# Properties

 Label 1170.2.a.d.1.1 Level $1170$ Weight $2$ Character 1170.1 Self dual yes Analytic conductor $9.342$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$9.34249703649$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 130) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1170.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{13} +4.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} +6.00000 q^{19} +1.00000 q^{20} -2.00000 q^{22} -6.00000 q^{23} +1.00000 q^{25} +1.00000 q^{26} -4.00000 q^{28} -2.00000 q^{29} -6.00000 q^{31} -1.00000 q^{32} +2.00000 q^{34} -4.00000 q^{35} -2.00000 q^{37} -6.00000 q^{38} -1.00000 q^{40} -10.0000 q^{41} -10.0000 q^{43} +2.00000 q^{44} +6.00000 q^{46} +12.0000 q^{47} +9.00000 q^{49} -1.00000 q^{50} -1.00000 q^{52} -2.00000 q^{53} +2.00000 q^{55} +4.00000 q^{56} +2.00000 q^{58} -10.0000 q^{59} +2.00000 q^{61} +6.00000 q^{62} +1.00000 q^{64} -1.00000 q^{65} -12.0000 q^{67} -2.00000 q^{68} +4.00000 q^{70} -10.0000 q^{71} +10.0000 q^{73} +2.00000 q^{74} +6.00000 q^{76} -8.00000 q^{77} -4.00000 q^{79} +1.00000 q^{80} +10.0000 q^{82} -2.00000 q^{85} +10.0000 q^{86} -2.00000 q^{88} +14.0000 q^{89} +4.00000 q^{91} -6.00000 q^{92} -12.0000 q^{94} +6.00000 q^{95} +14.0000 q^{97} -9.00000 q^{98} +O(q^{100})$$

## 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
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ −4.00000 −1.51186 −0.755929 0.654654i $$-0.772814\pi$$
−0.755929 + 0.654654i $$0.772814\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ −1.00000 −0.316228
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 4.00000 1.06904
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ 6.00000 1.37649 0.688247 0.725476i $$-0.258380\pi$$
0.688247 + 0.725476i $$0.258380\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 1.00000 0.196116
$$27$$ 0 0
$$28$$ −4.00000 −0.755929
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 2.00000 0.342997
$$35$$ −4.00000 −0.676123
$$36$$ 0 0
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ −6.00000 −0.973329
$$39$$ 0 0
$$40$$ −1.00000 −0.158114
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ −10.0000 −1.52499 −0.762493 0.646997i $$-0.776025\pi$$
−0.762493 + 0.646997i $$0.776025\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ 6.00000 0.884652
$$47$$ 12.0000 1.75038 0.875190 0.483779i $$-0.160736\pi$$
0.875190 + 0.483779i $$0.160736\pi$$
$$48$$ 0 0
$$49$$ 9.00000 1.28571
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ −1.00000 −0.138675
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ 0 0
$$55$$ 2.00000 0.269680
$$56$$ 4.00000 0.534522
$$57$$ 0 0
$$58$$ 2.00000 0.262613
$$59$$ −10.0000 −1.30189 −0.650945 0.759125i $$-0.725627\pi$$
−0.650945 + 0.759125i $$0.725627\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 6.00000 0.762001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −1.00000 −0.124035
$$66$$ 0 0
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ 0 0
$$70$$ 4.00000 0.478091
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ 0 0
$$73$$ 10.0000 1.17041 0.585206 0.810885i $$-0.301014\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ 2.00000 0.232495
$$75$$ 0 0
$$76$$ 6.00000 0.688247
$$77$$ −8.00000 −0.911685
$$78$$ 0 0
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 0 0
$$82$$ 10.0000 1.10432
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ 10.0000 1.07833
$$87$$ 0 0
$$88$$ −2.00000 −0.213201
$$89$$ 14.0000 1.48400 0.741999 0.670402i $$-0.233878\pi$$
0.741999 + 0.670402i $$0.233878\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ −6.00000 −0.625543
$$93$$ 0 0
$$94$$ −12.0000 −1.23771
$$95$$ 6.00000 0.615587
$$96$$ 0 0
$$97$$ 14.0000 1.42148 0.710742 0.703452i $$-0.248359\pi$$
0.710742 + 0.703452i $$0.248359\pi$$
$$98$$ −9.00000 −0.909137
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ −14.0000 −1.39305 −0.696526 0.717532i $$-0.745272\pi$$
−0.696526 + 0.717532i $$0.745272\pi$$
$$102$$ 0 0
$$103$$ −18.0000 −1.77359 −0.886796 0.462160i $$-0.847074\pi$$
−0.886796 + 0.462160i $$0.847074\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ 0 0
$$106$$ 2.00000 0.194257
$$107$$ −6.00000 −0.580042 −0.290021 0.957020i $$-0.593662\pi$$
