# Properties

 Label 2070.2.a.c.1.1 Level $2070$ Weight $2$ Character 2070.1 Self dual yes Analytic conductor $16.529$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2070.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$16.5290332184$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 690) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2070.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{8} +1.00000 q^{10} +2.00000 q^{11} +4.00000 q^{13} +1.00000 q^{16} -6.00000 q^{17} -8.00000 q^{19} -1.00000 q^{20} -2.00000 q^{22} +1.00000 q^{23} +1.00000 q^{25} -4.00000 q^{26} -4.00000 q^{29} -1.00000 q^{32} +6.00000 q^{34} -2.00000 q^{37} +8.00000 q^{38} +1.00000 q^{40} +2.00000 q^{41} +2.00000 q^{43} +2.00000 q^{44} -1.00000 q^{46} +12.0000 q^{47} -7.00000 q^{49} -1.00000 q^{50} +4.00000 q^{52} +6.00000 q^{53} -2.00000 q^{55} +4.00000 q^{58} -8.00000 q^{59} +2.00000 q^{61} +1.00000 q^{64} -4.00000 q^{65} -6.00000 q^{67} -6.00000 q^{68} -10.0000 q^{71} -2.00000 q^{73} +2.00000 q^{74} -8.00000 q^{76} -8.00000 q^{79} -1.00000 q^{80} -2.00000 q^{82} -8.00000 q^{83} +6.00000 q^{85} -2.00000 q^{86} -2.00000 q^{88} +12.0000 q^{89} +1.00000 q^{92} -12.0000 q^{94} +8.00000 q^{95} -16.0000 q^{97} +7.00000 q^{98} +O(q^{100})$$

## 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
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ −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
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ −8.00000 −1.83533 −0.917663 0.397360i $$-0.869927\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ 1.00000 0.208514
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ −4.00000 −0.784465
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 8.00000 1.29777
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ −1.00000 −0.147442
$$47$$ 12.0000 1.75038 0.875190 0.483779i $$-0.160736\pi$$
0.875190 + 0.483779i $$0.160736\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ 4.00000 0.554700
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ −2.00000 −0.269680
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 4.00000 0.525226
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 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
$$65$$ −4.00000 −0.496139
$$66$$ 0 0
$$67$$ −6.00000 −0.733017 −0.366508 0.930415i $$-0.619447\pi$$
−0.366508 + 0.930415i $$0.619447\pi$$
$$68$$ −6.00000 −0.727607
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ 0 0
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ 2.00000 0.232495
$$75$$ 0 0
$$76$$ −8.00000 −0.917663
$$77$$ 0 0
$$78$$ 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
$$82$$ −2.00000 −0.220863
$$83$$ −8.00000 −0.878114 −0.439057 0.898459i $$-0.644687\pi$$
−0.439057 + 0.898459i $$0.644687\pi$$
$$84$$ 0 0
$$85$$ 6.00000 0.650791
$$86$$ −2.00000 −0.215666
$$87$$ 0 0
$$88$$ −2.00000 −0.213201
$$89$$ 12.0000 1.27200 0.635999 0.771690i $$-0.280588\pi$$
0.635999 + 0.771690i $$0.280588\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 1.00000 0.104257
$$93$$ 0 0
$$94$$ −12.0000 −1.23771
$$95$$ 8.00000 0.820783
$$96$$ 0 0
$$97$$ −16.0000 −1.62455 −0.812277 0.583272i $$-0.801772\pi$$
−0.812277 + 0.583272i $$0.801772\pi$$
$$98$$ 7.00000 0.707107
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ −12.0000 −1.19404 −0.597022 0.802225i $$-0.703650\pi$$
−0.597022 + 0.802225i $$0.703650\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ −4.00000 −0.392232
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 2.00000 0.190693
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −18.0000 −1.69330 −0.846649 0.532152i $$-0.821383\pi$$
−0.846649 + 0.532152i $$0.821383\pi$$
$$114$$ 0 0
$$115$$ −1.00000 −0.0932505
$$116$$ −4.00000 −0.371391
$$117$$ 0 0
$$118$$ 8.00000 0.736460
$$119$$ 0 0
