# Properties

 Label 9200.2.a.cd.1.3 Level $9200$ Weight $2$ Character 9200.1 Self dual yes Analytic conductor $73.462$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9200 = 2^{4} \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9200.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$73.4623698596$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.621.1 Defining polynomial: $$x^{3} - 6 x - 3$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 920) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$2.66908$$ of defining polynomial Character $$\chi$$ $$=$$ 9200.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.66908 q^{3} +3.66908 q^{7} +4.12398 q^{9} +O(q^{10})$$ $$q+2.66908 q^{3} +3.66908 q^{7} +4.12398 q^{9} +1.21417 q^{11} -2.21417 q^{13} -1.21417 q^{17} +2.57889 q^{19} +9.79306 q^{21} +1.00000 q^{23} +3.00000 q^{27} +1.45490 q^{29} +6.46214 q^{31} +3.24073 q^{33} -4.00000 q^{37} -5.90981 q^{39} -10.9170 q^{41} +6.90981 q^{43} +5.45490 q^{47} +6.46214 q^{49} -3.24073 q^{51} -3.81962 q^{53} +6.88325 q^{57} +4.24797 q^{59} +6.78583 q^{61} +15.1312 q^{63} +12.8567 q^{67} +2.66908 q^{69} +6.91705 q^{71} +15.2214 q^{73} +4.45490 q^{77} -4.36471 q^{81} -15.5861 q^{83} +3.88325 q^{87} -10.9098 q^{89} -8.12398 q^{91} +17.2480 q^{93} -1.69563 q^{97} +5.00724 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 3 q^{7} + 3 q^{9} + O(q^{10})$$ $$3 q + 3 q^{7} + 3 q^{9} - 3 q^{11} + 3 q^{17} - 3 q^{19} + 12 q^{21} + 3 q^{23} + 9 q^{27} + 3 q^{29} - 6 q^{31} + 15 q^{33} - 12 q^{37} - 15 q^{39} - 6 q^{41} + 18 q^{43} + 15 q^{47} - 6 q^{49} - 15 q^{51} - 6 q^{53} + 6 q^{57} - 6 q^{59} + 27 q^{61} + 12 q^{63} + 12 q^{67} - 6 q^{71} + 15 q^{73} + 12 q^{77} - 9 q^{81} - 12 q^{83} - 3 q^{87} - 30 q^{89} - 15 q^{91} + 33 q^{93} - 9 q^{97} - 9 q^{99} + O(q^{100})$$

## 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
$$3$$ 2.66908 1.54099 0.770497 0.637444i $$-0.220008\pi$$
0.770497 + 0.637444i $$0.220008\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 3.66908 1.38678 0.693391 0.720562i $$-0.256116\pi$$
0.693391 + 0.720562i $$0.256116\pi$$
$$8$$ 0 0
$$9$$ 4.12398 1.37466
$$10$$ 0 0
$$11$$ 1.21417 0.366088 0.183044 0.983105i $$-0.441405\pi$$
0.183044 + 0.983105i $$0.441405\pi$$
$$12$$ 0 0
$$13$$ −2.21417 −0.614102 −0.307051 0.951693i $$-0.599342\pi$$
−0.307051 + 0.951693i $$0.599342\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1.21417 −0.294481 −0.147240 0.989101i $$-0.547039\pi$$
−0.147240 + 0.989101i $$0.547039\pi$$
$$18$$ 0 0
$$19$$ 2.57889 0.591637 0.295819 0.955244i $$-0.404408\pi$$
0.295819 + 0.955244i $$0.404408\pi$$
$$20$$ 0 0
$$21$$ 9.79306 2.13702
$$22$$ 0 0
$$23$$ 1.00000 0.208514
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 3.00000 0.577350
$$28$$ 0 0
$$29$$ 1.45490 0.270169 0.135084 0.990834i $$-0.456869\pi$$
0.135084 + 0.990834i $$0.456869\pi$$
$$30$$ 0 0
$$31$$ 6.46214 1.16063 0.580317 0.814390i $$-0.302928\pi$$
0.580317 + 0.814390i $$0.302928\pi$$
$$32$$ 0 0
$$33$$ 3.24073 0.564139
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −4.00000 −0.657596 −0.328798 0.944400i $$-0.606644\pi$$
−0.328798 + 0.944400i $$0.606644\pi$$
$$38$$ 0 0
$$39$$ −5.90981 −0.946327
$$40$$ 0 0
$$41$$ −10.9170 −1.70496 −0.852478 0.522763i $$-0.824901\pi$$
−0.852478 + 0.522763i $$0.824901\pi$$
$$42$$ 0 0
$$43$$ 6.90981 1.05374 0.526868 0.849947i $$-0.323366\pi$$
0.526868 + 0.849947i $$0.323366\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 5.45490 0.795680 0.397840 0.917455i $$-0.369760\pi$$
0.397840 + 0.917455i $$0.369760\pi$$
$$48$$ 0 0
$$49$$ 6.46214 0.923163
$$50$$ 0 0
$$51$$ −3.24073 −0.453793
$$52$$ 0 0
$$53$$ −3.81962 −0.524665 −0.262332 0.964978i $$-0.584492\pi$$
−0.262332 + 0.964978i $$0.584492\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 6.88325 0.911709
$$58$$ 0 0
$$59$$ 4.24797 0.553038 0.276519 0.961008i $$-0.410819\pi$$
0.276519 + 0.961008i $$0.410819\pi$$
$$60$$ 0 0
$$61$$ 6.78583 0.868836 0.434418 0.900711i $$-0.356954\pi$$
0.434418 + 0.900711i $$0.356954\pi$$
$$62$$ 0 0
$$63$$ 15.1312 1.90635
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 12.8567 1.57070 0.785348 0.619055i $$-0.212484\pi$$
