Properties

Label 845.2.d.c.844.8
Level $845$
Weight $2$
Character 845.844
Analytic conductor $6.747$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(844,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.844");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.d (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.49787136.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 844.8
Root \(0.228425 - 1.39564i\) of defining polynomial
Character \(\chi\) \(=\) 845.844
Dual form 845.2.d.c.844.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.18890 q^{2} +1.00000i q^{3} +2.79129 q^{4} +(0.456850 - 2.18890i) q^{5} +2.18890i q^{6} +1.73205 q^{7} +1.73205 q^{8} +2.00000 q^{9} +O(q^{10})\) \(q+2.18890 q^{2} +1.00000i q^{3} +2.79129 q^{4} +(0.456850 - 2.18890i) q^{5} +2.18890i q^{6} +1.73205 q^{7} +1.73205 q^{8} +2.00000 q^{9} +(1.00000 - 4.79129i) q^{10} +2.64575i q^{11} +2.79129i q^{12} +3.79129 q^{14} +(2.18890 + 0.456850i) q^{15} -1.79129 q^{16} -4.58258i q^{17} +4.37780 q^{18} +1.73205i q^{19} +(1.27520 - 6.10985i) q^{20} +1.73205i q^{21} +5.79129i q^{22} -4.58258i q^{23} +1.73205i q^{24} +(-4.58258 - 2.00000i) q^{25} +5.00000i q^{27} +4.83465 q^{28} +4.58258 q^{29} +(4.79129 + 1.00000i) q^{30} +9.66930i q^{31} -7.38505 q^{32} -2.64575 q^{33} -10.0308i q^{34} +(0.791288 - 3.79129i) q^{35} +5.58258 q^{36} +7.93725 q^{37} +3.79129i q^{38} +(0.791288 - 3.79129i) q^{40} -2.64575i q^{41} +3.79129i q^{42} +1.41742i q^{43} +7.38505i q^{44} +(0.913701 - 4.37780i) q^{45} -10.0308i q^{46} -8.75560 q^{47} -1.79129i q^{48} -4.00000 q^{49} +(-10.0308 - 4.37780i) q^{50} +4.58258 q^{51} -1.58258i q^{53} +10.9445i q^{54} +(5.79129 + 1.20871i) q^{55} +3.00000 q^{56} -1.73205 q^{57} +10.0308 q^{58} +3.36875i q^{59} +(6.10985 + 1.27520i) q^{60} -10.5826 q^{61} +21.1652i q^{62} +3.46410 q^{63} -12.5826 q^{64} -5.79129 q^{66} -14.8655 q^{67} -12.7913i q^{68} +4.58258 q^{69} +(1.73205 - 8.29875i) q^{70} +3.55945i q^{71} +3.46410 q^{72} +17.3739 q^{74} +(2.00000 - 4.58258i) q^{75} +4.83465i q^{76} +4.58258i q^{77} +6.00000 q^{79} +(-0.818350 + 3.92095i) q^{80} +1.00000 q^{81} -5.79129i q^{82} -11.3060 q^{83} +4.83465i q^{84} +(-10.0308 - 2.09355i) q^{85} +3.10260i q^{86} +4.58258i q^{87} +4.58258i q^{88} +4.28245i q^{89} +(2.00000 - 9.58258i) q^{90} -12.7913i q^{92} -9.66930 q^{93} -19.1652 q^{94} +(3.79129 + 0.791288i) q^{95} -7.38505i q^{96} -4.47315 q^{97} -8.75560 q^{98} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 16 q^{9} + 8 q^{10} + 12 q^{14} + 4 q^{16} + 20 q^{30} - 12 q^{35} + 8 q^{36} - 12 q^{40} - 32 q^{49} + 28 q^{55} + 24 q^{56} - 48 q^{61} - 64 q^{64} - 28 q^{66} + 84 q^{74} + 16 q^{75} + 48 q^{79} + 8 q^{81} + 16 q^{90} - 80 q^{94} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18890 1.54779 0.773893 0.633316i \(-0.218307\pi\)
0.773893 + 0.633316i \(0.218307\pi\)
\(3\) 1.00000i 0.577350i 0.957427 + 0.288675i \(0.0932147\pi\)
−0.957427 + 0.288675i \(0.906785\pi\)
\(4\) 2.79129 1.39564
\(5\) 0.456850 2.18890i 0.204310 0.978906i
\(6\) 2.18890i 0.893615i
\(7\) 1.73205 0.654654 0.327327 0.944911i \(-0.393852\pi\)
0.327327 + 0.944911i \(0.393852\pi\)
\(8\) 1.73205 0.612372
\(9\) 2.00000 0.666667
\(10\) 1.00000 4.79129i 0.316228 1.51514i
\(11\) 2.64575i 0.797724i 0.917011 + 0.398862i \(0.130595\pi\)
−0.917011 + 0.398862i \(0.869405\pi\)
\(12\) 2.79129i 0.805775i
\(13\) 0 0
\(14\) 3.79129 1.01326
\(15\) 2.18890 + 0.456850i 0.565172 + 0.117958i
\(16\) −1.79129 −0.447822
\(17\) 4.58258i 1.11144i −0.831370 0.555719i \(-0.812443\pi\)
0.831370 0.555719i \(-0.187557\pi\)
\(18\) 4.37780 1.03186
\(19\) 1.73205i 0.397360i 0.980064 + 0.198680i \(0.0636654\pi\)
−0.980064 + 0.198680i \(0.936335\pi\)
\(20\) 1.27520 6.10985i 0.285144 1.36620i
\(21\) 1.73205i 0.377964i
\(22\) 5.79129i 1.23471i
\(23\) 4.58258i 0.955533i −0.878487 0.477767i \(-0.841446\pi\)
0.878487 0.477767i \(-0.158554\pi\)
\(24\) 1.73205i 0.353553i
\(25\) −4.58258 2.00000i −0.916515 0.400000i
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 4.83465 0.913663
\(29\) 4.58258 0.850963 0.425481 0.904967i \(-0.360105\pi\)
0.425481 + 0.904967i \(0.360105\pi\)
\(30\) 4.79129 + 1.00000i 0.874765 + 0.182574i
\(31\) 9.66930i 1.73666i 0.495988 + 0.868329i \(0.334806\pi\)
−0.495988 + 0.868329i \(0.665194\pi\)
\(32\) −7.38505 −1.30551
\(33\) −2.64575 −0.460566
\(34\) 10.0308i 1.72027i
\(35\) 0.791288 3.79129i 0.133752 0.640845i
\(36\) 5.58258 0.930429
\(37\) 7.93725 1.30488 0.652438 0.757842i \(-0.273746\pi\)
0.652438 + 0.757842i \(0.273746\pi\)
\(38\) 3.79129i 0.615028i
\(39\) 0 0
\(40\) 0.791288 3.79129i 0.125114 0.599455i
\(41\) 2.64575i 0.413197i −0.978426 0.206598i \(-0.933761\pi\)
0.978426 0.206598i \(-0.0662394\pi\)
\(42\) 3.79129i 0.585008i
\(43\) 1.41742i 0.216155i 0.994142 + 0.108078i \(0.0344695\pi\)
−0.994142 + 0.108078i \(0.965531\pi\)
\(44\) 7.38505i 1.11334i
\(45\) 0.913701 4.37780i 0.136206 0.652604i
\(46\) 10.0308i 1.47896i
\(47\) −8.75560 −1.27714 −0.638568 0.769565i \(-0.720473\pi\)
−0.638568 + 0.769565i \(0.720473\pi\)
\(48\) 1.79129i 0.258550i
\(49\) −4.00000 −0.571429
\(50\) −10.0308 4.37780i −1.41857 0.619115i
\(51\) 4.58258 0.641689
\(52\) 0 0
\(53\) 1.58258i 0.217383i −0.994076 0.108692i \(-0.965334\pi\)
0.994076 0.108692i \(-0.0346661\pi\)
\(54\) 10.9445i 1.48936i
\(55\) 5.79129 + 1.20871i 0.780897 + 0.162983i
\(56\) 3.00000 0.400892
\(57\) −1.73205 −0.229416
\(58\) 10.0308 1.31711
\(59\) 3.36875i 0.438574i 0.975660 + 0.219287i \(0.0703731\pi\)
−0.975660 + 0.219287i \(0.929627\pi\)
\(60\) 6.10985 + 1.27520i 0.788779 + 0.164628i
\(61\) −10.5826 −1.35496 −0.677480 0.735541i \(-0.736928\pi\)
−0.677480 + 0.735541i \(0.736928\pi\)
\(62\) 21.1652i 2.68798i
\(63\) 3.46410 0.436436
\(64\) −12.5826 −1.57282
\(65\) 0 0
\(66\) −5.79129 −0.712858
\(67\) −14.8655 −1.81610 −0.908052 0.418857i \(-0.862431\pi\)
