Properties

 Label 7350.2.a.cc.1.1 Level $7350$ Weight $2$ Character 7350.1 Self dual yes Analytic conductor $58.690$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7350.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$58.6900454856$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 30) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7350.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} -1.00000 q^{12} +6.00000 q^{13} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +2.00000 q^{22} +4.00000 q^{23} -1.00000 q^{24} +6.00000 q^{26} -1.00000 q^{27} +8.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} +2.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} -6.00000 q^{39} -2.00000 q^{41} +4.00000 q^{43} +2.00000 q^{44} +4.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} -2.00000 q^{51} +6.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} -10.0000 q^{59} -2.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} -2.00000 q^{66} +8.00000 q^{67} +2.00000 q^{68} -4.00000 q^{69} +12.0000 q^{71} +1.00000 q^{72} -4.00000 q^{73} -2.00000 q^{74} -6.00000 q^{78} +1.00000 q^{81} -2.00000 q^{82} -4.00000 q^{83} +4.00000 q^{86} +2.00000 q^{88} +10.0000 q^{89} +4.00000 q^{92} -8.00000 q^{93} -8.00000 q^{94} -1.00000 q^{96} -8.00000 q^{97} +2.00000 q^{99} +O(q^{100})$$

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
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 2.00000 0.426401
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ 6.00000 1.17670
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 1.00000 0.176777
$$33$$ −2.00000 −0.348155
$$34$$ 2.00000 0.342997
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0 0
$$39$$ −6.00000 −0.960769
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −2.00000 −0.280056
$$52$$ 6.00000 0.832050
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −10.0000 −1.30189 −0.650945 0.759125i $$-0.725627\pi$$
−0.650945 + 0.759125i $$0.725627\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 8.00000 1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −2.00000 −0.246183
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 2.00000 0.242536
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −4.00000 −0.468165 −0.234082 0.972217i $$-0.575209\pi$$
−0.234082 + 0.972217i $$0.575209\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ −6.00000 −0.679366
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −2.00000 −0.220863
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ 2.00000 0.213201
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ −8.00000 −0.829561
$$94$$ −8.00000 −0.825137
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ −8.00000 −0.812277 −0.406138 0.913812i $$-0.633125\pi$$
−0.406138 + 0.913812i $$0.633125\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ 0 0
$$101$$ 8.00000 0.796030 0.398015 0.917379i $$-0.369699\pi$$
0.398015 + 0.917379i $$0.369699\pi$$
$$102$$ −2.00000 −0.198030
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ 0 0
$$111$$ 2.00000 0.189832
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 6.00000 0.554700
$$118$$ −10.0000 −0.920575
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ −2.00000 −0.181071
$$123$$ 2.00000 0.180334
$$124$$ 8.00000 0.718421
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ 18.0000 1.57267 0.786334 0.617802i $$-0.211977\pi$$
0.786334 + 0.617802i $$0.211977\pi$$
$$132$$ −2.00000 −0.174078
$$133$$ 0 0
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ 18.0000 1.53784 0.768922 0.639343i $$-0.220793\pi$$
0.768922 + 0.639343i $$0.220793\pi$$
$$138$$ −4.00000 −0.340503
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 0 0
$$141$$ 8.00000 0.673722
$$142$$ 12.0000 1.00702
$$143$$ 12.0000 1.00349
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ −20.0000 −1.63846 −0.819232 0.573462i $$-0.805600\pi$$
−0.819232 + 0.573462i $$0.805600\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −6.00000 −0.480384
$$157$$ 22.0000 1.75579 0.877896 0.478852i $$-0.158947\pi$$
0.877896 + 0.478852i $$0.158947\pi$$
