# Properties

 Label 950.2.a.l.1.3 Level $950$ Weight $2$ Character 950.1 Self dual yes Analytic conductor $7.586$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$7.58578819202$$ 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: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$-2.25342$$ of defining polynomial Character $$\chi$$ $$=$$ 950.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +3.25342 q^{3} +1.00000 q^{4} +3.25342 q^{6} -0.0778929 q^{7} +1.00000 q^{8} +7.58473 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +3.25342 q^{3} +1.00000 q^{4} +3.25342 q^{6} -0.0778929 q^{7} +1.00000 q^{8} +7.58473 q^{9} -4.50684 q^{11} +3.25342 q^{12} -5.33131 q^{13} -0.0778929 q^{14} +1.00000 q^{16} +7.33131 q^{17} +7.58473 q^{18} +1.00000 q^{19} -0.253418 q^{21} -4.50684 q^{22} +3.40920 q^{23} +3.25342 q^{24} -5.33131 q^{26} +14.9160 q^{27} -0.0778929 q^{28} -1.33131 q^{29} -2.50684 q^{31} +1.00000 q^{32} -14.6626 q^{33} +7.33131 q^{34} +7.58473 q^{36} -5.50684 q^{37} +1.00000 q^{38} -17.3450 q^{39} -0.253418 q^{42} +0.506836 q^{43} -4.50684 q^{44} +3.40920 q^{46} -5.66262 q^{47} +3.25342 q^{48} -6.99393 q^{49} +23.8518 q^{51} -5.33131 q^{52} -12.9358 q^{53} +14.9160 q^{54} -0.0778929 q^{56} +3.25342 q^{57} -1.33131 q^{58} +7.56499 q^{59} -2.15579 q^{61} -2.50684 q^{62} -0.590796 q^{63} +1.00000 q^{64} -14.6626 q^{66} -4.58473 q^{67} +7.33131 q^{68} +11.0916 q^{69} -10.8579 q^{71} +7.58473 q^{72} -5.09763 q^{73} -5.50684 q^{74} +1.00000 q^{76} +0.351050 q^{77} -17.3450 q^{78} +17.0137 q^{79} +25.7739 q^{81} -13.1695 q^{83} -0.253418 q^{84} +0.506836 q^{86} -4.33131 q^{87} -4.50684 q^{88} +15.0137 q^{89} +0.415271 q^{91} +3.40920 q^{92} -8.15579 q^{93} -5.66262 q^{94} +3.25342 q^{96} +7.67629 q^{97} -6.99393 q^{98} -34.1831 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + 5q^{9} + O(q^{10})$$ $$3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + 5q^{9} + 2q^{11} + 2q^{12} - 6q^{13} + 2q^{14} + 3q^{16} + 12q^{17} + 5q^{18} + 3q^{19} + 7q^{21} + 2q^{22} - 2q^{23} + 2q^{24} - 6q^{26} + 17q^{27} + 2q^{28} + 6q^{29} + 8q^{31} + 3q^{32} - 24q^{33} + 12q^{34} + 5q^{36} - q^{37} + 3q^{38} - 11q^{39} + 7q^{42} - 14q^{43} + 2q^{44} - 2q^{46} + 3q^{47} + 2q^{48} + 9q^{49} + 15q^{51} - 6q^{52} - 10q^{53} + 17q^{54} + 2q^{56} + 2q^{57} + 6q^{58} + 6q^{59} - 2q^{61} + 8q^{62} - 14q^{63} + 3q^{64} - 24q^{66} + 4q^{67} + 12q^{68} - 6q^{71} + 5q^{72} - 12q^{73} - q^{74} + 3q^{76} - 10q^{77} - 11q^{78} + 20q^{79} + 23q^{81} - 4q^{83} + 7q^{84} - 14q^{86} - 3q^{87} + 2q^{88} + 14q^{89} + 19q^{91} - 2q^{92} - 20q^{93} + 3q^{94} + 2q^{96} - 28q^{97} + 9q^{98} - 36q^{99} + O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 3.25342 1.87836 0.939181 0.343423i $$-0.111586\pi$$
0.939181 + 0.343423i $$0.111586\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 3.25342 1.32820
$$7$$ −0.0778929 −0.0294407 −0.0147204 0.999892i $$-0.504686\pi$$
−0.0147204 + 0.999892i $$0.504686\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 7.58473 2.52824
$$10$$ 0 0
$$11$$ −4.50684 −1.35886 −0.679431 0.733739i $$-0.737773\pi$$
−0.679431 + 0.733739i $$0.737773\pi$$
$$12$$ 3.25342 0.939181
$$13$$ −5.33131 −1.47864 −0.739320 0.673354i $$-0.764853\pi$$
−0.739320 + 0.673354i $$0.764853\pi$$
$$14$$ −0.0778929 −0.0208177
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 7.33131 1.77810 0.889052 0.457806i $$-0.151365\pi$$
0.889052 + 0.457806i $$0.151365\pi$$
$$18$$ 7.58473 1.78774
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ −0.253418 −0.0553003
$$22$$ −4.50684 −0.960861
$$23$$ 3.40920 0.710868 0.355434 0.934701i $$-0.384333\pi$$
0.355434 + 0.934701i $$0.384333\pi$$
$$24$$ 3.25342 0.664101
$$25$$ 0 0
$$26$$ −5.33131 −1.04556
$$27$$ 14.9160 2.87059
$$28$$ −0.0778929 −0.0147204
$$29$$ −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 $$-0.572278\pi$$
−0.225121 + 0.974331i $$0.572278\pi$$
$$32$$ 1.00000 0.176777
$$33$$ −14.6626 −2.55243
$$34$$ 7.33131 1.25731
$$35$$ 0 0
$$36$$ 7.58473 1.26412
$$37$$ −5.50684 −0.905318 −0.452659 0.891684i $$-0.649525\pi$$
−0.452659 + 0.891684i $$0.649525\pi$$
$$38$$ 1.00000 0.162221
$$39$$ −17.3450 −2.77742
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ −0.253418 −0.0391033
$$43$$ 0.506836 0.0772918 0.0386459 0.999253i $$-0.487696\pi$$
0.0386459 + 0.999253i $$0.487696\pi$$
$$44$$ −4.50684 −0.679431
$$45$$ 0 0
$$46$$ 3.40920 0.502660
$$47$$ −5.66262 −0.825978 −0.412989 0.910736i $$-0.635515\pi$$
−0.412989 + 0.910736i $$0.635515\pi$$
$$48$$ 3.25342 0.469590
$$49$$ −6.99393 −0.999133
$$50$$ 0 0
$$51$$ 23.8518 3.33992
$$52$$ −5.33131 −0.739320
$$53$$ −12.9358 −1.77687 −0.888433 0.459006i $$-0.848206\pi$$
