# Properties

 Label 7350.2.a.bb.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

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{12} -4.00000 q^{13} +1.00000 q^{16} +3.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} +3.00000 q^{23} -1.00000 q^{24} +4.00000 q^{26} +1.00000 q^{27} -1.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} -2.00000 q^{38} -4.00000 q^{39} -9.00000 q^{41} -10.0000 q^{43} -3.00000 q^{46} -3.00000 q^{47} +1.00000 q^{48} +3.00000 q^{51} -4.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} +2.00000 q^{57} -6.00000 q^{59} +8.00000 q^{61} +1.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} +3.00000 q^{68} +3.00000 q^{69} +3.00000 q^{71} -1.00000 q^{72} +14.0000 q^{73} +10.0000 q^{74} +2.00000 q^{76} +4.00000 q^{78} +11.0000 q^{79} +1.00000 q^{81} +9.00000 q^{82} +10.0000 q^{86} -15.0000 q^{89} +3.00000 q^{92} -1.00000 q^{93} +3.00000 q^{94} -1.00000 q^{96} -7.00000 q^{97} +O(q^{100})$$

## 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
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 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
$$26$$ 4.00000 0.784465
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −0.179605 −0.0898027 0.995960i $$-0.528624\pi$$
−0.0898027 + 0.995960i $$0.528624\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ −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 $$0.807139\pi$$
$$38$$ −2.00000 −0.324443
$$39$$ −4.00000 −0.640513
$$40$$ 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 $$-0.776025\pi$$
−0.762493 + 0.646997i $$0.776025\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −3.00000 −0.442326
$$47$$ −3.00000 −0.437595 −0.218797 0.975770i $$-0.570213\pi$$
−0.218797 + 0.975770i $$0.570213\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 3.00000 0.420084
$$52$$ −4.00000 −0.554700
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 2.00000 0.264906
$$58$$ 0 0
$$59$$ −6.00000 −0.781133 −0.390567 0.920575i $$-0.627721\pi$$
−0.390567 + 0.920575i $$0.627721\pi$$
$$60$$ 0 0
$$61$$ 8.00000 1.02430 0.512148 0.858898i $$-0.328850\pi$$
0.512148 + 0.858898i $$0.328850\pi$$
$$62$$ 1.00000 0.127000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −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
$$71$$ 3.00000 0.356034 0.178017 0.984027i $$-0.443032\pi$$
0.178017 + 0.984027i $$0.443032\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ 14.0000 1.63858 0.819288 0.573382i $$-0.194369\pi$$
0.819288 + 0.573382i $$0.194369\pi$$
$$74$$ 10.0000 1.16248
$$75$$ 0 0
$$76$$ 2.00000 0.229416
$$77$$ 0 0
$$78$$ 4.00000 0.452911
$$79$$ 11.0000 1.23760 0.618798 0.785550i $$-0.287620\pi$$
0.618798 + 0.785550i $$0.287620\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 9.00000 0.993884
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 10.0000 1.07833
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −15.0000 −1.59000 −0.794998 0.606612i $$-0.792528\pi$$
−0.794998 + 0.606612i $$0.792528\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 3.00000 0.312772
$$93$$ −1.00000 −0.103695
$$94$$ 3.00000 0.309426
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ −7.00000 −0.710742 −0.355371 0.934725i $$-0.615646\pi$$
−0.355371 + 0.934725i $$0.615646\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 18.0000 1.79107 0.895533 0.444994i $$-0.146794\pi$$
0.895533 + 0.444994i $$0.146794\pi$$
$$102$$ −3.00000 −0.297044
$$103$$ 5.00000 0.492665 0.246332 0.969185i $$-0.420775\pi$$
0.246332 + 0.969185i $$0.420775\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −18.0000 −1.74013 −0.870063 0.492941i $$-0.835922\pi$$
−0.870063 + 0.492941i $$0.835922\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 0 0
$$111$$ −10.0000 −0.949158
$$112$$ 0 0
$$113$$ 21.0000 1.97551 0.987757 0.156001i $$-0.0498603\pi$$
0.987757 + 0.156001i $$0.0498603\pi$$
$$114$$ −2.00000 −0.187317
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −4.00000 −0.369800
$$118$$ 6.00000 0.552345
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ −8.00000 −0.724286
