# Properties

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

# Related objects

## Newspace parameters

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

## Newform invariants

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

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} -2.00000 q^{21} -4.00000 q^{22} +1.00000 q^{24} +4.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} +4.00000 q^{29} +1.00000 q^{31} +1.00000 q^{32} -4.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} -4.00000 q^{37} +4.00000 q^{39} -6.00000 q^{41} -2.00000 q^{42} +8.00000 q^{43} -4.00000 q^{44} +12.0000 q^{47} +1.00000 q^{48} -3.00000 q^{49} +6.00000 q^{51} +4.00000 q^{52} +2.00000 q^{53} +1.00000 q^{54} -2.00000 q^{56} +4.00000 q^{58} +6.00000 q^{59} +10.0000 q^{61} +1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} +10.0000 q^{67} +6.00000 q^{68} -14.0000 q^{71} +1.00000 q^{72} -4.00000 q^{73} -4.00000 q^{74} +8.00000 q^{77} +4.00000 q^{78} -8.00000 q^{79} +1.00000 q^{81} -6.00000 q^{82} +4.00000 q^{83} -2.00000 q^{84} +8.00000 q^{86} +4.00000 q^{87} -4.00000 q^{88} -8.00000 q^{89} -8.00000 q^{91} +1.00000 q^{93} +12.0000 q^{94} +1.00000 q^{96} +2.00000 q^{97} -3.00000 q^{98} -4.00000 q^{99} +O(q^{100})$$

## 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
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ −2.00000 −0.534522
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 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
$$22$$ −4.00000 −0.852803
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 0 0
$$26$$ 4.00000 0.784465
$$27$$ 1.00000 0.192450
$$28$$ −2.00000 −0.377964
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ 1.00000 0.179605
$$32$$ 1.00000 0.176777
$$33$$ −4.00000 −0.696311
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −4.00000 −0.657596 −0.328798 0.944400i $$-0.606644\pi$$
−0.328798 + 0.944400i $$0.606644\pi$$
$$38$$ 0 0
$$39$$ 4.00000 0.640513
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ −2.00000 −0.308607
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 12.0000 1.75038 0.875190 0.483779i $$-0.160736\pi$$
0.875190 + 0.483779i $$0.160736\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 6.00000 0.840168
$$52$$ 4.00000 0.554700
$$53$$ 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
$$56$$ −2.00000 −0.267261
$$57$$ 0 0
$$58$$ 4.00000 0.525226
$$59$$ 6.00000 0.781133 0.390567 0.920575i $$-0.372279\pi$$
0.390567 + 0.920575i $$0.372279\pi$$
$$60$$ 0 0
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ 1.00000 0.127000
$$63$$ −2.00000 −0.251976
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −4.00000 −0.492366
$$67$$ 10.0000 1.22169 0.610847 0.791748i $$-0.290829\pi$$
0.610847 + 0.791748i $$0.290829\pi$$
$$68$$ 6.00000 0.727607
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −14.0000 −1.66149 −0.830747 0.556650i $$-0.812086\pi$$
−0.830747 + 0.556650i $$0.812086\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −4.00000 −0.468165 −0.234082 0.972217i $$-0.575209\pi$$
−0.234082 + 0.972217i $$0.575209\pi$$
$$74$$ −4.00000 −0.464991
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 8.00000 0.911685
$$78$$ 4.00000 0.452911
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −6.00000 −0.662589
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ −2.00000 −0.218218
$$85$$ 0 0
$$86$$ 8.00000 0.862662
$$87$$ 4.00000 0.428845
$$88$$ −4.00000 −0.426401
$$89$$ −8.00000 −0.847998 −0.423999 0.905663i $$-0.639374\pi$$
−0.423999 + 0.905663i $$0.639374\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.838628
$$92$$ 0 0
$$93$$ 1.00000 0.103695
$$94$$ 12.0000 1.23771
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ −3.00000 −0.303046
$$99$$ −4.00000 −0.402015
$$100$$ 0 0
$$101$$ 14.0000 1.39305 0.696526 0.717532i $$-0.254728\pi$$
0.696526 + 0.717532i $$0.254728\pi$$
$$102$$ 6.00000 0.594089
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 0 0
$$106$$ 2.00000 0.194257
$$107$$ 16.0000 1.54678 0.773389 0.633932i $$-0.218560\pi$$
0.773389 + 0.633932i $$0.218560\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 18.0000 1.72409 0.862044 0.506834i $$-0.169184\pi$$
