Properties

Label 207.6.a.f.1.5
Level $207$
Weight $6$
Character 207.1
Self dual yes
Analytic conductor $33.199$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.1994507013\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \( x^{5} - 113x^{3} - 257x^{2} + 1404x + 2197 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 69)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.42196\) of defining polynomial
Character \(\chi\) \(=\) 207.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.32729 q^{2} +54.9984 q^{4} -99.7124 q^{5} +125.983 q^{7} +214.513 q^{8} +O(q^{10})\) \(q+9.32729 q^{2} +54.9984 q^{4} -99.7124 q^{5} +125.983 q^{7} +214.513 q^{8} -930.047 q^{10} -177.715 q^{11} -919.618 q^{13} +1175.08 q^{14} +240.875 q^{16} -1568.24 q^{17} +447.960 q^{19} -5484.02 q^{20} -1657.60 q^{22} +529.000 q^{23} +6817.57 q^{25} -8577.55 q^{26} +6928.86 q^{28} +1298.72 q^{29} -6651.88 q^{31} -4617.70 q^{32} -14627.4 q^{34} -12562.1 q^{35} -8056.80 q^{37} +4178.25 q^{38} -21389.6 q^{40} -17941.4 q^{41} +10710.7 q^{43} -9774.04 q^{44} +4934.14 q^{46} +17886.9 q^{47} -935.293 q^{49} +63589.5 q^{50} -50577.5 q^{52} +20343.9 q^{53} +17720.4 q^{55} +27025.0 q^{56} +12113.5 q^{58} -28488.5 q^{59} +16222.3 q^{61} -62044.1 q^{62} -50778.6 q^{64} +91697.4 q^{65} +54128.0 q^{67} -86250.6 q^{68} -117170. q^{70} -42505.6 q^{71} +40936.2 q^{73} -75148.1 q^{74} +24637.1 q^{76} -22389.1 q^{77} -24760.6 q^{79} -24018.2 q^{80} -167345. q^{82} +30825.2 q^{83} +156373. q^{85} +99901.7 q^{86} -38122.1 q^{88} +66531.6 q^{89} -115856. q^{91} +29094.2 q^{92} +166836. q^{94} -44667.2 q^{95} -104506. q^{97} -8723.75 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 8 q^{2} + 118 q^{4} - 94 q^{5} + 272 q^{7} - 258 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 8 q^{2} + 118 q^{4} - 94 q^{5} + 272 q^{7} - 258 q^{8} - 172 q^{10} - 1100 q^{11} - 978 q^{13} + 344 q^{14} + 1218 q^{16} - 2522 q^{17} + 2060 q^{19} - 7720 q^{20} - 2572 q^{22} + 2645 q^{23} + 12035 q^{25} - 9280 q^{26} + 8072 q^{28} - 1526 q^{29} - 7392 q^{31} + 5086 q^{32} - 15608 q^{34} - 6056 q^{35} - 8210 q^{37} + 14276 q^{38} - 37472 q^{40} - 21250 q^{41} - 4548 q^{43} + 4260 q^{44} - 4232 q^{46} - 536 q^{47} - 27979 q^{49} + 81872 q^{50} - 76380 q^{52} + 11482 q^{53} - 77064 q^{55} + 28624 q^{56} - 79680 q^{58} - 74676 q^{59} - 44618 q^{61} - 64880 q^{62} - 137382 q^{64} + 24388 q^{65} - 1412 q^{67} - 80196 q^{68} - 222304 q^{70} - 37912 q^{71} + 46546 q^{73} - 111604 q^{74} - 79548 q^{76} - 157008 q^{77} + 50544 q^{79} - 69424 q^{80} - 233720 q^{82} - 89588 q^{83} + 147892 q^{85} - 77428 q^{86} + 54484 q^{88} - 280410 q^{89} - 27416 q^{91} + 62422 q^{92} + 113632 q^{94} - 203120 q^{95} + 90074 q^{97} - 32976 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.32729 1.64885 0.824424 0.565973i \(-0.191499\pi\)
0.824424 + 0.565973i \(0.191499\pi\)
\(3\) 0 0
\(4\) 54.9984 1.71870
\(5\) −99.7124 −1.78371 −0.891855 0.452321i \(-0.850596\pi\)
−0.891855 + 0.452321i \(0.850596\pi\)
\(6\) 0 0
\(7\) 125.983 0.971777 0.485889 0.874021i \(-0.338496\pi\)
0.485889 + 0.874021i \(0.338496\pi\)
\(8\) 214.513 1.18503
\(9\) 0 0
\(10\) −930.047 −2.94107
\(11\) −177.715 −0.442835 −0.221418 0.975179i \(-0.571068\pi\)
−0.221418 + 0.975179i \(0.571068\pi\)
\(12\) 0 0
\(13\) −919.618 −1.50921 −0.754604 0.656180i \(-0.772171\pi\)
−0.754604 + 0.656180i \(0.772171\pi\)
\(14\) 1175.08 1.60231
\(15\) 0 0
\(16\) 240.875 0.235229
\(17\) −1568.24 −1.31610 −0.658051 0.752973i \(-0.728619\pi\)
−0.658051 + 0.752973i \(0.728619\pi\)
\(18\) 0 0
\(19\) 447.960 0.284679 0.142339 0.989818i \(-0.454538\pi\)
0.142339 + 0.989818i \(0.454538\pi\)
\(20\) −5484.02 −3.06566
\(21\) 0 0
\(22\) −1657.60 −0.730168
\(23\) 529.000 0.208514
\(24\) 0 0
\(25\) 6817.57 2.18162
\(26\) −8577.55 −2.48846
\(27\) 0 0
\(28\) 6928.86 1.67019
\(29\) 1298.72 0.286760 0.143380 0.989668i \(-0.454203\pi\)
0.143380 + 0.989668i \(0.454203\pi\)
\(30\) 0 0
\(31\) −6651.88 −1.24320 −0.621599 0.783336i \(-0.713517\pi\)
−0.621599 + 0.783336i \(0.713517\pi\)
\(32\) −4617.70 −0.797169
\(33\) 0 0
\(34\) −14627.4 −2.17005
\(35\) −12562.1 −1.73337
\(36\) 0 0
\(37\) −8056.80 −0.967516 −0.483758 0.875202i \(-0.660728\pi\)
−0.483758 + 0.875202i \(0.660728\pi\)
\(38\) 4178.25 0.469392
\(39\) 0 0
\(40\) −21389.6 −2.11374
\(41\) −17941.4 −1.66685 −0.833427 0.552630i \(-0.813624\pi\)
−0.833427 + 0.552630i \(0.813624\pi\)
\(42\) 0 0
\(43\) 10710.7 0.883377 0.441688 0.897169i \(-0.354380\pi\)
0.441688 + 0.897169i \(0.354380\pi\)
\(44\) −9774.04 −0.761101
\(45\) 0 0
\(46\) 4934.14 0.343809
\(47\) 17886.9 1.18111 0.590555 0.806997i \(-0.298909\pi\)
0.590555 + 0.806997i \(0.298909\pi\)
\(48\) 0 0
