Properties

 Label 5166.2.a.o.1.1 Level $5166$ Weight $2$ Character 5166.1 Self dual yes Analytic conductor $41.251$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5166 = 2 \cdot 3^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5166.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$41.2507176842$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 574) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 5166.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} -8.00000 q^{19} +1.00000 q^{20} -2.00000 q^{22} +4.00000 q^{23} -4.00000 q^{25} +1.00000 q^{28} +5.00000 q^{29} -3.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} +1.00000 q^{35} +10.0000 q^{37} +8.00000 q^{38} -1.00000 q^{40} +1.00000 q^{41} -5.00000 q^{43} +2.00000 q^{44} -4.00000 q^{46} -6.00000 q^{47} +1.00000 q^{49} +4.00000 q^{50} +9.00000 q^{53} +2.00000 q^{55} -1.00000 q^{56} -5.00000 q^{58} +10.0000 q^{59} +13.0000 q^{61} +3.00000 q^{62} +1.00000 q^{64} -2.00000 q^{67} +3.00000 q^{68} -1.00000 q^{70} -9.00000 q^{71} +4.00000 q^{73} -10.0000 q^{74} -8.00000 q^{76} +2.00000 q^{77} -11.0000 q^{79} +1.00000 q^{80} -1.00000 q^{82} +14.0000 q^{83} +3.00000 q^{85} +5.00000 q^{86} -2.00000 q^{88} +1.00000 q^{89} +4.00000 q^{92} +6.00000 q^{94} -8.00000 q^{95} +7.00000 q^{97} -1.00000 q^{98} +O(q^{100})$$

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 0.223607 0.974679i $$-0.428217\pi$$
0.223607 + 0.974679i $$0.428217\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ −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 $$0.5\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 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
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ −4.00000 −0.800000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ 5.00000 0.928477 0.464238 0.885710i $$-0.346328\pi$$
0.464238 + 0.885710i $$0.346328\pi$$
$$30$$ 0 0
$$31$$ −3.00000 −0.538816 −0.269408 0.963026i $$-0.586828\pi$$
−0.269408 + 0.963026i $$0.586828\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ −3.00000 −0.514496
$$35$$ 1.00000 0.169031
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 8.00000 1.29777
$$39$$ 0 0
$$40$$ −1.00000 −0.158114
$$41$$ 1.00000 0.156174
$$42$$ 0 0
$$43$$ −5.00000 −0.762493 −0.381246 0.924473i $$-0.624505\pi$$
−0.381246 + 0.924473i $$0.624505\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ −4.00000 −0.589768
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 4.00000 0.565685
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ 0 0
$$55$$ 2.00000 0.269680
$$56$$ −1.00000 −0.133631
$$57$$ 0 0
$$58$$ −5.00000 −0.656532
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 0 0
$$61$$ 13.0000 1.66448 0.832240 0.554416i $$-0.187058\pi$$
0.832240 + 0.554416i $$0.187058\pi$$
$$62$$ 3.00000 0.381000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 3.00000 0.363803
$$69$$ 0 0
$$70$$ −1.00000 −0.119523
$$71$$ −9.00000 −1.06810 −0.534052 0.845452i $$-0.679331\pi$$
−0.534052 + 0.845452i $$0.679331\pi$$
$$72$$ 0 0
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ −10.0000 −1.16248
$$75$$ 0 0
$$76$$ −8.00000 −0.917663
$$77$$ 2.00000 0.227921
$$78$$ 0 0
$$79$$ −11.0000 −1.23760 −0.618798 0.785550i $$-0.712380\pi$$
−0.618798 + 0.785550i $$0.712380\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 0 0
$$82$$ −1.00000 −0.110432
$$83$$ 14.0000 1.53670 0.768350 0.640030i $$-0.221078\pi$$
0.768350 + 0.640030i $$0.221078\pi$$
$$84$$ 0 0
$$85$$ 3.00000 0.325396
$$86$$ 5.00000 0.539164
$$87$$ 0 0
$$88$$ −2.00000 −0.213201
$$89$$ 1.00000 0.106000 0.0529999 0.998595i $$-0.483122\pi$$
0.0529999 + 0.998595i $$0.483122\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 0 0
$$94$$ 6.00000 0.618853
$$95$$ −8.00000 −0.820783
$$96$$ 0 0
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0 0
$$100$$ −4.00000 −0.400000
$$101$$ 10.0000 0.995037 0.497519 0.867453i $$-0.334245\pi$$
0.497519 + 0.867453i $$0.334245\pi$$
$$102$$ 0 0
$$103$$ 13.0000 1.28093 0.640464 0.767988i $$-0.278742\pi$$
