# Properties

 Label 5733.2.a.bu.1.2 Level $5733$ Weight $2$ Character 5733.1 Self dual yes Analytic conductor $45.778$ Analytic rank $0$ Dimension $6$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5733,2,Mod(1,5733)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5733, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5733.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$5733 = 3^{2} \cdot 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5733.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: $$45.7782354788$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.6.4507648.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1$$ x^6 - 2*x^5 - 5*x^4 + 8*x^3 + 7*x^2 - 6*x - 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 637) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-0.146243$$ of defining polynomial Character $$\chi$$ $$=$$ 5733.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.83237 q^{2} +1.35758 q^{4} +2.62555 q^{5} +1.17715 q^{8} +O(q^{10})$$ $$q-1.83237 q^{2} +1.35758 q^{4} +2.62555 q^{5} +1.17715 q^{8} -4.81098 q^{10} -3.26469 q^{11} -1.00000 q^{13} -4.87214 q^{16} +4.53021 q^{17} -4.06615 q^{19} +3.56440 q^{20} +5.98212 q^{22} +4.53266 q^{23} +1.89352 q^{25} +1.83237 q^{26} +1.42268 q^{29} +2.80328 q^{31} +6.57326 q^{32} -8.30102 q^{34} -10.0503 q^{37} +7.45070 q^{38} +3.09067 q^{40} -2.84271 q^{41} +9.72632 q^{43} -4.43208 q^{44} -8.30551 q^{46} -9.44956 q^{47} -3.46963 q^{50} -1.35758 q^{52} -5.26439 q^{53} -8.57161 q^{55} -2.60687 q^{58} -2.56791 q^{59} +11.1830 q^{61} -5.13664 q^{62} -2.30037 q^{64} -2.62555 q^{65} -1.98172 q^{67} +6.15013 q^{68} +11.7544 q^{71} -12.1391 q^{73} +18.4159 q^{74} -5.52013 q^{76} +11.9089 q^{79} -12.7920 q^{80} +5.20889 q^{82} +13.2233 q^{83} +11.8943 q^{85} -17.8222 q^{86} -3.84303 q^{88} +10.6666 q^{89} +6.15345 q^{92} +17.3151 q^{94} -10.6759 q^{95} +13.7422 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 4 q^{4} + 6 q^{5}+O(q^{10})$$ 6 * q + 4 * q^4 + 6 * q^5 $$6 q + 4 q^{4} + 6 q^{5} - 4 q^{10} - 4 q^{11} - 6 q^{13} + 16 q^{17} - 2 q^{19} + 16 q^{20} - 12 q^{22} + 6 q^{23} - 4 q^{25} + 6 q^{29} - 6 q^{31} + 20 q^{32} + 8 q^{38} - 4 q^{40} - 8 q^{41} + 2 q^{43} + 4 q^{44} + 8 q^{46} + 30 q^{47} - 8 q^{50} - 4 q^{52} + 14 q^{53} + 8 q^{55} - 8 q^{58} + 24 q^{59} + 28 q^{62} - 20 q^{64} - 6 q^{65} + 16 q^{67} + 28 q^{68} - 8 q^{71} + 6 q^{73} + 12 q^{74} + 16 q^{76} - 22 q^{79} - 28 q^{80} + 40 q^{82} + 50 q^{83} - 8 q^{85} + 16 q^{86} - 44 q^{88} + 26 q^{89} - 20 q^{92} + 32 q^{94} + 6 q^{95} + 14 q^{97}+O(q^{100})$$ 6 * q + 4 * q^4 + 6 * q^5 - 4 * q^10 - 4 * q^11 - 6 * q^13 + 16 * q^17 - 2 * q^19 + 16 * q^20 - 12 * q^22 + 6 * q^23 - 4 * q^25 + 6 * q^29 - 6 * q^31 + 20 * q^32 + 8 * q^38 - 4 * q^40 - 8 * q^41 + 2 * q^43 + 4 * q^44 + 8 * q^46 + 30 * q^47 - 8 * q^50 - 4 * q^52 + 14 * q^53 + 8 * q^55 - 8 * q^58 + 24 * q^59 + 28 * q^62 - 20 * q^64 - 6 * q^65 + 16 * q^67 + 28 * q^68 - 8 * q^71 + 6 * q^73 + 12 * q^74 + 16 * q^76 - 22 * q^79 - 28 * q^80 + 40 * q^82 + 50 * q^83 - 8 * q^85 + 16 * q^86 - 44 * q^88 + 26 * q^89 - 20 * q^92 + 32 * q^94 + 6 * q^95 + 14 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.83237 −1.29568 −0.647841 0.761776i $$-0.724328\pi$$
−0.647841 + 0.761776i $$0.724328\pi$$
$$3$$ 0 0
$$4$$ 1.35758 0.678791
$$5$$ 2.62555 1.17418 0.587091 0.809521i $$-0.300273\pi$$
0.587091 + 0.809521i $$0.300273\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 1.17715 0.416185
$$9$$ 0 0
$$10$$ −4.81098 −1.52137
$$11$$ −3.26469 −0.984341 −0.492170 0.870499i $$-0.663796\pi$$
−0.492170 + 0.870499i $$0.663796\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −4.87214 −1.21803
$$17$$ 4.53021 1.09874 0.549369 0.835580i $$-0.314868\pi$$
0.549369 + 0.835580i $$0.314868\pi$$
$$18$$ 0 0
$$19$$ −4.06615 −0.932839 −0.466420 0.884564i $$-0.654456\pi$$
−0.466420 + 0.884564i $$0.654456\pi$$
$$20$$ 3.56440 0.797024
$$21$$ 0 0
$$22$$ 5.98212 1.27539
$$23$$ 4.53266 0.945125 0.472562 0.881297i $$-0.343329\pi$$
0.472562 + 0.881297i $$0.343329\pi$$
$$24$$ 0 0
$$25$$ 1.89352 0.378705
$$26$$ 1.83237 0.359357
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 1.42268 0.264184 0.132092 0.991237i $$-0.457831\pi$$
0.132092 + 0.991237i $$0.457831\pi$$
$$30$$ 0 0
$$31$$ 2.80328 0.503484 0.251742 0.967794i $$-0.418997\pi$$
0.251742 + 0.967794i $$0.418997\pi$$
$$32$$ 6.57326 1.16200
$$33$$ 0 0
$$34$$ −8.30102 −1.42361
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −10.0503 −1.65227 −0.826133 0.563475i $$-0.809464\pi$$
−0.826133 + 0.563475i $$0.809464\pi$$
$$38$$ 7.45070 1.20866
$$39$$ 0 0
$$40$$ 3.09067 0.488677
$$41$$ −2.84271 −0.443956 −0.221978 0.975052i $$-0.571251\pi$$
−0.221978 + 0.975052i $$0.571251\pi$$
$$42$$ 0 0
