Properties

Label 819.2.fm.e.622.1
Level $819$
Weight $2$
Character 819.622
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 622.1
Character \(\chi\) \(=\) 819.622
Dual form 819.2.fm.e.370.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.687394 + 2.56539i) q^{2} +(-4.37666 - 2.52687i) q^{4} +(1.17771 - 1.17771i) q^{5} +(-1.53750 + 2.15316i) q^{7} +(5.73490 - 5.73490i) q^{8} +O(q^{10})\) \(q+(-0.687394 + 2.56539i) q^{2} +(-4.37666 - 2.52687i) q^{4} +(1.17771 - 1.17771i) q^{5} +(-1.53750 + 2.15316i) q^{7} +(5.73490 - 5.73490i) q^{8} +(2.21174 + 3.83085i) q^{10} +(4.50301 + 1.20658i) q^{11} +(-3.59585 + 0.264293i) q^{13} +(-4.46682 - 5.42436i) q^{14} +(5.71638 + 9.90107i) q^{16} +(-3.15625 + 5.46679i) q^{17} +(-1.09384 - 4.08225i) q^{19} +(-8.13039 + 2.17853i) q^{20} +(-6.19069 + 10.7226i) q^{22} +(-3.67599 + 2.12233i) q^{23} +2.22598i q^{25} +(1.79375 - 9.40643i) q^{26} +(12.1699 - 5.53859i) q^{28} +(0.526889 + 0.912598i) q^{29} +(-5.61834 + 5.61834i) q^{31} +(-13.6615 + 3.66058i) q^{32} +(-11.8549 - 11.8549i) q^{34} +(0.725070 + 4.34654i) q^{35} +(0.572076 + 0.153287i) q^{37} +11.2245 q^{38} -13.5081i q^{40} +(-1.24468 - 0.333510i) q^{41} +(-9.27990 - 5.35775i) q^{43} +(-16.6593 - 16.6593i) q^{44} +(-2.91776 - 10.8892i) q^{46} +(-2.85718 - 2.85718i) q^{47} +(-2.27219 - 6.62096i) q^{49} +(-5.71050 - 1.53012i) q^{50} +(16.4057 + 7.92952i) q^{52} +0.398831 q^{53} +(6.72427 - 3.88226i) q^{55} +(3.53074 + 21.1656i) q^{56} +(-2.70335 + 0.724361i) q^{58} +(8.26243 - 2.21391i) q^{59} +(4.22976 + 2.44205i) q^{61} +(-10.5512 - 18.2752i) q^{62} -14.6977i q^{64} +(-3.92362 + 4.54615i) q^{65} +(-2.76762 + 10.3289i) q^{67} +(27.6277 - 15.9509i) q^{68} +(-11.6490 - 1.12770i) q^{70} +(-4.31760 + 1.15690i) q^{71} +(-0.935407 - 0.935407i) q^{73} +(-0.786484 + 1.36223i) q^{74} +(-5.52795 + 20.6306i) q^{76} +(-9.52134 + 7.84059i) q^{77} -0.927988 q^{79} +(18.3929 + 4.92836i) q^{80} +(1.71117 - 2.96383i) q^{82} +(-7.79378 + 7.79378i) q^{83} +(2.72115 + 10.1555i) q^{85} +(20.1237 - 20.1237i) q^{86} +(32.7439 - 18.9047i) q^{88} +(-1.28296 + 4.78807i) q^{89} +(4.95956 - 8.14879i) q^{91} +21.4514 q^{92} +(9.29378 - 5.36577i) q^{94} +(-6.09595 - 3.51950i) q^{95} +(-1.65635 - 6.18160i) q^{97} +(18.5472 - 1.27783i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.687394 + 2.56539i −0.486061 + 1.81400i 0.0891737 + 0.996016i \(0.471577\pi\)
−0.575235 + 0.817988i \(0.695089\pi\)
\(3\) 0 0
\(4\) −4.37666 2.52687i −2.18833 1.26343i
\(5\) 1.17771 1.17771i 0.526690 0.526690i −0.392894 0.919584i \(-0.628526\pi\)
0.919584 + 0.392894i \(0.128526\pi\)
\(6\) 0 0
\(7\) −1.53750 + 2.15316i −0.581120 + 0.813818i
\(8\) 5.73490 5.73490i 2.02759 2.02759i
\(9\) 0 0
\(10\) 2.21174 + 3.83085i 0.699414 + 1.21142i
\(11\) 4.50301 + 1.20658i 1.35771 + 0.363797i 0.862975 0.505247i \(-0.168599\pi\)
0.494734 + 0.869044i \(0.335265\pi\)
\(12\) 0 0
\(13\) −3.59585 + 0.264293i −0.997310 + 0.0733017i
\(14\) −4.46682 5.42436i −1.19381 1.44972i
\(15\) 0 0
\(16\) 5.71638 + 9.90107i 1.42910 + 2.47527i
\(17\) −3.15625 + 5.46679i −0.765503 + 1.32589i 0.174476 + 0.984661i \(0.444177\pi\)
−0.939980 + 0.341230i \(0.889157\pi\)
\(18\) 0 0
\(19\) −1.09384 4.08225i −0.250943 0.936532i −0.970303 0.241894i \(-0.922231\pi\)
0.719360 0.694638i \(-0.244435\pi\)
\(20\) −8.13039 + 2.17853i −1.81801 + 0.487134i
\(21\) 0 0
\(22\) −6.19069 + 10.7226i −1.31986 + 2.28606i
\(23\) −3.67599 + 2.12233i −0.766496 + 0.442537i −0.831623 0.555340i \(-0.812588\pi\)
0.0651270 + 0.997877i \(0.479255\pi\)
\(24\) 0 0
\(25\) 2.22598i 0.445196i
\(26\) 1.79375 9.40643i 0.351784 1.84475i
\(27\) 0 0
\(28\) 12.1699 5.53859i 2.29989 1.04670i
\(29\) 0.526889 + 0.912598i 0.0978408 + 0.169465i 0.910791 0.412868i \(-0.135473\pi\)
−0.812950 + 0.582334i \(0.802140\pi\)
\(30\) 0 0
\(31\) −5.61834 + 5.61834i −1.00908 + 1.00908i −0.00912491 + 0.999958i \(0.502905\pi\)
−0.999958 + 0.00912491i \(0.997095\pi\)
\(32\) −13.6615 + 3.66058i −2.41503 + 0.647105i
\(33\) 0 0
\(34\) −11.8549 11.8549i −2.03309 2.03309i
\(35\) 0.725070 + 4.34654i 0.122559 + 0.734700i
\(36\) 0 0
\(37\) 0.572076 + 0.153287i 0.0940488 + 0.0252003i 0.305537 0.952180i \(-0.401164\pi\)
−0.211488 + 0.977381i \(0.567831\pi\)
\(38\) 11.2245 1.82085
\(39\) 0 0
\(40\) 13.5081i 2.13583i
\(41\) −1.24468 0.333510i −0.194386 0.0520856i 0.160312 0.987066i \(-0.448750\pi\)
−0.354698 + 0.934981i \(0.615416\pi\)
\(42\) 0 0
\(43\) −9.27990 5.35775i −1.41517 0.817050i −0.419302 0.907847i \(-0.637725\pi\)
−0.995869 + 0.0907973i \(0.971058\pi\)
\(44\) −16.6593 16.6593i −2.51148 2.51148i
\(45\) 0 0
\(46\) −2.91776 10.8892i −0.430200 1.60553i
\(47\) −2.85718 2.85718i −0.416762 0.416762i 0.467324 0.884086i \(-0.345218\pi\)
−0.884086 + 0.467324i \(0.845218\pi\)
\(48\) 0 0
\(49\) −2.27219 6.62096i −0.324598 0.945852i
\(50\) −5.71050 1.53012i −0.807587 0.216392i
\(51\) 0 0
