# Properties

 Label 950.2.a.a.1.1 Level $950$ Weight $2$ Character 950.1 Self dual yes Analytic conductor $7.586$ Analytic rank $0$ Dimension $1$ 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: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 950.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} +2.00000 q^{18} +1.00000 q^{19} -1.00000 q^{21} -3.00000 q^{23} +1.00000 q^{24} -1.00000 q^{26} +5.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} -2.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} -1.00000 q^{39} +6.00000 q^{41} +1.00000 q^{42} -2.00000 q^{43} +3.00000 q^{46} -1.00000 q^{48} -6.00000 q^{49} -3.00000 q^{51} +1.00000 q^{52} -3.00000 q^{53} -5.00000 q^{54} -1.00000 q^{56} -1.00000 q^{57} +3.00000 q^{58} +3.00000 q^{59} +8.00000 q^{61} -2.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +7.00000 q^{67} +3.00000 q^{68} +3.00000 q^{69} +12.0000 q^{71} +2.00000 q^{72} +13.0000 q^{73} -10.0000 q^{74} +1.00000 q^{76} +1.00000 q^{78} +14.0000 q^{79} +1.00000 q^{81} -6.00000 q^{82} -6.00000 q^{83} -1.00000 q^{84} +2.00000 q^{86} +3.00000 q^{87} +6.00000 q^{89} +1.00000 q^{91} -3.00000 q^{92} -2.00000 q^{93} +1.00000 q^{96} +10.0000 q^{97} +6.00000 q^{98} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ −1.00000 −0.577350 −0.288675 0.957427i $$-0.593215\pi$$
−0.288675 + 0.957427i $$0.593215\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 1.00000 0.408248
$$7$$ 1.00000 0.377964 0.188982 0.981981i $$-0.439481\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 2.00000 0.471405
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ −3.00000 −0.625543 −0.312772 0.949828i $$-0.601257\pi$$
−0.312772 + 0.949828i $$0.601257\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 0 0
$$26$$ −1.00000 −0.196116
$$27$$ 5.00000 0.962250
$$28$$ 1.00000 0.188982
$$29$$ −3.00000 −0.557086 −0.278543 0.960424i $$-0.589851\pi$$
−0.278543 + 0.960424i $$0.589851\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ −3.00000 −0.514496
$$35$$ 0 0
$$36$$ −2.00000 −0.333333
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 1.00000 0.154303
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 3.00000 0.442326
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 1.00000 0.138675
$$53$$ −3.00000 −0.412082 −0.206041 0.978543i $$-0.566058\pi$$
−0.206041 + 0.978543i $$0.566058\pi$$
$$54$$ −5.00000 −0.680414
$$55$$ 0 0
$$56$$ −1.00000 −0.133631
$$57$$ −1.00000 −0.132453
$$58$$ 3.00000 0.393919
$$59$$ 3.00000 0.390567 0.195283 0.980747i $$-0.437437\pi$$
0.195283 + 0.980747i $$0.437437\pi$$
$$60$$ 0 0
$$61$$ 8.00000 1.02430 0.512148 0.858898i $$-0.328850\pi$$
0.512148 + 0.858898i $$0.328850\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ −2.00000 −0.251976
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 7.00000 0.855186 0.427593 0.903971i $$-0.359362\pi$$
0.427593 + 0.903971i $$0.359362\pi$$
$$68$$ 3.00000 0.363803
$$69$$ 3.00000 0.361158
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 2.00000 0.235702
$$73$$ 13.0000 1.52153 0.760767 0.649025i $$-0.224823\pi$$
0.760767 + 0.649025i $$0.224823\pi$$
$$74$$ −10.0000 −1.16248
$$75$$ 0 0
$$76$$ 1.00000 0.114708
$$77$$ 0 0
$$78$$ 1.00000 0.113228
$$79$$ 14.0000 1.57512 0.787562 0.616236i $$-0.211343\pi$$
0.787562 + 0.616236i $$0.211343\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −6.00000 −0.662589
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ −1.00000 −0.109109
$$85$$ 0 0
$$86$$ 2.00000 0.215666
$$87$$ 3.00000 0.321634
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 1.00000 0.104828
$$92$$ −3.00000 −0.312772
$$93$$ −2.00000 −0.207390
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 6.00000 0.606092
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 3.00000 0.297044
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ 3.00000 0.291386
$$107$$ −15.0000 −1.45010 −0.725052 0.688694i $$-0.758184\pi$$
−0.725052 + 0.688694i $$0.758184\pi$$
$$108$$ 5.00000 0.481125
$$109$$ 11.0000 1.05361 0.526804 0.849987i $$-0.323390\pi$$
0.526804 + 0.849987i $$0.323390\pi$$
$$110$$ 0 0
$$111$$ −10.0000 −0.949158
$$112$$ 1.00000 0.0944911
