Properties

Label 80.6.l.a.21.13
Level $80$
Weight $6$
Character 80.21
Analytic conductor $12.831$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [80,6,Mod(21,80)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(80, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("80.21");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.l (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: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 21.13
Character \(\chi\) \(=\) 80.21
Dual form 80.6.l.a.61.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.36114 + 4.55002i) q^{2} +(-18.2668 + 18.2668i) q^{3} +(-9.40545 - 30.5866i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-21.7171 - 144.512i) q^{6} +13.9157i q^{7} +(170.783 + 60.0107i) q^{8} -424.353i q^{9} +O(q^{10})\) \(q+(-3.36114 + 4.55002i) q^{2} +(-18.2668 + 18.2668i) q^{3} +(-9.40545 - 30.5866i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-21.7171 - 144.512i) q^{6} +13.9157i q^{7} +(170.783 + 60.0107i) q^{8} -424.353i q^{9} +(139.851 - 21.0167i) q^{10} +(-220.571 - 220.571i) q^{11} +(730.527 + 386.911i) q^{12} +(433.351 - 433.351i) q^{13} +(-63.3167 - 46.7726i) q^{14} +645.829 q^{15} +(-847.075 + 575.361i) q^{16} -25.9583 q^{17} +(1930.82 + 1426.31i) q^{18} +(-1566.86 + 1566.86i) q^{19} +(-374.433 + 706.965i) q^{20} +(-254.195 - 254.195i) q^{21} +(1744.97 - 262.232i) q^{22} +1496.29i q^{23} +(-4215.86 + 2023.45i) q^{24} +625.000i q^{25} +(515.203 + 3428.31i) q^{26} +(3312.74 + 3312.74i) q^{27} +(425.633 - 130.883i) q^{28} +(324.914 - 324.914i) q^{29} +(-2170.72 + 2938.54i) q^{30} +7904.77 q^{31} +(229.235 - 5788.08i) q^{32} +8058.24 q^{33} +(87.2494 - 118.111i) q^{34} +(245.997 - 245.997i) q^{35} +(-12979.5 + 3991.23i) q^{36} +(-3034.60 - 3034.60i) q^{37} +(-1862.82 - 12395.7i) q^{38} +15831.9i q^{39} +(-1958.19 - 4079.89i) q^{40} -17561.5i q^{41} +(2010.98 - 302.208i) q^{42} +(11258.4 + 11258.4i) q^{43} +(-4671.93 + 8821.06i) q^{44} +(-7501.57 + 7501.57i) q^{45} +(-6808.15 - 5029.24i) q^{46} +16959.8 q^{47} +(4963.36 - 25983.4i) q^{48} +16613.4 q^{49} +(-2843.77 - 2100.71i) q^{50} +(474.175 - 474.175i) q^{51} +(-17330.6 - 9178.85i) q^{52} +(15349.1 + 15349.1i) q^{53} +(-26207.7 + 3938.46i) q^{54} +7798.35i q^{55} +(-835.090 + 2376.56i) q^{56} -57243.3i q^{57} +(386.284 + 2570.45i) q^{58} +(-24469.4 - 24469.4i) q^{59} +(-6074.31 - 19753.7i) q^{60} +(-28968.0 + 28968.0i) q^{61} +(-26569.1 + 35966.9i) q^{62} +5905.16 q^{63} +(25565.4 + 20497.6i) q^{64} -15321.3 q^{65} +(-27084.9 + 36665.2i) q^{66} +(42714.5 - 42714.5i) q^{67} +(244.149 + 793.974i) q^{68} +(-27332.4 - 27332.4i) q^{69} +(292.461 + 1946.12i) q^{70} -40585.1i q^{71} +(25465.7 - 72472.1i) q^{72} -872.108i q^{73} +(24007.3 - 3607.79i) q^{74} +(-11416.8 - 11416.8i) q^{75} +(62662.1 + 33187.9i) q^{76} +(3069.39 - 3069.39i) q^{77} +(-72035.4 - 53213.2i) q^{78} +87124.5 q^{79} +(25145.3 + 4803.28i) q^{80} -17908.7 q^{81} +(79905.1 + 59026.6i) q^{82} +(-63039.3 + 63039.3i) q^{83} +(-5384.14 + 10165.8i) q^{84} +(458.881 + 458.881i) q^{85} +(-89066.8 + 13384.9i) q^{86} +11870.3i q^{87} +(-24433.0 - 50906.2i) q^{88} +51305.5i q^{89} +(-8918.49 - 59346.2i) q^{90} +(6030.37 + 6030.37i) q^{91} +(45766.3 - 14073.3i) q^{92} +(-144395. + 144395. i) q^{93} +(-57004.1 + 77167.3i) q^{94} +55397.0 q^{95} +(101542. + 109917. i) q^{96} +117514. q^{97} +(-55839.8 + 75591.2i) q^{98} +(-93599.8 + 93599.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.36114 + 4.55002i −0.594172 + 0.804338i
\(3\) −18.2668 + 18.2668i −1.17182 + 1.17182i −0.190040 + 0.981776i \(0.560862\pi\)
−0.981776 + 0.190040i \(0.939138\pi\)
\(4\) −9.40545 30.5866i −0.293920 0.955830i
\(5\) −17.6777 17.6777i −0.316228 0.316228i
\(6\) −21.7171 144.512i −0.246277 1.63880i
\(7\) 13.9157i 0.107339i 0.998559 + 0.0536697i \(0.0170918\pi\)
−0.998559 + 0.0536697i \(0.982908\pi\)
\(8\) 170.783 + 60.0107i 0.943450 + 0.331516i
\(9\) 424.353i 1.74631i
\(10\) 139.851 21.0167i 0.442248 0.0664606i
\(11\) −220.571 220.571i −0.549624 0.549624i 0.376708 0.926332i \(-0.377056\pi\)
−0.926332 + 0.376708i \(0.877056\pi\)
\(12\) 730.527 + 386.911i 1.46448 + 0.775637i
\(13\) 433.351 433.351i 0.711182 0.711182i −0.255600 0.966783i \(-0.582273\pi\)
0.966783 + 0.255600i \(0.0822731\pi\)
\(14\) −63.3167 46.7726i −0.0863372 0.0637781i
\(15\) 645.829 0.741122
\(16\) −847.075 + 575.361i −0.827222 + 0.561876i
\(17\) −25.9583 −0.0217848 −0.0108924 0.999941i \(-0.503467\pi\)
−0.0108924 + 0.999941i \(0.503467\pi\)
\(18\) 1930.82 + 1426.31i 1.40462 + 1.03761i
\(19\) −1566.86 + 1566.86i −0.995744 + 0.995744i −0.999991 0.00424742i \(-0.998648\pi\)
0.00424742 + 0.999991i \(0.498648\pi\)
\(20\) −374.433 + 706.965i −0.209314 + 0.395206i
\(21\) −254.195 254.195i −0.125782 0.125782i
\(22\) 1744.97 262.232i 0.768655 0.115513i
\(23\) 1496.29i 0.589787i 0.955530 + 0.294894i \(0.0952843\pi\)
−0.955530 + 0.294894i \(0.904716\pi\)
\(24\) −4215.86 + 2023.45i −1.49403 + 0.717075i
\(25\) 625.000i 0.200000i
\(26\) 515.203 + 3428.31i 0.149467 + 0.994596i
\(27\) 3312.74 + 3312.74i 0.874537 + 0.874537i
\(28\) 425.633 130.883i 0.102598 0.0315492i
\(29\) 324.914 324.914i 0.0717419 0.0717419i −0.670325 0.742067i \(-0.733845\pi\)
0.742067 + 0.670325i \(0.233845\pi\)
\(30\) −2170.72 + 2938.54i −0.440354 + 0.596113i
\(31\) 7904.77 1.47736 0.738678 0.674059i \(-0.235451\pi\)
0.738678 + 0.674059i \(0.235451\pi\)
\(32\) 229.235 5788.08i 0.0395736 0.999217i
\(33\) 8058.24 1.28812
\(34\) 87.2494 118.111i 0.0129439 0.0175223i
\(35\) 245.997 245.997i 0.0339437 0.0339437i
\(36\) −12979.5 + 3991.23i −1.66917 + 0.513275i
\(37\) −3034.60 3034.60i −0.364416 0.364416i 0.501020 0.865436i \(-0.332958\pi\)
−0.865436 + 0.501020i \(0.832958\pi\)
\(38\) −1862.82 12395.7i −0.209272 1.39256i
\(39\) 15831.9i 1.66675i
\(40\) −1958.19 4079.89i −0.193511 0.403179i
\(41\) 17561.5i 1.63155i −0.578367 0.815776i \(-0.696310\pi\)
0.578367 0.815776i \(-0.303690\pi\)
\(42\) 2010.98 302.208i 0.175908 0.0264352i
\(43\) 11258.4 + 11258.4i 0.928547 + 0.928547i 0.997612 0.0690650i \(-0.0220016\pi\)
−0.0690650 + 0.997612i \(0.522002\pi\)
\(44\) −4671.93 + 8821.06i −0.363802 + 0.686893i
\(45\) −7501.57 + 7501.57i −0.552231 + 0.552231i
\(46\) −6808.15 5029.24i −0.474389 0.350435i
\(47\) 16959.8 1.11989 0.559944 0.828530i \(-0.310822\pi\)
0.559944 + 0.828530i \(0.310822\pi\)
\(48\) 4963.36 25983.4i 0.310937 1.62777i
\(49\) 16613.4 0.988478
\(50\) −2843.77 2100.71i −0.160868 0.118834i
\(51\) 474.175 474.175i 0.0255278 0.0255278i
\(52\) −17330.6 9178.85i −0.888800 0.470739i
\(53\) 15349.1 + 15349.1i 0.750576 + 0.750576i 0.974587 0.224011i \(-0.0719151\pi\)
−0.224011 + 0.974587i \(0.571915\pi\)
\(54\) −26207.7 + 3938.46i −1.22305 + 0.183799i
\(55\) 7798.35i 0.347613i
\(56\) −835.090 + 2376.56i −0.0355847 + 0.101269i
\(57\) 57243.3i 2.33366i
\(58\) 386.284 + 2570.45i 0.0150778 + 0.100332i
\(59\) −24469.4 24469.4i −0.915151 0.915151i 0.0815203 0.996672i \(-0.474022\pi\)
−0.996672 + 0.0815203i \(0.974022\pi\)
\(60\) −6074.31 19753.7i −0.217831 0.708387i
\(61\) −28968.0 + 28968.0i −0.996768 + 0.996768i −0.999995 0.00322639i \(-0.998973\pi\)
0.00322639 + 0.999995i \(0.498973\pi\)
\(62\) −26569.1 + 35966.9i −0.877803 + 1.18829i
\(63\) 5905.16 0.187448
\(64\) 25565.4 + 20497.6i 0.780195 + 0.625537i
\(65\) −15321.3 −0.449791
\(66\) −27084.9 + 36665.2i −0.765363 + 1.03608i
\(67\) 42714.5 42714.5i 1.16249 1.16249i 0.178560 0.983929i \(-0.442856\pi\)
0.983929 0.178560i \(-0.0571438\pi\)
\(68\) 244.149 + 793.974i 0.00640299 + 0.0208225i
\(69\) −27332.4 27332.4i −0.691123 0.691123i
