Properties

Label 666.2.bs.a.89.1
Level $666$
Weight $2$
Character 666.89
Analytic conductor $5.318$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [666,2,Mod(17,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("666.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.bs (of order \(36\), degree \(12\), 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: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(6\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 89.1
Character \(\chi\) \(=\) 666.89
Dual form 666.2.bs.a.449.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-2.27330 + 1.59178i) q^{5} +(0.235550 - 1.33587i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\) \(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-2.27330 + 1.59178i) q^{5} +(0.235550 - 1.33587i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(1.38759 - 2.40338i) q^{10} +(-1.34547 - 2.33043i) q^{11} +(1.52507 - 0.133426i) q^{13} +(0.351082 + 1.31026i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(4.11867 + 0.360337i) q^{17} +(0.739989 - 1.58691i) q^{19} +(-0.241874 + 2.76463i) q^{20} +(2.20430 + 1.54346i) q^{22} +(1.05730 - 0.283302i) q^{23} +(0.924028 - 2.53875i) q^{25} +(-1.32580 + 0.765448i) q^{26} +(-0.871926 - 1.03912i) q^{28} +(5.38761 + 1.44361i) q^{29} +(3.32111 + 3.32111i) q^{31} +(0.573576 + 0.819152i) q^{32} +(-3.88507 + 1.41405i) q^{34} +(1.59094 + 3.41178i) q^{35} +(5.51738 - 2.56095i) q^{37} +1.75096i q^{38} +(-0.949171 - 2.60783i) q^{40} +(3.89852 + 3.27124i) q^{41} +(0.103083 - 0.103083i) q^{43} +(-2.65007 - 0.467278i) q^{44} +(-0.838509 + 0.703592i) q^{46} +(-8.88064 - 5.12724i) q^{47} +(4.84879 + 1.76481i) q^{49} +(0.235467 + 2.69140i) q^{50} +(0.878086 - 1.25404i) q^{52} +(7.13680 - 1.25841i) q^{53} +(6.76821 + 3.15607i) q^{55} +(1.22938 + 0.573271i) q^{56} +(-5.49293 + 0.968551i) q^{58} +(7.01467 - 10.0180i) q^{59} +(-0.282040 - 3.22373i) q^{61} +(-4.41351 - 1.60639i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.25456 + 2.73090i) q^{65} +(3.12376 + 0.550804i) q^{67} +(2.92347 - 2.92347i) q^{68} +(-2.88376 - 2.41976i) q^{70} +(1.48707 + 4.08569i) q^{71} +0.271239i q^{73} +(-3.91814 + 4.65276i) q^{74} +(-0.739989 - 1.58691i) q^{76} +(-3.43007 + 1.24844i) q^{77} +(3.80938 + 5.44036i) q^{79} +(1.96236 + 1.96236i) q^{80} +(-4.91574 - 1.31717i) q^{82} +(-3.10674 - 3.70246i) q^{83} +(-9.93657 + 5.73688i) q^{85} +(-0.0498601 + 0.136990i) q^{86} +(2.59926 - 0.696469i) q^{88} +(5.61411 + 3.93104i) q^{89} +(0.180990 - 2.06872i) q^{91} +(0.462596 - 0.992040i) q^{92} +(10.2155 + 0.893737i) q^{94} +(0.843800 + 4.78543i) q^{95} +(-0.863737 - 3.22351i) q^{97} +(-5.14034 + 0.449721i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{36}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.906308 + 0.422618i −0.640856 + 0.298836i
\(3\) 0 0
\(4\) 0.642788 0.766044i 0.321394 0.383022i
\(5\) −2.27330 + 1.59178i −1.01665 + 0.711867i −0.958105 0.286418i \(-0.907536\pi\)
−0.0585468 + 0.998285i \(0.518647\pi\)
\(6\) 0 0
\(7\) 0.235550 1.33587i 0.0890294 0.504911i −0.907385 0.420301i \(-0.861925\pi\)
0.996414 0.0846098i \(-0.0269644\pi\)
\(8\) −0.258819 + 0.965926i −0.0915064 + 0.341506i
\(9\) 0 0
\(10\) 1.38759 2.40338i 0.438796 0.760017i
\(11\) −1.34547 2.33043i −0.405676 0.702651i 0.588724 0.808334i \(-0.299630\pi\)
−0.994400 + 0.105683i \(0.966297\pi\)
\(12\) 0 0
\(13\) 1.52507 0.133426i 0.422979 0.0370058i 0.126320 0.991990i \(-0.459683\pi\)
0.296658 + 0.954984i \(0.404128\pi\)
\(14\) 0.351082 + 1.31026i 0.0938306 + 0.350180i
\(15\) 0 0
\(16\) −0.173648 0.984808i −0.0434120 0.246202i
\(17\) 4.11867 + 0.360337i 0.998925 + 0.0873946i 0.574873 0.818243i \(-0.305052\pi\)
0.424053 + 0.905638i \(0.360607\pi\)
\(18\) 0 0
\(19\) 0.739989 1.58691i 0.169765 0.364062i −0.802957 0.596037i \(-0.796741\pi\)
0.972722 + 0.231975i \(0.0745188\pi\)
\(20\) −0.241874 + 2.76463i −0.0540846 + 0.618190i
\(21\) 0 0
\(22\) 2.20430 + 1.54346i 0.469957 + 0.329068i
\(23\) 1.05730 0.283302i 0.220462 0.0590726i −0.146897 0.989152i \(-0.546929\pi\)
0.367359 + 0.930079i \(0.380262\pi\)
\(24\) 0 0
\(25\) 0.924028 2.53875i 0.184806 0.507749i
\(26\) −1.32580 + 0.765448i −0.260010 + 0.150117i
\(27\) 0 0
\(28\) −0.871926 1.03912i −0.164779 0.196375i
\(29\) 5.38761 + 1.44361i 1.00045 + 0.268071i 0.721636 0.692273i \(-0.243391\pi\)
0.278818 + 0.960344i \(0.410057\pi\)
\(30\) 0 0
\(31\) 3.32111 + 3.32111i 0.596489 + 0.596489i 0.939377 0.342887i \(-0.111405\pi\)
−0.342887 + 0.939377i \(0.611405\pi\)
\(32\) 0.573576 + 0.819152i 0.101395 + 0.144807i
\(33\) 0 0
\(34\) −3.88507 + 1.41405i −0.666284 + 0.242508i
\(35\) 1.59094 + 3.41178i 0.268917 + 0.576695i
\(36\) 0 0
\(37\) 5.51738 2.56095i 0.907052 0.421018i
\(38\) 1.75096i 0.284044i
\(39\) 0 0
\(40\) −0.949171 2.60783i −0.150077 0.412333i
\(41\) 3.89852 + 3.27124i 0.608846 + 0.510882i 0.894275 0.447517i \(-0.147692\pi\)
−0.285429 + 0.958400i \(0.592136\pi\)
\(42\) 0 0
\(43\) 0.103083 0.103083i 0.0157200 0.0157200i −0.699203 0.714923i \(-0.746462\pi\)
0.714923 + 0.699203i \(0.246462\pi\)
\(44\) −2.65007 0.467278i −0.399513 0.0704448i
\(45\) 0 0
\(46\) −0.838509 + 0.703592i −0.123631 + 0.103739i
\(47\) −8.88064 5.12724i −1.29537 0.747885i −0.315773 0.948835i \(-0.602264\pi\)
−0.979602 + 0.200950i \(0.935597\pi\)
\(48\) 0 0
\(49\) 4.84879 + 1.76481i 0.692684 + 0.252116i
\(50\) 0.235467 + 2.69140i 0.0333000 + 0.380621i
\(51\) 0 0
\(52\) 0.878086 1.25404i 0.121769 0.173904i
\(53\) 7.13680 1.25841i 0.980315 0.172856i 0.339546 0.940590i \(-0.389727\pi\)
0.640769 + 0.767734i \(0.278616\pi\)
\(54\) 0 0
\(55\) 6.76821 + 3.15607i 0.912625 + 0.425564i
\(56\) 1.22938 + 0.573271i 0.164283 + 0.0766066i
\(57\) 0 0
\(58\) −5.49293 + 0.968551i −0.721257 + 0.127177i
\(59\) 7.01467 10.0180i 0.913232 1.30423i −0.0391211 0.999234i \(-0.512456\pi\)
0.952353 0.304997i \(-0.0986553\pi\)
\(60\) 0 0
\(61\) −0.282040 3.22373i −0.0361115 0.412757i −0.992639 0.121113i \(-0.961354\pi\)
0.956527 0.291643i \(-0.0942020\pi\)
\(62\) −4.41351 1.60639i −0.560517 0.204011i
\(63\) 0 0
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) −3.25456 + 2.73090i −0.403679 + 0.338727i
\(66\) 0 0
\(67\) 3.12376 + 0.550804i 0.381628 + 0.0672914i 0.361172 0.932499i \(-0.382377\pi\)
0.0204567 + 0.999791i \(0.493488\pi\)
\(68\) 2.92347 2.92347i 0.354522 0.354522i
\(69\) 0 0