−0.290021 + 0.957020i $$0.593662\pi$$
$$108$$ 0 0
$$109$$ −6.00000 −0.574696 −0.287348 0.957826i $$-0.592774\pi$$
−0.287348 + 0.957826i $$0.592774\pi$$
$$110$$ −2.00000 −0.190693
$$111$$ 0 0
$$112$$ −4.00000 −0.377964
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ −6.00000 −0.559503
$$116$$ −2.00000 −0.185695
$$117$$ 0 0
$$118$$ 10.0000 0.920575
$$119$$ 8.00000 0.733359
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ −2.00000 −0.181071
$$123$$ 0 0
$$124$$ −6.00000 −0.538816
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −14.0000 −1.24230 −0.621150 0.783692i $$-0.713334\pi$$
−0.621150 + 0.783692i $$0.713334\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 1.00000 0.0877058
$$131$$ −4.00000 −0.349482 −0.174741 0.984614i $$-0.555909\pi$$
−0.174741 + 0.984614i $$0.555909\pi$$
$$132$$ 0 0
$$133$$ −24.0000 −2.08106
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ 18.0000 1.53784 0.768922 0.639343i $$-0.220793\pi$$
0.768922 + 0.639343i $$0.220793\pi$$
$$138$$ 0 0
$$139$$ −8.00000 −0.678551 −0.339276 0.940687i $$-0.610182\pi$$
−0.339276 + 0.940687i $$0.610182\pi$$
$$140$$ −4.00000 −0.338062
$$141$$ 0 0
$$142$$ 10.0000 0.839181
$$143$$ −2.00000 −0.167248
$$144$$ 0 0
$$145$$ −2.00000 −0.166091
$$146$$ −10.0000 −0.827606
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ −2.00000 −0.163846 −0.0819232 0.996639i $$-0.526106\pi$$
−0.0819232 + 0.996639i $$0.526106\pi$$
$$150$$ 0 0
$$151$$ 6.00000 0.488273 0.244137 0.969741i $$-0.421495\pi$$
0.244137 + 0.969741i $$0.421495\pi$$
$$152$$ −6.00000 −0.486664
$$153$$ 0 0
$$154$$ 8.00000 0.644658
$$155$$ −6.00000 −0.481932
$$156$$ 0 0
$$157$$ 10.0000 0.798087 0.399043 0.916932i $$-0.369342\pi$$
0.399043 + 0.916932i $$0.369342\pi$$
$$158$$ 4.00000 0.318223
$$159$$ 0 0
$$160$$ −1.00000 −0.0790569
$$161$$ 24.0000 1.89146
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ −10.0000 −0.780869
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −20.0000 −1.54765 −0.773823 0.633402i $$-0.781658\pi$$
−0.773823 + 0.633402i $$0.781658\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 2.00000 0.153393
$$171$$ 0 0
$$172$$ −10.0000 −0.762493
$$173$$ −10.0000 −0.760286 −0.380143 0.924928i $$-0.624125\pi$$
−0.380143 + 0.924928i $$0.624125\pi$$
$$174$$ 0 0
$$175$$ −4.00000 −0.302372
$$176$$ 2.00000 0.150756
$$177$$ 0 0
$$178$$ −14.0000 −1.04934
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ −4.00000 −0.296500
$$183$$ 0 0
$$184$$ 6.00000 0.442326
$$185$$ −2.00000 −0.147043
$$186$$ 0 0
$$187$$ −4.00000 −0.292509
$$188$$ 12.0000 0.875190
$$189$$ 0 0
$$190$$ −6.00000 −0.435286
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ −14.0000 −1.00514
$$195$$ 0 0
$$196$$ 9.00000 0.642857
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ 0 0
$$202$$ 14.0000 0.985037
$$203$$ 8.00000 0.561490
$$204$$ 0 0
$$205$$ −10.0000 −0.698430
$$206$$ 18.0000 1.25412
$$207$$ 0 0
$$208$$ −1.00000 −0.0693375
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ 28.0000 1.92760 0.963800 0.266627i $$-0.0859092\pi$$
0.963800 + 0.266627i $$0.0859092\pi$$
$$212$$ −2.00000 −0.137361
$$213$$ 0 0
$$214$$ 6.00000 0.410152
$$215$$ −10.0000 −0.681994
$$216$$ 0 0
$$217$$ 24.0000 1.62923
$$218$$ 6.00000 0.406371
$$219$$ 0 0
$$220$$ 2.00000 0.134840
$$221$$ 2.00000 0.134535
$$222$$ 0 0
$$223$$ 4.00000 0.267860 0.133930 0.990991i $$-0.457240\pi$$
0.133930 + 0.990991i $$0.457240\pi$$
$$224$$ 4.00000 0.267261
$$225$$ 0 0
$$226$$ 2.00000 0.133038
$$227$$ 4.00000 0.265489 0.132745 0.991150i $$-0.457621\pi$$
0.132745 + 0.991150i $$0.457621\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 6.00000 0.395628
$$231$$ 0 0
$$232$$ 2.00000 0.131306
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ 12.0000 0.782794
$$236$$ −10.0000 −0.650945
$$237$$ 0 0
$$238$$ −8.00000 −0.518563
$$239$$ 26.0000 1.68180 0.840900 0.541190i $$-0.182026\pi$$
0.840900 + 0.541190i $$0.182026\pi$$
$$240$$ 0 0
$$241$$ −22.0000 −1.41714 −0.708572 0.705638i $$-0.750660\pi$$
−0.708572 + 0.705638i $$0.750660\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ 9.00000 0.574989
$$246$$ 0 0
$$247$$ −6.00000 −0.381771
$$248$$ 6.00000 0.381000
$$249$$ 0 0
$$250$$ −1.00000 −0.0632456