\(70\) 292.461 + 1946.12i 0.00713384 + 0.0474706i
\(71\) 40585.1i 0.955478i −0.878502 0.477739i \(-0.841456\pi\)
0.878502 0.477739i \(-0.158544\pi\)
\(72\) 25465.7 72472.1i 0.578929 1.64755i
\(73\) 872.108i 0.0191542i −0.999954 0.00957708i \(-0.996951\pi\)
0.999954 0.00957708i \(-0.00304853\pi\)
\(74\) 24007.3 3607.79i 0.509640 0.0765881i
\(75\) −11416.8 11416.8i −0.234363 0.234363i
\(76\) 62662.1 + 33187.9i 1.24443 + 0.659092i
\(77\) 3069.39 3069.39i 0.0589964 0.0589964i
\(78\) −72035.4 53213.2i −1.34063 0.990336i
\(79\) 87124.5 1.57063 0.785313 0.619100i \(-0.212502\pi\)
0.785313 + 0.619100i \(0.212502\pi\)
\(80\) 25145.3 + 4803.28i 0.439271 + 0.0839098i
\(81\) −17908.7 −0.303285
\(82\) 79905.1 + 59026.6i 1.31232 + 0.969422i
\(83\) −63039.3 + 63039.3i −1.00442 + 1.00442i −0.00443164 + 0.999990i \(0.501411\pi\)
−0.999990 + 0.00443164i \(0.998589\pi\)
\(84\) −5384.14 + 10165.8i −0.0832564 + 0.157196i
\(85\) 458.881 + 458.881i 0.00688895 + 0.00688895i
\(86\) −89066.8 + 13384.9i −1.29858 + 0.195150i
\(87\) 11870.3i 0.168137i
\(88\) −24433.0 50906.2i −0.336334 0.700752i
\(89\) 51305.5i 0.686577i 0.939230 + 0.343288i \(0.111541\pi\)
−0.939230 + 0.343288i \(0.888459\pi\)
\(90\) −8918.49 59346.2i −0.116061 0.772301i
\(91\) 6030.37 + 6030.37i 0.0763379 + 0.0763379i
\(92\) 45766.3 14073.3i 0.563737 0.173350i
\(93\) −144395. + 144395.i −1.73119 + 1.73119i
\(94\) −57004.1 + 77167.3i −0.665406 + 0.900770i
\(95\) 55397.0 0.629764
\(96\) 101542. + 109917.i 1.12453 + 1.21727i
\(97\) 117514. 1.26812 0.634060 0.773284i \(-0.281387\pi\)
0.634060 + 0.773284i \(0.281387\pi\)
\(98\) −55839.8 + 75591.2i −0.587326 + 0.795071i
\(99\) −93599.8 + 93599.8i −0.959813 + 0.959813i
\(100\) 19116.6 5878.40i 0.191166 0.0587840i
\(101\) −43034.0 43034.0i −0.419767 0.419767i 0.465356 0.885123i \(-0.345926\pi\)
−0.885123 + 0.465356i \(0.845926\pi\)
\(102\) 563.738 + 3751.27i 0.00536509 + 0.0357008i
\(103\) 86467.5i 0.803082i 0.915841 + 0.401541i \(0.131525\pi\)
−0.915841 + 0.401541i \(0.868475\pi\)
\(104\) 100014. 48003.1i 0.906733 0.435197i
\(105\) 8987.16i 0.0795516i
\(106\) −121430. + 18248.3i −1.04969 + 0.157746i
\(107\) 6956.94 + 6956.94i 0.0587434 + 0.0587434i 0.735868 0.677125i \(-0.236774\pi\)
−0.677125 + 0.735868i \(0.736774\pi\)
\(108\) 70167.6 132483.i 0.578865 1.09295i
\(109\) 117017. 117017.i 0.943375 0.943375i −0.0551055 0.998481i \(-0.517550\pi\)
0.998481 + 0.0551055i \(0.0175495\pi\)
\(110\) −35482.7 26211.4i −0.279598 0.206542i
\(111\) 110865. 0.854058
\(112\) −8006.53 11787.6i −0.0603114 0.0887935i
\(113\) 32246.3 0.237566 0.118783 0.992920i \(-0.462101\pi\)
0.118783 + 0.992920i \(0.462101\pi\)
\(114\) 260458. + 192403.i 1.87705 + 1.38659i
\(115\) 26450.9 26450.9i 0.186507 0.186507i
\(116\) −12994.0 6882.03i −0.0896595 0.0474867i
\(117\) −183894. 183894.i −1.24194 1.24194i
\(118\) 193581. 29091.2i 1.27985 0.192334i
\(119\) 361.227i 0.00233837i
\(120\) 110296. + 38756.7i 0.699211 + 0.245694i
\(121\) 63748.3i 0.395827i
\(122\) −34439.6 229171.i −0.209488 1.39399i
\(123\) 320792. + 320792.i 1.91188 + 1.91188i
\(124\) −74347.9 241780.i −0.434225 1.41210i
\(125\) 11048.5 11048.5i 0.0632456 0.0632456i
\(126\) −19848.1 + 26868.6i −0.111376 + 0.150771i
\(127\) −312532. −1.71943 −0.859717 0.510772i \(-0.829360\pi\)
−0.859717 + 0.510772i \(0.829360\pi\)
\(128\) −179194. + 47428.0i −0.966713 + 0.255864i
\(129\) −411309. −2.17617
\(130\) 51496.9 69712.1i 0.267253 0.361784i
\(131\) 145389. 145389.i 0.740206 0.740206i −0.232411 0.972618i \(-0.574662\pi\)
0.972618 + 0.232411i \(0.0746615\pi\)
\(132\) −75791.4 246474.i −0.378604 1.23122i
\(133\) −21804.0 21804.0i −0.106883 0.106883i
\(134\) 50782.6 + 337922.i 0.244316 + 1.62575i
\(135\) 117123.i 0.553106i
\(136\) −4433.22 1557.77i −0.0205528 0.00722200i
\(137\) 337137.i 1.53464i −0.641267 0.767318i \(-0.721591\pi\)
0.641267 0.767318i \(-0.278409\pi\)
\(138\) 216231. 32495.0i 0.966542 0.145251i
\(139\) 193906. + 193906.i 0.851245 + 0.851245i 0.990287 0.139041i \(-0.0444020\pi\)
−0.139041 + 0.990287i \(0.544402\pi\)
\(140\) −9837.91 5210.49i −0.0424212 0.0224677i
\(141\) −309801. + 309801.i −1.31230 + 1.31230i
\(142\) 184663. + 136412.i 0.768527 + 0.567718i
\(143\) −191169. −0.781766
\(144\) 244156. + 359459.i 0.981208 + 1.44458i
\(145\) −11487.4 −0.0453736
\(146\) 3968.11 + 2931.28i 0.0154064 + 0.0113809i
\(147\) −303473. + 303473.i −1.15832 + 1.15832i
\(148\) −64276.3 + 121360.i −0.241211 + 0.455429i
\(149\) −218920. 218920.i −0.807829 0.807829i 0.176476 0.984305i \(-0.443530\pi\)
−0.984305 + 0.176476i \(0.943530\pi\)
\(150\) 90319.9 13573.2i 0.327759 0.0492554i
\(151\) 400584.i 1.42972i −0.699267 0.714861i \(-0.746490\pi\)
0.699267 0.714861i \(-0.253510\pi\)
\(152\) −361622. + 173565.i −1.26954 + 0.609329i
\(153\) 11015.5i 0.0380430i
\(154\) 3649.14 + 24282.5i 0.0123991 + 0.0825070i
\(155\) −139738. 139738.i −0.467181 0.467181i
\(156\) 484242. 148906.i 1.59313 0.489892i
\(157\) 244052. 244052.i 0.790192 0.790192i −0.191333 0.981525i \(-0.561281\pi\)
0.981525 + 0.191333i \(0.0612811\pi\)
\(158\) −292838. + 396419.i −0.933221 + 1.26331i
\(159\) −560760. −1.75907
\(160\) −106372. + 98267.4i −0.328494 + 0.303466i
\(161\) −20821.9 −0.0633075
\(162\) 60193.7 81485.0i 0.180204 0.243944i
\(163\) 129841. 129841.i 0.382774 0.382774i −0.489327 0.872101i \(-0.662757\pi\)
0.872101 + 0.489327i \(0.162757\pi\)
\(164\) −537145. + 165173.i −1.55949 + 0.479546i
\(165\) −142451. 142451.i −0.407339 0.407339i
\(166\) −74946.3 498714.i −0.211096 1.40469i
\(167\) 297250.i 0.824765i 0.911011 + 0.412383i \(0.135303\pi\)
−0.911011 + 0.412383i \(0.864697\pi\)
\(168\) −28157.7 58666.6i −0.0769704 0.160368i
\(169\) 4292.44i 0.0115608i
\(170\) −3630.29 + 545.556i −0.00963427 + 0.00144783i
\(171\) 664904. + 664904.i 1.73888 + 1.73888i
\(172\) 238465. 450244.i 0.614614 1.16045i
\(173\) 187953. 187953.i 0.477457 0.477457i −0.426861 0.904317i \(-0.640380\pi\)
0.904317 + 0.426861i \(0.140380\pi\)
\(174\) −54010.1 39897.7i −0.135239 0.0999021i
\(175\) −8697.30 −0.0214679
\(176\) 313747. + 59932.2i 0.763481 + 0.145841i
\(177\) 893955. 2.14478
\(178\) −233441. 172445.i −0.552240 0.407944i
\(179\) −368128. + 368128.i −0.858748 + 0.858748i −0.991191 0.132442i \(-0.957718\pi\)
0.132442 + 0.991191i \(0.457718\pi\)
\(180\) 300003. + 158892.i 0.690151 + 0.365527i
\(181\) 78950.2 + 78950.2i 0.179125 + 0.179125i 0.790974 0.611849i \(-0.209574\pi\)
−0.611849 + 0.790974i \(0.709574\pi\)
\(182\) −47707.3 + 7169.40i −0.106759 + 0.0160437i
\(183\) 1.05831e6i 2.33606i
\(184\) −89793.4 + 255540.i −0.195524 + 0.556435i
\(185\) 107289.i 0.230477i
\(186\) −171669. 1.14233e6i −0.363839 2.42109i
\(187\) 5725.63 + 5725.63i 0.0119734 + 0.0119734i
\(188\) −159514. 518741.i −0.329158 1.07042i
\(189\) −46099.1 + 46099.1i −0.0938723 + 0.0938723i
\(190\) −186197. + 252058.i −0.374188 + 0.506543i
\(191\) 160856. 0.319047 0.159524 0.987194i \(-0.449004\pi\)
0.159524 + 0.987194i \(0.449004\pi\)
\(192\) −841424. + 92573.2i −1.64726 + 0.181231i
\(193\) 543608. 1.05049 0.525246 0.850950i \(-0.323973\pi\)
0.525246 + 0.850950i \(0.323973\pi\)
\(194\) −394981. + 534692.i −0.753481 + 1.02000i
\(195\) 279871. 279871.i 0.527073 0.527073i
\(196\) −156256. 508145.i −0.290534 0.944817i
\(197\) −60916.8 60916.8i −0.111833 0.111833i 0.648976 0.760809i \(-0.275198\pi\)
−0.760809 + 0.648976i \(0.775198\pi\)
\(198\) −111279. 740483.i −0.201721 1.34231i
\(199\) 943709.i 1.68930i −0.535323 0.844648i \(-0.679810\pi\)
0.535323 0.844648i \(-0.320190\pi\)
\(200\) −37506.7 + 106739.i −0.0663031 + 0.188690i
