Properties

Label 1260.2.c.e.811.6
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.6
Root \(1.07312 + 0.921096i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.e.811.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.07312 + 0.921096i) q^{2} +(0.303166 - 1.97689i) q^{4} -1.00000i q^{5} +(1.82575 + 1.91485i) q^{7} +(1.49557 + 2.40068i) q^{8} +O(q^{10})\) \(q+(-1.07312 + 0.921096i) q^{2} +(0.303166 - 1.97689i) q^{4} -1.00000i q^{5} +(1.82575 + 1.91485i) q^{7} +(1.49557 + 2.40068i) q^{8} +(0.921096 + 1.07312i) q^{10} +6.24043i q^{11} +2.40312i q^{13} +(-3.72300 - 0.373174i) q^{14} +(-3.81618 - 1.19865i) q^{16} -1.30768i q^{17} +3.94796 q^{19} +(-1.97689 - 0.303166i) q^{20} +(-5.74803 - 6.69672i) q^{22} -3.55648i q^{23} -1.00000 q^{25} +(-2.21350 - 2.57883i) q^{26} +(4.33895 - 3.02878i) q^{28} -1.44221 q^{29} -10.9517 q^{31} +(5.19929 - 2.22877i) q^{32} +(1.20450 + 1.40329i) q^{34} +(1.91485 - 1.82575i) q^{35} -5.06265 q^{37} +(-4.23663 + 3.63645i) q^{38} +(2.40068 - 1.49557i) q^{40} +1.26175i q^{41} +2.19850i q^{43} +(12.3366 + 1.89189i) q^{44} +(3.27586 + 3.81652i) q^{46} +11.6743 q^{47} +(-0.333303 + 6.99206i) q^{49} +(1.07312 - 0.921096i) q^{50} +(4.75070 + 0.728544i) q^{52} -11.7545 q^{53} +6.24043 q^{55} +(-1.86641 + 7.24683i) q^{56} +(1.54766 - 1.32842i) q^{58} +0.415368 q^{59} +12.6848i q^{61} +(11.7524 - 10.0875i) q^{62} +(-3.52653 + 7.18078i) q^{64} +2.40312 q^{65} +3.10097i q^{67} +(-2.58513 - 0.396443i) q^{68} +(-0.373174 + 3.72300i) q^{70} +10.4762i q^{71} +1.64141i q^{73} +(5.43282 - 4.66319i) q^{74} +(1.19689 - 7.80468i) q^{76} +(-11.9495 + 11.3934i) q^{77} +9.18952i q^{79} +(-1.19865 + 3.81618i) q^{80} +(-1.16219 - 1.35401i) q^{82} +7.39922 q^{83} -1.30768 q^{85} +(-2.02502 - 2.35925i) q^{86} +(-14.9813 + 9.33301i) q^{88} +11.4448i q^{89} +(-4.60162 + 4.38749i) q^{91} +(-7.03076 - 1.07820i) q^{92} +(-12.5279 + 10.7531i) q^{94} -3.94796i q^{95} -12.4433i q^{97} +(-6.08268 - 7.81031i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07312 + 0.921096i −0.758809 + 0.651313i
\(3\) 0 0
\(4\) 0.303166 1.97689i 0.151583 0.988445i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 1.82575 + 1.91485i 0.690067 + 0.723745i
\(8\) 1.49557 + 2.40068i 0.528764 + 0.848769i
\(9\) 0 0
\(10\) 0.921096 + 1.07312i 0.291276 + 0.339350i
\(11\) 6.24043i 1.88156i 0.339016 + 0.940780i \(0.389906\pi\)
−0.339016 + 0.940780i \(0.610094\pi\)
\(12\) 0 0
\(13\) 2.40312i 0.666506i 0.942837 + 0.333253i \(0.108146\pi\)
−0.942837 + 0.333253i \(0.891854\pi\)
\(14\) −3.72300 0.373174i −0.995014 0.0997350i
\(15\) 0 0
\(16\) −3.81618 1.19865i −0.954045 0.299663i
\(17\) 1.30768i 0.317159i −0.987346 0.158579i \(-0.949309\pi\)
0.987346 0.158579i \(-0.0506913\pi\)
\(18\) 0 0
\(19\) 3.94796 0.905724 0.452862 0.891581i \(-0.350403\pi\)
0.452862 + 0.891581i \(0.350403\pi\)
\(20\) −1.97689 0.303166i −0.442046 0.0677899i
\(21\) 0 0
\(22\) −5.74803 6.69672i −1.22548 1.42775i
\(23\) 3.55648i 0.741577i −0.928717 0.370788i \(-0.879088\pi\)
0.928717 0.370788i \(-0.120912\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −2.21350 2.57883i −0.434104 0.505751i
\(27\) 0 0
\(28\) 4.33895 3.02878i 0.819985 0.572386i
\(29\) −1.44221 −0.267812 −0.133906 0.990994i \(-0.542752\pi\)
−0.133906 + 0.990994i \(0.542752\pi\)
\(30\) 0 0
\(31\) −10.9517 −1.96698 −0.983488 0.180974i \(-0.942075\pi\)
−0.983488 + 0.180974i \(0.942075\pi\)
\(32\) 5.19929 2.22877i 0.919112 0.393995i
\(33\) 0 0
\(34\) 1.20450 + 1.40329i 0.206569 + 0.240663i
\(35\) 1.91485 1.82575i 0.323669 0.308607i
\(36\) 0 0
\(37\) −5.06265 −0.832295 −0.416147 0.909297i \(-0.636620\pi\)
−0.416147 + 0.909297i \(0.636620\pi\)
\(38\) −4.23663 + 3.63645i −0.687272 + 0.589910i
\(39\) 0 0
\(40\) 2.40068 1.49557i 0.379581 0.236471i
\(41\) 1.26175i 0.197052i 0.995134 + 0.0985260i \(0.0314128\pi\)
−0.995134 + 0.0985260i \(0.968587\pi\)
\(42\) 0 0
\(43\) 2.19850i 0.335267i 0.985849 + 0.167634i \(0.0536126\pi\)
−0.985849 + 0.167634i \(0.946387\pi\)
\(44\) 12.3366 + 1.89189i 1.85982 + 0.285212i
\(45\) 0 0
\(46\) 3.27586 + 3.81652i 0.482999 + 0.562715i
\(47\) 11.6743 1.70287 0.851434 0.524462i \(-0.175733\pi\)
0.851434 + 0.524462i \(0.175733\pi\)
\(48\) 0 0
\(49\) −0.333303 + 6.99206i −0.0476147 + 0.998866i
\(50\) 1.07312 0.921096i 0.151762 0.130263i
\(51\) 0 0
\(52\) 4.75070 + 0.728544i 0.658804 + 0.101031i
\(53\) −11.7545 −1.61461 −0.807303 0.590137i \(-0.799074\pi\)
−0.807303 + 0.590137i \(0.799074\pi\)
\(54\) 0 0
