Properties

Label 230.3.k.a.223.12
Level $230$
Weight $3$
Character 230.223
Analytic conductor $6.267$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [230,3,Mod(3,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([33, 32]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.k (of order \(44\), degree \(20\), 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: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 223.12
Character \(\chi\) \(=\) 230.223
Dual form 230.3.k.a.197.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.100889 + 1.41061i) q^{2} +(5.40148 + 1.17502i) q^{3} +(-1.97964 + 0.284630i) q^{4} +(0.547749 - 4.96991i) q^{5} +(-1.11255 + 7.73793i) q^{6} +(1.85546 - 3.39802i) q^{7} +(-0.601225 - 2.76379i) q^{8} +(19.6086 + 8.95494i) q^{9} +O(q^{10})\) \(q+(0.100889 + 1.41061i) q^{2} +(5.40148 + 1.17502i) q^{3} +(-1.97964 + 0.284630i) q^{4} +(0.547749 - 4.96991i) q^{5} +(-1.11255 + 7.73793i) q^{6} +(1.85546 - 3.39802i) q^{7} +(-0.601225 - 2.76379i) q^{8} +(19.6086 + 8.95494i) q^{9} +(7.06586 + 0.271252i) q^{10} +(-7.45467 - 8.60315i) q^{11} +(-11.0274 - 0.788698i) q^{12} +(10.0919 + 18.4819i) q^{13} +(4.98047 + 2.27451i) q^{14} +(8.79839 - 26.2012i) q^{15} +(3.83797 - 1.12693i) q^{16} +(13.4331 + 17.9446i) q^{17} +(-10.6536 + 28.5635i) q^{18} +(-1.91303 + 0.275052i) q^{19} +(0.330236 + 9.99455i) q^{20} +(14.0149 - 16.1741i) q^{21} +(11.3836 - 11.3836i) q^{22} +(-15.7711 - 16.7414i) q^{23} -15.6350i q^{24} +(-24.3999 - 5.44452i) q^{25} +(-25.0527 + 16.1004i) q^{26} +(55.5660 + 41.5962i) q^{27} +(-2.70597 + 7.25498i) q^{28} +(-49.1214 - 7.06259i) q^{29} +(37.8474 + 9.76769i) q^{30} +(-25.6884 - 16.5089i) q^{31} +(1.97687 + 5.30019i) q^{32} +(-30.1574 - 55.2291i) q^{33} +(-23.9575 + 20.7593i) q^{34} +(-15.8715 - 11.0827i) q^{35} +(-41.3669 - 12.1464i) q^{36} +(3.11683 + 8.35656i) q^{37} +(-0.580995 - 2.67079i) q^{38} +(32.7945 + 111.688i) q^{39} +(-14.0651 + 1.47417i) q^{40} +(-5.29030 - 11.5841i) q^{41} +(24.2293 + 18.1378i) q^{42} +(26.2918 + 5.71943i) q^{43} +(17.2063 + 14.9093i) q^{44} +(55.2458 - 92.5478i) q^{45} +(22.0244 - 23.9359i) q^{46} +(-9.97197 + 9.97197i) q^{47} +(22.0549 - 1.57740i) q^{48} +(18.3876 + 28.6117i) q^{49} +(5.21842 - 34.9681i) q^{50} +(51.4735 + 112.711i) q^{51} +(-25.2389 - 33.7152i) q^{52} +(14.8104 + 8.08707i) q^{53} +(-53.0700 + 82.5786i) q^{54} +(-46.8401 + 32.3367i) q^{55} +(-10.5069 - 3.08512i) q^{56} +(-10.6564 - 0.762160i) q^{57} +(5.00676 - 70.0037i) q^{58} +(-4.19169 + 14.2756i) q^{59} +(-9.96002 + 54.3733i) q^{60} +(-88.7808 - 57.0559i) q^{61} +(20.6960 - 37.9019i) q^{62} +(66.8120 - 50.0148i) q^{63} +(-7.27706 + 3.32332i) q^{64} +(97.3814 - 40.0324i) q^{65} +(74.8642 - 48.1123i) q^{66} +(-2.89461 - 40.4719i) q^{67} +(-31.7004 - 31.7004i) q^{68} +(-65.5157 - 108.959i) q^{69} +(14.0321 - 23.5066i) q^{70} +(45.1082 - 52.0577i) q^{71} +(12.9604 - 59.5779i) q^{72} +(-82.9590 + 110.820i) q^{73} +(-11.4734 + 5.23972i) q^{74} +(-125.398 - 58.0789i) q^{75} +(3.70883 - 1.08901i) q^{76} +(-43.0655 + 9.36832i) q^{77} +(-154.240 + 57.5284i) q^{78} +(-16.2677 + 55.4028i) q^{79} +(-3.49849 - 19.6916i) q^{80} +(124.213 + 143.349i) q^{81} +(15.8070 - 8.63126i) q^{82} +(89.3656 - 33.3317i) q^{83} +(-23.1410 + 36.0080i) q^{84} +(96.5408 - 56.9323i) q^{85} +(-5.41534 + 37.6645i) q^{86} +(-257.029 - 95.8670i) q^{87} +(-19.2954 + 25.7756i) q^{88} +(7.04625 + 10.9642i) q^{89} +(136.123 + 68.5933i) q^{90} +81.5271 q^{91} +(35.9862 + 28.6530i) q^{92} +(-119.357 - 119.357i) q^{93} +(-15.0726 - 13.0605i) q^{94} +(0.319124 + 9.65824i) q^{95} +(4.45018 + 30.9517i) q^{96} +(-36.5362 - 13.6273i) q^{97} +(-38.5048 + 28.8243i) q^{98} +(-69.1349 - 235.452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 24 q^{2} - 4 q^{5} - 74 q^{7} + 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 24 q^{2} - 4 q^{5} - 74 q^{7} + 48 q^{8} - 16 q^{10} + 8 q^{11} + 44 q^{12} + 24 q^{13} + 24 q^{15} + 96 q^{16} + 12 q^{17} + 88 q^{18} - 24 q^{20} + 24 q^{21} + 8 q^{22} - 44 q^{23} - 128 q^{25} + 48 q^{26} - 60 q^{27} - 116 q^{28} + 120 q^{30} - 12 q^{31} + 96 q^{32} - 334 q^{33} - 224 q^{35} - 176 q^{36} + 188 q^{37} + 76 q^{38} - 16 q^{40} - 116 q^{41} + 24 q^{42} + 120 q^{43} + 204 q^{45} + 396 q^{46} - 144 q^{47} - 88 q^{48} + 170 q^{50} - 176 q^{51} + 48 q^{52} + 192 q^{53} - 312 q^{55} + 296 q^{56} + 88 q^{57} - 28 q^{58} - 72 q^{60} - 552 q^{61} - 12 q^{62} - 122 q^{63} - 392 q^{65} - 8 q^{66} - 72 q^{67} - 24 q^{68} + 100 q^{70} + 424 q^{71} - 176 q^{72} + 452 q^{73} + 604 q^{75} - 112 q^{76} + 356 q^{77} + 32 q^{78} + 16 q^{80} - 704 q^{81} + 148 q^{82} - 360 q^{83} + 428 q^{85} - 376 q^{86} - 462 q^{87} - 104 q^{88} - 510 q^{90} + 432 q^{91} - 192 q^{93} - 166 q^{95} - 1042 q^{97} - 88 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{4}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.100889 + 1.41061i 0.0504444 + 0.705305i
\(3\) 5.40148 + 1.17502i 1.80049 + 0.391673i 0.982902 0.184128i \(-0.0589460\pi\)
0.817590 + 0.575801i \(0.195310\pi\)
\(4\) −1.97964 + 0.284630i −0.494911 + 0.0711574i
\(5\) 0.547749 4.96991i 0.109550 0.993981i
\(6\) −1.11255 + 7.73793i −0.185424 + 1.28965i
\(7\) 1.85546 3.39802i 0.265065 0.485431i −0.710918 0.703275i \(-0.751720\pi\)
0.975984 + 0.217844i \(0.0699023\pi\)
\(8\) −0.601225 2.76379i −0.0751532 0.345474i
\(9\) 19.6086 + 8.95494i 2.17873 + 0.994994i
\(10\) 7.06586 + 0.271252i 0.706586 + 0.0271252i
\(11\) −7.45467 8.60315i −0.677698 0.782105i 0.307862 0.951431i \(-0.400386\pi\)
−0.985560 + 0.169326i \(0.945841\pi\)
\(12\) −11.0274 0.788698i −0.918953 0.0657248i
\(13\) 10.0919 + 18.4819i 0.776300 + 1.42169i 0.902952 + 0.429741i \(0.141395\pi\)
−0.126652 + 0.991947i \(0.540423\pi\)
\(14\) 4.98047 + 2.27451i 0.355748 + 0.162465i
\(15\) 8.79839 26.2012i 0.586559 1.74675i
\(16\) 3.83797 1.12693i 0.239873 0.0704331i
\(17\) 13.4331 + 17.9446i 0.790184 + 1.05556i 0.997017 + 0.0771863i \(0.0245936\pi\)
−0.206832 + 0.978376i \(0.566315\pi\)
\(18\) −10.6536 + 28.5635i −0.591869 + 1.58686i
\(19\) −1.91303 + 0.275052i −0.100686 + 0.0144764i −0.192474 0.981302i \(-0.561651\pi\)
0.0917877 + 0.995779i \(0.470742\pi\)
\(20\) 0.330236 + 9.99455i 0.0165118 + 0.499727i
\(21\) 14.0149 16.1741i 0.667378 0.770196i
\(22\) 11.3836 11.3836i 0.517436 0.517436i
\(23\) −15.7711 16.7414i −0.685699 0.727885i
\(24\) 15.6350i 0.651458i
\(25\) −24.3999 5.44452i −0.975998 0.217781i
\(26\) −25.0527 + 16.1004i −0.963564 + 0.619245i
\(27\) 55.5660 + 41.5962i 2.05800 + 1.54060i
\(28\) −2.70597 + 7.25498i −0.0966417 + 0.259106i
\(29\) −49.1214 7.06259i −1.69384 0.243538i −0.773260 0.634089i \(-0.781375\pi\)
−0.920581 + 0.390551i \(0.872285\pi\)
\(30\) 37.8474 + 9.76769i 1.26158 + 0.325590i
\(31\) −25.6884 16.5089i −0.828657 0.532546i 0.0561937 0.998420i \(-0.482104\pi\)
−0.884851 + 0.465874i \(0.845740\pi\)
\(32\) 1.97687 + 5.30019i 0.0617771 + 0.165631i
\(33\) −30.1574 55.2291i −0.913860 1.67361i
\(34\) −23.9575 + 20.7593i −0.704633 + 0.610568i
\(35\) −15.8715 11.0827i −0.453471 0.316649i
\(36\) −41.3669 12.1464i −1.14908 0.337400i
\(37\) 3.11683 + 8.35656i 0.0842388 + 0.225853i 0.972239 0.233990i \(-0.0751784\pi\)
−0.888000 + 0.459843i \(0.847906\pi\)
\(38\) −0.580995 2.67079i −0.0152893 0.0702840i
\(39\) 32.7945 + 111.688i 0.840886 + 2.86379i
\(40\) −14.0651 + 1.47417i −0.351627 + 0.0368543i
\(41\) −5.29030 11.5841i −0.129032 0.282540i 0.834079 0.551645i \(-0.186000\pi\)
−0.963111 + 0.269105i \(0.913272\pi\)
\(42\) 24.2293 + 18.1378i 0.576888 + 0.431853i
\(43\) 26.2918 + 5.71943i 0.611437 + 0.133010i 0.507612 0.861586i \(-0.330528\pi\)
0.103825 + 0.994596i \(0.466892\pi\)
\(44\) 17.2063 + 14.9093i 0.391052 + 0.338849i
\(45\) 55.2458 92.5478i 1.22768 2.05662i
\(46\) 22.0244 23.9359i 0.478792 0.520345i
\(47\) −9.97197 + 9.97197i −0.212170 + 0.212170i −0.805189 0.593019i \(-0.797936\pi\)
0.593019 + 0.805189i \(0.297936\pi\)
\(48\) 22.0549 1.57740i 0.459477 0.0328624i
\(49\) 18.3876 + 28.6117i 0.375257 + 0.583912i
\(50\) 5.21842 34.9681i 0.104368 0.699362i
\(51\) 51.4735 + 112.711i 1.00929 + 2.21003i
