# Properties

 Label 2450.2.a.a.1.1 Level $2450$ Weight $2$ Character 2450.1 Self dual yes Analytic conductor $19.563$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2450 = 2 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2450.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$19.5633484952$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 350) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2450.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} -5.00000 q^{11} -3.00000 q^{12} -6.00000 q^{13} +1.00000 q^{16} -1.00000 q^{17} -6.00000 q^{18} +3.00000 q^{19} +5.00000 q^{22} +3.00000 q^{24} +6.00000 q^{26} -9.00000 q^{27} -6.00000 q^{29} +4.00000 q^{31} -1.00000 q^{32} +15.0000 q^{33} +1.00000 q^{34} +6.00000 q^{36} -8.00000 q^{37} -3.00000 q^{38} +18.0000 q^{39} -11.0000 q^{41} +8.00000 q^{43} -5.00000 q^{44} +2.00000 q^{47} -3.00000 q^{48} +3.00000 q^{51} -6.00000 q^{52} -4.00000 q^{53} +9.00000 q^{54} -9.00000 q^{57} +6.00000 q^{58} -4.00000 q^{59} +2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -15.0000 q^{66} -9.00000 q^{67} -1.00000 q^{68} -10.0000 q^{71} -6.00000 q^{72} -7.00000 q^{73} +8.00000 q^{74} +3.00000 q^{76} -18.0000 q^{78} -2.00000 q^{79} +9.00000 q^{81} +11.0000 q^{82} +11.0000 q^{83} -8.00000 q^{86} +18.0000 q^{87} +5.00000 q^{88} +11.0000 q^{89} -12.0000 q^{93} -2.00000 q^{94} +3.00000 q^{96} -10.0000 q^{97} -30.0000 q^{99} +O(q^{100})$$

## 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
$$3$$ −3.00000 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 3.00000 1.22474
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 6.00000 2.00000
$$10$$ 0 0
$$11$$ −5.00000 −1.50756 −0.753778 0.657129i $$-0.771771\pi$$
−0.753778 + 0.657129i $$0.771771\pi$$
$$12$$ −3.00000 −0.866025
$$13$$ −6.00000 −1.66410 −0.832050 0.554700i $$-0.812833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −1.00000 −0.242536 −0.121268 0.992620i $$-0.538696\pi$$
−0.121268 + 0.992620i $$0.538696\pi$$
$$18$$ −6.00000 −1.41421
$$19$$ 3.00000 0.688247 0.344124 0.938924i $$-0.388176\pi$$
0.344124 + 0.938924i $$0.388176\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 5.00000 1.06600
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 3.00000 0.612372
$$25$$ 0 0
$$26$$ 6.00000 1.17670
$$27$$ −9.00000 −1.73205
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 15.0000 2.61116
$$34$$ 1.00000 0.171499
$$35$$ 0 0
$$36$$ 6.00000 1.00000
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ −3.00000 −0.486664
$$39$$ 18.0000 2.88231
$$40$$ 0 0
$$41$$ −11.0000 −1.71791 −0.858956 0.512050i $$-0.828886\pi$$
−0.858956 + 0.512050i $$0.828886\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ −5.00000 −0.753778
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.00000 0.291730 0.145865 0.989305i $$-0.453403\pi$$
0.145865 + 0.989305i $$0.453403\pi$$
$$48$$ −3.00000 −0.433013
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 3.00000 0.420084
$$52$$ −6.00000 −0.832050
$$53$$ −4.00000 −0.549442 −0.274721 0.961524i $$-0.588586\pi$$
−0.274721 + 0.961524i $$0.588586\pi$$
$$54$$ 9.00000 1.22474
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −9.00000 −1.19208
$$58$$ 6.00000 0.787839
$$59$$ −4.00000 −0.520756 −0.260378 0.965507i $$-0.583847\pi$$
−0.260378 + 0.965507i $$0.583847\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −15.0000 −1.84637
$$67$$ −9.00000 −1.09952 −0.549762 0.835321i $$-0.685282\pi$$
−0.549762 + 0.835321i $$0.685282\pi$$
$$68$$ −1.00000 −0.121268
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ −6.00000 −0.707107
$$73$$ −7.00000 −0.819288 −0.409644 0.912245i $$-0.634347\pi$$
−0.409644 + 0.912245i $$0.634347\pi$$
$$74$$ 8.00000 0.929981
$$75$$ 0 0
$$76$$ 3.00000 0.344124
$$77$$ 0 0
$$78$$ −18.0000 −2.03810
$$79$$ −2.00000 −0.225018 −0.112509 0.993651i $$-0.535889\pi$$
−0.112509 + 0.993651i $$0.535889\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 11.0000 1.21475
$$83$$ 11.0000 1.20741 0.603703 0.797209i $$-0.293691\pi$$
0.603703 + 0.797209i $$0.293691\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −8.00000 −0.862662
$$87$$ 18.0000 1.92980
$$88$$ 5.00000 0.533002
$$89$$ 11.0000 1.16600 0.582999 0.812473i $$-0.301879\pi$$
0.582999 + 0.812473i $$0.301879\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −12.0000 −1.24434
$$94$$ −2.00000 −0.206284
$$95$$ 0 0
