# Properties

 Label 7350.2.a.bh.1.1 Level $7350$ Weight $2$ Character 7350.1 Self dual yes Analytic conductor $58.690$ Analytic rank $1$ 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: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1470) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} +1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -2.00000 q^{22} -8.00000 q^{23} -1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} -2.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} -4.00000 q^{34} +1.00000 q^{36} -8.00000 q^{37} -2.00000 q^{39} -2.00000 q^{41} +2.00000 q^{43} +2.00000 q^{44} +8.00000 q^{46} -10.0000 q^{47} +1.00000 q^{48} +4.00000 q^{51} -2.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} +4.00000 q^{59} -10.0000 q^{61} +2.00000 q^{62} +1.00000 q^{64} -2.00000 q^{66} -2.00000 q^{67} +4.00000 q^{68} -8.00000 q^{69} -12.0000 q^{71} -1.00000 q^{72} -10.0000 q^{73} +8.00000 q^{74} +2.00000 q^{78} +16.0000 q^{79} +1.00000 q^{81} +2.00000 q^{82} -16.0000 q^{83} -2.00000 q^{86} -2.00000 q^{88} +14.0000 q^{89} -8.00000 q^{92} -2.00000 q^{93} +10.0000 q^{94} -1.00000 q^{96} -6.00000 q^{97} +2.00000 q^{99} +O(q^{100})$$

## 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
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ −8.00000 −1.66812 −0.834058 0.551677i $$-0.813988\pi$$
−0.834058 + 0.551677i $$0.813988\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ 2.00000 0.392232
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −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
$$34$$ −4.00000 −0.685994
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ 0 0
$$39$$ −2.00000 −0.320256
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ −10.0000 −1.45865 −0.729325 0.684167i $$-0.760166\pi$$
−0.729325 + 0.684167i $$0.760166\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ −2.00000 −0.277350
$$53$$ 2.00000 0.274721 0.137361 0.990521i $$-0.456138\pi$$
0.137361 + 0.990521i $$0.456138\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −10.0000 −1.28037 −0.640184 0.768221i $$-0.721142\pi$$
−0.640184 + 0.768221i $$0.721142\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −2.00000 −0.246183
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 4.00000 0.485071
$$69$$ −8.00000 −0.963087
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 8.00000 0.929981
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 2.00000 0.226455
$$79$$ 16.0000 1.80014 0.900070 0.435745i $$-0.143515\pi$$
0.900070 + 0.435745i $$0.143515\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 2.00000 0.220863
$$83$$ −16.0000 −1.75623 −0.878114 0.478451i $$-0.841198\pi$$
−0.878114 + 0.478451i $$0.841198\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 −0.215666
$$87$$ 0 0
$$88$$ −2.00000 −0.213201
$$89$$ 14.0000 1.48400 0.741999 0.670402i $$-0.233878\pi$$
0.741999 + 0.670402i $$0.233878\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −8.00000 −0.834058
$$93$$ −2.00000 −0.207390
$$94$$ 10.0000 1.03142
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ 0 0
$$101$$ −14.0000 −1.39305 −0.696526 0.717532i $$-0.745272\pi$$
−0.696526 + 0.717532i $$0.745272\pi$$
$$102$$ −4.00000 −0.396059
$$103$$ 20.0000 1.97066 0.985329 0.170664i $$-0.0545913\pi$$
0.985329 + 0.170664i $$0.0545913\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ −2.00000 −0.194257
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ −8.00000 −0.759326
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ −4.00000 −0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 10.0000 0.905357
$$123$$ −2.00000 −0.180334
$$124$$ −2.00000 −0.179605
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 12.0000 1.06483 0.532414 0.846484i $$-0.321285\pi$$
0.532414 + 0.846484i $$0.321285\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 2.00000 0.176090
$$130$$ 0 0