−0.908052 + 0.418857i \(0.862431\pi\)
\(68\) 12.7913i 1.55117i
\(69\) 4.58258 0.551677
\(70\) 1.73205 8.29875i 0.207020 0.991891i
\(71\) 3.55945i 0.422429i 0.977440 + 0.211215i \(0.0677419\pi\)
−0.977440 + 0.211215i \(0.932258\pi\)
\(72\) 3.46410 0.408248
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 17.3739 2.01967
\(75\) 2.00000 4.58258i 0.230940 0.529150i
\(76\) 4.83465i 0.554573i
\(77\) 4.58258i 0.522233i
\(78\) 0 0
\(79\) 6.00000 0.675053 0.337526 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) −0.818350 + 3.92095i −0.0914943 + 0.438376i
\(81\) 1.00000 0.111111
\(82\) 5.79129i 0.639541i
\(83\) −11.3060 −1.24100 −0.620498 0.784208i \(-0.713069\pi\)
−0.620498 + 0.784208i \(0.713069\pi\)
\(84\) 4.83465i 0.527504i
\(85\) −10.0308 2.09355i −1.08799 0.227077i
\(86\) 3.10260i 0.334562i
\(87\) 4.58258i 0.491304i
\(88\) 4.58258i 0.488504i
\(89\) 4.28245i 0.453939i 0.973902 + 0.226969i \(0.0728818\pi\)
−0.973902 + 0.226969i \(0.927118\pi\)
\(90\) 2.00000 9.58258i 0.210819 1.01009i
\(91\) 0 0
\(92\) 12.7913i 1.33358i
\(93\) −9.66930 −1.00266
\(94\) −19.1652 −1.97673
\(95\) 3.79129 + 0.791288i 0.388978 + 0.0811844i
\(96\) 7.38505i 0.753734i
\(97\) −4.47315 −0.454180 −0.227090 0.973874i \(-0.572921\pi\)
−0.227090 + 0.973874i \(0.572921\pi\)
\(98\) −8.75560 −0.884450
\(99\) 5.29150i 0.531816i
\(100\) −12.7913 5.58258i −1.27913 0.558258i
\(101\) 9.00000 0.895533 0.447767 0.894150i \(-0.352219\pi\)
0.447767 + 0.894150i \(0.352219\pi\)
\(102\) 10.0308 0.993198
\(103\) 15.1652i 1.49427i −0.664674 0.747133i \(-0.731430\pi\)
0.664674 0.747133i \(-0.268570\pi\)
\(104\) 0 0
\(105\) 3.79129 + 0.791288i 0.369992 + 0.0772218i
\(106\) 3.46410i 0.336463i
\(107\) 1.41742i 0.137028i 0.997650 + 0.0685138i \(0.0218257\pi\)
−0.997650 + 0.0685138i \(0.978174\pi\)
\(108\) 13.9564i 1.34296i
\(109\) 2.74110i 0.262550i −0.991346 0.131275i \(-0.958093\pi\)
0.991346 0.131275i \(-0.0419071\pi\)
\(110\) 12.6766 + 2.64575i 1.20866 + 0.252262i
\(111\) 7.93725i 0.753371i
\(112\) −3.10260 −0.293168
\(113\) 16.5826i 1.55996i −0.625806 0.779979i \(-0.715230\pi\)
0.625806 0.779979i \(-0.284770\pi\)
\(114\) −3.79129 −0.355087
\(115\) −10.0308 2.09355i −0.935377 0.195225i
\(116\) 12.7913 1.18764
\(117\) 0 0
\(118\) 7.37386i 0.678819i
\(119\) 7.93725i 0.727607i
\(120\) 3.79129 + 0.791288i 0.346096 + 0.0722344i
\(121\) 4.00000 0.363636
\(122\) −23.1642 −2.09719
\(123\) 2.64575 0.238559
\(124\) 26.9898i 2.42376i
\(125\) −6.47135 + 9.11710i −0.578815 + 0.815459i
\(126\) 7.58258 0.675510
\(127\) 9.74773i 0.864971i 0.901641 + 0.432485i \(0.142363\pi\)
−0.901641 + 0.432485i \(0.857637\pi\)
\(128\) −12.7719 −1.12889
\(129\) −1.41742 −0.124797
\(130\) 0 0
\(131\) 1.58258 0.138270 0.0691351 0.997607i \(-0.477976\pi\)
0.0691351 + 0.997607i \(0.477976\pi\)
\(132\) −7.38505 −0.642786
\(133\) 3.00000i 0.260133i
\(134\) −32.5390 −2.81094
\(135\) 10.9445 + 2.28425i 0.941953 + 0.196597i
\(136\) 7.93725i 0.680614i
\(137\) 0.0953502 0.00814632 0.00407316 0.999992i \(-0.498703\pi\)
0.00407316 + 0.999992i \(0.498703\pi\)
\(138\) 10.0308 0.853879
\(139\) −5.74773 −0.487516 −0.243758 0.969836i \(-0.578380\pi\)
−0.243758 + 0.969836i \(0.578380\pi\)
\(140\) 2.20871 10.5826i 0.186670 0.894391i
\(141\) 8.75560i 0.737355i
\(142\) 7.79129i 0.653830i
\(143\) 0 0
\(144\) −3.58258 −0.298548
\(145\) 2.09355 10.0308i 0.173860 0.833013i
\(146\) 0 0
\(147\) 4.00000i 0.329914i
\(148\) 22.1552 1.82114
\(149\) 9.76465i 0.799952i −0.916526 0.399976i \(-0.869019\pi\)
0.916526 0.399976i \(-0.130981\pi\)
\(150\) 4.37780 10.0308i 0.357446 0.819012i
\(151\) 6.20520i 0.504972i −0.967601 0.252486i \(-0.918752\pi\)
0.967601 0.252486i \(-0.0812482\pi\)
\(152\) 3.00000i 0.243332i
\(153\) 9.16515i 0.740959i
\(154\) 10.0308i 0.808305i
\(155\) 21.1652 + 4.41742i 1.70003 + 0.354816i
\(156\) 0 0
\(157\) 9.16515i 0.731459i 0.930721 + 0.365729i \(0.119180\pi\)
−0.930721 + 0.365729i \(0.880820\pi\)
\(158\) 13.1334 1.04484
\(159\) 1.58258 0.125506
\(160\) −3.37386 + 16.1652i −0.266727 + 1.27797i
\(161\) 7.93725i 0.625543i
\(162\) 2.18890 0.171976
\(163\) 10.6784 0.836393 0.418197 0.908357i \(-0.362662\pi\)
0.418197 + 0.908357i \(0.362662\pi\)
\(164\) 7.38505i 0.576676i
\(165\) −1.20871 + 5.79129i −0.0940981 + 0.450851i
\(166\) −24.7477 −1.92080
\(167\) 4.28245 0.331386 0.165693 0.986177i \(-0.447014\pi\)
0.165693 + 0.986177i \(0.447014\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 0 0
\(170\) −21.9564 4.58258i −1.68398 0.351468i
\(171\) 3.46410i 0.264906i
\(172\) 3.95644i 0.301676i
\(173\) 7.41742i 0.563936i −0.959424 0.281968i \(-0.909013\pi\)
0.959424 0.281968i \(-0.0909873\pi\)
\(174\) 10.0308i 0.760433i
\(175\) −7.93725 3.46410i −0.600000 0.261861i
\(176\) 4.73930i 0.357238i
\(177\) −3.36875 −0.253211
\(178\) 9.37386i 0.702601i
\(179\) 0.165151 0.0123440 0.00617200 0.999981i \(-0.498035\pi\)
0.00617200 + 0.999981i \(0.498035\pi\)
\(180\) 2.55040 12.2197i 0.190096 0.910803i
\(181\) −18.7477 −1.39351 −0.696754 0.717310i \(-0.745373\pi\)
−0.696754 + 0.717310i \(0.745373\pi\)
\(182\) 0 0
\(183\) 10.5826i 0.782287i
\(184\) 7.93725i 0.585142i
\(185\) 3.62614 17.3739i 0.266599 1.27735i
\(186\) −21.1652 −1.55190
\(187\) 12.1244 0.886621
\(188\) −24.4394 −1.78243
\(189\) 8.66025i 0.629941i
\(190\) 8.29875 + 1.73205i 0.602055 + 0.125656i
\(191\) −7.41742 −0.536706 −0.268353 0.963321i \(-0.586479\pi\)
−0.268353 + 0.963321i \(0.586479\pi\)
\(192\) 12.5826i 0.908069i
\(193\) 1.00905 0.0726331 0.0363165 0.999340i \(-0.488438\pi\)
0.0363165 + 0.999340i \(0.488438\pi\)
\(194\) −9.79129 −0.702973
\(195\) 0 0
\(196\) −11.1652 −0.797511
\(197\) 19.9663 1.42254 0.711269 0.702920i \(-0.248121\pi\)
0.711269 + 0.702920i \(0.248121\pi\)
\(198\) 11.5826i 0.823138i
\(199\) −1.41742 −0.100479 −0.0502393 0.998737i \(-0.515998\pi\)
−0.0502393 + 0.998737i \(0.515998\pi\)
\(200\) −7.93725 3.46410i −0.561249 0.244949i
