Properties

Label 325.6.a.j.1.7
Level $325$
Weight $6$
Character 325.1
Self dual yes
Analytic conductor $52.125$
Analytic rank $0$
Dimension $11$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [325,6,Mod(1,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(52.1247414392\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{6}\cdot 5^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.96479\) of defining polynomial
Character \(\chi\) \(=\) 325.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.96479 q^{2} +29.7675 q^{3} -28.1396 q^{4} +58.4868 q^{6} -176.972 q^{7} -118.162 q^{8} +643.103 q^{9} -62.7908 q^{11} -837.645 q^{12} -169.000 q^{13} -347.712 q^{14} +668.304 q^{16} +1825.19 q^{17} +1263.56 q^{18} +2509.78 q^{19} -5268.00 q^{21} -123.371 q^{22} -137.706 q^{23} -3517.37 q^{24} -332.049 q^{26} +11910.0 q^{27} +4979.91 q^{28} +5978.98 q^{29} -5203.47 q^{31} +5094.25 q^{32} -1869.12 q^{33} +3586.12 q^{34} -18096.7 q^{36} +4275.33 q^{37} +4931.19 q^{38} -5030.70 q^{39} +16780.1 q^{41} -10350.5 q^{42} +21508.6 q^{43} +1766.91 q^{44} -270.563 q^{46} -16741.5 q^{47} +19893.7 q^{48} +14511.9 q^{49} +54331.4 q^{51} +4755.59 q^{52} -2749.61 q^{53} +23400.7 q^{54} +20911.2 q^{56} +74709.8 q^{57} +11747.4 q^{58} +16631.5 q^{59} -25005.7 q^{61} -10223.7 q^{62} -113811. q^{63} -11376.6 q^{64} -3672.44 q^{66} -29425.1 q^{67} -51360.2 q^{68} -4099.16 q^{69} -26909.1 q^{71} -75990.1 q^{72} -33664.0 q^{73} +8400.13 q^{74} -70624.2 q^{76} +11112.2 q^{77} -9884.27 q^{78} -13528.9 q^{79} +198258. q^{81} +32969.4 q^{82} -790.985 q^{83} +148239. q^{84} +42259.9 q^{86} +177979. q^{87} +7419.47 q^{88} -72223.8 q^{89} +29908.2 q^{91} +3874.99 q^{92} -154894. q^{93} -32893.6 q^{94} +151643. q^{96} +5458.83 q^{97} +28512.9 q^{98} -40380.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q - 5 q^{2} - 11 q^{3} + 187 q^{4} + 351 q^{6} - 208 q^{7} - 165 q^{8} + 1372 q^{9} + 1276 q^{11} - 1533 q^{12} - 1859 q^{13} + 578 q^{14} + 5707 q^{16} - 2218 q^{17} + 6776 q^{18} + 3520 q^{19} + 1706 q^{21}+ \cdots + 426698 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.96479 0.347329 0.173664 0.984805i \(-0.444439\pi\)
0.173664 + 0.984805i \(0.444439\pi\)
\(3\) 29.7675 1.90958 0.954792 0.297274i \(-0.0960774\pi\)
0.954792 + 0.297274i \(0.0960774\pi\)
\(4\) −28.1396 −0.879363
\(5\) 0 0
\(6\) 58.4868 0.663254
\(7\) −176.972 −1.36508 −0.682540 0.730848i \(-0.739125\pi\)
−0.682540 + 0.730848i \(0.739125\pi\)
\(8\) −118.162 −0.652757
\(9\) 643.103 2.64651
\(10\) 0 0
\(11\) −62.7908 −0.156464 −0.0782320 0.996935i \(-0.524927\pi\)
−0.0782320 + 0.996935i \(0.524927\pi\)
\(12\) −837.645 −1.67922
\(13\) −169.000 −0.277350
\(14\) −347.712 −0.474132
\(15\) 0 0
\(16\) 668.304 0.652641
\(17\) 1825.19 1.53175 0.765873 0.642992i \(-0.222307\pi\)
0.765873 + 0.642992i \(0.222307\pi\)
\(18\) 1263.56 0.919211
\(19\) 2509.78 1.59497 0.797483 0.603342i \(-0.206165\pi\)
0.797483 + 0.603342i \(0.206165\pi\)
\(20\) 0 0
\(21\) −5268.00 −2.60674
\(22\) −123.371 −0.0543445
\(23\) −137.706 −0.0542791 −0.0271396 0.999632i \(-0.508640\pi\)
−0.0271396 + 0.999632i \(0.508640\pi\)
\(24\) −3517.37 −1.24649
\(25\) 0 0
\(26\) −332.049 −0.0963317
\(27\) 11910.0 3.14416
\(28\) 4979.91 1.20040
\(29\) 5978.98 1.32018 0.660088 0.751188i \(-0.270519\pi\)
0.660088 + 0.751188i \(0.270519\pi\)
\(30\) 0 0
\(31\) −5203.47 −0.972499 −0.486249 0.873820i \(-0.661635\pi\)
−0.486249 + 0.873820i \(0.661635\pi\)
\(32\) 5094.25 0.879438
\(33\) −1869.12 −0.298781
\(34\) 3586.12 0.532020
\(35\) 0 0
\(36\) −18096.7 −2.32724
\(37\) 4275.33 0.513412 0.256706 0.966490i \(-0.417363\pi\)
0.256706 + 0.966490i \(0.417363\pi\)
\(38\) 4931.19 0.553978
\(39\) −5030.70 −0.529623
\(40\) 0 0
\(41\) 16780.1 1.55896 0.779481 0.626426i \(-0.215483\pi\)
0.779481 + 0.626426i \(0.215483\pi\)
\(42\) −10350.5 −0.905395
\(43\) 21508.6 1.77395 0.886974 0.461819i \(-0.152803\pi\)
0.886974 + 0.461819i \(0.152803\pi\)
\(44\) 1766.91 0.137589
\(45\) 0 0
\(46\) −270.563 −0.0188527
\(47\) −16741.5 −1.10548 −0.552739 0.833354i \(-0.686417\pi\)
−0.552739 + 0.833354i \(0.686417\pi\)
\(48\) 19893.7 1.24627
\(49\) 14511.9 0.863445
\(50\) 0 0
\(51\) 54331.4 2.92500
\(52\) 4755.59 0.243891
\(53\) −2749.61 −0.134457 −0.0672283 0.997738i \(-0.521416\pi\)
−0.0672283 + 0.997738i \(0.521416\pi\)
\(54\) 23400.7 1.09206
\(55\) 0 0
\(56\) 20911.2 0.891066
\(57\) 74709.8 3.04572
\(58\) 11747.4 0.458536
\(59\) 16631.5 0.622015 0.311007 0.950407i \(-0.399334\pi\)
0.311007 + 0.950407i \(0.399334\pi\)
\(60\) 0 0
\(61\) −25005.7 −0.860429 −0.430214 0.902727i \(-0.641562\pi\)
−0.430214 + 0.902727i \(0.641562\pi\)
\(62\) −10223.7 −0.337777
\(63\) −113811. −3.61270
\(64\) −11376.6 −0.347187
\(65\) 0 0
\(66\) −3672.44 −0.103775
\(67\) −29425.1 −0.800812 −0.400406 0.916338i \(-0.631131\pi\)
−0.400406 + 0.916338i \(0.631131\pi\)
\(68\) −51360.2 −1.34696
\(69\) −4099.16 −0.103651
