Properties

Label 304.3.r.a.65.2
Level $304$
Weight $3$
Character 304.65
Analytic conductor $8.283$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 304.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.28340003655\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.2
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 304.65
Dual form 304.3.r.a.145.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.275255 - 0.158919i) q^{3} +(0.500000 - 0.866025i) q^{5} +2.89898 q^{7} +(-4.44949 - 7.70674i) q^{9} +O(q^{10})\) \(q+(-0.275255 - 0.158919i) q^{3} +(0.500000 - 0.866025i) q^{5} +2.89898 q^{7} +(-4.44949 - 7.70674i) q^{9} +5.10102 q^{11} +(-0.151531 + 0.0874863i) q^{13} +(-0.275255 + 0.158919i) q^{15} +(5.94949 - 10.3048i) q^{17} +(3.34847 - 18.7026i) q^{19} +(-0.797959 - 0.460702i) q^{21} +(-8.52270 - 14.7618i) q^{23} +(12.0000 + 20.7846i) q^{25} +5.68896i q^{27} +(38.5454 - 22.2542i) q^{29} -31.1769i q^{31} +(-1.40408 - 0.810647i) q^{33} +(1.44949 - 2.51059i) q^{35} -21.9917i q^{37} +0.0556128 q^{39} +(-46.9393 - 27.1004i) q^{41} +(18.6691 - 32.3359i) q^{43} -8.89898 q^{45} +(40.7702 + 70.6160i) q^{47} -40.5959 q^{49} +(-3.27526 + 1.89097i) q^{51} +(48.2878 - 27.8789i) q^{53} +(2.55051 - 4.41761i) q^{55} +(-3.89388 + 4.61586i) q^{57} +(29.9166 + 17.2723i) q^{59} +(38.0959 + 65.9841i) q^{61} +(-12.8990 - 22.3417i) q^{63} +0.174973i q^{65} +(-102.659 + 59.2702i) q^{67} +5.41767i q^{69} +(-65.4773 - 37.8033i) q^{71} +(-14.6918 + 25.4470i) q^{73} -7.62809i q^{75} +14.7878 q^{77} +(57.2196 + 33.0358i) q^{79} +(-39.1413 + 67.7948i) q^{81} +30.6969 q^{83} +(-5.94949 - 10.3048i) q^{85} -14.1464 q^{87} +(-8.84847 + 5.10867i) q^{89} +(-0.439285 + 0.253621i) q^{91} +(-4.95459 + 8.58161i) q^{93} +(-14.5227 - 12.2512i) q^{95} +(-128.848 - 74.3907i) q^{97} +(-22.6969 - 39.3123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} + 2 q^{5} - 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 4 q - 6 q^{3} + 2 q^{5} - 8 q^{7} - 8 q^{9} + 40 q^{11} - 30 q^{13} - 6 q^{15} + 14 q^{17} - 16 q^{19} + 36 q^{21} + 10 q^{23} + 48 q^{25} + 66 q^{29} - 84 q^{33} - 4 q^{35} + 108 q^{39} + 18 q^{41} - 38 q^{43} - 16 q^{45} + 70 q^{47} - 84 q^{49} - 18 q^{51} - 42 q^{53} + 20 q^{55} + 102 q^{57} - 42 q^{59} + 74 q^{61} - 32 q^{63} - 102 q^{67} - 306 q^{71} + 98 q^{73} - 176 q^{77} + 126 q^{79} + 10 q^{81} + 64 q^{83} - 14 q^{85} + 12 q^{87} - 6 q^{89} + 204 q^{91} - 108 q^{93} - 14 q^{95} - 486 q^{97} - 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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
\(3\) −0.275255 0.158919i −0.0917517 0.0529729i 0.453422 0.891296i \(-0.350203\pi\)
−0.545174 + 0.838323i \(0.683536\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.100000 0.173205i −0.811684 0.584096i \(-0.801449\pi\)
0.911684 + 0.410891i \(0.134782\pi\)
\(6\) 0 0
\(7\) 2.89898 0.414140 0.207070 0.978326i \(-0.433607\pi\)
0.207070 + 0.978326i \(0.433607\pi\)
\(8\) 0 0
\(9\) −4.44949 7.70674i −0.494388 0.856305i
\(10\) 0 0
\(11\) 5.10102 0.463729 0.231865 0.972748i \(-0.425517\pi\)
0.231865 + 0.972748i \(0.425517\pi\)
\(12\) 0 0
\(13\) −0.151531 + 0.0874863i −0.0116562 + 0.00672972i −0.505817 0.862641i \(-0.668809\pi\)
0.494161 + 0.869371i \(0.335475\pi\)
\(14\) 0 0
\(15\) −0.275255 + 0.158919i −0.0183503 + 0.0105946i
\(16\) 0 0
\(17\) 5.94949 10.3048i 0.349970 0.606166i −0.636274 0.771463i \(-0.719525\pi\)
0.986244 + 0.165298i \(0.0528584\pi\)
\(18\) 0 0
\(19\) 3.34847 18.7026i 0.176235 0.984348i
\(20\) 0 0
\(21\) −0.797959 0.460702i −0.0379980 0.0219382i
\(22\) 0 0
\(23\) −8.52270 14.7618i −0.370552 0.641815i 0.619098 0.785314i \(-0.287498\pi\)
−0.989651 + 0.143498i \(0.954165\pi\)
\(24\) 0 0
\(25\) 12.0000 + 20.7846i 0.480000 + 0.831384i
\(26\) 0 0
\(27\) 5.68896i 0.210702i
\(28\) 0 0
\(29\) 38.5454 22.2542i 1.32915 0.767386i 0.343983 0.938976i \(-0.388224\pi\)
0.985169 + 0.171589i \(0.0548903\pi\)
\(30\) 0 0
\(31\) 31.1769i 1.00571i −0.864372 0.502853i \(-0.832284\pi\)
0.864372 0.502853i \(-0.167716\pi\)
\(32\) 0 0
\(33\) −1.40408 0.810647i −0.0425479 0.0245651i
\(34\) 0 0
\(35\) 1.44949 2.51059i 0.0414140 0.0717311i
\(36\) 0 0
\(37\) 21.9917i 0.594371i −0.954820 0.297186i \(-0.903952\pi\)
0.954820 0.297186i \(-0.0960480\pi\)
