# Properties

 Label 3850.2.a.bb.1.1 Level $3850$ Weight $2$ Character 3850.1 Self dual yes Analytic conductor $30.742$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3850.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$30.7424047782$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 770) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 3850.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} +2.00000 q^{12} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{18} +2.00000 q^{21} +1.00000 q^{22} +4.00000 q^{23} +2.00000 q^{24} -4.00000 q^{27} +1.00000 q^{28} +2.00000 q^{29} -2.00000 q^{31} +1.00000 q^{32} +2.00000 q^{33} +1.00000 q^{36} +6.00000 q^{37} +8.00000 q^{41} +2.00000 q^{42} +12.0000 q^{43} +1.00000 q^{44} +4.00000 q^{46} +6.00000 q^{47} +2.00000 q^{48} +1.00000 q^{49} +6.00000 q^{53} -4.00000 q^{54} +1.00000 q^{56} +2.00000 q^{58} -10.0000 q^{59} -4.00000 q^{61} -2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{66} +8.00000 q^{67} +8.00000 q^{69} -4.00000 q^{71} +1.00000 q^{72} +4.00000 q^{73} +6.00000 q^{74} +1.00000 q^{77} -16.0000 q^{79} -11.0000 q^{81} +8.00000 q^{82} +2.00000 q^{84} +12.0000 q^{86} +4.00000 q^{87} +1.00000 q^{88} -6.00000 q^{89} +4.00000 q^{92} -4.00000 q^{93} +6.00000 q^{94} +2.00000 q^{96} -14.0000 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})$$

## 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
$$3$$ 2.00000 1.15470 0.577350 0.816497i $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 2.00000 0.816497
$$7$$ 1.00000 0.377964
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 1.00000 0.301511
$$12$$ 2.00000 0.577350
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 2.00000 0.436436
$$22$$ 1.00000 0.213201
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 2.00000 0.408248
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −4.00000 −0.769800
$$28$$ 1.00000 0.188982
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 2.00000 0.348155
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 8.00000 1.24939 0.624695 0.780869i $$-0.285223\pi$$
0.624695 + 0.780869i $$0.285223\pi$$
$$42$$ 2.00000 0.308607
$$43$$ 12.0000 1.82998 0.914991 0.403473i $$-0.132197\pi$$
0.914991 + 0.403473i $$0.132197\pi$$
$$44$$ 1.00000 0.150756
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ 2.00000 0.288675
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ −4.00000 −0.544331
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ 2.00000 0.262613
$$59$$ −10.0000 −1.30189 −0.650945 0.759125i $$-0.725627\pi$$
−0.650945 + 0.759125i $$0.725627\pi$$
$$60$$ 0 0
$$61$$ −4.00000 −0.512148 −0.256074 0.966657i $$-0.582429\pi$$
−0.256074 + 0.966657i $$0.582429\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ 1.00000 0.125988
$$64$$ 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 $$0.337479\pi$$
$$68$$ 0 0
$$69$$ 8.00000 0.963087
$$70$$ 0 0
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ 1.00000 0.117851
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 6.00000 0.697486
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1.00000 0.113961
$$78$$ 0 0
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 8.00000 0.883452
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 2.00000 0.218218
$$85$$ 0 0
$$86$$ 12.0000 1.29399
$$87$$ 4.00000 0.428845
$$88$$ 1.00000 0.106600
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ −4.00000 −0.414781
$$94$$ 6.00000 0.618853
$$95$$ 0 0
$$96$$ 2.00000 0.204124
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 1.00000 0.100504
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 14.0000 1.37946 0.689730 0.724066i $$-0.257729\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ −4.00000 −0.384900
$$109$$ −6.00000 −0.574696 −0.287348 0.957826i $$-0.592774\pi$$
−0.287348 + 0.957826i $$0.592774\pi$$
$$110$$ 0 0
$$111$$ 12.0000 1.13899
$$112$$ 1.00000 0.0944911
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 2.00000 0.185695
$$117$$ 0 0
$$118$$ −10.0000 −0.920575
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 0.0909091
$$122$$ −4.00000 −0.362143
