# Properties

 Label 1950.2.a.h.1.1 Level $1950$ Weight $2$ Character 1950.1 Self dual yes Analytic conductor $15.571$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$15.5708283941$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1950.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} -8.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} -2.00000 q^{21} -4.00000 q^{22} -6.00000 q^{23} -1.00000 q^{24} -1.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} -4.00000 q^{29} -1.00000 q^{32} +4.00000 q^{33} +8.00000 q^{34} +1.00000 q^{36} +2.00000 q^{37} +6.00000 q^{38} +1.00000 q^{39} -2.00000 q^{41} +2.00000 q^{42} +4.00000 q^{43} +4.00000 q^{44} +6.00000 q^{46} +1.00000 q^{48} -3.00000 q^{49} -8.00000 q^{51} +1.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} +2.00000 q^{56} -6.00000 q^{57} +4.00000 q^{58} +4.00000 q^{59} -10.0000 q^{61} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} -12.0000 q^{67} -8.00000 q^{68} -6.00000 q^{69} -8.00000 q^{71} -1.00000 q^{72} +8.00000 q^{73} -2.00000 q^{74} -6.00000 q^{76} -8.00000 q^{77} -1.00000 q^{78} +8.00000 q^{79} +1.00000 q^{81} +2.00000 q^{82} -12.0000 q^{83} -2.00000 q^{84} -4.00000 q^{86} -4.00000 q^{87} -4.00000 q^{88} -14.0000 q^{89} -2.00000 q^{91} -6.00000 q^{92} -1.00000 q^{96} +16.0000 q^{97} +3.00000 q^{98} +4.00000 q^{99} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 1.00000 0.577350
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 1.00000 0.277350
$$14$$ 2.00000 0.534522
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −8.00000 −1.94029 −0.970143 0.242536i $$-0.922021\pi$$
−0.970143 + 0.242536i $$0.922021\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −6.00000 −1.37649 −0.688247 0.725476i $$-0.741620\pi$$
−0.688247 + 0.725476i $$0.741620\pi$$
$$20$$ 0 0
$$21$$ −2.00000 −0.436436
$$22$$ −4.00000 −0.852803
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ −1.00000 −0.196116
$$27$$ 1.00000 0.192450
$$28$$ −2.00000 −0.377964
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 4.00000 0.696311
$$34$$ 8.00000 1.37199
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 6.00000 0.973329
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 2.00000 0.308607
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 0 0
$$46$$ 6.00000 0.884652
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ −8.00000 −1.12022
$$52$$ 1.00000 0.138675
$$53$$ 10.0000 1.37361 0.686803 0.726844i $$-0.259014\pi$$
0.686803 + 0.726844i $$0.259014\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 2.00000 0.267261
$$57$$ −6.00000 −0.794719
$$58$$ 4.00000 0.525226
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −10.0000 −1.28037 −0.640184 0.768221i $$-0.721142\pi$$
−0.640184 + 0.768221i $$0.721142\pi$$
$$62$$ 0 0
$$63$$ −2.00000 −0.251976
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −4.00000 −0.492366
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ −8.00000 −0.970143
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ 8.00000 0.936329 0.468165 0.883641i $$-0.344915\pi$$
0.468165 + 0.883641i $$0.344915\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 0 0
$$76$$ −6.00000 −0.688247
$$77$$ −8.00000 −0.911685
$$78$$ −1.00000 −0.113228
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 2.00000 0.220863
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ −2.00000 −0.218218
$$85$$ 0 0
$$86$$ −4.00000 −0.431331
$$87$$ −4.00000 −0.428845
$$88$$ −4.00000 −0.426401
$$89$$ −14.0000 −1.48400 −0.741999 0.670402i $$-0.766122\pi$$
−0.741999 + 0.670402i $$0.766122\pi$$
$$90$$ 0 0
$$91$$ −2.00000 −0.209657
$$92$$ −6.00000 −0.625543
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 16.0000 1.62455 0.812277 0.583272i $$-0.198228\pi$$
0.812277 + 0.583272i $$0.198228\pi$$
$$98$$ 3.00000 0.303046
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ −16.0000 −1.59206 −0.796030 0.605257i $$-0.793070\pi$$
−0.796030 + 0.605257i $$0.793070\pi$$
$$102$$ 8.00000 0.792118
$$103$$ 12.0000 1.18240 0.591198 0.806527i $$-0.298655\pi$$
0.591198 + 0.806527i $$0.298655\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ −10.0000 −0.971286
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 12.0000 1.14939 0.574696 0.818367i $$-0.305120\pi$$
0.574696 + 0.818367i $$0.305120\pi$$
$$110$$ 0 0
$$111$$ 2.00000 0.189832
