Properties

Label 297.2.n.b.37.8
Level $297$
Weight $2$
Character 297.37
Analytic conductor $2.372$
Analytic rank $0$
Dimension $72$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [297,2,Mod(37,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.n (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 37.8
Character \(\chi\) \(=\) 297.37
Dual form 297.2.n.b.289.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.161615 - 1.53767i) q^{2} +(-0.382004 - 0.0811974i) q^{4} +(0.0618842 + 0.588789i) q^{5} +(0.483079 - 0.536514i) q^{7} +(0.768973 - 2.36665i) q^{8} +0.915362 q^{10} +(2.56419 - 2.10355i) q^{11} +(-1.43880 + 0.640596i) q^{13} +(-0.746906 - 0.829524i) q^{14} +(-4.22840 - 1.88260i) q^{16} +(3.71501 - 2.69911i) q^{17} +(0.775200 - 2.38582i) q^{19} +(0.0241681 - 0.229944i) q^{20} +(-2.82014 - 4.28284i) q^{22} +(-2.22600 + 3.85554i) q^{23} +(4.54790 - 0.966685i) q^{25} +(0.752490 + 2.31593i) q^{26} +(-0.228102 + 0.165726i) q^{28} +(-4.66961 + 5.18613i) q^{29} +(-8.33906 + 3.71279i) q^{31} +(-1.08974 + 1.88749i) q^{32} +(-3.54993 - 6.14866i) q^{34} +(0.345788 + 0.251230i) q^{35} +(0.893583 + 2.75017i) q^{37} +(-3.54331 - 1.57758i) q^{38} +(1.44105 + 0.306304i) q^{40} +(0.772257 + 0.857678i) q^{41} +(2.10724 + 3.64985i) q^{43} +(-1.15033 + 0.595357i) q^{44} +(5.56879 + 4.04596i) q^{46} +(-0.222583 + 0.0473114i) q^{47} +(0.677218 + 6.44330i) q^{49} +(-0.751430 - 7.14938i) q^{50} +(0.601643 - 0.127883i) q^{52} +(-4.61430 - 3.35249i) q^{53} +(1.39723 + 1.37959i) q^{55} +(-0.898268 - 1.55585i) q^{56} +(7.21985 + 8.01846i) q^{58} +(6.97767 + 1.48315i) q^{59} +(4.16481 + 1.85429i) q^{61} +(4.36131 + 13.4227i) q^{62} +(-4.76295 - 3.46049i) q^{64} +(-0.466215 - 0.807507i) q^{65} +(4.04571 - 7.00738i) q^{67} +(-1.63831 + 0.729422i) q^{68} +(0.442192 - 0.491104i) q^{70} +(-9.95852 + 7.23528i) q^{71} +(4.78461 + 14.7255i) q^{73} +(4.37326 - 0.929564i) q^{74} +(-0.489852 + 0.848448i) q^{76} +(0.110128 - 2.39191i) q^{77} +(1.52816 - 14.5395i) q^{79} +(0.846785 - 2.60614i) q^{80} +(1.44363 - 1.04886i) q^{82} +(6.35188 + 2.82804i) q^{83} +(1.81911 + 2.02032i) q^{85} +(5.95281 - 2.65036i) q^{86} +(-3.00657 - 7.68613i) q^{88} -12.4803 q^{89} +(-0.351367 + 1.08140i) q^{91} +(1.16340 - 1.29209i) q^{92} +(0.0367764 + 0.349904i) q^{94} +(1.45272 + 0.308785i) q^{95} +(-1.48226 + 14.1028i) q^{97} +10.0171 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.161615 1.53767i 0.114279 1.08729i −0.775640 0.631176i \(-0.782573\pi\)
0.889919 0.456119i \(-0.150761\pi\)
\(3\) 0 0
\(4\) −0.382004 0.0811974i −0.191002 0.0405987i
\(5\) 0.0618842 + 0.588789i 0.0276755 + 0.263314i 0.999607 + 0.0280487i \(0.00892935\pi\)
−0.971931 + 0.235266i \(0.924404\pi\)
\(6\) 0 0
\(7\) 0.483079 0.536514i 0.182587 0.202783i −0.644902 0.764265i \(-0.723102\pi\)
0.827489 + 0.561482i \(0.189769\pi\)
\(8\) 0.768973 2.36665i 0.271873 0.836739i
\(9\) 0 0
\(10\) 0.915362 0.289463
\(11\) 2.56419 2.10355i 0.773134 0.634243i
\(12\) 0 0
\(13\) −1.43880 + 0.640596i −0.399052 + 0.177669i −0.596443 0.802656i \(-0.703420\pi\)
0.197391 + 0.980325i \(0.436753\pi\)
\(14\) −0.746906 0.829524i −0.199619 0.221699i
\(15\) 0 0
\(16\) −4.22840 1.88260i −1.05710 0.470651i
\(17\) 3.71501 2.69911i 0.901022 0.654631i −0.0377065 0.999289i \(-0.512005\pi\)
0.938728 + 0.344658i \(0.112005\pi\)
\(18\) 0 0
\(19\) 0.775200 2.38582i 0.177843 0.547345i −0.821909 0.569619i \(-0.807091\pi\)
0.999752 + 0.0222743i \(0.00709072\pi\)
\(20\) 0.0241681 0.229944i 0.00540416 0.0514171i
\(21\) 0 0
\(22\) −2.82014 4.28284i −0.601256 0.913105i
\(23\) −2.22600 + 3.85554i −0.464153 + 0.803937i −0.999163 0.0409092i \(-0.986975\pi\)
0.535010 + 0.844846i \(0.320308\pi\)
\(24\) 0 0
\(25\) 4.54790 0.966685i 0.909579 0.193337i
\(26\) 0.752490 + 2.31593i 0.147576 + 0.454191i
\(27\) 0 0
\(28\) −0.228102 + 0.165726i −0.0431072 + 0.0313192i
\(29\) −4.66961 + 5.18613i −0.867125 + 0.963039i −0.999604 0.0281463i \(-0.991040\pi\)
0.132479 + 0.991186i \(0.457706\pi\)
\(30\) 0 0
\(31\) −8.33906 + 3.71279i −1.49774 + 0.666837i −0.981822 0.189802i \(-0.939216\pi\)
−0.515917 + 0.856638i \(0.672549\pi\)
\(32\) −1.08974 + 1.88749i −0.192641 + 0.333664i
\(33\) 0 0
\(34\) −3.54993 6.14866i −0.608808 1.05449i
\(35\) 0.345788 + 0.251230i 0.0584489 + 0.0424656i
\(36\) 0 0
\(37\) 0.893583 + 2.75017i 0.146904 + 0.452125i 0.997251 0.0740981i \(-0.0236078\pi\)
−0.850347 + 0.526223i \(0.823608\pi\)
\(38\) −3.54331 1.57758i −0.574801 0.255918i
\(39\) 0 0
\(40\) 1.44105 + 0.306304i 0.227850 + 0.0484309i
\(41\) 0.772257 + 0.857678i 0.120606 + 0.133947i 0.800424 0.599434i \(-0.204608\pi\)
−0.679818 + 0.733381i \(0.737941\pi\)
\(42\) 0 0
\(43\) 2.10724 + 3.64985i 0.321351 + 0.556596i 0.980767 0.195182i \(-0.0625297\pi\)
−0.659416 + 0.751778i \(0.729196\pi\)
\(44\) −1.15033 + 0.595357i −0.173419 + 0.0897534i
\(45\) 0 0
\(46\) 5.56879 + 4.04596i 0.821073 + 0.596544i
\(47\) −0.222583 + 0.0473114i −0.0324670 + 0.00690108i −0.224117 0.974562i \(-0.571950\pi\)
0.191650 + 0.981463i \(0.438616\pi\)
\(48\) 0 0
\(49\) 0.677218 + 6.44330i 0.0967454 + 0.920471i
\(50\) −0.751430 7.14938i −0.106268 1.01107i
\(51\) 0 0
\(52\) 0.601643 0.127883i 0.0834328 0.0177342i
\(53\) −4.61430 3.35249i −0.633823 0.460500i 0.223899 0.974612i \(-0.428121\pi\)
−0.857723 + 0.514113i \(0.828121\pi\)
\(54\) 0 0
\(55\) 1.39723 + 1.37959i 0.188402 + 0.186024i
\(56\) −0.898268 1.55585i −0.120036 0.207909i
\(57\) 0 0
\(58\) 7.21985 + 8.01846i 0.948013 + 1.05288i
\(59\) 6.97767 + 1.48315i 0.908415 + 0.193090i 0.638344 0.769751i \(-0.279620\pi\)
0.270071 + 0.962841i \(0.412953\pi\)
\(60\) 0 0
\(61\) 4.16481 + 1.85429i 0.533250 + 0.237418i 0.655653 0.755062i \(-0.272393\pi\)
−0.122403 + 0.992480i \(0.539060\pi\)
\(62\) 4.36131 + 13.4227i 0.553887 + 1.70469i
\(63\) 0 0
\(64\) −4.76295 3.46049i −0.595369 0.432561i
\(65\) −0.466215 0.807507i −0.0578268 0.100159i
\(66\) 0 0
\(67\) 4.04571 7.00738i 0.494262 0.856087i −0.505716 0.862700i \(-0.668772\pi\)
0.999978 + 0.00661279i \(0.00210493\pi\)
\(68\) −1.63831 + 0.729422i −0.198674 + 0.0884554i
\(69\) 0 0
\(70\) 0.442192 0.491104i 0.0528521 0.0586982i
\(71\) −9.95852 + 7.23528i −1.18186 + 0.858670i −0.992380 0.123215i \(-0.960680\pi\)
−0.189478 + 0.981885i \(0.560680\pi\)
\(72\) 0 0
\(73\) 4.78461 + 14.7255i 0.559996 + 1.72349i 0.682370 + 0.731007i \(0.260950\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(74\) 4.37326 0.929564i 0.508381 0.108060i
\(75\) 0 0
