Properties

 Label 1008.6.a.i.1.1 Level $1008$ Weight $6$ Character 1008.1 Self dual yes Analytic conductor $161.667$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,6,Mod(1,1008)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1008.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 1008.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$161.666890371$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1008.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-26.0000 q^{5} +49.0000 q^{7} +O(q^{10})$$ $$q-26.0000 q^{5} +49.0000 q^{7} -470.000 q^{11} +642.000 q^{13} +1010.00 q^{17} -1532.00 q^{19} +430.000 q^{23} -2449.00 q^{25} +6736.00 q^{29} -2268.00 q^{31} -1274.00 q^{35} -9574.00 q^{37} +14406.0 q^{41} +9748.00 q^{43} -17004.0 q^{47} +2401.00 q^{49} +7596.00 q^{53} +12220.0 q^{55} +18908.0 q^{59} -36762.0 q^{61} -16692.0 q^{65} +36788.0 q^{67} -18326.0 q^{71} +36382.0 q^{73} -23030.0 q^{77} -29784.0 q^{79} +28240.0 q^{83} -26260.0 q^{85} -75954.0 q^{89} +31458.0 q^{91} +39832.0 q^{95} -80690.0 q^{97} +O(q^{100})$$

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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −26.0000 −0.465102 −0.232551 0.972584i $$-0.574707\pi$$
−0.232551 + 0.972584i $$0.574707\pi$$
$$6$$ 0 0
$$7$$ 49.0000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −470.000 −1.17116 −0.585580 0.810615i $$-0.699133\pi$$
−0.585580 + 0.810615i $$0.699133\pi$$
$$12$$ 0 0
$$13$$ 642.000 1.05360 0.526801 0.849989i $$-0.323391\pi$$
0.526801 + 0.849989i $$0.323391\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1010.00 0.847616 0.423808 0.905752i $$-0.360693\pi$$
0.423808 + 0.905752i $$0.360693\pi$$
$$18$$ 0 0
$$19$$ −1532.00 −0.973587 −0.486793 0.873517i $$-0.661834\pi$$
−0.486793 + 0.873517i $$0.661834\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 430.000 0.169492 0.0847459 0.996403i $$-0.472992\pi$$
0.0847459 + 0.996403i $$0.472992\pi$$
$$24$$ 0 0
$$25$$ −2449.00 −0.783680
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 6736.00 1.48733 0.743665 0.668553i $$-0.233086\pi$$
0.743665 + 0.668553i $$0.233086\pi$$
$$30$$ 0 0
$$31$$ −2268.00 −0.423876 −0.211938 0.977283i $$-0.567977\pi$$
−0.211938 + 0.977283i $$0.567977\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1274.00 −0.175792
$$36$$ 0 0
$$37$$ −9574.00 −1.14971 −0.574856 0.818255i $$-0.694942\pi$$
−0.574856 + 0.818255i $$0.694942\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 14406.0 1.33839 0.669197 0.743085i $$-0.266638\pi$$
0.669197 + 0.743085i $$0.266638\pi$$
$$42$$ 0 0
$$43$$ 9748.00 0.803978 0.401989 0.915644i $$-0.368319\pi$$
0.401989 + 0.915644i $$0.368319\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −17004.0 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 7596.00 0.371446 0.185723 0.982602i $$-0.440537\pi$$
0.185723 + 0.982602i $$0.440537\pi$$
$$54$$ 0 0
$$55$$ 12220.0 0.544709
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 18908.0 0.707157 0.353578 0.935405i $$-0.384965\pi$$
0.353578 + 0.935405i $$0.384965\pi$$
$$60$$ 0 0
$$61$$ −36762.0 −1.26495 −0.632477 0.774579i $$-0.717962\pi$$
−0.632477 + 0.774579i $$0.717962\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −16692.0 −0.490033
$$66$$ 0 0
$$67$$ 36788.0 1.00120 0.500598 0.865680i $$-0.333113\pi$$
0.500598 + 0.865680i $$0.333113\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −18326.0 −0.431441 −0.215721 0.976455i $$-0.569210\pi$$
−0.215721 + 0.976455i $$0.569210\pi$$
$$72$$ 0 0
$$73$$ 36382.0 0.799060 0.399530 0.916720i $$-0.369173\pi$$
0.399530 + 0.916720i $$0.369173\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −23030.0 −0.442657
$$78$$ 0 0
$$79$$ −29784.0 −0.536927 −0.268464 0.963290i $$-0.586516\pi$$
−0.268464 + 0.963290i $$0.586516\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 28240.0 0.449955 0.224978 0.974364i $$-0.427769\pi$$
0.224978 + 0.974364i $$0.427769\pi$$
$$84$$ 0 0
$$85$$ −26260.0 −0.394228
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −75954.0 −1.01643 −0.508213 0.861232i $$-0.669694\pi$$
