# Properties

 Label 1008.6.a.bx.1.1 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: $$\Q(\sqrt{429})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 107$$ x^2 - x - 107 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 504) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$10.8562$$ 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)

 $$f(q)$$ $$=$$ $$q-1.42463 q^{5} -49.0000 q^{7} +O(q^{10})$$ $$q-1.42463 q^{5} -49.0000 q^{7} -91.7261 q^{11} +224.794 q^{13} -1045.37 q^{17} +1013.21 q^{19} +2689.42 q^{23} -3122.97 q^{25} +7659.83 q^{29} -8188.32 q^{31} +69.8069 q^{35} +9108.73 q^{37} -18305.0 q^{41} +22387.1 q^{43} -4852.82 q^{47} +2401.00 q^{49} -940.063 q^{53} +130.676 q^{55} -13198.7 q^{59} +2987.79 q^{61} -320.248 q^{65} -37064.7 q^{67} +76872.6 q^{71} -50245.5 q^{73} +4494.58 q^{77} +10646.9 q^{79} +13803.0 q^{83} +1489.27 q^{85} -30996.7 q^{89} -11014.9 q^{91} -1443.44 q^{95} +99406.6 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 80 q^{5} - 98 q^{7}+O(q^{10})$$ 2 * q + 80 * q^5 - 98 * q^7 $$2 q + 80 q^{5} - 98 q^{7} - 432 q^{11} - 876 q^{13} - 848 q^{17} + 3352 q^{19} + 5296 q^{23} + 382 q^{25} - 256 q^{29} + 856 q^{31} - 3920 q^{35} + 3636 q^{37} - 3056 q^{41} + 26216 q^{43} - 2912 q^{47} + 4802 q^{49} - 27232 q^{53} - 27576 q^{55} - 59040 q^{59} - 40420 q^{61} - 89952 q^{65} - 52920 q^{67} + 52752 q^{71} + 18812 q^{73} + 21168 q^{77} - 50288 q^{79} + 66048 q^{83} + 17560 q^{85} - 131504 q^{89} + 42924 q^{91} + 188992 q^{95} + 164348 q^{97}+O(q^{100})$$ 2 * q + 80 * q^5 - 98 * q^7 - 432 * q^11 - 876 * q^13 - 848 * q^17 + 3352 * q^19 + 5296 * q^23 + 382 * q^25 - 256 * q^29 + 856 * q^31 - 3920 * q^35 + 3636 * q^37 - 3056 * q^41 + 26216 * q^43 - 2912 * q^47 + 4802 * q^49 - 27232 * q^53 - 27576 * q^55 - 59040 * q^59 - 40420 * q^61 - 89952 * q^65 - 52920 * q^67 + 52752 * q^71 + 18812 * q^73 + 21168 * q^77 - 50288 * q^79 + 66048 * q^83 + 17560 * q^85 - 131504 * q^89 + 42924 * q^91 + 188992 * q^95 + 164348 * 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
$$5$$ −1.42463 −0.0254846 −0.0127423 0.999919i $$-0.504056\pi$$
−0.0127423 + 0.999919i $$0.504056\pi$$
$$6$$ 0 0
$$7$$ −49.0000 −0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −91.7261 −0.228566 −0.114283 0.993448i $$-0.536457\pi$$
−0.114283 + 0.993448i $$0.536457\pi$$
$$12$$ 0 0
$$13$$ 224.794 0.368915 0.184458 0.982840i $$-0.440947\pi$$
0.184458 + 0.982840i $$0.440947\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1045.37 −0.877299 −0.438649 0.898658i $$-0.644543\pi$$
−0.438649 + 0.898658i $$0.644543\pi$$
$$18$$ 0 0
$$19$$ 1013.21 0.643893 0.321947 0.946758i $$-0.395663\pi$$
0.321947 + 0.946758i $$0.395663\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2689.42 1.06008 0.530041 0.847972i $$-0.322176\pi$$
0.530041 + 0.847972i $$0.322176\pi$$
$$24$$ 0 0
$$25$$ −3122.97 −0.999351
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 7659.83 1.69131 0.845657 0.533727i $$-0.179209\pi$$
0.845657 + 0.533727i $$0.179209\pi$$
$$30$$ 0 0
$$31$$ −8188.32 −1.53035 −0.765175 0.643822i $$-0.777348\pi$$
−0.765175 + 0.643822i $$0.777348\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 69.8069 0.00963226
$$36$$ 0 0
$$37$$ 9108.73 1.09384 0.546920 0.837185i $$-0.315800\pi$$
0.546920 + 0.837185i $$0.315800\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −18305.0 −1.70063 −0.850314 0.526275i $$-0.823588\pi$$
−0.850314 + 0.526275i $$0.823588\pi$$
$$42$$ 0 0
$$43$$ 22387.1 1.84641 0.923203 0.384314i $$-0.125562\pi$$
0.923203 + 0.384314i $$0.125562\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −4852.82 −0.320442 −0.160221 0.987081i $$-0.551221\pi$$
−0.160221 + 0.987081i $$0.551221\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −940.063 −0.0459692 −0.0229846 0.999736i $$-0.507317\pi$$
−0.0229846 + 0.999736i $$0.507317\pi$$
$$54$$ 0 0
$$55$$ 130.676 0.00582490
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −13198.7 −0.493629 −0.246815 0.969063i $$-0.579384\pi$$
−0.246815 + 0.969063i $$0.579384\pi$$
$$60$$ 0 0
$$61$$ 2987.79 0.102808 0.0514039 0.998678i $$-0.483630\pi$$
