Properties

Label 144.6.i.b.49.1
Level $144$
Weight $6$
Character 144.49
Analytic conductor $23.095$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [144,6,Mod(49,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.49");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 144.i (of order \(3\), degree \(2\), 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: \(23.0952700531\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.47347183152.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.1
Root \(0.500000 + 5.23712i\) of defining polynomial
Character \(\chi\) \(=\) 144.49
Dual form 144.6.i.b.97.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-15.5145 + 1.51695i) q^{3} +(33.0434 - 57.2329i) q^{5} +(57.0952 + 98.8918i) q^{7} +(238.398 - 47.0695i) q^{9} +O(q^{10})\) \(q+(-15.5145 + 1.51695i) q^{3} +(33.0434 - 57.2329i) q^{5} +(57.0952 + 98.8918i) q^{7} +(238.398 - 47.0695i) q^{9} +(-192.812 - 333.961i) q^{11} +(-516.287 + 894.236i) q^{13} +(-425.832 + 938.063i) q^{15} +959.020 q^{17} +464.576 q^{19} +(-1035.82 - 1447.64i) q^{21} +(1151.70 - 1994.81i) q^{23} +(-621.235 - 1076.01i) q^{25} +(-3627.21 + 1091.90i) q^{27} +(-3549.13 - 6147.28i) q^{29} +(3881.53 - 6723.00i) q^{31} +(3497.98 + 4888.74i) q^{33} +7546.48 q^{35} +9317.57 q^{37} +(6653.41 - 14656.8i) q^{39} +(6661.64 - 11538.3i) q^{41} +(-1056.29 - 1829.55i) q^{43} +(5183.55 - 15199.5i) q^{45} +(1247.40 + 2160.56i) q^{47} +(1883.78 - 3262.80i) q^{49} +(-14878.7 + 1454.79i) q^{51} -10044.2 q^{53} -25484.7 q^{55} +(-7207.66 + 704.741i) q^{57} +(2720.33 - 4711.75i) q^{59} +(-17094.4 - 29608.4i) q^{61} +(18266.1 + 20888.1i) q^{63} +(34119.8 + 59097.2i) q^{65} +(26792.6 - 46406.2i) q^{67} +(-14842.0 + 32695.5i) q^{69} +970.010 q^{71} -72400.3 q^{73} +(11270.4 + 15751.3i) q^{75} +(22017.3 - 38135.1i) q^{77} +(16098.9 + 27884.0i) q^{79} +(54617.9 - 22442.5i) q^{81} +(-18046.6 - 31257.6i) q^{83} +(31689.3 - 54887.5i) q^{85} +(64388.1 + 89987.9i) q^{87} +42622.2 q^{89} -117910. q^{91} +(-50021.4 + 110192. i) q^{93} +(15351.2 - 26589.0i) q^{95} +(21926.9 + 37978.6i) q^{97} +(-61685.4 - 70539.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9} + 315 q^{11} - 744 q^{13} - 2286 q^{15} + 2898 q^{17} - 2262 q^{19} - 11076 q^{21} + 3168 q^{23} - 2883 q^{25} - 18144 q^{27} - 5148 q^{29} + 8610 q^{31} + 17469 q^{33} - 2700 q^{35} + 39936 q^{37} + 49026 q^{39} + 5049 q^{41} + 31389 q^{43} + 2538 q^{45} - 12924 q^{47} - 52857 q^{49} - 36837 q^{51} - 96048 q^{53} - 126252 q^{55} - 17469 q^{57} - 62955 q^{59} - 75966 q^{61} - 49578 q^{63} + 108702 q^{65} + 32991 q^{67} - 29250 q^{69} + 129672 q^{71} - 8466 q^{73} + 105483 q^{75} + 88740 q^{77} - 89202 q^{79} + 123435 q^{81} - 32634 q^{83} + 71388 q^{85} + 151524 q^{87} + 66132 q^{89} + 301836 q^{91} + 57678 q^{93} + 82944 q^{95} + 46245 q^{97} - 282168 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −15.5145 + 1.51695i −0.995254 + 0.0973126i
\(4\) 0 0
\(5\) 33.0434 57.2329i 0.591099 1.02381i −0.402986 0.915206i \(-0.632028\pi\)
0.994085 0.108607i \(-0.0346389\pi\)
\(6\) 0 0
\(7\) 57.0952 + 98.8918i 0.440407 + 0.762808i 0.997720 0.0674952i \(-0.0215007\pi\)
−0.557312 + 0.830303i \(0.688167\pi\)
\(8\) 0 0
\(9\) 238.398 47.0695i 0.981061 0.193702i
\(10\) 0 0
\(11\) −192.812 333.961i −0.480455 0.832173i 0.519293 0.854596i \(-0.326195\pi\)
−0.999749 + 0.0224231i \(0.992862\pi\)
\(12\) 0 0
\(13\) −516.287 + 894.236i −0.847292 + 1.46755i 0.0363242 + 0.999340i \(0.488435\pi\)
−0.883616 + 0.468212i \(0.844898\pi\)
\(14\) 0 0
\(15\) −425.832 + 938.063i −0.488663 + 1.07648i
\(16\) 0 0
\(17\) 959.020 0.804832 0.402416 0.915457i \(-0.368171\pi\)
0.402416 + 0.915457i \(0.368171\pi\)
\(18\) 0 0
\(19\) 464.576 0.295239 0.147619 0.989044i \(-0.452839\pi\)
0.147619 + 0.989044i \(0.452839\pi\)
\(20\) 0 0
\(21\) −1035.82 1447.64i −0.512548 0.716330i
\(22\) 0 0
\(23\) 1151.70 1994.81i 0.453963 0.786288i −0.544664 0.838654i \(-0.683343\pi\)
0.998628 + 0.0523662i \(0.0166763\pi\)
\(24\) 0 0
\(25\) −621.235 1076.01i −0.198795 0.344323i
\(26\) 0 0
\(27\) −3627.21 + 1091.90i −0.957555 + 0.288252i
\(28\) 0 0
\(29\) −3549.13 6147.28i −0.783659 1.35734i −0.929797 0.368073i \(-0.880018\pi\)
0.146138 0.989264i \(-0.453316\pi\)
\(30\) 0 0
\(31\) 3881.53 6723.00i 0.725435 1.25649i −0.233360 0.972391i \(-0.574972\pi\)
0.958795 0.284100i \(-0.0916947\pi\)
\(32\) 0 0
\(33\) 3497.98 + 4888.74i 0.559156 + 0.781469i
\(34\) 0 0
\(35\) 7546.48 1.04130
\(36\) 0 0
\(37\) 9317.57 1.11892 0.559459 0.828858i \(-0.311009\pi\)
0.559459 + 0.828858i \(0.311009\pi\)
\(38\) 0 0
\(39\) 6653.41 14656.8i 0.700459 1.54304i
\(40\) 0 0
\(41\) 6661.64 11538.3i 0.618901 1.07197i −0.370785 0.928719i \(-0.620911\pi\)
0.989687 0.143250i \(-0.0457552\pi\)
\(42\) 0 0
\(43\) −1056.29 1829.55i −0.0871190 0.150895i 0.819173 0.573546i \(-0.194433\pi\)
−0.906292 + 0.422652i \(0.861099\pi\)
\(44\) 0 0
\(45\) 5183.55 15199.5i 0.381589 1.11892i
\(46\) 0 0
\(47\) 1247.40 + 2160.56i 0.0823686 + 0.142667i 0.904267 0.426968i \(-0.140418\pi\)
−0.821898 + 0.569634i \(0.807085\pi\)
\(48\) 0 0
\(49\) 1883.78 3262.80i 0.112083 0.194133i
\(50\) 0 0
\(51\) −14878.7 + 1454.79i −0.801012 + 0.0783203i
\(52\) 0 0
\(53\) −10044.2 −0.491163 −0.245582 0.969376i \(-0.578979\pi\)
−0.245582 + 0.969376i \(0.578979\pi\)
\(54\) 0 0
\(55\) −25484.7 −1.13599
\(56\) 0 0
\(57\) −7207.66 + 704.741i −0.293837 + 0.0287304i
\(58\) 0 0
\(59\) 2720.33 4711.75i 0.101740 0.176219i −0.810662 0.585515i \(-0.800892\pi\)
0.912402 + 0.409296i \(0.134226\pi\)
\(60\) 0 0
