Properties

Label 380.2.i.b.201.2
Level $380$
Weight $2$
Character 380.201
Analytic conductor $3.034$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(121,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.2
Root \(1.09935 + 1.90412i\) of defining polynomial
Character \(\chi\) \(=\) 380.201
Dual form 380.2.i.b.121.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.182224 - 0.315621i) q^{3} +(0.500000 - 0.866025i) q^{5} +0.635552 q^{7} +(1.43359 + 2.48305i) q^{9} +O(q^{10})\) \(q+(0.182224 - 0.315621i) q^{3} +(0.500000 - 0.866025i) q^{5} +0.635552 q^{7} +(1.43359 + 2.48305i) q^{9} +1.63555 q^{11} +(0.500000 + 0.866025i) q^{13} +(-0.182224 - 0.315621i) q^{15} +(3.29804 - 5.71237i) q^{17} +(0.0466721 - 4.35865i) q^{19} +(0.115813 - 0.200594i) q^{21} +(-0.433589 - 0.750998i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.13828 q^{27} +(4.54940 + 7.87979i) q^{29} -1.86718 q^{31} +(0.298037 - 0.516215i) q^{33} +(0.317776 - 0.550404i) q^{35} +0.635552 q^{37} +0.364448 q^{39} +(-0.953328 + 1.65121i) q^{41} +(-1.98026 + 3.42991i) q^{43} +2.86718 q^{45} +(-4.54940 - 7.87979i) q^{47} -6.59607 q^{49} +(-1.20196 - 2.08186i) q^{51} +(4.93359 + 8.54523i) q^{53} +(0.817776 - 1.41643i) q^{55} +(-1.36718 - 0.808981i) q^{57} +(-4.54940 + 7.87979i) q^{59} +(-1.13555 - 1.96683i) q^{61} +(0.911120 + 1.57811i) q^{63} +1.00000 q^{65} +(-6.23163 - 10.7935i) q^{67} -0.316041 q^{69} +(-1.25136 + 2.16743i) q^{71} +(0.201963 - 0.349810i) q^{73} -0.364448 q^{75} +1.03948 q^{77} +(-5.36445 + 9.29150i) q^{79} +(-3.91112 + 6.77426i) q^{81} -15.8672 q^{83} +(-3.29804 - 5.71237i) q^{85} +3.31604 q^{87} +(-0.271104 - 0.469566i) q^{89} +(0.317776 + 0.550404i) q^{91} +(-0.340245 + 0.589321i) q^{93} +(-3.75136 - 2.21974i) q^{95} +(3.68495 - 6.38253i) q^{97} +(2.34471 + 4.06116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9} + 10 q^{11} + 3 q^{13} - q^{15} + 3 q^{17} - 16 q^{21} + 14 q^{23} - 3 q^{25} - 20 q^{27} - 6 q^{29} + 22 q^{31} - 15 q^{33} + 2 q^{35} + 4 q^{37} + 2 q^{39} - 6 q^{41} + 5 q^{43} - 16 q^{45} + 6 q^{47} - 6 q^{49} - 24 q^{51} + 13 q^{53} + 5 q^{55} + 25 q^{57} + 6 q^{59} - 7 q^{61} + 5 q^{63} + 6 q^{65} - 4 q^{67} + 30 q^{69} + 9 q^{71} + 18 q^{73} - 2 q^{75} + 40 q^{77} - 32 q^{79} - 23 q^{81} - 62 q^{83} - 3 q^{85} - 12 q^{87} - 2 q^{89} + 2 q^{91} + 14 q^{93} - 6 q^{95} - 11 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.182224 0.315621i 0.105207 0.182224i −0.808616 0.588337i \(-0.799783\pi\)
0.913823 + 0.406113i \(0.133116\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 0.635552 0.240216 0.120108 0.992761i \(-0.461676\pi\)
0.120108 + 0.992761i \(0.461676\pi\)
\(8\) 0 0
\(9\) 1.43359 + 2.48305i 0.477863 + 0.827683i
\(10\) 0 0
\(11\) 1.63555 0.493137 0.246569 0.969125i \(-0.420697\pi\)
0.246569 + 0.969125i \(0.420697\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0 0
\(15\) −0.182224 0.315621i −0.0470500 0.0814931i
\(16\) 0 0
\(17\) 3.29804 5.71237i 0.799891 1.38545i −0.119795 0.992799i \(-0.538224\pi\)
0.919686 0.392654i \(-0.128443\pi\)
\(18\) 0 0
\(19\) 0.0466721 4.35865i 0.0107073 0.999943i
\(20\) 0 0
\(21\) 0.115813 0.200594i 0.0252724 0.0437731i
\(22\) 0 0
\(23\) −0.433589 0.750998i −0.0904095 0.156594i 0.817274 0.576249i \(-0.195484\pi\)
−0.907684 + 0.419655i \(0.862151\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 2.13828 0.411512
\(28\) 0 0
\(29\) 4.54940 + 7.87979i 0.844803 + 1.46324i 0.885792 + 0.464082i \(0.153616\pi\)
−0.0409898 + 0.999160i \(0.513051\pi\)
\(30\) 0 0
\(31\) −1.86718 −0.335355 −0.167677 0.985842i \(-0.553627\pi\)
−0.167677 + 0.985842i \(0.553627\pi\)
\(32\) 0 0
\(33\) 0.298037 0.516215i 0.0518816 0.0898615i
\(34\) 0 0
\(35\) 0.317776 0.550404i 0.0537139 0.0930353i
\(36\) 0 0
\(37\) 0.635552 0.104484 0.0522420 0.998634i \(-0.483363\pi\)
0.0522420 + 0.998634i \(0.483363\pi\)
\(38\) 0 0
\(39\) 0.364448 0.0583584
\(40\) 0 0
\(41\) −0.953328 + 1.65121i −0.148885 + 0.257876i −0.930816 0.365489i \(-0.880902\pi\)
0.781931 + 0.623365i \(0.214235\pi\)
\(42\) 0 0
\(43\) −1.98026 + 3.42991i −0.301987 + 0.523057i −0.976586 0.215128i \(-0.930983\pi\)
0.674599 + 0.738184i \(0.264317\pi\)
\(44\) 0 0
\(45\) 2.86718 0.427414
