# Properties

 Label 1710.2.a.n.1.1 Level $1710$ Weight $2$ Character 1710.1 Self dual yes Analytic conductor $13.654$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1710.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$13.6544187456$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 570) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1710.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -2.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{22} +8.00000 q^{23} +1.00000 q^{25} -2.00000 q^{28} +1.00000 q^{32} +2.00000 q^{34} +2.00000 q^{35} +4.00000 q^{37} +1.00000 q^{38} -1.00000 q^{40} +8.00000 q^{41} -6.00000 q^{43} +2.00000 q^{44} +8.00000 q^{46} +8.00000 q^{47} -3.00000 q^{49} +1.00000 q^{50} +10.0000 q^{53} -2.00000 q^{55} -2.00000 q^{56} +8.00000 q^{59} +2.00000 q^{61} +1.00000 q^{64} +2.00000 q^{68} +2.00000 q^{70} -8.00000 q^{71} -2.00000 q^{73} +4.00000 q^{74} +1.00000 q^{76} -4.00000 q^{77} -8.00000 q^{79} -1.00000 q^{80} +8.00000 q^{82} +16.0000 q^{83} -2.00000 q^{85} -6.00000 q^{86} +2.00000 q^{88} -16.0000 q^{89} +8.00000 q^{92} +8.00000 q^{94} -1.00000 q^{95} +8.00000 q^{97} -3.00000 q^{98} +O(q^{100})$$

## 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
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ 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
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ −2.00000 −0.534522
$$15$$ 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
$$19$$ 1.00000 0.229416
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ 2.00000 0.426401
$$23$$ 8.00000 1.66812 0.834058 0.551677i $$-0.186012\pi$$
0.834058 + 0.551677i $$0.186012\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ −2.00000 −0.377964
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 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
$$35$$ 2.00000 0.338062
$$36$$ 0 0
$$37$$ 4.00000 0.657596 0.328798 0.944400i $$-0.393356\pi$$
0.328798 + 0.944400i $$0.393356\pi$$
$$38$$ 1.00000 0.162221
$$39$$ 0 0
$$40$$ −1.00000 −0.158114
$$41$$ 8.00000 1.24939 0.624695 0.780869i $$-0.285223\pi$$
0.624695 + 0.780869i $$0.285223\pi$$
$$42$$ 0 0
$$43$$ −6.00000 −0.914991 −0.457496 0.889212i $$-0.651253\pi$$
−0.457496 + 0.889212i $$0.651253\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ 8.00000 1.16692 0.583460 0.812142i $$-0.301699\pi$$
0.583460 + 0.812142i $$0.301699\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 10.0000 1.37361 0.686803 0.726844i $$-0.259014\pi$$
0.686803 + 0.726844i $$0.259014\pi$$
$$54$$ 0 0
$$55$$ −2.00000 −0.269680
$$56$$ −2.00000 −0.267261
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 8.00000 1.04151 0.520756 0.853706i $$-0.325650\pi$$
0.520756 + 0.853706i $$0.325650\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 2.00000 0.242536
$$69$$ 0 0
$$70$$ 2.00000 0.239046
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ 0 0
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ 4.00000 0.464991
$$75$$ 0 0
$$76$$ 1.00000 0.114708
$$77$$ −4.00000 −0.455842
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ 8.00000 0.883452
$$83$$ 16.0000 1.75623 0.878114 0.478451i $$-0.158802\pi$$
0.878114 + 0.478451i $$0.158802\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ −6.00000 −0.646997
$$87$$ 0 0
$$88$$ 2.00000 0.213201
$$89$$ −16.0000 −1.69600 −0.847998 0.529999i $$-0.822192\pi$$
−0.847998 + 0.529999i $$0.822192\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 8.00000 0.834058
$$93$$ 0 0
$$94$$ 8.00000 0.825137
$$95$$ −1.00000 −0.102598
$$96$$ 0 0
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ −3.00000 −0.303046
$$99$$ 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
$$103$$ 12.0000 1.18240 0.591198 0.806527i $$-0.298655\pi$$
0.591198 + 0.806527i $$0.298655\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 10.0000 0.971286
$$107$$ −20.0000 −1.93347 −0.966736 0.255774i $$-0.917670\pi$$
