Properties

 Label 7350.2.a.ch.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 $1$

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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 210) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -5.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} -7.00000 q^{19} -5.00000 q^{22} -3.00000 q^{23} +1.00000 q^{24} +1.00000 q^{26} +1.00000 q^{27} +6.00000 q^{31} +1.00000 q^{32} -5.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} +5.00000 q^{37} -7.00000 q^{38} +1.00000 q^{39} +9.00000 q^{41} -10.0000 q^{43} -5.00000 q^{44} -3.00000 q^{46} -13.0000 q^{47} +1.00000 q^{48} -2.00000 q^{51} +1.00000 q^{52} +1.00000 q^{53} +1.00000 q^{54} -7.00000 q^{57} -4.00000 q^{59} +2.00000 q^{61} +6.00000 q^{62} +1.00000 q^{64} -5.00000 q^{66} -6.00000 q^{67} -2.00000 q^{68} -3.00000 q^{69} -2.00000 q^{71} +1.00000 q^{72} +4.00000 q^{73} +5.00000 q^{74} -7.00000 q^{76} +1.00000 q^{78} -14.0000 q^{79} +1.00000 q^{81} +9.00000 q^{82} -10.0000 q^{83} -10.0000 q^{86} -5.00000 q^{88} -10.0000 q^{89} -3.00000 q^{92} +6.00000 q^{93} -13.0000 q^{94} +1.00000 q^{96} +8.00000 q^{97} -5.00000 q^{99} +O(q^{100})$$

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
$$13$$ 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
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 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
$$23$$ −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
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 1.00000 0.176777
$$33$$ −5.00000 −0.870388
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 5.00000 0.821995 0.410997 0.911636i $$-0.365181\pi$$
0.410997 + 0.911636i $$0.365181\pi$$
$$38$$ −7.00000 −1.13555
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ 9.00000 1.40556 0.702782 0.711405i $$-0.251941\pi$$
0.702782 + 0.711405i $$0.251941\pi$$
$$42$$ 0 0
$$43$$ −10.0000 −1.52499 −0.762493 0.646997i $$-0.776025\pi$$
−0.762493 + 0.646997i $$0.776025\pi$$
$$44$$ −5.00000 −0.753778
$$45$$ 0 0
$$46$$ −3.00000 −0.442326
$$47$$ −13.0000 −1.89624 −0.948122 0.317905i $$-0.897021\pi$$
−0.948122 + 0.317905i $$0.897021\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −2.00000 −0.280056
$$52$$ 1.00000 0.138675
$$53$$ 1.00000 0.137361 0.0686803 0.997639i $$-0.478121\pi$$
0.0686803 + 0.997639i $$0.478121\pi$$
$$54$$ 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 $$-0.583847\pi$$
−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 $$0.459132\pi$$
$$62$$ 6.00000 0.762001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −5.00000 −0.615457
$$67$$ −6.00000 −0.733017 −0.366508 0.930415i $$-0.619447\pi$$
−0.366508 + 0.930415i $$0.619447\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ −3.00000 −0.361158
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ 1.00000 0.117851
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 5.00000 0.581238
$$75$$ 0 0
$$76$$ −7.00000 −0.802955
$$77$$ 0 0
$$78$$ 1.00000 0.113228
$$79$$ −14.0000 −1.57512 −0.787562 0.616236i $$-0.788657\pi$$
−0.787562 + 0.616236i $$0.788657\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 9.00000 0.993884
$$83$$ −10.0000 −1.09764 −0.548821 0.835940i $$-0.684923\pi$$
−0.548821 + 0.835940i $$0.684923\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −10.0000 −1.07833
$$87$$ 0 0
$$88$$ −5.00000 −0.533002
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −3.00000 −0.312772
$$93$$ 6.00000 0.622171
$$94$$ −13.0000 −1.34085
$$95$$ 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
$$101$$ −8.00000 −0.796030 −0.398015 0.917379i $$-0.630301\pi$$
−0.398015 + 0.917379i $$0.630301\pi$$
$$102$$ −2.00000 −0.198030
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ 0 0
$$106$$ 1.00000 0.0971286
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ −18.0000 −1.72409 −0.862044 0.506834i $$-0.830816\pi$$
−0.862044 + 0.506834i $$0.830816\pi$$
$$110$$ 0 0
$$111$$ 5.00000 0.474579
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ −7.00000 −0.655610
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 1.00000 0.0924500
$$118$$ −4.00000 −0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ 2.00000 0.181071
$$123$$ 9.00000 0.811503
$$124$$ 6.00000 0.538816
$$125$$ 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