$$123$$ −9.00000 −0.811503
$$124$$ −1.00000 −0.0898027
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −16.0000 −1.41977 −0.709885 0.704317i $$-0.751253\pi$$
−0.709885 + 0.704317i $$0.751253\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −10.0000 −0.880451
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 4.00000 0.345547
$$135$$ 0 0
$$136$$ −3.00000 −0.257248
$$137$$ −9.00000 −0.768922 −0.384461 0.923141i $$-0.625613\pi$$
−0.384461 + 0.923141i $$0.625613\pi$$
$$138$$ −3.00000 −0.255377
$$139$$ 2.00000 0.169638 0.0848189 0.996396i $$-0.472969\pi$$
0.0848189 + 0.996396i $$0.472969\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ −3.00000 −0.251754
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −14.0000 −1.15865
$$147$$ 0 0
$$148$$ −10.0000 −0.821995
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ −2.00000 −0.162221
$$153$$ 3.00000 0.242536
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −4.00000 −0.320256
$$157$$ 8.00000 0.638470 0.319235 0.947676i $$-0.396574\pi$$
0.319235 + 0.947676i $$0.396574\pi$$
$$158$$ −11.0000 −0.875113
$$159$$ −6.00000 −0.475831
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 8.00000 0.626608 0.313304 0.949653i $$-0.398564\pi$$
0.313304 + 0.949653i $$0.398564\pi$$
$$164$$ −9.00000 −0.702782
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −24.0000 −1.85718 −0.928588 0.371113i $$-0.878976\pi$$
−0.928588 + 0.371113i $$0.878976\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 2.00000 0.152944
$$172$$ −10.0000 −0.762493
$$173$$ −18.0000 −1.36851 −0.684257 0.729241i $$-0.739873\pi$$
−0.684257 + 0.729241i $$0.739873\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −6.00000 −0.450988
$$178$$ 15.0000 1.12430
$$179$$ −6.00000 −0.448461 −0.224231 0.974536i $$-0.571987\pi$$
−0.224231 + 0.974536i $$0.571987\pi$$
$$180$$ 0 0
$$181$$ 8.00000 0.594635 0.297318 0.954779i $$-0.403908\pi$$
0.297318 + 0.954779i $$0.403908\pi$$
$$182$$ 0 0
$$183$$ 8.00000 0.591377
$$184$$ −3.00000 −0.221163
$$185$$ 0 0
$$186$$ 1.00000 0.0733236
$$187$$ 0 0
$$188$$ −3.00000 −0.218797
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −21.0000 −1.51951 −0.759753 0.650211i $$-0.774680\pi$$
−0.759753 + 0.650211i $$0.774680\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 17.0000 1.22369 0.611843 0.790979i $$-0.290428\pi$$
0.611843 + 0.790979i $$0.290428\pi$$
$$194$$ 7.00000 0.502571
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ 11.0000 0.779769 0.389885 0.920864i $$-0.372515\pi$$
0.389885 + 0.920864i $$0.372515\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ −18.0000 −1.26648
$$203$$ 0 0
$$204$$ 3.00000 0.210042
$$205$$ 0 0
$$206$$ −5.00000 −0.348367
$$207$$ 3.00000 0.208514
$$208$$ −4.00000 −0.277350
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 14.0000 0.963800 0.481900 0.876226i $$-0.339947\pi$$
0.481900 + 0.876226i $$0.339947\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 3.00000 0.205557
$$214$$ 18.0000 1.23045
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ 14.0000 0.946032
$$220$$ 0 0
$$221$$ −12.0000 −0.807207
$$222$$ 10.0000 0.671156
$$223$$ −19.0000 −1.27233 −0.636167 0.771551i $$-0.719481\pi$$
−0.636167 + 0.771551i $$0.719481\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −21.0000 −1.39690
$$227$$ −6.00000 −0.398234 −0.199117 0.979976i $$-0.563807\pi$$
−0.199117 + 0.979976i $$0.563807\pi$$
$$228$$ 2.00000 0.132453
$$229$$ −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
$$233$$ −30.0000 −1.96537 −0.982683 0.185296i $$-0.940675\pi$$
−0.982683 + 0.185296i $$0.940675\pi$$
$$234$$ 4.00000 0.261488
$$235$$ 0 0
$$236$$ −6.00000 −0.390567
$$237$$ 11.0000 0.714527
$$238$$ 0 0
$$239$$ 15.0000 0.970269 0.485135 0.874439i $$-0.338771\pi$$
0.485135 + 0.874439i $$0.338771\pi$$
$$240$$ 0 0
$$241$$ 14.0000 0.901819 0.450910 0.892570i $$-0.351100\pi$$
0.450910 + 0.892570i $$0.351100\pi$$
$$242$$ 11.0000 0.707107
$$243$$ 1.00000 0.0641500
$$244$$ 8.00000 0.512148
$$245$$ 0 0
$$246$$ 9.00000 0.573819
$$247$$ −8.00000 −0.509028
$$248$$ 1.00000 0.0635001
