Properties

Label 756.2.n.b.19.8
Level $756$
Weight $2$
Character 756.19
Analytic conductor $6.037$
Analytic rank $0$
Dimension $84$
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] = [756,2,Mod(19,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.n (of order \(6\), degree \(2\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.8
Character \(\chi\) \(=\) 756.19
Dual form 756.2.n.b.199.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.17926 + 0.780599i) q^{2} +(0.781329 - 1.84107i) q^{4} +2.00240i q^{5} +(-2.64523 + 0.0525529i) q^{7} +(0.515742 + 2.78101i) q^{8} +O(q^{10})\) \(q+(-1.17926 + 0.780599i) q^{2} +(0.781329 - 1.84107i) q^{4} +2.00240i q^{5} +(-2.64523 + 0.0525529i) q^{7} +(0.515742 + 2.78101i) q^{8} +(-1.56307 - 2.36135i) q^{10} -5.03174i q^{11} +(3.29495 - 1.90234i) q^{13} +(3.07840 - 2.12684i) q^{14} +(-2.77905 - 2.87696i) q^{16} +(-1.61527 + 0.932579i) q^{17} +(3.12744 - 5.41689i) q^{19} +(3.68654 + 1.56453i) q^{20} +(3.92777 + 5.93375i) q^{22} +6.27581i q^{23} +0.990411 q^{25} +(-2.40065 + 4.81540i) q^{26} +(-1.97004 + 4.91110i) q^{28} +(1.23970 - 2.14722i) q^{29} +(-0.557613 + 0.965814i) q^{31} +(5.52299 + 1.22337i) q^{32} +(1.17687 - 2.36064i) q^{34} +(-0.105232 - 5.29680i) q^{35} +(0.559132 - 0.968445i) q^{37} +(0.540339 + 8.82923i) q^{38} +(-5.56868 + 1.03272i) q^{40} +(6.39139 - 3.69007i) q^{41} +(6.79358 + 3.92228i) q^{43} +(-9.26376 - 3.93144i) q^{44} +(-4.89889 - 7.40084i) q^{46} +(-1.95019 - 3.37783i) q^{47} +(6.99448 - 0.278029i) q^{49} +(-1.16796 + 0.773114i) q^{50} +(-0.927894 - 7.55257i) q^{52} +(-2.80349 - 4.85579i) q^{53} +10.0755 q^{55} +(-1.51040 - 7.32930i) q^{56} +(0.214186 + 3.49984i) q^{58} +(4.35302 - 7.53966i) q^{59} +(-1.83423 + 1.05899i) q^{61} +(-0.0963407 - 1.57422i) q^{62} +(-7.46802 + 2.86856i) q^{64} +(3.80924 + 6.59779i) q^{65} +(10.4118 + 6.01127i) q^{67} +(0.454879 + 3.70248i) q^{68} +(4.25877 + 6.16418i) q^{70} +3.84867i q^{71} +(-0.499355 + 0.288303i) q^{73} +(0.0966032 + 1.57851i) q^{74} +(-7.52929 - 9.99021i) q^{76} +(0.264432 + 13.3101i) q^{77} +(3.42902 - 1.97974i) q^{79} +(5.76081 - 5.56476i) q^{80} +(-4.65667 + 9.34068i) q^{82} +(5.34720 - 9.26162i) q^{83} +(-1.86739 - 3.23442i) q^{85} +(-11.0732 + 0.677665i) q^{86} +(13.9933 - 2.59508i) q^{88} +(5.13938 + 2.96722i) q^{89} +(-8.61592 + 5.20528i) q^{91} +(11.5542 + 4.90347i) q^{92} +(4.93652 + 2.46103i) q^{94} +(10.8468 + 6.26238i) q^{95} +(-14.0382 - 8.10496i) q^{97} +(-8.03131 + 5.78775i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17926 + 0.780599i −0.833866 + 0.551967i
\(3\) 0 0
\(4\) 0.781329 1.84107i 0.390665 0.920533i
\(5\) 2.00240i 0.895499i 0.894159 + 0.447749i \(0.147774\pi\)
−0.894159 + 0.447749i \(0.852226\pi\)
\(6\) 0 0
\(7\) −2.64523 + 0.0525529i −0.999803 + 0.0198631i
\(8\) 0.515742 + 2.78101i 0.182342 + 0.983235i
\(9\) 0 0
\(10\) −1.56307 2.36135i −0.494286 0.746726i
\(11\) 5.03174i 1.51713i −0.651600 0.758563i \(-0.725902\pi\)
0.651600 0.758563i \(-0.274098\pi\)
\(12\) 0 0
\(13\) 3.29495 1.90234i 0.913854 0.527614i 0.0321850 0.999482i \(-0.489753\pi\)
0.881669 + 0.471868i \(0.156420\pi\)
\(14\) 3.07840 2.12684i 0.822738 0.568421i
\(15\) 0 0
\(16\) −2.77905 2.87696i −0.694762 0.719239i
\(17\) −1.61527 + 0.932579i −0.391762 + 0.226184i −0.682923 0.730490i \(-0.739292\pi\)
0.291161 + 0.956674i \(0.405958\pi\)
\(18\) 0 0
\(19\) 3.12744 5.41689i 0.717485 1.24272i −0.244509 0.969647i \(-0.578627\pi\)
0.961993 0.273073i \(-0.0880400\pi\)
\(20\) 3.68654 + 1.56453i 0.824336 + 0.349840i
\(21\) 0 0
\(22\) 3.92777 + 5.93375i 0.837403 + 1.26508i
\(23\) 6.27581i 1.30860i 0.756236 + 0.654299i \(0.227036\pi\)
−0.756236 + 0.654299i \(0.772964\pi\)
\(24\) 0 0
\(25\) 0.990411 0.198082
\(26\) −2.40065 + 4.81540i −0.470806 + 0.944377i
\(27\) 0 0
\(28\) −1.97004 + 4.91110i −0.372303 + 0.928111i
\(29\) 1.23970 2.14722i 0.230206 0.398728i −0.727663 0.685935i \(-0.759393\pi\)
0.957869 + 0.287207i \(0.0927268\pi\)
\(30\) 0 0
\(31\) −0.557613 + 0.965814i −0.100150 + 0.173465i −0.911746 0.410753i \(-0.865266\pi\)
0.811596 + 0.584219i \(0.198599\pi\)
\(32\) 5.52299 + 1.22337i 0.976335 + 0.216263i
\(33\) 0 0
\(34\) 1.17687 2.36064i 0.201831 0.404846i
\(35\) −0.105232 5.29680i −0.0177874 0.895322i
\(36\) 0 0
\(37\) 0.559132 0.968445i 0.0919207 0.159211i −0.816399 0.577489i \(-0.804033\pi\)
0.908319 + 0.418277i \(0.137366\pi\)
\(38\) 0.540339 + 8.82923i 0.0876546 + 1.43229i
\(39\) 0 0
\(40\) −5.56868 + 1.03272i −0.880486 + 0.163287i
\(41\) 6.39139 3.69007i 0.998167 0.576292i 0.0904619 0.995900i \(-0.471166\pi\)
0.907706 + 0.419608i \(0.137832\pi\)
\(42\) 0 0
\(43\) 6.79358 + 3.92228i 1.03601 + 0.598141i 0.918701 0.394954i \(-0.129239\pi\)
0.117310 + 0.993095i \(0.462573\pi\)
\(44\) −9.26376 3.93144i −1.39656 0.592687i
\(45\) 0 0
\(46\) −4.89889 7.40084i −0.722303 1.09119i
\(47\) −1.95019 3.37783i −0.284464 0.492707i 0.688015 0.725697i \(-0.258482\pi\)
−0.972479 + 0.232990i \(0.925149\pi\)
\(48\) 0 0
\(49\) 6.99448 0.278029i 0.999211 0.0397184i
\(50\) −1.16796 + 0.773114i −0.165174 + 0.109335i
\(51\) 0 0
\(52\) −0.927894 7.55257i −0.128676 1.04735i
\(53\) −2.80349 4.85579i −0.385089 0.666994i 0.606692 0.794937i \(-0.292496\pi\)
−0.991782 + 0.127942i \(0.959163\pi\)
\(54\) 0 0
\(55\) 10.0755 1.35858
\(56\) −1.51040 7.32930i −0.201836 0.979419i
\(57\) 0 0
\(58\) 0.214186 + 3.49984i 0.0281241 + 0.459552i
\(59\) 4.35302 7.53966i 0.566715 0.981580i −0.430172 0.902747i \(-0.641547\pi\)
0.996888 0.0788331i \(-0.0251194\pi\)
\(60\) 0 0
\(61\) −1.83423 + 1.05899i −0.234849 + 0.135590i −0.612807 0.790232i \(-0.709960\pi\)
0.377958 + 0.925823i \(0.376626\pi\)
\(62\) −0.0963407 1.57422i −0.0122353 0.199927i
\(63\) 0 0
\(64\) −7.46802 + 2.86856i −0.933503 + 0.358570i
\(65\) 3.80924 + 6.59779i 0.472478 + 0.818355i
\(66\) 0 0
\(67\) 10.4118 + 6.01127i 1.27201 + 0.734394i 0.975366 0.220595i \(-0.0707998\pi\)
0.296642 + 0.954989i \(0.404133\pi\)
\(68\) 0.454879 + 3.70248i 0.0551622 + 0.448992i
\(69\) 0 0
\(70\) 4.25877 + 6.16418i 0.509021 + 0.736760i
\(71\) 3.84867i 0.456753i 0.973573 + 0.228377i \(0.0733417\pi\)
−0.973573 + 0.228377i \(0.926658\pi\)
\(72\) 0 0
\(73\) −0.499355 + 0.288303i −0.0584450 + 0.0337433i −0.528938 0.848661i \(-0.677410\pi\)
