# Properties

 Label 9702.2.a.cu.1.1 Level $9702$ Weight $2$ Character 9702.1 Self dual yes Analytic conductor $77.471$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9702.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$77.4708600410$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ Defining polynomial: $$x^{2} - x - 1$$ x^2 - x - 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 154) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-0.618034$$ of defining polynomial Character $$\chi$$ $$=$$ 9702.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.23607 q^{5} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.23607 q^{5} -1.00000 q^{8} +1.23607 q^{10} -1.00000 q^{11} +3.23607 q^{13} +1.00000 q^{16} +2.47214 q^{17} +7.23607 q^{19} -1.23607 q^{20} +1.00000 q^{22} -4.00000 q^{23} -3.47214 q^{25} -3.23607 q^{26} -4.47214 q^{29} -2.00000 q^{31} -1.00000 q^{32} -2.47214 q^{34} +6.94427 q^{37} -7.23607 q^{38} +1.23607 q^{40} -2.47214 q^{41} -10.4721 q^{43} -1.00000 q^{44} +4.00000 q^{46} -2.00000 q^{47} +3.47214 q^{50} +3.23607 q^{52} -8.47214 q^{53} +1.23607 q^{55} +4.47214 q^{58} +2.76393 q^{59} +0.763932 q^{61} +2.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} +11.4164 q^{67} +2.47214 q^{68} -6.47214 q^{71} -12.9443 q^{73} -6.94427 q^{74} +7.23607 q^{76} -1.23607 q^{80} +2.47214 q^{82} -12.1803 q^{83} -3.05573 q^{85} +10.4721 q^{86} +1.00000 q^{88} +10.0000 q^{89} -4.00000 q^{92} +2.00000 q^{94} -8.94427 q^{95} -12.4721 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8}+O(q^{10})$$ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 2 * q^8 $$2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8} - 2 q^{10} - 2 q^{11} + 2 q^{13} + 2 q^{16} - 4 q^{17} + 10 q^{19} + 2 q^{20} + 2 q^{22} - 8 q^{23} + 2 q^{25} - 2 q^{26} - 4 q^{31} - 2 q^{32} + 4 q^{34} - 4 q^{37} - 10 q^{38} - 2 q^{40} + 4 q^{41} - 12 q^{43} - 2 q^{44} + 8 q^{46} - 4 q^{47} - 2 q^{50} + 2 q^{52} - 8 q^{53} - 2 q^{55} + 10 q^{59} + 6 q^{61} + 4 q^{62} + 2 q^{64} - 8 q^{65} - 4 q^{67} - 4 q^{68} - 4 q^{71} - 8 q^{73} + 4 q^{74} + 10 q^{76} + 2 q^{80} - 4 q^{82} - 2 q^{83} - 24 q^{85} + 12 q^{86} + 2 q^{88} + 20 q^{89} - 8 q^{92} + 4 q^{94} - 16 q^{97}+O(q^{100})$$ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 2 * q^8 - 2 * q^10 - 2 * q^11 + 2 * q^13 + 2 * q^16 - 4 * q^17 + 10 * q^19 + 2 * q^20 + 2 * q^22 - 8 * q^23 + 2 * q^25 - 2 * q^26 - 4 * q^31 - 2 * q^32 + 4 * q^34 - 4 * q^37 - 10 * q^38 - 2 * q^40 + 4 * q^41 - 12 * q^43 - 2 * q^44 + 8 * q^46 - 4 * q^47 - 2 * q^50 + 2 * q^52 - 8 * q^53 - 2 * q^55 + 10 * q^59 + 6 * q^61 + 4 * q^62 + 2 * q^64 - 8 * q^65 - 4 * q^67 - 4 * q^68 - 4 * q^71 - 8 * q^73 + 4 * q^74 + 10 * q^76 + 2 * q^80 - 4 * q^82 - 2 * q^83 - 24 * q^85 + 12 * q^86 + 2 * q^88 + 20 * q^89 - 8 * q^92 + 4 * q^94 - 16 * q^97

## 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
$$5$$ −1.23607 −0.552786 −0.276393 0.961045i $$-0.589139\pi$$
−0.276393 + 0.961045i $$0.589139\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 1.23607 0.390879
$$11$$ −1.00000 −0.301511
$$12$$ 0 0
$$13$$ 3.23607 0.897524 0.448762 0.893651i $$-0.351865\pi$$
0.448762 + 0.893651i $$0.351865\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.47214 0.599581 0.299791 0.954005i $$-0.403083\pi$$
0.299791 + 0.954005i $$0.403083\pi$$
$$18$$ 0 0
$$19$$ 7.23607 1.66007 0.830034 0.557713i $$-0.188321\pi$$
0.830034 + 0.557713i $$0.188321\pi$$
$$20$$ −1.23607 −0.276393
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ −4.00000 −0.834058 −0.417029 0.908893i $$-0.636929\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ 0 0
$$25$$ −3.47214 −0.694427
$$26$$ −3.23607 −0.634645
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4.47214 −0.830455 −0.415227 0.909718i $$-0.636298\pi$$
−0.415227 + 0.909718i $$0.636298\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ −2.47214 −0.423968
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 6.94427 1.14163 0.570816 0.821078i $$-0.306627\pi$$
0.570816 + 0.821078i $$0.306627\pi$$
$$38$$ −7.23607 −1.17385
$$39$$ 0 0
$$40$$ 1.23607 0.195440
$$41$$ −2.47214 −0.386083 −0.193041 0.981191i $$-0.561835\pi$$
−0.193041 + 0.981191i $$0.561835\pi$$
$$42$$ 0 0
$$43$$ −10.4721 −1.59699 −0.798493 0.602004i $$-0.794369\pi$$
−0.798493 + 0.602004i $$0.794369\pi$$
$$44$$ −1.00000 −0.150756
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ −2.00000 −0.291730 −0.145865 0.989305i $$-0.546597\pi$$
−0.145865 + 0.989305i $$0.546597\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 3.47214 0.491034
$$51$$ 0 0
$$52$$ 3.23607 0.448762
$$53$$ −8.47214 −1.16374 −0.581869 0.813283i $$-0.697678\pi$$