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 16.0000 1.00393
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 30.0000 1.87135 0.935674 0.352865i $$-0.114792\pi$$
0.935674 + 0.352865i $$0.114792\pi$$
$$258$$ 10.0000 0.622573
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 12.0000 0.741362
$$263$$ 9.00000 0.554964 0.277482 0.960731i $$-0.410500\pi$$
0.277482 + 0.960731i $$0.410500\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −15.0000 −0.917985
$$268$$ −4.00000 −0.244339
$$269$$ −6.00000 −0.365826 −0.182913 0.983129i $$-0.558553\pi$$
−0.182913 + 0.983129i $$0.558553\pi$$
$$270$$ 0 0
$$271$$ −7.00000 −0.425220 −0.212610 0.977137i $$-0.568196\pi$$
−0.212610 + 0.977137i $$0.568196\pi$$
$$272$$ 3.00000 0.181902
$$273$$ 0 0
$$274$$ 9.00000 0.543710
$$275$$ 0 0
$$276$$ 3.00000 0.180579
$$277$$ −28.0000 −1.68236 −0.841178 0.540758i $$-0.818138\pi$$
−0.841178 + 0.540758i $$0.818138\pi$$
$$278$$ −2.00000 −0.119952
$$279$$ −1.00000 −0.0598684
$$280$$ 0 0
$$281$$ 9.00000 0.536895 0.268447 0.963294i $$-0.413489\pi$$
0.268447 + 0.963294i $$0.413489\pi$$
$$282$$ 3.00000 0.178647
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ 3.00000 0.178017
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ −7.00000 −0.410347
$$292$$ 14.0000 0.819288
$$293$$ −24.0000 −1.40209 −0.701047 0.713115i $$-0.747284\pi$$
−0.701047 + 0.713115i $$0.747284\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 10.0000 0.581238
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ −12.0000 −0.693978
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −8.00000 −0.460348
$$303$$ 18.0000 1.03407
$$304$$ 2.00000 0.114708
$$305$$ 0 0
$$306$$ −3.00000 −0.171499
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ 5.00000 0.284440
$$310$$ 0 0
$$311$$ 9.00000 0.510343 0.255172 0.966896i $$-0.417868\pi$$
0.255172 + 0.966896i $$0.417868\pi$$
$$312$$ 4.00000 0.226455
$$313$$ 5.00000 0.282617 0.141308 0.989966i $$-0.454869\pi$$
0.141308 + 0.989966i $$0.454869\pi$$
$$314$$ −8.00000 −0.451466
$$315$$ 0 0
$$316$$ 11.0000 0.618798
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 6.00000 0.336463
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −18.0000 −1.00466
$$322$$ 0 0
$$323$$ 6.00000 0.333849
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −8.00000 −0.443079
$$327$$ 2.00000 0.110600
$$328$$ 9.00000 0.496942
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −10.0000 −0.549650 −0.274825 0.961494i $$-0.588620\pi$$
−0.274825 + 0.961494i $$0.588620\pi$$
$$332$$ 0 0
$$333$$ −10.0000 −0.547997
$$334$$ 24.0000 1.31322
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 11.0000 0.599208 0.299604 0.954064i $$-0.403145\pi$$
0.299604 + 0.954064i $$0.403145\pi$$
$$338$$ −3.00000 −0.163178
$$339$$ 21.0000 1.14056
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −2.00000 −0.108148
$$343$$ 0 0
$$344$$ 10.0000 0.539164
$$345$$ 0 0
$$346$$ 18.0000 0.967686
$$347$$ −36.0000 −1.93258 −0.966291 0.257454i $$-0.917117\pi$$
−0.966291 + 0.257454i $$0.917117\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ −4.00000 −0.213504
$$352$$ 0 0
$$353$$ −15.0000 −0.798369 −0.399185 0.916871i $$-0.630707\pi$$
−0.399185 + 0.916871i $$0.630707\pi$$
$$354$$ 6.00000 0.318896
$$355$$ 0 0
$$356$$ −15.0000 −0.794998
$$357$$ 0 0
$$358$$ 6.00000 0.317110
$$359$$ 12.0000 0.633336 0.316668 0.948536i $$-0.397436\pi$$
0.316668 + 0.948536i $$0.397436\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ −8.00000 −0.420471
$$363$$ −11.0000 −0.577350
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −8.00000 −0.418167
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 3.00000 0.156386
$$369$$ −9.00000 −0.468521
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −1.00000 −0.0518476
$$373$$ −4.00000 −0.207112 −0.103556 0.994624i $$-0.533022\pi$$
−0.103556 + 0.994624i $$0.533022\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 3.00000 0.154713
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −16.0000 −0.821865 −0.410932 0.911666i $$-0.634797\pi$$
−0.410932 + 0.911666i $$0.634797\pi$$
