# Properties

 Label 7350.2.a.u.1.1 Level $7350$ Weight $2$ Character 7350.1 Self dual yes Analytic conductor $58.690$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7350.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$58.6900454856$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 210) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7350.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -5.00000 q^{11} +1.00000 q^{12} +5.00000 q^{13} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -7.00000 q^{19} +5.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} -5.00000 q^{26} +1.00000 q^{27} -2.00000 q^{31} -1.00000 q^{32} -5.00000 q^{33} -4.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} +7.00000 q^{38} +5.00000 q^{39} +5.00000 q^{41} -12.0000 q^{43} -5.00000 q^{44} +1.00000 q^{46} +11.0000 q^{47} +1.00000 q^{48} +4.00000 q^{51} +5.00000 q^{52} +9.00000 q^{53} -1.00000 q^{54} -7.00000 q^{57} +4.00000 q^{59} +4.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +5.00000 q^{66} +12.0000 q^{67} +4.00000 q^{68} -1.00000 q^{69} +2.00000 q^{71} -1.00000 q^{72} -10.0000 q^{73} +1.00000 q^{74} -7.00000 q^{76} -5.00000 q^{78} -12.0000 q^{79} +1.00000 q^{81} -5.00000 q^{82} +12.0000 q^{83} +12.0000 q^{86} +5.00000 q^{88} +14.0000 q^{89} -1.00000 q^{92} -2.00000 q^{93} -11.0000 q^{94} -1.00000 q^{96} +8.00000 q^{97} -5.00000 q^{99} +O(q^{100})$$

## 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
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −5.00000 −1.50756 −0.753778 0.657129i $$-0.771771\pi$$
−0.753778 + 0.657129i $$0.771771\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 5.00000 1.38675 0.693375 0.720577i $$-0.256123\pi$$
0.693375 + 0.720577i $$0.256123\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −7.00000 −1.60591 −0.802955 0.596040i $$-0.796740\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 5.00000 1.06600
$$23$$ −1.00000 −0.208514 −0.104257 0.994550i $$-0.533247\pi$$
−0.104257 + 0.994550i $$0.533247\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ −5.00000 −0.980581
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ −5.00000 −0.870388
$$34$$ −4.00000 −0.685994
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −1.00000 −0.164399 −0.0821995 0.996616i $$-0.526194\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ 7.00000 1.13555
$$39$$ 5.00000 0.800641
$$40$$ 0 0
$$41$$ 5.00000 0.780869 0.390434 0.920631i $$-0.372325\pi$$
0.390434 + 0.920631i $$0.372325\pi$$
$$42$$ 0 0
$$43$$ −12.0000 −1.82998 −0.914991 0.403473i $$-0.867803\pi$$
−0.914991 + 0.403473i $$0.867803\pi$$
$$44$$ −5.00000 −0.753778
$$45$$ 0 0
$$46$$ 1.00000 0.147442
$$47$$ 11.0000 1.60451 0.802257 0.596978i $$-0.203632\pi$$
0.802257 + 0.596978i $$0.203632\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ 5.00000 0.693375
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −7.00000 −0.927173
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ 4.00000 0.512148 0.256074 0.966657i $$-0.417571\pi$$
0.256074 + 0.966657i $$0.417571\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 5.00000 0.615457
$$67$$ 12.0000 1.46603 0.733017 0.680211i $$-0.238112\pi$$
0.733017 + 0.680211i $$0.238112\pi$$
$$68$$ 4.00000 0.485071
$$69$$ −1.00000 −0.120386
$$70$$ 0 0
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 1.00000 0.116248
$$75$$ 0 0
$$76$$ −7.00000 −0.802955
$$77$$ 0 0
$$78$$ −5.00000 −0.566139
$$79$$ −12.0000 −1.35011 −0.675053 0.737769i $$-0.735879\pi$$
−0.675053 + 0.737769i $$0.735879\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −5.00000 −0.552158
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 12.0000 1.29399
$$87$$ 0 0
$$88$$ 5.00000 0.533002
$$89$$ 14.0000 1.48400 0.741999 0.670402i $$-0.233878\pi$$
0.741999 + 0.670402i $$0.233878\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −1.00000 −0.104257
$$93$$ −2.00000 −0.207390
$$94$$ −11.0000 −1.13456
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ 0 0
$$99$$ −5.00000 −0.502519
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ −4.00000 −0.396059
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ −5.00000 −0.490290
$$105$$ 0 0
$$106$$ −9.00000 −0.874157
$$107$$ 2.00000 0.193347 0.0966736 0.995316i $$-0.469180\pi$$
0.0966736 + 0.995316i $$0.469180\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 7.00000 0.655610