−0.966736 + 0.255774i $$0.917670\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ −2.00000 −0.190693
$$111$$ 0 0
$$112$$ −2.00000 −0.188982
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ −8.00000 −0.746004
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 8.00000 0.736460
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 2.00000 0.181071
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 0 0
$$133$$ −2.00000 −0.173422
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ −18.0000 −1.53784 −0.768922 0.639343i $$-0.779207\pi$$
−0.768922 + 0.639343i $$0.779207\pi$$
$$138$$ 0 0
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 2.00000 0.169031
$$141$$ 0 0
$$142$$ −8.00000 −0.671345
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −2.00000 −0.165521
$$147$$ 0 0
$$148$$ 4.00000 0.328798
$$149$$ −2.00000 −0.163846 −0.0819232 0.996639i $$-0.526106\pi$$
−0.0819232 + 0.996639i $$0.526106\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 1.00000 0.0811107
$$153$$ 0 0
$$154$$ −4.00000 −0.322329
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −6.00000 −0.478852 −0.239426 0.970915i $$-0.576959\pi$$
−0.239426 + 0.970915i $$0.576959\pi$$
$$158$$ −8.00000 −0.636446
$$159$$ 0 0
$$160$$ −1.00000 −0.0790569
$$161$$ −16.0000 −1.26098
$$162$$ 0 0
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ 8.00000 0.624695
$$165$$ 0 0
$$166$$ 16.0000 1.24184
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ −2.00000 −0.153393
$$171$$ 0 0
$$172$$ −6.00000 −0.457496
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ −2.00000 −0.151186
$$176$$ 2.00000 0.150756
$$177$$ 0 0
$$178$$ −16.0000 −1.19925
$$179$$ 8.00000 0.597948 0.298974 0.954261i $$-0.403356\pi$$
0.298974 + 0.954261i $$0.403356\pi$$
$$180$$ 0 0
$$181$$ −6.00000 −0.445976 −0.222988 0.974821i $$-0.571581\pi$$
−0.222988 + 0.974821i $$0.571581\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 8.00000 0.589768
$$185$$ −4.00000 −0.294086
$$186$$ 0 0
$$187$$ 4.00000 0.292509
$$188$$ 8.00000 0.583460
$$189$$ 0 0
$$190$$ −1.00000 −0.0725476
$$191$$ −10.0000 −0.723575 −0.361787 0.932261i $$-0.617833\pi$$
−0.361787 + 0.932261i $$0.617833\pi$$
$$192$$ 0 0
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ 8.00000 0.574367
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ −10.0000 −0.712470 −0.356235 0.934396i $$-0.615940\pi$$
−0.356235 + 0.934396i $$0.615940\pi$$
$$198$$ 0 0
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 0 0
$$202$$ −2.00000 −0.140720
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −8.00000 −0.558744
$$206$$ 12.0000 0.836080
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 10.0000 0.686803
$$213$$ 0 0
$$214$$ −20.0000 −1.36717
$$215$$ 6.00000 0.409197
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 2.00000 0.135457
$$219$$ 0 0
$$220$$ −2.00000 −0.134840
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 12.0000 0.803579 0.401790 0.915732i $$-0.368388\pi$$
0.401790 + 0.915732i $$0.368388\pi$$
$$224$$ −2.00000 −0.133631
$$225$$ 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 $$0.392813\pi$$
$$230$$ −8.00000 −0.527504
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ −8.00000 −0.521862
$$236$$ 8.00000 0.520756
$$237$$ 0 0
$$238$$ −4.00000 −0.259281
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ 0 0
$$241$$ 10.0000 0.644157 0.322078 0.946713i $$-0.395619\pi$$
0.322078 + 0.946713i $$0.395619\pi$$
$$242$$ −7.00000 −0.449977
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ 3.00000 0.191663
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −1.00000 −0.0632456
$$251$$ −6.00000 −0.378717 −0.189358 0.981908i $$-0.560641\pi$$
−0.189358 + 0.981908i $$0.560641\pi$$
$$252$$ 0 0
$$253$$ 16.0000 1.00591
$$254$$ 16.0000 1.00393
$$255$$ 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
$$259$$ −8.00000 −0.497096
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 6.00000 0.370681
