# Properties

 Label 7350.2.a.t.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

# Learn more about

## 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 $$-0.203260\pi$$
0.802955 + 0.596040i $$0.203260\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 5.00000 1.06600
$$23$$ 3.00000 0.625543 0.312772 0.949828i $$-0.398743\pi$$
0.312772 + 0.949828i $$0.398743\pi$$
$$24$$ −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 $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ −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 $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ −7.00000 −1.13555
$$39$$ 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
$$43$$ 10.0000 1.52499 0.762493 0.646997i $$-0.223975\pi$$
0.762493 + 0.646997i $$0.223975\pi$$
$$44$$ −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 $$-0.521879\pi$$
−0.0686803 + 0.997639i $$0.521879\pi$$
$$54$$ −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
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 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 $$-0.380553\pi$$
0.366508 + 0.930415i $$0.380553\pi$$
$$68$$ −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 $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 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 $$-0.369699\pi$$
0.398015 + 0.917379i $$0.369699\pi$$
$$102$$ 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 $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 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 $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ −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 $$-0.369250\pi$$
0.399310 + 0.916816i $$0.369250\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 10.0000 0.880451
$$130$$ 0 0
$$131$$ −17.0000 −1.48530 −0.742648 0.669681i $$-0.766431\pi$$
−0.742648 + 0.669681i $$0.766431\pi$$
$$132$$ −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 $$-0.554658\pi$$
−0.170872 + 0.985293i $$0.554658\pi$$
$$138$$ −3.00000 −0.255377
$$139$$ −8.00000 −0.678551 −0.339276 0.940687i $$-0.610182\pi$$
−0.339276 + 0.940687i $$0.610182\pi$$
$$140$$ 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 $$-0.655730\pi$$
−0.469956 + 0.882690i $$0.655730\pi$$
$$164$$ −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 $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 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 $$-0.724325\pi$$
−0.647834 + 0.761781i $$0.724325\pi$$
$$194$$ −8.00000 −0.574367
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −27.0000 −1.92367 −0.961835 0.273629i $$-0.911776\pi$$
−0.961835 + 0.273629i $$0.911776\pi$$
$$198$$ 5.00000 0.355335
$$199$$ −14.0000 −0.992434 −0.496217 0.868199i $$-0.665278\pi$$
−0.496217 + 0.868199i $$0.665278\pi$$
$$200$$ 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 $$-0.542192\pi$$
−0.132164 + 0.991228i $$0.542192\pi$$
$$230$$ 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 $$-0.510254\pi$$
−0.0322078 + 0.999481i $$0.510254\pi$$
$$242$$ −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 $$-0.530183\pi$$
−0.0946792 + 0.995508i $$0.530183\pi$$
$$252$$ 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 $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 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 $$-0.359642\pi$$
0.426798 + 0.904347i $$0.359642\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ −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 $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ 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 $$-0.763835\pi$$
−0.737162 + 0.675716i $$0.763835\pi$$
$$312$$ −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 $$-0.482113\pi$$
0.0561656 + 0.998421i $$0.482113\pi$$
