# Properties

 Label 882.2.a.b.1.1 Level $882$ Weight $2$ Character 882.1 Self dual yes Analytic conductor $7.043$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 882.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$7.04280545828$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 882.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{8} +2.00000 q^{10} +4.00000 q^{11} -6.00000 q^{13} +1.00000 q^{16} +2.00000 q^{17} +4.00000 q^{19} -2.00000 q^{20} -4.00000 q^{22} -8.00000 q^{23} -1.00000 q^{25} +6.00000 q^{26} +2.00000 q^{29} -1.00000 q^{32} -2.00000 q^{34} -10.0000 q^{37} -4.00000 q^{38} +2.00000 q^{40} -6.00000 q^{41} -4.00000 q^{43} +4.00000 q^{44} +8.00000 q^{46} +1.00000 q^{50} -6.00000 q^{52} -6.00000 q^{53} -8.00000 q^{55} -2.00000 q^{58} +4.00000 q^{59} -6.00000 q^{61} +1.00000 q^{64} +12.0000 q^{65} +4.00000 q^{67} +2.00000 q^{68} -8.00000 q^{71} -10.0000 q^{73} +10.0000 q^{74} +4.00000 q^{76} -2.00000 q^{80} +6.00000 q^{82} -4.00000 q^{83} -4.00000 q^{85} +4.00000 q^{86} -4.00000 q^{88} -6.00000 q^{89} -8.00000 q^{92} -8.00000 q^{95} +14.0000 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −2.00000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 2.00000 0.632456
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 0 0
$$13$$ −6.00000 −1.66410 −0.832050 0.554700i $$-0.812833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ −2.00000 −0.447214
$$21$$ 0 0
$$22$$ −4.00000 −0.852803
$$23$$ −8.00000 −1.66812 −0.834058 0.551677i $$-0.813988\pi$$
−0.834058 + 0.551677i $$0.813988\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 6.00000 1.17670
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ 0 0
$$40$$ 2.00000 0.316228
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ −6.00000 −0.832050
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ −8.00000 −1.07872
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −2.00000 −0.262613
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 12.0000 1.48842
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 2.00000 0.242536
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ 0 0
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 10.0000 1.16248
$$75$$ 0 0
$$76$$ 4.00000 0.458831
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ −2.00000 −0.223607
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ −4.00000 −0.426401
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −8.00000 −0.834058
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −8.00000 −0.820783
$$96$$ 0 0
$$97$$ 14.0000 1.42148 0.710742 0.703452i $$-0.248359\pi$$
0.710742 + 0.703452i $$0.248359\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ −2.00000 −0.199007 −0.0995037 0.995037i $$-0.531726\pi$$
−0.0995037 + 0.995037i $$0.531726\pi$$
$$102$$ 0 0
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 8.00000 0.762770
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ 16.0000 1.49201
$$116$$ 2.00000 0.185695
$$117$$ 0 0
$$118$$ −4.00000 −0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 6.00000 0.543214
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ −12.0000 −1.05247
$$131$$ −20.0000 −1.74741 −0.873704 0.486458i $$-0.838289\pi$$
−0.873704 + 0.486458i $$0.838289\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ −2.00000 −0.171499
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 8.00000 0.671345
$$143$$ −24.0000 −2.00698
$$144$$ 0 0
$$145$$ −4.00000 −0.332182
$$146$$ 10.0000 0.827606
$$147$$ 0 0
$$148$$ −10.0000 −0.821995
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 10.0000 0.798087 0.399043 0.916932i $$-0.369342\pi$$
0.399043 + 0.916932i $$0.369342\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 2.00000 0.158114
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ −8.00000 −0.619059 −0.309529 0.950890i $$-0.600171\pi$$