0.862044 + 0.506834i $$0.169184\pi$$
$$110$$ 0 0
$$111$$ −4.00000 −0.379663
$$112$$ −2.00000 −0.188982
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 4.00000 0.371391
$$117$$ 4.00000 0.369800
$$118$$ 6.00000 0.552345
$$119$$ −12.0000 −1.10004
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 10.0000 0.905357
$$123$$ −6.00000 −0.541002
$$124$$ 1.00000 0.0898027
$$125$$ 0 0
$$126$$ −2.00000 −0.178174
$$127$$ 12.0000 1.06483 0.532414 0.846484i $$-0.321285\pi$$
0.532414 + 0.846484i $$0.321285\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 8.00000 0.704361
$$130$$ 0 0
$$131$$ 14.0000 1.22319 0.611593 0.791173i $$-0.290529\pi$$
0.611593 + 0.791173i $$0.290529\pi$$
$$132$$ −4.00000 −0.348155
$$133$$ 0 0
$$134$$ 10.0000 0.863868
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ 18.0000 1.53784 0.768922 0.639343i $$-0.220793\pi$$
0.768922 + 0.639343i $$0.220793\pi$$
$$138$$ 0 0
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 0 0
$$141$$ 12.0000 1.01058
$$142$$ −14.0000 −1.17485
$$143$$ −16.0000 −1.33799
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −4.00000 −0.331042
$$147$$ −3.00000 −0.247436
$$148$$ −4.00000 −0.328798
$$149$$ 14.0000 1.14692 0.573462 0.819232i $$-0.305600\pi$$
0.573462 + 0.819232i $$0.305600\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 6.00000 0.485071
$$154$$ 8.00000 0.644658
$$155$$ 0 0
$$156$$ 4.00000 0.320256
$$157$$ 6.00000 0.478852 0.239426 0.970915i $$-0.423041\pi$$
0.239426 + 0.970915i $$0.423041\pi$$
$$158$$ −8.00000 −0.636446
$$159$$ 2.00000 0.158610
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000 0.0785674
$$163$$ −6.00000 −0.469956 −0.234978 0.972001i $$-0.575502\pi$$
−0.234978 + 0.972001i $$0.575502\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ −2.00000 −0.154303
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 4.00000 0.303239
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ 6.00000 0.450988
$$178$$ −8.00000 −0.599625
$$179$$ −4.00000 −0.298974 −0.149487 0.988764i $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 0 0
$$181$$ 18.0000 1.33793 0.668965 0.743294i $$-0.266738\pi$$
0.668965 + 0.743294i $$0.266738\pi$$
$$182$$ −8.00000 −0.592999
$$183$$ 10.0000 0.739221
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 1.00000 0.0733236
$$187$$ −24.0000 −1.75505
$$188$$ 12.0000 0.875190
$$189$$ −2.00000 −0.145479
$$190$$ 0 0
$$191$$ −10.0000 −0.723575 −0.361787 0.932261i $$-0.617833\pi$$
−0.361787 + 0.932261i $$0.617833\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 2.00000 0.143963 0.0719816 0.997406i $$-0.477068\pi$$
0.0719816 + 0.997406i $$0.477068\pi$$
$$194$$ 2.00000 0.143592
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ −4.00000 −0.284268
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ 10.0000 0.705346
$$202$$ 14.0000 0.985037
$$203$$ −8.00000 −0.561490
$$204$$ 6.00000 0.420084
$$205$$ 0 0
$$206$$ −14.0000 −0.975426
$$207$$ 0 0
$$208$$ 4.00000 0.277350
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 16.0000 1.10149 0.550743 0.834675i $$-0.314345\pi$$
0.550743 + 0.834675i $$0.314345\pi$$
$$212$$ 2.00000 0.137361
$$213$$ −14.0000 −0.959264
$$214$$ 16.0000 1.09374
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ −2.00000 −0.135769
$$218$$ 18.0000 1.21911
$$219$$ −4.00000 −0.270295
$$220$$ 0 0
$$221$$ 24.0000 1.61441
$$222$$ −4.00000 −0.268462
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ −2.00000 −0.133631
$$225$$ 0 0
$$226$$ 6.00000 0.399114
$$227$$ −20.0000 −1.32745 −0.663723 0.747978i $$-0.731025\pi$$
−0.663723 + 0.747978i $$0.731025\pi$$
$$228$$ 0 0
$$229$$ −26.0000 −1.71813 −0.859064 0.511868i $$-0.828954\pi$$
−0.859064 + 0.511868i $$0.828954\pi$$
$$230$$ 0 0
$$231$$ 8.00000 0.526361
$$232$$ 4.00000 0.262613
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 4.00000 0.261488
$$235$$ 0 0
$$236$$ 6.00000 0.390567
$$237$$ −8.00000 −0.519656
$$238$$ −12.0000 −0.777844
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ 10.0000 0.644157 0.322078 0.946713i $$-0.395619\pi$$
0.322078 + 0.946713i $$0.395619\pi$$
$$242$$ 5.00000 0.321412
$$243$$ 1.00000 0.0641500