$$158$$ 0 0
$$159$$ 6.00000 0.475831
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000 0.0785674
$$163$$ −16.0000 −1.25322 −0.626608 0.779334i $$-0.715557\pi$$
−0.626608 + 0.779334i $$0.715557\pi$$
$$164$$ −2.00000 −0.156174
$$165$$ 0 0
$$166$$ −4.00000 −0.310460
$$167$$ 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
$$172$$ 4.00000 0.304997
$$173$$ −14.0000 −1.06440 −0.532200 0.846619i $$-0.678635\pi$$
−0.532200 + 0.846619i $$0.678635\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 2.00000 0.150756
$$177$$ 10.0000 0.751646
$$178$$ 10.0000 0.749532
$$179$$ 10.0000 0.747435 0.373718 0.927543i $$-0.378083\pi$$
0.373718 + 0.927543i $$0.378083\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ 4.00000 0.294884
$$185$$ 0 0
$$186$$ −8.00000 −0.586588
$$187$$ 4.00000 0.292509
$$188$$ −8.00000 −0.583460
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 4.00000 0.287926 0.143963 0.989583i $$-0.454015\pi$$
0.143963 + 0.989583i $$0.454015\pi$$
$$194$$ −8.00000 −0.574367
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −22.0000 −1.56744 −0.783718 0.621117i $$-0.786679\pi$$
−0.783718 + 0.621117i $$0.786679\pi$$
$$198$$ 2.00000 0.142134
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −8.00000 −0.564276
$$202$$ 8.00000 0.562878
$$203$$ 0 0
$$204$$ −2.00000 −0.140028
$$205$$ 0 0
$$206$$ −14.0000 −0.975426
$$207$$ 4.00000 0.278019
$$208$$ 6.00000 0.416025
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ −12.0000 −0.822226
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 10.0000 0.677285
$$219$$ 4.00000 0.270295
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 2.00000 0.134231
$$223$$ 26.0000 1.74109 0.870544 0.492090i $$-0.163767\pi$$
0.870544 + 0.492090i $$0.163767\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −28.0000 −1.85843 −0.929213 0.369546i $$-0.879513\pi$$
−0.929213 + 0.369546i $$0.879513\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 14.0000 0.917170 0.458585 0.888650i $$-0.348356\pi$$
0.458585 + 0.888650i $$0.348356\pi$$
$$234$$ 6.00000 0.392232
$$235$$ 0 0
$$236$$ −10.0000 −0.650945
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ −22.0000 −1.41714 −0.708572 0.705638i $$-0.750660\pi$$
−0.708572 + 0.705638i $$0.750660\pi$$
$$242$$ −7.00000 −0.449977
$$243$$ −1.00000 −0.0641500
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ 2.00000 0.127515
$$247$$ 0 0
$$248$$ 8.00000 0.508001
$$249$$ 4.00000 0.253490
$$250$$ 0 0
$$251$$ 18.0000 1.13615 0.568075 0.822977i $$-0.307688\pi$$
0.568075 + 0.822977i $$0.307688\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ −2.00000 −0.125491
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 18.0000 1.11204
$$263$$ 4.00000 0.246651 0.123325 0.992366i $$-0.460644\pi$$
0.123325 + 0.992366i $$0.460644\pi$$
$$264$$ −2.00000 −0.123091
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −10.0000 −0.611990
$$268$$ 8.00000 0.488678
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 18.0000 1.08742
$$275$$ 0 0
$$276$$ −4.00000 −0.240772
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 20.0000 1.19952
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 8.00000 0.476393
$$283$$ 16.0000 0.951101 0.475551 0.879688i $$-0.342249\pi$$
0.475551 + 0.879688i $$0.342249\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ 12.0000 0.709575
$$287$$ 0 0
$$288$$ 1.00000 0.0589256
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ −4.00000 −0.234082
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −2.00000 −0.116248
$$297$$ −2.00000 −0.116052
$$298$$ −20.0000 −1.15857
$$299$$ 24.0000 1.38796
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −8.00000 −0.460348
$$303$$ −8.00000 −0.459588
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 2.00000 0.114332
$$307$$ 12.0000 0.684876 0.342438 0.939540i $$-0.388747\pi$$
0.342438 + 0.939540i $$0.388747\pi$$
$$308$$ 0 0
$$309$$ 14.0000 0.796432
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ −6.00000 −0.339683
$$313$$ −4.00000 −0.226093 −0.113047 0.993590i $$-0.536061\pi$$
−0.113047 + 0.993590i $$0.536061\pi$$