\(201\) 14.8655i 1.04853i
\(202\) 19.7001 1.38609
\(203\) 7.93725 0.557086
\(204\) 12.7913 0.895569
\(205\) −5.79129 1.20871i −0.404481 0.0844201i
\(206\) 33.1950i 2.31281i
\(207\) 9.16515i 0.637022i
\(208\) 0 0
\(209\) −4.58258 −0.316983
\(210\) 8.29875 + 1.73205i 0.572668 + 0.119523i
\(211\) 18.1652 1.25054 0.625270 0.780408i \(-0.284989\pi\)
0.625270 + 0.780408i \(0.284989\pi\)
\(212\) 4.41742i 0.303390i
\(213\) −3.55945 −0.243890
\(214\) 3.10260i 0.212089i
\(215\) 3.10260 + 0.647551i 0.211596 + 0.0441626i
\(216\) 8.66025i 0.589256i
\(217\) 16.7477i 1.13691i
\(218\) 6.00000i 0.406371i
\(219\) 0 0
\(220\) 16.1652 + 3.37386i 1.08985 + 0.227466i
\(221\) 0 0
\(222\) 17.3739i 1.16606i
\(223\) 8.66025 0.579934 0.289967 0.957037i \(-0.406356\pi\)
0.289967 + 0.957037i \(0.406356\pi\)
\(224\) −12.7913 −0.854654
\(225\) −9.16515 4.00000i −0.611010 0.266667i
\(226\) 36.2976i 2.41448i
\(227\) −6.10985 −0.405525 −0.202763 0.979228i \(-0.564992\pi\)
−0.202763 + 0.979228i \(0.564992\pi\)
\(228\) −4.83465 −0.320183
\(229\) 5.48220i 0.362274i 0.983458 + 0.181137i \(0.0579778\pi\)
−0.983458 + 0.181137i \(0.942022\pi\)
\(230\) −21.9564 4.58258i −1.44776 0.302166i
\(231\) −4.58258 −0.301511
\(232\) 7.93725 0.521106
\(233\) 21.1652i 1.38658i 0.720661 + 0.693288i \(0.243838\pi\)
−0.720661 + 0.693288i \(0.756162\pi\)
\(234\) 0 0
\(235\) −4.00000 + 19.1652i −0.260931 + 1.25020i
\(236\) 9.40315i 0.612093i
\(237\) 6.00000i 0.389742i
\(238\) 17.3739i 1.12618i
\(239\) 20.9753i 1.35678i 0.734702 + 0.678390i \(0.237322\pi\)
−0.734702 + 0.678390i \(0.762678\pi\)
\(240\) −3.92095 0.818350i −0.253096 0.0528243i
\(241\) 1.73205i 0.111571i 0.998443 + 0.0557856i \(0.0177663\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 8.75560 0.562832
\(243\) 16.0000i 1.02640i
\(244\) −29.5390 −1.89104
\(245\) −1.82740 + 8.75560i −0.116748 + 0.559375i
\(246\) 5.79129 0.369239
\(247\) 0 0
\(248\) 16.7477i 1.06348i
\(249\) 11.3060i 0.716489i
\(250\) −14.1652 + 19.9564i −0.895883 + 1.26216i
\(251\) 18.1652 1.14657 0.573287 0.819355i \(-0.305668\pi\)
0.573287 + 0.819355i \(0.305668\pi\)
\(252\) 9.66930 0.609109
\(253\) 12.1244 0.762252
\(254\) 21.3368i 1.33879i
\(255\) 2.09355 10.0308i 0.131103 0.628153i
\(256\) −2.79129 −0.174455
\(257\) 0.165151i 0.0103019i −0.999987 0.00515093i \(-0.998360\pi\)
0.999987 0.00515093i \(-0.00163960\pi\)
\(258\) −3.10260 −0.193160
\(259\) 13.7477 0.854242
\(260\) 0 0
\(261\) 9.16515 0.567309
\(262\) 3.46410 0.214013
\(263\) 9.00000i 0.554964i 0.960731 + 0.277482i \(0.0894999\pi\)
−0.960731 + 0.277482i \(0.910500\pi\)
\(264\) −4.58258 −0.282038
\(265\) −3.46410 0.723000i −0.212798 0.0444135i
\(266\) 6.56670i 0.402630i
\(267\) −4.28245 −0.262082
\(268\) −41.4938 −2.53464
\(269\) 15.0000 0.914566 0.457283 0.889321i \(-0.348823\pi\)
0.457283 + 0.889321i \(0.348823\pi\)
\(270\) 23.9564 + 5.00000i 1.45794 + 0.304290i
\(271\) 8.66025i 0.526073i 0.964786 + 0.263036i \(0.0847240\pi\)
−0.964786 + 0.263036i \(0.915276\pi\)
\(272\) 8.20871i 0.497726i
\(273\) 0 0
\(274\) 0.208712 0.0126088
\(275\) 5.29150 12.1244i 0.319090 0.731126i
\(276\) 12.7913 0.769945
\(277\) 16.5826i 0.996350i 0.867076 + 0.498175i \(0.165996\pi\)
−0.867076 + 0.498175i \(0.834004\pi\)
\(278\) −12.5812 −0.754571
\(279\) 19.3386i 1.15777i
\(280\) 1.37055 6.56670i 0.0819061 0.392436i
\(281\) 17.5112i 1.04463i 0.852752 + 0.522316i \(0.174932\pi\)
−0.852752 + 0.522316i \(0.825068\pi\)
\(282\) 19.1652i 1.14127i
\(283\) 0.252273i 0.0149961i −0.999972 0.00749803i \(-0.997613\pi\)
0.999972 0.00749803i \(-0.00238672\pi\)
\(284\) 9.93545i 0.589561i
\(285\) −0.791288 + 3.79129i −0.0468718 + 0.224577i
\(286\) 0 0
\(287\) 4.58258i 0.270501i
\(288\) −14.7701 −0.870337
\(289\) −4.00000 −0.235294
\(290\) 4.58258 21.9564i 0.269098 1.28933i
\(291\) 4.47315i 0.262221i
\(292\) 0 0
\(293\) 23.4304 1.36882 0.684408 0.729099i \(-0.260061\pi\)
0.684408 + 0.729099i \(0.260061\pi\)
\(294\) 8.75560i 0.510637i
\(295\) 7.37386 + 1.53901i 0.429323 + 0.0896049i
\(296\) 13.7477 0.799070
\(297\) −13.2288 −0.767610
\(298\) 21.3739i 1.23815i
\(299\) 0 0
\(300\) 5.58258 12.7913i 0.322310 0.738505i
\(301\) 2.45505i 0.141507i
\(302\) 13.5826i 0.781589i
\(303\) 9.00000i 0.517036i
\(304\) 3.10260i 0.177946i
\(305\) −4.83465 + 23.1642i −0.276831 + 1.32638i
\(306\) 20.0616i 1.14685i
\(307\) 24.2487 1.38395 0.691974 0.721923i \(-0.256741\pi\)
0.691974 + 0.721923i \(0.256741\pi\)
\(308\) 12.7913i 0.728851i
\(309\) 15.1652 0.862715
\(310\) 46.3284 + 9.66930i 2.63128 + 0.549180i
\(311\) −1.58258 −0.0897396 −0.0448698 0.998993i \(-0.514287\pi\)
−0.0448698 + 0.998993i \(0.514287\pi\)
\(312\) 0 0
\(313\) 30.7477i 1.73796i −0.494843 0.868982i \(-0.664775\pi\)
0.494843 0.868982i \(-0.335225\pi\)
\(314\) 20.0616i 1.13214i
\(315\) 1.58258 7.58258i 0.0891680 0.427230i
\(316\) 16.7477 0.942133
\(317\) 20.9753 1.17809 0.589045 0.808100i \(-0.299504\pi\)
0.589045 + 0.808100i \(0.299504\pi\)
\(318\) 3.46410 0.194257
\(319\) 12.1244i 0.678834i
\(320\) −5.74835 + 27.5420i −0.321343 + 1.53965i
\(321\) −1.41742 −0.0791129
\(322\) 17.3739i 0.968208i
\(323\) 7.93725 0.441641
\(324\) 2.79129 0.155072
\(325\) 0 0
\(326\) 23.3739 1.29456
\(327\) 2.74110 0.151583
\(328\) 4.58258i 0.253030i
\(329\) −15.1652 −0.836082
\(330\) −2.64575 + 12.6766i −0.145644 + 0.697821i
\(331\) 11.4014i 0.626675i −0.949642 0.313338i \(-0.898553\pi\)
0.949642 0.313338i \(-0.101447\pi\)
\(332\) −31.5583 −1.73199
\(333\) 15.8745 0.869918
\(334\) 9.37386 0.512915
\(335\) −6.79129 + 32.5390i −0.371048 + 1.77780i
\(336\) 3.10260i 0.169261i
\(337\) 3.25227i 0.177163i −0.996069 0.0885813i \(-0.971767\pi\)
0.996069 0.0885813i \(-0.0282333\pi\)
\(338\) 0 0
\(339\) 16.5826 0.900642
\(340\) −27.9989 5.84370i −1.51845 0.316919i
\(341\) −25.5826 −1.38537
\(342\) 7.58258i 0.410019i
\(343\) −19.0526 −1.02874
\(344\) 2.45505i 0.132367i
