# Properties

 Label 9576.2.a.co.1.1 Level $9576$ Weight $2$ Character 9576.1 Self dual yes Analytic conductor $76.465$ Analytic rank $0$ Dimension $5$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9576.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$76.4647449756$$ Analytic rank: $$0$$ Dimension: $$5$$ Coefficient field: 5.5.135076.1 Defining polynomial: $$x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 2$$ x^5 - x^4 - 5*x^3 + 4*x^2 + 4*x - 2 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{5}$$ Twist minimal: no (minimal twist has level 3192) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$2.15154$$ of defining polynomial Character $$\chi$$ $$=$$ 9576.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-4.30308 q^{5} +1.00000 q^{7} +O(q^{10})$$ $$q-4.30308 q^{5} +1.00000 q^{7} +2.56627 q^{11} +2.81429 q^{13} +7.96536 q^{17} +1.00000 q^{19} +0.814291 q^{23} +13.5165 q^{25} -3.48879 q^{29} +3.38056 q^{31} -4.30308 q^{35} +3.75198 q^{37} -6.60615 q^{41} -10.2533 q^{47} +1.00000 q^{49} -0.511215 q^{53} -11.0428 q^{55} +13.9901 q^{59} +6.00000 q^{61} -12.1101 q^{65} +11.9805 q^{67} -5.02768 q^{71} +16.0204 q^{73} +2.56627 q^{77} -14.8347 q^{79} +2.01517 q^{83} -34.2756 q^{85} -17.6490 q^{89} +2.81429 q^{91} -4.30308 q^{95} -5.66847 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$5 q - 2 q^{5} + 5 q^{7}+O(q^{10})$$ 5 * q - 2 * q^5 + 5 * q^7 $$5 q - 2 q^{5} + 5 q^{7} - 2 q^{11} + 8 q^{13} + 2 q^{17} + 5 q^{19} - 2 q^{23} + 19 q^{25} - 4 q^{29} - 4 q^{31} - 2 q^{35} + 10 q^{37} + 6 q^{41} + 2 q^{47} + 5 q^{49} - 16 q^{53} - 16 q^{55} + 12 q^{59} + 30 q^{61} - 4 q^{65} + 18 q^{67} + 10 q^{71} + 14 q^{73} - 2 q^{77} - 2 q^{79} + 6 q^{83} + 12 q^{85} - 10 q^{89} + 8 q^{91} - 2 q^{95} + 8 q^{97}+O(q^{100})$$ 5 * q - 2 * q^5 + 5 * q^7 - 2 * q^11 + 8 * q^13 + 2 * q^17 + 5 * q^19 - 2 * q^23 + 19 * q^25 - 4 * q^29 - 4 * q^31 - 2 * q^35 + 10 * q^37 + 6 * q^41 + 2 * q^47 + 5 * q^49 - 16 * q^53 - 16 * q^55 + 12 * q^59 + 30 * q^61 - 4 * q^65 + 18 * q^67 + 10 * q^71 + 14 * q^73 - 2 * q^77 - 2 * q^79 + 6 * q^83 + 12 * q^85 - 10 * q^89 + 8 * q^91 - 2 * q^95 + 8 * 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
$$5$$ −4.30308 −1.92439 −0.962197 0.272354i $$-0.912198\pi$$
−0.962197 + 0.272354i $$0.912198\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.56627 0.773759 0.386880 0.922130i $$-0.373553\pi$$
0.386880 + 0.922130i $$0.373553\pi$$
$$12$$ 0 0
$$13$$ 2.81429 0.780544 0.390272 0.920700i $$-0.372381\pi$$
0.390272 + 0.920700i $$0.372381\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 7.96536 1.93188 0.965942 0.258757i $$-0.0833130\pi$$
0.965942 + 0.258757i $$0.0833130\pi$$
$$18$$ 0 0
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0.814291 0.169791 0.0848957 0.996390i $$-0.472944\pi$$
0.0848957 + 0.996390i $$0.472944\pi$$
$$24$$ 0 0
$$25$$ 13.5165 2.70329
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −3.48879 −0.647851 −0.323926 0.946083i $$-0.605003\pi$$
−0.323926 + 0.946083i $$0.605003\pi$$
$$30$$ 0 0
$$31$$ 3.38056 0.607166 0.303583 0.952805i $$-0.401817\pi$$
0.303583 + 0.952805i $$0.401817\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −4.30308 −0.727353
$$36$$ 0 0
$$37$$ 3.75198 0.616821 0.308411 0.951253i $$-0.400203\pi$$
0.308411 + 0.951253i $$0.400203\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −6.60615 −1.03171 −0.515854 0.856677i $$-0.672525\pi$$
−0.515854 + 0.856677i $$0.672525\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −10.2533 −1.49559 −0.747797 0.663928i $$-0.768888\pi$$
−0.747797 + 0.663928i $$0.768888\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −0.511215 −0.0702207 −0.0351104 0.999383i $$-0.511178\pi$$
−0.0351104 + 0.999383i $$0.511178\pi$$
$$54$$ 0 0
$$55$$ −11.0428 −1.48902
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 13.9901 1.82135 0.910677 0.413120i $$-0.135561\pi$$
0.910677 + 0.413120i $$0.135561\pi$$
$$60$$ 0 0
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −12.1101 −1.50207