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 5.00000 0.462250
$$118$$ −4.00000 −0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ −4.00000 −0.362143
$$123$$ 5.00000 0.450835
$$124$$ −2.00000 −0.179605
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −9.00000 −0.798621 −0.399310 0.916816i $$-0.630750\pi$$
−0.399310 + 0.916816i $$0.630750\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −12.0000 −1.05654
$$130$$ 0 0
$$131$$ −9.00000 −0.786334 −0.393167 0.919467i $$-0.628621\pi$$
−0.393167 + 0.919467i $$0.628621\pi$$
$$132$$ −5.00000 −0.435194
$$133$$ 0 0
$$134$$ −12.0000 −1.03664
$$135$$ 0 0
$$136$$ −4.00000 −0.342997
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 1.00000 0.0851257
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ 11.0000 0.926367
$$142$$ −2.00000 −0.167836
$$143$$ −25.0000 −2.09061
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 10.0000 0.827606
$$147$$ 0 0
$$148$$ −1.00000 −0.0821995
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ 0 0
$$151$$ 14.0000 1.13930 0.569652 0.821886i $$-0.307078\pi$$
0.569652 + 0.821886i $$0.307078\pi$$
$$152$$ 7.00000 0.567775
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 5.00000 0.400320
$$157$$ −11.0000 −0.877896 −0.438948 0.898513i $$-0.644649\pi$$
−0.438948 + 0.898513i $$0.644649\pi$$
$$158$$ 12.0000 0.954669
$$159$$ 9.00000 0.713746
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 24.0000 1.87983 0.939913 0.341415i $$-0.110906\pi$$
0.939913 + 0.341415i $$0.110906\pi$$
$$164$$ 5.00000 0.390434
$$165$$ 0 0
$$166$$ −12.0000 −0.931381
$$167$$ −11.0000 −0.851206 −0.425603 0.904910i $$-0.639938\pi$$
−0.425603 + 0.904910i $$0.639938\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ −7.00000 −0.535303
$$172$$ −12.0000 −0.914991
$$173$$ 13.0000 0.988372 0.494186 0.869356i $$-0.335466\pi$$
0.494186 + 0.869356i $$0.335466\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −5.00000 −0.376889
$$177$$ 4.00000 0.300658
$$178$$ −14.0000 −1.04934
$$179$$ −23.0000 −1.71910 −0.859550 0.511051i $$-0.829256\pi$$
−0.859550 + 0.511051i $$0.829256\pi$$
$$180$$ 0 0
$$181$$ 20.0000 1.48659 0.743294 0.668965i $$-0.233262\pi$$
0.743294 + 0.668965i $$0.233262\pi$$
$$182$$ 0 0
$$183$$ 4.00000 0.295689
$$184$$ 1.00000 0.0737210
$$185$$ 0 0
$$186$$ 2.00000 0.146647
$$187$$ −20.0000 −1.46254
$$188$$ 11.0000 0.802257
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 14.0000 1.01300 0.506502 0.862239i $$-0.330938\pi$$
0.506502 + 0.862239i $$0.330938\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ −10.0000 −0.719816 −0.359908 0.932988i $$-0.617192\pi$$
−0.359908 + 0.932988i $$0.617192\pi$$
$$194$$ −8.00000 −0.574367
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 3.00000 0.213741 0.106871 0.994273i $$-0.465917\pi$$
0.106871 + 0.994273i $$0.465917\pi$$
$$198$$ 5.00000 0.355335
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 0 0
$$201$$ 12.0000 0.846415
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 4.00000 0.280056
$$205$$ 0 0
$$206$$ 8.00000 0.557386
$$207$$ −1.00000 −0.0695048
$$208$$ 5.00000 0.346688
$$209$$ 35.0000 2.42100
$$210$$ 0 0
$$211$$ 17.0000 1.17033 0.585164 0.810915i $$-0.301030\pi$$
0.585164 + 0.810915i $$0.301030\pi$$
$$212$$ 9.00000 0.618123
$$213$$ 2.00000 0.137038
$$214$$ −2.00000 −0.136717
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 2.00000 0.135457
$$219$$ −10.0000 −0.675737
$$220$$ 0 0
$$221$$ 20.0000 1.34535
$$222$$ 1.00000 0.0671156
$$223$$ 12.0000 0.803579 0.401790 0.915732i $$-0.368388\pi$$
0.401790 + 0.915732i $$0.368388\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −14.0000 −0.931266
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ −7.00000 −0.463586
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 14.0000 0.917170 0.458585 0.888650i $$-0.348356\pi$$
0.458585 + 0.888650i $$0.348356\pi$$
$$234$$ −5.00000 −0.326860
$$235$$ 0 0
$$236$$ 4.00000 0.260378
$$237$$ −12.0000 −0.779484
$$238$$ 0 0
$$239$$ −22.0000 −1.42306 −0.711531 0.702655i $$-0.751998\pi$$
−0.711531 + 0.702655i $$0.751998\pi$$
$$240$$ 0 0
$$241$$ 15.0000 0.966235 0.483117 0.875556i $$-0.339504\pi$$
0.483117 + 0.875556i $$0.339504\pi$$
$$242$$ −14.0000 −0.899954
$$243$$ 1.00000 0.0641500
$$244$$ 4.00000 0.256074
$$245$$ 0 0
$$246$$ −5.00000 −0.318788
$$247$$ −35.0000 −2.22700
