Properties

Label 819.2.fm.e.370.1
Level $819$
Weight $2$
Character 819.370
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 370.1
Character \(\chi\) \(=\) 819.370
Dual form 819.2.fm.e.622.1

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\)

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 −0.575235 0.817988i \(-0.695089\pi\)
0.0891737 0.996016i \(-0.471577\pi\)
\(3\) 0 0
\(4\) −4.37666 + 2.52687i −2.18833 + 1.26343i
\(5\) 1.17771 + 1.17771i 0.526690 + 0.526690i 0.919584 0.392894i \(-0.128526\pi\)
−0.392894 + 0.919584i \(0.628526\pi\)
\(6\) 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 0.494734 0.869044i \(-0.335265\pi\)
0.862975 + 0.505247i \(0.168599\pi\)
\(12\) 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 −0.939980 0.341230i \(-0.889157\pi\)
0.174476 0.984661i \(-0.444177\pi\)
\(18\) 0 0
\(19\) −1.09384 + 4.08225i −0.250943 + 0.936532i 0.719360 + 0.694638i \(0.244435\pi\)
−0.970303 + 0.241894i \(0.922231\pi\)
\(20\) −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 0.0651270 0.997877i \(-0.479255\pi\)
−0.831623 + 0.555340i \(0.812588\pi\)
\(24\) 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 −0.812950 0.582334i \(-0.802140\pi\)
0.910791 + 0.412868i \(0.135473\pi\)
\(30\) 0 0
\(31\) −5.61834 5.61834i −1.00908 1.00908i −0.999958 0.00912491i \(-0.997095\pi\)
−0.00912491 0.999958i \(-0.502905\pi\)
\(32\) −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 −0.211488 0.977381i \(-0.567831\pi\)
0.305537 + 0.952180i \(0.401164\pi\)
\(38\) 11.2245 1.82085
\(39\) 0 0
\(40\) 13.5081i 2.13583i
\(41\) −1.24468 + 0.333510i −0.194386 + 0.0520856i −0.354698 0.934981i \(-0.615416\pi\)
0.160312 + 0.987066i \(0.448750\pi\)
\(42\) 0 0
\(43\) −9.27990 + 5.35775i −1.41517 + 0.817050i −0.995869 0.0907973i \(-0.971058\pi\)
−0.419302 + 0.907847i \(0.637725\pi\)
\(44\) −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 −0.884086 0.467324i \(-0.845218\pi\)
0.467324 + 0.884086i \(0.345218\pi\)
\(48\) 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 0.752824 0.658222i \(-0.228691\pi\)
0.322854 + 0.946449i \(0.395358\pi\)
\(60\) 0 0
\(61\) 4.22976 2.44205i 0.541565 0.312673i −0.204148 0.978940i \(-0.565442\pi\)
0.745713 + 0.666267i \(0.232109\pi\)
\(62\) −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 −0.900449 0.434962i \(-0.856762\pi\)
0.562330 0.826913i \(-0.309905\pi\)
\(68\) 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 −0.00665372 0.999978i \(-0.502118\pi\)
−0.505751 + 0.862679i \(0.668785\pi\)
\(72\) 0 0
\(73\) −0.935407 + 0.935407i −0.109481 + 0.109481i −0.759725 0.650244i \(-0.774667\pi\)
0.650244 + 0.759725i \(0.274667\pi\)
\(74\) −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 0.135323 0.990802i \(-0.456793\pi\)
−0.990802 + 0.135323i \(0.956793\pi\)
\(84\) 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 −0.999992 0.00403982i \(-0.998714\pi\)
0.863998 0.503495i \(-0.167953\pi\)
\(90\) 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 0.829436 + 0.558601i \(0.188662\pi\)
−0.997614 + 0.0690447i \(0.978005\pi\)
\(98\) 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 −0.841555 0.540171i \(-0.818360\pi\)
0.888579 + 0.458723i \(0.151693\pi\)
\(102\) 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 −0.0785320 0.996912i \(-0.525023\pi\)
0.902617 0.430445i \(-0.141643\pi\)
\(108\) 0 0
\(109\) 1.56781 1.56781i 0.150169 0.150169i −0.628025 0.778193i \(-0.716136\pi\)
0.778193 + 0.628025i \(0.216136\pi\)