$$113$$ 12.0000 1.12887 0.564433 0.825479i $$-0.309095\pi$$
0.564433 + 0.825479i $$0.309095\pi$$
$$114$$ 1.00000 0.0936586
$$115$$ 0 0
$$116$$ −3.00000 −0.278543
$$117$$ −2.00000 −0.184900
$$118$$ −3.00000 −0.276172
$$119$$ 3.00000 0.275010
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ −8.00000 −0.724286
$$123$$ −6.00000 −0.541002
$$124$$ 2.00000 0.179605
$$125$$ 0 0
$$126$$ 2.00000 0.178174
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 2.00000 0.176090
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 1.00000 0.0867110
$$134$$ −7.00000 −0.604708
$$135$$ 0 0
$$136$$ −3.00000 −0.257248
$$137$$ −9.00000 −0.768922 −0.384461 0.923141i $$-0.625613\pi$$
−0.384461 + 0.923141i $$0.625613\pi$$
$$138$$ −3.00000 −0.255377
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −12.0000 −1.00702
$$143$$ 0 0
$$144$$ −2.00000 −0.166667
$$145$$ 0 0
$$146$$ −13.0000 −1.07589
$$147$$ 6.00000 0.494872
$$148$$ 10.0000 0.821995
$$149$$ −12.0000 −0.983078 −0.491539 0.870855i $$-0.663566\pi$$
−0.491539 + 0.870855i $$0.663566\pi$$
$$150$$ 0 0
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ −1.00000 −0.0811107
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −1.00000 −0.0800641
$$157$$ 10.0000 0.798087 0.399043 0.916932i $$-0.369342\pi$$
0.399043 + 0.916932i $$0.369342\pi$$
$$158$$ −14.0000 −1.11378
$$159$$ 3.00000 0.237915
$$160$$ 0 0
$$161$$ −3.00000 −0.236433
$$162$$ −1.00000 −0.0785674
$$163$$ 22.0000 1.72317 0.861586 0.507611i $$-0.169471\pi$$
0.861586 + 0.507611i $$0.169471\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 0 0
$$166$$ 6.00000 0.465690
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −2.00000 −0.152944
$$172$$ −2.00000 −0.152499
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ −3.00000 −0.227429
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −3.00000 −0.225494
$$178$$ −6.00000 −0.449719
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ −1.00000 −0.0741249
$$183$$ −8.00000 −0.591377
$$184$$ 3.00000 0.221163
$$185$$ 0 0
$$186$$ 2.00000 0.146647
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 5.00000 0.363696
$$190$$ 0 0
$$191$$ −27.0000 −1.95365 −0.976826 0.214036i $$-0.931339\pi$$
−0.976826 + 0.214036i $$0.931339\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 22.0000 1.58359 0.791797 0.610784i $$-0.209146\pi$$
0.791797 + 0.610784i $$0.209146\pi$$
$$194$$ −10.0000 −0.717958
$$195$$ 0 0
$$196$$ −6.00000 −0.428571
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ −19.0000 −1.34687 −0.673437 0.739244i $$-0.735183\pi$$
−0.673437 + 0.739244i $$0.735183\pi$$
$$200$$ 0 0
$$201$$ −7.00000 −0.493742
$$202$$ −12.0000 −0.844317
$$203$$ −3.00000 −0.210559
$$204$$ −3.00000 −0.210042
$$205$$ 0 0
$$206$$ 8.00000 0.557386
$$207$$ 6.00000 0.417029
$$208$$ 1.00000 0.0693375
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −25.0000 −1.72107 −0.860535 0.509390i $$-0.829871\pi$$
−0.860535 + 0.509390i $$0.829871\pi$$
$$212$$ −3.00000 −0.206041
$$213$$ −12.0000 −0.822226
$$214$$ 15.0000 1.02538
$$215$$ 0 0
$$216$$ −5.00000 −0.340207
$$217$$ 2.00000 0.135769
$$218$$ −11.0000 −0.745014
$$219$$ −13.0000 −0.878459
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 10.0000 0.671156
$$223$$ −14.0000 −0.937509 −0.468755 0.883328i $$-0.655297\pi$$
−0.468755 + 0.883328i $$0.655297\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ −12.0000 −0.798228
$$227$$ 15.0000 0.995585 0.497792 0.867296i $$-0.334144\pi$$
0.497792 + 0.867296i $$0.334144\pi$$
$$228$$ −1.00000 −0.0662266
$$229$$ 26.0000 1.71813 0.859064 0.511868i $$-0.171046\pi$$
0.859064 + 0.511868i $$0.171046\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 3.00000 0.196960
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 2.00000 0.130744
$$235$$ 0 0
$$236$$ 3.00000 0.195283
$$237$$ −14.0000 −0.909398
$$238$$ −3.00000 −0.194461
$$239$$ −15.0000 −0.970269 −0.485135 0.874439i $$-0.661229\pi$$
−0.485135 + 0.874439i $$0.661229\pi$$
$$240$$ 0 0
$$241$$ −4.00000 −0.257663 −0.128831 0.991667i $$-0.541123\pi$$
−0.128831 + 0.991667i $$0.541123\pi$$
$$242$$ 11.0000 0.707107
$$243$$ −16.0000 −1.02640
$$244$$ 8.00000 0.512148
$$245$$ 0 0