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 2.00000 0.174078
$$133$$ 0 0
$$134$$ 2.00000 0.172774
$$135$$ 0 0
$$136$$ −4.00000 −0.342997
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 8.00000 0.681005
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ −10.0000 −0.842152
$$142$$ 12.0000 1.00702
$$143$$ −4.00000 −0.334497
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 10.0000 0.827606
$$147$$ 0 0
$$148$$ −8.00000 −0.657596
$$149$$ −16.0000 −1.31077 −0.655386 0.755295i $$-0.727494\pi$$
−0.655386 + 0.755295i $$0.727494\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −2.00000 −0.160128
$$157$$ 10.0000 0.798087 0.399043 0.916932i $$-0.369342\pi$$
0.399043 + 0.916932i $$0.369342\pi$$
$$158$$ −16.0000 −1.27289
$$159$$ 2.00000 0.158610
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 10.0000 0.783260 0.391630 0.920123i $$-0.371911\pi$$
0.391630 + 0.920123i $$0.371911\pi$$
$$164$$ −2.00000 −0.156174
$$165$$ 0 0
$$166$$ 16.0000 1.24184
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.00000 0.152499
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 2.00000 0.150756
$$177$$ 4.00000 0.300658
$$178$$ −14.0000 −1.04934
$$179$$ −2.00000 −0.149487 −0.0747435 0.997203i $$-0.523814\pi$$
−0.0747435 + 0.997203i $$0.523814\pi$$
$$180$$ 0 0
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 0 0
$$183$$ −10.0000 −0.739221
$$184$$ 8.00000 0.589768
$$185$$ 0 0
$$186$$ 2.00000 0.146647
$$187$$ 8.00000 0.585018
$$188$$ −10.0000 −0.729325
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 18.0000 1.29567 0.647834 0.761781i $$-0.275675\pi$$
0.647834 + 0.761781i $$0.275675\pi$$
$$194$$ 6.00000 0.430775
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ −2.00000 −0.142134
$$199$$ 10.0000 0.708881 0.354441 0.935079i $$-0.384671\pi$$
0.354441 + 0.935079i $$0.384671\pi$$
$$200$$ 0 0
$$201$$ −2.00000 −0.141069
$$202$$ 14.0000 0.985037
$$203$$ 0 0
$$204$$ 4.00000 0.280056
$$205$$ 0 0
$$206$$ −20.0000 −1.39347
$$207$$ −8.00000 −0.556038
$$208$$ −2.00000 −0.138675
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 2.00000 0.137361
$$213$$ −12.0000 −0.822226
$$214$$ 12.0000 0.820303
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 2.00000 0.135457
$$219$$ −10.0000 −0.675737
$$220$$ 0 0
$$221$$ −8.00000 −0.538138
$$222$$ 8.00000 0.536925
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −14.0000 −0.931266
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 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 $$0.348356\pi$$
$$234$$ 2.00000 0.130744
$$235$$ 0 0
$$236$$ 4.00000 0.260378
$$237$$ 16.0000 1.03931
$$238$$ 0 0
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ 0 0
$$241$$ −20.0000 −1.28831 −0.644157 0.764894i $$-0.722792\pi$$
−0.644157 + 0.764894i $$0.722792\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 1.00000 0.0641500
$$244$$ −10.0000 −0.640184
$$245$$ 0 0
$$246$$ 2.00000 0.127515
$$247$$ 0 0
$$248$$ 2.00000 0.127000
$$249$$ −16.0000 −1.01396
$$250$$ 0 0
$$251$$ −20.0000 −1.26239 −0.631194 0.775625i $$-0.717435\pi$$
−0.631194 + 0.775625i $$0.717435\pi$$
$$252$$ 0 0
$$253$$ −16.0000 −1.00591
$$254$$ −12.0000 −0.752947
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −12.0000 −0.748539 −0.374270 0.927320i $$-0.622107\pi$$
−0.374270 + 0.927320i $$0.622107\pi$$
$$258$$ −2.00000 −0.124515
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −12.0000 −0.741362
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ −2.00000 −0.123091
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 14.0000 0.856786
$$268$$ −2.00000 −0.122169
$$269$$ −10.0000 −0.609711 −0.304855 0.952399i $$-0.598608\pi$$
−0.304855 + 0.952399i $$0.598608\pi$$
$$270$$ 0 0
$$271$$ −14.0000 −0.850439 −0.425220 0.905090i $$-0.639803\pi$$
−0.425220 + 0.905090i $$0.639803\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 0 0
$$276$$ −8.00000 −0.481543