0.785348 + 0.619055i $$0.212484\pi$$
$$68$$ 0 0
$$69$$ 2.66908 0.321319
$$70$$ 0 0
$$71$$ 6.91705 0.820902 0.410451 0.911883i $$-0.365371\pi$$
0.410451 + 0.911883i $$0.365371\pi$$
$$72$$ 0 0
$$73$$ 15.2214 1.78153 0.890766 0.454463i $$-0.150169\pi$$
0.890766 + 0.454463i $$0.150169\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.45490 0.507683
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ −4.36471 −0.484968
$$82$$ 0 0
$$83$$ −15.5861 −1.71080 −0.855400 0.517968i $$-0.826688\pi$$
−0.855400 + 0.517968i $$0.826688\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 3.88325 0.416329
$$88$$ 0 0
$$89$$ −10.9098 −1.15644 −0.578219 0.815882i $$-0.696252\pi$$
−0.578219 + 0.815882i $$0.696252\pi$$
$$90$$ 0 0
$$91$$ −8.12398 −0.851625
$$92$$ 0 0
$$93$$ 17.2480 1.78853
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.69563 −0.172165 −0.0860827 0.996288i $$-0.527435\pi$$
−0.0860827 + 0.996288i $$0.527435\pi$$
$$98$$ 0 0
$$99$$ 5.00724 0.503246
$$100$$ 0 0
$$101$$ −2.24797 −0.223681 −0.111841 0.993726i $$-0.535675\pi$$
−0.111841 + 0.993726i $$0.535675\pi$$
$$102$$ 0 0
$$103$$ −2.78583 −0.274495 −0.137248 0.990537i $$-0.543826\pi$$
−0.137248 + 0.990537i $$0.543826\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 13.1578 1.27201 0.636005 0.771685i $$-0.280586\pi$$
0.636005 + 0.771685i $$0.280586\pi$$
$$108$$ 0 0
$$109$$ 3.42111 0.327683 0.163842 0.986487i $$-0.447611\pi$$
0.163842 + 0.986487i $$0.447611\pi$$
$$110$$ 0 0
$$111$$ −10.6763 −1.01335
$$112$$ 0 0
$$113$$ 10.0000 0.940721 0.470360 0.882474i $$-0.344124\pi$$
0.470360 + 0.882474i $$0.344124\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −9.13122 −0.844182
$$118$$ 0 0
$$119$$ −4.45490 −0.408380
$$120$$ 0 0
$$121$$ −9.52578 −0.865980
$$122$$ 0 0
$$123$$ −29.1385 −2.62733
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 19.9508 1.77035 0.885175 0.465258i $$-0.154038\pi$$
0.885175 + 0.465258i $$0.154038\pi$$
$$128$$ 0 0
$$129$$ 18.4428 1.62380
$$130$$ 0 0
$$131$$ 9.70287 0.847744 0.423872 0.905722i $$-0.360671\pi$$
0.423872 + 0.905722i $$0.360671\pi$$
$$132$$ 0 0
$$133$$ 9.46214 0.820472
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2.82685 −0.241514 −0.120757 0.992682i $$-0.538532\pi$$
−0.120757 + 0.992682i $$0.538532\pi$$
$$138$$ 0 0
$$139$$ −2.36471 −0.200572 −0.100286 0.994959i $$-0.531976\pi$$
−0.100286 + 0.994959i $$0.531976\pi$$
$$140$$ 0 0
$$141$$ 14.5596 1.22614
$$142$$ 0 0
$$143$$ −2.68840 −0.224815
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 17.2480 1.42259
$$148$$ 0 0
$$149$$ −11.9170 −0.976282 −0.488141 0.872765i $$-0.662325\pi$$
−0.488141 + 0.872765i $$0.662325\pi$$
$$150$$ 0 0
$$151$$ −9.57889 −0.779519 −0.389759 0.920917i $$-0.627442\pi$$
−0.389759 + 0.920917i $$0.627442\pi$$
$$152$$ 0 0
$$153$$ −5.00724 −0.404811
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 18.7439 1.49593 0.747963 0.663740i $$-0.231032\pi$$
0.747963 + 0.663740i $$0.231032\pi$$
$$158$$ 0 0
$$159$$ −10.1949 −0.808505
$$160$$ 0 0
$$161$$ 3.66908 0.289164
$$162$$ 0 0
$$163$$ −19.3188 −1.51317 −0.756584 0.653896i $$-0.773133\pi$$
−0.756584 + 0.653896i $$0.773133\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1.81962 −0.140806 −0.0704031 0.997519i $$-0.522429\pi$$
−0.0704031 + 0.997519i $$0.522429\pi$$
$$168$$ 0 0
$$169$$ −8.09743 −0.622879
$$170$$ 0 0
$$171$$ 10.6353 0.813301
$$172$$ 0 0
$$173$$ −15.9581 −1.21327 −0.606635 0.794981i $$-0.707481\pi$$
−0.606635 + 0.794981i $$0.707481\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 11.3382 0.852228
$$178$$ 0 0
$$179$$ −17.9508 −1.34171 −0.670854 0.741589i $$-0.734072\pi$$
−0.670854 + 0.741589i $$0.734072\pi$$
$$180$$ 0 0
$$181$$ 6.33092 0.470574 0.235287 0.971926i $$-0.424397\pi$$
0.235287 + 0.971926i $$0.424397\pi$$
$$182$$ 0 0
$$183$$ 18.1119 1.33887
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −1.47422 −0.107806
$$188$$ 0 0
$$189$$ 11.0072 0.800659
$$190$$ 0 0
$$191$$ 15.1578 1.09678 0.548389 0.836223i $$-0.315241\pi$$
0.548389 + 0.836223i $$0.315241\pi$$
$$192$$ 0 0
$$193$$ −18.9879 −1.36678 −0.683390 0.730053i $$-0.739495\pi$$