\(46\) 0 0
\(47\) −4.54940 7.87979i −0.663598 1.14939i −0.979663 0.200649i \(-0.935695\pi\)
0.316065 0.948738i \(-0.397638\pi\)
\(48\) 0 0
\(49\) −6.59607 −0.942296
\(50\) 0 0
\(51\) −1.20196 2.08186i −0.168309 0.291519i
\(52\) 0 0
\(53\) 4.93359 + 8.54523i 0.677681 + 1.17378i 0.975678 + 0.219210i \(0.0703481\pi\)
−0.297997 + 0.954567i \(0.596319\pi\)
\(54\) 0 0
\(55\) 0.817776 1.41643i 0.110269 0.190991i
\(56\) 0 0
\(57\) −1.36718 0.808981i −0.181087 0.107152i
\(58\) 0 0
\(59\) −4.54940 + 7.87979i −0.592282 + 1.02586i 0.401643 + 0.915796i \(0.368439\pi\)
−0.993924 + 0.110065i \(0.964894\pi\)
\(60\) 0 0
\(61\) −1.13555 1.96683i −0.145393 0.251827i 0.784127 0.620601i \(-0.213111\pi\)
−0.929519 + 0.368773i \(0.879778\pi\)
\(62\) 0 0
\(63\) 0.911120 + 1.57811i 0.114790 + 0.198823i
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −6.23163 10.7935i −0.761314 1.31863i −0.942173 0.335126i \(-0.891221\pi\)
0.180859 0.983509i \(-0.442112\pi\)
\(68\) 0 0
\(69\) −0.316041 −0.0380469
\(70\) 0 0
\(71\) −1.25136 + 2.16743i −0.148510 + 0.257226i −0.930677 0.365842i \(-0.880781\pi\)
0.782167 + 0.623069i \(0.214114\pi\)
\(72\) 0 0
\(73\) 0.201963 0.349810i 0.0236380 0.0409422i −0.853964 0.520331i \(-0.825808\pi\)
0.877602 + 0.479389i \(0.159142\pi\)
\(74\) 0 0
\(75\) −0.364448 −0.0420828
\(76\) 0 0
\(77\) 1.03948 0.118460
\(78\) 0 0
\(79\) −5.36445 + 9.29150i −0.603548 + 1.04538i 0.388732 + 0.921351i \(0.372913\pi\)
−0.992279 + 0.124024i \(0.960420\pi\)
\(80\) 0 0
\(81\) −3.91112 + 6.77426i −0.434569 + 0.752695i
\(82\) 0 0
\(83\) −15.8672 −1.74165 −0.870825 0.491594i \(-0.836414\pi\)
−0.870825 + 0.491594i \(0.836414\pi\)
\(84\) 0 0
\(85\) −3.29804 5.71237i −0.357722 0.619593i
\(86\) 0 0
\(87\) 3.31604 0.355517
\(88\) 0 0
\(89\) −0.271104 0.469566i −0.0287370 0.0497739i 0.851299 0.524680i \(-0.175815\pi\)
−0.880036 + 0.474907i \(0.842482\pi\)
\(90\) 0 0
\(91\) 0.317776 + 0.550404i 0.0333120 + 0.0576980i
\(92\) 0 0
\(93\) −0.340245 + 0.589321i −0.0352817 + 0.0611097i
\(94\) 0 0
\(95\) −3.75136 2.21974i −0.384882 0.227741i
\(96\) 0 0
\(97\) 3.68495 6.38253i 0.374150 0.648047i −0.616049 0.787708i \(-0.711268\pi\)
0.990199 + 0.139660i \(0.0446011\pi\)
\(98\) 0 0
\(99\) 2.34471 + 4.06116i 0.235652 + 0.408161i
\(100\) 0 0
\(101\) 4.66248 + 8.07566i 0.463935 + 0.803558i 0.999153 0.0411556i \(-0.0131039\pi\)
−0.535218 + 0.844714i \(0.679771\pi\)
\(102\) 0 0
\(103\) −10.8672 −1.07077 −0.535387 0.844607i \(-0.679834\pi\)
−0.535387 + 0.844607i \(0.679834\pi\)
\(104\) 0 0
\(105\) −0.115813 0.200594i −0.0113022 0.0195759i
\(106\) 0 0
\(107\) 11.3304 1.09535 0.547677 0.836690i \(-0.315512\pi\)
0.547677 + 0.836690i \(0.315512\pi\)
\(108\) 0 0
\(109\) −6.61581 + 11.4589i −0.633680 + 1.09757i 0.353113 + 0.935581i \(0.385123\pi\)
−0.986793 + 0.161985i \(0.948210\pi\)
\(110\) 0 0
\(111\) 0.115813 0.200594i 0.0109925 0.0190395i
\(112\) 0 0
\(113\) 7.09334 0.667286 0.333643 0.942700i \(-0.391722\pi\)
0.333643 + 0.942700i \(0.391722\pi\)
\(114\) 0 0
\(115\) −0.867178 −0.0808647
\(116\) 0 0
\(117\) −1.43359 + 2.48305i −0.132535 + 0.229558i
\(118\) 0 0
\(119\) 2.09607 3.63051i 0.192147 0.332808i
\(120\) 0 0
\(121\) −8.32497 −0.756815
\(122\) 0 0
\(123\) 0.347439 + 0.601781i 0.0313275 + 0.0542608i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −8.13828 14.0959i −0.722156 1.25081i −0.960134 0.279540i \(-0.909818\pi\)
0.237978 0.971270i \(-0.423515\pi\)
\(128\) 0 0
\(129\) 0.721702 + 1.25002i 0.0635423 + 0.110059i
\(130\) 0 0
\(131\) 5.31778 9.21066i 0.464616 0.804739i −0.534568 0.845126i \(-0.679526\pi\)
0.999184 + 0.0403866i \(0.0128590\pi\)
\(132\) 0 0
\(133\) 0.0296625 2.77015i 0.00257207 0.240202i
\(134\) 0 0
\(135\) 1.06914 1.85181i 0.0920170 0.159378i
\(136\) 0 0
\(137\) −1.74864 3.02873i −0.149396 0.258761i 0.781608 0.623769i \(-0.214400\pi\)
−0.931004 + 0.365008i \(0.881066\pi\)
\(138\) 0 0
\(139\) −0.367178 0.635970i −0.0311436 0.0539423i 0.850034 0.526729i \(-0.176582\pi\)
−0.881177 + 0.472786i \(0.843248\pi\)
\(140\) 0 0
\(141\) −3.31604 −0.279261
\(142\) 0 0
\(143\) 0.817776 + 1.41643i 0.0683859 + 0.118448i
\(144\) 0 0
\(145\) 9.09880 0.755614
\(146\) 0 0