−0.508213 + 0.861232i $$0.669694\pi$$
$$90$$ 0 0
$$91$$ 31458.0 0.398224
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 39832.0 0.452817
$$96$$ 0 0
$$97$$ −80690.0 −0.870744 −0.435372 0.900251i $$-0.643383\pi$$
−0.435372 + 0.900251i $$0.643383\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 31306.0 0.305368 0.152684 0.988275i $$-0.451208\pi$$
0.152684 + 0.988275i $$0.451208\pi$$
$$102$$ 0 0
$$103$$ −102908. −0.955776 −0.477888 0.878421i $$-0.658598\pi$$
−0.477888 + 0.878421i $$0.658598\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 172482. 1.45641 0.728206 0.685358i $$-0.240354\pi$$
0.728206 + 0.685358i $$0.240354\pi$$
$$108$$ 0 0
$$109$$ −135470. −1.09214 −0.546068 0.837741i $$-0.683876\pi$$
−0.546068 + 0.837741i $$0.683876\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −135632. −0.999231 −0.499616 0.866247i $$-0.666525\pi$$
−0.499616 + 0.866247i $$0.666525\pi$$
$$114$$ 0 0
$$115$$ −11180.0 −0.0788310
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 49490.0 0.320369
$$120$$ 0 0
$$121$$ 59849.0 0.371615
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 144924. 0.829593
$$126$$ 0 0
$$127$$ 275976. 1.51832 0.759158 0.650907i $$-0.225611\pi$$
0.759158 + 0.650907i $$0.225611\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −50488.0 −0.257045 −0.128523 0.991707i $$-0.541024\pi$$
−0.128523 + 0.991707i $$0.541024\pi$$
$$132$$ 0 0
$$133$$ −75068.0 −0.367981
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 137212. 0.624584 0.312292 0.949986i $$-0.398903\pi$$
0.312292 + 0.949986i $$0.398903\pi$$
$$138$$ 0 0
$$139$$ −21040.0 −0.0923653 −0.0461826 0.998933i $$-0.514706\pi$$
−0.0461826 + 0.998933i $$0.514706\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −301740. −1.23394
$$144$$ 0 0
$$145$$ −175136. −0.691760
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 240468. 0.887343 0.443672 0.896189i $$-0.353676\pi$$
0.443672 + 0.896189i $$0.353676\pi$$
$$150$$ 0 0
$$151$$ −325048. −1.16013 −0.580063 0.814572i $$-0.696972\pi$$
−0.580063 + 0.814572i $$0.696972\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 58968.0 0.197146
$$156$$ 0 0
$$157$$ 537734. 1.74108 0.870539 0.492099i $$-0.163770\pi$$
0.870539 + 0.492099i $$0.163770\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 21070.0 0.0640619
$$162$$ 0 0
$$163$$ −403748. −1.19026 −0.595129 0.803630i $$-0.702899\pi$$
−0.595129 + 0.803630i $$0.702899\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −702412. −1.94895 −0.974475 0.224496i $$-0.927927\pi$$
−0.974475 + 0.224496i $$0.927927\pi$$
$$168$$ 0 0
$$169$$ 40871.0 0.110077
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −726926. −1.84661 −0.923304 0.384069i $$-0.874523\pi$$
−0.923304 + 0.384069i $$0.874523\pi$$
$$174$$ 0 0
$$175$$ −120001. −0.296203
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −722418. −1.68522 −0.842609 0.538526i $$-0.818981\pi$$
−0.842609 + 0.538526i $$0.818981\pi$$
$$180$$ 0 0
$$181$$ −333486. −0.756626 −0.378313 0.925678i $$-0.623496\pi$$
−0.378313 + 0.925678i $$0.623496\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 248924. 0.534734
$$186$$ 0 0
$$187$$ −474700. −0.992694
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 669138. 1.32719 0.663594 0.748093i $$-0.269030\pi$$
0.663594 + 0.748093i $$0.269030\pi$$
$$192$$ 0 0
$$193$$ −115066. −0.222359 −0.111179 0.993800i $$-0.535463\pi$$
−0.111179 + 0.993800i $$0.535463\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −213364. −0.391702 −0.195851 0.980634i $$-0.562747\pi$$
−0.195851 + 0.980634i $$0.562747\pi$$
$$198$$ 0 0
$$199$$ −795296. −1.42363 −0.711813 0.702369i $$-0.752126\pi$$
−0.711813 + 0.702369i $$0.752126\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 330064. 0.562158
$$204$$ 0 0
$$205$$ −374556. −0.622490
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 720040. 1.14023
$$210$$ 0 0
$$211$$ −218468. −0.337817 −0.168909 0.985632i $$-0.554024\pi$$
