# Properties

 Label 704.6.a.e.1.1 Level $704$ Weight $6$ Character 704.1 Self dual yes Analytic conductor $112.910$ Analytic rank $0$ 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] = [704,6,Mod(1,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("704.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$704 = 2^{6} \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 704.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: $$112.910209148$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 22) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 704.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} +51.0000 q^{5} -166.000 q^{7} -242.000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} +51.0000 q^{5} -166.000 q^{7} -242.000 q^{9} +121.000 q^{11} -692.000 q^{13} -51.0000 q^{15} -738.000 q^{17} -1424.00 q^{19} +166.000 q^{21} -1779.00 q^{23} -524.000 q^{25} +485.000 q^{27} +2064.00 q^{29} +6245.00 q^{31} -121.000 q^{33} -8466.00 q^{35} +14785.0 q^{37} +692.000 q^{39} +5304.00 q^{41} -17798.0 q^{43} -12342.0 q^{45} -17184.0 q^{47} +10749.0 q^{49} +738.000 q^{51} +30726.0 q^{53} +6171.00 q^{55} +1424.00 q^{57} +34989.0 q^{59} +45940.0 q^{61} +40172.0 q^{63} -35292.0 q^{65} -25343.0 q^{67} +1779.00 q^{69} +13311.0 q^{71} -53260.0 q^{73} +524.000 q^{75} -20086.0 q^{77} +77234.0 q^{79} +58321.0 q^{81} -55014.0 q^{83} -37638.0 q^{85} -2064.00 q^{87} +125415. q^{89} +114872. q^{91} -6245.00 q^{93} -72624.0 q^{95} -88807.0 q^{97} -29282.0 q^{99} +O(q^{100})$$

## 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
$$3$$ −1.00000 −0.0641500 −0.0320750 0.999485i $$-0.510212\pi$$
−0.0320750 + 0.999485i $$0.510212\pi$$
$$4$$ 0 0
$$5$$ 51.0000 0.912316 0.456158 0.889899i $$-0.349225\pi$$
0.456158 + 0.889899i $$0.349225\pi$$
$$6$$ 0 0
$$7$$ −166.000 −1.28045 −0.640226 0.768187i $$-0.721159\pi$$
−0.640226 + 0.768187i $$0.721159\pi$$
$$8$$ 0 0
$$9$$ −242.000 −0.995885
$$10$$ 0 0
$$11$$ 121.000 0.301511
$$12$$ 0 0
$$13$$ −692.000 −1.13566 −0.567829 0.823146i $$-0.692217\pi$$
−0.567829 + 0.823146i $$0.692217\pi$$
$$14$$ 0 0
$$15$$ −51.0000 −0.0585251
$$16$$ 0 0
$$17$$ −738.000 −0.619347 −0.309674 0.950843i $$-0.600220\pi$$
−0.309674 + 0.950843i $$0.600220\pi$$
$$18$$ 0 0
$$19$$ −1424.00 −0.904953 −0.452476 0.891776i $$-0.649459\pi$$
−0.452476 + 0.891776i $$0.649459\pi$$
$$20$$ 0 0
$$21$$ 166.000 0.0821410
$$22$$ 0 0
$$23$$ −1779.00 −0.701223 −0.350612 0.936521i $$-0.614026\pi$$
−0.350612 + 0.936521i $$0.614026\pi$$
$$24$$ 0 0
$$25$$ −524.000 −0.167680
$$26$$ 0 0
$$27$$ 485.000 0.128036
$$28$$ 0 0
$$29$$ 2064.00 0.455737 0.227869 0.973692i $$-0.426824\pi$$
0.227869 + 0.973692i $$0.426824\pi$$
$$30$$ 0 0
$$31$$ 6245.00 1.16715 0.583577 0.812058i $$-0.301653\pi$$
0.583577 + 0.812058i $$0.301653\pi$$
$$32$$ 0 0
$$33$$ −121.000 −0.0193420
$$34$$ 0 0
$$35$$ −8466.00 −1.16818
$$36$$ 0 0
$$37$$ 14785.0 1.77549 0.887743 0.460340i $$-0.152273\pi$$
0.887743 + 0.460340i $$0.152273\pi$$
$$38$$ 0 0
$$39$$ 692.000 0.0728525
$$40$$ 0 0
$$41$$ 5304.00 0.492770 0.246385 0.969172i $$-0.420757\pi$$
0.246385 + 0.969172i $$0.420757\pi$$
$$42$$ 0 0
$$43$$ −17798.0 −1.46791 −0.733956 0.679197i $$-0.762328\pi$$
−0.733956 + 0.679197i $$0.762328\pi$$
$$44$$ 0 0
$$45$$ −12342.0 −0.908561
$$46$$ 0 0
$$47$$ −17184.0 −1.13470 −0.567348 0.823478i $$-0.692031\pi$$
−0.567348 + 0.823478i $$0.692031\pi$$
$$48$$ 0 0
$$49$$ 10749.0 0.639555
$$50$$ 0 0
$$51$$ 738.000 0.0397311
$$52$$ 0 0
$$53$$ 30726.0 1.50251 0.751253 0.660014i $$-0.229450\pi$$
0.751253 + 0.660014i $$0.229450\pi$$
$$54$$ 0 0
$$55$$ 6171.00 0.275074
$$56$$ 0 0
$$57$$ 1424.00 0.0580528
$$58$$ 0 0
$$59$$ 34989.0 1.30858 0.654292 0.756242i $$-0.272967\pi$$
0.654292 + 0.756242i $$0.272967\pi$$
$$60$$ 0 0
$$61$$ 45940.0 1.58076 0.790381 0.612616i $$-0.209883\pi$$
0.790381 + 0.612616i $$0.209883\pi$$
$$62$$ 0 0
$$63$$ 40172.0 1.27518
$$64$$ 0 0
$$65$$ −35292.0 −1.03608
$$66$$ 0 0
$$67$$ −25343.0 −0.689717 −0.344859 0.938655i $$-0.612073\pi$$
−0.344859 + 0.938655i $$0.612073\pi$$
$$68$$ 0 0
$$69$$ 1779.00 0.0449835
$$70$$ 0 0
$$71$$ 13311.0 0.313375 0.156688 0.987648i $$-0.449918\pi$$
0.156688 + 0.987648i $$0.449918\pi$$
$$72$$ 0 0
$$73$$ −53260.0 −1.16975 −0.584876 0.811123i $$-0.698857\pi$$
−0.584876 + 0.811123i $$0.698857\pi$$