\(52\) −25.2389 33.7152i −0.485363 0.648369i
\(53\) 14.8104 + 8.08707i 0.279441 + 0.152586i 0.612858 0.790193i \(-0.290020\pi\)
−0.333417 + 0.942779i \(0.608202\pi\)
\(54\) −53.0700 + 82.5786i −0.982778 + 1.52923i
\(55\) −46.8401 + 32.3367i −0.851639 + 0.587939i
\(56\) −10.5069 3.08512i −0.187624 0.0550914i
\(57\) −10.6564 0.762160i −0.186954 0.0133712i
\(58\) 5.00676 70.0037i 0.0863235 1.20696i
\(59\) −4.19169 + 14.2756i −0.0710455 + 0.241959i −0.987358 0.158505i \(-0.949333\pi\)
0.916313 + 0.400464i \(0.131151\pi\)
\(60\) −9.96002 + 54.3733i −0.166000 + 0.906222i
\(61\) −88.7808 57.0559i −1.45542 0.935343i −0.998960 0.0456010i \(-0.985480\pi\)
−0.456463 0.889742i \(-0.650884\pi\)
\(62\) 20.6960 37.9019i 0.333806 0.611320i
\(63\) 66.8120 50.0148i 1.06051 0.793886i
\(64\) −7.27706 + 3.32332i −0.113704 + 0.0519269i
\(65\) 97.3814 40.0324i 1.49817 0.615883i
\(66\) 74.8642 48.1123i 1.13431 0.728974i
\(67\) −2.89461 40.4719i −0.0432031 0.604058i −0.972227 0.234039i \(-0.924806\pi\)
0.929024 0.370019i \(-0.120649\pi\)
\(68\) −31.7004 31.7004i −0.466182 0.466182i
\(69\) −65.5157 108.959i −0.949502 1.57912i
\(70\) 14.0321 23.5066i 0.200459 0.335809i
\(71\) 45.1082 52.0577i 0.635327 0.733207i −0.343214 0.939257i \(-0.611516\pi\)
0.978541 + 0.206050i \(0.0660611\pi\)
\(72\) 12.9604 59.5779i 0.180005 0.827472i
\(73\) −82.9590 + 110.820i −1.13643 + 1.51809i −0.313812 + 0.949485i \(0.601606\pi\)
−0.822613 + 0.568601i \(0.807485\pi\)
\(74\) −11.4734 + 5.23972i −0.155046 + 0.0708071i
\(75\) −125.398 58.0789i −1.67198 0.774385i
\(76\) 3.70883 1.08901i 0.0488004 0.0143291i
\(77\) −43.0655 + 9.36832i −0.559292 + 0.121667i
\(78\) −154.240 + 57.5284i −1.97743 + 0.737544i
\(79\) −16.2677 + 55.4028i −0.205921 + 0.701301i 0.790164 + 0.612895i \(0.209995\pi\)
−0.996085 + 0.0884055i \(0.971823\pi\)
\(80\) −3.49849 19.6916i −0.0437312 0.246145i
\(81\) 124.213 + 143.349i 1.53349 + 1.76974i
\(82\) 15.8070 8.63126i 0.192768 0.105259i
\(83\) 89.3656 33.3317i 1.07669 0.401586i 0.252327 0.967642i \(-0.418804\pi\)
0.824367 + 0.566056i \(0.191531\pi\)
\(84\) −23.1410 + 36.0080i −0.275488 + 0.428667i
\(85\) 96.5408 56.9323i 1.13577 0.669792i
\(86\) −5.41534 + 37.6645i −0.0629690 + 0.437959i
\(87\) −257.029 95.8670i −2.95436 1.10192i
\(88\) −19.2954 + 25.7756i −0.219265 + 0.292904i
\(89\) 7.04625 + 10.9642i 0.0791714 + 0.123193i 0.878581 0.477593i \(-0.158491\pi\)
−0.799410 + 0.600786i \(0.794854\pi\)
\(90\) 136.123 + 68.5933i 1.51247 + 0.762148i
\(91\) 81.5271 0.895902
\(92\) 35.9862 + 28.6530i 0.391154 + 0.311446i
\(93\) −119.357 119.357i −1.28341 1.28341i
\(94\) −15.0726 13.0605i −0.160347 0.138942i
\(95\) 0.319124 + 9.65824i 0.00335920 + 0.101666i
\(96\) 4.45018 + 30.9517i 0.0463561 + 0.322414i
\(97\) −36.5362 13.6273i −0.376662 0.140488i 0.154001 0.988071i \(-0.450784\pi\)
−0.530663 + 0.847583i \(0.678057\pi\)
\(98\) −38.5048 + 28.8243i −0.392906 + 0.294126i
\(99\) −69.1349 235.452i −0.698332 2.37830i
\(100\) 49.8528 + 3.83326i 0.498528 + 0.0383326i
\(101\) 52.8800 115.791i 0.523564 1.14645i −0.444508 0.895775i \(-0.646621\pi\)
0.968072 0.250671i \(-0.0806512\pi\)
\(102\) −153.799 + 83.9804i −1.50783 + 0.823338i
\(103\) 4.09873 57.3077i 0.0397935 0.556385i −0.937976 0.346701i \(-0.887302\pi\)
0.977769 0.209684i \(-0.0672436\pi\)
\(104\) 45.0127 39.0037i 0.432814 0.375036i
\(105\) −72.7071 78.5123i −0.692449 0.747736i
\(106\) −9.91350 + 21.7075i −0.0935236 + 0.204788i
\(107\) −91.2407 + 19.8482i −0.852717 + 0.185497i −0.617622 0.786475i \(-0.711904\pi\)
−0.235095 + 0.971972i \(0.575540\pi\)
\(108\) −121.840 66.5299i −1.12815 0.616017i
\(109\) 112.796 + 16.2176i 1.03483 + 0.148786i 0.638736 0.769426i \(-0.279458\pi\)
0.396091 + 0.918211i \(0.370367\pi\)
\(110\) −50.3401 62.8108i −0.457637 0.571007i
\(111\) 7.01639 + 48.8001i 0.0632108 + 0.439640i
\(112\) 3.29187 15.1325i 0.0293917 0.135111i
\(113\) −96.9191 + 6.93179i −0.857691 + 0.0613433i −0.493254 0.869885i \(-0.664193\pi\)
−0.364436 + 0.931228i \(0.618738\pi\)
\(114\) 15.1089i 0.132534i
\(115\) −91.8416 + 69.2107i −0.798623 + 0.601832i
\(116\) 99.2531 0.855630
\(117\) 32.3833 + 452.777i 0.276780 + 3.86989i
\(118\) −20.5602 4.47259i −0.174239 0.0379033i
\(119\) 85.9005 12.3506i 0.721853 0.103787i
\(120\) −77.7044 8.56405i −0.647537 0.0713671i
\(121\) −1.22197 + 8.49898i −0.0100989 + 0.0702395i
\(122\) 71.5267 130.991i 0.586285 1.07370i
\(123\) −14.9638 68.7877i −0.121657 0.559249i
\(124\) 55.5527 + 25.3701i 0.448006 + 0.204597i
\(125\) −40.4238 + 118.283i −0.323390 + 0.946266i
\(126\) 77.2920 + 89.1997i 0.613428 + 0.707934i
\(127\) 157.312 + 11.2512i 1.23868 + 0.0885922i 0.675261 0.737579i \(-0.264031\pi\)
0.563420 + 0.826171i \(0.309485\pi\)
\(128\) −5.42208 9.92980i −0.0423600 0.0775766i
\(129\) 135.294 + 61.7867i 1.04879 + 0.478967i
\(130\) 66.2948 + 133.328i 0.509960 + 1.02560i
\(131\) −28.9578 + 8.50277i −0.221052 + 0.0649067i −0.390383 0.920653i \(-0.627657\pi\)
0.169331 + 0.985559i \(0.445839\pi\)
\(132\) 75.4207 + 100.750i 0.571369 + 0.763259i
\(133\) −2.61491 + 7.01086i −0.0196610 + 0.0527132i
\(134\) 56.7981 8.16633i 0.423866 0.0609427i
\(135\) 237.165 253.374i 1.75678 1.87684i
\(136\) 41.5186 47.9151i 0.305284 0.352317i
\(137\) 70.2576 70.2576i 0.512829 0.512829i −0.402563 0.915392i \(-0.631881\pi\)
0.915392 + 0.402563i \(0.131881\pi\)
\(138\) 147.089 103.410i 1.06587 0.749347i
\(139\) 248.673i 1.78901i 0.447054 + 0.894507i \(0.352473\pi\)
−0.447054 + 0.894507i \(0.647527\pi\)
\(140\) 34.5744 + 17.4223i 0.246960 + 0.124445i
\(141\) −65.5806 + 42.1461i −0.465111 + 0.298909i
\(142\) 77.9840 + 58.3781i 0.549183 + 0.411113i
\(143\) 83.7711 224.599i 0.585812 1.57062i
\(144\) 85.3488 + 12.2713i 0.592700 + 0.0852174i
\(145\) −62.0066 + 240.260i −0.427632 + 1.65697i
\(146\) −164.694 105.842i −1.12804 0.724948i
\(147\) 65.7010 + 176.151i 0.446945 + 1.19831i
\(148\) −8.54874 15.6559i −0.0577618 0.105783i
\(149\) 17.8556 15.4719i 0.119836 0.103838i −0.592881 0.805290i \(-0.702010\pi\)
0.712717 + 0.701451i \(0.247464\pi\)
\(150\) 69.2753 182.748i 0.461836 1.21832i
\(151\) 212.102 + 62.2787i 1.40465 + 0.412442i 0.894277 0.447514i \(-0.147690\pi\)
0.510370 + 0.859955i \(0.329509\pi\)
\(152\) 1.91035 + 5.12184i 0.0125681 + 0.0336963i
\(153\) 102.712 + 472.161i 0.671322 + 3.08602i
\(154\) −17.5599 59.8035i −0.114025 0.388334i
\(155\) −96.1186 + 118.626i −0.620120 + 0.765330i
\(156\) −96.7112 211.768i −0.619944 1.35749i
\(157\) −38.2617 28.6424i −0.243705 0.182436i 0.470442 0.882431i \(-0.344094\pi\)
−0.714147 + 0.699995i \(0.753185\pi\)
\(158\) −79.7930 17.3579i −0.505019 0.109860i
\(159\) 70.4953 + 61.0846i 0.443367 + 0.384180i
\(160\) 27.4243 6.92168i 0.171402 0.0432605i
\(161\) −86.1500 + 22.5275i −0.535093 + 0.139922i
\(162\) −189.678 + 189.678i −1.17085 + 1.17085i
\(163\) −3.43605 + 0.245751i −0.0210801 + 0.00150768i −0.0818752 0.996643i \(-0.526091\pi\)
0.0607952 + 0.998150i \(0.480636\pi\)
\(164\) 13.7701 + 21.4267i 0.0839640 + 0.130651i
\(165\) −291.002 + 119.628i −1.76365 + 0.725016i
\(166\) 56.0340 + 122.697i 0.337554 + 0.739140i
\(167\) −101.175 135.153i −0.605836 0.809302i 0.387823 0.921734i \(-0.373227\pi\)
−0.993659 + 0.112432i \(0.964136\pi\)
\(168\) −53.1280 29.0101i −0.316238 0.172679i
\(169\) −148.367 + 230.864i −0.877914 + 1.36606i
\(170\) 90.0492 + 130.438i 0.529701 + 0.767280i
\(171\) −39.9749 11.7377i −0.233771 0.0686415i
\(172\) −53.6763 3.83900i −0.312071 0.0223198i
\(173\) −3.31999 + 46.4195i −0.0191907 + 0.268321i 0.978793 + 0.204851i \(0.0656711\pi\)
−0.997984 + 0.0634696i \(0.979783\pi\)
\(174\) 109.300 372.240i 0.628159 2.13931i
\(175\) −63.7736 + 72.8093i −0.364421 + 0.416053i
\(176\) −38.3060 24.6178i −0.217648 0.139874i
\(177\) −39.4154 + 72.1839i −0.222686 + 0.407819i
\(178\) −14.7553 + 11.0457i −0.0828949 + 0.0620544i
\(179\) 68.4794 31.2735i 0.382566 0.174712i −0.214843 0.976649i \(-0.568924\pi\)
0.597409 + 0.801936i \(0.296197\pi\)
\(180\) −83.0251 + 198.936i −0.461251 + 1.10520i
\(181\) −274.694 + 176.535i −1.51765 + 0.975333i −0.525428 + 0.850838i \(0.676095\pi\)
