# Properties

 Label 630.2.a.h.1.1 Level $630$ Weight $2$ Character 630.1 Self dual yes Analytic conductor $5.031$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$630 = 2 \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 630.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$5.03057532734$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 210) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 630.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +8.00000 q^{19} -1.00000 q^{20} +1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} -1.00000 q^{35} -10.0000 q^{37} +8.00000 q^{38} -1.00000 q^{40} +6.00000 q^{41} -4.00000 q^{43} +1.00000 q^{49} +1.00000 q^{50} +2.00000 q^{52} +6.00000 q^{53} +1.00000 q^{56} -6.00000 q^{58} +12.0000 q^{59} -10.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -2.00000 q^{65} -4.00000 q^{67} +6.00000 q^{68} -1.00000 q^{70} -12.0000 q^{71} -10.0000 q^{73} -10.0000 q^{74} +8.00000 q^{76} +8.00000 q^{79} -1.00000 q^{80} +6.00000 q^{82} -12.0000 q^{83} -6.00000 q^{85} -4.00000 q^{86} +6.00000 q^{89} +2.00000 q^{91} -8.00000 q^{95} -10.0000 q^{97} +1.00000 q^{98} +O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −1.00000 −0.316228
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 0 0
$$19$$ 8.00000 1.83533 0.917663 0.397360i $$-0.130073\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 2.00000 0.392232
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 6.00000 1.02899
$$35$$ −1.00000 −0.169031
$$36$$ 0 0
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 8.00000 1.29777
$$39$$ 0 0
$$40$$ −1.00000 −0.158114
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ 2.00000 0.277350
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ −6.00000 −0.787839
$$59$$ 12.0000 1.56227 0.781133 0.624364i $$-0.214642\pi$$
0.781133 + 0.624364i $$0.214642\pi$$
$$60$$ 0 0
$$61$$ −10.0000 −1.28037 −0.640184 0.768221i $$-0.721142\pi$$
−0.640184 + 0.768221i $$0.721142\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −2.00000 −0.248069
$$66$$ 0 0
$$67$$ −4.00000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ 6.00000 0.727607
$$69$$ 0 0
$$70$$ −1.00000 −0.119523
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0 0
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ −10.0000 −1.16248
$$75$$ 0 0
$$76$$ 8.00000 0.917663
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ −6.00000 −0.650791
$$86$$ −4.00000 −0.431331
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −8.00000 −0.820783
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 0 0
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 1.00000 0.0944911
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −6.00000 −0.557086
$$117$$ 0 0
$$118$$ 12.0000 1.10469
$$119$$ 6.00000 0.550019
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ −10.0000 −0.905357
$$123$$ 0 0
$$124$$ −4.00000 −0.359211
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ −2.00000 −0.175412
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 0 0
$$133$$ 8.00000 0.693688
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 0 0
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ −1.00000 −0.0845154
$$141$$ 0 0
$$142$$ −12.0000 −1.00702
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 6.00000 0.498273
$$146$$ −10.0000 −0.827606
$$147$$ 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 $$0.394462\pi$$
$$152$$ 8.00000 0.648886
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 4.00000 0.321288
$$156$$ 0 0
$$157$$ −22.0000 −1.75579 −0.877896 0.478852i $$-0.841053\pi$$
−0.877896 + 0.478852i $$0.841053\pi$$
$$158$$ 8.00000 0.636446
$$159$$ 0 0
$$160$$ −1.00000 −0.0790569
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 0 0
$$166$$ −12.0000 −0.931381
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ −6.00000 −0.460179
$$171$$ 0 0
$$172$$ −4.00000 −0.304997
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 0 0
$$175$$ 1.00000 0.0755929