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 14.0000 0.878438
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 30.0000 1.87135 0.935674 0.352865i $$-0.114792\pi$$
0.935674 + 0.352865i $$0.114792\pi$$
$$258$$ 0 0
$$259$$ 8.00000 0.497096
$$260$$ −1.00000 −0.0620174
$$261$$ 0 0
$$262$$ 4.00000 0.247121
$$263$$ −2.00000 −0.123325 −0.0616626 0.998097i $$-0.519640\pi$$
−0.0616626 + 0.998097i $$0.519640\pi$$
$$264$$ 0 0
$$265$$ −2.00000 −0.122859
$$266$$ 24.0000 1.47153
$$267$$ 0 0
$$268$$ −12.0000 −0.733017
$$269$$ −6.00000 −0.365826 −0.182913 0.983129i $$-0.558553\pi$$
−0.182913 + 0.983129i $$0.558553\pi$$
$$270$$ 0 0
$$271$$ −2.00000 −0.121491 −0.0607457 0.998153i $$-0.519348\pi$$
−0.0607457 + 0.998153i $$0.519348\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ −18.0000 −1.08742
$$275$$ 2.00000 0.120605
$$276$$ 0 0
$$277$$ 2.00000 0.120168 0.0600842 0.998193i $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 0 0
$$280$$ 4.00000 0.239046
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 14.0000 0.832214 0.416107 0.909316i $$-0.363394\pi$$
0.416107 + 0.909316i $$0.363394\pi$$
$$284$$ −10.0000 −0.593391
$$285$$ 0 0
$$286$$ 2.00000 0.118262
$$287$$ 40.0000 2.36113
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 2.00000 0.117444
$$291$$ 0 0
$$292$$ 10.0000 0.585206
$$293$$ −22.0000 −1.28525 −0.642627 0.766179i $$-0.722155\pi$$
−0.642627 + 0.766179i $$0.722155\pi$$
$$294$$ 0 0
$$295$$ −10.0000 −0.582223
$$296$$ 2.00000 0.116248
$$297$$ 0 0
$$298$$ 2.00000 0.115857
$$299$$ 6.00000 0.346989
$$300$$ 0 0
$$301$$ 40.0000 2.30556
$$302$$ −6.00000 −0.345261
$$303$$ 0 0
$$304$$ 6.00000 0.344124
$$305$$ 2.00000 0.114520
$$306$$ 0 0
$$307$$ 24.0000 1.36975 0.684876 0.728659i $$-0.259856\pi$$
0.684876 + 0.728659i $$0.259856\pi$$
$$308$$ −8.00000 −0.455842
$$309$$ 0 0
$$310$$ 6.00000 0.340777
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 0 0
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ −10.0000 −0.564333
$$315$$ 0 0
$$316$$ −4.00000 −0.225018
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ −4.00000 −0.223957
$$320$$ 1.00000 0.0559017
$$321$$ 0 0
$$322$$ −24.0000 −1.33747
$$323$$ −12.0000 −0.667698
$$324$$ 0 0
$$325$$ −1.00000 −0.0554700
$$326$$ 4.00000 0.221540
$$327$$ 0 0
$$328$$ 10.0000 0.552158
$$329$$ −48.0000 −2.64633
$$330$$ 0 0
$$331$$ −14.0000 −0.769510 −0.384755 0.923019i $$-0.625714\pi$$
−0.384755 + 0.923019i $$0.625714\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 20.0000 1.09435
$$335$$ −12.0000 −0.655630
$$336$$ 0 0
$$337$$ −22.0000 −1.19842 −0.599208 0.800593i $$-0.704518\pi$$
−0.599208 + 0.800593i $$0.704518\pi$$
$$338$$ −1.00000 −0.0543928
$$339$$ 0 0
$$340$$ −2.00000 −0.108465
$$341$$ −12.0000 −0.649836
$$342$$ 0 0
$$343$$ −8.00000 −0.431959
$$344$$ 10.0000 0.539164
$$345$$ 0 0
$$346$$ 10.0000 0.537603
$$347$$ −6.00000 −0.322097 −0.161048 0.986947i $$-0.551488\pi$$
−0.161048 + 0.986947i $$0.551488\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ −2.00000 −0.106600
$$353$$ −34.0000 −1.80964 −0.904819 0.425797i $$-0.859994\pi$$
−0.904819 + 0.425797i $$0.859994\pi$$
$$354$$ 0 0
$$355$$ −10.0000 −0.530745
$$356$$ 14.0000 0.741999
$$357$$ 0 0
$$358$$ −4.00000 −0.211407
$$359$$ 6.00000 0.316668 0.158334 0.987386i $$-0.449388\pi$$
0.158334 + 0.987386i $$0.449388\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ −10.0000 −0.525588
$$363$$ 0 0
$$364$$ 4.00000 0.209657
$$365$$ 10.0000 0.523424
$$366$$ 0 0
$$367$$ 30.0000 1.56599 0.782994 0.622030i $$-0.213692\pi$$
0.782994 + 0.622030i $$0.213692\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 0 0
$$370$$ 2.00000 0.103975
$$371$$ 8.00000 0.415339
$$372$$ 0 0
$$373$$ −14.0000 −0.724893 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$374$$ 4.00000 0.206835
$$375$$ 0 0
$$376$$ −12.0000 −0.618853
$$377$$ 2.00000 0.103005
$$378$$ 0 0
$$379$$ 6.00000 0.308199 0.154100 0.988055i $$-0.450752\pi$$
0.154100 + 0.988055i $$0.450752\pi$$
$$380$$ 6.00000 0.307794
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −12.0000 −0.613171 −0.306586 0.951843i $$-0.599187\pi$$
−0.306586 + 0.951843i $$0.599187\pi$$
$$384$$ 0 0
$$385$$ −8.00000 −0.407718
$$386$$ −14.0000 −0.712581
