Properties

Label 1859.2.a.t.1.18
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.23194 q^{2} +1.36188 q^{3} +2.98154 q^{4} +4.28736 q^{5} +3.03963 q^{6} +0.384100 q^{7} +2.19073 q^{8} -1.14528 q^{9} +O(q^{10})\) \(q+2.23194 q^{2} +1.36188 q^{3} +2.98154 q^{4} +4.28736 q^{5} +3.03963 q^{6} +0.384100 q^{7} +2.19073 q^{8} -1.14528 q^{9} +9.56911 q^{10} +1.00000 q^{11} +4.06050 q^{12} +0.857286 q^{14} +5.83888 q^{15} -1.07351 q^{16} -4.75294 q^{17} -2.55618 q^{18} -2.17281 q^{19} +12.7829 q^{20} +0.523099 q^{21} +2.23194 q^{22} +2.70390 q^{23} +2.98352 q^{24} +13.3814 q^{25} -5.64538 q^{27} +1.14521 q^{28} -10.2556 q^{29} +13.0320 q^{30} +3.64487 q^{31} -6.77746 q^{32} +1.36188 q^{33} -10.6083 q^{34} +1.64677 q^{35} -3.41468 q^{36} -4.30010 q^{37} -4.84956 q^{38} +9.39245 q^{40} +6.28472 q^{41} +1.16752 q^{42} +0.639237 q^{43} +2.98154 q^{44} -4.91021 q^{45} +6.03493 q^{46} +4.82001 q^{47} -1.46199 q^{48} -6.85247 q^{49} +29.8665 q^{50} -6.47295 q^{51} +3.32193 q^{53} -12.6001 q^{54} +4.28736 q^{55} +0.841459 q^{56} -2.95911 q^{57} -22.8898 q^{58} -8.90125 q^{59} +17.4088 q^{60} +8.06080 q^{61} +8.13512 q^{62} -0.439900 q^{63} -12.9798 q^{64} +3.03963 q^{66} +14.7519 q^{67} -14.1711 q^{68} +3.68239 q^{69} +3.67549 q^{70} -13.9356 q^{71} -2.50899 q^{72} -11.4254 q^{73} -9.59755 q^{74} +18.2240 q^{75} -6.47830 q^{76} +0.384100 q^{77} +7.58183 q^{79} -4.60251 q^{80} -4.25252 q^{81} +14.0271 q^{82} -13.8004 q^{83} +1.55964 q^{84} -20.3776 q^{85} +1.42674 q^{86} -13.9669 q^{87} +2.19073 q^{88} +4.74761 q^{89} -10.9593 q^{90} +8.06178 q^{92} +4.96389 q^{93} +10.7580 q^{94} -9.31560 q^{95} -9.23010 q^{96} +15.3780 q^{97} -15.2943 q^{98} -1.14528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23194 1.57822 0.789109 0.614254i \(-0.210543\pi\)
0.789109 + 0.614254i \(0.210543\pi\)
\(3\) 1.36188 0.786283 0.393142 0.919478i \(-0.371388\pi\)
0.393142 + 0.919478i \(0.371388\pi\)
\(4\) 2.98154 1.49077
\(5\) 4.28736 1.91737 0.958683 0.284478i \(-0.0918202\pi\)
0.958683 + 0.284478i \(0.0918202\pi\)
\(6\) 3.03963 1.24093
\(7\) 0.384100 0.145176 0.0725880 0.997362i \(-0.476874\pi\)
0.0725880 + 0.997362i \(0.476874\pi\)
\(8\) 2.19073 0.774540
\(9\) −1.14528 −0.381759
\(10\) 9.56911 3.02602
\(11\) 1.00000 0.301511
\(12\) 4.06050 1.17217
\(13\) 0 0
\(14\) 0.857286 0.229119
\(15\) 5.83888 1.50759
\(16\) −1.07351 −0.268377
\(17\) −4.75294 −1.15276 −0.576379 0.817182i \(-0.695535\pi\)
−0.576379 + 0.817182i \(0.695535\pi\)
\(18\) −2.55618 −0.602498
\(19\) −2.17281 −0.498476 −0.249238 0.968442i \(-0.580180\pi\)
−0.249238 + 0.968442i \(0.580180\pi\)
\(20\) 12.7829 2.85835
\(21\) 0.523099 0.114149
\(22\) 2.23194 0.475850
\(23\) 2.70390 0.563802 0.281901 0.959444i \(-0.409035\pi\)
0.281901 + 0.959444i \(0.409035\pi\)
\(24\) 2.98352 0.609008
\(25\) 13.3814 2.67629
\(26\) 0 0
\(27\) −5.64538 −1.08645
\(28\) 1.14521 0.216424
\(29\) −10.2556 −1.90442 −0.952209 0.305449i \(-0.901194\pi\)
−0.952209 + 0.305449i \(0.901194\pi\)
\(30\) 13.0320 2.37931
\(31\) 3.64487 0.654638 0.327319 0.944914i \(-0.393855\pi\)
0.327319 + 0.944914i \(0.393855\pi\)
\(32\) −6.77746 −1.19810
\(33\) 1.36188 0.237073
\(34\) −10.6083 −1.81930
\(35\) 1.64677 0.278355
\(36\) −3.41468 −0.569114
\(37\) −4.30010 −0.706932 −0.353466 0.935447i \(-0.614997\pi\)
−0.353466 + 0.935447i \(0.614997\pi\)
\(38\) −4.84956 −0.786703
\(39\) 0 0
\(40\) 9.39245 1.48508
\(41\) 6.28472 0.981508 0.490754 0.871298i \(-0.336721\pi\)
0.490754 + 0.871298i \(0.336721\pi\)
\(42\) 1.16752 0.180153
\(43\) 0.639237 0.0974827 0.0487414 0.998811i \(-0.484479\pi\)
0.0487414 + 0.998811i \(0.484479\pi\)
\(44\) 2.98154 0.449484
\(45\) −4.91021 −0.731971
\(46\) 6.03493 0.889801
\(47\) 4.82001 0.703071 0.351536 0.936174i \(-0.385660\pi\)
0.351536 + 0.936174i \(0.385660\pi\)
\(48\) −1.46199 −0.211020
\(49\) −6.85247 −0.978924
\(50\) 29.8665 4.22377
\(51\) −6.47295 −0.906395
\(52\) 0 0
\(53\) 3.32193 0.456302 0.228151 0.973626i \(-0.426732\pi\)
0.228151 + 0.973626i \(0.426732\pi\)
\(54\) −12.6001 −1.71466
\(55\) 4.28736 0.578107
\(56\) 0.841459 0.112445
\(57\) −2.95911 −0.391943
\(58\) −22.8898 −3.00558
\(59\) −8.90125 −1.15884 −0.579422 0.815028i \(-0.696722\pi\)
−0.579422 + 0.815028i \(0.696722\pi\)
\(60\) 17.4088 2.24747
\(61\) 8.06080 1.03208 0.516040 0.856565i \(-0.327406\pi\)
0.516040 + 0.856565i \(0.327406\pi\)
\(62\) 8.13512 1.03316
\(63\) −0.439900 −0.0554222
\(64\) −12.9798 −1.62248
\(65\) 0 0
\(66\) 3.03963 0.374153
\(67\) 14.7519 1.80223 0.901114 0.433583i \(-0.142751\pi\)
0.901114 + 0.433583i \(0.142751\pi\)
\(68\) −14.1711 −1.71850
\(69\) 3.68239 0.443308
\(70\) 3.67549 0.439305
\(71\) −13.9356 −1.65385 −0.826927 0.562309i \(-0.809913\pi\)
−0.826927 + 0.562309i \(0.809913\pi\)
\(72\) −2.50899 −0.295687
\(73\) −11.4254 −1.33725 −0.668623 0.743602i \(-0.733116\pi\)
−0.668623 + 0.743602i \(0.733116\pi\)
\(74\) −9.59755 −1.11569