\(49\) −935.293 −0.0556490
\(50\) 63589.5 3.59716
\(51\) 0 0
\(52\) −50577.5 −2.59388
\(53\) 20343.9 0.994820 0.497410 0.867516i \(-0.334284\pi\)
0.497410 + 0.867516i \(0.334284\pi\)
\(54\) 0 0
\(55\) 17720.4 0.789890
\(56\) 27025.0 1.15158
\(57\) 0 0
\(58\) 12113.5 0.472824
\(59\) −28488.5 −1.06547 −0.532734 0.846283i \(-0.678835\pi\)
−0.532734 + 0.846283i \(0.678835\pi\)
\(60\) 0 0
\(61\) 16222.3 0.558196 0.279098 0.960263i \(-0.409965\pi\)
0.279098 + 0.960263i \(0.409965\pi\)
\(62\) −62044.1 −2.04984
\(63\) 0 0
\(64\) −50778.6 −1.54964
\(65\) 91697.4 2.69199
\(66\) 0 0
\(67\) 54128.0 1.47311 0.736555 0.676378i \(-0.236451\pi\)
0.736555 + 0.676378i \(0.236451\pi\)
\(68\) −86250.6 −2.26198
\(69\) 0 0
\(70\) −117170. −2.85806
\(71\) −42505.6 −1.00069 −0.500346 0.865826i \(-0.666794\pi\)
−0.500346 + 0.865826i \(0.666794\pi\)
\(72\) 0 0
\(73\) 40936.2 0.899084 0.449542 0.893259i \(-0.351587\pi\)
0.449542 + 0.893259i \(0.351587\pi\)
\(74\) −75148.1 −1.59529
\(75\) 0 0
\(76\) 24637.1 0.489277
\(77\) −22389.1 −0.430337
\(78\) 0 0
\(79\) −24760.6 −0.446369 −0.223185 0.974776i \(-0.571645\pi\)
−0.223185 + 0.974776i \(0.571645\pi\)
\(80\) −24018.2 −0.419581
\(81\) 0 0
\(82\) −167345. −2.74839
\(83\) 30825.2 0.491147 0.245573 0.969378i \(-0.421024\pi\)
0.245573 + 0.969378i \(0.421024\pi\)
\(84\) 0 0
\(85\) 156373. 2.34755
\(86\) 99901.7 1.45655
\(87\) 0 0
\(88\) −38122.1 −0.524772
\(89\) 66531.6 0.890334 0.445167 0.895448i \(-0.353144\pi\)
0.445167 + 0.895448i \(0.353144\pi\)
\(90\) 0 0
\(91\) −115856. −1.46661
\(92\) 29094.2 0.358374
\(93\) 0 0
\(94\) 166836. 1.94747
\(95\) −44667.2 −0.507784
\(96\) 0 0
\(97\) −104506. −1.12774 −0.563872 0.825862i \(-0.690689\pi\)
−0.563872 + 0.825862i \(0.690689\pi\)
\(98\) −8723.75 −0.0917568
\(99\) 0 0
\(100\) 374956. 3.74956
\(101\) 203117. 1.98127 0.990635 0.136540i \(-0.0435982\pi\)
0.990635 + 0.136540i \(0.0435982\pi\)
\(102\) 0 0
\(103\) −148132. −1.37580 −0.687901 0.725805i \(-0.741468\pi\)
−0.687901 + 0.725805i \(0.741468\pi\)
\(104\) −197270. −1.78845
\(105\) 0 0
\(106\) 189754. 1.64031
\(107\) 43750.9 0.369426 0.184713 0.982793i \(-0.440864\pi\)
0.184713 + 0.982793i \(0.440864\pi\)
\(108\) 0 0
\(109\) 189052. 1.52410 0.762052 0.647516i \(-0.224192\pi\)
0.762052 + 0.647516i \(0.224192\pi\)
\(110\) 165283. 1.30241
\(111\) 0 0
\(112\) 30346.1 0.228591
\(113\) 82382.3 0.606929 0.303465 0.952843i \(-0.401857\pi\)
0.303465 + 0.952843i \(0.401857\pi\)
\(114\) 0 0
\(115\) −52747.9 −0.371929
\(116\) 71427.2 0.492855
\(117\) 0 0
\(118\) −265721. −1.75679
\(119\) −197571. −1.27896
\(120\) 0 0
\(121\) −129468. −0.803897
\(122\) 151310. 0.920381
\(123\) 0 0
\(124\) −365843. −2.13668
\(125\) −368195. −2.10767
\(126\) 0 0
\(127\) −95322.4 −0.524428 −0.262214 0.965010i \(-0.584453\pi\)
−0.262214 + 0.965010i \(0.584453\pi\)
\(128\) −325861. −1.75795
\(129\) 0 0
\(130\) 855288. 4.43868
\(131\) −181975. −0.926474 −0.463237 0.886234i \(-0.653312\pi\)
−0.463237 + 0.886234i \(0.653312\pi\)
\(132\) 0 0
\(133\) 56435.3 0.276644
\(134\) 504868. 2.42893
\(135\) 0 0
\(136\) −336407. −1.55962
\(137\) −175024. −0.796705 −0.398352 0.917232i \(-0.630418\pi\)
−0.398352 + 0.917232i \(0.630418\pi\)
\(138\) 0 0
\(139\) 199672. 0.876556 0.438278 0.898839i \(-0.355588\pi\)
0.438278 + 0.898839i \(0.355588\pi\)
\(140\) −690894. −2.97914
\(141\) 0 0
\(142\) −396462. −1.64999
\(143\) 163430. 0.668331
\(144\) 0 0
\(145\) −129498. −0.511497
\(146\) 381824. 1.48245
\(147\) 0 0
\(148\) −443111. −1.66287
\(149\) −71174.8 −0.262640 −0.131320 0.991340i \(-0.541921\pi\)
−0.131320 + 0.991340i \(0.541921\pi\)
\(150\) 0 0
\(151\) 133491. 0.476440 0.238220 0.971211i \(-0.423436\pi\)
0.238220 + 0.971211i \(0.423436\pi\)
\(152\) 96093.1 0.337352
\(153\) 0 0
\(154\) −208829. −0.709561
\(155\) 663276. 2.21751
\(156\) 0 0
\(157\) −361773. −1.17135 −0.585675 0.810546i \(-0.699171\pi\)
−0.585675 + 0.810546i \(0.699171\pi\)
\(158\) −230950. −0.735995
\(159\) 0 0
\(160\) 460442. 1.42192
\(161\) 66645.0 0.202630
\(162\) 0 0
\(163\) −627275. −1.84922 −0.924611 0.380912i \(-0.875610\pi\)
−0.924611 + 0.380912i \(0.875610\pi\)
\(164\) −986750. −2.86482
\(165\) 0 0
\(166\) 287516. 0.809826
\(167\) −9849.85 −0.0273299 −0.0136650 0.999907i \(-0.504350\pi\)
−0.0136650 + 0.999907i \(0.504350\pi\)
\(168\) 0 0
\(169\) 474405. 1.27771
\(170\) 1.45854e6 3.87075
\(171\) 0 0
\(172\) 589070. 1.51826
\(173\) 250617. 0.636641 0.318320 0.947983i \(-0.396881\pi\)
0.318320 + 0.947983i \(0.396881\pi\)
\(174\) 0 0
\(175\) 858898. 2.12005
\(176\) −42807.1 −0.104168
\(177\) 0 0
\(178\) 620560. 1.46802
\(179\) −742331. −1.73167 −0.865835 0.500330i \(-0.833212\pi\)
−0.865835 + 0.500330i \(0.833212\pi\)
\(180\) 0 0