\(55\) 6.24043 0.841460
\(56\) −1.86641 + 7.24683i −0.249410 + 0.968398i
\(57\) 0 0
\(58\) 1.54766 1.32842i 0.203218 0.174430i
\(59\) 0.415368 0.0540763 0.0270382 0.999634i \(-0.491392\pi\)
0.0270382 + 0.999634i \(0.491392\pi\)
\(60\) 0 0
\(61\) 12.6848i 1.62412i 0.583574 + 0.812060i \(0.301654\pi\)
−0.583574 + 0.812060i \(0.698346\pi\)
\(62\) 11.7524 10.0875i 1.49256 1.28112i
\(63\) 0 0
\(64\) −3.52653 + 7.18078i −0.440817 + 0.897597i
\(65\) 2.40312 0.298070
\(66\) 0 0
\(67\) 3.10097i 0.378844i 0.981896 + 0.189422i \(0.0606614\pi\)
−0.981896 + 0.189422i \(0.939339\pi\)
\(68\) −2.58513 0.396443i −0.313494 0.0480758i
\(69\) 0 0
\(70\) −0.373174 + 3.72300i −0.0446029 + 0.444984i
\(71\) 10.4762i 1.24330i 0.783296 + 0.621649i \(0.213537\pi\)
−0.783296 + 0.621649i \(0.786463\pi\)
\(72\) 0 0
\(73\) 1.64141i 0.192112i 0.995376 + 0.0960562i \(0.0306229\pi\)
−0.995376 + 0.0960562i \(0.969377\pi\)
\(74\) 5.43282 4.66319i 0.631553 0.542084i
\(75\) 0 0
\(76\) 1.19689 7.80468i 0.137292 0.895258i
\(77\) −11.9495 + 11.3934i −1.36177 + 1.29840i
\(78\) 0 0
\(79\) 9.18952i 1.03390i 0.856015 + 0.516951i \(0.172933\pi\)
−0.856015 + 0.516951i \(0.827067\pi\)
\(80\) −1.19865 + 3.81618i −0.134013 + 0.426662i
\(81\) 0 0
\(82\) −1.16219 1.35401i −0.128343 0.149525i
\(83\) 7.39922 0.812170 0.406085 0.913835i \(-0.366894\pi\)
0.406085 + 0.913835i \(0.366894\pi\)
\(84\) 0 0
\(85\) −1.30768 −0.141838
\(86\) −2.02502 2.35925i −0.218364 0.254404i
\(87\) 0 0
\(88\) −14.9813 + 9.33301i −1.59701 + 0.994902i
\(89\) 11.4448i 1.21314i 0.795028 + 0.606572i \(0.207456\pi\)
−0.795028 + 0.606572i \(0.792544\pi\)
\(90\) 0 0
\(91\) −4.60162 + 4.38749i −0.482380 + 0.459934i
\(92\) −7.03076 1.07820i −0.733008 0.112410i
\(93\) 0 0
\(94\) −12.5279 + 10.7531i −1.29215 + 1.10910i
\(95\) 3.94796i 0.405052i
\(96\) 0 0
\(97\) 12.4433i 1.26343i −0.775202 0.631714i \(-0.782352\pi\)
0.775202 0.631714i \(-0.217648\pi\)
\(98\) −6.08268 7.81031i −0.614444 0.788961i
\(99\) 0 0
\(100\) −0.303166 + 1.97689i −0.0303166 + 0.197689i
\(101\) 4.25585i 0.423473i −0.977327 0.211737i \(-0.932088\pi\)
0.977327 0.211737i \(-0.0679119\pi\)
\(102\) 0 0
\(103\) 15.3254 1.51006 0.755029 0.655691i \(-0.227623\pi\)
0.755029 + 0.655691i \(0.227623\pi\)
\(104\) −5.76913 + 3.59404i −0.565709 + 0.352424i
\(105\) 0 0
\(106\) 12.6140 10.8270i 1.22518 1.05161i
\(107\) 4.83844i 0.467750i −0.972267 0.233875i \(-0.924859\pi\)
0.972267 0.233875i \(-0.0751406\pi\)
\(108\) 0 0
\(109\) 8.77146 0.840153 0.420077 0.907489i \(-0.362003\pi\)
0.420077 + 0.907489i \(0.362003\pi\)
\(110\) −6.69672 + 5.74803i −0.638507 + 0.548054i
\(111\) 0 0
\(112\) −4.67214 9.49585i −0.441476 0.897273i
\(113\) −4.09511 −0.385236 −0.192618 0.981274i \(-0.561698\pi\)
−0.192618 + 0.981274i \(0.561698\pi\)
\(114\) 0 0
\(115\) −3.55648 −0.331643
\(116\) −0.437230 + 2.85109i −0.0405957 + 0.264717i
\(117\) 0 0
\(118\) −0.445739 + 0.382594i −0.0410336 + 0.0352206i
\(119\) 2.50401 2.38749i 0.229542 0.218861i
\(120\) 0 0
\(121\) −27.9430 −2.54027
\(122\) −11.6839 13.6123i −1.05781 1.23240i
\(123\) 0 0
\(124\) −3.32017 + 21.6502i −0.298160 + 1.94425i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 6.68595i 0.593282i −0.954989 0.296641i \(-0.904134\pi\)
0.954989 0.296641i \(-0.0958664\pi\)
\(128\) −2.82979 10.9541i −0.250121 0.968215i
\(129\) 0 0
\(130\) −2.57883 + 2.21350i −0.226179 + 0.194137i
\(131\) 13.3308 1.16472 0.582360 0.812931i \(-0.302129\pi\)
0.582360 + 0.812931i \(0.302129\pi\)
\(132\) 0 0
\(133\) 7.20797 + 7.55975i 0.625010 + 0.655513i
\(134\) −2.85629 3.32771i −0.246746 0.287470i
\(135\) 0 0
\(136\) 3.13932 1.95573i 0.269194 0.167702i
\(137\) −5.59837 −0.478301 −0.239151 0.970982i \(-0.576869\pi\)
−0.239151 + 0.970982i \(0.576869\pi\)
\(138\) 0 0
\(139\) 6.13537 0.520395 0.260198 0.965555i \(-0.416212\pi\)
0.260198 + 0.965555i \(0.416212\pi\)
\(140\) −3.02878 4.33895i −0.255979 0.366708i
\(141\) 0 0
\(142\) −9.64959 11.2422i −0.809776 0.943425i
\(143\) −14.9965 −1.25407
\(144\) 0 0
\(145\) 1.44221i 0.119769i
\(146\) −1.51189 1.76143i −0.125125 0.145777i
\(147\) 0 0
\(148\) −1.53482 + 10.0083i −0.126162 + 0.822677i
\(149\) 12.3505 1.01179 0.505895 0.862595i \(-0.331162\pi\)
0.505895 + 0.862595i \(0.331162\pi\)
\(150\) 0 0
\(151\) 15.9654i 1.29924i −0.760258 0.649621i \(-0.774928\pi\)
0.760258 0.649621i \(-0.225072\pi\)
\(152\) 5.90445 + 9.47779i 0.478914 + 0.768750i
\(153\) 0 0
\(154\) 2.32877 23.2331i 0.187658 1.87218i
\(155\) 10.9517i 0.879658i