\(70\) −2.88376 2.41976i −0.344675 0.289217i
\(71\) 1.48707 + 4.08569i 0.176483 + 0.484882i 0.996120 0.0879998i \(-0.0280475\pi\)
−0.819638 + 0.572882i \(0.805825\pi\)
\(72\) 0 0
\(73\) 0.271239i 0.0317461i 0.999874 + 0.0158731i \(0.00505276\pi\)
−0.999874 + 0.0158731i \(0.994947\pi\)
\(74\) −3.91814 + 4.65276i −0.455475 + 0.540872i
\(75\) 0 0
\(76\) −0.739989 1.58691i −0.0848825 0.182031i
\(77\) −3.43007 + 1.24844i −0.390893 + 0.142273i
\(78\) 0 0
\(79\) 3.80938 + 5.44036i 0.428589 + 0.612088i 0.974128 0.225997i \(-0.0725640\pi\)
−0.545539 + 0.838085i \(0.683675\pi\)
\(80\) 1.96236 + 1.96236i 0.219398 + 0.219398i
\(81\) 0 0
\(82\) −4.91574 1.31717i −0.542853 0.145457i
\(83\) −3.10674 3.70246i −0.341009 0.406398i 0.568099 0.822961i \(-0.307679\pi\)
−0.909107 + 0.416562i \(0.863235\pi\)
\(84\) 0 0
\(85\) −9.93657 + 5.73688i −1.07777 + 0.622252i
\(86\) −0.0498601 + 0.136990i −0.00537656 + 0.0147720i
\(87\) 0 0
\(88\) 2.59926 0.696469i 0.277082 0.0742438i
\(89\) 5.61411 + 3.93104i 0.595094 + 0.416689i 0.831946 0.554856i \(-0.187227\pi\)
−0.236852 + 0.971546i \(0.576116\pi\)
\(90\) 0 0
\(91\) 0.180990 2.06872i 0.0189729 0.216861i
\(92\) 0.462596 0.992040i 0.0482290 0.103427i
\(93\) 0 0
\(94\) 10.2155 + 0.893737i 1.05364 + 0.0921819i
\(95\) 0.843800 + 4.78543i 0.0865721 + 0.490975i
\(96\) 0 0
\(97\) −0.863737 3.22351i −0.0876992 0.327298i 0.908112 0.418726i \(-0.137523\pi\)
−0.995812 + 0.0914286i \(0.970857\pi\)
\(98\) −5.14034 + 0.449721i −0.519253 + 0.0454287i
\(99\) 0 0
\(100\) −1.35084 2.33972i −0.135084 0.233972i
\(101\) 4.68631 8.11693i 0.466306 0.807665i −0.532954 0.846144i \(-0.678918\pi\)
0.999259 + 0.0384794i \(0.0122514\pi\)
\(102\) 0 0
\(103\) −1.93545 + 7.22319i −0.190705 + 0.711722i 0.802632 + 0.596475i \(0.203433\pi\)
−0.993337 + 0.115247i \(0.963234\pi\)
\(104\) −0.265837 + 1.50764i −0.0260675 + 0.147836i
\(105\) 0 0
\(106\) −5.93631 + 4.15665i −0.576585 + 0.403729i
\(107\) 2.82287 3.36417i 0.272897 0.325226i −0.612137 0.790751i \(-0.709690\pi\)
0.885035 + 0.465525i \(0.154134\pi\)
\(108\) 0 0
\(109\) −12.2377 + 5.70652i −1.17216 + 0.546585i −0.908440 0.418015i \(-0.862726\pi\)
−0.263716 + 0.964600i \(0.584948\pi\)
\(110\) −7.46789 −0.712035
\(111\) 0 0
\(112\) −1.35648 −0.128175
\(113\) 2.75210 1.28332i 0.258895 0.120725i −0.288838 0.957378i \(-0.593269\pi\)
0.547733 + 0.836653i \(0.315491\pi\)
\(114\) 0 0
\(115\) −1.95260 + 2.32702i −0.182081 + 0.216996i
\(116\) 4.56895 3.19922i 0.424217 0.297040i
\(117\) 0 0
\(118\) −2.12367 + 12.0439i −0.195499 + 1.10873i
\(119\) 1.45151 5.41713i 0.133060 0.496587i
\(120\) 0 0
\(121\) 1.87940 3.25521i 0.170854 0.295929i
\(122\) 1.61802 + 2.80250i 0.146489 + 0.253726i
\(123\) 0 0
\(124\) 4.67889 0.409350i 0.420177 0.0367607i
\(125\) −1.65082 6.16095i −0.147654 0.551052i
\(126\) 0 0
\(127\) 3.42243 + 19.4096i 0.303692 + 1.72232i 0.629599 + 0.776920i \(0.283219\pi\)
−0.325907 + 0.945402i \(0.605670\pi\)
\(128\) 0.996195 + 0.0871557i 0.0880520 + 0.00770355i
\(129\) 0 0
\(130\) 1.79551 3.85047i 0.157476 0.337709i
\(131\) 1.75945 20.1106i 0.153723 1.75707i −0.392801 0.919624i \(-0.628494\pi\)
0.546524 0.837443i \(-0.315951\pi\)
\(132\) 0 0
\(133\) −1.94560 1.36232i −0.168705 0.118128i
\(134\) −3.06387 + 0.820962i −0.264678 + 0.0709203i
\(135\) 0 0
\(136\) −1.41405 + 3.88507i −0.121254 + 0.333142i
\(137\) −11.2022 + 6.46757i −0.957066 + 0.552562i −0.895269 0.445527i \(-0.853016\pi\)
−0.0617971 + 0.998089i \(0.519683\pi\)
\(138\) 0 0
\(139\) −11.8850 14.1640i −1.00807 1.20137i −0.979430 0.201785i \(-0.935326\pi\)
−0.0286430 0.999590i \(-0.509119\pi\)
\(140\) 3.63621 + 0.974319i 0.307316 + 0.0823449i
\(141\) 0 0
\(142\) −3.07443 3.07443i −0.258000 0.258000i
\(143\) −2.36288 3.37455i −0.197594 0.282194i
\(144\) 0 0
\(145\) −14.5456 + 5.29415i −1.20794 + 0.439656i
\(146\) −0.114631 0.245826i −0.00948689 0.0203447i
\(147\) 0 0
\(148\) 1.58470 5.87271i 0.130262 0.482734i
\(149\) 0.645327i 0.0528672i 0.999651 + 0.0264336i \(0.00841506\pi\)
−0.999651 + 0.0264336i \(0.991585\pi\)
\(150\) 0 0
\(151\) −4.25678 11.6954i −0.346412 0.951758i −0.983491 0.180960i \(-0.942080\pi\)
0.637079 0.770799i \(-0.280143\pi\)
\(152\) 1.34132 + 1.12550i 0.108795 + 0.0912899i
\(153\) 0 0
\(154\) 2.58109 2.58109i 0.207990 0.207990i
\(155\) −12.8364 2.26340i −1.03104 0.181801i
\(156\) 0 0
\(157\) −13.4610 + 11.2951i −1.07431 + 0.901449i −0.995436 0.0954355i \(-0.969576\pi\)
−0.0788700 + 0.996885i \(0.525131\pi\)
\(158\) −5.75167 3.32073i −0.457578 0.264183i
\(159\) 0 0
\(160\) −2.60783 0.949171i −0.206167 0.0750385i
\(161\) −0.129408 1.47914i −0.0101988 0.116573i
\(162\) 0 0
\(163\) 6.68363 9.54522i 0.523502 0.747639i −0.467131 0.884188i \(-0.654712\pi\)
0.990633 + 0.136549i \(0.0436012\pi\)
\(164\) 5.01184 0.883722i 0.391359 0.0690071i
\(165\) 0 0
\(166\) 4.38039 + 2.04261i 0.339984 + 0.158537i
\(167\) 4.23656 + 1.97554i 0.327835 + 0.152872i 0.579566 0.814925i \(-0.303222\pi\)
−0.251731 + 0.967797i \(0.581000\pi\)
\(168\) 0 0
\(169\) −10.4945 + 1.85046i −0.807266 + 0.142343i
\(170\) 6.58108 9.39875i 0.504746 0.720852i
\(171\) 0 0
\(172\) −0.0127057 0.145227i −0.000968798 0.0110734i
\(173\) −15.8625 5.77348i −1.20600 0.438950i −0.340688 0.940176i \(-0.610660\pi\)
−0.865316 + 0.501226i \(0.832882\pi\)
\(174\) 0 0
\(175\) −3.17378 1.83238i −0.239915 0.138515i
\(176\) −2.06139 + 1.72971i −0.155383 + 0.130382i
\(177\) 0 0
\(178\) −6.74944 1.19011i −0.505892 0.0892023i
\(179\) −0.596793 + 0.596793i −0.0446064 + 0.0446064i −0.729058 0.684452i \(-0.760042\pi\)
0.684452 + 0.729058i \(0.260042\pi\)
\(180\) 0 0
\(181\) 18.6602 + 15.6578i 1.38700 + 1.16383i 0.966537 + 0.256527i \(0.0825782\pi\)
0.420467 + 0.907308i \(0.361866\pi\)
\(182\) 0.710247 + 1.95139i 0.0526470 + 0.144647i
\(183\) 0 0
\(184\) 1.09460i 0.0806946i
\(185\) −8.46620 + 14.6043i −0.622447 + 1.07373i
\(186\) 0 0
\(187\) −4.70183 10.0831i −0.343832 0.737349i
\(188\) −9.63606 + 3.50724i −0.702782 + 0.255792i
\(189\) 0 0
\(190\) −2.78715 3.98047i −0.202201 0.288773i
\(191\) −16.3470 16.3470i −1.18283 1.18283i −0.979008 0.203822i \(-0.934664\pi\)
−0.203822 0.979008i \(-0.565336\pi\)
\(192\) 0 0
\(193\) −14.9668 4.01035i −1.07734 0.288671i −0.323832 0.946115i \(-0.604971\pi\)
−0.753504 + 0.657443i \(0.771638\pi\)
\(194\) 2.14513 + 2.55646i 0.154011 + 0.183543i
\(195\) 0 0
\(196\) 4.46867 2.57999i 0.319191 0.184285i