\(147\) −1.20196 + 2.08186i −0.0991362 + 0.171709i
\(148\) 0 0
\(149\) −5.06914 + 8.78001i −0.415280 + 0.719286i −0.995458 0.0952036i \(-0.969650\pi\)
0.580178 + 0.814490i \(0.302983\pi\)
\(150\) 0 0
\(151\) 2.81331 0.228944 0.114472 0.993426i \(-0.463482\pi\)
0.114472 + 0.993426i \(0.463482\pi\)
\(152\) 0 0
\(153\) 18.9121 1.52895
\(154\) 0 0
\(155\) −0.933589 + 1.61702i −0.0749877 + 0.129882i
\(156\) 0 0
\(157\) −0.480261 + 0.831836i −0.0383290 + 0.0663878i −0.884554 0.466439i \(-0.845537\pi\)
0.846225 + 0.532826i \(0.178870\pi\)
\(158\) 0 0
\(159\) 3.59607 0.285187
\(160\) 0 0
\(161\) −0.275568 0.477298i −0.0217178 0.0376164i
\(162\) 0 0
\(163\) 3.13828 0.245809 0.122905 0.992418i \(-0.460779\pi\)
0.122905 + 0.992418i \(0.460779\pi\)
\(164\) 0 0
\(165\) −0.298037 0.516215i −0.0232021 0.0401873i
\(166\) 0 0
\(167\) 5.31778 + 9.21066i 0.411502 + 0.712742i 0.995054 0.0993334i \(-0.0316710\pi\)
−0.583552 + 0.812076i \(0.698338\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) 10.8896 6.13262i 0.832752 0.468973i
\(172\) 0 0
\(173\) −6.18495 + 10.7127i −0.470233 + 0.814468i −0.999421 0.0340371i \(-0.989164\pi\)
0.529187 + 0.848505i \(0.322497\pi\)
\(174\) 0 0
\(175\) −0.317776 0.550404i −0.0240216 0.0416066i
\(176\) 0 0
\(177\) 1.65802 + 2.87178i 0.124624 + 0.215856i
\(178\) 0 0
\(179\) −0.324970 −0.0242894 −0.0121447 0.999926i \(-0.503866\pi\)
−0.0121447 + 0.999926i \(0.503866\pi\)
\(180\) 0 0
\(181\) −4.40666 7.63255i −0.327544 0.567323i 0.654480 0.756079i \(-0.272888\pi\)
−0.982024 + 0.188756i \(0.939554\pi\)
\(182\) 0 0
\(183\) −0.827699 −0.0611853
\(184\) 0 0
\(185\) 0.317776 0.550404i 0.0233634 0.0404665i
\(186\) 0 0
\(187\) 5.39411 9.34287i 0.394456 0.683219i
\(188\) 0 0
\(189\) 1.35899 0.0988519
\(190\) 0 0
\(191\) 25.1921 1.82284 0.911420 0.411478i \(-0.134987\pi\)
0.911420 + 0.411478i \(0.134987\pi\)
\(192\) 0 0
\(193\) 9.43632 16.3442i 0.679241 1.17648i −0.295969 0.955198i \(-0.595642\pi\)
0.975210 0.221282i \(-0.0710243\pi\)
\(194\) 0 0
\(195\) 0.182224 0.315621i 0.0130493 0.0226021i
\(196\) 0 0
\(197\) −7.36445 −0.524695 −0.262348 0.964973i \(-0.584497\pi\)
−0.262348 + 0.964973i \(0.584497\pi\)
\(198\) 0 0
\(199\) −1.38419 2.39748i −0.0981224 0.169953i 0.812785 0.582564i \(-0.197950\pi\)
−0.910907 + 0.412611i \(0.864617\pi\)
\(200\) 0 0
\(201\) −4.54221 −0.320383
\(202\) 0 0
\(203\) 2.89138 + 5.00802i 0.202935 + 0.351494i
\(204\) 0 0
\(205\) 0.953328 + 1.65121i 0.0665833 + 0.115326i
\(206\) 0 0
\(207\) 1.24318 2.15324i 0.0864067 0.149661i
\(208\) 0 0
\(209\) 0.0763346 7.12880i 0.00528018 0.493109i
\(210\) 0 0
\(211\) −8.46325 + 14.6588i −0.582634 + 1.00915i 0.412532 + 0.910943i \(0.364645\pi\)
−0.995166 + 0.0982088i \(0.968689\pi\)
\(212\) 0 0
\(213\) 0.456057 + 0.789915i 0.0312485 + 0.0541241i
\(214\) 0 0
\(215\) 1.98026 + 3.42991i 0.135053 + 0.233918i
\(216\) 0 0
\(217\) −1.18669 −0.0805577
\(218\) 0 0
\(219\) −0.0736051 0.127488i −0.00497377 0.00861482i
\(220\) 0 0
\(221\) 6.59607 0.443700
\(222\) 0 0
\(223\) −4.32051 + 7.48334i −0.289322 + 0.501121i −0.973648 0.228055i \(-0.926763\pi\)
0.684326 + 0.729176i \(0.260097\pi\)
\(224\) 0 0
\(225\) 1.43359 2.48305i 0.0955726 0.165537i
\(226\) 0 0
\(227\) 20.9265 1.38894 0.694470 0.719521i \(-0.255639\pi\)
0.694470 + 0.719521i \(0.255639\pi\)
\(228\) 0 0
\(229\) 22.3754 1.47861 0.739303 0.673373i \(-0.235155\pi\)
0.739303 + 0.673373i \(0.235155\pi\)
\(230\) 0 0
\(231\) 0.189418 0.328081i 0.0124628 0.0215862i
\(232\) 0 0
\(233\) 9.61854 16.6598i 0.630132 1.09142i −0.357393 0.933954i \(-0.616334\pi\)
0.987524 0.157466i \(-0.0503324\pi\)
\(234\) 0 0
\(235\) −9.09880 −0.593540
\(236\) 0 0
\(237\) 1.95506 + 3.38627i 0.126995 + 0.219962i
\(238\) 0 0
\(239\) −2.13282 −0.137961 −0.0689804 0.997618i \(-0.521975\pi\)
−0.0689804 + 0.997618i \(0.521975\pi\)
\(240\) 0 0
\(241\) −12.2316 21.1858i −0.787908 1.36470i −0.927246 0.374452i \(-0.877831\pi\)
0.139338 0.990245i \(-0.455503\pi\)
\(242\) 0 0
\(243\) 4.63282 + 8.02428i 0.297196 + 0.514758i
\(244\) 0 0
\(245\) −3.29804 + 5.71237i −0.210704 + 0.364950i
\(246\) 0 0
\(247\) 3.79804 2.13891i 0.241663 0.136095i
\(248\) 0 0
\(249\) −2.89138 + 5.00802i −0.183234 + 0.317370i