$$129$$ −10.0000 −0.880451
$$130$$ 0 0
$$131$$ 17.0000 1.48530 0.742648 0.669681i $$-0.233569\pi$$
0.742648 + 0.669681i $$0.233569\pi$$
$$132$$ −5.00000 −0.435194
$$133$$ 0 0
$$134$$ −6.00000 −0.518321
$$135$$ 0 0
$$136$$ −2.00000 −0.171499
$$137$$ 4.00000 0.341743 0.170872 0.985293i $$-0.445342\pi$$
0.170872 + 0.985293i $$0.445342\pi$$
$$138$$ −3.00000 −0.255377
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 0 0
$$141$$ −13.0000 −1.09480
$$142$$ −2.00000 −0.167836
$$143$$ −5.00000 −0.418121
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 4.00000 0.331042
$$147$$ 0 0
$$148$$ 5.00000 0.410997
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ −22.0000 −1.79033 −0.895167 0.445730i $$-0.852944\pi$$
−0.895167 + 0.445730i $$0.852944\pi$$
$$152$$ −7.00000 −0.567775
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 1.00000 0.0800641
$$157$$ 13.0000 1.03751 0.518756 0.854922i $$-0.326395\pi$$
0.518756 + 0.854922i $$0.326395\pi$$
$$158$$ −14.0000 −1.11378
$$159$$ 1.00000 0.0793052
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000 0.0785674
$$163$$ 12.0000 0.939913 0.469956 0.882690i $$-0.344270\pi$$
0.469956 + 0.882690i $$0.344270\pi$$
$$164$$ 9.00000 0.702782
$$165$$ 0 0
$$166$$ −10.0000 −0.776151
$$167$$ −19.0000 −1.47026 −0.735132 0.677924i $$-0.762880\pi$$
−0.735132 + 0.677924i $$0.762880\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −7.00000 −0.535303
$$172$$ −10.0000 −0.762493
$$173$$ 7.00000 0.532200 0.266100 0.963945i $$-0.414265\pi$$
0.266100 + 0.963945i $$0.414265\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −5.00000 −0.376889
$$177$$ −4.00000 −0.300658
$$178$$ −10.0000 −0.749532
$$179$$ −11.0000 −0.822179 −0.411089 0.911595i $$-0.634852\pi$$
−0.411089 + 0.911595i $$0.634852\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ −3.00000 −0.221163
$$185$$ 0 0
$$186$$ 6.00000 0.439941
$$187$$ 10.0000 0.731272
$$188$$ −13.0000 −0.948122
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −16.0000 −1.15772 −0.578860 0.815427i $$-0.696502\pi$$
−0.578860 + 0.815427i $$0.696502\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 18.0000 1.29567 0.647834 0.761781i $$-0.275675\pi$$
0.647834 + 0.761781i $$0.275675\pi$$
$$194$$ 8.00000 0.574367
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 27.0000 1.92367 0.961835 0.273629i $$-0.0882242\pi$$
0.961835 + 0.273629i $$0.0882242\pi$$
$$198$$ −5.00000 −0.355335
$$199$$ 14.0000 0.992434 0.496217 0.868199i $$-0.334722\pi$$
0.496217 + 0.868199i $$0.334722\pi$$
$$200$$ 0 0
$$201$$ −6.00000 −0.423207
$$202$$ −8.00000 −0.562878
$$203$$ 0 0
$$204$$ −2.00000 −0.140028
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −3.00000 −0.208514
$$208$$ 1.00000 0.0693375
$$209$$ 35.0000 2.42100
$$210$$ 0 0
$$211$$ 19.0000 1.30801 0.654007 0.756489i $$-0.273087\pi$$
0.654007 + 0.756489i $$0.273087\pi$$
$$212$$ 1.00000 0.0686803
$$213$$ −2.00000 −0.137038
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ −18.0000 −1.21911
$$219$$ 4.00000 0.270295
$$220$$ 0 0
$$221$$ −2.00000 −0.134535
$$222$$ 5.00000 0.335578
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ 14.0000 0.929213 0.464606 0.885517i $$-0.346196\pi$$
0.464606 + 0.885517i $$0.346196\pi$$
$$228$$ −7.00000 −0.463586
$$229$$ 4.00000 0.264327 0.132164 0.991228i $$-0.457808\pi$$
0.132164 + 0.991228i $$0.457808\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 1.00000 0.0653720
$$235$$ 0 0
$$236$$ −4.00000 −0.260378
$$237$$ −14.0000 −0.909398
$$238$$ 0 0
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ 1.00000 0.0644157 0.0322078 0.999481i $$-0.489746\pi$$
0.0322078 + 0.999481i $$0.489746\pi$$
$$242$$ 14.0000 0.899954
$$243$$ 1.00000 0.0641500
$$244$$ 2.00000 0.128037
$$245$$ 0 0
$$246$$ 9.00000 0.573819
$$247$$ −7.00000 −0.445399
$$248$$ 6.00000 0.381000
$$249$$ −10.0000 −0.633724
$$250$$ 0 0
$$251$$ 3.00000 0.189358 0.0946792 0.995508i $$-0.469817\pi$$
0.0946792 + 0.995508i $$0.469817\pi$$
$$252$$ 0 0
$$253$$ 15.0000 0.943042
$$254$$ −9.00000 −0.564710
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −10.0000 −0.623783 −0.311891 0.950118i $$-0.600963\pi$$
−0.311891 + 0.950118i $$0.600963\pi$$
$$258$$ −10.0000 −0.622573
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 17.0000 1.05026