$$314$$ 22.0000 1.24153
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.00000 −0.112331 −0.0561656 0.998421i $$-0.517887\pi$$
−0.0561656 + 0.998421i $$0.517887\pi$$
$$318$$ 6.00000 0.336463
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −16.0000 −0.886158
$$327$$ −10.0000 −0.553001
$$328$$ −2.00000 −0.110432
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ −4.00000 −0.219529
$$333$$ −2.00000 −0.109599
$$334$$ 12.0000 0.656611
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 28.0000 1.52526 0.762629 0.646837i $$-0.223908\pi$$
0.762629 + 0.646837i $$0.223908\pi$$
$$338$$ 23.0000 1.25104
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ 16.0000 0.866449
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ −14.0000 −0.752645
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ 0 0
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ 0 0
$$351$$ −6.00000 −0.320256
$$352$$ 2.00000 0.106600
$$353$$ −14.0000 −0.745145 −0.372572 0.928003i $$-0.621524\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ 10.0000 0.531494
$$355$$ 0 0
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ 10.0000 0.528516
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ −2.00000 −0.105118
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 2.00000 0.104542
$$367$$ 2.00000 0.104399 0.0521996 0.998637i $$-0.483377\pi$$
0.0521996 + 0.998637i $$0.483377\pi$$
$$368$$ 4.00000 0.208514
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −8.00000 −0.414781
$$373$$ −6.00000 −0.310668 −0.155334 0.987862i $$-0.549645\pi$$
−0.155334 + 0.987862i $$0.549645\pi$$
$$374$$ 4.00000 0.206835
$$375$$ 0 0
$$376$$ −8.00000 −0.412568
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 0 0
$$381$$ 2.00000 0.102463
$$382$$ 12.0000 0.613973
$$383$$ 16.0000 0.817562 0.408781 0.912633i $$-0.365954\pi$$
0.408781 + 0.912633i $$0.365954\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ 4.00000 0.203595
$$387$$ 4.00000 0.203331
$$388$$ −8.00000 −0.406138
$$389$$ 20.0000 1.01404 0.507020 0.861934i $$-0.330747\pi$$
0.507020 + 0.861934i $$0.330747\pi$$
$$390$$ 0 0
$$391$$ 8.00000 0.404577
$$392$$ 0 0
$$393$$ −18.0000 −0.907980
$$394$$ −22.0000 −1.10834
$$395$$ 0 0
$$396$$ 2.00000 0.100504
$$397$$ 2.00000 0.100377 0.0501886 0.998740i $$-0.484018\pi$$
0.0501886 + 0.998740i $$0.484018\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 22.0000 1.09863 0.549314 0.835616i $$-0.314889\pi$$
0.549314 + 0.835616i $$0.314889\pi$$
$$402$$ −8.00000 −0.399004
$$403$$ 48.0000 2.39105
$$404$$ 8.00000 0.398015
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −4.00000 −0.198273
$$408$$ −2.00000 −0.0990148
$$409$$ 10.0000 0.494468 0.247234 0.968956i $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ 0 0
$$411$$ −18.0000 −0.887875
$$412$$ −14.0000 −0.689730
$$413$$ 0 0
$$414$$ 4.00000 0.196589
$$415$$ 0 0
$$416$$ 6.00000 0.294174
$$417$$ −20.0000 −0.979404
$$418$$ 0 0
$$419$$ 10.0000 0.488532 0.244266 0.969708i $$-0.421453\pi$$
0.244266 + 0.969708i $$0.421453\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ 12.0000 0.584151
$$423$$ −8.00000 −0.388973
$$424$$ −6.00000 −0.291386
$$425$$ 0 0
$$426$$ −12.0000 −0.581402
$$427$$ 0 0
$$428$$ −12.0000 −0.580042
$$429$$ −12.0000 −0.579365
$$430$$ 0 0
$$431$$ 32.0000 1.54139 0.770693 0.637207i $$-0.219910\pi$$
0.770693 + 0.637207i $$0.219910\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ −4.00000 −0.192228 −0.0961139 0.995370i $$-0.530641\pi$$
−0.0961139 + 0.995370i $$0.530641\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 10.0000 0.478913
$$437$$ 0 0
$$438$$ 4.00000 0.191127
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 12.0000 0.570782
$$443$$ −36.0000 −1.71041 −0.855206 0.518289i $$-0.826569\pi$$
−0.855206 + 0.518289i $$0.826569\pi$$
$$444$$ 2.00000 0.0949158
$$445$$ 0 0
$$446$$ 26.0000 1.23114
$$447$$ 20.0000 0.945968
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ −4.00000 −0.188353
$$452$$ −6.00000 −0.282216
$$453$$ 8.00000 0.375873
$$454$$ −28.0000 −1.31411