$$112$$ −2.00000 −0.188982
$$113$$ −20.0000 −1.88144 −0.940721 0.339182i $$-0.889850\pi$$
−0.940721 + 0.339182i $$0.889850\pi$$
$$114$$ 6.00000 0.561951
$$115$$ 0 0
$$116$$ −4.00000 −0.371391
$$117$$ 1.00000 0.0924500
$$118$$ −4.00000 −0.368230
$$119$$ 16.0000 1.46672
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 10.0000 0.905357
$$123$$ −2.00000 −0.180334
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 2.00000 0.178174
$$127$$ −4.00000 −0.354943 −0.177471 0.984126i $$-0.556792\pi$$
−0.177471 + 0.984126i $$0.556792\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 4.00000 0.352180
$$130$$ 0 0
$$131$$ 10.0000 0.873704 0.436852 0.899533i $$-0.356093\pi$$
0.436852 + 0.899533i $$0.356093\pi$$
$$132$$ 4.00000 0.348155
$$133$$ 12.0000 1.04053
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ 8.00000 0.685994
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 6.00000 0.510754
$$139$$ −8.00000 −0.678551 −0.339276 0.940687i $$-0.610182\pi$$
−0.339276 + 0.940687i $$0.610182\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 8.00000 0.671345
$$143$$ 4.00000 0.334497
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −8.00000 −0.662085
$$147$$ −3.00000 −0.247436
$$148$$ 2.00000 0.164399
$$149$$ −10.0000 −0.819232 −0.409616 0.912258i $$-0.634337\pi$$
−0.409616 + 0.912258i $$0.634337\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 6.00000 0.486664
$$153$$ −8.00000 −0.646762
$$154$$ 8.00000 0.644658
$$155$$ 0 0
$$156$$ 1.00000 0.0800641
$$157$$ −22.0000 −1.75579 −0.877896 0.478852i $$-0.841053\pi$$
−0.877896 + 0.478852i $$0.841053\pi$$
$$158$$ −8.00000 −0.636446
$$159$$ 10.0000 0.793052
$$160$$ 0 0
$$161$$ 12.0000 0.945732
$$162$$ −1.00000 −0.0785674
$$163$$ 16.0000 1.25322 0.626608 0.779334i $$-0.284443\pi$$
0.626608 + 0.779334i $$0.284443\pi$$
$$164$$ −2.00000 −0.156174
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ 4.00000 0.309529 0.154765 0.987951i $$-0.450538\pi$$
0.154765 + 0.987951i $$0.450538\pi$$
$$168$$ 2.00000 0.154303
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ −6.00000 −0.458831
$$172$$ 4.00000 0.304997
$$173$$ −22.0000 −1.67263 −0.836315 0.548250i $$-0.815294\pi$$
−0.836315 + 0.548250i $$0.815294\pi$$
$$174$$ 4.00000 0.303239
$$175$$ 0 0
$$176$$ 4.00000 0.301511
$$177$$ 4.00000 0.300658
$$178$$ 14.0000 1.04934
$$179$$ −10.0000 −0.747435 −0.373718 0.927543i $$-0.621917\pi$$
−0.373718 + 0.927543i $$0.621917\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 2.00000 0.148250
$$183$$ −10.0000 −0.739221
$$184$$ 6.00000 0.442326
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −32.0000 −2.34007
$$188$$ 0 0
$$189$$ −2.00000 −0.145479
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 4.00000 0.287926 0.143963 0.989583i $$-0.454015\pi$$
0.143963 + 0.989583i $$0.454015\pi$$
$$194$$ −16.0000 −1.14873
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ −4.00000 −0.284268
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −12.0000 −0.846415
$$202$$ 16.0000 1.12576
$$203$$ 8.00000 0.561490
$$204$$ −8.00000 −0.560112
$$205$$ 0 0
$$206$$ −12.0000 −0.836080
$$207$$ −6.00000 −0.417029
$$208$$ 1.00000 0.0693375
$$209$$ −24.0000 −1.66011
$$210$$ 0 0
$$211$$ −20.0000 −1.37686 −0.688428 0.725304i $$-0.741699\pi$$
−0.688428 + 0.725304i $$0.741699\pi$$
$$212$$ 10.0000 0.686803
$$213$$ −8.00000 −0.548151
$$214$$ 12.0000 0.820303
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ −12.0000 −0.812743
$$219$$ 8.00000 0.540590
$$220$$ 0 0
$$221$$ −8.00000 −0.538138
$$222$$ −2.00000 −0.134231
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ 2.00000 0.133631
$$225$$ 0 0
$$226$$ 20.0000 1.33038
$$227$$ 4.00000 0.265489 0.132745 0.991150i $$-0.457621\pi$$
0.132745 + 0.991150i $$0.457621\pi$$
$$228$$ −6.00000 −0.397360
$$229$$ 4.00000 0.264327 0.132164 0.991228i $$-0.457808\pi$$
0.132164 + 0.991228i $$0.457808\pi$$
$$230$$ 0 0
$$231$$ −8.00000 −0.526361
$$232$$ 4.00000 0.262613
$$233$$ −24.0000 −1.57229 −0.786146 0.618041i $$-0.787927\pi$$
−0.786146 + 0.618041i $$0.787927\pi$$
$$234$$ −1.00000 −0.0653720
$$235$$ 0 0
$$236$$ 4.00000 0.260378
$$237$$ 8.00000 0.519656
$$238$$ −16.0000 −1.03713
$$239$$ 16.0000 1.03495 0.517477 0.855697i $$-0.326871\pi$$
0.517477 + 0.855697i $$0.326871\pi$$
$$240$$ 0 0