\(52\) 16.4057 + 7.92952i 2.27506 + 1.09963i
\(53\) 0.398831 0.0547836 0.0273918 0.999625i \(-0.491280\pi\)
0.0273918 + 0.999625i \(0.491280\pi\)
\(54\) 0 0
\(55\) 6.72427 3.88226i 0.906700 0.523483i
\(56\) 3.53074 + 21.1656i 0.471815 + 2.82837i
\(57\) 0 0
\(58\) −2.70335 + 0.724361i −0.354967 + 0.0951132i
\(59\) 8.26243 2.21391i 1.07568 0.288227i 0.322854 0.946449i \(-0.395358\pi\)
0.752824 + 0.658222i \(0.228691\pi\)
\(60\) 0 0
\(61\) 4.22976 + 2.44205i 0.541565 + 0.312673i 0.745713 0.666267i \(-0.232109\pi\)
−0.204148 + 0.978940i \(0.565442\pi\)
\(62\) −10.5512 18.2752i −1.34001 2.32096i
\(63\) 0 0
\(64\) 14.6977i 1.83721i
\(65\) −3.92362 + 4.54615i −0.486666 + 0.563880i
\(66\) 0 0
\(67\) −2.76762 + 10.3289i −0.338118 + 1.26188i 0.562330 + 0.826913i \(0.309905\pi\)
−0.900449 + 0.434962i \(0.856762\pi\)
\(68\) 27.6277 15.9509i 3.35035 1.93433i
\(69\) 0 0
\(70\) −11.6490 1.12770i −1.39232 0.134786i
\(71\) −4.31760 + 1.15690i −0.512405 + 0.137298i −0.505751 0.862679i \(-0.668785\pi\)
−0.00665372 + 0.999978i \(0.502118\pi\)
\(72\) 0 0
\(73\) −0.935407 0.935407i −0.109481 0.109481i 0.650244 0.759725i \(-0.274667\pi\)
−0.759725 + 0.650244i \(0.774667\pi\)
\(74\) −0.786484 + 1.36223i −0.0914269 + 0.158356i
\(75\) 0 0
\(76\) −5.52795 + 20.6306i −0.634100 + 2.36649i
\(77\) −9.52134 + 7.84059i −1.08506 + 0.893518i
\(78\) 0 0
\(79\) −0.927988 −0.104407 −0.0522034 0.998636i \(-0.516624\pi\)
−0.0522034 + 0.998636i \(0.516624\pi\)
\(80\) 18.3929 + 4.92836i 2.05639 + 0.551008i
\(81\) 0 0
\(82\) 1.71117 2.96383i 0.188967 0.327300i
\(83\) −7.79378 + 7.79378i −0.855479 + 0.855479i −0.990802 0.135323i \(-0.956793\pi\)
0.135323 + 0.990802i \(0.456793\pi\)
\(84\) 0 0
\(85\) 2.72115 + 10.1555i 0.295150 + 1.10152i
\(86\) 20.1237 20.1237i 2.16999 2.16999i
\(87\) 0 0
\(88\) 32.7439 18.9047i 3.49052 2.01525i
\(89\) −1.28296 + 4.78807i −0.135993 + 0.507534i 0.863998 + 0.503495i \(0.167953\pi\)
−0.999992 + 0.00403982i \(0.998714\pi\)
\(90\) 0 0
\(91\) 4.95956 8.14879i 0.519903 0.854225i
\(92\) 21.4514 2.23646
\(93\) 0 0
\(94\) 9.29378 5.36577i 0.958580 0.553436i
\(95\) −6.09595 3.51950i −0.625431 0.361093i
\(96\) 0 0
\(97\) −1.65635 6.18160i −0.168177 0.627646i −0.997614 0.0690447i \(-0.978005\pi\)
0.829436 0.558601i \(-0.188662\pi\)
\(98\) 18.5472 1.27783i 1.87355 0.129081i
\(99\) 0 0
\(100\) 5.62475 9.74235i 0.562475 0.974235i
\(101\) 0.472587 + 0.818544i 0.0470241 + 0.0814482i 0.888579 0.458723i \(-0.151693\pi\)
−0.841555 + 0.540171i \(0.818360\pi\)
\(102\) 0 0
\(103\) −8.04965 −0.793156 −0.396578 0.918001i \(-0.629802\pi\)
−0.396578 + 0.918001i \(0.629802\pi\)
\(104\) −19.1062 + 22.1375i −1.87351 + 2.17077i
\(105\) 0 0
\(106\) −0.274154 + 1.02316i −0.0266282 + 0.0993777i
\(107\) 8.52440 + 14.7647i 0.824085 + 1.42736i 0.902617 + 0.430445i \(0.141643\pi\)
−0.0785320 + 0.996912i \(0.525023\pi\)
\(108\) 0 0
\(109\) 1.56781 + 1.56781i 0.150169 + 0.150169i 0.778193 0.628025i \(-0.216136\pi\)
−0.628025 + 0.778193i \(0.716136\pi\)
\(110\) 5.33728 + 19.9190i 0.508890 + 1.89920i
\(111\) 0 0
\(112\) −30.1075 2.91461i −2.84489 0.275405i
\(113\) 3.02535 5.24006i 0.284601 0.492943i −0.687911 0.725795i \(-0.741472\pi\)
0.972512 + 0.232852i \(0.0748056\pi\)
\(114\) 0 0
\(115\) −1.82976 + 6.82876i −0.170626 + 0.636786i
\(116\) 5.32551i 0.494462i
\(117\) 0 0
\(118\) 22.7182i 2.09138i
\(119\) −6.91813 15.2011i −0.634184 1.39348i
\(120\) 0 0
\(121\) 9.29500 + 5.36647i 0.845000 + 0.487861i
\(122\) −9.17232 + 9.17232i −0.830423 + 0.830423i
\(123\) 0 0
\(124\) 38.7864 10.3928i 3.48312 0.933299i
\(125\) 8.51014 + 8.51014i 0.761170 + 0.761170i
\(126\) 0 0
\(127\) −1.60575 + 0.927079i −0.142487 + 0.0822650i −0.569549 0.821958i \(-0.692882\pi\)
0.427062 + 0.904222i \(0.359549\pi\)
\(128\) 10.3824 + 2.78196i 0.917684 + 0.245893i
\(129\) 0 0
\(130\) −8.96556 13.1906i −0.786332 1.15689i
\(131\) 4.94735i 0.432252i −0.976365 0.216126i \(-0.930658\pi\)
0.976365 0.216126i \(-0.0693422\pi\)
\(132\) 0 0
\(133\) 10.4715 + 3.92126i 0.907994 + 0.340016i
\(134\) −24.5952 14.2000i −2.12470 1.22670i
\(135\) 0 0
\(136\) 13.2507 + 49.4523i 1.13624 + 4.24050i
\(137\) −1.82558 6.81316i −0.155970 0.582088i −0.999020 0.0442531i \(-0.985909\pi\)
0.843050 0.537834i \(-0.180757\pi\)
\(138\) 0 0
\(139\) 10.4051 + 6.00737i 0.882547 + 0.509539i 0.871497 0.490400i \(-0.163149\pi\)
0.0110494 + 0.999939i \(0.496483\pi\)
\(140\) 7.80975 20.8555i 0.660044 1.76261i
\(141\) 0 0
\(142\) 11.8716i 0.996240i
\(143\) −16.5111 3.14856i −1.38072 0.263296i
\(144\) 0 0
\(145\) 1.69530 + 0.454256i 0.140787 + 0.0377239i
\(146\) 3.04268 1.75669i 0.251814 0.145385i
\(147\) 0 0
\(148\) −2.11645 2.11645i −0.173971 0.173971i
\(149\) 4.76731 1.27740i 0.390553 0.104648i −0.0581981 0.998305i \(-0.518535\pi\)
0.448752 + 0.893657i \(0.351869\pi\)
\(150\) 0 0
\(151\) −13.7886 + 13.7886i −1.12210 + 1.12210i −0.130675 + 0.991425i \(0.541714\pi\)