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 6.00000 0.449719
$$179$$ 24.0000 1.79384 0.896922 0.442189i $$-0.145798\pi$$
0.896922 + 0.442189i $$0.145798\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 2.00000 0.148250
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 10.0000 0.735215
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −8.00000 −0.580381
$$191$$ −12.0000 −0.868290 −0.434145 0.900843i $$-0.642949\pi$$
−0.434145 + 0.900843i $$0.642949\pi$$
$$192$$ 0 0
$$193$$ 2.00000 0.143963 0.0719816 0.997406i $$-0.477068\pi$$
0.0719816 + 0.997406i $$0.477068\pi$$
$$194$$ −10.0000 −0.717958
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 20.0000 1.41776 0.708881 0.705328i $$-0.249200\pi$$
0.708881 + 0.705328i $$0.249200\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 0 0
$$202$$ −6.00000 −0.422159
$$203$$ −6.00000 −0.421117
$$204$$ 0 0
$$205$$ −6.00000 −0.419058
$$206$$ 8.00000 0.557386
$$207$$ 0 0
$$208$$ 2.00000 0.138675
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 6.00000 0.412082
$$213$$ 0 0
$$214$$ −12.0000 −0.820303
$$215$$ 4.00000 0.272798
$$216$$ 0 0
$$217$$ −4.00000 −0.271538
$$218$$ 14.0000 0.948200
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 0 0
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ −30.0000 −1.96537 −0.982683 0.185296i $$-0.940675\pi$$
−0.982683 + 0.185296i $$0.940675\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 12.0000 0.781133
$$237$$ 0 0
$$238$$ 6.00000 0.388922
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ 26.0000 1.67481 0.837404 0.546585i $$-0.184072\pi$$
0.837404 + 0.546585i $$0.184072\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ 0 0
$$244$$ −10.0000 −0.640184
$$245$$ −1.00000 −0.0638877
$$246$$ 0 0
$$247$$ 16.0000 1.01806
$$248$$ −4.00000 −0.254000
$$249$$ 0 0
$$250$$ −1.00000 −0.0632456
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 8.00000 0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 30.0000 1.87135 0.935674 0.352865i $$-0.114792\pi$$
0.935674 + 0.352865i $$0.114792\pi$$
$$258$$ 0 0
$$259$$ −10.0000 −0.621370
$$260$$ −2.00000 −0.124035
$$261$$ 0 0
$$262$$ 12.0000 0.741362
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ 8.00000 0.490511
$$267$$ 0 0
$$268$$ −4.00000 −0.244339
$$269$$ 18.0000 1.09748 0.548740 0.835993i $$-0.315108\pi$$
0.548740 + 0.835993i $$0.315108\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ 0 0
$$280$$ −1.00000 −0.0597614
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 6.00000 0.354169
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 6.00000 0.352332
$$291$$ 0 0
$$292$$ −10.0000 −0.585206
$$293$$ −30.0000 −1.75262 −0.876309 0.481749i $$-0.840002\pi$$
−0.876309 + 0.481749i $$0.840002\pi$$
$$294$$ 0 0
$$295$$ −12.0000 −0.698667
$$296$$ −10.0000 −0.581238
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −4.00000 −0.230556
$$302$$ 8.00000 0.460348
$$303$$ 0 0
$$304$$ 8.00000 0.458831
$$305$$ 10.0000 0.572598
$$306$$ 0 0
$$307$$ −4.00000 −0.228292 −0.114146 0.993464i $$-0.536413\pi$$
−0.114146 + 0.993464i $$0.536413\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 4.00000 0.227185
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 0 0
$$313$$ 14.0000 0.791327 0.395663 0.918396i $$-0.370515\pi$$
0.395663 + 0.918396i $$0.370515\pi$$
$$314$$ −22.0000 −1.24153
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −1.00000 −0.0559017
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 48.0000 2.67079
$$324$$ 0 0
$$325$$ 2.00000 0.110940
$$326$$ 20.0000 1.10770
$$327$$ 0 0
$$328$$ 6.00000 0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 4.00000 0.218543
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ −9.00000 −0.489535
$$339$$ 0 0
$$340$$ −6.00000 −0.325396
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ −4.00000 −0.215666
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ 0 0
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ 1.00000 0.0534522
