# Properties

 Label 1134.2.a.h.1.1 Level $1134$ Weight $2$ Character 1134.1 Self dual yes Analytic conductor $9.055$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1134.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{10} +6.00000 q^{11} +2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -7.00000 q^{19} +3.00000 q^{20} +6.00000 q^{22} -3.00000 q^{23} +4.00000 q^{25} +2.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} +2.00000 q^{31} +1.00000 q^{32} -6.00000 q^{34} +3.00000 q^{35} +2.00000 q^{37} -7.00000 q^{38} +3.00000 q^{40} +2.00000 q^{43} +6.00000 q^{44} -3.00000 q^{46} +1.00000 q^{49} +4.00000 q^{50} +2.00000 q^{52} -6.00000 q^{53} +18.0000 q^{55} +1.00000 q^{56} -6.00000 q^{58} +5.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +8.00000 q^{67} -6.00000 q^{68} +3.00000 q^{70} -3.00000 q^{71} +2.00000 q^{73} +2.00000 q^{74} -7.00000 q^{76} +6.00000 q^{77} +5.00000 q^{79} +3.00000 q^{80} -12.0000 q^{83} -18.0000 q^{85} +2.00000 q^{86} +6.00000 q^{88} +2.00000 q^{91} -3.00000 q^{92} -21.0000 q^{95} +2.00000 q^{97} +1.00000 q^{98} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 3.00000 1.34164 0.670820 0.741620i $$-0.265942\pi$$
0.670820 + 0.741620i $$0.265942\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 3.00000 0.948683
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 0 0
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ −7.00000 −1.60591 −0.802955 0.596040i $$-0.796740\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 3.00000 0.670820
$$21$$ 0 0
$$22$$ 6.00000 1.27920
$$23$$ −3.00000 −0.625543 −0.312772 0.949828i $$-0.601257\pi$$
−0.312772 + 0.949828i $$0.601257\pi$$
$$24$$ 0 0
$$25$$ 4.00000 0.800000
$$26$$ 2.00000 0.392232
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −6.00000 −1.02899
$$35$$ 3.00000 0.507093
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ −7.00000 −1.13555
$$39$$ 0 0
$$40$$ 3.00000 0.474342
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 6.00000 0.904534
$$45$$ 0 0
$$46$$ −3.00000 −0.442326
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 4.00000 0.565685
$$51$$ 0 0
$$52$$ 2.00000 0.277350
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 18.0000 2.42712
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ −6.00000 −0.787839
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 5.00000 0.640184 0.320092 0.947386i $$-0.396286\pi$$
0.320092 + 0.947386i $$0.396286\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 0.744208
$$66$$ 0 0
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ −6.00000 −0.727607
$$69$$ 0 0
$$70$$ 3.00000 0.358569
$$71$$ −3.00000 −0.356034 −0.178017 0.984027i $$-0.556968\pi$$
−0.178017 + 0.984027i $$0.556968\pi$$
$$72$$ 0 0
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ 2.00000 0.232495
$$75$$ 0 0
$$76$$ −7.00000 −0.802955
$$77$$ 6.00000 0.683763
$$78$$ 0 0
$$79$$ 5.00000 0.562544 0.281272 0.959628i $$-0.409244\pi$$
0.281272 + 0.959628i $$0.409244\pi$$
$$80$$ 3.00000 0.335410
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ −18.0000 −1.95237
$$86$$ 2.00000 0.215666
$$87$$ 0 0
$$88$$ 6.00000 0.639602
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ −3.00000 −0.312772
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −21.0000 −2.15455
$$96$$ 0 0
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ 4.00000 0.400000
$$101$$ −9.00000 −0.895533 −0.447767 0.894150i $$-0.647781\pi$$
−0.447767 + 0.894150i $$0.647781\pi$$
$$102$$ 0 0
$$103$$ −10.0000 −0.985329 −0.492665 0.870219i $$-0.663977\pi$$
−0.492665 + 0.870219i $$0.663977\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 18.0000 1.71623
$$111$$ 0 0
$$112$$ 1.00000 0.0944911
$$113$$ −15.0000 −1.41108 −0.705541 0.708669i $$-0.749296\pi$$
−0.705541 + 0.708669i $$0.749296\pi$$
$$114$$ 0 0
$$115$$ −9.00000 −0.839254
$$116$$ −6.00000 −0.557086
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −6.00000 −0.550019
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 5.00000 0.452679
$$123$$ 0 0
$$124$$ 2.00000 0.179605
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ 17.0000 1.50851 0.754253 0.656584i $$-0.227999\pi$$