$$241$$ 2.00000 0.128831 0.0644157 0.997923i $$-0.479482\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 1.00000 0.0641500
$$244$$ −10.0000 −0.640184
$$245$$ 0 0
$$246$$ 2.00000 0.127515
$$247$$ −6.00000 −0.381771
$$248$$ 0 0
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ 6.00000 0.378717 0.189358 0.981908i $$-0.439359\pi$$
0.189358 + 0.981908i $$0.439359\pi$$
$$252$$ −2.00000 −0.125988
$$253$$ −24.0000 −1.50887
$$254$$ 4.00000 0.250982
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −12.0000 −0.748539 −0.374270 0.927320i $$-0.622107\pi$$
−0.374270 + 0.927320i $$0.622107\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ −4.00000 −0.248548
$$260$$ 0 0
$$261$$ −4.00000 −0.247594
$$262$$ −10.0000 −0.617802
$$263$$ −2.00000 −0.123325 −0.0616626 0.998097i $$-0.519640\pi$$
−0.0616626 + 0.998097i $$0.519640\pi$$
$$264$$ −4.00000 −0.246183
$$265$$ 0 0
$$266$$ −12.0000 −0.735767
$$267$$ −14.0000 −0.856786
$$268$$ −12.0000 −0.733017
$$269$$ −24.0000 −1.46331 −0.731653 0.681677i $$-0.761251\pi$$
−0.731653 + 0.681677i $$0.761251\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ −8.00000 −0.485071
$$273$$ −2.00000 −0.121046
$$274$$ −6.00000 −0.362473
$$275$$ 0 0
$$276$$ −6.00000 −0.361158
$$277$$ 10.0000 0.600842 0.300421 0.953807i $$-0.402873\pi$$
0.300421 + 0.953807i $$0.402873\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −6.00000 −0.357930 −0.178965 0.983855i $$-0.557275\pi$$
−0.178965 + 0.983855i $$0.557275\pi$$
$$282$$ 0 0
$$283$$ 4.00000 0.237775 0.118888 0.992908i $$-0.462067\pi$$
0.118888 + 0.992908i $$0.462067\pi$$
$$284$$ −8.00000 −0.474713
$$285$$ 0 0
$$286$$ −4.00000 −0.236525
$$287$$ 4.00000 0.236113
$$288$$ −1.00000 −0.0589256
$$289$$ 47.0000 2.76471
$$290$$ 0 0
$$291$$ 16.0000 0.937937
$$292$$ 8.00000 0.468165
$$293$$ 26.0000 1.51894 0.759468 0.650545i $$-0.225459\pi$$
0.759468 + 0.650545i $$0.225459\pi$$
$$294$$ 3.00000 0.174964
$$295$$ 0 0
$$296$$ −2.00000 −0.116248
$$297$$ 4.00000 0.232104
$$298$$ 10.0000 0.579284
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 0 0
$$303$$ −16.0000 −0.919176
$$304$$ −6.00000 −0.344124
$$305$$ 0 0
$$306$$ 8.00000 0.457330
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ −8.00000 −0.455842
$$309$$ 12.0000 0.682656
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ −1.00000 −0.0566139
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ 22.0000 1.24153
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ 30.0000 1.68497 0.842484 0.538721i $$-0.181092\pi$$
0.842484 + 0.538721i $$0.181092\pi$$
$$318$$ −10.0000 −0.560772
$$319$$ −16.0000 −0.895828
$$320$$ 0 0
$$321$$ −12.0000 −0.669775
$$322$$ −12.0000 −0.668734
$$323$$ 48.0000 2.67079
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −16.0000 −0.886158
$$327$$ 12.0000 0.663602
$$328$$ 2.00000 0.110432
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 10.0000 0.549650 0.274825 0.961494i $$-0.411380\pi$$
0.274825 + 0.961494i $$0.411380\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 2.00000 0.109599
$$334$$ −4.00000 −0.218870
$$335$$ 0 0
$$336$$ −2.00000 −0.109109
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ −1.00000 −0.0543928
$$339$$ −20.0000 −1.08625
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 6.00000 0.324443
$$343$$ 20.0000 1.07990
$$344$$ −4.00000 −0.215666
$$345$$ 0 0
$$346$$ 22.0000 1.18273
$$347$$ 24.0000 1.28839 0.644194 0.764862i $$-0.277193\pi$$
0.644194 + 0.764862i $$0.277193\pi$$
$$348$$ −4.00000 −0.214423
$$349$$ −28.0000 −1.49881 −0.749403 0.662114i $$-0.769659\pi$$
−0.749403 + 0.662114i $$0.769659\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ −4.00000 −0.213201
$$353$$ 14.0000 0.745145 0.372572 0.928003i $$-0.378476\pi$$
0.372572 + 0.928003i $$0.378476\pi$$
$$354$$ −4.00000 −0.212598
$$355$$ 0 0
$$356$$ −14.0000 −0.741999
$$357$$ 16.0000 0.846810
$$358$$ 10.0000 0.528516
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ −10.0000 −0.525588
$$363$$ 5.00000 0.262432
$$364$$ −2.00000 −0.104828
$$365$$ 0 0
$$366$$ 10.0000 0.522708
$$367$$ 36.0000 1.87918 0.939592 0.342296i $$-0.111204\pi$$
0.939592 + 0.342296i $$0.111204\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ −20.0000 −1.03835
$$372$$ 0 0
$$373$$ 2.00000 0.103556 0.0517780 0.998659i $$-0.483511\pi$$
0.0517780 + 0.998659i $$0.483511\pi$$
$$374$$ 32.0000 1.65468