\(75\) 18.2240 2.10432
\(76\) −6.47830 −0.743112
\(77\) 0.384100 0.0437722
\(78\) 0 0
\(79\) 7.58183 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(80\) −4.60251 −0.514576
\(81\) −4.25252 −0.472502
\(82\) 14.0271 1.54903
\(83\) −13.8004 −1.51479 −0.757394 0.652958i \(-0.773528\pi\)
−0.757394 + 0.652958i \(0.773528\pi\)
\(84\) 1.55964 0.170171
\(85\) −20.3776 −2.21026
\(86\) 1.42674 0.153849
\(87\) −13.9669 −1.49741
\(88\) 2.19073 0.233533
\(89\) 4.74761 0.503245 0.251623 0.967825i \(-0.419036\pi\)
0.251623 + 0.967825i \(0.419036\pi\)
\(90\) −10.9593 −1.15521
\(91\) 0 0
\(92\) 8.06178 0.840498
\(93\) 4.96389 0.514731
\(94\) 10.7580 1.10960
\(95\) −9.31560 −0.955760
\(96\) −9.23010 −0.942044
\(97\) 15.3780 1.56140 0.780700 0.624906i \(-0.214863\pi\)
0.780700 + 0.624906i \(0.214863\pi\)
\(98\) −15.2943 −1.54495
\(99\) −1.14528 −0.115105
\(100\) 39.8973 3.98973
\(101\) 5.03341 0.500843 0.250422 0.968137i \(-0.419431\pi\)
0.250422 + 0.968137i \(0.419431\pi\)
\(102\) −14.4472 −1.43049
\(103\) 11.2981 1.11323 0.556617 0.830769i \(-0.312099\pi\)
0.556617 + 0.830769i \(0.312099\pi\)
\(104\) 0 0
\(105\) 2.24271 0.218866
\(106\) 7.41433 0.720143
\(107\) 10.3551 1.00106 0.500532 0.865718i \(-0.333138\pi\)
0.500532 + 0.865718i \(0.333138\pi\)
\(108\) −16.8319 −1.61965
\(109\) 0.406377 0.0389239 0.0194619 0.999811i \(-0.493805\pi\)
0.0194619 + 0.999811i \(0.493805\pi\)
\(110\) 9.56911 0.912379
\(111\) −5.85623 −0.555849
\(112\) −0.412334 −0.0389619
\(113\) −0.904703 −0.0851073 −0.0425536 0.999094i \(-0.513549\pi\)
−0.0425536 + 0.999094i \(0.513549\pi\)
\(114\) −6.60453 −0.618571
\(115\) 11.5926 1.08101
\(116\) −30.5775 −2.83905
\(117\) 0 0
\(118\) −19.8670 −1.82891
\(119\) −1.82560 −0.167353
\(120\) 12.7914 1.16769
\(121\) 1.00000 0.0909091
\(122\) 17.9912 1.62885
\(123\) 8.55905 0.771743
\(124\) 10.8673 0.975915
\(125\) 35.9343 3.21406
\(126\) −0.981829 −0.0874682
\(127\) 0.830064 0.0736563 0.0368281 0.999322i \(-0.488275\pi\)
0.0368281 + 0.999322i \(0.488275\pi\)
\(128\) −15.4153 −1.36253
\(129\) 0.870566 0.0766490
\(130\) 0 0
\(131\) 1.61595 0.141187 0.0705933 0.997505i \(-0.477511\pi\)
0.0705933 + 0.997505i \(0.477511\pi\)
\(132\) 4.06050 0.353422
\(133\) −0.834574 −0.0723667
\(134\) 32.9252 2.84431
\(135\) −24.2038 −2.08313
\(136\) −10.4124 −0.892858
\(137\) 2.65513 0.226843 0.113421 0.993547i \(-0.463819\pi\)
0.113421 + 0.993547i \(0.463819\pi\)
\(138\) 8.21886 0.699636
\(139\) 0.619987 0.0525866 0.0262933 0.999654i \(-0.491630\pi\)
0.0262933 + 0.999654i \(0.491630\pi\)
\(140\) 4.90992 0.414964
\(141\) 6.56429 0.552813
\(142\) −31.1034 −2.61014
\(143\) 0 0
\(144\) 1.22946 0.102455
\(145\) −43.9694 −3.65146
\(146\) −25.5008 −2.11046
\(147\) −9.33226 −0.769712
\(148\) −12.8209 −1.05387
\(149\) 3.82208 0.313117 0.156559 0.987669i \(-0.449960\pi\)
0.156559 + 0.987669i \(0.449960\pi\)
\(150\) 40.6747 3.32108
\(151\) −17.1470 −1.39540 −0.697702 0.716388i \(-0.745794\pi\)
−0.697702 + 0.716388i \(0.745794\pi\)
\(152\) −4.76003 −0.386089
\(153\) 5.44343 0.440075
\(154\) 0.857286 0.0690821
\(155\) 15.6269 1.25518
\(156\) 0 0
\(157\) −10.0397 −0.801254 −0.400627 0.916241i \(-0.631208\pi\)
−0.400627 + 0.916241i \(0.631208\pi\)
\(158\) 16.9222 1.34626
\(159\) 4.52407 0.358782
\(160\) −29.0574 −2.29719
\(161\) 1.03857 0.0818505
\(162\) −9.49135 −0.745711
\(163\) 7.10088 0.556184 0.278092 0.960554i \(-0.410298\pi\)
0.278092 + 0.960554i \(0.410298\pi\)
\(164\) 18.7381 1.46320
\(165\) 5.83888 0.454556
\(166\) −30.8016 −2.39066
\(167\) −18.1467 −1.40423 −0.702116 0.712062i \(-0.747761\pi\)
−0.702116 + 0.712062i \(0.747761\pi\)
\(168\) 1.14597 0.0884133
\(169\) 0 0
\(170\) −45.4815 −3.48827
\(171\) 2.48846 0.190297
\(172\) 1.90591 0.145324
\(173\) 10.1392 0.770866 0.385433 0.922736i \(-0.374052\pi\)
0.385433 + 0.922736i \(0.374052\pi\)
\(174\) −31.1733 −2.36324
\(175\) 5.13981 0.388533
\(176\) −1.07351 −0.0809186
\(177\) −12.1225 −0.911180
\(178\) 10.5964 0.794230
\(179\) −14.5995 −1.09122 −0.545610 0.838039i \(-0.683702\pi\)
−0.545610 + 0.838039i \(0.683702\pi\)
\(180\) −14.6400 −1.09120
\(181\) 15.2448 1.13313 0.566567 0.824016i \(-0.308271\pi\)
0.566567 + 0.824016i \(0.308271\pi\)
\(182\) 0 0
\(183\) 10.9779 0.811507
\(184\) 5.92351 0.436687
\(185\) −18.4361 −1.35545
\(186\) 11.0791 0.812358
\(187\) −4.75294 −0.347570
\(188\) 14.3711 1.04812
\(189\) −2.16839 −0.157727
\(190\) −20.7918 −1.50840
\(191\) 16.1594 1.16926 0.584628 0.811301i \(-0.301240\pi\)
0.584628 + 0.811301i \(0.301240\pi\)
\(192\) −17.6770 −1.27573
\(193\) 4.84928 0.349059 0.174529 0.984652i \(-0.444160\pi\)
0.174529 + 0.984652i \(0.444160\pi\)
\(194\) 34.3227 2.46423
\(195\) 0 0
\(196\) −20.4309 −1.45935
\(197\) 19.1751 1.36617 0.683084 0.730340i \(-0.260638\pi\)
0.683084 + 0.730340i \(0.260638\pi\)
\(198\) −2.55618 −0.181660
\(199\) 3.42451 0.242757 0.121379 0.992606i \(-0.461269\pi\)