0.754253 + 0.656584i $$0.227999\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 6.00000 0.526235
$$131$$ 9.00000 0.786334 0.393167 0.919467i $$-0.371379\pi$$
0.393167 + 0.919467i $$0.371379\pi$$
$$132$$ 0 0
$$133$$ −7.00000 −0.606977
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 0 0
$$139$$ 5.00000 0.424094 0.212047 0.977259i $$-0.431987\pi$$
0.212047 + 0.977259i $$0.431987\pi$$
$$140$$ 3.00000 0.253546
$$141$$ 0 0
$$142$$ −3.00000 −0.251754
$$143$$ 12.0000 1.00349
$$144$$ 0 0
$$145$$ −18.0000 −1.49482
$$146$$ 2.00000 0.165521
$$147$$ 0 0
$$148$$ 2.00000 0.164399
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 23.0000 1.87171 0.935857 0.352381i $$-0.114628\pi$$
0.935857 + 0.352381i $$0.114628\pi$$
$$152$$ −7.00000 −0.567775
$$153$$ 0 0
$$154$$ 6.00000 0.483494
$$155$$ 6.00000 0.481932
$$156$$ 0 0
$$157$$ −13.0000 −1.03751 −0.518756 0.854922i $$-0.673605\pi$$
−0.518756 + 0.854922i $$0.673605\pi$$
$$158$$ 5.00000 0.397779
$$159$$ 0 0
$$160$$ 3.00000 0.237171
$$161$$ −3.00000 −0.236433
$$162$$ 0 0
$$163$$ 2.00000 0.156652 0.0783260 0.996928i $$-0.475042\pi$$
0.0783260 + 0.996928i $$0.475042\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −12.0000 −0.931381
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ −18.0000 −1.38054
$$171$$ 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
$$175$$ 4.00000 0.302372
$$176$$ 6.00000 0.452267
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −18.0000 −1.34538 −0.672692 0.739923i $$-0.734862\pi$$
−0.672692 + 0.739923i $$0.734862\pi$$
$$180$$ 0 0
$$181$$ −25.0000 −1.85824 −0.929118 0.369784i $$-0.879432\pi$$
−0.929118 + 0.369784i $$0.879432\pi$$
$$182$$ 2.00000 0.148250
$$183$$ 0 0
$$184$$ −3.00000 −0.221163
$$185$$ 6.00000 0.441129
$$186$$ 0 0
$$187$$ −36.0000 −2.63258
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −21.0000 −1.52350
$$191$$ 9.00000 0.651217 0.325609 0.945505i $$-0.394431\pi$$
0.325609 + 0.945505i $$0.394431\pi$$
$$192$$ 0 0
$$193$$ 17.0000 1.22369 0.611843 0.790979i $$-0.290428\pi$$
0.611843 + 0.790979i $$0.290428\pi$$
$$194$$ 2.00000 0.143592
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 14.0000 0.992434 0.496217 0.868199i $$-0.334722\pi$$
0.496217 + 0.868199i $$0.334722\pi$$
$$200$$ 4.00000 0.282843
$$201$$ 0 0
$$202$$ −9.00000 −0.633238
$$203$$ −6.00000 −0.421117
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −10.0000 −0.696733
$$207$$ 0 0
$$208$$ 2.00000 0.138675
$$209$$ −42.0000 −2.90520
$$210$$ 0 0
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 0 0
$$214$$ 12.0000 0.820303
$$215$$ 6.00000 0.409197
$$216$$ 0 0
$$217$$ 2.00000 0.135769
$$218$$ −10.0000 −0.677285
$$219$$ 0 0
$$220$$ 18.0000 1.21356
$$221$$ −12.0000 −0.807207
$$222$$ 0 0
$$223$$ −28.0000 −1.87502 −0.937509 0.347960i $$-0.886874\pi$$
−0.937509 + 0.347960i $$0.886874\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −15.0000 −0.997785
$$227$$ 15.0000 0.995585 0.497792 0.867296i $$-0.334144\pi$$
0.497792 + 0.867296i $$0.334144\pi$$
$$228$$ 0 0
$$229$$ −1.00000 −0.0660819 −0.0330409 0.999454i $$-0.510519\pi$$
−0.0330409 + 0.999454i $$0.510519\pi$$
$$230$$ −9.00000 −0.593442
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ −9.00000 −0.589610 −0.294805 0.955557i $$-0.595255\pi$$
−0.294805 + 0.955557i $$0.595255\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ −6.00000 −0.388922
$$239$$ 15.0000 0.970269 0.485135 0.874439i $$-0.338771\pi$$
0.485135 + 0.874439i $$0.338771\pi$$
$$240$$ 0 0
$$241$$ 8.00000 0.515325 0.257663 0.966235i $$-0.417048\pi$$
0.257663 + 0.966235i $$0.417048\pi$$
$$242$$ 25.0000 1.60706
$$243$$ 0 0
$$244$$ 5.00000 0.320092
$$245$$ 3.00000 0.191663
$$246$$ 0 0
$$247$$ −14.0000 −0.890799
$$248$$ 2.00000 0.127000
$$249$$ 0 0
$$250$$ −3.00000 −0.189737
$$251$$ −3.00000 −0.189358 −0.0946792 0.995508i $$-0.530183\pi$$
−0.0946792 + 0.995508i $$0.530183\pi$$
$$252$$ 0 0
$$253$$ −18.0000 −1.13165
$$254$$ 17.0000 1.06667
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ 2.00000 0.124274
$$260$$ 6.00000 0.372104
$$261$$ 0 0