$$123$$ 16.0000 1.44267
$$124$$ −2.00000 −0.179605
$$125$$ 0 0
$$126$$ 1.00000 0.0890871
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 24.0000 2.11308
$$130$$ 0 0
$$131$$ 4.00000 0.349482 0.174741 0.984614i $$-0.444091\pi$$
0.174741 + 0.984614i $$0.444091\pi$$
$$132$$ 2.00000 0.174078
$$133$$ 0 0
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 8.00000 0.681005
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 0 0
$$141$$ 12.0000 1.01058
$$142$$ −4.00000 −0.335673
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 4.00000 0.331042
$$147$$ 2.00000 0.164957
$$148$$ 6.00000 0.493197
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 1.00000 0.0805823
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −6.00000 −0.478852 −0.239426 0.970915i $$-0.576959\pi$$
−0.239426 + 0.970915i $$0.576959\pi$$
$$158$$ −16.0000 −1.27289
$$159$$ 12.0000 0.951662
$$160$$ 0 0
$$161$$ 4.00000 0.315244
$$162$$ −11.0000 −0.864242
$$163$$ 8.00000 0.626608 0.313304 0.949653i $$-0.398564\pi$$
0.313304 + 0.949653i $$0.398564\pi$$
$$164$$ 8.00000 0.624695
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −16.0000 −1.23812 −0.619059 0.785345i $$-0.712486\pi$$
−0.619059 + 0.785345i $$0.712486\pi$$
$$168$$ 2.00000 0.154303
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 12.0000 0.914991
$$173$$ −24.0000 −1.82469 −0.912343 0.409426i $$-0.865729\pi$$
−0.912343 + 0.409426i $$0.865729\pi$$
$$174$$ 4.00000 0.303239
$$175$$ 0 0
$$176$$ 1.00000 0.0753778
$$177$$ −20.0000 −1.50329
$$178$$ −6.00000 −0.449719
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −6.00000 −0.445976 −0.222988 0.974821i $$-0.571581\pi$$
−0.222988 + 0.974821i $$0.571581\pi$$
$$182$$ 0 0
$$183$$ −8.00000 −0.591377
$$184$$ 4.00000 0.294884
$$185$$ 0 0
$$186$$ −4.00000 −0.293294
$$187$$ 0 0
$$188$$ 6.00000 0.437595
$$189$$ −4.00000 −0.290957
$$190$$ 0 0
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ 2.00000 0.144338
$$193$$ 22.0000 1.58359 0.791797 0.610784i $$-0.209146\pi$$
0.791797 + 0.610784i $$0.209146\pi$$
$$194$$ −14.0000 −1.00514
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −14.0000 −0.997459 −0.498729 0.866758i $$-0.666200\pi$$
−0.498729 + 0.866758i $$0.666200\pi$$
$$198$$ 1.00000 0.0710669
$$199$$ −6.00000 −0.425329 −0.212664 0.977125i $$-0.568214\pi$$
−0.212664 + 0.977125i $$0.568214\pi$$
$$200$$ 0 0
$$201$$ 16.0000 1.12855
$$202$$ 0 0
$$203$$ 2.00000 0.140372
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 14.0000 0.975426
$$207$$ 4.00000 0.278019
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 6.00000 0.412082
$$213$$ −8.00000 −0.548151
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ −4.00000 −0.272166
$$217$$ −2.00000 −0.135769
$$218$$ −6.00000 −0.406371
$$219$$ 8.00000 0.540590
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 12.0000 0.805387
$$223$$ 6.00000 0.401790 0.200895 0.979613i $$-0.435615\pi$$
0.200895 + 0.979613i $$0.435615\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −2.00000 −0.133038
$$227$$ −4.00000 −0.265489 −0.132745 0.991150i $$-0.542379\pi$$
−0.132745 + 0.991150i $$0.542379\pi$$
$$228$$ 0 0
$$229$$ 2.00000 0.132164 0.0660819 0.997814i $$-0.478950\pi$$
0.0660819 + 0.997814i $$0.478950\pi$$
$$230$$ 0 0
$$231$$ 2.00000 0.131590
$$232$$ 2.00000 0.131306
$$233$$ 18.0000 1.17922 0.589610 0.807688i $$-0.299282\pi$$
0.589610 + 0.807688i $$0.299282\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −10.0000 −0.650945
$$237$$ −32.0000 −2.07862
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −16.0000 −1.03065 −0.515325 0.856995i $$-0.672329\pi$$
−0.515325 + 0.856995i $$0.672329\pi$$
$$242$$ 1.00000 0.0642824
$$243$$ −10.0000 −0.641500
$$244$$ −4.00000 −0.256074
$$245$$ 0 0
$$246$$ 16.0000 1.02012
$$247$$ 0 0
$$248$$ −2.00000 −0.127000
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 10.0000 0.631194 0.315597 0.948893i $$-0.397795\pi$$
0.315597 + 0.948893i $$0.397795\pi$$
$$252$$ 1.00000 0.0629941
$$253$$ 4.00000 0.251478
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 14.0000 0.873296 0.436648 0.899632i $$-0.356166\pi$$
