Properties

Label 252.2.be.a.107.11
Level $252$
Weight $2$
Character 252.107
Analytic conductor $2.012$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,2,Mod(107,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.be (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.11
Character \(\chi\) \(=\) 252.107
Dual form 252.2.be.a.179.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.754782 + 1.19595i) q^{2} +(-0.860607 + 1.80537i) q^{4} +(1.80224 + 1.04052i) q^{5} +(1.89429 - 1.84707i) q^{7} +(-2.80871 + 0.333415i) q^{8} +O(q^{10})\) \(q+(0.754782 + 1.19595i) q^{2} +(-0.860607 + 1.80537i) q^{4} +(1.80224 + 1.04052i) q^{5} +(1.89429 - 1.84707i) q^{7} +(-2.80871 + 0.333415i) q^{8} +(0.115881 + 2.94076i) q^{10} +(2.13406 + 3.69630i) q^{11} -4.80655 q^{13} +(3.63879 + 0.871343i) q^{14} +(-2.51871 - 3.10743i) q^{16} +(2.77574 - 1.60257i) q^{17} +(-2.43886 - 1.40807i) q^{19} +(-3.42954 + 2.35822i) q^{20} +(-2.80985 + 5.34213i) q^{22} +(-2.33061 + 4.03674i) q^{23} +(-0.334629 - 0.579595i) q^{25} +(-3.62790 - 5.74841i) q^{26} +(1.70441 + 5.00949i) q^{28} -3.87198i q^{29} +(8.90803 - 5.14305i) q^{31} +(1.81526 - 5.35769i) q^{32} +(4.01168 + 2.11006i) q^{34} +(5.33587 - 1.35781i) q^{35} +(-0.136891 + 0.237102i) q^{37} +(-0.156815 - 3.97955i) q^{38} +(-5.40888 - 2.32163i) q^{40} -0.387186i q^{41} -0.907954i q^{43} +(-8.50977 + 0.671702i) q^{44} +(-6.58686 + 0.259557i) q^{46} +(3.92882 - 6.80492i) q^{47} +(0.176657 - 6.99777i) q^{49} +(0.440596 - 0.837668i) q^{50} +(4.13655 - 8.67759i) q^{52} +(-10.1385 + 5.85348i) q^{53} +8.88214i q^{55} +(-4.70466 + 5.81947i) q^{56} +(4.63071 - 2.92250i) q^{58} +(-1.85252 - 3.20865i) q^{59} +(4.01168 - 6.94844i) q^{61} +(12.8745 + 6.77170i) q^{62} +(7.77767 - 1.87293i) q^{64} +(-8.66254 - 5.00132i) q^{65} +(-1.21588 + 0.701986i) q^{67} +(0.504416 + 6.39042i) q^{68} +(5.65130 + 5.35660i) q^{70} -11.9134 q^{71} +(6.14118 + 10.6368i) q^{73} +(-0.386885 + 0.0152453i) q^{74} +(4.64099 - 3.19124i) q^{76} +(10.8698 + 3.06010i) q^{77} +(0.715577 + 0.413138i) q^{79} +(-1.30597 - 8.22109i) q^{80} +(0.463056 - 0.292241i) q^{82} +5.69055 q^{83} +6.67006 q^{85} +(1.08587 - 0.685308i) q^{86} +(-7.22635 - 9.67029i) q^{88} +(2.61763 + 1.51129i) q^{89} +(-9.10499 + 8.87804i) q^{91} +(-5.28206 - 7.68166i) q^{92} +(11.1038 - 0.437547i) q^{94} +(-2.93026 - 5.07536i) q^{95} -15.2972 q^{97} +(8.50234 - 5.07052i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.754782 + 1.19595i 0.533712 + 0.845666i
\(3\) 0 0
\(4\) −0.860607 + 1.80537i −0.430304 + 0.902684i
\(5\) 1.80224 + 1.04052i 0.805985 + 0.465335i 0.845560 0.533881i \(-0.179267\pi\)
−0.0395749 + 0.999217i \(0.512600\pi\)
\(6\) 0 0
\(7\) 1.89429 1.84707i 0.715974 0.698127i
\(8\) −2.80871 + 0.333415i −0.993028 + 0.117880i
\(9\) 0 0
\(10\) 0.115881 + 2.94076i 0.0366449 + 0.929949i
\(11\) 2.13406 + 3.69630i 0.643443 + 1.11448i 0.984659 + 0.174491i \(0.0558279\pi\)
−0.341216 + 0.939985i \(0.610839\pi\)
\(12\) 0 0
\(13\) −4.80655 −1.33310 −0.666548 0.745462i \(-0.732229\pi\)
−0.666548 + 0.745462i \(0.732229\pi\)
\(14\) 3.63879 + 0.871343i 0.972506 + 0.232876i
\(15\) 0 0
\(16\) −2.51871 3.10743i −0.629678 0.776856i
\(17\) 2.77574 1.60257i 0.673216 0.388681i −0.124078 0.992272i \(-0.539597\pi\)
0.797294 + 0.603591i \(0.206264\pi\)
\(18\) 0 0
\(19\) −2.43886 1.40807i −0.559512 0.323034i 0.193438 0.981113i \(-0.438036\pi\)
−0.752950 + 0.658078i \(0.771370\pi\)
\(20\) −3.42954 + 2.35822i −0.766869 + 0.527314i
\(21\) 0 0
\(22\) −2.80985 + 5.34213i −0.599062 + 1.13895i
\(23\) −2.33061 + 4.03674i −0.485966 + 0.841718i −0.999870 0.0161296i \(-0.994866\pi\)
0.513904 + 0.857848i \(0.328199\pi\)
\(24\) 0 0
\(25\) −0.334629 0.579595i −0.0669258 0.115919i
\(26\) −3.62790 5.74841i −0.711489 1.12735i
\(27\) 0 0
\(28\) 1.70441 + 5.00949i 0.322102 + 0.946705i
\(29\) 3.87198i 0.719009i −0.933143 0.359504i \(-0.882946\pi\)
0.933143 0.359504i \(-0.117054\pi\)
\(30\) 0 0
\(31\) 8.90803 5.14305i 1.59993 0.923720i 0.608431 0.793607i \(-0.291799\pi\)
0.991499 0.130113i \(-0.0415339\pi\)
\(32\) 1.81526 5.35769i 0.320895 0.947115i
\(33\) 0 0
\(34\) 4.01168 + 2.11006i 0.687998 + 0.361872i
\(35\) 5.33587 1.35781i 0.901927 0.229512i
\(36\) 0 0
\(37\) −0.136891 + 0.237102i −0.0225047 + 0.0389793i −0.877058 0.480384i \(-0.840497\pi\)
0.854554 + 0.519363i \(0.173831\pi\)
\(38\) −0.156815 3.97955i −0.0254388 0.645568i
\(39\) 0 0
\(40\) −5.40888 2.32163i −0.855219 0.367082i
\(41\) 0.387186i 0.0604683i −0.999543 0.0302341i \(-0.990375\pi\)
0.999543 0.0302341i \(-0.00962529\pi\)
\(42\) 0 0
\(43\) 0.907954i 0.138462i −0.997601 0.0692308i \(-0.977945\pi\)
0.997601 0.0692308i \(-0.0220545\pi\)
\(44\) −8.50977 + 0.671702i −1.28290 + 0.101263i
\(45\) 0 0
\(46\) −6.58686 + 0.259557i −0.971179 + 0.0382696i
\(47\) 3.92882 6.80492i 0.573078 0.992599i −0.423170 0.906050i \(-0.639083\pi\)
0.996248 0.0865492i \(-0.0275840\pi\)
\(48\) 0 0
\(49\) 0.176657 6.99777i 0.0252367 0.999682i
\(50\) 0.440596 0.837668i 0.0623096 0.118464i
\(51\) 0 0
\(52\) 4.13655 8.67759i 0.573636 1.20337i
\(53\) −10.1385 + 5.85348i −1.39263 + 0.804037i −0.993606 0.112902i \(-0.963985\pi\)
−0.399027 + 0.916939i \(0.630652\pi\)
\(54\) 0 0
\(55\) 8.88214i 1.19767i
\(56\) −4.70466 + 5.81947i −0.628687 + 0.777659i
\(57\) 0 0
\(58\) 4.63071 2.92250i 0.608041 0.383743i
\(59\) −1.85252 3.20865i −0.241177 0.417731i 0.719873 0.694106i \(-0.244200\pi\)
−0.961050 + 0.276375i \(0.910867\pi\)
\(60\) 0 0
\(61\) 4.01168 6.94844i 0.513644 0.889657i −0.486231 0.873830i \(-0.661629\pi\)
0.999875 0.0158266i \(-0.00503796\pi\)
\(62\) 12.8745 + 6.77170i 1.63506 + 0.860007i
\(63\) 0 0
\(64\) 7.77767 1.87293i 0.972209 0.234116i
\(65\) −8.66254 5.00132i −1.07446 0.620337i
\(66\) 0 0
\(67\) −1.21588 + 0.701986i −0.148543 + 0.0857613i −0.572429 0.819954i \(-0.693999\pi\)
0.423886 + 0.905715i \(0.360666\pi\)
\(68\) 0.504416 + 6.39042i 0.0611694 + 0.774953i
\(69\) 0 0
\(70\) 5.65130 + 5.35660i 0.675460 + 0.640236i
\(71\) −11.9134 −1.41386 −0.706931 0.707282i \(-0.749921\pi\)
−0.706931 + 0.707282i \(0.749921\pi\)
\(72\) 0 0
\(73\) 6.14118 + 10.6368i 0.718770 + 1.24495i 0.961487 + 0.274850i \(0.0886281\pi\)
−0.242717 + 0.970097i \(0.578039\pi\)
\(74\) −0.386885 + 0.0152453i −0.0449745 + 0.00177223i