−0.992220 + 0.124495i \(0.960269\pi\)
\(182\) 8.22517 + 115.003i 0.0451932 + 0.631884i
\(183\) −412.506 412.506i −2.25413 2.25413i
\(184\) −36.7876 + 53.6532i −0.199933 + 0.291594i
\(185\) 43.2385 10.9131i 0.233722 0.0589896i
\(186\) 156.324 180.408i 0.840453 0.969934i
\(187\) 54.2402 249.338i 0.290055 1.33336i
\(188\) 16.9026 22.5793i 0.0899076 0.120102i
\(189\) 244.445 111.634i 1.29336 0.590657i
\(190\) −13.5918 + 1.42457i −0.0715359 + 0.00749773i
\(191\) 172.910 50.7709i 0.905288 0.265816i 0.204232 0.978923i \(-0.434530\pi\)
0.701056 + 0.713106i \(0.252712\pi\)
\(192\) −43.2118 + 9.40015i −0.225062 + 0.0489591i
\(193\) 2.87732 1.07318i 0.0149084 0.00556054i −0.341999 0.939700i \(-0.611104\pi\)
0.356907 + 0.934140i \(0.383831\pi\)
\(194\) 15.5367 52.9132i 0.0800862 0.272748i
\(195\) 573.042 101.809i 2.93868 0.522097i
\(196\) −44.5446 51.4072i −0.227268 0.262282i
\(197\) 214.215 116.970i 1.08739 0.593759i 0.167473 0.985877i \(-0.446439\pi\)
0.919915 + 0.392118i \(0.128258\pi\)
\(198\) 325.156 121.277i 1.64220 0.612510i
\(199\) −13.1690 + 20.4914i −0.0661761 + 0.102972i −0.872765 0.488141i \(-0.837675\pi\)
0.806588 + 0.591113i \(0.201311\pi\)
\(200\) −0.377639 + 70.7097i −0.00188819 + 0.353548i
\(201\) 31.9201 222.009i 0.158807 1.10452i
\(202\) 168.671 + 62.9110i 0.835005 + 0.311441i
\(203\) −115.141 + 153.811i −0.567199 + 0.757690i
\(204\) −133.980 208.477i −0.656766 1.02195i
\(205\) −60.4699 + 19.9471i −0.294975 + 0.0973029i
\(206\) 81.2523 0.394429
\(207\) −159.331 469.504i −0.769713 2.26813i
\(208\) 59.5603 + 59.5603i 0.286348 + 0.286348i
\(209\) 16.6273 + 14.4077i 0.0795566 + 0.0689362i
\(210\) 103.415 110.482i 0.492452 0.526107i
\(211\) 45.6530 + 317.524i 0.216365 + 1.50485i 0.751301 + 0.659959i \(0.229426\pi\)
−0.534936 + 0.844892i \(0.679664\pi\)
\(212\) −31.6210 11.7940i −0.149156 0.0556322i
\(213\) 304.820 228.185i 1.43108 1.07129i
\(214\) −37.2032 126.703i −0.173847 0.592068i
\(215\) 42.8263 127.535i 0.199192 0.593186i
\(216\) 81.5554 178.581i 0.377571 0.826766i
\(217\) −103.761 + 56.6579i −0.478162 + 0.261096i
\(218\) −11.4969 + 160.748i −0.0527380 + 0.737374i
\(219\) −578.317 + 501.115i −2.64072 + 2.28820i
\(220\) 83.5228 77.3471i 0.379649 0.351578i
\(221\) −196.085 + 429.365i −0.887260 + 1.94283i
\(222\) −68.1300 + 14.8208i −0.306892 + 0.0667603i
\(223\) 56.9334 + 31.0880i 0.255307 + 0.139408i 0.601806 0.798642i \(-0.294448\pi\)
−0.346500 + 0.938050i \(0.612630\pi\)
\(224\) 21.6781 + 3.11684i 0.0967773 + 0.0139145i
\(225\) −429.693 325.260i −1.90975 1.44560i
\(226\) −19.5561 136.016i −0.0865314 0.601839i
\(227\) 54.7215 251.550i 0.241064 1.10815i −0.684338 0.729165i \(-0.739909\pi\)
0.925402 0.378987i \(-0.123728\pi\)
\(228\) 21.3128 1.52432i 0.0934770 0.00668561i
\(229\) 418.794i 1.82880i −0.404816 0.914398i \(-0.632665\pi\)
0.404816 0.914398i \(-0.367335\pi\)
\(230\) −106.895 122.570i −0.464761 0.532914i
\(231\) −243.625 −1.05465
\(232\) 10.0135 + 140.007i 0.0431618 + 0.603480i
\(233\) −1.49612 0.325461i −0.00642112 0.00139683i 0.209354 0.977840i \(-0.432864\pi\)
−0.215775 + 0.976443i \(0.569228\pi\)
\(234\) −635.425 + 91.3604i −2.71549 + 0.390429i
\(235\) 44.0976 + 55.0219i 0.187649 + 0.234136i
\(236\) 4.23479 29.4536i 0.0179440 0.124803i
\(237\) −152.969 + 280.142i −0.645439 + 1.18203i
\(238\) 26.0883 + 119.926i 0.109615 + 0.503891i
\(239\) 69.7012 + 31.8315i 0.291637 + 0.133186i 0.555861 0.831275i \(-0.312389\pi\)
−0.264224 + 0.964461i \(0.585116\pi\)
\(240\) 4.24102 110.475i 0.0176709 0.460311i
\(241\) 232.222 + 267.999i 0.963578 + 1.11203i 0.993654 + 0.112480i \(0.0358795\pi\)
−0.0300764 + 0.999548i \(0.509575\pi\)
\(242\) −12.1120 0.866270i −0.0500497 0.00357963i
\(243\) 203.110 + 371.969i 0.835845 + 1.53074i
\(244\) 191.994 + 87.6808i 0.786861 + 0.359347i
\(245\) 152.269 75.7127i 0.621507 0.309031i
\(246\) 95.5229 28.0481i 0.388305 0.114017i
\(247\) −24.3896 32.5807i −0.0987434 0.131906i
\(248\) −30.1827 + 80.9228i −0.121704 + 0.326302i
\(249\) 521.872 75.0338i 2.09587 0.301341i
\(250\) −170.930 45.0888i −0.683719 0.180355i
\(251\) 110.121 127.086i 0.438727 0.506318i −0.492723 0.870186i \(-0.663998\pi\)
0.931451 + 0.363868i \(0.118544\pi\)
\(252\) −118.028 + 118.028i −0.468366 + 0.468366i
\(253\) −26.4603 + 260.482i −0.104586 + 1.02957i
\(254\) 223.042i 0.878117i
\(255\) 588.359 194.081i 2.30729 0.761103i
\(256\) 13.4601 8.65025i 0.0525783 0.0337901i
\(257\) −34.7237 25.9938i −0.135112 0.101143i 0.529584 0.848257i \(-0.322348\pi\)
−0.664696 + 0.747114i \(0.731439\pi\)
\(258\) −73.5073 + 197.081i −0.284912 + 0.763879i
\(259\) 34.1789 + 4.91418i 0.131965 + 0.0189737i
\(260\) −181.386 + 106.967i −0.697638 + 0.411413i
\(261\) −899.957 578.367i −3.44811 2.21597i
\(262\) −14.9156 39.9903i −0.0569298 0.152635i
\(263\) −98.3200 180.060i −0.373840 0.684638i 0.621249 0.783613i \(-0.286625\pi\)
−0.995090 + 0.0989753i \(0.968444\pi\)
\(264\) −134.510 + 116.554i −0.509508 + 0.441492i
\(265\) 48.3043 69.1764i 0.182280 0.261043i
\(266\) −10.1534 2.98131i −0.0381707 0.0112079i
\(267\) 25.1770 + 67.5022i 0.0942960 + 0.252817i
\(268\) 17.2498 + 79.2960i 0.0643649 + 0.295881i
\(269\) 88.2386 + 300.513i 0.328025 + 1.11715i 0.944154 + 0.329505i \(0.106882\pi\)
−0.616129 + 0.787645i \(0.711300\pi\)
\(270\) 381.339 + 308.985i 1.41237 + 1.14439i
\(271\) −42.7471 93.6030i −0.157738 0.345398i 0.814218 0.580559i \(-0.197166\pi\)
−0.971957 + 0.235160i \(0.924439\pi\)
\(272\) 71.7783 + 53.7325i 0.263891 + 0.197546i
\(273\) 440.366 + 95.7959i 1.61306 + 0.350901i
\(274\) 106.194 + 92.0179i 0.387570 + 0.335832i
\(275\) 135.054 + 250.504i 0.491104 + 0.910922i
\(276\) 160.711 + 197.053i 0.582285 + 0.713960i
\(277\) 6.77143 6.77143i 0.0244456 0.0244456i −0.694778 0.719224i \(-0.744498\pi\)
0.719224 + 0.694778i \(0.244498\pi\)
\(278\) −350.781 + 25.0883i −1.26180 + 0.0902458i
\(279\) −355.876 553.755i −1.27554 1.98478i
\(280\) −21.0879 + 50.5287i −0.0753140 + 0.180460i
\(281\) −125.627 275.084i −0.447070 0.978946i −0.990246 0.139328i \(-0.955506\pi\)
0.543176 0.839619i \(-0.317221\pi\)
\(282\) −66.0681 88.2566i −0.234284 0.312967i
\(283\) 177.135 + 96.7230i 0.625918 + 0.341777i 0.760705 0.649097i \(-0.224853\pi\)
−0.134787 + 0.990875i \(0.543035\pi\)
\(284\) −74.4810 + 115.895i −0.262257 + 0.408080i
\(285\) −9.62488 + 52.5438i −0.0337715 + 0.184364i
\(286\) 325.273 + 95.5089i 1.13732 + 0.333947i
\(287\) −49.1790 3.51735i −0.171356 0.0122556i
\(288\) −8.69929 + 121.632i −0.0302059 + 0.422333i
\(289\) −60.1377 + 204.810i −0.208089 + 0.708685i
\(290\) −345.169 63.2276i −1.19024 0.218026i
\(291\) −181.337 116.538i −0.623152 0.400475i
\(292\) 132.687 242.997i 0.454406 0.832182i
\(293\) −305.850 + 228.956i −1.04386 + 0.781420i −0.976328 0.216297i \(-0.930602\pi\)
−0.0675278 + 0.997717i \(0.521511\pi\)
\(294\) −241.852 + 110.450i −0.822626 + 0.375681i
\(295\) 68.6523 + 28.6517i 0.232720 + 0.0971245i
\(296\) 21.2218 13.6384i 0.0716954 0.0460758i
\(297\) −56.3681 788.129i −0.189792 2.65363i
\(298\) 23.6263 + 23.6263i 0.0792829 + 0.0792829i
\(299\) 150.253 460.432i 0.502518 1.53991i
\(300\) 264.775 + 79.2833i 0.882583 + 0.264278i
\(301\) 68.2180 78.7278i 0.226638 0.261554i
\(302\) −66.4522 + 305.476i −0.220041 + 1.01151i
\(303\) 421.687 563.308i 1.39171 1.85910i
\(304\) −7.03219 + 3.21150i −0.0231322 + 0.0105641i
\(305\) −332.192 + 409.980i −1.08916 + 1.34420i
\(306\) −655.672 + 192.523i −2.14272 + 0.629159i
\(307\) 63.8034 13.8796i 0.207829 0.0452103i −0.107446 0.994211i \(-0.534267\pi\)
0.315274 + 0.949001i \(0.397904\pi\)
\(308\) 82.5878 30.8036i 0.268142 0.100012i
\(309\) 89.4768 304.730i 0.289569 0.986181i
\(310\) −177.032 123.618i −0.571072 0.398767i
\(311\) −277.235 319.947i −0.891432 1.02877i −0.999401 0.0346133i \(-0.988980\pi\)
0.107969 0.994154i \(-0.465565\pi\)
\(312\) 288.965 157.787i 0.926170 0.505727i
\(313\) −178.426 + 66.5496i −0.570053 + 0.212619i −0.617928 0.786235i \(-0.712028\pi\)
0.0478755 + 0.998853i \(0.484755\pi\)
\(314\) 36.5431 56.8621i 0.116379 0.181090i
\(315\) −211.973 359.445i −0.672929 1.14109i