−0.309529 + 0.950890i $$0.600171\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 4.00000 0.306786
$$171$$ 0 0
$$172$$ −4.00000 −0.304997
$$173$$ 22.0000 1.67263 0.836315 0.548250i $$-0.184706\pi$$
0.836315 + 0.548250i $$0.184706\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 4.00000 0.301511
$$177$$ 0 0
$$178$$ 6.00000 0.449719
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ 18.0000 1.33793 0.668965 0.743294i $$-0.266738\pi$$
0.668965 + 0.743294i $$0.266738\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 8.00000 0.589768
$$185$$ 20.0000 1.47043
$$186$$ 0 0
$$187$$ 8.00000 0.585018
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 8.00000 0.580381
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 2.00000 0.143963 0.0719816 0.997406i $$-0.477068\pi$$
0.0719816 + 0.997406i $$0.477068\pi$$
$$194$$ −14.0000 −1.00514
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 10.0000 0.712470 0.356235 0.934396i $$-0.384060\pi$$
0.356235 + 0.934396i $$0.384060\pi$$
$$198$$ 0 0
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 0 0
$$202$$ 2.00000 0.140720
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 12.0000 0.838116
$$206$$ 8.00000 0.557386
$$207$$ 0 0
$$208$$ −6.00000 −0.416025
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ 20.0000 1.37686 0.688428 0.725304i $$-0.258301\pi$$
0.688428 + 0.725304i $$0.258301\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 0 0
$$214$$ 12.0000 0.820303
$$215$$ 8.00000 0.545595
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 2.00000 0.135457
$$219$$ 0 0
$$220$$ −8.00000 −0.539360
$$221$$ −12.0000 −0.807207
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −14.0000 −0.931266
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 0 0
$$229$$ 2.00000 0.132164 0.0660819 0.997814i $$-0.478950\pi$$
0.0660819 + 0.997814i $$0.478950\pi$$
$$230$$ −16.0000 −1.05501
$$231$$ 0 0
$$232$$ −2.00000 −0.131306
$$233$$ 22.0000 1.44127 0.720634 0.693316i $$-0.243851\pi$$
0.720634 + 0.693316i $$0.243851\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 4.00000 0.260378
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −2.00000 −0.128831 −0.0644157 0.997923i $$-0.520518\pi$$
−0.0644157 + 0.997923i $$0.520518\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 0 0
$$244$$ −6.00000 −0.384111
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −24.0000 −1.52708
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −12.0000 −0.758947
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ −32.0000 −2.01182
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −30.0000 −1.87135 −0.935674 0.352865i $$-0.885208\pi$$
−0.935674 + 0.352865i $$0.885208\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 12.0000 0.744208
$$261$$ 0 0
$$262$$ 20.0000 1.23560
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ 12.0000 0.737154
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 4.00000 0.244339
$$269$$ 22.0000 1.34136 0.670682 0.741745i $$-0.266002\pi$$
0.670682 + 0.741745i $$0.266002\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 10.0000 0.604122
$$275$$ −4.00000 −0.241209
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 4.00000 0.239904
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −26.0000 −1.55103 −0.775515 0.631329i $$-0.782510\pi$$
−0.775515 + 0.631329i $$0.782510\pi$$
$$282$$ 0 0
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ −8.00000 −0.474713
$$285$$ 0 0
$$286$$ 24.0000 1.41915
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 4.00000 0.234888
$$291$$ 0 0
$$292$$ −10.0000 −0.585206
$$293$$ 30.0000 1.75262 0.876309 0.481749i $$-0.159998\pi$$
0.876309 + 0.481749i $$0.159998\pi$$
$$294$$ 0 0
$$295$$ −8.00000 −0.465778
$$296$$ 10.0000 0.581238