$$246$$ 6.00000 0.382546
$$247$$ 1.00000 0.0636285
$$248$$ −2.00000 −0.127000
$$249$$ 6.00000 0.380235
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ −2.00000 −0.125988
$$253$$ 0 0
$$254$$ 2.00000 0.125491
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ −2.00000 −0.124515
$$259$$ 10.0000 0.621370
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −1.00000 −0.0613139
$$267$$ −6.00000 −0.367194
$$268$$ 7.00000 0.427593
$$269$$ 18.0000 1.09748 0.548740 0.835993i $$-0.315108\pi$$
0.548740 + 0.835993i $$0.315108\pi$$
$$270$$ 0 0
$$271$$ −7.00000 −0.425220 −0.212610 0.977137i $$-0.568196\pi$$
−0.212610 + 0.977137i $$0.568196\pi$$
$$272$$ 3.00000 0.181902
$$273$$ −1.00000 −0.0605228
$$274$$ 9.00000 0.543710
$$275$$ 0 0
$$276$$ 3.00000 0.180579
$$277$$ −8.00000 −0.480673 −0.240337 0.970690i $$-0.577258\pi$$
−0.240337 + 0.970690i $$0.577258\pi$$
$$278$$ −8.00000 −0.479808
$$279$$ −4.00000 −0.239474
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ −14.0000 −0.832214 −0.416107 0.909316i $$-0.636606\pi$$
−0.416107 + 0.909316i $$0.636606\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 6.00000 0.354169
$$288$$ 2.00000 0.117851
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ −10.0000 −0.586210
$$292$$ 13.0000 0.760767
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ −6.00000 −0.349927
$$295$$ 0 0
$$296$$ −10.0000 −0.581238
$$297$$ 0 0
$$298$$ 12.0000 0.695141
$$299$$ −3.00000 −0.173494
$$300$$ 0 0
$$301$$ −2.00000 −0.115278
$$302$$ 10.0000 0.575435
$$303$$ −12.0000 −0.689382
$$304$$ 1.00000 0.0573539
$$305$$ 0 0
$$306$$ 6.00000 0.342997
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ 8.00000 0.455104
$$310$$ 0 0
$$311$$ −3.00000 −0.170114 −0.0850572 0.996376i $$-0.527107\pi$$
−0.0850572 + 0.996376i $$0.527107\pi$$
$$312$$ 1.00000 0.0566139
$$313$$ 1.00000 0.0565233 0.0282617 0.999601i $$-0.491003\pi$$
0.0282617 + 0.999601i $$0.491003\pi$$
$$314$$ −10.0000 −0.564333
$$315$$ 0 0
$$316$$ 14.0000 0.787562
$$317$$ −9.00000 −0.505490 −0.252745 0.967533i $$-0.581333\pi$$
−0.252745 + 0.967533i $$0.581333\pi$$
$$318$$ −3.00000 −0.168232
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 15.0000 0.837218
$$322$$ 3.00000 0.167183
$$323$$ 3.00000 0.166924
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −22.0000 −1.21847
$$327$$ −11.0000 −0.608301
$$328$$ −6.00000 −0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 5.00000 0.274825 0.137412 0.990514i $$-0.456121\pi$$
0.137412 + 0.990514i $$0.456121\pi$$
$$332$$ −6.00000 −0.329293
$$333$$ −20.0000 −1.09599
$$334$$ 18.0000 0.984916
$$335$$ 0 0
$$336$$ −1.00000 −0.0545545
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ 12.0000 0.652714
$$339$$ −12.0000 −0.651751
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 2.00000 0.108148
$$343$$ −13.0000 −0.701934
$$344$$ 2.00000 0.107833
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ 30.0000 1.61048 0.805242 0.592946i $$-0.202035\pi$$
0.805242 + 0.592946i $$0.202035\pi$$
$$348$$ 3.00000 0.160817
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 5.00000 0.266880
$$352$$ 0 0
$$353$$ 33.0000 1.75641 0.878206 0.478282i $$-0.158740\pi$$
0.878206 + 0.478282i $$0.158740\pi$$
$$354$$ 3.00000 0.159448
$$355$$ 0 0
$$356$$ 6.00000 0.317999
$$357$$ −3.00000 −0.158777
$$358$$ 0 0
$$359$$ −33.0000 −1.74167 −0.870837 0.491572i $$-0.836422\pi$$
−0.870837 + 0.491572i $$0.836422\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ −2.00000 −0.105118
$$363$$ 11.0000 0.577350
$$364$$ 1.00000 0.0524142
$$365$$ 0 0
$$366$$ 8.00000 0.418167
$$367$$ 16.0000 0.835193 0.417597 0.908633i $$-0.362873\pi$$
0.417597 + 0.908633i $$0.362873\pi$$
$$368$$ −3.00000 −0.156386
$$369$$ −12.0000 −0.624695
$$370$$ 0 0
$$371$$ −3.00000 −0.155752
$$372$$ −2.00000 −0.103695
$$373$$ 31.0000 1.60512 0.802560 0.596572i $$-0.203471\pi$$
0.802560 + 0.596572i $$0.203471\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −3.00000 −0.154508
$$378$$ −5.00000 −0.257172
$$379$$ 35.0000 1.79783 0.898915 0.438124i $$-0.144357\pi$$
0.898915 + 0.438124i $$0.144357\pi$$
$$380$$ 0 0
$$381$$ 2.00000 0.102463
$$382$$ 27.0000 1.38144