\(197\) −8.04789 + 22.1114i −0.573388 + 1.57537i 0.225725 + 0.974191i \(0.427525\pi\)
−0.799113 + 0.601181i \(0.794697\pi\)
\(198\) 0 0
\(199\) 6.48384 1.73734i 0.459627 0.123157i −0.0215733 0.999767i \(-0.506868\pi\)
0.481201 + 0.876610i \(0.340201\pi\)
\(200\) 2.21308 + 1.54962i 0.156489 + 0.109575i
\(201\) 0 0
\(202\) −0.816878 + 9.33696i −0.0574753 + 0.656946i
\(203\) 3.19752 6.85709i 0.224422 0.481274i
\(204\) 0 0
\(205\) −14.0696 1.23093i −0.982665 0.0859720i
\(206\) −1.29854 7.36439i −0.0904736 0.513101i
\(207\) 0 0
\(208\) −0.396225 1.47873i −0.0274733 0.102532i
\(209\) −4.69382 + 0.410656i −0.324678 + 0.0284057i
\(210\) 0 0
\(211\) −3.40637 5.90001i −0.234504 0.406173i 0.724624 0.689144i \(-0.242013\pi\)
−0.959129 + 0.282971i \(0.908680\pi\)
\(212\) 3.62345 6.27600i 0.248859 0.431037i
\(213\) 0 0
\(214\) −1.13663 + 4.24197i −0.0776986 + 0.289975i
\(215\) −0.0702529 + 0.398424i −0.00479121 + 0.0271723i
\(216\) 0 0
\(217\) 5.21885 3.65428i 0.354279 0.248069i
\(218\) 8.67941 10.3437i 0.587844 0.700565i
\(219\) 0 0
\(220\) 6.76821 3.15607i 0.456312 0.212782i
\(221\) 6.32935 0.425758
\(222\) 0 0
\(223\) 12.8235 0.858723 0.429362 0.903133i \(-0.358739\pi\)
0.429362 + 0.903133i \(0.358739\pi\)
\(224\) 1.22938 0.573271i 0.0821417 0.0383033i
\(225\) 0 0
\(226\) −1.95189 + 2.32617i −0.129838 + 0.154735i
\(227\) −13.7372 + 9.61888i −0.911769 + 0.638428i −0.932427 0.361359i \(-0.882313\pi\)
0.0206575 + 0.999787i \(0.493424\pi\)
\(228\) 0 0
\(229\) 3.84303 21.7949i 0.253954 1.44025i −0.544788 0.838574i \(-0.683390\pi\)
0.798743 0.601673i \(-0.205499\pi\)
\(230\) 0.786217 2.93420i 0.0518416 0.193476i
\(231\) 0 0
\(232\) −2.78883 + 4.83040i −0.183096 + 0.317131i
\(233\) 1.20514 + 2.08736i 0.0789513 + 0.136748i 0.902798 0.430065i \(-0.141509\pi\)
−0.823846 + 0.566813i \(0.808176\pi\)
\(234\) 0 0
\(235\) 28.3498 2.48029i 1.84934 0.161796i
\(236\) −3.16528 11.8130i −0.206042 0.768960i
\(237\) 0 0
\(238\) 0.973858 + 5.52302i 0.0631258 + 0.358004i
\(239\) 19.2353 + 1.68287i 1.24423 + 0.108856i 0.690186 0.723632i \(-0.257529\pi\)
0.554043 + 0.832488i \(0.313084\pi\)
\(240\) 0 0
\(241\) −0.0206898 + 0.0443695i −0.00133275 + 0.00285809i −0.906973 0.421189i \(-0.861613\pi\)
0.905640 + 0.424047i \(0.139391\pi\)
\(242\) −0.327601 + 3.74449i −0.0210590 + 0.240705i
\(243\) 0 0
\(244\) −2.65081 1.85612i −0.169701 0.118826i
\(245\) −13.8320 + 3.70626i −0.883692 + 0.236785i
\(246\) 0 0
\(247\) 0.916800 2.51889i 0.0583346 0.160273i
\(248\) −4.06751 + 2.34838i −0.258287 + 0.149122i
\(249\) 0 0
\(250\) 4.09988 + 4.88605i 0.259299 + 0.309021i
\(251\) 9.30495 + 2.49325i 0.587323 + 0.157373i 0.540229 0.841518i \(-0.318337\pi\)
0.0470936 + 0.998890i \(0.485004\pi\)
\(252\) 0 0
\(253\) −2.08278 2.08278i −0.130943 0.130943i
\(254\) −11.3046 16.1447i −0.709315 1.01301i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) 5.88349 + 12.6172i 0.367002 + 0.787038i 0.999918 + 0.0128178i \(0.00408013\pi\)
−0.632916 + 0.774221i \(0.718142\pi\)
\(258\) 0 0
\(259\) −2.12148 7.97373i −0.131822 0.495463i
\(260\) 4.24853i 0.263483i
\(261\) 0 0
\(262\) 6.90449 + 18.9699i 0.426561 + 1.17197i
\(263\) 10.1497 + 8.51663i 0.625859 + 0.525158i 0.899639 0.436634i \(-0.143830\pi\)
−0.273780 + 0.961792i \(0.588274\pi\)
\(264\) 0 0
\(265\) −14.2210 + 14.2210i −0.873588 + 0.873588i
\(266\) 2.33905 + 0.412438i 0.143417 + 0.0252882i
\(267\) 0 0
\(268\) 2.42986 2.03889i 0.148427 0.124545i
\(269\) 13.9187 + 8.03598i 0.848640 + 0.489962i 0.860192 0.509971i \(-0.170344\pi\)
−0.0115519 + 0.999933i \(0.503677\pi\)
\(270\) 0 0
\(271\) −2.27924 0.829576i −0.138454 0.0503931i 0.271864 0.962336i \(-0.412360\pi\)
−0.410318 + 0.911943i \(0.634582\pi\)
\(272\) −0.360337 4.11867i −0.0218487 0.249731i
\(273\) 0 0
\(274\) 7.41930 10.5959i 0.448216 0.640119i
\(275\) −7.15962 + 1.26244i −0.431742 + 0.0761277i
\(276\) 0 0
\(277\) 25.4745 + 11.8789i 1.53061 + 0.713736i 0.991694 0.128622i \(-0.0410555\pi\)
0.538918 + 0.842358i \(0.318833\pi\)
\(278\) 16.7574 + 7.81412i 1.00504 + 0.468660i
\(279\) 0 0
\(280\) −3.70729 + 0.653695i −0.221553 + 0.0390657i
\(281\) 2.74940 3.92655i 0.164015 0.234238i −0.728728 0.684803i \(-0.759888\pi\)
0.892744 + 0.450564i \(0.148777\pi\)
\(282\) 0 0
\(283\) −0.493350 5.63902i −0.0293266 0.335205i −0.996658 0.0816891i \(-0.973969\pi\)
0.967331 0.253516i \(-0.0815870\pi\)
\(284\) 4.08569 + 1.48707i 0.242441 + 0.0882414i
\(285\) 0 0
\(286\) 3.56765 + 2.05978i 0.210959 + 0.121797i
\(287\) 5.28824 4.43736i 0.312155 0.261929i
\(288\) 0 0
\(289\) 0.0918971 + 0.0162039i 0.00540571 + 0.000953172i
\(290\) 10.9454 10.9454i 0.642734 0.642734i
\(291\) 0 0
\(292\) 0.207781 + 0.174349i 0.0121595 + 0.0102030i
\(293\) 9.77701 + 26.8621i 0.571179 + 1.56930i 0.802644 + 0.596458i \(0.203426\pi\)
−0.231465 + 0.972843i \(0.574352\pi\)
\(294\) 0 0
\(295\) 33.9398i 1.97605i
\(296\) 1.04569 + 5.99221i 0.0607793 + 0.348290i
\(297\) 0 0
\(298\) −0.272727 0.584865i −0.0157986 0.0338803i
\(299\) 1.57465 0.573127i 0.0910646 0.0331448i
\(300\) 0 0
\(301\) −0.113424 0.161986i −0.00653765 0.00933673i
\(302\) 8.80064 + 8.80064i 0.506420 + 0.506420i
\(303\) 0 0
\(304\) −1.69130 0.453182i −0.0970027 0.0259918i
\(305\) 5.77265 + 6.87957i 0.330541 + 0.393923i
\(306\) 0 0
\(307\) −5.04283 + 2.91148i −0.287810 + 0.166167i −0.636954 0.770902i \(-0.719806\pi\)
0.349144 + 0.937069i \(0.386472\pi\)
\(308\) −1.24844 + 3.43007i −0.0711367 + 0.195446i
\(309\) 0 0
\(310\) 12.5903 3.37355i 0.715079 0.191605i
\(311\) 21.9726 + 15.3854i 1.24595 + 0.872426i 0.995412 0.0956804i \(-0.0305027\pi\)
0.250541 + 0.968106i \(0.419392\pi\)
\(312\) 0 0
\(313\) −0.614936 + 7.02875i −0.0347583 + 0.397289i 0.958810 + 0.284050i \(0.0916781\pi\)
−0.993568 + 0.113239i \(0.963877\pi\)
\(314\) 7.42629 15.9257i 0.419090 0.898741i
\(315\) 0 0
\(316\) 6.61618 + 0.578841i 0.372189 + 0.0325623i
\(317\) 1.71711 + 9.73820i 0.0964424 + 0.546952i 0.994296 + 0.106657i \(0.0340148\pi\)
−0.897853 + 0.440294i \(0.854874\pi\)
\(318\) 0 0
\(319\) −3.88467 14.4978i −0.217500 0.811720i
\(320\) 2.76463 0.241874i 0.154547 0.0135212i
\(321\) 0 0
\(322\) 0.742396 + 1.28587i 0.0413721 + 0.0716586i
\(323\) 3.61960 6.26932i 0.201400 0.348834i
\(324\) 0 0
\(325\) 1.07047 3.99506i 0.0593791 0.221606i
\(326\) −2.02345 + 11.4755i −0.112068 + 0.635571i
\(327\) 0 0
\(328\) −4.16879 + 2.91902i −0.230183 + 0.161176i
