Properties

Label 804.2.y.b.49.1
Level 804
Weight 2
Character 804.49
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 49.1
Character \(\chi\) = 804.49
Dual form 804.2.y.b.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{3} +(-0.597458 - 4.15542i) q^{5} +(3.22256 + 0.307717i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{3} +(-0.597458 - 4.15542i) q^{5} +(3.22256 + 0.307717i) q^{7} +(0.415415 + 0.909632i) q^{9} +(2.67720 + 1.07179i) q^{11} +(3.73782 + 3.56401i) q^{13} +(-1.74397 + 3.81877i) q^{15} +(2.37683 - 6.86740i) q^{17} +(0.298813 - 0.0285332i) q^{19} +(-2.54463 - 2.00112i) q^{21} +(-0.141620 + 2.97297i) q^{23} +(-12.1131 + 3.55671i) q^{25} +(0.142315 - 0.989821i) q^{27} +(3.33398 - 5.77462i) q^{29} +(2.44794 - 2.33411i) q^{31} +(-1.67275 - 2.34905i) q^{33} +(-0.646653 - 13.5749i) q^{35} +(-0.336012 - 0.581990i) q^{37} +(-1.21761 - 5.01905i) q^{39} +(-10.3429 + 1.99343i) q^{41} +(-4.38396 - 5.05936i) q^{43} +(3.53171 - 2.26969i) q^{45} +(-5.85388 + 3.01789i) q^{47} +(3.41670 + 0.658515i) q^{49} +(-5.71231 + 4.49221i) q^{51} +(-3.08733 + 3.56297i) q^{53} +(2.85421 - 11.7652i) q^{55} +(-0.266804 - 0.137547i) q^{57} +(10.2488 + 3.00933i) q^{59} +(-0.658869 + 0.263772i) q^{61} +(1.05879 + 3.05917i) q^{63} +(12.5767 - 17.6616i) q^{65} +(6.48863 + 4.98975i) q^{67} +(1.72645 - 2.42446i) q^{69} +(-0.131683 - 0.380473i) q^{71} +(-1.44202 + 0.577298i) q^{73} +(12.1131 + 3.55671i) q^{75} +(8.29762 + 4.27772i) q^{77} +(1.94006 - 7.99702i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(8.00214 - 6.29295i) q^{83} +(-29.9570 - 5.77373i) q^{85} +(-5.92671 + 3.05543i) q^{87} +(-5.98146 + 3.84405i) q^{89} +(10.9487 + 12.6354i) q^{91} +(-3.32126 + 0.640120i) q^{93} +(-0.297095 - 1.22464i) q^{95} +(7.50149 + 12.9930i) q^{97} +(0.137215 + 2.88050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{33}\right)\) \(1\)

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 0
\(3\) −0.841254 0.540641i −0.485698 0.312139i
\(4\) 0 0
\(5\) −0.597458 4.15542i −0.267192 1.85836i −0.474730 0.880131i \(-0.657454\pi\)
0.207539 0.978227i \(-0.433455\pi\)
\(6\) 0 0
\(7\) 3.22256 + 0.307717i 1.21801 + 0.116306i 0.684199 0.729296i \(-0.260152\pi\)
0.533814 + 0.845602i \(0.320758\pi\)
\(8\) 0 0
\(9\) 0.415415 + 0.909632i 0.138472 + 0.303211i
\(10\) 0 0
\(11\) 2.67720 + 1.07179i 0.807206 + 0.323156i 0.738305 0.674467i \(-0.235627\pi\)
0.0689008 + 0.997624i \(0.478051\pi\)
\(12\) 0 0
\(13\) 3.73782 + 3.56401i 1.03669 + 0.988478i 0.999941 0.0108467i \(-0.00345269\pi\)
0.0367447 + 0.999325i \(0.488301\pi\)
\(14\) 0 0
\(15\) −1.74397 + 3.81877i −0.450292 + 0.986002i
\(16\) 0 0
\(17\) 2.37683 6.86740i 0.576466 1.66559i −0.158398 0.987375i \(-0.550633\pi\)
0.734864 0.678214i \(-0.237246\pi\)
\(18\) 0 0
\(19\) 0.298813 0.0285332i 0.0685524 0.00654596i −0.0607235 0.998155i \(-0.519341\pi\)
0.129276 + 0.991609i \(0.458735\pi\)
\(20\) 0 0
\(21\) −2.54463 2.00112i −0.555283 0.436679i
\(22\) 0 0
\(23\) −0.141620 + 2.97297i −0.0295298 + 0.619908i 0.934795 + 0.355187i \(0.115583\pi\)
−0.964325 + 0.264721i \(0.914720\pi\)
\(24\) 0 0
\(25\) −12.1131 + 3.55671i −2.42261 + 0.711343i
\(26\) 0 0
\(27\) 0.142315 0.989821i 0.0273885 0.190491i
\(28\) 0 0
\(29\) 3.33398 5.77462i 0.619104 1.07232i −0.370546 0.928814i \(-0.620829\pi\)
0.989650 0.143505i \(-0.0458374\pi\)
\(30\) 0 0
\(31\) 2.44794 2.33411i 0.439664 0.419219i −0.437643 0.899149i \(-0.644187\pi\)
0.877307 + 0.479930i \(0.159338\pi\)
\(32\) 0 0
\(33\) −1.67275 2.34905i −0.291188 0.408917i
\(34\) 0 0
\(35\) −0.646653 13.5749i −0.109304 2.29458i
\(36\) 0 0
\(37\) −0.336012 0.581990i −0.0552401 0.0956786i 0.837083 0.547076i \(-0.184259\pi\)
−0.892323 + 0.451397i \(0.850926\pi\)
\(38\) 0 0
\(39\) −1.21761 5.01905i −0.194974 0.803692i
\(40\) 0 0
\(41\) −10.3429 + 1.99343i −1.61529 + 0.311322i −0.915282 0.402814i \(-0.868032\pi\)
−0.700008 + 0.714135i \(0.746820\pi\)
\(42\) 0 0
\(43\) −4.38396 5.05936i −0.668547 0.771545i 0.315601 0.948892i \(-0.397794\pi\)
−0.984148 + 0.177347i \(0.943248\pi\)
\(44\) 0 0
\(45\) 3.53171 2.26969i 0.526476 0.338345i
\(46\) 0 0
\(47\) −5.85388 + 3.01789i −0.853876 + 0.440204i −0.828842 0.559483i \(-0.811000\pi\)
−0.0250343 + 0.999687i \(0.507969\pi\)
\(48\) 0 0
\(49\) 3.41670 + 0.658515i 0.488100 + 0.0940735i
\(50\) 0 0
\(51\) −5.71231 + 4.49221i −0.799884 + 0.629036i
\(52\) 0 0