$$120$$ 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
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 4.00000 0.350823
$$131$$ 4.00000 0.349482 0.174741 0.984614i $$-0.444091\pi$$
0.174741 + 0.984614i $$0.444091\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 6.00000 0.518321
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ −2.00000 −0.170872 −0.0854358 0.996344i $$-0.527228\pi$$
−0.0854358 + 0.996344i $$0.527228\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 10.0000 0.839181
$$143$$ 8.00000 0.668994
$$144$$ 0 0
$$145$$ 4.00000 0.332182
$$146$$ 2.00000 0.165521
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ −14.0000 −1.14692 −0.573462 0.819232i $$-0.694400\pi$$
−0.573462 + 0.819232i $$0.694400\pi$$
$$150$$ 0 0
$$151$$ −4.00000 −0.325515 −0.162758 0.986666i $$-0.552039\pi$$
−0.162758 + 0.986666i $$0.552039\pi$$
$$152$$ 8.00000 0.648886
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −10.0000 −0.798087 −0.399043 0.916932i $$-0.630658\pi$$
−0.399043 + 0.916932i $$0.630658\pi$$
$$158$$ 8.00000 0.636446
$$159$$ 0 0
$$160$$ 1.00000 0.0790569
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −16.0000 −1.25322 −0.626608 0.779334i $$-0.715557\pi$$
−0.626608 + 0.779334i $$0.715557\pi$$
$$164$$ 2.00000 0.156174
$$165$$ 0 0
$$166$$ 8.00000 0.620920
$$167$$ 16.0000 1.23812 0.619059 0.785345i $$-0.287514\pi$$
0.619059 + 0.785345i $$0.287514\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ −6.00000 −0.460179
$$171$$ 0 0
$$172$$ 2.00000 0.152499
$$173$$ 10.0000 0.760286 0.380143 0.924928i $$-0.375875\pi$$
0.380143 + 0.924928i $$0.375875\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 2.00000 0.150756
$$177$$ 0 0
$$178$$ −12.0000 −0.899438
$$179$$ −16.0000 −1.19590 −0.597948 0.801535i $$-0.704017\pi$$
−0.597948 + 0.801535i $$0.704017\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −1.00000 −0.0737210
$$185$$ 2.00000 0.147043
$$186$$ 0 0
$$187$$ −12.0000 −0.877527
$$188$$ 12.0000 0.875190
$$189$$ 0 0
$$190$$ −8.00000 −0.580381
$$191$$ −24.0000 −1.73658 −0.868290 0.496058i $$-0.834780\pi$$
−0.868290 + 0.496058i $$0.834780\pi$$
$$192$$ 0 0
$$193$$ 26.0000 1.87152 0.935760 0.352636i $$-0.114715\pi$$
0.935760 + 0.352636i $$0.114715\pi$$
$$194$$ 16.0000 1.14873
$$195$$ 0 0
$$196$$ −7.00000 −0.500000
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ 0 0
$$202$$ 12.0000 0.844317
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −2.00000 −0.139686
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 4.00000 0.277350
$$209$$ −16.0000 −1.10674
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 6.00000 0.412082
$$213$$ 0 0
$$214$$ −12.0000 −0.820303
$$215$$ −2.00000 −0.136399
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 10.0000 0.677285
$$219$$ 0 0
$$220$$ −2.00000 −0.134840
$$221$$ −24.0000 −1.61441
$$222$$ 0 0
$$223$$ −2.00000 −0.133930 −0.0669650 0.997755i $$-0.521332\pi$$
−0.0669650 + 0.997755i $$0.521332\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 18.0000 1.19734
$$227$$ −28.0000 −1.85843 −0.929213 0.369546i $$-0.879513\pi$$
−0.929213 + 0.369546i $$0.879513\pi$$
$$228$$ 0 0
$$229$$ −10.0000 −0.660819 −0.330409 0.943838i $$-0.607187\pi$$
−0.330409 + 0.943838i $$0.607187\pi$$
$$230$$ 1.00000 0.0659380
$$231$$ 0 0
$$232$$ 4.00000 0.262613
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ −12.0000 −0.782794
$$236$$ −8.00000 −0.520756
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 14.0000 0.905585 0.452792 0.891616i $$-0.350428\pi$$
0.452792 + 0.891616i $$0.350428\pi$$
$$240$$ 0 0
$$241$$ −6.00000 −0.386494 −0.193247 0.981150i $$-0.561902\pi$$
−0.193247 + 0.981150i $$0.561902\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ 7.00000 0.447214
$$246$$ 0 0
$$247$$ −32.0000 −2.03611
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 1.00000 0.0632456