0.0514039 + 0.998678i $$0.483630\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −320.248 −0.00940164
$$66$$ 0 0
$$67$$ −37064.7 −1.00873 −0.504363 0.863492i $$-0.668273\pi$$
−0.504363 + 0.863492i $$0.668273\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 76872.6 1.80978 0.904890 0.425645i $$-0.139953\pi$$
0.904890 + 0.425645i $$0.139953\pi$$
$$72$$ 0 0
$$73$$ −50245.5 −1.10354 −0.551772 0.833995i $$-0.686048\pi$$
−0.551772 + 0.833995i $$0.686048\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4494.58 0.0863898
$$78$$ 0 0
$$79$$ 10646.9 0.191935 0.0959676 0.995384i $$-0.469405\pi$$
0.0959676 + 0.995384i $$0.469405\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 13803.0 0.219926 0.109963 0.993936i $$-0.464927\pi$$
0.109963 + 0.993936i $$0.464927\pi$$
$$84$$ 0 0
$$85$$ 1489.27 0.0223576
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −30996.7 −0.414802 −0.207401 0.978256i $$-0.566501\pi$$
−0.207401 + 0.978256i $$0.566501\pi$$
$$90$$ 0 0
$$91$$ −11014.9 −0.139437
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −1443.44 −0.0164093
$$96$$ 0 0
$$97$$ 99406.6 1.07272 0.536360 0.843990i $$-0.319799\pi$$
0.536360 + 0.843990i $$0.319799\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −190238. −1.85564 −0.927821 0.373027i $$-0.878320\pi$$
−0.927821 + 0.373027i $$0.878320\pi$$
$$102$$ 0 0
$$103$$ −24516.0 −0.227697 −0.113848 0.993498i $$-0.536318\pi$$
−0.113848 + 0.993498i $$0.536318\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 142231. 1.20098 0.600491 0.799632i $$-0.294972\pi$$
0.600491 + 0.799632i $$0.294972\pi$$
$$108$$ 0 0
$$109$$ −123869. −0.998612 −0.499306 0.866426i $$-0.666412\pi$$
−0.499306 + 0.866426i $$0.666412\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −49772.7 −0.366686 −0.183343 0.983049i $$-0.558692\pi$$
−0.183343 + 0.983049i $$0.558692\pi$$
$$114$$ 0 0
$$115$$ −3831.44 −0.0270157
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 51223.1 0.331588
$$120$$ 0 0
$$121$$ −152637. −0.947758
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 8901.05 0.0509526
$$126$$ 0 0
$$127$$ −168621. −0.927687 −0.463844 0.885917i $$-0.653530\pi$$
−0.463844 + 0.885917i $$0.653530\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 165483. 0.842512 0.421256 0.906942i $$-0.361589\pi$$
0.421256 + 0.906942i $$0.361589\pi$$
$$132$$ 0 0
$$133$$ −49647.1 −0.243369
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −224888. −1.02368 −0.511842 0.859080i $$-0.671037\pi$$
−0.511842 + 0.859080i $$0.671037\pi$$
$$138$$ 0 0
$$139$$ 81205.3 0.356490 0.178245 0.983986i $$-0.442958\pi$$
0.178245 + 0.983986i $$0.442958\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −20619.5 −0.0843214
$$144$$ 0 0
$$145$$ −10912.4 −0.0431024
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −28149.2 −0.103873 −0.0519363 0.998650i $$-0.516539\pi$$
−0.0519363 + 0.998650i $$0.516539\pi$$
$$150$$ 0 0
$$151$$ −159410. −0.568948 −0.284474 0.958684i $$-0.591819\pi$$
−0.284474 + 0.958684i $$0.591819\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 11665.3 0.0390003
$$156$$ 0 0
$$157$$ 301600. 0.976522 0.488261 0.872698i $$-0.337631\pi$$
0.488261 + 0.872698i $$0.337631\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −131782. −0.400674
$$162$$ 0 0
$$163$$ −259215. −0.764173 −0.382086 0.924127i $$-0.624794\pi$$
−0.382086 + 0.924127i $$0.624794\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 670935. 1.86161 0.930807 0.365512i $$-0.119106\pi$$
0.930807 + 0.365512i $$0.119106\pi$$
$$168$$ 0 0
$$169$$ −320761. −0.863902
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −425338. −1.08049 −0.540243 0.841509i $$-0.681668\pi$$
−0.540243 + 0.841509i $$0.681668\pi$$
$$174$$ 0 0
$$175$$ 153026. 0.377719
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 457231. 1.06660 0.533301 0.845925i $$-0.320951\pi$$
0.533301 + 0.845925i $$0.320951\pi$$
$$180$$ 0 0
$$181$$ −622087. −1.41141 −0.705707 0.708504i $$-0.749371\pi$$
−0.705707 + 0.708504i $$0.749371\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −12976.6 −0.0278760
$$186$$ 0 0
$$187$$ 95887.7 0.200520