\(250\) 0 0
\(251\) −1.64002 2.84059i −0.103517 0.179297i 0.809614 0.586962i \(-0.199676\pi\)
−0.913131 + 0.407666i \(0.866343\pi\)
\(252\) 0 0
\(253\) −0.709157 1.22830i −0.0445843 0.0772223i
\(254\) 0 0
\(255\) −2.40393 −0.150540
\(256\) 0 0
\(257\) 3.81778 + 6.61258i 0.238146 + 0.412482i 0.960182 0.279374i \(-0.0901269\pi\)
−0.722036 + 0.691855i \(0.756794\pi\)
\(258\) 0 0
\(259\) 0.403926 0.0250988
\(260\) 0 0
\(261\) −13.0439 + 22.5928i −0.807400 + 1.39846i
\(262\) 0 0
\(263\) −7.36445 + 12.7556i −0.454111 + 0.786544i −0.998637 0.0522005i \(-0.983376\pi\)
0.544525 + 0.838744i \(0.316710\pi\)
\(264\) 0 0
\(265\) 9.86718 0.606136
\(266\) 0 0
\(267\) −0.197607 −0.0120933
\(268\) 0 0
\(269\) 6.73163 11.6595i 0.410434 0.710893i −0.584503 0.811392i \(-0.698710\pi\)
0.994937 + 0.100498i \(0.0320437\pi\)
\(270\) 0 0
\(271\) −1.93086 + 3.34435i −0.117291 + 0.203155i −0.918693 0.394971i \(-0.870754\pi\)
0.801402 + 0.598126i \(0.204088\pi\)
\(272\) 0 0
\(273\) 0.231626 0.0140186
\(274\) 0 0
\(275\) −0.817776 1.41643i −0.0493137 0.0854139i
\(276\) 0 0
\(277\) −24.2766 −1.45864 −0.729319 0.684174i \(-0.760163\pi\)
−0.729319 + 0.684174i \(0.760163\pi\)
\(278\) 0 0
\(279\) −2.67676 4.63629i −0.160254 0.277568i
\(280\) 0 0
\(281\) −0.248635 0.430649i −0.0148323 0.0256904i 0.858514 0.512790i \(-0.171388\pi\)
−0.873346 + 0.487100i \(0.838055\pi\)
\(282\) 0 0
\(283\) 7.57906 13.1273i 0.450529 0.780338i −0.547890 0.836550i \(-0.684569\pi\)
0.998419 + 0.0562118i \(0.0179022\pi\)
\(284\) 0 0
\(285\) −1.38419 + 0.779520i −0.0819922 + 0.0461748i
\(286\) 0 0
\(287\) −0.605889 + 1.04943i −0.0357645 + 0.0619460i
\(288\) 0 0
\(289\) −13.2541 22.9568i −0.779653 1.35040i
\(290\) 0 0
\(291\) −1.34297 2.32610i −0.0787265 0.136358i
\(292\) 0 0
\(293\) −13.4094 −0.783385 −0.391692 0.920096i \(-0.628110\pi\)
−0.391692 + 0.920096i \(0.628110\pi\)
\(294\) 0 0
\(295\) 4.54940 + 7.87979i 0.264876 + 0.458779i
\(296\) 0 0
\(297\) 3.49727 0.202932
\(298\) 0 0
\(299\) 0.433589 0.750998i 0.0250751 0.0434313i
\(300\) 0 0
\(301\) −1.25856 + 2.17989i −0.0725421 + 0.125647i
\(302\) 0 0
\(303\) 3.39847 0.195237
\(304\) 0 0
\(305\) −2.27110 −0.130043
\(306\) 0 0
\(307\) −16.1033 + 27.8917i −0.919062 + 1.59186i −0.118219 + 0.992988i \(0.537719\pi\)
−0.800843 + 0.598875i \(0.795615\pi\)
\(308\) 0 0
\(309\) −1.98026 + 3.42991i −0.112653 + 0.195121i
\(310\) 0 0
\(311\) 12.3699 0.701433 0.350717 0.936482i \(-0.385938\pi\)
0.350717 + 0.936482i \(0.385938\pi\)
\(312\) 0 0
\(313\) −12.3941 21.4672i −0.700557 1.21340i −0.968271 0.249901i \(-0.919602\pi\)
0.267715 0.963498i \(-0.413732\pi\)
\(314\) 0 0
\(315\) 1.82224 0.102672
\(316\) 0 0
\(317\) −3.65529 6.33115i −0.205302 0.355593i 0.744927 0.667146i \(-0.232484\pi\)
−0.950229 + 0.311553i \(0.899151\pi\)
\(318\) 0 0
\(319\) 7.44078 + 12.8878i 0.416604 + 0.721579i
\(320\) 0 0
\(321\) 2.06468 3.57612i 0.115239 0.199600i
\(322\) 0 0
\(323\) −24.7443 14.6416i −1.37681 0.814680i
\(324\) 0 0
\(325\) 0.500000 0.866025i 0.0277350 0.0480384i
\(326\) 0 0
\(327\) 2.41112 + 4.17618i 0.133335 + 0.230943i
\(328\) 0 0
\(329\) −2.89138 5.00802i −0.159407 0.276101i
\(330\) 0 0
\(331\) 18.4722 1.01532 0.507661 0.861557i \(-0.330510\pi\)
0.507661 + 0.861557i \(0.330510\pi\)
\(332\) 0 0
\(333\) 0.911120 + 1.57811i 0.0499291 + 0.0864797i
\(334\) 0 0
\(335\) −12.4633 −0.680940
\(336\) 0 0
\(337\) −15.2316 + 26.3819i −0.829720 + 1.43712i 0.0685388 + 0.997648i \(0.478166\pi\)
−0.898258 + 0.439468i \(0.855167\pi\)
\(338\) 0 0
\(339\) 1.29258 2.23881i 0.0702032 0.121595i
\(340\) 0 0
\(341\) −3.05387 −0.165376
\(342\) 0 0
\(343\) −8.64101 −0.466571
\(344\) 0 0
\(345\) −0.158021 + 0.273700i −0.00850754 + 0.0147355i
\(346\) 0 0
\(347\) −11.6608 + 20.1970i −0.625982 + 1.08423i 0.362368 + 0.932035i \(0.381968\pi\)
−0.988350 + 0.152197i \(0.951365\pi\)
\(348\) 0 0
\(349\) −17.6894 −0.946893 −0.473446 0.880823i \(-0.656990\pi\)
−0.473446 + 0.880823i \(0.656990\pi\)
\(350\) 0 0
\(351\) 1.06914 + 1.85181i 0.0570665 + 0.0988421i
\(352\) 0 0
\(353\) −7.13828 −0.379932 −0.189966 0.981791i \(-0.560838\pi\)
−0.189966 + 0.981791i \(0.560838\pi\)
\(354\) 0 0
\(355\) 1.25136 + 2.16743i 0.0664155 + 0.115035i