$$277$$ 28.0000 1.68236 0.841178 0.540758i $$-0.181862\pi$$
0.841178 + 0.540758i $$0.181862\pi$$
$$278$$ 4.00000 0.239904
$$279$$ −2.00000 −0.119737
$$280$$ 0 0
$$281$$ 14.0000 0.835170 0.417585 0.908638i $$-0.362877\pi$$
0.417585 + 0.908638i $$0.362877\pi$$
$$282$$ 10.0000 0.595491
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ 0 0
$$286$$ 4.00000 0.236525
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ −6.00000 −0.351726
$$292$$ −10.0000 −0.585206
$$293$$ −30.0000 −1.75262 −0.876309 0.481749i $$-0.840002\pi$$
−0.876309 + 0.481749i $$0.840002\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 8.00000 0.464991
$$297$$ 2.00000 0.116052
$$298$$ 16.0000 0.926855
$$299$$ 16.0000 0.925304
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −14.0000 −0.804279
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −4.00000 −0.228665
$$307$$ 20.0000 1.14146 0.570730 0.821138i $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ 0 0
$$309$$ 20.0000 1.13776
$$310$$ 0 0
$$311$$ −20.0000 −1.13410 −0.567048 0.823685i $$-0.691915\pi$$
−0.567048 + 0.823685i $$0.691915\pi$$
$$312$$ 2.00000 0.113228
$$313$$ 26.0000 1.46961 0.734803 0.678280i $$-0.237274\pi$$
0.734803 + 0.678280i $$0.237274\pi$$
$$314$$ −10.0000 −0.564333
$$315$$ 0 0
$$316$$ 16.0000 0.900070
$$317$$ −6.00000 −0.336994 −0.168497 0.985702i $$-0.553891\pi$$
−0.168497 + 0.985702i $$0.553891\pi$$
$$318$$ −2.00000 −0.112154
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −12.0000 −0.669775
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −10.0000 −0.553849
$$327$$ −2.00000 −0.110600
$$328$$ 2.00000 0.110432
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ −16.0000 −0.878114
$$333$$ −8.00000 −0.438397
$$334$$ 18.0000 0.984916
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 9.00000 0.489535
$$339$$ 14.0000 0.760376
$$340$$ 0 0
$$341$$ −4.00000 −0.216612
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −2.00000 −0.107833
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ 4.00000 0.214731 0.107366 0.994220i $$-0.465758\pi$$
0.107366 + 0.994220i $$0.465758\pi$$
$$348$$ 0 0
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −0.106752
$$352$$ −2.00000 −0.106600
$$353$$ −24.0000 −1.27739 −0.638696 0.769460i $$-0.720526\pi$$
−0.638696 + 0.769460i $$0.720526\pi$$
$$354$$ −4.00000 −0.212598
$$355$$ 0 0
$$356$$ 14.0000 0.741999
$$357$$ 0 0
$$358$$ 2.00000 0.105703
$$359$$ −20.0000 −1.05556 −0.527780 0.849381i $$-0.676975\pi$$
−0.527780 + 0.849381i $$0.676975\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 22.0000 1.15629
$$363$$ −7.00000 −0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 10.0000 0.522708
$$367$$ 28.0000 1.46159 0.730794 0.682598i $$-0.239150\pi$$
0.730794 + 0.682598i $$0.239150\pi$$
$$368$$ −8.00000 −0.417029
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −2.00000 −0.103695
$$373$$ 36.0000 1.86401 0.932005 0.362446i $$-0.118058\pi$$
0.932005 + 0.362446i $$0.118058\pi$$
$$374$$ −8.00000 −0.413670
$$375$$ 0 0
$$376$$ 10.0000 0.515711
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 8.00000 0.410932 0.205466 0.978664i $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ 0 0
$$381$$ 12.0000 0.614779
$$382$$ 0 0
$$383$$ −14.0000 −0.715367 −0.357683 0.933843i $$-0.616433\pi$$
−0.357683 + 0.933843i $$0.616433\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −18.0000 −0.916176
$$387$$ 2.00000 0.101666
$$388$$ −6.00000 −0.304604
$$389$$ −24.0000 −1.21685 −0.608424 0.793612i $$-0.708198\pi$$
−0.608424 + 0.793612i $$0.708198\pi$$
$$390$$ 0 0
$$391$$ −32.0000 −1.61831
$$392$$ 0 0
$$393$$ 12.0000 0.605320
$$394$$ 18.0000 0.906827
$$395$$ 0 0
$$396$$ 2.00000 0.100504
$$397$$ −14.0000 −0.702640 −0.351320 0.936255i $$-0.614267\pi$$
−0.351320 + 0.936255i $$0.614267\pi$$
$$398$$ −10.0000 −0.501255
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −14.0000 −0.699127 −0.349563 0.936913i $$-0.613670\pi$$