\(53\) −3.08733 + 3.56297i −0.424078 + 0.489412i −0.927075 0.374876i \(-0.877685\pi\)
0.502997 + 0.864288i \(0.332231\pi\)
\(54\) 0 0
\(55\) 2.85421 11.7652i 0.384862 1.58642i
\(56\) 0 0
\(57\) −0.266804 0.137547i −0.0353390 0.0182185i
\(58\) 0 0
\(59\) 10.2488 + 3.00933i 1.33429 + 0.391781i 0.869627 0.493709i \(-0.164359\pi\)
0.464658 + 0.885490i \(0.346177\pi\)
\(60\) 0 0
\(61\) −0.658869 + 0.263772i −0.0843596 + 0.0337725i −0.413458 0.910523i \(-0.635679\pi\)
0.329099 + 0.944295i \(0.393255\pi\)
\(62\) 0 0
\(63\) 1.05879 + 3.05917i 0.133395 + 0.385420i
\(64\) 0 0
\(65\) 12.5767 17.6616i 1.55995 2.19065i
\(66\) 0 0
\(67\) 6.48863 + 4.98975i 0.792713 + 0.609596i
\(68\) 0 0
\(69\) 1.72645 2.42446i 0.207840 0.291871i
\(70\) 0 0
\(71\) −0.131683 0.380473i −0.0156279 0.0451538i 0.936917 0.349552i \(-0.113666\pi\)
−0.952545 + 0.304398i \(0.901545\pi\)
\(72\) 0 0
\(73\) −1.44202 + 0.577298i −0.168776 + 0.0675676i −0.454512 0.890741i \(-0.650186\pi\)
0.285736 + 0.958308i \(0.407762\pi\)
\(74\) 0 0
\(75\) 12.1131 + 3.55671i 1.39869 + 0.410694i
\(76\) 0 0
\(77\) 8.29762 + 4.27772i 0.945602 + 0.487492i
\(78\) 0 0
\(79\) 1.94006 7.99702i 0.218273 0.899736i −0.752279 0.658845i \(-0.771045\pi\)
0.970552 0.240891i \(-0.0774395\pi\)
\(80\) 0 0
\(81\) −0.654861 + 0.755750i −0.0727623 + 0.0839722i
\(82\) 0 0
\(83\) 8.00214 6.29295i 0.878349 0.690741i −0.0735047 0.997295i \(-0.523418\pi\)
0.951853 + 0.306554i \(0.0991760\pi\)
\(84\) 0 0
\(85\) −29.9570 5.77373i −3.24929 0.626249i
\(86\) 0 0
\(87\) −5.92671 + 3.05543i −0.635410 + 0.327577i
\(88\) 0 0
\(89\) −5.98146 + 3.84405i −0.634034 + 0.407469i −0.817801 0.575501i \(-0.804807\pi\)
0.183767 + 0.982970i \(0.441171\pi\)
\(90\) 0 0
\(91\) 10.9487 + 12.6354i 1.14773 + 1.32455i
\(92\) 0 0
\(93\) −3.32126 + 0.640120i −0.344398 + 0.0663773i
\(94\) 0 0
\(95\) −0.297095 1.22464i −0.0304814 0.125646i
\(96\) 0 0
\(97\) 7.50149 + 12.9930i 0.761660 + 1.31923i 0.941994 + 0.335629i \(0.108949\pi\)
−0.180334 + 0.983605i \(0.557718\pi\)
\(98\) 0 0
\(99\) 0.137215 + 2.88050i 0.0137907 + 0.289501i
\(100\) 0 0
\(101\) 6.10629 + 8.57509i 0.607599 + 0.853253i 0.997719 0.0675108i \(-0.0215057\pi\)
−0.390120 + 0.920764i \(0.627566\pi\)
\(102\) 0 0
\(103\) 1.18498 1.12988i 0.116760 0.111330i −0.629450 0.777041i \(-0.716720\pi\)
0.746210 + 0.665711i \(0.231871\pi\)
\(104\) 0 0
\(105\) −6.79516 + 11.7696i −0.663139 + 1.14859i
\(106\) 0 0
\(107\) −0.259425 + 1.80434i −0.0250796 + 0.174432i −0.998511 0.0545452i \(-0.982629\pi\)
0.973432 + 0.228977i \(0.0735382\pi\)
\(108\) 0 0
\(109\) −9.69108 + 2.84556i −0.928237 + 0.272555i −0.710698 0.703497i \(-0.751621\pi\)
−0.217539 + 0.976052i \(0.569803\pi\)
\(110\) 0 0
\(111\) −0.0319762 + 0.671263i −0.00303505 + 0.0637135i
\(112\) 0 0
\(113\) −14.1378 11.1181i −1.32998 1.04590i −0.994596 0.103822i \(-0.966893\pi\)
−0.335380 0.942083i \(-0.608865\pi\)
\(114\) 0 0
\(115\) 12.4386 1.18774i 1.15990 0.110757i
\(116\) 0 0
\(117\) −1.68919 + 4.88059i −0.156165 + 0.451210i
\(118\) 0 0
\(119\) 9.77270 21.3992i 0.895862 1.96166i
\(120\) 0 0
\(121\) −1.94241 1.85209i −0.176583 0.168372i
\(122\) 0 0
\(123\) 9.77873 + 3.91481i 0.881719 + 0.352987i
\(124\) 0 0
\(125\) 13.2968 + 29.1159i 1.18930 + 2.60421i
\(126\) 0 0
\(127\) −10.7891 1.03023i −0.957377 0.0914184i −0.395344 0.918533i \(-0.629375\pi\)
−0.562033 + 0.827115i \(0.689981\pi\)
\(128\) 0 0
\(129\) 0.952725 + 6.62635i 0.0838828 + 0.583417i
\(130\) 0 0
\(131\) 5.73349 + 3.68469i 0.500938 + 0.321933i 0.766591 0.642135i \(-0.221951\pi\)
−0.265653 + 0.964069i \(0.585588\pi\)
\(132\) 0 0
\(133\) 0.971723 0.0842590
\(134\) 0 0
\(135\) −4.19815 −0.361319
\(136\) 0 0
\(137\) 0.658190 + 0.422993i 0.0562329 + 0.0361387i 0.568455 0.822714i \(-0.307541\pi\)
−0.512222 + 0.858853i \(0.671178\pi\)
\(138\) 0 0
\(139\) −2.41814 16.8185i −0.205104 1.42653i −0.788848 0.614589i \(-0.789322\pi\)
0.583744 0.811938i \(-0.301587\pi\)
\(140\) 0 0
\(141\) 6.55619 + 0.626040i 0.552131 + 0.0527221i
\(142\) 0 0
\(143\) 6.18703 + 13.5477i 0.517386 + 1.13292i
\(144\) 0 0
\(145\) −25.9878 10.4040i −2.15817 0.864002i
\(146\) 0 0
\(147\) −2.51829 2.40118i −0.207705 0.198046i
\(148\) 0 0
\(149\) −5.84791 + 12.8051i −0.479079 + 1.04904i 0.503636 + 0.863916i \(0.331995\pi\)
−0.982716 + 0.185121i \(0.940732\pi\)
\(150\) 0 0
\(151\) −5.13443 + 14.8350i −0.417834 + 1.20725i 0.518174 + 0.855275i \(0.326612\pi\)