−0.168909 + 0.985632i $$0.554024\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −253448. −0.373932
$$216$$ 0 0
$$217$$ −111132. −0.160210
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 648420. 0.893050
$$222$$ 0 0
$$223$$ −656888. −0.884564 −0.442282 0.896876i $$-0.645831\pi$$
−0.442282 + 0.896876i $$0.645831\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 971532. 1.25139 0.625695 0.780068i $$-0.284816\pi$$
0.625695 + 0.780068i $$0.284816\pi$$
$$228$$ 0 0
$$229$$ −459350. −0.578835 −0.289418 0.957203i $$-0.593462\pi$$
−0.289418 + 0.957203i $$0.593462\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −1.23704e6 −1.49277 −0.746384 0.665515i $$-0.768212\pi$$
−0.746384 + 0.665515i $$0.768212\pi$$
$$234$$ 0 0
$$235$$ 442104. 0.522222
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 1.53433e6 1.73749 0.868746 0.495258i $$-0.164926\pi$$
0.868746 + 0.495258i $$0.164926\pi$$
$$240$$ 0 0
$$241$$ −1.41990e6 −1.57476 −0.787380 0.616468i $$-0.788563\pi$$
−0.787380 + 0.616468i $$0.788563\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −62426.0 −0.0664432
$$246$$ 0 0
$$247$$ −983544. −1.02577
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1.61197e6 −1.61500 −0.807501 0.589866i $$-0.799181\pi$$
−0.807501 + 0.589866i $$0.799181\pi$$
$$252$$ 0 0
$$253$$ −202100. −0.198502
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −851442. −0.804123 −0.402061 0.915613i $$-0.631706\pi$$
−0.402061 + 0.915613i $$0.631706\pi$$
$$258$$ 0 0
$$259$$ −469126. −0.434550
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.06738e6 0.951548 0.475774 0.879568i $$-0.342168\pi$$
0.475774 + 0.879568i $$0.342168\pi$$
$$264$$ 0 0
$$265$$ −197496. −0.172760
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 871870. 0.734634 0.367317 0.930096i $$-0.380276\pi$$
0.367317 + 0.930096i $$0.380276\pi$$
$$270$$ 0 0
$$271$$ 1.40737e6 1.16409 0.582044 0.813157i $$-0.302253\pi$$
0.582044 + 0.813157i $$0.302253\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.15103e6 0.917814
$$276$$ 0 0
$$277$$ 888782. 0.695979 0.347989 0.937499i $$-0.386865\pi$$
0.347989 + 0.937499i $$0.386865\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −2.00038e6 −1.51129 −0.755643 0.654984i $$-0.772676\pi$$
−0.755643 + 0.654984i $$0.772676\pi$$
$$282$$ 0 0
$$283$$ −150460. −0.111675 −0.0558374 0.998440i $$-0.517783\pi$$
−0.0558374 + 0.998440i $$0.517783\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 705894. 0.505865
$$288$$ 0 0
$$289$$ −399757. −0.281547
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 2.73669e6 1.86233 0.931165 0.364599i $$-0.118794\pi$$
0.931165 + 0.364599i $$0.118794\pi$$
$$294$$ 0 0
$$295$$ −491608. −0.328900
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 276060. 0.178577
$$300$$ 0 0
$$301$$ 477652. 0.303875
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 955812. 0.588333
$$306$$ 0 0
$$307$$ −714436. −0.432631 −0.216315 0.976324i $$-0.569404\pi$$
−0.216315 + 0.976324i $$0.569404\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.34019e6 −0.785714 −0.392857 0.919599i $$-0.628513\pi$$
−0.392857 + 0.919599i $$0.628513\pi$$
$$312$$ 0 0
$$313$$ −2.59201e6 −1.49547 −0.747733 0.664000i $$-0.768858\pi$$
−0.747733 + 0.664000i $$0.768858\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1.54753e6 −0.864951 −0.432475 0.901646i $$-0.642360\pi$$
−0.432475 + 0.901646i $$0.642360\pi$$
$$318$$ 0 0
$$319$$ −3.16592e6 −1.74190
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1.54732e6 −0.825228
$$324$$ 0 0
$$325$$ −1.57226e6 −0.825687
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −833196. −0.424382
$$330$$ 0 0
$$331$$ 672892. 0.337579 0.168789 0.985652i $$-0.446014\pi$$
0.168789 + 0.985652i $$0.446014\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −956488. −0.465658
$$336$$ 0 0
$$337$$ −3.00127e6 −1.43956 −0.719780 0.694202i $$-0.755757\pi$$
−0.719780 + 0.694202i $$0.755757\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.06596e6 0.496427
$$342$$ 0 0