$$262$$ 9.00000 0.556022
$$263$$ 21.0000 1.29492 0.647458 0.762101i $$-0.275832\pi$$
0.647458 + 0.762101i $$0.275832\pi$$
$$264$$ 0 0
$$265$$ −18.0000 −1.10573
$$266$$ −7.00000 −0.429198
$$267$$ 0 0
$$268$$ 8.00000 0.488678
$$269$$ 9.00000 0.548740 0.274370 0.961624i $$-0.411531\pi$$
0.274370 + 0.961624i $$0.411531\pi$$
$$270$$ 0 0
$$271$$ −28.0000 −1.70088 −0.850439 0.526073i $$-0.823664\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ −6.00000 −0.363803
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ 24.0000 1.44725
$$276$$ 0 0
$$277$$ −16.0000 −0.961347 −0.480673 0.876900i $$-0.659608\pi$$
−0.480673 + 0.876900i $$0.659608\pi$$
$$278$$ 5.00000 0.299880
$$279$$ 0 0
$$280$$ 3.00000 0.179284
$$281$$ 27.0000 1.61068 0.805342 0.592810i $$-0.201981\pi$$
0.805342 + 0.592810i $$0.201981\pi$$
$$282$$ 0 0
$$283$$ −19.0000 −1.12943 −0.564716 0.825285i $$-0.691014\pi$$
−0.564716 + 0.825285i $$0.691014\pi$$
$$284$$ −3.00000 −0.178017
$$285$$ 0 0
$$286$$ 12.0000 0.709575
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ −18.0000 −1.05700
$$291$$ 0 0
$$292$$ 2.00000 0.117041
$$293$$ 3.00000 0.175262 0.0876309 0.996153i $$-0.472070\pi$$
0.0876309 + 0.996153i $$0.472070\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 2.00000 0.116248
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ 2.00000 0.115278
$$302$$ 23.0000 1.32350
$$303$$ 0 0
$$304$$ −7.00000 −0.401478
$$305$$ 15.0000 0.858898
$$306$$ 0 0
$$307$$ −25.0000 −1.42683 −0.713413 0.700744i $$-0.752851\pi$$
−0.713413 + 0.700744i $$0.752851\pi$$
$$308$$ 6.00000 0.341882
$$309$$ 0 0
$$310$$ 6.00000 0.340777
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ −13.0000 −0.733632
$$315$$ 0 0
$$316$$ 5.00000 0.281272
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ −36.0000 −2.01561
$$320$$ 3.00000 0.167705
$$321$$ 0 0
$$322$$ −3.00000 −0.167183
$$323$$ 42.0000 2.33694
$$324$$ 0 0
$$325$$ 8.00000 0.443760
$$326$$ 2.00000 0.110770
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 26.0000 1.42909 0.714545 0.699590i $$-0.246634\pi$$
0.714545 + 0.699590i $$0.246634\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 24.0000 1.31126
$$336$$ 0 0
$$337$$ −22.0000 −1.19842 −0.599208 0.800593i $$-0.704518\pi$$
−0.599208 + 0.800593i $$0.704518\pi$$
$$338$$ −9.00000 −0.489535
$$339$$ 0 0
$$340$$ −18.0000 −0.976187
$$341$$ 12.0000 0.649836
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 2.00000 0.107833
$$345$$ 0 0
$$346$$ 6.00000 0.322562
$$347$$ 24.0000 1.28839 0.644194 0.764862i $$-0.277193\pi$$
0.644194 + 0.764862i $$0.277193\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ 6.00000 0.319801
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 0 0
$$355$$ −9.00000 −0.477670
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −18.0000 −0.951330
$$359$$ 3.00000 0.158334 0.0791670 0.996861i $$-0.474774\pi$$
0.0791670 + 0.996861i $$0.474774\pi$$
$$360$$ 0 0
$$361$$ 30.0000 1.57895
$$362$$ −25.0000 −1.31397
$$363$$ 0 0
$$364$$ 2.00000 0.104828
$$365$$ 6.00000 0.314054
$$366$$ 0 0
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ −3.00000 −0.156386
$$369$$ 0 0
$$370$$ 6.00000 0.311925
$$371$$ −6.00000 −0.311504
$$372$$ 0 0
$$373$$ 14.0000 0.724893 0.362446 0.932005i $$-0.381942\pi$$
0.362446 + 0.932005i $$0.381942\pi$$
$$374$$ −36.0000 −1.86152
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ 2.00000 0.102733 0.0513665 0.998680i $$-0.483642\pi$$
0.0513665 + 0.998680i $$0.483642\pi$$
$$380$$ −21.0000 −1.07728
$$381$$ 0 0
$$382$$ 9.00000 0.460480
$$383$$ 18.0000 0.919757 0.459879 0.887982i $$-0.347893\pi$$
0.459879 + 0.887982i $$0.347893\pi$$
$$384$$ 0 0
$$385$$ 18.0000 0.917365
$$386$$ 17.0000 0.865277
$$387$$ 0 0
$$388$$ 2.00000 0.101535
$$389$$ −24.0000 −1.21685 −0.608424 0.793612i $$-0.708198\pi$$
−0.608424 + 0.793612i $$0.708198\pi$$
$$390$$ 0 0
$$391$$ 18.0000 0.910299
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ −18.0000 −0.906827
$$395$$ 15.0000 0.754732
$$396$$ 0 0
$$397$$ 26.0000 1.30490 0.652451 0.757831i $$-0.273741\pi$$
0.652451 + 0.757831i $$0.273741\pi$$
$$398$$ 14.0000 0.701757
