# Properties

 Label 7350.2.a.r.1.1 Level $7350$ Weight $2$ Character 7350.1 Self dual yes Analytic conductor $58.690$ Analytic rank $1$ 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: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1050) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +6.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} -6.00000 q^{22} -3.00000 q^{23} +1.00000 q^{24} -1.00000 q^{26} -1.00000 q^{27} +3.00000 q^{29} -5.00000 q^{31} -1.00000 q^{32} -6.00000 q^{33} +3.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} -4.00000 q^{38} -1.00000 q^{39} -9.00000 q^{41} -1.00000 q^{43} +6.00000 q^{44} +3.00000 q^{46} -1.00000 q^{48} +3.00000 q^{51} +1.00000 q^{52} +9.00000 q^{53} +1.00000 q^{54} -4.00000 q^{57} -3.00000 q^{58} -9.00000 q^{59} -11.0000 q^{61} +5.00000 q^{62} +1.00000 q^{64} +6.00000 q^{66} -4.00000 q^{67} -3.00000 q^{68} +3.00000 q^{69} -12.0000 q^{71} -1.00000 q^{72} +10.0000 q^{73} +10.0000 q^{74} +4.00000 q^{76} +1.00000 q^{78} -10.0000 q^{79} +1.00000 q^{81} +9.00000 q^{82} -9.00000 q^{83} +1.00000 q^{86} -3.00000 q^{87} -6.00000 q^{88} +6.00000 q^{89} -3.00000 q^{92} +5.00000 q^{93} +1.00000 q^{96} -14.0000 q^{97} +6.00000 q^{99} +O(q^{100})$$

## 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
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −3.00000 −0.727607 −0.363803 0.931476i $$-0.618522\pi$$
−0.363803 + 0.931476i $$0.618522\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −6.00000 −1.27920
$$23$$ −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
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 3.00000 0.557086 0.278543 0.960424i $$-0.410149\pi$$
0.278543 + 0.960424i $$0.410149\pi$$
$$30$$ 0 0
$$31$$ −5.00000 −0.898027 −0.449013 0.893525i $$-0.648224\pi$$
−0.449013 + 0.893525i $$0.648224\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ −6.00000 −1.04447
$$34$$ 3.00000 0.514496
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ −9.00000 −1.40556 −0.702782 0.711405i $$-0.748059\pi$$
−0.702782 + 0.711405i $$0.748059\pi$$
$$42$$ 0 0
$$43$$ −1.00000 −0.152499 −0.0762493 0.997089i $$-0.524294\pi$$
−0.0762493 + 0.997089i $$0.524294\pi$$
$$44$$ 6.00000 0.904534
$$45$$ 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
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 3.00000 0.420084
$$52$$ 1.00000 0.138675
$$53$$ 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
$$57$$ −4.00000 −0.529813
$$58$$ −3.00000 −0.393919
$$59$$ −9.00000 −1.17170 −0.585850 0.810419i $$-0.699239\pi$$
−0.585850 + 0.810419i $$0.699239\pi$$
$$60$$ 0 0
$$61$$ −11.0000 −1.40841 −0.704203 0.709999i $$-0.748695\pi$$
−0.704203 + 0.709999i $$0.748695\pi$$
$$62$$ 5.00000 0.635001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 6.00000 0.738549
$$67$$ −4.00000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ −3.00000 −0.363803
$$69$$ 3.00000 0.361158
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ 10.0000 1.17041 0.585206 0.810885i $$-0.301014\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ 10.0000 1.16248
$$75$$ 0 0
$$76$$ 4.00000 0.458831
$$77$$ 0 0
$$78$$ 1.00000 0.113228
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 9.00000 0.993884
$$83$$ −9.00000 −0.987878 −0.493939 0.869496i $$-0.664443\pi$$
−0.493939 + 0.869496i $$0.664443\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.00000 0.107833
$$87$$ −3.00000 −0.321634
$$88$$ −6.00000 −0.639602
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −3.00000 −0.312772
$$93$$ 5.00000 0.518476
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ 6.00000 0.603023
$$100$$ 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
$$103$$ −17.0000 −1.67506 −0.837530 0.546392i $$-0.816001\pi$$
−0.837530 + 0.546392i $$0.816001\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ −9.00000 −0.874157
$$107$$ 18.0000 1.74013 0.870063 0.492941i $$-0.164078\pi$$
0.870063 + 0.492941i $$0.164078\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ 8.00000 0.766261 0.383131 0.923694i $$-0.374846\pi$$
0.383131 + 0.923694i $$0.374846\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 4.00000 0.374634
$$115$$ 0 0
$$116$$ 3.00000 0.278543