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.00000 −0.206010
$$378$$ 2.00000 0.102869
$$379$$ −18.0000 −0.924598 −0.462299 0.886724i $$-0.652975\pi$$
−0.462299 + 0.886724i $$0.652975\pi$$
$$380$$ 0 0
$$381$$ −4.00000 −0.204926
$$382$$ 0 0
$$383$$ 12.0000 0.613171 0.306586 0.951843i $$-0.400813\pi$$
0.306586 + 0.951843i $$0.400813\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −4.00000 −0.203595
$$387$$ 4.00000 0.203331
$$388$$ 16.0000 0.812277
$$389$$ 8.00000 0.405616 0.202808 0.979219i $$-0.434993\pi$$
0.202808 + 0.979219i $$0.434993\pi$$
$$390$$ 0 0
$$391$$ 48.0000 2.42746
$$392$$ 3.00000 0.151523
$$393$$ 10.0000 0.504433
$$394$$ −18.0000 −0.906827
$$395$$ 0 0
$$396$$ 4.00000 0.201008
$$397$$ −14.0000 −0.702640 −0.351320 0.936255i $$-0.614267\pi$$
−0.351320 + 0.936255i $$0.614267\pi$$
$$398$$ 0 0
$$399$$ 12.0000 0.600751
$$400$$ 0 0
$$401$$ 30.0000 1.49813 0.749064 0.662497i $$-0.230503\pi$$
0.749064 + 0.662497i $$0.230503\pi$$
$$402$$ 12.0000 0.598506
$$403$$ 0 0
$$404$$ −16.0000 −0.796030
$$405$$ 0 0
$$406$$ −8.00000 −0.397033
$$407$$ 8.00000 0.396545
$$408$$ 8.00000 0.396059
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 0 0
$$411$$ 6.00000 0.295958
$$412$$ 12.0000 0.591198
$$413$$ −8.00000 −0.393654
$$414$$ 6.00000 0.294884
$$415$$ 0 0
$$416$$ −1.00000 −0.0490290
$$417$$ −8.00000 −0.391762
$$418$$ 24.0000 1.17388
$$419$$ 10.0000 0.488532 0.244266 0.969708i $$-0.421453\pi$$
0.244266 + 0.969708i $$0.421453\pi$$
$$420$$ 0 0
$$421$$ −8.00000 −0.389896 −0.194948 0.980814i $$-0.562454\pi$$
−0.194948 + 0.980814i $$0.562454\pi$$
$$422$$ 20.0000 0.973585
$$423$$ 0 0
$$424$$ −10.0000 −0.485643
$$425$$ 0 0
$$426$$ 8.00000 0.387601
$$427$$ 20.0000 0.967868
$$428$$ −12.0000 −0.580042
$$429$$ 4.00000 0.193122
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 12.0000 0.574696
$$437$$ 36.0000 1.72211
$$438$$ −8.00000 −0.382255
$$439$$ −32.0000 −1.52728 −0.763638 0.645644i $$-0.776589\pi$$
−0.763638 + 0.645644i $$0.776589\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 8.00000 0.380521
$$443$$ −16.0000 −0.760183 −0.380091 0.924949i $$-0.624107\pi$$
−0.380091 + 0.924949i $$0.624107\pi$$
$$444$$ 2.00000 0.0949158
$$445$$ 0 0
$$446$$ −2.00000 −0.0947027
$$447$$ −10.0000 −0.472984
$$448$$ −2.00000 −0.0944911
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ 0 0
$$451$$ −8.00000 −0.376705
$$452$$ −20.0000 −0.940721
$$453$$ 0 0
$$454$$ −4.00000 −0.187729
$$455$$ 0 0
$$456$$ 6.00000 0.280976
$$457$$ −8.00000 −0.374224 −0.187112 0.982339i $$-0.559913\pi$$
−0.187112 + 0.982339i $$0.559913\pi$$
$$458$$ −4.00000 −0.186908
$$459$$ −8.00000 −0.373408
$$460$$ 0 0
$$461$$ −6.00000 −0.279448 −0.139724 0.990190i $$-0.544622\pi$$
−0.139724 + 0.990190i $$0.544622\pi$$
$$462$$ 8.00000 0.372194
$$463$$ 26.0000 1.20832 0.604161 0.796862i $$-0.293508\pi$$
0.604161 + 0.796862i $$0.293508\pi$$
$$464$$ −4.00000 −0.185695
$$465$$ 0 0
$$466$$ 24.0000 1.11178
$$467$$ −28.0000 −1.29569 −0.647843 0.761774i $$-0.724329\pi$$
−0.647843 + 0.761774i $$0.724329\pi$$
$$468$$ 1.00000 0.0462250
$$469$$ 24.0000 1.10822
$$470$$ 0 0
$$471$$ −22.0000 −1.01371
$$472$$ −4.00000 −0.184115
$$473$$ 16.0000 0.735681
$$474$$ −8.00000 −0.367452
$$475$$ 0 0
$$476$$ 16.0000 0.733359
$$477$$ 10.0000 0.457869
$$478$$ −16.0000 −0.731823
$$479$$ 32.0000 1.46212 0.731059 0.682315i $$-0.239027\pi$$
0.731059 + 0.682315i $$0.239027\pi$$
$$480$$ 0 0
$$481$$ 2.00000 0.0911922
$$482$$ −2.00000 −0.0910975
$$483$$ 12.0000 0.546019
$$484$$ 5.00000 0.227273
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ −26.0000 −1.17817 −0.589086 0.808070i $$-0.700512\pi$$
−0.589086 + 0.808070i $$0.700512\pi$$
$$488$$ 10.0000 0.452679
$$489$$ 16.0000 0.723545
$$490$$ 0 0
$$491$$ 42.0000 1.89543 0.947717 0.319113i $$-0.103385\pi$$
0.947717 + 0.319113i $$0.103385\pi$$
$$492$$ −2.00000 −0.0901670
$$493$$ 32.0000 1.44121
$$494$$ 6.00000 0.269953
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 16.0000 0.717698
$$498$$ 12.0000 0.537733
$$499$$ 38.0000 1.70111 0.850557 0.525883i $$-0.176265\pi$$
0.850557 + 0.525883i $$0.176265\pi$$
$$500$$ 0 0
$$501$$ 4.00000 0.178707
$$502$$ −6.00000 −0.267793
$$503$$ −10.0000 −0.445878 −0.222939 0.974832i $$-0.571565\pi$$
−0.222939 + 0.974832i $$0.571565\pi$$
$$504$$ 2.00000 0.0890871
$$505$$ 0 0
$$506$$ 24.0000 1.06693
$$507$$ 1.00000 0.0444116