0.640464 + 0.767988i $$0.278742\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −9.00000 −0.874157
$$107$$ −3.00000 −0.290021 −0.145010 0.989430i $$-0.546322\pi$$
−0.145010 + 0.989430i $$0.546322\pi$$
$$108$$ 0 0
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ −2.00000 −0.190693
$$111$$ 0 0
$$112$$ 1.00000 0.0944911
$$113$$ −9.00000 −0.846649 −0.423324 0.905978i $$-0.639137\pi$$
−0.423324 + 0.905978i $$0.639137\pi$$
$$114$$ 0 0
$$115$$ 4.00000 0.373002
$$116$$ 5.00000 0.464238
$$117$$ 0 0
$$118$$ −10.0000 −0.920575
$$119$$ 3.00000 0.275010
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ −13.0000 −1.17696
$$123$$ 0 0
$$124$$ −3.00000 −0.269408
$$125$$ −9.00000 −0.804984
$$126$$ 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
$$130$$ 0 0
$$131$$ 8.00000 0.698963 0.349482 0.936943i $$-0.386358\pi$$
0.349482 + 0.936943i $$0.386358\pi$$
$$132$$ 0 0
$$133$$ −8.00000 −0.693688
$$134$$ 2.00000 0.172774
$$135$$ 0 0
$$136$$ −3.00000 −0.257248
$$137$$ −12.0000 −1.02523 −0.512615 0.858619i $$-0.671323\pi$$
−0.512615 + 0.858619i $$0.671323\pi$$
$$138$$ 0 0
$$139$$ 14.0000 1.18746 0.593732 0.804663i $$-0.297654\pi$$
0.593732 + 0.804663i $$0.297654\pi$$
$$140$$ 1.00000 0.0845154
$$141$$ 0 0
$$142$$ 9.00000 0.755263
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 5.00000 0.415227
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ 10.0000 0.821995
$$149$$ −3.00000 −0.245770 −0.122885 0.992421i $$-0.539215\pi$$
−0.122885 + 0.992421i $$0.539215\pi$$
$$150$$ 0 0
$$151$$ 19.0000 1.54620 0.773099 0.634285i $$-0.218706\pi$$
0.773099 + 0.634285i $$0.218706\pi$$
$$152$$ 8.00000 0.648886
$$153$$ 0 0
$$154$$ −2.00000 −0.161165
$$155$$ −3.00000 −0.240966
$$156$$ 0 0
$$157$$ 4.00000 0.319235 0.159617 0.987179i $$-0.448974\pi$$
0.159617 + 0.987179i $$0.448974\pi$$
$$158$$ 11.0000 0.875113
$$159$$ 0 0
$$160$$ −1.00000 −0.0790569
$$161$$ 4.00000 0.315244
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 1.00000 0.0780869
$$165$$ 0 0
$$166$$ −14.0000 −1.08661
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ −3.00000 −0.230089
$$171$$ 0 0
$$172$$ −5.00000 −0.381246
$$173$$ 1.00000 0.0760286 0.0380143 0.999277i $$-0.487897\pi$$
0.0380143 + 0.999277i $$0.487897\pi$$
$$174$$ 0 0
$$175$$ −4.00000 −0.302372
$$176$$ 2.00000 0.150756
$$177$$ 0 0
$$178$$ −1.00000 −0.0749532
$$179$$ 16.0000 1.19590 0.597948 0.801535i $$-0.295983\pi$$
0.597948 + 0.801535i $$0.295983\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −4.00000 −0.294884
$$185$$ 10.0000 0.735215
$$186$$ 0 0
$$187$$ 6.00000 0.438763
$$188$$ −6.00000 −0.437595
$$189$$ 0 0
$$190$$ 8.00000 0.580381
$$191$$ 11.0000 0.795932 0.397966 0.917400i $$-0.369716\pi$$
0.397966 + 0.917400i $$0.369716\pi$$
$$192$$ 0 0
$$193$$ 12.0000 0.863779 0.431889 0.901927i $$-0.357847\pi$$
0.431889 + 0.901927i $$0.357847\pi$$
$$194$$ −7.00000 −0.502571
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ 12.0000 0.854965 0.427482 0.904024i $$-0.359401\pi$$
0.427482 + 0.904024i $$0.359401\pi$$
$$198$$ 0 0
$$199$$ −24.0000 −1.70131 −0.850657 0.525720i $$-0.823796\pi$$
−0.850657 + 0.525720i $$0.823796\pi$$
$$200$$ 4.00000 0.282843
$$201$$ 0 0
$$202$$ −10.0000 −0.703598
$$203$$ 5.00000 0.350931
$$204$$ 0 0
$$205$$ 1.00000 0.0698430
$$206$$ −13.0000 −0.905753
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −16.0000 −1.10674
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 9.00000 0.618123
$$213$$ 0 0
$$214$$ 3.00000 0.205076
$$215$$ −5.00000 −0.340997
$$216$$ 0 0
$$217$$ −3.00000 −0.203653
$$218$$ 2.00000 0.135457
$$219$$ 0 0
$$220$$ 2.00000 0.134840
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 21.0000 1.40626 0.703132 0.711059i $$-0.251784\pi$$
0.703132 + 0.711059i $$0.251784\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ 9.00000 0.598671
$$227$$ −25.0000 −1.65931 −0.829654 0.558278i $$-0.811462\pi$$
−0.829654 + 0.558278i $$0.811462\pi$$
$$228$$ 0 0
$$229$$ 20.0000 1.32164 0.660819 0.750546i $$-0.270209\pi$$
0.660819 + 0.750546i $$0.270209\pi$$
$$230$$ −4.00000 −0.263752
$$231$$ 0 0