−0.581869 + 0.813283i $$0.697678\pi$$
$$54$$ 0 0
$$55$$ 1.23607 0.166671
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 4.47214 0.587220
$$59$$ 2.76393 0.359833 0.179917 0.983682i $$-0.442417\pi$$
0.179917 + 0.983682i $$0.442417\pi$$
$$60$$ 0 0
$$61$$ 0.763932 0.0978115 0.0489057 0.998803i $$-0.484427\pi$$
0.0489057 + 0.998803i $$0.484427\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −4.00000 −0.496139
$$66$$ 0 0
$$67$$ 11.4164 1.39474 0.697368 0.716713i $$-0.254354\pi$$
0.697368 + 0.716713i $$0.254354\pi$$
$$68$$ 2.47214 0.299791
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −6.47214 −0.768101 −0.384051 0.923312i $$-0.625471\pi$$
−0.384051 + 0.923312i $$0.625471\pi$$
$$72$$ 0 0
$$73$$ −12.9443 −1.51501 −0.757506 0.652828i $$-0.773582\pi$$
−0.757506 + 0.652828i $$0.773582\pi$$
$$74$$ −6.94427 −0.807255
$$75$$ 0 0
$$76$$ 7.23607 0.830034
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ −1.23607 −0.138197
$$81$$ 0 0
$$82$$ 2.47214 0.273002
$$83$$ −12.1803 −1.33697 −0.668483 0.743727i $$-0.733056\pi$$
−0.668483 + 0.743727i $$0.733056\pi$$
$$84$$ 0 0
$$85$$ −3.05573 −0.331440
$$86$$ 10.4721 1.12924
$$87$$ 0 0
$$88$$ 1.00000 0.106600
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −4.00000 −0.417029
$$93$$ 0 0
$$94$$ 2.00000 0.206284
$$95$$ −8.94427 −0.917663
$$96$$ 0 0
$$97$$ −12.4721 −1.26635 −0.633177 0.774007i $$-0.718249\pi$$
−0.633177 + 0.774007i $$0.718249\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −3.47214 −0.347214
$$101$$ 8.18034 0.813974 0.406987 0.913434i $$-0.366579\pi$$
0.406987 + 0.913434i $$0.366579\pi$$
$$102$$ 0 0
$$103$$ 14.9443 1.47250 0.736251 0.676708i $$-0.236594\pi$$
0.736251 + 0.676708i $$0.236594\pi$$
$$104$$ −3.23607 −0.317323
$$105$$ 0 0
$$106$$ 8.47214 0.822887
$$107$$ −2.47214 −0.238990 −0.119495 0.992835i $$-0.538128\pi$$
−0.119495 + 0.992835i $$0.538128\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ −1.23607 −0.117854
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.472136 0.0444148 0.0222074 0.999753i $$-0.492931\pi$$
0.0222074 + 0.999753i $$0.492931\pi$$
$$114$$ 0 0
$$115$$ 4.94427 0.461056
$$116$$ −4.47214 −0.415227
$$117$$ 0 0
$$118$$ −2.76393 −0.254441
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 0.0909091
$$122$$ −0.763932 −0.0691632
$$123$$ 0 0
$$124$$ −2.00000 −0.179605
$$125$$ 10.4721 0.936656
$$126$$ 0 0
$$127$$ −12.0000 −1.06483 −0.532414 0.846484i $$-0.678715\pi$$
−0.532414 + 0.846484i $$0.678715\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 4.00000 0.350823
$$131$$ 4.76393 0.416227 0.208113 0.978105i $$-0.433268\pi$$
0.208113 + 0.978105i $$0.433268\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −11.4164 −0.986227
$$135$$ 0 0
$$136$$ −2.47214 −0.211984
$$137$$ 19.8885 1.69919 0.849596 0.527433i $$-0.176846\pi$$
0.849596 + 0.527433i $$0.176846\pi$$
$$138$$ 0 0
$$139$$ 21.7082 1.84127 0.920633 0.390429i $$-0.127673\pi$$
0.920633 + 0.390429i $$0.127673\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 6.47214 0.543130
$$143$$ −3.23607 −0.270614
$$144$$ 0 0
$$145$$ 5.52786 0.459064
$$146$$ 12.9443 1.07128
$$147$$ 0 0
$$148$$ 6.94427 0.570816
$$149$$ 22.3607 1.83186 0.915929 0.401340i $$-0.131455\pi$$
0.915929 + 0.401340i $$0.131455\pi$$
$$150$$ 0 0
$$151$$ 12.0000 0.976546 0.488273 0.872691i $$-0.337627\pi$$
0.488273 + 0.872691i $$0.337627\pi$$
$$152$$ −7.23607 −0.586923
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 2.47214 0.198567
$$156$$ 0 0
$$157$$ 12.6525 1.00978 0.504889 0.863184i $$-0.331534\pi$$
0.504889 + 0.863184i $$0.331534\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 1.23607 0.0977198
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −19.4164 −1.52081 −0.760405 0.649449i $$-0.775000\pi$$
−0.760405 + 0.649449i $$0.775000\pi$$
$$164$$ −2.47214 −0.193041
$$165$$ 0 0
$$166$$ 12.1803 0.945378
$$167$$ 11.4164 0.883428 0.441714 0.897156i $$-0.354371\pi$$
0.441714 + 0.897156i $$0.354371\pi$$
$$168$$ 0 0
$$169$$ −2.52786 −0.194451
$$170$$ 3.05573 0.234364
$$171$$ 0 0
$$172$$ −10.4721 −0.798493
$$173$$ −3.23607 −0.246034 −0.123017 0.992405i $$-0.539257\pi$$
−0.123017 + 0.992405i $$0.539257\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1.00000 −0.0753778
$$177$$ 0 0
$$178$$ −10.0000 −0.749532
$$179$$ 8.94427 0.668526 0.334263 0.942480i $$-0.391513\pi$$
0.334263 + 0.942480i $$0.391513\pi$$
$$180$$ 0 0
$$181$$ −9.23607 −0.686512 −0.343256 0.939242i $$-0.611530\pi$$
−0.343256 + 0.939242i $$0.611530\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 4.00000 0.294884
$$185$$ −8.58359 −0.631078
$$186$$ 0 0
$$187$$ −2.47214 −0.180780
$$188$$ −2.00000 −0.145865
$$189$$ 0 0
$$190$$ 8.94427 0.648886