\(156\) 0 0
\(157\) 5.15966i 0.411786i 0.978575 + 0.205893i \(0.0660098\pi\)
−0.978575 + 0.205893i \(0.933990\pi\)
\(158\) −8.46443 9.86144i −0.673394 0.784534i
\(159\) 0 0
\(160\) −2.22877 5.19929i −0.176200 0.411040i
\(161\) 6.81012 6.49322i 0.536713 0.511738i
\(162\) 0 0
\(163\) 1.27295i 0.0997052i −0.998757 0.0498526i \(-0.984125\pi\)
0.998757 0.0498526i \(-0.0158751\pi\)
\(164\) 2.49434 + 0.382519i 0.194775 + 0.0298697i
\(165\) 0 0
\(166\) −7.94023 + 6.81539i −0.616282 + 0.528977i
\(167\) −21.6628 −1.67632 −0.838158 0.545428i \(-0.816367\pi\)
−0.838158 + 0.545428i \(0.816367\pi\)
\(168\) 0 0
\(169\) 7.22501 0.555770
\(170\) 1.40329 1.20450i 0.107628 0.0923807i
\(171\) 0 0
\(172\) 4.34618 + 0.666509i 0.331393 + 0.0508208i
\(173\) 12.9769i 0.986617i 0.869855 + 0.493308i \(0.164213\pi\)
−0.869855 + 0.493308i \(0.835787\pi\)
\(174\) 0 0
\(175\) −1.82575 1.91485i −0.138013 0.144749i
\(176\) 7.48010 23.8146i 0.563833 1.79509i
\(177\) 0 0
\(178\) −10.5417 12.2816i −0.790137 0.920545i
\(179\) 15.1508i 1.13242i 0.824261 + 0.566210i \(0.191591\pi\)
−0.824261 + 0.566210i \(0.808409\pi\)
\(180\) 0 0
\(181\) 2.92356i 0.217307i −0.994080 0.108653i \(-0.965346\pi\)
0.994080 0.108653i \(-0.0346538\pi\)
\(182\) 0.896783 8.94682i 0.0664740 0.663183i
\(183\) 0 0
\(184\) 8.53797 5.31896i 0.629427 0.392119i
\(185\) 5.06265i 0.372214i
\(186\) 0 0
\(187\) 8.16048 0.596753
\(188\) 3.53924 23.0788i 0.258126 1.68319i
\(189\) 0 0
\(190\) 3.63645 + 4.23663i 0.263816 + 0.307357i
\(191\) 13.9477i 1.00922i 0.863348 + 0.504608i \(0.168363\pi\)
−0.863348 + 0.504608i \(0.831637\pi\)
\(192\) 0 0
\(193\) −13.3869 −0.963607 −0.481803 0.876279i \(-0.660018\pi\)
−0.481803 + 0.876279i \(0.660018\pi\)
\(194\) 11.4615 + 13.3532i 0.822887 + 0.958701i
\(195\) 0 0
\(196\) 13.7215 + 2.77866i 0.980106 + 0.198476i
\(197\) −4.07989 −0.290680 −0.145340 0.989382i \(-0.546428\pi\)
−0.145340 + 0.989382i \(0.546428\pi\)
\(198\) 0 0
\(199\) −3.66884 −0.260077 −0.130039 0.991509i \(-0.541510\pi\)
−0.130039 + 0.991509i \(0.541510\pi\)
\(200\) −1.49557 2.40068i −0.105753 0.169754i
\(201\) 0 0
\(202\) 3.92005 + 4.56703i 0.275814 + 0.321335i
\(203\) −2.63311 2.76162i −0.184808 0.193828i
\(204\) 0 0
\(205\) 1.26175 0.0881244
\(206\) −16.4460 + 14.1162i −1.14585 + 0.983521i
\(207\) 0 0
\(208\) 2.88050 9.17074i 0.199727 0.635877i
\(209\) 24.6370i 1.70417i
\(210\) 0 0
\(211\) 5.67817i 0.390901i 0.980714 + 0.195451i \(0.0626170\pi\)
−0.980714 + 0.195451i \(0.937383\pi\)
\(212\) −3.56357 + 23.2374i −0.244747 + 1.59595i
\(213\) 0 0
\(214\) 4.45667 + 5.19222i 0.304651 + 0.354933i
\(215\) 2.19850 0.149936
\(216\) 0 0
\(217\) −19.9949 20.9708i −1.35735 1.42359i
\(218\) −9.41281 + 8.07935i −0.637516 + 0.547203i
\(219\) 0 0
\(220\) 1.89189 12.3366i 0.127551 0.831736i
\(221\) 3.14251 0.211388
\(222\) 0 0
\(223\) −3.97664 −0.266296 −0.133148 0.991096i \(-0.542509\pi\)
−0.133148 + 0.991096i \(0.542509\pi\)
\(224\) 13.7603 + 5.88668i 0.919402 + 0.393320i
\(225\) 0 0
\(226\) 4.39454 3.77199i 0.292321 0.250909i
\(227\) −2.54691 −0.169045 −0.0845223 0.996422i \(-0.526936\pi\)
−0.0845223 + 0.996422i \(0.526936\pi\)
\(228\) 0 0
\(229\) 10.6638i 0.704681i −0.935872 0.352341i \(-0.885386\pi\)
0.935872 0.352341i \(-0.114614\pi\)
\(230\) 3.81652 3.27586i 0.251654 0.216004i
\(231\) 0 0
\(232\) −2.15693 3.46229i −0.141609 0.227311i
\(233\) 20.4421 1.33921 0.669605 0.742718i \(-0.266464\pi\)
0.669605 + 0.742718i \(0.266464\pi\)
\(234\) 0 0
\(235\) 11.6743i 0.761546i
\(236\) 0.125925 0.821137i 0.00819705 0.0534515i
\(237\) 0 0
\(238\) −0.487992 + 4.86849i −0.0316318 + 0.315577i
\(239\) 4.38800i 0.283836i −0.989878 0.141918i \(-0.954673\pi\)
0.989878 0.141918i \(-0.0453270\pi\)
\(240\) 0 0
\(241\) 22.5909i 1.45521i −0.685996 0.727605i \(-0.740633\pi\)
0.685996 0.727605i \(-0.259367\pi\)
\(242\) 29.9861 25.7382i 1.92758 1.65451i
\(243\) 0 0
\(244\) 25.0764 + 3.84559i 1.60535 + 0.246189i
\(245\) 6.99206 + 0.333303i 0.446706 + 0.0212940i
\(246\) 0 0
\(247\) 9.48742i 0.603670i
\(248\) −16.3790 26.2914i −1.04007 1.66951i
\(249\) 0 0
\(250\) −0.921096 1.07312i −0.0582552 0.0678700i
\(251\) 12.0822 0.762624 0.381312 0.924446i \(-0.375472\pi\)
0.381312 + 0.924446i \(0.375472\pi\)
\(252\) 0 0
\(253\) 22.1940 1.39532
\(254\) 6.15840 + 7.17481i 0.386412 + 0.450188i
\(255\) 0 0
\(256\) 13.1265 + 9.14853i 0.820405 + 0.571783i
\(257\) 14.1869i 0.884957i −0.896779 0.442478i \(-0.854099\pi\)
0.896779 0.442478i \(-0.145901\pi\)
