Properties

Label 16.6.e.a.5.1
Level $16$
Weight $6$
Character 16.5
Analytic conductor $2.566$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,6,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.56614111701\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} - 297472 x^{9} + 265216 x^{8} + 1368064 x^{7} + 11894784 x^{6} + \cdots + 68719476736 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{36} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.1
Root \(-1.58716 + 3.67164i\) of defining polynomial
Character \(\chi\) \(=\) 16.5
Dual form 16.6.e.a.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.25880 + 2.08448i) q^{2} +(-3.18000 + 3.18000i) q^{3} +(23.3098 - 21.9238i) q^{4} +(-67.3647 - 67.3647i) q^{5} +(10.0943 - 23.3517i) q^{6} -148.379i q^{7} +(-76.8820 + 163.882i) q^{8} +222.775i q^{9} +O(q^{10})\) \(q+(-5.25880 + 2.08448i) q^{2} +(-3.18000 + 3.18000i) q^{3} +(23.3098 - 21.9238i) q^{4} +(-67.3647 - 67.3647i) q^{5} +(10.0943 - 23.3517i) q^{6} -148.379i q^{7} +(-76.8820 + 163.882i) q^{8} +222.775i q^{9} +(494.678 + 213.836i) q^{10} +(-256.205 - 256.205i) q^{11} +(-4.40780 + 143.843i) q^{12} +(-218.586 + 218.586i) q^{13} +(309.293 + 780.294i) q^{14} +428.440 q^{15} +(62.6982 - 1022.08i) q^{16} -463.168 q^{17} +(-464.371 - 1171.53i) q^{18} +(920.791 - 920.791i) q^{19} +(-3047.15 - 93.3741i) q^{20} +(471.845 + 471.845i) q^{21} +(1881.39 + 813.276i) q^{22} -1053.65i q^{23} +(-276.659 - 765.629i) q^{24} +5951.00i q^{25} +(693.860 - 1605.14i) q^{26} +(-1481.17 - 1481.17i) q^{27} +(-3253.02 - 3458.69i) q^{28} +(1290.79 - 1290.79i) q^{29} +(-2253.08 + 893.076i) q^{30} +10036.9 q^{31} +(1800.79 + 5505.60i) q^{32} +1629.47 q^{33} +(2435.71 - 965.466i) q^{34} +(-9995.50 + 9995.50i) q^{35} +(4884.07 + 5192.86i) q^{36} +(-9409.85 - 9409.85i) q^{37} +(-2922.88 + 6761.62i) q^{38} -1390.21i q^{39} +(16219.0 - 5860.70i) q^{40} -368.682i q^{41} +(-3464.89 - 1497.78i) q^{42} +(-9168.57 - 9168.57i) q^{43} +(-11589.1 - 355.126i) q^{44} +(15007.2 - 15007.2i) q^{45} +(2196.32 + 5540.94i) q^{46} -7638.65 q^{47} +(3050.83 + 3449.59i) q^{48} -5209.29 q^{49} +(-12404.8 - 31295.1i) q^{50} +(1472.88 - 1472.88i) q^{51} +(-302.982 + 9887.43i) q^{52} +(-1242.05 - 1242.05i) q^{53} +(10876.6 + 4701.68i) q^{54} +34518.4i q^{55} +(24316.6 + 11407.7i) q^{56} +5856.24i q^{57} +(-4097.36 + 9478.62i) q^{58} +(16255.3 + 16255.3i) q^{59} +(9986.87 - 9393.01i) q^{60} +(-1394.11 + 1394.11i) q^{61} +(-52782.1 + 20921.8i) q^{62} +33055.1 q^{63} +(-20946.3 - 25199.1i) q^{64} +29449.9 q^{65} +(-8569.04 + 3396.60i) q^{66} +(-17400.9 + 17400.9i) q^{67} +(-10796.4 + 10154.4i) q^{68} +(3350.62 + 3350.62i) q^{69} +(31728.8 - 73399.7i) q^{70} -67414.6i q^{71} +(-36508.7 - 17127.4i) q^{72} +19543.2i q^{73} +(69099.2 + 29869.8i) q^{74} +(-18924.2 - 18924.2i) q^{75} +(1276.31 - 41650.7i) q^{76} +(-38015.5 + 38015.5i) q^{77} +(2897.87 + 7310.82i) q^{78} -43996.5 q^{79} +(-73075.7 + 64628.4i) q^{80} -44714.1 q^{81} +(768.512 + 1938.82i) q^{82} +(73286.1 - 73286.1i) q^{83} +(21343.3 + 654.024i) q^{84} +(31201.2 + 31201.2i) q^{85} +(67327.4 + 29103.9i) q^{86} +8209.42i q^{87} +(61684.9 - 22289.8i) q^{88} -88671.1i q^{89} +(-47637.4 + 110202. i) q^{90} +(32433.5 + 32433.5i) q^{91} +(-23100.0 - 24560.5i) q^{92} +(-31917.5 + 31917.5i) q^{93} +(40170.1 - 15922.6i) q^{94} -124058. q^{95} +(-23234.3 - 11781.3i) q^{96} -73610.3 q^{97} +(27394.6 - 10858.7i) q^{98} +(57076.2 - 57076.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.25880 + 2.08448i −0.929632 + 0.368488i
\(3\) −3.18000 + 3.18000i −0.203997 + 0.203997i −0.801710 0.597713i \(-0.796076\pi\)
0.597713 + 0.801710i \(0.296076\pi\)
\(4\) 23.3098 21.9238i 0.728433 0.685117i
\(5\) −67.3647 67.3647i −1.20506 1.20506i −0.972609 0.232447i \(-0.925327\pi\)
−0.232447 0.972609i \(-0.574673\pi\)
\(6\) 10.0943 23.3517i 0.114472 0.264813i
\(7\) 148.379i 1.14453i −0.820069 0.572265i \(-0.806065\pi\)
0.820069 0.572265i \(-0.193935\pi\)
\(8\) −76.8820 + 163.882i −0.424717 + 0.905326i
\(9\) 222.775i 0.916770i
\(10\) 494.678 + 213.836i 1.56431 + 0.676210i
\(11\) −256.205 256.205i −0.638420 0.638420i 0.311745 0.950166i \(-0.399086\pi\)
−0.950166 + 0.311745i \(0.899086\pi\)
\(12\) −4.40780 + 143.843i −0.00883626 + 0.288360i
\(13\) −218.586 + 218.586i −0.358727 + 0.358727i −0.863343 0.504617i \(-0.831634\pi\)
0.504617 + 0.863343i \(0.331634\pi\)
\(14\) 309.293 + 780.294i 0.421746 + 1.06399i
\(15\) 428.440 0.491657
\(16\) 62.6982 1022.08i 0.0612287 0.998124i
\(17\) −463.168 −0.388701 −0.194351 0.980932i \(-0.562260\pi\)
−0.194351 + 0.980932i \(0.562260\pi\)
\(18\) −464.371 1171.53i −0.337819 0.852259i
\(19\) 920.791 920.791i 0.585163 0.585163i −0.351154 0.936318i \(-0.614211\pi\)
0.936318 + 0.351154i \(0.114211\pi\)
\(20\) −3047.15 93.3741i −1.70341 0.0521977i
\(21\) 471.845 + 471.845i 0.233481 + 0.233481i
\(22\) 1881.39 + 813.276i 0.828746 + 0.358246i
\(23\) 1053.65i 0.415315i −0.978202 0.207657i \(-0.933416\pi\)
0.978202 0.207657i \(-0.0665839\pi\)
\(24\) −276.659 765.629i −0.0980430 0.271325i
\(25\) 5951.00i 1.90432i
\(26\) 693.860 1605.14i 0.201297 0.465671i
\(27\) −1481.17 1481.17i −0.391016 0.391016i
\(28\) −3253.02 3458.69i −0.784137 0.833713i
\(29\) 1290.79 1290.79i 0.285010 0.285010i −0.550093 0.835103i \(-0.685408\pi\)
0.835103 + 0.550093i \(0.185408\pi\)
\(30\) −2253.08 + 893.076i −0.457060 + 0.181170i
\(31\) 10036.9 1.87584 0.937921 0.346848i \(-0.112748\pi\)
0.937921 + 0.346848i \(0.112748\pi\)
\(32\) 1800.79 + 5505.60i 0.310877 + 0.950450i
\(33\) 1629.47 0.260472
\(34\) 2435.71 965.466i 0.361349 0.143232i
\(35\) −9995.50 + 9995.50i −1.37922 + 1.37922i
\(36\) 4884.07 + 5192.86i 0.628095 + 0.667805i
\(37\) −9409.85 9409.85i −1.13000 1.13000i −0.990176 0.139824i \(-0.955346\pi\)
−0.139824 0.990176i \(-0.544654\pi\)
\(38\) −2922.88 + 6761.62i −0.328361 + 0.759612i
\(39\) 1390.21i 0.146359i
\(40\) 16219.0 5860.70i 1.60278 0.579161i
\(41\) 368.682i 0.0342525i −0.999853 0.0171263i \(-0.994548\pi\)
0.999853 0.0171263i \(-0.00545173\pi\)
\(42\) −3464.89 1497.78i −0.303086 0.131016i
\(43\) −9168.57 9168.57i −0.756189 0.756189i 0.219438 0.975627i \(-0.429578\pi\)
−0.975627 + 0.219438i \(0.929578\pi\)
\(44\) −11589.1 355.126i −0.902439 0.0276535i
\(45\) 15007.2 15007.2i 1.10476 1.10476i
\(46\) 2196.32 + 5540.94i 0.153039 + 0.386090i
\(47\) −7638.65 −0.504396 −0.252198 0.967676i \(-0.581153\pi\)
−0.252198 + 0.967676i \(0.581153\pi\)
\(48\) 3050.83 + 3449.59i 0.191124 + 0.216105i
\(49\) −5209.29 −0.309948
\(50\) −12404.8 31295.1i −0.701720 1.77032i
\(51\) 1472.88 1472.88i 0.0792941 0.0792941i
\(52\) −302.982 + 9887.43i −0.0155385 + 0.507078i
\(53\) −1242.05 1242.05i −0.0607363 0.0607363i 0.676086 0.736823i \(-0.263675\pi\)
−0.736823 + 0.676086i \(0.763675\pi\)
\(54\) 10876.6 + 4701.68i 0.507586 + 0.219416i
\(55\) 34518.4i 1.53866i
\(56\) 24316.6 + 11407.7i 1.03617 + 0.486101i
\(57\) 5856.24i 0.238743i
\(58\) −4097.36 + 9478.62i −0.159932 + 0.369977i
\(59\) 16255.3 + 16255.3i 0.607945 + 0.607945i 0.942409 0.334464i \(-0.108555\pi\)
−0.334464 + 0.942409i \(0.608555\pi\)
\(60\) 9986.87 9393.01i 0.358139 0.336842i
\(61\) −1394.11 + 1394.11i −0.0479704 + 0.0479704i −0.730685 0.682715i \(-0.760799\pi\)
0.682715 + 0.730685i \(0.260799\pi\)
\(62\) −52782.1 + 20921.8i −1.74384 + 0.691226i
\(63\) 33055.1 1.04927
\(64\) −20946.3 25199.1i −0.639231 0.769015i
\(65\) 29449.9 0.864572
\(66\) −8569.04 + 3396.60i −0.242143 + 0.0959809i
\(67\) −17400.9 + 17400.9i −0.473569 + 0.473569i −0.903068 0.429498i \(-0.858690\pi\)
0.429498 + 0.903068i \(0.358690\pi\)
\(68\) −10796.4 + 10154.4i −0.283143 + 0.266306i
\(69\) 3350.62 + 3350.62i 0.0847231 + 0.0847231i