−0.683390 + 0.730053i $$0.739495\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 19.1650 1.36545 0.682725 0.730675i $$-0.260795\pi$$
0.682725 + 0.730675i $$0.260795\pi$$
$$198$$ 0 0
$$199$$ 5.76651 0.408777 0.204388 0.978890i $$-0.434479\pi$$
0.204388 + 0.978890i $$0.434479\pi$$
$$200$$ 0 0
$$201$$ 34.3155 2.42043
$$202$$ 0 0
$$203$$ 5.33816 0.374665
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 4.12398 0.286637
$$208$$ 0 0
$$209$$ 3.13122 0.216591
$$210$$ 0 0
$$211$$ 17.4057 1.19826 0.599130 0.800652i $$-0.295513\pi$$
0.599130 + 0.800652i $$0.295513\pi$$
$$212$$ 0 0
$$213$$ 18.4621 1.26501
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 23.7101 1.60955
$$218$$ 0 0
$$219$$ 40.6272 2.74533
$$220$$ 0 0
$$221$$ 2.68840 0.180841
$$222$$ 0 0
$$223$$ −14.6763 −0.982799 −0.491399 0.870934i $$-0.663514\pi$$
−0.491399 + 0.870934i $$0.663514\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 16.4283 1.09039 0.545194 0.838310i $$-0.316456\pi$$
0.545194 + 0.838310i $$0.316456\pi$$
$$228$$ 0 0
$$229$$ 19.3526 1.27886 0.639429 0.768850i $$-0.279171\pi$$
0.639429 + 0.768850i $$0.279171\pi$$
$$230$$ 0 0
$$231$$ 11.8905 0.782337
$$232$$ 0 0
$$233$$ 19.4549 1.27453 0.637267 0.770643i $$-0.280065\pi$$
0.637267 + 0.770643i $$0.280065\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −23.7029 −1.53321 −0.766606 0.642118i $$-0.778056\pi$$
−0.766606 + 0.642118i $$0.778056\pi$$
$$240$$ 0 0
$$241$$ 0.233492 0.0150405 0.00752027 0.999972i $$-0.497606\pi$$
0.00752027 + 0.999972i $$0.497606\pi$$
$$242$$ 0 0
$$243$$ −20.6498 −1.32468
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −5.71011 −0.363325
$$248$$ 0 0
$$249$$ −41.6006 −2.63633
$$250$$ 0 0
$$251$$ −21.7511 −1.37292 −0.686460 0.727168i $$-0.740836\pi$$
−0.686460 + 0.727168i $$0.740836\pi$$
$$252$$ 0 0
$$253$$ 1.21417 0.0763345
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 16.3116 1.01749 0.508745 0.860917i $$-0.330110\pi$$
0.508745 + 0.860917i $$0.330110\pi$$
$$258$$ 0 0
$$259$$ −14.6763 −0.911942
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ 0 0
$$263$$ −2.53786 −0.156491 −0.0782455 0.996934i $$-0.524932\pi$$
−0.0782455 + 0.996934i $$0.524932\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −29.1191 −1.78206
$$268$$ 0 0
$$269$$ −2.54510 −0.155177 −0.0775886 0.996985i $$-0.524722\pi$$
−0.0775886 + 0.996985i $$0.524722\pi$$
$$270$$ 0 0
$$271$$ −24.1795 −1.46880 −0.734400 0.678717i $$-0.762536\pi$$
−0.734400 + 0.678717i $$0.762536\pi$$
$$272$$ 0 0
$$273$$ −21.6836 −1.31235
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 21.2359 1.27594 0.637970 0.770061i $$-0.279774\pi$$
0.637970 + 0.770061i $$0.279774\pi$$
$$278$$ 0 0
$$279$$ 26.6498 1.59548
$$280$$ 0 0
$$281$$ −13.8872 −0.828441 −0.414220 0.910177i $$-0.635946\pi$$
−0.414220 + 0.910177i $$0.635946\pi$$
$$282$$ 0 0
$$283$$ −29.5330 −1.75556 −0.877778 0.479068i $$-0.840975\pi$$
−0.877778 + 0.479068i $$0.840975\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −40.0555 −2.36440
$$288$$ 0 0
$$289$$ −15.5258 −0.913281
$$290$$ 0 0
$$291$$ −4.52578 −0.265306
$$292$$ 0 0
$$293$$ 24.0821 1.40689 0.703444 0.710750i $$-0.251644\pi$$
0.703444 + 0.710750i $$0.251644\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 3.64252 0.211361
$$298$$ 0 0
$$299$$ −2.21417 −0.128049
$$300$$ 0 0
$$301$$ 25.3526 1.46130
$$302$$ 0 0
$$303$$ −6.00000 −0.344691
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 19.9436 1.13824 0.569121 0.822254i $$-0.307284\pi$$
0.569121 + 0.822254i $$0.307284\pi$$
$$308$$ 0 0
$$309$$ −7.43559 −0.422996
$$310$$ 0 0
$$311$$ 2.97345 0.168609 0.0843043 0.996440i $$-0.473133\pi$$
0.0843043 + 0.996440i $$0.473133\pi$$
$$312$$ 0 0
$$313$$ −15.4887 −0.875473 −0.437736 0.899103i $$-0.644220\pi$$
−0.437736 + 0.899103i $$0.644220\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −8.82685 −0.495765 −0.247883 0.968790i $$-0.579735\pi$$
−0.247883 + 0.968790i $$0.579735\pi$$
$$318$$ 0 0
$$319$$ 1.76651 0.0989055
$$320$$ 0 0
$$321$$ 35.1191 1.96016
$$322$$ 0 0
$$323$$ −3.13122 −0.174226
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 9.13122 0.504958