$$74$$ 0 0
$$75$$ 524.000 0.0107567
$$76$$ 0 0
$$77$$ −20086.0 −0.386071
$$78$$ 0 0
$$79$$ 77234.0 1.39233 0.696163 0.717884i $$-0.254889\pi$$
0.696163 + 0.717884i $$0.254889\pi$$
$$80$$ 0 0
$$81$$ 58321.0 0.987671
$$82$$ 0 0
$$83$$ −55014.0 −0.876553 −0.438276 0.898840i $$-0.644411\pi$$
−0.438276 + 0.898840i $$0.644411\pi$$
$$84$$ 0 0
$$85$$ −37638.0 −0.565040
$$86$$ 0 0
$$87$$ −2064.00 −0.0292356
$$88$$ 0 0
$$89$$ 125415. 1.67832 0.839159 0.543886i $$-0.183047\pi$$
0.839159 + 0.543886i $$0.183047\pi$$
$$90$$ 0 0
$$91$$ 114872. 1.45416
$$92$$ 0 0
$$93$$ −6245.00 −0.0748730
$$94$$ 0 0
$$95$$ −72624.0 −0.825603
$$96$$ 0 0
$$97$$ −88807.0 −0.958336 −0.479168 0.877723i $$-0.659062\pi$$
−0.479168 + 0.877723i $$0.659062\pi$$
$$98$$ 0 0
$$99$$ −29282.0 −0.300271
$$100$$ 0 0
$$101$$ −1482.00 −0.0144559 −0.00722794 0.999974i $$-0.502301\pi$$
−0.00722794 + 0.999974i $$0.502301\pi$$
$$102$$ 0 0
$$103$$ −117496. −1.09126 −0.545632 0.838025i $$-0.683710\pi$$
−0.545632 + 0.838025i $$0.683710\pi$$
$$104$$ 0 0
$$105$$ 8466.00 0.0749385
$$106$$ 0 0
$$107$$ 79362.0 0.670121 0.335060 0.942197i $$-0.391243\pi$$
0.335060 + 0.942197i $$0.391243\pi$$
$$108$$ 0 0
$$109$$ −87842.0 −0.708167 −0.354084 0.935214i $$-0.615207\pi$$
−0.354084 + 0.935214i $$0.615207\pi$$
$$110$$ 0 0
$$111$$ −14785.0 −0.113897
$$112$$ 0 0
$$113$$ −47247.0 −0.348079 −0.174040 0.984739i $$-0.555682\pi$$
−0.174040 + 0.984739i $$0.555682\pi$$
$$114$$ 0 0
$$115$$ −90729.0 −0.639737
$$116$$ 0 0
$$117$$ 167464. 1.13098
$$118$$ 0 0
$$119$$ 122508. 0.793044
$$120$$ 0 0
$$121$$ 14641.0 0.0909091
$$122$$ 0 0
$$123$$ −5304.00 −0.0316112
$$124$$ 0 0
$$125$$ −186099. −1.06529
$$126$$ 0 0
$$127$$ −239416. −1.31718 −0.658588 0.752504i $$-0.728846\pi$$
−0.658588 + 0.752504i $$0.728846\pi$$
$$128$$ 0 0
$$129$$ 17798.0 0.0941666
$$130$$ 0 0
$$131$$ 98142.0 0.499662 0.249831 0.968289i $$-0.419625\pi$$
0.249831 + 0.968289i $$0.419625\pi$$
$$132$$ 0 0
$$133$$ 236384. 1.15875
$$134$$ 0 0
$$135$$ 24735.0 0.116809
$$136$$ 0 0
$$137$$ 400137. 1.82141 0.910704 0.413059i $$-0.135540\pi$$
0.910704 + 0.413059i $$0.135540\pi$$
$$138$$ 0 0
$$139$$ −205766. −0.903310 −0.451655 0.892193i $$-0.649166\pi$$
−0.451655 + 0.892193i $$0.649166\pi$$
$$140$$ 0 0
$$141$$ 17184.0 0.0727908
$$142$$ 0 0
$$143$$ −83732.0 −0.342414
$$144$$ 0 0
$$145$$ 105264. 0.415776
$$146$$ 0 0
$$147$$ −10749.0 −0.0410275
$$148$$ 0 0
$$149$$ −87726.0 −0.323715 −0.161857 0.986814i $$-0.551748\pi$$
−0.161857 + 0.986814i $$0.551748\pi$$
$$150$$ 0 0
$$151$$ −432778. −1.54462 −0.772312 0.635243i $$-0.780900\pi$$
−0.772312 + 0.635243i $$0.780900\pi$$
$$152$$ 0 0
$$153$$ 178596. 0.616798
$$154$$ 0 0
$$155$$ 318495. 1.06481
$$156$$ 0 0
$$157$$ 34075.0 0.110328 0.0551641 0.998477i $$-0.482432\pi$$
0.0551641 + 0.998477i $$0.482432\pi$$
$$158$$ 0 0
$$159$$ −30726.0 −0.0963858
$$160$$ 0 0
$$161$$ 295314. 0.897882
$$162$$ 0 0
$$163$$ −45020.0 −0.132720 −0.0663600 0.997796i $$-0.521139\pi$$
−0.0663600 + 0.997796i $$0.521139\pi$$
$$164$$ 0 0
$$165$$ −6171.00 −0.0176460
$$166$$ 0 0
$$167$$ 482556. 1.33893 0.669463 0.742845i $$-0.266524\pi$$
0.669463 + 0.742845i $$0.266524\pi$$
$$168$$ 0 0
$$169$$ 107571. 0.289720
$$170$$ 0 0
$$171$$ 344608. 0.901229
$$172$$ 0 0
$$173$$ 766254. 1.94651 0.973257 0.229719i $$-0.0737808\pi$$
0.973257 + 0.229719i $$0.0737808\pi$$
$$174$$ 0 0
$$175$$ 86984.0 0.214706
$$176$$ 0 0
$$177$$ −34989.0 −0.0839457
$$178$$ 0 0
$$179$$ −303399. −0.707753 −0.353876 0.935292i $$-0.615137\pi$$
−0.353876 + 0.935292i $$0.615137\pi$$
$$180$$ 0 0
$$181$$ 285181. 0.647030 0.323515 0.946223i $$-0.395135\pi$$
0.323515 + 0.946223i $$0.395135\pi$$
$$182$$ 0 0
$$183$$ −45940.0 −0.101406
$$184$$ 0 0
$$185$$ 754035. 1.61980
$$186$$ 0 0
$$187$$ −89298.0 −0.186740
$$188$$ 0 0
$$189$$ −80510.0 −0.163944
$$190$$ 0 0
$$191$$ 767067. 1.52142 0.760711 0.649090i $$-0.224850\pi$$
0.760711 + 0.649090i $$0.224850\pi$$
$$192$$ 0 0
$$193$$ 411668. 0.795525 0.397763 0.917488i $$-0.369787\pi$$
0.397763 + 0.917488i $$0.369787\pi$$
$$194$$ 0 0
$$195$$ 35292.0 0.0664645
$$196$$ 0 0
$$197$$ 759258. 1.39387 0.696937 0.717132i $$-0.254545\pi$$
0.696937 + 0.717132i $$0.254545\pi$$
$$198$$ 0 0
$$199$$ −46600.0 −0.0834167 −0.0417084 0.999130i $$-0.513280\pi$$
−0.0417084 + 0.999130i $$0.513280\pi$$
$$200$$ 0 0
