# Properties

 Label 4650.2.a.bv.1.1 Level $4650$ Weight $2$ Character 4650.1 Self dual yes Analytic conductor $37.130$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4650.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$37.1304369399$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 930) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 4650.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} -3.00000 q^{19} +3.00000 q^{21} +3.00000 q^{22} -5.00000 q^{23} +1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} +3.00000 q^{28} +4.00000 q^{29} +1.00000 q^{31} +1.00000 q^{32} +3.00000 q^{33} +4.00000 q^{34} +1.00000 q^{36} -3.00000 q^{38} +2.00000 q^{39} +4.00000 q^{41} +3.00000 q^{42} -1.00000 q^{43} +3.00000 q^{44} -5.00000 q^{46} -10.0000 q^{47} +1.00000 q^{48} +2.00000 q^{49} +4.00000 q^{51} +2.00000 q^{52} -3.00000 q^{53} +1.00000 q^{54} +3.00000 q^{56} -3.00000 q^{57} +4.00000 q^{58} +6.00000 q^{59} -2.00000 q^{61} +1.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +3.00000 q^{66} -2.00000 q^{67} +4.00000 q^{68} -5.00000 q^{69} +7.00000 q^{71} +1.00000 q^{72} -5.00000 q^{73} -3.00000 q^{76} +9.00000 q^{77} +2.00000 q^{78} -1.00000 q^{79} +1.00000 q^{81} +4.00000 q^{82} -12.0000 q^{83} +3.00000 q^{84} -1.00000 q^{86} +4.00000 q^{87} +3.00000 q^{88} +1.00000 q^{89} +6.00000 q^{91} -5.00000 q^{92} +1.00000 q^{93} -10.0000 q^{94} +1.00000 q^{96} +10.0000 q^{97} +2.00000 q^{98} +3.00000 q^{99} +O(q^{100})$$

## 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
$$3$$ 1.00000 0.577350
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 1.00000 0.408248
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 3.00000 0.801784
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −3.00000 −0.688247 −0.344124 0.938924i $$-0.611824\pi$$
−0.344124 + 0.938924i $$0.611824\pi$$
$$20$$ 0 0
$$21$$ 3.00000 0.654654
$$22$$ 3.00000 0.639602
$$23$$ −5.00000 −1.04257 −0.521286 0.853382i $$-0.674548\pi$$
−0.521286 + 0.853382i $$0.674548\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 0 0
$$26$$ 2.00000 0.392232
$$27$$ 1.00000 0.192450
$$28$$ 3.00000 0.566947
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ 1.00000 0.179605
$$32$$ 1.00000 0.176777
$$33$$ 3.00000 0.522233
$$34$$ 4.00000 0.685994
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ −3.00000 −0.486664
$$39$$ 2.00000 0.320256
$$40$$ 0 0
$$41$$ 4.00000 0.624695 0.312348 0.949968i $$-0.398885\pi$$
0.312348 + 0.949968i $$0.398885\pi$$
$$42$$ 3.00000 0.462910
$$43$$ −1.00000 −0.152499 −0.0762493 0.997089i $$-0.524294\pi$$
−0.0762493 + 0.997089i $$0.524294\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 0 0
$$46$$ −5.00000 −0.737210
$$47$$ −10.0000 −1.45865 −0.729325 0.684167i $$-0.760166\pi$$
−0.729325 + 0.684167i $$0.760166\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 2.00000 0.285714
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ 2.00000 0.277350
$$53$$ −3.00000 −0.412082 −0.206041 0.978543i $$-0.566058\pi$$
−0.206041 + 0.978543i $$0.566058\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 0 0
$$56$$ 3.00000 0.400892
$$57$$ −3.00000 −0.397360
$$58$$ 4.00000 0.525226
$$59$$ 6.00000 0.781133 0.390567 0.920575i $$-0.372279\pi$$
0.390567 + 0.920575i $$0.372279\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 1.00000 0.127000
$$63$$ 3.00000 0.377964
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 3.00000 0.369274
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 4.00000 0.485071
$$69$$ −5.00000 −0.601929
$$70$$ 0 0
$$71$$ 7.00000 0.830747 0.415374 0.909651i $$-0.363651\pi$$
0.415374 + 0.909651i $$0.363651\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −5.00000 −0.585206 −0.292603 0.956234i $$-0.594521\pi$$
−0.292603 + 0.956234i $$0.594521\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −3.00000 −0.344124
$$77$$ 9.00000 1.02565
$$78$$ 2.00000 0.226455
$$79$$ −1.00000 −0.112509 −0.0562544 0.998416i $$-0.517916\pi$$
−0.0562544 + 0.998416i $$0.517916\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 4.00000 0.441726
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 3.00000 0.327327
$$85$$ 0 0
$$86$$ −1.00000 −0.107833
$$87$$ 4.00000 0.428845
$$88$$ 3.00000 0.319801
$$89$$ 1.00000 0.106000 0.0529999 0.998595i $$-0.483122\pi$$
0.0529999 + 0.998595i $$0.483122\pi$$
$$90$$ 0 0
$$91$$ 6.00000 0.628971
$$92$$ −5.00000 −0.521286