$$343$$ 117649. 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −3.29114e6 −1.46731 −0.733656 0.679521i $$-0.762188\pi$$
−0.733656 + 0.679521i $$0.762188\pi$$
$$348$$ 0 0
$$349$$ −2.96059e6 −1.30111 −0.650557 0.759458i $$-0.725464\pi$$
−0.650557 + 0.759458i $$0.725464\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.65899e6 0.708611 0.354306 0.935130i $$-0.384717\pi$$
0.354306 + 0.935130i $$0.384717\pi$$
$$354$$ 0 0
$$355$$ 476476. 0.200664
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −2.33841e6 −0.957603 −0.478801 0.877923i $$-0.658929\pi$$
−0.478801 + 0.877923i $$0.658929\pi$$
$$360$$ 0 0
$$361$$ −129075. −0.0521284
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −945932. −0.371645
$$366$$ 0 0
$$367$$ 1.77875e6 0.689367 0.344683 0.938719i $$-0.387986\pi$$
0.344683 + 0.938719i $$0.387986\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 372204. 0.140393
$$372$$ 0 0
$$373$$ −1.38079e6 −0.513874 −0.256937 0.966428i $$-0.582713\pi$$
−0.256937 + 0.966428i $$0.582713\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 4.32451e6 1.56705
$$378$$ 0 0
$$379$$ −4.18575e6 −1.49684 −0.748419 0.663226i $$-0.769187\pi$$
−0.748419 + 0.663226i $$0.769187\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 586216. 0.204202 0.102101 0.994774i $$-0.467443\pi$$
0.102101 + 0.994774i $$0.467443\pi$$
$$384$$ 0 0
$$385$$ 598780. 0.205881
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1.50212e6 −0.503304 −0.251652 0.967818i $$-0.580974\pi$$
−0.251652 + 0.967818i $$0.580974\pi$$
$$390$$ 0 0
$$391$$ 434300. 0.143664
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 774384. 0.249726
$$396$$ 0 0
$$397$$ −2.01988e6 −0.643205 −0.321603 0.946875i $$-0.604222\pi$$
−0.321603 + 0.946875i $$0.604222\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −2.67558e6 −0.830916 −0.415458 0.909612i $$-0.636379\pi$$
−0.415458 + 0.909612i $$0.636379\pi$$
$$402$$ 0 0
$$403$$ −1.45606e6 −0.446597
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 4.49978e6 1.34650
$$408$$ 0 0
$$409$$ −1.32378e6 −0.391297 −0.195649 0.980674i $$-0.562681\pi$$
−0.195649 + 0.980674i $$0.562681\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 926492. 0.267280
$$414$$ 0 0
$$415$$ −734240. −0.209275
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 451212. 0.125558 0.0627792 0.998027i $$-0.480004\pi$$
0.0627792 + 0.998027i $$0.480004\pi$$
$$420$$ 0 0
$$421$$ −3.88005e6 −1.06692 −0.533460 0.845825i $$-0.679109\pi$$
−0.533460 + 0.845825i $$0.679109\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −2.47349e6 −0.664260
$$426$$ 0 0
$$427$$ −1.80134e6 −0.478107
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −5.31469e6 −1.37811 −0.689056 0.724708i $$-0.741975\pi$$
−0.689056 + 0.724708i $$0.741975\pi$$
$$432$$ 0 0
$$433$$ 2.68951e6 0.689373 0.344686 0.938718i $$-0.387985\pi$$
0.344686 + 0.938718i $$0.387985\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −658760. −0.165015
$$438$$ 0 0
$$439$$ 643392. 0.159336 0.0796681 0.996821i $$-0.474614\pi$$
0.0796681 + 0.996821i $$0.474614\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 2.53601e6 0.613961 0.306981 0.951716i $$-0.400681\pi$$
0.306981 + 0.951716i $$0.400681\pi$$
$$444$$ 0 0
$$445$$ 1.97480e6 0.472742
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 4.79178e6 1.12171 0.560856 0.827913i $$-0.310472\pi$$
0.560856 + 0.827913i $$0.310472\pi$$
$$450$$ 0 0
$$451$$ −6.77082e6 −1.56747
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −817908. −0.185215
$$456$$ 0 0
$$457$$ 6.39833e6 1.43310 0.716549 0.697537i $$-0.245721\pi$$
0.716549 + 0.697537i $$0.245721\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −8.59151e6 −1.88286 −0.941428 0.337214i $$-0.890516\pi$$
−0.941428 + 0.337214i $$0.890516\pi$$
$$462$$ 0 0
$$463$$ 1.66558e6 0.361089 0.180544 0.983567i $$-0.442214\pi$$
0.180544 + 0.983567i $$0.442214\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 7.88124e6 1.67225 0.836127 0.548536i $$-0.184815\pi$$
0.836127 + 0.548536i $$0.184815\pi$$
$$468$$ 0 0
$$469$$ 1.80261e6 0.378417
