Properties

Label 245.6.a.l.1.7
Level $245$
Weight $6$
Character 245.1
Self dual yes
Analytic conductor $39.294$
Analytic rank $1$
Dimension $10$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(39.2940358542\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \( x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + 7583055 x^{2} + 5935300 x - 22888100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{3}\cdot 7^{5} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-4.37629\) of defining polynomial
Character \(\chi\) \(=\) 245.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.37629 q^{2} +16.5213 q^{3} -3.09546 q^{4} -25.0000 q^{5} +88.8236 q^{6} -188.684 q^{8} +29.9545 q^{9} +O(q^{10})\) \(q+5.37629 q^{2} +16.5213 q^{3} -3.09546 q^{4} -25.0000 q^{5} +88.8236 q^{6} -188.684 q^{8} +29.9545 q^{9} -134.407 q^{10} -11.0558 q^{11} -51.1411 q^{12} +367.295 q^{13} -413.033 q^{15} -915.363 q^{16} -1173.52 q^{17} +161.044 q^{18} -342.504 q^{19} +77.3865 q^{20} -59.4393 q^{22} -2072.14 q^{23} -3117.30 q^{24} +625.000 q^{25} +1974.69 q^{26} -3519.80 q^{27} -2627.73 q^{29} -2220.59 q^{30} -8264.94 q^{31} +1116.61 q^{32} -182.657 q^{33} -6309.19 q^{34} -92.7229 q^{36} +4807.69 q^{37} -1841.40 q^{38} +6068.21 q^{39} +4717.09 q^{40} -2909.16 q^{41} -10245.5 q^{43} +34.2228 q^{44} -748.862 q^{45} -11140.4 q^{46} -19728.5 q^{47} -15123.0 q^{48} +3360.18 q^{50} -19388.1 q^{51} -1136.95 q^{52} +39395.2 q^{53} -18923.5 q^{54} +276.395 q^{55} -5658.63 q^{57} -14127.4 q^{58} +8056.38 q^{59} +1278.53 q^{60} -46149.3 q^{61} -44434.7 q^{62} +35294.9 q^{64} -9182.38 q^{65} -982.016 q^{66} +39912.1 q^{67} +3632.58 q^{68} -34234.5 q^{69} +60453.6 q^{71} -5651.92 q^{72} +46818.8 q^{73} +25847.6 q^{74} +10325.8 q^{75} +1060.21 q^{76} +32624.5 q^{78} -12641.1 q^{79} +22884.1 q^{80} -65430.7 q^{81} -15640.5 q^{82} +4899.74 q^{83} +29338.0 q^{85} -55082.8 q^{86} -43413.5 q^{87} +2086.05 q^{88} +69297.5 q^{89} -4026.10 q^{90} +6414.22 q^{92} -136548. q^{93} -106066. q^{94} +8562.61 q^{95} +18447.9 q^{96} -14604.2 q^{97} -331.171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9} - 250 q^{10} + 794 q^{11} - 2560 q^{12} - 474 q^{13} + 1450 q^{15} + 2394 q^{16} - 802 q^{17} + 3702 q^{18} - 7292 q^{19} - 4550 q^{20} + 3948 q^{22} + 3708 q^{23} - 2092 q^{24} + 6250 q^{25} - 6576 q^{26} - 11818 q^{27} - 8866 q^{29} + 3600 q^{30} - 13292 q^{31} + 2590 q^{32} - 9854 q^{33} - 44468 q^{34} - 10690 q^{36} + 16124 q^{37} - 2180 q^{38} - 24982 q^{39} - 6750 q^{40} - 34836 q^{41} - 28604 q^{43} - 31120 q^{44} - 17500 q^{45} - 39732 q^{46} - 18106 q^{47} - 101788 q^{48} + 6250 q^{50} + 31602 q^{51} + 22480 q^{52} + 36440 q^{53} - 80836 q^{54} - 19850 q^{55} + 126988 q^{57} - 100356 q^{58} - 18644 q^{59} + 64000 q^{60} - 68120 q^{61} - 181052 q^{62} - 59358 q^{64} + 11850 q^{65} - 157780 q^{66} + 92328 q^{67} - 288540 q^{68} - 170888 q^{69} + 5044 q^{71} - 61654 q^{72} - 170160 q^{73} - 216584 q^{74} - 36250 q^{75} - 505180 q^{76} - 158008 q^{78} + 26442 q^{79} - 59850 q^{80} - 56314 q^{81} - 353948 q^{82} - 353360 q^{83} + 20050 q^{85} - 52940 q^{86} + 3190 q^{87} - 114916 q^{88} - 90704 q^{89} - 92550 q^{90} + 183520 q^{92} + 188560 q^{93} + 121388 q^{94} + 182300 q^{95} - 442220 q^{96} - 236382 q^{97} + 109024 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.37629 0.950404 0.475202 0.879877i \(-0.342375\pi\)
0.475202 + 0.879877i \(0.342375\pi\)
\(3\) 16.5213 1.05984 0.529922 0.848046i \(-0.322221\pi\)
0.529922 + 0.848046i \(0.322221\pi\)
\(4\) −3.09546 −0.0967331
\(5\) −25.0000 −0.447214
\(6\) 88.8236 1.00728
\(7\) 0 0
\(8\) −188.684 −1.04234
\(9\) 29.9545 0.123269
\(10\) −134.407 −0.425033
\(11\) −11.0558 −0.0275492 −0.0137746 0.999905i \(-0.504385\pi\)
−0.0137746 + 0.999905i \(0.504385\pi\)
\(12\) −51.1411 −0.102522
\(13\) 367.295 0.602777 0.301389 0.953501i \(-0.402550\pi\)
0.301389 + 0.953501i \(0.402550\pi\)
\(14\) 0 0
\(15\) −413.033 −0.473977
\(16\) −915.363 −0.893910
\(17\) −1173.52 −0.984846 −0.492423 0.870356i \(-0.663889\pi\)
−0.492423 + 0.870356i \(0.663889\pi\)
\(18\) 161.044 0.117156
\(19\) −342.504 −0.217662 −0.108831 0.994060i \(-0.534711\pi\)
−0.108831 + 0.994060i \(0.534711\pi\)
\(20\) 77.3865 0.0432604
\(21\) 0 0
\(22\) −59.4393 −0.0261828
\(23\) −2072.14 −0.816769 −0.408384 0.912810i \(-0.633908\pi\)
−0.408384 + 0.912810i \(0.633908\pi\)
\(24\) −3117.30 −1.10472
\(25\) 625.000 0.200000
\(26\) 1974.69 0.572882
\(27\) −3519.80 −0.929198
\(28\) 0 0
\(29\) −2627.73 −0.580210 −0.290105 0.956995i \(-0.593690\pi\)
−0.290105 + 0.956995i \(0.593690\pi\)
\(30\) −2220.59 −0.450469
\(31\) −8264.94 −1.54467 −0.772335 0.635216i \(-0.780911\pi\)
−0.772335 + 0.635216i \(0.780911\pi\)
\(32\) 1116.61 0.192764
\(33\) −182.657 −0.0291978
\(34\) −6309.19 −0.936001
\(35\) 0 0
\(36\) −92.7229 −0.0119242
\(37\) 4807.69 0.577341 0.288670 0.957429i \(-0.406787\pi\)
0.288670 + 0.957429i \(0.406787\pi\)
\(38\) −1841.40 −0.206866
\(39\) 6068.21 0.638850
\(40\) 4717.09 0.466148
\(41\) −2909.16 −0.270276 −0.135138 0.990827i \(-0.543148\pi\)
−0.135138 + 0.990827i \(0.543148\pi\)
\(42\) 0 0
\(43\) −10245.5 −0.845011 −0.422505 0.906360i \(-0.638849\pi\)