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ −22.0000 −1.11977
$$387$$ 4.00000 0.203331
$$388$$ 10.0000 0.507673
$$389$$ −24.0000 −1.21685 −0.608424 0.793612i $$-0.708198\pi$$
−0.608424 + 0.793612i $$0.708198\pi$$
$$390$$ 0 0
$$391$$ −9.00000 −0.455150
$$392$$ 6.00000 0.303046
$$393$$ 0 0
$$394$$ 6.00000 0.302276
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −8.00000 −0.401508 −0.200754 0.979642i $$-0.564339\pi$$
−0.200754 + 0.979642i $$0.564339\pi$$
$$398$$ 19.0000 0.952384
$$399$$ −1.00000 −0.0500626
$$400$$ 0 0
$$401$$ 6.00000 0.299626 0.149813 0.988714i $$-0.452133\pi$$
0.149813 + 0.988714i $$0.452133\pi$$
$$402$$ 7.00000 0.349128
$$403$$ 2.00000 0.0996271
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ 3.00000 0.148888
$$407$$ 0 0
$$408$$ 3.00000 0.148522
$$409$$ −22.0000 −1.08783 −0.543915 0.839140i $$-0.683059\pi$$
−0.543915 + 0.839140i $$0.683059\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ −8.00000 −0.394132
$$413$$ 3.00000 0.147620
$$414$$ −6.00000 −0.294884
$$415$$ 0 0
$$416$$ −1.00000 −0.0490290
$$417$$ −8.00000 −0.391762
$$418$$ 0 0
$$419$$ −30.0000 −1.46560 −0.732798 0.680446i $$-0.761786\pi$$
−0.732798 + 0.680446i $$0.761786\pi$$
$$420$$ 0 0
$$421$$ 17.0000 0.828529 0.414265 0.910156i $$-0.364039\pi$$
0.414265 + 0.910156i $$0.364039\pi$$
$$422$$ 25.0000 1.21698
$$423$$ 0 0
$$424$$ 3.00000 0.145693
$$425$$ 0 0
$$426$$ 12.0000 0.581402
$$427$$ 8.00000 0.387147
$$428$$ −15.0000 −0.725052
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 24.0000 1.15604 0.578020 0.816023i $$-0.303826\pi$$
0.578020 + 0.816023i $$0.303826\pi$$
$$432$$ 5.00000 0.240563
$$433$$ 4.00000 0.192228 0.0961139 0.995370i $$-0.469359\pi$$
0.0961139 + 0.995370i $$0.469359\pi$$
$$434$$ −2.00000 −0.0960031
$$435$$ 0 0
$$436$$ 11.0000 0.526804
$$437$$ −3.00000 −0.143509
$$438$$ 13.0000 0.621164
$$439$$ 38.0000 1.81364 0.906821 0.421517i $$-0.138502\pi$$
0.906821 + 0.421517i $$0.138502\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ −3.00000 −0.142695
$$443$$ 24.0000 1.14027 0.570137 0.821549i $$-0.306890\pi$$
0.570137 + 0.821549i $$0.306890\pi$$
$$444$$ −10.0000 −0.474579
$$445$$ 0 0
$$446$$ 14.0000 0.662919
$$447$$ 12.0000 0.567581
$$448$$ 1.00000 0.0472456
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 12.0000 0.564433
$$453$$ 10.0000 0.469841
$$454$$ −15.0000 −0.703985
$$455$$ 0 0
$$456$$ 1.00000 0.0468293
$$457$$ −35.0000 −1.63723 −0.818615 0.574342i $$-0.805258\pi$$
−0.818615 + 0.574342i $$0.805258\pi$$
$$458$$ −26.0000 −1.21490
$$459$$ 15.0000 0.700140
$$460$$ 0 0
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −3.00000 −0.139272
$$465$$ 0 0
$$466$$ −6.00000 −0.277945
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ −2.00000 −0.0924500
$$469$$ 7.00000 0.323230
$$470$$ 0 0
$$471$$ −10.0000 −0.460776
$$472$$ −3.00000 −0.138086
$$473$$ 0 0
$$474$$ 14.0000 0.643041
$$475$$ 0 0
$$476$$ 3.00000 0.137505
$$477$$ 6.00000 0.274721
$$478$$ 15.0000 0.686084
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 0 0
$$481$$ 10.0000 0.455961
$$482$$ 4.00000 0.182195
$$483$$ 3.00000 0.136505
$$484$$ −11.0000 −0.500000
$$485$$ 0 0
$$486$$ 16.0000 0.725775
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ −8.00000 −0.362143
$$489$$ −22.0000 −0.994874
$$490$$ 0 0
$$491$$ 30.0000 1.35388 0.676941 0.736038i $$-0.263305\pi$$
0.676941 + 0.736038i $$0.263305\pi$$
$$492$$ −6.00000 −0.270501
$$493$$ −9.00000 −0.405340
$$494$$ −1.00000 −0.0449921
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ 12.0000 0.538274
$$498$$ −6.00000 −0.268866
$$499$$ −10.0000 −0.447661 −0.223831 0.974628i $$-0.571856\pi$$
−0.223831 + 0.974628i $$0.571856\pi$$
$$500$$ 0 0
$$501$$ 18.0000 0.804181
$$502$$ 0 0
$$503$$ −39.0000 −1.73892 −0.869462 0.494000i $$-0.835534\pi$$
−0.869462 + 0.494000i $$0.835534\pi$$
$$504$$ 2.00000 0.0890871
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 12.0000 0.532939
$$508$$ −2.00000 −0.0887357
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ 13.0000 0.575086
$$512$$ −1.00000 −0.0441942
$$513$$ 5.00000 0.220755
$$514$$ 18.0000 0.793946
$$515$$ 0 0
$$516$$ 2.00000 0.0880451
$$517$$ 0 0
$$518$$ −10.0000 −0.439375