$$328$$ 0 0
$$329$$ 20.0145 1.10343
$$330$$ 0 0
$$331$$ −17.4018 −0.956489 −0.478245 0.878227i $$-0.658727\pi$$
−0.478245 + 0.878227i $$0.658727\pi$$
$$332$$ 0 0
$$333$$ −16.4959 −0.903972
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −26.9541 −1.46828 −0.734142 0.678995i $$-0.762416\pi$$
−0.734142 + 0.678995i $$0.762416\pi$$
$$338$$ 0 0
$$339$$ 26.6908 1.44964
$$340$$ 0 0
$$341$$ 7.84617 0.424894
$$342$$ 0 0
$$343$$ −1.97345 −0.106556
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −10.1240 −0.543484 −0.271742 0.962370i $$-0.587600\pi$$
−0.271742 + 0.962370i $$0.587600\pi$$
$$348$$ 0 0
$$349$$ 7.38732 0.395434 0.197717 0.980259i $$-0.436647\pi$$
0.197717 + 0.980259i $$0.436647\pi$$
$$350$$ 0 0
$$351$$ −6.64252 −0.354552
$$352$$ 0 0
$$353$$ −13.8833 −0.738931 −0.369466 0.929244i $$-0.620459\pi$$
−0.369466 + 0.929244i $$0.620459\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −11.8905 −0.629312
$$358$$ 0 0
$$359$$ −15.0902 −0.796430 −0.398215 0.917292i $$-0.630370\pi$$
−0.398215 + 0.917292i $$0.630370\pi$$
$$360$$ 0 0
$$361$$ −12.3493 −0.649965
$$362$$ 0 0
$$363$$ −25.4251 −1.33447
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −24.0289 −1.25430 −0.627150 0.778898i $$-0.715779\pi$$
−0.627150 + 0.778898i $$0.715779\pi$$
$$368$$ 0 0
$$369$$ −45.0217 −2.34374
$$370$$ 0 0
$$371$$ −14.0145 −0.727595
$$372$$ 0 0
$$373$$ −30.6908 −1.58911 −0.794554 0.607193i $$-0.792296\pi$$
−0.794554 + 0.607193i $$0.792296\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −3.22141 −0.165911
$$378$$ 0 0
$$379$$ −2.07087 −0.106374 −0.0531869 0.998585i $$-0.516938\pi$$
−0.0531869 + 0.998585i $$0.516938\pi$$
$$380$$ 0 0
$$381$$ 53.2504 2.72810
$$382$$ 0 0
$$383$$ −1.58612 −0.0810472 −0.0405236 0.999179i $$-0.512903\pi$$
−0.0405236 + 0.999179i $$0.512903\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 28.4959 1.44853
$$388$$ 0 0
$$389$$ 21.2142 1.07560 0.537801 0.843072i $$-0.319255\pi$$
0.537801 + 0.843072i $$0.319255\pi$$
$$390$$ 0 0
$$391$$ −1.21417 −0.0614035
$$392$$ 0 0
$$393$$ 25.8977 1.30637
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1.93965 0.0973485 0.0486742 0.998815i $$-0.484500\pi$$
0.0486742 + 0.998815i $$0.484500\pi$$
$$398$$ 0 0
$$399$$ 25.2552 1.26434
$$400$$ 0 0
$$401$$ −5.69893 −0.284591 −0.142295 0.989824i $$-0.545448\pi$$
−0.142295 + 0.989824i $$0.545448\pi$$
$$402$$ 0 0
$$403$$ −14.3083 −0.712748
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −4.85670 −0.240738
$$408$$ 0 0
$$409$$ 3.53786 0.174936 0.0874679 0.996167i $$-0.472122\pi$$
0.0874679 + 0.996167i $$0.472122\pi$$
$$410$$ 0 0
$$411$$ −7.54510 −0.372172
$$412$$ 0 0
$$413$$ 15.5861 0.766943
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −6.31160 −0.309081
$$418$$ 0 0
$$419$$ −28.2624 −1.38071 −0.690355 0.723471i $$-0.742546\pi$$
−0.690355 + 0.723471i $$0.742546\pi$$
$$420$$ 0 0
$$421$$ 34.0974 1.66181 0.830904 0.556417i $$-0.187824\pi$$
0.830904 + 0.556417i $$0.187824\pi$$
$$422$$ 0 0
$$423$$ 22.4959 1.09379
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 24.8977 1.20489
$$428$$ 0 0
$$429$$ −7.17554 −0.346438
$$430$$ 0 0
$$431$$ 13.2850 0.639918 0.319959 0.947431i $$-0.396331\pi$$
0.319959 + 0.947431i $$0.396331\pi$$
$$432$$ 0 0
$$433$$ −11.0603 −0.531526 −0.265763 0.964038i $$-0.585624\pi$$
−0.265763 + 0.964038i $$0.585624\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 2.57889 0.123365
$$438$$ 0 0
$$439$$ 19.1916 0.915963 0.457982 0.888962i $$-0.348573\pi$$
0.457982 + 0.888962i $$0.348573\pi$$
$$440$$ 0 0
$$441$$ 26.6498 1.26904
$$442$$ 0 0
$$443$$ 24.2818 1.15366 0.576831 0.816864i $$-0.304289\pi$$
0.576831 + 0.816864i $$0.304289\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −31.8075 −1.50444
$$448$$ 0 0
$$449$$ 14.8413 0.700406 0.350203 0.936674i $$-0.386113\pi$$
0.350203 + 0.936674i $$0.386113\pi$$
$$450$$ 0 0
$$451$$ −13.2552 −0.624163
$$452$$ 0 0
$$453$$ −25.5668 −1.20123
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −15.5861 −0.729088 −0.364544 0.931186i $$-0.618775\pi$$
−0.364544 + 0.931186i $$0.618775\pi$$
$$458$$ 0 0
$$459$$ −3.64252 −0.170019
$$460$$ 0 0
