# Properties

 Label 1008.6.a.bq.1.2 Level $1008$ Weight $6$ Character 1008.1 Self dual yes Analytic conductor $161.667$ Analytic rank $1$ Dimension $2$ 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: $$2$$ Coefficient field: $$\Q(\sqrt{57})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 14$$ x^2 - x - 14 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 7) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$4.27492$$ of defining polynomial 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)

 $$f(q)$$ $$=$$ $$q+46.7492 q^{5} -49.0000 q^{7} +O(q^{10})$$ $$q+46.7492 q^{5} -49.0000 q^{7} +666.090 q^{11} -650.640 q^{13} -1186.89 q^{17} +1565.05 q^{19} -1100.15 q^{23} -939.515 q^{25} -2396.72 q^{29} +2048.46 q^{31} -2290.71 q^{35} +1077.54 q^{37} -1098.21 q^{41} -16564.3 q^{43} -8298.39 q^{47} +2401.00 q^{49} -5519.18 q^{53} +31139.1 q^{55} -14230.4 q^{59} -14234.7 q^{61} -30416.9 q^{65} -19730.4 q^{67} +64562.7 q^{71} +28567.0 q^{73} -32638.4 q^{77} +30633.4 q^{79} -675.946 q^{83} -55486.3 q^{85} -125971. q^{89} +31881.3 q^{91} +73164.9 q^{95} -22906.8 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 18 q^{5} - 98 q^{7}+O(q^{10})$$ 2 * q + 18 * q^5 - 98 * q^7 $$2 q + 18 q^{5} - 98 q^{7} + 396 q^{11} - 350 q^{13} - 1800 q^{17} + 3266 q^{19} + 2088 q^{23} - 3238 q^{25} - 6696 q^{29} + 20 q^{31} - 882 q^{35} + 6232 q^{37} + 6048 q^{41} + 3020 q^{43} + 11700 q^{47} + 4802 q^{49} - 9468 q^{53} + 38904 q^{55} - 43938 q^{59} - 64754 q^{61} - 39060 q^{65} - 24784 q^{67} + 97416 q^{71} + 17452 q^{73} - 19404 q^{77} - 51256 q^{79} + 117558 q^{83} - 37860 q^{85} - 84276 q^{89} + 17150 q^{91} + 24264 q^{95} + 20776 q^{97}+O(q^{100})$$ 2 * q + 18 * q^5 - 98 * q^7 + 396 * q^11 - 350 * q^13 - 1800 * q^17 + 3266 * q^19 + 2088 * q^23 - 3238 * q^25 - 6696 * q^29 + 20 * q^31 - 882 * q^35 + 6232 * q^37 + 6048 * q^41 + 3020 * q^43 + 11700 * q^47 + 4802 * q^49 - 9468 * q^53 + 38904 * q^55 - 43938 * q^59 - 64754 * q^61 - 39060 * q^65 - 24784 * q^67 + 97416 * q^71 + 17452 * q^73 - 19404 * q^77 - 51256 * q^79 + 117558 * q^83 - 37860 * q^85 - 84276 * q^89 + 17150 * q^91 + 24264 * q^95 + 20776 * q^97

## 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
$$5$$ 46.7492 0.836275 0.418137 0.908384i $$-0.362683\pi$$
0.418137 + 0.908384i $$0.362683\pi$$
$$6$$ 0 0
$$7$$ −49.0000 −0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 666.090 1.65978 0.829891 0.557926i $$-0.188403\pi$$
0.829891 + 0.557926i $$0.188403\pi$$
$$12$$ 0 0
$$13$$ −650.640 −1.06778 −0.533890 0.845554i $$-0.679271\pi$$
−0.533890 + 0.845554i $$0.679271\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1186.89 −0.996069 −0.498035 0.867157i $$-0.665945\pi$$
−0.498035 + 0.867157i $$0.665945\pi$$
$$18$$ 0 0
$$19$$ 1565.05 0.994591 0.497296 0.867581i $$-0.334326\pi$$
0.497296 + 0.867581i $$0.334326\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1100.15 −0.433644 −0.216822 0.976211i $$-0.569569\pi$$
−0.216822 + 0.976211i $$0.569569\pi$$
$$24$$ 0 0
$$25$$ −939.515 −0.300645
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2396.72 −0.529203 −0.264602 0.964358i $$-0.585240\pi$$
−0.264602 + 0.964358i $$0.585240\pi$$
$$30$$ 0 0
$$31$$ 2048.46 0.382844 0.191422 0.981508i $$-0.438690\pi$$
0.191422 + 0.981508i $$0.438690\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −2290.71 −0.316082
$$36$$ 0 0
$$37$$ 1077.54 0.129399 0.0646995 0.997905i $$-0.479391\pi$$
0.0646995 + 0.997905i $$0.479391\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1098.21 −0.102029 −0.0510147 0.998698i $$-0.516246\pi$$
−0.0510147 + 0.998698i $$0.516246\pi$$
$$42$$ 0 0
$$43$$ −16564.3 −1.36616 −0.683081 0.730343i $$-0.739360\pi$$
−0.683081 + 0.730343i $$0.739360\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −8298.39 −0.547960 −0.273980 0.961735i $$-0.588340\pi$$
−0.273980 + 0.961735i $$0.588340\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −5519.18 −0.269889 −0.134944 0.990853i $$-0.543086\pi$$
−0.134944 + 0.990853i $$0.543086\pi$$
$$54$$ 0 0
$$55$$ 31139.1 1.38803
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −14230.4 −0.532216 −0.266108 0.963943i $$-0.585738\pi$$
−0.266108 + 0.963943i $$0.585738\pi$$
$$60$$ 0 0
$$61$$ −14234.7 −0.489807 −0.244904 0.969547i $$-0.578756\pi$$