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −42570.1 −0.0844347 −0.0422173 0.999108i $$-0.513442\pi$$
−0.0422173 + 0.999108i $$0.513442\pi$$
$$192$$ 0 0
$$193$$ 108849. 0.210345 0.105173 0.994454i $$-0.466460\pi$$
0.105173 + 0.994454i $$0.466460\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −445387. −0.817658 −0.408829 0.912611i $$-0.634063\pi$$
−0.408829 + 0.912611i $$0.634063\pi$$
$$198$$ 0 0
$$199$$ −203894. −0.364983 −0.182492 0.983207i $$-0.558416\pi$$
−0.182492 + 0.983207i $$0.558416\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −375332. −0.639256
$$204$$ 0 0
$$205$$ 26077.8 0.0433398
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −92937.4 −0.147172
$$210$$ 0 0
$$211$$ −442304. −0.683934 −0.341967 0.939712i $$-0.611093\pi$$
−0.341967 + 0.939712i $$0.611093\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −31893.4 −0.0470548
$$216$$ 0 0
$$217$$ 401228. 0.578418
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −234993. −0.323649
$$222$$ 0 0
$$223$$ −988850. −1.33158 −0.665792 0.746138i $$-0.731906\pi$$
−0.665792 + 0.746138i $$0.731906\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 908650. 1.17039 0.585197 0.810891i $$-0.301017\pi$$
0.585197 + 0.810891i $$0.301017\pi$$
$$228$$ 0 0
$$229$$ −822273. −1.03616 −0.518080 0.855332i $$-0.673353\pi$$
−0.518080 + 0.855332i $$0.673353\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −756277. −0.912623 −0.456311 0.889820i $$-0.650830\pi$$
−0.456311 + 0.889820i $$0.650830\pi$$
$$234$$ 0 0
$$235$$ 6913.47 0.00816633
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 530659. 0.600926 0.300463 0.953794i $$-0.402859\pi$$
0.300463 + 0.953794i $$0.402859\pi$$
$$240$$ 0 0
$$241$$ −1.67683e6 −1.85972 −0.929858 0.367919i $$-0.880070\pi$$
−0.929858 + 0.367919i $$0.880070\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −3420.54 −0.00364065
$$246$$ 0 0
$$247$$ 227763. 0.237542
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1.29896e6 −1.30140 −0.650701 0.759334i $$-0.725525\pi$$
−0.650701 + 0.759334i $$0.725525\pi$$
$$252$$ 0 0
$$253$$ −246690. −0.242299
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1.05589e6 0.997208 0.498604 0.866830i $$-0.333846\pi$$
0.498604 + 0.866830i $$0.333846\pi$$
$$258$$ 0 0
$$259$$ −446328. −0.413433
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −461318. −0.411255 −0.205627 0.978630i $$-0.565923\pi$$
−0.205627 + 0.978630i $$0.565923\pi$$
$$264$$ 0 0
$$265$$ 1339.24 0.00117151
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.50754e6 1.27025 0.635123 0.772411i $$-0.280949\pi$$
0.635123 + 0.772411i $$0.280949\pi$$
$$270$$ 0 0
$$271$$ −1.80207e6 −1.49056 −0.745278 0.666754i $$-0.767683\pi$$
−0.745278 + 0.666754i $$0.767683\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 286458. 0.228417
$$276$$ 0 0
$$277$$ −827961. −0.648352 −0.324176 0.945997i $$-0.605087\pi$$
−0.324176 + 0.945997i $$0.605087\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 444663. 0.335943 0.167971 0.985792i $$-0.446278\pi$$
0.167971 + 0.985792i $$0.446278\pi$$
$$282$$ 0 0
$$283$$ −1.30880e6 −0.971422 −0.485711 0.874119i $$-0.661439\pi$$
−0.485711 + 0.874119i $$0.661439\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 896944. 0.642777
$$288$$ 0 0
$$289$$ −327060. −0.230347
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.04355e6 −0.710138 −0.355069 0.934840i $$-0.615543\pi$$
−0.355069 + 0.934840i $$0.615543\pi$$
$$294$$ 0 0
$$295$$ 18803.3 0.0125799
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 604567. 0.391081
$$300$$ 0 0
$$301$$ −1.09697e6 −0.697876
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −4256.50 −0.00262001
$$306$$ 0 0
$$307$$ 609911. 0.369335 0.184668 0.982801i $$-0.440879\pi$$
0.184668 + 0.982801i $$0.440879\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −2.83834e6 −1.66404 −0.832021 0.554744i $$-0.812816\pi$$
−0.832021 + 0.554744i $$0.812816\pi$$
$$312$$ 0 0
$$313$$ 966888. 0.557847 0.278924 0.960313i $$-0.410022\pi$$
0.278924 + 0.960313i $$0.410022\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.88081e6 1.05123 0.525615 0.850723i $$-0.323835\pi$$
0.525615 + 0.850723i $$0.323835\pi$$