\(38\) 0 0
\(39\) 0.0556128 0.00142597
\(40\) 0 0
\(41\) −46.9393 27.1004i −1.14486 0.660986i −0.197231 0.980357i \(-0.563195\pi\)
−0.947630 + 0.319371i \(0.896528\pi\)
\(42\) 0 0
\(43\) 18.6691 32.3359i 0.434166 0.751997i −0.563061 0.826415i \(-0.690377\pi\)
0.997227 + 0.0744178i \(0.0237098\pi\)
\(44\) 0 0
\(45\) −8.89898 −0.197755
\(46\) 0 0
\(47\) 40.7702 + 70.6160i 0.867450 + 1.50247i 0.864594 + 0.502472i \(0.167576\pi\)
0.00285637 + 0.999996i \(0.499091\pi\)
\(48\) 0 0
\(49\) −40.5959 −0.828488
\(50\) 0 0
\(51\) −3.27526 + 1.89097i −0.0642207 + 0.0370778i
\(52\) 0 0
\(53\) 48.2878 27.8789i 0.911090 0.526018i 0.0303081 0.999541i \(-0.490351\pi\)
0.880782 + 0.473523i \(0.157018\pi\)
\(54\) 0 0
\(55\) 2.55051 4.41761i 0.0463729 0.0803202i
\(56\) 0 0
\(57\) −3.89388 + 4.61586i −0.0683136 + 0.0809799i
\(58\) 0 0
\(59\) 29.9166 + 17.2723i 0.507061 + 0.292752i 0.731625 0.681708i \(-0.238762\pi\)
−0.224564 + 0.974459i \(0.572096\pi\)
\(60\) 0 0
\(61\) 38.0959 + 65.9841i 0.624523 + 1.08171i 0.988633 + 0.150350i \(0.0480400\pi\)
−0.364110 + 0.931356i \(0.618627\pi\)
\(62\) 0 0
\(63\) −12.8990 22.3417i −0.204746 0.354630i
\(64\) 0 0
\(65\) 0.174973i 0.00269189i
\(66\) 0 0
\(67\) −102.659 + 59.2702i −1.53222 + 0.884629i −0.532964 + 0.846138i \(0.678922\pi\)
−0.999259 + 0.0384912i \(0.987745\pi\)
\(68\) 0 0
\(69\) 5.41767i 0.0785169i
\(70\) 0 0
\(71\) −65.4773 37.8033i −0.922215 0.532441i −0.0378743 0.999283i \(-0.512059\pi\)
−0.884341 + 0.466841i \(0.845392\pi\)
\(72\) 0 0
\(73\) −14.6918 + 25.4470i −0.201258 + 0.348589i −0.948934 0.315475i \(-0.897836\pi\)
0.747676 + 0.664064i \(0.231170\pi\)
\(74\) 0 0
\(75\) 7.62809i 0.101708i
\(76\) 0 0
\(77\) 14.7878 0.192049
\(78\) 0 0
\(79\) 57.2196 + 33.0358i 0.724299 + 0.418174i 0.816333 0.577582i \(-0.196003\pi\)
−0.0920338 + 0.995756i \(0.529337\pi\)
\(80\) 0 0
\(81\) −39.1413 + 67.7948i −0.483226 + 0.836972i
\(82\) 0 0
\(83\) 30.6969 0.369843 0.184921 0.982753i \(-0.440797\pi\)
0.184921 + 0.982753i \(0.440797\pi\)
\(84\) 0 0
\(85\) −5.94949 10.3048i −0.0699940 0.121233i
\(86\) 0 0
\(87\) −14.1464 −0.162603
\(88\) 0 0
\(89\) −8.84847 + 5.10867i −0.0994210 + 0.0574007i −0.548886 0.835897i \(-0.684948\pi\)
0.449465 + 0.893298i \(0.351615\pi\)
\(90\) 0 0
\(91\) −0.439285 + 0.253621i −0.00482730 + 0.00278704i
\(92\) 0 0
\(93\) −4.95459 + 8.58161i −0.0532752 + 0.0922753i
\(94\) 0 0
\(95\) −14.5227 12.2512i −0.152871 0.128960i
\(96\) 0 0
\(97\) −128.848 74.3907i −1.32833 0.766914i −0.343293 0.939228i \(-0.611542\pi\)
−0.985042 + 0.172314i \(0.944876\pi\)
\(98\) 0 0
\(99\) −22.6969 39.3123i −0.229262 0.397093i
\(100\) 0 0
\(101\) 70.2423 + 121.663i 0.695469 + 1.20459i 0.970022 + 0.243015i \(0.0781366\pi\)
−0.274554 + 0.961572i \(0.588530\pi\)
\(102\) 0 0
\(103\) 113.965i 1.10646i 0.833028 + 0.553230i \(0.186605\pi\)
−0.833028 + 0.553230i \(0.813395\pi\)
\(104\) 0 0
\(105\) −0.797959 + 0.460702i −0.00759961 + 0.00438764i
\(106\) 0 0
\(107\) 113.965i 1.06510i 0.846399 + 0.532549i \(0.178766\pi\)
−0.846399 + 0.532549i \(0.821234\pi\)
\(108\) 0 0
\(109\) 59.2423 + 34.2036i 0.543508 + 0.313794i 0.746499 0.665386i \(-0.231733\pi\)
−0.202992 + 0.979180i \(0.565066\pi\)
\(110\) 0 0
\(111\) −3.49490 + 6.05334i −0.0314856 + 0.0545346i
\(112\) 0 0
\(113\) 81.9313i 0.725056i 0.931973 + 0.362528i \(0.118086\pi\)
−0.931973 + 0.362528i \(0.881914\pi\)
\(114\) 0 0
\(115\) −17.0454 −0.148221
\(116\) 0 0
\(117\) 1.34847 + 0.778539i 0.0115254 + 0.00665418i
\(118\) 0 0
\(119\) 17.2474 29.8735i 0.144937 0.251037i
\(120\) 0 0
\(121\) −94.9796 −0.784955
\(122\) 0 0
\(123\) 8.61352 + 14.9191i 0.0700286 + 0.121293i
\(124\) 0 0
\(125\) 49.0000 0.392000
\(126\) 0 0
\(127\) −116.174 + 67.0732i −0.914758 + 0.528136i −0.881959 0.471326i \(-0.843775\pi\)
−0.0327989 + 0.999462i \(0.510442\pi\)
\(128\) 0 0
\(129\) −10.2775 + 5.93375i −0.0796709 + 0.0459980i
\(130\) 0 0
\(131\) 41.3763 71.6658i 0.315849 0.547067i −0.663768 0.747938i \(-0.731044\pi\)
0.979618 + 0.200871i \(0.0643772\pi\)
\(132\) 0 0
\(133\) 9.70714 54.2185i 0.0729860 0.407658i
\(134\) 0 0
\(135\) 4.92679 + 2.84448i 0.0364947 + 0.0210702i
\(136\) 0 0
\(137\) 5.94949 + 10.3048i 0.0434269 + 0.0752177i 0.886922 0.461919i \(-0.152839\pi\)
−0.843495 + 0.537137i \(0.819506\pi\)