$$96$$ 3.00000 0.306186
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ −30.0000 −3.01511
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ −3.00000 −0.297044
$$103$$ 4.00000 0.394132 0.197066 0.980390i $$-0.436859\pi$$
0.197066 + 0.980390i $$0.436859\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ 4.00000 0.388514
$$107$$ −3.00000 −0.290021 −0.145010 0.989430i $$-0.546322\pi$$
−0.145010 + 0.989430i $$0.546322\pi$$
$$108$$ −9.00000 −0.866025
$$109$$ −18.0000 −1.72409 −0.862044 0.506834i $$-0.830816\pi$$
−0.862044 + 0.506834i $$0.830816\pi$$
$$110$$ 0 0
$$111$$ 24.0000 2.27798
$$112$$ 0 0
$$113$$ 1.00000 0.0940721 0.0470360 0.998893i $$-0.485022\pi$$
0.0470360 + 0.998893i $$0.485022\pi$$
$$114$$ 9.00000 0.842927
$$115$$ 0 0
$$116$$ −6.00000 −0.557086
$$117$$ −36.0000 −3.32820
$$118$$ 4.00000 0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ −2.00000 −0.181071
$$123$$ 33.0000 2.97551
$$124$$ 4.00000 0.359211
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 14.0000 1.24230 0.621150 0.783692i $$-0.286666\pi$$
0.621150 + 0.783692i $$0.286666\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −24.0000 −2.11308
$$130$$ 0 0
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 15.0000 1.30558
$$133$$ 0 0
$$134$$ 9.00000 0.777482
$$135$$ 0 0
$$136$$ 1.00000 0.0857493
$$137$$ 3.00000 0.256307 0.128154 0.991754i $$-0.459095\pi$$
0.128154 + 0.991754i $$0.459095\pi$$
$$138$$ 0 0
$$139$$ 11.0000 0.933008 0.466504 0.884519i $$-0.345513\pi$$
0.466504 + 0.884519i $$0.345513\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 10.0000 0.839181
$$143$$ 30.0000 2.50873
$$144$$ 6.00000 0.500000
$$145$$ 0 0
$$146$$ 7.00000 0.579324
$$147$$ 0 0
$$148$$ −8.00000 −0.657596
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ −3.00000 −0.243332
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 18.0000 1.44115
$$157$$ 4.00000 0.319235 0.159617 0.987179i $$-0.448974\pi$$
0.159617 + 0.987179i $$0.448974\pi$$
$$158$$ 2.00000 0.159111
$$159$$ 12.0000 0.951662
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −9.00000 −0.707107
$$163$$ 19.0000 1.48819 0.744097 0.668071i $$-0.232880\pi$$
0.744097 + 0.668071i $$0.232880\pi$$
$$164$$ −11.0000 −0.858956
$$165$$ 0 0
$$166$$ −11.0000 −0.853766
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 18.0000 1.37649
$$172$$ 8.00000 0.609994
$$173$$ 2.00000 0.152057 0.0760286 0.997106i $$-0.475776\pi$$
0.0760286 + 0.997106i $$0.475776\pi$$
$$174$$ −18.0000 −1.36458
$$175$$ 0 0
$$176$$ −5.00000 −0.376889
$$177$$ 12.0000 0.901975
$$178$$ −11.0000 −0.824485
$$179$$ 3.00000 0.224231 0.112115 0.993695i $$-0.464237\pi$$
0.112115 + 0.993695i $$0.464237\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ −6.00000 −0.443533
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 12.0000 0.879883
$$187$$ 5.00000 0.365636
$$188$$ 2.00000 0.145865
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −6.00000 −0.434145 −0.217072 0.976156i $$-0.569651\pi$$
−0.217072 + 0.976156i $$0.569651\pi$$
$$192$$ −3.00000 −0.216506
$$193$$ 19.0000 1.36765 0.683825 0.729646i $$-0.260315\pi$$
0.683825 + 0.729646i $$0.260315\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 22.0000 1.56744 0.783718 0.621117i $$-0.213321\pi$$
0.783718 + 0.621117i $$0.213321\pi$$
$$198$$ 30.0000 2.13201
$$199$$ 10.0000 0.708881 0.354441 0.935079i $$-0.384671\pi$$
0.354441 + 0.935079i $$0.384671\pi$$
$$200$$ 0 0
$$201$$ 27.0000 1.90443
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 3.00000 0.210042
$$205$$ 0 0
$$206$$ −4.00000 −0.278693
$$207$$ 0 0
$$208$$ −6.00000 −0.416025
$$209$$ −15.0000 −1.03757
$$210$$ 0 0
$$211$$ 1.00000 0.0688428 0.0344214 0.999407i $$-0.489041\pi$$
0.0344214 + 0.999407i $$0.489041\pi$$
$$212$$ −4.00000 −0.274721
$$213$$ 30.0000 2.05557
$$214$$ 3.00000 0.205076
$$215$$ 0 0
$$216$$ 9.00000 0.612372
$$217$$ 0 0
$$218$$ 18.0000 1.21911
$$219$$ 21.0000 1.41905
$$220$$ 0 0
$$221$$ 6.00000 0.403604
$$222$$ −24.0000 −1.61077
$$223$$ 22.0000 1.47323 0.736614 0.676313i $$-0.236423\pi$$
0.736614 + 0.676313i $$0.236423\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −1.00000 −0.0665190
$$227$$ −28.0000 −1.85843 −0.929213 0.369546i $$-0.879513\pi$$
−0.929213 + 0.369546i $$0.879513\pi$$
$$228$$ −9.00000 −0.596040
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 36.0000 2.35339
$$235$$ 0 0