\(201\) 1.56052e6i 2.72445i
\(202\) 340449. 51162.4i 0.587049 0.0882211i
\(203\) 4521.40 + 4521.40i 0.00770074 + 0.00770074i
\(204\) −18963.2 10043.5i −0.0319033 0.0168971i
\(205\) −310446. + 310446.i −0.515942 + 0.515942i
\(206\) −393429. 290630.i −0.645950 0.477169i
\(207\) 634954. 1.02995
\(208\) −117748. + 616413.i −0.188710 + 0.987902i
\(209\) 691208. 1.09457
\(210\) −40891.8 30207.1i −0.0639864 0.0472673i
\(211\) 60603.7 60603.7i 0.0937115 0.0937115i −0.658697 0.752408i \(-0.728892\pi\)
0.752408 + 0.658697i \(0.228892\pi\)
\(212\) 325112. 613843.i 0.496813 0.938032i
\(213\) 741360. + 741360.i 1.11964 + 1.11964i
\(214\) −55037.5 + 8270.99i −0.0821532 + 0.0123459i
\(215\) 398043.i 0.587265i
\(216\) 366959. + 764559.i 0.535159 + 1.11500i
\(217\) 110000.i 0.158579i
\(218\) 139120. + 925745.i 0.198266 + 1.31932i
\(219\) 15930.6 + 15930.6i 0.0224452 + 0.0224452i
\(220\) 238525. 73346.9i 0.332259 0.102170i
\(221\) −11249.0 + 11249.0i −0.0154930 + 0.0154930i
\(222\) −372633. + 504439.i −0.507457 + 0.686951i
\(223\) 286362. 0.385614 0.192807 0.981237i \(-0.438241\pi\)
0.192807 + 0.981237i \(0.438241\pi\)
\(224\) 80545.1 + 3189.96i 0.107255 + 0.00424781i
\(225\) 265221. 0.349262
\(226\) −108384. + 146721.i −0.141155 + 0.191083i
\(227\) 173972. 173972.i 0.224086 0.224086i −0.586130 0.810217i \(-0.699349\pi\)
0.810217 + 0.586130i \(0.199349\pi\)
\(228\) −1.75087e6 + 538398.i −2.23058 + 0.685909i
\(229\) 670007. + 670007.i 0.844287 + 0.844287i 0.989413 0.145126i \(-0.0463587\pi\)
−0.145126 + 0.989413i \(0.546359\pi\)
\(230\) 31447.0 + 209257.i 0.0391976 + 0.260832i
\(231\) 112136.i 0.138266i
\(232\) 74987.9 35991.3i 0.0914685 0.0439013i
\(233\) 855139.i 1.03192i 0.856612 + 0.515961i \(0.172565\pi\)
−0.856612 + 0.515961i \(0.827435\pi\)
\(234\) 1.45481e6 218628.i 1.73687 0.261015i
\(235\) −299809. 299809.i −0.354140 0.354140i
\(236\) −518289. + 978580.i −0.605748 + 1.14371i
\(237\) −1.59149e6 + 1.59149e6i −1.84048 + 1.84048i
\(238\) 1643.59 + 1214.13i 0.00188084 + 0.00138939i
\(239\) −1.24908e6 −1.41448 −0.707238 0.706975i \(-0.750059\pi\)
−0.707238 + 0.706975i \(0.750059\pi\)
\(240\) −547066. + 371585.i −0.613072 + 0.416418i
\(241\) 738534. 0.819083 0.409542 0.912291i \(-0.365689\pi\)
0.409542 + 0.912291i \(0.365689\pi\)
\(242\) 290056. + 214267.i 0.318378 + 0.235189i
\(243\) −477861. + 477861.i −0.519142 + 0.519142i
\(244\) 1.15849e6 + 613575.i 1.24571 + 0.659771i
\(245\) −293685. 293685.i −0.312584 0.312584i
\(246\) −2.53784e6 + 381384.i −2.67378 + 0.401814i
\(247\) 1.35800e6i 1.41631i
\(248\) 1.35000e6 + 474371.i 1.39381 + 0.489767i
\(249\) 2.30305e6i 2.35400i
\(250\) 13135.4 + 87406.9i 0.0132921 + 0.0884495i
\(251\) −180182. 180182.i −0.180520 0.180520i 0.611062 0.791583i \(-0.290742\pi\)
−0.791583 + 0.611062i \(0.790742\pi\)
\(252\) −55540.7 180619.i −0.0550947 0.179168i
\(253\) 330037. 330037.i 0.324161 0.324161i
\(254\) 1.05046e6 1.42203e6i 1.02164 1.38301i
\(255\) −16764.6 −0.0161452
\(256\) 386496. 974747.i 0.368592 0.929591i
\(257\) 1.33681e6 1.26251 0.631256 0.775575i \(-0.282540\pi\)
0.631256 + 0.775575i \(0.282540\pi\)
\(258\) 1.38247e6 1.87146e6i 1.29302 1.75038i
\(259\) 42228.6 42228.6i 0.0391162 0.0391162i
\(260\) 144103. + 468625.i 0.132203 + 0.429924i
\(261\) −137878. 137878.i −0.125284 0.125284i
\(262\) 172850. + 1.15020e6i 0.155567 + 1.03519i
\(263\) 265597.i 0.236774i −0.992968 0.118387i \(-0.962228\pi\)
0.992968 0.118387i \(-0.0377724\pi\)
\(264\) 1.37621e6 + 483581.i 1.21527 + 0.427031i
\(265\) 542674.i 0.474706i
\(266\) 172495. 25922.4i 0.149476 0.0224632i
\(267\) −937188. 937188.i −0.804542 0.804542i
\(268\) −1.70824e6 904741.i −1.45282 0.769463i
\(269\) 525286. 525286.i 0.442603 0.442603i −0.450283 0.892886i \(-0.648677\pi\)
0.892886 + 0.450283i \(0.148677\pi\)
\(270\) 532913. + 393667.i 0.444884 + 0.328640i
\(271\) −404175. −0.334308 −0.167154 0.985931i \(-0.553458\pi\)
−0.167154 + 0.985931i \(0.553458\pi\)
\(272\) 21988.6 14935.4i 0.0180208 0.0122403i
\(273\) −220311. −0.178908
\(274\) 1.53398e6 + 1.13317e6i 1.23437 + 0.911837i
\(275\) 137857. 137857.i 0.109925 0.109925i
\(276\) −578931. + 1.09308e6i −0.457461 + 0.863731i
\(277\) −359520. 359520.i −0.281529 0.281529i 0.552189 0.833719i \(-0.313793\pi\)
−0.833719 + 0.552189i \(0.813793\pi\)
\(278\) −1.53402e6 + 230532.i −1.19048 + 0.178903i
\(279\) 3.35441e6i 2.57992i
\(280\) 56774.4 27249.5i 0.0432771 0.0207713i
\(281\) 2.11992e6i 1.60160i −0.598932 0.800800i \(-0.704408\pi\)
0.598932 0.800800i \(-0.295592\pi\)
\(282\) −368317. 2.45089e6i −0.275803 1.83527i
\(283\) −644887. 644887.i −0.478650 0.478650i 0.426050 0.904700i \(-0.359905\pi\)
−0.904700 + 0.426050i \(0.859905\pi\)
\(284\) −1.24136e6 + 381721.i −0.913274 + 0.280834i
\(285\) −1.01193e6 + 1.01193e6i −0.737967 + 0.737967i
\(286\) 642545. 869823.i 0.464503 0.628804i
\(287\) 244380. 0.175130
\(288\) −2.45619e6 97276.6i −1.74494 0.0691078i
\(289\) −1.41918e6 −0.999525
\(290\) 38610.9 52268.1i 0.0269597 0.0364957i
\(291\) −2.14661e6 + 2.14661e6i −1.48600 + 1.48600i
\(292\) −26674.8 + 8202.57i −0.0183081 + 0.00562980i
\(293\) 811411. + 811411.i 0.552169 + 0.552169i 0.927066 0.374898i \(-0.122322\pi\)
−0.374898 + 0.927066i \(0.622322\pi\)
\(294\) −360794. 2.40083e6i −0.243439 1.61992i
\(295\) 865123.i 0.578793i
\(296\) −336149. 700366.i −0.222999 0.464618i
\(297\) 1.46139e6i 0.961333i
\(298\) 1.73191e6 260270.i 1.12976 0.169779i
\(299\) 648417. + 648417.i 0.419446 + 0.419446i
\(300\) −241820. + 456579.i −0.155127 + 0.292896i
\(301\) −156668. + 156668.i −0.0996697 + 0.0996697i
\(302\) 1.82267e6 + 1.34642e6i 1.14998 + 0.849500i
\(303\) 1.57219e6 0.983780
\(304\) 425740. 2.22876e6i 0.264217 1.38318i
\(305\) 1.02417e6 0.630412
\(306\) −50120.6 37024.5i −0.0305994 0.0226040i
\(307\) 231288. 231288.i 0.140058 0.140058i −0.633602 0.773660i \(-0.718424\pi\)
0.773660 + 0.633602i \(0.218424\pi\)
\(308\) −122751. 65013.1i −0.0737307 0.0390503i
\(309\) −1.57949e6 1.57949e6i −0.941065 0.941065i
\(310\) 1.10549e6 166132.i 0.653357 0.0981859i
\(311\) 1.08331e6i 0.635114i 0.948239 + 0.317557i \(0.102863\pi\)
−0.948239 + 0.317557i \(0.897137\pi\)
\(312\) −950082. + 2.70381e6i −0.552554 + 1.57250i
\(313\) 2.42505e6i 1.39914i 0.714566 + 0.699568i \(0.246624\pi\)
−0.714566 + 0.699568i \(0.753376\pi\)
\(314\) 290149. + 1.93073e6i 0.166072 + 1.10509i
\(315\) −104389. 104389.i −0.0592762 0.0592762i
\(316\) −819445. 2.66484e6i −0.461639 1.50125i
\(317\) −601112. + 601112.i −0.335975 + 0.335975i −0.854850 0.518875i \(-0.826351\pi\)
0.518875 + 0.854850i \(0.326351\pi\)
\(318\) 1.88479e6 2.55147e6i 1.04519 1.41489i
\(319\) −143333. −0.0788622
\(320\) −89587.5 814287.i −0.0489071 0.444531i
\(321\) −254162. −0.137673
\(322\) 69985.3 94740.0i 0.0376155 0.0509206i
\(323\) 40673.1 40673.1i 0.0216921 0.0216921i
\(324\) 168439. + 547765.i 0.0891417 + 0.289889i
\(325\) 270844. + 270844.i 0.142236 + 0.142236i
\(326\) 154366. + 1.02719e6i 0.0804464 + 0.535313i
\(327\) 4.27507e6i 2.21093i
\(328\) 1.05388e6 2.99919e6i 0.540885 1.53929i
\(329\) 236007.i 0.120208i
\(330\) 1.12695e6 169357.i 0.569667 0.0856090i
\(331\) −510922. 510922.i −0.256321 0.256321i 0.567235 0.823556i \(-0.308013\pi\)
−0.823556 + 0.567235i \(0.808013\pi\)
\(332\) 2.52107e6 + 1.33524e6i 1.25528 + 0.664837i
\(333\) −1.28774e6 + 1.28774e6i −0.636383 + 0.636383i
\(334\) −1.35249e6 999099.i −0.663390 0.490052i
\(335\) −1.51019e6 −0.735222
\(336\) 361576. + 69068.5i 0.174724 + 0.0333758i
\(337\) 2.57019e6 1.23279 0.616397 0.787436i \(-0.288592\pi\)