\(76\) −0.489852 + 0.848448i −0.0561899 + 0.0973237i
\(77\) 0.110128 2.39191i 0.0125502 0.272583i
\(78\) 0 0
\(79\) 1.52816 14.5395i 0.171931 1.63582i −0.479807 0.877374i \(-0.659293\pi\)
0.651738 0.758444i \(-0.274040\pi\)
\(80\) 0.846785 2.60614i 0.0946734 0.291375i
\(81\) 0 0
\(82\) 1.44363 1.04886i 0.159422 0.115827i
\(83\) 6.35188 + 2.82804i 0.697210 + 0.310418i 0.724564 0.689208i \(-0.242041\pi\)
−0.0273537 + 0.999626i \(0.508708\pi\)
\(84\) 0 0
\(85\) 1.81911 + 2.02032i 0.197310 + 0.219135i
\(86\) 5.95281 2.65036i 0.641908 0.285796i
\(87\) 0 0
\(88\) −3.00657 7.68613i −0.320502 0.819344i
\(89\) −12.4803 −1.32291 −0.661453 0.749986i \(-0.730060\pi\)
−0.661453 + 0.749986i \(0.730060\pi\)
\(90\) 0 0
\(91\) −0.351367 + 1.08140i −0.0368332 + 0.113361i
\(92\) 1.16340 1.29209i 0.121293 0.134709i
\(93\) 0 0
\(94\) 0.0367764 + 0.349904i 0.00379320 + 0.0360899i
\(95\) 1.45272 + 0.308785i 0.149046 + 0.0316806i
\(96\) 0 0
\(97\) −1.48226 + 14.1028i −0.150501 + 1.43192i 0.615021 + 0.788511i \(0.289148\pi\)
−0.765522 + 0.643410i \(0.777519\pi\)
\(98\) 10.0171 1.01188
\(99\) 0 0
\(100\) −1.81581 −0.181581
\(101\) −1.50192 + 14.2898i −0.149447 + 1.42189i 0.620712 + 0.784039i \(0.286844\pi\)
−0.770159 + 0.637852i \(0.779823\pi\)
\(102\) 0 0
\(103\) 4.33207 + 0.920810i 0.426852 + 0.0907301i 0.416328 0.909214i \(-0.363317\pi\)
0.0105237 + 0.999945i \(0.496650\pi\)
\(104\) 0.409670 + 3.89775i 0.0401714 + 0.382206i
\(105\) 0 0
\(106\) −5.90075 + 6.55345i −0.573132 + 0.636527i
\(107\) 4.86529 14.9738i 0.470345 1.44757i −0.381788 0.924250i \(-0.624692\pi\)
0.852134 0.523324i \(-0.175308\pi\)
\(108\) 0 0
\(109\) −13.6970 −1.31194 −0.655969 0.754788i \(-0.727740\pi\)
−0.655969 + 0.754788i \(0.727740\pi\)
\(110\) 2.34717 1.92551i 0.223794 0.183590i
\(111\) 0 0
\(112\) −3.05269 + 1.35915i −0.288452 + 0.128427i
\(113\) −5.37321 5.96755i −0.505469 0.561380i 0.435363 0.900255i \(-0.356620\pi\)
−0.940831 + 0.338875i \(0.889954\pi\)
\(114\) 0 0
\(115\) −2.40786 1.07205i −0.224534 0.0999688i
\(116\) 2.20491 1.60196i 0.204721 0.148738i
\(117\) 0 0
\(118\) 3.40829 10.4896i 0.313758 0.965648i
\(119\) 0.346533 3.29704i 0.0317666 0.302239i
\(120\) 0 0
\(121\) 2.15019 10.7878i 0.195472 0.980709i
\(122\) 3.52438 6.10441i 0.319083 0.552668i
\(123\) 0 0
\(124\) 3.48702 0.741190i 0.313144 0.0665608i
\(125\) 1.76536 + 5.43321i 0.157898 + 0.485961i
\(126\) 0 0
\(127\) 9.70522 7.05126i 0.861199 0.625698i −0.0670118 0.997752i \(-0.521347\pi\)
0.928211 + 0.372054i \(0.121347\pi\)
\(128\) −9.00756 + 10.0039i −0.796163 + 0.884229i
\(129\) 0 0
\(130\) −1.31702 + 0.586377i −0.115511 + 0.0514287i
\(131\) −3.44555 + 5.96786i −0.301039 + 0.521414i −0.976372 0.216099i \(-0.930667\pi\)
0.675333 + 0.737513i \(0.264000\pi\)
\(132\) 0 0
\(133\) −0.905543 1.56845i −0.0785205 0.136002i
\(134\) −10.1212 7.35345i −0.874335 0.635242i
\(135\) 0 0
\(136\) −3.53112 10.8677i −0.302791 0.931896i
\(137\) −8.44714 3.76091i −0.721688 0.321316i 0.0128184 0.999918i \(-0.495920\pi\)
−0.734507 + 0.678602i \(0.762586\pi\)
\(138\) 0 0
\(139\) −21.1390 4.49324i −1.79299 0.381112i −0.813334 0.581797i \(-0.802350\pi\)
−0.979656 + 0.200685i \(0.935683\pi\)
\(140\) −0.111693 0.124048i −0.00943980 0.0104840i
\(141\) 0 0
\(142\) 9.51601 + 16.4822i 0.798566 + 1.38316i
\(143\) −2.34184 + 4.66920i −0.195835 + 0.390458i
\(144\) 0 0
\(145\) −3.34251 2.42847i −0.277580 0.201674i
\(146\) 23.4162 4.97727i 1.93794 0.411922i
\(147\) 0 0
\(148\) −0.118046 1.12313i −0.00970331 0.0923208i
\(149\) −0.119835 1.14015i −0.00981725 0.0934049i 0.988516 0.151116i \(-0.0482866\pi\)
−0.998333 + 0.0577107i \(0.981620\pi\)
\(150\) 0 0
\(151\) −0.861396 + 0.183095i −0.0700994 + 0.0149001i −0.242828 0.970069i \(-0.578075\pi\)
0.172728 + 0.984969i \(0.444742\pi\)
\(152\) −5.05031 3.66926i −0.409634 0.297616i
\(153\) 0 0
\(154\) −3.66015 0.555908i −0.294944 0.0447963i
\(155\) −2.70211 4.68018i −0.217038 0.375921i
\(156\) 0 0
\(157\) −6.54825 7.27257i −0.522608 0.580415i 0.422834 0.906207i \(-0.361035\pi\)
−0.945441 + 0.325793i \(0.894369\pi\)
\(158\) −22.1099 4.69960i −1.75897 0.373880i
\(159\) 0 0
\(160\) −1.17877 0.524822i −0.0931899 0.0414908i
\(161\) 0.993219 + 3.05681i 0.0782766 + 0.240911i
\(162\) 0 0
\(163\) −3.74555 2.72130i −0.293374 0.213149i 0.431355 0.902182i \(-0.358035\pi\)
−0.724730 + 0.689033i \(0.758035\pi\)
\(164\) −0.225364 0.390342i −0.0175980 0.0304806i
\(165\) 0 0
\(166\) 5.37515 9.31002i 0.417192 0.722598i
\(167\) 15.5187 6.90939i 1.20088 0.534665i 0.293896 0.955837i \(-0.405048\pi\)
0.906980 + 0.421173i \(0.138381\pi\)
\(168\) 0 0
\(169\) −7.03891 + 7.81750i −0.541455 + 0.601346i
\(170\) 3.40058 2.47066i 0.260812 0.189491i
\(171\) 0 0
\(172\) −0.508616 1.56536i −0.0387816 0.119357i
\(173\) −0.578140 + 0.122887i −0.0439551 + 0.00934296i −0.229837 0.973229i \(-0.573819\pi\)
0.185882 + 0.982572i \(0.440486\pi\)
\(174\) 0 0
\(175\) 1.67835 2.90699i 0.126872 0.219748i
\(176\) −14.8026 + 4.06727i −1.11579 + 0.306582i
\(177\) 0 0
\(178\) −2.01700 + 19.1905i −0.151181 + 1.43839i
\(179\) 2.97921 9.16907i 0.222677 0.685328i −0.775842 0.630927i \(-0.782675\pi\)
0.998519 0.0544017i \(-0.0173251\pi\)
\(180\) 0 0
\(181\) 3.85243 2.79896i 0.286349 0.208045i −0.435333 0.900270i \(-0.643369\pi\)
0.721682 + 0.692225i \(0.243369\pi\)
\(182\) 1.60604 + 0.715055i 0.119048 + 0.0530034i
\(183\) 0 0
\(184\) 7.41301 + 8.23298i 0.546494 + 0.606943i
\(185\) −1.56397 + 0.696324i −0.114985 + 0.0511947i
\(186\) 0 0
\(187\) 3.84830 14.7357i 0.281415 1.07758i
\(188\) 0.0888691 0.00648144
\(189\) 0 0
\(190\) 0.709589 2.18389i 0.0514790 0.158436i
\(191\) 3.47816 3.86289i 0.251671 0.279509i −0.604050 0.796946i \(-0.706447\pi\)
0.855721 + 0.517438i \(0.173114\pi\)
\(192\) 0 0
\(193\) −0.341604 3.25014i −0.0245892 0.233950i −0.999913 0.0131723i \(-0.995807\pi\)
0.975324 0.220778i \(-0.0708597\pi\)
\(194\) 21.4458 + 4.55845i 1.53972 + 0.327278i
\(195\) 0 0
\(196\) 0.264479 2.51635i 0.0188914 0.179739i
\(197\) 22.4626 1.60039 0.800197 0.599737i \(-0.204728\pi\)
0.800197 + 0.599737i \(0.204728\pi\)
\(198\) 0 0
\(199\) −20.8291 −1.47654 −0.738269 0.674507i \(-0.764356\pi\)
−0.738269 + 0.674507i \(0.764356\pi\)
\(200\) 1.20940 11.5067i 0.0855173 0.813643i
\(201\) 0 0
\(202\) 21.7303 + 4.61891i 1.52894 + 0.324985i
\(203\) 0.526637 + 5.01062i 0.0369627 + 0.351677i
\(204\) 0 0
\(205\) −0.457201 + 0.507773i −0.0319323 + 0.0354644i
\(206\) 2.11603 6.51246i 0.147431 0.453745i
\(207\) 0 0