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −32.0000 −1.49690 −0.748448 0.663193i $$-0.769201\pi$$
−0.748448 + 0.663193i $$0.769201\pi$$
$$458$$ 10.0000 0.467269
$$459$$ −2.00000 −0.0933520
$$460$$ 0 0
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ −6.00000 −0.278844 −0.139422 0.990233i $$-0.544524\pi$$
−0.139422 + 0.990233i $$0.544524\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 14.0000 0.648537
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 6.00000 0.277350
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −22.0000 −1.01371
$$472$$ −10.0000 −0.460287
$$473$$ 8.00000 0.367840
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ 20.0000 0.914779
$$479$$ −20.0000 −0.913823 −0.456912 0.889512i $$-0.651044\pi$$
−0.456912 + 0.889512i $$0.651044\pi$$
$$480$$ 0 0
$$481$$ −12.0000 −0.547153
$$482$$ −22.0000 −1.00207
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 18.0000 0.815658 0.407829 0.913058i $$-0.366286\pi$$
0.407829 + 0.913058i $$0.366286\pi$$
$$488$$ −2.00000 −0.0905357
$$489$$ 16.0000 0.723545
$$490$$ 0 0
$$491$$ −18.0000 −0.812329 −0.406164 0.913800i $$-0.633134\pi$$
−0.406164 + 0.913800i $$0.633134\pi$$
$$492$$ 2.00000 0.0901670
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ 4.00000 0.179244
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 0 0
$$501$$ −12.0000 −0.536120
$$502$$ 18.0000 0.803379
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 8.00000 0.355643
$$507$$ −23.0000 −1.02147
$$508$$ −2.00000 −0.0887357
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −18.0000 −0.793946
$$515$$ 0 0
$$516$$ −4.00000 −0.176090
$$517$$ −16.0000 −0.703679
$$518$$ 0 0
$$519$$ 14.0000 0.614532
$$520$$ 0 0
$$521$$ −22.0000 −0.963837 −0.481919 0.876216i $$-0.660060\pi$$
−0.481919 + 0.876216i $$0.660060\pi$$
$$522$$ 0 0
$$523$$ 16.0000 0.699631 0.349816 0.936819i $$-0.386244\pi$$
0.349816 + 0.936819i $$0.386244\pi$$
$$524$$ 18.0000 0.786334
$$525$$ 0 0
$$526$$ 4.00000 0.174408
$$527$$ 16.0000 0.696971
$$528$$ −2.00000 −0.0870388
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ −10.0000 −0.433963
$$532$$ 0 0
$$533$$ −12.0000 −0.519778
$$534$$ −10.0000 −0.432742
$$535$$ 0 0
$$536$$ 8.00000 0.345547
$$537$$ −10.0000 −0.431532
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −38.0000 −1.63375 −0.816874 0.576816i $$-0.804295\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 8.00000 0.343629
$$543$$ 2.00000 0.0858282
$$544$$ 2.00000 0.0857493
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 28.0000 1.19719 0.598597 0.801050i $$-0.295725\pi$$
0.598597 + 0.801050i $$0.295725\pi$$
$$548$$ 18.0000 0.768922
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −4.00000 −0.170251
$$553$$ 0 0
$$554$$ −2.00000 −0.0849719
$$555$$ 0 0
$$556$$ 20.0000 0.848189
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ 8.00000 0.338667
$$559$$ 24.0000 1.01509
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ −18.0000 −0.759284
$$563$$ −44.0000 −1.85438 −0.927189 0.374593i $$-0.877783\pi$$
−0.927189 + 0.374593i $$0.877783\pi$$
$$564$$ 8.00000 0.336861
$$565$$ 0 0
$$566$$ 16.0000 0.672530
$$567$$ 0 0
$$568$$ 12.0000 0.503509
$$569$$ −10.0000 −0.419222 −0.209611 0.977785i $$-0.567220\pi$$
−0.209611 + 0.977785i $$0.567220\pi$$
$$570$$ 0 0
$$571$$ −8.00000 −0.334790 −0.167395 0.985890i $$-0.553535\pi$$
−0.167395 + 0.985890i $$0.553535\pi$$
$$572$$ 12.0000 0.501745
$$573$$ −12.0000 −0.501307
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 32.0000 1.33218 0.666089 0.745873i $$-0.267967\pi$$
0.666089 + 0.745873i $$0.267967\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ −4.00000 −0.166234
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 8.00000 0.331611
$$583$$ −12.0000 −0.496989
$$584$$ −4.00000 −0.165521
$$585$$ 0 0
$$586$$ 6.00000 0.247858
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 22.0000 0.904959
$$592$$ −2.00000 −0.0821995
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ −2.00000 −0.0820610
$$595$$ 0 0
$$596$$ −20.0000 −0.819232
$$597$$ 0 0
$$598$$ 24.0000 0.981433
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −2.00000 −0.0815817 −0.0407909 0.999168i $$-0.512988\pi$$