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 12.0000 0.636894
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ 24.0000 1.26844
$$359$$ 12.0000 0.633336 0.316668 0.948536i $$-0.397436\pi$$
0.316668 + 0.948536i $$0.397436\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ −10.0000 −0.525588
$$363$$ 0 0
$$364$$ 2.00000 0.104828
$$365$$ 10.0000 0.523424
$$366$$ 0 0
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 10.0000 0.519875
$$371$$ 6.00000 0.311504
$$372$$ 0 0
$$373$$ −34.0000 −1.76045 −0.880227 0.474554i $$-0.842610\pi$$
−0.880227 + 0.474554i $$0.842610\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ −8.00000 −0.410391
$$381$$ 0 0
$$382$$ −12.0000 −0.613973
$$383$$ −24.0000 −1.22634 −0.613171 0.789950i $$-0.710106\pi$$
−0.613171 + 0.789950i $$0.710106\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 2.00000 0.101797
$$387$$ 0 0
$$388$$ −10.0000 −0.507673
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ −18.0000 −0.906827
$$395$$ −8.00000 −0.402524
$$396$$ 0 0
$$397$$ 2.00000 0.100377 0.0501886 0.998740i $$-0.484018\pi$$
0.0501886 + 0.998740i $$0.484018\pi$$
$$398$$ 20.0000 1.00251
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 30.0000 1.49813 0.749064 0.662497i $$-0.230503\pi$$
0.749064 + 0.662497i $$0.230503\pi$$
$$402$$ 0 0
$$403$$ −8.00000 −0.398508
$$404$$ −6.00000 −0.298511
$$405$$ 0 0
$$406$$ −6.00000 −0.297775
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 26.0000 1.28562 0.642809 0.766027i $$-0.277769\pi$$
0.642809 + 0.766027i $$0.277769\pi$$
$$410$$ −6.00000 −0.296319
$$411$$ 0 0
$$412$$ 8.00000 0.394132
$$413$$ 12.0000 0.590481
$$414$$ 0 0
$$415$$ 12.0000 0.589057
$$416$$ 2.00000 0.0980581
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ 38.0000 1.85201 0.926003 0.377515i $$-0.123221\pi$$
0.926003 + 0.377515i $$0.123221\pi$$
$$422$$ −4.00000 −0.194717
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ 6.00000 0.291043
$$426$$ 0 0
$$427$$ −10.0000 −0.483934
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ 4.00000 0.192897
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 0 0
$$433$$ −10.0000 −0.480569 −0.240285 0.970702i $$-0.577241\pi$$
−0.240285 + 0.970702i $$0.577241\pi$$
$$434$$ −4.00000 −0.192006
$$435$$ 0 0
$$436$$ 14.0000 0.670478
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −28.0000 −1.33637 −0.668184 0.743996i $$-0.732928\pi$$
−0.668184 + 0.743996i $$0.732928\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 12.0000 0.570782
$$443$$ 12.0000 0.570137 0.285069 0.958507i $$-0.407984\pi$$
0.285069 + 0.958507i $$0.407984\pi$$
$$444$$ 0 0
$$445$$ −6.00000 −0.284427
$$446$$ 8.00000 0.378811
$$447$$ 0 0
$$448$$ 1.00000 0.0472456
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −6.00000 −0.282216
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ −2.00000 −0.0937614
$$456$$ 0 0
$$457$$ 2.00000 0.0935561 0.0467780 0.998905i $$-0.485105\pi$$
0.0467780 + 0.998905i $$0.485105\pi$$
$$458$$ 14.0000 0.654177
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 18.0000 0.838344 0.419172 0.907907i $$-0.362320\pi$$
0.419172 + 0.907907i $$0.362320\pi$$
$$462$$ 0 0
$$463$$ −40.0000 −1.85896 −0.929479 0.368875i $$-0.879743\pi$$
−0.929479 + 0.368875i $$0.879743\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 0 0
$$466$$ −30.0000 −1.38972
$$467$$ 36.0000 1.66588 0.832941 0.553362i $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 12.0000 0.552345
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 8.00000 0.367065
$$476$$ 6.00000 0.275010
$$477$$ 0 0
$$478$$ 12.0000 0.548867
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −20.0000 −0.911922
$$482$$ 26.0000 1.18427
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ 10.0000 0.454077
$$486$$ 0 0
$$487$$ 32.0000 1.45006 0.725029 0.688718i $$-0.241826\pi$$
0.725029 + 0.688718i $$0.241826\pi$$
$$488$$ −10.0000 −0.452679
$$489$$ 0 0
$$490$$ −1.00000 −0.0451754
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ −36.0000 −1.62136