0.616397 + 0.787436i \(0.288592\pi\)
\(338\) 19530.7 + 14427.5i 0.00929878 + 0.00686909i
\(339\) −589037. + 589037.i −0.278383 + 0.278383i
\(340\) 9719.62 18351.6i 0.00455986 0.00860947i
\(341\) −1.74356e6 1.74356e6i −0.811990 0.811990i
\(342\) −5.26016e6 + 790492.i −2.43183 + 0.365454i
\(343\) 465067.i 0.213442i
\(344\) 1.24711e6 + 2.59835e6i 0.568210 + 1.18387i
\(345\) 966347.i 0.437104i
\(346\) 223454. + 1.48693e6i 0.100346 + 0.667728i
\(347\) −1.28231e6 1.28231e6i −0.571701 0.571701i 0.360903 0.932603i \(-0.382469\pi\)
−0.932603 + 0.360903i \(0.882469\pi\)
\(348\) 363071. 111645.i 0.160710 0.0494188i
\(349\) 888285. 888285.i 0.390381 0.390381i −0.484442 0.874823i \(-0.660977\pi\)
0.874823 + 0.484442i \(0.160977\pi\)
\(350\) 29232.9 39572.9i 0.0127556 0.0172674i
\(351\) 2.87116e6 1.24391
\(352\) −1.32724e6 + 1.22612e6i −0.570944 + 0.527443i
\(353\) −806589. −0.344521 −0.172260 0.985051i \(-0.555107\pi\)
−0.172260 + 0.985051i \(0.555107\pi\)
\(354\) −3.00471e6 + 4.06752e6i −1.27437 + 1.72513i
\(355\) −717450. + 717450.i −0.302149 + 0.302149i
\(356\) 1.56926e6 482551.i 0.656250 0.201799i
\(357\) 6598.46 + 6598.46i 0.00274014 + 0.00274014i
\(358\) −437661. 2.91232e6i −0.180480 1.20097i
\(359\) 3.12013e6i 1.27772i −0.769322 0.638861i \(-0.779406\pi\)
0.769322 0.638861i \(-0.220594\pi\)
\(360\) −1.73131e6 + 830963.i −0.704076 + 0.337929i
\(361\) 2.43403e6i 0.983010i
\(362\) −624588. + 93862.5i −0.250508 + 0.0376462i
\(363\) 1.16448e6 + 1.16448e6i 0.463836 + 0.463836i
\(364\) 127730. 241167.i 0.0505288 0.0954033i
\(365\) −15416.8 + 15416.8i −0.00605708 + 0.00605708i
\(366\) 4.81532e6 + 3.55712e6i 1.87898 + 1.38802i
\(367\) −2.36989e6 −0.918466 −0.459233 0.888316i \(-0.651876\pi\)
−0.459233 + 0.888316i \(0.651876\pi\)
\(368\) −860905. 1.26747e6i −0.331387 0.487885i
\(369\) −7.45226e6 −2.84920
\(370\) −488170. 360615.i −0.185381 0.136943i
\(371\) −213594. + 213594.i −0.0805664 + 0.0805664i
\(372\) 5.77465e6 + 3.05845e6i 2.16356 + 1.14589i
\(373\) 592951. + 592951.i 0.220672 + 0.220672i 0.808781 0.588110i \(-0.200128\pi\)
−0.588110 + 0.808781i \(0.700128\pi\)
\(374\) −45296.4 + 6807.10i −0.0167450 + 0.00251642i
\(375\) 403643.i 0.148224i
\(376\) 2.89643e6 + 1.01777e6i 1.05656 + 0.371261i
\(377\) 281603.i 0.102043i
\(378\) −54806.4 364697.i −0.0197288 0.131281i
\(379\) 1.55802e6 + 1.55802e6i 0.557152 + 0.557152i 0.928496 0.371343i \(-0.121103\pi\)
−0.371343 + 0.928496i \(0.621103\pi\)
\(380\) −521034. 1.69440e6i −0.185100 0.601947i
\(381\) 5.70896e6 5.70896e6i 2.01486 2.01486i
\(382\) −540661. + 731901.i −0.189569 + 0.256622i
\(383\) −1.73646e6 −0.604877 −0.302439 0.953169i \(-0.597801\pi\)
−0.302439 + 0.953169i \(0.597801\pi\)
\(384\) 2.40694e6 4.13965e6i 0.832984 1.43264i
\(385\) −108519. −0.0373126
\(386\) −1.82714e6 + 2.47343e6i −0.624173 + 0.844951i
\(387\) 4.77752e6 4.77752e6i 1.62153 1.62153i
\(388\) −1.10527e6 3.59435e6i −0.372726 1.21211i
\(389\) 1.66357e6 + 1.66357e6i 0.557400 + 0.557400i 0.928566 0.371166i \(-0.121042\pi\)
−0.371166 + 0.928566i \(0.621042\pi\)
\(390\) 332733. + 2.21410e6i 0.110773 + 0.737117i
\(391\) 38841.0i 0.0128484i
\(392\) 2.83727e6 + 996980.i 0.932580 + 0.327696i
\(393\) 5.31158e6i 1.73477i
\(394\) 481923. 72422.9i 0.156400 0.0235037i
\(395\) −1.54016e6 1.54016e6i −0.496675 0.496675i
\(396\) 3.74324e6 + 1.98255e6i 1.19953 + 0.635310i
\(397\) −3.80404e6 + 3.80404e6i −1.21135 + 1.21135i −0.240763 + 0.970584i \(0.577398\pi\)
−0.970584 + 0.240763i \(0.922602\pi\)
\(398\) 4.29390e6 + 3.17194e6i 1.35876 + 1.00373i
\(399\) 796579. 0.250494
\(400\) −359600. 529422.i −0.112375 0.165444i
\(401\) 2.69674e6 0.837487 0.418744 0.908105i \(-0.362471\pi\)
0.418744 + 0.908105i \(0.362471\pi\)
\(402\) −7.10039e6 5.24512e6i −2.19138 1.61879i
\(403\) 3.42554e6 3.42554e6i 1.05067 1.05067i
\(404\) −911508. + 1.72102e6i −0.277848 + 0.524604i
\(405\) 316584. + 316584.i 0.0959073 + 0.0959073i
\(406\) −35769.5 + 5375.41i −0.0107696 + 0.00161844i
\(407\) 1.33869e6i 0.400584i
\(408\) 109436. 52525.2i 0.0325470 0.0156213i
\(409\) 4.46773e6i 1.32062i 0.750992 + 0.660311i \(0.229576\pi\)
−0.750992 + 0.660311i \(0.770424\pi\)
\(410\) −369084. 2.45599e6i −0.108434 0.721550i
\(411\) 6.15842e6 + 6.15842e6i 1.79831 + 1.79831i
\(412\) 2.64474e6 813266.i 0.767610 0.236042i
\(413\) 340508. 340508.i 0.0982319 0.0982319i
\(414\) −2.13417e6 + 2.88906e6i −0.611968 + 0.828429i
\(415\) 2.22878e6 0.635252
\(416\) −2.40893e6 2.60761e6i −0.682481 0.738769i
\(417\) −7.08410e6 −1.99501
\(418\) −2.32325e6 + 3.14502e6i −0.650362 + 0.880404i
\(419\) 1.17941e6 1.17941e6i 0.328193 0.328193i −0.523706 0.851899i \(-0.675451\pi\)
0.851899 + 0.523706i \(0.175451\pi\)
\(420\) 274886. 84528.2i 0.0760378 0.0233818i
\(421\) −846196. 846196.i −0.232684 0.232684i 0.581128 0.813812i \(-0.302611\pi\)
−0.813812 + 0.581128i \(0.802611\pi\)
\(422\) 72050.6 + 479446.i 0.0196950 + 0.131056i
\(423\) 7.19692e6i 1.95567i
\(424\) 1.70025e6 + 3.54248e6i 0.459303 + 0.956958i
\(425\) 16223.9i 0.00435696i
\(426\) −5.86503e6 + 881390.i −1.56583 + 0.235312i
\(427\) −403110. 403110.i −0.106993 0.106993i
\(428\) 147356. 278222.i 0.0388828 0.0734146i
\(429\) 3.49204e6 3.49204e6i 0.916086 0.916086i
\(430\) 1.81111e6 + 1.33788e6i 0.472360 + 0.348936i
\(431\) −3.51459e6 −0.911342 −0.455671 0.890148i \(-0.650601\pi\)
−0.455671 + 0.890148i \(0.650601\pi\)
\(432\) −4.71216e6 900120.i −1.21482 0.232055i
\(433\) −2.50659e6 −0.642485 −0.321243 0.946997i \(-0.604101\pi\)
−0.321243 + 0.946997i \(0.604101\pi\)
\(434\) −500504. 369727.i −0.127551 0.0942229i
\(435\) 209839. 209839.i 0.0531695 0.0531695i
\(436\) −4.67976e6 2.47856e6i −1.17898 0.624429i
\(437\) −2.34448e6 2.34448e6i −0.587277 0.587277i
\(438\) −126030. + 18939.7i −0.0313898 + 0.00471723i
\(439\) 7.36523e6i 1.82400i 0.410189 + 0.912001i \(0.365463\pi\)
−0.410189 + 0.912001i \(0.634537\pi\)
\(440\) −467985. + 1.33182e6i −0.115239 + 0.327955i
\(441\) 7.04993e6i 1.72619i
\(442\) −13373.8 88992.9i −0.00325610 0.0216670i
\(443\) 707148. + 707148.i 0.171199 + 0.171199i 0.787506 0.616307i \(-0.211372\pi\)
−0.616307 + 0.787506i \(0.711372\pi\)
\(444\) −1.04274e6 3.39098e6i −0.251025 0.816334i
\(445\) 906962. 906962.i 0.217115 0.217115i
\(446\) −962502. + 1.30295e6i −0.229121 + 0.310164i
\(447\) 7.99793e6 1.89325
\(448\) −285238. + 355760.i −0.0671448 + 0.0837457i
\(449\) −3.60308e6 −0.843449 −0.421724 0.906724i \(-0.638575\pi\)
−0.421724 + 0.906724i \(0.638575\pi\)
\(450\) −891444. + 1.20676e6i −0.207521 + 0.280925i
\(451\) −3.87354e6 + 3.87354e6i −0.896741 + 0.896741i
\(452\) −303291. 986303.i −0.0698253 0.227072i
\(453\) 7.31740e6 + 7.31740e6i 1.67537 + 1.67537i
\(454\) 206833. + 1.37632e6i 0.0470955 + 0.313387i
\(455\) 213206.i 0.0482803i
\(456\) 3.43521e6 9.77615e6i 0.773644 2.20169i
\(457\) 4.29166e6i 0.961246i 0.876927 + 0.480623i \(0.159589\pi\)
−0.876927 + 0.480623i \(0.840411\pi\)
\(458\) −5.30053e6 + 796559.i −1.18074 + 0.177441i
\(459\) −85993.0 85993.0i −0.0190516 0.0190516i
\(460\) −1.05782e6 560259.i −0.233087 0.123451i
\(461\) 3.12730e6 3.12730e6i 0.685358 0.685358i −0.275845 0.961202i \(-0.588958\pi\)
0.961202 + 0.275845i \(0.0889575\pi\)
\(462\) −510221. 376905.i −0.111213 0.0821536i
\(463\) −3.19121e6 −0.691836 −0.345918 0.938265i \(-0.612433\pi\)
−0.345918 + 0.938265i \(0.612433\pi\)
\(464\) −88283.8 + 462169.i −0.0190365 + 0.0996565i
\(465\) 5.10513e6 1.09490
\(466\) −3.89090e6 2.87424e6i −0.830014 0.613138i
\(467\) 1.85914e6 1.85914e6i 0.394476 0.394476i −0.481803 0.876279i \(-0.660018\pi\)
0.876279 + 0.481803i \(0.160018\pi\)