$$93$$ 1.00000 0.103695
$$94$$ −10.0000 −1.03142
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 2.00000 0.202031
$$99$$ 3.00000 0.301511
$$100$$ 0 0
$$101$$ −1.00000 −0.0995037 −0.0497519 0.998762i $$-0.515843\pi$$
−0.0497519 + 0.998762i $$0.515843\pi$$
$$102$$ 4.00000 0.396059
$$103$$ −16.0000 −1.57653 −0.788263 0.615338i $$-0.789020\pi$$
−0.788263 + 0.615338i $$0.789020\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ −3.00000 −0.291386
$$107$$ −9.00000 −0.870063 −0.435031 0.900415i $$-0.643263\pi$$
−0.435031 + 0.900415i $$0.643263\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 20.0000 1.91565 0.957826 0.287348i $$-0.0927736\pi$$
0.957826 + 0.287348i $$0.0927736\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 3.00000 0.283473
$$113$$ −9.00000 −0.846649 −0.423324 0.905978i $$-0.639137\pi$$
−0.423324 + 0.905978i $$0.639137\pi$$
$$114$$ −3.00000 −0.280976
$$115$$ 0 0
$$116$$ 4.00000 0.371391
$$117$$ 2.00000 0.184900
$$118$$ 6.00000 0.552345
$$119$$ 12.0000 1.10004
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ −2.00000 −0.181071
$$123$$ 4.00000 0.360668
$$124$$ 1.00000 0.0898027
$$125$$ 0 0
$$126$$ 3.00000 0.267261
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −1.00000 −0.0880451
$$130$$ 0 0
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 3.00000 0.261116
$$133$$ −9.00000 −0.780399
$$134$$ −2.00000 −0.172774
$$135$$ 0 0
$$136$$ 4.00000 0.342997
$$137$$ 10.0000 0.854358 0.427179 0.904167i $$-0.359507\pi$$
0.427179 + 0.904167i $$0.359507\pi$$
$$138$$ −5.00000 −0.425628
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 0 0
$$141$$ −10.0000 −0.842152
$$142$$ 7.00000 0.587427
$$143$$ 6.00000 0.501745
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −5.00000 −0.413803
$$147$$ 2.00000 0.164957
$$148$$ 0 0
$$149$$ −11.0000 −0.901155 −0.450578 0.892737i $$-0.648782\pi$$
−0.450578 + 0.892737i $$0.648782\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ −3.00000 −0.243332
$$153$$ 4.00000 0.323381
$$154$$ 9.00000 0.725241
$$155$$ 0 0
$$156$$ 2.00000 0.160128
$$157$$ 5.00000 0.399043 0.199522 0.979893i $$-0.436061\pi$$
0.199522 + 0.979893i $$0.436061\pi$$
$$158$$ −1.00000 −0.0795557
$$159$$ −3.00000 −0.237915
$$160$$ 0 0
$$161$$ −15.0000 −1.18217
$$162$$ 1.00000 0.0785674
$$163$$ −14.0000 −1.09656 −0.548282 0.836293i $$-0.684718\pi$$
−0.548282 + 0.836293i $$0.684718\pi$$
$$164$$ 4.00000 0.312348
$$165$$ 0 0
$$166$$ −12.0000 −0.931381
$$167$$ 19.0000 1.47026 0.735132 0.677924i $$-0.237120\pi$$
0.735132 + 0.677924i $$0.237120\pi$$
$$168$$ 3.00000 0.231455
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −3.00000 −0.229416
$$172$$ −1.00000 −0.0762493
$$173$$ 22.0000 1.67263 0.836315 0.548250i $$-0.184706\pi$$
0.836315 + 0.548250i $$0.184706\pi$$
$$174$$ 4.00000 0.303239
$$175$$ 0 0
$$176$$ 3.00000 0.226134
$$177$$ 6.00000 0.450988
$$178$$ 1.00000 0.0749532
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ 5.00000 0.371647 0.185824 0.982583i $$-0.440505\pi$$
0.185824 + 0.982583i $$0.440505\pi$$
$$182$$ 6.00000 0.444750
$$183$$ −2.00000 −0.147844
$$184$$ −5.00000 −0.368605
$$185$$ 0 0
$$186$$ 1.00000 0.0733236
$$187$$ 12.0000 0.877527
$$188$$ −10.0000 −0.729325
$$189$$ 3.00000 0.218218
$$190$$ 0 0
$$191$$ 16.0000 1.15772 0.578860 0.815427i $$-0.303498\pi$$
0.578860 + 0.815427i $$0.303498\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 6.00000 0.431889 0.215945 0.976406i $$-0.430717\pi$$
0.215945 + 0.976406i $$0.430717\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ 2.00000 0.142857
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 3.00000 0.213201
$$199$$ 7.00000 0.496217 0.248108 0.968732i $$-0.420191\pi$$
0.248108 + 0.968732i $$0.420191\pi$$
$$200$$ 0 0
$$201$$ −2.00000 −0.141069
$$202$$ −1.00000 −0.0703598
$$203$$ 12.0000 0.842235
$$204$$ 4.00000 0.280056
$$205$$ 0 0
$$206$$ −16.0000 −1.11477
$$207$$ −5.00000 −0.347524
$$208$$ 2.00000 0.138675
$$209$$ −9.00000 −0.622543
$$210$$ 0 0
$$211$$ −19.0000 −1.30801 −0.654007 0.756489i $$-0.726913\pi$$
−0.654007 + 0.756489i $$0.726913\pi$$
$$212$$ −3.00000 −0.206041
$$213$$ 7.00000 0.479632
$$214$$ −9.00000 −0.615227
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 3.00000 0.203653
$$218$$ 20.0000 1.35457
$$219$$ −5.00000 −0.337869
$$220$$ 0 0
$$221$$ 8.00000 0.538138
$$222$$ 0 0
$$223$$ 6.00000 0.401790 0.200895 0.979613i $$-0.435615\pi$$