\(110\) 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 0.972512 0.232852i \(-0.0748056\pi\)
−0.687911 + 0.725795i \(0.741472\pi\)
\(114\) 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 0.427062 0.904222i \(-0.359549\pi\)
−0.569549 + 0.821958i \(0.692882\pi\)
\(128\) 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 \(0.0693422\pi\)
−0.976365 + 0.216126i \(0.930658\pi\)
\(132\) 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 0.843050 + 0.537834i \(0.180757\pi\)
−0.999020 + 0.0442531i \(0.985909\pi\)
\(138\) 0 0
\(139\) 10.4051 6.00737i 0.882547 0.509539i 0.0110494 0.999939i \(-0.496483\pi\)
0.871497 + 0.490400i \(0.163149\pi\)
\(140\) 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 0.448752 0.893657i \(-0.351869\pi\)
−0.0581981 + 0.998305i \(0.518535\pi\)
\(150\) 0 0
\(151\) −13.7886 13.7886i −1.12210 1.12210i −0.991425 0.130675i \(-0.958286\pi\)
−0.130675 0.991425i \(-0.541714\pi\)
\(152\) −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 \(0.293777\pi\)
−0.603489 + 0.797371i \(0.706223\pi\)
\(158\) 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 −0.999274 0.0380934i \(-0.987872\pi\)
0.884444 + 0.466647i \(0.154538\pi\)
\(164\) 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 0.910073 0.414448i \(-0.136025\pi\)
−0.995370 + 0.0961143i \(0.969359\pi\)
\(168\) 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 0.830890 0.556437i \(-0.187832\pi\)
−0.897333 + 0.441353i \(0.854499\pi\)
\(174\) 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 0.999656 0.0262285i \(-0.00834976\pi\)
0.477113 + 0.878842i \(0.341683\pi\)
\(180\) 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 0.561362 0.827570i \(-0.310277\pi\)
−0.997378 + 0.0723688i \(0.976944\pi\)
\(192\) 0 0
\(193\) −4.42174 + 1.18480i −0.318284 + 0.0852838i −0.414424 0.910084i \(-0.636017\pi\)
0.0961404 + 0.995368i \(0.469350\pi\)
\(194\) 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 −0.873625 0.486599i \(-0.838237\pi\)
0.513282 0.858220i \(-0.328430\pi\)
\(198\) 0 0
\(199\) −12.2497 21.2170i −0.868355 1.50403i −0.863677 0.504046i \(-0.831844\pi\)
−0.00467796 0.999989i \(-0.501489\pi\)
\(200\) 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 0.142544 + 0.989788i \(0.454472\pi\)
−0.928454 + 0.371448i \(0.878862\pi\)
\(212\) −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 −0.644294 0.764778i \(-0.722849\pi\)
−0.175586 + 0.984464i \(0.556182\pi\)
\(224\) 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 −0.792499 0.609874i \(-0.791220\pi\)
0.991261 0.131917i \(-0.0421131\pi\)
\(228\) 0 0
\(229\) 9.10742 9.10742i 0.601835 0.601835i −0.338964 0.940799i \(-0.610077\pi\)
0.940799 + 0.338964i \(0.110077\pi\)
\(230\) −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 \(0.0156079\pi\)
−0.998798 + 0.0490139i \(0.984392\pi\)
\(234\) 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 −0.596252 0.802798i \(-0.703344\pi\)
0.802798 + 0.596252i \(0.203344\pi\)
\(240\) 0 0
\(241\) 9.27435 + 2.48506i 0.597414 + 0.160076i 0.544839 0.838541i \(-0.316591\pi\)
0.0525744 + 0.998617i \(0.483257\pi\)
\(242\) −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 0.908230 + 0.418472i \(0.137434\pi\)
−0.0917077 + 0.995786i \(0.529233\pi\)
\(252\) 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 −0.250011 0.968243i \(-0.580434\pi\)
0.963528 0.267606i \(-0.0862326\pi\)
\(258\) 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 −0.303844 0.952722i \(-0.598270\pi\)