$$461$$ −14.1312 −0.658157 −0.329078 0.944303i $$-0.606738\pi$$
−0.329078 + 0.944303i $$0.606738\pi$$
$$462$$ 0 0
$$463$$ 26.7584 1.24357 0.621784 0.783189i $$-0.286408\pi$$
0.621784 + 0.783189i $$0.286408\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 26.6908 1.23510 0.617551 0.786531i $$-0.288125\pi$$
0.617551 + 0.786531i $$0.288125\pi$$
$$468$$ 0 0
$$469$$ 47.1722 2.17821
$$470$$ 0 0
$$471$$ 50.0289 2.30521
$$472$$ 0 0
$$473$$ 8.38972 0.385760
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −15.7520 −0.721236
$$478$$ 0 0
$$479$$ −4.90981 −0.224335 −0.112167 0.993689i $$-0.535779\pi$$
−0.112167 + 0.993689i $$0.535779\pi$$
$$480$$ 0 0
$$481$$ 8.85670 0.403831
$$482$$ 0 0
$$483$$ 9.79306 0.445600
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 16.7786 0.760310 0.380155 0.924923i $$-0.375871\pi$$
0.380155 + 0.924923i $$0.375871\pi$$
$$488$$ 0 0
$$489$$ −51.5635 −2.33178
$$490$$ 0 0
$$491$$ −41.4839 −1.87214 −0.936070 0.351814i $$-0.885565\pi$$
−0.936070 + 0.351814i $$0.885565\pi$$
$$492$$ 0 0
$$493$$ −1.76651 −0.0795595
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 25.3792 1.13841
$$498$$ 0 0
$$499$$ 6.47751 0.289973 0.144987 0.989434i $$-0.453686\pi$$
0.144987 + 0.989434i $$0.453686\pi$$
$$500$$ 0 0
$$501$$ −4.85670 −0.216981
$$502$$ 0 0
$$503$$ 37.3825 1.66680 0.833401 0.552669i $$-0.186390\pi$$
0.833401 + 0.552669i $$0.186390\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −21.6127 −0.959853
$$508$$ 0 0
$$509$$ −15.0410 −0.666682 −0.333341 0.942806i $$-0.608176\pi$$
−0.333341 + 0.942806i $$0.608176\pi$$
$$510$$ 0 0
$$511$$ 55.8486 2.47060
$$512$$ 0 0
$$513$$ 7.73666 0.341582
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 6.62321 0.291288
$$518$$ 0 0
$$519$$ −42.5934 −1.86964
$$520$$ 0 0
$$521$$ 15.9469 0.698646 0.349323 0.937002i $$-0.386412\pi$$
0.349323 + 0.937002i $$0.386412\pi$$
$$522$$ 0 0
$$523$$ 10.8567 0.474730 0.237365 0.971420i $$-0.423716\pi$$
0.237365 + 0.971420i $$0.423716\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −7.84617 −0.341785
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 17.5185 0.760240
$$532$$ 0 0
$$533$$ 24.1722 1.04702
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −47.9122 −2.06756
$$538$$ 0 0
$$539$$ 7.84617 0.337958
$$540$$ 0 0
$$541$$ −30.3792 −1.30610 −0.653052 0.757313i $$-0.726512\pi$$
−0.653052 + 0.757313i $$0.726512\pi$$
$$542$$ 0 0
$$543$$ 16.8977 0.725151
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 28.4090 1.21468 0.607341 0.794441i $$-0.292236\pi$$
0.607341 + 0.794441i $$0.292236\pi$$
$$548$$ 0 0
$$549$$ 27.9846 1.19435
$$550$$ 0 0
$$551$$ 3.75203 0.159842
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −36.7584 −1.55750 −0.778751 0.627333i $$-0.784147\pi$$
−0.778751 + 0.627333i $$0.784147\pi$$
$$558$$ 0 0
$$559$$ −15.2995 −0.647101
$$560$$ 0 0
$$561$$ −3.93481 −0.166128
$$562$$ 0 0
$$563$$ −3.03708 −0.127998 −0.0639989 0.997950i $$-0.520385\pi$$
−0.0639989 + 0.997950i $$0.520385\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −16.0145 −0.672545
$$568$$ 0 0
$$569$$ −32.2093 −1.35029 −0.675143 0.737687i $$-0.735918\pi$$
−0.675143 + 0.737687i $$0.735918\pi$$
$$570$$ 0 0
$$571$$ −27.7777 −1.16246 −0.581230 0.813739i $$-0.697428\pi$$
−0.581230 + 0.813739i $$0.697428\pi$$
$$572$$ 0 0
$$573$$ 40.4573 1.69013
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −11.2890 −0.469967 −0.234984 0.971999i $$-0.575504\pi$$
−0.234984 + 0.971999i $$0.575504\pi$$
$$578$$ 0 0
$$579$$ −50.6803 −2.10620
$$580$$ 0 0
$$581$$ −57.1867 −2.37251
$$582$$ 0 0
$$583$$ −4.63768 −0.192073
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 23.6609 0.976592 0.488296 0.872678i $$-0.337619\pi$$
0.488296 + 0.872678i $$0.337619\pi$$
$$588$$ 0 0
$$589$$ 16.6651 0.686675
$$590$$ 0 0
$$591$$ 51.1529 2.10415
$$592$$ 0 0
$$593$$ 17.8341 0.732358 0.366179 0.930544i $$-0.380666\pi$$
0.366179 + 0.930544i $$0.380666\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 15.3913 0.629923
$$598$$ 0 0
$$599$$ 23.8308 0.973700 0.486850 0.873486i $$-0.338146\pi$$
0.486850 + 0.873486i $$0.338146\pi$$
$$600$$ 0 0
$$601$$ 12.5297 0.511098 0.255549 0.966796i $$-0.417744\pi$$