0.200895 + 0.979613i $$0.435615\pi$$
$$224$$ 3.00000 0.200446
$$225$$ 0 0
$$226$$ −9.00000 −0.598671
$$227$$ 27.0000 1.79205 0.896026 0.444001i $$-0.146441\pi$$
0.896026 + 0.444001i $$0.146441\pi$$
$$228$$ −3.00000 −0.198680
$$229$$ 13.0000 0.859064 0.429532 0.903052i $$-0.358679\pi$$
0.429532 + 0.903052i $$0.358679\pi$$
$$230$$ 0 0
$$231$$ 9.00000 0.592157
$$232$$ 4.00000 0.262613
$$233$$ −15.0000 −0.982683 −0.491341 0.870967i $$-0.663493\pi$$
−0.491341 + 0.870967i $$0.663493\pi$$
$$234$$ 2.00000 0.130744
$$235$$ 0 0
$$236$$ 6.00000 0.390567
$$237$$ −1.00000 −0.0649570
$$238$$ 12.0000 0.777844
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ −2.00000 −0.128565
$$243$$ 1.00000 0.0641500
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ 4.00000 0.255031
$$247$$ −6.00000 −0.381771
$$248$$ 1.00000 0.0635001
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 3.00000 0.188982
$$253$$ −15.0000 −0.943042
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 23.0000 1.43470 0.717350 0.696713i $$-0.245355\pi$$
0.717350 + 0.696713i $$0.245355\pi$$
$$258$$ −1.00000 −0.0622573
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 4.00000 0.247594
$$262$$ 6.00000 0.370681
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ 3.00000 0.184637
$$265$$ 0 0
$$266$$ −9.00000 −0.551825
$$267$$ 1.00000 0.0611990
$$268$$ −2.00000 −0.122169
$$269$$ 2.00000 0.121942 0.0609711 0.998140i $$-0.480580\pi$$
0.0609711 + 0.998140i $$0.480580\pi$$
$$270$$ 0 0
$$271$$ 13.0000 0.789694 0.394847 0.918747i $$-0.370798\pi$$
0.394847 + 0.918747i $$0.370798\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 6.00000 0.363137
$$274$$ 10.0000 0.604122
$$275$$ 0 0
$$276$$ −5.00000 −0.300965
$$277$$ −12.0000 −0.721010 −0.360505 0.932757i $$-0.617396\pi$$
−0.360505 + 0.932757i $$0.617396\pi$$
$$278$$ −14.0000 −0.839664
$$279$$ 1.00000 0.0598684
$$280$$ 0 0
$$281$$ 16.0000 0.954480 0.477240 0.878773i $$-0.341637\pi$$
0.477240 + 0.878773i $$0.341637\pi$$
$$282$$ −10.0000 −0.595491
$$283$$ 24.0000 1.42665 0.713326 0.700832i $$-0.247188\pi$$
0.713326 + 0.700832i $$0.247188\pi$$
$$284$$ 7.00000 0.415374
$$285$$ 0 0
$$286$$ 6.00000 0.354787
$$287$$ 12.0000 0.708338
$$288$$ 1.00000 0.0589256
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 10.0000 0.586210
$$292$$ −5.00000 −0.292603
$$293$$ −30.0000 −1.75262 −0.876309 0.481749i $$-0.840002\pi$$
−0.876309 + 0.481749i $$0.840002\pi$$
$$294$$ 2.00000 0.116642
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 3.00000 0.174078
$$298$$ −11.0000 −0.637213
$$299$$ −10.0000 −0.578315
$$300$$ 0 0
$$301$$ −3.00000 −0.172917
$$302$$ 0 0
$$303$$ −1.00000 −0.0574485
$$304$$ −3.00000 −0.172062
$$305$$ 0 0
$$306$$ 4.00000 0.228665
$$307$$ −16.0000 −0.913168 −0.456584 0.889680i $$-0.650927\pi$$
−0.456584 + 0.889680i $$0.650927\pi$$
$$308$$ 9.00000 0.512823
$$309$$ −16.0000 −0.910208
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 2.00000 0.113228
$$313$$ −30.0000 −1.69570 −0.847850 0.530236i $$-0.822103\pi$$
−0.847850 + 0.530236i $$0.822103\pi$$
$$314$$ 5.00000 0.282166
$$315$$ 0 0
$$316$$ −1.00000 −0.0562544
$$317$$ 8.00000 0.449325 0.224662 0.974437i $$-0.427872\pi$$
0.224662 + 0.974437i $$0.427872\pi$$
$$318$$ −3.00000 −0.168232
$$319$$ 12.0000 0.671871
$$320$$ 0 0
$$321$$ −9.00000 −0.502331
$$322$$ −15.0000 −0.835917
$$323$$ −12.0000 −0.667698
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −14.0000 −0.775388
$$327$$ 20.0000 1.10600
$$328$$ 4.00000 0.220863
$$329$$ −30.0000 −1.65395
$$330$$ 0 0
$$331$$ 12.0000 0.659580 0.329790 0.944054i $$-0.393022\pi$$
0.329790 + 0.944054i $$0.393022\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 0 0
$$334$$ 19.0000 1.03963
$$335$$ 0 0
$$336$$ 3.00000 0.163663
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ −9.00000 −0.489535
$$339$$ −9.00000 −0.488813
$$340$$ 0 0
$$341$$ 3.00000 0.162459
$$342$$ −3.00000 −0.162221
$$343$$ −15.0000 −0.809924
$$344$$ −1.00000 −0.0539164
$$345$$ 0 0
$$346$$ 22.0000 1.18273
$$347$$ 32.0000 1.71785 0.858925 0.512101i $$-0.171133\pi$$
0.858925 + 0.512101i $$0.171133\pi$$
$$348$$ 4.00000 0.214423
$$349$$ −24.0000 −1.28469 −0.642345 0.766415i $$-0.722038\pi$$
−0.642345 + 0.766415i $$0.722038\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ 3.00000 0.159901
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ 6.00000 0.318896
$$355$$ 0 0
$$356$$ 1.00000 0.0529999