−0.244904 + 0.969547i $$0.578756\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −30416.9 −0.892958
$$66$$ 0 0
$$67$$ −19730.4 −0.536970 −0.268485 0.963284i $$-0.586523\pi$$
−0.268485 + 0.963284i $$0.586523\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 64562.7 1.51997 0.759986 0.649940i $$-0.225206\pi$$
0.759986 + 0.649940i $$0.225206\pi$$
$$72$$ 0 0
$$73$$ 28567.0 0.627418 0.313709 0.949519i $$-0.398428\pi$$
0.313709 + 0.949519i $$0.398428\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −32638.4 −0.627339
$$78$$ 0 0
$$79$$ 30633.4 0.552239 0.276119 0.961123i $$-0.410951\pi$$
0.276119 + 0.961123i $$0.410951\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −675.946 −0.0107700 −0.00538501 0.999986i $$-0.501714\pi$$
−0.00538501 + 0.999986i $$0.501714\pi$$
$$84$$ 0 0
$$85$$ −55486.3 −0.832987
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −125971. −1.68576 −0.842882 0.538098i $$-0.819143\pi$$
−0.842882 + 0.538098i $$0.819143\pi$$
$$90$$ 0 0
$$91$$ 31881.3 0.403583
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 73164.9 0.831751
$$96$$ 0 0
$$97$$ −22906.8 −0.247192 −0.123596 0.992333i $$-0.539443\pi$$
−0.123596 + 0.992333i $$0.539443\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 181474. 1.77015 0.885077 0.465444i $$-0.154105\pi$$
0.885077 + 0.465444i $$0.154105\pi$$
$$102$$ 0 0
$$103$$ −64772.0 −0.601581 −0.300791 0.953690i $$-0.597251\pi$$
−0.300791 + 0.953690i $$0.597251\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −148170. −1.25112 −0.625562 0.780175i $$-0.715130\pi$$
−0.625562 + 0.780175i $$0.715130\pi$$
$$108$$ 0 0
$$109$$ −111294. −0.897237 −0.448618 0.893723i $$-0.648084\pi$$
−0.448618 + 0.893723i $$0.648084\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 43175.5 0.318084 0.159042 0.987272i $$-0.449160\pi$$
0.159042 + 0.987272i $$0.449160\pi$$
$$114$$ 0 0
$$115$$ −51431.2 −0.362646
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 58157.8 0.376479
$$120$$ 0 0
$$121$$ 282625. 1.75488
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −190013. −1.08770
$$126$$ 0 0
$$127$$ 131449. 0.723182 0.361591 0.932337i $$-0.382234\pi$$
0.361591 + 0.932337i $$0.382234\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −349458. −1.77916 −0.889582 0.456775i $$-0.849005\pi$$
−0.889582 + 0.456775i $$0.849005\pi$$
$$132$$ 0 0
$$133$$ −76687.5 −0.375920
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −386434. −1.75903 −0.879516 0.475869i $$-0.842134\pi$$
−0.879516 + 0.475869i $$0.842134\pi$$
$$138$$ 0 0
$$139$$ −17289.3 −0.0758997 −0.0379498 0.999280i $$-0.512083\pi$$
−0.0379498 + 0.999280i $$0.512083\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −433384. −1.77228
$$144$$ 0 0
$$145$$ −112045. −0.442559
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 112171. 0.413917 0.206959 0.978350i $$-0.433643\pi$$
0.206959 + 0.978350i $$0.433643\pi$$
$$150$$ 0 0
$$151$$ −30495.4 −0.108841 −0.0544205 0.998518i $$-0.517331\pi$$
−0.0544205 + 0.998518i $$0.517331\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 95763.6 0.320163
$$156$$ 0 0
$$157$$ 523509. 1.69502 0.847510 0.530780i $$-0.178101\pi$$
0.847510 + 0.530780i $$0.178101\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 53907.5 0.163902
$$162$$ 0 0
$$163$$ 439646. 1.29609 0.648043 0.761604i $$-0.275588\pi$$
0.648043 + 0.761604i $$0.275588\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 279353. 0.775107 0.387554 0.921847i $$-0.373320\pi$$
0.387554 + 0.921847i $$0.373320\pi$$
$$168$$ 0 0
$$169$$ 52038.8 0.140156
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −99699.4 −0.253266 −0.126633 0.991950i $$-0.540417\pi$$
−0.126633 + 0.991950i $$0.540417\pi$$
$$174$$ 0 0
$$175$$ 46036.2 0.113633
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 329980. 0.769760 0.384880 0.922967i $$-0.374243\pi$$
0.384880 + 0.922967i $$0.374243\pi$$
$$180$$ 0 0
$$181$$ −505810. −1.14760 −0.573800 0.818995i $$-0.694531\pi$$
−0.573800 + 0.818995i $$0.694531\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 50374.3 0.108213
$$186$$ 0 0
$$187$$ −790578. −1.65326
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −63835.6 −0.126613 −0.0633067 0.997994i $$-0.520165\pi$$