\(70\) 0 0
\(71\) −26909.1 −0.633509 −0.316754 0.948508i \(-0.602593\pi\)
−0.316754 + 0.948508i \(0.602593\pi\)
\(72\) −75990.1 −1.72753
\(73\) −33664.0 −0.739365 −0.369683 0.929158i \(-0.620534\pi\)
−0.369683 + 0.929158i \(0.620534\pi\)
\(74\) 8400.13 0.178323
\(75\) 0 0
\(76\) −70624.2 −1.40255
\(77\) 11112.2 0.213586
\(78\) −9884.27 −0.183954
\(79\) −13528.9 −0.243891 −0.121945 0.992537i \(-0.538913\pi\)
−0.121945 + 0.992537i \(0.538913\pi\)
\(80\) 0 0
\(81\) 198258. 3.35752
\(82\) 32969.4 0.541473
\(83\) −790.985 −0.0126030 −0.00630148 0.999980i \(-0.502006\pi\)
−0.00630148 + 0.999980i \(0.502006\pi\)
\(84\) 148239. 2.29227
\(85\) 0 0
\(86\) 42259.9 0.616144
\(87\) 177979. 2.52099
\(88\) 7419.47 0.102133
\(89\) −72223.8 −0.966508 −0.483254 0.875480i \(-0.660545\pi\)
−0.483254 + 0.875480i \(0.660545\pi\)
\(90\) 0 0
\(91\) 29908.2 0.378605
\(92\) 3874.99 0.0477310
\(93\) −154894. −1.85707
\(94\) −32893.6 −0.383965
\(95\) 0 0
\(96\) 151643. 1.67936
\(97\) 5458.83 0.0589075 0.0294538 0.999566i \(-0.490623\pi\)
0.0294538 + 0.999566i \(0.490623\pi\)
\(98\) 28512.9 0.299899
\(99\) −40380.9 −0.414084
\(100\) 0 0
\(101\) −87461.4 −0.853125 −0.426563 0.904458i \(-0.640276\pi\)
−0.426563 + 0.904458i \(0.640276\pi\)
\(102\) 106750. 1.01594
\(103\) 75287.7 0.699248 0.349624 0.936890i \(-0.386309\pi\)
0.349624 + 0.936890i \(0.386309\pi\)
\(104\) 19969.3 0.181042
\(105\) 0 0
\(106\) −5402.41 −0.0467007
\(107\) −77781.0 −0.656771 −0.328386 0.944544i \(-0.606505\pi\)
−0.328386 + 0.944544i \(0.606505\pi\)
\(108\) −335144. −2.76485
\(109\) 175666. 1.41619 0.708096 0.706116i \(-0.249554\pi\)
0.708096 + 0.706116i \(0.249554\pi\)
\(110\) 0 0
\(111\) 127266. 0.980403
\(112\) −118271. −0.890908
\(113\) 2350.11 0.0173138 0.00865691 0.999963i \(-0.497244\pi\)
0.00865691 + 0.999963i \(0.497244\pi\)
\(114\) 146789. 1.05787
\(115\) 0 0
\(116\) −168246. −1.16091
\(117\) −108684. −0.734011
\(118\) 32677.4 0.216044
\(119\) −323007. −2.09096
\(120\) 0 0
\(121\) −157108. −0.975519
\(122\) −49131.0 −0.298852
\(123\) 499502. 2.97697
\(124\) 146424. 0.855179
\(125\) 0 0
\(126\) −223614. −1.25480
\(127\) 266534. 1.46637 0.733183 0.680031i \(-0.238034\pi\)
0.733183 + 0.680031i \(0.238034\pi\)
\(128\) −185369. −1.00003
\(129\) 640257. 3.38750
\(130\) 0 0
\(131\) 118703. 0.604341 0.302170 0.953254i \(-0.402289\pi\)
0.302170 + 0.953254i \(0.402289\pi\)
\(132\) 52596.4 0.262737
\(133\) −444159. −2.17726
\(134\) −57814.1 −0.278145
\(135\) 0 0
\(136\) −215668. −0.999858
\(137\) 163850. 0.745838 0.372919 0.927864i \(-0.378357\pi\)
0.372919 + 0.927864i \(0.378357\pi\)
\(138\) −8053.98 −0.0360008
\(139\) 218277. 0.958231 0.479115 0.877752i \(-0.340958\pi\)
0.479115 + 0.877752i \(0.340958\pi\)
\(140\) 0 0
\(141\) −498353. −2.11100
\(142\) −52870.6 −0.220036
\(143\) 10611.6 0.0433953
\(144\) 429788. 1.72722
\(145\) 0 0
\(146\) −66142.7 −0.256803
\(147\) 431983. 1.64882
\(148\) −120306. −0.451475
\(149\) −79310.9 −0.292663 −0.146331 0.989236i \(-0.546747\pi\)
−0.146331 + 0.989236i \(0.546747\pi\)
\(150\) 0 0
\(151\) 368505. 1.31523 0.657615 0.753355i \(-0.271566\pi\)
0.657615 + 0.753355i \(0.271566\pi\)
\(152\) −296560. −1.04113
\(153\) 1.17379e6 4.05378
\(154\) 21833.1 0.0741846
\(155\) 0 0
\(156\) 141562. 0.465731
\(157\) −30957.2 −0.100233 −0.0501166 0.998743i \(-0.515959\pi\)
−0.0501166 + 0.998743i \(0.515959\pi\)
\(158\) −26581.5 −0.0847103
\(159\) −81849.1 −0.256756
\(160\) 0 0
\(161\) 24370.0 0.0740954
\(162\) 389535. 1.16616
\(163\) 204546. 0.603006 0.301503 0.953465i \(-0.402512\pi\)
0.301503 + 0.953465i \(0.402512\pi\)
\(164\) −472186. −1.37089
\(165\) 0 0
\(166\) −1554.12 −0.00437738
\(167\) −158449. −0.439641 −0.219821 0.975540i \(-0.570547\pi\)
−0.219821 + 0.975540i \(0.570547\pi\)
\(168\) 622475. 1.70157
\(169\) 28561.0 0.0769231
\(170\) 0 0
\(171\) 1.61404e6 4.22110
\(172\) −605243. −1.55994
\(173\) −230663. −0.585952 −0.292976 0.956120i \(-0.594646\pi\)
−0.292976 + 0.956120i \(0.594646\pi\)
\(174\) 349692. 0.875613
\(175\) 0 0
\(176\) −41963.4 −0.102115
\(177\) 495077. 1.18779
\(178\) −141905. −0.335696
\(179\) 791891. 1.84728 0.923640 0.383260i \(-0.125199\pi\)
0.923640 + 0.383260i \(0.125199\pi\)
\(180\) 0 0
\(181\) −272694. −0.618699 −0.309350 0.950948i \(-0.600111\pi\)
−0.309350 + 0.950948i \(0.600111\pi\)
\(182\) 58763.3 0.131501
\(183\) −744358. −1.64306
\(184\) 16271.5 0.0354311
\(185\) 0 0
\(186\) −304335. −0.645014
\(187\) −114605. −0.239663
\(188\) 471100. 0.972116
\(189\) −2.10774e6 −4.29203
\(190\) 0 0
\(191\) 603069. 1.19614 0.598072 0.801442i \(-0.295933\pi\)
0.598072 + 0.801442i \(0.295933\pi\)
\(192\) −338653. −0.662982
\(193\) 59043.0 0.114097 0.0570486 0.998371i \(-0.481831\pi\)
0.0570486 + 0.998371i \(0.481831\pi\)
\(194\) 10725.5 0.0204603
\(195\) 0 0
\(196\) −408360. −0.759281
\(197\) −815964. −1.49798 −0.748989 0.662582i \(-0.769461\pi\)