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 48.0000 2.77591
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 8.00000 0.460348
$$303$$ 0 0
$$304$$ 4.00000 0.229416
$$305$$ 12.0000 0.687118
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −8.00000 −0.453638 −0.226819 0.973937i $$-0.572833\pi$$
−0.226819 + 0.973937i $$0.572833\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ −10.0000 −0.564333
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ 8.00000 0.447914
$$320$$ −2.00000 −0.111803
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000 0.445132
$$324$$ 0 0
$$325$$ 6.00000 0.332820
$$326$$ −20.0000 −1.10770
$$327$$ 0 0
$$328$$ 6.00000 0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ −4.00000 −0.219529
$$333$$ 0 0
$$334$$ 8.00000 0.437741
$$335$$ −8.00000 −0.437087
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ −23.0000 −1.25104
$$339$$ 0 0
$$340$$ −4.00000 −0.216930
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ −22.0000 −1.18273
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ 0 0
$$349$$ −22.0000 −1.17763 −0.588817 0.808267i $$-0.700406\pi$$
−0.588817 + 0.808267i $$0.700406\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −4.00000 −0.213201
$$353$$ −30.0000 −1.59674 −0.798369 0.602168i $$-0.794304\pi$$
−0.798369 + 0.602168i $$0.794304\pi$$
$$354$$ 0 0
$$355$$ 16.0000 0.849192
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ 8.00000 0.422224 0.211112 0.977462i $$-0.432292\pi$$
0.211112 + 0.977462i $$0.432292\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −18.0000 −0.946059
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 20.0000 1.04685
$$366$$ 0 0
$$367$$ −32.0000 −1.67039 −0.835193 0.549957i $$-0.814644\pi$$
−0.835193 + 0.549957i $$0.814644\pi$$
$$368$$ −8.00000 −0.417029
$$369$$ 0 0
$$370$$ −20.0000 −1.03975
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 22.0000 1.13912 0.569558 0.821951i $$-0.307114\pi$$
0.569558 + 0.821951i $$0.307114\pi$$
$$374$$ −8.00000 −0.413670
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ −8.00000 −0.410391
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −16.0000 −0.817562 −0.408781 0.912633i $$-0.634046\pi$$
−0.408781 + 0.912633i $$0.634046\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.00000 −0.101797
$$387$$ 0 0
$$388$$ 14.0000 0.710742
$$389$$ 26.0000 1.31825 0.659126 0.752032i $$-0.270926\pi$$
0.659126 + 0.752032i $$0.270926\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −10.0000 −0.503793
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −6.00000 −0.301131 −0.150566 0.988600i $$-0.548110\pi$$
−0.150566 + 0.988600i $$0.548110\pi$$
$$398$$ 8.00000 0.401004
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −2.00000 −0.0995037
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −40.0000 −1.98273
$$408$$ 0 0
$$409$$ 22.0000 1.08783 0.543915 0.839140i $$-0.316941\pi$$
0.543915 + 0.839140i $$0.316941\pi$$
$$410$$ −12.0000 −0.592638
$$411$$ 0 0
$$412$$ −8.00000 −0.394132
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 8.00000 0.392705
$$416$$ 6.00000 0.294174
$$417$$ 0 0
$$418$$ −16.0000 −0.782586
$$419$$ −36.0000 −1.75872 −0.879358 0.476162i $$-0.842028\pi$$
−0.879358 + 0.476162i $$0.842028\pi$$
$$420$$ 0 0
$$421$$ 6.00000 0.292422 0.146211 0.989253i $$-0.453292\pi$$
0.146211 + 0.989253i $$0.453292\pi$$
$$422$$ −20.0000 −0.973585
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ −2.00000 −0.0970143
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ −8.00000 −0.385794
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −2.00000 −0.0957826
$$437$$ −32.0000 −1.53077
$$438$$ 0 0
$$439$$ 24.0000 1.14546 0.572729 0.819745i $$-0.305885\pi$$
0.572729 + 0.819745i $$0.305885\pi$$
$$440$$ 8.00000 0.381385
$$441$$ 0 0
$$442$$ 12.0000 0.570782
