# Properties

 Label 1584.4.a.bj.1.2 Level $1584$ Weight $4$ Character 1584.1 Self dual yes Analytic conductor $93.459$ Analytic rank $0$ 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] = [1584,4,Mod(1,1584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1584, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1584.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1584 = 2^{4} \cdot 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1584.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: $$93.4590254491$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{97})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 24$$ x^2 - x - 24 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 33) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-4.42443$$ of defining polynomial Character $$\chi$$ $$=$$ 1584.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+16.8489 q^{5} +7.69772 q^{7} +O(q^{10})$$ $$q+16.8489 q^{5} +7.69772 q^{7} -11.0000 q^{11} +24.8489 q^{13} +15.9420 q^{17} -15.1511 q^{19} +17.7557 q^{23} +158.884 q^{25} +128.547 q^{29} -219.395 q^{31} +129.698 q^{35} +92.0703 q^{37} +459.942 q^{41} -64.9648 q^{43} +497.408 q^{47} -283.745 q^{49} +526.919 q^{53} -185.337 q^{55} -578.443 q^{59} -221.569 q^{61} +418.675 q^{65} +860.745 q^{67} +580.919 q^{71} +510.116 q^{73} -84.6749 q^{77} -1035.12 q^{79} +606.211 q^{83} +268.605 q^{85} +23.4411 q^{89} +191.279 q^{91} -255.279 q^{95} +719.490 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 14 q^{5} - 24 q^{7}+O(q^{10})$$ 2 * q + 14 * q^5 - 24 * q^7 $$2 q + 14 q^{5} - 24 q^{7} - 22 q^{11} + 30 q^{13} - 106 q^{17} - 50 q^{19} + 134 q^{23} + 42 q^{25} + 198 q^{29} - 360 q^{31} + 220 q^{35} - 328 q^{37} + 782 q^{41} - 386 q^{43} + 266 q^{47} + 378 q^{49} + 522 q^{53} - 154 q^{55} - 172 q^{59} - 778 q^{61} + 404 q^{65} + 776 q^{67} + 630 q^{71} + 1296 q^{73} + 264 q^{77} - 652 q^{79} - 324 q^{83} + 616 q^{85} + 756 q^{89} + 28 q^{91} - 156 q^{95} - 452 q^{97}+O(q^{100})$$ 2 * q + 14 * q^5 - 24 * q^7 - 22 * q^11 + 30 * q^13 - 106 * q^17 - 50 * q^19 + 134 * q^23 + 42 * q^25 + 198 * q^29 - 360 * q^31 + 220 * q^35 - 328 * q^37 + 782 * q^41 - 386 * q^43 + 266 * q^47 + 378 * q^49 + 522 * q^53 - 154 * q^55 - 172 * q^59 - 778 * q^61 + 404 * q^65 + 776 * q^67 + 630 * q^71 + 1296 * q^73 + 264 * q^77 - 652 * q^79 - 324 * q^83 + 616 * q^85 + 756 * q^89 + 28 * q^91 - 156 * q^95 - 452 * 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
$$5$$ 16.8489 1.50701 0.753504 0.657444i $$-0.228362\pi$$
0.753504 + 0.657444i $$0.228362\pi$$
$$6$$ 0 0
$$7$$ 7.69772 0.415638 0.207819 0.978167i $$-0.433364\pi$$
0.207819 + 0.978167i $$0.433364\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −11.0000 −0.301511
$$12$$ 0 0
$$13$$ 24.8489 0.530141 0.265071 0.964229i $$-0.414605\pi$$
0.265071 + 0.964229i $$0.414605\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 15.9420 0.227441 0.113721 0.993513i $$-0.463723\pi$$
0.113721 + 0.993513i $$0.463723\pi$$
$$18$$ 0 0
$$19$$ −15.1511 −0.182943 −0.0914713 0.995808i $$-0.529157\pi$$
−0.0914713 + 0.995808i $$0.529157\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 17.7557 0.160971 0.0804853 0.996756i $$-0.474353\pi$$
0.0804853 + 0.996756i $$0.474353\pi$$
$$24$$ 0 0
$$25$$ 158.884 1.27107
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 128.547 0.823121 0.411560 0.911383i $$-0.364984\pi$$
0.411560 + 0.911383i $$0.364984\pi$$
$$30$$ 0 0
$$31$$ −219.395 −1.27112 −0.635558 0.772053i $$-0.719230\pi$$
−0.635558 + 0.772053i $$0.719230\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 129.698 0.626369
$$36$$ 0 0
$$37$$ 92.0703 0.409088 0.204544 0.978857i $$-0.434429\pi$$
0.204544 + 0.978857i $$0.434429\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 459.942 1.75197 0.875986 0.482336i $$-0.160212\pi$$
0.875986 + 0.482336i $$0.160212\pi$$
$$42$$ 0 0
$$43$$ −64.9648 −0.230396 −0.115198 0.993343i $$-0.536750\pi$$
−0.115198 + 0.993343i $$0.536750\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 497.408 1.54371 0.771855 0.635799i $$-0.219329\pi$$
0.771855 + 0.635799i $$0.219329\pi$$
$$48$$ 0 0
$$49$$ −283.745 −0.827245