$$387$$ 0 0
$$388$$ 14.0000 0.710742
$$389$$ 10.0000 0.507020 0.253510 0.967333i $$-0.418415\pi$$
0.253510 + 0.967333i $$0.418415\pi$$
$$390$$ 0 0
$$391$$ 12.0000 0.606866
$$392$$ −9.00000 −0.454569
$$393$$ 0 0
$$394$$ −6.00000 −0.302276
$$395$$ −4.00000 −0.201262
$$396$$ 0 0
$$397$$ 38.0000 1.90717 0.953583 0.301131i $$-0.0973643\pi$$
0.953583 + 0.301131i $$0.0973643\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 6.00000 0.299626 0.149813 0.988714i $$-0.452133\pi$$
0.149813 + 0.988714i $$0.452133\pi$$
$$402$$ 0 0
$$403$$ 6.00000 0.298881
$$404$$ −14.0000 −0.696526
$$405$$ 0 0
$$406$$ −8.00000 −0.397033
$$407$$ −4.00000 −0.198273
$$408$$ 0 0
$$409$$ 34.0000 1.68119 0.840596 0.541663i $$-0.182205\pi$$
0.840596 + 0.541663i $$0.182205\pi$$
$$410$$ 10.0000 0.493865
$$411$$ 0 0
$$412$$ −18.0000 −0.886796
$$413$$ 40.0000 1.96827
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.00000 0.0490290
$$417$$ 0 0
$$418$$ −12.0000 −0.586939
$$419$$ −16.0000 −0.781651 −0.390826 0.920465i $$-0.627810\pi$$
−0.390826 + 0.920465i $$0.627810\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ −28.0000 −1.36302
$$423$$ 0 0
$$424$$ 2.00000 0.0971286
$$425$$ −2.00000 −0.0970143
$$426$$ 0 0
$$427$$ −8.00000 −0.387147
$$428$$ −6.00000 −0.290021
$$429$$ 0 0
$$430$$ 10.0000 0.482243
$$431$$ −18.0000 −0.867029 −0.433515 0.901146i $$-0.642727\pi$$
−0.433515 + 0.901146i $$0.642727\pi$$
$$432$$ 0 0
$$433$$ −38.0000 −1.82616 −0.913082 0.407777i $$-0.866304\pi$$
−0.913082 + 0.407777i $$0.866304\pi$$
$$434$$ −24.0000 −1.15204
$$435$$ 0 0
$$436$$ −6.00000 −0.287348
$$437$$ −36.0000 −1.72211
$$438$$ 0 0
$$439$$ −32.0000 −1.52728 −0.763638 0.645644i $$-0.776589\pi$$
−0.763638 + 0.645644i $$0.776589\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ 0 0
$$442$$ −2.00000 −0.0951303
$$443$$ 14.0000 0.665160 0.332580 0.943075i $$-0.392081\pi$$
0.332580 + 0.943075i $$0.392081\pi$$
$$444$$ 0 0
$$445$$ 14.0000 0.663664
$$446$$ −4.00000 −0.189405
$$447$$ 0 0
$$448$$ −4.00000 −0.188982
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ −20.0000 −0.941763
$$452$$ −2.00000 −0.0940721
$$453$$ 0 0
$$454$$ −4.00000 −0.187729
$$455$$ 4.00000 0.187523
$$456$$ 0 0
$$457$$ −10.0000 −0.467780 −0.233890 0.972263i $$-0.575146\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 0 0
$$460$$ −6.00000 −0.279751
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ 0 0
$$466$$ −6.00000 −0.277945
$$467$$ −10.0000 −0.462745 −0.231372 0.972865i $$-0.574322\pi$$
−0.231372 + 0.972865i $$0.574322\pi$$
$$468$$ 0 0
$$469$$ 48.0000 2.21643
$$470$$ −12.0000 −0.553519
$$471$$ 0 0
$$472$$ 10.0000 0.460287
$$473$$ −20.0000 −0.919601
$$474$$ 0 0
$$475$$ 6.00000 0.275299
$$476$$ 8.00000 0.366679
$$477$$ 0 0
$$478$$ −26.0000 −1.18921
$$479$$ −2.00000 −0.0913823 −0.0456912 0.998956i $$-0.514549\pi$$
−0.0456912 + 0.998956i $$0.514549\pi$$
$$480$$ 0 0
$$481$$ 2.00000 0.0911922
$$482$$ 22.0000 1.00207
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 14.0000 0.635707
$$486$$ 0 0
$$487$$ −16.0000 −0.725029 −0.362515 0.931978i $$-0.618082\pi$$
−0.362515 + 0.931978i $$0.618082\pi$$
$$488$$ −2.00000 −0.0905357
$$489$$ 0 0
$$490$$ −9.00000 −0.406579
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 4.00000 0.180151
$$494$$ 6.00000 0.269953
$$495$$ 0 0
$$496$$ −6.00000 −0.269408
$$497$$ 40.0000 1.79425
$$498$$ 0 0
$$499$$ 38.0000 1.70111 0.850557 0.525883i $$-0.176265\pi$$
0.850557 + 0.525883i $$0.176265\pi$$
$$500$$ 1.00000 0.0447214
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 14.0000 0.624229 0.312115 0.950044i $$-0.398963\pi$$
0.312115 + 0.950044i $$0.398963\pi$$
$$504$$ 0 0
$$505$$ −14.0000 −0.622992
$$506$$ 12.0000 0.533465
$$507$$ 0 0
$$508$$ −14.0000 −0.621150
$$509$$ 6.00000 0.265945 0.132973 0.991120i $$-0.457548\pi$$
0.132973 + 0.991120i $$0.457548\pi$$
$$510$$ 0 0
$$511$$ −40.0000 −1.76950
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −30.0000 −1.32324
$$515$$ −18.0000 −0.793175
$$516$$ 0 0
$$517$$ 24.0000 1.05552
$$518$$ −8.00000 −0.351500
$$519$$ 0 0
$$520$$ 1.00000 0.0438529
$$521$$ 26.0000 1.13908 0.569540 0.821963i $$-0.307121\pi$$
0.569540 + 0.821963i $$0.307121\pi$$
$$522$$ 0 0