$$318$$ 0 0
$$319$$ −702606. −0.386576
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1.05917e6 −0.564887
$$324$$ 0 0
$$325$$ −702025. −0.368676
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 237788. 0.121116
$$330$$ 0 0
$$331$$ −1.80336e6 −0.904717 −0.452359 0.891836i $$-0.649417\pi$$
−0.452359 + 0.891836i $$0.649417\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 52803.5 0.0257070
$$336$$ 0 0
$$337$$ −2.08491e6 −1.00003 −0.500015 0.866017i $$-0.666672\pi$$
−0.500015 + 0.866017i $$0.666672\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 751083. 0.349786
$$342$$ 0 0
$$343$$ −117649. −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1.41483e6 −0.630783 −0.315391 0.948962i $$-0.602136\pi$$
−0.315391 + 0.948962i $$0.602136\pi$$
$$348$$ 0 0
$$349$$ −929394. −0.408447 −0.204224 0.978924i $$-0.565467\pi$$
−0.204224 + 0.978924i $$0.565467\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −539719. −0.230532 −0.115266 0.993335i $$-0.536772\pi$$
−0.115266 + 0.993335i $$0.536772\pi$$
$$354$$ 0 0
$$355$$ −109515. −0.0461215
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −3.43124e6 −1.40512 −0.702562 0.711623i $$-0.747961\pi$$
−0.702562 + 0.711623i $$0.747961\pi$$
$$360$$ 0 0
$$361$$ −1.44951e6 −0.585402
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 71581.2 0.0281233
$$366$$ 0 0
$$367$$ −757163. −0.293443 −0.146722 0.989178i $$-0.546872\pi$$
−0.146722 + 0.989178i $$0.546872\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 46063.1 0.0173747
$$372$$ 0 0
$$373$$ −1.81560e6 −0.675690 −0.337845 0.941202i $$-0.609698\pi$$
−0.337845 + 0.941202i $$0.609698\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 1.72188e6 0.623951
$$378$$ 0 0
$$379$$ −1.95161e6 −0.697903 −0.348951 0.937141i $$-0.613462\pi$$
−0.348951 + 0.937141i $$0.613462\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −1.31041e6 −0.456467 −0.228234 0.973606i $$-0.573295\pi$$
−0.228234 + 0.973606i $$0.573295\pi$$
$$384$$ 0 0
$$385$$ −6403.11 −0.00220161
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 2.81982e6 0.944816 0.472408 0.881380i $$-0.343385\pi$$
0.472408 + 0.881380i $$0.343385\pi$$
$$390$$ 0 0
$$391$$ −2.81144e6 −0.930009
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −15167.9 −0.00489138
$$396$$ 0 0
$$397$$ −3.74747e6 −1.19334 −0.596668 0.802489i $$-0.703509\pi$$
−0.596668 + 0.802489i $$0.703509\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1.57222e6 0.488260 0.244130 0.969743i $$-0.421498\pi$$
0.244130 + 0.969743i $$0.421498\pi$$
$$402$$ 0 0
$$403$$ −1.84069e6 −0.564569
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −835509. −0.250014
$$408$$ 0 0
$$409$$ 3.65811e6 1.08130 0.540652 0.841246i $$-0.318178\pi$$
0.540652 + 0.841246i $$0.318178\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 646736. 0.186574
$$414$$ 0 0
$$415$$ −19664.1 −0.00560473
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −477218. −0.132795 −0.0663975 0.997793i $$-0.521151\pi$$
−0.0663975 + 0.997793i $$0.521151\pi$$
$$420$$ 0 0
$$421$$ 3.78986e6 1.04212 0.521060 0.853520i $$-0.325537\pi$$
0.521060 + 0.853520i $$0.325537\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 3.26466e6 0.876729
$$426$$ 0 0
$$427$$ −146402. −0.0388577
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 4.58044e6 1.18772 0.593860 0.804569i $$-0.297603\pi$$
0.593860 + 0.804569i $$0.297603\pi$$
$$432$$ 0 0
$$433$$ −3.45781e6 −0.886301 −0.443150 0.896447i $$-0.646139\pi$$
−0.443150 + 0.896447i $$0.646139\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 2.72494e6 0.682580
$$438$$ 0 0
$$439$$ 4.95610e6 1.22738 0.613689 0.789548i $$-0.289685\pi$$
0.613689 + 0.789548i $$0.289685\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −3.88556e6 −0.940685 −0.470343 0.882484i $$-0.655870\pi$$
−0.470343 + 0.882484i $$0.655870\pi$$
$$444$$ 0 0
$$445$$ 44158.9 0.0105710
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 590043. 0.138124 0.0690618 0.997612i $$-0.477999\pi$$
0.0690618 + 0.997612i $$0.477999\pi$$
$$450$$ 0 0
$$451$$ 1.67904e6 0.388706
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 15692.2 0.00355349