−0.422505 + 0.906360i \(0.638849\pi\)
\(44\) 34.2228 0.00266492
\(45\) −748.862 −0.0551278
\(46\) −11140.4 −0.776260
\(47\) −19728.5 −1.30271 −0.651357 0.758771i \(-0.725800\pi\)
−0.651357 + 0.758771i \(0.725800\pi\)
\(48\) −15123.0 −0.947405
\(49\) 0 0
\(50\) 3360.18 0.190081
\(51\) −19388.1 −1.04378
\(52\) −1136.95 −0.0583085
\(53\) 39395.2 1.92643 0.963217 0.268725i \(-0.0866024\pi\)
0.963217 + 0.268725i \(0.0866024\pi\)
\(54\) −18923.5 −0.883113
\(55\) 276.395 0.0123204
\(56\) 0 0
\(57\) −5658.63 −0.230687
\(58\) −14127.4 −0.551433
\(59\) 8056.38 0.301308 0.150654 0.988587i \(-0.451862\pi\)
0.150654 + 0.988587i \(0.451862\pi\)
\(60\) 1278.53 0.0458492
\(61\) −46149.3 −1.58796 −0.793982 0.607941i \(-0.791996\pi\)
−0.793982 + 0.607941i \(0.791996\pi\)
\(62\) −44434.7 −1.46806
\(63\) 0 0
\(64\) 35294.9 1.07711
\(65\) −9182.38 −0.269570
\(66\) −982.016 −0.0277497
\(67\) 39912.1 1.08622 0.543110 0.839662i \(-0.317247\pi\)
0.543110 + 0.839662i \(0.317247\pi\)
\(68\) 3632.58 0.0952672
\(69\) −34234.5 −0.865647
\(70\) 0 0
\(71\) 60453.6 1.42323 0.711617 0.702567i \(-0.247963\pi\)
0.711617 + 0.702567i \(0.247963\pi\)
\(72\) −5651.92 −0.128489
\(73\) 46818.8 1.02828 0.514142 0.857705i \(-0.328110\pi\)
0.514142 + 0.857705i \(0.328110\pi\)
\(74\) 25847.6 0.548706
\(75\) 10325.8 0.211969
\(76\) 1060.21 0.0210551
\(77\) 0 0
\(78\) 32624.5 0.607165
\(79\) −12641.1 −0.227885 −0.113943 0.993487i \(-0.536348\pi\)
−0.113943 + 0.993487i \(0.536348\pi\)
\(80\) 22884.1 0.399769
\(81\) −65430.7 −1.10807
\(82\) −15640.5 −0.256872
\(83\) 4899.74 0.0780689 0.0390344 0.999238i \(-0.487572\pi\)
0.0390344 + 0.999238i \(0.487572\pi\)
\(84\) 0 0
\(85\) 29338.0 0.440436
\(86\) −55082.8 −0.803101
\(87\) −43413.5 −0.614932
\(88\) 2086.05 0.0287156
\(89\) 69297.5 0.927348 0.463674 0.886006i \(-0.346531\pi\)
0.463674 + 0.886006i \(0.346531\pi\)
\(90\) −4026.10 −0.0523936
\(91\) 0 0
\(92\) 6414.22 0.0790086
\(93\) −136548. −1.63711
\(94\) −106066. −1.23810
\(95\) 8562.61 0.0973413
\(96\) 18447.9 0.204300
\(97\) −14604.2 −0.157597 −0.0787984 0.996891i \(-0.525108\pi\)
−0.0787984 + 0.996891i \(0.525108\pi\)
\(98\) 0 0
\(99\) −331.171 −0.00339597
\(100\) −1934.66 −0.0193466
\(101\) 153606. 1.49832 0.749160 0.662389i \(-0.230457\pi\)
0.749160 + 0.662389i \(0.230457\pi\)
\(102\) −104236. −0.992015
\(103\) −131855. −1.22463 −0.612315 0.790614i \(-0.709762\pi\)
−0.612315 + 0.790614i \(0.709762\pi\)
\(104\) −69302.5 −0.628298
\(105\) 0 0
\(106\) 211800. 1.83089
\(107\) −169892. −1.43454 −0.717270 0.696795i \(-0.754609\pi\)
−0.717270 + 0.696795i \(0.754609\pi\)
\(108\) 10895.4 0.0898842
\(109\) 21967.1 0.177095 0.0885477 0.996072i \(-0.471777\pi\)
0.0885477 + 0.996072i \(0.471777\pi\)
\(110\) 1485.98 0.0117093
\(111\) 79429.4 0.611891
\(112\) 0 0
\(113\) −135136. −0.995575 −0.497787 0.867299i \(-0.665854\pi\)
−0.497787 + 0.867299i \(0.665854\pi\)
\(114\) −30422.4 −0.219246
\(115\) 51803.4 0.365270
\(116\) 8134.02 0.0561255
\(117\) 11002.1 0.0743040
\(118\) 43313.5 0.286364
\(119\) 0 0
\(120\) 77932.6 0.494044
\(121\) −160929. −0.999241
\(122\) −248112. −1.50921
\(123\) −48063.2 −0.286451
\(124\) 25583.8 0.149421
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) −286149. −1.57429 −0.787143 0.616771i \(-0.788440\pi\)
−0.787143 + 0.616771i \(0.788440\pi\)
\(128\) 154024. 0.830928
\(129\) −169269. −0.895579
\(130\) −49367.2 −0.256200
\(131\) 39360.5 0.200393 0.100196 0.994968i \(-0.468053\pi\)
0.100196 + 0.994968i \(0.468053\pi\)
\(132\) 565.406 0.00282440
\(133\) 0 0
\(134\) 214579. 1.03235
\(135\) 87994.9 0.415550
\(136\) 221424. 1.02654
\(137\) 256567. 1.16788 0.583942 0.811796i \(-0.301510\pi\)
0.583942 + 0.811796i \(0.301510\pi\)
\(138\) −184055. −0.822714
\(139\) −51525.4 −0.226196 −0.113098 0.993584i \(-0.536077\pi\)
−0.113098 + 0.993584i \(0.536077\pi\)
\(140\) 0 0
\(141\) −325941. −1.38067
\(142\) 325017. 1.35265
\(143\) −4060.74 −0.0166060
\(144\) −27419.2 −0.110192
\(145\) 65693.2 0.259478
\(146\) 251712. 0.977286
\(147\) 0 0
\(148\) −14882.0 −0.0558480
\(149\) 420194. 1.55055 0.775273 0.631627i \(-0.217612\pi\)
0.775273 + 0.631627i \(0.217612\pi\)
\(150\) 55514.7 0.201456
\(151\) 79551.5 0.283926 0.141963 0.989872i \(-0.454659\pi\)
0.141963 + 0.989872i \(0.454659\pi\)
\(152\) 64624.9 0.226877
\(153\) −35152.2 −0.121401
\(154\) 0 0
\(155\) 206623. 0.690797
\(156\) −18783.9 −0.0617979
\(157\) −143038. −0.463131 −0.231565 0.972819i \(-0.574385\pi\)
−0.231565 + 0.972819i \(0.574385\pi\)
\(158\) −67962.1 −0.216583
\(159\) 650862. 2.04172
\(160\) −27915.2 −0.0862068
\(161\) 0 0
\(162\) −351775. −1.05312
\(163\) 528116. 1.55690 0.778449 0.627708i \(-0.216007\pi\)
0.778449 + 0.627708i \(0.216007\pi\)
\(164\) 9005.19 0.0261447
\(165\) 4566.42 0.0130577
\(166\) 26342.4 0.0741969
\(167\) −181743. −0.504274 −0.252137 0.967692i \(-0.581133\pi\)
−0.252137 + 0.967692i \(0.581133\pi\)
\(168\) 0 0
\(169\) −236387. −0.636660
\(170\) 157730. 0.418592
\(171\) −10259.5 −0.0268310
\(172\) 31714.5 0.0817405
\(173\) −640689. −1.62754 −0.813771 0.581186i \(-0.802589\pi\)
−0.813771 + 0.581186i \(0.802589\pi\)