\(468\) −3.89507e6 + 7.35427e6i −0.822055 + 1.55212i
\(469\) 594402. + 594402.i 0.124781 + 0.124781i
\(470\) 2.37184e6 356438.i 0.495268 0.0744284i
\(471\) 8.91609e6i 1.85192i
\(472\) −2.71052e6 5.64737e6i −0.560012 1.16679i
\(473\) 4.96652e6i 1.02070i
\(474\) −1.89209e6 1.25905e7i −0.386809 2.57394i
\(475\) −979290. 979290.i −0.199149 0.199149i
\(476\) −11048.7 + 3397.50i −0.00223508 + 0.000687293i
\(477\) 6.51346e6 6.51346e6i 1.31074 1.31074i
\(478\) 4.19834e6 5.68335e6i 0.840442 1.13772i
\(479\) 1.42822e6 0.284418 0.142209 0.989837i \(-0.454579\pi\)
0.142209 + 0.989837i \(0.454579\pi\)
\(480\) 148047. 3.73811e6i 0.0293289 0.740541i
\(481\) −2.63009e6 −0.518333
\(482\) −2.48232e6 + 3.36035e6i −0.486676 + 0.658820i
\(483\) 380349. 380349.i 0.0741848 0.0741848i
\(484\) −1.94984e6 + 599581.i −0.378343 + 0.116341i
\(485\) −2.07737e6 2.07737e6i −0.401015 0.401015i
\(486\) −568121. 3.78044e6i −0.109106 0.726025i
\(487\) 6.60517e6i 1.26201i 0.775780 + 0.631003i \(0.217357\pi\)
−0.775780 + 0.631003i \(0.782643\pi\)
\(488\) −6.68563e6 + 3.20884e6i −1.27085 + 0.609957i
\(489\) 4.74356e6i 0.897082i
\(490\) 2.32339e6 349157.i 0.437152 0.0656948i
\(491\) −65912.2 65912.2i −0.0123385 0.0123385i 0.700911 0.713249i \(-0.252777\pi\)
−0.713249 + 0.700911i \(0.752777\pi\)
\(492\) 6.79473e6 1.28291e7i 1.26549 2.38937i
\(493\) −8434.19 + 8434.19i −0.00156288 + 0.00156288i
\(494\) −6.17895e6 4.56444e6i −1.13919 0.841531i
\(495\) 3.30925e6 0.607039
\(496\) −6.69593e6 + 4.54809e6i −1.22210 + 0.830090i
\(497\) 564769. 0.102560
\(498\) 1.04790e7 + 7.74089e6i 1.89341 + 1.39868i
\(499\) 3.20050e6 3.20050e6i 0.575396 0.575396i −0.358235 0.933631i \(-0.616621\pi\)
0.933631 + 0.358235i \(0.116621\pi\)
\(500\) −441853. 234020.i −0.0790411 0.0418628i
\(501\) −5.42981e6 5.42981e6i −0.966474 0.966474i
\(502\) 1.42545e6 214215.i 0.252459 0.0379394i
\(503\) 2.12538e6i 0.374555i −0.982307 0.187278i \(-0.940034\pi\)
0.982307 0.187278i \(-0.0599664\pi\)
\(504\) 1.00850e6 + 354373.i 0.176848 + 0.0621419i
\(505\) 1.52148e6i 0.265484i
\(506\) 392375. + 2.61098e6i 0.0681280 + 0.453343i
\(507\) 78409.2 + 78409.2i 0.0135471 + 0.0135471i
\(508\) 2.93950e6 + 9.55928e6i 0.505376 + 1.64349i
\(509\) 6.65339e6 6.65339e6i 1.13828 1.13828i 0.149519 0.988759i \(-0.452227\pi\)
0.988759 0.149519i \(-0.0477726\pi\)
\(510\) 56348.2 76279.4i 0.00959301 0.0129862i
\(511\) 12136.0 0.00205600
\(512\) 3.13605e6 + 5.03483e6i 0.528699 + 0.848809i
\(513\) −1.03812e7 −1.74163
\(514\) −4.49319e6 + 6.08250e6i −0.750149 + 1.01549i
\(515\) 1.52854e6 1.52854e6i 0.253957 0.253957i
\(516\) 3.86854e6 + 1.25805e7i 0.639622 + 2.08005i
\(517\) −3.74082e6 3.74082e6i −0.615518 0.615518i
\(518\) 50204.8 + 334077.i 0.00822093 + 0.0547044i
\(519\) 6.86661e6i 1.11898i
\(520\) −2.61660e6 919440.i −0.424355 0.149113i
\(521\) 6.43393e6i 1.03844i 0.854640 + 0.519220i \(0.173778\pi\)
−0.854640 + 0.519220i \(0.826222\pi\)
\(522\) 1.09078e6 163921.i 0.175210 0.0263304i
\(523\) −5.14301e6 5.14301e6i −0.822172 0.822172i 0.164247 0.986419i \(-0.447481\pi\)
−0.986419 + 0.164247i \(0.947481\pi\)
\(524\) −5.81439e6 3.07950e6i −0.925073 0.489950i
\(525\) 158872. 158872.i 0.0251564 0.0251564i
\(526\) 1.20847e6 + 892711.i 0.190447 + 0.140685i
\(527\) −205194. −0.0321839
\(528\) −6.82594e6 + 4.63639e6i −1.06556 + 0.723762i
\(529\) 4.19747e6 0.652151
\(530\) 2.46918e6 + 1.82401e6i 0.381824 + 0.282057i
\(531\) −1.03837e7 + 1.03837e7i −1.59814 + 1.59814i
\(532\) −461833. + 871985.i −0.0707466 + 0.133577i
\(533\) −7.61027e6 7.61027e6i −1.16033 1.16033i
\(534\) 7.41425e6 1.11421e6i 1.12516 0.169088i
\(535\) 245965.i 0.0371526i
\(536\) 9.85823e6 4.73157e6i 1.48213 0.711366i
\(537\) 1.34490e7i 2.01259i
\(538\) 624503. + 4.15562e6i 0.0930205 + 0.618985i
\(539\) −3.66442e6 3.66442e6i −0.543292 0.543292i
\(540\) −3.58239e6 + 1.10160e6i −0.528675 + 0.162569i
\(541\) −6.17708e6 + 6.17708e6i −0.907381 + 0.907381i −0.996060 0.0886790i \(-0.971735\pi\)
0.0886790 + 0.996060i \(0.471735\pi\)
\(542\) 1.35849e6 1.83901e6i 0.198636 0.268896i
\(543\) −2.88434e6 −0.419804
\(544\) −5950.54 + 150248.i −0.000862103 + 0.0217677i
\(545\) −4.13719e6 −0.596643
\(546\) 740497. 1.00242e6i 0.106302 0.143903i
\(547\) 5.33988e6 5.33988e6i 0.763068 0.763068i −0.213808 0.976876i \(-0.568587\pi\)
0.976876 + 0.213808i \(0.0685866\pi\)
\(548\) −1.03119e7 + 3.17093e6i −1.46685 + 0.451060i
\(549\) 1.22927e7 + 1.22927e7i 1.74067 + 1.74067i
\(550\) 163895. + 1.09061e6i 0.0231025 + 0.153731i
\(551\) 1.01819e6i 0.142873i
\(552\) −3.02766e6 6.30814e6i −0.422922 0.881158i
\(553\) 1.21240e6i 0.168590i
\(554\) 2.84422e6 427427.i 0.393722 0.0591681i
\(555\) −1.95984e6 1.95984e6i −0.270077 0.270077i
\(556\) 4.10715e6 7.75470e6i 0.563448 1.06384i
\(557\) −1.67989e6 + 1.67989e6i −0.229426 + 0.229426i −0.812453 0.583027i \(-0.801868\pi\)
0.583027 + 0.812453i \(0.301868\pi\)
\(558\) 1.52627e7 + 1.12747e7i 2.07513 + 1.53291i
\(559\) 9.75763e6 1.32073
\(560\) −66840.9 + 349915.i −0.00900684 + 0.0471511i
\(561\) −209178. −0.0280614
\(562\) 9.64570e6 + 7.12536e6i 1.28823 + 0.951625i
\(563\) 5.06107e6 5.06107e6i 0.672933 0.672933i −0.285458 0.958391i \(-0.592146\pi\)
0.958391 + 0.285458i \(0.0921458\pi\)
\(564\) 1.23896e7 + 6.56192e6i 1.64005 + 0.868627i
\(565\) −570039. 570039.i −0.0751248 0.0751248i
\(566\) 5.10181e6 766695.i 0.669396 0.100596i
\(567\) 249212.i 0.0325545i
\(568\) 2.43554e6 6.93123e6i 0.316756 0.901445i
\(569\) 8.18380e6i 1.05968i −0.848098 0.529839i \(-0.822252\pi\)
0.848098 0.529839i \(-0.177748\pi\)
\(570\) −1.20306e6 8.00553e6i −0.155096 1.03205i
\(571\) −3.05274e6 3.05274e6i −0.391832 0.391832i 0.483508 0.875340i \(-0.339362\pi\)
−0.875340 + 0.483508i \(0.839362\pi\)
\(572\) 1.79803e6 + 5.84719e6i 0.229777 + 0.747235i
\(573\) −2.93833e6 + 2.93833e6i −0.373865 + 0.373865i
\(574\) −821395. + 1.11193e6i −0.104057 + 0.140864i
\(575\) −935180. −0.117957
\(576\) 8.69821e6 1.08488e7i 1.09238 1.36246i
\(577\) −4.77219e6 −0.596730 −0.298365 0.954452i \(-0.596441\pi\)
−0.298365 + 0.954452i \(0.596441\pi\)
\(578\) 4.77008e6 6.45732e6i 0.593890 0.803957i
\(579\) −9.92999e6 + 9.92999e6i −1.23098 + 1.23098i
\(580\) 108044. + 351361.i 0.0133362 + 0.0433694i
\(581\) −877235. 877235.i −0.107814 0.107814i
\(582\) −2.55206e6 1.69822e7i −0.312309 2.07819i
\(583\) 6.77114e6i 0.825069i
\(584\) 52335.9 148941.i 0.00634991 0.0180710i
\(585\) 6.50162e6i 0.785474i
\(586\) −6.41921e6 + 964672.i −0.772213 + 0.116047i
\(587\) −7.77494e6 7.77494e6i −0.931327 0.931327i 0.0664624 0.997789i \(-0.478829\pi\)
−0.997789 + 0.0664624i \(0.978829\pi\)
\(588\) 1.21365e7 + 6.42790e6i 1.44760 + 0.766700i
\(589\) −1.23857e7 + 1.23857e7i −1.47107 + 1.47107i
\(590\) −3.93633e6 2.90780e6i −0.465545 0.343902i
\(591\) 2.22551e6 0.262097
\(592\) 4.31653e6 + 824546.i 0.506209 + 0.0966964i
\(593\) 1.63675e7 1.91137 0.955687 0.294384i \(-0.0951146\pi\)
0.955687 + 0.294384i \(0.0951146\pi\)
\(594\) 6.64934e6 + 4.91193e6i 0.773237 + 0.571197i
\(595\) −6385.65 + 6385.65i −0.000739456 + 0.000739456i
\(596\) −4.63696e6 + 8.75504e6i −0.534710 + 1.00958i
\(597\) 1.72386e7 + 1.72386e7i 1.97954 + 1.97954i
\(598\) −5.12974e6 + 770892.i −0.586600 + 0.0881537i
\(599\) 9.42265e6i 1.07302i 0.843895 + 0.536508i \(0.180257\pi\)
−0.843895 + 0.536508i \(0.819743\pi\)
\(600\) −1.26466e6 2.63491e6i −0.143415 0.298805i
\(601\) 3.73432e6i 0.421722i 0.977516 + 0.210861i \(0.0676267\pi\)
−0.977516 + 0.210861i \(0.932373\pi\)
\(602\) −186260. 1.23942e6i −0.0209473 0.139389i
\(603\) −1.81260e7 1.81260e7i −2.03006 2.03006i
\(604\) −1.22525e7 + 3.76767e6i −1.36657 + 0.420224i