$$117$$ 1.00000 0.0924500
$$118$$ 9.00000 0.828517
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 11.0000 0.995893
$$123$$ 9.00000 0.811503
$$124$$ −5.00000 −0.449013
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −10.0000 −0.887357 −0.443678 0.896186i $$-0.646327\pi$$
−0.443678 + 0.896186i $$0.646327\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 1.00000 0.0880451
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ −6.00000 −0.522233
$$133$$ 0 0
$$134$$ 4.00000 0.345547
$$135$$ 0 0
$$136$$ 3.00000 0.257248
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ −3.00000 −0.255377
$$139$$ 16.0000 1.35710 0.678551 0.734553i $$-0.262608\pi$$
0.678551 + 0.734553i $$0.262608\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 12.0000 1.00702
$$143$$ 6.00000 0.501745
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −10.0000 −0.827606
$$147$$ 0 0
$$148$$ −10.0000 −0.821995
$$149$$ −9.00000 −0.737309 −0.368654 0.929567i $$-0.620181\pi$$
−0.368654 + 0.929567i $$0.620181\pi$$
$$150$$ 0 0
$$151$$ 2.00000 0.162758 0.0813788 0.996683i $$-0.474068\pi$$
0.0813788 + 0.996683i $$0.474068\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ −3.00000 −0.242536
$$154$$ 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 $$0.369342\pi$$
$$158$$ 10.0000 0.795557
$$159$$ −9.00000 −0.713746
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 5.00000 0.391630 0.195815 0.980641i $$-0.437265\pi$$
0.195815 + 0.980641i $$0.437265\pi$$
$$164$$ −9.00000 −0.702782
$$165$$ 0 0
$$166$$ 9.00000 0.698535
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ −1.00000 −0.0762493
$$173$$ 12.0000 0.912343 0.456172 0.889892i $$-0.349220\pi$$
0.456172 + 0.889892i $$0.349220\pi$$
$$174$$ 3.00000 0.227429
$$175$$ 0 0
$$176$$ 6.00000 0.452267
$$177$$ 9.00000 0.676481
$$178$$ −6.00000 −0.449719
$$179$$ 18.0000 1.34538 0.672692 0.739923i $$-0.265138\pi$$
0.672692 + 0.739923i $$0.265138\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 11.0000 0.813143
$$184$$ 3.00000 0.221163
$$185$$ 0 0
$$186$$ −5.00000 −0.366618
$$187$$ −18.0000 −1.31629
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −15.0000 −1.08536 −0.542681 0.839939i $$-0.682591\pi$$
−0.542681 + 0.839939i $$0.682591\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ −22.0000 −1.58359 −0.791797 0.610784i $$-0.790854\pi$$
−0.791797 + 0.610784i $$0.790854\pi$$
$$194$$ 14.0000 1.00514
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −15.0000 −1.06871 −0.534353 0.845262i $$-0.679445\pi$$
−0.534353 + 0.845262i $$0.679445\pi$$
$$198$$ −6.00000 −0.426401
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ 4.00000 0.282138
$$202$$ −12.0000 −0.844317
$$203$$ 0 0
$$204$$ 3.00000 0.210042
$$205$$ 0 0
$$206$$ 17.0000 1.18445
$$207$$ −3.00000 −0.208514
$$208$$ 1.00000 0.0693375
$$209$$ 24.0000 1.66011
$$210$$ 0 0
$$211$$ −25.0000 −1.72107 −0.860535 0.509390i $$-0.829871\pi$$
−0.860535 + 0.509390i $$0.829871\pi$$
$$212$$ 9.00000 0.618123
$$213$$ 12.0000 0.822226
$$214$$ −18.0000 −1.23045
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ −8.00000 −0.541828
$$219$$ −10.0000 −0.675737
$$220$$ 0 0
$$221$$ −3.00000 −0.201802
$$222$$ −10.0000 −0.671156
$$223$$ 19.0000 1.27233 0.636167 0.771551i $$-0.280519\pi$$
0.636167 + 0.771551i $$0.280519\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 6.00000 0.399114
$$227$$ −3.00000 −0.199117 −0.0995585 0.995032i $$-0.531743\pi$$
−0.0995585 + 0.995032i $$0.531743\pi$$
$$228$$ −4.00000 −0.264906
$$229$$ 22.0000 1.45380 0.726900 0.686743i $$-0.240960\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −3.00000 −0.196960
$$233$$ 12.0000 0.786146 0.393073 0.919507i $$-0.371412\pi$$
0.393073 + 0.919507i $$0.371412\pi$$
$$234$$ −1.00000 −0.0653720
$$235$$ 0 0
$$236$$ −9.00000 −0.585850
$$237$$ 10.0000 0.649570
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −2.00000 −0.128831 −0.0644157 0.997923i $$-0.520518\pi$$
−0.0644157 + 0.997923i $$0.520518\pi$$
$$242$$ −25.0000 −1.60706
$$243$$ −1.00000 −0.0641500
$$244$$ −11.0000 −0.704203
$$245$$ 0 0
$$246$$ −9.00000 −0.573819
$$247$$ 4.00000 0.254514
$$248$$ 5.00000 0.317500
$$249$$ 9.00000 0.570352
$$250$$ 0 0