$$380$$ 0 0
$$381$$ −16.0000 −0.819705
$$382$$ 21.0000 1.07445
$$383$$ 21.0000 1.07305 0.536525 0.843884i $$-0.319737\pi$$
0.536525 + 0.843884i $$0.319737\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −17.0000 −0.865277
$$387$$ −10.0000 −0.508329
$$388$$ −7.00000 −0.355371
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ 0 0
$$393$$ −12.0000 −0.605320
$$394$$ 12.0000 0.604551
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −22.0000 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ −11.0000 −0.551380
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 4.00000 0.199502
$$403$$ 4.00000 0.199254
$$404$$ 18.0000 0.895533
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −3.00000 −0.148522
$$409$$ 5.00000 0.247234 0.123617 0.992330i $$-0.460551\pi$$
0.123617 + 0.992330i $$0.460551\pi$$
$$410$$ 0 0
$$411$$ −9.00000 −0.443937
$$412$$ 5.00000 0.246332
$$413$$ 0 0
$$414$$ −3.00000 −0.147442
$$415$$ 0 0
$$416$$ 4.00000 0.196116
$$417$$ 2.00000 0.0979404
$$418$$ 0 0
$$419$$ 18.0000 0.879358 0.439679 0.898155i $$-0.355092\pi$$
0.439679 + 0.898155i $$0.355092\pi$$
$$420$$ 0 0
$$421$$ −40.0000 −1.94948 −0.974740 0.223341i $$-0.928304\pi$$
−0.974740 + 0.223341i $$0.928304\pi$$
$$422$$ −14.0000 −0.681509
$$423$$ −3.00000 −0.145865
$$424$$ 6.00000 0.291386
$$425$$ 0 0
$$426$$ −3.00000 −0.145350
$$427$$ 0 0
$$428$$ −18.0000 −0.870063
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −27.0000 −1.30054 −0.650272 0.759701i $$-0.725345\pi$$
−0.650272 + 0.759701i $$0.725345\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ 29.0000 1.39365 0.696826 0.717241i $$-0.254595\pi$$
0.696826 + 0.717241i $$0.254595\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 2.00000 0.0957826
$$437$$ 6.00000 0.287019
$$438$$ −14.0000 −0.668946
$$439$$ 5.00000 0.238637 0.119318 0.992856i $$-0.461929\pi$$
0.119318 + 0.992856i $$0.461929\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 12.0000 0.570782
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ −10.0000 −0.474579
$$445$$ 0 0
$$446$$ 19.0000 0.899676
$$447$$ −6.00000 −0.283790
$$448$$ 0 0
$$449$$ −21.0000 −0.991051 −0.495526 0.868593i $$-0.665025\pi$$
−0.495526 + 0.868593i $$0.665025\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 21.0000 0.987757
$$453$$ 8.00000 0.375873
$$454$$ 6.00000 0.281594
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ 2.00000 0.0935561 0.0467780 0.998905i $$-0.485105\pi$$
0.0467780 + 0.998905i $$0.485105\pi$$
$$458$$ 4.00000 0.186908
$$459$$ 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
$$463$$ 5.00000 0.232370 0.116185 0.993228i $$-0.462933\pi$$
0.116185 + 0.993228i $$0.462933\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 30.0000 1.38972
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ −4.00000 −0.184900
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 8.00000 0.368621
$$472$$ 6.00000 0.276172
$$473$$ 0 0
$$474$$ −11.0000 −0.505247
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ −15.0000 −0.686084
$$479$$ −27.0000 −1.23366 −0.616831 0.787096i $$-0.711584\pi$$
−0.616831 + 0.787096i $$0.711584\pi$$
$$480$$ 0 0
$$481$$ 40.0000 1.82384
$$482$$ −14.0000 −0.637683
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ −31.0000 −1.40474 −0.702372 0.711810i $$-0.747876\pi$$
−0.702372 + 0.711810i $$0.747876\pi$$
$$488$$ −8.00000 −0.362143
$$489$$ 8.00000 0.361773
$$490$$ 0 0
$$491$$ −6.00000 −0.270776 −0.135388 0.990793i $$-0.543228\pi$$
−0.135388 + 0.990793i $$0.543228\pi$$
$$492$$ −9.00000 −0.405751
$$493$$ 0 0
$$494$$ 8.00000 0.359937
$$495$$ 0 0
$$496$$ −1.00000 −0.0449013
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 32.0000 1.43252 0.716258 0.697835i $$-0.245853\pi$$
0.716258 + 0.697835i $$0.245853\pi$$
$$500$$ 0 0
$$501$$ −24.0000 −1.07224
$$502$$ −12.0000 −0.535586
$$503$$ −36.0000 −1.60516 −0.802580 0.596544i $$-0.796540\pi$$
−0.802580 + 0.596544i $$0.796540\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 3.00000 0.133235
$$508$$ −16.0000 −0.709885
$$509$$ −36.0000 −1.59567 −0.797836 0.602875i $$-0.794022\pi$$