$$191$$ 2.47214 0.178877 0.0894387 0.995992i $$-0.471493\pi$$
0.0894387 + 0.995992i $$0.471493\pi$$
$$192$$ 0 0
$$193$$ −14.9443 −1.07571 −0.537856 0.843037i $$-0.680766\pi$$
−0.537856 + 0.843037i $$0.680766\pi$$
$$194$$ 12.4721 0.895447
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ −18.9443 −1.34292 −0.671462 0.741039i $$-0.734333\pi$$
−0.671462 + 0.741039i $$0.734333\pi$$
$$200$$ 3.47214 0.245517
$$201$$ 0 0
$$202$$ −8.18034 −0.575567
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 3.05573 0.213421
$$206$$ −14.9443 −1.04122
$$207$$ 0 0
$$208$$ 3.23607 0.224381
$$209$$ −7.23607 −0.500529
$$210$$ 0 0
$$211$$ −13.5279 −0.931297 −0.465648 0.884970i $$-0.654179\pi$$
−0.465648 + 0.884970i $$0.654179\pi$$
$$212$$ −8.47214 −0.581869
$$213$$ 0 0
$$214$$ 2.47214 0.168992
$$215$$ 12.9443 0.882792
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 10.0000 0.677285
$$219$$ 0 0
$$220$$ 1.23607 0.0833357
$$221$$ 8.00000 0.538138
$$222$$ 0 0
$$223$$ 0.472136 0.0316166 0.0158083 0.999875i $$-0.494968\pi$$
0.0158083 + 0.999875i $$0.494968\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −0.472136 −0.0314060
$$227$$ −19.2361 −1.27674 −0.638371 0.769729i $$-0.720392\pi$$
−0.638371 + 0.769729i $$0.720392\pi$$
$$228$$ 0 0
$$229$$ −17.2361 −1.13899 −0.569496 0.821994i $$-0.692861\pi$$
−0.569496 + 0.821994i $$0.692861\pi$$
$$230$$ −4.94427 −0.326016
$$231$$ 0 0
$$232$$ 4.47214 0.293610
$$233$$ 14.9443 0.979032 0.489516 0.871994i $$-0.337174\pi$$
0.489516 + 0.871994i $$0.337174\pi$$
$$234$$ 0 0
$$235$$ 2.47214 0.161264
$$236$$ 2.76393 0.179917
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 0 0
$$241$$ −15.4164 −0.993058 −0.496529 0.868020i $$-0.665392\pi$$
−0.496529 + 0.868020i $$0.665392\pi$$
$$242$$ −1.00000 −0.0642824
$$243$$ 0 0
$$244$$ 0.763932 0.0489057
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 23.4164 1.48995
$$248$$ 2.00000 0.127000
$$249$$ 0 0
$$250$$ −10.4721 −0.662316
$$251$$ 29.2361 1.84536 0.922682 0.385562i $$-0.125992\pi$$
0.922682 + 0.385562i $$0.125992\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ 12.0000 0.752947
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 6.94427 0.433172 0.216586 0.976264i $$-0.430508\pi$$
0.216586 + 0.976264i $$0.430508\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −4.00000 −0.248069
$$261$$ 0 0
$$262$$ −4.76393 −0.294317
$$263$$ 4.94427 0.304877 0.152438 0.988313i $$-0.451287\pi$$
0.152438 + 0.988313i $$0.451287\pi$$
$$264$$ 0 0
$$265$$ 10.4721 0.643298
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 11.4164 0.697368
$$269$$ −22.7639 −1.38794 −0.693971 0.720003i $$-0.744140\pi$$
−0.693971 + 0.720003i $$0.744140\pi$$
$$270$$ 0 0
$$271$$ −0.944272 −0.0573604 −0.0286802 0.999589i $$-0.509130\pi$$
−0.0286802 + 0.999589i $$0.509130\pi$$
$$272$$ 2.47214 0.149895
$$273$$ 0 0
$$274$$ −19.8885 −1.20151
$$275$$ 3.47214 0.209378
$$276$$ 0 0
$$277$$ 3.52786 0.211969 0.105984 0.994368i $$-0.466201\pi$$
0.105984 + 0.994368i $$0.466201\pi$$
$$278$$ −21.7082 −1.30197
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −28.8328 −1.72002 −0.860011 0.510276i $$-0.829543\pi$$
−0.860011 + 0.510276i $$0.829543\pi$$
$$282$$ 0 0
$$283$$ −14.6525 −0.870999 −0.435500 0.900189i $$-0.643428\pi$$
−0.435500 + 0.900189i $$0.643428\pi$$
$$284$$ −6.47214 −0.384051
$$285$$ 0 0
$$286$$ 3.23607 0.191353
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −10.8885 −0.640503
$$290$$ −5.52786 −0.324607
$$291$$ 0 0
$$292$$ −12.9443 −0.757506
$$293$$ −26.6525 −1.55705 −0.778527 0.627611i $$-0.784033\pi$$
−0.778527 + 0.627611i $$0.784033\pi$$
$$294$$ 0 0
$$295$$ −3.41641 −0.198911
$$296$$ −6.94427 −0.403628
$$297$$ 0 0
$$298$$ −22.3607 −1.29532
$$299$$ −12.9443 −0.748587
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −12.0000 −0.690522
$$303$$ 0 0
$$304$$ 7.23607 0.415017
$$305$$ −0.944272 −0.0540689
$$306$$ 0 0
$$307$$ 26.0689 1.48783 0.743915 0.668274i $$-0.232967\pi$$
0.743915 + 0.668274i $$0.232967\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −2.47214 −0.140408
$$311$$ −21.4164 −1.21441 −0.607207 0.794544i $$-0.707710\pi$$
−0.607207 + 0.794544i $$0.707710\pi$$
$$312$$ 0 0
$$313$$ −19.5279 −1.10378 −0.551890 0.833917i $$-0.686093\pi$$
−0.551890 + 0.833917i $$0.686093\pi$$
$$314$$ −12.6525 −0.714021
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 30.9443 1.73800 0.869002 0.494809i $$-0.164762\pi$$
0.869002 + 0.494809i $$0.164762\pi$$
$$318$$ 0 0
$$319$$ 4.47214 0.250392
$$320$$ −1.23607 −0.0690983
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 17.8885 0.995345
$$324$$ 0 0
$$325$$ −11.2361 −0.623265
$$326$$ 19.4164 1.07538
$$327$$ 0 0
$$328$$ 2.47214 0.136501