$$251$$ 27.0000 1.70422 0.852112 0.523359i $$-0.175321\pi$$
0.852112 + 0.523359i $$0.175321\pi$$
$$252$$ 0 0
$$253$$ −18.0000 −1.13165
$$254$$ 10.0000 0.627456
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −15.0000 −0.935674 −0.467837 0.883815i $$-0.654967\pi$$
−0.467837 + 0.883815i $$0.654967\pi$$
$$258$$ −1.00000 −0.0622573
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 3.00000 0.185695
$$262$$ 0 0
$$263$$ 9.00000 0.554964 0.277482 0.960731i $$-0.410500\pi$$
0.277482 + 0.960731i $$0.410500\pi$$
$$264$$ 6.00000 0.369274
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ −4.00000 −0.244339
$$269$$ 18.0000 1.09748 0.548740 0.835993i $$-0.315108\pi$$
0.548740 + 0.835993i $$0.315108\pi$$
$$270$$ 0 0
$$271$$ −20.0000 −1.21491 −0.607457 0.794353i $$-0.707810\pi$$
−0.607457 + 0.794353i $$0.707810\pi$$
$$272$$ −3.00000 −0.181902
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 3.00000 0.180579
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ −5.00000 −0.299342
$$280$$ 0 0
$$281$$ −24.0000 −1.43172 −0.715860 0.698244i $$-0.753965\pi$$
−0.715860 + 0.698244i $$0.753965\pi$$
$$282$$ 0 0
$$283$$ 4.00000 0.237775 0.118888 0.992908i $$-0.462067\pi$$
0.118888 + 0.992908i $$0.462067\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ 0 0
$$286$$ −6.00000 −0.354787
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 14.0000 0.820695
$$292$$ 10.0000 0.585206
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 10.0000 0.581238
$$297$$ −6.00000 −0.348155
$$298$$ 9.00000 0.521356
$$299$$ −3.00000 −0.173494
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −2.00000 −0.115087
$$303$$ −12.0000 −0.689382
$$304$$ 4.00000 0.229416
$$305$$ 0 0
$$306$$ 3.00000 0.171499
$$307$$ −2.00000 −0.114146 −0.0570730 0.998370i $$-0.518177\pi$$
−0.0570730 + 0.998370i $$0.518177\pi$$
$$308$$ 0 0
$$309$$ 17.0000 0.967096
$$310$$ 0 0
$$311$$ 18.0000 1.02069 0.510343 0.859971i $$-0.329518\pi$$
0.510343 + 0.859971i $$0.329518\pi$$
$$312$$ 1.00000 0.0566139
$$313$$ 10.0000 0.565233 0.282617 0.959233i $$-0.408798\pi$$
0.282617 + 0.959233i $$0.408798\pi$$
$$314$$ −10.0000 −0.564333
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ −27.0000 −1.51647 −0.758236 0.651981i $$-0.773938\pi$$
−0.758236 + 0.651981i $$0.773938\pi$$
$$318$$ 9.00000 0.504695
$$319$$ 18.0000 1.00781
$$320$$ 0 0
$$321$$ −18.0000 −1.00466
$$322$$ 0 0
$$323$$ −12.0000 −0.667698
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −5.00000 −0.276924
$$327$$ −8.00000 −0.442401
$$328$$ 9.00000 0.496942
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −19.0000 −1.04433 −0.522167 0.852843i $$-0.674876\pi$$
−0.522167 + 0.852843i $$0.674876\pi$$
$$332$$ −9.00000 −0.493939
$$333$$ −10.0000 −0.547997
$$334$$ 18.0000 0.984916
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −13.0000 −0.708155 −0.354078 0.935216i $$-0.615205\pi$$
−0.354078 + 0.935216i $$0.615205\pi$$
$$338$$ 12.0000 0.652714
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ −30.0000 −1.62459
$$342$$ −4.00000 −0.216295
$$343$$ 0 0
$$344$$ 1.00000 0.0539164
$$345$$ 0 0
$$346$$ −12.0000 −0.645124
$$347$$ 18.0000 0.966291 0.483145 0.875540i $$-0.339494\pi$$
0.483145 + 0.875540i $$0.339494\pi$$
$$348$$ −3.00000 −0.160817
$$349$$ −17.0000 −0.909989 −0.454995 0.890494i $$-0.650359\pi$$
−0.454995 + 0.890494i $$0.650359\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −0.0533761
$$352$$ −6.00000 −0.319801
$$353$$ 30.0000 1.59674 0.798369 0.602168i $$-0.205696\pi$$
0.798369 + 0.602168i $$0.205696\pi$$
$$354$$ −9.00000 −0.478345
$$355$$ 0 0
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −18.0000 −0.951330
$$359$$ −3.00000 −0.158334 −0.0791670 0.996861i $$-0.525226\pi$$
−0.0791670 + 0.996861i $$0.525226\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 2.00000 0.105118
$$363$$ −25.0000 −1.31216
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −11.0000 −0.574979
$$367$$ 37.0000 1.93138 0.965692 0.259690i $$-0.0836203\pi$$
0.965692 + 0.259690i $$0.0836203\pi$$
$$368$$ −3.00000 −0.156386
$$369$$ −9.00000 −0.468521
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 5.00000 0.259238
$$373$$ 8.00000 0.414224 0.207112 0.978317i $$-0.433593\pi$$