0.255549 + 0.966796i $$0.417744\pi$$
$$602$$ 0 0
$$603$$ 53.0208 2.15917
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −23.1722 −0.940533 −0.470266 0.882525i $$-0.655842\pi$$
−0.470266 + 0.882525i $$0.655842\pi$$
$$608$$ 0 0
$$609$$ 14.2480 0.577357
$$610$$ 0 0
$$611$$ −12.0781 −0.488628
$$612$$ 0 0
$$613$$ 44.5780 1.80049 0.900244 0.435386i $$-0.143388\pi$$
0.900244 + 0.435386i $$0.143388\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 32.1385 1.29385 0.646923 0.762556i $$-0.276056\pi$$
0.646923 + 0.762556i $$0.276056\pi$$
$$618$$ 0 0
$$619$$ −31.5708 −1.26894 −0.634468 0.772949i $$-0.718781\pi$$
−0.634468 + 0.772949i $$0.718781\pi$$
$$620$$ 0 0
$$621$$ 3.00000 0.120386
$$622$$ 0 0
$$623$$ −40.0289 −1.60373
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 8.35748 0.333765
$$628$$ 0 0
$$629$$ 4.85670 0.193649
$$630$$ 0 0
$$631$$ −24.0145 −0.956001 −0.478001 0.878360i $$-0.658638\pi$$
−0.478001 + 0.878360i $$0.658638\pi$$
$$632$$ 0 0
$$633$$ 46.4573 1.84651
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −14.3083 −0.566916
$$638$$ 0 0
$$639$$ 28.5258 1.12846
$$640$$ 0 0
$$641$$ −10.4428 −0.412467 −0.206233 0.978503i $$-0.566121\pi$$
−0.206233 + 0.978503i $$0.566121\pi$$
$$642$$ 0 0
$$643$$ 4.39940 0.173495 0.0867477 0.996230i $$-0.472353\pi$$
0.0867477 + 0.996230i $$0.472353\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −23.6498 −0.929768 −0.464884 0.885372i $$-0.653904\pi$$
−0.464884 + 0.885372i $$0.653904\pi$$
$$648$$ 0 0
$$649$$ 5.15777 0.202460
$$650$$ 0 0
$$651$$ 63.2842 2.48030
$$652$$ 0 0
$$653$$ −40.9194 −1.60130 −0.800651 0.599131i $$-0.795513\pi$$
−0.800651 + 0.599131i $$0.795513\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 62.7728 2.44900
$$658$$ 0 0
$$659$$ −48.8567 −1.90319 −0.951593 0.307360i $$-0.900555\pi$$
−0.951593 + 0.307360i $$0.900555\pi$$
$$660$$ 0 0
$$661$$ −12.1529 −0.472694 −0.236347 0.971669i $$-0.575950\pi$$
−0.236347 + 0.971669i $$0.575950\pi$$
$$662$$ 0 0
$$663$$ 7.17554 0.278675
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.45490 0.0563341
$$668$$ 0 0
$$669$$ −39.1722 −1.51449
$$670$$ 0 0
$$671$$ 8.23918 0.318070
$$672$$ 0 0
$$673$$ −9.20694 −0.354901 −0.177451 0.984130i $$-0.556785\pi$$
−0.177451 + 0.984130i $$0.556785\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 39.8196 1.53039 0.765196 0.643797i $$-0.222642\pi$$
0.765196 + 0.643797i $$0.222642\pi$$
$$678$$ 0 0
$$679$$ −6.22141 −0.238756
$$680$$ 0 0
$$681$$ 43.8486 1.68028
$$682$$ 0 0
$$683$$ −5.60544 −0.214486 −0.107243 0.994233i $$-0.534202\pi$$
−0.107243 + 0.994233i $$0.534202\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 51.6537 1.97071
$$688$$ 0 0
$$689$$ 8.45730 0.322197
$$690$$ 0 0
$$691$$ 2.84223 0.108123 0.0540617 0.998538i $$-0.482783\pi$$
0.0540617 + 0.998538i $$0.482783\pi$$
$$692$$ 0 0
$$693$$ 18.3719 0.697893
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 13.2552 0.502077
$$698$$ 0 0
$$699$$ 51.9267 1.96405
$$700$$ 0 0
$$701$$ −24.4130 −0.922065 −0.461033 0.887383i $$-0.652521\pi$$
−0.461033 + 0.887383i $$0.652521\pi$$
$$702$$ 0 0
$$703$$ −10.3155 −0.389058
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −8.24797 −0.310197
$$708$$ 0 0
$$709$$ 0.123983 0.00465629 0.00232814 0.999997i $$-0.499259\pi$$
0.00232814 + 0.999997i $$0.499259\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 6.46214 0.242009
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −63.2648 −2.36267
$$718$$ 0 0
$$719$$ −47.1569 −1.75865 −0.879327 0.476218i $$-0.842007\pi$$
−0.879327 + 0.476218i $$0.842007\pi$$
$$720$$ 0 0
$$721$$ −10.2214 −0.380665
$$722$$ 0 0
$$723$$ 0.623208 0.0231774
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 43.2962 1.60577 0.802884 0.596135i $$-0.203298\pi$$
0.802884 + 0.596135i $$0.203298\pi$$
$$728$$ 0 0
$$729$$ −42.0217 −1.55636
$$730$$ 0 0
$$731$$ −8.38972 −0.310305
$$732$$ 0 0
$$733$$ −11.5861 −0.427943 −0.213972 0.976840i $$-0.568640\pi$$
−0.213972 + 0.976840i $$0.568640\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 15.6103 0.575012
$$738$$ 0 0
$$739$$ 30.3792 1.11752 0.558758 0.829331i $$-0.311278\pi$$