$$519$$ −6.00000 −0.263371
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ −6.00000 −0.262613
$$523$$ −11.0000 −0.480996 −0.240498 0.970650i $$-0.577311\pi$$
−0.240498 + 0.970650i $$0.577311\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 6.00000 0.261364
$$528$$ 0 0
$$529$$ −14.0000 −0.608696
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 1.00000 0.0433555
$$533$$ 6.00000 0.259889
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ −7.00000 −0.302354
$$537$$ 0 0
$$538$$ −18.0000 −0.776035
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 20.0000 0.859867 0.429934 0.902861i $$-0.358537\pi$$
0.429934 + 0.902861i $$0.358537\pi$$
$$542$$ 7.00000 0.300676
$$543$$ −2.00000 −0.0858282
$$544$$ −3.00000 −0.128624
$$545$$ 0 0
$$546$$ 1.00000 0.0427960
$$547$$ 4.00000 0.171028 0.0855138 0.996337i $$-0.472747\pi$$
0.0855138 + 0.996337i $$0.472747\pi$$
$$548$$ −9.00000 −0.384461
$$549$$ −16.0000 −0.682863
$$550$$ 0 0
$$551$$ −3.00000 −0.127804
$$552$$ −3.00000 −0.127688
$$553$$ 14.0000 0.595341
$$554$$ 8.00000 0.339887
$$555$$ 0 0
$$556$$ 8.00000 0.339276
$$557$$ 12.0000 0.508456 0.254228 0.967144i $$-0.418179\pi$$
0.254228 + 0.967144i $$0.418179\pi$$
$$558$$ 4.00000 0.169334
$$559$$ −2.00000 −0.0845910
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −18.0000 −0.759284
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 14.0000 0.588464
$$567$$ 1.00000 0.0419961
$$568$$ −12.0000 −0.503509
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ −22.0000 −0.920671 −0.460336 0.887745i $$-0.652271\pi$$
−0.460336 + 0.887745i $$0.652271\pi$$
$$572$$ 0 0
$$573$$ 27.0000 1.12794
$$574$$ −6.00000 −0.250435
$$575$$ 0 0
$$576$$ −2.00000 −0.0833333
$$577$$ 7.00000 0.291414 0.145707 0.989328i $$-0.453454\pi$$
0.145707 + 0.989328i $$0.453454\pi$$
$$578$$ 8.00000 0.332756
$$579$$ −22.0000 −0.914289
$$580$$ 0 0
$$581$$ −6.00000 −0.248922
$$582$$ 10.0000 0.414513
$$583$$ 0 0
$$584$$ −13.0000 −0.537944
$$585$$ 0 0
$$586$$ 21.0000 0.867502
$$587$$ −30.0000 −1.23823 −0.619116 0.785299i $$-0.712509\pi$$
−0.619116 + 0.785299i $$0.712509\pi$$
$$588$$ 6.00000 0.247436
$$589$$ 2.00000 0.0824086
$$590$$ 0 0
$$591$$ 6.00000 0.246807
$$592$$ 10.0000 0.410997
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −12.0000 −0.491539
$$597$$ 19.0000 0.777618
$$598$$ 3.00000 0.122679
$$599$$ −30.0000 −1.22577 −0.612883 0.790173i $$-0.709990\pi$$
−0.612883 + 0.790173i $$0.709990\pi$$
$$600$$ 0 0
$$601$$ −34.0000 −1.38689 −0.693444 0.720510i $$-0.743908\pi$$
−0.693444 + 0.720510i $$0.743908\pi$$
$$602$$ 2.00000 0.0815139
$$603$$ −14.0000 −0.570124
$$604$$ −10.0000 −0.406894
$$605$$ 0 0
$$606$$ 12.0000 0.487467
$$607$$ 10.0000 0.405887 0.202944 0.979190i $$-0.434949\pi$$
0.202944 + 0.979190i $$0.434949\pi$$
$$608$$ −1.00000 −0.0405554
$$609$$ 3.00000 0.121566
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −6.00000 −0.242536
$$613$$ 16.0000 0.646234 0.323117 0.946359i $$-0.395269\pi$$
0.323117 + 0.946359i $$0.395269\pi$$
$$614$$ 20.0000 0.807134
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ −8.00000 −0.321807
$$619$$ 44.0000 1.76851 0.884255 0.467005i $$-0.154667\pi$$
0.884255 + 0.467005i $$0.154667\pi$$
$$620$$ 0 0
$$621$$ −15.0000 −0.601929
$$622$$ 3.00000 0.120289
$$623$$ 6.00000 0.240385
$$624$$ −1.00000 −0.0400320
$$625$$ 0 0
$$626$$ −1.00000 −0.0399680
$$627$$ 0 0
$$628$$ 10.0000 0.399043
$$629$$ 30.0000 1.19618
$$630$$ 0 0
$$631$$ 32.0000 1.27390 0.636950 0.770905i $$-0.280196\pi$$
0.636950 + 0.770905i $$0.280196\pi$$
$$632$$ −14.0000 −0.556890
$$633$$ 25.0000 0.993661
$$634$$ 9.00000 0.357436
$$635$$ 0 0
$$636$$ 3.00000 0.118958
$$637$$ −6.00000 −0.237729
$$638$$ 0 0
$$639$$ −24.0000 −0.949425
$$640$$ 0 0
$$641$$ −12.0000 −0.473972 −0.236986 0.971513i $$-0.576159\pi$$
−0.236986 + 0.971513i $$0.576159\pi$$
$$642$$ −15.0000 −0.592003
$$643$$ −50.0000 −1.97181 −0.985904 0.167313i $$-0.946491\pi$$
−0.985904 + 0.167313i $$0.946491\pi$$
$$644$$ −3.00000 −0.118217
$$645$$ 0 0
$$646$$ −3.00000 −0.118033
$$647$$ 33.0000 1.29736 0.648682 0.761060i $$-0.275321\pi$$
0.648682 + 0.761060i $$0.275321\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −2.00000 −0.0783862