\(258\) 0 0
\(259\) −9.24311 9.69422i −0.574339 0.602369i
\(260\) 0.728544 4.75070i 0.0451824 0.294626i
\(261\) 0 0
\(262\) −14.3056 + 12.2790i −0.883801 + 0.758598i
\(263\) 13.5093i 0.833021i 0.909131 + 0.416511i \(0.136747\pi\)
−0.909131 + 0.416511i \(0.863253\pi\)
\(264\) 0 0
\(265\) 11.7545i 0.722074i
\(266\) −14.6983 1.47328i −0.901208 0.0903324i
\(267\) 0 0
\(268\) 6.13027 + 0.940108i 0.374466 + 0.0574262i
\(269\) 9.57770i 0.583963i −0.956424 0.291981i \(-0.905685\pi\)
0.956424 0.291981i \(-0.0943145\pi\)
\(270\) 0 0
\(271\) −7.20379 −0.437599 −0.218800 0.975770i \(-0.570214\pi\)
−0.218800 + 0.975770i \(0.570214\pi\)
\(272\) −1.56745 + 4.99034i −0.0950406 + 0.302584i
\(273\) 0 0
\(274\) 6.00771 5.15663i 0.362939 0.311524i
\(275\) 6.24043i 0.376312i
\(276\) 0 0
\(277\) 22.2563 1.33725 0.668627 0.743598i \(-0.266882\pi\)
0.668627 + 0.743598i \(0.266882\pi\)
\(278\) −6.58398 + 5.65126i −0.394881 + 0.338940i
\(279\) 0 0
\(280\) 7.24683 + 1.86641i 0.433081 + 0.111539i
\(281\) −27.2215 −1.62390 −0.811950 0.583727i \(-0.801594\pi\)
−0.811950 + 0.583727i \(0.801594\pi\)
\(282\) 0 0
\(283\) 18.6312 1.10751 0.553754 0.832680i \(-0.313195\pi\)
0.553754 + 0.832680i \(0.313195\pi\)
\(284\) 20.7103 + 3.17603i 1.22893 + 0.188463i
\(285\) 0 0
\(286\) 16.0930 13.8132i 0.951601 0.816793i
\(287\) −2.41606 + 2.30363i −0.142616 + 0.135979i
\(288\) 0 0
\(289\) 15.2900 0.899410
\(290\) −1.32842 1.54766i −0.0780073 0.0908820i
\(291\) 0 0
\(292\) 3.24488 + 0.497619i 0.189892 + 0.0291210i
\(293\) 15.4578i 0.903057i −0.892257 0.451528i \(-0.850879\pi\)
0.892257 0.451528i \(-0.149121\pi\)
\(294\) 0 0
\(295\) 0.415368i 0.0241837i
\(296\) −7.57155 12.1538i −0.440088 0.706426i
\(297\) 0 0
\(298\) −13.2535 + 11.3760i −0.767756 + 0.658992i
\(299\) 8.54664 0.494265
\(300\) 0 0
\(301\) −4.20979 + 4.01389i −0.242648 + 0.231357i
\(302\) 14.7056 + 17.1327i 0.846213 + 0.985877i
\(303\) 0 0
\(304\) −15.0661 4.73222i −0.864101 0.271412i
\(305\) 12.6848 0.726329
\(306\) 0 0
\(307\) 30.4225 1.73630 0.868151 0.496299i \(-0.165308\pi\)
0.868151 + 0.496299i \(0.165308\pi\)
\(308\) 18.9009 + 27.0769i 1.07698 + 1.54285i
\(309\) 0 0
\(310\) −10.0875 11.7524i −0.572933 0.667493i
\(311\) −6.24557 −0.354154 −0.177077 0.984197i \(-0.556664\pi\)
−0.177077 + 0.984197i \(0.556664\pi\)
\(312\) 0 0
\(313\) 14.5063i 0.819945i −0.912098 0.409973i \(-0.865538\pi\)
0.912098 0.409973i \(-0.134462\pi\)
\(314\) −4.75254 5.53692i −0.268201 0.312467i
\(315\) 0 0
\(316\) 18.1667 + 2.78595i 1.02195 + 0.156722i
\(317\) −2.29755 −0.129043 −0.0645215 0.997916i \(-0.520552\pi\)
−0.0645215 + 0.997916i \(0.520552\pi\)
\(318\) 0 0
\(319\) 9.00003i 0.503905i
\(320\) 7.18078 + 3.52653i 0.401418 + 0.197139i
\(321\) 0 0
\(322\) −1.32719 + 13.2408i −0.0739612 + 0.737879i
\(323\) 5.16266i 0.287258i
\(324\) 0 0
\(325\) 2.40312i 0.133301i
\(326\) 1.17251 + 1.36603i 0.0649393 + 0.0756572i
\(327\) 0 0
\(328\) −3.02906 + 1.88704i −0.167252 + 0.104194i
\(329\) 21.3143 + 22.3545i 1.17509 + 1.23244i
\(330\) 0 0
\(331\) 23.4483i 1.28884i 0.764673 + 0.644419i \(0.222901\pi\)
−0.764673 + 0.644419i \(0.777099\pi\)
\(332\) 2.24319 14.6274i 0.123111 0.802785i
\(333\) 0 0
\(334\) 23.2467 19.9535i 1.27200 1.09181i
\(335\) 3.10097 0.169424
\(336\) 0 0
\(337\) 14.6709 0.799174 0.399587 0.916695i \(-0.369153\pi\)
0.399587 + 0.916695i \(0.369153\pi\)
\(338\) −7.75329 + 6.65493i −0.421723 + 0.361980i
\(339\) 0 0
\(340\) −0.396443 + 2.58513i −0.0215002 + 0.140199i
\(341\) 68.3431i 3.70099i
\(342\) 0 0
\(343\) −13.9973 + 12.1275i −0.755782 + 0.654823i
\(344\) −5.27789 + 3.28801i −0.284565 + 0.177277i
\(345\) 0 0
\(346\) −11.9530 13.9258i −0.642596 0.748654i
\(347\) 21.6099i 1.16008i 0.814587 + 0.580041i \(0.196964\pi\)
−0.814587 + 0.580041i \(0.803036\pi\)
\(348\) 0 0
\(349\) 0.885917i 0.0474220i −0.999719 0.0237110i \(-0.992452\pi\)
0.999719 0.0237110i \(-0.00754816\pi\)
\(350\) 3.72300 + 0.373174i 0.199003 + 0.0199470i
\(351\) 0 0
\(352\) 13.9085 + 32.4458i 0.741326 + 1.72937i
\(353\) 14.2476i 0.758325i −0.925330 0.379163i \(-0.876212\pi\)
0.925330 0.379163i \(-0.123788\pi\)
\(354\) 0 0
\(355\) 10.4762 0.556019
\(356\) 22.6251 + 3.46967i 1.19913 + 0.183892i
\(357\) 0 0
\(358\) −13.9553 16.2586i −0.737560 0.859291i
\(359\) 23.9005i 1.26142i −0.776018 0.630710i \(-0.782764\pi\)
0.776018 0.630710i \(-0.217236\pi\)
\(360\) 0 0
\(361\) −3.41362 −0.179664
\(362\) 2.69288 + 3.13733i 0.141535 + 0.164894i
\(363\) 0 0