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ −5.00000 −0.307729
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −10.0000 −0.611990
$$268$$ −6.00000 −0.366508
$$269$$ −14.0000 −0.853595 −0.426798 0.904347i $$-0.640358\pi$$
−0.426798 + 0.904347i $$0.640358\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ 4.00000 0.241649
$$275$$ 0 0
$$276$$ −3.00000 −0.180579
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 6.00000 0.359211
$$280$$ 0 0
$$281$$ −11.0000 −0.656205 −0.328102 0.944642i $$-0.606409\pi$$
−0.328102 + 0.944642i $$0.606409\pi$$
$$282$$ −13.0000 −0.774139
$$283$$ 26.0000 1.54554 0.772770 0.634686i $$-0.218871\pi$$
0.772770 + 0.634686i $$0.218871\pi$$
$$284$$ −2.00000 −0.118678
$$285$$ 0 0
$$286$$ −5.00000 −0.295656
$$287$$ 0 0
$$288$$ 1.00000 0.0589256
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ 4.00000 0.234082
$$293$$ 1.00000 0.0584206 0.0292103 0.999573i $$-0.490701\pi$$
0.0292103 + 0.999573i $$0.490701\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 5.00000 0.290619
$$297$$ −5.00000 −0.290129
$$298$$ −6.00000 −0.347571
$$299$$ −3.00000 −0.173494
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −22.0000 −1.26596
$$303$$ −8.00000 −0.459588
$$304$$ −7.00000 −0.401478
$$305$$ 0 0
$$306$$ −2.00000 −0.114332
$$307$$ 2.00000 0.114146 0.0570730 0.998370i $$-0.481823\pi$$
0.0570730 + 0.998370i $$0.481823\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 26.0000 1.47432 0.737162 0.675716i $$-0.236165\pi$$
0.737162 + 0.675716i $$0.236165\pi$$
$$312$$ 1.00000 0.0566139
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 13.0000 0.733632
$$315$$ 0 0
$$316$$ −14.0000 −0.787562
$$317$$ −2.00000 −0.112331 −0.0561656 0.998421i $$-0.517887\pi$$
−0.0561656 + 0.998421i $$0.517887\pi$$
$$318$$ 1.00000 0.0560772
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −12.0000 −0.669775
$$322$$ 0 0
$$323$$ 14.0000 0.778981
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 12.0000 0.664619
$$327$$ −18.0000 −0.995402
$$328$$ 9.00000 0.496942
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −15.0000 −0.824475 −0.412237 0.911077i $$-0.635253\pi$$
−0.412237 + 0.911077i $$0.635253\pi$$
$$332$$ −10.0000 −0.548821
$$333$$ 5.00000 0.273998
$$334$$ −19.0000 −1.03963
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ −12.0000 −0.652714
$$339$$ −6.00000 −0.325875
$$340$$ 0 0
$$341$$ −30.0000 −1.62459
$$342$$ −7.00000 −0.378517
$$343$$ 0 0
$$344$$ −10.0000 −0.539164
$$345$$ 0 0
$$346$$ 7.00000 0.376322
$$347$$ 16.0000 0.858925 0.429463 0.903085i $$-0.358703\pi$$
0.429463 + 0.903085i $$0.358703\pi$$
$$348$$ 0 0
$$349$$ 24.0000 1.28469 0.642345 0.766415i $$-0.277962\pi$$
0.642345 + 0.766415i $$0.277962\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ −5.00000 −0.266501
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ −4.00000 −0.212598
$$355$$ 0 0
$$356$$ −10.0000 −0.529999
$$357$$ 0 0
$$358$$ −11.0000 −0.581368
$$359$$ −28.0000 −1.47778 −0.738892 0.673824i $$-0.764651\pi$$
−0.738892 + 0.673824i $$0.764651\pi$$
$$360$$ 0 0
$$361$$ 30.0000 1.57895
$$362$$ 2.00000 0.105118
$$363$$ 14.0000 0.734809
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 2.00000 0.104542
$$367$$ −37.0000 −1.93138 −0.965692 0.259690i $$-0.916380\pi$$
−0.965692 + 0.259690i $$0.916380\pi$$
$$368$$ −3.00000 −0.156386
$$369$$ 9.00000 0.468521
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 6.00000 0.311086
$$373$$ −6.00000 −0.310668 −0.155334 0.987862i $$-0.549645\pi$$
−0.155334 + 0.987862i $$0.549645\pi$$
$$374$$ 10.0000 0.517088
$$375$$ 0 0
$$376$$ −13.0000 −0.670424
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −1.00000 −0.0513665 −0.0256833 0.999670i $$-0.508176\pi$$
−0.0256833 + 0.999670i $$0.508176\pi$$
$$380$$ 0 0
$$381$$ −9.00000 −0.461084
$$382$$ −16.0000 −0.818631
$$383$$ −9.00000 −0.459879 −0.229939 0.973205i $$-0.573853\pi$$
−0.229939 + 0.973205i $$0.573853\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ 18.0000 0.916176
$$387$$ −10.0000 −0.508329
$$388$$ 8.00000 0.406138
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 6.00000 0.303433
$$392$$ 0 0
$$393$$ 17.0000 0.857537
$$394$$ 27.0000 1.36024
$$395$$ 0 0
$$396$$ −5.00000 −0.251259
$$397$$ −2.00000 −0.100377 −0.0501886 0.998740i $$-0.515982\pi$$
−0.0501886 + 0.998740i $$0.515982\pi$$