−0.936008 + 0.351978i \(0.885509\pi\)
\(152\) 0 0
\(153\) 7.23418 0.690780i 0.584849 0.0558463i
\(154\) 0 0
\(155\) −11.1617 8.77769i −0.896533 0.705041i
\(156\) 0 0
\(157\) −0.850546 + 17.8552i −0.0678810 + 1.42500i 0.666118 + 0.745846i \(0.267955\pi\)
−0.733999 + 0.679150i \(0.762348\pi\)
\(158\) 0 0
\(159\) 4.52352 1.32822i 0.358738 0.105335i
\(160\) 0 0
\(161\) −1.37121 + 9.53701i −0.108067 + 0.751621i
\(162\) 0 0
\(163\) −5.52152 + 9.56354i −0.432478 + 0.749075i −0.997086 0.0762848i \(-0.975694\pi\)
0.564608 + 0.825359i \(0.309028\pi\)
\(164\) 0 0
\(165\) −8.76187 + 8.35443i −0.682111 + 0.650392i
\(166\) 0 0
\(167\) −2.73971 3.84739i −0.212005 0.297720i 0.694856 0.719149i \(-0.255468\pi\)
−0.906861 + 0.421429i \(0.861529\pi\)
\(168\) 0 0
\(169\) 0.650610 + 13.6580i 0.0500470 + 1.05061i
\(170\) 0 0
\(171\) 0.150086 + 0.259957i 0.0114774 + 0.0198794i
\(172\) 0 0
\(173\) −3.40137 14.0206i −0.258601 1.06597i −0.941917 0.335846i \(-0.890978\pi\)
0.683315 0.730123i \(-0.260537\pi\)
\(174\) 0 0
\(175\) −40.1295 + 7.73433i −3.03350 + 0.584660i
\(176\) 0 0
\(177\) −6.99490 8.07255i −0.525769 0.606770i
\(178\) 0 0
\(179\) 11.2940 7.25819i 0.844150 0.542503i −0.0455948 0.998960i \(-0.514518\pi\)
0.889745 + 0.456458i \(0.150882\pi\)
\(180\) 0 0
\(181\) 19.7014 10.1568i 1.46440 0.754949i 0.472420 0.881373i \(-0.343380\pi\)
0.991976 + 0.126425i \(0.0403502\pi\)
\(182\) 0 0
\(183\) 0.696882 + 0.134313i 0.0515150 + 0.00992870i
\(184\) 0 0
\(185\) −2.21766 + 1.74398i −0.163045 + 0.128220i
\(186\) 0 0
\(187\) 13.7237 15.8379i 1.00357 1.15818i
\(188\) 0 0
\(189\) 0.763203 3.14597i 0.0555149 0.228835i
\(190\) 0 0
\(191\) −4.31102 2.22248i −0.311934 0.160813i 0.295150 0.955451i \(-0.404630\pi\)
−0.607084 + 0.794638i \(0.707661\pi\)
\(192\) 0 0
\(193\) 15.4476 + 4.53583i 1.11194 + 0.326496i 0.785587 0.618751i \(-0.212361\pi\)
0.326356 + 0.945247i \(0.394179\pi\)
\(194\) 0 0
\(195\) −20.1288 + 8.05835i −1.44145 + 0.577070i
\(196\) 0 0
\(197\) −4.95218 14.3084i −0.352828 1.01943i −0.972163 0.234304i \(-0.924719\pi\)
0.619335 0.785127i \(-0.287402\pi\)
\(198\) 0 0
\(199\) −2.83988 + 3.98806i −0.201314 + 0.282706i −0.902875 0.429904i \(-0.858547\pi\)
0.701561 + 0.712610i \(0.252487\pi\)
\(200\) 0 0
\(201\) −2.76092 7.70567i −0.194740 0.543516i
\(202\) 0 0
\(203\) 12.5209 17.5831i 0.878794 1.23409i
\(204\) 0 0
\(205\) 14.4630 + 41.7881i 1.01014 + 2.91860i
\(206\) 0 0
\(207\) −2.76314 + 1.10620i −0.192052 + 0.0768859i
\(208\) 0 0
\(209\) 0.830563 + 0.243875i 0.0574512 + 0.0168692i
\(210\) 0 0
\(211\) 21.6564 + 11.1646i 1.49089 + 0.768606i 0.995009 0.0997856i \(-0.0318157\pi\)
0.495879 + 0.868392i \(0.334846\pi\)
\(212\) 0 0
\(213\) −0.0949203 + 0.391267i −0.00650383 + 0.0268092i
\(214\) 0 0
\(215\) −18.4045 + 21.2399i −1.25518 + 1.44855i
\(216\) 0 0
\(217\) 8.60689 6.76854i 0.584274 0.459478i
\(218\) 0 0
\(219\) 1.52522 + 0.293961i 0.103065 + 0.0198641i
\(220\) 0 0
\(221\) 33.3596 17.1981i 2.24401 1.15687i
\(222\) 0 0
\(223\) 2.46772 1.58591i 0.165251 0.106200i −0.455401 0.890286i \(-0.650504\pi\)
0.620652 + 0.784086i \(0.286868\pi\)
\(224\) 0 0
\(225\) −8.26724 9.54091i −0.551150 0.636061i
\(226\) 0 0
\(227\) 22.1093 4.26121i 1.46744 0.282827i 0.607951 0.793974i \(-0.291992\pi\)
0.859493 + 0.511148i \(0.170780\pi\)
\(228\) 0 0
\(229\) −1.72808 7.12322i −0.114194 0.470716i −0.999978 0.00661749i \(-0.997894\pi\)
0.885784 0.464098i \(-0.153622\pi\)
\(230\) 0 0
\(231\) −4.66769 8.08468i −0.307112 0.531933i
\(232\) 0 0
\(233\) 0.282930 + 5.93943i 0.0185354 + 0.389105i 0.989005 + 0.147882i \(0.0472456\pi\)
−0.970470 + 0.241223i \(0.922451\pi\)
\(234\) 0 0
\(235\) 16.0380 + 22.5222i 1.04620 + 1.46919i
\(236\) 0 0
\(237\) −5.95560 + 5.67865i −0.386858 + 0.368868i
\(238\) 0 0
\(239\) −9.25594 + 16.0318i −0.598717 + 1.03701i 0.394294 + 0.918985i \(0.370989\pi\)
−0.993011 + 0.118024i \(0.962344\pi\)
\(240\) 0 0
\(241\) −1.87457 + 13.0379i −0.120751 + 0.839845i 0.835957 + 0.548796i \(0.184913\pi\)
−0.956708 + 0.291049i \(0.905996\pi\)
\(242\) 0 0
\(243\) 0.959493 0.281733i 0.0615515 0.0180732i
\(244\) 0 0
\(245\) 0.695066 14.5912i 0.0444062 0.932200i
\(246\) 0 0
\(247\) 1.21860 + 0.958320i 0.0775378 + 0.0609764i
\(248\) 0 0
\(249\) −10.1341 + 0.967685i −0.642219 + 0.0613245i
\(250\) 0 0
\(251\) −9.24635 + 26.7156i −0.583624 + 1.68627i 0.134977 + 0.990849i \(0.456904\pi\)