\(364\) 7.27852 + 10.4270i 0.381498 + 0.546524i
\(365\) 1.64141 0.0859153
\(366\) 0 0
\(367\) −32.8358 −1.71401 −0.857007 0.515304i \(-0.827679\pi\)
−0.857007 + 0.515304i \(0.827679\pi\)
\(368\) −4.26297 + 13.5722i −0.222223 + 0.707498i
\(369\) 0 0
\(370\) −4.66319 5.43282i −0.242427 0.282439i
\(371\) −21.4608 22.5081i −1.11419 1.16856i
\(372\) 0 0
\(373\) 11.9520 0.618852 0.309426 0.950923i \(-0.399863\pi\)
0.309426 + 0.950923i \(0.399863\pi\)
\(374\) −8.75716 + 7.51658i −0.452822 + 0.388673i
\(375\) 0 0
\(376\) 17.4597 + 28.0262i 0.900416 + 1.44534i
\(377\) 3.46581i 0.178498i
\(378\) 0 0
\(379\) 21.9351i 1.12673i 0.826208 + 0.563366i \(0.190494\pi\)
−0.826208 + 0.563366i \(0.809506\pi\)
\(380\) −7.80468 1.19689i −0.400371 0.0613990i
\(381\) 0 0
\(382\) −12.8471 14.9675i −0.657316 0.765803i
\(383\) 28.3845 1.45038 0.725190 0.688549i \(-0.241752\pi\)
0.725190 + 0.688549i \(0.241752\pi\)
\(384\) 0 0
\(385\) 11.3934 + 11.9495i 0.580664 + 0.609003i
\(386\) 14.3657 12.3306i 0.731194 0.627610i
\(387\) 0 0
\(388\) −24.5991 3.77239i −1.24883 0.191514i
\(389\) −22.0568 −1.11832 −0.559162 0.829058i \(-0.688877\pi\)
−0.559162 + 0.829058i \(0.688877\pi\)
\(390\) 0 0
\(391\) −4.65073 −0.235197
\(392\) −17.2842 + 9.65697i −0.872983 + 0.487751i
\(393\) 0 0
\(394\) 4.37821 3.75797i 0.220571 0.189324i
\(395\) 9.18952 0.462375
\(396\) 0 0
\(397\) 37.0058i 1.85727i −0.370997 0.928634i \(-0.620984\pi\)
0.370997 0.928634i \(-0.379016\pi\)
\(398\) 3.93710 3.37935i 0.197349 0.169392i
\(399\) 0 0
\(400\) 3.81618 + 1.19865i 0.190809 + 0.0599325i
\(401\) 1.70729 0.0852580 0.0426290 0.999091i \(-0.486427\pi\)
0.0426290 + 0.999091i \(0.486427\pi\)
\(402\) 0 0
\(403\) 26.3182i 1.31100i
\(404\) −8.41335 1.29023i −0.418580 0.0641913i
\(405\) 0 0
\(406\) 5.36936 + 0.538197i 0.266477 + 0.0267103i
\(407\) 31.5931i 1.56601i
\(408\) 0 0
\(409\) 26.3062i 1.30076i 0.759609 + 0.650379i \(0.225390\pi\)
−0.759609 + 0.650379i \(0.774610\pi\)
\(410\) −1.35401 + 1.16219i −0.0668696 + 0.0573965i
\(411\) 0 0
\(412\) 4.64614 30.2967i 0.228899 1.49261i
\(413\) 0.758357 + 0.795368i 0.0373163 + 0.0391375i
\(414\) 0 0
\(415\) 7.39922i 0.363213i
\(416\) 5.35601 + 12.4945i 0.262600 + 0.612594i
\(417\) 0 0
\(418\) −22.6930 26.4384i −1.10995 1.29314i
\(419\) 5.33293 0.260531 0.130265 0.991479i \(-0.458417\pi\)
0.130265 + 0.991479i \(0.458417\pi\)
\(420\) 0 0
\(421\) −14.7096 −0.716903 −0.358451 0.933548i \(-0.616695\pi\)
−0.358451 + 0.933548i \(0.616695\pi\)
\(422\) −5.23014 6.09335i −0.254599 0.296620i
\(423\) 0 0
\(424\) −17.5797 28.2188i −0.853746 1.37043i
\(425\) 1.30768i 0.0634317i
\(426\) 0 0
\(427\) −24.2895 + 23.1592i −1.17545 + 1.12075i
\(428\) −9.56506 1.46685i −0.462345 0.0709029i
\(429\) 0 0
\(430\) −2.35925 + 2.02502i −0.113773 + 0.0976554i
\(431\) 20.0200i 0.964331i −0.876080 0.482166i \(-0.839850\pi\)
0.876080 0.482166i \(-0.160150\pi\)
\(432\) 0 0
\(433\) 8.87770i 0.426635i 0.976983 + 0.213317i \(0.0684268\pi\)
−0.976983 + 0.213317i \(0.931573\pi\)
\(434\) 40.7730 + 4.08688i 1.95717 + 0.196176i
\(435\) 0 0
\(436\) 2.65921 17.3402i 0.127353 0.830445i
\(437\) 14.0408i 0.671664i
\(438\) 0 0
\(439\) −25.3037 −1.20768 −0.603841 0.797105i \(-0.706364\pi\)
−0.603841 + 0.797105i \(0.706364\pi\)
\(440\) 9.33301 + 14.9813i 0.444934 + 0.714205i
\(441\) 0 0
\(442\) −3.37228 + 2.89455i −0.160403 + 0.137680i
\(443\) 27.9709i 1.32894i −0.747317 0.664468i \(-0.768658\pi\)
0.747317 0.664468i \(-0.231342\pi\)
\(444\) 0 0
\(445\) 11.4448 0.542535
\(446\) 4.26741 3.66287i 0.202068 0.173442i
\(447\) 0 0
\(448\) −20.1887 + 6.35749i −0.953825 + 0.300363i
\(449\) 36.0790 1.70267 0.851337 0.524619i \(-0.175792\pi\)
0.851337 + 0.524619i \(0.175792\pi\)
\(450\) 0 0
\(451\) −7.87386 −0.370765
\(452\) −1.24150 + 8.09559i −0.0583952 + 0.380784i
\(453\) 0 0
\(454\) 2.73314 2.34595i 0.128273 0.110101i
\(455\) 4.38749 + 4.60162i 0.205689 + 0.215727i
\(456\) 0 0
\(457\) −4.26370 −0.199448 −0.0997238 0.995015i \(-0.531796\pi\)
−0.0997238 + 0.995015i \(0.531796\pi\)
\(458\) 9.82235 + 11.4435i 0.458968 + 0.534719i
\(459\) 0 0
\(460\) −1.07820 + 7.03076i −0.0502714 + 0.327811i
\(461\) 18.7953i 0.875386i 0.899124 + 0.437693i \(0.144204\pi\)
−0.899124 + 0.437693i \(0.855796\pi\)
\(462\) 0 0
\(463\) 38.2151i 1.77601i −0.459836 0.888004i \(-0.652092\pi\)
0.459836 0.888004i \(-0.347908\pi\)
\(464\) 5.50374 + 1.72871i 0.255505 + 0.0802533i
\(465\) 0 0
\(466\) −21.9368 + 18.8292i −1.01620 + 0.872244i
