# Properties

 Label 7600.2.a.bz.1.3 Level $7600$ Weight $2$ Character 7600.1 Self dual yes Analytic conductor $60.686$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7600 = 2^{4} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7600.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$60.6863055362$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.993.1 Defining polynomial: $$x^{3} - x^{2} - 6 x + 3$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 950) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$-2.25342$$ of defining polynomial Character $$\chi$$ $$=$$ 7600.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.25342 q^{3} -0.0778929 q^{7} +7.58473 q^{9} +O(q^{10})$$ $$q+3.25342 q^{3} -0.0778929 q^{7} +7.58473 q^{9} +4.50684 q^{11} +5.33131 q^{13} -7.33131 q^{17} -1.00000 q^{19} -0.253418 q^{21} +3.40920 q^{23} +14.9160 q^{27} -1.33131 q^{29} +2.50684 q^{31} +14.6626 q^{33} +5.50684 q^{37} +17.3450 q^{39} +0.506836 q^{43} -5.66262 q^{47} -6.99393 q^{49} -23.8518 q^{51} +12.9358 q^{53} -3.25342 q^{57} -7.56499 q^{59} -2.15579 q^{61} -0.590796 q^{63} -4.58473 q^{67} +11.0916 q^{69} +10.8579 q^{71} +5.09763 q^{73} -0.351050 q^{77} -17.0137 q^{79} +25.7739 q^{81} -13.1695 q^{83} -4.33131 q^{87} +15.0137 q^{89} -0.415271 q^{91} +8.15579 q^{93} -7.67629 q^{97} +34.1831 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3q + 2q^{3} + 2q^{7} + 5q^{9} + O(q^{10})$$ $$3q + 2q^{3} + 2q^{7} + 5q^{9} - 2q^{11} + 6q^{13} - 12q^{17} - 3q^{19} + 7q^{21} - 2q^{23} + 17q^{27} + 6q^{29} - 8q^{31} + 24q^{33} + q^{37} + 11q^{39} - 14q^{43} + 3q^{47} + 9q^{49} - 15q^{51} + 10q^{53} - 2q^{57} - 6q^{59} - 2q^{61} - 14q^{63} + 4q^{67} + 6q^{71} + 12q^{73} + 10q^{77} - 20q^{79} + 23q^{81} - 4q^{83} - 3q^{87} + 14q^{89} - 19q^{91} + 20q^{93} + 28q^{97} + 36q^{99} + O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 3.25342 1.87836 0.939181 0.343423i $$-0.111586\pi$$
0.939181 + 0.343423i $$0.111586\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −0.0778929 −0.0294407 −0.0147204 0.999892i $$-0.504686\pi$$
−0.0147204 + 0.999892i $$0.504686\pi$$
$$8$$ 0 0
$$9$$ 7.58473 2.52824
$$10$$ 0 0
$$11$$ 4.50684 1.35886 0.679431 0.733739i $$-0.262227\pi$$
0.679431 + 0.733739i $$0.262227\pi$$
$$12$$ 0 0
$$13$$ 5.33131 1.47864 0.739320 0.673354i $$-0.235147\pi$$
0.739320 + 0.673354i $$0.235147\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −7.33131 −1.77810 −0.889052 0.457806i $$-0.848635\pi$$
−0.889052 + 0.457806i $$0.848635\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −0.229416
$$20$$ 0 0
$$21$$ −0.253418 −0.0553003
$$22$$ 0 0
$$23$$ 3.40920 0.710868 0.355434 0.934701i $$-0.384333\pi$$
0.355434 + 0.934701i $$0.384333\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 14.9160 2.87059
$$28$$ 0 0
$$29$$ −1.33131 −0.247218 −0.123609 0.992331i $$-0.539447\pi$$
−0.123609 + 0.992331i $$0.539447\pi$$
$$30$$ 0 0
$$31$$ 2.50684 0.450241 0.225121 0.974331i $$-0.427722\pi$$
0.225121 + 0.974331i $$0.427722\pi$$
$$32$$ 0 0
$$33$$ 14.6626 2.55243
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 5.50684 0.905318 0.452659 0.891684i $$-0.350475\pi$$
0.452659 + 0.891684i $$0.350475\pi$$
$$38$$ 0 0
$$39$$ 17.3450 2.77742
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 0.506836 0.0772918 0.0386459 0.999253i $$-0.487696\pi$$
0.0386459 + 0.999253i $$0.487696\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −5.66262 −0.825978 −0.412989 0.910736i $$-0.635515\pi$$
−0.412989 + 0.910736i $$0.635515\pi$$
$$48$$ 0 0
$$49$$ −6.99393 −0.999133
$$50$$ 0 0
$$51$$ −23.8518 −3.33992
$$52$$ 0 0
$$53$$ 12.9358 1.77687 0.888433 0.459006i $$-0.151794\pi$$
0.888433 + 0.459006i $$0.151794\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −3.25342 −0.430926
$$58$$ 0 0
$$59$$ −7.56499 −0.984878 −0.492439 0.870347i $$-0.663894\pi$$
−0.492439 + 0.870347i $$0.663894\pi$$
$$60$$ 0 0
$$61$$ −2.15579 −0.276020 −0.138010 0.990431i $$-0.544071\pi$$
−0.138010 + 0.990431i $$0.544071\pi$$
$$62$$ 0 0
$$63$$ −0.590796 −0.0744333
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −4.58473 −0.560114 −0.280057 0.959983i $$-0.590353\pi$$