\(316\) 16.4350 114.308i 0.0520095 0.361734i
\(317\) 122.179 + 45.5705i 0.385423 + 0.143755i 0.534704 0.845039i \(-0.320423\pi\)
−0.149281 + 0.988795i \(0.547696\pi\)
\(318\) −79.0543 + 105.604i −0.248598 + 0.332089i
\(319\) 305.424 + 475.248i 0.957440 + 1.48981i
\(320\) 12.5306 + 37.9866i 0.0391581 + 0.118708i
\(321\) −516.156 −1.60796
\(322\) −40.4691 119.251i −0.125680 0.370346i
\(323\) −30.6337 30.6337i −0.0948412 0.0948412i
\(324\) −286.699 248.426i −0.884872 0.766746i
\(325\) −145.617 505.904i −0.448051 1.55663i
\(326\) −0.693318 4.82213i −0.00212674 0.0147918i
\(327\) 590.210 + 220.137i 1.80492 + 0.673201i
\(328\) −28.8355 + 21.5860i −0.0879130 + 0.0658108i
\(329\) 15.3824 + 52.3875i 0.0467549 + 0.159233i
\(330\) −198.107 398.422i −0.600324 1.20734i
\(331\) 94.0603 205.963i 0.284170 0.622245i −0.712686 0.701483i \(-0.752521\pi\)
0.996856 + 0.0792380i \(0.0252487\pi\)
\(332\) −167.425 + 91.4209i −0.504292 + 0.275364i
\(333\) −13.7158 + 191.771i −0.0411885 + 0.575890i
\(334\) 180.441 156.353i 0.540244 0.468124i
\(335\) −202.727 7.78251i −0.605156 0.0232314i
\(336\) 35.5619 77.8696i 0.105839 0.231755i
\(337\) 652.497 141.942i 1.93619 0.421193i 0.939235 0.343276i \(-0.111537\pi\)
0.996960 0.0779171i \(-0.0248270\pi\)
\(338\) −340.628 185.997i −1.00778 0.550287i
\(339\) −531.651 76.4399i −1.56829 0.225486i
\(340\) −174.912 + 140.184i −0.514446 + 0.412306i
\(341\) 49.4697 + 344.070i 0.145073 + 1.00900i
\(342\) 12.5243 57.5732i 0.0366207 0.168343i
\(343\) 320.565 22.9273i 0.934592 0.0668433i
\(344\) 76.1036i 0.221231i
\(345\) −577.404 + 265.924i −1.67364 + 0.770795i
\(346\) −65.8148 −0.190216
\(347\) −2.76360 38.6402i −0.00796428 0.111355i 0.991915 0.126906i \(-0.0405045\pi\)
−0.999879 + 0.0155504i \(0.995050\pi\)
\(348\) 536.113 + 116.624i 1.54056 + 0.335127i
\(349\) 160.287 23.0458i 0.459276 0.0660339i 0.0912061 0.995832i \(-0.470928\pi\)
0.368070 + 0.929798i \(0.380019\pi\)
\(350\) −109.140 82.6141i −0.311828 0.236040i
\(351\) −208.012 + 1446.75i −0.592626 + 4.12180i
\(352\) 30.8614 56.5185i 0.0876745 0.160564i
\(353\) 25.0431 + 115.121i 0.0709436 + 0.326123i 0.998917 0.0465234i \(-0.0148142\pi\)
−0.927974 + 0.372646i \(0.878451\pi\)
\(354\) −105.800 48.3172i −0.298870 0.136489i
\(355\) −234.014 252.698i −0.659194 0.711826i
\(356\) −17.0698 19.6996i −0.0479489 0.0553359i
\(357\) 478.502 + 34.2231i 1.34034 + 0.0958631i
\(358\) 51.0235 + 93.4426i 0.142524 + 0.261013i
\(359\) 189.166 + 86.3892i 0.526925 + 0.240639i 0.661071 0.750323i \(-0.270102\pi\)
−0.134147 + 0.990962i \(0.542829\pi\)
\(360\) −288.998 97.0457i −0.802772 0.269571i
\(361\) −342.793 + 100.653i −0.949565 + 0.278817i
\(362\) −276.736 369.676i −0.764464 1.02120i
\(363\) −16.5869 + 44.4712i −0.0456940 + 0.122510i
\(364\) −161.394 + 23.2050i −0.443391 + 0.0637501i
\(365\) 505.326 + 473.000i 1.38445 + 1.29589i
\(366\) 540.267 623.502i 1.47614 1.70356i
\(367\) −397.881 + 397.881i −1.08414 + 1.08414i −0.0880262 + 0.996118i \(0.528056\pi\)
−0.996118 + 0.0880262i \(0.971944\pi\)
\(368\) −79.3953 46.4800i −0.215748 0.126304i
\(369\) 274.523i 0.743965i
\(370\) 19.7564 + 59.8917i 0.0533957 + 0.161870i
\(371\) 54.9600 35.3206i 0.148140 0.0952038i
\(372\) 270.256 + 202.311i 0.726496 + 0.543848i
\(373\) 109.229 292.855i 0.292840 0.785135i −0.704324 0.709879i \(-0.748750\pi\)
0.997164 0.0752565i \(-0.0239775\pi\)
\(374\) 357.191 + 51.3563i 0.955057 + 0.137316i
\(375\) −357.333 + 591.405i −0.952889 + 1.57708i
\(376\) 33.5558 + 21.5650i 0.0892442 + 0.0573538i
\(377\) −365.198 979.134i −0.968695 2.59717i
\(378\) 182.134 + 333.554i 0.481836 + 0.882418i
\(379\) −478.920 + 414.987i −1.26364 + 1.09495i −0.272498 + 0.962156i \(0.587850\pi\)
−0.991143 + 0.132796i \(0.957605\pi\)
\(380\) −3.38077 19.0290i −0.00889677 0.0500764i
\(381\) 836.499 + 245.618i 2.19554 + 0.644668i
\(382\) 89.0627 + 238.786i 0.233148 + 0.625095i
\(383\) 99.4016 + 456.942i 0.259534 + 1.19306i 0.903697 + 0.428172i \(0.140842\pi\)
−0.644163 + 0.764888i \(0.722794\pi\)
\(384\) −17.6195 60.0067i −0.0458842 0.156267i
\(385\) 22.9706 + 219.163i 0.0596639 + 0.569254i
\(386\) 1.80413 + 3.95050i 0.00467392 + 0.0102345i
\(387\) 464.328 + 347.592i 1.19981 + 0.898169i
\(388\) 76.2074 + 16.5779i 0.196411 + 0.0427266i
\(389\) −189.841 164.498i −0.488023 0.422874i 0.375777 0.926710i \(-0.377376\pi\)
−0.863799 + 0.503836i \(0.831921\pi\)
\(390\) 201.426 + 798.068i 0.516477 + 2.04633i
\(391\) 88.5616 507.894i 0.226500 1.29896i
\(392\) 68.0215 68.0215i 0.173524 0.173524i
\(393\) −166.406 + 11.9016i −0.423424 + 0.0302839i
\(394\) 186.612 + 290.373i 0.473634 + 0.736988i
\(395\) 266.436 + 111.196i 0.674521 + 0.281508i
\(396\) 203.879 + 446.433i 0.514846 + 1.12736i
\(397\) −255.902 341.845i −0.644589 0.861071i 0.352617 0.935768i \(-0.385292\pi\)
−0.997206 + 0.0746972i \(0.976201\pi\)
\(398\) −30.2340 16.5090i −0.0759649 0.0414800i
\(399\) −22.3623 + 34.7964i −0.0560459 + 0.0872090i
\(400\) −99.7819 + 6.60112i −0.249455 + 0.0165028i
\(401\) 685.328 + 201.231i 1.70905 + 0.501822i 0.982653 0.185455i \(-0.0593759\pi\)
0.726396 + 0.687277i \(0.241194\pi\)
\(402\) 316.389 + 22.6286i 0.787037 + 0.0562900i
\(403\) 45.8722 641.378i 0.113827 1.59151i
\(404\) −71.7259 + 244.276i −0.177539 + 0.604644i
\(405\) 780.470 538.807i 1.92709 1.33039i
\(406\) −228.584 146.902i −0.563015 0.361827i
\(407\) 48.6577 89.1100i 0.119552 0.218944i
\(408\) 280.563 210.027i 0.687655 0.514772i
\(409\) 330.543 150.954i 0.808173 0.369080i 0.0319112 0.999491i \(-0.489841\pi\)
0.776262 + 0.630410i \(0.217113\pi\)
\(410\) −34.2383 83.2870i −0.0835081 0.203139i
\(411\) 462.049 296.941i 1.12421 0.722483i
\(412\) 8.19745 + 114.615i 0.0198967 + 0.278193i
\(413\) 40.7311 + 40.7311i 0.0986226 + 0.0986226i
\(414\) 646.212 272.121i 1.56090 0.657297i
\(415\) −116.705 462.396i −0.281218 1.11421i
\(416\) −78.0074 + 90.0254i −0.187518 + 0.216407i
\(417\) −292.195 + 1343.20i −0.700709 + 3.22111i
\(418\) −18.6461 + 24.9083i −0.0446079 + 0.0595891i
\(419\) 182.808 83.4858i 0.436297 0.199250i −0.185143 0.982711i \(-0.559275\pi\)
0.621441 + 0.783461i \(0.286548\pi\)
\(420\) 166.281 + 134.732i 0.395907 + 0.320790i
\(421\) 169.851 49.8728i 0.403447 0.118463i −0.0737122 0.997280i \(-0.523485\pi\)
0.477159 + 0.878817i \(0.341666\pi\)
\(422\) −443.296 + 96.4332i −1.05047 + 0.228515i
\(423\) −284.835 + 106.238i −0.673368 + 0.251153i
\(424\) 13.4466 45.7948i 0.0317136 0.108007i
\(425\) −230.068 510.983i −0.541337 1.20231i
\(426\) 352.633 + 406.961i 0.827778 + 0.955307i
\(427\) −358.606 + 195.814i −0.839827 + 0.458580i
\(428\) 174.975 65.2621i 0.408819 0.152482i
\(429\) 716.396 1114.73i 1.66992 2.59845i
\(430\) 184.223 + 47.5444i 0.428425 + 0.110568i
\(431\) 13.6962 95.2591i 0.0317777 0.221019i −0.967744 0.251935i \(-0.918933\pi\)
0.999522 + 0.0309157i \(0.00984233\pi\)
\(432\) 260.137 + 97.0260i 0.602168 + 0.224597i
\(433\) −67.4095 + 90.0486i −0.155680 + 0.207964i −0.871600 0.490219i \(-0.836917\pi\)
0.715919 + 0.698183i \(0.246008\pi\)
\(434\) −90.3906 140.651i −0.208273 0.324080i
\(435\) −617.238 + 1224.90i −1.41894 + 2.81587i
\(436\) −227.912 −0.522734
\(437\) 34.7753 + 27.6889i 0.0795773 + 0.0633613i
\(438\) −765.223 765.223i −1.74709 1.74709i
\(439\) −337.277 292.252i −0.768284 0.665722i 0.179814 0.983701i \(-0.442450\pi\)
−0.948098 + 0.317979i \(0.896996\pi\)
\(440\) 117.533 + 110.015i 0.267121 + 0.250033i
\(441\) 104.339 + 725.695i 0.236597 + 1.64557i
\(442\) −625.450 233.281i −1.41504 0.527784i
\(443\) −95.5502 + 71.5280i −0.215689 + 0.161463i −0.701659 0.712513i \(-0.747557\pi\)
0.485970 + 0.873975i \(0.338466\pi\)
\(444\) −27.7799 94.6097i −0.0625674 0.213085i
\(445\) 58.3505 29.0136i 0.131125 0.0651991i
\(446\) −38.1091 + 83.4472i −0.0854463 + 0.187101i
\(447\) 114.626 62.5906i 0.256434 0.140024i
\(448\) −2.20957 + 30.8938i −0.00493208 + 0.0689595i
\(449\) 69.7654 60.4521i 0.155380 0.134637i −0.573702 0.819064i \(-0.694493\pi\)
0.729081 + 0.684427i \(0.239948\pi\)
\(450\) 415.463 638.945i 0.923252 1.41988i
\(451\) −60.2227 + 131.869i −0.133531 + 0.292393i
\(452\) 189.892 41.3085i 0.420115 0.0913905i