\(70\) 31728.8 73399.7i 0.773943 1.79040i
\(71\) 67414.6i 1.58711i −0.608495 0.793557i \(-0.708227\pi\)
0.608495 0.793557i \(-0.291773\pi\)
\(72\) −36508.7 17127.4i −0.829976 0.389368i
\(73\) 19543.2i 0.429228i 0.976699 + 0.214614i \(0.0688494\pi\)
−0.976699 + 0.214614i \(0.931151\pi\)
\(74\) 69099.2 + 29869.8i 1.46688 + 0.634093i
\(75\) −18924.2 18924.2i −0.388476 0.388476i
\(76\) 1276.31 41650.7i 0.0253467 0.827157i
\(77\) −38015.5 + 38015.5i −0.730691 + 0.730691i
\(78\) 2897.87 + 7310.82i 0.0539314 + 0.136060i
\(79\) −43996.5 −0.793140 −0.396570 0.918004i \(-0.629800\pi\)
−0.396570 + 0.918004i \(0.629800\pi\)
\(80\) −73075.7 + 64628.4i −1.27658 + 1.12901i
\(81\) −44714.1 −0.757238
\(82\) 768.512 + 1938.82i 0.0126217 + 0.0318423i
\(83\) 73286.1 73286.1i 1.16769 1.16769i 0.184937 0.982750i \(-0.440792\pi\)
0.982750 0.184937i \(-0.0592080\pi\)
\(84\) 21343.3 + 654.024i 0.330037 + 0.0101134i
\(85\) 31201.2 + 31201.2i 0.468407 + 0.468407i
\(86\) 67327.4 + 29103.9i 0.981625 + 0.424331i
\(87\) 8209.42i 0.116283i
\(88\) 61684.9 22289.8i 0.849126 0.306831i
\(89\) 88671.1i 1.18661i −0.804979 0.593304i \(-0.797823\pi\)
0.804979 0.593304i \(-0.202177\pi\)
\(90\) −47637.4 + 110202.i −0.619929 + 1.43411i
\(91\) 32433.5 + 32433.5i 0.410573 + 0.410573i
\(92\) −23100.0 24560.5i −0.284539 0.302529i
\(93\) −31917.5 + 31917.5i −0.382667 + 0.382667i
\(94\) 40170.1 15922.6i 0.468903 0.185864i
\(95\) −124058. −1.41031
\(96\) −23234.3 11781.3i −0.257307 0.130471i
\(97\) −73610.3 −0.794345 −0.397173 0.917744i \(-0.630009\pi\)
−0.397173 + 0.917744i \(0.630009\pi\)
\(98\) 27394.6 10858.7i 0.288137 0.114212i
\(99\) 57076.2 57076.2i 0.585285 0.585285i
\(100\) 130468. + 138717.i 1.30468 + 1.38717i
\(101\) 78062.3 + 78062.3i 0.761444 + 0.761444i 0.976583 0.215139i \(-0.0690206\pi\)
−0.215139 + 0.976583i \(0.569021\pi\)
\(102\) −4675.37 + 10815.7i −0.0444954 + 0.102933i
\(103\) 3655.48i 0.0339509i −0.999856 0.0169754i \(-0.994596\pi\)
0.999856 0.0169754i \(-0.00540371\pi\)
\(104\) −19016.9 52627.5i −0.172407 0.477122i
\(105\) 63571.4i 0.562715i
\(106\) 9120.70 + 3942.64i 0.0788431 + 0.0340818i
\(107\) 44702.0 + 44702.0i 0.377457 + 0.377457i 0.870184 0.492727i \(-0.164000\pi\)
−0.492727 + 0.870184i \(0.664000\pi\)
\(108\) −66998.5 2053.04i −0.552721 0.0169371i
\(109\) −68265.8 + 68265.8i −0.550348 + 0.550348i −0.926541 0.376193i \(-0.877233\pi\)
0.376193 + 0.926541i \(0.377233\pi\)
\(110\) −71953.1 181525.i −0.566980 1.43039i
\(111\) 59846.7 0.461034
\(112\) −151655. 9303.09i −1.14238 0.0700781i
\(113\) 176086. 1.29726 0.648632 0.761102i \(-0.275341\pi\)
0.648632 + 0.761102i \(0.275341\pi\)
\(114\) −12207.2 30796.8i −0.0879742 0.221944i
\(115\) −70978.9 + 70978.9i −0.500478 + 0.500478i
\(116\) 1789.16 58387.0i 0.0123454 0.402876i
\(117\) −48695.5 48695.5i −0.328870 0.328870i
\(118\) −119367. 51599.3i −0.789186 0.341145i
\(119\) 68724.3i 0.444880i
\(120\) −32939.3 + 70213.4i −0.208815 + 0.445110i
\(121\) 29768.6i 0.184839i
\(122\) 4425.35 10237.4i 0.0269183 0.0622714i
\(123\) 1172.41 + 1172.41i 0.00698743 + 0.00698743i
\(124\) 233959. 220047.i 1.36643 1.28517i
\(125\) 190373. 190373.i 1.08976 1.08976i
\(126\) −173830. + 68902.9i −0.975436 + 0.386644i
\(127\) −77564.5 −0.426730 −0.213365 0.976973i \(-0.568442\pi\)
−0.213365 + 0.976973i \(0.568442\pi\)
\(128\) 162679. + 88854.5i 0.877623 + 0.479352i
\(129\) 58312.2 0.308521
\(130\) −154871. + 61388.0i −0.803734 + 0.318585i
\(131\) −102943. + 102943.i −0.524105 + 0.524105i −0.918809 0.394703i \(-0.870847\pi\)
0.394703 + 0.918809i \(0.370847\pi\)
\(132\) 37982.7 35724.1i 0.189736 0.178454i
\(133\) −136626. 136626.i −0.669737 0.669737i
\(134\) 55235.7 127779.i 0.265741 0.614750i
\(135\) 199557.i 0.942393i
\(136\) 35609.3 75904.7i 0.165088 0.351902i
\(137\) 103866.i 0.472792i 0.971657 + 0.236396i \(0.0759662\pi\)
−0.971657 + 0.236396i \(0.924034\pi\)
\(138\) −24604.5 10635.9i −0.109981 0.0475419i
\(139\) 199447. + 199447.i 0.875569 + 0.875569i 0.993072 0.117503i \(-0.0374891\pi\)
−0.117503 + 0.993072i \(0.537489\pi\)
\(140\) −13854.7 + 452132.i −0.0597418 + 1.94960i
\(141\) 24290.9 24290.9i 0.102895 0.102895i
\(142\) 140525. + 354520.i 0.584833 + 1.47543i
\(143\) 112006. 0.458037
\(144\) 227694. + 13967.6i 0.915050 + 0.0561327i
\(145\) −173907. −0.686906
\(146\) −40737.5 102774.i −0.158166 0.399025i
\(147\) 16565.6 16565.6i 0.0632285 0.0632285i
\(148\) −425642. 13043.0i −1.59731 0.0489466i
\(149\) 111883. + 111883.i 0.412855 + 0.412855i 0.882732 0.469877i \(-0.155702\pi\)
−0.469877 + 0.882732i \(0.655702\pi\)
\(150\) 138966. + 60071.3i 0.504289 + 0.217991i
\(151\) 270469.i 0.965330i −0.875805 0.482665i \(-0.839669\pi\)
0.875805 0.482665i \(-0.160331\pi\)
\(152\) 80108.4 + 221693.i 0.281235 + 0.778292i
\(153\) 103182.i 0.356350i
\(154\) 120673. 279158.i 0.410023 0.948525i
\(155\) −676134. 676134.i −2.26050 2.26050i
\(156\) −30478.6 32405.5i −0.100273 0.106612i
\(157\) −105844. + 105844.i −0.342703 + 0.342703i −0.857383 0.514679i \(-0.827911\pi\)
0.514679 + 0.857383i \(0.327911\pi\)
\(158\) 231368. 91709.9i 0.737329 0.292263i
\(159\) 7899.43 0.0247801
\(160\) 249573. 492192.i 0.770722 1.51997i
\(161\) −156340. −0.475340
\(162\) 235142. 93205.9i 0.703953 0.279033i
\(163\) 3832.26 3832.26i 0.0112976 0.0112976i −0.701435 0.712733i \(-0.747457\pi\)
0.712733 + 0.701435i \(0.247457\pi\)
\(164\) −8082.90 8593.93i −0.0234670 0.0249507i
\(165\) −109769. 109769.i −0.313883 0.313883i
\(166\) −232633. + 538160.i −0.655241 + 1.51580i
\(167\) 94932.2i 0.263404i −0.991289 0.131702i \(-0.957956\pi\)
0.991289 0.131702i \(-0.0420442\pi\)
\(168\) −113603. + 41050.3i −0.310540 + 0.112213i
\(169\) 275733.i 0.742630i
\(170\) −229119. 99042.2i −0.608049 0.262844i
\(171\) 205129. + 205129.i 0.536460 + 0.536460i
\(172\) −414727. 12708.5i −1.06891 0.0327548i
\(173\) 267579. 267579.i 0.679732 0.679732i −0.280208 0.959939i \(-0.590403\pi\)
0.959939 + 0.280208i \(0.0904034\pi\)
\(174\) −17112.4 43171.7i −0.0428487 0.108100i
\(175\) 883003. 2.17955
\(176\) −277926. + 245798.i −0.676312 + 0.598133i
\(177\) −103384. −0.248038
\(178\) 184834. + 466303.i 0.437251 + 1.10311i
\(179\) −153517. + 153517.i −0.358116 + 0.358116i −0.863118 0.505002i \(-0.831492\pi\)
0.505002 + 0.863118i \(0.331492\pi\)
\(180\) 20801.4 678829.i 0.0478533 1.56163i
\(181\) −286803. 286803.i −0.650711 0.650711i 0.302453 0.953164i \(-0.402194\pi\)
−0.953164 + 0.302453i \(0.902194\pi\)
\(182\) −238169. 102954.i −0.532974 0.230391i
\(183\) 8866.57i 0.0195717i
\(184\) 172674. + 81006.9i 0.375995 + 0.176391i
\(185\) 1.26778e6i 2.72343i
\(186\) 101316. 234379.i 0.214731 0.496748i
\(187\) 118666. + 118666.i 0.248155 + 0.248155i
\(188\) −178056. + 167468.i −0.367419 + 0.345571i
\(189\) −219774. + 219774.i −0.447529 + 0.447529i
\(190\) 652393. 258596.i 1.31107 0.519682i
\(191\) −266466. −0.528517 −0.264258 0.964452i \(-0.585127\pi\)
−0.264258 + 0.964452i \(0.585127\pi\)
\(192\) 146743. + 13523.8i 0.287278 + 0.0264756i
\(193\) 953848. 1.84326 0.921628 0.388074i \(-0.126859\pi\)
0.921628 + 0.388074i \(0.126859\pi\)
\(194\) 387101. 153440.i 0.738449 0.292707i
\(195\) −93650.9 + 93650.9i −0.176370 + 0.176370i
\(196\) −121428. + 114207.i −0.225776 + 0.212351i
\(197\) 223796. + 223796.i 0.410853 + 0.410853i 0.882036 0.471183i \(-0.156173\pi\)
−0.471183 + 0.882036i \(0.656173\pi\)
\(198\) −181178. + 419126.i −0.328429 + 0.759770i
\(199\) 562835.i 1.00751i −0.863847 0.503754i \(-0.831952\pi\)
0.863847 0.503754i \(-0.168048\pi\)
\(200\) −975259. 457525.i −1.72403 0.808798i
\(201\) 110670.i 0.193214i
\(202\) −573233. 247794.i −0.988446 0.427280i
\(203\) −191526. 191526.i −0.326202 0.326202i