$$43$$ 9.72632 1.48325 0.741625 0.670815i $$-0.234056\pi$$
0.741625 + 0.670815i $$0.234056\pi$$
$$44$$ −4.43208 −0.668161
$$45$$ 0 0
$$46$$ −8.30551 −1.22458
$$47$$ −9.44956 −1.37836 −0.689180 0.724590i $$-0.742029\pi$$
−0.689180 + 0.724590i $$0.742029\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −3.46963 −0.490680
$$51$$ 0 0
$$52$$ −1.35758 −0.188263
$$53$$ −5.26439 −0.723119 −0.361559 0.932349i $$-0.617756\pi$$
−0.361559 + 0.932349i $$0.617756\pi$$
$$54$$ 0 0
$$55$$ −8.57161 −1.15580
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −2.60687 −0.342299
$$59$$ −2.56791 −0.334313 −0.167156 0.985930i $$-0.553458\pi$$
−0.167156 + 0.985930i $$0.553458\pi$$
$$60$$ 0 0
$$61$$ 11.1830 1.43183 0.715917 0.698185i $$-0.246009\pi$$
0.715917 + 0.698185i $$0.246009\pi$$
$$62$$ −5.13664 −0.652354
$$63$$ 0 0
$$64$$ −2.30037 −0.287546
$$65$$ −2.62555 −0.325660
$$66$$ 0 0
$$67$$ −1.98172 −0.242106 −0.121053 0.992646i $$-0.538627\pi$$
−0.121053 + 0.992646i $$0.538627\pi$$
$$68$$ 6.15013 0.745813
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 11.7544 1.39499 0.697495 0.716590i $$-0.254298\pi$$
0.697495 + 0.716590i $$0.254298\pi$$
$$72$$ 0 0
$$73$$ −12.1391 −1.42078 −0.710388 0.703810i $$-0.751481\pi$$
−0.710388 + 0.703810i $$0.751481\pi$$
$$74$$ 18.4159 2.14081
$$75$$ 0 0
$$76$$ −5.52013 −0.633202
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 11.9089 1.33986 0.669928 0.742426i $$-0.266325\pi$$
0.669928 + 0.742426i $$0.266325\pi$$
$$80$$ −12.7920 −1.43019
$$81$$ 0 0
$$82$$ 5.20889 0.575226
$$83$$ 13.2233 1.45145 0.725723 0.687987i $$-0.241505\pi$$
0.725723 + 0.687987i $$0.241505\pi$$
$$84$$ 0 0
$$85$$ 11.8943 1.29012
$$86$$ −17.8222 −1.92182
$$87$$ 0 0
$$88$$ −3.84303 −0.409668
$$89$$ 10.6666 1.13065 0.565326 0.824867i $$-0.308750\pi$$
0.565326 + 0.824867i $$0.308750\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 6.15345 0.641542
$$93$$ 0 0
$$94$$ 17.3151 1.78592
$$95$$ −10.6759 −1.09532
$$96$$ 0 0
$$97$$ 13.7422 1.39531 0.697655 0.716433i $$-0.254227\pi$$
0.697655 + 0.716433i $$0.254227\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 2.57061 0.257061
$$101$$ 5.89458 0.586533 0.293266 0.956031i $$-0.405258\pi$$
0.293266 + 0.956031i $$0.405258\pi$$
$$102$$ 0 0
$$103$$ −2.78737 −0.274647 −0.137324 0.990526i $$-0.543850\pi$$
−0.137324 + 0.990526i $$0.543850\pi$$
$$104$$ −1.17715 −0.115429
$$105$$ 0 0
$$106$$ 9.64630 0.936932
$$107$$ 17.6647 1.70771 0.853856 0.520509i $$-0.174258\pi$$
0.853856 + 0.520509i $$0.174258\pi$$
$$108$$ 0 0
$$109$$ −9.56450 −0.916113 −0.458057 0.888923i $$-0.651454\pi$$
−0.458057 + 0.888923i $$0.651454\pi$$
$$110$$ 15.7064 1.49754
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 17.6017 1.65583 0.827916 0.560852i $$-0.189526\pi$$
0.827916 + 0.560852i $$0.189526\pi$$
$$114$$ 0 0
$$115$$ 11.9007 1.10975
$$116$$ 1.93140 0.179326
$$117$$ 0 0
$$118$$ 4.70535 0.433163
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.341808 −0.0310735
$$122$$ −20.4914 −1.85520
$$123$$ 0 0
$$124$$ 3.80568 0.341760
$$125$$ −8.15622 −0.729514
$$126$$ 0 0
$$127$$ −1.59482 −0.141517 −0.0707586 0.997493i $$-0.522542\pi$$
−0.0707586 + 0.997493i $$0.522542\pi$$
$$128$$ −8.93138 −0.789430
$$129$$ 0 0
$$130$$ 4.81098 0.421951
$$131$$ 4.30279 0.375937 0.187968 0.982175i $$-0.439810\pi$$
0.187968 + 0.982175i $$0.439810\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 3.63125 0.313692
$$135$$ 0 0
$$136$$ 5.33273 0.457278
$$137$$ −9.82234 −0.839179 −0.419590 0.907714i $$-0.637826\pi$$
−0.419590 + 0.907714i $$0.637826\pi$$
$$138$$ 0 0
$$139$$ −10.0811 −0.855070 −0.427535 0.903999i $$-0.640618\pi$$
−0.427535 + 0.903999i $$0.640618\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −21.5384 −1.80746
$$143$$ 3.26469 0.273007
$$144$$ 0 0
$$145$$ 3.73531 0.310201
$$146$$ 22.2434 1.84087
$$147$$ 0 0
$$148$$ −13.6442 −1.12154
$$149$$ 13.8124 1.13155 0.565777 0.824558i $$-0.308576\pi$$
0.565777 + 0.824558i $$0.308576\pi$$
$$150$$ 0 0
$$151$$ 21.2123 1.72623 0.863117 0.505004i $$-0.168509\pi$$
0.863117 + 0.505004i $$0.168509\pi$$
$$152$$ −4.78647 −0.388234
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 7.36015 0.591182
$$156$$ 0 0
$$157$$ −23.5155 −1.87674 −0.938372 0.345627i $$-0.887666\pi$$
−0.938372 + 0.345627i $$0.887666\pi$$
$$158$$ −21.8215 −1.73603
$$159$$ 0 0
$$160$$ 17.2584 1.36440
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 7.83062 0.613341 0.306671 0.951816i $$-0.400785\pi$$
0.306671 + 0.951816i $$0.400785\pi$$
$$164$$ −3.85920 −0.301353
$$165$$ 0 0
$$166$$ −24.2300 −1.88061
$$167$$ 12.7116 0.983654 0.491827 0.870693i $$-0.336329\pi$$
0.491827 + 0.870693i $$0.336329\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ −21.7948 −1.67158
$$171$$ 0 0
$$172$$ 13.2043 1.00682