−0.718601 + 0.695423i \(0.755217\pi\)
\(252\) 0 0
\(253\) −3.56554 + 7.80745i −0.224164 + 0.490850i
\(254\) 0 0
\(255\) 22.0799 + 21.0531i 1.38270 + 1.31840i
\(256\) 0 0
\(257\) −6.67318 2.67154i −0.416262 0.166646i 0.154071 0.988060i \(-0.450762\pi\)
−0.570333 + 0.821414i \(0.693186\pi\)
\(258\) 0 0
\(259\) −0.903731 1.97889i −0.0561551 0.122963i
\(260\) 0 0
\(261\) 6.63776 + 0.633829i 0.410867 + 0.0392330i
\(262\) 0 0
\(263\) −4.05250 28.1858i −0.249888 1.73801i −0.598840 0.800868i \(-0.704372\pi\)
0.348952 0.937140i \(-0.386538\pi\)
\(264\) 0 0
\(265\) 16.6502 + 10.7004i 1.02281 + 0.657321i
\(266\) 0 0
\(267\) 7.11018 0.435136
\(268\) 0 0
\(269\) 2.67808 0.163285 0.0816427 0.996662i \(-0.473983\pi\)
0.0816427 + 0.996662i \(0.473983\pi\)
\(270\) 0 0
\(271\) 20.6705 + 13.2841i 1.25564 + 0.806952i 0.987681 0.156478i \(-0.0500141\pi\)
0.267960 + 0.963430i \(0.413651\pi\)
\(272\) 0 0
\(273\) −2.37937 16.5489i −0.144006 1.00158i
\(274\) 0 0
\(275\) −36.2411 3.46060i −2.18542 0.208682i
\(276\) 0 0
\(277\) −6.47129 14.1701i −0.388822 0.851401i −0.998282 0.0585850i \(-0.981341\pi\)
0.609460 0.792817i \(-0.291386\pi\)
\(278\) 0 0
\(279\) 3.14009 + 1.25710i 0.187993 + 0.0752609i
\(280\) 0 0
\(281\) 11.8573 + 11.3059i 0.707349 + 0.674456i 0.955743 0.294203i \(-0.0950542\pi\)
−0.248394 + 0.968659i \(0.579903\pi\)
\(282\) 0 0
\(283\) −7.01697 + 15.3650i −0.417116 + 0.913356i 0.578129 + 0.815946i \(0.303783\pi\)
−0.995244 + 0.0974104i \(0.968944\pi\)
\(284\) 0 0
\(285\) −0.412160 + 1.19086i −0.0244143 + 0.0705404i
\(286\) 0 0
\(287\) −33.9440 + 3.24126i −2.00365 + 0.191326i
\(288\) 0 0
\(289\) −28.1490 22.1366i −1.65582 1.30215i
\(290\) 0 0
\(291\) 0.713870 14.9860i 0.0418478 0.878494i
\(292\) 0 0
\(293\) 2.13705 0.627493i 0.124848 0.0366586i −0.218712 0.975789i \(-0.570185\pi\)
0.343559 + 0.939131i \(0.388367\pi\)
\(294\) 0 0
\(295\) 6.38176 44.3861i 0.371561 2.58426i
\(296\) 0 0
\(297\) 1.44188 2.49742i 0.0836666 0.144915i
\(298\) 0 0
\(299\) −11.1251 + 10.6077i −0.643378 + 0.613460i
\(300\) 0 0
\(301\) −12.5707 17.6531i −0.724564 1.01751i
\(302\) 0 0
\(303\) −0.500898 10.5151i −0.0287758 0.604079i
\(304\) 0 0
\(305\) 1.48973 + 2.58028i 0.0853015 + 0.147747i
\(306\) 0 0
\(307\) 5.16990 + 21.3106i 0.295062 + 1.21626i 0.905551 + 0.424237i \(0.139457\pi\)
−0.610490 + 0.792024i \(0.709027\pi\)
\(308\) 0 0
\(309\) −1.60773 + 0.309864i −0.0914604 + 0.0176276i
\(310\) 0 0
\(311\) 22.5944 + 26.0753i 1.28121 + 1.47860i 0.797434 + 0.603407i \(0.206190\pi\)
0.483778 + 0.875191i \(0.339264\pi\)
\(312\) 0 0
\(313\) 24.0524 15.4575i 1.35952 0.873711i 0.361248 0.932470i \(-0.382351\pi\)
0.998272 + 0.0587592i \(0.0187144\pi\)
\(314\) 0 0
\(315\) 12.0796 6.22744i 0.680606 0.350877i
\(316\) 0 0
\(317\) −8.28154 1.59614i −0.465137 0.0896479i −0.0487023 0.998813i \(-0.515509\pi\)
−0.416435 + 0.909165i \(0.636721\pi\)
\(318\) 0 0
\(319\) 15.1149 11.8865i 0.846271 0.665515i
\(320\) 0 0
\(321\) 1.19374 1.37765i 0.0666282 0.0768931i
\(322\) 0 0
\(323\) 0.514279 2.11989i 0.0286152 0.117954i
\(324\) 0 0
\(325\) −57.9526 29.8766i −3.21463 1.65726i
\(326\) 0 0
\(327\) 9.69108 + 2.84556i 0.535918 + 0.157360i
\(328\) 0 0
\(329\) −19.7931 + 7.92398i −1.09123 + 0.436863i
\(330\) 0 0
\(331\) 2.89959 + 8.37782i 0.159376 + 0.460487i 0.996211 0.0869683i \(-0.0277179\pi\)
−0.836835 + 0.547455i \(0.815597\pi\)
\(332\) 0 0
\(333\) 0.389812 0.547415i 0.0213616 0.0299981i
\(334\) 0 0
\(335\) 16.8578 29.9441i 0.921041 1.63602i
\(336\) 0 0
\(337\) 8.81222 12.3750i 0.480032 0.674111i −0.501555 0.865126i \(-0.667238\pi\)
0.981587 + 0.191015i \(0.0611778\pi\)
\(338\) 0 0
\(339\) 5.88260 + 16.9967i 0.319499 + 0.923131i
\(340\) 0 0
\(341\) 9.05531 3.62520i 0.490372 0.196315i
\(342\) 0 0
\(343\) −10.9347 3.21073i −0.590420 0.173363i
\(344\) 0 0
\(345\) −11.1061 5.72560i −0.597933 0.308256i
\(346\) 0 0
\(347\) 1.01610 4.18844i 0.0545474 0.224847i −0.938013 0.346600i \(-0.887336\pi\)
0.992561 + 0.121752i \(0.0388514\pi\)
\(348\) 0 0
\(349\) 3.30990 3.81983i 0.177175 0.204471i −0.660215 0.751077i \(-0.729535\pi\)
0.837390 + 0.546606i \(0.184080\pi\)
\(350\) 0 0
\(351\) 4.05968 3.19257i 0.216690 0.170407i
\(352\) 0 0
\(353\) −12.1180 2.33555i −0.644976 0.124309i −0.143735 0.989616i \(-0.545911\pi\)
−0.501242 + 0.865307i \(0.667123\pi\)
\(354\) 0 0
\(355\) −1.50235 + 0.774513i −0.0797363 + 0.0411069i
\(356\) 0 0