$$66$$ 0 0
$$67$$ 11.9805 1.46366 0.731828 0.681490i $$-0.238668\pi$$
0.731828 + 0.681490i $$0.238668\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −5.02768 −0.596676 −0.298338 0.954460i $$-0.596432\pi$$
−0.298338 + 0.954460i $$0.596432\pi$$
$$72$$ 0 0
$$73$$ 16.0204 1.87505 0.937524 0.347920i $$-0.113112\pi$$
0.937524 + 0.347920i $$0.113112\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 2.56627 0.292453
$$78$$ 0 0
$$79$$ −14.8347 −1.66904 −0.834518 0.550981i $$-0.814254\pi$$
−0.834518 + 0.550981i $$0.814254\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 2.01517 0.221194 0.110597 0.993865i $$-0.464724\pi$$
0.110597 + 0.993865i $$0.464724\pi$$
$$84$$ 0 0
$$85$$ −34.2756 −3.71771
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −17.6490 −1.87079 −0.935395 0.353604i $$-0.884956\pi$$
−0.935395 + 0.353604i $$0.884956\pi$$
$$90$$ 0 0
$$91$$ 2.81429 0.295018
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −4.30308 −0.441486
$$96$$ 0 0
$$97$$ −5.66847 −0.575545 −0.287773 0.957699i $$-0.592915\pi$$
−0.287773 + 0.957699i $$0.592915\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 4.90923 0.488486 0.244243 0.969714i $$-0.421460\pi$$
0.244243 + 0.969714i $$0.421460\pi$$
$$102$$ 0 0
$$103$$ 1.47025 0.144868 0.0724339 0.997373i $$-0.476923\pi$$
0.0724339 + 0.997373i $$0.476923\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 10.3767 1.00315 0.501575 0.865114i $$-0.332754\pi$$
0.501575 + 0.865114i $$0.332754\pi$$
$$108$$ 0 0
$$109$$ −5.98671 −0.573423 −0.286711 0.958017i $$-0.592562\pi$$
−0.286711 + 0.958017i $$0.592562\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 9.14771 0.860544 0.430272 0.902699i $$-0.358418\pi$$
0.430272 + 0.902699i $$0.358418\pi$$
$$114$$ 0 0
$$115$$ −3.50396 −0.326746
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 7.96536 0.730184
$$120$$ 0 0
$$121$$ −4.41427 −0.401297
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −36.6470 −3.27781
$$126$$ 0 0
$$127$$ 0.599976 0.0532392 0.0266196 0.999646i $$-0.491526\pi$$
0.0266196 + 0.999646i $$0.491526\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −7.14771 −0.624498 −0.312249 0.950000i $$-0.601082\pi$$
−0.312249 + 0.950000i $$0.601082\pi$$
$$132$$ 0 0
$$133$$ 1.00000 0.0867110
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −11.6286 −0.993497 −0.496748 0.867895i $$-0.665473\pi$$
−0.496748 + 0.867895i $$0.665473\pi$$
$$138$$ 0 0
$$139$$ −3.01251 −0.255518 −0.127759 0.991805i $$-0.540778\pi$$
−0.127759 + 0.991805i $$0.540778\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 7.22223 0.603953
$$144$$ 0 0
$$145$$ 15.0125 1.24672
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −12.8542 −1.05306 −0.526528 0.850158i $$-0.676506\pi$$
−0.526528 + 0.850158i $$0.676506\pi$$
$$150$$ 0 0
$$151$$ −17.8123 −1.44954 −0.724771 0.688989i $$-0.758055\pi$$
−0.724771 + 0.688989i $$0.758055\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −14.5468 −1.16843
$$156$$ 0 0
$$157$$ 1.92023 0.153251 0.0766256 0.997060i $$-0.475585\pi$$
0.0766256 + 0.997060i $$0.475585\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0.814291 0.0641751
$$162$$ 0 0
$$163$$ 22.5468 1.76600 0.883001 0.469371i $$-0.155519\pi$$
0.883001 + 0.469371i $$0.155519\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 10.5165 0.813788 0.406894 0.913475i $$-0.366612\pi$$
0.406894 + 0.913475i $$0.366612\pi$$
$$168$$ 0 0
$$169$$ −5.07977 −0.390751
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 24.4101 1.85587 0.927933 0.372746i $$-0.121584\pi$$
0.927933 + 0.372746i $$0.121584\pi$$
$$174$$ 0 0
$$175$$ 13.5165 1.02175
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −7.08703 −0.529709 −0.264855 0.964288i $$-0.585324\pi$$
−0.264855 + 0.964288i $$0.585324\pi$$
$$180$$ 0 0
$$181$$ 2.56964 0.191000 0.0954998 0.995429i $$-0.469555\pi$$
0.0954998 + 0.995429i $$0.469555\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −16.1450 −1.18701
$$186$$ 0 0
$$187$$ 20.4413 1.49481