\(453\) 1072.48 + 585.620i 2.36751 + 1.29276i
\(454\) 360.360 + 51.8120i 0.793745 + 0.114123i
\(455\) 44.6563 405.182i 0.0981458 0.890510i
\(456\) 4.30044 + 29.9102i 0.00943079 + 0.0655926i
\(457\) 105.016 482.749i 0.229793 1.05634i −0.707205 0.707009i \(-0.750044\pi\)
0.936998 0.349334i \(-0.113592\pi\)
\(458\) 590.756 42.2517i 1.28986 0.0922526i
\(459\) 1555.88i 3.38971i
\(460\) 162.114 163.153i 0.352422 0.354681i
\(461\) 444.984 0.965258 0.482629 0.875825i \(-0.339682\pi\)
0.482629 + 0.875825i \(0.339682\pi\)
\(462\) −24.5791 343.660i −0.0532014 0.743853i
\(463\) 510.468 + 111.045i 1.10252 + 0.239839i 0.726770 0.686881i \(-0.241021\pi\)
0.375752 + 0.926720i \(0.377384\pi\)
\(464\) −196.486 + 28.2504i −0.423460 + 0.0608844i
\(465\) −658.570 + 527.815i −1.41628 + 1.13509i
\(466\) 0.308157 2.14328i 0.000661281 0.00459931i
\(467\) 98.7523 180.851i 0.211461 0.387262i −0.750323 0.661072i \(-0.770102\pi\)
0.961784 + 0.273810i \(0.0882838\pi\)
\(468\) −192.981 887.120i −0.412353 1.89556i
\(469\) −142.895 65.2580i −0.304680 0.139143i
\(470\) −73.1655 + 67.7557i −0.155671 + 0.144161i
\(471\) −173.015 199.669i −0.367335 0.423927i
\(472\) 41.9748 + 3.00210i 0.0889297 + 0.00636038i
\(473\) −146.792 268.829i −0.310342 0.568348i
\(474\) −410.604 187.517i −0.866253 0.395604i
\(475\) 48.1754 + 3.70428i 0.101422 + 0.00779847i
\(476\) −166.537 + 48.8997i −0.349868 + 0.102730i
\(477\) 217.991 + 291.202i 0.457004 + 0.610486i
\(478\) −37.8697 + 101.533i −0.0792254 + 0.212411i
\(479\) −232.774 + 33.4679i −0.485958 + 0.0698703i −0.380939 0.924600i \(-0.624399\pi\)
−0.105019 + 0.994470i \(0.533490\pi\)
\(480\) 156.265 5.16324i 0.325551 0.0107567i
\(481\) −122.991 + 141.939i −0.255698 + 0.295091i
\(482\) −354.613 + 354.613i −0.735712 + 0.735712i
\(483\) −491.807 + 20.4537i −1.01823 + 0.0423473i
\(484\) 17.1728i 0.0354809i
\(485\) −87.7391 + 174.117i −0.180905 + 0.359005i
\(486\) −504.212 + 324.037i −1.03747 + 0.666743i
\(487\) 4.50193 + 3.37010i 0.00924421 + 0.00692013i 0.603890 0.797068i \(-0.293617\pi\)
−0.594646 + 0.803988i \(0.702708\pi\)
\(488\) −104.313 + 279.675i −0.213757 + 0.573104i
\(489\) −18.8485 2.71000i −0.0385450 0.00554193i
\(490\) 122.163 + 207.154i 0.249313 + 0.422763i
\(491\) 753.546 + 484.275i 1.53472 + 0.986303i 0.988931 + 0.148378i \(0.0474053\pi\)
0.545786 + 0.837925i \(0.316231\pi\)
\(492\) 49.2021 + 131.916i 0.100004 + 0.268122i
\(493\) −533.119 976.335i −1.08138 1.98040i
\(494\) 43.4981 37.6913i 0.0880528 0.0762982i
\(495\) −1208.04 + 214.626i −2.44049 + 0.433587i
\(496\) −117.196 34.4118i −0.236282 0.0693785i
\(497\) −93.1964 249.869i −0.187518 0.502755i
\(498\) 158.495 + 728.588i 0.318262 + 1.46303i
\(499\) −116.590 397.068i −0.233646 0.795727i −0.989939 0.141493i \(-0.954810\pi\)
0.756293 0.654233i \(-0.227009\pi\)
\(500\) 46.3578 245.664i 0.0927155 0.491329i
\(501\) −387.684 848.910i −0.773821 1.69443i
\(502\) 190.379 + 142.516i 0.379240 + 0.283896i
\(503\) 518.705 + 112.837i 1.03122 + 0.224329i 0.696175 0.717872i \(-0.254884\pi\)
0.335048 + 0.942201i \(0.391247\pi\)
\(504\) −178.399 154.584i −0.353967 0.306714i
\(505\) −546.506 326.233i −1.08219 0.646006i
\(506\) −370.109 11.0454i −0.731440 0.0218289i
\(507\) −1072.67 + 1072.67i −2.11573 + 2.11573i
\(508\) −314.625 + 22.5024i −0.619340 + 0.0442961i
\(509\) 52.2262 + 81.2655i 0.102605 + 0.159657i 0.888760 0.458373i \(-0.151567\pi\)
−0.786155 + 0.618030i \(0.787931\pi\)
\(510\) 333.132 + 810.365i 0.653200 + 1.58895i
\(511\) 222.642 + 487.519i 0.435699 + 0.954048i
\(512\) 13.5601 + 18.1142i 0.0264846 + 0.0353793i
\(513\) −117.741 64.2912i −0.229514 0.125324i
\(514\) 33.1639 51.6041i 0.0645213 0.100397i
\(515\) −282.569 51.7605i −0.548677 0.100506i
\(516\) −285.420 83.8070i −0.553140 0.162417i
\(517\) 160.128 + 11.4526i 0.309726 + 0.0221520i
\(518\) −3.48373 + 48.7089i −0.00672534 + 0.0940325i
\(519\) −72.4767 + 246.833i −0.139647 + 0.475593i
\(520\) −169.189 245.073i −0.325364 0.471294i
\(521\) 221.276 + 142.206i 0.424715 + 0.272948i 0.735490 0.677536i \(-0.236952\pi\)
−0.310775 + 0.950484i \(0.600589\pi\)
\(522\) 725.055 1327.84i 1.38899 2.54375i
\(523\) 570.523 427.088i 1.09087 0.816612i 0.106776 0.994283i \(-0.465947\pi\)
0.984090 + 0.177671i \(0.0568563\pi\)
\(524\) 54.9059 25.0747i 0.104782 0.0478525i
\(525\) −430.024 + 318.343i −0.819094 + 0.606367i
\(526\) 244.075 156.857i 0.464020 0.298208i
\(527\) −48.8300 682.733i −0.0926566 1.29551i
\(528\) −177.983 177.983i −0.337088 0.337088i
\(529\) −31.5466 + 528.059i −0.0596343 + 0.998220i
\(530\) 102.454 + 61.1594i 0.193310 + 0.115395i
\(531\) −210.030 + 242.388i −0.395537 + 0.456474i
\(532\) 3.18110 14.6233i 0.00597951 0.0274874i
\(533\) 160.708 214.681i 0.301516 0.402779i
\(534\) −92.6793 + 42.3252i −0.173557 + 0.0792607i
\(535\) 48.6667 + 464.329i 0.0909658 + 0.867905i
\(536\) −110.115 + 32.3328i −0.205439 + 0.0603224i
\(537\) 406.637 88.4584i 0.757238 0.164727i
\(538\) −415.005 + 154.789i −0.771384 + 0.287711i
\(539\) 109.077 371.482i 0.202369 0.689206i
\(540\) −397.385 + 569.094i −0.735898 + 1.05388i
\(541\) −431.023 497.427i −0.796716 0.919459i 0.201481 0.979492i \(-0.435425\pi\)
−0.998196 + 0.0600337i \(0.980879\pi\)
\(542\) 127.725 69.7429i 0.235654 0.128677i
\(543\) −1691.19 + 630.780i −3.11453 + 1.16166i
\(544\) −68.5540 + 106.672i −0.126018 + 0.196089i
\(545\) 142.384 551.703i 0.261255 1.01230i
\(546\) −90.7026 + 630.850i −0.166122 + 1.15540i
\(547\) −452.817 168.892i −0.827820 0.308761i −0.100394 0.994948i \(-0.532010\pi\)
−0.727425 + 0.686187i \(0.759283\pi\)
\(548\) −119.088 + 159.082i −0.217313 + 0.290296i
\(549\) −1229.93 1913.81i −2.24032 3.48600i
\(550\) −339.737 + 215.781i −0.617704 + 0.392329i
\(551\) 95.9133 0.174071
\(552\) −261.751 + 246.581i −0.474187 + 0.446704i
\(553\) 158.075 + 158.075i 0.285851 + 0.285851i
\(554\) 10.2350 + 8.86869i 0.0184748 + 0.0160085i
\(555\) 246.375 8.14063i 0.443919 0.0146678i
\(556\) −70.7797 492.284i −0.127302 0.885402i
\(557\) −572.999 213.718i −1.02872 0.383694i −0.222266 0.974986i \(-0.571345\pi\)
−0.806458 + 0.591292i \(0.798618\pi\)
\(558\) 745.228 557.871i 1.33553 0.999768i
\(559\) 159.628 + 543.643i 0.285560 + 0.972528i
\(560\) −73.4038 24.6491i −0.131078 0.0440162i
\(561\) 585.954 1283.06i 1.04448 2.28710i
\(562\) 375.362 204.963i 0.667904 0.364703i
\(563\) 29.3526 410.403i 0.0521361 0.728957i −0.902407 0.430885i \(-0.858202\pi\)
0.954543 0.298073i \(-0.0963438\pi\)
\(564\) 117.830 102.100i 0.208919 0.181029i
\(565\) −18.6370 + 485.476i −0.0329858 + 0.859249i
\(566\) −118.567 + 259.627i −0.209483 + 0.458704i
\(567\) 717.575 156.099i 1.26556 0.275307i
\(568\) −170.997 93.3712i −0.301050 0.164386i
\(569\) −998.061 143.499i −1.75406 0.252196i −0.811055 0.584970i \(-0.801106\pi\)
−0.943006 + 0.332774i \(0.892015\pi\)
\(570\) −75.0898 8.27588i −0.131736 0.0145191i
\(571\) −65.0205 452.227i −0.113871 0.791992i −0.964093 0.265566i \(-0.914441\pi\)
0.850221 0.526425i \(-0.176468\pi\)
\(572\) −101.909 + 468.470i −0.178163 + 0.819003i
\(573\) 993.626 71.0655i 1.73408 0.124024i
\(574\) 69.7273i 0.121476i
\(575\) 293.665 + 494.354i 0.510721 + 0.859747i
\(576\) −172.453 −0.299398
\(577\) 41.0900 + 574.513i 0.0712131 + 0.995689i 0.899934 + 0.436027i \(0.143615\pi\)
−0.828721 + 0.559662i \(0.810931\pi\)
\(578\) −294.974 64.1678i −0.510336 0.111017i
\(579\) 16.8028 2.41587i 0.0290203 0.00417249i
\(580\) 54.3657 493.278i 0.0937340 0.850480i
\(581\) 52.5526 365.511i 0.0904520 0.629107i
\(582\) 146.095 267.554i 0.251023 0.459714i
\(583\) −40.8321 187.702i −0.0700379 0.321959i
\(584\) 356.161 + 162.653i 0.609865 + 0.278516i
\(585\) 2268.00 + 87.0664i 3.87692 + 0.148831i
\(586\) −353.825 408.336i −0.603797 0.696818i
\(587\) −72.1189 5.15805i −0.122860 0.00878713i 0.00977370 0.999952i \(-0.496889\pi\)
−0.132634 + 0.991165i \(0.542343\pi\)
\(588\) −180.202 330.016i −0.306466 0.561251i
\(589\) 53.6835 + 24.5164i 0.0911434 + 0.0416238i
\(590\) −33.4902 + 99.7323i −0.0567630 + 0.169038i
\(591\) 1294.52 380.106i 2.19039 0.643157i
\(592\) 21.3796 + 28.5598i 0.0361142 + 0.0482429i