−0.991425 + 0.130675i \(0.958286\pi\)
\(152\) −29.6843 17.1383i −2.40772 1.39010i
\(153\) 0 0
\(154\) −13.5692 29.8155i −1.09344 2.40260i
\(155\) 13.2336i 1.06295i
\(156\) 0 0
\(157\) 19.9821i 1.59474i −0.603489 0.797371i \(-0.706223\pi\)
0.603489 0.797371i \(-0.293777\pi\)
\(158\) 0.637894 2.38065i 0.0507481 0.189394i
\(159\) 0 0
\(160\) −11.7782 + 20.4004i −0.931147 + 1.61279i
\(161\) 1.08211 11.1781i 0.0852824 0.880955i
\(162\) 0 0
\(163\) −1.46606 5.47141i −0.114831 0.428554i 0.884444 0.466647i \(-0.154538\pi\)
−0.999274 + 0.0380934i \(0.987872\pi\)
\(164\) 4.60480 + 4.60480i 0.359574 + 0.359574i
\(165\) 0 0
\(166\) −14.6367 25.3515i −1.13603 1.96766i
\(167\) −1.10228 + 4.11377i −0.0852972 + 0.318333i −0.995370 0.0961143i \(-0.969359\pi\)
0.910073 + 0.414448i \(0.136025\pi\)
\(168\) 0 0
\(169\) 12.8603 1.90072i 0.989254 0.146209i
\(170\) −27.9233 −2.14162
\(171\) 0 0
\(172\) 27.0767 + 46.8982i 2.06458 + 3.57595i
\(173\) −0.873930 + 1.51369i −0.0664437 + 0.115084i −0.897333 0.441353i \(-0.854499\pi\)
0.830890 + 0.556437i \(0.187832\pi\)
\(174\) 0 0
\(175\) −4.79288 3.42244i −0.362308 0.258712i
\(176\) 13.7945 + 51.4819i 1.03980 + 3.88059i
\(177\) 0 0
\(178\) −11.4014 6.58258i −0.854568 0.493385i
\(179\) 19.7578 11.4072i 1.47677 0.852613i 0.477113 0.878842i \(-0.341683\pi\)
0.999656 + 0.0262285i \(0.00834976\pi\)
\(180\) 0 0
\(181\) 13.7425 1.02147 0.510737 0.859737i \(-0.329372\pi\)
0.510737 + 0.859737i \(0.329372\pi\)
\(182\) 17.4957 + 18.3246i 1.29686 + 1.35831i
\(183\) 0 0
\(184\) −8.91006 + 33.2528i −0.656858 + 2.45143i
\(185\) 0.854271 0.493214i 0.0628073 0.0362618i
\(186\) 0 0
\(187\) −20.8087 + 20.8087i −1.52169 + 1.52169i
\(188\) 5.28519 + 19.7246i 0.385462 + 1.43856i
\(189\) 0 0
\(190\) 13.2192 13.2192i 0.959021 0.959021i
\(191\) −6.02586 + 10.4371i −0.436016 + 0.755201i −0.997378 0.0723688i \(-0.976944\pi\)
0.561362 + 0.827570i \(0.310277\pi\)
\(192\) 0 0
\(193\) −4.42174 1.18480i −0.318284 0.0852838i 0.0961404 0.995368i \(-0.469350\pi\)
−0.414424 + 0.910084i \(0.636017\pi\)
\(194\) 16.9968 1.22030
\(195\) 0 0
\(196\) −6.78570 + 34.7192i −0.484693 + 2.47995i
\(197\) −5.05766 + 18.8754i −0.360343 + 1.34482i 0.513282 + 0.858220i \(0.328430\pi\)
−0.873625 + 0.486599i \(0.838237\pi\)
\(198\) 0 0
\(199\) −12.2497 + 21.2170i −0.868355 + 1.50403i −0.00467796 + 0.999989i \(0.501489\pi\)
−0.863677 + 0.504046i \(0.831844\pi\)
\(200\) 12.7658 + 12.7658i 0.902676 + 0.902676i
\(201\) 0 0
\(202\) −2.42474 + 0.649707i −0.170604 + 0.0457132i
\(203\) −2.77506 0.268644i −0.194771 0.0188551i
\(204\) 0 0
\(205\) −1.85865 + 1.07309i −0.129814 + 0.0749482i
\(206\) 5.53328 20.6505i 0.385522 1.43879i
\(207\) 0 0
\(208\) −23.1721 34.0920i −1.60669 2.36385i
\(209\) 19.7022i 1.36283i
\(210\) 0 0
\(211\) −11.4160 19.7731i −0.785910 1.36124i −0.928454 0.371448i \(-0.878862\pi\)
0.142544 0.989788i \(-0.454472\pi\)
\(212\) −1.74555 1.00779i −0.119885 0.0692154i
\(213\) 0 0
\(214\) −43.7368 + 11.7192i −2.98979 + 0.801111i
\(215\) −17.2390 + 4.61917i −1.17569 + 0.315025i
\(216\) 0 0
\(217\) −3.45898 20.7354i −0.234811 1.40761i
\(218\) −5.09973 + 2.94433i −0.345397 + 0.199415i
\(219\) 0 0
\(220\) −39.2398 −2.64555
\(221\) 9.90458 20.4919i 0.666254 1.37844i
\(222\) 0 0
\(223\) −12.2434 3.28062i −0.819881 0.219686i −0.175586 0.984464i \(-0.556182\pi\)
−0.644294 + 0.764778i \(0.722849\pi\)
\(224\) 13.1227 35.0434i 0.876797 2.34144i
\(225\) 0 0
\(226\) 11.3632 + 11.3632i 0.755868 + 0.755868i
\(227\) 2.99465 + 11.1762i 0.198762 + 0.741790i 0.991261 + 0.131917i \(0.0421131\pi\)
−0.792499 + 0.609874i \(0.791220\pi\)
\(228\) 0 0
\(229\) 9.10742 + 9.10742i 0.601835 + 0.601835i 0.940799 0.338964i \(-0.110077\pi\)
−0.338964 + 0.940799i \(0.610077\pi\)
\(230\) −16.2607 9.38810i −1.07220 0.619033i
\(231\) 0 0
\(232\) 8.25532 + 2.21201i 0.541988 + 0.145225i
\(233\) 1.49633i 0.0980277i −0.998798 0.0490139i \(-0.984392\pi\)
0.998798 0.0490139i \(-0.0156079\pi\)
\(234\) 0 0
\(235\) −6.72988 −0.439009
\(236\) −41.7562 11.1885i −2.71809 0.728311i
\(237\) 0 0
\(238\) 43.7522 7.29855i 2.83604 0.473095i
\(239\) 3.19313 + 3.19313i 0.206546 + 0.206546i 0.802798 0.596252i \(-0.203344\pi\)
−0.596252 + 0.802798i \(0.703344\pi\)
\(240\) 0 0
\(241\) 9.27435 2.48506i 0.597414 0.160076i 0.0525744 0.998617i \(-0.483257\pi\)
0.544839 + 0.838541i \(0.316591\pi\)
\(242\) −20.1564 + 20.1564i −1.29570 + 1.29570i
\(243\) 0 0
\(244\) −12.3415 21.3761i −0.790082 1.36846i
\(245\) −10.4736 5.12162i −0.669133 0.327208i
\(246\) 0 0
\(247\) 5.01218 + 14.3901i 0.318917 + 0.915618i
\(248\) 64.4412i 4.09202i
\(249\) 0 0
\(250\) −27.6816 + 15.9820i −1.75074 + 1.01079i
\(251\) 12.9361 22.4061i 0.816522 1.41426i −0.0917077 0.995786i \(-0.529233\pi\)
0.908230 0.418472i \(-0.137434\pi\)
\(252\) 0 0
\(253\) −19.1138 + 5.12152i −1.20167 + 0.321987i