−0.797836 + 0.602875i $$0.794022\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 2.00000 0.0883022
$$514$$ −30.0000 −1.32324
$$515$$ 0 0
$$516$$ −10.0000 −0.440225
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −18.0000 −0.790112
$$520$$ 0 0
$$521$$ 15.0000 0.657162 0.328581 0.944476i $$-0.393430\pi$$
0.328581 + 0.944476i $$0.393430\pi$$
$$522$$ 0 0
$$523$$ 32.0000 1.39926 0.699631 0.714504i $$-0.253348\pi$$
0.699631 + 0.714504i $$0.253348\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 0 0
$$526$$ −9.00000 −0.392419
$$527$$ −3.00000 −0.130682
$$528$$ 0 0
$$529$$ −14.0000 −0.608696
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 0 0
$$533$$ 36.0000 1.55933
$$534$$ 15.0000 0.649113
$$535$$ 0 0
$$536$$ 4.00000 0.172774
$$537$$ −6.00000 −0.258919
$$538$$ 6.00000 0.258678
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −16.0000 −0.687894 −0.343947 0.938989i $$-0.611764\pi$$
−0.343947 + 0.938989i $$0.611764\pi$$
$$542$$ 7.00000 0.300676
$$543$$ 8.00000 0.343313
$$544$$ −3.00000 −0.128624
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 26.0000 1.11168 0.555840 0.831289i $$-0.312397\pi$$
0.555840 + 0.831289i $$0.312397\pi$$
$$548$$ −9.00000 −0.384461
$$549$$ 8.00000 0.341432
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −3.00000 −0.127688
$$553$$ 0 0
$$554$$ 28.0000 1.18961
$$555$$ 0 0
$$556$$ 2.00000 0.0848189
$$557$$ 6.00000 0.254228 0.127114 0.991888i $$-0.459429\pi$$
0.127114 + 0.991888i $$0.459429\pi$$
$$558$$ 1.00000 0.0423334
$$559$$ 40.0000 1.69182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −9.00000 −0.379642
$$563$$ −30.0000 −1.26435 −0.632175 0.774826i $$-0.717837\pi$$
−0.632175 + 0.774826i $$0.717837\pi$$
$$564$$ −3.00000 −0.126323
$$565$$ 0 0
$$566$$ 4.00000 0.168133
$$567$$ 0 0
$$568$$ −3.00000 −0.125877
$$569$$ 27.0000 1.13190 0.565949 0.824440i $$-0.308510\pi$$
0.565949 + 0.824440i $$0.308510\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ 0 0
$$573$$ −21.0000 −0.877288
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 14.0000 0.582828 0.291414 0.956597i $$-0.405874\pi$$
0.291414 + 0.956597i $$0.405874\pi$$
$$578$$ 8.00000 0.332756
$$579$$ 17.0000 0.706496
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 7.00000 0.290159
$$583$$ 0 0
$$584$$ −14.0000 −0.579324
$$585$$ 0 0
$$586$$ 24.0000 0.991431
$$587$$ 42.0000 1.73353 0.866763 0.498721i $$-0.166197\pi$$
0.866763 + 0.498721i $$0.166197\pi$$
$$588$$ 0 0
$$589$$ −2.00000 −0.0824086
$$590$$ 0 0
$$591$$ −12.0000 −0.493614
$$592$$ −10.0000 −0.410997
$$593$$ 21.0000 0.862367 0.431183 0.902264i $$-0.358096\pi$$
0.431183 + 0.902264i $$0.358096\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ 11.0000 0.450200
$$598$$ 12.0000 0.490716
$$599$$ −3.00000 −0.122577 −0.0612883 0.998120i $$-0.519521\pi$$
−0.0612883 + 0.998120i $$0.519521\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 0 0
$$603$$ −4.00000 −0.162893
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ −18.0000 −0.731200
$$607$$ −7.00000 −0.284121 −0.142061 0.989858i $$-0.545373\pi$$
−0.142061 + 0.989858i $$0.545373\pi$$
$$608$$ −2.00000 −0.0811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 12.0000 0.485468
$$612$$ 3.00000 0.121268
$$613$$ −16.0000 −0.646234 −0.323117 0.946359i $$-0.604731\pi$$
−0.323117 + 0.946359i $$0.604731\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −15.0000 −0.603877 −0.301939 0.953327i $$-0.597634\pi$$
−0.301939 + 0.953327i $$0.597634\pi$$
$$618$$ −5.00000 −0.201129
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ 0 0
$$621$$ 3.00000 0.120386
$$622$$ −9.00000 −0.360867
$$623$$ 0 0
$$624$$ −4.00000 −0.160128
$$625$$ 0 0
$$626$$ −5.00000 −0.199840
$$627$$ 0 0
$$628$$ 8.00000 0.319235
$$629$$ −30.0000 −1.19618
$$630$$ 0 0
$$631$$ −37.0000 −1.47295 −0.736473 0.676467i $$-0.763510\pi$$
−0.736473 + 0.676467i $$0.763510\pi$$
$$632$$ −11.0000 −0.437557
$$633$$ 14.0000 0.556450
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 3.00000 0.118678
$$640$$ 0 0
$$641$$ −33.0000 −1.30342 −0.651711 0.758468i $$-0.725948\pi$$