−0.0407909 + 0.999168i $$0.512988\pi$$
$$602$$ 0 0
$$603$$ 8.00000 0.325785
$$604$$ −8.00000 −0.325515
$$605$$ 0 0
$$606$$ −8.00000 −0.324978
$$607$$ 22.0000 0.892952 0.446476 0.894795i $$-0.352679\pi$$
0.446476 + 0.894795i $$0.352679\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −48.0000 −1.94187
$$612$$ 2.00000 0.0808452
$$613$$ −26.0000 −1.05013 −0.525065 0.851062i $$-0.675959\pi$$
−0.525065 + 0.851062i $$0.675959\pi$$
$$614$$ 12.0000 0.484281
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −2.00000 −0.0805170 −0.0402585 0.999189i $$-0.512818\pi$$
−0.0402585 + 0.999189i $$0.512818\pi$$
$$618$$ 14.0000 0.563163
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 0 0
$$621$$ −4.00000 −0.160514
$$622$$ −12.0000 −0.481156
$$623$$ 0 0
$$624$$ −6.00000 −0.240192
$$625$$ 0 0
$$626$$ −4.00000 −0.159872
$$627$$ 0 0
$$628$$ 22.0000 0.877896
$$629$$ −4.00000 −0.159490
$$630$$ 0 0
$$631$$ 32.0000 1.27390 0.636950 0.770905i $$-0.280196\pi$$
0.636950 + 0.770905i $$0.280196\pi$$
$$632$$ 0 0
$$633$$ −12.0000 −0.476957
$$634$$ −2.00000 −0.0794301
$$635$$ 0 0
$$636$$ 6.00000 0.237915
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 12.0000 0.474713
$$640$$ 0 0
$$641$$ 2.00000 0.0789953 0.0394976 0.999220i $$-0.487424\pi$$
0.0394976 + 0.999220i $$0.487424\pi$$
$$642$$ 12.0000 0.473602
$$643$$ −24.0000 −0.946468 −0.473234 0.880937i $$-0.656913\pi$$
−0.473234 + 0.880937i $$0.656913\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −48.0000 −1.88707 −0.943537 0.331266i $$-0.892524\pi$$
−0.943537 + 0.331266i $$0.892524\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ −20.0000 −0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −16.0000 −0.626608
$$653$$ −26.0000 −1.01746 −0.508729 0.860927i $$-0.669885\pi$$
−0.508729 + 0.860927i $$0.669885\pi$$
$$654$$ −10.0000 −0.391031
$$655$$ 0 0
$$656$$ −2.00000 −0.0780869
$$657$$ −4.00000 −0.156055
$$658$$ 0 0
$$659$$ −50.0000 −1.94772 −0.973862 0.227142i $$-0.927062\pi$$
−0.973862 + 0.227142i $$0.927062\pi$$
$$660$$ 0 0
$$661$$ −2.00000 −0.0777910 −0.0388955 0.999243i $$-0.512384\pi$$
−0.0388955 + 0.999243i $$0.512384\pi$$
$$662$$ −8.00000 −0.310929
$$663$$ −12.0000 −0.466041
$$664$$ −4.00000 −0.155230
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ 0 0
$$668$$ 12.0000 0.464294
$$669$$ −26.0000 −1.00522
$$670$$ 0 0
$$671$$ −4.00000 −0.154418
$$672$$ 0 0
$$673$$ −36.0000 −1.38770 −0.693849 0.720121i $$-0.744086\pi$$
−0.693849 + 0.720121i $$0.744086\pi$$
$$674$$ 28.0000 1.07852
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ 2.00000 0.0768662 0.0384331 0.999261i $$-0.487763\pi$$
0.0384331 + 0.999261i $$0.487763\pi$$
$$678$$ 6.00000 0.230429
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 28.0000 1.07296
$$682$$ 16.0000 0.612672
$$683$$ 4.00000 0.153056 0.0765279 0.997067i $$-0.475617\pi$$
0.0765279 + 0.997067i $$0.475617\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −10.0000 −0.381524
$$688$$ 4.00000 0.152499
$$689$$ −36.0000 −1.37149
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ −14.0000 −0.532200
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −4.00000 −0.151511
$$698$$ −10.0000 −0.378506
$$699$$ −14.0000 −0.529529
$$700$$ 0 0
$$701$$ 32.0000 1.20862 0.604312 0.796748i $$-0.293448\pi$$
0.604312 + 0.796748i $$0.293448\pi$$
$$702$$ −6.00000 −0.226455
$$703$$ 0 0
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ −14.0000 −0.526897
$$707$$ 0 0
$$708$$ 10.0000 0.375823
$$709$$ 30.0000 1.12667 0.563337 0.826227i $$-0.309517\pi$$
0.563337 + 0.826227i $$0.309517\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 10.0000 0.374766
$$713$$ 32.0000 1.19841
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 10.0000 0.373718
$$717$$ −20.0000 −0.746914
$$718$$ 0 0
$$719$$ 40.0000 1.49175 0.745874 0.666087i $$-0.232032\pi$$
0.745874 + 0.666087i $$0.232032\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −19.0000 −0.707107
$$723$$ 22.0000 0.818189
$$724$$ −2.00000 −0.0743294
$$725$$ 0 0
$$726$$ 7.00000 0.259794