0.470493 + 0.882404i \(0.344076\pi\)
\(74\) 0.0966032 + 1.57851i 0.0112299 + 0.183498i
\(75\) 0 0
\(76\) −7.52929 9.99021i −0.863669 1.14596i
\(77\) 0.264432 + 13.3101i 0.0301349 + 1.51683i
\(78\) 0 0
\(79\) 3.42902 1.97974i 0.385794 0.222739i −0.294542 0.955639i \(-0.595167\pi\)
0.680336 + 0.732900i \(0.261834\pi\)
\(80\) 5.76081 5.56476i 0.644078 0.622159i
\(81\) 0 0
\(82\) −4.65667 + 9.34068i −0.514243 + 1.03151i
\(83\) 5.34720 9.26162i 0.586931 1.01660i −0.407700 0.913116i \(-0.633669\pi\)
0.994632 0.103479i \(-0.0329975\pi\)
\(84\) 0 0
\(85\) −1.86739 3.23442i −0.202547 0.350822i
\(86\) −11.0732 + 0.677665i −1.19405 + 0.0730745i
\(87\) 0 0
\(88\) 13.9933 2.59508i 1.49169 0.276636i
\(89\) 5.13938 + 2.96722i 0.544773 + 0.314525i 0.747011 0.664811i \(-0.231488\pi\)
−0.202238 + 0.979336i \(0.564821\pi\)
\(90\) 0 0
\(91\) −8.61592 + 5.20528i −0.903194 + 0.545662i
\(92\) 11.5542 + 4.90347i 1.20461 + 0.511222i
\(93\) 0 0
\(94\) 4.93652 + 2.46103i 0.509163 + 0.253836i
\(95\) 10.8468 + 6.26238i 1.11285 + 0.642507i
\(96\) 0 0
\(97\) −14.0382 8.10496i −1.42536 0.822934i −0.428613 0.903488i \(-0.640997\pi\)
−0.996750 + 0.0805547i \(0.974331\pi\)
\(98\) −8.03131 + 5.78775i −0.811285 + 0.584651i
\(99\) 0 0
\(100\) 0.773837 1.82341i 0.0773837 0.182341i
\(101\) 3.79391i 0.377508i −0.982024 0.188754i \(-0.939555\pi\)
0.982024 0.188754i \(-0.0604449\pi\)
\(102\) 0 0
\(103\) 9.26720 0.913125 0.456562 0.889691i \(-0.349081\pi\)
0.456562 + 0.889691i \(0.349081\pi\)
\(104\) 6.98976 + 8.18217i 0.685403 + 0.802327i
\(105\) 0 0
\(106\) 7.09649 + 3.53786i 0.689272 + 0.343627i
\(107\) 6.79221 + 3.92148i 0.656628 + 0.379104i 0.790991 0.611828i \(-0.209566\pi\)
−0.134363 + 0.990932i \(0.542899\pi\)
\(108\) 0 0
\(109\) 8.27240 + 14.3282i 0.792353 + 1.37239i 0.924507 + 0.381166i \(0.124477\pi\)
−0.132154 + 0.991229i \(0.542189\pi\)
\(110\) −11.8817 + 7.86495i −1.13288 + 0.749894i
\(111\) 0 0
\(112\) 7.50242 + 7.46416i 0.708912 + 0.705297i
\(113\) −9.70786 16.8145i −0.913238 1.58178i −0.809460 0.587175i \(-0.800240\pi\)
−0.103778 0.994600i \(-0.533093\pi\)
\(114\) 0 0
\(115\) −12.5667 −1.17185
\(116\) −2.98456 3.96004i −0.277109 0.367681i
\(117\) 0 0
\(118\) 0.752087 + 12.2892i 0.0692352 + 1.13131i
\(119\) 4.22376 2.55177i 0.387192 0.233921i
\(120\) 0 0
\(121\) −14.3184 −1.30167
\(122\) 1.33639 2.68063i 0.120991 0.242693i
\(123\) 0 0
\(124\) 1.34245 + 1.78122i 0.120555 + 0.159958i
\(125\) 11.9952i 1.07288i
\(126\) 0 0
\(127\) 2.21609i 0.196646i −0.995155 0.0983232i \(-0.968652\pi\)
0.995155 0.0983232i \(-0.0313479\pi\)
\(128\) 6.56757 9.21233i 0.580497 0.814262i
\(129\) 0 0
\(130\) −9.64233 4.80705i −0.845688 0.421606i
\(131\) −15.9027 −1.38943 −0.694714 0.719286i \(-0.744469\pi\)
−0.694714 + 0.719286i \(0.744469\pi\)
\(132\) 0 0
\(133\) −7.98813 + 14.4933i −0.692659 + 1.25673i
\(134\) −16.9707 + 1.03859i −1.46605 + 0.0897204i
\(135\) 0 0
\(136\) −3.42658 4.01112i −0.293826 0.343951i
\(137\) 4.30171 0.367520 0.183760 0.982971i \(-0.441173\pi\)
0.183760 + 0.982971i \(0.441173\pi\)
\(138\) 0 0
\(139\) −2.19727 3.80579i −0.186370 0.322803i 0.757667 0.652641i \(-0.226339\pi\)
−0.944037 + 0.329838i \(0.893006\pi\)
\(140\) −9.83397 3.94480i −0.831122 0.333397i
\(141\) 0 0
\(142\) −3.00427 4.53860i −0.252113 0.380871i
\(143\) −9.57207 16.5793i −0.800457 1.38643i
\(144\) 0 0
\(145\) 4.29958 + 2.48236i 0.357060 + 0.206149i
\(146\) 0.363822 0.729781i 0.0301102 0.0603971i
\(147\) 0 0
\(148\) −1.34611 1.78607i −0.110649 0.146814i
\(149\) −4.58475 −0.375597 −0.187799 0.982208i \(-0.560135\pi\)
−0.187799 + 0.982208i \(0.560135\pi\)
\(150\) 0 0
\(151\) 23.4942i 1.91193i −0.293475 0.955967i \(-0.594812\pi\)
0.293475 0.955967i \(-0.405188\pi\)
\(152\) 16.6774 + 5.90373i 1.35271 + 0.478856i
\(153\) 0 0
\(154\) −10.7017 15.4897i −0.862367 1.24820i
\(155\) −1.93394 1.11656i −0.155338 0.0896844i
\(156\) 0 0
\(157\) −14.1976 8.19699i −1.13309 0.654191i −0.188381 0.982096i \(-0.560324\pi\)
−0.944711 + 0.327905i \(0.893657\pi\)
\(158\) −2.49833 + 5.01133i −0.198756 + 0.398680i
\(159\) 0 0
\(160\) −2.44967 + 11.0592i −0.193663 + 0.874307i
\(161\) −0.329812 16.6010i −0.0259928 1.30834i
\(162\) 0 0
\(163\) −4.37894 2.52818i −0.342985 0.198022i 0.318606 0.947887i \(-0.396785\pi\)
−0.661591 + 0.749865i \(0.730119\pi\)
\(164\) −1.79989 14.6501i −0.140547 1.14398i
\(165\) 0 0
\(166\) 0.923854 + 15.0959i 0.0717050 + 1.17167i
\(167\) 4.45705 + 7.71983i 0.344897 + 0.597378i 0.985335 0.170631i \(-0.0545806\pi\)
−0.640438 + 0.768010i \(0.721247\pi\)
\(168\) 0 0
\(169\) 0.737790 1.27789i 0.0567530 0.0982992i
\(170\) 4.72694 + 2.35655i 0.362539 + 0.180739i
\(171\) 0 0
\(172\) 12.5292 9.44284i 0.955342 0.720010i
\(173\) −2.63021 + 1.51855i −0.199971 + 0.115453i −0.596642 0.802508i \(-0.703499\pi\)
0.396671 + 0.917961i \(0.370165\pi\)
\(174\) 0 0
\(175\) −2.61986 + 0.0520490i −0.198043 + 0.00393453i
\(176\) −14.4761 + 13.9834i −1.09118 + 1.05404i
\(177\) 0 0
\(178\) −8.37690 + 0.512657i −0.627875 + 0.0384253i
\(179\) 4.01804 2.31982i 0.300323 0.173391i −0.342265 0.939603i \(-0.611194\pi\)
0.642588 + 0.766212i \(0.277861\pi\)
\(180\) 0 0
\(181\) 3.81679i 0.283700i −0.989888 0.141850i \(-0.954695\pi\)
0.989888 0.141850i \(-0.0453050\pi\)
\(182\) 6.09721 12.8640i 0.451955 0.953542i
\(183\) 0 0
\(184\) −17.4531 + 3.23670i −1.28666 + 0.238612i
\(185\) 1.93921 + 1.11960i 0.142574 + 0.0823149i
\(186\) 0 0
\(187\) 4.69249 + 8.12764i 0.343149 + 0.594352i
\(188\) −7.74254 + 0.951233i −0.564683 + 0.0693758i
\(189\) 0 0
\(190\) −17.6796 + 1.08197i −1.28261 + 0.0784946i
\(191\) −3.26838 + 1.88700i −0.236492 + 0.136539i −0.613563 0.789645i \(-0.710264\pi\)
0.377071 + 0.926184i \(0.376931\pi\)
\(192\) 0 0
\(193\) 6.06896 10.5117i 0.436853 0.756652i −0.560592 0.828092i \(-0.689426\pi\)
0.997445 + 0.0714404i \(0.0227596\pi\)
\(194\) 22.8815 1.40032i 1.64279 0.100537i
\(195\) 0 0
\(196\) 4.95312 13.0945i 0.353794 0.935323i
\(197\) 6.35688 0.452909 0.226455 0.974022i \(-0.427287\pi\)
0.226455 + 0.974022i \(0.427287\pi\)
\(198\) 0 0
\(199\) −1.00759 1.74520i −0.0714262 0.123714i 0.828100 0.560580i \(-0.189422\pi\)
−0.899527 + 0.436866i \(0.856088\pi\)
\(200\) 0.510796 + 2.75434i 0.0361187 + 0.194761i
\(201\) 0 0
\(202\) 2.96152 + 4.47402i 0.208372 + 0.314791i