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −4.58156e6 −0.941587
$$474$$ 0 0
$$475$$ 3.75187e6 0.762981
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 2.25396e6 0.448857 0.224429 0.974491i $$-0.427948\pi$$
0.224429 + 0.974491i $$0.427948\pi$$
$$480$$ 0 0
$$481$$ −6.14651e6 −1.21134
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 2.09794e6 0.404985
$$486$$ 0 0
$$487$$ −6.29194e6 −1.20216 −0.601080 0.799189i $$-0.705263\pi$$
−0.601080 + 0.799189i $$0.705263\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 460542. 0.0862116 0.0431058 0.999071i $$-0.486275\pi$$
0.0431058 + 0.999071i $$0.486275\pi$$
$$492$$ 0 0
$$493$$ 6.80336e6 1.26068
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −897974. −0.163070
$$498$$ 0 0
$$499$$ −9.33924e6 −1.67904 −0.839519 0.543331i $$-0.817163\pi$$
−0.839519 + 0.543331i $$0.817163\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 2.89982e6 0.511036 0.255518 0.966804i $$-0.417754\pi$$
0.255518 + 0.966804i $$0.417754\pi$$
$$504$$ 0 0
$$505$$ −813956. −0.142028
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 1.97477e6 0.337849 0.168925 0.985629i $$-0.445971\pi$$
0.168925 + 0.985629i $$0.445971\pi$$
$$510$$ 0 0
$$511$$ 1.78272e6 0.302016
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 2.67561e6 0.444533
$$516$$ 0 0
$$517$$ 7.99188e6 1.31499
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −4.31576e6 −0.696567 −0.348283 0.937389i $$-0.613235\pi$$
−0.348283 + 0.937389i $$0.613235\pi$$
$$522$$ 0 0
$$523$$ 1.01477e7 1.62223 0.811116 0.584885i $$-0.198860\pi$$
0.811116 + 0.584885i $$0.198860\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.29068e6 −0.359284
$$528$$ 0 0
$$529$$ −6.25144e6 −0.971273
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 9.24865e6 1.41013
$$534$$ 0 0
$$535$$ −4.48453e6 −0.677380
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −1.12847e6 −0.167309
$$540$$ 0 0
$$541$$ −1.57718e6 −0.231679 −0.115840 0.993268i $$-0.536956\pi$$
−0.115840 + 0.993268i $$0.536956\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 3.52222e6 0.507955
$$546$$ 0 0
$$547$$ 6.24229e6 0.892022 0.446011 0.895027i $$-0.352844\pi$$
0.446011 + 0.895027i $$0.352844\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1.03196e7 −1.44804
$$552$$ 0 0
$$553$$ −1.45942e6 −0.202939
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −8.36277e6 −1.14212 −0.571061 0.820908i $$-0.693468\pi$$
−0.571061 + 0.820908i $$0.693468\pi$$
$$558$$ 0 0
$$559$$ 6.25822e6 0.847073
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −9.91051e6 −1.31773 −0.658863 0.752263i $$-0.728962\pi$$
−0.658863 + 0.752263i $$0.728962\pi$$
$$564$$ 0 0
$$565$$ 3.52643e6 0.464745
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 7.44344e6 0.963814 0.481907 0.876222i $$-0.339944\pi$$
0.481907 + 0.876222i $$0.339944\pi$$
$$570$$ 0 0
$$571$$ 4.08068e6 0.523773 0.261886 0.965099i $$-0.415655\pi$$
0.261886 + 0.965099i $$0.415655\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.05307e6 −0.132827
$$576$$ 0 0
$$577$$ 5.65712e6 0.707385 0.353693 0.935362i $$-0.384926\pi$$
0.353693 + 0.935362i $$0.384926\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1.38376e6 0.170067
$$582$$ 0 0
$$583$$ −3.57012e6 −0.435022
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1.38451e7 1.65845 0.829223 0.558917i $$-0.188783\pi$$
0.829223 + 0.558917i $$0.188783\pi$$
$$588$$ 0 0
$$589$$ 3.47458e6 0.412680
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.22720e7 1.43311 0.716553 0.697533i $$-0.245719\pi$$
0.716553 + 0.697533i $$0.245719\pi$$
$$594$$ 0 0
$$595$$ −1.28674e6 −0.149004
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −920118. −0.104780 −0.0523898 0.998627i $$-0.516684\pi$$
−0.0523898 + 0.998627i $$0.516684\pi$$
$$600$$ 0 0
$$601$$ −1.30680e7 −1.47579 −0.737893 0.674917i $$-0.764179\pi$$
−0.737893 + 0.674917i $$0.764179\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1.55607e6 −0.172839
$$606$$ 0 0
$$607$$ −6.07692e6 −0.669440 −0.334720 0.942318i $$-0.608642\pi$$