$$173$$ 5.24907 0.399079 0.199540 0.979890i $$-0.436055\pi$$
0.199540 + 0.979890i $$0.436055\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 15.9060 1.19896
$$177$$ 0 0
$$178$$ −19.5451 −1.46497
$$179$$ 10.5255 0.786714 0.393357 0.919386i $$-0.371314\pi$$
0.393357 + 0.919386i $$0.371314\pi$$
$$180$$ 0 0
$$181$$ 18.8177 1.39871 0.699356 0.714774i $$-0.253470\pi$$
0.699356 + 0.714774i $$0.253470\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 5.33562 0.393347
$$185$$ −26.3877 −1.94006
$$186$$ 0 0
$$187$$ −14.7897 −1.08153
$$188$$ −12.8285 −0.935618
$$189$$ 0 0
$$190$$ 19.5622 1.41919
$$191$$ −14.9144 −1.07917 −0.539585 0.841931i $$-0.681419\pi$$
−0.539585 + 0.841931i $$0.681419\pi$$
$$192$$ 0 0
$$193$$ −0.0531356 −0.00382479 −0.00191239 0.999998i $$-0.500609\pi$$
−0.00191239 + 0.999998i $$0.500609\pi$$
$$194$$ −25.1808 −1.80788
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −10.0478 −0.715875 −0.357938 0.933745i $$-0.616520\pi$$
−0.357938 + 0.933745i $$0.616520\pi$$
$$198$$ 0 0
$$199$$ −23.2914 −1.65109 −0.825543 0.564340i $$-0.809131\pi$$
−0.825543 + 0.564340i $$0.809131\pi$$
$$200$$ 2.22896 0.157611
$$201$$ 0 0
$$202$$ −10.8011 −0.759959
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −7.46367 −0.521285
$$206$$ 5.10749 0.355855
$$207$$ 0 0
$$208$$ 4.87214 0.337822
$$209$$ 13.2747 0.918232
$$210$$ 0 0
$$211$$ −2.47457 −0.170356 −0.0851780 0.996366i $$-0.527146\pi$$
−0.0851780 + 0.996366i $$0.527146\pi$$
$$212$$ −7.14683 −0.490846
$$213$$ 0 0
$$214$$ −32.3683 −2.21265
$$215$$ 25.5369 1.74161
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 17.5257 1.18699
$$219$$ 0 0
$$220$$ −11.6367 −0.784543
$$221$$ −4.53021 −0.304735
$$222$$ 0 0
$$223$$ −6.17027 −0.413192 −0.206596 0.978426i $$-0.566239\pi$$
−0.206596 + 0.978426i $$0.566239\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −32.2529 −2.14543
$$227$$ 11.5939 0.769513 0.384757 0.923018i $$-0.374285\pi$$
0.384757 + 0.923018i $$0.374285\pi$$
$$228$$ 0 0
$$229$$ 10.2382 0.676558 0.338279 0.941046i $$-0.390155\pi$$
0.338279 + 0.941046i $$0.390155\pi$$
$$230$$ −21.8065 −1.43788
$$231$$ 0 0
$$232$$ 1.67470 0.109950
$$233$$ −21.4822 −1.40735 −0.703673 0.710524i $$-0.748458\pi$$
−0.703673 + 0.710524i $$0.748458\pi$$
$$234$$ 0 0
$$235$$ −24.8103 −1.61845
$$236$$ −3.48614 −0.226928
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −1.08591 −0.0702414 −0.0351207 0.999383i $$-0.511182\pi$$
−0.0351207 + 0.999383i $$0.511182\pi$$
$$240$$ 0 0
$$241$$ 19.9830 1.28722 0.643608 0.765355i $$-0.277437\pi$$
0.643608 + 0.765355i $$0.277437\pi$$
$$242$$ 0.626319 0.0402613
$$243$$ 0 0
$$244$$ 15.1818 0.971915
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 4.06615 0.258723
$$248$$ 3.29988 0.209542
$$249$$ 0 0
$$250$$ 14.9452 0.945218
$$251$$ 20.1497 1.27184 0.635920 0.771755i $$-0.280621\pi$$
0.635920 + 0.771755i $$0.280621\pi$$
$$252$$ 0 0
$$253$$ −14.7977 −0.930325
$$254$$ 2.92230 0.183361
$$255$$ 0 0
$$256$$ 20.9663 1.31040
$$257$$ −15.0174 −0.936759 −0.468379 0.883527i $$-0.655162\pi$$
−0.468379 + 0.883527i $$0.655162\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −3.56440 −0.221055
$$261$$ 0 0
$$262$$ −7.88431 −0.487094
$$263$$ 21.1662 1.30516 0.652582 0.757718i $$-0.273686\pi$$
0.652582 + 0.757718i $$0.273686\pi$$
$$264$$ 0 0
$$265$$ −13.8219 −0.849074
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −2.69035 −0.164339
$$269$$ −4.10480 −0.250274 −0.125137 0.992139i $$-0.539937\pi$$
−0.125137 + 0.992139i $$0.539937\pi$$
$$270$$ 0 0
$$271$$ −3.43244 −0.208506 −0.104253 0.994551i $$-0.533245\pi$$
−0.104253 + 0.994551i $$0.533245\pi$$
$$272$$ −22.0718 −1.33830
$$273$$ 0 0
$$274$$ 17.9982 1.08731
$$275$$ −6.18176 −0.372774
$$276$$ 0 0
$$277$$ −0.361012 −0.0216911 −0.0108455 0.999941i $$-0.503452\pi$$
−0.0108455 + 0.999941i $$0.503452\pi$$
$$278$$ 18.4724 1.10790
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.5213 −1.10489 −0.552445 0.833550i $$-0.686305\pi$$
−0.552445 + 0.833550i $$0.686305\pi$$
$$282$$ 0 0
$$283$$ 1.61158 0.0957983 0.0478991 0.998852i $$-0.484747\pi$$
0.0478991 + 0.998852i $$0.484747\pi$$
$$284$$ 15.9575 0.946906
$$285$$ 0 0
$$286$$ −5.98212 −0.353730
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 3.52281 0.207224
$$290$$ −6.84447 −0.401921
$$291$$ 0 0
$$292$$ −16.4798 −0.964410
$$293$$ −4.41671 −0.258027 −0.129013 0.991643i $$-0.541181\pi$$
−0.129013 + 0.991643i $$0.541181\pi$$
$$294$$ 0 0
$$295$$ −6.74217 −0.392544
$$296$$ −11.8308 −0.687649
$$297$$ 0 0
$$298$$ −25.3094 −1.46613
$$299$$ −4.53266 −0.262130
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −38.8688 −2.23665
$$303$$ 0 0
$$304$$ 19.8108 1.13623
$$305$$ 29.3615 1.68123
$$306$$ 0 0
$$307$$ 5.78353 0.330083 0.165042 0.986287i $$-0.447224\pi$$