$$508$$ −4.00000 −0.177471
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ −16.0000 −0.707798
$$512$$ −1.00000 −0.0441942
$$513$$ −6.00000 −0.264906
$$514$$ 12.0000 0.529297
$$515$$ 0 0
$$516$$ 4.00000 0.176090
$$517$$ 0 0
$$518$$ 4.00000 0.175750
$$519$$ −22.0000 −0.965693
$$520$$ 0 0
$$521$$ −26.0000 −1.13908 −0.569540 0.821963i $$-0.692879\pi$$
−0.569540 + 0.821963i $$0.692879\pi$$
$$522$$ 4.00000 0.175075
$$523$$ −36.0000 −1.57417 −0.787085 0.616844i $$-0.788411\pi$$
−0.787085 + 0.616844i $$0.788411\pi$$
$$524$$ 10.0000 0.436852
$$525$$ 0 0
$$526$$ 2.00000 0.0872041
$$527$$ 0 0
$$528$$ 4.00000 0.174078
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 12.0000 0.520266
$$533$$ −2.00000 −0.0866296
$$534$$ 14.0000 0.605839
$$535$$ 0 0
$$536$$ 12.0000 0.518321
$$537$$ −10.0000 −0.431532
$$538$$ 24.0000 1.03471
$$539$$ −12.0000 −0.516877
$$540$$ 0 0
$$541$$ −8.00000 −0.343947 −0.171973 0.985102i $$-0.555014\pi$$
−0.171973 + 0.985102i $$0.555014\pi$$
$$542$$ −16.0000 −0.687259
$$543$$ 10.0000 0.429141
$$544$$ 8.00000 0.342997
$$545$$ 0 0
$$546$$ 2.00000 0.0855921
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ 6.00000 0.256307
$$549$$ −10.0000 −0.426790
$$550$$ 0 0
$$551$$ 24.0000 1.02243
$$552$$ 6.00000 0.255377
$$553$$ −16.0000 −0.680389
$$554$$ −10.0000 −0.424859
$$555$$ 0 0
$$556$$ −8.00000 −0.339276
$$557$$ −2.00000 −0.0847427 −0.0423714 0.999102i $$-0.513491\pi$$
−0.0423714 + 0.999102i $$0.513491\pi$$
$$558$$ 0 0
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ −32.0000 −1.35104
$$562$$ 6.00000 0.253095
$$563$$ −24.0000 −1.01148 −0.505740 0.862686i $$-0.668780\pi$$
−0.505740 + 0.862686i $$0.668780\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −4.00000 −0.168133
$$567$$ −2.00000 −0.0839921
$$568$$ 8.00000 0.335673
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 40.0000 1.67395 0.836974 0.547243i $$-0.184323\pi$$
0.836974 + 0.547243i $$0.184323\pi$$
$$572$$ 4.00000 0.167248
$$573$$ 0 0
$$574$$ −4.00000 −0.166957
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −12.0000 −0.499567 −0.249783 0.968302i $$-0.580359\pi$$
−0.249783 + 0.968302i $$0.580359\pi$$
$$578$$ −47.0000 −1.95494
$$579$$ 4.00000 0.166234
$$580$$ 0 0
$$581$$ 24.0000 0.995688
$$582$$ −16.0000 −0.663221
$$583$$ 40.0000 1.65663
$$584$$ −8.00000 −0.331042
$$585$$ 0 0
$$586$$ −26.0000 −1.07405
$$587$$ −36.0000 −1.48588 −0.742940 0.669359i $$-0.766569\pi$$
−0.742940 + 0.669359i $$0.766569\pi$$
$$588$$ −3.00000 −0.123718
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 18.0000 0.740421
$$592$$ 2.00000 0.0821995
$$593$$ −22.0000 −0.903432 −0.451716 0.892162i $$-0.649188\pi$$
−0.451716 + 0.892162i $$0.649188\pi$$
$$594$$ −4.00000 −0.164122
$$595$$ 0 0
$$596$$ −10.0000 −0.409616
$$597$$ 0 0
$$598$$ 6.00000 0.245358
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ 22.0000 0.897399 0.448699 0.893683i $$-0.351887\pi$$
0.448699 + 0.893683i $$0.351887\pi$$
$$602$$ 8.00000 0.326056
$$603$$ −12.0000 −0.488678
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 16.0000 0.649956
$$607$$ 28.0000 1.13648 0.568242 0.822861i $$-0.307624\pi$$
0.568242 + 0.822861i $$0.307624\pi$$
$$608$$ 6.00000 0.243332
$$609$$ 8.00000 0.324176
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −8.00000 −0.323381
$$613$$ 10.0000 0.403896 0.201948 0.979396i $$-0.435273\pi$$
0.201948 + 0.979396i $$0.435273\pi$$
$$614$$ 12.0000 0.484281
$$615$$ 0 0
$$616$$ 8.00000 0.322329
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ −12.0000 −0.482711
$$619$$ −10.0000 −0.401934 −0.200967 0.979598i $$-0.564408\pi$$
−0.200967 + 0.979598i $$0.564408\pi$$
$$620$$ 0 0
$$621$$ −6.00000 −0.240772
$$622$$ −24.0000 −0.962312
$$623$$ 28.0000 1.12180
$$624$$ 1.00000 0.0400320
$$625$$ 0 0
$$626$$ 6.00000 0.239808
$$627$$ −24.0000 −0.958468
$$628$$ −22.0000 −0.877896
$$629$$ −16.0000 −0.637962
$$630$$ 0 0
$$631$$ 12.0000 0.477712 0.238856 0.971055i $$-0.423228\pi$$
0.238856 + 0.971055i $$0.423228\pi$$
$$632$$ −8.00000 −0.318223
$$633$$ −20.0000 −0.794929
$$634$$ −30.0000 −1.19145
$$635$$ 0 0
$$636$$ 10.0000 0.396526
$$637$$ −3.00000 −0.118864
$$638$$ 16.0000 0.633446
$$639$$ −8.00000 −0.316475
$$640$$ 0 0
$$641$$ 18.0000 0.710957 0.355479 0.934684i $$-0.384318\pi$$
0.355479 + 0.934684i $$0.384318\pi$$
$$642$$ 12.0000 0.473602