\(75\) 0 0
\(76\) 4.64099 3.19124i 0.532358 0.366060i
\(77\) 10.8698 + 3.06010i 1.23873 + 0.348730i
\(78\) 0 0
\(79\) 0.715577 + 0.413138i 0.0805087 + 0.0464817i 0.539714 0.841848i \(-0.318532\pi\)
−0.459205 + 0.888330i \(0.651866\pi\)
\(80\) −1.30597 8.22109i −0.146012 0.919146i
\(81\) 0 0
\(82\) 0.463056 0.292241i 0.0511360 0.0322726i
\(83\) 5.69055 0.624619 0.312310 0.949980i \(-0.398897\pi\)
0.312310 + 0.949980i \(0.398897\pi\)
\(84\) 0 0
\(85\) 6.67006 0.723469
\(86\) 1.08587 0.685308i 0.117092 0.0738986i
\(87\) 0 0
\(88\) −7.22635 9.67029i −0.770331 1.03086i
\(89\) 2.61763 + 1.51129i 0.277469 + 0.160197i 0.632277 0.774742i \(-0.282121\pi\)
−0.354808 + 0.934939i \(0.615454\pi\)
\(90\) 0 0
\(91\) −9.10499 + 8.87804i −0.954462 + 0.930671i
\(92\) −5.28206 7.68166i −0.550693 0.800868i
\(93\) 0 0
\(94\) 11.1038 0.437547i 1.14527 0.0451295i
\(95\) −2.93026 5.07536i −0.300639 0.520721i
\(96\) 0 0
\(97\) −15.2972 −1.55319 −0.776595 0.630000i \(-0.783055\pi\)
−0.776595 + 0.630000i \(0.783055\pi\)
\(98\) 8.50234 5.07052i 0.858866 0.512200i
\(99\) 0 0
\(100\) 1.33437 0.105326i 0.133437 0.0105326i
\(101\) −0.335313 + 0.193593i −0.0333649 + 0.0192632i −0.516590 0.856233i \(-0.672799\pi\)
0.483225 + 0.875496i \(0.339465\pi\)
\(102\) 0 0
\(103\) −11.7225 6.76797i −1.15505 0.666868i −0.204937 0.978775i \(-0.565699\pi\)
−0.950113 + 0.311907i \(0.899032\pi\)
\(104\) 13.5002 1.60257i 1.32380 0.157145i
\(105\) 0 0
\(106\) −14.6529 7.70709i −1.42321 0.748579i
\(107\) −5.44204 + 9.42590i −0.526102 + 0.911236i 0.473435 + 0.880829i \(0.343014\pi\)
−0.999538 + 0.0304073i \(0.990320\pi\)
\(108\) 0 0
\(109\) 9.35800 + 16.2085i 0.896334 + 1.55250i 0.832145 + 0.554558i \(0.187113\pi\)
0.0641884 + 0.997938i \(0.479554\pi\)
\(110\) −10.6226 + 6.70408i −1.01283 + 0.639209i
\(111\) 0 0
\(112\) −10.5108 1.23412i −0.993177 0.116614i
\(113\) 13.1377i 1.23589i 0.786221 + 0.617945i \(0.212035\pi\)
−0.786221 + 0.617945i \(0.787965\pi\)
\(114\) 0 0
\(115\) −8.40063 + 4.85011i −0.783363 + 0.452275i
\(116\) 6.99035 + 3.33225i 0.649038 + 0.309392i
\(117\) 0 0
\(118\) 2.43915 4.63736i 0.224542 0.426904i
\(119\) 2.29798 8.16273i 0.210656 0.748276i
\(120\) 0 0
\(121\) −3.60841 + 6.24995i −0.328037 + 0.568177i
\(122\) 11.3380 0.446775i 1.02649 0.0404491i
\(123\) 0 0
\(124\) 1.61879 + 20.5084i 0.145372 + 1.84171i
\(125\) 11.7980i 1.05524i
\(126\) 0 0
\(127\) 4.80602i 0.426465i −0.977001 0.213233i \(-0.931601\pi\)
0.977001 0.213233i \(-0.0683992\pi\)
\(128\) 8.11038 + 7.88807i 0.716863 + 0.697214i
\(129\) 0 0
\(130\) −0.556989 14.1349i −0.0488512 1.23971i
\(131\) −7.35836 + 12.7451i −0.642903 + 1.11354i 0.341878 + 0.939744i \(0.388937\pi\)
−0.984782 + 0.173797i \(0.944396\pi\)
\(132\) 0 0
\(133\) −7.22071 + 1.83744i −0.626115 + 0.159326i
\(134\) −1.75726 0.924284i −0.151805 0.0798459i
\(135\) 0 0
\(136\) −7.26192 + 5.42664i −0.622705 + 0.465330i
\(137\) 3.43633 1.98397i 0.293585 0.169502i −0.345972 0.938245i \(-0.612451\pi\)
0.639558 + 0.768743i \(0.279118\pi\)
\(138\) 0 0
\(139\) 19.1682i 1.62583i 0.582383 + 0.812915i \(0.302121\pi\)
−0.582383 + 0.812915i \(0.697879\pi\)
\(140\) −2.14074 + 10.8018i −0.180926 + 0.912915i
\(141\) 0 0
\(142\) −8.99204 14.2479i −0.754595 1.19566i
\(143\) −10.2575 17.7664i −0.857771 1.48570i
\(144\) 0 0
\(145\) 4.02888 6.97822i 0.334580 0.579510i
\(146\) −8.08590 + 15.3731i −0.669194 + 1.27228i
\(147\) 0 0
\(148\) −0.310247 0.451190i −0.0255022 0.0370876i
\(149\) −4.89898 2.82843i −0.401340 0.231714i 0.285722 0.958313i \(-0.407767\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(150\) 0 0
\(151\) 8.38179 4.83923i 0.682100 0.393811i −0.118546 0.992949i \(-0.537823\pi\)
0.800646 + 0.599138i \(0.204490\pi\)
\(152\) 7.31950 + 3.14172i 0.593690 + 0.254827i
\(153\) 0 0
\(154\) 4.54464 + 15.3095i 0.366217 + 1.23368i
\(155\) 21.4058 1.71936
\(156\) 0 0
\(157\) −2.94304 5.09749i −0.234880 0.406824i 0.724358 0.689424i \(-0.242136\pi\)
−0.959238 + 0.282600i \(0.908803\pi\)
\(158\) 0.0460106 + 1.16763i 0.00366041 + 0.0928913i
\(159\) 0 0
\(160\) 8.84631 7.76701i 0.699363 0.614036i
\(161\) 3.04129 + 11.9516i 0.239687 + 0.941914i
\(162\) 0 0
\(163\) −8.40063 4.85011i −0.657988 0.379890i 0.133522 0.991046i \(-0.457371\pi\)
−0.791510 + 0.611156i \(0.790705\pi\)
\(164\) 0.699013 + 0.333215i 0.0545837 + 0.0260197i
\(165\) 0 0
\(166\) 4.29513 + 6.80563i 0.333367 + 0.528220i
\(167\) −18.4218 −1.42552 −0.712759 0.701409i \(-0.752555\pi\)
−0.712759 + 0.701409i \(0.752555\pi\)
\(168\) 0 0
\(169\) 10.1029 0.777146
\(170\) 5.03444 + 7.97707i 0.386124 + 0.611814i
\(171\) 0 0
\(172\) 1.63919 + 0.781392i 0.124987 + 0.0595805i
\(173\) 6.13279 + 3.54077i 0.466267 + 0.269199i 0.714676 0.699456i \(-0.246574\pi\)
−0.248409 + 0.968655i \(0.579908\pi\)
\(174\) 0 0
\(175\) −1.70444 0.479836i −0.128843 0.0362722i
\(176\) 6.11089 15.9413i 0.460626 1.20162i
\(177\) 0 0
\(178\) 0.168310 + 4.27126i 0.0126154 + 0.320145i
\(179\) 10.5602 + 18.2908i 0.789305 + 1.36712i 0.926393 + 0.376557i \(0.122892\pi\)
−0.137088 + 0.990559i \(0.543774\pi\)
\(180\) 0 0
\(181\) −6.13809 −0.456240 −0.228120 0.973633i \(-0.573258\pi\)
−0.228120 + 0.973633i \(0.573258\pi\)
\(182\) −17.4900 4.18815i −1.29644 0.310446i
\(183\) 0 0
\(184\) 5.20010 12.1151i 0.383356 0.893135i
\(185\) −0.493419 + 0.284876i −0.0362769 + 0.0209445i
\(186\) 0 0
\(187\) 11.8472 + 6.83998i 0.866352 + 0.500189i
\(188\) 8.90422 + 12.9493i 0.649407 + 0.944427i
\(189\) 0 0
\(190\) 3.85819 7.33525i 0.279902 0.532155i
\(191\) 5.89895 10.2173i 0.426833 0.739297i −0.569756 0.821814i \(-0.692962\pi\)
0.996590 + 0.0825166i \(0.0262958\pi\)
\(192\) 0 0
\(193\) 7.90367 + 13.6896i 0.568919 + 0.985396i 0.996673 + 0.0815013i \(0.0259715\pi\)
−0.427754 + 0.903895i \(0.640695\pi\)
\(194\) −11.5460 18.2947i −0.828956 1.31348i
\(195\) 0 0
\(196\) 12.4815 + 6.34126i 0.891537 + 0.452947i
\(197\) 2.17812i 0.155185i −0.996985 0.0775924i \(-0.975277\pi\)
0.996985 0.0775924i \(-0.0247233\pi\)
\(198\) 0 0
\(199\) 4.74590 2.74005i 0.336428 0.194237i −0.322263 0.946650i \(-0.604444\pi\)
0.658691 + 0.752413i \(0.271110\pi\)
\(200\) 1.13312 + 1.51634i 0.0801237 + 0.107222i
\(201\) 0 0
\(202\) −0.484616 0.254898i −0.0340975 0.0179345i
\(203\) −7.15182 7.33465i −0.501959 0.514791i