\(467\) −15.7945 −0.730882 −0.365441 0.930834i \(-0.619082\pi\)
−0.365441 + 0.930834i \(0.619082\pi\)
\(468\) 0 0
\(469\) −5.93789 + 5.66158i −0.274186 + 0.261428i
\(470\) 10.7531 + 12.5279i 0.496005 + 0.577868i
\(471\) 0 0
\(472\) 0.621213 + 0.997166i 0.0285936 + 0.0458983i
\(473\) −13.7196 −0.630826
\(474\) 0 0
\(475\) −3.94796 −0.181145
\(476\) −3.96067 5.67395i −0.181537 0.260065i
\(477\) 0 0
\(478\) 4.04177 + 4.70885i 0.184866 + 0.215378i
\(479\) −33.1809 −1.51608 −0.758038 0.652210i \(-0.773842\pi\)
−0.758038 + 0.652210i \(0.773842\pi\)
\(480\) 0 0
\(481\) 12.1662i 0.554729i
\(482\) 20.8084 + 24.2428i 0.947798 + 1.10423i
\(483\) 0 0
\(484\) −8.47136 + 55.2402i −0.385062 + 2.51092i
\(485\) −12.4433 −0.565022
\(486\) 0 0
\(487\) 18.8854i 0.855781i 0.903831 + 0.427891i \(0.140743\pi\)
−0.903831 + 0.427891i \(0.859257\pi\)
\(488\) −30.4521 + 18.9710i −1.37850 + 0.858777i
\(489\) 0 0
\(490\) −7.81031 + 6.08268i −0.352834 + 0.274788i
\(491\) 1.14336i 0.0515989i 0.999667 + 0.0257995i \(0.00821314\pi\)
−0.999667 + 0.0257995i \(0.991787\pi\)
\(492\) 0 0
\(493\) 1.88595i 0.0849389i
\(494\) −8.73882 10.1811i −0.393178 0.458070i
\(495\) 0 0
\(496\) 41.7935 + 13.1272i 1.87658 + 0.589429i
\(497\) −20.0604 + 19.1269i −0.899831 + 0.857959i
\(498\) 0 0
\(499\) 18.8734i 0.844890i 0.906389 + 0.422445i \(0.138828\pi\)
−0.906389 + 0.422445i \(0.861172\pi\)
\(500\) 1.97689 + 0.303166i 0.0884092 + 0.0135580i
\(501\) 0 0
\(502\) −12.9657 + 11.1289i −0.578686 + 0.496707i
\(503\) 18.8624 0.841035 0.420517 0.907284i \(-0.361849\pi\)
0.420517 + 0.907284i \(0.361849\pi\)
\(504\) 0 0
\(505\) −4.25585 −0.189383
\(506\) −23.8167 + 20.4428i −1.05878 + 0.908791i
\(507\) 0 0
\(508\) −13.2174 2.02695i −0.586426 0.0899314i
\(509\) 24.1765i 1.07160i −0.844344 0.535801i \(-0.820010\pi\)
0.844344 0.535801i \(-0.179990\pi\)
\(510\) 0 0
\(511\) −3.14305 + 2.99680i −0.139040 + 0.132570i
\(512\) −22.5129 + 2.27328i −0.994941 + 0.100466i
\(513\) 0 0
\(514\) 13.0675 + 15.2243i 0.576384 + 0.671513i
\(515\) 15.3254i 0.675319i
\(516\) 0 0
\(517\) 72.8525i 3.20405i
\(518\) 18.8483 + 1.88925i 0.828145 + 0.0830089i
\(519\) 0 0
\(520\) 3.59404 + 5.76913i 0.157609 + 0.252993i
\(521\) 17.2367i 0.755152i 0.925979 + 0.377576i \(0.123242\pi\)
−0.925979 + 0.377576i \(0.876758\pi\)
\(522\) 0 0
\(523\) 14.1555 0.618975 0.309487 0.950904i \(-0.399843\pi\)
0.309487 + 0.950904i \(0.399843\pi\)
\(524\) 4.04145 26.3536i 0.176552 1.15126i
\(525\) 0 0
\(526\) −12.4434 14.4971i −0.542557 0.632104i
\(527\) 14.3212i 0.623843i
\(528\) 0 0
\(529\) 10.3515 0.450064
\(530\) −10.8270 12.6140i −0.470296 0.547916i
\(531\) 0 0
\(532\) 17.1300 11.9575i 0.742680 0.518423i
\(533\) −3.03213 −0.131336
\(534\) 0 0
\(535\) −4.83844 −0.209184
\(536\) −7.44444 + 4.63772i −0.321551 + 0.200319i
\(537\) 0 0
\(538\) 8.82198 + 10.2780i 0.380342 + 0.443116i
\(539\) −43.6335 2.07996i −1.87943 0.0895900i
\(540\) 0 0
\(541\) 20.6842 0.889283 0.444642 0.895709i \(-0.353331\pi\)
0.444642 + 0.895709i \(0.353331\pi\)
\(542\) 7.73052 6.63538i 0.332054 0.285014i
\(543\) 0 0
\(544\) −2.91452 6.79899i −0.124959 0.291504i
\(545\) 8.77146i 0.375728i
\(546\) 0 0
\(547\) 14.1854i 0.606526i −0.952907 0.303263i \(-0.901924\pi\)
0.952907 0.303263i \(-0.0980760\pi\)
\(548\) −1.69723 + 11.0674i −0.0725023 + 0.472774i
\(549\) 0 0
\(550\) 5.74803 + 6.69672i 0.245097 + 0.285549i
\(551\) −5.69380 −0.242564
\(552\) 0 0
\(553\) −17.5966 + 16.7777i −0.748282 + 0.713462i
\(554\) −23.8837 + 20.5002i −1.01472 + 0.870971i
\(555\) 0 0
\(556\) 1.86003 12.1289i 0.0788830 0.514382i
\(557\) 23.5297 0.996987 0.498494 0.866893i \(-0.333887\pi\)
0.498494 + 0.866893i \(0.333887\pi\)
\(558\) 0 0
\(559\) −5.28325 −0.223458
\(560\) −9.49585 + 4.67214i −0.401273 + 0.197434i
\(561\) 0 0
\(562\) 29.2119 25.0736i 1.23223 1.05767i
\(563\) 30.5742 1.28855 0.644275 0.764794i \(-0.277159\pi\)
0.644275 + 0.764794i \(0.277159\pi\)
\(564\) 0 0
\(565\) 4.09511i 0.172283i
\(566\) −19.9935 + 17.1611i −0.840388 + 0.721335i
\(567\) 0 0
\(568\) −25.1500 + 15.6679i −1.05527 + 0.657411i
\(569\) −12.0943 −0.507018 −0.253509 0.967333i \(-0.581585\pi\)
−0.253509 + 0.967333i \(0.581585\pi\)
\(570\) 0 0
\(571\) 20.1686i 0.844029i 0.906589 + 0.422015i \(0.138677\pi\)
−0.906589 + 0.422015i \(0.861323\pi\)
\(572\) −4.54643 + 29.6464i −0.190096 + 1.23958i
\(573\) 0 0
\(574\) 0.470852 4.69749i 0.0196530 0.196070i
\(575\) 3.55648i 0.148315i
\(576\) 0 0
\(577\) 2.82405i 0.117567i −0.998271 0.0587834i \(-0.981278\pi\)