$$456$$ 0 0
$$457$$ −2.08724e6 −0.467501 −0.233750 0.972297i $$-0.575100\pi$$
−0.233750 + 0.972297i $$0.575100\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 492088. 0.107843 0.0539213 0.998545i $$-0.482828\pi$$
0.0539213 + 0.998545i $$0.482828\pi$$
$$462$$ 0 0
$$463$$ 2.51852e6 0.546000 0.273000 0.962014i $$-0.411984\pi$$
0.273000 + 0.962014i $$0.411984\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −8.39504e6 −1.78127 −0.890637 0.454715i $$-0.849741\pi$$
−0.890637 + 0.454715i $$0.849741\pi$$
$$468$$ 0 0
$$469$$ 1.81617e6 0.381263
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −2.05348e6 −0.422025
$$474$$ 0 0
$$475$$ −3.16421e6 −0.643475
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −8.01184e6 −1.59549 −0.797744 0.602996i $$-0.793973\pi$$
−0.797744 + 0.602996i $$0.793973\pi$$
$$480$$ 0 0
$$481$$ 2.04759e6 0.403534
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −141618. −0.0273378
$$486$$ 0 0
$$487$$ −5.72223e6 −1.09331 −0.546654 0.837358i $$-0.684099\pi$$
−0.546654 + 0.837358i $$0.684099\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 8.23498e6 1.54155 0.770777 0.637105i $$-0.219868\pi$$
0.770777 + 0.637105i $$0.219868\pi$$
$$492$$ 0 0
$$493$$ −8.00735e6 −1.48379
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −3.76676e6 −0.684033
$$498$$ 0 0
$$499$$ −1.23344e6 −0.221752 −0.110876 0.993834i $$-0.535366\pi$$
−0.110876 + 0.993834i $$0.535366\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 3.21980e6 0.567425 0.283713 0.958909i $$-0.408434\pi$$
0.283713 + 0.958909i $$0.408434\pi$$
$$504$$ 0 0
$$505$$ 271019. 0.0472902
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −7.87503e6 −1.34728 −0.673640 0.739060i $$-0.735270\pi$$
−0.673640 + 0.739060i $$0.735270\pi$$
$$510$$ 0 0
$$511$$ 2.46203e6 0.417101
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 34926.3 0.00580276
$$516$$ 0 0
$$517$$ 445130. 0.0732421
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 9.29172e6 1.49969 0.749846 0.661613i $$-0.230128\pi$$
0.749846 + 0.661613i $$0.230128\pi$$
$$522$$ 0 0
$$523$$ −8.51310e6 −1.36092 −0.680461 0.732784i $$-0.738221\pi$$
−0.680461 + 0.732784i $$0.738221\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 8.55982e6 1.34257
$$528$$ 0 0
$$529$$ 796662. 0.123776
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −4.11485e6 −0.627388
$$534$$ 0 0
$$535$$ −202627. −0.0306065
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −220234. −0.0326523
$$540$$ 0 0
$$541$$ 2.50333e6 0.367727 0.183864 0.982952i $$-0.441140\pi$$
0.183864 + 0.982952i $$0.441140\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 176468. 0.0254492
$$546$$ 0 0
$$547$$ 1.58615e6 0.226661 0.113330 0.993557i $$-0.463848\pi$$
0.113330 + 0.993557i $$0.463848\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 7.76099e6 1.08903
$$552$$ 0 0
$$553$$ −521697. −0.0725447
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −3.66566e6 −0.500627 −0.250314 0.968165i $$-0.580534\pi$$
−0.250314 + 0.968165i $$0.580534\pi$$
$$558$$ 0 0
$$559$$ 5.03249e6 0.681167
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.37431e6 −0.182731 −0.0913656 0.995817i $$-0.529123\pi$$
−0.0913656 + 0.995817i $$0.529123\pi$$
$$564$$ 0 0
$$565$$ 70907.7 0.00934484
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 640716. 0.0829631 0.0414815 0.999139i $$-0.486792\pi$$
0.0414815 + 0.999139i $$0.486792\pi$$
$$570$$ 0 0
$$571$$ 1.50255e7 1.92858 0.964289 0.264852i $$-0.0853230\pi$$
0.964289 + 0.264852i $$0.0853230\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −8.39899e6 −1.05939
$$576$$ 0 0
$$577$$ 1.14721e7 1.43451 0.717253 0.696813i $$-0.245399\pi$$
0.717253 + 0.696813i $$0.245399\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −676346. −0.0831244
$$582$$ 0 0
$$583$$ 86228.3 0.0105070
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7.77624e6 0.931482 0.465741 0.884921i $$-0.345788\pi$$
0.465741 + 0.884921i $$0.345788\pi$$
$$588$$ 0 0
$$589$$ −8.29646e6 −0.985382
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.48233e6 −0.173104 −0.0865521 0.996247i $$-0.527585\pi$$