\(203\) −3.16644 + 5.74503i −0.222240 + 0.403222i
\(204\) 0 0
\(205\) 7.38898 + 12.7981i 0.516069 + 0.893858i
\(206\) −10.9285 + 7.23397i −0.761424 + 0.504015i
\(207\) 0 0
\(208\) −14.6298 4.19273i −1.01439 0.290714i
\(209\) −27.2564 15.7365i −1.88536 1.08851i
\(210\) 0 0
\(211\) −15.8266 + 9.13752i −1.08955 + 0.629053i −0.933457 0.358690i \(-0.883224\pi\)
−0.156094 + 0.987742i \(0.549890\pi\)
\(212\) −11.1303 + 1.36744i −0.764431 + 0.0939165i
\(213\) 0 0
\(214\) −11.0709 + 0.677528i −0.756792 + 0.0463149i
\(215\) −7.85395 + 13.6034i −0.535635 + 0.927747i
\(216\) 0 0
\(217\) 1.42426 2.58410i 0.0966850 0.175420i
\(218\) −20.9400 10.4393i −1.41823 0.707041i
\(219\) 0 0
\(220\) 7.87230 18.5497i 0.530751 1.25062i
\(221\) −3.54816 + 6.14560i −0.238675 + 0.413398i
\(222\) 0 0
\(223\) −8.23280 + 14.2596i −0.551309 + 0.954896i 0.446871 + 0.894598i \(0.352538\pi\)
−0.998180 + 0.0602974i \(0.980795\pi\)
\(224\) −14.6739 2.94584i −0.980438 0.196827i
\(225\) 0 0
\(226\) 24.5735 + 12.2508i 1.63461 + 0.814911i
\(227\) −0.441421 −0.0292982 −0.0146491 0.999893i \(-0.504663\pi\)
−0.0146491 + 0.999893i \(0.504663\pi\)
\(228\) 0 0
\(229\) 5.37457i 0.355161i −0.984106 0.177581i \(-0.943173\pi\)
0.984106 0.177581i \(-0.0568271\pi\)
\(230\) 14.8194 9.80953i 0.977163 0.646821i
\(231\) 0 0
\(232\) 6.61079 + 2.34020i 0.434020 + 0.153641i
\(233\) −3.38198 + 5.85776i −0.221561 + 0.383754i −0.955282 0.295696i \(-0.904448\pi\)
0.733721 + 0.679450i \(0.237782\pi\)
\(234\) 0 0
\(235\) 6.76375 3.90505i 0.441218 0.254737i
\(236\) −10.4799 13.9052i −0.682181 0.905149i
\(237\) 0 0
\(238\) −2.98902 + 6.30628i −0.193749 + 0.408776i
\(239\) −0.169520 + 0.0978724i −0.0109653 + 0.00633084i −0.505473 0.862843i \(-0.668682\pi\)
0.494507 + 0.869173i \(0.335349\pi\)
\(240\) 0 0
\(241\) 12.8524i 0.827897i 0.910300 + 0.413948i \(0.135851\pi\)
−0.910300 + 0.413948i \(0.864149\pi\)
\(242\) 16.8851 11.1769i 1.08542 0.718479i
\(243\) 0 0
\(244\) 0.516540 + 4.20437i 0.0330681 + 0.269157i
\(245\) 0.556724 + 14.0057i 0.0355678 + 0.894792i
\(246\) 0 0
\(247\) 23.7978i 1.51422i
\(248\) −2.97352 1.05262i −0.188819 0.0668412i
\(249\) 0 0
\(250\) −9.36343 14.1455i −0.592195 0.894639i
\(251\) −13.7723 −0.869299 −0.434650 0.900600i \(-0.643128\pi\)
−0.434650 + 0.900600i \(0.643128\pi\)
\(252\) 0 0
\(253\) 31.5782 1.98531
\(254\) 1.72988 + 2.61336i 0.108542 + 0.163977i
\(255\) 0 0
\(256\) −0.553766 + 15.9904i −0.0346104 + 0.999401i
\(257\) 13.8537i 0.864170i −0.901833 0.432085i \(-0.857778\pi\)
0.901833 0.432085i \(-0.142222\pi\)
\(258\) 0 0
\(259\) −1.42814 + 2.59114i −0.0887402 + 0.161006i
\(260\) 15.1232 1.85801i 0.937903 0.115229i
\(261\) 0 0
\(262\) 18.7535 12.4137i 1.15860 0.766919i
\(263\) 1.61839i 0.0997945i 0.998754 + 0.0498972i \(0.0158894\pi\)
−0.998754 + 0.0498972i \(0.984111\pi\)
\(264\) 0 0
\(265\) 9.72322 5.61370i 0.597293 0.344847i
\(266\) −1.89332 23.3269i −0.116087 1.43027i
\(267\) 0 0
\(268\) 19.2022 14.4721i 1.17296 0.884024i
\(269\) 3.95786 2.28507i 0.241315 0.139323i −0.374466 0.927241i \(-0.622174\pi\)
0.615781 + 0.787917i \(0.288841\pi\)
\(270\) 0 0
\(271\) −11.9451 + 20.6896i −0.725615 + 1.25680i 0.233105 + 0.972452i \(0.425111\pi\)
−0.958720 + 0.284351i \(0.908222\pi\)
\(272\) 7.17192 + 2.05539i 0.434861 + 0.124626i
\(273\) 0 0
\(274\) −5.07285 + 3.35791i −0.306462 + 0.202859i
\(275\) 4.98349i 0.300516i
\(276\) 0 0
\(277\) 12.3054 0.739363 0.369681 0.929159i \(-0.379467\pi\)
0.369681 + 0.929159i \(0.379467\pi\)
\(278\) 5.56196 + 2.77284i 0.333584 + 0.166304i
\(279\) 0 0
\(280\) 14.6762 3.02443i 0.877069 0.180744i
\(281\) 6.68674 11.5818i 0.398897 0.690910i −0.594693 0.803953i \(-0.702726\pi\)
0.993590 + 0.113043i \(0.0360597\pi\)
\(282\) 0 0
\(283\) −3.22533 + 5.58643i −0.191726 + 0.332079i −0.945822 0.324685i \(-0.894742\pi\)
0.754097 + 0.656764i \(0.228075\pi\)
\(284\) 7.08566 + 3.00708i 0.420456 + 0.178437i
\(285\) 0 0
\(286\) 24.2298 + 12.0794i 1.43274 + 0.714272i
\(287\) −16.7128 + 10.0970i −0.986524 + 0.596005i
\(288\) 0 0
\(289\) −6.76059 + 11.7097i −0.397682 + 0.688805i
\(290\) −7.00807 + 0.428886i −0.411528 + 0.0251851i
\(291\) 0 0
\(292\) 0.140624 + 1.14460i 0.00822938 + 0.0669829i
\(293\) −18.9236 + 10.9255i −1.10553 + 0.638277i −0.937668 0.347534i \(-0.887019\pi\)
−0.167861 + 0.985811i \(0.553686\pi\)
\(294\) 0 0
\(295\) 15.0974 + 8.71648i 0.879003 + 0.507493i
\(296\) 2.98162 + 1.05548i 0.173303 + 0.0613487i
\(297\) 0 0
\(298\) 5.40663 3.57885i 0.313198 0.207317i
\(299\) 11.9387 + 20.6785i 0.690434 + 1.19587i
\(300\) 0 0
\(301\) −18.1767 10.0183i −1.04769 0.577445i
\(302\) 18.3396 + 27.7059i 1.05532 + 1.59430i
\(303\) 0 0
\(304\) −24.2755 + 6.05629i −1.39229 + 0.347352i
\(305\) −2.12053 3.67286i −0.121421 0.210307i
\(306\) 0 0
\(307\) 5.00234 0.285499 0.142749 0.989759i \(-0.454406\pi\)
0.142749 + 0.989759i \(0.454406\pi\)
\(308\) 24.7114 + 9.91273i 1.40806 + 0.564830i
\(309\) 0 0
\(310\) 3.15222 0.192912i 0.179034 0.0109567i
\(311\) 10.1968 17.6613i 0.578206 1.00148i −0.417479 0.908687i \(-0.637086\pi\)
0.995685 0.0927962i \(-0.0295805\pi\)
\(312\) 0 0
\(313\) −18.2484 + 10.5357i −1.03146 + 0.595515i −0.917403 0.397959i \(-0.869718\pi\)
−0.114059 + 0.993474i \(0.536385\pi\)
\(314\) 23.1413 1.41622i 1.30594 0.0799220i
\(315\) 0 0
\(316\) −0.965649 7.85988i −0.0543220 0.442153i
\(317\) 6.03814 + 10.4584i 0.339136 + 0.587400i 0.984270 0.176669i \(-0.0565321\pi\)
−0.645135 + 0.764069i \(0.723199\pi\)
\(318\) 0 0
\(319\) −10.8042 6.23782i −0.604920 0.349251i
\(320\) −5.74400 14.9539i −0.321099 0.835950i
\(321\) 0 0
\(322\) 13.3476 + 19.3195i 0.743835 + 1.07663i
\(323\) 11.6664i 0.649133i
\(324\) 0 0
\(325\) 3.26335 1.88410i 0.181018 0.104511i
\(326\) 7.13742 0.436802i 0.395305 0.0241922i
\(327\) 0 0
\(328\) 13.5584 + 15.8714i 0.748639 + 0.876351i
\(329\) 5.33621 + 8.83264i 0.294195 + 0.486959i
\(330\) 0 0
\(331\) 1.10382 0.637288i 0.0606712 0.0350285i −0.469358 0.883008i \(-0.655514\pi\)
0.530029 + 0.847980i \(0.322181\pi\)
\(332\) −12.8733 17.0809i −0.706516 0.937437i
\(333\) 0 0
\(334\) −11.2821 5.62455i −0.617331 0.307762i
\(335\) −12.0370 + 20.8486i −0.657649 + 1.13908i
\(336\) 0 0
\(337\) −6.12539 10.6095i −0.333671 0.577935i 0.649558 0.760312i \(-0.274954\pi\)