0.121379 + 0.992606i \(0.461269\pi\)
\(200\) 29.3151 2.07289
\(201\) 20.0903 1.41706
\(202\) 11.2343 0.790440
\(203\) −3.93917 −0.276476
\(204\) −19.2994 −1.35123
\(205\) 26.9448 1.88191
\(206\) 25.2166 1.75692
\(207\) −3.09671 −0.215236
\(208\) 0 0
\(209\) −2.17281 −0.150296
\(210\) 5.00559 0.345418
\(211\) 22.3140 1.53616 0.768079 0.640355i \(-0.221213\pi\)
0.768079 + 0.640355i \(0.221213\pi\)
\(212\) 9.90445 0.680240
\(213\) −18.9787 −1.30040
\(214\) 23.1119 1.57990
\(215\) 2.74064 0.186910
\(216\) −12.3675 −0.841502
\(217\) 1.39999 0.0950378
\(218\) 0.907008 0.0614303
\(219\) −15.5601 −1.05145
\(220\) 12.7829 0.861825
\(221\) 0 0
\(222\) −13.0707 −0.877250
\(223\) 4.73412 0.317020 0.158510 0.987357i \(-0.449331\pi\)
0.158510 + 0.987357i \(0.449331\pi\)
\(224\) −2.60322 −0.173935
\(225\) −15.3254 −1.02170
\(226\) −2.01924 −0.134318
\(227\) −5.54598 −0.368100 −0.184050 0.982917i \(-0.558921\pi\)
−0.184050 + 0.982917i \(0.558921\pi\)
\(228\) −8.82269 −0.584297
\(229\) −9.51261 −0.628611 −0.314305 0.949322i \(-0.601772\pi\)
−0.314305 + 0.949322i \(0.601772\pi\)
\(230\) 25.8739 1.70607
\(231\) 0.523099 0.0344174
\(232\) −22.4672 −1.47505
\(233\) 4.49964 0.294781 0.147391 0.989078i \(-0.452913\pi\)
0.147391 + 0.989078i \(0.452913\pi\)
\(234\) 0 0
\(235\) 20.6651 1.34804
\(236\) −26.5394 −1.72757
\(237\) 10.3256 0.670718
\(238\) −4.07463 −0.264119
\(239\) −2.97813 −0.192639 −0.0963196 0.995350i \(-0.530707\pi\)
−0.0963196 + 0.995350i \(0.530707\pi\)
\(240\) −6.26808 −0.404603
\(241\) −17.6425 −1.13645 −0.568227 0.822872i \(-0.692370\pi\)
−0.568227 + 0.822872i \(0.692370\pi\)
\(242\) 2.23194 0.143474
\(243\) 11.1447 0.714933
\(244\) 24.0336 1.53859
\(245\) −29.3790 −1.87695
\(246\) 19.1032 1.21798
\(247\) 0 0
\(248\) 7.98493 0.507044
\(249\) −18.7945 −1.19105
\(250\) 80.2030 5.07248
\(251\) 11.9658 0.755273 0.377636 0.925954i \(-0.376737\pi\)
0.377636 + 0.925954i \(0.376737\pi\)
\(252\) −1.31158 −0.0826217
\(253\) 2.70390 0.169993
\(254\) 1.85265 0.116246
\(255\) −27.7519 −1.73789
\(256\) −8.44618 −0.527886
\(257\) 4.13033 0.257643 0.128822 0.991668i \(-0.458881\pi\)
0.128822 + 0.991668i \(0.458881\pi\)
\(258\) 1.94305 0.120969
\(259\) −1.65167 −0.102630
\(260\) 0 0
\(261\) 11.7455 0.727027
\(262\) 3.60671 0.222823
\(263\) −10.0479 −0.619581 −0.309790 0.950805i \(-0.600259\pi\)
−0.309790 + 0.950805i \(0.600259\pi\)
\(264\) 2.98352 0.183623
\(265\) 14.2423 0.874897
\(266\) −1.86272 −0.114210
\(267\) 6.46568 0.395693
\(268\) 43.9832 2.68670
\(269\) −7.95591 −0.485080 −0.242540 0.970141i \(-0.577981\pi\)
−0.242540 + 0.970141i \(0.577981\pi\)
\(270\) −54.0213 −3.28763
\(271\) −29.1531 −1.77092 −0.885462 0.464712i \(-0.846158\pi\)
−0.885462 + 0.464712i \(0.846158\pi\)
\(272\) 5.10232 0.309374
\(273\) 0 0
\(274\) 5.92607 0.358007
\(275\) 13.3814 0.806932
\(276\) 10.9792 0.660870
\(277\) 2.20405 0.132428 0.0662142 0.997805i \(-0.478908\pi\)
0.0662142 + 0.997805i \(0.478908\pi\)
\(278\) 1.38377 0.0829931
\(279\) −4.17438 −0.249914
\(280\) 3.60764 0.215597
\(281\) 28.6515 1.70920 0.854602 0.519284i \(-0.173801\pi\)
0.854602 + 0.519284i \(0.173801\pi\)
\(282\) 14.6511 0.872459
\(283\) −3.89684 −0.231643 −0.115821 0.993270i \(-0.536950\pi\)
−0.115821 + 0.993270i \(0.536950\pi\)
\(284\) −41.5496 −2.46552
\(285\) −12.6867 −0.751498
\(286\) 0 0
\(287\) 2.41396 0.142491
\(288\) 7.76206 0.457384
\(289\) 5.59049 0.328852
\(290\) −98.1370 −5.76280
\(291\) 20.9430 1.22770
\(292\) −34.0654 −1.99352
\(293\) −7.85353 −0.458808 −0.229404 0.973331i \(-0.573678\pi\)
−0.229404 + 0.973331i \(0.573678\pi\)
\(294\) −20.8290 −1.21477
\(295\) −38.1629 −2.22193
\(296\) −9.42036 −0.547547
\(297\) −5.64538 −0.327578
\(298\) 8.53065 0.494167
\(299\) 0 0
\(300\) 54.3354 3.13706
\(301\) 0.245531 0.0141522
\(302\) −38.2710 −2.20225
\(303\) 6.85492 0.393805
\(304\) 2.33252 0.133779
\(305\) 34.5595 1.97887
\(306\) 12.1494 0.694534
\(307\) −19.3947 −1.10691 −0.553456 0.832878i \(-0.686691\pi\)
−0.553456 + 0.832878i \(0.686691\pi\)
\(308\) 1.14521 0.0652543
\(309\) 15.3867 0.875317
\(310\) 34.8782 1.98095
\(311\) −23.4655 −1.33060 −0.665302 0.746574i \(-0.731697\pi\)
−0.665302 + 0.746574i \(0.731697\pi\)
\(312\) 0 0
\(313\) 7.41942 0.419370 0.209685 0.977769i \(-0.432756\pi\)
0.209685 + 0.977769i \(0.432756\pi\)
\(314\) −22.4079 −1.26455
\(315\) −1.88601 −0.106265
\(316\) 22.6055 1.27166
\(317\) 6.18430 0.347345 0.173672 0.984803i \(-0.444437\pi\)
0.173672 + 0.984803i \(0.444437\pi\)
\(318\) 10.0974 0.566236
\(319\) −10.2556 −0.574203
\(320\) −55.6492 −3.11089
\(321\) 14.1024 0.787120
\(322\) 2.31801 0.129178
\(323\) 10.3272 0.574622
\(324\) −12.6790 −0.704391
\(325\) 0 0
\(326\) 15.8487 0.877779
\(327\) 0.553438 0.0306052
\(328\) 13.7681 0.760217
\(329\) 1.85137 0.102069
\(330\) 13.0320 0.717388
\(331\) −13.7493 −0.755730 −0.377865 0.925861i \(-0.623342\pi\)
−0.377865 + 0.925861i \(0.623342\pi\)
