Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(211,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.j (of order \(3\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.3 | ||
Root | \(2.33086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.211 |
Dual form | 630.2.j.l.421.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.657430 | − | 1.60243i | −0.379567 | − | 0.925164i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −1.05903 | + | 1.37057i | −0.432348 | + | 0.559531i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.13557 | + | 2.10697i | −0.711857 | + | 0.702324i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.37389 | − | 2.37965i | −0.414244 | − | 0.717491i | 0.581105 | − | 0.813829i | \(-0.302621\pi\) |
−0.995349 | + | 0.0963374i | \(0.969287\pi\) | |||||||
\(12\) | 1.71646 | + | 0.231865i | 0.495500 | + | 0.0669335i | ||||
\(13\) | 2.01859 | − | 3.49629i | 0.559855 | − | 0.969698i | −0.437653 | − | 0.899144i | \(-0.644190\pi\) |
0.997508 | − | 0.0705536i | \(-0.0224766\pi\) | |||||||
\(14\) | 0.500000 | − | 0.866025i | 0.133631 | − | 0.231455i | ||||
\(15\) | −1.71646 | − | 0.231865i | −0.443188 | − | 0.0598672i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −7.58816 | −1.84040 | −0.920199 | − | 0.391450i | \(-0.871974\pi\) | ||||
−0.920199 | + | 0.391450i | \(0.871974\pi\) | |||||||
\(18\) | 2.89248 | + | 0.795973i | 0.681764 | + | 0.187613i | ||||
\(19\) | −4.27114 | −0.979868 | −0.489934 | − | 0.871760i | \(-0.662979\pi\) | ||||
−0.489934 | + | 0.871760i | \(0.662979\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | 1.05903 | − | 1.37057i | 0.231100 | − | 0.299082i | ||||
\(22\) | −1.37389 | + | 2.37965i | −0.292915 | + | 0.507343i | ||||
\(23\) | 0.873891 | − | 1.51362i | 0.182219 | − | 0.315612i | −0.760417 | − | 0.649435i | \(-0.775005\pi\) |
0.942636 | + | 0.333823i | \(0.108339\pi\) | |||||||
\(24\) | −0.657430 | − | 1.60243i | −0.134197 | − | 0.327095i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −4.03717 | −0.791755 | ||||||||
\(27\) | 4.78027 | + | 2.03692i | 0.919963 | + | 0.392005i | ||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −4.67709 | − | 8.10096i | −0.868514 | − | 1.50431i | −0.863515 | − | 0.504324i | \(-0.831742\pi\) |
−0.00499981 | − | 0.999988i | \(-0.501591\pi\) | |||||||
\(30\) | 0.657430 | + | 1.60243i | 0.120030 | + | 0.292563i | ||||
\(31\) | −5.27114 | + | 9.12989i | −0.946725 | + | 1.63978i | −0.194466 | + | 0.980909i | \(0.562297\pi\) |
−0.752259 | + | 0.658867i | \(0.771036\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.90999 | + | 3.76602i | −0.506564 | + | 0.655580i | ||||
\(34\) | 3.79408 | + | 6.57154i | 0.650679 | + | 1.12701i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −0.756906 | − | 2.90295i | −0.126151 | − | 0.483824i | ||||
\(37\) | 7.30832 | 1.20148 | 0.600740 | − | 0.799445i | \(-0.294873\pi\) | ||||
0.600740 | + | 0.799445i | \(0.294873\pi\) | |||||||
\(38\) | 2.13557 | + | 3.69892i | 0.346435 | + | 0.600044i | ||||
\(39\) | −6.92965 | − | 0.936078i | −1.10963 | − | 0.149892i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −1.51859 | + | 2.63027i | −0.237163 | + | 0.410779i | −0.959899 | − | 0.280345i | \(-0.909551\pi\) |
0.722736 | + | 0.691124i | \(0.242884\pi\) | |||||||
\(42\) | −1.71646 | − | 0.231865i | −0.264856 | − | 0.0357775i | ||||
\(43\) | 0.644696 | + | 1.11665i | 0.0983151 | + | 0.170287i | 0.910987 | − | 0.412434i | \(-0.135321\pi\) |
−0.812672 | + | 0.582721i | \(0.801988\pi\) | |||||||
\(44\) | 2.74778 | 0.414244 | ||||||||
\(45\) | 0.756906 | + | 2.90295i | 0.112833 | + | 0.432746i | ||||
\(46\) | −1.74778 | −0.257696 | ||||||||
\(47\) | 0.378666 | + | 0.655869i | 0.0552341 | + | 0.0956683i | 0.892320 | − | 0.451403i | \(-0.149076\pi\) |
−0.837086 | + | 0.547071i | \(0.815743\pi\) | |||||||
\(48\) | −1.05903 | + | 1.37057i | −0.152858 | + | 0.197824i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 4.98868 | + | 12.1595i | 0.698555 | + | 1.70267i | ||||
\(52\) | 2.01859 | + | 3.49629i | 0.279928 | + | 0.484849i | ||||
\(53\) | 7.23397 | 0.993662 | 0.496831 | − | 0.867847i | \(-0.334497\pi\) | ||||
0.496831 | + | 0.867847i | \(0.334497\pi\) | |||||||
\(54\) | −0.626109 | − | 5.15829i | −0.0852026 | − | 0.701955i | ||||
\(55\) | −2.74778 | −0.370511 | ||||||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 2.80798 | + | 6.84421i | 0.371926 | + | 0.906538i | ||||
\(58\) | −4.67709 | + | 8.10096i | −0.614132 | + | 1.06371i | ||||
\(59\) | 0.612210 | − | 1.06038i | 0.0797030 | − | 0.138050i | −0.823419 | − | 0.567434i | \(-0.807936\pi\) |
0.903122 | + | 0.429385i | \(0.141269\pi\) | |||||||
\(60\) | 1.05903 | − | 1.37057i | 0.136720 | − | 0.176939i | ||||
\(61\) | −6.16797 | − | 10.6832i | −0.789728 | − | 1.36785i | −0.926134 | − | 0.377195i | \(-0.876889\pi\) |
0.136406 | − | 0.990653i | \(-0.456445\pi\) | |||||||
\(62\) | 10.5423 | 1.33887 | ||||||||
\(63\) | −2.89248 | − | 0.795973i | −0.364418 | − | 0.100283i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.01859 | − | 3.49629i | −0.250375 | − | 0.433662i | ||||
\(66\) | 4.71646 | + | 0.637113i | 0.580556 | + | 0.0784232i | ||||
\(67\) | −6.64938 | + | 11.5171i | −0.812351 | + | 1.40703i | 0.0988627 | + | 0.995101i | \(0.468480\pi\) |
−0.911214 | + | 0.411933i | \(0.864854\pi\) | |||||||
\(68\) | 3.79408 | − | 6.57154i | 0.460100 | − | 0.796916i | ||||
\(69\) | −3.00000 | − | 0.405249i | −0.361158 | − | 0.0487862i | ||||
\(70\) | −0.500000 | − | 0.866025i | −0.0597614 | − | 0.103510i | ||||
\(71\) | −0.550985 | −0.0653899 | −0.0326949 | − | 0.999465i | \(-0.510409\pi\) | ||||
−0.0326949 | + | 0.999465i | \(0.510409\pi\) | |||||||
\(72\) | −2.13557 | + | 2.10697i | −0.251680 | + | 0.248309i | ||||
\(73\) | −9.07435 | −1.06207 | −0.531036 | − | 0.847349i | \(-0.678197\pi\) | ||||
−0.531036 | + | 0.847349i | \(0.678197\pi\) | |||||||
\(74\) | −3.65416 | − | 6.32919i | −0.424787 | − | 0.735753i | ||||
\(75\) | −1.05903 | + | 1.37057i | −0.122286 | + | 0.158259i | ||||
\(76\) | 2.13557 | − | 3.69892i | 0.244967 | − | 0.424295i | ||||
\(77\) | 1.37389 | − | 2.37965i | 0.156569 | − | 0.271186i | ||||
\(78\) | 2.65416 | + | 6.46929i | 0.300524 | + | 0.732503i | ||||
\(79\) | −3.14470 | − | 5.44677i | −0.353806 | − | 0.612810i | 0.633107 | − | 0.774064i | \(-0.281779\pi\) |
−0.986913 | + | 0.161255i | \(0.948446\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0.121334 | − | 8.99918i | 0.0134816 | − | 0.999909i | ||||
\(82\) | 3.03717 | 0.335400 | ||||||||
\(83\) | −6.18187 | − | 10.7073i | −0.678548 | − | 1.17528i | −0.975418 | − | 0.220362i | \(-0.929276\pi\) |
0.296870 | − | 0.954918i | \(-0.404057\pi\) | |||||||
\(84\) | 0.657430 | + | 1.60243i | 0.0717315 | + | 0.174840i | ||||
\(85\) | −3.79408 | + | 6.57154i | −0.411526 | + | 0.712783i | ||||
\(86\) | 0.644696 | − | 1.11665i | 0.0695193 | − | 0.120411i | ||||
\(87\) | −9.90638 | + | 12.8205i | −1.06208 | + | 1.37451i | ||||
\(88\) | −1.37389 | − | 2.37965i | −0.146457 | − | 0.253671i | ||||
\(89\) | 7.02762 | 0.744927 | 0.372463 | − | 0.928047i | \(-0.378513\pi\) | ||||
0.372463 | + | 0.928047i | \(0.378513\pi\) | |||||||
\(90\) | 2.13557 | − | 2.10697i | 0.225109 | − | 0.222094i | ||||
\(91\) | 4.03717 | 0.423211 | ||||||||
\(92\) | 0.873891 | + | 1.51362i | 0.0911094 | + | 0.157806i | ||||
\(93\) | 18.0954 | + | 2.44438i | 1.87641 | + | 0.253471i | ||||
\(94\) | 0.378666 | − | 0.655869i | 0.0390564 | − | 0.0676477i | ||||
\(95\) | −2.13557 | + | 3.69892i | −0.219105 | + | 0.379501i | ||||
\(96\) | 1.71646 | + | 0.231865i | 0.175186 | + | 0.0236646i | ||||
\(97\) | 7.79877 | + | 13.5079i | 0.791845 | + | 1.37152i | 0.924823 | + | 0.380397i | \(0.124212\pi\) |
−0.132979 | + | 0.991119i | \(0.542454\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 7.94790 | + | 2.18716i | 0.798794 | + | 0.219818i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −7.98175 | − | 13.8248i | −0.794214 | − | 1.37562i | −0.923337 | − | 0.383991i | \(-0.874550\pi\) |
0.129123 | − | 0.991629i | \(-0.458784\pi\) | |||||||
\(102\) | 8.03610 | − | 10.4001i | 0.795692 | − | 1.02976i | ||||
\(103\) | 7.36477 | − | 12.7562i | 0.725672 | − | 1.25690i | −0.233025 | − | 0.972471i | \(-0.574862\pi\) |
0.958697 | − | 0.284430i | \(-0.0918044\pi\) | |||||||
\(104\) | 2.01859 | − | 3.49629i | 0.197939 | − | 0.342840i | ||||
\(105\) | −0.657430 | − | 1.60243i | −0.0641586 | − | 0.156381i | ||||
\(106\) | −3.61699 | − | 6.26480i | −0.351313 | − | 0.608491i | ||||
\(107\) | 8.66474 | 0.837652 | 0.418826 | − | 0.908067i | \(-0.362442\pi\) | ||||
0.418826 | + | 0.908067i | \(0.362442\pi\) | |||||||
\(108\) | −4.15416 | + | 3.12137i | −0.399734 | + | 0.300354i | ||||
\(109\) | 3.56923 | 0.341870 | 0.170935 | − | 0.985282i | \(-0.445321\pi\) | ||||
0.170935 | + | 0.985282i | \(0.445321\pi\) | |||||||
\(110\) | 1.37389 | + | 2.37965i | 0.130995 | + | 0.226891i | ||||
\(111\) | −4.80471 | − | 11.7111i | −0.456043 | − | 1.11157i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | 4.04186 | − | 7.00071i | 0.380226 | − | 0.658571i | −0.610868 | − | 0.791732i | \(-0.709179\pi\) |
0.991094 | + | 0.133161i | \(0.0425128\pi\) | |||||||
\(114\) | 4.52327 | − | 5.85389i | 0.423643 | − | 0.548267i | ||||
\(115\) | −0.873891 | − | 1.51362i | −0.0814908 | − | 0.141146i | ||||
\(116\) | 9.35419 | 0.868514 | ||||||||
\(117\) | 3.05576 | + | 11.7197i | 0.282505 | + | 1.08349i | ||||
\(118\) | −1.22442 | −0.112717 | ||||||||
\(119\) | −3.79408 | − | 6.57154i | −0.347803 | − | 0.602412i | ||||
\(120\) | −1.71646 | − | 0.231865i | −0.156691 | − | 0.0211662i | ||||
\(121\) | 1.72485 | − | 2.98752i | 0.156804 | − | 0.271593i | ||||
\(122\) | −6.16797 | + | 10.6832i | −0.558422 | + | 0.967215i | ||||
\(123\) | 5.21319 | + | 0.704213i | 0.470057 | + | 0.0634967i | ||||