−0.983229 + 0.182377i \(0.941621\pi\)
\(338\) 0.127470 + 2.08289i 0.00693348 + 0.113294i
\(339\) 0 0
\(340\) −7.41383 + 0.910848i −0.402071 + 0.0493977i
\(341\) 4.85972 + 2.80576i 0.263169 + 0.151941i
\(342\) 0 0
\(343\) −18.4874 + 1.10303i −0.998225 + 0.0595581i
\(344\) −7.40415 + 20.9159i −0.399205 + 1.12771i
\(345\) 0 0
\(346\) 1.91633 3.84391i 0.103023 0.206650i
\(347\) 7.47885 + 4.31792i 0.401486 + 0.231798i 0.687125 0.726539i \(-0.258873\pi\)
−0.285639 + 0.958337i \(0.592206\pi\)
\(348\) 0 0
\(349\) −6.91380 3.99168i −0.370087 0.213670i 0.303409 0.952860i \(-0.401875\pi\)
−0.673497 + 0.739190i \(0.735208\pi\)
\(350\) 3.04888 2.10644i 0.162970 0.112594i
\(351\) 0 0
\(352\) 6.15567 27.7902i 0.328098 1.48122i
\(353\) 18.9233i 1.00719i 0.863941 + 0.503594i \(0.167989\pi\)
−0.863941 + 0.503594i \(0.832011\pi\)
\(354\) 0 0
\(355\) −7.70656 −0.409022
\(356\) 9.47840 7.14356i 0.502354 0.378608i
\(357\) 0 0
\(358\) −2.92749 + 5.87216i −0.154722 + 0.310353i
\(359\) 22.7971 + 13.1619i 1.20319 + 0.694659i 0.961262 0.275636i \(-0.0888885\pi\)
0.241923 + 0.970295i \(0.422222\pi\)
\(360\) 0 0
\(361\) −10.0618 17.4276i −0.529569 0.917240i
\(362\) 2.97939 + 4.50101i 0.156593 + 0.236568i
\(363\) 0 0
\(364\) 2.85140 + 19.9295i 0.149454 + 1.04459i
\(365\) −0.577296 0.999906i −0.0302170 0.0523375i
\(366\) 0 0
\(367\) −1.55991 −0.0814269 −0.0407134 0.999171i \(-0.512963\pi\)
−0.0407134 + 0.999171i \(0.512963\pi\)
\(368\) 18.0552 17.4408i 0.941194 0.909164i
\(369\) 0 0
\(370\) −3.16080 + 0.193438i −0.164322 + 0.0100564i
\(371\) 7.67107 + 12.6974i 0.398262 + 0.659214i
\(372\) 0 0
\(373\) 35.9979 1.86390 0.931950 0.362588i \(-0.118107\pi\)
0.931950 + 0.362588i \(0.118107\pi\)
\(374\) −11.8781 5.92168i −0.614203 0.306203i
\(375\) 0 0
\(376\) 8.38797 7.16558i 0.432577 0.369537i
\(377\) 9.43329i 0.485839i
\(378\) 0 0
\(379\) 19.4764i 1.00044i 0.865899 + 0.500219i \(0.166747\pi\)
−0.865899 + 0.500219i \(0.833253\pi\)
\(380\) 20.0043 15.0766i 1.02620 0.773414i
\(381\) 0 0
\(382\) 2.38130 4.77657i 0.121838 0.244391i
\(383\) 0.0991517 0.00506641 0.00253321 0.999997i \(-0.499194\pi\)
0.00253321 + 0.999997i \(0.499194\pi\)
\(384\) 0 0
\(385\) −26.6521 + 0.529498i −1.35832 + 0.0269857i
\(386\) 1.04855 + 17.1336i 0.0533700 + 0.872075i
\(387\) 0 0
\(388\) −25.8902 + 19.5126i −1.31438 + 0.990603i
\(389\) 26.5662 1.34696 0.673481 0.739204i \(-0.264798\pi\)
0.673481 + 0.739204i \(0.264798\pi\)
\(390\) 0 0
\(391\) −5.85269 10.1372i −0.295983 0.512658i
\(392\) 4.38054 + 19.3083i 0.221251 + 0.975217i
\(393\) 0 0
\(394\) −7.49645 + 4.96218i −0.377665 + 0.249991i
\(395\) 3.96423 + 6.86625i 0.199462 + 0.345478i
\(396\) 0 0
\(397\) 23.4405 + 13.5334i 1.17645 + 0.679221i 0.955190 0.295995i \(-0.0956511\pi\)
0.221256 + 0.975216i \(0.428984\pi\)
\(398\) 2.55052 + 1.27153i 0.127846 + 0.0637358i
\(399\) 0 0
\(400\) −2.75240 2.84937i −0.137620 0.142469i
\(401\) 31.9981 1.59791 0.798954 0.601392i \(-0.205387\pi\)
0.798954 + 0.601392i \(0.205387\pi\)
\(402\) 0 0
\(403\) 4.24308i 0.211363i
\(404\) −6.98484 2.96429i −0.347509 0.147479i
\(405\) 0 0
\(406\) −0.750499 9.24662i −0.0372466 0.458902i
\(407\) −4.87296 2.81340i −0.241544 0.139455i
\(408\) 0 0
\(409\) 18.9401 + 10.9351i 0.936527 + 0.540704i 0.888870 0.458160i \(-0.151491\pi\)
0.0476569 + 0.998864i \(0.484825\pi\)
\(410\) −18.7037 9.32450i −0.923712 0.460504i
\(411\) 0 0
\(412\) 7.24074 17.0615i 0.356726 0.840562i
\(413\) −11.1185 + 20.1729i −0.547106 + 0.992643i
\(414\) 0 0
\(415\) 18.5454 + 10.7072i 0.910359 + 0.525596i
\(416\) 20.5252 6.47566i 1.00633 0.317495i
\(417\) 0 0
\(418\) 44.4263 2.71884i 2.17296 0.132983i
\(419\) −9.62802 16.6762i −0.470360 0.814687i 0.529066 0.848581i \(-0.322542\pi\)
−0.999425 + 0.0338939i \(0.989209\pi\)
\(420\) 0 0
\(421\) 16.8866 29.2484i 0.823002 1.42548i −0.0804343 0.996760i \(-0.525631\pi\)
0.903437 0.428722i \(-0.141036\pi\)
\(422\) 11.5311 23.1298i 0.561323 1.12594i
\(423\) 0 0
\(424\) 12.0581 10.3009i 0.585594 0.500255i
\(425\) −1.59979 + 0.923637i −0.0776010 + 0.0448030i
\(426\) 0 0
\(427\) 4.79631 2.89768i 0.232110 0.140228i
\(428\) 12.5267 9.44094i 0.605499 0.456345i
\(429\) 0 0
\(430\) −1.35695 22.1728i −0.0654381 1.06927i
\(431\) 2.57782 1.48830i 0.124169 0.0716890i −0.436629 0.899642i \(-0.643828\pi\)
0.560798 + 0.827953i \(0.310494\pi\)
\(432\) 0 0
\(433\) 25.5918i 1.22986i −0.788580 0.614932i \(-0.789183\pi\)
0.788580 0.614932i \(-0.210817\pi\)
\(434\) 0.337573 + 4.15912i 0.0162040 + 0.199644i
\(435\) 0 0
\(436\) 32.8427 4.03498i 1.57288 0.193241i
\(437\) 33.9954 + 19.6272i 1.62622 + 0.938898i
\(438\) 0 0
\(439\) −14.5655 25.2282i −0.695174 1.20408i −0.970122 0.242618i \(-0.921994\pi\)
0.274947 0.961459i \(-0.411340\pi\)
\(440\) 5.19637 + 28.0201i 0.247727 + 1.33581i
\(441\) 0 0
\(442\) −0.613029 10.0170i −0.0291588 0.476459i
\(443\) −21.9919 + 12.6970i −1.04487 + 0.603254i −0.921208 0.389070i \(-0.872796\pi\)
−0.123659 + 0.992325i \(0.539463\pi\)
\(444\) 0 0
\(445\) −5.94155 + 10.2911i −0.281657 + 0.487844i
\(446\) −1.42241 23.2424i −0.0673530 1.10056i
\(447\) 0 0
\(448\) 19.6039 7.98048i 0.926196 0.377042i
\(449\) −30.7532 −1.45133 −0.725667 0.688046i \(-0.758469\pi\)
−0.725667 + 0.688046i \(0.758469\pi\)
\(450\) 0 0
\(451\) −18.5675 32.1598i −0.874308 1.51435i
\(452\) −38.5416 + 4.73515i −1.81285 + 0.222723i
\(453\) 0 0
\(454\) 0.520552 0.344573i 0.0244307 0.0161716i
\(455\) −10.4230 17.2525i −0.488639 0.808809i
\(456\) 0 0
\(457\) 5.49304 + 9.51423i 0.256954 + 0.445057i 0.965424 0.260683i \(-0.0839479\pi\)
−0.708471 + 0.705740i \(0.750615\pi\)
\(458\) 4.19538 + 6.33804i 0.196037 + 0.296157i
\(459\) 0 0
\(460\) −9.81870 + 23.1360i −0.457799 + 1.07872i
\(461\) −14.3875 8.30665i −0.670095 0.386879i 0.126018 0.992028i \(-0.459780\pi\)
−0.796113 + 0.605149i \(0.793114\pi\)
\(462\) 0 0
\(463\) −6.92387 + 3.99750i −0.321779 + 0.185779i −0.652185 0.758059i \(-0.726148\pi\)
0.330406 + 0.943839i \(0.392814\pi\)
\(464\) −9.62262 + 2.40067i −0.446719 + 0.111448i
\(465\) 0 0
\(466\) −0.584316 9.54781i −0.0270679 0.442294i
\(467\) 12.6639 21.9346i 0.586017 1.01501i −0.408731 0.912655i \(-0.634029\pi\)
0.994748 0.102356i \(-0.0326381\pi\)
\(468\) 0 0
\(469\) −27.8576 15.3540i −1.28634 0.708983i
\(470\) −4.92797 + 9.88487i −0.227310 + 0.455955i