\(345\) 2.09355 10.0308i 0.112713 0.540040i
\(346\) 16.2360i 0.872853i
\(347\) 15.3303i 0.822974i −0.911416 0.411487i \(-0.865010\pi\)
0.911416 0.411487i \(-0.134990\pi\)
\(348\) 12.7913i 0.685685i
\(349\) 18.3296i 0.981159i 0.871396 + 0.490579i \(0.163215\pi\)
−0.871396 + 0.490579i \(0.836785\pi\)
\(350\) −17.3739 7.58258i −0.928672 0.405306i
\(351\) 0 0
\(352\) 19.5390i 1.04143i
\(353\) −17.4159 −0.926953 −0.463476 0.886109i \(-0.653398\pi\)
−0.463476 + 0.886109i \(0.653398\pi\)
\(354\) −7.37386 −0.391916
\(355\) 7.79129 + 1.62614i 0.413519 + 0.0863064i
\(356\) 11.9536i 0.633537i
\(357\) 7.93725 0.420084
\(358\) 0.361500 0.0191059
\(359\) 33.3857i 1.76203i −0.473088 0.881015i \(-0.656861\pi\)
0.473088 0.881015i \(-0.343139\pi\)
\(360\) 1.58258 7.58258i 0.0834091 0.399637i
\(361\) 16.0000 0.842105
\(362\) −41.0369 −2.15685
\(363\) 4.00000i 0.209946i
\(364\) 0 0
\(365\) 0 0
\(366\) 23.1642i 1.21081i
\(367\) 25.7477i 1.34402i −0.740542 0.672010i \(-0.765431\pi\)
0.740542 0.672010i \(-0.234569\pi\)
\(368\) 8.20871i 0.427909i
\(369\) 5.29150i 0.275465i
\(370\) 7.93725 38.0297i 0.412638 1.97707i
\(371\) 2.74110i 0.142311i
\(372\) −26.9898 −1.39936
\(373\) 13.0000i 0.673114i −0.941663 0.336557i \(-0.890737\pi\)
0.941663 0.336557i \(-0.109263\pi\)
\(374\) 26.5390 1.37230
\(375\) −9.11710 6.47135i −0.470805 0.334179i
\(376\) −15.1652 −0.782083
\(377\) 0 0
\(378\) 18.9564i 0.975014i
\(379\) 21.0707i 1.08233i 0.840917 + 0.541164i \(0.182016\pi\)
−0.840917 + 0.541164i \(0.817984\pi\)
\(380\) 10.5826 + 2.20871i 0.542875 + 0.113305i
\(381\) −9.74773 −0.499391
\(382\) −16.2360 −0.830706
\(383\) 2.83645 0.144936 0.0724680 0.997371i \(-0.476912\pi\)
0.0724680 + 0.997371i \(0.476912\pi\)
\(384\) 12.7719i 0.651764i
\(385\) 10.0308 + 2.09355i 0.511217 + 0.106697i
\(386\) 2.20871 0.112420
\(387\) 2.83485i 0.144103i
\(388\) −12.4859 −0.633873
\(389\) −15.1652 −0.768904 −0.384452 0.923145i \(-0.625610\pi\)
−0.384452 + 0.923145i \(0.625610\pi\)
\(390\) 0 0
\(391\) −21.0000 −1.06202
\(392\) −6.92820 −0.349927
\(393\) 1.58258i 0.0798304i
\(394\) 43.7042 2.20178
\(395\) 2.74110 13.1334i 0.137920 0.660813i
\(396\) 14.7701i 0.742226i
\(397\) −27.2759 −1.36894 −0.684468 0.729043i \(-0.739966\pi\)
−0.684468 + 0.729043i \(0.739966\pi\)
\(398\) −3.10260 −0.155519
\(399\) −3.00000 −0.150188
\(400\) 8.20871 + 3.58258i 0.410436 + 0.179129i
\(401\) 12.5058i 0.624508i 0.949999 + 0.312254i \(0.101084\pi\)
−0.949999 + 0.312254i \(0.898916\pi\)
\(402\) 32.5390i 1.62290i
\(403\) 0 0
\(404\) 25.1216 1.24985
\(405\) 0.456850 2.18890i 0.0227011 0.108767i
\(406\) 17.3739 0.862250
\(407\) 21.0000i 1.04093i
\(408\) 7.93725 0.392953
\(409\) 8.66025i 0.428222i −0.976809 0.214111i \(-0.931315\pi\)
0.976809 0.214111i \(-0.0686854\pi\)
\(410\) −12.6766 2.64575i −0.626050 0.130664i
\(411\) 0.0953502i 0.00470328i
\(412\) 42.3303i 2.08546i
\(413\) 5.83485i 0.287114i
\(414\) 20.0616i 0.985974i
\(415\) −5.16515 + 24.7477i −0.253547 + 1.21482i
\(416\) 0 0
\(417\) 5.74773i 0.281467i
\(418\) −10.0308 −0.490623
\(419\) 24.1652 1.18054 0.590272 0.807204i \(-0.299020\pi\)
0.590272 + 0.807204i \(0.299020\pi\)
\(420\) 10.5826 + 2.20871i 0.516377 + 0.107774i
\(421\) 26.2668i 1.28017i 0.768306 + 0.640083i \(0.221100\pi\)
−0.768306 + 0.640083i \(0.778900\pi\)
\(422\) 39.7617 1.93557
\(423\) −17.5112 −0.851424
\(424\) 2.74110i 0.133120i
\(425\) −9.16515 + 21.0000i −0.444575 + 1.01865i
\(426\) −7.79129 −0.377489
\(427\) −18.3296 −0.887030
\(428\) 3.95644i 0.191242i
\(429\) 0 0
\(430\) 6.79129 + 1.41742i 0.327505 + 0.0683543i
\(431\) 29.6356i 1.42749i 0.700403 + 0.713747i \(0.253004\pi\)
−0.700403 + 0.713747i \(0.746996\pi\)
\(432\) 8.95644i 0.430917i
\(433\) 17.7477i 0.852901i −0.904511 0.426451i \(-0.859764\pi\)
0.904511 0.426451i \(-0.140236\pi\)
\(434\) 36.6591i 1.75969i
\(435\) 10.0308 + 2.09355i 0.480940 + 0.100378i
\(436\) 7.65120i 0.366426i
\(437\) 7.93725 0.379690
\(438\) 0 0
\(439\) −40.4955 −1.93274 −0.966371 0.257151i \(-0.917216\pi\)
−0.966371 + 0.257151i \(0.917216\pi\)
\(440\) 10.0308 + 2.09355i 0.478200 + 0.0998061i
\(441\) −8.00000 −0.380952
\(442\) 0 0
\(443\) 25.9129i 1.23116i −0.788075 0.615579i \(-0.788922\pi\)
0.788075 0.615579i \(-0.211078\pi\)
\(444\) 22.1552i 1.05144i
\(445\) 9.37386 + 1.95644i 0.444364 + 0.0927441i
\(446\) 18.9564 0.897613
\(447\) 9.76465 0.461852
\(448\) −21.7937 −1.02965
\(449\) 37.4775i 1.76867i −0.466852 0.884336i \(-0.654612\pi\)
0.466852 0.884336i \(-0.345388\pi\)
\(450\) −20.0616 8.75560i −0.945713 0.412743i
\(451\) 7.00000 0.329617
\(452\) 46.2867i 2.17715i
\(453\) 6.20520 0.291546
\(454\) −13.3739 −0.627667
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) −1.73205 −0.0810219 −0.0405110 0.999179i \(-0.512899\pi\)
−0.0405110 + 0.999179i \(0.512899\pi\)
\(458\) 12.0000i 0.560723i
\(459\) 22.9129 1.06948
\(460\) −27.9989 5.84370i −1.30545 0.272464i
\(461\) 1.19975i 0.0558780i 0.999610 + 0.0279390i \(0.00889441\pi\)
−0.999610 + 0.0279390i \(0.991106\pi\)
\(462\) −10.0308 −0.466675
\(463\) −8.22330 −0.382169 −0.191085 0.981574i \(-0.561201\pi\)
−0.191085 + 0.981574i \(0.561201\pi\)
\(464\) −8.20871 −0.381080
\(465\) −4.41742 + 21.1652i −0.204853 + 0.981510i
\(466\) 46.3284i 2.14612i
\(467\) 12.3303i 0.570578i −0.958441 0.285289i \(-0.907910\pi\)
0.958441 0.285289i \(-0.0920896\pi\)
\(468\) 0 0
\(469\) −25.7477 −1.18892
\(470\) −8.75560 + 41.9506i −0.403866 + 1.93504i
\(471\) −9.16515 −0.422308
\(472\) 5.83485i 0.268571i
\(473\) −3.75015 −0.172432
\(474\) 13.1334i 0.603237i
\(475\) 3.46410 7.93725i 0.158944 0.364186i
\(476\) 22.1552i 1.01548i
\(477\) 3.16515i 0.144922i
\(478\) 45.9129i 2.10001i
\(479\) 32.3767i 1.47933i −0.672977 0.739664i \(-0.734985\pi\)
0.672977 0.739664i \(-0.265015\pi\)
\(480\) −16.1652 3.37386i −0.737835 0.153995i
\(481\) 0 0
\(482\) 3.79129i 0.172688i
\(483\) 7.93725 0.361158