\(138\) 0 0
\(139\) 20.8712 + 36.1499i 0.150152 + 0.260071i 0.931283 0.364296i \(-0.118690\pi\)
−0.781131 + 0.624367i \(0.785357\pi\)
\(140\) 0 0
\(141\) 25.9165i 0.183805i
\(142\) 0 0
\(143\) −0.772962 + 0.446270i −0.00540533 + 0.00312077i
\(144\) 0 0
\(145\) 44.5084i 0.306955i
\(146\) 0 0
\(147\) 11.1742 + 6.45145i 0.0760152 + 0.0438874i
\(148\) 0 0
\(149\) 17.8383 30.8968i 0.119720 0.207361i −0.799937 0.600084i \(-0.795134\pi\)
0.919657 + 0.392723i \(0.128467\pi\)
\(150\) 0 0
\(151\) 85.5527i 0.566574i −0.959035 0.283287i \(-0.908575\pi\)
0.959035 0.283287i \(-0.0914249\pi\)
\(152\) 0 0
\(153\) −105.889 −0.692083
\(154\) 0 0
\(155\) −27.0000 15.5885i −0.174194 0.100571i
\(156\) 0 0
\(157\) 100.076 173.336i 0.637424 1.10405i −0.348573 0.937282i \(-0.613333\pi\)
0.985996 0.166768i \(-0.0533332\pi\)
\(158\) 0 0
\(159\) −17.7219 −0.111459
\(160\) 0 0
\(161\) −24.7071 42.7940i −0.153461 0.265801i
\(162\) 0 0
\(163\) 127.303 0.781000 0.390500 0.920603i \(-0.372302\pi\)
0.390500 + 0.920603i \(0.372302\pi\)
\(164\) 0 0
\(165\) −1.40408 + 0.810647i −0.00850959 + 0.00491301i
\(166\) 0 0
\(167\) 158.917 91.7505i 0.951596 0.549404i 0.0580198 0.998315i \(-0.481521\pi\)
0.893576 + 0.448911i \(0.148188\pi\)
\(168\) 0 0
\(169\) −84.4847 + 146.332i −0.499909 + 0.865869i
\(170\) 0 0
\(171\) −159.035 + 57.4113i −0.930030 + 0.335739i
\(172\) 0 0
\(173\) −57.6214 33.2677i −0.333072 0.192299i 0.324132 0.946012i \(-0.394928\pi\)
−0.657204 + 0.753713i \(0.728261\pi\)
\(174\) 0 0
\(175\) 34.7878 + 60.2542i 0.198787 + 0.344309i
\(176\) 0 0
\(177\) −5.48979 9.50860i −0.0310158 0.0537209i
\(178\) 0 0
\(179\) 24.2134i 0.135270i −0.997710 0.0676351i \(-0.978455\pi\)
0.997710 0.0676351i \(-0.0215454\pi\)
\(180\) 0 0
\(181\) 30.8939 17.8366i 0.170684 0.0985447i −0.412224 0.911082i \(-0.635248\pi\)
0.582909 + 0.812538i \(0.301915\pi\)
\(182\) 0 0
\(183\) 24.2166i 0.132331i
\(184\) 0 0
\(185\) −19.0454 10.9959i −0.102948 0.0594371i
\(186\) 0 0
\(187\) 30.3485 52.5651i 0.162291 0.281097i
\(188\) 0 0
\(189\) 16.4922i 0.0872602i
\(190\) 0 0
\(191\) 180.252 0.943728 0.471864 0.881671i \(-0.343581\pi\)
0.471864 + 0.881671i \(0.343581\pi\)
\(192\) 0 0
\(193\) 188.985 + 109.110i 0.979195 + 0.565339i 0.902027 0.431679i \(-0.142079\pi\)
0.0771682 + 0.997018i \(0.475412\pi\)
\(194\) 0 0
\(195\) 0.0278064 0.0481621i 0.000142597 0.000246985i
\(196\) 0 0
\(197\) 340.091 1.72635 0.863175 0.504905i \(-0.168473\pi\)
0.863175 + 0.504905i \(0.168473\pi\)
\(198\) 0 0
\(199\) −166.694 288.723i −0.837659 1.45087i −0.891847 0.452337i \(-0.850590\pi\)
0.0541881 0.998531i \(-0.482743\pi\)
\(200\) 0 0
\(201\) 37.6765 0.187445
\(202\) 0 0
\(203\) 111.742 64.5145i 0.550455 0.317805i
\(204\) 0 0
\(205\) −46.9393 + 27.1004i −0.228972 + 0.132197i
\(206\) 0 0
\(207\) −75.8434 + 131.365i −0.366393 + 0.634611i
\(208\) 0 0
\(209\) 17.0806 95.4024i 0.0817254 0.456471i
\(210\) 0 0
\(211\) −302.750 174.793i −1.43483 0.828401i −0.437349 0.899292i \(-0.644082\pi\)
−0.997484 + 0.0708908i \(0.977416\pi\)
\(212\) 0 0
\(213\) 12.0153 + 20.8111i 0.0564099 + 0.0977048i
\(214\) 0 0
\(215\) −18.6691 32.3359i −0.0868332 0.150399i
\(216\) 0 0
\(217\) 90.3812i 0.416503i
\(218\) 0 0
\(219\) 8.08801 4.66961i 0.0369315 0.0213224i
\(220\) 0 0
\(221\) 2.08200i 0.00942080i
\(222\) 0 0
\(223\) 27.5227 + 15.8902i 0.123420 + 0.0712567i 0.560439 0.828196i \(-0.310632\pi\)
−0.437019 + 0.899452i \(0.643966\pi\)
\(224\) 0 0
\(225\) 106.788 184.962i 0.474612 0.822053i
\(226\) 0 0
\(227\) 249.730i 1.10013i −0.835121 0.550066i \(-0.814603\pi\)
0.835121 0.550066i \(-0.185397\pi\)
\(228\) 0 0
\(229\) −259.687 −1.13400 −0.567002 0.823717i \(-0.691897\pi\)
−0.567002 + 0.823717i \(0.691897\pi\)
\(230\) 0 0
\(231\) −4.07041 2.35005i −0.0176208 0.0101734i
\(232\) 0 0
\(233\) 195.141 337.995i 0.837516 1.45062i −0.0544486 0.998517i \(-0.517340\pi\)
0.891965 0.452104i \(-0.149327\pi\)
\(234\) 0 0
\(235\) 81.5403 0.346980
\(236\) 0 0
\(237\) −10.5000 18.1865i −0.0443038 0.0767364i
\(238\) 0 0
\(239\) 296.677 1.24132 0.620662 0.784078i \(-0.286864\pi\)
0.620662 + 0.784078i \(0.286864\pi\)
\(240\) 0 0
\(241\) −99.7270 + 57.5774i −0.413805 + 0.238911i −0.692423 0.721491i \(-0.743457\pi\)
0.278618 + 0.960402i \(0.410124\pi\)