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −27.2265 −1.97004 −0.985022 0.172429i $$-0.944838\pi$$
−0.985022 + 0.172429i $$0.944838\pi$$
$$192$$ 0 0
$$193$$ −14.5369 −1.04639 −0.523194 0.852214i $$-0.675260\pi$$
−0.523194 + 0.852214i $$0.675260\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 8.32779 0.593330 0.296665 0.954982i $$-0.404125\pi$$
0.296665 + 0.954982i $$0.404125\pi$$
$$198$$ 0 0
$$199$$ 14.0204 0.993881 0.496941 0.867785i $$-0.334457\pi$$
0.496941 + 0.867785i $$0.334457\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −3.48879 −0.244865
$$204$$ 0 0
$$205$$ 28.4268 1.98541
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 2.56627 0.177512
$$210$$ 0 0
$$211$$ 4.44624 0.306092 0.153046 0.988219i $$-0.451092\pi$$
0.153046 + 0.988219i $$0.451092\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 3.38056 0.229487
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 22.4169 1.50792
$$222$$ 0 0
$$223$$ 16.0238 1.07303 0.536516 0.843890i $$-0.319740\pi$$
0.536516 + 0.843890i $$0.319740\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −3.25930 −0.216327 −0.108164 0.994133i $$-0.534497\pi$$
−0.108164 + 0.994133i $$0.534497\pi$$
$$228$$ 0 0
$$229$$ 23.7387 1.56870 0.784348 0.620321i $$-0.212998\pi$$
0.784348 + 0.620321i $$0.212998\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −21.3673 −1.39982 −0.699908 0.714233i $$-0.746776\pi$$
−0.699908 + 0.714233i $$0.746776\pi$$
$$234$$ 0 0
$$235$$ 44.1206 2.87811
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 29.3208 1.89661 0.948303 0.317365i $$-0.102798\pi$$
0.948303 + 0.317365i $$0.102798\pi$$
$$240$$ 0 0
$$241$$ −14.6216 −0.941862 −0.470931 0.882170i $$-0.656082\pi$$
−0.470931 + 0.882170i $$0.656082\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −4.30308 −0.274913
$$246$$ 0 0
$$247$$ 2.81429 0.179069
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 20.8931 1.31876 0.659381 0.751809i $$-0.270818\pi$$
0.659381 + 0.751809i $$0.270818\pi$$
$$252$$ 0 0
$$253$$ 2.08969 0.131378
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −8.54680 −0.533135 −0.266567 0.963816i $$-0.585890\pi$$
−0.266567 + 0.963816i $$0.585890\pi$$
$$258$$ 0 0
$$259$$ 3.75198 0.233137
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.24107 0.0765274 0.0382637 0.999268i $$-0.487817\pi$$
0.0382637 + 0.999268i $$0.487817\pi$$
$$264$$ 0 0
$$265$$ 2.19980 0.135132
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 20.6266 1.25762 0.628812 0.777557i $$-0.283541\pi$$
0.628812 + 0.777557i $$0.283541\pi$$
$$270$$ 0 0
$$271$$ −17.7758 −1.07980 −0.539900 0.841729i $$-0.681538\pi$$
−0.539900 + 0.841729i $$0.681538\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 34.6869 2.09170
$$276$$ 0 0
$$277$$ −22.8613 −1.37360 −0.686801 0.726845i $$-0.740986\pi$$
−0.686801 + 0.726845i $$0.740986\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 16.0949 0.960143 0.480072 0.877229i $$-0.340611\pi$$
0.480072 + 0.877229i $$0.340611\pi$$
$$282$$ 0 0
$$283$$ 16.4042 0.975128 0.487564 0.873087i $$-0.337886\pi$$
0.487564 + 0.873087i $$0.337886\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −6.60615 −0.389949
$$288$$ 0 0
$$289$$ 46.4470 2.73218
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 14.3918 0.840780 0.420390 0.907343i $$-0.361893\pi$$
0.420390 + 0.907343i $$0.361893\pi$$
$$294$$ 0 0
$$295$$ −60.2004 −3.50500
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 2.29165 0.132530
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −25.8185 −1.47836
$$306$$ 0 0
$$307$$ 17.9901 1.02675 0.513374 0.858165i $$-0.328395\pi$$
0.513374 + 0.858165i $$0.328395\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 12.0916 0.685650 0.342825 0.939399i $$-0.388616\pi$$
0.342825 + 0.939399i $$0.388616\pi$$
$$312$$ 0 0
$$313$$ −25.2024 −1.42452 −0.712261 0.701914i $$-0.752329\pi$$
−0.712261 + 0.701914i $$0.752329\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 11.8806 0.667282 0.333641 0.942700i $$-0.391723\pi$$