\(204\) 2041.55 66623.5i 0.00343467 0.112086i
\(205\) −24836.2 + 24836.2i −0.0412762 + 0.0412762i
\(206\) 7619.79 + 19223.4i 0.0125105 + 0.0315619i
\(207\) 234727. 0.380748
\(208\) 209707. + 237117.i 0.336089 + 0.380018i
\(209\) −471823. −0.747160
\(210\) 132514. + 334309.i 0.207354 + 0.523118i
\(211\) 507141. 507141.i 0.784192 0.784192i −0.196343 0.980535i \(-0.562907\pi\)
0.980535 + 0.196343i \(0.0629067\pi\)
\(212\) −56182.3 1721.60i −0.0858538 0.00263083i
\(213\) 214379. + 214379.i 0.323767 + 0.323767i
\(214\) −328259. 141898.i −0.489985 0.211808i
\(215\) 1.23528e6i 1.82250i
\(216\) 356611. 128861.i 0.520068 0.187926i
\(217\) 1.48927e6i 2.14696i
\(218\) 216697. 501295.i 0.308824 0.714418i
\(219\) −62147.4 62147.4i −0.0875615 0.0875615i
\(220\) 756773. + 804619.i 1.05417 + 1.12081i
\(221\) 101242. 101242.i 0.139438 0.139438i
\(222\) −314722. + 124750.i −0.428592 + 0.169886i
\(223\) −963165. −1.29700 −0.648498 0.761217i \(-0.724602\pi\)
−0.648498 + 0.761217i \(0.724602\pi\)
\(224\) 816914. 267199.i 1.08782 0.355808i
\(225\) −1.32574e6 −1.74582
\(226\) −926000. + 367048.i −1.20598 + 0.478027i
\(227\) −288197. + 288197.i −0.371214 + 0.371214i −0.867919 0.496705i \(-0.834543\pi\)
0.496705 + 0.867919i \(0.334543\pi\)
\(228\) 128391. + 136508.i 0.163567 + 0.173909i
\(229\) −294327. 294327.i −0.370887 0.370887i 0.496913 0.867800i \(-0.334467\pi\)
−0.867800 + 0.496913i \(0.834467\pi\)
\(230\) 225309. 521218.i 0.280840 0.649681i
\(231\) 241779.i 0.298118i
\(232\) 112298. + 310775.i 0.136978 + 0.379075i
\(233\) 1.27046e6i 1.53311i −0.642180 0.766554i \(-0.721970\pi\)
0.642180 0.766554i \(-0.278030\pi\)
\(234\) 357585. + 154575.i 0.426913 + 0.184543i
\(235\) 514575. + 514575.i 0.607826 + 0.607826i
\(236\) 735285. + 22531.4i 0.859361 + 0.0263335i
\(237\) 139909. 139909.i 0.161799 0.161799i
\(238\) −143255. 361407.i −0.163933 0.413575i
\(239\) −1.09946e6 −1.24504 −0.622522 0.782603i \(-0.713892\pi\)
−0.622522 + 0.782603i \(0.713892\pi\)
\(240\) 26862.4 437899.i 0.0301035 0.490734i
\(241\) 1.31349e6 1.45675 0.728376 0.685178i \(-0.240275\pi\)
0.728376 + 0.685178i \(0.240275\pi\)
\(242\) 62052.1 + 156547.i 0.0681111 + 0.171833i
\(243\) 502115. 502115.i 0.545491 0.545491i
\(244\) −1932.38 + 63060.8i −0.00207787 + 0.0678086i
\(245\) 350922. + 350922.i 0.373504 + 0.373504i
\(246\) −8609.34 3721.60i −0.00907052 0.00392095i
\(247\) 402544.i 0.419827i
\(248\) −771659. + 1.64487e6i −0.796703 + 1.69825i
\(249\) 466100.i 0.476410i
\(250\) −604302. + 1.39796e6i −0.611511 + 1.41464i
\(251\) 444145. + 444145.i 0.444980 + 0.444980i 0.893682 0.448701i \(-0.148113\pi\)
−0.448701 + 0.893682i \(0.648113\pi\)
\(252\) 770510. 724692.i 0.764323 0.718873i
\(253\) −269951. + 269951.i −0.265145 + 0.265145i
\(254\) 407896. 161682.i 0.396702 0.157245i
\(255\) −198440. −0.191108
\(256\) −1.04071e6 128165.i −0.992502 0.122228i
\(257\) 664856. 0.627906 0.313953 0.949438i \(-0.398347\pi\)
0.313953 + 0.949438i \(0.398347\pi\)
\(258\) −306652. + 121551.i −0.286811 + 0.113686i
\(259\) −1.39622e6 + 1.39622e6i −1.29332 + 1.29332i
\(260\) 686474. 645653.i 0.629783 0.592333i
\(261\) 287555. + 287555.i 0.261289 + 0.261289i
\(262\) 326773. 755939.i 0.294099 0.680352i
\(263\) 1.50708e6i 1.34353i −0.740765 0.671764i \(-0.765537\pi\)
0.740765 0.671764i \(-0.234463\pi\)
\(264\) −125277. + 267040.i −0.110627 + 0.235812i
\(265\) 167340.i 0.146381i
\(266\) 1.00328e6 + 433693.i 0.869399 + 0.375819i
\(267\) 281975. + 281975.i 0.242065 + 0.242065i
\(268\) −24119.3 + 787103.i −0.0205129 + 0.669414i
\(269\) −581250. + 581250.i −0.489759 + 0.489759i −0.908230 0.418471i \(-0.862566\pi\)
0.418471 + 0.908230i \(0.362566\pi\)
\(270\) −415973. 1.04943e6i −0.347261 0.876079i
\(271\) 821841. 0.679774 0.339887 0.940466i \(-0.389611\pi\)
0.339887 + 0.940466i \(0.389611\pi\)
\(272\) −29039.8 + 473394.i −0.0237997 + 0.387972i
\(273\) −206278. −0.167512
\(274\) −216506. 546207.i −0.174218 0.439523i
\(275\) 1.52468e6 1.52468e6i 1.21576 1.21576i
\(276\) 151560. + 4644.28i 0.119760 + 0.00366983i
\(277\) −285729. 285729.i −0.223746 0.223746i 0.586328 0.810074i \(-0.300573\pi\)
−0.810074 + 0.586328i \(0.800573\pi\)
\(278\) −1.46459e6 633107.i −1.13659 0.491320i
\(279\) 2.23598e6i 1.71972i
\(280\) −869604. 2.40655e6i −0.662867 1.83443i
\(281\) 1.38882e6i 1.04925i −0.851334 0.524625i \(-0.824206\pi\)
0.851334 0.524625i \(-0.175794\pi\)
\(282\) −77107.0 + 178375.i −0.0577392 + 0.133571i
\(283\) 62485.8 + 62485.8i 0.0463784 + 0.0463784i 0.729916 0.683537i \(-0.239559\pi\)
−0.683537 + 0.729916i \(0.739559\pi\)
\(284\) −1.47798e6 1.57142e6i −1.08736 1.15611i
\(285\) 394504. 394504.i 0.287699 0.287699i
\(286\) −589016. + 233474.i −0.425806 + 0.168781i
\(287\) −54704.7 −0.0392030
\(288\) −1.22651e6 + 401171.i −0.871344 + 0.285002i
\(289\) −1.20533e6 −0.848911
\(290\) 914542. 362507.i 0.638570 0.253117i
\(291\) 234081. 234081.i 0.162044 0.162044i
\(292\) 428460. + 455549.i 0.294072 + 0.312664i
\(293\) 1.58326e6 + 1.58326e6i 1.07741 + 1.07741i 0.996741 + 0.0806745i \(0.0257074\pi\)
0.0806745 + 0.996741i \(0.474293\pi\)
\(294\) −52584.3 + 121646.i −0.0354803 + 0.0820782i
\(295\) 2.19006e6i 1.46522i
\(296\) 2.26555e6 818653.i 1.50295 0.543088i
\(297\) 758966.i 0.499265i
\(298\) −821586. 355150.i −0.535935 0.231671i
\(299\) 230313. + 230313.i 0.148985 + 0.148985i
\(300\) −856010. 26230.8i −0.549131 0.0168271i
\(301\) −1.36042e6 + 1.36042e6i −0.865481 + 0.865481i
\(302\) 563789. + 1.42234e6i 0.355713 + 0.897402i
\(303\) −496477. −0.310665
\(304\) −883389. 998853.i −0.548236 0.619894i
\(305\) 187828. 0.115614
\(306\) 215082. + 542615.i 0.131311 + 0.331274i
\(307\) 1.31667e6 1.31667e6i 0.797314 0.797314i −0.185357 0.982671i \(-0.559344\pi\)
0.982671 + 0.185357i \(0.0593441\pi\)
\(308\) −52693.2 + 1.71958e6i −0.0316503 + 1.03287i
\(309\) 11624.4 + 11624.4i 0.00692589 + 0.00692589i
\(310\) 4.96504e6 + 2.14626e6i 2.93440 + 1.26846i
\(311\) 564228.i 0.330791i 0.986227 + 0.165395i \(0.0528900\pi\)
−0.986227 + 0.165395i \(0.947110\pi\)
\(312\) 227829. + 106882.i 0.132502 + 0.0621610i
\(313\) 2.17165e6i 1.25294i 0.779446 + 0.626469i \(0.215500\pi\)
−0.779446 + 0.626469i \(0.784500\pi\)
\(314\) 335983. 777244.i 0.192306 0.444870i
\(315\) −2.22675e6 2.22675e6i −1.26443 1.26443i
\(316\) −1.02555e6 + 964568.i −0.577749 + 0.543394i
\(317\) −266259. + 266259.i −0.148818 + 0.148818i −0.777590 0.628772i \(-0.783558\pi\)
0.628772 + 0.777590i \(0.283558\pi\)
\(318\) −41541.5 + 16466.2i −0.0230364 + 0.00913117i
\(319\) −661414. −0.363912
\(320\) −286486. + 3.10857e6i −0.156397 + 1.69702i
\(321\) −284305. −0.154000
\(322\) 822158. 325888.i 0.441892 0.175157i
\(323\) −426481. + 426481.i −0.227454 + 0.227454i
\(324\) −1.04228e6 + 980301.i −0.551597 + 0.518797i
\(325\) −1.30081e6 1.30081e6i −0.683131 0.683131i
\(326\) −12164.8 + 28141.4i −0.00633958 + 0.0146656i
\(327\) 434171.i 0.224539i
\(328\) 60420.2 + 28345.0i 0.0310097 + 0.0145476i
\(329\) 1.13341e6i 0.577296i
\(330\) 806062. + 348440.i 0.407459 + 0.176134i
\(331\) 1.05180e6 + 1.05180e6i 0.527670 + 0.527670i 0.919877 0.392207i \(-0.128288\pi\)
−0.392207 + 0.919877i \(0.628288\pi\)
\(332\) 101582. 3.31500e6i 0.0505790 1.65058i
\(333\) 2.09628e6 2.09628e6i 1.03595 1.03595i
\(334\) 197885. + 499229.i 0.0970613 + 0.244869i
\(335\) 2.34441e6 1.14136
\(336\) 511847. 452679.i 0.247339 0.218747i
\(337\) 228933. 0.109808 0.0549040 0.998492i \(-0.482515\pi\)
0.0549040 + 0.998492i \(0.482515\pi\)
\(338\) −574762. 1.45003e6i −0.273650 0.690373i
\(339\) −559954. + 559954.i −0.264639 + 0.264639i
\(340\) 1.41134e6 + 43247.9i 0.662117 + 0.0202893i
\(341\) −2.57151e6 2.57151e6i −1.19758 1.19758i
\(342\) −1.50632e6 651144.i −0.696390 0.301031i