0.207112 + 0.978317i $$0.433593\pi$$
$$374$$ 18.0000 0.930758
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3.00000 0.154508
$$378$$ 0 0
$$379$$ 35.0000 1.79783 0.898915 0.438124i $$-0.144357\pi$$
0.898915 + 0.438124i $$0.144357\pi$$
$$380$$ 0 0
$$381$$ 10.0000 0.512316
$$382$$ 15.0000 0.767467
$$383$$ 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
$$387$$ −1.00000 −0.0508329
$$388$$ −14.0000 −0.710742
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 15.0000 0.755689
$$395$$ 0 0
$$396$$ 6.00000 0.301511
$$397$$ −29.0000 −1.45547 −0.727734 0.685859i $$-0.759427\pi$$
−0.727734 + 0.685859i $$0.759427\pi$$
$$398$$ 8.00000 0.401004
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −12.0000 −0.599251 −0.299626 0.954057i $$-0.596862\pi$$
−0.299626 + 0.954057i $$0.596862\pi$$
$$402$$ −4.00000 −0.199502
$$403$$ −5.00000 −0.249068
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −60.0000 −2.97409
$$408$$ −3.00000 −0.148522
$$409$$ −38.0000 −1.87898 −0.939490 0.342578i $$-0.888700\pi$$
−0.939490 + 0.342578i $$0.888700\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −17.0000 −0.837530
$$413$$ 0 0
$$414$$ 3.00000 0.147442
$$415$$ 0 0
$$416$$ −1.00000 −0.0490290
$$417$$ −16.0000 −0.783523
$$418$$ −24.0000 −1.17388
$$419$$ 21.0000 1.02592 0.512959 0.858413i $$-0.328549\pi$$
0.512959 + 0.858413i $$0.328549\pi$$
$$420$$ 0 0
$$421$$ −34.0000 −1.65706 −0.828529 0.559946i $$-0.810822\pi$$
−0.828529 + 0.559946i $$0.810822\pi$$
$$422$$ 25.0000 1.21698
$$423$$ 0 0
$$424$$ −9.00000 −0.437079
$$425$$ 0 0
$$426$$ −12.0000 −0.581402
$$427$$ 0 0
$$428$$ 18.0000 0.870063
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ −15.0000 −0.722525 −0.361262 0.932464i $$-0.617654\pi$$
−0.361262 + 0.932464i $$0.617654\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ −38.0000 −1.82616 −0.913082 0.407777i $$-0.866304\pi$$
−0.913082 + 0.407777i $$0.866304\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 8.00000 0.383131
$$437$$ −12.0000 −0.574038
$$438$$ 10.0000 0.477818
$$439$$ −41.0000 −1.95682 −0.978412 0.206666i $$-0.933739\pi$$
−0.978412 + 0.206666i $$0.933739\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 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
$$446$$ −19.0000 −0.899676
$$447$$ 9.00000 0.425685
$$448$$ 0 0
$$449$$ 24.0000 1.13263 0.566315 0.824189i $$-0.308369\pi$$
0.566315 + 0.824189i $$0.308369\pi$$
$$450$$ 0 0
$$451$$ −54.0000 −2.54276
$$452$$ −6.00000 −0.282216
$$453$$ −2.00000 −0.0939682
$$454$$ 3.00000 0.140797
$$455$$ 0 0
$$456$$ 4.00000 0.187317
$$457$$ −25.0000 −1.16945 −0.584725 0.811231i $$-0.698798\pi$$
−0.584725 + 0.811231i $$0.698798\pi$$
$$458$$ −22.0000 −1.02799
$$459$$ 3.00000 0.140028
$$460$$ 0 0
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ 32.0000 1.48717 0.743583 0.668644i $$-0.233125\pi$$
0.743583 + 0.668644i $$0.233125\pi$$
$$464$$ 3.00000 0.139272
$$465$$ 0 0
$$466$$ −12.0000 −0.555889
$$467$$ 3.00000 0.138823 0.0694117 0.997588i $$-0.477888\pi$$
0.0694117 + 0.997588i $$0.477888\pi$$
$$468$$ 1.00000 0.0462250
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −10.0000 −0.460776
$$472$$ 9.00000 0.414259
$$473$$ −6.00000 −0.275880
$$474$$ −10.0000 −0.459315
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 9.00000 0.412082
$$478$$ 0 0
$$479$$ −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
$$482$$ 2.00000 0.0910975
$$483$$ 0 0
$$484$$ 25.0000 1.13636
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ 2.00000 0.0906287 0.0453143 0.998973i $$-0.485571\pi$$
0.0453143 + 0.998973i $$0.485571\pi$$
$$488$$ 11.0000 0.497947
$$489$$ −5.00000 −0.226108
$$490$$ 0 0
$$491$$ 42.0000 1.89543 0.947717 0.319113i $$-0.103385\pi$$
0.947717 + 0.319113i $$0.103385\pi$$
$$492$$ 9.00000 0.405751
$$493$$ −9.00000 −0.405340
$$494$$ −4.00000 −0.179969
$$495$$ 0 0
$$496$$ −5.00000 −0.224507
$$497$$ 0 0
$$498$$ −9.00000 −0.403300
$$499$$ −19.0000 −0.850557 −0.425278 0.905063i $$-0.639824\pi$$
−0.425278 + 0.905063i $$0.639824\pi$$
$$500$$ 0 0
$$501$$ 18.0000 0.804181
$$502$$ −27.0000 −1.20507
$$503$$ −6.00000 −0.267527 −0.133763 0.991013i $$-0.542706\pi$$
−0.133763 + 0.991013i $$0.542706\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 18.0000 0.800198