$$443$$ 4.00000 0.190046 0.0950229 0.995475i $$-0.469708\pi$$
0.0950229 + 0.995475i $$0.469708\pi$$
$$444$$ 0 0
$$445$$ 12.0000 0.568855
$$446$$ −16.0000 −0.757622
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −34.0000 −1.60456 −0.802280 0.596948i $$-0.796380\pi$$
−0.802280 + 0.596948i $$0.796380\pi$$
$$450$$ 0 0
$$451$$ −24.0000 −1.13012
$$452$$ 14.0000 0.658505
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 10.0000 0.467780 0.233890 0.972263i $$-0.424854\pi$$
0.233890 + 0.972263i $$0.424854\pi$$
$$458$$ −2.00000 −0.0934539
$$459$$ 0 0
$$460$$ 16.0000 0.746004
$$461$$ 22.0000 1.02464 0.512321 0.858794i $$-0.328786\pi$$
0.512321 + 0.858794i $$0.328786\pi$$
$$462$$ 0 0
$$463$$ −32.0000 −1.48717 −0.743583 0.668644i $$-0.766875\pi$$
−0.743583 + 0.668644i $$0.766875\pi$$
$$464$$ 2.00000 0.0928477
$$465$$ 0 0
$$466$$ −22.0000 −1.01913
$$467$$ 28.0000 1.29569 0.647843 0.761774i $$-0.275671\pi$$
0.647843 + 0.761774i $$0.275671\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −4.00000 −0.184115
$$473$$ −16.0000 −0.735681
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −16.0000 −0.731059 −0.365529 0.930800i $$-0.619112\pi$$
−0.365529 + 0.930800i $$0.619112\pi$$
$$480$$ 0 0
$$481$$ 60.0000 2.73576
$$482$$ 2.00000 0.0910975
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ −28.0000 −1.27141
$$486$$ 0 0
$$487$$ 8.00000 0.362515 0.181257 0.983436i $$-0.441983\pi$$
0.181257 + 0.983436i $$0.441983\pi$$
$$488$$ 6.00000 0.271607
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 0 0
$$493$$ 4.00000 0.180151
$$494$$ 24.0000 1.07981
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −44.0000 −1.96971 −0.984855 0.173379i $$-0.944532\pi$$
−0.984855 + 0.173379i $$0.944532\pi$$
$$500$$ 12.0000 0.536656
$$501$$ 0 0
$$502$$ 12.0000 0.535586
$$503$$ 24.0000 1.07011 0.535054 0.844818i $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 0 0
$$505$$ 4.00000 0.177998
$$506$$ 32.0000 1.42257
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 6.00000 0.265945 0.132973 0.991120i $$-0.457548\pi$$
0.132973 + 0.991120i $$0.457548\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 30.0000 1.32324
$$515$$ 16.0000 0.705044
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −12.0000 −0.526235
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ 0 0
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ −20.0000 −0.873704
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 41.0000 1.78261
$$530$$ −12.0000 −0.521247
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 36.0000 1.55933
$$534$$ 0 0
$$535$$ 24.0000 1.03761
$$536$$ −4.00000 −0.172774
$$537$$ 0 0
$$538$$ −22.0000 −0.948487
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 30.0000 1.28980 0.644900 0.764267i $$-0.276899\pi$$
0.644900 + 0.764267i $$0.276899\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −2.00000 −0.0857493
$$545$$ 4.00000 0.171341
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ −10.0000 −0.427179
$$549$$ 0 0
$$550$$ 4.00000 0.170561
$$551$$ 8.00000 0.340811
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 10.0000 0.424859
$$555$$ 0 0
$$556$$ −4.00000 −0.169638
$$557$$ 2.00000 0.0847427 0.0423714 0.999102i $$-0.486509\pi$$
0.0423714 + 0.999102i $$0.486509\pi$$
$$558$$ 0 0
$$559$$ 24.0000 1.01509
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 26.0000 1.09674
$$563$$ 44.0000 1.85438 0.927189 0.374593i $$-0.122217\pi$$
0.927189 + 0.374593i $$0.122217\pi$$
$$564$$ 0 0
$$565$$ −28.0000 −1.17797
$$566$$ 4.00000 0.168133
$$567$$ 0 0
$$568$$ 8.00000 0.335673
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ −24.0000 −1.00349
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 8.00000 0.333623
$$576$$ 0 0
$$577$$ −34.0000 −1.41544 −0.707719 0.706494i $$-0.750276\pi$$