\(343\) 1.72085e6i 0.789785i
\(344\) 2.20746e6 797661.i 1.00576 0.363431i
\(345\) 451427.i 0.204192i
\(346\) −849380. + 1.96491e6i −0.381427 + 0.882374i
\(347\) −1.61497e6 1.61497e6i −0.720014 0.720014i 0.248594 0.968608i \(-0.420031\pi\)
−0.968608 + 0.248594i \(0.920031\pi\)
\(348\) 179981. + 191360.i 0.0796672 + 0.0847040i
\(349\) 341998. 341998.i 0.150300 0.150300i −0.627952 0.778252i \(-0.716107\pi\)
0.778252 + 0.627952i \(0.216107\pi\)
\(350\) −4.64353e6 + 1.84061e6i −2.02618 + 0.803139i
\(351\) 647524. 0.280536
\(352\) 949191. 1.87194e6i 0.408317 0.805257i
\(353\) −1986.21 −0.000848377 −0.000424188 1.00000i \(-0.500135\pi\)
−0.000424188 1.00000i \(0.500135\pi\)
\(354\) 543674. 215502.i 0.230585 0.0913992i
\(355\) −4.54137e6 + 4.54137e6i −1.91256 + 1.91256i
\(356\) −1.94400e6 2.06691e6i −0.812965 0.864364i
\(357\) −218544. 218544.i −0.0907544 0.0907544i
\(358\) 487311. 1.12732e6i 0.200955 0.464878i
\(359\) 1.77409e6i 0.726505i 0.931691 + 0.363253i \(0.118334\pi\)
−0.931691 + 0.363253i \(0.881666\pi\)
\(360\) 1.30562e6 + 3.61318e6i 0.530957 + 1.46938i
\(361\) 780387.i 0.315168i
\(362\) 2.10608e6 + 910403.i 0.844701 + 0.365142i
\(363\) 94664.1 + 94664.1i 0.0377067 + 0.0377067i
\(364\) 1.46709e6 + 44956.1i 0.580366 + 0.0177842i
\(365\) 1.31652e6 1.31652e6i 0.517244 0.517244i
\(366\) 18482.2 + 46627.5i 0.00721193 + 0.0181945i
\(367\) 4.40691e6 1.70793 0.853963 0.520334i \(-0.174193\pi\)
0.853963 + 0.520334i \(0.174193\pi\)
\(368\) −1.07692e6 66062.1i −0.414536 0.0254292i
\(369\) 82133.3 0.0314017
\(370\) −2.64268e6 6.66702e6i −1.00355 2.53179i
\(371\) −184294. + 184294.i −0.0695145 + 0.0695145i
\(372\) −44240.7 + 1.44374e6i −0.0165754 + 0.540919i
\(373\) 1.23878e6 + 1.23878e6i 0.461024 + 0.461024i 0.898991 0.437967i \(-0.144301\pi\)
−0.437967 + 0.898991i \(0.644301\pi\)
\(374\) −871399. 376683.i −0.322135 0.139251i
\(375\) 1.21077e6i 0.444615i
\(376\) 587275. 1.25183e6i 0.214226 0.456643i
\(377\) 564296.i 0.204481i
\(378\) 697631. 1.61386e6i 0.251128 0.580947i
\(379\) −608015. 608015.i −0.217428 0.217428i 0.589986 0.807414i \(-0.299133\pi\)
−0.807414 + 0.589986i \(0.799133\pi\)
\(380\) −2.89176e6 + 2.71981e6i −1.02732 + 0.966227i
\(381\) 246655. 246655.i 0.0870519 0.0870519i
\(382\) 1.40129e6 555445.i 0.491326 0.194752i
\(383\) −1.17463e6 −0.409172 −0.204586 0.978849i \(-0.565585\pi\)
−0.204586 + 0.978849i \(0.565585\pi\)
\(384\) −799879. + 234764.i −0.276819 + 0.0812461i
\(385\) 5.12180e6 1.76105
\(386\) −5.01609e6 + 1.98828e6i −1.71355 + 0.679218i
\(387\) 2.04253e6 2.04253e6i 0.693252 0.693252i
\(388\) −1.71585e6 + 1.61381e6i −0.578627 + 0.544220i
\(389\) −612458. 612458.i −0.205212 0.205212i 0.597017 0.802229i \(-0.296353\pi\)
−0.802229 + 0.597017i \(0.796353\pi\)
\(390\) 297277. 687705.i 0.0989692 0.228950i
\(391\) 488018.i 0.161434i
\(392\) 400501. 853707.i 0.131640 0.280604i
\(393\) 654718.i 0.213832i
\(394\) −1.64339e6 710397.i −0.533337 0.230548i
\(395\) 2.96381e6 + 2.96381e6i 0.955779 + 0.955779i
\(396\) 79113.2 2.58176e6i 0.0253519 0.827329i
\(397\) −127882. + 127882.i −0.0407224 + 0.0407224i −0.727175 0.686452i \(-0.759167\pi\)
0.686452 + 0.727175i \(0.259167\pi\)
\(398\) 1.17322e6 + 2.95983e6i 0.371255 + 0.936612i
\(399\) 868942. 0.273249
\(400\) 6.08239e6 + 373117.i 1.90075 + 0.116599i
\(401\) −5.67113e6 −1.76120 −0.880600 0.473861i \(-0.842860\pi\)
−0.880600 + 0.473861i \(0.842860\pi\)
\(402\) 230689. + 581989.i 0.0711970 + 0.179618i
\(403\) −2.19393e6 + 2.19393e6i −0.672915 + 0.672915i
\(404\) 3.53104e6 + 108202.i 1.07634 + 0.0329824i
\(405\) 3.01215e6 + 3.01215e6i 0.912514 + 0.912514i
\(406\) 1.40643e6 + 607962.i 0.423450 + 0.183046i
\(407\) 4.82171e6i 1.44283i
\(408\) 128139. + 354615.i 0.0381094 + 0.105465i
\(409\) 156604.i 0.0462907i 0.999732 + 0.0231453i \(0.00736805\pi\)
−0.999732 + 0.0231453i \(0.992632\pi\)
\(410\) 78837.7 182379.i 0.0231619 0.0535815i
\(411\) −330293. 330293.i −0.0964483 0.0964483i
\(412\) −80141.8 85208.7i −0.0232603 0.0247309i
\(413\) 2.41194e6 2.41194e6i 0.695811 0.695811i
\(414\) −1.23438e6 + 489286.i −0.353956 + 0.140301i
\(415\) −9.87379e6 −2.81426
\(416\) −1.59707e6 809818.i −0.452472 0.229432i
\(417\) −1.26848e6 −0.357227
\(418\) 2.48122e6 983508.i 0.694584 0.275320i
\(419\) 3.22837e6 3.22837e6i 0.898357 0.898357i −0.0969342 0.995291i \(-0.530904\pi\)
0.995291 + 0.0969342i \(0.0309036\pi\)
\(420\) −1.39372e6 1.48184e6i −0.385526 0.409900i
\(421\) −3.16092e6 3.16092e6i −0.869176 0.869176i 0.123205 0.992381i \(-0.460683\pi\)
−0.992381 + 0.123205i \(0.960683\pi\)
\(422\) −1.60982e6 + 3.72408e6i −0.440045 + 1.01798i
\(423\) 1.70170e6i 0.462415i
\(424\) 299040. 108058.i 0.0807819 0.0291904i
\(425\) 2.75631e6i 0.740212i
\(426\) −1.57424e6 680505.i −0.420289 0.181680i
\(427\) 206857. + 206857.i 0.0549036 + 0.0549036i
\(428\) 2.02203e6 + 61961.3i 0.533554 + 0.0163498i
\(429\) −356179. + 356179.i −0.0934383 + 0.0934383i
\(430\) −2.57491e6 6.49606e6i −0.671570 1.69426i
\(431\) 6.23411e6 1.61652 0.808260 0.588826i \(-0.200410\pi\)
0.808260 + 0.588826i \(0.200410\pi\)
\(432\) −1.60674e6 + 1.42100e6i −0.414224 + 0.366341i
\(433\) 4.15896e6 1.06602 0.533010 0.846109i \(-0.321061\pi\)
0.533010 + 0.846109i \(0.321061\pi\)
\(434\) 3.10436e6 + 7.83175e6i 0.791129 + 1.99588i
\(435\) 553025. 553025.i 0.140127 0.140127i
\(436\) −94623.1 + 3.08791e6i −0.0238386 + 0.777944i
\(437\) −970193. 970193.i −0.243027 0.243027i
\(438\) 456366. + 197275.i 0.113665 + 0.0491346i
\(439\) 5.80927e6i 1.43867i −0.694664 0.719334i \(-0.744447\pi\)
0.694664 0.719334i \(-0.255553\pi\)
\(440\) −5.65693e6 2.65384e6i −1.39299 0.653497i
\(441\) 1.16050e6i 0.284151i
\(442\) −321374. + 743448.i −0.0782446 + 0.181007i
\(443\) −4.91288e6 4.91288e6i −1.18940 1.18940i −0.977234 0.212162i \(-0.931949\pi\)
−0.212162 0.977234i \(-0.568051\pi\)
\(444\) 1.39502e6 1.31207e6i 0.335832 0.315862i
\(445\) −5.97330e6 + 5.97330e6i −1.42993 + 1.42993i
\(446\) 5.06509e6 2.00770e6i 1.20573 0.477928i
\(447\) −711575. −0.168443
\(448\) −3.73901e6 + 3.10799e6i −0.880160 + 0.731618i
\(449\) −5.08115e6 −1.18945 −0.594725 0.803929i \(-0.702739\pi\)
−0.594725 + 0.803929i \(0.702739\pi\)
\(450\) 6.97177e6 2.76348e6i 1.62298 0.643316i
\(451\) −94458.4 + 94458.4i −0.0218675 + 0.0218675i
\(452\) 4.10454e6 3.86047e6i 0.944970 0.888779i
\(453\) 860094. + 860094.i 0.196925 + 0.196925i
\(454\) 914825. 2.11631e6i 0.208304 0.481880i
\(455\) 4.36975e6i 0.989528i
\(456\) −959729. 450239.i −0.216141 0.101398i
\(457\) 166114.i 0.0372061i −0.999827 0.0186031i \(-0.994078\pi\)
0.999827 0.0186031i \(-0.00592188\pi\)
\(458\) 2.16133e6 + 934286.i 0.481456 + 0.208121i
\(459\) 686029. + 686029.i 0.151988 + 0.151988i
\(460\) −98383.8 + 3.21063e6i −0.0216785 + 0.707450i
\(461\) −3.52977e6 + 3.52977e6i −0.773560 + 0.773560i −0.978727 0.205167i \(-0.934226\pi\)
0.205167 + 0.978727i \(0.434226\pi\)
\(462\) 503984. + 1.27146e6i 0.109853 + 0.277140i
\(463\) −3.31500e6 −0.718673 −0.359337 0.933208i \(-0.616997\pi\)
−0.359337 + 0.933208i \(0.616997\pi\)
\(464\) −1.23836e6 1.40022e6i −0.267024 0.301926i
\(465\) 4.30022e6 0.922270
\(466\) 2.64826e6 + 6.68111e6i 0.564932 + 1.42523i
\(467\) 1.83160e6 1.83160e6i 0.388632 0.388632i −0.485567 0.874199i \(-0.661387\pi\)
0.874199 + 0.485567i \(0.161387\pi\)
\(468\) −2.20267e6 67496.8i −0.464874 0.0142452i
\(469\) 2.58192e6 + 2.58192e6i 0.542014 + 0.542014i
\(470\) −3.77867e6 1.63342e6i −0.789031 0.341078i
\(471\) 673171.i 0.139821i
\(472\) −3.91368e6 + 1.41420e6i −0.808593 + 0.292184i
\(473\) 4.69807e6i 0.965533i
\(474\) −444114. + 1.02739e6i −0.0907923 + 0.210034i
\(475\) 5.47963e6 + 5.47963e6i 1.11434 + 1.11434i