$$357$$ 12.0000 0.635107
$$358$$ 4.00000 0.211407
$$359$$ 15.0000 0.791670 0.395835 0.918322i $$-0.370455\pi$$
0.395835 + 0.918322i $$0.370455\pi$$
$$360$$ 0 0
$$361$$ −10.0000 −0.526316
$$362$$ 5.00000 0.262794
$$363$$ −2.00000 −0.104973
$$364$$ 6.00000 0.314485
$$365$$ 0 0
$$366$$ −2.00000 −0.104542
$$367$$ −2.00000 −0.104399 −0.0521996 0.998637i $$-0.516623\pi$$
−0.0521996 + 0.998637i $$0.516623\pi$$
$$368$$ −5.00000 −0.260643
$$369$$ 4.00000 0.208232
$$370$$ 0 0
$$371$$ −9.00000 −0.467257
$$372$$ 1.00000 0.0518476
$$373$$ 9.00000 0.466002 0.233001 0.972476i $$-0.425145\pi$$
0.233001 + 0.972476i $$0.425145\pi$$
$$374$$ 12.0000 0.620505
$$375$$ 0 0
$$376$$ −10.0000 −0.515711
$$377$$ 8.00000 0.412021
$$378$$ 3.00000 0.154303
$$379$$ 15.0000 0.770498 0.385249 0.922813i $$-0.374116\pi$$
0.385249 + 0.922813i $$0.374116\pi$$
$$380$$ 0 0
$$381$$ −8.00000 −0.409852
$$382$$ 16.0000 0.818631
$$383$$ −12.0000 −0.613171 −0.306586 0.951843i $$-0.599187\pi$$
−0.306586 + 0.951843i $$0.599187\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ 6.00000 0.305392
$$387$$ −1.00000 −0.0508329
$$388$$ 10.0000 0.507673
$$389$$ −26.0000 −1.31825 −0.659126 0.752032i $$-0.729074\pi$$
−0.659126 + 0.752032i $$0.729074\pi$$
$$390$$ 0 0
$$391$$ −20.0000 −1.01144
$$392$$ 2.00000 0.101015
$$393$$ 6.00000 0.302660
$$394$$ 6.00000 0.302276
$$395$$ 0 0
$$396$$ 3.00000 0.150756
$$397$$ −35.0000 −1.75660 −0.878300 0.478110i $$-0.841322\pi$$
−0.878300 + 0.478110i $$0.841322\pi$$
$$398$$ 7.00000 0.350878
$$399$$ −9.00000 −0.450564
$$400$$ 0 0
$$401$$ 25.0000 1.24844 0.624220 0.781248i $$-0.285417\pi$$
0.624220 + 0.781248i $$0.285417\pi$$
$$402$$ −2.00000 −0.0997509
$$403$$ 2.00000 0.0996271
$$404$$ −1.00000 −0.0497519
$$405$$ 0 0
$$406$$ 12.0000 0.595550
$$407$$ 0 0
$$408$$ 4.00000 0.198030
$$409$$ 8.00000 0.395575 0.197787 0.980245i $$-0.436624\pi$$
0.197787 + 0.980245i $$0.436624\pi$$
$$410$$ 0 0
$$411$$ 10.0000 0.493264
$$412$$ −16.0000 −0.788263
$$413$$ 18.0000 0.885722
$$414$$ −5.00000 −0.245737
$$415$$ 0 0
$$416$$ 2.00000 0.0980581
$$417$$ −14.0000 −0.685583
$$418$$ −9.00000 −0.440204
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ −19.0000 −0.924906
$$423$$ −10.0000 −0.486217
$$424$$ −3.00000 −0.145693
$$425$$ 0 0
$$426$$ 7.00000 0.339151
$$427$$ −6.00000 −0.290360
$$428$$ −9.00000 −0.435031
$$429$$ 6.00000 0.289683
$$430$$ 0 0
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ 1.00000 0.0480569 0.0240285 0.999711i $$-0.492351\pi$$
0.0240285 + 0.999711i $$0.492351\pi$$
$$434$$ 3.00000 0.144005
$$435$$ 0 0
$$436$$ 20.0000 0.957826
$$437$$ 15.0000 0.717547
$$438$$ −5.00000 −0.238909
$$439$$ 18.0000 0.859093 0.429547 0.903045i $$-0.358673\pi$$
0.429547 + 0.903045i $$0.358673\pi$$
$$440$$ 0 0
$$441$$ 2.00000 0.0952381
$$442$$ 8.00000 0.380521
$$443$$ −15.0000 −0.712672 −0.356336 0.934358i $$-0.615974\pi$$
−0.356336 + 0.934358i $$0.615974\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 6.00000 0.284108
$$447$$ −11.0000 −0.520282
$$448$$ 3.00000 0.141737
$$449$$ 2.00000 0.0943858 0.0471929 0.998886i $$-0.484972\pi$$
0.0471929 + 0.998886i $$0.484972\pi$$
$$450$$ 0 0
$$451$$ 12.0000 0.565058
$$452$$ −9.00000 −0.423324
$$453$$ 0 0
$$454$$ 27.0000 1.26717
$$455$$ 0 0
$$456$$ −3.00000 −0.140488
$$457$$ −10.0000 −0.467780 −0.233890 0.972263i $$-0.575146\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ 13.0000 0.607450
$$459$$ 4.00000 0.186704
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 9.00000 0.418718
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ 4.00000 0.185695
$$465$$ 0 0
$$466$$ −15.0000 −0.694862
$$467$$ −24.0000 −1.11059 −0.555294 0.831654i $$-0.687394\pi$$
−0.555294 + 0.831654i $$0.687394\pi$$
$$468$$ 2.00000 0.0924500
$$469$$ −6.00000 −0.277054
$$470$$ 0 0
$$471$$ 5.00000 0.230388
$$472$$ 6.00000 0.276172
$$473$$ −3.00000 −0.137940
$$474$$ −1.00000 −0.0459315
$$475$$ 0 0
$$476$$ 12.0000 0.550019
$$477$$ −3.00000 −0.137361
$$478$$ 12.0000 0.548867
$$479$$ 3.00000 0.137073 0.0685367 0.997649i $$-0.478167\pi$$
0.0685367 + 0.997649i $$0.478167\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −18.0000 −0.819878
$$483$$ −15.0000 −0.682524
$$484$$ −2.00000 −0.0909091
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ −32.0000 −1.45006 −0.725029 0.688718i $$-0.758174\pi$$
−0.725029 + 0.688718i $$0.758174\pi$$
$$488$$ −2.00000 −0.0905357