−0.707719 + 0.706494i $$0.750276\pi$$
$$578$$ 13.0000 0.540729
$$579$$ 0 0
$$580$$ −4.00000 −0.166091
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −24.0000 −0.993978
$$584$$ 10.0000 0.413803
$$585$$ 0 0
$$586$$ −30.0000 −1.23929
$$587$$ −28.0000 −1.15568 −0.577842 0.816149i $$-0.696105\pi$$
−0.577842 + 0.816149i $$0.696105\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 8.00000 0.329355
$$591$$ 0 0
$$592$$ −10.0000 −0.410997
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ 0 0
$$598$$ −48.0000 −1.96287
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −8.00000 −0.325515
$$605$$ −10.0000 −0.406558
$$606$$ 0 0
$$607$$ −48.0000 −1.94826 −0.974130 0.225989i $$-0.927439\pi$$
−0.974130 + 0.225989i $$0.927439\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 0 0
$$610$$ −12.0000 −0.485866
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −42.0000 −1.69636 −0.848182 0.529705i $$-0.822303\pi$$
−0.848182 + 0.529705i $$0.822303\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 22.0000 0.885687 0.442843 0.896599i $$-0.353970\pi$$
0.442843 + 0.896599i $$0.353970\pi$$
$$618$$ 0 0
$$619$$ 44.0000 1.76851 0.884255 0.467005i $$-0.154667\pi$$
0.884255 + 0.467005i $$0.154667\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 8.00000 0.320771
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 10.0000 0.399680
$$627$$ 0 0
$$628$$ 10.0000 0.399043
$$629$$ −20.0000 −0.797452
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −18.0000 −0.714871
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −8.00000 −0.316723
$$639$$ 0 0
$$640$$ 2.00000 0.0790569
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 0 0
$$643$$ 4.00000 0.157745 0.0788723 0.996885i $$-0.474868\pi$$
0.0788723 + 0.996885i $$0.474868\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −8.00000 −0.314756
$$647$$ 24.0000 0.943537 0.471769 0.881722i $$-0.343616\pi$$
0.471769 + 0.881722i $$0.343616\pi$$
$$648$$ 0 0
$$649$$ 16.0000 0.628055
$$650$$ −6.00000 −0.235339
$$651$$ 0 0
$$652$$ 20.0000 0.783260
$$653$$ 18.0000 0.704394 0.352197 0.935926i $$-0.385435\pi$$
0.352197 + 0.935926i $$0.385435\pi$$
$$654$$ 0 0
$$655$$ 40.0000 1.56293
$$656$$ −6.00000 −0.234261
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 28.0000 1.09073 0.545363 0.838200i $$-0.316392\pi$$
0.545363 + 0.838200i $$0.316392\pi$$
$$660$$ 0 0
$$661$$ 2.00000 0.0777910 0.0388955 0.999243i $$-0.487616\pi$$
0.0388955 + 0.999243i $$0.487616\pi$$
$$662$$ 4.00000 0.155464
$$663$$ 0 0
$$664$$ 4.00000 0.155230
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −16.0000 −0.619522
$$668$$ −8.00000 −0.309529
$$669$$ 0 0
$$670$$ 8.00000 0.309067
$$671$$ −24.0000 −0.926510
$$672$$ 0 0
$$673$$ 2.00000 0.0770943 0.0385472 0.999257i $$-0.487727\pi$$
0.0385472 + 0.999257i $$0.487727\pi$$
$$674$$ −18.0000 −0.693334
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ −18.0000 −0.691796 −0.345898 0.938272i $$-0.612426\pi$$
−0.345898 + 0.938272i $$0.612426\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 4.00000 0.153393
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ 20.0000 0.764161
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −4.00000 −0.152499
$$689$$ 36.0000 1.37149
$$690$$ 0 0
$$691$$ 4.00000 0.152167 0.0760836 0.997101i $$-0.475758\pi$$
0.0760836 + 0.997101i $$0.475758\pi$$
$$692$$ 22.0000 0.836315
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 8.00000 0.303457
$$696$$ 0 0
$$697$$ −12.0000 −0.454532
$$698$$ 22.0000 0.832712
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 2.00000 0.0755390 0.0377695 0.999286i $$-0.487975\pi$$
0.0377695 + 0.999286i $$0.487975\pi$$
$$702$$ 0 0
$$703$$ −40.0000 −1.50863
$$704$$ 4.00000 0.150756
$$705$$ 0 0
$$706$$ 30.0000 1.12906
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ −16.0000 −0.600469