$$251$$ −2.00000 −0.126239 −0.0631194 0.998006i $$-0.520105\pi$$
−0.0631194 + 0.998006i $$0.520105\pi$$
$$252$$ 0 0
$$253$$ 2.00000 0.125739
$$254$$ −2.00000 −0.125491
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −22.0000 −1.37232 −0.686161 0.727450i $$-0.740706\pi$$
−0.686161 + 0.727450i $$0.740706\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −4.00000 −0.248069
$$261$$ 0 0
$$262$$ −4.00000 −0.247121
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −6.00000 −0.366508
$$269$$ −8.00000 −0.487769 −0.243884 0.969804i $$-0.578422\pi$$
−0.243884 + 0.969804i $$0.578422\pi$$
$$270$$ 0 0
$$271$$ 24.0000 1.45790 0.728948 0.684569i $$-0.240010\pi$$
0.728948 + 0.684569i $$0.240010\pi$$
$$272$$ −6.00000 −0.363803
$$273$$ 0 0
$$274$$ 2.00000 0.120824
$$275$$ 2.00000 0.120605
$$276$$ 0 0
$$277$$ −28.0000 −1.68236 −0.841178 0.540758i $$-0.818138\pi$$
−0.841178 + 0.540758i $$0.818138\pi$$
$$278$$ −4.00000 −0.239904
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 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
$$286$$ −8.00000 −0.473050
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ −4.00000 −0.234888
$$291$$ 0 0
$$292$$ −2.00000 −0.117041
$$293$$ 14.0000 0.817889 0.408944 0.912559i $$-0.365897\pi$$
0.408944 + 0.912559i $$0.365897\pi$$
$$294$$ 0 0
$$295$$ 8.00000 0.465778
$$296$$ 2.00000 0.116248
$$297$$ 0 0
$$298$$ 14.0000 0.810998
$$299$$ 4.00000 0.231326
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 4.00000 0.230174
$$303$$ 0 0
$$304$$ −8.00000 −0.458831
$$305$$ −2.00000 −0.114520
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −26.0000 −1.47432 −0.737162 0.675716i $$-0.763835\pi$$
−0.737162 + 0.675716i $$0.763835\pi$$
$$312$$ 0 0
$$313$$ 28.0000 1.58265 0.791327 0.611393i $$-0.209391\pi$$
0.791327 + 0.611393i $$0.209391\pi$$
$$314$$ 10.0000 0.564333
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ −8.00000 −0.447914
$$320$$ −1.00000 −0.0559017
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 48.0000 2.67079
$$324$$ 0 0
$$325$$ 4.00000 0.221880
$$326$$ 16.0000 0.886158
$$327$$ 0 0
$$328$$ −2.00000 −0.110432
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 28.0000 1.53902 0.769510 0.638635i $$-0.220501\pi$$
0.769510 + 0.638635i $$0.220501\pi$$
$$332$$ −8.00000 −0.439057
$$333$$ 0 0
$$334$$ −16.0000 −0.875481
$$335$$ 6.00000 0.327815
$$336$$ 0 0
$$337$$ −28.0000 −1.52526 −0.762629 0.646837i $$-0.776092\pi$$
−0.762629 + 0.646837i $$0.776092\pi$$
$$338$$ −3.00000 −0.163178
$$339$$ 0 0
$$340$$ 6.00000 0.325396
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −2.00000 −0.107833
$$345$$ 0 0
$$346$$ −10.0000 −0.537603
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −2.00000 −0.106600
$$353$$ −10.0000 −0.532246 −0.266123 0.963939i $$-0.585743\pi$$
−0.266123 + 0.963939i $$0.585743\pi$$
$$354$$ 0 0
$$355$$ 10.0000 0.530745
$$356$$ 12.0000 0.635999
$$357$$ 0 0
$$358$$ 16.0000 0.845626
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ −10.0000 −0.525588
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.00000 0.104685
$$366$$ 0 0
$$367$$ 16.0000 0.835193 0.417597 0.908633i $$-0.362873\pi$$
0.417597 + 0.908633i $$0.362873\pi$$
$$368$$ 1.00000 0.0521286
$$369$$ 0 0
$$370$$ −2.00000 −0.103975
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 6.00000 0.310668 0.155334 0.987862i $$-0.450355\pi$$
0.155334 + 0.987862i $$0.450355\pi$$
$$374$$ 12.0000 0.620505
$$375$$ 0 0
$$376$$ −12.0000 −0.618853
$$377$$ −16.0000 −0.824042
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 8.00000 0.410391
$$381$$ 0 0
$$382$$ 24.0000 1.22795
$$383$$ 32.0000 1.63512 0.817562 0.575841i $$-0.195325\pi$$
0.817562 + 0.575841i $$0.195325\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −26.0000 −1.32337
$$387$$ 0 0
$$388$$ −16.0000 −0.812277