−0.0633067 + 0.997994i $$0.520165\pi$$
$$192$$ 0 0
$$193$$ 469355. 0.907001 0.453501 0.891256i $$-0.350175\pi$$
0.453501 + 0.891256i $$0.350175\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −268021. −0.492043 −0.246021 0.969264i $$-0.579123\pi$$
−0.246021 + 0.969264i $$0.579123\pi$$
$$198$$ 0 0
$$199$$ 605167. 1.08328 0.541642 0.840609i $$-0.317803\pi$$
0.541642 + 0.840609i $$0.317803\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 117439. 0.200020
$$204$$ 0 0
$$205$$ −51340.4 −0.0853246
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1.04246e6 1.65080
$$210$$ 0 0
$$211$$ −335389. −0.518612 −0.259306 0.965795i $$-0.583494\pi$$
−0.259306 + 0.965795i $$0.583494\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −774367. −1.14249
$$216$$ 0 0
$$217$$ −100374. −0.144702
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 772240. 1.06358
$$222$$ 0 0
$$223$$ −1.02526e6 −1.38061 −0.690305 0.723518i $$-0.742524\pi$$
−0.690305 + 0.723518i $$0.742524\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −504226. −0.649473 −0.324736 0.945805i $$-0.605276\pi$$
−0.324736 + 0.945805i $$0.605276\pi$$
$$228$$ 0 0
$$229$$ −1.11939e6 −1.41057 −0.705283 0.708925i $$-0.749180\pi$$
−0.705283 + 0.708925i $$0.749180\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −770703. −0.930031 −0.465015 0.885303i $$-0.653951\pi$$
−0.465015 + 0.885303i $$0.653951\pi$$
$$234$$ 0 0
$$235$$ −387943. −0.458245
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −171646. −0.194374 −0.0971871 0.995266i $$-0.530985\pi$$
−0.0971871 + 0.995266i $$0.530985\pi$$
$$240$$ 0 0
$$241$$ −383779. −0.425637 −0.212818 0.977092i $$-0.568264\pi$$
−0.212818 + 0.977092i $$0.568264\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 112245. 0.119468
$$246$$ 0 0
$$247$$ −1.01828e6 −1.06201
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1.57046e6 −1.57342 −0.786708 0.617325i $$-0.788216\pi$$
−0.786708 + 0.617325i $$0.788216\pi$$
$$252$$ 0 0
$$253$$ −732801. −0.719755
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −790656. −0.746715 −0.373357 0.927688i $$-0.621793\pi$$
−0.373357 + 0.927688i $$0.621793\pi$$
$$258$$ 0 0
$$259$$ −52799.7 −0.0489082
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 464416. 0.414017 0.207008 0.978339i $$-0.433627\pi$$
0.207008 + 0.978339i $$0.433627\pi$$
$$264$$ 0 0
$$265$$ −258017. −0.225701
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.99959e6 −1.68484 −0.842422 0.538818i $$-0.818871\pi$$
−0.842422 + 0.538818i $$0.818871\pi$$
$$270$$ 0 0
$$271$$ −1.61296e6 −1.33414 −0.667070 0.744995i $$-0.732452\pi$$
−0.667070 + 0.744995i $$0.732452\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −625801. −0.499005
$$276$$ 0 0
$$277$$ −2.08119e6 −1.62972 −0.814860 0.579658i $$-0.803186\pi$$
−0.814860 + 0.579658i $$0.803186\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 982035. 0.741927 0.370964 0.928647i $$-0.379027\pi$$
0.370964 + 0.928647i $$0.379027\pi$$
$$282$$ 0 0
$$283$$ 1.39622e6 1.03630 0.518152 0.855289i $$-0.326620\pi$$
0.518152 + 0.855289i $$0.326620\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 53812.3 0.0385635
$$288$$ 0 0
$$289$$ −11140.3 −0.00784609
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −2.56205e6 −1.74348 −0.871742 0.489965i $$-0.837010\pi$$
−0.871742 + 0.489965i $$0.837010\pi$$
$$294$$ 0 0
$$295$$ −665260. −0.445078
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 715803. 0.463037
$$300$$ 0 0
$$301$$ 811651. 0.516361
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −665463. −0.409613
$$306$$ 0 0
$$307$$ 884855. 0.535829 0.267915 0.963443i $$-0.413666\pi$$
0.267915 + 0.963443i $$0.413666\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1.80120e6 1.05599 0.527997 0.849246i $$-0.322943\pi$$
0.527997 + 0.849246i $$0.322943\pi$$
$$312$$ 0 0
$$313$$ 950366. 0.548315 0.274158 0.961685i $$-0.411601\pi$$
0.274158 + 0.961685i $$0.411601\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −3.04277e6 −1.70068 −0.850338 0.526237i $$-0.823602\pi$$
−0.850338 + 0.526237i $$0.823602\pi$$
$$318$$ 0 0
$$319$$ −1.59643e6 −0.878362
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1.85755e6 −0.990682
$$324$$ 0 0
$$325$$ 611286. 0.321023