$$643$$ −44.0000 −1.73519 −0.867595 0.497271i $$-0.834335\pi$$
−0.867595 + 0.497271i $$0.834335\pi$$
$$644$$ 12.0000 0.472866
$$645$$ 0 0
$$646$$ −48.0000 −1.88853
$$647$$ 30.0000 1.17942 0.589711 0.807614i $$-0.299242\pi$$
0.589711 + 0.807614i $$0.299242\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 16.0000 0.628055
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 16.0000 0.626608
$$653$$ −42.0000 −1.64359 −0.821794 0.569785i $$-0.807026\pi$$
−0.821794 + 0.569785i $$0.807026\pi$$
$$654$$ −12.0000 −0.469237
$$655$$ 0 0
$$656$$ −2.00000 −0.0780869
$$657$$ 8.00000 0.312110
$$658$$ 0 0
$$659$$ 2.00000 0.0779089 0.0389545 0.999241i $$-0.487597\pi$$
0.0389545 + 0.999241i $$0.487597\pi$$
$$660$$ 0 0
$$661$$ 48.0000 1.86698 0.933492 0.358599i $$-0.116745\pi$$
0.933492 + 0.358599i $$0.116745\pi$$
$$662$$ −10.0000 −0.388661
$$663$$ −8.00000 −0.310694
$$664$$ 12.0000 0.465690
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ 24.0000 0.929284
$$668$$ 4.00000 0.154765
$$669$$ 2.00000 0.0773245
$$670$$ 0 0
$$671$$ −40.0000 −1.54418
$$672$$ 2.00000 0.0771517
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ 14.0000 0.539260
$$675$$ 0 0
$$676$$ 1.00000 0.0384615
$$677$$ 30.0000 1.15299 0.576497 0.817099i $$-0.304419\pi$$
0.576497 + 0.817099i $$0.304419\pi$$
$$678$$ 20.0000 0.768095
$$679$$ −32.0000 −1.22805
$$680$$ 0 0
$$681$$ 4.00000 0.153280
$$682$$ 0 0
$$683$$ 44.0000 1.68361 0.841807 0.539779i $$-0.181492\pi$$
0.841807 + 0.539779i $$0.181492\pi$$
$$684$$ −6.00000 −0.229416
$$685$$ 0 0
$$686$$ −20.0000 −0.763604
$$687$$ 4.00000 0.152610
$$688$$ 4.00000 0.152499
$$689$$ 10.0000 0.380970
$$690$$ 0 0
$$691$$ −14.0000 −0.532585 −0.266293 0.963892i $$-0.585799\pi$$
−0.266293 + 0.963892i $$0.585799\pi$$
$$692$$ −22.0000 −0.836315
$$693$$ −8.00000 −0.303895
$$694$$ −24.0000 −0.911028
$$695$$ 0 0
$$696$$ 4.00000 0.151620
$$697$$ 16.0000 0.606043
$$698$$ 28.0000 1.05982
$$699$$ −24.0000 −0.907763
$$700$$ 0 0
$$701$$ 32.0000 1.20862 0.604312 0.796748i $$-0.293448\pi$$
0.604312 + 0.796748i $$0.293448\pi$$
$$702$$ −1.00000 −0.0377426
$$703$$ −12.0000 −0.452589
$$704$$ 4.00000 0.150756
$$705$$ 0 0
$$706$$ −14.0000 −0.526897
$$707$$ 32.0000 1.20348
$$708$$ 4.00000 0.150329
$$709$$ −4.00000 −0.150223 −0.0751116 0.997175i $$-0.523931\pi$$
−0.0751116 + 0.997175i $$0.523931\pi$$
$$710$$ 0 0
$$711$$ 8.00000 0.300023
$$712$$ 14.0000 0.524672
$$713$$ 0 0
$$714$$ −16.0000 −0.598785
$$715$$ 0 0
$$716$$ −10.0000 −0.373718
$$717$$ 16.0000 0.597531
$$718$$ 24.0000 0.895672
$$719$$ 36.0000 1.34257 0.671287 0.741198i $$-0.265742\pi$$
0.671287 + 0.741198i $$0.265742\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ −17.0000 −0.632674
$$723$$ 2.00000 0.0743808
$$724$$ 10.0000 0.371647
$$725$$ 0 0
$$726$$ −5.00000 −0.185567
$$727$$ −16.0000 −0.593407 −0.296704 0.954970i $$-0.595887\pi$$
−0.296704 + 0.954970i $$0.595887\pi$$
$$728$$ 2.00000 0.0741249
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −32.0000 −1.18356
$$732$$ −10.0000 −0.369611
$$733$$ −38.0000 −1.40356 −0.701781 0.712393i $$-0.747612\pi$$
−0.701781 + 0.712393i $$0.747612\pi$$
$$734$$ −36.0000 −1.32878
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ −48.0000 −1.76810
$$738$$ 2.00000 0.0736210
$$739$$ 30.0000 1.10357 0.551784 0.833987i $$-0.313947\pi$$
0.551784 + 0.833987i $$0.313947\pi$$
$$740$$ 0 0
$$741$$ −6.00000 −0.220416
$$742$$ 20.0000 0.734223
$$743$$ −12.0000 −0.440237 −0.220119 0.975473i $$-0.570644\pi$$
−0.220119 + 0.975473i $$0.570644\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −2.00000 −0.0732252
$$747$$ −12.0000 −0.439057
$$748$$ −32.0000 −1.17004
$$749$$ 24.0000 0.876941
$$750$$ 0 0
$$751$$ −16.0000 −0.583848 −0.291924 0.956441i $$-0.594295\pi$$
−0.291924 + 0.956441i $$0.594295\pi$$
$$752$$ 0 0
$$753$$ 6.00000 0.218652
$$754$$ 4.00000 0.145671
$$755$$ 0 0
$$756$$ −2.00000 −0.0727393
$$757$$ 6.00000 0.218074 0.109037 0.994038i $$-0.465223\pi$$
0.109037 + 0.994038i $$0.465223\pi$$
$$758$$ 18.0000 0.653789
$$759$$ −24.0000 −0.871145
$$760$$ 0 0
$$761$$ 22.0000 0.797499 0.398750 0.917060i $$-0.369444\pi$$
0.398750 + 0.917060i $$0.369444\pi$$
$$762$$ 4.00000 0.144905
$$763$$ −24.0000 −0.868858
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −12.0000 −0.433578
$$767$$ 4.00000 0.144432
$$768$$ 1.00000 0.0360844