$$263$$ 12.0000 0.739952 0.369976 0.929041i $$-0.379366\pi$$
0.369976 + 0.929041i $$0.379366\pi$$
$$264$$ 0 0
$$265$$ −10.0000 −0.614295
$$266$$ −2.00000 −0.122628
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −8.00000 −0.487769 −0.243884 0.969804i $$-0.578422\pi$$
−0.243884 + 0.969804i $$0.578422\pi$$
$$270$$ 0 0
$$271$$ −4.00000 −0.242983 −0.121491 0.992592i $$-0.538768\pi$$
−0.121491 + 0.992592i $$0.538768\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ −18.0000 −1.08742
$$275$$ 2.00000 0.120605
$$276$$ 0 0
$$277$$ −14.0000 −0.841178 −0.420589 0.907251i $$-0.638177\pi$$
−0.420589 + 0.907251i $$0.638177\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 0 0
$$280$$ 2.00000 0.119523
$$281$$ 20.0000 1.19310 0.596550 0.802576i $$-0.296538\pi$$
0.596550 + 0.802576i $$0.296538\pi$$
$$282$$ 0 0
$$283$$ −2.00000 −0.118888 −0.0594438 0.998232i $$-0.518933\pi$$
−0.0594438 + 0.998232i $$0.518933\pi$$
$$284$$ −8.00000 −0.474713
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −16.0000 −0.944450
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −2.00000 −0.117041
$$293$$ 22.0000 1.28525 0.642627 0.766179i $$-0.277845\pi$$
0.642627 + 0.766179i $$0.277845\pi$$
$$294$$ 0 0
$$295$$ −8.00000 −0.465778
$$296$$ 4.00000 0.232495
$$297$$ 0 0
$$298$$ −2.00000 −0.115857
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 12.0000 0.691669
$$302$$ −8.00000 −0.460348
$$303$$ 0 0
$$304$$ 1.00000 0.0573539
$$305$$ −2.00000 −0.114520
$$306$$ 0 0
$$307$$ −24.0000 −1.36975 −0.684876 0.728659i $$-0.740144\pi$$
−0.684876 + 0.728659i $$0.740144\pi$$
$$308$$ −4.00000 −0.227921
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 14.0000 0.793867 0.396934 0.917847i $$-0.370074\pi$$
0.396934 + 0.917847i $$0.370074\pi$$
$$312$$ 0 0
$$313$$ 18.0000 1.01742 0.508710 0.860938i $$-0.330123\pi$$
0.508710 + 0.860938i $$0.330123\pi$$
$$314$$ −6.00000 −0.338600
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ −6.00000 −0.336994 −0.168497 0.985702i $$-0.553891\pi$$
−0.168497 + 0.985702i $$0.553891\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −1.00000 −0.0559017
$$321$$ 0 0
$$322$$ −16.0000 −0.891645
$$323$$ 2.00000 0.111283
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −10.0000 −0.553849
$$327$$ 0 0
$$328$$ 8.00000 0.441726
$$329$$ −16.0000 −0.882109
$$330$$ 0 0
$$331$$ −12.0000 −0.659580 −0.329790 0.944054i $$-0.606978\pi$$
−0.329790 + 0.944054i $$0.606978\pi$$
$$332$$ 16.0000 0.878114
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −16.0000 −0.871576 −0.435788 0.900049i $$-0.643530\pi$$
−0.435788 + 0.900049i $$0.643530\pi$$
$$338$$ −13.0000 −0.707107
$$339$$ 0 0
$$340$$ −2.00000 −0.108465
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 20.0000 1.07990
$$344$$ −6.00000 −0.323498
$$345$$ 0 0
$$346$$ 6.00000 0.322562
$$347$$ 8.00000 0.429463 0.214731 0.976673i $$-0.431112\pi$$
0.214731 + 0.976673i $$0.431112\pi$$
$$348$$ 0 0
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ −2.00000 −0.106904
$$351$$ 0 0
$$352$$ 2.00000 0.106600
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ 0 0
$$355$$ 8.00000 0.424596
$$356$$ −16.0000 −0.847998
$$357$$ 0 0
$$358$$ 8.00000 0.422813
$$359$$ 30.0000 1.58334 0.791670 0.610949i $$-0.209212\pi$$
0.791670 + 0.610949i $$0.209212\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ −6.00000 −0.315353
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.00000 0.104685
$$366$$ 0 0
$$367$$ 26.0000 1.35719 0.678594 0.734513i $$-0.262589\pi$$
0.678594 + 0.734513i $$0.262589\pi$$
$$368$$ 8.00000 0.417029
$$369$$ 0 0
$$370$$ −4.00000 −0.207950
$$371$$ −20.0000 −1.03835
$$372$$ 0 0
$$373$$ 32.0000 1.65690 0.828449 0.560065i $$-0.189224\pi$$
0.828449 + 0.560065i $$0.189224\pi$$
$$374$$ 4.00000 0.206835
$$375$$ 0 0
$$376$$ 8.00000 0.412568
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ −1.00000 −0.0512989
$$381$$ 0 0
$$382$$ −10.0000 −0.511645
$$383$$ −8.00000 −0.408781 −0.204390 0.978889i $$-0.565521\pi$$