0.165042 + 0.986287i $$0.447224\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −13.4865 −0.765983
$$311$$ 14.2895 0.810284 0.405142 0.914254i $$-0.367222\pi$$
0.405142 + 0.914254i $$0.367222\pi$$
$$312$$ 0 0
$$313$$ −2.73725 −0.154718 −0.0773592 0.997003i $$-0.524649\pi$$
−0.0773592 + 0.997003i $$0.524649\pi$$
$$314$$ 43.0892 2.43166
$$315$$ 0 0
$$316$$ 16.1673 0.909481
$$317$$ −10.6512 −0.598231 −0.299116 0.954217i $$-0.596692\pi$$
−0.299116 + 0.954217i $$0.596692\pi$$
$$318$$ 0 0
$$319$$ −4.64460 −0.260047
$$320$$ −6.03975 −0.337632
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −18.4205 −1.02495
$$324$$ 0 0
$$325$$ −1.89352 −0.105034
$$326$$ −14.3486 −0.794695
$$327$$ 0 0
$$328$$ −3.34629 −0.184768
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −3.41626 −0.187774 −0.0938872 0.995583i $$-0.529929\pi$$
−0.0938872 + 0.995583i $$0.529929\pi$$
$$332$$ 17.9517 0.985228
$$333$$ 0 0
$$334$$ −23.2924 −1.27450
$$335$$ −5.20312 −0.284277
$$336$$ 0 0
$$337$$ 24.9606 1.35969 0.679844 0.733357i $$-0.262047\pi$$
0.679844 + 0.733357i $$0.262047\pi$$
$$338$$ −1.83237 −0.0996678
$$339$$ 0 0
$$340$$ 16.1475 0.875720
$$341$$ −9.15183 −0.495599
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 11.4493 0.617306
$$345$$ 0 0
$$346$$ −9.61824 −0.517080
$$347$$ 19.1833 1.02981 0.514907 0.857246i $$-0.327827\pi$$
0.514907 + 0.857246i $$0.327827\pi$$
$$348$$ 0 0
$$349$$ 3.94421 0.211129 0.105564 0.994412i $$-0.466335\pi$$
0.105564 + 0.994412i $$0.466335\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −21.4596 −1.14380
$$353$$ 28.0232 1.49152 0.745762 0.666212i $$-0.232086\pi$$
0.745762 + 0.666212i $$0.232086\pi$$
$$354$$ 0 0
$$355$$ 30.8618 1.63797
$$356$$ 14.4807 0.767476
$$357$$ 0 0
$$358$$ −19.2866 −1.01933
$$359$$ −33.2232 −1.75345 −0.876726 0.480989i $$-0.840278\pi$$
−0.876726 + 0.480989i $$0.840278\pi$$
$$360$$ 0 0
$$361$$ −2.46641 −0.129811
$$362$$ −34.4811 −1.81228
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −31.8719 −1.66825
$$366$$ 0 0
$$367$$ 28.3091 1.47772 0.738862 0.673857i $$-0.235363\pi$$
0.738862 + 0.673857i $$0.235363\pi$$
$$368$$ −22.0837 −1.15119
$$369$$ 0 0
$$370$$ 48.3520 2.51370
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −12.9515 −0.670602 −0.335301 0.942111i $$-0.608838\pi$$
−0.335301 + 0.942111i $$0.608838\pi$$
$$374$$ 27.1003 1.40132
$$375$$ 0 0
$$376$$ −11.1235 −0.573653
$$377$$ −1.42268 −0.0732716
$$378$$ 0 0
$$379$$ 0.168981 0.00867995 0.00433997 0.999991i $$-0.498619\pi$$
0.00433997 + 0.999991i $$0.498619\pi$$
$$380$$ −14.4934 −0.743495
$$381$$ 0 0
$$382$$ 27.3288 1.39826
$$383$$ 10.1933 0.520854 0.260427 0.965494i $$-0.416137\pi$$
0.260427 + 0.965494i $$0.416137\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0.0973641 0.00495570
$$387$$ 0 0
$$388$$ 18.6562 0.947124
$$389$$ 28.6665 1.45345 0.726723 0.686930i $$-0.241042\pi$$
0.726723 + 0.686930i $$0.241042\pi$$
$$390$$ 0 0
$$391$$ 20.5339 1.03844
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 18.4113 0.927547
$$395$$ 31.2674 1.57323
$$396$$ 0 0
$$397$$ 28.6411 1.43746 0.718728 0.695292i $$-0.244725\pi$$
0.718728 + 0.695292i $$0.244725\pi$$
$$398$$ 42.6785 2.13928
$$399$$ 0 0
$$400$$ −9.22550 −0.461275
$$401$$ 14.2963 0.713922 0.356961 0.934119i $$-0.383813\pi$$
0.356961 + 0.934119i $$0.383813\pi$$
$$402$$ 0 0
$$403$$ −2.80328 −0.139641
$$404$$ 8.00237 0.398133
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 32.8112 1.62639
$$408$$ 0 0
$$409$$ −25.6988 −1.27072 −0.635362 0.772215i $$-0.719149\pi$$
−0.635362 + 0.772215i $$0.719149\pi$$
$$410$$ 13.6762 0.675420
$$411$$ 0 0
$$412$$ −3.78408 −0.186428
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 34.7185 1.70426
$$416$$ −6.57326 −0.322281
$$417$$ 0 0
$$418$$ −24.3242 −1.18974
$$419$$ 18.7999 0.918433 0.459216 0.888324i $$-0.348130\pi$$
0.459216 + 0.888324i $$0.348130\pi$$
$$420$$ 0 0
$$421$$ −18.0283 −0.878645 −0.439322 0.898329i $$-0.644781\pi$$
−0.439322 + 0.898329i $$0.644781\pi$$
$$422$$ 4.53432 0.220727
$$423$$ 0 0
$$424$$ −6.19697 −0.300951
$$425$$ 8.57806 0.416097
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 23.9813 1.15918
$$429$$ 0 0
$$430$$ −46.7931 −2.25657
$$431$$ −20.5583 −0.990256 −0.495128 0.868820i $$-0.664879\pi$$
−0.495128 + 0.868820i $$0.664879\pi$$
$$432$$ 0 0
$$433$$ −18.9235 −0.909404 −0.454702 0.890644i $$-0.650254\pi$$
−0.454702 + 0.890644i $$0.650254\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −12.9846 −0.621849
$$437$$ −18.4305 −0.881650
$$438$$ 0 0
$$439$$ 14.6550 0.699445 0.349723 0.936853i $$-0.386276\pi$$
0.349723 + 0.936853i $$0.386276\pi$$
$$440$$ −10.0901 −0.481025
$$441$$ 0 0
$$442$$ 8.30102 0.394839
$$443$$ 11.9592 0.568201 0.284100 0.958795i $$-0.408305\pi$$
0.284100 + 0.958795i $$0.408305\pi$$
$$444$$ 0 0
$$445$$ 28.0056 1.32759