\(124\) | −5.27114 | − | 9.12989i | −0.473363 | − | 0.819888i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.756906 | + | 2.90295i | 0.0674305 | + | 0.258615i | ||||
\(127\) | −3.74778 | −0.332562 | −0.166281 | − | 0.986078i | \(-0.553176\pi\) | ||||
−0.166281 | + | 0.986078i | \(0.553176\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.36551 | − | 1.76720i | 0.120226 | − | 0.155593i | ||||
\(130\) | −2.01859 | + | 3.49629i | −0.177042 | + | 0.306645i | ||||
\(131\) | −6.25691 | + | 10.8373i | −0.546668 | + | 0.946857i | 0.451831 | + | 0.892103i | \(0.350771\pi\) |
−0.998500 | + | 0.0547541i | \(0.982563\pi\) | |||||||
\(132\) | −1.80647 | − | 4.40313i | −0.157233 | − | 0.383243i | ||||
\(133\) | −2.13557 | − | 3.69892i | −0.185178 | − | 0.320737i | ||||
\(134\) | 13.2988 | 1.14884 | ||||||||
\(135\) | 4.15416 | − | 3.12137i | 0.357533 | − | 0.268645i | ||||
\(136\) | −7.58816 | −0.650679 | ||||||||
\(137\) | −8.77549 | − | 15.1996i | −0.749741 | − | 1.29859i | −0.947947 | − | 0.318429i | \(-0.896845\pi\) |
0.198206 | − | 0.980160i | \(-0.436489\pi\) | |||||||
\(138\) | 1.14904 | + | 2.80070i | 0.0978131 | + | 0.238411i | ||||
\(139\) | 0.195680 | − | 0.338928i | 0.0165974 | − | 0.0287475i | −0.857607 | − | 0.514305i | \(-0.828050\pi\) |
0.874205 | + | 0.485557i | \(0.161383\pi\) | |||||||
\(140\) | −0.500000 | + | 0.866025i | −0.0422577 | + | 0.0731925i | ||||
\(141\) | 0.802038 | − | 1.03797i | 0.0675438 | − | 0.0874132i | ||||
\(142\) | 0.275492 | + | 0.477167i | 0.0231188 | + | 0.0400429i | ||||
\(143\) | −11.0933 | −0.927666 | ||||||||
\(144\) | 2.89248 | + | 0.795973i | 0.241040 | + | 0.0663311i | ||||
\(145\) | −9.35419 | −0.776823 | ||||||||
\(146\) | 4.53717 | + | 7.85861i | 0.375499 | + | 0.650384i | ||||
\(147\) | 1.71646 | + | 0.231865i | 0.141571 | + | 0.0191239i | ||||
\(148\) | −3.65416 | + | 6.32919i | −0.300370 | + | 0.520256i | ||||
\(149\) | 1.61264 | − | 2.79317i | 0.132112 | − | 0.228825i | −0.792378 | − | 0.610030i | \(-0.791157\pi\) |
0.924491 | + | 0.381205i | \(0.124491\pi\) | |||||||
\(150\) | 1.71646 | + | 0.231865i | 0.140148 | + | 0.0189317i | ||||
\(151\) | 2.69568 | + | 4.66906i | 0.219371 | + | 0.379962i | 0.954616 | − | 0.297840i | \(-0.0962660\pi\) |
−0.735245 | + | 0.677802i | \(0.762933\pi\) | |||||||
\(152\) | −4.27114 | −0.346435 | ||||||||
\(153\) | 16.2051 | − | 15.9880i | 1.31010 | − | 1.29256i | ||||
\(154\) | −2.74778 | −0.221423 | ||||||||
\(155\) | 5.27114 | + | 9.12989i | 0.423388 | + | 0.733330i | ||||
\(156\) | 4.27549 | − | 5.53321i | 0.342313 | − | 0.443012i | ||||
\(157\) | 11.5696 | − | 20.0391i | 0.923352 | − | 1.59929i | 0.129162 | − | 0.991623i | \(-0.458771\pi\) |
0.794190 | − | 0.607670i | \(-0.207896\pi\) | |||||||
\(158\) | −3.14470 | + | 5.44677i | −0.250179 | + | 0.433322i | ||||
\(159\) | −4.75583 | − | 11.5919i | −0.377162 | − | 0.919301i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 1.74778 | 0.137745 | ||||||||
\(162\) | −7.85419 | + | 4.39451i | −0.617083 | + | 0.345266i | ||||
\(163\) | −4.58816 | −0.359372 | −0.179686 | − | 0.983724i | \(-0.557508\pi\) | ||||
−0.179686 | + | 0.983724i | \(0.557508\pi\) | |||||||
\(164\) | −1.51859 | − | 2.63027i | −0.118582 | − | 0.205390i | ||||
\(165\) | 1.80647 | + | 4.40313i | 0.140634 | + | 0.342783i | ||||
\(166\) | −6.18187 | + | 10.7073i | −0.479806 | + | 0.831048i | ||||
\(167\) | 4.74343 | − | 8.21587i | 0.367058 | − | 0.635763i | −0.622046 | − | 0.782981i | \(-0.713698\pi\) |
0.989104 | + | 0.147218i | \(0.0470318\pi\) | |||||||
\(168\) | 1.05903 | − | 1.37057i | 0.0817060 | − | 0.105742i | ||||
\(169\) | −1.64938 | − | 2.85682i | −0.126876 | − | 0.219755i | ||||
\(170\) | 7.58816 | 0.581985 | ||||||||
\(171\) | 9.12133 | − | 8.99918i | 0.697526 | − | 0.688185i | ||||
\(172\) | −1.28939 | −0.0983151 | ||||||||
\(173\) | −5.27114 | − | 9.12989i | −0.400758 | − | 0.694133i | 0.593060 | − | 0.805158i | \(-0.297920\pi\) |
−0.993818 | + | 0.111026i | \(0.964586\pi\) | |||||||
\(174\) | 16.0561 | + | 2.16891i | 1.21721 | + | 0.164424i | ||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | −1.37389 | + | 2.37965i | −0.103561 | + | 0.179373i | ||||
\(177\) | −2.10167 | − | 0.283900i | −0.157971 | − | 0.0213392i | ||||
\(178\) | −3.51381 | − | 6.08610i | −0.263371 | − | 0.456172i | ||||
\(179\) | −11.9052 | −0.889834 | −0.444917 | − | 0.895572i | \(-0.646767\pi\) | ||||
−0.444917 | + | 0.895572i | \(0.646767\pi\) | |||||||
\(180\) | −2.89248 | − | 0.795973i | −0.215593 | − | 0.0593283i | ||||
\(181\) | 10.5232 | 0.782182 | 0.391091 | − | 0.920352i | \(-0.372098\pi\) | ||||
0.391091 | + | 0.920352i | \(0.372098\pi\) | |||||||
\(182\) | −2.01859 | − | 3.49629i | −0.149628 | − | 0.259163i | ||||
\(183\) | −13.0641 | + | 16.9072i | −0.965729 | + | 1.24982i | ||||
\(184\) | 0.873891 | − | 1.51362i | 0.0644241 | − | 0.111586i | ||||
\(185\) | 3.65416 | − | 6.32919i | 0.268659 | − | 0.465331i | ||||
\(186\) | −6.93082 | − | 16.8933i | −0.508192 | − | 1.23868i | ||||
\(187\) | 10.4253 | + | 18.0572i | 0.762374 | + | 1.32047i | ||||
\(188\) | −0.757332 | −0.0552341 | ||||||||
\(189\) | 0.626109 | + | 5.15829i | 0.0455427 | + | 0.375211i | ||||
\(190\) | 4.27114 | 0.309861 | ||||||||
\(191\) | 9.37311 | + | 16.2347i | 0.678215 | + | 1.17470i | 0.975518 | + | 0.219919i | \(0.0705794\pi\) |
−0.297303 | + | 0.954783i | \(0.596087\pi\) | |||||||
\(192\) | −0.657430 | − | 1.60243i | −0.0474459 | − | 0.115646i | ||||
\(193\) | 5.81267 | − | 10.0678i | 0.418405 | − | 0.724698i | −0.577374 | − | 0.816480i | \(-0.695923\pi\) |
0.995779 | + | 0.0917811i | \(0.0292560\pi\) | |||||||
\(194\) | 7.79877 | − | 13.5079i | 0.559919 | − | 0.969808i | ||||
\(195\) | −4.27549 | + | 5.53321i | −0.306174 | + | 0.396242i | ||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | 22.8039 | 1.62471 | 0.812355 | − | 0.583164i | \(-0.198185\pi\) | ||||
0.812355 | + | 0.583164i | \(0.198185\pi\) | |||||||
\(198\) | −2.07981 | − | 7.97666i | −0.147806 | − | 0.566877i | ||||
\(199\) | 14.8498 | 1.05267 | 0.526335 | − | 0.850277i | \(-0.323566\pi\) | ||||
0.526335 | + | 0.850277i | \(0.323566\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 22.8268 | + | 3.08351i | 1.61008 | + | 0.217494i | ||||
\(202\) | −7.98175 | + | 13.8248i | −0.561594 | + | 0.972710i | ||||
\(203\) | 4.67709 | − | 8.10096i | 0.328268 | − | 0.568576i | ||||
\(204\) | −13.0248 | − | 1.75943i | −0.911917 | − | 0.123184i | ||||
\(205\) | 1.51859 | + | 2.63027i | 0.106063 | + | 0.183706i | ||||
\(206\) | −14.7295 | −1.02626 | ||||||||
\(207\) | 1.32291 | + | 5.07372i | 0.0919483 | + | 0.352648i | ||||
\(208\) | −4.03717 | −0.279928 | ||||||||
\(209\) | 5.86809 | + | 10.1638i | 0.405904 | + | 0.703046i | ||||
\(210\) | −1.05903 | + | 1.37057i | −0.0730801 | + | 0.0945781i | ||||
\(211\) | 4.90203 | − | 8.49056i | 0.337469 | − | 0.584514i | −0.646487 | − | 0.762925i | \(-0.723762\pi\) |
0.983956 | + | 0.178411i | \(0.0570957\pi\) | |||||||
\(212\) | −3.61699 | + | 6.26480i | −0.248416 | + | 0.430268i | ||||
\(213\) | 0.362234 | + | 0.882915i | 0.0248199 | + | 0.0604963i | ||||
\(214\) | −4.33237 | − | 7.50388i | −0.296155 | − | 0.512955i | ||||
\(215\) | 1.28939 | 0.0879357 | ||||||||
\(216\) | 4.78027 | + | 2.03692i | 0.325256 | + | 0.138595i | ||||
\(217\) | −10.5423 | −0.715657 | ||||||||
\(218\) | −1.78462 | − | 3.09105i | −0.120869 | − | 0.209352i | ||||
\(219\) | 5.96575 | + | 14.5410i | 0.403128 | + | 0.982591i | ||||
\(220\) | 1.37389 | − | 2.37965i | 0.0926277 | − | 0.160436i | ||||
\(221\) | −15.3174 | + | 26.5304i | −1.03036 | + | 1.78463i | ||||
\(222\) | −7.73974 | + | 10.0165i | −0.519457 | + | 0.672266i | ||||
\(223\) | −1.28504 | − | 2.22576i | −0.0860528 | − | 0.149048i | 0.819787 | − | 0.572669i | \(-0.194092\pi\) |
−0.905839 | + | 0.423621i | \(0.860759\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 2.89248 | + | 0.795973i | 0.192832 | + | 0.0530649i | ||||
\(226\) | −8.08372 | −0.537721 | ||||||||
\(227\) | −4.37858 | − | 7.58392i | −0.290616 | − | 0.503363i | 0.683339 | − | 0.730101i | \(-0.260527\pi\) |
−0.973956 | + | 0.226739i | \(0.927194\pi\) | |||||||
\(228\) | −7.33125 | − | 0.990327i | −0.485524 | − | 0.0655860i | ||||
\(229\) | 0.0936237 | − | 0.162161i | 0.00618683 | − | 0.0107159i | −0.862915 | − | 0.505348i | \(-0.831364\pi\) |
0.869102 | + | 0.494632i | \(0.164697\pi\) | |||||||
\(230\) | −0.873891 | + | 1.51362i | −0.0576227 | + | 0.0998054i | ||||
\(231\) | −4.71646 | − | 0.637113i | −0.310320 | − | 0.0419190i | ||||
\(232\) | −4.67709 | − | 8.10096i | −0.307066 | − | 0.531854i | ||||
\(233\) | 15.5795 | 1.02064 | 0.510322 | − | 0.859983i | \(-0.329526\pi\) | ||||
0.510322 | + | 0.859983i | \(0.329526\pi\) | |||||||
\(234\) | 8.62167 | − | 8.50621i | 0.563616 | − | 0.556069i | ||||
\(235\) | 0.757332 | 0.0494029 | ||||||||
\(236\) | 0.612210 | + | 1.06038i | 0.0398515 | + | 0.0690248i | ||||
\(237\) | −6.66066 | + | 8.62003i | −0.432656 | + | 0.559931i | ||||
\(238\) | −3.79408 | + | 6.57154i | −0.245934 | + | 0.425970i | ||||
\(239\) | −2.46794 | + | 4.27460i | −0.159638 | + | 0.276501i | −0.934738 | − | 0.355337i | \(-0.884366\pi\) |
0.775100 | + | 0.631838i | \(0.217699\pi\) | |||||||
\(240\) | 0.657430 | + | 1.60243i | 0.0424369 | + | 0.103436i | ||||
\(241\) | −12.6348 | − | 21.8841i | −0.813879 | − | 1.40968i | −0.910130 | − | 0.414322i | \(-0.864019\pi\) |
0.0962517 | − | 0.995357i | \(-0.469315\pi\) | |||||||
\(242\) | −3.44969 | −0.221755 | ||||||||
\(243\) | −14.5003 | + | 5.72190i | −0.930197 | + | 0.367060i | ||||
\(244\) | 12.3359 | 0.789728 | ||||||||
\(245\) | 0.500000 | + | 0.866025i | 0.0319438 | + | 0.0553283i | ||||
\(246\) | −1.99673 | − | 4.86686i | −0.127307 | − | 0.310300i | ||||