$$236$$ −4.00000 −0.260378
$$237$$ 6.00000 0.389742
$$238$$ 0 0
$$239$$ 4.00000 0.258738 0.129369 0.991596i $$-0.458705\pi$$
0.129369 + 0.991596i $$0.458705\pi$$
$$240$$ 0 0
$$241$$ 5.00000 0.322078 0.161039 0.986948i $$-0.448515\pi$$
0.161039 + 0.986948i $$0.448515\pi$$
$$242$$ −14.0000 −0.899954
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ 0 0
$$246$$ −33.0000 −2.10400
$$247$$ −18.0000 −1.14531
$$248$$ −4.00000 −0.254000
$$249$$ −33.0000 −2.09129
$$250$$ 0 0
$$251$$ −27.0000 −1.70422 −0.852112 0.523359i $$-0.824679\pi$$
−0.852112 + 0.523359i $$0.824679\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −14.0000 −0.878438
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 2.00000 0.124757 0.0623783 0.998053i $$-0.480131\pi$$
0.0623783 + 0.998053i $$0.480131\pi$$
$$258$$ 24.0000 1.49417
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −36.0000 −2.22834
$$262$$ 8.00000 0.494242
$$263$$ 10.0000 0.616626 0.308313 0.951285i $$-0.400236\pi$$
0.308313 + 0.951285i $$0.400236\pi$$
$$264$$ −15.0000 −0.923186
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −33.0000 −2.01957
$$268$$ −9.00000 −0.549762
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ 6.00000 0.364474 0.182237 0.983255i $$-0.441666\pi$$
0.182237 + 0.983255i $$0.441666\pi$$
$$272$$ −1.00000 −0.0606339
$$273$$ 0 0
$$274$$ −3.00000 −0.181237
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 30.0000 1.80253 0.901263 0.433273i $$-0.142641\pi$$
0.901263 + 0.433273i $$0.142641\pi$$
$$278$$ −11.0000 −0.659736
$$279$$ 24.0000 1.43684
$$280$$ 0 0
$$281$$ 14.0000 0.835170 0.417585 0.908638i $$-0.362877\pi$$
0.417585 + 0.908638i $$0.362877\pi$$
$$282$$ 6.00000 0.357295
$$283$$ −13.0000 −0.772770 −0.386385 0.922338i $$-0.626276\pi$$
−0.386385 + 0.922338i $$0.626276\pi$$
$$284$$ −10.0000 −0.593391
$$285$$ 0 0
$$286$$ −30.0000 −1.77394
$$287$$ 0 0
$$288$$ −6.00000 −0.353553
$$289$$ −16.0000 −0.941176
$$290$$ 0 0
$$291$$ 30.0000 1.75863
$$292$$ −7.00000 −0.409644
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 8.00000 0.464991
$$297$$ 45.0000 2.61116
$$298$$ −12.0000 −0.695141
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −8.00000 −0.460348
$$303$$ 0 0
$$304$$ 3.00000 0.172062
$$305$$ 0 0
$$306$$ 6.00000 0.342997
$$307$$ 13.0000 0.741949 0.370975 0.928643i $$-0.379024\pi$$
0.370975 + 0.928643i $$0.379024\pi$$
$$308$$ 0 0
$$309$$ −12.0000 −0.682656
$$310$$ 0 0
$$311$$ −6.00000 −0.340229 −0.170114 0.985424i $$-0.554414\pi$$
−0.170114 + 0.985424i $$0.554414\pi$$
$$312$$ −18.0000 −1.01905
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ 0 0
$$316$$ −2.00000 −0.112509
$$317$$ −4.00000 −0.224662 −0.112331 0.993671i $$-0.535832\pi$$
−0.112331 + 0.993671i $$0.535832\pi$$
$$318$$ −12.0000 −0.672927
$$319$$ 30.0000 1.67968
$$320$$ 0 0
$$321$$ 9.00000 0.502331
$$322$$ 0 0
$$323$$ −3.00000 −0.166924
$$324$$ 9.00000 0.500000
$$325$$ 0 0
$$326$$ −19.0000 −1.05231
$$327$$ 54.0000 2.98621
$$328$$ 11.0000 0.607373
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −17.0000 −0.934405 −0.467202 0.884150i $$-0.654738\pi$$
−0.467202 + 0.884150i $$0.654738\pi$$
$$332$$ 11.0000 0.603703
$$333$$ −48.0000 −2.63038
$$334$$ −12.0000 −0.656611
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 29.0000 1.57973 0.789865 0.613280i $$-0.210150\pi$$
0.789865 + 0.613280i $$0.210150\pi$$
$$338$$ −23.0000 −1.25104
$$339$$ −3.00000 −0.162938
$$340$$ 0 0
$$341$$ −20.0000 −1.08306
$$342$$ −18.0000 −0.973329
$$343$$ 0 0
$$344$$ −8.00000 −0.431331
$$345$$ 0 0
$$346$$ −2.00000 −0.107521
$$347$$ −19.0000 −1.01997 −0.509987 0.860182i $$-0.670350\pi$$
−0.509987 + 0.860182i $$0.670350\pi$$
$$348$$ 18.0000 0.964901
$$349$$ 8.00000 0.428230 0.214115 0.976808i $$-0.431313\pi$$
0.214115 + 0.976808i $$0.431313\pi$$
$$350$$ 0 0
$$351$$ 54.0000 2.88231
$$352$$ 5.00000 0.266501
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ −12.0000 −0.637793
$$355$$ 0 0
$$356$$ 11.0000 0.582999
$$357$$ 0 0
$$358$$ −3.00000 −0.158555
$$359$$ 26.0000 1.37223 0.686114 0.727494i $$-0.259315\pi$$
0.686114 + 0.727494i $$0.259315\pi$$
$$360$$ 0 0
$$361$$ −10.0000 −0.526316
$$362$$ 10.0000 0.525588
$$363$$ −42.0000 −2.20443
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 6.00000 0.313625
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 0 0
$$369$$ −66.0000 −3.43582
