Properties

 Label 3150.2.a.bq.1.1 Level $3150$ Weight $2$ Character 3150.1 Self dual yes Analytic conductor $25.153$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3150.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$25.1528766367$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 350) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 3150.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +5.00000 q^{11} +6.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} -3.00000 q^{19} +5.00000 q^{22} +6.00000 q^{26} +1.00000 q^{28} +6.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{34} -8.00000 q^{37} -3.00000 q^{38} -11.0000 q^{41} +8.00000 q^{43} +5.00000 q^{44} +2.00000 q^{47} +1.00000 q^{49} +6.00000 q^{52} +4.00000 q^{53} +1.00000 q^{56} +6.00000 q^{58} -4.00000 q^{59} -2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -9.00000 q^{67} -1.00000 q^{68} +10.0000 q^{71} +7.00000 q^{73} -8.00000 q^{74} -3.00000 q^{76} +5.00000 q^{77} -2.00000 q^{79} -11.0000 q^{82} +11.0000 q^{83} +8.00000 q^{86} +5.00000 q^{88} +11.0000 q^{89} +6.00000 q^{91} +2.00000 q^{94} +10.0000 q^{97} +1.00000 q^{98} +O(q^{100})$$

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
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 0 0
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −1.00000 −0.242536 −0.121268 0.992620i $$-0.538696\pi$$
−0.121268 + 0.992620i $$0.538696\pi$$
$$18$$ 0 0
$$19$$ −3.00000 −0.688247 −0.344124 0.938924i $$-0.611824\pi$$
−0.344124 + 0.938924i $$0.611824\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 5.00000 1.06600
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 6.00000 1.17670
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −1.00000 −0.171499
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ −3.00000 −0.486664
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −11.0000 −1.71791 −0.858956 0.512050i $$-0.828886\pi$$
−0.858956 + 0.512050i $$0.828886\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 5.00000 0.753778
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.00000 0.291730 0.145865 0.989305i $$-0.453403\pi$$
0.145865 + 0.989305i $$0.453403\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 6.00000 0.832050
$$53$$ 4.00000 0.549442 0.274721 0.961524i $$-0.411414\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ 6.00000 0.787839
$$59$$ −4.00000 −0.520756 −0.260378 0.965507i $$-0.583847\pi$$
−0.260378 + 0.965507i $$0.583847\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −9.00000 −1.09952 −0.549762 0.835321i $$-0.685282\pi$$
−0.549762 + 0.835321i $$0.685282\pi$$
$$68$$ −1.00000 −0.121268
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 10.0000 1.18678 0.593391 0.804914i $$-0.297789\pi$$
0.593391 + 0.804914i $$0.297789\pi$$
$$72$$ 0 0
$$73$$ 7.00000 0.819288 0.409644 0.912245i $$-0.365653\pi$$
0.409644 + 0.912245i $$0.365653\pi$$
$$74$$ −8.00000 −0.929981
$$75$$ 0 0
$$76$$ −3.00000 −0.344124
$$77$$ 5.00000 0.569803
$$78$$ 0 0
$$79$$ −2.00000 −0.225018 −0.112509 0.993651i $$-0.535889\pi$$
−0.112509 + 0.993651i $$0.535889\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −11.0000 −1.21475
$$83$$ 11.0000 1.20741 0.603703 0.797209i $$-0.293691\pi$$
0.603703 + 0.797209i $$0.293691\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 8.00000 0.862662
$$87$$ 0 0
$$88$$ 5.00000 0.533002
$$89$$ 11.0000 1.16600 0.582999 0.812473i $$-0.301879\pi$$
0.582999 + 0.812473i $$0.301879\pi$$
$$90$$ 0 0
$$91$$ 6.00000 0.628971
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 2.00000 0.206284
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −4.00000 −0.394132 −0.197066 0.980390i $$-0.563141\pi$$
−0.197066 + 0.980390i $$0.563141\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ 4.00000 0.388514
$$107$$ 3.00000 0.290021 0.145010 0.989430i $$-0.453678\pi$$
0.145010 + 0.989430i $$0.453678\pi$$
$$108$$ 0 0
$$109$$ −18.0000 −1.72409 −0.862044 0.506834i $$-0.830816\pi$$
−0.862044 + 0.506834i $$0.830816\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 1.00000 0.0944911