$$248$$ 2.00000 0.127000
$$249$$ 12.0000 0.760469
$$250$$ 0 0
$$251$$ 1.00000 0.0631194 0.0315597 0.999502i $$-0.489953\pi$$
0.0315597 + 0.999502i $$0.489953\pi$$
$$252$$ 0 0
$$253$$ 5.00000 0.314347
$$254$$ 9.00000 0.564710
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 16.0000 0.998053 0.499026 0.866587i $$-0.333691\pi$$
0.499026 + 0.866587i $$0.333691\pi$$
$$258$$ 12.0000 0.747087
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 9.00000 0.556022
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 5.00000 0.307729
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 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
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 0 0
$$276$$ −1.00000 −0.0601929
$$277$$ −14.0000 −0.841178 −0.420589 0.907251i $$-0.638177\pi$$
−0.420589 + 0.907251i $$0.638177\pi$$
$$278$$ 4.00000 0.239904
$$279$$ −2.00000 −0.119737
$$280$$ 0 0
$$281$$ 7.00000 0.417585 0.208792 0.977960i $$-0.433047\pi$$
0.208792 + 0.977960i $$0.433047\pi$$
$$282$$ −11.0000 −0.655040
$$283$$ 10.0000 0.594438 0.297219 0.954809i $$-0.403941\pi$$
0.297219 + 0.954809i $$0.403941\pi$$
$$284$$ 2.00000 0.118678
$$285$$ 0 0
$$286$$ 25.0000 1.47828
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ −10.0000 −0.585206
$$293$$ −9.00000 −0.525786 −0.262893 0.964825i $$-0.584677\pi$$
−0.262893 + 0.964825i $$0.584677\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 1.00000 0.0581238
$$297$$ −5.00000 −0.290129
$$298$$ −12.0000 −0.695141
$$299$$ −5.00000 −0.289157
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −14.0000 −0.805609
$$303$$ 0 0
$$304$$ −7.00000 −0.401478
$$305$$ 0 0
$$306$$ −4.00000 −0.228665
$$307$$ −8.00000 −0.456584 −0.228292 0.973593i $$-0.573314\pi$$
−0.228292 + 0.973593i $$0.573314\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ 8.00000 0.453638 0.226819 0.973937i $$-0.427167\pi$$
0.226819 + 0.973937i $$0.427167\pi$$
$$312$$ −5.00000 −0.283069
$$313$$ −16.0000 −0.904373 −0.452187 0.891923i $$-0.649356\pi$$
−0.452187 + 0.891923i $$0.649356\pi$$
$$314$$ 11.0000 0.620766
$$315$$ 0 0
$$316$$ −12.0000 −0.675053
$$317$$ 22.0000 1.23564 0.617822 0.786318i $$-0.288015\pi$$
0.617822 + 0.786318i $$0.288015\pi$$
$$318$$ −9.00000 −0.504695
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 2.00000 0.111629
$$322$$ 0 0
$$323$$ −28.0000 −1.55796
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −24.0000 −1.32924
$$327$$ −2.00000 −0.110600
$$328$$ −5.00000 −0.276079
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 31.0000 1.70391 0.851957 0.523612i $$-0.175416\pi$$
0.851957 + 0.523612i $$0.175416\pi$$
$$332$$ 12.0000 0.658586
$$333$$ −1.00000 −0.0547997
$$334$$ 11.0000 0.601893
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 16.0000 0.871576 0.435788 0.900049i $$-0.356470\pi$$
0.435788 + 0.900049i $$0.356470\pi$$
$$338$$ −12.0000 −0.652714
$$339$$ 14.0000 0.760376
$$340$$ 0 0
$$341$$ 10.0000 0.541530
$$342$$ 7.00000 0.378517
$$343$$ 0 0
$$344$$ 12.0000 0.646997
$$345$$ 0 0
$$346$$ −13.0000 −0.698884
$$347$$ 18.0000 0.966291 0.483145 0.875540i $$-0.339494\pi$$
0.483145 + 0.875540i $$0.339494\pi$$
$$348$$ 0 0
$$349$$ −4.00000 −0.214115 −0.107058 0.994253i $$-0.534143\pi$$
−0.107058 + 0.994253i $$0.534143\pi$$
$$350$$ 0 0
$$351$$ 5.00000 0.266880
$$352$$ 5.00000 0.266501
$$353$$ −24.0000 −1.27739 −0.638696 0.769460i $$-0.720526\pi$$
−0.638696 + 0.769460i $$0.720526\pi$$
$$354$$ −4.00000 −0.212598
$$355$$ 0 0
$$356$$ 14.0000 0.741999
$$357$$ 0 0
$$358$$ 23.0000 1.21559
$$359$$ −20.0000 −1.05556 −0.527780 0.849381i $$-0.676975\pi$$
−0.527780 + 0.849381i $$0.676975\pi$$
$$360$$ 0 0
$$361$$ 30.0000 1.57895
$$362$$ −20.0000 −1.05118
$$363$$ 14.0000 0.734809
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −4.00000 −0.209083
$$367$$ −7.00000 −0.365397 −0.182699 0.983169i $$-0.558483\pi$$
−0.182699 + 0.983169i $$0.558483\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ 5.00000 0.260290
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −2.00000 −0.103695
$$373$$ 22.0000 1.13912 0.569558 0.821951i $$-0.307114\pi$$
0.569558 + 0.821951i $$0.307114\pi$$
$$374$$ 20.0000 1.03418
$$375$$ 0 0
$$376$$ −11.0000 −0.567282
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.00000 0.0513665 0.0256833 0.999670i $$-0.491824\pi$$
0.0256833 + 0.999670i $$0.491824\pi$$
$$380$$ 0 0