$$244$$ 10.0000 0.640184
$$245$$ 0 0
$$246$$ −6.00000 −0.382546
$$247$$ 0 0
$$248$$ 1.00000 0.0635001
$$249$$ 4.00000 0.253490
$$250$$ 0 0
$$251$$ −28.0000 −1.76734 −0.883672 0.468106i $$-0.844936\pi$$
−0.883672 + 0.468106i $$0.844936\pi$$
$$252$$ −2.00000 −0.125988
$$253$$ 0 0
$$254$$ 12.0000 0.752947
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 2.00000 0.124757 0.0623783 0.998053i $$-0.480131\pi$$
0.0623783 + 0.998053i $$0.480131\pi$$
$$258$$ 8.00000 0.498058
$$259$$ 8.00000 0.497096
$$260$$ 0 0
$$261$$ 4.00000 0.247594
$$262$$ 14.0000 0.864923
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ −4.00000 −0.246183
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −8.00000 −0.489592
$$268$$ 10.0000 0.610847
$$269$$ −12.0000 −0.731653 −0.365826 0.930683i $$-0.619214\pi$$
−0.365826 + 0.930683i $$0.619214\pi$$
$$270$$ 0 0
$$271$$ −24.0000 −1.45790 −0.728948 0.684569i $$-0.759990\pi$$
−0.728948 + 0.684569i $$0.759990\pi$$
$$272$$ 6.00000 0.363803
$$273$$ −8.00000 −0.484182
$$274$$ 18.0000 1.08742
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ −12.0000 −0.719712
$$279$$ 1.00000 0.0598684
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 12.0000 0.714590
$$283$$ −14.0000 −0.832214 −0.416107 0.909316i $$-0.636606\pi$$
−0.416107 + 0.909316i $$0.636606\pi$$
$$284$$ −14.0000 −0.830747
$$285$$ 0 0
$$286$$ −16.0000 −0.946100
$$287$$ 12.0000 0.708338
$$288$$ 1.00000 0.0589256
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 2.00000 0.117242
$$292$$ −4.00000 −0.234082
$$293$$ −26.0000 −1.51894 −0.759468 0.650545i $$-0.774541\pi$$
−0.759468 + 0.650545i $$0.774541\pi$$
$$294$$ −3.00000 −0.174964
$$295$$ 0 0
$$296$$ −4.00000 −0.232495
$$297$$ −4.00000 −0.232104
$$298$$ 14.0000 0.810998
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −16.0000 −0.922225
$$302$$ −16.0000 −0.920697
$$303$$ 14.0000 0.804279
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 6.00000 0.342997
$$307$$ −2.00000 −0.114146 −0.0570730 0.998370i $$-0.518177\pi$$
−0.0570730 + 0.998370i $$0.518177\pi$$
$$308$$ 8.00000 0.455842
$$309$$ −14.0000 −0.796432
$$310$$ 0 0
$$311$$ 6.00000 0.340229 0.170114 0.985424i $$-0.445586\pi$$
0.170114 + 0.985424i $$0.445586\pi$$
$$312$$ 4.00000 0.226455
$$313$$ 4.00000 0.226093 0.113047 0.993590i $$-0.463939\pi$$
0.113047 + 0.993590i $$0.463939\pi$$
$$314$$ 6.00000 0.338600
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ −26.0000 −1.46031 −0.730153 0.683284i $$-0.760551\pi$$
−0.730153 + 0.683284i $$0.760551\pi$$
$$318$$ 2.00000 0.112154
$$319$$ −16.0000 −0.895828
$$320$$ 0 0
$$321$$ 16.0000 0.893033
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −6.00000 −0.332309
$$327$$ 18.0000 0.995402
$$328$$ −6.00000 −0.331295
$$329$$ −24.0000 −1.32316
$$330$$ 0 0
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ 4.00000 0.219529
$$333$$ −4.00000 −0.219199
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −2.00000 −0.109109
$$337$$ −8.00000 −0.435788 −0.217894 0.975972i $$-0.569919\pi$$
−0.217894 + 0.975972i $$0.569919\pi$$
$$338$$ 3.00000 0.163178
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ −4.00000 −0.216612
$$342$$ 0 0
$$343$$ 20.0000 1.07990
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ −4.00000 −0.214731 −0.107366 0.994220i $$-0.534242\pi$$
−0.107366 + 0.994220i $$0.534242\pi$$
$$348$$ 4.00000 0.214423
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 0 0
$$351$$ 4.00000 0.213504
$$352$$ −4.00000 −0.213201
$$353$$ −10.0000 −0.532246 −0.266123 0.963939i $$-0.585743\pi$$
−0.266123 + 0.963939i $$0.585743\pi$$
$$354$$ 6.00000 0.318896
$$355$$ 0 0
$$356$$ −8.00000 −0.423999
$$357$$ −12.0000 −0.635107
$$358$$ −4.00000 −0.211407
$$359$$ 30.0000 1.58334 0.791670 0.610949i $$-0.209212\pi$$
0.791670 + 0.610949i $$0.209212\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 18.0000 0.946059
$$363$$ 5.00000 0.262432
$$364$$ −8.00000 −0.419314
$$365$$ 0 0
$$366$$ 10.0000 0.522708
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ −4.00000 −0.207670
$$372$$ 1.00000 0.0518476
$$373$$ −18.0000 −0.932005 −0.466002 0.884783i $$-0.654306\pi$$
−0.466002 + 0.884783i $$0.654306\pi$$
$$374$$ −24.0000 −1.24101