0.436648 + 0.899632i $$0.356166\pi$$
$$258$$ 24.0000 1.49417
$$259$$ 6.00000 0.372822
$$260$$ 0 0
$$261$$ 2.00000 0.123797
$$262$$ 4.00000 0.247121
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 2.00000 0.123091
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −12.0000 −0.734388
$$268$$ 8.00000 0.488678
$$269$$ 10.0000 0.609711 0.304855 0.952399i $$-0.401392\pi$$
0.304855 + 0.952399i $$0.401392\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ 0 0
$$276$$ 8.00000 0.481543
$$277$$ 2.00000 0.120168 0.0600842 0.998193i $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ 8.00000 0.479808
$$279$$ −2.00000 −0.119737
$$280$$ 0 0
$$281$$ −2.00000 −0.119310 −0.0596550 0.998219i $$-0.519000\pi$$
−0.0596550 + 0.998219i $$0.519000\pi$$
$$282$$ 12.0000 0.714590
$$283$$ −28.0000 −1.66443 −0.832214 0.554455i $$-0.812927\pi$$
−0.832214 + 0.554455i $$0.812927\pi$$
$$284$$ −4.00000 −0.237356
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 8.00000 0.472225
$$288$$ 1.00000 0.0589256
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ −28.0000 −1.64139
$$292$$ 4.00000 0.234082
$$293$$ 4.00000 0.233682 0.116841 0.993151i $$-0.462723\pi$$
0.116841 + 0.993151i $$0.462723\pi$$
$$294$$ 2.00000 0.116642
$$295$$ 0 0
$$296$$ 6.00000 0.348743
$$297$$ −4.00000 −0.232104
$$298$$ 6.00000 0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 12.0000 0.691669
$$302$$ −8.00000 −0.460348
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 1.00000 0.0569803
$$309$$ 28.0000 1.59286
$$310$$ 0 0
$$311$$ −6.00000 −0.340229 −0.170114 0.985424i $$-0.554414\pi$$
−0.170114 + 0.985424i $$0.554414\pi$$
$$312$$ 0 0
$$313$$ −2.00000 −0.113047 −0.0565233 0.998401i $$-0.518002\pi$$
−0.0565233 + 0.998401i $$0.518002\pi$$
$$314$$ −6.00000 −0.338600
$$315$$ 0 0
$$316$$ −16.0000 −0.900070
$$317$$ 2.00000 0.112331 0.0561656 0.998421i $$-0.482113\pi$$
0.0561656 + 0.998421i $$0.482113\pi$$
$$318$$ 12.0000 0.672927
$$319$$ 2.00000 0.111979
$$320$$ 0 0
$$321$$ −24.0000 −1.33955
$$322$$ 4.00000 0.222911
$$323$$ 0 0
$$324$$ −11.0000 −0.611111
$$325$$ 0 0
$$326$$ 8.00000 0.443079
$$327$$ −12.0000 −0.663602
$$328$$ 8.00000 0.441726
$$329$$ 6.00000 0.330791
$$330$$ 0 0
$$331$$ 28.0000 1.53902 0.769510 0.638635i $$-0.220501\pi$$
0.769510 + 0.638635i $$0.220501\pi$$
$$332$$ 0 0
$$333$$ 6.00000 0.328798
$$334$$ −16.0000 −0.875481
$$335$$ 0 0
$$336$$ 2.00000 0.109109
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ −13.0000 −0.707107
$$339$$ −4.00000 −0.217250
$$340$$ 0 0
$$341$$ −2.00000 −0.108306
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 12.0000 0.646997
$$345$$ 0 0
$$346$$ −24.0000 −1.29025
$$347$$ −28.0000 −1.50312 −0.751559 0.659665i $$-0.770698\pi$$
−0.751559 + 0.659665i $$0.770698\pi$$
$$348$$ 4.00000 0.214423
$$349$$ −20.0000 −1.07058 −0.535288 0.844670i $$-0.679797\pi$$
−0.535288 + 0.844670i $$0.679797\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.00000 0.0533002
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ −20.0000 −1.06299
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ −8.00000 −0.422224 −0.211112 0.977462i $$-0.567708\pi$$
−0.211112 + 0.977462i $$0.567708\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ −6.00000 −0.315353
$$363$$ 2.00000 0.104973
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −8.00000 −0.418167
$$367$$ 22.0000 1.14839 0.574195 0.818718i $$-0.305315\pi$$
0.574195 + 0.818718i $$0.305315\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 8.00000 0.416463
$$370$$ 0 0
$$371$$ 6.00000 0.311504
$$372$$ −4.00000 −0.207390
$$373$$ −14.0000 −0.724893 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 6.00000 0.309426
$$377$$ 0 0
$$378$$ −4.00000 −0.205738
$$379$$ −16.0000 −0.821865 −0.410932 0.911666i $$-0.634797\pi$$
−0.410932 + 0.911666i $$0.634797\pi$$
$$380$$ 0 0
$$381$$ −16.0000 −0.819705
$$382$$ −8.00000 −0.409316
$$383$$ 2.00000 0.102195 0.0510976 0.998694i $$-0.483728\pi$$
0.0510976 + 0.998694i $$0.483728\pi$$
$$384$$ 2.00000 0.102062
$$385$$ 0 0
$$386$$ 22.0000 1.11977
$$387$$ 12.0000 0.609994
$$388$$ −14.0000 −0.710742