0.977003 0.213225i \(-0.0683966\pi\)
\(264\) 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 −0.647127 0.762383i \(-0.724029\pi\)
0.336679 + 0.941619i \(0.390696\pi\)
\(270\) 0 0
\(271\) −1.80033 6.71891i −0.109362 0.408145i 0.889441 0.457049i \(-0.151094\pi\)
−0.998803 + 0.0489044i \(0.984427\pi\)
\(272\) −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 −0.142420 0.989806i \(-0.545488\pi\)
0.785988 + 0.618242i \(0.212155\pi\)
\(278\) −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 0.997936 0.0642154i \(-0.0204545\pi\)
−0.0642154 + 0.997936i \(0.520454\pi\)
\(282\) 0 0
\(283\) 14.3579 24.8687i 0.853490 1.47829i −0.0245489 0.999699i \(-0.507815\pi\)
0.878039 0.478589i \(-0.158852\pi\)
\(284\) 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 0.843011 0.537897i \(-0.180781\pi\)
0.461120 + 0.887338i \(0.347448\pi\)
\(294\) 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 −0.847005 0.531585i \(-0.821596\pi\)
0.531585 + 0.847005i \(0.321596\pi\)
\(308\) 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 \(-0.798457\pi\)
0.806157 0.591701i \(-0.201543\pi\)
\(314\) 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 −0.903509 0.428569i \(-0.859018\pi\)
0.428569 + 0.903509i \(0.359018\pi\)
\(318\) 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 0.870084 0.492903i \(-0.164064\pi\)
0.507064 + 0.861909i \(0.330731\pi\)
\(332\) 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 \(0.252092\pi\)
−0.702445 + 0.711738i \(0.747908\pi\)
\(338\) −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 0.747990 0.663710i \(-0.231019\pi\)
−0.948785 + 0.315923i \(0.897686\pi\)
\(348\) 0 0
\(349\) 0.528661 + 1.97299i 0.0282986 + 0.105612i 0.978631 0.205626i \(-0.0659231\pi\)
−0.950332 + 0.311238i \(0.899256\pi\)
\(350\) 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 0.0785047 0.996914i \(-0.474985\pi\)
0.566444 + 0.824100i \(0.308319\pi\)
\(354\) 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 0.865920 0.500182i \(-0.166733\pi\)
−0.500182 + 0.865920i \(0.666733\pi\)
\(360\) 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 0.945808 0.324727i \(-0.105272\pi\)
0.191682 + 0.981457i \(0.438606\pi\)
\(368\) −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 0.976424 0.215862i \(-0.0692562\pi\)
−0.675154 + 0.737677i \(0.735923\pi\)
\(374\) −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 −0.893517 0.449029i \(-0.851770\pi\)
0.549294 0.835629i \(-0.314897\pi\)
\(380\) 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 0.865992 + 0.500058i \(0.166688\pi\)
−1.00000 6.67944e-5i \(0.999979\pi\)
\(384\) 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 \(0.222740\pi\)
−0.764999 + 0.644032i \(0.777260\pi\)
\(390\) 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 −0.389140 0.921179i \(-0.627228\pi\)
−0.797594 + 0.603194i \(0.793894\pi\)
\(398\) −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 −0.701111 0.713052i \(-0.747312\pi\)
−0.250654 + 0.968077i \(0.580646\pi\)
\(402\) 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 −0.583622 0.812025i \(-0.698365\pi\)
0.911444 0.411423i \(-0.134968\pi\)
\(410\) −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 0.437945 0.899002i \(-0.355706\pi\)
−0.559586 + 0.828772i \(0.689040\pi\)
\(420\) 0 0
\(421\) −13.5970 + 13.5970i −0.662676 + 0.662676i −0.956010 0.293334i \(-0.905235\pi\)
0.293334 + 0.956010i \(0.405235\pi\)
\(422\) 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 −0.682089 0.731269i \(-0.738928\pi\)