$$389$$ −26.0000 −1.31825 −0.659126 0.752032i $$-0.729074\pi$$
−0.659126 + 0.752032i $$0.729074\pi$$
$$390$$ 0 0
$$391$$ −6.00000 −0.303433
$$392$$ 7.00000 0.353553
$$393$$ 0 0
$$394$$ −18.0000 −0.906827
$$395$$ 8.00000 0.402524
$$396$$ 0 0
$$397$$ 28.0000 1.40528 0.702640 0.711546i $$-0.252005\pi$$
0.702640 + 0.711546i $$0.252005\pi$$
$$398$$ 16.0000 0.802008
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 8.00000 0.399501 0.199750 0.979847i $$-0.435987\pi$$
0.199750 + 0.979847i $$0.435987\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −12.0000 −0.597022
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −4.00000 −0.198273
$$408$$ 0 0
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 2.00000 0.0987730
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 8.00000 0.392705
$$416$$ −4.00000 −0.196116
$$417$$ 0 0
$$418$$ 16.0000 0.782586
$$419$$ −30.0000 −1.46560 −0.732798 0.680446i $$-0.761786\pi$$
−0.732798 + 0.680446i $$0.761786\pi$$
$$420$$ 0 0
$$421$$ −14.0000 −0.682318 −0.341159 0.940006i $$-0.610819\pi$$
−0.341159 + 0.940006i $$0.610819\pi$$
$$422$$ −4.00000 −0.194717
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ −6.00000 −0.291043
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 2.00000 0.0964486
$$431$$ 8.00000 0.385346 0.192673 0.981263i $$-0.438284\pi$$
0.192673 + 0.981263i $$0.438284\pi$$
$$432$$ 0 0
$$433$$ 16.0000 0.768911 0.384455 0.923144i $$-0.374389\pi$$
0.384455 + 0.923144i $$0.374389\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −10.0000 −0.478913
$$437$$ −8.00000 −0.382692
$$438$$ 0 0
$$439$$ 28.0000 1.33637 0.668184 0.743996i $$-0.267072\pi$$
0.668184 + 0.743996i $$0.267072\pi$$
$$440$$ 2.00000 0.0953463
$$441$$ 0 0
$$442$$ 24.0000 1.14156
$$443$$ 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
$$446$$ 2.00000 0.0947027
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 4.00000 0.188353
$$452$$ −18.0000 −0.846649
$$453$$ 0 0
$$454$$ 28.0000 1.31411
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −8.00000 −0.374224 −0.187112 0.982339i $$-0.559913\pi$$
−0.187112 + 0.982339i $$0.559913\pi$$
$$458$$ 10.0000 0.467269
$$459$$ 0 0
$$460$$ −1.00000 −0.0466252
$$461$$ 12.0000 0.558896 0.279448 0.960161i $$-0.409849\pi$$
0.279448 + 0.960161i $$0.409849\pi$$
$$462$$ 0 0
$$463$$ −26.0000 −1.20832 −0.604161 0.796862i $$-0.706492\pi$$
−0.604161 + 0.796862i $$0.706492\pi$$
$$464$$ −4.00000 −0.185695
$$465$$ 0 0
$$466$$ 6.00000 0.277945
$$467$$ 24.0000 1.11059 0.555294 0.831654i $$-0.312606\pi$$
0.555294 + 0.831654i $$0.312606\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 12.0000 0.553519
$$471$$ 0 0
$$472$$ 8.00000 0.368230
$$473$$ 4.00000 0.183920
$$474$$ 0 0
$$475$$ −8.00000 −0.367065
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −14.0000 −0.640345
$$479$$ 16.0000 0.731059 0.365529 0.930800i $$-0.380888\pi$$
0.365529 + 0.930800i $$0.380888\pi$$
$$480$$ 0 0
$$481$$ −8.00000 −0.364769
$$482$$ 6.00000 0.273293
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 16.0000 0.726523
$$486$$ 0 0
$$487$$ −26.0000 −1.17817 −0.589086 0.808070i $$-0.700512\pi$$
−0.589086 + 0.808070i $$0.700512\pi$$
$$488$$ −2.00000 −0.0905357
$$489$$ 0 0
$$490$$ −7.00000 −0.316228
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ 0 0
$$493$$ 24.0000 1.08091
$$494$$ 32.0000 1.43975
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 0 0
$$502$$ 2.00000 0.0892644
$$503$$ 16.0000 0.713405 0.356702 0.934218i $$-0.383901\pi$$
0.356702 + 0.934218i $$0.383901\pi$$
$$504$$ 0 0
$$505$$ 12.0000 0.533993
$$506$$ −2.00000 −0.0889108
$$507$$ 0 0
$$508$$ 2.00000 0.0887357
$$509$$ −20.0000 −0.886484 −0.443242 0.896402i $$-0.646172\pi$$
−0.443242 + 0.896402i $$0.646172\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 22.0000 0.970378