$$652$$ 22.0000 0.861586
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 11.0000 0.430134
$$655$$ 0 0
$$656$$ 6.00000 0.234261
$$657$$ −26.0000 −1.01436
$$658$$ 0 0
$$659$$ 21.0000 0.818044 0.409022 0.912525i $$-0.365870\pi$$
0.409022 + 0.912525i $$0.365870\pi$$
$$660$$ 0 0
$$661$$ −49.0000 −1.90588 −0.952940 0.303160i $$-0.901958\pi$$
−0.952940 + 0.303160i $$0.901958\pi$$
$$662$$ −5.00000 −0.194331
$$663$$ −3.00000 −0.116510
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ 20.0000 0.774984
$$667$$ 9.00000 0.348481
$$668$$ −18.0000 −0.696441
$$669$$ 14.0000 0.541271
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 1.00000 0.0385758
$$673$$ −20.0000 −0.770943 −0.385472 0.922720i $$-0.625961\pi$$
−0.385472 + 0.922720i $$0.625961\pi$$
$$674$$ 2.00000 0.0770371
$$675$$ 0 0
$$676$$ −12.0000 −0.461538
$$677$$ 15.0000 0.576497 0.288248 0.957556i $$-0.406927\pi$$
0.288248 + 0.957556i $$0.406927\pi$$
$$678$$ 12.0000 0.460857
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ −15.0000 −0.574801
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ −2.00000 −0.0764719
$$685$$ 0 0
$$686$$ 13.0000 0.496342
$$687$$ −26.0000 −0.991962
$$688$$ −2.00000 −0.0762493
$$689$$ −3.00000 −0.114291
$$690$$ 0 0
$$691$$ −10.0000 −0.380418 −0.190209 0.981744i $$-0.560917\pi$$
−0.190209 + 0.981744i $$0.560917\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ −30.0000 −1.13878
$$695$$ 0 0
$$696$$ −3.00000 −0.113715
$$697$$ 18.0000 0.681799
$$698$$ −14.0000 −0.529908
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ 48.0000 1.81293 0.906467 0.422276i $$-0.138769\pi$$
0.906467 + 0.422276i $$0.138769\pi$$
$$702$$ −5.00000 −0.188713
$$703$$ 10.0000 0.377157
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −33.0000 −1.24197
$$707$$ 12.0000 0.451306
$$708$$ −3.00000 −0.112747
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 0 0
$$711$$ −28.0000 −1.05008
$$712$$ −6.00000 −0.224860
$$713$$ −6.00000 −0.224702
$$714$$ 3.00000 0.112272
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 15.0000 0.560185
$$718$$ 33.0000 1.23155
$$719$$ 33.0000 1.23069 0.615346 0.788257i $$-0.289016\pi$$
0.615346 + 0.788257i $$0.289016\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ −1.00000 −0.0372161
$$723$$ 4.00000 0.148762
$$724$$ 2.00000 0.0743294
$$725$$ 0 0
$$726$$ −11.0000 −0.408248
$$727$$ 13.0000 0.482143 0.241072 0.970507i $$-0.422501\pi$$
0.241072 + 0.970507i $$0.422501\pi$$
$$728$$ −1.00000 −0.0370625
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −6.00000 −0.221918
$$732$$ −8.00000 −0.295689
$$733$$ 4.00000 0.147743 0.0738717 0.997268i $$-0.476464\pi$$
0.0738717 + 0.997268i $$0.476464\pi$$
$$734$$ −16.0000 −0.590571
$$735$$ 0 0
$$736$$ 3.00000 0.110581
$$737$$ 0 0
$$738$$ 12.0000 0.441726
$$739$$ 2.00000 0.0735712 0.0367856 0.999323i $$-0.488288\pi$$
0.0367856 + 0.999323i $$0.488288\pi$$
$$740$$ 0 0
$$741$$ −1.00000 −0.0367359
$$742$$ 3.00000 0.110133
$$743$$ −18.0000 −0.660356 −0.330178 0.943919i $$-0.607109\pi$$
−0.330178 + 0.943919i $$0.607109\pi$$
$$744$$ 2.00000 0.0733236
$$745$$ 0 0
$$746$$ −31.0000 −1.13499
$$747$$ 12.0000 0.439057
$$748$$ 0 0
$$749$$ −15.0000 −0.548088
$$750$$ 0 0
$$751$$ 2.00000 0.0729810 0.0364905 0.999334i $$-0.488382\pi$$
0.0364905 + 0.999334i $$0.488382\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 3.00000 0.109254
$$755$$ 0 0
$$756$$ 5.00000 0.181848
$$757$$ −2.00000 −0.0726912 −0.0363456 0.999339i $$-0.511572\pi$$
−0.0363456 + 0.999339i $$0.511572\pi$$
$$758$$ −35.0000 −1.27126
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −21.0000 −0.761249 −0.380625 0.924730i $$-0.624291\pi$$
−0.380625 + 0.924730i $$0.624291\pi$$
$$762$$ −2.00000 −0.0724524
$$763$$ 11.0000 0.398227
$$764$$ −27.0000 −0.976826
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ 3.00000 0.108324
$$768$$ −1.00000 −0.0360844
$$769$$ −55.0000 −1.98335 −0.991675 0.128763i $$-0.958899\pi$$
−0.991675 + 0.128763i $$0.958899\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 22.0000 0.791797
$$773$$ −21.0000 −0.755318 −0.377659 0.925945i $$-0.623271\pi$$
−0.377659 + 0.925945i $$0.623271\pi$$