0.225071 0.974342i \(-0.427738\pi\)
\(432\) 0 0
\(433\) −0.0741930 0.128506i −0.00356549 0.00617561i 0.864237 0.503085i \(-0.167802\pi\)
−0.867803 + 0.496909i \(0.834468\pi\)
\(434\) 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 −0.752805 0.658244i \(-0.771300\pi\)
0.946458 + 0.322826i \(0.104633\pi\)
\(440\) 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 −0.984770 0.173864i \(-0.944375\pi\)
0.939768 + 0.341814i \(0.111041\pi\)
\(450\) 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 0.999416 0.0341660i \(-0.0108775\pi\)
−0.882603 + 0.470119i \(0.844211\pi\)
\(458\) −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 −0.907158 0.420789i \(-0.861753\pi\)
0.996017 + 0.0891650i \(0.0284198\pi\)
\(462\) 0 0
\(463\) 10.2671 + 10.2671i 0.477153 + 0.477153i 0.904220 0.427067i \(-0.140453\pi\)
−0.427067 + 0.904220i \(0.640453\pi\)
\(464\) −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 −0.774316 0.632799i \(-0.781906\pi\)
0.354178 0.935178i \(-0.384761\pi\)
\(480\) 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 0.720433 0.693525i \(-0.243943\pi\)
0.277150 + 0.960827i \(0.410610\pi\)
\(488\) 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 0.180741 0.983531i \(-0.442150\pi\)
−0.761392 + 0.648292i \(0.775484\pi\)
\(492\) 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 −0.912270 0.409590i \(-0.865672\pi\)
0.409590 + 0.912270i \(0.365672\pi\)
\(500\) −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 −0.775209 0.631705i \(-0.782355\pi\)
0.159468 + 0.987203i \(0.449022\pi\)
\(504\) 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 0.243846 0.969814i \(-0.421591\pi\)
0.696084 + 0.717961i \(0.254924\pi\)
\(510\) 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 \(-0.790612\pi\)
0.791332 0.611387i \(-0.209388\pi\)
\(522\) 0 0
\(523\) 14.4506 + 8.34306i 0.631881 + 0.364817i 0.781480 0.623930i \(-0.214465\pi\)
−0.149599 + 0.988747i \(0.547798\pi\)
\(524\) −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 0.308295 0.951291i \(-0.400242\pi\)
−0.951291 + 0.308295i \(0.900242\pi\)
\(542\) −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 −0.221598 0.975138i \(-0.571127\pi\)
0.295660 + 0.955293i \(0.404460\pi\)
\(558\) 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 0.926797 0.375564i \(-0.122551\pi\)
−0.788646 + 0.614847i \(0.789218\pi\)
\(564\) 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 0.653329 0.757074i \(-0.273372\pi\)
−0.328981 + 0.944337i \(0.606705\pi\)
\(570\) 0 0
\(571\) 21.0842i 0.882348i −0.897422 0.441174i \(-0.854562\pi\)
0.897422 0.441174i \(-0.145438\pi\)
\(572\) 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 0.600903 0.799322i \(-0.294808\pi\)
−0.799322 + 0.600903i \(0.794808\pi\)
\(578\) 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 −0.523515 0.852017i \(-0.675379\pi\)
−0.0273686 + 0.999625i \(0.508713\pi\)
\(588\) 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 −0.258353 0.966051i \(-0.583180\pi\)
0.966051 + 0.258353i \(0.0831796\pi\)
\(594\) 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 0.535255 0.844691i \(-0.320216\pi\)
−0.463896 + 0.885889i \(0.653549\pi\)
\(602\) 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 −0.934473 0.356035i \(-0.884128\pi\)
−0.158901 + 0.987295i \(0.550795\pi\)
\(608\) 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 0.997850 0.0655381i \(-0.0208764\pi\)
−0.896933 + 0.442167i \(0.854210\pi\)