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −16.9443 −0.931341 −0.465671 0.884958i $$-0.654187\pi$$
−0.465671 + 0.884958i $$0.654187\pi$$
$$332$$ −12.1803 −0.668483
$$333$$ 0 0
$$334$$ −11.4164 −0.624678
$$335$$ −14.1115 −0.770991
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 2.52786 0.137498
$$339$$ 0 0
$$340$$ −3.05573 −0.165720
$$341$$ 2.00000 0.108306
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 10.4721 0.564620
$$345$$ 0 0
$$346$$ 3.23607 0.173972
$$347$$ −2.47214 −0.132711 −0.0663556 0.997796i $$-0.521137\pi$$
−0.0663556 + 0.997796i $$0.521137\pi$$
$$348$$ 0 0
$$349$$ −21.7082 −1.16201 −0.581007 0.813899i $$-0.697341\pi$$
−0.581007 + 0.813899i $$0.697341\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.00000 0.0533002
$$353$$ −17.0557 −0.907785 −0.453892 0.891056i $$-0.649965\pi$$
−0.453892 + 0.891056i $$0.649965\pi$$
$$354$$ 0 0
$$355$$ 8.00000 0.424596
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ −8.94427 −0.472719
$$359$$ −26.8328 −1.41618 −0.708091 0.706121i $$-0.750443\pi$$
−0.708091 + 0.706121i $$0.750443\pi$$
$$360$$ 0 0
$$361$$ 33.3607 1.75583
$$362$$ 9.23607 0.485437
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 16.0000 0.837478
$$366$$ 0 0
$$367$$ 5.41641 0.282734 0.141367 0.989957i $$-0.454850\pi$$
0.141367 + 0.989957i $$0.454850\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 0 0
$$370$$ 8.58359 0.446240
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −6.00000 −0.310668 −0.155334 0.987862i $$-0.549645\pi$$
−0.155334 + 0.987862i $$0.549645\pi$$
$$374$$ 2.47214 0.127831
$$375$$ 0 0
$$376$$ 2.00000 0.103142
$$377$$ −14.4721 −0.745353
$$378$$ 0 0
$$379$$ 14.4721 0.743384 0.371692 0.928356i $$-0.378778\pi$$
0.371692 + 0.928356i $$0.378778\pi$$
$$380$$ −8.94427 −0.458831
$$381$$ 0 0
$$382$$ −2.47214 −0.126485
$$383$$ −23.8885 −1.22065 −0.610324 0.792152i $$-0.708961\pi$$
−0.610324 + 0.792152i $$0.708961\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 14.9443 0.760643
$$387$$ 0 0
$$388$$ −12.4721 −0.633177
$$389$$ −33.4164 −1.69428 −0.847140 0.531370i $$-0.821677\pi$$
−0.847140 + 0.531370i $$0.821677\pi$$
$$390$$ 0 0
$$391$$ −9.88854 −0.500085
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 18.0000 0.906827
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 23.7082 1.18988 0.594940 0.803770i $$-0.297176\pi$$
0.594940 + 0.803770i $$0.297176\pi$$
$$398$$ 18.9443 0.949591
$$399$$ 0 0
$$400$$ −3.47214 −0.173607
$$401$$ −14.3607 −0.717138 −0.358569 0.933503i $$-0.616735\pi$$
−0.358569 + 0.933503i $$0.616735\pi$$
$$402$$ 0 0
$$403$$ −6.47214 −0.322400
$$404$$ 8.18034 0.406987
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −6.94427 −0.344215
$$408$$ 0 0
$$409$$ −3.41641 −0.168930 −0.0844652 0.996426i $$-0.526918\pi$$
−0.0844652 + 0.996426i $$0.526918\pi$$
$$410$$ −3.05573 −0.150912
$$411$$ 0 0
$$412$$ 14.9443 0.736251
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 15.0557 0.739057
$$416$$ −3.23607 −0.158661
$$417$$ 0 0
$$418$$ 7.23607 0.353928
$$419$$ 17.2361 0.842037 0.421019 0.907052i $$-0.361673\pi$$
0.421019 + 0.907052i $$0.361673\pi$$
$$420$$ 0 0
$$421$$ 16.4721 0.802803 0.401401 0.915902i $$-0.368523\pi$$
0.401401 + 0.915902i $$0.368523\pi$$
$$422$$ 13.5279 0.658526
$$423$$ 0 0
$$424$$ 8.47214 0.411443
$$425$$ −8.58359 −0.416365
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −2.47214 −0.119495
$$429$$ 0 0
$$430$$ −12.9443 −0.624228
$$431$$ −23.0557 −1.11056 −0.555278 0.831665i $$-0.687388\pi$$
−0.555278 + 0.831665i $$0.687388\pi$$
$$432$$ 0 0
$$433$$ −28.4721 −1.36828 −0.684142 0.729349i $$-0.739823\pi$$
−0.684142 + 0.729349i $$0.739823\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −10.0000 −0.478913
$$437$$ −28.9443 −1.38459
$$438$$ 0 0
$$439$$ −8.94427 −0.426887 −0.213443 0.976955i $$-0.568468\pi$$
−0.213443 + 0.976955i $$0.568468\pi$$
$$440$$ −1.23607 −0.0589272
$$441$$ 0 0
$$442$$ −8.00000 −0.380521
$$443$$ 24.9443 1.18514 0.592569 0.805520i $$-0.298114\pi$$
0.592569 + 0.805520i $$0.298114\pi$$
$$444$$ 0 0
$$445$$ −12.3607 −0.585952
$$446$$ −0.472136 −0.0223563
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −18.9443 −0.894035 −0.447018 0.894525i $$-0.647514\pi$$
−0.447018 + 0.894525i $$0.647514\pi$$
$$450$$ 0 0
$$451$$ 2.47214 0.116408
$$452$$ 0.472136 0.0222074
$$453$$ 0 0
$$454$$ 19.2361 0.902793
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 26.9443 1.26040 0.630200 0.776433i $$-0.282973\pi$$
0.630200 + 0.776433i $$0.282973\pi$$
$$458$$ 17.2361 0.805389
$$459$$ 0 0
$$460$$ 4.94427 0.230528
$$461$$ 24.7639 1.15337 0.576686 0.816966i $$-0.304346\pi$$
0.576686 + 0.816966i $$0.304346\pi$$
$$462$$ 0 0