\(181\) −292957. −0.664673 −0.332336 0.943161i \(-0.607837\pi\)
−0.332336 + 0.943161i \(0.607837\pi\)
\(182\) −1.08062e6 −2.41822
\(183\) 0 0
\(184\) 113477. 0.247095
\(185\) 803363. 1.72577
\(186\) 0 0
\(187\) 278699. 0.582817
\(188\) 983751. 2.02997
\(189\) 0 0
\(190\) −416624. −0.837259
\(191\) −57674.2 −0.114393 −0.0571963 0.998363i \(-0.518216\pi\)
−0.0571963 + 0.998363i \(0.518216\pi\)
\(192\) 0 0
\(193\) −178690. −0.345308 −0.172654 0.984983i \(-0.555234\pi\)
−0.172654 + 0.984983i \(0.555234\pi\)
\(194\) −974754. −1.85948
\(195\) 0 0
\(196\) −51439.6 −0.0956439
\(197\) 525992. 0.965636 0.482818 0.875721i \(-0.339613\pi\)
0.482818 + 0.875721i \(0.339613\pi\)
\(198\) 0 0
\(199\) −184283. −0.329877 −0.164939 0.986304i \(-0.552743\pi\)
−0.164939 + 0.986304i \(0.552743\pi\)
\(200\) 1.46246e6 2.58528
\(201\) 0 0
\(202\) 1.89453e6 3.26681
\(203\) 163616. 0.278667
\(204\) 0 0
\(205\) 1.78898e6 2.97318
\(206\) −1.38167e6 −2.26849
\(207\) 0 0
\(208\) −221513. −0.355010
\(209\) −79609.1 −0.126066
\(210\) 0 0
\(211\) −313460. −0.484703 −0.242352 0.970188i \(-0.577919\pi\)
−0.242352 + 0.970188i \(0.577919\pi\)
\(212\) 1.11888e6 1.70980
\(213\) 0 0
\(214\) 408077. 0.609127
\(215\) −1.06799e6 −1.57569
\(216\) 0 0
\(217\) −838024. −1.20811
\(218\) 1.76334e6 2.51302
\(219\) 0 0
\(220\) 974593. 1.35758
\(221\) 1.44218e6 1.98627
\(222\) 0 0
\(223\) −1.00274e6 −1.35028 −0.675141 0.737689i \(-0.735917\pi\)
−0.675141 + 0.737689i \(0.735917\pi\)
\(224\) −581751. −0.774671
\(225\) 0 0
\(226\) 768404. 1.00073
\(227\) 1.02818e6 1.32435 0.662176 0.749348i \(-0.269633\pi\)
0.662176 + 0.749348i \(0.269633\pi\)
\(228\) 0 0
\(229\) −83843.9 −0.105653 −0.0528266 0.998604i \(-0.516823\pi\)
−0.0528266 + 0.998604i \(0.516823\pi\)
\(230\) −491995. −0.613255
\(231\) 0 0
\(232\) 278591. 0.339819
\(233\) 241626. 0.291577 0.145789 0.989316i \(-0.453428\pi\)
0.145789 + 0.989316i \(0.453428\pi\)
\(234\) 0 0
\(235\) −1.78355e6 −2.10676
\(236\) −1.56682e6 −1.83122
\(237\) 0 0
\(238\) −1.84281e6 −2.10881
\(239\) −1.32779e6 −1.50361 −0.751806 0.659384i \(-0.770817\pi\)
−0.751806 + 0.659384i \(0.770817\pi\)
\(240\) 0 0
\(241\) −1.21493e6 −1.34744 −0.673721 0.738986i \(-0.735305\pi\)
−0.673721 + 0.738986i \(0.735305\pi\)
\(242\) −1.20759e6 −1.32550
\(243\) 0 0
\(244\) 892199. 0.959372
\(245\) 93260.3 0.0992617
\(246\) 0 0
\(247\) −411952. −0.429639
\(248\) −1.42691e6 −1.47322
\(249\) 0 0
\(250\) −3.43427e6 −3.47523
\(251\) −1.21766e6 −1.21995 −0.609977 0.792419i \(-0.708821\pi\)
−0.609977 + 0.792419i \(0.708821\pi\)
\(252\) 0 0
\(253\) −94011.2 −0.0923376
\(254\) −889100. −0.864702
\(255\) 0 0
\(256\) −1.41448e6 −1.34896
\(257\) −1.21439e6 −1.14690 −0.573450 0.819241i \(-0.694395\pi\)
−0.573450 + 0.819241i \(0.694395\pi\)
\(258\) 0 0
\(259\) −1.01502e6 −0.940210
\(260\) 5.04321e6 4.62672
\(261\) 0 0
\(262\) −1.69733e6 −1.52761
\(263\) −93687.8 −0.0835206 −0.0417603 0.999128i \(-0.513297\pi\)
−0.0417603 + 0.999128i \(0.513297\pi\)
\(264\) 0 0
\(265\) −2.02854e6 −1.77447
\(266\) 526388. 0.456144
\(267\) 0 0
\(268\) 2.97695e6 2.53183
\(269\) 323647. 0.272703 0.136352 0.990660i \(-0.456462\pi\)
0.136352 + 0.990660i \(0.456462\pi\)
\(270\) 0 0
\(271\) 1.76235e6 1.45771 0.728853 0.684670i \(-0.240054\pi\)
0.728853 + 0.684670i \(0.240054\pi\)
\(272\) −377749. −0.309586
\(273\) 0 0
\(274\) −1.63250e6 −1.31364
\(275\) −1.21158e6 −0.966100
\(276\) 0 0
\(277\) −1.83478e6 −1.43676 −0.718381 0.695650i \(-0.755117\pi\)
−0.718381 + 0.695650i \(0.755117\pi\)
\(278\) 1.86240e6 1.44531
\(279\) 0 0
\(280\) −2.69472e6 −2.05409
\(281\) 1.71252e6 1.29381 0.646903 0.762572i \(-0.276064\pi\)
0.646903 + 0.762572i \(0.276064\pi\)
\(282\) 0 0
\(283\) 1.53094e6 1.13629 0.568147 0.822927i \(-0.307660\pi\)
0.568147 + 0.822927i \(0.307660\pi\)
\(284\) −2.33774e6 −1.71989
\(285\) 0 0
\(286\) 1.52436e6 1.10198
\(287\) −2.26031e6 −1.61981
\(288\) 0 0
\(289\) 1.03951e6 0.732125
\(290\) −1.20787e6 −0.843381
\(291\) 0 0
\(292\) 2.25142e6 1.54526
\(293\) 2.02997e6 1.38140 0.690701 0.723141i \(-0.257302\pi\)
0.690701 + 0.723141i \(0.257302\pi\)
\(294\) 0 0
\(295\) 2.84066e6 1.90049
\(296\) −1.72829e6 −1.14653
\(297\) 0 0
\(298\) −663868. −0.433053
\(299\) −486478. −0.314692
\(300\) 0 0
\(301\) 1.34936e6 0.858445
\(302\) 1.24511e6 0.785578
\(303\) 0 0
\(304\) 107902. 0.0669648
\(305\) −1.61756e6 −0.995661
\(306\) 0 0
\(307\) 396907. 0.240349 0.120175 0.992753i \(-0.461655\pi\)
0.120175 + 0.992753i \(0.461655\pi\)
\(308\) −1.23136e6 −0.739621
\(309\) 0 0
\(310\) 6.18657e6 3.65633
\(311\) −1.27993e6 −0.750385 −0.375192 0.926947i \(-0.622423\pi\)
−0.375192 + 0.926947i \(0.622423\pi\)
\(312\) 0 0
\(313\) −2.41300e6 −1.39218 −0.696091 0.717953i \(-0.745079\pi\)