$$507$$ 12.0000 0.532939
$$508$$ −10.0000 −0.443678
$$509$$ 24.0000 1.06378 0.531891 0.846813i $$-0.321482\pi$$
0.531891 + 0.846813i $$0.321482\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ −4.00000 −0.176604
$$514$$ 15.0000 0.661622
$$515$$ 0 0
$$516$$ 1.00000 0.0440225
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −12.0000 −0.526742
$$520$$ 0 0
$$521$$ 21.0000 0.920027 0.460013 0.887912i $$-0.347845\pi$$
0.460013 + 0.887912i $$0.347845\pi$$
$$522$$ −3.00000 −0.131306
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −9.00000 −0.392419
$$527$$ 15.0000 0.653410
$$528$$ −6.00000 −0.261116
$$529$$ −14.0000 −0.608696
$$530$$ 0 0
$$531$$ −9.00000 −0.390567
$$532$$ 0 0
$$533$$ −9.00000 −0.389833
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ 4.00000 0.172774
$$537$$ −18.0000 −0.776757
$$538$$ −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 $$0.358537\pi$$
$$542$$ 20.0000 0.859074
$$543$$ 2.00000 0.0858282
$$544$$ 3.00000 0.128624
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 17.0000 0.726868 0.363434 0.931620i $$-0.381604\pi$$
0.363434 + 0.931620i $$0.381604\pi$$
$$548$$ 0 0
$$549$$ −11.0000 −0.469469
$$550$$ 0 0
$$551$$ 12.0000 0.511217
$$552$$ −3.00000 −0.127688
$$553$$ 0 0
$$554$$ 10.0000 0.424859
$$555$$ 0 0
$$556$$ 16.0000 0.678551
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ 5.00000 0.211667
$$559$$ −1.00000 −0.0422955
$$560$$ 0 0
$$561$$ 18.0000 0.759961
$$562$$ 24.0000 1.01238
$$563$$ −21.0000 −0.885044 −0.442522 0.896758i $$-0.645916\pi$$
−0.442522 + 0.896758i $$0.645916\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −4.00000 −0.168133
$$567$$ 0 0
$$568$$ 12.0000 0.503509
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ −13.0000 −0.544033 −0.272017 0.962293i $$-0.587691\pi$$
−0.272017 + 0.962293i $$0.587691\pi$$
$$572$$ 6.00000 0.250873
$$573$$ 15.0000 0.626634
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 34.0000 1.41544 0.707719 0.706494i $$-0.249724\pi$$
0.707719 + 0.706494i $$0.249724\pi$$
$$578$$ 8.00000 0.332756
$$579$$ 22.0000 0.914289
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −14.0000 −0.580319
$$583$$ 54.0000 2.23645
$$584$$ −10.0000 −0.413803
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −33.0000 −1.36206 −0.681028 0.732257i $$-0.738467\pi$$
−0.681028 + 0.732257i $$0.738467\pi$$
$$588$$ 0 0
$$589$$ −20.0000 −0.824086
$$590$$ 0 0
$$591$$ 15.0000 0.617018
$$592$$ −10.0000 −0.410997
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 6.00000 0.246183
$$595$$ 0 0
$$596$$ −9.00000 −0.368654
$$597$$ 8.00000 0.327418
$$598$$ 3.00000 0.122679
$$599$$ 9.00000 0.367730 0.183865 0.982952i $$-0.441139\pi$$
0.183865 + 0.982952i $$0.441139\pi$$
$$600$$ 0 0
$$601$$ 4.00000 0.163163 0.0815817 0.996667i $$-0.474003\pi$$
0.0815817 + 0.996667i $$0.474003\pi$$
$$602$$ 0 0
$$603$$ −4.00000 −0.162893
$$604$$ 2.00000 0.0813788
$$605$$ 0 0
$$606$$ 12.0000 0.487467
$$607$$ 28.0000 1.13648 0.568242 0.822861i $$-0.307624\pi$$
0.568242 + 0.822861i $$0.307624\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −3.00000 −0.121268
$$613$$ 2.00000 0.0807792 0.0403896 0.999184i $$-0.487140\pi$$
0.0403896 + 0.999184i $$0.487140\pi$$
$$614$$ 2.00000 0.0807134
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ −17.0000 −0.683840
$$619$$ −26.0000 −1.04503 −0.522514 0.852631i $$-0.675006\pi$$
−0.522514 + 0.852631i $$0.675006\pi$$
$$620$$ 0 0
$$621$$ 3.00000 0.120386
$$622$$ −18.0000 −0.721734
$$623$$ 0 0
$$624$$ −1.00000 −0.0400320
$$625$$ 0 0
$$626$$ −10.0000 −0.399680
$$627$$ −24.0000 −0.958468
$$628$$ 10.0000 0.399043
$$629$$ 30.0000 1.19618
$$630$$ 0 0
$$631$$ −22.0000 −0.875806 −0.437903 0.899022i $$-0.644279\pi$$
−0.437903 + 0.899022i $$0.644279\pi$$
$$632$$ 10.0000 0.397779
$$633$$ 25.0000 0.993661
$$634$$ 27.0000 1.07231
$$635$$ 0 0
$$636$$ −9.00000 −0.356873
$$637$$ 0 0
$$638$$ −18.0000 −0.712627
$$639$$ −12.0000 −0.474713
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 18.0000 0.710403
$$643$$ −14.0000 −0.552106 −0.276053 0.961142i $$-0.589027\pi$$
−0.276053 + 0.961142i $$0.589027\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 12.0000 0.472134