\(471\) 0 0
\(472\) 23.2129 + 8.21728i 1.06846 + 0.378231i
\(473\) 19.7359 34.1835i 0.907456 1.57176i
\(474\) 0 0
\(475\) 3.09745 5.36495i 0.142121 0.246161i
\(476\) −1.39784 9.77000i −0.0640697 0.447807i
\(477\) 0 0
\(478\) 0.123510 0.247745i 0.00564920 0.0113316i
\(479\) 4.18768 0.191340 0.0956701 0.995413i \(-0.469501\pi\)
0.0956701 + 0.995413i \(0.469501\pi\)
\(480\) 0 0
\(481\) 4.25464i 0.193995i
\(482\) −10.0326 15.1564i −0.456972 0.690355i
\(483\) 0 0
\(484\) −11.1874 + 26.3611i −0.508516 + 1.19823i
\(485\) 16.2293 28.1100i 0.736936 1.27641i
\(486\) 0 0
\(487\) −29.8039 + 17.2073i −1.35054 + 0.779737i −0.988326 0.152356i \(-0.951314\pi\)
−0.362219 + 0.932093i \(0.617981\pi\)
\(488\) −3.89106 4.55485i −0.176140 0.206188i
\(489\) 0 0
\(490\) −11.5894 16.0819i −0.523555 0.726504i
\(491\) −12.1909 + 7.03839i −0.550166 + 0.317638i −0.749189 0.662357i \(-0.769556\pi\)
0.199023 + 0.979995i \(0.436223\pi\)
\(492\) 0 0
\(493\) 4.62446i 0.208275i
\(494\) 18.5766 + 28.0639i 0.835800 + 1.26266i
\(495\) 0 0
\(496\) 4.32824 1.07982i 0.194344 0.0484852i
\(497\) −0.202259 10.1806i −0.00907255 0.456663i
\(498\) 0 0
\(499\) 15.6889i 0.702331i 0.936313 + 0.351166i \(0.114215\pi\)
−0.936313 + 0.351166i \(0.885785\pi\)
\(500\) 22.0839 + 9.37218i 0.987622 + 0.419137i
\(501\) 0 0
\(502\) 16.2412 10.7506i 0.724879 0.479825i
\(503\) 9.76063 0.435205 0.217603 0.976037i \(-0.430176\pi\)
0.217603 + 0.976037i \(0.430176\pi\)
\(504\) 0 0
\(505\) 7.59691 0.338058
\(506\) −37.2391 + 24.6499i −1.65548 + 1.09582i
\(507\) 0 0
\(508\) −4.07997 1.73150i −0.181019 0.0768228i
\(509\) 33.1208i 1.46806i −0.679120 0.734028i \(-0.737638\pi\)
0.679120 0.734028i \(-0.262362\pi\)
\(510\) 0 0
\(511\) 1.30576 0.788869i 0.0577633 0.0348975i
\(512\) −11.8291 19.2892i −0.522776 0.852470i
\(513\) 0 0
\(514\) 10.8142 + 16.3372i 0.476993 + 0.720602i
\(515\) 18.5566i 0.817702i
\(516\) 0 0
\(517\) −16.9963 + 9.81284i −0.747498 + 0.431568i
\(518\) −0.338493 4.17045i −0.0148725 0.183239i
\(519\) 0 0
\(520\) −16.3839 + 13.9963i −0.718483 + 0.613777i
\(521\) −12.6595 + 7.30899i −0.554624 + 0.320213i −0.750985 0.660319i \(-0.770421\pi\)
0.196361 + 0.980532i \(0.437088\pi\)
\(522\) 0 0
\(523\) 6.22510 10.7822i 0.272205 0.471472i −0.697221 0.716856i \(-0.745581\pi\)
0.969426 + 0.245383i \(0.0789139\pi\)
\(524\) −12.4253 + 29.2780i −0.542800 + 1.27901i
\(525\) 0 0
\(526\) −1.26332 1.90852i −0.0550833 0.0832152i
\(527\) 2.08007i 0.0906094i
\(528\) 0 0
\(529\) −16.3858 −0.712426
\(530\) −7.08419 + 14.2100i −0.307718 + 0.617242i
\(531\) 0 0
\(532\) 20.4417 + 26.0307i 0.886261 + 1.12857i
\(533\) 14.0395 24.3172i 0.608120 1.05329i
\(534\) 0 0
\(535\) −7.85236 + 13.6007i −0.339487 + 0.588009i
\(536\) −11.3476 + 32.0557i −0.490141 + 1.38459i
\(537\) 0 0
\(538\) −2.88364 + 5.78420i −0.124322 + 0.249375i
\(539\) −1.39897 35.1944i −0.0602579 1.51593i
\(540\) 0 0
\(541\) −18.8784 + 32.6984i −0.811647 + 1.40581i 0.100064 + 0.994981i \(0.468095\pi\)
−0.911711 + 0.410832i \(0.865238\pi\)
\(542\) −2.06380 33.7229i −0.0886479 1.44852i
\(543\) 0 0
\(544\) −10.0620 + 3.17455i −0.431406 + 0.136108i
\(545\) −28.6908 + 16.5646i −1.22898 + 0.709551i
\(546\) 0 0
\(547\) 4.46357 + 2.57704i 0.190848 + 0.110186i 0.592380 0.805659i \(-0.298189\pi\)
−0.401531 + 0.915845i \(0.631522\pi\)
\(548\) 3.36105 7.91973i 0.143577 0.338314i
\(549\) 0 0
\(550\) 3.89011 + 5.87685i 0.165875 + 0.250590i
\(551\) −7.75416 13.4306i −0.330338 0.572162i
\(552\) 0 0
\(553\) −8.96649 + 5.41708i −0.381294 + 0.230358i
\(554\) −14.5114 + 9.60562i −0.616529 + 0.408104i
\(555\) 0 0
\(556\) −8.72350 + 1.07175i −0.369959 + 0.0454524i
\(557\) 21.0386 + 36.4399i 0.891434 + 1.54401i 0.838156 + 0.545430i \(0.183634\pi\)
0.0532780 + 0.998580i \(0.483033\pi\)
\(558\) 0 0
\(559\) 29.8460 1.26235
\(560\) −14.9462 + 15.0228i −0.631593 + 0.634829i
\(561\) 0 0
\(562\) 1.15529 + 18.8776i 0.0487330 + 0.796305i
\(563\) −16.2896 + 28.2145i −0.686526 + 1.18910i 0.286429 + 0.958102i \(0.407532\pi\)
−0.972955 + 0.230996i \(0.925801\pi\)
\(564\) 0 0
\(565\) 33.6693 19.4390i 1.41648 0.817804i
\(566\) −0.557251 9.10556i −0.0234230 0.382735i
\(567\) 0 0
\(568\) −10.7032 + 1.98492i −0.449096 + 0.0832854i
\(569\) 20.3694 + 35.2808i 0.853930 + 1.47905i 0.877635 + 0.479330i \(0.159120\pi\)
−0.0237050 + 0.999719i \(0.507546\pi\)
\(570\) 0 0
\(571\) 23.1787 + 13.3822i 0.969998 + 0.560029i 0.899236 0.437465i \(-0.144123\pi\)
0.0707624 + 0.997493i \(0.477457\pi\)
\(572\) −38.0025 + 4.66892i −1.58897 + 0.195217i
\(573\) 0 0
\(574\) 11.8271 24.9530i 0.493653 1.04152i
\(575\) 6.21563i 0.259210i
\(576\) 0 0
\(577\) 4.34065 2.50607i 0.180704 0.104329i −0.406920 0.913464i \(-0.633397\pi\)
0.587623 + 0.809135i \(0.300064\pi\)
\(578\) −1.16805 19.0861i −0.0485845 0.793878i
\(579\) 0 0
\(580\) 7.92957 5.97626i 0.329258 0.248151i
\(581\) −13.6578 + 24.7801i −0.566623 + 1.02805i
\(582\) 0 0
\(583\) −24.4331 + 14.1064i −1.01191 + 0.584229i
\(584\) −1.05931 1.24002i −0.0438346 0.0513124i
\(585\) 0 0
\(586\) 13.7875 27.6559i 0.569554 1.14245i
\(587\) 10.2852 17.8145i 0.424517 0.735285i −0.571858 0.820352i \(-0.693777\pi\)
0.996375 + 0.0850676i \(0.0271106\pi\)
\(588\) 0 0
\(589\) 3.48781 + 6.04106i 0.143713 + 0.248918i
\(590\) −24.6079 + 1.50598i −1.01309 + 0.0620000i
\(591\) 0 0
\(592\) −4.34003 + 1.08276i −0.178374 + 0.0445011i
\(593\) 15.5093 + 8.95431i 0.636891 + 0.367709i 0.783416 0.621498i \(-0.213475\pi\)
−0.146525 + 0.989207i \(0.546809\pi\)
\(594\) 0 0
\(595\) 5.10966 + 8.45764i 0.209476 + 0.346730i
\(596\) −3.58220 + 8.44082i −0.146732 + 0.345750i
\(597\) 0 0
\(598\) −30.2205 15.0660i −1.23581 0.616096i
\(599\) −18.2010 10.5083i −0.743672 0.429360i 0.0797306 0.996816i \(-0.474594\pi\)
−0.823403 + 0.567457i \(0.807927\pi\)
\(600\) 0 0
\(601\) −17.3571 10.0211i −0.708012 0.408771i 0.102312 0.994752i \(-0.467376\pi\)
−0.810325 + 0.585981i \(0.800709\pi\)
\(602\) 29.2554 2.37451i 1.19236 0.0967776i
\(603\) 0 0
\(604\) −43.2544 18.3567i −1.76000 0.746925i
\(605\) 28.6710i 1.16564i
\(606\) 0 0
\(607\) 18.5971 0.754833 0.377417 0.926044i \(-0.376812\pi\)
0.377417 + 0.926044i \(0.376812\pi\)
\(608\) 23.8997 26.0914i 0.969260 1.05815i
\(609\) 0 0
\(610\) 5.36769 + 2.67599i 0.217331 + 0.108348i