\(356\) 0 0
\(357\) −0.763910 1.32313i −0.0404304 0.0700275i
\(358\) 0 0
\(359\) 15.0719 26.1052i 0.795463 1.37778i −0.127082 0.991892i \(-0.540561\pi\)
0.922545 0.385890i \(-0.126106\pi\)
\(360\) 0 0
\(361\) −18.9956 0.406855i −0.999771 0.0214134i
\(362\) 0 0
\(363\) −1.51701 + 2.62754i −0.0796224 + 0.137910i
\(364\) 0 0
\(365\) −0.201963 0.349810i −0.0105712 0.0183099i
\(366\) 0 0
\(367\) 15.1015 + 26.1566i 0.788294 + 1.36536i 0.927012 + 0.375033i \(0.122369\pi\)
−0.138718 + 0.990332i \(0.544298\pi\)
\(368\) 0 0
\(369\) −5.46672 −0.284586
\(370\) 0 0
\(371\) 3.13555 + 5.43094i 0.162790 + 0.281960i
\(372\) 0 0
\(373\) 29.0449 1.50389 0.751945 0.659226i \(-0.229116\pi\)
0.751945 + 0.659226i \(0.229116\pi\)
\(374\) 0 0
\(375\) −0.182224 + 0.315621i −0.00941001 + 0.0162986i
\(376\) 0 0
\(377\) −4.54940 + 7.87979i −0.234306 + 0.405830i
\(378\) 0 0
\(379\) 2.76837 0.142202 0.0711009 0.997469i \(-0.477349\pi\)
0.0711009 + 0.997469i \(0.477349\pi\)
\(380\) 0 0
\(381\) −5.93196 −0.303904
\(382\) 0 0
\(383\) −13.3052 + 23.0453i −0.679866 + 1.17756i 0.295156 + 0.955449i \(0.404629\pi\)
−0.975021 + 0.222112i \(0.928705\pi\)
\(384\) 0 0
\(385\) 0.519739 0.900215i 0.0264884 0.0458792i
\(386\) 0 0
\(387\) −11.3555 −0.577233
\(388\) 0 0
\(389\) 2.77830 + 4.81215i 0.140865 + 0.243986i 0.927823 0.373021i \(-0.121678\pi\)
−0.786957 + 0.617007i \(0.788345\pi\)
\(390\) 0 0
\(391\) −5.71997 −0.289271
\(392\) 0 0
\(393\) −1.93805 3.35681i −0.0977618 0.169328i
\(394\) 0 0
\(395\) 5.36445 + 9.29150i 0.269915 + 0.467506i
\(396\) 0 0
\(397\) −1.35725 + 2.35083i −0.0681186 + 0.117985i −0.898073 0.439846i \(-0.855033\pi\)
0.829955 + 0.557831i \(0.188366\pi\)
\(398\) 0 0
\(399\) −0.868912 0.514150i −0.0435000 0.0257397i
\(400\) 0 0
\(401\) 8.94078 15.4859i 0.446481 0.773328i −0.551673 0.834061i \(-0.686010\pi\)
0.998154 + 0.0607322i \(0.0193436\pi\)
\(402\) 0 0
\(403\) −0.933589 1.61702i −0.0465054 0.0805497i
\(404\) 0 0
\(405\) 3.91112 + 6.77426i 0.194345 + 0.336616i
\(406\) 0 0
\(407\) 1.03948 0.0515250
\(408\) 0 0
\(409\) −13.1625 22.7981i −0.650843 1.12729i −0.982919 0.184040i \(-0.941082\pi\)
0.332076 0.943253i \(-0.392251\pi\)
\(410\) 0 0
\(411\) −1.27457 −0.0628701
\(412\) 0 0
\(413\) −2.89138 + 5.00802i −0.142276 + 0.246428i
\(414\) 0 0
\(415\) −7.93359 + 13.7414i −0.389445 + 0.674538i
\(416\) 0 0
\(417\) −0.267634 −0.0131061
\(418\) 0 0
\(419\) 15.3250 0.748674 0.374337 0.927293i \(-0.377870\pi\)
0.374337 + 0.927293i \(0.377870\pi\)
\(420\) 0 0
\(421\) −10.9166 + 18.9081i −0.532042 + 0.921523i 0.467259 + 0.884121i \(0.345242\pi\)
−0.999300 + 0.0374023i \(0.988092\pi\)
\(422\) 0 0
\(423\) 13.0439 22.5928i 0.634218 1.09850i
\(424\) 0 0
\(425\) −6.59607 −0.319957
\(426\) 0 0
\(427\) −0.721702 1.25002i −0.0349256 0.0604929i
\(428\) 0 0
\(429\) 0.596074 0.0287787
\(430\) 0 0
\(431\) −11.6427 20.1658i −0.560811 0.971354i −0.997426 0.0717050i \(-0.977156\pi\)
0.436615 0.899649i \(-0.356177\pi\)
\(432\) 0 0
\(433\) 1.95060 + 3.37854i 0.0937398 + 0.162362i 0.909082 0.416617i \(-0.136784\pi\)
−0.815342 + 0.578979i \(0.803451\pi\)
\(434\) 0 0
\(435\) 1.65802 2.87178i 0.0794960 0.137691i
\(436\) 0 0
\(437\) −3.29357 + 1.85481i −0.157553 + 0.0887276i
\(438\) 0 0
\(439\) 9.73882 16.8681i 0.464808 0.805072i −0.534384 0.845242i \(-0.679457\pi\)
0.999193 + 0.0401697i \(0.0127898\pi\)
\(440\) 0 0
\(441\) −9.45606 16.3784i −0.450288 0.779922i
\(442\) 0 0
\(443\) −0.953328 1.65121i −0.0452940 0.0784515i 0.842490 0.538713i \(-0.181089\pi\)
−0.887784 + 0.460261i \(0.847756\pi\)
\(444\) 0 0
\(445\) −0.542208 −0.0257031
\(446\) 0 0
\(447\) 1.84744 + 3.19986i 0.0873808 + 0.151348i
\(448\) 0 0
\(449\) −8.05933 −0.380343 −0.190172 0.981751i \(-0.560904\pi\)
−0.190172 + 0.981751i \(0.560904\pi\)
\(450\) 0 0
\(451\) −1.55922 + 2.70064i −0.0734207 + 0.127168i
\(452\) 0 0
\(453\) 0.512653 0.887941i 0.0240865 0.0417191i
\(454\) 0 0
\(455\) 0.635552 0.0297951
\(456\) 0 0
\(457\) 11.3250 0.529760 0.264880 0.964281i \(-0.414668\pi\)
0.264880 + 0.964281i \(0.414668\pi\)
\(458\) 0 0
\(459\) 7.05213 12.2146i 0.329165 0.570131i
\(460\) 0 0
\(461\) −10.0521 + 17.4108i −0.468174 + 0.810902i −0.999338 0.0363671i \(-0.988421\pi\)