$$647$$ −6.00000 −0.235884 −0.117942 0.993020i $$-0.537630\pi$$
−0.117942 + 0.993020i $$0.537630\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ −54.0000 −2.11969
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 5.00000 0.195815
$$653$$ 18.0000 0.704394 0.352197 0.935926i $$-0.385435\pi$$
0.352197 + 0.935926i $$0.385435\pi$$
$$654$$ 8.00000 0.312825
$$655$$ 0 0
$$656$$ −9.00000 −0.351391
$$657$$ 10.0000 0.390137
$$658$$ 0 0
$$659$$ 42.0000 1.63609 0.818044 0.575156i $$-0.195059\pi$$
0.818044 + 0.575156i $$0.195059\pi$$
$$660$$ 0 0
$$661$$ −38.0000 −1.47803 −0.739014 0.673690i $$-0.764708\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ 19.0000 0.738456
$$663$$ 3.00000 0.116510
$$664$$ 9.00000 0.349268
$$665$$ 0 0
$$666$$ 10.0000 0.387492
$$667$$ −9.00000 −0.348481
$$668$$ −18.0000 −0.696441
$$669$$ −19.0000 −0.734582
$$670$$ 0 0
$$671$$ −66.0000 −2.54790
$$672$$ 0 0
$$673$$ −37.0000 −1.42625 −0.713123 0.701039i $$-0.752720\pi$$
−0.713123 + 0.701039i $$0.752720\pi$$
$$674$$ 13.0000 0.500741
$$675$$ 0 0
$$676$$ −12.0000 −0.461538
$$677$$ 12.0000 0.461197 0.230599 0.973049i $$-0.425932\pi$$
0.230599 + 0.973049i $$0.425932\pi$$
$$678$$ −6.00000 −0.230429
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 3.00000 0.114960
$$682$$ 30.0000 1.14876
$$683$$ 18.0000 0.688751 0.344375 0.938832i $$-0.388091\pi$$
0.344375 + 0.938832i $$0.388091\pi$$
$$684$$ 4.00000 0.152944
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −22.0000 −0.839352
$$688$$ −1.00000 −0.0381246
$$689$$ 9.00000 0.342873
$$690$$ 0 0
$$691$$ 34.0000 1.29342 0.646710 0.762736i $$-0.276144\pi$$
0.646710 + 0.762736i $$0.276144\pi$$
$$692$$ 12.0000 0.456172
$$693$$ 0 0
$$694$$ −18.0000 −0.683271
$$695$$ 0 0
$$696$$ 3.00000 0.113715
$$697$$ 27.0000 1.02270
$$698$$ 17.0000 0.643459
$$699$$ −12.0000 −0.453882
$$700$$ 0 0
$$701$$ 3.00000 0.113308 0.0566542 0.998394i $$-0.481957\pi$$
0.0566542 + 0.998394i $$0.481957\pi$$
$$702$$ 1.00000 0.0377426
$$703$$ −40.0000 −1.50863
$$704$$ 6.00000 0.226134
$$705$$ 0 0
$$706$$ −30.0000 −1.12906
$$707$$ 0 0
$$708$$ 9.00000 0.338241
$$709$$ −40.0000 −1.50223 −0.751116 0.660171i $$-0.770484\pi$$
−0.751116 + 0.660171i $$0.770484\pi$$
$$710$$ 0 0
$$711$$ −10.0000 −0.375029
$$712$$ −6.00000 −0.224860
$$713$$ 15.0000 0.561754
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 18.0000 0.672692
$$717$$ 0 0
$$718$$ 3.00000 0.111959
$$719$$ −30.0000 −1.11881 −0.559406 0.828894i $$-0.688971\pi$$
−0.559406 + 0.828894i $$0.688971\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 3.00000 0.111648
$$723$$ 2.00000 0.0743808
$$724$$ −2.00000 −0.0743294
$$725$$ 0 0
$$726$$ 25.0000 0.927837
$$727$$ 7.00000 0.259616 0.129808 0.991539i $$-0.458564\pi$$
0.129808 + 0.991539i $$0.458564\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 3.00000 0.110959
$$732$$ 11.0000 0.406572
$$733$$ −29.0000 −1.07114 −0.535570 0.844491i $$-0.679903\pi$$
−0.535570 + 0.844491i $$0.679903\pi$$
$$734$$ −37.0000 −1.36569
$$735$$ 0 0
$$736$$ 3.00000 0.110581
$$737$$ −24.0000 −0.884051
$$738$$ 9.00000 0.331295
$$739$$ −37.0000 −1.36107 −0.680534 0.732717i $$-0.738252\pi$$
−0.680534 + 0.732717i $$0.738252\pi$$
$$740$$ 0 0
$$741$$ −4.00000 −0.146944
$$742$$ 0 0
$$743$$ −9.00000 −0.330178 −0.165089 0.986279i $$-0.552791\pi$$
−0.165089 + 0.986279i $$0.552791\pi$$
$$744$$ −5.00000 −0.183309
$$745$$ 0 0
$$746$$ −8.00000 −0.292901
$$747$$ −9.00000 −0.329293
$$748$$ −18.0000 −0.658145
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ 0 0
$$753$$ −27.0000 −0.983935
$$754$$ −3.00000 −0.109254
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 14.0000 0.508839 0.254419 0.967094i $$-0.418116\pi$$
0.254419 + 0.967094i $$0.418116\pi$$
$$758$$ −35.0000 −1.27126
$$759$$ 18.0000 0.653359
$$760$$ 0 0
$$761$$ −18.0000 −0.652499 −0.326250 0.945284i $$-0.605785\pi$$
−0.326250 + 0.945284i $$0.605785\pi$$
$$762$$ −10.0000 −0.362262
$$763$$ 0 0
$$764$$ −15.0000 −0.542681
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ −9.00000 −0.324971
$$768$$ −1.00000 −0.0360844
$$769$$ 4.00000 0.144244 0.0721218 0.997396i $$-0.477023\pi$$
0.0721218 + 0.997396i $$0.477023\pi$$