$$463$$ −30.4721 −1.41616 −0.708080 0.706132i $$-0.750438\pi$$
−0.708080 + 0.706132i $$0.750438\pi$$
$$464$$ −4.47214 −0.207614
$$465$$ 0 0
$$466$$ −14.9443 −0.692280
$$467$$ −27.1246 −1.25518 −0.627589 0.778545i $$-0.715958\pi$$
−0.627589 + 0.778545i $$0.715958\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −2.47214 −0.114031
$$471$$ 0 0
$$472$$ −2.76393 −0.127220
$$473$$ 10.4721 0.481509
$$474$$ 0 0
$$475$$ −25.1246 −1.15280
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 20.0000 0.914779
$$479$$ 12.3607 0.564774 0.282387 0.959301i $$-0.408874\pi$$
0.282387 + 0.959301i $$0.408874\pi$$
$$480$$ 0 0
$$481$$ 22.4721 1.02464
$$482$$ 15.4164 0.702198
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 15.4164 0.700023
$$486$$ 0 0
$$487$$ 16.9443 0.767818 0.383909 0.923371i $$-0.374578\pi$$
0.383909 + 0.923371i $$0.374578\pi$$
$$488$$ −0.763932 −0.0345816
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 16.9443 0.764684 0.382342 0.924021i $$-0.375118\pi$$
0.382342 + 0.924021i $$0.375118\pi$$
$$492$$ 0 0
$$493$$ −11.0557 −0.497925
$$494$$ −23.4164 −1.05355
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −32.3607 −1.44866 −0.724331 0.689452i $$-0.757851\pi$$
−0.724331 + 0.689452i $$0.757851\pi$$
$$500$$ 10.4721 0.468328
$$501$$ 0 0
$$502$$ −29.2361 −1.30487
$$503$$ 4.00000 0.178351 0.0891756 0.996016i $$-0.471577\pi$$
0.0891756 + 0.996016i $$0.471577\pi$$
$$504$$ 0 0
$$505$$ −10.1115 −0.449954
$$506$$ −4.00000 −0.177822
$$507$$ 0 0
$$508$$ −12.0000 −0.532414
$$509$$ 24.0689 1.06683 0.533417 0.845852i $$-0.320908\pi$$
0.533417 + 0.845852i $$0.320908\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −6.94427 −0.306299
$$515$$ −18.4721 −0.813980
$$516$$ 0 0
$$517$$ 2.00000 0.0879599
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 4.00000 0.175412
$$521$$ −10.3607 −0.453910 −0.226955 0.973905i $$-0.572877\pi$$
−0.226955 + 0.973905i $$0.572877\pi$$
$$522$$ 0 0
$$523$$ 14.2918 0.624937 0.312468 0.949928i $$-0.398844\pi$$
0.312468 + 0.949928i $$0.398844\pi$$
$$524$$ 4.76393 0.208113
$$525$$ 0 0
$$526$$ −4.94427 −0.215580
$$527$$ −4.94427 −0.215376
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ −10.4721 −0.454881
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −8.00000 −0.346518
$$534$$ 0 0
$$535$$ 3.05573 0.132111
$$536$$ −11.4164 −0.493114
$$537$$ 0 0
$$538$$ 22.7639 0.981423
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −26.9443 −1.15842 −0.579212 0.815177i $$-0.696640\pi$$
−0.579212 + 0.815177i $$0.696640\pi$$
$$542$$ 0.944272 0.0405600
$$543$$ 0 0
$$544$$ −2.47214 −0.105992
$$545$$ 12.3607 0.529473
$$546$$ 0 0
$$547$$ −0.944272 −0.0403742 −0.0201871 0.999796i $$-0.506426\pi$$
−0.0201871 + 0.999796i $$0.506426\pi$$
$$548$$ 19.8885 0.849596
$$549$$ 0 0
$$550$$ −3.47214 −0.148052
$$551$$ −32.3607 −1.37861
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −3.52786 −0.149885
$$555$$ 0 0
$$556$$ 21.7082 0.920633
$$557$$ −24.8328 −1.05220 −0.526100 0.850423i $$-0.676346\pi$$
−0.526100 + 0.850423i $$0.676346\pi$$
$$558$$ 0 0
$$559$$ −33.8885 −1.43333
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 28.8328 1.21624
$$563$$ 31.2361 1.31644 0.658222 0.752824i $$-0.271309\pi$$
0.658222 + 0.752824i $$0.271309\pi$$
$$564$$ 0 0
$$565$$ −0.583592 −0.0245519
$$566$$ 14.6525 0.615889
$$567$$ 0 0
$$568$$ 6.47214 0.271565
$$569$$ 36.8328 1.54411 0.772056 0.635555i $$-0.219228\pi$$
0.772056 + 0.635555i $$0.219228\pi$$
$$570$$ 0 0
$$571$$ −10.1115 −0.423151 −0.211576 0.977362i $$-0.567859\pi$$
−0.211576 + 0.977362i $$0.567859\pi$$
$$572$$ −3.23607 −0.135307
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 13.8885 0.579192
$$576$$ 0 0
$$577$$ −26.9443 −1.12170 −0.560852 0.827916i $$-0.689526\pi$$
−0.560852 + 0.827916i $$0.689526\pi$$
$$578$$ 10.8885 0.452904
$$579$$ 0 0
$$580$$ 5.52786 0.229532
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 8.47214 0.350880
$$584$$ 12.9443 0.535638
$$585$$ 0 0
$$586$$ 26.6525 1.10100
$$587$$ −5.81966 −0.240203 −0.120102 0.992762i $$-0.538322\pi$$
−0.120102 + 0.992762i $$0.538322\pi$$
$$588$$ 0 0
$$589$$ −14.4721 −0.596314
$$590$$ 3.41641 0.140651
$$591$$ 0 0
$$592$$ 6.94427 0.285408
$$593$$ 24.0000 0.985562 0.492781 0.870153i $$-0.335980\pi$$
0.492781 + 0.870153i $$0.335980\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 22.3607 0.915929
$$597$$ 0 0
$$598$$ 12.9443 0.529331
$$599$$ 32.3607 1.32222 0.661111 0.750288i $$-0.270085\pi$$
0.661111 + 0.750288i $$0.270085\pi$$
$$600$$ 0 0
$$601$$ 34.8328 1.42086 0.710430 0.703768i $$-0.248500\pi$$
0.710430 + 0.703768i $$0.248500\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 12.0000 0.488273
$$605$$ −1.23607 −0.0502533