\(332\) −41.1463 −2.25820
\(333\) 4.92480 0.269877
\(334\) −40.5022 −2.21618
\(335\) 63.2465 3.45553
\(336\) −0.561550 −0.0306351
\(337\) −8.57461 −0.467089 −0.233544 0.972346i \(-0.575032\pi\)
−0.233544 + 0.972346i \(0.575032\pi\)
\(338\) 0 0
\(339\) −1.23210 −0.0669184
\(340\) −60.7565 −3.29499
\(341\) 3.64487 0.197381
\(342\) 5.55409 0.300331
\(343\) −5.32073 −0.287292
\(344\) 1.40040 0.0755043
\(345\) 15.7877 0.849983
\(346\) 22.6300 1.21659
\(347\) 9.73625 0.522669 0.261335 0.965248i \(-0.415837\pi\)
0.261335 + 0.965248i \(0.415837\pi\)
\(348\) −41.6429 −2.23229
\(349\) 10.3236 0.552608 0.276304 0.961070i \(-0.410890\pi\)
0.276304 + 0.961070i \(0.410890\pi\)
\(350\) 11.4717 0.613190
\(351\) 0 0
\(352\) −6.77746 −0.361240
\(353\) −3.38311 −0.180065 −0.0900324 0.995939i \(-0.528697\pi\)
−0.0900324 + 0.995939i \(0.528697\pi\)
\(354\) −27.0565 −1.43804
\(355\) −59.7470 −3.17104
\(356\) 14.1552 0.750222
\(357\) −2.48626 −0.131587
\(358\) −32.5852 −1.72218
\(359\) −14.4639 −0.763376 −0.381688 0.924291i \(-0.624657\pi\)
−0.381688 + 0.924291i \(0.624657\pi\)
\(360\) −10.7569 −0.566940
\(361\) −14.2789 −0.751522
\(362\) 34.0253 1.78833
\(363\) 1.36188 0.0714803
\(364\) 0 0
\(365\) −48.9849 −2.56399
\(366\) 24.5019 1.28073
\(367\) −21.5437 −1.12457 −0.562286 0.826943i \(-0.690078\pi\)
−0.562286 + 0.826943i \(0.690078\pi\)
\(368\) −2.90265 −0.151311
\(369\) −7.19773 −0.374699
\(370\) −41.1481 −2.13919
\(371\) 1.27595 0.0662441
\(372\) 14.8000 0.767345
\(373\) −25.6291 −1.32703 −0.663513 0.748165i \(-0.730935\pi\)
−0.663513 + 0.748165i \(0.730935\pi\)
\(374\) −10.6083 −0.548541
\(375\) 48.9383 2.52716
\(376\) 10.5593 0.544557
\(377\) 0 0
\(378\) −4.83970 −0.248927
\(379\) −9.41163 −0.483443 −0.241722 0.970346i \(-0.577712\pi\)
−0.241722 + 0.970346i \(0.577712\pi\)
\(380\) −27.7748 −1.42482
\(381\) 1.13045 0.0579147
\(382\) 36.0668 1.84534
\(383\) −9.95412 −0.508632 −0.254316 0.967121i \(-0.581850\pi\)
−0.254316 + 0.967121i \(0.581850\pi\)
\(384\) −20.9938 −1.07133
\(385\) 1.64677 0.0839273
\(386\) 10.8233 0.550891
\(387\) −0.732102 −0.0372149
\(388\) 45.8501 2.32769
\(389\) −3.75782 −0.190529 −0.0952646 0.995452i \(-0.530370\pi\)
−0.0952646 + 0.995452i \(0.530370\pi\)
\(390\) 0 0
\(391\) −12.8515 −0.649927
\(392\) −15.0119 −0.758216
\(393\) 2.20074 0.111013
\(394\) 42.7975 2.15611
\(395\) 32.5060 1.63556
\(396\) −3.41468 −0.171594
\(397\) −16.9510 −0.850748 −0.425374 0.905018i \(-0.639857\pi\)
−0.425374 + 0.905018i \(0.639857\pi\)
\(398\) 7.64329 0.383123
\(399\) −1.13659 −0.0569007
\(400\) −14.3651 −0.718254
\(401\) 14.0800 0.703120 0.351560 0.936165i \(-0.385651\pi\)
0.351560 + 0.936165i \(0.385651\pi\)
\(402\) 44.8403 2.23643
\(403\) 0 0
\(404\) 15.0073 0.746642
\(405\) −18.2321 −0.905959
\(406\) −8.79198 −0.436339
\(407\) −4.30010 −0.213148
\(408\) −14.1805 −0.702039
\(409\) 34.6483 1.71325 0.856624 0.515941i \(-0.172557\pi\)
0.856624 + 0.515941i \(0.172557\pi\)
\(410\) 60.1391 2.97006
\(411\) 3.61597 0.178363
\(412\) 33.6857 1.65957
\(413\) −3.41897 −0.168236
\(414\) −6.91166 −0.339689
\(415\) −59.1672 −2.90440
\(416\) 0 0
\(417\) 0.844350 0.0413480
\(418\) −4.84956 −0.237200
\(419\) −0.846364 −0.0413476 −0.0206738 0.999786i \(-0.506581\pi\)
−0.0206738 + 0.999786i \(0.506581\pi\)
\(420\) 6.68673 0.326279
\(421\) 11.2318 0.547406 0.273703 0.961814i \(-0.411751\pi\)
0.273703 + 0.961814i \(0.411751\pi\)
\(422\) 49.8034 2.42439
\(423\) −5.52024 −0.268403
\(424\) 7.27744 0.353424
\(425\) −63.6013 −3.08512
\(426\) −42.3592 −2.05231
\(427\) 3.09615 0.149833
\(428\) 30.8741 1.49236
\(429\) 0 0
\(430\) 6.11693 0.294985
\(431\) −11.6680 −0.562030 −0.281015 0.959703i \(-0.590671\pi\)
−0.281015 + 0.959703i \(0.590671\pi\)
\(432\) 6.06035 0.291579
\(433\) −4.80473 −0.230901 −0.115450 0.993313i \(-0.536831\pi\)
−0.115450 + 0.993313i \(0.536831\pi\)
\(434\) 3.12470 0.149990
\(435\) −59.8812 −2.87108
\(436\) 1.21163 0.0580265
\(437\) −5.87504 −0.281041
\(438\) −34.7291 −1.65942
\(439\) 14.8238 0.707504 0.353752 0.935339i \(-0.384906\pi\)
0.353752 + 0.935339i \(0.384906\pi\)
\(440\) 9.39245 0.447767
\(441\) 7.84796 0.373713
\(442\) 0 0
\(443\) 11.2007 0.532162 0.266081 0.963951i \(-0.414271\pi\)
0.266081 + 0.963951i \(0.414271\pi\)
\(444\) −17.4606 −0.828642
\(445\) 20.3547 0.964905
\(446\) 10.5662 0.500326
\(447\) 5.20523 0.246199
\(448\) −4.98555 −0.235545
\(449\) 27.5634 1.30080 0.650399 0.759593i \(-0.274602\pi\)
0.650399 + 0.759593i \(0.274602\pi\)
\(450\) −34.2054 −1.61246
\(451\) 6.28472 0.295936
\(452\) −2.69741 −0.126875
\(453\) −23.3522 −1.09718
\(454\) −12.3783 −0.580941
\(455\) 0 0
\(456\) −6.48260 −0.303576
\(457\) 36.7079 1.71712 0.858562 0.512710i \(-0.171358\pi\)
0.858562 + 0.512710i \(0.171358\pi\)
\(458\) −21.2315 −0.992084
\(459\) 26.8322 1.25242
\(460\) 34.5637 1.61154
\(461\) 1.28568 0.0598803 0.0299401 0.999552i \(-0.490468\pi\)
0.0299401 + 0.999552i \(0.490468\pi\)