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 526.919 1.36562 0.682811 0.730596i $$-0.260757\pi$$
0.682811 + 0.730596i $$0.260757\pi$$
$$54$$ 0 0
$$55$$ −185.337 −0.454380
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −578.443 −1.27639 −0.638194 0.769876i $$-0.720318\pi$$
−0.638194 + 0.769876i $$0.720318\pi$$
$$60$$ 0 0
$$61$$ −221.569 −0.465067 −0.232533 0.972588i $$-0.574701\pi$$
−0.232533 + 0.972588i $$0.574701\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 418.675 0.798927
$$66$$ 0 0
$$67$$ 860.745 1.56950 0.784752 0.619810i $$-0.212790\pi$$
0.784752 + 0.619810i $$0.212790\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 580.919 0.971020 0.485510 0.874231i $$-0.338634\pi$$
0.485510 + 0.874231i $$0.338634\pi$$
$$72$$ 0 0
$$73$$ 510.116 0.817871 0.408935 0.912563i $$-0.365900\pi$$
0.408935 + 0.912563i $$0.365900\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −84.6749 −0.125319
$$78$$ 0 0
$$79$$ −1035.12 −1.47418 −0.737088 0.675797i $$-0.763800\pi$$
−0.737088 + 0.675797i $$0.763800\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 606.211 0.801690 0.400845 0.916146i $$-0.368717\pi$$
0.400845 + 0.916146i $$0.368717\pi$$
$$84$$ 0 0
$$85$$ 268.605 0.342756
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 23.4411 0.0279186 0.0139593 0.999903i $$-0.495556\pi$$
0.0139593 + 0.999903i $$0.495556\pi$$
$$90$$ 0 0
$$91$$ 191.279 0.220347
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −255.279 −0.275696
$$96$$ 0 0
$$97$$ 719.490 0.753126 0.376563 0.926391i $$-0.377106\pi$$
0.376563 + 0.926391i $$0.377106\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1871.27 −1.84355 −0.921774 0.387727i $$-0.873260\pi$$
−0.921774 + 0.387727i $$0.873260\pi$$
$$102$$ 0 0
$$103$$ 428.745 0.410151 0.205075 0.978746i $$-0.434256\pi$$
0.205075 + 0.978746i $$0.434256\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 1148.02 1.03723 0.518616 0.855008i $$-0.326448\pi$$
0.518616 + 0.855008i $$0.326448\pi$$
$$108$$ 0 0
$$109$$ −1828.32 −1.60662 −0.803308 0.595564i $$-0.796929\pi$$
−0.803308 + 0.595564i $$0.796929\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1126.40 −0.937722 −0.468861 0.883272i $$-0.655335\pi$$
−0.468861 + 0.883272i $$0.655335\pi$$
$$114$$ 0 0
$$115$$ 299.163 0.242584
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 122.717 0.0945332
$$120$$ 0 0
$$121$$ 121.000 0.0909091
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 570.907 0.408508
$$126$$ 0 0
$$127$$ −661.304 −0.462057 −0.231029 0.972947i $$-0.574209\pi$$
−0.231029 + 0.972947i $$0.574209\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 622.186 0.414967 0.207483 0.978239i $$-0.433473\pi$$
0.207483 + 0.978239i $$0.433473\pi$$
$$132$$ 0 0
$$133$$ −116.629 −0.0760378
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1872.84 1.16794 0.583969 0.811776i $$-0.301499\pi$$
0.583969 + 0.811776i $$0.301499\pi$$
$$138$$ 0 0
$$139$$ 954.058 0.582174 0.291087 0.956697i $$-0.405983\pi$$
0.291087 + 0.956697i $$0.405983\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −273.337 −0.159844
$$144$$ 0 0
$$145$$ 2165.86 1.24045
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2047.01 1.12549 0.562745 0.826631i $$-0.309745\pi$$
0.562745 + 0.826631i $$0.309745\pi$$
$$150$$ 0 0
$$151$$ −475.863 −0.256458 −0.128229 0.991745i $$-0.540929\pi$$
−0.128229 + 0.991745i $$0.540929\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3696.56 −1.91558
$$156$$ 0 0
$$157$$ −647.466 −0.329130 −0.164565 0.986366i $$-0.552622\pi$$
−0.164565 + 0.986366i $$0.552622\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 136.678 0.0669054
$$162$$ 0 0
$$163$$ −1093.23 −0.525329 −0.262665 0.964887i $$-0.584601\pi$$
−0.262665 + 0.964887i $$0.584601\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1123.25 0.520479 0.260240 0.965544i $$-0.416198\pi$$
0.260240 + 0.965544i $$0.416198\pi$$
$$168$$ 0 0
$$169$$ −1579.53 −0.718951
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −46.0123 −0.0202211 −0.0101106 0.999949i $$-0.503218\pi$$
−0.0101106 + 0.999949i $$0.503218\pi$$
$$174$$ 0 0
$$175$$ 1223.04 0.528305
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −831.975 −0.347401 −0.173700 0.984799i $$-0.555572\pi$$
−0.173700 + 0.984799i $$0.555572\pi$$