\(484\) 11.1652 0.507507
\(485\) −2.04356 + 9.79129i −0.0927933 + 0.444599i
\(486\) 35.0224i 1.58865i
\(487\) 21.0707 0.954803 0.477401 0.878685i \(-0.341579\pi\)
0.477401 + 0.878685i \(0.341579\pi\)
\(488\) −18.3296 −0.829740
\(489\) 10.6784i 0.482892i
\(490\) −4.00000 + 19.1652i −0.180702 + 0.865793i
\(491\) 28.5826 1.28991 0.644957 0.764219i \(-0.276875\pi\)
0.644957 + 0.764219i \(0.276875\pi\)
\(492\) 7.38505 0.332944
\(493\) 21.0000i 0.945792i
\(494\) 0 0
\(495\) 11.5826 + 2.41742i 0.520598 + 0.108655i
\(496\) 17.3205i 0.777714i
\(497\) 6.16515i 0.276545i
\(498\) 24.7477i 1.10897i
\(499\) 16.5975i 0.743006i −0.928432 0.371503i \(-0.878842\pi\)
0.928432 0.371503i \(-0.121158\pi\)
\(500\) −18.0634 + 25.4485i −0.807820 + 1.13809i
\(501\) 4.28245i 0.191326i
\(502\) 39.7617 1.77465
\(503\) 18.1652i 0.809944i −0.914329 0.404972i \(-0.867281\pi\)
0.914329 0.404972i \(-0.132719\pi\)
\(504\) 6.00000 0.267261
\(505\) 4.11165 19.7001i 0.182966 0.876643i
\(506\) 26.5390 1.17980
\(507\) 0 0
\(508\) 27.2087i 1.20719i
\(509\) 29.6356i 1.31357i −0.754076 0.656787i \(-0.771915\pi\)
0.754076 0.656787i \(-0.228085\pi\)
\(510\) 4.58258 21.9564i 0.202920 0.972247i
\(511\) 0 0
\(512\) 19.4340 0.858868
\(513\) −8.66025 −0.382360
\(514\) 0.361500i 0.0159451i
\(515\) −33.1950 6.92820i −1.46275 0.305293i
\(516\) −3.95644 −0.174173
\(517\) 23.1652i 1.01880i
\(518\) 30.0924 1.32218
\(519\) 7.41742 0.325589
\(520\) 0 0
\(521\) −27.4955 −1.20460 −0.602299 0.798271i \(-0.705748\pi\)
−0.602299 + 0.798271i \(0.705748\pi\)
\(522\) 20.0616 0.878073
\(523\) 18.1652i 0.794307i −0.917752 0.397153i \(-0.869998\pi\)
0.917752 0.397153i \(-0.130002\pi\)
\(524\) 4.41742 0.192976
\(525\) 3.46410 7.93725i 0.151186 0.346410i
\(526\) 19.7001i 0.858966i
\(527\) 44.3103 1.93019
\(528\) 4.73930 0.206252
\(529\) 2.00000 0.0869565
\(530\) −7.58258 1.58258i −0.329366 0.0687427i
\(531\) 6.73750i 0.292383i
\(532\) 8.37386i 0.363053i
\(533\) 0 0
\(534\) −9.37386 −0.405647
\(535\) 3.10260 + 0.647551i 0.134137 + 0.0279961i
\(536\) −25.7477 −1.11213
\(537\) 0.165151i 0.00712681i
\(538\) 32.8335 1.41555
\(539\) 10.5830i 0.455842i
\(540\) 30.5493 + 6.37600i 1.31463 + 0.274379i
\(541\) 10.3923i 0.446800i 0.974727 + 0.223400i \(0.0717156\pi\)
−0.974727 + 0.223400i \(0.928284\pi\)
\(542\) 18.9564i 0.814249i
\(543\) 18.7477i 0.804542i
\(544\) 33.8426i 1.45099i
\(545\) −6.00000 1.25227i −0.257012 0.0536415i
\(546\) 0 0
\(547\) 1.25227i 0.0535433i −0.999642 0.0267717i \(-0.991477\pi\)
0.999642 0.0267717i \(-0.00852270\pi\)
\(548\) 0.266150 0.0113694
\(549\) −21.1652 −0.903307
\(550\) 11.5826 26.5390i 0.493883 1.13163i
\(551\) 7.93725i 0.338138i
\(552\) 7.93725 0.337832
\(553\) 10.3923 0.441926
\(554\) 36.2976i 1.54214i
\(555\) 17.3739 + 3.62614i 0.737479 + 0.153921i
\(556\) −16.0436 −0.680399
\(557\) −13.0381 −0.552440 −0.276220 0.961094i \(-0.589082\pi\)
−0.276220 + 0.961094i \(0.589082\pi\)
\(558\) 42.3303i 1.79198i
\(559\) 0 0
\(560\) −1.41742 + 6.79129i −0.0598971 + 0.286984i
\(561\) 12.1244i 0.511891i
\(562\) 38.3303i 1.61687i
\(563\) 9.00000i 0.379305i −0.981851 0.189652i \(-0.939264\pi\)
0.981851 0.189652i \(-0.0607361\pi\)
\(564\) 24.4394i 1.02908i
\(565\) −36.2976 7.57575i −1.52705 0.318714i
\(566\) 0.552200i 0.0232107i
\(567\) 1.73205 0.0727393
\(568\) 6.16515i 0.258684i
\(569\) 19.7477 0.827868 0.413934 0.910307i \(-0.364154\pi\)
0.413934 + 0.910307i \(0.364154\pi\)
\(570\) −1.73205 + 8.29875i −0.0725476 + 0.347597i
\(571\) 29.0780 1.21688 0.608439 0.793601i \(-0.291796\pi\)
0.608439 + 0.793601i \(0.291796\pi\)
\(572\) 0 0
\(573\) 7.41742i 0.309867i
\(574\) 10.0308i 0.418678i
\(575\) −9.16515 + 21.0000i −0.382213 + 0.875761i
\(576\) −25.1652 −1.04855
\(577\) −6.92820 −0.288425 −0.144212 0.989547i \(-0.546065\pi\)
−0.144212 + 0.989547i \(0.546065\pi\)
\(578\) −8.75560 −0.364185
\(579\) 1.00905i 0.0419347i
\(580\) 5.84370 27.9989i 0.242647 1.16259i
\(581\) −19.5826 −0.812422
\(582\) 9.79129i 0.405862i
\(583\) 4.18710 0.173412
\(584\) 0 0
\(585\) 0 0
\(586\) 51.2867 2.11864
\(587\) 18.7110 0.772284 0.386142 0.922439i \(-0.373807\pi\)
0.386142 + 0.922439i \(0.373807\pi\)
\(588\) 11.1652i 0.460443i
\(589\) −16.7477 −0.690078
\(590\) 16.1407 + 3.36875i 0.664500 + 0.138689i
\(591\) 19.9663i 0.821302i
\(592\) −14.2179 −0.584352
\(593\) 21.1660 0.869184 0.434592 0.900627i \(-0.356893\pi\)
0.434592 + 0.900627i \(0.356893\pi\)
\(594\) −28.9564 −1.18810
\(595\) −17.3739 3.62614i −0.712259 0.148657i
\(596\) 27.2560i 1.11645i
\(597\) 1.41742i 0.0580113i
\(598\) 0 0
\(599\) 39.4955 1.61374 0.806870 0.590729i \(-0.201160\pi\)
0.806870 + 0.590729i \(0.201160\pi\)
\(600\) 3.46410 7.93725i 0.141421 0.324037i
\(601\) −28.9129 −1.17938 −0.589690 0.807629i \(-0.700750\pi\)
−0.589690 + 0.807629i \(0.700750\pi\)
\(602\) 5.37386i 0.219022i
\(603\) −29.7309 −1.21074
\(604\) 17.3205i 0.704761i
\(605\) 1.82740 8.75560i 0.0742944 0.355966i
\(606\) 19.7001i 0.800262i
\(607\) 19.7477i 0.801536i 0.916180 + 0.400768i \(0.131257\pi\)
−0.916180 + 0.400768i \(0.868743\pi\)
\(608\) 12.7913i 0.518755i
\(609\) 7.93725i 0.321634i
\(610\) −10.5826 + 50.7042i −0.428476 + 2.05295i
\(611\) 0 0
\(612\) 25.5826i 1.03411i
\(613\) 21.7937 0.880238 0.440119 0.897940i \(-0.354936\pi\)
0.440119 + 0.897940i \(0.354936\pi\)
\(614\) 53.0780 2.14205
\(615\) 1.20871 5.79129i 0.0487400 0.233527i
\(616\) 7.93725i 0.319801i
\(617\) 3.36875 0.135621 0.0678104 0.997698i \(-0.478399\pi\)
0.0678104 + 0.997698i \(0.478399\pi\)
\(618\) 33.1950 1.33530
\(619\) 2.01810i 0.0811143i −0.999177 0.0405572i \(-0.987087\pi\)
0.999177 0.0405572i \(-0.0129133\pi\)
\(620\) 59.0780 + 12.3303i 2.37263 + 0.495197i
\(621\) 22.9129 0.919462
\(622\) −3.46410 −0.138898
\(623\) 7.41742i 0.297173i
\(624\) 0 0
\(625\) 17.0000 + 18.3303i 0.680000 + 0.733212i
\(626\) 67.3037i 2.69000i
\(627\) 4.58258i 0.183010i