$$375$$ 0 0
$$376$$ 12.0000 0.618853
$$377$$ 16.0000 0.824042
$$378$$ −2.00000 −0.102869
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 0 0
$$381$$ 12.0000 0.614779
$$382$$ −10.0000 −0.511645
$$383$$ −24.0000 −1.22634 −0.613171 0.789950i $$-0.710106\pi$$
−0.613171 + 0.789950i $$0.710106\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ 2.00000 0.101797
$$387$$ 8.00000 0.406663
$$388$$ 2.00000 0.101535
$$389$$ 36.0000 1.82527 0.912636 0.408773i $$-0.134043\pi$$
0.912636 + 0.408773i $$0.134043\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −3.00000 −0.151523
$$393$$ 14.0000 0.706207
$$394$$ −2.00000 −0.100759
$$395$$ 0 0
$$396$$ −4.00000 −0.201008
$$397$$ 18.0000 0.903394 0.451697 0.892171i $$-0.350819\pi$$
0.451697 + 0.892171i $$0.350819\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −4.00000 −0.199750 −0.0998752 0.995000i $$-0.531844\pi$$
−0.0998752 + 0.995000i $$0.531844\pi$$
$$402$$ 10.0000 0.498755
$$403$$ 4.00000 0.199254
$$404$$ 14.0000 0.696526
$$405$$ 0 0
$$406$$ −8.00000 −0.397033
$$407$$ 16.0000 0.793091
$$408$$ 6.00000 0.297044
$$409$$ 6.00000 0.296681 0.148340 0.988936i $$-0.452607\pi$$
0.148340 + 0.988936i $$0.452607\pi$$
$$410$$ 0 0
$$411$$ 18.0000 0.887875
$$412$$ −14.0000 −0.689730
$$413$$ −12.0000 −0.590481
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 4.00000 0.196116
$$417$$ −12.0000 −0.587643
$$418$$ 0 0
$$419$$ −30.0000 −1.46560 −0.732798 0.680446i $$-0.761786\pi$$
−0.732798 + 0.680446i $$0.761786\pi$$
$$420$$ 0 0
$$421$$ −30.0000 −1.46211 −0.731055 0.682318i $$-0.760972\pi$$
−0.731055 + 0.682318i $$0.760972\pi$$
$$422$$ 16.0000 0.778868
$$423$$ 12.0000 0.583460
$$424$$ 2.00000 0.0971286
$$425$$ 0 0
$$426$$ −14.0000 −0.678302
$$427$$ −20.0000 −0.967868
$$428$$ 16.0000 0.773389
$$429$$ −16.0000 −0.772487
$$430$$ 0 0
$$431$$ −10.0000 −0.481683 −0.240842 0.970564i $$-0.577423\pi$$
−0.240842 + 0.970564i $$0.577423\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ 4.00000 0.192228 0.0961139 0.995370i $$-0.469359\pi$$
0.0961139 + 0.995370i $$0.469359\pi$$
$$434$$ −2.00000 −0.0960031
$$435$$ 0 0
$$436$$ 18.0000 0.862044
$$437$$ 0 0
$$438$$ −4.00000 −0.191127
$$439$$ 24.0000 1.14546 0.572729 0.819745i $$-0.305885\pi$$
0.572729 + 0.819745i $$0.305885\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 24.0000 1.14156
$$443$$ 12.0000 0.570137 0.285069 0.958507i $$-0.407984\pi$$
0.285069 + 0.958507i $$0.407984\pi$$
$$444$$ −4.00000 −0.189832
$$445$$ 0 0
$$446$$ −16.0000 −0.757622
$$447$$ 14.0000 0.662177
$$448$$ −2.00000 −0.0944911
$$449$$ 20.0000 0.943858 0.471929 0.881636i $$-0.343558\pi$$
0.471929 + 0.881636i $$0.343558\pi$$
$$450$$ 0 0
$$451$$ 24.0000 1.13012
$$452$$ 6.00000 0.282216
$$453$$ −16.0000 −0.751746
$$454$$ −20.0000 −0.938647
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 4.00000 0.187112 0.0935561 0.995614i $$-0.470177\pi$$
0.0935561 + 0.995614i $$0.470177\pi$$
$$458$$ −26.0000 −1.21490
$$459$$ 6.00000 0.280056
$$460$$ 0 0
$$461$$ 24.0000 1.11779 0.558896 0.829238i $$-0.311225\pi$$
0.558896 + 0.829238i $$0.311225\pi$$
$$462$$ 8.00000 0.372194
$$463$$ −12.0000 −0.557687 −0.278844 0.960337i $$-0.589951\pi$$
−0.278844 + 0.960337i $$0.589951\pi$$
$$464$$ 4.00000 0.185695
$$465$$ 0 0
$$466$$ −6.00000 −0.277945
$$467$$ 24.0000 1.11059 0.555294 0.831654i $$-0.312606\pi$$
0.555294 + 0.831654i $$0.312606\pi$$
$$468$$ 4.00000 0.184900
$$469$$ −20.0000 −0.923514
$$470$$ 0 0
$$471$$ 6.00000 0.276465
$$472$$ 6.00000 0.276172
$$473$$ −32.0000 −1.47136
$$474$$ −8.00000 −0.367452
$$475$$ 0 0
$$476$$ −12.0000 −0.550019
$$477$$ 2.00000 0.0915737
$$478$$ 20.0000 0.914779
$$479$$ −14.0000 −0.639676 −0.319838 0.947472i $$-0.603629\pi$$
−0.319838 + 0.947472i $$0.603629\pi$$
$$480$$ 0 0
$$481$$ −16.0000 −0.729537
$$482$$ 10.0000 0.455488
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ 28.0000 1.26880 0.634401 0.773004i $$-0.281247\pi$$
0.634401 + 0.773004i $$0.281247\pi$$
$$488$$ 10.0000 0.452679
$$489$$ −6.00000 −0.271329
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ −6.00000 −0.270501
$$493$$ 24.0000 1.08091
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 1.00000 0.0449013