$$494$$ 16.0000 0.719874
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ −12.0000 −0.538274
$$498$$ 0 0
$$499$$ 20.0000 0.895323 0.447661 0.894203i $$-0.352257\pi$$
0.447661 + 0.894203i $$0.352257\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 0 0
$$502$$ 12.0000 0.535586
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 6.00000 0.266996
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 8.00000 0.354943
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 0 0
$$511$$ −10.0000 −0.442374
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 30.0000 1.32324
$$515$$ −8.00000 −0.352522
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −10.0000 −0.439375
$$519$$ 0 0
$$520$$ −2.00000 −0.0877058
$$521$$ 6.00000 0.262865 0.131432 0.991325i $$-0.458042\pi$$
0.131432 + 0.991325i $$0.458042\pi$$
$$522$$ 0 0
$$523$$ −28.0000 −1.22435 −0.612177 0.790721i $$-0.709706\pi$$
−0.612177 + 0.790721i $$0.709706\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ −24.0000 −1.04546
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ −6.00000 −0.260623
$$531$$ 0 0
$$532$$ 8.00000 0.346844
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ 12.0000 0.518805
$$536$$ −4.00000 −0.172774
$$537$$ 0 0
$$538$$ 18.0000 0.776035
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −34.0000 −1.46177 −0.730887 0.682498i $$-0.760893\pi$$
−0.730887 + 0.682498i $$0.760893\pi$$
$$542$$ 20.0000 0.859074
$$543$$ 0 0
$$544$$ 6.00000 0.257248
$$545$$ −14.0000 −0.599694
$$546$$ 0 0
$$547$$ 44.0000 1.88130 0.940652 0.339372i $$-0.110215\pi$$
0.940652 + 0.339372i $$0.110215\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −48.0000 −2.04487
$$552$$ 0 0
$$553$$ 8.00000 0.340195
$$554$$ −10.0000 −0.424859
$$555$$ 0 0
$$556$$ −16.0000 −0.678551
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ −1.00000 −0.0422577
$$561$$ 0 0
$$562$$ −18.0000 −0.759284
$$563$$ −36.0000 −1.51722 −0.758610 0.651546i $$-0.774121\pi$$
−0.758610 + 0.651546i $$0.774121\pi$$
$$564$$ 0 0
$$565$$ 6.00000 0.252422
$$566$$ −4.00000 −0.168133
$$567$$ 0 0
$$568$$ −12.0000 −0.503509
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 6.00000 0.250435
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −10.0000 −0.416305 −0.208153 0.978096i $$-0.566745\pi$$
−0.208153 + 0.978096i $$0.566745\pi$$
$$578$$ 19.0000 0.790296
$$579$$ 0 0
$$580$$ 6.00000 0.249136
$$581$$ −12.0000 −0.497844
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −10.0000 −0.413803
$$585$$ 0 0
$$586$$ −30.0000 −1.23929
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ −32.0000 −1.31854
$$590$$ −12.0000 −0.494032
$$591$$ 0 0
$$592$$ −10.0000 −0.410997
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ −6.00000 −0.245976
$$596$$ −6.00000 −0.245770
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −36.0000 −1.47092 −0.735460 0.677568i $$-0.763034\pi$$
−0.735460 + 0.677568i $$0.763034\pi$$
$$600$$ 0 0
$$601$$ 2.00000 0.0815817 0.0407909 0.999168i $$-0.487012\pi$$
0.0407909 + 0.999168i $$0.487012\pi$$
$$602$$ −4.00000 −0.163028
$$603$$ 0 0
$$604$$ 8.00000 0.325515
$$605$$ 11.0000 0.447214
$$606$$ 0 0
$$607$$ 8.00000 0.324710 0.162355 0.986732i $$-0.448091\pi$$
0.162355 + 0.986732i $$0.448091\pi$$
$$608$$ 8.00000 0.324443
$$609$$ 0 0
$$610$$ 10.0000 0.404888
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 38.0000 1.53481 0.767403 0.641165i $$-0.221549\pi$$
0.767403 + 0.641165i $$0.221549\pi$$
$$614$$ −4.00000 −0.161427
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000 0.724653 0.362326 0.932051i $$-0.381983\pi$$
0.362326 + 0.932051i $$0.381983\pi$$
$$618$$ 0 0
$$619$$ 32.0000 1.28619 0.643094 0.765787i $$-0.277650\pi$$
0.643094 + 0.765787i $$0.277650\pi$$
$$620$$ 4.00000 0.160644
$$621$$ 0 0
$$622$$ −24.0000 −0.962312
$$623$$ 6.00000 0.240385
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 14.0000 0.559553
$$627$$ 0 0
$$628$$ −22.0000 −0.877896
$$629$$ −60.0000 −2.39236