\(247\) | −8.62167 | + | 14.9332i | −0.548584 | + | 0.950175i | ||||
\(248\) | −5.27114 | + | 9.12989i | −0.334718 | + | 0.579749i | ||||
\(249\) | −13.0936 | + | 16.9453i | −0.829772 | + | 1.07387i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −16.6741 | −1.05246 | −0.526230 | − | 0.850342i | \(-0.676395\pi\) | ||||
−0.526230 | + | 0.850342i | \(0.676395\pi\) | |||||||
\(252\) | 2.13557 | − | 2.10697i | 0.134528 | − | 0.132727i | ||||
\(253\) | −4.80252 | −0.301932 | ||||||||
\(254\) | 1.87389 | + | 3.24567i | 0.117578 | + | 0.203652i | ||||
\(255\) | 13.0248 | + | 1.75943i | 0.815643 | + | 0.110179i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −11.0699 | + | 19.1736i | −0.690522 | + | 1.19602i | 0.281145 | + | 0.959665i | \(0.409286\pi\) |
−0.971667 | + | 0.236354i | \(0.924048\pi\) | |||||||
\(258\) | −2.21319 | − | 0.298964i | −0.137787 | − | 0.0186127i | ||||
\(259\) | 3.65416 | + | 6.32919i | 0.227058 | + | 0.393277i | ||||
\(260\) | 4.03717 | 0.250375 | ||||||||
\(261\) | 27.0568 | + | 7.44568i | 1.67477 | + | 0.460876i | ||||
\(262\) | 12.5138 | 0.773106 | ||||||||
\(263\) | 0.911064 | + | 1.57801i | 0.0561786 | + | 0.0973042i | 0.892747 | − | 0.450558i | \(-0.148775\pi\) |
−0.836568 | + | 0.547862i | \(0.815442\pi\) | |||||||
\(264\) | −2.90999 | + | 3.76602i | −0.179097 | + | 0.231782i | ||||
\(265\) | 3.61699 | − | 6.26480i | 0.222190 | − | 0.384844i | ||||
\(266\) | −2.13557 | + | 3.69892i | −0.130940 | + | 0.226795i | ||||
\(267\) | −4.62017 | − | 11.2613i | −0.282750 | − | 0.689179i | ||||
\(268\) | −6.64938 | − | 11.5171i | −0.406176 | − | 0.703517i | ||||
\(269\) | −6.26159 | −0.381776 | −0.190888 | − | 0.981612i | \(-0.561137\pi\) | ||||
−0.190888 | + | 0.981612i | \(0.561137\pi\) | |||||||
\(270\) | −4.78027 | − | 2.03692i | −0.290918 | − | 0.123963i | ||||
\(271\) | −5.91387 | −0.359242 | −0.179621 | − | 0.983736i | \(-0.557487\pi\) | ||||
−0.179621 | + | 0.983736i | \(0.557487\pi\) | |||||||
\(272\) | 3.79408 | + | 6.57154i | 0.230050 | + | 0.398458i | ||||
\(273\) | −2.65416 | − | 6.46929i | −0.160637 | − | 0.391539i | ||||
\(274\) | −8.77549 | + | 15.1996i | −0.530147 | + | 0.918241i | ||||
\(275\) | −1.37389 | + | 2.37965i | −0.0828487 | + | 0.143498i | ||||
\(276\) | 1.85096 | − | 2.39545i | 0.111414 | − | 0.144189i | ||||
\(277\) | 7.98175 | + | 13.8248i | 0.479577 | + | 0.830652i | 0.999726 | − | 0.0234240i | \(-0.00745677\pi\) |
−0.520149 | + | 0.854076i | \(0.674123\pi\) | |||||||
\(278\) | −0.391360 | −0.0234722 | ||||||||
\(279\) | −7.97952 | − | 30.6037i | −0.477721 | − | 1.83219i | ||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −1.60795 | − | 2.78505i | −0.0959222 | − | 0.166142i | 0.814071 | − | 0.580765i | \(-0.197247\pi\) |
−0.909993 | + | 0.414623i | \(0.863913\pi\) | |||||||
\(282\) | −1.29993 | − | 0.175599i | −0.0774098 | − | 0.0104567i | ||||
\(283\) | 0.621334 | − | 1.07618i | 0.0369345 | − | 0.0639724i | −0.846967 | − | 0.531645i | \(-0.821574\pi\) |
0.883902 | + | 0.467673i | \(0.154907\pi\) | |||||||
\(284\) | 0.275492 | − | 0.477167i | 0.0163475 | − | 0.0283146i | ||||
\(285\) | 7.33125 | + | 0.990327i | 0.434266 | + | 0.0586619i | ||||
\(286\) | 5.54664 | + | 9.60706i | 0.327979 | + | 0.568077i | ||||
\(287\) | −3.03717 | −0.179279 | ||||||||
\(288\) | −0.756906 | − | 2.90295i | −0.0446011 | − | 0.171058i | ||||
\(289\) | 40.5801 | 2.38707 | ||||||||
\(290\) | 4.67709 | + | 8.10096i | 0.274648 | + | 0.475705i | ||||
\(291\) | 16.5183 | − | 21.3775i | 0.968318 | − | 1.25317i | ||||
\(292\) | 4.53717 | − | 7.85861i | 0.265518 | − | 0.459891i | ||||
\(293\) | −10.7419 | + | 18.6055i | −0.627548 | + | 1.08694i | 0.360494 | + | 0.932761i | \(0.382608\pi\) |
−0.988042 | + | 0.154183i | \(0.950725\pi\) | |||||||
\(294\) | −0.657430 | − | 1.60243i | −0.0383421 | − | 0.0934557i | ||||
\(295\) | −0.612210 | − | 1.06038i | −0.0356443 | − | 0.0617377i | ||||
\(296\) | 7.30832 | 0.424787 | ||||||||
\(297\) | −1.72041 | − | 14.1739i | −0.0998284 | − | 0.822451i | ||||
\(298\) | −3.22527 | −0.186835 | ||||||||
\(299\) | −3.52805 | − | 6.11076i | −0.204032 | − | 0.353394i | ||||
\(300\) | −0.657430 | − | 1.60243i | −0.0379567 | − | 0.0925164i | ||||
\(301\) | −0.644696 | + | 1.11665i | −0.0371596 | + | 0.0643624i | ||||
\(302\) | 2.69568 | − | 4.66906i | 0.155119 | − | 0.268674i | ||||
\(303\) | −16.9059 | + | 21.8790i | −0.971216 | + | 1.25692i | ||||
\(304\) | 2.13557 | + | 3.69892i | 0.122483 | + | 0.212148i | ||||
\(305\) | −12.3359 | −0.706354 | ||||||||
\(306\) | −21.9486 | − | 6.03997i | −1.25472 | − | 0.345282i | ||||
\(307\) | 31.1369 | 1.77708 | 0.888539 | − | 0.458802i | \(-0.151721\pi\) | ||||
0.888539 | + | 0.458802i | \(0.151721\pi\) | |||||||
\(308\) | 1.37389 | + | 2.37965i | 0.0782847 | + | 0.135593i | ||||
\(309\) | −25.2827 | − | 3.41526i | −1.43828 | − | 0.194287i | ||||
\(310\) | 5.27114 | − | 9.12989i | 0.299381 | − | 0.518543i | ||||
\(311\) | −12.8498 | + | 22.2564i | −0.728643 | + | 1.26205i | 0.228814 | + | 0.973470i | \(0.426515\pi\) |
−0.957457 | + | 0.288576i | \(0.906818\pi\) | |||||||
\(312\) | −6.92965 | − | 0.936078i | −0.392314 | − | 0.0529950i | ||||
\(313\) | −11.2375 | − | 19.4640i | −0.635183 | − | 1.10017i | −0.986476 | − | 0.163904i | \(-0.947591\pi\) |
0.351293 | − | 0.936266i | \(-0.385742\pi\) | |||||||
\(314\) | −23.1391 | −1.30582 | ||||||||
\(315\) | −2.13557 | + | 2.10697i | −0.120326 | + | 0.118714i | ||||
\(316\) | 6.28939 | 0.353806 | ||||||||
\(317\) | −1.18622 | − | 2.05459i | −0.0666246 | − | 0.115397i | 0.830789 | − | 0.556588i | \(-0.187890\pi\) |
−0.897413 | + | 0.441190i | \(0.854556\pi\) | |||||||
\(318\) | −7.66100 | + | 9.91464i | −0.429608 | + | 0.555985i | ||||
\(319\) | −12.8516 | + | 22.2597i | −0.719553 | + | 1.24630i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −5.69646 | − | 13.8846i | −0.317945 | − | 0.774965i | ||||
\(322\) | −0.873891 | − | 1.51362i | −0.0487000 | − | 0.0843510i | ||||
\(323\) | 32.4101 | 1.80335 | ||||||||
\(324\) | 7.73285 | + | 4.60467i | 0.429603 | + | 0.255815i | ||||
\(325\) | −4.03717 | −0.223942 | ||||||||
\(326\) | 2.29408 | + | 3.97346i | 0.127057 | + | 0.220070i | ||||
\(327\) | −2.34652 | − | 5.71945i | −0.129763 | − | 0.316286i | ||||
\(328\) | −1.51859 | + | 2.63027i | −0.0838499 | + | 0.145232i | ||||
\(329\) | −0.378666 | + | 0.655869i | −0.0208765 | + | 0.0361592i | ||||
\(330\) | 2.90999 | − | 3.76602i | 0.160190 | − | 0.207312i | ||||
\(331\) | 0.649810 | + | 1.12550i | 0.0357168 | + | 0.0618633i | 0.883331 | − | 0.468749i | \(-0.155295\pi\) |
−0.847614 | + | 0.530613i | \(0.821962\pi\) | |||||||
\(332\) | 12.3637 | 0.678548 | ||||||||
\(333\) | −15.6074 | + | 15.3984i | −0.855282 | + | 0.843828i | ||||
\(334\) | −9.48687 | −0.519098 | ||||||||
\(335\) | 6.64938 | + | 11.5171i | 0.363295 | + | 0.629245i | ||||
\(336\) | −1.71646 | − | 0.231865i | −0.0936406 | − | 0.0126493i | ||||
\(337\) | −1.29885 | + | 2.24968i | −0.0707531 | + | 0.122548i | −0.899232 | − | 0.437473i | \(-0.855874\pi\) |
0.828478 | + | 0.560021i | \(0.189207\pi\) | |||||||
\(338\) | −1.64938 | + | 2.85682i | −0.0897146 | + | 0.155390i | ||||
\(339\) | −13.8754 | − | 1.87433i | −0.753608 | − | 0.101800i | ||||
\(340\) | −3.79408 | − | 6.57154i | −0.205763 | − | 0.356392i | ||||
\(341\) | 28.9679 | 1.56870 | ||||||||
\(342\) | −12.3542 | − | 3.39972i | −0.668038 | − | 0.183836i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.644696 | + | 1.11665i | 0.0347597 | + | 0.0602055i | ||||
\(345\) | −1.85096 | + | 2.39545i | −0.0996521 | + | 0.128967i | ||||
\(346\) | −5.27114 | + | 9.12989i | −0.283378 | + | 0.490826i | ||||
\(347\) | 6.16319 | − | 10.6750i | 0.330858 | − | 0.573062i | −0.651823 | − | 0.758371i | \(-0.725995\pi\) |
0.982680 | + | 0.185309i | \(0.0593287\pi\) | |||||||
\(348\) | −6.14972 | − | 14.9894i | −0.329660 | − | 0.803518i | ||||
\(349\) | 6.79554 | + | 11.7702i | 0.363757 | + | 0.630045i | 0.988576 | − | 0.150724i | \(-0.0481606\pi\) |
−0.624819 | + | 0.780770i | \(0.714827\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 16.7711 | − | 12.6015i | 0.895173 | − | 0.672620i | ||||
\(352\) | 2.74778 | 0.146457 | ||||||||
\(353\) | 4.71904 | + | 8.17362i | 0.251169 | + | 0.435038i | 0.963848 | − | 0.266453i | \(-0.0858516\pi\) |
−0.712679 | + | 0.701491i | \(0.752518\pi\) | |||||||
\(354\) | 0.804971 | + | 1.96205i | 0.0427837 | + | 0.104282i | ||||
\(355\) | −0.275492 | + | 0.477167i | −0.0146216 | + | 0.0253254i | ||||
\(356\) | −3.51381 | + | 6.08610i | −0.186232 | + | 0.322563i | ||||
\(357\) | −8.03610 | + | 10.4001i | −0.425315 | + | 0.550430i | ||||
\(358\) | 5.95259 | + | 10.3102i | 0.314604 | + | 0.544910i | ||||
\(359\) | −14.2251 | −0.750772 | −0.375386 | − | 0.926869i | \(-0.622490\pi\) | ||||
−0.375386 | + | 0.926869i | \(0.622490\pi\) | |||||||
\(360\) | 0.756906 | + | 2.90295i | 0.0398924 | + | 0.152999i | ||||
\(361\) | −0.757332 | −0.0398596 | ||||||||
\(362\) | −5.26159 | − | 9.11335i | −0.276543 | − | 0.478987i | ||||
\(363\) | −5.92127 | − | 0.799862i | −0.310786 | − | 0.0419819i | ||||
\(364\) | −2.01859 | + | 3.49629i | −0.105803 | + | 0.183256i | ||||
\(365\) | −4.53717 | + | 7.85861i | −0.237486 | + | 0.411339i | ||||
\(366\) | 21.1742 | + | 2.86027i | 1.10679 | + | 0.149509i | ||||
\(367\) | −12.3870 | − | 21.4549i | −0.646597 | − | 1.11994i | −0.983930 | − | 0.178553i | \(-0.942858\pi\) |
0.337334 | − | 0.941385i | \(-0.390475\pi\) | |||||||
\(368\) | −1.74778 | −0.0911094 | ||||||||
\(369\) | −2.29885 | − | 8.81675i | −0.119674 | − | 0.458982i | ||||
\(370\) | −7.30832 | −0.379941 | ||||||||
\(371\) | 3.61699 | + | 6.26480i | 0.187785 | + | 0.325252i | ||||
\(372\) | −11.1646 | + | 14.4489i | −0.578858 | + | 0.749141i | ||||