−0.888433 + 0.459006i $$0.848206\pi$$
$$54$$ 14.9160 2.02982
$$55$$ 0 0
$$56$$ −0.0778929 −0.0104089
$$57$$ 3.25342 0.430926
$$58$$ −1.33131 −0.174810
$$59$$ 7.56499 0.984878 0.492439 0.870347i $$-0.336106\pi$$
0.492439 + 0.870347i $$0.336106\pi$$
$$60$$ 0 0
$$61$$ −2.15579 −0.276020 −0.138010 0.990431i $$-0.544071\pi$$
−0.138010 + 0.990431i $$0.544071\pi$$
$$62$$ −2.50684 −0.318369
$$63$$ −0.590796 −0.0744333
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −14.6626 −1.80484
$$67$$ −4.58473 −0.560114 −0.280057 0.959983i $$-0.590353\pi$$
−0.280057 + 0.959983i $$0.590353\pi$$
$$68$$ 7.33131 0.889052
$$69$$ 11.0916 1.33527
$$70$$ 0 0
$$71$$ −10.8579 −1.28859 −0.644297 0.764775i $$-0.722850\pi$$
−0.644297 + 0.764775i $$0.722850\pi$$
$$72$$ 7.58473 0.893869
$$73$$ −5.09763 −0.596633 −0.298316 0.954467i $$-0.596425\pi$$
−0.298316 + 0.954467i $$0.596425\pi$$
$$74$$ −5.50684 −0.640157
$$75$$ 0 0
$$76$$ 1.00000 0.114708
$$77$$ 0.351050 0.0400059
$$78$$ −17.3450 −1.96393
$$79$$ 17.0137 1.91419 0.957094 0.289778i $$-0.0935815\pi$$
0.957094 + 0.289778i $$0.0935815\pi$$
$$80$$ 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 $$0.757130\pi$$
$$84$$ −0.253418 −0.0276502
$$85$$ 0 0
$$86$$ 0.506836 0.0546535
$$87$$ −4.33131 −0.464365
$$88$$ −4.50684 −0.480430
$$89$$ 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
$$92$$ 3.40920 0.355434
$$93$$ −8.15579 −0.845716
$$94$$ −5.66262 −0.584055
$$95$$ 0 0
$$96$$ 3.25342 0.332051
$$97$$ 7.67629 0.779410 0.389705 0.920940i $$-0.372577\pi$$
0.389705 + 0.920940i $$0.372577\pi$$
$$98$$ −6.99393 −0.706494
$$99$$ −34.1831 −3.43553
$$100$$ 0 0
$$101$$ −4.15579 −0.413516 −0.206758 0.978392i $$-0.566291\pi$$
−0.206758 + 0.978392i $$0.566291\pi$$
$$102$$ 23.8518 2.36168
$$103$$ 2.35105 0.231656 0.115828 0.993269i $$-0.463048\pi$$
0.115828 + 0.993269i $$0.463048\pi$$
$$104$$ −5.33131 −0.522778
$$105$$ 0 0
$$106$$ −12.9358 −1.25643
$$107$$ −14.0334 −1.35666 −0.678331 0.734757i $$-0.737296\pi$$
−0.678331 + 0.734757i $$0.737296\pi$$
$$108$$ 14.9160 1.43530
$$109$$ −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
$$112$$ −0.0778929 −0.00736018
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 3.25342 0.304711
$$115$$ 0 0
$$116$$ −1.33131 −0.123609
$$117$$ −40.4365 −3.73836
$$118$$ 7.56499 0.696414
$$119$$ −0.571057 −0.0523487
$$120$$ 0 0
$$121$$ 9.31157 0.846506
$$122$$ −2.15579 −0.195176
$$123$$ 0 0
$$124$$ −2.50684 −0.225121
$$125$$ 0 0
$$126$$ −0.590796 −0.0526323
$$127$$ 17.8321 1.58234 0.791171 0.611596i $$-0.209472\pi$$
0.791171 + 0.611596i $$0.209472\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 1.64895 0.145182
$$130$$ 0 0
$$131$$ −1.49316 −0.130458 −0.0652292 0.997870i $$-0.520778\pi$$
−0.0652292 + 0.997870i $$0.520778\pi$$
$$132$$ −14.6626 −1.27622
$$133$$ −0.0778929 −0.00675417
$$134$$ −4.58473 −0.396060
$$135$$ 0 0
$$136$$ 7.33131 0.628655
$$137$$ −8.42894 −0.720133 −0.360067 0.932927i $$-0.617246\pi$$
−0.360067 + 0.932927i $$0.617246\pi$$
$$138$$ 11.0916 0.944177
$$139$$ 8.81841 0.747968 0.373984 0.927435i $$-0.377992\pi$$
0.373984 + 0.927435i $$0.377992\pi$$
$$140$$ 0 0
$$141$$ −18.4229 −1.55149
$$142$$ −10.8579 −0.911174
$$143$$ 24.0273 2.00927
$$144$$ 7.58473 0.632061
$$145$$ 0 0
$$146$$ −5.09763 −0.421883
$$147$$ −22.7542 −1.87673
$$148$$ −5.50684 −0.452659
$$149$$ 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 $$-0.197401\pi$$
0.813788 + 0.581161i $$0.197401\pi$$
$$152$$ 1.00000 0.0811107
$$153$$ 55.6060 4.49548
$$154$$ 0.351050 0.0282884
$$155$$ 0 0
$$156$$ −17.3450 −1.38871
$$157$$ 0.506836 0.0404499 0.0202250 0.999795i $$-0.493562\pi$$
0.0202250 + 0.999795i $$0.493562\pi$$
$$158$$ 17.0137 1.35354
$$159$$ −42.0855 −3.33760
$$160$$ 0 0
$$161$$ −0.265553 −0.0209285
$$162$$ 25.7739 2.02499
$$163$$ 0.830542 0.0650531 0.0325265 0.999471i $$-0.489645\pi$$
0.0325265 + 0.999471i $$0.489645\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −13.1695 −1.02215
$$167$$ 16.5068 1.27734 0.638669 0.769482i $$-0.279485\pi$$
0.638669 + 0.769482i $$0.279485\pi$$
$$168$$ −0.253418 −0.0195516
$$169$$ 15.4229 1.18638
$$170$$ 0 0
$$171$$ 7.58473 0.580019
$$172$$ 0.506836 0.0386459
$$173$$ 18.8321 1.43178 0.715888 0.698215i $$-0.246022\pi$$
0.715888 + 0.698215i $$0.246022\pi$$
$$174$$ −4.33131 −0.328356
$$175$$ 0 0
$$176$$ −4.50684 −0.339716
$$177$$ 24.6121 1.84996
$$178$$ 15.0137 1.12532
$$179$$ −7.15579 −0.534849 −0.267424 0.963579i $$-0.586173\pi$$
−0.267424 + 0.963579i $$0.586173\pi$$
$$180$$ 0 0
$$181$$ 12.5205 0.930642 0.465321 0.885142i $$-0.345939\pi$$
0.465321 + 0.885142i $$0.345939\pi$$
$$182$$ 0.415271 0.0307819
$$183$$ −7.01367 −0.518466
$$184$$ 3.40920 0.251330
$$185$$ 0 0
$$186$$ −8.15579 −0.598011