$$497$$ 28.0000 1.25597
$$498$$ 4.00000 0.179244
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −28.0000 −1.24970
$$503$$ 12.0000 0.535054 0.267527 0.963550i $$-0.413794\pi$$
0.267527 + 0.963550i $$0.413794\pi$$
$$504$$ −2.00000 −0.0890871
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 3.00000 0.133235
$$508$$ 12.0000 0.532414
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 8.00000 0.353899
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 2.00000 0.0882162
$$515$$ 0 0
$$516$$ 8.00000 0.352180
$$517$$ −48.0000 −2.11104
$$518$$ 8.00000 0.351500
$$519$$ −6.00000 −0.263371
$$520$$ 0 0
$$521$$ 18.0000 0.788594 0.394297 0.918983i $$-0.370988\pi$$
0.394297 + 0.918983i $$0.370988\pi$$
$$522$$ 4.00000 0.175075
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 14.0000 0.611593
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ 6.00000 0.261364
$$528$$ −4.00000 −0.174078
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ 6.00000 0.260378
$$532$$ 0 0
$$533$$ −24.0000 −1.03956
$$534$$ −8.00000 −0.346194
$$535$$ 0 0
$$536$$ 10.0000 0.431934
$$537$$ −4.00000 −0.172613
$$538$$ −12.0000 −0.517357
$$539$$ 12.0000 0.516877
$$540$$ 0 0
$$541$$ −30.0000 −1.28980 −0.644900 0.764267i $$-0.723101\pi$$
−0.644900 + 0.764267i $$0.723101\pi$$
$$542$$ −24.0000 −1.03089
$$543$$ 18.0000 0.772454
$$544$$ 6.00000 0.257248
$$545$$ 0 0
$$546$$ −8.00000 −0.342368
$$547$$ −46.0000 −1.96682 −0.983409 0.181402i $$-0.941936\pi$$
−0.983409 + 0.181402i $$0.941936\pi$$
$$548$$ 18.0000 0.768922
$$549$$ 10.0000 0.426790
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ 8.00000 0.339887
$$555$$ 0 0
$$556$$ −12.0000 −0.508913
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ 1.00000 0.0423334
$$559$$ 32.0000 1.35346
$$560$$ 0 0
$$561$$ −24.0000 −1.01328
$$562$$ 6.00000 0.253095
$$563$$ −8.00000 −0.337160 −0.168580 0.985688i $$-0.553918\pi$$
−0.168580 + 0.985688i $$0.553918\pi$$
$$564$$ 12.0000 0.505291
$$565$$ 0 0
$$566$$ −14.0000 −0.588464
$$567$$ −2.00000 −0.0839921
$$568$$ −14.0000 −0.587427
$$569$$ −20.0000 −0.838444 −0.419222 0.907884i $$-0.637697\pi$$
−0.419222 + 0.907884i $$0.637697\pi$$
$$570$$ 0 0
$$571$$ −28.0000 −1.17176 −0.585882 0.810397i $$-0.699252\pi$$
−0.585882 + 0.810397i $$0.699252\pi$$
$$572$$ −16.0000 −0.668994
$$573$$ −10.0000 −0.417756
$$574$$ 12.0000 0.500870
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −42.0000 −1.74848 −0.874241 0.485491i $$-0.838641\pi$$
−0.874241 + 0.485491i $$0.838641\pi$$
$$578$$ 19.0000 0.790296
$$579$$ 2.00000 0.0831172
$$580$$ 0 0
$$581$$ −8.00000 −0.331896
$$582$$ 2.00000 0.0829027
$$583$$ −8.00000 −0.331326
$$584$$ −4.00000 −0.165521
$$585$$ 0 0
$$586$$ −26.0000 −1.07405
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ −3.00000 −0.123718
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −2.00000 −0.0822690
$$592$$ −4.00000 −0.164399
$$593$$ 46.0000 1.88899 0.944497 0.328521i $$-0.106550\pi$$
0.944497 + 0.328521i $$0.106550\pi$$
$$594$$ −4.00000 −0.164122
$$595$$ 0 0
$$596$$ 14.0000 0.573462
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 6.00000 0.245153 0.122577 0.992459i $$-0.460884\pi$$
0.122577 + 0.992459i $$0.460884\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ −16.0000 −0.652111
$$603$$ 10.0000 0.407231
$$604$$ −16.0000 −0.651031
$$605$$ 0 0
$$606$$ 14.0000 0.568711
$$607$$ −14.0000 −0.568242 −0.284121 0.958788i $$-0.591702\pi$$
−0.284121 + 0.958788i $$0.591702\pi$$
$$608$$ 0 0
$$609$$ −8.00000 −0.324176
$$610$$ 0 0
$$611$$ 48.0000 1.94187
$$612$$ 6.00000 0.242536
$$613$$ 24.0000 0.969351 0.484675 0.874694i $$-0.338938\pi$$
0.484675 + 0.874694i $$0.338938\pi$$
$$614$$ −2.00000 −0.0807134
$$615$$ 0 0
$$616$$ 8.00000 0.322329
$$617$$ −26.0000 −1.04672 −0.523360 0.852111i $$-0.675322\pi$$
−0.523360 + 0.852111i $$0.675322\pi$$
$$618$$ −14.0000 −0.563163
$$619$$ 28.0000 1.12542 0.562708 0.826656i $$-0.309760\pi$$
0.562708 + 0.826656i $$0.309760\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 6.00000 0.240578
$$623$$ 16.0000 0.641026
$$624$$ 4.00000 0.160128
$$625$$ 0 0
$$626$$ 4.00000 0.159872
$$627$$ 0 0
$$628$$ 6.00000 0.239426