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −12.0000 −0.622171
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ −5.00000 −0.258544
$$375$$ 0 0
$$376$$ −2.00000 −0.103142
$$377$$ 36.0000 1.85409
$$378$$ 0 0
$$379$$ 9.00000 0.462299 0.231149 0.972918i $$-0.425751\pi$$
0.231149 + 0.972918i $$0.425751\pi$$
$$380$$ 0 0
$$381$$ −42.0000 −2.15173
$$382$$ 6.00000 0.306987
$$383$$ −6.00000 −0.306586 −0.153293 0.988181i $$-0.548988\pi$$
−0.153293 + 0.988181i $$0.548988\pi$$
$$384$$ 3.00000 0.153093
$$385$$ 0 0
$$386$$ −19.0000 −0.967075
$$387$$ 48.0000 2.43998
$$388$$ −10.0000 −0.507673
$$389$$ 8.00000 0.405616 0.202808 0.979219i $$-0.434993\pi$$
0.202808 + 0.979219i $$0.434993\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 24.0000 1.21064
$$394$$ −22.0000 −1.10834
$$395$$ 0 0
$$396$$ −30.0000 −1.50756
$$397$$ 10.0000 0.501886 0.250943 0.968002i $$-0.419259\pi$$
0.250943 + 0.968002i $$0.419259\pi$$
$$398$$ −10.0000 −0.501255
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 37.0000 1.84769 0.923846 0.382765i $$-0.125028\pi$$
0.923846 + 0.382765i $$0.125028\pi$$
$$402$$ −27.0000 −1.34664
$$403$$ −24.0000 −1.19553
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 40.0000 1.98273
$$408$$ −3.00000 −0.148522
$$409$$ 21.0000 1.03838 0.519192 0.854658i $$-0.326233\pi$$
0.519192 + 0.854658i $$0.326233\pi$$
$$410$$ 0 0
$$411$$ −9.00000 −0.443937
$$412$$ 4.00000 0.197066
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 6.00000 0.294174
$$417$$ −33.0000 −1.61602
$$418$$ 15.0000 0.733674
$$419$$ 39.0000 1.90527 0.952637 0.304109i $$-0.0983586\pi$$
0.952637 + 0.304109i $$0.0983586\pi$$
$$420$$ 0 0
$$421$$ 20.0000 0.974740 0.487370 0.873195i $$-0.337956\pi$$
0.487370 + 0.873195i $$0.337956\pi$$
$$422$$ −1.00000 −0.0486792
$$423$$ 12.0000 0.583460
$$424$$ 4.00000 0.194257
$$425$$ 0 0
$$426$$ −30.0000 −1.45350
$$427$$ 0 0
$$428$$ −3.00000 −0.145010
$$429$$ −90.0000 −4.34524
$$430$$ 0 0
$$431$$ −36.0000 −1.73406 −0.867029 0.498257i $$-0.833974\pi$$
−0.867029 + 0.498257i $$0.833974\pi$$
$$432$$ −9.00000 −0.433013
$$433$$ −1.00000 −0.0480569 −0.0240285 0.999711i $$-0.507649\pi$$
−0.0240285 + 0.999711i $$0.507649\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −18.0000 −0.862044
$$437$$ 0 0
$$438$$ −21.0000 −1.00342
$$439$$ −28.0000 −1.33637 −0.668184 0.743996i $$-0.732928\pi$$
−0.668184 + 0.743996i $$0.732928\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −6.00000 −0.285391
$$443$$ −37.0000 −1.75792 −0.878962 0.476893i $$-0.841763\pi$$
−0.878962 + 0.476893i $$0.841763\pi$$
$$444$$ 24.0000 1.13899
$$445$$ 0 0
$$446$$ −22.0000 −1.04173
$$447$$ −36.0000 −1.70274
$$448$$ 0 0
$$449$$ 33.0000 1.55737 0.778683 0.627417i $$-0.215888\pi$$
0.778683 + 0.627417i $$0.215888\pi$$
$$450$$ 0 0
$$451$$ 55.0000 2.58985
$$452$$ 1.00000 0.0470360
$$453$$ −24.0000 −1.12762
$$454$$ 28.0000 1.31411
$$455$$ 0 0
$$456$$ 9.00000 0.421464
$$457$$ −25.0000 −1.16945 −0.584725 0.811231i $$-0.698798\pi$$
−0.584725 + 0.811231i $$0.698798\pi$$
$$458$$ −14.0000 −0.654177
$$459$$ 9.00000 0.420084
$$460$$ 0 0
$$461$$ 38.0000 1.76984 0.884918 0.465746i $$-0.154214\pi$$
0.884918 + 0.465746i $$0.154214\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 0 0
$$466$$ 6.00000 0.277945
$$467$$ −4.00000 −0.185098 −0.0925490 0.995708i $$-0.529501\pi$$
−0.0925490 + 0.995708i $$0.529501\pi$$
$$468$$ −36.0000 −1.66410
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −12.0000 −0.552931
$$472$$ 4.00000 0.184115
$$473$$ −40.0000 −1.83920
$$474$$ −6.00000 −0.275589
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −24.0000 −1.09888
$$478$$ −4.00000 −0.182956
$$479$$ 6.00000 0.274147 0.137073 0.990561i $$-0.456230\pi$$
0.137073 + 0.990561i $$0.456230\pi$$
$$480$$ 0 0
$$481$$ 48.0000 2.18861
$$482$$ −5.00000 −0.227744
$$483$$ 0 0
$$484$$ 14.0000 0.636364
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 34.0000 1.54069 0.770344 0.637629i $$-0.220085\pi$$
0.770344 + 0.637629i $$0.220085\pi$$
$$488$$ −2.00000 −0.0905357
$$489$$ −57.0000 −2.57763
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 33.0000 1.48775
$$493$$ 6.00000 0.270226
$$494$$ 18.0000 0.809858
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ 0 0
$$498$$ 33.0000 1.47877
$$499$$ 36.0000 1.61158 0.805791 0.592200i $$-0.201741\pi$$
0.805791 + 0.592200i $$0.201741\pi$$
$$500$$ 0 0