0.558758 + 0.829331i $$0.311278\pi$$
$$740$$ 0 0
$$741$$ −15.2407 −0.559882
$$742$$ 0 0
$$743$$ 35.5708 1.30496 0.652482 0.757804i $$-0.273728\pi$$
0.652482 + 0.757804i $$0.273728\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −64.2769 −2.35177
$$748$$ 0 0
$$749$$ 48.2769 1.76400
$$750$$ 0 0
$$751$$ 24.9774 0.911438 0.455719 0.890124i $$-0.349382\pi$$
0.455719 + 0.890124i $$0.349382\pi$$
$$752$$ 0 0
$$753$$ −58.0555 −2.11566
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −9.35263 −0.339927 −0.169964 0.985450i $$-0.554365\pi$$
−0.169964 + 0.985450i $$0.554365\pi$$
$$758$$ 0 0
$$759$$ 3.24073 0.117631
$$760$$ 0 0
$$761$$ −18.1466 −0.657813 −0.328907 0.944362i $$-0.606680\pi$$
−0.328907 + 0.944362i $$0.606680\pi$$
$$762$$ 0 0
$$763$$ 12.5523 0.454425
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −9.40574 −0.339622
$$768$$ 0 0
$$769$$ 44.3445 1.59910 0.799552 0.600597i $$-0.205070\pi$$
0.799552 + 0.600597i $$0.205070\pi$$
$$770$$ 0 0
$$771$$ 43.5370 1.56795
$$772$$ 0 0
$$773$$ 10.8036 0.388578 0.194289 0.980944i $$-0.437760\pi$$
0.194289 + 0.980944i $$0.437760\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −39.1722 −1.40530
$$778$$ 0 0
$$779$$ −28.1538 −1.00872
$$780$$ 0 0
$$781$$ 8.39850 0.300522
$$782$$ 0 0
$$783$$ 4.36471 0.155982
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −31.7810 −1.13287 −0.566435 0.824107i $$-0.691678\pi$$
−0.566435 + 0.824107i $$0.691678\pi$$
$$788$$ 0 0
$$789$$ −6.77375 −0.241152
$$790$$ 0 0
$$791$$ 36.6908 1.30457
$$792$$ 0 0
$$793$$ −15.0250 −0.533554
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −35.0594 −1.24187 −0.620935 0.783862i $$-0.713247\pi$$
−0.620935 + 0.783862i $$0.713247\pi$$
$$798$$ 0 0
$$799$$ −6.62321 −0.234312
$$800$$ 0 0
$$801$$ −44.9919 −1.58971
$$802$$ 0 0
$$803$$ 18.4815 0.652196
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −6.79306 −0.239127
$$808$$ 0 0
$$809$$ −51.4911 −1.81033 −0.905165 0.425060i $$-0.860253\pi$$
−0.905165 + 0.425060i $$0.860253\pi$$
$$810$$ 0 0
$$811$$ 19.7705 0.694235 0.347117 0.937822i $$-0.387161\pi$$
0.347117 + 0.937822i $$0.387161\pi$$
$$812$$ 0 0
$$813$$ −64.5370 −2.26341
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 17.8196 0.623429
$$818$$ 0 0
$$819$$ −33.5032 −1.17070
$$820$$ 0 0
$$821$$ 31.8486 1.11152 0.555761 0.831342i $$-0.312427\pi$$
0.555761 + 0.831342i $$0.312427\pi$$
$$822$$ 0 0
$$823$$ 9.34210 0.325645 0.162823 0.986655i $$-0.447940\pi$$
0.162823 + 0.986655i $$0.447940\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −30.9243 −1.07534 −0.537671 0.843155i $$-0.680696\pi$$
−0.537671 + 0.843155i $$0.680696\pi$$
$$828$$ 0 0
$$829$$ −32.5701 −1.13121 −0.565603 0.824678i $$-0.691357\pi$$
−0.565603 + 0.824678i $$0.691357\pi$$
$$830$$ 0 0
$$831$$ 56.6803 1.96622
$$832$$ 0 0
$$833$$ −7.84617 −0.271854
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 19.3864 0.670093
$$838$$ 0 0
$$839$$ −48.5635 −1.67660 −0.838299 0.545210i $$-0.816450\pi$$
−0.838299 + 0.545210i $$0.816450\pi$$
$$840$$ 0 0
$$841$$ −26.8833 −0.927009
$$842$$ 0 0
$$843$$ −37.0660 −1.27662
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −34.9508 −1.20092
$$848$$ 0 0
$$849$$ −78.8260 −2.70530
$$850$$ 0 0
$$851$$ −4.00000 −0.137118
$$852$$ 0 0
$$853$$ 33.6546 1.15231 0.576156 0.817340i $$-0.304552\pi$$
0.576156 + 0.817340i $$0.304552\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −24.4081 −0.833766 −0.416883 0.908960i $$-0.636878\pi$$
−0.416883 + 0.908960i $$0.636878\pi$$
$$858$$ 0 0
$$859$$ 11.1394 0.380070 0.190035 0.981777i $$-0.439140\pi$$
0.190035 + 0.981777i $$0.439140\pi$$
$$860$$ 0 0
$$861$$ −106.911 −3.64353
$$862$$ 0 0
$$863$$ −15.7173 −0.535025 −0.267512 0.963554i $$-0.586202\pi$$
−0.267512 + 0.963554i $$0.586202\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −41.4395 −1.40736
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −28.4670 −0.964567
$$872$$ 0 0
$$873$$ −6.99276 −0.236669
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 33.2818 1.12385 0.561923 0.827190i $$-0.310062\pi$$
0.561923 + 0.827190i $$0.310062\pi$$
$$878$$ 0 0
$$879$$ 64.2769 2.16801
$$880$$ 0 0