\(254\) −1.27454 4.75664i −0.0799716 0.298458i
\(255\) 0 0
\(256\) 0.424093 0.734550i 0.0265058 0.0459094i
\(257\) 11.4386 + 19.8122i 0.713518 + 1.23585i 0.963528 + 0.267606i \(0.0862326\pi\)
−0.250011 + 0.968243i \(0.580434\pi\)
\(258\) 0 0
\(259\) −1.20962 + 0.996092i −0.0751621 + 0.0618941i
\(260\) 28.6599 9.98248i 1.77741 0.619087i
\(261\) 0 0
\(262\) 12.6919 + 3.40078i 0.784107 + 0.210101i
\(263\) 10.9168 + 18.9085i 0.673160 + 1.16595i 0.977003 + 0.213225i \(0.0683966\pi\)
−0.303844 + 0.952722i \(0.598270\pi\)
\(264\) 0 0
\(265\) 0.469709 0.469709i 0.0288540 0.0288540i
\(266\) −17.2576 + 24.1680i −1.05813 + 1.48184i
\(267\) 0 0
\(268\) 38.2127 38.2127i 2.33421 2.33421i
\(269\) −5.09171 2.93970i −0.310447 0.179237i 0.336679 0.941619i \(-0.390696\pi\)
−0.647127 + 0.762383i \(0.724029\pi\)
\(270\) 0 0
\(271\) −1.80033 + 6.71891i −0.109362 + 0.408145i −0.998803 0.0489044i \(-0.984427\pi\)
0.889441 + 0.457049i \(0.151094\pi\)
\(272\) −72.1694 −4.37591
\(273\) 0 0
\(274\) 18.7333 1.13172
\(275\) −2.68582 + 10.0236i −0.161961 + 0.604446i
\(276\) 0 0
\(277\) 10.7111 + 6.18406i 0.643568 + 0.371564i 0.785988 0.618242i \(-0.212155\pi\)
−0.142420 + 0.989806i \(0.545488\pi\)
\(278\) −22.5636 + 22.5636i −1.35328 + 1.35328i
\(279\) 0 0
\(280\) 29.0852 + 20.7688i 1.73817 + 1.24117i
\(281\) 15.6520 15.6520i 0.933721 0.933721i −0.0642154 0.997936i \(-0.520454\pi\)
0.997936 + 0.0642154i \(0.0204545\pi\)
\(282\) 0 0
\(283\) 14.3579 + 24.8687i 0.853490 + 1.47829i 0.878039 + 0.478589i \(0.158852\pi\)
−0.0245489 + 0.999699i \(0.507815\pi\)
\(284\) 21.8200 + 5.84665i 1.29478 + 0.346935i
\(285\) 0 0
\(286\) 19.4269 40.1930i 1.14874 2.37666i
\(287\) 2.63179 2.16722i 0.155350 0.127927i
\(288\) 0 0
\(289\) −11.4238 19.7867i −0.671991 1.16392i
\(290\) −2.33069 + 4.03687i −0.136863 + 0.237053i
\(291\) 0 0
\(292\) 1.73031 + 6.45761i 0.101259 + 0.377903i
\(293\) 22.3231 5.98146i 1.30413 0.349441i 0.461120 0.887338i \(-0.347448\pi\)
0.843011 + 0.537897i \(0.180781\pi\)
\(294\) 0 0
\(295\) 7.12343 12.3381i 0.414742 0.718355i
\(296\) 4.15989 2.40171i 0.241789 0.139597i
\(297\) 0 0
\(298\) 13.1081i 0.759331i
\(299\) 12.6574 8.60313i 0.731996 0.497532i
\(300\) 0 0
\(301\) 25.8039 11.7436i 1.48731 0.676887i
\(302\) −25.8949 44.8513i −1.49009 2.58090i
\(303\) 0 0
\(304\) 34.1658 34.1658i 1.95954 1.95954i
\(305\) 7.85749 2.10541i 0.449918 0.120555i
\(306\) 0 0
\(307\) −5.52660 5.52660i −0.315419 0.315419i 0.531585 0.847005i \(-0.321596\pi\)
−0.847005 + 0.531585i \(0.821596\pi\)
\(308\) 61.4838 10.2564i 3.50336 0.584415i
\(309\) 0 0
\(310\) −33.9493 9.09669i −1.92819 0.516658i
\(311\) 10.3208 0.585239 0.292620 0.956229i \(-0.405473\pi\)
0.292620 + 0.956229i \(0.405473\pi\)
\(312\) 0 0
\(313\) 20.9365i 1.18340i 0.806157 + 0.591701i \(0.201543\pi\)
−0.806157 + 0.591701i \(0.798457\pi\)
\(314\) 51.2618 + 13.7356i 2.89287 + 0.775142i
\(315\) 0 0
\(316\) 4.06149 + 2.34490i 0.228477 + 0.131911i
\(317\) −8.45606 8.45606i −0.474940 0.474940i 0.428569 0.903509i \(-0.359018\pi\)
−0.903509 + 0.428569i \(0.859018\pi\)
\(318\) 0 0
\(319\) 1.27147 + 4.74517i 0.0711884 + 0.265679i
\(320\) −17.3097 17.3097i −0.967641 0.967641i
\(321\) 0 0
\(322\) 27.9323 + 10.4598i 1.55660 + 0.582901i
\(323\) 25.7692 + 6.90484i 1.43384 + 0.384195i
\(324\) 0 0
\(325\) −0.588311 8.00429i −0.0326336 0.443998i
\(326\) 15.0441 0.833213
\(327\) 0 0
\(328\) −9.05075 + 5.22545i −0.499744 + 0.288527i
\(329\) 10.5449 1.75905i 0.581357 0.0969794i
\(330\) 0 0
\(331\) 25.0550 6.71347i 1.37715 0.369006i 0.507064 0.861909i \(-0.330731\pi\)
0.870084 + 0.492903i \(0.164064\pi\)
\(332\) 53.8046 14.4169i 2.95291 0.791230i
\(333\) 0 0
\(334\) −9.79573 5.65557i −0.535999 0.309459i
\(335\) 8.90502 + 15.4240i 0.486533 + 0.842700i
\(336\) 0 0
\(337\) 26.1315i 1.42348i −0.702445 0.711738i \(-0.747908\pi\)
0.702445 0.711738i \(-0.252092\pi\)
\(338\) −3.96401 + 34.2982i −0.215614 + 1.86558i
\(339\) 0 0
\(340\) 13.7520 51.3231i 0.745806 2.78339i
\(341\) −32.0784 + 18.5205i −1.73714 + 1.00294i
\(342\) 0 0
\(343\) 17.7495 + 5.28735i 0.958382 + 0.285490i
\(344\) −83.9455 + 22.4931i −4.52604 + 1.21275i
\(345\) 0 0
\(346\) −3.28247 3.28247i −0.176467 0.176467i
\(347\) −3.74039 + 6.47855i −0.200795 + 0.347787i −0.948785 0.315923i \(-0.897686\pi\)
0.747990 + 0.663710i \(0.231019\pi\)
\(348\) 0 0
\(349\) 0.528661 1.97299i 0.0282986 0.105612i −0.950332 0.311238i \(-0.899256\pi\)
0.978631 + 0.205626i \(0.0659231\pi\)
\(350\) 12.0745 9.94305i 0.645409 0.531478i
\(351\) 0 0
\(352\) −65.9345 −3.51432
\(353\) 12.1175 + 3.24687i 0.644949 + 0.172813i 0.566444 0.824100i \(-0.308319\pi\)
0.0785047 + 0.996914i \(0.474985\pi\)
\(354\) 0 0
\(355\) −3.72241 + 6.44740i −0.197565 + 0.342192i
\(356\) 17.7139 17.7139i 0.938835 0.938835i
\(357\) 0 0
\(358\) 15.6825 + 58.5278i 0.828844 + 3.09329i
\(359\) 6.92976 6.92976i 0.365739 0.365739i −0.500182 0.865920i \(-0.666733\pi\)