−0.349563 + 0.936913i $$0.613670\pi$$
$$402$$ 2.00000 0.0997509
$$403$$ 4.00000 0.199254
$$404$$ −14.0000 −0.696526
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −16.0000 −0.793091
$$408$$ −4.00000 −0.198030
$$409$$ −32.0000 −1.58230 −0.791149 0.611623i $$-0.790517\pi$$
−0.791149 + 0.611623i $$0.790517\pi$$
$$410$$ 0 0
$$411$$ 2.00000 0.0986527
$$412$$ 20.0000 0.985329
$$413$$ 0 0
$$414$$ 8.00000 0.393179
$$415$$ 0 0
$$416$$ 2.00000 0.0980581
$$417$$ −4.00000 −0.195881
$$418$$ 0 0
$$419$$ 36.0000 1.75872 0.879358 0.476162i $$-0.157972\pi$$
0.879358 + 0.476162i $$0.157972\pi$$
$$420$$ 0 0
$$421$$ 38.0000 1.85201 0.926003 0.377515i $$-0.123221\pi$$
0.926003 + 0.377515i $$0.123221\pi$$
$$422$$ 4.00000 0.194717
$$423$$ −10.0000 −0.486217
$$424$$ −2.00000 −0.0971286
$$425$$ 0 0
$$426$$ 12.0000 0.581402
$$427$$ 0 0
$$428$$ −12.0000 −0.580042
$$429$$ −4.00000 −0.193122
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −38.0000 −1.82616 −0.913082 0.407777i $$-0.866304\pi$$
−0.913082 + 0.407777i $$0.866304\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −2.00000 −0.0957826
$$437$$ 0 0
$$438$$ 10.0000 0.477818
$$439$$ −26.0000 −1.24091 −0.620456 0.784241i $$-0.713053\pi$$
−0.620456 + 0.784241i $$0.713053\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 8.00000 0.380521
$$443$$ −28.0000 −1.33032 −0.665160 0.746701i $$-0.731637\pi$$
−0.665160 + 0.746701i $$0.731637\pi$$
$$444$$ −8.00000 −0.379663
$$445$$ 0 0
$$446$$ 16.0000 0.757622
$$447$$ −16.0000 −0.756774
$$448$$ 0 0
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ −4.00000 −0.188353
$$452$$ 14.0000 0.658505
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 42.0000 1.96468 0.982339 0.187112i $$-0.0599128\pi$$
0.982339 + 0.187112i $$0.0599128\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 4.00000 0.186704
$$460$$ 0 0
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −14.0000 −0.648537
$$467$$ −8.00000 −0.370196 −0.185098 0.982720i $$-0.559260\pi$$
−0.185098 + 0.982720i $$0.559260\pi$$
$$468$$ −2.00000 −0.0924500
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 10.0000 0.460776
$$472$$ −4.00000 −0.184115
$$473$$ 4.00000 0.183920
$$474$$ −16.0000 −0.734904
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 2.00000 0.0915737
$$478$$ 8.00000 0.365911
$$479$$ 4.00000 0.182765 0.0913823 0.995816i $$-0.470871\pi$$
0.0913823 + 0.995816i $$0.470871\pi$$
$$480$$ 0 0
$$481$$ 16.0000 0.729537
$$482$$ 20.0000 0.910975
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ −28.0000 −1.26880 −0.634401 0.773004i $$-0.718753\pi$$
−0.634401 + 0.773004i $$0.718753\pi$$
$$488$$ 10.0000 0.452679
$$489$$ 10.0000 0.452216
$$490$$ 0 0
$$491$$ 6.00000 0.270776 0.135388 0.990793i $$-0.456772\pi$$
0.135388 + 0.990793i $$0.456772\pi$$
$$492$$ −2.00000 −0.0901670
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ 0 0
$$498$$ 16.0000 0.716977
$$499$$ 40.0000 1.79065 0.895323 0.445418i $$-0.146945\pi$$
0.895323 + 0.445418i $$0.146945\pi$$
$$500$$ 0 0
$$501$$ −18.0000 −0.804181
$$502$$ 20.0000 0.892644
$$503$$ 6.00000 0.267527 0.133763 0.991013i $$-0.457294\pi$$
0.133763 + 0.991013i $$0.457294\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 16.0000 0.711287
$$507$$ −9.00000 −0.399704
$$508$$ 12.0000 0.532414
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 12.0000 0.529297
$$515$$ 0 0
$$516$$ 2.00000 0.0880451
$$517$$ −20.0000 −0.879599
$$518$$ 0 0
$$519$$ 6.00000 0.263371
$$520$$ 0 0
$$521$$ 30.0000 1.31432 0.657162 0.753749i $$-0.271757\pi$$
0.657162 + 0.753749i $$0.271757\pi$$
$$522$$ 0 0
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −8.00000 −0.348485
$$528$$ 2.00000 0.0870388
$$529$$ 41.0000 1.78261
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ 4.00000 0.173259
$$534$$ −14.0000 −0.605839
$$535$$ 0 0
$$536$$ 2.00000 0.0863868
$$537$$ −2.00000 −0.0863064
$$538$$ 10.0000 0.431131