\(61\) −17094.4 29608.4i −0.588206 1.01880i −0.994467 0.105046i \(-0.966501\pi\)
0.406261 0.913757i \(-0.366832\pi\)
\(62\) 0 0
\(63\) 18266.1 + 20888.1i 0.579823 + 0.663053i
\(64\) 0 0
\(65\) 34119.8 + 59097.2i 1.00167 + 1.73494i
\(66\) 0 0
\(67\) 26792.6 46406.2i 0.729169 1.26296i −0.228066 0.973646i \(-0.573240\pi\)
0.957235 0.289311i \(-0.0934263\pi\)
\(68\) 0 0
\(69\) −14842.0 + 32695.5i −0.375293 + 0.826732i
\(70\) 0 0
\(71\) 970.010 0.0228365 0.0114183 0.999935i \(-0.496365\pi\)
0.0114183 + 0.999935i \(0.496365\pi\)
\(72\) 0 0
\(73\) −72400.3 −1.59013 −0.795066 0.606523i \(-0.792564\pi\)
−0.795066 + 0.606523i \(0.792564\pi\)
\(74\) 0 0
\(75\) 11270.4 + 15751.3i 0.231359 + 0.323344i
\(76\) 0 0
\(77\) 22017.3 38135.1i 0.423192 0.732990i
\(78\) 0 0
\(79\) 16098.9 + 27884.0i 0.290220 + 0.502676i 0.973862 0.227142i \(-0.0729382\pi\)
−0.683642 + 0.729818i \(0.739605\pi\)
\(80\) 0 0
\(81\) 54617.9 22442.5i 0.924959 0.380066i
\(82\) 0 0
\(83\) −18046.6 31257.6i −0.287541 0.498036i 0.685681 0.727902i \(-0.259504\pi\)
−0.973222 + 0.229866i \(0.926171\pi\)
\(84\) 0 0
\(85\) 31689.3 54887.5i 0.475735 0.823998i
\(86\) 0 0
\(87\) 64388.1 + 89987.9i 0.912026 + 1.27464i
\(88\) 0 0
\(89\) 42622.2 0.570375 0.285188 0.958472i \(-0.407944\pi\)
0.285188 + 0.958472i \(0.407944\pi\)
\(90\) 0 0
\(91\) −117910. −1.49261
\(92\) 0 0
\(93\) −50021.4 + 110192.i −0.599720 + 1.32112i
\(94\) 0 0
\(95\) 15351.2 26589.0i 0.174515 0.302269i
\(96\) 0 0
\(97\) 21926.9 + 37978.6i 0.236618 + 0.409835i 0.959742 0.280884i \(-0.0906275\pi\)
−0.723123 + 0.690719i \(0.757294\pi\)
\(98\) 0 0
\(99\) −61685.4 70539.9i −0.632549 0.723347i
\(100\) 0 0
\(101\) −12056.7 20882.8i −0.117604 0.203697i 0.801213 0.598379i \(-0.204188\pi\)
−0.918818 + 0.394682i \(0.870855\pi\)
\(102\) 0 0
\(103\) −68610.4 + 118837.i −0.637231 + 1.10372i 0.348807 + 0.937195i \(0.386587\pi\)
−0.986038 + 0.166522i \(0.946746\pi\)
\(104\) 0 0
\(105\) −117080. + 11447.7i −1.03635 + 0.101331i
\(106\) 0 0
\(107\) 167979. 1.41839 0.709195 0.705012i \(-0.249059\pi\)
0.709195 + 0.705012i \(0.249059\pi\)
\(108\) 0 0
\(109\) −21224.0 −0.171104 −0.0855521 0.996334i \(-0.527265\pi\)
−0.0855521 + 0.996334i \(0.527265\pi\)
\(110\) 0 0
\(111\) −144557. + 14134.3i −1.11361 + 0.108885i
\(112\) 0 0
\(113\) 14420.8 24977.5i 0.106241 0.184015i −0.808003 0.589178i \(-0.799452\pi\)
0.914245 + 0.405163i \(0.132785\pi\)
\(114\) 0 0
\(115\) −76112.4 131831.i −0.536674 0.929547i
\(116\) 0 0
\(117\) −80990.5 + 237485.i −0.546977 + 1.60388i
\(118\) 0 0
\(119\) 54755.4 + 94839.2i 0.354454 + 0.613932i
\(120\) 0 0
\(121\) 6172.35 10690.8i 0.0383255 0.0663816i
\(122\) 0 0
\(123\) −85848.7 + 189116.i −0.511648 + 1.12711i
\(124\) 0 0
\(125\) 124410. 0.712167
\(126\) 0 0
\(127\) 215062. 1.18319 0.591594 0.806236i \(-0.298499\pi\)
0.591594 + 0.806236i \(0.298499\pi\)
\(128\) 0 0
\(129\) 19163.2 + 26782.2i 0.101389 + 0.141701i
\(130\) 0 0
\(131\) −94654.7 + 163947.i −0.481908 + 0.834688i −0.999784 0.0207668i \(-0.993389\pi\)
0.517877 + 0.855455i \(0.326723\pi\)
\(132\) 0 0
\(133\) 26525.1 + 45942.8i 0.130025 + 0.225210i
\(134\) 0 0
\(135\) −57363.1 + 243676.i −0.270893 + 1.15074i
\(136\) 0 0
\(137\) 1809.78 + 3134.63i 0.00823805 + 0.0142687i 0.870115 0.492849i \(-0.164044\pi\)
−0.861877 + 0.507117i \(0.830711\pi\)
\(138\) 0 0
\(139\) 60440.1 104685.i 0.265331 0.459567i −0.702319 0.711862i \(-0.747852\pi\)
0.967650 + 0.252295i \(0.0811854\pi\)
\(140\) 0 0
\(141\) −22630.2 31627.7i −0.0958609 0.133974i
\(142\) 0 0
\(143\) 398186. 1.62834
\(144\) 0 0
\(145\) −469102. −1.85288
\(146\) 0 0
\(147\) −24276.3 + 53478.2i −0.0926594 + 0.204119i
\(148\) 0 0
\(149\) −37408.2 + 64792.9i −0.138039 + 0.239090i −0.926754 0.375668i \(-0.877413\pi\)
0.788715 + 0.614758i \(0.210746\pi\)
\(150\) 0 0
\(151\) −179976. 311728.i −0.642352 1.11259i −0.984906 0.173088i \(-0.944625\pi\)
0.342554 0.939498i \(-0.388708\pi\)
\(152\) 0 0
\(153\) 228628. 45140.6i 0.789589 0.155897i
\(154\) 0 0
\(155\) −256518. 444302.i −0.857607 1.48542i
\(156\) 0 0
\(157\) −23983.3 + 41540.3i −0.0776533 + 0.134499i −0.902237 0.431241i \(-0.858076\pi\)
0.824584 + 0.565740i \(0.191409\pi\)
\(158\) 0 0
\(159\) 155831. 15236.6i 0.488832 0.0477964i
\(160\) 0 0
\(161\) 263027. 0.799715
\(162\) 0 0
\(163\) −361063. −1.06442 −0.532212 0.846611i \(-0.678639\pi\)
−0.532212 + 0.846611i \(0.678639\pi\)
\(164\) 0 0
\(165\) 395382. 38659.1i 1.13059 0.110546i
\(166\) 0 0
\(167\) 58233.2 100863.i 0.161577 0.279860i −0.773857 0.633360i \(-0.781675\pi\)
0.935434 + 0.353500i \(0.115009\pi\)
\(168\) 0 0
\(169\) −347458. 601816.i −0.935807 1.62086i
\(170\) 0 0
\(171\) 110754. 21867.4i 0.289647 0.0571882i
\(172\) 0 0
\(173\) −51762.9 89656.0i −0.131493 0.227753i 0.792759 0.609535i \(-0.208644\pi\)
−0.924252 + 0.381782i \(0.875311\pi\)
\(174\) 0 0
\(175\) 70939.0 122870.i 0.175102 0.303285i
\(176\) 0 0
\(177\) −35057.0 + 77226.9i −0.0841088 + 0.185283i
\(178\) 0 0
\(179\) 78941.2 0.184150 0.0920748 0.995752i \(-0.470650\pi\)
0.0920748 + 0.995752i \(0.470650\pi\)
\(180\) 0 0
\(181\) 586108. 1.32978 0.664892 0.746940i \(-0.268478\pi\)
0.664892 + 0.746940i \(0.268478\pi\)
\(182\) 0 0
\(183\) 310125. + 433427.i 0.684557 + 0.956728i
\(184\) 0 0
\(185\) 307884. 533271.i 0.661391 1.14556i
\(186\) 0 0
\(187\) −184911. 320275.i −0.386686 0.669760i
\(188\) 0 0
\(189\) −315076. 296359.i −0.641595 0.603482i
\(190\) 0 0
\(191\) 386026. + 668617.i 0.765656 + 1.32615i 0.939899 + 0.341452i \(0.110919\pi\)
−0.174243 + 0.984703i \(0.555748\pi\)
\(192\) 0 0