−0.280057 + 0.959983i $$0.590353\pi$$
$$68$$ 0 0
$$69$$ 11.0916 1.33527
$$70$$ 0 0
$$71$$ 10.8579 1.28859 0.644297 0.764775i $$-0.277150\pi$$
0.644297 + 0.764775i $$0.277150\pi$$
$$72$$ 0 0
$$73$$ 5.09763 0.596633 0.298316 0.954467i $$-0.403575\pi$$
0.298316 + 0.954467i $$0.403575\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −0.351050 −0.0400059
$$78$$ 0 0
$$79$$ −17.0137 −1.91419 −0.957094 0.289778i $$-0.906418\pi$$
−0.957094 + 0.289778i $$0.906418\pi$$
$$80$$ 0 0
$$81$$ 25.7739 2.86377
$$82$$ 0 0
$$83$$ −13.1695 −1.44554 −0.722768 0.691091i $$-0.757130\pi$$
−0.722768 + 0.691091i $$0.757130\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −4.33131 −0.464365
$$88$$ 0 0
$$89$$ 15.0137 1.59145 0.795723 0.605661i $$-0.207091\pi$$
0.795723 + 0.605661i $$0.207091\pi$$
$$90$$ 0 0
$$91$$ −0.415271 −0.0435322
$$92$$ 0 0
$$93$$ 8.15579 0.845716
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −7.67629 −0.779410 −0.389705 0.920940i $$-0.627423\pi$$
−0.389705 + 0.920940i $$0.627423\pi$$
$$98$$ 0 0
$$99$$ 34.1831 3.43553
$$100$$ 0 0
$$101$$ −4.15579 −0.413516 −0.206758 0.978392i $$-0.566291\pi$$
−0.206758 + 0.978392i $$0.566291\pi$$
$$102$$ 0 0
$$103$$ 2.35105 0.231656 0.115828 0.993269i $$-0.463048\pi$$
0.115828 + 0.993269i $$0.463048\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −14.0334 −1.35666 −0.678331 0.734757i $$-0.737296\pi$$
−0.678331 + 0.734757i $$0.737296\pi$$
$$108$$ 0 0
$$109$$ −0.0778929 −0.00746078 −0.00373039 0.999993i $$-0.501187\pi$$
−0.00373039 + 0.999993i $$0.501187\pi$$
$$110$$ 0 0
$$111$$ 17.9160 1.70052
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 40.4365 3.73836
$$118$$ 0 0
$$119$$ 0.571057 0.0523487
$$120$$ 0 0
$$121$$ 9.31157 0.846506
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 17.8321 1.58234 0.791171 0.611596i $$-0.209472\pi$$
0.791171 + 0.611596i $$0.209472\pi$$
$$128$$ 0 0
$$129$$ 1.64895 0.145182
$$130$$ 0 0
$$131$$ 1.49316 0.130458 0.0652292 0.997870i $$-0.479222\pi$$
0.0652292 + 0.997870i $$0.479222\pi$$
$$132$$ 0 0
$$133$$ 0.0778929 0.00675417
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 8.42894 0.720133 0.360067 0.932927i $$-0.382754\pi$$
0.360067 + 0.932927i $$0.382754\pi$$
$$138$$ 0 0
$$139$$ −8.81841 −0.747968 −0.373984 0.927435i $$-0.622008\pi$$
−0.373984 + 0.927435i $$0.622008\pi$$
$$140$$ 0 0
$$141$$ −18.4229 −1.55149
$$142$$ 0 0
$$143$$ 24.0273 2.00927
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −22.7542 −1.87673
$$148$$ 0 0
$$149$$ 17.6763 1.44810 0.724049 0.689748i $$-0.242279\pi$$
0.724049 + 0.689748i $$0.242279\pi$$
$$150$$ 0 0
$$151$$ −20.0000 −1.62758 −0.813788 0.581161i $$-0.802599\pi$$
−0.813788 + 0.581161i $$0.802599\pi$$
$$152$$ 0 0
$$153$$ −55.6060 −4.49548
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −0.506836 −0.0404499 −0.0202250 0.999795i $$-0.506438\pi$$
−0.0202250 + 0.999795i $$0.506438\pi$$
$$158$$ 0 0
$$159$$ 42.0855 3.33760
$$160$$ 0 0
$$161$$ −0.265553 −0.0209285
$$162$$ 0 0
$$163$$ 0.830542 0.0650531 0.0325265 0.999471i $$-0.489645\pi$$
0.0325265 + 0.999471i $$0.489645\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 16.5068 1.27734 0.638669 0.769482i $$-0.279485\pi$$
0.638669 + 0.769482i $$0.279485\pi$$
$$168$$ 0 0
$$169$$ 15.4229 1.18638
$$170$$ 0 0
$$171$$ −7.58473 −0.580019
$$172$$ 0 0
$$173$$ −18.8321 −1.43178 −0.715888 0.698215i $$-0.753978\pi$$
−0.715888 + 0.698215i $$0.753978\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −24.6121 −1.84996
$$178$$ 0 0
$$179$$ 7.15579 0.534849 0.267424 0.963579i $$-0.413827\pi$$
0.267424 + 0.963579i $$0.413827\pi$$
$$180$$ 0 0
$$181$$ 12.5205 0.930642 0.465321 0.885142i $$-0.345939\pi$$
0.465321 + 0.885142i $$0.345939\pi$$
$$182$$ 0 0
$$183$$ −7.01367 −0.518466
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −33.0410 −2.41620
$$188$$ 0 0
$$189$$ −1.16185 −0.0845124
$$190$$ 0 0
$$191$$ 4.90237 0.354723 0.177361 0.984146i $$-0.443244\pi$$
0.177361 + 0.984146i $$0.443244\pi$$
$$192$$ 0 0
$$193$$ −18.1558 −1.30688 −0.653441 0.756977i $$-0.726675\pi$$