$$606$$ 0 0
$$607$$ 32.0000 1.29884 0.649420 0.760430i $$-0.275012\pi$$
0.649420 + 0.760430i $$0.275012\pi$$
$$608$$ −7.23607 −0.293461
$$609$$ 0 0
$$610$$ 0.944272 0.0382325
$$611$$ −6.47214 −0.261835
$$612$$ 0 0
$$613$$ 28.4721 1.14998 0.574989 0.818161i $$-0.305006\pi$$
0.574989 + 0.818161i $$0.305006\pi$$
$$614$$ −26.0689 −1.05205
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −21.4164 −0.862192 −0.431096 0.902306i $$-0.641873\pi$$
−0.431096 + 0.902306i $$0.641873\pi$$
$$618$$ 0 0
$$619$$ −18.5410 −0.745227 −0.372613 0.927987i $$-0.621538\pi$$
−0.372613 + 0.927987i $$0.621538\pi$$
$$620$$ 2.47214 0.0992834
$$621$$ 0 0
$$622$$ 21.4164 0.858720
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 4.41641 0.176656
$$626$$ 19.5279 0.780490
$$627$$ 0 0
$$628$$ 12.6525 0.504889
$$629$$ 17.1672 0.684500
$$630$$ 0 0
$$631$$ −31.4164 −1.25067 −0.625334 0.780357i $$-0.715037\pi$$
−0.625334 + 0.780357i $$0.715037\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −30.9443 −1.22895
$$635$$ 14.8328 0.588622
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −4.47214 −0.177054
$$639$$ 0 0
$$640$$ 1.23607 0.0488599
$$641$$ −27.5279 −1.08729 −0.543643 0.839317i $$-0.682955\pi$$
−0.543643 + 0.839317i $$0.682955\pi$$
$$642$$ 0 0
$$643$$ 18.7639 0.739977 0.369989 0.929036i $$-0.379362\pi$$
0.369989 + 0.929036i $$0.379362\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −17.8885 −0.703815
$$647$$ −28.8328 −1.13353 −0.566767 0.823878i $$-0.691806\pi$$
−0.566767 + 0.823878i $$0.691806\pi$$
$$648$$ 0 0
$$649$$ −2.76393 −0.108494
$$650$$ 11.2361 0.440715
$$651$$ 0 0
$$652$$ −19.4164 −0.760405
$$653$$ −46.3607 −1.81423 −0.907117 0.420879i $$-0.861722\pi$$
−0.907117 + 0.420879i $$0.861722\pi$$
$$654$$ 0 0
$$655$$ −5.88854 −0.230084
$$656$$ −2.47214 −0.0965207
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −16.5836 −0.646005 −0.323003 0.946398i $$-0.604692\pi$$
−0.323003 + 0.946398i $$0.604692\pi$$
$$660$$ 0 0
$$661$$ 3.12461 0.121533 0.0607667 0.998152i $$-0.480645\pi$$
0.0607667 + 0.998152i $$0.480645\pi$$
$$662$$ 16.9443 0.658558
$$663$$ 0 0
$$664$$ 12.1803 0.472689
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 17.8885 0.692647
$$668$$ 11.4164 0.441714
$$669$$ 0 0
$$670$$ 14.1115 0.545173
$$671$$ −0.763932 −0.0294913
$$672$$ 0 0
$$673$$ −3.88854 −0.149892 −0.0749462 0.997188i $$-0.523878\pi$$
−0.0749462 + 0.997188i $$0.523878\pi$$
$$674$$ −18.0000 −0.693334
$$675$$ 0 0
$$676$$ −2.52786 −0.0972255
$$677$$ −26.0689 −1.00191 −0.500954 0.865474i $$-0.667018\pi$$
−0.500954 + 0.865474i $$0.667018\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 3.05573 0.117182
$$681$$ 0 0
$$682$$ −2.00000 −0.0765840
$$683$$ −32.9443 −1.26058 −0.630289 0.776361i $$-0.717064\pi$$
−0.630289 + 0.776361i $$0.717064\pi$$
$$684$$ 0 0
$$685$$ −24.5836 −0.939291
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −10.4721 −0.399246
$$689$$ −27.4164 −1.04448
$$690$$ 0 0
$$691$$ −12.6525 −0.481323 −0.240661 0.970609i $$-0.577364\pi$$
−0.240661 + 0.970609i $$0.577364\pi$$
$$692$$ −3.23607 −0.123017
$$693$$ 0 0
$$694$$ 2.47214 0.0938410
$$695$$ −26.8328 −1.01783
$$696$$ 0 0
$$697$$ −6.11146 −0.231488
$$698$$ 21.7082 0.821668
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 42.7214 1.61356 0.806782 0.590850i $$-0.201207\pi$$
0.806782 + 0.590850i $$0.201207\pi$$
$$702$$ 0 0
$$703$$ 50.2492 1.89519
$$704$$ −1.00000 −0.0376889
$$705$$ 0 0
$$706$$ 17.0557 0.641901
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 4.47214 0.167955 0.0839773 0.996468i $$-0.473238\pi$$
0.0839773 + 0.996468i $$0.473238\pi$$
$$710$$ −8.00000 −0.300235
$$711$$ 0 0
$$712$$ −10.0000 −0.374766
$$713$$ 8.00000 0.299602
$$714$$ 0 0
$$715$$ 4.00000 0.149592
$$716$$ 8.94427 0.334263
$$717$$ 0 0
$$718$$ 26.8328 1.00139
$$719$$ 16.8328 0.627758 0.313879 0.949463i $$-0.398371\pi$$
0.313879 + 0.949463i $$0.398371\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −33.3607 −1.24156
$$723$$ 0 0
$$724$$ −9.23607 −0.343256
$$725$$ 15.5279 0.576690
$$726$$ 0 0
$$727$$ −18.0000 −0.667583 −0.333792 0.942647i $$-0.608328\pi$$
−0.333792 + 0.942647i $$0.608328\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −16.0000 −0.592187
$$731$$ −25.8885 −0.957522
$$732$$ 0 0
$$733$$ −49.1246 −1.81446 −0.907229 0.420636i $$-0.861807\pi$$
−0.907229 + 0.420636i $$0.861807\pi$$
$$734$$ −5.41641 −0.199923
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ −11.4164 −0.420529
$$738$$ 0 0
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ −8.58359 −0.315539
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −21.8885 −0.803013 −0.401506 0.915856i $$-0.631513\pi$$
−0.401506 + 0.915856i $$0.631513\pi$$