−0.0865521 + 0.996247i $$0.527585\pi$$
$$594$$ 0 0
$$595$$ −72974.0 −0.00845037
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 2.50168e6 0.284882 0.142441 0.989803i $$-0.454505\pi$$
0.142441 + 0.989803i $$0.454505\pi$$
$$600$$ 0 0
$$601$$ 7.48878e6 0.845717 0.422858 0.906196i $$-0.361027\pi$$
0.422858 + 0.906196i $$0.361027\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 217452. 0.0241532
$$606$$ 0 0
$$607$$ −6.14962e6 −0.677449 −0.338724 0.940886i $$-0.609995\pi$$
−0.338724 + 0.940886i $$0.609995\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.09089e6 −0.118216
$$612$$ 0 0
$$613$$ −6.50878e6 −0.699598 −0.349799 0.936825i $$-0.613750\pi$$
−0.349799 + 0.936825i $$0.613750\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.38532e7 −1.46499 −0.732497 0.680770i $$-0.761645\pi$$
−0.732497 + 0.680770i $$0.761645\pi$$
$$618$$ 0 0
$$619$$ −1.19631e6 −0.125492 −0.0627459 0.998030i $$-0.519986\pi$$
−0.0627459 + 0.998030i $$0.519986\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 1.51884e6 0.156780
$$624$$ 0 0
$$625$$ 9.74660e6 0.998052
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −9.52199e6 −0.959624
$$630$$ 0 0
$$631$$ 2.25678e6 0.225640 0.112820 0.993615i $$-0.464012\pi$$
0.112820 + 0.993615i $$0.464012\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 240222. 0.0236417
$$636$$ 0 0
$$637$$ 539731. 0.0527022
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −1.62873e7 −1.56569 −0.782843 0.622219i $$-0.786231\pi$$
−0.782843 + 0.622219i $$0.786231\pi$$
$$642$$ 0 0
$$643$$ 1.68780e6 0.160988 0.0804942 0.996755i $$-0.474350\pi$$
0.0804942 + 0.996755i $$0.474350\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.80330e6 0.169359 0.0846794 0.996408i $$-0.473013\pi$$
0.0846794 + 0.996408i $$0.473013\pi$$
$$648$$ 0 0
$$649$$ 1.21066e6 0.112827
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.55291e7 1.42516 0.712581 0.701590i $$-0.247526\pi$$
0.712581 + 0.701590i $$0.247526\pi$$
$$654$$ 0 0
$$655$$ −235753. −0.0214711
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 2.05891e7 1.84682 0.923409 0.383816i $$-0.125390\pi$$
0.923409 + 0.383816i $$0.125390\pi$$
$$660$$ 0 0
$$661$$ −8.11279e6 −0.722215 −0.361108 0.932524i $$-0.617601\pi$$
−0.361108 + 0.932524i $$0.617601\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 70728.8 0.00620214
$$666$$ 0 0
$$667$$ 2.06005e7 1.79293
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −274059. −0.0234983
$$672$$ 0 0
$$673$$ 1.86442e7 1.58674 0.793370 0.608740i $$-0.208325\pi$$
0.793370 + 0.608740i $$0.208325\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 1.86500e7 1.56389 0.781947 0.623345i $$-0.214227\pi$$
0.781947 + 0.623345i $$0.214227\pi$$
$$678$$ 0 0
$$679$$ −4.87093e6 −0.405450
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.70213e7 1.39618 0.698091 0.716009i $$-0.254033\pi$$
0.698091 + 0.716009i $$0.254033\pi$$
$$684$$ 0 0
$$685$$ 320383. 0.0260881
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −211321. −0.0169587
$$690$$ 0 0
$$691$$ 2.22823e7 1.77527 0.887636 0.460546i $$-0.152347\pi$$
0.887636 + 0.460546i $$0.152347\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −115688. −0.00908500
$$696$$ 0 0
$$697$$ 1.91355e7 1.49196
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1.01249e7 −0.778212 −0.389106 0.921193i $$-0.627216\pi$$
−0.389106 + 0.921193i $$0.627216\pi$$
$$702$$ 0 0
$$703$$ 9.22902e6 0.704316
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 9.32167e6 0.701366
$$708$$ 0 0
$$709$$ 1.39102e7 1.03924 0.519622 0.854396i $$-0.326073\pi$$
0.519622 + 0.854396i $$0.326073\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −2.20219e7 −1.62230
$$714$$ 0 0
$$715$$ 29375.1 0.00214889
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.37453e6 0.0991589 0.0495794 0.998770i $$-0.484212\pi$$
0.0495794 + 0.998770i $$0.484212\pi$$
$$720$$ 0 0
$$721$$ 1.20129e6 0.0860613
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2.39214e7 −1.69022
$$726$$ 0 0
$$727$$ 5.92812e6 0.415988 0.207994 0.978130i $$-0.433307\pi$$
0.207994 + 0.978130i $$0.433307\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −2.34028e7 −1.61985