$$727$$ −18.0000 −0.667583 −0.333792 0.942647i $$-0.608328\pi$$
−0.333792 + 0.942647i $$0.608328\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 8.00000 0.295891
$$732$$ 2.00000 0.0739221
$$733$$ −14.0000 −0.517102 −0.258551 0.965998i $$-0.583245\pi$$
−0.258551 + 0.965998i $$0.583245\pi$$
$$734$$ 2.00000 0.0738213
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 16.0000 0.589368
$$738$$ −2.00000 −0.0736210
$$739$$ 40.0000 1.47142 0.735712 0.677295i $$-0.236848\pi$$
0.735712 + 0.677295i $$0.236848\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ −8.00000 −0.293294
$$745$$ 0 0
$$746$$ −6.00000 −0.219676
$$747$$ −4.00000 −0.146352
$$748$$ 4.00000 0.146254
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ −8.00000 −0.291730
$$753$$ −18.0000 −0.655956
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −2.00000 −0.0726912 −0.0363456 0.999339i $$-0.511572\pi$$
−0.0363456 + 0.999339i $$0.511572\pi$$
$$758$$ 20.0000 0.726433
$$759$$ −8.00000 −0.290382
$$760$$ 0 0
$$761$$ 18.0000 0.652499 0.326250 0.945284i $$-0.394215\pi$$
0.326250 + 0.945284i $$0.394215\pi$$
$$762$$ 2.00000 0.0724524
$$763$$ 0 0
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ 16.0000 0.578103
$$767$$ −60.0000 −2.16647
$$768$$ −1.00000 −0.0360844
$$769$$ 30.0000 1.08183 0.540914 0.841078i $$-0.318079\pi$$
0.540914 + 0.841078i $$0.318079\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 4.00000 0.143963
$$773$$ −54.0000 −1.94225 −0.971123 0.238581i $$-0.923318\pi$$
−0.971123 + 0.238581i $$0.923318\pi$$
$$774$$ 4.00000 0.143777
$$775$$ 0 0
$$776$$ −8.00000 −0.287183
$$777$$ 0 0
$$778$$ 20.0000 0.717035
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 24.0000 0.858788
$$782$$ 8.00000 0.286079
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −18.0000 −0.642039
$$787$$ 32.0000 1.14068 0.570338 0.821410i $$-0.306812\pi$$
0.570338 + 0.821410i $$0.306812\pi$$
$$788$$ −22.0000 −0.783718
$$789$$ −4.00000 −0.142404
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 2.00000 0.0710669
$$793$$ −12.0000 −0.426132
$$794$$ 2.00000 0.0709773
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 2.00000 0.0708436 0.0354218 0.999372i $$-0.488723\pi$$
0.0354218 + 0.999372i $$0.488723\pi$$
$$798$$ 0 0
$$799$$ −16.0000 −0.566039
$$800$$ 0 0
$$801$$ 10.0000 0.353333
$$802$$ 22.0000 0.776847
$$803$$ −8.00000 −0.282314
$$804$$ −8.00000 −0.282138
$$805$$ 0 0
$$806$$ 48.0000 1.69073
$$807$$ 0 0
$$808$$ 8.00000 0.281439
$$809$$ −30.0000 −1.05474 −0.527372 0.849635i $$-0.676823\pi$$
−0.527372 + 0.849635i $$0.676823\pi$$
$$810$$ 0 0
$$811$$ −52.0000 −1.82597 −0.912983 0.407997i $$-0.866228\pi$$
−0.912983 + 0.407997i $$0.866228\pi$$
$$812$$ 0 0
$$813$$ −8.00000 −0.280572
$$814$$ −4.00000 −0.140200
$$815$$ 0 0
$$816$$ −2.00000 −0.0700140
$$817$$ 0 0
$$818$$ 10.0000 0.349642
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −8.00000 −0.279202 −0.139601 0.990208i $$-0.544582\pi$$
−0.139601 + 0.990208i $$0.544582\pi$$
$$822$$ −18.0000 −0.627822
$$823$$ −6.00000 −0.209147 −0.104573 0.994517i $$-0.533348\pi$$
−0.104573 + 0.994517i $$0.533348\pi$$
$$824$$ −14.0000 −0.487713
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 28.0000 0.973655 0.486828 0.873498i $$-0.338154\pi$$
0.486828 + 0.873498i $$0.338154\pi$$
$$828$$ 4.00000 0.139010
$$829$$ 30.0000 1.04194 0.520972 0.853574i $$-0.325570\pi$$
0.520972 + 0.853574i $$0.325570\pi$$
$$830$$ 0 0
$$831$$ 2.00000 0.0693792
$$832$$ 6.00000 0.208013
$$833$$ 0 0
$$834$$ −20.0000 −0.692543
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −8.00000 −0.276520
$$838$$ 10.0000 0.345444
$$839$$ −40.0000 −1.38095 −0.690477 0.723355i $$-0.742599\pi$$
−0.690477 + 0.723355i $$0.742599\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ 22.0000 0.758170
$$843$$ 18.0000 0.619953
$$844$$ 12.0000 0.413057
$$845$$ 0 0
$$846$$ −8.00000 −0.275046
$$847$$ 0 0
$$848$$ −6.00000 −0.206041
$$849$$ −16.0000 −0.549119
$$850$$ 0 0
$$851$$ −8.00000 −0.274236
$$852$$ −12.0000 −0.411113
$$853$$ −14.0000 −0.479351 −0.239675 0.970853i $$-0.577041\pi$$