$$711$$ 0 0
$$712$$ 6.00000 0.224860
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 48.0000 1.79510
$$716$$ 12.0000 0.448461
$$717$$ 0 0
$$718$$ −8.00000 −0.298557
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 3.00000 0.111648
$$723$$ 0 0
$$724$$ 18.0000 0.668965
$$725$$ −2.00000 −0.0742781
$$726$$ 0 0
$$727$$ 8.00000 0.296704 0.148352 0.988935i $$-0.452603\pi$$
0.148352 + 0.988935i $$0.452603\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −20.0000 −0.740233
$$731$$ −8.00000 −0.295891
$$732$$ 0 0
$$733$$ −6.00000 −0.221615 −0.110808 0.993842i $$-0.535344\pi$$
−0.110808 + 0.993842i $$0.535344\pi$$
$$734$$ 32.0000 1.18114
$$735$$ 0 0
$$736$$ 8.00000 0.294884
$$737$$ 16.0000 0.589368
$$738$$ 0 0
$$739$$ −12.0000 −0.441427 −0.220714 0.975339i $$-0.570839\pi$$
−0.220714 + 0.975339i $$0.570839\pi$$
$$740$$ 20.0000 0.735215
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ 12.0000 0.439646
$$746$$ −22.0000 −0.805477
$$747$$ 0 0
$$748$$ 8.00000 0.292509
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 48.0000 1.75154 0.875772 0.482724i $$-0.160353\pi$$
0.875772 + 0.482724i $$0.160353\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 12.0000 0.437014
$$755$$ 16.0000 0.582300
$$756$$ 0 0
$$757$$ 6.00000 0.218074 0.109037 0.994038i $$-0.465223\pi$$
0.109037 + 0.994038i $$0.465223\pi$$
$$758$$ 20.0000 0.726433
$$759$$ 0 0
$$760$$ 8.00000 0.290191
$$761$$ −22.0000 −0.797499 −0.398750 0.917060i $$-0.630556\pi$$
−0.398750 + 0.917060i $$0.630556\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 16.0000 0.578103
$$767$$ −24.0000 −0.866590
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 2.00000 0.0719816
$$773$$ −2.00000 −0.0719350 −0.0359675 0.999353i $$-0.511451\pi$$
−0.0359675 + 0.999353i $$0.511451\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −14.0000 −0.502571
$$777$$ 0 0
$$778$$ −26.0000 −0.932145
$$779$$ −24.0000 −0.859889
$$780$$ 0 0
$$781$$ −32.0000 −1.14505
$$782$$ 16.0000 0.572159
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −20.0000 −0.713831
$$786$$ 0 0
$$787$$ 36.0000 1.28326 0.641631 0.767014i $$-0.278258\pi$$
0.641631 + 0.767014i $$0.278258\pi$$
$$788$$ 10.0000 0.356235
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 36.0000 1.27840
$$794$$ 6.00000 0.212932
$$795$$ 0 0
$$796$$ −8.00000 −0.283552
$$797$$ 6.00000 0.212531 0.106265 0.994338i $$-0.466111\pi$$
0.106265 + 0.994338i $$0.466111\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.00000 0.0353553
$$801$$ 0 0
$$802$$ 18.0000 0.635602
$$803$$ −40.0000 −1.41157
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 2.00000 0.0703598
$$809$$ −10.0000 −0.351581 −0.175791 0.984428i $$-0.556248\pi$$
−0.175791 + 0.984428i $$0.556248\pi$$
$$810$$ 0 0
$$811$$ 44.0000 1.54505 0.772524 0.634985i $$-0.218994\pi$$
0.772524 + 0.634985i $$0.218994\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 40.0000 1.40200
$$815$$ −40.0000 −1.40114
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ −22.0000 −0.769212
$$819$$ 0 0
$$820$$ 12.0000 0.419058
$$821$$ −38.0000 −1.32621 −0.663105 0.748527i $$-0.730762\pi$$
−0.663105 + 0.748527i $$0.730762\pi$$
$$822$$ 0 0
$$823$$ −56.0000 −1.95204 −0.976019 0.217687i $$-0.930149\pi$$
−0.976019 + 0.217687i $$0.930149\pi$$
$$824$$ 8.00000 0.278693
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 36.0000 1.25184 0.625921 0.779886i $$-0.284723\pi$$
0.625921 + 0.779886i $$0.284723\pi$$
$$828$$ 0 0
$$829$$ 26.0000 0.903017 0.451509 0.892267i $$-0.350886\pi$$
0.451509 + 0.892267i $$0.350886\pi$$
$$830$$ −8.00000 −0.277684
$$831$$ 0 0
$$832$$ −6.00000 −0.208013
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 16.0000 0.553703
$$836$$ 16.0000 0.553372
$$837$$ 0 0
$$838$$ 36.0000 1.24360