\(373\) | 8.00000 | − | 13.8564i | 0.414224 | − | 0.717458i | −0.581122 | − | 0.813816i | \(-0.697386\pi\) |
0.995347 | + | 0.0963587i | \(0.0307196\pi\) | |||||||
\(374\) | 10.4253 | − | 18.0572i | 0.539080 | − | 0.933713i | ||||
\(375\) | 0.657430 | + | 1.60243i | 0.0339495 | + | 0.0827492i | ||||
\(376\) | 0.378666 | + | 0.655869i | 0.0195282 | + | 0.0338239i | ||||
\(377\) | −37.7645 | −1.94497 | ||||||||
\(378\) | 4.15416 | − | 3.12137i | 0.213667 | − | 0.160546i | ||||
\(379\) | −24.4570 | −1.25627 | −0.628136 | − | 0.778103i | \(-0.716182\pi\) | ||||
−0.628136 | + | 0.778103i | \(0.716182\pi\) | |||||||
\(380\) | −2.13557 | − | 3.69892i | −0.109553 | − | 0.189751i | ||||
\(381\) | 2.46390 | + | 6.00556i | 0.126230 | + | 0.307674i | ||||
\(382\) | 9.37311 | − | 16.2347i | 0.479570 | − | 0.830640i | ||||
\(383\) | 0.461710 | − | 0.799705i | 0.0235923 | − | 0.0408630i | −0.853988 | − | 0.520292i | \(-0.825823\pi\) |
0.877580 | + | 0.479429i | \(0.159156\pi\) | |||||||
\(384\) | −1.05903 | + | 1.37057i | −0.0540435 | + | 0.0699414i | ||||
\(385\) | −1.37389 | − | 2.37965i | −0.0700200 | − | 0.121278i | ||||
\(386\) | −11.6253 | −0.591714 | ||||||||
\(387\) | −3.72953 | − | 1.02632i | −0.189583 | − | 0.0521708i | ||||
\(388\) | −15.5975 | −0.791845 | ||||||||
\(389\) | 8.68698 | + | 15.0463i | 0.440448 | + | 0.762877i | 0.997723 | − | 0.0674504i | \(-0.0214865\pi\) |
−0.557275 | + | 0.830328i | \(0.688153\pi\) | |||||||
\(390\) | 6.92965 | + | 0.936078i | 0.350897 | + | 0.0474001i | ||||
\(391\) | −6.63122 | + | 11.4856i | −0.335355 | + | 0.580853i | ||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | 21.4795 | + | 2.90151i | 1.08350 | + | 0.146362i | ||||
\(394\) | −11.4019 | − | 19.7487i | −0.574421 | − | 0.994927i | ||||
\(395\) | −6.28939 | −0.316454 | ||||||||
\(396\) | −5.86809 | + | 5.78950i | −0.294882 | + | 0.290933i | ||||
\(397\) | −28.4562 | −1.42817 | −0.714087 | − | 0.700057i | \(-0.753158\pi\) | ||||
−0.714087 | + | 0.700057i | \(0.753158\pi\) | |||||||
\(398\) | −7.42488 | − | 12.8603i | −0.372175 | − | 0.644627i | ||||
\(399\) | −4.52327 | + | 5.85389i | −0.226447 | + | 0.293061i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −7.55210 | + | 13.0806i | −0.377134 | + | 0.653215i | −0.990644 | − | 0.136472i | \(-0.956424\pi\) |
0.613510 | + | 0.789687i | \(0.289757\pi\) | |||||||
\(402\) | −8.74301 | − | 21.3104i | −0.436062 | − | 1.06286i | ||||
\(403\) | 21.2805 | + | 36.8589i | 1.06006 | + | 1.83607i | ||||
\(404\) | 15.9635 | 0.794214 | ||||||||
\(405\) | −7.73285 | − | 4.60467i | −0.384249 | − | 0.228808i | ||||
\(406\) | −9.35419 | −0.464241 | ||||||||
\(407\) | −10.0408 | − | 17.3912i | −0.497706 | − | 0.862051i | ||||
\(408\) | 4.98868 | + | 12.1595i | 0.246977 | + | 0.601985i | ||||
\(409\) | 16.1257 | − | 27.9305i | 0.797363 | − | 1.38107i | −0.123965 | − | 0.992287i | \(-0.539561\pi\) |
0.921328 | − | 0.388787i | \(-0.127106\pi\) | |||||||
\(410\) | 1.51859 | − | 2.63027i | 0.0749976 | − | 0.129900i | ||||
\(411\) | −18.5870 | + | 24.0548i | −0.916831 | + | 1.18654i | ||||
\(412\) | 7.36477 | + | 12.7562i | 0.362836 | + | 0.628450i | ||||
\(413\) | 1.22442 | 0.0602498 | ||||||||
\(414\) | 3.73251 | − | 3.68253i | 0.183443 | − | 0.180986i | ||||
\(415\) | −12.3637 | −0.606912 | ||||||||
\(416\) | 2.01859 | + | 3.49629i | 0.0989693 | + | 0.171420i | ||||
\(417\) | −0.671755 | − | 0.0907426i | −0.0328960 | − | 0.00444369i | ||||
\(418\) | 5.86809 | − | 10.1638i | 0.287017 | − | 0.497129i | ||||
\(419\) | −3.31300 | + | 5.73829i | −0.161851 | + | 0.280334i | −0.935532 | − | 0.353241i | \(-0.885080\pi\) |
0.773682 | + | 0.633575i | \(0.218413\pi\) | |||||||
\(420\) | 1.71646 | + | 0.231865i | 0.0837547 | + | 0.0113138i | ||||
\(421\) | 0.335601 | + | 0.581277i | 0.0163562 | + | 0.0283297i | 0.874088 | − | 0.485768i | \(-0.161460\pi\) |
−0.857731 | + | 0.514098i | \(0.828127\pi\) | |||||||
\(422\) | −9.80406 | −0.477254 | ||||||||
\(423\) | −2.19057 | − | 0.602816i | −0.106509 | − | 0.0293099i | ||||
\(424\) | 7.23397 | 0.351313 | ||||||||
\(425\) | 3.79408 | + | 6.57154i | 0.184040 | + | 0.318766i | ||||
\(426\) | 0.583510 | − | 0.755161i | 0.0282712 | − | 0.0365877i | ||||
\(427\) | 6.16797 | − | 10.6832i | 0.298489 | − | 0.516998i | ||||
\(428\) | −4.33237 | + | 7.50388i | −0.209413 | + | 0.362714i | ||||
\(429\) | 7.29305 | + | 17.7762i | 0.352112 | + | 0.858243i | ||||
\(430\) | −0.644696 | − | 1.11665i | −0.0310900 | − | 0.0538494i | ||||
\(431\) | 25.3914 | 1.22306 | 0.611529 | − | 0.791222i | \(-0.290555\pi\) | ||||
0.611529 | + | 0.791222i | \(0.290555\pi\) | |||||||
\(432\) | −0.626109 | − | 5.15829i | −0.0301237 | − | 0.248178i | ||||
\(433\) | 31.1376 | 1.49638 | 0.748188 | − | 0.663486i | \(-0.230924\pi\) | ||||
0.748188 | + | 0.663486i | \(0.230924\pi\) | |||||||
\(434\) | 5.27114 | + | 9.12989i | 0.253023 | + | 0.438249i | ||||
\(435\) | 6.14972 | + | 14.9894i | 0.294857 | + | 0.718689i | ||||
\(436\) | −1.78462 | + | 3.09105i | −0.0854676 | + | 0.148034i | ||||
\(437\) | −3.73251 | + | 6.46490i | −0.178550 | + | 0.309258i | ||||
\(438\) | 9.61002 | − | 12.4370i | 0.459184 | − | 0.594263i | ||||
\(439\) | 0.368777 | + | 0.638740i | 0.0176008 | + | 0.0304854i | 0.874692 | − | 0.484680i | \(-0.161064\pi\) |
−0.857091 | + | 0.515165i | \(0.827731\pi\) | |||||||
\(440\) | −2.74778 | −0.130995 | ||||||||
\(441\) | −0.756906 | − | 2.90295i | −0.0360431 | − | 0.138236i | ||||
\(442\) | 30.6347 | 1.45714 | ||||||||
\(443\) | −13.5499 | − | 23.4691i | −0.643774 | − | 1.11505i | −0.984583 | − | 0.174916i | \(-0.944035\pi\) |
0.340810 | − | 0.940132i | \(-0.389299\pi\) | |||||||
\(444\) | 12.5444 | + | 1.69454i | 0.595333 | + | 0.0804193i | ||||
\(445\) | 3.51381 | − | 6.08610i | 0.166571 | − | 0.288509i | ||||
\(446\) | −1.28504 | + | 2.22576i | −0.0608485 | + | 0.105393i | ||||
\(447\) | −5.53606 | − | 0.747827i | −0.261846 | − | 0.0353710i | ||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | −5.16917 | −0.243948 | −0.121974 | − | 0.992533i | \(-0.538923\pi\) | ||||
−0.121974 | + | 0.992533i | \(0.538923\pi\) | |||||||
\(450\) | −0.756906 | − | 2.90295i | −0.0356809 | − | 0.136846i | ||||
\(451\) | 8.34549 | 0.392974 | ||||||||
\(452\) | 4.04186 | + | 7.00071i | 0.190113 | + | 0.329286i | ||||
\(453\) | 5.70962 | − | 7.38922i | 0.268261 | − | 0.347176i | ||||
\(454\) | −4.37858 | + | 7.58392i | −0.205497 | + | 0.355931i | ||||
\(455\) | 2.01859 | − | 3.49629i | 0.0946328 | − | 0.163909i | ||||
\(456\) | 2.80798 | + | 6.84421i | 0.131496 | + | 0.320510i | ||||
\(457\) | 2.56446 | + | 4.44177i | 0.119960 | + | 0.207777i | 0.919752 | − | 0.392501i | \(-0.128390\pi\) |
−0.799791 | + | 0.600278i | \(0.795057\pi\) | |||||||
\(458\) | −0.187247 | −0.00874950 | ||||||||
\(459\) | −36.2734 | − | 15.4565i | −1.69310 | − | 0.721446i | ||||
\(460\) | 1.74778 | 0.0814908 | ||||||||
\(461\) | 6.54040 | + | 11.3283i | 0.304617 | + | 0.527612i | 0.977176 | − | 0.212431i | \(-0.0681382\pi\) |
−0.672559 | + | 0.740044i | \(0.734805\pi\) | |||||||
\(462\) | 1.80647 | + | 4.40313i | 0.0840448 | + | 0.204852i | ||||
\(463\) | 9.76671 | − | 16.9164i | 0.453897 | − | 0.786173i | −0.544727 | − | 0.838614i | \(-0.683367\pi\) |
0.998624 | + | 0.0524403i | \(0.0166999\pi\) | |||||||
\(464\) | −4.67709 | + | 8.10096i | −0.217129 | + | 0.376078i | ||||
\(465\) | 11.1646 | − | 14.4489i | 0.517746 | − | 0.670052i | ||||
\(466\) | −7.78973 | − | 13.4922i | −0.360852 | − | 0.625014i | ||||
\(467\) | −0.510899 | −0.0236416 | −0.0118208 | − | 0.999930i | \(-0.503763\pi\) | ||||
−0.0118208 | + | 0.999930i | \(0.503763\pi\) | |||||||
\(468\) | −11.6774 | − | 3.21348i | −0.539790 | − | 0.148543i | ||||
\(469\) | −13.2988 | −0.614080 | ||||||||
\(470\) | −0.378666 | − | 0.655869i | −0.0174666 | − | 0.0302530i | ||||
\(471\) | −39.7174 | − | 5.36515i | −1.83008 | − | 0.247213i | ||||
\(472\) | 0.612210 | − | 1.06038i | 0.0281793 | − | 0.0488079i | ||||
\(473\) | 1.77148 | − | 3.06830i | 0.0814529 | − | 0.141081i | ||||
\(474\) | 10.7955 | + | 1.45829i | 0.495854 | + | 0.0669814i | ||||
\(475\) | 2.13557 | + | 3.69892i | 0.0979868 | + | 0.169718i | ||||
\(476\) | 7.58816 | 0.347803 | ||||||||
\(477\) | −15.4487 | + | 15.2418i | −0.707346 | + | 0.697873i | ||||
\(478\) | 4.93588 | 0.225762 | ||||||||
\(479\) | −4.17283 | − | 7.22756i | −0.190662 | − | 0.330236i | 0.754808 | − | 0.655946i | \(-0.227730\pi\) |
−0.945470 | + | 0.325710i | \(0.894397\pi\) | |||||||
\(480\) | 1.05903 | − | 1.37057i | 0.0483379 | − | 0.0625575i | ||||
\(481\) | 14.7525 | − | 25.5520i | 0.672655 | − | 1.16507i | ||||
\(482\) | −12.6348 | + | 21.8841i | −0.575499 | + | 0.996794i | ||||
\(483\) | −1.14904 | − | 2.80070i | −0.0522833 | − | 0.127436i | ||||
\(484\) | 1.72485 | + | 2.98752i | 0.0784021 | + | 0.135796i | ||||
\(485\) | 15.5975 | 0.708248 | ||||||||
\(486\) | 12.2055 | + | 9.69671i | 0.553652 | + | 0.439852i | ||||
\(487\) | 21.8847 | 0.991690 | 0.495845 | − | 0.868411i | \(-0.334858\pi\) | ||||
0.495845 | + | 0.868411i | \(0.334858\pi\) | |||||||
\(488\) | −6.16797 | − | 10.6832i | −0.279211 | − | 0.483607i | ||||
\(489\) | 3.01639 | + | 7.35221i | 0.136406 | + | 0.332478i | ||||
\(490\) | 0.500000 | − | 0.866025i | 0.0225877 | − | 0.0391230i | ||||
\(491\) | 14.2103 | − | 24.6129i | 0.641300 | − | 1.11076i | −0.343843 | − | 0.939027i | \(-0.611729\pi\) |
0.985143 | − | 0.171737i | \(-0.0549379\pi\) | |||||||
\(492\) | −3.21646 | + | 4.16265i | −0.145009 | + | 0.187667i | ||||
\(493\) | 35.4905 | + | 61.4714i | 1.59841 | + | 2.76853i | ||||
\(494\) | 17.2433 | 0.775815 | ||||||||
\(495\) | 5.86809 | − | 5.78950i | 0.263751 | − | 0.260219i | ||||
\(496\) | 10.5423 | 0.473363 | ||||||||
\(497\) | −0.275492 | − | 0.477167i | −0.0123575 | − | 0.0214039i | ||||