\(462\) 1.16752 0.0543181
\(463\) 25.8691 1.20224 0.601120 0.799159i \(-0.294721\pi\)
0.601120 + 0.799159i \(0.294721\pi\)
\(464\) 11.0095 0.511101
\(465\) 21.2820 0.986928
\(466\) 10.0429 0.465228
\(467\) −19.9050 −0.921095 −0.460548 0.887635i \(-0.652347\pi\)
−0.460548 + 0.887635i \(0.652347\pi\)
\(468\) 0 0
\(469\) 5.66619 0.261640
\(470\) 46.1232 2.12751
\(471\) −13.6729 −0.630013
\(472\) −19.5002 −0.897571
\(473\) 0.639237 0.0293921
\(474\) 23.0460 1.05854
\(475\) −29.0753 −1.33407
\(476\) −5.44311 −0.249485
\(477\) −3.80452 −0.174197
\(478\) −6.64699 −0.304026
\(479\) −41.7901 −1.90944 −0.954720 0.297507i \(-0.903845\pi\)
−0.954720 + 0.297507i \(0.903845\pi\)
\(480\) −39.5728 −1.80624
\(481\) 0 0
\(482\) −39.3770 −1.79357
\(483\) 1.41441 0.0643577
\(484\) 2.98154 0.135524
\(485\) 65.9310 2.99377
\(486\) 24.8743 1.12832
\(487\) −25.1408 −1.13924 −0.569619 0.821909i \(-0.692909\pi\)
−0.569619 + 0.821909i \(0.692909\pi\)
\(488\) 17.6590 0.799387
\(489\) 9.67057 0.437318
\(490\) −65.5720 −2.96224
\(491\) −33.4637 −1.51020 −0.755098 0.655612i \(-0.772411\pi\)
−0.755098 + 0.655612i \(0.772411\pi\)
\(492\) 25.5191 1.15049
\(493\) 48.7443 2.19533
\(494\) 0 0
\(495\) −4.91021 −0.220697
\(496\) −3.91280 −0.175690
\(497\) −5.35267 −0.240100
\(498\) −41.9481 −1.87974
\(499\) −32.1808 −1.44061 −0.720305 0.693657i \(-0.755998\pi\)
−0.720305 + 0.693657i \(0.755998\pi\)
\(500\) 107.139 4.79142
\(501\) −24.7137 −1.10412
\(502\) 26.7068 1.19198
\(503\) 25.3959 1.13235 0.566173 0.824287i \(-0.308424\pi\)
0.566173 + 0.824287i \(0.308424\pi\)
\(504\) −0.963702 −0.0429267
\(505\) 21.5801 0.960300
\(506\) 6.03493 0.268285
\(507\) 0 0
\(508\) 2.47487 0.109805
\(509\) −40.0559 −1.77545 −0.887723 0.460378i \(-0.847714\pi\)
−0.887723 + 0.460378i \(0.847714\pi\)
\(510\) −61.9404 −2.74277
\(511\) −4.38850 −0.194136
\(512\) 11.9792 0.529410
\(513\) 12.2663 0.541571
\(514\) 9.21864 0.406617
\(515\) 48.4389 2.13447
\(516\) 2.59562 0.114266
\(517\) 4.82001 0.211984
\(518\) −3.68641 −0.161972
\(519\) 13.8084 0.606119
\(520\) 0 0
\(521\) 9.99187 0.437752 0.218876 0.975753i \(-0.429761\pi\)
0.218876 + 0.975753i \(0.429761\pi\)
\(522\) 26.2152 1.14741
\(523\) 16.7831 0.733873 0.366937 0.930246i \(-0.380407\pi\)
0.366937 + 0.930246i \(0.380407\pi\)
\(524\) 4.81803 0.210477
\(525\) 6.99982 0.305497
\(526\) −22.4263 −0.977833
\(527\) −17.3239 −0.754640
\(528\) −1.46199 −0.0636250
\(529\) −15.6889 −0.682128
\(530\) 31.7879 1.38078
\(531\) 10.1944 0.442399
\(532\) −2.48831 −0.107882
\(533\) 0 0
\(534\) 14.4310 0.624490
\(535\) 44.3960 1.91941
\(536\) 32.3174 1.39590
\(537\) −19.8829 −0.858009
\(538\) −17.7571 −0.765562
\(539\) −6.85247 −0.295157
\(540\) −72.1645 −3.10546
\(541\) 9.22570 0.396644 0.198322 0.980137i \(-0.436451\pi\)
0.198322 + 0.980137i \(0.436451\pi\)
\(542\) −65.0678 −2.79490
\(543\) 20.7616 0.890965
\(544\) 32.2129 1.38112
\(545\) 1.74228 0.0746313
\(546\) 0 0
\(547\) −39.1085 −1.67216 −0.836079 0.548609i \(-0.815158\pi\)
−0.836079 + 0.548609i \(0.815158\pi\)
\(548\) 7.91636 0.338170
\(549\) −9.23183 −0.394005
\(550\) 29.8665 1.27351
\(551\) 22.2834 0.949306
\(552\) 8.06713 0.343360
\(553\) 2.91218 0.123838
\(554\) 4.91929 0.209001
\(555\) −25.1078 −1.06577
\(556\) 1.84852 0.0783945
\(557\) −23.3254 −0.988327 −0.494164 0.869369i \(-0.664526\pi\)
−0.494164 + 0.869369i \(0.664526\pi\)
\(558\) −9.31696 −0.394418
\(559\) 0 0
\(560\) −1.76782 −0.0747041
\(561\) −6.47295 −0.273288
\(562\) 63.9482 2.69749
\(563\) 8.48003 0.357391 0.178695 0.983904i \(-0.442812\pi\)
0.178695 + 0.983904i \(0.442812\pi\)
\(564\) 19.5717 0.824117
\(565\) −3.87879 −0.163182
\(566\) −8.69749 −0.365583
\(567\) −1.63339 −0.0685959
\(568\) −30.5292 −1.28098
\(569\) 6.74179 0.282630 0.141315 0.989965i \(-0.454867\pi\)
0.141315 + 0.989965i \(0.454867\pi\)
\(570\) −28.3160 −1.18603
\(571\) 16.4075 0.686632 0.343316 0.939220i \(-0.388450\pi\)
0.343316 + 0.939220i \(0.388450\pi\)
\(572\) 0 0
\(573\) 22.0073 0.919367
\(574\) 5.38780 0.224882
\(575\) 36.1821 1.50890
\(576\) 14.8655 0.619396
\(577\) 12.7296 0.529939 0.264969 0.964257i \(-0.414638\pi\)
0.264969 + 0.964257i \(0.414638\pi\)
\(578\) 12.4776 0.519000
\(579\) 6.60415 0.274459
\(580\) −131.097 −5.44349
\(581\) −5.30072 −0.219911
\(582\) 46.7435 1.93758
\(583\) 3.32193 0.137580
\(584\) −25.0300 −1.03575
\(585\) 0 0
\(586\) −17.5286 −0.724099
\(587\) 32.3761 1.33630 0.668152 0.744025i \(-0.267085\pi\)
0.668152 + 0.744025i \(0.267085\pi\)
\(588\) −27.8245 −1.14746
\(589\) −7.91960 −0.326321
\(590\) −85.1770 −3.50668
\(591\) 26.1142 1.07419
\(592\) 4.61619 0.189724
\(593\) 26.6848 1.09581 0.547907 0.836539i \(-0.315425\pi\)
0.547907 + 0.836539i \(0.315425\pi\)
\(594\) −12.6001 −0.516989
\(595\) −7.82702 −0.320877
\(596\) 11.3957 0.466786
\(597\) 4.66378 0.190876
\(598\) 0 0
\(599\) 16.3472 0.667928 0.333964 0.942586i \(-0.391614\pi\)