\(193\) 8719.67 15102.9i 0.0168503 0.0291855i −0.857477 0.514522i \(-0.827969\pi\)
0.874328 + 0.485336i \(0.161303\pi\)
\(194\) 0 0
\(195\) −618998. 865104.i −1.16574 1.62923i
\(196\) 0 0
\(197\) 340729. 0.625524 0.312762 0.949832i \(-0.398746\pi\)
0.312762 + 0.949832i \(0.398746\pi\)
\(198\) 0 0
\(199\) −14239.7 −0.0254899 −0.0127450 0.999919i \(-0.504057\pi\)
−0.0127450 + 0.999919i \(0.504057\pi\)
\(200\) 0 0
\(201\) −345277. + 760610.i −0.602806 + 1.32792i
\(202\) 0 0
\(203\) 405277. 701960.i 0.690258 1.19556i
\(204\) 0 0
\(205\) −440246. 762529.i −0.731663 1.26728i
\(206\) 0 0
\(207\) 180669. 529768.i 0.293061 0.859329i
\(208\) 0 0
\(209\) −89576.0 155150.i −0.141849 0.245690i
\(210\) 0 0
\(211\) −24049.2 + 41654.4i −0.0371873 + 0.0644102i −0.884020 0.467449i \(-0.845173\pi\)
0.846833 + 0.531859i \(0.178506\pi\)
\(212\) 0 0
\(213\) −15049.2 + 1471.46i −0.0227282 + 0.00222228i
\(214\) 0 0
\(215\) −139614. −0.205984
\(216\) 0 0
\(217\) 886466. 1.27795
\(218\) 0 0
\(219\) 1.12325e6 109828.i 1.58258 0.154740i
\(220\) 0 0
\(221\) −495130. + 857590.i −0.681928 + 1.18113i
\(222\) 0 0
\(223\) 391988. + 678944.i 0.527851 + 0.914264i 0.999473 + 0.0324633i \(0.0103352\pi\)
−0.471622 + 0.881801i \(0.656331\pi\)
\(224\) 0 0
\(225\) −198748. 227277.i −0.261726 0.299295i
\(226\) 0 0
\(227\) −277898. 481334.i −0.357949 0.619986i 0.629669 0.776863i \(-0.283190\pi\)
−0.987618 + 0.156878i \(0.949857\pi\)
\(228\) 0 0
\(229\) −57346.2 + 99326.6i −0.0722630 + 0.125163i −0.899893 0.436111i \(-0.856355\pi\)
0.827630 + 0.561274i \(0.189689\pi\)
\(230\) 0 0
\(231\) −283738. + 625045.i −0.349854 + 0.770693i
\(232\) 0 0
\(233\) −111177. −0.134161 −0.0670805 0.997748i \(-0.521368\pi\)
−0.0670805 + 0.997748i \(0.521368\pi\)
\(234\) 0 0
\(235\) 164874. 0.194752
\(236\) 0 0
\(237\) −292064. 408185.i −0.337759 0.472048i
\(238\) 0 0
\(239\) −369523. + 640033.i −0.418453 + 0.724782i −0.995784 0.0917279i \(-0.970761\pi\)
0.577331 + 0.816510i \(0.304094\pi\)
\(240\) 0 0
\(241\) 645180. + 1.11748e6i 0.715547 + 1.23936i 0.962748 + 0.270400i \(0.0871559\pi\)
−0.247201 + 0.968964i \(0.579511\pi\)
\(242\) 0 0
\(243\) −813324. + 431036.i −0.883584 + 0.468272i
\(244\) 0 0
\(245\) −124493. 215628.i −0.132504 0.229504i
\(246\) 0 0
\(247\) −239855. + 415441.i −0.250153 + 0.433278i
\(248\) 0 0
\(249\) 327400. + 457569.i 0.334641 + 0.467690i
\(250\) 0 0
\(251\) −1.29383e6 −1.29626 −0.648129 0.761530i \(-0.724448\pi\)
−0.648129 + 0.761530i \(0.724448\pi\)
\(252\) 0 0
\(253\) −888250. −0.872437
\(254\) 0 0
\(255\) −408381. + 899621.i −0.393292 + 0.866382i
\(256\) 0 0
\(257\) −312181. + 540713.i −0.294831 + 0.510663i −0.974946 0.222443i \(-0.928597\pi\)
0.680114 + 0.733106i \(0.261930\pi\)
\(258\) 0 0
\(259\) 531988. + 921431.i 0.492780 + 0.853519i
\(260\) 0 0
\(261\) −1.13545e6 1.29844e6i −1.03174 1.17983i
\(262\) 0 0
\(263\) −582495. 1.00891e6i −0.519281 0.899421i −0.999749 0.0224089i \(-0.992866\pi\)
0.480468 0.877012i \(-0.340467\pi\)
\(264\) 0 0
\(265\) −331895. + 574859.i −0.290326 + 0.502859i
\(266\) 0 0
\(267\) −661261. + 64655.9i −0.567668 + 0.0555047i
\(268\) 0 0
\(269\) 1.58951e6 1.33932 0.669659 0.742669i \(-0.266440\pi\)
0.669659 + 0.742669i \(0.266440\pi\)
\(270\) 0 0
\(271\) 977878. 0.808837 0.404419 0.914574i \(-0.367474\pi\)
0.404419 + 0.914574i \(0.367474\pi\)
\(272\) 0 0
\(273\) 1.82931e6 178864.i 1.48553 0.145250i
\(274\) 0 0
\(275\) −239563. + 414936.i −0.191024 + 0.330864i
\(276\) 0 0
\(277\) 645243. + 1.11759e6i 0.505271 + 0.875154i 0.999981 + 0.00609677i \(0.00194067\pi\)
−0.494711 + 0.869058i \(0.664726\pi\)
\(278\) 0 0
\(279\) 608899. 1.78545e6i 0.468312 1.37321i
\(280\) 0 0
\(281\) −833662. 1.44395e6i −0.629831 1.09090i −0.987585 0.157084i \(-0.949791\pi\)
0.357754 0.933816i \(-0.383543\pi\)
\(282\) 0 0
\(283\) 564568. 977861.i 0.419035 0.725790i −0.576808 0.816880i \(-0.695702\pi\)
0.995843 + 0.0910901i \(0.0290351\pi\)
\(284\) 0 0
\(285\) −197831. + 435802.i −0.144272 + 0.317817i
\(286\) 0 0
\(287\) 1.52139e6 1.09027
\(288\) 0 0
\(289\) −500138. −0.352245
\(290\) 0 0
\(291\) −397797. 555955.i −0.275378 0.384864i
\(292\) 0 0
\(293\) −1.02815e6 + 1.78081e6i −0.699663 + 1.21185i 0.268921 + 0.963162i \(0.413333\pi\)
−0.968583 + 0.248689i \(0.920000\pi\)
\(294\) 0 0
\(295\) −179778. 311385.i −0.120277 0.208325i
\(296\) 0 0
\(297\) 1.06402e6 + 1.00082e6i 0.699937 + 0.658359i
\(298\) 0 0
\(299\) 1.18922e6 + 2.05979e6i 0.769279 + 1.33243i
\(300\) 0 0
\(301\) 120618. 208917.i 0.0767357 0.132910i
\(302\) 0 0
\(303\) 218731. + 305696.i 0.136869 + 0.191286i
\(304\) 0 0
\(305\) −2.25943e6 −1.39075
\(306\) 0 0
\(307\) −1.52149e6 −0.921346 −0.460673 0.887570i \(-0.652392\pi\)
−0.460673 + 0.887570i \(0.652392\pi\)
\(308\) 0 0
\(309\) 884184. 1.94777e6i 0.526801 1.16049i
\(310\) 0 0
\(311\) −1.35420e6 + 2.34554e6i −0.793928 + 1.37512i 0.129589 + 0.991568i \(0.458634\pi\)
−0.923517 + 0.383556i \(0.874699\pi\)
\(312\) 0 0
\(313\) 325583. + 563926.i 0.187845 + 0.325358i 0.944532 0.328420i \(-0.106516\pi\)
−0.756686 + 0.653778i \(0.773183\pi\)
\(314\) 0 0
\(315\) 1.79906e6 355209.i 1.02157 0.201701i
\(316\) 0 0
\(317\) 58055.3 + 100555.i 0.0324484 + 0.0562024i 0.881794 0.471636i \(-0.156336\pi\)
−0.849345 + 0.527838i \(0.823003\pi\)
\(318\) 0 0
\(319\) −1.36863e6 + 2.37054e6i −0.753026 + 1.30428i
\(320\) 0 0
\(321\) −2.60611e6 + 254816.i −1.41166 + 0.138027i
\(322\) 0 0
\(323\) 445538. 0.237618
\(324\) 0 0
\(325\) 1.28294e6 0.673750
\(326\) 0 0
\(327\) 329279. 32195.8i 0.170292 0.0166506i
\(328\) 0 0
\(329\) −142441. + 246715.i −0.0725514 + 0.125663i