\(174\) −233404. −0.584434
\(175\) 0 0
\(176\) 10120.1 0.0246265
\(177\) 133102. 0.319339
\(178\) 372564. 0.881354
\(179\) 565927. 1.32016 0.660082 0.751193i \(-0.270521\pi\)
0.660082 + 0.751193i \(0.270521\pi\)
\(180\) 2318.07 0.00533268
\(181\) 461950. 1.04809 0.524045 0.851690i \(-0.324422\pi\)
0.524045 + 0.851690i \(0.324422\pi\)
\(182\) 0 0
\(183\) −762448. −1.68299
\(184\) 390978. 0.851350
\(185\) −120192. −0.258195
\(186\) −734121. −1.55591
\(187\) 12974.2 0.0271317
\(188\) 61068.8 0.126016
\(189\) 0 0
\(190\) 46035.1 0.0925135
\(191\) −372488. −0.738804 −0.369402 0.929270i \(-0.620437\pi\)
−0.369402 + 0.929270i \(0.620437\pi\)
\(192\) 583118. 1.14157
\(193\) 19371.9 0.0374351 0.0187176 0.999825i \(-0.494042\pi\)
0.0187176 + 0.999825i \(0.494042\pi\)
\(194\) −78516.3 −0.149781
\(195\) −151705. −0.285702
\(196\) 0 0
\(197\) −129308. −0.237388 −0.118694 0.992931i \(-0.537871\pi\)
−0.118694 + 0.992931i \(0.537871\pi\)
\(198\) −1780.47 −0.00322754
\(199\) −439258. −0.786298 −0.393149 0.919475i \(-0.628614\pi\)
−0.393149 + 0.919475i \(0.628614\pi\)
\(200\) −117927. −0.208468
\(201\) 659402. 1.15122
\(202\) 825831. 1.42401
\(203\) 0 0
\(204\) 60015.1 0.100968
\(205\) 72729.0 0.120871
\(206\) −708894. −1.16389
\(207\) −62069.8 −0.100683
\(208\) −336208. −0.538828
\(209\) 3786.66 0.00599640
\(210\) 0 0
\(211\) −275198. −0.425540 −0.212770 0.977102i \(-0.568248\pi\)
−0.212770 + 0.977102i \(0.568248\pi\)
\(212\) −121946. −0.186350
\(213\) 998775. 1.50841
\(214\) −913388. −1.36339
\(215\) 256138. 0.377900
\(216\) 664128. 0.968539
\(217\) 0 0
\(218\) 118102. 0.168312
\(219\) 773510. 1.08982
\(220\) −855.570 −0.00119179
\(221\) −431028. −0.593642
\(222\) 427036. 0.581543
\(223\) 1.10303e6 1.48534 0.742672 0.669655i \(-0.233558\pi\)
0.742672 + 0.669655i \(0.233558\pi\)
\(224\) 0 0
\(225\) 18721.5 0.0246539
\(226\) −726529. −0.946198
\(227\) −773342. −0.996110 −0.498055 0.867145i \(-0.665952\pi\)
−0.498055 + 0.867145i \(0.665952\pi\)
\(228\) 17516.1 0.0223151
\(229\) 1.43998e6 1.81454 0.907271 0.420547i \(-0.138162\pi\)
0.907271 + 0.420547i \(0.138162\pi\)
\(230\) 278511. 0.347154
\(231\) 0 0
\(232\) 495809. 0.604775
\(233\) −5656.54 −0.00682592 −0.00341296 0.999994i \(-0.501086\pi\)
−0.00341296 + 0.999994i \(0.501086\pi\)
\(234\) 59150.7 0.0706188
\(235\) 493212. 0.582592
\(236\) −24938.2 −0.0291464
\(237\) −208847. −0.241523
\(238\) 0 0
\(239\) 1.62686e6 1.84227 0.921137 0.389238i \(-0.127262\pi\)
0.921137 + 0.389238i \(0.127262\pi\)
\(240\) 378076. 0.423692
\(241\) −1.38641e6 −1.53762 −0.768810 0.639478i \(-0.779151\pi\)
−0.768810 + 0.639478i \(0.779151\pi\)
\(242\) −865200. −0.949682
\(243\) −225691. −0.245188
\(244\) 142853. 0.153609
\(245\) 0 0
\(246\) −258402. −0.272244
\(247\) −125800. −0.131201
\(248\) 1.55946e6 1.61007
\(249\) 80950.2 0.0827408
\(250\) −84004.6 −0.0850067
\(251\) −398018. −0.398766 −0.199383 0.979922i \(-0.563894\pi\)
−0.199383 + 0.979922i \(0.563894\pi\)
\(252\) 0 0
\(253\) 22909.2 0.0225013
\(254\) −1.53842e6 −1.49621
\(255\) 484703. 0.466794
\(256\) −301357. −0.287396
\(257\) −510302. −0.481942 −0.240971 0.970532i \(-0.577466\pi\)
−0.240971 + 0.970532i \(0.577466\pi\)
\(258\) −910042. −0.851162
\(259\) 0 0
\(260\) 28423.7 0.0260764
\(261\) −78712.2 −0.0715222
\(262\) 211614. 0.190454
\(263\) 1.37462e6 1.22544 0.612722 0.790298i \(-0.290074\pi\)
0.612722 + 0.790298i \(0.290074\pi\)
\(264\) 34464.3 0.0304340
\(265\) −984881. −0.861527
\(266\) 0 0
\(267\) 1.14489e6 0.982844
\(268\) −123546. −0.105073
\(269\) 263149. 0.221728 0.110864 0.993836i \(-0.464638\pi\)
0.110864 + 0.993836i \(0.464638\pi\)
\(270\) 473087. 0.394940
\(271\) −1.25268e6 −1.03614 −0.518069 0.855339i \(-0.673349\pi\)
−0.518069 + 0.855339i \(0.673349\pi\)
\(272\) 1.07420e6 0.880363
\(273\) 0 0
\(274\) 1.37938e6 1.10996
\(275\) −6909.88 −0.00550984
\(276\) 105971. 0.0837368
\(277\) −980534. −0.767827 −0.383914 0.923369i \(-0.625424\pi\)
−0.383914 + 0.923369i \(0.625424\pi\)
\(278\) −277016. −0.214977
\(279\) −247572. −0.190411
\(280\) 0 0
\(281\) −1.52611e6 −1.15298 −0.576489 0.817105i \(-0.695578\pi\)
−0.576489 + 0.817105i \(0.695578\pi\)
\(282\) −1.75236e6 −1.31220
\(283\) 260267. 0.193176 0.0965881 0.995324i \(-0.469207\pi\)
0.0965881 + 0.995324i \(0.469207\pi\)
\(284\) −187132. −0.137674
\(285\) 141466. 0.103167
\(286\) −21831.8 −0.0157824
\(287\) 0 0
\(288\) 33447.5 0.0237619
\(289\) −42707.6 −0.0300788
\(290\) 353186. 0.246609
\(291\) −241280. −0.167028
\(292\) −144926. −0.0994692
\(293\) −2.44271e6 −1.66228 −0.831138 0.556067i \(-0.812310\pi\)
−0.831138 + 0.556067i \(0.812310\pi\)
\(294\) 0 0
\(295\) −201410. −0.134749
\(296\) −907132. −0.601785
\(297\) 38914.2 0.0255986
\(298\) 2.25909e6 1.47364
\(299\) −761086. −0.492329
\(300\) −31963.2 −0.0205044
\(301\) 0 0
\(302\) 427692. 0.269845
\(303\) 2.53778e6 1.58799
\(304\) 313516. 0.194570
\(305\) 1.15373e6 0.710159
\(306\) −188988. −0.115380
\(307\) −179892. −0.108934 −0.0544672 0.998516i \(-0.517346\pi\)
−0.0544672 + 0.998516i \(0.517346\pi\)
\(308\) 0 0
\(309\) −2.17843e6 −1.29792
\(310\) 1.11087e6 0.656536
\(311\) −2.64551e6 −1.55099 −0.775494 0.631355i \(-0.782499\pi\)