\(498\) | 21.2219 | + | 2.86671i | 0.950975 | + | 0.128460i | ||||
\(499\) | 7.70983 | − | 13.3538i | 0.345139 | − | 0.597799i | −0.640240 | − | 0.768175i | \(-0.721165\pi\) |
0.985379 | + | 0.170376i | \(0.0544983\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | −16.2838 | − | 2.19967i | −0.727508 | − | 0.0982740i | ||||
\(502\) | 8.33706 | + | 14.4402i | 0.372101 | + | 0.644498i | ||||
\(503\) | 39.0058 | 1.73918 | 0.869590 | − | 0.493774i | \(-0.164383\pi\) | ||||
0.869590 | + | 0.493774i | \(0.164383\pi\) | |||||||
\(504\) | −2.89248 | − | 0.795973i | −0.128841 | − | 0.0354555i | ||||
\(505\) | −15.9635 | −0.710367 | ||||||||
\(506\) | 2.40126 | + | 4.15911i | 0.106749 | + | 0.184895i | ||||
\(507\) | −3.49350 | + | 4.52118i | −0.155152 | + | 0.200793i | ||||
\(508\) | 1.87389 | − | 3.24567i | 0.0831405 | − | 0.144004i | ||||
\(509\) | −6.16797 | + | 10.6832i | −0.273390 | + | 0.473526i | −0.969728 | − | 0.244188i | \(-0.921478\pi\) |
0.696337 | + | 0.717715i | \(0.254812\pi\) | |||||||
\(510\) | −4.98868 | − | 12.1595i | −0.220903 | − | 0.538432i | ||||
\(511\) | −4.53717 | − | 7.85861i | −0.200713 | − | 0.347645i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −20.4172 | − | 8.69998i | −0.901442 | − | 0.384113i | ||||
\(514\) | 22.1398 | 0.976546 | ||||||||
\(515\) | −7.36477 | − | 12.7562i | −0.324530 | − | 0.562103i | ||||
\(516\) | 0.847684 | + | 2.06616i | 0.0373172 | + | 0.0909576i | ||||
\(517\) | 1.04049 | − | 1.80218i | 0.0457608 | − | 0.0792600i | ||||
\(518\) | 3.65416 | − | 6.32919i | 0.160555 | − | 0.278089i | ||||
\(519\) | −11.1646 | + | 14.4489i | −0.490072 | + | 0.634237i | ||||
\(520\) | −2.01859 | − | 3.49629i | −0.0885209 | − | 0.153323i | ||||
\(521\) | 6.55986 | 0.287393 | 0.143696 | − | 0.989622i | \(-0.454101\pi\) | ||||
0.143696 | + | 0.989622i | \(0.454101\pi\) | |||||||
\(522\) | −7.08024 | − | 27.1547i | −0.309894 | − | 1.18853i | ||||
\(523\) | −10.2070 | −0.446322 | −0.223161 | − | 0.974782i | \(-0.571638\pi\) | ||||
−0.223161 | + | 0.974782i | \(0.571638\pi\) | |||||||
\(524\) | −6.25691 | − | 10.8373i | −0.273334 | − | 0.473429i | ||||
\(525\) | −1.71646 | − | 0.231865i | −0.0749125 | − | 0.0101194i | ||||
\(526\) | 0.911064 | − | 1.57801i | 0.0397243 | − | 0.0688045i | ||||
\(527\) | 39.9983 | − | 69.2790i | 1.74235 | − | 3.01784i | ||||
\(528\) | 4.71646 | + | 0.637113i | 0.205258 | + | 0.0277268i | ||||
\(529\) | 9.97263 | + | 17.2731i | 0.433593 | + | 0.751004i | ||||
\(530\) | −7.23397 | −0.314224 | ||||||||
\(531\) | 0.926771 | + | 3.55443i | 0.0402184 | + | 0.154249i | ||||
\(532\) | 4.27114 | 0.185178 | ||||||||
\(533\) | 6.13080 | + | 10.6189i | 0.265554 | + | 0.459954i | ||||
\(534\) | −7.44247 | + | 9.63183i | −0.322067 | + | 0.416810i | ||||
\(535\) | 4.33237 | − | 7.50388i | 0.187305 | − | 0.324421i | ||||
\(536\) | −6.64938 | + | 11.5171i | −0.287210 | + | 0.497462i | ||||
\(537\) | 7.82682 | + | 19.0772i | 0.337752 | + | 0.823243i | ||||
\(538\) | 3.13080 | + | 5.42270i | 0.134978 | + | 0.233789i | ||||
\(539\) | 2.74778 | 0.118355 | ||||||||
\(540\) | 0.626109 | + | 5.15829i | 0.0269434 | + | 0.221978i | ||||
\(541\) | −22.1741 | −0.953338 | −0.476669 | − | 0.879083i | \(-0.658156\pi\) | ||||
−0.476669 | + | 0.879083i | \(0.658156\pi\) | |||||||
\(542\) | 2.95693 | + | 5.12156i | 0.127011 | + | 0.219990i | ||||
\(543\) | −6.91826 | − | 16.8627i | −0.296891 | − | 0.723647i | ||||
\(544\) | 3.79408 | − | 6.57154i | 0.162670 | − | 0.281752i | ||||
\(545\) | 1.78462 | − | 3.09105i | 0.0764446 | − | 0.132406i | ||||
\(546\) | −4.27549 | + | 5.53321i | −0.182974 | + | 0.236800i | ||||
\(547\) | 0.364002 | + | 0.630470i | 0.0155636 | + | 0.0269569i | 0.873702 | − | 0.486461i | \(-0.161712\pi\) |
−0.858139 | + | 0.513418i | \(0.828379\pi\) | |||||||
\(548\) | 17.5510 | 0.749741 | ||||||||
\(549\) | 35.6814 | + | 9.81908i | 1.52285 | + | 0.419068i | ||||
\(550\) | 2.74778 | 0.117166 | ||||||||
\(551\) | 19.9765 | + | 34.6004i | 0.851029 | + | 1.47403i | ||||
\(552\) | −3.00000 | − | 0.405249i | −0.127688 | − | 0.0172485i | ||||
\(553\) | 3.14470 | − | 5.44677i | 0.133726 | − | 0.231620i | ||||
\(554\) | 7.98175 | − | 13.8248i | 0.339112 | − | 0.587360i | ||||
\(555\) | −12.5444 | − | 1.69454i | −0.532482 | − | 0.0719292i | ||||
\(556\) | 0.195680 | + | 0.338928i | 0.00829869 | + | 0.0143738i | ||||
\(557\) | −9.64426 | −0.408640 | −0.204320 | − | 0.978904i | \(-0.565498\pi\) | ||||
−0.204320 | + | 0.978904i | \(0.565498\pi\) | |||||||
\(558\) | −22.5138 | + | 22.2123i | −0.953086 | + | 0.940322i | ||||
\(559\) | 5.20549 | 0.220169 | ||||||||
\(560\) | −0.500000 | − | 0.866025i | −0.0211289 | − | 0.0365963i | ||||
\(561\) | 22.0814 | − | 28.5771i | 0.932279 | − | 1.20653i | ||||
\(562\) | −1.60795 | + | 2.78505i | −0.0678272 | + | 0.117480i | ||||
\(563\) | −9.84183 | + | 17.0466i | −0.414784 | + | 0.718427i | −0.995406 | − | 0.0957467i | \(-0.969476\pi\) |
0.580622 | + | 0.814173i | \(0.302809\pi\) | |||||||
\(564\) | 0.497893 | + | 1.21357i | 0.0209651 | + | 0.0511006i | ||||
\(565\) | −4.04186 | − | 7.00071i | −0.170042 | − | 0.294522i | ||||
\(566\) | −1.24267 | −0.0522332 | ||||||||
\(567\) | 7.85419 | − | 4.39451i | 0.329845 | − | 0.184552i | ||||
\(568\) | −0.550985 | −0.0231188 | ||||||||
\(569\) | 12.0928 | + | 20.9454i | 0.506958 | + | 0.878078i | 0.999968 | + | 0.00805366i | \(0.00256359\pi\) |
−0.493009 | + | 0.870024i | \(0.664103\pi\) | |||||||
\(570\) | −2.80798 | − | 6.84421i | −0.117613 | − | 0.286673i | ||||
\(571\) | −6.62125 | + | 11.4683i | −0.277091 | + | 0.479935i | −0.970660 | − | 0.240454i | \(-0.922704\pi\) |
0.693570 | + | 0.720389i | \(0.256037\pi\) | |||||||
\(572\) | 5.54664 | − | 9.60706i | 0.231917 | − | 0.401691i | ||||
\(573\) | 19.8528 | − | 25.6930i | 0.829364 | − | 1.07334i | ||||
\(574\) | 1.51859 | + | 2.63027i | 0.0633846 | + | 0.109785i | ||||
\(575\) | −1.74778 | −0.0728876 | ||||||||
\(576\) | −2.13557 | + | 2.10697i | −0.0889822 | + | 0.0877905i | ||||
\(577\) | 7.45822 | 0.310490 | 0.155245 | − | 0.987876i | \(-0.450383\pi\) | ||||
0.155245 | + | 0.987876i | \(0.450383\pi\) | |||||||
\(578\) | −20.2901 | − | 35.1434i | −0.843956 | − | 1.46177i | ||||
\(579\) | −19.9544 | − | 2.69550i | −0.829278 | − | 0.112021i | ||||
\(580\) | 4.67709 | − | 8.10096i | 0.194206 | − | 0.336374i | ||||
\(581\) | 6.18187 | − | 10.7073i | 0.256467 | − | 0.444214i | ||||
\(582\) | −26.7726 | − | 3.61652i | −1.10976 | − | 0.149909i | ||||
\(583\) | −9.93869 | − | 17.2143i | −0.411618 | − | 0.712944i | ||||
\(584\) | −9.07435 | −0.375499 | ||||||||
\(585\) | 11.6774 | + | 3.21348i | 0.482802 | + | 0.132861i | ||||
\(586\) | 21.4838 | 0.887487 | ||||||||
\(587\) | −4.56514 | − | 7.90705i | −0.188423 | − | 0.326359i | 0.756301 | − | 0.654223i | \(-0.227004\pi\) |
−0.944725 | + | 0.327865i | \(0.893671\pi\) | |||||||
\(588\) | −1.05903 | + | 1.37057i | −0.0436737 | + | 0.0565212i | ||||
\(589\) | 22.5138 | − | 38.9951i | 0.927665 | − | 1.60676i | ||||
\(590\) | −0.612210 | + | 1.06038i | −0.0252043 | + | 0.0436551i | ||||
\(591\) | −14.9920 | − | 36.5417i | −0.616687 | − | 1.50312i | ||||
\(592\) | −3.65416 | − | 6.32919i | −0.150185 | − | 0.260128i | ||||
\(593\) | −34.3068 | −1.40881 | −0.704405 | − | 0.709798i | \(-0.748786\pi\) | ||||
−0.704405 | + | 0.709798i | \(0.748786\pi\) | |||||||
\(594\) | −11.4147 | + | 8.57685i | −0.468352 | + | 0.351913i | ||||
\(595\) | −7.58816 | −0.311084 | ||||||||
\(596\) | 1.61264 | + | 2.79317i | 0.0660562 | + | 0.114413i | ||||
\(597\) | −9.76267 | − | 23.7957i | −0.399560 | − | 0.973893i | ||||
\(598\) | −3.52805 | + | 6.11076i | −0.144273 | + | 0.249888i | ||||
\(599\) | −12.9573 | + | 22.4427i | −0.529420 | + | 0.916982i | 0.469991 | + | 0.882671i | \(0.344257\pi\) |
−0.999411 | + | 0.0343111i | \(0.989076\pi\) | |||||||
\(600\) | −1.05903 | + | 1.37057i | −0.0432348 | + | 0.0559531i | ||||
\(601\) | −11.4055 | − | 19.7549i | −0.465241 | − | 0.805820i | 0.533972 | − | 0.845502i | \(-0.320699\pi\) |
−0.999212 | + | 0.0396821i | \(0.987365\pi\) | |||||||
\(602\) | 1.28939 | 0.0525517 | ||||||||
\(603\) | −10.0659 | − | 38.6056i | −0.409916 | − | 1.57214i | ||||
\(604\) | −5.39136 | −0.219371 | ||||||||
\(605\) | −1.72485 | − | 2.98752i | −0.0701250 | − | 0.121460i | ||||
\(606\) | 27.4007 | + | 3.70137i | 1.11308 | + | 0.150358i | ||||
\(607\) | −7.10197 | + | 12.3010i | −0.288260 | + | 0.499281i | −0.973395 | − | 0.229136i | \(-0.926410\pi\) |
0.685134 | + | 0.728417i | \(0.259743\pi\) | |||||||
\(608\) | 2.13557 | − | 3.69892i | 0.0866089 | − | 0.150011i | ||||
\(609\) | −16.0561 | − | 2.16891i | −0.650626 | − | 0.0878885i | ||||
\(610\) | 6.16797 | + | 10.6832i | 0.249734 | + | 0.432552i | ||||
\(611\) | 3.05748 | 0.123692 | ||||||||
\(612\) | 5.74352 | + | 22.0280i | 0.232168 | + | 0.890430i | ||||
\(613\) | 16.2418 | 0.656000 | 0.328000 | − | 0.944678i | \(-0.393625\pi\) | ||||
0.328000 | + | 0.944678i | \(0.393625\pi\) | |||||||
\(614\) | −15.5685 | − | 26.9654i | −0.628292 | − | 1.08823i | ||||
\(615\) | 3.21646 | − | 4.16265i | 0.129700 | − | 0.167854i | ||||
\(616\) | 1.37389 | − | 2.37965i | 0.0553556 | − | 0.0958788i | ||||
\(617\) | 15.4008 | − | 26.6750i | 0.620014 | − | 1.07390i | −0.369469 | − | 0.929243i | \(-0.620460\pi\) |
0.989483 | − | 0.144652i | \(-0.0462063\pi\) | |||||||
\(618\) | 9.68364 | + | 23.6031i | 0.389533 | + | 0.949455i | ||||
\(619\) | 12.9157 | + | 22.3706i | 0.519124 | + | 0.899150i | 0.999753 | + | 0.0222256i | \(0.00707520\pi\) |
−0.480629 | + | 0.876924i | \(0.659591\pi\) | |||||||
\(620\) | −10.5423 | −0.423388 | ||||||||
\(621\) | 7.26056 | − | 5.45548i | 0.291356 | − | 0.218921i | ||||
\(622\) | 25.6995 | 1.03046 | ||||||||
\(623\) | 3.51381 | + | 6.08610i | 0.140778 | + | 0.243834i | ||||