−0.653441 + 0.756977i $$0.726675\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.98633 0.212767 0.106384 0.994325i $$-0.466073\pi$$
0.106384 + 0.994325i $$0.466073\pi$$
$$198$$ 0 0
$$199$$ 3.06422 0.217217 0.108608 0.994085i $$-0.465361\pi$$
0.108608 + 0.994085i $$0.465361\pi$$
$$200$$ 0 0
$$201$$ −14.9160 −1.05210
$$202$$ 0 0
$$203$$ 0.103700 0.00727829
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 25.8579 1.79725
$$208$$ 0 0
$$209$$ −4.50684 −0.311744
$$210$$ 0 0
$$211$$ −19.2534 −1.32546 −0.662730 0.748858i $$-0.730602\pi$$
−0.662730 + 0.748858i $$0.730602\pi$$
$$212$$ 0 0
$$213$$ 35.3252 2.42045
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −0.195265 −0.0132554
$$218$$ 0 0
$$219$$ 16.5847 1.12069
$$220$$ 0 0
$$221$$ −39.0855 −2.62918
$$222$$ 0 0
$$223$$ −14.5068 −0.971450 −0.485725 0.874112i $$-0.661444\pi$$
−0.485725 + 0.874112i $$0.661444\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −21.5984 −1.43354 −0.716768 0.697312i $$-0.754379\pi$$
−0.716768 + 0.697312i $$0.754379\pi$$
$$228$$ 0 0
$$229$$ −19.0137 −1.25646 −0.628229 0.778028i $$-0.716220\pi$$
−0.628229 + 0.778028i $$0.716220\pi$$
$$230$$ 0 0
$$231$$ −1.14211 −0.0751456
$$232$$ 0 0
$$233$$ 6.01367 0.393969 0.196984 0.980407i $$-0.436885\pi$$
0.196984 + 0.980407i $$0.436885\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −55.3526 −3.59554
$$238$$ 0 0
$$239$$ −15.4092 −0.996739 −0.498369 0.866965i $$-0.666068\pi$$
−0.498369 + 0.866965i $$0.666068\pi$$
$$240$$ 0 0
$$241$$ −4.81841 −0.310381 −0.155190 0.987885i $$-0.549599\pi$$
−0.155190 + 0.987885i $$0.549599\pi$$
$$242$$ 0 0
$$243$$ 39.1052 2.50860
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −5.33131 −0.339223
$$248$$ 0 0
$$249$$ −42.8458 −2.71524
$$250$$ 0 0
$$251$$ −1.52051 −0.0959736 −0.0479868 0.998848i $$-0.515281\pi$$
−0.0479868 + 0.998848i $$0.515281\pi$$
$$252$$ 0 0
$$253$$ 15.3647 0.965972
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −16.5068 −1.02967 −0.514834 0.857290i $$-0.672146\pi$$
−0.514834 + 0.857290i $$0.672146\pi$$
$$258$$ 0 0
$$259$$ −0.428943 −0.0266532
$$260$$ 0 0
$$261$$ −10.0976 −0.625028
$$262$$ 0 0
$$263$$ −18.0273 −1.11161 −0.555807 0.831311i $$-0.687591\pi$$
−0.555807 + 0.831311i $$0.687591\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 48.8458 2.98931
$$268$$ 0 0
$$269$$ 20.2089 1.23216 0.616080 0.787683i $$-0.288720\pi$$
0.616080 + 0.787683i $$0.288720\pi$$
$$270$$ 0 0
$$271$$ −6.08396 −0.369574 −0.184787 0.982779i $$-0.559160\pi$$
−0.184787 + 0.982779i $$0.559160\pi$$
$$272$$ 0 0
$$273$$ −1.35105 −0.0817693
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 31.3647 1.88452 0.942262 0.334877i $$-0.108695\pi$$
0.942262 + 0.334877i $$0.108695\pi$$
$$278$$ 0 0
$$279$$ 19.0137 1.13832
$$280$$ 0 0
$$281$$ 11.3252 0.675607 0.337804 0.941217i $$-0.390316\pi$$
0.337804 + 0.941217i $$0.390316\pi$$
$$282$$ 0 0
$$283$$ 26.1437 1.55408 0.777039 0.629452i $$-0.216721\pi$$
0.777039 + 0.629452i $$0.216721\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 36.7481 2.16165
$$290$$ 0 0
$$291$$ −24.9742 −1.46401
$$292$$ 0 0
$$293$$ −1.33131 −0.0777760 −0.0388880 0.999244i $$-0.512382\pi$$
−0.0388880 + 0.999244i $$0.512382\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 67.2241 3.90074
$$298$$ 0 0
$$299$$ 18.1755 1.05112
$$300$$ 0 0
$$301$$ −0.0394789 −0.00227553
$$302$$ 0 0
$$303$$ −13.5205 −0.776733
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −2.84421 −0.162328 −0.0811639 0.996701i $$-0.525864\pi$$
−0.0811639 + 0.996701i $$0.525864\pi$$
$$308$$ 0 0
$$309$$ 7.64895 0.435134
$$310$$ 0 0
$$311$$ 16.3895 0.929361 0.464681 0.885478i $$-0.346169\pi$$
0.464681 + 0.885478i $$0.346169\pi$$
$$312$$ 0 0
$$313$$ 21.0471 1.18965 0.594826 0.803855i $$-0.297221\pi$$
0.594826 + 0.803855i $$0.297221\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 30.8902 1.73497 0.867484 0.497465i $$-0.165736\pi$$
0.867484 + 0.497465i $$0.165736\pi$$
$$318$$ 0 0
$$319$$ −6.00000 −0.335936
$$320$$ 0 0
$$321$$ −45.6566 −2.54830
$$322$$ 0 0
$$323$$ 7.33131 0.407925
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −0.253418 −0.0140140
$$328$$ 0 0