$$770$$ 0 0
$$771$$ 15.0000 0.540212
$$772$$ −22.0000 −0.791797
$$773$$ 48.0000 1.72644 0.863220 0.504828i $$-0.168444\pi$$
0.863220 + 0.504828i $$0.168444\pi$$
$$774$$ 1.00000 0.0359443
$$775$$ 0 0
$$776$$ 14.0000 0.502571
$$777$$ 0 0
$$778$$ 6.00000 0.215110
$$779$$ −36.0000 −1.28983
$$780$$ 0 0
$$781$$ −72.0000 −2.57636
$$782$$ −9.00000 −0.321839
$$783$$ −3.00000 −0.107211
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −26.0000 −0.926800 −0.463400 0.886149i $$-0.653371\pi$$
−0.463400 + 0.886149i $$0.653371\pi$$
$$788$$ −15.0000 −0.534353
$$789$$ −9.00000 −0.320408
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −6.00000 −0.213201
$$793$$ −11.0000 −0.390621
$$794$$ 29.0000 1.02917
$$795$$ 0 0
$$796$$ −8.00000 −0.283552
$$797$$ 6.00000 0.212531 0.106265 0.994338i $$-0.466111\pi$$
0.106265 + 0.994338i $$0.466111\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ 12.0000 0.423735
$$803$$ 60.0000 2.11735
$$804$$ 4.00000 0.141069
$$805$$ 0 0
$$806$$ 5.00000 0.176117
$$807$$ −18.0000 −0.633630
$$808$$ −12.0000 −0.422159
$$809$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$810$$ 0 0
$$811$$ 34.0000 1.19390 0.596951 0.802278i $$-0.296379\pi$$
0.596951 + 0.802278i $$0.296379\pi$$
$$812$$ 0 0
$$813$$ 20.0000 0.701431
$$814$$ 60.0000 2.10300
$$815$$ 0 0
$$816$$ 3.00000 0.105021
$$817$$ −4.00000 −0.139942
$$818$$ 38.0000 1.32864
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −42.0000 −1.46581 −0.732905 0.680331i $$-0.761836\pi$$
−0.732905 + 0.680331i $$0.761836\pi$$
$$822$$ 0 0
$$823$$ −34.0000 −1.18517 −0.592583 0.805510i $$-0.701892\pi$$
−0.592583 + 0.805510i $$0.701892\pi$$
$$824$$ 17.0000 0.592223
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 6.00000 0.208640 0.104320 0.994544i $$-0.466733\pi$$
0.104320 + 0.994544i $$0.466733\pi$$
$$828$$ −3.00000 −0.104257
$$829$$ −29.0000 −1.00721 −0.503606 0.863934i $$-0.667994\pi$$
−0.503606 + 0.863934i $$0.667994\pi$$
$$830$$ 0 0
$$831$$ 10.0000 0.346896
$$832$$ 1.00000 0.0346688
$$833$$ 0 0
$$834$$ 16.0000 0.554035
$$835$$ 0 0
$$836$$ 24.0000 0.830057
$$837$$ 5.00000 0.172825
$$838$$ −21.0000 −0.725433
$$839$$ −36.0000 −1.24286 −0.621429 0.783470i $$-0.713448\pi$$
−0.621429 + 0.783470i $$0.713448\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ 34.0000 1.17172
$$843$$ 24.0000 0.826604
$$844$$ −25.0000 −0.860535
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 9.00000 0.309061
$$849$$ −4.00000 −0.137280
$$850$$ 0 0
$$851$$ 30.0000 1.02839
$$852$$ 12.0000 0.411113
$$853$$ 19.0000 0.650548 0.325274 0.945620i $$-0.394544\pi$$
0.325274 + 0.945620i $$0.394544\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −18.0000 −0.615227
$$857$$ −18.0000 −0.614868 −0.307434 0.951569i $$-0.599470\pi$$
−0.307434 + 0.951569i $$0.599470\pi$$
$$858$$ 6.00000 0.204837
$$859$$ 40.0000 1.36478 0.682391 0.730987i $$-0.260940\pi$$
0.682391 + 0.730987i $$0.260940\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 15.0000 0.510902
$$863$$ −48.0000 −1.63394 −0.816970 0.576681i $$-0.804348\pi$$
−0.816970 + 0.576681i $$0.804348\pi$$
$$864$$ 1.00000 0.0340207
$$865$$ 0 0
$$866$$ 38.0000 1.29129
$$867$$ 8.00000 0.271694
$$868$$ 0 0
$$869$$ −60.0000 −2.03536
$$870$$ 0 0
$$871$$ −4.00000 −0.135535
$$872$$ −8.00000 −0.270914
$$873$$ −14.0000 −0.473828
$$874$$ 12.0000 0.405906
$$875$$ 0 0
$$876$$ −10.0000 −0.337869
$$877$$ 32.0000 1.08056 0.540282 0.841484i $$-0.318318\pi$$
0.540282 + 0.841484i $$0.318318\pi$$
$$878$$ 41.0000 1.38368
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −33.0000 −1.11180 −0.555899 0.831250i $$-0.687626\pi$$
−0.555899 + 0.831250i $$0.687626\pi$$
$$882$$ 0 0
$$883$$ 5.00000 0.168263 0.0841317 0.996455i $$-0.473188\pi$$
0.0841317 + 0.996455i $$0.473188\pi$$
$$884$$ −3.00000 −0.100901
$$885$$ 0 0
$$886$$ −24.0000 −0.806296
$$887$$ −54.0000 −1.81314 −0.906571 0.422053i $$-0.861310\pi$$
−0.906571 + 0.422053i $$0.861310\pi$$
$$888$$ −10.0000 −0.335578
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 6.00000 0.201008
$$892$$ 19.0000 0.636167
$$893$$ 0 0
$$894$$ −9.00000 −0.301005
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 3.00000 0.100167
$$898$$ −24.0000 −0.800890