\(624\) | 2.65416 | + | 6.46929i | 0.106251 | + | 0.258979i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −11.2375 | + | 19.4640i | −0.449142 | + | 0.777938i | ||||
\(627\) | 12.4290 | − | 16.0852i | 0.496365 | − | 0.642381i | ||||
\(628\) | 11.5696 | + | 20.0391i | 0.461676 | + | 0.799647i | ||||
\(629\) | −55.4567 | −2.21120 | ||||||||
\(630\) | 2.89248 | + | 0.795973i | 0.115239 | + | 0.0317123i | ||||
\(631\) | −29.6908 | −1.18197 | −0.590986 | − | 0.806682i | \(-0.701261\pi\) | ||||
−0.590986 | + | 0.806682i | \(0.701261\pi\) | |||||||
\(632\) | −3.14470 | − | 5.44677i | −0.125089 | − | 0.216661i | ||||
\(633\) | −16.8283 | − | 2.27321i | −0.668864 | − | 0.0903521i | ||||
\(634\) | −1.18622 | + | 2.05459i | −0.0471107 | + | 0.0815981i | ||||
\(635\) | −1.87389 | + | 3.24567i | −0.0743631 | + | 0.128801i | ||||
\(636\) | 12.4168 | + | 1.67730i | 0.492359 | + | 0.0665093i | ||||
\(637\) | 2.01859 | + | 3.49629i | 0.0799793 | + | 0.138528i | ||||
\(638\) | 25.7033 | 1.01760 | ||||||||
\(639\) | 1.17667 | − | 1.16091i | 0.0465482 | − | 0.0459249i | ||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −15.6961 | − | 27.1865i | −0.619959 | − | 1.07380i | −0.989493 | − | 0.144583i | \(-0.953816\pi\) |
0.369534 | − | 0.929217i | \(-0.379517\pi\) | |||||||
\(642\) | −9.17623 | + | 11.8756i | −0.362157 | + | 0.468693i | ||||
\(643\) | −5.37858 | + | 9.31597i | −0.212110 | + | 0.367386i | −0.952375 | − | 0.304930i | \(-0.901367\pi\) |
0.740264 | + | 0.672316i | \(0.234700\pi\) | |||||||
\(644\) | −0.873891 | + | 1.51362i | −0.0344361 | + | 0.0596451i | ||||
\(645\) | −0.847684 | − | 2.06616i | −0.0333775 | − | 0.0813550i | ||||
\(646\) | −16.2051 | − | 28.0680i | −0.637579 | − | 1.10432i | ||||
\(647\) | −3.10438 | −0.122046 | −0.0610228 | − | 0.998136i | \(-0.519436\pi\) | ||||
−0.0610228 | + | 0.998136i | \(0.519436\pi\) | |||||||
\(648\) | 0.121334 | − | 8.99918i | 0.00476645 | − | 0.353521i | ||||
\(649\) | −3.36444 | −0.132066 | ||||||||
\(650\) | 2.01859 | + | 3.49629i | 0.0791755 | + | 0.137136i | ||||
\(651\) | 6.93082 | + | 16.8933i | 0.271640 | + | 0.662100i | ||||
\(652\) | 2.29408 | − | 3.97346i | 0.0898431 | − | 0.155613i | ||||
\(653\) | −20.4292 | + | 35.3844i | −0.799457 | + | 1.38470i | 0.120513 | + | 0.992712i | \(0.461546\pi\) |
−0.919970 | + | 0.391988i | \(0.871787\pi\) | |||||||
\(654\) | −3.77993 | + | 4.89187i | −0.147807 | + | 0.191287i | ||||
\(655\) | 6.25691 | + | 10.8373i | 0.244478 | + | 0.423448i | ||||
\(656\) | 3.03717 | 0.118582 | ||||||||
\(657\) | 19.3789 | − | 19.1194i | 0.756044 | − | 0.745919i | ||||
\(658\) | 0.757332 | 0.0295239 | ||||||||
\(659\) | 15.4158 | + | 26.7010i | 0.600516 | + | 1.04012i | 0.992743 | + | 0.120256i | \(0.0383714\pi\) |
−0.392227 | + | 0.919868i | \(0.628295\pi\) | |||||||
\(660\) | −4.71646 | − | 0.637113i | −0.183588 | − | 0.0247996i | ||||
\(661\) | 22.5795 | − | 39.1088i | 0.878239 | − | 1.52115i | 0.0249676 | − | 0.999688i | \(-0.492052\pi\) |
0.853272 | − | 0.521467i | \(-0.174615\pi\) | |||||||
\(662\) | 0.649810 | − | 1.12550i | 0.0252556 | − | 0.0437439i | ||||
\(663\) | 52.5833 | + | 7.10310i | 2.04217 | + | 0.275862i | ||||
\(664\) | −6.18187 | − | 10.7073i | −0.239903 | − | 0.415524i | ||||
\(665\) | −4.27114 | −0.165628 | ||||||||
\(666\) | 21.1391 | + | 5.81722i | 0.819125 | + | 0.225413i | ||||
\(667\) | −16.3491 | −0.633039 | ||||||||
\(668\) | 4.74343 | + | 8.21587i | 0.183529 | + | 0.317881i | ||||
\(669\) | −2.72180 | + | 3.52247i | −0.105231 | + | 0.136187i | ||||
\(670\) | 6.64938 | − | 11.5171i | 0.256888 | − | 0.444943i | ||||
\(671\) | −16.9482 | + | 29.3552i | −0.654279 | + | 1.13325i | ||||
\(672\) | 0.657430 | + | 1.60243i | 0.0253609 | + | 0.0618151i | ||||
\(673\) | −2.01893 | − | 3.49688i | −0.0778239 | − | 0.134795i | 0.824487 | − | 0.565881i | \(-0.191464\pi\) |
−0.902311 | + | 0.431086i | \(0.858131\pi\) | |||||||
\(674\) | 2.59771 | 0.100060 | ||||||||
\(675\) | −0.626109 | − | 5.15829i | −0.0240989 | − | 0.198543i | ||||
\(676\) | 3.29877 | 0.126876 | ||||||||
\(677\) | −13.4770 | − | 23.3428i | −0.517962 | − | 0.897137i | −0.999782 | − | 0.0208668i | \(-0.993357\pi\) |
0.481820 | − | 0.876270i | \(-0.339976\pi\) | |||||||
\(678\) | 5.31448 | + | 12.9536i | 0.204101 | + | 0.497480i | ||||
\(679\) | −7.79877 | + | 13.5079i | −0.299289 | + | 0.518384i | ||||
\(680\) | −3.79408 | + | 6.57154i | −0.145496 | + | 0.252007i | ||||
\(681\) | −9.27410 | + | 12.0023i | −0.355384 | + | 0.459928i | ||||
\(682\) | −14.4840 | − | 25.0869i | −0.554619 | − | 0.960629i | ||||
\(683\) | 43.7302 | 1.67329 | 0.836645 | − | 0.547745i | \(-0.184514\pi\) | ||||
0.836645 | + | 0.547745i | \(0.184514\pi\) | |||||||
\(684\) | 3.23285 | + | 12.3989i | 0.123611 | + | 0.474084i | ||||
\(685\) | −17.5510 | −0.670589 | ||||||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | −0.321403 | − | 0.0434161i | −0.0122623 | − | 0.00165643i | ||||
\(688\) | 0.644696 | − | 1.11665i | 0.0245788 | − | 0.0425717i | ||||
\(689\) | 14.6024 | − | 25.2921i | 0.556307 | − | 0.963552i | ||||
\(690\) | 3.00000 | + | 0.405249i | 0.114208 | + | 0.0154276i | ||||
\(691\) | −4.10420 | − | 7.10869i | −0.156131 | − | 0.270427i | 0.777339 | − | 0.629082i | \(-0.216569\pi\) |
−0.933470 | + | 0.358655i | \(0.883236\pi\) | |||||||
\(692\) | 10.5423 | 0.400758 | ||||||||
\(693\) | 2.07981 | + | 7.97666i | 0.0790055 | + | 0.303008i | ||||
\(694\) | −12.3264 | −0.467903 | ||||||||
\(695\) | −0.195680 | − | 0.338928i | −0.00742257 | − | 0.0128563i | ||||
\(696\) | −9.90638 | + | 12.8205i | −0.375500 | + | 0.485961i | ||||
\(697\) | 11.5233 | − | 19.9589i | 0.436475 | − | 0.755997i | ||||
\(698\) | 6.79554 | − | 11.7702i | 0.257215 | − | 0.445509i | ||||
\(699\) | −10.2424 | − | 24.9650i | −0.387403 | − | 0.944264i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | −13.9263 | −0.525990 | −0.262995 | − | 0.964797i | \(-0.584710\pi\) | ||||
−0.262995 | + | 0.964797i | \(0.584710\pi\) | |||||||
\(702\) | −19.2988 | − | 8.22340i | −0.728385 | − | 0.310372i | ||||
\(703\) | −31.2149 | −1.17729 | ||||||||
\(704\) | −1.37389 | − | 2.37965i | −0.0517805 | − | 0.0896864i | ||||
\(705\) | −0.497893 | − | 1.21357i | −0.0187517 | − | 0.0457058i | ||||
\(706\) | 4.71904 | − | 8.17362i | 0.177603 | − | 0.307618i | ||||
\(707\) | 7.98175 | − | 13.8248i | 0.300185 | − | 0.519935i | ||||
\(708\) | 1.29670 | − | 1.67815i | 0.0487330 | − | 0.0630687i | ||||
\(709\) | −8.99411 | − | 15.5783i | −0.337781 | − | 0.585054i | 0.646234 | − | 0.763139i | \(-0.276343\pi\) |
−0.984015 | + | 0.178086i | \(0.943010\pi\) | |||||||
\(710\) | 0.550985 | 0.0206781 | ||||||||
\(711\) | 18.1919 | + | 5.00619i | 0.682250 | + | 0.187747i | ||||
\(712\) | 7.02762 | 0.263371 | ||||||||
\(713\) | 9.21281 | + | 15.9571i | 0.345022 | + | 0.597596i | ||||
\(714\) | 13.0248 | + | 1.75943i | 0.487440 | + | 0.0658448i | ||||
\(715\) | −5.54664 | + | 9.60706i | −0.207432 | + | 0.359283i | ||||
\(716\) | 5.95259 | − | 10.3102i | 0.222459 | − | 0.385310i | ||||
\(717\) | 8.47225 | + | 1.14446i | 0.316402 | + | 0.0427405i | ||||
\(718\) | 7.11255 | + | 12.3193i | 0.265438 | + | 0.459752i | ||||
\(719\) | 6.41966 | 0.239413 | 0.119706 | − | 0.992809i | \(-0.461805\pi\) | ||||
0.119706 | + | 0.992809i | \(0.461805\pi\) | |||||||
\(720\) | 2.13557 | − | 2.10697i | 0.0795881 | − | 0.0785222i | ||||
\(721\) | 14.7295 | 0.548557 | ||||||||
\(722\) | 0.378666 | + | 0.655869i | 0.0140925 | + | 0.0244089i | ||||
\(723\) | −26.7613 | + | 34.6337i | −0.995263 | + | 1.28804i | ||||
\(724\) | −5.26159 | + | 9.11335i | −0.195546 | + | 0.338695i | ||||
\(725\) | −4.67709 | + | 8.10096i | −0.173703 | + | 0.300862i | ||||
\(726\) | 2.26793 | + | 5.52790i | 0.0841708 | + | 0.205159i | ||||
\(727\) | 7.48830 | + | 12.9701i | 0.277726 | + | 0.481035i | 0.970819 | − | 0.239813i | \(-0.0770860\pi\) |
−0.693093 | + | 0.720848i | \(0.743753\pi\) | |||||||
\(728\) | 4.03717 | 0.149628 | ||||||||
\(729\) | 18.7019 | + | 19.4740i | 0.692663 | + | 0.721261i | ||||
\(730\) | 9.07435 | 0.335857 | ||||||||
\(731\) | −4.89205 | − | 8.47328i | −0.180939 | − | 0.313396i | ||||
\(732\) | −8.11002 | − | 19.7675i | −0.299755 | − | 0.730628i | ||||
\(733\) | −15.0320 | + | 26.0361i | −0.555218 | + | 0.961666i | 0.442668 | + | 0.896685i | \(0.354032\pi\) |
−0.997887 | + | 0.0649806i | \(0.979301\pi\) | |||||||
\(734\) | −12.3870 | + | 21.4549i | −0.457213 | + | 0.791916i | ||||
\(735\) | 1.05903 | − | 1.37057i | 0.0390630 | − | 0.0505541i | ||||
\(736\) | 0.873891 | + | 1.51362i | 0.0322121 | + | 0.0557929i | ||||
\(737\) | 36.5421 | 1.34605 | ||||||||
\(738\) | −6.48610 | + | 6.39924i | −0.238757 | + | 0.235559i | ||||
\(739\) | 33.4089 | 1.22897 | 0.614483 | − | 0.788930i | \(-0.289365\pi\) | ||||
0.614483 | + | 0.788930i | \(0.289365\pi\) | |||||||
\(740\) | 3.65416 | + | 6.32919i | 0.134330 | + | 0.232666i | ||||
\(741\) | 29.5975 | + | 3.99812i | 1.08729 | + | 0.146875i | ||||
\(742\) | 3.61699 | − | 6.26480i | 0.132784 | − | 0.229988i | ||||
\(743\) | −0.710609 | + | 1.23081i | −0.0260697 | + | 0.0451541i | −0.878766 | − | 0.477253i | \(-0.841633\pi\) |
0.852696 | + | 0.522407i | \(0.174966\pi\) | |||||||
\(744\) | 18.0954 | + | 2.44438i | 0.663411 | + | 0.0896154i | ||||
\(745\) | −1.61264 | − | 2.79317i | −0.0590824 | − | 0.102334i | ||||
\(746\) | −16.0000 | −0.585802 | ||||||||
\(747\) | 35.7618 | + | 9.84120i | 1.30846 | + | 0.360071i | ||||
\(748\) | −20.8506 | −0.762374 | ||||||||
\(749\) | 4.33237 | + | 7.50388i | 0.158301 | + | 0.274186i | ||||
\(750\) | 1.05903 | − | 1.37057i | 0.0386704 | − | 0.0500460i | ||||
\(751\) | −21.0551 | + | 36.4684i | −0.768310 | + | 1.33075i | 0.170168 | + | 0.985415i | \(0.445569\pi\) |
−0.938479 | + | 0.345338i | \(0.887764\pi\) | |||||||