$$774$$ −4.00000 −0.143777
$$775$$ 0 0
$$776$$ −10.0000 −0.358979
$$777$$ −10.0000 −0.358748
$$778$$ 24.0000 0.860442
$$779$$ 6.00000 0.214972
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 9.00000 0.321839
$$783$$ −15.0000 −0.536056
$$784$$ −6.00000 −0.214286
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −5.00000 −0.178231 −0.0891154 0.996021i $$-0.528404\pi$$
−0.0891154 + 0.996021i $$0.528404\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 12.0000 0.426671
$$792$$ 0 0
$$793$$ 8.00000 0.284088
$$794$$ 8.00000 0.283909
$$795$$ 0 0
$$796$$ −19.0000 −0.673437
$$797$$ 33.0000 1.16892 0.584460 0.811423i $$-0.301306\pi$$
0.584460 + 0.811423i $$0.301306\pi$$
$$798$$ 1.00000 0.0353996
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −12.0000 −0.423999
$$802$$ −6.00000 −0.211867
$$803$$ 0 0
$$804$$ −7.00000 −0.246871
$$805$$ 0 0
$$806$$ −2.00000 −0.0704470
$$807$$ −18.0000 −0.633630
$$808$$ −12.0000 −0.422159
$$809$$ 33.0000 1.16022 0.580109 0.814539i $$-0.303010\pi$$
0.580109 + 0.814539i $$0.303010\pi$$
$$810$$ 0 0
$$811$$ −7.00000 −0.245803 −0.122902 0.992419i $$-0.539220\pi$$
−0.122902 + 0.992419i $$0.539220\pi$$
$$812$$ −3.00000 −0.105279
$$813$$ 7.00000 0.245501
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −3.00000 −0.105021
$$817$$ −2.00000 −0.0699711
$$818$$ 22.0000 0.769212
$$819$$ −2.00000 −0.0698857
$$820$$ 0 0
$$821$$ −12.0000 −0.418803 −0.209401 0.977830i $$-0.567152\pi$$
−0.209401 + 0.977830i $$0.567152\pi$$
$$822$$ −9.00000 −0.313911
$$823$$ 31.0000 1.08059 0.540296 0.841475i $$-0.318312\pi$$
0.540296 + 0.841475i $$0.318312\pi$$
$$824$$ 8.00000 0.278693
$$825$$ 0 0
$$826$$ −3.00000 −0.104383
$$827$$ −33.0000 −1.14752 −0.573761 0.819023i $$-0.694516\pi$$
−0.573761 + 0.819023i $$0.694516\pi$$
$$828$$ 6.00000 0.208514
$$829$$ −13.0000 −0.451509 −0.225754 0.974184i $$-0.572485\pi$$
−0.225754 + 0.974184i $$0.572485\pi$$
$$830$$ 0 0
$$831$$ 8.00000 0.277517
$$832$$ 1.00000 0.0346688
$$833$$ −18.0000 −0.623663
$$834$$ 8.00000 0.277017
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 10.0000 0.345651
$$838$$ 30.0000 1.03633
$$839$$ 36.0000 1.24286 0.621429 0.783470i $$-0.286552\pi$$
0.621429 + 0.783470i $$0.286552\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ −17.0000 −0.585859
$$843$$ −18.0000 −0.619953
$$844$$ −25.0000 −0.860535
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −11.0000 −0.377964
$$848$$ −3.00000 −0.103020
$$849$$ 14.0000 0.480479
$$850$$ 0 0
$$851$$ −30.0000 −1.02839
$$852$$ −12.0000 −0.411113
$$853$$ −50.0000 −1.71197 −0.855984 0.517003i $$-0.827048\pi$$
−0.855984 + 0.517003i $$0.827048\pi$$
$$854$$ −8.00000 −0.273754
$$855$$ 0 0
$$856$$ 15.0000 0.512689
$$857$$ −48.0000 −1.63965 −0.819824 0.572615i $$-0.805929\pi$$
−0.819824 + 0.572615i $$0.805929\pi$$
$$858$$ 0 0
$$859$$ −16.0000 −0.545913 −0.272956 0.962026i $$-0.588002\pi$$
−0.272956 + 0.962026i $$0.588002\pi$$
$$860$$ 0 0
$$861$$ −6.00000 −0.204479
$$862$$ −24.0000 −0.817443
$$863$$ 12.0000 0.408485 0.204242 0.978920i $$-0.434527\pi$$
0.204242 + 0.978920i $$0.434527\pi$$
$$864$$ −5.00000 −0.170103
$$865$$ 0 0
$$866$$ −4.00000 −0.135926
$$867$$ 8.00000 0.271694
$$868$$ 2.00000 0.0678844
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 7.00000 0.237186
$$872$$ −11.0000 −0.372507
$$873$$ −20.0000 −0.676897
$$874$$ 3.00000 0.101477
$$875$$ 0 0
$$876$$ −13.0000 −0.439229
$$877$$ 31.0000 1.04680 0.523398 0.852088i $$-0.324664\pi$$
0.523398 + 0.852088i $$0.324664\pi$$
$$878$$ −38.0000 −1.28244
$$879$$ 21.0000 0.708312
$$880$$ 0 0
$$881$$ 42.0000 1.41502 0.707508 0.706705i $$-0.249819\pi$$
0.707508 + 0.706705i $$0.249819\pi$$
$$882$$ −12.0000 −0.404061
$$883$$ −38.0000 −1.27880 −0.639401 0.768874i $$-0.720818\pi$$
−0.639401 + 0.768874i $$0.720818\pi$$
$$884$$ 3.00000 0.100901
$$885$$ 0 0
$$886$$ −24.0000 −0.806296
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ 10.0000 0.335578
$$889$$ −2.00000 −0.0670778
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −14.0000 −0.468755
$$893$$ 0 0
$$894$$ −12.0000 −0.401340
$$895$$ 0 0
$$896$$ −1.00000 −0.0334077
$$897$$ 3.00000 0.100167
$$898$$ 30.0000 1.00111