0.531164 + 0.847269i \(0.321755\pi\)
\(462\) 0 0
\(463\) 1.33043 0.0618303 0.0309151 0.999522i \(-0.490158\pi\)
0.0309151 + 0.999522i \(0.490158\pi\)
\(464\) 0 0
\(465\) 0.340245 + 0.589321i 0.0157785 + 0.0273291i
\(466\) 0 0
\(467\) 10.0844 0.466651 0.233326 0.972399i \(-0.425039\pi\)
0.233326 + 0.972399i \(0.425039\pi\)
\(468\) 0 0
\(469\) −3.96052 6.85982i −0.182880 0.316757i
\(470\) 0 0
\(471\) 0.175030 + 0.303161i 0.00806496 + 0.0139689i
\(472\) 0 0
\(473\) −3.23882 + 5.60980i −0.148921 + 0.257939i
\(474\) 0 0
\(475\) −3.79804 + 2.13891i −0.174266 + 0.0981397i
\(476\) 0 0
\(477\) −14.1455 + 24.5007i −0.647677 + 1.12181i
\(478\) 0 0
\(479\) −4.44078 7.69166i −0.202905 0.351441i 0.746559 0.665320i \(-0.231705\pi\)
−0.949463 + 0.313879i \(0.898371\pi\)
\(480\) 0 0
\(481\) 0.317776 + 0.550404i 0.0144893 + 0.0250963i
\(482\) 0 0
\(483\) −0.200861 −0.00913947
\(484\) 0 0
\(485\) −3.68495 6.38253i −0.167325 0.289816i
\(486\) 0 0
\(487\) 5.32497 0.241297 0.120649 0.992695i \(-0.461503\pi\)
0.120649 + 0.992695i \(0.461503\pi\)
\(488\) 0 0
\(489\) 0.571870 0.990508i 0.0258609 0.0447923i
\(490\) 0 0
\(491\) 9.70469 16.8090i 0.437967 0.758580i −0.559566 0.828786i \(-0.689032\pi\)
0.997533 + 0.0702054i \(0.0223655\pi\)
\(492\) 0 0
\(493\) 60.0164 2.70300
\(494\) 0 0
\(495\) 4.68942 0.210774
\(496\) 0 0
\(497\) −0.795307 + 1.37751i −0.0356744 + 0.0617899i
\(498\) 0 0
\(499\) −5.79357 + 10.0348i −0.259356 + 0.449218i −0.966070 0.258282i \(-0.916844\pi\)
0.706714 + 0.707500i \(0.250177\pi\)
\(500\) 0 0
\(501\) 3.87611 0.173172
\(502\) 0 0
\(503\) −17.5521 30.4012i −0.782611 1.35552i −0.930416 0.366505i \(-0.880554\pi\)
0.147805 0.989017i \(-0.452779\pi\)
\(504\) 0 0
\(505\) 9.32497 0.414956
\(506\) 0 0
\(507\) −2.18669 3.78746i −0.0971142 0.168207i
\(508\) 0 0
\(509\) 7.93359 + 13.7414i 0.351650 + 0.609076i 0.986539 0.163528i \(-0.0522873\pi\)
−0.634889 + 0.772604i \(0.718954\pi\)
\(510\) 0 0
\(511\) 0.128358 0.222323i 0.00567823 0.00983498i
\(512\) 0 0
\(513\) 0.0997981 9.32002i 0.00440619 0.411489i
\(514\) 0 0
\(515\) −5.43359 + 9.41125i −0.239433 + 0.414709i
\(516\) 0 0
\(517\) −7.44078 12.8878i −0.327245 0.566805i
\(518\) 0 0
\(519\) 2.25409 + 3.90421i 0.0989438 + 0.171376i
\(520\) 0 0
\(521\) 36.6949 1.60763 0.803816 0.594878i \(-0.202800\pi\)
0.803816 + 0.594878i \(0.202800\pi\)
\(522\) 0 0
\(523\) 15.5127 + 26.8687i 0.678321 + 1.17489i 0.975486 + 0.220060i \(0.0706254\pi\)
−0.297165 + 0.954826i \(0.596041\pi\)
\(524\) 0 0
\(525\) −0.231626 −0.0101090
\(526\) 0 0
\(527\) −6.15802 + 10.6660i −0.268248 + 0.464618i
\(528\) 0 0
\(529\) 11.1240 19.2673i 0.483652 0.837710i
\(530\) 0 0
\(531\) −26.0879 −1.13212
\(532\) 0 0
\(533\) −1.90666 −0.0825864
\(534\) 0 0
\(535\) 5.66521 9.81244i 0.244929 0.424229i
\(536\) 0 0
\(537\) −0.0592173 + 0.102567i −0.00255542 + 0.00442611i
\(538\) 0 0
\(539\) −10.7882 −0.464682
\(540\) 0 0
\(541\) 3.79357 + 6.57066i 0.163098 + 0.282495i 0.935978 0.352058i \(-0.114518\pi\)
−0.772880 + 0.634552i \(0.781185\pi\)
\(542\) 0 0
\(543\) −3.21199 −0.137840
\(544\) 0 0
\(545\) 6.61581 + 11.4589i 0.283390 + 0.490846i
\(546\) 0 0
\(547\) 15.3914 + 26.6587i 0.658088 + 1.13984i 0.981110 + 0.193450i \(0.0619678\pi\)
−0.323022 + 0.946391i \(0.604699\pi\)
\(548\) 0 0
\(549\) 3.25583 5.63926i 0.138955 0.240678i
\(550\) 0 0
\(551\) 34.5576 19.4615i 1.47220 0.829087i
\(552\) 0 0
\(553\) −3.40939 + 5.90523i −0.144982 + 0.251116i
\(554\) 0 0
\(555\) −0.115813 0.200594i −0.00491598 0.00851473i
\(556\) 0 0
\(557\) −15.5369 26.9106i −0.658318 1.14024i −0.981051 0.193750i \(-0.937935\pi\)
0.322733 0.946490i \(-0.395398\pi\)
\(558\) 0 0
\(559\) −3.96052 −0.167512
\(560\) 0 0
\(561\) −1.96587 3.40499i −0.0829992 0.143759i
\(562\) 0 0
\(563\) −23.2766 −0.980990 −0.490495 0.871444i \(-0.663184\pi\)
−0.490495 + 0.871444i \(0.663184\pi\)
\(564\) 0 0
\(565\) 3.54667 6.14302i 0.149210 0.258439i
\(566\) 0 0
\(567\) −2.48572 + 4.30539i −0.104390 + 0.180810i
\(568\) 0 0
\(569\) 24.1976 1.01442 0.507208 0.861824i \(-0.330678\pi\)
0.507208 + 0.861824i \(0.330678\pi\)
\(570\) 0 0
\(571\) 29.8475 1.24908 0.624540 0.780992i \(-0.285286\pi\)
0.624540 + 0.780992i \(0.285286\pi\)