$$501$$ −36.0000 −1.60836
$$502$$ 27.0000 1.20507
$$503$$ −30.0000 −1.33763 −0.668817 0.743427i $$-0.733199\pi$$
−0.668817 + 0.743427i $$0.733199\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −69.0000 −3.06440
$$508$$ 14.0000 0.621150
$$509$$ 14.0000 0.620539 0.310270 0.950649i $$-0.399581\pi$$
0.310270 + 0.950649i $$0.399581\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ −27.0000 −1.19208
$$514$$ −2.00000 −0.0882162
$$515$$ 0 0
$$516$$ −24.0000 −1.05654
$$517$$ −10.0000 −0.439799
$$518$$ 0 0
$$519$$ −6.00000 −0.263371
$$520$$ 0 0
$$521$$ −11.0000 −0.481919 −0.240959 0.970535i $$-0.577462\pi$$
−0.240959 + 0.970535i $$0.577462\pi$$
$$522$$ 36.0000 1.57568
$$523$$ 13.0000 0.568450 0.284225 0.958758i $$-0.408264\pi$$
0.284225 + 0.958758i $$0.408264\pi$$
$$524$$ −8.00000 −0.349482
$$525$$ 0 0
$$526$$ −10.0000 −0.436021
$$527$$ −4.00000 −0.174243
$$528$$ 15.0000 0.652791
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ −24.0000 −1.04151
$$532$$ 0 0
$$533$$ 66.0000 2.85878
$$534$$ 33.0000 1.42805
$$535$$ 0 0
$$536$$ 9.00000 0.388741
$$537$$ −9.00000 −0.388379
$$538$$ 18.0000 0.776035
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −42.0000 −1.80572 −0.902861 0.429934i $$-0.858537\pi$$
−0.902861 + 0.429934i $$0.858537\pi$$
$$542$$ −6.00000 −0.257722
$$543$$ 30.0000 1.28742
$$544$$ 1.00000 0.0428746
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −27.0000 −1.15444 −0.577218 0.816590i $$-0.695862\pi$$
−0.577218 + 0.816590i $$0.695862\pi$$
$$548$$ 3.00000 0.128154
$$549$$ 12.0000 0.512148
$$550$$ 0 0
$$551$$ −18.0000 −0.766826
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −30.0000 −1.27458
$$555$$ 0 0
$$556$$ 11.0000 0.466504
$$557$$ −4.00000 −0.169485 −0.0847427 0.996403i $$-0.527007\pi$$
−0.0847427 + 0.996403i $$0.527007\pi$$
$$558$$ −24.0000 −1.01600
$$559$$ −48.0000 −2.03018
$$560$$ 0 0
$$561$$ −15.0000 −0.633300
$$562$$ −14.0000 −0.590554
$$563$$ 20.0000 0.842900 0.421450 0.906852i $$-0.361521\pi$$
0.421450 + 0.906852i $$0.361521\pi$$
$$564$$ −6.00000 −0.252646
$$565$$ 0 0
$$566$$ 13.0000 0.546431
$$567$$ 0 0
$$568$$ 10.0000 0.419591
$$569$$ 21.0000 0.880366 0.440183 0.897908i $$-0.354914\pi$$
0.440183 + 0.897908i $$0.354914\pi$$
$$570$$ 0 0
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ 30.0000 1.25436
$$573$$ 18.0000 0.751961
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 6.00000 0.250000
$$577$$ 13.0000 0.541197 0.270599 0.962692i $$-0.412778\pi$$
0.270599 + 0.962692i $$0.412778\pi$$
$$578$$ 16.0000 0.665512
$$579$$ −57.0000 −2.36884
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −30.0000 −1.24354
$$583$$ 20.0000 0.828315
$$584$$ 7.00000 0.289662
$$585$$ 0 0
$$586$$ 14.0000 0.578335
$$587$$ −13.0000 −0.536567 −0.268284 0.963340i $$-0.586456\pi$$
−0.268284 + 0.963340i $$0.586456\pi$$
$$588$$ 0 0
$$589$$ 12.0000 0.494451
$$590$$ 0 0
$$591$$ −66.0000 −2.71488
$$592$$ −8.00000 −0.328798
$$593$$ −39.0000 −1.60154 −0.800769 0.598973i $$-0.795576\pi$$
−0.800769 + 0.598973i $$0.795576\pi$$
$$594$$ −45.0000 −1.84637
$$595$$ 0 0
$$596$$ 12.0000 0.491539
$$597$$ −30.0000 −1.22782
$$598$$ 0 0
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ −21.0000 −0.856608 −0.428304 0.903635i $$-0.640889\pi$$
−0.428304 + 0.903635i $$0.640889\pi$$
$$602$$ 0 0
$$603$$ −54.0000 −2.19905
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 28.0000 1.13648 0.568242 0.822861i $$-0.307624\pi$$
0.568242 + 0.822861i $$0.307624\pi$$
$$608$$ −3.00000 −0.121666
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −12.0000 −0.485468
$$612$$ −6.00000 −0.242536
$$613$$ −18.0000 −0.727013 −0.363507 0.931592i $$-0.618421\pi$$
−0.363507 + 0.931592i $$0.618421\pi$$
$$614$$ −13.0000 −0.524637
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −14.0000 −0.563619 −0.281809 0.959470i $$-0.590935\pi$$
−0.281809 + 0.959470i $$0.590935\pi$$
$$618$$ 12.0000 0.482711
$$619$$ 4.00000 0.160774 0.0803868 0.996764i $$-0.474384\pi$$
0.0803868 + 0.996764i $$0.474384\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 6.00000 0.240578
$$623$$ 0 0
$$624$$ 18.0000 0.720577
$$625$$ 0 0
$$626$$ 10.0000 0.399680
$$627$$ 45.0000 1.79713
$$628$$ 4.00000 0.159617
$$629$$ 8.00000 0.318981
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 2.00000 0.0795557
$$633$$ −3.00000 −0.119239
$$634$$ 4.00000 0.158860
$$635$$ 0 0
$$636$$ 12.0000 0.475831