$$180$$ 0 0
$$181$$ −1810.63 −0.743553 −0.371776 0.928322i $$-0.621251\pi$$
−0.371776 + 0.928322i $$0.621251\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1551.28 0.616499
$$186$$ 0 0
$$187$$ −175.362 −0.0685762
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 458.898 0.173847 0.0869233 0.996215i $$-0.472296\pi$$
0.0869233 + 0.996215i $$0.472296\pi$$
$$192$$ 0 0
$$193$$ 1778.91 0.663465 0.331733 0.943373i $$-0.392367\pi$$
0.331733 + 0.943373i $$0.392367\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −5304.53 −1.91844 −0.959218 0.282666i $$-0.908781\pi$$
−0.959218 + 0.282666i $$0.908781\pi$$
$$198$$ 0 0
$$199$$ 5138.40 1.83041 0.915205 0.402989i $$-0.132029\pi$$
0.915205 + 0.402989i $$0.132029\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 989.515 0.342120
$$204$$ 0 0
$$205$$ 7749.50 2.64024
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 166.663 0.0551593
$$210$$ 0 0
$$211$$ 4262.36 1.39068 0.695339 0.718682i $$-0.255254\pi$$
0.695339 + 0.718682i $$0.255254\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −1094.58 −0.347209
$$216$$ 0 0
$$217$$ −1688.84 −0.528323
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 396.141 0.120576
$$222$$ 0 0
$$223$$ 1377.80 0.413740 0.206870 0.978368i $$-0.433672\pi$$
0.206870 + 0.978368i $$0.433672\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1227.28 −0.358843 −0.179422 0.983772i $$-0.557423\pi$$
−0.179422 + 0.983772i $$0.557423\pi$$
$$228$$ 0 0
$$229$$ 3890.28 1.12261 0.561304 0.827610i $$-0.310300\pi$$
0.561304 + 0.827610i $$0.310300\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 3218.14 0.904837 0.452419 0.891806i $$-0.350561\pi$$
0.452419 + 0.891806i $$0.350561\pi$$
$$234$$ 0 0
$$235$$ 8380.75 2.32638
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −428.098 −0.115864 −0.0579318 0.998321i $$-0.518451\pi$$
−0.0579318 + 0.998321i $$0.518451\pi$$
$$240$$ 0 0
$$241$$ 1231.16 0.329070 0.164535 0.986371i $$-0.447388\pi$$
0.164535 + 0.986371i $$0.447388\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −4780.78 −1.24667
$$246$$ 0 0
$$247$$ −376.489 −0.0969854
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2838.22 0.713732 0.356866 0.934156i $$-0.383845\pi$$
0.356866 + 0.934156i $$0.383845\pi$$
$$252$$ 0 0
$$253$$ −195.313 −0.0485344
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −342.007 −0.0830110 −0.0415055 0.999138i $$-0.513215\pi$$
−0.0415055 + 0.999138i $$0.513215\pi$$
$$258$$ 0 0
$$259$$ 708.731 0.170032
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 5895.00 1.38213 0.691067 0.722791i $$-0.257141\pi$$
0.691067 + 0.722791i $$0.257141\pi$$
$$264$$ 0 0
$$265$$ 8877.99 2.05800
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 2496.18 0.565779 0.282890 0.959152i $$-0.408707\pi$$
0.282890 + 0.959152i $$0.408707\pi$$
$$270$$ 0 0
$$271$$ 2249.68 0.504274 0.252137 0.967692i $$-0.418867\pi$$
0.252137 + 0.967692i $$0.418867\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1747.72 −0.383243
$$276$$ 0 0
$$277$$ 4082.59 0.885556 0.442778 0.896631i $$-0.353993\pi$$
0.442778 + 0.896631i $$0.353993\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1033.79 0.219468 0.109734 0.993961i $$-0.465000\pi$$
0.109734 + 0.993961i $$0.465000\pi$$
$$282$$ 0 0
$$283$$ 7809.14 1.64030 0.820150 0.572148i $$-0.193890\pi$$
0.820150 + 0.572148i $$0.193890\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 3540.50 0.728186
$$288$$ 0 0
$$289$$ −4658.85 −0.948270
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1949.19 0.388645 0.194323 0.980938i $$-0.437749\pi$$
0.194323 + 0.980938i $$0.437749\pi$$
$$294$$ 0 0
$$295$$ −9746.10 −1.92353
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 441.209 0.0853371
$$300$$ 0 0
$$301$$ −500.081 −0.0957614
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −3733.19 −0.700859
$$306$$ 0 0
$$307$$ −2364.09 −0.439497 −0.219748 0.975557i $$-0.570524\pi$$
−0.219748 + 0.975557i $$0.570524\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1989.17 −0.362686 −0.181343 0.983420i $$-0.558044\pi$$
−0.181343 + 0.983420i $$0.558044\pi$$
$$312$$ 0 0
$$313$$ −3878.67 −0.700433 −0.350216 0.936669i $$-0.613892\pi$$