\(242\) 0 0
\(243\) 65.8888 38.0409i 0.271147 0.156547i
\(244\) 0 0
\(245\) −20.2980 + 35.1571i −0.0828488 + 0.143498i
\(246\) 0 0
\(247\) 1.12883 + 3.12697i 0.00457015 + 0.0126598i
\(248\) 0 0
\(249\) −8.44949 4.87832i −0.0339337 0.0195916i
\(250\) 0 0
\(251\) 244.962 + 424.287i 0.975944 + 1.69038i 0.676783 + 0.736182i \(0.263373\pi\)
0.299161 + 0.954203i \(0.403293\pi\)
\(252\) 0 0
\(253\) −43.4745 75.3000i −0.171836 0.297629i
\(254\) 0 0
\(255\) 3.78194i 0.0148311i
\(256\) 0 0
\(257\) −197.379 + 113.957i −0.768010 + 0.443411i −0.832164 0.554529i \(-0.812898\pi\)
0.0641543 + 0.997940i \(0.479565\pi\)
\(258\) 0 0
\(259\) 63.7536i 0.246153i
\(260\) 0 0
\(261\) −343.015 198.040i −1.31423 0.758773i
\(262\) 0 0
\(263\) 67.9620 117.714i 0.258411 0.447580i −0.707406 0.706808i \(-0.750135\pi\)
0.965816 + 0.259227i \(0.0834679\pi\)
\(264\) 0 0
\(265\) 55.7579i 0.210407i
\(266\) 0 0
\(267\) 3.24745 0.0121627
\(268\) 0 0
\(269\) 225.090 + 129.956i 0.836767 + 0.483108i 0.856164 0.516704i \(-0.172841\pi\)
−0.0193970 + 0.999812i \(0.506175\pi\)
\(270\) 0 0
\(271\) −116.492 + 201.770i −0.429860 + 0.744540i −0.996860 0.0791780i \(-0.974770\pi\)
0.567000 + 0.823718i \(0.308104\pi\)
\(272\) 0 0
\(273\) 0.161220 0.000590551
\(274\) 0 0
\(275\) 61.2122 + 106.023i 0.222590 + 0.385537i
\(276\) 0 0
\(277\) −9.44387 −0.0340934 −0.0170467 0.999855i \(-0.505426\pi\)
−0.0170467 + 0.999855i \(0.505426\pi\)
\(278\) 0 0
\(279\) −240.272 + 138.721i −0.861192 + 0.497209i
\(280\) 0 0
\(281\) 135.591 78.2834i 0.482530 0.278589i −0.238940 0.971034i \(-0.576800\pi\)
0.721470 + 0.692446i \(0.243467\pi\)
\(282\) 0 0
\(283\) 1.46709 2.54108i 0.00518407 0.00897907i −0.863422 0.504483i \(-0.831683\pi\)
0.868606 + 0.495504i \(0.165017\pi\)
\(284\) 0 0
\(285\) 2.05051 + 5.68012i 0.00719477 + 0.0199303i
\(286\) 0 0
\(287\) −136.076 78.5635i −0.474132 0.273741i
\(288\) 0 0
\(289\) 73.7071 + 127.665i 0.255042 + 0.441746i
\(290\) 0 0
\(291\) 23.6441 + 40.9528i 0.0812513 + 0.140731i
\(292\) 0 0
\(293\) 332.361i 1.13434i 0.823601 + 0.567169i \(0.191961\pi\)
−0.823601 + 0.567169i \(0.808039\pi\)
\(294\) 0 0
\(295\) 29.9166 17.2723i 0.101412 0.0585503i
\(296\) 0 0
\(297\) 29.0195i 0.0977088i
\(298\) 0 0
\(299\) 2.58290 + 1.49124i 0.00863847 + 0.00498743i
\(300\) 0 0
\(301\) 54.1214 93.7411i 0.179805 0.311432i
\(302\) 0 0
\(303\) 44.6513i 0.147364i
\(304\) 0 0
\(305\) 76.1918 0.249809
\(306\) 0 0
\(307\) −222.962 128.727i −0.726261 0.419307i 0.0907920 0.995870i \(-0.471060\pi\)
−0.817053 + 0.576563i \(0.804393\pi\)
\(308\) 0 0
\(309\) 18.1112 31.3696i 0.0586124 0.101520i
\(310\) 0 0
\(311\) −217.666 −0.699892 −0.349946 0.936770i \(-0.613800\pi\)
−0.349946 + 0.936770i \(0.613800\pi\)
\(312\) 0 0
\(313\) 155.121 + 268.677i 0.495594 + 0.858394i 0.999987 0.00508018i \(-0.00161708\pi\)
−0.504393 + 0.863474i \(0.668284\pi\)
\(314\) 0 0
\(315\) −25.7980 −0.0818983
\(316\) 0 0
\(317\) −298.939 + 172.593i −0.943026 + 0.544456i −0.890908 0.454185i \(-0.849931\pi\)
−0.0521185 + 0.998641i \(0.516597\pi\)
\(318\) 0 0
\(319\) 196.621 113.519i 0.616367 0.355859i
\(320\) 0 0
\(321\) 18.1112 31.3696i 0.0564213 0.0977245i
\(322\) 0 0
\(323\) −172.805 145.776i −0.535001 0.451320i
\(324\) 0 0
\(325\) −3.63674 2.09967i −0.0111900 0.00646053i
\(326\) 0 0
\(327\) −10.8712 18.8294i −0.0332452 0.0575823i
\(328\) 0 0
\(329\) 118.192 + 204.714i 0.359246 + 0.622232i
\(330\) 0 0
\(331\) 487.318i 1.47226i 0.676841 + 0.736130i \(0.263349\pi\)
−0.676841 + 0.736130i \(0.736651\pi\)
\(332\) 0 0
\(333\) −169.485 + 97.8520i −0.508963 + 0.293850i
\(334\) 0 0
\(335\) 118.540i 0.353852i
\(336\) 0 0
\(337\) 144.393 + 83.3655i 0.428467 + 0.247376i 0.698693 0.715421i \(-0.253765\pi\)
−0.270226 + 0.962797i \(0.587099\pi\)
\(338\) 0 0
\(339\) 13.0204 22.5520i 0.0384083 0.0665251i
\(340\) 0 0
\(341\) 159.034i 0.466376i
\(342\) 0 0
\(343\) −259.737 −0.757250
\(344\) 0 0
\(345\) 4.69184 + 2.70883i 0.0135995 + 0.00785169i
\(346\) 0 0
\(347\) 188.871 327.134i 0.544297 0.942751i −0.454353 0.890822i \(-0.650130\pi\)
0.998651 0.0519291i \(-0.0165370\pi\)
\(348\) 0 0
\(349\) −586.434 −1.68033 −0.840163 0.542334i \(-0.817541\pi\)
−0.840163 + 0.542334i \(0.817541\pi\)
\(350\) 0 0
\(351\) −0.497706 0.862053i −0.00141797 0.00245599i