\(752\) | 0.378666 | − | 0.655869i | 0.0138085 | − | 0.0239171i | ||||
\(753\) | 10.9621 | + | 26.7191i | 0.399480 | + | 0.973699i | ||||
\(754\) | 18.8822 | + | 32.7050i | 0.687651 | + | 1.19105i | ||||
\(755\) | 5.39136 | 0.196212 | ||||||||
\(756\) | −4.78027 | − | 2.03692i | −0.173857 | − | 0.0740821i | ||||
\(757\) | −22.8765 | −0.831461 | −0.415731 | − | 0.909488i | \(-0.636474\pi\) | ||||
−0.415731 | + | 0.909488i | \(0.636474\pi\) | |||||||
\(758\) | 12.2285 | + | 21.1804i | 0.444159 | + | 0.769306i | ||||
\(759\) | 3.15732 | + | 7.69571i | 0.114604 | + | 0.279337i | ||||
\(760\) | −2.13557 | + | 3.69892i | −0.0774653 | + | 0.134174i | ||||
\(761\) | −2.87978 | + | 4.98793i | −0.104392 | + | 0.180812i | −0.913490 | − | 0.406862i | \(-0.866623\pi\) |
0.809098 | + | 0.587674i | \(0.199956\pi\) | |||||||
\(762\) | 3.96902 | − | 5.13659i | 0.143782 | − | 0.186079i | ||||
\(763\) | 1.78462 | + | 3.09105i | 0.0646074 | + | 0.111903i | ||||
\(764\) | −18.7462 | −0.678215 | ||||||||
\(765\) | −5.74352 | − | 22.0280i | −0.207657 | − | 0.796424i | ||||
\(766\) | −0.923419 | −0.0333645 | ||||||||
\(767\) | −2.47160 | − | 4.28093i | −0.0892443 | − | 0.154576i | ||||
\(768\) | 1.71646 | + | 0.231865i | 0.0619375 | + | 0.00836669i | ||||
\(769\) | −15.0886 | + | 26.1342i | −0.544108 | + | 0.942423i | 0.454554 | + | 0.890719i | \(0.349799\pi\) |
−0.998662 | + | 0.0517041i | \(0.983535\pi\) | |||||||
\(770\) | −1.37389 | + | 2.37965i | −0.0495116 | + | 0.0857566i | ||||
\(771\) | 38.0021 | + | 5.13344i | 1.36861 | + | 0.184876i | ||||
\(772\) | 5.81267 | + | 10.0678i | 0.209202 | + | 0.362349i | ||||
\(773\) | −34.6156 | −1.24504 | −0.622518 | − | 0.782605i | \(-0.713890\pi\) | ||||
−0.622518 | + | 0.782605i | \(0.713890\pi\) | |||||||
\(774\) | 0.975948 | + | 3.74303i | 0.0350797 | + | 0.134541i | ||||
\(775\) | 10.5423 | 0.378690 | ||||||||
\(776\) | 7.79877 | + | 13.5079i | 0.279959 | + | 0.484904i | ||||
\(777\) | 7.73974 | − | 10.0165i | 0.277661 | − | 0.359341i | ||||
\(778\) | 8.68698 | − | 15.0463i | 0.311443 | − | 0.539436i | ||||
\(779\) | 6.48610 | − | 11.2343i | 0.232389 | − | 0.402509i | ||||
\(780\) | −2.65416 | − | 6.46929i | −0.0950341 | − | 0.231638i | ||||
\(781\) | 0.756993 | + | 1.31115i | 0.0270873 | + | 0.0469166i | ||||
\(782\) | 13.2624 | 0.474264 | ||||||||
\(783\) | −5.85674 | − | 48.2516i | −0.209303 | − | 1.72437i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −11.5696 | − | 20.0391i | −0.412936 | − | 0.715226i | ||||
\(786\) | −8.22695 | − | 20.0525i | −0.293446 | − | 0.715250i | ||||
\(787\) | −17.4530 | + | 30.2295i | −0.622133 | + | 1.07757i | 0.366955 | + | 0.930239i | \(0.380400\pi\) |
−0.989088 | + | 0.147327i | \(0.952933\pi\) | |||||||
\(788\) | −11.4019 | + | 19.7487i | −0.406177 | + | 0.703520i | ||||
\(789\) | 1.92969 | − | 2.49735i | 0.0686988 | − | 0.0889080i | ||||
\(790\) | 3.14470 | + | 5.44677i | 0.111883 | + | 0.193787i | ||||
\(791\) | 8.08372 | 0.287424 | ||||||||
\(792\) | 7.94790 | + | 2.18716i | 0.282416 | + | 0.0777174i | ||||
\(793\) | −49.8023 | −1.76853 | ||||||||
\(794\) | 14.2281 | + | 24.6438i | 0.504936 | + | 0.874574i | ||||
\(795\) | −12.4168 | − | 1.67730i | −0.440380 | − | 0.0594878i | ||||
\(796\) | −7.42488 | + | 12.8603i | −0.263168 | + | 0.455820i | ||||
\(797\) | 22.6403 | − | 39.2141i | 0.801959 | − | 1.38903i | −0.116366 | − | 0.993206i | \(-0.537124\pi\) |
0.918325 | − | 0.395828i | \(-0.129542\pi\) | |||||||
\(798\) | 7.33125 | + | 0.990327i | 0.259524 | + | 0.0350572i | ||||
\(799\) | −2.87338 | − | 4.97684i | −0.101653 | − | 0.176068i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −15.0080 | + | 14.8070i | −0.530281 | + | 0.523180i | ||||
\(802\) | 15.1042 | 0.533348 | ||||||||
\(803\) | 12.4672 | + | 21.5938i | 0.439957 | + | 0.762027i | ||||
\(804\) | −14.0838 | + | 18.2268i | −0.496698 | + | 0.642811i | ||||
\(805\) | 0.873891 | − | 1.51362i | 0.0308006 | − | 0.0533482i | ||||
\(806\) | 21.2805 | − | 36.8589i | 0.749574 | − | 1.29830i | ||||
\(807\) | 4.11656 | + | 10.0338i | 0.144910 | + | 0.353206i | ||||
\(808\) | −7.98175 | − | 13.8248i | −0.280797 | − | 0.486355i | ||||
\(809\) | 10.1482 | 0.356791 | 0.178396 | − | 0.983959i | \(-0.442909\pi\) | ||||
0.178396 | + | 0.983959i | \(0.442909\pi\) | |||||||
\(810\) | −0.121334 | + | 8.99918i | −0.00426324 | + | 0.316199i | ||||
\(811\) | −5.76671 | −0.202496 | −0.101248 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101248 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(812\) | 4.67709 | + | 8.10096i | 0.164134 | + | 0.284288i | ||||
\(813\) | 3.88795 | + | 9.47657i | 0.136357 | + | 0.332358i | ||||
\(814\) | −10.0408 | + | 17.3912i | −0.351931 | + | 0.609562i | ||||
\(815\) | −2.29408 | + | 3.97346i | −0.0803581 | + | 0.139184i | ||||
\(816\) | 8.03610 | − | 10.4001i | 0.281320 | − | 0.364075i | ||||
\(817\) | −2.75359 | − | 4.76935i | −0.0963358 | − | 0.166859i | ||||
\(818\) | −32.2513 | −1.12764 | ||||||||
\(819\) | −8.62167 | + | 8.50621i | −0.301266 | + | 0.297231i | ||||
\(820\) | −3.03717 | −0.106063 | ||||||||
\(821\) | 4.68332 | + | 8.11176i | 0.163449 | + | 0.283102i | 0.936103 | − | 0.351725i | \(-0.114405\pi\) |
−0.772654 | + | 0.634827i | \(0.781071\pi\) | |||||||
\(822\) | 30.1256 | + | 4.06945i | 1.05075 | + | 0.141938i | ||||
\(823\) | 25.5088 | − | 44.1825i | 0.889180 | − | 1.54010i | 0.0483333 | − | 0.998831i | \(-0.484609\pi\) |
0.840847 | − | 0.541273i | \(-0.182058\pi\) | |||||||
\(824\) | 7.36477 | − | 12.7562i | 0.256564 | − | 0.444382i | ||||
\(825\) | 4.71646 | + | 0.637113i | 0.164206 | + | 0.0221814i | ||||
\(826\) | −0.612210 | − | 1.06038i | −0.0213015 | − | 0.0368953i | ||||
\(827\) | 20.4582 | 0.711402 | 0.355701 | − | 0.934600i | \(-0.384242\pi\) | ||||
0.355701 | + | 0.934600i | \(0.384242\pi\) | |||||||
\(828\) | −5.05542 | − | 1.39119i | −0.175688 | − | 0.0483471i | ||||
\(829\) | −36.5801 | −1.27048 | −0.635240 | − | 0.772314i | \(-0.719099\pi\) | ||||
−0.635240 | + | 0.772314i | \(0.719099\pi\) | |||||||
\(830\) | 6.18187 | + | 10.7073i | 0.214576 | + | 0.371656i | ||||
\(831\) | 16.9059 | − | 21.8790i | 0.586457 | − | 0.758976i | ||||
\(832\) | 2.01859 | − | 3.49629i | 0.0699819 | − | 0.121212i | ||||
\(833\) | 3.79408 | − | 6.57154i | 0.131457 | − | 0.227690i | ||||
\(834\) | 0.257292 | + | 0.627128i | 0.00890929 | + | 0.0217157i | ||||
\(835\) | −4.74343 | − | 8.21587i | −0.164153 | − | 0.284322i | ||||
\(836\) | −11.7362 | −0.405904 | ||||||||
\(837\) | −43.7943 | + | 32.9064i | −1.51375 | + | 1.13741i | ||||
\(838\) | 6.62601 | 0.228892 | ||||||||
\(839\) | 6.89214 | + | 11.9375i | 0.237943 | + | 0.412129i | 0.960124 | − | 0.279575i | \(-0.0901935\pi\) |
−0.722181 | + | 0.691704i | \(0.756860\pi\) | |||||||
\(840\) | −0.657430 | − | 1.60243i | −0.0226835 | − | 0.0552891i | ||||
\(841\) | −29.2504 | + | 50.6632i | −1.00863 | + | 1.74701i | ||||
\(842\) | 0.335601 | − | 0.581277i | 0.0115656 | − | 0.0200321i | ||||
\(843\) | −3.40574 | + | 4.40760i | −0.117300 | + | 0.151806i | ||||
\(844\) | 4.90203 | + | 8.49056i | 0.168735 | + | 0.292257i | ||||
\(845\) | −3.29877 | −0.113481 | ||||||||
\(846\) | 0.573229 | + | 2.19849i | 0.0197080 | + | 0.0755858i | ||||
\(847\) | 3.44969 | 0.118533 | ||||||||
\(848\) | −3.61699 | − | 6.26480i | −0.124208 | − | 0.215134i | ||||
\(849\) | −2.13299 | − | 0.288131i | −0.0732041 | − | 0.00988862i | ||||
\(850\) | 3.79408 | − | 6.57154i | 0.130136 | − | 0.225402i | ||||
\(851\) | 6.38667 | − | 11.0620i | 0.218932 | − | 0.379202i | ||||
\(852\) | −0.945744 | − | 0.127754i | −0.0324006 | − | 0.00437677i | ||||
\(853\) | 9.06480 | + | 15.7007i | 0.310373 | + | 0.537581i | 0.978443 | − | 0.206517i | \(-0.0662128\pi\) |
−0.668070 | + | 0.744098i | \(0.732879\pi\) | |||||||
\(854\) | −12.3359 | −0.422127 | ||||||||
\(855\) | −3.23285 | − | 12.3989i | −0.110561 | − | 0.424033i | ||||
\(856\) | 8.66474 | 0.296155 | ||||||||
\(857\) | −10.9993 | − | 19.0514i | −0.375729 | − | 0.650782i | 0.614707 | − | 0.788756i | \(-0.289274\pi\) |
−0.990436 | + | 0.137974i | \(0.955941\pi\) | |||||||
\(858\) | 11.7481 | − | 15.2041i | 0.401074 | − | 0.519058i | ||||
\(859\) | −1.15364 | + | 1.99817i | −0.0393619 | + | 0.0681767i | −0.885035 | − | 0.465524i | \(-0.845866\pi\) |
0.845673 | + | 0.533701i | \(0.179199\pi\) | |||||||
\(860\) | −0.644696 | + | 1.11665i | −0.0219839 | + | 0.0380773i | ||||
\(861\) | 1.99673 | + | 4.86686i | 0.0680483 | + | 0.165862i | ||||
\(862\) | −12.6957 | − | 21.9896i | −0.432417 | − | 0.748967i | ||||
\(863\) | −56.2987 | −1.91643 | −0.958216 | − | 0.286047i | \(-0.907659\pi\) | ||||
−0.958216 | + | 0.286047i | \(0.907659\pi\) | |||||||
\(864\) | −4.15416 | + | 3.12137i | −0.141327 | + | 0.106191i | ||||
\(865\) | −10.5423 | −0.358449 | ||||||||
\(866\) | −15.5688 | − | 26.9659i | −0.529049 | − | 0.916340i | ||||
\(867\) | −26.6786 | − | 65.0269i | −0.906053 | − | 2.20843i | ||||
\(868\) | 5.27114 | − | 9.12989i | 0.178914 | − | 0.309889i | ||||
\(869\) | −8.64094 | + | 14.9665i | −0.293124 | + | 0.507705i | ||||
\(870\) | 9.90638 | − | 12.8205i | 0.335858 | − | 0.434657i | ||||
\(871\) | 26.8447 | + | 46.4964i | 0.909598 | + | 1.57547i | ||||
\(872\) | 3.56923 | 0.120869 | ||||||||
\(873\) | −45.1155 | − | 12.4152i | −1.52693 | − | 0.420191i | ||||
\(874\) | 7.46503 | 0.252508 | ||||||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | −15.5758 | − | 2.10402i | −0.526256 | − | 0.0710882i | ||||
\(877\) | −18.4754 | + | 32.0004i | −0.623871 | + | 1.08058i | 0.364887 | + | 0.931052i | \(0.381108\pi\) |
−0.988758 | + | 0.149525i | \(0.952226\pi\) | |||||||
\(878\) | 0.368777 | − | 0.638740i | 0.0124456 | − | 0.0215564i | ||||
\(879\) | 36.8761 | + | 4.98133i | 1.24380 | + | 0.168016i | ||||
\(880\) | 1.37389 | + | 2.37965i | 0.0463139 | + | 0.0802180i | ||||