−0.204390 + 0.978889i $$0.565521\pi$$
$$384$$ 0 0
$$385$$ 4.00000 0.203859
$$386$$ −4.00000 −0.203595
$$387$$ 0 0
$$388$$ 8.00000 0.406138
$$389$$ −14.0000 −0.709828 −0.354914 0.934899i $$-0.615490\pi$$
−0.354914 + 0.934899i $$0.615490\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ −3.00000 −0.151523
$$393$$ 0 0
$$394$$ −10.0000 −0.503793
$$395$$ 8.00000 0.402524
$$396$$ 0 0
$$397$$ −6.00000 −0.301131 −0.150566 0.988600i $$-0.548110\pi$$
−0.150566 + 0.988600i $$0.548110\pi$$
$$398$$ −4.00000 −0.200502
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 12.0000 0.599251 0.299626 0.954057i $$-0.403138\pi$$
0.299626 + 0.954057i $$0.403138\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −2.00000 −0.0995037
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 8.00000 0.396545
$$408$$ 0 0
$$409$$ −18.0000 −0.890043 −0.445021 0.895520i $$-0.646804\pi$$
−0.445021 + 0.895520i $$0.646804\pi$$
$$410$$ −8.00000 −0.395092
$$411$$ 0 0
$$412$$ 12.0000 0.591198
$$413$$ −16.0000 −0.787309
$$414$$ 0 0
$$415$$ −16.0000 −0.785409
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 2.00000 0.0978232
$$419$$ −30.0000 −1.46560 −0.732798 0.680446i $$-0.761786\pi$$
−0.732798 + 0.680446i $$0.761786\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 4.00000 0.194717
$$423$$ 0 0
$$424$$ 10.0000 0.485643
$$425$$ 2.00000 0.0970143
$$426$$ 0 0
$$427$$ −4.00000 −0.193574
$$428$$ −20.0000 −0.966736
$$429$$ 0 0
$$430$$ 6.00000 0.289346
$$431$$ −20.0000 −0.963366 −0.481683 0.876346i $$-0.659974\pi$$
−0.481683 + 0.876346i $$0.659974\pi$$
$$432$$ 0 0
$$433$$ −12.0000 −0.576683 −0.288342 0.957528i $$-0.593104\pi$$
−0.288342 + 0.957528i $$0.593104\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 2.00000 0.0957826
$$437$$ 8.00000 0.382692
$$438$$ 0 0
$$439$$ 16.0000 0.763638 0.381819 0.924237i $$-0.375298\pi$$
0.381819 + 0.924237i $$0.375298\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −12.0000 −0.570137 −0.285069 0.958507i $$-0.592016\pi$$
−0.285069 + 0.958507i $$0.592016\pi$$
$$444$$ 0 0
$$445$$ 16.0000 0.758473
$$446$$ 12.0000 0.568216
$$447$$ 0 0
$$448$$ −2.00000 −0.0944911
$$449$$ −24.0000 −1.13263 −0.566315 0.824189i $$-0.691631\pi$$
−0.566315 + 0.824189i $$0.691631\pi$$
$$450$$ 0 0
$$451$$ 16.0000 0.753411
$$452$$ 2.00000 0.0940721
$$453$$ 0 0
$$454$$ 4.00000 0.187729
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −22.0000 −1.02912 −0.514558 0.857455i $$-0.672044\pi$$
−0.514558 + 0.857455i $$0.672044\pi$$
$$458$$ 10.0000 0.467269
$$459$$ 0 0
$$460$$ −8.00000 −0.373002
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ 18.0000 0.836531 0.418265 0.908325i $$-0.362638\pi$$
0.418265 + 0.908325i $$0.362638\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 6.00000 0.277945
$$467$$ −20.0000 −0.925490 −0.462745 0.886492i $$-0.653135\pi$$
−0.462745 + 0.886492i $$0.653135\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −8.00000 −0.369012
$$471$$ 0 0
$$472$$ 8.00000 0.368230
$$473$$ −12.0000 −0.551761
$$474$$ 0 0
$$475$$ 1.00000 0.0458831
$$476$$ −4.00000 −0.183340
$$477$$ 0 0
$$478$$ −6.00000 −0.274434
$$479$$ 30.0000 1.37073 0.685367 0.728197i $$-0.259642\pi$$
0.685367 + 0.728197i $$0.259642\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 10.0000 0.455488
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ −8.00000 −0.363261
$$486$$ 0 0
$$487$$ 20.0000 0.906287 0.453143 0.891438i $$-0.350303\pi$$
0.453143 + 0.891438i $$0.350303\pi$$
$$488$$ 2.00000 0.0905357
$$489$$ 0 0
$$490$$ 3.00000 0.135526
$$491$$ 30.0000 1.35388 0.676941 0.736038i $$-0.263305\pi$$
0.676941 + 0.736038i $$0.263305\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 16.0000 0.717698
$$498$$ 0 0
$$499$$ −16.0000 −0.716258 −0.358129 0.933672i $$-0.616585\pi$$
−0.358129 + 0.933672i $$0.616585\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 0 0
$$502$$ −6.00000 −0.267793
$$503$$ −28.0000 −1.24846 −0.624229 0.781241i $$-0.714587\pi$$