$$389$$ 22.0000 1.11544 0.557722 0.830028i $$-0.311675\pi$$
0.557722 + 0.830028i $$0.311675\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.00000 0.0505076
$$393$$ 8.00000 0.403547
$$394$$ −14.0000 −0.705310
$$395$$ 0 0
$$396$$ 1.00000 0.0502519
$$397$$ 34.0000 1.70641 0.853206 0.521575i $$-0.174655\pi$$
0.853206 + 0.521575i $$0.174655\pi$$
$$398$$ −6.00000 −0.300753
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 16.0000 0.798007
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 2.00000 0.0992583
$$407$$ 6.00000 0.297409
$$408$$ 0 0
$$409$$ 4.00000 0.197787 0.0988936 0.995098i $$-0.468470\pi$$
0.0988936 + 0.995098i $$0.468470\pi$$
$$410$$ 0 0
$$411$$ −12.0000 −0.591916
$$412$$ 14.0000 0.689730
$$413$$ −10.0000 −0.492068
$$414$$ 4.00000 0.196589
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 16.0000 0.783523
$$418$$ 0 0
$$419$$ −26.0000 −1.27018 −0.635092 0.772437i $$-0.719038\pi$$
−0.635092 + 0.772437i $$0.719038\pi$$
$$420$$ 0 0
$$421$$ 18.0000 0.877266 0.438633 0.898666i $$-0.355463\pi$$
0.438633 + 0.898666i $$0.355463\pi$$
$$422$$ −12.0000 −0.584151
$$423$$ 6.00000 0.291730
$$424$$ 6.00000 0.291386
$$425$$ 0 0
$$426$$ −8.00000 −0.387601
$$427$$ −4.00000 −0.193574
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 8.00000 0.385346 0.192673 0.981263i $$-0.438284\pi$$
0.192673 + 0.981263i $$0.438284\pi$$
$$432$$ −4.00000 −0.192450
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ −2.00000 −0.0960031
$$435$$ 0 0
$$436$$ −6.00000 −0.287348
$$437$$ 0 0
$$438$$ 8.00000 0.382255
$$439$$ 4.00000 0.190910 0.0954548 0.995434i $$-0.469569\pi$$
0.0954548 + 0.995434i $$0.469569\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ 0 0
$$443$$ 20.0000 0.950229 0.475114 0.879924i $$-0.342407\pi$$
0.475114 + 0.879924i $$0.342407\pi$$
$$444$$ 12.0000 0.569495
$$445$$ 0 0
$$446$$ 6.00000 0.284108
$$447$$ 12.0000 0.567581
$$448$$ 1.00000 0.0472456
$$449$$ −10.0000 −0.471929 −0.235965 0.971762i $$-0.575825\pi$$
−0.235965 + 0.971762i $$0.575825\pi$$
$$450$$ 0 0
$$451$$ 8.00000 0.376705
$$452$$ −2.00000 −0.0940721
$$453$$ −16.0000 −0.751746
$$454$$ −4.00000 −0.187729
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −26.0000 −1.21623 −0.608114 0.793849i $$-0.708074\pi$$
−0.608114 + 0.793849i $$0.708074\pi$$
$$458$$ 2.00000 0.0934539
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −20.0000 −0.931493 −0.465746 0.884918i $$-0.654214\pi$$
−0.465746 + 0.884918i $$0.654214\pi$$
$$462$$ 2.00000 0.0930484
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ 2.00000 0.0928477
$$465$$ 0 0
$$466$$ 18.0000 0.833834
$$467$$ 30.0000 1.38823 0.694117 0.719862i $$-0.255795\pi$$
0.694117 + 0.719862i $$0.255795\pi$$
$$468$$ 0 0
$$469$$ 8.00000 0.369406
$$470$$ 0 0
$$471$$ −12.0000 −0.552931
$$472$$ −10.0000 −0.460287
$$473$$ 12.0000 0.551761
$$474$$ −32.0000 −1.46981
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 0 0
$$479$$ 20.0000 0.913823 0.456912 0.889512i $$-0.348956\pi$$
0.456912 + 0.889512i $$0.348956\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −16.0000 −0.728780
$$483$$ 8.00000 0.364013
$$484$$ 1.00000 0.0454545
$$485$$ 0 0
$$486$$ −10.0000 −0.453609
$$487$$ −20.0000 −0.906287 −0.453143 0.891438i $$-0.649697\pi$$
−0.453143 + 0.891438i $$0.649697\pi$$
$$488$$ −4.00000 −0.181071
$$489$$ 16.0000 0.723545
$$490$$ 0 0
$$491$$ 36.0000 1.62466 0.812329 0.583200i $$-0.198200\pi$$
0.812329 + 0.583200i $$0.198200\pi$$
$$492$$ 16.0000 0.721336
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ −4.00000 −0.179425
$$498$$ 0 0
$$499$$ −40.0000 −1.79065 −0.895323 0.445418i $$-0.853055\pi$$
−0.895323 + 0.445418i $$0.853055\pi$$
$$500$$ 0 0
$$501$$ −32.0000 −1.42965
$$502$$ 10.0000 0.446322
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 1.00000 0.0445435
$$505$$ 0 0
$$506$$ 4.00000 0.177822
$$507$$ −26.0000 −1.15470
$$508$$ −8.00000 −0.354943
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ 4.00000 0.176950
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 14.0000 0.617514
$$515$$ 0 0
$$516$$ 24.0000 1.05654
$$517$$ 6.00000 0.263880
$$518$$ 6.00000 0.263625