$$399$$ 0 0
$$400$$ 4.00000 0.200000
$$401$$ −3.00000 −0.149813 −0.0749064 0.997191i $$-0.523866\pi$$
−0.0749064 + 0.997191i $$0.523866\pi$$
$$402$$ 0 0
$$403$$ 4.00000 0.199254
$$404$$ −9.00000 −0.447767
$$405$$ 0 0
$$406$$ −6.00000 −0.297775
$$407$$ 12.0000 0.594818
$$408$$ 0 0
$$409$$ 32.0000 1.58230 0.791149 0.611623i $$-0.209483\pi$$
0.791149 + 0.611623i $$0.209483\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −10.0000 −0.492665
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −36.0000 −1.76717
$$416$$ 2.00000 0.0980581
$$417$$ 0 0
$$418$$ −42.0000 −2.05429
$$419$$ −15.0000 −0.732798 −0.366399 0.930458i $$-0.619409\pi$$
−0.366399 + 0.930458i $$0.619409\pi$$
$$420$$ 0 0
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ 8.00000 0.389434
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ −24.0000 −1.16417
$$426$$ 0 0
$$427$$ 5.00000 0.241967
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 6.00000 0.289346
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 2.00000 0.0960031
$$435$$ 0 0
$$436$$ −10.0000 −0.478913
$$437$$ 21.0000 1.00457
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 18.0000 0.858116
$$441$$ 0 0
$$442$$ −12.0000 −0.570782
$$443$$ −18.0000 −0.855206 −0.427603 0.903967i $$-0.640642\pi$$
−0.427603 + 0.903967i $$0.640642\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −28.0000 −1.32584
$$447$$ 0 0
$$448$$ 1.00000 0.0472456
$$449$$ −33.0000 −1.55737 −0.778683 0.627417i $$-0.784112\pi$$
−0.778683 + 0.627417i $$0.784112\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −15.0000 −0.705541
$$453$$ 0 0
$$454$$ 15.0000 0.703985
$$455$$ 6.00000 0.281284
$$456$$ 0 0
$$457$$ 29.0000 1.35656 0.678281 0.734802i $$-0.262725\pi$$
0.678281 + 0.734802i $$0.262725\pi$$
$$458$$ −1.00000 −0.0467269
$$459$$ 0 0
$$460$$ −9.00000 −0.419627
$$461$$ 33.0000 1.53696 0.768482 0.639872i $$-0.221013\pi$$
0.768482 + 0.639872i $$0.221013\pi$$
$$462$$ 0 0
$$463$$ −13.0000 −0.604161 −0.302081 0.953282i $$-0.597681\pi$$
−0.302081 + 0.953282i $$0.597681\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 0 0
$$466$$ −9.00000 −0.416917
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ 0 0
$$469$$ 8.00000 0.369406
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 12.0000 0.551761
$$474$$ 0 0
$$475$$ −28.0000 −1.28473
$$476$$ −6.00000 −0.275010
$$477$$ 0 0
$$478$$ 15.0000 0.686084
$$479$$ 6.00000 0.274147 0.137073 0.990561i $$-0.456230\pi$$
0.137073 + 0.990561i $$0.456230\pi$$
$$480$$ 0 0
$$481$$ 4.00000 0.182384
$$482$$ 8.00000 0.364390
$$483$$ 0 0
$$484$$ 25.0000 1.13636
$$485$$ 6.00000 0.272446
$$486$$ 0 0
$$487$$ 29.0000 1.31412 0.657058 0.753840i $$-0.271801\pi$$
0.657058 + 0.753840i $$0.271801\pi$$
$$488$$ 5.00000 0.226339
$$489$$ 0 0
$$490$$ 3.00000 0.135526
$$491$$ −18.0000 −0.812329 −0.406164 0.913800i $$-0.633134\pi$$
−0.406164 + 0.913800i $$0.633134\pi$$
$$492$$ 0 0
$$493$$ 36.0000 1.62136
$$494$$ −14.0000 −0.629890
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ −3.00000 −0.134568
$$498$$ 0 0
$$499$$ 32.0000 1.43252 0.716258 0.697835i $$-0.245853\pi$$
0.716258 + 0.697835i $$0.245853\pi$$
$$500$$ −3.00000 −0.134164
$$501$$ 0 0
$$502$$ −3.00000 −0.133897
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ −27.0000 −1.20148
$$506$$ −18.0000 −0.800198
$$507$$ 0 0
$$508$$ 17.0000 0.754253
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 0 0
$$511$$ 2.00000 0.0884748
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −18.0000 −0.793946
$$515$$ −30.0000 −1.32196
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 2.00000 0.0878750
$$519$$ 0 0
$$520$$ 6.00000 0.263117
$$521$$ −24.0000 −1.05146 −0.525730 0.850652i $$-0.676208\pi$$
−0.525730 + 0.850652i $$0.676208\pi$$
$$522$$ 0 0
$$523$$ −13.0000 −0.568450 −0.284225 0.958758i $$-0.591736\pi$$
−0.284225 + 0.958758i $$0.591736\pi$$
$$524$$ 9.00000 0.393167
$$525$$ 0 0
$$526$$ 21.0000 0.915644
$$527$$ −12.0000 −0.522728
$$528$$ 0 0
$$529$$ −14.0000 −0.608696
$$530$$ −18.0000 −0.781870
$$531$$ 0 0
$$532$$ −7.00000 −0.303488
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 36.0000 1.55642