\(352\) 0 0
\(353\) 476.817 1.35076 0.675379 0.737471i \(-0.263980\pi\)
0.675379 + 0.737471i \(0.263980\pi\)
\(354\) 0 0
\(355\) −65.4773 + 37.8033i −0.184443 + 0.106488i
\(356\) 0 0
\(357\) −9.49490 + 5.48188i −0.0265964 + 0.0153554i
\(358\) 0 0
\(359\) −123.704 + 214.262i −0.344580 + 0.596831i −0.985277 0.170963i \(-0.945312\pi\)
0.640697 + 0.767794i \(0.278645\pi\)
\(360\) 0 0
\(361\) −338.576 125.250i −0.937882 0.346954i
\(362\) 0 0
\(363\) 26.1436 + 15.0940i 0.0720210 + 0.0415813i
\(364\) 0 0
\(365\) 14.6918 + 25.4470i 0.0402516 + 0.0697178i
\(366\) 0 0
\(367\) 241.962 + 419.090i 0.659297 + 1.14194i 0.980798 + 0.195027i \(0.0624793\pi\)
−0.321501 + 0.946909i \(0.604187\pi\)
\(368\) 0 0
\(369\) 482.332i 1.30713i
\(370\) 0 0
\(371\) 139.985 80.8205i 0.377319 0.217845i
\(372\) 0 0
\(373\) 140.908i 0.377768i 0.981999 + 0.188884i \(0.0604871\pi\)
−0.981999 + 0.188884i \(0.939513\pi\)
\(374\) 0 0
\(375\) −13.4875 7.78701i −0.0359667 0.0207654i
\(376\) 0 0
\(377\) −3.89388 + 6.74439i −0.0103286 + 0.0178896i
\(378\) 0 0
\(379\) 468.633i 1.23650i 0.785982 + 0.618249i \(0.212158\pi\)
−0.785982 + 0.618249i \(0.787842\pi\)
\(380\) 0 0
\(381\) 42.6367 0.111907
\(382\) 0 0
\(383\) 482.552 + 278.602i 1.25993 + 0.727420i 0.973060 0.230551i \(-0.0740528\pi\)
0.286867 + 0.957970i \(0.407386\pi\)
\(384\) 0 0
\(385\) 7.39388 12.8066i 0.0192049 0.0332638i
\(386\) 0 0
\(387\) −332.272 −0.858585
\(388\) 0 0
\(389\) −46.5602 80.6446i −0.119692 0.207313i 0.799954 0.600062i \(-0.204857\pi\)
−0.919646 + 0.392749i \(0.871524\pi\)
\(390\) 0 0
\(391\) −202.823 −0.518729
\(392\) 0 0
\(393\) −22.7781 + 13.1509i −0.0579595 + 0.0334629i
\(394\) 0 0
\(395\) 57.2196 33.0358i 0.144860 0.0836349i
\(396\) 0 0
\(397\) −129.682 + 224.615i −0.326654 + 0.565781i −0.981846 0.189681i \(-0.939255\pi\)
0.655192 + 0.755463i \(0.272588\pi\)
\(398\) 0 0
\(399\) −11.2883 + 13.3813i −0.0282914 + 0.0335370i
\(400\) 0 0
\(401\) −389.484 224.869i −0.971282 0.560770i −0.0716553 0.997429i \(-0.522828\pi\)
−0.899627 + 0.436659i \(0.856161\pi\)
\(402\) 0 0
\(403\) 2.72755 + 4.72426i 0.00676812 + 0.0117227i
\(404\) 0 0
\(405\) 39.1413 + 67.7948i 0.0966452 + 0.167394i
\(406\) 0 0
\(407\) 112.180i 0.275627i
\(408\) 0 0
\(409\) 90.8326 52.4423i 0.222085 0.128221i −0.384830 0.922987i \(-0.625740\pi\)
0.606915 + 0.794767i \(0.292407\pi\)
\(410\) 0 0
\(411\) 3.78194i 0.00920180i
\(412\) 0 0
\(413\) 86.7276 + 50.0722i 0.209994 + 0.121240i
\(414\) 0 0
\(415\) 15.3485 26.5843i 0.0369843 0.0640586i
\(416\) 0 0
\(417\) 13.2673i 0.0318160i
\(418\) 0 0
\(419\) −463.121 −1.10530 −0.552651 0.833413i \(-0.686384\pi\)
−0.552651 + 0.833413i \(0.686384\pi\)
\(420\) 0 0
\(421\) −418.711 241.743i −0.994563 0.574211i −0.0879282 0.996127i \(-0.528025\pi\)
−0.906635 + 0.421915i \(0.861358\pi\)
\(422\) 0 0
\(423\) 362.813 628.410i 0.857713 1.48560i
\(424\) 0 0
\(425\) 285.576 0.671942
\(426\) 0 0
\(427\) 110.439 + 191.286i 0.258640 + 0.447978i
\(428\) 0 0
\(429\) 0.283682 0.000661264
\(430\) 0 0
\(431\) −392.447 + 226.579i −0.910549 + 0.525706i −0.880608 0.473846i \(-0.842865\pi\)
−0.0299413 + 0.999552i \(0.509532\pi\)
\(432\) 0 0
\(433\) 650.651 375.654i 1.50266 0.867560i 0.502663 0.864482i \(-0.332354\pi\)
0.999995 0.00307767i \(-0.000979653\pi\)
\(434\) 0 0
\(435\) −7.07321 + 12.2512i −0.0162603 + 0.0281636i
\(436\) 0 0
\(437\) −304.621 + 109.968i −0.697074 + 0.251642i
\(438\) 0 0
\(439\) −543.325 313.689i −1.23764 0.714553i −0.269031 0.963132i \(-0.586703\pi\)
−0.968612 + 0.248578i \(0.920037\pi\)
\(440\) 0 0
\(441\) 180.631 + 312.862i 0.409594 + 0.709438i
\(442\) 0 0
\(443\) 220.628 + 382.139i 0.498032 + 0.862617i 0.999997 0.00227061i \(-0.000722758\pi\)
−0.501965 + 0.864888i \(0.667389\pi\)
\(444\) 0 0
\(445\) 10.2173i 0.0229603i
\(446\) 0 0
\(447\) −9.82015 + 5.66966i −0.0219690 + 0.0126838i
\(448\) 0 0
\(449\) 347.932i 0.774904i −0.921890 0.387452i \(-0.873355\pi\)
0.921890 0.387452i \(-0.126645\pi\)
\(450\) 0 0
\(451\) −239.438 138.240i −0.530905 0.306518i
\(452\) 0 0
\(453\) −13.5959 + 23.5488i −0.0300131 + 0.0519842i
\(454\) 0 0
\(455\) 0.507242i 0.00111482i
\(456\) 0 0
\(457\) 443.576 0.970625 0.485312 0.874341i \(-0.338706\pi\)
0.485312 + 0.874341i \(0.338706\pi\)
\(458\) 0 0