$$201$$ 25343.0 0.0442454
$$202$$ 0 0
$$203$$ −342624. −0.583549
$$204$$ 0 0
$$205$$ 270504. 0.449561
$$206$$ 0 0
$$207$$ 430518. 0.698338
$$208$$ 0 0
$$209$$ −172304. −0.272854
$$210$$ 0 0
$$211$$ 932428. 1.44181 0.720907 0.693032i $$-0.243726\pi$$
0.720907 + 0.693032i $$0.243726\pi$$
$$212$$ 0 0
$$213$$ −13311.0 −0.0201030
$$214$$ 0 0
$$215$$ −907698. −1.33920
$$216$$ 0 0
$$217$$ −1.03667e6 −1.49448
$$218$$ 0 0
$$219$$ 53260.0 0.0750397
$$220$$ 0 0
$$221$$ 510696. 0.703367
$$222$$ 0 0
$$223$$ 169745. 0.228578 0.114289 0.993448i $$-0.463541\pi$$
0.114289 + 0.993448i $$0.463541\pi$$
$$224$$ 0 0
$$225$$ 126808. 0.166990
$$226$$ 0 0
$$227$$ −198078. −0.255136 −0.127568 0.991830i $$-0.540717\pi$$
−0.127568 + 0.991830i $$0.540717\pi$$
$$228$$ 0 0
$$229$$ 849997. 1.07110 0.535548 0.844505i $$-0.320105\pi$$
0.535548 + 0.844505i $$0.320105\pi$$
$$230$$ 0 0
$$231$$ 20086.0 0.0247664
$$232$$ 0 0
$$233$$ −401832. −0.484903 −0.242451 0.970164i $$-0.577952\pi$$
−0.242451 + 0.970164i $$0.577952\pi$$
$$234$$ 0 0
$$235$$ −876384. −1.03520
$$236$$ 0 0
$$237$$ −77234.0 −0.0893177
$$238$$ 0 0
$$239$$ 855174. 0.968411 0.484206 0.874954i $$-0.339109\pi$$
0.484206 + 0.874954i $$0.339109\pi$$
$$240$$ 0 0
$$241$$ 1.12546e6 1.24821 0.624107 0.781339i $$-0.285463\pi$$
0.624107 + 0.781339i $$0.285463\pi$$
$$242$$ 0 0
$$243$$ −176176. −0.191395
$$244$$ 0 0
$$245$$ 548199. 0.583476
$$246$$ 0 0
$$247$$ 985408. 1.02772
$$248$$ 0 0
$$249$$ 55014.0 0.0562309
$$250$$ 0 0
$$251$$ 1.19751e6 1.19976 0.599882 0.800088i $$-0.295214\pi$$
0.599882 + 0.800088i $$0.295214\pi$$
$$252$$ 0 0
$$253$$ −215259. −0.211427
$$254$$ 0 0
$$255$$ 37638.0 0.0362473
$$256$$ 0 0
$$257$$ 37758.0 0.0356596 0.0178298 0.999841i $$-0.494324\pi$$
0.0178298 + 0.999841i $$0.494324\pi$$
$$258$$ 0 0
$$259$$ −2.45431e6 −2.27342
$$260$$ 0 0
$$261$$ −499488. −0.453862
$$262$$ 0 0
$$263$$ −631254. −0.562749 −0.281375 0.959598i $$-0.590790\pi$$
−0.281375 + 0.959598i $$0.590790\pi$$
$$264$$ 0 0
$$265$$ 1.56703e6 1.37076
$$266$$ 0 0
$$267$$ −125415. −0.107664
$$268$$ 0 0
$$269$$ 1.08034e6 0.910292 0.455146 0.890417i $$-0.349587\pi$$
0.455146 + 0.890417i $$0.349587\pi$$
$$270$$ 0 0
$$271$$ −816100. −0.675025 −0.337513 0.941321i $$-0.609586\pi$$
−0.337513 + 0.941321i $$0.609586\pi$$
$$272$$ 0 0
$$273$$ −114872. −0.0932841
$$274$$ 0 0
$$275$$ −63404.0 −0.0505574
$$276$$ 0 0
$$277$$ −1.68820e6 −1.32198 −0.660989 0.750396i $$-0.729863\pi$$
−0.660989 + 0.750396i $$0.729863\pi$$
$$278$$ 0 0
$$279$$ −1.51129e6 −1.16235
$$280$$ 0 0
$$281$$ −879042. −0.664116 −0.332058 0.943259i $$-0.607743\pi$$
−0.332058 + 0.943259i $$0.607743\pi$$
$$282$$ 0 0
$$283$$ −1.54027e6 −1.14322 −0.571611 0.820525i $$-0.693681\pi$$
−0.571611 + 0.820525i $$0.693681\pi$$
$$284$$ 0 0
$$285$$ 72624.0 0.0529624
$$286$$ 0 0
$$287$$ −880464. −0.630967
$$288$$ 0 0
$$289$$ −875213. −0.616409
$$290$$ 0 0
$$291$$ 88807.0 0.0614773
$$292$$ 0 0
$$293$$ −720840. −0.490535 −0.245267 0.969455i $$-0.578876\pi$$
−0.245267 + 0.969455i $$0.578876\pi$$
$$294$$ 0 0
$$295$$ 1.78444e6 1.19384
$$296$$ 0 0
$$297$$ 58685.0 0.0386043
$$298$$ 0 0
$$299$$ 1.23107e6 0.796350
$$300$$ 0 0
$$301$$ 2.95447e6 1.87959
$$302$$ 0 0
$$303$$ 1482.00 0.000927346 0
$$304$$ 0 0
$$305$$ 2.34294e6 1.44215
$$306$$ 0 0
$$307$$ 1.03905e6 0.629201 0.314601 0.949224i $$-0.398129\pi$$
0.314601 + 0.949224i $$0.398129\pi$$
$$308$$ 0 0
$$309$$ 117496. 0.0700046
$$310$$ 0 0
$$311$$ −1.25135e6 −0.733630 −0.366815 0.930294i $$-0.619552\pi$$
−0.366815 + 0.930294i $$0.619552\pi$$
$$312$$ 0 0
$$313$$ −1.44336e6 −0.832749 −0.416375 0.909193i $$-0.636699\pi$$
−0.416375 + 0.909193i $$0.636699\pi$$
$$314$$ 0 0
$$315$$ 2.04877e6 1.16337
$$316$$ 0 0
$$317$$ 2.01208e6 1.12460 0.562298 0.826934i $$-0.309917\pi$$
0.562298 + 0.826934i $$0.309917\pi$$
$$318$$ 0 0
$$319$$ 249744. 0.137410
$$320$$ 0 0
$$321$$ −79362.0 −0.0429883
$$322$$ 0 0
$$323$$ 1.05091e6 0.560480
$$324$$ 0 0
$$325$$ 362608. 0.190427
$$326$$ 0 0
$$327$$ 87842.0 0.0454290
$$328$$ 0 0
$$329$$ 2.85254e6 1.45292
$$330$$ 0 0
$$331$$ −2.01734e6 −1.01207 −0.506033 0.862514i $$-0.668888\pi$$
−0.506033 + 0.862514i $$0.668888\pi$$
$$332$$ 0 0
$$333$$ −3.57797e6 −1.76818
$$334$$ 0 0
$$335$$ −1.29249e6 −0.629240
$$336$$ 0 0
$$337$$ 264122. 0.126686 0.0633432 0.997992i $$-0.479824\pi$$