−0.748989 + 0.662582i \(0.769461\pi\)
\(198\) −79340.1 −0.143823
\(199\) 490593. 0.878190 0.439095 0.898441i \(-0.355299\pi\)
0.439095 + 0.898441i \(0.355299\pi\)
\(200\) 0 0
\(201\) −875911. −1.52922
\(202\) −171843. −0.296315
\(203\) −1.05811e6 −1.80215
\(204\) −1.52886e6 −2.57213
\(205\) 0 0
\(206\) 147925. 0.242869
\(207\) −88559.0 −0.143650
\(208\) −112943. −0.181010
\(209\) −157591. −0.249555
\(210\) 0 0
\(211\) 593914. 0.918370 0.459185 0.888341i \(-0.348142\pi\)
0.459185 + 0.888341i \(0.348142\pi\)
\(212\) 77373.0 0.118236
\(213\) −801015. −1.20974
\(214\) −152823. −0.228116
\(215\) 0 0
\(216\) −1.40731e6 −2.05237
\(217\) 920866. 1.32754
\(218\) 345147. 0.491884
\(219\) −1.00209e6 −1.41188
\(220\) 0 0
\(221\) −308458. −0.424830
\(222\) 250051. 0.340522
\(223\) 893543. 1.20324 0.601621 0.798781i \(-0.294522\pi\)
0.601621 + 0.798781i \(0.294522\pi\)
\(224\) −901537. −1.20050
\(225\) 0 0
\(226\) 4617.48 0.00601359
\(227\) −1.10400e6 −1.42201 −0.711006 0.703186i \(-0.751760\pi\)
−0.711006 + 0.703186i \(0.751760\pi\)
\(228\) −2.10230e6 −2.67829
\(229\) −662093. −0.834315 −0.417158 0.908834i \(-0.636974\pi\)
−0.417158 + 0.908834i \(0.636974\pi\)
\(230\) 0 0
\(231\) 330782. 0.407860
\(232\) −706486. −0.861755
\(233\) −828333. −0.999574 −0.499787 0.866148i \(-0.666588\pi\)
−0.499787 + 0.866148i \(0.666588\pi\)
\(234\) −213542. −0.254943
\(235\) 0 0
\(236\) −468003. −0.546977
\(237\) −402722. −0.465730
\(238\) −634641. −0.726250
\(239\) 359216. 0.406781 0.203391 0.979098i \(-0.434804\pi\)
0.203391 + 0.979098i \(0.434804\pi\)
\(240\) 0 0
\(241\) −928812. −1.03011 −0.515057 0.857156i \(-0.672229\pi\)
−0.515057 + 0.857156i \(0.672229\pi\)
\(242\) −308685. −0.338826
\(243\) 3.00750e6 3.26731
\(244\) 703651. 0.756629
\(245\) 0 0
\(246\) 981416. 1.03399
\(247\) −424152. −0.442364
\(248\) 614851. 0.634805
\(249\) −23545.6 −0.0240664
\(250\) 0 0
\(251\) −102334. −0.102526 −0.0512631 0.998685i \(-0.516325\pi\)
−0.0512631 + 0.998685i \(0.516325\pi\)
\(252\) 3.20259e6 3.17688
\(253\) 8646.66 0.00849273
\(254\) 523682. 0.509312
\(255\) 0 0
\(256\) −158.767 −0.000151412 0
\(257\) −1.17461e6 −1.10933 −0.554664 0.832075i \(-0.687153\pi\)
−0.554664 + 0.832075i \(0.687153\pi\)
\(258\) 1.25797e6 1.17658
\(259\) −756612. −0.700848
\(260\) 0 0
\(261\) 3.84510e6 3.49387
\(262\) 233226. 0.209905
\(263\) −99506.0 −0.0887074 −0.0443537 0.999016i \(-0.514123\pi\)
−0.0443537 + 0.999016i \(0.514123\pi\)
\(264\) 220859. 0.195032
\(265\) 0 0
\(266\) −872679. −0.756224
\(267\) −2.14992e6 −1.84563
\(268\) 828010. 0.704204
\(269\) −558985. −0.470999 −0.235499 0.971874i \(-0.575673\pi\)
−0.235499 + 0.971874i \(0.575673\pi\)
\(270\) 0 0
\(271\) −503763. −0.416680 −0.208340 0.978056i \(-0.566806\pi\)
−0.208340 + 0.978056i \(0.566806\pi\)
\(272\) 1.21978e6 0.999680
\(273\) 890291. 0.722979
\(274\) 321930. 0.259051
\(275\) 0 0
\(276\) 115349. 0.0911464
\(277\) 1.08351e6 0.848466 0.424233 0.905553i \(-0.360544\pi\)
0.424233 + 0.905553i \(0.360544\pi\)
\(278\) 428867. 0.332821
\(279\) −3.34637e6 −2.57373
\(280\) 0 0
\(281\) −1.46593e6 −1.10751 −0.553756 0.832679i \(-0.686806\pi\)
−0.553756 + 0.832679i \(0.686806\pi\)
\(282\) −979158. −0.733213
\(283\) −2.11337e6 −1.56859 −0.784294 0.620390i \(-0.786974\pi\)
−0.784294 + 0.620390i \(0.786974\pi\)
\(284\) 757210. 0.557084
\(285\) 0 0
\(286\) 20849.7 0.0150724
\(287\) −2.96960e6 −2.12811
\(288\) 3.27613e6 2.32744
\(289\) 1.91147e6 1.34624
\(290\) 0 0
\(291\) 162496. 0.112489
\(292\) 947293. 0.650170
\(293\) 2.71115e6 1.84495 0.922475 0.386057i \(-0.126163\pi\)
0.922475 + 0.386057i \(0.126163\pi\)
\(294\) 848756. 0.572683
\(295\) 0 0
\(296\) −505180. −0.335133
\(297\) −747842. −0.491947
\(298\) −155829. −0.101650
\(299\) 23272.3 0.0150543
\(300\) 0 0
\(301\) −3.80641e6 −2.42158
\(302\) 724035. 0.456817
\(303\) −2.60350e6 −1.62911
\(304\) 1.67730e6 1.04094
\(305\) 0 0
\(306\) 2.30624e6 1.40800
\(307\) −1.55774e6 −0.943297 −0.471648 0.881787i \(-0.656341\pi\)
−0.471648 + 0.881787i \(0.656341\pi\)
\(308\) −312693. −0.187820
\(309\) 2.24113e6 1.33527
\(310\) 0 0
\(311\) −2.57327e6 −1.50863 −0.754316 0.656511i \(-0.772032\pi\)
−0.754316 + 0.656511i \(0.772032\pi\)
\(312\) 594436. 0.345715
\(313\) 563667. 0.325208 0.162604 0.986691i \(-0.448011\pi\)
0.162604 + 0.986691i \(0.448011\pi\)
\(314\) −60824.3 −0.0348139
\(315\) 0 0
\(316\) 380698. 0.214468
\(317\) 1.49727e6 0.836858 0.418429 0.908250i \(-0.362581\pi\)
0.418429 + 0.908250i \(0.362581\pi\)
\(318\) −160816. −0.0891789
\(319\) −375425. −0.206560
\(320\) 0 0
\(321\) −2.31534e6 −1.25416
\(322\) 47881.9 0.0257355
\(323\) 4.58083e6 2.44308
\(324\) −5.57890e6 −2.95248
\(325\) 0 0
\(326\) 401889. 0.209441
\(327\) 5.22914e6 2.70434
\(328\) −1.98277e6 −1.01762
\(329\) 2.96277e6 1.50907
\(330\) 0 0
\(331\) 2.48241e6 1.24538 0.622692 0.782467i \(-0.286039\pi\)
0.622692 + 0.782467i \(0.286039\pi\)