0.998271 0.0587834i \(-0.0187221\pi\)
\(578\) −16.4080 + 14.0835i −0.682481 + 0.585798i
\(579\) 0 0
\(580\) 2.85109 + 0.437230i 0.118385 + 0.0181550i
\(581\) 13.5091 + 14.1684i 0.560451 + 0.587804i
\(582\) 0 0
\(583\) 73.3532i 3.03798i
\(584\) −3.94050 + 2.45484i −0.163059 + 0.101582i
\(585\) 0 0
\(586\) 14.2381 + 16.5881i 0.588172 + 0.685248i
\(587\) −0.0213868 −0.000882727 −0.000441363 1.00000i \(-0.500140\pi\)
−0.000441363 1.00000i \(0.500140\pi\)
\(588\) 0 0
\(589\) −43.2367 −1.78154
\(590\) 0.382594 + 0.445739i 0.0157511 + 0.0183508i
\(591\) 0 0
\(592\) 19.3200 + 6.06835i 0.794047 + 0.249408i
\(593\) 31.7082i 1.30210i −0.759036 0.651049i \(-0.774329\pi\)
0.759036 0.651049i \(-0.225671\pi\)
\(594\) 0 0
\(595\) −2.38749 2.50401i −0.0978775 0.102654i
\(596\) 3.74424 24.4155i 0.153370 1.00010i
\(597\) 0 0
\(598\) −9.17156 + 7.87228i −0.375053 + 0.321921i
\(599\) 17.4804i 0.714229i −0.934061 0.357114i \(-0.883761\pi\)
0.934061 0.357114i \(-0.116239\pi\)
\(600\) 0 0
\(601\) 45.4399i 1.85353i −0.375637 0.926767i \(-0.622576\pi\)
0.375637 0.926767i \(-0.377424\pi\)
\(602\) 0.820422 8.18500i 0.0334379 0.333596i
\(603\) 0 0
\(604\) −31.5617 4.84015i −1.28423 0.196943i
\(605\) 27.9430i 1.13604i
\(606\) 0 0
\(607\) 12.3160 0.499893 0.249946 0.968260i \(-0.419587\pi\)
0.249946 + 0.968260i \(0.419587\pi\)
\(608\) 20.5266 8.79911i 0.832462 0.356851i
\(609\) 0 0
\(610\) −13.6123 + 11.6839i −0.551145 + 0.473067i
\(611\) 28.0547i 1.13497i
\(612\) 0 0
\(613\) 27.3548 1.10485 0.552424 0.833563i \(-0.313703\pi\)
0.552424 + 0.833563i \(0.313703\pi\)
\(614\) −32.6469 + 28.0220i −1.31752 + 1.13088i
\(615\) 0 0
\(616\) −45.2233 11.6472i −1.82210 0.469280i
\(617\) 44.5457 1.79334 0.896671 0.442698i \(-0.145979\pi\)
0.896671 + 0.442698i \(0.145979\pi\)
\(618\) 0 0
\(619\) 23.1713 0.931334 0.465667 0.884960i \(-0.345815\pi\)
0.465667 + 0.884960i \(0.345815\pi\)
\(620\) 21.6502 + 3.32017i 0.869494 + 0.133341i
\(621\) 0 0
\(622\) 6.70223 5.75276i 0.268735 0.230665i
\(623\) −21.9150 + 20.8953i −0.878008 + 0.837151i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 13.3617 + 15.5670i 0.534041 + 0.622182i
\(627\) 0 0
\(628\) 10.2001 + 1.56423i 0.407027 + 0.0624197i
\(629\) 6.62032i 0.263969i
\(630\) 0 0
\(631\) 10.4615i 0.416464i 0.978079 + 0.208232i \(0.0667709\pi\)
−0.978079 + 0.208232i \(0.933229\pi\)
\(632\) −22.0611 + 13.7436i −0.877543 + 0.546690i
\(633\) 0 0
\(634\) 2.46554 2.11626i 0.0979190 0.0840474i
\(635\) −6.68595 −0.265324
\(636\) 0 0
\(637\) −16.8028 0.800968i −0.665750 0.0317355i
\(638\) 8.28989 + 9.65810i 0.328200 + 0.382368i
\(639\) 0 0
\(640\) −10.9541 + 2.82979i −0.432999 + 0.111857i
\(641\) −21.4122 −0.845731 −0.422866 0.906192i \(-0.638976\pi\)
−0.422866 + 0.906192i \(0.638976\pi\)
\(642\) 0 0
\(643\) 26.2531 1.03532 0.517661 0.855586i \(-0.326803\pi\)
0.517661 + 0.855586i \(0.326803\pi\)
\(644\) −10.7718 15.4314i −0.424468 0.608081i
\(645\) 0 0
\(646\) 4.75530 + 5.54014i 0.187095 + 0.217974i
\(647\) −6.99553 −0.275023 −0.137511 0.990500i \(-0.543910\pi\)
−0.137511 + 0.990500i \(0.543910\pi\)
\(648\) 0 0
\(649\) 2.59208i 0.101748i
\(650\) 2.21350 + 2.57883i 0.0868208 + 0.101150i
\(651\) 0 0
\(652\) −2.51648 0.385915i −0.0985530 0.0151136i
\(653\) −21.1729 −0.828559 −0.414280 0.910150i \(-0.635966\pi\)
−0.414280 + 0.910150i \(0.635966\pi\)
\(654\) 0 0
\(655\) 13.3308i 0.520879i
\(656\) 1.51240 4.81506i 0.0590491 0.187997i
\(657\) 0 0
\(658\) −43.4634 4.35654i −1.69438 0.169836i
\(659\) 21.4552i 0.835774i 0.908499 + 0.417887i \(0.137229\pi\)
−0.908499 + 0.417887i \(0.862771\pi\)
\(660\) 0 0
\(661\) 19.5116i 0.758914i −0.925209 0.379457i \(-0.876111\pi\)
0.925209 0.379457i \(-0.123889\pi\)
\(662\) −21.5982 25.1628i −0.839437 0.977982i
\(663\) 0 0
\(664\) 11.0661 + 17.7632i 0.429446 + 0.689344i
\(665\) 7.55975 7.20797i 0.293155 0.279513i
\(666\) 0 0
\(667\) 5.12920i 0.198603i
\(668\) −6.56741 + 42.8249i −0.254101 + 1.65695i
\(669\) 0 0
\(670\) −3.32771 + 2.85629i −0.128561 + 0.110348i
\(671\) −79.1585 −3.05588
\(672\) 0 0
\(673\) 2.26978 0.0874936 0.0437468 0.999043i \(-0.486071\pi\)
0.0437468 + 0.999043i \(0.486071\pi\)
\(674\) −15.7436 + 13.5133i −0.606421 + 0.520513i
\(675\) 0 0
\(676\) 2.19038 14.2830i 0.0842452 0.549348i
\(677\) 17.8761i 0.687035i 0.939146 + 0.343518i \(0.111619\pi\)
−0.939146 + 0.343518i \(0.888381\pi\)
\(678\) 0 0
\(679\) 23.8271 22.7183i 0.914400 0.871850i
\(680\) −1.95573 3.13932i −0.0749986 0.120387i