0.333641 + 0.942700i $$0.391723\pi$$
$$318$$ 0 0
$$319$$ −8.95316 −0.501281
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 7.96536 0.443205
$$324$$ 0 0
$$325$$ 38.0393 2.11004
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −10.2533 −0.565281
$$330$$ 0 0
$$331$$ 6.28454 0.345429 0.172715 0.984972i $$-0.444746\pi$$
0.172715 + 0.984972i $$0.444746\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −51.5532 −2.81665
$$336$$ 0 0
$$337$$ 31.1430 1.69647 0.848235 0.529621i $$-0.177666\pi$$
0.848235 + 0.529621i $$0.177666\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8.67542 0.469800
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −31.3196 −1.68132 −0.840662 0.541560i $$-0.817834\pi$$
−0.840662 + 0.541560i $$0.817834\pi$$
$$348$$ 0 0
$$349$$ −14.6432 −0.783834 −0.391917 0.920001i $$-0.628188\pi$$
−0.391917 + 0.920001i $$0.628188\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 9.85309 0.524427 0.262214 0.965010i $$-0.415548\pi$$
0.262214 + 0.965010i $$0.415548\pi$$
$$354$$ 0 0
$$355$$ 21.6345 1.14824
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −3.26548 −0.172345 −0.0861726 0.996280i $$-0.527464\pi$$
−0.0861726 + 0.996280i $$0.527464\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −68.9371 −3.60833
$$366$$ 0 0
$$367$$ −4.03034 −0.210382 −0.105191 0.994452i $$-0.533545\pi$$
−0.105191 + 0.994452i $$0.533545\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −0.511215 −0.0265409
$$372$$ 0 0
$$373$$ 14.6194 0.756966 0.378483 0.925608i $$-0.376446\pi$$
0.378483 + 0.925608i $$0.376446\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −9.81846 −0.505676
$$378$$ 0 0
$$379$$ 19.3175 0.992272 0.496136 0.868245i $$-0.334752\pi$$
0.496136 + 0.868245i $$0.334752\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 14.2954 0.730462 0.365231 0.930917i $$-0.380990\pi$$
0.365231 + 0.930917i $$0.380990\pi$$
$$384$$ 0 0
$$385$$ −11.0428 −0.562796
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 20.9946 1.06447 0.532235 0.846597i $$-0.321352\pi$$
0.532235 + 0.846597i $$0.321352\pi$$
$$390$$ 0 0
$$391$$ 6.48612 0.328017
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 63.8349 3.21188
$$396$$ 0 0
$$397$$ −10.6365 −0.533830 −0.266915 0.963720i $$-0.586004\pi$$
−0.266915 + 0.963720i $$0.586004\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 35.0011 1.74787 0.873936 0.486041i $$-0.161560\pi$$
0.873936 + 0.486041i $$0.161560\pi$$
$$402$$ 0 0
$$403$$ 9.51388 0.473920
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 9.62858 0.477271
$$408$$ 0 0
$$409$$ 4.98845 0.246663 0.123331 0.992366i $$-0.460642\pi$$
0.123331 + 0.992366i $$0.460642\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 13.9901 0.688407
$$414$$ 0 0
$$415$$ −8.67143 −0.425664
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −13.6991 −0.669245 −0.334623 0.942352i $$-0.608609\pi$$
−0.334623 + 0.942352i $$0.608609\pi$$
$$420$$ 0 0
$$421$$ 18.9399 0.923073 0.461536 0.887121i $$-0.347298\pi$$
0.461536 + 0.887121i $$0.347298\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 107.664 5.22245
$$426$$ 0 0
$$427$$ 6.00000 0.290360
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −9.20706 −0.443488 −0.221744 0.975105i $$-0.571175\pi$$
−0.221744 + 0.975105i $$0.571175\pi$$
$$432$$ 0 0
$$433$$ −11.6236 −0.558595 −0.279297 0.960205i $$-0.590102\pi$$
−0.279297 + 0.960205i $$0.590102\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0.814291 0.0389528
$$438$$ 0 0
$$439$$ 4.43333 0.211591 0.105796 0.994388i $$-0.466261\pi$$
0.105796 + 0.994388i $$0.466261\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −13.2847 −0.631175 −0.315587 0.948897i $$-0.602202\pi$$
−0.315587 + 0.948897i $$0.602202\pi$$
$$444$$ 0 0
$$445$$ 75.9450 3.60014
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 38.9213 1.83681 0.918406 0.395640i $$-0.129477\pi$$
0.918406 + 0.395640i $$0.129477\pi$$
$$450$$ 0 0
$$451$$ −16.9532 −0.798293
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −12.1101 −0.567731