\(572\) 0 0
\(573\) 4.59061 7.95118i 0.191776 0.332165i
\(574\) 0 0
\(575\) −0.433589 + 0.750998i −0.0180819 + 0.0313188i
\(576\) 0 0
\(577\) 33.7882 1.40662 0.703311 0.710882i \(-0.251704\pi\)
0.703311 + 0.710882i \(0.251704\pi\)
\(578\) 0 0
\(579\) −3.43905 5.95661i −0.142922 0.247548i
\(580\) 0 0
\(581\) −10.0844 −0.418372
\(582\) 0 0
\(583\) 8.06914 + 13.9762i 0.334190 + 0.578833i
\(584\) 0 0
\(585\) 1.43359 + 2.48305i 0.0592716 + 0.102661i
\(586\) 0 0
\(587\) 15.3474 26.5825i 0.633457 1.09718i −0.353383 0.935479i \(-0.614969\pi\)
0.986840 0.161700i \(-0.0516978\pi\)
\(588\) 0 0
\(589\) −0.0871451 + 8.13837i −0.00359075 + 0.335336i
\(590\) 0 0
\(591\) −1.34198 + 2.32438i −0.0552017 + 0.0956121i
\(592\) 0 0
\(593\) −3.49727 6.05745i −0.143616 0.248750i 0.785240 0.619192i \(-0.212540\pi\)
−0.928856 + 0.370442i \(0.879206\pi\)
\(594\) 0 0
\(595\) −2.09607 3.63051i −0.0859306 0.148836i
\(596\) 0 0
\(597\) −1.00893 −0.0412927
\(598\) 0 0
\(599\) 2.26837 + 3.92894i 0.0926833 + 0.160532i 0.908639 0.417582i \(-0.137122\pi\)
−0.815956 + 0.578114i \(0.803789\pi\)
\(600\) 0 0
\(601\) 16.0790 0.655874 0.327937 0.944700i \(-0.393647\pi\)
0.327937 + 0.944700i \(0.393647\pi\)
\(602\) 0 0
\(603\) 17.8672 30.9469i 0.727608 1.26025i
\(604\) 0 0
\(605\) −4.16248 + 7.20964i −0.169229 + 0.293113i
\(606\) 0 0
\(607\) −34.0702 −1.38287 −0.691434 0.722439i \(-0.743021\pi\)
−0.691434 + 0.722439i \(0.743021\pi\)
\(608\) 0 0
\(609\) 2.10752 0.0854009
\(610\) 0 0
\(611\) 4.54940 7.87979i 0.184049 0.318782i
\(612\) 0 0
\(613\) 19.7191 34.1544i 0.796446 1.37949i −0.125471 0.992097i \(-0.540044\pi\)
0.921917 0.387388i \(-0.126623\pi\)
\(614\) 0 0
\(615\) 0.694877 0.0280201
\(616\) 0 0
\(617\) 19.6257 + 33.9928i 0.790102 + 1.36850i 0.925903 + 0.377761i \(0.123306\pi\)
−0.135801 + 0.990736i \(0.543361\pi\)
\(618\) 0 0
\(619\) 24.3644 0.979290 0.489645 0.871922i \(-0.337126\pi\)
0.489645 + 0.871922i \(0.337126\pi\)
\(620\) 0 0
\(621\) −0.927135 1.60584i −0.0372046 0.0644403i
\(622\) 0 0
\(623\) −0.172301 0.298433i −0.00690308 0.0119565i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −2.23609 1.32313i −0.0893008 0.0528408i
\(628\) 0 0
\(629\) 2.09607 3.63051i 0.0835759 0.144758i
\(630\) 0 0
\(631\) 17.6949 + 30.6484i 0.704422 + 1.22009i 0.966900 + 0.255157i \(0.0821270\pi\)
−0.262478 + 0.964938i \(0.584540\pi\)
\(632\) 0 0
\(633\) 3.08442 + 5.34236i 0.122595 + 0.212340i
\(634\) 0 0
\(635\) −16.2766 −0.645916
\(636\) 0 0
\(637\) −3.29804 5.71237i −0.130673 0.226332i
\(638\) 0 0
\(639\) −7.17577 −0.283869
\(640\) 0 0
\(641\) −17.8546 + 30.9251i −0.705216 + 1.22147i 0.261398 + 0.965231i \(0.415816\pi\)
−0.966614 + 0.256238i \(0.917517\pi\)
\(642\) 0 0
\(643\) −10.5549 + 18.2816i −0.416243 + 0.720954i −0.995558 0.0941496i \(-0.969987\pi\)
0.579315 + 0.815104i \(0.303320\pi\)
\(644\) 0 0
\(645\) 1.44340 0.0568340
\(646\) 0 0
\(647\) 43.7058 1.71825 0.859126 0.511764i \(-0.171008\pi\)
0.859126 + 0.511764i \(0.171008\pi\)
\(648\) 0 0
\(649\) −7.44078 + 12.8878i −0.292076 + 0.505891i
\(650\) 0 0
\(651\) −0.216243 + 0.374544i −0.00847524 + 0.0146795i
\(652\) 0 0
\(653\) −24.1887 −0.946576 −0.473288 0.880908i \(-0.656933\pi\)
−0.473288 + 0.880908i \(0.656933\pi\)
\(654\) 0 0
\(655\) −5.31778 9.21066i −0.207783 0.359890i
\(656\) 0 0
\(657\) 1.15813 0.0451829
\(658\) 0 0
\(659\) −16.9956 29.4373i −0.662056 1.14672i −0.980074 0.198630i \(-0.936351\pi\)
0.318018 0.948085i \(-0.396983\pi\)
\(660\) 0 0
\(661\) −2.27830 3.94613i −0.0886155 0.153487i 0.818311 0.574776i \(-0.194911\pi\)
−0.906926 + 0.421290i \(0.861578\pi\)
\(662\) 0 0
\(663\) 1.20196 2.08186i 0.0466804 0.0808528i
\(664\) 0 0
\(665\) −2.38419 1.41076i −0.0924548 0.0547070i
\(666\) 0 0
\(667\) 3.94514 6.83318i 0.152756 0.264582i
\(668\) 0 0
\(669\) 1.57460 + 2.72729i 0.0608775 + 0.105443i
\(670\) 0 0
\(671\) −1.85725 3.21686i −0.0716985 0.124185i
\(672\) 0 0
\(673\) −22.7487 −0.876900 −0.438450 0.898756i \(-0.644472\pi\)
−0.438450 + 0.898756i \(0.644472\pi\)
\(674\) 0 0
\(675\) −1.06914 1.85181i −0.0411512 0.0712760i
\(676\) 0 0
\(677\) −15.6949 −0.603203 −0.301602 0.953434i \(-0.597521\pi\)
−0.301602 + 0.953434i \(0.597521\pi\)