0.0633432 + 0.997992i $$0.479824\pi$$
$$338$$ 0 0
$$339$$ 47247.0 0.0223293
$$340$$ 0 0
$$341$$ 755645. 0.351910
$$342$$ 0 0
$$343$$ 1.00563e6 0.461532
$$344$$ 0 0
$$345$$ 90729.0 0.0410392
$$346$$ 0 0
$$347$$ 1.71049e6 0.762601 0.381300 0.924451i $$-0.375476\pi$$
0.381300 + 0.924451i $$0.375476\pi$$
$$348$$ 0 0
$$349$$ −218822. −0.0961673 −0.0480836 0.998843i $$-0.515311\pi$$
−0.0480836 + 0.998843i $$0.515311\pi$$
$$350$$ 0 0
$$351$$ −335620. −0.145405
$$352$$ 0 0
$$353$$ 3.68192e6 1.57267 0.786334 0.617802i $$-0.211977\pi$$
0.786334 + 0.617802i $$0.211977\pi$$
$$354$$ 0 0
$$355$$ 678861. 0.285897
$$356$$ 0 0
$$357$$ −122508. −0.0508738
$$358$$ 0 0
$$359$$ 1.88528e6 0.772042 0.386021 0.922490i $$-0.373849\pi$$
0.386021 + 0.922490i $$0.373849\pi$$
$$360$$ 0 0
$$361$$ −448323. −0.181060
$$362$$ 0 0
$$363$$ −14641.0 −0.00583182
$$364$$ 0 0
$$365$$ −2.71626e6 −1.06718
$$366$$ 0 0
$$367$$ −3.11666e6 −1.20788 −0.603940 0.797029i $$-0.706404\pi$$
−0.603940 + 0.797029i $$0.706404\pi$$
$$368$$ 0 0
$$369$$ −1.28357e6 −0.490742
$$370$$ 0 0
$$371$$ −5.10052e6 −1.92389
$$372$$ 0 0
$$373$$ −1.39441e6 −0.518943 −0.259471 0.965751i $$-0.583548\pi$$
−0.259471 + 0.965751i $$0.583548\pi$$
$$374$$ 0 0
$$375$$ 186099. 0.0683386
$$376$$ 0 0
$$377$$ −1.42829e6 −0.517562
$$378$$ 0 0
$$379$$ 4.26036e6 1.52352 0.761759 0.647860i $$-0.224336\pi$$
0.761759 + 0.647860i $$0.224336\pi$$
$$380$$ 0 0
$$381$$ 239416. 0.0844969
$$382$$ 0 0
$$383$$ 201765. 0.0702828 0.0351414 0.999382i $$-0.488812\pi$$
0.0351414 + 0.999382i $$0.488812\pi$$
$$384$$ 0 0
$$385$$ −1.02439e6 −0.352218
$$386$$ 0 0
$$387$$ 4.30712e6 1.46187
$$388$$ 0 0
$$389$$ −1.94882e6 −0.652977 −0.326489 0.945201i $$-0.605865\pi$$
−0.326489 + 0.945201i $$0.605865\pi$$
$$390$$ 0 0
$$391$$ 1.31290e6 0.434301
$$392$$ 0 0
$$393$$ −98142.0 −0.0320534
$$394$$ 0 0
$$395$$ 3.93893e6 1.27024
$$396$$ 0 0
$$397$$ 1.46826e6 0.467548 0.233774 0.972291i $$-0.424892\pi$$
0.233774 + 0.972291i $$0.424892\pi$$
$$398$$ 0 0
$$399$$ −236384. −0.0743337
$$400$$ 0 0
$$401$$ 2.24618e6 0.697563 0.348781 0.937204i $$-0.386596\pi$$
0.348781 + 0.937204i $$0.386596\pi$$
$$402$$ 0 0
$$403$$ −4.32154e6 −1.32549
$$404$$ 0 0
$$405$$ 2.97437e6 0.901068
$$406$$ 0 0
$$407$$ 1.78898e6 0.535329
$$408$$ 0 0
$$409$$ −3.61488e6 −1.06853 −0.534263 0.845318i $$-0.679411\pi$$
−0.534263 + 0.845318i $$0.679411\pi$$
$$410$$ 0 0
$$411$$ −400137. −0.116843
$$412$$ 0 0
$$413$$ −5.80817e6 −1.67558
$$414$$ 0 0
$$415$$ −2.80571e6 −0.799693
$$416$$ 0 0
$$417$$ 205766. 0.0579473
$$418$$ 0 0
$$419$$ 3.81239e6 1.06087 0.530435 0.847726i $$-0.322029\pi$$
0.530435 + 0.847726i $$0.322029\pi$$
$$420$$ 0 0
$$421$$ −1.97346e6 −0.542655 −0.271327 0.962487i $$-0.587463\pi$$
−0.271327 + 0.962487i $$0.587463\pi$$
$$422$$ 0 0
$$423$$ 4.15853e6 1.13003
$$424$$ 0 0
$$425$$ 386712. 0.103852
$$426$$ 0 0
$$427$$ −7.62604e6 −2.02409
$$428$$ 0 0
$$429$$ 83732.0 0.0219659
$$430$$ 0 0
$$431$$ −2.08359e6 −0.540280 −0.270140 0.962821i $$-0.587070\pi$$
−0.270140 + 0.962821i $$0.587070\pi$$
$$432$$ 0 0
$$433$$ −72691.0 −0.0186321 −0.00931603 0.999957i $$-0.502965\pi$$
−0.00931603 + 0.999957i $$0.502965\pi$$
$$434$$ 0 0
$$435$$ −105264. −0.0266721
$$436$$ 0 0
$$437$$ 2.53330e6 0.634574
$$438$$ 0 0
$$439$$ 594392. 0.147201 0.0736007 0.997288i $$-0.476551\pi$$
0.0736007 + 0.997288i $$0.476551\pi$$
$$440$$ 0 0
$$441$$ −2.60126e6 −0.636923
$$442$$ 0 0
$$443$$ −4.56651e6 −1.10554 −0.552770 0.833334i $$-0.686429\pi$$
−0.552770 + 0.833334i $$0.686429\pi$$
$$444$$ 0 0
$$445$$ 6.39616e6 1.53116
$$446$$ 0 0
$$447$$ 87726.0 0.0207663
$$448$$ 0 0
$$449$$ −5.44382e6 −1.27435 −0.637174 0.770720i $$-0.719897\pi$$
−0.637174 + 0.770720i $$0.719897\pi$$
$$450$$ 0 0
$$451$$ 641784. 0.148576
$$452$$ 0 0
$$453$$ 432778. 0.0990877
$$454$$ 0 0
$$455$$ 5.85847e6 1.32665
$$456$$ 0 0
$$457$$ 6.70312e6 1.50137 0.750683 0.660662i $$-0.229724\pi$$
0.750683 + 0.660662i $$0.229724\pi$$
$$458$$ 0 0
$$459$$ −357930. −0.0792988
$$460$$ 0 0
$$461$$ 1.25994e6 0.276120 0.138060 0.990424i $$-0.455913\pi$$
0.138060 + 0.990424i $$0.455913\pi$$
$$462$$ 0 0
$$463$$ −5.02308e6 −1.08897 −0.544487 0.838769i $$-0.683276\pi$$
−0.544487 + 0.838769i $$0.683276\pi$$
$$464$$ 0 0
$$465$$ −318495. −0.0683078
$$466$$ 0 0
$$467$$ 2.35660e6 0.500028 0.250014 0.968242i $$-0.419565\pi$$