$$232$$ −5.00000 −0.328266
$$233$$ −10.0000 −0.655122 −0.327561 0.944830i $$-0.606227\pi$$
−0.327561 + 0.944830i $$0.606227\pi$$
$$234$$ 0 0
$$235$$ −6.00000 −0.391397
$$236$$ 10.0000 0.650945
$$237$$ 0 0
$$238$$ −3.00000 −0.194461
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 0 0
$$244$$ 13.0000 0.832240
$$245$$ 1.00000 0.0638877
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 3.00000 0.190500
$$249$$ 0 0
$$250$$ 9.00000 0.569210
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ −2.00000 −0.125491
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 15.0000 0.935674 0.467837 0.883815i $$-0.345033\pi$$
0.467837 + 0.883815i $$0.345033\pi$$
$$258$$ 0 0
$$259$$ 10.0000 0.621370
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −8.00000 −0.494242
$$263$$ 16.0000 0.986602 0.493301 0.869859i $$-0.335790\pi$$
0.493301 + 0.869859i $$0.335790\pi$$
$$264$$ 0 0
$$265$$ 9.00000 0.552866
$$266$$ 8.00000 0.490511
$$267$$ 0 0
$$268$$ −2.00000 −0.122169
$$269$$ 10.0000 0.609711 0.304855 0.952399i $$-0.401392\pi$$
0.304855 + 0.952399i $$0.401392\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ 3.00000 0.181902
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ −8.00000 −0.482418
$$276$$ 0 0
$$277$$ 26.0000 1.56219 0.781094 0.624413i $$-0.214662\pi$$
0.781094 + 0.624413i $$0.214662\pi$$
$$278$$ −14.0000 −0.839664
$$279$$ 0 0
$$280$$ −1.00000 −0.0597614
$$281$$ −2.00000 −0.119310 −0.0596550 0.998219i $$-0.519000\pi$$
−0.0596550 + 0.998219i $$0.519000\pi$$
$$282$$ 0 0
$$283$$ 18.0000 1.06999 0.534994 0.844856i $$-0.320314\pi$$
0.534994 + 0.844856i $$0.320314\pi$$
$$284$$ −9.00000 −0.534052
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 1.00000 0.0590281
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ −5.00000 −0.293610
$$291$$ 0 0
$$292$$ 4.00000 0.234082
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ 0 0
$$295$$ 10.0000 0.582223
$$296$$ −10.0000 −0.581238
$$297$$ 0 0
$$298$$ 3.00000 0.173785
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −5.00000 −0.288195
$$302$$ −19.0000 −1.09333
$$303$$ 0 0
$$304$$ −8.00000 −0.458831
$$305$$ 13.0000 0.744378
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 2.00000 0.113961
$$309$$ 0 0
$$310$$ 3.00000 0.170389
$$311$$ −18.0000 −1.02069 −0.510343 0.859971i $$-0.670482\pi$$
−0.510343 + 0.859971i $$0.670482\pi$$
$$312$$ 0 0
$$313$$ −22.0000 −1.24351 −0.621757 0.783210i $$-0.713581\pi$$
−0.621757 + 0.783210i $$0.713581\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ 0 0
$$316$$ −11.0000 −0.618798
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ 10.0000 0.559893
$$320$$ 1.00000 0.0559017
$$321$$ 0 0
$$322$$ −4.00000 −0.222911
$$323$$ −24.0000 −1.33540
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 4.00000 0.221540
$$327$$ 0 0
$$328$$ −1.00000 −0.0552158
$$329$$ −6.00000 −0.330791
$$330$$ 0 0
$$331$$ −32.0000 −1.75888 −0.879440 0.476011i $$-0.842082\pi$$
−0.879440 + 0.476011i $$0.842082\pi$$
$$332$$ 14.0000 0.768350
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −2.00000 −0.109272
$$336$$ 0 0
$$337$$ −19.0000 −1.03500 −0.517498 0.855684i $$-0.673136\pi$$
−0.517498 + 0.855684i $$0.673136\pi$$
$$338$$ 13.0000 0.707107
$$339$$ 0 0
$$340$$ 3.00000 0.162698
$$341$$ −6.00000 −0.324918
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 5.00000 0.269582
$$345$$ 0 0
$$346$$ −1.00000 −0.0537603
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ −2.00000 −0.106600
$$353$$ 24.0000 1.27739 0.638696 0.769460i $$-0.279474\pi$$
0.638696 + 0.769460i $$0.279474\pi$$
$$354$$ 0 0
$$355$$ −9.00000 −0.477670
$$356$$ 1.00000 0.0529999
$$357$$ 0 0
$$358$$ −16.0000 −0.845626
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ 14.0000 0.735824
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 4.00000 0.209370
$$366$$ 0 0
$$367$$ −17.0000 −0.887393 −0.443696 0.896177i $$-0.646333\pi$$
−0.443696 + 0.896177i $$0.646333\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 0 0
$$370$$ −10.0000 −0.519875
$$371$$ 9.00000 0.467257
$$372$$ 0 0