$$629$$ −24.0000 −0.956943
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ −8.00000 −0.318223
$$633$$ 16.0000 0.635943
$$634$$ −26.0000 −1.03259
$$635$$ 0 0
$$636$$ 2.00000 0.0793052
$$637$$ −12.0000 −0.475457
$$638$$ −16.0000 −0.633446
$$639$$ −14.0000 −0.553831
$$640$$ 0 0
$$641$$ 36.0000 1.42191 0.710957 0.703235i $$-0.248262\pi$$
0.710957 + 0.703235i $$0.248262\pi$$
$$642$$ 16.0000 0.631470
$$643$$ −40.0000 −1.57745 −0.788723 0.614749i $$-0.789257\pi$$
−0.788723 + 0.614749i $$0.789257\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −32.0000 −1.25805 −0.629025 0.777385i $$-0.716546\pi$$
−0.629025 + 0.777385i $$0.716546\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ −24.0000 −0.942082
$$650$$ 0 0
$$651$$ −2.00000 −0.0783862
$$652$$ −6.00000 −0.234978
$$653$$ 22.0000 0.860927 0.430463 0.902608i $$-0.358350\pi$$
0.430463 + 0.902608i $$0.358350\pi$$
$$654$$ 18.0000 0.703856
$$655$$ 0 0
$$656$$ −6.00000 −0.234261
$$657$$ −4.00000 −0.156055
$$658$$ −24.0000 −0.935617
$$659$$ −22.0000 −0.856998 −0.428499 0.903542i $$-0.640958\pi$$
−0.428499 + 0.903542i $$0.640958\pi$$
$$660$$ 0 0
$$661$$ −18.0000 −0.700119 −0.350059 0.936727i $$-0.613839\pi$$
−0.350059 + 0.936727i $$0.613839\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 24.0000 0.932083
$$664$$ 4.00000 0.155230
$$665$$ 0 0
$$666$$ −4.00000 −0.154997
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −16.0000 −0.618596
$$670$$ 0 0
$$671$$ −40.0000 −1.54418
$$672$$ −2.00000 −0.0771517
$$673$$ 16.0000 0.616755 0.308377 0.951264i $$-0.400214\pi$$
0.308377 + 0.951264i $$0.400214\pi$$
$$674$$ −8.00000 −0.308148
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ 34.0000 1.30673 0.653363 0.757045i $$-0.273358\pi$$
0.653363 + 0.757045i $$0.273358\pi$$
$$678$$ 6.00000 0.230429
$$679$$ −4.00000 −0.153506
$$680$$ 0 0
$$681$$ −20.0000 −0.766402
$$682$$ −4.00000 −0.153168
$$683$$ −4.00000 −0.153056 −0.0765279 0.997067i $$-0.524383\pi$$
−0.0765279 + 0.997067i $$0.524383\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 20.0000 0.763604
$$687$$ −26.0000 −0.991962
$$688$$ 8.00000 0.304997
$$689$$ 8.00000 0.304776
$$690$$ 0 0
$$691$$ −4.00000 −0.152167 −0.0760836 0.997101i $$-0.524242\pi$$
−0.0760836 + 0.997101i $$0.524242\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 8.00000 0.303895
$$694$$ −4.00000 −0.151838
$$695$$ 0 0
$$696$$ 4.00000 0.151620
$$697$$ −36.0000 −1.36360
$$698$$ 2.00000 0.0757011
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ 50.0000 1.88847 0.944237 0.329267i $$-0.106802\pi$$
0.944237 + 0.329267i $$0.106802\pi$$
$$702$$ 4.00000 0.150970
$$703$$ 0 0
$$704$$ −4.00000 −0.150756
$$705$$ 0 0
$$706$$ −10.0000 −0.376355
$$707$$ −28.0000 −1.05305
$$708$$ 6.00000 0.225494
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ −8.00000 −0.299813
$$713$$ 0 0
$$714$$ −12.0000 −0.449089
$$715$$ 0 0
$$716$$ −4.00000 −0.149487
$$717$$ 20.0000 0.746914
$$718$$ 30.0000 1.11959
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 0 0
$$721$$ 28.0000 1.04277
$$722$$ −19.0000 −0.707107
$$723$$ 10.0000 0.371904
$$724$$ 18.0000 0.668965
$$725$$ 0 0
$$726$$ 5.00000 0.185567
$$727$$ 30.0000 1.11264 0.556319 0.830969i $$-0.312213\pi$$
0.556319 + 0.830969i $$0.312213\pi$$
$$728$$ −8.00000 −0.296500
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 48.0000 1.77534
$$732$$ 10.0000 0.369611
$$733$$ 26.0000 0.960332 0.480166 0.877178i $$-0.340576\pi$$
0.480166 + 0.877178i $$0.340576\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −40.0000 −1.47342
$$738$$ −6.00000 −0.220863
$$739$$ −44.0000 −1.61857 −0.809283 0.587419i $$-0.800144\pi$$
−0.809283 + 0.587419i $$0.800144\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −4.00000 −0.146845
$$743$$ −8.00000 −0.293492 −0.146746 0.989174i $$-0.546880\pi$$
−0.146746 + 0.989174i $$0.546880\pi$$
$$744$$ 1.00000 0.0366618
$$745$$ 0 0
$$746$$ −18.0000 −0.659027
$$747$$ 4.00000 0.146352
$$748$$ −24.0000 −0.877527
$$749$$ −32.0000 −1.16925
$$750$$ 0 0
$$751$$ 16.0000 0.583848 0.291924 0.956441i $$-0.405705\pi$$
0.291924 + 0.956441i $$0.405705\pi$$
$$752$$ 12.0000 0.437595
$$753$$ −28.0000 −1.02038
$$754$$ 16.0000 0.582686