−0.350216 + 0.936669i $$0.613892\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2913.73 −0.516251 −0.258126 0.966111i $$-0.583105\pi$$
−0.258126 + 0.966111i $$0.583105\pi$$
$$318$$ 0 0
$$319$$ −1414.01 −0.248180
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −241.540 −0.0416087
$$324$$ 0 0
$$325$$ 3948.09 0.673847
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 3828.90 0.641624
$$330$$ 0 0
$$331$$ −8104.46 −1.34580 −0.672902 0.739731i $$-0.734953\pi$$
−0.672902 + 0.739731i $$0.734953\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 14502.6 2.36525
$$336$$ 0 0
$$337$$ 5919.19 0.956792 0.478396 0.878144i $$-0.341218\pi$$
0.478396 + 0.878144i $$0.341218\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 2413.35 0.383256
$$342$$ 0 0
$$343$$ −4824.51 −0.759472
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −8540.59 −1.32128 −0.660638 0.750705i $$-0.729714\pi$$
−0.660638 + 0.750705i $$0.729714\pi$$
$$348$$ 0 0
$$349$$ 937.337 0.143767 0.0718833 0.997413i $$-0.477099\pi$$
0.0718833 + 0.997413i $$0.477099\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 211.118 0.0318319 0.0159160 0.999873i $$-0.494934\pi$$
0.0159160 + 0.999873i $$0.494934\pi$$
$$354$$ 0 0
$$355$$ 9787.82 1.46333
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1376.31 −0.202337 −0.101169 0.994869i $$-0.532258\pi$$
−0.101169 + 0.994869i $$0.532258\pi$$
$$360$$ 0 0
$$361$$ −6629.44 −0.966532
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 8594.87 1.23254
$$366$$ 0 0
$$367$$ −1030.45 −0.146564 −0.0732821 0.997311i $$-0.523347\pi$$
−0.0732821 + 0.997311i $$0.523347\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 4056.07 0.567603
$$372$$ 0 0
$$373$$ 9365.39 1.30006 0.650029 0.759909i $$-0.274757\pi$$
0.650029 + 0.759909i $$0.274757\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3194.24 0.436370
$$378$$ 0 0
$$379$$ 7120.23 0.965017 0.482509 0.875891i $$-0.339726\pi$$
0.482509 + 0.875891i $$0.339726\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −1163.56 −0.155235 −0.0776176 0.996983i $$-0.524731\pi$$
−0.0776176 + 0.996983i $$0.524731\pi$$
$$384$$ 0 0
$$385$$ −1426.67 −0.188857
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 10958.9 1.42838 0.714188 0.699954i $$-0.246796\pi$$
0.714188 + 0.699954i $$0.246796\pi$$
$$390$$ 0 0
$$391$$ 283.062 0.0366114
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −17440.6 −2.22159
$$396$$ 0 0
$$397$$ −2172.09 −0.274595 −0.137298 0.990530i $$-0.543842\pi$$
−0.137298 + 0.990530i $$0.543842\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −7830.71 −0.975180 −0.487590 0.873073i $$-0.662124\pi$$
−0.487590 + 0.873073i $$0.662124\pi$$
$$402$$ 0 0
$$403$$ −5451.73 −0.673870
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −1012.77 −0.123345
$$408$$ 0 0
$$409$$ −10731.2 −1.29736 −0.648682 0.761060i $$-0.724679\pi$$
−0.648682 + 0.761060i $$0.724679\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −4452.69 −0.530515
$$414$$ 0 0
$$415$$ 10214.0 1.20815
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −7315.88 −0.852994 −0.426497 0.904489i $$-0.640252\pi$$
−0.426497 + 0.904489i $$0.640252\pi$$
$$420$$ 0 0
$$421$$ −12495.7 −1.44657 −0.723284 0.690551i $$-0.757368\pi$$
−0.723284 + 0.690551i $$0.757368\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2532.93 0.289094
$$426$$ 0 0
$$427$$ −1705.58 −0.193299
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 6075.01 0.678939 0.339470 0.940617i $$-0.389752\pi$$
0.339470 + 0.940617i $$0.389752\pi$$
$$432$$ 0 0
$$433$$ 5641.79 0.626160 0.313080 0.949727i $$-0.398639\pi$$
0.313080 + 0.949727i $$0.398639\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −269.019 −0.0294484
$$438$$ 0 0
$$439$$ −10897.0 −1.18470 −0.592351 0.805680i $$-0.701800\pi$$
−0.592351 + 0.805680i $$0.701800\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −7720.83 −0.828054 −0.414027 0.910265i $$-0.635878\pi$$
−0.414027 + 0.910265i $$0.635878\pi$$
$$444$$ 0 0
$$445$$ 394.956 0.0420735
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 7473.86 0.785553 0.392776 0.919634i $$-0.371515\pi$$
0.392776 + 0.919634i $$0.371515\pi$$
$$450$$ 0 0
$$451$$ −5059.36 −0.528240
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 3222.84 0.332064