\(611\) −12.8515 7.41984i −0.519918 0.300175i
\(612\) 0 0
\(613\) 16.7357 + 28.9871i 0.675949 + 1.17078i 0.976191 + 0.216915i \(0.0695993\pi\)
−0.300242 + 0.953863i \(0.597067\pi\)
\(614\) −5.89908 + 3.90483i −0.238068 + 0.157586i
\(615\) 0 0
\(616\) −36.8791 + 7.59996i −1.48590 + 0.306211i
\(617\) 12.3643 + 21.4156i 0.497769 + 0.862161i 0.999997 0.00257408i \(-0.000819356\pi\)
−0.502228 + 0.864735i \(0.667486\pi\)
\(618\) 0 0
\(619\) 42.6300 1.71345 0.856723 0.515777i \(-0.172497\pi\)
0.856723 + 0.515777i \(0.172497\pi\)
\(620\) −3.56671 + 2.68811i −0.143243 + 0.107957i
\(621\) 0 0
\(622\) 1.76173 + 28.7870i 0.0706391 + 1.15425i
\(623\) −13.7508 7.57889i −0.550913 0.303642i
\(624\) 0 0
\(625\) −19.0670 −0.762681
\(626\) 13.2955 26.6691i 0.531396 1.06591i
\(627\) 0 0
\(628\) −26.1842 + 19.7342i −1.04486 + 0.787479i
\(629\) 2.08574i 0.0831639i
\(630\) 0 0
\(631\) 43.8344i 1.74502i −0.488596 0.872510i \(-0.662491\pi\)
0.488596 0.872510i \(-0.337509\pi\)
\(632\) 7.27417 + 8.51509i 0.289351 + 0.338712i
\(633\) 0 0
\(634\) −15.2844 7.61981i −0.607019 0.302621i
\(635\) 4.43749 0.176097
\(636\) 0 0
\(637\) 22.5175 14.2220i 0.892177 0.563495i
\(638\) 17.6103 1.07773i 0.697197 0.0426677i
\(639\) 0 0
\(640\) 18.4467 + 13.1509i 0.729171 + 0.519834i
\(641\) −26.2084 −1.03517 −0.517584 0.855632i \(-0.673168\pi\)
−0.517584 + 0.855632i \(0.673168\pi\)
\(642\) 0 0
\(643\) −24.8988 43.1259i −0.981911 1.70072i −0.654930 0.755690i \(-0.727302\pi\)
−0.326981 0.945031i \(-0.606031\pi\)
\(644\) −30.8212 12.3636i −1.21452 0.487194i
\(645\) 0 0
\(646\) −9.10675 13.7577i −0.358300 0.541290i
\(647\) 7.44967 + 12.9032i 0.292877 + 0.507277i 0.974489 0.224436i \(-0.0720541\pi\)
−0.681612 + 0.731714i \(0.738721\pi\)
\(648\) 0 0
\(649\) −37.9376 21.9033i −1.48918 0.859778i
\(650\) −2.37763 + 4.76922i −0.0932583 + 0.187064i
\(651\) 0 0
\(652\) −8.07594 + 6.08657i −0.316278 + 0.238369i
\(653\) −43.2148 −1.69113 −0.845563 0.533876i \(-0.820735\pi\)
−0.845563 + 0.533876i \(0.820735\pi\)
\(654\) 0 0
\(655\) 31.8436i 1.24423i
\(656\) −28.3782 8.13287i −1.10798 0.317535i
\(657\) 0 0
\(658\) −13.1876 6.25057i −0.514105 0.243673i
\(659\) 28.1704 + 16.2642i 1.09736 + 0.633562i 0.935527 0.353256i \(-0.114925\pi\)
0.161835 + 0.986818i \(0.448259\pi\)
\(660\) 0 0
\(661\) 26.1675 + 15.1078i 1.01780 + 0.587627i 0.913466 0.406916i \(-0.133396\pi\)
0.104333 + 0.994542i \(0.466729\pi\)
\(662\) −0.804223 + 1.61317i −0.0312570 + 0.0626976i
\(663\) 0 0
\(664\) 28.5144 + 10.0940i 1.10657 + 0.391723i
\(665\) −29.0213 15.9954i −1.12540 0.620275i
\(666\) 0 0
\(667\) 13.4755 + 7.78009i 0.521774 + 0.301246i
\(668\) 17.6951 2.17399i 0.684646 0.0841142i
\(669\) 0 0
\(670\) −2.07967 33.9821i −0.0803445 1.31284i
\(671\) 5.32858 + 9.22937i 0.205708 + 0.356296i
\(672\) 0 0
\(673\) −7.60245 + 13.1678i −0.293053 + 0.507582i −0.974530 0.224257i \(-0.928005\pi\)
0.681477 + 0.731839i \(0.261338\pi\)
\(674\) 15.5052 + 7.72991i 0.597238 + 0.297745i
\(675\) 0 0
\(676\) −1.77622 2.35677i −0.0683162 0.0906451i
\(677\) −35.2936 + 20.3768i −1.35644 + 0.783143i −0.989143 0.146959i \(-0.953052\pi\)
−0.367301 + 0.930102i \(0.619718\pi\)
\(678\) 0 0
\(679\) 37.5602 + 20.7017i 1.44143 + 0.794459i
\(680\) 8.03186 6.86136i 0.308008 0.263121i
\(681\) 0 0
\(682\) −7.92108 + 0.484761i −0.303314 + 0.0185625i
\(683\) 1.67736 0.968424i 0.0641824 0.0370557i −0.467565 0.883958i \(-0.654869\pi\)
0.531748 + 0.846903i \(0.321535\pi\)
\(684\) 0 0
\(685\) 8.61373i 0.329114i
\(686\) 20.9405 15.7320i 0.799512 0.600651i
\(687\) 0 0
\(688\) −7.59548 30.4450i −0.289575 1.16071i
\(689\) −18.4747 10.6664i −0.703831 0.406357i
\(690\) 0 0
\(691\) 8.02376 + 13.8976i 0.305238 + 0.528688i 0.977314 0.211794i \(-0.0679306\pi\)
−0.672076 + 0.740482i \(0.734597\pi\)
\(692\) 0.740696 + 6.02888i 0.0281570 + 0.229184i
\(693\) 0 0
\(694\) −12.1901 + 0.746021i −0.462730 + 0.0283186i
\(695\) 7.62070 4.39981i 0.289069 0.166894i
\(696\) 0 0
\(697\) −6.88257 + 11.9210i −0.260696 + 0.451538i
\(698\) 11.2691 0.689657i 0.426542 0.0261039i
\(699\) 0 0
\(700\) −1.95115 + 4.86401i −0.0737466 + 0.183842i
\(701\) 15.9608 0.602830 0.301415 0.953493i \(-0.402541\pi\)
0.301415 + 0.953493i \(0.402541\pi\)
\(702\) 0 0
\(703\) −3.49731 6.05751i −0.131903 0.228463i
\(704\) 14.4339 + 37.5771i 0.543996 + 1.41624i
\(705\) 0 0
\(706\) −14.7715 22.3156i −0.555934 0.839859i
\(707\) 0.199381 + 10.0358i 0.00749849 + 0.377433i
\(708\) 0 0
\(709\) 1.54644 + 2.67851i 0.0580776 + 0.100593i 0.893602 0.448859i \(-0.148170\pi\)
−0.835525 + 0.549453i \(0.814836\pi\)
\(710\) 9.08807 6.01574i 0.341069 0.225767i
\(711\) 0 0
\(712\) −5.60128 + 15.8230i −0.209917 + 0.592991i
\(713\) −6.06127 3.49947i −0.226996 0.131056i
\(714\) 0 0
\(715\) 33.1983 19.1671i 1.24155 0.716808i
\(716\) −1.13152 9.21002i −0.0422871 0.344195i
\(717\) 0 0
\(718\) −37.1580 + 2.27403i −1.38672 + 0.0848660i
\(719\) 12.5658 21.7645i 0.468624 0.811680i −0.530733 0.847539i \(-0.678083\pi\)
0.999357 + 0.0358588i \(0.0114167\pi\)
\(720\) 0 0
\(721\) −24.5139 + 0.487019i −0.912945 + 0.0181375i
\(722\) 25.4695 + 12.6975i 0.947876 + 0.472551i
\(723\) 0 0
\(724\) −7.02697 2.98217i −0.261155 0.110831i
\(725\) 1.22781 2.12663i 0.0455996 0.0789809i
\(726\) 0 0
\(727\) −26.4226 + 45.7653i −0.979960 + 1.69734i −0.317474 + 0.948267i \(0.602835\pi\)
−0.662486 + 0.749074i \(0.730499\pi\)
\(728\) −18.9195 21.2764i −0.701204 0.788555i
\(729\) 0 0
\(730\) 1.46131 + 0.728516i 0.0540855 + 0.0269636i
\(731\) −14.6313 −0.541159
\(732\) 0 0
\(733\) 3.85524i 0.142397i 0.997462 + 0.0711983i \(0.0226823\pi\)
−0.997462 + 0.0711983i \(0.977318\pi\)
\(734\) 1.83955 1.21767i 0.0678991 0.0449450i
\(735\) 0 0
\(736\) −7.67763 + 34.6612i −0.283001 + 1.27763i
\(737\) 30.2471 52.3896i 1.11417 1.92980i
\(738\) 0 0
\(739\) −3.15539 + 1.82177i −0.116073 + 0.0670148i −0.556912 0.830571i \(-0.688014\pi\)
0.440840 + 0.897586i \(0.354681\pi\)
\(740\) 3.57643 2.69544i 0.131472 0.0990862i
\(741\) 0 0
\(742\) −18.9578 8.98551i −0.695961 0.329868i
\(743\) 10.9054 6.29626i 0.400082 0.230987i −0.286437 0.958099i \(-0.592471\pi\)
0.686519 + 0.727112i \(0.259138\pi\)
\(744\) 0 0
\(745\) 9.18048i 0.336347i
\(746\) −42.4510 + 28.0999i −1.55424 + 1.02881i
\(747\) 0 0
\(748\) 18.6299 2.28883i 0.681177 0.0836880i