$$373$$ −18.0000 −0.932005 −0.466002 0.884783i $$-0.654306\pi$$
−0.466002 + 0.884783i $$0.654306\pi$$
$$374$$ −6.00000 −0.310253
$$375$$ 0 0
$$376$$ 6.00000 0.309426
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 37.0000 1.90056 0.950281 0.311393i $$-0.100796\pi$$
0.950281 + 0.311393i $$0.100796\pi$$
$$380$$ −8.00000 −0.410391
$$381$$ 0 0
$$382$$ −11.0000 −0.562809
$$383$$ 22.0000 1.12415 0.562074 0.827087i $$-0.310004\pi$$
0.562074 + 0.827087i $$0.310004\pi$$
$$384$$ 0 0
$$385$$ 2.00000 0.101929
$$386$$ −12.0000 −0.610784
$$387$$ 0 0
$$388$$ 7.00000 0.355371
$$389$$ 2.00000 0.101404 0.0507020 0.998714i $$-0.483854\pi$$
0.0507020 + 0.998714i $$0.483854\pi$$
$$390$$ 0 0
$$391$$ 12.0000 0.606866
$$392$$ −1.00000 −0.0505076
$$393$$ 0 0
$$394$$ −12.0000 −0.604551
$$395$$ −11.0000 −0.553470
$$396$$ 0 0
$$397$$ 20.0000 1.00377 0.501886 0.864934i $$-0.332640\pi$$
0.501886 + 0.864934i $$0.332640\pi$$
$$398$$ 24.0000 1.20301
$$399$$ 0 0
$$400$$ −4.00000 −0.200000
$$401$$ 25.0000 1.24844 0.624220 0.781248i $$-0.285417\pi$$
0.624220 + 0.781248i $$0.285417\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 10.0000 0.497519
$$405$$ 0 0
$$406$$ −5.00000 −0.248146
$$407$$ 20.0000 0.991363
$$408$$ 0 0
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ −1.00000 −0.0493865
$$411$$ 0 0
$$412$$ 13.0000 0.640464
$$413$$ 10.0000 0.492068
$$414$$ 0 0
$$415$$ 14.0000 0.687233
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 16.0000 0.782586
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ 0 0
$$421$$ −19.0000 −0.926003 −0.463002 0.886357i $$-0.653228\pi$$
−0.463002 + 0.886357i $$0.653228\pi$$
$$422$$ 12.0000 0.584151
$$423$$ 0 0
$$424$$ −9.00000 −0.437079
$$425$$ −12.0000 −0.582086
$$426$$ 0 0
$$427$$ 13.0000 0.629114
$$428$$ −3.00000 −0.145010
$$429$$ 0 0
$$430$$ 5.00000 0.241121
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 3.00000 0.144005
$$435$$ 0 0
$$436$$ −2.00000 −0.0957826
$$437$$ −32.0000 −1.53077
$$438$$ 0 0
$$439$$ 34.0000 1.62273 0.811366 0.584539i $$-0.198725\pi$$
0.811366 + 0.584539i $$0.198725\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 25.0000 1.18779 0.593893 0.804544i $$-0.297590\pi$$
0.593893 + 0.804544i $$0.297590\pi$$
$$444$$ 0 0
$$445$$ 1.00000 0.0474045
$$446$$ −21.0000 −0.994379
$$447$$ 0 0
$$448$$ 1.00000 0.0472456
$$449$$ 33.0000 1.55737 0.778683 0.627417i $$-0.215888\pi$$
0.778683 + 0.627417i $$0.215888\pi$$
$$450$$ 0 0
$$451$$ 2.00000 0.0941763
$$452$$ −9.00000 −0.423324
$$453$$ 0 0
$$454$$ 25.0000 1.17331
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −18.0000 −0.842004 −0.421002 0.907060i $$-0.638322\pi$$
−0.421002 + 0.907060i $$0.638322\pi$$
$$458$$ −20.0000 −0.934539
$$459$$ 0 0
$$460$$ 4.00000 0.186501
$$461$$ 21.0000 0.978068 0.489034 0.872265i $$-0.337349\pi$$
0.489034 + 0.872265i $$0.337349\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ 5.00000 0.232119
$$465$$ 0 0
$$466$$ 10.0000 0.463241
$$467$$ −6.00000 −0.277647 −0.138823 0.990317i $$-0.544332\pi$$
−0.138823 + 0.990317i $$0.544332\pi$$
$$468$$ 0 0
$$469$$ −2.00000 −0.0923514
$$470$$ 6.00000 0.276759
$$471$$ 0 0
$$472$$ −10.0000 −0.460287
$$473$$ −10.0000 −0.459800
$$474$$ 0 0
$$475$$ 32.0000 1.46826
$$476$$ 3.00000 0.137505
$$477$$ 0 0
$$478$$ −12.0000 −0.548867
$$479$$ 10.0000 0.456912 0.228456 0.973554i $$-0.426632\pi$$
0.228456 + 0.973554i $$0.426632\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 10.0000 0.455488
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 7.00000 0.317854
$$486$$ 0 0
$$487$$ 12.0000 0.543772 0.271886 0.962329i $$-0.412353\pi$$
0.271886 + 0.962329i $$0.412353\pi$$
$$488$$ −13.0000 −0.588482
$$489$$ 0 0
$$490$$ −1.00000 −0.0451754
$$491$$ −37.0000 −1.66979 −0.834893 0.550412i $$-0.814471\pi$$
−0.834893 + 0.550412i $$0.814471\pi$$
$$492$$ 0 0
$$493$$ 15.0000 0.675566
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −3.00000 −0.134704
$$497$$ −9.00000 −0.403705
$$498$$ 0 0
$$499$$ 10.0000 0.447661 0.223831 0.974628i $$-0.428144\pi$$
0.223831 + 0.974628i $$0.428144\pi$$