−0.696091 + 0.717953i \(0.745079\pi\)
\(314\) −3.37436e6 −1.93138
\(315\) 0 0
\(316\) −1.36180e6 −0.767175
\(317\) −1.03063e6 −0.576043 −0.288022 0.957624i \(-0.592998\pi\)
−0.288022 + 0.957624i \(0.592998\pi\)
\(318\) 0 0
\(319\) −230801. −0.126988
\(320\) 5.06326e6 2.76411
\(321\) 0 0
\(322\) 621617. 0.334105
\(323\) −702507. −0.374666
\(324\) 0 0
\(325\) −6.26956e6 −3.29252
\(326\) −5.85078e6 −3.04909
\(327\) 0 0
\(328\) −3.84867e6 −1.97527
\(329\) 2.25345e6 1.14778
\(330\) 0 0
\(331\) 231656. 0.116218 0.0581089 0.998310i \(-0.481493\pi\)
0.0581089 + 0.998310i \(0.481493\pi\)
\(332\) 1.69534e6 0.844134
\(333\) 0 0
\(334\) −91872.4 −0.0450629
\(335\) −5.39723e6 −2.62760
\(336\) 0 0
\(337\) −351073. −0.168393 −0.0841963 0.996449i \(-0.526832\pi\)
−0.0841963 + 0.996449i \(0.526832\pi\)
\(338\) 4.42491e6 2.10675
\(339\) 0 0
\(340\) 8.60026e6 4.03473
\(341\) 1.18214e6 0.550532
\(342\) 0 0
\(343\) −2.23523e6 −1.02586
\(344\) 2.29758e6 1.04683
\(345\) 0 0
\(346\) 2.33757e6 1.04972
\(347\) 550941. 0.245630 0.122815 0.992430i \(-0.460808\pi\)
0.122815 + 0.992430i \(0.460808\pi\)
\(348\) 0 0
\(349\) −1.30593e6 −0.573928 −0.286964 0.957941i \(-0.592646\pi\)
−0.286964 + 0.957941i \(0.592646\pi\)
\(350\) 8.01119e6 3.49564
\(351\) 0 0
\(352\) 820634. 0.353015
\(353\) −2.13442e6 −0.911682 −0.455841 0.890061i \(-0.650661\pi\)
−0.455841 + 0.890061i \(0.650661\pi\)
\(354\) 0 0
\(355\) 4.23834e6 1.78494
\(356\) 3.65913e6 1.53022
\(357\) 0 0
\(358\) −6.92394e6 −2.85526
\(359\) −1.06632e6 −0.436670 −0.218335 0.975874i \(-0.570063\pi\)
−0.218335 + 0.975874i \(0.570063\pi\)
\(360\) 0 0
\(361\) −2.27543e6 −0.918958
\(362\) −2.73250e6 −1.09594
\(363\) 0 0
\(364\) −6.37191e6 −2.52067
\(365\) −4.08185e6 −1.60371
\(366\) 0 0
\(367\) 1.34294e6 0.520464 0.260232 0.965546i \(-0.416201\pi\)
0.260232 + 0.965546i \(0.416201\pi\)
\(368\) 127423. 0.0490487
\(369\) 0 0
\(370\) 7.49320e6 2.84553
\(371\) 2.56299e6 0.966744
\(372\) 0 0
\(373\) 3.22658e6 1.20080 0.600400 0.799700i \(-0.295008\pi\)
0.600400 + 0.799700i \(0.295008\pi\)
\(374\) 2.59951e6 0.960976
\(375\) 0 0
\(376\) 3.83697e6 1.39965
\(377\) −1.19432e6 −0.432781
\(378\) 0 0
\(379\) −2.41939e6 −0.865184 −0.432592 0.901590i \(-0.642401\pi\)
−0.432592 + 0.901590i \(0.642401\pi\)
\(380\) −2.45662e6 −0.872729
\(381\) 0 0
\(382\) −537944. −0.188616
\(383\) −1.03280e6 −0.359764 −0.179882 0.983688i \(-0.557572\pi\)
−0.179882 + 0.983688i \(0.557572\pi\)
\(384\) 0 0
\(385\) 2.23247e6 0.767597
\(386\) −1.66669e6 −0.569360
\(387\) 0 0
\(388\) −5.74764e6 −1.93825
\(389\) −2.56135e6 −0.858212 −0.429106 0.903254i \(-0.641171\pi\)
−0.429106 + 0.903254i \(0.641171\pi\)
\(390\) 0 0
\(391\) −829598. −0.274426
\(392\) −200632. −0.0659456
\(393\) 0 0
\(394\) 4.90608e6 1.59219
\(395\) 2.46894e6 0.796193
\(396\) 0 0
\(397\) −2.07970e6 −0.662255 −0.331128 0.943586i \(-0.607429\pi\)
−0.331128 + 0.943586i \(0.607429\pi\)
\(398\) −1.71886e6 −0.543917
\(399\) 0 0
\(400\) 1.64218e6 0.513182
\(401\) 1.97329e6 0.612817 0.306408 0.951900i \(-0.400873\pi\)
0.306408 + 0.951900i \(0.400873\pi\)
\(402\) 0 0
\(403\) 6.11719e6 1.87624
\(404\) 1.11711e7 3.40521
\(405\) 0 0
\(406\) 1.52609e6 0.459480
\(407\) 1.43181e6 0.428450
\(408\) 0 0
\(409\) 1.68806e6 0.498975 0.249488 0.968378i \(-0.419738\pi\)
0.249488 + 0.968378i \(0.419738\pi\)
\(410\) 1.66864e7 4.90233
\(411\) 0 0
\(412\) −8.14702e6 −2.36459
\(413\) −3.58907e6 −1.03540
\(414\) 0 0
\(415\) −3.07366e6 −0.876064
\(416\) 4.24652e6 1.20309
\(417\) 0 0
\(418\) −742538. −0.207863
\(419\) −1.72868e6 −0.481039 −0.240520 0.970644i \(-0.577318\pi\)
−0.240520 + 0.970644i \(0.577318\pi\)
\(420\) 0 0
\(421\) 932870. 0.256517 0.128258 0.991741i \(-0.459061\pi\)
0.128258 + 0.991741i \(0.459061\pi\)
\(422\) −2.92373e6 −0.799202
\(423\) 0 0
\(424\) 4.36403e6 1.17889
\(425\) −1.06916e7 −2.87124
\(426\) 0 0
\(427\) 2.04373e6 0.542443
\(428\) 2.40623e6 0.634932
\(429\) 0 0
\(430\) −9.96144e6 −2.59807
\(431\) 7.62939e6 1.97832 0.989161 0.146838i \(-0.0469095\pi\)
0.989161 + 0.146838i \(0.0469095\pi\)
\(432\) 0 0
\(433\) 4.68013e6 1.19960 0.599802 0.800148i \(-0.295246\pi\)
0.599802 + 0.800148i \(0.295246\pi\)
\(434\) −7.81650e6 −1.99199
\(435\) 0 0
\(436\) 1.03976e7 2.61948
\(437\) 236971. 0.0593596
\(438\) 0 0
\(439\) 1.21981e6 0.302087 0.151043 0.988527i \(-0.451737\pi\)
0.151043 + 0.988527i \(0.451737\pi\)
\(440\) 3.80125e6 0.936041
\(441\) 0 0
\(442\) 1.34516e7 3.27506
\(443\) 1.82127e6 0.440926 0.220463 0.975395i \(-0.429243\pi\)
0.220463 + 0.975395i \(0.429243\pi\)
\(444\) 0 0
\(445\) −6.63403e6 −1.58810
\(446\) −9.35281e6 −2.22641
\(447\) 0 0
\(448\) −6.39724e6 −1.50591
\(449\) 3.31712e6 0.776506 0.388253 0.921553i \(-0.373079\pi\)