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 24.0000 1.05552
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 4.00000 0.175412
$$521$$ 20.0000 0.876216 0.438108 0.898922i $$-0.355649\pi$$
0.438108 + 0.898922i $$0.355649\pi$$
$$522$$ 0 0
$$523$$ 30.0000 1.31181 0.655904 0.754844i $$-0.272288\pi$$
0.655904 + 0.754844i $$0.272288\pi$$
$$524$$ 4.00000 0.174741
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 6.00000 0.260623
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 8.00000 0.346518
$$534$$ 0 0
$$535$$ −12.0000 −0.518805
$$536$$ 6.00000 0.259161
$$537$$ 0 0
$$538$$ 8.00000 0.344904
$$539$$ −14.0000 −0.603023
$$540$$ 0 0
$$541$$ −22.0000 −0.945854 −0.472927 0.881102i $$-0.656803\pi$$
−0.472927 + 0.881102i $$0.656803\pi$$
$$542$$ −24.0000 −1.03089
$$543$$ 0 0
$$544$$ 6.00000 0.257248
$$545$$ 10.0000 0.428353
$$546$$ 0 0
$$547$$ 4.00000 0.171028 0.0855138 0.996337i $$-0.472747\pi$$
0.0855138 + 0.996337i $$0.472747\pi$$
$$548$$ −2.00000 −0.0854358
$$549$$ 0 0
$$550$$ −2.00000 −0.0852803
$$551$$ 32.0000 1.36325
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 28.0000 1.18961
$$555$$ 0 0
$$556$$ 4.00000 0.169638
$$557$$ −38.0000 −1.61011 −0.805056 0.593199i $$-0.797865\pi$$
−0.805056 + 0.593199i $$0.797865\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 12.0000 0.506189
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ 0 0
$$565$$ 18.0000 0.757266
$$566$$ −14.0000 −0.588464
$$567$$ 0 0
$$568$$ 10.0000 0.419591
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 8.00000 0.334497
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.00000 0.0417029
$$576$$ 0 0
$$577$$ 38.0000 1.58196 0.790980 0.611842i $$-0.209571\pi$$
0.790980 + 0.611842i $$0.209571\pi$$
$$578$$ −19.0000 −0.790296
$$579$$ 0 0
$$580$$ 4.00000 0.166091
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 12.0000 0.496989
$$584$$ 2.00000 0.0827606
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ −4.00000 −0.165098 −0.0825488 0.996587i $$-0.526306\pi$$
−0.0825488 + 0.996587i $$0.526306\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −8.00000 −0.329355
$$591$$ 0 0
$$592$$ −2.00000 −0.0821995
$$593$$ −6.00000 −0.246390 −0.123195 0.992382i $$-0.539314\pi$$
−0.123195 + 0.992382i $$0.539314\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −14.0000 −0.573462
$$597$$ 0 0
$$598$$ −4.00000 −0.163572
$$599$$ 34.0000 1.38920 0.694601 0.719395i $$-0.255581\pi$$
0.694601 + 0.719395i $$0.255581\pi$$
$$600$$ 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
$$604$$ −4.00000 −0.162758
$$605$$ 7.00000 0.284590
$$606$$ 0 0
$$607$$ −10.0000 −0.405887 −0.202944 0.979190i $$-0.565051\pi$$
−0.202944 + 0.979190i $$0.565051\pi$$
$$608$$ 8.00000 0.324443
$$609$$ 0 0
$$610$$ 2.00000 0.0809776
$$611$$ 48.0000 1.94187
$$612$$ 0 0
$$613$$ −30.0000 −1.21169 −0.605844 0.795583i $$-0.707165\pi$$
−0.605844 + 0.795583i $$0.707165\pi$$
$$614$$ −28.0000 −1.12999
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000 0.724653 0.362326 0.932051i $$-0.381983\pi$$
0.362326 + 0.932051i $$0.381983\pi$$
$$618$$ 0 0
$$619$$ 32.0000 1.28619 0.643094 0.765787i $$-0.277650\pi$$
0.643094 + 0.765787i $$0.277650\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 26.0000 1.04251
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ −28.0000 −1.11911
$$627$$ 0 0
$$628$$ −10.0000 −0.399043
$$629$$ 12.0000 0.478471
$$630$$ 0 0
$$631$$ −32.0000 −1.27390 −0.636950 0.770905i $$-0.719804\pi$$
−0.636950 + 0.770905i $$0.719804\pi$$
$$632$$ 8.00000 0.318223
$$633$$ 0 0
$$634$$ 18.0000 0.714871
$$635$$ −2.00000 −0.0793676
$$636$$ 0 0
$$637$$ −28.0000 −1.10940
$$638$$ 8.00000 0.316723
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ 4.00000 0.157991 0.0789953 0.996875i $$-0.474829\pi$$
0.0789953 + 0.996875i $$0.474829\pi$$
$$642$$ 0 0