$$519$$ −48.0000 −2.10697
$$520$$ 0 0
$$521$$ −34.0000 −1.48957 −0.744784 0.667306i $$-0.767447\pi$$
−0.744784 + 0.667306i $$0.767447\pi$$
$$522$$ 2.00000 0.0875376
$$523$$ −28.0000 −1.22435 −0.612177 0.790721i $$-0.709706\pi$$
−0.612177 + 0.790721i $$0.709706\pi$$
$$524$$ 4.00000 0.174741
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ 0 0
$$528$$ 2.00000 0.0870388
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ −10.0000 −0.433963
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −12.0000 −0.519291
$$535$$ 0 0
$$536$$ 8.00000 0.345547
$$537$$ 24.0000 1.03568
$$538$$ 10.0000 0.431131
$$539$$ 1.00000 0.0430730
$$540$$ 0 0
$$541$$ −10.0000 −0.429934 −0.214967 0.976621i $$-0.568964\pi$$
−0.214967 + 0.976621i $$0.568964\pi$$
$$542$$ 20.0000 0.859074
$$543$$ −12.0000 −0.514969
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 44.0000 1.88130 0.940652 0.339372i $$-0.110215\pi$$
0.940652 + 0.339372i $$0.110215\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ −4.00000 −0.170716
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 8.00000 0.340503
$$553$$ −16.0000 −0.680389
$$554$$ 2.00000 0.0849719
$$555$$ 0 0
$$556$$ 8.00000 0.339276
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ −2.00000 −0.0846668
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −2.00000 −0.0843649
$$563$$ −32.0000 −1.34864 −0.674320 0.738440i $$-0.735563\pi$$
−0.674320 + 0.738440i $$0.735563\pi$$
$$564$$ 12.0000 0.505291
$$565$$ 0 0
$$566$$ −28.0000 −1.17693
$$567$$ −11.0000 −0.461957
$$568$$ −4.00000 −0.167836
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 0 0
$$573$$ −16.0000 −0.668410
$$574$$ 8.00000 0.333914
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 26.0000 1.08239 0.541197 0.840896i $$-0.317971\pi$$
0.541197 + 0.840896i $$0.317971\pi$$
$$578$$ −17.0000 −0.707107
$$579$$ 44.0000 1.82858
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −28.0000 −1.16064
$$583$$ 6.00000 0.248495
$$584$$ 4.00000 0.165521
$$585$$ 0 0
$$586$$ 4.00000 0.165238
$$587$$ −2.00000 −0.0825488 −0.0412744 0.999148i $$-0.513142\pi$$
−0.0412744 + 0.999148i $$0.513142\pi$$
$$588$$ 2.00000 0.0824786
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −28.0000 −1.15177
$$592$$ 6.00000 0.246598
$$593$$ 12.0000 0.492781 0.246390 0.969171i $$-0.420755\pi$$
0.246390 + 0.969171i $$0.420755\pi$$
$$594$$ −4.00000 −0.164122
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ −12.0000 −0.491127
$$598$$ 0 0
$$599$$ 20.0000 0.817178 0.408589 0.912719i $$-0.366021\pi$$
0.408589 + 0.912719i $$0.366021\pi$$
$$600$$ 0 0
$$601$$ −8.00000 −0.326327 −0.163163 0.986599i $$-0.552170\pi$$
−0.163163 + 0.986599i $$0.552170\pi$$
$$602$$ 12.0000 0.489083
$$603$$ 8.00000 0.325785
$$604$$ −8.00000 −0.325515
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −24.0000 −0.974130 −0.487065 0.873366i $$-0.661933\pi$$
−0.487065 + 0.873366i $$0.661933\pi$$
$$608$$ 0 0
$$609$$ 4.00000 0.162088
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 6.00000 0.242338 0.121169 0.992632i $$-0.461336\pi$$
0.121169 + 0.992632i $$0.461336\pi$$
$$614$$ −28.0000 −1.12999
$$615$$ 0 0
$$616$$ 1.00000 0.0402911
$$617$$ 42.0000 1.69086 0.845428 0.534089i $$-0.179345\pi$$
0.845428 + 0.534089i $$0.179345\pi$$
$$618$$ 28.0000 1.12633
$$619$$ −22.0000 −0.884255 −0.442127 0.896952i $$-0.645776\pi$$
−0.442127 + 0.896952i $$0.645776\pi$$
$$620$$ 0 0
$$621$$ −16.0000 −0.642058
$$622$$ −6.00000 −0.240578
$$623$$ −6.00000 −0.240385
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −2.00000 −0.0799361
$$627$$ 0 0
$$628$$ −6.00000 −0.239426
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ −16.0000 −0.636446
$$633$$ −24.0000 −0.953914
$$634$$ 2.00000 0.0794301
$$635$$ 0 0
$$636$$ 12.0000 0.475831
$$637$$ 0 0
$$638$$ 2.00000 0.0791808
$$639$$ −4.00000 −0.158238
$$640$$ 0 0
$$641$$ 46.0000 1.81689 0.908445 0.418004i $$-0.137270\pi$$
0.908445 + 0.418004i $$0.137270\pi$$
$$642$$ −24.0000 −0.947204
$$643$$ −34.0000 −1.34083 −0.670415 0.741987i $$-0.733884\pi$$
−0.670415 + 0.741987i $$0.733884\pi$$
$$644$$ 4.00000 0.157622