0.250014 + 0.968242i $$0.419565\pi$$
$$468$$ 0 0
$$469$$ 4.20694e6 0.883149
$$470$$ 0 0
$$471$$ −34075.0 −0.00707756
$$472$$ 0 0
$$473$$ −2.15356e6 −0.442592
$$474$$ 0 0
$$475$$ 746176. 0.151743
$$476$$ 0 0
$$477$$ −7.43569e6 −1.49632
$$478$$ 0 0
$$479$$ −6.72258e6 −1.33874 −0.669371 0.742928i $$-0.733437\pi$$
−0.669371 + 0.742928i $$0.733437\pi$$
$$480$$ 0 0
$$481$$ −1.02312e7 −2.01634
$$482$$ 0 0
$$483$$ −295314. −0.0575992
$$484$$ 0 0
$$485$$ −4.52916e6 −0.874305
$$486$$ 0 0
$$487$$ 1.96001e6 0.374487 0.187243 0.982314i $$-0.440045\pi$$
0.187243 + 0.982314i $$0.440045\pi$$
$$488$$ 0 0
$$489$$ 45020.0 0.00851399
$$490$$ 0 0
$$491$$ 579624. 0.108503 0.0542516 0.998527i $$-0.482723\pi$$
0.0542516 + 0.998527i $$0.482723\pi$$
$$492$$ 0 0
$$493$$ −1.52323e6 −0.282260
$$494$$ 0 0
$$495$$ −1.49338e6 −0.273942
$$496$$ 0 0
$$497$$ −2.20963e6 −0.401262
$$498$$ 0 0
$$499$$ −1.36905e6 −0.246132 −0.123066 0.992398i $$-0.539273\pi$$
−0.123066 + 0.992398i $$0.539273\pi$$
$$500$$ 0 0
$$501$$ −482556. −0.0858921
$$502$$ 0 0
$$503$$ 1.83343e6 0.323105 0.161552 0.986864i $$-0.448350\pi$$
0.161552 + 0.986864i $$0.448350\pi$$
$$504$$ 0 0
$$505$$ −75582.0 −0.0131883
$$506$$ 0 0
$$507$$ −107571. −0.0185855
$$508$$ 0 0
$$509$$ 1.71266e6 0.293006 0.146503 0.989210i $$-0.453198\pi$$
0.146503 + 0.989210i $$0.453198\pi$$
$$510$$ 0 0
$$511$$ 8.84116e6 1.49781
$$512$$ 0 0
$$513$$ −690640. −0.115867
$$514$$ 0 0
$$515$$ −5.99230e6 −0.995578
$$516$$ 0 0
$$517$$ −2.07926e6 −0.342124
$$518$$ 0 0
$$519$$ −766254. −0.124869
$$520$$ 0 0
$$521$$ −789435. −0.127415 −0.0637077 0.997969i $$-0.520293\pi$$
−0.0637077 + 0.997969i $$0.520293\pi$$
$$522$$ 0 0
$$523$$ −627392. −0.100296 −0.0501481 0.998742i $$-0.515969\pi$$
−0.0501481 + 0.998742i $$0.515969\pi$$
$$524$$ 0 0
$$525$$ −86984.0 −0.0137734
$$526$$ 0 0
$$527$$ −4.60881e6 −0.722873
$$528$$ 0 0
$$529$$ −3.27150e6 −0.508286
$$530$$ 0 0
$$531$$ −8.46734e6 −1.30320
$$532$$ 0 0
$$533$$ −3.67037e6 −0.559618
$$534$$ 0 0
$$535$$ 4.04746e6 0.611362
$$536$$ 0 0
$$537$$ 303399. 0.0454024
$$538$$ 0 0
$$539$$ 1.30063e6 0.192833
$$540$$ 0 0
$$541$$ −3.20895e6 −0.471379 −0.235689 0.971828i $$-0.575735\pi$$
−0.235689 + 0.971828i $$0.575735\pi$$
$$542$$ 0 0
$$543$$ −285181. −0.0415070
$$544$$ 0 0
$$545$$ −4.47994e6 −0.646072
$$546$$ 0 0
$$547$$ −3.42658e6 −0.489658 −0.244829 0.969566i $$-0.578732\pi$$
−0.244829 + 0.969566i $$0.578732\pi$$
$$548$$ 0 0
$$549$$ −1.11175e7 −1.57426
$$550$$ 0 0
$$551$$ −2.93914e6 −0.412421
$$552$$ 0 0
$$553$$ −1.28208e7 −1.78280
$$554$$ 0 0
$$555$$ −754035. −0.103910
$$556$$ 0 0
$$557$$ −1.05198e7 −1.43672 −0.718358 0.695674i $$-0.755106\pi$$
−0.718358 + 0.695674i $$0.755106\pi$$
$$558$$ 0 0
$$559$$ 1.23162e7 1.66705
$$560$$ 0 0
$$561$$ 89298.0 0.0119794
$$562$$ 0 0
$$563$$ −5.47288e6 −0.727687 −0.363844 0.931460i $$-0.618536\pi$$
−0.363844 + 0.931460i $$0.618536\pi$$
$$564$$ 0 0
$$565$$ −2.40960e6 −0.317558
$$566$$ 0 0
$$567$$ −9.68129e6 −1.26466
$$568$$ 0 0
$$569$$ −1.17787e7 −1.52516 −0.762580 0.646893i $$-0.776068\pi$$
−0.762580 + 0.646893i $$0.776068\pi$$
$$570$$ 0 0
$$571$$ 8.35628e6 1.07256 0.536281 0.844039i $$-0.319829\pi$$
0.536281 + 0.844039i $$0.319829\pi$$
$$572$$ 0 0
$$573$$ −767067. −0.0975993
$$574$$ 0 0
$$575$$ 932196. 0.117581
$$576$$ 0 0
$$577$$ −1.37758e7 −1.72258 −0.861288 0.508117i $$-0.830342\pi$$
−0.861288 + 0.508117i $$0.830342\pi$$
$$578$$ 0 0
$$579$$ −411668. −0.0510330
$$580$$ 0 0
$$581$$ 9.13232e6 1.12238
$$582$$ 0 0
$$583$$ 3.71785e6 0.453023
$$584$$ 0 0
$$585$$ 8.54066e6 1.03182
$$586$$ 0 0
$$587$$ 1.27093e7 1.52239 0.761196 0.648522i $$-0.224612\pi$$
0.761196 + 0.648522i $$0.224612\pi$$
$$588$$ 0 0
$$589$$ −8.89288e6 −1.05622
$$590$$ 0 0
$$591$$ −759258. −0.0894171
$$592$$ 0 0
$$593$$ 1.00825e6 0.117742 0.0588711 0.998266i $$-0.481250\pi$$
0.0588711 + 0.998266i $$0.481250\pi$$
$$594$$ 0 0
$$595$$ 6.24791e6 0.723506
$$596$$ 0 0
$$597$$ 46600.0 0.00535119
$$598$$ 0 0
$$599$$ 1.05100e7 1.19684 0.598421 0.801182i $$-0.295795\pi$$
0.598421 + 0.801182i $$0.295795\pi$$
$$600$$ 0 0
$$601$$ −199390. −0.0225173 −0.0112587 0.999937i $$-0.503584\pi$$
−0.0112587 + 0.999937i $$0.503584\pi$$
$$602$$ 0 0
$$603$$ 6.13301e6 0.686879
$$604$$ 0 0
$$605$$ 746691. 0.0829378
$$606$$ 0 0
$$607$$ 16190.0 0.00178351 0.000891754 1.00000i $$-0.499716\pi$$