$$489$$ −14.0000 −0.633102
$$490$$ 0 0
$$491$$ −37.0000 −1.66979 −0.834893 0.550412i $$-0.814471\pi$$
−0.834893 + 0.550412i $$0.814471\pi$$
$$492$$ 4.00000 0.180334
$$493$$ 16.0000 0.720604
$$494$$ −6.00000 −0.269953
$$495$$ 0 0
$$496$$ 1.00000 0.0449013
$$497$$ 21.0000 0.941979
$$498$$ −12.0000 −0.537733
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 0 0
$$501$$ 19.0000 0.848857
$$502$$ −12.0000 −0.535586
$$503$$ −20.0000 −0.891756 −0.445878 0.895094i $$-0.647108\pi$$
−0.445878 + 0.895094i $$0.647108\pi$$
$$504$$ 3.00000 0.133631
$$505$$ 0 0
$$506$$ −15.0000 −0.666831
$$507$$ −9.00000 −0.399704
$$508$$ −8.00000 −0.354943
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ −15.0000 −0.663561
$$512$$ 1.00000 0.0441942
$$513$$ −3.00000 −0.132453
$$514$$ 23.0000 1.01449
$$515$$ 0 0
$$516$$ −1.00000 −0.0440225
$$517$$ −30.0000 −1.31940
$$518$$ 0 0
$$519$$ 22.0000 0.965693
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 4.00000 0.175075
$$523$$ 43.0000 1.88026 0.940129 0.340818i $$-0.110704\pi$$
0.940129 + 0.340818i $$0.110704\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ 4.00000 0.174243
$$528$$ 3.00000 0.130558
$$529$$ 2.00000 0.0869565
$$530$$ 0 0
$$531$$ 6.00000 0.260378
$$532$$ −9.00000 −0.390199
$$533$$ 8.00000 0.346518
$$534$$ 1.00000 0.0432742
$$535$$ 0 0
$$536$$ −2.00000 −0.0863868
$$537$$ 4.00000 0.172613
$$538$$ 2.00000 0.0862261
$$539$$ 6.00000 0.258438
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ 13.0000 0.558398
$$543$$ 5.00000 0.214571
$$544$$ 4.00000 0.171499
$$545$$ 0 0
$$546$$ 6.00000 0.256776
$$547$$ −22.0000 −0.940652 −0.470326 0.882493i $$-0.655864\pi$$
−0.470326 + 0.882493i $$0.655864\pi$$
$$548$$ 10.0000 0.427179
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ −12.0000 −0.511217
$$552$$ −5.00000 −0.212814
$$553$$ −3.00000 −0.127573
$$554$$ −12.0000 −0.509831
$$555$$ 0 0
$$556$$ −14.0000 −0.593732
$$557$$ 1.00000 0.0423714 0.0211857 0.999776i $$-0.493256\pi$$
0.0211857 + 0.999776i $$0.493256\pi$$
$$558$$ 1.00000 0.0423334
$$559$$ −2.00000 −0.0845910
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ 16.0000 0.674919
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ −10.0000 −0.421076
$$565$$ 0 0
$$566$$ 24.0000 1.00880
$$567$$ 3.00000 0.125988
$$568$$ 7.00000 0.293713
$$569$$ −23.0000 −0.964210 −0.482105 0.876113i $$-0.660128\pi$$
−0.482105 + 0.876113i $$0.660128\pi$$
$$570$$ 0 0
$$571$$ 22.0000 0.920671 0.460336 0.887745i $$-0.347729\pi$$
0.460336 + 0.887745i $$0.347729\pi$$
$$572$$ 6.00000 0.250873
$$573$$ 16.0000 0.668410
$$574$$ 12.0000 0.500870
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −4.00000 −0.166522 −0.0832611 0.996528i $$-0.526534\pi$$
−0.0832611 + 0.996528i $$0.526534\pi$$
$$578$$ −1.00000 −0.0415945
$$579$$ 6.00000 0.249351
$$580$$ 0 0
$$581$$ −36.0000 −1.49353
$$582$$ 10.0000 0.414513
$$583$$ −9.00000 −0.372742
$$584$$ −5.00000 −0.206901
$$585$$ 0 0
$$586$$ −30.0000 −1.23929
$$587$$ −44.0000 −1.81607 −0.908037 0.418890i $$-0.862419\pi$$
−0.908037 + 0.418890i $$0.862419\pi$$
$$588$$ 2.00000 0.0824786
$$589$$ −3.00000 −0.123613
$$590$$ 0 0
$$591$$ 6.00000 0.246807
$$592$$ 0 0
$$593$$ −22.0000 −0.903432 −0.451716 0.892162i $$-0.649188\pi$$
−0.451716 + 0.892162i $$0.649188\pi$$
$$594$$ 3.00000 0.123091
$$595$$ 0 0
$$596$$ −11.0000 −0.450578
$$597$$ 7.00000 0.286491
$$598$$ −10.0000 −0.408930
$$599$$ −27.0000 −1.10319 −0.551595 0.834112i $$-0.685981\pi$$
−0.551595 + 0.834112i $$0.685981\pi$$
$$600$$ 0 0
$$601$$ 42.0000 1.71322 0.856608 0.515968i $$-0.172568\pi$$
0.856608 + 0.515968i $$0.172568\pi$$
$$602$$ −3.00000 −0.122271
$$603$$ −2.00000 −0.0814463
$$604$$ 0 0
$$605$$ 0 0
$$606$$ −1.00000 −0.0406222
$$607$$ −29.0000 −1.17707 −0.588537 0.808470i $$-0.700296\pi$$
−0.588537 + 0.808470i $$0.700296\pi$$
$$608$$ −3.00000 −0.121666
$$609$$ 12.0000 0.486265
$$610$$ 0 0
$$611$$ −20.0000 −0.809113
$$612$$ 4.00000 0.161690
$$613$$ 22.0000 0.888572 0.444286 0.895885i $$-0.353457\pi$$
0.444286 + 0.895885i $$0.353457\pi$$
$$614$$ −16.0000 −0.645707
$$615$$ 0 0
$$616$$ 9.00000 0.362620
$$617$$ 27.0000 1.08698 0.543490 0.839416i $$-0.317103\pi$$
0.543490 + 0.839416i $$0.317103\pi$$
$$618$$ −16.0000 −0.643614
$$619$$ −38.0000 −1.52735 −0.763674 0.645601i $$-0.776607\pi$$
−0.763674 + 0.645601i $$0.776607\pi$$
$$620$$ 0 0
$$621$$ −5.00000 −0.200643
$$622$$ 0 0
$$623$$ 3.00000 0.120192