$$398$$ 14.0000 0.701757
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −27.0000 −1.34832 −0.674158 0.738587i $$-0.735493\pi$$
−0.674158 + 0.738587i $$0.735493\pi$$
$$402$$ −6.00000 −0.299253
$$403$$ 6.00000 0.298881
$$404$$ −8.00000 −0.398015
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −25.0000 −1.23920
$$408$$ −2.00000 −0.0990148
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 0 0
$$411$$ 4.00000 0.197305
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −3.00000 −0.147442
$$415$$ 0 0
$$416$$ 1.00000 0.0490290
$$417$$ 8.00000 0.391762
$$418$$ 35.0000 1.71191
$$419$$ −3.00000 −0.146560 −0.0732798 0.997311i $$-0.523347\pi$$
−0.0732798 + 0.997311i $$0.523347\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ 19.0000 0.924906
$$423$$ −13.0000 −0.632082
$$424$$ 1.00000 0.0485643
$$425$$ 0 0
$$426$$ −2.00000 −0.0969003
$$427$$ 0 0
$$428$$ −12.0000 −0.580042
$$429$$ −5.00000 −0.241402
$$430$$ 0 0
$$431$$ 18.0000 0.867029 0.433515 0.901146i $$-0.357273\pi$$
0.433515 + 0.901146i $$0.357273\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ 4.00000 0.192228 0.0961139 0.995370i $$-0.469359\pi$$
0.0961139 + 0.995370i $$0.469359\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −18.0000 −0.862044
$$437$$ 21.0000 1.00457
$$438$$ 4.00000 0.191127
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −2.00000 −0.0951303
$$443$$ 6.00000 0.285069 0.142534 0.989790i $$-0.454475\pi$$
0.142534 + 0.989790i $$0.454475\pi$$
$$444$$ 5.00000 0.237289
$$445$$ 0 0
$$446$$ 16.0000 0.757622
$$447$$ −6.00000 −0.283790
$$448$$ 0 0
$$449$$ 9.00000 0.424736 0.212368 0.977190i $$-0.431882\pi$$
0.212368 + 0.977190i $$0.431882\pi$$
$$450$$ 0 0
$$451$$ −45.0000 −2.11897
$$452$$ −6.00000 −0.282216
$$453$$ −22.0000 −1.03365
$$454$$ 14.0000 0.657053
$$455$$ 0 0
$$456$$ −7.00000 −0.327805
$$457$$ 38.0000 1.77757 0.888783 0.458329i $$-0.151552\pi$$
0.888783 + 0.458329i $$0.151552\pi$$
$$458$$ 4.00000 0.186908
$$459$$ −2.00000 −0.0933520
$$460$$ 0 0
$$461$$ 12.0000 0.558896 0.279448 0.960161i $$-0.409849\pi$$
0.279448 + 0.960161i $$0.409849\pi$$
$$462$$ 0 0
$$463$$ 15.0000 0.697109 0.348555 0.937288i $$-0.386673\pi$$
0.348555 + 0.937288i $$0.386673\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2.00000 0.0925490 0.0462745 0.998929i $$-0.485265\pi$$
0.0462745 + 0.998929i $$0.485265\pi$$
$$468$$ 1.00000 0.0462250
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 13.0000 0.599008
$$472$$ −4.00000 −0.184115
$$473$$ 50.0000 2.29900
$$474$$ −14.0000 −0.643041
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 1.00000 0.0457869
$$478$$ 20.0000 0.914779
$$479$$ −8.00000 −0.365529 −0.182765 0.983157i $$-0.558505\pi$$
−0.182765 + 0.983157i $$0.558505\pi$$
$$480$$ 0 0
$$481$$ 5.00000 0.227980
$$482$$ 1.00000 0.0455488
$$483$$ 0 0
$$484$$ 14.0000 0.636364
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ −24.0000 −1.08754 −0.543772 0.839233i $$-0.683004\pi$$
−0.543772 + 0.839233i $$0.683004\pi$$
$$488$$ 2.00000 0.0905357
$$489$$ 12.0000 0.542659
$$490$$ 0 0
$$491$$ 24.0000 1.08310 0.541552 0.840667i $$-0.317837\pi$$
0.541552 + 0.840667i $$0.317837\pi$$
$$492$$ 9.00000 0.405751
$$493$$ 0 0
$$494$$ −7.00000 −0.314945
$$495$$ 0 0
$$496$$ 6.00000 0.269408
$$497$$ 0 0
$$498$$ −10.0000 −0.448111
$$499$$ −28.0000 −1.25345 −0.626726 0.779240i $$-0.715605\pi$$
−0.626726 + 0.779240i $$0.715605\pi$$
$$500$$ 0 0
$$501$$ −19.0000 −0.848857
$$502$$ 3.00000 0.133897
$$503$$ 24.0000 1.07011 0.535054 0.844818i $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 15.0000 0.666831
$$507$$ −12.0000 −0.532939
$$508$$ −9.00000 −0.399310
$$509$$ −14.0000 −0.620539 −0.310270 0.950649i $$-0.600419\pi$$
−0.310270 + 0.950649i $$0.600419\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ −7.00000 −0.309058
$$514$$ −10.0000 −0.441081
$$515$$ 0 0
$$516$$ −10.0000 −0.440225
$$517$$ 65.0000 2.85870
$$518$$ 0 0
$$519$$ 7.00000 0.307266
$$520$$ 0 0
$$521$$ 15.0000 0.657162 0.328581 0.944476i $$-0.393430\pi$$
0.328581 + 0.944476i $$0.393430\pi$$
$$522$$ 0 0
$$523$$ 12.0000 0.524723 0.262362 0.964970i $$-0.415499\pi$$
0.262362 + 0.964970i $$0.415499\pi$$
$$524$$ 17.0000 0.742648
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ −12.0000 −0.522728
$$528$$ −5.00000 −0.217597
$$529$$ −14.0000 −0.608696