$$446$$ 11.3062 0.535365
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 2.32245 0.109603 0.0548015 0.998497i $$-0.482547\pi$$
0.0548015 + 0.998497i $$0.482547\pi$$
$$450$$ 0 0
$$451$$ 9.28055 0.437004
$$452$$ 23.8958 1.12396
$$453$$ 0 0
$$454$$ −21.2443 −0.997044
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −18.5805 −0.869157 −0.434579 0.900634i $$-0.643103\pi$$
−0.434579 + 0.900634i $$0.643103\pi$$
$$458$$ −18.7601 −0.876604
$$459$$ 0 0
$$460$$ 16.1562 0.753287
$$461$$ 27.8926 1.29909 0.649543 0.760325i $$-0.274960\pi$$
0.649543 + 0.760325i $$0.274960\pi$$
$$462$$ 0 0
$$463$$ −3.66462 −0.170309 −0.0851547 0.996368i $$-0.527138\pi$$
−0.0851547 + 0.996368i $$0.527138\pi$$
$$464$$ −6.93147 −0.321786
$$465$$ 0 0
$$466$$ 39.3634 1.82347
$$467$$ 38.7532 1.79328 0.896641 0.442757i $$-0.146000\pi$$
0.896641 + 0.442757i $$0.146000\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 45.4617 2.09699
$$471$$ 0 0
$$472$$ −3.02281 −0.139136
$$473$$ −31.7534 −1.46002
$$474$$ 0 0
$$475$$ −7.69935 −0.353270
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 1.98978 0.0910105
$$479$$ −6.03430 −0.275714 −0.137857 0.990452i $$-0.544021\pi$$
−0.137857 + 0.990452i $$0.544021\pi$$
$$480$$ 0 0
$$481$$ 10.0503 0.458256
$$482$$ −36.6162 −1.66782
$$483$$ 0 0
$$484$$ −0.464032 −0.0210924
$$485$$ 36.0809 1.63835
$$486$$ 0 0
$$487$$ −3.80249 −0.172307 −0.0861537 0.996282i $$-0.527458\pi$$
−0.0861537 + 0.996282i $$0.527458\pi$$
$$488$$ 13.1640 0.595908
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0.381464 0.0172152 0.00860761 0.999963i $$-0.497260\pi$$
0.00860761 + 0.999963i $$0.497260\pi$$
$$492$$ 0 0
$$493$$ 6.44502 0.290269
$$494$$ −7.45070 −0.335223
$$495$$ 0 0
$$496$$ −13.6580 −0.613260
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 34.5739 1.54774 0.773871 0.633343i $$-0.218318\pi$$
0.773871 + 0.633343i $$0.218318\pi$$
$$500$$ −11.0727 −0.495187
$$501$$ 0 0
$$502$$ −36.9218 −1.64790
$$503$$ −2.41090 −0.107497 −0.0537485 0.998555i $$-0.517117\pi$$
−0.0537485 + 0.998555i $$0.517117\pi$$
$$504$$ 0 0
$$505$$ 15.4765 0.688696
$$506$$ 27.1149 1.20540
$$507$$ 0 0
$$508$$ −2.16509 −0.0960605
$$509$$ −21.9153 −0.971380 −0.485690 0.874131i $$-0.661432\pi$$
−0.485690 + 0.874131i $$0.661432\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −20.5553 −0.908426
$$513$$ 0 0
$$514$$ 27.5174 1.21374
$$515$$ −7.31837 −0.322486
$$516$$ 0 0
$$517$$ 30.8499 1.35678
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −3.09067 −0.135535
$$521$$ −30.1450 −1.32068 −0.660338 0.750968i $$-0.729587\pi$$
−0.660338 + 0.750968i $$0.729587\pi$$
$$522$$ 0 0
$$523$$ 18.0993 0.791428 0.395714 0.918374i $$-0.370497\pi$$
0.395714 + 0.918374i $$0.370497\pi$$
$$524$$ 5.84139 0.255182
$$525$$ 0 0
$$526$$ −38.7843 −1.69108
$$527$$ 12.6994 0.553196
$$528$$ 0 0
$$529$$ −2.45500 −0.106739
$$530$$ 25.3269 1.10013
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 2.84271 0.123131
$$534$$ 0 0
$$535$$ 46.3796 2.00517
$$536$$ −2.33278 −0.100761
$$537$$ 0 0
$$538$$ 7.52151 0.324275
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 4.08890 0.175795 0.0878977 0.996130i $$-0.471985\pi$$
0.0878977 + 0.996130i $$0.471985\pi$$
$$542$$ 6.28950 0.270157
$$543$$ 0 0
$$544$$ 29.7782 1.27673
$$545$$ −25.1121 −1.07568
$$546$$ 0 0
$$547$$ −40.4264 −1.72851 −0.864255 0.503055i $$-0.832209\pi$$
−0.864255 + 0.503055i $$0.832209\pi$$
$$548$$ −13.3346 −0.569627
$$549$$ 0 0
$$550$$ 11.3273 0.482997
$$551$$ −5.78482 −0.246442
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0.661507 0.0281047
$$555$$ 0 0
$$556$$ −13.6859 −0.580413
$$557$$ −19.7690 −0.837640 −0.418820 0.908069i $$-0.637556\pi$$
−0.418820 + 0.908069i $$0.637556\pi$$
$$558$$ 0 0
$$559$$ −9.72632 −0.411379
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 33.9379 1.43158
$$563$$ 8.22392 0.346597 0.173298 0.984869i $$-0.444557\pi$$
0.173298 + 0.984869i $$0.444557\pi$$
$$564$$ 0 0
$$565$$ 46.2143 1.94425
$$566$$ −2.95300 −0.124124
$$567$$ 0 0
$$568$$ 13.8367 0.580574
$$569$$ −14.5770 −0.611099 −0.305550 0.952176i $$-0.598840\pi$$
−0.305550 + 0.952176i $$0.598840\pi$$
$$570$$ 0 0
$$571$$ −2.58822 −0.108314 −0.0541568 0.998532i $$-0.517247\pi$$
−0.0541568 + 0.998532i $$0.517247\pi$$
$$572$$ 4.43208 0.185315
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 8.58269 0.357923
$$576$$ 0 0
$$577$$ 23.8937 0.994707 0.497353 0.867548i $$-0.334305\pi$$
0.497353 + 0.867548i $$0.334305\pi$$
$$578$$ −6.45509 −0.268496
$$579$$ 0 0
$$580$$ 5.07099 0.210561
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 17.1866 0.711795
$$584$$ −14.2896 −0.591306
$$585$$ 0 0
$$586$$ 8.09304 0.334320
$$587$$ 28.5759 1.17945 0.589726 0.807604i $$-0.299236\pi$$
0.589726 + 0.807604i $$0.299236\pi$$
$$588$$ 0 0
$$589$$ −11.3986 −0.469669