\(329\) −8.94115 + 10.6556i −0.492941 + 0.587465i
\(330\) 0 0
\(331\) 28.2675 13.1813i 1.55372 0.724512i 0.559198 0.829034i \(-0.311109\pi\)
0.994523 + 0.104522i \(0.0333312\pi\)
\(332\) −4.83322 −0.265258
\(333\) 0 0
\(334\) −4.67453 −0.255779
\(335\) −7.97802 + 3.72021i −0.435886 + 0.203257i
\(336\) 0 0
\(337\) −5.22153 + 6.22278i −0.284435 + 0.338976i −0.889277 0.457369i \(-0.848792\pi\)
0.604842 + 0.796346i \(0.293236\pi\)
\(338\) 8.72918 6.11223i 0.474805 0.332462i
\(339\) 0 0
\(340\) −1.99240 + 11.2994i −0.108053 + 0.612799i
\(341\) 3.27115 12.2081i 0.177143 0.661105i
\(342\) 0 0
\(343\) 8.24736 14.2848i 0.445315 0.771309i
\(344\) 0.0728906 + 0.126250i 0.00393000 + 0.00680696i
\(345\) 0 0
\(346\) 16.8163 1.47124i 0.904050 0.0790941i
\(347\) −1.55103 5.78853i −0.0832637 0.310744i 0.911716 0.410821i \(-0.134758\pi\)
−0.994980 + 0.100077i \(0.968091\pi\)
\(348\) 0 0
\(349\) −1.83880 10.4284i −0.0984289 0.558218i −0.993643 0.112581i \(-0.964088\pi\)
0.895214 0.445637i \(-0.147023\pi\)
\(350\) 3.65081 + 0.319405i 0.195144 + 0.0170729i
\(351\) 0 0
\(352\) 1.13724 2.43883i 0.0606153 0.129990i
\(353\) 0.999484 11.4241i 0.0531971 0.608046i −0.922071 0.387021i \(-0.873504\pi\)
0.975268 0.221025i \(-0.0709403\pi\)
\(354\) 0 0
\(355\) −9.88409 6.92092i −0.524593 0.367324i
\(356\) 6.62003 1.77383i 0.350861 0.0940129i
\(357\) 0 0
\(358\) 0.288662 0.793093i 0.0152563 0.0419163i
\(359\) −25.1016 + 14.4924i −1.32481 + 0.764882i −0.984492 0.175427i \(-0.943869\pi\)
−0.340322 + 0.940309i \(0.610536\pi\)
\(360\) 0 0
\(361\) 10.2423 + 12.2063i 0.539066 + 0.642434i
\(362\) −23.5292 6.30463i −1.23667 0.331364i
\(363\) 0 0
\(364\) −1.46839 1.46839i −0.0769648 0.0769648i
\(365\) −0.431754 0.616608i −0.0225990 0.0322747i
\(366\) 0 0
\(367\) −16.8701 + 6.14020i −0.880611 + 0.320516i −0.742456 0.669895i \(-0.766339\pi\)
−0.138154 + 0.990411i \(0.544117\pi\)
\(368\) −0.462596 0.992040i −0.0241145 0.0517137i
\(369\) 0 0
\(370\) 1.50094 16.8140i 0.0780300 0.874116i
\(371\) 9.83024i 0.510361i
\(372\) 0 0
\(373\) −3.33319 9.15786i −0.172586 0.474176i 0.822999 0.568043i \(-0.192299\pi\)
−0.995585 + 0.0938671i \(0.970077\pi\)
\(374\) 8.52261 + 7.15132i 0.440693 + 0.369786i
\(375\) 0 0
\(376\) 7.25101 7.25101i 0.373942 0.373942i
\(377\) 8.40910 + 1.48275i 0.433091 + 0.0763656i
\(378\) 0 0
\(379\) 14.2239 11.9353i 0.730634 0.613075i −0.199670 0.979863i \(-0.563987\pi\)
0.930304 + 0.366788i \(0.119543\pi\)
\(380\) 4.20824 + 2.42963i 0.215878 + 0.124637i
\(381\) 0 0
\(382\) 21.7240 + 7.90689i 1.11150 + 0.404552i
\(383\) −0.108584 1.24113i −0.00554841 0.0634186i 0.992916 0.118821i \(-0.0379114\pi\)
−0.998464 + 0.0554023i \(0.982356\pi\)
\(384\) 0 0
\(385\) 5.81034 8.29802i 0.296122 0.422906i
\(386\) 15.2594 2.69064i 0.776683 0.136950i
\(387\) 0 0
\(388\) −3.02455 1.41037i −0.153548 0.0716007i
\(389\) 29.6625 + 13.8318i 1.50395 + 0.701302i 0.987876 0.155245i \(-0.0496167\pi\)
0.516070 + 0.856546i \(0.327394\pi\)
\(390\) 0 0
\(391\) 4.45675 0.785845i 0.225387 0.0397419i
\(392\) −2.95964 + 4.22680i −0.149484 + 0.213486i
\(393\) 0 0
\(394\) −2.05081 23.4409i −0.103319 1.18094i
\(395\) −17.3197 6.30387i −0.871451 0.317182i
\(396\) 0 0
\(397\) −21.5055 12.4162i −1.07933 0.623151i −0.148614 0.988895i \(-0.547481\pi\)
−0.930715 + 0.365744i \(0.880814\pi\)
\(398\) −5.14213 + 4.31476i −0.257751 + 0.216279i
\(399\) 0 0
\(400\) −2.66063 0.469141i −0.133032 0.0234571i
\(401\) −13.8195 + 13.8195i −0.690113 + 0.690113i −0.962257 0.272143i \(-0.912267\pi\)
0.272143 + 0.962257i \(0.412267\pi\)
\(402\) 0 0
\(403\) 5.50805 + 4.62181i 0.274376 + 0.230229i
\(404\) −3.20563 8.80739i −0.159486 0.438184i
\(405\) 0 0
\(406\) 7.56597i 0.375493i
\(407\) −13.3916 9.41218i −0.663798 0.466544i
\(408\) 0 0
\(409\) −8.45778 18.1378i −0.418210 0.896855i −0.996701 0.0811654i \(-0.974136\pi\)
0.578490 0.815689i \(-0.303642\pi\)
\(410\) 13.2716 4.83047i 0.655439 0.238560i
\(411\) 0 0
\(412\) 4.28920 + 6.12561i 0.211314 + 0.301787i
\(413\) −11.7304 11.7304i −0.577216 0.577216i
\(414\) 0 0
\(415\) 12.9561 + 3.47157i 0.635989 + 0.170413i
\(416\) 0.984041 + 1.17273i 0.0482466 + 0.0574980i
\(417\) 0 0
\(418\) 4.08049 2.35587i 0.199584 0.115230i
\(419\) −1.65269 + 4.54072i −0.0807390 + 0.221829i −0.973493 0.228715i \(-0.926548\pi\)
0.892754 + 0.450544i \(0.148770\pi\)
\(420\) 0 0
\(421\) 4.30723 1.15412i 0.209922 0.0562484i −0.152326 0.988330i \(-0.548676\pi\)
0.362247 + 0.932082i \(0.382010\pi\)
\(422\) 5.58067 + 3.90763i 0.271663 + 0.190220i
\(423\) 0 0
\(424\) −0.631609 + 7.21932i −0.0306736 + 0.350601i
\(425\) 4.72057 10.1233i 0.228982 0.491052i
\(426\) 0 0
\(427\) −4.37292 0.382581i −0.211620 0.0185144i
\(428\) −0.762595 4.32489i −0.0368614 0.209052i
\(429\) 0 0
\(430\) −0.104711 0.390785i −0.00504959 0.0188453i
\(431\) 18.4810 1.61688i 0.890201 0.0778825i 0.367128 0.930170i \(-0.380341\pi\)
0.523073 + 0.852288i \(0.324786\pi\)
\(432\) 0 0
\(433\) −3.97483 6.88461i −0.191018 0.330853i 0.754570 0.656220i \(-0.227846\pi\)
−0.945588 + 0.325367i \(0.894512\pi\)
\(434\) −3.18552 + 5.51749i −0.152910 + 0.264848i
\(435\) 0 0
\(436\) −3.49477 + 13.0427i −0.167369 + 0.624631i
\(437\) 0.332813 1.88748i 0.0159206 0.0902903i
\(438\) 0 0
\(439\) −14.0454 + 9.83466i −0.670348 + 0.469383i −0.858538 0.512750i \(-0.828627\pi\)
0.188190 + 0.982133i \(0.439738\pi\)
\(440\) −4.80027 + 5.72074i −0.228844 + 0.272725i
\(441\) 0 0
\(442\) −5.73634 + 2.67490i −0.272850 + 0.127232i
\(443\) −29.8379 −1.41764 −0.708821 0.705388i \(-0.750773\pi\)
−0.708821 + 0.705388i \(0.750773\pi\)
\(444\) 0 0
\(445\) −19.0199 −0.901631
\(446\) −11.6220 + 5.41943i −0.550318 + 0.256618i
\(447\) 0 0
\(448\) −0.871926 + 1.03912i −0.0411946 + 0.0490938i
\(449\) 3.39752 2.37897i 0.160339 0.112270i −0.490653 0.871355i \(-0.663242\pi\)
0.650992 + 0.759084i \(0.274353\pi\)
\(450\) 0 0
\(451\) 2.37805 13.4866i 0.111978 0.635059i
\(452\) 0.785930 2.93313i 0.0369670 0.137963i
\(453\) 0 0
\(454\) 8.38501 14.5233i 0.393528 0.681610i
\(455\) 2.88151 + 4.99093i 0.135087 + 0.233978i
\(456\) 0 0
\(457\) 24.3633 2.13152i 1.13967 0.0997081i 0.498345 0.866979i \(-0.333941\pi\)
0.641324 + 0.767270i \(0.278386\pi\)
\(458\) 5.72795 + 21.3770i 0.267650 + 0.998882i
\(459\) 0 0
\(460\) 0.527493 + 2.99156i 0.0245945 + 0.139482i
\(461\) −25.4764 2.22890i −1.18655 0.103810i −0.523263 0.852171i \(-0.675285\pi\)