0.000891754 1.00000i $$0.499716\pi$$
$$608$$ 0 0
$$609$$ 342624. 0.0374347
$$610$$ 0 0
$$611$$ 1.18913e7 1.28863
$$612$$ 0 0
$$613$$ 1.15253e7 1.23880 0.619402 0.785074i $$-0.287375\pi$$
0.619402 + 0.785074i $$0.287375\pi$$
$$614$$ 0 0
$$615$$ −270504. −0.0288394
$$616$$ 0 0
$$617$$ 1.69974e7 1.79750 0.898751 0.438459i $$-0.144476\pi$$
0.898751 + 0.438459i $$0.144476\pi$$
$$618$$ 0 0
$$619$$ 1.84875e7 1.93933 0.969663 0.244445i $$-0.0786058\pi$$
0.969663 + 0.244445i $$0.0786058\pi$$
$$620$$ 0 0
$$621$$ −862815. −0.0897819
$$622$$ 0 0
$$623$$ −2.08189e7 −2.14901
$$624$$ 0 0
$$625$$ −7.85355e6 −0.804203
$$626$$ 0 0
$$627$$ 172304. 0.0175036
$$628$$ 0 0
$$629$$ −1.09113e7 −1.09964
$$630$$ 0 0
$$631$$ −4.54281e6 −0.454204 −0.227102 0.973871i $$-0.572925\pi$$
−0.227102 + 0.973871i $$0.572925\pi$$
$$632$$ 0 0
$$633$$ −932428. −0.0924924
$$634$$ 0 0
$$635$$ −1.22102e7 −1.20168
$$636$$ 0 0
$$637$$ −7.43831e6 −0.726316
$$638$$ 0 0
$$639$$ −3.22126e6 −0.312086
$$640$$ 0 0
$$641$$ 1.84286e7 1.77153 0.885764 0.464136i $$-0.153635\pi$$
0.885764 + 0.464136i $$0.153635\pi$$
$$642$$ 0 0
$$643$$ −9.66604e6 −0.921979 −0.460989 0.887406i $$-0.652505\pi$$
−0.460989 + 0.887406i $$0.652505\pi$$
$$644$$ 0 0
$$645$$ 907698. 0.0859097
$$646$$ 0 0
$$647$$ −4.51430e6 −0.423965 −0.211982 0.977273i $$-0.567992\pi$$
−0.211982 + 0.977273i $$0.567992\pi$$
$$648$$ 0 0
$$649$$ 4.23367e6 0.394553
$$650$$ 0 0
$$651$$ 1.03667e6 0.0958712
$$652$$ 0 0
$$653$$ 5.37235e6 0.493039 0.246519 0.969138i $$-0.420713\pi$$
0.246519 + 0.969138i $$0.420713\pi$$
$$654$$ 0 0
$$655$$ 5.00524e6 0.455850
$$656$$ 0 0
$$657$$ 1.28889e7 1.16494
$$658$$ 0 0
$$659$$ −9.87956e6 −0.886184 −0.443092 0.896476i $$-0.646119\pi$$
−0.443092 + 0.896476i $$0.646119\pi$$
$$660$$ 0 0
$$661$$ −1.08052e7 −0.961898 −0.480949 0.876748i $$-0.659708\pi$$
−0.480949 + 0.876748i $$0.659708\pi$$
$$662$$ 0 0
$$663$$ −510696. −0.0451210
$$664$$ 0 0
$$665$$ 1.20556e7 1.05714
$$666$$ 0 0
$$667$$ −3.67186e6 −0.319574
$$668$$ 0 0
$$669$$ −169745. −0.0146633
$$670$$ 0 0
$$671$$ 5.55874e6 0.476618
$$672$$ 0 0
$$673$$ 1.13275e7 0.964042 0.482021 0.876160i $$-0.339903\pi$$
0.482021 + 0.876160i $$0.339903\pi$$
$$674$$ 0 0
$$675$$ −254140. −0.0214691
$$676$$ 0 0
$$677$$ 1.20595e7 1.01125 0.505624 0.862754i $$-0.331262\pi$$
0.505624 + 0.862754i $$0.331262\pi$$
$$678$$ 0 0
$$679$$ 1.47420e7 1.22710
$$680$$ 0 0
$$681$$ 198078. 0.0163670
$$682$$ 0 0
$$683$$ 5.14166e6 0.421747 0.210873 0.977513i $$-0.432369\pi$$
0.210873 + 0.977513i $$0.432369\pi$$
$$684$$ 0 0
$$685$$ 2.04070e7 1.66170
$$686$$ 0 0
$$687$$ −849997. −0.0687109
$$688$$ 0 0
$$689$$ −2.12624e7 −1.70633
$$690$$ 0 0
$$691$$ −1.31243e7 −1.04563 −0.522817 0.852445i $$-0.675119\pi$$
−0.522817 + 0.852445i $$0.675119\pi$$
$$692$$ 0 0
$$693$$ 4.86081e6 0.384482
$$694$$ 0 0
$$695$$ −1.04941e7 −0.824104
$$696$$ 0 0
$$697$$ −3.91435e6 −0.305195
$$698$$ 0 0
$$699$$ 401832. 0.0311065
$$700$$ 0 0
$$701$$ −3.65956e6 −0.281277 −0.140638 0.990061i $$-0.544916\pi$$
−0.140638 + 0.990061i $$0.544916\pi$$
$$702$$ 0 0
$$703$$ −2.10538e7 −1.60673
$$704$$ 0 0
$$705$$ 876384. 0.0664082
$$706$$ 0 0
$$707$$ 246012. 0.0185101
$$708$$ 0 0
$$709$$ −1.02252e7 −0.763935 −0.381968 0.924176i $$-0.624753\pi$$
−0.381968 + 0.924176i $$0.624753\pi$$
$$710$$ 0 0
$$711$$ −1.86906e7 −1.38660
$$712$$ 0 0
$$713$$ −1.11099e7 −0.818436
$$714$$ 0 0
$$715$$ −4.27033e6 −0.312390
$$716$$ 0 0
$$717$$ −855174. −0.0621236
$$718$$ 0 0
$$719$$ 2.41683e7 1.74351 0.871753 0.489945i $$-0.162983\pi$$
0.871753 + 0.489945i $$0.162983\pi$$
$$720$$ 0 0
$$721$$ 1.95043e7 1.39731
$$722$$ 0 0
$$723$$ −1.12546e6 −0.0800730
$$724$$ 0 0
$$725$$ −1.08154e6 −0.0764181
$$726$$ 0 0
$$727$$ 1.68246e7 1.18062 0.590310 0.807177i $$-0.299006\pi$$
0.590310 + 0.807177i $$0.299006\pi$$
$$728$$ 0 0
$$729$$ −1.39958e7 −0.975393
$$730$$ 0 0
$$731$$ 1.31349e7 0.909147
$$732$$ 0 0
$$733$$ 5.04168e6 0.346590 0.173295 0.984870i $$-0.444559\pi$$
0.173295 + 0.984870i $$0.444559\pi$$
$$734$$ 0 0
$$735$$ −548199. −0.0374300
$$736$$ 0 0
$$737$$ −3.06650e6 −0.207958
$$738$$ 0 0
$$739$$ 6.26375e6 0.421913 0.210957 0.977495i $$-0.432342\pi$$
0.210957 + 0.977495i $$0.432342\pi$$
$$740$$ 0 0
$$741$$ −985408. −0.0659281
$$742$$ 0 0
$$743$$ 3.63976e6 0.241880 0.120940 0.992660i $$-0.461409\pi$$