$$187$$ −33.0410 −2.41620
$$188$$ −5.66262 −0.412989
$$189$$ −1.16185 −0.0845124
$$190$$ 0 0
$$191$$ −4.90237 −0.354723 −0.177361 0.984146i $$-0.556756\pi$$
−0.177361 + 0.984146i $$0.556756\pi$$
$$192$$ 3.25342 0.234795
$$193$$ 18.1558 1.30688 0.653441 0.756977i $$-0.273325\pi$$
0.653441 + 0.756977i $$0.273325\pi$$
$$194$$ 7.67629 0.551126
$$195$$ 0 0
$$196$$ −6.99393 −0.499567
$$197$$ −2.98633 −0.212767 −0.106384 0.994325i $$-0.533927\pi$$
−0.106384 + 0.994325i $$0.533927\pi$$
$$198$$ −34.1831 −2.42929
$$199$$ −3.06422 −0.217217 −0.108608 0.994085i $$-0.534639\pi$$
−0.108608 + 0.994085i $$0.534639\pi$$
$$200$$ 0 0
$$201$$ −14.9160 −1.05210
$$202$$ −4.15579 −0.292400
$$203$$ 0.103700 0.00727829
$$204$$ 23.8518 1.66996
$$205$$ 0 0
$$206$$ 2.35105 0.163805
$$207$$ 25.8579 1.79725
$$208$$ −5.33131 −0.369660
$$209$$ −4.50684 −0.311744
$$210$$ 0 0
$$211$$ 19.2534 1.32546 0.662730 0.748858i $$-0.269398\pi$$
0.662730 + 0.748858i $$0.269398\pi$$
$$212$$ −12.9358 −0.888433
$$213$$ −35.3252 −2.42045
$$214$$ −14.0334 −0.959304
$$215$$ 0 0
$$216$$ 14.9160 1.01491
$$217$$ 0.195265 0.0132554
$$218$$ −0.0778929 −0.00527557
$$219$$ −16.5847 −1.12069
$$220$$ 0 0
$$221$$ −39.0855 −2.62918
$$222$$ −17.9160 −1.20245
$$223$$ −14.5068 −0.971450 −0.485725 0.874112i $$-0.661444\pi$$
−0.485725 + 0.874112i $$0.661444\pi$$
$$224$$ −0.0778929 −0.00520444
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −21.5984 −1.43354 −0.716768 0.697312i $$-0.754379\pi$$
−0.716768 + 0.697312i $$0.754379\pi$$
$$228$$ 3.25342 0.215463
$$229$$ −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
$$232$$ −1.33131 −0.0874048
$$233$$ −6.01367 −0.393969 −0.196984 0.980407i $$-0.563115\pi$$
−0.196984 + 0.980407i $$0.563115\pi$$
$$234$$ −40.4365 −2.64342
$$235$$ 0 0
$$236$$ 7.56499 0.492439
$$237$$ 55.3526 3.59554
$$238$$ −0.571057 −0.0370161
$$239$$ 15.4092 0.996739 0.498369 0.866965i $$-0.333932\pi$$
0.498369 + 0.866965i $$0.333932\pi$$
$$240$$ 0 0
$$241$$ −4.81841 −0.310381 −0.155190 0.987885i $$-0.549599\pi$$
−0.155190 + 0.987885i $$0.549599\pi$$
$$242$$ 9.31157 0.598570
$$243$$ 39.1052 2.50860
$$244$$ −2.15579 −0.138010
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −5.33131 −0.339223
$$248$$ −2.50684 −0.159184
$$249$$ −42.8458 −2.71524
$$250$$ 0 0
$$251$$ 1.52051 0.0959736 0.0479868 0.998848i $$-0.484719\pi$$
0.0479868 + 0.998848i $$0.484719\pi$$
$$252$$ −0.590796 −0.0372167
$$253$$ −15.3647 −0.965972
$$254$$ 17.8321 1.11888
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 16.5068 1.02967 0.514834 0.857290i $$-0.327854\pi$$
0.514834 + 0.857290i $$0.327854\pi$$
$$258$$ 1.64895 0.102659
$$259$$ 0.428943 0.0266532
$$260$$ 0 0
$$261$$ −10.0976 −0.625028
$$262$$ −1.49316 −0.0922480
$$263$$ −18.0273 −1.11161 −0.555807 0.831311i $$-0.687591\pi$$
−0.555807 + 0.831311i $$0.687591\pi$$
$$264$$ −14.6626 −0.902422
$$265$$ 0 0
$$266$$ −0.0778929 −0.00477592
$$267$$ 48.8458 2.98931
$$268$$ −4.58473 −0.280057
$$269$$ 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 $$-0.440840\pi$$
0.184787 + 0.982779i $$0.440840\pi$$
$$272$$ 7.33131 0.444526
$$273$$ 1.35105 0.0817693
$$274$$ −8.42894 −0.509211
$$275$$ 0 0
$$276$$ 11.0916 0.667634
$$277$$ −31.3647 −1.88452 −0.942262 0.334877i $$-0.891305\pi$$
−0.942262 + 0.334877i $$0.891305\pi$$
$$278$$ 8.81841 0.528893
$$279$$ −19.0137 −1.13832
$$280$$ 0 0
$$281$$ 11.3252 0.675607 0.337804 0.941217i $$-0.390316\pi$$
0.337804 + 0.941217i $$0.390316\pi$$
$$282$$ −18.4229 −1.09707
$$283$$ 26.1437 1.55408 0.777039 0.629452i $$-0.216721\pi$$
0.777039 + 0.629452i $$0.216721\pi$$
$$284$$ −10.8579 −0.644297
$$285$$ 0 0
$$286$$ 24.0273 1.42077
$$287$$ 0 0
$$288$$ 7.58473 0.446934
$$289$$ 36.7481 2.16165
$$290$$ 0 0
$$291$$ 24.9742 1.46401
$$292$$ −5.09763 −0.298316
$$293$$ 1.33131 0.0777760 0.0388880 0.999244i $$-0.487618\pi$$
0.0388880 + 0.999244i $$0.487618\pi$$
$$294$$ −22.7542 −1.32705
$$295$$ 0 0
$$296$$ −5.50684 −0.320078
$$297$$ −67.2241 −3.90074
$$298$$ 17.6763 1.02396
$$299$$ −18.1755 −1.05112
$$300$$ 0 0
$$301$$ −0.0394789 −0.00227553
$$302$$ 20.0000 1.15087
$$303$$ −13.5205 −0.776733
$$304$$ 1.00000 0.0573539
$$305$$ 0 0
$$306$$ 55.6060 3.17878
$$307$$ −2.84421 −0.162328 −0.0811639 0.996701i $$-0.525864\pi$$
−0.0811639 + 0.996701i $$0.525864\pi$$
$$308$$ 0.351050 0.0200030
$$309$$ 7.64895 0.435134
$$310$$ 0 0
$$311$$ −16.3895 −0.929361 −0.464681 0.885478i $$-0.653831\pi$$
−0.464681 + 0.885478i $$0.653831\pi$$
$$312$$ −17.3450 −0.981966
$$313$$ −21.0471 −1.18965 −0.594826 0.803855i $$-0.702779\pi$$
−0.594826 + 0.803855i $$0.702779\pi$$
$$314$$ 0.506836 0.0286024
$$315$$ 0 0
$$316$$ 17.0137 0.957094
$$317$$ −30.8902 −1.73497 −0.867484 0.497465i $$-0.834264\pi$$