$$523$$ −6.00000 −0.262362 −0.131181 0.991358i $$-0.541877\pi$$
−0.131181 + 0.991358i $$0.541877\pi$$
$$524$$ −4.00000 −0.174741
$$525$$ 0 0
$$526$$ 2.00000 0.0872041
$$527$$ 12.0000 0.522728
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 2.00000 0.0868744
$$531$$ 0 0
$$532$$ −24.0000 −1.04053
$$533$$ 10.0000 0.433148
$$534$$ 0 0
$$535$$ −6.00000 −0.259403
$$536$$ 12.0000 0.518321
$$537$$ 0 0
$$538$$ 6.00000 0.258678
$$539$$ 18.0000 0.775315
$$540$$ 0 0
$$541$$ −38.0000 −1.63375 −0.816874 0.576816i $$-0.804295\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 2.00000 0.0859074
$$543$$ 0 0
$$544$$ 2.00000 0.0857493
$$545$$ −6.00000 −0.257012
$$546$$ 0 0
$$547$$ 22.0000 0.940652 0.470326 0.882493i $$-0.344136\pi$$
0.470326 + 0.882493i $$0.344136\pi$$
$$548$$ 18.0000 0.768922
$$549$$ 0 0
$$550$$ −2.00000 −0.0852803
$$551$$ −12.0000 −0.511217
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ −2.00000 −0.0849719
$$555$$ 0 0
$$556$$ −8.00000 −0.339276
$$557$$ −38.0000 −1.61011 −0.805056 0.593199i $$-0.797865\pi$$
−0.805056 + 0.593199i $$0.797865\pi$$
$$558$$ 0 0
$$559$$ 10.0000 0.422955
$$560$$ −4.00000 −0.169031
$$561$$ 0 0
$$562$$ −6.00000 −0.253095
$$563$$ −6.00000 −0.252870 −0.126435 0.991975i $$-0.540353\pi$$
−0.126435 + 0.991975i $$0.540353\pi$$
$$564$$ 0 0
$$565$$ −2.00000 −0.0841406
$$566$$ −14.0000 −0.588464
$$567$$ 0 0
$$568$$ 10.0000 0.419591
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ −32.0000 −1.33916 −0.669579 0.742741i $$-0.733526\pi$$
−0.669579 + 0.742741i $$0.733526\pi$$
$$572$$ −2.00000 −0.0836242
$$573$$ 0 0
$$574$$ −40.0000 −1.66957
$$575$$ −6.00000 −0.250217
$$576$$ 0 0
$$577$$ 18.0000 0.749350 0.374675 0.927156i $$-0.377754\pi$$
0.374675 + 0.927156i $$0.377754\pi$$
$$578$$ 13.0000 0.540729
$$579$$ 0 0
$$580$$ −2.00000 −0.0830455
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −4.00000 −0.165663
$$584$$ −10.0000 −0.413803
$$585$$ 0 0
$$586$$ 22.0000 0.908812
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ −36.0000 −1.48335
$$590$$ 10.0000 0.411693
$$591$$ 0 0
$$592$$ −2.00000 −0.0821995
$$593$$ 2.00000 0.0821302 0.0410651 0.999156i $$-0.486925\pi$$
0.0410651 + 0.999156i $$0.486925\pi$$
$$594$$ 0 0
$$595$$ 8.00000 0.327968
$$596$$ −2.00000 −0.0819232
$$597$$ 0 0
$$598$$ −6.00000 −0.245358
$$599$$ 12.0000 0.490307 0.245153 0.969484i $$-0.421162\pi$$
0.245153 + 0.969484i $$0.421162\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ −40.0000 −1.63028
$$603$$ 0 0
$$604$$ 6.00000 0.244137
$$605$$ −7.00000 −0.284590
$$606$$ 0 0
$$607$$ −34.0000 −1.38002 −0.690009 0.723801i $$-0.742393\pi$$
−0.690009 + 0.723801i $$0.742393\pi$$
$$608$$ −6.00000 −0.243332
$$609$$ 0 0
$$610$$ −2.00000 −0.0809776
$$611$$ −12.0000 −0.485468
$$612$$ 0 0
$$613$$ 26.0000 1.05013 0.525065 0.851062i $$-0.324041\pi$$
0.525065 + 0.851062i $$0.324041\pi$$
$$614$$ −24.0000 −0.968561
$$615$$ 0 0
$$616$$ 8.00000 0.322329
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 0 0
$$619$$ −46.0000 −1.84890 −0.924448 0.381308i $$-0.875474\pi$$
−0.924448 + 0.381308i $$0.875474\pi$$
$$620$$ −6.00000 −0.240966
$$621$$ 0 0
$$622$$ −12.0000 −0.481156
$$623$$ −56.0000 −2.24359
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 6.00000 0.239808
$$627$$ 0 0
$$628$$ 10.0000 0.399043
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ 30.0000 1.19428 0.597141 0.802137i $$-0.296303\pi$$
0.597141 + 0.802137i $$0.296303\pi$$
$$632$$ 4.00000 0.159111
$$633$$ 0 0
$$634$$ −18.0000 −0.714871
$$635$$ −14.0000 −0.555573
$$636$$ 0 0
$$637$$ −9.00000 −0.356593
$$638$$ 4.00000 0.158362
$$639$$ 0 0
$$640$$ −1.00000 −0.0395285
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 0 0
$$643$$ −16.0000 −0.630978 −0.315489 0.948929i $$-0.602169\pi$$
−0.315489 + 0.948929i $$0.602169\pi$$
$$644$$ 24.0000 0.945732
$$645$$ 0 0
$$646$$ 12.0000 0.472134
$$647$$ −42.0000 −1.65119 −0.825595 0.564263i $$-0.809160\pi$$
−0.825595 + 0.564263i $$0.809160\pi$$
$$648$$ 0 0
$$649$$ −20.0000 −0.785069
$$650$$ 1.00000 0.0392232
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ 6.00000 0.234798 0.117399 0.993085i $$-0.462544\pi$$
0.117399 + 0.993085i $$0.462544\pi$$
$$654$$ 0 0
$$655$$ −4.00000 −0.156293
$$656$$ −10.0000 −0.390434