0.333964 + 0.942586i \(0.391614\pi\)
\(600\) 39.9238 1.62988
\(601\) −15.9276 −0.649700 −0.324850 0.945766i \(-0.605314\pi\)
−0.324850 + 0.945766i \(0.605314\pi\)
\(602\) 0.548009 0.0223352
\(603\) −16.8950 −0.688016
\(604\) −51.1245 −2.08023
\(605\) 4.28736 0.174306
\(606\) 15.2997 0.621509
\(607\) −33.1705 −1.34635 −0.673175 0.739483i \(-0.735070\pi\)
−0.673175 + 0.739483i \(0.735070\pi\)
\(608\) 14.7261 0.597222
\(609\) −5.36469 −0.217388
\(610\) 77.1347 3.12309
\(611\) 0 0
\(612\) 16.2298 0.656051
\(613\) 15.0843 0.609251 0.304626 0.952472i \(-0.401469\pi\)
0.304626 + 0.952472i \(0.401469\pi\)
\(614\) −43.2876 −1.74695
\(615\) 36.6957 1.47971
\(616\) 0.841459 0.0339033
\(617\) 12.1043 0.487302 0.243651 0.969863i \(-0.421655\pi\)
0.243651 + 0.969863i \(0.421655\pi\)
\(618\) 34.3421 1.38144
\(619\) −9.71704 −0.390561 −0.195280 0.980747i \(-0.562562\pi\)
−0.195280 + 0.980747i \(0.562562\pi\)
\(620\) 46.5921 1.87118
\(621\) −15.2645 −0.612544
\(622\) −52.3734 −2.09998
\(623\) 1.82355 0.0730591
\(624\) 0 0
\(625\) 87.1559 3.48624
\(626\) 16.5597 0.661858
\(627\) −2.95911 −0.118175
\(628\) −29.9337 −1.19449
\(629\) 20.4381 0.814922
\(630\) −4.20945 −0.167709
\(631\) 38.4391 1.53024 0.765118 0.643890i \(-0.222680\pi\)
0.765118 + 0.643890i \(0.222680\pi\)
\(632\) 16.6097 0.660700
\(633\) 30.3890 1.20786
\(634\) 13.8030 0.548185
\(635\) 3.55878 0.141226
\(636\) 13.4887 0.534862
\(637\) 0 0
\(638\) −22.8898 −0.906217
\(639\) 15.9601 0.631373
\(640\) −66.0907 −2.61247
\(641\) −2.30218 −0.0909308 −0.0454654 0.998966i \(-0.514477\pi\)
−0.0454654 + 0.998966i \(0.514477\pi\)
\(642\) 31.4757 1.24225
\(643\) 13.5933 0.536067 0.268033 0.963410i \(-0.413626\pi\)
0.268033 + 0.963410i \(0.413626\pi\)
\(644\) 3.09653 0.122020
\(645\) 3.73243 0.146964
\(646\) 23.0497 0.906878
\(647\) −25.3906 −0.998209 −0.499104 0.866542i \(-0.666338\pi\)
−0.499104 + 0.866542i \(0.666338\pi\)
\(648\) −9.31612 −0.365972
\(649\) −8.90125 −0.349405
\(650\) 0 0
\(651\) 1.90663 0.0747266
\(652\) 21.1715 0.829142
\(653\) −24.1446 −0.944853 −0.472426 0.881370i \(-0.656622\pi\)
−0.472426 + 0.881370i \(0.656622\pi\)
\(654\) 1.23524 0.0483016
\(655\) 6.92817 0.270706
\(656\) −6.74669 −0.263414
\(657\) 13.0853 0.510505
\(658\) 4.13213 0.161087
\(659\) 34.3980 1.33996 0.669978 0.742381i \(-0.266304\pi\)
0.669978 + 0.742381i \(0.266304\pi\)
\(660\) 17.4088 0.677638
\(661\) 17.4355 0.678163 0.339081 0.940757i \(-0.389884\pi\)
0.339081 + 0.940757i \(0.389884\pi\)
\(662\) −30.6876 −1.19271
\(663\) 0 0
\(664\) −30.2329 −1.17326
\(665\) −3.57812 −0.138753
\(666\) 10.9918 0.425925
\(667\) −27.7301 −1.07371
\(668\) −54.1050 −2.09339
\(669\) 6.44731 0.249267
\(670\) 141.162 5.45357
\(671\) 8.06080 0.311184
\(672\) −3.54528 −0.136762
\(673\) −43.1928 −1.66496 −0.832479 0.554056i \(-0.813079\pi\)
−0.832479 + 0.554056i \(0.813079\pi\)
\(674\) −19.1380 −0.737167
\(675\) −75.5433 −2.90766
\(676\) 0 0
\(677\) 22.7599 0.874732 0.437366 0.899284i \(-0.355911\pi\)
0.437366 + 0.899284i \(0.355911\pi\)
\(678\) −2.74997 −0.105612
\(679\) 5.90669 0.226678
\(680\) −44.6418 −1.71193
\(681\) −7.55297 −0.289431
\(682\) 8.13512 0.311510
\(683\) −16.9629 −0.649066 −0.324533 0.945874i \(-0.605207\pi\)
−0.324533 + 0.945874i \(0.605207\pi\)
\(684\) 7.41944 0.283689
\(685\) 11.3835 0.434940
\(686\) −11.8755 −0.453410
\(687\) −12.9551 −0.494266
\(688\) −0.686225 −0.0261621
\(689\) 0 0
\(690\) 35.2372 1.34146
\(691\) 4.52167 0.172012 0.0860061 0.996295i \(-0.472590\pi\)
0.0860061 + 0.996295i \(0.472590\pi\)
\(692\) 30.2303 1.14918
\(693\) −0.439900 −0.0167104
\(694\) 21.7307 0.824885
\(695\) 2.65811 0.100828
\(696\) −30.5978 −1.15981
\(697\) −29.8709 −1.13144
\(698\) 23.0415 0.872135
\(699\) 6.12798 0.231781
\(700\) 15.3245 0.579213
\(701\) 38.4564 1.45248 0.726239 0.687442i \(-0.241267\pi\)
0.726239 + 0.687442i \(0.241267\pi\)
\(702\) 0 0
\(703\) 9.34328 0.352388
\(704\) −12.9798 −0.489196
\(705\) 28.1435 1.05994
\(706\) −7.55089 −0.284181
\(707\) 1.93333 0.0727105
\(708\) −36.1436 −1.35836
\(709\) 37.4050 1.40477 0.702386 0.711796i \(-0.252118\pi\)
0.702386 + 0.711796i \(0.252118\pi\)
\(710\) −133.352 −5.00459
\(711\) −8.68329 −0.325649
\(712\) 10.4007 0.389784
\(713\) 9.85536 0.369086
\(714\) −5.54917 −0.207673
\(715\) 0 0
\(716\) −43.5291 −1.62676
\(717\) −4.05586 −0.151469
\(718\) −32.2825 −1.20477
\(719\) 30.7619 1.14722 0.573612 0.819127i \(-0.305542\pi\)
0.573612 + 0.819127i \(0.305542\pi\)
\(720\) 5.27114 0.196444
\(721\) 4.33959 0.161615
\(722\) −31.8696 −1.18606
\(723\) −24.0270 −0.893575
\(724\) 45.4528 1.68924
\(725\) −137.235 −5.09677
\(726\) 3.03963 0.112811
\(727\) 22.7199 0.842636 0.421318 0.906913i \(-0.361568\pi\)
0.421318 + 0.906913i \(0.361568\pi\)
\(728\) 0 0
\(729\) 27.9353 1.03464
\(730\) −109.331 −4.04653
\(731\) −3.03826 −0.112374
\(732\) 32.7309 1.20977
\(733\) 18.1398 0.670008 0.335004 0.942217i \(-0.391262\pi\)