\(628\) 25.5826i 1.02086i
\(629\) 36.3731i 1.45029i
\(630\) 3.46410 16.5975i 0.138013 0.661261i
\(631\) 21.7937i 0.867592i 0.901011 + 0.433796i \(0.142826\pi\)
−0.901011 + 0.433796i \(0.857174\pi\)
\(632\) 10.3923 0.413384
\(633\) 18.1652i 0.722000i
\(634\) 45.9129 1.82343
\(635\) 21.3368 + 4.45325i 0.846725 + 0.176722i
\(636\) 4.41742 0.175162
\(637\) 0 0
\(638\) 26.5390i 1.05069i
\(639\) 7.11890i 0.281619i
\(640\) −5.83485 + 27.9564i −0.230643 + 1.10508i
\(641\) −0.165151 −0.00652309 −0.00326154 0.999995i \(-0.501038\pi\)
−0.00326154 + 0.999995i \(0.501038\pi\)
\(642\) −3.10260 −0.122450
\(643\) 5.91915 0.233429 0.116714 0.993166i \(-0.462764\pi\)
0.116714 + 0.993166i \(0.462764\pi\)
\(644\) 22.1552i 0.873036i
\(645\) −0.647551 + 3.10260i −0.0254973 + 0.122165i
\(646\) 17.3739 0.683566
\(647\) 27.0000i 1.06148i −0.847535 0.530740i \(-0.821914\pi\)
0.847535 0.530740i \(-0.178086\pi\)
\(648\) 1.73205 0.0680414
\(649\) −8.91288 −0.349861
\(650\) 0 0
\(651\) −16.7477 −0.656395
\(652\) 29.8064 1.16731
\(653\) 48.8258i 1.91070i 0.295477 + 0.955350i \(0.404521\pi\)
−0.295477 + 0.955350i \(0.595479\pi\)
\(654\) 6.00000 0.234619
\(655\) 0.723000 3.46410i 0.0282500 0.135354i
\(656\) 4.73930i 0.185039i
\(657\) 0 0
\(658\) −33.1950 −1.29408
\(659\) 24.4955 0.954207 0.477104 0.878847i \(-0.341687\pi\)
0.477104 + 0.878847i \(0.341687\pi\)
\(660\) −3.37386 + 16.1652i −0.131327 + 0.629228i
\(661\) 2.45505i 0.0954904i 0.998860 + 0.0477452i \(0.0152036\pi\)
−0.998860 + 0.0477452i \(0.984796\pi\)
\(662\) 24.9564i 0.969960i
\(663\) 0 0
\(664\) −19.5826 −0.759951
\(665\) 6.56670 + 1.37055i 0.254646 + 0.0531477i
\(666\) 34.7477 1.34645
\(667\) 21.0000i 0.813123i
\(668\) 11.9536 0.462497
\(669\) 8.66025i 0.334825i
\(670\) −14.8655 + 71.2247i −0.574303 + 2.75165i
\(671\) 27.9989i 1.08088i
\(672\) 12.7913i 0.493435i
\(673\) 5.83485i 0.224917i −0.993656 0.112458i \(-0.964127\pi\)
0.993656 0.112458i \(-0.0358725\pi\)
\(674\) 7.11890i 0.274210i
\(675\) 10.0000 22.9129i 0.384900 0.881917i
\(676\) 0 0
\(677\) 21.1652i 0.813443i 0.913552 + 0.406721i \(0.133328\pi\)
−0.913552 + 0.406721i \(0.866672\pi\)
\(678\) 36.2976 1.39400
\(679\) −7.74773 −0.297330
\(680\) −17.3739 3.62614i −0.666257 0.139056i
\(681\) 6.10985i 0.234130i
\(682\) −55.9977 −2.14426
\(683\) −11.9337 −0.456629 −0.228314 0.973587i \(-0.573321\pi\)
−0.228314 + 0.973587i \(0.573321\pi\)
\(684\) 9.66930i 0.369715i
\(685\) 0.0435608 0.208712i 0.00166437 0.00797448i
\(686\) −41.7042 −1.59227
\(687\) −5.48220 −0.209159
\(688\) 2.53901i 0.0967990i
\(689\) 0 0
\(690\) 4.58258 21.9564i 0.174456 0.835867i
\(691\) 35.6501i 1.35619i 0.734973 + 0.678096i \(0.237195\pi\)
−0.734973 + 0.678096i \(0.762805\pi\)
\(692\) 20.7042i 0.787054i
\(693\) 9.16515i 0.348155i
\(694\) 33.5565i 1.27379i
\(695\) −2.62585 + 12.5812i −0.0996042 + 0.477232i
\(696\) 7.93725i 0.300861i
\(697\) −12.1244 −0.459243
\(698\) 40.1216i 1.51862i
\(699\) −21.1652 −0.800540
\(700\) −22.1552 9.66930i −0.837386 0.365465i
\(701\) −2.83485 −0.107071 −0.0535354 0.998566i \(-0.517049\pi\)
−0.0535354 + 0.998566i \(0.517049\pi\)
\(702\) 0 0
\(703\) 13.7477i 0.518505i
\(704\) 33.2904i 1.25468i
\(705\) −19.1652 4.00000i −0.721801 0.150649i
\(706\) −38.1216 −1.43472
\(707\) 15.5885 0.586264
\(708\) −9.40315 −0.353392
\(709\) 36.3731i 1.36602i −0.730409 0.683010i \(-0.760671\pi\)
0.730409 0.683010i \(-0.239329\pi\)
\(710\) 17.0544 + 3.55945i 0.640039 + 0.133584i
\(711\) 12.0000 0.450035
\(712\) 7.41742i 0.277980i
\(713\) 44.3103 1.65943
\(714\) 17.3739 0.650201
\(715\) 0 0
\(716\) 0.460985 0.0172278
\(717\) −20.9753 −0.783337
\(718\) 73.0780i 2.72725i
\(719\) −30.4955 −1.13729 −0.568644 0.822584i \(-0.692532\pi\)
−0.568644 + 0.822584i \(0.692532\pi\)
\(720\) −1.63670 + 7.84190i −0.0609962 + 0.292250i
\(721\) 26.2668i 0.978227i
\(722\) 35.0224 1.30340
\(723\) −1.73205 −0.0644157
\(724\) −52.3303 −1.94484
\(725\) −21.0000 9.16515i −0.779920 0.340385i
\(726\) 8.75560i 0.324951i
\(727\) 42.7477i 1.58543i 0.609595 + 0.792713i \(0.291332\pi\)
−0.609595 + 0.792713i \(0.708668\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 6.49545 0.240243
\(732\) 29.5390i 1.09179i
\(733\) −8.94630 −0.330439 −0.165220 0.986257i \(-0.552833\pi\)
−0.165220 + 0.986257i \(0.552833\pi\)
\(734\) 56.3592i 2.08026i
\(735\) −8.75560 1.82740i −0.322955 0.0674047i
\(736\) 33.8426i 1.24745i
\(737\) 39.3303i 1.44875i
\(738\) 11.5826i 0.426361i
\(739\) 48.7835i 1.79453i −0.441493 0.897265i \(-0.645551\pi\)
0.441493 0.897265i \(-0.354449\pi\)
\(740\) 10.1216 48.4955i 0.372077 1.78273i
\(741\) 0 0
\(742\) 6.00000i 0.220267i
\(743\) −42.7690 −1.56904 −0.784521 0.620103i \(-0.787091\pi\)
−0.784521 + 0.620103i \(0.787091\pi\)
\(744\) −16.7477 −0.614001
\(745\) −21.3739 4.46099i −0.783078 0.163438i
\(746\) 28.4557i 1.04184i
\(747\) −22.6120 −0.827330
\(748\) 33.8426 1.23741
\(749\) 2.45505i 0.0897056i
\(750\) −19.9564 14.1652i −0.728706 0.517238i
\(751\) −15.7477 −0.574643 −0.287321 0.957834i \(-0.592765\pi\)
−0.287321 + 0.957834i \(0.592765\pi\)
\(752\) 15.6838 0.571930
\(753\) 18.1652i 0.661975i
\(754\) 0 0
\(755\) −13.5826 2.83485i −0.494321 0.103171i
\(756\) 24.1733i 0.879173i
\(757\) 17.7477i 0.645052i 0.946561 + 0.322526i \(0.104532\pi\)
−0.946561 + 0.322526i \(0.895468\pi\)
\(758\) 46.1216i 1.67521i
\(759\) 12.1244i 0.440086i
\(760\) 6.56670 + 1.37055i 0.238199 + 0.0497151i
\(761\) 40.7509i 1.47722i 0.674134 + 0.738609i \(0.264517\pi\)
−0.674134 + 0.738609i \(0.735483\pi\)
\(762\) −21.3368 −0.772951
\(763\) 4.74773i 0.171879i
\(764\) −20.7042 −0.749050
\(765\) −20.0616 4.18710i −0.725329 0.151385i
\(766\) 6.20871 0.224330
\(767\) 0 0
\(768\) 2.79129i 0.100722i
\(769\) 15.5885i 0.562134i −0.959688 0.281067i \(-0.909312\pi\)
0.959688 0.281067i \(-0.0906883\pi\)
\(770\) 21.9564 + 4.58258i 0.791255 + 0.165145i
\(771\) 0.165151 0.00594778