$$657$$ 0 0
$$658$$ 48.0000 1.87123
$$659$$ −8.00000 −0.311636 −0.155818 0.987786i $$-0.549801\pi$$
−0.155818 + 0.987786i $$0.549801\pi$$
$$660$$ 0 0
$$661$$ −30.0000 −1.16686 −0.583432 0.812162i $$-0.698291\pi$$
−0.583432 + 0.812162i $$0.698291\pi$$
$$662$$ 14.0000 0.544125
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −24.0000 −0.930680
$$666$$ 0 0
$$667$$ 12.0000 0.464642
$$668$$ −20.0000 −0.773823
$$669$$ 0 0
$$670$$ 12.0000 0.463600
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ 2.00000 0.0770943 0.0385472 0.999257i $$-0.487727\pi$$
0.0385472 + 0.999257i $$0.487727\pi$$
$$674$$ 22.0000 0.847408
$$675$$ 0 0
$$676$$ 1.00000 0.0384615
$$677$$ 6.00000 0.230599 0.115299 0.993331i $$-0.463217\pi$$
0.115299 + 0.993331i $$0.463217\pi$$
$$678$$ 0 0
$$679$$ −56.0000 −2.14908
$$680$$ 2.00000 0.0766965
$$681$$ 0 0
$$682$$ 12.0000 0.459504
$$683$$ 44.0000 1.68361 0.841807 0.539779i $$-0.181492\pi$$
0.841807 + 0.539779i $$0.181492\pi$$
$$684$$ 0 0
$$685$$ 18.0000 0.687745
$$686$$ 8.00000 0.305441
$$687$$ 0 0
$$688$$ −10.0000 −0.381246
$$689$$ 2.00000 0.0761939
$$690$$ 0 0
$$691$$ −38.0000 −1.44559 −0.722794 0.691063i $$-0.757142\pi$$
−0.722794 + 0.691063i $$0.757142\pi$$
$$692$$ −10.0000 −0.380143
$$693$$ 0 0
$$694$$ 6.00000 0.227757
$$695$$ −8.00000 −0.303457
$$696$$ 0 0
$$697$$ 20.0000 0.757554
$$698$$ −2.00000 −0.0757011
$$699$$ 0 0
$$700$$ −4.00000 −0.151186
$$701$$ −38.0000 −1.43524 −0.717620 0.696435i $$-0.754769\pi$$
−0.717620 + 0.696435i $$0.754769\pi$$
$$702$$ 0 0
$$703$$ −12.0000 −0.452589
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ 34.0000 1.27961
$$707$$ 56.0000 2.10610
$$708$$ 0 0
$$709$$ −22.0000 −0.826227 −0.413114 0.910679i $$-0.635559\pi$$
−0.413114 + 0.910679i $$0.635559\pi$$
$$710$$ 10.0000 0.375293
$$711$$ 0 0
$$712$$ −14.0000 −0.524672
$$713$$ 36.0000 1.34821
$$714$$ 0 0
$$715$$ −2.00000 −0.0747958
$$716$$ 4.00000 0.149487
$$717$$ 0 0
$$718$$ −6.00000 −0.223918
$$719$$ −48.0000 −1.79010 −0.895049 0.445968i $$-0.852860\pi$$
−0.895049 + 0.445968i $$0.852860\pi$$
$$720$$ 0 0
$$721$$ 72.0000 2.68142
$$722$$ −17.0000 −0.632674
$$723$$ 0 0
$$724$$ 10.0000 0.371647
$$725$$ −2.00000 −0.0742781
$$726$$ 0 0
$$727$$ −14.0000 −0.519231 −0.259616 0.965712i $$-0.583596\pi$$
−0.259616 + 0.965712i $$0.583596\pi$$
$$728$$ −4.00000 −0.148250
$$729$$ 0 0
$$730$$ −10.0000 −0.370117
$$731$$ 20.0000 0.739727
$$732$$ 0 0
$$733$$ 2.00000 0.0738717 0.0369358 0.999318i $$-0.488240\pi$$
0.0369358 + 0.999318i $$0.488240\pi$$
$$734$$ −30.0000 −1.10732
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ −24.0000 −0.884051
$$738$$ 0 0
$$739$$ 42.0000 1.54499 0.772497 0.635018i $$-0.219007\pi$$
0.772497 + 0.635018i $$0.219007\pi$$
$$740$$ −2.00000 −0.0735215
$$741$$ 0 0
$$742$$ −8.00000 −0.293689
$$743$$ 12.0000 0.440237 0.220119 0.975473i $$-0.429356\pi$$
0.220119 + 0.975473i $$0.429356\pi$$
$$744$$ 0 0
$$745$$ −2.00000 −0.0732743
$$746$$ 14.0000 0.512576
$$747$$ 0 0
$$748$$ −4.00000 −0.146254
$$749$$ 24.0000 0.876941
$$750$$ 0 0
$$751$$ 44.0000 1.60558 0.802791 0.596260i $$-0.203347\pi$$
0.802791 + 0.596260i $$0.203347\pi$$
$$752$$ 12.0000 0.437595
$$753$$ 0 0
$$754$$ −2.00000 −0.0728357
$$755$$ 6.00000 0.218362
$$756$$ 0 0
$$757$$ 18.0000 0.654221 0.327111 0.944986i $$-0.393925\pi$$
0.327111 + 0.944986i $$0.393925\pi$$
$$758$$ −6.00000 −0.217930
$$759$$ 0 0
$$760$$ −6.00000 −0.217643
$$761$$ 14.0000 0.507500 0.253750 0.967270i $$-0.418336\pi$$
0.253750 + 0.967270i $$0.418336\pi$$
$$762$$ 0 0
$$763$$ 24.0000 0.868858
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 12.0000 0.433578
$$767$$ 10.0000 0.361079
$$768$$ 0 0
$$769$$ 10.0000 0.360609 0.180305 0.983611i $$-0.442292\pi$$
0.180305 + 0.983611i $$0.442292\pi$$
$$770$$ 8.00000 0.288300
$$771$$ 0 0
$$772$$ 14.0000 0.503871
$$773$$ 34.0000 1.22290 0.611448 0.791285i $$-0.290588\pi$$
0.611448 + 0.791285i $$0.290588\pi$$
$$774$$ 0 0
$$775$$ −6.00000 −0.215526
$$776$$ −14.0000 −0.502571
$$777$$ 0 0
$$778$$ −10.0000 −0.358517
$$779$$ −60.0000 −2.14972
$$780$$ 0 0
$$781$$ −20.0000 −0.715656
$$782$$ −12.0000 −0.429119
$$783$$ 0 0
$$784$$ 9.00000 0.321429
$$785$$ 10.0000 0.356915
$$786$$ 0 0