$$624$$ 2.00000 0.0800641
$$625$$ 0 0
$$626$$ −30.0000 −1.19904
$$627$$ −9.00000 −0.359425
$$628$$ 5.00000 0.199522
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 17.0000 0.676759 0.338380 0.941010i $$-0.390121\pi$$
0.338380 + 0.941010i $$0.390121\pi$$
$$632$$ −1.00000 −0.0397779
$$633$$ −19.0000 −0.755182
$$634$$ 8.00000 0.317721
$$635$$ 0 0
$$636$$ −3.00000 −0.118958
$$637$$ 4.00000 0.158486
$$638$$ 12.0000 0.475085
$$639$$ 7.00000 0.276916
$$640$$ 0 0
$$641$$ 26.0000 1.02694 0.513469 0.858108i $$-0.328360\pi$$
0.513469 + 0.858108i $$0.328360\pi$$
$$642$$ −9.00000 −0.355202
$$643$$ −19.0000 −0.749287 −0.374643 0.927169i $$-0.622235\pi$$
−0.374643 + 0.927169i $$0.622235\pi$$
$$644$$ −15.0000 −0.591083
$$645$$ 0 0
$$646$$ −12.0000 −0.472134
$$647$$ −3.00000 −0.117942 −0.0589711 0.998260i $$-0.518782\pi$$
−0.0589711 + 0.998260i $$0.518782\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 18.0000 0.706562
$$650$$ 0 0
$$651$$ 3.00000 0.117579
$$652$$ −14.0000 −0.548282
$$653$$ 26.0000 1.01746 0.508729 0.860927i $$-0.330115\pi$$
0.508729 + 0.860927i $$0.330115\pi$$
$$654$$ 20.0000 0.782062
$$655$$ 0 0
$$656$$ 4.00000 0.156174
$$657$$ −5.00000 −0.195069
$$658$$ −30.0000 −1.16952
$$659$$ −4.00000 −0.155818 −0.0779089 0.996960i $$-0.524824\pi$$
−0.0779089 + 0.996960i $$0.524824\pi$$
$$660$$ 0 0
$$661$$ −14.0000 −0.544537 −0.272268 0.962221i $$-0.587774\pi$$
−0.272268 + 0.962221i $$0.587774\pi$$
$$662$$ 12.0000 0.466393
$$663$$ 8.00000 0.310694
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −20.0000 −0.774403
$$668$$ 19.0000 0.735132
$$669$$ 6.00000 0.231973
$$670$$ 0 0
$$671$$ −6.00000 −0.231627
$$672$$ 3.00000 0.115728
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ 2.00000 0.0770371
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −27.0000 −1.03769 −0.518847 0.854867i $$-0.673639\pi$$
−0.518847 + 0.854867i $$0.673639\pi$$
$$678$$ −9.00000 −0.345643
$$679$$ 30.0000 1.15129
$$680$$ 0 0
$$681$$ 27.0000 1.03464
$$682$$ 3.00000 0.114876
$$683$$ 19.0000 0.727015 0.363507 0.931591i $$-0.381579\pi$$
0.363507 + 0.931591i $$0.381579\pi$$
$$684$$ −3.00000 −0.114708
$$685$$ 0 0
$$686$$ −15.0000 −0.572703
$$687$$ 13.0000 0.495981
$$688$$ −1.00000 −0.0381246
$$689$$ −6.00000 −0.228582
$$690$$ 0 0
$$691$$ −31.0000 −1.17930 −0.589648 0.807661i $$-0.700733\pi$$
−0.589648 + 0.807661i $$0.700733\pi$$
$$692$$ 22.0000 0.836315
$$693$$ 9.00000 0.341882
$$694$$ 32.0000 1.21470
$$695$$ 0 0
$$696$$ 4.00000 0.151620
$$697$$ 16.0000 0.606043
$$698$$ −24.0000 −0.908413
$$699$$ −15.0000 −0.567352
$$700$$ 0 0
$$701$$ −21.0000 −0.793159 −0.396580 0.918000i $$-0.629803\pi$$
−0.396580 + 0.918000i $$0.629803\pi$$
$$702$$ 2.00000 0.0754851
$$703$$ 0 0
$$704$$ 3.00000 0.113067
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ −3.00000 −0.112827
$$708$$ 6.00000 0.225494
$$709$$ −25.0000 −0.938895 −0.469447 0.882960i $$-0.655547\pi$$
−0.469447 + 0.882960i $$0.655547\pi$$
$$710$$ 0 0
$$711$$ −1.00000 −0.0375029
$$712$$ 1.00000 0.0374766
$$713$$ −5.00000 −0.187251
$$714$$ 12.0000 0.449089
$$715$$ 0 0
$$716$$ 4.00000 0.149487
$$717$$ 12.0000 0.448148
$$718$$ 15.0000 0.559795
$$719$$ 26.0000 0.969636 0.484818 0.874615i $$-0.338886\pi$$
0.484818 + 0.874615i $$0.338886\pi$$
$$720$$ 0 0
$$721$$ −48.0000 −1.78761
$$722$$ −10.0000 −0.372161
$$723$$ −18.0000 −0.669427
$$724$$ 5.00000 0.185824
$$725$$ 0 0
$$726$$ −2.00000 −0.0742270
$$727$$ −45.0000 −1.66896 −0.834479 0.551040i $$-0.814231\pi$$
−0.834479 + 0.551040i $$0.814231\pi$$
$$728$$ 6.00000 0.222375
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −4.00000 −0.147945
$$732$$ −2.00000 −0.0739221
$$733$$ 18.0000 0.664845 0.332423 0.943131i $$-0.392134\pi$$
0.332423 + 0.943131i $$0.392134\pi$$
$$734$$ −2.00000 −0.0738213
$$735$$ 0 0
$$736$$ −5.00000 −0.184302
$$737$$ −6.00000 −0.221013
$$738$$ 4.00000 0.147242
$$739$$ −20.0000 −0.735712 −0.367856 0.929883i $$-0.619908\pi$$
−0.367856 + 0.929883i $$0.619908\pi$$
$$740$$ 0 0
$$741$$ −6.00000 −0.220416
$$742$$ −9.00000 −0.330400
$$743$$ 37.0000 1.35740 0.678699 0.734416i $$-0.262544\pi$$
0.678699 + 0.734416i $$0.262544\pi$$
$$744$$ 1.00000 0.0366618
$$745$$ 0 0
$$746$$ 9.00000 0.329513
$$747$$ −12.0000 −0.439057
$$748$$ 12.0000 0.438763
$$749$$ −27.0000 −0.986559
$$750$$ 0 0
$$751$$ −50.0000 −1.82453 −0.912263 0.409605i $$-0.865667\pi$$
−0.912263 + 0.409605i $$0.865667\pi$$