\(204\) 0 0
\(205\) 0.402875 0.697800i 0.0281380 0.0487365i
\(206\) −0.753739 19.1279i −0.0525155 1.33270i
\(207\) 0 0
\(208\) 12.1063 + 14.9360i 0.839421 + 1.03562i
\(209\) 12.0196i 0.831416i
\(210\) 0 0
\(211\) 8.80046i 0.605849i −0.953015 0.302924i \(-0.902037\pi\)
0.953015 0.302924i \(-0.0979629\pi\)
\(212\) −1.84240 23.3413i −0.126537 1.60309i
\(213\) 0 0
\(214\) −15.3805 + 0.606073i −1.05139 + 0.0414303i
\(215\) 0.944746 1.63635i 0.0644311 0.111598i
\(216\) 0 0
\(217\) 7.37479 26.1962i 0.500634 1.77831i
\(218\) −12.3214 + 23.4256i −0.834510 + 1.58658i
\(219\) 0 0
\(220\) −16.0355 7.64403i −1.08112 0.515360i
\(221\) −13.3417 + 7.70285i −0.897462 + 0.518150i
\(222\) 0 0
\(223\) 21.1499i 1.41630i −0.706060 0.708152i \(-0.749529\pi\)
0.706060 0.708152i \(-0.250471\pi\)
\(224\) −6.45742 13.5019i −0.431454 0.902135i
\(225\) 0 0
\(226\) −15.7121 + 9.91610i −1.04515 + 0.659609i
\(227\) 14.0475 + 24.3309i 0.932364 + 1.61490i 0.779269 + 0.626690i \(0.215591\pi\)
0.153095 + 0.988211i \(0.451076\pi\)
\(228\) 0 0
\(229\) 6.81783 11.8088i 0.450535 0.780350i −0.547884 0.836554i \(-0.684567\pi\)
0.998419 + 0.0562045i \(0.0178999\pi\)
\(230\) −12.1411 6.38598i −0.800563 0.421079i
\(231\) 0 0
\(232\) 1.29098 + 10.8753i 0.0847567 + 0.713996i
\(233\) 3.73493 + 2.15637i 0.244684 + 0.141268i 0.617328 0.786706i \(-0.288215\pi\)
−0.372644 + 0.927974i \(0.621549\pi\)
\(234\) 0 0
\(235\) 14.1613 8.17605i 0.923783 0.533347i
\(236\) 7.38709 0.583086i 0.480859 0.0379557i
\(237\) 0 0
\(238\) 11.4967 3.41280i 0.745222 0.221219i
\(239\) 7.22142 0.467115 0.233558 0.972343i \(-0.424963\pi\)
0.233558 + 0.972343i \(0.424963\pi\)
\(240\) 0 0
\(241\) −2.36740 4.10045i −0.152497 0.264133i 0.779648 0.626219i \(-0.215398\pi\)
−0.932145 + 0.362085i \(0.882065\pi\)
\(242\) −10.1982 + 0.401863i −0.655566 + 0.0258328i
\(243\) 0 0
\(244\) 9.09201 + 13.2224i 0.582057 + 0.846480i
\(245\) 7.59971 12.4278i 0.485528 0.793984i
\(246\) 0 0
\(247\) 11.7225 + 6.76797i 0.745883 + 0.430636i
\(248\) −23.3053 + 17.4154i −1.47989 + 1.10588i
\(249\) 0 0
\(250\) 14.1098 8.90490i 0.892383 0.563195i
\(251\) 2.26312 0.142847 0.0714233 0.997446i \(-0.477246\pi\)
0.0714233 + 0.997446i \(0.477246\pi\)
\(252\) 0 0
\(253\) −19.8947 −1.25077
\(254\) 5.74777 3.62750i 0.360647 0.227610i
\(255\) 0 0
\(256\) −3.31219 + 15.6534i −0.207012 + 0.978338i
\(257\) −15.6241 9.02055i −0.974602 0.562687i −0.0739657 0.997261i \(-0.523566\pi\)
−0.900636 + 0.434574i \(0.856899\pi\)
\(258\) 0 0
\(259\) 0.178633 + 0.701986i 0.0110997 + 0.0436193i
\(260\) 16.4843 11.3349i 1.02231 0.702961i
\(261\) 0 0
\(262\) −20.7965 + 0.819490i −1.28481 + 0.0506283i
\(263\) −0.335353 0.580849i −0.0206788 0.0358167i 0.855501 0.517801i \(-0.173249\pi\)
−0.876180 + 0.481985i \(0.839916\pi\)
\(264\) 0 0
\(265\) −24.3627 −1.49659
\(266\) −7.64756 7.24876i −0.468902 0.444450i
\(267\) 0 0
\(268\) −0.220953 2.79924i −0.0134968 0.170991i
\(269\) −8.22457 + 4.74846i −0.501461 + 0.289518i −0.729317 0.684176i \(-0.760162\pi\)
0.227856 + 0.973695i \(0.426829\pi\)
\(270\) 0 0
\(271\) 14.8698 + 8.58509i 0.903276 + 0.521507i 0.878262 0.478180i \(-0.158703\pi\)
0.0250146 + 0.999687i \(0.492037\pi\)
\(272\) −11.9712 4.58899i −0.725859 0.278248i
\(273\) 0 0
\(274\) 4.96641 + 2.61223i 0.300032 + 0.157810i
\(275\) 1.42824 2.47378i 0.0861259 0.149174i
\(276\) 0 0
\(277\) −4.92436 8.52923i −0.295876 0.512472i 0.679312 0.733849i \(-0.262278\pi\)
−0.975188 + 0.221377i \(0.928945\pi\)
\(278\) −22.9243 + 14.4679i −1.37491 + 0.867724i
\(279\) 0 0
\(280\) −14.5342 + 5.59275i −0.868584 + 0.334231i
\(281\) 7.25476i 0.432783i −0.976307 0.216391i \(-0.930571\pi\)
0.976307 0.216391i \(-0.0694287\pi\)
\(282\) 0 0
\(283\) −2.43886 + 1.40807i −0.144975 + 0.0837013i −0.570733 0.821136i \(-0.693341\pi\)
0.425758 + 0.904837i \(0.360007\pi\)
\(284\) 10.2528 21.5081i 0.608390 1.27627i
\(285\) 0 0
\(286\) 13.5057 25.6772i 0.798607 1.51833i
\(287\) −0.715160 0.733441i −0.0422145 0.0432937i
\(288\) 0 0
\(289\) −3.36351 + 5.82577i −0.197853 + 0.342692i
\(290\) 11.3866 0.448690i 0.668641 0.0263480i
\(291\) 0 0
\(292\) −24.4885 + 1.93296i −1.43308 + 0.113118i
\(293\) 6.86151i 0.400854i −0.979709 0.200427i \(-0.935767\pi\)
0.979709 0.200427i \(-0.0642329\pi\)
\(294\) 0 0
\(295\) 7.71034i 0.448913i
\(296\) 0.305433 0.711591i 0.0177529 0.0413604i
\(297\) 0 0
\(298\) −0.314998 7.99380i −0.0182473 0.463068i
\(299\) 11.2022 19.4028i 0.647840 1.12209i
\(300\) 0 0
\(301\) −1.67706 1.71993i −0.0966639 0.0991349i
\(302\) 12.1139 + 6.37166i 0.697077 + 0.366648i
\(303\) 0 0
\(304\) 1.76729 + 11.1251i 0.101361 + 0.638068i
\(305\) 14.4600 8.34849i 0.827978 0.478033i
\(306\) 0 0
\(307\) 8.29624i 0.473491i −0.971572 0.236746i \(-0.923919\pi\)
0.971572 0.236746i \(-0.0760808\pi\)
\(308\) −14.8793 + 16.9905i −0.847825 + 0.968126i
\(309\) 0 0
\(310\) 16.1568 + 25.6004i 0.917642 + 1.45400i
\(311\) 8.68043 + 15.0349i 0.492222 + 0.852553i 0.999960 0.00895813i \(-0.00285150\pi\)
−0.507738 + 0.861512i \(0.669518\pi\)
\(312\) 0 0
\(313\) −3.97581 + 6.88630i −0.224726 + 0.389237i −0.956237 0.292593i \(-0.905482\pi\)
0.731511 + 0.681829i \(0.238815\pi\)
\(314\) 3.87501 7.36724i 0.218679 0.415757i
\(315\) 0 0
\(316\) −1.36170 + 0.936330i −0.0766015 + 0.0526727i
\(317\) 1.89058 + 1.09153i 0.106186 + 0.0613063i 0.552152 0.833743i \(-0.313807\pi\)
−0.445967 + 0.895050i \(0.647140\pi\)
\(318\) 0 0
\(319\) 14.3120 8.26303i 0.801318 0.462641i
\(320\) 15.9660 + 4.71737i 0.892528 + 0.263709i
\(321\) 0 0
\(322\) −11.9980 + 12.6581i −0.668621 + 0.705406i
\(323\) −9.02618 −0.502230
\(324\) 0 0
\(325\) 1.60841 + 2.78585i 0.0892186 + 0.154531i
\(326\) −0.540149 13.7075i −0.0299161 0.759190i
\(327\) 0 0
\(328\) 0.129094 + 1.08749i 0.00712800 + 0.0600467i
\(329\) −5.12685 20.1473i −0.282652 1.11076i
\(330\) 0 0
\(331\) 11.6706 + 6.73802i 0.641473 + 0.370355i 0.785182 0.619265i \(-0.212569\pi\)
−0.143709 + 0.989620i \(0.545903\pi\)
\(332\) −4.89733 + 10.2735i −0.268776 + 0.563834i
\(333\) 0 0
\(334\) −13.9044 22.0316i −0.760816 1.20551i
\(335\) −2.92173 −0.159631
\(336\) 0 0
\(337\) 17.4188 0.948865 0.474432 0.880292i \(-0.342653\pi\)
0.474432 + 0.880292i \(0.342653\pi\)
\(338\) 7.62549 + 12.0826i 0.414772 + 0.657207i
\(339\) 0 0