$$744$$ 0 0
$$745$$ −27.6393 −1.01263
$$746$$ 6.00000 0.219676
$$747$$ 0 0
$$748$$ −2.47214 −0.0903902
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −16.9443 −0.618305 −0.309153 0.951012i $$-0.600045\pi$$
−0.309153 + 0.951012i $$0.600045\pi$$
$$752$$ −2.00000 −0.0729325
$$753$$ 0 0
$$754$$ 14.4721 0.527044
$$755$$ −14.8328 −0.539821
$$756$$ 0 0
$$757$$ −23.3050 −0.847033 −0.423516 0.905888i $$-0.639204\pi$$
−0.423516 + 0.905888i $$0.639204\pi$$
$$758$$ −14.4721 −0.525652
$$759$$ 0 0
$$760$$ 8.94427 0.324443
$$761$$ −11.4164 −0.413844 −0.206922 0.978357i $$-0.566345\pi$$
−0.206922 + 0.978357i $$0.566345\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 2.47214 0.0894387
$$765$$ 0 0
$$766$$ 23.8885 0.863128
$$767$$ 8.94427 0.322959
$$768$$ 0 0
$$769$$ 43.4164 1.56564 0.782818 0.622251i $$-0.213782\pi$$
0.782818 + 0.622251i $$0.213782\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −14.9443 −0.537856
$$773$$ 15.7082 0.564985 0.282492 0.959270i $$-0.408839\pi$$
0.282492 + 0.959270i $$0.408839\pi$$
$$774$$ 0 0
$$775$$ 6.94427 0.249446
$$776$$ 12.4721 0.447724
$$777$$ 0 0
$$778$$ 33.4164 1.19804
$$779$$ −17.8885 −0.640924
$$780$$ 0 0
$$781$$ 6.47214 0.231591
$$782$$ 9.88854 0.353614
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −15.6393 −0.558191
$$786$$ 0 0
$$787$$ 28.1803 1.00452 0.502260 0.864716i $$-0.332502\pi$$
0.502260 + 0.864716i $$0.332502\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 2.47214 0.0877881
$$794$$ −23.7082 −0.841373
$$795$$ 0 0
$$796$$ −18.9443 −0.671462
$$797$$ −41.5967 −1.47343 −0.736716 0.676202i $$-0.763625\pi$$
−0.736716 + 0.676202i $$0.763625\pi$$
$$798$$ 0 0
$$799$$ −4.94427 −0.174916
$$800$$ 3.47214 0.122759
$$801$$ 0 0
$$802$$ 14.3607 0.507093
$$803$$ 12.9443 0.456793
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 6.47214 0.227971
$$807$$ 0 0
$$808$$ −8.18034 −0.287783
$$809$$ 21.0557 0.740280 0.370140 0.928976i $$-0.379310\pi$$
0.370140 + 0.928976i $$0.379310\pi$$
$$810$$ 0 0
$$811$$ −4.76393 −0.167284 −0.0836421 0.996496i $$-0.526655\pi$$
−0.0836421 + 0.996496i $$0.526655\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 6.94427 0.243397
$$815$$ 24.0000 0.840683
$$816$$ 0 0
$$817$$ −75.7771 −2.65110
$$818$$ 3.41641 0.119452
$$819$$ 0 0
$$820$$ 3.05573 0.106711
$$821$$ 1.41641 0.0494330 0.0247165 0.999695i $$-0.492132\pi$$
0.0247165 + 0.999695i $$0.492132\pi$$
$$822$$ 0 0
$$823$$ −46.2492 −1.61215 −0.806073 0.591816i $$-0.798411\pi$$
−0.806073 + 0.591816i $$0.798411\pi$$
$$824$$ −14.9443 −0.520608
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −16.9443 −0.589210 −0.294605 0.955619i $$-0.595188\pi$$
−0.294605 + 0.955619i $$0.595188\pi$$
$$828$$ 0 0
$$829$$ −11.7082 −0.406643 −0.203321 0.979112i $$-0.565174\pi$$
−0.203321 + 0.979112i $$0.565174\pi$$
$$830$$ −15.0557 −0.522592
$$831$$ 0 0
$$832$$ 3.23607 0.112190
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −14.1115 −0.488347
$$836$$ −7.23607 −0.250265
$$837$$ 0 0
$$838$$ −17.2361 −0.595410
$$839$$ 16.8328 0.581133 0.290567 0.956855i $$-0.406156\pi$$
0.290567 + 0.956855i $$0.406156\pi$$
$$840$$ 0 0
$$841$$ −9.00000 −0.310345
$$842$$ −16.4721 −0.567667
$$843$$ 0 0
$$844$$ −13.5279 −0.465648
$$845$$ 3.12461 0.107490
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −8.47214 −0.290934
$$849$$ 0 0
$$850$$ 8.58359 0.294415
$$851$$ −27.7771 −0.952186
$$852$$ 0 0
$$853$$ −32.5410 −1.11418 −0.557092 0.830451i $$-0.688083\pi$$
−0.557092 + 0.830451i $$0.688083\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 2.47214 0.0844959
$$857$$ −46.4721 −1.58746 −0.793729 0.608272i $$-0.791863\pi$$
−0.793729 + 0.608272i $$0.791863\pi$$
$$858$$ 0 0
$$859$$ −15.1246 −0.516045 −0.258023 0.966139i $$-0.583071\pi$$
−0.258023 + 0.966139i $$0.583071\pi$$
$$860$$ 12.9443 0.441396
$$861$$ 0 0
$$862$$ 23.0557 0.785281
$$863$$ −0.583592 −0.0198657 −0.00993285 0.999951i $$-0.503162\pi$$
−0.00993285 + 0.999951i $$0.503162\pi$$
$$864$$ 0 0
$$865$$ 4.00000 0.136004
$$866$$ 28.4721 0.967523
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 36.9443 1.25181
$$872$$ 10.0000 0.338643
$$873$$ 0 0
$$874$$ 28.9443 0.979055
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 9.05573 0.305790 0.152895 0.988242i $$-0.451140\pi$$
0.152895 + 0.988242i $$0.451140\pi$$
$$878$$ 8.94427 0.301855
$$879$$ 0 0
$$880$$ 1.23607 0.0416678
$$881$$ 28.8328 0.971402 0.485701 0.874125i $$-0.338564\pi$$
0.485701 + 0.874125i $$0.338564\pi$$
$$882$$ 0 0
$$883$$ −2.83282 −0.0953318 −0.0476659 0.998863i $$-0.515178\pi$$
−0.0476659 + 0.998863i $$0.515178\pi$$
$$884$$ 8.00000 0.269069
$$885$$ 0 0
$$886$$ −24.9443 −0.838019