\(332\) 22258.0 0.0110826
\(333\) 2.74948e6 1.35875
\(334\) −311319. −0.152700
\(335\) 0 0
\(336\) −3.52063e6 −1.70126
\(337\) −2.17057e6 −1.04112 −0.520558 0.853827i \(-0.674276\pi\)
−0.520558 + 0.853827i \(0.674276\pi\)
\(338\) 56116.4 0.0267176
\(339\) 69957.0 0.0330622
\(340\) 0 0
\(341\) 326730. 0.152161
\(342\) 3.17126e6 1.46611
\(343\) 406164. 0.186409
\(344\) −2.54149e6 −1.15796
\(345\) 0 0
\(346\) −453204. −0.203518
\(347\) −3.93089e6 −1.75254 −0.876269 0.481821i \(-0.839975\pi\)
−0.876269 + 0.481821i \(0.839975\pi\)
\(348\) −5.00826e6 −2.21686
\(349\) 378915. 0.166524 0.0832622 0.996528i \(-0.473466\pi\)
0.0832622 + 0.996528i \(0.473466\pi\)
\(350\) 0 0
\(351\) −2.01280e6 −0.872032
\(352\) −319872. −0.137600
\(353\) 1.13031e6 0.482792 0.241396 0.970427i \(-0.422395\pi\)
0.241396 + 0.970427i \(0.422395\pi\)
\(354\) 972722. 0.412554
\(355\) 0 0
\(356\) 2.03235e6 0.849911
\(357\) −9.61511e6 −3.99286
\(358\) 1.55590e6 0.641614
\(359\) 3.35579e6 1.37423 0.687114 0.726550i \(-0.258877\pi\)
0.687114 + 0.726550i \(0.258877\pi\)
\(360\) 0 0
\(361\) 3.82289e6 1.54391
\(362\) −535787. −0.214892
\(363\) −4.67672e6 −1.86284
\(364\) −841605. −0.332931
\(365\) 0 0
\(366\) −1.46251e6 −0.570683
\(367\) −1.99093e6 −0.771597 −0.385799 0.922583i \(-0.626074\pi\)
−0.385799 + 0.922583i \(0.626074\pi\)
\(368\) −92029.4 −0.0354248
\(369\) 1.07913e7 4.12581
\(370\) 0 0
\(371\) 486603. 0.183544
\(372\) 4.35866e6 1.63304
\(373\) −1.39554e6 −0.519362 −0.259681 0.965694i \(-0.583617\pi\)
−0.259681 + 0.965694i \(0.583617\pi\)
\(374\) −225175. −0.0832419
\(375\) 0 0
\(376\) 1.97821e6 0.721609
\(377\) −1.01045e6 −0.366151
\(378\) −4.14126e6 −1.49075
\(379\) 3.81965e6 1.36592 0.682960 0.730455i \(-0.260692\pi\)
0.682960 + 0.730455i \(0.260692\pi\)
\(380\) 0 0
\(381\) 7.93403e6 2.80015
\(382\) 1.18490e6 0.415456
\(383\) −4.30052e6 −1.49804 −0.749020 0.662547i \(-0.769475\pi\)
−0.749020 + 0.662547i \(0.769475\pi\)
\(384\) −5.51796e6 −1.90963
\(385\) 0 0
\(386\) 116007. 0.0396293
\(387\) 1.38322e7 4.69478
\(388\) −153609. −0.0518011
\(389\) 5.63218e6 1.88713 0.943567 0.331182i \(-0.107447\pi\)
0.943567 + 0.331182i \(0.107447\pi\)
\(390\) 0 0
\(391\) −251340. −0.0831418
\(392\) −1.71475e6 −0.563620
\(393\) 3.53348e6 1.15404
\(394\) −1.60320e6 −0.520291
\(395\) 0 0
\(396\) 1.13630e6 0.364130
\(397\) −1.02692e6 −0.327011 −0.163505 0.986542i \(-0.552280\pi\)
−0.163505 + 0.986542i \(0.552280\pi\)
\(398\) 963911. 0.305021
\(399\) −1.32215e7 −4.15766
\(400\) 0 0
\(401\) −1.07636e6 −0.334269 −0.167134 0.985934i \(-0.553451\pi\)
−0.167134 + 0.985934i \(0.553451\pi\)
\(402\) −1.72098e6 −0.531142
\(403\) 879387. 0.269723
\(404\) 2.46113e6 0.750206
\(405\) 0 0
\(406\) −2.07896e6 −0.625938
\(407\) −268452. −0.0803304
\(408\) −6.41989e6 −1.90931
\(409\) −4.48956e6 −1.32708 −0.663538 0.748143i \(-0.730946\pi\)
−0.663538 + 0.748143i \(0.730946\pi\)
\(410\) 0 0
\(411\) 4.87739e6 1.42424
\(412\) −2.11857e6 −0.614892
\(413\) −2.94330e6 −0.849100
\(414\) −174000. −0.0498939
\(415\) 0 0
\(416\) −860928. −0.243912
\(417\) 6.49754e6 1.82982
\(418\) −309633. −0.0866776
\(419\) −2.90095e6 −0.807245 −0.403622 0.914926i \(-0.632249\pi\)
−0.403622 + 0.914926i \(0.632249\pi\)
\(420\) 0 0
\(421\) −5.69840e6 −1.56692 −0.783461 0.621441i \(-0.786548\pi\)
−0.783461 + 0.621441i \(0.786548\pi\)
\(422\) 1.16692e6 0.318977
\(423\) −1.07665e7 −2.92566
\(424\) 324899. 0.0877675
\(425\) 0 0
\(426\) −1.57383e6 −0.420177
\(427\) 4.42530e6 1.17455
\(428\) 2.18873e6 0.577540
\(429\) 315882. 0.0828670
\(430\) 0 0
\(431\) 7.25477e6 1.88118 0.940590 0.339545i \(-0.110273\pi\)
0.940590 + 0.339545i \(0.110273\pi\)
\(432\) 7.95954e6 2.05201
\(433\) −2.92650e6 −0.750115 −0.375058 0.927001i \(-0.622377\pi\)
−0.375058 + 0.927001i \(0.622377\pi\)
\(434\) 1.80931e6 0.461093
\(435\) 0 0
\(436\) −4.94318e6 −1.24535
\(437\) −345611. −0.0865733
\(438\) −1.96890e6 −0.490387
\(439\) 2.15422e6 0.533492 0.266746 0.963767i \(-0.414051\pi\)
0.266746 + 0.963767i \(0.414051\pi\)
\(440\) 0 0
\(441\) 9.33266e6 2.28512
\(442\) −606054. −0.147556
\(443\) −7.40975e6 −1.79388 −0.896942 0.442148i \(-0.854217\pi\)
−0.896942 + 0.442148i \(0.854217\pi\)
\(444\) −3.58121e6 −0.862130
\(445\) 0 0
\(446\) 1.75562e6 0.417921
\(447\) −2.36088e6 −0.558864
\(448\) 2.01334e6 0.473938
\(449\) −1.90284e6 −0.445438 −0.222719 0.974883i \(-0.571493\pi\)
−0.222719 + 0.974883i \(0.571493\pi\)
\(450\) 0 0
\(451\) −1.05364e6 −0.243921
\(452\) −66131.3 −0.0152251
\(453\) 1.09695e7 2.51154
\(454\) −2.16912e6 −0.493906
\(455\) 0 0
\(456\) −8.82783e6 −1.98812
\(457\) −2.79693e6 −0.626457 −0.313229 0.949678i \(-0.601411\pi\)
−0.313229 + 0.949678i \(0.601411\pi\)
\(458\) −1.30087e6 −0.289782
\(459\) 2.17381e7 4.81605
\(460\) 0 0
\(461\) 4.18307e6 0.916733 0.458366 0.888763i \(-0.348435\pi\)
0.458366 + 0.888763i \(0.348435\pi\)
\(462\) 649917. 0.141662