$$329$$ 0.441078 0.0243174
$$330$$ 0 0
$$331$$ −28.3845 −1.56015 −0.780076 0.625685i $$-0.784819\pi$$
−0.780076 + 0.625685i $$0.784819\pi$$
$$332$$ 0 0
$$333$$ 41.7679 2.28886
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 17.8716 0.973526 0.486763 0.873534i $$-0.338178\pi$$
0.486763 + 0.873534i $$0.338178\pi$$
$$338$$ 0 0
$$339$$ 19.5205 1.06021
$$340$$ 0 0
$$341$$ 11.2979 0.611816
$$342$$ 0 0
$$343$$ 1.09003 0.0588560
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 33.0410 1.77373 0.886867 0.462024i $$-0.152877\pi$$
0.886867 + 0.462024i $$0.152877\pi$$
$$348$$ 0 0
$$349$$ −19.7158 −1.05536 −0.527681 0.849443i $$-0.676938\pi$$
−0.527681 + 0.849443i $$0.676938\pi$$
$$350$$ 0 0
$$351$$ 79.5220 4.24457
$$352$$ 0 0
$$353$$ 5.90997 0.314556 0.157278 0.987554i $$-0.449728\pi$$
0.157278 + 0.987554i $$0.449728\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 1.85789 0.0983298
$$358$$ 0 0
$$359$$ 7.00760 0.369847 0.184924 0.982753i $$-0.440796\pi$$
0.184924 + 0.982753i $$0.440796\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ 30.2944 1.59005
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 17.7158 0.924756 0.462378 0.886683i $$-0.346996\pi$$
0.462378 + 0.886683i $$0.346996\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −1.00760 −0.0523122
$$372$$ 0 0
$$373$$ −15.4487 −0.799902 −0.399951 0.916536i $$-0.630973\pi$$
−0.399951 + 0.916536i $$0.630973\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −7.09763 −0.365547
$$378$$ 0 0
$$379$$ −34.4563 −1.76990 −0.884950 0.465685i $$-0.845808\pi$$
−0.884950 + 0.465685i $$0.845808\pi$$
$$380$$ 0 0
$$381$$ 58.0152 2.97221
$$382$$ 0 0
$$383$$ −12.0273 −0.614569 −0.307284 0.951618i $$-0.599420\pi$$
−0.307284 + 0.951618i $$0.599420\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 3.84421 0.195412
$$388$$ 0 0
$$389$$ −15.3647 −0.779022 −0.389511 0.921022i $$-0.627356\pi$$
−0.389511 + 0.921022i $$0.627356\pi$$
$$390$$ 0 0
$$391$$ −24.9939 −1.26400
$$392$$ 0 0
$$393$$ 4.85789 0.245048
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −1.32524 −0.0665121 −0.0332560 0.999447i $$-0.510588\pi$$
−0.0332560 + 0.999447i $$0.510588\pi$$
$$398$$ 0 0
$$399$$ 0.253418 0.0126868
$$400$$ 0 0
$$401$$ −6.46736 −0.322964 −0.161482 0.986876i $$-0.551627\pi$$
−0.161482 + 0.986876i $$0.551627\pi$$
$$402$$ 0 0
$$403$$ 13.3647 0.665744
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 24.8184 1.23020
$$408$$ 0 0
$$409$$ −1.36472 −0.0674812 −0.0337406 0.999431i $$-0.510742\pi$$
−0.0337406 + 0.999431i $$0.510742\pi$$
$$410$$ 0 0
$$411$$ 27.4229 1.35267
$$412$$ 0 0
$$413$$ 0.589259 0.0289955
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −28.6900 −1.40495
$$418$$ 0 0
$$419$$ −16.6231 −0.812094 −0.406047 0.913852i $$-0.633093\pi$$
−0.406047 + 0.913852i $$0.633093\pi$$
$$420$$ 0 0
$$421$$ −31.1128 −1.51635 −0.758174 0.652053i $$-0.773908\pi$$
−0.758174 + 0.652053i $$0.773908\pi$$
$$422$$ 0 0
$$423$$ −42.9495 −2.08827
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0.167920 0.00812623
$$428$$ 0 0
$$429$$ 78.1710 3.77413
$$430$$ 0 0
$$431$$ 10.1831 0.490504 0.245252 0.969459i $$-0.421129\pi$$
0.245252 + 0.969459i $$0.421129\pi$$
$$432$$ 0 0
$$433$$ −22.1953 −1.06664 −0.533318 0.845915i $$-0.679055\pi$$
−0.533318 + 0.845915i $$0.679055\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3.40920 −0.163084
$$438$$ 0 0
$$439$$ 9.32524 0.445070 0.222535 0.974925i $$-0.428567\pi$$
0.222535 + 0.974925i $$0.428567\pi$$
$$440$$ 0 0
$$441$$ −53.0471 −2.52605
$$442$$ 0 0
$$443$$ −13.9879 −0.664584 −0.332292 0.943177i $$-0.607822\pi$$
−0.332292 + 0.943177i $$0.607822\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 57.5084 2.72005
$$448$$ 0 0
$$449$$ 13.4932 0.636782 0.318391 0.947960i $$-0.396858\pi$$
0.318391 + 0.947960i $$0.396858\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −65.0684 −3.05718
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −9.68236 −0.452922 −0.226461 0.974020i $$-0.572716\pi$$
−0.226461 + 0.974020i $$0.572716\pi$$
$$458$$ 0 0
$$459$$ −109.354 −5.10421
$$460$$ 0 0
$$461$$ 8.66262 0.403459 0.201729 0.979441i $$-0.435344\pi$$