$$752$$ −10.0000 −0.364662
$$753$$ −12.0000 −0.437304
$$754$$ 8.00000 0.291343
$$755$$ 0 0
$$756$$ 3.00000 0.109109
$$757$$ −50.0000 −1.81728 −0.908640 0.417579i $$-0.862879\pi$$
−0.908640 + 0.417579i $$0.862879\pi$$
$$758$$ 15.0000 0.544825
$$759$$ −15.0000 −0.544466
$$760$$ 0 0
$$761$$ 45.0000 1.63125 0.815624 0.578582i $$-0.196394\pi$$
0.815624 + 0.578582i $$0.196394\pi$$
$$762$$ −8.00000 −0.289809
$$763$$ 60.0000 2.17215
$$764$$ 16.0000 0.578860
$$765$$ 0 0
$$766$$ −12.0000 −0.433578
$$767$$ 12.0000 0.433295
$$768$$ 1.00000 0.0360844
$$769$$ 9.00000 0.324548 0.162274 0.986746i $$-0.448117\pi$$
0.162274 + 0.986746i $$0.448117\pi$$
$$770$$ 0 0
$$771$$ 23.0000 0.828325
$$772$$ 6.00000 0.215945
$$773$$ 31.0000 1.11499 0.557496 0.830179i $$-0.311762\pi$$
0.557496 + 0.830179i $$0.311762\pi$$
$$774$$ −1.00000 −0.0359443
$$775$$ 0 0
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ −26.0000 −0.932145
$$779$$ −12.0000 −0.429945
$$780$$ 0 0
$$781$$ 21.0000 0.751439
$$782$$ −20.0000 −0.715199
$$783$$ 4.00000 0.142948
$$784$$ 2.00000 0.0714286
$$785$$ 0 0
$$786$$ 6.00000 0.214013
$$787$$ 35.0000 1.24762 0.623808 0.781578i $$-0.285585\pi$$
0.623808 + 0.781578i $$0.285585\pi$$
$$788$$ 6.00000 0.213741
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ −27.0000 −0.960009
$$792$$ 3.00000 0.106600
$$793$$ −4.00000 −0.142044
$$794$$ −35.0000 −1.24210
$$795$$ 0 0
$$796$$ 7.00000 0.248108
$$797$$ −2.00000 −0.0708436 −0.0354218 0.999372i $$-0.511277\pi$$
−0.0354218 + 0.999372i $$0.511277\pi$$
$$798$$ −9.00000 −0.318597
$$799$$ −40.0000 −1.41510
$$800$$ 0 0
$$801$$ 1.00000 0.0353333
$$802$$ 25.0000 0.882781
$$803$$ −15.0000 −0.529339
$$804$$ −2.00000 −0.0705346
$$805$$ 0 0
$$806$$ 2.00000 0.0704470
$$807$$ 2.00000 0.0704033
$$808$$ −1.00000 −0.0351799
$$809$$ 17.0000 0.597688 0.298844 0.954302i $$-0.403399\pi$$
0.298844 + 0.954302i $$0.403399\pi$$
$$810$$ 0 0
$$811$$ −27.0000 −0.948098 −0.474049 0.880498i $$-0.657208\pi$$
−0.474049 + 0.880498i $$0.657208\pi$$
$$812$$ 12.0000 0.421117
$$813$$ 13.0000 0.455930
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 4.00000 0.140028
$$817$$ 3.00000 0.104957
$$818$$ 8.00000 0.279713
$$819$$ 6.00000 0.209657
$$820$$ 0 0
$$821$$ 40.0000 1.39601 0.698005 0.716093i $$-0.254071\pi$$
0.698005 + 0.716093i $$0.254071\pi$$
$$822$$ 10.0000 0.348790
$$823$$ 18.0000 0.627441 0.313720 0.949515i $$-0.398425\pi$$
0.313720 + 0.949515i $$0.398425\pi$$
$$824$$ −16.0000 −0.557386
$$825$$ 0 0
$$826$$ 18.0000 0.626300
$$827$$ −20.0000 −0.695468 −0.347734 0.937593i $$-0.613049\pi$$
−0.347734 + 0.937593i $$0.613049\pi$$
$$828$$ −5.00000 −0.173762
$$829$$ −35.0000 −1.21560 −0.607800 0.794090i $$-0.707948\pi$$
−0.607800 + 0.794090i $$0.707948\pi$$
$$830$$ 0 0
$$831$$ −12.0000 −0.416275
$$832$$ 2.00000 0.0693375
$$833$$ 8.00000 0.277184
$$834$$ −14.0000 −0.484780
$$835$$ 0 0
$$836$$ −9.00000 −0.311272
$$837$$ 1.00000 0.0345651
$$838$$ 12.0000 0.414533
$$839$$ 51.0000 1.76072 0.880358 0.474310i $$-0.157302\pi$$
0.880358 + 0.474310i $$0.157302\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ −22.0000 −0.758170
$$843$$ 16.0000 0.551069
$$844$$ −19.0000 −0.654007
$$845$$ 0 0
$$846$$ −10.0000 −0.343807
$$847$$ −6.00000 −0.206162
$$848$$ −3.00000 −0.103020
$$849$$ 24.0000 0.823678
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 7.00000 0.239816
$$853$$ 41.0000 1.40381 0.701907 0.712269i $$-0.252332\pi$$
0.701907 + 0.712269i $$0.252332\pi$$
$$854$$ −6.00000 −0.205316
$$855$$ 0 0
$$856$$ −9.00000 −0.307614
$$857$$ −42.0000 −1.43469 −0.717346 0.696717i $$-0.754643\pi$$
−0.717346 + 0.696717i $$0.754643\pi$$
$$858$$ 6.00000 0.204837
$$859$$ 32.0000 1.09183 0.545913 0.837842i $$-0.316183\pi$$
0.545913 + 0.837842i $$0.316183\pi$$
$$860$$ 0 0
$$861$$ 12.0000 0.408959
$$862$$ 16.0000 0.544962
$$863$$ −43.0000 −1.46374 −0.731869 0.681446i $$-0.761351\pi$$
−0.731869 + 0.681446i $$0.761351\pi$$
$$864$$ 1.00000 0.0340207
$$865$$ 0 0
$$866$$ 1.00000 0.0339814
$$867$$ −1.00000 −0.0339618
$$868$$ 3.00000 0.101827
$$869$$ −3.00000 −0.101768
$$870$$ 0 0
$$871$$ −4.00000 −0.135535
$$872$$ 20.0000 0.677285
$$873$$ 10.0000 0.338449
$$874$$ 15.0000 0.507383
$$875$$ 0 0
$$876$$ −5.00000 −0.168934
$$877$$ −46.0000 −1.55331 −0.776655 0.629926i $$-0.783085\pi$$
−0.776655 + 0.629926i $$0.783085\pi$$
$$878$$ 18.0000 0.607471
$$879$$ −30.0000 −1.01187
$$880$$ 0 0