$$500$$ −9.00000 −0.402492
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 10.0000 0.444994
$$506$$ −8.00000 −0.355643
$$507$$ 0 0
$$508$$ 2.00000 0.0887357
$$509$$ 36.0000 1.59567 0.797836 0.602875i $$-0.205978\pi$$
0.797836 + 0.602875i $$0.205978\pi$$
$$510$$ 0 0
$$511$$ 4.00000 0.176950
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −15.0000 −0.661622
$$515$$ 13.0000 0.572848
$$516$$ 0 0
$$517$$ −12.0000 −0.527759
$$518$$ −10.0000 −0.439375
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 38.0000 1.66481 0.832405 0.554168i $$-0.186963\pi$$
0.832405 + 0.554168i $$0.186963\pi$$
$$522$$ 0 0
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ 8.00000 0.349482
$$525$$ 0 0
$$526$$ −16.0000 −0.697633
$$527$$ −9.00000 −0.392046
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ −9.00000 −0.390935
$$531$$ 0 0
$$532$$ −8.00000 −0.346844
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −3.00000 −0.129701
$$536$$ 2.00000 0.0863868
$$537$$ 0 0
$$538$$ −10.0000 −0.431131
$$539$$ 2.00000 0.0861461
$$540$$ 0 0
$$541$$ 10.0000 0.429934 0.214967 0.976621i $$-0.431036\pi$$
0.214967 + 0.976621i $$0.431036\pi$$
$$542$$ −20.0000 −0.859074
$$543$$ 0 0
$$544$$ −3.00000 −0.128624
$$545$$ −2.00000 −0.0856706
$$546$$ 0 0
$$547$$ 2.00000 0.0855138 0.0427569 0.999086i $$-0.486386\pi$$
0.0427569 + 0.999086i $$0.486386\pi$$
$$548$$ −12.0000 −0.512615
$$549$$ 0 0
$$550$$ 8.00000 0.341121
$$551$$ −40.0000 −1.70406
$$552$$ 0 0
$$553$$ −11.0000 −0.467768
$$554$$ −26.0000 −1.10463
$$555$$ 0 0
$$556$$ 14.0000 0.593732
$$557$$ −33.0000 −1.39825 −0.699127 0.714997i $$-0.746428\pi$$
−0.699127 + 0.714997i $$0.746428\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 1.00000 0.0422577
$$561$$ 0 0
$$562$$ 2.00000 0.0843649
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 0 0
$$565$$ −9.00000 −0.378633
$$566$$ −18.0000 −0.756596
$$567$$ 0 0
$$568$$ 9.00000 0.377632
$$569$$ 25.0000 1.04805 0.524027 0.851701i $$-0.324429\pi$$
0.524027 + 0.851701i $$0.324429\pi$$
$$570$$ 0 0
$$571$$ −44.0000 −1.84134 −0.920671 0.390339i $$-0.872358\pi$$
−0.920671 + 0.390339i $$0.872358\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −1.00000 −0.0417392
$$575$$ −16.0000 −0.667246
$$576$$ 0 0
$$577$$ 46.0000 1.91501 0.957503 0.288425i $$-0.0931316\pi$$
0.957503 + 0.288425i $$0.0931316\pi$$
$$578$$ 8.00000 0.332756
$$579$$ 0 0
$$580$$ 5.00000 0.207614
$$581$$ 14.0000 0.580818
$$582$$ 0 0
$$583$$ 18.0000 0.745484
$$584$$ −4.00000 −0.165521
$$585$$ 0 0
$$586$$ 14.0000 0.578335
$$587$$ 21.0000 0.866763 0.433381 0.901211i $$-0.357320\pi$$
0.433381 + 0.901211i $$0.357320\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ −10.0000 −0.411693
$$591$$ 0 0
$$592$$ 10.0000 0.410997
$$593$$ 43.0000 1.76580 0.882899 0.469563i $$-0.155588\pi$$
0.882899 + 0.469563i $$0.155588\pi$$
$$594$$ 0 0
$$595$$ 3.00000 0.122988
$$596$$ −3.00000 −0.122885
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 44.0000 1.79779 0.898896 0.438163i $$-0.144371\pi$$
0.898896 + 0.438163i $$0.144371\pi$$
$$600$$ 0 0
$$601$$ 21.0000 0.856608 0.428304 0.903635i $$-0.359111\pi$$
0.428304 + 0.903635i $$0.359111\pi$$
$$602$$ 5.00000 0.203785
$$603$$ 0 0
$$604$$ 19.0000 0.773099
$$605$$ −7.00000 −0.284590
$$606$$ 0 0
$$607$$ −43.0000 −1.74532 −0.872658 0.488332i $$-0.837606\pi$$
−0.872658 + 0.488332i $$0.837606\pi$$
$$608$$ 8.00000 0.324443
$$609$$ 0 0
$$610$$ −13.0000 −0.526355
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −16.0000 −0.646234 −0.323117 0.946359i $$-0.604731\pi$$
−0.323117 + 0.946359i $$0.604731\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 0 0
$$616$$ −2.00000 −0.0805823
$$617$$ −30.0000 −1.20775 −0.603877 0.797077i $$-0.706378\pi$$
−0.603877 + 0.797077i $$0.706378\pi$$
$$618$$ 0 0
$$619$$ −24.0000 −0.964641 −0.482321 0.875995i $$-0.660206\pi$$
−0.482321 + 0.875995i $$0.660206\pi$$
$$620$$ −3.00000 −0.120483
$$621$$ 0 0
$$622$$ 18.0000 0.721734
$$623$$ 1.00000 0.0400642
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ 22.0000 0.879297
$$627$$ 0 0