$$381$$ −9.00000 −0.461084
$$382$$ −14.0000 −0.716302
$$383$$ −21.0000 −1.07305 −0.536525 0.843884i $$-0.680263\pi$$
−0.536525 + 0.843884i $$0.680263\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ 10.0000 0.508987
$$387$$ −12.0000 −0.609994
$$388$$ 8.00000 0.406138
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ 0 0
$$393$$ −9.00000 −0.453990
$$394$$ −3.00000 −0.151138
$$395$$ 0 0
$$396$$ −5.00000 −0.251259
$$397$$ 14.0000 0.702640 0.351320 0.936255i $$-0.385733\pi$$
0.351320 + 0.936255i $$0.385733\pi$$
$$398$$ 4.00000 0.200502
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −21.0000 −1.04869 −0.524345 0.851506i $$-0.675690\pi$$
−0.524345 + 0.851506i $$0.675690\pi$$
$$402$$ −12.0000 −0.598506
$$403$$ −10.0000 −0.498135
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 5.00000 0.247841
$$408$$ −4.00000 −0.198030
$$409$$ 10.0000 0.494468 0.247234 0.968956i $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ 0 0
$$411$$ 2.00000 0.0986527
$$412$$ −8.00000 −0.394132
$$413$$ 0 0
$$414$$ 1.00000 0.0491473
$$415$$ 0 0
$$416$$ −5.00000 −0.245145
$$417$$ −4.00000 −0.195881
$$418$$ −35.0000 −1.71191
$$419$$ 15.0000 0.732798 0.366399 0.930458i $$-0.380591\pi$$
0.366399 + 0.930458i $$0.380591\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ −17.0000 −0.827547
$$423$$ 11.0000 0.534838
$$424$$ −9.00000 −0.437079
$$425$$ 0 0
$$426$$ −2.00000 −0.0969003
$$427$$ 0 0
$$428$$ 2.00000 0.0966736
$$429$$ −25.0000 −1.20701
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −24.0000 −1.15337 −0.576683 0.816968i $$-0.695653\pi$$
−0.576683 + 0.816968i $$0.695653\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −2.00000 −0.0957826
$$437$$ 7.00000 0.334855
$$438$$ 10.0000 0.477818
$$439$$ −40.0000 −1.90910 −0.954548 0.298057i $$-0.903661\pi$$
−0.954548 + 0.298057i $$0.903661\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −20.0000 −0.951303
$$443$$ 28.0000 1.33032 0.665160 0.746701i $$-0.268363\pi$$
0.665160 + 0.746701i $$0.268363\pi$$
$$444$$ −1.00000 −0.0474579
$$445$$ 0 0
$$446$$ −12.0000 −0.568216
$$447$$ 12.0000 0.567581
$$448$$ 0 0
$$449$$ −29.0000 −1.36859 −0.684297 0.729203i $$-0.739891\pi$$
−0.684297 + 0.729203i $$0.739891\pi$$
$$450$$ 0 0
$$451$$ −25.0000 −1.17720
$$452$$ 14.0000 0.658505
$$453$$ 14.0000 0.657777
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ 7.00000 0.327805
$$457$$ 14.0000 0.654892 0.327446 0.944870i $$-0.393812\pi$$
0.327446 + 0.944870i $$0.393812\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 4.00000 0.186704
$$460$$ 0 0
$$461$$ −4.00000 −0.186299 −0.0931493 0.995652i $$-0.529693\pi$$
−0.0931493 + 0.995652i $$0.529693\pi$$
$$462$$ 0 0
$$463$$ 19.0000 0.883005 0.441502 0.897260i $$-0.354446\pi$$
0.441502 + 0.897260i $$0.354446\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −14.0000 −0.648537
$$467$$ 20.0000 0.925490 0.462745 0.886492i $$-0.346865\pi$$
0.462745 + 0.886492i $$0.346865\pi$$
$$468$$ 5.00000 0.231125
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −11.0000 −0.506853
$$472$$ −4.00000 −0.184115
$$473$$ 60.0000 2.75880
$$474$$ 12.0000 0.551178
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 9.00000 0.412082
$$478$$ 22.0000 1.00626
$$479$$ 18.0000 0.822441 0.411220 0.911536i $$-0.365103\pi$$
0.411220 + 0.911536i $$0.365103\pi$$
$$480$$ 0 0
$$481$$ −5.00000 −0.227980
$$482$$ −15.0000 −0.683231
$$483$$ 0 0
$$484$$ 14.0000 0.636364
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ −4.00000 −0.181071
$$489$$ 24.0000 1.08532
$$490$$ 0 0
$$491$$ −36.0000 −1.62466 −0.812329 0.583200i $$-0.801800\pi$$
−0.812329 + 0.583200i $$0.801800\pi$$
$$492$$ 5.00000 0.225417
$$493$$ 0 0
$$494$$ 35.0000 1.57472
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ 0 0
$$498$$ −12.0000 −0.537733
$$499$$ 40.0000 1.79065 0.895323 0.445418i $$-0.146945\pi$$
0.895323 + 0.445418i $$0.146945\pi$$
$$500$$ 0 0
$$501$$ −11.0000 −0.491444
$$502$$ −1.00000 −0.0446322
$$503$$ 20.0000 0.891756 0.445878 0.895094i $$-0.352892\pi$$
0.445878 + 0.895094i $$0.352892\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −5.00000 −0.222277
$$507$$ 12.0000 0.532939
$$508$$ −9.00000 −0.399310
$$509$$ −10.0000 −0.443242 −0.221621 0.975133i $$-0.571135\pi$$
−0.221621 + 0.975133i $$0.571135\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ −7.00000 −0.309058