$$755$$ 0 0
$$756$$ −2.00000 −0.0727393
$$757$$ 12.0000 0.436147 0.218074 0.975932i $$-0.430023\pi$$
0.218074 + 0.975932i $$0.430023\pi$$
$$758$$ −8.00000 −0.290573
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 36.0000 1.30500 0.652499 0.757789i $$-0.273720\pi$$
0.652499 + 0.757789i $$0.273720\pi$$
$$762$$ 12.0000 0.434714
$$763$$ −36.0000 −1.30329
$$764$$ −10.0000 −0.361787
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ 24.0000 0.866590
$$768$$ 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
$$771$$ 2.00000 0.0720282
$$772$$ 2.00000 0.0719816
$$773$$ −6.00000 −0.215805 −0.107903 0.994161i $$-0.534413\pi$$
−0.107903 + 0.994161i $$0.534413\pi$$
$$774$$ 8.00000 0.287554
$$775$$ 0 0
$$776$$ 2.00000 0.0717958
$$777$$ 8.00000 0.286998
$$778$$ 36.0000 1.29066
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 56.0000 2.00384
$$782$$ 0 0
$$783$$ 4.00000 0.142948
$$784$$ −3.00000 −0.107143
$$785$$ 0 0
$$786$$ 14.0000 0.499363
$$787$$ −20.0000 −0.712923 −0.356462 0.934310i $$-0.616017\pi$$
−0.356462 + 0.934310i $$0.616017\pi$$
$$788$$ −2.00000 −0.0712470
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ −12.0000 −0.426671
$$792$$ −4.00000 −0.142134
$$793$$ 40.0000 1.42044
$$794$$ 18.0000 0.638796
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 6.00000 0.212531 0.106265 0.994338i $$-0.466111\pi$$
0.106265 + 0.994338i $$0.466111\pi$$
$$798$$ 0 0
$$799$$ 72.0000 2.54718
$$800$$ 0 0
$$801$$ −8.00000 −0.282666
$$802$$ −4.00000 −0.141245
$$803$$ 16.0000 0.564628
$$804$$ 10.0000 0.352673
$$805$$ 0 0
$$806$$ 4.00000 0.140894
$$807$$ −12.0000 −0.422420
$$808$$ 14.0000 0.492518
$$809$$ 20.0000 0.703163 0.351581 0.936157i $$-0.385644\pi$$
0.351581 + 0.936157i $$0.385644\pi$$
$$810$$ 0 0
$$811$$ −40.0000 −1.40459 −0.702295 0.711886i $$-0.747841\pi$$
−0.702295 + 0.711886i $$0.747841\pi$$
$$812$$ −8.00000 −0.280745
$$813$$ −24.0000 −0.841717
$$814$$ 16.0000 0.560800
$$815$$ 0 0
$$816$$ 6.00000 0.210042
$$817$$ 0 0
$$818$$ 6.00000 0.209785
$$819$$ −8.00000 −0.279543
$$820$$ 0 0
$$821$$ 12.0000 0.418803 0.209401 0.977830i $$-0.432848\pi$$
0.209401 + 0.977830i $$0.432848\pi$$
$$822$$ 18.0000 0.627822
$$823$$ 4.00000 0.139431 0.0697156 0.997567i $$-0.477791\pi$$
0.0697156 + 0.997567i $$0.477791\pi$$
$$824$$ −14.0000 −0.487713
$$825$$ 0 0
$$826$$ −12.0000 −0.417533
$$827$$ 4.00000 0.139094 0.0695468 0.997579i $$-0.477845\pi$$
0.0695468 + 0.997579i $$0.477845\pi$$
$$828$$ 0 0
$$829$$ 2.00000 0.0694629 0.0347314 0.999397i $$-0.488942\pi$$
0.0347314 + 0.999397i $$0.488942\pi$$
$$830$$ 0 0
$$831$$ 8.00000 0.277517
$$832$$ 4.00000 0.138675
$$833$$ −18.0000 −0.623663
$$834$$ −12.0000 −0.415526
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 1.00000 0.0345651
$$838$$ −30.0000 −1.03633
$$839$$ −34.0000 −1.17381 −0.586905 0.809656i $$-0.699654\pi$$
−0.586905 + 0.809656i $$0.699654\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ −30.0000 −1.03387
$$843$$ 6.00000 0.206651
$$844$$ 16.0000 0.550743
$$845$$ 0 0
$$846$$ 12.0000 0.412568
$$847$$ −10.0000 −0.343604
$$848$$ 2.00000 0.0686803
$$849$$ −14.0000 −0.480479
$$850$$ 0 0
$$851$$ 0 0
$$852$$ −14.0000 −0.479632
$$853$$ −30.0000 −1.02718 −0.513590 0.858036i $$-0.671685\pi$$
−0.513590 + 0.858036i $$0.671685\pi$$
$$854$$ −20.0000 −0.684386
$$855$$ 0 0
$$856$$ 16.0000 0.546869
$$857$$ −42.0000 −1.43469 −0.717346 0.696717i $$-0.754643\pi$$
−0.717346 + 0.696717i $$0.754643\pi$$
$$858$$ −16.0000 −0.546231
$$859$$ 28.0000 0.955348 0.477674 0.878537i $$-0.341480\pi$$
0.477674 + 0.878537i $$0.341480\pi$$
$$860$$ 0 0
$$861$$ 12.0000 0.408959
$$862$$ −10.0000 −0.340601
$$863$$ 24.0000 0.816970 0.408485 0.912765i $$-0.366057\pi$$
0.408485 + 0.912765i $$0.366057\pi$$
$$864$$ 1.00000 0.0340207
$$865$$ 0 0
$$866$$ 4.00000 0.135926
$$867$$ 19.0000 0.645274
$$868$$ −2.00000 −0.0678844
$$869$$ 32.0000 1.08553
$$870$$ 0 0
$$871$$ 40.0000 1.35535
$$872$$ 18.0000 0.609557
$$873$$ 2.00000 0.0676897
$$874$$ 0 0
$$875$$ 0 0
$$876$$ −4.00000 −0.135147
$$877$$ 18.0000 0.607817 0.303908 0.952701i $$-0.401708\pi$$
0.303908 + 0.952701i $$0.401708\pi$$
$$878$$ 24.0000 0.809961
$$879$$ −26.0000 −0.876958