$$456$$ 0 0
$$457$$ 11140.5 1.14033 0.570167 0.821529i $$-0.306879\pi$$
0.570167 + 0.821529i $$0.306879\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −14328.8 −1.44763 −0.723817 0.689992i $$-0.757614\pi$$
−0.723817 + 0.689992i $$0.757614\pi$$
$$462$$ 0 0
$$463$$ −11760.7 −1.18049 −0.590246 0.807223i $$-0.700969\pi$$
−0.590246 + 0.807223i $$0.700969\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 11854.9 1.17469 0.587343 0.809338i $$-0.300174\pi$$
0.587343 + 0.809338i $$0.300174\pi$$
$$468$$ 0 0
$$469$$ 6625.77 0.652345
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 714.613 0.0694671
$$474$$ 0 0
$$475$$ −2407.27 −0.232533
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −1324.68 −0.126359 −0.0631796 0.998002i $$-0.520124\pi$$
−0.0631796 + 0.998002i $$0.520124\pi$$
$$480$$ 0 0
$$481$$ 2287.84 0.216874
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 12122.6 1.13497
$$486$$ 0 0
$$487$$ −18636.4 −1.73408 −0.867040 0.498239i $$-0.833980\pi$$
−0.867040 + 0.498239i $$0.833980\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 124.552 0.0114480 0.00572398 0.999984i $$-0.498178\pi$$
0.00572398 + 0.999984i $$0.498178\pi$$
$$492$$ 0 0
$$493$$ 2049.29 0.187212
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 4471.75 0.403592
$$498$$ 0 0
$$499$$ −10230.2 −0.917768 −0.458884 0.888496i $$-0.651751\pi$$
−0.458884 + 0.888496i $$0.651751\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 5150.81 0.456587 0.228294 0.973592i $$-0.426685\pi$$
0.228294 + 0.973592i $$0.426685\pi$$
$$504$$ 0 0
$$505$$ −31528.8 −2.77824
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 22.7715 0.00198296 0.000991481 1.00000i $$-0.499684\pi$$
0.000991481 1.00000i $$0.499684\pi$$
$$510$$ 0 0
$$511$$ 3926.73 0.339938
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 7223.87 0.618100
$$516$$ 0 0
$$517$$ −5471.49 −0.465446
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −21521.7 −1.80976 −0.904879 0.425669i $$-0.860039\pi$$
−0.904879 + 0.425669i $$0.860039\pi$$
$$522$$ 0 0
$$523$$ −2923.36 −0.244416 −0.122208 0.992504i $$-0.538998\pi$$
−0.122208 + 0.992504i $$0.538998\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −3497.60 −0.289104
$$528$$ 0 0
$$529$$ −11851.7 −0.974088
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 11429.0 0.928792
$$534$$ 0 0
$$535$$ 19342.9 1.56312
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3121.20 0.249424
$$540$$ 0 0
$$541$$ 21272.8 1.69056 0.845278 0.534327i $$-0.179435\pi$$
0.845278 + 0.534327i $$0.179435\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −30805.1 −2.42118
$$546$$ 0 0
$$547$$ 18730.5 1.46409 0.732046 0.681256i $$-0.238566\pi$$
0.732046 + 0.681256i $$0.238566\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1947.63 −0.150584
$$552$$ 0 0
$$553$$ −7968.04 −0.612723
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 18885.0 1.43659 0.718297 0.695736i $$-0.244922\pi$$
0.718297 + 0.695736i $$0.244922\pi$$
$$558$$ 0 0
$$559$$ −1614.30 −0.122143
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 10285.1 0.769922 0.384961 0.922933i $$-0.374215\pi$$
0.384961 + 0.922933i $$0.374215\pi$$
$$564$$ 0 0
$$565$$ −18978.5 −1.41315
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −18008.8 −1.32683 −0.663415 0.748251i $$-0.730894\pi$$
−0.663415 + 0.748251i $$0.730894\pi$$
$$570$$ 0 0
$$571$$ 7010.79 0.513822 0.256911 0.966435i $$-0.417295\pi$$
0.256911 + 0.966435i $$0.417295\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 2821.10 0.204605
$$576$$ 0 0
$$577$$ −16398.9 −1.18318 −0.591589 0.806240i $$-0.701499\pi$$
−0.591589 + 0.806240i $$0.701499\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 4666.44 0.333213
$$582$$ 0 0
$$583$$ −5796.11 −0.411750
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 12823.5 0.901671 0.450836 0.892607i $$-0.351126\pi$$
0.450836 + 0.892607i $$0.351126\pi$$
$$588$$ 0 0
$$589$$ 3324.09 0.232541
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −16899.5 −1.17029 −0.585144 0.810929i $$-0.698962\pi$$
−0.585144 + 0.810929i $$0.698962\pi$$
$$594$$ 0 0
$$595$$ 2067.64 0.142462
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −15074.9 −1.02829 −0.514143 0.857704i $$-0.671890\pi$$