$$899$$ −15.0000 −0.500278
$$900$$ 0 0
$$901$$ −27.0000 −0.899500
$$902$$ 54.0000 1.79800
$$903$$ 0 0
$$904$$ 6.00000 0.199557
$$905$$ 0 0
$$906$$ 2.00000 0.0664455
$$907$$ 53.0000 1.75984 0.879918 0.475125i $$-0.157597\pi$$
0.879918 + 0.475125i $$0.157597\pi$$
$$908$$ −3.00000 −0.0995585
$$909$$ 12.0000 0.398015
$$910$$ 0 0
$$911$$ 15.0000 0.496972 0.248486 0.968635i $$-0.420067\pi$$
0.248486 + 0.968635i $$0.420067\pi$$
$$912$$ −4.00000 −0.132453
$$913$$ −54.0000 −1.78714
$$914$$ 25.0000 0.826927
$$915$$ 0 0
$$916$$ 22.0000 0.726900
$$917$$ 0 0
$$918$$ −3.00000 −0.0990148
$$919$$ 20.0000 0.659739 0.329870 0.944027i $$-0.392995\pi$$
0.329870 + 0.944027i $$0.392995\pi$$
$$920$$ 0 0
$$921$$ 2.00000 0.0659022
$$922$$ 12.0000 0.395199
$$923$$ −12.0000 −0.394985
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −32.0000 −1.05159
$$927$$ −17.0000 −0.558353
$$928$$ −3.00000 −0.0984798
$$929$$ 27.0000 0.885841 0.442921 0.896561i $$-0.353942\pi$$
0.442921 + 0.896561i $$0.353942\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 12.0000 0.393073
$$933$$ −18.0000 −0.589294
$$934$$ −3.00000 −0.0981630
$$935$$ 0 0
$$936$$ −1.00000 −0.0326860
$$937$$ −2.00000 −0.0653372 −0.0326686 0.999466i $$-0.510401\pi$$
−0.0326686 + 0.999466i $$0.510401\pi$$
$$938$$ 0 0
$$939$$ −10.0000 −0.326338
$$940$$ 0 0
$$941$$ −24.0000 −0.782378 −0.391189 0.920310i $$-0.627936\pi$$
−0.391189 + 0.920310i $$0.627936\pi$$
$$942$$ 10.0000 0.325818
$$943$$ 27.0000 0.879241
$$944$$ −9.00000 −0.292925
$$945$$ 0 0
$$946$$ 6.00000 0.195077
$$947$$ −24.0000 −0.779895 −0.389948 0.920837i $$-0.627507\pi$$
−0.389948 + 0.920837i $$0.627507\pi$$
$$948$$ 10.0000 0.324785
$$949$$ 10.0000 0.324614
$$950$$ 0 0
$$951$$ 27.0000 0.875535
$$952$$ 0 0
$$953$$ 24.0000 0.777436 0.388718 0.921357i $$-0.372918\pi$$
0.388718 + 0.921357i $$0.372918\pi$$
$$954$$ −9.00000 −0.291386
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −18.0000 −0.581857
$$958$$ 24.0000 0.775405
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ 10.0000 0.322413
$$963$$ 18.0000 0.580042
$$964$$ −2.00000 −0.0644157
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −28.0000 −0.900419 −0.450210 0.892923i $$-0.648651\pi$$
−0.450210 + 0.892923i $$0.648651\pi$$
$$968$$ −25.0000 −0.803530
$$969$$ 12.0000 0.385496
$$970$$ 0 0
$$971$$ 12.0000 0.385098 0.192549 0.981287i $$-0.438325\pi$$
0.192549 + 0.981287i $$0.438325\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ −2.00000 −0.0640841
$$975$$ 0 0
$$976$$ −11.0000 −0.352101
$$977$$ 42.0000 1.34370 0.671850 0.740688i $$-0.265500\pi$$
0.671850 + 0.740688i $$0.265500\pi$$
$$978$$ 5.00000 0.159882
$$979$$ 36.0000 1.15056
$$980$$ 0 0
$$981$$ 8.00000 0.255420
$$982$$ −42.0000 −1.34027
$$983$$ −24.0000 −0.765481 −0.382741 0.923856i $$-0.625020\pi$$
−0.382741 + 0.923856i $$0.625020\pi$$
$$984$$ −9.00000 −0.286910
$$985$$ 0 0
$$986$$ 9.00000 0.286618
$$987$$ 0 0
$$988$$ 4.00000 0.127257
$$989$$ 3.00000 0.0953945
$$990$$ 0 0
$$991$$ −16.0000 −0.508257 −0.254128 0.967170i $$-0.581789\pi$$
−0.254128 + 0.967170i $$0.581789\pi$$
$$992$$ 5.00000 0.158750
$$993$$ 19.0000 0.602947
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 9.00000 0.285176
$$997$$ −26.0000 −0.823428 −0.411714 0.911313i $$-0.635070\pi$$
−0.411714 + 0.911313i $$0.635070\pi$$
$$998$$ 19.0000 0.601434
$$999$$ 10.0000 0.316386
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.r.1.1 1
5.4 even 2 7350.2.a.cz.1.1 1
7.6 odd 2 1050.2.a.j.1.1 1
21.20 even 2 3150.2.a.bg.1.1 1
28.27 even 2 8400.2.a.a.1.1 1
35.13 even 4 1050.2.g.e.799.2 2
35.27 even 4 1050.2.g.e.799.1 2
35.34 odd 2 1050.2.a.l.1.1 yes 1
105.62 odd 4 3150.2.g.a.2899.2 2
105.83 odd 4 3150.2.g.a.2899.1 2
105.104 even 2 3150.2.a.a.1.1 1
140.139 even 2 8400.2.a.ci.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.a.j.1.1 1 7.6 odd 2
1050.2.a.l.1.1 yes 1 35.34 odd 2
1050.2.g.e.799.1 2 35.27 even 4
1050.2.g.e.799.2 2 35.13 even 4
3150.2.a.a.1.1 1 105.104 even 2
3150.2.a.bg.1.1 1 21.20 even 2
3150.2.g.a.2899.1 2 105.83 odd 4
3150.2.g.a.2899.2 2 105.62 odd 4
7350.2.a.r.1.1 1 1.1 even 1 trivial
7350.2.a.cz.1.1 1 5.4 even 2
8400.2.a.a.1.1 1 28.27 even 2
8400.2.a.ci.1.1 1 140.139 even 2