\(459\) 58.6237 + 33.8464i 0.127721 + 0.0737395i
\(460\) 0 0
\(461\) −97.8076 + 169.408i −0.212164 + 0.367479i −0.952392 0.304878i \(-0.901384\pi\)
0.740227 + 0.672357i \(0.234718\pi\)
\(462\) 0 0
\(463\) 720.958 1.55715 0.778573 0.627555i \(-0.215944\pi\)
0.778573 + 0.627555i \(0.215944\pi\)
\(464\) 0 0
\(465\) 4.95459 + 8.58161i 0.0106550 + 0.0184551i
\(466\) 0 0
\(467\) −271.889 −0.582203 −0.291101 0.956692i \(-0.594022\pi\)
−0.291101 + 0.956692i \(0.594022\pi\)
\(468\) 0 0
\(469\) −297.606 + 171.823i −0.634555 + 0.366360i
\(470\) 0 0
\(471\) −55.0926 + 31.8077i −0.116969 + 0.0675323i
\(472\) 0 0
\(473\) 95.2316 164.946i 0.201335 0.348723i
\(474\) 0 0
\(475\) 428.908 154.835i 0.902965 0.325968i
\(476\) 0 0
\(477\) −429.712 248.094i −0.900863 0.520114i
\(478\) 0 0
\(479\) 173.599 + 300.682i 0.362419 + 0.627728i 0.988358 0.152144i \(-0.0486176\pi\)
−0.625939 + 0.779872i \(0.715284\pi\)
\(480\) 0 0
\(481\) 1.92398 + 3.33243i 0.00399995 + 0.00692812i
\(482\) 0 0
\(483\) 15.7057i 0.0325170i
\(484\) 0 0
\(485\) −128.848 + 74.3907i −0.265667 + 0.153383i
\(486\) 0 0
\(487\) 495.960i 1.01840i −0.860648 0.509200i \(-0.829942\pi\)
0.860648 0.509200i \(-0.170058\pi\)
\(488\) 0 0
\(489\) −35.0408 20.2308i −0.0716581 0.0413718i
\(490\) 0 0
\(491\) 267.174 462.759i 0.544143 0.942483i −0.454517 0.890738i \(-0.650188\pi\)
0.998660 0.0517455i \(-0.0164785\pi\)
\(492\) 0 0
\(493\) 529.605i 1.07425i
\(494\) 0 0
\(495\) −45.3939 −0.0917048
\(496\) 0 0
\(497\) −189.817 109.591i −0.381926 0.220505i
\(498\) 0 0
\(499\) 395.457 684.951i 0.792499 1.37265i −0.131917 0.991261i \(-0.542113\pi\)
0.924415 0.381387i \(-0.124554\pi\)
\(500\) 0 0
\(501\) −58.3235 −0.116414
\(502\) 0 0
\(503\) 209.841 + 363.455i 0.417178 + 0.722574i 0.995654 0.0931256i \(-0.0296858\pi\)
−0.578476 + 0.815699i \(0.696352\pi\)
\(504\) 0 0
\(505\) 140.485 0.278188
\(506\) 0 0
\(507\) 46.5097 26.8524i 0.0917351 0.0529633i
\(508\) 0 0
\(509\) 695.515 401.556i 1.36643 0.788911i 0.375963 0.926635i \(-0.377312\pi\)
0.990471 + 0.137724i \(0.0439786\pi\)
\(510\) 0 0
\(511\) −42.5913 + 73.7703i −0.0833490 + 0.144365i
\(512\) 0 0
\(513\) 106.398 + 19.0493i 0.207404 + 0.0371332i
\(514\) 0 0
\(515\) 98.6969 + 56.9827i 0.191645 + 0.110646i
\(516\) 0 0
\(517\) 207.969 + 360.214i 0.402262 + 0.696738i
\(518\) 0 0
\(519\) 10.5737 + 18.3142i 0.0203733 + 0.0352875i
\(520\) 0 0
\(521\) 413.663i 0.793979i 0.917823 + 0.396990i \(0.129945\pi\)
−0.917823 + 0.396990i \(0.870055\pi\)
\(522\) 0 0
\(523\) −434.144 + 250.653i −0.830103 + 0.479260i −0.853888 0.520457i \(-0.825762\pi\)
0.0237853 + 0.999717i \(0.492428\pi\)
\(524\) 0 0
\(525\) 22.1137i 0.0421213i
\(526\) 0 0
\(527\) −321.272 185.487i −0.609625 0.351967i
\(528\) 0 0
\(529\) 119.227 206.507i 0.225382 0.390373i
\(530\) 0 0
\(531\) 307.413i 0.578931i
\(532\) 0 0
\(533\) 9.48366 0.0177930
\(534\) 0 0
\(535\) 98.6969 + 56.9827i 0.184480 + 0.106510i
\(536\) 0 0
\(537\) −3.84795 + 6.66485i −0.00716565 + 0.0124113i
\(538\) 0 0
\(539\) −207.081 −0.384194
\(540\) 0 0
\(541\) 196.576 + 340.480i 0.363357 + 0.629352i 0.988511 0.151149i \(-0.0482973\pi\)
−0.625154 + 0.780501i \(0.714964\pi\)
\(542\) 0 0
\(543\) −11.3383 −0.0208808
\(544\) 0 0
\(545\) 59.2423 34.2036i 0.108702 0.0627589i
\(546\) 0 0
\(547\) 418.159 241.424i 0.764460 0.441361i −0.0664350 0.997791i \(-0.521162\pi\)
0.830895 + 0.556430i \(0.187829\pi\)
\(548\) 0 0
\(549\) 339.015 587.191i 0.617513 1.06956i
\(550\) 0 0
\(551\) −287.144 795.417i −0.521132 1.44359i
\(552\) 0 0
\(553\) 165.879 + 95.7700i 0.299961 + 0.173183i
\(554\) 0 0
\(555\) 3.49490 + 6.05334i 0.00629711 + 0.0109069i
\(556\) 0 0
\(557\) 75.8531 + 131.381i 0.136181 + 0.235873i 0.926048 0.377405i \(-0.123184\pi\)
−0.789867 + 0.613279i \(0.789850\pi\)
\(558\) 0 0
\(559\) 6.53318i 0.0116873i
\(560\) 0 0
\(561\) −16.7071 + 9.64587i −0.0297810 + 0.0171941i
\(562\) 0 0
\(563\) 176.634i 0.313737i −0.987620 0.156868i \(-0.949860\pi\)
0.987620 0.156868i \(-0.0501399\pi\)
\(564\) 0 0
\(565\) 70.9546 + 40.9657i 0.125583 + 0.0725056i
\(566\) 0 0
\(567\) −113.470 + 196.536i −0.200123 + 0.346624i
\(568\) 0 0
\(569\) 957.928i 1.68353i −0.539844 0.841765i \(-0.681517\pi\)
0.539844 0.841765i \(-0.318483\pi\)
\(570\) 0 0
\(571\) −833.242 −1.45927 −0.729634 0.683838i \(-0.760309\pi\)