$$113$$ −1.00000 −0.0940721 −0.0470360 0.998893i $$-0.514978\pi$$
−0.0470360 + 0.998893i $$0.514978\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 6.00000 0.557086
$$117$$ 0 0
$$118$$ −4.00000 −0.368230
$$119$$ −1.00000 −0.0916698
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ −2.00000 −0.181071
$$123$$ 0 0
$$124$$ −4.00000 −0.359211
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 14.0000 1.24230 0.621150 0.783692i $$-0.286666\pi$$
0.621150 + 0.783692i $$0.286666\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 0 0
$$133$$ −3.00000 −0.260133
$$134$$ −9.00000 −0.777482
$$135$$ 0 0
$$136$$ −1.00000 −0.0857493
$$137$$ −3.00000 −0.256307 −0.128154 0.991754i $$-0.540905\pi$$
−0.128154 + 0.991754i $$0.540905\pi$$
$$138$$ 0 0
$$139$$ −11.0000 −0.933008 −0.466504 0.884519i $$-0.654487\pi$$
−0.466504 + 0.884519i $$0.654487\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 10.0000 0.839181
$$143$$ 30.0000 2.50873
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 7.00000 0.579324
$$147$$ 0 0
$$148$$ −8.00000 −0.657596
$$149$$ −12.0000 −0.983078 −0.491539 0.870855i $$-0.663566\pi$$
−0.491539 + 0.870855i $$0.663566\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ −3.00000 −0.243332
$$153$$ 0 0
$$154$$ 5.00000 0.402911
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −4.00000 −0.319235 −0.159617 0.987179i $$-0.551026\pi$$
−0.159617 + 0.987179i $$0.551026\pi$$
$$158$$ −2.00000 −0.159111
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 19.0000 1.48819 0.744097 0.668071i $$-0.232880\pi$$
0.744097 + 0.668071i $$0.232880\pi$$
$$164$$ −11.0000 −0.858956
$$165$$ 0 0
$$166$$ 11.0000 0.853766
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ 2.00000 0.152057 0.0760286 0.997106i $$-0.475776\pi$$
0.0760286 + 0.997106i $$0.475776\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 5.00000 0.376889
$$177$$ 0 0
$$178$$ 11.0000 0.824485
$$179$$ −3.00000 −0.224231 −0.112115 0.993695i $$-0.535763\pi$$
−0.112115 + 0.993695i $$0.535763\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 6.00000 0.444750
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −5.00000 −0.365636
$$188$$ 2.00000 0.145865
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 6.00000 0.434145 0.217072 0.976156i $$-0.430349\pi$$
0.217072 + 0.976156i $$0.430349\pi$$
$$192$$ 0 0
$$193$$ 19.0000 1.36765 0.683825 0.729646i $$-0.260315\pi$$
0.683825 + 0.729646i $$0.260315\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −22.0000 −1.56744 −0.783718 0.621117i $$-0.786679\pi$$
−0.783718 + 0.621117i $$0.786679\pi$$
$$198$$ 0 0
$$199$$ −10.0000 −0.708881 −0.354441 0.935079i $$-0.615329\pi$$
−0.354441 + 0.935079i $$0.615329\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 6.00000 0.421117
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −4.00000 −0.278693
$$207$$ 0 0
$$208$$ 6.00000 0.416025
$$209$$ −15.0000 −1.03757
$$210$$ 0 0
$$211$$ 1.00000 0.0688428 0.0344214 0.999407i $$-0.489041\pi$$
0.0344214 + 0.999407i $$0.489041\pi$$
$$212$$ 4.00000 0.274721
$$213$$ 0 0
$$214$$ 3.00000 0.205076
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −4.00000 −0.271538
$$218$$ −18.0000 −1.21911
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −6.00000 −0.403604
$$222$$ 0 0
$$223$$ −22.0000 −1.47323 −0.736614 0.676313i $$-0.763577\pi$$
−0.736614 + 0.676313i $$0.763577\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −1.00000 −0.0665190
$$227$$ −28.0000 −1.85843 −0.929213 0.369546i $$-0.879513\pi$$
−0.929213 + 0.369546i $$0.879513\pi$$
$$228$$ 0 0
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −4.00000 −0.260378
$$237$$ 0 0
$$238$$ −1.00000 −0.0648204
$$239$$ −4.00000 −0.258738 −0.129369 0.991596i $$-0.541295\pi$$
−0.129369 + 0.991596i $$0.541295\pi$$
$$240$$ 0 0
$$241$$ −5.00000 −0.322078 −0.161039 0.986948i $$-0.551485\pi$$
−0.161039 + 0.986948i $$0.551485\pi$$
$$242$$ 14.0000 0.899954
$$243$$ 0 0
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −18.0000 −1.14531
$$248$$ −4.00000 −0.254000
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −27.0000 −1.70422 −0.852112 0.523359i $$-0.824679\pi$$