$$530$$ 0 0
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ 9.00000 0.389833
$$534$$ −10.0000 −0.432742
$$535$$ 0 0
$$536$$ −6.00000 −0.259161
$$537$$ −11.0000 −0.474685
$$538$$ −14.0000 −0.603583
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 4.00000 0.171973 0.0859867 0.996296i $$-0.472596\pi$$
0.0859867 + 0.996296i $$0.472596\pi$$
$$542$$ −8.00000 −0.343629
$$543$$ 2.00000 0.0858282
$$544$$ −2.00000 −0.0857493
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 14.0000 0.598597 0.299298 0.954160i $$-0.403247\pi$$
0.299298 + 0.954160i $$0.403247\pi$$
$$548$$ 4.00000 0.170872
$$549$$ 2.00000 0.0853579
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −3.00000 −0.127688
$$553$$ 0 0
$$554$$ −2.00000 −0.0849719
$$555$$ 0 0
$$556$$ 8.00000 0.339276
$$557$$ 39.0000 1.65248 0.826242 0.563316i $$-0.190475\pi$$
0.826242 + 0.563316i $$0.190475\pi$$
$$558$$ 6.00000 0.254000
$$559$$ −10.0000 −0.422955
$$560$$ 0 0
$$561$$ 10.0000 0.422200
$$562$$ −11.0000 −0.464007
$$563$$ 30.0000 1.26435 0.632175 0.774826i $$-0.282163\pi$$
0.632175 + 0.774826i $$0.282163\pi$$
$$564$$ −13.0000 −0.547399
$$565$$ 0 0
$$566$$ 26.0000 1.09286
$$567$$ 0 0
$$568$$ −2.00000 −0.0839181
$$569$$ −3.00000 −0.125767 −0.0628833 0.998021i $$-0.520030\pi$$
−0.0628833 + 0.998021i $$0.520030\pi$$
$$570$$ 0 0
$$571$$ −8.00000 −0.334790 −0.167395 0.985890i $$-0.553535\pi$$
−0.167395 + 0.985890i $$0.553535\pi$$
$$572$$ −5.00000 −0.209061
$$573$$ −16.0000 −0.668410
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 24.0000 0.999133 0.499567 0.866276i $$-0.333493\pi$$
0.499567 + 0.866276i $$0.333493\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ 18.0000 0.748054
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 8.00000 0.331611
$$583$$ −5.00000 −0.207079
$$584$$ 4.00000 0.165521
$$585$$ 0 0
$$586$$ 1.00000 0.0413096
$$587$$ 2.00000 0.0825488 0.0412744 0.999148i $$-0.486858\pi$$
0.0412744 + 0.999148i $$0.486858\pi$$
$$588$$ 0 0
$$589$$ −42.0000 −1.73058
$$590$$ 0 0
$$591$$ 27.0000 1.11063
$$592$$ 5.00000 0.205499
$$593$$ −34.0000 −1.39621 −0.698106 0.715994i $$-0.745974\pi$$
−0.698106 + 0.715994i $$0.745974\pi$$
$$594$$ −5.00000 −0.205152
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ 14.0000 0.572982
$$598$$ −3.00000 −0.122679
$$599$$ −28.0000 −1.14405 −0.572024 0.820237i $$-0.693842\pi$$
−0.572024 + 0.820237i $$0.693842\pi$$
$$600$$ 0 0
$$601$$ 30.0000 1.22373 0.611863 0.790964i $$-0.290420\pi$$
0.611863 + 0.790964i $$0.290420\pi$$
$$602$$ 0 0
$$603$$ −6.00000 −0.244339
$$604$$ −22.0000 −0.895167
$$605$$ 0 0
$$606$$ −8.00000 −0.324978
$$607$$ 13.0000 0.527654 0.263827 0.964570i $$-0.415015\pi$$
0.263827 + 0.964570i $$0.415015\pi$$
$$608$$ −7.00000 −0.283887
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −13.0000 −0.525924
$$612$$ −2.00000 −0.0808452
$$613$$ −19.0000 −0.767403 −0.383701 0.923457i $$-0.625351\pi$$
−0.383701 + 0.923457i $$0.625351\pi$$
$$614$$ 2.00000 0.0807134
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −30.0000 −1.20775 −0.603877 0.797077i $$-0.706378\pi$$
−0.603877 + 0.797077i $$0.706378\pi$$
$$618$$ 0 0
$$619$$ −15.0000 −0.602901 −0.301450 0.953482i $$-0.597471\pi$$
−0.301450 + 0.953482i $$0.597471\pi$$
$$620$$ 0 0
$$621$$ −3.00000 −0.120386
$$622$$ 26.0000 1.04251
$$623$$ 0 0
$$624$$ 1.00000 0.0400320
$$625$$ 0 0
$$626$$ −10.0000 −0.399680
$$627$$ 35.0000 1.39777
$$628$$ 13.0000 0.518756
$$629$$ −10.0000 −0.398726
$$630$$ 0 0
$$631$$ 18.0000 0.716569 0.358284 0.933613i $$-0.383362\pi$$
0.358284 + 0.933613i $$0.383362\pi$$
$$632$$ −14.0000 −0.556890
$$633$$ 19.0000 0.755182
$$634$$ −2.00000 −0.0794301
$$635$$ 0 0
$$636$$ 1.00000 0.0396526
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −2.00000 −0.0791188
$$640$$ 0 0
$$641$$ −33.0000 −1.30342 −0.651711 0.758468i $$-0.725948\pi$$
−0.651711 + 0.758468i $$0.725948\pi$$
$$642$$ −12.0000 −0.473602
$$643$$ 38.0000 1.49857 0.749287 0.662246i $$-0.230396\pi$$
0.749287 + 0.662246i $$0.230396\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 14.0000 0.550823
$$647$$ −1.00000 −0.0393141 −0.0196570 0.999807i $$-0.506257\pi$$
−0.0196570 + 0.999807i $$0.506257\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 20.0000 0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 12.0000 0.469956