−0.867484 + 0.497465i $$0.834264\pi$$
$$318$$ −42.0855 −2.36004
$$319$$ 6.00000 0.335936
$$320$$ 0 0
$$321$$ −45.6566 −2.54830
$$322$$ −0.265553 −0.0147987
$$323$$ 7.33131 0.407925
$$324$$ 25.7739 1.43188
$$325$$ 0 0
$$326$$ 0.830542 0.0459995
$$327$$ −0.253418 −0.0140140
$$328$$ 0 0
$$329$$ 0.441078 0.0243174
$$330$$ 0 0
$$331$$ 28.3845 1.56015 0.780076 0.625685i $$-0.215181\pi$$
0.780076 + 0.625685i $$0.215181\pi$$
$$332$$ −13.1695 −0.722768
$$333$$ −41.7679 −2.28886
$$334$$ 16.5068 0.903214
$$335$$ 0 0
$$336$$ −0.253418 −0.0138251
$$337$$ −17.8716 −0.973526 −0.486763 0.873534i $$-0.661822\pi$$
−0.486763 + 0.873534i $$0.661822\pi$$
$$338$$ 15.4229 0.838894
$$339$$ −19.5205 −1.06021
$$340$$ 0 0
$$341$$ 11.2979 0.611816
$$342$$ 7.58473 0.410135
$$343$$ 1.09003 0.0588560
$$344$$ 0.506836 0.0273268
$$345$$ 0 0
$$346$$ 18.8321 1.01242
$$347$$ 33.0410 1.77373 0.886867 0.462024i $$-0.152877\pi$$
0.886867 + 0.462024i $$0.152877\pi$$
$$348$$ −4.33131 −0.232183
$$349$$ −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
$$352$$ −4.50684 −0.240215
$$353$$ −5.90997 −0.314556 −0.157278 0.987554i $$-0.550272\pi$$
−0.157278 + 0.987554i $$0.550272\pi$$
$$354$$ 24.6121 1.30812
$$355$$ 0 0
$$356$$ 15.0137 0.795723
$$357$$ −1.85789 −0.0983298
$$358$$ −7.15579 −0.378195
$$359$$ −7.00760 −0.369847 −0.184924 0.982753i $$-0.559204\pi$$
−0.184924 + 0.982753i $$0.559204\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 12.5205 0.658063
$$363$$ 30.2944 1.59005
$$364$$ 0.415271 0.0217661
$$365$$ 0 0
$$366$$ −7.01367 −0.366611
$$367$$ 17.7158 0.924756 0.462378 0.886683i $$-0.346996\pi$$
0.462378 + 0.886683i $$0.346996\pi$$
$$368$$ 3.40920 0.177717
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1.00760 0.0523122
$$372$$ −8.15579 −0.422858
$$373$$ 15.4487 0.799902 0.399951 0.916536i $$-0.369027\pi$$
0.399951 + 0.916536i $$0.369027\pi$$
$$374$$ −33.0410 −1.70851
$$375$$ 0 0
$$376$$ −5.66262 −0.292027
$$377$$ 7.09763 0.365547
$$378$$ −1.16185 −0.0597593
$$379$$ 34.4563 1.76990 0.884950 0.465685i $$-0.154192\pi$$
0.884950 + 0.465685i $$0.154192\pi$$
$$380$$ 0 0
$$381$$ 58.0152 2.97221
$$382$$ −4.90237 −0.250827
$$383$$ −12.0273 −0.614569 −0.307284 0.951618i $$-0.599420\pi$$
−0.307284 + 0.951618i $$0.599420\pi$$
$$384$$ 3.25342 0.166025
$$385$$ 0 0
$$386$$ 18.1558 0.924105
$$387$$ 3.84421 0.195412
$$388$$ 7.67629 0.389705
$$389$$ −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
$$392$$ −6.99393 −0.353247
$$393$$ −4.85789 −0.245048
$$394$$ −2.98633 −0.150449
$$395$$ 0 0
$$396$$ −34.1831 −1.71777
$$397$$ 1.32524 0.0665121 0.0332560 0.999447i $$-0.489412\pi$$
0.0332560 + 0.999447i $$0.489412\pi$$
$$398$$ −3.06422 −0.153596
$$399$$ −0.253418 −0.0126868
$$400$$ 0 0
$$401$$ −6.46736 −0.322964 −0.161482 0.986876i $$-0.551627\pi$$
−0.161482 + 0.986876i $$0.551627\pi$$
$$402$$ −14.9160 −0.743944
$$403$$ 13.3647 0.665744
$$404$$ −4.15579 −0.206758
$$405$$ 0 0
$$406$$ 0.103700 0.00514653
$$407$$ 24.8184 1.23020
$$408$$ 23.8518 1.18084
$$409$$ −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
$$412$$ 2.35105 0.115828
$$413$$ −0.589259 −0.0289955
$$414$$ 25.8579 1.27085
$$415$$ 0 0
$$416$$ −5.33131 −0.261389
$$417$$ 28.6900 1.40495
$$418$$ −4.50684 −0.220437
$$419$$ 16.6231 0.812094 0.406047 0.913852i $$-0.366907\pi$$
0.406047 + 0.913852i $$0.366907\pi$$
$$420$$ 0 0
$$421$$ −31.1128 −1.51635 −0.758174 0.652053i $$-0.773908\pi$$
−0.758174 + 0.652053i $$0.773908\pi$$
$$422$$ 19.2534 0.937242
$$423$$ −42.9495 −2.08827
$$424$$ −12.9358 −0.628217
$$425$$ 0 0
$$426$$ −35.3252 −1.71151
$$427$$ 0.167920 0.00812623
$$428$$ −14.0334 −0.678331
$$429$$ 78.1710 3.77413
$$430$$ 0 0
$$431$$ −10.1831 −0.490504 −0.245252 0.969459i $$-0.578871\pi$$
−0.245252 + 0.969459i $$0.578871\pi$$
$$432$$ 14.9160 0.717648
$$433$$ 22.1953 1.06664 0.533318 0.845915i $$-0.320945\pi$$
0.533318 + 0.845915i $$0.320945\pi$$
$$434$$ 0.195265 0.00937300
$$435$$ 0 0
$$436$$ −0.0778929 −0.00373039
$$437$$ 3.40920 0.163084
$$438$$ −16.5847 −0.792449
$$439$$ −9.32524 −0.445070 −0.222535 0.974925i $$-0.571433\pi$$
−0.222535 + 0.974925i $$0.571433\pi$$
$$440$$ 0 0
$$441$$ −53.0471 −2.52605
$$442$$ −39.0855 −1.85911
$$443$$ −13.9879 −0.664584 −0.332292 0.943177i $$-0.607822\pi$$
−0.332292 + 0.943177i $$0.607822\pi$$
$$444$$ −17.9160 −0.850258
$$445$$ 0 0
$$446$$ −14.5068 −0.686919
$$447$$ 57.5084 2.72005
$$448$$ −0.0778929 −0.00368009
$$449$$ 13.4932 0.636782 0.318391 0.947960i $$-0.396858\pi$$
0.318391 + 0.947960i $$0.396858\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −6.00000 −0.282216
$$453$$ 65.0684 3.05718
$$454$$ −21.5984 −1.01366
$$455$$ 0 0
$$456$$ 3.25342 0.152355
