + 6.77051i 0.684024 + 0.222253i
\(929\) −0.645898 + 1.98787i −0.0211912 + 0.0652199i −0.961093 0.276225i \(-0.910916\pi\)
0.939902 + 0.341445i \(0.110916\pi\)
\(930\) 0 0
\(931\) −13.0000 40.0099i −0.426058 1.31127i
\(932\) 14.6180i 0.478830i
\(933\) −4.08174 + 1.32624i −0.133630 + 0.0434191i
\(934\) 4.70820 + 3.42071i 0.154057 + 0.111929i
\(935\) 0 0
\(936\) 8.20820 5.96361i 0.268294 0.194927i
\(937\) −6.86940 + 9.45492i −0.224413 + 0.308879i −0.906346 0.422537i \(-0.861140\pi\)
0.681932 + 0.731415i \(0.261140\pi\)
\(938\) 13.7638 18.9443i 0.449405 0.618552i
\(939\) 6.85410 4.97980i 0.223675 0.162510i
\(940\) 0 0
\(941\) −4.30902 3.13068i −0.140470 0.102057i 0.515331 0.856991i \(-0.327669\pi\)
−0.655801 + 0.754934i \(0.727669\pi\)
\(942\) −13.1230 + 4.26393i −0.427572 + 0.138926i
\(943\) 6.18034i 0.201260i
\(944\) −1.23607 3.80423i −0.0402306 0.123817i
\(945\) 0 0
\(946\) −5.70820 + 17.5680i −0.185590 + 0.571186i
\(947\) −27.9767 9.09017i −0.909120 0.295391i −0.183124 0.983090i \(-0.558621\pi\)
−0.725996 + 0.687699i \(0.758621\pi\)
\(948\) 0 0
\(949\) −10.4508 −0.339249
\(950\) 0 0
\(951\) −24.8328 −0.805259
\(952\) 22.5074 + 30.9787i 0.729468 + 1.00403i
\(953\) 9.59632 + 3.11803i 0.310855 + 0.101003i 0.460290 0.887769i \(-0.347745\pi\)
−0.149435 + 0.988772i \(0.547745\pi\)
\(954\) −0.427051 + 1.31433i −0.0138263 + 0.0425529i
\(955\) 0 0
\(956\) 2.18034 + 6.71040i 0.0705172 + 0.217030i
\(957\) 14.1803i 0.458385i
\(958\) −1.00406 + 0.326238i −0.0324396 + 0.0105403i
\(959\) −19.4721 14.1473i −0.628788 0.456841i
\(960\) 0 0
\(961\) −17.2812 + 12.5555i −0.557457 + 0.405016i
\(962\) −16.0822 + 22.1353i −0.518511 + 0.713669i
\(963\) 9.68208 13.3262i 0.312001 0.429432i
\(964\) 0.836881 0.608030i 0.0269541 0.0195833i
\(965\) 0 0
\(966\) 16.1803 + 11.7557i 0.520594 + 0.378234i
\(967\) 33.1280 10.7639i 1.06532 0.346145i 0.276659 0.960968i \(-0.410773\pi\)
0.788665 + 0.614823i \(0.210773\pi\)
\(968\) 1.58359i 0.0508986i
\(969\) −2.85410 8.78402i −0.0916870 0.282183i
\(970\) 0 0
\(971\) −2.03444 + 6.26137i −0.0652883 + 0.200937i −0.978379 0.206819i \(-0.933689\pi\)
0.913091 + 0.407756i \(0.133689\pi\)
\(972\) 0.951057 + 0.309017i 0.0305052 + 0.00991172i
\(973\) 13.2898 + 18.2918i 0.426050 + 0.586408i
\(974\) 3.70820 0.118819
\(975\) 0 0
\(976\) 0.618034 0.0197828
\(977\) −26.8869 37.0066i −0.860187 1.18395i −0.981525 0.191334i \(-0.938719\pi\)
0.121338 0.992611i \(-0.461281\pi\)
\(978\) 2.80017 + 0.909830i 0.0895395 + 0.0290932i
\(979\) −7.61803 + 23.4459i −0.243473 + 0.749334i
\(980\) 0 0
\(981\) −5.89919 18.1558i −0.188347 0.579671i
\(982\) 29.8885i 0.953782i
\(983\) −20.6457 + 6.70820i −0.658496 + 0.213958i −0.619157 0.785267i \(-0.712525\pi\)
−0.0393397 + 0.999226i \(0.512525\pi\)
\(984\) 3.35410 + 2.43690i 0.106925 + 0.0776855i
\(985\) 0 0
\(986\) 10.1180 7.35118i 0.322224 0.234109i
\(987\) 13.7638 18.9443i 0.438107 0.603003i
\(988\) 6.43288 8.85410i 0.204657 0.281687i
\(989\) 20.6525 15.0049i 0.656711 0.477128i
\(990\) 0 0
\(991\) 2.52786 + 1.83660i 0.0803002 + 0.0583415i 0.627211 0.778849i \(-0.284196\pi\)
−0.546911 + 0.837191i \(0.684196\pi\)
\(992\) 34.4095 11.1803i 1.09250 0.354976i
\(993\) 10.9443i 0.347306i
\(994\) 1.05573 + 3.24920i 0.0334857 + 0.103058i
\(995\) 0 0
\(996\) −1.09017 + 3.35520i −0.0345434 + 0.106314i
\(997\) −8.95554 2.90983i −0.283625 0.0921552i 0.163750 0.986502i \(-0.447641\pi\)
−0.447375 + 0.894347i \(0.647641\pi\)
\(998\) 3.52671 + 4.85410i 0.111636 + 0.153654i
\(999\) −8.09017 −0.255962
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.a.199.2 8
5.2 odd 4 75.2.g.a.61.1 yes 4
5.3 odd 4 375.2.g.a.301.1 4
5.4 even 2 inner 375.2.i.a.199.1 8
15.2 even 4 225.2.h.a.136.1 4
25.3 odd 20 1875.2.a.a.1.1 2
25.4 even 10 1875.2.b.b.1249.4 4
25.9 even 10 inner 375.2.i.a.49.2 8
25.12 odd 20 75.2.g.a.16.1 4
25.13 odd 20 375.2.g.a.76.1 4
25.16 even 5 inner 375.2.i.a.49.1 8
25.21 even 5 1875.2.b.b.1249.1 4
25.22 odd 20 1875.2.a.d.1.2 2
75.47 even 20 5625.2.a.a.1.2 2
75.53 even 20 5625.2.a.h.1.1 2
75.62 even 20 225.2.h.a.91.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.a.16.1 4 25.12 odd 20
75.2.g.a.61.1 yes 4 5.2 odd 4
225.2.h.a.91.1 4 75.62 even 20
225.2.h.a.136.1 4 15.2 even 4
375.2.g.a.76.1 4 25.13 odd 20
375.2.g.a.301.1 4 5.3 odd 4
375.2.i.a.49.1 8 25.16 even 5 inner
375.2.i.a.49.2 8 25.9 even 10 inner
375.2.i.a.199.1 8 5.4 even 2 inner
375.2.i.a.199.2 8 1.1 even 1 trivial
1875.2.a.a.1.1 2 25.3 odd 20
1875.2.a.d.1.2 2 25.22 odd 20
1875.2.b.b.1249.1 4 25.21 even 5
1875.2.b.b.1249.4 4 25.4 even 10
5625.2.a.a.1.2 2 75.47 even 20
5625.2.a.h.1.1 2 75.53 even 20