0.865920 + 0.500182i \(0.166733\pi\)
\(360\) 0 0
\(361\) 0.986209 0.569388i 0.0519057 0.0299678i
\(362\) −9.44654 + 35.2550i −0.496499 + 1.85296i
\(363\) 0 0
\(364\) −42.2972 + 23.1324i −2.21698 + 1.21247i
\(365\) −2.20328 −0.115325
\(366\) 0 0
\(367\) 21.7912 12.5811i 1.13749 0.656730i 0.191682 0.981457i \(-0.438606\pi\)
0.945808 + 0.324727i \(0.105272\pi\)
\(368\) −42.0267 24.2641i −2.19079 1.26486i
\(369\) 0 0
\(370\) 0.678064 + 2.53057i 0.0352509 + 0.131558i
\(371\) −0.613202 + 0.858746i −0.0318359 + 0.0445839i
\(372\) 0 0
\(373\) 5.81848 10.0779i 0.301270 0.521814i −0.675154 0.737677i \(-0.735923\pi\)
0.976424 + 0.215862i \(0.0692562\pi\)
\(374\) −39.0787 67.6864i −2.02071 3.49998i
\(375\) 0 0
\(376\) −32.7713 −1.69005
\(377\) −2.13581 3.14232i −0.110000 0.161837i
\(378\) 0 0
\(379\) −6.70131 + 25.0096i −0.344223 + 1.28466i 0.549294 + 0.835629i \(0.314897\pi\)
−0.893517 + 0.449029i \(0.851770\pi\)
\(380\) 17.7866 + 30.8073i 0.912434 + 1.58038i
\(381\) 0 0
\(382\) −22.6331 22.6331i −1.15801 1.15801i
\(383\) −2.62259 9.78763i −0.134008 0.500125i −1.00000 6.67944e-5i \(-0.999979\pi\)
0.865992 0.500058i \(-0.166688\pi\)
\(384\) 0 0
\(385\) −1.97944 + 20.4474i −0.100882 + 1.04210i
\(386\) 6.07895 10.5291i 0.309410 0.535915i
\(387\) 0 0
\(388\) −8.37077 + 31.2401i −0.424962 + 1.58598i
\(389\) 25.4046i 1.28806i −0.764999 0.644032i \(-0.777260\pi\)
0.764999 0.644032i \(-0.222740\pi\)
\(390\) 0 0
\(391\) 26.7945i 1.35505i
\(392\) −51.0013 24.9398i −2.57596 1.25965i
\(393\) 0 0
\(394\) −44.9463 25.9497i −2.26436 1.30733i
\(395\) −1.09291 + 1.09291i −0.0549900 + 0.0549900i
\(396\) 0 0
\(397\) −23.6455 + 6.33580i −1.18673 + 0.317984i −0.797594 0.603194i \(-0.793894\pi\)
−0.389140 + 0.921179i \(0.627228\pi\)
\(398\) −46.0096 46.0096i −2.30625 2.30625i
\(399\) 0 0
\(400\) −22.0396 + 12.7245i −1.10198 + 0.636227i
\(401\) −19.0591 5.10686i −0.951765 0.255025i −0.250654 0.968077i \(-0.580646\pi\)
−0.701111 + 0.713052i \(0.747312\pi\)
\(402\) 0 0
\(403\) 18.7178 21.6876i 0.932401 1.08034i
\(404\) 4.77666i 0.237647i
\(405\) 0 0
\(406\) 2.59674 6.93445i 0.128874 0.344151i
\(407\) 2.39111 + 1.38051i 0.118523 + 0.0684293i
\(408\) 0 0
\(409\) 6.62979 + 24.7427i 0.327822 + 1.22345i 0.911444 + 0.411423i \(0.134968\pi\)
−0.583622 + 0.812025i \(0.698365\pi\)
\(410\) −1.47528 5.50581i −0.0728588 0.271913i
\(411\) 0 0
\(412\) 35.2306 + 20.3404i 1.73569 + 1.00210i
\(413\) −7.93659 + 21.1942i −0.390534 + 1.04290i
\(414\) 0 0
\(415\) 18.3577i 0.901144i
\(416\) 48.1571 16.7735i 2.36110 0.822390i
\(417\) 0 0
\(418\) 50.5438 + 13.5432i 2.47218 + 0.662419i
\(419\) −2.48993 + 1.43756i −0.121641 + 0.0702295i −0.559586 0.828772i \(-0.689040\pi\)
0.437945 + 0.899002i \(0.355706\pi\)
\(420\) 0 0
\(421\) −13.5970 13.5970i −0.662676 0.662676i 0.293334 0.956010i \(-0.405235\pi\)
−0.956010 + 0.293334i \(0.905235\pi\)
\(422\) 58.5730 15.6946i 2.85129 0.764000i
\(423\) 0 0
\(424\) 2.28725 2.28725i 0.111079 0.111079i
\(425\) −12.1689 7.02575i −0.590281 0.340799i
\(426\) 0 0
\(427\) −11.7614 + 5.35269i −0.569173 + 0.259035i
\(428\) 86.1601i 4.16471i
\(429\) 0 0
\(430\) 47.3999i 2.28582i
\(431\) −9.48793 + 35.4094i −0.457017 + 1.70561i 0.225071 + 0.974342i \(0.427738\pi\)
−0.682089 + 0.731269i \(0.738928\pi\)
\(432\) 0 0
\(433\) −0.0741930 + 0.128506i −0.00356549 + 0.00617561i −0.867803 0.496909i \(-0.834468\pi\)
0.864237 + 0.503085i \(0.167802\pi\)
\(434\) 55.5720 + 5.37974i 2.66754 + 0.258236i
\(435\) 0 0
\(436\) −2.90012 10.8234i −0.138891 0.518346i
\(437\) 12.6848 + 12.6848i 0.606797 + 0.606797i
\(438\) 0 0
\(439\) 4.05749 + 7.02778i 0.193654 + 0.335418i 0.946458 0.322826i \(-0.104633\pi\)
−0.752805 + 0.658244i \(0.771300\pi\)
\(440\) 16.2986 60.8274i 0.777007 2.89983i
\(441\) 0 0
\(442\) 45.7615 + 39.4951i 2.17665 + 1.87859i
\(443\) 26.1952 1.24457 0.622285 0.782790i \(-0.286204\pi\)
0.622285 + 0.782790i \(0.286204\pi\)
\(444\) 0 0
\(445\) 4.12802 + 7.14994i 0.195687 + 0.338940i
\(446\) 16.8321 29.1541i 0.797024 1.38049i
\(447\) 0 0
\(448\) 31.6465 + 22.5977i 1.49516 + 1.06764i
\(449\) −0.953576 3.55879i −0.0450020 0.167950i 0.939768 0.341814i \(-0.111041\pi\)
−0.984770 + 0.173864i \(0.944375\pi\)
\(450\) 0 0
\(451\) −5.20239 3.00360i −0.244971 0.141434i
\(452\) −26.4819 + 15.2893i −1.24560 + 0.719148i
\(453\) 0 0
\(454\) −30.7298 −1.44222
\(455\) −3.75601 15.4379i −0.176084 0.723739i
\(456\) 0 0
\(457\) 2.49719 9.31962i 0.116813 0.435954i −0.882603 0.470119i \(-0.844211\pi\)
0.999416 + 0.0341660i \(0.0108775\pi\)
\(458\) −29.6245 + 17.1037i −1.38426 + 0.799203i
\(459\) 0 0
\(460\) 25.2636 25.2636i 1.17792 1.17792i
\(461\) 1.90787 + 7.12028i 0.0888585 + 0.331624i 0.996017 0.0891650i \(-0.0284198\pi\)
−0.907158 + 0.420789i \(0.861753\pi\)
\(462\) 0 0
\(463\) 10.2671 10.2671i 0.477153 0.477153i −0.427067 0.904220i \(-0.640453\pi\)