$$653$$ −5.00000 −0.195665 −0.0978326 0.995203i $$-0.531191\pi$$
−0.0978326 + 0.995203i $$0.531191\pi$$
$$654$$ −18.0000 −0.703856
$$655$$ 0 0
$$656$$ 9.00000 0.351391
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −40.0000 −1.55582 −0.777910 0.628376i $$-0.783720\pi$$
−0.777910 + 0.628376i $$0.783720\pi$$
$$662$$ −15.0000 −0.582992
$$663$$ −2.00000 −0.0776736
$$664$$ −10.0000 −0.388075
$$665$$ 0 0
$$666$$ 5.00000 0.193746
$$667$$ 0 0
$$668$$ −19.0000 −0.735132
$$669$$ 16.0000 0.618596
$$670$$ 0 0
$$671$$ −10.0000 −0.386046
$$672$$ 0 0
$$673$$ −36.0000 −1.38770 −0.693849 0.720121i $$-0.744086\pi$$
−0.693849 + 0.720121i $$0.744086\pi$$
$$674$$ 14.0000 0.539260
$$675$$ 0 0
$$676$$ −12.0000 −0.461538
$$677$$ 33.0000 1.26829 0.634147 0.773213i $$-0.281352\pi$$
0.634147 + 0.773213i $$0.281352\pi$$
$$678$$ −6.00000 −0.230429
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 14.0000 0.536481
$$682$$ −30.0000 −1.14876
$$683$$ 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
$$687$$ 4.00000 0.152610
$$688$$ −10.0000 −0.381246
$$689$$ 1.00000 0.0380970
$$690$$ 0 0
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ 7.00000 0.266100
$$693$$ 0 0
$$694$$ 16.0000 0.607352
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −18.0000 −0.681799
$$698$$ 24.0000 0.908413
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 1.00000 0.0377426
$$703$$ −35.0000 −1.32005
$$704$$ −5.00000 −0.188445
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ −4.00000 −0.150329
$$709$$ 16.0000 0.600893 0.300446 0.953799i $$-0.402864\pi$$
0.300446 + 0.953799i $$0.402864\pi$$
$$710$$ 0 0
$$711$$ −14.0000 −0.525041
$$712$$ −10.0000 −0.374766
$$713$$ −18.0000 −0.674105
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −11.0000 −0.411089
$$717$$ 20.0000 0.746914
$$718$$ −28.0000 −1.04495
$$719$$ 2.00000 0.0745874 0.0372937 0.999304i $$-0.488126\pi$$
0.0372937 + 0.999304i $$0.488126\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 30.0000 1.11648
$$723$$ 1.00000 0.0371904
$$724$$ 2.00000 0.0743294
$$725$$ 0 0
$$726$$ 14.0000 0.519589
$$727$$ 53.0000 1.96566 0.982831 0.184510i $$-0.0590699\pi$$
0.982831 + 0.184510i $$0.0590699\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 20.0000 0.739727
$$732$$ 2.00000 0.0739221
$$733$$ −21.0000 −0.775653 −0.387826 0.921732i $$-0.626774\pi$$
−0.387826 + 0.921732i $$0.626774\pi$$
$$734$$ −37.0000 −1.36569
$$735$$ 0 0
$$736$$ −3.00000 −0.110581
$$737$$ 30.0000 1.10506
$$738$$ 9.00000 0.331295
$$739$$ 47.0000 1.72892 0.864461 0.502699i $$-0.167660\pi$$
0.864461 + 0.502699i $$0.167660\pi$$
$$740$$ 0 0
$$741$$ −7.00000 −0.257151
$$742$$ 0 0
$$743$$ 31.0000 1.13728 0.568640 0.822587i $$-0.307470\pi$$
0.568640 + 0.822587i $$0.307470\pi$$
$$744$$ 6.00000 0.219971
$$745$$ 0 0
$$746$$ −6.00000 −0.219676
$$747$$ −10.0000 −0.365881
$$748$$ 10.0000 0.365636
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 4.00000 0.145962 0.0729810 0.997333i $$-0.476749\pi$$
0.0729810 + 0.997333i $$0.476749\pi$$
$$752$$ −13.0000 −0.474061
$$753$$ 3.00000 0.109326
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ −1.00000 −0.0363216
$$759$$ 15.0000 0.544466
$$760$$ 0 0
$$761$$ 3.00000 0.108750 0.0543750 0.998521i $$-0.482683\pi$$
0.0543750 + 0.998521i $$0.482683\pi$$
$$762$$ −9.00000 −0.326036
$$763$$ 0 0
$$764$$ −16.0000 −0.578860
$$765$$ 0 0
$$766$$ −9.00000 −0.325183
$$767$$ −4.00000 −0.144432
$$768$$ 1.00000 0.0360844
$$769$$ −51.0000 −1.83911 −0.919554 0.392965i $$-0.871449\pi$$
−0.919554 + 0.392965i $$0.871449\pi$$
$$770$$ 0 0
$$771$$ −10.0000 −0.360141
$$772$$ 18.0000 0.647834
$$773$$ −37.0000 −1.33080 −0.665399 0.746488i $$-0.731738\pi$$
−0.665399 + 0.746488i $$0.731738\pi$$
$$774$$ −10.0000 −0.359443
$$775$$ 0 0
$$776$$ 8.00000 0.287183
$$777$$ 0 0
$$778$$ 6.00000 0.215110
$$779$$ −63.0000 −2.25721
$$780$$ 0 0
$$781$$ 10.0000 0.357828
$$782$$ 6.00000 0.214560
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 17.0000 0.606370
$$787$$ 38.0000 1.35455 0.677277 0.735728i $$-0.263160\pi$$
0.677277 + 0.735728i $$0.263160\pi$$
$$788$$ 27.0000 0.961835
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −5.00000 −0.177667
$$793$$ 2.00000 0.0710221
$$794$$ −2.00000 −0.0709773
$$795$$ 0 0
$$796$$ 14.0000 0.496217
$$797$$ −30.0000 −1.06265 −0.531327 0.847167i $$-0.678307\pi$$