\(463\) 2.51126e6 0.544427 0.272213 0.962237i \(-0.412244\pi\)
0.272213 + 0.962237i \(0.412244\pi\)
\(464\) 3.99578e6 0.861602
\(465\) 0 0
\(466\) −1.62750e6 −0.347181
\(467\) −2.17175e6 −0.460806 −0.230403 0.973095i \(-0.574004\pi\)
−0.230403 + 0.973095i \(0.574004\pi\)
\(468\) 3.05833e6 0.645462
\(469\) 5.20740e6 1.09317
\(470\) 0 0
\(471\) −921517. −0.191404
\(472\) −1.96520e6 −0.406025
\(473\) −1.35054e6 −0.277559
\(474\) −791263. −0.161761
\(475\) 0 0
\(476\) 9.08930e6 1.83871
\(477\) −1.76828e6 −0.355841
\(478\) 705784. 0.141287
\(479\) −9.46791e6 −1.88545 −0.942726 0.333568i \(-0.891747\pi\)
−0.942726 + 0.333568i \(0.891747\pi\)
\(480\) 0 0
\(481\) −722531. −0.142395
\(482\) −1.82492e6 −0.357788
\(483\) 725434. 0.141491
\(484\) 4.42097e6 0.857835
\(485\) 0 0
\(486\) 5.90911e6 1.13483
\(487\) −4.87785e6 −0.931979 −0.465989 0.884790i \(-0.654302\pi\)
−0.465989 + 0.884790i \(0.654302\pi\)
\(488\) 2.95472e6 0.561651
\(489\) 6.08881e6 1.15149
\(490\) 0 0
\(491\) −3.86456e6 −0.723429 −0.361715 0.932289i \(-0.617808\pi\)
−0.361715 + 0.932289i \(0.617808\pi\)
\(492\) −1.40558e7 −2.61784
\(493\) 1.09128e7 2.02217
\(494\) −833370. −0.153646
\(495\) 0 0
\(496\) −3.47750e6 −0.634693
\(497\) 4.76214e6 0.864791
\(498\) −46262.2 −0.00835897
\(499\) 5.75229e6 1.03416 0.517082 0.855936i \(-0.327018\pi\)
0.517082 + 0.855936i \(0.327018\pi\)
\(500\) 0 0
\(501\) −4.71663e6 −0.839532
\(502\) −201064. −0.0356103
\(503\) 5.93696e6 1.04627 0.523136 0.852249i \(-0.324762\pi\)
0.523136 + 0.852249i \(0.324762\pi\)
\(504\) 1.34481e7 2.35822
\(505\) 0 0
\(506\) 16988.9 0.00294977
\(507\) 850189. 0.146891
\(508\) −7.50015e6 −1.28947
\(509\) −563930. −0.0964785 −0.0482393 0.998836i \(-0.515361\pi\)
−0.0482393 + 0.998836i \(0.515361\pi\)
\(510\) 0 0
\(511\) 5.95758e6 1.00929
\(512\) 5.93149e6 0.999974
\(513\) 2.98916e7 5.01482
\(514\) −2.30786e6 −0.385302
\(515\) 0 0
\(516\) −1.80166e7 −2.97884
\(517\) 1.05121e6 0.172968
\(518\) −1.48658e6 −0.243425
\(519\) −6.86625e6 −1.11892
\(520\) 0 0
\(521\) 1.09272e6 0.176366 0.0881828 0.996104i \(-0.471894\pi\)
0.0881828 + 0.996104i \(0.471894\pi\)
\(522\) 7.55481e6 1.21352
\(523\) −2.47626e6 −0.395861 −0.197930 0.980216i \(-0.563422\pi\)
−0.197930 + 0.980216i \(0.563422\pi\)
\(524\) −3.34024e6 −0.531435
\(525\) 0 0
\(526\) −195508. −0.0308107
\(527\) −9.49734e6 −1.48962
\(528\) −1.24914e6 −0.194997
\(529\) −6.41738e6 −0.997054
\(530\) 0 0
\(531\) 1.06957e7 1.64617
\(532\) 1.24985e7 1.91460
\(533\) −2.83584e6 −0.432378
\(534\) −4.22414e6 −0.641041
\(535\) 0 0
\(536\) 3.47692e6 0.522736
\(537\) 2.35726e7 3.52754
\(538\) −1.09829e6 −0.163592
\(539\) −911215. −0.135098
\(540\) 0 0
\(541\) −5.78515e6 −0.849810 −0.424905 0.905238i \(-0.639692\pi\)
−0.424905 + 0.905238i \(0.639692\pi\)
\(542\) −989788. −0.144725
\(543\) −8.11742e6 −1.18146
\(544\) 9.29799e6 1.34708
\(545\) 0 0
\(546\) 1.74923e6 0.251111
\(547\) 1.26151e7 1.80269 0.901345 0.433102i \(-0.142581\pi\)
0.901345 + 0.433102i \(0.142581\pi\)
\(548\) −4.61067e6 −0.655862
\(549\) −1.60813e7 −2.27714
\(550\) 0 0
\(551\) 1.50059e7 2.10564
\(552\) 484363. 0.0676586
\(553\) 2.39423e6 0.332930
\(554\) 2.12887e6 0.294697
\(555\) 0 0
\(556\) −6.14222e6 −0.842632
\(557\) 9.93482e6 1.35682 0.678409 0.734684i \(-0.262670\pi\)
0.678409 + 0.734684i \(0.262670\pi\)
\(558\) −6.57491e6 −0.893931
\(559\) −3.63495e6 −0.492005
\(560\) 0 0
\(561\) −3.41151e6 −0.457657
\(562\) −2.88025e6 −0.384671
\(563\) −8.72418e6 −1.15999 −0.579994 0.814621i \(-0.696945\pi\)
−0.579994 + 0.814621i \(0.696945\pi\)
\(564\) 1.40234e7 1.85634
\(565\) 0 0
\(566\) −4.15232e6 −0.544816
\(567\) −3.50860e7 −4.58328
\(568\) 3.17962e6 0.413527
\(569\) 5.33272e6 0.690508 0.345254 0.938509i \(-0.387793\pi\)
0.345254 + 0.938509i \(0.387793\pi\)
\(570\) 0 0
\(571\) −1.46290e7 −1.87769 −0.938847 0.344334i \(-0.888105\pi\)
−0.938847 + 0.344334i \(0.888105\pi\)
\(572\) −298608. −0.0381602
\(573\) 1.79519e7 2.28414
\(574\) −5.83465e6 −0.739154
\(575\) 0 0
\(576\) −7.31633e6 −0.918834
\(577\) −7.62278e6 −0.953177 −0.476589 0.879126i \(-0.658127\pi\)
−0.476589 + 0.879126i \(0.658127\pi\)
\(578\) 3.75564e6 0.467590
\(579\) 1.75756e6 0.217878
\(580\) 0 0
\(581\) 139982. 0.0172041
\(582\) 319270. 0.0390706
\(583\) 172650. 0.0210376
\(584\) 3.97780e6 0.482626
\(585\) 0 0
\(586\) 5.32684e6 0.640805
\(587\) −7.92637e6 −0.949465 −0.474732 0.880130i \(-0.657455\pi\)
−0.474732 + 0.880130i \(0.657455\pi\)
\(588\) −1.21558e7 −1.44991
\(589\) −1.30596e7 −1.55110
\(590\) 0 0
\(591\) −2.42892e7 −2.86052
\(592\) 2.85722e6 0.335074
\(593\) −1.13806e7 −1.32901 −0.664507 0.747282i \(-0.731358\pi\)
−0.664507 + 0.747282i \(0.731358\pi\)
\(594\) −1.46935e6 −0.170868
\(595\) 0 0
\(596\) 2.23178e6 0.257356
\(597\) 1.46037e7 1.67698
\(598\) 45725.1 0.00522880
\(599\) 7.12203e6 0.811030 0.405515 0.914088i \(-0.367092\pi\)
0.405515 + 0.914088i \(0.367092\pi\)
\(600\) 0 0