−0.663292 + 0.748361i \(0.730841\pi\)
\(462\) 0 0
\(463\) 1.12825 2.41955i 0.0524344 0.112446i −0.878345 0.478027i \(-0.841352\pi\)
0.930779 + 0.365581i \(0.119130\pi\)
\(464\) 0.486125 5.55644i 0.0225678 0.257951i
\(465\) 0 0
\(466\) −1.97439 1.38248i −0.0914617 0.0640421i
\(467\) −33.8235 + 9.06299i −1.56517 + 0.419385i −0.934295 0.356501i \(-0.883970\pi\)
−0.630872 + 0.775887i \(0.717303\pi\)
\(468\) 0 0
\(469\) 1.47160 4.04319i 0.0679523 0.186697i
\(470\) −24.6455 + 14.2291i −1.13681 + 0.656338i
\(471\) 0 0
\(472\) 7.86110 + 9.36850i 0.361837 + 0.431220i
\(473\) −0.378923 0.101532i −0.0174229 0.00466845i
\(474\) 0 0
\(475\) −3.34499 3.34499i −0.153479 0.153479i
\(476\) −3.21674 4.59399i −0.147439 0.210565i
\(477\) 0 0
\(478\) −18.1443 + 6.60399i −0.829902 + 0.302060i
\(479\) 7.36452 + 15.7933i 0.336493 + 0.721612i 0.999639 0.0268783i \(-0.00855666\pi\)
−0.663145 + 0.748491i \(0.730779\pi\)
\(480\) 0 0
\(481\) 8.07270 4.64180i 0.368084 0.211648i
\(482\) 0.0489563i 0.00222990i
\(483\) 0 0
\(484\) −1.28558 3.53211i −0.0584357 0.160551i
\(485\) 7.09466 + 5.95313i 0.322152 + 0.270318i
\(486\) 0 0
\(487\) −24.1126 + 24.1126i −1.09265 + 1.09265i −0.0974024 + 0.995245i \(0.531053\pi\)
−0.995245 + 0.0974024i \(0.968947\pi\)
\(488\) 3.18688 + 0.561934i 0.144263 + 0.0254375i
\(489\) 0 0
\(490\) 10.9697 9.20466i 0.495560 0.415824i
\(491\) 21.1432 + 12.2070i 0.954178 + 0.550895i 0.894376 0.447315i \(-0.147620\pi\)
0.0598019 + 0.998210i \(0.480953\pi\)
\(492\) 0 0
\(493\) 21.6696 + 7.88710i 0.975951 + 0.355217i
\(494\) 0.233625 + 2.67034i 0.0105113 + 0.120144i
\(495\) 0 0
\(496\) 2.69395 3.84736i 0.120962 0.172752i
\(497\) 5.80822 1.02415i 0.260534 0.0459392i
\(498\) 0 0
\(499\) 31.9048 + 14.8775i 1.42826 + 0.666007i 0.974349 0.225043i \(-0.0722521\pi\)
0.453907 + 0.891049i \(0.350030\pi\)
\(500\) −5.78069 2.69558i −0.258520 0.120550i
\(501\) 0 0
\(502\) −9.48684 + 1.67279i −0.423418 + 0.0746601i
\(503\) 12.7986 18.2783i 0.570661 0.814989i −0.425274 0.905065i \(-0.639822\pi\)
0.995935 + 0.0900761i \(0.0287110\pi\)
\(504\) 0 0
\(505\) 2.26699 + 25.9118i 0.100880 + 1.15306i
\(506\) 2.76786 + 1.00742i 0.123047 + 0.0447853i
\(507\) 0 0
\(508\) 17.0685 + 9.85451i 0.757292 + 0.437223i
\(509\) 0.772986 0.648613i 0.0342620 0.0287492i −0.625496 0.780227i \(-0.715103\pi\)
0.659758 + 0.751478i \(0.270659\pi\)
\(510\) 0 0
\(511\) 0.362339 + 0.0638902i 0.0160290 + 0.00282634i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) −10.6645 8.94858i −0.470391 0.394705i
\(515\) −7.09789 19.5013i −0.312770 0.859330i
\(516\) 0 0
\(517\) 27.5943i 1.21359i
\(518\) 5.29255 + 6.33008i 0.232542 + 0.278128i
\(519\) 0 0
\(520\) −1.79551 3.85047i −0.0787381 0.168854i
\(521\) 8.30810 3.02390i 0.363984 0.132479i −0.153552 0.988141i \(-0.549071\pi\)
0.517537 + 0.855661i \(0.326849\pi\)
\(522\) 0 0
\(523\) −6.97982 9.96822i −0.305206 0.435880i 0.637025 0.770843i \(-0.280165\pi\)
−0.942231 + 0.334964i \(0.891276\pi\)
\(524\) −14.2746 14.2746i −0.623590 0.623590i
\(525\) 0 0
\(526\) −12.7981 3.42923i −0.558022 0.149522i
\(527\) 12.4819 + 14.8753i 0.543718 + 0.647978i
\(528\) 0 0
\(529\) −18.8810 + 10.9009i −0.820912 + 0.473954i
\(530\) 6.87854 18.8986i 0.298785 0.820904i
\(531\) 0 0
\(532\) −2.29421 + 0.614731i −0.0994665 + 0.0266520i
\(533\) 6.38198 + 4.46871i 0.276434 + 0.193561i
\(534\) 0 0
\(535\) −1.06222 + 12.1412i −0.0459236 + 0.524909i
\(536\) −1.34052 + 2.87476i −0.0579018 + 0.124171i
\(537\) 0 0
\(538\) −16.0108 1.40076i −0.690275 0.0603912i
\(539\) −2.41114 13.6743i −0.103855 0.588993i
\(540\) 0 0
\(541\) −6.44160 24.0404i −0.276946 1.03358i −0.954526 0.298128i \(-0.903638\pi\)
0.677580 0.735449i \(-0.263029\pi\)
\(542\) 2.41629 0.211398i 0.103788 0.00908031i
\(543\) 0 0
\(544\) 2.06720 + 3.58050i 0.0886306 + 0.153513i
\(545\) 18.7364 32.4523i 0.802578 1.39011i
\(546\) 0 0
\(547\) 1.68985 6.30661i 0.0722528 0.269651i −0.920344 0.391111i \(-0.872091\pi\)
0.992596 + 0.121460i \(0.0387575\pi\)
\(548\) −2.24617 + 12.7386i −0.0959514 + 0.544168i
\(549\) 0 0
\(550\) 5.95530 4.16994i 0.253935 0.177807i
\(551\) 6.27764 7.48140i 0.267437 0.318719i
\(552\) 0 0
\(553\) 8.16490 3.80736i 0.347207 0.161905i
\(554\) −28.1079 −1.19419
\(555\) 0 0
\(556\) −18.4898 −0.784142
\(557\) −16.8705 + 7.86685i −0.714827 + 0.333329i −0.745781 0.666192i \(-0.767923\pi\)
0.0309538 + 0.999521i \(0.490146\pi\)
\(558\) 0 0
\(559\) 0.143455 0.170963i 0.00606749 0.00723095i
\(560\) 3.08368 2.15922i 0.130309 0.0912435i
\(561\) 0 0
\(562\) −0.832371 + 4.72061i −0.0351114 + 0.199127i
\(563\) 4.50975 16.8306i 0.190063 0.709325i −0.803427 0.595404i \(-0.796992\pi\)
0.993490 0.113921i \(-0.0363412\pi\)
\(564\) 0 0
\(565\) −4.21357 + 7.29812i −0.177266 + 0.307034i
\(566\) 2.83028 + 4.90219i 0.118966 + 0.206054i
\(567\) 0 0
\(568\) −4.33136 + 0.378945i −0.181740 + 0.0159002i
\(569\) 6.29363 + 23.4881i 0.263843 + 0.984674i 0.962955 + 0.269662i \(0.0869120\pi\)
−0.699112 + 0.715012i \(0.746421\pi\)
\(570\) 0 0
\(571\) 4.13085 + 23.4272i 0.172871 + 0.980399i 0.940573 + 0.339592i \(0.110289\pi\)
−0.767702 + 0.640807i \(0.778600\pi\)
\(572\) −4.10389 0.359044i −0.171592 0.0150124i
\(573\) 0 0
\(574\) −2.91747 + 6.25653i −0.121773 + 0.261142i
\(575\) 0.257741 2.94599i 0.0107485 0.122856i
\(576\) 0 0
\(577\) −34.3983 24.0859i −1.43202 1.00271i −0.994636 0.103434i \(-0.967017\pi\)
−0.437382 0.899276i \(-0.644094\pi\)
\(578\) −0.0901351 + 0.0241516i −0.00374913 + 0.00100458i
\(579\) 0 0
\(580\) −5.29415 + 14.5456i −0.219828 + 0.603972i
\(581\) −5.67779 + 3.27808i −0.235555 + 0.135998i
\(582\) 0 0
\(583\) −12.5350 14.9386i −0.519147 0.618696i
\(584\) −0.261997 0.0702018i −0.0108415 0.00290497i
\(585\) 0 0
\(586\) −20.2134 20.2134i −0.835008 0.835008i
\(587\) −0.983918 1.40518i −0.0406106 0.0579980i 0.798333 0.602216i \(-0.205715\pi\)
−0.838944 + 0.544218i \(0.816826\pi\)
\(588\) 0 0
\(589\) 7.72789 2.81272i 0.318422 0.115896i
\(590\) −14.3436 30.7599i −0.590515 1.26636i
\(591\) 0 0
\(592\) −3.48013 4.98886i −0.143032 0.205041i
\(593\) 22.4283i 0.921020i −0.887655 0.460510i \(-0.847667\pi\)
0.887655 0.460510i \(-0.152333\pi\)
\(594\) 0 0
\(595\) 5.32316 + 14.6253i 0.218228 + 0.599577i
\(596\) 0.494349 + 0.414808i 0.0202493 + 0.0169912i
\(597\) 0 0
\(598\) −1.18491 + 1.18491i −0.0484545 + 0.0484545i
\(599\) 11.3133 + 1.99483i 0.462248 + 0.0815067i 0.399922 0.916549i \(-0.369037\pi\)