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 406621. 0.207110
$$330$$ 0 0
$$331$$ 2.19616e6 1.10178 0.550889 0.834579i $$-0.314289\pi$$
0.550889 + 0.834579i $$0.314289\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −922382. −0.449054
$$336$$ 0 0
$$337$$ −2.41491e6 −1.15832 −0.579158 0.815216i $$-0.696618\pi$$
−0.579158 + 0.815216i $$0.696618\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.36446e6 0.635438
$$342$$ 0 0
$$343$$ −117649. −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1.08833e6 −0.485219 −0.242609 0.970124i $$-0.578003\pi$$
−0.242609 + 0.970124i $$0.578003\pi$$
$$348$$ 0 0
$$349$$ 2.79267e6 1.22731 0.613657 0.789573i $$-0.289698\pi$$
0.613657 + 0.789573i $$0.289698\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −2.53134e6 −1.08122 −0.540610 0.841273i $$-0.681807\pi$$
−0.540610 + 0.841273i $$0.681807\pi$$
$$354$$ 0 0
$$355$$ 3.01825e6 1.27111
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 1.09028e6 0.446480 0.223240 0.974763i $$-0.428337\pi$$
0.223240 + 0.974763i $$0.428337\pi$$
$$360$$ 0 0
$$361$$ −26712.8 −0.0107883
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1.33548e6 0.524694
$$366$$ 0 0
$$367$$ −188070. −0.0728879 −0.0364439 0.999336i $$-0.511603\pi$$
−0.0364439 + 0.999336i $$0.511603\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 270440. 0.102008
$$372$$ 0 0
$$373$$ −1.79371e6 −0.667545 −0.333772 0.942654i $$-0.608322\pi$$
−0.333772 + 0.942654i $$0.608322\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 1.55940e6 0.565073
$$378$$ 0 0
$$379$$ −3.58806e6 −1.28310 −0.641551 0.767080i $$-0.721709\pi$$
−0.641551 + 0.767080i $$0.721709\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −3.42457e6 −1.19291 −0.596457 0.802645i $$-0.703425\pi$$
−0.596457 + 0.802645i $$0.703425\pi$$
$$384$$ 0 0
$$385$$ −1.52582e6 −0.524627
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −8625.27 −0.00289001 −0.00144500 0.999999i $$-0.500460\pi$$
−0.00144500 + 0.999999i $$0.500460\pi$$
$$390$$ 0 0
$$391$$ 1.30576e6 0.431940
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 1.43208e6 0.461823
$$396$$ 0 0
$$397$$ 1.25709e6 0.400306 0.200153 0.979765i $$-0.435856\pi$$
0.200153 + 0.979765i $$0.435856\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1.42670e6 −0.443070 −0.221535 0.975152i $$-0.571107\pi$$
−0.221535 + 0.975152i $$0.571107\pi$$
$$402$$ 0 0
$$403$$ −1.33281e6 −0.408794
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 717741. 0.214774
$$408$$ 0 0
$$409$$ −3.06529e6 −0.906073 −0.453036 0.891492i $$-0.649659\pi$$
−0.453036 + 0.891492i $$0.649659\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 697291. 0.201159
$$414$$ 0 0
$$415$$ −31599.9 −0.00900670
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −248240. −0.0690776 −0.0345388 0.999403i $$-0.510996\pi$$
−0.0345388 + 0.999403i $$0.510996\pi$$
$$420$$ 0 0
$$421$$ 5.96280e6 1.63963 0.819814 0.572630i $$-0.194077\pi$$
0.819814 + 0.572630i $$0.194077\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.11510e6 0.299463
$$426$$ 0 0
$$427$$ 697503. 0.185130
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −4.93538e6 −1.27976 −0.639879 0.768476i $$-0.721015\pi$$
−0.639879 + 0.768476i $$0.721015\pi$$
$$432$$ 0 0
$$433$$ 4.15513e6 1.06504 0.532519 0.846418i $$-0.321245\pi$$
0.532519 + 0.846418i $$0.321245\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −1.72180e6 −0.431299
$$438$$ 0 0
$$439$$ 227955. 0.0564531 0.0282265 0.999602i $$-0.491014\pi$$
0.0282265 + 0.999602i $$0.491014\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −1.98462e6 −0.480472 −0.240236 0.970715i $$-0.577225\pi$$
−0.240236 + 0.970715i $$0.577225\pi$$
$$444$$ 0 0
$$445$$ −5.88906e6 −1.40976
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −2.61077e6 −0.611157 −0.305579 0.952167i $$-0.598850\pi$$
−0.305579 + 0.952167i $$0.598850\pi$$
$$450$$ 0 0
$$451$$ −731506. −0.169347
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 1.49043e6 0.337506
$$456$$ 0 0
$$457$$ −4.09917e6 −0.918132 −0.459066 0.888402i $$-0.651816\pi$$
−0.459066 + 0.888402i $$0.651816\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2.62378e6 0.575009 0.287505 0.957779i $$-0.407174\pi$$
0.287505 + 0.957779i $$0.407174\pi$$
$$462$$ 0 0