−0.624229 + 0.781241i $$0.714587\pi$$
$$504$$ 0 0
$$505$$ 2.00000 0.0889988
$$506$$ 16.0000 0.711287
$$507$$ 0 0
$$508$$ 16.0000 0.709885
$$509$$ −20.0000 −0.886484 −0.443242 0.896402i $$-0.646172\pi$$
−0.443242 + 0.896402i $$0.646172\pi$$
$$510$$ 0 0
$$511$$ 4.00000 0.176950
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −30.0000 −1.32324
$$515$$ −12.0000 −0.528783
$$516$$ 0 0
$$517$$ 16.0000 0.703679
$$518$$ −8.00000 −0.351500
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 20.0000 0.876216 0.438108 0.898922i $$-0.355649\pi$$
0.438108 + 0.898922i $$0.355649\pi$$
$$522$$ 0 0
$$523$$ 28.0000 1.22435 0.612177 0.790721i $$-0.290294\pi$$
0.612177 + 0.790721i $$0.290294\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ 12.0000 0.523225
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 41.0000 1.78261
$$530$$ −10.0000 −0.434372
$$531$$ 0 0
$$532$$ −2.00000 −0.0867110
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 20.0000 0.864675
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −8.00000 −0.344904
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 14.0000 0.601907 0.300954 0.953639i $$-0.402695\pi$$
0.300954 + 0.953639i $$0.402695\pi$$
$$542$$ −4.00000 −0.171815
$$543$$ 0 0
$$544$$ 2.00000 0.0857493
$$545$$ −2.00000 −0.0856706
$$546$$ 0 0
$$547$$ −40.0000 −1.71028 −0.855138 0.518400i $$-0.826528\pi$$
−0.855138 + 0.518400i $$0.826528\pi$$
$$548$$ −18.0000 −0.768922
$$549$$ 0 0
$$550$$ 2.00000 0.0852803
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ −14.0000 −0.594803
$$555$$ 0 0
$$556$$ 8.00000 0.339276
$$557$$ 2.00000 0.0847427 0.0423714 0.999102i $$-0.486509\pi$$
0.0423714 + 0.999102i $$0.486509\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 2.00000 0.0845154
$$561$$ 0 0
$$562$$ 20.0000 0.843649
$$563$$ 36.0000 1.51722 0.758610 0.651546i $$-0.225879\pi$$
0.758610 + 0.651546i $$0.225879\pi$$
$$564$$ 0 0
$$565$$ −2.00000 −0.0841406
$$566$$ −2.00000 −0.0840663
$$567$$ 0 0
$$568$$ −8.00000 −0.335673
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −16.0000 −0.667827
$$575$$ 8.00000 0.333623
$$576$$ 0 0
$$577$$ −14.0000 −0.582828 −0.291414 0.956597i $$-0.594126\pi$$
−0.291414 + 0.956597i $$0.594126\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −32.0000 −1.32758
$$582$$ 0 0
$$583$$ 20.0000 0.828315
$$584$$ −2.00000 −0.0827606
$$585$$ 0 0
$$586$$ 22.0000 0.908812
$$587$$ 44.0000 1.81607 0.908037 0.418890i $$-0.137581\pi$$
0.908037 + 0.418890i $$0.137581\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −8.00000 −0.329355
$$591$$ 0 0
$$592$$ 4.00000 0.164399
$$593$$ −34.0000 −1.39621 −0.698106 0.715994i $$-0.745974\pi$$
−0.698106 + 0.715994i $$0.745974\pi$$
$$594$$ 0 0
$$595$$ 4.00000 0.163984
$$596$$ −2.00000 −0.0819232
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 4.00000 0.163436 0.0817178 0.996656i $$-0.473959\pi$$
0.0817178 + 0.996656i $$0.473959\pi$$
$$600$$ 0 0
$$601$$ −42.0000 −1.71322 −0.856608 0.515968i $$-0.827432\pi$$
−0.856608 + 0.515968i $$0.827432\pi$$
$$602$$ 12.0000 0.489083
$$603$$ 0 0
$$604$$ −8.00000 −0.325515
$$605$$ 7.00000 0.284590
$$606$$ 0 0
$$607$$ 44.0000 1.78590 0.892952 0.450151i $$-0.148630\pi$$
0.892952 + 0.450151i $$0.148630\pi$$
$$608$$ 1.00000 0.0405554
$$609$$ 0 0
$$610$$ −2.00000 −0.0809776
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −46.0000 −1.85792 −0.928961 0.370177i $$-0.879297\pi$$
−0.928961 + 0.370177i $$0.879297\pi$$
$$614$$ −24.0000 −0.968561
$$615$$ 0 0
$$616$$ −4.00000 −0.161165
$$617$$ 42.0000 1.69086 0.845428 0.534089i $$-0.179345\pi$$
0.845428 + 0.534089i $$0.179345\pi$$
$$618$$ 0 0
$$619$$ −32.0000 −1.28619 −0.643094 0.765787i $$-0.722350\pi$$
−0.643094 + 0.765787i $$0.722350\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 14.0000 0.561349
$$623$$ 32.0000 1.28205
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 18.0000 0.719425
$$627$$ 0 0
$$628$$ −6.00000 −0.239426