$$457$$ 9.68236 0.452922 0.226461 0.974020i $$-0.427284\pi$$
0.226461 + 0.974020i $$0.427284\pi$$
$$458$$ −19.0137 −0.888451
$$459$$ 109.354 5.10421
$$460$$ 0 0
$$461$$ 8.66262 0.403459 0.201729 0.979441i $$-0.435344\pi$$
0.201729 + 0.979441i $$0.435344\pi$$
$$462$$ 1.14211 0.0531359
$$463$$ 28.0015 1.30134 0.650671 0.759360i $$-0.274488\pi$$
0.650671 + 0.759360i $$0.274488\pi$$
$$464$$ −1.33131 −0.0618046
$$465$$ 0 0
$$466$$ −6.01367 −0.278578
$$467$$ 16.9742 0.785472 0.392736 0.919651i $$-0.371529\pi$$
0.392736 + 0.919651i $$0.371529\pi$$
$$468$$ −40.4365 −1.86918
$$469$$ 0.357118 0.0164902
$$470$$ 0 0
$$471$$ 1.64895 0.0759796
$$472$$ 7.56499 0.348207
$$473$$ −2.28423 −0.105029
$$474$$ 55.3526 2.54243
$$475$$ 0 0
$$476$$ −0.571057 −0.0261743
$$477$$ −98.1144 −4.49235
$$478$$ 15.4092 0.704801
$$479$$ 10.0532 0.459340 0.229670 0.973269i $$-0.426235\pi$$
0.229670 + 0.973269i $$0.426235\pi$$
$$480$$ 0 0
$$481$$ 29.3587 1.33864
$$482$$ −4.81841 −0.219472
$$483$$ −0.863954 −0.0393113
$$484$$ 9.31157 0.423253
$$485$$ 0 0
$$486$$ 39.1052 1.77385
$$487$$ 19.2089 0.870440 0.435220 0.900324i $$-0.356671\pi$$
0.435220 + 0.900324i $$0.356671\pi$$
$$488$$ −2.15579 −0.0975878
$$489$$ 2.70210 0.122193
$$490$$ 0 0
$$491$$ 5.32524 0.240325 0.120162 0.992754i $$-0.461658\pi$$
0.120162 + 0.992754i $$0.461658\pi$$
$$492$$ 0 0
$$493$$ −9.76025 −0.439580
$$494$$ −5.33131 −0.239867
$$495$$ 0 0
$$496$$ −2.50684 −0.112560
$$497$$ 0.845752 0.0379372
$$498$$ −42.8458 −1.91996
$$499$$ −11.9605 −0.535426 −0.267713 0.963499i $$-0.586268\pi$$
−0.267713 + 0.963499i $$0.586268\pi$$
$$500$$ 0 0
$$501$$ 53.7036 2.39930
$$502$$ 1.52051 0.0678636
$$503$$ −19.3313 −0.861941 −0.430970 0.902366i $$-0.641829\pi$$
−0.430970 + 0.902366i $$0.641829\pi$$
$$504$$ −0.590796 −0.0263162
$$505$$ 0 0
$$506$$ −15.3647 −0.683045
$$507$$ 50.1771 2.22844
$$508$$ 17.8321 0.791171
$$509$$ −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
$$512$$ 1.00000 0.0441942
$$513$$ 14.9160 0.658559
$$514$$ 16.5068 0.728085
$$515$$ 0 0
$$516$$ 1.64895 0.0725910
$$517$$ 25.5205 1.12239
$$518$$ 0.428943 0.0188467
$$519$$ 61.2686 2.68939
$$520$$ 0 0
$$521$$ −31.5205 −1.38094 −0.690469 0.723362i $$-0.742596\pi$$
−0.690469 + 0.723362i $$0.742596\pi$$
$$522$$ −10.0976 −0.441961
$$523$$ 5.59840 0.244801 0.122400 0.992481i $$-0.460941\pi$$
0.122400 + 0.992481i $$0.460941\pi$$
$$524$$ −1.49316 −0.0652292
$$525$$ 0 0
$$526$$ −18.0273 −0.786030
$$527$$ −18.3784 −0.800575
$$528$$ −14.6626 −0.638109
$$529$$ −11.3773 −0.494667
$$530$$ 0 0
$$531$$ 57.3784 2.49001
$$532$$ −0.0778929 −0.00337708
$$533$$ 0 0
$$534$$ 48.8458 2.11376
$$535$$ 0 0
$$536$$ −4.58473 −0.198030
$$537$$ −23.2808 −1.00464
$$538$$ 20.2089 0.871269
$$539$$ 31.5205 1.35768
$$540$$ 0 0
$$541$$ 15.1968 0.653362 0.326681 0.945135i $$-0.394070\pi$$
0.326681 + 0.945135i $$0.394070\pi$$
$$542$$ 6.08396 0.261328
$$543$$ 40.7344 1.74808
$$544$$ 7.33131 0.314327
$$545$$ 0 0
$$546$$ 1.35105 0.0578196
$$547$$ −26.6505 −1.13949 −0.569746 0.821821i $$-0.692959\pi$$
−0.569746 + 0.821821i $$0.692959\pi$$
$$548$$ −8.42894 −0.360067
$$549$$ −16.3511 −0.697846
$$550$$ 0 0
$$551$$ −1.33131 −0.0567158
$$552$$ 11.0916 0.472088
$$553$$ −1.32524 −0.0563551
$$554$$ −31.3647 −1.33256
$$555$$ 0 0
$$556$$ 8.81841 0.373984
$$557$$ 12.8458 0.544292 0.272146 0.962256i $$-0.412267\pi$$
0.272146 + 0.962256i $$0.412267\pi$$
$$558$$ −19.0137 −0.804913
$$559$$ −2.70210 −0.114287
$$560$$ 0 0
$$561$$ −107.496 −4.53849
$$562$$ 11.3252 0.477727
$$563$$ 10.1968 0.429744 0.214872 0.976642i $$-0.431067\pi$$
0.214872 + 0.976642i $$0.431067\pi$$
$$564$$ −18.4229 −0.775743
$$565$$ 0 0
$$566$$ 26.1437 1.09890
$$567$$ −2.00760 −0.0843115
$$568$$ −10.8579 −0.455587
$$569$$ −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 $$-0.444276\pi$$
0.174168 + 0.984716i $$0.444276\pi$$
$$572$$ 24.0273 1.00463
$$573$$ −15.9495 −0.666298
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 7.58473 0.316030
$$577$$ −7.29290 −0.303607 −0.151804 0.988411i $$-0.548508\pi$$
−0.151804 + 0.988411i $$0.548508\pi$$
$$578$$ 36.7481 1.52852
$$579$$ 59.0684 2.45480
$$580$$ 0 0
$$581$$ 1.02581 0.0425576
$$582$$ 24.9742 1.03521
$$583$$ 58.2994 2.41452
$$584$$ −5.09763 −0.210942
$$585$$ 0 0
$$586$$ 1.33131 0.0549959
$$587$$ 5.53264 0.228357 0.114178 0.993460i $$-0.463576\pi$$
0.114178 + 0.993460i $$0.463576\pi$$
$$588$$ −22.7542 −0.938367
$$589$$ −2.50684 −0.103292
$$590$$ 0 0
$$591$$ −9.71577 −0.399653
$$592$$ −5.50684 −0.226330
$$593$$ −26.3252 −1.08105 −0.540524 0.841329i $$-0.681774\pi$$
−0.540524 + 0.841329i $$0.681774\pi$$
$$594$$ −67.2241 −2.75824
$$595$$ 0 0
$$596$$ 17.6763 0.724049
$$597$$ −9.96919 −0.408012
$$598$$ −18.1755 −0.743252