$$456$$ 0 0
$$457$$ 19.1820 0.897294 0.448647 0.893709i $$-0.351906\pi$$
0.448647 + 0.893709i $$0.351906\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −10.6356 −0.495348 −0.247674 0.968843i $$-0.579666\pi$$
−0.247674 + 0.968843i $$0.579666\pi$$
$$462$$ 0 0
$$463$$ −12.1794 −0.566024 −0.283012 0.959116i $$-0.591334\pi$$
−0.283012 + 0.959116i $$0.591334\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 19.3765 0.896638 0.448319 0.893874i $$-0.352023\pi$$
0.448319 + 0.893874i $$0.352023\pi$$
$$468$$ 0 0
$$469$$ 11.9805 0.553210
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 13.5165 0.620178
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −4.65503 −0.212694 −0.106347 0.994329i $$-0.533915\pi$$
−0.106347 + 0.994329i $$0.533915\pi$$
$$480$$ 0 0
$$481$$ 10.5592 0.481456
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 24.3918 1.10758
$$486$$ 0 0
$$487$$ 28.5431 1.29341 0.646705 0.762740i $$-0.276147\pi$$
0.646705 + 0.762740i $$0.276147\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −20.2443 −0.913611 −0.456806 0.889566i $$-0.651007\pi$$
−0.456806 + 0.889566i $$0.651007\pi$$
$$492$$ 0 0
$$493$$ −27.7894 −1.25157
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −5.02768 −0.225522
$$498$$ 0 0
$$499$$ −29.6345 −1.32662 −0.663311 0.748344i $$-0.730849\pi$$
−0.663311 + 0.748344i $$0.730849\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4.03089 0.179729 0.0898643 0.995954i $$-0.471357\pi$$
0.0898643 + 0.995954i $$0.471357\pi$$
$$504$$ 0 0
$$505$$ −21.1248 −0.940040
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 14.5409 0.644513 0.322256 0.946652i $$-0.395559\pi$$
0.322256 + 0.946652i $$0.395559\pi$$
$$510$$ 0 0
$$511$$ 16.0204 0.708702
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −6.32659 −0.278783
$$516$$ 0 0
$$517$$ −26.3126 −1.15723
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 32.0631 1.40471 0.702355 0.711827i $$-0.252132\pi$$
0.702355 + 0.711827i $$0.252132\pi$$
$$522$$ 0 0
$$523$$ −39.0837 −1.70901 −0.854505 0.519443i $$-0.826139\pi$$
−0.854505 + 0.519443i $$0.826139\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 26.9274 1.17298
$$528$$ 0 0
$$529$$ −22.3369 −0.971171
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −18.5916 −0.805293
$$534$$ 0 0
$$535$$ −44.6516 −1.93046
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 2.56627 0.110537
$$540$$ 0 0
$$541$$ 28.3166 1.21743 0.608714 0.793390i $$-0.291686\pi$$
0.608714 + 0.793390i $$0.291686\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 25.7613 1.10349
$$546$$ 0 0
$$547$$ −25.2621 −1.08013 −0.540065 0.841623i $$-0.681600\pi$$
−0.540065 + 0.841623i $$0.681600\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −3.48879 −0.148627
$$552$$ 0 0
$$553$$ −14.8347 −0.630836
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −8.67480 −0.367563 −0.183781 0.982967i $$-0.558834\pi$$
−0.183781 + 0.982967i $$0.558834\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 5.97958 0.252009 0.126005 0.992030i $$-0.459785\pi$$
0.126005 + 0.992030i $$0.459785\pi$$
$$564$$ 0 0
$$565$$ −39.3633 −1.65603
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 30.7830 1.29049 0.645246 0.763975i $$-0.276755\pi$$
0.645246 + 0.763975i $$0.276755\pi$$
$$570$$ 0 0
$$571$$ 11.5389 0.482888 0.241444 0.970415i $$-0.422379\pi$$
0.241444 + 0.970415i $$0.422379\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 11.0063 0.458996
$$576$$ 0 0
$$577$$ 24.7345 1.02971 0.514856 0.857277i $$-0.327845\pi$$
0.514856 + 0.857277i $$0.327845\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 2.01517 0.0836033
$$582$$ 0 0
$$583$$ −1.31191 −0.0543339
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 23.5745 0.973023 0.486511 0.873674i $$-0.338269\pi$$
0.486511 + 0.873674i $$0.338269\pi$$
$$588$$ 0 0
$$589$$ 3.38056 0.139294
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 13.0608 0.536344 0.268172 0.963371i $$-0.413580\pi$$
0.268172 + 0.963371i $$0.413580\pi$$
$$594$$ 0 0