−0.651711 + 0.758468i $$0.725948\pi$$
$$642$$ 18.0000 0.710403
$$643$$ 38.0000 1.49857 0.749287 0.662246i $$-0.230396\pi$$
0.749287 + 0.662246i $$0.230396\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −6.00000 −0.236067
$$647$$ 24.0000 0.943537 0.471769 0.881722i $$-0.343616\pi$$
0.471769 + 0.881722i $$0.343616\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 8.00000 0.313304
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ −2.00000 −0.0782062
$$655$$ 0 0
$$656$$ −9.00000 −0.351391
$$657$$ 14.0000 0.546192
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −10.0000 −0.388955 −0.194477 0.980907i $$-0.562301\pi$$
−0.194477 + 0.980907i $$0.562301\pi$$
$$662$$ 10.0000 0.388661
$$663$$ −12.0000 −0.466041
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 10.0000 0.387492
$$667$$ 0 0
$$668$$ −24.0000 −0.928588
$$669$$ −19.0000 −0.734582
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ −11.0000 −0.423704
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ −12.0000 −0.461197 −0.230599 0.973049i $$-0.574068\pi$$
−0.230599 + 0.973049i $$0.574068\pi$$
$$678$$ −21.0000 −0.806500
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −6.00000 −0.229920
$$682$$ 0 0
$$683$$ 6.00000 0.229584 0.114792 0.993390i $$-0.463380\pi$$
0.114792 + 0.993390i $$0.463380\pi$$
$$684$$ 2.00000 0.0764719
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −4.00000 −0.152610
$$688$$ −10.0000 −0.381246
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ 36.0000 1.36654
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −27.0000 −1.02270
$$698$$ −26.0000 −0.984115
$$699$$ −30.0000 −1.13470
$$700$$ 0 0
$$701$$ −12.0000 −0.453234 −0.226617 0.973984i $$-0.572767\pi$$
−0.226617 + 0.973984i $$0.572767\pi$$
$$702$$ 4.00000 0.150970
$$703$$ −20.0000 −0.754314
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 15.0000 0.564532
$$707$$ 0 0
$$708$$ −6.00000 −0.225494
$$709$$ −34.0000 −1.27690 −0.638448 0.769665i $$-0.720423\pi$$
−0.638448 + 0.769665i $$0.720423\pi$$
$$710$$ 0 0
$$711$$ 11.0000 0.412532
$$712$$ 15.0000 0.562149
$$713$$ −3.00000 −0.112351
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −6.00000 −0.224231
$$717$$ 15.0000 0.560185
$$718$$ −12.0000 −0.447836
$$719$$ −27.0000 −1.00693 −0.503465 0.864016i $$-0.667942\pi$$
−0.503465 + 0.864016i $$0.667942\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 15.0000 0.558242
$$723$$ 14.0000 0.520666
$$724$$ 8.00000 0.297318
$$725$$ 0 0
$$726$$ 11.0000 0.408248
$$727$$ −37.0000 −1.37225 −0.686127 0.727482i $$-0.740691\pi$$
−0.686127 + 0.727482i $$0.740691\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −30.0000 −1.10959
$$732$$ 8.00000 0.295689
$$733$$ 14.0000 0.517102 0.258551 0.965998i $$-0.416755\pi$$
0.258551 + 0.965998i $$0.416755\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ −3.00000 −0.110581
$$737$$ 0 0
$$738$$ 9.00000 0.331295
$$739$$ 2.00000 0.0735712 0.0367856 0.999323i $$-0.488288\pi$$
0.0367856 + 0.999323i $$0.488288\pi$$
$$740$$ 0 0
$$741$$ −8.00000 −0.293887
$$742$$ 0 0
$$743$$ −51.0000 −1.87101 −0.935504 0.353315i $$-0.885054\pi$$
−0.935504 + 0.353315i $$0.885054\pi$$
$$744$$ 1.00000 0.0366618
$$745$$ 0 0
$$746$$ 4.00000 0.146450
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −16.0000 −0.583848 −0.291924 0.956441i $$-0.594295\pi$$
−0.291924 + 0.956441i $$0.594295\pi$$
$$752$$ −3.00000 −0.109399
$$753$$ 12.0000 0.437304
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −16.0000 −0.581530 −0.290765 0.956795i $$-0.593910\pi$$
−0.290765 + 0.956795i $$0.593910\pi$$
$$758$$ 16.0000 0.581146
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 27.0000 0.978749 0.489375 0.872074i $$-0.337225\pi$$
0.489375 + 0.872074i $$0.337225\pi$$
$$762$$ 16.0000 0.579619
$$763$$ 0 0
$$764$$ −21.0000 −0.759753
$$765$$ 0 0
$$766$$ −21.0000 −0.758761
$$767$$ 24.0000 0.866590
$$768$$ 1.00000 0.0360844
$$769$$ 26.0000 0.937584 0.468792 0.883309i $$-0.344689\pi$$
0.468792 + 0.883309i $$0.344689\pi$$
$$770$$ 0 0
$$771$$ 30.0000 1.08042
$$772$$ 17.0000 0.611843