−0.239675 + 0.970853i $$0.577041\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ −12.0000 −0.409673
$$859$$ −20.0000 −0.682391 −0.341196 0.939992i $$-0.610832\pi$$
−0.341196 + 0.939992i $$0.610832\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 32.0000 1.08992
$$863$$ −36.0000 −1.22545 −0.612727 0.790295i $$-0.709928\pi$$
−0.612727 + 0.790295i $$0.709928\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ −4.00000 −0.135926
$$867$$ 13.0000 0.441503
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 48.0000 1.62642
$$872$$ 10.0000 0.338643
$$873$$ −8.00000 −0.270759
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 4.00000 0.135147
$$877$$ −22.0000 −0.742887 −0.371444 0.928456i $$-0.621137\pi$$
−0.371444 + 0.928456i $$0.621137\pi$$
$$878$$ 0 0
$$879$$ −6.00000 −0.202375
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ 24.0000 0.807664 0.403832 0.914833i $$-0.367678\pi$$
0.403832 + 0.914833i $$0.367678\pi$$
$$884$$ 12.0000 0.403604
$$885$$ 0 0
$$886$$ −36.0000 −1.20944
$$887$$ 12.0000 0.402921 0.201460 0.979497i $$-0.435431\pi$$
0.201460 + 0.979497i $$0.435431\pi$$
$$888$$ 2.00000 0.0671156
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 2.00000 0.0670025
$$892$$ 26.0000 0.870544
$$893$$ 0 0
$$894$$ 20.0000 0.668900
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −24.0000 −0.801337
$$898$$ 30.0000 1.00111
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −12.0000 −0.399778
$$902$$ −4.00000 −0.133185
$$903$$ 0 0
$$904$$ −6.00000 −0.199557
$$905$$ 0 0
$$906$$ 8.00000 0.265782
$$907$$ −12.0000 −0.398453 −0.199227 0.979953i $$-0.563843\pi$$
−0.199227 + 0.979953i $$0.563843\pi$$
$$908$$ −28.0000 −0.929213
$$909$$ 8.00000 0.265343
$$910$$ 0 0
$$911$$ −48.0000 −1.59031 −0.795155 0.606406i $$-0.792611\pi$$
−0.795155 + 0.606406i $$0.792611\pi$$
$$912$$ 0 0
$$913$$ −8.00000 −0.264761
$$914$$ −32.0000 −1.05847
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ 0 0
$$918$$ −2.00000 −0.0660098
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ −12.0000 −0.395413
$$922$$ −12.0000 −0.395199
$$923$$ 72.0000 2.36991
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −6.00000 −0.197172
$$927$$ −14.0000 −0.459820
$$928$$ 0 0
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 14.0000 0.458585
$$933$$ 12.0000 0.392862
$$934$$ 12.0000 0.392652
$$935$$ 0 0
$$936$$ 6.00000 0.196116
$$937$$ −8.00000 −0.261349 −0.130674 0.991425i $$-0.541714\pi$$
−0.130674 + 0.991425i $$0.541714\pi$$
$$938$$ 0 0
$$939$$ 4.00000 0.130535
$$940$$ 0 0
$$941$$ 28.0000 0.912774 0.456387 0.889781i $$-0.349143\pi$$
0.456387 + 0.889781i $$0.349143\pi$$
$$942$$ −22.0000 −0.716799
$$943$$ −8.00000 −0.260516
$$944$$ −10.0000 −0.325472
$$945$$ 0 0
$$946$$ 8.00000 0.260102
$$947$$ −12.0000 −0.389948 −0.194974 0.980808i $$-0.562462\pi$$
−0.194974 + 0.980808i $$0.562462\pi$$
$$948$$ 0 0
$$949$$ −24.0000 −0.779073
$$950$$ 0 0
$$951$$ 2.00000 0.0648544
$$952$$ 0 0
$$953$$ −46.0000 −1.49009 −0.745043 0.667016i $$-0.767571\pi$$
−0.745043 + 0.667016i $$0.767571\pi$$
$$954$$ −6.00000 −0.194257
$$955$$ 0 0
$$956$$ 20.0000 0.646846
$$957$$ 0 0
$$958$$ −20.0000 −0.646171
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ −12.0000 −0.386896
$$963$$ −12.0000 −0.386695
$$964$$ −22.0000 −0.708572
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 38.0000 1.22200 0.610999 0.791632i $$-0.290768\pi$$
0.610999 + 0.791632i $$0.290768\pi$$
$$968$$ −7.00000 −0.224989
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 18.0000 0.577647 0.288824 0.957382i $$-0.406736\pi$$
0.288824 + 0.957382i $$0.406736\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ 18.0000 0.576757
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ −42.0000 −1.34370 −0.671850 0.740688i $$-0.734500\pi$$
−0.671850 + 0.740688i $$0.734500\pi$$
$$978$$ 16.0000 0.511624
$$979$$ 20.0000 0.639203
$$980$$ 0 0
$$981$$ 10.0000 0.319275
$$982$$ −18.0000 −0.574403
$$983$$ 16.0000 0.510321 0.255160 0.966899i $$-0.417872\pi$$
0.255160 + 0.966899i $$0.417872\pi$$
$$984$$ 2.00000 0.0637577
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 16.0000 0.508770