$$590$$ 12.3541 0.508612
$$591$$ 0 0
$$592$$ 48.9666 2.01252
$$593$$ −19.9575 −0.819556 −0.409778 0.912185i $$-0.634394\pi$$
−0.409778 + 0.912185i $$0.634394\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 18.7514 0.768088
$$597$$ 0 0
$$598$$ 8.30551 0.339638
$$599$$ −1.17716 −0.0480973 −0.0240486 0.999711i $$-0.507656\pi$$
−0.0240486 + 0.999711i $$0.507656\pi$$
$$600$$ 0 0
$$601$$ 30.9250 1.26146 0.630729 0.776003i $$-0.282756\pi$$
0.630729 + 0.776003i $$0.282756\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 28.7974 1.17175
$$605$$ −0.897435 −0.0364859
$$606$$ 0 0
$$607$$ −2.40708 −0.0977005 −0.0488503 0.998806i $$-0.515556\pi$$
−0.0488503 + 0.998806i $$0.515556\pi$$
$$608$$ −26.7279 −1.08396
$$609$$ 0 0
$$610$$ −53.8011 −2.17834
$$611$$ 9.44956 0.382288
$$612$$ 0 0
$$613$$ −27.7742 −1.12179 −0.560895 0.827887i $$-0.689543\pi$$
−0.560895 + 0.827887i $$0.689543\pi$$
$$614$$ −10.5976 −0.427683
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −26.2125 −1.05527 −0.527637 0.849470i $$-0.676922\pi$$
−0.527637 + 0.849470i $$0.676922\pi$$
$$618$$ 0 0
$$619$$ 17.2357 0.692763 0.346381 0.938094i $$-0.387410\pi$$
0.346381 + 0.938094i $$0.387410\pi$$
$$620$$ 9.99200 0.401288
$$621$$ 0 0
$$622$$ −26.1837 −1.04987
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −30.8822 −1.23529
$$626$$ 5.01565 0.200466
$$627$$ 0 0
$$628$$ −31.9242 −1.27392
$$629$$ −45.5302 −1.81541
$$630$$ 0 0
$$631$$ 39.2125 1.56103 0.780513 0.625140i $$-0.214958\pi$$
0.780513 + 0.625140i $$0.214958\pi$$
$$632$$ 14.0185 0.557628
$$633$$ 0 0
$$634$$ 19.5170 0.775117
$$635$$ −4.18728 −0.166167
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 8.51062 0.336939
$$639$$ 0 0
$$640$$ −23.4498 −0.926935
$$641$$ 22.8735 0.903451 0.451725 0.892157i $$-0.350809\pi$$
0.451725 + 0.892157i $$0.350809\pi$$
$$642$$ 0 0
$$643$$ 46.7072 1.84195 0.920976 0.389620i $$-0.127394\pi$$
0.920976 + 0.389620i $$0.127394\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 33.7532 1.32800
$$647$$ 5.93075 0.233162 0.116581 0.993181i $$-0.462807\pi$$
0.116581 + 0.993181i $$0.462807\pi$$
$$648$$ 0 0
$$649$$ 8.38341 0.329078
$$650$$ 3.46963 0.136090
$$651$$ 0 0
$$652$$ 10.6307 0.416330
$$653$$ 18.8046 0.735881 0.367940 0.929849i $$-0.380063\pi$$
0.367940 + 0.929849i $$0.380063\pi$$
$$654$$ 0 0
$$655$$ 11.2972 0.441419
$$656$$ 13.8500 0.540754
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −23.1086 −0.900184 −0.450092 0.892982i $$-0.648609\pi$$
−0.450092 + 0.892982i $$0.648609\pi$$
$$660$$ 0 0
$$661$$ 33.9087 1.31889 0.659447 0.751751i $$-0.270790\pi$$
0.659447 + 0.751751i $$0.270790\pi$$
$$662$$ 6.25985 0.243296
$$663$$ 0 0
$$664$$ 15.5658 0.604071
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 6.44851 0.249687
$$668$$ 17.2570 0.667695
$$669$$ 0 0
$$670$$ 9.53404 0.368332
$$671$$ −36.5090 −1.40941
$$672$$ 0 0
$$673$$ 6.00430 0.231449 0.115724 0.993281i $$-0.463081\pi$$
0.115724 + 0.993281i $$0.463081\pi$$
$$674$$ −45.7370 −1.76172
$$675$$ 0 0
$$676$$ 1.35758 0.0522147
$$677$$ 20.2075 0.776637 0.388318 0.921525i $$-0.373056\pi$$
0.388318 + 0.921525i $$0.373056\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 14.0014 0.536928
$$681$$ 0 0
$$682$$ 16.7695 0.642139
$$683$$ 31.6508 1.21108 0.605541 0.795814i $$-0.292957\pi$$
0.605541 + 0.795814i $$0.292957\pi$$
$$684$$ 0 0
$$685$$ −25.7891 −0.985350
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −47.3879 −1.80665
$$689$$ 5.26439 0.200557
$$690$$ 0 0
$$691$$ −9.69199 −0.368701 −0.184350 0.982861i $$-0.559018\pi$$
−0.184350 + 0.982861i $$0.559018\pi$$
$$692$$ 7.12604 0.270891
$$693$$ 0 0
$$694$$ −35.1509 −1.33431
$$695$$ −26.4685 −1.00401
$$696$$ 0 0
$$697$$ −12.8781 −0.487791
$$698$$ −7.22725 −0.273556
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 5.10365 0.192762 0.0963811 0.995345i $$-0.469273\pi$$
0.0963811 + 0.995345i $$0.469273\pi$$
$$702$$ 0 0
$$703$$ 40.8662 1.54130
$$704$$ 7.51000 0.283044
$$705$$ 0 0
$$706$$ −51.3489 −1.93254
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 26.1445 0.981878 0.490939 0.871194i $$-0.336654\pi$$
0.490939 + 0.871194i $$0.336654\pi$$
$$710$$ −56.5502 −2.12229
$$711$$ 0 0
$$712$$ 12.5561 0.470561
$$713$$ 12.7063 0.475855
$$714$$ 0 0
$$715$$ 8.57161 0.320560
$$716$$ 14.2892 0.534014
$$717$$ 0 0
$$718$$ 60.8772 2.27192
$$719$$ −8.72884 −0.325531 −0.162765 0.986665i $$-0.552041\pi$$
−0.162765 + 0.986665i $$0.552041\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 4.51937 0.168193
$$723$$ 0 0
$$724$$ 25.5466 0.949432
$$725$$ 2.69387 0.100048
$$726$$ 0 0
$$727$$ 21.8712 0.811158 0.405579 0.914060i $$-0.367070\pi$$
0.405579 + 0.914060i $$0.367070\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 58.4011 2.16152
$$731$$ 44.0623 1.62970
$$732$$ 0 0