\(605\) −1.12692e6 + 1.12692e6i −0.125171 + 0.125171i
\(606\) −5.28435e6 + 7.15350e6i −0.584534 + 0.791292i
\(607\) −6.00207e6 −0.661195 −0.330598 0.943772i \(-0.607250\pi\)
−0.330598 + 0.943772i \(0.607250\pi\)
\(608\) 8.70996e6 + 9.42832e6i 0.955558 + 1.03437i
\(609\) −165183. −0.0180477
\(610\) −3.44240e6 + 4.66002e6i −0.374573 + 0.507064i
\(611\) 7.34952e6 7.34952e6i 0.796445 0.796445i
\(612\) 336925. 103605.i 0.0363626 0.0111816i
\(613\) 7.64426e6 + 7.64426e6i 0.821645 + 0.821645i 0.986344 0.164699i \(-0.0526652\pi\)
−0.164699 + 0.986344i \(0.552665\pi\)
\(614\) 274975. + 1.82976e6i 0.0294355 + 0.195872i
\(615\) 1.13417e7i 1.20918i
\(616\) 708395. 340002.i 0.0752183 0.0361019i
\(617\) 1.13245e7i 1.19759i −0.800903 0.598794i \(-0.795647\pi\)
0.800903 0.598794i \(-0.204353\pi\)
\(618\) 1.24956e7 1.87782e6i 1.31609 0.197781i
\(619\) 9.72348e6 + 9.72348e6i 1.01999 + 1.01999i 0.999796 + 0.0201917i \(0.00642766\pi\)
0.0201917 + 0.999796i \(0.493572\pi\)
\(620\) −2.95980e6 + 5.58840e6i −0.309232 + 0.583859i
\(621\) −4.95682e6 + 4.95682e6i −0.515791 + 0.515791i
\(622\) −4.92909e6 3.64116e6i −0.510847 0.377367i
\(623\) −713951. −0.0736968
\(624\) −9.10903e6 1.34108e7i −0.936507 1.37877i
\(625\) −390625. −0.0400000
\(626\) −1.10340e7 8.15094e6i −1.12538 0.831327i
\(627\) −1.26262e7 + 1.26262e7i −1.28263 + 1.28263i
\(628\) −9.76011e6 5.16928e6i −0.987542 0.523036i
\(629\) 78773.0 + 78773.0i 0.00793873 + 0.00793873i
\(630\) 825843. 124107.i 0.0828984 0.0124579i
\(631\) 6.32498e6i 0.632392i −0.948694 0.316196i \(-0.897594\pi\)
0.948694 0.316196i \(-0.102406\pi\)
\(632\) 1.48794e7 + 5.22841e6i 1.48181 + 0.520687i
\(633\) 2.21407e6i 0.219625i
\(634\) −714652. 4.75550e6i −0.0706108 0.469865i
\(635\) 5.52484e6 + 5.52484e6i 0.543732 + 0.543732i
\(636\) 5.27420e6 + 1.71517e7i 0.517028 + 1.68138i
\(637\) 7.19941e6 7.19941e6i 0.702988 0.702988i
\(638\) 481762. 652168.i 0.0468577 0.0634319i
\(639\) −1.72224e7 −1.66856
\(640\) 4.00614e6 + 2.32931e6i 0.386613 + 0.224790i
\(641\) 1.14227e7 1.09805 0.549025 0.835806i \(-0.314999\pi\)
0.549025 + 0.835806i \(0.314999\pi\)
\(642\) 854276. 1.15644e6i 0.0818014 0.110736i
\(643\) 6.23986e6 6.23986e6i 0.595179 0.595179i −0.343847 0.939026i \(-0.611730\pi\)
0.939026 + 0.343847i \(0.111730\pi\)
\(644\) 195839. + 636869.i 0.0186073 + 0.0605112i
\(645\) 7.27098e6 + 7.27098e6i 0.688167 + 0.688167i
\(646\) 48355.5 + 321771.i 0.00455895 + 0.0303366i
\(647\) 1.32619e7i 1.24550i 0.782420 + 0.622751i \(0.213985\pi\)
−0.782420 + 0.622751i \(0.786015\pi\)
\(648\) −3.05849e6 1.07471e6i −0.286135 0.100544i
\(649\) 1.07944e7i 1.00598i
\(650\) −2.14269e6 + 322002.i −0.198919 + 0.0298934i
\(651\) −2.00935e6 2.00935e6i −0.185825 0.185825i
\(652\) −5.19260e6 2.75017e6i −0.478372 0.253362i
\(653\) −6.10202e6 + 6.10202e6i −0.560003 + 0.560003i −0.929308 0.369305i \(-0.879596\pi\)
0.369305 + 0.929308i \(0.379596\pi\)
\(654\) −1.94517e7 1.43691e7i −1.77833 1.31367i
\(655\) −5.14027e6 −0.468148
\(656\) 1.01042e7 + 1.48759e7i 0.916730 + 1.34966i
\(657\) −370082. −0.0334491
\(658\) −1.07384e6 793252.i −0.0966881 0.0714243i
\(659\) 7.32830e6 7.32830e6i 0.657339 0.657339i −0.297411 0.954750i \(-0.596123\pi\)
0.954750 + 0.297411i \(0.0961230\pi\)
\(660\) −3.01727e6 + 5.69690e6i −0.269621 + 0.509071i
\(661\) −1.04059e7 1.04059e7i −0.926356 0.926356i 0.0711126 0.997468i \(-0.477345\pi\)
−0.997468 + 0.0711126i \(0.977345\pi\)
\(662\) 4.04199e6 607426.i 0.358468 0.0538702i
\(663\) 410968.i 0.0363098i
\(664\) −1.45491e7 + 6.98298e6i −1.28060 + 0.614640i
\(665\) 770888.i 0.0675985i
\(666\) −1.53098e6 1.01875e7i −0.133747 0.889988i
\(667\) 486164. + 486164.i 0.0423125 + 0.0423125i
\(668\) 9.09185e6 2.79577e6i 0.788335 0.242415i
\(669\) −5.23091e6 + 5.23091e6i −0.451869 + 0.451869i
\(670\) 5.07595e6 6.87139e6i 0.436848 0.591368i
\(671\) 1.27790e7 1.09570
\(672\) −1.52957e6 + 1.41303e6i −0.130661 + 0.120706i
\(673\) −9.64151e6 −0.820554 −0.410277 0.911961i \(-0.634568\pi\)
−0.410277 + 0.911961i \(0.634568\pi\)
\(674\) −8.63877e6 + 1.16944e7i −0.732491 + 0.991583i
\(675\) −2.07046e6 + 2.07046e6i −0.174907 + 0.174907i
\(676\) −131291. + 40372.3i −0.0110501 + 0.00339795i
\(677\) 7.87407e6 + 7.87407e6i 0.660279 + 0.660279i 0.955446 0.295167i \(-0.0953752\pi\)
−0.295167 + 0.955446i \(0.595375\pi\)
\(678\) −700296. 4.65997e6i −0.0585069 0.389322i
\(679\) 1.63529e6i 0.136119i
\(680\) 50831.2 + 105907.i 0.00421558 + 0.00878318i
\(681\) 6.35584e6i 0.525176i
\(682\) 1.37936e7 2.07289e6i 1.13558 0.170653i
\(683\) −6.41872e6 6.41872e6i −0.526498 0.526498i 0.393028 0.919526i \(-0.371427\pi\)
−0.919526 + 0.393028i \(0.871427\pi\)
\(684\) 1.40834e7 2.65908e7i 1.15098 2.17316i
\(685\) −5.95980e6 + 5.95980e6i −0.485294 + 0.485294i
\(686\) −2.11607e6 1.56316e6i −0.171680 0.126821i
\(687\) −2.44778e7 −1.97870
\(688\) −1.60143e7 3.05906e6i −1.28984 0.246386i
\(689\) 1.33031e7 1.06759
\(690\) −4.39690e6 3.24803e6i −0.351580 0.259715i
\(691\) 5.22227e6 5.22227e6i 0.416068 0.416068i −0.467778 0.883846i \(-0.654945\pi\)
0.883846 + 0.467778i \(0.154945\pi\)
\(692\) −7.51662e6 3.98105e6i −0.596702 0.316033i
\(693\) −1.30250e6 1.30250e6i −0.103026 0.103026i
\(694\) 1.01446e7 1.52451e6i 0.799529 0.120152i
\(695\) 6.85562e6i 0.538375i
\(696\) −712344. + 2.02724e6i −0.0557400 + 0.158629i
\(697\) 455865.i 0.0355430i
\(698\) 1.05607e6 + 7.02737e6i 0.0820451 + 0.545952i
\(699\) −1.56207e7 1.56207e7i −1.20922 1.20922i
\(700\) 81802.0 + 266021.i 0.00630985 + 0.0205197i
\(701\) 6.26872e6 6.26872e6i 0.481819 0.481819i −0.423894 0.905712i \(-0.639337\pi\)
0.905712 + 0.423894i \(0.139337\pi\)
\(702\) −9.65037e6 + 1.30638e7i −0.739096 + 1.00052i
\(703\) 9.50963e6 0.725730
\(704\) −1.11781e6 1.01601e7i −0.0850038 0.772624i
\(705\) 1.09531e7 0.829974
\(706\) 2.71106e6 3.67000e6i 0.204705 0.277111i
\(707\) 598848. 598848.i 0.0450576 0.0450576i
\(708\) −8.40805e6 2.73430e7i −0.630394 2.05004i
\(709\) −9.04563e6 9.04563e6i −0.675808 0.675808i 0.283241 0.959049i \(-0.408590\pi\)
−0.959049 + 0.283241i \(0.908590\pi\)
\(710\) −852964. 5.67587e6i −0.0635016 0.422558i
\(711\) 3.69715e7i 2.74280i
\(712\) −3.07888e6 + 8.76209e6i −0.227611 + 0.647750i
\(713\) 1.18278e7i 0.871326i
\(714\) −52201.5 + 7844.80i −0.00383211 + 0.000575886i
\(715\) 3.37942e6 + 3.37942e6i 0.247216 + 0.247216i
\(716\) 1.47222e7 + 7.79735e6i 1.07322 + 0.568414i
\(717\) 2.28167e7 2.28167e7i 1.65751 1.65751i
\(718\) 1.41967e7 + 1.04872e7i 1.02772 + 0.759186i
\(719\) 6.51627e6 0.470085 0.235043 0.971985i \(-0.424477\pi\)
0.235043 + 0.971985i \(0.424477\pi\)
\(720\) 2.03829e6 1.06705e7i 0.146532 0.767103i
\(721\) −1.20325e6 −0.0862024
\(722\) 1.10749e7 + 8.18112e6i 0.790673 + 0.584077i
\(723\) −1.34907e7 + 1.34907e7i −0.959815 + 0.959815i
\(724\) 1.67225e6 3.15738e6i 0.118565 0.223862i
\(725\) 203071. + 203071.i 0.0143484 + 0.0143484i
\(726\) −9.21238e6 + 1.38443e6i −0.648680 + 0.0974829i
\(727\) 2.20343e7i 1.54619i −0.634290 0.773095i \(-0.718707\pi\)
0.634290 0.773095i \(-0.281293\pi\)
\(728\) 667995. + 1.39177e6i 0.0467138 + 0.0973282i
\(729\) 2.18098e7i 1.51996i
\(730\) −18328.8 121965.i −0.00127300 0.00847088i
\(731\) −292247. 292247.i −0.0202282 0.0202282i
\(732\) −3.23700e7 + 9.95385e6i −2.23288 + 0.686615i
\(733\) 3.96665e6 3.96665e6i 0.272687 0.272687i −0.557494 0.830181i \(-0.688237\pi\)
0.830181 + 0.557494i \(0.188237\pi\)
\(734\) 7.96554e6 1.07831e7i 0.545726 0.738757i
\(735\) 1.07294e7 0.732583
\(736\) 8.66064e6 + 343002.i 0.589325 + 0.0233400i
\(737\) −1.88431e7 −1.27786
\(738\) 2.50481e7 3.39080e7i 1.69291 2.29172i