$$773$$ 18.0000 0.647415 0.323708 0.946157i $$-0.395071\pi$$
0.323708 + 0.946157i $$0.395071\pi$$
$$774$$ 10.0000 0.359443
$$775$$ 0 0
$$776$$ 7.00000 0.251285
$$777$$ 0 0
$$778$$ −6.00000 −0.215110
$$779$$ −18.0000 −0.644917
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −9.00000 −0.321839
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 12.0000 0.428026
$$787$$ −22.0000 −0.784215 −0.392108 0.919919i $$-0.628254\pi$$
−0.392108 + 0.919919i $$0.628254\pi$$
$$788$$ −12.0000 −0.427482
$$789$$ 9.00000 0.320408
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −32.0000 −1.13635
$$794$$ 22.0000 0.780751
$$795$$ 0 0
$$796$$ 11.0000 0.389885
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ −9.00000 −0.318397
$$800$$ 0 0
$$801$$ −15.0000 −0.529999
$$802$$ −18.0000 −0.635602
$$803$$ 0 0
$$804$$ −4.00000 −0.141069
$$805$$ 0 0
$$806$$ −4.00000 −0.140894
$$807$$ −6.00000 −0.211210
$$808$$ −18.0000 −0.633238
$$809$$ 6.00000 0.210949 0.105474 0.994422i $$-0.466364\pi$$
0.105474 + 0.994422i $$0.466364\pi$$
$$810$$ 0 0
$$811$$ 56.0000 1.96643 0.983213 0.182462i $$-0.0584065\pi$$
0.983213 + 0.182462i $$0.0584065\pi$$
$$812$$ 0 0
$$813$$ −7.00000 −0.245501
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 3.00000 0.105021
$$817$$ −20.0000 −0.699711
$$818$$ −5.00000 −0.174821
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −54.0000 −1.88461 −0.942306 0.334751i $$-0.891348\pi$$
−0.942306 + 0.334751i $$0.891348\pi$$
$$822$$ 9.00000 0.313911
$$823$$ 32.0000 1.11545 0.557725 0.830026i $$-0.311674\pi$$
0.557725 + 0.830026i $$0.311674\pi$$
$$824$$ −5.00000 −0.174183
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 48.0000 1.66912 0.834562 0.550914i $$-0.185721\pi$$
0.834562 + 0.550914i $$0.185721\pi$$
$$828$$ 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
$$831$$ −28.0000 −0.971309
$$832$$ −4.00000 −0.138675
$$833$$ 0 0
$$834$$ −2.00000 −0.0692543
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −1.00000 −0.0345651
$$838$$ −18.0000 −0.621800
$$839$$ 27.0000 0.932144 0.466072 0.884747i $$-0.345669\pi$$
0.466072 + 0.884747i $$0.345669\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ 40.0000 1.37849
$$843$$ 9.00000 0.309976
$$844$$ 14.0000 0.481900
$$845$$ 0 0
$$846$$ 3.00000 0.103142
$$847$$ 0 0
$$848$$ −6.00000 −0.206041
$$849$$ −4.00000 −0.137280
$$850$$ 0 0
$$851$$ −30.0000 −1.02839
$$852$$ 3.00000 0.102778
$$853$$ 26.0000 0.890223 0.445112 0.895475i $$-0.353164\pi$$
0.445112 + 0.895475i $$0.353164\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 18.0000 0.615227
$$857$$ 54.0000 1.84460 0.922302 0.386469i $$-0.126305\pi$$
0.922302 + 0.386469i $$0.126305\pi$$
$$858$$ 0 0
$$859$$ −4.00000 −0.136478 −0.0682391 0.997669i $$-0.521738\pi$$
−0.0682391 + 0.997669i $$0.521738\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 27.0000 0.919624
$$863$$ −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
$$866$$ −29.0000 −0.985460
$$867$$ −8.00000 −0.271694
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 16.0000 0.542139
$$872$$ −2.00000 −0.0677285
$$873$$ −7.00000 −0.236914
$$874$$ −6.00000 −0.202953
$$875$$ 0 0
$$876$$ 14.0000 0.473016
$$877$$ 38.0000 1.28317 0.641584 0.767052i $$-0.278277\pi$$
0.641584 + 0.767052i $$0.278277\pi$$
$$878$$ −5.00000 −0.168742
$$879$$ −24.0000 −0.809500
$$880$$ 0 0
$$881$$ −3.00000 −0.101073 −0.0505363 0.998722i $$-0.516093\pi$$
−0.0505363 + 0.998722i $$0.516093\pi$$
$$882$$ 0 0
$$883$$ 38.0000 1.27880 0.639401 0.768874i $$-0.279182\pi$$
0.639401 + 0.768874i $$0.279182\pi$$
$$884$$ −12.0000 −0.403604
$$885$$ 0 0
$$886$$ 6.00000 0.201574
$$887$$ 48.0000 1.61168 0.805841 0.592132i $$-0.201714\pi$$
0.805841 + 0.592132i $$0.201714\pi$$
$$888$$ 10.0000 0.335578
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −19.0000 −0.636167
$$893$$ −6.00000 −0.200782
$$894$$ 6.00000 0.200670
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −12.0000 −0.400668
$$898$$ 21.0000 0.700779
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −18.0000 −0.599667