$$899$$ −6.00000 −0.200111
$$900$$ 0 0
$$901$$ −9.00000 −0.299833
$$902$$ 0 0
$$903$$ 2.00000 0.0665558
$$904$$ −12.0000 −0.399114
$$905$$ 0 0
$$906$$ −10.0000 −0.332228
$$907$$ −35.0000 −1.16216 −0.581078 0.813848i $$-0.697369\pi$$
−0.581078 + 0.813848i $$0.697369\pi$$
$$908$$ 15.0000 0.497792
$$909$$ −24.0000 −0.796030
$$910$$ 0 0
$$911$$ −36.0000 −1.19273 −0.596367 0.802712i $$-0.703390\pi$$
−0.596367 + 0.802712i $$0.703390\pi$$
$$912$$ −1.00000 −0.0331133
$$913$$ 0 0
$$914$$ 35.0000 1.15770
$$915$$ 0 0
$$916$$ 26.0000 0.859064
$$917$$ 0 0
$$918$$ −15.0000 −0.495074
$$919$$ −1.00000 −0.0329870 −0.0164935 0.999864i $$-0.505250\pi$$
−0.0164935 + 0.999864i $$0.505250\pi$$
$$920$$ 0 0
$$921$$ 20.0000 0.659022
$$922$$ −6.00000 −0.197599
$$923$$ 12.0000 0.394985
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −16.0000 −0.525793
$$927$$ 16.0000 0.525509
$$928$$ 3.00000 0.0984798
$$929$$ 21.0000 0.688988 0.344494 0.938789i $$-0.388051\pi$$
0.344494 + 0.938789i $$0.388051\pi$$
$$930$$ 0 0
$$931$$ −6.00000 −0.196642
$$932$$ 6.00000 0.196537
$$933$$ 3.00000 0.0982156
$$934$$ 12.0000 0.392652
$$935$$ 0 0
$$936$$ 2.00000 0.0653720
$$937$$ −47.0000 −1.53542 −0.767712 0.640796i $$-0.778605\pi$$
−0.767712 + 0.640796i $$0.778605\pi$$
$$938$$ −7.00000 −0.228558
$$939$$ −1.00000 −0.0326338
$$940$$ 0 0
$$941$$ 45.0000 1.46696 0.733479 0.679712i $$-0.237895\pi$$
0.733479 + 0.679712i $$0.237895\pi$$
$$942$$ 10.0000 0.325818
$$943$$ −18.0000 −0.586161
$$944$$ 3.00000 0.0976417
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −24.0000 −0.779895 −0.389948 0.920837i $$-0.627507\pi$$
−0.389948 + 0.920837i $$0.627507\pi$$
$$948$$ −14.0000 −0.454699
$$949$$ 13.0000 0.421998
$$950$$ 0 0
$$951$$ 9.00000 0.291845
$$952$$ −3.00000 −0.0972306
$$953$$ 36.0000 1.16615 0.583077 0.812417i $$-0.301849\pi$$
0.583077 + 0.812417i $$0.301849\pi$$
$$954$$ −6.00000 −0.194257
$$955$$ 0 0
$$956$$ −15.0000 −0.485135
$$957$$ 0 0
$$958$$ 24.0000 0.775405
$$959$$ −9.00000 −0.290625
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ −10.0000 −0.322413
$$963$$ 30.0000 0.966736
$$964$$ −4.00000 −0.128831
$$965$$ 0 0
$$966$$ −3.00000 −0.0965234
$$967$$ −44.0000 −1.41494 −0.707472 0.706741i $$-0.750165\pi$$
−0.707472 + 0.706741i $$0.750165\pi$$
$$968$$ 11.0000 0.353553
$$969$$ −3.00000 −0.0963739
$$970$$ 0 0
$$971$$ 12.0000 0.385098 0.192549 0.981287i $$-0.438325\pi$$
0.192549 + 0.981287i $$0.438325\pi$$
$$972$$ −16.0000 −0.513200
$$973$$ 8.00000 0.256468
$$974$$ 2.00000 0.0640841
$$975$$ 0 0
$$976$$ 8.00000 0.256074
$$977$$ −6.00000 −0.191957 −0.0959785 0.995383i $$-0.530598\pi$$
−0.0959785 + 0.995383i $$0.530598\pi$$
$$978$$ 22.0000 0.703482
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −22.0000 −0.702406
$$982$$ −30.0000 −0.957338
$$983$$ −54.0000 −1.72233 −0.861166 0.508323i $$-0.830265\pi$$
−0.861166 + 0.508323i $$0.830265\pi$$
$$984$$ 6.00000 0.191273
$$985$$ 0 0
$$986$$ 9.00000 0.286618
$$987$$ 0 0
$$988$$ 1.00000 0.0318142
$$989$$ 6.00000 0.190789
$$990$$ 0 0
$$991$$ 2.00000 0.0635321 0.0317660 0.999495i $$-0.489887\pi$$
0.0317660 + 0.999495i $$0.489887\pi$$
$$992$$ −2.00000 −0.0635001
$$993$$ −5.00000 −0.158670
$$994$$ −12.0000 −0.380617
$$995$$ 0 0
$$996$$ 6.00000 0.190117
$$997$$ 46.0000 1.45683 0.728417 0.685134i $$-0.240256\pi$$
0.728417 + 0.685134i $$0.240256\pi$$
$$998$$ 10.0000 0.316544
$$999$$ 50.0000 1.58193
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.a.1.1 1
3.2 odd 2 8550.2.a.bd.1.1 1
4.3 odd 2 7600.2.a.m.1.1 1
5.2 odd 4 950.2.b.e.799.1 2
5.3 odd 4 950.2.b.e.799.2 2
5.4 even 2 190.2.a.c.1.1 1
15.14 odd 2 1710.2.a.d.1.1 1
20.19 odd 2 1520.2.a.d.1.1 1
35.34 odd 2 9310.2.a.o.1.1 1
40.19 odd 2 6080.2.a.p.1.1 1
40.29 even 2 6080.2.a.h.1.1 1
95.94 odd 2 3610.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.c.1.1 1 5.4 even 2
950.2.a.a.1.1 1 1.1 even 1 trivial
950.2.b.e.799.1 2 5.2 odd 4
950.2.b.e.799.2 2 5.3 odd 4
1520.2.a.d.1.1 1 20.19 odd 2
1710.2.a.d.1.1 1 15.14 odd 2
3610.2.a.b.1.1 1 95.94 odd 2
6080.2.a.h.1.1 1 40.29 even 2
6080.2.a.p.1.1 1 40.19 odd 2
7600.2.a.m.1.1 1 4.3 odd 2
8550.2.a.bd.1.1 1 3.2 odd 2
9310.2.a.o.1.1 1 35.34 odd 2