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 42.0000 1.65119 0.825595 0.564263i $$-0.190840\pi$$
0.825595 + 0.564263i $$0.190840\pi$$
$$648$$ −11.0000 −0.432121
$$649$$ −10.0000 −0.392534
$$650$$ 0 0
$$651$$ −4.00000 −0.156772
$$652$$ 8.00000 0.313304
$$653$$ −22.0000 −0.860927 −0.430463 0.902608i $$-0.641650\pi$$
−0.430463 + 0.902608i $$0.641650\pi$$
$$654$$ −12.0000 −0.469237
$$655$$ 0 0
$$656$$ 8.00000 0.312348
$$657$$ 4.00000 0.156055
$$658$$ 6.00000 0.233904
$$659$$ −20.0000 −0.779089 −0.389545 0.921008i $$-0.627368\pi$$
−0.389545 + 0.921008i $$0.627368\pi$$
$$660$$ 0 0
$$661$$ 46.0000 1.78919 0.894596 0.446875i $$-0.147463\pi$$
0.894596 + 0.446875i $$0.147463\pi$$
$$662$$ 28.0000 1.08825
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ 8.00000 0.309761
$$668$$ −16.0000 −0.619059
$$669$$ 12.0000 0.463947
$$670$$ 0 0
$$671$$ −4.00000 −0.154418
$$672$$ 2.00000 0.0771517
$$673$$ −14.0000 −0.539660 −0.269830 0.962908i $$-0.586968\pi$$
−0.269830 + 0.962908i $$0.586968\pi$$
$$674$$ −14.0000 −0.539260
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ −4.00000 −0.153619
$$679$$ −14.0000 −0.537271
$$680$$ 0 0
$$681$$ −8.00000 −0.306561
$$682$$ −2.00000 −0.0765840
$$683$$ −20.0000 −0.765279 −0.382639 0.923898i $$-0.624985\pi$$
−0.382639 + 0.923898i $$0.624985\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1.00000 0.0381802
$$687$$ 4.00000 0.152610
$$688$$ 12.0000 0.457496
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 6.00000 0.228251 0.114125 0.993466i $$-0.463593\pi$$
0.114125 + 0.993466i $$0.463593\pi$$
$$692$$ −24.0000 −0.912343
$$693$$ 1.00000 0.0379869
$$694$$ −28.0000 −1.06287
$$695$$ 0 0
$$696$$ 4.00000 0.151620
$$697$$ 0 0
$$698$$ −20.0000 −0.757011
$$699$$ 36.0000 1.36165
$$700$$ 0 0
$$701$$ −14.0000 −0.528773 −0.264386 0.964417i $$-0.585169\pi$$
−0.264386 + 0.964417i $$0.585169\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 1.00000 0.0376889
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ 0 0
$$708$$ −20.0000 −0.751646
$$709$$ 30.0000 1.12667 0.563337 0.826227i $$-0.309517\pi$$
0.563337 + 0.826227i $$0.309517\pi$$
$$710$$ 0 0
$$711$$ −16.0000 −0.600047
$$712$$ −6.00000 −0.224860
$$713$$ −8.00000 −0.299602
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 0 0
$$718$$ −8.00000 −0.298557
$$719$$ −34.0000 −1.26799 −0.633993 0.773339i $$-0.718585\pi$$
−0.633993 + 0.773339i $$0.718585\pi$$
$$720$$ 0 0
$$721$$ 14.0000 0.521387
$$722$$ −19.0000 −0.707107
$$723$$ −32.0000 −1.19009
$$724$$ −6.00000 −0.222988
$$725$$ 0 0
$$726$$ 2.00000 0.0742270
$$727$$ −14.0000 −0.519231 −0.259616 0.965712i $$-0.583596\pi$$
−0.259616 + 0.965712i $$0.583596\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −8.00000 −0.295689
$$733$$ −4.00000 −0.147743 −0.0738717 0.997268i $$-0.523536\pi$$
−0.0738717 + 0.997268i $$0.523536\pi$$
$$734$$ 22.0000 0.812035
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 8.00000 0.294684
$$738$$ 8.00000 0.294484
$$739$$ 12.0000 0.441427 0.220714 0.975339i $$-0.429161\pi$$
0.220714 + 0.975339i $$0.429161\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 6.00000 0.220267
$$743$$ 8.00000 0.293492 0.146746 0.989174i $$-0.453120\pi$$
0.146746 + 0.989174i $$0.453120\pi$$
$$744$$ −4.00000 −0.146647
$$745$$ 0 0
$$746$$ −14.0000 −0.512576
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −12.0000 −0.438470
$$750$$ 0 0
$$751$$ 52.0000 1.89751 0.948753 0.316017i $$-0.102346\pi$$
0.948753 + 0.316017i $$0.102346\pi$$
$$752$$ 6.00000 0.218797
$$753$$ 20.0000 0.728841
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −4.00000 −0.145479
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ −16.0000 −0.581146
$$759$$ 8.00000 0.290382
$$760$$ 0 0
$$761$$ 12.0000 0.435000 0.217500 0.976060i $$-0.430210\pi$$
0.217500 + 0.976060i $$0.430210\pi$$
$$762$$ −16.0000 −0.579619
$$763$$ −6.00000 −0.217215
$$764$$ −8.00000 −0.289430
$$765$$ 0 0
$$766$$ 2.00000 0.0722629
$$767$$ 0 0
$$768$$ 2.00000 0.0721688
$$769$$ 12.0000 0.432731 0.216366 0.976312i $$-0.430580\pi$$
0.216366 + 0.976312i $$0.430580\pi$$
$$770$$ 0 0
$$771$$ 28.0000 1.00840