$$787$$ −8.00000 −0.285169 −0.142585 0.989783i $$-0.545541\pi$$
−0.142585 + 0.989783i $$0.545541\pi$$
$$788$$ 6.00000 0.213741
$$789$$ 0 0
$$790$$ 4.00000 0.142314
$$791$$ 8.00000 0.284447
$$792$$ 0 0
$$793$$ −2.00000 −0.0710221
$$794$$ −38.0000 −1.34857
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 22.0000 0.779280 0.389640 0.920967i $$-0.372599\pi$$
0.389640 + 0.920967i $$0.372599\pi$$
$$798$$ 0 0
$$799$$ −24.0000 −0.849059
$$800$$ −1.00000 −0.0353553
$$801$$ 0 0
$$802$$ −6.00000 −0.211867
$$803$$ 20.0000 0.705785
$$804$$ 0 0
$$805$$ 24.0000 0.845889
$$806$$ −6.00000 −0.211341
$$807$$ 0 0
$$808$$ 14.0000 0.492518
$$809$$ 34.0000 1.19538 0.597688 0.801729i $$-0.296086\pi$$
0.597688 + 0.801729i $$0.296086\pi$$
$$810$$ 0 0
$$811$$ −38.0000 −1.33436 −0.667180 0.744896i $$-0.732499\pi$$
−0.667180 + 0.744896i $$0.732499\pi$$
$$812$$ 8.00000 0.280745
$$813$$ 0 0
$$814$$ 4.00000 0.140200
$$815$$ −4.00000 −0.140114
$$816$$ 0 0
$$817$$ −60.0000 −2.09913
$$818$$ −34.0000 −1.18878
$$819$$ 0 0
$$820$$ −10.0000 −0.349215
$$821$$ −50.0000 −1.74501 −0.872506 0.488603i $$-0.837507\pi$$
−0.872506 + 0.488603i $$0.837507\pi$$
$$822$$ 0 0
$$823$$ 14.0000 0.488009 0.244005 0.969774i $$-0.421539\pi$$
0.244005 + 0.969774i $$0.421539\pi$$
$$824$$ 18.0000 0.627060
$$825$$ 0 0
$$826$$ −40.0000 −1.39178
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 2.00000 0.0694629 0.0347314 0.999397i $$-0.488942\pi$$
0.0347314 + 0.999397i $$0.488942\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −1.00000 −0.0346688
$$833$$ −18.0000 −0.623663
$$834$$ 0 0
$$835$$ −20.0000 −0.692129
$$836$$ 12.0000 0.415029
$$837$$ 0 0
$$838$$ 16.0000 0.552711
$$839$$ −26.0000 −0.897620 −0.448810 0.893627i $$-0.648152\pi$$
−0.448810 + 0.893627i $$0.648152\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ −10.0000 −0.344623
$$843$$ 0 0
$$844$$ 28.0000 0.963800
$$845$$ 1.00000 0.0344010
$$846$$ 0 0
$$847$$ 28.0000 0.962091
$$848$$ −2.00000 −0.0686803
$$849$$ 0 0
$$850$$ 2.00000 0.0685994
$$851$$ 12.0000 0.411355
$$852$$ 0 0
$$853$$ −26.0000 −0.890223 −0.445112 0.895475i $$-0.646836\pi$$
−0.445112 + 0.895475i $$0.646836\pi$$
$$854$$ 8.00000 0.273754
$$855$$ 0 0
$$856$$ 6.00000 0.205076
$$857$$ 14.0000 0.478231 0.239115 0.970991i $$-0.423143\pi$$
0.239115 + 0.970991i $$0.423143\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ −10.0000 −0.340997
$$861$$ 0 0
$$862$$ 18.0000 0.613082
$$863$$ 36.0000 1.22545 0.612727 0.790295i $$-0.290072\pi$$
0.612727 + 0.790295i $$0.290072\pi$$
$$864$$ 0 0
$$865$$ −10.0000 −0.340010
$$866$$ 38.0000 1.29129
$$867$$ 0 0
$$868$$ 24.0000 0.814613
$$869$$ −8.00000 −0.271381
$$870$$ 0 0
$$871$$ 12.0000 0.406604
$$872$$ 6.00000 0.203186
$$873$$ 0 0
$$874$$ 36.0000 1.21772
$$875$$ −4.00000 −0.135225
$$876$$ 0 0
$$877$$ −14.0000 −0.472746 −0.236373 0.971662i $$-0.575959\pi$$
−0.236373 + 0.971662i $$0.575959\pi$$
$$878$$ 32.0000 1.07995
$$879$$ 0 0
$$880$$ 2.00000 0.0674200
$$881$$ −6.00000 −0.202145 −0.101073 0.994879i $$-0.532227\pi$$
−0.101073 + 0.994879i $$0.532227\pi$$
$$882$$ 0 0
$$883$$ 38.0000 1.27880 0.639401 0.768874i $$-0.279182\pi$$
0.639401 + 0.768874i $$0.279182\pi$$
$$884$$ 2.00000 0.0672673
$$885$$ 0 0
$$886$$ −14.0000 −0.470339
$$887$$ −22.0000 −0.738688 −0.369344 0.929293i $$-0.620418\pi$$
−0.369344 + 0.929293i $$0.620418\pi$$
$$888$$ 0 0
$$889$$ 56.0000 1.87818
$$890$$ −14.0000 −0.469281
$$891$$ 0 0
$$892$$ 4.00000 0.133930
$$893$$ 72.0000 2.40939
$$894$$ 0 0
$$895$$ 4.00000 0.133705
$$896$$ 4.00000 0.133631
$$897$$ 0 0
$$898$$ −6.00000 −0.200223
$$899$$ 12.0000 0.400222
$$900$$ 0 0
$$901$$ 4.00000 0.133259
$$902$$ 20.0000 0.665927
$$903$$ 0 0
$$904$$ 2.00000 0.0665190
$$905$$ 10.0000 0.332411
$$906$$ 0 0
$$907$$ −14.0000 −0.464862 −0.232431 0.972613i $$-0.574668\pi$$
−0.232431 + 0.972613i $$0.574668\pi$$
$$908$$ 4.00000 0.132745
$$909$$ 0 0
$$910$$ −4.00000 −0.132599
$$911$$ −16.0000 −0.530104 −0.265052 0.964234i $$-0.585389\pi$$
−0.265052 + 0.964234i $$0.585389\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 10.0000 0.330771
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ 16.0000 0.528367
$$918$$ 0 0
$$919$$ 4.00000 0.131948 0.0659739 0.997821i $$-0.478985\pi$$