$$990$$ 0 0
$$991$$ −8.00000 −0.254128 −0.127064 0.991894i $$-0.540555\pi$$
−0.127064 + 0.991894i $$0.540555\pi$$
$$992$$ 8.00000 0.254000
$$993$$ 8.00000 0.253872
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 4.00000 0.126745
$$997$$ −18.0000 −0.570066 −0.285033 0.958518i $$-0.592005\pi$$
−0.285033 + 0.958518i $$0.592005\pi$$
$$998$$ 0 0
$$999$$ 2.00000 0.0632772
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 7350.2.a.cc.1.1 1
5.2 odd 4 1470.2.g.g.589.2 2
5.3 odd 4 1470.2.g.g.589.1 2
5.4 even 2 7350.2.a.bg.1.1 1
7.6 odd 2 150.2.a.c.1.1 1
21.20 even 2 450.2.a.b.1.1 1
28.27 even 2 1200.2.a.g.1.1 1
35.2 odd 12 1470.2.n.a.949.2 4
35.3 even 12 1470.2.n.h.79.2 4
35.12 even 12 1470.2.n.h.949.2 4
35.13 even 4 30.2.c.a.19.1 2
35.17 even 12 1470.2.n.h.79.1 4
35.18 odd 12 1470.2.n.a.79.2 4
35.23 odd 12 1470.2.n.a.949.1 4
35.27 even 4 30.2.c.a.19.2 yes 2
35.32 odd 12 1470.2.n.a.79.1 4
35.33 even 12 1470.2.n.h.949.1 4
35.34 odd 2 150.2.a.a.1.1 1
56.13 odd 2 4800.2.a.l.1.1 1
56.27 even 2 4800.2.a.cj.1.1 1
84.83 odd 2 3600.2.a.bg.1.1 1
105.62 odd 4 90.2.c.a.19.1 2
105.83 odd 4 90.2.c.a.19.2 2
105.104 even 2 450.2.a.f.1.1 1
140.27 odd 4 240.2.f.a.49.2 2
140.83 odd 4 240.2.f.a.49.1 2
140.139 even 2 1200.2.a.m.1.1 1
280.13 even 4 960.2.f.h.769.1 2
280.27 odd 4 960.2.f.i.769.1 2
280.69 odd 2 4800.2.a.cg.1.1 1
280.83 odd 4 960.2.f.i.769.2 2
280.139 even 2 4800.2.a.m.1.1 1
280.237 even 4 960.2.f.h.769.2 2
315.13 even 12 810.2.i.e.379.2 4
315.83 odd 12 810.2.i.b.109.2 4
315.97 even 12 810.2.i.e.109.2 4
315.167 odd 12 810.2.i.b.379.2 4
315.202 even 12 810.2.i.e.379.1 4
315.223 even 12 810.2.i.e.109.1 4
315.272 odd 12 810.2.i.b.109.1 4
315.293 odd 12 810.2.i.b.379.1 4
420.83 even 4 720.2.f.f.289.2 2
420.167 even 4 720.2.f.f.289.1 2
420.419 odd 2 3600.2.a.o.1.1 1
560.13 even 4 3840.2.d.g.2689.2 2
560.27 odd 4 3840.2.d.x.2689.1 2
560.83 odd 4 3840.2.d.x.2689.2 2
560.237 even 4 3840.2.d.y.2689.2 2
560.293 even 4 3840.2.d.y.2689.1 2
560.307 odd 4 3840.2.d.j.2689.2 2
560.363 odd 4 3840.2.d.j.2689.1 2
560.517 even 4 3840.2.d.g.2689.1 2
840.83 even 4 2880.2.f.c.1729.1 2
840.293 odd 4 2880.2.f.e.1729.1 2
840.587 even 4 2880.2.f.c.1729.2 2
840.797 odd 4 2880.2.f.e.1729.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
30.2.c.a.19.1 2 35.13 even 4
30.2.c.a.19.2 yes 2 35.27 even 4
90.2.c.a.19.1 2 105.62 odd 4
90.2.c.a.19.2 2 105.83 odd 4
150.2.a.a.1.1 1 35.34 odd 2
150.2.a.c.1.1 1 7.6 odd 2
240.2.f.a.49.1 2 140.83 odd 4
240.2.f.a.49.2 2 140.27 odd 4
450.2.a.b.1.1 1 21.20 even 2
450.2.a.f.1.1 1 105.104 even 2
720.2.f.f.289.1 2 420.167 even 4
720.2.f.f.289.2 2 420.83 even 4
810.2.i.b.109.1 4 315.272 odd 12
810.2.i.b.109.2 4 315.83 odd 12
810.2.i.b.379.1 4 315.293 odd 12
810.2.i.b.379.2 4 315.167 odd 12
810.2.i.e.109.1 4 315.223 even 12
810.2.i.e.109.2 4 315.97 even 12
810.2.i.e.379.1 4 315.202 even 12
810.2.i.e.379.2 4 315.13 even 12
960.2.f.h.769.1 2 280.13 even 4
960.2.f.h.769.2 2 280.237 even 4
960.2.f.i.769.1 2 280.27 odd 4
960.2.f.i.769.2 2 280.83 odd 4
1200.2.a.g.1.1 1 28.27 even 2
1200.2.a.m.1.1 1 140.139 even 2
1470.2.g.g.589.1 2 5.3 odd 4
1470.2.g.g.589.2 2 5.2 odd 4
1470.2.n.a.79.1 4 35.32 odd 12
1470.2.n.a.79.2 4 35.18 odd 12
1470.2.n.a.949.1 4 35.23 odd 12
1470.2.n.a.949.2 4 35.2 odd 12
1470.2.n.h.79.1 4 35.17 even 12
1470.2.n.h.79.2 4 35.3 even 12
1470.2.n.h.949.1 4 35.33 even 12
1470.2.n.h.949.2 4 35.12 even 12
2880.2.f.c.1729.1 2 840.83 even 4
2880.2.f.c.1729.2 2 840.587 even 4
2880.2.f.e.1729.1 2 840.293 odd 4
2880.2.f.e.1729.2 2 840.797 odd 4
3600.2.a.o.1.1 1 420.419 odd 2
3600.2.a.bg.1.1 1 84.83 odd 2
3840.2.d.g.2689.1 2 560.517 even 4
3840.2.d.g.2689.2 2 560.13 even 4
3840.2.d.j.2689.1 2 560.363 odd 4
3840.2.d.j.2689.2 2 560.307 odd 4
3840.2.d.x.2689.1 2 560.27 odd 4
3840.2.d.x.2689.2 2 560.83 odd 4
3840.2.d.y.2689.1 2 560.293 even 4
3840.2.d.y.2689.2 2 560.237 even 4
4800.2.a.l.1.1 1 56.13 odd 2
4800.2.a.m.1.1 1 280.139 even 2
4800.2.a.cg.1.1 1 280.69 odd 2
4800.2.a.cj.1.1 1 56.27 even 2
7350.2.a.bg.1.1 1 5.4 even 2
7350.2.a.cc.1.1 1 1.1 even 1 trivial