$$733$$ 35.5640 1.31359 0.656793 0.754071i $$-0.271912\pi$$
0.656793 + 0.754071i $$0.271912\pi$$
$$734$$ −51.8728 −1.91466
$$735$$ 0 0
$$736$$ 29.7943 1.09823
$$737$$ 6.46971 0.238315
$$738$$ 0 0
$$739$$ −36.4894 −1.34228 −0.671142 0.741329i $$-0.734196\pi$$
−0.671142 + 0.741329i $$0.734196\pi$$
$$740$$ −35.8234 −1.31690
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −12.4588 −0.457071 −0.228535 0.973536i $$-0.573394\pi$$
−0.228535 + 0.973536i $$0.573394\pi$$
$$744$$ 0 0
$$745$$ 36.2651 1.32865
$$746$$ 23.7319 0.868886
$$747$$ 0 0
$$748$$ −20.0783 −0.734134
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −18.9424 −0.691217 −0.345608 0.938379i $$-0.612327\pi$$
−0.345608 + 0.938379i $$0.612327\pi$$
$$752$$ 46.0395 1.67889
$$753$$ 0 0
$$754$$ 2.60687 0.0949366
$$755$$ 55.6940 2.02691
$$756$$ 0 0
$$757$$ −25.0956 −0.912114 −0.456057 0.889951i $$-0.650739\pi$$
−0.456057 + 0.889951i $$0.650739\pi$$
$$758$$ −0.309635 −0.0112464
$$759$$ 0 0
$$760$$ −12.5671 −0.455857
$$761$$ 28.0617 1.01723 0.508617 0.860993i $$-0.330157\pi$$
0.508617 + 0.860993i $$0.330157\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −20.2476 −0.732531
$$765$$ 0 0
$$766$$ −18.6779 −0.674861
$$767$$ 2.56791 0.0927217
$$768$$ 0 0
$$769$$ 23.2636 0.838907 0.419454 0.907777i $$-0.362222\pi$$
0.419454 + 0.907777i $$0.362222\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −0.0721359 −0.00259623
$$773$$ 45.8118 1.64774 0.823869 0.566781i $$-0.191811\pi$$
0.823869 + 0.566781i $$0.191811\pi$$
$$774$$ 0 0
$$775$$ 5.30807 0.190672
$$776$$ 16.1766 0.580708
$$777$$ 0 0
$$778$$ −52.5276 −1.88320
$$779$$ 11.5589 0.414140
$$780$$ 0 0
$$781$$ −38.3744 −1.37315
$$782$$ −37.6257 −1.34549
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −61.7413 −2.20364
$$786$$ 0 0
$$787$$ −31.2715 −1.11471 −0.557355 0.830274i $$-0.688184\pi$$
−0.557355 + 0.830274i $$0.688184\pi$$
$$788$$ −13.6407 −0.485929
$$789$$ 0 0
$$790$$ −57.2935 −2.03841
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −11.1830 −0.397119
$$794$$ −52.4811 −1.86248
$$795$$ 0 0
$$796$$ −31.6200 −1.12074
$$797$$ −11.6121 −0.411323 −0.205661 0.978623i $$-0.565935\pi$$
−0.205661 + 0.978623i $$0.565935\pi$$
$$798$$ 0 0
$$799$$ −42.8085 −1.51446
$$800$$ 12.4466 0.440054
$$801$$ 0 0
$$802$$ −26.1961 −0.925016
$$803$$ 39.6304 1.39853
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 5.13664 0.180931
$$807$$ 0 0
$$808$$ 6.93880 0.244106
$$809$$ −7.30665 −0.256888 −0.128444 0.991717i $$-0.540998\pi$$
−0.128444 + 0.991717i $$0.540998\pi$$
$$810$$ 0 0
$$811$$ 15.9662 0.560651 0.280325 0.959905i $$-0.409558\pi$$
0.280325 + 0.959905i $$0.409558\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ −60.1223 −2.10729
$$815$$ 20.5597 0.720175
$$816$$ 0 0
$$817$$ −39.5487 −1.38363
$$818$$ 47.0897 1.64645
$$819$$ 0 0
$$820$$ −10.1325 −0.353844
$$821$$ −1.12788 −0.0393634 −0.0196817 0.999806i $$-0.506265\pi$$
−0.0196817 + 0.999806i $$0.506265\pi$$
$$822$$ 0 0
$$823$$ 22.4044 0.780968 0.390484 0.920610i $$-0.372308\pi$$
0.390484 + 0.920610i $$0.372308\pi$$
$$824$$ −3.28115 −0.114304
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 6.32296 0.219871 0.109935 0.993939i $$-0.464936\pi$$
0.109935 + 0.993939i $$0.464936\pi$$
$$828$$ 0 0
$$829$$ 44.3704 1.54105 0.770523 0.637412i $$-0.219995\pi$$
0.770523 + 0.637412i $$0.219995\pi$$
$$830$$ −63.6171 −2.20818
$$831$$ 0 0
$$832$$ 2.30037 0.0797510
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 33.3750 1.15499
$$836$$ 18.0215 0.623287
$$837$$ 0 0
$$838$$ −34.4483 −1.19000
$$839$$ −9.89476 −0.341605 −0.170803 0.985305i $$-0.554636\pi$$
−0.170803 + 0.985305i $$0.554636\pi$$
$$840$$ 0 0
$$841$$ −26.9760 −0.930207
$$842$$ 33.0345 1.13844
$$843$$ 0 0
$$844$$ −3.35942 −0.115636
$$845$$ 2.62555 0.0903217
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 25.6488 0.880783
$$849$$ 0 0
$$850$$ −15.7182 −0.539129
$$851$$ −45.5548 −1.56160
$$852$$ 0 0
$$853$$ −25.9407 −0.888193 −0.444097 0.895979i $$-0.646475\pi$$
−0.444097 + 0.895979i $$0.646475\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 20.7940 0.710725
$$857$$ 10.0244 0.342426 0.171213 0.985234i $$-0.445231\pi$$
0.171213 + 0.985234i $$0.445231\pi$$
$$858$$ 0 0
$$859$$ −37.4378 −1.27736 −0.638680 0.769472i $$-0.720519\pi$$
−0.638680 + 0.769472i $$0.720519\pi$$
$$860$$ 34.6685 1.18219
$$861$$ 0 0
$$862$$ 37.6703 1.28306
$$863$$ −21.0026 −0.714938 −0.357469 0.933925i $$-0.616360\pi$$
−0.357469 + 0.933925i $$0.616360\pi$$
$$864$$ 0 0
$$865$$ 13.7817 0.468592
$$866$$ 34.6748 1.17830
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −38.8788 −1.31887
$$870$$ 0 0
$$871$$ 1.98172 0.0671481
$$872$$ −11.2588 −0.381273
$$873$$ 0 0
$$874$$ 33.7715 1.14234
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 7.56302 0.255385 0.127692 0.991814i $$-0.459243\pi$$