0.0623255 + 0.998056i \(0.480148\pi\)
\(600\) 0 0
\(601\) 19.8035 16.6171i 0.807803 0.677827i −0.142279 0.989827i \(-0.545443\pi\)
0.950082 + 0.311999i \(0.100999\pi\)
\(602\) 0.171255 + 0.0988744i 0.00697985 + 0.00402982i
\(603\) 0 0
\(604\) −11.6954 4.25678i −0.475879 0.173206i
\(605\) 0.909154 + 10.3917i 0.0369624 + 0.422482i
\(606\) 0 0
\(607\) −15.6819 + 22.3960i −0.636507 + 0.909027i −0.999743 0.0226707i \(-0.992783\pi\)
0.363236 + 0.931697i \(0.381672\pi\)
\(608\) 1.72436 0.304051i 0.0699321 0.0123309i
\(609\) 0 0
\(610\) −8.13923 3.79538i −0.329548 0.153671i
\(611\) −14.2277 6.63449i −0.575592 0.268403i
\(612\) 0 0
\(613\) 14.4650 2.55057i 0.584236 0.103017i 0.126285 0.991994i \(-0.459695\pi\)
0.457951 + 0.888977i \(0.348584\pi\)
\(614\) 3.33991 4.76989i 0.134788 0.192497i
\(615\) 0 0
\(616\) −0.318136 3.63632i −0.0128181 0.146511i
\(617\) −44.2733 16.1141i −1.78237 0.648731i −0.999653 0.0263596i \(-0.991608\pi\)
−0.782722 0.622372i \(-0.786169\pi\)
\(618\) 0 0
\(619\) −30.5984 17.6660i −1.22985 0.710057i −0.262855 0.964835i \(-0.584664\pi\)
−0.966999 + 0.254779i \(0.917997\pi\)
\(620\) −9.98493 + 8.37835i −0.401005 + 0.336483i
\(621\) 0 0
\(622\) −26.4161 4.65787i −1.05919 0.186764i
\(623\) 6.57375 6.57375i 0.263372 0.263372i
\(624\) 0 0
\(625\) 23.9077 + 20.0610i 0.956309 + 0.802439i
\(626\) −2.41316 6.63010i −0.0964492 0.264992i
\(627\) 0 0
\(628\) 17.5721i 0.701203i
\(629\) 23.6471 8.55961i 0.942872 0.341294i
\(630\) 0 0
\(631\) −7.14015 15.3121i −0.284245 0.609565i 0.711401 0.702787i \(-0.248061\pi\)
−0.995645 + 0.0932220i \(0.970283\pi\)
\(632\) −6.24092 + 2.27151i −0.248251 + 0.0903558i
\(633\) 0 0
\(634\) −5.67177 8.10013i −0.225255 0.321697i
\(635\) −38.6761 38.6761i −1.53481 1.53481i
\(636\) 0 0
\(637\) 7.63022 + 2.04451i 0.302320 + 0.0810065i
\(638\) 9.64773 + 11.4977i 0.381957 + 0.455199i
\(639\) 0 0
\(640\) −2.40338 + 1.38759i −0.0950021 + 0.0548495i
\(641\) −3.08971 + 8.48891i −0.122036 + 0.335292i −0.985635 0.168887i \(-0.945983\pi\)
0.863599 + 0.504179i \(0.168205\pi\)
\(642\) 0 0
\(643\) −27.7873 + 7.44559i −1.09583 + 0.293625i −0.761064 0.648677i \(-0.775322\pi\)
−0.334762 + 0.942303i \(0.608656\pi\)
\(644\) −1.21627 0.851642i −0.0479278 0.0335594i
\(645\) 0 0
\(646\) −0.630937 + 7.21164i −0.0248239 + 0.283738i
\(647\) 1.38466 2.96942i 0.0544367 0.116740i −0.877208 0.480111i \(-0.840596\pi\)
0.931645 + 0.363371i \(0.118374\pi\)
\(648\) 0 0
\(649\) −32.7843 2.86825i −1.28690 0.112589i
\(650\) 0.718207 + 4.07315i 0.0281704 + 0.159762i
\(651\) 0 0
\(652\) −3.01590 11.2555i −0.118112 0.440800i
\(653\) 26.6996 2.33591i 1.04484 0.0914112i 0.448208 0.893929i \(-0.352063\pi\)
0.596628 + 0.802518i \(0.296507\pi\)
\(654\) 0 0
\(655\) 28.0119 + 48.5180i 1.09452 + 1.89576i
\(656\) 2.54458 4.40733i 0.0993490 0.172078i
\(657\) 0 0
\(658\) 3.60016 13.4360i 0.140349 0.523789i
\(659\) 2.20416 12.5004i 0.0858620 0.486948i −0.911305 0.411731i \(-0.864924\pi\)
0.997167 0.0752162i \(-0.0239647\pi\)
\(660\) 0 0
\(661\) −41.3646 + 28.9638i −1.60890 + 1.12656i −0.696264 + 0.717786i \(0.745156\pi\)
−0.912634 + 0.408777i \(0.865955\pi\)
\(662\) −20.0484 + 23.8927i −0.779202 + 0.928616i
\(663\) 0 0
\(664\) 4.38039 2.04261i 0.169992 0.0792686i
\(665\) 6.59146 0.255606
\(666\) 0 0
\(667\) 6.10528 0.236398
\(668\) 4.23656 1.97554i 0.163917 0.0764360i
\(669\) 0 0
\(670\) 5.65831 6.74331i 0.218600 0.260517i
\(671\) −7.13320 + 4.99472i −0.275374 + 0.192819i
\(672\) 0 0
\(673\) 6.03500 34.2262i 0.232632 1.31932i −0.614911 0.788597i \(-0.710808\pi\)
0.847543 0.530726i \(-0.178081\pi\)
\(674\) 2.10245 7.84647i 0.0809835 0.302235i
\(675\) 0 0
\(676\) −5.32818 + 9.22868i −0.204930 + 0.354949i
\(677\) −4.30315 7.45327i −0.165383 0.286452i 0.771408 0.636341i \(-0.219553\pi\)
−0.936791 + 0.349888i \(0.886219\pi\)
\(678\) 0 0
\(679\) −4.50964 + 0.394542i −0.173064 + 0.0151411i
\(680\) −2.96963 11.0828i −0.113880 0.425006i
\(681\) 0 0
\(682\) 2.19469 + 12.4467i 0.0840392 + 0.476610i
\(683\) −21.1770 1.85275i −0.810315 0.0708934i −0.325536 0.945530i \(-0.605545\pi\)
−0.484780 + 0.874636i \(0.661100\pi\)
\(684\) 0 0
\(685\) 15.1709 32.5342i 0.579652 1.24307i
\(686\) −1.43761 + 16.4319i −0.0548882 + 0.627374i
\(687\) 0 0
\(688\) −0.119417 0.0836167i −0.00455273 0.00318786i
\(689\) 10.7162 2.87140i 0.408255 0.109392i
\(690\) 0 0
\(691\) −11.8540 + 32.5686i −0.450948 + 1.23897i 0.481110 + 0.876660i \(0.340234\pi\)
−0.932058 + 0.362309i \(0.881989\pi\)
\(692\) −14.6190 + 8.44027i −0.555730 + 0.320851i
\(693\) 0 0
\(694\) 3.85205 + 4.59069i 0.146222 + 0.174260i
\(695\) 49.5642 + 13.2807i 1.88008 + 0.503765i
\(696\) 0 0
\(697\) 14.8780 + 14.8780i 0.563543 + 0.563543i
\(698\) 6.07375 + 8.67421i 0.229895 + 0.328324i
\(699\) 0 0
\(700\) −3.44375 + 1.25342i −0.130161 + 0.0473749i
\(701\) −10.5239 22.5686i −0.397482 0.852403i −0.998582 0.0532295i \(-0.983049\pi\)
0.601100 0.799174i \(-0.294729\pi\)
\(702\) 0 0
\(703\) 0.0187967 10.6507i 0.000708930 0.401698i
\(704\) 2.69095i 0.101419i
\(705\) 0 0
\(706\) 3.92221 + 10.7762i 0.147614 + 0.405567i
\(707\) −9.73929 8.17223i −0.366284 0.307349i
\(708\) 0 0
\(709\) 24.2046 24.2046i 0.909023 0.909023i −0.0871702 0.996193i \(-0.527782\pi\)
0.996193 + 0.0871702i \(0.0277824\pi\)
\(710\) 11.8829 + 2.09528i 0.445959 + 0.0786345i
\(711\) 0 0
\(712\) −5.25013 + 4.40538i −0.196757 + 0.165099i
\(713\) 4.45228 + 2.57053i 0.166739 + 0.0962670i
\(714\) 0 0
\(715\) 10.7431 + 3.91017i 0.401769 + 0.146232i
\(716\) 0.0735588 + 0.840781i 0.00274902 + 0.0314215i
\(717\) 0 0
\(718\) 16.6250 23.7430i 0.620441 0.886082i
\(719\) −18.8332 + 3.32080i −0.702359 + 0.123845i −0.513412 0.858143i \(-0.671619\pi\)
−0.188947 + 0.981987i \(0.560507\pi\)
\(720\) 0 0
\(721\) 9.19333 + 4.28692i 0.342377 + 0.159653i
\(722\) −14.4412 6.73405i −0.537447 0.250616i
\(723\) 0 0
\(724\) 23.9891 4.22993i 0.891549 0.157204i
\(725\) 8.64325 12.3438i 0.321002 0.458439i
\(726\) 0 0
\(727\) 4.37674 + 50.0263i 0.162324 + 1.85537i 0.444205 + 0.895925i \(0.353486\pi\)
−0.281881 + 0.959449i \(0.590958\pi\)
\(728\) 1.95139 + 0.710247i 0.0723233 + 0.0263235i
\(729\) 0 0
\(730\) 0.651892 + 0.376370i 0.0241276 + 0.0139301i
\(731\) 0.461709 0.387420i 0.0170769 0.0143293i
\(732\) 0 0
\(733\) −34.9543 6.16338i −1.29107 0.227650i −0.514393 0.857555i \(-0.671983\pi\)