\(681\) 0 0
\(682\) 62.9505 + 73.3402i 2.41050 + 2.80834i
\(683\) 4.47109i 0.171081i −0.996335 0.0855407i \(-0.972738\pi\)
0.996335 0.0855407i \(-0.0272618\pi\)
\(684\) 0 0
\(685\) 5.59837i 0.213903i
\(686\) 3.85015 25.9071i 0.146999 0.989137i
\(687\) 0 0
\(688\) 2.63523 8.38986i 0.100467 0.319860i
\(689\) 28.2475i 1.07614i
\(690\) 0 0
\(691\) −2.13713 −0.0813003 −0.0406502 0.999173i \(-0.512943\pi\)
−0.0406502 + 0.999173i \(0.512943\pi\)
\(692\) 25.6539 + 3.93416i 0.975216 + 0.149554i
\(693\) 0 0
\(694\) −19.9048 23.1900i −0.755577 0.880281i
\(695\) 6.13537i 0.232728i
\(696\) 0 0
\(697\) 1.64996 0.0624967
\(698\) 0.816014 + 0.950694i 0.0308866 + 0.0359843i
\(699\) 0 0
\(700\) −4.33895 + 3.02878i −0.163997 + 0.114477i
\(701\) −2.37715 −0.0897836 −0.0448918 0.998992i \(-0.514294\pi\)
−0.0448918 + 0.998992i \(0.514294\pi\)
\(702\) 0 0
\(703\) −19.9871 −0.753829
\(704\) −44.8111 22.0071i −1.68888 0.829424i
\(705\) 0 0
\(706\) 13.1234 + 15.2894i 0.493907 + 0.575424i
\(707\) 8.14932 7.77011i 0.306487 0.292225i
\(708\) 0 0
\(709\) −11.2074 −0.420904 −0.210452 0.977604i \(-0.567494\pi\)
−0.210452 + 0.977604i \(0.567494\pi\)
\(710\) −11.2422 + 9.64959i −0.421913 + 0.362143i
\(711\) 0 0
\(712\) −27.4753 + 17.1165i −1.02968 + 0.641467i
\(713\) 38.9493i 1.45866i
\(714\) 0 0
\(715\) 14.9965i 0.560838i
\(716\) 29.9514 + 4.59319i 1.11934 + 0.171656i
\(717\) 0 0
\(718\) 22.0147 + 25.6481i 0.821580 + 0.957178i
\(719\) 43.4702 1.62116 0.810582 0.585624i \(-0.199151\pi\)
0.810582 + 0.585624i \(0.199151\pi\)
\(720\) 0 0
\(721\) 27.9803 + 29.3459i 1.04204 + 1.09290i
\(722\) 3.66322 3.14427i 0.136331 0.117018i
\(723\) 0 0
\(724\) −5.77956 0.886324i −0.214795 0.0329400i
\(725\) 1.44221 0.0535624
\(726\) 0 0
\(727\) −8.53645 −0.316599 −0.158300 0.987391i \(-0.550601\pi\)
−0.158300 + 0.987391i \(0.550601\pi\)
\(728\) −17.4150 4.48521i −0.645443 0.166233i
\(729\) 0 0
\(730\) −1.76143 + 1.51189i −0.0651933 + 0.0559577i
\(731\) 2.87492 0.106333
\(732\) 0 0
\(733\) 12.7274i 0.470098i −0.971984 0.235049i \(-0.924475\pi\)
0.971984 0.235049i \(-0.0755250\pi\)
\(734\) 35.2367 30.2449i 1.30061 1.11636i
\(735\) 0 0
\(736\) −7.92658 18.4911i −0.292178 0.681592i
\(737\) −19.3514 −0.712818
\(738\) 0 0
\(739\) 17.6922i 0.650817i −0.945573 0.325409i \(-0.894498\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(740\) 10.0083 + 1.53482i 0.367912 + 0.0564212i
\(741\) 0 0
\(742\) 43.7621 + 4.38648i 1.60656 + 0.161033i
\(743\) 11.0428i 0.405122i −0.979270 0.202561i \(-0.935074\pi\)
0.979270 0.202561i \(-0.0649265\pi\)
\(744\) 0 0
\(745\) 12.3505i 0.452486i
\(746\) −12.8259 + 11.0090i −0.469591 + 0.403066i
\(747\) 0 0
\(748\) 2.47398 16.1324i 0.0904576 0.589857i
\(749\) 9.26489 8.83376i 0.338532 0.322779i
\(750\) 0 0
\(751\) 18.4917i 0.674771i 0.941367 + 0.337385i \(0.109543\pi\)
−0.941367 + 0.337385i \(0.890457\pi\)
\(752\) −44.5512 13.9934i −1.62461 0.510286i
\(753\) 0 0
\(754\) 3.19234 + 3.71923i 0.116258 + 0.135446i
\(755\) −15.9654 −0.581039
\(756\) 0 0
\(757\) −20.2498 −0.735992 −0.367996 0.929827i \(-0.619956\pi\)
−0.367996 + 0.929827i \(0.619956\pi\)
\(758\) −20.2043 23.5390i −0.733855 0.854974i
\(759\) 0 0
\(760\) 9.47779 5.90445i 0.343795 0.214177i
\(761\) 25.4306i 0.921857i 0.887437 + 0.460928i \(0.152484\pi\)
−0.887437 + 0.460928i \(0.847516\pi\)
\(762\) 0 0
\(763\) 16.0145 + 16.7960i 0.579762 + 0.608057i
\(764\) 27.5730 + 4.22845i 0.997555 + 0.152980i
\(765\) 0 0
\(766\) −30.4599 + 26.1448i −1.10056 + 0.944651i
\(767\) 0.998180i 0.0360422i
\(768\) 0 0
\(769\) 31.4563i 1.13434i −0.823600 0.567172i \(-0.808038\pi\)
0.823600 0.567172i \(-0.191962\pi\)
\(770\) −23.2331 2.32877i −0.837264 0.0839230i
\(771\) 0 0
\(772\) −4.05844 + 26.4643i −0.146066 + 0.952472i
\(773\) 9.51127i 0.342097i 0.985263 + 0.171048i \(0.0547154\pi\)
−0.985263 + 0.171048i \(0.945285\pi\)
\(774\) 0 0
\(775\) 10.9517 0.393395
\(776\) 29.8724 18.6099i 1.07236 0.668055i
\(777\) 0 0
\(778\) 23.6696 20.3164i 0.848595 0.728379i
\(779\) 4.98133i 0.178475i
\(780\) 0 0
\(781\) −65.3761 −2.33934
\(782\) 4.99078 4.28376i 0.178470 0.153187i
\(783\) 0 0
\(784\) 9.65298 26.2835i 0.344749 0.938695i
\(785\) 5.15966 0.184156
\(786\) 0 0
\(787\) −23.8141 −0.848880 −0.424440 0.905456i \(-0.639529\pi\)
−0.424440 + 0.905456i \(0.639529\pi\)
\(788\) −1.23688 + 8.06550i −0.0440622 + 0.287321i
\(789\) 0 0
\(790\) −9.86144 + 8.46443i −0.350854 + 0.301151i
\(791\) −7.47664 7.84153i −0.265839 0.278813i
\(792\) 0