$$643$$ −10.0000 −0.394362 −0.197181 0.980367i $$-0.563179\pi$$
−0.197181 + 0.980367i $$0.563179\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −48.0000 −1.88853
$$647$$ 28.0000 1.10079 0.550397 0.834903i $$-0.314476\pi$$
0.550397 + 0.834903i $$0.314476\pi$$
$$648$$ 0 0
$$649$$ −16.0000 −0.628055
$$650$$ −4.00000 −0.156893
$$651$$ 0 0
$$652$$ −16.0000 −0.626608
$$653$$ −2.00000 −0.0782660 −0.0391330 0.999234i $$-0.512460\pi$$
−0.0391330 + 0.999234i $$0.512460\pi$$
$$654$$ 0 0
$$655$$ −4.00000 −0.156293
$$656$$ 2.00000 0.0780869
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 26.0000 1.01282 0.506408 0.862294i $$-0.330973\pi$$
0.506408 + 0.862294i $$0.330973\pi$$
$$660$$ 0 0
$$661$$ −50.0000 −1.94477 −0.972387 0.233373i $$-0.925024\pi$$
−0.972387 + 0.233373i $$0.925024\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 0 0
$$664$$ 8.00000 0.310460
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −4.00000 −0.154881
$$668$$ 16.0000 0.619059
$$669$$ 0 0
$$670$$ −6.00000 −0.231800
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ 28.0000 1.07852
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ 10.0000 0.384331 0.192166 0.981363i $$-0.438449\pi$$
0.192166 + 0.981363i $$0.438449\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −6.00000 −0.230089
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ 2.00000 0.0764161
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 2.00000 0.0762493
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ 10.0000 0.380143
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ −4.00000 −0.151729
$$696$$ 0 0
$$697$$ −12.0000 −0.454532
$$698$$ −26.0000 −0.984115
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 14.0000 0.528773 0.264386 0.964417i $$-0.414831\pi$$
0.264386 + 0.964417i $$0.414831\pi$$
$$702$$ 0 0
$$703$$ 16.0000 0.603451
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ 10.0000 0.376355
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 38.0000 1.42712 0.713560 0.700594i $$-0.247082\pi$$
0.713560 + 0.700594i $$0.247082\pi$$
$$710$$ −10.0000 −0.375293
$$711$$ 0 0
$$712$$ −12.0000 −0.449719
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −8.00000 −0.299183
$$716$$ −16.0000 −0.597948
$$717$$ 0 0
$$718$$ −16.0000 −0.597115
$$719$$ 2.00000 0.0745874 0.0372937 0.999304i $$-0.488126\pi$$
0.0372937 + 0.999304i $$0.488126\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −45.0000 −1.67473
$$723$$ 0 0
$$724$$ 10.0000 0.371647
$$725$$ −4.00000 −0.148556
$$726$$ 0 0
$$727$$ 28.0000 1.03846 0.519231 0.854634i $$-0.326218\pi$$
0.519231 + 0.854634i $$0.326218\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −2.00000 −0.0740233
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ −42.0000 −1.55131 −0.775653 0.631160i $$-0.782579\pi$$
−0.775653 + 0.631160i $$0.782579\pi$$
$$734$$ −16.0000 −0.590571
$$735$$ 0 0
$$736$$ −1.00000 −0.0368605
$$737$$ −12.0000 −0.442026
$$738$$ 0 0
$$739$$ −36.0000 −1.32428 −0.662141 0.749380i $$-0.730352\pi$$
−0.662141 + 0.749380i $$0.730352\pi$$
$$740$$ 2.00000 0.0735215
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 0 0
$$745$$ 14.0000 0.512920
$$746$$ −6.00000 −0.219676
$$747$$ 0 0
$$748$$ −12.0000 −0.438763
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 12.0000 0.437595
$$753$$ 0 0
$$754$$ 16.0000 0.582686
$$755$$ 4.00000 0.145575
$$756$$ 0 0
$$757$$ −6.00000 −0.218074 −0.109037 0.994038i $$-0.534777\pi$$
−0.109037 + 0.994038i $$0.534777\pi$$
$$758$$ −12.0000 −0.435860
$$759$$ 0 0
$$760$$ −8.00000 −0.290191
$$761$$ 22.0000 0.797499 0.398750 0.917060i $$-0.369444\pi$$
0.398750 + 0.917060i $$0.369444\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −24.0000 −0.868290
$$765$$ 0 0
$$766$$ −32.0000 −1.15621
$$767$$ −32.0000 −1.15545
$$768$$ 0 0
$$769$$ −2.00000 −0.0721218 −0.0360609 0.999350i $$-0.511481\pi$$