\(476\) 1.50670e6 + 1.60195e6i 0.304795 + 0.324065i
\(477\) 276697. 276697.i 0.0556812 0.0556812i
\(478\) 5.78183e6 2.29181e6i 1.15743 0.458784i
\(479\) 2.00716e6 0.399708 0.199854 0.979826i \(-0.435953\pi\)
0.199854 + 0.979826i \(0.435953\pi\)
\(480\) 771530. + 2.35882e6i 0.152845 + 0.467295i
\(481\) 4.11372e6 0.810723
\(482\) −6.90740e6 + 2.73796e6i −1.35424 + 0.536796i
\(483\) 497161. 497161.i 0.0969681 0.0969681i
\(484\) −652639. 693901.i −0.126637 0.134643i
\(485\) 4.95874e6 + 4.95874e6i 0.957231 + 0.957231i
\(486\) −1.59387e6 + 3.68717e6i −0.306099 + 0.708113i
\(487\) 2.41202e6i 0.460850i 0.973090 + 0.230425i \(0.0740116\pi\)
−0.973090 + 0.230425i \(0.925988\pi\)
\(488\) −121287. 335652.i −0.0230550 0.0638027i
\(489\) 24373.2i 0.00460936i
\(490\) −2.57692e6 1.11394e6i −0.484854 0.209590i
\(491\) 5.10857e6 + 5.10857e6i 0.956303 + 0.956303i 0.999084 0.0427811i \(-0.0136218\pi\)
−0.0427811 + 0.999084i \(0.513622\pi\)
\(492\) 53032.4 + 1625.08i 0.00987708 + 0.000302664i
\(493\) −597852. + 597852.i −0.110784 + 0.110784i
\(494\) −839096. 2.11690e6i −0.154701 0.390285i
\(495\) −7.68984e6 −1.41060
\(496\) 629297. 1.02585e7i 0.114855 1.87232i
\(497\) −1.00029e7 −1.81650
\(498\) −971579. 2.45113e6i −0.175552 0.442886i
\(499\) 7.47209e6 7.47209e6i 1.34335 1.34335i 0.450658 0.892697i \(-0.351189\pi\)
0.892697 0.450658i \(-0.148811\pi\)
\(500\) 263875. 8.61125e6i 0.0472035 1.54043i
\(501\) 301885. + 301885.i 0.0537337 + 0.0537337i
\(502\) −3.26148e6 1.40986e6i −0.577638 0.249698i
\(503\) 7.72508e6i 1.36139i 0.732566 + 0.680696i \(0.238322\pi\)
−0.732566 + 0.680696i \(0.761678\pi\)
\(504\) −2.54134e6 + 5.41712e6i −0.445643 + 0.949932i
\(505\) 1.05173e7i 1.83517i
\(506\) 856909. 1.98233e6i 0.148785 0.344191i
\(507\) −876833. 876833.i −0.151495 0.151495i
\(508\) −1.80802e6 + 1.70050e6i −0.310844 + 0.292360i
\(509\) 3.58467e6 3.58467e6i 0.613274 0.613274i −0.330524 0.943798i \(-0.607225\pi\)
0.943798 + 0.330524i \(0.107225\pi\)
\(510\) 1.04355e6 413644.i 0.177660 0.0704209i
\(511\) 2.89980e6 0.491265
\(512\) 5.74006e6 1.49536e6i 0.967702 0.252099i
\(513\) −2.72769e6 −0.457616
\(514\) −3.49634e6 + 1.38588e6i −0.583722 + 0.231376i
\(515\) −246250. + 246250.i −0.0409127 + 0.0409127i
\(516\) 1.35925e6 1.27842e6i 0.224737 0.211373i
\(517\) 1.95706e6 + 1.95706e6i 0.322017 + 0.322017i
\(518\) 4.43205e6 1.02529e7i 0.725738 1.67888i
\(519\) 1.70181e6i 0.277327i
\(520\) −2.26417e6 + 4.82630e6i −0.367198 + 0.782720i
\(521\) 2.53713e6i 0.409495i −0.978815 0.204748i \(-0.934363\pi\)
0.978815 0.204748i \(-0.0656374\pi\)
\(522\) −2.11160e6 912790.i −0.339184 0.146621i
\(523\) −4.65944e6 4.65944e6i −0.744868 0.744868i 0.228642 0.973510i \(-0.426571\pi\)
−0.973510 + 0.228642i \(0.926571\pi\)
\(524\) −142689. + 4.65648e6i −0.0227019 + 0.740849i
\(525\) −2.80795e6 + 2.80795e6i −0.444623 + 0.444623i
\(526\) 3.14148e6 + 7.92542e6i 0.495074 + 1.24899i
\(527\) −4.64878e6 −0.729143
\(528\) 102165. 1.66545e6i 0.0159484 0.259983i
\(529\) 5.32616e6 0.827514
\(530\) −348818. 880008.i −0.0539398 0.136081i
\(531\) −3.62127e6 + 3.62127e6i −0.557346 + 0.557346i
\(532\) −6.18008e6 189377.i −0.946706 0.0290100i
\(533\) 80588.8 + 80588.8i 0.0122873 + 0.0122873i
\(534\) −2.07062e6 895075.i −0.314229 0.135833i
\(535\) 6.02267e6i 0.909714i
\(536\) −1.51387e6 4.18949e6i −0.227602 0.629868i
\(537\) 976370.i 0.146110i
\(538\) 1.84507e6 4.26828e6i 0.274825 0.635766i
\(539\) 1.33465e6 + 1.33465e6i 0.197877 + 0.197877i
\(540\) 4.37503e6 + 4.65164e6i 0.645649 + 0.686470i
\(541\) 2.06112e6 2.06112e6i 0.302768 0.302768i −0.539328 0.842096i \(-0.681322\pi\)
0.842096 + 0.539328i \(0.181322\pi\)
\(542\) −4.32189e6 + 1.71311e6i −0.631940 + 0.250489i
\(543\) 1.82407e6 0.265486
\(544\) −834068. 2.55002e6i −0.120838 0.369441i
\(545\) 9.19741e6 1.32640
\(546\) 1.08477e6 429982.i 0.155724 0.0617261i
\(547\) −7.60525e6 + 7.60525e6i −1.08679 + 1.08679i −0.0909315 + 0.995857i \(0.528984\pi\)
−0.995857 + 0.0909315i \(0.971016\pi\)
\(548\) 2.27712e6 + 2.42109e6i 0.323918 + 0.344397i
\(549\) −310574. 310574.i −0.0439779 0.0439779i
\(550\) −4.83981e6 + 1.11961e7i −0.682215 + 1.57820i
\(551\) 2.37709e6i 0.333555i
\(552\) −806706. + 291502.i −0.112685 + 0.0407187i
\(553\) 6.52815e6i 0.907773i
\(554\) 2.09819e6 + 906992.i 0.290449 + 0.125554i
\(555\) −4.03156e6 4.03156e6i −0.555572 0.555572i
\(556\) 9.02170e6 + 276453.i 1.23766 + 0.0379258i
\(557\) 2.69598e6 2.69598e6i 0.368196 0.368196i −0.498623 0.866819i \(-0.666161\pi\)
0.866819 + 0.498623i \(0.166161\pi\)
\(558\) −4.66086e6 1.17585e7i −0.633695 1.59870i
\(559\) 4.00824e6 0.542531
\(560\) 9.58949e6 + 1.08429e7i 1.29219 + 1.46108i
\(561\) −754718. −0.101246
\(562\) 2.89496e6 + 7.30350e6i 0.386636 + 0.975416i
\(563\) −4.79425e6 + 4.79425e6i −0.637455 + 0.637455i −0.949927 0.312472i \(-0.898843\pi\)
0.312472 + 0.949927i \(0.398843\pi\)
\(564\) 33669.6 1.09877e6i 0.00445698 0.145448i
\(565\) −1.18620e7 1.18620e7i −1.56328 1.56328i
\(566\) −458851. 198349.i −0.0602047 0.0260249i
\(567\) 6.63463e6i 0.866681i
\(568\) 1.10480e7 + 5.18297e6i 1.43686 + 0.674075i
\(569\) 5.78452e6i 0.749008i −0.927225 0.374504i \(-0.877813\pi\)
0.927225 0.374504i \(-0.122187\pi\)
\(570\) −1.25228e6 + 2.89695e6i −0.161441 + 0.373468i
\(571\) 6.78200e6 + 6.78200e6i 0.870498 + 0.870498i 0.992527 0.122029i \(-0.0389401\pi\)
−0.122029 + 0.992527i \(0.538940\pi\)
\(572\) 2.61084e6 2.45559e6i 0.333649 0.313809i
\(573\) 847364. 847364.i 0.107816 0.107816i
\(574\) 287681. 114031.i 0.0364444 0.0144459i
\(575\) 6.27028e6 0.790893
\(576\) 5.61373e6 4.66632e6i 0.705010 0.586028i
\(577\) −1.33602e7 −1.67060 −0.835300 0.549795i \(-0.814706\pi\)
−0.835300 + 0.549795i \(0.814706\pi\)
\(578\) 6.33860e6 2.51250e6i 0.789175 0.312814i
\(579\) −3.03324e6 + 3.03324e6i −0.376019 + 0.376019i
\(580\) −4.05375e6 + 3.81269e6i −0.500365 + 0.470611i
\(581\) −1.08741e7 1.08741e7i −1.33645 1.33645i
\(582\) −743046. + 1.71892e6i −0.0909302 + 0.210353i
\(583\) 636438.i 0.0775506i
\(584\) −3.20277e6 1.50252e6i −0.388592 0.182301i
\(585\) 6.56072e6i 0.792614i
\(586\) −1.16263e7 5.02576e6i −1.39861 0.604585i
\(587\) −4.29558e6 4.29558e6i −0.514549 0.514549i 0.401368 0.915917i \(-0.368535\pi\)
−0.915917 + 0.401368i \(0.868535\pi\)
\(588\) 22961.5 749320.i 0.00273878 0.0893767i
\(589\) 9.24191e6 9.24191e6i 1.09767 1.09767i
\(590\) 4.56515e6 + 1.15171e7i 0.539915 + 1.36211i
\(591\) −1.42334e6 −0.167626
\(592\) −1.02076e7 + 9.02763e6i −1.19707 + 1.05869i
\(593\) 1.13393e7 1.32418 0.662092 0.749423i \(-0.269669\pi\)
0.662092 + 0.749423i \(0.269669\pi\)
\(594\) −1.58205e6 3.99125e6i −0.183973 0.464133i
\(595\) 4.62959e6 4.62959e6i 0.536106 0.536106i
\(596\) 5.06086e6 + 155080.i 0.583591 + 0.0178830i
\(597\) 1.78982e6 + 1.78982e6i 0.205529 + 0.205529i
\(598\) −1.69126e6 731086.i −0.193400 0.0836018i
\(599\) 1.32953e6i 0.151402i 0.997131 + 0.0757011i \(0.0241195\pi\)
−0.997131 + 0.0757011i \(0.975881\pi\)
\(600\) 4.55626e6 1.64640e6i 0.516690 0.186705i
\(601\) 1.21817e7i 1.37569i 0.725858 + 0.687845i \(0.241443\pi\)
−0.725858 + 0.687845i \(0.758557\pi\)
\(602\) 4.31840e6 9.98996e6i 0.485659 1.12350i
\(603\) −3.87648e6 3.87648e6i −0.434154 0.434154i
\(604\) −5.92970e6 6.30460e6i −0.661364 0.703178i
\(605\) −2.00535e6 + 2.00535e6i −0.222742 + 0.222742i
\(606\) 2.61087e6 1.03490e6i 0.288804 0.114476i
\(607\) 8.54612e6 0.941450 0.470725 0.882280i \(-0.343992\pi\)
0.470725 + 0.882280i \(0.343992\pi\)
\(608\) 6.72765e6 + 3.41135e6i 0.738082 + 0.374255i
\(609\) 1.21810e6 0.133089
\(610\) −987749. + 391525.i −0.107479 + 0.0426024i
\(611\) 1.66970e6 1.66970e6i 0.180940 0.180940i
\(612\) −2.26214e6 2.40516e6i −0.244141 0.259577i