\(593\) −137.847 + 369.581i −0.232456 + 0.623240i −0.999839 0.0179499i \(-0.994286\pi\)
0.767382 + 0.641190i \(0.221559\pi\)
\(594\) 1106.06 159.027i 1.86205 0.267722i
\(595\) −14.3296 433.683i −0.0240833 0.728878i
\(596\) −30.9439 + 35.7111i −0.0519192 + 0.0599180i
\(597\) −95.2101 + 95.2101i −0.159481 + 0.159481i
\(598\) 664.649 + 165.496i 1.11145 + 0.276749i
\(599\) 894.523i 1.49336i 0.665183 + 0.746680i \(0.268354\pi\)
−0.665183 + 0.746680i \(0.731646\pi\)
\(600\) −85.1250 + 381.493i −0.141875 + 0.635822i
\(601\) −573.339 + 368.463i −0.953976 + 0.613083i −0.922325 0.386416i \(-0.873713\pi\)
−0.0316511 + 0.999499i \(0.510077\pi\)
\(602\) 117.937 + 88.2863i 0.195908 + 0.146655i
\(603\) 305.664 819.518i 0.506906 1.35907i
\(604\) −437.612 62.9191i −0.724523 0.104171i
\(605\) 41.5698 + 10.7284i 0.0687105 + 0.0177329i
\(606\) 837.151 + 538.004i 1.38144 + 0.887796i
\(607\) 250.450 + 671.483i 0.412603 + 1.10623i 0.962567 + 0.271044i \(0.0873688\pi\)
−0.549964 + 0.835189i \(0.685358\pi\)
\(608\) −5.23964 9.59568i −0.00861783 0.0157824i
\(609\) −802.665 + 695.513i −1.31800 + 1.14206i
\(610\) −611.836 427.231i −1.00301 0.700379i
\(611\) −284.938 83.6652i −0.466346 0.136932i
\(612\) −337.725 905.475i −0.551837 1.47953i
\(613\) 117.387 + 539.617i 0.191495 + 0.880289i 0.968152 + 0.250365i \(0.0805506\pi\)
−0.776656 + 0.629925i \(0.783086\pi\)
\(614\) 26.0157 + 88.6014i 0.0423709 + 0.144302i
\(615\) −350.065 + 36.6905i −0.569211 + 0.0596594i
\(616\) 51.7841 + 113.391i 0.0840651 + 0.184077i
\(617\) 382.474 + 286.317i 0.619893 + 0.464046i 0.862485 0.506082i \(-0.168907\pi\)
−0.242592 + 0.970128i \(0.577998\pi\)
\(618\) 438.883 + 95.4731i 0.710166 + 0.154487i
\(619\) −661.052 572.805i −1.06794 0.925372i −0.0705413 0.997509i \(-0.522473\pi\)
−0.997395 + 0.0721371i \(0.977018\pi\)
\(620\) 156.516 262.195i 0.252445 0.422896i
\(621\) −179.959 1586.27i −0.289788 2.55438i
\(622\) 423.350 423.350i 0.680627 0.680627i
\(623\) 50.3305 3.59971i 0.0807873 0.00577802i
\(624\) 251.729 + 391.698i 0.403412 + 0.627721i
\(625\) 565.714 + 265.692i 0.905143 + 0.425107i
\(626\) −111.877 244.976i −0.178717 0.391336i
\(627\) 72.8829 + 97.3601i 0.116241 + 0.155279i
\(628\) 83.8971 + 45.8113i 0.133594 + 0.0729479i
\(629\) −108.086 + 168.185i −0.171838 + 0.267385i
\(630\) 485.651 335.275i 0.770874 0.532182i
\(631\) −1054.50 309.629i −1.67116 0.490696i −0.697095 0.716979i \(-0.745524\pi\)
−0.974062 + 0.226283i \(0.927343\pi\)
\(632\) 162.902 + 11.6510i 0.257757 + 0.0184351i
\(633\) −126.503 + 1768.74i −0.199846 + 2.79422i
\(634\) −51.9557 + 176.945i −0.0819490 + 0.279093i
\(635\) 142.085 775.665i 0.223756 1.22152i
\(636\) −156.942 100.861i −0.246764 0.158586i
\(637\) −343.233 + 628.585i −0.538828 + 0.986790i
\(638\) −639.576 + 478.781i −1.00247 + 0.750440i
\(639\) 1350.68 616.836i 2.11374 0.965315i
\(640\) −52.3201 + 21.5082i −0.0817502 + 0.0336066i
\(641\) −478.161 + 307.295i −0.745961 + 0.479400i −0.857580 0.514351i \(-0.828033\pi\)
0.111619 + 0.993751i \(0.464396\pi\)
\(642\) −52.0744 728.095i −0.0811128 1.13411i
\(643\) 163.557 + 163.557i 0.254366 + 0.254366i 0.822758 0.568392i \(-0.192434\pi\)
−0.568392 + 0.822758i \(0.692434\pi\)
\(644\) 164.134 69.1172i 0.254867 0.107325i
\(645\) 381.181 638.555i 0.590979 0.990008i
\(646\) 40.1216 46.3028i 0.0621077 0.0716762i
\(647\) −4.60265 + 21.1580i −0.00711383 + 0.0327017i −0.980567 0.196185i \(-0.937145\pi\)
0.973453 + 0.228886i \(0.0735084\pi\)
\(648\) 321.507 429.483i 0.496153 0.662783i
\(649\) 154.063 70.3580i 0.237385 0.108410i
\(650\) 698.942 256.448i 1.07530 0.394536i
\(651\) −627.038 + 184.115i −0.963192 + 0.282819i
\(652\) 6.73220 1.46450i 0.0103255 0.00224617i
\(653\) −147.088 + 54.8609i −0.225249 + 0.0840136i −0.459555 0.888149i \(-0.651991\pi\)
0.234306 + 0.972163i \(0.424718\pi\)
\(654\) −250.982 + 854.765i −0.383764 + 1.30698i
\(655\) 26.3964 + 148.575i 0.0402998 + 0.226832i
\(656\) −33.3585 38.4978i −0.0508514 0.0586857i
\(657\) −2619.10 + 1430.14i −3.98645 + 2.17677i
\(658\) −72.3464 + 26.9838i −0.109949 + 0.0410088i
\(659\) 590.898 919.455i 0.896658 1.39523i −0.0218228 0.999762i \(-0.506947\pi\)
0.918481 0.395465i \(-0.129417\pi\)
\(660\) 542.031 319.648i 0.821259 0.484315i
\(661\) −34.1898 + 237.795i −0.0517244 + 0.359751i 0.947478 + 0.319821i \(0.103623\pi\)
−0.999202 + 0.0399303i \(0.987286\pi\)
\(662\) 300.024 + 111.903i 0.453208 + 0.169038i
\(663\) −1563.66 + 2088.80i −2.35846 + 3.15053i
\(664\) −145.851 226.948i −0.219654 0.341789i
\(665\) 33.4110 + 16.8361i 0.0502421 + 0.0253174i
\(666\) −271.898 −0.408256
\(667\) 656.460 + 933.744i 0.984198 + 1.39992i
\(668\) 238.758 + 238.758i 0.357423 + 0.357423i
\(669\) 270.995 + 234.819i 0.405075 + 0.351000i
\(670\) −9.47482 286.754i −0.0141415 0.427991i
\(671\) 170.971 + 1189.13i 0.254800 + 1.77217i
\(672\) 113.432 + 42.3078i 0.168797 + 0.0629580i
\(673\) 41.1748 30.8231i 0.0611809 0.0457995i −0.568250 0.822856i \(-0.692379\pi\)
0.629430 + 0.777057i \(0.283288\pi\)
\(674\) 266.055 + 906.099i 0.394740 + 1.34436i
\(675\) −1129.34 1317.47i −1.67309 1.95181i
\(676\) 228.004 499.258i 0.337284 0.738548i
\(677\) 169.277 92.4321i 0.250040 0.136532i −0.349342 0.936995i \(-0.613595\pi\)
0.599382 + 0.800463i \(0.295413\pi\)
\(678\) 54.1892 757.664i 0.0799251 1.11750i
\(679\) −114.097 + 98.8658i −0.168037 + 0.145605i
\(680\) −215.392 232.589i −0.316752 0.342043i
\(681\) 591.153 1294.45i 0.868067 1.90080i
\(682\) −480.357 + 104.495i −0.704336 + 0.153219i
\(683\) −492.969 269.181i −0.721770 0.394116i 0.0759760 0.997110i \(-0.475793\pi\)
−0.797746 + 0.602993i \(0.793975\pi\)
\(684\) 82.4770 + 11.8584i 0.120580 + 0.0173368i
\(685\) −310.690 387.657i −0.453562 0.565923i
\(686\) 64.6829 + 449.879i 0.0942899 + 0.655801i
\(687\) 492.091 2262.11i 0.716290 3.29273i
\(688\) 107.353 7.67801i 0.156036 0.0111599i
\(689\) 355.338i 0.515730i
\(690\) −433.369 787.664i −0.628071 1.14154i
\(691\) 729.215 1.05530 0.527652 0.849461i \(-0.323072\pi\)
0.527652 + 0.849461i \(0.323072\pi\)
\(692\) −6.63998 92.8391i −0.00959535 0.134161i
\(693\) −928.346 201.949i −1.33961 0.291413i
\(694\) 54.2275 7.79674i 0.0781376 0.0112345i
\(695\) 1235.88 + 136.210i 1.77825 + 0.195986i
\(696\) −110.424 + 768.013i −0.158655 + 1.10347i
\(697\) 136.807 250.544i 0.196280 0.359460i
\(698\) 48.6799 + 223.778i 0.0697420 + 0.320599i
\(699\) −7.69883 3.51594i −0.0110141 0.00502996i
\(700\) 105.525 162.288i 0.150750 0.231840i
\(701\) −276.810 319.456i −0.394879 0.455714i 0.523143 0.852245i \(-0.324759\pi\)
−0.918021 + 0.396531i \(0.870214\pi\)
\(702\) −2061.79 147.462i −2.93702 0.210060i
\(703\) −8.26109 15.1291i −0.0117512 0.0215207i
\(704\) 82.8391 + 37.8314i 0.117669 + 0.0537377i
\(705\) 173.541 + 349.015i 0.246157 + 0.495057i
\(706\) −159.865 + 46.9405i −0.226437 + 0.0664880i
\(707\) −295.343 394.532i −0.417742 0.558037i
\(708\) 57.4827 154.117i 0.0811903 0.217680i
\(709\) 798.393 114.792i 1.12608 0.161906i 0.445994 0.895036i \(-0.352850\pi\)
0.680089 + 0.733129i \(0.261941\pi\)
\(710\) 332.849 355.597i 0.468802 0.500841i
\(711\) −815.116 + 940.694i −1.14644 + 1.32306i
\(712\) 26.0663 26.0663i 0.0366100 0.0366100i
\(713\) 128.751 + 690.422i 0.180577 + 0.968333i
\(714\) 678.433i 0.950186i
\(715\) −1070.35 539.358i −1.49699 0.754348i
\(716\) −126.663 + 81.4016i −0.176904 + 0.113689i
\(717\) 339.087 + 253.837i 0.472924 + 0.354027i
\(718\) −102.777 + 275.555i −0.143143 + 0.383782i
\(719\) 1281.79 + 184.293i 1.78273 + 0.256318i 0.953244 0.302202i \(-0.0977219\pi\)
0.829490 + 0.558521i \(0.188631\pi\)
\(720\) 107.737 417.454i 0.149635 0.579797i
\(721\) −187.127 120.260i −0.259539 0.166795i
\(722\) −176.566 473.392i −0.244552 0.655668i
\(723\) 939.439 + 1720.45i 1.29936 + 2.37960i
\(724\) 493.549 427.663i 0.681698 0.590695i
\(725\) 1160.11 + 439.769i 1.60015 + 0.606578i
\(726\) −64.4050 18.9110i −0.0887121 0.0260482i
\(727\) −335.622 899.838i −0.461654 1.23774i −0.934299 0.356489i \(-0.883974\pi\)
0.472646 0.881253i \(-0.343299\pi\)
\(728\) −49.0161 225.324i −0.0673299 0.309510i
\(729\) 179.079 + 609.885i 0.245650 + 0.836605i