$$839$$ 56.0000 1.93333 0.966667 0.256036i $$-0.0824164\pi$$
0.966667 + 0.256036i $$0.0824164\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ −6.00000 −0.206774
$$843$$ 0 0
$$844$$ 20.0000 0.688428
$$845$$ −46.0000 −1.58245
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −6.00000 −0.206041
$$849$$ 0 0
$$850$$ 2.00000 0.0685994
$$851$$ 80.0000 2.74236
$$852$$ 0 0
$$853$$ −14.0000 −0.479351 −0.239675 0.970853i $$-0.577041\pi$$
−0.239675 + 0.970853i $$0.577041\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 12.0000 0.410152
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ −20.0000 −0.682391 −0.341196 0.939992i $$-0.610832\pi$$
−0.341196 + 0.939992i $$0.610832\pi$$
$$860$$ 8.00000 0.272798
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 32.0000 1.08929 0.544646 0.838666i $$-0.316664\pi$$
0.544646 + 0.838666i $$0.316664\pi$$
$$864$$ 0 0
$$865$$ −44.0000 −1.49604
$$866$$ 2.00000 0.0679628
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −24.0000 −0.813209
$$872$$ 2.00000 0.0677285
$$873$$ 0 0
$$874$$ 32.0000 1.08242
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −2.00000 −0.0675352 −0.0337676 0.999430i $$-0.510751\pi$$
−0.0337676 + 0.999430i $$0.510751\pi$$
$$878$$ −24.0000 −0.809961
$$879$$ 0 0
$$880$$ −8.00000 −0.269680
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ 20.0000 0.673054 0.336527 0.941674i $$-0.390748\pi$$
0.336527 + 0.941674i $$0.390748\pi$$
$$884$$ −12.0000 −0.403604
$$885$$ 0 0
$$886$$ −4.00000 −0.134383
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ −12.0000 −0.402241
$$891$$ 0 0
$$892$$ 16.0000 0.535720
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −24.0000 −0.802232
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 34.0000 1.13459
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −12.0000 −0.399778
$$902$$ 24.0000 0.799113
$$903$$ 0 0
$$904$$ −14.0000 −0.465633
$$905$$ −36.0000 −1.19668
$$906$$ 0 0
$$907$$ 12.0000 0.398453 0.199227 0.979953i $$-0.436157\pi$$
0.199227 + 0.979953i $$0.436157\pi$$
$$908$$ 12.0000 0.398234
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ −16.0000 −0.529523
$$914$$ −10.0000 −0.330771
$$915$$ 0 0
$$916$$ 2.00000 0.0660819
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 40.0000 1.31948 0.659739 0.751495i $$-0.270667\pi$$
0.659739 + 0.751495i $$0.270667\pi$$
$$920$$ −16.0000 −0.527504
$$921$$ 0 0
$$922$$ −22.0000 −0.724531
$$923$$ 48.0000 1.57994
$$924$$ 0 0
$$925$$ 10.0000 0.328798
$$926$$ 32.0000 1.05159
$$927$$ 0 0
$$928$$ −2.00000 −0.0656532
$$929$$ 18.0000 0.590561 0.295280 0.955411i $$-0.404587\pi$$
0.295280 + 0.955411i $$0.404587\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 22.0000 0.720634
$$933$$ 0 0
$$934$$ −28.0000 −0.916188
$$935$$ −16.0000 −0.523256
$$936$$ 0 0
$$937$$ 22.0000 0.718709 0.359354 0.933201i $$-0.382997\pi$$
0.359354 + 0.933201i $$0.382997\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −26.0000 −0.847576 −0.423788 0.905761i $$-0.639300\pi$$
−0.423788 + 0.905761i $$0.639300\pi$$
$$942$$ 0 0
$$943$$ 48.0000 1.56310
$$944$$ 4.00000 0.130189
$$945$$ 0 0
$$946$$ 16.0000 0.520205
$$947$$ −4.00000 −0.129983 −0.0649913 0.997886i $$-0.520702\pi$$
−0.0649913 + 0.997886i $$0.520702\pi$$
$$948$$ 0 0
$$949$$ 60.0000 1.94768
$$950$$ 4.00000 0.129777
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −26.0000 −0.842223 −0.421111 0.907009i $$-0.638360\pi$$
−0.421111 + 0.907009i $$0.638360\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 16.0000 0.516937
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ −60.0000 −1.93448
$$963$$ 0 0
$$964$$ −2.00000 −0.0644157
$$965$$ −4.00000 −0.128765
$$966$$ 0 0
$$967$$ 8.00000 0.257263 0.128631 0.991692i $$-0.458942\pi$$
0.128631 + 0.991692i $$0.458942\pi$$
$$968$$ −5.00000 −0.160706
$$969$$ 0 0
$$970$$ 28.0000 0.899026