$$595$$ −34.2756 −1.40516
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 5.38643 0.220084 0.110042 0.993927i $$-0.464902\pi$$
0.110042 + 0.993927i $$0.464902\pi$$
$$600$$ 0 0
$$601$$ −25.8213 −1.05327 −0.526636 0.850091i $$-0.676547\pi$$
−0.526636 + 0.850091i $$0.676547\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 18.9949 0.772253
$$606$$ 0 0
$$607$$ −26.6095 −1.08005 −0.540024 0.841650i $$-0.681585\pi$$
−0.540024 + 0.841650i $$0.681585\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −28.8557 −1.16738
$$612$$ 0 0
$$613$$ −12.4101 −0.501240 −0.250620 0.968086i $$-0.580634\pi$$
−0.250620 + 0.968086i $$0.580634\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 36.3448 1.46319 0.731594 0.681740i $$-0.238777\pi$$
0.731594 + 0.681740i $$0.238777\pi$$
$$618$$ 0 0
$$619$$ −26.3371 −1.05858 −0.529288 0.848442i $$-0.677541\pi$$
−0.529288 + 0.848442i $$0.677541\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −17.6490 −0.707092
$$624$$ 0 0
$$625$$ 90.1125 3.60450
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 29.8859 1.19163
$$630$$ 0 0
$$631$$ −23.2024 −0.923672 −0.461836 0.886965i $$-0.652809\pi$$
−0.461836 + 0.886965i $$0.652809\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −2.58174 −0.102453
$$636$$ 0 0
$$637$$ 2.81429 0.111506
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −27.8540 −1.10017 −0.550084 0.835109i $$-0.685404\pi$$
−0.550084 + 0.835109i $$0.685404\pi$$
$$642$$ 0 0
$$643$$ 33.5593 1.32345 0.661725 0.749747i $$-0.269825\pi$$
0.661725 + 0.749747i $$0.269825\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 22.0534 0.867010 0.433505 0.901151i $$-0.357277\pi$$
0.433505 + 0.901151i $$0.357277\pi$$
$$648$$ 0 0
$$649$$ 35.9023 1.40929
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.41949 0.0555489 0.0277745 0.999614i $$-0.491158\pi$$
0.0277745 + 0.999614i $$0.491158\pi$$
$$654$$ 0 0
$$655$$ 30.7571 1.20178
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 2.46852 0.0961600 0.0480800 0.998843i $$-0.484690\pi$$
0.0480800 + 0.998843i $$0.484690\pi$$
$$660$$ 0 0
$$661$$ −6.78771 −0.264011 −0.132006 0.991249i $$-0.542142\pi$$
−0.132006 + 0.991249i $$0.542142\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −4.30308 −0.166866
$$666$$ 0 0
$$667$$ −2.84089 −0.110000
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 15.3976 0.594418
$$672$$ 0 0
$$673$$ 23.6087 0.910050 0.455025 0.890479i $$-0.349630\pi$$
0.455025 + 0.890479i $$0.349630\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 14.2817 0.548891 0.274446 0.961603i $$-0.411506\pi$$
0.274446 + 0.961603i $$0.411506\pi$$
$$678$$ 0 0
$$679$$ −5.66847 −0.217536
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −38.0560 −1.45617 −0.728086 0.685485i $$-0.759590\pi$$
−0.728086 + 0.685485i $$0.759590\pi$$
$$684$$ 0 0
$$685$$ 50.0387 1.91188
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −1.43871 −0.0548104
$$690$$ 0 0
$$691$$ −18.3838 −0.699352 −0.349676 0.936871i $$-0.613708\pi$$
−0.349676 + 0.936871i $$0.613708\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 12.9631 0.491717
$$696$$ 0 0
$$697$$ −52.6204 −1.99314
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −32.7583 −1.23726 −0.618632 0.785681i $$-0.712313\pi$$
−0.618632 + 0.785681i $$0.712313\pi$$
$$702$$ 0 0
$$703$$ 3.75198 0.141509
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 4.90923 0.184631
$$708$$ 0 0
$$709$$ 2.39583 0.0899773 0.0449886 0.998987i $$-0.485675\pi$$
0.0449886 + 0.998987i $$0.485675\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 2.75276 0.103092
$$714$$ 0 0
$$715$$ −31.0778 −1.16224
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −17.7999 −0.663825 −0.331912 0.943310i $$-0.607694\pi$$
−0.331912 + 0.943310i $$0.607694\pi$$
$$720$$ 0 0
$$721$$ 1.47025 0.0547549
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −47.1560 −1.75133
$$726$$ 0 0
$$727$$ −20.0921 −0.745175 −0.372588 0.927997i $$-0.621529\pi$$