$$463$$ 4.28563e6 0.929100 0.464550 0.885547i $$-0.346216\pi$$
0.464550 + 0.885547i $$0.346216\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 990118. 0.210085 0.105042 0.994468i $$-0.466502\pi$$
0.105042 + 0.994468i $$0.466502\pi$$
$$468$$ 0 0
$$469$$ 966792. 0.202955
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −1.10333e7 −2.26753
$$474$$ 0 0
$$475$$ −1.47039e6 −0.299019
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 2.57976e6 0.513737 0.256868 0.966446i $$-0.417309\pi$$
0.256868 + 0.966446i $$0.417309\pi$$
$$480$$ 0 0
$$481$$ −701093. −0.138170
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.07087e6 −0.206720
$$486$$ 0 0
$$487$$ −3.21474e6 −0.614219 −0.307109 0.951674i $$-0.599362\pi$$
−0.307109 + 0.951674i $$0.599362\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −7.86108e6 −1.47156 −0.735781 0.677220i $$-0.763185\pi$$
−0.735781 + 0.677220i $$0.763185\pi$$
$$492$$ 0 0
$$493$$ 2.84465e6 0.527123
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −3.16357e6 −0.574495
$$498$$ 0 0
$$499$$ 1.35382e6 0.243395 0.121697 0.992567i $$-0.461166\pi$$
0.121697 + 0.992567i $$0.461166\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 3.85775e6 0.679851 0.339926 0.940452i $$-0.389598\pi$$
0.339926 + 0.940452i $$0.389598\pi$$
$$504$$ 0 0
$$505$$ 8.48376e6 1.48034
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 1.06060e7 1.81451 0.907253 0.420585i $$-0.138175\pi$$
0.907253 + 0.420585i $$0.138175\pi$$
$$510$$ 0 0
$$511$$ −1.39978e6 −0.237142
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −3.02804e6 −0.503087
$$516$$ 0 0
$$517$$ −5.52747e6 −0.909495
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 9.17989e6 1.48164 0.740821 0.671703i $$-0.234437\pi$$
0.740821 + 0.671703i $$0.234437\pi$$
$$522$$ 0 0
$$523$$ −9.05585e6 −1.44769 −0.723844 0.689964i $$-0.757627\pi$$
−0.723844 + 0.689964i $$0.757627\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.43130e6 −0.381339
$$528$$ 0 0
$$529$$ −5.22601e6 −0.811953
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 714539. 0.108945
$$534$$ 0 0
$$535$$ −6.92681e6 −1.04628
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 1.59928e6 0.237112
$$540$$ 0 0
$$541$$ 1.21783e7 1.78894 0.894468 0.447132i $$-0.147555\pi$$
0.894468 + 0.447132i $$0.147555\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −5.20292e6 −0.750336
$$546$$ 0 0
$$547$$ 9.00451e6 1.28674 0.643372 0.765554i $$-0.277535\pi$$
0.643372 + 0.765554i $$0.277535\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −3.75099e6 −0.526341
$$552$$ 0 0
$$553$$ −1.50103e6 −0.208727
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −1.54461e6 −0.210950 −0.105475 0.994422i $$-0.533636\pi$$
−0.105475 + 0.994422i $$0.533636\pi$$
$$558$$ 0 0
$$559$$ 1.07774e7 1.45876
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.18748e7 −1.57890 −0.789449 0.613816i $$-0.789634\pi$$
−0.789449 + 0.613816i $$0.789634\pi$$
$$564$$ 0 0
$$565$$ 2.01842e6 0.266005
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.54308e6 0.199806 0.0999031 0.994997i $$-0.468147\pi$$
0.0999031 + 0.994997i $$0.468147\pi$$
$$570$$ 0 0
$$571$$ 7.01812e6 0.900804 0.450402 0.892826i $$-0.351281\pi$$
0.450402 + 0.892826i $$0.351281\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.03361e6 0.130373
$$576$$ 0 0
$$577$$ −5.37543e6 −0.672162 −0.336081 0.941833i $$-0.609102\pi$$
−0.336081 + 0.941833i $$0.609102\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 33121.4 0.00407069
$$582$$ 0 0
$$583$$ −3.67627e6 −0.447957
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −2.06682e6 −0.247575 −0.123788 0.992309i $$-0.539504\pi$$
−0.123788 + 0.992309i $$0.539504\pi$$
$$588$$ 0 0
$$589$$ 3.20594e6 0.380774
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 5.46947e6 0.638717 0.319358 0.947634i $$-0.396533\pi$$
0.319358 + 0.947634i $$0.396533\pi$$
$$594$$ 0 0
$$595$$ 2.71883e6 0.314840
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 1.09943e7 1.25199 0.625996 0.779826i $$-0.284693\pi$$
0.625996 + 0.779826i $$0.284693\pi$$
$$600$$ 0 0
$$601$$ 1.58788e7 1.79322 0.896608 0.442826i $$-0.146024\pi$$
0.896608 + 0.442826i $$0.146024\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 1.32125e7 1.46756
$$606$$ 0 0