$$881$$ 8.99187 0.302944 0.151472 0.988462i $$-0.451599\pi$$
0.151472 + 0.988462i $$0.451599\pi$$
$$882$$ 0 0
$$883$$ 58.5258 1.96955 0.984775 0.173836i $$-0.0556162\pi$$
0.984775 + 0.173836i $$0.0556162\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 32.8220 1.10206 0.551028 0.834487i $$-0.314236\pi$$
0.551028 + 0.834487i $$0.314236\pi$$
$$888$$ 0 0
$$889$$ 73.2012 2.45509
$$890$$ 0 0
$$891$$ −5.29952 −0.177541
$$892$$ 0 0
$$893$$ 14.0676 0.470754
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −5.90981 −0.197323
$$898$$ 0 0
$$899$$ 9.40180 0.313567
$$900$$ 0 0
$$901$$ 4.63768 0.154504
$$902$$ 0 0
$$903$$ 67.6682 2.25186
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 28.3300 0.940683 0.470341 0.882484i $$-0.344131\pi$$
0.470341 + 0.882484i $$0.344131\pi$$
$$908$$ 0 0
$$909$$ −9.27058 −0.307486
$$910$$ 0 0
$$911$$ −15.3382 −0.508176 −0.254088 0.967181i $$-0.581775\pi$$
−0.254088 + 0.967181i $$0.581775\pi$$
$$912$$ 0 0
$$913$$ −18.9243 −0.626302
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 35.6006 1.17564
$$918$$ 0 0
$$919$$ 38.8036 1.28001 0.640006 0.768370i $$-0.278932\pi$$
0.640006 + 0.768370i $$0.278932\pi$$
$$920$$ 0 0
$$921$$ 53.2310 1.75402
$$922$$ 0 0
$$923$$ −15.3155 −0.504117
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −11.4887 −0.377338
$$928$$ 0 0
$$929$$ 4.01053 0.131581 0.0657906 0.997833i $$-0.479043\pi$$
0.0657906 + 0.997833i $$0.479043\pi$$
$$930$$ 0 0
$$931$$ 16.6651 0.546178
$$932$$ 0 0
$$933$$ 7.93636 0.259825
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −43.6836 −1.42708 −0.713540 0.700615i $$-0.752909\pi$$
−0.713540 + 0.700615i $$0.752909\pi$$
$$938$$ 0 0
$$939$$ −41.3406 −1.34910
$$940$$ 0 0
$$941$$ −24.8534 −0.810198 −0.405099 0.914273i $$-0.632763\pi$$
−0.405099 + 0.914273i $$0.632763\pi$$
$$942$$ 0 0
$$943$$ −10.9170 −0.355508
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −22.1690 −0.720394 −0.360197 0.932876i $$-0.617291\pi$$
−0.360197 + 0.932876i $$0.617291\pi$$
$$948$$ 0 0
$$949$$ −33.7029 −1.09404
$$950$$ 0 0
$$951$$ −23.5596 −0.763971
$$952$$ 0 0
$$953$$ −15.9050 −0.515212 −0.257606 0.966250i $$-0.582934\pi$$
−0.257606 + 0.966250i $$0.582934\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 4.71495 0.152413
$$958$$ 0 0
$$959$$ −10.3719 −0.334928
$$960$$ 0 0
$$961$$ 10.7593 0.347073
$$962$$ 0 0
$$963$$ 54.2624 1.74858
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 50.6272 1.62806 0.814030 0.580823i $$-0.197269\pi$$
0.814030 + 0.580823i $$0.197269\pi$$
$$968$$ 0 0
$$969$$ −8.35748 −0.268481
$$970$$ 0 0
$$971$$ 52.4009 1.68162 0.840812 0.541327i $$-0.182078\pi$$
0.840812 + 0.541327i $$0.182078\pi$$
$$972$$ 0 0
$$973$$ −8.67632 −0.278150
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −10.5258 −0.336750 −0.168375 0.985723i $$-0.553852\pi$$
−0.168375 + 0.985723i $$0.553852\pi$$
$$978$$ 0 0
$$979$$ −13.2464 −0.423357
$$980$$ 0 0
$$981$$ 14.1086 0.450453
$$982$$ 0 0
$$983$$ 9.44767 0.301334 0.150667 0.988585i $$-0.451858\pi$$
0.150667 + 0.988585i $$0.451858\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 53.4202 1.70038
$$988$$ 0 0
$$989$$ 6.90981 0.219719
$$990$$ 0 0
$$991$$ −33.3252 −1.05861 −0.529305 0.848432i $$-0.677547\pi$$
−0.529305 + 0.848432i $$0.677547\pi$$
$$992$$ 0 0
$$993$$ −46.4468 −1.47394
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −54.0289 −1.71111 −0.855557 0.517709i $$-0.826785\pi$$
−0.855557 + 0.517709i $$0.826785\pi$$
$$998$$ 0 0
$$999$$ −12.0000 −0.379663
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 9200.2.a.cd.1.3 3
4.3 odd 2 4600.2.a.y.1.1 3
5.4 even 2 1840.2.a.t.1.1 3
20.3 even 4 4600.2.e.r.4049.1 6
20.7 even 4 4600.2.e.r.4049.6 6
20.19 odd 2 920.2.a.g.1.3 3
40.19 odd 2 7360.2.a.cb.1.1 3
40.29 even 2 7360.2.a.ca.1.3 3
60.59 even 2 8280.2.a.bo.1.3 3

By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.g.1.3 3 20.19 odd 2
1840.2.a.t.1.1 3 5.4 even 2
4600.2.a.y.1.1 3 4.3 odd 2
4600.2.e.r.4049.1 6 20.3 even 4
4600.2.e.r.4049.6 6 20.7 even 4
7360.2.a.ca.1.3 3 40.29 even 2
7360.2.a.cb.1.1 3 40.19 odd 2
8280.2.a.bo.1.3 3 60.59 even 2
9200.2.a.cd.1.3 3 1.1 even 1 trivial