$$599$$ 22.2994 0.911130 0.455565 0.890202i $$-0.349437\pi$$
0.455565 + 0.890202i $$0.349437\pi$$
$$600$$ 0 0
$$601$$ 32.4947 1.32549 0.662743 0.748847i $$-0.269392\pi$$
0.662743 + 0.748847i $$0.269392\pi$$
$$602$$ −0.0394789 −0.00160904
$$603$$ −34.7739 −1.41610
$$604$$ 20.0000 0.813788
$$605$$ 0 0
$$606$$ −13.5205 −0.549233
$$607$$ 8.35105 0.338959 0.169479 0.985534i $$-0.445791\pi$$
0.169479 + 0.985534i $$0.445791\pi$$
$$608$$ 1.00000 0.0405554
$$609$$ 0.337378 0.0136713
$$610$$ 0 0
$$611$$ 30.1892 1.22132
$$612$$ 55.6060 2.24774
$$613$$ −38.2994 −1.54690 −0.773450 0.633858i $$-0.781471\pi$$
−0.773450 + 0.633858i $$0.781471\pi$$
$$614$$ −2.84421 −0.114783
$$615$$ 0 0
$$616$$ 0.351050 0.0141442
$$617$$ −14.3526 −0.577813 −0.288907 0.957357i $$-0.593292\pi$$
−0.288907 + 0.957357i $$0.593292\pi$$
$$618$$ 7.64895 0.307686
$$619$$ −8.62314 −0.346593 −0.173297 0.984870i $$-0.555442\pi$$
−0.173297 + 0.984870i $$0.555442\pi$$
$$620$$ 0 0
$$621$$ 50.8518 2.04061
$$622$$ −16.3895 −0.657158
$$623$$ −1.16946 −0.0468533
$$624$$ −17.3450 −0.694355
$$625$$ 0 0
$$626$$ −21.0471 −0.841211
$$627$$ −14.6626 −0.585569
$$628$$ 0.506836 0.0202250
$$629$$ −40.3723 −1.60975
$$630$$ 0 0
$$631$$ −10.3374 −0.411525 −0.205762 0.978602i $$-0.565967\pi$$
−0.205762 + 0.978602i $$0.565967\pi$$
$$632$$ 17.0137 0.676768
$$633$$ 62.6394 2.48969
$$634$$ −30.8902 −1.22681
$$635$$ 0 0
$$636$$ −42.0855 −1.66880
$$637$$ 37.2868 1.47736
$$638$$ 6.00000 0.237542
$$639$$ −82.3541 −3.25788
$$640$$ 0 0
$$641$$ 5.88369 0.232392 0.116196 0.993226i $$-0.462930\pi$$
0.116196 + 0.993226i $$0.462930\pi$$
$$642$$ −45.6566 −1.80192
$$643$$ −25.5084 −1.00595 −0.502976 0.864300i $$-0.667762\pi$$
−0.502976 + 0.864300i $$0.667762\pi$$
$$644$$ −0.265553 −0.0104642
$$645$$ 0 0
$$646$$ 7.33131 0.288447
$$647$$ −5.09157 −0.200170 −0.100085 0.994979i $$-0.531911\pi$$
−0.100085 + 0.994979i $$0.531911\pi$$
$$648$$ 25.7739 1.01250
$$649$$ −34.0942 −1.33831
$$650$$ 0 0
$$651$$ 0.635277 0.0248985
$$652$$ 0.830542 0.0325265
$$653$$ −11.1816 −0.437570 −0.218785 0.975773i $$-0.570209\pi$$
−0.218785 + 0.975773i $$0.570209\pi$$
$$654$$ −0.253418 −0.00990943
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −38.6642 −1.50843
$$658$$ 0.441078 0.0171950
$$659$$ −13.7542 −0.535787 −0.267894 0.963449i $$-0.586328\pi$$
−0.267894 + 0.963449i $$0.586328\pi$$
$$660$$ 0 0
$$661$$ −12.6171 −0.490747 −0.245374 0.969429i $$-0.578911\pi$$
−0.245374 + 0.969429i $$0.578911\pi$$
$$662$$ 28.3845 1.10319
$$663$$ −127.161 −4.93854
$$664$$ −13.1695 −0.511074
$$665$$ 0 0
$$666$$ −41.7679 −1.61847
$$667$$ −4.53871 −0.175740
$$668$$ 16.5068 0.638669
$$669$$ −47.1968 −1.82473
$$670$$ 0 0
$$671$$ 9.71577 0.375073
$$672$$ −0.253418 −0.00977581
$$673$$ 2.35105 0.0906263 0.0453132 0.998973i $$-0.485571\pi$$
0.0453132 + 0.998973i $$0.485571\pi$$
$$674$$ −17.8716 −0.688387
$$675$$ 0 0
$$676$$ 15.4229 0.593188
$$677$$ −23.7663 −0.913414 −0.456707 0.889617i $$-0.650971\pi$$
−0.456707 + 0.889617i $$0.650971\pi$$
$$678$$ −19.5205 −0.749681
$$679$$ −0.597928 −0.0229464
$$680$$ 0 0
$$681$$ −70.2686 −2.69270
$$682$$ 11.2979 0.432619
$$683$$ 28.1695 1.07787 0.538937 0.842346i $$-0.318826\pi$$
0.538937 + 0.842346i $$0.318826\pi$$
$$684$$ 7.58473 0.290009
$$685$$ 0 0
$$686$$ 1.09003 0.0416174
$$687$$ −61.8594 −2.36008
$$688$$ 0.506836 0.0193229
$$689$$ 68.9647 2.62734
$$690$$ 0 0
$$691$$ 2.32371 0.0883979 0.0441990 0.999023i $$-0.485926\pi$$
0.0441990 + 0.999023i $$0.485926\pi$$
$$692$$ 18.8321 0.715888
$$693$$ 2.66262 0.101145
$$694$$ 33.0410 1.25422
$$695$$ 0 0
$$696$$ −4.33131 −0.164178
$$697$$ 0 0
$$698$$ −19.7158 −0.746253
$$699$$ −19.5650 −0.740016
$$700$$ 0 0
$$701$$ 23.7036 0.895274 0.447637 0.894215i $$-0.352266\pi$$
0.447637 + 0.894215i $$0.352266\pi$$
$$702$$ −79.5220 −3.00137
$$703$$ −5.50684 −0.207694
$$704$$ −4.50684 −0.169858
$$705$$ 0 0
$$706$$ −5.90997 −0.222425
$$707$$ 0.323706 0.0121742
$$708$$ 24.6121 0.924978
$$709$$ 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
$$712$$ 15.0137 0.562661
$$713$$ −8.54631 −0.320062
$$714$$ −1.85789 −0.0695297
$$715$$ 0 0
$$716$$ −7.15579 −0.267424
$$717$$ 50.1326 1.87224
$$718$$ −7.00760 −0.261521
$$719$$ 35.0734 1.30802 0.654008 0.756488i $$-0.273086\pi$$
0.654008 + 0.756488i $$0.273086\pi$$
$$720$$ 0 0
$$721$$ −0.183130 −0.00682012
$$722$$ 1.00000 0.0372161
$$723$$ −15.6763 −0.583008
$$724$$ 12.5205 0.465321
$$725$$ 0 0
$$726$$ 30.2944 1.12433
$$727$$ 30.1386 1.11778 0.558890 0.829242i $$-0.311227\pi$$
0.558890 + 0.829242i $$0.311227\pi$$
$$728$$ 0.415271 0.0153910
$$729$$ 49.9039 1.84829
$$730$$ 0 0
$$731$$ 3.71577 0.137433
$$732$$ −7.01367 −0.259233
$$733$$ 47.8321 1.76672 0.883359 0.468697i $$-0.155276\pi$$