−0.775494 + 0.631355i \(0.782499\pi\)
\(312\) −1.14497e6 −0.665898
\(313\) −2.02011e6 −1.16550 −0.582752 0.812650i \(-0.698024\pi\)
−0.582752 + 0.812650i \(0.698024\pi\)
\(314\) −769016. −0.440161
\(315\) 0 0
\(316\) 39129.9 0.0220441
\(317\) −2.88723e6 −1.61374 −0.806868 0.590731i \(-0.798839\pi\)
−0.806868 + 0.590731i \(0.798839\pi\)
\(318\) 3.49922e6 1.94046
\(319\) 29051.6 0.0159843
\(320\) −882371. −0.481700
\(321\) −2.80684e6 −1.52039
\(322\) 0 0
\(323\) 401936. 0.214363
\(324\) 202538. 0.107187
\(325\) 229559. 0.120555
\(326\) 2.83931e6 1.47968
\(327\) 362927. 0.187694
\(328\) 548910. 0.281719
\(329\) 0 0
\(330\) 24550.4 0.0124101
\(331\) 1.44013e6 0.722492 0.361246 0.932471i \(-0.382351\pi\)
0.361246 + 0.932471i \(0.382351\pi\)
\(332\) −15167.0 −0.00755185
\(333\) 144012. 0.0711685
\(334\) −977104. −0.479264
\(335\) −997803. −0.485772
\(336\) 0 0
\(337\) 401552. 0.192605 0.0963024 0.995352i \(-0.469298\pi\)
0.0963024 + 0.995352i \(0.469298\pi\)
\(338\) −1.27089e6 −0.605084
\(339\) −2.23262e6 −1.05515
\(340\) −90814.6 −0.0426048
\(341\) 91375.6 0.0425544
\(342\) −55158.3 −0.0255003
\(343\) 0 0
\(344\) 1.93316e6 0.880788
\(345\) 855862. 0.387129
\(346\) −3.44453e6 −1.54682
\(347\) 2.48643e6 1.10854 0.554272 0.832336i \(-0.312997\pi\)
0.554272 + 0.832336i \(0.312997\pi\)
\(348\) 134385. 0.0594843
\(349\) −760055. −0.334027 −0.167013 0.985955i \(-0.553412\pi\)
−0.167013 + 0.985955i \(0.553412\pi\)
\(350\) 0 0
\(351\) −1.29280e6 −0.560099
\(352\) −12345.0 −0.00531050
\(353\) 322965. 0.137949 0.0689746 0.997618i \(-0.478027\pi\)
0.0689746 + 0.997618i \(0.478027\pi\)
\(354\) 715596. 0.303501
\(355\) −1.51134e6 −0.636490
\(356\) −214508. −0.0897052
\(357\) 0 0
\(358\) 3.04259e6 1.25469
\(359\) −3.78096e6 −1.54834 −0.774170 0.632978i \(-0.781833\pi\)
−0.774170 + 0.632978i \(0.781833\pi\)
\(360\) 141298. 0.0574618
\(361\) −2.35879e6 −0.952623
\(362\) 2.48358e6 0.996109
\(363\) −2.65876e6 −1.05904
\(364\) 0 0
\(365\) −1.17047e6 −0.459863
\(366\) −4.09915e6 −1.59952
\(367\) −4.30592e6 −1.66879 −0.834393 0.551170i \(-0.814182\pi\)
−0.834393 + 0.551170i \(0.814182\pi\)
\(368\) 1.89676e6 0.730117
\(369\) −87142.4 −0.0333168
\(370\) −646189. −0.245389
\(371\) 0 0
\(372\) 422678. 0.158363
\(373\) 4.33886e6 1.61474 0.807371 0.590044i \(-0.200890\pi\)
0.807371 + 0.590044i \(0.200890\pi\)
\(374\) 69753.2 0.0257861
\(375\) −258146. −0.0947953
\(376\) 3.72244e6 1.35787
\(377\) −965151. −0.349737
\(378\) 0 0
\(379\) −3.27628e6 −1.17161 −0.585805 0.810452i \(-0.699222\pi\)
−0.585805 + 0.810452i \(0.699222\pi\)
\(380\) −26505.2 −0.00941612
\(381\) −4.72757e6 −1.66850
\(382\) −2.00261e6 −0.702162
\(383\) −3.60923e6 −1.25724 −0.628619 0.777713i \(-0.716380\pi\)
−0.628619 + 0.777713i \(0.716380\pi\)
\(384\) 2.54468e6 0.880654
\(385\) 0 0
\(386\) 104149. 0.0355785
\(387\) −306899. −0.104164
\(388\) 45206.6 0.0152448
\(389\) 1.60910e6 0.539148 0.269574 0.962980i \(-0.413117\pi\)
0.269574 + 0.962980i \(0.413117\pi\)
\(390\) −815611. −0.271532
\(391\) 2.43170e6 0.804391
\(392\) 0 0
\(393\) 650288. 0.212385
\(394\) −695197. −0.225615
\(395\) 316027. 0.101913
\(396\) 1025.13 0.000328503 0
\(397\) −121454. −0.0386755 −0.0193377 0.999813i \(-0.506156\pi\)
−0.0193377 + 0.999813i \(0.506156\pi\)
\(398\) −2.36158e6 −0.747300
\(399\) 0 0
\(400\) −572102. −0.178782
\(401\) −5.11280e6 −1.58781 −0.793904 0.608043i \(-0.791955\pi\)
−0.793904 + 0.608043i \(0.791955\pi\)
\(402\) 3.54514e6 1.09413
\(403\) −3.03567e6 −0.931091
\(404\) −475481. −0.144937
\(405\) 1.63577e6 0.495546
\(406\) 0 0
\(407\) −53152.9 −0.0159053
\(408\) 3.65822e6 1.08798
\(409\) 4.66827e6 1.37990 0.689950 0.723857i \(-0.257632\pi\)
0.689950 + 0.723857i \(0.257632\pi\)
\(410\) 391012. 0.114876
\(411\) 4.23883e6 1.23777
\(412\) 408153. 0.118462
\(413\) 0 0
\(414\) −333706. −0.0956891
\(415\) −122494. −0.0349135
\(416\) 410125. 0.116194
\(417\) −851268. −0.239732
\(418\) 20358.2 0.00569900
\(419\) 5.36826e6 1.49382 0.746910 0.664925i \(-0.231537\pi\)
0.746910 + 0.664925i \(0.231537\pi\)
\(420\) 0 0
\(421\) −1.72529e6 −0.474413 −0.237206 0.971459i \(-0.576232\pi\)
−0.237206 + 0.971459i \(0.576232\pi\)
\(422\) −1.47955e6 −0.404434
\(423\) −590957. −0.160585
\(424\) −7.43323e6 −2.00800
\(425\) −733450. −0.196969
\(426\) 5.36971e6 1.43360
\(427\) 0 0
\(428\) 525893. 0.138768
\(429\) −67088.9 −0.0175998
\(430\) 1.37707e6 0.359158
\(431\) −3.97363e6 −1.03037 −0.515186 0.857078i \(-0.672277\pi\)
−0.515186 + 0.857078i \(0.672277\pi\)
\(432\) 3.22189e6 0.830619
\(433\) −1.75813e6 −0.450642 −0.225321 0.974285i \(-0.572343\pi\)
−0.225321 + 0.974285i \(0.572343\pi\)
\(434\) 0 0
\(435\) 1.08534e6 0.275006
\(436\) −67998.4 −0.0171310
\(437\) 709716. 0.177779
\(438\) 4.15862e6 1.03577
\(439\) −5.12207e6 −1.26848 −0.634241 0.773135i \(-0.718687\pi\)
−0.634241 + 0.773135i \(0.718687\pi\)
\(440\) −52151.2 −0.0128420
\(441\) 0 0
\(442\) −2.31733e6 −0.564200
\(443\) 6.51360e6 1.57693 0.788464 0.615081i \(-0.210877\pi\)
0.788464 + 0.615081i \(0.210877\pi\)
\(444\) −245871. −0.0591901
\(445\) −1.73244e6 −0.414722
\(446\) 5.93024e6 1.41168