\(330\) 0 0
\(331\) 158828. + 275099.i 0.0796816 + 0.138013i 0.903113 0.429404i \(-0.141276\pi\)
−0.823431 + 0.567416i \(0.807943\pi\)
\(332\) 0 0
\(333\) 2.22129e6 438573.i 1.09773 0.216736i
\(334\) 0 0
\(335\) −1.77064e6 3.06684e6i −0.862021 1.49306i
\(336\) 0 0
\(337\) −215275. + 372867.i −0.103257 + 0.178846i −0.913025 0.407904i \(-0.866260\pi\)
0.809768 + 0.586750i \(0.199593\pi\)
\(338\) 0 0
\(339\) −185841. + 409389.i −0.0878299 + 0.193480i
\(340\) 0 0
\(341\) −2.99363e6 −1.39416
\(342\) 0 0
\(343\) 2.34942e6 1.07826
\(344\) 0 0
\(345\) 1.38082e6 + 1.92982e6i 0.624584 + 0.872910i
\(346\) 0 0
\(347\) −2.07020e6 + 3.58569e6i −0.922971 + 1.59863i −0.128178 + 0.991751i \(0.540913\pi\)
−0.794793 + 0.606881i \(0.792420\pi\)
\(348\) 0 0
\(349\) 1.73048e6 + 2.99727e6i 0.760505 + 1.31723i 0.942590 + 0.333951i \(0.108382\pi\)
−0.182085 + 0.983283i \(0.558285\pi\)
\(350\) 0 0
\(351\) 896271. 3.80731e6i 0.388304 1.64949i
\(352\) 0 0
\(353\) −1.32229e6 2.29027e6i −0.564792 0.978249i −0.997069 0.0765076i \(-0.975623\pi\)
0.432277 0.901741i \(-0.357710\pi\)
\(354\) 0 0
\(355\) 32052.5 55516.5i 0.0134987 0.0233804i
\(356\) 0 0
\(357\) −993368. 1.38832e6i −0.412515 0.576526i
\(358\) 0 0
\(359\) −2.13123e6 −0.872761 −0.436380 0.899762i \(-0.643740\pi\)
−0.436380 + 0.899762i \(0.643740\pi\)
\(360\) 0 0
\(361\) −2.26027e6 −0.912834
\(362\) 0 0
\(363\) −79543.3 + 175226.i −0.0316838 + 0.0697961i
\(364\) 0 0
\(365\) −2.39235e6 + 4.14368e6i −0.939925 + 1.62800i
\(366\) 0 0
\(367\) −640035. 1.10857e6i −0.248049 0.429634i 0.714935 0.699191i \(-0.246456\pi\)
−0.962985 + 0.269557i \(0.913123\pi\)
\(368\) 0 0
\(369\) 1.04502e6 3.06426e6i 0.399538 1.17155i
\(370\) 0 0
\(371\) −573476. 993289.i −0.216312 0.374663i
\(372\) 0 0
\(373\) 1.94733e6 3.37288e6i 0.724716 1.25524i −0.234375 0.972146i \(-0.575304\pi\)
0.959091 0.283099i \(-0.0913623\pi\)
\(374\) 0 0
\(375\) −1.93016e6 + 188725.i −0.708787 + 0.0693028i
\(376\) 0 0
\(377\) 7.32949e6 2.65595
\(378\) 0 0
\(379\) 2.83335e6 1.01322 0.506609 0.862176i \(-0.330899\pi\)
0.506609 + 0.862176i \(0.330899\pi\)
\(380\) 0 0
\(381\) −3.33657e6 + 326239.i −1.17757 + 0.115139i
\(382\) 0 0
\(383\) 1.18249e6 2.04814e6i 0.411909 0.713448i −0.583189 0.812336i \(-0.698195\pi\)
0.995099 + 0.0988883i \(0.0315287\pi\)
\(384\) 0 0
\(385\) −1.45505e6 2.52023e6i −0.500296 0.866539i
\(386\) 0 0
\(387\) −337934. 386442.i −0.114698 0.131162i
\(388\) 0 0
\(389\) 871692. + 1.50981e6i 0.292071 + 0.505882i 0.974299 0.225257i \(-0.0723222\pi\)
−0.682228 + 0.731139i \(0.738989\pi\)
\(390\) 0 0
\(391\) 1.10451e6 1.91306e6i 0.365364 0.632830i
\(392\) 0 0
\(393\) 1.21982e6 2.68713e6i 0.398395 0.877623i
\(394\) 0 0
\(395\) 2.12785e6 0.686195
\(396\) 0 0
\(397\) 4.81109e6 1.53203 0.766015 0.642823i \(-0.222237\pi\)
0.766015 + 0.642823i \(0.222237\pi\)
\(398\) 0 0
\(399\) −481216. 672541.i −0.151324 0.211488i
\(400\) 0 0
\(401\) 2.27703e6 3.94394e6i 0.707145 1.22481i −0.258767 0.965940i \(-0.583316\pi\)
0.965912 0.258871i \(-0.0833506\pi\)
\(402\) 0 0
\(403\) 4.00797e6 + 6.94200e6i 1.22931 + 2.12923i
\(404\) 0 0
\(405\) 520314. 3.86752e6i 0.157626 1.17164i
\(406\) 0 0
\(407\) −1.79654e6 3.11170e6i −0.537590 0.931133i
\(408\) 0 0
\(409\) −956414. + 1.65656e6i −0.282708 + 0.489664i −0.972051 0.234771i \(-0.924566\pi\)
0.689343 + 0.724435i \(0.257899\pi\)
\(410\) 0 0
\(411\) −32832.9 45886.8i −0.00958748 0.0133993i
\(412\) 0 0
\(413\) 621271. 0.179228
\(414\) 0 0
\(415\) −2.38528e6 −0.679860
\(416\) 0 0
\(417\) −778894. + 1.71582e6i −0.219350 + 0.483206i
\(418\) 0 0
\(419\) 2.20697e6 3.82259e6i 0.614132 1.06371i −0.376404 0.926456i \(-0.622839\pi\)
0.990536 0.137252i \(-0.0438272\pi\)
\(420\) 0 0
\(421\) 872253. + 1.51079e6i 0.239848 + 0.415430i 0.960671 0.277690i \(-0.0895689\pi\)
−0.720822 + 0.693120i \(0.756236\pi\)
\(422\) 0 0
\(423\) 399074. + 456359.i 0.108443 + 0.124010i
\(424\) 0 0
\(425\) −595777. 1.03192e6i −0.159997 0.277122i
\(426\) 0 0
\(427\) 1.95202e6 3.38099e6i 0.518100 0.897376i
\(428\) 0 0
\(429\) −6.17765e6 + 604030.i −1.62061 + 0.158458i
\(430\) 0 0
\(431\) 2.21740e6 0.574976 0.287488 0.957784i \(-0.407180\pi\)
0.287488 + 0.957784i \(0.407180\pi\)
\(432\) 0 0
\(433\) −3.63511e6 −0.931746 −0.465873 0.884851i \(-0.654260\pi\)
−0.465873 + 0.884851i \(0.654260\pi\)
\(434\) 0 0
\(435\) 7.27787e6 711606.i 1.84409 0.180309i
\(436\) 0 0
\(437\) 535054. 926741.i 0.134028 0.232143i
\(438\) 0 0
\(439\) −1.54413e6 2.67452e6i −0.382405 0.662345i 0.609001 0.793170i \(-0.291571\pi\)
−0.991405 + 0.130825i \(0.958237\pi\)
\(440\) 0 0
\(441\) 295510. 866512.i 0.0723562 0.212167i
\(442\) 0 0
\(443\) −3.50048e6 6.06302e6i −0.847459 1.46784i −0.883468 0.468491i \(-0.844798\pi\)
0.0360092 0.999351i \(-0.488535\pi\)
\(444\) 0 0
\(445\) 1.40838e6 2.43939e6i 0.337148 0.583958i
\(446\) 0 0
\(447\) 482080. 1.06197e6i 0.114117 0.251388i
\(448\) 0 0
\(449\) −5.00196e6 −1.17091 −0.585456 0.810704i \(-0.699084\pi\)
−0.585456 + 0.810704i \(0.699084\pi\)
\(450\) 0 0
\(451\) −5.13778e6 −1.18942
\(452\) 0 0
\(453\) 3.26511e6 + 4.56328e6i 0.747572 + 1.04480i
\(454\) 0 0
\(455\) −3.89615e6 + 6.74833e6i −0.882282 + 1.52816i
\(456\) 0 0
\(457\) −1.78581e6 3.09311e6i −0.399985 0.692795i 0.593738 0.804658i \(-0.297651\pi\)
−0.993724 + 0.111863i \(0.964318\pi\)
\(458\) 0 0
\(459\) −3.47857e6 + 1.04715e6i −0.770671 + 0.231994i
\(460\) 0 0
\(461\) −2.75061e6 4.76420e6i −0.602805 1.04409i −0.992394 0.123100i \(-0.960716\pi\)
0.389589 0.920989i \(-0.372617\pi\)
\(462\) 0 0