$$971$$ −12.0000 −0.385098 −0.192549 0.981287i $$-0.561675\pi$$
−0.192549 + 0.981287i $$0.561675\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ −8.00000 −0.256337
$$975$$ 0 0
$$976$$ −6.00000 −0.192055
$$977$$ −18.0000 −0.575871 −0.287936 0.957650i $$-0.592969\pi$$
−0.287936 + 0.957650i $$0.592969\pi$$
$$978$$ 0 0
$$979$$ −24.0000 −0.767043
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 12.0000 0.382935
$$983$$ −24.0000 −0.765481 −0.382741 0.923856i $$-0.625020\pi$$
−0.382741 + 0.923856i $$0.625020\pi$$
$$984$$ 0 0
$$985$$ −20.0000 −0.637253
$$986$$ −4.00000 −0.127386
$$987$$ 0 0
$$988$$ −24.0000 −0.763542
$$989$$ 32.0000 1.01754
$$990$$ 0 0
$$991$$ −16.0000 −0.508257 −0.254128 0.967170i $$-0.581789\pi$$
−0.254128 + 0.967170i $$0.581789\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 16.0000 0.507234
$$996$$ 0 0
$$997$$ −14.0000 −0.443384 −0.221692 0.975117i $$-0.571158\pi$$
−0.221692 + 0.975117i $$0.571158\pi$$
$$998$$ 44.0000 1.39280
$$999$$ 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 882.2.a.b.1.1 1
3.2 odd 2 294.2.a.g.1.1 1
4.3 odd 2 7056.2.a.k.1.1 1
7.2 even 3 882.2.g.j.361.1 2
7.3 odd 6 882.2.g.h.667.1 2
7.4 even 3 882.2.g.j.667.1 2
7.5 odd 6 882.2.g.h.361.1 2
7.6 odd 2 126.2.a.a.1.1 1
12.11 even 2 2352.2.a.l.1.1 1
15.14 odd 2 7350.2.a.f.1.1 1
21.2 odd 6 294.2.e.a.67.1 2
21.5 even 6 294.2.e.c.67.1 2
21.11 odd 6 294.2.e.a.79.1 2
21.17 even 6 294.2.e.c.79.1 2
21.20 even 2 42.2.a.a.1.1 1
24.5 odd 2 9408.2.a.n.1.1 1
24.11 even 2 9408.2.a.bw.1.1 1
28.27 even 2 1008.2.a.j.1.1 1
35.13 even 4 3150.2.g.r.2899.2 2
35.27 even 4 3150.2.g.r.2899.1 2
35.34 odd 2 3150.2.a.bo.1.1 1
56.13 odd 2 4032.2.a.e.1.1 1
56.27 even 2 4032.2.a.m.1.1 1
63.13 odd 6 1134.2.f.j.379.1 2
63.20 even 6 1134.2.f.g.757.1 2
63.34 odd 6 1134.2.f.j.757.1 2
63.41 even 6 1134.2.f.g.379.1 2
84.11 even 6 2352.2.q.n.961.1 2
84.23 even 6 2352.2.q.n.1537.1 2
84.47 odd 6 2352.2.q.i.1537.1 2
84.59 odd 6 2352.2.q.i.961.1 2
84.83 odd 2 336.2.a.d.1.1 1
105.62 odd 4 1050.2.g.a.799.2 2
105.83 odd 4 1050.2.g.a.799.1 2
105.104 even 2 1050.2.a.i.1.1 1
168.83 odd 2 1344.2.a.i.1.1 1
168.125 even 2 1344.2.a.q.1.1 1
231.230 odd 2 5082.2.a.d.1.1 1
273.272 even 2 7098.2.a.f.1.1 1
336.83 odd 4 5376.2.c.e.2689.2 2
336.125 even 4 5376.2.c.bc.2689.1 2
336.251 odd 4 5376.2.c.e.2689.1 2
336.293 even 4 5376.2.c.bc.2689.2 2
420.419 odd 2 8400.2.a.k.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.a.a.1.1 1 21.20 even 2
126.2.a.a.1.1 1 7.6 odd 2
294.2.a.g.1.1 1 3.2 odd 2
294.2.e.a.67.1 2 21.2 odd 6
294.2.e.a.79.1 2 21.11 odd 6
294.2.e.c.67.1 2 21.5 even 6
294.2.e.c.79.1 2 21.17 even 6
336.2.a.d.1.1 1 84.83 odd 2
882.2.a.b.1.1 1 1.1 even 1 trivial
882.2.g.h.361.1 2 7.5 odd 6
882.2.g.h.667.1 2 7.3 odd 6
882.2.g.j.361.1 2 7.2 even 3
882.2.g.j.667.1 2 7.4 even 3
1008.2.a.j.1.1 1 28.27 even 2
1050.2.a.i.1.1 1 105.104 even 2
1050.2.g.a.799.1 2 105.83 odd 4
1050.2.g.a.799.2 2 105.62 odd 4
1134.2.f.g.379.1 2 63.41 even 6
1134.2.f.g.757.1 2 63.20 even 6
1134.2.f.j.379.1 2 63.13 odd 6
1134.2.f.j.757.1 2 63.34 odd 6
1344.2.a.i.1.1 1 168.83 odd 2
1344.2.a.q.1.1 1 168.125 even 2
2352.2.a.l.1.1 1 12.11 even 2
2352.2.q.i.961.1 2 84.59 odd 6
2352.2.q.i.1537.1 2 84.47 odd 6
2352.2.q.n.961.1 2 84.11 even 6
2352.2.q.n.1537.1 2 84.23 even 6
3150.2.a.bo.1.1 1 35.34 odd 2
3150.2.g.r.2899.1 2 35.27 even 4
3150.2.g.r.2899.2 2 35.13 even 4
4032.2.a.e.1.1 1 56.13 odd 2
4032.2.a.m.1.1 1 56.27 even 2
5082.2.a.d.1.1 1 231.230 odd 2
5376.2.c.e.2689.1 2 336.251 odd 4
5376.2.c.e.2689.2 2 336.83 odd 4
5376.2.c.bc.2689.1 2 336.125 even 4
5376.2.c.bc.2689.2 2 336.293 even 4
7056.2.a.k.1.1 1 4.3 odd 2
7098.2.a.f.1.1 1 273.272 even 2
7350.2.a.f.1.1 1 15.14 odd 2
8400.2.a.k.1.1 1 420.419 odd 2
9408.2.a.n.1.1 1 24.5 odd 2
9408.2.a.bw.1.1 1 24.11 even 2