−0.852112 + 0.523359i $$0.824679\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 14.0000 0.878438
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 2.00000 0.124757 0.0623783 0.998053i $$-0.480131\pi$$
0.0623783 + 0.998053i $$0.480131\pi$$
$$258$$ 0 0
$$259$$ −8.00000 −0.497096
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −8.00000 −0.494242
$$263$$ −10.0000 −0.616626 −0.308313 0.951285i $$-0.599764\pi$$
−0.308313 + 0.951285i $$0.599764\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −3.00000 −0.183942
$$267$$ 0 0
$$268$$ −9.00000 −0.549762
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ −6.00000 −0.364474 −0.182237 0.983255i $$-0.558334\pi$$
−0.182237 + 0.983255i $$0.558334\pi$$
$$272$$ −1.00000 −0.0606339
$$273$$ 0 0
$$274$$ −3.00000 −0.181237
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 30.0000 1.80253 0.901263 0.433273i $$-0.142641\pi$$
0.901263 + 0.433273i $$0.142641\pi$$
$$278$$ −11.0000 −0.659736
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −14.0000 −0.835170 −0.417585 0.908638i $$-0.637123\pi$$
−0.417585 + 0.908638i $$0.637123\pi$$
$$282$$ 0 0
$$283$$ 13.0000 0.772770 0.386385 0.922338i $$-0.373724\pi$$
0.386385 + 0.922338i $$0.373724\pi$$
$$284$$ 10.0000 0.593391
$$285$$ 0 0
$$286$$ 30.0000 1.77394
$$287$$ −11.0000 −0.649309
$$288$$ 0 0
$$289$$ −16.0000 −0.941176
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 7.00000 0.409644
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −8.00000 −0.464991
$$297$$ 0 0
$$298$$ −12.0000 −0.695141
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 8.00000 0.461112
$$302$$ 8.00000 0.460348
$$303$$ 0 0
$$304$$ −3.00000 −0.172062
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −13.0000 −0.741949 −0.370975 0.928643i $$-0.620976\pi$$
−0.370975 + 0.928643i $$0.620976\pi$$
$$308$$ 5.00000 0.284901
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −6.00000 −0.340229 −0.170114 0.985424i $$-0.554414\pi$$
−0.170114 + 0.985424i $$0.554414\pi$$
$$312$$ 0 0
$$313$$ 10.0000 0.565233 0.282617 0.959233i $$-0.408798\pi$$
0.282617 + 0.959233i $$0.408798\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ 0 0
$$316$$ −2.00000 −0.112509
$$317$$ 4.00000 0.224662 0.112331 0.993671i $$-0.464168\pi$$
0.112331 + 0.993671i $$0.464168\pi$$
$$318$$ 0 0
$$319$$ 30.0000 1.67968
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 3.00000 0.166924
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 19.0000 1.05231
$$327$$ 0 0
$$328$$ −11.0000 −0.607373
$$329$$ 2.00000 0.110264
$$330$$ 0 0
$$331$$ −17.0000 −0.934405 −0.467202 0.884150i $$-0.654738\pi$$
−0.467202 + 0.884150i $$0.654738\pi$$
$$332$$ 11.0000 0.603703
$$333$$ 0 0
$$334$$ 12.0000 0.656611
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 29.0000 1.57973 0.789865 0.613280i $$-0.210150\pi$$
0.789865 + 0.613280i $$0.210150\pi$$
$$338$$ 23.0000 1.25104
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −20.0000 −1.08306
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ 2.00000 0.107521
$$347$$ 19.0000 1.01997 0.509987 0.860182i $$-0.329650\pi$$
0.509987 + 0.860182i $$0.329650\pi$$
$$348$$ 0 0
$$349$$ −8.00000 −0.428230 −0.214115 0.976808i $$-0.568687\pi$$
−0.214115 + 0.976808i $$0.568687\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 5.00000 0.266501
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 11.0000 0.582999
$$357$$ 0 0
$$358$$ −3.00000 −0.158555
$$359$$ −26.0000 −1.37223 −0.686114 0.727494i $$-0.740685\pi$$
−0.686114 + 0.727494i $$0.740685\pi$$
$$360$$ 0 0
$$361$$ −10.0000 −0.526316
$$362$$ 10.0000 0.525588
$$363$$ 0 0
$$364$$ 6.00000 0.314485
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 4.00000 0.207670
$$372$$ 0 0
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ −5.00000 −0.258544
$$375$$ 0 0
$$376$$ 2.00000 0.103142
$$377$$ 36.0000 1.85409
$$378$$ 0 0
$$379$$ 9.00000 0.462299 0.231149 0.972918i $$-0.425751\pi$$
0.231149 + 0.972918i $$0.425751\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 6.00000 0.306987
$$383$$ −6.00000 −0.306586 −0.153293 0.988181i $$-0.548988\pi$$