\(357\) −19.7906 + 12.7187i −1.04743 + 0.673142i
\(358\) 0 0
\(359\) −14.3866 16.6031i −0.759298 0.876277i 0.236137 0.971720i \(-0.424119\pi\)
−0.995435 + 0.0954432i \(0.969573\pi\)
\(360\) 0 0
\(361\) −18.5682 + 3.57872i −0.977272 + 0.188354i
\(362\) 0 0
\(363\) 0.632748 + 2.60822i 0.0332107 + 0.136896i
\(364\) 0 0
\(365\) 3.26046 + 5.64728i 0.170660 + 0.295592i
\(366\) 0 0
\(367\) 0.677261 + 14.2175i 0.0353527 + 0.742145i 0.945060 + 0.326896i \(0.106003\pi\)
−0.909708 + 0.415249i \(0.863694\pi\)
\(368\) 0 0
\(369\) −6.10989 8.58013i −0.318068 0.446664i
\(370\) 0 0
\(371\) −11.0455 + 10.5319i −0.573454 + 0.546787i
\(372\) 0 0
\(373\) 15.9465 27.6201i 0.825676 1.43011i −0.0757255 0.997129i \(-0.524127\pi\)
0.901402 0.432984i \(-0.142539\pi\)
\(374\) 0 0
\(375\) 4.55528 31.6827i 0.235234 1.63609i
\(376\) 0 0
\(377\) 33.0426 9.70218i 1.70178 0.499688i
\(378\) 0 0
\(379\) −0.786153 + 16.5034i −0.0403819 + 0.847721i 0.884286 + 0.466946i \(0.154646\pi\)
−0.924668 + 0.380775i \(0.875657\pi\)
\(380\) 0 0
\(381\) 8.51937 + 6.69971i 0.436461 + 0.343237i
\(382\) 0 0
\(383\) −32.5999 + 3.11291i −1.66578 + 0.159062i −0.884950 0.465687i \(-0.845807\pi\)
−0.780826 + 0.624749i \(0.785201\pi\)
\(384\) 0 0
\(385\) 12.8182 37.0358i 0.653277 1.88752i
\(386\) 0 0
\(387\) 2.78099 6.08952i 0.141366 0.309548i
\(388\) 0 0
\(389\) 10.4651 + 9.97848i 0.530603 + 0.505929i 0.907344 0.420390i \(-0.138107\pi\)
−0.376740 + 0.926319i \(0.622955\pi\)
\(390\) 0 0
\(391\) 20.0800 + 8.03882i 1.01549 + 0.406540i
\(392\) 0 0
\(393\) −2.83123 6.19952i −0.142817 0.312725i
\(394\) 0 0
\(395\) −34.3901 3.28385i −1.73035 0.165229i
\(396\) 0 0
\(397\) −2.65801 18.4869i −0.133402 0.927830i −0.941075 0.338199i \(-0.890182\pi\)
0.807673 0.589631i \(-0.200727\pi\)
\(398\) 0 0
\(399\) −0.817465 0.525353i −0.0409244 0.0263005i
\(400\) 0 0
\(401\) 23.4162 1.16935 0.584676 0.811267i \(-0.301222\pi\)
0.584676 + 0.811267i \(0.301222\pi\)
\(402\) 0 0
\(403\) 17.4688 0.870182
\(404\) 0 0
\(405\) 3.53171 + 2.26969i 0.175492 + 0.112782i
\(406\) 0 0
\(407\) −0.275801 1.91824i −0.0136709 0.0950835i
\(408\) 0 0
\(409\) 28.5071 + 2.72210i 1.40959 + 0.134599i 0.771923 0.635716i \(-0.219295\pi\)
0.637663 + 0.770315i \(0.279901\pi\)
\(410\) 0 0
\(411\) −0.325017 0.711688i −0.0160319 0.0351050i
\(412\) 0 0
\(413\) 32.1015 + 12.8515i 1.57961 + 0.632380i
\(414\) 0 0
\(415\) −30.9308 29.4924i −1.51833 1.44773i
\(416\) 0 0
\(417\) −7.05850 + 15.4560i −0.345656 + 0.756882i
\(418\) 0 0
\(419\) −1.04337 + 3.01461i −0.0509718 + 0.147273i −0.967613 0.252437i \(-0.918768\pi\)
0.916642 + 0.399710i \(0.130889\pi\)
\(420\) 0 0
\(421\) −24.7668 + 2.36494i −1.20706 + 0.115260i −0.679123 0.734024i \(-0.737640\pi\)
−0.527936 + 0.849284i \(0.677034\pi\)
\(422\) 0 0
\(423\) −5.17695 4.07120i −0.251712 0.197949i
\(424\) 0 0
\(425\) −4.36530 + 91.6389i −0.211748 + 4.44514i
\(426\) 0 0
\(427\) −2.20441 + 0.647274i −0.106679 + 0.0313238i
\(428\) 0 0
\(429\) 2.11958 14.7420i 0.102334 0.711752i
\(430\) 0 0
\(431\) −12.3405 + 21.3744i −0.594422 + 1.02957i 0.399206 + 0.916861i \(0.369286\pi\)
−0.993628 + 0.112708i \(0.964047\pi\)
\(432\) 0 0
\(433\) −15.9458 + 15.2043i −0.766305 + 0.730670i −0.968592 0.248656i \(-0.920011\pi\)
0.202287 + 0.979326i \(0.435163\pi\)
\(434\) 0 0
\(435\) 16.2376 + 22.8025i 0.778531 + 1.09329i
\(436\) 0 0
\(437\) 0.0425104 + 0.892404i 0.00203355 + 0.0426895i
\(438\) 0 0
\(439\) −15.7672 27.3096i −0.752526 1.30341i −0.946595 0.322426i \(-0.895502\pi\)
0.194068 0.980988i \(-0.437832\pi\)
\(440\) 0 0
\(441\) 0.820342 + 3.38150i 0.0390639 + 0.161024i
\(442\) 0 0
\(443\) −6.06177 + 1.16831i −0.288003 + 0.0555081i −0.331207 0.943558i \(-0.607456\pi\)
0.0432033 + 0.999066i \(0.486244\pi\)
\(444\) 0 0
\(445\) 19.5473 + 22.5588i 0.926631 + 1.06939i
\(446\) 0 0
\(447\) 11.8425 7.61074i 0.560133 0.359976i
\(448\) 0 0
\(449\) −16.6575 + 8.58753i −0.786115 + 0.405271i −0.804045 0.594569i \(-0.797323\pi\)
0.0179295 + 0.999839i \(0.494293\pi\)
\(450\) 0 0
\(451\) −29.8265 5.74859i −1.40448 0.270691i
\(452\) 0 0
\(453\) 12.3398 9.70409i 0.579772 0.455938i
\(454\) 0 0
\(455\) 45.9640 53.0453i 2.15483 2.48680i
\(456\) 0 0
\(457\) 1.95338 8.05192i 0.0913751 0.376653i −0.907702 0.419616i \(-0.862165\pi\)
0.999077 + 0.0429631i \(0.0136798\pi\)
\(458\) 0 0
\(459\) −6.45924 3.32997i −0.301492 0.155430i
\(460\) 0 0