−0.514143 + 0.857704i $$0.671890\pi$$
$$600$$ 0 0
$$601$$ −11418.8 −0.775014 −0.387507 0.921867i $$-0.626664\pi$$
−0.387507 + 0.921867i $$0.626664\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2038.71 0.137001
$$606$$ 0 0
$$607$$ 17952.8 1.20046 0.600232 0.799826i $$-0.295075\pi$$
0.600232 + 0.799826i $$0.295075\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 12360.0 0.818384
$$612$$ 0 0
$$613$$ 12528.9 0.825507 0.412753 0.910843i $$-0.364567\pi$$
0.412753 + 0.910843i $$0.364567\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 8586.10 0.560232 0.280116 0.959966i $$-0.409627\pi$$
0.280116 + 0.959966i $$0.409627\pi$$
$$618$$ 0 0
$$619$$ −18415.4 −1.19576 −0.597882 0.801584i $$-0.703991\pi$$
−0.597882 + 0.801584i $$0.703991\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 180.443 0.0116040
$$624$$ 0 0
$$625$$ −10241.4 −0.655448
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1467.79 0.0930436
$$630$$ 0 0
$$631$$ −2374.38 −0.149798 −0.0748989 0.997191i $$-0.523863\pi$$
−0.0748989 + 0.997191i $$0.523863\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −11142.2 −0.696324
$$636$$ 0 0
$$637$$ −7050.74 −0.438557
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −11086.0 −0.683104 −0.341552 0.939863i $$-0.610953\pi$$
−0.341552 + 0.939863i $$0.610953\pi$$
$$642$$ 0 0
$$643$$ −19934.1 −1.22259 −0.611294 0.791403i $$-0.709351\pi$$
−0.611294 + 0.791403i $$0.709351\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −30634.8 −1.86148 −0.930739 0.365684i $$-0.880835\pi$$
−0.930739 + 0.365684i $$0.880835\pi$$
$$648$$ 0 0
$$649$$ 6362.87 0.384845
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 9818.07 0.588378 0.294189 0.955747i $$-0.404951\pi$$
0.294189 + 0.955747i $$0.404951\pi$$
$$654$$ 0 0
$$655$$ 10483.1 0.625358
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 16478.5 0.974070 0.487035 0.873383i $$-0.338078\pi$$
0.487035 + 0.873383i $$0.338078\pi$$
$$660$$ 0 0
$$661$$ 2958.12 0.174066 0.0870328 0.996205i $$-0.472262\pi$$
0.0870328 + 0.996205i $$0.472262\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −1965.07 −0.114590
$$666$$ 0 0
$$667$$ 2282.44 0.132498
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 2437.26 0.140223
$$672$$ 0 0
$$673$$ −29960.3 −1.71602 −0.858012 0.513630i $$-0.828300\pi$$
−0.858012 + 0.513630i $$0.828300\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 4514.73 0.256300 0.128150 0.991755i $$-0.459096\pi$$
0.128150 + 0.991755i $$0.459096\pi$$
$$678$$ 0 0
$$679$$ 5538.43 0.313027
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −13555.7 −0.759438 −0.379719 0.925102i $$-0.623979\pi$$
−0.379719 + 0.925102i $$0.623979\pi$$
$$684$$ 0 0
$$685$$ 31555.2 1.76009
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 13093.3 0.723972
$$690$$ 0 0
$$691$$ 11471.3 0.631535 0.315768 0.948837i $$-0.397738\pi$$
0.315768 + 0.948837i $$0.397738\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 16074.8 0.877340
$$696$$ 0 0
$$697$$ 7332.40 0.398471
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −22229.0 −1.19769 −0.598843 0.800866i $$-0.704373\pi$$
−0.598843 + 0.800866i $$0.704373\pi$$
$$702$$ 0 0
$$703$$ −1394.97 −0.0748397
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −14404.5 −0.766248
$$708$$ 0 0
$$709$$ −15081.2 −0.798851 −0.399426 0.916766i $$-0.630790\pi$$
−0.399426 + 0.916766i $$0.630790\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −3895.52 −0.204612
$$714$$ 0 0
$$715$$ −4605.42 −0.240885
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −7399.80 −0.383819 −0.191910 0.981413i $$-0.561468\pi$$
−0.191910 + 0.981413i $$0.561468\pi$$
$$720$$ 0 0
$$721$$ 3300.36 0.170474
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 20424.0 1.04625
$$726$$ 0 0
$$727$$ −1705.77 −0.0870202 −0.0435101 0.999053i $$-0.513854\pi$$
−0.0435101 + 0.999053i $$0.513854\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1035.67 −0.0524017
$$732$$ 0 0
$$733$$ 37122.6 1.87061 0.935303 0.353847i $$-0.115127\pi$$
0.935303 + 0.353847i $$0.115127\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −9468.20 −0.473223
$$738$$ 0 0
$$739$$ −34256.3 −1.70520 −0.852598 0.522568i $$-0.824974\pi$$