−0.153293 + 0.988181i $$0.548988\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 19.0000 0.967075
$$387$$ 0 0
$$388$$ 10.0000 0.507673
$$389$$ −8.00000 −0.405616 −0.202808 0.979219i $$-0.565007\pi$$
−0.202808 + 0.979219i $$0.565007\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ −22.0000 −1.10834
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −10.0000 −0.501886 −0.250943 0.968002i $$-0.580741\pi$$
−0.250943 + 0.968002i $$0.580741\pi$$
$$398$$ −10.0000 −0.501255
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −37.0000 −1.84769 −0.923846 0.382765i $$-0.874972\pi$$
−0.923846 + 0.382765i $$0.874972\pi$$
$$402$$ 0 0
$$403$$ −24.0000 −1.19553
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 6.00000 0.297775
$$407$$ −40.0000 −1.98273
$$408$$ 0 0
$$409$$ −21.0000 −1.03838 −0.519192 0.854658i $$-0.673767\pi$$
−0.519192 + 0.854658i $$0.673767\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −4.00000 −0.197066
$$413$$ −4.00000 −0.196827
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 6.00000 0.294174
$$417$$ 0 0
$$418$$ −15.0000 −0.733674
$$419$$ 39.0000 1.90527 0.952637 0.304109i $$-0.0983586\pi$$
0.952637 + 0.304109i $$0.0983586\pi$$
$$420$$ 0 0
$$421$$ 20.0000 0.974740 0.487370 0.873195i $$-0.337956\pi$$
0.487370 + 0.873195i $$0.337956\pi$$
$$422$$ 1.00000 0.0486792
$$423$$ 0 0
$$424$$ 4.00000 0.194257
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −2.00000 −0.0967868
$$428$$ 3.00000 0.145010
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 36.0000 1.73406 0.867029 0.498257i $$-0.166026\pi$$
0.867029 + 0.498257i $$0.166026\pi$$
$$432$$ 0 0
$$433$$ 1.00000 0.0480569 0.0240285 0.999711i $$-0.492351\pi$$
0.0240285 + 0.999711i $$0.492351\pi$$
$$434$$ −4.00000 −0.192006
$$435$$ 0 0
$$436$$ −18.0000 −0.862044
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 28.0000 1.33637 0.668184 0.743996i $$-0.267072\pi$$
0.668184 + 0.743996i $$0.267072\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −6.00000 −0.285391
$$443$$ 37.0000 1.75792 0.878962 0.476893i $$-0.158237\pi$$
0.878962 + 0.476893i $$0.158237\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −22.0000 −1.04173
$$447$$ 0 0
$$448$$ 1.00000 0.0472456
$$449$$ −33.0000 −1.55737 −0.778683 0.627417i $$-0.784112\pi$$
−0.778683 + 0.627417i $$0.784112\pi$$
$$450$$ 0 0
$$451$$ −55.0000 −2.58985
$$452$$ −1.00000 −0.0470360
$$453$$ 0 0
$$454$$ −28.0000 −1.31411
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −25.0000 −1.16945 −0.584725 0.811231i $$-0.698798\pi$$
−0.584725 + 0.811231i $$0.698798\pi$$
$$458$$ −14.0000 −0.654177
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 38.0000 1.76984 0.884918 0.465746i $$-0.154214\pi$$
0.884918 + 0.465746i $$0.154214\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ 6.00000 0.278543
$$465$$ 0 0
$$466$$ 6.00000 0.277945
$$467$$ −4.00000 −0.185098 −0.0925490 0.995708i $$-0.529501\pi$$
−0.0925490 + 0.995708i $$0.529501\pi$$
$$468$$ 0 0
$$469$$ −9.00000 −0.415581
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −4.00000 −0.184115
$$473$$ 40.0000 1.83920
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −1.00000 −0.0458349
$$477$$ 0 0
$$478$$ −4.00000 −0.182956
$$479$$ 6.00000 0.274147 0.137073 0.990561i $$-0.456230\pi$$
0.137073 + 0.990561i $$0.456230\pi$$
$$480$$ 0 0
$$481$$ −48.0000 −2.18861
$$482$$ −5.00000 −0.227744
$$483$$ 0 0
$$484$$ 14.0000 0.636364
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 34.0000 1.54069 0.770344 0.637629i $$-0.220085\pi$$
0.770344 + 0.637629i $$0.220085\pi$$
$$488$$ −2.00000 −0.0905357
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ 0 0
$$493$$ −6.00000 −0.270226
$$494$$ −18.0000 −0.809858
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ 10.0000 0.448561
$$498$$ 0 0
$$499$$ 36.0000 1.61158 0.805791 0.592200i $$-0.201741\pi$$
0.805791 + 0.592200i $$0.201741\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −27.0000 −1.20507
$$503$$ −30.0000 −1.33763 −0.668817 0.743427i $$-0.733199\pi$$
−0.668817 + 0.743427i $$0.733199\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 14.0000 0.621150