\(340\) −5.74030 + 12.0419i −0.311311 + 0.653064i
\(341\) 38.0205 + 21.9512i 2.05893 + 1.18872i
\(342\) 0 0
\(343\) −12.5907 13.5821i −0.679836 0.733364i
\(344\) 0.302725 + 2.55018i 0.0163219 + 0.137496i
\(345\) 0 0
\(346\) 0.394330 + 10.0070i 0.0211993 + 0.537981i
\(347\) −1.10433 1.91275i −0.0592833 0.102682i 0.834861 0.550461i \(-0.185548\pi\)
−0.894144 + 0.447780i \(0.852215\pi\)
\(348\) 0 0
\(349\) 31.3253 1.67681 0.838403 0.545051i \(-0.183490\pi\)
0.838403 + 0.545051i \(0.183490\pi\)
\(350\) −0.712618 2.40060i −0.0380910 0.128317i
\(351\) 0 0
\(352\) 23.6775 4.72390i 1.26201 0.251785i
\(353\) −5.97612 + 3.45031i −0.318077 + 0.183642i −0.650535 0.759476i \(-0.725455\pi\)
0.332458 + 0.943118i \(0.392122\pi\)
\(354\) 0 0
\(355\) −21.4708 12.3962i −1.13955 0.657920i
\(356\) −4.98119 + 3.42517i −0.264003 + 0.181533i
\(357\) 0 0
\(358\) −13.9043 + 26.4350i −0.734863 + 1.39713i
\(359\) −6.57360 + 11.3858i −0.346941 + 0.600920i −0.985705 0.168483i \(-0.946113\pi\)
0.638763 + 0.769404i \(0.279446\pi\)
\(360\) 0 0
\(361\) −5.53466 9.58630i −0.291298 0.504542i
\(362\) −4.63292 7.34086i −0.243501 0.385827i
\(363\) 0 0
\(364\) −8.19231 24.0784i −0.429394 1.26205i
\(365\) 25.5601i 1.33788i
\(366\) 0 0
\(367\) −9.79102 + 5.65285i −0.511087 + 0.295076i −0.733280 0.679926i \(-0.762012\pi\)
0.222193 + 0.975003i \(0.428678\pi\)
\(368\) 18.4140 2.92518i 0.959896 0.152485i
\(369\) 0 0
\(370\) −0.713122 0.375087i −0.0370735 0.0194998i
\(371\) −8.39349 + 29.8147i −0.435768 + 1.54790i
\(372\) 0 0
\(373\) −7.07682 + 12.2574i −0.366424 + 0.634665i −0.989004 0.147892i \(-0.952751\pi\)
0.622580 + 0.782556i \(0.286085\pi\)
\(374\) 0.761758 + 19.3314i 0.0393896 + 0.999601i
\(375\) 0 0
\(376\) −8.76605 + 20.4230i −0.452074 + 1.05323i
\(377\) 18.6109i 0.958508i
\(378\) 0 0
\(379\) 16.2405i 0.834216i 0.908857 + 0.417108i \(0.136956\pi\)
−0.908857 + 0.417108i \(0.863044\pi\)
\(380\) 11.6847 0.922311i 0.599413 0.0473135i
\(381\) 0 0
\(382\) 16.6718 0.656958i 0.853005 0.0336129i
\(383\) −1.35904 + 2.35392i −0.0694436 + 0.120280i −0.898657 0.438653i \(-0.855456\pi\)
0.829213 + 0.558933i \(0.188789\pi\)
\(384\) 0 0
\(385\) 16.4059 + 16.8253i 0.836124 + 0.857498i
\(386\) −10.4065 + 19.7851i −0.529678 + 1.00703i
\(387\) 0 0
\(388\) 13.1648 27.6170i 0.668343 1.40204i
\(389\) −17.4029 + 10.0476i −0.882363 + 0.509432i −0.871437 0.490508i \(-0.836811\pi\)
−0.0109262 + 0.999940i \(0.503478\pi\)
\(390\) 0 0
\(391\) 14.9399i 0.755544i
\(392\) 1.83698 + 19.7136i 0.0927817 + 0.995686i
\(393\) 0 0
\(394\) 2.60493 1.64401i 0.131235 0.0828239i
\(395\) 0.859759 + 1.48915i 0.0432592 + 0.0749271i
\(396\) 0 0
\(397\) −7.93175 + 13.7382i −0.398083 + 0.689501i −0.993489 0.113924i \(-0.963658\pi\)
0.595406 + 0.803425i \(0.296991\pi\)
\(398\) 6.85909 + 3.60773i 0.343815 + 0.180839i
\(399\) 0 0
\(400\) −0.958213 + 2.49967i −0.0479107 + 0.124983i
\(401\) 27.7148 + 16.0012i 1.38401 + 0.799060i 0.992632 0.121169i \(-0.0386642\pi\)
0.391381 + 0.920229i \(0.371998\pi\)
\(402\) 0 0
\(403\) −42.8169 + 24.7203i −2.13286 + 1.23141i
\(404\) −0.0609340 0.771970i −0.00303158 0.0384070i
\(405\) 0 0
\(406\) 3.37382 14.0893i 0.167440 0.699240i
\(407\) −1.16853 −0.0579220
\(408\) 0 0
\(409\) −2.42047 4.19237i −0.119684 0.207300i 0.799958 0.600056i \(-0.204855\pi\)
−0.919643 + 0.392756i \(0.871522\pi\)
\(410\) 1.13862 0.0448676i 0.0562324 0.00221585i
\(411\) 0 0
\(412\) 22.3071 15.3388i 1.09899 0.755690i
\(413\) −9.43582 2.65639i −0.464306 0.130712i
\(414\) 0 0
\(415\) 10.2557 + 5.92114i 0.503434 + 0.290658i
\(416\) −8.72511 + 25.7520i −0.427784 + 1.26260i
\(417\) 0 0
\(418\) 14.3749 9.07222i 0.703101 0.443737i
\(419\) −9.95079 −0.486128 −0.243064 0.970010i \(-0.578152\pi\)
−0.243064 + 0.970010i \(0.578152\pi\)
\(420\) 0 0
\(421\) −2.27378 −0.110817 −0.0554087 0.998464i \(-0.517646\pi\)
−0.0554087 + 0.998464i \(0.517646\pi\)
\(422\) 10.5249 6.64243i 0.512346 0.323349i
\(423\) 0 0
\(424\) 26.5245 19.8210i 1.28814 0.962595i
\(425\) −1.85769 1.07254i −0.0901111 0.0520257i
\(426\) 0 0
\(427\) −5.23498 20.5722i −0.253338 0.995559i
\(428\) −12.3338 17.9369i −0.596175 0.867012i
\(429\) 0 0
\(430\) 2.67007 0.105215i 0.128762 0.00507392i
\(431\) −14.2652 24.7081i −0.687131 1.19015i −0.972762 0.231806i \(-0.925536\pi\)
0.285631 0.958340i \(-0.407797\pi\)
\(432\) 0 0
\(433\) −7.86191 −0.377819 −0.188910 0.981994i \(-0.560495\pi\)
−0.188910 + 0.981994i \(0.560495\pi\)
\(434\) 36.8958 10.9525i 1.77105 0.525738i
\(435\) 0 0
\(436\) −37.3159 + 2.94546i −1.78711 + 0.141062i
\(437\) 11.3681 6.56335i 0.543808 0.313968i
\(438\) 0 0
\(439\) −9.24092 5.33525i −0.441045 0.254637i 0.262996 0.964797i \(-0.415289\pi\)
−0.704041 + 0.710160i \(0.748623\pi\)
\(440\) −2.96144 24.9473i −0.141181 1.18932i
\(441\) 0 0
\(442\) −19.2824 10.1421i −0.917168 0.482411i
\(443\) 18.9902 32.8921i 0.902254 1.56275i 0.0776916 0.996977i \(-0.475245\pi\)
0.824562 0.565772i \(-0.191422\pi\)
\(444\) 0 0
\(445\) 3.14506 + 5.44741i 0.149090 + 0.258232i
\(446\) 25.2943 15.9636i 1.19772 0.755898i
\(447\) 0 0
\(448\) 11.2737 17.9138i 0.532633 0.846346i
\(449\) 24.0046i 1.13285i −0.824114 0.566423i \(-0.808327\pi\)
0.824114 0.566423i \(-0.191673\pi\)
\(450\) 0 0
\(451\) 1.43115 0.826277i 0.0673904 0.0389079i
\(452\) −23.7184 11.3064i −1.11562 0.531808i
\(453\) 0 0
\(454\) −18.4959 + 35.1647i −0.868054 + 1.65036i
\(455\) −25.6471 + 6.52638i −1.20236 + 0.305962i
\(456\) 0 0
\(457\) −7.52257 + 13.0295i −0.351891 + 0.609493i −0.986581 0.163274i \(-0.947795\pi\)
0.634690 + 0.772767i \(0.281128\pi\)
\(458\) 19.2688 0.759292i 0.900371 0.0354794i
\(459\) 0 0
\(460\) −1.52659 19.3403i −0.0711775 0.901745i
\(461\) 30.3714i 1.41454i −0.706946 0.707268i \(-0.749927\pi\)
0.706946 0.707268i \(-0.250073\pi\)
\(462\) 0 0
\(463\) 23.7810i 1.10519i 0.833448 + 0.552597i \(0.186363\pi\)
−0.833448 + 0.552597i \(0.813637\pi\)
\(464\) −12.0319 + 9.75240i −0.558566 + 0.452744i
\(465\) 0 0
\(466\) 0.240151 + 6.09439i 0.0111248 + 0.282317i
\(467\) 2.35180 4.07343i 0.108828 0.188496i −0.806468 0.591278i \(-0.798623\pi\)
0.915296 + 0.402782i \(0.131957\pi\)
\(468\) 0 0
\(469\) −1.00660 + 3.57557i −0.0464805 + 0.165105i
\(470\) 20.4669 + 10.7651i 0.944067 + 0.496559i
\(471\) 0 0
\(472\) 6.27299 + 8.39451i 0.288738 + 0.386389i