$$628$$ 4.00000 0.159617
$$629$$ 30.0000 1.19618
$$630$$ 0 0
$$631$$ 30.0000 1.19428 0.597141 0.802137i $$-0.296303\pi$$
0.597141 + 0.802137i $$0.296303\pi$$
$$632$$ 11.0000 0.437557
$$633$$ 0 0
$$634$$ −18.0000 −0.714871
$$635$$ 2.00000 0.0793676
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −10.0000 −0.395904
$$639$$ 0 0
$$640$$ −1.00000 −0.0395285
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 0 0
$$643$$ −7.00000 −0.276053 −0.138027 0.990429i $$-0.544076\pi$$
−0.138027 + 0.990429i $$0.544076\pi$$
$$644$$ 4.00000 0.157622
$$645$$ 0 0
$$646$$ 24.0000 0.944267
$$647$$ 3.00000 0.117942 0.0589711 0.998260i $$-0.481218\pi$$
0.0589711 + 0.998260i $$0.481218\pi$$
$$648$$ 0 0
$$649$$ 20.0000 0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ −3.00000 −0.117399 −0.0586995 0.998276i $$-0.518695\pi$$
−0.0586995 + 0.998276i $$0.518695\pi$$
$$654$$ 0 0
$$655$$ 8.00000 0.312586
$$656$$ 1.00000 0.0390434
$$657$$ 0 0
$$658$$ 6.00000 0.233904
$$659$$ −44.0000 −1.71400 −0.856998 0.515319i $$-0.827673\pi$$
−0.856998 + 0.515319i $$0.827673\pi$$
$$660$$ 0 0
$$661$$ −38.0000 −1.47803 −0.739014 0.673690i $$-0.764708\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ 32.0000 1.24372
$$663$$ 0 0
$$664$$ −14.0000 −0.543305
$$665$$ −8.00000 −0.310227
$$666$$ 0 0
$$667$$ 20.0000 0.774403
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 2.00000 0.0772667
$$671$$ 26.0000 1.00372
$$672$$ 0 0
$$673$$ 30.0000 1.15642 0.578208 0.815890i $$-0.303752\pi$$
0.578208 + 0.815890i $$0.303752\pi$$
$$674$$ 19.0000 0.731853
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ −6.00000 −0.230599 −0.115299 0.993331i $$-0.536783\pi$$
−0.115299 + 0.993331i $$0.536783\pi$$
$$678$$ 0 0
$$679$$ 7.00000 0.268635
$$680$$ −3.00000 −0.115045
$$681$$ 0 0
$$682$$ 6.00000 0.229752
$$683$$ −40.0000 −1.53056 −0.765279 0.643699i $$-0.777399\pi$$
−0.765279 + 0.643699i $$0.777399\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ −1.00000 −0.0381802
$$687$$ 0 0
$$688$$ −5.00000 −0.190623
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 13.0000 0.494543 0.247272 0.968946i $$-0.420466\pi$$
0.247272 + 0.968946i $$0.420466\pi$$
$$692$$ 1.00000 0.0380143
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 14.0000 0.531050
$$696$$ 0 0
$$697$$ 3.00000 0.113633
$$698$$ −14.0000 −0.529908
$$699$$ 0 0
$$700$$ −4.00000 −0.151186
$$701$$ −16.0000 −0.604312 −0.302156 0.953259i $$-0.597706\pi$$
−0.302156 + 0.953259i $$0.597706\pi$$
$$702$$ 0 0
$$703$$ −80.0000 −3.01726
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ −24.0000 −0.903252
$$707$$ 10.0000 0.376089
$$708$$ 0 0
$$709$$ 3.00000 0.112667 0.0563337 0.998412i $$-0.482059\pi$$
0.0563337 + 0.998412i $$0.482059\pi$$
$$710$$ 9.00000 0.337764
$$711$$ 0 0
$$712$$ −1.00000 −0.0374766
$$713$$ −12.0000 −0.449404
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 16.0000 0.597948
$$717$$ 0 0
$$718$$ 24.0000 0.895672
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 0 0
$$721$$ 13.0000 0.484145
$$722$$ −45.0000 −1.67473
$$723$$ 0 0
$$724$$ −14.0000 −0.520306
$$725$$ −20.0000 −0.742781
$$726$$ 0 0
$$727$$ −28.0000 −1.03846 −0.519231 0.854634i $$-0.673782\pi$$
−0.519231 + 0.854634i $$0.673782\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −4.00000 −0.148047
$$731$$ −15.0000 −0.554795
$$732$$ 0 0
$$733$$ 13.0000 0.480166 0.240083 0.970752i $$-0.422825\pi$$
0.240083 + 0.970752i $$0.422825\pi$$
$$734$$ 17.0000 0.627481
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ −4.00000 −0.147342
$$738$$ 0 0
$$739$$ 19.0000 0.698926 0.349463 0.936950i $$-0.386364\pi$$
0.349463 + 0.936950i $$0.386364\pi$$
$$740$$ 10.0000 0.367607
$$741$$ 0 0
$$742$$ −9.00000 −0.330400
$$743$$ 12.0000 0.440237 0.220119 0.975473i $$-0.429356\pi$$
0.220119 + 0.975473i $$0.429356\pi$$
$$744$$ 0 0
$$745$$ −3.00000 −0.109911
$$746$$ 18.0000 0.659027
$$747$$ 0 0
$$748$$ 6.00000 0.219382
$$749$$ −3.00000 −0.109618
$$750$$ 0 0
$$751$$ 24.0000 0.875772 0.437886 0.899030i $$-0.355727\pi$$
0.437886 + 0.899030i $$0.355727\pi$$
$$752$$ −6.00000 −0.218797