0.904220 + 0.427067i \(0.140453\pi\)
\(464\) −6.02380 + 10.4335i −0.279648 + 0.484364i
\(465\) 0 0
\(466\) 3.83867 + 1.02857i 0.177823 + 0.0476475i
\(467\) −34.1823 −1.58177 −0.790883 0.611967i \(-0.790379\pi\)
−0.790883 + 0.611967i \(0.790379\pi\)
\(468\) 0 0
\(469\) −17.9845 21.8398i −0.830449 1.00847i
\(470\) 4.62608 17.2648i 0.213385 0.796364i
\(471\) 0 0
\(472\) 34.6877 60.0808i 1.59663 2.76544i
\(473\) −35.3229 35.3229i −1.62415 1.62415i
\(474\) 0 0
\(475\) 9.08699 2.43485i 0.416940 0.111719i
\(476\) −8.13285 + 84.0113i −0.372769 + 3.85065i
\(477\) 0 0
\(478\) −10.3865 + 5.99668i −0.475070 + 0.274282i
\(479\) −9.19517 + 34.3169i −0.420138 + 1.56798i 0.354178 + 0.935178i \(0.384761\pi\)
−0.774316 + 0.632799i \(0.781906\pi\)
\(480\) 0 0
\(481\) −2.09761 0.400003i −0.0956430 0.0182386i
\(482\) 25.5005i 1.16152i
\(483\) 0 0
\(484\) −27.1207 46.9745i −1.23276 2.13520i
\(485\) −9.23087 5.32944i −0.419152 0.241998i
\(486\) 0 0
\(487\) 22.0147 5.89883i 0.997583 0.267302i 0.277150 0.960827i \(-0.410610\pi\)
0.720433 + 0.693525i \(0.243943\pi\)
\(488\) 38.2622 10.2523i 1.73205 0.464101i
\(489\) 0 0
\(490\) 20.3384 23.3483i 0.918797 1.05477i
\(491\) −12.8664 + 7.42840i −0.580651 + 0.335239i −0.761392 0.648292i \(-0.775484\pi\)
0.180741 + 0.983531i \(0.442150\pi\)
\(492\) 0 0
\(493\) −6.65198 −0.299590
\(494\) −40.3615 + 2.96655i −1.81595 + 0.133471i
\(495\) 0 0
\(496\) −87.7441 23.5110i −3.93983 1.05567i
\(497\) 4.14733 11.0752i 0.186033 0.496791i
\(498\) 0 0
\(499\) −11.2290 11.2290i −0.502679 0.502679i 0.409590 0.912270i \(-0.365672\pi\)
−0.912270 + 0.409590i \(0.865672\pi\)
\(500\) −15.7420 58.7500i −0.704004 2.62738i
\(501\) 0 0
\(502\) 48.5880 + 48.5880i 2.16859 + 2.16859i
\(503\) −13.8096 7.97299i −0.615741 0.355498i 0.159468 0.987203i \(-0.449022\pi\)
−0.775209 + 0.631705i \(0.782355\pi\)
\(504\) 0 0
\(505\) 1.52058 + 0.407439i 0.0676651 + 0.0181308i
\(506\) 52.5548i 2.33635i
\(507\) 0 0
\(508\) 9.37043 0.415745
\(509\) 21.2058 + 5.68207i 0.939930 + 0.251853i 0.696084 0.717961i \(-0.254924\pi\)
0.243846 + 0.969814i \(0.421591\pi\)
\(510\) 0 0
\(511\) 3.45227 0.575892i 0.152719 0.0254759i
\(512\) 16.7938 + 16.7938i 0.742187 + 0.742187i
\(513\) 0 0
\(514\) −58.6887 + 15.7256i −2.58865 + 0.693626i
\(515\) −9.48019 + 9.48019i −0.417747 + 0.417747i
\(516\) 0 0
\(517\) −9.41849 16.3133i −0.414225 0.717458i
\(518\) −1.72388 3.78785i −0.0757429 0.166429i
\(519\) 0 0
\(520\) 3.57011 + 48.5733i 0.156560 + 2.13008i
\(521\) 27.9103i 1.22277i 0.791332 + 0.611387i \(0.209388\pi\)
−0.791332 + 0.611387i \(0.790612\pi\)
\(522\) 0 0
\(523\) 14.4506 8.34306i 0.631881 0.364817i −0.149599 0.988747i \(-0.547798\pi\)
0.781480 + 0.623930i \(0.214465\pi\)
\(524\) −12.5013 + 21.6529i −0.546122 + 0.945911i
\(525\) 0 0
\(526\) −56.0118 + 15.0083i −2.44223 + 0.654393i
\(527\) −12.9814 48.4472i −0.565478 2.11039i
\(528\) 0 0
\(529\) −2.49141 + 4.31525i −0.108322 + 0.187620i
\(530\) 0.882111 + 1.52786i 0.0383164 + 0.0663660i
\(531\) 0 0
\(532\) −35.9217 43.6221i −1.55740 1.89126i
\(533\) 4.56382 + 0.870294i 0.197681 + 0.0376966i
\(534\) 0 0
\(535\) 27.4279 + 7.34928i 1.18581 + 0.317737i
\(536\) 43.3632 + 75.1072i 1.87300 + 3.24414i
\(537\) 0 0
\(538\) 11.0415 11.0415i 0.476032 0.476032i
\(539\) −2.24297 32.5559i −0.0966117 1.40228i
\(540\) 0 0
\(541\) −14.9557 + 14.9557i −0.642996 + 0.642996i −0.951291 0.308295i \(-0.900242\pi\)
0.308295 + 0.951291i \(0.400242\pi\)
\(542\) −15.9991 9.23708i −0.687220 0.396767i
\(543\) 0 0
\(544\) 23.1074 86.2380i 0.990722 3.69743i
\(545\) 3.69285 0.158184
\(546\) 0 0
\(547\) 39.1844 1.67540 0.837702 0.546127i \(-0.183898\pi\)
0.837702 + 0.546127i \(0.183898\pi\)
\(548\) −9.22600 + 34.4319i −0.394115 + 1.47086i
\(549\) 0 0
\(550\) −23.8682 13.7803i −1.01775 0.587595i
\(551\) 3.14912 3.14912i 0.134157 0.134157i
\(552\) 0 0
\(553\) 1.42678 1.99811i 0.0606729 0.0849681i
\(554\) −23.2273 + 23.2273i −0.986833 + 0.986833i
\(555\) 0 0
\(556\) −30.3597 52.5845i −1.28754 2.23008i
\(557\) 1.74793 + 0.468357i 0.0740623 + 0.0198449i 0.295660 0.955293i \(-0.404460\pi\)
−0.221598 + 0.975138i \(0.571127\pi\)
\(558\) 0 0
\(559\) 34.7852 + 16.8131i 1.47126 + 0.711117i
\(560\) −38.8906 + 32.0255i −1.64343 + 1.35332i
\(561\) 0 0
\(562\) 29.3944 + 50.9126i 1.23993 + 2.14762i
\(563\) 3.27798 5.67763i 0.138150 0.239284i −0.788646 0.614847i \(-0.789218\pi\)
0.926797 + 0.375564i \(0.122551\pi\)
\(564\) 0 0
\(565\) −2.60829 9.73429i −0.109732 0.409524i
\(566\) −73.6673 + 19.7391i −3.09647 + 0.829696i
\(567\) 0 0
\(568\) −18.1263 + 31.3957i −0.760563 + 1.31733i
\(569\) 7.73692 4.46691i 0.324349 0.187263i −0.328981 0.944337i \(-0.606705\pi\)
0.653329 + 0.757074i \(0.273372\pi\)
\(570\) 0 0
\(571\) 21.0842i 0.882348i 0.897422 + 0.441174i \(0.145438\pi\)
−0.897422 + 0.441174i \(0.854562\pi\)
\(572\) 64.3073 + 55.5014i 2.68882 + 2.32063i