\(473\) 3.35607 1.93763i 0.154312 0.0890922i
\(474\) 0 0
\(475\) 1.88473i 0.0864774i
\(476\) 12.7591 + 11.1736i 0.584811 + 0.512142i
\(477\) 0 0
\(478\) 5.45060 + 8.63648i 0.249305 + 0.395024i
\(479\) 2.04513 + 3.54227i 0.0934444 + 0.161850i 0.908958 0.416887i \(-0.136879\pi\)
−0.815514 + 0.578737i \(0.803546\pi\)
\(480\) 0 0
\(481\) 0.657972 1.13964i 0.0300010 0.0519632i
\(482\) 3.11708 5.92624i 0.141979 0.269933i
\(483\) 0 0
\(484\) −8.17804 11.8933i −0.371729 0.540603i
\(485\) −27.5691 15.9170i −1.25185 0.722755i
\(486\) 0 0
\(487\) −4.85177 + 2.80117i −0.219854 + 0.126933i −0.605883 0.795554i \(-0.707180\pi\)
0.386028 + 0.922487i \(0.373847\pi\)
\(488\) −8.95093 + 20.8537i −0.405190 + 0.944002i
\(489\) 0 0
\(490\) 20.5992 0.291406i 0.930578 0.0131644i
\(491\) −10.3094 −0.465257 −0.232629 0.972566i \(-0.574733\pi\)
−0.232629 + 0.972566i \(0.574733\pi\)
\(492\) 0 0
\(493\) −6.20514 10.7476i −0.279465 0.484048i
\(494\) 0.753739 + 19.1279i 0.0339123 + 0.860604i
\(495\) 0 0
\(496\) −38.4184 14.7272i −1.72504 0.661270i
\(497\) −22.5674 + 22.0049i −1.01229 + 0.987056i
\(498\) 0 0
\(499\) 6.14548 + 3.54809i 0.275109 + 0.158835i 0.631207 0.775614i \(-0.282560\pi\)
−0.356098 + 0.934449i \(0.615893\pi\)
\(500\) 21.2997 + 10.1534i 0.952551 + 0.454075i
\(501\) 0 0
\(502\) 1.70816 + 2.70658i 0.0762389 + 0.120801i
\(503\) 6.79674 0.303052 0.151526 0.988453i \(-0.451581\pi\)
0.151526 + 0.988453i \(0.451581\pi\)
\(504\) 0 0
\(505\) −0.805750 −0.0358554
\(506\) −15.0161 23.7931i −0.667549 1.05773i
\(507\) 0 0
\(508\) 8.67664 + 4.13609i 0.384963 + 0.183509i
\(509\) −16.8641 9.73648i −0.747487 0.431562i 0.0772979 0.997008i \(-0.475371\pi\)
−0.824785 + 0.565446i \(0.808704\pi\)
\(510\) 0 0
\(511\) 31.2801 + 8.80603i 1.38375 + 0.389556i
\(512\) −21.2207 + 7.85370i −0.937833 + 0.347088i
\(513\) 0 0
\(514\) −1.00461 25.4942i −0.0443113 1.12450i
\(515\) −14.0844 24.3950i −0.620635 1.07497i
\(516\) 0 0
\(517\) 33.5373 1.47497
\(518\) −0.704713 + 0.743484i −0.0309633 + 0.0326668i
\(519\) 0 0
\(520\) 25.9980 + 11.1590i 1.14009 + 0.489355i
\(521\) −29.8381 + 17.2270i −1.30723 + 0.754729i −0.981633 0.190779i \(-0.938898\pi\)
−0.325597 + 0.945509i \(0.605565\pi\)
\(522\) 0 0
\(523\) −18.6920 10.7918i −0.817342 0.471893i 0.0321570 0.999483i \(-0.489762\pi\)
−0.849499 + 0.527590i \(0.823096\pi\)
\(524\) −16.6769 24.2530i −0.728533 1.05950i
\(525\) 0 0
\(526\) 0.441549 0.839482i 0.0192525 0.0366031i
\(527\) 16.4843 28.5516i 0.718066 1.24373i
\(528\) 0 0
\(529\) 0.636492 + 1.10244i 0.0276736 + 0.0479320i
\(530\) −18.3885 29.1366i −0.798746 1.26561i
\(531\) 0 0
\(532\) 2.89693 14.6174i 0.125598 0.633743i
\(533\) 1.86103i 0.0806100i
\(534\) 0 0
\(535\) −19.6157 + 11.3251i −0.848061 + 0.489628i
\(536\) 3.18099 2.37707i 0.137398 0.102674i
\(537\) 0 0
\(538\) −11.8867 6.25214i −0.512472 0.269549i
\(539\) 26.2428 14.2807i 1.13036 0.615112i
\(540\) 0 0
\(541\) 21.1762 36.6783i 0.910437 1.57692i 0.0969897 0.995285i \(-0.469079\pi\)
0.813448 0.581638i \(-0.197588\pi\)
\(542\) 0.956108 + 24.2635i 0.0410684 + 1.04220i
\(543\) 0 0
\(544\) −3.54742 17.7806i −0.152094 0.762339i
\(545\) 38.9488i 1.66838i
\(546\) 0 0
\(547\) 36.9243i 1.57877i 0.613899 + 0.789385i \(0.289600\pi\)
−0.613899 + 0.789385i \(0.710400\pi\)
\(548\) 0.624460 + 7.91125i 0.0266756 + 0.337952i
\(549\) 0 0
\(550\) 4.03653 0.159061i 0.172118 0.00678236i
\(551\) −5.45203 + 9.44320i −0.232264 + 0.402294i
\(552\) 0 0
\(553\) 2.11861 0.539118i 0.0900922 0.0229256i
\(554\) 6.48375 12.3270i 0.275468 0.523725i
\(555\) 0 0
\(556\) −34.6057 16.4963i −1.46761 0.699600i
\(557\) 13.1808 7.60993i 0.558488 0.322443i −0.194050 0.980992i \(-0.562163\pi\)
0.752538 + 0.658548i \(0.228829\pi\)
\(558\) 0 0
\(559\) 4.36412i 0.184583i
\(560\) −17.6588 13.1609i −0.746221 0.556149i
\(561\) 0 0
\(562\) 8.67635 5.47577i 0.365990 0.230981i
\(563\) −8.71740 15.0990i −0.367395 0.636346i 0.621763 0.783206i \(-0.286417\pi\)
−0.989157 + 0.146859i \(0.953084\pi\)
\(564\) 0 0
\(565\) −13.6701 + 23.6772i −0.575104 + 0.996109i
\(566\) −3.52480 1.85397i −0.148158 0.0779281i
\(567\) 0 0
\(568\) 33.4613 3.97211i 1.40400 0.166666i
\(569\) 18.0368 + 10.4136i 0.756144 + 0.436560i 0.827909 0.560862i \(-0.189530\pi\)
−0.0717659 + 0.997422i \(0.522863\pi\)
\(570\) 0 0
\(571\) 17.8090 10.2820i 0.745282 0.430289i −0.0787048 0.996898i \(-0.525078\pi\)
0.823987 + 0.566609i \(0.191745\pi\)
\(572\) 40.9026 3.22857i 1.71022 0.134993i
\(573\) 0 0
\(574\) 0.337372 1.40889i 0.0140816 0.0588058i
\(575\) 3.11956 0.130095
\(576\) 0 0
\(577\) −1.58033 2.73721i −0.0657900 0.113952i 0.831254 0.555893i \(-0.187623\pi\)
−0.897044 + 0.441941i \(0.854290\pi\)
\(578\) −9.50606 + 0.374589i −0.395400 + 0.0155808i
\(579\) 0 0
\(580\) 9.13098 + 13.2791i 0.379143 + 0.551385i
\(581\) 10.7795 10.5109i 0.447211 0.436064i
\(582\) 0 0
\(583\) −43.2724 24.9833i −1.79216 1.03470i
\(584\) −20.7952 27.8282i −0.860513 1.15154i
\(585\) 0 0
\(586\) 8.20605 5.17895i 0.338989 0.213940i
\(587\) −22.1152 −0.912792 −0.456396 0.889777i \(-0.650860\pi\)
−0.456396 + 0.889777i \(0.650860\pi\)
\(588\) 0 0
\(589\) −28.9672 −1.19357
\(590\) 9.22120 5.81963i 0.379631 0.239590i
\(591\) 0 0
\(592\) 1.08156 0.171813i 0.0444520 0.00706147i
\(593\) −36.0411 20.8083i −1.48003 0.854496i −0.480286 0.877112i \(-0.659467\pi\)
−0.999744 + 0.0226166i \(0.992800\pi\)
\(594\) 0 0
\(595\) 12.6350 12.3201i 0.517985 0.505074i
\(596\) 9.32245 6.41030i 0.381862 0.262576i
\(597\) 0 0
\(598\) 31.6600 1.24757i 1.29468 0.0510170i
\(599\) 19.1656 + 33.1958i 0.783086 + 1.35634i 0.930136 + 0.367215i \(0.119689\pi\)
−0.147050 + 0.989129i \(0.546978\pi\)
\(600\) 0 0
\(601\) 29.3369 1.19668 0.598338 0.801244i \(-0.295828\pi\)
0.598338 + 0.801244i \(0.295828\pi\)
\(602\) 0.791139 3.30385i 0.0322444 0.134655i
\(603\) 0 0
\(604\) 1.52316 + 19.2969i 0.0619766 + 0.785179i
\(605\) −13.0064 + 7.50926i −0.528786 + 0.305295i
\(606\) 0 0
\(607\) 31.4700 + 18.1692i 1.27733 + 0.737465i 0.976356 0.216168i \(-0.0693558\pi\)
0.300971 + 0.953633i \(0.402689\pi\)
\(608\) −11.9712 + 10.5106i −0.485495 + 0.426262i
\(609\) 0 0
\(610\) 20.8986 + 10.9922i 0.846158 + 0.445061i
\(611\) −18.8841 + 32.7082i −0.763968 + 1.32323i
\(612\) 0 0