\(614\) 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 0.404768 0.914419i \(-0.367352\pi\)
−0.106670 + 0.994294i \(0.534019\pi\)
\(618\) 0 0
\(619\) −23.5040 + 23.5040i −0.944707 + 0.944707i −0.998549 0.0538424i \(-0.982853\pi\)
0.0538424 + 0.998549i \(0.482853\pi\)
\(620\) 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 0.730684 + 0.682716i \(0.239201\pi\)
−0.974149 + 0.225907i \(0.927465\pi\)
\(632\) −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 −0.478328 0.878181i \(-0.658757\pi\)
0.521363 + 0.853335i \(0.325424\pi\)
\(642\) 0 0
\(643\) −8.43652 + 31.4855i −0.332704 + 1.24167i 0.573633 + 0.819113i \(0.305534\pi\)
−0.906337 + 0.422556i \(0.861133\pi\)
\(644\) −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 −0.760018 0.649902i \(-0.774810\pi\)
0.942841 + 0.333244i \(0.108143\pi\)
\(648\) 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 −0.474483 0.880264i \(-0.657365\pi\)
0.999573 0.0292175i \(-0.00930153\pi\)
\(654\) 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 0.978356 0.206928i \(-0.0663467\pi\)
−0.668383 + 0.743817i \(0.733013\pi\)
\(660\) 0 0
\(661\) 0.555848 + 2.07445i 0.0216200 + 0.0806868i 0.975893 0.218250i \(-0.0700348\pi\)
−0.954273 + 0.298937i \(0.903368\pi\)
\(662\) 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 −0.306472 0.951880i \(-0.599148\pi\)
−0.977588 + 0.210528i \(0.932482\pi\)
\(674\) 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 \(0.113015\pi\)
−0.937630 + 0.347634i \(0.886985\pi\)
\(678\) 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 −0.536827 0.843693i \(-0.680377\pi\)
0.886752 0.462246i \(-0.152956\pi\)
\(684\) 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 −0.594906 0.803795i \(-0.702811\pi\)
−0.113306 + 0.993560i \(0.536144\pi\)
\(692\) 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 \(-0.806092\pi\)
0.820118 0.572194i \(-0.193908\pi\)
\(702\) 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 0.845527 + 0.533932i \(0.179286\pi\)
−0.999214 + 0.0396350i \(0.987380\pi\)
\(710\) −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 0.759202 0.650855i \(-0.225589\pi\)
−0.943258 + 0.332061i \(0.892256\pi\)
\(720\) 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 0.425531 0.904944i \(-0.360087\pi\)
−0.904944 + 0.425531i \(0.860087\pi\)
\(734\) 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 −0.720505 0.693450i \(-0.756090\pi\)
−0.277251 + 0.960798i \(0.589423\pi\)
\(740\) −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 0.992748 + 0.120218i \(0.0383592\pi\)
−0.799636 + 0.600485i \(0.794974\pi\)
\(744\) 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 −0.145230 0.989398i \(-0.546392\pi\)
−0.929459 + 0.368926i \(0.879725\pi\)
\(752\) 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 −0.997799 0.0663153i \(-0.978876\pi\)
0.556330 + 0.830961i \(0.312209\pi\)
\(758\) −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 0.548362 0.836241i \(-0.315252\pi\)
0.0567745 + 0.998387i \(0.481918\pi\)
\(762\) 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 −0.0660568 0.997816i \(-0.521042\pi\)
0.441701 + 0.897162i \(0.354375\pi\)
\(770\) −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 0.459219 + 0.888323i \(0.348129\pi\)
−0.841857 + 0.539701i \(0.818537\pi\)
\(774\) 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 −0.251926 0.967747i \(-0.581064\pi\)
−0.702047 + 0.712130i \(0.747731\pi\)
\(788\) 69.8314 + 69.8314i 2.48764 + 2.48764i