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −21.0000 −0.698450
$$905$$ 0 0
$$906$$ −8.00000 −0.265782
$$907$$ −16.0000 −0.531271 −0.265636 0.964073i $$-0.585582\pi$$
−0.265636 + 0.964073i $$0.585582\pi$$
$$908$$ −6.00000 −0.199117
$$909$$ 18.0000 0.597022
$$910$$ 0 0
$$911$$ 39.0000 1.29213 0.646064 0.763283i $$-0.276414\pi$$
0.646064 + 0.763283i $$0.276414\pi$$
$$912$$ 2.00000 0.0662266
$$913$$ 0 0
$$914$$ −2.00000 −0.0661541
$$915$$ 0 0
$$916$$ −4.00000 −0.132164
$$917$$ 0 0
$$918$$ −3.00000 −0.0990148
$$919$$ −19.0000 −0.626752 −0.313376 0.949629i $$-0.601460\pi$$
−0.313376 + 0.949629i $$0.601460\pi$$
$$920$$ 0 0
$$921$$ −28.0000 −0.922631
$$922$$ 12.0000 0.395199
$$923$$ −12.0000 −0.394985
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −5.00000 −0.164310
$$927$$ 5.00000 0.164222
$$928$$ 0 0
$$929$$ 18.0000 0.590561 0.295280 0.955411i $$-0.404587\pi$$
0.295280 + 0.955411i $$0.404587\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −30.0000 −0.982683
$$933$$ 9.00000 0.294647
$$934$$ −12.0000 −0.392652
$$935$$ 0 0
$$936$$ 4.00000 0.130744
$$937$$ 26.0000 0.849383 0.424691 0.905338i $$-0.360383\pi$$
0.424691 + 0.905338i $$0.360383\pi$$
$$938$$ 0 0
$$939$$ 5.00000 0.163169
$$940$$ 0 0
$$941$$ 30.0000 0.977972 0.488986 0.872292i $$-0.337367\pi$$
0.488986 + 0.872292i $$0.337367\pi$$
$$942$$ −8.00000 −0.260654
$$943$$ −27.0000 −0.879241
$$944$$ −6.00000 −0.195283
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −48.0000 −1.55979 −0.779895 0.625910i $$-0.784728\pi$$
−0.779895 + 0.625910i $$0.784728\pi$$
$$948$$ 11.0000 0.357263
$$949$$ −56.0000 −1.81784
$$950$$ 0 0
$$951$$ −18.0000 −0.583690
$$952$$ 0 0
$$953$$ 6.00000 0.194359 0.0971795 0.995267i $$-0.469018\pi$$
0.0971795 + 0.995267i $$0.469018\pi$$
$$954$$ 6.00000 0.194257
$$955$$ 0 0
$$956$$ 15.0000 0.485135
$$957$$ 0 0
$$958$$ 27.0000 0.872330
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −30.0000 −0.967742
$$962$$ −40.0000 −1.28965
$$963$$ −18.0000 −0.580042
$$964$$ 14.0000 0.450910
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −49.0000 −1.57573 −0.787867 0.615846i $$-0.788815\pi$$
−0.787867 + 0.615846i $$0.788815\pi$$
$$968$$ 11.0000 0.353553
$$969$$ 6.00000 0.192748
$$970$$ 0 0
$$971$$ −36.0000 −1.15529 −0.577647 0.816286i $$-0.696029\pi$$
−0.577647 + 0.816286i $$0.696029\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 0 0
$$974$$ 31.0000 0.993304
$$975$$ 0 0
$$976$$ 8.00000 0.256074
$$977$$ 27.0000 0.863807 0.431903 0.901920i $$-0.357842\pi$$
0.431903 + 0.901920i $$0.357842\pi$$
$$978$$ −8.00000 −0.255812
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 2.00000 0.0638551
$$982$$ 6.00000 0.191468
$$983$$ −12.0000 −0.382741 −0.191370 0.981518i $$-0.561293\pi$$
−0.191370 + 0.981518i $$0.561293\pi$$
$$984$$ 9.00000 0.286910
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −8.00000 −0.254514
$$989$$ −30.0000 −0.953945
$$990$$ 0 0
$$991$$ 59.0000 1.87420 0.937098 0.349065i $$-0.113501\pi$$
0.937098 + 0.349065i $$0.113501\pi$$
$$992$$ 1.00000 0.0317500
$$993$$ −10.0000 −0.317340
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −40.0000 −1.26681 −0.633406 0.773819i $$-0.718344\pi$$
−0.633406 + 0.773819i $$0.718344\pi$$
$$998$$ −32.0000 −1.01294
$$999$$ −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.bb.1.1 1
5.4 even 2 7350.2.a.by.1.1 1
7.2 even 3 1050.2.i.m.151.1 yes 2
7.4 even 3 1050.2.i.m.751.1 yes 2
7.6 odd 2 7350.2.a.n.1.1 1
35.2 odd 12 1050.2.o.e.949.1 4
35.4 even 6 1050.2.i.h.751.1 yes 2
35.9 even 6 1050.2.i.h.151.1 2
35.18 odd 12 1050.2.o.e.499.1 4
35.23 odd 12 1050.2.o.e.949.2 4
35.32 odd 12 1050.2.o.e.499.2 4
35.34 odd 2 7350.2.a.cq.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.h.151.1 2 35.9 even 6
1050.2.i.h.751.1 yes 2 35.4 even 6
1050.2.i.m.151.1 yes 2 7.2 even 3
1050.2.i.m.751.1 yes 2 7.4 even 3
1050.2.o.e.499.1 4 35.18 odd 12
1050.2.o.e.499.2 4 35.32 odd 12
1050.2.o.e.949.1 4 35.2 odd 12
1050.2.o.e.949.2 4 35.23 odd 12
7350.2.a.n.1.1 1 7.6 odd 2
7350.2.a.bb.1.1 1 1.1 even 1 trivial
7350.2.a.by.1.1 1 5.4 even 2
7350.2.a.cq.1.1 1 35.34 odd 2