$$629$$ 8.00000 0.318981
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ −8.00000 −0.318223
$$633$$ 0 0
$$634$$ −6.00000 −0.238290
$$635$$ −16.0000 −0.634941
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.00000 −0.0395285
$$641$$ −16.0000 −0.631962 −0.315981 0.948766i $$-0.602334\pi$$
−0.315981 + 0.948766i $$0.602334\pi$$
$$642$$ 0 0
$$643$$ 46.0000 1.81406 0.907031 0.421063i $$-0.138343\pi$$
0.907031 + 0.421063i $$0.138343\pi$$
$$644$$ −16.0000 −0.630488
$$645$$ 0 0
$$646$$ 2.00000 0.0786889
$$647$$ −36.0000 −1.41531 −0.707653 0.706560i $$-0.750246\pi$$
−0.707653 + 0.706560i $$0.750246\pi$$
$$648$$ 0 0
$$649$$ 16.0000 0.628055
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −10.0000 −0.391630
$$653$$ 30.0000 1.17399 0.586995 0.809590i $$-0.300311\pi$$
0.586995 + 0.809590i $$0.300311\pi$$
$$654$$ 0 0
$$655$$ −6.00000 −0.234439
$$656$$ 8.00000 0.312348
$$657$$ 0 0
$$658$$ −16.0000 −0.623745
$$659$$ 44.0000 1.71400 0.856998 0.515319i $$-0.172327\pi$$
0.856998 + 0.515319i $$0.172327\pi$$
$$660$$ 0 0
$$661$$ −38.0000 −1.47803 −0.739014 0.673690i $$-0.764708\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ −12.0000 −0.466393
$$663$$ 0 0
$$664$$ 16.0000 0.620920
$$665$$ 2.00000 0.0775567
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ −16.0000 −0.616755 −0.308377 0.951264i $$-0.599786\pi$$
−0.308377 + 0.951264i $$0.599786\pi$$
$$674$$ −16.0000 −0.616297
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ 0 0
$$679$$ −16.0000 −0.614024
$$680$$ −2.00000 −0.0766965
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ 18.0000 0.687745
$$686$$ 20.0000 0.763604
$$687$$ 0 0
$$688$$ −6.00000 −0.228748
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 40.0000 1.52167 0.760836 0.648944i $$-0.224789\pi$$
0.760836 + 0.648944i $$0.224789\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ 8.00000 0.303676
$$695$$ −8.00000 −0.303457
$$696$$ 0 0
$$697$$ 16.0000 0.606043
$$698$$ −26.0000 −0.984115
$$699$$ 0 0
$$700$$ −2.00000 −0.0755929
$$701$$ 38.0000 1.43524 0.717620 0.696435i $$-0.245231\pi$$
0.717620 + 0.696435i $$0.245231\pi$$
$$702$$ 0 0
$$703$$ 4.00000 0.150863
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ 4.00000 0.150435
$$708$$ 0 0
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 8.00000 0.300235
$$711$$ 0 0
$$712$$ −16.0000 −0.599625
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 8.00000 0.298974
$$717$$ 0 0
$$718$$ 30.0000 1.11959
$$719$$ −22.0000 −0.820462 −0.410231 0.911982i $$-0.634552\pi$$
−0.410231 + 0.911982i $$0.634552\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ 1.00000 0.0372161
$$723$$ 0 0
$$724$$ −6.00000 −0.222988
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −22.0000 −0.815935 −0.407967 0.912996i $$-0.633762\pi$$
−0.407967 + 0.912996i $$0.633762\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 2.00000 0.0740233
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ −26.0000 −0.960332 −0.480166 0.877178i $$-0.659424\pi$$
−0.480166 + 0.877178i $$0.659424\pi$$
$$734$$ 26.0000 0.959678
$$735$$ 0 0
$$736$$ 8.00000 0.294884
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −20.0000 −0.735712 −0.367856 0.929883i $$-0.619908\pi$$
−0.367856 + 0.929883i $$0.619908\pi$$
$$740$$ −4.00000 −0.147043
$$741$$ 0 0
$$742$$ −20.0000 −0.734223
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ 2.00000 0.0732743
$$746$$ 32.0000 1.17160
$$747$$ 0 0
$$748$$ 4.00000 0.146254
$$749$$ 40.0000 1.46157
$$750$$ 0 0
$$751$$ −8.00000 −0.291924 −0.145962 0.989290i $$-0.546628\pi$$
−0.145962 + 0.989290i $$0.546628\pi$$
$$752$$ 8.00000 0.291730
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ −28.0000 −1.01701
$$759$$ 0 0
$$760$$ −1.00000 −0.0362738
$$761$$ 10.0000 0.362500 0.181250 0.983437i $$-0.441986\pi$$
0.181250 + 0.983437i $$0.441986\pi$$
$$762$$ 0 0
$$763$$ −4.00000 −0.144810
$$764$$ −10.0000 −0.361787
$$765$$ 0 0
$$766$$ −8.00000 −0.289052