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 2.00000 0.0859867 0.0429934 0.999075i $$-0.486311\pi$$
0.0429934 + 0.999075i $$0.486311\pi$$
$$542$$ 14.0000 0.601351
$$543$$ −22.0000 −0.944110
$$544$$ −4.00000 −0.171499
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 14.0000 0.598597 0.299298 0.954160i $$-0.403247\pi$$
0.299298 + 0.954160i $$0.403247\pi$$
$$548$$ 2.00000 0.0854358
$$549$$ −10.0000 −0.426790
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 8.00000 0.340503
$$553$$ 0 0
$$554$$ −28.0000 −1.18961
$$555$$ 0 0
$$556$$ −4.00000 −0.169638
$$557$$ −30.0000 −1.27114 −0.635570 0.772043i $$-0.719235\pi$$
−0.635570 + 0.772043i $$0.719235\pi$$
$$558$$ 2.00000 0.0846668
$$559$$ −4.00000 −0.169182
$$560$$ 0 0
$$561$$ 8.00000 0.337760
$$562$$ −14.0000 −0.590554
$$563$$ −24.0000 −1.01148 −0.505740 0.862686i $$-0.668780\pi$$
−0.505740 + 0.862686i $$0.668780\pi$$
$$564$$ −10.0000 −0.421076
$$565$$ 0 0
$$566$$ 4.00000 0.168133
$$567$$ 0 0
$$568$$ 12.0000 0.503509
$$569$$ −38.0000 −1.59304 −0.796521 0.604610i $$-0.793329\pi$$
−0.796521 + 0.604610i $$0.793329\pi$$
$$570$$ 0 0
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ −4.00000 −0.167248
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ 18.0000 0.748054
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 6.00000 0.248708
$$583$$ 4.00000 0.165663
$$584$$ 10.0000 0.413803
$$585$$ 0 0
$$586$$ 30.0000 1.23929
$$587$$ 16.0000 0.660391 0.330195 0.943913i $$-0.392885\pi$$
0.330195 + 0.943913i $$0.392885\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −18.0000 −0.740421
$$592$$ −8.00000 −0.328798
$$593$$ 20.0000 0.821302 0.410651 0.911793i $$-0.365302\pi$$
0.410651 + 0.911793i $$0.365302\pi$$
$$594$$ −2.00000 −0.0820610
$$595$$ 0 0
$$596$$ −16.0000 −0.655386
$$597$$ 10.0000 0.409273
$$598$$ −16.0000 −0.654289
$$599$$ 32.0000 1.30748 0.653742 0.756717i $$-0.273198\pi$$
0.653742 + 0.756717i $$0.273198\pi$$
$$600$$ 0 0
$$601$$ 4.00000 0.163163 0.0815817 0.996667i $$-0.474003\pi$$
0.0815817 + 0.996667i $$0.474003\pi$$
$$602$$ 0 0
$$603$$ −2.00000 −0.0814463
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 14.0000 0.568711
$$607$$ −8.00000 −0.324710 −0.162355 0.986732i $$-0.551909\pi$$
−0.162355 + 0.986732i $$0.551909\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 20.0000 0.809113
$$612$$ 4.00000 0.161690
$$613$$ 8.00000 0.323117 0.161558 0.986863i $$-0.448348\pi$$
0.161558 + 0.986863i $$0.448348\pi$$
$$614$$ −20.0000 −0.807134
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ −20.0000 −0.804518
$$619$$ −24.0000 −0.964641 −0.482321 0.875995i $$-0.660206\pi$$
−0.482321 + 0.875995i $$0.660206\pi$$
$$620$$ 0 0
$$621$$ −8.00000 −0.321029
$$622$$ 20.0000 0.801927
$$623$$ 0 0
$$624$$ −2.00000 −0.0800641
$$625$$ 0 0
$$626$$ −26.0000 −1.03917
$$627$$ 0 0
$$628$$ 10.0000 0.399043
$$629$$ −32.0000 −1.27592
$$630$$ 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
$$633$$ −4.00000 −0.158986
$$634$$ 6.00000 0.238290
$$635$$ 0 0
$$636$$ 2.00000 0.0793052
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −12.0000 −0.474713
$$640$$ 0 0
$$641$$ 42.0000 1.65890 0.829450 0.558581i $$-0.188654\pi$$
0.829450 + 0.558581i $$0.188654\pi$$
$$642$$ 12.0000 0.473602
$$643$$ 36.0000 1.41970 0.709851 0.704352i $$-0.248762\pi$$
0.709851 + 0.704352i $$0.248762\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 2.00000 0.0786281 0.0393141 0.999227i $$-0.487483\pi$$
0.0393141 + 0.999227i $$0.487483\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 8.00000 0.314027
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 10.0000 0.391630
$$653$$ −2.00000 −0.0782660 −0.0391330 0.999234i $$-0.512460\pi$$
−0.0391330 + 0.999234i $$0.512460\pi$$
$$654$$ 2.00000 0.0782062
$$655$$ 0 0
$$656$$ −2.00000 −0.0780869
$$657$$ −10.0000 −0.390137
$$658$$ 0 0
$$659$$ −34.0000 −1.32445 −0.662226 0.749304i $$-0.730388\pi$$