−0.852598 + 0.522568i $$0.824974\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 1567.88 0.0774160 0.0387080 0.999251i $$-0.487676\pi$$
0.0387080 + 0.999251i $$0.487676\pi$$
$$744$$ 0 0
$$745$$ 34489.8 1.69612
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 8837.17 0.431112
$$750$$ 0 0
$$751$$ 955.613 0.0464325 0.0232163 0.999730i $$-0.492609\pi$$
0.0232163 + 0.999730i $$0.492609\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −8017.75 −0.386484
$$756$$ 0 0
$$757$$ −14015.4 −0.672918 −0.336459 0.941698i $$-0.609229\pi$$
−0.336459 + 0.941698i $$0.609229\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 36271.0 1.72776 0.863879 0.503699i $$-0.168028\pi$$
0.863879 + 0.503699i $$0.168028\pi$$
$$762$$ 0 0
$$763$$ −14073.9 −0.667770
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −14373.6 −0.676665
$$768$$ 0 0
$$769$$ −18163.6 −0.851749 −0.425874 0.904782i $$-0.640033\pi$$
−0.425874 + 0.904782i $$0.640033\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 8345.65 0.388321 0.194160 0.980970i $$-0.437802\pi$$
0.194160 + 0.980970i $$0.437802\pi$$
$$774$$ 0 0
$$775$$ −34858.4 −1.61568
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −6968.65 −0.320510
$$780$$ 0 0
$$781$$ −6390.11 −0.292774
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −10909.1 −0.496001
$$786$$ 0 0
$$787$$ 22996.2 1.04158 0.520791 0.853684i $$-0.325637\pi$$
0.520791 + 0.853684i $$0.325637\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −8670.69 −0.389752
$$792$$ 0 0
$$793$$ −5505.75 −0.246551
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 2743.82 0.121946 0.0609730 0.998139i $$-0.480580\pi$$
0.0609730 + 0.998139i $$0.480580\pi$$
$$798$$ 0 0
$$799$$ 7929.68 0.351104
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −5611.28 −0.246597
$$804$$ 0 0
$$805$$ 2302.88 0.100827
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −41241.7 −1.79231 −0.896156 0.443738i $$-0.853652\pi$$
−0.896156 + 0.443738i $$0.853652\pi$$
$$810$$ 0 0
$$811$$ −12832.9 −0.555641 −0.277820 0.960633i $$-0.589612\pi$$
−0.277820 + 0.960633i $$0.589612\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −18419.7 −0.791675
$$816$$ 0 0
$$817$$ 984.292 0.0421493
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −16368.5 −0.695817 −0.347908 0.937529i $$-0.613108\pi$$
−0.347908 + 0.937529i $$0.613108\pi$$
$$822$$ 0 0
$$823$$ −3869.53 −0.163892 −0.0819461 0.996637i $$-0.526114\pi$$
−0.0819461 + 0.996637i $$0.526114\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 7388.69 0.310677 0.155339 0.987861i $$-0.450353\pi$$
0.155339 + 0.987861i $$0.450353\pi$$
$$828$$ 0 0
$$829$$ 23990.1 1.00508 0.502539 0.864554i $$-0.332399\pi$$
0.502539 + 0.864554i $$0.332399\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −4523.47 −0.188150
$$834$$ 0 0
$$835$$ 18925.6 0.784367
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −18228.3 −0.750074 −0.375037 0.927010i $$-0.622370\pi$$
−0.375037 + 0.927010i $$0.622370\pi$$
$$840$$ 0 0
$$841$$ −7864.78 −0.322472
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −26613.3 −1.08346
$$846$$ 0 0
$$847$$ 931.424 0.0377852
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 1634.77 0.0658511
$$852$$ 0 0
$$853$$ −21737.3 −0.872534 −0.436267 0.899817i $$-0.643700\pi$$
−0.436267 + 0.899817i $$0.643700\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 18712.2 0.745852 0.372926 0.927861i $$-0.378355\pi$$
0.372926 + 0.927861i $$0.378355\pi$$
$$858$$ 0 0
$$859$$ −30527.6 −1.21256 −0.606279 0.795252i $$-0.707339\pi$$
−0.606279 + 0.795252i $$0.707339\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 10906.4 0.430196 0.215098 0.976592i $$-0.430993\pi$$
0.215098 + 0.976592i $$0.430993\pi$$
$$864$$ 0 0
$$865$$ −775.255 −0.0304734
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 11386.3 0.444481
$$870$$ 0 0
$$871$$ 21388.5 0.832058
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 4394.68 0.169791
$$876$$ 0 0
$$877$$ 21770.9 0.838256 0.419128 0.907927i $$-0.362336\pi$$
0.419128 + 0.907927i $$0.362336\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −47206.9 −1.80527 −0.902634 0.430409i $$-0.858369\pi$$
−0.902634 + 0.430409i $$0.858369\pi$$