$$637$$ 0 0
$$638$$ −30.0000 −1.18771
$$639$$ −60.0000 −2.37356
$$640$$ 0 0
$$641$$ 2.00000 0.0789953 0.0394976 0.999220i $$-0.487424\pi$$
0.0394976 + 0.999220i $$0.487424\pi$$
$$642$$ −9.00000 −0.355202
$$643$$ 16.0000 0.630978 0.315489 0.948929i $$-0.397831\pi$$
0.315489 + 0.948929i $$0.397831\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 3.00000 0.118033
$$647$$ −8.00000 −0.314512 −0.157256 0.987558i $$-0.550265\pi$$
−0.157256 + 0.987558i $$0.550265\pi$$
$$648$$ −9.00000 −0.353553
$$649$$ 20.0000 0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 19.0000 0.744097
$$653$$ 28.0000 1.09572 0.547862 0.836569i $$-0.315442\pi$$
0.547862 + 0.836569i $$0.315442\pi$$
$$654$$ −54.0000 −2.11157
$$655$$ 0 0
$$656$$ −11.0000 −0.429478
$$657$$ −42.0000 −1.63858
$$658$$ 0 0
$$659$$ 1.00000 0.0389545 0.0194772 0.999810i $$-0.493800\pi$$
0.0194772 + 0.999810i $$0.493800\pi$$
$$660$$ 0 0
$$661$$ 50.0000 1.94477 0.972387 0.233373i $$-0.0749763\pi$$
0.972387 + 0.233373i $$0.0749763\pi$$
$$662$$ 17.0000 0.660724
$$663$$ −18.0000 −0.699062
$$664$$ −11.0000 −0.426883
$$665$$ 0 0
$$666$$ 48.0000 1.85996
$$667$$ 0 0
$$668$$ 12.0000 0.464294
$$669$$ −66.0000 −2.55171
$$670$$ 0 0
$$671$$ −10.0000 −0.386046
$$672$$ 0 0
$$673$$ −34.0000 −1.31060 −0.655302 0.755367i $$-0.727459\pi$$
−0.655302 + 0.755367i $$0.727459\pi$$
$$674$$ −29.0000 −1.11704
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ −48.0000 −1.84479 −0.922395 0.386248i $$-0.873771\pi$$
−0.922395 + 0.386248i $$0.873771\pi$$
$$678$$ 3.00000 0.115214
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 84.0000 3.21889
$$682$$ 20.0000 0.765840
$$683$$ 13.0000 0.497431 0.248716 0.968577i $$-0.419992\pi$$
0.248716 + 0.968577i $$0.419992\pi$$
$$684$$ 18.0000 0.688247
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −42.0000 −1.60240
$$688$$ 8.00000 0.304997
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ −49.0000 −1.86405 −0.932024 0.362397i $$-0.881959\pi$$
−0.932024 + 0.362397i $$0.881959\pi$$
$$692$$ 2.00000 0.0760286
$$693$$ 0 0
$$694$$ 19.0000 0.721230
$$695$$ 0 0
$$696$$ −18.0000 −0.682288
$$697$$ 11.0000 0.416655
$$698$$ −8.00000 −0.302804
$$699$$ 18.0000 0.680823
$$700$$ 0 0
$$701$$ −32.0000 −1.20862 −0.604312 0.796748i $$-0.706552\pi$$
−0.604312 + 0.796748i $$0.706552\pi$$
$$702$$ −54.0000 −2.03810
$$703$$ −24.0000 −0.905177
$$704$$ −5.00000 −0.188445
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ 0 0
$$708$$ 12.0000 0.450988
$$709$$ 4.00000 0.150223 0.0751116 0.997175i $$-0.476069\pi$$
0.0751116 + 0.997175i $$0.476069\pi$$
$$710$$ 0 0
$$711$$ −12.0000 −0.450035
$$712$$ −11.0000 −0.412242
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 3.00000 0.112115
$$717$$ −12.0000 −0.448148
$$718$$ −26.0000 −0.970311
$$719$$ 48.0000 1.79010 0.895049 0.445968i $$-0.147140\pi$$
0.895049 + 0.445968i $$0.147140\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 10.0000 0.372161
$$723$$ −15.0000 −0.557856
$$724$$ −10.0000 −0.371647
$$725$$ 0 0
$$726$$ 42.0000 1.55877
$$727$$ 6.00000 0.222528 0.111264 0.993791i $$-0.464510\pi$$
0.111264 + 0.993791i $$0.464510\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −8.00000 −0.295891
$$732$$ −6.00000 −0.221766
$$733$$ 40.0000 1.47743 0.738717 0.674016i $$-0.235432\pi$$
0.738717 + 0.674016i $$0.235432\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 45.0000 1.65760
$$738$$ 66.0000 2.42949
$$739$$ 4.00000 0.147142 0.0735712 0.997290i $$-0.476560\pi$$
0.0735712 + 0.997290i $$0.476560\pi$$
$$740$$ 0 0
$$741$$ 54.0000 1.98374
$$742$$ 0 0
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 12.0000 0.439941
$$745$$ 0 0
$$746$$ −4.00000 −0.146450
$$747$$ 66.0000 2.41481
$$748$$ 5.00000 0.182818
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 50.0000 1.82453 0.912263 0.409605i $$-0.134333\pi$$
0.912263 + 0.409605i $$0.134333\pi$$
$$752$$ 2.00000 0.0729325
$$753$$ 81.0000 2.95180
$$754$$ −36.0000 −1.31104
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ −9.00000 −0.326895
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −27.0000 −0.978749 −0.489375 0.872074i $$-0.662775\pi$$
−0.489375 + 0.872074i $$0.662775\pi$$
$$762$$ 42.0000 1.52150
$$763$$ 0 0
$$764$$ −6.00000 −0.217072
$$765$$ 0 0
$$766$$ 6.00000 0.216789
$$767$$ 24.0000 0.866590
$$768$$ −3.00000 −0.108253