\(461\) −27.7495 8.14800i −1.29242 0.379490i −0.437957 0.898996i \(-0.644298\pi\)
−0.854467 + 0.519506i \(0.826116\pi\)
\(462\) 0 0
\(463\) 24.6246 9.85818i 1.14440 0.458149i 0.279526 0.960138i \(-0.409823\pi\)
0.864874 + 0.501989i \(0.167398\pi\)
\(464\) 0 0
\(465\) 4.64428 + 13.4188i 0.215373 + 0.622280i
\(466\) 0 0
\(467\) −4.86215 + 6.82793i −0.224993 + 0.315959i −0.911607 0.411064i \(-0.865157\pi\)
0.686613 + 0.727023i \(0.259097\pi\)
\(468\) 0 0
\(469\) 19.3746 + 18.0764i 0.894635 + 0.834693i
\(470\) 0 0
\(471\) 10.3688 14.5609i 0.477767 0.670930i
\(472\) 0 0
\(473\) −6.31416 18.2436i −0.290326 0.838841i
\(474\) 0 0
\(475\) −3.51805 + 1.40842i −0.161419 + 0.0646225i
\(476\) 0 0
\(477\) −4.52352 1.32822i −0.207118 0.0608152i
\(478\) 0 0
\(479\) 10.5449 + 5.43629i 0.481810 + 0.248390i 0.681980 0.731371i \(-0.261119\pi\)
−0.200170 + 0.979761i \(0.564149\pi\)
\(480\) 0 0
\(481\) 0.818263 3.37293i 0.0373096 0.153792i
\(482\) 0 0
\(483\) 6.30963 7.28170i 0.287098 0.331329i
\(484\) 0 0
\(485\) 49.5093 38.9345i 2.24810 1.76793i
\(486\) 0 0
\(487\) 35.8119 + 6.90217i 1.62279 + 0.312767i 0.917979 0.396628i \(-0.129820\pi\)
0.704811 + 0.709395i \(0.251032\pi\)
\(488\) 0 0
\(489\) 9.81544 5.06021i 0.443869 0.228831i
\(490\) 0 0
\(491\) −13.6106 + 8.74698i −0.614237 + 0.394746i −0.810444 0.585817i \(-0.800774\pi\)
0.196207 + 0.980562i \(0.437138\pi\)
\(492\) 0 0
\(493\) −31.7323 36.6210i −1.42915 1.64933i
\(494\) 0 0
\(495\) 11.8877 2.29117i 0.534313 0.102980i
\(496\) 0 0
\(497\) −0.307278 1.26662i −0.0137833 0.0568155i
\(498\) 0 0
\(499\) 16.2826 + 28.2023i 0.728911 + 1.26251i 0.957344 + 0.288951i \(0.0933064\pi\)
−0.228433 + 0.973560i \(0.573360\pi\)
\(500\) 0 0
\(501\) 0.224738 + 4.71783i 0.0100405 + 0.210777i
\(502\) 0 0
\(503\) 23.7335 + 33.3290i 1.05822 + 1.48607i 0.862929 + 0.505324i \(0.168627\pi\)
0.195295 + 0.980744i \(0.437433\pi\)
\(504\) 0 0
\(505\) 31.9848 30.4974i 1.42331 1.35712i
\(506\) 0 0
\(507\) 6.83674 11.8416i 0.303630 0.525903i
\(508\) 0 0
\(509\) 1.38766 9.65137i 0.0615068 0.427789i −0.935681 0.352847i \(-0.885214\pi\)
0.997188 0.0749424i \(-0.0238773\pi\)
\(510\) 0 0
\(511\) −4.82464 + 1.41664i −0.213430 + 0.0626686i
\(512\) 0 0
\(513\) 0.0142828 0.299832i 0.000630599 0.0132379i
\(514\) 0 0
\(515\) −5.40309 4.24903i −0.238088 0.187235i
\(516\) 0 0
\(517\) −18.9065 + 1.80536i −0.831509 + 0.0793994i
\(518\) 0 0
\(519\) −4.71871 + 13.6338i −0.207129 + 0.598459i
\(520\) 0 0
\(521\) −4.17214 + 9.13572i −0.182785 + 0.400243i −0.978738 0.205115i \(-0.934243\pi\)
0.795953 + 0.605359i \(0.206970\pi\)
\(522\) 0 0
\(523\) −6.39580 6.09838i −0.279669 0.266664i 0.537241 0.843429i \(-0.319466\pi\)
−0.816910 + 0.576765i \(0.804315\pi\)
\(524\) 0 0
\(525\) 37.9406 + 15.1891i 1.65586 + 0.662907i
\(526\) 0 0
\(527\) −10.2109 22.3588i −0.444795 0.973965i
\(528\) 0 0
\(529\) 14.0773 + 1.34422i 0.612058 + 0.0584445i
\(530\) 0 0
\(531\) 1.52014 + 10.5728i 0.0659684 + 0.458820i
\(532\) 0 0
\(533\) −45.7645 29.4111i −1.98228 1.27394i
\(534\) 0 0
\(535\) 7.65278 0.330859
\(536\) 0 0
\(537\) −13.4252 −0.579338
\(538\) 0 0
\(539\) 8.44139 + 5.42495i 0.363597 + 0.233669i
\(540\) 0 0
\(541\) −1.79045 12.4529i −0.0769776 0.535391i −0.991424 0.130684i \(-0.958283\pi\)
0.914447 0.404707i \(-0.132626\pi\)
\(542\) 0 0
\(543\) −22.0651 2.10696i −0.946903 0.0904183i
\(544\) 0 0
\(545\) 17.6145 + 38.5704i 0.754522 + 1.65217i
\(546\) 0 0
\(547\) −26.4967 10.6077i −1.13292 0.453551i −0.271999 0.962297i \(-0.587685\pi\)
−0.860916 + 0.508746i \(0.830109\pi\)
\(548\) 0 0
\(549\) −0.513639 0.489754i −0.0219216 0.0209022i
\(550\) 0 0
\(551\) 0.831467 1.82066i 0.0354217 0.0775627i
\(552\) 0 0
\(553\) 8.71277 25.1739i 0.370505 1.07050i
\(554\) 0 0
\(555\) 2.80848 0.268177i 0.119213 0.0113835i
\(556\) 0 0
\(557\) −20.3421 15.9972i −0.861924 0.677825i 0.0860090 0.996294i \(-0.472589\pi\)
−0.947933 + 0.318470i \(0.896831\pi\)
\(558\) 0 0
\(559\) 1.64513 34.5354i 0.0695814 1.46069i
\(560\) 0 0
\(561\) −20.1077 + 5.90416i −0.848948 + 0.249274i
\(562\) 0 0
\(563\) −1.92814 + 13.4105i −0.0812612 + 0.565184i 0.907994 + 0.418984i \(0.137614\pi\)
−0.989255 + 0.146201i \(0.953296\pi\)
\(564\) 0 0
\(565\) −37.7536 + 65.3912i −1.58831 + 2.75103i
\(566\) 0 0
\(567\) −2.34288 + 2.23394i −0.0983919 + 0.0938165i
\(568\) 0 0
\(569\) 21.5140 + 30.2122i 0.901914 + 1.26656i 0.963295 + 0.268446i \(0.0865102\pi\)