$$769$$ 10.0000 0.360609 0.180305 0.983611i $$-0.442292\pi$$
0.180305 + 0.983611i $$0.442292\pi$$
$$770$$ 0 0
$$771$$ −12.0000 −0.432169
$$772$$ 4.00000 0.143963
$$773$$ −38.0000 −1.36677 −0.683383 0.730061i $$-0.739492\pi$$
−0.683383 + 0.730061i $$0.739492\pi$$
$$774$$ −4.00000 −0.143777
$$775$$ 0 0
$$776$$ −16.0000 −0.574367
$$777$$ −4.00000 −0.143499
$$778$$ −8.00000 −0.286814
$$779$$ 12.0000 0.429945
$$780$$ 0 0
$$781$$ −32.0000 −1.14505
$$782$$ −48.0000 −1.71648
$$783$$ −4.00000 −0.142948
$$784$$ −3.00000 −0.107143
$$785$$ 0 0
$$786$$ −10.0000 −0.356688
$$787$$ 32.0000 1.14068 0.570338 0.821410i $$-0.306812\pi$$
0.570338 + 0.821410i $$0.306812\pi$$
$$788$$ 18.0000 0.641223
$$789$$ −2.00000 −0.0712019
$$790$$ 0 0
$$791$$ 40.0000 1.42224
$$792$$ −4.00000 −0.142134
$$793$$ −10.0000 −0.355110
$$794$$ 14.0000 0.496841
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 10.0000 0.354218 0.177109 0.984191i $$-0.443325\pi$$
0.177109 + 0.984191i $$0.443325\pi$$
$$798$$ −12.0000 −0.424795
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −14.0000 −0.494666
$$802$$ −30.0000 −1.05934
$$803$$ 32.0000 1.12926
$$804$$ −12.0000 −0.423207
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −24.0000 −0.844840
$$808$$ 16.0000 0.562878
$$809$$ 2.00000 0.0703163 0.0351581 0.999382i $$-0.488807\pi$$
0.0351581 + 0.999382i $$0.488807\pi$$
$$810$$ 0 0
$$811$$ −38.0000 −1.33436 −0.667180 0.744896i $$-0.732499\pi$$
−0.667180 + 0.744896i $$0.732499\pi$$
$$812$$ 8.00000 0.280745
$$813$$ 16.0000 0.561144
$$814$$ −8.00000 −0.280400
$$815$$ 0 0
$$816$$ −8.00000 −0.280056
$$817$$ −24.0000 −0.839654
$$818$$ 26.0000 0.909069
$$819$$ −2.00000 −0.0698857
$$820$$ 0 0
$$821$$ −10.0000 −0.349002 −0.174501 0.984657i $$-0.555831\pi$$
−0.174501 + 0.984657i $$0.555831\pi$$
$$822$$ −6.00000 −0.209274
$$823$$ 52.0000 1.81261 0.906303 0.422628i $$-0.138892\pi$$
0.906303 + 0.422628i $$0.138892\pi$$
$$824$$ −12.0000 −0.418040
$$825$$ 0 0
$$826$$ 8.00000 0.278356
$$827$$ 12.0000 0.417281 0.208640 0.977992i $$-0.433096\pi$$
0.208640 + 0.977992i $$0.433096\pi$$
$$828$$ −6.00000 −0.208514
$$829$$ −10.0000 −0.347314 −0.173657 0.984806i $$-0.555558\pi$$
−0.173657 + 0.984806i $$0.555558\pi$$
$$830$$ 0 0
$$831$$ 10.0000 0.346896
$$832$$ 1.00000 0.0346688
$$833$$ 24.0000 0.831551
$$834$$ 8.00000 0.277017
$$835$$ 0 0
$$836$$ −24.0000 −0.830057
$$837$$ 0 0
$$838$$ −10.0000 −0.345444
$$839$$ −40.0000 −1.38095 −0.690477 0.723355i $$-0.742599\pi$$
−0.690477 + 0.723355i $$0.742599\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ 8.00000 0.275698
$$843$$ −6.00000 −0.206651
$$844$$ −20.0000 −0.688428
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −10.0000 −0.343604
$$848$$ 10.0000 0.343401
$$849$$ 4.00000 0.137280
$$850$$ 0 0
$$851$$ −12.0000 −0.411355
$$852$$ −8.00000 −0.274075
$$853$$ −46.0000 −1.57501 −0.787505 0.616308i $$-0.788628\pi$$
−0.787505 + 0.616308i $$0.788628\pi$$
$$854$$ −20.0000 −0.684386
$$855$$ 0 0
$$856$$ 12.0000 0.410152
$$857$$ −4.00000 −0.136637 −0.0683187 0.997664i $$-0.521763\pi$$
−0.0683187 + 0.997664i $$0.521763\pi$$
$$858$$ −4.00000 −0.136558
$$859$$ 36.0000 1.22830 0.614152 0.789188i $$-0.289498\pi$$
0.614152 + 0.789188i $$0.289498\pi$$
$$860$$ 0 0
$$861$$ 4.00000 0.136320
$$862$$ 0 0
$$863$$ 12.0000 0.408485 0.204242 0.978920i $$-0.434527\pi$$
0.204242 + 0.978920i $$0.434527\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ −2.00000 −0.0679628
$$867$$ 47.0000 1.59620
$$868$$ 0 0
$$869$$ 32.0000 1.08553
$$870$$ 0 0
$$871$$ −12.0000 −0.406604
$$872$$ −12.0000 −0.406371
$$873$$ 16.0000 0.541518
$$874$$ −36.0000 −1.21772
$$875$$ 0 0
$$876$$ 8.00000 0.270295
$$877$$ 14.0000 0.472746 0.236373 0.971662i $$-0.424041\pi$$
0.236373 + 0.971662i $$0.424041\pi$$
$$878$$ 32.0000 1.07995
$$879$$ 26.0000 0.876958
$$880$$ 0 0
$$881$$ −18.0000 −0.606435 −0.303218 0.952921i $$-0.598061\pi$$
−0.303218 + 0.952921i $$0.598061\pi$$
$$882$$ 3.00000 0.101015
$$883$$ 28.0000 0.942275 0.471138 0.882060i $$-0.343844\pi$$
0.471138 + 0.882060i $$0.343844\pi$$
$$884$$ −8.00000 −0.269069
$$885$$ 0 0
$$886$$ 16.0000 0.537531
$$887$$ 2.00000 0.0671534 0.0335767 0.999436i $$-0.489310\pi$$
0.0335767 + 0.999436i $$0.489310\pi$$
$$888$$ −2.00000 −0.0671156
$$889$$ 8.00000 0.268311
$$890$$ 0 0
$$891$$ 4.00000 0.134005
$$892$$ 2.00000 0.0669650