\(208\) 7.28981 0.505457
\(209\) −3.03092 7.74838i −0.209653 0.535966i
\(210\) 0 0
\(211\) 3.09877 1.37966i 0.213328 0.0949797i −0.297291 0.954787i \(-0.596083\pi\)
0.510619 + 0.859807i \(0.329416\pi\)
\(212\) 1.49047 + 1.65533i 0.102366 + 0.113689i
\(213\) 0 0
\(214\) −22.2384 9.90119i −1.52019 0.676831i
\(215\) −2.01858 + 1.46659i −0.137666 + 0.100020i
\(216\) 0 0
\(217\) −2.03646 + 6.26759i −0.138244 + 0.425472i
\(218\) −2.21365 + 21.0615i −0.149927 + 1.42646i
\(219\) 0 0
\(220\) −0.421727 0.640461i −0.0284328 0.0431799i
\(221\) −3.61612 + 6.26330i −0.243247 + 0.421315i
\(222\) 0 0
\(223\) 10.7854 2.29252i 0.722246 0.153518i 0.167900 0.985804i \(-0.446302\pi\)
0.554347 + 0.832286i \(0.312968\pi\)
\(224\) 0.486232 + 1.49647i 0.0324877 + 0.0999870i
\(225\) 0 0
\(226\) −10.0445 + 7.29775i −0.668150 + 0.485439i
\(227\) 3.99263 4.43426i 0.265000 0.294312i −0.595929 0.803037i \(-0.703216\pi\)
0.860929 + 0.508725i \(0.169883\pi\)
\(228\) 0 0
\(229\) 22.6109 10.0670i 1.49417 0.665246i 0.512998 0.858390i \(-0.328535\pi\)
0.981171 + 0.193144i \(0.0618683\pi\)
\(230\) −2.03760 + 3.52922i −0.134355 + 0.232710i
\(231\) 0 0
\(232\) 8.68297 + 15.0393i 0.570065 + 0.987381i
\(233\) 3.38850 + 2.46189i 0.221988 + 0.161284i 0.693221 0.720725i \(-0.256191\pi\)
−0.471233 + 0.882009i \(0.656191\pi\)
\(234\) 0 0
\(235\) −0.0416308 0.128126i −0.00271569 0.00835805i
\(236\) −2.54507 1.13314i −0.165670 0.0737610i
\(237\) 0 0
\(238\) −5.01374 1.06570i −0.324992 0.0690793i
\(239\) 4.93340 + 5.47909i 0.319115 + 0.354413i 0.881265 0.472622i \(-0.156692\pi\)
−0.562150 + 0.827035i \(0.690026\pi\)
\(240\) 0 0
\(241\) 4.41462 + 7.64634i 0.284371 + 0.492544i 0.972456 0.233085i \(-0.0748821\pi\)
−0.688086 + 0.725629i \(0.741549\pi\)
\(242\) −16.2405 5.04975i −1.04398 0.324610i
\(243\) 0 0
\(244\) −1.44041 1.04652i −0.0922129 0.0669966i
\(245\) −3.75183 + 0.797476i −0.239696 + 0.0509489i
\(246\) 0 0
\(247\) 0.412987 + 3.92931i 0.0262778 + 0.250016i
\(248\) 2.37438 + 22.5907i 0.150773 + 1.43451i
\(249\) 0 0
\(250\) 8.63977 1.83644i 0.546427 0.116147i
\(251\) 16.6439 + 12.0925i 1.05056 + 0.763274i 0.972318 0.233661i \(-0.0750704\pi\)
0.0782385 + 0.996935i \(0.475070\pi\)
\(252\) 0 0
\(253\) 2.40242 + 14.5689i 0.151039 + 0.915936i
\(254\) −9.27397 16.0630i −0.581901 1.00788i
\(255\) 0 0
\(256\) 6.04813 + 6.71713i 0.378008 + 0.419820i
\(257\) −3.30847 0.703238i −0.206377 0.0438668i 0.103563 0.994623i \(-0.466976\pi\)
−0.309940 + 0.950756i \(0.600309\pi\)
\(258\) 0 0
\(259\) 1.90717 + 0.849129i 0.118506 + 0.0527623i
\(260\) 0.112528 + 0.346326i 0.00697871 + 0.0214783i
\(261\) 0 0
\(262\) 8.61973 + 6.26260i 0.532528 + 0.386905i
\(263\) −7.14112 12.3688i −0.440341 0.762692i 0.557374 0.830262i \(-0.311809\pi\)
−0.997715 + 0.0675692i \(0.978476\pi\)
\(264\) 0 0
\(265\) 1.68836 2.92432i 0.103715 0.179639i
\(266\) −2.55810 + 1.13894i −0.156847 + 0.0698328i
\(267\) 0 0
\(268\) −2.11446 + 2.34834i −0.129161 + 0.143448i
\(269\) 5.43693 3.95016i 0.331495 0.240845i −0.409570 0.912279i \(-0.634321\pi\)
0.741065 + 0.671433i \(0.234321\pi\)
\(270\) 0 0
\(271\) −1.23000 3.78554i −0.0747170 0.229955i 0.906722 0.421728i \(-0.138576\pi\)
−0.981439 + 0.191773i \(0.938576\pi\)
\(272\) −20.7899 + 4.41903i −1.26057 + 0.267943i
\(273\) 0 0
\(274\) −7.14821 + 12.3811i −0.431839 + 0.747968i
\(275\) 9.62822 12.0455i 0.580604 0.726370i
\(276\) 0 0
\(277\) 1.37267 13.0601i 0.0824756 0.784703i −0.872619 0.488402i \(-0.837580\pi\)
0.955094 0.296301i \(-0.0957533\pi\)
\(278\) −10.3255 + 31.7786i −0.619282 + 1.90595i
\(279\) 0 0
\(280\) 0.860476 0.625172i 0.0514233 0.0373612i
\(281\) 2.71128 + 1.20714i 0.161742 + 0.0720120i 0.486011 0.873953i \(-0.338452\pi\)
−0.324269 + 0.945965i \(0.605118\pi\)
\(282\) 0 0
\(283\) 5.41512 + 6.01410i 0.321896 + 0.357501i 0.882275 0.470735i \(-0.156011\pi\)
−0.560379 + 0.828236i \(0.689345\pi\)
\(284\) 4.39168 1.95530i 0.260598 0.116026i
\(285\) 0 0
\(286\) 6.80119 + 4.35559i 0.402163 + 0.257551i
\(287\) 0.833217 0.0491833
\(288\) 0 0
\(289\) 1.26279 3.88648i 0.0742820 0.228616i
\(290\) −4.27438 + 4.74718i −0.251000 + 0.278764i
\(291\) 0 0
\(292\) −0.632066 6.01370i −0.0369888 0.351925i
\(293\) −15.3722 3.26745i −0.898051 0.190887i −0.264315 0.964436i \(-0.585146\pi\)
−0.633736 + 0.773550i \(0.718479\pi\)
\(294\) 0 0
\(295\) −0.441454 + 4.20016i −0.0257025 + 0.244543i
\(296\) 7.19584 0.418249
\(297\) 0 0
\(298\) −1.77254 −0.102681
\(299\) 0.732926 6.97333i 0.0423862 0.403278i
\(300\) 0 0
\(301\) 2.97616 + 0.632602i 0.171543 + 0.0364626i
\(302\) 0.142325 + 1.35413i 0.00818988 + 0.0779215i
\(303\) 0 0
\(304\) −7.76941 + 8.62880i −0.445606 + 0.494896i
\(305\) −0.834052 + 2.56695i −0.0477577 + 0.146983i
\(306\) 0 0
\(307\) −3.51315 −0.200506 −0.100253 0.994962i \(-0.531965\pi\)
−0.100253 + 0.994962i \(0.531965\pi\)
\(308\) −0.236286 + 0.904775i −0.0134636 + 0.0515543i
\(309\) 0 0
\(310\) −7.63326 + 3.39855i −0.433540 + 0.193025i
\(311\) −17.6212 19.5703i −0.999205 1.10973i −0.993960 0.109743i \(-0.964997\pi\)
−0.00524459 0.999986i \(-0.501669\pi\)
\(312\) 0 0
\(313\) −2.24836 1.00104i −0.127085 0.0565819i 0.342209 0.939624i \(-0.388825\pi\)
−0.469294 + 0.883042i \(0.655492\pi\)
\(314\) −12.2411 + 8.89367i −0.690805 + 0.501899i
\(315\) 0 0
\(316\) −1.76433 + 5.43005i −0.0992513 + 0.305464i
\(317\) −2.77075 + 26.3619i −0.155621 + 1.48063i 0.586271 + 0.810115i \(0.300595\pi\)
−0.741892 + 0.670519i \(0.766071\pi\)
\(318\) 0 0
\(319\) −1.06453 + 23.1210i −0.0596023 + 1.29453i
\(320\) 1.74274 3.01852i 0.0974224 0.168741i
\(321\) 0 0
\(322\) 4.86088 1.03321i 0.270886 0.0575786i
\(323\) −3.55972 10.9557i −0.198068 0.609591i
\(324\) 0 0
\(325\) −5.92427 + 4.30423i −0.328619 + 0.238756i
\(326\) −4.78980 + 5.31961i −0.265282 + 0.294626i
\(327\) 0 0
\(328\) 2.62367 1.16813i 0.144868 0.0644994i
\(329\) −0.0821419 + 0.142274i −0.00452863 + 0.00784382i
\(330\) 0 0
\(331\) −4.05198 7.01824i −0.222717 0.385757i 0.732915 0.680320i \(-0.238159\pi\)
−0.955632 + 0.294563i \(0.904826\pi\)
\(332\) −2.19681 1.59608i −0.120566 0.0875962i
\(333\) 0 0
\(334\) −8.11627 24.9793i −0.444103 1.36681i
\(335\) 4.37623 + 1.94842i 0.239099 + 0.106454i
\(336\) 0 0
\(337\) −24.1804 5.13971i −1.31719 0.279978i −0.504874 0.863193i \(-0.668461\pi\)
−0.812318 + 0.583215i \(0.801794\pi\)
\(338\) 10.8831 + 12.0869i 0.591964 + 0.657442i
\(339\) 0 0
\(340\) −0.530861 0.919478i −0.0287900 0.0498657i
\(341\) −13.5730 + 27.0619i −0.735017 + 1.46549i