$$880$$ 0 0
$$881$$ −56.0000 −1.88669 −0.943344 0.331816i $$-0.892339\pi$$
−0.943344 + 0.331816i $$0.892339\pi$$
$$882$$ −3.00000 −0.101015
$$883$$ 20.0000 0.673054 0.336527 0.941674i $$-0.390748\pi$$
0.336527 + 0.941674i $$0.390748\pi$$
$$884$$ 24.0000 0.807207
$$885$$ 0 0
$$886$$ 12.0000 0.403148
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ −4.00000 −0.134231
$$889$$ −24.0000 −0.804934
$$890$$ 0 0
$$891$$ −4.00000 −0.134005
$$892$$ −16.0000 −0.535720
$$893$$ 0 0
$$894$$ 14.0000 0.468230
$$895$$ 0 0
$$896$$ −2.00000 −0.0668153
$$897$$ 0 0
$$898$$ 20.0000 0.667409
$$899$$ 4.00000 0.133407
$$900$$ 0 0
$$901$$ 12.0000 0.399778
$$902$$ 24.0000 0.799113
$$903$$ −16.0000 −0.532447
$$904$$ 6.00000 0.199557
$$905$$ 0 0
$$906$$ −16.0000 −0.531564
$$907$$ −58.0000 −1.92586 −0.962929 0.269754i $$-0.913058\pi$$
−0.962929 + 0.269754i $$0.913058\pi$$
$$908$$ −20.0000 −0.663723
$$909$$ 14.0000 0.464351
$$910$$ 0 0
$$911$$ 8.00000 0.265052 0.132526 0.991180i $$-0.457691\pi$$
0.132526 + 0.991180i $$0.457691\pi$$
$$912$$ 0 0
$$913$$ −16.0000 −0.529523
$$914$$ 4.00000 0.132308
$$915$$ 0 0
$$916$$ −26.0000 −0.859064
$$917$$ −28.0000 −0.924641
$$918$$ 6.00000 0.198030
$$919$$ −36.0000 −1.18753 −0.593765 0.804638i $$-0.702359\pi$$
−0.593765 + 0.804638i $$0.702359\pi$$
$$920$$ 0 0
$$921$$ −2.00000 −0.0659022
$$922$$ 24.0000 0.790398
$$923$$ −56.0000 −1.84326
$$924$$ 8.00000 0.263181
$$925$$ 0 0
$$926$$ −12.0000 −0.394344
$$927$$ −14.0000 −0.459820
$$928$$ 4.00000 0.131306
$$929$$ 24.0000 0.787414 0.393707 0.919236i $$-0.371192\pi$$
0.393707 + 0.919236i $$0.371192\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −6.00000 −0.196537
$$933$$ 6.00000 0.196431
$$934$$ 24.0000 0.785304
$$935$$ 0 0
$$936$$ 4.00000 0.130744
$$937$$ 2.00000 0.0653372 0.0326686 0.999466i $$-0.489599\pi$$
0.0326686 + 0.999466i $$0.489599\pi$$
$$938$$ −20.0000 −0.653023
$$939$$ 4.00000 0.130535
$$940$$ 0 0
$$941$$ 12.0000 0.391189 0.195594 0.980685i $$-0.437336\pi$$
0.195594 + 0.980685i $$0.437336\pi$$
$$942$$ 6.00000 0.195491
$$943$$ 0 0
$$944$$ 6.00000 0.195283
$$945$$ 0 0
$$946$$ −32.0000 −1.04041
$$947$$ 28.0000 0.909878 0.454939 0.890523i $$-0.349661\pi$$
0.454939 + 0.890523i $$0.349661\pi$$
$$948$$ −8.00000 −0.259828
$$949$$ −16.0000 −0.519382
$$950$$ 0 0
$$951$$ −26.0000 −0.843108
$$952$$ −12.0000 −0.388922
$$953$$ 50.0000 1.61966 0.809829 0.586665i $$-0.199560\pi$$
0.809829 + 0.586665i $$0.199560\pi$$
$$954$$ 2.00000 0.0647524
$$955$$ 0 0
$$956$$ 20.0000 0.646846
$$957$$ −16.0000 −0.517207
$$958$$ −14.0000 −0.452319
$$959$$ −36.0000 −1.16250
$$960$$ 0 0
$$961$$ 1.00000 0.0322581
$$962$$ −16.0000 −0.515861
$$963$$ 16.0000 0.515593
$$964$$ 10.0000 0.322078
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 40.0000 1.28631 0.643157 0.765735i $$-0.277624\pi$$
0.643157 + 0.765735i $$0.277624\pi$$
$$968$$ 5.00000 0.160706
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −6.00000 −0.192549 −0.0962746 0.995355i $$-0.530693\pi$$
−0.0962746 + 0.995355i $$0.530693\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 24.0000 0.769405
$$974$$ 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 $$0.340676\pi$$
$$978$$ −6.00000 −0.191859
$$979$$ 32.0000 1.02272
$$980$$ 0 0
$$981$$ 18.0000 0.574696
$$982$$ 0 0
$$983$$ −24.0000 −0.765481 −0.382741 0.923856i $$-0.625020\pi$$
−0.382741 + 0.923856i $$0.625020\pi$$
$$984$$ −6.00000 −0.191273
$$985$$ 0 0
$$986$$ 24.0000 0.764316
$$987$$ −24.0000 −0.763928
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 8.00000 0.254128 0.127064 0.991894i $$-0.459445\pi$$
0.127064 + 0.991894i $$0.459445\pi$$
$$992$$ 1.00000 0.0317500
$$993$$ −28.0000 −0.888553
$$994$$ 28.0000 0.888106
$$995$$ 0 0
$$996$$ 4.00000 0.126745
$$997$$ −18.0000 −0.570066 −0.285033 0.958518i $$-0.592005\pi$$
−0.285033 + 0.958518i $$0.592005\pi$$
$$998$$ −4.00000 −0.126618
$$999$$ −4.00000 −0.126554
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4650.2.a.bl.1.1 1
5.2 odd 4 4650.2.d.p.3349.2 2
5.3 odd 4 4650.2.d.p.3349.1 2
5.4 even 2 930.2.a.d.1.1 1
15.14 odd 2 2790.2.a.t.1.1 1
20.19 odd 2 7440.2.a.y.1.1 1

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