\(447\) 6.94217e6 1.64334
\(448\) 0 0
\(449\) −3.84667e6 −0.900469 −0.450234 0.892910i \(-0.648660\pi\)
−0.450234 + 0.892910i \(0.648660\pi\)
\(450\) 100653. 0.0234311
\(451\) 32163.1 0.00744589
\(452\) 418307. 0.0963051
\(453\) 1.31430e6 0.300918
\(454\) −4.15772e6 −0.946706
\(455\) 0 0
\(456\) 1.06769e6 0.240455
\(457\) 4.07431e6 0.912564 0.456282 0.889835i \(-0.349181\pi\)
0.456282 + 0.889835i \(0.349181\pi\)
\(458\) 7.74174e6 1.72455
\(459\) 4.13055e6 0.915116
\(460\) −160355. −0.0353337
\(461\) −863488. −0.189236 −0.0946180 0.995514i \(-0.530163\pi\)
−0.0946180 + 0.995514i \(0.530163\pi\)
\(462\) 0 0
\(463\) 7.54412e6 1.63552 0.817761 0.575559i \(-0.195215\pi\)
0.817761 + 0.575559i \(0.195215\pi\)
\(464\) 2.40532e6 0.518655
\(465\) 3.41370e6 0.732137
\(466\) −30411.2 −0.00648738
\(467\) −2.75815e6 −0.585229 −0.292614 0.956231i \(-0.594525\pi\)
−0.292614 + 0.956231i \(0.594525\pi\)
\(468\) −34056.7 −0.00718766
\(469\) 0 0
\(470\) 2.65166e6 0.553697
\(471\) −2.36318e6 −0.490846
\(472\) −1.52011e6 −0.314065
\(473\) 113272. 0.0232793
\(474\) −1.12282e6 −0.229544
\(475\) −214065. −0.0435323
\(476\) 0 0
\(477\) 1.18006e6 0.237470
\(478\) 8.74646e6 1.75090
\(479\) 3.00065e6 0.597553 0.298776 0.954323i \(-0.403422\pi\)
0.298776 + 0.954323i \(0.403422\pi\)
\(480\) −461197. −0.0913657
\(481\) 1.76584e6 0.348008
\(482\) −7.45375e6 −1.46136
\(483\) 0 0
\(484\) 498149. 0.0966597
\(485\) 365104. 0.0704794
\(486\) −1.21338e6 −0.233028
\(487\) −855280. −0.163413 −0.0817064 0.996656i \(-0.526037\pi\)
−0.0817064 + 0.996656i \(0.526037\pi\)
\(488\) 8.70761e6 1.65520
\(489\) 8.72518e6 1.65007
\(490\) 0 0
\(491\) 6.37895e6 1.19411 0.597056 0.802199i \(-0.296337\pi\)
0.597056 + 0.802199i \(0.296337\pi\)
\(492\) 148778. 0.0277093
\(493\) 3.08369e6 0.571417
\(494\) −676339. −0.124694
\(495\) 8279.27 0.00151873
\(496\) 7.56542e6 1.38079
\(497\) 0 0
\(498\) 435212. 0.0786372
\(499\) −1.75331e6 −0.315216 −0.157608 0.987502i \(-0.550378\pi\)
−0.157608 + 0.987502i \(0.550378\pi\)
\(500\) 48366.6 0.00865207
\(501\) −3.00264e6 −0.534452
\(502\) −2.13986e6 −0.378989
\(503\) −261372. −0.0460617 −0.0230308 0.999735i \(-0.507332\pi\)
−0.0230308 + 0.999735i \(0.507332\pi\)
\(504\) 0 0
\(505\) −3.84015e6 −0.670069
\(506\) 123166. 0.0213853
\(507\) −3.90543e6 −0.674760
\(508\) 885764. 0.152286
\(509\) 32421.3 0.00554672 0.00277336 0.999996i \(-0.499117\pi\)
0.00277336 + 0.999996i \(0.499117\pi\)
\(510\) 2.60591e6 0.443643
\(511\) 0 0
\(512\) −6.54895e6 −1.10407
\(513\) 1.20555e6 0.202251
\(514\) −2.74353e6 −0.458039
\(515\) 3.29639e6 0.547671
\(516\) 523967. 0.0866322
\(517\) 218114. 0.0358887
\(518\) 0 0
\(519\) −1.05850e7 −1.72494
\(520\) 1.73256e6 0.280983
\(521\) 5.56412e6 0.898053 0.449027 0.893518i \(-0.351771\pi\)
0.449027 + 0.893518i \(0.351771\pi\)
\(522\) −423180. −0.0679749
\(523\) −3.94058e6 −0.629950 −0.314975 0.949100i \(-0.601996\pi\)
−0.314975 + 0.949100i \(0.601996\pi\)
\(524\) −121839. −0.0193846
\(525\) 0 0
\(526\) 7.39037e6 1.16467
\(527\) 9.69907e6 1.52126
\(528\) 167197. 0.0261002
\(529\) −2.14259e6 −0.332889
\(530\) −5.29501e6 −0.818799
\(531\) 241325. 0.0371420
\(532\) 0 0
\(533\) −1.06852e6 −0.162916
\(534\) 6.15525e6 0.934098
\(535\) 4.24729e6 0.641546
\(536\) −7.53076e6 −1.13221
\(537\) 9.34988e6 1.39917
\(538\) 1.41476e6 0.210731
\(539\) 0 0
\(540\) −272385. −0.0401974
\(541\) 7.33948e6 1.07813 0.539066 0.842263i \(-0.318777\pi\)
0.539066 + 0.842263i \(0.318777\pi\)
\(542\) −6.73479e6 −0.984750
\(543\) 7.63204e6 1.11081
\(544\) −1.31036e6 −0.189843
\(545\) −549179. −0.0791995
\(546\) 0 0
\(547\) −5.92706e6 −0.846976 −0.423488 0.905902i \(-0.639194\pi\)
−0.423488 + 0.905902i \(0.639194\pi\)
\(548\) −794193. −0.112973
\(549\) −1.38238e6 −0.195747
\(550\) −37149.5 −0.00523657
\(551\) 900007. 0.126289
\(552\) 6.45948e6 0.902298
\(553\) 0 0
\(554\) −5.27164e6 −0.729746
\(555\) −1.98574e6 −0.273646
\(556\) 159495. 0.0218806
\(557\) 3.87133e6 0.528715 0.264358 0.964425i \(-0.414840\pi\)
0.264358 + 0.964425i \(0.414840\pi\)
\(558\) −1.33102e6 −0.180967
\(559\) −3.76312e6 −0.509353
\(560\) 0 0
\(561\) 214351. 0.0287554
\(562\) −8.20484e6 −1.09579
\(563\) 1.25365e6 0.166688 0.0833442 0.996521i \(-0.473440\pi\)
0.0833442 + 0.996521i \(0.473440\pi\)
\(564\) 1.00894e6 0.133557
\(565\) 3.37839e6 0.445235
\(566\) 1.39927e6 0.183595
\(567\) 0 0
\(568\) −1.14066e7 −1.48349
\(569\) −1.00618e7 −1.30285 −0.651425 0.758713i \(-0.725829\pi\)
−0.651425 + 0.758713i \(0.725829\pi\)
\(570\) 760561. 0.0980499
\(571\) −1.20255e7 −1.54352 −0.771759 0.635915i \(-0.780623\pi\)
−0.771759 + 0.635915i \(0.780623\pi\)
\(572\) 12569.9 0.00160635
\(573\) −6.15400e6 −0.783017
\(574\) 0 0
\(575\) −1.29509e6 −0.163354
\(576\) 1.05724e6 0.132775
\(577\) −1.46566e7 −1.83271 −0.916355 0.400366i \(-0.868883\pi\)
−0.916355 + 0.400366i \(0.868883\pi\)
\(578\) −229609. −0.0285870
\(579\) 320050. 0.0396754
\(580\) −203351. −0.0251001
\(581\) 0 0
\(582\) −1.29719e6 −0.158744
\(583\) −435546. −0.0530717
\(584\) −8.83394e6 −1.07182
\(585\) −275053. −0.0332298
\(586\) −1.31327e7 −1.57983
\(587\) −610951. −0.0731832 −0.0365916 0.999330i \(-0.511650\pi\)