0.335004 + 0.942217i \(0.391262\pi\)
\(734\) −48.0842 −1.77482
\(735\) −40.0107 −1.47582
\(736\) −18.3256 −0.675489
\(737\) 14.7519 0.543392
\(738\) −16.0649 −0.591356
\(739\) −38.3992 −1.41254 −0.706268 0.707945i \(-0.749623\pi\)
−0.706268 + 0.707945i \(0.749623\pi\)
\(740\) −54.9679 −2.02066
\(741\) 0 0
\(742\) 2.84784 0.104548
\(743\) −36.1752 −1.32714 −0.663571 0.748114i \(-0.730960\pi\)
−0.663571 + 0.748114i \(0.730960\pi\)
\(744\) 10.8745 0.398680
\(745\) 16.3866 0.600360
\(746\) −57.2026 −2.09434
\(747\) 15.8052 0.578283
\(748\) −14.1711 −0.518146
\(749\) 3.97739 0.145331
\(750\) 109.227 3.98841
\(751\) −12.5624 −0.458408 −0.229204 0.973378i \(-0.573612\pi\)
−0.229204 + 0.973378i \(0.573612\pi\)
\(752\) −5.17432 −0.188688
\(753\) 16.2960 0.593858
\(754\) 0 0
\(755\) −73.5154 −2.67550
\(756\) −6.46513 −0.235135
\(757\) 32.0717 1.16566 0.582832 0.812593i \(-0.301945\pi\)
0.582832 + 0.812593i \(0.301945\pi\)
\(758\) −21.0062 −0.762978
\(759\) 3.68239 0.133662
\(760\) −20.4080 −0.740274
\(761\) −2.45600 −0.0890300 −0.0445150 0.999009i \(-0.514174\pi\)
−0.0445150 + 0.999009i \(0.514174\pi\)
\(762\) 2.52309 0.0914020
\(763\) 0.156089 0.00565081
\(764\) 48.1800 1.74309
\(765\) 23.3379 0.843785
\(766\) −22.2170 −0.802732
\(767\) 0 0
\(768\) −11.5027 −0.415068
\(769\) 1.97248 0.0711296 0.0355648 0.999367i \(-0.488677\pi\)
0.0355648 + 0.999367i \(0.488677\pi\)
\(770\) 3.67549 0.132456
\(771\) 5.62503 0.202581
\(772\) 14.4583 0.520366
\(773\) −25.9419 −0.933064 −0.466532 0.884504i \(-0.654497\pi\)
−0.466532 + 0.884504i \(0.654497\pi\)
\(774\) −1.63401 −0.0587331
\(775\) 48.7737 1.75200
\(776\) 33.6891 1.20937
\(777\) −2.24938 −0.0806959
\(778\) −8.38722 −0.300696
\(779\) −13.6555 −0.489258
\(780\) 0 0
\(781\) −13.9356 −0.498656
\(782\) −28.6837 −1.02573
\(783\) 57.8967 2.06906
\(784\) 7.35617 0.262720
\(785\) −43.0438 −1.53630
\(786\) 4.91191 0.175202
\(787\) 45.8214 1.63336 0.816679 0.577093i \(-0.195813\pi\)
0.816679 + 0.577093i \(0.195813\pi\)
\(788\) 57.1712 2.03664
\(789\) −13.6841 −0.487166
\(790\) 72.5514 2.58126
\(791\) −0.347496 −0.0123555
\(792\) −2.50899 −0.0891531
\(793\) 0 0
\(794\) −37.8336 −1.34267
\(795\) 19.3963 0.687917
\(796\) 10.2103 0.361895
\(797\) 25.4970 0.903152 0.451576 0.892233i \(-0.350862\pi\)
0.451576 + 0.892233i \(0.350862\pi\)
\(798\) −2.53680 −0.0898017
\(799\) −22.9093 −0.810471
\(800\) −90.6922 −3.20645
\(801\) −5.43732 −0.192118
\(802\) 31.4256 1.10968
\(803\) −11.4254 −0.403195
\(804\) 59.9000 2.11251
\(805\) 4.45271 0.156937
\(806\) 0 0
\(807\) −10.8350 −0.381411
\(808\) 11.0269 0.387923
\(809\) 46.8717 1.64792 0.823960 0.566648i \(-0.191760\pi\)
0.823960 + 0.566648i \(0.191760\pi\)
\(810\) −40.6928 −1.42980
\(811\) −2.41983 −0.0849717 −0.0424859 0.999097i \(-0.513528\pi\)
−0.0424859 + 0.999097i \(0.513528\pi\)
\(812\) −11.7448 −0.412161
\(813\) −39.7031 −1.39245
\(814\) −9.59755 −0.336394
\(815\) 30.4440 1.06641
\(816\) 6.94876 0.243255
\(817\) −1.38894 −0.0485928
\(818\) 77.3328 2.70388
\(819\) 0 0
\(820\) 80.3370 2.80549
\(821\) −8.76673 −0.305961 −0.152980 0.988229i \(-0.548887\pi\)
−0.152980 + 0.988229i \(0.548887\pi\)
\(822\) 8.07061 0.281495
\(823\) −41.7652 −1.45584 −0.727921 0.685661i \(-0.759513\pi\)
−0.727921 + 0.685661i \(0.759513\pi\)
\(824\) 24.7511 0.862244
\(825\) 18.2240 0.634477
\(826\) −7.63091 −0.265513
\(827\) 38.4530 1.33714 0.668570 0.743649i \(-0.266907\pi\)
0.668570 + 0.743649i \(0.266907\pi\)
\(828\) −9.23295 −0.320867
\(829\) 1.12630 0.0391179 0.0195590 0.999809i \(-0.493774\pi\)
0.0195590 + 0.999809i \(0.493774\pi\)
\(830\) −132.057 −4.58378
\(831\) 3.00165 0.104126
\(832\) 0 0
\(833\) 32.5694 1.12846
\(834\) 1.88453 0.0652561
\(835\) −77.8014 −2.69243
\(836\) −6.47830 −0.224057
\(837\) −20.5767 −0.711234
\(838\) −1.88903 −0.0652555
\(839\) −8.13825 −0.280964 −0.140482 0.990083i \(-0.544865\pi\)
−0.140482 + 0.990083i \(0.544865\pi\)
\(840\) 4.91318 0.169521
\(841\) 76.1773 2.62680
\(842\) 25.0688 0.863926
\(843\) 39.0199 1.34392
\(844\) 66.5300 2.29006
\(845\) 0 0
\(846\) −12.3208 −0.423599
\(847\) 0.384100 0.0131978
\(848\) −3.56611 −0.122461
\(849\) −5.30704 −0.182137
\(850\) −141.954 −4.86898
\(851\) −11.6270 −0.398570
\(852\) −56.5857 −1.93859
\(853\) 23.5017 0.804682 0.402341 0.915490i \(-0.368197\pi\)
0.402341 + 0.915490i \(0.368197\pi\)
\(854\) 6.91041 0.236469
\(855\) 10.6689 0.364870
\(856\) 22.6852 0.775364
\(857\) −26.1485 −0.893217 −0.446608 0.894730i \(-0.647368\pi\)
−0.446608 + 0.894730i \(0.647368\pi\)
\(858\) 0 0
\(859\) 14.9787 0.511065 0.255533 0.966800i \(-0.417749\pi\)
0.255533 + 0.966800i \(0.417749\pi\)
\(860\) 8.17132 0.278640
\(861\) 3.28753 0.112039
\(862\) −26.0423 −0.887005
\(863\) 45.0286 1.53279 0.766396 0.642369i \(-0.222048\pi\)
0.766396 + 0.642369i \(0.222048\pi\)
\(864\) 38.2613 1.30168
\(865\) 43.4702 1.47803
\(866\) −10.7238 −0.364411