\(730\) −616.237 + 760.538i −0.844161 + 1.04183i
\(731\) 250.549 + 548.625i 0.342748 + 0.750513i
\(732\) 934.025 + 699.202i 1.27599 + 0.955194i
\(733\) −399.137 86.8269i −0.544525 0.118454i −0.0681150 0.997677i \(-0.521698\pi\)
−0.476410 + 0.879223i \(0.658062\pi\)
\(734\) −601.397 521.113i −0.819342 0.709964i
\(735\) 911.442 230.041i 1.24006 0.312981i
\(736\) 57.5551 116.685i 0.0781998 0.158540i
\(737\) −326.608 + 326.608i −0.443158 + 0.443158i
\(738\) 387.245 27.6963i 0.524722 0.0375289i
\(739\) −469.242 730.155i −0.634969 0.988031i −0.998408 0.0564129i \(-0.982034\pi\)
0.363438 0.931618i \(-0.381603\pi\)
\(740\) −82.4907 + 33.9110i −0.111474 + 0.0458256i
\(741\) −93.4570 204.642i −0.126123 0.276170i
\(742\) 55.3685 + 73.9636i 0.0746206 + 0.0996815i
\(743\) −593.151 323.885i −0.798320 0.435915i 0.0276587 0.999617i \(-0.491195\pi\)
−0.825978 + 0.563702i \(0.809377\pi\)
\(744\) −258.117 + 401.638i −0.346931 + 0.539835i
\(745\) −67.1137 97.2152i −0.0900855 0.130490i
\(746\) 424.125 + 124.534i 0.568532 + 0.166936i
\(747\) 2050.82 + 146.677i 2.74540 + 0.196355i
\(748\) −36.4072 + 509.039i −0.0486727 + 0.680533i
\(749\) −101.849 + 346.865i −0.135980 + 0.463104i
\(750\) −870.293 444.392i −1.16039 0.592522i
\(751\) 64.6339 + 41.5377i 0.0860638 + 0.0553098i 0.582965 0.812497i \(-0.301892\pi\)
−0.496901 + 0.867807i \(0.665529\pi\)
\(752\) −27.0344 + 49.5099i −0.0359500 + 0.0658376i
\(753\) 744.142 557.058i 0.988237 0.739785i
\(754\) 1344.33 613.936i 1.78293 0.814239i
\(755\) 425.698 1020.01i 0.563838 1.35101i
\(756\) −452.139 + 290.572i −0.598068 + 0.384355i
\(757\) 0.235016 + 3.28595i 0.000310457 + 0.00434075i 0.997605 0.0691686i \(-0.0220347\pi\)
−0.997295 + 0.0735094i \(0.976580\pi\)
\(758\) −633.702 633.702i −0.836019 0.836019i
\(759\) −448.997 + 1375.90i −0.591563 + 1.81278i
\(760\) 26.5015 6.68877i 0.0348704 0.00880102i
\(761\) −178.186 + 205.638i −0.234147 + 0.270220i −0.860648 0.509201i \(-0.829941\pi\)
0.626501 + 0.779421i \(0.284487\pi\)
\(762\) −262.078 + 1204.75i −0.343935 + 1.58104i
\(763\) 264.396 353.192i 0.346522 0.462899i
\(764\) −327.849 + 149.724i −0.429122 + 0.195973i
\(765\) 2402.85 251.845i 3.14099 0.329209i
\(766\) −634.538 + 186.317i −0.828379 + 0.243234i
\(767\) −306.143 + 66.5972i −0.399143 + 0.0868282i
\(768\) 82.8684 30.9083i 0.107902 0.0402452i
\(769\) −104.376 + 355.473i −0.135730 + 0.462254i −0.999105 0.0423098i \(-0.986528\pi\)
0.863375 + 0.504563i \(0.168347\pi\)
\(770\) −306.836 + 54.5137i −0.398488 + 0.0707970i
\(771\) −157.016 181.206i −0.203652 0.235027i
\(772\) −5.39060 + 2.94349i −0.00698264 + 0.00381281i
\(773\) −1347.88 + 502.732i −1.74369 + 0.650364i −0.999838 0.0179753i \(-0.994278\pi\)
−0.743856 + 0.668340i \(0.767005\pi\)
\(774\) −443.471 + 690.054i −0.572960 + 0.891542i
\(775\) 536.912 + 542.678i 0.692789 + 0.700229i
\(776\) −15.6965 + 109.171i −0.0202274 + 0.140685i
\(777\) 178.842 + 66.7047i 0.230170 + 0.0858490i
\(778\) 212.890 284.387i 0.273637 0.365537i
\(779\) 13.3068 + 20.7057i 0.0170818 + 0.0265799i
\(780\) −1105.44 + 364.650i −1.41723 + 0.467500i
\(781\) −784.127 −1.00400
\(782\) 725.375 + 73.6851i 0.927590 + 0.0942264i
\(783\) −2435.70 2435.70i −3.11073 3.11073i
\(784\) 102.814 + 89.0892i 0.131141 + 0.113634i
\(785\) −163.308 + 174.468i −0.208035 + 0.222253i
\(786\) −33.5770 233.533i −0.0427188 0.297116i
\(787\) 783.643 + 292.284i 0.995734 + 0.371390i 0.793912 0.608033i \(-0.208041\pi\)
0.201822 + 0.979422i \(0.435314\pi\)
\(788\) −390.777 + 292.532i −0.495909 + 0.371233i
\(789\) −319.500 1088.12i −0.404943 1.37911i
\(790\) −129.974 + 387.056i −0.164524 + 0.489944i
\(791\) −156.275 + 342.194i −0.197566 + 0.432610i
\(792\) −609.174 + 332.634i −0.769159 + 0.419992i
\(793\) 158.538 2216.64i 0.199921 2.79526i
\(794\) 456.392 395.466i 0.574802 0.498068i
\(795\) 342.198 316.896i 0.430438 0.398612i
\(796\) 20.2375 44.3140i 0.0254240 0.0556709i
\(797\) −1119.12 + 243.450i −1.40417 + 0.305458i −0.849927 0.526900i \(-0.823354\pi\)
−0.554239 + 0.832358i \(0.686991\pi\)
\(798\) −51.3403 28.0339i −0.0643362 0.0351302i
\(799\) −312.898 44.9879i −0.391611 0.0563052i
\(800\) −19.3785 140.087i −0.0242231 0.175109i
\(801\) 39.9834 + 278.091i 0.0499169 + 0.347180i
\(802\) −214.716 + 987.033i −0.267726 + 1.23071i
\(803\) 1571.84 112.420i 1.95746 0.140000i
\(804\) 448.584i 0.557941i
\(805\) 64.7709 + 440.497i 0.0804607 + 0.547201i
\(806\) 909.362 1.12824
\(807\) 123.510 + 1726.90i 0.153048 + 2.13990i
\(808\) −351.815 76.5326i −0.435414 0.0947186i
\(809\) −493.537 + 70.9598i −0.610058 + 0.0877130i −0.440418 0.897793i \(-0.645170\pi\)
−0.169640 + 0.985506i \(0.554260\pi\)
\(810\) 838.788 + 1046.58i 1.03554 + 1.29207i
\(811\) 167.783 1166.96i 0.206884 1.43891i −0.576359 0.817197i \(-0.695527\pi\)
0.783243 0.621716i \(-0.213564\pi\)
\(812\) 184.160 337.264i 0.226798 0.415349i
\(813\) −120.912 555.823i −0.148723 0.683669i
\(814\) 130.609 + 59.6469i 0.160453 + 0.0732763i
\(815\) −0.660732 + 17.2114i −0.000810714 + 0.0211183i
\(816\) 324.572 + 374.576i 0.397760 + 0.459039i
\(817\) −51.8701 3.70983i −0.0634886 0.00454079i
\(818\) 246.285 + 451.038i 0.301082 + 0.551391i
\(819\) 1598.63 + 730.070i 1.95193 + 0.891417i
\(820\) 114.031 56.6997i 0.139062 0.0691459i
\(821\) 857.050 251.652i 1.04391 0.306519i 0.285555 0.958362i \(-0.407822\pi\)
0.758354 + 0.651843i \(0.226004\pi\)
\(822\) 465.483 + 621.813i 0.566281 + 0.756463i
\(823\) −153.068 + 410.392i −0.185988 + 0.498654i −0.996161 0.0875369i \(-0.972100\pi\)
0.810173 + 0.586191i \(0.199373\pi\)
\(824\) −160.851 + 23.1268i −0.195207 + 0.0280665i
\(825\) 435.142 + 1511.78i 0.527445 + 1.83246i
\(826\) −53.3465 + 61.5651i −0.0645841 + 0.0745340i
\(827\) −676.950 + 676.950i −0.818561 + 0.818561i −0.985899 0.167339i \(-0.946483\pi\)
0.167339 + 0.985899i \(0.446483\pi\)
\(828\) 449.052 + 884.099i 0.542334 + 1.06775i
\(829\) 841.928i 1.01559i 0.861477 + 0.507797i \(0.169540\pi\)
−0.861477 + 0.507797i \(0.830460\pi\)
\(830\) 640.487 211.276i 0.771671 0.254550i
\(831\) 44.5323 28.6192i 0.0535888 0.0344394i
\(832\) −134.861 100.956i −0.162092 0.121341i
\(833\) −266.421 + 714.302i −0.319833 + 0.857505i
\(834\) −1924.21 276.660i −2.30721 0.331727i
\(835\) −727.118 + 428.798i −0.870800 + 0.513531i
\(836\) −37.0170 23.7894i −0.0442788 0.0284562i
\(837\) −740.692 1985.87i −0.884937 2.37261i
\(838\) 136.209 + 249.449i 0.162541 + 0.297672i
\(839\) −510.781 + 442.594i −0.608797 + 0.527526i −0.903791 0.427973i \(-0.859228\pi\)
0.294994 + 0.955499i \(0.404682\pi\)
\(840\) −173.278 + 248.151i −0.206283 + 0.295418i
\(841\) 1556.10 + 456.912i 1.85030 + 0.543296i
\(842\) 87.4872 + 234.562i 0.103904 + 0.278578i
\(843\) −355.340 1633.47i −0.421519 1.93769i
\(844\) −180.753 615.589i −0.214163 0.729371i
\(845\) 1066.11 + 863.828i 1.26166 + 1.02228i
\(846\) −178.597 391.073i −0.211107 0.462261i
\(847\) 26.6124 + 19.9218i 0.0314196 + 0.0235204i
\(848\) 65.9553 + 14.3477i 0.0777775 + 0.0169195i
\(849\) 843.139 + 730.584i 0.993096 + 0.860523i
\(850\) 697.587 376.089i 0.820691 0.442458i
\(851\) 90.7443 183.972i 0.106633 0.216183i
\(852\) −538.486 + 538.486i −0.632026 + 0.632026i
\(853\) 798.631 57.1192i 0.936261 0.0669627i 0.405136 0.914256i \(-0.367224\pi\)
0.531125 + 0.847293i \(0.321769\pi\)
\(854\) −312.396 486.098i −0.365803 0.569201i
\(855\) −80.2315 + 192.242i −0.0938380 + 0.224845i
\(856\) 109.712 + 240.237i 0.128169 + 0.280650i
\(857\) 272.381 + 363.858i 0.317831 + 0.424572i 0.930797 0.365537i \(-0.119115\pi\)
−0.612966 + 0.790109i \(0.710024\pi\)
\(858\) 1644.73 + 898.091i 1.91694 + 1.04673i
\(859\) −70.3512 + 109.469i −0.0818990 + 0.127437i −0.879786 0.475369i \(-0.842315\pi\)
0.797887 + 0.602806i \(0.205951\pi\)
\(860\) −48.4806 + 264.663i −0.0563728 + 0.307748i
\(861\) −261.506 76.7852i −0.303724 0.0891814i
\(862\) 135.755 + 9.70941i 0.157489 + 0.0112638i
\(863\) 97.3529 1361.17i 0.112807 1.57725i −0.554315 0.832307i \(-0.687020\pi\)
0.667123 0.744948i \(-0.267526\pi\)
\(864\) −110.621 + 376.740i −0.128034 + 0.436042i
\(865\) 228.882 + 41.9263i 0.264604 + 0.0484697i