$$772$$ 22.0000 0.791797
$$773$$ −18.0000 −0.647415 −0.323708 0.946157i $$-0.604929\pi$$
−0.323708 + 0.946157i $$0.604929\pi$$
$$774$$ 12.0000 0.431331
$$775$$ 0 0
$$776$$ −14.0000 −0.502571
$$777$$ 12.0000 0.430498
$$778$$ 22.0000 0.788738
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −4.00000 −0.143131
$$782$$ 0 0
$$783$$ −8.00000 −0.285897
$$784$$ 1.00000 0.0357143
$$785$$ 0 0
$$786$$ 8.00000 0.285351
$$787$$ −48.0000 −1.71102 −0.855508 0.517790i $$-0.826755\pi$$
−0.855508 + 0.517790i $$0.826755\pi$$
$$788$$ −14.0000 −0.498729
$$789$$ 48.0000 1.70885
$$790$$ 0 0
$$791$$ −2.00000 −0.0711118
$$792$$ 1.00000 0.0355335
$$793$$ 0 0
$$794$$ 34.0000 1.20661
$$795$$ 0 0
$$796$$ −6.00000 −0.212664
$$797$$ −6.00000 −0.212531 −0.106265 0.994338i $$-0.533889\pi$$
−0.106265 + 0.994338i $$0.533889\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ −6.00000 −0.211867
$$803$$ 4.00000 0.141157
$$804$$ 16.0000 0.564276
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 20.0000 0.704033
$$808$$ 0 0
$$809$$ 18.0000 0.632846 0.316423 0.948618i $$-0.397518\pi$$
0.316423 + 0.948618i $$0.397518\pi$$
$$810$$ 0 0
$$811$$ −44.0000 −1.54505 −0.772524 0.634985i $$-0.781006\pi$$
−0.772524 + 0.634985i $$0.781006\pi$$
$$812$$ 2.00000 0.0701862
$$813$$ 40.0000 1.40286
$$814$$ 6.00000 0.210300
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 4.00000 0.139857
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −34.0000 −1.18661 −0.593304 0.804978i $$-0.702177\pi$$
−0.593304 + 0.804978i $$0.702177\pi$$
$$822$$ −12.0000 −0.418548
$$823$$ −32.0000 −1.11545 −0.557725 0.830026i $$-0.688326\pi$$
−0.557725 + 0.830026i $$0.688326\pi$$
$$824$$ 14.0000 0.487713
$$825$$ 0 0
$$826$$ −10.0000 −0.347945
$$827$$ 36.0000 1.25184 0.625921 0.779886i $$-0.284723\pi$$
0.625921 + 0.779886i $$0.284723\pi$$
$$828$$ 4.00000 0.139010
$$829$$ −10.0000 −0.347314 −0.173657 0.984806i $$-0.555558\pi$$
−0.173657 + 0.984806i $$0.555558\pi$$
$$830$$ 0 0
$$831$$ 4.00000 0.138758
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 16.0000 0.554035
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 8.00000 0.276520
$$838$$ −26.0000 −0.898155
$$839$$ −10.0000 −0.345238 −0.172619 0.984989i $$-0.555223\pi$$
−0.172619 + 0.984989i $$0.555223\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 18.0000 0.620321
$$843$$ −4.00000 −0.137767
$$844$$ −12.0000 −0.413057
$$845$$ 0 0
$$846$$ 6.00000 0.206284
$$847$$ 1.00000 0.0343604
$$848$$ 6.00000 0.206041
$$849$$ −56.0000 −1.92192
$$850$$ 0 0
$$851$$ 24.0000 0.822709
$$852$$ −8.00000 −0.274075
$$853$$ 8.00000 0.273915 0.136957 0.990577i $$-0.456268\pi$$
0.136957 + 0.990577i $$0.456268\pi$$
$$854$$ −4.00000 −0.136877
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ −12.0000 −0.409912 −0.204956 0.978771i $$-0.565705\pi$$
−0.204956 + 0.978771i $$0.565705\pi$$
$$858$$ 0 0
$$859$$ 2.00000 0.0682391 0.0341196 0.999418i $$-0.489137\pi$$
0.0341196 + 0.999418i $$0.489137\pi$$
$$860$$ 0 0
$$861$$ 16.0000 0.545279
$$862$$ 8.00000 0.272481
$$863$$ 32.0000 1.08929 0.544646 0.838666i $$-0.316664\pi$$
0.544646 + 0.838666i $$0.316664\pi$$
$$864$$ −4.00000 −0.136083
$$865$$ 0 0
$$866$$ −14.0000 −0.475739
$$867$$ −34.0000 −1.15470
$$868$$ −2.00000 −0.0678844
$$869$$ −16.0000 −0.542763
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −6.00000 −0.203186
$$873$$ −14.0000 −0.473828
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 8.00000 0.270295
$$877$$ −10.0000 −0.337676 −0.168838 0.985644i $$-0.554001\pi$$
−0.168838 + 0.985644i $$0.554001\pi$$
$$878$$ 4.00000 0.134993
$$879$$ 8.00000 0.269833
$$880$$ 0 0
$$881$$ −26.0000 −0.875962 −0.437981 0.898984i $$-0.644306\pi$$
−0.437981 + 0.898984i $$0.644306\pi$$
$$882$$ 1.00000 0.0336718
$$883$$ 44.0000 1.48072 0.740359 0.672212i $$-0.234656\pi$$
0.740359 + 0.672212i $$0.234656\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 20.0000 0.671913
$$887$$ 52.0000 1.74599 0.872995 0.487730i $$-0.162175\pi$$
0.872995 + 0.487730i $$0.162175\pi$$
$$888$$ 12.0000 0.402694
$$889$$ −8.00000 −0.268311
$$890$$ 0 0
$$891$$ −11.0000 −0.368514
$$892$$ 6.00000 0.200895