0.201729 + 0.979441i $$0.435344\pi$$
$$462$$ 0 0
$$463$$ 28.0015 1.30134 0.650671 0.759360i $$-0.274488\pi$$
0.650671 + 0.759360i $$0.274488\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 16.9742 0.785472 0.392736 0.919651i $$-0.371529\pi$$
0.392736 + 0.919651i $$0.371529\pi$$
$$468$$ 0 0
$$469$$ 0.357118 0.0164902
$$470$$ 0 0
$$471$$ −1.64895 −0.0759796
$$472$$ 0 0
$$473$$ 2.28423 0.105029
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 98.1144 4.49235
$$478$$ 0 0
$$479$$ −10.0532 −0.459340 −0.229670 0.973269i $$-0.573765\pi$$
−0.229670 + 0.973269i $$0.573765\pi$$
$$480$$ 0 0
$$481$$ 29.3587 1.33864
$$482$$ 0 0
$$483$$ −0.863954 −0.0393113
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 19.2089 0.870440 0.435220 0.900324i $$-0.356671\pi$$
0.435220 + 0.900324i $$0.356671\pi$$
$$488$$ 0 0
$$489$$ 2.70210 0.122193
$$490$$ 0 0
$$491$$ −5.32524 −0.240325 −0.120162 0.992754i $$-0.538342\pi$$
−0.120162 + 0.992754i $$0.538342\pi$$
$$492$$ 0 0
$$493$$ 9.76025 0.439580
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −0.845752 −0.0379372
$$498$$ 0 0
$$499$$ 11.9605 0.535426 0.267713 0.963499i $$-0.413732\pi$$
0.267713 + 0.963499i $$0.413732\pi$$
$$500$$ 0 0
$$501$$ 53.7036 2.39930
$$502$$ 0 0
$$503$$ −19.3313 −0.861941 −0.430970 0.902366i $$-0.641829\pi$$
−0.430970 + 0.902366i $$0.641829\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 50.1771 2.22844
$$508$$ 0 0
$$509$$ −36.1573 −1.60265 −0.801323 0.598232i $$-0.795870\pi$$
−0.801323 + 0.598232i $$0.795870\pi$$
$$510$$ 0 0
$$511$$ −0.397069 −0.0175653
$$512$$ 0 0
$$513$$ −14.9160 −0.658559
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −25.5205 −1.12239
$$518$$ 0 0
$$519$$ −61.2686 −2.68939
$$520$$ 0 0
$$521$$ −31.5205 −1.38094 −0.690469 0.723362i $$-0.742596\pi$$
−0.690469 + 0.723362i $$0.742596\pi$$
$$522$$ 0 0
$$523$$ 5.59840 0.244801 0.122400 0.992481i $$-0.460941\pi$$
0.122400 + 0.992481i $$0.460941\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −18.3784 −0.800575
$$528$$ 0 0
$$529$$ −11.3773 −0.494667
$$530$$ 0 0
$$531$$ −57.3784 −2.49001
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 23.2808 1.00464
$$538$$ 0 0
$$539$$ −31.5205 −1.35768
$$540$$ 0 0
$$541$$ 15.1968 0.653362 0.326681 0.945135i $$-0.394070\pi$$
0.326681 + 0.945135i $$0.394070\pi$$
$$542$$ 0 0
$$543$$ 40.7344 1.74808
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −26.6505 −1.13949 −0.569746 0.821821i $$-0.692959\pi$$
−0.569746 + 0.821821i $$0.692959\pi$$
$$548$$ 0 0
$$549$$ −16.3511 −0.697846
$$550$$ 0 0
$$551$$ 1.33131 0.0567158
$$552$$ 0 0
$$553$$ 1.32524 0.0563551
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −12.8458 −0.544292 −0.272146 0.962256i $$-0.587733\pi$$
−0.272146 + 0.962256i $$0.587733\pi$$
$$558$$ 0 0
$$559$$ 2.70210 0.114287
$$560$$ 0 0
$$561$$ −107.496 −4.53849
$$562$$ 0 0
$$563$$ 10.1968 0.429744 0.214872 0.976642i $$-0.431067\pi$$
0.214872 + 0.976642i $$0.431067\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −2.00760 −0.0843115
$$568$$ 0 0
$$569$$ −24.3784 −1.02200 −0.510998 0.859582i $$-0.670724\pi$$
−0.510998 + 0.859582i $$0.670724\pi$$
$$570$$ 0 0
$$571$$ −8.32371 −0.348336 −0.174168 0.984716i $$-0.555724\pi$$
−0.174168 + 0.984716i $$0.555724\pi$$
$$572$$ 0 0
$$573$$ 15.9495 0.666298
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 7.29290 0.303607 0.151804 0.988411i $$-0.451492\pi$$
0.151804 + 0.988411i $$0.451492\pi$$
$$578$$ 0 0
$$579$$ −59.0684 −2.45480
$$580$$ 0 0
$$581$$ 1.02581 0.0425576
$$582$$ 0 0
$$583$$ 58.2994 2.41452
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 5.53264 0.228357 0.114178 0.993460i $$-0.463576\pi$$
0.114178 + 0.993460i $$0.463576\pi$$
$$588$$ 0 0
$$589$$ −2.50684 −0.103292
$$590$$ 0 0
$$591$$ 9.71577 0.399653
$$592$$ 0 0
$$593$$ 26.3252 1.08105 0.540524 0.841329i $$-0.318226\pi$$
0.540524 + 0.841329i $$0.318226\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 9.96919 0.408012
$$598$$ 0 0
$$599$$ −22.2994 −0.911130 −0.455565 0.890202i $$-0.650563\pi$$
−0.455565 + 0.890202i $$0.650563\pi$$
$$600$$ 0 0
$$601$$ 32.4947 1.32549 0.662743 0.748847i $$-0.269392\pi$$