$$607$$ −5.33262e6 −0.587447 −0.293724 0.955890i $$-0.594895\pi$$
−0.293724 + 0.955890i $$0.594895\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 5.39926e6 0.585102
$$612$$ 0 0
$$613$$ −8.91838e6 −0.958594 −0.479297 0.877653i $$-0.659108\pi$$
−0.479297 + 0.877653i $$0.659108\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −9.63586e6 −1.01901 −0.509504 0.860468i $$-0.670171\pi$$
−0.509504 + 0.860468i $$0.670171\pi$$
$$618$$ 0 0
$$619$$ −1.21747e7 −1.27712 −0.638560 0.769572i $$-0.720470\pi$$
−0.638560 + 0.769572i $$0.720470\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 6.17260e6 0.637159
$$624$$ 0 0
$$625$$ −5.94695e6 −0.608968
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −1.27893e6 −0.128890
$$630$$ 0 0
$$631$$ 1.30854e7 1.30832 0.654161 0.756356i $$-0.273022\pi$$
0.654161 + 0.756356i $$0.273022\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 6.14513e6 0.604779
$$636$$ 0 0
$$637$$ −1.56219e6 −0.152540
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 441107. 0.0424032 0.0212016 0.999775i $$-0.493251\pi$$
0.0212016 + 0.999775i $$0.493251\pi$$
$$642$$ 0 0
$$643$$ 4.18888e6 0.399550 0.199775 0.979842i $$-0.435979\pi$$
0.199775 + 0.979842i $$0.435979\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.87822e7 1.76395 0.881973 0.471300i $$-0.156215\pi$$
0.881973 + 0.471300i $$0.156215\pi$$
$$648$$ 0 0
$$649$$ −9.47874e6 −0.883362
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.51733e6 0.139251 0.0696254 0.997573i $$-0.477820\pi$$
0.0696254 + 0.997573i $$0.477820\pi$$
$$654$$ 0 0
$$655$$ −1.63368e7 −1.48787
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 1.84809e7 1.65772 0.828859 0.559458i $$-0.188991\pi$$
0.828859 + 0.559458i $$0.188991\pi$$
$$660$$ 0 0
$$661$$ −1.03952e7 −0.925403 −0.462702 0.886514i $$-0.653120\pi$$
−0.462702 + 0.886514i $$0.653120\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −3.58508e6 −0.314372
$$666$$ 0 0
$$667$$ 2.63676e6 0.229486
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −9.48162e6 −0.812973
$$672$$ 0 0
$$673$$ −1.10398e7 −0.939556 −0.469778 0.882785i $$-0.655666\pi$$
−0.469778 + 0.882785i $$0.655666\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 8.23485e6 0.690532 0.345266 0.938505i $$-0.387789\pi$$
0.345266 + 0.938505i $$0.387789\pi$$
$$678$$ 0 0
$$679$$ 1.12243e6 0.0934298
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.98437e7 1.62768 0.813842 0.581086i $$-0.197372\pi$$
0.813842 + 0.581086i $$0.197372\pi$$
$$684$$ 0 0
$$685$$ −1.80655e7 −1.47103
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 3.59100e6 0.288182
$$690$$ 0 0
$$691$$ 2.37019e6 0.188837 0.0944185 0.995533i $$-0.469901\pi$$
0.0944185 + 0.995533i $$0.469901\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −808259. −0.0634730
$$696$$ 0 0
$$697$$ 1.30346e6 0.101628
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.56833e7 1.20543 0.602714 0.797957i $$-0.294086\pi$$
0.602714 + 0.797957i $$0.294086\pi$$
$$702$$ 0 0
$$703$$ 1.68641e6 0.128699
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −8.89223e6 −0.669056
$$708$$ 0 0
$$709$$ 3.68544e6 0.275343 0.137671 0.990478i $$-0.456038\pi$$
0.137671 + 0.990478i $$0.456038\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −2.25361e6 −0.166018
$$714$$ 0 0
$$715$$ −2.02604e7 −1.48212
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.56427e7 −1.12847 −0.564233 0.825615i $$-0.690828\pi$$
−0.564233 + 0.825615i $$0.690828\pi$$
$$720$$ 0 0
$$721$$ 3.17383e6 0.227376
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.25175e6 0.159102
$$726$$ 0 0
$$727$$ −1.85908e7 −1.30456 −0.652279 0.757979i $$-0.726187\pi$$
−0.652279 + 0.757979i $$0.726187\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 1.96601e7 1.36079
$$732$$ 0 0
$$733$$ 2.49466e7 1.71495 0.857476 0.514524i $$-0.172031\pi$$
0.857476 + 0.514524i $$0.172031\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −1.31422e7 −0.891253
$$738$$ 0 0
$$739$$ 2.42944e7 1.63642 0.818211 0.574918i $$-0.194966\pi$$
0.818211 + 0.574918i $$0.194966\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 4.16541e6 0.276812 0.138406 0.990376i $$-0.455802\pi$$
0.138406 + 0.990376i $$0.455802\pi$$
$$744$$ 0 0
$$745$$ 5.24388e6 0.346148