\(749\) −18.1730 10.0163i −0.664028 0.365987i
\(750\) 0 0
\(751\) 13.3856i 0.488447i 0.969719 + 0.244223i \(0.0785330\pi\)
−0.969719 + 0.244223i \(0.921467\pi\)
\(752\) −4.29819 + 14.9978i −0.156739 + 0.546912i
\(753\) 0 0
\(754\) 7.36362 + 11.1243i 0.268167 + 0.405125i
\(755\) 47.0448 1.71213
\(756\) 0 0
\(757\) 1.72257 0.0626080 0.0313040 0.999510i \(-0.490034\pi\)
0.0313040 + 0.999510i \(0.490034\pi\)
\(758\) −15.2033 22.9679i −0.552208 0.834230i
\(759\) 0 0
\(760\) −11.8216 + 33.3947i −0.428815 + 1.21135i
\(761\) 20.7093i 0.750710i −0.926881 0.375355i \(-0.877521\pi\)
0.926881 0.375355i \(-0.122479\pi\)
\(762\) 0 0
\(763\) −22.6354 37.4667i −0.819456 1.35639i
\(764\) 0.920413 + 7.49168i 0.0332994 + 0.271040i
\(765\) 0 0
\(766\) −0.116926 + 0.0773977i −0.00422471 + 0.00279649i
\(767\) 33.1237i 1.19603i
\(768\) 0 0
\(769\) −6.19700 + 3.57784i −0.223470 + 0.129020i −0.607556 0.794277i \(-0.707850\pi\)
0.384086 + 0.923297i \(0.374517\pi\)
\(770\) 31.0165 21.4290i 1.11776 0.772248i
\(771\) 0 0
\(772\) −14.6110 19.3865i −0.525860 0.697735i
\(773\) −28.6131 + 16.5198i −1.02914 + 0.594176i −0.916739 0.399487i \(-0.869188\pi\)
−0.112404 + 0.993663i \(0.535855\pi\)
\(774\) 0 0
\(775\) −0.552266 + 0.956553i −0.0198380 + 0.0343604i
\(776\) 15.2999 43.2204i 0.549233 1.55152i
\(777\) 0 0
\(778\) −31.3286 + 20.7376i −1.12319 + 0.743479i
\(779\) 46.1620i 1.65392i
\(780\) 0 0
\(781\) 19.3655 0.692952
\(782\) 14.8149 + 7.38578i 0.529781 + 0.264115i
\(783\) 0 0
\(784\) −20.2379 19.3502i −0.722781 0.691077i
\(785\) 16.4136 28.4292i 0.585827 1.01468i
\(786\) 0 0
\(787\) −11.7413 + 20.3366i −0.418533 + 0.724920i −0.995792 0.0916406i \(-0.970789\pi\)
0.577259 + 0.816561i \(0.304122\pi\)
\(788\) 4.96682 11.7034i 0.176936 0.416918i
\(789\) 0 0
\(790\) −10.0347 5.00265i −0.357017 0.177986i
\(791\) 26.5632 + 43.9680i 0.944477 + 1.56332i
\(792\) 0 0
\(793\) −4.02913 + 6.97866i −0.143079 + 0.247820i
\(794\) −38.2067 + 2.33821i −1.35591 + 0.0829799i
\(795\) 0 0
\(796\) −4.00029 + 0.491467i −0.141786 + 0.0174196i
\(797\) −15.6061 + 9.01016i −0.552795 + 0.319156i −0.750248 0.661156i \(-0.770066\pi\)
0.197454 + 0.980312i \(0.436733\pi\)
\(798\) 0 0
\(799\) 6.30018 + 3.63741i 0.222884 + 0.128682i
\(800\) 5.47003 + 1.21164i 0.193395 + 0.0428379i
\(801\) 0 0
\(802\) −37.7342 + 24.9777i −1.33244 + 0.881993i
\(803\) 1.45066 + 2.51262i 0.0511928 + 0.0886685i
\(804\) 0 0
\(805\) 33.2417 0.660415i 1.17162 0.0232766i
\(806\) −3.31214 5.00371i −0.116665 0.176248i
\(807\) 0 0
\(808\) 10.5509 1.95668i 0.371179 0.0688356i
\(809\) −6.22093 10.7750i −0.218716 0.378828i 0.735699 0.677308i \(-0.236854\pi\)
−0.954416 + 0.298480i \(0.903520\pi\)
\(810\) 0 0
\(811\) 11.5370 0.405118 0.202559 0.979270i \(-0.435074\pi\)
0.202559 + 0.979270i \(0.435074\pi\)
\(812\) 8.10295 + 10.3184i 0.284358 + 0.362104i
\(813\) 0 0
\(814\) 7.94265 0.486082i 0.278390 0.0170372i
\(815\) 5.06242 8.76836i 0.177329 0.307142i
\(816\) 0 0
\(817\) 42.4931 24.5334i 1.48664 0.858315i
\(818\) −30.8713 + 1.88929i −1.07939 + 0.0660574i
\(819\) 0 0
\(820\) 29.3354 3.60408i 1.02444 0.125860i
\(821\) 15.3484 + 26.5841i 0.535661 + 0.927792i 0.999131 + 0.0416797i \(0.0132709\pi\)
−0.463470 + 0.886113i \(0.653396\pi\)
\(822\) 0 0
\(823\) 37.4029 + 21.5946i 1.30378 + 0.752740i 0.981051 0.193749i \(-0.0620649\pi\)
0.322734 + 0.946490i \(0.395398\pi\)
\(824\) 4.77948 + 25.7722i 0.166501 + 0.897816i
\(825\) 0 0
\(826\) −2.63528 32.4683i −0.0916930 1.12972i
\(827\) 24.5381i 0.853273i −0.904423 0.426637i \(-0.859698\pi\)
0.904423 0.426637i \(-0.140302\pi\)
\(828\) 0 0
\(829\) −44.2845 + 25.5676i −1.53806 + 0.888001i −0.539110 + 0.842235i \(0.681239\pi\)
−0.998952 + 0.0457657i \(0.985427\pi\)
\(830\) −30.2280 + 1.84992i −1.04923 + 0.0642117i
\(831\) 0 0
\(832\) −19.1498 + 23.6585i −0.663899 + 0.820210i
\(833\) −11.0387 + 6.97200i −0.382469 + 0.241565i
\(834\) 0 0
\(835\) −15.4582 + 8.92477i −0.534952 + 0.308854i
\(836\) −50.2681 + 37.8854i −1.73856 + 1.31029i
\(837\) 0 0
\(838\) 24.3714 + 12.1500i 0.841897 + 0.419717i
\(839\) 14.4267 24.9878i 0.498066 0.862675i −0.501932 0.864907i \(-0.667377\pi\)
0.999998 + 0.00223194i \(0.000710448\pi\)
\(840\) 0 0
\(841\) 11.4263 + 19.7909i 0.394011 + 0.682447i
\(842\) 2.91755 + 47.6733i 0.100546 + 1.64293i
\(843\) 0 0
\(844\) 4.45696 + 36.2773i 0.153415 + 1.24872i
\(845\) 2.55884 + 1.47735i 0.0880268 + 0.0508223i
\(846\) 0 0
\(847\) 37.8754 0.752472i 1.30141 0.0258552i
\(848\) −6.17886 + 21.5600i −0.212183 + 0.740374i
\(849\) 0 0
\(850\) 1.16558 2.33800i 0.0399791 0.0801929i
\(851\) 6.07778 + 3.50901i 0.208344 + 0.120287i
\(852\) 0 0
\(853\) −2.27160 1.31151i −0.0777781 0.0449052i 0.460607 0.887604i \(-0.347632\pi\)
−0.538385 + 0.842699i \(0.680965\pi\)
\(854\) −3.39419 + 7.16113i −0.116147 + 0.245049i
\(855\) 0 0
\(856\) −7.40266 + 20.9117i −0.253018 + 0.714746i
\(857\) 20.7061i 0.707307i −0.935376 0.353654i \(-0.884939\pi\)
0.935376 0.353654i \(-0.115061\pi\)
\(858\) 0 0
\(859\) −54.5095 −1.85984 −0.929920 0.367763i \(-0.880124\pi\)
−0.929920 + 0.367763i \(0.880124\pi\)
\(860\) 18.9083 + 25.0884i 0.644768 + 0.855507i
\(861\) 0 0
\(862\) −1.87816 + 3.76734i −0.0639703 + 0.128316i
\(863\) −27.4054 15.8225i −0.932891 0.538605i −0.0451662 0.998979i \(-0.514382\pi\)
−0.887725 + 0.460375i \(0.847715\pi\)
\(864\) 0 0
\(865\) −3.04074 5.26672i −0.103388 0.179074i
\(866\) 19.9770 + 30.1795i 0.678845 + 1.02554i
\(867\) 0 0
\(868\) −3.64469 4.64119i −0.123709 0.157532i
\(869\) −9.96155 17.2539i −0.337922 0.585299i
\(870\) 0 0
\(871\) 45.7419 1.54991
\(872\) −35.5805 + 30.3953i −1.20491 + 1.02931i
\(873\) 0 0
\(874\) −55.4106 + 3.39107i −1.87429 + 0.114705i
\(875\) −0.630381 31.7300i −0.0213108 1.07267i
\(876\) 0 0
\(877\) 7.91019 0.267108 0.133554 0.991042i \(-0.457361\pi\)
0.133554 + 0.991042i \(0.457361\pi\)
\(878\) 36.8697 + 18.3809i 1.24429 + 0.620326i
\(879\) 0 0
\(880\) −28.0004 28.9869i −0.943893 0.977147i
\(881\) 22.7935i 0.767932i 0.923347 + 0.383966i \(0.125442\pi\)
−0.923347 + 0.383966i \(0.874558\pi\)
\(882\) 0 0
\(883\) 13.4192i 0.451591i −0.974175 0.225795i \(-0.927502\pi\)
0.974175 0.225795i \(-0.0724981\pi\)
\(884\) 8.54217 + 11.3341i 0.287304 + 0.381208i
\(885\) 0 0