\(601\) 1.50084e6 0.169492 0.0847458 0.996403i \(-0.472992\pi\)
0.0847458 + 0.996403i \(0.472992\pi\)
\(602\) −7.47879e6 −0.841086
\(603\) −1.89234e7 −2.11936
\(604\) −1.03696e7 −1.15656
\(605\) 0 0
\(606\) −5.11534e6 −0.565839
\(607\) 1.39958e7 1.54179 0.770897 0.636960i \(-0.219808\pi\)
0.770897 + 0.636960i \(0.219808\pi\)
\(608\) 1.27854e7 1.40267
\(609\) −3.14972e7 −3.44135
\(610\) 0 0
\(611\) 2.82932e6 0.306604
\(612\) −3.30299e7 −3.56475
\(613\) −4.60575e6 −0.495050 −0.247525 0.968882i \(-0.579617\pi\)
−0.247525 + 0.968882i \(0.579617\pi\)
\(614\) −3.06063e6 −0.327634
\(615\) 0 0
\(616\) −1.31303e6 −0.139420
\(617\) −5.55212e6 −0.587146 −0.293573 0.955937i \(-0.594844\pi\)
−0.293573 + 0.955937i \(0.594844\pi\)
\(618\) 4.40334e6 0.463779
\(619\) −2.71815e6 −0.285133 −0.142566 0.989785i \(-0.545535\pi\)
−0.142566 + 0.989785i \(0.545535\pi\)
\(620\) 0 0
\(621\) −1.64008e6 −0.170662
\(622\) −5.05592e6 −0.523992
\(623\) 1.27816e7 1.31936
\(624\) −3.36204e6 −0.345654
\(625\) 0 0
\(626\) 1.10749e6 0.112954
\(627\) −4.69109e6 −0.476546
\(628\) 871122. 0.0881414
\(629\) 7.80331e6 0.786416
\(630\) 0 0
\(631\) −1.93426e6 −0.193393 −0.0966964 0.995314i \(-0.530828\pi\)
−0.0966964 + 0.995314i \(0.530828\pi\)
\(632\) 1.59860e6 0.159201
\(633\) 1.76793e7 1.75371
\(634\) 2.94182e6 0.290665
\(635\) 0 0
\(636\) 2.30320e6 0.225782
\(637\) −2.45251e6 −0.239477
\(638\) −737631. −0.0717443
\(639\) −1.73053e7 −1.67659
\(640\) 0 0
\(641\) 9.58248e6 0.921155 0.460578 0.887619i \(-0.347642\pi\)
0.460578 + 0.887619i \(0.347642\pi\)
\(642\) −4.54916e6 −0.435606
\(643\) −2.46659e6 −0.235272 −0.117636 0.993057i \(-0.537532\pi\)
−0.117636 + 0.993057i \(0.537532\pi\)
\(644\) −685762. −0.0651567
\(645\) 0 0
\(646\) 9.00037e6 0.848553
\(647\) 2.72804e6 0.256207 0.128103 0.991761i \(-0.459111\pi\)
0.128103 + 0.991761i \(0.459111\pi\)
\(648\) −2.34265e7 −2.19164
\(649\) −1.04430e6 −0.0973229
\(650\) 0 0
\(651\) 2.74119e7 2.53505
\(652\) −5.75584e6 −0.530261
\(653\) −9.94071e6 −0.912293 −0.456147 0.889905i \(-0.650771\pi\)
−0.456147 + 0.889905i \(0.650771\pi\)
\(654\) 1.02742e7 0.939295
\(655\) 0 0
\(656\) 1.12142e7 1.01744
\(657\) −2.16494e7 −1.95674
\(658\) 5.82122e6 0.524143
\(659\) 440385. 0.0395019 0.0197510 0.999805i \(-0.493713\pi\)
0.0197510 + 0.999805i \(0.493713\pi\)
\(660\) 0 0
\(661\) 4.85089e6 0.431835 0.215918 0.976412i \(-0.430726\pi\)
0.215918 + 0.976412i \(0.430726\pi\)
\(662\) 4.87741e6 0.432558
\(663\) −9.18201e6 −0.811248
\(664\) 93464.0 0.00822668
\(665\) 0 0
\(666\) 5.40215e6 0.471933
\(667\) −823340. −0.0716580
\(668\) 4.45869e6 0.386604
\(669\) 2.65985e7 2.29769
\(670\) 0 0
\(671\) 1.57013e6 0.134626
\(672\) −2.68365e7 −2.29246
\(673\) −2.15372e6 −0.183296 −0.0916479 0.995791i \(-0.529213\pi\)
−0.0916479 + 0.995791i \(0.529213\pi\)
\(674\) −4.26471e6 −0.361609
\(675\) 0 0
\(676\) −803695. −0.0676433
\(677\) −4.93215e6 −0.413585 −0.206792 0.978385i \(-0.566302\pi\)
−0.206792 + 0.978385i \(0.566302\pi\)
\(678\) 137451. 0.0114835
\(679\) −966058. −0.0804135
\(680\) 0 0
\(681\) −3.28632e7 −2.71545
\(682\) 641956. 0.0528499
\(683\) 1.39352e7 1.14304 0.571521 0.820588i \(-0.306354\pi\)
0.571521 + 0.820588i \(0.306354\pi\)
\(684\) −4.54186e7 −3.71187
\(685\) 0 0
\(686\) 798026. 0.0647451
\(687\) −1.97088e7 −1.59320
\(688\) 1.43743e7 1.15775
\(689\) 464685. 0.0372915
\(690\) 0 0
\(691\) 1.71835e7 1.36904 0.684520 0.728994i \(-0.260012\pi\)
0.684520 + 0.728994i \(0.260012\pi\)
\(692\) 6.49076e6 0.515264
\(693\) 7.14628e6 0.565258
\(694\) −7.72338e6 −0.608708
\(695\) 0 0
\(696\) −2.10303e7 −1.64559
\(697\) 3.06270e7 2.38793
\(698\) 744488. 0.0578387
\(699\) −2.46574e7 −1.90877
\(700\) 0 0
\(701\) 4.18640e6 0.321770 0.160885 0.986973i \(-0.448565\pi\)
0.160885 + 0.986973i \(0.448565\pi\)
\(702\) −3.95472e6 −0.302882
\(703\) 1.07301e7 0.818874
\(704\) 714347. 0.0543222
\(705\) 0 0
\(706\) 2.22082e6 0.167688
\(707\) 1.54782e7 1.16458
\(708\) −1.39313e7 −1.04450
\(709\) −7.30623e6 −0.545855 −0.272928 0.962035i \(-0.587992\pi\)
−0.272928 + 0.962035i \(0.587992\pi\)
\(710\) 0 0
\(711\) −8.70048e6 −0.645460
\(712\) 8.53409e6 0.630895
\(713\) 716548. 0.0527864
\(714\) −1.88917e7 −1.38684
\(715\) 0 0
\(716\) −2.22835e7 −1.62443
\(717\) 1.06930e7 0.776783
\(718\) 6.59342e6 0.477309
\(719\) −1.22435e7 −0.883249 −0.441625 0.897200i \(-0.645598\pi\)
−0.441625 + 0.897200i \(0.645598\pi\)
\(720\) 0 0
\(721\) −1.33238e7 −0.954530
\(722\) 7.51117e6 0.536246
\(723\) −2.76484e7 −1.96709
\(724\) 7.67351e6 0.544061
\(725\) 0 0
\(726\) −9.18877e6 −0.647017
\(727\) −612630. −0.0429895 −0.0214947 0.999769i \(-0.506843\pi\)
−0.0214947 + 0.999769i \(0.506843\pi\)
\(728\) −3.53400e6 −0.247137
\(729\) 4.13490e7 2.88169
\(730\) 0 0
\(731\) 3.92574e7 2.71724
\(732\) 2.09459e7 1.44485
\(733\) −1.54190e7 −1.05998 −0.529989 0.848004i \(-0.677804\pi\)
−0.529989 + 0.848004i \(0.677804\pi\)