$$536$$ 8.00000 0.345547
$$537$$ 0 0
$$538$$ 9.00000 0.388018
$$539$$ 6.00000 0.258438
$$540$$ 0 0
$$541$$ 38.0000 1.63375 0.816874 0.576816i $$-0.195705\pi$$
0.816874 + 0.576816i $$0.195705\pi$$
$$542$$ −28.0000 −1.20270
$$543$$ 0 0
$$544$$ −6.00000 −0.257248
$$545$$ −30.0000 −1.28506
$$546$$ 0 0
$$547$$ 32.0000 1.36822 0.684111 0.729378i $$-0.260191\pi$$
0.684111 + 0.729378i $$0.260191\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 0 0
$$550$$ 24.0000 1.02336
$$551$$ 42.0000 1.78926
$$552$$ 0 0
$$553$$ 5.00000 0.212622
$$554$$ −16.0000 −0.679775
$$555$$ 0 0
$$556$$ 5.00000 0.212047
$$557$$ 24.0000 1.01691 0.508456 0.861088i $$-0.330216\pi$$
0.508456 + 0.861088i $$0.330216\pi$$
$$558$$ 0 0
$$559$$ 4.00000 0.169182
$$560$$ 3.00000 0.126773
$$561$$ 0 0
$$562$$ 27.0000 1.13893
$$563$$ 33.0000 1.39078 0.695392 0.718631i $$-0.255231\pi$$
0.695392 + 0.718631i $$0.255231\pi$$
$$564$$ 0 0
$$565$$ −45.0000 −1.89316
$$566$$ −19.0000 −0.798630
$$567$$ 0 0
$$568$$ −3.00000 −0.125877
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ 12.0000 0.501745
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −12.0000 −0.500435
$$576$$ 0 0
$$577$$ −4.00000 −0.166522 −0.0832611 0.996528i $$-0.526534\pi$$
−0.0832611 + 0.996528i $$0.526534\pi$$
$$578$$ 19.0000 0.790296
$$579$$ 0 0
$$580$$ −18.0000 −0.747409
$$581$$ −12.0000 −0.497844
$$582$$ 0 0
$$583$$ −36.0000 −1.49097
$$584$$ 2.00000 0.0827606
$$585$$ 0 0
$$586$$ 3.00000 0.123929
$$587$$ 3.00000 0.123823 0.0619116 0.998082i $$-0.480280\pi$$
0.0619116 + 0.998082i $$0.480280\pi$$
$$588$$ 0 0
$$589$$ −14.0000 −0.576860
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 2.00000 0.0821995
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ −18.0000 −0.737928
$$596$$ 6.00000 0.245770
$$597$$ 0 0
$$598$$ −6.00000 −0.245358
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ 14.0000 0.571072 0.285536 0.958368i $$-0.407828\pi$$
0.285536 + 0.958368i $$0.407828\pi$$
$$602$$ 2.00000 0.0815139
$$603$$ 0 0
$$604$$ 23.0000 0.935857
$$605$$ 75.0000 3.04918
$$606$$ 0 0
$$607$$ −22.0000 −0.892952 −0.446476 0.894795i $$-0.647321\pi$$
−0.446476 + 0.894795i $$0.647321\pi$$
$$608$$ −7.00000 −0.283887
$$609$$ 0 0
$$610$$ 15.0000 0.607332
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 8.00000 0.323117 0.161558 0.986863i $$-0.448348\pi$$
0.161558 + 0.986863i $$0.448348\pi$$
$$614$$ −25.0000 −1.00892
$$615$$ 0 0
$$616$$ 6.00000 0.241747
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ 0 0
$$619$$ −7.00000 −0.281354 −0.140677 0.990056i $$-0.544928\pi$$
−0.140677 + 0.990056i $$0.544928\pi$$
$$620$$ 6.00000 0.240966
$$621$$ 0 0
$$622$$ −12.0000 −0.481156
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −29.0000 −1.16000
$$626$$ −10.0000 −0.399680
$$627$$ 0 0
$$628$$ −13.0000 −0.518756
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −7.00000 −0.278666 −0.139333 0.990246i $$-0.544496\pi$$
−0.139333 + 0.990246i $$0.544496\pi$$
$$632$$ 5.00000 0.198889
$$633$$ 0 0
$$634$$ −18.0000 −0.714871
$$635$$ 51.0000 2.02387
$$636$$ 0 0
$$637$$ 2.00000 0.0792429
$$638$$ −36.0000 −1.42525
$$639$$ 0 0
$$640$$ 3.00000 0.118585
$$641$$ −27.0000 −1.06644 −0.533218 0.845978i $$-0.679017\pi$$
−0.533218 + 0.845978i $$0.679017\pi$$
$$642$$ 0 0
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ −3.00000 −0.118217
$$645$$ 0 0
$$646$$ 42.0000 1.65247
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 8.00000 0.313786
$$651$$ 0 0
$$652$$ 2.00000 0.0783260
$$653$$ 36.0000 1.40879 0.704394 0.709809i $$-0.251219\pi$$
0.704394 + 0.709809i $$0.251219\pi$$
$$654$$ 0 0
$$655$$ 27.0000 1.05498
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −42.0000 −1.63609 −0.818044 0.575156i $$-0.804941\pi$$
−0.818044 + 0.575156i $$0.804941\pi$$
$$660$$ 0 0
$$661$$ 5.00000 0.194477 0.0972387 0.995261i $$-0.468999\pi$$
0.0972387 + 0.995261i $$0.468999\pi$$
$$662$$ 26.0000 1.01052
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ −21.0000 −0.814345
$$666$$ 0 0
$$667$$ 18.0000 0.696963
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 24.0000 0.927201