\(678\) 0 0
\(679\) 2.34198 4.05643i 0.0898769 0.155671i
\(680\) 0 0
\(681\) 3.81331 6.60485i 0.146126 0.253098i
\(682\) 0 0
\(683\) −8.82770 −0.337783 −0.168891 0.985635i \(-0.554019\pi\)
−0.168891 + 0.985635i \(0.554019\pi\)
\(684\) 0 0
\(685\) −3.49727 −0.133624
\(686\) 0 0
\(687\) 4.07733 7.06214i 0.155560 0.269438i
\(688\) 0 0
\(689\) −4.93359 + 8.54523i −0.187955 + 0.325547i
\(690\) 0 0
\(691\) −23.0198 −0.875716 −0.437858 0.899044i \(-0.644263\pi\)
−0.437858 + 0.899044i \(0.644263\pi\)
\(692\) 0 0
\(693\) 1.49018 + 2.58107i 0.0566074 + 0.0980469i
\(694\) 0 0
\(695\) −0.734355 −0.0278557
\(696\) 0 0
\(697\) 6.28822 + 10.8915i 0.238183 + 0.412546i
\(698\) 0 0
\(699\) −3.50546 6.07163i −0.132589 0.229650i
\(700\) 0 0
\(701\) 4.95606 8.58414i 0.187188 0.324219i −0.757124 0.653271i \(-0.773396\pi\)
0.944312 + 0.329053i \(0.106729\pi\)
\(702\) 0 0
\(703\) 0.0296625 2.77015i 0.00111874 0.104478i
\(704\) 0 0
\(705\) −1.65802 + 2.87178i −0.0624447 + 0.108157i
\(706\) 0 0
\(707\) 2.96325 + 5.13250i 0.111445 + 0.193028i
\(708\) 0 0
\(709\) 18.0521 + 31.2672i 0.677962 + 1.17426i 0.975594 + 0.219584i \(0.0704700\pi\)
−0.297632 + 0.954681i \(0.596197\pi\)
\(710\) 0 0
\(711\) −30.7617 −1.15365
\(712\) 0 0
\(713\) 0.809587 + 1.40225i 0.0303193 + 0.0525145i
\(714\) 0 0
\(715\) 1.63555 0.0611662
\(716\) 0 0
\(717\) −0.388651 + 0.673164i −0.0145145 + 0.0251398i
\(718\) 0 0
\(719\) 9.50546 16.4639i 0.354494 0.614001i −0.632537 0.774530i \(-0.717987\pi\)
0.987031 + 0.160529i \(0.0513199\pi\)
\(720\) 0 0
\(721\) −6.90666 −0.257217
\(722\) 0 0
\(723\) −8.91558 −0.331574
\(724\) 0 0
\(725\) 4.54940 7.87979i 0.168961 0.292648i
\(726\) 0 0
\(727\) 1.44351 2.50024i 0.0535369 0.0927286i −0.838015 0.545647i \(-0.816284\pi\)
0.891552 + 0.452919i \(0.149617\pi\)
\(728\) 0 0
\(729\) −20.0899 −0.744069
\(730\) 0 0
\(731\) 13.0619 + 22.6240i 0.483114 + 0.836777i
\(732\) 0 0
\(733\) 44.9463 1.66013 0.830066 0.557666i \(-0.188303\pi\)
0.830066 + 0.557666i \(0.188303\pi\)
\(734\) 0 0
\(735\) 1.20196 + 2.08186i 0.0443351 + 0.0767906i
\(736\) 0 0
\(737\) −10.1921 17.6533i −0.375433 0.650268i
\(738\) 0 0
\(739\) −25.4956 + 44.1597i −0.937872 + 1.62444i −0.168442 + 0.985711i \(0.553874\pi\)
−0.769430 + 0.638731i \(0.779460\pi\)
\(740\) 0 0
\(741\) 0.0170096 1.58850i 0.000624862 0.0583550i
\(742\) 0 0
\(743\) −9.43805 + 16.3472i −0.346249 + 0.599720i −0.985580 0.169211i \(-0.945878\pi\)
0.639331 + 0.768931i \(0.279211\pi\)
\(744\) 0 0
\(745\) 5.06914 + 8.78001i 0.185719 + 0.321675i
\(746\) 0 0
\(747\) −22.7470 39.3990i −0.832270 1.44153i
\(748\) 0 0
\(749\) 7.20108 0.263122
\(750\) 0 0
\(751\) −13.0127 22.5386i −0.474838 0.822444i 0.524746 0.851259i \(-0.324160\pi\)
−0.999585 + 0.0288143i \(0.990827\pi\)
\(752\) 0 0
\(753\) −1.19540 −0.0435629
\(754\) 0 0
\(755\) 1.40666 2.43640i 0.0511934 0.0886697i
\(756\) 0 0
\(757\) 5.95779 10.3192i 0.216540 0.375058i −0.737208 0.675666i \(-0.763856\pi\)
0.953748 + 0.300608i \(0.0971896\pi\)
\(758\) 0 0
\(759\) −0.516902 −0.0187623
\(760\) 0 0
\(761\) −2.39500 −0.0868186 −0.0434093 0.999057i \(-0.513822\pi\)
−0.0434093 + 0.999057i \(0.513822\pi\)
\(762\) 0 0
\(763\) −4.20469 + 7.28274i −0.152220 + 0.263653i
\(764\) 0 0
\(765\) 9.45606 16.3784i 0.341884 0.592161i
\(766\) 0 0
\(767\) −9.09880 −0.328539
\(768\) 0 0
\(769\) −2.66248 4.61156i −0.0960117 0.166297i 0.814019 0.580839i \(-0.197275\pi\)
−0.910030 + 0.414542i \(0.863942\pi\)
\(770\) 0 0
\(771\) 2.78276 0.100219
\(772\) 0 0
\(773\) 12.2486 + 21.2153i 0.440553 + 0.763060i 0.997731 0.0673334i \(-0.0214491\pi\)
−0.557178 + 0.830393i \(0.688116\pi\)
\(774\) 0 0
\(775\) 0.933589 + 1.61702i 0.0335355 + 0.0580852i
\(776\) 0 0
\(777\) 0.0736051 0.127488i 0.00264057 0.00457360i
\(778\) 0 0
\(779\) 7.15256 + 4.23229i 0.256267 + 0.151637i
\(780\) 0 0
\(781\) −2.04667 + 3.54494i −0.0732357 + 0.126848i
\(782\) 0 0
\(783\) 9.72790 + 16.8492i 0.347647 + 0.602142i
\(784\) 0 0
\(785\) 0.480261 + 0.831836i 0.0171412 + 0.0296895i
\(786\) 0 0
\(787\) −20.5171 −0.731356 −0.365678 0.930741i \(-0.619163\pi\)
−0.365678 + 0.930741i \(0.619163\pi\)
\(788\) 0 0
\(789\) 2.68396 + 4.64875i 0.0955515 + 0.165500i
\(790\)