\(881\) | −41.7471 | −1.40649 | −0.703247 | − | 0.710945i | \(-0.748267\pi\) | ||||
−0.703247 | + | 0.710945i | \(0.748267\pi\) | |||||||
\(882\) | −2.13557 | + | 2.10697i | −0.0719084 | + | 0.0709455i | ||||
\(883\) | −5.69236 | −0.191563 | −0.0957816 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957816 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(884\) | −15.3174 | − | 26.5304i | −0.515178 | − | 0.892315i | ||||
\(885\) | −1.29670 | + | 1.67815i | −0.0435881 | + | 0.0564104i | ||||
\(886\) | −13.5499 | + | 23.4691i | −0.455217 | + | 0.788458i | ||||
\(887\) | −18.9052 | + | 32.7447i | −0.634774 | + | 1.09946i | 0.351790 | + | 0.936079i | \(0.385573\pi\) |
−0.986563 | + | 0.163381i | \(0.947760\pi\) | |||||||
\(888\) | −4.80471 | − | 11.7111i | −0.161235 | − | 0.392998i | ||||
\(889\) | −1.87389 | − | 3.24567i | −0.0628483 | − | 0.108856i | ||||
\(890\) | −7.02762 | −0.235566 | ||||||||
\(891\) | −21.5816 | + | 12.0752i | −0.723011 | + | 0.404533i | ||||
\(892\) | 2.57008 | 0.0860528 | ||||||||
\(893\) | −1.61734 | − | 2.80131i | −0.0541221 | − | 0.0937423i | ||||
\(894\) | 2.12039 | + | 5.16828i | 0.0709165 | + | 0.172853i | ||||
\(895\) | −5.95259 | + | 10.3102i | −0.198973 | + | 0.344631i | ||||
\(896\) | 0.500000 | − | 0.866025i | 0.0167038 | − | 0.0289319i | ||||
\(897\) | −7.47263 | + | 9.67085i | −0.249504 | + | 0.322900i | ||||
\(898\) | 2.58459 | + | 4.47664i | 0.0862488 | + | 0.149387i | ||||
\(899\) | 98.6145 | 3.28898 | ||||||||
\(900\) | −2.13557 | + | 2.10697i | −0.0711857 | + | 0.0702324i | ||||
\(901\) | −54.8925 | −1.82873 | ||||||||
\(902\) | −4.17274 | − | 7.22741i | −0.138937 | − | 0.240646i | ||||
\(903\) | 2.21319 | + | 0.298964i | 0.0736503 | + | 0.00994890i | ||||
\(904\) | 4.04186 | − | 7.00071i | 0.134430 | − | 0.232840i | ||||
\(905\) | 5.26159 | − | 9.11335i | 0.174901 | − | 0.302938i | ||||
\(906\) | −9.25406 | − | 1.25007i | −0.307446 | − | 0.0415307i | ||||
\(907\) | −20.6779 | − | 35.8151i | −0.686597 | − | 1.18922i | −0.972932 | − | 0.231091i | \(-0.925770\pi\) |
0.286335 | − | 0.958130i | \(-0.407563\pi\) | |||||||
\(908\) | 8.75716 | 0.290616 | ||||||||
\(909\) | 46.1741 | + | 12.7065i | 1.53150 | + | 0.421449i | ||||
\(910\) | −4.03717 | −0.133831 | ||||||||
\(911\) | −8.48167 | − | 14.6907i | −0.281010 | − | 0.486724i | 0.690624 | − | 0.723214i | \(-0.257336\pi\) |
−0.971634 | + | 0.236491i | \(0.924003\pi\) | |||||||
\(912\) | 4.52327 | − | 5.85389i | 0.149781 | − | 0.193842i | ||||
\(913\) | −16.9864 | + | 29.4214i | −0.562169 | + | 0.973705i | ||||
\(914\) | 2.56446 | − | 4.44177i | 0.0848247 | − | 0.146921i | ||||
\(915\) | 8.11002 | + | 19.7675i | 0.268109 | + | 0.653493i | ||||
\(916\) | 0.0936237 | + | 0.162161i | 0.00309341 | + | 0.00535795i | ||||
\(917\) | −12.5138 | −0.413242 | ||||||||
\(918\) | 4.75101 | + | 39.1419i | 0.156807 | + | 1.29188i | ||||
\(919\) | −3.49350 | −0.115240 | −0.0576200 | − | 0.998339i | \(-0.518351\pi\) | ||||
−0.0576200 | + | 0.998339i | \(0.518351\pi\) | |||||||
\(920\) | −0.873891 | − | 1.51362i | −0.0288113 | − | 0.0499027i | ||||
\(921\) | −20.4703 | − | 49.8948i | −0.674520 | − | 1.64409i | ||||
\(922\) | 6.54040 | − | 11.3283i | 0.215397 | − | 0.373078i | ||||
\(923\) | −1.11221 | + | 1.92640i | −0.0366088 | + | 0.0634084i | ||||
\(924\) | 2.90999 | − | 3.76602i | 0.0957315 | − | 0.123893i | ||||
\(925\) | −3.65416 | − | 6.32919i | −0.120148 | − | 0.208102i | ||||
\(926\) | −19.5334 | −0.641908 | ||||||||
\(927\) | 11.1489 | + | 42.7590i | 0.366177 | + | 1.40439i | ||||
\(928\) | 9.35419 | 0.307066 | ||||||||
\(929\) | 9.76603 | + | 16.9153i | 0.320413 | + | 0.554972i | 0.980573 | − | 0.196153i | \(-0.0628450\pi\) |
−0.660160 | + | 0.751125i | \(0.729512\pi\) | |||||||
\(930\) | −18.0954 | − | 2.44438i | −0.593372 | − | 0.0801545i | ||||
\(931\) | 2.13557 | − | 3.69892i | 0.0699905 | − | 0.121227i | ||||
\(932\) | −7.78973 | + | 13.4922i | −0.255161 | + | 0.441952i | ||||
\(933\) | 44.1122 | + | 5.95881i | 1.44417 | + | 0.195083i | ||||
\(934\) | 0.255449 | + | 0.442451i | 0.00835856 | + | 0.0144775i | ||||
\(935\) | 20.8506 | 0.681888 | ||||||||
\(936\) | 3.05576 | + | 11.7197i | 0.0998806 | + | 0.383070i | ||||
\(937\) | −21.5129 | −0.702797 | −0.351398 | − | 0.936226i | \(-0.614294\pi\) | ||||
−0.351398 | + | 0.936226i | \(0.614294\pi\) | |||||||
\(938\) | 6.64938 | + | 11.5171i | 0.217110 | + | 0.376046i | ||||
\(939\) | −23.8018 | + | 30.8036i | −0.776743 | + | 1.00524i | ||||
\(940\) | −0.378666 | + | 0.655869i | −0.0123507 | + | 0.0213921i | ||||
\(941\) | −20.3550 | + | 35.2560i | −0.663555 | + | 1.14931i | 0.316119 | + | 0.948719i | \(0.397620\pi\) |
−0.979675 | + | 0.200592i | \(0.935713\pi\) | |||||||
\(942\) | 15.2124 | + | 37.0789i | 0.495646 | + | 1.20810i | ||||
\(943\) | 2.65416 | + | 4.59714i | 0.0864313 | + | 0.149703i | ||||
\(944\) | −1.22442 | −0.0398515 | ||||||||
\(945\) | 4.78027 | + | 2.03692i | 0.155502 | + | 0.0662610i | ||||
\(946\) | −3.54297 | −0.115192 | ||||||||
\(947\) | −25.0156 | − | 43.3282i | −0.812897 | − | 1.40798i | −0.910828 | − | 0.412786i | \(-0.864556\pi\) |
0.0979313 | − | 0.995193i | \(-0.468777\pi\) | |||||||
\(948\) | −4.13483 | − | 10.0783i | −0.134293 | − | 0.327329i | ||||
\(949\) | −18.3174 | + | 31.7266i | −0.594606 | + | 1.02989i | ||||
\(950\) | 2.13557 | − | 3.69892i | 0.0692871 | − | 0.120009i | ||||
\(951\) | −2.51248 | + | 3.25158i | −0.0814728 | + | 0.105440i | ||||
\(952\) | −3.79408 | − | 6.57154i | −0.122967 | − | 0.212985i | ||||
\(953\) | −27.4321 | −0.888614 | −0.444307 | − | 0.895875i | \(-0.646550\pi\) | ||||
−0.444307 | + | 0.895875i | \(0.646550\pi\) | |||||||
\(954\) | 20.9241 | + | 5.75805i | 0.677443 | + | 0.186424i | ||||
\(955\) | 18.7462 | 0.606614 | ||||||||
\(956\) | −2.46794 | − | 4.27460i | −0.0798189 | − | 0.138250i | ||||
\(957\) | 44.1187 | + | 5.95968i | 1.42615 | + | 0.192649i | ||||
\(958\) | −4.17283 | + | 7.22756i | −0.134818 | + | 0.233512i | ||||
\(959\) | 8.77549 | − | 15.1996i | 0.283375 | − | 0.490821i | ||||
\(960\) | −1.71646 | − | 0.231865i | −0.0553985 | − | 0.00748340i | ||||
\(961\) | −40.0699 | − | 69.4031i | −1.29258 | − | 2.23881i | ||||
\(962\) | −29.5049 | −0.951277 | ||||||||
\(963\) | −18.5042 | + | 18.2564i | −0.596289 | + | 0.588303i | ||||
\(964\) | 25.2696 | 0.813879 | ||||||||
\(965\) | −5.81267 | − | 10.0678i | −0.187116 | − | 0.324095i | ||||
\(966\) | −1.85096 | + | 2.39545i | −0.0595535 | + | 0.0770724i | ||||
\(967\) | 13.1603 | − | 22.7943i | 0.423207 | − | 0.733016i | −0.573044 | − | 0.819524i | \(-0.694238\pi\) |
0.996251 | + | 0.0865087i | \(0.0275710\pi\) | |||||||
\(968\) | 1.72485 | − | 2.98752i | 0.0554387 | − | 0.0960226i | ||||
\(969\) | −21.3074 | − | 51.9350i | −0.684492 | − | 1.66839i | ||||
\(970\) | −7.79877 | − | 13.5079i | −0.250403 | − | 0.433711i | ||||
\(971\) | 12.4301 | 0.398901 | 0.199450 | − | 0.979908i | \(-0.436084\pi\) | ||||
0.199450 | + | 0.979908i | \(0.436084\pi\) | |||||||
\(972\) | 2.29486 | − | 15.4186i | 0.0736076 | − | 0.494552i | ||||
\(973\) | 0.391360 | 0.0125464 | ||||||||
\(974\) | −10.9423 | − | 18.9527i | −0.350615 | − | 0.607284i | ||||
\(975\) | 2.65416 | + | 6.46929i | 0.0850011 | + | 0.207183i | ||||
\(976\) | −6.16797 | + | 10.6832i | −0.197432 | + | 0.341962i | ||||
\(977\) | −11.3914 | + | 19.7306i | −0.364445 | + | 0.631237i | −0.988687 | − | 0.149994i | \(-0.952075\pi\) |
0.624242 | + | 0.781231i | \(0.285408\pi\) | |||||||
\(978\) | 4.85900 | − | 6.28838i | 0.155374 | − | 0.201080i | ||||
\(979\) | −9.65519 | − | 16.7233i | −0.308581 | − | 0.534478i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −7.62235 | + | 7.52027i | −0.243363 | + | 0.240104i | ||||
\(982\) | −28.4205 | −0.906935 | ||||||||
\(983\) | 26.6220 | + | 46.1107i | 0.849110 | + | 1.47070i | 0.882003 | + | 0.471243i | \(0.156195\pi\) |
−0.0328929 | + | 0.999459i | \(0.510472\pi\) | |||||||
\(984\) | 5.21319 | + | 0.704213i | 0.166190 | + | 0.0224495i | ||||
\(985\) | 11.4019 | − | 19.7487i | 0.363296 | − | 0.629247i | ||||
\(986\) | 35.4905 | − | 61.4714i | 1.13025 | − | 1.95765i | ||||
\(987\) | 1.29993 | + | 0.175599i | 0.0413773 | + | 0.00558936i | ||||
\(988\) | −8.62167 | − | 14.9332i | −0.274292 | − | 0.475088i | ||||
\(989\) | 2.25357 | 0.0716595 | ||||||||
\(990\) | −7.94790 | − | 2.18716i | −0.252601 | − | 0.0695125i | ||||
\(991\) | −33.2993 | −1.05779 | −0.528893 | − | 0.848688i | \(-0.677393\pi\) | ||||
−0.528893 | + | 0.848688i | \(0.677393\pi\) | |||||||
\(992\) | −5.27114 | − | 9.12989i | −0.167359 | − | 0.289874i | ||||
\(993\) | 1.37634 | − | 1.78121i | 0.0436767 | − | 0.0565251i | ||||
\(994\) | −0.275492 | + | 0.477167i | −0.00873809 | + | 0.0151348i | ||||
\(995\) | 7.42488 | − | 12.8603i | 0.235384 | − | 0.407698i | ||||
\(996\) | −8.12829 | − | 19.8120i | −0.257555 | − | 0.627768i | ||||
\(997\) | 4.82230 | + | 8.35247i | 0.152724 | + | 0.264525i | 0.932228 | − | 0.361872i | \(-0.117862\pi\) |
−0.779504 | + | 0.626397i | \(0.784529\pi\) | |||||||
\(998\) | −15.4197 | −0.488101 | ||||||||
\(999\) | 34.9357 | + | 14.8865i | 1.10532 | + | 0.470987i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 630.2.j.l.211.3 | ✓ | 8 | |
3.2 | odd | 2 | 1890.2.j.l.631.3 | 8 | |||
9.2 | odd | 6 | 1890.2.j.l.1261.3 | 8 | |||
9.4 | even | 3 | 5670.2.a.bw.1.3 | 4 | |||
9.5 | odd | 6 | 5670.2.a.bv.1.2 | 4 | |||
9.7 | even | 3 | inner | 630.2.j.l.421.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.j.l.211.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
630.2.j.l.421.3 | yes | 8 | 9.7 | even | 3 | inner | |
1890.2.j.l.631.3 | 8 | 3.2 | odd | 2 | |||
1890.2.j.l.1261.3 | 8 | 9.2 | odd | 6 | |||
5670.2.a.bv.1.2 | 4 | 9.5 | odd | 6 | |||
5670.2.a.bw.1.3 | 4 | 9.4 | even | 3 |