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 18.0000 0.649097 0.324548 0.945869i $$-0.394788\pi$$
0.324548 + 0.945869i $$0.394788\pi$$
$$770$$ 4.00000 0.144150
$$771$$ 0 0
$$772$$ −4.00000 −0.143963
$$773$$ 42.0000 1.51064 0.755318 0.655359i $$-0.227483\pi$$
0.755318 + 0.655359i $$0.227483\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 8.00000 0.287183
$$777$$ 0 0
$$778$$ −14.0000 −0.501924
$$779$$ 8.00000 0.286630
$$780$$ 0 0
$$781$$ −16.0000 −0.572525
$$782$$ 16.0000 0.572159
$$783$$ 0 0
$$784$$ −3.00000 −0.107143
$$785$$ 6.00000 0.214149
$$786$$ 0 0
$$787$$ 52.0000 1.85360 0.926800 0.375555i $$-0.122548\pi$$
0.926800 + 0.375555i $$0.122548\pi$$
$$788$$ −10.0000 −0.356235
$$789$$ 0 0
$$790$$ 8.00000 0.284627
$$791$$ −4.00000 −0.142224
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −6.00000 −0.212932
$$795$$ 0 0
$$796$$ −4.00000 −0.141776
$$797$$ 22.0000 0.779280 0.389640 0.920967i $$-0.372599\pi$$
0.389640 + 0.920967i $$0.372599\pi$$
$$798$$ 0 0
$$799$$ 16.0000 0.566039
$$800$$ 1.00000 0.0353553
$$801$$ 0 0
$$802$$ 12.0000 0.423735
$$803$$ −4.00000 −0.141157
$$804$$ 0 0
$$805$$ 16.0000 0.563926
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −2.00000 −0.0703598
$$809$$ −18.0000 −0.632846 −0.316423 0.948618i $$-0.602482\pi$$
−0.316423 + 0.948618i $$0.602482\pi$$
$$810$$ 0 0
$$811$$ 28.0000 0.983213 0.491606 0.870817i $$-0.336410\pi$$
0.491606 + 0.870817i $$0.336410\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 8.00000 0.280400
$$815$$ 10.0000 0.350285
$$816$$ 0 0
$$817$$ −6.00000 −0.209913
$$818$$ −18.0000 −0.629355
$$819$$ 0 0
$$820$$ −8.00000 −0.279372
$$821$$ 6.00000 0.209401 0.104701 0.994504i $$-0.466612\pi$$
0.104701 + 0.994504i $$0.466612\pi$$
$$822$$ 0 0
$$823$$ 34.0000 1.18517 0.592583 0.805510i $$-0.298108\pi$$
0.592583 + 0.805510i $$0.298108\pi$$
$$824$$ 12.0000 0.418040
$$825$$ 0 0
$$826$$ −16.0000 −0.556711
$$827$$ −12.0000 −0.417281 −0.208640 0.977992i $$-0.566904\pi$$
−0.208640 + 0.977992i $$0.566904\pi$$
$$828$$ 0 0
$$829$$ −46.0000 −1.59765 −0.798823 0.601566i $$-0.794544\pi$$
−0.798823 + 0.601566i $$0.794544\pi$$
$$830$$ −16.0000 −0.555368
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −6.00000 −0.207888
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 2.00000 0.0691714
$$837$$ 0 0
$$838$$ −30.0000 −1.03633
$$839$$ −24.0000 −0.828572 −0.414286 0.910147i $$-0.635969\pi$$
−0.414286 + 0.910147i $$0.635969\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ −26.0000 −0.896019
$$843$$ 0 0
$$844$$ 4.00000 0.137686
$$845$$ 13.0000 0.447214
$$846$$ 0 0
$$847$$ 14.0000 0.481046
$$848$$ 10.0000 0.343401
$$849$$ 0 0
$$850$$ 2.00000 0.0685994
$$851$$ 32.0000 1.09695
$$852$$ 0 0
$$853$$ 6.00000 0.205436 0.102718 0.994711i $$-0.467246\pi$$
0.102718 + 0.994711i $$0.467246\pi$$
$$854$$ −4.00000 −0.136877
$$855$$ 0 0
$$856$$ −20.0000 −0.683586
$$857$$ 30.0000 1.02478 0.512390 0.858753i $$-0.328760\pi$$
0.512390 + 0.858753i $$0.328760\pi$$
$$858$$ 0 0
$$859$$ −20.0000 −0.682391 −0.341196 0.939992i $$-0.610832\pi$$
−0.341196 + 0.939992i $$0.610832\pi$$
$$860$$ 6.00000 0.204598
$$861$$ 0 0
$$862$$ −20.0000 −0.681203
$$863$$ 16.0000 0.544646 0.272323 0.962206i $$-0.412208\pi$$
0.272323 + 0.962206i $$0.412208\pi$$
$$864$$ 0 0
$$865$$ −6.00000 −0.204006
$$866$$ −12.0000 −0.407777
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −16.0000 −0.542763
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 2.00000 0.0677285
$$873$$ 0 0
$$874$$ 8.00000 0.270604
$$875$$ 2.00000 0.0676123
$$876$$ 0 0
$$877$$ 8.00000 0.270141 0.135070 0.990836i $$-0.456874\pi$$
0.135070 + 0.990836i $$0.456874\pi$$
$$878$$ 16.0000 0.539974
$$879$$ 0 0
$$880$$ −2.00000 −0.0674200
$$881$$ −30.0000 −1.01073 −0.505363 0.862907i $$-0.668641\pi$$
−0.505363 + 0.862907i $$0.668641\pi$$
$$882$$ 0 0
$$883$$ −18.0000 −0.605748 −0.302874 0.953031i $$-0.597946\pi$$