\(573\) 0 0
\(574\) 3.75068 + 8.24131i 0.156550 + 0.343986i
\(575\) −4.72426 8.18267i −0.197015 0.341241i
\(576\) 0 0
\(577\) −4.76619 + 4.76619i −0.198419 + 0.198419i −0.799322 0.600903i \(-0.794808\pi\)
0.600903 + 0.799322i \(0.294808\pi\)
\(578\) 58.6133 15.7054i 2.43799 0.653257i
\(579\) 0 0
\(580\) −6.27193 6.27193i −0.260428 0.260428i
\(581\) −4.79831 28.7642i −0.199067 1.19334i
\(582\) 0 0
\(583\) 1.79594 + 0.481220i 0.0743802 + 0.0199301i
\(584\) −10.7289 −0.443966
\(585\) 0 0
\(586\) 61.3791i 2.53555i
\(587\) −13.3468 3.57628i −0.550883 0.147609i −0.0273686 0.999625i \(-0.508713\pi\)
−0.523515 + 0.852017i \(0.675379\pi\)
\(588\) 0 0
\(589\) 29.0810 + 16.7899i 1.19826 + 0.691816i
\(590\) 26.7555 + 26.7555i 1.10151 + 1.10151i
\(591\) 0 0
\(592\) 1.75250 + 6.54042i 0.0720273 + 0.268809i
\(593\) 17.2336 + 17.2336i 0.707698 + 0.707698i 0.966051 0.258353i \(-0.0831796\pi\)
−0.258353 + 0.966051i \(0.583180\pi\)
\(594\) 0 0
\(595\) −26.0501 9.75497i −1.06795 0.399915i
\(596\) −24.0927 6.45563i −0.986877 0.264433i
\(597\) 0 0
\(598\) 13.3698 + 38.3849i 0.546730 + 1.56967i
\(599\) −35.8803 −1.46603 −0.733015 0.680212i \(-0.761888\pi\)
−0.733015 + 0.680212i \(0.761888\pi\)
\(600\) 0 0
\(601\) 1.74937 1.01000i 0.0713582 0.0411987i −0.463896 0.885889i \(-0.653549\pi\)
0.535255 + 0.844691i \(0.320216\pi\)
\(602\) 12.3893 + 74.2696i 0.504951 + 3.02700i
\(603\) 0 0
\(604\) 95.1900 25.5061i 3.87323 1.03783i
\(605\) 17.2670 4.62669i 0.702005 0.188102i
\(606\) 0 0
\(607\) −26.9378 15.5526i −1.09337 0.631259i −0.158901 0.987295i \(-0.550795\pi\)
−0.934473 + 0.356035i \(0.884128\pi\)
\(608\) 29.8868 + 51.7654i 1.21207 + 2.09936i
\(609\) 0 0
\(610\) 21.6048i 0.874751i
\(611\) 11.0291 + 9.51885i 0.446190 + 0.385092i
\(612\) 0 0
\(613\) 2.49860 9.32490i 0.100917 0.376629i −0.896933 0.442167i \(-0.854210\pi\)
0.997850 + 0.0655381i \(0.0208764\pi\)
\(614\) 17.9768 10.3789i 0.725485 0.418859i
\(615\) 0 0
\(616\) −9.63893 + 99.5689i −0.388364 + 4.01175i
\(617\) 7.40462 1.98406i 0.298099 0.0798753i −0.106670 0.994294i \(-0.534019\pi\)
0.404768 + 0.914419i \(0.367352\pi\)
\(618\) 0 0
\(619\) −23.5040 23.5040i −0.944707 0.944707i 0.0538424 0.998549i \(-0.482853\pi\)
−0.998549 + 0.0538424i \(0.982853\pi\)
\(620\) 33.4395 57.9190i 1.34296 2.32608i
\(621\) 0 0
\(622\) −7.09446 + 26.4769i −0.284462 + 1.06163i
\(623\) −8.33692 10.1241i −0.334012 0.405612i
\(624\) 0 0
\(625\) 8.91513 0.356605
\(626\) −53.7104 14.3916i −2.14670 0.575206i
\(627\) 0 0
\(628\) −50.4920 + 87.4548i −2.01485 + 3.48983i
\(629\) −2.64361 + 2.64361i −0.105408 + 0.105408i
\(630\) 0 0
\(631\) −6.11577 22.8244i −0.243465 0.908623i −0.974149 0.225907i \(-0.927465\pi\)
0.730684 0.682716i \(-0.239201\pi\)
\(632\) −5.32192 + 5.32192i −0.211695 + 0.211695i
\(633\) 0 0
\(634\) 27.5057 15.8804i 1.09239 0.630693i
\(635\) −0.799278 + 2.98295i −0.0317184 + 0.118375i
\(636\) 0 0
\(637\) 9.92032 + 23.2075i 0.393058 + 0.919514i
\(638\) −13.0472 −0.516544
\(639\) 0 0
\(640\) 15.5039 8.95116i 0.612844 0.353826i
\(641\) 1.08956 + 0.629057i 0.0430350 + 0.0248463i 0.521363 0.853335i \(-0.325424\pi\)
−0.478328 + 0.878181i \(0.658757\pi\)
\(642\) 0 0
\(643\) −8.43652 31.4855i −0.332704 1.24167i −0.906337 0.422556i \(-0.861133\pi\)
0.573633 0.819113i \(-0.305534\pi\)
\(644\) −32.9815 + 46.1883i −1.29965 + 1.82007i
\(645\) 0 0
\(646\) −35.4272 + 61.3617i −1.39386 + 2.41424i
\(647\) 4.65030 + 8.05456i 0.182822 + 0.316657i 0.942841 0.333244i \(-0.108143\pi\)
−0.760018 + 0.649902i \(0.774810\pi\)
\(648\) 0 0
\(649\) 39.8771 1.56531
\(650\) 20.9385 + 3.99285i 0.821276 + 0.156613i
\(651\) 0 0
\(652\) −7.40908 + 27.6510i −0.290162 + 1.08290i
\(653\) 13.4181 + 23.2408i 0.525090 + 0.909482i 0.999573 + 0.0292175i \(0.00930153\pi\)
−0.474483 + 0.880264i \(0.657365\pi\)
\(654\) 0 0
\(655\) −5.82657 5.82657i −0.227663 0.227663i
\(656\) −3.81295 14.2301i −0.148871 0.555593i
\(657\) 0 0
\(658\) −2.73584 + 28.2608i −0.106654 + 1.10172i
\(659\) 7.95731 13.7825i 0.309973 0.536889i −0.668383 0.743817i \(-0.733013\pi\)
0.978356 + 0.206928i \(0.0663467\pi\)
\(660\) 0 0
\(661\) 0.555848 2.07445i 0.0216200 0.0806868i −0.954273 0.298937i \(-0.903368\pi\)
0.975893 + 0.218250i \(0.0700348\pi\)
\(662\) 68.8907i 2.67751i
\(663\) 0 0
\(664\) 89.3931i 3.46913i
\(665\) 16.9506 7.71432i 0.657314 0.299148i
\(666\) 0 0
\(667\) −3.87367 2.23647i −0.149989 0.0865963i
\(668\) 15.2193 15.2193i 0.588852 0.588852i
\(669\) 0 0
\(670\) −45.6897 + 12.2425i −1.76515 + 0.472970i
\(671\) 16.1001 + 16.1001i 0.621538 + 0.621538i
\(672\) 0 0
\(673\) −33.3114 + 19.2323i −1.28406 + 0.741352i −0.977588 0.210528i \(-0.932482\pi\)
−0.306472 + 0.951880i \(0.599148\pi\)
\(674\) 67.0376 + 17.9627i 2.58219 + 0.691896i
\(675\) 0 0
\(676\) −61.0881 24.1775i −2.34954 0.929903i
\(677\) 18.0903i 0.695268i −0.937630 0.347634i \(-0.886985\pi\)
0.937630 0.347634i \(-0.113015\pi\)