$$509$$ 14.0000 0.620539 0.310270 0.950649i $$-0.399581\pi$$
0.310270 + 0.950649i $$0.399581\pi$$
$$510$$ 0 0
$$511$$ 7.00000 0.309662
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 2.00000 0.0882162
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 10.0000 0.439799
$$518$$ −8.00000 −0.351500
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −11.0000 −0.481919 −0.240959 0.970535i $$-0.577462\pi$$
−0.240959 + 0.970535i $$0.577462\pi$$
$$522$$ 0 0
$$523$$ −13.0000 −0.568450 −0.284225 0.958758i $$-0.591736\pi$$
−0.284225 + 0.958758i $$0.591736\pi$$
$$524$$ −8.00000 −0.349482
$$525$$ 0 0
$$526$$ −10.0000 −0.436021
$$527$$ 4.00000 0.174243
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −3.00000 −0.130066
$$533$$ −66.0000 −2.85878
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −9.00000 −0.388741
$$537$$ 0 0
$$538$$ −18.0000 −0.776035
$$539$$ 5.00000 0.215365
$$540$$ 0 0
$$541$$ −42.0000 −1.80572 −0.902861 0.429934i $$-0.858537\pi$$
−0.902861 + 0.429934i $$0.858537\pi$$
$$542$$ −6.00000 −0.257722
$$543$$ 0 0
$$544$$ −1.00000 −0.0428746
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −27.0000 −1.15444 −0.577218 0.816590i $$-0.695862\pi$$
−0.577218 + 0.816590i $$0.695862\pi$$
$$548$$ −3.00000 −0.128154
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −18.0000 −0.766826
$$552$$ 0 0
$$553$$ −2.00000 −0.0850487
$$554$$ 30.0000 1.27458
$$555$$ 0 0
$$556$$ −11.0000 −0.466504
$$557$$ 4.00000 0.169485 0.0847427 0.996403i $$-0.472993\pi$$
0.0847427 + 0.996403i $$0.472993\pi$$
$$558$$ 0 0
$$559$$ 48.0000 2.03018
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −14.0000 −0.590554
$$563$$ 20.0000 0.842900 0.421450 0.906852i $$-0.361521\pi$$
0.421450 + 0.906852i $$0.361521\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 13.0000 0.546431
$$567$$ 0 0
$$568$$ 10.0000 0.419591
$$569$$ −21.0000 −0.880366 −0.440183 0.897908i $$-0.645086\pi$$
−0.440183 + 0.897908i $$0.645086\pi$$
$$570$$ 0 0
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ 30.0000 1.25436
$$573$$ 0 0
$$574$$ −11.0000 −0.459131
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −13.0000 −0.541197 −0.270599 0.962692i $$-0.587222\pi$$
−0.270599 + 0.962692i $$0.587222\pi$$
$$578$$ −16.0000 −0.665512
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 11.0000 0.456357
$$582$$ 0 0
$$583$$ 20.0000 0.828315
$$584$$ 7.00000 0.289662
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ −13.0000 −0.536567 −0.268284 0.963340i $$-0.586456\pi$$
−0.268284 + 0.963340i $$0.586456\pi$$
$$588$$ 0 0
$$589$$ 12.0000 0.494451
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −8.00000 −0.328798
$$593$$ −39.0000 −1.60154 −0.800769 0.598973i $$-0.795576\pi$$
−0.800769 + 0.598973i $$0.795576\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −12.0000 −0.491539
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ 21.0000 0.856608 0.428304 0.903635i $$-0.359111\pi$$
0.428304 + 0.903635i $$0.359111\pi$$
$$602$$ 8.00000 0.326056
$$603$$ 0 0
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −28.0000 −1.13648 −0.568242 0.822861i $$-0.692376\pi$$
−0.568242 + 0.822861i $$0.692376\pi$$
$$608$$ −3.00000 −0.121666
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 12.0000 0.485468
$$612$$ 0 0
$$613$$ −18.0000 −0.727013 −0.363507 0.931592i $$-0.618421\pi$$
−0.363507 + 0.931592i $$0.618421\pi$$
$$614$$ −13.0000 −0.524637
$$615$$ 0 0
$$616$$ 5.00000 0.201456
$$617$$ 14.0000 0.563619 0.281809 0.959470i $$-0.409065\pi$$
0.281809 + 0.959470i $$0.409065\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −6.00000 −0.240578
$$623$$ 11.0000 0.440706
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 10.0000 0.399680
$$627$$ 0 0
$$628$$ −4.00000 −0.159617
$$629$$ 8.00000 0.318981
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ −2.00000 −0.0795557
$$633$$ 0 0
$$634$$ 4.00000 0.158860
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.00000 0.237729
$$638$$ 30.0000 1.18771
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 0 0
$$643$$ −16.0000 −0.630978 −0.315489 0.948929i $$-0.602169\pi$$