0.120940 + 0.992660i $$0.461409\pi$$
$$744$$ 0 0
$$745$$ −4.47403e6 −0.295330
$$746$$ 0 0
$$747$$ 1.33134e7 0.872945
$$748$$ 0 0
$$749$$ −1.31741e7 −0.858057
$$750$$ 0 0
$$751$$ −1.87370e7 −1.21227 −0.606135 0.795362i $$-0.707281\pi$$
−0.606135 + 0.795362i $$0.707281\pi$$
$$752$$ 0 0
$$753$$ −1.19751e6 −0.0769649
$$754$$ 0 0
$$755$$ −2.20717e7 −1.40918
$$756$$ 0 0
$$757$$ −489242. −0.0310302 −0.0155151 0.999880i $$-0.504939\pi$$
−0.0155151 + 0.999880i $$0.504939\pi$$
$$758$$ 0 0
$$759$$ 215259. 0.0135630
$$760$$ 0 0
$$761$$ 1.46969e7 0.919952 0.459976 0.887931i $$-0.347858\pi$$
0.459976 + 0.887931i $$0.347858\pi$$
$$762$$ 0 0
$$763$$ 1.45818e7 0.906774
$$764$$ 0 0
$$765$$ 9.10840e6 0.562715
$$766$$ 0 0
$$767$$ −2.42124e7 −1.48610
$$768$$ 0 0
$$769$$ 2.42072e7 1.47615 0.738073 0.674721i $$-0.235736\pi$$
0.738073 + 0.674721i $$0.235736\pi$$
$$770$$ 0 0
$$771$$ −37758.0 −0.00228756
$$772$$ 0 0
$$773$$ −1.35260e7 −0.814181 −0.407091 0.913388i $$-0.633457\pi$$
−0.407091 + 0.913388i $$0.633457\pi$$
$$774$$ 0 0
$$775$$ −3.27238e6 −0.195708
$$776$$ 0 0
$$777$$ 2.45431e6 0.145840
$$778$$ 0 0
$$779$$ −7.55290e6 −0.445933
$$780$$ 0 0
$$781$$ 1.61063e6 0.0944862
$$782$$ 0 0
$$783$$ 1.00104e6 0.0583508
$$784$$ 0 0
$$785$$ 1.73782e6 0.100654
$$786$$ 0 0
$$787$$ −1.42094e7 −0.817786 −0.408893 0.912582i $$-0.634085\pi$$
−0.408893 + 0.912582i $$0.634085\pi$$
$$788$$ 0 0
$$789$$ 631254. 0.0361004
$$790$$ 0 0
$$791$$ 7.84300e6 0.445698
$$792$$ 0 0
$$793$$ −3.17905e7 −1.79521
$$794$$ 0 0
$$795$$ −1.56703e6 −0.0879343
$$796$$ 0 0
$$797$$ 7.93333e6 0.442395 0.221197 0.975229i $$-0.429003\pi$$
0.221197 + 0.975229i $$0.429003\pi$$
$$798$$ 0 0
$$799$$ 1.26818e7 0.702771
$$800$$ 0 0
$$801$$ −3.03504e7 −1.67141
$$802$$ 0 0
$$803$$ −6.44446e6 −0.352694
$$804$$ 0 0
$$805$$ 1.50610e7 0.819152
$$806$$ 0 0
$$807$$ −1.08034e6 −0.0583952
$$808$$ 0 0
$$809$$ −1.04685e7 −0.562359 −0.281180 0.959655i $$-0.590726\pi$$
−0.281180 + 0.959655i $$0.590726\pi$$
$$810$$ 0 0
$$811$$ −1.19147e7 −0.636110 −0.318055 0.948072i $$-0.603030\pi$$
−0.318055 + 0.948072i $$0.603030\pi$$
$$812$$ 0 0
$$813$$ 816100. 0.0433029
$$814$$ 0 0
$$815$$ −2.29602e6 −0.121083
$$816$$ 0 0
$$817$$ 2.53444e7 1.32839
$$818$$ 0 0
$$819$$ −2.77990e7 −1.44817
$$820$$ 0 0
$$821$$ 1.86112e6 0.0963645 0.0481822 0.998839i $$-0.484657\pi$$
0.0481822 + 0.998839i $$0.484657\pi$$
$$822$$ 0 0
$$823$$ 2.30153e7 1.18445 0.592225 0.805773i $$-0.298250\pi$$
0.592225 + 0.805773i $$0.298250\pi$$
$$824$$ 0 0
$$825$$ 63404.0 0.00324326
$$826$$ 0 0
$$827$$ 1.68351e7 0.855959 0.427980 0.903788i $$-0.359225\pi$$
0.427980 + 0.903788i $$0.359225\pi$$
$$828$$ 0 0
$$829$$ 2.35299e7 1.18914 0.594570 0.804044i $$-0.297322\pi$$
0.594570 + 0.804044i $$0.297322\pi$$
$$830$$ 0 0
$$831$$ 1.68820e6 0.0848049
$$832$$ 0 0
$$833$$ −7.93276e6 −0.396106
$$834$$ 0 0
$$835$$ 2.46104e7 1.22152
$$836$$ 0 0
$$837$$ 3.02882e6 0.149438
$$838$$ 0 0
$$839$$ 2.91549e7 1.42990 0.714952 0.699173i $$-0.246448\pi$$
0.714952 + 0.699173i $$0.246448\pi$$
$$840$$ 0 0
$$841$$ −1.62511e7 −0.792303
$$842$$ 0 0
$$843$$ 879042. 0.0426030
$$844$$ 0 0
$$845$$ 5.48612e6 0.264316
$$846$$ 0 0
$$847$$ −2.43041e6 −0.116405
$$848$$ 0 0
$$849$$ 1.54027e6 0.0733377
$$850$$ 0 0
$$851$$ −2.63025e7 −1.24501
$$852$$ 0 0
$$853$$ 9.49052e6 0.446599 0.223299 0.974750i $$-0.428317\pi$$
0.223299 + 0.974750i $$0.428317\pi$$
$$854$$ 0 0
$$855$$ 1.75750e7 0.822205
$$856$$ 0 0
$$857$$ −1.81553e6 −0.0844405 −0.0422203 0.999108i $$-0.513443\pi$$
−0.0422203 + 0.999108i $$0.513443\pi$$
$$858$$ 0 0
$$859$$ 1.07812e7 0.498522 0.249261 0.968436i $$-0.419812\pi$$
0.249261 + 0.968436i $$0.419812\pi$$
$$860$$ 0 0
$$861$$ 880464. 0.0404766
$$862$$ 0 0
$$863$$ −2.83355e7 −1.29510 −0.647550 0.762023i $$-0.724206\pi$$
−0.647550 + 0.762023i $$0.724206\pi$$
$$864$$ 0 0
$$865$$ 3.90790e7 1.77584
$$866$$ 0 0
$$867$$ 875213. 0.0395427
$$868$$ 0 0
$$869$$ 9.34531e6 0.419802
$$870$$ 0 0
$$871$$ 1.75374e7 0.783283
$$872$$ 0 0
$$873$$ 2.14913e7 0.954392
$$874$$ 0 0
$$875$$ 3.08924e7 1.36406
$$876$$ 0 0
$$877$$ 2.68919e7 1.18065 0.590326 0.807165i $$-0.298999\pi$$
0.590326 + 0.807165i $$0.298999\pi$$
$$878$$ 0 0
$$879$$ 720840. 0.0314678
$$880$$ 0 0
$$881$$ −1.92132e7 −0.833989 −0.416995 0.908909i $$-0.636917\pi$$