$$514$$ −16.0000 −0.705730
$$515$$ 0 0
$$516$$ −12.0000 −0.528271
$$517$$ −55.0000 −2.41890
$$518$$ 0 0
$$519$$ 13.0000 0.570637
$$520$$ 0 0
$$521$$ −33.0000 −1.44576 −0.722878 0.690976i $$-0.757181\pi$$
−0.722878 + 0.690976i $$0.757181\pi$$
$$522$$ 0 0
$$523$$ 22.0000 0.961993 0.480996 0.876723i $$-0.340275\pi$$
0.480996 + 0.876723i $$0.340275\pi$$
$$524$$ −9.00000 −0.393167
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −8.00000 −0.348485
$$528$$ −5.00000 −0.217597
$$529$$ −22.0000 −0.956522
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ 25.0000 1.08287
$$534$$ −14.0000 −0.605839
$$535$$ 0 0
$$536$$ −12.0000 −0.518321
$$537$$ −23.0000 −0.992523
$$538$$ 24.0000 1.03471
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 2.00000 0.0859867 0.0429934 0.999075i $$-0.486311\pi$$
0.0429934 + 0.999075i $$0.486311\pi$$
$$542$$ 0 0
$$543$$ 20.0000 0.858282
$$544$$ −4.00000 −0.171499
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −28.0000 −1.19719 −0.598597 0.801050i $$-0.704275\pi$$
−0.598597 + 0.801050i $$0.704275\pi$$
$$548$$ 2.00000 0.0854358
$$549$$ 4.00000 0.170716
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 1.00000 0.0425628
$$553$$ 0 0
$$554$$ 14.0000 0.594803
$$555$$ 0 0
$$556$$ −4.00000 −0.169638
$$557$$ −37.0000 −1.56774 −0.783870 0.620925i $$-0.786757\pi$$
−0.783870 + 0.620925i $$0.786757\pi$$
$$558$$ 2.00000 0.0846668
$$559$$ −60.0000 −2.53773
$$560$$ 0 0
$$561$$ −20.0000 −0.844401
$$562$$ −7.00000 −0.295277
$$563$$ 18.0000 0.758610 0.379305 0.925272i $$-0.376163\pi$$
0.379305 + 0.925272i $$0.376163\pi$$
$$564$$ 11.0000 0.463184
$$565$$ 0 0
$$566$$ −10.0000 −0.420331
$$567$$ 0 0
$$568$$ −2.00000 −0.0839181
$$569$$ 39.0000 1.63497 0.817483 0.575953i $$-0.195369\pi$$
0.817483 + 0.575953i $$0.195369\pi$$
$$570$$ 0 0
$$571$$ 40.0000 1.67395 0.836974 0.547243i $$-0.184323\pi$$
0.836974 + 0.547243i $$0.184323\pi$$
$$572$$ −25.0000 −1.04530
$$573$$ 14.0000 0.584858
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −26.0000 −1.08239 −0.541197 0.840896i $$-0.682029\pi$$
−0.541197 + 0.840896i $$0.682029\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ −10.0000 −0.415586
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −8.00000 −0.331611
$$583$$ −45.0000 −1.86371
$$584$$ 10.0000 0.413803
$$585$$ 0 0
$$586$$ 9.00000 0.371787
$$587$$ 30.0000 1.23823 0.619116 0.785299i $$-0.287491\pi$$
0.619116 + 0.785299i $$0.287491\pi$$
$$588$$ 0 0
$$589$$ 14.0000 0.576860
$$590$$ 0 0
$$591$$ 3.00000 0.123404
$$592$$ −1.00000 −0.0410997
$$593$$ −36.0000 −1.47834 −0.739171 0.673517i $$-0.764783\pi$$
−0.739171 + 0.673517i $$0.764783\pi$$
$$594$$ 5.00000 0.205152
$$595$$ 0 0
$$596$$ 12.0000 0.491539
$$597$$ −4.00000 −0.163709
$$598$$ 5.00000 0.204465
$$599$$ −10.0000 −0.408589 −0.204294 0.978909i $$-0.565490\pi$$
−0.204294 + 0.978909i $$0.565490\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 0 0
$$603$$ 12.0000 0.488678
$$604$$ 14.0000 0.569652
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 27.0000 1.09590 0.547948 0.836512i $$-0.315409\pi$$
0.547948 + 0.836512i $$0.315409\pi$$
$$608$$ 7.00000 0.283887
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 55.0000 2.22506
$$612$$ 4.00000 0.161690
$$613$$ 43.0000 1.73675 0.868377 0.495905i $$-0.165164\pi$$
0.868377 + 0.495905i $$0.165164\pi$$
$$614$$ 8.00000 0.322854
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 8.00000 0.322068 0.161034 0.986949i $$-0.448517\pi$$
0.161034 + 0.986949i $$0.448517\pi$$
$$618$$ 8.00000 0.321807
$$619$$ 25.0000 1.00483 0.502417 0.864625i $$-0.332444\pi$$
0.502417 + 0.864625i $$0.332444\pi$$
$$620$$ 0 0
$$621$$ −1.00000 −0.0401286
$$622$$ −8.00000 −0.320771
$$623$$ 0 0
$$624$$ 5.00000 0.200160
$$625$$ 0 0
$$626$$ 16.0000 0.639489
$$627$$ 35.0000 1.39777
$$628$$ −11.0000 −0.438948
$$629$$ −4.00000 −0.159490
$$630$$ 0 0
$$631$$ 6.00000 0.238856 0.119428 0.992843i $$-0.461894\pi$$
0.119428 + 0.992843i $$0.461894\pi$$
$$632$$ 12.0000 0.477334
$$633$$ 17.0000 0.675689
$$634$$ −22.0000 −0.873732
$$635$$ 0 0
$$636$$ 9.00000 0.356873
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 2.00000 0.0791188
$$640$$ 0 0
$$641$$ 21.0000 0.829450 0.414725 0.909947i $$-0.363878\pi$$
0.414725 + 0.909947i $$0.363878\pi$$
$$642$$ −2.00000 −0.0789337
$$643$$ −34.0000 −1.34083 −0.670415 0.741987i $$-0.733884\pi$$