$$671$$ 30.0000 1.15814
$$672$$ 0 0
$$673$$ −37.0000 −1.42625 −0.713123 0.701039i $$-0.752720\pi$$
−0.713123 + 0.701039i $$0.752720\pi$$
$$674$$ −22.0000 −0.847408
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −42.0000 −1.61419 −0.807096 0.590421i $$-0.798962\pi$$
−0.807096 + 0.590421i $$0.798962\pi$$
$$678$$ 0 0
$$679$$ 2.00000 0.0767530
$$680$$ −18.0000 −0.690268
$$681$$ 0 0
$$682$$ 12.0000 0.459504
$$683$$ 6.00000 0.229584 0.114792 0.993390i $$-0.463380\pi$$
0.114792 + 0.993390i $$0.463380\pi$$
$$684$$ 0 0
$$685$$ −18.0000 −0.687745
$$686$$ 1.00000 0.0381802
$$687$$ 0 0
$$688$$ 2.00000 0.0762493
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ 47.0000 1.78796 0.893982 0.448103i $$-0.147900\pi$$
0.893982 + 0.448103i $$0.147900\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ 24.0000 0.911028
$$695$$ 15.0000 0.568982
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 26.0000 0.984115
$$699$$ 0 0
$$700$$ 4.00000 0.151186
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 0 0
$$703$$ −14.0000 −0.528020
$$704$$ 6.00000 0.226134
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ −9.00000 −0.338480
$$708$$ 0 0
$$709$$ −52.0000 −1.95290 −0.976450 0.215742i $$-0.930783\pi$$
−0.976450 + 0.215742i $$0.930783\pi$$
$$710$$ −9.00000 −0.337764
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −6.00000 −0.224702
$$714$$ 0 0
$$715$$ 36.0000 1.34632
$$716$$ −18.0000 −0.672692
$$717$$ 0 0
$$718$$ 3.00000 0.111959
$$719$$ 36.0000 1.34257 0.671287 0.741198i $$-0.265742\pi$$
0.671287 + 0.741198i $$0.265742\pi$$
$$720$$ 0 0
$$721$$ −10.0000 −0.372419
$$722$$ 30.0000 1.11648
$$723$$ 0 0
$$724$$ −25.0000 −0.929118
$$725$$ −24.0000 −0.891338
$$726$$ 0 0
$$727$$ 8.00000 0.296704 0.148352 0.988935i $$-0.452603\pi$$
0.148352 + 0.988935i $$0.452603\pi$$
$$728$$ 2.00000 0.0741249
$$729$$ 0 0
$$730$$ 6.00000 0.222070
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ 29.0000 1.07114 0.535570 0.844491i $$-0.320097\pi$$
0.535570 + 0.844491i $$0.320097\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ −3.00000 −0.110581
$$737$$ 48.0000 1.76810
$$738$$ 0 0
$$739$$ 26.0000 0.956425 0.478213 0.878244i $$-0.341285\pi$$
0.478213 + 0.878244i $$0.341285\pi$$
$$740$$ 6.00000 0.220564
$$741$$ 0 0
$$742$$ −6.00000 −0.220267
$$743$$ −36.0000 −1.32071 −0.660356 0.750953i $$-0.729595\pi$$
−0.660356 + 0.750953i $$0.729595\pi$$
$$744$$ 0 0
$$745$$ 18.0000 0.659469
$$746$$ 14.0000 0.512576
$$747$$ 0 0
$$748$$ −36.0000 −1.31629
$$749$$ 12.0000 0.438470
$$750$$ 0 0
$$751$$ −31.0000 −1.13121 −0.565603 0.824678i $$-0.691357\pi$$
−0.565603 + 0.824678i $$0.691357\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −12.0000 −0.437014
$$755$$ 69.0000 2.51117
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ 2.00000 0.0726433
$$759$$ 0 0
$$760$$ −21.0000 −0.761750
$$761$$ 42.0000 1.52250 0.761249 0.648459i $$-0.224586\pi$$
0.761249 + 0.648459i $$0.224586\pi$$
$$762$$ 0 0
$$763$$ −10.0000 −0.362024
$$764$$ 9.00000 0.325609
$$765$$ 0 0
$$766$$ 18.0000 0.650366
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 18.0000 0.648675
$$771$$ 0 0
$$772$$ 17.0000 0.611843
$$773$$ 51.0000 1.83434 0.917171 0.398493i $$-0.130467\pi$$
0.917171 + 0.398493i $$0.130467\pi$$
$$774$$ 0 0
$$775$$ 8.00000 0.287368
$$776$$ 2.00000 0.0717958
$$777$$ 0 0
$$778$$ −24.0000 −0.860442
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −18.0000 −0.644091
$$782$$ 18.0000 0.643679
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ −39.0000 −1.39197
$$786$$ 0 0
$$787$$ 20.0000 0.712923 0.356462 0.934310i $$-0.383983\pi$$
0.356462 + 0.934310i $$0.383983\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ 0 0
$$790$$ 15.0000 0.533676
$$791$$ −15.0000 −0.533339
$$792$$ 0 0
$$793$$ 10.0000 0.355110
$$794$$ 26.0000 0.922705
$$795$$ 0 0
$$796$$ 14.0000 0.496217
$$797$$ −3.00000 −0.106265 −0.0531327 0.998587i $$-0.516921\pi$$
−0.0531327 + 0.998587i $$0.516921\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 4.00000 0.141421
$$801$$ 0 0
$$802$$ −3.00000 −0.105934
$$803$$ 12.0000 0.423471
$$804$$ 0 0
$$805$$ −9.00000 −0.317208