−0.315489 + 0.948929i $$0.602169\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 3.00000 0.118033
$$647$$ −8.00000 −0.314512 −0.157256 0.987558i $$-0.550265\pi$$
−0.157256 + 0.987558i $$0.550265\pi$$
$$648$$ 0 0
$$649$$ −20.0000 −0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 19.0000 0.744097
$$653$$ −28.0000 −1.09572 −0.547862 0.836569i $$-0.684558\pi$$
−0.547862 + 0.836569i $$0.684558\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −11.0000 −0.429478
$$657$$ 0 0
$$658$$ 2.00000 0.0779681
$$659$$ −1.00000 −0.0389545 −0.0194772 0.999810i $$-0.506200\pi$$
−0.0194772 + 0.999810i $$0.506200\pi$$
$$660$$ 0 0
$$661$$ −50.0000 −1.94477 −0.972387 0.233373i $$-0.925024\pi$$
−0.972387 + 0.233373i $$0.925024\pi$$
$$662$$ −17.0000 −0.660724
$$663$$ 0 0
$$664$$ 11.0000 0.426883
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 12.0000 0.464294
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −10.0000 −0.386046
$$672$$ 0 0
$$673$$ −34.0000 −1.31060 −0.655302 0.755367i $$-0.727459\pi$$
−0.655302 + 0.755367i $$0.727459\pi$$
$$674$$ 29.0000 1.11704
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ −48.0000 −1.84479 −0.922395 0.386248i $$-0.873771\pi$$
−0.922395 + 0.386248i $$0.873771\pi$$
$$678$$ 0 0
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −20.0000 −0.765840
$$683$$ −13.0000 −0.497431 −0.248716 0.968577i $$-0.580008\pi$$
−0.248716 + 0.968577i $$0.580008\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1.00000 0.0381802
$$687$$ 0 0
$$688$$ 8.00000 0.304997
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ 49.0000 1.86405 0.932024 0.362397i $$-0.118041\pi$$
0.932024 + 0.362397i $$0.118041\pi$$
$$692$$ 2.00000 0.0760286
$$693$$ 0 0
$$694$$ 19.0000 0.721230
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 11.0000 0.416655
$$698$$ −8.00000 −0.302804
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 32.0000 1.20862 0.604312 0.796748i $$-0.293448\pi$$
0.604312 + 0.796748i $$0.293448\pi$$
$$702$$ 0 0
$$703$$ 24.0000 0.905177
$$704$$ 5.00000 0.188445
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 4.00000 0.150223 0.0751116 0.997175i $$-0.476069\pi$$
0.0751116 + 0.997175i $$0.476069\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 11.0000 0.412242
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −3.00000 −0.112115
$$717$$ 0 0
$$718$$ −26.0000 −0.970311
$$719$$ 48.0000 1.79010 0.895049 0.445968i $$-0.147140\pi$$
0.895049 + 0.445968i $$0.147140\pi$$
$$720$$ 0 0
$$721$$ −4.00000 −0.148968
$$722$$ −10.0000 −0.372161
$$723$$ 0 0
$$724$$ 10.0000 0.371647
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −6.00000 −0.222528 −0.111264 0.993791i $$-0.535490\pi$$
−0.111264 + 0.993791i $$0.535490\pi$$
$$728$$ 6.00000 0.222375
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −8.00000 −0.295891
$$732$$ 0 0
$$733$$ −40.0000 −1.47743 −0.738717 0.674016i $$-0.764568\pi$$
−0.738717 + 0.674016i $$0.764568\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −45.0000 −1.65760
$$738$$ 0 0
$$739$$ 4.00000 0.147142 0.0735712 0.997290i $$-0.476560\pi$$
0.0735712 + 0.997290i $$0.476560\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 4.00000 0.146845
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 4.00000 0.146450
$$747$$ 0 0
$$748$$ −5.00000 −0.182818
$$749$$ 3.00000 0.109618
$$750$$ 0 0
$$751$$ 50.0000 1.82453 0.912263 0.409605i $$-0.134333\pi$$
0.912263 + 0.409605i $$0.134333\pi$$
$$752$$ 2.00000 0.0729325
$$753$$ 0 0
$$754$$ 36.0000 1.31104
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 9.00000 0.326895
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −27.0000 −0.978749 −0.489375 0.872074i $$-0.662775\pi$$
−0.489375 + 0.872074i $$0.662775\pi$$
$$762$$ 0 0
$$763$$ −18.0000 −0.651644
$$764$$ 6.00000 0.217072
$$765$$ 0 0
$$766$$ −6.00000 −0.216789
$$767$$ −24.0000 −0.866590
$$768$$ 0 0
$$769$$ 19.0000 0.685158 0.342579 0.939489i $$-0.388700\pi$$
0.342579 + 0.939489i $$0.388700\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 19.0000 0.683825
$$773$$ 36.0000 1.29483 0.647415 0.762138i $$-0.275850\pi$$