\(613\) −13.9621 24.1831i −0.563925 0.976746i −0.997149 0.0754602i \(-0.975957\pi\)
0.433224 0.901286i \(-0.357376\pi\)
\(614\) 9.92191 6.26185i 0.400416 0.252708i
\(615\) 0 0
\(616\) −31.5505 4.97074i −1.27121 0.200277i
\(617\) 1.74855i 0.0703940i −0.999380 0.0351970i \(-0.988794\pi\)
0.999380 0.0351970i \(-0.0112059\pi\)
\(618\) 0 0
\(619\) 17.8090 10.2820i 0.715803 0.413269i −0.0974033 0.995245i \(-0.531054\pi\)
0.813206 + 0.581976i \(0.197720\pi\)
\(620\) −18.4220 + 38.6454i −0.739846 + 1.55204i
\(621\) 0 0
\(622\) −11.4293 + 21.7295i −0.458271 + 0.871273i
\(623\) 7.75002 1.97213i 0.310498 0.0790119i
\(624\) 0 0
\(625\) 10.6029 18.3648i 0.424116 0.734591i
\(626\) −11.2366 + 0.442780i −0.449103 + 0.0176970i
\(627\) 0 0
\(628\) 11.7357 0.926332i 0.468304 0.0369647i
\(629\) 0.877511i 0.0349887i
\(630\) 0 0
\(631\) 14.5144i 0.577810i −0.957358 0.288905i \(-0.906709\pi\)
0.957358 0.288905i \(-0.0932912\pi\)
\(632\) −2.14759 0.921801i −0.0854266 0.0366673i
\(633\) 0 0
\(634\) 0.121562 + 3.08491i 0.00482784 + 0.122518i
\(635\) 5.00077 8.66158i 0.198449 0.343724i
\(636\) 0 0
\(637\) −0.849109 + 33.6351i −0.0336429 + 1.33267i
\(638\) 20.6846 + 10.8797i 0.818912 + 0.430730i
\(639\) 0 0
\(640\) 6.40912 + 22.6552i 0.253343 + 0.895525i
\(641\) 43.6375 25.1941i 1.72358 0.995108i 0.812391 0.583113i \(-0.198165\pi\)
0.911186 0.411995i \(-0.135168\pi\)
\(642\) 0 0
\(643\) 40.2212i 1.58617i −0.609111 0.793085i \(-0.708474\pi\)
0.609111 0.793085i \(-0.291526\pi\)
\(644\) −24.1943 4.79494i −0.953390 0.188947i
\(645\) 0 0
\(646\) −6.81280 10.7949i −0.268046 0.424719i
\(647\) 10.1498 + 17.5800i 0.399031 + 0.691142i 0.993607 0.112898i \(-0.0360133\pi\)
−0.594576 + 0.804040i \(0.702680\pi\)
\(648\) 0 0
\(649\) 7.90676 13.6949i 0.310368 0.537572i
\(650\) −2.11774 + 4.02629i −0.0830648 + 0.157924i
\(651\) 0 0
\(652\) 15.9859 10.9922i 0.626055 0.430488i
\(653\) 16.4671 + 9.50728i 0.644407 + 0.372049i 0.786310 0.617832i \(-0.211989\pi\)
−0.141903 + 0.989881i \(0.545322\pi\)
\(654\) 0 0
\(655\) −26.5230 + 15.3131i −1.03634 + 0.598331i
\(656\) −1.20315 + 0.975209i −0.0469751 + 0.0380755i
\(657\) 0 0
\(658\) 20.2256 21.3383i 0.788474 0.831853i
\(659\) −20.4920 −0.798256 −0.399128 0.916895i \(-0.630687\pi\)
−0.399128 + 0.916895i \(0.630687\pi\)
\(660\) 0 0
\(661\) 9.67706 + 16.7612i 0.376394 + 0.651933i 0.990535 0.137263i \(-0.0438306\pi\)
−0.614141 + 0.789197i \(0.710497\pi\)
\(662\) 0.750403 + 19.0432i 0.0291652 + 0.740135i
\(663\) 0 0
\(664\) −15.9831 + 1.89732i −0.620264 + 0.0736301i
\(665\) −14.9253 4.20180i −0.578779 0.162939i
\(666\) 0 0
\(667\) 15.6302 + 9.02408i 0.605203 + 0.349414i
\(668\) 15.8539 33.2581i 0.613406 1.28679i
\(669\) 0 0
\(670\) −2.20527 3.49425i −0.0851970 0.134995i
\(671\) 34.2447 1.32200
\(672\) 0 0
\(673\) −18.9180 −0.729236 −0.364618 0.931157i \(-0.618800\pi\)
−0.364618 + 0.931157i \(0.618800\pi\)
\(674\) 13.1474 + 20.8321i 0.506420 + 0.802423i
\(675\) 0 0
\(676\) −8.69463 + 18.2395i −0.334409 + 0.701518i
\(677\) 5.94225 + 3.43076i 0.228379 + 0.131855i 0.609824 0.792537i \(-0.291240\pi\)
−0.381445 + 0.924392i \(0.624573\pi\)
\(678\) 0 0
\(679\) −28.9772 + 28.2549i −1.11204 + 1.08432i
\(680\) −18.7342 + 2.22390i −0.718425 + 0.0852825i
\(681\) 0 0
\(682\) 2.44467 + 62.0391i 0.0936112 + 2.37560i
\(683\) −11.2294 19.4499i −0.429682 0.744232i 0.567163 0.823606i \(-0.308041\pi\)
−0.996845 + 0.0793743i \(0.974708\pi\)
\(684\) 0 0
\(685\) 8.25744 0.315500
\(686\) 6.74027 25.3095i 0.257345 0.966320i
\(687\) 0 0
\(688\) −2.82140 + 2.28687i −0.107565 + 0.0871862i
\(689\) 48.7313 28.1350i 1.85651 1.07186i
\(690\) 0 0
\(691\) 37.8628 + 21.8601i 1.44037 + 0.831598i 0.997874 0.0651733i \(-0.0207600\pi\)
0.442495 + 0.896771i \(0.354093\pi\)
\(692\) −11.6703 + 8.02473i −0.443638 + 0.305054i
\(693\) 0 0
\(694\) 1.45403 2.76443i 0.0551943 0.104936i
\(695\) −19.9450 + 34.5457i −0.756556 + 1.31039i
\(696\) 0 0
\(697\) −0.620494 1.07473i −0.0235029 0.0407082i
\(698\) 23.6438 + 37.4636i 0.894931 + 1.41802i
\(699\) 0 0
\(700\) 2.33313 2.66419i 0.0881840 0.100697i
\(701\) 5.48856i 0.207300i 0.994614 + 0.103650i \(0.0330522\pi\)
−0.994614 + 0.103650i \(0.966948\pi\)
\(702\) 0 0
\(703\) 0.667714 0.385505i 0.0251833 0.0145396i
\(704\) 23.5209 + 24.7516i 0.886477 + 0.932862i
\(705\) 0 0
\(706\) −8.63708 4.54292i −0.325061 0.170975i
\(707\) −0.277599 + 0.986067i −0.0104402 + 0.0370849i
\(708\) 0 0
\(709\) 5.37290 9.30614i 0.201784 0.349500i −0.747320 0.664465i \(-0.768660\pi\)
0.949103 + 0.314965i \(0.101993\pi\)
\(710\) −1.38054 35.0345i −0.0518109 1.31482i
\(711\) 0 0
\(712\) −7.85606 3.37202i −0.294418 0.126372i
\(713\) 47.9459i 1.79559i
\(714\) 0 0
\(715\) 42.6924i 1.59661i
\(716\) −42.1097 + 3.32385i −1.57371 + 0.124218i
\(717\) 0 0
\(718\) −18.5785 + 0.732092i −0.693345 + 0.0273214i
\(719\) −1.88369 + 3.26265i −0.0702498 + 0.121676i −0.899011 0.437927i \(-0.855713\pi\)
0.828761 + 0.559603i \(0.189046\pi\)
\(720\) 0 0
\(721\) −34.7067 + 8.83175i −1.29254 + 0.328912i
\(722\) 7.28731 13.8548i 0.271206 0.515621i
\(723\) 0 0
\(724\) 5.28248 11.0815i 0.196322 0.411841i
\(725\) −2.24418 + 1.29568i −0.0833467 + 0.0481202i
\(726\) 0 0
\(727\) 50.2752i 1.86460i −0.361683 0.932301i \(-0.617798\pi\)
0.361683 0.932301i \(-0.382202\pi\)
\(728\) 22.6132 27.9715i 0.838100 1.03669i
\(729\) 0 0
\(730\) −30.5687 + 19.2923i −1.13140 + 0.714041i
\(731\) −1.45506 2.52025i −0.0538175 0.0932146i
\(732\) 0 0
\(733\) −4.70703 + 8.15281i −0.173858 + 0.301131i −0.939765 0.341820i \(-0.888957\pi\)
0.765907 + 0.642951i \(0.222290\pi\)
\(734\) −14.1506 7.44293i −0.522309 0.274724i
\(735\) 0 0
\(736\) 17.3969 + 19.8144i 0.641260 + 0.730369i
\(737\) −5.18950 2.99616i −0.191158 0.110365i
\(738\) 0 0
\(739\) 23.0267 13.2944i 0.847049 0.489044i −0.0126048 0.999921i \(-0.504012\pi\)
0.859654 + 0.510876i \(0.170679\pi\)
\(740\) −0.0896656 1.13597i −0.00329617 0.0417591i
\(741\) 0 0
\(742\) −41.9923 + 12.4654i −1.54159 + 0.457620i
\(743\) 52.2920 1.91841 0.959204 0.282715i \(-0.0912352\pi\)
0.959204 + 0.282715i \(0.0912352\pi\)
\(744\) 0 0
\(745\) −5.88608 10.1950i −0.215649 0.373516i
\(746\) −20.0007 + 0.788135i −0.732279 + 0.0288557i
\(747\) 0 0
\(748\) −22.5445 + 15.5020i −0.824307 + 0.566810i
\(749\) 7.10150 + 27.9072i 0.259483 + 1.01971i