$$732$$ 0 0
$$733$$ 1.21732e7 0.836844 0.418422 0.908253i $$-0.362583\pi$$
0.418422 + 0.908253i $$0.362583\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 3.39980e6 0.230560
$$738$$ 0 0
$$739$$ −1.91339e7 −1.28882 −0.644409 0.764681i $$-0.722897\pi$$
−0.644409 + 0.764681i $$0.722897\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 1.61539e7 1.07351 0.536754 0.843739i $$-0.319650\pi$$
0.536754 + 0.843739i $$0.319650\pi$$
$$744$$ 0 0
$$745$$ 40102.2 0.00264715
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −6.96934e6 −0.453928
$$750$$ 0 0
$$751$$ 886544. 0.0573589 0.0286794 0.999589i $$-0.490870\pi$$
0.0286794 + 0.999589i $$0.490870\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 227100. 0.0144994
$$756$$ 0 0
$$757$$ −7.32720e6 −0.464727 −0.232364 0.972629i $$-0.574646\pi$$
−0.232364 + 0.972629i $$0.574646\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.06984e7 −0.669664 −0.334832 0.942278i $$-0.608680\pi$$
−0.334832 + 0.942278i $$0.608680\pi$$
$$762$$ 0 0
$$763$$ 6.06959e6 0.377440
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −2.96699e6 −0.182107
$$768$$ 0 0
$$769$$ −1.55599e7 −0.948835 −0.474418 0.880300i $$-0.657341\pi$$
−0.474418 + 0.880300i $$0.657341\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 2.40758e7 1.44921 0.724607 0.689162i $$-0.242021\pi$$
0.724607 + 0.689162i $$0.242021\pi$$
$$774$$ 0 0
$$775$$ 2.55719e7 1.52936
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1.85467e7 −1.09502
$$780$$ 0 0
$$781$$ −7.05123e6 −0.413654
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −429668. −0.0248862
$$786$$ 0 0
$$787$$ −2.82983e6 −0.162863 −0.0814316 0.996679i $$-0.525949\pi$$
−0.0814316 + 0.996679i $$0.525949\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2.43886e6 0.138594
$$792$$ 0 0
$$793$$ 671638. 0.0379273
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −8.89218e6 −0.495864 −0.247932 0.968777i $$-0.579751\pi$$
−0.247932 + 0.968777i $$0.579751\pi$$
$$798$$ 0 0
$$799$$ 5.07299e6 0.281123
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 4.60882e6 0.252232
$$804$$ 0 0
$$805$$ 187740. 0.0102110
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 3.43931e7 1.84756 0.923782 0.382918i $$-0.125081\pi$$
0.923782 + 0.382918i $$0.125081\pi$$
$$810$$ 0 0
$$811$$ −2.07305e7 −1.10677 −0.553384 0.832926i $$-0.686664\pi$$
−0.553384 + 0.832926i $$0.686664\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 369286. 0.0194746
$$816$$ 0 0
$$817$$ 2.26828e7 1.18889
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −2.54818e7 −1.31939 −0.659694 0.751535i $$-0.729314\pi$$
−0.659694 + 0.751535i $$0.729314\pi$$
$$822$$ 0 0
$$823$$ 1.43584e7 0.738933 0.369467 0.929244i $$-0.379540\pi$$
0.369467 + 0.929244i $$0.379540\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 5.17982e6 0.263361 0.131680 0.991292i $$-0.457963\pi$$
0.131680 + 0.991292i $$0.457963\pi$$
$$828$$ 0 0
$$829$$ 1.98018e7 1.00073 0.500366 0.865814i $$-0.333199\pi$$
0.500366 + 0.865814i $$0.333199\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −2.50993e6 −0.125328
$$834$$ 0 0
$$835$$ −955835. −0.0474424
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 1.83283e7 0.898914 0.449457 0.893302i $$-0.351617\pi$$
0.449457 + 0.893302i $$0.351617\pi$$
$$840$$ 0 0
$$841$$ 3.81619e7 1.86054
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 456965. 0.0220162
$$846$$ 0 0
$$847$$ 7.47923e6 0.358219
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 2.44973e7 1.15956
$$852$$ 0 0
$$853$$ −1.30941e7 −0.616175 −0.308087 0.951358i $$-0.599689\pi$$
−0.308087 + 0.951358i $$0.599689\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 3.33903e7 1.55299 0.776494 0.630124i $$-0.216996\pi$$
0.776494 + 0.630124i $$0.216996\pi$$
$$858$$ 0 0
$$859$$ 1.20144e7 0.555545 0.277772 0.960647i $$-0.410404\pi$$
0.277772 + 0.960647i $$0.410404\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −2.99226e7 −1.36764 −0.683821 0.729649i $$-0.739683\pi$$
−0.683821 + 0.729649i $$0.739683\pi$$
$$864$$ 0 0
$$865$$ 605950. 0.0275357