\(866\) −133.824 86.0037i −0.154532 0.0993114i
\(867\) −565.488 + 1035.61i −0.652235 + 1.19448i
\(868\) 189.284 141.696i 0.218069 0.163244i
\(869\) 597.909 273.056i 0.688043 0.314219i
\(870\) −1790.13 747.103i −2.05762 0.858739i
\(871\) 718.787 461.937i 0.825244 0.530352i
\(872\) −22.9938 321.495i −0.0263690 0.368687i
\(873\) −594.392 594.392i −0.680861 0.680861i
\(874\) −35.5498 + 51.8479i −0.0406748 + 0.0593225i
\(875\) 326.924 + 356.830i 0.373627 + 0.407806i
\(876\) 1002.23 1156.63i 1.14410 1.32036i
\(877\) 4.32742 19.8928i 0.00493434 0.0226828i −0.974614 0.223892i \(-0.928124\pi\)
0.979548 + 0.201210i \(0.0644872\pi\)
\(878\) 378.226 505.251i 0.430781 0.575457i
\(879\) −1921.07 + 877.322i −2.18552 + 0.998091i
\(880\) −143.330 + 176.893i −0.162875 + 0.201015i
\(881\) −569.055 + 167.090i −0.645919 + 0.189659i −0.588253 0.808677i \(-0.700184\pi\)
−0.0576663 + 0.998336i \(0.518366\pi\)
\(882\) −1013.15 + 220.396i −1.14869 + 0.249882i
\(883\) 236.892 88.3562i 0.268281 0.100064i −0.211724 0.977330i \(-0.567908\pi\)
0.480005 + 0.877266i \(0.340635\pi\)
\(884\) 265.967 905.801i 0.300868 1.02466i
\(885\) 337.157 + 235.429i 0.380969 + 0.266022i
\(886\) −110.538 127.568i −0.124761 0.143982i
\(887\) 528.570 288.621i 0.595907 0.325390i −0.152835 0.988252i \(-0.548840\pi\)
0.748742 + 0.662862i \(0.230658\pi\)
\(888\) 130.655 48.7317i 0.147134 0.0548780i
\(889\) 330.118 513.674i 0.371337 0.577811i
\(890\) 46.8138 + 79.3827i 0.0525998 + 0.0891941i
\(891\) 307.289 2137.24i 0.344882 2.39870i
\(892\) −121.556 45.3381i −0.136274 0.0508275i
\(893\) 16.3339 21.8195i 0.0182910 0.0244339i
\(894\) 99.8555 + 155.378i 0.111695 + 0.173801i
\(895\) −117.917 357.466i −0.131751 0.399403i
\(896\) −43.8021 −0.0488863
\(897\) 1352.60 2310.46i 1.50792 2.57577i
\(898\) 92.3129 + 92.3129i 0.102798 + 0.102798i
\(899\) 1145.25 + 992.368i 1.27392 + 1.10386i
\(900\) 943.218 + 521.594i 1.04802 + 0.579549i
\(901\) 53.8306 + 374.400i 0.0597454 + 0.415538i
\(902\) −192.092 71.6466i −0.212962 0.0794308i
\(903\) 460.985 345.089i 0.510504 0.382158i
\(904\) 77.4282 + 263.696i 0.0856507 + 0.291699i
\(905\) 726.901 + 1461.90i 0.803205 + 1.61536i
\(906\) −717.880 + 1571.94i −0.792363 + 1.73503i
\(907\) 1293.10 706.086i 1.42569 0.778486i 0.433257 0.901271i \(-0.357364\pi\)
0.992433 + 0.122785i \(0.0391826\pi\)
\(908\) −36.7302 + 513.555i −0.0404518 + 0.565590i
\(909\) 2073.80 1796.96i 2.28141 1.97686i
\(910\) 576.059 + 22.1144i 0.633032 + 0.0243015i
\(911\) −16.9504 + 37.1162i −0.0186064 + 0.0407423i −0.918707 0.394940i \(-0.870765\pi\)
0.900101 + 0.435682i \(0.143493\pi\)
\(912\) −41.7578 + 9.08385i −0.0457871 + 0.00996036i
\(913\) −952.949 520.349i −1.04376 0.569934i
\(914\) 691.565 + 99.4321i 0.756636 + 0.108788i
\(915\) −2276.06 + 1824.16i −2.48750 + 1.99362i
\(916\) 119.201 + 829.063i 0.130132 + 0.905091i
\(917\) −24.8374 + 114.176i −0.0270855 + 0.124510i
\(918\) −2194.73 + 156.970i −2.39078 + 0.170992i
\(919\) 568.151i 0.618227i −0.951025 0.309113i \(-0.899968\pi\)
0.951025 0.309113i \(-0.100032\pi\)
\(920\) 246.501 + 212.220i 0.267936 + 0.230673i
\(921\) 360.941 0.391901
\(922\) 44.8939 + 627.699i 0.0486919 + 0.680801i
\(923\) 1417.36 + 308.327i 1.53560 + 0.334049i
\(924\) 482.291 69.3429i 0.521960 0.0750465i
\(925\) −30.5531 220.869i −0.0330304 0.238777i
\(926\) −105.141 + 731.274i −0.113544 + 0.789713i
\(927\) 593.557 1087.02i 0.640299 1.17262i
\(928\) −59.6735 274.315i −0.0643033 0.295598i
\(929\) −333.466 152.289i −0.358951 0.163928i 0.227773 0.973714i \(-0.426856\pi\)
−0.586724 + 0.809787i \(0.699583\pi\)
\(930\) −810.984 875.735i −0.872025 0.941651i
\(931\) −43.0458 49.6775i −0.0462360 0.0533592i
\(932\) 3.05442 + 0.218456i 0.00327727 + 0.000234395i
\(933\) −1121.54 2053.94i −1.20208 2.20144i
\(934\) 265.074 + 121.055i 0.283805 + 0.129609i
\(935\) −1209.48 406.143i −1.29356 0.434378i
\(936\) 1231.91 361.722i 1.31614 0.386455i
\(937\) −248.645 332.151i −0.265363 0.354483i 0.647992 0.761647i \(-0.275609\pi\)
−0.913355 + 0.407164i \(0.866518\pi\)
\(938\) 77.6370 208.153i 0.0827687 0.221911i
\(939\) −1041.96 + 149.812i −1.10965 + 0.159544i
\(940\) −102.958 96.3722i −0.109530 0.102524i
\(941\) −953.900 + 1100.86i −1.01371 + 1.16988i −0.0283135 + 0.999599i \(0.509014\pi\)
−0.985395 + 0.170283i \(0.945532\pi\)
\(942\) 264.201 264.201i 0.280468 0.280468i
\(943\) −110.501 + 271.261i −0.117180 + 0.287658i
\(944\) 59.5130i 0.0630434i
\(945\) −420.917 1276.02i −0.445415 1.35028i
\(946\) 364.403 234.188i 0.385204 0.247556i
\(947\) −276.704 207.138i −0.292191 0.218731i 0.443118 0.896463i \(-0.353872\pi\)
−0.735309 + 0.677732i \(0.762963\pi\)
\(948\) 223.087 598.120i 0.235324 0.630929i
\(949\) −2885.39 414.856i −3.04045 0.437151i
\(950\) −0.364932 + 68.3304i −0.000384139 + 0.0719267i
\(951\) 606.402 + 389.711i 0.637647 + 0.409791i
\(952\) −85.7801 229.985i −0.0901052 0.241581i
\(953\) 501.171 + 917.827i 0.525888 + 0.963092i 0.996725 + 0.0808714i \(0.0257703\pi\)
−0.470837 + 0.882220i \(0.656048\pi\)
\(954\) −388.780 + 336.879i −0.407526 + 0.353123i
\(955\) −157.616 887.156i −0.165043 0.928959i
\(956\) −147.044 43.1759i −0.153811 0.0451631i
\(957\) 1091.31 + 2925.92i 1.14035 + 3.05739i
\(958\) −70.6944 324.977i −0.0737937 0.339224i
\(959\) −108.376 369.096i −0.113010 0.384876i
\(960\) 23.0487 + 219.908i 0.0240090 + 0.229070i
\(961\) −11.8655 25.9818i −0.0123470 0.0270362i
\(962\) −212.629 159.172i −0.221028 0.165459i
\(963\) −1966.84 427.860i −2.04241 0.444299i
\(964\) −535.997 464.444i −0.556014 0.481789i
\(965\) −3.75758 14.8878i −0.00389386 0.0154278i
\(966\) −78.4701 691.685i −0.0812320 0.716030i
\(967\) −722.895 + 722.895i −0.747565 + 0.747565i −0.974021 0.226456i \(-0.927286\pi\)
0.226456 + 0.974021i \(0.427286\pi\)
\(968\) 24.2241 1.73254i 0.0250249 0.00178981i
\(969\) −129.472 201.462i −0.133614 0.207907i
\(970\) −254.463 106.199i −0.262333 0.109484i
\(971\) 268.436 + 587.792i 0.276453 + 0.605348i 0.996025 0.0890699i \(-0.0283894\pi\)
−0.719572 + 0.694417i \(0.755662\pi\)
\(972\) −507.960 678.555i −0.522592 0.698101i
\(973\) 844.995 + 461.402i 0.868443 + 0.474206i
\(974\) −4.29971 + 6.69048i −0.00441449 + 0.00686907i
\(975\) −192.098 2903.73i −0.197023 2.97819i
\(976\) −405.036 118.929i −0.414996 0.121854i
\(977\) −1328.46 95.0136i −1.35974 0.0972503i −0.627668 0.778481i \(-0.715991\pi\)
−0.732069 + 0.681230i \(0.761445\pi\)
\(978\) 1.92116 26.8613i 0.00196437 0.0274655i
\(979\) 41.7990 142.354i 0.0426956 0.145408i
\(980\) −279.888 + 193.224i −0.285600 + 0.197168i
\(981\) 2066.55 + 1328.09i 2.10657 + 1.35381i
\(982\) −607.098 + 1111.82i −0.618226 + 1.13220i
\(983\) −1413.26 + 1057.95i −1.43770 + 1.07625i −0.455118 + 0.890431i \(0.650403\pi\)
−0.982584 + 0.185819i \(0.940506\pi\)
\(984\) −181.118 + 82.7138i −0.184063 + 0.0840588i
\(985\) −463.996 1128.70i −0.471062 1.14589i
\(986\) 1323.44 850.525i 1.34223 0.862601i
\(987\) 21.5311 + 301.044i 0.0218147 + 0.305010i
\(988\) 57.5562 + 57.5562i 0.0582553 + 0.0582553i
\(989\) −318.899 530.362i −0.322446 0.536261i
\(990\) −424.631 1682.42i −0.428920 1.69942i
\(991\) −1187.72 + 1370.70i −1.19851 + 1.38315i −0.294487 + 0.955656i \(0.595149\pi\)
−0.904019 + 0.427493i \(0.859397\pi\)
\(992\) 36.7178 168.789i 0.0370139 0.170150i
\(993\) 750.075 1001.98i 0.755363 1.00905i
\(994\) 343.066 156.673i 0.345137 0.157619i
\(995\) 94.6272 + 76.6731i 0.0951027 + 0.0770584i
\(996\) −1011.76 + 297.080i −1.01583 + 0.298273i
\(997\) 174.560 37.9733i 0.175086 0.0380875i −0.124168 0.992261i \(-0.539626\pi\)
0.299253 + 0.954174i \(0.403262\pi\)
\(998\) 548.345 204.522i 0.549444 0.204932i
\(999\) −174.411 + 593.989i −0.174585 + 0.594584i
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 230.3.k.a.223.12 yes 240
5.2 odd 4 inner 230.3.k.a.177.12 yes 240
23.13 even 11 inner 230.3.k.a.13.12 240
115.82 odd 44 inner 230.3.k.a.197.12 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.3.k.a.13.12 240 23.13 even 11 inner
230.3.k.a.177.12 yes 240 5.2 odd 4 inner
230.3.k.a.197.12 yes 240 115.82 odd 44 inner
230.3.k.a.223.12 yes 240 1.1 even 1 trivial