\(750\) 0 0
\(751\) −3.21343 1.85527i −0.117260 0.0676999i 0.440223 0.897888i \(-0.354899\pi\)
−0.557483 + 0.830189i \(0.688233\pi\)
\(752\) −31.0413 + 4.93110i −1.13196 + 0.179819i
\(753\) 0 0
\(754\) −22.2577 + 14.0471i −0.810578 + 0.511567i
\(755\) 20.1413 0.733016
\(756\) 0 0
\(757\) 3.20123 0.116351 0.0581753 0.998306i \(-0.481472\pi\)
0.0581753 + 0.998306i \(0.481472\pi\)
\(758\) −19.4228 + 12.2580i −0.705469 + 0.445231i
\(759\) 0 0
\(760\) 9.92245 + 13.2782i 0.359925 + 0.481652i
\(761\) −30.1032 17.3801i −1.09124 0.630027i −0.157333 0.987546i \(-0.550290\pi\)
−0.933906 + 0.357519i \(0.883623\pi\)
\(762\) 0 0
\(763\) 47.6651 + 13.4187i 1.72559 + 0.485791i
\(764\) 13.3693 + 19.4429i 0.483684 + 0.703418i
\(765\) 0 0
\(766\) −3.84096 + 0.151354i −0.138780 + 0.00546865i
\(767\) 8.90422 + 15.4226i 0.321513 + 0.556876i
\(768\) 0 0
\(769\) −21.6622 −0.781160 −0.390580 0.920569i \(-0.627726\pi\)
−0.390580 + 0.920569i \(0.627726\pi\)
\(770\) −7.73939 + 32.3202i −0.278908 + 1.16474i
\(771\) 0 0
\(772\) −31.5167 + 2.48771i −1.13431 + 0.0895346i
\(773\) 20.9104 12.0727i 0.752096 0.434223i −0.0743545 0.997232i \(-0.523690\pi\)
0.826451 + 0.563009i \(0.190356\pi\)
\(774\) 0 0
\(775\) −5.96177 3.44203i −0.214153 0.123641i
\(776\) 42.9652 5.10030i 1.54236 0.183090i
\(777\) 0 0
\(778\) −25.1518 13.2293i −0.901737 0.474295i
\(779\) −0.545186 + 0.944290i −0.0195333 + 0.0338327i
\(780\) 0 0
\(781\) −25.4239 44.0355i −0.909740 1.57572i
\(782\) −17.8674 + 11.2764i −0.638939 + 0.403243i
\(783\) 0 0
\(784\) −22.1900 + 17.0764i −0.792500 + 0.609872i
\(785\) 12.2492i 0.437192i
\(786\) 0 0
\(787\) 3.52292 2.03396i 0.125578 0.0725028i −0.435895 0.899998i \(-0.643568\pi\)
0.561473 + 0.827495i \(0.310235\pi\)
\(788\) 3.93231 + 1.87451i 0.140083 + 0.0667765i
\(789\) 0 0
\(790\) −1.13202 + 2.15221i −0.0402754 + 0.0765723i
\(791\) 24.2663 + 24.8866i 0.862809 + 0.884865i
\(792\) 0 0
\(793\) −19.2824 + 33.3980i −0.684736 + 1.18600i
\(794\) −22.4170 + 0.883348i −0.795549 + 0.0313488i
\(795\) 0 0
\(796\) 0.862439 + 10.9262i 0.0305683 + 0.387269i
\(797\) 19.6098i 0.694614i −0.937752 0.347307i \(-0.887096\pi\)
0.937752 0.347307i \(-0.112904\pi\)
\(798\) 0 0
\(799\) 25.1849i 0.890979i
\(800\) −3.71273 + 0.740727i −0.131265 + 0.0261886i
\(801\) 0 0
\(802\) 1.78203 + 45.2230i 0.0629255 + 1.59688i
\(803\) −26.2113 + 45.3992i −0.924975 + 1.60210i
\(804\) 0 0
\(805\) −6.95472 + 24.7041i −0.245122 + 0.870704i
\(806\) −61.8818 32.5485i −2.17969 1.14647i
\(807\) 0 0
\(808\) 0.877248 0.655544i 0.0308615 0.0230620i
\(809\) 36.1801 20.8886i 1.27203 0.734405i 0.296657 0.954984i \(-0.404128\pi\)
0.975369 + 0.220580i \(0.0707948\pi\)
\(810\) 0 0
\(811\) 4.61271i 0.161974i −0.996715 0.0809870i \(-0.974193\pi\)
0.996715 0.0809870i \(-0.0258072\pi\)
\(812\) 19.3966 6.59943i 0.680689 0.231594i
\(813\) 0 0
\(814\) −0.881987 1.39751i −0.0309136 0.0489827i
\(815\) −10.0933 17.4821i −0.353552 0.612370i
\(816\) 0 0
\(817\) −1.27847 + 2.21437i −0.0447279 + 0.0774710i
\(818\) 3.18695 6.05910i 0.111429 0.211851i
\(819\) 0 0
\(820\) 0.913069 + 1.32787i 0.0318858 + 0.0463712i
\(821\) −14.0211 8.09506i −0.489339 0.282520i 0.234961 0.972005i \(-0.424504\pi\)
−0.724300 + 0.689485i \(0.757837\pi\)
\(822\) 0 0
\(823\) −13.6183 + 7.86255i −0.474705 + 0.274071i −0.718207 0.695829i \(-0.755037\pi\)
0.243502 + 0.969900i \(0.421704\pi\)
\(824\) 35.1815 + 15.1008i 1.22561 + 0.526062i
\(825\) 0 0
\(826\) −3.94508 13.2898i −0.137267 0.462411i
\(827\) −13.1854 −0.458500 −0.229250 0.973368i \(-0.573627\pi\)
−0.229250 + 0.973368i \(0.573627\pi\)
\(828\) 0 0
\(829\) −17.4266 30.1838i −0.605252 1.04833i −0.992012 0.126147i \(-0.959739\pi\)
0.386759 0.922181i \(-0.373594\pi\)
\(830\) 0.659429 + 16.7345i 0.0228891 + 0.580864i
\(831\) 0 0
\(832\) −37.3837 + 9.00233i −1.29605 + 0.312099i
\(833\) −10.7241 19.7071i −0.371568 0.682811i
\(834\) 0 0
\(835\) −33.2004 19.1682i −1.14895 0.663345i
\(836\) 21.6999 + 10.3442i 0.750507 + 0.357761i
\(837\) 0 0
\(838\) −7.51068 11.9007i −0.259452 0.411102i
\(839\) 10.2242 0.352978 0.176489 0.984303i \(-0.443526\pi\)
0.176489 + 0.984303i \(0.443526\pi\)
\(840\) 0 0
\(841\) 14.0078 0.483027
\(842\) −1.71621 2.71934i −0.0591445 0.0937145i
\(843\) 0 0
\(844\) 15.8881 + 7.57374i 0.546890 + 0.260699i
\(845\) 18.2078 + 10.5123i 0.626368 + 0.361634i
\(846\) 0 0
\(847\) 4.70873 + 18.5042i 0.161794 + 0.635812i
\(848\) 43.7253 + 16.7615i 1.50153 + 0.575592i
\(849\) 0 0
\(850\) −0.119447 3.03124i −0.00409699 0.103971i
\(851\) −0.638079 1.10519i −0.0218731 0.0378853i
\(852\) 0 0
\(853\) 47.4094 1.62327 0.811634 0.584167i \(-0.198578\pi\)
0.811634 + 0.584167i \(0.198578\pi\)
\(854\) 20.6521 21.7883i 0.706702 0.745582i
\(855\) 0 0
\(856\) 12.1424 28.2890i 0.415018 0.966900i
\(857\) 14.6387 8.45163i 0.500047 0.288702i −0.228686 0.973500i \(-0.573443\pi\)
0.728733 + 0.684798i \(0.240110\pi\)
\(858\) 0 0
\(859\) 9.83178 + 5.67638i 0.335456 + 0.193676i 0.658261 0.752790i \(-0.271292\pi\)
−0.322805 + 0.946466i \(0.604626\pi\)
\(860\) 2.14116 + 3.11387i 0.0730128 + 0.106182i
\(861\) 0 0
\(862\) 18.7826 35.7097i 0.639737 1.21628i
\(863\) 15.1464 26.2343i 0.515590 0.893027i −0.484247 0.874932i \(-0.660906\pi\)
0.999836 0.0180959i \(-0.00576043\pi\)
\(864\) 0 0
\(865\) 7.36849 + 12.7626i 0.250536 + 0.433941i
\(866\) −5.93403 9.40248i −0.201647 0.319509i
\(867\) 0 0
\(868\) 40.9470 + 35.8589i 1.38983 + 1.21713i
\(869\) 3.52665i 0.119633i
\(870\) 0 0
\(871\) 5.84417 3.37413i 0.198022 0.114328i
\(872\) −31.6880 42.4049i −1.07309 1.43601i
\(873\) 0 0
\(874\) 16.4299 + 8.64176i 0.555748 + 0.292312i
\(875\) −21.7917 22.3488i −0.736694 0.755526i
\(876\) 0 0
\(877\) 7.82172 13.5476i 0.264121 0.457471i −0.703212 0.710980i \(-0.748252\pi\)
0.967333 + 0.253510i \(0.0815849\pi\)
\(878\) −0.594178 15.0787i −0.0200526 0.508880i
\(879\) 0 0
\(880\) 27.6006 22.3715i 0.930415 0.754144i
\(881\) 23.0836i 0.777705i 0.921300 + 0.388853i \(0.127128\pi\)
−0.921300 + 0.388853i \(0.872872\pi\)
\(882\) 0 0
\(883\) 13.4161i 0.451488i −0.974187 0.225744i \(-0.927519\pi\)
0.974187 0.225744i \(-0.0724813\pi\)
\(884\) −2.42450 30.7159i −0.0815447 1.03309i
\(885\) 0 0
\(886\) 53.6709 2.11492i 1.80311 0.0710520i