\(342\) 0 0
\(343\) 7.87256 + 5.71975i 0.425078 + 0.308837i
\(344\) 10.2583 2.18048i 0.553092 0.117563i
\(345\) 0 0
\(346\) 0.0955236 + 0.908847i 0.00513538 + 0.0488599i
\(347\) −0.216337 2.05831i −0.0116136 0.110496i 0.987179 0.159615i \(-0.0510252\pi\)
−0.998793 + 0.0491192i \(0.984359\pi\)
\(348\) 0 0
\(349\) 5.10032 1.08411i 0.273014 0.0580309i −0.0693701 0.997591i \(-0.522099\pi\)
0.342384 + 0.939560i \(0.388766\pi\)
\(350\) −4.19874 3.05056i −0.224432 0.163059i
\(351\) 0 0
\(352\) 1.17611 + 7.13221i 0.0626868 + 0.380148i
\(353\) 10.8363 + 18.7689i 0.576756 + 0.998970i 0.995848 + 0.0910266i \(0.0290148\pi\)
−0.419093 + 0.907943i \(0.637652\pi\)
\(354\) 0 0
\(355\) −4.87633 5.41571i −0.258809 0.287436i
\(356\) 4.76751 + 1.01337i 0.252678 + 0.0537083i
\(357\) 0 0
\(358\) −13.6175 6.06290i −0.719706 0.320434i
\(359\) −2.70478 8.32446i −0.142753 0.439348i 0.853962 0.520335i \(-0.174193\pi\)
−0.996715 + 0.0809868i \(0.974193\pi\)
\(360\) 0 0
\(361\) 10.2801 + 7.46894i 0.541059 + 0.393102i
\(362\) −3.68125 6.37611i −0.193482 0.335121i
\(363\) 0 0
\(364\) 0.222030 0.384567i 0.0116375 0.0201568i
\(365\) −8.37413 + 3.72840i −0.438322 + 0.195153i
\(366\) 0 0
\(367\) −4.52749 + 5.02829i −0.236333 + 0.262474i −0.849631 0.527377i \(-0.823176\pi\)
0.613298 + 0.789851i \(0.289842\pi\)
\(368\) 16.6709 12.1121i 0.869029 0.631387i
\(369\) 0 0
\(370\) 0.817952 + 2.51740i 0.0425233 + 0.130873i
\(371\) −4.02773 + 0.856121i −0.209109 + 0.0444476i
\(372\) 0 0
\(373\) 10.9467 18.9602i 0.566797 0.981722i −0.430083 0.902790i \(-0.641516\pi\)
0.996880 0.0789323i \(-0.0251511\pi\)
\(374\) −22.0367 8.29892i −1.13949 0.429127i
\(375\) 0 0
\(376\) −0.0591903 + 0.563158i −0.00305251 + 0.0290426i
\(377\) 3.39643 10.4531i 0.174925 0.538364i
\(378\) 0 0
\(379\) 27.3639 19.8810i 1.40559 1.02122i 0.411642 0.911346i \(-0.364955\pi\)
0.993946 0.109873i \(-0.0350445\pi\)
\(380\) −0.529871 0.235914i −0.0271818 0.0121021i
\(381\) 0 0
\(382\) −5.37771 5.97255i −0.275147 0.305582i
\(383\) 16.7854 7.47333i 0.857693 0.381869i 0.0697105 0.997567i \(-0.477792\pi\)
0.787982 + 0.615698i \(0.211126\pi\)
\(384\) 0 0
\(385\) 1.41514 0.0831793i 0.0721223 0.00423921i
\(386\) −5.05284 −0.257183
\(387\) 0 0
\(388\) 1.71134 5.26696i 0.0868801 0.267390i
\(389\) 20.6136 22.8937i 1.04515 1.16076i 0.0584370 0.998291i \(-0.481388\pi\)
0.986714 0.162467i \(-0.0519450\pi\)
\(390\) 0 0
\(391\) 2.13694 + 20.3316i 0.108070 + 1.02821i
\(392\) 15.7698 + 3.35198i 0.796496 + 0.169300i
\(393\) 0 0
\(394\) 3.63030 34.5400i 0.182892 1.74010i
\(395\) 8.65524 0.435493
\(396\) 0 0
\(397\) −8.29578 −0.416353 −0.208177 0.978091i \(-0.566753\pi\)
−0.208177 + 0.978091i \(0.566753\pi\)
\(398\) −3.36630 + 32.0282i −0.168738 + 1.60543i
\(399\) 0 0
\(400\) −21.0502 4.47436i −1.05251 0.223718i
\(401\) −0.411175 3.91207i −0.0205331 0.195360i 0.979447 0.201703i \(-0.0646475\pi\)
−0.999980 + 0.00634326i \(0.997981\pi\)
\(402\) 0 0
\(403\) 9.61986 10.6839i 0.479199 0.532205i
\(404\) 1.73404 5.33682i 0.0862716 0.265517i
\(405\) 0 0
\(406\) 7.78977 0.386600
\(407\) 8.07642 + 5.17227i 0.400333 + 0.256380i
\(408\) 0 0
\(409\) −2.28775 + 1.01857i −0.113122 + 0.0503651i −0.462517 0.886610i \(-0.653054\pi\)
0.349395 + 0.936975i \(0.386387\pi\)
\(410\) 0.706895 + 0.785086i 0.0349110 + 0.0387726i
\(411\) 0 0
\(412\) −1.58010 0.703506i −0.0778460 0.0346593i
\(413\) 4.16650 3.02714i 0.205020 0.148956i
\(414\) 0 0
\(415\) −1.27204 + 3.91493i −0.0624419 + 0.192176i
\(416\) 0.358805 3.41381i 0.0175919 0.167376i
\(417\) 0 0
\(418\) −12.4043 + 3.40829i −0.606712 + 0.166705i
\(419\) 5.36970 9.30060i 0.262327 0.454364i −0.704533 0.709672i \(-0.748843\pi\)
0.966860 + 0.255307i \(0.0821767\pi\)
\(420\) 0 0
\(421\) −21.7026 + 4.61303i −1.05772 + 0.224825i −0.703762 0.710436i \(-0.748498\pi\)
−0.353958 + 0.935261i \(0.615164\pi\)
\(422\) −1.62065 4.98785i −0.0788920 0.242805i
\(423\) 0 0
\(424\) −11.4825 + 8.34249i −0.557637 + 0.405147i
\(425\) 14.2863 15.8665i 0.692986 0.769639i
\(426\) 0 0
\(427\) 3.00679 1.33871i 0.145509 0.0647847i
\(428\) −3.07440 + 5.32501i −0.148606 + 0.257394i
\(429\) 0 0
\(430\) 1.92889 + 3.34093i 0.0930192 + 0.161114i
\(431\) −14.9330 10.8495i −0.719297 0.522600i 0.166862 0.985980i \(-0.446636\pi\)
−0.886160 + 0.463380i \(0.846636\pi\)
\(432\) 0 0
\(433\) 4.67130 + 14.3768i 0.224488 + 0.690904i 0.998343 + 0.0575408i \(0.0183259\pi\)
−0.773855 + 0.633363i \(0.781674\pi\)
\(434\) 9.30835 + 4.14434i 0.446815 + 0.198935i
\(435\) 0 0
\(436\) 5.23232 + 1.11216i 0.250583 + 0.0532630i
\(437\) 7.47304 + 8.29965i 0.357484 + 0.397026i
\(438\) 0 0
\(439\) −11.9777 20.7459i −0.571663 0.990150i −0.996395 0.0848306i \(-0.972965\pi\)
0.424732 0.905319i \(-0.360368\pi\)
\(440\) 4.33945 2.24589i 0.206875 0.107068i
\(441\) 0 0
\(442\) 9.04645 + 6.57263i 0.430296 + 0.312628i
\(443\) 24.9405 5.30127i 1.18496 0.251871i 0.427049 0.904229i \(-0.359553\pi\)
0.757911 + 0.652358i \(0.226220\pi\)
\(444\) 0 0
\(445\) −0.772332 7.34825i −0.0366120 0.348340i
\(446\) −1.78203 16.9549i −0.0843817 0.802838i
\(447\) 0 0
\(448\) −4.15748 + 0.883700i −0.196423 + 0.0417509i
\(449\) −18.1886 13.2148i −0.858375 0.623646i 0.0690672 0.997612i \(-0.477998\pi\)
−0.927442 + 0.373966i \(0.877998\pi\)
\(450\) 0 0
\(451\) 3.78438 + 0.574776i 0.178200 + 0.0270651i
\(452\) 1.56804 + 2.71592i 0.0737542 + 0.127746i
\(453\) 0 0
\(454\) −6.17315 6.85598i −0.289720 0.321767i
\(455\) −0.658458 0.139959i −0.0308690 0.00656140i
\(456\) 0 0
\(457\) 19.8144 + 8.82195i 0.926879 + 0.412673i 0.813953 0.580930i \(-0.197311\pi\)
0.112926 + 0.993603i \(0.463978\pi\)
\(458\) −11.8254 36.3950i −0.552566 1.70062i
\(459\) 0 0
\(460\) 0.832763 + 0.605037i 0.0388278 + 0.0282100i
\(461\) −6.05182 10.4821i −0.281861 0.488198i 0.689982 0.723827i \(-0.257618\pi\)
−0.971843 + 0.235629i \(0.924285\pi\)
\(462\) 0 0
\(463\) −10.0154 + 17.3472i −0.465455 + 0.806192i −0.999222 0.0394398i \(-0.987443\pi\)
0.533767 + 0.845632i \(0.320776\pi\)
\(464\) 29.5084 13.1380i 1.36989 0.609915i
\(465\) 0 0
\(466\) 4.33320 4.81250i 0.200731 0.222935i
\(467\) 4.90871 3.56639i 0.227148 0.165033i −0.468390 0.883522i \(-0.655166\pi\)
0.695538 + 0.718489i \(0.255166\pi\)
\(468\) 0 0
\(469\) −1.80516 5.55570i −0.0833543 0.256538i
\(470\) −0.203744 + 0.0433071i −0.00939801 + 0.00199761i
\(471\) 0 0
\(472\) 8.87574 15.3732i 0.408539 0.707610i
\(473\) 13.0810 + 4.92624i 0.601465 + 0.226509i
\(474\) 0 0