\(463\) −1.42708e6 + 2.47177e6i −0.309382 + 0.535866i −0.978227 0.207536i \(-0.933456\pi\)
0.668845 + 0.743402i \(0.266789\pi\)
\(464\) 0 0
\(465\) 4.65373e6 + 6.50399e6i 0.998087 + 1.39491i
\(466\) 0 0
\(467\) 7.16552e6 1.52039 0.760196 0.649694i \(-0.225103\pi\)
0.760196 + 0.649694i \(0.225103\pi\)
\(468\) 0 0
\(469\) 6.11892e6 1.28452
\(470\) 0 0
\(471\) 309074. 680857.i 0.0641962 0.141418i
\(472\) 0 0
\(473\) −407332. + 705520.i −0.0837136 + 0.144996i
\(474\) 0 0
\(475\) −288611. 499889.i −0.0586920 0.101658i
\(476\) 0 0
\(477\) −2.39452e6 + 472775.i −0.481861 + 0.0951391i
\(478\) 0 0
\(479\) 1.64185e6 + 2.84377e6i 0.326961 + 0.566312i 0.981907 0.189363i \(-0.0606423\pi\)
−0.654947 + 0.755675i \(0.727309\pi\)
\(480\) 0 0
\(481\) −4.81054e6 + 8.33210e6i −0.948050 + 1.64207i
\(482\) 0 0
\(483\) −4.08072e6 + 398999.i −0.795920 + 0.0778224i
\(484\) 0 0
\(485\) 2.89816e6 0.559459
\(486\) 0 0
\(487\) −2.18097e6 −0.416704 −0.208352 0.978054i \(-0.566810\pi\)
−0.208352 + 0.978054i \(0.566810\pi\)
\(488\) 0 0
\(489\) 5.60171e6 547716.i 1.05937 0.103582i
\(490\) 0 0
\(491\) −4.96974e6 + 8.60785e6i −0.930315 + 1.61135i −0.147534 + 0.989057i \(0.547134\pi\)
−0.782782 + 0.622297i \(0.786200\pi\)
\(492\) 0 0
\(493\) −3.40369e6 5.89536e6i −0.630714 1.09243i
\(494\) 0 0
\(495\) −6.07550e6 + 1.19955e6i −1.11447 + 0.220042i
\(496\) 0 0
\(497\) 55382.9 + 95926.0i 0.0100574 + 0.0174199i
\(498\) 0 0
\(499\) −2.26386e6 + 3.92112e6i −0.407004 + 0.704951i −0.994552 0.104238i \(-0.966760\pi\)
0.587549 + 0.809189i \(0.300093\pi\)
\(500\) 0 0
\(501\) −750453. + 1.65317e6i −0.133576 + 0.294255i
\(502\) 0 0
\(503\) 4.40282e6 0.775909 0.387955 0.921679i \(-0.373182\pi\)
0.387955 + 0.921679i \(0.373182\pi\)
\(504\) 0 0
\(505\) −1.59357e6 −0.278063
\(506\) 0 0
\(507\) 6.30356e6 + 8.80977e6i 1.08910 + 1.52211i
\(508\) 0 0
\(509\) −2.91063e6 + 5.04135e6i −0.497957 + 0.862487i −0.999997 0.00235703i \(-0.999250\pi\)
0.502040 + 0.864844i \(0.332583\pi\)
\(510\) 0 0
\(511\) −4.13371e6 7.15979e6i −0.700306 1.21296i
\(512\) 0 0
\(513\) −1.68512e6 + 507269.i −0.282707 + 0.0851030i
\(514\) 0 0
\(515\) 4.53424e6 + 7.85354e6i 0.753333 + 1.30481i
\(516\) 0 0
\(517\) 481028. 833166.i 0.0791488 0.137090i
\(518\) 0 0
\(519\) 939078. + 1.31244e6i 0.153032 + 0.213876i
\(520\) 0 0
\(521\) 1.09649e7 1.76975 0.884875 0.465829i \(-0.154244\pi\)
0.884875 + 0.465829i \(0.154244\pi\)
\(522\) 0 0
\(523\) 3.83705e6 0.613399 0.306700 0.951806i \(-0.400775\pi\)
0.306700 + 0.951806i \(0.400775\pi\)
\(524\) 0 0
\(525\) −914194. + 2.01387e6i −0.144757 + 0.318885i
\(526\) 0 0
\(527\) 3.72246e6 6.44750e6i 0.583854 1.01126i
\(528\) 0 0
\(529\) 565332. + 979183.i 0.0878343 + 0.152133i
\(530\) 0 0
\(531\) 426741. 1.25131e6i 0.0656792 0.192588i
\(532\) 0 0
\(533\) 6.87864e6 + 1.19141e7i 1.04878 + 1.81654i
\(534\) 0 0
\(535\) 5.55060e6 9.61392e6i 0.838408 1.45217i
\(536\) 0 0
\(537\) −1.22473e6 + 119750.i −0.183276 + 0.0179201i
\(538\) 0 0
\(539\) −1.45286e6 −0.215403
\(540\) 0 0
\(541\) −4.88767e6 −0.717974 −0.358987 0.933343i \(-0.616878\pi\)
−0.358987 + 0.933343i \(0.616878\pi\)
\(542\) 0 0
\(543\) −9.09315e6 + 889098.i −1.32347 + 0.129405i
\(544\) 0 0
\(545\) −701313. + 1.21471e6i −0.101139 + 0.175179i
\(546\) 0 0
\(547\) −3.46672e6 6.00454e6i −0.495394 0.858047i 0.504592 0.863358i \(-0.331643\pi\)
−0.999986 + 0.00531061i \(0.998310\pi\)
\(548\) 0 0
\(549\) −5.46892e6 6.25395e6i −0.774410 0.885571i
\(550\) 0 0
\(551\) −1.64884e6 2.85588e6i −0.231366 0.400739i
\(552\) 0 0
\(553\) −1.83834e6 + 3.18409e6i −0.255630 + 0.442764i
\(554\) 0 0
\(555\) −3.96772e6 + 8.74047e6i −0.546774 + 1.20449i
\(556\) 0 0
\(557\) −9.83771e6 −1.34356 −0.671778 0.740752i \(-0.734469\pi\)
−0.671778 + 0.740752i \(0.734469\pi\)
\(558\) 0 0
\(559\) 2.18140e6 0.295261
\(560\) 0 0
\(561\) 3.35464e6 + 4.68840e6i 0.450027 + 0.628951i
\(562\) 0 0
\(563\) 1.36609e6 2.36613e6i 0.181638 0.314607i −0.760800 0.648986i \(-0.775193\pi\)
0.942439 + 0.334379i \(0.108527\pi\)
\(564\) 0 0
\(565\) −953024. 1.65069e6i −0.125598 0.217542i
\(566\) 0 0
\(567\) 5.33780e6 + 4.11990e6i 0.697276 + 0.538182i
\(568\) 0 0
\(569\) −4.71998e6 8.17525e6i −0.611167 1.05857i −0.991044 0.133535i \(-0.957367\pi\)
0.379877 0.925037i \(-0.375966\pi\)
\(570\) 0 0
\(571\) −6.33948e6 + 1.09803e7i −0.813698 + 1.40937i 0.0965611 + 0.995327i \(0.469216\pi\)
−0.910259 + 0.414039i \(0.864118\pi\)
\(572\) 0 0
\(573\) −7.00326e6 9.78766e6i −0.891073 1.24535i
\(574\) 0 0
\(575\) −2.86191e6 −0.360983
\(576\) 0 0
\(577\) −1.51657e7 −1.89637 −0.948187 0.317712i \(-0.897086\pi\)
−0.948187 + 0.317712i \(0.897086\pi\)
\(578\) 0 0
\(579\) −112371. + 247541.i −0.0139302 + 0.0306867i
\(580\) 0 0
\(581\) 2.06075e6 3.56932e6i 0.253270 0.438677i
\(582\) 0 0
\(583\) 1.93665e6 + 3.35437e6i 0.235982 + 0.408733i
\(584\) 0 0
\(585\) 1.09158e7 + 1.24826e7i 1.31875 + 1.50805i
\(586\) 0 0
\(587\) 911702. + 1.57911e6i 0.109209 + 0.189155i 0.915450 0.402432i \(-0.131835\pi\)
−0.806241 + 0.591587i \(0.798502\pi\)
\(588\) 0 0
\(589\) 1.80327e6 3.12335e6i 0.214176 0.370965i
\(590\) 0 0
\(591\) −5.28623e6 + 516870.i −0.622555 + 0.0608713i
\(592\) 0 0
\(593\) 1.27957e7 1.49427 0.747133 0.664674i \(-0.231430\pi\)
0.747133 + 0.664674i \(0.231430\pi\)
\(594\) 0 0
\(595\) 7.23723e6 0.838069
\(596\) 0 0
\(597\) 220922. 21601.0i 0.0253689 0.00248049i
\(598\) 0 0
\(599\) 4.38212e6 7.59006e6i 0.499020 0.864327i −0.500980 0.865459i \(-0.667027\pi\)
0.999999 + 0.00113166i \(0.000360218\pi\)
\(600\) 0 0
\(601\) −834793. 1.44590e6i −0.0942741 0.163288i 0.815031 0.579417i \(-0.196720\pi\)