0.388253 + 0.921553i \(0.373079\pi\)
\(450\) 0 0
\(451\) 3.18846e6 0.738142
\(452\) 4.53090e6 1.04313
\(453\) 0 0
\(454\) 9.59012e6 2.18366
\(455\) 1.15523e7 2.61602
\(456\) 0 0
\(457\) −2.14897e6 −0.481326 −0.240663 0.970609i \(-0.577365\pi\)
−0.240663 + 0.970609i \(0.577365\pi\)
\(458\) −782036. −0.174206
\(459\) 0 0
\(460\) −2.90105e6 −0.639235
\(461\) 6.83686e6 1.49832 0.749160 0.662389i \(-0.230457\pi\)
0.749160 + 0.662389i \(0.230457\pi\)
\(462\) 0 0
\(463\) 3.26293e6 0.707385 0.353692 0.935362i \(-0.384926\pi\)
0.353692 + 0.935362i \(0.384926\pi\)
\(464\) 312828. 0.0674544
\(465\) 0 0
\(466\) 2.25372e6 0.480767
\(467\) 4.30238e6 0.912886 0.456443 0.889753i \(-0.349123\pi\)
0.456443 + 0.889753i \(0.349123\pi\)
\(468\) 0 0
\(469\) 6.81920e6 1.43153
\(470\) −1.66357e7 −3.47373
\(471\) 0 0
\(472\) −6.11116e6 −1.26261
\(473\) −1.90345e6 −0.391191
\(474\) 0 0
\(475\) 3.05400e6 0.621061
\(476\) −1.08661e7 −2.19815
\(477\) 0 0
\(478\) −1.23847e7 −2.47923
\(479\) −3.15612e6 −0.628514 −0.314257 0.949338i \(-0.601755\pi\)
−0.314257 + 0.949338i \(0.601755\pi\)
\(480\) 0 0
\(481\) 7.40918e6 1.46018
\(482\) −1.13320e7 −2.22173
\(483\) 0 0
\(484\) −7.12055e6 −1.38166
\(485\) 1.04205e7 2.01157
\(486\) 0 0
\(487\) −1.04981e6 −0.200581 −0.100290 0.994958i \(-0.531977\pi\)
−0.100290 + 0.994958i \(0.531977\pi\)
\(488\) 3.47988e6 0.661478
\(489\) 0 0
\(490\) 869867. 0.163667
\(491\) −1.67278e6 −0.313138 −0.156569 0.987667i \(-0.550043\pi\)
−0.156569 + 0.987667i \(0.550043\pi\)
\(492\) 0 0
\(493\) −2.03669e6 −0.377406
\(494\) −3.84240e6 −0.708410
\(495\) 0 0
\(496\) −1.60227e6 −0.292437
\(497\) −5.35498e6 −0.972449
\(498\) 0 0
\(499\) −3.07979e6 −0.553695 −0.276847 0.960914i \(-0.589290\pi\)
−0.276847 + 0.960914i \(0.589290\pi\)
\(500\) −2.02502e7 −3.62246
\(501\) 0 0
\(502\) −1.13575e7 −2.01152
\(503\) −4.06934e6 −0.717140 −0.358570 0.933503i \(-0.616736\pi\)
−0.358570 + 0.933503i \(0.616736\pi\)
\(504\) 0 0
\(505\) −2.02533e7 −3.53401
\(506\) −876870. −0.152251
\(507\) 0 0
\(508\) −5.24258e6 −0.901334
\(509\) −5.65269e6 −0.967077 −0.483538 0.875323i \(-0.660649\pi\)
−0.483538 + 0.875323i \(0.660649\pi\)
\(510\) 0 0
\(511\) 5.15726e6 0.873709
\(512\) −2.76575e6 −0.466271
\(513\) 0 0
\(514\) −1.13270e7 −1.89106
\(515\) 1.47706e7 2.45403
\(516\) 0 0
\(517\) −3.17877e6 −0.523038
\(518\) −9.46738e6 −1.55026
\(519\) 0 0
\(520\) 1.96703e7 3.19008
\(521\) 729056. 0.117670 0.0588351 0.998268i \(-0.481261\pi\)
0.0588351 + 0.998268i \(0.481261\pi\)
\(522\) 0 0
\(523\) 5.74086e6 0.917747 0.458873 0.888502i \(-0.348253\pi\)
0.458873 + 0.888502i \(0.348253\pi\)
\(524\) −1.00083e7 −1.59233
\(525\) 0 0
\(526\) −873853. −0.137713
\(527\) 1.04317e7 1.63618
\(528\) 0 0
\(529\) 279841. 0.0434783
\(530\) −1.89208e7 −2.92583
\(531\) 0 0
\(532\) 3.10385e6 0.475468
\(533\) 1.64993e7 2.51563
\(534\) 0 0
\(535\) −4.36250e6 −0.658948
\(536\) 1.16111e7 1.74567
\(537\) 0 0
\(538\) 3.01875e6 0.449647
\(539\) 166216. 0.0246434
\(540\) 0 0
\(541\) 1.12666e7 1.65500 0.827500 0.561466i \(-0.189762\pi\)
0.827500 + 0.561466i \(0.189762\pi\)
\(542\) 1.64380e7 2.40354
\(543\) 0 0
\(544\) 7.24165e6 1.04916
\(545\) −1.88508e7 −2.71856
\(546\) 0 0
\(547\) 1.92802e6 0.275513 0.137757 0.990466i \(-0.456011\pi\)
0.137757 + 0.990466i \(0.456011\pi\)
\(548\) −9.62606e6 −1.36930
\(549\) 0 0
\(550\) −1.13008e7 −1.59295
\(551\) 581772. 0.0816345
\(552\) 0 0
\(553\) −3.11942e6 −0.433771
\(554\) −1.71135e7 −2.36900
\(555\) 0 0
\(556\) 1.09816e7 1.50654
\(557\) 1.27385e7 1.73973 0.869865 0.493290i \(-0.164206\pi\)
0.869865 + 0.493290i \(0.164206\pi\)
\(558\) 0 0
\(559\) −9.84974e6 −1.33320
\(560\) −3.02589e6 −0.407739
\(561\) 0 0
\(562\) 1.59732e7 2.13329
\(563\) −1.30970e7 −1.74140 −0.870702 0.491810i \(-0.836335\pi\)
−0.870702 + 0.491810i \(0.836335\pi\)
\(564\) 0 0
\(565\) −8.21454e6 −1.08259
\(566\) 1.42795e7 1.87358
\(567\) 0 0
\(568\) −9.11799e6 −1.18585
\(569\) −1.32454e7 −1.71509 −0.857543 0.514413i \(-0.828010\pi\)
−0.857543 + 0.514413i \(0.828010\pi\)
\(570\) 0 0
\(571\) −4.22643e6 −0.542480 −0.271240 0.962512i \(-0.587434\pi\)
−0.271240 + 0.962512i \(0.587434\pi\)
\(572\) 8.98838e6 1.14866
\(573\) 0 0
\(574\) −2.10826e7 −2.67082
\(575\) 3.60650e6 0.454900
\(576\) 0 0
\(577\) −224943. −0.0281276 −0.0140638 0.999901i \(-0.504477\pi\)
−0.0140638 + 0.999901i \(0.504477\pi\)
\(578\) 9.69584e6 1.20716
\(579\) 0 0
\(580\) −7.12219e6 −0.879110
\(581\) 3.88346e6 0.477285
\(582\) 0 0
\(583\) −3.61542e6 −0.440542
\(584\) 8.78134e6 1.06544
\(585\) 0 0
\(586\) 1.89341e7 2.27772
\(587\) −4.80198e6 −0.575209 −0.287604 0.957749i \(-0.592859\pi\)
−0.287604 + 0.957749i \(0.592859\pi\)
\(588\) 0 0
\(589\) −2.97978e6 −0.353912