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 7.26032e6 0.472880
$$750$$ 0 0
$$751$$ 2.36434e7 1.52972 0.764858 0.644199i $$-0.222809\pi$$
0.764858 + 0.644199i $$0.222809\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −1.42564e6 −0.0910209
$$756$$ 0 0
$$757$$ 1.50108e7 0.952062 0.476031 0.879429i $$-0.342075\pi$$
0.476031 + 0.879429i $$0.342075\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −2.92191e6 −0.182897 −0.0914483 0.995810i $$-0.529150\pi$$
−0.0914483 + 0.995810i $$0.529150\pi$$
$$762$$ 0 0
$$763$$ 5.45343e6 0.339124
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 9.25887e6 0.568290
$$768$$ 0 0
$$769$$ 1.42847e7 0.871073 0.435536 0.900171i $$-0.356559\pi$$
0.435536 + 0.900171i $$0.356559\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1.09012e7 0.656186 0.328093 0.944645i $$-0.393594\pi$$
0.328093 + 0.944645i $$0.393594\pi$$
$$774$$ 0 0
$$775$$ −1.92455e6 −0.115100
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1.71875e6 −0.101478
$$780$$ 0 0
$$781$$ 4.30045e7 2.52282
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 2.44736e7 1.41750
$$786$$ 0 0
$$787$$ 2.56449e7 1.47593 0.737963 0.674841i $$-0.235788\pi$$
0.737963 + 0.674841i $$0.235788\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −2.11560e6 −0.120224
$$792$$ 0 0
$$793$$ 9.26169e6 0.523007
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −7.73086e6 −0.431104 −0.215552 0.976492i $$-0.569155\pi$$
−0.215552 + 0.976492i $$0.569155\pi$$
$$798$$ 0 0
$$799$$ 9.84931e6 0.545807
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 1.90282e7 1.04138
$$804$$ 0 0
$$805$$ 2.52013e6 0.137067
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1.87811e7 1.00890 0.504452 0.863440i $$-0.331695\pi$$
0.504452 + 0.863440i $$0.331695\pi$$
$$810$$ 0 0
$$811$$ 9.00729e6 0.480886 0.240443 0.970663i $$-0.422707\pi$$
0.240443 + 0.970663i $$0.422707\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 2.05531e7 1.08388
$$816$$ 0 0
$$817$$ −2.59240e7 −1.35877
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 9.27965e6 0.480478 0.240239 0.970714i $$-0.422774\pi$$
0.240239 + 0.970714i $$0.422774\pi$$
$$822$$ 0 0
$$823$$ 1.08308e7 0.557393 0.278697 0.960379i $$-0.410098\pi$$
0.278697 + 0.960379i $$0.410098\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −2.05230e7 −1.04346 −0.521731 0.853110i $$-0.674714\pi$$
−0.521731 + 0.853110i $$0.674714\pi$$
$$828$$ 0 0
$$829$$ −1.42216e7 −0.718724 −0.359362 0.933198i $$-0.617006\pi$$
−0.359362 + 0.933198i $$0.617006\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −2.84973e6 −0.142296
$$834$$ 0 0
$$835$$ 1.30595e7 0.648202
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −9.29934e6 −0.456087 −0.228043 0.973651i $$-0.573233\pi$$
−0.228043 + 0.973651i $$0.573233\pi$$
$$840$$ 0 0
$$841$$ −1.47669e7 −0.719944
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 2.43277e6 0.117209
$$846$$ 0 0
$$847$$ −1.38486e7 −0.663281
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −1.18546e6 −0.0561131
$$852$$ 0 0
$$853$$ −3.07436e6 −0.144671 −0.0723357 0.997380i $$-0.523045\pi$$
−0.0723357 + 0.997380i $$0.523045\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −3.45835e7 −1.60848 −0.804242 0.594302i $$-0.797428\pi$$
−0.804242 + 0.594302i $$0.797428\pi$$
$$858$$ 0 0
$$859$$ −1.63022e7 −0.753814 −0.376907 0.926251i $$-0.623012\pi$$
−0.376907 + 0.926251i $$0.623012\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 2.56962e7 1.17447 0.587235 0.809416i $$-0.300216\pi$$
0.587235 + 0.809416i $$0.300216\pi$$
$$864$$ 0 0
$$865$$ −4.66087e6 −0.211800
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 2.04046e7 0.916596
$$870$$ 0 0
$$871$$ 1.28374e7 0.573366
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 9.31062e6 0.411111
$$876$$ 0 0
$$877$$ 3.30060e7 1.44908 0.724542 0.689230i $$-0.242051\pi$$
0.724542 + 0.689230i $$0.242051\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −2.26705e6 −0.0984060 −0.0492030 0.998789i $$-0.515668\pi$$
−0.0492030 + 0.998789i $$0.515668\pi$$
$$882$$ 0 0
$$883$$ −1.97779e7 −0.853649 −0.426825 0.904334i $$-0.640368\pi$$
−0.426825 + 0.904334i $$0.640368\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −36468.3 −0.00155635 −0.000778173 1.00000i $$-0.500248\pi$$