\(475\) 1.21919 11.5998i 0.0559404 0.532237i
\(476\) −0.400088 + 1.23134i −0.0183380 + 0.0564385i
\(477\) 0 0
\(478\) 9.22233 6.70041i 0.421819 0.306470i
\(479\) −33.1369 14.7535i −1.51406 0.674104i −0.529367 0.848393i \(-0.677571\pi\)
−0.984695 + 0.174289i \(0.944237\pi\)
\(480\) 0 0
\(481\) −3.04743 3.38452i −0.138951 0.154321i
\(482\) 12.4710 5.55244i 0.568038 0.252907i
\(483\) 0 0
\(484\) −1.69732 + 3.94639i −0.0771510 + 0.179381i
\(485\) −8.39529 −0.381211
\(486\) 0 0
\(487\) −2.68379 + 8.25986i −0.121614 + 0.374290i −0.993269 0.115830i \(-0.963047\pi\)
0.871655 + 0.490120i \(0.163047\pi\)
\(488\) 7.59110 8.43077i 0.343633 0.381643i
\(489\) 0 0
\(490\) 0.619900 + 5.89795i 0.0280042 + 0.266442i
\(491\) −32.4719 6.90211i −1.46544 0.311488i −0.594982 0.803739i \(-0.702841\pi\)
−0.870453 + 0.492251i \(0.836174\pi\)
\(492\) 0 0
\(493\) −3.34970 + 31.8703i −0.150863 + 1.43537i
\(494\) 6.10872 0.274844
\(495\) 0 0
\(496\) 42.2506 1.89711
\(497\) −0.928921 + 8.83810i −0.0416678 + 0.396443i
\(498\) 0 0
\(499\) −20.4207 4.34055i −0.914155 0.194310i −0.273262 0.961940i \(-0.588103\pi\)
−0.640893 + 0.767630i \(0.721436\pi\)
\(500\) −0.233210 2.21885i −0.0104295 0.0992299i
\(501\) 0 0
\(502\) 21.2842 23.6385i 0.949961 1.05504i
\(503\) −7.20593 + 22.1776i −0.321297 + 0.988850i 0.651788 + 0.758401i \(0.274019\pi\)
−0.973085 + 0.230448i \(0.925981\pi\)
\(504\) 0 0
\(505\) −8.50663 −0.378540
\(506\) 22.7903 1.33957i 1.01315 0.0595511i
\(507\) 0 0
\(508\) −4.27998 + 1.90557i −0.189893 + 0.0845459i
\(509\) −4.33678 4.81648i −0.192224 0.213487i 0.639327 0.768935i \(-0.279213\pi\)
−0.831551 + 0.555449i \(0.812547\pi\)
\(510\) 0 0
\(511\) 10.2118 + 4.54658i 0.451743 + 0.201129i
\(512\) −10.4751 + 7.61063i −0.462940 + 0.336346i
\(513\) 0 0
\(514\) −1.61605 + 4.97368i −0.0712807 + 0.219379i
\(515\) −0.274076 + 2.60766i −0.0120772 + 0.114907i
\(516\) 0 0
\(517\) −0.471224 + 0.589529i −0.0207244 + 0.0259275i
\(518\) 1.61390 2.79537i 0.0709109 0.122821i
\(519\) 0 0
\(520\) −2.26960 + 0.482418i −0.0995284 + 0.0211554i
\(521\) 10.2625 + 31.5848i 0.449610 + 1.38376i 0.877348 + 0.479855i \(0.159311\pi\)
−0.427738 + 0.903903i \(0.640689\pi\)
\(522\) 0 0
\(523\) 32.4728 23.5929i 1.41994 1.03164i 0.428154 0.903706i \(-0.359164\pi\)
0.991782 0.127938i \(-0.0408359\pi\)
\(524\) 1.80079 1.99998i 0.0786677 0.0873694i
\(525\) 0 0
\(526\) −20.1732 + 8.98168i −0.879593 + 0.391620i
\(527\) −20.9585 + 36.3011i −0.912965 + 1.58130i
\(528\) 0 0
\(529\) 1.58985 + 2.75370i 0.0691240 + 0.119726i
\(530\) −4.22376 3.06874i −0.183468 0.133298i
\(531\) 0 0
\(532\) 0.218567 + 0.672680i 0.00947608 + 0.0291644i
\(533\) −1.66055 0.739324i −0.0719264 0.0320237i
\(534\) 0 0
\(535\) 9.11750 + 1.93798i 0.394184 + 0.0837864i
\(536\) −13.4730 14.9633i −0.581945 0.646315i
\(537\) 0 0
\(538\) −5.19534 8.99859i −0.223987 0.387957i
\(539\) 15.2903 + 15.0973i 0.658599 + 0.650287i
\(540\) 0 0
\(541\) −19.9410 14.4880i −0.857332 0.622888i 0.0698260 0.997559i \(-0.477756\pi\)
−0.927158 + 0.374671i \(0.877756\pi\)
\(542\) −6.01969 + 1.27952i −0.258568 + 0.0549602i
\(543\) 0 0
\(544\) 1.04614 + 9.95337i 0.0448529 + 0.426747i
\(545\) −0.847630 8.06466i −0.0363085 0.345452i
\(546\) 0 0
\(547\) −25.1583 + 5.34756i −1.07569 + 0.228645i −0.711505 0.702681i \(-0.751986\pi\)
−0.364186 + 0.931326i \(0.618653\pi\)
\(548\) 2.92147 + 2.12257i 0.124799 + 0.0906716i
\(549\) 0 0
\(550\) −16.9659 16.7517i −0.723427 0.714296i
\(551\) 8.75329 + 15.1611i 0.372902 + 0.645886i
\(552\) 0 0
\(553\) −7.06240 7.84359i −0.300324 0.333543i
\(554\) −19.8602 4.22141i −0.843778 0.179351i
\(555\) 0 0
\(556\) 7.71035 + 3.43287i 0.326992 + 0.145586i
\(557\) −3.60979 11.1098i −0.152952 0.470737i 0.844996 0.534773i \(-0.179603\pi\)
−0.997948 + 0.0640357i \(0.979603\pi\)
\(558\) 0 0
\(559\) −5.36998 3.90152i −0.227126 0.165017i
\(560\) −0.989164 1.71328i −0.0417998 0.0723994i
\(561\) 0 0
\(562\) 2.29436 3.97396i 0.0967819 0.167631i
\(563\) −7.41991 + 3.30356i −0.312712 + 0.139228i −0.557091 0.830451i \(-0.688083\pi\)
0.244379 + 0.969680i \(0.421416\pi\)
\(564\) 0 0
\(565\) 3.18111 3.53298i 0.133830 0.148634i
\(566\) 10.1229 7.35468i 0.425495 0.309140i
\(567\) 0 0
\(568\) 9.46559 + 29.1321i 0.397167 + 1.22236i
\(569\) −17.6131 + 3.74379i −0.738381 + 0.156948i −0.561724 0.827325i \(-0.689862\pi\)
−0.176657 + 0.984272i \(0.556528\pi\)
\(570\) 0 0
\(571\) 1.30322 2.25725i 0.0545382 0.0944629i −0.837467 0.546487i \(-0.815965\pi\)
0.892006 + 0.452024i \(0.149298\pi\)
\(572\) 1.27372 1.59350i 0.0532569 0.0666276i
\(573\) 0 0
\(574\) 0.134661 1.28121i 0.00562063 0.0534767i
\(575\) −6.39652 + 19.6865i −0.266753 + 0.820982i
\(576\) 0 0
\(577\) −28.4684 + 20.6835i −1.18515 + 0.861064i −0.992744 0.120251i \(-0.961630\pi\)
−0.192409 + 0.981315i \(0.561630\pi\)
\(578\) −5.77202 2.56987i −0.240084 0.106893i
\(579\) 0 0
\(580\) 1.07967 + 1.19909i 0.0448307 + 0.0497895i
\(581\) 4.58575 2.04171i 0.190249 0.0847042i
\(582\) 0 0
\(583\) −18.8841 + 1.10997i −0.782099 + 0.0459702i
\(584\) 38.5294 1.59436
\(585\) 0 0
\(586\) −7.50863 + 23.1092i −0.310179 + 0.954631i
\(587\) −15.7596 + 17.5029i −0.650470 + 0.722420i −0.974690 0.223562i \(-0.928232\pi\)
0.324220 + 0.945982i \(0.394898\pi\)
\(588\) 0 0
\(589\) 2.39361 + 22.7737i 0.0986269 + 0.938372i
\(590\) 6.38709 + 1.35762i 0.262952 + 0.0558923i
\(591\) 0 0
\(592\) 1.39905 13.3111i 0.0575005 0.547081i
\(593\) −13.1828 −0.541354 −0.270677 0.962670i \(-0.587248\pi\)
−0.270677 + 0.962670i \(0.587248\pi\)
\(594\) 0 0
\(595\) 1.96270 0.0804630
\(596\) −0.0468001 + 0.445273i −0.00191701 + 0.0182391i
\(597\) 0 0
\(598\) −10.6042 2.25399i −0.433638 0.0921726i
\(599\) 3.57659 + 34.0290i 0.146135 + 1.39039i 0.784250 + 0.620445i \(0.213048\pi\)
−0.638115 + 0.769941i \(0.720285\pi\)
\(600\) 0 0
\(601\) 19.4239 21.5724i 0.792316 0.879956i −0.202744 0.979232i \(-0.564986\pi\)
0.995060 + 0.0992759i \(0.0316526\pi\)
\(602\) 1.45372 4.47410i 0.0592493 0.182351i
\(603\) 0 0
\(604\) 0.343924 0.0139941
\(605\) 6.48480 + 0.598412i 0.263645 + 0.0243289i
\(606\) 0 0
\(607\) −2.88347 + 1.28380i −0.117037 + 0.0521080i −0.464420 0.885615i \(-0.653737\pi\)
0.347383 + 0.937723i \(0.387070\pi\)
\(608\) 3.65844 + 4.06311i 0.148369 + 0.164781i
\(609\) 0 0
\(610\) 3.81231 + 1.69735i 0.154356 + 0.0687238i
\(611\) 0.289945 0.210657i 0.0117299 0.00852229i
\(612\) 0 0
\(613\) 10.4884 32.2798i 0.423620 1.30377i −0.480689 0.876891i \(-0.659613\pi\)
0.904309 0.426878i \(-0.140387\pi\)