−0.334720 + 0.942318i $$0.608642\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.09166e7 −1.18300
$$612$$ 0 0
$$613$$ 1.40826e7 1.51367 0.756835 0.653606i $$-0.226745\pi$$
0.756835 + 0.653606i $$0.226745\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −3.45617e6 −0.365496 −0.182748 0.983160i $$-0.558499\pi$$
−0.182748 + 0.983160i $$0.558499\pi$$
$$618$$ 0 0
$$619$$ −1.29450e6 −0.135793 −0.0678964 0.997692i $$-0.521629\pi$$
−0.0678964 + 0.997692i $$0.521629\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −3.72175e6 −0.384173
$$624$$ 0 0
$$625$$ 3.88510e6 0.397834
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −9.66974e6 −0.974514
$$630$$ 0 0
$$631$$ 1.51131e7 1.51106 0.755529 0.655116i $$-0.227380\pi$$
0.755529 + 0.655116i $$0.227380\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −7.17538e6 −0.706172
$$636$$ 0 0
$$637$$ 1.54144e6 0.150515
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2.22343e6 0.213736 0.106868 0.994273i $$-0.465918\pi$$
0.106868 + 0.994273i $$0.465918\pi$$
$$642$$ 0 0
$$643$$ −2.02821e6 −0.193458 −0.0967288 0.995311i $$-0.530838\pi$$
−0.0967288 + 0.995311i $$0.530838\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.31471e7 1.23472 0.617360 0.786681i $$-0.288202\pi$$
0.617360 + 0.786681i $$0.288202\pi$$
$$648$$ 0 0
$$649$$ −8.88676e6 −0.828193
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.07280e7 0.984550 0.492275 0.870440i $$-0.336165\pi$$
0.492275 + 0.870440i $$0.336165\pi$$
$$654$$ 0 0
$$655$$ 1.31269e6 0.119552
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1.71881e7 −1.54176 −0.770878 0.636983i $$-0.780182\pi$$
−0.770878 + 0.636983i $$0.780182\pi$$
$$660$$ 0 0
$$661$$ 1.48793e7 1.32459 0.662293 0.749245i $$-0.269583\pi$$
0.662293 + 0.749245i $$0.269583\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 1.95177e6 0.171149
$$666$$ 0 0
$$667$$ 2.89648e6 0.252090
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 1.72781e7 1.48146
$$672$$ 0 0
$$673$$ −1.02649e7 −0.873611 −0.436806 0.899556i $$-0.643890\pi$$
−0.436806 + 0.899556i $$0.643890\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 5.21750e6 0.437513 0.218756 0.975780i $$-0.429800\pi$$
0.218756 + 0.975780i $$0.429800\pi$$
$$678$$ 0 0
$$679$$ −3.95381e6 −0.329110
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.36733e7 1.12156 0.560780 0.827965i $$-0.310501\pi$$
0.560780 + 0.827965i $$0.310501\pi$$
$$684$$ 0 0
$$685$$ −3.56751e6 −0.290495
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 4.87663e6 0.391356
$$690$$ 0 0
$$691$$ 2.09599e7 1.66991 0.834956 0.550317i $$-0.185493\pi$$
0.834956 + 0.550317i $$0.185493\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 547040. 0.0429593
$$696$$ 0 0
$$697$$ 1.45501e7 1.13444
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 6.76672e6 0.520096 0.260048 0.965596i $$-0.416262\pi$$
0.260048 + 0.965596i $$0.416262\pi$$
$$702$$ 0 0
$$703$$ 1.46674e7 1.11934
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1.53399e6 0.115418
$$708$$ 0 0
$$709$$ 1.52983e7 1.14295 0.571477 0.820618i $$-0.306371\pi$$
0.571477 + 0.820618i $$0.306371\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −975240. −0.0718435
$$714$$ 0 0
$$715$$ 7.84524e6 0.573906
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −932736. −0.0672878 −0.0336439 0.999434i $$-0.510711\pi$$
−0.0336439 + 0.999434i $$0.510711\pi$$
$$720$$ 0 0
$$721$$ −5.04249e6 −0.361249
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1.64965e7 −1.16559
$$726$$ 0 0
$$727$$ 2.19675e7 1.54150 0.770751 0.637137i $$-0.219881\pi$$
0.770751 + 0.637137i $$0.219881\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 9.84548e6 0.681465
$$732$$ 0 0
$$733$$ −3.41626e6 −0.234850 −0.117425 0.993082i $$-0.537464\pi$$
−0.117425 + 0.993082i $$0.537464\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −1.72904e7 −1.17256
$$738$$ 0 0
$$739$$ 2.00714e7 1.35197 0.675983 0.736917i $$-0.263719\pi$$