\(590\) 2.64957e7 3.13361
\(591\) 0 0
\(592\) −1.94068e6 −0.227588
\(593\) 9.07891e6 1.06022 0.530111 0.847928i \(-0.322150\pi\)
0.530111 + 0.847928i \(0.322150\pi\)
\(594\) 0 0
\(595\) 1.97003e7 2.28129
\(596\) −3.91450e6 −0.451399
\(597\) 0 0
\(598\) −4.53752e6 −0.518879
\(599\) 487665. 0.0555334 0.0277667 0.999614i \(-0.491160\pi\)
0.0277667 + 0.999614i \(0.491160\pi\)
\(600\) 0 0
\(601\) −9.72337e6 −1.09807 −0.549036 0.835799i \(-0.685005\pi\)
−0.549036 + 0.835799i \(0.685005\pi\)
\(602\) 1.25859e7 1.41545
\(603\) 0 0
\(604\) 7.34177e6 0.818858
\(605\) 1.29096e7 1.43392
\(606\) 0 0
\(607\) −3.30773e6 −0.364384 −0.182192 0.983263i \(-0.558319\pi\)
−0.182192 + 0.983263i \(0.558319\pi\)
\(608\) −2.06854e6 −0.226937
\(609\) 0 0
\(610\) −1.50875e7 −1.64169
\(611\) −1.64491e7 −1.78254
\(612\) 0 0
\(613\) −234065. −0.0251585 −0.0125793 0.999921i \(-0.504004\pi\)
−0.0125793 + 0.999921i \(0.504004\pi\)
\(614\) 3.70207e6 0.396300
\(615\) 0 0
\(616\) −4.80274e6 −0.509961
\(617\) 9.19095e6 0.971958 0.485979 0.873970i \(-0.338463\pi\)
0.485979 + 0.873970i \(0.338463\pi\)
\(618\) 0 0
\(619\) 7.15853e6 0.750926 0.375463 0.926837i \(-0.377484\pi\)
0.375463 + 0.926837i \(0.377484\pi\)
\(620\) 3.64791e7 3.81123
\(621\) 0 0
\(622\) −1.19382e7 −1.23727
\(623\) 8.38185e6 0.865206
\(624\) 0 0
\(625\) 1.54088e7 1.57786
\(626\) −2.25067e7 −2.29550
\(627\) 0 0
\(628\) −1.98969e7 −2.01320
\(629\) 1.26350e7 1.27335
\(630\) 0 0
\(631\) 1.00474e7 1.00457 0.502283 0.864703i \(-0.332493\pi\)
0.502283 + 0.864703i \(0.332493\pi\)
\(632\) −5.31147e6 −0.528960
\(633\) 0 0
\(634\) −9.61300e6 −0.949808
\(635\) 9.50483e6 0.935427
\(636\) 0 0
\(637\) 860112. 0.0839859
\(638\) −2.15275e6 −0.209383
\(639\) 0 0
\(640\) 3.24924e7 3.13568
\(641\) −4.21517e6 −0.405201 −0.202600 0.979262i \(-0.564939\pi\)
−0.202600 + 0.979262i \(0.564939\pi\)
\(642\) 0 0
\(643\) 9.48561e6 0.904770 0.452385 0.891823i \(-0.350573\pi\)
0.452385 + 0.891823i \(0.350573\pi\)
\(644\) 3.66537e6 0.348259
\(645\) 0 0
\(646\) −6.55249e6 −0.617768
\(647\) −2.54033e6 −0.238578 −0.119289 0.992860i \(-0.538061\pi\)
−0.119289 + 0.992860i \(0.538061\pi\)
\(648\) 0 0
\(649\) 5.06284e6 0.471827
\(650\) −5.84781e7 −5.42887
\(651\) 0 0
\(652\) −3.44991e7 −3.17826
\(653\) −9.06671e6 −0.832083 −0.416042 0.909346i \(-0.636583\pi\)
−0.416042 + 0.909346i \(0.636583\pi\)
\(654\) 0 0
\(655\) 1.81452e7 1.65256
\(656\) −4.32164e6 −0.392093
\(657\) 0 0
\(658\) 2.10185e7 1.89251
\(659\) 1.63938e7 1.47050 0.735251 0.677795i \(-0.237064\pi\)
0.735251 + 0.677795i \(0.237064\pi\)
\(660\) 0 0
\(661\) −1.06203e7 −0.945435 −0.472717 0.881214i \(-0.656727\pi\)
−0.472717 + 0.881214i \(0.656727\pi\)
\(662\) 2.16072e6 0.191626
\(663\) 0 0
\(664\) 6.61241e6 0.582022
\(665\) −5.62730e6 −0.493453
\(666\) 0 0
\(667\) 687020. 0.0597936
\(668\) −541726. −0.0469719
\(669\) 0 0
\(670\) −5.03416e7 −4.33251
\(671\) −2.88294e6 −0.247189
\(672\) 0 0
\(673\) −1.19056e7 −1.01324 −0.506620 0.862169i \(-0.669105\pi\)
−0.506620 + 0.862169i \(0.669105\pi\)
\(674\) −3.27456e6 −0.277654
\(675\) 0 0
\(676\) 2.60915e7 2.19600
\(677\) −2.17878e7 −1.82701 −0.913507 0.406822i \(-0.866637\pi\)
−0.913507 + 0.406822i \(0.866637\pi\)
\(678\) 0 0
\(679\) −1.31659e7 −1.09592
\(680\) 3.35440e7 2.78190
\(681\) 0 0
\(682\) 1.10262e7 0.907744
\(683\) −8.27503e6 −0.678762 −0.339381 0.940649i \(-0.610218\pi\)
−0.339381 + 0.940649i \(0.610218\pi\)
\(684\) 0 0
\(685\) 1.74521e7 1.42109
\(686\) −2.08486e7 −1.69148
\(687\) 0 0
\(688\) 2.57993e6 0.207796
\(689\) −1.87086e7 −1.50139
\(690\) 0 0
\(691\) 8.37140e6 0.666965 0.333483 0.942756i \(-0.391776\pi\)
0.333483 + 0.942756i \(0.391776\pi\)
\(692\) 1.37835e7 1.09419
\(693\) 0 0
\(694\) 5.13879e6 0.405007
\(695\) −1.99098e7 −1.56352
\(696\) 0 0
\(697\) 2.81364e7 2.19375
\(698\) −1.21808e7 −0.946320
\(699\) 0 0
\(700\) 4.72380e7 3.64373
\(701\) −3.01421e6 −0.231675 −0.115837 0.993268i \(-0.536955\pi\)
−0.115837 + 0.993268i \(0.536955\pi\)
\(702\) 0 0
\(703\) −3.60912e6 −0.275431
\(704\) 9.02412e6 0.686236
\(705\) 0 0
\(706\) −1.99084e7 −1.50323
\(707\) 2.55893e7 1.92535
\(708\) 0 0
\(709\) −5.74628e6 −0.429310 −0.214655 0.976690i \(-0.568863\pi\)
−0.214655 + 0.976690i \(0.568863\pi\)
\(710\) 3.95322e7 2.94310
\(711\) 0 0
\(712\) 1.42719e7 1.05507
\(713\) −3.51885e6 −0.259225
\(714\) 0 0
\(715\) −1.62960e7 −1.19211
\(716\) −4.08270e7 −2.97622
\(717\) 0 0
\(718\) −9.94592e6 −0.720002
\(719\) 1.64352e7 1.18564 0.592821 0.805334i \(-0.298014\pi\)
0.592821 + 0.805334i \(0.298014\pi\)
\(720\) 0 0
\(721\) −1.86621e7 −1.33697
\(722\) −2.12236e7 −1.51522
\(723\) 0 0
\(724\) −1.61122e7 −1.14237
\(725\) 8.85408e6 0.625603
\(726\) 0 0
\(727\) −4.65331e6 −0.326532 −0.163266 0.986582i \(-0.552203\pi\)