$$806$$ 4.00000 0.140894
$$807$$ 0 0
$$808$$ −9.00000 −0.316619
$$809$$ 30.0000 1.05474 0.527372 0.849635i $$-0.323177\pi$$
0.527372 + 0.849635i $$0.323177\pi$$
$$810$$ 0 0
$$811$$ −16.0000 −0.561836 −0.280918 0.959732i $$-0.590639\pi$$
−0.280918 + 0.959732i $$0.590639\pi$$
$$812$$ −6.00000 −0.210559
$$813$$ 0 0
$$814$$ 12.0000 0.420600
$$815$$ 6.00000 0.210171
$$816$$ 0 0
$$817$$ −14.0000 −0.489798
$$818$$ 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 $$0.362450\pi$$
$$822$$ 0 0
$$823$$ 8.00000 0.278862 0.139431 0.990232i $$-0.455473\pi$$
0.139431 + 0.990232i $$0.455473\pi$$
$$824$$ −10.0000 −0.348367
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −36.0000 −1.25184 −0.625921 0.779886i $$-0.715277\pi$$
−0.625921 + 0.779886i $$0.715277\pi$$
$$828$$ 0 0
$$829$$ −34.0000 −1.18087 −0.590434 0.807086i $$-0.701044\pi$$
−0.590434 + 0.807086i $$0.701044\pi$$
$$830$$ −36.0000 −1.24958
$$831$$ 0 0
$$832$$ 2.00000 0.0693375
$$833$$ −6.00000 −0.207888
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −42.0000 −1.45260
$$837$$ 0 0
$$838$$ −15.0000 −0.518166
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ −10.0000 −0.344623
$$843$$ 0 0
$$844$$ 8.00000 0.275371
$$845$$ −27.0000 −0.928828
$$846$$ 0 0
$$847$$ 25.0000 0.859010
$$848$$ −6.00000 −0.206041
$$849$$ 0 0
$$850$$ −24.0000 −0.823193
$$851$$ −6.00000 −0.205677
$$852$$ 0 0
$$853$$ 35.0000 1.19838 0.599189 0.800608i $$-0.295490\pi$$
0.599189 + 0.800608i $$0.295490\pi$$
$$854$$ 5.00000 0.171096
$$855$$ 0 0
$$856$$ 12.0000 0.410152
$$857$$ −54.0000 −1.84460 −0.922302 0.386469i $$-0.873695\pi$$
−0.922302 + 0.386469i $$0.873695\pi$$
$$858$$ 0 0
$$859$$ −4.00000 −0.136478 −0.0682391 0.997669i $$-0.521738\pi$$
−0.0682391 + 0.997669i $$0.521738\pi$$
$$860$$ 6.00000 0.204598
$$861$$ 0 0
$$862$$ −12.0000 −0.408722
$$863$$ −9.00000 −0.306364 −0.153182 0.988198i $$-0.548952\pi$$
−0.153182 + 0.988198i $$0.548952\pi$$
$$864$$ 0 0
$$865$$ 18.0000 0.612018
$$866$$ 14.0000 0.475739
$$867$$ 0 0
$$868$$ 2.00000 0.0678844
$$869$$ 30.0000 1.01768
$$870$$ 0 0
$$871$$ 16.0000 0.542139
$$872$$ −10.0000 −0.338643
$$873$$ 0 0
$$874$$ 21.0000 0.710336
$$875$$ −3.00000 −0.101419
$$876$$ 0 0
$$877$$ −22.0000 −0.742887 −0.371444 0.928456i $$-0.621137\pi$$
−0.371444 + 0.928456i $$0.621137\pi$$
$$878$$ 8.00000 0.269987
$$879$$ 0 0
$$880$$ 18.0000 0.606780
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ −34.0000 −1.14419 −0.572096 0.820187i $$-0.693869\pi$$
−0.572096 + 0.820187i $$0.693869\pi$$
$$884$$ −12.0000 −0.403604
$$885$$ 0 0
$$886$$ −18.0000 −0.604722
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ 0 0
$$889$$ 17.0000 0.570162
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −28.0000 −0.937509
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −54.0000 −1.80502
$$896$$ 1.00000 0.0334077
$$897$$ 0 0
$$898$$ −33.0000 −1.10122
$$899$$ −12.0000 −0.400222
$$900$$ 0 0
$$901$$ 36.0000 1.19933
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −15.0000 −0.498893
$$905$$ −75.0000 −2.49308
$$906$$ 0 0
$$907$$ 32.0000 1.06254 0.531271 0.847202i $$-0.321714\pi$$
0.531271 + 0.847202i $$0.321714\pi$$
$$908$$ 15.0000 0.497792
$$909$$ 0 0
$$910$$ 6.00000 0.198898
$$911$$ −15.0000 −0.496972 −0.248486 0.968635i $$-0.579933\pi$$
−0.248486 + 0.968635i $$0.579933\pi$$
$$912$$ 0 0
$$913$$ −72.0000 −2.38285
$$914$$ 29.0000 0.959235
$$915$$ 0 0
$$916$$ −1.00000 −0.0330409
$$917$$ 9.00000 0.297206
$$918$$ 0 0
$$919$$ 11.0000 0.362857 0.181428 0.983404i $$-0.441928\pi$$
0.181428 + 0.983404i $$0.441928\pi$$
$$920$$ −9.00000 −0.296721
$$921$$ 0 0
$$922$$ 33.0000 1.08680
$$923$$ −6.00000 −0.197492
$$924$$ 0 0
$$925$$ 8.00000 0.263038
$$926$$ −13.0000 −0.427207
$$927$$ 0 0
$$928$$ −6.00000 −0.196960
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 0 0
$$931$$ −7.00000 −0.229416
$$932$$ −9.00000 −0.294805
$$933$$ 0 0
$$934$$ −12.0000 −0.392652
$$935$$ −108.000 −3.53198
$$936$$ 0 0
$$937$$ 38.0000 1.24141 0.620703 0.784046i $$-0.286847\pi$$
0.620703 + 0.784046i $$0.286847\pi$$
$$938$$ 8.00000 0.261209