−0.0360609 + 0.999350i $$0.511481\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 26.0000 0.935760
$$773$$ 6.00000 0.215805 0.107903 0.994161i $$-0.465587\pi$$
0.107903 + 0.994161i $$0.465587\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 16.0000 0.574367
$$777$$ 0 0
$$778$$ 26.0000 0.932145
$$779$$ −16.0000 −0.573259
$$780$$ 0 0
$$781$$ −20.0000 −0.715656
$$782$$ 6.00000 0.214560
$$783$$ 0 0
$$784$$ −7.00000 −0.250000
$$785$$ 10.0000 0.356915
$$786$$ 0 0
$$787$$ 22.0000 0.784215 0.392108 0.919919i $$-0.371746\pi$$
0.392108 + 0.919919i $$0.371746\pi$$
$$788$$ 18.0000 0.641223
$$789$$ 0 0
$$790$$ −8.00000 −0.284627
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 8.00000 0.284088
$$794$$ −28.0000 −0.993683
$$795$$ 0 0
$$796$$ −16.0000 −0.567105
$$797$$ −14.0000 −0.495905 −0.247953 0.968772i $$-0.579758\pi$$
−0.247953 + 0.968772i $$0.579758\pi$$
$$798$$ 0 0
$$799$$ −72.0000 −2.54718
$$800$$ −1.00000 −0.0353553
$$801$$ 0 0
$$802$$ −8.00000 −0.282490
$$803$$ −4.00000 −0.141157
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 12.0000 0.422159
$$809$$ 46.0000 1.61727 0.808637 0.588308i $$-0.200206\pi$$
0.808637 + 0.588308i $$0.200206\pi$$
$$810$$ 0 0
$$811$$ 4.00000 0.140459 0.0702295 0.997531i $$-0.477627\pi$$
0.0702295 + 0.997531i $$0.477627\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 4.00000 0.140200
$$815$$ 16.0000 0.560456
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ 10.0000 0.349642
$$819$$ 0 0
$$820$$ −2.00000 −0.0698430
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ −22.0000 −0.766872 −0.383436 0.923567i $$-0.625259\pi$$
−0.383436 + 0.923567i $$0.625259\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −12.0000 −0.417281 −0.208640 0.977992i $$-0.566904\pi$$
−0.208640 + 0.977992i $$0.566904\pi$$
$$828$$ 0 0
$$829$$ −38.0000 −1.31979 −0.659897 0.751356i $$-0.729400\pi$$
−0.659897 + 0.751356i $$0.729400\pi$$
$$830$$ −8.00000 −0.277684
$$831$$ 0 0
$$832$$ 4.00000 0.138675
$$833$$ 42.0000 1.45521
$$834$$ 0 0
$$835$$ −16.0000 −0.553703
$$836$$ −16.0000 −0.553372
$$837$$ 0 0
$$838$$ 30.0000 1.03633
$$839$$ 12.0000 0.414286 0.207143 0.978311i $$-0.433583\pi$$
0.207143 + 0.978311i $$0.433583\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ 14.0000 0.482472
$$843$$ 0 0
$$844$$ 4.00000 0.137686
$$845$$ −3.00000 −0.103203
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 6.00000 0.206041
$$849$$ 0 0
$$850$$ 6.00000 0.205798
$$851$$ −2.00000 −0.0685591
$$852$$ 0 0
$$853$$ 36.0000 1.23262 0.616308 0.787505i $$-0.288628\pi$$
0.616308 + 0.787505i $$0.288628\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ −18.0000 −0.614868 −0.307434 0.951569i $$-0.599470\pi$$
−0.307434 + 0.951569i $$0.599470\pi$$
$$858$$ 0 0
$$859$$ −28.0000 −0.955348 −0.477674 0.878537i $$-0.658520\pi$$
−0.477674 + 0.878537i $$0.658520\pi$$
$$860$$ −2.00000 −0.0681994
$$861$$ 0 0
$$862$$ −8.00000 −0.272481
$$863$$ 20.0000 0.680808 0.340404 0.940279i $$-0.389436\pi$$
0.340404 + 0.940279i $$0.389436\pi$$
$$864$$ 0 0
$$865$$ −10.0000 −0.340010
$$866$$ −16.0000 −0.543702
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −16.0000 −0.542763
$$870$$ 0 0
$$871$$ −24.0000 −0.813209
$$872$$ 10.0000 0.338643
$$873$$ 0 0
$$874$$ 8.00000 0.270604
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −20.0000 −0.675352 −0.337676 0.941262i $$-0.609641\pi$$
−0.337676 + 0.941262i $$0.609641\pi$$
$$878$$ −28.0000 −0.944954
$$879$$ 0 0
$$880$$ −2.00000 −0.0674200
$$881$$ −4.00000 −0.134763 −0.0673817 0.997727i $$-0.521465\pi$$
−0.0673817 + 0.997727i $$0.521465\pi$$
$$882$$ 0 0
$$883$$ 32.0000 1.07689 0.538443 0.842662i $$-0.319013\pi$$
0.538443 + 0.842662i $$0.319013\pi$$
$$884$$ −24.0000 −0.807207
$$885$$ 0 0
$$886$$ −4.00000 −0.134383
$$887$$ −36.0000 −1.20876 −0.604381 0.796696i $$-0.706579\pi$$