−0.0613808 + 0.998114i \(0.519550\pi\)
\(570\) 0 0
\(571\) 1.26165 + 26.4853i 0.0527984 + 1.10838i 0.857430 + 0.514601i \(0.172060\pi\)
−0.804631 + 0.593775i \(0.797637\pi\)
\(572\) 0 0
\(573\) 2.42509 + 4.20038i 0.101310 + 0.175474i
\(574\) 0 0
\(575\) −8.85856 36.5155i −0.369428 1.52280i
\(576\) 0 0
\(577\) −39.0541 + 7.52705i −1.62584 + 0.313355i −0.919072 0.394089i \(-0.871060\pi\)
−0.706769 + 0.707444i \(0.749848\pi\)
\(578\) 0 0
\(579\) −10.5431 12.1674i −0.438157 0.505660i
\(580\) 0 0
\(581\) 27.7238 17.8170i 1.15018 0.739174i
\(582\) 0 0
\(583\) −12.0842 + 6.22981i −0.500474 + 0.258013i
\(584\) 0 0
\(585\) 21.2901 + 4.10333i 0.880237 + 0.169652i
\(586\) 0 0
\(587\) 19.7922 15.5648i 0.816912 0.642427i −0.119694 0.992811i \(-0.538191\pi\)
0.936606 + 0.350384i \(0.113949\pi\)
\(588\) 0 0
\(589\) 0.664878 0.767310i 0.0273958 0.0316165i
\(590\) 0 0
\(591\) −3.56966 + 14.7143i −0.146836 + 0.605267i
\(592\) 0 0
\(593\) −15.1461 7.80837i −0.621977 0.320651i 0.118275 0.992981i \(-0.462263\pi\)
−0.740252 + 0.672330i \(0.765294\pi\)
\(594\) 0 0
\(595\) −94.7614 27.8245i −3.88484 1.14069i
\(596\) 0 0
\(597\) 4.54517 1.81961i 0.186021 0.0744717i
\(598\) 0 0
\(599\) −9.32475 26.9421i −0.380999 1.10082i −0.958662 0.284549i \(-0.908156\pi\)
0.577662 0.816276i \(-0.303965\pi\)
\(600\) 0 0
\(601\) 17.6993 24.8552i 0.721971 1.01387i −0.276630 0.960977i \(-0.589218\pi\)
0.998600 0.0528892i \(-0.0168430\pi\)
\(602\) 0 0
\(603\) −1.84337 + 7.97509i −0.0750676 + 0.324771i
\(604\) 0 0
\(605\) −6.53568 + 9.17808i −0.265713 + 0.373142i
\(606\) 0 0
\(607\) 9.31515 + 26.9144i 0.378090 + 1.09242i 0.960201 + 0.279310i \(0.0901058\pi\)
−0.582111 + 0.813110i \(0.697773\pi\)
\(608\) 0 0
\(609\) −20.0394 + 8.02256i −0.812037 + 0.325091i
\(610\) 0 0
\(611\) −32.6365 9.58295i −1.32033 0.387685i
\(612\) 0 0
\(613\) 6.42185 + 3.31069i 0.259376 + 0.133718i 0.583011 0.812465i \(-0.301875\pi\)
−0.323635 + 0.946182i \(0.604905\pi\)
\(614\) 0 0
\(615\) 10.4253 42.9736i 0.420388 1.73286i
\(616\) 0 0
\(617\) −16.3521 + 18.8713i −0.658309 + 0.759729i −0.982500 0.186262i \(-0.940363\pi\)
0.324191 + 0.945992i \(0.394908\pi\)
\(618\) 0 0
\(619\) −1.46817 + 1.15459i −0.0590109 + 0.0464067i −0.647229 0.762296i \(-0.724072\pi\)
0.588218 + 0.808702i \(0.299830\pi\)
\(620\) 0 0
\(621\) 2.92256 + 0.563277i 0.117278 + 0.0226035i
\(622\) 0 0
\(623\) −20.4585 + 10.5471i −0.819652 + 0.422560i
\(624\) 0 0
\(625\) 59.9428 38.5229i 2.39771 1.54091i
\(626\) 0 0
\(627\) −0.566865 0.654197i −0.0226384 0.0261261i
\(628\) 0 0
\(629\) −4.79540 + 0.924238i −0.191205 + 0.0368518i
\(630\) 0 0
\(631\) −0.528557 2.17874i −0.0210415 0.0867343i 0.960323 0.278891i \(-0.0899669\pi\)
−0.981364 + 0.192157i \(0.938452\pi\)
\(632\) 0 0
\(633\) −12.1825 21.1006i −0.484209 0.838675i
\(634\) 0 0
\(635\) 2.16499 + 45.4487i 0.0859149 + 1.80358i
\(636\) 0 0
\(637\) 10.4241 + 14.6386i 0.413017 + 0.580001i
\(638\) 0 0
\(639\) 0.291387 0.277837i 0.0115271 0.0109911i
\(640\) 0 0
\(641\) −5.27413 + 9.13506i −0.208316 + 0.360813i −0.951184 0.308624i \(-0.900131\pi\)
0.742869 + 0.669437i \(0.233465\pi\)
\(642\) 0 0
\(643\) 4.72164 32.8397i 0.186203 1.29507i −0.655526 0.755173i \(-0.727553\pi\)
0.841729 0.539900i \(-0.181538\pi\)
\(644\) 0 0
\(645\) 26.9660 7.91793i 1.06179 0.311768i
\(646\) 0 0
\(647\) −0.482874 + 10.1368i −0.0189837 + 0.398517i 0.969299 + 0.245884i \(0.0790783\pi\)
−0.988283 + 0.152633i \(0.951225\pi\)
\(648\) 0 0
\(649\) 24.2128 + 19.0412i 0.950436 + 0.747431i
\(650\) 0 0
\(651\) −10.8999 + 1.04082i −0.427202 + 0.0407928i
\(652\) 0 0
\(653\) −5.48144 + 15.8376i −0.214505 + 0.619772i 0.785494 + 0.618869i \(0.212409\pi\)
−1.00000 0.000903348i \(0.999712\pi\)
\(654\) 0 0
\(655\) 11.8859 26.0265i 0.464421 1.01694i
\(656\) 0 0
\(657\) −1.12417 1.07189i −0.0438579 0.0418184i
\(658\) 0 0
\(659\) 13.5829 + 5.43776i 0.529113 + 0.211825i 0.620809 0.783962i \(-0.286804\pi\)
−0.0916955 + 0.995787i \(0.529229\pi\)
\(660\) 0 0
\(661\) 8.04874 + 17.6243i 0.313060 + 0.685505i 0.999116 0.0420437i \(-0.0133869\pi\)
−0.686056 + 0.727549i \(0.740660\pi\)
\(662\) 0 0
\(663\) −37.3619 3.56763i −1.45102 0.138555i
\(664\) 0 0
\(665\) −0.580564 4.03791i −0.0225133 0.156583i
\(666\) 0 0
\(667\) 16.6956 + 10.7296i 0.646457 + 0.415453i
\(668\) 0 0
\(669\) −2.93339 −0.113411
\(670\) 0 0
\(671\) −2.04663 −0.0790093
\(672\) 0 0