−0.662226 + 0.749304i $$0.730388\pi$$
$$660$$ 0 0
$$661$$ −26.0000 −1.01128 −0.505641 0.862744i $$-0.668744\pi$$
−0.505641 + 0.862744i $$0.668744\pi$$
$$662$$ 4.00000 0.155464
$$663$$ −8.00000 −0.310694
$$664$$ 16.0000 0.620920
$$665$$ 0 0
$$666$$ 8.00000 0.309994
$$667$$ 0 0
$$668$$ −18.0000 −0.696441
$$669$$ −16.0000 −0.618596
$$670$$ 0 0
$$671$$ −20.0000 −0.772091
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ −2.00000 −0.0770371
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −26.0000 −0.999261 −0.499631 0.866239i $$-0.666531\pi$$
−0.499631 + 0.866239i $$0.666531\pi$$
$$678$$ −14.0000 −0.537667
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 4.00000 0.153168
$$683$$ −24.0000 −0.918334 −0.459167 0.888350i $$-0.651852\pi$$
−0.459167 + 0.888350i $$0.651852\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 10.0000 0.381524
$$688$$ 2.00000 0.0762493
$$689$$ −4.00000 −0.152388
$$690$$ 0 0
$$691$$ −28.0000 −1.06517 −0.532585 0.846376i $$-0.678779\pi$$
−0.532585 + 0.846376i $$0.678779\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ −4.00000 −0.151838
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −8.00000 −0.303022
$$698$$ −10.0000 −0.378506
$$699$$ 14.0000 0.529529
$$700$$ 0 0
$$701$$ 16.0000 0.604312 0.302156 0.953259i $$-0.402294\pi$$
0.302156 + 0.953259i $$0.402294\pi$$
$$702$$ 2.00000 0.0754851
$$703$$ 0 0
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ 24.0000 0.903252
$$707$$ 0 0
$$708$$ 4.00000 0.150329
$$709$$ 42.0000 1.57734 0.788672 0.614815i $$-0.210769\pi$$
0.788672 + 0.614815i $$0.210769\pi$$
$$710$$ 0 0
$$711$$ 16.0000 0.600047
$$712$$ −14.0000 −0.524672
$$713$$ 16.0000 0.599205
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −2.00000 −0.0747435
$$717$$ −8.00000 −0.298765
$$718$$ 20.0000 0.746393
$$719$$ −48.0000 −1.79010 −0.895049 0.445968i $$-0.852860\pi$$
−0.895049 + 0.445968i $$0.852860\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 19.0000 0.707107
$$723$$ −20.0000 −0.743808
$$724$$ −22.0000 −0.817624
$$725$$ 0 0
$$726$$ 7.00000 0.259794
$$727$$ −32.0000 −1.18681 −0.593407 0.804902i $$-0.702218\pi$$
−0.593407 + 0.804902i $$0.702218\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 8.00000 0.295891
$$732$$ −10.0000 −0.369611
$$733$$ −30.0000 −1.10808 −0.554038 0.832492i $$-0.686914\pi$$
−0.554038 + 0.832492i $$0.686914\pi$$
$$734$$ −28.0000 −1.03350
$$735$$ 0 0
$$736$$ 8.00000 0.294884
$$737$$ −4.00000 −0.147342
$$738$$ 2.00000 0.0736210
$$739$$ 48.0000 1.76571 0.882854 0.469647i $$-0.155619\pi$$
0.882854 + 0.469647i $$0.155619\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 48.0000 1.76095 0.880475 0.474093i $$-0.157224\pi$$
0.880475 + 0.474093i $$0.157224\pi$$
$$744$$ 2.00000 0.0733236
$$745$$ 0 0
$$746$$ −36.0000 −1.31805
$$747$$ −16.0000 −0.585409
$$748$$ 8.00000 0.292509
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −8.00000 −0.291924 −0.145962 0.989290i $$-0.546628\pi$$
−0.145962 + 0.989290i $$0.546628\pi$$
$$752$$ −10.0000 −0.364662
$$753$$ −20.0000 −0.728841
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 20.0000 0.726912 0.363456 0.931611i $$-0.381597\pi$$
0.363456 + 0.931611i $$0.381597\pi$$
$$758$$ −8.00000 −0.290573
$$759$$ −16.0000 −0.580763
$$760$$ 0 0
$$761$$ −30.0000 −1.08750 −0.543750 0.839248i $$-0.682996\pi$$
−0.543750 + 0.839248i $$0.682996\pi$$
$$762$$ −12.0000 −0.434714
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 14.0000 0.505841
$$767$$ −8.00000 −0.288863
$$768$$ 1.00000 0.0360844
$$769$$ 16.0000 0.576975 0.288487 0.957484i $$-0.406848\pi$$
0.288487 + 0.957484i $$0.406848\pi$$
$$770$$ 0 0
$$771$$ −12.0000 −0.432169
$$772$$ 18.0000 0.647834
$$773$$ −30.0000 −1.07903 −0.539513 0.841978i $$-0.681391\pi$$
−0.539513 + 0.841978i $$0.681391\pi$$
$$774$$ −2.00000 −0.0718885
$$775$$ 0 0
$$776$$ 6.00000 0.215387
$$777$$ 0 0
$$778$$ 24.0000 0.860442