\(614\) −0.567779 + 5.40206i −0.0229137 + 0.218009i
\(615\) 0 0
\(616\) −5.57613 2.09994i −0.224669 0.0846091i
\(617\) −10.8039 + 18.7129i −0.434948 + 0.753351i −0.997291 0.0735523i \(-0.976566\pi\)
0.562344 + 0.826904i \(0.309900\pi\)
\(618\) 0 0
\(619\) −20.0643 + 4.26481i −0.806454 + 0.171417i −0.592651 0.805460i \(-0.701919\pi\)
−0.213803 + 0.976877i \(0.568585\pi\)
\(620\) 0.652196 + 2.00725i 0.0261928 + 0.0806132i
\(621\) 0 0
\(622\) −32.9404 + 23.9326i −1.32079 + 0.959611i
\(623\) −6.02896 + 6.69584i −0.241545 + 0.268263i
\(624\) 0 0
\(625\) 18.1479 8.07996i 0.725915 0.323198i
\(626\) −1.90263 + 3.29545i −0.0760444 + 0.131713i
\(627\) 0 0
\(628\) 1.91094 + 3.30985i 0.0762550 + 0.132078i
\(629\) 10.7427 + 7.80501i 0.428339 + 0.311206i
\(630\) 0 0
\(631\) 9.22863 + 28.4028i 0.367386 + 1.13070i 0.948473 + 0.316857i \(0.102628\pi\)
−0.581087 + 0.813841i \(0.697372\pi\)
\(632\) −33.2348 14.7971i −1.32201 0.588596i
\(633\) 0 0
\(634\) 40.0881 + 8.52098i 1.59210 + 0.338411i
\(635\) 4.75230 + 5.27796i 0.188589 + 0.209450i
\(636\) 0 0
\(637\) −5.10193 8.83680i −0.202146 0.350127i
\(638\) 35.3803 + 5.37360i 1.40072 + 0.212743i
\(639\) 0 0
\(640\) −6.44762 4.68447i −0.254864 0.185170i
\(641\) −37.2870 + 7.92561i −1.47275 + 0.313043i −0.873226 0.487315i \(-0.837976\pi\)
−0.599523 + 0.800357i \(0.704643\pi\)
\(642\) 0 0
\(643\) 1.75871 + 16.7330i 0.0693566 + 0.659884i 0.972875 + 0.231333i \(0.0743088\pi\)
−0.903518 + 0.428550i \(0.859024\pi\)
\(644\) −0.131208 1.24836i −0.00517032 0.0491923i
\(645\) 0 0
\(646\) −17.4215 + 3.70306i −0.685440 + 0.145695i
\(647\) −16.9687 12.3285i −0.667109 0.484683i 0.201947 0.979396i \(-0.435273\pi\)
−0.869056 + 0.494713i \(0.835273\pi\)
\(648\) 0 0
\(649\) 21.0120 10.8748i 0.824792 0.426872i
\(650\) 5.66102 + 9.80517i 0.222043 + 0.384591i
\(651\) 0 0
\(652\) 1.20985 + 1.34368i 0.0473815 + 0.0526225i
\(653\) 19.3345 + 4.10968i 0.756619 + 0.160824i 0.570041 0.821616i \(-0.306927\pi\)
0.186577 + 0.982440i \(0.440261\pi\)
\(654\) 0 0
\(655\) −3.72703 1.65938i −0.145627 0.0648374i
\(656\) −1.65074 5.08046i −0.0644506 0.198358i
\(657\) 0 0
\(658\) 0.205494 + 0.149300i 0.00801101 + 0.00582034i
\(659\) −5.90277 10.2239i −0.229939 0.398267i 0.727851 0.685736i \(-0.240519\pi\)
−0.957790 + 0.287469i \(0.907186\pi\)
\(660\) 0 0
\(661\) −8.90382 + 15.4219i −0.346318 + 0.599841i −0.985592 0.169138i \(-0.945902\pi\)
0.639274 + 0.768979i \(0.279235\pi\)
\(662\) −11.4466 + 5.09634i −0.444884 + 0.198075i
\(663\) 0 0
\(664\) 11.5774 12.8580i 0.449291 0.498988i
\(665\) 0.867445 0.630235i 0.0336381 0.0244395i
\(666\) 0 0
\(667\) −9.60079 29.5482i −0.371744 1.14411i
\(668\) −6.48925 + 1.37933i −0.251076 + 0.0533679i
\(669\) 0 0
\(670\) 3.70329 6.41429i 0.143071 0.247806i
\(671\) 14.5800 4.00611i 0.562854 0.154654i
\(672\) 0 0
\(673\) −2.05976 + 19.5973i −0.0793980 + 0.755422i 0.880306 + 0.474407i \(0.157338\pi\)
−0.959704 + 0.281014i \(0.909329\pi\)
\(674\) −11.8111 + 36.3508i −0.454946 + 1.40018i
\(675\) 0 0
\(676\) 3.32365 2.41477i 0.127833 0.0928760i
\(677\) 11.3407 + 5.04919i 0.435857 + 0.194056i 0.612923 0.790143i \(-0.289994\pi\)
−0.177065 + 0.984199i \(0.556660\pi\)
\(678\) 0 0
\(679\) 6.85029 + 7.60802i 0.262890 + 0.291969i
\(680\) 6.18025 2.75162i 0.237002 0.105520i
\(681\) 0 0
\(682\) 39.4186 + 25.2443i 1.50942 + 0.966654i
\(683\) −2.02837 −0.0776135 −0.0388068 0.999247i \(-0.512356\pi\)
−0.0388068 + 0.999247i \(0.512356\pi\)
\(684\) 0 0
\(685\) 1.69164 5.20632i 0.0646341 0.198923i
\(686\) 10.0674 11.1810i 0.384375 0.426891i
\(687\) 0 0
\(688\) −2.03903 19.4001i −0.0777374 0.739622i
\(689\) 8.78666 + 1.86766i 0.334745 + 0.0711523i
\(690\) 0 0
\(691\) −0.244897 + 2.33004i −0.00931631 + 0.0886387i −0.998192 0.0601053i \(-0.980856\pi\)
0.988876 + 0.148744i \(0.0475230\pi\)
\(692\) 0.230830 0.00877483
\(693\) 0 0
\(694\) −3.19995 −0.121469
\(695\) 1.33740 12.7245i 0.0507304 0.482667i
\(696\) 0 0
\(697\) 5.18391 + 1.10187i 0.196355 + 0.0417364i
\(698\) −0.842705 8.01780i −0.0318969 0.303478i
\(699\) 0 0
\(700\) −0.877178 + 0.974205i −0.0331542 + 0.0368215i
\(701\) 1.37008 4.21668i 0.0517473 0.159262i −0.921843 0.387563i \(-0.873317\pi\)
0.973591 + 0.228301i \(0.0733170\pi\)
\(702\) 0 0
\(703\) 7.25411 0.273594
\(704\) −19.4924 + 1.14573i −0.734649 + 0.0431812i
\(705\) 0 0
\(706\) 30.6117 13.6292i 1.15209 0.512942i
\(707\) 6.94114 + 7.70892i 0.261049 + 0.289924i
\(708\) 0 0
\(709\) 27.2990 + 12.1543i 1.02524 + 0.456465i 0.849286 0.527934i \(-0.177033\pi\)
0.175952 + 0.984399i \(0.443700\pi\)
\(710\) −9.11565 + 6.62291i −0.342104 + 0.248553i
\(711\) 0 0
\(712\) −9.59699 + 29.5365i −0.359662 + 1.10693i
\(713\) 4.24792 40.4163i 0.159086 1.51360i
\(714\) 0 0
\(715\) −2.89409 1.08990i −0.108233 0.0407600i
\(716\) −1.88258 + 3.26072i −0.0703551 + 0.121859i
\(717\) 0 0
\(718\) −13.2374 + 2.81369i −0.494014 + 0.105006i
\(719\) 6.68469 + 20.5734i 0.249297 + 0.767257i 0.994900 + 0.100867i \(0.0321616\pi\)
−0.745603 + 0.666390i \(0.767838\pi\)
\(720\) 0 0
\(721\) 2.58676 1.87939i 0.0963360 0.0699922i
\(722\) 13.1462 14.6003i 0.489250 0.543367i
\(723\) 0 0
\(724\) −1.69891 + 0.756405i −0.0631396 + 0.0281116i
\(725\) −16.2235 + 28.1000i −0.602527 + 1.04361i
\(726\) 0 0
\(727\) 6.22109 + 10.7752i 0.230727 + 0.399631i 0.958022 0.286694i \(-0.0925561\pi\)
−0.727295 + 0.686325i \(0.759223\pi\)
\(728\) 2.28910 + 1.66313i 0.0848396 + 0.0616396i
\(729\) 0 0
\(730\) 4.37965 + 13.4792i 0.162098 + 0.498887i
\(731\) 17.6798 + 7.87154i 0.653909 + 0.291139i
\(732\) 0 0
\(733\) 51.2082 + 10.8846i 1.89142 + 0.402033i 0.998809 0.0487988i \(-0.0155393\pi\)
0.892609 + 0.450832i \(0.148873\pi\)
\(734\) 7.00012 + 7.77442i 0.258379 + 0.286959i
\(735\) 0 0
\(736\) −4.85153 8.40310i −0.178830 0.309742i
\(737\) −4.36635 26.4786i −0.160837 0.975352i
\(738\) 0 0
\(739\) 37.7617 + 27.4355i 1.38909 + 1.00923i 0.995965 + 0.0897445i \(0.0286051\pi\)
0.393122 + 0.919486i \(0.371395\pi\)
\(740\) 0.653982 0.139008i 0.0240408 0.00511004i
\(741\) 0 0
\(742\) 0.665485 + 6.33167i 0.0244307 + 0.232443i
\(743\) −2.28623 21.7521i −0.0838738 0.798006i −0.952909 0.303256i \(-0.901926\pi\)
0.869035 0.494750i \(-0.164740\pi\)
\(744\) 0 0
\(745\) 0.663893 0.141115i 0.0243232 0.00517005i
\(746\) −27.3853 19.8966i −1.00265 0.728466i
\(747\) 0 0
\(748\) −2.66657 + 5.31664i −0.0974994 + 0.194395i
\(749\) −5.68334 9.84384i −0.207665 0.359686i
\(750\) 0 0