−0.776672 + 0.629905i \(0.783094\pi\)
\(734\) 12.6945 12.6945i 0.468563 0.468563i
\(735\) 0 0
\(736\) 0.838509 + 0.703592i 0.0309078 + 0.0259348i
\(737\) −2.91933 8.02080i −0.107535 0.295450i
\(738\) 0 0
\(739\) 4.68216i 0.172236i 0.996285 + 0.0861180i \(0.0274462\pi\)
−0.996285 + 0.0861180i \(0.972554\pi\)
\(740\) 5.74558 + 15.8729i 0.211212 + 0.583501i
\(741\) 0 0
\(742\) 4.15444 + 8.90922i 0.152514 + 0.327068i
\(743\) 34.8359 12.6792i 1.27800 0.465155i 0.388232 0.921562i \(-0.373086\pi\)
0.889771 + 0.456406i \(0.150864\pi\)
\(744\) 0 0
\(745\) −1.02722 1.46702i −0.0376344 0.0537476i
\(746\) 6.89117 + 6.89117i 0.252304 + 0.252304i
\(747\) 0 0
\(748\) −10.7464 2.87948i −0.392927 0.105284i
\(749\) −3.82916 4.56341i −0.139914 0.166743i
\(750\) 0 0
\(751\) −12.7605 + 7.36726i −0.465636 + 0.268835i −0.714411 0.699726i \(-0.753305\pi\)
0.248775 + 0.968561i \(0.419972\pi\)
\(752\) −3.50724 + 9.63606i −0.127896 + 0.351391i
\(753\) 0 0
\(754\) −8.24787 + 2.21001i −0.300370 + 0.0804838i
\(755\) 28.2935 + 19.8113i 1.02971 + 0.721008i
\(756\) 0 0
\(757\) −4.35699 + 49.8006i −0.158358 + 1.81004i 0.337171 + 0.941444i \(0.390530\pi\)
−0.495528 + 0.868592i \(0.665026\pi\)
\(758\) −7.84719 + 16.8283i −0.285023 + 0.611233i
\(759\) 0 0
\(760\) −4.84076 0.423512i −0.175593 0.0153624i
\(761\) −5.93150 33.6392i −0.215017 1.21942i −0.880878 0.473344i \(-0.843047\pi\)
0.665861 0.746076i \(-0.268064\pi\)
\(762\) 0 0
\(763\) 4.74058 + 17.6921i 0.171620 + 0.640496i
\(764\) −23.0302 + 2.01488i −0.833205 + 0.0728959i
\(765\) 0 0
\(766\) 0.622934 + 1.07895i 0.0225075 + 0.0389841i
\(767\) 9.36121 16.2141i 0.338014 0.585457i
\(768\) 0 0
\(769\) −13.8103 + 51.5408i −0.498012 + 1.85861i 0.0144461 + 0.999896i \(0.495402\pi\)
−0.512458 + 0.858712i \(0.671265\pi\)
\(770\) −1.75906 + 9.97612i −0.0633921 + 0.359514i
\(771\) 0 0
\(772\) −12.6926 + 8.88745i −0.456817 + 0.319866i
\(773\) −13.2760 + 15.8218i −0.477506 + 0.569070i −0.949994 0.312267i \(-0.898912\pi\)
0.472488 + 0.881337i \(0.343356\pi\)
\(774\) 0 0
\(775\) 11.5003 5.36266i 0.413102 0.192632i
\(776\) 3.33722 0.119799
\(777\) 0 0
\(778\) −32.7289 −1.17339
\(779\) 8.07603 3.76592i 0.289354 0.134928i
\(780\) 0 0
\(781\) 7.52060 8.96270i 0.269108 0.320711i
\(782\) −3.70707 + 2.59572i −0.132565 + 0.0928228i
\(783\) 0 0
\(784\) 0.896020 5.08158i 0.0320007 0.181485i
\(785\) 12.6215 47.1043i 0.450482 1.68122i
\(786\) 0 0
\(787\) 27.7603 48.0823i 0.989549 1.71395i 0.369898 0.929073i \(-0.379393\pi\)
0.619652 0.784877i \(-0.287274\pi\)
\(788\) 11.7652 + 20.3780i 0.419119 + 0.725935i
\(789\) 0 0
\(790\) 18.3612 1.60639i 0.653261 0.0571529i
\(791\) −1.06610 3.97872i −0.0379060 0.141467i
\(792\) 0 0
\(793\) −0.860262 4.87879i −0.0305488 0.173251i
\(794\) 24.7379 + 2.16428i 0.877915 + 0.0768076i
\(795\) 0 0
\(796\) 2.83685 6.08365i 0.100550 0.215629i
\(797\) −0.565149 + 6.45969i −0.0200186 + 0.228814i 0.979594 + 0.200986i \(0.0644146\pi\)
−0.999613 + 0.0278278i \(0.991141\pi\)
\(798\) 0 0
\(799\) −34.7289 24.3175i −1.22862 0.860290i
\(800\) 2.60962 0.699246i 0.0922640 0.0247221i
\(801\) 0 0
\(802\) 6.68435 18.3651i 0.236033 0.648494i
\(803\) 0.632103 0.364945i 0.0223064 0.0128786i
\(804\) 0 0
\(805\) 2.64866 + 3.15655i 0.0933529 + 0.111254i
\(806\) −6.94525 1.86097i −0.244636 0.0655500i
\(807\) 0 0
\(808\) 6.62745 + 6.62745i 0.233153 + 0.233153i
\(809\) 24.6778 + 35.2435i 0.867624 + 1.23910i 0.969695 + 0.244318i \(0.0785642\pi\)
−0.102071 + 0.994777i \(0.532547\pi\)
\(810\) 0 0
\(811\) −27.7929 + 10.1158i −0.975940 + 0.355213i −0.780260 0.625455i \(-0.784913\pi\)
−0.195679 + 0.980668i \(0.562691\pi\)
\(812\) −3.19752 6.85709i −0.112211 0.240637i
\(813\) 0 0
\(814\) 16.1147 + 2.87079i 0.564819 + 0.100621i
\(815\) 32.3381i 1.13275i
\(816\) 0 0
\(817\) −0.0873032 0.239864i −0.00305435 0.00839177i
\(818\) 15.3307 + 12.8640i 0.536025 + 0.449779i
\(819\) 0 0
\(820\) −9.98672 + 9.98672i −0.348752 + 0.348752i
\(821\) −8.42050 1.48476i −0.293877 0.0518185i 0.0247657 0.999693i \(-0.492116\pi\)
−0.318643 + 0.947875i \(0.603227\pi\)
\(822\) 0 0
\(823\) 38.1828 32.0392i 1.33097 1.11682i 0.347119 0.937821i \(-0.387160\pi\)
0.983850 0.178995i \(-0.0572846\pi\)
\(824\) −6.47613 3.73900i −0.225607 0.130254i
\(825\) 0 0
\(826\) 15.5888 + 5.67388i 0.542405 + 0.197419i
\(827\) 2.16286 + 24.7216i 0.0752099 + 0.859654i 0.936300 + 0.351201i \(0.114227\pi\)
−0.861090 + 0.508452i \(0.830218\pi\)
\(828\) 0 0
\(829\) 8.63776 12.3360i 0.300002 0.428447i −0.640643 0.767839i \(-0.721332\pi\)
0.940645 + 0.339392i \(0.110221\pi\)
\(830\) −13.2093 + 2.32916i −0.458503 + 0.0808464i
\(831\) 0 0
\(832\) −1.38746 0.646985i −0.0481016 0.0224302i
\(833\) 19.3346 + 9.01590i 0.669906 + 0.312382i
\(834\) 0 0
\(835\) −12.7756 + 2.25269i −0.442118 + 0.0779574i
\(836\) −2.70255 + 3.85964i −0.0934696 + 0.133488i
\(837\) 0 0
\(838\) −0.421148 4.81374i −0.0145483 0.166288i
\(839\) 40.4395 + 14.7188i 1.39613 + 0.508148i 0.927026 0.374997i \(-0.122356\pi\)
0.469099 + 0.883145i \(0.344579\pi\)
\(840\) 0 0
\(841\) 1.82760 + 1.05516i 0.0630207 + 0.0363850i
\(842\) −3.41593 + 2.86630i −0.117721 + 0.0987794i
\(843\) 0 0
\(844\) −6.70924 1.18302i −0.230942 0.0407213i
\(845\) 20.9116 20.9116i 0.719379 0.719379i
\(846\) 0 0
\(847\) −3.90585 3.27739i −0.134206 0.112613i
\(848\) −2.47858 6.80985i −0.0851149 0.233851i
\(849\) 0 0
\(850\) 11.1698i 0.383122i
\(851\) 5.10799 4.27078i 0.175100 0.146400i
\(852\) 0 0
\(853\) 2.34409 + 5.02693i 0.0802603 + 0.172119i 0.942343 0.334649i \(-0.108618\pi\)
−0.862082 + 0.506768i \(0.830840\pi\)
\(854\) 4.12489 1.50134i 0.141151 0.0513747i
\(855\) 0 0
\(856\) 2.51892 + 3.59740i 0.0860951 + 0.122956i
\(857\) −10.8517 10.8517i −0.370687 0.370687i 0.497041 0.867727i \(-0.334420\pi\)
−0.867727 + 0.497041i \(0.834420\pi\)
\(858\) 0 0
\(859\) −34.9875 9.37486i −1.19376 0.319866i −0.393387 0.919373i \(-0.628697\pi\)
−0.800370 + 0.599507i \(0.795363\pi\)
\(860\) 0.260053 + 0.309919i 0.00886773 + 0.0105682i
\(861\) 0 0
\(862\) −16.0662 + 9.27582i −0.547217 + 0.315936i
\(863\) −7.68909 + 21.1256i −0.261740 + 0.719124i 0.737311 + 0.675554i \(0.236095\pi\)
−0.999050 + 0.0435701i \(0.986127\pi\)
\(864\) 0 0
\(865\) 45.2504 12.1248i 1.53856 0.412256i
\(866\) 6.51198 + 4.55974i 0.221286 + 0.154946i
\(867\) 0 0
\(868\) 0.555273 6.34680i 0.0188472 0.215424i
\(869\) 7.55295 16.1974i 0.256216 0.549458i