$$318$$ 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 $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ 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 $$-0.641297\pi$$
−0.429463 + 0.903085i $$0.641297\pi$$
$$348$$ 0 0
$$349$$ −24.0000 −1.28469 −0.642345 0.766415i $$-0.722038\pi$$
−0.642345 + 0.766415i $$0.722038\pi$$
$$350$$ 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 $$-0.450355\pi$$
0.155334 + 0.987862i $$0.450355\pi$$
$$374$$ −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 $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ 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 $$-0.476653\pi$$
0.0732798 + 0.997311i $$0.476653\pi$$
$$420$$ 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 $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ −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 $$-0.848448\pi$$
−0.888783 + 0.458329i $$0.848448\pi$$
$$458$$ 4.00000 0.186908
$$459$$ −2.00000 −0.0933520
$$460$$ 0 0
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ −15.0000 −0.697109 −0.348555 0.937288i $$-0.613327\pi$$
−0.348555 + 0.937288i $$0.613327\pi$$
$$464$$ 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 $$-0.441495\pi$$
0.182765 + 0.983157i $$0.441495\pi$$
$$480$$ 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 $$-0.316996\pi$$
0.543772 + 0.839233i $$0.316996\pi$$
$$488$$ 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 $$-0.399581\pi$$
0.310270 + 0.950649i $$0.399581\pi$$
$$510$$ 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 $$-0.606570\pi$$
−0.328581 + 0.944476i $$0.606570\pi$$
$$522$$ 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 $$-0.596753\pi$$
−0.299298 + 0.954160i $$0.596753\pi$$
$$548$$ −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 $$-0.809525\pi$$
−0.826242 + 0.563316i $$0.809525\pi$$
$$558$$ 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 $$-0.709580\pi$$
−0.611863 + 0.790964i $$0.709580\pi$$
$$602$$ 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 $$-0.374649\pi$$
0.383701 + 0.923457i $$0.374649\pi$$
$$614$$ −2.00000 −0.0807134
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 30.0000 1.20775 0.603877 0.797077i $$-0.293622\pi$$
0.603877 + 0.797077i $$0.293622\pi$$
$$618$$ 0 0
$$619$$ 15.0000 0.602901 0.301450 0.953482i $$-0.402529\pi$$
0.301450 + 0.953482i $$0.402529\pi$$
$$620$$ 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 $$-0.468809\pi$$
0.0978326 + 0.995203i $$0.468809\pi$$
$$654$$ 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 $$-0.216280\pi$$
0.777910 + 0.628376i $$0.216280\pi$$
$$662$$ 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 $$-0.255914\pi$$
0.693849 + 0.720121i $$0.255914\pi$$
$$674$$ 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 $$-0.524383\pi$$
−0.0765279 + 0.997067i $$0.524383\pi$$
$$684$$ 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 $$-0.624220\pi$$
−0.380418 + 0.924815i $$0.624220\pi$$
$$692$$ 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 $$-0.511874\pi$$
−0.0372937 + 0.999304i $$0.511874\pi$$
$$720$$ 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 $$-0.692530\pi$$
−0.568640 + 0.822587i $$0.692530\pi$$
$$744$$ 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 $$-0.656646\pi$$
−0.472493 + 0.881334i $$0.656646\pi$$
$$758$$ 1.00000 0.0363216
$$759$$ −15.0000 −0.544466
$$760$$ 0 0
$$761$$ −3.00000 −0.108750 −0.0543750 0.998521i $$-0.517317\pi$$
−0.0543750 + 0.998521i $$0.517317\pi$$
$$762$$ −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 $$-0.128551\pi$$
0.919554 + 0.392965i $$0.128551\pi$$
$$770$$ 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 $$-0.438136\pi$$
0.193131 + 0.981173i $$0.438136\pi$$
$$812$$ 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 $$-0.544527\pi$$