$$893$$ 0 0
$$894$$ 12.0000 0.401340
$$895$$ 0 0
$$896$$ 1.00000 0.0334077
$$897$$ 0 0
$$898$$ −10.0000 −0.333704
$$899$$ −4.00000 −0.133407
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 8.00000 0.266371
$$903$$ 24.0000 0.798670
$$904$$ −2.00000 −0.0665190
$$905$$ 0 0
$$906$$ −16.0000 −0.531564
$$907$$ −48.0000 −1.59381 −0.796907 0.604102i $$-0.793532\pi$$
−0.796907 + 0.604102i $$0.793532\pi$$
$$908$$ −4.00000 −0.132745
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 28.0000 0.927681 0.463841 0.885919i $$-0.346471\pi$$
0.463841 + 0.885919i $$0.346471\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ −26.0000 −0.860004
$$915$$ 0 0
$$916$$ 2.00000 0.0660819
$$917$$ 4.00000 0.132092
$$918$$ 0 0
$$919$$ −8.00000 −0.263896 −0.131948 0.991257i $$-0.542123\pi$$
−0.131948 + 0.991257i $$0.542123\pi$$
$$920$$ 0 0
$$921$$ −56.0000 −1.84526
$$922$$ −20.0000 −0.658665
$$923$$ 0 0
$$924$$ 2.00000 0.0657952
$$925$$ 0 0
$$926$$ −4.00000 −0.131448
$$927$$ 14.0000 0.459820
$$928$$ 2.00000 0.0656532
$$929$$ 30.0000 0.984268 0.492134 0.870519i $$-0.336217\pi$$
0.492134 + 0.870519i $$0.336217\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 18.0000 0.589610
$$933$$ −12.0000 −0.392862
$$934$$ 30.0000 0.981630
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −36.0000 −1.17607 −0.588034 0.808836i $$-0.700098\pi$$
−0.588034 + 0.808836i $$0.700098\pi$$
$$938$$ 8.00000 0.261209
$$939$$ −4.00000 −0.130535
$$940$$ 0 0
$$941$$ −60.0000 −1.95594 −0.977972 0.208736i $$-0.933065\pi$$
−0.977972 + 0.208736i $$0.933065\pi$$
$$942$$ −12.0000 −0.390981
$$943$$ 32.0000 1.04206
$$944$$ −10.0000 −0.325472
$$945$$ 0 0
$$946$$ 12.0000 0.390154
$$947$$ 12.0000 0.389948 0.194974 0.980808i $$-0.437538\pi$$
0.194974 + 0.980808i $$0.437538\pi$$
$$948$$ −32.0000 −1.03931
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 4.00000 0.129709
$$952$$ 0 0
$$953$$ 6.00000 0.194359 0.0971795 0.995267i $$-0.469018\pi$$
0.0971795 + 0.995267i $$0.469018\pi$$
$$954$$ 6.00000 0.194257
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 4.00000 0.129302
$$958$$ 20.0000 0.646171
$$959$$ −6.00000 −0.193750
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 0 0
$$963$$ −12.0000 −0.386695
$$964$$ −16.0000 −0.515325
$$965$$ 0 0
$$966$$ 8.00000 0.257396
$$967$$ 48.0000 1.54358 0.771788 0.635880i $$-0.219363\pi$$
0.771788 + 0.635880i $$0.219363\pi$$
$$968$$ 1.00000 0.0321412
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 26.0000 0.834380 0.417190 0.908819i $$-0.363015\pi$$
0.417190 + 0.908819i $$0.363015\pi$$
$$972$$ −10.0000 −0.320750
$$973$$ 8.00000 0.256468
$$974$$ −20.0000 −0.640841
$$975$$ 0 0
$$976$$ −4.00000 −0.128037
$$977$$ −42.0000 −1.34370 −0.671850 0.740688i $$-0.734500\pi$$
−0.671850 + 0.740688i $$0.734500\pi$$
$$978$$ 16.0000 0.511624
$$979$$ −6.00000 −0.191761
$$980$$ 0 0
$$981$$ −6.00000 −0.191565
$$982$$ 36.0000 1.14881
$$983$$ 22.0000 0.701691 0.350846 0.936433i $$-0.385894\pi$$
0.350846 + 0.936433i $$0.385894\pi$$
$$984$$ 16.0000 0.510061
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 12.0000 0.381964
$$988$$ 0 0
$$989$$ 48.0000 1.52631
$$990$$ 0 0
$$991$$ −4.00000 −0.127064 −0.0635321 0.997980i $$-0.520237\pi$$
−0.0635321 + 0.997980i $$0.520237\pi$$
$$992$$ −2.00000 −0.0635001
$$993$$ 56.0000 1.77711
$$994$$ −4.00000 −0.126872
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 48.0000 1.52018 0.760088 0.649821i $$-0.225156\pi$$
0.760088 + 0.649821i $$0.225156\pi$$
$$998$$ −40.0000 −1.26618
$$999$$ −24.0000 −0.759326
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 3850.2.a.bb.1.1 1
5.2 odd 4 3850.2.c.p.1849.2 2
5.3 odd 4 3850.2.c.p.1849.1 2
5.4 even 2 770.2.a.b.1.1 1
15.14 odd 2 6930.2.a.s.1.1 1
20.19 odd 2 6160.2.a.p.1.1 1
35.34 odd 2 5390.2.a.q.1.1 1
55.54 odd 2 8470.2.a.v.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.a.b.1.1 1 5.4 even 2
3850.2.a.bb.1.1 1 1.1 even 1 trivial
3850.2.c.p.1849.1 2 5.3 odd 4
3850.2.c.p.1849.2 2 5.2 odd 4
5390.2.a.q.1.1 1 35.34 odd 2
6160.2.a.p.1.1 1 20.19 odd 2
6930.2.a.s.1.1 1 15.14 odd 2
8470.2.a.v.1.1 1 55.54 odd 2