−0.0365916 + 0.999330i \(0.511650\pi\)
\(588\) 0 0
\(589\) 2.83078e6 0.336215
\(590\) −1.08284e6 −0.128066
\(591\) −2.13634e6 −0.251595
\(592\) −4.40078e6 −0.516090
\(593\) 8.89186e6 1.03838 0.519190 0.854659i \(-0.326234\pi\)
0.519190 + 0.854659i \(0.326234\pi\)
\(594\) 209214. 0.0243290
\(595\) 0 0
\(596\) −1.30069e6 −0.149989
\(597\) −7.25713e6 −0.833353
\(598\) −4.09182e6 −0.467912
\(599\) 5.57297e6 0.634629 0.317314 0.948320i \(-0.397219\pi\)
0.317314 + 0.948320i \(0.397219\pi\)
\(600\) −1.94831e6 −0.220943
\(601\) −9.30873e6 −1.05125 −0.525623 0.850718i \(-0.676168\pi\)
−0.525623 + 0.850718i \(0.676168\pi\)
\(602\) 0 0
\(603\) 1.19555e6 0.133898
\(604\) −246248. −0.0274651
\(605\) 4.02322e6 0.446874
\(606\) 1.36438e7 1.50923
\(607\) −626627. −0.0690300 −0.0345150 0.999404i \(-0.510989\pi\)
−0.0345150 + 0.999404i \(0.510989\pi\)
\(608\) −382444. −0.0419574
\(609\) 0 0
\(610\) 6.20281e6 0.674938
\(611\) −7.24618e6 −0.785247
\(612\) 108812. 0.0117435
\(613\) 2.98473e6 0.320814 0.160407 0.987051i \(-0.448719\pi\)
0.160407 + 0.987051i \(0.448719\pi\)
\(614\) −967151. −0.103532
\(615\) 1.20158e6 0.128105
\(616\) 0 0
\(617\) 345728. 0.0365613 0.0182806 0.999833i \(-0.494181\pi\)
0.0182806 + 0.999833i \(0.494181\pi\)
\(618\) −1.17119e7 −1.23355
\(619\) −2.73766e6 −0.287179 −0.143589 0.989637i \(-0.545864\pi\)
−0.143589 + 0.989637i \(0.545864\pi\)
\(620\) −639595. −0.0668230
\(621\) 7.29350e6 0.758939
\(622\) −1.42230e7 −1.47406
\(623\) 0 0
\(624\) −5.55461e6 −0.571074
\(625\) 390625. 0.0400000
\(626\) −1.08607e7 −1.10770
\(627\) 62560.7 0.00635525
\(628\) 442770. 0.0448001
\(629\) −5.64192e6 −0.568591
\(630\) 0 0
\(631\) 4.80556e6 0.480474 0.240237 0.970714i \(-0.422775\pi\)
0.240237 + 0.970714i \(0.422775\pi\)
\(632\) 2.38516e6 0.237534
\(633\) −4.54665e6 −0.451006
\(634\) −1.55226e7 −1.53370
\(635\) 7.15373e6 0.704042
\(636\) −2.01472e6 −0.197502
\(637\) 0 0
\(638\) 156190. 0.0151915
\(639\) 1.81086e6 0.175441
\(640\) −3.85060e6 −0.371602
\(641\) 3.79928e6 0.365221 0.182611 0.983185i \(-0.441545\pi\)
0.182611 + 0.983185i \(0.441545\pi\)
\(642\) −1.50904e7 −1.44498
\(643\) 2.46468e6 0.235089 0.117545 0.993068i \(-0.462498\pi\)
0.117545 + 0.993068i \(0.462498\pi\)
\(644\) 0 0
\(645\) 4.23173e6 0.400515
\(646\) 2.16092e6 0.203732
\(647\) 5.72708e6 0.537865 0.268932 0.963159i \(-0.413329\pi\)
0.268932 + 0.963159i \(0.413329\pi\)
\(648\) 1.23457e7 1.15499
\(649\) −89069.8 −0.00830078
\(650\) 1.23418e6 0.114576
\(651\) 0 0
\(652\) −1.63476e6 −0.150604
\(653\) −2.62713e6 −0.241101 −0.120550 0.992707i \(-0.538466\pi\)
−0.120550 + 0.992707i \(0.538466\pi\)
\(654\) 1.95120e6 0.178385
\(655\) −984012. −0.0896184
\(656\) 2.66294e6 0.241603
\(657\) 1.40243e6 0.126756
\(658\) 0 0
\(659\) 1.46417e7 1.31334 0.656671 0.754177i \(-0.271964\pi\)
0.656671 + 0.754177i \(0.271964\pi\)
\(660\) −14135.2 −0.00126311
\(661\) 1.34296e7 1.19553 0.597763 0.801673i \(-0.296056\pi\)
0.597763 + 0.801673i \(0.296056\pi\)
\(662\) 7.74259e6 0.686659
\(663\) −7.12116e6 −0.629168
\(664\) −924500. −0.0813742
\(665\) 0 0
\(666\) 774250. 0.0676387
\(667\) 5.44501e6 0.473897
\(668\) 562579. 0.0487800
\(669\) 1.82236e7 1.57423
\(670\) −5.36448e6 −0.461680
\(671\) 510218. 0.0437471
\(672\) 0 0
\(673\) 8.25651e6 0.702682 0.351341 0.936248i \(-0.385726\pi\)
0.351341 + 0.936248i \(0.385726\pi\)
\(674\) 2.15886e6 0.183052
\(675\) −2.19987e6 −0.185840
\(676\) 731727. 0.0615861
\(677\) 4.92012e6 0.412576 0.206288 0.978491i \(-0.433862\pi\)
0.206288 + 0.978491i \(0.433862\pi\)
\(678\) −1.20032e7 −1.00282
\(679\) 0 0
\(680\) −5.53560e6 −0.459084
\(681\) −1.27766e7 −1.05572
\(682\) 491262. 0.0404438
\(683\) −1.47407e7 −1.20911 −0.604556 0.796563i \(-0.706649\pi\)
−0.604556 + 0.796563i \(0.706649\pi\)
\(684\) 31758.0 0.00259545
\(685\) −6.41418e6 −0.522293
\(686\) 0 0
\(687\) 2.37903e7 1.92313
\(688\) 9.37836e6 0.755363
\(689\) 1.44697e7 1.16121
\(690\) 4.60137e6 0.367929
\(691\) −1.37360e7 −1.09437 −0.547185 0.837012i \(-0.684301\pi\)
−0.547185 + 0.837012i \(0.684301\pi\)
\(692\) 1.98323e6 0.157437
\(693\) 0 0
\(694\) 1.33678e7 1.05356
\(695\) 1.28813e6 0.101158
\(696\) 8.19142e6 0.640968
\(697\) 3.41396e6 0.266180
\(698\) −4.08628e6 −0.317460
\(699\) −93453.6 −0.00723441
\(700\) 0 0
\(701\) −9.23895e6 −0.710113 −0.355057 0.934845i \(-0.615538\pi\)
−0.355057 + 0.934845i \(0.615538\pi\)
\(702\) −6.95049e6 −0.532320
\(703\) −1.64665e6 −0.125665
\(704\) −390213. −0.0296736
\(705\) 8.14853e6 0.617457
\(706\) 1.73636e6 0.131107
\(707\) 0 0
\(708\) −412012. −0.0308907
\(709\) −1.56718e7 −1.17086 −0.585428 0.810724i \(-0.699074\pi\)
−0.585428 + 0.810724i \(0.699074\pi\)
\(710\) −8.12541e6 −0.604922
\(711\) −378657. −0.0280913
\(712\) −1.30753e7 −0.966611
\(713\) 1.71261e7 1.26164
\(714\) 0 0
\(715\) 101519. 0.00742644
\(716\) −1.75181e6 −0.127704
\(717\) 2.68778e7 1.95252
\(718\) −2.03276e7 −1.47155
\(719\) 7.77979e6 0.561236 0.280618 0.959819i \(-0.409461\pi\)
0.280618 + 0.959819i \(0.409461\pi\)
\(720\) 685481. 0.0492792
\(721\) 0 0
\(722\) −1.26815e7 −0.905377
\(723\) −2.29053e7 −1.62964
\(724\) −1.42995e6 −0.101385
\(725\) −1.64233e6 −0.116042