−0.531327 + 0.847167i $$0.678307\pi$$
$$798$$ 0 0
$$799$$ 26.0000 0.919814
$$800$$ 0 0
$$801$$ −10.0000 −0.353333
$$802$$ −27.0000 −0.953403
$$803$$ −20.0000 −0.705785
$$804$$ −6.00000 −0.211604
$$805$$ 0 0
$$806$$ 6.00000 0.211341
$$807$$ −14.0000 −0.492823
$$808$$ −8.00000 −0.281439
$$809$$ −9.00000 −0.316423 −0.158212 0.987405i $$-0.550573\pi$$
−0.158212 + 0.987405i $$0.550573\pi$$
$$810$$ 0 0
$$811$$ −11.0000 −0.386262 −0.193131 0.981173i $$-0.561864\pi$$
−0.193131 + 0.981173i $$0.561864\pi$$
$$812$$ 0 0
$$813$$ −8.00000 −0.280572
$$814$$ −25.0000 −0.876250
$$815$$ 0 0
$$816$$ −2.00000 −0.0700140
$$817$$ 70.0000 2.44899
$$818$$ −10.0000 −0.349642
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 6.00000 0.209401 0.104701 0.994504i $$-0.466612\pi$$
0.104701 + 0.994504i $$0.466612\pi$$
$$822$$ 4.00000 0.139516
$$823$$ 8.00000 0.278862 0.139431 0.990232i $$-0.455473\pi$$
0.139431 + 0.990232i $$0.455473\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 42.0000 1.46048 0.730242 0.683189i $$-0.239408\pi$$
0.730242 + 0.683189i $$0.239408\pi$$
$$828$$ −3.00000 −0.104257
$$829$$ −2.00000 −0.0694629 −0.0347314 0.999397i $$-0.511058\pi$$
−0.0347314 + 0.999397i $$0.511058\pi$$
$$830$$ 0 0
$$831$$ −2.00000 −0.0693792
$$832$$ 1.00000 0.0346688
$$833$$ 0 0
$$834$$ 8.00000 0.277017
$$835$$ 0 0
$$836$$ 35.0000 1.21050
$$837$$ 6.00000 0.207390
$$838$$ −3.00000 −0.103633
$$839$$ −2.00000 −0.0690477 −0.0345238 0.999404i $$-0.510991\pi$$
−0.0345238 + 0.999404i $$0.510991\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ −20.0000 −0.689246
$$843$$ −11.0000 −0.378860
$$844$$ 19.0000 0.654007
$$845$$ 0 0
$$846$$ −13.0000 −0.446949
$$847$$ 0 0
$$848$$ 1.00000 0.0343401
$$849$$ 26.0000 0.892318
$$850$$ 0 0
$$851$$ −15.0000 −0.514193
$$852$$ −2.00000 −0.0685189
$$853$$ −49.0000 −1.67773 −0.838864 0.544341i $$-0.816780\pi$$
−0.838864 + 0.544341i $$0.816780\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ −56.0000 −1.91292 −0.956462 0.291858i $$-0.905727\pi$$
−0.956462 + 0.291858i $$0.905727\pi$$
$$858$$ −5.00000 −0.170697
$$859$$ −36.0000 −1.22830 −0.614152 0.789188i $$-0.710502\pi$$
−0.614152 + 0.789188i $$0.710502\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 18.0000 0.613082
$$863$$ −15.0000 −0.510606 −0.255303 0.966861i $$-0.582175\pi$$
−0.255303 + 0.966861i $$0.582175\pi$$
$$864$$ 1.00000 0.0340207
$$865$$ 0 0
$$866$$ 4.00000 0.135926
$$867$$ −13.0000 −0.441503
$$868$$ 0 0
$$869$$ 70.0000 2.37459
$$870$$ 0 0
$$871$$ −6.00000 −0.203302
$$872$$ −18.0000 −0.609557
$$873$$ 8.00000 0.270759
$$874$$ 21.0000 0.710336
$$875$$ 0 0
$$876$$ 4.00000 0.135147
$$877$$ 27.0000 0.911725 0.455863 0.890050i $$-0.349331\pi$$
0.455863 + 0.890050i $$0.349331\pi$$
$$878$$ 0 0
$$879$$ 1.00000 0.0337292
$$880$$ 0 0
$$881$$ 3.00000 0.101073 0.0505363 0.998722i $$-0.483907\pi$$
0.0505363 + 0.998722i $$0.483907\pi$$
$$882$$ 0 0
$$883$$ 52.0000 1.74994 0.874970 0.484178i $$-0.160881\pi$$
0.874970 + 0.484178i $$0.160881\pi$$
$$884$$ −2.00000 −0.0672673
$$885$$ 0 0
$$886$$ 6.00000 0.201574
$$887$$ −12.0000 −0.402921 −0.201460 0.979497i $$-0.564569\pi$$
−0.201460 + 0.979497i $$0.564569\pi$$
$$888$$ 5.00000 0.167789
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −5.00000 −0.167506
$$892$$ 16.0000 0.535720
$$893$$ 91.0000 3.04520
$$894$$ −6.00000 −0.200670
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −3.00000 −0.100167
$$898$$ 9.00000 0.300334
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −2.00000 −0.0666297
$$902$$ −45.0000 −1.49834
$$903$$ 0 0
$$904$$ −6.00000 −0.199557
$$905$$ 0 0
$$906$$ −22.0000 −0.730901
$$907$$ 16.0000 0.531271 0.265636 0.964073i $$-0.414418\pi$$
0.265636 + 0.964073i $$0.414418\pi$$
$$908$$ 14.0000 0.464606
$$909$$ −8.00000 −0.265343
$$910$$ 0 0
$$911$$ −6.00000 −0.198789 −0.0993944 0.995048i $$-0.531691\pi$$
−0.0993944 + 0.995048i $$0.531691\pi$$
$$912$$ −7.00000 −0.231793
$$913$$ 50.0000 1.65476
$$914$$ 38.0000 1.25693
$$915$$ 0 0
$$916$$ 4.00000 0.132164
$$917$$ 0 0
$$918$$ −2.00000 −0.0660098
$$919$$ 56.0000 1.84727 0.923635 0.383274i $$-0.125203\pi$$
0.923635 + 0.383274i $$0.125203\pi$$
$$920$$ 0 0
$$921$$ 2.00000 0.0659022
$$922$$ 12.0000 0.395199
$$923$$ −2.00000 −0.0658308