\(751\) 26.4923 + 29.4227i 0.966718 + 1.07365i 0.997250 + 0.0741152i \(0.0236132\pi\)
−0.0305318 + 0.999534i \(0.509720\pi\)
\(752\) 1.03024 + 0.218984i 0.0375689 + 0.00798551i
\(753\) 0 0
\(754\) −15.5245 6.91196i −0.565370 0.251719i
\(755\) −0.161111 0.495850i −0.00586344 0.0180458i
\(756\) 0 0
\(757\) −18.7253 13.6047i −0.680583 0.494472i 0.192968 0.981205i \(-0.438189\pi\)
−0.873551 + 0.486733i \(0.838189\pi\)
\(758\) −26.1480 45.2896i −0.949736 1.64499i
\(759\) 0 0
\(760\) 1.84789 3.20063i 0.0670299 0.116099i
\(761\) 13.6053 6.05747i 0.493192 0.219583i −0.145042 0.989425i \(-0.546332\pi\)
0.638234 + 0.769842i \(0.279665\pi\)
\(762\) 0 0
\(763\) −6.61675 + 7.34864i −0.239542 + 0.266039i
\(764\) −1.64233 + 1.19322i −0.0594173 + 0.0431692i
\(765\) 0 0
\(766\) −8.77872 27.0181i −0.317188 0.976204i
\(767\) −10.9896 + 2.33591i −0.396811 + 0.0843447i
\(768\) 0 0
\(769\) −10.8117 + 18.7264i −0.389879 + 0.675290i −0.992433 0.122788i \(-0.960816\pi\)
0.602554 + 0.798078i \(0.294150\pi\)
\(770\) 0.100807 2.18946i 0.00363282 0.0789026i
\(771\) 0 0
\(772\) −0.133409 + 1.26930i −0.00480151 + 0.0456833i
\(773\) 1.87664 5.77569i 0.0674979 0.207737i −0.911619 0.411037i \(-0.865167\pi\)
0.979117 + 0.203300i \(0.0651666\pi\)
\(774\) 0 0
\(775\) −34.3361 + 24.9466i −1.23339 + 0.896109i
\(776\) 32.2366 + 14.3527i 1.15723 + 0.515231i
\(777\) 0 0
\(778\) −31.8714 35.3968i −1.14265 1.26904i
\(779\) 2.64492 1.17759i 0.0947641 0.0421917i
\(780\) 0 0
\(781\) −10.3158 + 39.5009i −0.369129 + 1.41345i
\(782\) 31.6086 1.13032
\(783\) 0 0
\(784\) 9.26663 28.5197i 0.330951 1.01856i
\(785\) 3.87678 4.30560i 0.138368 0.153673i
\(786\) 0 0
\(787\) −5.34719 50.8751i −0.190607 1.81350i −0.503808 0.863816i \(-0.668068\pi\)
0.313201 0.949687i \(-0.398599\pi\)
\(788\) −8.58080 1.82391i −0.305678 0.0649739i
\(789\) 0 0
\(790\) 1.39882 13.3089i 0.0497678 0.473509i
\(791\) −5.79736 −0.206130
\(792\) 0 0
\(793\) −7.18019 −0.254976
\(794\) −1.34072 + 12.7561i −0.0475805 + 0.452699i
\(795\) 0 0
\(796\) 7.95681 + 1.69127i 0.282022 + 0.0599455i
\(797\) −2.64052 25.1228i −0.0935319 0.889897i −0.936201 0.351465i \(-0.885684\pi\)
0.842669 0.538432i \(-0.180983\pi\)
\(798\) 0 0
\(799\) −0.699198 + 0.776538i −0.0247359 + 0.0274719i
\(800\) −3.13143 + 9.63754i −0.110713 + 0.340738i
\(801\) 0 0
\(802\) −6.08192 −0.214760
\(803\) 43.2445 + 27.6944i 1.52606 + 0.977316i
\(804\) 0 0
\(805\) −1.73835 + 0.773964i −0.0612689 + 0.0272787i
\(806\) −14.8736 16.5188i −0.523901 0.581851i
\(807\) 0 0
\(808\) 32.6641 + 14.5430i 1.14912 + 0.511621i
\(809\) 41.5248 30.1696i 1.45994 1.06071i 0.476556 0.879144i \(-0.341885\pi\)
0.983380 0.181561i \(-0.0581150\pi\)
\(810\) 0 0
\(811\) 1.40476 4.32339i 0.0493276 0.151815i −0.923359 0.383939i \(-0.874567\pi\)
0.972686 + 0.232124i \(0.0745674\pi\)
\(812\) 0.205672 1.95684i 0.00721767 0.0686715i
\(813\) 0 0
\(814\) 9.25850 11.5829i 0.324510 0.405981i
\(815\) 1.37048 2.37375i 0.0480059 0.0831487i
\(816\) 0 0
\(817\) 10.3414 2.19814i 0.361800 0.0769030i
\(818\) 1.19649 + 3.68241i 0.0418342 + 0.128753i
\(819\) 0 0
\(820\) 0.215882 0.156848i 0.00753894 0.00547736i
\(821\) −7.27599 + 8.08080i −0.253934 + 0.282022i −0.856611 0.515963i \(-0.827434\pi\)
0.602677 + 0.797985i \(0.294101\pi\)
\(822\) 0 0
\(823\) −21.5744 + 9.60555i −0.752037 + 0.334828i −0.746703 0.665157i \(-0.768364\pi\)
−0.00533378 + 0.999986i \(0.501698\pi\)
\(824\) 5.51048 9.54444i 0.191967 0.332496i
\(825\) 0 0
\(826\) −3.98136 6.89591i −0.138529 0.239940i
\(827\) −22.3321 16.2252i −0.776564 0.564207i 0.127382 0.991854i \(-0.459343\pi\)
−0.903946 + 0.427647i \(0.859343\pi\)
\(828\) 0 0
\(829\) −4.97546 15.3129i −0.172805 0.531839i 0.826722 0.562611i \(-0.190203\pi\)
−0.999526 + 0.0307727i \(0.990203\pi\)
\(830\) 5.81427 + 2.58868i 0.201816 + 0.0898545i
\(831\) 0 0
\(832\) 9.06972 + 1.92783i 0.314436 + 0.0668354i
\(833\) 19.9070 + 22.1090i 0.689738 + 0.766032i
\(834\) 0 0
\(835\) 5.02854 + 8.70968i 0.174020 + 0.301411i
\(836\) 0.528675 + 3.20601i 0.0182846 + 0.110882i
\(837\) 0 0
\(838\) −13.4334 9.75993i −0.464049 0.337151i
\(839\) −19.0073 + 4.04012i −0.656205 + 0.139481i −0.523968 0.851738i \(-0.675549\pi\)
−0.132236 + 0.991218i \(0.542216\pi\)
\(840\) 0 0
\(841\) −2.05933 19.5932i −0.0710114 0.675629i
\(842\) 3.58583 + 34.1169i 0.123576 + 1.17575i
\(843\) 0 0
\(844\) −1.29577 + 0.275424i −0.0446021 + 0.00948047i
\(845\) −5.03845 3.66065i −0.173328 0.125930i
\(846\) 0 0
\(847\) −4.74909 6.36497i −0.163181 0.218703i
\(848\) 13.1997 + 22.8626i 0.453280 + 0.785103i
\(849\) 0 0
\(850\) −22.0885 24.5318i −0.757631 0.841434i
\(851\) −12.5925 2.67662i −0.431666 0.0917533i
\(852\) 0 0
\(853\) −18.0750 8.04749i −0.618875 0.275541i 0.0732555 0.997313i \(-0.476661\pi\)
−0.692131 + 0.721772i \(0.743328\pi\)
\(854\) −1.57255 4.83980i −0.0538114 0.165614i
\(855\) 0 0
\(856\) −31.6966 23.0289i −1.08337 0.787112i
\(857\) −2.17032 3.75911i −0.0741369 0.128409i 0.826574 0.562828i \(-0.190287\pi\)
−0.900711 + 0.434420i \(0.856953\pi\)
\(858\) 0 0
\(859\) 2.58967 4.48545i 0.0883586 0.153042i −0.818459 0.574565i \(-0.805171\pi\)
0.906817 + 0.421524i \(0.138505\pi\)
\(860\) 0.890190 0.396338i 0.0303552 0.0135150i
\(861\) 0 0
\(862\) −19.0963 + 21.2085i −0.650421 + 0.722366i
\(863\) −2.17943 + 1.58345i −0.0741886 + 0.0539011i −0.624261 0.781216i \(-0.714600\pi\)
0.550073 + 0.835117i \(0.314600\pi\)
\(864\) 0 0
\(865\) −0.108132 0.332797i −0.00367661 0.0113155i
\(866\) 22.8616 4.85939i 0.776870 0.165129i
\(867\) 0 0
\(868\) 1.28685 2.22889i 0.0436785 0.0756534i
\(869\) −26.6659 40.4966i −0.904580 1.37375i
\(870\) 0 0
\(871\) −1.33208 + 12.6739i −0.0451358 + 0.429438i
\(872\) −10.5326 + 32.4161i −0.356680 + 1.09775i
\(873\) 0 0
\(874\) 13.9699 10.1497i 0.472538 0.343319i
\(875\) 3.76780 + 1.67753i 0.127375 + 0.0567109i
\(876\) 0 0
\(877\) −13.9479 15.4907i −0.470986 0.523083i 0.460107 0.887863i \(-0.347811\pi\)
−0.931094 + 0.364780i \(0.881144\pi\)
\(878\) −33.8361 + 15.0648i −1.14191 + 0.508413i
\(879\) 0 0
\(880\) −3.31081 8.46389i −0.111607 0.285318i
\(881\) −11.5843 −0.390286 −0.195143 0.980775i \(-0.562517\pi\)
−0.195143 + 0.980775i \(0.562517\pi\)
\(882\) 0 0
\(883\) 4.75801 14.6437i 0.160120 0.492798i −0.838524 0.544865i \(-0.816581\pi\)
0.998644 + 0.0520667i \(0.0165808\pi\)
\(884\) 1.88994 2.09899i 0.0635654 0.0705966i
\(885\) 0 0
\(886\) −4.12082 39.2070i −0.138442 1.31718i
\(887\) −5.78081 1.22875i −0.194101 0.0412574i 0.109835 0.993950i \(-0.464968\pi\)