−0.163266 + 0.986582i \(0.552203\pi\)
\(728\) −2.48526e7 −1.73798
\(729\) 0 0
\(730\) −3.80726e7 −2.64427
\(731\) −1.67969e7 −1.16261
\(732\) 0 0
\(733\) 1.76748e7 1.21505 0.607527 0.794299i \(-0.292162\pi\)
0.607527 + 0.794299i \(0.292162\pi\)
\(734\) 1.25260e7 0.858166
\(735\) 0 0
\(736\) −2.44276e6 −0.166221
\(737\) −9.61936e6 −0.652345
\(738\) 0 0
\(739\) 2.32944e7 1.56907 0.784533 0.620087i \(-0.212903\pi\)
0.784533 + 0.620087i \(0.212903\pi\)
\(740\) 4.41837e7 2.96608
\(741\) 0 0
\(742\) 2.39057e7 1.59401
\(743\) −1.77107e7 −1.17696 −0.588482 0.808511i \(-0.700274\pi\)
−0.588482 + 0.808511i \(0.700274\pi\)
\(744\) 0 0
\(745\) 7.09701e6 0.468473
\(746\) 3.00953e7 1.97994
\(747\) 0 0
\(748\) 1.53280e7 1.00169
\(749\) 5.51186e6 0.358999
\(750\) 0 0
\(751\) −9.59704e6 −0.620922 −0.310461 0.950586i \(-0.600483\pi\)
−0.310461 + 0.950586i \(0.600483\pi\)
\(752\) 4.30851e6 0.277832
\(753\) 0 0
\(754\) −1.11398e7 −0.713590
\(755\) −1.33107e7 −0.849832
\(756\) 0 0
\(757\) 1.81520e7 1.15129 0.575645 0.817700i \(-0.304751\pi\)
0.575645 + 0.817700i \(0.304751\pi\)
\(758\) −2.25664e7 −1.42656
\(759\) 0 0
\(760\) −9.58167e6 −0.601738
\(761\) −2.18570e7 −1.36813 −0.684067 0.729419i \(-0.739790\pi\)
−0.684067 + 0.729419i \(0.739790\pi\)
\(762\) 0 0
\(763\) 2.38173e7 1.48109
\(764\) −3.17199e6 −0.196607
\(765\) 0 0
\(766\) −9.63319e6 −0.593196
\(767\) 2.61986e7 1.60801
\(768\) 0 0
\(769\) −3.01818e6 −0.184047 −0.0920237 0.995757i \(-0.529334\pi\)
−0.0920237 + 0.995757i \(0.529334\pi\)
\(770\) 2.08229e7 1.26565
\(771\) 0 0
\(772\) −9.82765e6 −0.593480
\(773\) −7.09462e6 −0.427052 −0.213526 0.976937i \(-0.568495\pi\)
−0.213526 + 0.976937i \(0.568495\pi\)
\(774\) 0 0
\(775\) −4.53497e7 −2.71219
\(776\) −2.24178e7 −1.33641
\(777\) 0 0
\(778\) −2.38904e7 −1.41506
\(779\) −8.03704e6 −0.474518
\(780\) 0 0
\(781\) 7.55388e6 0.443142
\(782\) −7.73790e6 −0.452487
\(783\) 0 0
\(784\) −225289. −0.0130903
\(785\) 3.60732e7 2.08935
\(786\) 0 0
\(787\) 2.85125e7 1.64096 0.820482 0.571672i \(-0.193705\pi\)
0.820482 + 0.571672i \(0.193705\pi\)
\(788\) 2.89287e7 1.65964
\(789\) 0 0
\(790\) 2.30286e7 1.31280
\(791\) 1.03788e7 0.589800
\(792\) 0 0
\(793\) −1.49183e7 −0.842435
\(794\) −1.93980e7 −1.09196
\(795\) 0 0
\(796\) −1.01353e7 −0.566960
\(797\) −7.59475e6 −0.423514 −0.211757 0.977322i \(-0.567919\pi\)
−0.211757 + 0.977322i \(0.567919\pi\)
\(798\) 0 0
\(799\) −2.80509e7 −1.55446
\(800\) −3.14815e7 −1.73912
\(801\) 0 0
\(802\) 1.84055e7 1.01044
\(803\) −7.27497e6 −0.398146
\(804\) 0 0
\(805\) −6.64533e6 −0.361432
\(806\) 5.70568e7 3.09364
\(807\) 0 0
\(808\) 4.35713e7 2.34786
\(809\) −135394. −0.00727324 −0.00363662 0.999993i \(-0.501158\pi\)
−0.00363662 + 0.999993i \(0.501158\pi\)
\(810\) 0 0
\(811\) −2.84394e7 −1.51834 −0.759168 0.650895i \(-0.774394\pi\)
−0.759168 + 0.650895i \(0.774394\pi\)
\(812\) 8.99862e6 0.478945
\(813\) 0 0
\(814\) 1.33549e7 0.706449
\(815\) 6.25471e7 3.29848
\(816\) 0 0
\(817\) 4.79795e6 0.251479
\(818\) 1.57450e7 0.822735
\(819\) 0 0
\(820\) 9.83913e7 5.11001
\(821\) 9.25492e6 0.479198 0.239599 0.970872i \(-0.422984\pi\)
0.239599 + 0.970872i \(0.422984\pi\)
\(822\) 0 0
\(823\) 8.81289e6 0.453543 0.226772 0.973948i \(-0.427183\pi\)
0.226772 + 0.973948i \(0.427183\pi\)
\(824\) −3.17762e7 −1.63036
\(825\) 0 0
\(826\) −3.34763e7 −1.70721
\(827\) −2.40557e7 −1.22308 −0.611539 0.791214i \(-0.709449\pi\)
−0.611539 + 0.791214i \(0.709449\pi\)
\(828\) 0 0
\(829\) 3.34899e7 1.69249 0.846247 0.532791i \(-0.178857\pi\)
0.846247 + 0.532791i \(0.178857\pi\)
\(830\) −2.86689e7 −1.44450
\(831\) 0 0
\(832\) 4.66969e7 2.33873
\(833\) 1.46676e6 0.0732398
\(834\) 0 0
\(835\) 982153. 0.0487487
\(836\) −4.37838e6 −0.216669
\(837\) 0 0
\(838\) −1.61239e7 −0.793160
\(839\) −6.66922e6 −0.327092 −0.163546 0.986536i \(-0.552293\pi\)
−0.163546 + 0.986536i \(0.552293\pi\)
\(840\) 0 0
\(841\) −1.88245e7 −0.917769
\(842\) 8.70115e6 0.422957
\(843\) 0 0
\(844\) −1.72398e7 −0.833060
\(845\) −4.73040e7 −2.27906
\(846\) 0 0
\(847\) −1.63108e7 −0.781209
\(848\) 4.90034e6 0.234011
\(849\) 0 0
\(850\) −9.97235e7 −4.73424
\(851\) −4.26205e6 −0.201741
\(852\) 0 0
\(853\) 2.91274e6 0.137066 0.0685330 0.997649i \(-0.478168\pi\)
0.0685330 + 0.997649i \(0.478168\pi\)
\(854\) 1.90625e7 0.894405
\(855\) 0 0
\(856\) 9.38512e6 0.437779
\(857\) −1.52102e7 −0.707429 −0.353715 0.935353i \(-0.615082\pi\)
−0.353715 + 0.935353i \(0.615082\pi\)
\(858\) 0 0
\(859\) 1.06621e7 0.493016 0.246508 0.969141i \(-0.420717\pi\)
0.246508 + 0.969141i \(0.420717\pi\)
\(860\) −5.87376e7 −2.70814
\(861\) 0 0
\(862\) 7.11616e7 3.26195
\(863\) 3.79585e7 1.73493 0.867465 0.497498i \(-0.165748\pi\)