\(613\) 1.05598e7 + 1.05598e7i 1.13502 + 1.13502i 0.989331 + 0.145688i \(0.0465395\pi\)
0.145688 + 0.989331i \(0.453460\pi\)
\(614\) −4.17951e6 + 9.66864e6i −0.447408 + 1.03501i
\(615\) 157958.i 0.0168405i
\(616\) −3.30733e6 9.15274e6i −0.351177 0.971850i
\(617\) 3.42350e6i 0.362041i 0.983479 + 0.181021i \(0.0579401\pi\)
−0.983479 + 0.181021i \(0.942060\pi\)
\(618\) −85361.5 36899.6i −0.00899064 0.00388642i
\(619\) −9.52048e6 9.52048e6i −0.998693 0.998693i 0.00130592 0.999999i \(-0.499584\pi\)
−0.999999 + 0.00130592i \(0.999584\pi\)
\(620\) −3.05840e7 937189.i −3.19532 0.0979147i
\(621\) −1.56063e6 + 1.56063e6i −0.162395 + 0.162395i
\(622\) −1.17612e6 2.96716e6i −0.121893 0.307514i
\(623\) −1.31569e7 −1.35811
\(624\) −1.42090e6 87163.6i −0.146084 0.00896135i
\(625\) −7.05193e6 −0.722117
\(626\) −4.52678e6 1.14203e7i −0.461693 1.16477i
\(627\) 1.50040e6 1.50040e6i 0.152419 0.152419i
\(628\) −146711. + 4.78772e6i −0.0148444 + 0.484428i
\(629\) 4.35834e6 + 4.35834e6i 0.439233 + 0.439233i
\(630\) 1.63516e7 + 7.06839e6i 1.64138 + 0.709527i
\(631\) 7.08377e6i 0.708257i −0.935197 0.354129i \(-0.884777\pi\)
0.935197 0.354129i \(-0.115223\pi\)
\(632\) 3.38254e6 7.21021e6i 0.336860 0.718051i
\(633\) 3.22542e6i 0.319946i
\(634\) 845190. 1.95522e6i 0.0835086 0.193184i
\(635\) 5.22511e6 + 5.22511e6i 0.514234 + 0.514234i
\(636\) 184135. 173185.i 0.0180506 0.0169773i
\(637\) 1.13868e6 1.13868e6i 0.111187 0.111187i
\(638\) 3.47824e6 1.37871e6i 0.338304 0.134097i
\(639\) 1.50183e7 1.45502
\(640\) −4.97319e6 1.69445e7i −0.479938 1.63523i
\(641\) 1.32658e6 0.127523 0.0637617 0.997965i \(-0.479690\pi\)
0.0637617 + 0.997965i \(0.479690\pi\)
\(642\) 1.49510e6 592629.i 0.143164 0.0567473i
\(643\) 2.06573e6 2.06573e6i 0.197036 0.197036i −0.601692 0.798728i \(-0.705507\pi\)
0.798728 + 0.601692i \(0.205507\pi\)
\(644\) −3.64425e6 + 3.42755e6i −0.346253 + 0.325664i
\(645\) −3.92818e6 3.92818e6i −0.371785 0.371785i
\(646\) 1.35378e6 3.13177e6i 0.127634 0.295262i
\(647\) 879558.i 0.0826046i −0.999147 0.0413023i \(-0.986849\pi\)
0.999147 0.0413023i \(-0.0131507\pi\)
\(648\) 3.43771e6 7.32782e6i 0.321612 0.685547i
\(649\) 8.32938e6i 0.776249i
\(650\) 9.55218e6 + 4.12916e6i 0.886786 + 0.383335i
\(651\) 4.73588e6 + 4.73588e6i 0.437974 + 0.437974i
\(652\) 5311.89 173347.i 0.000489362 0.0159697i
\(653\) −9.65093e6 + 9.65093e6i −0.885699 + 0.885699i −0.994107 0.108407i \(-0.965425\pi\)
0.108407 + 0.994107i \(0.465425\pi\)
\(654\) 905023. + 2.28322e6i 0.0827400 + 0.208739i
\(655\) 1.38694e7 1.26315
\(656\) −376822. 23115.7i −0.0341883 0.00209724i
\(657\) −4.35374e6 −0.393504
\(658\) −2.36258e6 5.96039e6i −0.212727 0.536673i
\(659\) −7.38827e6 + 7.38827e6i −0.662719 + 0.662719i −0.956020 0.293301i \(-0.905246\pi\)
0.293301 + 0.956020i \(0.405246\pi\)
\(660\) −4.96523e6 152150.i −0.443690 0.0135960i
\(661\) 4.31263e6 + 4.31263e6i 0.383918 + 0.383918i 0.872512 0.488593i \(-0.162490\pi\)
−0.488593 + 0.872512i \(0.662490\pi\)
\(662\) −7.72364e6 3.33873e6i −0.684979 0.296099i
\(663\) 643900.i 0.0568898i
\(664\) 6.37586e6 + 1.76446e7i 0.561201 + 1.55307i
\(665\) 1.84075e7i 1.61414i
\(666\) −6.65425e6 + 1.53936e7i −0.581318 + 1.34479i
\(667\) −1.36004e6 1.36004e6i −0.118369 0.118369i
\(668\) −2.08127e6 2.21286e6i −0.180463 0.191872i
\(669\) 3.06287e6 3.06287e6i 0.264584 0.264584i
\(670\) −1.23288e7 + 4.88688e6i −1.06104 + 0.420576i
\(671\) 714359. 0.0612506
\(672\) −1.74810e6 + 3.44748e6i −0.149328 + 0.294496i
\(673\) 3.04784e6 0.259390 0.129695 0.991554i \(-0.458600\pi\)
0.129695 + 0.991554i \(0.458600\pi\)
\(674\) −1.20391e6 + 477208.i −0.102081 + 0.0404630i
\(675\) 8.81443e6 8.81443e6i 0.744620 0.744620i
\(676\) 6.04511e6 + 6.42730e6i 0.508789 + 0.540956i
\(677\) 2.15140e6 + 2.15140e6i 0.180405 + 0.180405i 0.791533 0.611127i \(-0.209284\pi\)
−0.611127 + 0.791533i \(0.709284\pi\)
\(678\) 1.77747e6 4.11190e6i 0.148500 0.343533i
\(679\) 1.09222e7i 0.909151i
\(680\) −7.51210e6 + 2.71449e6i −0.623002 + 0.225121i
\(681\) 1.83293e6i 0.151453i
\(682\) 1.88834e7 + 8.16279e6i 1.55460 + 0.672013i
\(683\) −6.10507e6 6.10507e6i −0.500770 0.500770i 0.410907 0.911677i \(-0.365212\pi\)
−0.911677 + 0.410907i \(0.865212\pi\)
\(684\) 9.27874e6 + 284329.i 0.758313 + 0.0232371i
\(685\) 6.99687e6 6.99687e6i 0.569741 0.569741i
\(686\) 3.58710e6 + 9.04962e6i 0.291027 + 0.734210i
\(687\) 1.87192e6 0.151320
\(688\) −9.94585e6 + 8.79615e6i −0.801071 + 0.708470i
\(689\) 542988. 0.0435755
\(690\) 940992. + 2.37396e6i 0.0752425 + 0.189824i
\(691\) −1.26085e7 + 1.26085e7i −1.00454 + 1.00454i −0.00455145 + 0.999990i \(0.501449\pi\)
−0.999990 + 0.00455145i \(0.998551\pi\)
\(692\) 370891. 1.21036e7i 0.0294430 0.960835i
\(693\) −8.46890e6 8.46890e6i −0.669875 0.669875i
\(694\) 1.18592e7 + 5.12642e6i 0.934665 + 0.404031i
\(695\) 2.68714e7i 2.11022i
\(696\) −1.34537e6 631157.i −0.105274 0.0493872i
\(697\) 170762.i 0.0133140i
\(698\) −1.08561e6 + 2.51138e6i −0.0843401 + 0.195108i
\(699\) 4.04008e6 + 4.04008e6i 0.312750 + 0.312750i
\(700\) 2.05827e7 1.93587e7i 1.58766 1.49325i
\(701\) −1.59123e7 + 1.59123e7i −1.22303 + 1.22303i −0.256487 + 0.966548i \(0.582565\pi\)
−0.966548 + 0.256487i \(0.917435\pi\)
\(702\) −3.40520e6 + 1.34975e6i −0.260795 + 0.103374i
\(703\) −1.73290e7 −1.32247
\(704\) −1.08958e6 + 1.18227e7i −0.0828568 + 0.899053i
\(705\) −3.27270e6 −0.247990
\(706\) 10445.1 4140.23i 0.000788678 0.000312617i
\(707\) 1.15828e7 1.15828e7i 0.871495 0.871495i
\(708\) −2.40986e6 + 2.26656e6i −0.180679 + 0.169935i
\(709\) −1.02088e7 1.02088e7i −0.762709 0.762709i 0.214103 0.976811i \(-0.431317\pi\)
−0.976811 + 0.214103i \(0.931317\pi\)
\(710\) 1.44157e7 3.33485e7i 1.07322 2.48274i
\(711\) 9.80132e6i 0.727127i
\(712\) 1.45316e7 + 6.81721e6i 1.07427 + 0.503973i
\(713\) 1.05754e7i 0.779066i
\(714\) 1.60483e6 + 693725.i 0.117810 + 0.0509263i
\(715\) −7.54524e6 7.54524e6i −0.551960 0.551960i
\(716\) −212790. + 6.94413e6i −0.0155120 + 0.506215i
\(717\) 3.49629e6 3.49629e6i 0.253986 0.253986i
\(718\) −3.69806e6 9.32956e6i −0.267709 0.675383i
\(719\) −1.72580e7 −1.24499 −0.622497 0.782622i \(-0.713882\pi\)
−0.622497 + 0.782622i \(0.713882\pi\)
\(720\) −1.43976e7 1.62794e7i −1.03504 1.17033i
\(721\) −542396. −0.0388578
\(722\) −1.62671e6 4.10390e6i −0.116136 0.292990i
\(723\) −4.17692e6 + 4.17692e6i −0.297174 + 0.297174i
\(724\) −1.29732e7 397538.i −0.919812 0.0281859i
\(725\) 7.68148e6 + 7.68148e6i 0.542750 + 0.542750i
\(726\) −695145. 300493.i −0.0489479 0.0211589i
\(727\) 1.06169e7i 0.745012i 0.928030 + 0.372506i \(0.121501\pi\)
−0.928030 + 0.372506i \(0.878499\pi\)
\(728\) −7.80881e6 + 2.82170e6i −0.546080 + 0.197325i
\(729\) 7.67208e6i 0.534680i
\(730\) −4.17905e6 + 9.66758e6i −0.290249 + 0.671446i
\(731\) 4.24659e6 + 4.24659e6i 0.293932 + 0.293932i
\(732\) −194389. 206678.i −0.0134089 0.0142567i
\(733\) 3.65326e6 3.65326e6i 0.251143 0.251143i −0.570296 0.821439i \(-0.693172\pi\)
0.821439 + 0.570296i \(0.193172\pi\)
\(734\) −2.31750e7 + 9.18613e6i −1.58774 + 0.629350i
\(735\) −2.23187e6 −0.152388
\(736\) 5.80098e6 1.89741e6i 0.394736 0.129112i
\(737\) 8.91639e6 0.604673
\(738\) −431922. + 171205.i −0.0291920 + 0.0115712i
\(739\) 1.91916e7 1.91916e7i 1.29271 1.29271i 0.359600 0.933106i \(-0.382913\pi\)
0.933106 0.359600i \(-0.117087\pi\)
\(740\) 2.77946e7 + 2.95519e7i 1.86587 + 1.98383i
\(741\) −1.28009e6 1.28009e6i −0.0856437 0.0856437i
\(742\) 585005. 1.35332e6i 0.0390077 0.0902382i
\(743\) 1.62809e7i 1.08195i 0.841039 + 0.540974i \(0.181944\pi\)
−0.841039 + 0.540974i \(0.818056\pi\)
\(744\) −2.77680e6 7.68456e6i −0.183913 0.508964i
\(745\) 1.50739e7i 0.995026i
\(746\) −9.09674e6 3.93229e6i −0.598465 0.258701i
\(747\) 1.63263e7 + 1.63263e7i 1.07050 + 1.07050i