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −24.0000 −0.858788
$$782$$ 32.0000 1.14432
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −12.0000 −0.428026
$$787$$ 12.0000 0.427754 0.213877 0.976861i $$-0.431391\pi$$
0.213877 + 0.976861i $$0.431391\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −2.00000 −0.0710669
$$793$$ 20.0000 0.710221
$$794$$ 14.0000 0.496841
$$795$$ 0 0
$$796$$ 10.0000 0.354441
$$797$$ −2.00000 −0.0708436 −0.0354218 0.999372i $$-0.511277\pi$$
−0.0354218 + 0.999372i $$0.511277\pi$$
$$798$$ 0 0
$$799$$ −40.0000 −1.41510
$$800$$ 0 0
$$801$$ 14.0000 0.494666
$$802$$ 14.0000 0.494357
$$803$$ −20.0000 −0.705785
$$804$$ −2.00000 −0.0705346
$$805$$ 0 0
$$806$$ −4.00000 −0.140894
$$807$$ −10.0000 −0.352017
$$808$$ 14.0000 0.492518
$$809$$ −10.0000 −0.351581 −0.175791 0.984428i $$-0.556248\pi$$
−0.175791 + 0.984428i $$0.556248\pi$$
$$810$$ 0 0
$$811$$ −28.0000 −0.983213 −0.491606 0.870817i $$-0.663590\pi$$
−0.491606 + 0.870817i $$0.663590\pi$$
$$812$$ 0 0
$$813$$ −14.0000 −0.491001
$$814$$ 16.0000 0.560800
$$815$$ 0 0
$$816$$ 4.00000 0.140028
$$817$$ 0 0
$$818$$ 32.0000 1.11885
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 24.0000 0.837606 0.418803 0.908077i $$-0.362450\pi$$
0.418803 + 0.908077i $$0.362450\pi$$
$$822$$ −2.00000 −0.0697580
$$823$$ 16.0000 0.557725 0.278862 0.960331i $$-0.410043\pi$$
0.278862 + 0.960331i $$0.410043\pi$$
$$824$$ −20.0000 −0.696733
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −8.00000 −0.278187 −0.139094 0.990279i $$-0.544419\pi$$
−0.139094 + 0.990279i $$0.544419\pi$$
$$828$$ −8.00000 −0.278019
$$829$$ −10.0000 −0.347314 −0.173657 0.984806i $$-0.555558\pi$$
−0.173657 + 0.984806i $$0.555558\pi$$
$$830$$ 0 0
$$831$$ 28.0000 0.971309
$$832$$ −2.00000 −0.0693375
$$833$$ 0 0
$$834$$ 4.00000 0.138509
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −2.00000 −0.0691301
$$838$$ −36.0000 −1.24360
$$839$$ 12.0000 0.414286 0.207143 0.978311i $$-0.433583\pi$$
0.207143 + 0.978311i $$0.433583\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ −38.0000 −1.30957
$$843$$ 14.0000 0.482186
$$844$$ −4.00000 −0.137686
$$845$$ 0 0
$$846$$ 10.0000 0.343807
$$847$$ 0 0
$$848$$ 2.00000 0.0686803
$$849$$ −4.00000 −0.137280
$$850$$ 0 0
$$851$$ 64.0000 2.19389
$$852$$ −12.0000 −0.411113
$$853$$ −38.0000 −1.30110 −0.650548 0.759465i $$-0.725461\pi$$
−0.650548 + 0.759465i $$0.725461\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 12.0000 0.410152
$$857$$ 12.0000 0.409912 0.204956 0.978771i $$-0.434295\pi$$
0.204956 + 0.978771i $$0.434295\pi$$
$$858$$ 4.00000 0.136558
$$859$$ −4.00000 −0.136478 −0.0682391 0.997669i $$-0.521738\pi$$
−0.0682391 + 0.997669i $$0.521738\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −12.0000 −0.408722
$$863$$ −24.0000 −0.816970 −0.408485 0.912765i $$-0.633943\pi$$
−0.408485 + 0.912765i $$0.633943\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ 38.0000 1.29129
$$867$$ −1.00000 −0.0339618
$$868$$ 0 0
$$869$$ 32.0000 1.08553
$$870$$ 0 0
$$871$$ 4.00000 0.135535
$$872$$ 2.00000 0.0677285
$$873$$ −6.00000 −0.203069
$$874$$ 0 0
$$875$$ 0 0
$$876$$ −10.0000 −0.337869
$$877$$ −12.0000 −0.405211 −0.202606 0.979260i $$-0.564941\pi$$
−0.202606 + 0.979260i $$0.564941\pi$$
$$878$$ 26.0000 0.877457
$$879$$ −30.0000 −1.01187
$$880$$ 0 0
$$881$$ −46.0000 −1.54978 −0.774890 0.632096i $$-0.782195\pi$$
−0.774890 + 0.632096i $$0.782195\pi$$
$$882$$ 0 0
$$883$$ −34.0000 −1.14419 −0.572096 0.820187i $$-0.693869\pi$$
−0.572096 + 0.820187i $$0.693869\pi$$
$$884$$ −8.00000 −0.269069
$$885$$ 0 0
$$886$$ 28.0000 0.940678
$$887$$ 2.00000 0.0671534 0.0335767 0.999436i $$-0.489310\pi$$
0.0335767 + 0.999436i $$0.489310\pi$$
$$888$$ 8.00000 0.268462
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 2.00000 0.0670025
$$892$$ −16.0000 −0.535720
$$893$$ 0 0
$$894$$ 16.0000 0.535120
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 16.0000 0.534224