0.127692 + 0.991814i $$0.459243\pi$$
$$878$$ −26.8534 −0.906258
$$879$$ 0 0
$$880$$ 41.7620 1.40780
$$881$$ −34.3550 −1.15745 −0.578725 0.815522i $$-0.696450\pi$$
−0.578725 + 0.815522i $$0.696450\pi$$
$$882$$ 0 0
$$883$$ 49.6697 1.67152 0.835759 0.549096i $$-0.185028\pi$$
0.835759 + 0.549096i $$0.185028\pi$$
$$884$$ −6.15013 −0.206851
$$885$$ 0 0
$$886$$ −21.9138 −0.736207
$$887$$ −48.0325 −1.61277 −0.806386 0.591389i $$-0.798580\pi$$
−0.806386 + 0.591389i $$0.798580\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ −51.3166 −1.72014
$$891$$ 0 0
$$892$$ −8.37665 −0.280471
$$893$$ 38.4234 1.28579
$$894$$ 0 0
$$895$$ 27.6353 0.923745
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −4.25558 −0.142011
$$899$$ 3.98816 0.133013
$$900$$ 0 0
$$901$$ −23.8488 −0.794518
$$902$$ −17.0054 −0.566218
$$903$$ 0 0
$$904$$ 20.7199 0.689133
$$905$$ 49.4069 1.64234
$$906$$ 0 0
$$907$$ 2.40195 0.0797556 0.0398778 0.999205i $$-0.487303\pi$$
0.0398778 + 0.999205i $$0.487303\pi$$
$$908$$ 15.7396 0.522338
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 33.9555 1.12500 0.562499 0.826798i $$-0.309840\pi$$
0.562499 + 0.826798i $$0.309840\pi$$
$$912$$ 0 0
$$913$$ −43.1700 −1.42872
$$914$$ 34.0463 1.12615
$$915$$ 0 0
$$916$$ 13.8992 0.459241
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −9.37134 −0.309132 −0.154566 0.987982i $$-0.549398\pi$$
−0.154566 + 0.987982i $$0.549398\pi$$
$$920$$ 14.0089 0.461861
$$921$$ 0 0
$$922$$ −51.1095 −1.68320
$$923$$ −11.7544 −0.386901
$$924$$ 0 0
$$925$$ −19.0306 −0.625721
$$926$$ 6.71494 0.220667
$$927$$ 0 0
$$928$$ 9.35162 0.306982
$$929$$ −43.4273 −1.42480 −0.712402 0.701771i $$-0.752393\pi$$
−0.712402 + 0.701771i $$0.752393\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −29.1639 −0.955294
$$933$$ 0 0
$$934$$ −71.0102 −2.32352
$$935$$ −38.8312 −1.26992
$$936$$ 0 0
$$937$$ −2.59416 −0.0847476 −0.0423738 0.999102i $$-0.513492\pi$$
−0.0423738 + 0.999102i $$0.513492\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ −33.6820 −1.09859
$$941$$ 43.4060 1.41499 0.707497 0.706716i $$-0.249824\pi$$
0.707497 + 0.706716i $$0.249824\pi$$
$$942$$ 0 0
$$943$$ −12.8850 −0.419594
$$944$$ 12.5112 0.407204
$$945$$ 0 0
$$946$$ 58.1840 1.89172
$$947$$ 7.50058 0.243736 0.121868 0.992546i $$-0.461112\pi$$
0.121868 + 0.992546i $$0.461112\pi$$
$$948$$ 0 0
$$949$$ 12.1391 0.394052
$$950$$ 14.1081 0.457726
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0.708439 0.0229486 0.0114743 0.999934i $$-0.496348\pi$$
0.0114743 + 0.999934i $$0.496348\pi$$
$$954$$ 0 0
$$955$$ −39.1586 −1.26714
$$956$$ −1.47421 −0.0476792
$$957$$ 0 0
$$958$$ 11.0571 0.357238
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −23.1416 −0.746504
$$962$$ −18.4159 −0.593754
$$963$$ 0 0
$$964$$ 27.1285 0.873750
$$965$$ −0.139510 −0.00449100
$$966$$ 0 0
$$967$$ −16.9761 −0.545915 −0.272957 0.962026i $$-0.588002\pi$$
−0.272957 + 0.962026i $$0.588002\pi$$
$$968$$ −0.402359 −0.0129323
$$969$$ 0 0
$$970$$ −66.1136 −2.12278
$$971$$ −6.86359 −0.220263 −0.110132 0.993917i $$-0.535127\pi$$
−0.110132 + 0.993917i $$0.535127\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 6.96757 0.223255
$$975$$ 0 0
$$976$$ −54.4850 −1.74402
$$977$$ −0.581913 −0.0186171 −0.00930853 0.999957i $$-0.502963\pi$$
−0.00930853 + 0.999957i $$0.502963\pi$$
$$978$$ 0 0
$$979$$ −34.8230 −1.11295
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −0.698983 −0.0223054
$$983$$ 34.7195 1.10738 0.553689 0.832723i $$-0.313220\pi$$
0.553689 + 0.832723i $$0.313220\pi$$
$$984$$ 0 0
$$985$$ −26.3810 −0.840568
$$986$$ −11.8097 −0.376097
$$987$$ 0 0
$$988$$ 5.52013 0.175619
$$989$$ 44.0861 1.40186
$$990$$ 0 0
$$991$$ 24.1688 0.767748 0.383874 0.923385i $$-0.374590\pi$$
0.383874 + 0.923385i $$0.374590\pi$$
$$992$$ 18.4267 0.585047
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −61.1528 −1.93868
$$996$$ 0 0
$$997$$ 35.1852 1.11433 0.557163 0.830403i $$-0.311890\pi$$
0.557163 + 0.830403i $$0.311890\pi$$
$$998$$ −63.3523 −2.00538
$$999$$ 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 5733.2.a.bu.1.2 6
3.2 odd 2 637.2.a.m.1.5 6
7.6 odd 2 5733.2.a.br.1.2 6
21.2 odd 6 637.2.e.o.508.2 12
21.5 even 6 637.2.e.n.508.2 12
21.11 odd 6 637.2.e.o.79.2 12
21.17 even 6 637.2.e.n.79.2 12
21.20 even 2 637.2.a.n.1.5 yes 6
39.38 odd 2 8281.2.a.cc.1.2 6
273.272 even 2 8281.2.a.cd.1.2 6

By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.a.m.1.5 6 3.2 odd 2
637.2.a.n.1.5 yes 6 21.20 even 2
637.2.e.n.79.2 12 21.17 even 6
637.2.e.n.508.2 12 21.5 even 6
637.2.e.o.79.2 12 21.11 odd 6
637.2.e.o.508.2 12 21.2 odd 6
5733.2.a.br.1.2 6 7.6 odd 2
5733.2.a.bu.1.2 6 1.1 even 1 trivial
8281.2.a.cc.1.2 6 39.38 odd 2
8281.2.a.cd.1.2 6 273.272 even 2