\(886\) 16.0230 32.1400i 0.538303 1.07977i
\(887\) 58.3174 1.95811 0.979053 0.203605i \(-0.0652659\pi\)
0.979053 + 0.203605i \(0.0652659\pi\)
\(888\) 0 0
\(889\) 0.116462 + 5.86207i 0.00390601 + 0.196608i
\(890\) −1.02654 16.7739i −0.0344098 0.562261i
\(891\) 0 0
\(892\) 19.8204 + 26.2986i 0.663636 + 0.880542i
\(893\) −24.3964 −0.816395
\(894\) 0 0
\(895\) 4.64519 + 8.04571i 0.155272 + 0.268938i
\(896\) −16.8886 + 24.7139i −0.564209 + 0.825632i
\(897\) 0 0
\(898\) 36.2662 24.0060i 1.21022 0.801089i
\(899\) 1.38254 + 2.39463i 0.0461103 + 0.0798654i
\(900\) 0 0
\(901\) 9.05682 + 5.22896i 0.301727 + 0.174202i
\(902\) 46.9999 + 23.4311i 1.56492 + 0.780172i
\(903\) 0 0
\(904\) 41.7545 35.6696i 1.38874 1.18635i
\(905\) 7.64273 0.254053
\(906\) 0 0
\(907\) 2.07741i 0.0689794i −0.999405 0.0344897i \(-0.989019\pi\)
0.999405 0.0344897i \(-0.0109806\pi\)
\(908\) −0.344895 + 0.812686i −0.0114457 + 0.0269699i
\(909\) 0 0
\(910\) 25.7588 + 12.2090i 0.853896 + 0.404725i
\(911\) −39.6927 22.9166i −1.31508 0.759261i −0.332147 0.943228i \(-0.607773\pi\)
−0.982933 + 0.183966i \(0.941106\pi\)
\(912\) 0 0
\(913\) −46.6020 26.9057i −1.54230 0.890449i
\(914\) −13.9046 6.93193i −0.459922 0.229288i
\(915\) 0 0
\(916\) −9.89494 4.19931i −0.326938 0.138749i
\(917\) 42.0664 0.835735i 1.38915 0.0275984i
\(918\) 0 0
\(919\) 3.35149 + 1.93498i 0.110555 + 0.0638292i 0.554258 0.832345i \(-0.313002\pi\)
−0.443703 + 0.896174i \(0.646335\pi\)
\(920\) −6.48115 34.9480i −0.213677 1.15220i
\(921\) 0 0
\(922\) 23.4509 1.43517i 0.772314 0.0472648i
\(923\) 7.32148 + 12.6812i 0.240989 + 0.417406i
\(924\) 0 0
\(925\) 0.553771 0.959159i 0.0182079 0.0315369i
\(926\) 5.04463 10.1189i 0.165777 0.332527i
\(927\) 0 0
\(928\) 9.47366 10.3424i 0.310988 0.339507i
\(929\) −6.96346 + 4.02036i −0.228464 + 0.131904i −0.609863 0.792507i \(-0.708776\pi\)
0.381399 + 0.924410i \(0.375442\pi\)
\(930\) 0 0
\(931\) 20.3688 38.7578i 0.667560 1.27024i
\(932\) 8.14208 + 10.8033i 0.266703 + 0.353873i
\(933\) 0 0
\(934\) 2.18799 + 35.7521i 0.0715932 + 1.16985i
\(935\) −16.2747 + 9.39623i −0.532241 + 0.307290i
\(936\) 0 0
\(937\) 51.2010i 1.67267i −0.548222 0.836333i \(-0.684695\pi\)
0.548222 0.836333i \(-0.315305\pi\)
\(938\) 44.8368 3.63916i 1.46397 0.118823i
\(939\) 0 0
\(940\) −1.90475 15.5036i −0.0621259 0.505673i
\(941\) 48.6046 + 28.0619i 1.58446 + 0.914790i 0.994196 + 0.107582i \(0.0343108\pi\)
0.590267 + 0.807208i \(0.299023\pi\)
\(942\) 0 0
\(943\) 23.1582 + 40.1112i 0.754134 + 1.30620i
\(944\) −33.7885 + 8.42962i −1.09972 + 0.274361i
\(945\) 0 0
\(946\) 3.40983 + 55.7172i 0.110863 + 1.81152i
\(947\) 7.57213 4.37177i 0.246061 0.142063i −0.371898 0.928274i \(-0.621293\pi\)
0.617959 + 0.786210i \(0.287960\pi\)
\(948\) 0 0
\(949\) −1.09690 + 1.89988i −0.0356068 + 0.0616728i
\(950\) 0.535158 + 8.74456i 0.0173628 + 0.283711i
\(951\) 0 0
\(952\) 9.27487 + 10.4303i 0.300600 + 0.338047i
\(953\) 0.861914 0.0279201 0.0139601 0.999903i \(-0.495556\pi\)
0.0139601 + 0.999903i \(0.495556\pi\)
\(954\) 0 0
\(955\) −3.77853 6.54460i −0.122270 0.211778i
\(956\) 0.0477387 + 0.388568i 0.00154398 + 0.0125672i
\(957\) 0 0
\(958\) −4.93839 + 3.26890i −0.159552 + 0.105613i
\(959\) −11.3790 + 0.226067i −0.367447 + 0.00730010i
\(960\) 0 0
\(961\) 14.8781 + 25.7697i 0.479940 + 0.831280i
\(962\) 3.32117 + 5.01734i 0.107079 + 0.161766i
\(963\) 0 0
\(964\) 23.6622 + 10.0420i 0.762107 + 0.323430i
\(965\) 21.0487 + 12.1525i 0.677581 + 0.391201i
\(966\) 0 0
\(967\) −34.3142 + 19.8113i −1.10347 + 0.637090i −0.937131 0.348979i \(-0.886529\pi\)
−0.166341 + 0.986068i \(0.553195\pi\)
\(968\) −7.38458 39.8195i −0.237349 1.27985i
\(969\) 0 0
\(970\) 2.80400 + 45.8178i 0.0900309 + 1.47112i
\(971\) −5.76791 + 9.99031i −0.185101 + 0.320604i −0.943611 0.331058i \(-0.892595\pi\)
0.758510 + 0.651662i \(0.225928\pi\)
\(972\) 0 0
\(973\) 6.01230 + 9.95171i 0.192745 + 0.319037i
\(974\) 21.7147 43.5569i 0.695784 1.39565i
\(975\) 0 0
\(976\) 8.14410 + 2.33401i 0.260686 + 0.0747098i
\(977\) −2.46473 + 4.26903i −0.0788536 + 0.136578i −0.902756 0.430154i \(-0.858459\pi\)
0.823902 + 0.566732i \(0.191793\pi\)
\(978\) 0 0
\(979\) 14.9303 25.8600i 0.477174 0.826489i
\(980\) 26.2204 + 9.91810i 0.837581 + 0.316822i
\(981\) 0 0
\(982\) 8.88207 17.8163i 0.283438 0.568541i
\(983\) −6.53487 −0.208430 −0.104215 0.994555i \(-0.533233\pi\)
−0.104215 + 0.994555i \(0.533233\pi\)
\(984\) 0 0
\(985\) 12.7290i 0.405579i
\(986\) −3.60985 5.45346i −0.114961 0.173673i
\(987\) 0 0
\(988\) −43.8134 18.5939i −1.39389 0.591552i
\(989\) −24.6155 + 42.6352i −0.782726 + 1.35572i
\(990\) 0 0
\(991\) −9.59915 + 5.54207i −0.304927 + 0.176050i −0.644654 0.764474i \(-0.722999\pi\)
0.339727 + 0.940524i \(0.389665\pi\)
\(992\) −4.26124 + 4.65201i −0.135294 + 0.147702i
\(993\) 0 0
\(994\) 8.18550 + 11.8478i 0.259628 + 0.375788i
\(995\) 3.49458 2.01760i 0.110786 0.0639621i
\(996\) 0 0
\(997\) 12.6388i 0.400275i −0.979768 0.200138i \(-0.935861\pi\)
0.979768 0.200138i \(-0.0641389\pi\)
\(998\) −12.2467 18.5014i −0.387664 0.585650i
\(999\) 0 0
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 756.2.n.b.19.8 84
3.2 odd 2 252.2.n.b.187.35 yes 84
4.3 odd 2 inner 756.2.n.b.19.36 84
7.3 odd 6 756.2.bj.b.451.21 84
9.4 even 3 756.2.bj.b.523.21 84
9.5 odd 6 252.2.bj.b.103.22 yes 84
12.11 even 2 252.2.n.b.187.7 yes 84
21.17 even 6 252.2.bj.b.115.22 yes 84
28.3 even 6 756.2.bj.b.451.22 84
36.23 even 6 252.2.bj.b.103.21 yes 84
36.31 odd 6 756.2.bj.b.523.22 84
63.31 odd 6 inner 756.2.n.b.199.36 84
63.59 even 6 252.2.n.b.31.7 84
84.59 odd 6 252.2.bj.b.115.21 yes 84
252.31 even 6 inner 756.2.n.b.199.8 84
252.59 odd 6 252.2.n.b.31.35 yes 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.n.b.31.7 84 63.59 even 6
252.2.n.b.31.35 yes 84 252.59 odd 6
252.2.n.b.187.7 yes 84 12.11 even 2
252.2.n.b.187.35 yes 84 3.2 odd 2
252.2.bj.b.103.21 yes 84 36.23 even 6
252.2.bj.b.103.22 yes 84 9.5 odd 6
252.2.bj.b.115.21 yes 84 84.59 odd 6
252.2.bj.b.115.22 yes 84 21.17 even 6
756.2.n.b.19.8 84 1.1 even 1 trivial
756.2.n.b.19.36 84 4.3 odd 2 inner
756.2.n.b.199.8 84 252.31 even 6 inner
756.2.n.b.199.36 84 63.31 odd 6 inner
756.2.bj.b.451.21 84 7.3 odd 6
756.2.bj.b.451.22 84 28.3 even 6
756.2.bj.b.523.21 84 9.4 even 3
756.2.bj.b.523.22 84 36.31 odd 6