\(734\) −3.91176e6 −0.267998
\(735\) 0 0
\(736\) −701508. −0.0477351
\(737\) 1.84763e6 0.125298
\(738\) 2.12027e7 1.43301
\(739\) 1.10414e7 0.743724 0.371862 0.928288i \(-0.378720\pi\)
0.371862 + 0.928288i \(0.378720\pi\)
\(740\) 0 0
\(741\) −1.26259e7 −0.844731
\(742\) 956073. 0.0637502
\(743\) 1.66010e7 1.10322 0.551611 0.834102i \(-0.314013\pi\)
0.551611 + 0.834102i \(0.314013\pi\)
\(744\) 1.83026e7 1.21221
\(745\) 0 0
\(746\) −2.74194e6 −0.180390
\(747\) −508684. −0.0333539
\(748\) 3.22495e6 0.210751
\(749\) 1.37650e7 0.896546
\(750\) 0 0
\(751\) 1.04497e6 0.0676089 0.0338045 0.999428i \(-0.489238\pi\)
0.0338045 + 0.999428i \(0.489238\pi\)
\(752\) −1.11884e7 −0.721481
\(753\) −3.04622e6 −0.195782
\(754\) −1.98532e6 −0.127175
\(755\) 0 0
\(756\) 5.93109e7 3.77425
\(757\) −5.93460e6 −0.376402 −0.188201 0.982131i \(-0.560266\pi\)
−0.188201 + 0.982131i \(0.560266\pi\)
\(758\) 7.50481e6 0.474424
\(759\) 257389. 0.0162176
\(760\) 0 0
\(761\) 5.89549e6 0.369027 0.184514 0.982830i \(-0.440929\pi\)
0.184514 + 0.982830i \(0.440929\pi\)
\(762\) 1.55887e7 0.972574
\(763\) −3.10879e7 −1.93322
\(764\) −1.69701e7 −1.05185
\(765\) 0 0
\(766\) −8.44961e6 −0.520313
\(767\) −2.81072e6 −0.172516
\(768\) −4726.10 −0.000289134 0
\(769\) −1.30498e7 −0.795769 −0.397884 0.917436i \(-0.630256\pi\)
−0.397884 + 0.917436i \(0.630256\pi\)
\(770\) 0 0
\(771\) −3.49651e7 −2.11835
\(772\) −1.66145e6 −0.100333
\(773\) 2.29371e7 1.38067 0.690334 0.723491i \(-0.257464\pi\)
0.690334 + 0.723491i \(0.257464\pi\)
\(774\) 2.71774e7 1.63063
\(775\) 0 0
\(776\) −645025. −0.0384523
\(777\) −2.25224e7 −1.33833
\(778\) 1.10661e7 0.655456
\(779\) 4.21144e7 2.48649
\(780\) 0 0
\(781\) 1.68964e6 0.0991213
\(782\) −493830. −0.0288775
\(783\) 7.12099e7 4.15084
\(784\) 9.69838e6 0.563520
\(785\) 0 0
\(786\) 6.94254e6 0.400831
\(787\) 1.68766e7 0.971291 0.485645 0.874156i \(-0.338585\pi\)
0.485645 + 0.874156i \(0.338585\pi\)
\(788\) 2.29609e7 1.31727
\(789\) −2.96204e6 −0.169394
\(790\) 0 0
\(791\) −415903. −0.0236348
\(792\) 4.77148e6 0.270296
\(793\) 4.22597e6 0.238640
\(794\) −2.01769e6 −0.113580
\(795\) 0 0
\(796\) −1.38051e7 −0.772247
\(797\) 4.13009e6 0.230311 0.115155 0.993348i \(-0.463263\pi\)
0.115155 + 0.993348i \(0.463263\pi\)
\(798\) −2.59775e7 −1.44407
\(799\) −3.05565e7 −1.69331
\(800\) 0 0
\(801\) −4.64474e7 −2.55788
\(802\) −2.11482e6 −0.116101
\(803\) 2.11379e6 0.115684
\(804\) 2.46478e7 1.34474
\(805\) 0 0
\(806\) 1.72781e6 0.0936825
\(807\) −1.66396e7 −0.899412
\(808\) 1.03346e7 0.556884
\(809\) 1.01709e7 0.546369 0.273185 0.961962i \(-0.411923\pi\)
0.273185 + 0.961962i \(0.411923\pi\)
\(810\) 0 0
\(811\) −2.22723e7 −1.18909 −0.594543 0.804064i \(-0.702667\pi\)
−0.594543 + 0.804064i \(0.702667\pi\)
\(812\) 2.97748e7 1.58474
\(813\) −1.49957e7 −0.795686
\(814\) −527451. −0.0279011
\(815\) 0 0
\(816\) 3.63099e7 1.90897
\(817\) 5.39818e7 2.82939
\(818\) −8.82104e6 −0.460932
\(819\) 1.92340e7 1.00198
\(820\) 0 0
\(821\) 3.65506e6 0.189250 0.0946251 0.995513i \(-0.469835\pi\)
0.0946251 + 0.995513i \(0.469835\pi\)
\(822\) 9.58305e6 0.494680
\(823\) 7.29867e6 0.375616 0.187808 0.982206i \(-0.439862\pi\)
0.187808 + 0.982206i \(0.439862\pi\)
\(824\) −8.89612e6 −0.456439
\(825\) 0 0
\(826\) −5.78296e6 −0.294917
\(827\) −3.19608e7 −1.62500 −0.812502 0.582958i \(-0.801895\pi\)
−0.812502 + 0.582958i \(0.801895\pi\)
\(828\) 2.49201e6 0.126321
\(829\) 9.74730e6 0.492604 0.246302 0.969193i \(-0.420785\pi\)
0.246302 + 0.969193i \(0.420785\pi\)
\(830\) 0 0
\(831\) 3.22534e7 1.62022
\(832\) 1.92265e6 0.0962923
\(833\) 2.64871e7 1.32258
\(834\) 1.27663e7 0.635550
\(835\) 0 0
\(836\) 4.43455e6 0.219449
\(837\) −6.19736e7 −3.05769
\(838\) −5.69976e6 −0.280380
\(839\) −6.75711e6 −0.331403 −0.165701 0.986176i \(-0.552989\pi\)
−0.165701 + 0.986176i \(0.552989\pi\)
\(840\) 0 0
\(841\) 1.52371e7 0.742867
\(842\) −1.11962e7 −0.544238
\(843\) −4.36371e7 −2.11489
\(844\) −1.67125e7 −0.807580
\(845\) 0 0
\(846\) −2.11539e7 −1.01617
\(847\) 2.78037e7 1.33166
\(848\) −1.83758e6 −0.0877519
\(849\) −6.29096e7 −2.99535
\(850\) 0 0
\(851\) −588738. −0.0278675
\(852\) 2.25402e7 1.06380
\(853\) −2.85698e7 −1.34442 −0.672209 0.740362i \(-0.734654\pi\)
−0.672209 + 0.740362i \(0.734654\pi\)
\(854\) 8.69479e6 0.407957
\(855\) 0 0
\(856\) 9.19073e6 0.428712
\(857\) −2.35895e6 −0.109715 −0.0548577 0.998494i \(-0.517471\pi\)
−0.0548577 + 0.998494i \(0.517471\pi\)
\(858\) 620642. 0.0287821
\(859\) 1.07995e7 0.499368 0.249684 0.968327i \(-0.419673\pi\)
0.249684 + 0.968327i \(0.419673\pi\)
\(860\) 0 0
\(861\) −8.83976e7 −4.06380
\(862\) 1.42541e7 0.653388
\(863\) 2.27989e7 1.04204 0.521022 0.853543i \(-0.325551\pi\)
0.521022 + 0.853543i \(0.325551\pi\)
\(864\) 6.06728e7 2.76509
\(865\) 0 0
\(866\) −5.74995e6 −0.260537
\(867\) 5.68998e7 2.57077
\(868\) −2.59128e7 −1.16739
\(869\) 849491. 0.0381601
\(870\) 0 0