−0.909305 + 0.416129i \(0.863386\pi\)
\(602\) 0 0
\(603\) 4.20298e6 1.23242e7i 0.470722 1.38028i
\(604\) 0 0
\(605\) −407911. 706523.i −0.0453082 0.0784762i
\(606\) 0 0
\(607\) −5.08535e6 + 8.80809e6i −0.560208 + 0.970308i 0.437270 + 0.899330i \(0.355945\pi\)
−0.997478 + 0.0709782i \(0.977388\pi\)
\(608\) 0 0
\(609\) −5.22282e6 + 1.15053e7i −0.570639 + 1.25706i
\(610\) 0 0
\(611\) −2.57607e6 −0.279161
\(612\) 0 0
\(613\) 1.37829e7 1.48146 0.740730 0.671803i \(-0.234480\pi\)
0.740730 + 0.671803i \(0.234480\pi\)
\(614\) 0 0
\(615\) 7.98691e6 + 1.11624e7i 0.851513 + 1.19006i
\(616\) 0 0
\(617\) 6.05409e6 1.04860e7i 0.640230 1.10891i −0.345152 0.938547i \(-0.612173\pi\)
0.985381 0.170363i \(-0.0544942\pi\)
\(618\) 0 0
\(619\) −8.48665e6 1.46993e7i −0.890245 1.54195i −0.839581 0.543234i \(-0.817200\pi\)
−0.0506641 0.998716i \(-0.516134\pi\)
\(620\) 0 0
\(621\) −1.99935e6 + 8.49313e6i −0.208046 + 0.883769i
\(622\) 0 0
\(623\) 2.43352e6 + 4.21498e6i 0.251197 + 0.435087i
\(624\) 0 0
\(625\) 6.05231e6 1.04829e7i 0.619756 1.07345i
\(626\) 0 0
\(627\) 1.62508e6 + 2.27119e6i 0.165084 + 0.230720i
\(628\) 0 0
\(629\) 8.93574e6 0.900541
\(630\) 0 0
\(631\) −7.90092e6 −0.789958 −0.394979 0.918690i \(-0.629248\pi\)
−0.394979 + 0.918690i \(0.629248\pi\)
\(632\) 0 0
\(633\) 309923. 682728.i 0.0307428 0.0677233i
\(634\) 0 0
\(635\) 7.10637e6 1.23086e7i 0.699381 1.21136i
\(636\) 0 0
\(637\) 1.94514e6 + 3.36908e6i 0.189934 + 0.328975i
\(638\) 0 0
\(639\) 231248. 45657.9i 0.0224040 0.00442347i
\(640\) 0 0
\(641\) −5.33807e6 9.24581e6i −0.513144 0.888792i −0.999884 0.0152446i \(-0.995147\pi\)
0.486740 0.873547i \(-0.338186\pi\)
\(642\) 0 0
\(643\) 4.68885e6 8.12132e6i 0.447238 0.774639i −0.550967 0.834527i \(-0.685741\pi\)
0.998205 + 0.0598882i \(0.0190744\pi\)
\(644\) 0 0
\(645\) 2.16604e6 211788.i 0.205006 0.0200448i
\(646\) 0 0
\(647\) 9.44013e6 0.886579 0.443289 0.896379i \(-0.353811\pi\)
0.443289 + 0.896379i \(0.353811\pi\)
\(648\) 0 0
\(649\) −2.09805e6 −0.195526
\(650\) 0 0
\(651\) −1.37531e7 + 1.34473e6i −1.27188 + 0.124360i
\(652\) 0 0
\(653\) −7.44455e6 + 1.28943e7i −0.683212 + 1.18336i 0.290783 + 0.956789i \(0.406084\pi\)
−0.973995 + 0.226569i \(0.927249\pi\)
\(654\) 0 0
\(655\) 6.25543e6 + 1.08347e7i 0.569710 + 0.986766i
\(656\) 0 0
\(657\) −1.72601e7 + 3.40784e6i −1.56002 + 0.308011i
\(658\) 0 0
\(659\) −3.82391e6 6.62320e6i −0.343000 0.594093i 0.641989 0.766714i \(-0.278110\pi\)
−0.984988 + 0.172621i \(0.944776\pi\)
\(660\) 0 0
\(661\) 2.50269e6 4.33479e6i 0.222794 0.385891i −0.732861 0.680378i \(-0.761816\pi\)
0.955655 + 0.294487i \(0.0951489\pi\)
\(662\) 0 0
\(663\) 6.38075e6 1.40561e7i 0.563752 1.24189i
\(664\) 0 0
\(665\) 3.50592e6 0.307431
\(666\) 0 0
\(667\) −1.63502e7 −1.42301
\(668\) 0 0
\(669\) −7.11142e6 9.93882e6i −0.614315 0.858558i
\(670\) 0 0
\(671\) −6.59202e6 + 1.14177e7i −0.565214 + 0.978979i
\(672\) 0 0
\(673\) −1.07220e6 1.85710e6i −0.0912511 0.158051i 0.816787 0.576940i \(-0.195753\pi\)
−0.908038 + 0.418888i \(0.862420\pi\)
\(674\) 0 0
\(675\) 3.42824e6 + 3.22459e6i 0.289609 + 0.272405i
\(676\) 0 0
\(677\) 4.75463e6 + 8.23526e6i 0.398699 + 0.690567i 0.993566 0.113257i \(-0.0361285\pi\)
−0.594867 + 0.803824i \(0.702795\pi\)
\(678\) 0 0
\(679\) −2.50385e6 + 4.33679e6i −0.208417 + 0.360989i
\(680\) 0 0
\(681\) 5.04161e6 + 7.04608e6i 0.416583 + 0.582210i
\(682\) 0 0
\(683\) 5.47266e6 0.448897 0.224449 0.974486i \(-0.427942\pi\)
0.224449 + 0.974486i \(0.427942\pi\)
\(684\) 0 0
\(685\) 239205. 0.0194780
\(686\) 0 0
\(687\) 739023. 1.62799e6i 0.0597401 0.131601i
\(688\) 0 0
\(689\) 5.18570e6 8.98189e6i 0.416159 0.720808i
\(690\) 0 0
\(691\) 3.44084e6 + 5.95970e6i 0.274138 + 0.474821i 0.969917 0.243435i \(-0.0782742\pi\)
−0.695779 + 0.718255i \(0.744941\pi\)
\(692\) 0 0
\(693\) 3.45388e6 1.01277e7i 0.273196 0.801080i
\(694\) 0 0
\(695\) −3.99430e6 6.91832e6i −0.313674 0.543299i
\(696\) 0 0
\(697\) 6.38864e6 1.10655e7i 0.498112 0.862755i
\(698\) 0 0
\(699\) 1.72486e6 168651.i 0.133524 0.0130556i
\(700\) 0 0
\(701\) 5.19615e6 0.399380 0.199690 0.979859i \(-0.436006\pi\)
0.199690 + 0.979859i \(0.436006\pi\)
\(702\) 0 0
\(703\) 4.32872e6 0.330348
\(704\) 0 0
\(705\) −2.55793e6 + 250106.i −0.193827 + 0.0189518i
\(706\) 0 0
\(707\) 1.37676e6 2.38461e6i 0.103588 0.179419i
\(708\) 0 0
\(709\) −287410. 497809.i −0.0214727 0.0371918i 0.855089 0.518481i \(-0.173502\pi\)
−0.876562 + 0.481289i \(0.840169\pi\)
\(710\) 0 0
\(711\) 5.15042e6 + 5.88973e6i 0.382093 + 0.436939i
\(712\) 0 0
\(713\) −8.94074e6 1.54858e7i −0.658642 1.14080i
\(714\) 0 0
\(715\) 1.31574e7 2.27893e7i 0.962511 1.66712i
\(716\) 0 0
\(717\) 4.76206e6 1.04903e7i 0.345937 0.762063i
\(718\) 0 0
\(719\) 400906. 0.0289215 0.0144607 0.999895i \(-0.495397\pi\)
0.0144607 + 0.999895i \(0.495397\pi\)
\(720\) 0 0
\(721\) −1.56693e7 −1.12256
\(722\) 0 0
\(723\) −1.17048e7 1.63585e7i −0.832757 1.16385i
\(724\) 0 0
\(725\) −4.40969e6 + 7.63781e6i −0.311575 + 0.539664i
\(726\) 0 0
\(727\) 5.27154e6 + 9.13058e6i 0.369915 + 0.640711i 0.989552 0.144177i \(-0.0460535\pi\)
−0.619637 + 0.784889i \(0.712720\pi\)
\(728\) 0 0
\(729\) 1.19644e7 7.92108e6i 0.833822 0.552034i
\(730\) 0 0
\(731\) −1.01301e6 1.75458e6i −0.0701162 0.121445i
\(732\) 0 0
\(733\) −6.96868e6 + 1.20701e7i −0.479061 + 0.829758i −0.999712 0.0240119i \(-0.992356\pi\)
0.520651 + 0.853770i \(0.325689\pi\)
\(734\) 0 0
\(735\) 2.25854e6 + 3.15651e6i 0.154209 + 0.215520i
\(736\) 0 0
\(737\) −2.06638e7 −1.40133
\(738\) 0 0
\(739\) 9.88034e6 0.665519 0.332760 0.943012i \(-0.392020\pi\)