\(748\) 5.36770e6 + 164483.i 0.350779 + 0.0107490i
\(749\) 6.63283e6 6.63283e6i 0.432011 0.432011i
\(750\) −2.52384e6 6.36720e6i −0.163836 0.413329i
\(751\) −9.94826e6 −0.643646 −0.321823 0.946800i \(-0.604296\pi\)
−0.321823 + 0.946800i \(0.604296\pi\)
\(752\) −478930. + 7.80730e6i −0.0308835 + 0.503450i
\(753\) −2.82477e6 −0.181550
\(754\) −1.17627e6 2.96752e6i −0.0753490 0.190092i
\(755\) −1.82201e7 + 1.82201e7i −1.16328 + 1.16328i
\(756\) −304628. + 9.94116e6i −0.0193850 + 0.632605i
\(757\) 1.01751e7 + 1.01751e7i 0.645356 + 0.645356i 0.951867 0.306511i \(-0.0991616\pi\)
−0.306511 + 0.951867i \(0.599162\pi\)
\(758\) 4.46482e6 + 1.93003e6i 0.282248 + 0.122009i
\(759\) 1.71689e6i 0.108178i
\(760\) 9.53780e6 2.03307e7i 0.598982 1.27679i
\(761\) 3.04334e7i 1.90497i −0.304583 0.952486i \(-0.598517\pi\)
0.304583 0.952486i \(-0.401483\pi\)
\(762\) −782961. + 1.81126e6i −0.0488487 + 0.113004i
\(763\) 1.01292e7 + 1.01292e7i 0.629889 + 0.629889i
\(764\) −6.21129e6 + 5.84194e6i −0.384989 + 0.362096i
\(765\) −6.95084e6 + 6.95084e6i −0.429422 + 0.429422i
\(766\) 6.17716e6 2.44851e6i 0.380379 0.150775i
\(767\) −7.10635e6 −0.436172
\(768\) 3.71704e6 2.90191e6i 0.227402 0.177534i
\(769\) −1.22268e7 −0.745587 −0.372794 0.927914i \(-0.621600\pi\)
−0.372794 + 0.927914i \(0.621600\pi\)
\(770\) −2.69345e7 + 1.06763e7i −1.63713 + 0.648925i
\(771\) −2.11424e6 + 2.11424e6i −0.128091 + 0.128091i
\(772\) 2.22340e7 2.09119e7i 1.34269 1.26285i
\(773\) 1.62595e7 + 1.62595e7i 0.978722 + 0.978722i 0.999778 0.0210561i \(-0.00670287\pi\)
−0.0210561 + 0.999778i \(0.506703\pi\)
\(774\) −6.48362e6 + 1.49989e7i −0.389014 + 0.899924i
\(775\) 5.97298e7i 3.57221i
\(776\) 5.65931e6 1.20634e7i 0.337372 0.719141i
\(777\) 8.87999e6i 0.527667i
\(778\) 4.49745e6 + 1.94413e6i 0.266390 + 0.115153i
\(779\) −339479. 339479.i −0.0200433 0.0200433i
\(780\) −129809. + 4.23617e6i −0.00763958 + 0.249308i
\(781\) −1.72720e7 + 1.72720e7i −1.01325 + 1.01325i
\(782\) −1.01727e6 2.56639e6i −0.0594864 0.150074i
\(783\) −3.82374e6 −0.222887
\(784\) −326613. + 5.32431e6i −0.0189777 + 0.309366i
\(785\) 1.42603e7 0.825954
\(786\) 1.36475e6 + 3.44303e6i 0.0787947 + 0.198785i
\(787\) 1.80208e7 1.80208e7i 1.03714 1.03714i 0.0378547 0.999283i \(-0.487948\pi\)
0.999283 0.0378547i \(-0.0120524\pi\)
\(788\) 1.01231e7 + 310203.i 0.580761 + 0.0177963i
\(789\) 4.79252e6 + 4.79252e6i 0.274076 + 0.274076i
\(790\) −2.17641e7 9.40805e6i −1.24072 0.536330i
\(791\) 2.61274e7i 1.48476i
\(792\) 4.96560e6 + 1.37419e7i 0.281293 + 0.778454i
\(793\) 609467.i 0.0344166i
\(794\) 405938. 939074.i 0.0228511 0.0528626i
\(795\) −532143. 532143.i −0.0298614 0.0298614i
\(796\) −1.23395e7 1.31196e7i −0.690261 0.733902i
\(797\) 2.43391e7 2.43391e7i 1.35725 1.35725i 0.479953 0.877294i \(-0.340654\pi\)
0.877294 0.479953i \(-0.159346\pi\)
\(798\) −4.56959e6 + 1.81130e6i −0.254021 + 0.100689i
\(799\) 3.53798e6 0.196060
\(800\) −3.27638e7 + 1.07165e7i −1.80996 + 0.592009i
\(801\) 1.97537e7 1.08785
\(802\) 2.98233e7 1.18214e7i 1.63727 0.648981i
\(803\) 5.00707e6 5.00707e6i 0.274028 0.274028i
\(804\) −2.42629e6 2.57969e6i −0.132374 0.140743i
\(805\) 1.05318e7 + 1.05318e7i 0.572812 + 0.572812i
\(806\) 6.96422e6 1.61106e7i 0.377602 0.873525i
\(807\) 3.69675e6i 0.199819i
\(808\) −1.87946e7 + 6.79138e6i −1.01275 + 0.365957i
\(809\) 2.45540e7i 1.31902i 0.751696 + 0.659509i \(0.229236\pi\)
−0.751696 + 0.659509i \(0.770764\pi\)
\(810\) −2.21191e7 9.56151e6i −1.18455 0.512052i
\(811\) 5.58766e6 + 5.58766e6i 0.298317 + 0.298317i 0.840354 0.542037i \(-0.182347\pi\)
−0.542037 + 0.840354i \(0.682347\pi\)
\(812\) −8.66340e6 265473.i −0.461103 0.0141296i
\(813\) −2.61346e6 + 2.61346e6i −0.138672 + 0.138672i
\(814\) −1.00508e7 2.53564e7i −0.531666 1.34130i
\(815\) −516318. −0.0272285
\(816\) −1.41305e6 1.59774e6i −0.0742902 0.0840004i
\(817\) −1.68847e7 −0.884988
\(818\) −326438. 823546.i −0.0170576 0.0430333i
\(819\) −7.22539e6 + 7.22539e6i −0.376401 + 0.376401i
\(820\) −34425.4 + 1.12343e6i −0.00178790 + 0.0583460i
\(821\) −2.26326e7 2.26326e7i −1.17186 1.17186i −0.981766 0.190094i \(-0.939121\pi\)
−0.190094 0.981766i \(-0.560879\pi\)
\(822\) 2.42543e6 + 1.04845e6i 0.125202 + 0.0541214i
\(823\) 2.57524e7i 1.32531i −0.748923 0.662657i \(-0.769429\pi\)
0.748923 0.662657i \(-0.230571\pi\)
\(824\) 599066. + 281041.i 0.0307366 + 0.0144195i
\(825\) 9.69697e6i 0.496022i
\(826\) −7.65625e6 + 1.77115e7i −0.390450 + 0.903247i
\(827\) −6.00028e6 6.00028e6i −0.305076 0.305076i 0.537920 0.842996i \(-0.319210\pi\)
−0.842996 + 0.537920i \(0.819210\pi\)
\(828\) 5.47146e6 5.14611e6i 0.277350 0.260857i
\(829\) −2.48171e7 + 2.48171e7i −1.25419 + 1.25419i −0.300368 + 0.953823i \(0.597110\pi\)
−0.953823 + 0.300368i \(0.902890\pi\)
\(830\) 5.19243e7 2.05818e7i 2.61622 1.03702i
\(831\) 1.81724e6 0.0912871
\(832\) 1.00867e7 + 929595.i 0.505175 + 0.0465571i
\(833\) 2.41278e6 0.120477
\(834\) 6.67070e6 2.64414e6i 0.332090 0.131634i
\(835\) −6.39508e6 + 6.39508e6i −0.317417 + 0.317417i
\(836\) −1.09981e7 + 1.03441e7i −0.544256 + 0.511892i
\(837\) −1.48664e7 1.48664e7i −0.733485 0.733485i
\(838\) −1.02479e7 + 2.37069e7i −0.504108 + 1.16618i
\(839\) 7.34159e6i 0.360069i −0.983660 0.180034i \(-0.942379\pi\)
0.983660 0.180034i \(-0.0576209\pi\)
\(840\) 1.04182e7 + 4.88750e6i 0.509441 + 0.238995i
\(841\) 1.71789e7i 0.837539i
\(842\) 2.32115e7 + 1.00337e7i 1.12830 + 0.487733i
\(843\) 4.41644e6 + 4.41644e6i 0.214044 + 0.214044i
\(844\) 702947. 2.29398e7i 0.0339677 1.10849i
\(845\) 1.85747e7 1.85747e7i 0.894911 0.894911i
\(846\) 3.54717e6 + 8.94890e6i 0.170395 + 0.429876i
\(847\) −4.41703e6 −0.211554
\(848\) −1.34734e6 + 1.19160e6i −0.0643412 + 0.0569035i
\(849\) −397410. −0.0189221
\(850\) 5.74549e6 + 1.44949e7i 0.272760 + 0.688125i
\(851\) −9.91471e6 + 9.91471e6i −0.469306 + 0.469306i
\(852\) 9.69713e6 + 297150.i 0.457661 + 0.0140242i
\(853\) −1.13091e7 1.13091e7i −0.532175 0.532175i 0.389044 0.921219i \(-0.372805\pi\)
−0.921219 + 0.389044i \(0.872805\pi\)
\(854\) −1.51901e6 656628.i −0.0712715 0.0308088i
\(855\) 2.76369e7i 1.29293i
\(856\) −1.07626e7 + 3.88905e6i −0.502034 + 0.181409i
\(857\) 9.03234e6i 0.420096i −0.977691 0.210048i \(-0.932638\pi\)
0.977691 0.210048i \(-0.0673620\pi\)
\(858\) 1.13062e6 2.61552e6i 0.0524324 0.121294i
\(859\) −9.00166e6 9.00166e6i −0.416236 0.416236i 0.467668 0.883904i \(-0.345094\pi\)
−0.883904 + 0.467668i \(0.845094\pi\)
\(860\) 2.70819e7 + 2.87941e7i 1.24863 + 1.32757i
\(861\) 173961. 173961.i 0.00799731 0.00799731i
\(862\) −3.27839e7 + 1.29949e7i −1.50277 + 0.595669i
\(863\) 3.76885e7 1.72259 0.861296 0.508104i \(-0.169654\pi\)
0.861296 + 0.508104i \(0.169654\pi\)
\(864\) 5.48744e6 1.08220e7i 0.250084 0.493199i
\(865\) −3.60508e7 −1.63823
\(866\) −2.18711e7 + 8.66929e6i −0.991006 + 0.392816i
\(867\) 3.83296e6 3.83296e6i 0.173176 0.173176i
\(868\) −3.26503e7 3.47146e7i −1.47092 1.56391i
\(869\) 1.12721e7 + 1.12721e7i 0.506357 + 0.506357i
\(870\) −1.75547e6 + 4.06102e6i −0.0786314 + 0.181902i
\(871\) 7.60716e6i 0.339764i
\(872\) −5.93910e6 1.64359e7i −0.264502 0.731986i
\(873\) 1.63985e7i 0.728232i
\(874\) 7.12440e6 + 3.07969e6i 0.315478 + 0.136373i
\(875\) −2.82473e7 2.82473e7i −1.24726 1.24726i
\(876\) −2.81115e6 86142.5i −0.123773 0.00379277i
\(877\) −7.81571e6 + 7.81571e6i −0.343139 + 0.343139i −0.857546 0.514407i \(-0.828012\pi\)
0.514407 + 0.857546i \(0.328012\pi\)
\(878\) 1.21093e7 + 3.05498e7i 0.530132 + 1.33743i
\(879\) −1.00695e7 −0.439580
\(880\) 3.52805e7 + 2.16424e6i 1.53578 + 0.0942105i
\(881\) 3.50352e7 1.52077 0.760387 0.649470i \(-0.225009\pi\)
0.760387 + 0.649470i \(0.225009\pi\)