\(772\) 2.81655 0.101370
\(773\) 34.7364 1.24938 0.624690 0.780873i \(-0.285225\pi\)
0.624690 + 0.780873i \(0.285225\pi\)
\(774\) 6.20520i 0.223041i
\(775\) 19.3386 44.3103i 0.694663 1.59167i
\(776\) −7.74773 −0.278127
\(777\) 13.7477i 0.493197i
\(778\) −33.1950 −1.19010
\(779\) 4.58258 0.164188
\(780\) 0 0
\(781\) −9.41742 −0.336982
\(782\) −45.9669 −1.64377
\(783\) 22.9129i 0.818839i
\(784\) 7.16515 0.255898
\(785\) 20.0616 + 4.18710i 0.716030 + 0.149444i
\(786\) 3.46410i 0.123560i
\(787\) −32.1860 −1.14731 −0.573653 0.819099i \(-0.694474\pi\)
−0.573653 + 0.819099i \(0.694474\pi\)
\(788\) 55.7316 1.98536
\(789\) −9.00000 −0.320408
\(790\) 6.00000 28.7477i 0.213470 1.02280i
\(791\) 28.7219i 1.02123i
\(792\) 9.16515i 0.325669i
\(793\) 0 0
\(794\) −59.7042 −2.11882
\(795\) 0.723000 3.46410i 0.0256422 0.122859i
\(796\) −3.95644 −0.140232
\(797\) 20.0780i 0.711200i 0.934638 + 0.355600i \(0.115724\pi\)
−0.934638 + 0.355600i \(0.884276\pi\)
\(798\) −6.56670 −0.232459
\(799\) 40.1232i 1.41946i
\(800\) 33.8426 + 14.7701i 1.19652 + 0.522202i
\(801\) 8.56490i 0.302626i
\(802\) 27.3739i 0.966605i
\(803\) 0 0
\(804\) 41.4938i 1.46337i
\(805\) −17.3739 3.62614i −0.612348 0.127805i
\(806\) 0 0
\(807\) 15.0000i 0.528025i
\(808\) 15.5885 0.548400
\(809\) −36.8258 −1.29472 −0.647362 0.762182i \(-0.724128\pi\)
−0.647362 + 0.762182i \(0.724128\pi\)
\(810\) 1.00000 4.79129i 0.0351364 0.168349i
\(811\) 18.7665i 0.658981i 0.944159 + 0.329491i \(0.106877\pi\)
−0.944159 + 0.329491i \(0.893123\pi\)
\(812\) 22.1552 0.777494
\(813\) −8.66025 −0.303728
\(814\) 45.9669i 1.61114i
\(815\) 4.87841 23.3739i 0.170883 0.818751i
\(816\) −8.20871 −0.287362
\(817\) −2.45505 −0.0858914
\(818\) 18.9564i 0.662796i
\(819\) 0 0
\(820\) −16.1652 3.37386i −0.564512 0.117820i
\(821\) 23.4304i 0.817725i 0.912596 + 0.408863i \(0.134074\pi\)
−0.912596 + 0.408863i \(0.865926\pi\)
\(822\) 0.208712i 0.00727967i
\(823\) 40.5826i 1.41462i −0.706904 0.707310i \(-0.749909\pi\)
0.706904 0.707310i \(-0.250091\pi\)
\(824\) 26.2668i 0.915048i
\(825\) 12.1244 + 5.29150i 0.422116 + 0.184226i
\(826\) 12.7719i 0.444391i
\(827\) −31.5583 −1.09739 −0.548695 0.836023i \(-0.684875\pi\)
−0.548695 + 0.836023i \(0.684875\pi\)
\(828\) 25.5826i 0.889056i
\(829\) −3.33030 −0.115666 −0.0578331 0.998326i \(-0.518419\pi\)
−0.0578331 + 0.998326i \(0.518419\pi\)
\(830\) −11.3060 + 54.1703i −0.392437 + 1.88028i
\(831\) −16.5826 −0.575243
\(832\) 0 0
\(833\) 18.3303i 0.635107i
\(834\) 12.5812i 0.435652i
\(835\) 1.95644 9.37386i 0.0677054 0.324396i
\(836\) −12.7913 −0.442396
\(837\) −48.3465 −1.67110
\(838\) 52.8951 1.82723
\(839\) 1.35065i 0.0466296i −0.999728 0.0233148i \(-0.992578\pi\)
0.999728 0.0233148i \(-0.00742201\pi\)
\(840\) 6.56670 + 1.37055i 0.226573 + 0.0472885i
\(841\) −8.00000 −0.275862
\(842\) 57.4955i 1.98142i
\(843\) −17.5112 −0.603118
\(844\) 50.7042 1.74531
\(845\) 0 0
\(846\) −38.3303 −1.31782
\(847\) 6.92820 0.238056
\(848\) 2.83485i 0.0973491i
\(849\) 0.252273 0.00865798
\(850\) −20.0616 + 45.9669i −0.688108 + 1.57665i
\(851\) 36.3731i 1.24685i
\(852\) −9.93545 −0.340383
\(853\) −53.2566 −1.82347 −0.911736 0.410777i \(-0.865258\pi\)
−0.911736 + 0.410777i \(0.865258\pi\)
\(854\) −40.1216 −1.37293
\(855\) 7.58258 + 1.58258i 0.259319 + 0.0541229i
\(856\) 2.45505i 0.0839119i
\(857\) 22.7477i 0.777048i −0.921439 0.388524i \(-0.872985\pi\)
0.921439 0.388524i \(-0.127015\pi\)
\(858\) 0 0
\(859\) −38.2432 −1.30484 −0.652420 0.757857i \(-0.726246\pi\)
−0.652420 + 0.757857i \(0.726246\pi\)
\(860\) 8.66025 + 1.80750i 0.295312 + 0.0616352i
\(861\) 4.58258 0.156174
\(862\) 64.8693i 2.20946i
\(863\) 34.8317 1.18569 0.592843 0.805318i \(-0.298006\pi\)
0.592843 + 0.805318i \(0.298006\pi\)
\(864\) 36.9253i 1.25622i
\(865\) −16.2360 3.38865i −0.552041 0.115218i
\(866\) 38.8480i 1.32011i
\(867\) 4.00000i 0.135847i
\(868\) 46.7477i 1.58672i
\(869\) 15.8745i 0.538506i
\(870\) 21.9564 + 4.58258i 0.744393 + 0.155364i
\(871\) 0 0
\(872\) 4.74773i 0.160778i
\(873\) −8.94630 −0.302787
\(874\) 17.3739 0.587680
\(875\) −11.2087 + 15.7913i −0.378924 + 0.533843i
\(876\) 0 0
\(877\) −7.93725 −0.268022 −0.134011 0.990980i \(-0.542786\pi\)
−0.134011 + 0.990980i \(0.542786\pi\)
\(878\) −88.6405 −2.99147
\(879\) 23.4304i 0.790286i
\(880\) −10.3739 2.16515i −0.349703 0.0729872i
\(881\) −18.4955 −0.623128 −0.311564 0.950225i \(-0.600853\pi\)
−0.311564 + 0.950225i \(0.600853\pi\)
\(882\) −17.5112 −0.589633
\(883\) 46.2432i 1.55621i −0.628136 0.778103i \(-0.716182\pi\)
0.628136 0.778103i \(-0.283818\pi\)
\(884\) 0 0
\(885\) −1.53901 + 7.37386i −0.0517334 + 0.247870i
\(886\) 56.7207i 1.90557i
\(887\) 0.495454i 0.0166357i 0.999965 + 0.00831786i \(0.00264769\pi\)
−0.999965 + 0.00831786i \(0.997352\pi\)
\(888\) 13.7477i 0.461344i
\(889\) 16.8836i 0.566256i
\(890\) 20.5185 + 4.28245i 0.687780 + 0.143548i
\(891\) 2.64575i 0.0886360i
\(892\) 24.1733 0.809381
\(893\) 15.1652i 0.507482i
\(894\) 21.3739 0.714849
\(895\) 0.0754495 0.361500i 0.00252200 0.0120836i
\(896\) −22.1216 −0.739030
\(897\) 0 0
\(898\) 82.0345i 2.73753i
\(899\) 44.3103i 1.47783i
\(900\) −25.5826 11.1652i −0.852753 0.372172i
\(901\) −7.25227 −0.241608
\(902\) 15.3223 0.510177
\(903\) −2.45505 −0.0816990
\(904\) 28.7219i 0.955275i
\(905\) −8.56490 + 41.0369i −0.284707 + 1.36411i
\(906\) 13.5826 0.451251
\(907\) 33.7477i 1.12057i 0.828298 + 0.560287i \(0.189309\pi\)
−0.828298 + 0.560287i \(0.810691\pi\)
\(908\) −17.0544 −0.565969
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) 37.9129 1.25611 0.628055 0.778169i \(-0.283851\pi\)
0.628055 + 0.778169i \(0.283851\pi\)
\(912\) 3.10260 0.102737
\(913\) 29.9129i 0.989972i
\(914\) −3.79129 −0.125405
\(915\) −23.1642 4.83465i −0.765785 0.159829i
\(916\) 15.3024i 0.505606i
\(917\) 2.74110 0.0905191
\(918\) 50.1540 1.65533
\(919\) −35.8348 −1.18208 −0.591041 0.806641i \(-0.701283\pi\)