\(726\) −1.42943e7 −1.00652
\(727\) 3.18266e6 0.223334 0.111667 0.993746i \(-0.464381\pi\)
0.111667 + 0.993746i \(0.464381\pi\)
\(728\) 0 0
\(729\) 1.21709e7 0.848213
\(730\) −6.29280e6 −0.437055
\(731\) 1.20233e7 0.832205
\(732\) 2.36013e6 0.162801
\(733\) −2.33890e7 −1.60787 −0.803935 0.594717i \(-0.797264\pi\)
−0.803935 + 0.594717i \(0.797264\pi\)
\(734\) −2.31499e7 −1.58602
\(735\) 0 0
\(736\) −2.31377e6 −0.157444
\(737\) −441261. −0.0299245
\(738\) −468503. −0.0316644
\(739\) 2.22717e6 0.150017 0.0750087 0.997183i \(-0.476102\pi\)
0.0750087 + 0.997183i \(0.476102\pi\)
\(740\) 372050. 0.0249760
\(741\) −2.07839e6 −0.139053
\(742\) 0 0
\(743\) −936803. −0.0622553 −0.0311276 0.999515i \(-0.509910\pi\)
−0.0311276 + 0.999515i \(0.509910\pi\)
\(744\) 2.57643e7 1.70642
\(745\) −1.05049e7 −0.693425
\(746\) 2.33270e7 1.53466
\(747\) 146769. 0.00962351
\(748\) −40161.2 −0.00262453
\(749\) 0 0
\(750\) −1.38787e6 −0.0900938
\(751\) −1.70492e6 −0.110307 −0.0551536 0.998478i \(-0.517565\pi\)
−0.0551536 + 0.998478i \(0.517565\pi\)
\(752\) 1.80587e7 1.16451
\(753\) −6.57579e6 −0.422630
\(754\) −5.18894e6 −0.332391
\(755\) −1.98879e6 −0.126976
\(756\) 0 0
\(757\) 2.53663e7 1.60886 0.804428 0.594051i \(-0.202472\pi\)
0.804428 + 0.594051i \(0.202472\pi\)
\(758\) −1.76143e7 −1.11350
\(759\) 378490. 0.0238479
\(760\) −1.61562e6 −0.101463
\(761\) 1.83989e7 1.15167 0.575837 0.817565i \(-0.304676\pi\)
0.575837 + 0.817565i \(0.304676\pi\)
\(762\) −2.54168e7 −1.58575
\(763\) 0 0
\(764\) 1.15302e6 0.0714668
\(765\) 878805. 0.0542924
\(766\) −1.94043e7 −1.19488
\(767\) 2.95907e6 0.181621
\(768\) −4.97882e6 −0.304595
\(769\) 619294. 0.0377643 0.0188821 0.999822i \(-0.493989\pi\)
0.0188821 + 0.999822i \(0.493989\pi\)
\(770\) 0 0
\(771\) −8.43087e6 −0.510783
\(772\) −59965.0 −0.00362122
\(773\) 1.09079e7 0.656588 0.328294 0.944576i \(-0.393526\pi\)
0.328294 + 0.944576i \(0.393526\pi\)
\(774\) −1.64998e6 −0.0989978
\(775\) −5.16559e6 −0.308934
\(776\) 2.75557e6 0.164269
\(777\) 0 0
\(778\) 8.65098e6 0.512408
\(779\) 996400. 0.0588288
\(780\) 469597. 0.0276369
\(781\) −668364. −0.0392090
\(782\) 1.30735e7 0.764496
\(783\) 9.24906e6 0.539130
\(784\) 0 0
\(785\) 3.57596e6 0.207118
\(786\) 3.49614e6 0.201852
\(787\) 184858. 0.0106390 0.00531951 0.999986i \(-0.498307\pi\)
0.00531951 + 0.999986i \(0.498307\pi\)
\(788\) 400267. 0.0229633
\(789\) 2.27106e7 1.29878
\(790\) 1.69905e6 0.0968588
\(791\) 0 0
\(792\) 62486.5 0.00353975
\(793\) −1.69504e7 −0.957188
\(794\) −652972. −0.0367573
\(795\) −1.62715e7 −0.913085
\(796\) 1.35971e6 0.0760611
\(797\) 3.23367e7 1.80323 0.901613 0.432543i \(-0.142384\pi\)
0.901613 + 0.432543i \(0.142384\pi\)
\(798\) 0 0
\(799\) 2.31518e7 1.28297
\(800\) 697881. 0.0385528
\(801\) 2.07577e6 0.114314
\(802\) −2.74879e7 −1.50906
\(803\) −517620. −0.0283284
\(804\) −2.04115e6 −0.111362
\(805\) 0 0
\(806\) −1.63207e7 −0.884912
\(807\) 4.34757e6 0.234997
\(808\) −2.89829e7 −1.56176
\(809\) 9.09846e6 0.488761 0.244381 0.969679i \(-0.421415\pi\)
0.244381 + 0.969679i \(0.421415\pi\)
\(810\) 8.79436e6 0.470968
\(811\) −3.70294e7 −1.97695 −0.988473 0.151396i \(-0.951623\pi\)
−0.988473 + 0.151396i \(0.951623\pi\)
\(812\) 0 0
\(813\) −2.06960e7 −1.09815
\(814\) −285765. −0.0151164
\(815\) −1.32029e7 −0.696266
\(816\) 1.77472e7 0.933048
\(817\) 3.50913e6 0.183926
\(818\) 2.50980e7 1.31146
\(819\) 0 0
\(820\) −225130. −0.0116923
\(821\) 3.14038e7 1.62601 0.813007 0.582254i \(-0.197829\pi\)
0.813007 + 0.582254i \(0.197829\pi\)
\(822\) 2.27892e7 1.17639
\(823\) −3.33574e7 −1.71669 −0.858346 0.513072i \(-0.828507\pi\)
−0.858346 + 0.513072i \(0.828507\pi\)
\(824\) 2.48789e7 1.27648
\(825\) −114160. −0.00583957
\(826\) 0 0
\(827\) 6.34159e6 0.322429 0.161215 0.986919i \(-0.448459\pi\)
0.161215 + 0.986919i \(0.448459\pi\)
\(828\) 192135. 0.00973934
\(829\) −1.57969e7 −0.798334 −0.399167 0.916878i \(-0.630701\pi\)
−0.399167 + 0.916878i \(0.630701\pi\)
\(830\) −658561. −0.0331819
\(831\) −1.61997e7 −0.813777
\(832\) 1.29636e7 0.649259
\(833\) 0 0
\(834\) −4.57667e6 −0.227842
\(835\) 4.54358e6 0.225518
\(836\) −11721.5 −0.000580051 0
\(837\) 2.90909e7 1.43530
\(838\) 2.88613e7 1.41973
\(839\) 1.88579e7 0.924888 0.462444 0.886649i \(-0.346973\pi\)
0.462444 + 0.886649i \(0.346973\pi\)
\(840\) 0 0
\(841\) −1.36062e7 −0.663357
\(842\) −9.27565e6 −0.450883
\(843\) −2.52134e7 −1.22198
\(844\) 851866. 0.0411638
\(845\) 5.90968e6 0.284723
\(846\) −3.17716e6 −0.152621
\(847\) 0 0
\(848\) −3.60610e7 −1.72206
\(849\) 4.29996e6 0.204737
\(850\) −3.94324e6 −0.187200
\(851\) −9.96219e6 −0.471554
\(852\) −3.09167e6 −0.145913
\(853\) 1.96760e7 0.925898 0.462949 0.886385i \(-0.346791\pi\)
0.462949 + 0.886385i \(0.346791\pi\)
\(854\) 0 0
\(855\) 256488. 0.0119992
\(856\) 3.20558e7 1.49528
\(857\) −1.15028e7 −0.534997 −0.267499 0.963558i \(-0.586197\pi\)
−0.267499 + 0.963558i \(0.586197\pi\)
\(858\) −360690. −0.0167269
\(859\) −9.91985e6 −0.458693 −0.229347 0.973345i \(-0.573659\pi\)
−0.229347 + 0.973345i \(0.573659\pi\)
\(860\) −792864. −0.0365555
\(861\) 0 0
\(862\) −2.13634e7 −0.979269
\(863\) 6.99312e6 0.319628 0.159814 0.987147i \(-0.448911\pi\)