0.883359 + 0.468697i $$0.155276\pi$$
$$734$$ 17.7158 0.653901
$$735$$ 0 0
$$736$$ 3.40920 0.125665
$$737$$ 20.6626 0.761117
$$738$$ 0 0
$$739$$ −22.4674 −0.826475 −0.413238 0.910623i $$-0.635602\pi$$
−0.413238 + 0.910623i $$0.635602\pi$$
$$740$$ 0 0
$$741$$ −17.3450 −0.637184
$$742$$ 1.00760 0.0369903
$$743$$ −11.7926 −0.432629 −0.216314 0.976324i $$-0.569404\pi$$
−0.216314 + 0.976324i $$0.569404\pi$$
$$744$$ −8.15579 −0.299006
$$745$$ 0 0
$$746$$ 15.4487 0.565616
$$747$$ −99.8868 −3.65467
$$748$$ −33.0410 −1.20810
$$749$$ 1.09310 0.0399411
$$750$$ 0 0
$$751$$ −2.03948 −0.0744216 −0.0372108 0.999307i $$-0.511847\pi$$
−0.0372108 + 0.999307i $$0.511847\pi$$
$$752$$ −5.66262 −0.206495
$$753$$ 4.94685 0.180273
$$754$$ 7.09763 0.258481
$$755$$ 0 0
$$756$$ −1.16185 −0.0422562
$$757$$ 43.3526 1.57568 0.787838 0.615882i $$-0.211200\pi$$
0.787838 + 0.615882i $$0.211200\pi$$
$$758$$ 34.4563 1.25151
$$759$$ −49.9879 −1.81444
$$760$$ 0 0
$$761$$ 6.62921 0.240309 0.120154 0.992755i $$-0.461661\pi$$
0.120154 + 0.992755i $$0.461661\pi$$
$$762$$ 58.0152 2.10167
$$763$$ 0.00606730 0.000219651 0
$$764$$ −4.90237 −0.177361
$$765$$ 0 0
$$766$$ −12.0273 −0.434566
$$767$$ −40.3313 −1.45628
$$768$$ 3.25342 0.117398
$$769$$ −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
$$772$$ 18.1558 0.653441
$$773$$ 14.4107 0.518318 0.259159 0.965835i $$-0.416555\pi$$
0.259159 + 0.965835i $$0.416555\pi$$
$$774$$ 3.84421 0.138177
$$775$$ 0 0
$$776$$ 7.67629 0.275563
$$777$$ 1.39553 0.0500644
$$778$$ −15.3647 −0.550852
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 48.9347 1.75102
$$782$$ 24.9939 0.893781
$$783$$ −19.8579 −0.709663
$$784$$ −6.99393 −0.249783
$$785$$ 0 0
$$786$$ −4.85789 −0.173275
$$787$$ 24.3176 0.866830 0.433415 0.901194i $$-0.357308\pi$$
0.433415 + 0.901194i $$0.357308\pi$$
$$788$$ −2.98633 −0.106384
$$789$$ −58.6505 −2.08801
$$790$$ 0 0
$$791$$ 0.467357 0.0166173
$$792$$ −34.1831 −1.21464
$$793$$ 11.4932 0.408134
$$794$$ 1.32524 0.0470311
$$795$$ 0 0
$$796$$ −3.06422 −0.108608
$$797$$ −7.30397 −0.258720 −0.129360 0.991598i $$-0.541292\pi$$
−0.129360 + 0.991598i $$0.541292\pi$$
$$798$$ −0.253418 −0.00897090
$$799$$ −41.5144 −1.46868
$$800$$ 0 0
$$801$$ 113.875 4.02356
$$802$$ −6.46736 −0.228370
$$803$$ 22.9742 0.810742
$$804$$ −14.9160 −0.526048
$$805$$ 0 0
$$806$$ 13.3647 0.470752
$$807$$ 65.7481 2.31444
$$808$$ −4.15579 −0.146200
$$809$$ −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 $$-0.489324\pi$$
0.0335341 + 0.999438i $$0.489324\pi$$
$$812$$ 0.103700 0.00363914
$$813$$ 19.7937 0.694194
$$814$$ 24.8184 0.869885
$$815$$ 0 0
$$816$$ 23.8518 0.834981
$$817$$ 0.506836 0.0177319
$$818$$ −1.36472 −0.0477164
$$819$$ 3.14972 0.110060
$$820$$ 0 0
$$821$$ −38.2226 −1.33398 −0.666989 0.745067i $$-0.732417\pi$$
−0.666989 + 0.745067i $$0.732417\pi$$
$$822$$ −27.4229 −0.956483
$$823$$ −45.7481 −1.59468 −0.797340 0.603531i $$-0.793760\pi$$
−0.797340 + 0.603531i $$0.793760\pi$$
$$824$$ 2.35105 0.0819027
$$825$$ 0 0
$$826$$ −0.589259 −0.0205029
$$827$$ −22.6687 −0.788268 −0.394134 0.919053i $$-0.628955\pi$$
−0.394134 + 0.919053i $$0.628955\pi$$
$$828$$ 25.8579 0.898624
$$829$$ −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
$$832$$ −5.33131 −0.184830
$$833$$ −51.2747 −1.77656
$$834$$ 28.6900 0.993452
$$835$$ 0 0
$$836$$ −4.50684 −0.155872
$$837$$ −37.3921 −1.29246
$$838$$ 16.6231 0.574237
$$839$$ −50.4826 −1.74285 −0.871426 0.490527i $$-0.836804\pi$$
−0.871426 + 0.490527i $$0.836804\pi$$
$$840$$ 0 0
$$841$$ −27.2276 −0.938883
$$842$$ −31.1128 −1.07222
$$843$$ 36.8458 1.26904
$$844$$ 19.2534 0.662730
$$845$$ 0 0
$$846$$ −42.9495 −1.47663
$$847$$ −0.725305 −0.0249218
$$848$$ −12.9358 −0.444216
$$849$$ 85.0562 2.91912
$$850$$ 0 0
$$851$$ −18.7739 −0.643562
$$852$$ −35.3252 −1.21022
$$853$$ 36.2105 1.23982 0.619912 0.784672i $$-0.287168\pi$$
0.619912 + 0.784672i $$0.287168\pi$$
$$854$$ 0.167920 0.00574611
$$855$$ 0 0
$$856$$ −14.0334 −0.479652
$$857$$ 25.1968 0.860706 0.430353 0.902661i $$-0.358389\pi$$
0.430353 + 0.902661i $$0.358389\pi$$
$$858$$ 78.1710 2.66871
$$859$$ 18.8579 0.643423 0.321711 0.946838i $$-0.395742\pi$$
0.321711 + 0.946838i $$0.395742\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −10.1831 −0.346839
$$863$$ 15.0137 0.511071 0.255536 0.966800i $$-0.417748\pi$$
0.255536 + 0.966800i $$0.417748\pi$$
$$864$$ 14.9160 0.507454
$$865$$ 0 0
$$866$$ 22.1953 0.754226
$$867$$ 119.557 4.06037
$$868$$ 0.195265 0.00662771
$$869$$ −76.6778 −2.60112
$$870$$ 0 0
$$871$$ 24.4426 0.828206
$$872$$ −0.0778929 −0.00263779
$$873$$ 58.2226 1.97054
$$874$$ 3.40920 0.115318
$$875$$ 0 0
$$876$$ −16.5847 −0.560346