\(739\) 1.60917e7 1.60917e7i 1.08391 1.08391i 0.0877647 0.996141i \(-0.472028\pi\)
0.996141 0.0877647i \(-0.0279724\pi\)
\(740\) 3.28161e6 1.00911e6i 0.220297 0.0677419i
\(741\) −2.48064e7 2.48064e7i −1.65966 1.65966i
\(742\) −253938. 1.68978e6i −0.0169324 0.112673i
\(743\) 9.94157e6i 0.660667i 0.943864 + 0.330334i \(0.107161\pi\)
−0.943864 + 0.330334i \(0.892839\pi\)
\(744\) −3.33254e7 + 1.59949e7i −2.20721 + 1.05937i
\(745\) 7.73998e6i 0.510916i
\(746\) −4.69093e6 + 704949.i −0.308612 + 0.0463779i
\(747\) 2.67509e7 + 2.67509e7i 1.75403 + 1.75403i
\(748\) 121275. 228979.i 0.00792534 0.0149638i
\(749\) −96810.6 + 96810.6i −0.00630548 + 0.00630548i
\(750\) −1.83659e6 1.35670e6i −0.119223 0.0880707i
\(751\) 1.68342e7 1.08916 0.544582 0.838708i \(-0.316688\pi\)
0.544582 + 0.838708i \(0.316688\pi\)
\(752\) −1.43662e7 + 9.75797e6i −0.926396 + 0.629238i
\(753\) 6.58268e6 0.423073
\(754\) 1.28130e6 + 946508.i 0.0820773 + 0.0606312i
\(755\) −7.08140e6 + 7.08140e6i −0.452118 + 0.452118i
\(756\) 1.84359e6 + 976429.i 0.117317 + 0.0621350i
\(757\) −9.43078e6 9.43078e6i −0.598147 0.598147i 0.341672 0.939819i \(-0.389007\pi\)
−0.939819 + 0.341672i \(0.889007\pi\)
\(758\) −1.23257e7 + 1.85230e6i −0.779183 + 0.117095i
\(759\) 1.20575e7i 0.759716i
\(760\) 9.46085e6 + 3.32442e6i 0.594150 + 0.208776i
\(761\) 7.83368e6i 0.490348i −0.969479 0.245174i \(-0.921155\pi\)
0.969479 0.245174i \(-0.0788450\pi\)
\(762\) 6.78729e6 + 4.51646e7i 0.423457 + 2.81780i
\(763\) 1.62838e6 + 1.62838e6i 0.101261 + 0.101261i
\(764\) −1.51293e6 4.92005e6i −0.0937745 0.304955i
\(765\) 194728. 194728.i 0.0120302 0.0120302i
\(766\) 5.83648e6 7.90092e6i 0.359401 0.486526i
\(767\) −2.12076e7 −1.30168
\(768\) 1.07455e7 + 2.48656e7i 0.657389 + 1.52123i
\(769\) 3.02031e7 1.84177 0.920887 0.389830i \(-0.127466\pi\)
0.920887 + 0.389830i \(0.127466\pi\)
\(770\) 364749. 493766.i 0.0221701 0.0300119i
\(771\) −2.44192e7 + 2.44192e7i −1.47943 + 1.47943i
\(772\) −5.11288e6 1.66271e7i −0.308761 1.00409i
\(773\) −1.06293e6 1.06293e6i −0.0639818 0.0639818i 0.674392 0.738374i \(-0.264406\pi\)
−0.738374 + 0.674392i \(0.764406\pi\)
\(774\) 5.67991e6 + 3.77957e7i 0.340792 + 2.26773i
\(775\) 4.94048e6i 0.295471i
\(776\) 2.00694e7 + 7.05210e6i 1.19641 + 0.420402i
\(777\) 1.54276e6i 0.0916741i
\(778\) −1.31608e7 + 1.97779e6i −0.779529 + 0.117147i
\(779\) 2.75164e7 + 2.75164e7i 1.62461 + 1.62461i
\(780\) −1.11926e7 5.92797e6i −0.658709 0.348875i
\(781\) −8.95188e6 + 8.95188e6i −0.525154 + 0.525154i
\(782\) 176728. + 130550.i 0.0103345 + 0.00763415i
\(783\) 2.15271e6 0.125482
\(784\) −1.40728e7 + 9.55867e6i −0.817691 + 0.555402i
\(785\) −8.62853e6 −0.499761
\(786\) −2.41678e7 1.78530e7i −1.39534 1.03075i
\(787\) −7.28531e6 + 7.28531e6i −0.419287 + 0.419287i −0.884958 0.465671i \(-0.845813\pi\)
0.465671 + 0.884958i \(0.345813\pi\)
\(788\) −1.29029e6 + 2.43619e6i −0.0740236 + 0.139764i
\(789\) 4.85162e6 + 4.85162e6i 0.277456 + 0.277456i
\(790\) 1.21844e7 1.83107e6i 0.694605 0.104385i
\(791\) 448729.i 0.0255002i
\(792\) −2.16022e7 + 1.03682e7i −1.22373 + 0.587343i
\(793\) 2.51066e7i 1.41777i
\(794\) −4.52255e6 3.00944e7i −0.254585 1.69408i
\(795\) 9.91293e6 + 9.91293e6i 0.556268 + 0.556268i
\(796\) −2.88648e7 + 8.87601e6i −1.61468 + 0.496518i
\(797\) 6.89591e6 6.89591e6i 0.384544 0.384544i −0.488192 0.872736i \(-0.662344\pi\)
0.872736 + 0.488192i \(0.162344\pi\)
\(798\) −2.67742e6 + 3.62445e6i −0.148836 + 0.201482i
\(799\) −440246. −0.0243965
\(800\) 3.61755e6 + 143272.i 0.199843 + 0.00791473i
\(801\) 2.17716e7 1.19897
\(802\) −9.06413e6 + 1.22702e7i −0.497611 + 0.673623i
\(803\) −192361. + 192361.i −0.0105276 + 0.0105276i
\(804\) 4.77309e7 1.46774e7i 2.60411 0.800770i
\(805\) 368082. + 368082.i 0.0200196 + 0.0200196i
\(806\) 4.07256e6 + 2.71000e7i 0.220816 + 1.46937i
\(807\) 1.91906e7i 1.03730i
\(808\) −4.76696e6 9.93197e6i −0.256870 0.535189i
\(809\) 2.38523e7i 1.28132i −0.767824 0.640661i \(-0.778660\pi\)
0.767824 0.640661i \(-0.221340\pi\)
\(810\) −2.50455e6 + 376381.i −0.134127 + 0.0201565i
\(811\) 1.58590e7 + 1.58590e7i 0.846690 + 0.846690i 0.989719 0.143028i \(-0.0456841\pi\)
−0.143028 + 0.989719i \(0.545684\pi\)
\(812\) 95768.2 180820.i 0.00509719 0.00962400i
\(813\) 7.38299e6 7.38299e6i 0.391747 0.391747i
\(814\) −6.09106e6 4.49952e6i −0.322205 0.238016i
\(815\) −4.59057e6 −0.242088
\(816\) −128840. + 674483.i −0.00677370 + 0.0354606i
\(817\) −3.52807e7 −1.84919
\(818\) −2.03283e7 1.50167e7i −1.06223 0.784676i
\(819\) 2.55901e6 2.55901e6i 0.133310 0.133310i
\(820\) 1.24154e7 + 6.57559e6i 0.644799 + 0.341507i
\(821\) 6.21577e6 + 6.21577e6i 0.321838 + 0.321838i 0.849472 0.527634i \(-0.176921\pi\)
−0.527634 + 0.849472i \(0.676921\pi\)
\(822\) −4.87203e7 + 7.32164e6i −2.51496 + 0.377945i
\(823\) 5.28235e6i 0.271849i 0.990719 + 0.135924i \(0.0434004\pi\)
−0.990719 + 0.135924i \(0.956600\pi\)
\(824\) −5.18898e6 + 1.47672e7i −0.266234 + 0.757668i
\(825\) 5.03640e6i 0.257624i
\(826\) 404824. + 2.69382e6i 0.0206451 + 0.137378i
\(827\) 2.61896e7 + 2.61896e7i 1.33157 + 1.33157i 0.903962 + 0.427613i \(0.140645\pi\)
0.427613 + 0.903962i \(0.359355\pi\)
\(828\) −5.97203e6 1.94211e7i −0.302723 0.984458i
\(829\) 4.93710e6 4.93710e6i 0.249509 0.249509i −0.571260 0.820769i \(-0.693545\pi\)
0.820769 + 0.571260i \(0.193545\pi\)
\(830\) −7.49123e6 + 1.01410e7i −0.377449 + 0.510958i
\(831\) 1.31346e7 0.659802
\(832\) 1.99614e7 2.19615e6i 0.999731 0.109990i
\(833\) −431254. −0.0215338
\(834\) 2.38107e7 3.22328e7i 1.18538 1.60466i
\(835\) 5.25468e6 5.25468e6i 0.260814 0.260814i
\(836\) −6.50112e6 2.11417e7i −0.321716 1.04622i
\(837\) 2.61865e7 + 2.61865e7i 1.29200 + 1.29200i
\(838\) 1.40218e6 + 9.33050e6i 0.0689752 + 0.458981i
\(839\) 4.12702e6i 0.202410i −0.994866 0.101205i \(-0.967730\pi\)
0.994866 0.101205i \(-0.0322698\pi\)
\(840\) −539326. + 1.53485e6i −0.0263726 + 0.0750530i
\(841\) 2.03000e7i 0.989706i
\(842\) 6.69440e6 1.00603e6i 0.325410 0.0489024i
\(843\) 3.87242e7 + 3.87242e7i 1.87678 + 1.87678i
\(844\) −2.42366e6 1.28365e6i −0.117116 0.0620285i
\(845\) −75880.3 + 75880.3i −0.00365584 + 0.00365584i
\(846\) 3.27462e7 + 2.41899e7i 1.57302 + 1.16200i
\(847\) 887101. 0.0424878
\(848\) −2.18332e7 4.17059e6i −1.04262 0.199162i
\(849\) 2.35601e7 1.12178
\(850\) 73819.2 + 54530.9i 0.00350447 + 0.00258878i
\(851\) 4.54064e6 4.54064e6i 0.214928 0.214928i
\(852\) 1.57028e7 2.96485e7i 0.741104 1.39928i
\(853\) −1.19481e7 1.19481e7i −0.562244 0.562244i 0.367700 0.929944i \(-0.380145\pi\)
−0.929944 + 0.367700i \(0.880145\pi\)
\(854\) 3.18907e6 479250.i 0.149630 0.0224863i
\(855\) 2.35079e7i 1.09976i
\(856\) 770634. + 1.60562e6i 0.0359471 + 0.0748958i
\(857\) 1.09807e7i 0.510712i 0.966847 + 0.255356i \(0.0821927\pi\)
−0.966847 + 0.255356i \(0.917807\pi\)
\(858\) 4.15163e6 + 2.76261e7i 0.192531 + 1.28116i
\(859\) −2.41728e7 2.41728e7i −1.11775 1.11775i −0.992071 0.125676i \(-0.959890\pi\)
−0.125676 0.992071i \(-0.540110\pi\)
\(860\) −1.21748e7 + 3.74377e6i −0.561325 + 0.172609i
\(861\) −4.46404e6 + 4.46404e6i −0.205220 + 0.205220i
\(862\) 1.18130e7 1.59915e7i 0.541493 0.733027i
\(863\) −4.01497e7 −1.83508 −0.917541 0.397642i \(-0.869828\pi\)
−0.917541 + 0.397642i \(0.869828\pi\)
\(864\) 1.99338e7 1.84150e7i 0.908461 0.839243i
\(865\) −6.64514e6 −0.301970
\(866\) 8.42500e6 1.14050e7i 0.381746 0.516776i
\(867\) 2.59240e7 2.59240e7i 1.17126 1.17126i
\(868\) 3.36453e6 1.03460e6i 0.151574 0.0466095i
\(869\) −1.92171e7 1.92171e7i −0.863253 0.863253i
\(870\) 249474. + 1.66007e6i 0.0111745 + 0.0743581i