$$893$$ 0 0
$$894$$ 10.0000 0.334450
$$895$$ 0 0
$$896$$ 2.00000 0.0668153
$$897$$ −6.00000 −0.200334
$$898$$ 6.00000 0.200223
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −80.0000 −2.66519
$$902$$ 8.00000 0.266371
$$903$$ −8.00000 −0.266223
$$904$$ 20.0000 0.665190
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −52.0000 −1.72663 −0.863316 0.504664i $$-0.831616\pi$$
−0.863316 + 0.504664i $$0.831616\pi$$
$$908$$ 4.00000 0.132745
$$909$$ −16.0000 −0.530687
$$910$$ 0 0
$$911$$ −20.0000 −0.662630 −0.331315 0.943520i $$-0.607492\pi$$
−0.331315 + 0.943520i $$0.607492\pi$$
$$912$$ −6.00000 −0.198680
$$913$$ −48.0000 −1.58857
$$914$$ 8.00000 0.264616
$$915$$ 0 0
$$916$$ 4.00000 0.132164
$$917$$ −20.0000 −0.660458
$$918$$ 8.00000 0.264039
$$919$$ 40.0000 1.31948 0.659739 0.751495i $$-0.270667\pi$$
0.659739 + 0.751495i $$0.270667\pi$$
$$920$$ 0 0
$$921$$ −12.0000 −0.395413
$$922$$ 6.00000 0.197599
$$923$$ −8.00000 −0.263323
$$924$$ −8.00000 −0.263181
$$925$$ 0 0
$$926$$ −26.0000 −0.854413
$$927$$ 12.0000 0.394132
$$928$$ 4.00000 0.131306
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 0 0
$$931$$ 18.0000 0.589926
$$932$$ −24.0000 −0.786146
$$933$$ 24.0000 0.785725
$$934$$ 28.0000 0.916188
$$935$$ 0 0
$$936$$ −1.00000 −0.0326860
$$937$$ −18.0000 −0.588034 −0.294017 0.955800i $$-0.594992\pi$$
−0.294017 + 0.955800i $$0.594992\pi$$
$$938$$ −24.0000 −0.783628
$$939$$ −6.00000 −0.195803
$$940$$ 0 0
$$941$$ −34.0000 −1.10837 −0.554184 0.832394i $$-0.686970\pi$$
−0.554184 + 0.832394i $$0.686970\pi$$
$$942$$ 22.0000 0.716799
$$943$$ 12.0000 0.390774
$$944$$ 4.00000 0.130189
$$945$$ 0 0
$$946$$ −16.0000 −0.520205
$$947$$ −4.00000 −0.129983 −0.0649913 0.997886i $$-0.520702\pi$$
−0.0649913 + 0.997886i $$0.520702\pi$$
$$948$$ 8.00000 0.259828
$$949$$ 8.00000 0.259691
$$950$$ 0 0
$$951$$ 30.0000 0.972817
$$952$$ −16.0000 −0.518563
$$953$$ −24.0000 −0.777436 −0.388718 0.921357i $$-0.627082\pi$$
−0.388718 + 0.921357i $$0.627082\pi$$
$$954$$ −10.0000 −0.323762
$$955$$ 0 0
$$956$$ 16.0000 0.517477
$$957$$ −16.0000 −0.517207
$$958$$ −32.0000 −1.03387
$$959$$ −12.0000 −0.387500
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ −2.00000 −0.0644826
$$963$$ −12.0000 −0.386695
$$964$$ 2.00000 0.0644157
$$965$$ 0 0
$$966$$ −12.0000 −0.386094
$$967$$ 14.0000 0.450210 0.225105 0.974335i $$-0.427728\pi$$
0.225105 + 0.974335i $$0.427728\pi$$
$$968$$ −5.00000 −0.160706
$$969$$ 48.0000 1.54198
$$970$$ 0 0
$$971$$ 38.0000 1.21948 0.609739 0.792602i $$-0.291274\pi$$
0.609739 + 0.792602i $$0.291274\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 16.0000 0.512936
$$974$$ 26.0000 0.833094
$$975$$ 0 0
$$976$$ −10.0000 −0.320092
$$977$$ −30.0000 −0.959785 −0.479893 0.877327i $$-0.659324\pi$$
−0.479893 + 0.877327i $$0.659324\pi$$
$$978$$ −16.0000 −0.511624
$$979$$ −56.0000 −1.78977
$$980$$ 0 0
$$981$$ 12.0000 0.383131
$$982$$ −42.0000 −1.34027
$$983$$ 52.0000 1.65854 0.829271 0.558846i $$-0.188756\pi$$
0.829271 + 0.558846i $$0.188756\pi$$
$$984$$ 2.00000 0.0637577
$$985$$ 0 0
$$986$$ −32.0000 −1.01909
$$987$$ 0 0
$$988$$ −6.00000 −0.190885
$$989$$ −24.0000 −0.763156
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 0 0
$$993$$ 10.0000 0.317340
$$994$$ −16.0000 −0.507489
$$995$$ 0 0
$$996$$ −12.0000 −0.380235
$$997$$ 26.0000 0.823428 0.411714 0.911313i $$-0.364930\pi$$
0.411714 + 0.911313i $$0.364930\pi$$
$$998$$ −38.0000 −1.20287
$$999$$ 2.00000 0.0632772
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 1950.2.a.h.1.1 1
3.2 odd 2 5850.2.a.bi.1.1 1
5.2 odd 4 1950.2.e.f.1249.1 2
5.3 odd 4 1950.2.e.f.1249.2 2
5.4 even 2 390.2.a.e.1.1 1
15.2 even 4 5850.2.e.i.5149.2 2
15.8 even 4 5850.2.e.i.5149.1 2
15.14 odd 2 1170.2.a.e.1.1 1
20.19 odd 2 3120.2.a.o.1.1 1
60.59 even 2 9360.2.a.bh.1.1 1
65.34 odd 4 5070.2.b.e.1351.2 2
65.44 odd 4 5070.2.b.e.1351.1 2
65.64 even 2 5070.2.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.a.e.1.1 1 5.4 even 2
1170.2.a.e.1.1 1 15.14 odd 2
1950.2.a.h.1.1 1 1.1 even 1 trivial
1950.2.e.f.1249.1 2 5.2 odd 4
1950.2.e.f.1249.2 2 5.3 odd 4
3120.2.a.o.1.1 1 20.19 odd 2
5070.2.a.e.1.1 1 65.64 even 2
5070.2.b.e.1351.1 2 65.44 odd 4
5070.2.b.e.1351.2 2 65.34 odd 4
5850.2.a.bi.1.1 1 3.2 odd 2
5850.2.e.i.5149.1 2 15.8 even 4
5850.2.e.i.5149.2 2 15.2 even 4
9360.2.a.bh.1.1 1 60.59 even 2