0.647415 + 0.762138i $$0.275850\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ −8.00000 −0.286814
$$779$$ 33.0000 1.18235
$$780$$ 0 0
$$781$$ 50.0000 1.78914
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −52.0000 −1.85360 −0.926800 0.375555i $$-0.877452\pi$$
−0.926800 + 0.375555i $$0.877452\pi$$
$$788$$ −22.0000 −0.783718
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −1.00000 −0.0355559
$$792$$ 0 0
$$793$$ −12.0000 −0.426132
$$794$$ −10.0000 −0.354887
$$795$$ 0 0
$$796$$ −10.0000 −0.354441
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ 0 0
$$799$$ −2.00000 −0.0707549
$$800$$ 0 0
$$801$$ 0 0
$$802$$ −37.0000 −1.30652
$$803$$ 35.0000 1.23512
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −24.0000 −0.845364
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −6.00000 −0.210949 −0.105474 0.994422i $$-0.533636\pi$$
−0.105474 + 0.994422i $$0.533636\pi$$
$$810$$ 0 0
$$811$$ −28.0000 −0.983213 −0.491606 0.870817i $$-0.663590\pi$$
−0.491606 + 0.870817i $$0.663590\pi$$
$$812$$ 6.00000 0.210559
$$813$$ 0 0
$$814$$ −40.0000 −1.40200
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −24.0000 −0.839654
$$818$$ −21.0000 −0.734248
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 24.0000 0.837606 0.418803 0.908077i $$-0.362450\pi$$
0.418803 + 0.908077i $$0.362450\pi$$
$$822$$ 0 0
$$823$$ −10.0000 −0.348578 −0.174289 0.984695i $$-0.555763\pi$$
−0.174289 + 0.984695i $$0.555763\pi$$
$$824$$ −4.00000 −0.139347
$$825$$ 0 0
$$826$$ −4.00000 −0.139178
$$827$$ 41.0000 1.42571 0.712855 0.701312i $$-0.247402\pi$$
0.712855 + 0.701312i $$0.247402\pi$$
$$828$$ 0 0
$$829$$ −4.00000 −0.138926 −0.0694629 0.997585i $$-0.522129\pi$$
−0.0694629 + 0.997585i $$0.522129\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 6.00000 0.208013
$$833$$ −1.00000 −0.0346479
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −15.0000 −0.518786
$$837$$ 0 0
$$838$$ 39.0000 1.34723
$$839$$ −2.00000 −0.0690477 −0.0345238 0.999404i $$-0.510991\pi$$
−0.0345238 + 0.999404i $$0.510991\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 20.0000 0.689246
$$843$$ 0 0
$$844$$ 1.00000 0.0344214
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 14.0000 0.481046
$$848$$ 4.00000 0.137361
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 34.0000 1.16414 0.582069 0.813139i $$-0.302243\pi$$
0.582069 + 0.813139i $$0.302243\pi$$
$$854$$ −2.00000 −0.0684386
$$855$$ 0 0
$$856$$ 3.00000 0.102538
$$857$$ 3.00000 0.102478 0.0512390 0.998686i $$-0.483683\pi$$
0.0512390 + 0.998686i $$0.483683\pi$$
$$858$$ 0 0
$$859$$ −51.0000 −1.74010 −0.870049 0.492966i $$-0.835913\pi$$
−0.870049 + 0.492966i $$0.835913\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 36.0000 1.22616
$$863$$ 4.00000 0.136162 0.0680808 0.997680i $$-0.478312\pi$$
0.0680808 + 0.997680i $$0.478312\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 1.00000 0.0339814
$$867$$ 0 0
$$868$$ −4.00000 −0.135769
$$869$$ −10.0000 −0.339227
$$870$$ 0 0
$$871$$ −54.0000 −1.82972
$$872$$ −18.0000 −0.609557
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −32.0000 −1.08056 −0.540282 0.841484i $$-0.681682\pi$$
−0.540282 + 0.841484i $$0.681682\pi$$
$$878$$ 28.0000 0.944954
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −26.0000 −0.875962 −0.437981 0.898984i $$-0.644306\pi$$
−0.437981 + 0.898984i $$0.644306\pi$$
$$882$$ 0 0
$$883$$ −15.0000 −0.504790 −0.252395 0.967624i $$-0.581218\pi$$
−0.252395 + 0.967624i $$0.581218\pi$$
$$884$$ −6.00000 −0.201802
$$885$$ 0 0
$$886$$ 37.0000 1.24304
$$887$$ −34.0000 −1.14161 −0.570804 0.821086i $$-0.693368\pi$$
−0.570804 + 0.821086i $$0.693368\pi$$
$$888$$ 0 0
$$889$$ 14.0000 0.469545
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −22.0000 −0.736614
$$893$$ −6.00000 −0.200782
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 1.00000 0.0334077
$$897$$ 0 0
$$898$$ −33.0000 −1.10122
$$899$$ −24.0000 −0.800445
$$900$$ 0 0
$$901$$ −4.00000 −0.133259
$$902$$ −55.0000 −1.83130
$$903$$ 0 0
$$904$$ −1.00000 −0.0332595