\(673\) 12.8845 + 8.28037i 0.496661 + 0.319185i 0.764880 0.644173i \(-0.222798\pi\)
−0.268218 + 0.963358i \(0.586435\pi\)
\(674\) 0 0
\(675\) 1.79664 + 12.4959i 0.0691529 + 0.480969i
\(676\) 0 0
\(677\) −16.6284 1.58782i −0.639081 0.0610248i −0.229515 0.973305i \(-0.573714\pi\)
−0.409566 + 0.912280i \(0.634320\pi\)
\(678\) 0 0
\(679\) 20.1758 + 44.1789i 0.774277 + 1.69543i
\(680\) 0 0
\(681\) −20.9033 8.36842i −0.801016 0.320678i
\(682\) 0 0
\(683\) −21.0060 20.0292i −0.803771 0.766394i 0.172021 0.985093i \(-0.444970\pi\)
−0.975792 + 0.218699i \(0.929819\pi\)
\(684\) 0 0
\(685\) 1.36447 2.98777i 0.0521337 0.114157i
\(686\) 0 0
\(687\) −2.39736 + 6.92670i −0.0914648 + 0.264270i
\(688\) 0 0
\(689\) −24.2384 + 2.31448i −0.923408 + 0.0881748i
\(690\) 0 0
\(691\) 26.8597 + 21.1227i 1.02179 + 0.803547i 0.980682 0.195608i \(-0.0626680\pi\)
0.0411106 + 0.999155i \(0.486910\pi\)
\(692\) 0 0
\(693\) −0.444196 + 9.32481i −0.0168736 + 0.354220i
\(694\) 0 0
\(695\) −68.4431 + 20.0967i −2.59620 + 0.762312i
\(696\) 0 0
\(697\) −10.8936 + 75.7669i −0.412626 + 2.86988i
\(698\) 0 0
\(699\) 2.97308 5.14953i 0.112452 0.194773i
\(700\) 0 0
\(701\) −3.97752 + 3.79256i −0.150229 + 0.143243i −0.761467 0.648204i \(-0.775520\pi\)
0.611238 + 0.791447i \(0.290672\pi\)
\(702\) 0 0
\(703\) −0.117011 0.164319i −0.00441315 0.00619740i
\(704\) 0 0
\(705\) −1.31559 27.6177i −0.0495481 1.04014i
\(706\) 0 0
\(707\) 17.0392 + 29.5128i 0.640825 + 1.10994i
\(708\) 0 0
\(709\) 7.19310 + 29.6504i 0.270143 + 1.11354i 0.931578 + 0.363541i \(0.118432\pi\)
−0.661436 + 0.750002i \(0.730053\pi\)
\(710\) 0 0
\(711\) 8.08028 1.55735i 0.303034 0.0584050i
\(712\) 0 0
\(713\) 6.59257 + 7.60823i 0.246894 + 0.284931i
\(714\) 0 0
\(715\) 52.5999 33.8039i 1.96712 1.26419i
\(716\) 0 0
\(717\) 16.4540 8.48264i 0.614487 0.316790i
\(718\) 0 0
\(719\) −6.83093 1.31655i −0.254751 0.0490992i 0.0602769 0.998182i \(-0.480802\pi\)
−0.315028 + 0.949083i \(0.602014\pi\)
\(720\) 0 0
\(721\) 4.16636 3.27646i 0.155163 0.122022i
\(722\) 0 0
\(723\) 8.62581 9.95471i 0.320797 0.370220i
\(724\) 0 0
\(725\) −19.8460 + 81.8062i −0.737061 + 3.03821i
\(726\) 0 0
\(727\) −15.2929 7.88405i −0.567183 0.292403i 0.150685 0.988582i \(-0.451852\pi\)
−0.717869 + 0.696178i \(0.754882\pi\)
\(728\) 0 0
\(729\) −0.959493 0.281733i −0.0355368 0.0104345i
\(730\) 0 0
\(731\) −45.1646 + 18.0812i −1.67047 + 0.668756i
\(732\) 0 0
\(733\) −5.29125 15.2881i −0.195437 0.564677i 0.804119 0.594468i \(-0.202637\pi\)
−0.999556 + 0.0297905i \(0.990516\pi\)
\(734\) 0 0
\(735\) −8.47335 + 11.8991i −0.312544 + 0.438907i
\(736\) 0 0
\(737\) 12.0234 + 20.3130i 0.442887 + 0.748239i
\(738\) 0 0
\(739\) −11.8231 + 16.6032i −0.434920 + 0.610760i −0.972627 0.232372i \(-0.925351\pi\)
0.537707 + 0.843132i \(0.319291\pi\)
\(740\) 0 0
\(741\) −0.507047 1.46502i −0.0186268 0.0538187i
\(742\) 0 0
\(743\) −19.0017 + 7.60715i −0.697106 + 0.279079i −0.693026 0.720913i \(-0.743723\pi\)
−0.00407985 + 0.999992i \(0.501299\pi\)
\(744\) 0 0
\(745\) 56.7045 + 16.6499i 2.07749 + 0.610007i
\(746\) 0 0
\(747\) 9.04848 + 4.66481i 0.331066 + 0.170677i
\(748\) 0 0
\(749\) −1.39124 + 5.73477i −0.0508348 + 0.209544i
\(750\) 0 0
\(751\) 2.67462 3.08668i 0.0975983 0.112634i −0.704849 0.709357i \(-0.748985\pi\)
0.802447 + 0.596723i \(0.203531\pi\)
\(752\) 0 0
\(753\) 22.2220 17.4756i 0.809816 0.636847i
\(754\) 0 0
\(755\) 64.7131 + 12.4724i 2.35515 + 0.453918i
\(756\) 0 0
\(757\) −1.21730 + 0.627562i −0.0442436 + 0.0228091i −0.480206 0.877156i \(-0.659438\pi\)
0.435963 + 0.899965i \(0.356408\pi\)
\(758\) 0 0
\(759\) 7.22056 4.64037i 0.262090 0.168435i
\(760\) 0 0
\(761\) 23.5188 + 27.1421i 0.852554 + 0.983900i 0.999987 0.00517231i \(-0.00164641\pi\)
−0.147433 + 0.989072i \(0.547101\pi\)
\(762\) 0 0
\(763\) −32.1057 + 6.18787i −1.16230 + 0.224016i
\(764\) 0 0
\(765\) −7.19260 29.6483i −0.260049 1.07194i
\(766\) 0 0
\(767\) 27.5831 + 47.7753i 0.995967 + 1.72507i
\(768\) 0 0
\(769\) −1.07546 22.5767i −0.0387821 0.814137i −0.931549 0.363617i \(-0.881542\pi\)
0.892766 0.450520i \(-0.148761\pi\)
\(770\) 0 0
\(771\) 4.16949 + 5.85524i 0.150161 + 0.210871i
\(772\) 0 0
\(773\) −11.1559 + 10.6371i −0.401250 + 0.382591i −0.863660 0.504075i \(-0.831833\pi\)
0.462410 + 0.886666i \(0.346985\pi\)
\(774\) 0 0
\(775\) −21.3503 + 36.9798i −0.766926 + 1.32836i
\(776\) 0 0
\(777\) −0.309604 + 2.15335i −0.0111070 + 0.0772509i
\(778\) 0