$$769$$ −19.0000 −0.685158 −0.342579 0.939489i $$-0.611300\pi$$
−0.342579 + 0.939489i $$0.611300\pi$$
$$770$$ 0 0
$$771$$ −6.00000 −0.216085
$$772$$ 19.0000 0.683825
$$773$$ 36.0000 1.29483 0.647415 0.762138i $$-0.275850\pi$$
0.647415 + 0.762138i $$0.275850\pi$$
$$774$$ −48.0000 −1.72532
$$775$$ 0 0
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ −8.00000 −0.286814
$$779$$ −33.0000 −1.18235
$$780$$ 0 0
$$781$$ 50.0000 1.78914
$$782$$ 0 0
$$783$$ 54.0000 1.92980
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −24.0000 −0.856052
$$787$$ 52.0000 1.85360 0.926800 0.375555i $$-0.122548\pi$$
0.926800 + 0.375555i $$0.122548\pi$$
$$788$$ 22.0000 0.783718
$$789$$ −30.0000 −1.06803
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 30.0000 1.06600
$$793$$ −12.0000 −0.426132
$$794$$ −10.0000 −0.354887
$$795$$ 0 0
$$796$$ 10.0000 0.354441
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ 0 0
$$799$$ −2.00000 −0.0707549
$$800$$ 0 0
$$801$$ 66.0000 2.33200
$$802$$ −37.0000 −1.30652
$$803$$ 35.0000 1.23512
$$804$$ 27.0000 0.952217
$$805$$ 0 0
$$806$$ 24.0000 0.845364
$$807$$ 54.0000 1.90089
$$808$$ 0 0
$$809$$ 6.00000 0.210949 0.105474 0.994422i $$-0.466364\pi$$
0.105474 + 0.994422i $$0.466364\pi$$
$$810$$ 0 0
$$811$$ 28.0000 0.983213 0.491606 0.870817i $$-0.336410\pi$$
0.491606 + 0.870817i $$0.336410\pi$$
$$812$$ 0 0
$$813$$ −18.0000 −0.631288
$$814$$ −40.0000 −1.40200
$$815$$ 0 0
$$816$$ 3.00000 0.105021
$$817$$ 24.0000 0.839654
$$818$$ −21.0000 −0.734248
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −24.0000 −0.837606 −0.418803 0.908077i $$-0.637550\pi$$
−0.418803 + 0.908077i $$0.637550\pi$$
$$822$$ 9.00000 0.313911
$$823$$ −10.0000 −0.348578 −0.174289 0.984695i $$-0.555763\pi$$
−0.174289 + 0.984695i $$0.555763\pi$$
$$824$$ −4.00000 −0.139347
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −41.0000 −1.42571 −0.712855 0.701312i $$-0.752598\pi$$
−0.712855 + 0.701312i $$0.752598\pi$$
$$828$$ 0 0
$$829$$ 4.00000 0.138926 0.0694629 0.997585i $$-0.477871\pi$$
0.0694629 + 0.997585i $$0.477871\pi$$
$$830$$ 0 0
$$831$$ −90.0000 −3.12207
$$832$$ −6.00000 −0.208013
$$833$$ 0 0
$$834$$ 33.0000 1.14270
$$835$$ 0 0
$$836$$ −15.0000 −0.518786
$$837$$ −36.0000 −1.24434
$$838$$ −39.0000 −1.34723
$$839$$ −2.00000 −0.0690477 −0.0345238 0.999404i $$-0.510991\pi$$
−0.0345238 + 0.999404i $$0.510991\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ −20.0000 −0.689246
$$843$$ −42.0000 −1.44656
$$844$$ 1.00000 0.0344214
$$845$$ 0 0
$$846$$ −12.0000 −0.412568
$$847$$ 0 0
$$848$$ −4.00000 −0.137361
$$849$$ 39.0000 1.33848
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 30.0000 1.02778
$$853$$ −34.0000 −1.16414 −0.582069 0.813139i $$-0.697757\pi$$
−0.582069 + 0.813139i $$0.697757\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 3.00000 0.102538
$$857$$ 3.00000 0.102478 0.0512390 0.998686i $$-0.483683\pi$$
0.0512390 + 0.998686i $$0.483683\pi$$
$$858$$ 90.0000 3.07255
$$859$$ 51.0000 1.74010 0.870049 0.492966i $$-0.164087\pi$$
0.870049 + 0.492966i $$0.164087\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 36.0000 1.22616
$$863$$ −4.00000 −0.136162 −0.0680808 0.997680i $$-0.521688\pi$$
−0.0680808 + 0.997680i $$0.521688\pi$$
$$864$$ 9.00000 0.306186
$$865$$ 0 0
$$866$$ 1.00000 0.0339814
$$867$$ 48.0000 1.63017
$$868$$ 0 0
$$869$$ 10.0000 0.339227
$$870$$ 0 0
$$871$$ 54.0000 1.82972
$$872$$ 18.0000 0.609557
$$873$$ −60.0000 −2.03069
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 21.0000 0.709524
$$877$$ −32.0000 −1.08056 −0.540282 0.841484i $$-0.681682\pi$$
−0.540282 + 0.841484i $$0.681682\pi$$
$$878$$ 28.0000 0.944954
$$879$$ 42.0000 1.41662
$$880$$ 0 0
$$881$$ −26.0000 −0.875962 −0.437981 0.898984i $$-0.644306\pi$$
−0.437981 + 0.898984i $$0.644306\pi$$
$$882$$ 0 0
$$883$$ −15.0000 −0.504790 −0.252395 0.967624i $$-0.581218\pi$$
−0.252395 + 0.967624i $$0.581218\pi$$
$$884$$ 6.00000 0.201802
$$885$$ 0 0
$$886$$ 37.0000 1.24304
$$887$$ −34.0000 −1.14161 −0.570804 0.821086i $$-0.693368\pi$$
−0.570804 + 0.821086i $$0.693368\pi$$
$$888$$ −24.0000 −0.805387
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −45.0000 −1.50756
$$892$$ 22.0000 0.736614
$$893$$ 6.00000 0.200782
$$894$$ 36.0000 1.20402
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −33.0000 −1.10122
$$899$$ −24.0000 −0.800445
$$900$$ 0 0
$$901$$ 4.00000 0.133259