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −21.0000 −0.684580 −0.342290 0.939594i $$-0.611203\pi$$
−0.342290 + 0.939594i $$0.611203\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 12.0000 0.390154
$$947$$ 24.0000 0.779895 0.389948 0.920837i $$-0.372493\pi$$
0.389948 + 0.920837i $$0.372493\pi$$
$$948$$ 0 0
$$949$$ 4.00000 0.129845
$$950$$ −28.0000 −0.908440
$$951$$ 0 0
$$952$$ −6.00000 −0.194461
$$953$$ −42.0000 −1.36051 −0.680257 0.732974i $$-0.738132\pi$$
−0.680257 + 0.732974i $$0.738132\pi$$
$$954$$ 0 0
$$955$$ 27.0000 0.873699
$$956$$ 15.0000 0.485135
$$957$$ 0 0
$$958$$ 6.00000 0.193851
$$959$$ −6.00000 −0.193750
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 4.00000 0.128965
$$963$$ 0 0
$$964$$ 8.00000 0.257663
$$965$$ 51.0000 1.64175
$$966$$ 0 0
$$967$$ 17.0000 0.546683 0.273342 0.961917i $$-0.411871\pi$$
0.273342 + 0.961917i $$0.411871\pi$$
$$968$$ 25.0000 0.803530
$$969$$ 0 0
$$970$$ 6.00000 0.192648
$$971$$ 15.0000 0.481373 0.240686 0.970603i $$-0.422627\pi$$
0.240686 + 0.970603i $$0.422627\pi$$
$$972$$ 0 0
$$973$$ 5.00000 0.160293
$$974$$ 29.0000 0.929220
$$975$$ 0 0
$$976$$ 5.00000 0.160046
$$977$$ −6.00000 −0.191957 −0.0959785 0.995383i $$-0.530598\pi$$
−0.0959785 + 0.995383i $$0.530598\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 3.00000 0.0958315
$$981$$ 0 0
$$982$$ −18.0000 −0.574403
$$983$$ −18.0000 −0.574111 −0.287055 0.957914i $$-0.592676\pi$$
−0.287055 + 0.957914i $$0.592676\pi$$
$$984$$ 0 0
$$985$$ −54.0000 −1.72058
$$986$$ 36.0000 1.14647
$$987$$ 0 0
$$988$$ −14.0000 −0.445399
$$989$$ −6.00000 −0.190789
$$990$$ 0 0
$$991$$ −40.0000 −1.27064 −0.635321 0.772248i $$-0.719132\pi$$
−0.635321 + 0.772248i $$0.719132\pi$$
$$992$$ 2.00000 0.0635001
$$993$$ 0 0
$$994$$ −3.00000 −0.0951542
$$995$$ 42.0000 1.33149
$$996$$ 0 0
$$997$$ −55.0000 −1.74187 −0.870934 0.491400i $$-0.836485\pi$$
−0.870934 + 0.491400i $$0.836485\pi$$
$$998$$ 32.0000 1.01294
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1134.2.a.h.1.1 1
3.2 odd 2 1134.2.a.a.1.1 1
4.3 odd 2 9072.2.a.w.1.1 1
7.6 odd 2 7938.2.a.u.1.1 1
9.2 odd 6 126.2.f.a.85.1 yes 2
9.4 even 3 378.2.f.a.127.1 2
9.5 odd 6 126.2.f.a.43.1 2
9.7 even 3 378.2.f.a.253.1 2
12.11 even 2 9072.2.a.c.1.1 1
21.20 even 2 7938.2.a.l.1.1 1
36.7 odd 6 3024.2.r.a.1009.1 2
36.11 even 6 1008.2.r.d.337.1 2
36.23 even 6 1008.2.r.d.673.1 2
36.31 odd 6 3024.2.r.a.2017.1 2
63.2 odd 6 882.2.h.j.67.1 2
63.4 even 3 2646.2.h.e.667.1 2
63.5 even 6 882.2.e.d.655.1 2
63.11 odd 6 882.2.e.b.373.1 2
63.13 odd 6 2646.2.f.c.883.1 2
63.16 even 3 2646.2.h.e.361.1 2
63.20 even 6 882.2.f.h.589.1 2
63.23 odd 6 882.2.e.b.655.1 2
63.25 even 3 2646.2.e.f.1549.1 2
63.31 odd 6 2646.2.h.a.667.1 2
63.32 odd 6 882.2.h.j.79.1 2
63.34 odd 6 2646.2.f.c.1765.1 2
63.38 even 6 882.2.e.d.373.1 2
63.40 odd 6 2646.2.e.j.2125.1 2
63.41 even 6 882.2.f.h.295.1 2
63.47 even 6 882.2.h.f.67.1 2
63.52 odd 6 2646.2.e.j.1549.1 2
63.58 even 3 2646.2.e.f.2125.1 2
63.59 even 6 882.2.h.f.79.1 2
63.61 odd 6 2646.2.h.a.361.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.f.a.43.1 2 9.5 odd 6
126.2.f.a.85.1 yes 2 9.2 odd 6
378.2.f.a.127.1 2 9.4 even 3
378.2.f.a.253.1 2 9.7 even 3
882.2.e.b.373.1 2 63.11 odd 6
882.2.e.b.655.1 2 63.23 odd 6
882.2.e.d.373.1 2 63.38 even 6
882.2.e.d.655.1 2 63.5 even 6
882.2.f.h.295.1 2 63.41 even 6
882.2.f.h.589.1 2 63.20 even 6
882.2.h.f.67.1 2 63.47 even 6
882.2.h.f.79.1 2 63.59 even 6
882.2.h.j.67.1 2 63.2 odd 6
882.2.h.j.79.1 2 63.32 odd 6
1008.2.r.d.337.1 2 36.11 even 6
1008.2.r.d.673.1 2 36.23 even 6
1134.2.a.a.1.1 1 3.2 odd 2
1134.2.a.h.1.1 1 1.1 even 1 trivial
2646.2.e.f.1549.1 2 63.25 even 3
2646.2.e.f.2125.1 2 63.58 even 3
2646.2.e.j.1549.1 2 63.52 odd 6
2646.2.e.j.2125.1 2 63.40 odd 6
2646.2.f.c.883.1 2 63.13 odd 6
2646.2.f.c.1765.1 2 63.34 odd 6
2646.2.h.a.361.1 2 63.61 odd 6
2646.2.h.a.667.1 2 63.31 odd 6
2646.2.h.e.361.1 2 63.16 even 3
2646.2.h.e.667.1 2 63.4 even 3
3024.2.r.a.1009.1 2 36.7 odd 6
3024.2.r.a.2017.1 2 36.31 odd 6
7938.2.a.l.1.1 1 21.20 even 2
7938.2.a.u.1.1 1 7.6 odd 2
9072.2.a.c.1.1 1 12.11 even 2
9072.2.a.w.1.1 1 4.3 odd 2