0.0659739 + 0.997821i $$0.478985\pi$$
$$920$$ 6.00000 0.197814
$$921$$ 0 0
$$922$$ −6.00000 −0.197599
$$923$$ 10.0000 0.329154
$$924$$ 0 0
$$925$$ −2.00000 −0.0657596
$$926$$ −16.0000 −0.525793
$$927$$ 0 0
$$928$$ 2.00000 0.0656532
$$929$$ 6.00000 0.196854 0.0984268 0.995144i $$-0.468619\pi$$
0.0984268 + 0.995144i $$0.468619\pi$$
$$930$$ 0 0
$$931$$ 54.0000 1.76978
$$932$$ 6.00000 0.196537
$$933$$ 0 0
$$934$$ 10.0000 0.327210
$$935$$ −4.00000 −0.130814
$$936$$ 0 0
$$937$$ 18.0000 0.588034 0.294017 0.955800i $$-0.405008\pi$$
0.294017 + 0.955800i $$0.405008\pi$$
$$938$$ −48.0000 −1.56726
$$939$$ 0 0
$$940$$ 12.0000 0.391397
$$941$$ −50.0000 −1.62995 −0.814977 0.579494i $$-0.803250\pi$$
−0.814977 + 0.579494i $$0.803250\pi$$
$$942$$ 0 0
$$943$$ 60.0000 1.95387
$$944$$ −10.0000 −0.325472
$$945$$ 0 0
$$946$$ 20.0000 0.650256
$$947$$ 8.00000 0.259965 0.129983 0.991516i $$-0.458508\pi$$
0.129983 + 0.991516i $$0.458508\pi$$
$$948$$ 0 0
$$949$$ −10.0000 −0.324614
$$950$$ −6.00000 −0.194666
$$951$$ 0 0
$$952$$ −8.00000 −0.259281
$$953$$ −18.0000 −0.583077 −0.291539 0.956559i $$-0.594167\pi$$
−0.291539 + 0.956559i $$0.594167\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 26.0000 0.840900
$$957$$ 0 0
$$958$$ 2.00000 0.0646171
$$959$$ −72.0000 −2.32500
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ −2.00000 −0.0644826
$$963$$ 0 0
$$964$$ −22.0000 −0.708572
$$965$$ 14.0000 0.450676
$$966$$ 0 0
$$967$$ −32.0000 −1.02905 −0.514525 0.857475i $$-0.672032\pi$$
−0.514525 + 0.857475i $$0.672032\pi$$
$$968$$ 7.00000 0.224989
$$969$$ 0 0
$$970$$ −14.0000 −0.449513
$$971$$ −20.0000 −0.641831 −0.320915 0.947108i $$-0.603990\pi$$
−0.320915 + 0.947108i $$0.603990\pi$$
$$972$$ 0 0
$$973$$ 32.0000 1.02587
$$974$$ 16.0000 0.512673
$$975$$ 0 0
$$976$$ 2.00000 0.0640184
$$977$$ 30.0000 0.959785 0.479893 0.877327i $$-0.340676\pi$$
0.479893 + 0.877327i $$0.340676\pi$$
$$978$$ 0 0
$$979$$ 28.0000 0.894884
$$980$$ 9.00000 0.287494
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 16.0000 0.510321 0.255160 0.966899i $$-0.417872\pi$$
0.255160 + 0.966899i $$0.417872\pi$$
$$984$$ 0 0
$$985$$ 6.00000 0.191176
$$986$$ −4.00000 −0.127386
$$987$$ 0 0
$$988$$ −6.00000 −0.190885
$$989$$ 60.0000 1.90789
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 6.00000 0.190500
$$993$$ 0 0
$$994$$ −40.0000 −1.26872
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 10.0000 0.316703 0.158352 0.987383i $$-0.449382\pi$$
0.158352 + 0.987383i $$0.449382\pi$$
$$998$$ −38.0000 −1.20287
$$999$$ 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 1170.2.a.d.1.1 1
3.2 odd 2 130.2.a.c.1.1 1
4.3 odd 2 9360.2.a.by.1.1 1
5.2 odd 4 5850.2.e.u.5149.1 2
5.3 odd 4 5850.2.e.u.5149.2 2
5.4 even 2 5850.2.a.cb.1.1 1
12.11 even 2 1040.2.a.b.1.1 1
15.2 even 4 650.2.b.g.599.2 2
15.8 even 4 650.2.b.g.599.1 2
15.14 odd 2 650.2.a.c.1.1 1
21.20 even 2 6370.2.a.l.1.1 1
24.5 odd 2 4160.2.a.c.1.1 1
24.11 even 2 4160.2.a.t.1.1 1
39.2 even 12 1690.2.l.a.1161.2 4
39.5 even 4 1690.2.d.e.1351.1 2
39.8 even 4 1690.2.d.e.1351.2 2
39.11 even 12 1690.2.l.a.1161.1 4
39.17 odd 6 1690.2.e.g.991.1 2
39.20 even 12 1690.2.l.a.361.2 4
39.23 odd 6 1690.2.e.g.191.1 2
39.29 odd 6 1690.2.e.a.191.1 2
39.32 even 12 1690.2.l.a.361.1 4
39.35 odd 6 1690.2.e.a.991.1 2
39.38 odd 2 1690.2.a.e.1.1 1
60.59 even 2 5200.2.a.bd.1.1 1
195.194 odd 2 8450.2.a.n.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.a.c.1.1 1 3.2 odd 2
650.2.a.c.1.1 1 15.14 odd 2
650.2.b.g.599.1 2 15.8 even 4
650.2.b.g.599.2 2 15.2 even 4
1040.2.a.b.1.1 1 12.11 even 2
1170.2.a.d.1.1 1 1.1 even 1 trivial
1690.2.a.e.1.1 1 39.38 odd 2
1690.2.d.e.1351.1 2 39.5 even 4
1690.2.d.e.1351.2 2 39.8 even 4
1690.2.e.a.191.1 2 39.29 odd 6
1690.2.e.a.991.1 2 39.35 odd 6
1690.2.e.g.191.1 2 39.23 odd 6
1690.2.e.g.991.1 2 39.17 odd 6
1690.2.l.a.361.1 4 39.32 even 12
1690.2.l.a.361.2 4 39.20 even 12
1690.2.l.a.1161.1 4 39.11 even 12
1690.2.l.a.1161.2 4 39.2 even 12
4160.2.a.c.1.1 1 24.5 odd 2
4160.2.a.t.1.1 1 24.11 even 2
5200.2.a.bd.1.1 1 60.59 even 2
5850.2.a.cb.1.1 1 5.4 even 2
5850.2.e.u.5149.1 2 5.2 odd 4
5850.2.e.u.5149.2 2 5.3 odd 4
6370.2.a.l.1.1 1 21.20 even 2
8450.2.a.n.1.1 1 195.194 odd 2
9360.2.a.by.1.1 1 4.3 odd 2