\(871\) 4.97284e6 0.222105
\(872\) −2.07570e7 −0.924429
\(873\) 3.51059e6 0.155899
\(874\) −679053. −0.0300694
\(875\) 0 0
\(876\) 2.81985e7 1.24155
\(877\) −3.23124e7 −1.41863 −0.709317 0.704890i \(-0.750997\pi\)
−0.709317 + 0.704890i \(0.750997\pi\)
\(878\) 4.23258e6 0.185297
\(879\) 8.07041e7 3.52309
\(880\) 0 0
\(881\) 1.40863e7 0.611447 0.305723 0.952120i \(-0.401102\pi\)
0.305723 + 0.952120i \(0.401102\pi\)
\(882\) 1.83367e7 0.793688
\(883\) −4.14803e7 −1.79036 −0.895180 0.445705i \(-0.852953\pi\)
−0.895180 + 0.445705i \(0.852953\pi\)
\(884\) 8.67988e6 0.373579
\(885\) 0 0
\(886\) −1.45586e7 −0.623068
\(887\) 6.64591e6 0.283626 0.141813 0.989893i \(-0.454707\pi\)
0.141813 + 0.989893i \(0.454707\pi\)
\(888\) −1.50379e7 −0.639965
\(889\) −4.71689e7 −2.00171
\(890\) 0 0
\(891\) −1.24488e7 −0.525331
\(892\) −2.51439e7 −1.05809
\(893\) −4.20175e7 −1.76320
\(894\) −4.63864e6 −0.194110
\(895\) 0 0
\(896\) 3.28050e7 1.36512
\(897\) 692757. 0.0287475
\(898\) −3.73869e6 −0.154713
\(899\) −3.11115e7 −1.28387
\(900\) 0 0
\(901\) −5.01858e6 −0.205953
\(902\) −2.07018e6 −0.0847210
\(903\) −1.13307e8 −4.62422
\(904\) −277693. −0.0113017
\(905\) 0 0
\(906\) 2.15527e7 0.872331
\(907\) −1.12437e7 −0.453827 −0.226914 0.973915i \(-0.572863\pi\)
−0.226914 + 0.973915i \(0.572863\pi\)
\(908\) 3.10660e7 1.25046
\(909\) −5.62466e7 −2.25781
\(910\) 0 0
\(911\) 2.28294e7 0.911377 0.455689 0.890139i \(-0.349393\pi\)
0.455689 + 0.890139i \(0.349393\pi\)
\(912\) 4.99289e7 1.98776
\(913\) 49666.6 0.00197191
\(914\) −5.49538e6 −0.217587
\(915\) 0 0
\(916\) 1.86310e7 0.733666
\(917\) −2.10070e7 −0.824974
\(918\) 4.27109e7 1.67275
\(919\) 3.58183e7 1.39899 0.699497 0.714635i \(-0.253407\pi\)
0.699497 + 0.714635i \(0.253407\pi\)
\(920\) 0 0
\(921\) −4.63699e7 −1.80130
\(922\) 8.21885e6 0.318408
\(923\) 4.54763e6 0.175704
\(924\) −9.30807e6 −0.358657
\(925\) 0 0
\(926\) 4.93410e6 0.189095
\(927\) 4.84177e7 1.85057
\(928\) 3.04584e7 1.16101
\(929\) −1.37009e7 −0.520847 −0.260424 0.965494i \(-0.583862\pi\)
−0.260424 + 0.965494i \(0.583862\pi\)
\(930\) 0 0
\(931\) 3.64217e7 1.37716
\(932\) 2.33090e7 0.878988
\(933\) −7.65996e7 −2.88086
\(934\) −4.26704e6 −0.160051
\(935\) 0 0
\(936\) 1.28423e7 0.479131
\(937\) −2.45732e7 −0.914352 −0.457176 0.889376i \(-0.651139\pi\)
−0.457176 + 0.889376i \(0.651139\pi\)
\(938\) 1.02315e7 0.379691
\(939\) 1.67789e7 0.621013
\(940\) 0 0
\(941\) 3.53611e7 1.30182 0.650912 0.759153i \(-0.274387\pi\)
0.650912 + 0.759153i \(0.274387\pi\)
\(942\) −1.81059e6 −0.0664801
\(943\) −2.31072e6 −0.0846191
\(944\) 1.11149e7 0.405952
\(945\) 0 0
\(946\) −2.65353e6 −0.0964043
\(947\) −4.90338e7 −1.77673 −0.888364 0.459140i \(-0.848158\pi\)
−0.888364 + 0.459140i \(0.848158\pi\)
\(948\) 1.13324e7 0.409545
\(949\) 5.68922e6 0.205063
\(950\) 0 0
\(951\) 4.45699e7 1.59805
\(952\) 3.81671e7 1.36489
\(953\) 1.81532e7 0.647472 0.323736 0.946147i \(-0.395061\pi\)
0.323736 + 0.946147i \(0.395061\pi\)
\(954\) −3.47431e6 −0.123594
\(955\) 0 0
\(956\) −1.01082e7 −0.357708
\(957\) −1.11755e7 −0.394444
\(958\) −1.86025e7 −0.654872
\(959\) −2.89967e7 −1.01813
\(960\) 0 0
\(961\) −1.55304e6 −0.0542466
\(962\) −1.41962e6 −0.0494578
\(963\) −5.00212e7 −1.73815
\(964\) 2.61364e7 0.905844
\(965\) 0 0
\(966\) 1.42532e6 0.0491441
\(967\) −5.23618e7 −1.80073 −0.900365 0.435135i \(-0.856701\pi\)
−0.900365 + 0.435135i \(0.856701\pi\)
\(968\) 1.85642e7 0.636777
\(969\) 1.36360e8 4.66527
\(970\) 0 0
\(971\) 2.95200e7 1.00477 0.502387 0.864643i \(-0.332455\pi\)
0.502387 + 0.864643i \(0.332455\pi\)
\(972\) −8.46299e7 −2.87315
\(973\) −3.86287e7 −1.30806
\(974\) −9.58395e6 −0.323703
\(975\) 0 0
\(976\) −1.67114e7 −0.561551
\(977\) 1.21759e7 0.408098 0.204049 0.978961i \(-0.434590\pi\)
0.204049 + 0.978961i \(0.434590\pi\)
\(978\) 1.19632e7 0.399946
\(979\) 4.53499e6 0.151224
\(980\) 0 0
\(981\) 1.12971e8 3.74797
\(982\) −7.59304e6 −0.251268
\(983\) 1.46087e6 0.0482200 0.0241100 0.999709i \(-0.492325\pi\)
0.0241100 + 0.999709i \(0.492325\pi\)
\(984\) −5.90220e7 −1.94324
\(985\) 0 0
\(986\) 2.14413e7 0.702360
\(987\) 8.81942e7 2.88169
\(988\) 1.19355e7 0.388998
\(989\) −2.96186e6 −0.0962883
\(990\) 0 0
\(991\) 3.16160e7 1.02264 0.511320 0.859390i \(-0.329157\pi\)
0.511320 + 0.859390i \(0.329157\pi\)
\(992\) −2.65078e7 −0.855252
\(993\) 7.38951e7 2.37817
\(994\) 9.35660e6 0.300367
\(995\) 0 0
\(996\) 662564. 0.0211631
\(997\) 3.93744e7 1.25452 0.627258 0.778812i \(-0.284177\pi\)
0.627258 + 0.778812i \(0.284177\pi\)
\(998\) 1.13020e7 0.359195
\(999\) 5.09194e7 1.61425
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 325.6.a.j.1.7 11
5.2 odd 4 325.6.b.i.274.13 22
5.3 odd 4 325.6.b.i.274.10 22
5.4 even 2 325.6.a.k.1.5 yes 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
325.6.a.j.1.7 11 1.1 even 1 trivial
325.6.a.k.1.5 yes 11 5.4 even 2
325.6.b.i.274.10 22 5.3 odd 4
325.6.b.i.274.13 22 5.2 odd 4