−0.303936 + 0.952692i \(0.598301\pi\)
\(888\) 0 0
\(889\) 0.905294 8.61330i 0.0303626 0.288881i
\(890\) −11.4240 −0.382932
\(891\) 0 0
\(892\) −4.30623 −0.144183
\(893\) −0.0596696 + 0.567719i −0.00199677 + 0.0189980i
\(894\) 0 0
\(895\) 5.58301 + 1.18671i 0.186619 + 0.0396672i
\(896\) 1.01587 + 9.66536i 0.0339378 + 0.322897i
\(897\) 0 0
\(898\) −23.2596 + 25.8324i −0.776182 + 0.862037i
\(899\) 19.6852 60.5847i 0.656537 2.02061i
\(900\) 0 0
\(901\) −26.1909 −0.872546
\(902\) 1.49543 5.72622i 0.0497923 0.190662i
\(903\) 0 0
\(904\) −18.2550 + 8.12764i −0.607152 + 0.270321i
\(905\) 1.88640 + 2.09506i 0.0627060 + 0.0696421i
\(906\) 0 0
\(907\) −6.75413 3.00713i −0.224267 0.0998502i 0.291527 0.956562i \(-0.405837\pi\)
−0.515795 + 0.856712i \(0.672503\pi\)
\(908\) −1.88525 + 1.36971i −0.0625642 + 0.0454556i
\(909\) 0 0
\(910\) −0.321628 + 0.989869i −0.0106619 + 0.0328138i
\(911\) −1.48418 + 14.1210i −0.0491730 + 0.467850i 0.942033 + 0.335521i \(0.108912\pi\)
−0.991206 + 0.132329i \(0.957754\pi\)
\(912\) 0 0
\(913\) 22.2364 6.10983i 0.735917 0.202206i
\(914\) 16.7675 29.0422i 0.554620 0.960631i
\(915\) 0 0
\(916\) −9.45485 + 2.00969i −0.312397 + 0.0664021i
\(917\) 1.53737 + 4.73153i 0.0507684 + 0.156249i
\(918\) 0 0
\(919\) 33.6895 24.4769i 1.11132 0.807418i 0.128445 0.991717i \(-0.459001\pi\)
0.982870 + 0.184299i \(0.0590013\pi\)
\(920\) −4.38874 + 4.87419i −0.144692 + 0.160697i
\(921\) 0 0
\(922\) −17.0960 + 7.61162i −0.563026 + 0.250675i
\(923\) 9.69344 16.7895i 0.319063 0.552634i
\(924\) 0 0
\(925\) 6.72247 + 11.6437i 0.221033 + 0.382841i
\(926\) 25.0555 + 18.2039i 0.823376 + 0.598218i
\(927\) 0 0
\(928\) −4.70008 14.4654i −0.154288 0.474849i
\(929\) 31.1818 + 13.8830i 1.02304 + 0.455488i 0.848519 0.529165i \(-0.177495\pi\)
0.174524 + 0.984653i \(0.444161\pi\)
\(930\) 0 0
\(931\) 15.8975 + 3.37912i 0.521020 + 0.110746i
\(932\) −1.09452 1.21559i −0.0358522 0.0398179i
\(933\) 0 0
\(934\) −4.69059 8.12434i −0.153481 0.265837i
\(935\) 8.91439 + 1.35393i 0.291532 + 0.0442781i
\(936\) 0 0
\(937\) −41.8118 30.3780i −1.36593 0.992407i −0.998043 0.0625376i \(-0.980081\pi\)
−0.367889 0.929870i \(-0.619919\pi\)
\(938\) −8.83455 + 1.87784i −0.288458 + 0.0613137i
\(939\) 0 0
\(940\) 0.00549959 + 0.0523251i 0.000179377 + 0.00170666i
\(941\) 1.88216 + 17.9075i 0.0613566 + 0.583769i 0.981403 + 0.191959i \(0.0614842\pi\)
−0.920046 + 0.391810i \(0.871849\pi\)
\(942\) 0 0
\(943\) −5.02586 + 1.06828i −0.163664 + 0.0347880i
\(944\) −26.7122 19.4075i −0.869407 0.631661i
\(945\) 0 0
\(946\) 9.68901 19.3181i 0.315017 0.628084i
\(947\) 14.3151 + 24.7946i 0.465180 + 0.805715i 0.999210 0.0397506i \(-0.0126563\pi\)
−0.534030 + 0.845466i \(0.679323\pi\)
\(948\) 0 0
\(949\) −16.3172 18.1221i −0.529679 0.588268i
\(950\) −17.6396 3.74942i −0.572306 0.121647i
\(951\) 0 0
\(952\) −7.53647 3.35545i −0.244259 0.108751i
\(953\) −5.15728 15.8725i −0.167061 0.514160i 0.832121 0.554594i \(-0.187126\pi\)
−0.999182 + 0.0404331i \(0.987126\pi\)
\(954\) 0 0
\(955\) 2.48967 + 1.80885i 0.0805637 + 0.0585330i
\(956\) −1.43969 2.49361i −0.0465628 0.0806492i
\(957\) 0 0
\(958\) −28.0414 + 48.5690i −0.905975 + 1.56919i
\(959\) −6.09842 + 2.71519i −0.196928 + 0.0876781i
\(960\) 0 0
\(961\) 35.0121 38.8849i 1.12942 1.25435i
\(962\) −5.69677 + 4.13895i −0.183671 + 0.133445i
\(963\) 0 0
\(964\) −1.06554 3.27939i −0.0343187 0.105622i
\(965\) 1.89251 0.402265i 0.0609220 0.0129494i
\(966\) 0 0
\(967\) −12.1597 + 21.0612i −0.391029 + 0.677281i −0.992585 0.121549i \(-0.961214\pi\)
0.601557 + 0.798830i \(0.294547\pi\)
\(968\) −23.8776 13.3843i −0.767454 0.430187i
\(969\) 0 0
\(970\) −1.35681 + 12.9092i −0.0435645 + 0.414488i
\(971\) −2.33367 + 7.18229i −0.0748910 + 0.230491i −0.981494 0.191495i \(-0.938667\pi\)
0.906603 + 0.421985i \(0.138667\pi\)
\(972\) 0 0
\(973\) −12.6225 + 9.17079i −0.404659 + 0.294002i
\(974\) 12.2672 + 5.46169i 0.393065 + 0.175004i
\(975\) 0 0
\(976\) −14.1196 15.6814i −0.451957 0.501949i
\(977\) −1.85659 + 0.826605i −0.0593974 + 0.0264454i −0.436220 0.899840i \(-0.643683\pi\)
0.376823 + 0.926285i \(0.377017\pi\)
\(978\) 0 0
\(979\) −32.0019 + 26.2528i −1.02278 + 0.839044i
\(980\) 1.49797 0.0478508
\(981\) 0 0
\(982\) −15.8611 + 48.8154i −0.506148 + 1.55776i
\(983\) −22.3755 + 24.8505i −0.713666 + 0.792607i −0.985489 0.169741i \(-0.945707\pi\)
0.271822 + 0.962347i \(0.412374\pi\)
\(984\) 0 0
\(985\) 1.39008 + 13.2257i 0.0442916 + 0.421407i
\(986\) 48.4645 + 10.3015i 1.54342 + 0.328065i
\(987\) 0 0
\(988\) 0.161287 1.53455i 0.00513123 0.0488204i
\(989\) −18.7629 −0.596624
\(990\) 0 0
\(991\) 40.1009 1.27385 0.636923 0.770927i \(-0.280207\pi\)
0.636923 + 0.770927i \(0.280207\pi\)
\(992\) 2.07958 19.7859i 0.0660267 0.628202i
\(993\) 0 0
\(994\) 13.4399 + 2.85674i 0.426288 + 0.0906104i
\(995\) −1.28899 12.2640i −0.0408638 0.388793i
\(996\) 0 0
\(997\) 10.7931 11.9870i 0.341822 0.379632i −0.547583 0.836751i \(-0.684452\pi\)
0.889405 + 0.457119i \(0.151119\pi\)
\(998\) −9.97461 + 30.6987i −0.315741 + 0.971750i
\(999\) 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 297.2.n.b.37.8 72
3.2 odd 2 99.2.m.b.4.2 72
9.2 odd 6 99.2.m.b.70.8 yes 72
9.4 even 3 891.2.f.e.730.8 36
9.5 odd 6 891.2.f.f.730.2 36
9.7 even 3 inner 297.2.n.b.235.2 72
11.3 even 5 inner 297.2.n.b.91.2 72
33.5 odd 10 1089.2.e.p.364.4 36
33.14 odd 10 99.2.m.b.58.8 yes 72
33.17 even 10 1089.2.e.o.364.15 36
99.5 odd 30 9801.2.a.cm.1.15 18
99.14 odd 30 891.2.f.f.487.2 36
99.25 even 15 inner 297.2.n.b.289.8 72
99.38 odd 30 1089.2.e.p.727.4 36
99.47 odd 30 99.2.m.b.25.2 yes 72
99.49 even 15 9801.2.a.cp.1.4 18
99.50 even 30 9801.2.a.co.1.4 18
99.58 even 15 891.2.f.e.487.8 36
99.83 even 30 1089.2.e.o.727.15 36
99.94 odd 30 9801.2.a.cn.1.15 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.2 72 3.2 odd 2
99.2.m.b.25.2 yes 72 99.47 odd 30
99.2.m.b.58.8 yes 72 33.14 odd 10
99.2.m.b.70.8 yes 72 9.2 odd 6
297.2.n.b.37.8 72 1.1 even 1 trivial
297.2.n.b.91.2 72 11.3 even 5 inner
297.2.n.b.235.2 72 9.7 even 3 inner
297.2.n.b.289.8 72 99.25 even 15 inner
891.2.f.e.487.8 36 99.58 even 15
891.2.f.e.730.8 36 9.4 even 3
891.2.f.f.487.2 36 99.14 odd 30
891.2.f.f.730.2 36 9.5 odd 6
1089.2.e.o.364.15 36 33.17 even 10
1089.2.e.o.727.15 36 99.83 even 30
1089.2.e.p.364.4 36 33.5 odd 10
1089.2.e.p.727.4 36 99.38 odd 30
9801.2.a.cm.1.15 18 99.5 odd 30
9801.2.a.cn.1.15 18 99.94 odd 30
9801.2.a.co.1.4 18 99.50 even 30
9801.2.a.cp.1.4 18 99.49 even 15