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 19.0000 0.691481
$$756$$ 0 0
$$757$$ −5.00000 −0.181728 −0.0908640 0.995863i $$-0.528963\pi$$
−0.0908640 + 0.995863i $$0.528963\pi$$
$$758$$ −37.0000 −1.34390
$$759$$ 0 0
$$760$$ 8.00000 0.290191
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ 0 0
$$763$$ −2.00000 −0.0724049
$$764$$ 11.0000 0.397966
$$765$$ 0 0
$$766$$ −22.0000 −0.794892
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ −2.00000 −0.0720750
$$771$$ 0 0
$$772$$ 12.0000 0.431889
$$773$$ 38.0000 1.36677 0.683383 0.730061i $$-0.260508\pi$$
0.683383 + 0.730061i $$0.260508\pi$$
$$774$$ 0 0
$$775$$ 12.0000 0.431053
$$776$$ −7.00000 −0.251285
$$777$$ 0 0
$$778$$ −2.00000 −0.0717035
$$779$$ −8.00000 −0.286630
$$780$$ 0 0
$$781$$ −18.0000 −0.644091
$$782$$ −12.0000 −0.429119
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 4.00000 0.142766
$$786$$ 0 0
$$787$$ −52.0000 −1.85360 −0.926800 0.375555i $$-0.877452\pi$$
−0.926800 + 0.375555i $$0.877452\pi$$
$$788$$ 12.0000 0.427482
$$789$$ 0 0
$$790$$ 11.0000 0.391362
$$791$$ −9.00000 −0.320003
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −20.0000 −0.709773
$$795$$ 0 0
$$796$$ −24.0000 −0.850657
$$797$$ −21.0000 −0.743858 −0.371929 0.928261i $$-0.621304\pi$$
−0.371929 + 0.928261i $$0.621304\pi$$
$$798$$ 0 0
$$799$$ −18.0000 −0.636794
$$800$$ 4.00000 0.141421
$$801$$ 0 0
$$802$$ −25.0000 −0.882781
$$803$$ 8.00000 0.282314
$$804$$ 0 0
$$805$$ 4.00000 0.140981
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −10.0000 −0.351799
$$809$$ −54.0000 −1.89854 −0.949269 0.314464i $$-0.898175\pi$$
−0.949269 + 0.314464i $$0.898175\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 5.00000 0.175466
$$813$$ 0 0
$$814$$ −20.0000 −0.701000
$$815$$ −4.00000 −0.140114
$$816$$ 0 0
$$817$$ 40.0000 1.39942
$$818$$ 10.0000 0.349642
$$819$$ 0 0
$$820$$ 1.00000 0.0349215
$$821$$ 4.00000 0.139601 0.0698005 0.997561i $$-0.477764\pi$$
0.0698005 + 0.997561i $$0.477764\pi$$
$$822$$ 0 0
$$823$$ −51.0000 −1.77775 −0.888874 0.458151i $$-0.848512\pi$$
−0.888874 + 0.458151i $$0.848512\pi$$
$$824$$ −13.0000 −0.452876
$$825$$ 0 0
$$826$$ −10.0000 −0.347945
$$827$$ −30.0000 −1.04320 −0.521601 0.853189i $$-0.674665\pi$$
−0.521601 + 0.853189i $$0.674665\pi$$
$$828$$ 0 0
$$829$$ 11.0000 0.382046 0.191023 0.981586i $$-0.438820\pi$$
0.191023 + 0.981586i $$0.438820\pi$$
$$830$$ −14.0000 −0.485947
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 3.00000 0.103944
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −16.0000 −0.553372
$$837$$ 0 0
$$838$$ 28.0000 0.967244
$$839$$ −14.0000 −0.483334 −0.241667 0.970359i $$-0.577694\pi$$
−0.241667 + 0.970359i $$0.577694\pi$$
$$840$$ 0 0
$$841$$ −4.00000 −0.137931
$$842$$ 19.0000 0.654783
$$843$$ 0 0
$$844$$ −12.0000 −0.413057
$$845$$ −13.0000 −0.447214
$$846$$ 0 0
$$847$$ −7.00000 −0.240523
$$848$$ 9.00000 0.309061
$$849$$ 0 0
$$850$$ 12.0000 0.411597
$$851$$ 40.0000 1.37118
$$852$$ 0 0
$$853$$ −21.0000 −0.719026 −0.359513 0.933140i $$-0.617057\pi$$
−0.359513 + 0.933140i $$0.617057\pi$$
$$854$$ −13.0000 −0.444851
$$855$$ 0 0
$$856$$ 3.00000 0.102538
$$857$$ 38.0000 1.29806 0.649028 0.760765i $$-0.275176\pi$$
0.649028 + 0.760765i $$0.275176\pi$$
$$858$$ 0 0
$$859$$ −8.00000 −0.272956 −0.136478 0.990643i $$-0.543578\pi$$
−0.136478 + 0.990643i $$0.543578\pi$$
$$860$$ −5.00000 −0.170499
$$861$$ 0 0
$$862$$ −16.0000 −0.544962
$$863$$ 32.0000 1.08929 0.544646 0.838666i $$-0.316664\pi$$
0.544646 + 0.838666i $$0.316664\pi$$
$$864$$ 0 0
$$865$$ 1.00000 0.0340010
$$866$$ 0 0
$$867$$ 0 0
$$868$$ −3.00000 −0.101827
$$869$$ −22.0000 −0.746299
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 2.00000 0.0677285
$$873$$ 0 0
$$874$$ 32.0000 1.08242
$$875$$ −9.00000 −0.304256
$$876$$ 0 0
$$877$$ −32.0000 −1.08056 −0.540282 0.841484i $$-0.681682\pi$$
−0.540282 + 0.841484i $$0.681682\pi$$
$$878$$ −34.0000 −1.14744
$$879$$ 0 0
$$880$$ 2.00000 0.0674200
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ −26.0000 −0.874970 −0.437485 0.899226i $$-0.644131\pi$$