−0.000778173 1.00000i $$0.500248\pi$$
$$888$$ 0 0
$$889$$ −6.44100e6 −0.273337
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −1.29874e7 −0.544997
$$894$$ 0 0
$$895$$ 1.54263e7 0.643730
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −4.90958e6 −0.202602
$$900$$ 0 0
$$901$$ 6.55068e6 0.268828
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −2.36462e7 −0.959709
$$906$$ 0 0
$$907$$ −1.62298e7 −0.655079 −0.327540 0.944837i $$-0.606219\pi$$
−0.327540 + 0.944837i $$0.606219\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −2.61699e7 −1.04474 −0.522368 0.852720i $$-0.674951\pi$$
−0.522368 + 0.852720i $$0.674951\pi$$
$$912$$ 0 0
$$913$$ −450241. −0.0178759
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 1.71234e7 0.672461
$$918$$ 0 0
$$919$$ −4.05973e6 −0.158565 −0.0792826 0.996852i $$-0.525263\pi$$
−0.0792826 + 0.996852i $$0.525263\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −4.20070e7 −1.62300
$$924$$ 0 0
$$925$$ −1.01237e6 −0.0389031
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −3.69518e6 −0.140474 −0.0702370 0.997530i $$-0.522376\pi$$
−0.0702370 + 0.997530i $$0.522376\pi$$
$$930$$ 0 0
$$931$$ 3.75769e6 0.142084
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −3.69589e7 −1.38258
$$936$$ 0 0
$$937$$ −1.91384e7 −0.712126 −0.356063 0.934462i $$-0.615881\pi$$
−0.356063 + 0.934462i $$0.615881\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −1.20954e7 −0.445294 −0.222647 0.974899i $$-0.571470\pi$$
−0.222647 + 0.974899i $$0.571470\pi$$
$$942$$ 0 0
$$943$$ 1.20820e6 0.0442445
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −1.95969e7 −0.710087 −0.355044 0.934850i $$-0.615534\pi$$
−0.355044 + 0.934850i $$0.615534\pi$$
$$948$$ 0 0
$$949$$ −1.85868e7 −0.669945
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −4.23265e7 −1.50966 −0.754832 0.655918i $$-0.772282\pi$$
−0.754832 + 0.655918i $$0.772282\pi$$
$$954$$ 0 0
$$955$$ −2.98426e6 −0.105884
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 1.89353e7 0.664852
$$960$$ 0 0
$$961$$ −2.44330e7 −0.853430
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 2.19419e7 0.758502
$$966$$ 0 0
$$967$$ −1.39211e6 −0.0478749 −0.0239375 0.999713i $$-0.507620\pi$$
−0.0239375 + 0.999713i $$0.507620\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 4.41877e7 1.50402 0.752009 0.659153i $$-0.229085\pi$$
0.752009 + 0.659153i $$0.229085\pi$$
$$972$$ 0 0
$$973$$ 847175. 0.0286874
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 5.60457e7 1.87848 0.939239 0.343264i $$-0.111533\pi$$
0.939239 + 0.343264i $$0.111533\pi$$
$$978$$ 0 0
$$979$$ −8.39082e7 −2.79800
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −5.00560e7 −1.65224 −0.826118 0.563497i $$-0.809456\pi$$
−0.826118 + 0.563497i $$0.809456\pi$$
$$984$$ 0 0
$$985$$ −1.25298e7 −0.411483
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 1.82233e7 0.592428
$$990$$ 0 0
$$991$$ −1.59116e7 −0.514670 −0.257335 0.966322i $$-0.582844\pi$$
−0.257335 + 0.966322i $$0.582844\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 2.82911e7 0.905924
$$996$$ 0 0
$$997$$ 4.25995e7 1.35727 0.678635 0.734476i $$-0.262572\pi$$
0.678635 + 0.734476i $$0.262572\pi$$
$$998$$ 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.bq.1.2 2
3.2 odd 2 112.6.a.h.1.1 2
4.3 odd 2 63.6.a.f.1.2 2
12.11 even 2 7.6.a.b.1.1 2
21.20 even 2 784.6.a.v.1.2 2
24.5 odd 2 448.6.a.u.1.2 2
24.11 even 2 448.6.a.w.1.1 2
28.27 even 2 441.6.a.l.1.2 2
60.23 odd 4 175.6.b.c.99.2 4
60.47 odd 4 175.6.b.c.99.3 4
60.59 even 2 175.6.a.c.1.2 2
84.11 even 6 49.6.c.e.30.2 4
84.23 even 6 49.6.c.e.18.2 4
84.47 odd 6 49.6.c.d.18.2 4
84.59 odd 6 49.6.c.d.30.2 4
84.83 odd 2 49.6.a.f.1.1 2
132.131 odd 2 847.6.a.c.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
7.6.a.b.1.1 2 12.11 even 2
49.6.a.f.1.1 2 84.83 odd 2
49.6.c.d.18.2 4 84.47 odd 6
49.6.c.d.30.2 4 84.59 odd 6
49.6.c.e.18.2 4 84.23 even 6
49.6.c.e.30.2 4 84.11 even 6
63.6.a.f.1.2 2 4.3 odd 2
112.6.a.h.1.1 2 3.2 odd 2
175.6.a.c.1.2 2 60.59 even 2
175.6.b.c.99.2 4 60.23 odd 4
175.6.b.c.99.3 4 60.47 odd 4
441.6.a.l.1.2 2 28.27 even 2
448.6.a.u.1.2 2 24.5 odd 2
448.6.a.w.1.1 2 24.11 even 2
784.6.a.v.1.2 2 21.20 even 2
847.6.a.c.1.2 2 132.131 odd 2
1008.6.a.bq.1.2 2 1.1 even 1 trivial