−0.372588 + 0.927997i $$0.621529\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 45.3474 1.67495 0.837473 0.546479i $$-0.184032\pi$$
0.837473 + 0.546479i $$0.184032\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 30.7453 1.13252
$$738$$ 0 0
$$739$$ −6.15710 −0.226493 −0.113246 0.993567i $$-0.536125\pi$$
−0.113246 + 0.993567i $$0.536125\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −31.5785 −1.15850 −0.579251 0.815149i $$-0.696655\pi$$
−0.579251 + 0.815149i $$0.696655\pi$$
$$744$$ 0 0
$$745$$ 55.3125 2.02649
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 10.3767 0.379155
$$750$$ 0 0
$$751$$ −38.3207 −1.39834 −0.699171 0.714955i $$-0.746447\pi$$
−0.699171 + 0.714955i $$0.746447\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 76.6476 2.78949
$$756$$ 0 0
$$757$$ −28.0924 −1.02104 −0.510518 0.859867i $$-0.670546\pi$$
−0.510518 + 0.859867i $$0.670546\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −16.4348 −0.595762 −0.297881 0.954603i $$-0.596280\pi$$
−0.297881 + 0.954603i $$0.596280\pi$$
$$762$$ 0 0
$$763$$ −5.98671 −0.216733
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 39.3721 1.42165
$$768$$ 0 0
$$769$$ 11.0679 0.399117 0.199559 0.979886i $$-0.436049\pi$$
0.199559 + 0.979886i $$0.436049\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0.596231 0.0214449 0.0107225 0.999943i $$-0.496587\pi$$
0.0107225 + 0.999943i $$0.496587\pi$$
$$774$$ 0 0
$$775$$ 45.6932 1.64135
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −6.60615 −0.236690
$$780$$ 0 0
$$781$$ −12.9024 −0.461683
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −8.26291 −0.294916
$$786$$ 0 0
$$787$$ −26.8567 −0.957339 −0.478670 0.877995i $$-0.658881\pi$$
−0.478670 + 0.877995i $$0.658881\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 9.14771 0.325255
$$792$$ 0 0
$$793$$ 16.8857 0.599630
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −7.04742 −0.249632 −0.124816 0.992180i $$-0.539834\pi$$
−0.124816 + 0.992180i $$0.539834\pi$$
$$798$$ 0 0
$$799$$ −81.6710 −2.88931
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 41.1127 1.45084
$$804$$ 0 0
$$805$$ −3.50396 −0.123498
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −28.1531 −0.989811 −0.494905 0.868947i $$-0.664797\pi$$
−0.494905 + 0.868947i $$0.664797\pi$$
$$810$$ 0 0
$$811$$ −6.75550 −0.237218 −0.118609 0.992941i $$-0.537843\pi$$
−0.118609 + 0.992941i $$0.537843\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −97.0206 −3.39848
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −35.1260 −1.22591 −0.612953 0.790120i $$-0.710018\pi$$
−0.612953 + 0.790120i $$0.710018\pi$$
$$822$$ 0 0
$$823$$ −11.4393 −0.398748 −0.199374 0.979923i $$-0.563891\pi$$
−0.199374 + 0.979923i $$0.563891\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −18.7134 −0.650730 −0.325365 0.945588i $$-0.605487\pi$$
−0.325365 + 0.945588i $$0.605487\pi$$
$$828$$ 0 0
$$829$$ 37.2244 1.29286 0.646429 0.762974i $$-0.276262\pi$$
0.646429 + 0.762974i $$0.276262\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 7.96536 0.275984
$$834$$ 0 0
$$835$$ −45.2531 −1.56605
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 32.6127 1.12591 0.562957 0.826486i $$-0.309664\pi$$
0.562957 + 0.826486i $$0.309664\pi$$
$$840$$ 0 0
$$841$$ −16.8284 −0.580289
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 21.8586 0.751960
$$846$$ 0 0
$$847$$ −4.41427 −0.151676
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 3.05520 0.104731
$$852$$ 0 0
$$853$$ 6.56346 0.224729 0.112364 0.993667i $$-0.464158\pi$$
0.112364 + 0.993667i $$0.464158\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −19.6939 −0.672729 −0.336365 0.941732i $$-0.609197\pi$$
−0.336365 + 0.941732i $$0.609197\pi$$
$$858$$ 0 0
$$859$$ −1.41988 −0.0484458 −0.0242229 0.999707i $$-0.507711\pi$$
−0.0242229 + 0.999707i $$0.507711\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 31.9991 1.08926 0.544631 0.838676i $$-0.316670\pi$$
0.544631 + 0.838676i $$0.316670\pi$$
$$864$$ 0 0
$$865$$ −105.039 −3.57142