−0.670415 + 0.741987i $$0.733884\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 28.0000 1.10165
$$647$$ 23.0000 0.904223 0.452112 0.891961i $$-0.350671\pi$$
0.452112 + 0.891961i $$0.350671\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ −20.0000 −0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 24.0000 0.939913
$$653$$ 19.0000 0.743527 0.371764 0.928327i $$-0.378753\pi$$
0.371764 + 0.928327i $$0.378753\pi$$
$$654$$ 2.00000 0.0782062
$$655$$ 0 0
$$656$$ 5.00000 0.195217
$$657$$ −10.0000 −0.390137
$$658$$ 0 0
$$659$$ −20.0000 −0.779089 −0.389545 0.921008i $$-0.627368\pi$$
−0.389545 + 0.921008i $$0.627368\pi$$
$$660$$ 0 0
$$661$$ −40.0000 −1.55582 −0.777910 0.628376i $$-0.783720\pi$$
−0.777910 + 0.628376i $$0.783720\pi$$
$$662$$ −31.0000 −1.20485
$$663$$ 20.0000 0.776736
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ 1.00000 0.0387492
$$667$$ 0 0
$$668$$ −11.0000 −0.425603
$$669$$ 12.0000 0.463947
$$670$$ 0 0
$$671$$ −20.0000 −0.772091
$$672$$ 0 0
$$673$$ 4.00000 0.154189 0.0770943 0.997024i $$-0.475436\pi$$
0.0770943 + 0.997024i $$0.475436\pi$$
$$674$$ −16.0000 −0.616297
$$675$$ 0 0
$$676$$ 12.0000 0.461538
$$677$$ −33.0000 −1.26829 −0.634147 0.773213i $$-0.718648\pi$$
−0.634147 + 0.773213i $$0.718648\pi$$
$$678$$ −14.0000 −0.537667
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ −10.0000 −0.382920
$$683$$ 4.00000 0.153056 0.0765279 0.997067i $$-0.475617\pi$$
0.0765279 + 0.997067i $$0.475617\pi$$
$$684$$ −7.00000 −0.267652
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 10.0000 0.381524
$$688$$ −12.0000 −0.457496
$$689$$ 45.0000 1.71436
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ 13.0000 0.494186
$$693$$ 0 0
$$694$$ −18.0000 −0.683271
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 20.0000 0.757554
$$698$$ 4.00000 0.151402
$$699$$ 14.0000 0.529529
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ −5.00000 −0.188713
$$703$$ 7.00000 0.264010
$$704$$ −5.00000 −0.188445
$$705$$ 0 0
$$706$$ 24.0000 0.903252
$$707$$ 0 0
$$708$$ 4.00000 0.150329
$$709$$ 28.0000 1.05156 0.525781 0.850620i $$-0.323773\pi$$
0.525781 + 0.850620i $$0.323773\pi$$
$$710$$ 0 0
$$711$$ −12.0000 −0.450035
$$712$$ −14.0000 −0.524672
$$713$$ 2.00000 0.0749006
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −23.0000 −0.859550
$$717$$ −22.0000 −0.821605
$$718$$ 20.0000 0.746393
$$719$$ −6.00000 −0.223762 −0.111881 0.993722i $$-0.535688\pi$$
−0.111881 + 0.993722i $$0.535688\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −30.0000 −1.11648
$$723$$ 15.0000 0.557856
$$724$$ 20.0000 0.743294
$$725$$ 0 0
$$726$$ −14.0000 −0.519589
$$727$$ 3.00000 0.111264 0.0556319 0.998451i $$-0.482283\pi$$
0.0556319 + 0.998451i $$0.482283\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −48.0000 −1.77534
$$732$$ 4.00000 0.147844
$$733$$ −9.00000 −0.332423 −0.166211 0.986090i $$-0.553153\pi$$
−0.166211 + 0.986090i $$0.553153\pi$$
$$734$$ 7.00000 0.258375
$$735$$ 0 0
$$736$$ 1.00000 0.0368605
$$737$$ −60.0000 −2.21013
$$738$$ −5.00000 −0.184053
$$739$$ −15.0000 −0.551784 −0.275892 0.961189i $$-0.588973\pi$$
−0.275892 + 0.961189i $$0.588973\pi$$
$$740$$ 0 0
$$741$$ −35.0000 −1.28576
$$742$$ 0 0
$$743$$ −15.0000 −0.550297 −0.275148 0.961402i $$-0.588727\pi$$
−0.275148 + 0.961402i $$0.588727\pi$$
$$744$$ 2.00000 0.0733236
$$745$$ 0 0
$$746$$ −22.0000 −0.805477
$$747$$ 12.0000 0.439057
$$748$$ −20.0000 −0.731272
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −50.0000 −1.82453 −0.912263 0.409605i $$-0.865667\pi$$
−0.912263 + 0.409605i $$0.865667\pi$$
$$752$$ 11.0000 0.401129
$$753$$ 1.00000 0.0364420
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 34.0000 1.23575 0.617876 0.786276i $$-0.287994\pi$$
0.617876 + 0.786276i $$0.287994\pi$$
$$758$$ −1.00000 −0.0363216
$$759$$ 5.00000 0.181489
$$760$$ 0 0
$$761$$ −37.0000 −1.34125 −0.670624 0.741797i $$-0.733974\pi$$
−0.670624 + 0.741797i $$0.733974\pi$$
$$762$$ 9.00000 0.326036
$$763$$ 0 0
$$764$$ 14.0000 0.506502
$$765$$ 0 0
$$766$$ 21.0000 0.758761
$$767$$ 20.0000 0.722158
$$768$$ 1.00000 0.0360844
$$769$$ −5.00000 −0.180305 −0.0901523 0.995928i $$-0.528735\pi$$
−0.0901523 + 0.995928i $$0.528735\pi$$
$$770$$ 0 0
$$771$$ 16.0000 0.576226
$$772$$ −10.0000 −0.359908
$$773$$ 5.00000 0.179838 0.0899188 0.995949i $$-0.471339\pi$$
0.0899188 + 0.995949i $$0.471339\pi$$