0.662743 + 0.748847i $$0.269392\pi$$
$$602$$ 0 0
$$603$$ −34.7739 −1.41610
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 8.35105 0.338959 0.169479 0.985534i $$-0.445791\pi$$
0.169479 + 0.985534i $$0.445791\pi$$
$$608$$ 0 0
$$609$$ 0.337378 0.0136713
$$610$$ 0 0
$$611$$ −30.1892 −1.22132
$$612$$ 0 0
$$613$$ 38.2994 1.54690 0.773450 0.633858i $$-0.218529\pi$$
0.773450 + 0.633858i $$0.218529\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 14.3526 0.577813 0.288907 0.957357i $$-0.406708\pi$$
0.288907 + 0.957357i $$0.406708\pi$$
$$618$$ 0 0
$$619$$ 8.62314 0.346593 0.173297 0.984870i $$-0.444558\pi$$
0.173297 + 0.984870i $$0.444558\pi$$
$$620$$ 0 0
$$621$$ 50.8518 2.04061
$$622$$ 0 0
$$623$$ −1.16946 −0.0468533
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −14.6626 −0.585569
$$628$$ 0 0
$$629$$ −40.3723 −1.60975
$$630$$ 0 0
$$631$$ 10.3374 0.411525 0.205762 0.978602i $$-0.434033\pi$$
0.205762 + 0.978602i $$0.434033\pi$$
$$632$$ 0 0
$$633$$ −62.6394 −2.48969
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −37.2868 −1.47736
$$638$$ 0 0
$$639$$ 82.3541 3.25788
$$640$$ 0 0
$$641$$ 5.88369 0.232392 0.116196 0.993226i $$-0.462930\pi$$
0.116196 + 0.993226i $$0.462930\pi$$
$$642$$ 0 0
$$643$$ −25.5084 −1.00595 −0.502976 0.864300i $$-0.667762\pi$$
−0.502976 + 0.864300i $$0.667762\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −5.09157 −0.200170 −0.100085 0.994979i $$-0.531911\pi$$
−0.100085 + 0.994979i $$0.531911\pi$$
$$648$$ 0 0
$$649$$ −34.0942 −1.33831
$$650$$ 0 0
$$651$$ −0.635277 −0.0248985
$$652$$ 0 0
$$653$$ 11.1816 0.437570 0.218785 0.975773i $$-0.429791\pi$$
0.218785 + 0.975773i $$0.429791\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 38.6642 1.50843
$$658$$ 0 0
$$659$$ 13.7542 0.535787 0.267894 0.963449i $$-0.413672\pi$$
0.267894 + 0.963449i $$0.413672\pi$$
$$660$$ 0 0
$$661$$ −12.6171 −0.490747 −0.245374 0.969429i $$-0.578911\pi$$
−0.245374 + 0.969429i $$0.578911\pi$$
$$662$$ 0 0
$$663$$ −127.161 −4.93854
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −4.53871 −0.175740
$$668$$ 0 0
$$669$$ −47.1968 −1.82473
$$670$$ 0 0
$$671$$ −9.71577 −0.375073
$$672$$ 0 0
$$673$$ −2.35105 −0.0906263 −0.0453132 0.998973i $$-0.514429\pi$$
−0.0453132 + 0.998973i $$0.514429\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 23.7663 0.913414 0.456707 0.889617i $$-0.349029\pi$$
0.456707 + 0.889617i $$0.349029\pi$$
$$678$$ 0 0
$$679$$ 0.597928 0.0229464
$$680$$ 0 0
$$681$$ −70.2686 −2.69270
$$682$$ 0 0
$$683$$ 28.1695 1.07787 0.538937 0.842346i $$-0.318826\pi$$
0.538937 + 0.842346i $$0.318826\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −61.8594 −2.36008
$$688$$ 0 0
$$689$$ 68.9647 2.62734
$$690$$ 0 0
$$691$$ −2.32371 −0.0883979 −0.0441990 0.999023i $$-0.514074\pi$$
−0.0441990 + 0.999023i $$0.514074\pi$$
$$692$$ 0 0
$$693$$ −2.66262 −0.101145
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 19.5650 0.740016
$$700$$ 0 0
$$701$$ 23.7036 0.895274 0.447637 0.894215i $$-0.352266\pi$$
0.447637 + 0.894215i $$0.352266\pi$$
$$702$$ 0 0
$$703$$ −5.50684 −0.207694
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0.323706 0.0121742
$$708$$ 0 0
$$709$$ 9.05315 0.339998 0.169999 0.985444i $$-0.445624\pi$$
0.169999 + 0.985444i $$0.445624\pi$$
$$710$$ 0 0
$$711$$ −129.044 −4.83953
$$712$$ 0 0
$$713$$ 8.54631 0.320062
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −50.1326 −1.87224
$$718$$ 0 0
$$719$$ −35.0734 −1.30802 −0.654008 0.756488i $$-0.726914\pi$$
−0.654008 + 0.756488i $$0.726914\pi$$
$$720$$ 0 0
$$721$$ −0.183130 −0.00682012
$$722$$ 0 0
$$723$$ −15.6763 −0.583008
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 30.1386 1.11778 0.558890 0.829242i $$-0.311227\pi$$
0.558890 + 0.829242i $$0.311227\pi$$
$$728$$ 0 0
$$729$$ 49.9039 1.84829
$$730$$ 0 0
$$731$$ −3.71577 −0.137433
$$732$$ 0 0
$$733$$ −47.8321 −1.76672 −0.883359 0.468697i $$-0.844724\pi$$
−0.883359 + 0.468697i $$0.844724\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −20.6626 −0.761117
$$738$$ 0 0
$$739$$ 22.4674 0.826475 0.413238 0.910623i $$-0.364398\pi$$