$$882$$ 0 0
$$883$$ 6059.68 0.230945 0.115473 0.993311i $$-0.463162\pi$$
0.115473 + 0.993311i $$0.463162\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −37130.2 −1.40553 −0.702767 0.711420i $$-0.748052\pi$$
−0.702767 + 0.711420i $$0.748052\pi$$
$$888$$ 0 0
$$889$$ −5090.53 −0.192048
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −7536.30 −0.282410
$$894$$ 0 0
$$895$$ −14017.8 −0.523536
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −28202.5 −1.04628
$$900$$ 0 0
$$901$$ 8400.15 0.310599
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −30507.0 −1.12054
$$906$$ 0 0
$$907$$ −1182.94 −0.0433064 −0.0216532 0.999766i $$-0.506893\pi$$
−0.0216532 + 0.999766i $$0.506893\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 37676.4 1.37022 0.685112 0.728438i $$-0.259753\pi$$
0.685112 + 0.728438i $$0.259753\pi$$
$$912$$ 0 0
$$913$$ −6668.32 −0.241719
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 4789.41 0.172476
$$918$$ 0 0
$$919$$ −8697.82 −0.312203 −0.156101 0.987741i $$-0.549893\pi$$
−0.156101 + 0.987741i $$0.549893\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 14435.2 0.514778
$$924$$ 0 0
$$925$$ 14628.5 0.519981
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 17247.5 0.609119 0.304559 0.952493i $$-0.401491\pi$$
0.304559 + 0.952493i $$0.401491\pi$$
$$930$$ 0 0
$$931$$ 4299.06 0.151338
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −2954.65 −0.103345
$$936$$ 0 0
$$937$$ −41812.4 −1.45779 −0.728896 0.684624i $$-0.759966\pi$$
−0.728896 + 0.684624i $$0.759966\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −37655.9 −1.30451 −0.652257 0.757998i $$-0.726178\pi$$
−0.652257 + 0.757998i $$0.726178\pi$$
$$942$$ 0 0
$$943$$ 8166.60 0.282016
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −21244.4 −0.728986 −0.364493 0.931206i $$-0.618758\pi$$
−0.364493 + 0.931206i $$0.618758\pi$$
$$948$$ 0 0
$$949$$ 12675.8 0.433587
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −1324.27 −0.0450130 −0.0225065 0.999747i $$-0.507165\pi$$
−0.0225065 + 0.999747i $$0.507165\pi$$
$$954$$ 0 0
$$955$$ 7731.91 0.261988
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 14416.6 0.485439
$$960$$ 0 0
$$961$$ 18343.4 0.615735
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 29972.6 0.999847
$$966$$ 0 0
$$967$$ −52267.1 −1.73815 −0.869077 0.494676i $$-0.835287\pi$$
−0.869077 + 0.494676i $$0.835287\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −52489.8 −1.73479 −0.867394 0.497622i $$-0.834207\pi$$
−0.867394 + 0.497622i $$0.834207\pi$$
$$972$$ 0 0
$$973$$ 7344.07 0.241973
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −8324.11 −0.272581 −0.136291 0.990669i $$-0.543518\pi$$
−0.136291 + 0.990669i $$0.543518\pi$$
$$978$$ 0 0
$$979$$ −257.852 −0.00841777
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −44407.1 −1.44086 −0.720431 0.693527i $$-0.756056\pi$$
−0.720431 + 0.693527i $$0.756056\pi$$
$$984$$ 0 0
$$985$$ −89375.3 −2.89110
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −1153.50 −0.0370870
$$990$$ 0 0
$$991$$ 45124.7 1.44645 0.723226 0.690612i $$-0.242659\pi$$
0.723226 + 0.690612i $$0.242659\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 86576.2 2.75844
$$996$$ 0 0
$$997$$ 5480.61 0.174095 0.0870474 0.996204i $$-0.472257\pi$$
0.0870474 + 0.996204i $$0.472257\pi$$
$$998$$ 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 1584.4.a.bj.1.2 2
3.2 odd 2 528.4.a.p.1.1 2
4.3 odd 2 99.4.a.f.1.1 2
12.11 even 2 33.4.a.c.1.2 2
20.19 odd 2 2475.4.a.p.1.2 2
24.5 odd 2 2112.4.a.bg.1.2 2
24.11 even 2 2112.4.a.bn.1.2 2
44.43 even 2 1089.4.a.u.1.2 2
60.23 odd 4 825.4.c.h.199.1 4
60.47 odd 4 825.4.c.h.199.4 4
60.59 even 2 825.4.a.l.1.1 2
84.83 odd 2 1617.4.a.k.1.2 2
132.131 odd 2 363.4.a.i.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
33.4.a.c.1.2 2 12.11 even 2
99.4.a.f.1.1 2 4.3 odd 2
363.4.a.i.1.1 2 132.131 odd 2
528.4.a.p.1.1 2 3.2 odd 2
825.4.a.l.1.1 2 60.59 even 2
825.4.c.h.199.1 4 60.23 odd 4
825.4.c.h.199.4 4 60.47 odd 4
1089.4.a.u.1.2 2 44.43 even 2
1584.4.a.bj.1.2 2 1.1 even 1 trivial
1617.4.a.k.1.2 2 84.83 odd 2
2112.4.a.bg.1.2 2 24.5 odd 2
2112.4.a.bn.1.2 2 24.11 even 2
2475.4.a.p.1.2 2 20.19 odd 2