$$877$$ 35.1128 1.18568 0.592838 0.805322i $$-0.298007\pi$$
0.592838 + 0.805322i $$0.298007\pi$$
$$878$$ −9.32524 −0.314712
$$879$$ 4.33131 0.146091
$$880$$ 0 0
$$881$$ −41.3389 −1.39274 −0.696372 0.717681i $$-0.745203\pi$$
−0.696372 + 0.717681i $$0.745203\pi$$
$$882$$ −53.0471 −1.78619
$$883$$ −12.6353 −0.425211 −0.212605 0.977138i $$-0.568195\pi$$
−0.212605 + 0.977138i $$0.568195\pi$$
$$884$$ −39.0855 −1.31459
$$885$$ 0 0
$$886$$ −13.9879 −0.469932
$$887$$ 4.15579 0.139538 0.0697688 0.997563i $$-0.477774\pi$$
0.0697688 + 0.997563i $$0.477774\pi$$
$$888$$ −17.9160 −0.601223
$$889$$ −1.38899 −0.0465853
$$890$$ 0 0
$$891$$ −116.159 −3.89147
$$892$$ −14.5068 −0.485725
$$893$$ −5.66262 −0.189492
$$894$$ 57.5084 1.92337
$$895$$ 0 0
$$896$$ −0.0778929 −0.00260222
$$897$$ −59.1326 −1.97438
$$898$$ 13.4932 0.450273
$$899$$ 3.33738 0.111308
$$900$$ 0 0
$$901$$ −94.8362 −3.15945
$$902$$ 0 0
$$903$$ −0.128441 −0.00427426
$$904$$ −6.00000 −0.199557
$$905$$ 0 0
$$906$$ 65.0684 2.16175
$$907$$ −41.7542 −1.38643 −0.693213 0.720733i $$-0.743805\pi$$
−0.693213 + 0.720733i $$0.743805\pi$$
$$908$$ −21.5984 −0.716768
$$909$$ −31.5205 −1.04547
$$910$$ 0 0
$$911$$ −9.12998 −0.302490 −0.151245 0.988496i $$-0.548328\pi$$
−0.151245 + 0.988496i $$0.548328\pi$$
$$912$$ 3.25342 0.107731
$$913$$ 59.3526 1.96428
$$914$$ 9.68236 0.320264
$$915$$ 0 0
$$916$$ −19.0137 −0.628229
$$917$$ 0.116307 0.00384079
$$918$$ 109.354 3.60922
$$919$$ 19.0197 0.627403 0.313702 0.949522i $$-0.398431\pi$$
0.313702 + 0.949522i $$0.398431\pi$$
$$920$$ 0 0
$$921$$ −9.25342 −0.304910
$$922$$ 8.66262 0.285288
$$923$$ 57.8868 1.90537
$$924$$ 1.14211 0.0375728
$$925$$ 0 0
$$926$$ 28.0015 0.920188
$$927$$ 17.8321 0.585682
$$928$$ −1.33131 −0.0437024
$$929$$ −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
$$932$$ −6.01367 −0.196984
$$933$$ −53.3218 −1.74568
$$934$$ 16.9742 0.555413
$$935$$ 0 0
$$936$$ −40.4365 −1.32171
$$937$$ −45.9818 −1.50216 −0.751080 0.660211i $$-0.770467\pi$$
−0.751080 + 0.660211i $$0.770467\pi$$
$$938$$ 0.357118 0.0116603
$$939$$ −68.4750 −2.23460
$$940$$ 0 0
$$941$$ −40.6242 −1.32431 −0.662156 0.749366i $$-0.730358\pi$$
−0.662156 + 0.749366i $$0.730358\pi$$
$$942$$ 1.64895 0.0537257
$$943$$ 0 0
$$944$$ 7.56499 0.246219
$$945$$ 0 0
$$946$$ −2.28423 −0.0742666
$$947$$ −2.28423 −0.0742274 −0.0371137 0.999311i $$-0.511816\pi$$
−0.0371137 + 0.999311i $$0.511816\pi$$
$$948$$ 55.3526 1.79777
$$949$$ 27.1771 0.882205
$$950$$ 0 0
$$951$$ −100.499 −3.25890
$$952$$ −0.571057 −0.0185081
$$953$$ −57.5084 −1.86288 −0.931439 0.363896i $$-0.881446\pi$$
−0.931439 + 0.363896i $$0.881446\pi$$
$$954$$ −98.1144 −3.17657
$$955$$ 0 0
$$956$$ 15.4092 0.498369
$$957$$ 19.5205 0.631008
$$958$$ 10.0532 0.324803
$$959$$ 0.656555 0.0212013
$$960$$ 0 0
$$961$$ −24.7158 −0.797283
$$962$$ 29.3587 0.946561
$$963$$ −106.440 −3.42997
$$964$$ −4.81841 −0.155190
$$965$$ 0 0
$$966$$ −0.863954 −0.0277973
$$967$$ −4.70210 −0.151209 −0.0756047 0.997138i $$-0.524089\pi$$
−0.0756047 + 0.997138i $$0.524089\pi$$
$$968$$ 9.31157 0.299285
$$969$$ 23.8518 0.766231
$$970$$ 0 0
$$971$$ 14.9863 0.480934 0.240467 0.970657i $$-0.422699\pi$$
0.240467 + 0.970657i $$0.422699\pi$$
$$972$$ 39.1052 1.25430
$$973$$ −0.686891 −0.0220207
$$974$$ 19.2089 0.615494
$$975$$ 0 0
$$976$$ −2.15579 −0.0690050
$$977$$ 8.89737 0.284652 0.142326 0.989820i $$-0.454542\pi$$
0.142326 + 0.989820i $$0.454542\pi$$
$$978$$ 2.70210 0.0864037
$$979$$ −67.6642 −2.16256
$$980$$ 0 0
$$981$$ −0.590796 −0.0188627
$$982$$ 5.32524 0.169935
$$983$$ −1.60947 −0.0513341 −0.0256671 0.999671i $$-0.508171\pi$$
−0.0256671 + 0.999671i $$0.508171\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −9.76025 −0.310830
$$987$$ 1.43501 0.0456769
$$988$$ −5.33131 −0.169612
$$989$$ 1.72791 0.0549443
$$990$$ 0 0
$$991$$ 16.8974 0.536763 0.268381 0.963313i $$-0.413511\pi$$
0.268381 + 0.963313i $$0.413511\pi$$
$$992$$ −2.50684 −0.0795921
$$993$$ 92.3465 2.93053
$$994$$ 0.845752 0.0268256
$$995$$ 0 0
$$996$$ −42.8458 −1.35762
$$997$$ 24.1558 0.765021 0.382511 0.923951i $$-0.375060\pi$$
0.382511 + 0.923951i $$0.375060\pi$$
$$998$$ −11.9605 −0.378604
$$999$$ −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 950.2.a.l.1.3 yes 3
3.2 odd 2 8550.2.a.ci.1.2 3
4.3 odd 2 7600.2.a.bk.1.1 3
5.2 odd 4 950.2.b.h.799.4 6
5.3 odd 4 950.2.b.h.799.3 6
5.4 even 2 950.2.a.j.1.1 3
15.14 odd 2 8550.2.a.cp.1.2 3
20.19 odd 2 7600.2.a.bz.1.3 3

By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.1 3 5.4 even 2
950.2.a.l.1.3 yes 3 1.1 even 1 trivial
950.2.b.h.799.3 6 5.3 odd 4
950.2.b.h.799.4 6 5.2 odd 4
7600.2.a.bk.1.1 3 4.3 odd 2
7600.2.a.bz.1.3 3 20.19 odd 2
8550.2.a.ci.1.2 3 3.2 odd 2
8550.2.a.cp.1.2 3 15.14 odd 2