0.413238 + 0.910623i $$0.364398\pi$$
$$740$$ 0 0
$$741$$ −17.3450 −0.637184
$$742$$ 0 0
$$743$$ −11.7926 −0.432629 −0.216314 0.976324i $$-0.569404\pi$$
−0.216314 + 0.976324i $$0.569404\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −99.8868 −3.65467
$$748$$ 0 0
$$749$$ 1.09310 0.0399411
$$750$$ 0 0
$$751$$ 2.03948 0.0744216 0.0372108 0.999307i $$-0.488153\pi$$
0.0372108 + 0.999307i $$0.488153\pi$$
$$752$$ 0 0
$$753$$ −4.94685 −0.180273
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −43.3526 −1.57568 −0.787838 0.615882i $$-0.788800\pi$$
−0.787838 + 0.615882i $$0.788800\pi$$
$$758$$ 0 0
$$759$$ 49.9879 1.81444
$$760$$ 0 0
$$761$$ 6.62921 0.240309 0.120154 0.992755i $$-0.461661\pi$$
0.120154 + 0.992755i $$0.461661\pi$$
$$762$$ 0 0
$$763$$ 0.00606730 0.000219651 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −40.3313 −1.45628
$$768$$ 0 0
$$769$$ −19.6429 −0.708340 −0.354170 0.935181i $$-0.615237\pi$$
−0.354170 + 0.935181i $$0.615237\pi$$
$$770$$ 0 0
$$771$$ −53.7036 −1.93409
$$772$$ 0 0
$$773$$ −14.4107 −0.518318 −0.259159 0.965835i $$-0.583445\pi$$
−0.259159 + 0.965835i $$0.583445\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −1.39553 −0.0500644
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 48.9347 1.75102
$$782$$ 0 0
$$783$$ −19.8579 −0.709663
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 24.3176 0.866830 0.433415 0.901194i $$-0.357308\pi$$
0.433415 + 0.901194i $$0.357308\pi$$
$$788$$ 0 0
$$789$$ −58.6505 −2.08801
$$790$$ 0 0
$$791$$ −0.467357 −0.0166173
$$792$$ 0 0
$$793$$ −11.4932 −0.408134
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 7.30397 0.258720 0.129360 0.991598i $$-0.458708\pi$$
0.129360 + 0.991598i $$0.458708\pi$$
$$798$$ 0 0
$$799$$ 41.5144 1.46868
$$800$$ 0 0
$$801$$ 113.875 4.02356
$$802$$ 0 0
$$803$$ 22.9742 0.810742
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 65.7481 2.31444
$$808$$ 0 0
$$809$$ −0.584729 −0.0205580 −0.0102790 0.999947i $$-0.503272\pi$$
−0.0102790 + 0.999947i $$0.503272\pi$$
$$810$$ 0 0
$$811$$ −1.90997 −0.0670682 −0.0335341 0.999438i $$-0.510676\pi$$
−0.0335341 + 0.999438i $$0.510676\pi$$
$$812$$ 0 0
$$813$$ −19.7937 −0.694194
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −0.506836 −0.0177319
$$818$$ 0 0
$$819$$ −3.14972 −0.110060
$$820$$ 0 0
$$821$$ −38.2226 −1.33398 −0.666989 0.745067i $$-0.732417\pi$$
−0.666989 + 0.745067i $$0.732417\pi$$
$$822$$ 0 0
$$823$$ −45.7481 −1.59468 −0.797340 0.603531i $$-0.793760\pi$$
−0.797340 + 0.603531i $$0.793760\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −22.6687 −0.788268 −0.394134 0.919053i $$-0.628955\pi$$
−0.394134 + 0.919053i $$0.628955\pi$$
$$828$$ 0 0
$$829$$ −4.63028 −0.160816 −0.0804081 0.996762i $$-0.525622\pi$$
−0.0804081 + 0.996762i $$0.525622\pi$$
$$830$$ 0 0
$$831$$ 102.043 3.53982
$$832$$ 0 0
$$833$$ 51.2747 1.77656
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 37.3921 1.29246
$$838$$ 0 0
$$839$$ 50.4826 1.74285 0.871426 0.490527i $$-0.163196\pi$$
0.871426 + 0.490527i $$0.163196\pi$$
$$840$$ 0 0
$$841$$ −27.2276 −0.938883
$$842$$ 0 0
$$843$$ 36.8458 1.26904
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −0.725305 −0.0249218
$$848$$ 0 0
$$849$$ 85.0562 2.91912
$$850$$ 0 0
$$851$$ 18.7739 0.643562
$$852$$ 0 0
$$853$$ −36.2105 −1.23982 −0.619912 0.784672i $$-0.712832\pi$$
−0.619912 + 0.784672i $$0.712832\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −25.1968 −0.860706 −0.430353 0.902661i $$-0.641611\pi$$
−0.430353 + 0.902661i $$0.641611\pi$$
$$858$$ 0 0
$$859$$ −18.8579 −0.643423 −0.321711 0.946838i $$-0.604258\pi$$
−0.321711 + 0.946838i $$0.604258\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 15.0137 0.511071 0.255536 0.966800i $$-0.417748\pi$$
0.255536 + 0.966800i $$0.417748\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 119.557 4.06037
$$868$$ 0 0
$$869$$ −76.6778 −2.60112
$$870$$ 0 0
$$871$$ −24.4426 −0.828206
$$872$$ 0 0
$$873$$ −58.2226 −1.97054
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −35.1128 −1.18568 −0.592838 0.805322i $$-0.701993\pi$$
−0.592838 + 0.805322i $$0.701993\pi$$