$$902$$ −55.0000 −1.83130
$$903$$ 0 0
$$904$$ −1.00000 −0.0332595
$$905$$ 0 0
$$906$$ 24.0000 0.797347
$$907$$ 4.00000 0.132818 0.0664089 0.997792i $$-0.478846\pi$$
0.0664089 + 0.997792i $$0.478846\pi$$
$$908$$ −28.0000 −0.929213
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −12.0000 −0.397578 −0.198789 0.980042i $$-0.563701\pi$$
−0.198789 + 0.980042i $$0.563701\pi$$
$$912$$ −9.00000 −0.298020
$$913$$ −55.0000 −1.82023
$$914$$ 25.0000 0.826927
$$915$$ 0 0
$$916$$ 14.0000 0.462573
$$917$$ 0 0
$$918$$ −9.00000 −0.297044
$$919$$ −34.0000 −1.12156 −0.560778 0.827966i $$-0.689498\pi$$
−0.560778 + 0.827966i $$0.689498\pi$$
$$920$$ 0 0
$$921$$ −39.0000 −1.28509
$$922$$ −38.0000 −1.25146
$$923$$ 60.0000 1.97492
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 8.00000 0.262896
$$927$$ 24.0000 0.788263
$$928$$ 6.00000 0.196960
$$929$$ −46.0000 −1.50921 −0.754606 0.656179i $$-0.772172\pi$$
−0.754606 + 0.656179i $$0.772172\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −6.00000 −0.196537
$$933$$ 18.0000 0.589294
$$934$$ 4.00000 0.130884
$$935$$ 0 0
$$936$$ 36.0000 1.17670
$$937$$ −7.00000 −0.228680 −0.114340 0.993442i $$-0.536475\pi$$
−0.114340 + 0.993442i $$0.536475\pi$$
$$938$$ 0 0
$$939$$ 30.0000 0.979013
$$940$$ 0 0
$$941$$ −56.0000 −1.82555 −0.912774 0.408465i $$-0.866064\pi$$
−0.912774 + 0.408465i $$0.866064\pi$$
$$942$$ 12.0000 0.390981
$$943$$ 0 0
$$944$$ −4.00000 −0.130189
$$945$$ 0 0
$$946$$ 40.0000 1.30051
$$947$$ 4.00000 0.129983 0.0649913 0.997886i $$-0.479298\pi$$
0.0649913 + 0.997886i $$0.479298\pi$$
$$948$$ 6.00000 0.194871
$$949$$ 42.0000 1.36338
$$950$$ 0 0
$$951$$ 12.0000 0.389127
$$952$$ 0 0
$$953$$ −9.00000 −0.291539 −0.145769 0.989319i $$-0.546566\pi$$
−0.145769 + 0.989319i $$0.546566\pi$$
$$954$$ 24.0000 0.777029
$$955$$ 0 0
$$956$$ 4.00000 0.129369
$$957$$ −90.0000 −2.90929
$$958$$ −6.00000 −0.193851
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ −48.0000 −1.54758
$$963$$ −18.0000 −0.580042
$$964$$ 5.00000 0.161039
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 2.00000 0.0643157 0.0321578 0.999483i $$-0.489762\pi$$
0.0321578 + 0.999483i $$0.489762\pi$$
$$968$$ −14.0000 −0.449977
$$969$$ 9.00000 0.289122
$$970$$ 0 0
$$971$$ 51.0000 1.63667 0.818334 0.574743i $$-0.194898\pi$$
0.818334 + 0.574743i $$0.194898\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ −34.0000 −1.08943
$$975$$ 0 0
$$976$$ 2.00000 0.0640184
$$977$$ −21.0000 −0.671850 −0.335925 0.941889i $$-0.609049\pi$$
−0.335925 + 0.941889i $$0.609049\pi$$
$$978$$ 57.0000 1.82266
$$979$$ −55.0000 −1.75781
$$980$$ 0 0
$$981$$ −108.000 −3.44817
$$982$$ 12.0000 0.382935
$$983$$ −4.00000 −0.127580 −0.0637901 0.997963i $$-0.520319\pi$$
−0.0637901 + 0.997963i $$0.520319\pi$$
$$984$$ −33.0000 −1.05200
$$985$$ 0 0
$$986$$ −6.00000 −0.191079
$$987$$ 0 0
$$988$$ −18.0000 −0.572656
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 4.00000 0.127064 0.0635321 0.997980i $$-0.479763\pi$$
0.0635321 + 0.997980i $$0.479763\pi$$
$$992$$ −4.00000 −0.127000
$$993$$ 51.0000 1.61844
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −33.0000 −1.04565
$$997$$ −58.0000 −1.83688 −0.918439 0.395562i $$-0.870550\pi$$
−0.918439 + 0.395562i $$0.870550\pi$$
$$998$$ −36.0000 −1.13956
$$999$$ 72.0000 2.27798
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 2450.2.a.a.1.1 1
5.2 odd 4 2450.2.c.r.99.1 2
5.3 odd 4 2450.2.c.r.99.2 2
5.4 even 2 2450.2.a.bg.1.1 1
7.6 odd 2 350.2.a.c.1.1 1
21.20 even 2 3150.2.a.bq.1.1 1
28.27 even 2 2800.2.a.b.1.1 1
35.13 even 4 350.2.c.a.99.2 2
35.27 even 4 350.2.c.a.99.1 2
35.34 odd 2 350.2.a.d.1.1 yes 1
105.62 odd 4 3150.2.g.v.2899.2 2
105.83 odd 4 3150.2.g.v.2899.1 2
105.104 even 2 3150.2.a.j.1.1 1
140.27 odd 4 2800.2.g.a.449.2 2
140.83 odd 4 2800.2.g.a.449.1 2
140.139 even 2 2800.2.a.bg.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.a.c.1.1 1 7.6 odd 2
350.2.a.d.1.1 yes 1 35.34 odd 2
350.2.c.a.99.1 2 35.27 even 4
350.2.c.a.99.2 2 35.13 even 4
2450.2.a.a.1.1 1 1.1 even 1 trivial
2450.2.a.bg.1.1 1 5.4 even 2
2450.2.c.r.99.1 2 5.2 odd 4
2450.2.c.r.99.2 2 5.3 odd 4
2800.2.a.b.1.1 1 28.27 even 2
2800.2.a.bg.1.1 1 140.139 even 2
2800.2.g.a.449.1 2 140.83 odd 4
2800.2.g.a.449.2 2 140.27 odd 4
3150.2.a.j.1.1 1 105.104 even 2
3150.2.a.bq.1.1 1 21.20 even 2
3150.2.g.v.2899.1 2 105.83 odd 4
3150.2.g.v.2899.2 2 105.62 odd 4