$$774$$ 12.0000 0.431331
$$775$$ 0 0
$$776$$ −8.00000 −0.287183
$$777$$ 0 0
$$778$$ −18.0000 −0.645331
$$779$$ −35.0000 −1.25401
$$780$$ 0 0
$$781$$ −10.0000 −0.357828
$$782$$ 4.00000 0.143040
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 9.00000 0.321019
$$787$$ −2.00000 −0.0712923 −0.0356462 0.999364i $$-0.511349\pi$$
−0.0356462 + 0.999364i $$0.511349\pi$$
$$788$$ 3.00000 0.106871
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 5.00000 0.177667
$$793$$ 20.0000 0.710221
$$794$$ −14.0000 −0.496841
$$795$$ 0 0
$$796$$ −4.00000 −0.141776
$$797$$ 54.0000 1.91278 0.956389 0.292096i $$-0.0943526\pi$$
0.956389 + 0.292096i $$0.0943526\pi$$
$$798$$ 0 0
$$799$$ 44.0000 1.55661
$$800$$ 0 0
$$801$$ 14.0000 0.494666
$$802$$ 21.0000 0.741536
$$803$$ 50.0000 1.76446
$$804$$ 12.0000 0.423207
$$805$$ 0 0
$$806$$ 10.0000 0.352235
$$807$$ −24.0000 −0.844840
$$808$$ 0 0
$$809$$ 25.0000 0.878953 0.439477 0.898254i $$-0.355164\pi$$
0.439477 + 0.898254i $$0.355164\pi$$
$$810$$ 0 0
$$811$$ 21.0000 0.737410 0.368705 0.929547i $$-0.379801\pi$$
0.368705 + 0.929547i $$0.379801\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ −5.00000 −0.175250
$$815$$ 0 0
$$816$$ 4.00000 0.140028
$$817$$ 84.0000 2.93879
$$818$$ −10.0000 −0.349642
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 10.0000 0.349002 0.174501 0.984657i $$-0.444169\pi$$
0.174501 + 0.984657i $$0.444169\pi$$
$$822$$ −2.00000 −0.0697580
$$823$$ −40.0000 −1.39431 −0.697156 0.716919i $$-0.745552\pi$$
−0.697156 + 0.716919i $$0.745552\pi$$
$$824$$ 8.00000 0.278693
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 6.00000 0.208640 0.104320 0.994544i $$-0.466733\pi$$
0.104320 + 0.994544i $$0.466733\pi$$
$$828$$ −1.00000 −0.0347524
$$829$$ −52.0000 −1.80603 −0.903017 0.429604i $$-0.858653\pi$$
−0.903017 + 0.429604i $$0.858653\pi$$
$$830$$ 0 0
$$831$$ −14.0000 −0.485655
$$832$$ 5.00000 0.173344
$$833$$ 0 0
$$834$$ 4.00000 0.138509
$$835$$ 0 0
$$836$$ 35.0000 1.21050
$$837$$ −2.00000 −0.0691301
$$838$$ −15.0000 −0.518166
$$839$$ 12.0000 0.414286 0.207143 0.978311i $$-0.433583\pi$$
0.207143 + 0.978311i $$0.433583\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ −10.0000 −0.344623
$$843$$ 7.00000 0.241093
$$844$$ 17.0000 0.585164
$$845$$ 0 0
$$846$$ −11.0000 −0.378188
$$847$$ 0 0
$$848$$ 9.00000 0.309061
$$849$$ 10.0000 0.343199
$$850$$ 0 0
$$851$$ 1.00000 0.0342796
$$852$$ 2.00000 0.0685189
$$853$$ 11.0000 0.376633 0.188316 0.982108i $$-0.439697\pi$$
0.188316 + 0.982108i $$0.439697\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −2.00000 −0.0683586
$$857$$ −2.00000 −0.0683187 −0.0341593 0.999416i $$-0.510875\pi$$
−0.0341593 + 0.999416i $$0.510875\pi$$
$$858$$ 25.0000 0.853486
$$859$$ −4.00000 −0.136478 −0.0682391 0.997669i $$-0.521738\pi$$
−0.0682391 + 0.997669i $$0.521738\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −12.0000 −0.408722
$$863$$ −45.0000 −1.53182 −0.765909 0.642949i $$-0.777711\pi$$
−0.765909 + 0.642949i $$0.777711\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ 24.0000 0.815553
$$867$$ −1.00000 −0.0339618
$$868$$ 0 0
$$869$$ 60.0000 2.03536
$$870$$ 0 0
$$871$$ 60.0000 2.03302
$$872$$ 2.00000 0.0677285
$$873$$ 8.00000 0.270759
$$874$$ −7.00000 −0.236779
$$875$$ 0 0
$$876$$ −10.0000 −0.337869
$$877$$ 37.0000 1.24940 0.624701 0.780864i $$-0.285221\pi$$
0.624701 + 0.780864i $$0.285221\pi$$
$$878$$ 40.0000 1.34993
$$879$$ −9.00000 −0.303562
$$880$$ 0 0
$$881$$ 3.00000 0.101073 0.0505363 0.998722i $$-0.483907\pi$$
0.0505363 + 0.998722i $$0.483907\pi$$
$$882$$ 0 0
$$883$$ 50.0000 1.68263 0.841317 0.540542i $$-0.181781\pi$$
0.841317 + 0.540542i $$0.181781\pi$$
$$884$$ 20.0000 0.672673
$$885$$ 0 0
$$886$$ −28.0000 −0.940678
$$887$$ 44.0000 1.47738 0.738688 0.674048i $$-0.235446\pi$$
0.738688 + 0.674048i $$0.235446\pi$$
$$888$$ 1.00000 0.0335578
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −5.00000 −0.167506
$$892$$ 12.0000 0.401790
$$893$$ −77.0000 −2.57671
$$894$$ −12.0000 −0.401340
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −5.00000 −0.166945
$$898$$ 29.0000 0.967743
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 36.0000 1.19933
$$902$$ 25.0000 0.832409
$$903$$ 0 0
$$904$$ −14.0000 −0.465633
$$905$$ 0 0
$$906$$ −14.0000 −0.465119
$$907$$ 18.0000 0.597680 0.298840 0.954303i $$-0.403400\pi$$