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −976597. −0.0438698
$$870$$ 0 0
$$871$$ −8.33193e6 −0.372135
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −436151. −0.0192583
$$876$$ 0 0
$$877$$ −2.48936e7 −1.09292 −0.546460 0.837485i $$-0.684025\pi$$
−0.546460 + 0.837485i $$0.684025\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 3.37037e7 1.46298 0.731490 0.681852i $$-0.238825\pi$$
0.731490 + 0.681852i $$0.238825\pi$$
$$882$$ 0 0
$$883$$ 2.47973e7 1.07029 0.535147 0.844759i $$-0.320256\pi$$
0.535147 + 0.844759i $$0.320256\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −2.64431e7 −1.12851 −0.564253 0.825602i $$-0.690836\pi$$
−0.564253 + 0.825602i $$0.690836\pi$$
$$888$$ 0 0
$$889$$ 8.26241e6 0.350633
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −4.91691e6 −0.206330
$$894$$ 0 0
$$895$$ −651385. −0.0271819
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −6.27212e7 −2.58830
$$900$$ 0 0
$$901$$ 982713. 0.0403288
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 886244. 0.0359693
$$906$$ 0 0
$$907$$ 2.96507e7 1.19679 0.598393 0.801203i $$-0.295806\pi$$
0.598393 + 0.801203i $$0.295806\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 1.47849e7 0.590230 0.295115 0.955462i $$-0.404642\pi$$
0.295115 + 0.955462i $$0.404642\pi$$
$$912$$ 0 0
$$913$$ −1.26609e6 −0.0502677
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −8.10869e6 −0.318440
$$918$$ 0 0
$$919$$ 1.87883e6 0.0733837 0.0366918 0.999327i $$-0.488318\pi$$
0.0366918 + 0.999327i $$0.488318\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 1.72805e7 0.667655
$$924$$ 0 0
$$925$$ −2.84463e7 −1.09313
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 2.03881e7 0.775062 0.387531 0.921857i $$-0.373328\pi$$
0.387531 + 0.921857i $$0.373328\pi$$
$$930$$ 0 0
$$931$$ 2.43271e6 0.0919847
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −136604. −0.00511018
$$936$$ 0 0
$$937$$ 4.20402e7 1.56429 0.782143 0.623099i $$-0.214127\pi$$
0.782143 + 0.623099i $$0.214127\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 2.74914e7 1.01210 0.506049 0.862504i $$-0.331105\pi$$
0.506049 + 0.862504i $$0.331105\pi$$
$$942$$ 0 0
$$943$$ −4.92299e7 −1.80281
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −1.95466e7 −0.708266 −0.354133 0.935195i $$-0.615224\pi$$
−0.354133 + 0.935195i $$0.615224\pi$$
$$948$$ 0 0
$$949$$ −1.12949e7 −0.407114
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −3.93873e7 −1.40483 −0.702416 0.711767i $$-0.747895\pi$$
−0.702416 + 0.711767i $$0.747895\pi$$
$$954$$ 0 0
$$955$$ 60646.6 0.00215178
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 1.10195e7 0.386916
$$960$$ 0 0
$$961$$ 3.84195e7 1.34197
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −155070. −0.00536056
$$966$$ 0 0
$$967$$ −245882. −0.00845591 −0.00422796 0.999991i $$-0.501346\pi$$
−0.00422796 + 0.999991i $$0.501346\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −2.96422e7 −1.00893 −0.504466 0.863431i $$-0.668311\pi$$
−0.504466 + 0.863431i $$0.668311\pi$$
$$972$$ 0 0
$$973$$ −3.97906e6 −0.134741
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −5.14882e7 −1.72572 −0.862861 0.505441i $$-0.831330\pi$$
−0.862861 + 0.505441i $$0.831330\pi$$
$$978$$ 0 0
$$979$$ 2.84321e6 0.0948096
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −4.19970e7 −1.38623 −0.693114 0.720828i $$-0.743762\pi$$
−0.693114 + 0.720828i $$0.743762\pi$$
$$984$$ 0 0
$$985$$ 634511. 0.0208377
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 6.02085e7 1.95734
$$990$$ 0 0
$$991$$ −2.14353e7 −0.693339 −0.346670 0.937987i $$-0.612687\pi$$
−0.346670 + 0.937987i $$0.612687\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 290474. 0.00930143
$$996$$ 0 0
$$997$$ −1.94096e7 −0.618413 −0.309207 0.950995i $$-0.600063\pi$$
−0.309207 + 0.950995i $$0.600063\pi$$
$$998$$ 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.bx.1.1 2
3.2 odd 2 1008.6.a.be.1.2 2
4.3 odd 2 504.6.a.w.1.1 yes 2
12.11 even 2 504.6.a.j.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.j.1.2 2 12.11 even 2
504.6.a.w.1.1 yes 2 4.3 odd 2
1008.6.a.be.1.2 2 3.2 odd 2
1008.6.a.bx.1.1 2 1.1 even 1 trivial