−0.437485 + 0.899226i $$0.644131\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ −25.0000 −0.839891
$$887$$ −20.0000 −0.671534 −0.335767 0.941945i $$-0.608996\pi$$
−0.335767 + 0.941945i $$0.608996\pi$$
$$888$$ 0 0
$$889$$ 2.00000 0.0670778
$$890$$ −1.00000 −0.0335201
$$891$$ 0 0
$$892$$ 21.0000 0.703132
$$893$$ 48.0000 1.60626
$$894$$ 0 0
$$895$$ 16.0000 0.534821
$$896$$ −1.00000 −0.0334077
$$897$$ 0 0
$$898$$ −33.0000 −1.10122
$$899$$ −15.0000 −0.500278
$$900$$ 0 0
$$901$$ 27.0000 0.899500
$$902$$ −2.00000 −0.0665927
$$903$$ 0 0
$$904$$ 9.00000 0.299336
$$905$$ −14.0000 −0.465376
$$906$$ 0 0
$$907$$ 19.0000 0.630885 0.315442 0.948945i $$-0.397847\pi$$
0.315442 + 0.948945i $$0.397847\pi$$
$$908$$ −25.0000 −0.829654
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −2.00000 −0.0662630 −0.0331315 0.999451i $$-0.510548\pi$$
−0.0331315 + 0.999451i $$0.510548\pi$$
$$912$$ 0 0
$$913$$ 28.0000 0.926665
$$914$$ 18.0000 0.595387
$$915$$ 0 0
$$916$$ 20.0000 0.660819
$$917$$ 8.00000 0.264183
$$918$$ 0 0
$$919$$ 3.00000 0.0989609 0.0494804 0.998775i $$-0.484243\pi$$
0.0494804 + 0.998775i $$0.484243\pi$$
$$920$$ −4.00000 −0.131876
$$921$$ 0 0
$$922$$ −21.0000 −0.691598
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −40.0000 −1.31519
$$926$$ −16.0000 −0.525793
$$927$$ 0 0
$$928$$ −5.00000 −0.164133
$$929$$ 50.0000 1.64045 0.820223 0.572043i $$-0.193849\pi$$
0.820223 + 0.572043i $$0.193849\pi$$
$$930$$ 0 0
$$931$$ −8.00000 −0.262189
$$932$$ −10.0000 −0.327561
$$933$$ 0 0
$$934$$ 6.00000 0.196326
$$935$$ 6.00000 0.196221
$$936$$ 0 0
$$937$$ 7.00000 0.228680 0.114340 0.993442i $$-0.463525\pi$$
0.114340 + 0.993442i $$0.463525\pi$$
$$938$$ 2.00000 0.0653023
$$939$$ 0 0
$$940$$ −6.00000 −0.195698
$$941$$ −18.0000 −0.586783 −0.293392 0.955992i $$-0.594784\pi$$
−0.293392 + 0.955992i $$0.594784\pi$$
$$942$$ 0 0
$$943$$ 4.00000 0.130258
$$944$$ 10.0000 0.325472
$$945$$ 0 0
$$946$$ 10.0000 0.325128
$$947$$ 4.00000 0.129983 0.0649913 0.997886i $$-0.479298\pi$$
0.0649913 + 0.997886i $$0.479298\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ −32.0000 −1.03822
$$951$$ 0 0
$$952$$ −3.00000 −0.0972306
$$953$$ −30.0000 −0.971795 −0.485898 0.874016i $$-0.661507\pi$$
−0.485898 + 0.874016i $$0.661507\pi$$
$$954$$ 0 0
$$955$$ 11.0000 0.355952
$$956$$ 12.0000 0.388108
$$957$$ 0 0
$$958$$ −10.0000 −0.323085
$$959$$ −12.0000 −0.387500
$$960$$ 0 0
$$961$$ −22.0000 −0.709677
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −10.0000 −0.322078
$$965$$ 12.0000 0.386294
$$966$$ 0 0
$$967$$ −47.0000 −1.51142 −0.755709 0.654907i $$-0.772708\pi$$
−0.755709 + 0.654907i $$0.772708\pi$$
$$968$$ 7.00000 0.224989
$$969$$ 0 0
$$970$$ −7.00000 −0.224756
$$971$$ −13.0000 −0.417190 −0.208595 0.978002i $$-0.566889\pi$$
−0.208595 + 0.978002i $$0.566889\pi$$
$$972$$ 0 0
$$973$$ 14.0000 0.448819
$$974$$ −12.0000 −0.384505
$$975$$ 0 0
$$976$$ 13.0000 0.416120
$$977$$ −54.0000 −1.72761 −0.863807 0.503824i $$-0.831926\pi$$
−0.863807 + 0.503824i $$0.831926\pi$$
$$978$$ 0 0
$$979$$ 2.00000 0.0639203
$$980$$ 1.00000 0.0319438
$$981$$ 0 0
$$982$$ 37.0000 1.18072
$$983$$ 3.00000 0.0956851 0.0478426 0.998855i $$-0.484765\pi$$
0.0478426 + 0.998855i $$0.484765\pi$$
$$984$$ 0 0
$$985$$ 12.0000 0.382352
$$986$$ −15.0000 −0.477697
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −20.0000 −0.635963
$$990$$ 0 0
$$991$$ 40.0000 1.27064 0.635321 0.772248i $$-0.280868\pi$$
0.635321 + 0.772248i $$0.280868\pi$$
$$992$$ 3.00000 0.0952501
$$993$$ 0 0
$$994$$ 9.00000 0.285463
$$995$$ −24.0000 −0.760851
$$996$$ 0 0
$$997$$ 4.00000 0.126681 0.0633406 0.997992i $$-0.479825\pi$$
0.0633406 + 0.997992i $$0.479825\pi$$
$$998$$ −10.0000 −0.316544
$$999$$ 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 5166.2.a.o.1.1 1
3.2 odd 2 574.2.a.g.1.1 1
12.11 even 2 4592.2.a.l.1.1 1
21.20 even 2 4018.2.a.s.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.a.g.1.1 1 3.2 odd 2
4018.2.a.s.1.1 1 21.20 even 2
4592.2.a.l.1.1 1 12.11 even 2
5166.2.a.o.1.1 1 1.1 even 1 trivial