0.867465 + 0.497498i \(0.165748\pi\)
\(864\) 0 0
\(865\) −2.49896e7 −1.13558
\(866\) 4.36529e7 1.97796
\(867\) 0 0
\(868\) −4.60900e7 −2.07638
\(869\) 4.40034e6 0.197668
\(870\) 0 0
\(871\) −4.97771e7 −2.22323
\(872\) 4.05540e7 1.80610
\(873\) 0 0
\(874\) 2.21029e6 0.0978750
\(875\) −4.63863e7 −2.04819
\(876\) 0 0
\(877\) 2.72329e7 1.19562 0.597812 0.801636i \(-0.296037\pi\)
0.597812 + 0.801636i \(0.296037\pi\)
\(878\) 1.13775e7 0.498095
\(879\) 0 0
\(880\) 4.26840e6 0.185805
\(881\) −8.49018e6 −0.368534 −0.184267 0.982876i \(-0.558991\pi\)
−0.184267 + 0.982876i \(0.558991\pi\)
\(882\) 0 0
\(883\) −2.58940e7 −1.11763 −0.558815 0.829292i \(-0.688744\pi\)
−0.558815 + 0.829292i \(0.688744\pi\)
\(884\) 7.93176e7 3.41381
\(885\) 0 0
\(886\) 1.69875e7 0.727020
\(887\) 1.57892e7 0.673832 0.336916 0.941535i \(-0.390616\pi\)
0.336916 + 0.941535i \(0.390616\pi\)
\(888\) 0 0
\(889\) −1.20090e7 −0.509627
\(890\) −6.18775e7 −2.61853
\(891\) 0 0
\(892\) −5.51489e7 −2.32073
\(893\) 8.01261e6 0.336237
\(894\) 0 0
\(895\) 7.40196e7 3.08880
\(896\) −4.10529e7 −1.70834
\(897\) 0 0
\(898\) 3.09397e7 1.28034
\(899\) −8.63890e6 −0.356500
\(900\) 0 0
\(901\) −3.19041e7 −1.30929
\(902\) 2.97397e7 1.21708
\(903\) 0 0
\(904\) 1.76721e7 0.719227
\(905\) 2.92115e7 1.18558
\(906\) 0 0
\(907\) −1.12308e7 −0.453305 −0.226653 0.973976i \(-0.572778\pi\)
−0.226653 + 0.973976i \(0.572778\pi\)
\(908\) 5.65481e7 2.27616
\(909\) 0 0
\(910\) 1.07752e8 4.31341
\(911\) −2.61794e7 −1.04511 −0.522557 0.852604i \(-0.675022\pi\)
−0.522557 + 0.852604i \(0.675022\pi\)
\(912\) 0 0
\(913\) −5.47811e6 −0.217497
\(914\) −2.00441e7 −0.793634
\(915\) 0 0
\(916\) −4.61128e6 −0.181586
\(917\) −2.29257e7 −0.900326
\(918\) 0 0
\(919\) 4.07119e7 1.59013 0.795065 0.606524i \(-0.207437\pi\)
0.795065 + 0.606524i \(0.207437\pi\)
\(920\) −1.13151e7 −0.440746
\(921\) 0 0
\(922\) 6.37694e7 2.47050
\(923\) 3.90889e7 1.51025
\(924\) 0 0
\(925\) −5.49278e7 −2.11075
\(926\) 3.04343e7 1.16637
\(927\) 0 0
\(928\) −5.99707e6 −0.228596
\(929\) −8.89152e6 −0.338015 −0.169008 0.985615i \(-0.554056\pi\)
−0.169008 + 0.985615i \(0.554056\pi\)
\(930\) 0 0
\(931\) −418973. −0.0158421
\(932\) 1.32890e7 0.501134
\(933\) 0 0
\(934\) 4.01296e7 1.50521
\(935\) −2.77898e7 −1.03958
\(936\) 0 0
\(937\) 4.07318e6 0.151560 0.0757799 0.997125i \(-0.475855\pi\)
0.0757799 + 0.997125i \(0.475855\pi\)
\(938\) 6.36047e7 2.36038
\(939\) 0 0
\(940\) −9.80922e7 −3.62089
\(941\) 1.08008e7 0.397634 0.198817 0.980037i \(-0.436290\pi\)
0.198817 + 0.980037i \(0.436290\pi\)
\(942\) 0 0
\(943\) −9.49102e6 −0.347563
\(944\) −6.86218e6 −0.250629
\(945\) 0 0
\(946\) −1.77540e7 −0.645014
\(947\) −6.93307e6 −0.251218 −0.125609 0.992080i \(-0.540088\pi\)
−0.125609 + 0.992080i \(0.540088\pi\)
\(948\) 0 0
\(949\) −3.76457e7 −1.35690
\(950\) 2.84855e7 1.02404
\(951\) 0 0
\(952\) −4.23816e7 −1.51560
\(953\) −3.81395e7 −1.36033 −0.680163 0.733060i \(-0.738091\pi\)
−0.680163 + 0.733060i \(0.738091\pi\)
\(954\) 0 0
\(955\) 5.75084e6 0.204043
\(956\) −7.30265e7 −2.58426
\(957\) 0 0
\(958\) −2.94381e7 −1.03632
\(959\) −2.20501e7 −0.774219
\(960\) 0 0
\(961\) 1.56184e7 0.545542
\(962\) 6.91076e7 2.40762
\(963\) 0 0
\(964\) −6.68194e7 −2.31585
\(965\) 1.78176e7 0.615929
\(966\) 0 0
\(967\) 1.52545e6 0.0524603 0.0262302 0.999656i \(-0.491650\pi\)
0.0262302 + 0.999656i \(0.491650\pi\)
\(968\) −2.77726e7 −0.952639
\(969\) 0 0
\(970\) 9.71951e7 3.31677
\(971\) 4.37167e7 1.48799 0.743993 0.668187i \(-0.232929\pi\)
0.743993 + 0.668187i \(0.232929\pi\)
\(972\) 0 0
\(973\) 2.51553e7 0.851817
\(974\) −9.79190e6 −0.330727
\(975\) 0 0
\(976\) 3.90754e6 0.131304
\(977\) −1.59223e6 −0.0533666 −0.0266833 0.999644i \(-0.508495\pi\)
−0.0266833 + 0.999644i \(0.508495\pi\)
\(978\) 0 0
\(979\) −1.18237e7 −0.394271
\(980\) 5.12917e6 0.170601
\(981\) 0 0
\(982\) −1.56025e7 −0.516316
\(983\) −1.98366e7 −0.654762 −0.327381 0.944892i \(-0.606166\pi\)
−0.327381 + 0.944892i \(0.606166\pi\)
\(984\) 0 0
\(985\) −5.24479e7 −1.72241
\(986\) −1.89968e7 −0.622285
\(987\) 0 0
\(988\) −2.26567e7 −0.738421
\(989\) 5.66595e6 0.184197
\(990\) 0 0
\(991\) 5.77793e7 1.86891 0.934454 0.356083i \(-0.115888\pi\)
0.934454 + 0.356083i \(0.115888\pi\)
\(992\) 3.07164e7 0.991040
\(993\) 0 0
\(994\) −4.99475e7 −1.60342
\(995\) 1.83753e7 0.588405
\(996\) 0 0
\(997\) −2.48258e7 −0.790980 −0.395490 0.918470i \(-0.629425\pi\)
−0.395490 + 0.918470i \(0.629425\pi\)
\(998\) −2.87261e7 −0.912958
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 207.6.a.f.1.5 5
3.2 odd 2 69.6.a.e.1.1 5
12.11 even 2 1104.6.a.r.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.a.e.1.1 5 3.2 odd 2
207.6.a.f.1.5 5 1.1 even 1 trivial
1104.6.a.r.1.5 5 12.11 even 2