−0.729634 + 0.683838i \(0.760309\pi\)
\(572\) 0 0
\(573\) −49.6153 28.6454i −0.0865887 0.0499920i
\(574\) 0 0
\(575\) 204.545 354.282i 0.355730 0.616143i
\(576\) 0 0
\(577\) −484.595 −0.839852 −0.419926 0.907558i \(-0.637944\pi\)
−0.419926 + 0.907558i \(0.637944\pi\)
\(578\) 0 0
\(579\) −34.6793 60.0664i −0.0598952 0.103742i
\(580\) 0 0
\(581\) 88.9898 0.153167
\(582\) 0 0
\(583\) 246.317 142.211i 0.422499 0.243930i
\(584\) 0 0
\(585\) 1.34847 0.778539i 0.00230508 0.00133084i
\(586\) 0 0
\(587\) −309.432 + 535.952i −0.527141 + 0.913035i 0.472358 + 0.881407i \(0.343403\pi\)
−0.999500 + 0.0316288i \(0.989931\pi\)
\(588\) 0 0
\(589\) −583.090 104.395i −0.989966 0.177241i
\(590\) 0 0
\(591\) −93.6117 54.0468i −0.158396 0.0914497i
\(592\) 0 0
\(593\) 93.9699 + 162.761i 0.158465 + 0.274470i 0.934315 0.356447i \(-0.116012\pi\)
−0.775850 + 0.630917i \(0.782679\pi\)
\(594\) 0 0
\(595\) −17.2474 29.8735i −0.0289873 0.0502075i
\(596\) 0 0
\(597\) 105.963i 0.177493i
\(598\) 0 0
\(599\) 69.5533 40.1566i 0.116116 0.0670394i −0.440817 0.897597i \(-0.645311\pi\)
0.556933 + 0.830557i \(0.311978\pi\)
\(600\) 0 0
\(601\) 665.929i 1.10804i 0.832505 + 0.554018i \(0.186906\pi\)
−0.832505 + 0.554018i \(0.813094\pi\)
\(602\) 0 0
\(603\) 913.560 + 527.444i 1.51502 + 0.874700i
\(604\) 0 0
\(605\) −47.4898 + 82.2547i −0.0784955 + 0.135958i
\(606\) 0 0
\(607\) 105.952i 0.174550i 0.996184 + 0.0872751i \(0.0278159\pi\)
−0.996184 + 0.0872751i \(0.972184\pi\)
\(608\) 0 0
\(609\) −41.0102 −0.0673402
\(610\) 0 0
\(611\) −12.3559 7.13366i −0.0202224 0.0116754i
\(612\) 0 0
\(613\) 569.171 985.833i 0.928501 1.60821i 0.142668 0.989771i \(-0.454432\pi\)
0.785832 0.618440i \(-0.212235\pi\)
\(614\) 0 0
\(615\) 17.2270 0.0280114
\(616\) 0 0
\(617\) −459.131 795.238i −0.744135 1.28888i −0.950598 0.310425i \(-0.899529\pi\)
0.206463 0.978454i \(-0.433805\pi\)
\(618\) 0 0
\(619\) 1123.85 1.81559 0.907793 0.419418i \(-0.137766\pi\)
0.907793 + 0.419418i \(0.137766\pi\)
\(620\) 0 0
\(621\) 83.9791 48.4853i 0.135232 0.0780762i
\(622\) 0 0
\(623\) −25.6515 + 14.8099i −0.0411742 + 0.0237719i
\(624\) 0 0
\(625\) −275.500 + 477.180i −0.440800 + 0.763488i
\(626\) 0 0
\(627\) −19.8627 + 23.5456i −0.0316790 + 0.0375528i
\(628\) 0 0
\(629\) −226.621 130.840i −0.360288 0.208012i
\(630\) 0 0
\(631\) 40.2753 + 69.7588i 0.0638277 + 0.110553i 0.896173 0.443704i \(-0.146336\pi\)
−0.832346 + 0.554257i \(0.813003\pi\)
\(632\) 0 0
\(633\) 55.5556 + 96.2251i 0.0877656 + 0.152014i
\(634\) 0 0
\(635\) 134.146i 0.211254i
\(636\) 0 0
\(637\) 6.15153 3.55159i 0.00965703 0.00557549i
\(638\) 0 0
\(639\) 672.822i 1.05293i
\(640\) 0 0
\(641\) −428.893 247.621i −0.669100 0.386305i 0.126636 0.991949i \(-0.459582\pi\)
−0.795735 + 0.605644i \(0.792915\pi\)
\(642\) 0 0
\(643\) 245.123 424.566i 0.381218 0.660289i −0.610019 0.792387i \(-0.708838\pi\)
0.991237 + 0.132098i \(0.0421714\pi\)
\(644\) 0 0
\(645\) 11.8675i 0.0183992i
\(646\) 0 0
\(647\) 494.132 0.763727 0.381864 0.924219i \(-0.375282\pi\)
0.381864 + 0.924219i \(0.375282\pi\)
\(648\) 0 0
\(649\) 152.605 + 88.1066i 0.235139 + 0.135757i
\(650\) 0 0
\(651\) −14.3633 + 24.8779i −0.0220634 + 0.0382149i
\(652\) 0 0
\(653\) 475.383 0.727998 0.363999 0.931399i \(-0.381411\pi\)
0.363999 + 0.931399i \(0.381411\pi\)
\(654\) 0 0
\(655\) −41.3763 71.6658i −0.0631699 0.109413i
\(656\) 0 0
\(657\) 261.485 0.397998
\(658\) 0 0
\(659\) −494.082 + 285.259i −0.749746 + 0.432866i −0.825602 0.564253i \(-0.809164\pi\)
0.0758563 + 0.997119i \(0.475831\pi\)
\(660\) 0 0
\(661\) −18.6964 + 10.7944i −0.0282851 + 0.0163304i −0.514076 0.857745i \(-0.671865\pi\)
0.485791 + 0.874075i \(0.338532\pi\)
\(662\) 0 0
\(663\) 0.330868 0.573080i 0.000499047 0.000864374i
\(664\) 0 0
\(665\) −42.1010 35.5159i −0.0633098 0.0534073i
\(666\) 0 0
\(667\) −657.022 379.332i −0.985041 0.568714i
\(668\) 0 0
\(669\) −5.05051 8.74774i −0.00754934 0.0130758i
\(670\) 0 0
\(671\) 194.328 + 336.586i 0.289610 + 0.501619i
\(672\) 0 0
\(673\) 256.395i 0.380973i −0.981690 0.190486i \(-0.938993\pi\)
0.981690 0.190486i \(-0.0610065\pi\)
\(674\) 0 0
\(675\) −118.243 + 68.2675i −0.175175 + 0.101137i
\(676\) 0 0
\(677\) 662.815i 0.979048i 0.871990 + 0.489524i \(0.162829\pi\)