\(678\) 0 0
\(679\) 15.8566 + 5.93781i 0.608521 + 0.227872i
\(680\) 73.8462 + 42.6351i 2.83187 + 1.63498i
\(681\) 0 0
\(682\) −25.4617 95.0245i −0.974980 3.63868i
\(683\) 9.14504 + 34.1297i 0.349925 + 1.30594i 0.886752 + 0.462246i \(0.152956\pi\)
−0.536827 + 0.843693i \(0.680377\pi\)
\(684\) 0 0
\(685\) −10.1740 5.87394i −0.388727 0.224432i
\(686\) −25.7650 + 41.8998i −0.983712 + 1.59974i
\(687\) 0 0
\(688\) 122.508i 4.67057i
\(689\) −1.43414 + 0.105408i −0.0546362 + 0.00401573i
\(690\) 0 0
\(691\) −18.6167 4.98833i −0.708213 0.189765i −0.113306 0.993560i \(-0.536144\pi\)
−0.594906 + 0.803795i \(0.702811\pi\)
\(692\) 7.64980 4.41661i 0.290802 0.167894i
\(693\) 0 0
\(694\) −14.0489 14.0489i −0.533289 0.533289i
\(695\) 19.3292 5.17924i 0.733197 0.196460i
\(696\) 0 0
\(697\) 5.75175 5.75175i 0.217863 0.217863i
\(698\) 4.69809 + 2.71244i 0.177825 + 0.102668i
\(699\) 0 0
\(700\) 12.3288 + 27.0899i 0.465984 + 1.02390i
\(701\) 30.2993i 1.14439i 0.820118 + 0.572194i \(0.193908\pi\)
−0.820118 + 0.572194i \(0.806092\pi\)
\(702\) 0 0
\(703\) 2.50303i 0.0944035i
\(704\) 17.7339 66.1839i 0.668373 2.49440i
\(705\) 0 0
\(706\) −16.6590 + 28.8542i −0.626969 + 1.08594i
\(707\) −2.48906 0.240957i −0.0936106 0.00906214i
\(708\) 0 0
\(709\) −4.09223 15.2724i −0.153687 0.573567i −0.999214 0.0396350i \(-0.987380\pi\)
0.845527 0.533932i \(-0.179286\pi\)
\(710\) −13.9813 13.9813i −0.524710 0.524710i
\(711\) 0 0
\(712\) 20.1015 + 34.8167i 0.753334 + 1.30481i
\(713\) 8.72896 32.5769i 0.326902 1.22002i
\(714\) 0 0
\(715\) −23.1534 + 15.7372i −0.865888 + 0.588538i
\(716\) −115.298 −4.30888
\(717\) 0 0
\(718\) 13.0141 + 22.5410i 0.485680 + 0.841223i
\(719\) −4.93530 + 8.54819i −0.184056 + 0.318794i −0.943258 0.332061i \(-0.892256\pi\)
0.759202 + 0.650855i \(0.225589\pi\)
\(720\) 0 0
\(721\) 12.3763 17.3322i 0.460919 0.645484i
\(722\) 0.782788 + 2.92140i 0.0291324 + 0.108723i
\(723\) 0 0
\(724\) −60.1465 34.7256i −2.23533 1.29057i
\(725\) −2.03142 + 1.17284i −0.0754452 + 0.0435583i
\(726\) 0 0
\(727\) 24.0371 0.891486 0.445743 0.895161i \(-0.352939\pi\)
0.445743 + 0.895161i \(0.352939\pi\)
\(728\) −18.2899 75.1751i −0.677870 2.78617i
\(729\) 0 0
\(730\) 1.51452 5.65228i 0.0560551 0.209200i
\(731\) 58.5794 33.8208i 2.16664 1.25091i
\(732\) 0 0
\(733\) −12.9796 + 12.9796i −0.479413 + 0.479413i −0.904944 0.425531i \(-0.860087\pi\)
0.425531 + 0.904944i \(0.360087\pi\)
\(734\) 17.2964 + 64.5510i 0.638422 + 2.38262i
\(735\) 0 0
\(736\) 42.4504 42.4504i 1.56474 1.56474i
\(737\) −24.9252 + 43.1718i −0.918133 + 1.59025i
\(738\) 0 0
\(739\) −27.1236 7.26773i −0.997756 0.267348i −0.277251 0.960798i \(-0.589423\pi\)
−0.720505 + 0.693450i \(0.756090\pi\)
\(740\) −4.98514 −0.183258
\(741\) 0 0
\(742\) −1.78151 2.16340i −0.0654011 0.0794209i
\(743\) 5.26385 19.6449i 0.193112 0.720703i −0.799636 0.600485i \(-0.794974\pi\)
0.992748 0.120218i \(-0.0383592\pi\)
\(744\) 0 0
\(745\) 4.11012 7.11894i 0.150583 0.260818i
\(746\) 21.8542 + 21.8542i 0.800138 + 0.800138i
\(747\) 0 0
\(748\) 143.654 38.4919i 5.25250 1.40740i
\(749\) −44.8970 4.34633i −1.64050 0.158811i
\(750\) 0 0
\(751\) −29.4512 + 17.0036i −1.07469 + 0.620472i −0.929459 0.368926i \(-0.879725\pi\)
−0.145230 + 0.989398i \(0.546392\pi\)
\(752\) 11.9564 44.6218i 0.436004 1.62719i
\(753\) 0 0
\(754\) 9.52941 3.31917i 0.347040 0.120877i
\(755\) 32.4781i 1.18200i
\(756\) 0 0
\(757\) −12.1464 21.0382i −0.441469 0.764646i 0.556330 0.830961i \(-0.312209\pi\)
−0.997799 + 0.0663153i \(0.978876\pi\)
\(758\) −59.5530 34.3830i −2.16306 1.24885i
\(759\) 0 0
\(760\) −55.1436 + 14.7757i −2.00027 + 0.535971i
\(761\) 16.6934 4.47299i 0.605136 0.162146i 0.0567745 0.998387i \(-0.481918\pi\)
0.548362 + 0.836241i \(0.315252\pi\)
\(762\) 0 0
\(763\) −5.78624 + 0.965233i −0.209476 + 0.0349438i
\(764\) 52.7463 30.4531i 1.90829 1.10175i
\(765\) 0 0
\(766\) 26.9118 0.972364
\(767\) −29.1254 + 10.1446i −1.05166 + 0.366301i
\(768\) 0 0
\(769\) 10.4169 + 2.79121i 0.375644 + 0.100654i 0.441701 0.897162i \(-0.354375\pi\)
−0.0660568 + 0.997816i \(0.521042\pi\)
\(770\) −51.0949 19.1335i −1.84133 0.689522i
\(771\) 0 0
\(772\) 16.3586 + 16.3586i 0.588759 + 0.588759i
\(773\) −10.6384 39.7032i −0.382638 1.42802i −0.841857 0.539701i \(-0.818537\pi\)
0.459219 0.888323i \(-0.348129\pi\)
\(774\) 0 0
\(775\) −12.5063 12.5063i −0.449239 0.449239i
\(776\) −44.9499 25.9518i −1.61361 0.931616i
\(777\) 0 0
\(778\) 65.1727 + 17.4630i 2.33655 + 0.626078i
\(779\) 5.44589i 0.195119i
\(780\) 0 0
\(781\) −20.8381 −0.745646
\(782\) 68.7382 + 18.4184i 2.45807 + 0.658639i
\(783\) 0 0
\(784\) 52.5659 60.3450i 1.87735 2.15518i
\(785\) −23.5332 23.5332i −0.839935 0.839935i
\(786\) 0 0
\(787\) −26.7623 + 7.17094i −0.953973 + 0.255616i −0.702047 0.712130i \(-0.747731\pi\)
−0.251926 + 0.967747i \(0.581064\pi\)
\(788\) 69.8314 69.8314i 2.48764 2.48764i