−0.302874 + 0.953031i $$0.597946\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ −12.0000 −0.403148
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ 0 0
$$889$$ −32.0000 −1.07325
$$890$$ 16.0000 0.536321
$$891$$ 0 0
$$892$$ 12.0000 0.401790
$$893$$ 8.00000 0.267710
$$894$$ 0 0
$$895$$ −8.00000 −0.267411
$$896$$ −2.00000 −0.0668153
$$897$$ 0 0
$$898$$ −24.0000 −0.800890
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 20.0000 0.666297
$$902$$ 16.0000 0.532742
$$903$$ 0 0
$$904$$ 2.00000 0.0665190
$$905$$ 6.00000 0.199447
$$906$$ 0 0
$$907$$ −44.0000 −1.46100 −0.730498 0.682915i $$-0.760712\pi$$
−0.730498 + 0.682915i $$0.760712\pi$$
$$908$$ 4.00000 0.132745
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −48.0000 −1.59031 −0.795155 0.606406i $$-0.792611\pi$$
−0.795155 + 0.606406i $$0.792611\pi$$
$$912$$ 0 0
$$913$$ 32.0000 1.05905
$$914$$ −22.0000 −0.727695
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ −12.0000 −0.396275
$$918$$ 0 0
$$919$$ 40.0000 1.31948 0.659739 0.751495i $$-0.270667\pi$$
0.659739 + 0.751495i $$0.270667\pi$$
$$920$$ −8.00000 −0.263752
$$921$$ 0 0
$$922$$ 6.00000 0.197599
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 4.00000 0.131519
$$926$$ 18.0000 0.591517
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 6.00000 0.196854 0.0984268 0.995144i $$-0.468619\pi$$
0.0984268 + 0.995144i $$0.468619\pi$$
$$930$$ 0 0
$$931$$ −3.00000 −0.0983210
$$932$$ 6.00000 0.196537
$$933$$ 0 0
$$934$$ −20.0000 −0.654420
$$935$$ −4.00000 −0.130814
$$936$$ 0 0
$$937$$ −58.0000 −1.89478 −0.947389 0.320085i $$-0.896288\pi$$
−0.947389 + 0.320085i $$0.896288\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ −8.00000 −0.260931
$$941$$ −16.0000 −0.521585 −0.260793 0.965395i $$-0.583984\pi$$
−0.260793 + 0.965395i $$0.583984\pi$$
$$942$$ 0 0
$$943$$ 64.0000 2.08413
$$944$$ 8.00000 0.260378
$$945$$ 0 0
$$946$$ −12.0000 −0.390154
$$947$$ 32.0000 1.03986 0.519930 0.854209i $$-0.325958\pi$$
0.519930 + 0.854209i $$0.325958\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 1.00000 0.0324443
$$951$$ 0 0
$$952$$ −4.00000 −0.129641
$$953$$ 18.0000 0.583077 0.291539 0.956559i $$-0.405833\pi$$
0.291539 + 0.956559i $$0.405833\pi$$
$$954$$ 0 0
$$955$$ 10.0000 0.323592
$$956$$ −6.00000 −0.194054
$$957$$ 0 0
$$958$$ 30.0000 0.969256
$$959$$ 36.0000 1.16250
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 10.0000 0.322078
$$965$$ 4.00000 0.128765
$$966$$ 0 0
$$967$$ −6.00000 −0.192947 −0.0964735 0.995336i $$-0.530756\pi$$
−0.0964735 + 0.995336i $$0.530756\pi$$
$$968$$ −7.00000 −0.224989
$$969$$ 0 0
$$970$$ −8.00000 −0.256865
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ 0 0
$$973$$ −16.0000 −0.512936
$$974$$ 20.0000 0.640841
$$975$$ 0 0
$$976$$ 2.00000 0.0640184
$$977$$ −18.0000 −0.575871 −0.287936 0.957650i $$-0.592969\pi$$
−0.287936 + 0.957650i $$0.592969\pi$$
$$978$$ 0 0
$$979$$ −32.0000 −1.02272
$$980$$ 3.00000 0.0958315
$$981$$ 0 0
$$982$$ 30.0000 0.957338
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 10.0000 0.318626
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −48.0000 −1.52631
$$990$$ 0 0
$$991$$ 40.0000 1.27064 0.635321 0.772248i $$-0.280868\pi$$
0.635321 + 0.772248i $$0.280868\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 16.0000 0.507489
$$995$$ 4.00000 0.126809
$$996$$ 0 0
$$997$$ −22.0000 −0.696747 −0.348373 0.937356i $$-0.613266\pi$$
−0.348373 + 0.937356i $$0.613266\pi$$
$$998$$ −16.0000 −0.506471
$$999$$ 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 1710.2.a.n.1.1 1
3.2 odd 2 570.2.a.c.1.1 1
5.4 even 2 8550.2.a.o.1.1 1
12.11 even 2 4560.2.a.bd.1.1 1
15.2 even 4 2850.2.d.n.799.1 2
15.8 even 4 2850.2.d.n.799.2 2
15.14 odd 2 2850.2.a.ba.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.c.1.1 1 3.2 odd 2
1710.2.a.n.1.1 1 1.1 even 1 trivial
2850.2.a.ba.1.1 1 15.14 odd 2
2850.2.d.n.799.1 2 15.2 even 4
2850.2.d.n.799.2 2 15.8 even 4
4560.2.a.bd.1.1 1 12.11 even 2
8550.2.a.o.1.1 1 5.4 even 2