−0.871990 + 0.489524i \(0.837171\pi\)
\(678\) 0 0
\(679\) −373.529 215.657i −0.550116 0.317610i
\(680\) 0 0
\(681\) −39.6867 + 68.7394i −0.0582771 + 0.100939i
\(682\) 0 0
\(683\) 310.334i 0.454369i −0.973852 0.227184i \(-0.927048\pi\)
0.973852 0.227184i \(-0.0729520\pi\)
\(684\) 0 0
\(685\) 11.8990 0.0173708
\(686\) 0 0
\(687\) 71.4801 + 41.2691i 0.104047 + 0.0600714i
\(688\) 0 0
\(689\) −4.87805 + 8.44904i −0.00707990 + 0.0122628i
\(690\) 0 0
\(691\) −187.789 −0.271764 −0.135882 0.990725i \(-0.543387\pi\)
−0.135882 + 0.990725i \(0.543387\pi\)
\(692\) 0 0
\(693\) −65.7980 113.965i −0.0949465 0.164452i
\(694\) 0 0
\(695\) 41.7423 0.0600609
\(696\) 0 0
\(697\) −558.530 + 322.467i −0.801334 + 0.462650i
\(698\) 0 0
\(699\) −107.427 + 62.0232i −0.153687 + 0.0887313i
\(700\) 0 0
\(701\) −270.818 + 469.070i −0.386331 + 0.669144i −0.991953 0.126608i \(-0.959591\pi\)
0.605622 + 0.795752i \(0.292924\pi\)
\(702\) 0 0
\(703\) −411.303 73.6387i −0.585068 0.104749i
\(704\) 0 0
\(705\) −22.4444 12.9583i −0.0318360 0.0183805i
\(706\) 0 0
\(707\) 203.631 + 352.699i 0.288021 + 0.498868i
\(708\) 0 0
\(709\) 245.621 + 425.429i 0.346434 + 0.600041i 0.985613 0.169017i \(-0.0540593\pi\)
−0.639180 + 0.769058i \(0.720726\pi\)
\(710\) 0 0
\(711\) 587.969i 0.826961i
\(712\) 0 0
\(713\) −460.226 + 265.712i −0.645478 + 0.372667i
\(714\) 0 0
\(715\) 0.892539i 0.00124831i
\(716\) 0 0
\(717\) −81.6617 47.1474i −0.113894 0.0657565i
\(718\) 0 0
\(719\) −287.734 + 498.370i −0.400186 + 0.693143i −0.993748 0.111645i \(-0.964388\pi\)
0.593562 + 0.804788i \(0.297721\pi\)
\(720\) 0 0
\(721\) 330.383i 0.458229i
\(722\) 0 0
\(723\) 36.6005 0.0506231
\(724\) 0 0
\(725\) 925.090 + 534.101i 1.27599 + 0.736691i
\(726\) 0 0
\(727\) −409.552 + 709.365i −0.563346 + 0.975743i 0.433856 + 0.900982i \(0.357153\pi\)
−0.997201 + 0.0747610i \(0.976181\pi\)
\(728\) 0 0
\(729\) 680.362 0.933282
\(730\) 0 0
\(731\) −222.144 384.764i −0.303890 0.526353i
\(732\) 0 0
\(733\) 804.332 1.09731 0.548657 0.836047i \(-0.315139\pi\)
0.548657 + 0.836047i \(0.315139\pi\)
\(734\) 0 0
\(735\) 11.1742 6.45145i 0.0152030 0.00877748i
\(736\) 0 0
\(737\) −523.665 + 302.338i −0.710536 + 0.410228i
\(738\) 0 0
\(739\) 37.9314 65.6991i 0.0513280 0.0889027i −0.839220 0.543792i \(-0.816988\pi\)
0.890548 + 0.454890i \(0.150321\pi\)
\(740\) 0 0
\(741\) 0.186218 1.04011i 0.000251306 0.00140365i
\(742\) 0 0
\(743\) −505.810 292.030i −0.680767 0.393041i 0.119377 0.992849i \(-0.461910\pi\)
−0.800144 + 0.599808i \(0.795244\pi\)
\(744\) 0 0
\(745\) −17.8383 30.8968i −0.0239440 0.0414722i
\(746\) 0 0
\(747\) −136.586 236.573i −0.182846 0.316698i
\(748\) 0 0
\(749\) 330.383i 0.441099i
\(750\) 0 0
\(751\) −513.931 + 296.718i −0.684329 + 0.395098i −0.801484 0.598016i \(-0.795956\pi\)
0.117155 + 0.993114i \(0.462623\pi\)
\(752\) 0 0
\(753\) 155.716i 0.206794i
\(754\) 0 0
\(755\) −74.0908 42.7764i −0.0981335 0.0566574i
\(756\) 0 0
\(757\) 278.257 481.956i 0.367579 0.636665i −0.621608 0.783329i \(-0.713520\pi\)
0.989186 + 0.146664i \(0.0468535\pi\)
\(758\) 0 0
\(759\) 27.6356i 0.0364106i
\(760\) 0 0
\(761\) −1211.85 −1.59244 −0.796219 0.605008i \(-0.793170\pi\)
−0.796219 + 0.605008i \(0.793170\pi\)
\(762\) 0 0
\(763\) 171.742 + 99.1555i 0.225088 + 0.129955i
\(764\) 0 0
\(765\) −52.9444 + 91.7024i −0.0692083 + 0.119872i
\(766\) 0 0
\(767\) −6.04438 −0.00788054
\(768\) 0 0
\(769\) 479.115 + 829.852i 0.623037 + 1.07913i 0.988917 + 0.148469i \(0.0474347\pi\)
−0.365880 + 0.930662i \(0.619232\pi\)
\(770\) 0 0
\(771\) 72.4393 0.0939550
\(772\) 0 0
\(773\) −404.409 + 233.486i −0.523168 + 0.302051i −0.738230 0.674549i \(-0.764338\pi\)
0.215062 + 0.976600i \(0.431005\pi\)
\(774\) 0 0
\(775\) 648.000 374.123i 0.836129 0.482739i
\(776\) 0 0
\(777\) −10.1316 + 17.5485i −0.0130394 + 0.0225850i
\(778\) 0 0
\(779\) −664.023 + 787.142i −0.852405 + 1.01045i
\(780\) 0 0
\(781\) −334.001 192.836i −0.427658 0.246909i
\(782\) 0 0
\(783\) 126.603 + 219.283i 0.161690 + 0.280055i
\(784\) 0 0
\(785\) −100.076 173.336i −0.127485 0.220810i
\(786\) 0 0
\(787\) 1410.48i 1.79223i 0.443824 + 0.896114i \(0.353621\pi\)
−0.443824 + 0.896114i \(0.646379\pi\)
\(788\) 0 0
\(789\) −37.4138 + 21.6009i −0.0474192 + 0.0273775i
\(790\) 0 0
\(791\) 237.517i 0.300275i
\(792\) 0 0