\(867\) 7.61359 0.258571
\(868\) 4.17414 0.141679
\(869\) 7.58183 0.257196
\(870\) −133.651 −4.53119
\(871\) 0 0
\(872\) 0.890262 0.0301481
\(873\) −17.6121 −0.596078
\(874\) −13.1127 −0.443544
\(875\) 13.8023 0.466604
\(876\) −46.3930 −1.56748
\(877\) −15.9277 −0.537839 −0.268920 0.963163i \(-0.586667\pi\)
−0.268920 + 0.963163i \(0.586667\pi\)
\(878\) 33.0859 1.11659
\(879\) −10.6956 −0.360753
\(880\) −4.60251 −0.155151
\(881\) 47.6435 1.60515 0.802575 0.596551i \(-0.203463\pi\)
0.802575 + 0.596551i \(0.203463\pi\)
\(882\) 17.5162 0.589800
\(883\) 23.9450 0.805815 0.402907 0.915241i \(-0.368000\pi\)
0.402907 + 0.915241i \(0.368000\pi\)
\(884\) 0 0
\(885\) −51.9733 −1.74706
\(886\) 24.9993 0.839867
\(887\) 26.8935 0.902996 0.451498 0.892272i \(-0.350890\pi\)
0.451498 + 0.892272i \(0.350890\pi\)
\(888\) −12.8294 −0.430527
\(889\) 0.318827 0.0106931
\(890\) 45.4304 1.52283
\(891\) −4.25252 −0.142465
\(892\) 14.1150 0.472604
\(893\) −10.4730 −0.350464
\(894\) 11.6177 0.388555
\(895\) −62.5935 −2.09227
\(896\) −5.92099 −0.197807
\(897\) 0 0
\(898\) 61.5197 2.05294
\(899\) −37.3804 −1.24670
\(900\) −45.6934 −1.52311
\(901\) −15.7889 −0.526006
\(902\) 14.0271 0.467051
\(903\) 0.334384 0.0111276
\(904\) −1.98196 −0.0659190
\(905\) 65.3598 2.17263
\(906\) −52.1207 −1.73159
\(907\) 31.8951 1.05906 0.529530 0.848291i \(-0.322368\pi\)
0.529530 + 0.848291i \(0.322368\pi\)
\(908\) −16.5355 −0.548751
\(909\) −5.76465 −0.191201
\(910\) 0 0
\(911\) −14.6773 −0.486280 −0.243140 0.969991i \(-0.578177\pi\)
−0.243140 + 0.969991i \(0.578177\pi\)
\(912\) 3.17662 0.105188
\(913\) −13.8004 −0.456726
\(914\) 81.9297 2.70999
\(915\) 47.0660 1.55595
\(916\) −28.3622 −0.937114
\(917\) 0.620687 0.0204969
\(918\) 59.8877 1.97659
\(919\) 28.8671 0.952239 0.476119 0.879381i \(-0.342043\pi\)
0.476119 + 0.879381i \(0.342043\pi\)
\(920\) 25.3962 0.837288
\(921\) −26.4133 −0.870346
\(922\) 2.86956 0.0945041
\(923\) 0 0
\(924\) 1.55964 0.0513083
\(925\) −57.5416 −1.89195
\(926\) 57.7382 1.89740
\(927\) −12.9394 −0.424986
\(928\) 69.5069 2.28168
\(929\) −50.7771 −1.66594 −0.832972 0.553316i \(-0.813362\pi\)
−0.832972 + 0.553316i \(0.813362\pi\)
\(930\) 47.5000 1.55759
\(931\) 14.8891 0.487970
\(932\) 13.4158 0.439450
\(933\) −31.9572 −1.04623
\(934\) −44.4268 −1.45369
\(935\) −20.3776 −0.666418
\(936\) 0 0
\(937\) 19.2380 0.628478 0.314239 0.949344i \(-0.398251\pi\)
0.314239 + 0.949344i \(0.398251\pi\)
\(938\) 12.6466 0.412925
\(939\) 10.1044 0.329744
\(940\) 61.6139 2.00962
\(941\) −9.69418 −0.316021 −0.158011 0.987437i \(-0.550508\pi\)
−0.158011 + 0.987437i \(0.550508\pi\)
\(942\) −30.5170 −0.994297
\(943\) 16.9932 0.553376
\(944\) 9.55555 0.311007
\(945\) −9.29666 −0.302420
\(946\) 1.42674 0.0463872
\(947\) −50.0296 −1.62574 −0.812871 0.582444i \(-0.802097\pi\)
−0.812871 + 0.582444i \(0.802097\pi\)
\(948\) 30.7861 0.999885
\(949\) 0 0
\(950\) −64.8942 −2.10544
\(951\) 8.42229 0.273111
\(952\) −3.99941 −0.129622
\(953\) −41.2685 −1.33682 −0.668409 0.743794i \(-0.733024\pi\)
−0.668409 + 0.743794i \(0.733024\pi\)
\(954\) −8.49145 −0.274921
\(955\) 69.2813 2.24189
\(956\) −8.87941 −0.287181
\(957\) −13.9669 −0.451487
\(958\) −93.2729 −3.01351
\(959\) 1.01983 0.0329321
\(960\) −75.7877 −2.44604
\(961\) −17.7149 −0.571449
\(962\) 0 0
\(963\) −11.8594 −0.382165
\(964\) −52.6018 −1.69419
\(965\) 20.7906 0.669273
\(966\) 3.15686 0.101570
\(967\) −9.89332 −0.318148 −0.159074 0.987267i \(-0.550851\pi\)
−0.159074 + 0.987267i \(0.550851\pi\)
\(968\) 2.19073 0.0704127
\(969\) 14.0645 0.451816
\(970\) 147.154 4.72482
\(971\) −0.640473 −0.0205537 −0.0102769 0.999947i \(-0.503271\pi\)
−0.0102769 + 0.999947i \(0.503271\pi\)
\(972\) 33.2284 1.06580
\(973\) 0.238137 0.00763432
\(974\) −56.1126 −1.79796
\(975\) 0 0
\(976\) −8.65332 −0.276986
\(977\) 19.9838 0.639338 0.319669 0.947529i \(-0.396428\pi\)
0.319669 + 0.947529i \(0.396428\pi\)
\(978\) 21.5841 0.690183
\(979\) 4.74761 0.151734
\(980\) −87.5946 −2.79811
\(981\) −0.465414 −0.0148595
\(982\) −74.6889 −2.38342
\(983\) 50.7308 1.61806 0.809031 0.587766i \(-0.199993\pi\)
0.809031 + 0.587766i \(0.199993\pi\)
\(984\) 18.7506 0.597746
\(985\) 82.2104 2.61944
\(986\) 108.794 3.46471
\(987\) 2.52134 0.0802552
\(988\) 0 0
\(989\) 1.72843 0.0549609
\(990\) −10.9593 −0.348308
\(991\) 27.3294 0.868147 0.434073 0.900878i \(-0.357076\pi\)
0.434073 + 0.900878i \(0.357076\pi\)
\(992\) −24.7030 −0.784320
\(993\) −18.7249 −0.594218
\(994\) −11.9468 −0.378930
\(995\) 14.6821 0.465454
\(996\) −56.0365 −1.77558
\(997\) 28.7308 0.909915 0.454958 0.890513i \(-0.349654\pi\)
0.454958 + 0.890513i \(0.349654\pi\)
\(998\) −71.8255 −2.27360
\(999\) 24.2757 0.768049
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 1859.2.a.t.1.18 yes 21
13.12 even 2 1859.2.a.s.1.4 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.4 21 13.12 even 2
1859.2.a.t.1.18 yes 21 1.1 even 1 trivial