0.332760 + 0.943012i \(0.392020\pi\)
\(740\) 0 0
\(741\) 3.09102e6 6.80919e6i 0.206803 0.455565i
\(742\) 0 0
\(743\) −4.66695e6 + 8.08339e6i −0.310142 + 0.537182i −0.978393 0.206754i \(-0.933710\pi\)
0.668251 + 0.743936i \(0.267043\pi\)
\(744\) 0 0
\(745\) 2.47219e6 + 4.28195e6i 0.163189 + 0.282652i
\(746\) 0 0
\(747\) −5.77354e6 6.60230e6i −0.378565 0.432906i
\(748\) 0 0
\(749\) 9.59080e6 + 1.66117e7i 0.624669 + 1.08196i
\(750\) 0 0
\(751\) 1.43761e7 2.49001e7i 0.930124 1.61102i 0.147018 0.989134i \(-0.453032\pi\)
0.783106 0.621888i \(-0.213634\pi\)
\(752\) 0 0
\(753\) 2.00730e7 1.96267e6i 1.29011 0.126142i
\(754\) 0 0
\(755\) −2.37881e7 −1.51877
\(756\) 0 0
\(757\) −4.94587e6 −0.313691 −0.156846 0.987623i \(-0.550133\pi\)
−0.156846 + 0.987623i \(0.550133\pi\)
\(758\) 0 0
\(759\) 1.37807e7 1.34743e6i 0.868296 0.0848991i
\(760\) 0 0
\(761\) −4.56829e6 + 7.91251e6i −0.285951 + 0.495282i −0.972839 0.231481i \(-0.925643\pi\)
0.686888 + 0.726763i \(0.258976\pi\)
\(762\) 0 0
\(763\) −1.21179e6 2.09888e6i −0.0753555 0.130520i
\(764\) 0 0
\(765\) 4.97113e6 1.45766e7i 0.307115 0.900542i
\(766\) 0 0
\(767\) 2.80894e6 + 4.86523e6i 0.172407 + 0.298617i
\(768\) 0 0
\(769\) −8.26221e6 + 1.43106e7i −0.503826 + 0.872652i 0.496164 + 0.868229i \(0.334741\pi\)
−0.999990 + 0.00442349i \(0.998592\pi\)
\(770\) 0 0
\(771\) 4.02309e6 8.86244e6i 0.243738 0.536930i
\(772\) 0 0
\(773\) 1.01763e7 0.612550 0.306275 0.951943i \(-0.400917\pi\)
0.306275 + 0.951943i \(0.400917\pi\)
\(774\) 0 0
\(775\) −9.64536e6 −0.576852
\(776\) 0 0
\(777\) −9.65129e6 1.34885e7i −0.573499 0.801515i
\(778\) 0 0
\(779\) 3.09484e6 5.36042e6i 0.182724 0.316486i
\(780\) 0 0
\(781\) −187030. 323945.i −0.0109719 0.0190040i
\(782\) 0 0
\(783\) 1.95856e7 + 1.84222e7i 1.14165 + 1.07383i
\(784\) 0 0
\(785\) 1.58498e6 + 2.74527e6i 0.0918015 + 0.159005i
\(786\) 0 0
\(787\) −9.38173e6 + 1.62496e7i −0.539941 + 0.935205i 0.458966 + 0.888454i \(0.348220\pi\)
−0.998907 + 0.0467507i \(0.985113\pi\)
\(788\) 0 0
\(789\) 1.05676e7 + 1.47691e7i 0.604342 + 0.844620i
\(790\) 0 0
\(791\) 3.29343e6 0.187158
\(792\) 0 0
\(793\) 3.53025e7 1.99353
\(794\) 0 0
\(795\) 4.27714e6 9.42210e6i 0.240014 0.528725i
\(796\) 0 0
\(797\) 1.23982e6 2.14744e6i 0.0691376 0.119750i −0.829384 0.558678i \(-0.811309\pi\)
0.898522 + 0.438929i \(0.144642\pi\)
\(798\) 0 0
\(799\) 1.19628e6 + 2.07202e6i 0.0662929 + 0.114823i
\(800\) 0 0
\(801\) 1.01610e7 2.00620e6i 0.559573 0.110483i
\(802\) 0 0
\(803\) 1.39597e7 + 2.41788e7i 0.763987 + 1.32326i
\(804\) 0 0
\(805\) 8.69130e6 1.50538e7i 0.472711 0.818759i
\(806\) 0 0
\(807\) −2.46605e7 + 2.41122e6i −1.33296 + 0.130332i
\(808\) 0 0
\(809\) −2.50880e7 −1.34770 −0.673852 0.738867i \(-0.735361\pi\)
−0.673852 + 0.738867i \(0.735361\pi\)
\(810\) 0 0
\(811\) 4.28465e6 0.228751 0.114376 0.993438i \(-0.463513\pi\)
0.114376 + 0.993438i \(0.463513\pi\)
\(812\) 0 0
\(813\) −1.51713e7 + 1.48339e6i −0.804999 + 0.0787101i
\(814\) 0 0
\(815\) −1.19308e7 + 2.06647e7i −0.629179 + 1.08977i
\(816\) 0 0
\(817\) −490728. 849967.i −0.0257209 0.0445499i
\(818\) 0 0
\(819\) −2.81095e7 + 5.54996e6i −1.46434 + 0.289121i
\(820\) 0 0
\(821\) −1.01563e7 1.75913e7i −0.525871 0.910836i −0.999546 0.0301356i \(-0.990406\pi\)
0.473675 0.880700i \(-0.342927\pi\)
\(822\) 0 0
\(823\) −6.58313e6 + 1.14023e7i −0.338792 + 0.586804i −0.984206 0.177029i \(-0.943351\pi\)
0.645414 + 0.763833i \(0.276685\pi\)
\(824\) 0 0
\(825\) 3.08726e6 6.80092e6i 0.157920 0.347883i
\(826\) 0 0
\(827\) −2.82859e7 −1.43816 −0.719079 0.694928i \(-0.755436\pi\)
−0.719079 + 0.694928i \(0.755436\pi\)
\(828\) 0 0
\(829\) 1.36608e7 0.690381 0.345190 0.938533i \(-0.387814\pi\)
0.345190 + 0.938533i \(0.387814\pi\)
\(830\) 0 0
\(831\) −1.17059e7 1.63601e7i −0.588036 0.821832i
\(832\) 0 0
\(833\) 1.80658e6 3.12909e6i 0.0902080 0.156245i
\(834\) 0 0
\(835\) −3.84845e6 6.66571e6i −0.191016 0.330849i
\(836\) 0 0
\(837\) −6.73831e6 + 2.86240e7i −0.332458 + 1.41227i
\(838\) 0 0
\(839\) −75641.6 131015.i −0.00370984 0.00642564i 0.864165 0.503209i \(-0.167848\pi\)
−0.867874 + 0.496784i \(0.834514\pi\)
\(840\) 0 0
\(841\) −1.49371e7 + 2.58718e7i −0.728244 + 1.26135i
\(842\) 0 0
\(843\) 1.51242e7 + 2.11374e7i 0.733000 + 1.02443i
\(844\) 0 0
\(845\) −4.59249e7 −2.21262
\(846\) 0 0
\(847\) 1.40965e6 0.0675152
\(848\) 0 0
\(849\) −7.27561e6 + 1.60274e7i −0.346418 + 0.763123i
\(850\) 0 0
\(851\) 1.07311e7 1.85868e7i 0.507948 0.879792i
\(852\) 0 0
\(853\) 1.38831e7 + 2.40462e7i 0.653301 + 1.13155i 0.982317 + 0.187226i \(0.0599498\pi\)
−0.329015 + 0.944325i \(0.606717\pi\)
\(854\) 0 0
\(855\) 2.40816e6 7.06134e6i 0.112660 0.330348i
\(856\) 0 0
\(857\) 1.76136e7 + 3.05077e7i 0.819212 + 1.41892i 0.906263 + 0.422713i \(0.138922\pi\)
−0.0870512 + 0.996204i \(0.527744\pi\)
\(858\) 0 0
\(859\) −2.02341e7 + 3.50464e7i −0.935622 + 1.62054i −0.162100 + 0.986774i \(0.551827\pi\)
−0.773522 + 0.633770i \(0.781507\pi\)
\(860\) 0 0
\(861\) −2.36036e7 + 2.30788e6i −1.08510 + 0.106097i
\(862\) 0 0
\(863\) 1.96865e7 0.899789 0.449895 0.893082i \(-0.351462\pi\)
0.449895 + 0.893082i \(0.351462\pi\)
\(864\) 0 0
\(865\) −6.84170e6 −0.310902
\(866\) 0 0
\(867\) 7.75937e6 758686.i 0.350573 0.0342779i
\(868\) 0 0
\(869\) 6.20812e6 1.07528e7i 0.278876 0.483027i
\(870\) 0 0
\(871\) 2.76654e7 + 4.79178e7i 1.23564 + 2.14019i
\(872\) 0 0
\(873\) 7.01496e6 + 8.02191e6i 0.311523 + 0.356240i
\(874\) 0 0
\(875\) 7.10324e6 + 1.23032e7i 0.313644 + 0.543247i
\(876\) 0 0
\(877\) −1.31221e7 + 2.27282e7i −0.576109 + 0.997850i 0.419811 + 0.907611i \(0.362096\pi\)