0.298840 + 0.954303i $$0.403400\pi$$
$$908$$ 12.0000 0.398234
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 30.0000 0.993944 0.496972 0.867766i $$-0.334445\pi$$
0.496972 + 0.867766i $$0.334445\pi$$
$$912$$ −7.00000 −0.231793
$$913$$ −60.0000 −1.98571
$$914$$ −14.0000 −0.463079
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ 0 0
$$918$$ −4.00000 −0.132020
$$919$$ 28.0000 0.923635 0.461817 0.886975i $$-0.347198\pi$$
0.461817 + 0.886975i $$0.347198\pi$$
$$920$$ 0 0
$$921$$ −8.00000 −0.263609
$$922$$ 4.00000 0.131733
$$923$$ 10.0000 0.329154
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −19.0000 −0.624379
$$927$$ −8.00000 −0.262754
$$928$$ 0 0
$$929$$ 19.0000 0.623370 0.311685 0.950186i $$-0.399107\pi$$
0.311685 + 0.950186i $$0.399107\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 14.0000 0.458585
$$933$$ 8.00000 0.261908
$$934$$ −20.0000 −0.654420
$$935$$ 0 0
$$936$$ −5.00000 −0.163430
$$937$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$938$$ 0 0
$$939$$ −16.0000 −0.522140
$$940$$ 0 0
$$941$$ −6.00000 −0.195594 −0.0977972 0.995206i $$-0.531180\pi$$
−0.0977972 + 0.995206i $$0.531180\pi$$
$$942$$ 11.0000 0.358399
$$943$$ −5.00000 −0.162822
$$944$$ 4.00000 0.130189
$$945$$ 0 0
$$946$$ −60.0000 −1.95077
$$947$$ 42.0000 1.36482 0.682408 0.730971i $$-0.260933\pi$$
0.682408 + 0.730971i $$0.260933\pi$$
$$948$$ −12.0000 −0.389742
$$949$$ −50.0000 −1.62307
$$950$$ 0 0
$$951$$ 22.0000 0.713399
$$952$$ 0 0
$$953$$ −12.0000 −0.388718 −0.194359 0.980930i $$-0.562263\pi$$
−0.194359 + 0.980930i $$0.562263\pi$$
$$954$$ −9.00000 −0.291386
$$955$$ 0 0
$$956$$ −22.0000 −0.711531
$$957$$ 0 0
$$958$$ −18.0000 −0.581554
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 5.00000 0.161206
$$963$$ 2.00000 0.0644491
$$964$$ 15.0000 0.483117
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −4.00000 −0.128631 −0.0643157 0.997930i $$-0.520486\pi$$
−0.0643157 + 0.997930i $$0.520486\pi$$
$$968$$ −14.0000 −0.449977
$$969$$ −28.0000 −0.899490
$$970$$ 0 0
$$971$$ 15.0000 0.481373 0.240686 0.970603i $$-0.422627\pi$$
0.240686 + 0.970603i $$0.422627\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 4.00000 0.128037
$$977$$ 30.0000 0.959785 0.479893 0.877327i $$-0.340676\pi$$
0.479893 + 0.877327i $$0.340676\pi$$
$$978$$ −24.0000 −0.767435
$$979$$ −70.0000 −2.23721
$$980$$ 0 0
$$981$$ −2.00000 −0.0638551
$$982$$ 36.0000 1.14881
$$983$$ 25.0000 0.797376 0.398688 0.917087i $$-0.369466\pi$$
0.398688 + 0.917087i $$0.369466\pi$$
$$984$$ −5.00000 −0.159394
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −35.0000 −1.11350
$$989$$ 12.0000 0.381578
$$990$$ 0 0
$$991$$ −38.0000 −1.20711 −0.603555 0.797321i $$-0.706250\pi$$
−0.603555 + 0.797321i $$0.706250\pi$$
$$992$$ 2.00000 0.0635001
$$993$$ 31.0000 0.983755
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 12.0000 0.380235
$$997$$ 22.0000 0.696747 0.348373 0.937356i $$-0.386734\pi$$
0.348373 + 0.937356i $$0.386734\pi$$
$$998$$ −40.0000 −1.26618
$$999$$ −1.00000 −0.0316386
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 7350.2.a.u.1.1 1
5.4 even 2 1470.2.a.l.1.1 1
7.2 even 3 1050.2.i.p.151.1 2
7.4 even 3 1050.2.i.p.751.1 2
7.6 odd 2 7350.2.a.a.1.1 1
15.14 odd 2 4410.2.a.j.1.1 1
35.2 odd 12 1050.2.o.g.949.1 4
35.4 even 6 210.2.i.b.121.1 2
35.9 even 6 210.2.i.b.151.1 yes 2
35.18 odd 12 1050.2.o.g.499.1 4
35.19 odd 6 1470.2.i.e.361.1 2
35.23 odd 12 1050.2.o.g.949.2 4
35.24 odd 6 1470.2.i.e.961.1 2
35.32 odd 12 1050.2.o.g.499.2 4
35.34 odd 2 1470.2.a.o.1.1 1
105.44 odd 6 630.2.k.g.361.1 2
105.74 odd 6 630.2.k.g.541.1 2
105.104 even 2 4410.2.a.u.1.1 1
140.39 odd 6 1680.2.bg.d.961.1 2
140.79 odd 6 1680.2.bg.d.1201.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.i.b.121.1 2 35.4 even 6
210.2.i.b.151.1 yes 2 35.9 even 6
630.2.k.g.361.1 2 105.44 odd 6
630.2.k.g.541.1 2 105.74 odd 6
1050.2.i.p.151.1 2 7.2 even 3
1050.2.i.p.751.1 2 7.4 even 3
1050.2.o.g.499.1 4 35.18 odd 12
1050.2.o.g.499.2 4 35.32 odd 12
1050.2.o.g.949.1 4 35.2 odd 12
1050.2.o.g.949.2 4 35.23 odd 12
1470.2.a.l.1.1 1 5.4 even 2
1470.2.a.o.1.1 1 35.34 odd 2
1470.2.i.e.361.1 2 35.19 odd 6
1470.2.i.e.961.1 2 35.24 odd 6
1680.2.bg.d.961.1 2 140.39 odd 6
1680.2.bg.d.1201.1 2 140.79 odd 6
4410.2.a.j.1.1 1 15.14 odd 2
4410.2.a.u.1.1 1 105.104 even 2
7350.2.a.a.1.1 1 7.6 odd 2
7350.2.a.u.1.1 1 1.1 even 1 trivial