$$887$$ −44.3607 −1.48949 −0.744743 0.667351i $$-0.767428\pi$$
−0.744743 + 0.667351i $$0.767428\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 12.3607 0.414331
$$891$$ 0 0
$$892$$ 0.472136 0.0158083
$$893$$ −14.4721 −0.484292
$$894$$ 0 0
$$895$$ −11.0557 −0.369552
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 18.9443 0.632179
$$899$$ 8.94427 0.298308
$$900$$ 0 0
$$901$$ −20.9443 −0.697755
$$902$$ −2.47214 −0.0823131
$$903$$ 0 0
$$904$$ −0.472136 −0.0157030
$$905$$ 11.4164 0.379494
$$906$$ 0 0
$$907$$ −24.3607 −0.808883 −0.404442 0.914564i $$-0.632534\pi$$
−0.404442 + 0.914564i $$0.632534\pi$$
$$908$$ −19.2361 −0.638371
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 28.0000 0.927681 0.463841 0.885919i $$-0.346471\pi$$
0.463841 + 0.885919i $$0.346471\pi$$
$$912$$ 0 0
$$913$$ 12.1803 0.403110
$$914$$ −26.9443 −0.891237
$$915$$ 0 0
$$916$$ −17.2361 −0.569496
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −22.1115 −0.729390 −0.364695 0.931127i $$-0.618827\pi$$
−0.364695 + 0.931127i $$0.618827\pi$$
$$920$$ −4.94427 −0.163008
$$921$$ 0 0
$$922$$ −24.7639 −0.815557
$$923$$ −20.9443 −0.689389
$$924$$ 0 0
$$925$$ −24.1115 −0.792780
$$926$$ 30.4721 1.00138
$$927$$ 0 0
$$928$$ 4.47214 0.146805
$$929$$ 40.2492 1.32053 0.660267 0.751031i $$-0.270443\pi$$
0.660267 + 0.751031i $$0.270443\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 14.9443 0.489516
$$933$$ 0 0
$$934$$ 27.1246 0.887544
$$935$$ 3.05573 0.0999330
$$936$$ 0 0
$$937$$ 3.05573 0.0998263 0.0499131 0.998754i $$-0.484106\pi$$
0.0499131 + 0.998754i $$0.484106\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 2.47214 0.0806322
$$941$$ −11.8197 −0.385310 −0.192655 0.981267i $$-0.561710\pi$$
−0.192655 + 0.981267i $$0.561710\pi$$
$$942$$ 0 0
$$943$$ 9.88854 0.322015
$$944$$ 2.76393 0.0899583
$$945$$ 0 0
$$946$$ −10.4721 −0.340479
$$947$$ −16.9443 −0.550615 −0.275307 0.961356i $$-0.588780\pi$$
−0.275307 + 0.961356i $$0.588780\pi$$
$$948$$ 0 0
$$949$$ −41.8885 −1.35976
$$950$$ 25.1246 0.815150
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −22.9443 −0.743238 −0.371619 0.928385i $$-0.621197\pi$$
−0.371619 + 0.928385i $$0.621197\pi$$
$$954$$ 0 0
$$955$$ −3.05573 −0.0988810
$$956$$ −20.0000 −0.646846
$$957$$ 0 0
$$958$$ −12.3607 −0.399355
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ −22.4721 −0.724531
$$963$$ 0 0
$$964$$ −15.4164 −0.496529
$$965$$ 18.4721 0.594639
$$966$$ 0 0
$$967$$ 45.8885 1.47568 0.737838 0.674978i $$-0.235847\pi$$
0.737838 + 0.674978i $$0.235847\pi$$
$$968$$ −1.00000 −0.0321412
$$969$$ 0 0
$$970$$ −15.4164 −0.494991
$$971$$ 50.5410 1.62194 0.810969 0.585089i $$-0.198940\pi$$
0.810969 + 0.585089i $$0.198940\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ −16.9443 −0.542929
$$975$$ 0 0
$$976$$ 0.763932 0.0244529
$$977$$ 28.8328 0.922443 0.461222 0.887285i $$-0.347411\pi$$
0.461222 + 0.887285i $$0.347411\pi$$
$$978$$ 0 0
$$979$$ −10.0000 −0.319601
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −16.9443 −0.540713
$$983$$ 14.0000 0.446531 0.223265 0.974758i $$-0.428328\pi$$
0.223265 + 0.974758i $$0.428328\pi$$
$$984$$ 0 0
$$985$$ 22.2492 0.708919
$$986$$ 11.0557 0.352086
$$987$$ 0 0
$$988$$ 23.4164 0.744975
$$989$$ 41.8885 1.33198
$$990$$ 0 0
$$991$$ −0.360680 −0.0114574 −0.00572869 0.999984i $$-0.501824\pi$$
−0.00572869 + 0.999984i $$0.501824\pi$$
$$992$$ 2.00000 0.0635001
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 23.4164 0.742350
$$996$$ 0 0
$$997$$ −24.1803 −0.765799 −0.382900 0.923790i $$-0.625074\pi$$
−0.382900 + 0.923790i $$0.625074\pi$$
$$998$$ 32.3607 1.02436
$$999$$ 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 9702.2.a.cu.1.1 2
3.2 odd 2 1078.2.a.w.1.1 2
7.6 odd 2 1386.2.a.m.1.2 2
12.11 even 2 8624.2.a.bf.1.2 2
21.2 odd 6 1078.2.e.n.67.2 4
21.5 even 6 1078.2.e.q.67.1 4
21.11 odd 6 1078.2.e.n.177.2 4
21.17 even 6 1078.2.e.q.177.1 4
21.20 even 2 154.2.a.d.1.2 2
84.83 odd 2 1232.2.a.p.1.1 2
105.62 odd 4 3850.2.c.q.1849.3 4
105.83 odd 4 3850.2.c.q.1849.2 4
105.104 even 2 3850.2.a.bj.1.1 2
168.83 odd 2 4928.2.a.bk.1.2 2
168.125 even 2 4928.2.a.bt.1.1 2
231.230 odd 2 1694.2.a.l.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.a.d.1.2 2 21.20 even 2
1078.2.a.w.1.1 2 3.2 odd 2
1078.2.e.n.67.2 4 21.2 odd 6
1078.2.e.n.177.2 4 21.11 odd 6
1078.2.e.q.67.1 4 21.5 even 6
1078.2.e.q.177.1 4 21.17 even 6
1232.2.a.p.1.1 2 84.83 odd 2
1386.2.a.m.1.2 2 7.6 odd 2
1694.2.a.l.1.2 2 231.230 odd 2
3850.2.a.bj.1.1 2 105.104 even 2
3850.2.c.q.1849.2 4 105.83 odd 4
3850.2.c.q.1849.3 4 105.62 odd 4
4928.2.a.bk.1.2 2 168.83 odd 2
4928.2.a.bt.1.1 2 168.125 even 2
8624.2.a.bf.1.2 2 12.11 even 2
9702.2.a.cu.1.1 2 1.1 even 1 trivial