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 4.00000 0.132818 0.0664089 0.997792i $$-0.478846\pi$$
0.0664089 + 0.997792i $$0.478846\pi$$
$$908$$ −28.0000 −0.929213
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ 55.0000 1.82023
$$914$$ −25.0000 −0.826927
$$915$$ 0 0
$$916$$ −14.0000 −0.462573
$$917$$ −8.00000 −0.264183
$$918$$ 0 0
$$919$$ −34.0000 −1.12156 −0.560778 0.827966i $$-0.689498\pi$$
−0.560778 + 0.827966i $$0.689498\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 38.0000 1.25146
$$923$$ 60.0000 1.97492
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −8.00000 −0.262896
$$927$$ 0 0
$$928$$ 6.00000 0.196960
$$929$$ −46.0000 −1.50921 −0.754606 0.656179i $$-0.772172\pi$$
−0.754606 + 0.656179i $$0.772172\pi$$
$$930$$ 0 0
$$931$$ −3.00000 −0.0983210
$$932$$ 6.00000 0.196537
$$933$$ 0 0
$$934$$ −4.00000 −0.130884
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 7.00000 0.228680 0.114340 0.993442i $$-0.463525\pi$$
0.114340 + 0.993442i $$0.463525\pi$$
$$938$$ −9.00000 −0.293860
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −56.0000 −1.82555 −0.912774 0.408465i $$-0.866064\pi$$
−0.912774 + 0.408465i $$0.866064\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −4.00000 −0.130189
$$945$$ 0 0
$$946$$ 40.0000 1.30051
$$947$$ −4.00000 −0.129983 −0.0649913 0.997886i $$-0.520702\pi$$
−0.0649913 + 0.997886i $$0.520702\pi$$
$$948$$ 0 0
$$949$$ 42.0000 1.36338
$$950$$ 0 0
$$951$$ 0 0
$$952$$ −1.00000 −0.0324102
$$953$$ 9.00000 0.291539 0.145769 0.989319i $$-0.453434\pi$$
0.145769 + 0.989319i $$0.453434\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −4.00000 −0.129369
$$957$$ 0 0
$$958$$ 6.00000 0.193851
$$959$$ −3.00000 −0.0968751
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ −48.0000 −1.54758
$$963$$ 0 0
$$964$$ −5.00000 −0.161039
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 2.00000 0.0643157 0.0321578 0.999483i $$-0.489762\pi$$
0.0321578 + 0.999483i $$0.489762\pi$$
$$968$$ 14.0000 0.449977
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 51.0000 1.63667 0.818334 0.574743i $$-0.194898\pi$$
0.818334 + 0.574743i $$0.194898\pi$$
$$972$$ 0 0
$$973$$ −11.0000 −0.352644
$$974$$ 34.0000 1.08943
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ 21.0000 0.671850 0.335925 0.941889i $$-0.390951\pi$$
0.335925 + 0.941889i $$0.390951\pi$$
$$978$$ 0 0
$$979$$ 55.0000 1.75781
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 12.0000 0.382935
$$983$$ −4.00000 −0.127580 −0.0637901 0.997963i $$-0.520319\pi$$
−0.0637901 + 0.997963i $$0.520319\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −6.00000 −0.191079
$$987$$ 0 0
$$988$$ −18.0000 −0.572656
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 4.00000 0.127064 0.0635321 0.997980i $$-0.479763\pi$$
0.0635321 + 0.997980i $$0.479763\pi$$
$$992$$ −4.00000 −0.127000
$$993$$ 0 0
$$994$$ 10.0000 0.317181
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 58.0000 1.83688 0.918439 0.395562i $$-0.129450\pi$$
0.918439 + 0.395562i $$0.129450\pi$$
$$998$$ 36.0000 1.13956
$$999$$ 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 3150.2.a.bq.1.1 1
3.2 odd 2 350.2.a.c.1.1 1
5.2 odd 4 3150.2.g.v.2899.2 2
5.3 odd 4 3150.2.g.v.2899.1 2
5.4 even 2 3150.2.a.j.1.1 1
12.11 even 2 2800.2.a.b.1.1 1
15.2 even 4 350.2.c.a.99.1 2
15.8 even 4 350.2.c.a.99.2 2
15.14 odd 2 350.2.a.d.1.1 yes 1
21.20 even 2 2450.2.a.a.1.1 1
60.23 odd 4 2800.2.g.a.449.1 2
60.47 odd 4 2800.2.g.a.449.2 2
60.59 even 2 2800.2.a.bg.1.1 1
105.62 odd 4 2450.2.c.r.99.1 2
105.83 odd 4 2450.2.c.r.99.2 2
105.104 even 2 2450.2.a.bg.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.a.c.1.1 1 3.2 odd 2
350.2.a.d.1.1 yes 1 15.14 odd 2
350.2.c.a.99.1 2 15.2 even 4
350.2.c.a.99.2 2 15.8 even 4
2450.2.a.a.1.1 1 21.20 even 2
2450.2.a.bg.1.1 1 105.104 even 2
2450.2.c.r.99.1 2 105.62 odd 4
2450.2.c.r.99.2 2 105.83 odd 4
2800.2.a.b.1.1 1 12.11 even 2
2800.2.a.bg.1.1 1 60.59 even 2
2800.2.g.a.449.1 2 60.23 odd 4
2800.2.g.a.449.2 2 60.47 odd 4
3150.2.a.j.1.1 1 5.4 even 2
3150.2.a.bq.1.1 1 1.1 even 1 trivial
3150.2.g.v.2899.1 2 5.3 odd 4
3150.2.g.v.2899.2 2 5.2 odd 4