−0.591041 + 0.806641i \(0.701283\pi\)
\(920\) −17.3739 3.62614i −0.572799 0.119550i
\(921\) 24.2487i 0.799022i
\(922\) 2.62614i 0.0864872i
\(923\) 0 0
\(924\) −12.7913 −0.420802
\(925\) −36.3731 15.8745i −1.19594 0.521951i
\(926\) −18.0000 −0.591517
\(927\) 30.3303i 0.996178i
\(928\) −33.8426 −1.11094
\(929\) 15.9699i 0.523954i 0.965074 + 0.261977i \(0.0843745\pi\)
−0.965074 + 0.261977i \(0.915626\pi\)
\(930\) −9.66930 + 46.3284i −0.317069 + 1.51917i
\(931\) 6.92820i 0.227063i
\(932\) 59.0780i 1.93517i
\(933\) 1.58258i 0.0518112i
\(934\) 26.9898i 0.883134i
\(935\) 5.53901 26.5390i 0.181145 0.867919i
\(936\) 0 0
\(937\) 23.4955i 0.767563i 0.923424 + 0.383782i \(0.125378\pi\)
−0.923424 + 0.383782i \(0.874622\pi\)
\(938\) −56.3592 −1.84019
\(939\) 30.7477 1.00341
\(940\) −11.1652 + 53.4955i −0.364167 + 1.74483i
\(941\) 26.4575i 0.862490i −0.902235 0.431245i \(-0.858074\pi\)
0.902235 0.431245i \(-0.141926\pi\)
\(942\) −20.0616 −0.653643
\(943\) −12.1244 −0.394823
\(944\) 6.03440i 0.196403i
\(945\) 18.9564 + 3.95644i 0.616653 + 0.128703i
\(946\) −8.20871 −0.266888
\(947\) 38.5819 1.25374 0.626871 0.779123i \(-0.284335\pi\)
0.626871 + 0.779123i \(0.284335\pi\)
\(948\) 16.7477i 0.543941i
\(949\) 0 0
\(950\) 7.58258 17.3739i 0.246011 0.563683i
\(951\) 20.9753i 0.680171i
\(952\) 13.7477i 0.445566i
\(953\) 56.0780i 1.81655i 0.418378 + 0.908273i \(0.362599\pi\)
−0.418378 + 0.908273i \(0.637401\pi\)
\(954\) 6.92820i 0.224309i
\(955\) −3.38865 + 16.2360i −0.109654 + 0.525385i
\(956\) 58.5481i 1.89358i
\(957\) −12.1244 −0.391925
\(958\) 70.8693i 2.28968i
\(959\) 0.165151 0.00533302
\(960\) −27.5420 5.74835i −0.888915 0.185527i
\(961\) −62.4955 −2.01598
\(962\) 0 0
\(963\) 2.83485i 0.0913517i
\(964\) 4.83465i 0.155714i
\(965\) 0.460985 2.20871i 0.0148396 0.0711010i
\(966\) 17.3739 0.558995
\(967\) −21.5076 −0.691638 −0.345819 0.938301i \(-0.612399\pi\)
−0.345819 + 0.938301i \(0.612399\pi\)
\(968\) 6.92820 0.222681
\(969\) 7.93725i 0.254981i
\(970\) −4.47315 + 21.4322i −0.143624 + 0.688145i
\(971\) 36.4955 1.17119 0.585597 0.810602i \(-0.300860\pi\)
0.585597 + 0.810602i \(0.300860\pi\)
\(972\) 44.6606i 1.43249i
\(973\) −9.95536 −0.319154
\(974\) 46.1216 1.47783
\(975\) 0 0
\(976\) 18.9564 0.606781
\(977\) −38.7726 −1.24044 −0.620222 0.784426i \(-0.712958\pi\)
−0.620222 + 0.784426i \(0.712958\pi\)
\(978\) 23.3739i 0.747414i
\(979\) −11.3303 −0.362118
\(980\) −5.10080 + 24.4394i −0.162939 + 0.780688i
\(981\) 5.48220i 0.175033i
\(982\) 62.5644 1.99651
\(983\) −3.12250 −0.0995924 −0.0497962 0.998759i \(-0.515857\pi\)
−0.0497962 + 0.998759i \(0.515857\pi\)
\(984\) 4.58258 0.146087
\(985\) 9.12159 43.7042i 0.290638 1.39253i
\(986\) 45.9669i 1.46389i
\(987\) 15.1652i 0.482712i
\(988\) 0 0
\(989\) 6.49545 0.206543
\(990\) 25.3531 + 5.29150i 0.805775 + 0.168175i
\(991\) −13.0000 −0.412959 −0.206479 0.978451i \(-0.566201\pi\)
−0.206479 + 0.978451i \(0.566201\pi\)
\(992\) 71.4083i 2.26722i
\(993\) 11.4014 0.361811
\(994\) 13.4949i 0.428032i
\(995\) −0.647551 + 3.10260i −0.0205287 + 0.0983591i
\(996\) 31.5583i 0.999963i
\(997\) 18.1652i 0.575296i 0.957736 + 0.287648i \(0.0928733\pi\)
−0.957736 + 0.287648i \(0.907127\pi\)
\(998\) 36.3303i 1.15002i
\(999\) 39.6863i 1.25562i
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 845.2.d.c.844.8 8
5.4 even 2 inner 845.2.d.c.844.1 8
13.2 odd 12 845.2.n.d.529.3 8
13.3 even 3 845.2.l.c.654.1 8
13.4 even 6 845.2.l.c.699.4 8
13.5 odd 4 845.2.b.f.339.2 8
13.6 odd 12 845.2.n.c.484.2 8
13.7 odd 12 845.2.n.d.484.4 8
13.8 odd 4 845.2.b.f.339.8 8
13.9 even 3 65.2.l.a.49.1 yes 8
13.10 even 6 65.2.l.a.4.4 yes 8
13.11 odd 12 845.2.n.c.529.1 8
13.12 even 2 inner 845.2.d.c.844.2 8
39.23 odd 6 585.2.bf.a.199.1 8
39.35 odd 6 585.2.bf.a.244.4 8
52.23 odd 6 1040.2.df.b.849.3 8
52.35 odd 6 1040.2.df.b.49.2 8
65.4 even 6 845.2.l.c.699.1 8
65.8 even 4 4225.2.a.bj.1.4 4
65.9 even 6 65.2.l.a.49.4 yes 8
65.18 even 4 4225.2.a.bj.1.1 4
65.19 odd 12 845.2.n.d.484.3 8
65.22 odd 12 325.2.n.c.101.2 4
65.23 odd 12 325.2.n.b.251.1 4
65.24 odd 12 845.2.n.d.529.4 8
65.29 even 6 845.2.l.c.654.4 8
65.34 odd 4 845.2.b.f.339.1 8
65.44 odd 4 845.2.b.f.339.7 8
65.47 even 4 4225.2.a.bk.1.1 4
65.48 odd 12 325.2.n.b.101.1 4
65.49 even 6 65.2.l.a.4.1 8
65.54 odd 12 845.2.n.c.529.2 8
65.57 even 4 4225.2.a.bk.1.4 4
65.59 odd 12 845.2.n.c.484.1 8
65.62 odd 12 325.2.n.c.251.2 4
65.64 even 2 inner 845.2.d.c.844.7 8
195.74 odd 6 585.2.bf.a.244.1 8
195.179 odd 6 585.2.bf.a.199.4 8
260.139 odd 6 1040.2.df.b.49.3 8
260.179 odd 6 1040.2.df.b.849.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.l.a.4.1 8 65.49 even 6
65.2.l.a.4.4 yes 8 13.10 even 6
65.2.l.a.49.1 yes 8 13.9 even 3
65.2.l.a.49.4 yes 8 65.9 even 6
325.2.n.b.101.1 4 65.48 odd 12
325.2.n.b.251.1 4 65.23 odd 12
325.2.n.c.101.2 4 65.22 odd 12
325.2.n.c.251.2 4 65.62 odd 12
585.2.bf.a.199.1 8 39.23 odd 6
585.2.bf.a.199.4 8 195.179 odd 6
585.2.bf.a.244.1 8 195.74 odd 6
585.2.bf.a.244.4 8 39.35 odd 6
845.2.b.f.339.1 8 65.34 odd 4
845.2.b.f.339.2 8 13.5 odd 4
845.2.b.f.339.7 8 65.44 odd 4
845.2.b.f.339.8 8 13.8 odd 4
845.2.d.c.844.1 8 5.4 even 2 inner
845.2.d.c.844.2 8 13.12 even 2 inner
845.2.d.c.844.7 8 65.64 even 2 inner
845.2.d.c.844.8 8 1.1 even 1 trivial
845.2.l.c.654.1 8 13.3 even 3
845.2.l.c.654.4 8 65.29 even 6
845.2.l.c.699.1 8 65.4 even 6
845.2.l.c.699.4 8 13.4 even 6
845.2.n.c.484.1 8 65.59 odd 12
845.2.n.c.484.2 8 13.6 odd 12
845.2.n.c.529.1 8 13.11 odd 12
845.2.n.c.529.2 8 65.54 odd 12
845.2.n.d.484.3 8 65.19 odd 12
845.2.n.d.484.4 8 13.7 odd 12
845.2.n.d.529.3 8 13.2 odd 12
845.2.n.d.529.4 8 65.24 odd 12
1040.2.df.b.49.2 8 52.35 odd 6
1040.2.df.b.49.3 8 260.139 odd 6
1040.2.df.b.849.2 8 260.179 odd 6
1040.2.df.b.849.3 8 52.23 odd 6
4225.2.a.bj.1.1 4 65.18 even 4
4225.2.a.bj.1.4 4 65.8 even 4
4225.2.a.bk.1.1 4 65.47 even 4
4225.2.a.bk.1.4 4 65.57 even 4