\(882\) 2.41905e6 + 6.10284e6i 0.104706 + 0.264156i
\(883\) 1.00918e6 1.00918e6i 0.0435581 0.0435581i −0.684992 0.728550i \(-0.740194\pi\)
0.728550 + 0.684992i \(0.240194\pi\)
\(884\) 140331. 4.57954e6i 0.00603982 0.197102i
\(885\) 6.96441e6 + 6.96441e6i 0.298900 + 0.298900i
\(886\) 3.60766e7 + 1.55950e7i 1.54398 + 0.667423i
\(887\) 3.68389e7i 1.57216i 0.618122 + 0.786082i \(0.287894\pi\)
−0.618122 + 0.786082i \(0.712106\pi\)
\(888\) −4.60114e6 + 9.80778e6i −0.195809 + 0.417386i
\(889\) 1.15089e7i 0.488406i
\(890\) 1.89611e7 4.38636e7i 0.802396 1.85622i
\(891\) 1.14560e7 + 1.14560e7i 0.483436 + 0.483436i
\(892\) −2.24512e7 + 2.11162e7i −0.944774 + 0.888594i
\(893\) −7.03360e6 + 7.03360e6i −0.295154 + 0.295154i
\(894\) 3.74203e6 1.48327e6i 0.156590 0.0620691i
\(895\) 2.06833e7 0.863101
\(896\) 1.31841e7 2.41382e7i 0.548633 1.00446i
\(897\) −1.46480e6 −0.0607849
\(898\) 2.67207e7 1.05916e7i 1.10575 0.438298i
\(899\) 1.29555e7 1.29555e7i 0.534634 0.534634i
\(900\) −3.09027e7 + 2.90651e7i −1.27172 + 1.19609i
\(901\) 575276. + 575276.i 0.0236083 + 0.0236083i
\(902\) 299840. 693634.i 0.0122708 0.0283867i
\(903\) 8.65229e6i 0.353111i
\(904\) −1.35378e7 + 2.88572e7i −0.550971 + 1.17445i
\(905\) 3.86408e7i 1.56829i
\(906\) −6.31591e6 2.73020e6i −0.255632 0.110503i
\(907\) −3.03199e7 3.03199e7i −1.22380 1.22380i −0.966271 0.257527i \(-0.917093\pi\)
−0.257527 0.966271i \(-0.582907\pi\)
\(908\) −399469. + 1.30362e7i −0.0160793 + 0.524729i
\(909\) −1.73903e7 + 1.73903e7i −0.698069 + 0.698069i
\(910\) 9.10868e6 + 2.29796e7i 0.364629 + 0.919897i
\(911\) −1.32865e6 −0.0530413 −0.0265207 0.999648i \(-0.508443\pi\)
−0.0265207 + 0.999648i \(0.508443\pi\)
\(912\) 5.98554e6 + 367176.i 0.238296 + 0.0146180i
\(913\) −3.75526e7 −1.49095
\(914\) 346261. + 873557.i 0.0137100 + 0.0345880i
\(915\) −597294. + 597294.i −0.0235850 + 0.0235850i
\(916\) −1.33135e7 407966.i −0.524267 0.0160652i
\(917\) 1.52746e7 + 1.52746e7i 0.599854 + 0.599854i
\(918\) −5.03770e6 2.17767e6i −0.197299 0.0852875i
\(919\) 1.81854e7i 0.710286i 0.934812 + 0.355143i \(0.115568\pi\)
−0.934812 + 0.355143i \(0.884432\pi\)
\(920\) −6.17513e6 1.70891e7i −0.240534 0.665657i
\(921\) 8.37400e6i 0.325300i
\(922\) 1.12046e7 2.59201e7i 0.434079 1.00417i
\(923\) 1.47359e7 + 1.47359e7i 0.569341 + 0.569341i
\(924\) −5.30070e6 5.63583e6i −0.204246 0.217159i
\(925\) 5.59981e7 5.59981e7i 2.15188 2.15188i
\(926\) 1.74329e7 6.91007e6i 0.668102 0.264823i
\(927\) 814350. 0.0311252
\(928\) 9.43099e6 + 4.78212e6i 0.359491 + 0.182285i
\(929\) −2.08621e7 −0.793085 −0.396542 0.918016i \(-0.629790\pi\)
−0.396542 + 0.918016i \(0.629790\pi\)
\(930\) −2.26140e7 + 8.96374e6i −0.857372 + 0.339846i
\(931\) −4.79667e6 + 4.79667e6i −0.181370 + 0.181370i
\(932\) −2.78533e7 2.96143e7i −1.05036 1.11677i
\(933\) −1.79425e6 1.79425e6i −0.0674804 0.0674804i
\(934\) −5.81408e6 + 1.34500e7i −0.218079 + 0.504492i
\(935\) 1.59878e7i 0.598081i
\(936\) 1.17241e7 4.23649e6i 0.437411 0.158058i
\(937\) 8.88420e6i 0.330574i 0.986245 + 0.165287i \(0.0528551\pi\)
−0.986245 + 0.165287i \(0.947145\pi\)
\(938\) −1.89598e7 8.19581e6i −0.703600 0.304148i
\(939\) −6.90586e6 6.90586e6i −0.255596 0.255596i
\(940\) 2.32761e7 + 713252.i 0.859192 + 0.0263283i
\(941\) −1.15274e7 + 1.15274e7i −0.424381 + 0.424381i −0.886709 0.462328i \(-0.847014\pi\)
0.462328 + 0.886709i \(0.347014\pi\)
\(942\) 1.40321e6 + 3.54007e6i 0.0515225 + 0.129982i
\(943\) −388463. −0.0142256
\(944\) 1.76334e7 1.55950e7i 0.644028 0.569581i
\(945\) 2.96100e7 1.07860
\(946\) −9.79306e6 2.47062e7i −0.355787 0.897590i
\(947\) 3.66420e6 3.66420e6i 0.132771 0.132771i −0.637598 0.770369i \(-0.720072\pi\)
0.770369 + 0.637598i \(0.220072\pi\)
\(948\) 193928. 6.32858e6i 0.00700840 0.228710i
\(949\) −4.27187e6 4.27187e6i −0.153976 0.153976i
\(950\) −4.02384e7 1.73940e7i −1.44655 0.625305i
\(951\) 1.69341e6i 0.0607172i
\(952\) −1.12626e7 5.28366e6i −0.402762 0.188948i
\(953\) 2.62115e7i 0.934887i 0.884023 + 0.467444i \(0.154825\pi\)
−0.884023 + 0.467444i \(0.845175\pi\)
\(954\) −878323. + 2.03187e6i −0.0312452 + 0.0722810i
\(955\) 1.79504e7 + 1.79504e7i 0.636892 + 0.636892i
\(956\) −2.56282e7 + 2.41043e7i −0.906930 + 0.853001i
\(957\) 2.10330e6 2.10330e6i 0.0742371 0.0742371i
\(958\) −1.05552e7 + 4.18389e6i −0.371582 + 0.147288i
\(959\) 1.54114e7 0.541124
\(960\) −8.97424e6 1.07963e7i −0.314282 0.378091i
\(961\) 7.21107e7 2.51879
\(962\) −2.16332e7 + 8.57499e6i −0.753674 + 0.298742i
\(963\) −9.95849e6 + 9.95849e6i −0.346041 + 0.346041i
\(964\) 3.06174e7 2.87967e7i 1.06115 0.998046i
\(965\) −6.42557e7 6.42557e7i −2.22123 2.22123i
\(966\) −1.57814e6 + 3.65079e6i −0.0544131 + 0.125876i
\(967\) 5.78618e6i 0.198988i 0.995038 + 0.0994938i \(0.0317223\pi\)
−0.995038 + 0.0994938i \(0.968278\pi\)
\(968\) 4.87852e6 + 2.28867e6i 0.167340 + 0.0785044i
\(969\) 2.71242e6i 0.0927999i
\(970\) −3.64134e7 1.57406e7i −1.24260 0.537144i
\(971\) 1.05214e7 + 1.05214e7i 0.358116 + 0.358116i 0.863118 0.505002i \(-0.168508\pi\)
−0.505002 + 0.863118i \(0.668508\pi\)
\(972\) 695980. 2.27125e7i 0.0236282 0.771078i
\(973\) 2.95937e7 2.95937e7i 1.00211 1.00211i
\(974\) −5.02783e6 1.26843e7i −0.169818 0.428421i
\(975\) 8.27313e6 0.278714
\(976\) 1.33749e6 + 1.51230e6i 0.0449433 + 0.0508176i
\(977\) −1.96506e7 −0.658626 −0.329313 0.944221i \(-0.606817\pi\)
−0.329313 + 0.944221i \(0.606817\pi\)
\(978\) −50805.6 128174.i −0.00169849 0.00428501i
\(979\) −2.27180e7 + 2.27180e7i −0.757554 + 0.757554i
\(980\) 1.58735e7 + 486413.i 0.527967 + 0.0161786i
\(981\) −1.52079e7 1.52079e7i −0.504542 0.504542i
\(982\) −3.75137e7 1.62162e7i −1.24140 0.536624i
\(983\) 8.36026e6i 0.275954i 0.990435 + 0.137977i \(0.0440600\pi\)
−0.990435 + 0.137977i \(0.955940\pi\)
\(984\) −282274. + 101999.i −0.00929358 + 0.00335822i
\(985\) 3.01519e7i 0.990202i
\(986\) 1.89777e6 4.39019e6i 0.0621656 0.143811i
\(987\) −3.60426e6 3.60426e6i −0.117767 0.117767i
\(988\) 8.82527e6 + 9.38324e6i 0.287631 + 0.305816i
\(989\) −9.66048e6 + 9.66048e6i −0.314057 + 0.314057i
\(990\) 4.04393e7 1.60294e7i 1.31134 0.519790i
\(991\) 2.37286e7 0.767515 0.383758 0.923434i \(-0.374630\pi\)
0.383758 + 0.923434i \(0.374630\pi\)
\(992\) 1.80744e7 + 5.52593e7i 0.583156 + 1.78290i
\(993\) −6.68944e6 −0.215286
\(994\) 5.26032e7 2.08509e7i 1.68868 0.669359i
\(995\) −3.79152e7 + 3.79152e7i −1.21410 + 1.21410i
\(996\) 1.02187e7 + 1.08647e7i 0.326397 + 0.347033i
\(997\) 3.90437e7 + 3.90437e7i 1.24398 + 1.24398i 0.958336 + 0.285644i \(0.0922074\pi\)
0.285644 + 0.958336i \(0.407793\pi\)
\(998\) −2.37187e7 + 5.48696e7i −0.753816 + 1.74384i
\(999\) 2.78751e7i 0.883697i
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 16.6.e.a.5.1 18
3.2 odd 2 144.6.k.a.37.9 18
4.3 odd 2 64.6.e.a.49.5 18
8.3 odd 2 128.6.e.a.97.5 18
8.5 even 2 128.6.e.b.97.5 18
12.11 even 2 576.6.k.a.433.9 18
16.3 odd 4 64.6.e.a.17.5 18
16.5 even 4 128.6.e.b.33.5 18
16.11 odd 4 128.6.e.a.33.5 18
16.13 even 4 inner 16.6.e.a.13.1 yes 18
32.3 odd 8 1024.6.a.l.1.10 18
32.13 even 8 1024.6.a.k.1.10 18
32.19 odd 8 1024.6.a.l.1.9 18
32.29 even 8 1024.6.a.k.1.9 18
48.29 odd 4 144.6.k.a.109.9 18
48.35 even 4 576.6.k.a.145.9 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.6.e.a.5.1 18 1.1 even 1 trivial
16.6.e.a.13.1 yes 18 16.13 even 4 inner
64.6.e.a.17.5 18 16.3 odd 4
64.6.e.a.49.5 18 4.3 odd 2
128.6.e.a.33.5 18 16.11 odd 4
128.6.e.a.97.5 18 8.3 odd 2
128.6.e.b.33.5 18 16.5 even 4
128.6.e.b.97.5 18 8.5 even 2
144.6.k.a.37.9 18 3.2 odd 2
144.6.k.a.109.9 18 48.29 odd 4
576.6.k.a.145.9 18 48.35 even 4
576.6.k.a.433.9 18 12.11 even 2
1024.6.a.k.1.9 18 32.29 even 8
1024.6.a.k.1.10 18 32.13 even 8
1024.6.a.l.1.9 18 32.19 odd 8
1024.6.a.l.1.10 18 32.3 odd 8