$$878$$ 0 0
$$879$$ −4.33131 −0.146091
$$880$$ 0 0
$$881$$ −41.3389 −1.39274 −0.696372 0.717681i $$-0.745203\pi$$
−0.696372 + 0.717681i $$0.745203\pi$$
$$882$$ 0 0
$$883$$ −12.6353 −0.425211 −0.212605 0.977138i $$-0.568195\pi$$
−0.212605 + 0.977138i $$0.568195\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 4.15579 0.139538 0.0697688 0.997563i $$-0.477774\pi$$
0.0697688 + 0.997563i $$0.477774\pi$$
$$888$$ 0 0
$$889$$ −1.38899 −0.0465853
$$890$$ 0 0
$$891$$ 116.159 3.89147
$$892$$ 0 0
$$893$$ 5.66262 0.189492
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 59.1326 1.97438
$$898$$ 0 0
$$899$$ −3.33738 −0.111308
$$900$$ 0 0
$$901$$ −94.8362 −3.15945
$$902$$ 0 0
$$903$$ −0.128441 −0.00427426
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −41.7542 −1.38643 −0.693213 0.720733i $$-0.743805\pi$$
−0.693213 + 0.720733i $$0.743805\pi$$
$$908$$ 0 0
$$909$$ −31.5205 −1.04547
$$910$$ 0 0
$$911$$ 9.12998 0.302490 0.151245 0.988496i $$-0.451672\pi$$
0.151245 + 0.988496i $$0.451672\pi$$
$$912$$ 0 0
$$913$$ −59.3526 −1.96428
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −0.116307 −0.00384079
$$918$$ 0 0
$$919$$ −19.0197 −0.627403 −0.313702 0.949522i $$-0.601569\pi$$
−0.313702 + 0.949522i $$0.601569\pi$$
$$920$$ 0 0
$$921$$ −9.25342 −0.304910
$$922$$ 0 0
$$923$$ 57.8868 1.90537
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 17.8321 0.585682
$$928$$ 0 0
$$929$$ −7.77239 −0.255004 −0.127502 0.991838i $$-0.540696\pi$$
−0.127502 + 0.991838i $$0.540696\pi$$
$$930$$ 0 0
$$931$$ 6.99393 0.229217
$$932$$ 0 0
$$933$$ 53.3218 1.74568
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 45.9818 1.50216 0.751080 0.660211i $$-0.229533\pi$$
0.751080 + 0.660211i $$0.229533\pi$$
$$938$$ 0 0
$$939$$ 68.4750 2.23460
$$940$$ 0 0
$$941$$ −40.6242 −1.32431 −0.662156 0.749366i $$-0.730358\pi$$
−0.662156 + 0.749366i $$0.730358\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −2.28423 −0.0742274 −0.0371137 0.999311i $$-0.511816\pi$$
−0.0371137 + 0.999311i $$0.511816\pi$$
$$948$$ 0 0
$$949$$ 27.1771 0.882205
$$950$$ 0 0
$$951$$ 100.499 3.25890
$$952$$ 0 0
$$953$$ 57.5084 1.86288 0.931439 0.363896i $$-0.118554\pi$$
0.931439 + 0.363896i $$0.118554\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −19.5205 −0.631008
$$958$$ 0 0
$$959$$ −0.656555 −0.0212013
$$960$$ 0 0
$$961$$ −24.7158 −0.797283
$$962$$ 0 0
$$963$$ −106.440 −3.42997
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −4.70210 −0.151209 −0.0756047 0.997138i $$-0.524089\pi$$
−0.0756047 + 0.997138i $$0.524089\pi$$
$$968$$ 0 0
$$969$$ 23.8518 0.766231
$$970$$ 0 0
$$971$$ −14.9863 −0.480934 −0.240467 0.970657i $$-0.577301\pi$$
−0.240467 + 0.970657i $$0.577301\pi$$
$$972$$ 0 0
$$973$$ 0.686891 0.0220207
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −8.89737 −0.284652 −0.142326 0.989820i $$-0.545458\pi$$
−0.142326 + 0.989820i $$0.545458\pi$$
$$978$$ 0 0
$$979$$ 67.6642 2.16256
$$980$$ 0 0
$$981$$ −0.590796 −0.0188627
$$982$$ 0 0
$$983$$ −1.60947 −0.0513341 −0.0256671 0.999671i $$-0.508171\pi$$
−0.0256671 + 0.999671i $$0.508171\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 1.43501 0.0456769
$$988$$ 0 0
$$989$$ 1.72791 0.0549443
$$990$$ 0 0
$$991$$ −16.8974 −0.536763 −0.268381 0.963313i $$-0.586489\pi$$
−0.268381 + 0.963313i $$0.586489\pi$$
$$992$$ 0 0
$$993$$ −92.3465 −2.93053
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −24.1558 −0.765021 −0.382511 0.923951i $$-0.624940\pi$$
−0.382511 + 0.923951i $$0.624940\pi$$
$$998$$ 0 0
$$999$$ 82.1402 2.59880
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 7600.2.a.bz.1.3 3
4.3 odd 2 950.2.a.j.1.1 3
5.4 even 2 7600.2.a.bk.1.1 3
12.11 even 2 8550.2.a.cp.1.2 3
20.3 even 4 950.2.b.h.799.4 6
20.7 even 4 950.2.b.h.799.3 6
20.19 odd 2 950.2.a.l.1.3 yes 3
60.59 even 2 8550.2.a.ci.1.2 3

By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.1 3 4.3 odd 2
950.2.a.l.1.3 yes 3 20.19 odd 2
950.2.b.h.799.3 6 20.7 even 4
950.2.b.h.799.4 6 20.3 even 4
7600.2.a.bk.1.1 3 5.4 even 2
7600.2.a.bz.1.3 3 1.1 even 1 trivial
8550.2.a.ci.1.2 3 60.59 even 2
8550.2.a.cp.1.2 3 12.11 even 2