\(870\) 0 0
\(871\) 4.83745 + 0.423222i 0.163911 + 0.0143403i
\(872\) −2.34473 13.2976i −0.0794026 0.450315i
\(873\) 0 0
\(874\) 0.496051 + 1.85129i 0.0167792 + 0.0626208i
\(875\) −8.61906 + 0.754070i −0.291377 + 0.0254922i
\(876\) 0 0
\(877\) 21.3295 + 36.9438i 0.720246 + 1.24750i 0.960901 + 0.276892i \(0.0893044\pi\)
−0.240655 + 0.970611i \(0.577362\pi\)
\(878\) 8.57310 14.8491i 0.289328 0.501131i
\(879\) 0 0
\(880\) 1.93283 7.21343i 0.0651558 0.243165i
\(881\) 2.21108 12.5396i 0.0744931 0.422471i −0.924640 0.380842i \(-0.875634\pi\)
0.999133 0.0416290i \(-0.0132548\pi\)
\(882\) 0 0
\(883\) −2.33065 + 1.63194i −0.0784327 + 0.0549192i −0.612135 0.790753i \(-0.709689\pi\)
0.533702 + 0.845672i \(0.320800\pi\)
\(884\) 4.06843 4.84856i 0.136836 0.163075i
\(885\) 0 0
\(886\) 27.0423 12.6101i 0.908505 0.423643i
\(887\) −42.6779 −1.43298 −0.716492 0.697596i \(-0.754253\pi\)
−0.716492 + 0.697596i \(0.754253\pi\)
\(888\) 0 0
\(889\) 26.7348 0.896656
\(890\) 17.2379 8.03817i 0.577816 0.269440i
\(891\) 0 0
\(892\) 8.24277 9.82335i 0.275988 0.328910i
\(893\) −14.7081 + 10.2987i −0.492186 + 0.344632i
\(894\) 0 0
\(895\) 0.406726 2.30666i 0.0135953 0.0771030i
\(896\) 0.351082 1.31026i 0.0117288 0.0437726i
\(897\) 0 0
\(898\) −2.07380 + 3.59193i −0.0692037 + 0.119864i
\(899\) 13.0985 + 22.6872i 0.436859 + 0.756661i
\(900\) 0 0
\(901\) 29.8476 2.61133i 0.994368 0.0869959i
\(902\) 3.54443 + 13.2280i 0.118017 + 0.440445i
\(903\) 0 0
\(904\) 0.527300 + 2.99047i 0.0175377 + 0.0994615i
\(905\) −67.3442 5.89185i −2.23860 0.195852i
\(906\) 0 0
\(907\) −3.31501 + 7.10907i −0.110073 + 0.236053i −0.953626 0.300993i \(-0.902682\pi\)
0.843553 + 0.537046i \(0.180460\pi\)
\(908\) −1.46160 + 16.7062i −0.0485050 + 0.554415i
\(909\) 0 0
\(910\) −4.72079 3.30554i −0.156493 0.109577i
\(911\) 44.9264 12.0380i 1.48848 0.398837i 0.579256 0.815146i \(-0.303343\pi\)
0.909223 + 0.416309i \(0.136676\pi\)
\(912\) 0 0
\(913\) −4.44830 + 12.2216i −0.147217 + 0.404476i
\(914\) −21.1799 + 12.2282i −0.700568 + 0.404473i
\(915\) 0 0
\(916\) −14.2256 16.9534i −0.470027 0.560156i
\(917\) −26.4506 7.08742i −0.873476 0.234047i
\(918\) 0 0
\(919\) −29.6589 29.6589i −0.978356 0.978356i 0.0214146 0.999771i \(-0.493183\pi\)
−0.999771 + 0.0214146i \(0.993183\pi\)
\(920\) −1.74236 2.48835i −0.0574439 0.0820383i
\(921\) 0 0
\(922\) 24.0314 8.74673i 0.791433 0.288058i
\(923\) 2.81303 + 6.03255i 0.0925919 + 0.198564i
\(924\) 0 0
\(925\) −1.40339 16.3736i −0.0461433 0.538362i
\(926\) 2.66967i 0.0877309i
\(927\) 0 0
\(928\) 1.90767 + 5.24129i 0.0626224 + 0.172054i
\(929\) 10.0235 + 8.41071i 0.328860 + 0.275946i 0.792235 0.610216i \(-0.208917\pi\)
−0.463375 + 0.886162i \(0.653362\pi\)
\(930\) 0 0
\(931\) 6.38865 6.38865i 0.209380 0.209380i
\(932\) 2.37366 + 0.418541i 0.0777519 + 0.0137098i
\(933\) 0 0
\(934\) 26.8244 22.5083i 0.877720 0.736494i
\(935\) 26.7388 + 15.4376i 0.874452 + 0.504865i
\(936\) 0 0
\(937\) 48.9981 + 17.8339i 1.60070 + 0.582607i 0.979570 0.201102i \(-0.0644521\pi\)
0.621129 + 0.783708i \(0.286674\pi\)
\(938\) 0.375003 + 4.28630i 0.0122443 + 0.139953i
\(939\) 0 0
\(940\) 16.3229 23.3115i 0.532395 0.760338i
\(941\) −37.5432 + 6.61988i −1.22387 + 0.215802i −0.747992 0.663708i \(-0.768982\pi\)
−0.475881 + 0.879509i \(0.657871\pi\)
\(942\) 0 0
\(943\) 5.04864 + 2.35422i 0.164406 + 0.0766640i
\(944\) −11.0839 5.16850i −0.360749 0.168220i
\(945\) 0 0
\(946\) 0.386330 0.0681204i 0.0125607 0.00221479i
\(947\) −33.1019 + 47.2745i −1.07567 + 1.53621i −0.253191 + 0.967416i \(0.581480\pi\)
−0.822478 + 0.568797i \(0.807409\pi\)
\(948\) 0 0
\(949\) 0.0361904 + 0.413659i 0.00117479 + 0.0134279i
\(950\) 4.44525 + 1.61794i 0.144223 + 0.0524929i
\(951\) 0 0
\(952\) 4.85686 + 2.80411i 0.157412 + 0.0908818i
\(953\) −42.4220 + 35.5963i −1.37418 + 1.15308i −0.402874 + 0.915256i \(0.631989\pi\)
−0.971309 + 0.237821i \(0.923567\pi\)
\(954\) 0 0
\(955\) 63.1827 + 11.1408i 2.04454 + 0.360508i
\(956\) 13.6534 13.6534i 0.441582 0.441582i
\(957\) 0 0
\(958\) −13.3490 11.2012i −0.431288 0.361893i
\(959\) 6.00116 + 16.4881i 0.193788 + 0.532427i
\(960\) 0 0
\(961\) 8.94043i 0.288401i
\(962\) −5.35464 + 7.61857i −0.172641 + 0.245633i
\(963\) 0 0
\(964\) 0.0206898 + 0.0443695i 0.000666375 + 0.00142905i
\(965\) 40.4077 14.7072i 1.30077 0.473442i
\(966\) 0 0
\(967\) −10.6157 15.1607i −0.341376 0.487536i 0.611352 0.791359i \(-0.290626\pi\)
−0.952729 + 0.303823i \(0.901737\pi\)
\(968\) 2.65787 + 2.65787i 0.0854272 + 0.0854272i
\(969\) 0 0
\(970\) −8.94585 2.39703i −0.287234 0.0769641i
\(971\) −17.8806 21.3093i −0.573816 0.683847i 0.398594 0.917128i \(-0.369498\pi\)
−0.972409 + 0.233281i \(0.925054\pi\)
\(972\) 0 0
\(973\) −21.7207 + 12.5405i −0.696335 + 0.402029i
\(974\) 11.6630 32.0439i 0.373707 1.02675i
\(975\) 0 0
\(976\) −3.12578 + 0.837551i −0.100054 + 0.0268093i
\(977\) −0.578714 0.405220i −0.0185147 0.0129641i 0.564282 0.825582i \(-0.309153\pi\)
−0.582797 + 0.812618i \(0.698042\pi\)
\(978\) 0 0
\(979\) 1.60738 18.3724i 0.0513719 0.587184i
\(980\) −6.05185 + 12.9782i −0.193319 + 0.414575i
\(981\) 0 0
\(982\) −24.3211 2.12782i −0.776119 0.0679016i
\(983\) 0.855643 + 4.85259i 0.0272908 + 0.154774i 0.995408 0.0957243i \(-0.0305167\pi\)
−0.968117 + 0.250498i \(0.919406\pi\)
\(984\) 0 0
\(985\) −16.9013 63.0764i −0.538519 2.00978i
\(986\) −22.9726 + 2.00984i −0.731596 + 0.0640063i
\(987\) 0 0
\(988\) −1.34027 2.32142i −0.0426397 0.0738541i
\(989\) 0.0797857 0.138193i 0.00253704 0.00439428i
\(990\) 0 0
\(991\) 7.11901 26.5685i 0.226143 0.843976i −0.755801 0.654802i \(-0.772752\pi\)
0.981944 0.189174i \(-0.0605811\pi\)
\(992\) −0.815584 + 4.62541i −0.0258948 + 0.146857i
\(993\) 0 0
\(994\) −4.83121 + 3.38285i −0.153237 + 0.107298i
\(995\) −11.9743 + 14.2704i −0.379610 + 0.452401i
\(996\) 0 0
\(997\) 0.941623 0.439086i 0.0298215 0.0139060i −0.407650 0.913138i \(-0.633652\pi\)
0.437472 + 0.899232i \(0.355874\pi\)
\(998\) −35.2031 −1.11433
\(999\) 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 666.2.bs.a.89.1 72
3.2 odd 2 inner 666.2.bs.a.89.6 yes 72
37.5 odd 36 inner 666.2.bs.a.449.6 yes 72
111.5 even 36 inner 666.2.bs.a.449.1 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
666.2.bs.a.89.1 72 1.1 even 1 trivial
666.2.bs.a.89.6 yes 72 3.2 odd 2 inner
666.2.bs.a.449.1 yes 72 111.5 even 36 inner
666.2.bs.a.449.6 yes 72 37.5 odd 36 inner