−0.604381 + 0.796696i $$0.706579\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 12.0000 0.402241
$$891$$ 0 0
$$892$$ −2.00000 −0.0669650
$$893$$ −96.0000 −3.21252
$$894$$ 0 0
$$895$$ 16.0000 0.534821
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 30.0000 1.00111
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −36.0000 −1.19933
$$902$$ −4.00000 −0.133185
$$903$$ 0 0
$$904$$ 18.0000 0.598671
$$905$$ −10.0000 −0.332411
$$906$$ 0 0
$$907$$ −22.0000 −0.730498 −0.365249 0.930910i $$-0.619016\pi$$
−0.365249 + 0.930910i $$0.619016\pi$$
$$908$$ −28.0000 −0.929213
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 4.00000 0.132526 0.0662630 0.997802i $$-0.478892\pi$$
0.0662630 + 0.997802i $$0.478892\pi$$
$$912$$ 0 0
$$913$$ −16.0000 −0.529523
$$914$$ 8.00000 0.264616
$$915$$ 0 0
$$916$$ −10.0000 −0.330409
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 40.0000 1.31948 0.659739 0.751495i $$-0.270667\pi$$
0.659739 + 0.751495i $$0.270667\pi$$
$$920$$ 1.00000 0.0329690
$$921$$ 0 0
$$922$$ −12.0000 −0.395199
$$923$$ −40.0000 −1.31662
$$924$$ 0 0
$$925$$ −2.00000 −0.0657596
$$926$$ 26.0000 0.854413
$$927$$ 0 0
$$928$$ 4.00000 0.131306
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 0 0
$$931$$ 56.0000 1.83533
$$932$$ −6.00000 −0.196537
$$933$$ 0 0
$$934$$ −24.0000 −0.785304
$$935$$ 12.0000 0.392442
$$936$$ 0 0
$$937$$ 32.0000 1.04539 0.522697 0.852518i $$-0.324926\pi$$
0.522697 + 0.852518i $$0.324926\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ −12.0000 −0.391397
$$941$$ −38.0000 −1.23876 −0.619382 0.785090i $$-0.712617\pi$$
−0.619382 + 0.785090i $$0.712617\pi$$
$$942$$ 0 0
$$943$$ 2.00000 0.0651290
$$944$$ −8.00000 −0.260378
$$945$$ 0 0
$$946$$ −4.00000 −0.130051
$$947$$ −4.00000 −0.129983 −0.0649913 0.997886i $$-0.520702\pi$$
−0.0649913 + 0.997886i $$0.520702\pi$$
$$948$$ 0 0
$$949$$ −8.00000 −0.259691
$$950$$ 8.00000 0.259554
$$951$$ 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
$$955$$ 24.0000 0.776622
$$956$$ 14.0000 0.452792
$$957$$ 0 0
$$958$$ −16.0000 −0.516937
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 8.00000 0.257930
$$963$$ 0 0
$$964$$ −6.00000 −0.193247
$$965$$ −26.0000 −0.836970
$$966$$ 0 0
$$967$$ −42.0000 −1.35063 −0.675314 0.737530i $$-0.735992\pi$$
−0.675314 + 0.737530i $$0.735992\pi$$
$$968$$ 7.00000 0.224989
$$969$$ 0 0
$$970$$ −16.0000 −0.513729
$$971$$ 14.0000 0.449281 0.224641 0.974442i $$-0.427879\pi$$
0.224641 + 0.974442i $$0.427879\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 26.0000 0.833094
$$975$$ 0 0
$$976$$ 2.00000 0.0640184
$$977$$ 42.0000 1.34370 0.671850 0.740688i $$-0.265500\pi$$
0.671850 + 0.740688i $$0.265500\pi$$
$$978$$ 0 0
$$979$$ 24.0000 0.767043
$$980$$ 7.00000 0.223607
$$981$$ 0 0
$$982$$ 20.0000 0.638226
$$983$$ −48.0000 −1.53096 −0.765481 0.643458i $$-0.777499\pi$$
−0.765481 + 0.643458i $$0.777499\pi$$
$$984$$ 0 0
$$985$$ −18.0000 −0.573528
$$986$$ −24.0000 −0.764316
$$987$$ 0 0
$$988$$ −32.0000 −1.01806
$$989$$ 2.00000 0.0635963
$$990$$ 0 0
$$991$$ 12.0000 0.381193 0.190596 0.981669i $$-0.438958\pi$$
0.190596 + 0.981669i $$0.438958\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 16.0000 0.507234
$$996$$ 0 0
$$997$$ −4.00000 −0.126681 −0.0633406 0.997992i $$-0.520175\pi$$
−0.0633406 + 0.997992i $$0.520175\pi$$
$$998$$ 4.00000 0.126618
$$999$$ 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 2070.2.a.c.1.1 1
3.2 odd 2 690.2.a.j.1.1 1
12.11 even 2 5520.2.a.l.1.1 1
15.2 even 4 3450.2.d.m.2899.2 2
15.8 even 4 3450.2.d.m.2899.1 2
15.14 odd 2 3450.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.a.j.1.1 1 3.2 odd 2
2070.2.a.c.1.1 1 1.1 even 1 trivial
3450.2.a.b.1.1 1 15.14 odd 2
3450.2.d.m.2899.1 2 15.8 even 4
3450.2.d.m.2899.2 2 15.2 even 4
5520.2.a.l.1.1 1 12.11 even 2