$$881$$ 26.0000 0.875962 0.437981 0.898984i $$-0.355694\pi$$
0.437981 + 0.898984i $$0.355694\pi$$
$$882$$ 2.00000 0.0673435
$$883$$ −11.0000 −0.370179 −0.185090 0.982722i $$-0.559258\pi$$
−0.185090 + 0.982722i $$0.559258\pi$$
$$884$$ 8.00000 0.269069
$$885$$ 0 0
$$886$$ −15.0000 −0.503935
$$887$$ 46.0000 1.54453 0.772264 0.635301i $$-0.219124\pi$$
0.772264 + 0.635301i $$0.219124\pi$$
$$888$$ 0 0
$$889$$ −24.0000 −0.804934
$$890$$ 0 0
$$891$$ 3.00000 0.100504
$$892$$ 6.00000 0.200895
$$893$$ 30.0000 1.00391
$$894$$ −11.0000 −0.367895
$$895$$ 0 0
$$896$$ 3.00000 0.100223
$$897$$ −10.0000 −0.333890
$$898$$ 2.00000 0.0667409
$$899$$ 4.00000 0.133407
$$900$$ 0 0
$$901$$ −12.0000 −0.399778
$$902$$ 12.0000 0.399556
$$903$$ −3.00000 −0.0998337
$$904$$ −9.00000 −0.299336
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 52.0000 1.72663 0.863316 0.504664i $$-0.168384\pi$$
0.863316 + 0.504664i $$0.168384\pi$$
$$908$$ 27.0000 0.896026
$$909$$ −1.00000 −0.0331679
$$910$$ 0 0
$$911$$ 20.0000 0.662630 0.331315 0.943520i $$-0.392508\pi$$
0.331315 + 0.943520i $$0.392508\pi$$
$$912$$ −3.00000 −0.0993399
$$913$$ −36.0000 −1.19143
$$914$$ −10.0000 −0.330771
$$915$$ 0 0
$$916$$ 13.0000 0.429532
$$917$$ 18.0000 0.594412
$$918$$ 4.00000 0.132020
$$919$$ −38.0000 −1.25350 −0.626752 0.779219i $$-0.715616\pi$$
−0.626752 + 0.779219i $$0.715616\pi$$
$$920$$ 0 0
$$921$$ −16.0000 −0.527218
$$922$$ 0 0
$$923$$ 14.0000 0.460816
$$924$$ 9.00000 0.296078
$$925$$ 0 0
$$926$$ −4.00000 −0.131448
$$927$$ −16.0000 −0.525509
$$928$$ 4.00000 0.131306
$$929$$ −41.0000 −1.34517 −0.672583 0.740022i $$-0.734815\pi$$
−0.672583 + 0.740022i $$0.734815\pi$$
$$930$$ 0 0
$$931$$ −6.00000 −0.196642
$$932$$ −15.0000 −0.491341
$$933$$ 0 0
$$934$$ −24.0000 −0.785304
$$935$$ 0 0
$$936$$ 2.00000 0.0653720
$$937$$ 52.0000 1.69877 0.849383 0.527777i $$-0.176974\pi$$
0.849383 + 0.527777i $$0.176974\pi$$
$$938$$ −6.00000 −0.195907
$$939$$ −30.0000 −0.979013
$$940$$ 0 0
$$941$$ 40.0000 1.30396 0.651981 0.758235i $$-0.273938\pi$$
0.651981 + 0.758235i $$0.273938\pi$$
$$942$$ 5.00000 0.162909
$$943$$ −20.0000 −0.651290
$$944$$ 6.00000 0.195283
$$945$$ 0 0
$$946$$ −3.00000 −0.0975384
$$947$$ −30.0000 −0.974869 −0.487435 0.873160i $$-0.662067\pi$$
−0.487435 + 0.873160i $$0.662067\pi$$
$$948$$ −1.00000 −0.0324785
$$949$$ −10.0000 −0.324614
$$950$$ 0 0
$$951$$ 8.00000 0.259418
$$952$$ 12.0000 0.388922
$$953$$ 52.0000 1.68445 0.842223 0.539130i $$-0.181247\pi$$
0.842223 + 0.539130i $$0.181247\pi$$
$$954$$ −3.00000 −0.0971286
$$955$$ 0 0
$$956$$ 12.0000 0.388108
$$957$$ 12.0000 0.387905
$$958$$ 3.00000 0.0969256
$$959$$ 30.0000 0.968751
$$960$$ 0 0
$$961$$ 1.00000 0.0322581
$$962$$ 0 0
$$963$$ −9.00000 −0.290021
$$964$$ −18.0000 −0.579741
$$965$$ 0 0
$$966$$ −15.0000 −0.482617
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ −2.00000 −0.0642824
$$969$$ −12.0000 −0.385496
$$970$$ 0 0
$$971$$ −54.0000 −1.73294 −0.866471 0.499227i $$-0.833617\pi$$
−0.866471 + 0.499227i $$0.833617\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ −42.0000 −1.34646
$$974$$ −32.0000 −1.02535
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ −38.0000 −1.21573 −0.607864 0.794041i $$-0.707973\pi$$
−0.607864 + 0.794041i $$0.707973\pi$$
$$978$$ −14.0000 −0.447671
$$979$$ 3.00000 0.0958804
$$980$$ 0 0
$$981$$ 20.0000 0.638551
$$982$$ −37.0000 −1.18072
$$983$$ 56.0000 1.78612 0.893061 0.449935i $$-0.148553\pi$$
0.893061 + 0.449935i $$0.148553\pi$$
$$984$$ 4.00000 0.127515
$$985$$ 0 0
$$986$$ 16.0000 0.509544
$$987$$ −30.0000 −0.954911
$$988$$ −6.00000 −0.190885
$$989$$ 5.00000 0.158991
$$990$$ 0 0
$$991$$ −25.0000 −0.794151 −0.397076 0.917786i $$-0.629975\pi$$
−0.397076 + 0.917786i $$0.629975\pi$$
$$992$$ 1.00000 0.0317500
$$993$$ 12.0000 0.380808
$$994$$ 21.0000 0.666080
$$995$$ 0 0
$$996$$ −12.0000 −0.380235
$$997$$ 42.0000 1.33015 0.665077 0.746775i $$-0.268399\pi$$
0.665077 + 0.746775i $$0.268399\pi$$
$$998$$ 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 4650.2.a.bv.1.1 1
5.2 odd 4 4650.2.d.y.3349.2 2
5.3 odd 4 4650.2.d.y.3349.1 2
5.4 even 2 930.2.a.a.1.1 1
15.14 odd 2 2790.2.a.y.1.1 1
20.19 odd 2 7440.2.a.v.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.a.1.1 1 5.4 even 2
2790.2.a.y.1.1 1 15.14 odd 2
4650.2.a.bv.1.1 1 1.1 even 1 trivial
4650.2.d.y.3349.1 2 5.3 odd 4
4650.2.d.y.3349.2 2 5.2 odd 4
7440.2.a.v.1.1 1 20.19 odd 2