−0.139431 + 0.990232i $$0.544527\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −42.0000 −1.46048 −0.730242 0.683189i $$-0.760592\pi$$
−0.730242 + 0.683189i $$0.760592\pi$$
$$828$$ 3.00000 0.104257
$$829$$ 2.00000 0.0694629 0.0347314 0.999397i $$-0.488942\pi$$
0.0347314 + 0.999397i $$0.488942\pi$$
$$830$$ 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 $$-0.489009\pi$$
0.0345238 + 0.999404i $$0.489009\pi$$
$$840$$ 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 $$-0.289498\pi$$
0.614152 + 0.789188i $$0.289498\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −18.0000 −0.613082
$$863$$ 15.0000 0.510606 0.255303 0.966861i $$-0.417825\pi$$
0.255303 + 0.966861i $$0.417825\pi$$
$$864$$ −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 $$-0.650669\pi$$
−0.455863 + 0.890050i $$0.650669\pi$$
$$878$$ 0 0
$$879$$ 1.00000 0.0337292
$$880$$ 0 0
$$881$$ −3.00000 −0.101073 −0.0505363 0.998722i $$-0.516093\pi$$
−0.0505363 + 0.998722i $$0.516093\pi$$
$$882$$ 0 0
$$883$$ −52.0000 −1.74994 −0.874970 0.484178i $$-0.839119\pi$$
−0.874970 + 0.484178i $$0.839119\pi$$
$$884$$ −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 $$-0.585582\pi$$
−0.265636 + 0.964073i $$0.585582\pi$$
$$908$$ 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 $$-0.317914\pi$$
0.541347 + 0.840799i $$0.317914\pi$$
$$930$$ 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 $$-0.437538\pi$$
0.194974 + 0.980808i $$0.437538\pi$$
$$948$$ −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 $$-0.627082\pi$$
−0.388718 + 0.921357i $$0.627082\pi$$
$$954$$ 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 $$-0.626107\pi$$
−0.385894 + 0.922543i $$0.626107\pi$$
$$968$$ −14.0000 −0.449977
$$969$$ −14.0000 −0.449745
$$970$$ 0 0
$$971$$ 39.0000 1.25157 0.625785 0.779996i $$-0.284779\pi$$
0.625785 + 0.779996i $$0.284779\pi$$
$$972$$ 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 $$-0.265500\pi$$
0.671850 + 0.740688i $$0.265500\pi$$
$$978$$ 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.t.1.1 1
5.2 odd 4 1470.2.g.f.589.1 2
5.3 odd 4 1470.2.g.f.589.2 2
5.4 even 2 7350.2.a.bn.1.1 1
7.2 even 3 1050.2.i.o.151.1 2
7.4 even 3 1050.2.i.o.751.1 2
7.6 odd 2 7350.2.a.b.1.1 1
35.2 odd 12 210.2.n.a.109.1 yes 4
35.3 even 12 1470.2.n.i.79.1 4
35.4 even 6 1050.2.i.f.751.1 2
35.9 even 6 1050.2.i.f.151.1 2
35.12 even 12 1470.2.n.i.949.1 4
35.13 even 4 1470.2.g.a.589.2 2
35.17 even 12 1470.2.n.i.79.2 4
35.18 odd 12 210.2.n.a.79.1 4
35.23 odd 12 210.2.n.a.109.2 yes 4
35.27 even 4 1470.2.g.a.589.1 2
35.32 odd 12 210.2.n.a.79.2 yes 4
35.33 even 12 1470.2.n.i.949.2 4
35.34 odd 2 7350.2.a.ch.1.1 1
105.2 even 12 630.2.u.c.109.2 4
105.23 even 12 630.2.u.c.109.1 4
105.32 even 12 630.2.u.c.289.1 4
105.53 even 12 630.2.u.c.289.2 4
140.23 even 12 1680.2.di.a.529.2 4
140.67 even 12 1680.2.di.a.289.2 4
140.107 even 12 1680.2.di.a.529.1 4
140.123 even 12 1680.2.di.a.289.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.n.a.79.1 4 35.18 odd 12
210.2.n.a.79.2 yes 4 35.32 odd 12
210.2.n.a.109.1 yes 4 35.2 odd 12
210.2.n.a.109.2 yes 4 35.23 odd 12
630.2.u.c.109.1 4 105.23 even 12
630.2.u.c.109.2 4 105.2 even 12
630.2.u.c.289.1 4 105.32 even 12
630.2.u.c.289.2 4 105.53 even 12
1050.2.i.f.151.1 2 35.9 even 6
1050.2.i.f.751.1 2 35.4 even 6
1050.2.i.o.151.1 2 7.2 even 3
1050.2.i.o.751.1 2 7.4 even 3
1470.2.g.a.589.1 2 35.27 even 4
1470.2.g.a.589.2 2 35.13 even 4
1470.2.g.f.589.1 2 5.2 odd 4
1470.2.g.f.589.2 2 5.3 odd 4
1470.2.n.i.79.1 4 35.3 even 12
1470.2.n.i.79.2 4 35.17 even 12
1470.2.n.i.949.1 4 35.12 even 12
1470.2.n.i.949.2 4 35.33 even 12
1680.2.di.a.289.1 4 140.123 even 12
1680.2.di.a.289.2 4 140.67 even 12
1680.2.di.a.529.1 4 140.107 even 12
1680.2.di.a.529.2 4 140.23 even 12
7350.2.a.b.1.1 1 7.6 odd 2
7350.2.a.t.1.1 1 1.1 even 1 trivial
7350.2.a.bn.1.1 1 5.4 even 2
7350.2.a.ch.1.1 1 35.34 odd 2