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −38.0698 −1.29143
$$870$$ 0 0
$$871$$ 33.7167 1.14245
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −36.6470 −1.23889
$$876$$ 0 0
$$877$$ −26.4933 −0.894614 −0.447307 0.894381i $$-0.647617\pi$$
−0.447307 + 0.894381i $$0.647617\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 17.5630 0.591713 0.295856 0.955232i $$-0.404395\pi$$
0.295856 + 0.955232i $$0.404395\pi$$
$$882$$ 0 0
$$883$$ −5.05551 −0.170132 −0.0850658 0.996375i $$-0.527110\pi$$
−0.0850658 + 0.996375i $$0.527110\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 15.7390 0.528464 0.264232 0.964459i $$-0.414882\pi$$
0.264232 + 0.964459i $$0.414882\pi$$
$$888$$ 0 0
$$889$$ 0.599976 0.0201225
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −10.2533 −0.343113
$$894$$ 0 0
$$895$$ 30.4960 1.01937
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −11.7940 −0.393353
$$900$$ 0 0
$$901$$ −4.07201 −0.135658
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −11.0573 −0.367558
$$906$$ 0 0
$$907$$ 19.0379 0.632142 0.316071 0.948736i $$-0.397636\pi$$
0.316071 + 0.948736i $$0.397636\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −52.9775 −1.75522 −0.877611 0.479373i $$-0.840864\pi$$
−0.877611 + 0.479373i $$0.840864\pi$$
$$912$$ 0 0
$$913$$ 5.17147 0.171151
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −7.14771 −0.236038
$$918$$ 0 0
$$919$$ −37.5222 −1.23774 −0.618872 0.785492i $$-0.712410\pi$$
−0.618872 + 0.785492i $$0.712410\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −14.1493 −0.465731
$$924$$ 0 0
$$925$$ 50.7135 1.66745
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 57.3372 1.88117 0.940586 0.339555i $$-0.110276\pi$$
0.940586 + 0.339555i $$0.110276\pi$$
$$930$$ 0 0
$$931$$ 1.00000 0.0327737
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −87.9603 −2.87661
$$936$$ 0 0
$$937$$ −11.3469 −0.370685 −0.185343 0.982674i $$-0.559340\pi$$
−0.185343 + 0.982674i $$0.559340\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 34.7123 1.13159 0.565794 0.824547i $$-0.308570\pi$$
0.565794 + 0.824547i $$0.308570\pi$$
$$942$$ 0 0
$$943$$ −5.37933 −0.175175
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 16.2357 0.527589 0.263794 0.964579i $$-0.415026\pi$$
0.263794 + 0.964579i $$0.415026\pi$$
$$948$$ 0 0
$$949$$ 45.0861 1.46356
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 19.4158 0.628938 0.314469 0.949268i $$-0.398174\pi$$
0.314469 + 0.949268i $$0.398174\pi$$
$$954$$ 0 0
$$955$$ 117.158 3.79114
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −11.6286 −0.375506
$$960$$ 0 0
$$961$$ −19.5718 −0.631349
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 62.5533 2.01366
$$966$$ 0 0
$$967$$ −1.38578 −0.0445638 −0.0222819 0.999752i $$-0.507093\pi$$
−0.0222819 + 0.999752i $$0.507093\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 1.33450 0.0428261 0.0214131 0.999771i $$-0.493183\pi$$
0.0214131 + 0.999771i $$0.493183\pi$$
$$972$$ 0 0
$$973$$ −3.01251 −0.0965766
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 13.0460 0.417377 0.208689 0.977982i $$-0.433080\pi$$
0.208689 + 0.977982i $$0.433080\pi$$
$$978$$ 0 0
$$979$$ −45.2921 −1.44754
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −13.0877 −0.417433 −0.208717 0.977976i $$-0.566929\pi$$
−0.208717 + 0.977976i $$0.566929\pi$$
$$984$$ 0 0
$$985$$ −35.8351 −1.14180
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −4.81643 −0.152999 −0.0764994 0.997070i $$-0.524374\pi$$
−0.0764994 + 0.997070i $$0.524374\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −60.3309 −1.91262
$$996$$ 0 0
$$997$$ −11.1127 −0.351943 −0.175971 0.984395i $$-0.556307\pi$$
−0.175971 + 0.984395i $$0.556307\pi$$
$$998$$ 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 9576.2.a.co.1.1 5
3.2 odd 2 3192.2.a.ba.1.5 5
12.11 even 2 6384.2.a.ce.1.5 5

By twisted newform
Twist Min Dim Char Parity Ord Type
3192.2.a.ba.1.5 5 3.2 odd 2
6384.2.a.ce.1.5 5 12.11 even 2
9576.2.a.co.1.1 5 1.1 even 1 trivial