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 15.0000 0.492931
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −33.0000 −1.08269 −0.541347 0.840799i $$-0.682086\pi$$
−0.541347 + 0.840799i $$0.682086\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 26.0000 0.851202
$$934$$ 2.00000 0.0654420
$$935$$ 0 0
$$936$$ 1.00000 0.0326860
$$937$$ −34.0000 −1.11073 −0.555366 0.831606i $$-0.687422\pi$$
−0.555366 + 0.831606i $$0.687422\pi$$
$$938$$ 0 0
$$939$$ −10.0000 −0.326338
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 13.0000 0.423563
$$943$$ −27.0000 −0.879241
$$944$$ −4.00000 −0.130189
$$945$$ 0 0
$$946$$ 50.0000 1.62564
$$947$$ −12.0000 −0.389948 −0.194974 0.980808i $$-0.562462\pi$$
−0.194974 + 0.980808i $$0.562462\pi$$
$$948$$ −14.0000 −0.454699
$$949$$ 4.00000 0.129845
$$950$$ 0 0
$$951$$ −2.00000 −0.0648544
$$952$$ 0 0
$$953$$ 24.0000 0.777436 0.388718 0.921357i $$-0.372918\pi$$
0.388718 + 0.921357i $$0.372918\pi$$
$$954$$ 1.00000 0.0323762
$$955$$ 0 0
$$956$$ 20.0000 0.646846
$$957$$ 0 0
$$958$$ −8.00000 −0.258468
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ 5.00000 0.161206
$$963$$ −12.0000 −0.386695
$$964$$ 1.00000 0.0322078
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 24.0000 0.771788 0.385894 0.922543i $$-0.373893\pi$$
0.385894 + 0.922543i $$0.373893\pi$$
$$968$$ 14.0000 0.449977
$$969$$ 14.0000 0.449745
$$970$$ 0 0
$$971$$ −39.0000 −1.25157 −0.625785 0.779996i $$-0.715221\pi$$
−0.625785 + 0.779996i $$0.715221\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 0 0
$$974$$ −24.0000 −0.769010
$$975$$ 0 0
$$976$$ 2.00000 0.0640184
$$977$$ −42.0000 −1.34370 −0.671850 0.740688i $$-0.734500\pi$$
−0.671850 + 0.740688i $$0.734500\pi$$
$$978$$ 12.0000 0.383718
$$979$$ 50.0000 1.59801
$$980$$ 0 0
$$981$$ −18.0000 −0.574696
$$982$$ 24.0000 0.765871
$$983$$ 33.0000 1.05254 0.526268 0.850319i $$-0.323591\pi$$
0.526268 + 0.850319i $$0.323591\pi$$
$$984$$ 9.00000 0.286910
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −7.00000 −0.222700
$$989$$ 30.0000 0.953945
$$990$$ 0 0
$$991$$ −36.0000 −1.14358 −0.571789 0.820401i $$-0.693750\pi$$
−0.571789 + 0.820401i $$0.693750\pi$$
$$992$$ 6.00000 0.190500
$$993$$ −15.0000 −0.476011
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −10.0000 −0.316862
$$997$$ −10.0000 −0.316703 −0.158352 0.987383i $$-0.550618\pi$$
−0.158352 + 0.987383i $$0.550618\pi$$
$$998$$ −28.0000 −0.886325
$$999$$ 5.00000 0.158193
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.ch.1.1 1
5.2 odd 4 1470.2.g.a.589.2 2
5.3 odd 4 1470.2.g.a.589.1 2
5.4 even 2 7350.2.a.b.1.1 1
7.3 odd 6 1050.2.i.f.751.1 2
7.5 odd 6 1050.2.i.f.151.1 2
7.6 odd 2 7350.2.a.bn.1.1 1
35.2 odd 12 1470.2.n.i.949.2 4
35.3 even 12 210.2.n.a.79.2 yes 4
35.12 even 12 210.2.n.a.109.2 yes 4
35.13 even 4 1470.2.g.f.589.1 2
35.17 even 12 210.2.n.a.79.1 4
35.18 odd 12 1470.2.n.i.79.2 4
35.19 odd 6 1050.2.i.o.151.1 2
35.23 odd 12 1470.2.n.i.949.1 4
35.24 odd 6 1050.2.i.o.751.1 2
35.27 even 4 1470.2.g.f.589.2 2
35.32 odd 12 1470.2.n.i.79.1 4
35.33 even 12 210.2.n.a.109.1 yes 4
35.34 odd 2 7350.2.a.t.1.1 1
105.17 odd 12 630.2.u.c.289.2 4
105.38 odd 12 630.2.u.c.289.1 4
105.47 odd 12 630.2.u.c.109.1 4
105.68 odd 12 630.2.u.c.109.2 4
140.3 odd 12 1680.2.di.a.289.2 4
140.47 odd 12 1680.2.di.a.529.2 4
140.87 odd 12 1680.2.di.a.289.1 4
140.103 odd 12 1680.2.di.a.529.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.n.a.79.1 4 35.17 even 12
210.2.n.a.79.2 yes 4 35.3 even 12
210.2.n.a.109.1 yes 4 35.33 even 12
210.2.n.a.109.2 yes 4 35.12 even 12
630.2.u.c.109.1 4 105.47 odd 12
630.2.u.c.109.2 4 105.68 odd 12
630.2.u.c.289.1 4 105.38 odd 12
630.2.u.c.289.2 4 105.17 odd 12
1050.2.i.f.151.1 2 7.5 odd 6
1050.2.i.f.751.1 2 7.3 odd 6
1050.2.i.o.151.1 2 35.19 odd 6
1050.2.i.o.751.1 2 35.24 odd 6
1470.2.g.a.589.1 2 5.3 odd 4
1470.2.g.a.589.2 2 5.2 odd 4
1470.2.g.f.589.1 2 35.13 even 4
1470.2.g.f.589.2 2 35.27 even 4
1470.2.n.i.79.1 4 35.32 odd 12
1470.2.n.i.79.2 4 35.18 odd 12
1470.2.n.i.949.1 4 35.23 odd 12
1470.2.n.i.949.2 4 35.2 odd 12
1680.2.di.a.289.1 4 140.87 odd 12
1680.2.di.a.289.2 4 140.3 odd 12
1680.2.di.a.529.1 4 140.103 odd 12
1680.2.di.a.529.2 4 140.47 odd 12
7350.2.a.b.1.1 1 5.4 even 2
7350.2.a.t.1.1 1 35.34 odd 2
7350.2.a.bn.1.1 1 7.6 odd 2
7350.2.a.ch.1.1 1 1.1 even 1 trivial