\(887\) −23.9872 + 41.5471i −0.805412 + 1.39501i 0.110600 + 0.993865i \(0.464723\pi\)
−0.916012 + 0.401150i \(0.868611\pi\)
\(888\) 0 0
\(889\) −8.87706 9.10399i −0.297727 0.305338i
\(890\) −4.14101 + 7.87296i −0.138807 + 0.263902i
\(891\) 0 0
\(892\) 38.1834 + 18.2018i 1.27847 + 0.609440i
\(893\) −19.1637 + 11.0641i −0.641287 + 0.370247i
\(894\) 0 0
\(895\) 43.9524i 1.46917i
\(896\) 29.9332 0.0381723i 0.999999 0.00127525i
\(897\) 0 0
\(898\) 28.7084 18.1182i 0.958010 0.604614i
\(899\) −19.9138 34.4917i −0.664162 1.15036i
\(900\) 0 0
\(901\) −18.7613 + 32.4955i −0.625029 + 1.08258i
\(902\) 2.06840 + 1.08793i 0.0688701 + 0.0362242i
\(903\) 0 0
\(904\) −4.38030 36.8999i −0.145687 1.22727i
\(905\) −11.0623 6.38681i −0.367723 0.212305i
\(906\) 0 0
\(907\) 8.04388 4.64414i 0.267093 0.154206i −0.360473 0.932770i \(-0.617385\pi\)
0.627566 + 0.778564i \(0.284051\pi\)
\(908\) −56.0157 + 4.42149i −1.85895 + 0.146732i
\(909\) 0 0
\(910\) −27.1632 25.7468i −0.900453 0.853497i
\(911\) −32.4981 −1.07671 −0.538354 0.842719i \(-0.680954\pi\)
−0.538354 + 0.842719i \(0.680954\pi\)
\(912\) 0 0
\(913\) 12.1440 + 21.0340i 0.401907 + 0.696123i
\(914\) −21.2605 + 0.837778i −0.703236 + 0.0277112i
\(915\) 0 0
\(916\) 15.4518 + 22.4715i 0.510543 + 0.742478i
\(917\) 9.60217 + 37.7342i 0.317092 + 1.24609i
\(918\) 0 0
\(919\) −0.384776 0.222151i −0.0126926 0.00732808i 0.493640 0.869666i \(-0.335666\pi\)
−0.506333 + 0.862338i \(0.668999\pi\)
\(920\) 21.9778 16.4234i 0.724587 0.541464i
\(921\) 0 0
\(922\) 36.3227 22.9238i 1.19623 0.754955i
\(923\) 57.2624 1.88482
\(924\) 0 0
\(925\) 0.183231 0.00602459
\(926\) −28.4409 + 17.9494i −0.934626 + 0.589855i
\(927\) 0 0
\(928\) −20.7449 7.02863i −0.680984 0.230726i
\(929\) 14.1031 + 8.14244i 0.462708 + 0.267145i 0.713182 0.700979i \(-0.247253\pi\)
−0.250474 + 0.968123i \(0.580586\pi\)
\(930\) 0 0
\(931\) −10.2842 + 16.8178i −0.337052 + 0.551181i
\(932\) −7.10735 + 4.88715i −0.232809 + 0.160084i
\(933\) 0 0
\(934\) 6.64673 0.261916i 0.217488 0.00857016i
\(935\) 14.2343 + 24.6545i 0.465511 + 0.806289i
\(936\) 0 0
\(937\) 30.9796 1.01206 0.506029 0.862516i \(-0.331113\pi\)
0.506029 + 0.862516i \(0.331113\pi\)
\(938\) −5.03598 + 1.49493i −0.164431 + 0.0488113i
\(939\) 0 0
\(940\) 2.57344 + 32.6028i 0.0839364 + 1.06339i
\(941\) −9.45740 + 5.46023i −0.308302 + 0.177998i −0.646167 0.763196i \(-0.723629\pi\)
0.337864 + 0.941195i \(0.390296\pi\)
\(942\) 0 0
\(943\) 1.56297 + 0.902380i 0.0508972 + 0.0293855i
\(944\) −5.30470 + 13.8382i −0.172653 + 0.450396i
\(945\) 0 0
\(946\) 4.85041 + 2.55121i 0.157700 + 0.0829471i
\(947\) −8.39495 + 14.5405i −0.272799 + 0.472502i −0.969577 0.244785i \(-0.921283\pi\)
0.696778 + 0.717286i \(0.254616\pi\)
\(948\) 0 0
\(949\) −29.5179 51.1264i −0.958190 1.65963i
\(950\) −2.25405 + 1.42256i −0.0731310 + 0.0461540i
\(951\) 0 0
\(952\) −3.73279 + 23.6929i −0.120980 + 0.767891i
\(953\) 39.3512i 1.27471i −0.770570 0.637355i \(-0.780028\pi\)
0.770570 0.637355i \(-0.219972\pi\)
\(954\) 0 0
\(955\) 21.2626 12.2760i 0.688042 0.397241i
\(956\) −6.21481 + 13.0373i −0.201001 + 0.421657i
\(957\) 0 0
\(958\) −2.69276 + 5.11952i −0.0869991 + 0.165404i
\(959\) 2.84487 10.1053i 0.0918657 0.326319i
\(960\) 0 0
\(961\) 37.4020 64.7822i 1.20652 2.08975i
\(962\) 1.85958 0.0732774i 0.0599554 0.00236256i
\(963\) 0 0
\(964\) 9.44022 0.745146i 0.304049 0.0239995i
\(965\) 32.8958i 1.05895i
\(966\) 0 0
\(967\) 9.26652i 0.297991i 0.988838 + 0.148996i \(0.0476040\pi\)
−0.988838 + 0.148996i \(0.952396\pi\)
\(968\) 8.05114 18.7574i 0.258773 0.602885i
\(969\) 0 0
\(970\) −1.77265 44.9852i −0.0569165 1.44439i
\(971\) 14.5837 25.2598i 0.468014 0.810624i −0.531318 0.847173i \(-0.678303\pi\)
0.999332 + 0.0365484i \(0.0116363\pi\)
\(972\) 0 0
\(973\) 35.4051 + 36.3102i 1.13504 + 1.16405i
\(974\) −7.01209 3.68821i −0.224682 0.118178i
\(975\) 0 0
\(976\) −31.6960 + 5.03511i −1.01457 + 0.161170i
\(977\) −43.6149 + 25.1811i −1.39537 + 0.805615i −0.993903 0.110261i \(-0.964831\pi\)
−0.401463 + 0.915875i \(0.631498\pi\)
\(978\) 0 0
\(979\) 12.9007i 0.412309i
\(980\) 15.8964 + 24.4157i 0.507793 + 0.779932i
\(981\) 0 0
\(982\) −7.78136 12.3296i −0.248313 0.393452i
\(983\) −22.4873 38.9491i −0.717233 1.24228i −0.962092 0.272725i \(-0.912075\pi\)
0.244859 0.969559i \(-0.421258\pi\)
\(984\) 0 0
\(985\) 2.26638 3.92549i 0.0722130 0.125077i
\(986\) 8.17011 15.5332i 0.260189 0.494677i
\(987\) 0 0
\(988\) −22.3071 + 15.3388i −0.709684 + 0.487993i
\(989\) 3.66517 + 2.11609i 0.116546 + 0.0672877i
\(990\) 0 0
\(991\) −28.7650 + 16.6075i −0.913749 + 0.527553i −0.881635 0.471931i \(-0.843557\pi\)
−0.0321135 + 0.999484i \(0.510224\pi\)
\(992\) −11.3845 57.0624i −0.361459 1.81173i
\(993\) 0 0
\(994\) −43.3504 10.3807i −1.37499 0.329255i
\(995\) 11.4043 0.361541
\(996\) 0 0
\(997\) 4.80964 + 8.33054i 0.152323 + 0.263831i 0.932081 0.362250i \(-0.117991\pi\)
−0.779758 + 0.626081i \(0.784658\pi\)
\(998\) 0.395146 + 10.0277i 0.0125081 + 0.317423i
\(999\) 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 252.2.be.a.107.11 yes 32
3.2 odd 2 inner 252.2.be.a.107.6 yes 32
4.3 odd 2 inner 252.2.be.a.107.16 yes 32
7.2 even 3 1764.2.e.i.1079.11 16
7.4 even 3 inner 252.2.be.a.179.1 yes 32
7.5 odd 6 1764.2.e.h.1079.11 16
12.11 even 2 inner 252.2.be.a.107.1 32
21.2 odd 6 1764.2.e.i.1079.6 16
21.5 even 6 1764.2.e.h.1079.6 16
21.11 odd 6 inner 252.2.be.a.179.16 yes 32
28.11 odd 6 inner 252.2.be.a.179.6 yes 32
28.19 even 6 1764.2.e.h.1079.5 16
28.23 odd 6 1764.2.e.i.1079.5 16
84.11 even 6 inner 252.2.be.a.179.11 yes 32
84.23 even 6 1764.2.e.i.1079.12 16
84.47 odd 6 1764.2.e.h.1079.12 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.be.a.107.1 32 12.11 even 2 inner
252.2.be.a.107.6 yes 32 3.2 odd 2 inner
252.2.be.a.107.11 yes 32 1.1 even 1 trivial
252.2.be.a.107.16 yes 32 4.3 odd 2 inner
252.2.be.a.179.1 yes 32 7.4 even 3 inner
252.2.be.a.179.6 yes 32 28.11 odd 6 inner
252.2.be.a.179.11 yes 32 84.11 even 6 inner
252.2.be.a.179.16 yes 32 21.11 odd 6 inner
1764.2.e.h.1079.5 16 28.19 even 6
1764.2.e.h.1079.6 16 21.5 even 6
1764.2.e.h.1079.11 16 7.5 odd 6
1764.2.e.h.1079.12 16 84.47 odd 6
1764.2.e.i.1079.5 16 28.23 odd 6
1764.2.e.i.1079.6 16 21.2 odd 6
1764.2.e.i.1079.11 16 7.2 even 3
1764.2.e.i.1079.12 16 84.23 even 6