0.159814 + 0.987147i \(0.448911\pi\)
\(864\) −3.93024e6 −0.179116
\(865\) 1.60172e7 0.727859
\(866\) −9.45224e6 −0.428292
\(867\) −705587. −0.0318788
\(868\) 0 0
\(869\) 139757. 0.00627805
\(870\) 5.83510e6 0.261367
\(871\) 1.46595e7 0.654749
\(872\) −4.14484e6 −0.184594
\(873\) −437460. −0.0194269
\(874\) 3.81564e6 0.168962
\(875\) 0 0
\(876\) −2.39437e6 −0.105422
\(877\) 4.60833e6 0.202323 0.101161 0.994870i \(-0.467744\pi\)
0.101161 + 0.994870i \(0.467744\pi\)
\(878\) −2.75378e7 −1.20557
\(879\) −4.03568e7 −1.76175
\(880\) −253002. −0.0110133
\(881\) 3.09916e7 1.34525 0.672627 0.739982i \(-0.265166\pi\)
0.672627 + 0.739982i \(0.265166\pi\)
\(882\) 0 0
\(883\) −2.62829e7 −1.13441 −0.567207 0.823575i \(-0.691976\pi\)
−0.567207 + 0.823575i \(0.691976\pi\)
\(884\) 1.33423e6 0.0574249
\(885\) −3.32755e6 −0.142813
\(886\) 3.50190e7 1.49872
\(887\) −1.77899e6 −0.0759215 −0.0379607 0.999279i \(-0.512086\pi\)
−0.0379607 + 0.999279i \(0.512086\pi\)
\(888\) −1.49870e7 −0.637798
\(889\) 0 0
\(890\) −9.31409e6 −0.394154
\(891\) 723389. 0.0305265
\(892\) −3.41440e6 −0.143682
\(893\) 6.75709e6 0.283551
\(894\) 3.73232e7 1.56183
\(895\) −1.41482e7 −0.590396
\(896\) 0 0
\(897\) −1.25742e7 −0.521792
\(898\) −2.06808e7 −0.855809
\(899\) 2.17180e7 0.896232
\(900\) −57951.8 −0.00238485
\(901\) −4.62311e7 −1.89724
\(902\) 172918. 0.00707660
\(903\) 0 0
\(904\) 2.54979e7 1.03773
\(905\) −1.15488e7 −0.468720
\(906\) 7.06604e6 0.285993
\(907\) −2.60166e7 −1.05010 −0.525051 0.851071i \(-0.675954\pi\)
−0.525051 + 0.851071i \(0.675954\pi\)
\(908\) 2.39385e6 0.0963568
\(909\) 4.60119e6 0.184697
\(910\) 0 0
\(911\) −2.82785e7 −1.12891 −0.564457 0.825463i \(-0.690914\pi\)
−0.564457 + 0.825463i \(0.690914\pi\)
\(912\) 5.17970e6 0.206214
\(913\) −54170.6 −0.00215073
\(914\) 2.19047e7 0.867304
\(915\) 1.90612e7 0.752658
\(916\) −4.45739e6 −0.175526
\(917\) 0 0
\(918\) 2.22071e7 0.869730
\(919\) 3.48158e7 1.35984 0.679920 0.733286i \(-0.262014\pi\)
0.679920 + 0.733286i \(0.262014\pi\)
\(920\) −9.77446e6 −0.380735
\(921\) −2.97205e6 −0.115454
\(922\) −4.64236e6 −0.179851
\(923\) 2.22043e7 0.857893
\(924\) 0 0
\(925\) 3.00481e6 0.115468
\(926\) 4.05594e7 1.55440
\(927\) −3.94966e6 −0.150960
\(928\) −2.93414e6 −0.111844
\(929\) −2.23517e7 −0.849710 −0.424855 0.905261i \(-0.639675\pi\)
−0.424855 + 0.905261i \(0.639675\pi\)
\(930\) 1.83530e7 0.695826
\(931\) 0 0
\(932\) 17509.6 0.000660292 0
\(933\) −4.37074e7 −1.64381
\(934\) −1.48286e7 −0.556203
\(935\) −324355. −0.0121337
\(936\) −2.07592e6 −0.0774500
\(937\) −6.87782e6 −0.255919 −0.127959 0.991779i \(-0.540843\pi\)
−0.127959 + 0.991779i \(0.540843\pi\)
\(938\) 0 0
\(939\) −3.33749e7 −1.23525
\(940\) −1.52672e6 −0.0563559
\(941\) 3.65000e7 1.34375 0.671875 0.740664i \(-0.265489\pi\)
0.671875 + 0.740664i \(0.265489\pi\)
\(942\) −1.27052e7 −0.466502
\(943\) 6.02818e6 0.220753
\(944\) −7.37452e6 −0.269342
\(945\) 0 0
\(946\) 608985. 0.0221248
\(947\) 3.53650e7 1.28144 0.640721 0.767773i \(-0.278635\pi\)
0.640721 + 0.767773i \(0.278635\pi\)
\(948\) 646479. 0.0233633
\(949\) 1.71963e7 0.619827
\(950\) −1.15088e6 −0.0413733
\(951\) −4.77008e7 −1.71031
\(952\) 0 0
\(953\) −8.09150e6 −0.288600 −0.144300 0.989534i \(-0.546093\pi\)
−0.144300 + 0.989534i \(0.546093\pi\)
\(954\) 6.34437e6 0.225693
\(955\) 9.31221e6 0.330403
\(956\) −5.03587e6 −0.178209
\(957\) 479972. 0.0169409
\(958\) 1.61324e7 0.567916
\(959\) 0 0
\(960\) −1.45780e7 −0.510527
\(961\) 3.96801e7 1.38600
\(962\) 9.49368e6 0.330748
\(963\) −5.08902e6 −0.176835
\(964\) 4.29158e6 0.148739
\(965\) −484298. −0.0167415
\(966\) 0 0
\(967\) 1.82499e7 0.627617 0.313808 0.949486i \(-0.398395\pi\)
0.313808 + 0.949486i \(0.398395\pi\)
\(968\) 3.03646e7 1.04155
\(969\) 6.64051e6 0.227192
\(970\) 1.96291e6 0.0669839
\(971\) −1.53154e7 −0.521292 −0.260646 0.965434i \(-0.583935\pi\)
−0.260646 + 0.965434i \(0.583935\pi\)
\(972\) 698619. 0.0237178
\(973\) 0 0
\(974\) −4.59824e6 −0.155308
\(975\) 3.79263e6 0.127770
\(976\) 4.22434e7 1.41950
\(977\) 1.80410e7 0.604679 0.302339 0.953200i \(-0.402232\pi\)
0.302339 + 0.953200i \(0.402232\pi\)
\(978\) 4.69091e7 1.56823
\(979\) −766140. −0.0255477
\(980\) 0 0
\(981\) 658014. 0.0218305
\(982\) 3.42951e7 1.13489
\(983\) 1.41126e7 0.465824 0.232912 0.972498i \(-0.425175\pi\)
0.232912 + 0.972498i \(0.425175\pi\)
\(984\) 9.06873e6 0.298579
\(985\) 3.23270e6 0.106163
\(986\) 1.65788e7 0.543077
\(987\) 0 0
\(988\) 389409. 0.0126915
\(989\) 2.12301e7 0.690178
\(990\) 44511.8 0.00144340
\(991\) −5.56339e6 −0.179952 −0.0899758 0.995944i \(-0.528679\pi\)
−0.0899758 + 0.995944i \(0.528679\pi\)
\(992\) −9.22871e6 −0.297757
\(993\) 2.37929e7 0.765729
\(994\) 0 0
\(995\) 1.09815e7 0.351643
\(996\) −250578. −0.00800378
\(997\) −2.71962e6 −0.0866503 −0.0433252 0.999061i \(-0.513795\pi\)
−0.0433252 + 0.999061i \(0.513795\pi\)
\(998\) −9.42632e6 −0.299582
\(999\) −1.69221e7 −0.536463
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 245.6.a.l.1.7 10
7.6 odd 2 245.6.a.m.1.7 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.6.a.l.1.7 10 1.1 even 1 trivial
245.6.a.m.1.7 yes 10 7.6 odd 2