$$898$$ −6.00000 −0.200223
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 8.00000 0.266519
$$902$$ 4.00000 0.133185
$$903$$ 0 0
$$904$$ −14.0000 −0.465633
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −10.0000 −0.332045 −0.166022 0.986122i $$-0.553092\pi$$
−0.166022 + 0.986122i $$0.553092\pi$$
$$908$$ 12.0000 0.398234
$$909$$ −14.0000 −0.464351
$$910$$ 0 0
$$911$$ 16.0000 0.530104 0.265052 0.964234i $$-0.414611\pi$$
0.265052 + 0.964234i $$0.414611\pi$$
$$912$$ 0 0
$$913$$ −32.0000 −1.05905
$$914$$ −42.0000 −1.38924
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ 0 0
$$918$$ −4.00000 −0.132020
$$919$$ 56.0000 1.84727 0.923635 0.383274i $$-0.125203\pi$$
0.923635 + 0.383274i $$0.125203\pi$$
$$920$$ 0 0
$$921$$ 20.0000 0.659022
$$922$$ 18.0000 0.592798
$$923$$ 24.0000 0.789970
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 16.0000 0.525793
$$927$$ 20.0000 0.656886
$$928$$ 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
$$933$$ −20.0000 −0.654771
$$934$$ 8.00000 0.261768
$$935$$ 0 0
$$936$$ 2.00000 0.0653720
$$937$$ −42.0000 −1.37208 −0.686040 0.727564i $$-0.740653\pi$$
−0.686040 + 0.727564i $$0.740653\pi$$
$$938$$ 0 0
$$939$$ 26.0000 0.848478
$$940$$ 0 0
$$941$$ 50.0000 1.62995 0.814977 0.579494i $$-0.196750\pi$$
0.814977 + 0.579494i $$0.196750\pi$$
$$942$$ −10.0000 −0.325818
$$943$$ 16.0000 0.521032
$$944$$ 4.00000 0.130189
$$945$$ 0 0
$$946$$ −4.00000 −0.130051
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 16.0000 0.519656
$$949$$ 20.0000 0.649227
$$950$$ 0 0
$$951$$ −6.00000 −0.194563
$$952$$ 0 0
$$953$$ 58.0000 1.87880 0.939402 0.342817i $$-0.111381\pi$$
0.939402 + 0.342817i $$0.111381\pi$$
$$954$$ −2.00000 −0.0647524
$$955$$ 0 0
$$956$$ −8.00000 −0.258738
$$957$$ 0 0
$$958$$ −4.00000 −0.129234
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ −16.0000 −0.515861
$$963$$ −12.0000 −0.386695
$$964$$ −20.0000 −0.644157
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −32.0000 −1.02905 −0.514525 0.857475i $$-0.672032\pi$$
−0.514525 + 0.857475i $$0.672032\pi$$
$$968$$ 7.00000 0.224989
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −20.0000 −0.641831 −0.320915 0.947108i $$-0.603990\pi$$
−0.320915 + 0.947108i $$0.603990\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 0 0
$$974$$ 28.0000 0.897178
$$975$$ 0 0
$$976$$ −10.0000 −0.320092
$$977$$ 30.0000 0.959785 0.479893 0.877327i $$-0.340676\pi$$
0.479893 + 0.877327i $$0.340676\pi$$
$$978$$ −10.0000 −0.319765
$$979$$ 28.0000 0.894884
$$980$$ 0 0
$$981$$ −2.00000 −0.0638551
$$982$$ −6.00000 −0.191468
$$983$$ 46.0000 1.46717 0.733586 0.679597i $$-0.237845\pi$$
0.733586 + 0.679597i $$0.237845\pi$$
$$984$$ 2.00000 0.0637577
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −16.0000 −0.508770
$$990$$ 0 0
$$991$$ −24.0000 −0.762385 −0.381193 0.924496i $$-0.624487\pi$$
−0.381193 + 0.924496i $$0.624487\pi$$
$$992$$ 2.00000 0.0635001
$$993$$ −4.00000 −0.126936
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −16.0000 −0.506979
$$997$$ −6.00000 −0.190022 −0.0950110 0.995476i $$-0.530289\pi$$
−0.0950110 + 0.995476i $$0.530289\pi$$
$$998$$ −40.0000 −1.26618
$$999$$ −8.00000 −0.253109
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.bh.1.1 1
5.4 even 2 1470.2.a.n.1.1 1
7.6 odd 2 7350.2.a.o.1.1 1
15.14 odd 2 4410.2.a.e.1.1 1
35.4 even 6 1470.2.i.g.961.1 2
35.9 even 6 1470.2.i.g.361.1 2
35.19 odd 6 1470.2.i.c.361.1 2
35.24 odd 6 1470.2.i.c.961.1 2
35.34 odd 2 1470.2.a.p.1.1 yes 1
105.104 even 2 4410.2.a.n.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.a.n.1.1 1 5.4 even 2
1470.2.a.p.1.1 yes 1 35.34 odd 2
1470.2.i.c.361.1 2 35.19 odd 6
1470.2.i.c.961.1 2 35.24 odd 6
1470.2.i.g.361.1 2 35.9 even 6
1470.2.i.g.961.1 2 35.4 even 6
4410.2.a.e.1.1 1 15.14 odd 2
4410.2.a.n.1.1 1 105.104 even 2
7350.2.a.o.1.1 1 7.6 odd 2
7350.2.a.bh.1.1 1 1.1 even 1 trivial