−0.416995 + 0.908909i $$0.636917\pi$$
$$882$$ 0 0
$$883$$ −1.15931e7 −0.500378 −0.250189 0.968197i $$-0.580493\pi$$
−0.250189 + 0.968197i $$0.580493\pi$$
$$884$$ 0 0
$$885$$ −1.78444e6 −0.0765850
$$886$$ 0 0
$$887$$ 1.31857e7 0.562721 0.281361 0.959602i $$-0.409214\pi$$
0.281361 + 0.959602i $$0.409214\pi$$
$$888$$ 0 0
$$889$$ 3.97431e7 1.68658
$$890$$ 0 0
$$891$$ 7.05684e6 0.297794
$$892$$ 0 0
$$893$$ 2.44700e7 1.02685
$$894$$ 0 0
$$895$$ −1.54733e7 −0.645694
$$896$$ 0 0
$$897$$ −1.23107e6 −0.0510859
$$898$$ 0 0
$$899$$ 1.28897e7 0.531916
$$900$$ 0 0
$$901$$ −2.26758e7 −0.930573
$$902$$ 0 0
$$903$$ −2.95447e6 −0.120576
$$904$$ 0 0
$$905$$ 1.45442e7 0.590295
$$906$$ 0 0
$$907$$ −2.98195e6 −0.120360 −0.0601800 0.998188i $$-0.519167\pi$$
−0.0601800 + 0.998188i $$0.519167\pi$$
$$908$$ 0 0
$$909$$ 358644. 0.0143964
$$910$$ 0 0
$$911$$ 2.96579e7 1.18398 0.591989 0.805946i $$-0.298343\pi$$
0.591989 + 0.805946i $$0.298343\pi$$
$$912$$ 0 0
$$913$$ −6.65669e6 −0.264291
$$914$$ 0 0
$$915$$ −2.34294e6 −0.0925142
$$916$$ 0 0
$$917$$ −1.62916e7 −0.639793
$$918$$ 0 0
$$919$$ 3.18057e7 1.24227 0.621135 0.783704i $$-0.286672\pi$$
0.621135 + 0.783704i $$0.286672\pi$$
$$920$$ 0 0
$$921$$ −1.03905e6 −0.0403633
$$922$$ 0 0
$$923$$ −9.21121e6 −0.355887
$$924$$ 0 0
$$925$$ −7.74734e6 −0.297713
$$926$$ 0 0
$$927$$ 2.84340e7 1.08677
$$928$$ 0 0
$$929$$ −2.33444e7 −0.887451 −0.443725 0.896163i $$-0.646343\pi$$
−0.443725 + 0.896163i $$0.646343\pi$$
$$930$$ 0 0
$$931$$ −1.53066e7 −0.578767
$$932$$ 0 0
$$933$$ 1.25135e6 0.0470624
$$934$$ 0 0
$$935$$ −4.55420e6 −0.170366
$$936$$ 0 0
$$937$$ 2.07372e7 0.771616 0.385808 0.922579i $$-0.373923\pi$$
0.385808 + 0.922579i $$0.373923\pi$$
$$938$$ 0 0
$$939$$ 1.44336e6 0.0534209
$$940$$ 0 0
$$941$$ −2.69193e7 −0.991036 −0.495518 0.868598i $$-0.665022\pi$$
−0.495518 + 0.868598i $$0.665022\pi$$
$$942$$ 0 0
$$943$$ −9.43582e6 −0.345542
$$944$$ 0 0
$$945$$ −4.10601e6 −0.149569
$$946$$ 0 0
$$947$$ −1.01896e7 −0.369216 −0.184608 0.982812i $$-0.559102\pi$$
−0.184608 + 0.982812i $$0.559102\pi$$
$$948$$ 0 0
$$949$$ 3.68559e7 1.32844
$$950$$ 0 0
$$951$$ −2.01208e6 −0.0721429
$$952$$ 0 0
$$953$$ 1.03924e7 0.370665 0.185333 0.982676i $$-0.440664\pi$$
0.185333 + 0.982676i $$0.440664\pi$$
$$954$$ 0 0
$$955$$ 3.91204e7 1.38802
$$956$$ 0 0
$$957$$ −249744. −0.00881486
$$958$$ 0 0
$$959$$ −6.64227e7 −2.33222
$$960$$ 0 0
$$961$$ 1.03709e7 0.362249
$$962$$ 0 0
$$963$$ −1.92056e7 −0.667363
$$964$$ 0 0
$$965$$ 2.09951e7 0.725770
$$966$$ 0 0
$$967$$ −8.18877e6 −0.281613 −0.140806 0.990037i $$-0.544970\pi$$
−0.140806 + 0.990037i $$0.544970\pi$$
$$968$$ 0 0
$$969$$ −1.05091e6 −0.0359548
$$970$$ 0 0
$$971$$ 1.73274e7 0.589775 0.294887 0.955532i $$-0.404718\pi$$
0.294887 + 0.955532i $$0.404718\pi$$
$$972$$ 0 0
$$973$$ 3.41572e7 1.15664
$$974$$ 0 0
$$975$$ −362608. −0.0122159
$$976$$ 0 0
$$977$$ −438963. −0.0147127 −0.00735634 0.999973i $$-0.502342\pi$$
−0.00735634 + 0.999973i $$0.502342\pi$$
$$978$$ 0 0
$$979$$ 1.51752e7 0.506032
$$980$$ 0 0
$$981$$ 2.12578e7 0.705253
$$982$$ 0 0
$$983$$ −2.79124e7 −0.921326 −0.460663 0.887575i $$-0.652388\pi$$
−0.460663 + 0.887575i $$0.652388\pi$$
$$984$$ 0 0
$$985$$ 3.87222e7 1.27165
$$986$$ 0 0
$$987$$ −2.85254e6 −0.0932051
$$988$$ 0 0
$$989$$ 3.16626e7 1.02933
$$990$$ 0 0
$$991$$ −4.26846e7 −1.38066 −0.690331 0.723494i $$-0.742535\pi$$
−0.690331 + 0.723494i $$0.742535\pi$$
$$992$$ 0 0
$$993$$ 2.01734e6 0.0649240
$$994$$ 0 0
$$995$$ −2.37660e6 −0.0761024
$$996$$ 0 0
$$997$$ 2.21044e7 0.704273 0.352137 0.935949i $$-0.385455\pi$$
0.352137 + 0.935949i $$0.385455\pi$$
$$998$$ 0 0
$$999$$ 7.17072e6 0.227326
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 704.6.a.e.1.1 1
4.3 odd 2 704.6.a.f.1.1 1
8.3 odd 2 176.6.a.b.1.1 1
8.5 even 2 22.6.a.b.1.1 1
24.5 odd 2 198.6.a.i.1.1 1
40.13 odd 4 550.6.b.f.199.2 2
40.29 even 2 550.6.a.f.1.1 1
40.37 odd 4 550.6.b.f.199.1 2
56.13 odd 2 1078.6.a.a.1.1 1
88.21 odd 2 242.6.a.d.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
22.6.a.b.1.1 1 8.5 even 2
176.6.a.b.1.1 1 8.3 odd 2
198.6.a.i.1.1 1 24.5 odd 2
242.6.a.d.1.1 1 88.21 odd 2
550.6.a.f.1.1 1 40.29 even 2
550.6.b.f.199.1 2 40.37 odd 4
550.6.b.f.199.2 2 40.13 odd 4
704.6.a.e.1.1 1 1.1 even 1 trivial
704.6.a.f.1.1 1 4.3 odd 2
1078.6.a.a.1.1 1 56.13 odd 2