0.675983 + 0.736917i $$0.263719\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −3.87764e6 −0.257689 −0.128844 0.991665i $$-0.541127\pi$$
−0.128844 + 0.991665i $$0.541127\pi$$
$$744$$ 0 0
$$745$$ −6.25217e6 −0.412705
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 8.45162e6 0.550472
$$750$$ 0 0
$$751$$ −965112. −0.0624422 −0.0312211 0.999513i $$-0.509940\pi$$
−0.0312211 + 0.999513i $$0.509940\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 8.45125e6 0.539577
$$756$$ 0 0
$$757$$ 1.51809e6 0.0962848 0.0481424 0.998840i $$-0.484670\pi$$
0.0481424 + 0.998840i $$0.484670\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −2.78210e7 −1.74145 −0.870724 0.491772i $$-0.836349\pi$$
−0.870724 + 0.491772i $$0.836349\pi$$
$$762$$ 0 0
$$763$$ −6.63803e6 −0.412789
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1.21389e7 0.745062
$$768$$ 0 0
$$769$$ 1.29011e7 0.786704 0.393352 0.919388i $$-0.371315\pi$$
0.393352 + 0.919388i $$0.371315\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.03741e7 −1.22640 −0.613198 0.789929i $$-0.710117\pi$$
−0.613198 + 0.789929i $$0.710117\pi$$
$$774$$ 0 0
$$775$$ 5.55433e6 0.332183
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −2.20700e7 −1.30304
$$780$$ 0 0
$$781$$ 8.61322e6 0.505287
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −1.39811e7 −0.809779
$$786$$ 0 0
$$787$$ 8.69990e6 0.500700 0.250350 0.968155i $$-0.419454\pi$$
0.250350 + 0.968155i $$0.419454\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −6.64597e6 −0.377674
$$792$$ 0 0
$$793$$ −2.36012e7 −1.33276
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −3.56281e7 −1.98677 −0.993383 0.114845i $$-0.963363\pi$$
−0.993383 + 0.114845i $$0.963363\pi$$
$$798$$ 0 0
$$799$$ −1.71740e7 −0.951712
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −1.70995e7 −0.935827
$$804$$ 0 0
$$805$$ −547820. −0.0297953
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 2.12912e7 1.14375 0.571873 0.820342i $$-0.306217\pi$$
0.571873 + 0.820342i $$0.306217\pi$$
$$810$$ 0 0
$$811$$ −1.83458e7 −0.979455 −0.489728 0.871875i $$-0.662904\pi$$
−0.489728 + 0.871875i $$0.662904\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 1.04974e7 0.553592
$$816$$ 0 0
$$817$$ −1.49339e7 −0.782743
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 2.50359e7 1.29630 0.648149 0.761514i $$-0.275544\pi$$
0.648149 + 0.761514i $$0.275544\pi$$
$$822$$ 0 0
$$823$$ −3.30923e6 −0.170305 −0.0851525 0.996368i $$-0.527138\pi$$
−0.0851525 + 0.996368i $$0.527138\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 1.25220e7 0.636664 0.318332 0.947979i $$-0.396877\pi$$
0.318332 + 0.947979i $$0.396877\pi$$
$$828$$ 0 0
$$829$$ 8.72677e6 0.441029 0.220515 0.975384i $$-0.429226\pi$$
0.220515 + 0.975384i $$0.429226\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 2.42501e6 0.121088
$$834$$ 0 0
$$835$$ 1.82627e7 0.906461
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −3.17349e7 −1.55644 −0.778221 0.627991i $$-0.783877\pi$$
−0.778221 + 0.627991i $$0.783877\pi$$
$$840$$ 0 0
$$841$$ 2.48625e7 1.21215
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −1.06265e6 −0.0511973
$$846$$ 0 0
$$847$$ 2.93260e6 0.140457
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −4.11682e6 −0.194867
$$852$$ 0 0
$$853$$ 3.40388e7 1.60178 0.800888 0.598814i $$-0.204361\pi$$
0.800888 + 0.598814i $$0.204361\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 2.84100e7 1.32135 0.660676 0.750671i $$-0.270270\pi$$
0.660676 + 0.750671i $$0.270270\pi$$
$$858$$ 0 0
$$859$$ −1.44582e7 −0.668545 −0.334272 0.942477i $$-0.608491\pi$$
−0.334272 + 0.942477i $$0.608491\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 1.46943e7 0.671619 0.335809 0.941930i $$-0.390990\pi$$
0.335809 + 0.941930i $$0.390990\pi$$
$$864$$ 0 0
$$865$$ 1.89001e7 0.858862
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 1.39985e7 0.628827
$$870$$ 0 0
$$871$$ 2.36179e7 1.05486
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 7.10128e6 0.313557
$$876$$ 0 0
$$877$$ 2.47228e7 1.08542 0.542711 0.839920i $$-0.317398\pi$$