\(871\) 3.70207e7i 1.65348i
\(872\) 2.70069e7 1.29622e7i 1.20277 0.577283i
\(873\) 4.98674e7i 2.21453i
\(874\) 1.85476e7 2.78731e6i 0.821313 0.123426i
\(875\) 153748. + 153748.i 0.00678874 + 0.00678874i
\(876\) 337429. 637098.i 0.0148567 0.0280509i
\(877\) −1.59056e7 + 1.59056e7i −0.698313 + 0.698313i −0.964047 0.265734i \(-0.914386\pi\)
0.265734 + 0.964047i \(0.414386\pi\)
\(878\) −3.35120e7 2.47556e7i −1.46711 1.08377i
\(879\) −2.96438e7 −1.29408
\(880\) −4.48686e6 6.60579e6i −0.195315 0.287553i
\(881\) 1.28495e7 0.557760 0.278880 0.960326i \(-0.410037\pi\)
0.278880 + 0.960326i \(0.410037\pi\)
\(882\) 3.20773e7 + 2.36958e7i 1.38844 + 1.02565i
\(883\) 1.73039e7 1.73039e7i 0.746863 0.746863i −0.227025 0.973889i \(-0.572900\pi\)
0.973889 + 0.227025i \(0.0729001\pi\)
\(884\) 449871. + 238267.i 0.0193623 + 0.0102549i
\(885\) −1.58030e7 1.58030e7i −0.678239 0.678239i
\(886\) −5.59436e6 + 840716.i −0.239423 + 0.0359803i
\(887\) 5.87969e6i 0.250926i −0.992098 0.125463i \(-0.959958\pi\)
0.992098 0.125463i \(-0.0400416\pi\)
\(888\) 1.89338e7 + 6.65310e6i 0.805761 + 0.283134i
\(889\) 4.34910e6i 0.184563i
\(890\) 1.07827e6 + 7.17513e6i 0.0456303 + 0.303637i
\(891\) 3.95013e6 + 3.95013e6i 0.166693 + 0.166693i
\(892\) −2.69336e6 8.75882e6i −0.113340 0.368581i
\(893\) −2.65736e7 + 2.65736e7i −1.11512 + 1.11512i
\(894\) −2.68822e7 + 3.63908e7i −1.12492 + 1.52282i
\(895\) 1.30153e7 0.543120
\(896\) −659993. 2.49360e6i −0.0274643 0.103766i
\(897\) −2.36890e7 −0.983029
\(898\) 1.21105e7 1.63941e7i 0.501153 0.678418i
\(899\) 2.56837e6 2.56837e6i 0.105988 0.105988i
\(900\) −2.49452e6 8.11219e6i −0.102655 0.333835i
\(901\) −398437. 398437.i −0.0163511 0.0163511i
\(902\) −4.60519e6 3.06442e7i −0.188465 1.25410i
\(903\) 5.72364e6i 0.233589i
\(904\) 5.50710e6 + 1.93512e6i 0.224131 + 0.0787567i
\(905\) 2.79131e6i 0.113289i
\(906\) −5.78892e7 + 8.69953e6i −2.34302 + 0.352107i
\(907\) −7.51633e6 7.51633e6i −0.303380 0.303380i 0.538954 0.842335i \(-0.318819\pi\)
−0.842335 + 0.538954i \(0.818819\pi\)
\(908\) −6.95750e6 3.68493e6i −0.280052 0.148325i
\(909\) −1.82616e7 + 1.82616e7i −0.733043 + 0.733043i
\(910\) 970091. + 716615.i 0.0388337 + 0.0286868i
\(911\) −6.38354e6 −0.254839 −0.127419 0.991849i \(-0.540669\pi\)
−0.127419 + 0.991849i \(0.540669\pi\)
\(912\) 3.29355e7 + 4.84893e7i 1.31123 + 1.93045i
\(913\) 2.78092e7 1.10411
\(914\) −1.95271e7 1.44249e7i −0.773167 0.571145i
\(915\) −1.87084e7 + 1.87084e7i −0.738727 + 0.738727i
\(916\) 1.41915e7 2.67949e7i 0.558842 1.05515i
\(917\) 2.02318e6 + 2.02318e6i 0.0794533 + 0.0794533i
\(918\) 680305. 102236.i 0.0266438 0.00400401i
\(919\) 3.04004e7i 1.18738i 0.804693 + 0.593692i \(0.202330\pi\)
−0.804693 + 0.593692i \(0.797670\pi\)
\(920\) 6.10469e6 2.93001e6i 0.237790 0.114130i
\(921\) 8.44980e6i 0.328245i
\(922\) 3.71799e6 + 2.47406e7i 0.144039 + 0.958479i
\(923\) −1.75876e7 1.75876e7i −0.679519 0.679519i
\(924\) 3.42985e6 1.05469e6i 0.132159 0.0406391i
\(925\) 1.89663e6 1.89663e6i 0.0728832 0.0728832i
\(926\) 1.07261e7 1.45201e7i 0.411070 0.556471i
\(927\) 3.66928e7 1.40243
\(928\) −1.80615e6 1.95511e6i −0.0688466 0.0745248i
\(929\) −4.62504e7 −1.75823 −0.879116 0.476609i \(-0.841866\pi\)
−0.879116 + 0.476609i \(0.841866\pi\)
\(930\) −1.71591e7 + 2.32285e7i −0.650559 + 0.880671i
\(931\) −2.60309e7 + 2.60309e7i −0.984271 + 0.984271i
\(932\) 2.61557e7 8.04296e6i 0.986342 0.303303i
\(933\) −1.97886e7 1.97886e7i −0.744237 0.744237i
\(934\) 2.21030e6 + 1.47080e7i 0.0829058 + 0.551679i
\(935\) 202431.i 0.00757267i
\(936\) −2.03702e7 4.24414e7i −0.759988 1.58344i
\(937\) 3.17166e6i 0.118015i 0.998258 + 0.0590075i \(0.0187936\pi\)
−0.998258 + 0.0590075i \(0.981206\pi\)
\(938\) −4.70241e6 + 706674.i −0.174507 + 0.0262248i
\(939\) −4.42980e7 4.42980e7i −1.63953 1.63953i
\(940\) −6.35029e6 + 1.19900e7i −0.234409 + 0.442586i
\(941\) −2.61002e7 + 2.61002e7i −0.960880 + 0.960880i −0.999263 0.0383828i \(-0.987779\pi\)
0.0383828 + 0.999263i \(0.487779\pi\)
\(942\) −4.05684e7 2.99682e7i −1.48957 1.10036i
\(943\) 2.62770e7 0.962269
\(944\) 3.48061e7 + 6.64869e6i 1.27123 + 0.242832i
\(945\) 1.62985e6 0.0593701
\(946\) 2.25978e7 + 1.66932e7i 0.820991 + 0.606473i
\(947\) −2.58430e7 + 2.58430e7i −0.936412 + 0.936412i −0.998096 0.0616833i \(-0.980353\pi\)
0.0616833 + 0.998096i \(0.480353\pi\)
\(948\) 6.36468e7 + 3.37095e7i 2.30015 + 1.21823i
\(949\) −377929. 377929.i −0.0136221 0.0136221i
\(950\) 7.74733e6 1.16426e6i 0.278511 0.0418544i
\(951\) 2.19608e7i 0.787403i
\(952\) 21677.5 61691.3i 0.000775205 0.00220613i
\(953\) 3.68799e7i 1.31540i −0.753280 0.657700i \(-0.771529\pi\)
0.753280 0.657700i \(-0.228471\pi\)
\(954\) 7.74373e6 + 5.15290e7i 0.275473 + 1.83308i
\(955\) −2.84357e6 2.84357e6i −0.100892 0.100892i
\(956\) 1.17482e7 + 3.82051e7i 0.415743 + 1.35200i
\(957\) 2.61823e6 2.61823e6i 0.0924120 0.0924120i
\(958\) −4.80046e6 + 6.49845e6i −0.168993 + 0.228768i
\(959\) 4.69149e6 0.164727
\(960\) 1.65109e7 + 1.32379e7i 0.578219 + 0.463599i
\(961\) 3.38563e7 1.18258
\(962\) 8.84012e6 1.19670e7i 0.307979 0.416915i
\(963\) 2.95220e6 2.95220e6i 0.102584 0.102584i
\(964\) −6.94625e6 2.25892e7i −0.240745 0.782904i
\(965\) −9.60973e6 9.60973e6i −0.332195 0.332195i
\(966\) 452190. + 3.00901e6i 0.0155912 + 0.103748i
\(967\) 5.08603e7i 1.74909i −0.484941 0.874547i \(-0.661159\pi\)
0.484941 0.874547i \(-0.338841\pi\)
\(968\) 3.82558e6 1.08871e7i 0.131223 0.373442i
\(969\) 1.48594e6i 0.0508382i
\(970\) 1.64345e7 2.46975e6i 0.560823 0.0842799i
\(971\) 1.70236e7 + 1.70236e7i 0.579434 + 0.579434i 0.934747 0.355313i \(-0.115626\pi\)
−0.355313 + 0.934747i \(0.615626\pi\)
\(972\) 1.91106e7 + 1.01216e7i 0.648798 + 0.343625i
\(973\) −2.69834e6 + 2.69834e6i −0.0913722 + 0.0913722i
\(974\) −3.00537e7 2.22009e7i −1.01508 0.749848i
\(975\) −9.89492e6 −0.333350
\(976\) 7.87103e6 4.12051e7i 0.264489 1.38461i
\(977\) −7.72986e6 −0.259081 −0.129540 0.991574i \(-0.541350\pi\)
−0.129540 + 0.991574i \(0.541350\pi\)
\(978\) −2.15833e7 1.59438e7i −0.721557 0.533021i
\(979\) 1.13165e7 1.13165e7i 0.377359 0.377359i
\(980\) −6.22058e6 + 1.17451e7i −0.206903 + 0.390652i
\(981\) −4.96567e7 4.96567e7i −1.64742 1.64742i
\(982\) 521443. 78361.9i 0.0172555 0.00259314i
\(983\) 2.68033e7i 0.884717i 0.896838 + 0.442358i \(0.145858\pi\)
−0.896838 + 0.442358i \(0.854142\pi\)
\(984\) 3.55347e7 + 7.40367e7i 1.16995 + 2.43758i
\(985\) 2.15373e6i 0.0707297i
\(986\) −10027.3 66724.3i −0.000328466 0.00218571i
\(987\) −4.31109e6 4.31109e6i −0.140862 0.140862i
\(988\) 4.15367e7 1.27726e7i 1.35375 0.416282i
\(989\) −1.68457e7 + 1.68457e7i −0.547645 + 0.547645i
\(990\) −1.11229e7 + 1.50572e7i −0.360686 + 0.488265i
\(991\) −1.13975e7 −0.368661 −0.184330 0.982864i \(-0.559012\pi\)
−0.184330 + 0.982864i \(0.559012\pi\)
\(992\) 1.81205e6 4.57535e7i 0.0584643 1.47620i
\(993\) 1.86658e7 0.600723
\(994\) −1.89827e6 + 2.56971e6i −0.0609385 + 0.0824933i
\(995\) −1.66826e7 + 1.66826e7i −0.534202 + 0.534202i
\(996\) −7.04425e7 + 2.16613e7i −2.25002 + 0.691887i
\(997\) 8.77758e6 + 8.77758e6i 0.279664 + 0.279664i 0.832975 0.553311i \(-0.186636\pi\)
−0.553311 + 0.832975i \(0.686636\pi\)
\(998\) 3.80502e6 + 2.53197e7i 0.120929 + 0.804697i
\(999\) 2.01057e7i 0.637391i
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 80.6.l.a.21.13 80
4.3 odd 2 320.6.l.a.241.36 80
16.3 odd 4 320.6.l.a.81.36 80
16.13 even 4 inner 80.6.l.a.61.13 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.6.l.a.21.13 80 1.1 even 1 trivial
80.6.l.a.61.13 yes 80 16.13 even 4 inner
320.6.l.a.81.36 80 16.3 odd 4
320.6.l.a.241.36 80 4.3 odd 2