−0.995920 + 0.0902384i \(0.971237\pi\)
\(878\) 0 0
\(879\) 1.32498e7 2.91880e7i 0.578414 1.27419i
\(880\) 0 0
\(881\) −1.29423e7 −0.561786 −0.280893 0.959739i \(-0.590631\pi\)
−0.280893 + 0.959739i \(0.590631\pi\)
\(882\) 0 0
\(883\) −3.39097e6 −0.146360 −0.0731800 0.997319i \(-0.523315\pi\)
−0.0731800 + 0.997319i \(0.523315\pi\)
\(884\) 0 0
\(885\) 3.26152e6 + 4.55825e6i 0.139979 + 0.195632i
\(886\) 0 0
\(887\) 3.83796e6 6.64753e6i 0.163791 0.283695i −0.772434 0.635095i \(-0.780961\pi\)
0.936225 + 0.351400i \(0.114294\pi\)
\(888\) 0 0
\(889\) 1.22790e7 + 2.12678e7i 0.521085 + 0.902545i
\(890\) 0 0
\(891\) −1.80259e7 1.39130e7i −0.760682 0.587122i
\(892\) 0 0
\(893\) 579513. + 1.00375e6i 0.0243184 + 0.0421207i
\(894\) 0 0
\(895\) 2.60849e6 4.51803e6i 0.108851 0.188535i
\(896\) 0 0
\(897\) −2.15747e7 3.01525e7i −0.895290 1.25125i
\(898\) 0 0
\(899\) −5.51042e7 −2.27398
\(900\) 0 0
\(901\) −9.63260e6 −0.395304
\(902\) 0 0
\(903\) −1.55441e6 + 3.42421e6i −0.0634377 + 0.139747i
\(904\) 0 0
\(905\) 1.93670e7 3.35446e7i 0.786033 1.36145i
\(906\) 0 0
\(907\) 5.44435e6 + 9.42990e6i 0.219750 + 0.380618i 0.954731 0.297469i \(-0.0961426\pi\)
−0.734982 + 0.678087i \(0.762809\pi\)
\(908\) 0 0
\(909\) −3.85722e6 4.41090e6i −0.154834 0.177059i
\(910\) 0 0
\(911\) −90239.2 156299.i −0.00360246 0.00623964i 0.864219 0.503117i \(-0.167813\pi\)
−0.867821 + 0.496877i \(0.834480\pi\)
\(912\) 0 0
\(913\) −6.95920e6 + 1.20537e7i −0.276301 + 0.478568i
\(914\) 0 0
\(915\) 3.50539e7 3.42745e6i 1.38415 0.135338i
\(916\) 0 0
\(917\) −2.16173e7 −0.848942
\(918\) 0 0
\(919\) 2.24831e7 0.878148 0.439074 0.898451i \(-0.355307\pi\)
0.439074 + 0.898451i \(0.355307\pi\)
\(920\) 0 0
\(921\) 2.36051e7 2.30803e6i 0.916973 0.0896586i
\(922\) 0 0
\(923\) −500804. + 867418.i −0.0193492 + 0.0335138i
\(924\) 0 0
\(925\) −5.78840e6 1.00258e7i −0.222436 0.385270i
\(926\) 0 0
\(927\) −1.07630e7 + 3.15598e7i −0.411371 + 1.20625i
\(928\) 0 0
\(929\) 2.06620e7 + 3.57877e7i 0.785477 + 1.36049i 0.928714 + 0.370797i \(0.120916\pi\)
−0.143237 + 0.989688i \(0.545751\pi\)
\(930\) 0 0
\(931\) 875159. 1.51582e6i 0.0330912 0.0573157i
\(932\) 0 0
\(933\) 1.74516e7 3.84441e7i 0.656343 1.44586i
\(934\) 0 0
\(935\) −2.44403e7 −0.914278
\(936\) 0 0
\(937\) 2.56470e7 0.954305 0.477153 0.878820i \(-0.341669\pi\)
0.477153 + 0.878820i \(0.341669\pi\)
\(938\) 0 0
\(939\) −5.90670e6 8.25512e6i −0.218615 0.305534i
\(940\) 0 0
\(941\) −8.99880e6 + 1.55864e7i −0.331292 + 0.573814i −0.982765 0.184857i \(-0.940818\pi\)
0.651474 + 0.758671i \(0.274151\pi\)
\(942\) 0 0
\(943\) −1.53445e7 2.65774e7i −0.561917 0.973269i
\(944\) 0 0
\(945\) −2.73727e7 + 8.23997e6i −0.997098 + 0.300155i
\(946\) 0 0
\(947\) −2.25398e7 3.90400e7i −0.816723 1.41461i −0.908084 0.418788i \(-0.862455\pi\)
0.0913614 0.995818i \(-0.470878\pi\)
\(948\) 0 0
\(949\) 3.73793e7 6.47429e7i 1.34731 2.33360i
\(950\) 0 0
\(951\) −1.05323e6 1.47199e6i −0.0377636 0.0527780i
\(952\) 0 0
\(953\) 2.21374e7 0.789577 0.394788 0.918772i \(-0.370818\pi\)
0.394788 + 0.918772i \(0.370818\pi\)
\(954\) 0 0
\(955\) 5.10225e7 1.81031
\(956\) 0 0
\(957\) 1.76376e7 3.88539e7i 0.622530 1.37137i
\(958\) 0 0
\(959\) −206660. + 357945.i −0.00725619 + 0.0125681i
\(960\) 0 0
\(961\) −1.58180e7 2.73975e7i −0.552512 0.956979i
\(962\) 0 0
\(963\) 4.00458e7 7.90668e6i 1.39153 0.274744i
\(964\) 0 0
\(965\) −576255. 998103.i −0.0199203 0.0345030i
\(966\) 0 0
\(967\) −9.81614e6 + 1.70020e7i −0.337578 + 0.584703i −0.983977 0.178297i \(-0.942941\pi\)
0.646398 + 0.763000i \(0.276274\pi\)
\(968\) 0 0
\(969\) −6.91229e6 + 675861.i −0.236490 + 0.0231232i
\(970\) 0 0
\(971\) 3.46539e7 1.17952 0.589758 0.807580i \(-0.299223\pi\)
0.589758 + 0.807580i \(0.299223\pi\)
\(972\) 0 0
\(973\) 1.38034e7 0.467415
\(974\) 0 0
\(975\) −1.99042e7 + 1.94616e6i −0.670552 + 0.0655644i
\(976\) 0 0
\(977\) −1.34006e7 + 2.32106e7i −0.449148 + 0.777947i −0.998331 0.0577553i \(-0.981606\pi\)
0.549183 + 0.835702i \(0.314939\pi\)
\(978\) 0 0
\(979\) −8.21808e6 1.42341e7i −0.274040 0.474651i
\(980\) 0 0
\(981\) −5.05975e6 + 999002.i −0.167864 + 0.0331431i
\(982\) 0 0
\(983\) −1.19040e7 2.06183e7i −0.392924 0.680565i 0.599910 0.800068i \(-0.295203\pi\)
−0.992834 + 0.119503i \(0.961870\pi\)
\(984\) 0 0
\(985\) 1.12589e7 1.95009e7i 0.369746 0.640419i
\(986\) 0 0
\(987\) 1.83564e6 4.04374e6i 0.0599785 0.132126i
\(988\) 0 0
\(989\) −4.86614e6 −0.158195
\(990\) 0 0
\(991\) 2.37156e7 0.767096 0.383548 0.923521i \(-0.374702\pi\)
0.383548 + 0.923521i \(0.374702\pi\)
\(992\) 0 0
\(993\) −2.88145e6 4.02708e6i −0.0927338 0.129603i
\(994\) 0 0
\(995\) −470529. + 814980.i −0.0150671 + 0.0260969i
\(996\) 0 0
\(997\) 2.04170e7 + 3.53633e7i 0.650511 + 1.12672i 0.982999 + 0.183610i \(0.0587785\pi\)
−0.332488 + 0.943107i \(0.607888\pi\)
\(998\) 0 0
\(999\) −3.37968e7 + 1.01738e7i −1.07143 + 0.322530i
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 144.6.i.b.49.1 6
3.2 odd 2 432.6.i.b.145.1 6
4.3 odd 2 18.6.c.b.13.3 yes 6
9.2 odd 6 432.6.i.b.289.1 6
9.7 even 3 inner 144.6.i.b.97.1 6
12.11 even 2 54.6.c.b.37.1 6
36.7 odd 6 18.6.c.b.7.3 6
36.11 even 6 54.6.c.b.19.1 6
36.23 even 6 162.6.a.i.1.3 3
36.31 odd 6 162.6.a.j.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.6.c.b.7.3 6 36.7 odd 6
18.6.c.b.13.3 yes 6 4.3 odd 2
54.6.c.b.19.1 6 36.11 even 6
54.6.c.b.37.1 6 12.11 even 2
144.6.i.b.49.1 6 1.1 even 1 trivial
144.6.i.b.97.1 6 9.7 even 3 inner
162.6.a.i.1.3 3 36.23 even 6
162.6.a.j.1.1 3 36.31 odd 6
432.6.i.b.145.1 6 3.2 odd 2
432.6.i.b.289.1 6 9.2 odd 6