0.542711 + 0.839920i $$0.317398\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −3.50211e6 −0.152016 −0.0760081 0.997107i $$-0.524217\pi$$
−0.0760081 + 0.997107i $$0.524217\pi$$
$$882$$ 0 0
$$883$$ 767908. 0.0331442 0.0165721 0.999863i $$-0.494725\pi$$
0.0165721 + 0.999863i $$0.494725\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.14209e7 0.487405 0.243703 0.969850i $$-0.421638\pi$$
0.243703 + 0.969850i $$0.421638\pi$$
$$888$$ 0 0
$$889$$ 1.35228e7 0.573869
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 2.60501e7 1.09315
$$894$$ 0 0
$$895$$ 1.87829e7 0.783798
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −1.52772e7 −0.630443
$$900$$ 0 0
$$901$$ 7.67196e6 0.314843
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 8.67064e6 0.351908
$$906$$ 0 0
$$907$$ 1.31900e7 0.532387 0.266194 0.963920i $$-0.414234\pi$$
0.266194 + 0.963920i $$0.414234\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −2.99072e7 −1.19393 −0.596965 0.802267i $$-0.703627\pi$$
−0.596965 + 0.802267i $$0.703627\pi$$
$$912$$ 0 0
$$913$$ −1.32728e7 −0.526970
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −2.47391e6 −0.0971540
$$918$$ 0 0
$$919$$ −2.53866e7 −0.991552 −0.495776 0.868450i $$-0.665116\pi$$
−0.495776 + 0.868450i $$0.665116\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −1.17653e7 −0.454568
$$924$$ 0 0
$$925$$ 2.34467e7 0.901006
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 2.29559e7 0.872680 0.436340 0.899782i $$-0.356274\pi$$
0.436340 + 0.899782i $$0.356274\pi$$
$$930$$ 0 0
$$931$$ −3.67833e6 −0.139084
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 1.23422e7 0.461704
$$936$$ 0 0
$$937$$ 1.16444e7 0.433280 0.216640 0.976252i $$-0.430490\pi$$
0.216640 + 0.976252i $$0.430490\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 2.04943e7 0.754500 0.377250 0.926111i $$-0.376870\pi$$
0.377250 + 0.926111i $$0.376870\pi$$
$$942$$ 0 0
$$943$$ 6.19458e6 0.226847
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 2.91160e7 1.05501 0.527505 0.849552i $$-0.323128\pi$$
0.527505 + 0.849552i $$0.323128\pi$$
$$948$$ 0 0
$$949$$ 2.33572e7 0.841891
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −5.20790e6 −0.185751 −0.0928753 0.995678i $$-0.529606\pi$$
−0.0928753 + 0.995678i $$0.529606\pi$$
$$954$$ 0 0
$$955$$ −1.73976e7 −0.617278
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 6.72339e6 0.236070
$$960$$ 0 0
$$961$$ −2.34853e7 −0.820329
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 2.99172e6 0.103419
$$966$$ 0 0
$$967$$ 4.28147e6 0.147240 0.0736202 0.997286i $$-0.476545\pi$$
0.0736202 + 0.997286i $$0.476545\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 1.20741e7 0.410966 0.205483 0.978661i $$-0.434124\pi$$
0.205483 + 0.978661i $$0.434124\pi$$
$$972$$ 0 0
$$973$$ −1.03096e6 −0.0349108
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 1.06568e7 0.357183 0.178591 0.983923i $$-0.442846\pi$$
0.178591 + 0.983923i $$0.442846\pi$$
$$978$$ 0 0
$$979$$ 3.56984e7 1.19040
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −3.55409e7 −1.17312 −0.586562 0.809904i $$-0.699519\pi$$
−0.586562 + 0.809904i $$0.699519\pi$$
$$984$$ 0 0
$$985$$ 5.54746e6 0.182181
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 4.19164e6 0.136268
$$990$$ 0 0
$$991$$ −2.83700e7 −0.917647 −0.458823 0.888527i $$-0.651729\pi$$
−0.458823 + 0.888527i $$0.651729\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 2.06777e7 0.662132
$$996$$ 0 0
$$997$$ −6.15275e6 −0.196034 −0.0980169 0.995185i $$-0.531250\pi$$
−0.0980169 + 0.995185i $$0.531250\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1008.6.a.i.1.1 1
3.2 odd 2 1008.6.a.r.1.1 1
4.3 odd 2 126.6.a.j.1.1 yes 1
12.11 even 2 126.6.a.d.1.1 1
28.27 even 2 882.6.a.u.1.1 1
84.83 odd 2 882.6.a.c.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
126.6.a.d.1.1 1 12.11 even 2
126.6.a.j.1.1 yes 1 4.3 odd 2
882.6.a.c.1.1 1 84.83 odd 2
882.6.a.u.1.1 1 28.27 even 2
1008.6.a.i.1.1 1 1.1 even 1 trivial
1008.6.a.r.1.1 1 3.2 odd 2