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 8.00000 0.318223
$$633$$ 0 0
$$634$$ −18.0000 −0.714871
$$635$$ −8.00000 −0.317470
$$636$$ 0 0
$$637$$ 2.00000 0.0792429
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.00000 −0.0395285
$$641$$ −42.0000 −1.65890 −0.829450 0.558581i $$-0.811346\pi$$
−0.829450 + 0.558581i $$0.811346\pi$$
$$642$$ 0 0
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 48.0000 1.88853
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 2.00000 0.0784465
$$651$$ 0 0
$$652$$ 20.0000 0.783260
$$653$$ 6.00000 0.234798 0.117399 0.993085i $$-0.462544\pi$$
0.117399 + 0.993085i $$0.462544\pi$$
$$654$$ 0 0
$$655$$ −12.0000 −0.468879
$$656$$ 6.00000 0.234261
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −48.0000 −1.86981 −0.934907 0.354892i $$-0.884518\pi$$
−0.934907 + 0.354892i $$0.884518\pi$$
$$660$$ 0 0
$$661$$ −34.0000 −1.32245 −0.661223 0.750189i $$-0.729962\pi$$
−0.661223 + 0.750189i $$0.729962\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ −8.00000 −0.310227
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 4.00000 0.154533
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 26.0000 1.00223 0.501113 0.865382i $$-0.332924\pi$$
0.501113 + 0.865382i $$0.332924\pi$$
$$674$$ 2.00000 0.0770371
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ 0 0
$$679$$ −10.0000 −0.383765
$$680$$ −6.00000 −0.230089
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 6.00000 0.229248
$$686$$ 1.00000 0.0381802
$$687$$ 0 0
$$688$$ −4.00000 −0.152499
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ −16.0000 −0.608669 −0.304334 0.952565i $$-0.598434\pi$$
−0.304334 + 0.952565i $$0.598434\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 16.0000 0.606915
$$696$$ 0 0
$$697$$ 36.0000 1.36360
$$698$$ −10.0000 −0.378506
$$699$$ 0 0
$$700$$ 1.00000 0.0377964
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 0 0
$$703$$ −80.0000 −3.01726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 6.00000 0.225813
$$707$$ −6.00000 −0.225653
$$708$$ 0 0
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ 12.0000 0.450352
$$711$$ 0 0
$$712$$ 6.00000 0.224860
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 24.0000 0.896922
$$717$$ 0 0
$$718$$ 12.0000 0.447836
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ 8.00000 0.297936
$$722$$ 45.0000 1.67473
$$723$$ 0 0
$$724$$ −10.0000 −0.371647
$$725$$ −6.00000 −0.222834
$$726$$ 0 0
$$727$$ 32.0000 1.18681 0.593407 0.804902i $$-0.297782\pi$$
0.593407 + 0.804902i $$0.297782\pi$$
$$728$$ 2.00000 0.0741249
$$729$$ 0 0
$$730$$ 10.0000 0.370117
$$731$$ −24.0000 −0.887672
$$732$$ 0 0
$$733$$ 2.00000 0.0738717 0.0369358 0.999318i $$-0.488240\pi$$
0.0369358 + 0.999318i $$0.488240\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −28.0000 −1.03000 −0.514998 0.857191i $$-0.672207\pi$$
−0.514998 + 0.857191i $$0.672207\pi$$
$$740$$ 10.0000 0.367607
$$741$$ 0 0
$$742$$ 6.00000 0.220267
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 0 0
$$745$$ 6.00000 0.219823
$$746$$ −34.0000 −1.24483
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −12.0000 −0.438470
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −12.0000 −0.437014
$$755$$ −8.00000 −0.291150
$$756$$ 0 0
$$757$$ −34.0000 −1.23575 −0.617876 0.786276i $$-0.712006\pi$$
−0.617876 + 0.786276i $$0.712006\pi$$
$$758$$ −4.00000 −0.145287
$$759$$ 0 0
$$760$$ −8.00000 −0.290191
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 0 0
$$763$$ 14.0000 0.506834
$$764$$ −12.0000 −0.434145
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ 24.0000 0.866590
$$768$$ 0 0
$$769$$ 26.0000 0.937584 0.468792 0.883309i $$-0.344689\pi$$
0.468792 + 0.883309i $$0.344689\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 2.00000 0.0719816
$$773$$ 18.0000 0.647415 0.323708 0.946157i $$-0.395071\pi$$
0.323708 + 0.946157i $$0.395071\pi$$
$$774$$ 0 0
$$775$$ −4.00000 −0.143684
$$776$$ −10.0000 −0.358979
$$777$$ 0 0
$$778$$ −6.00000 −0.215110
$$779$$ 48.0000 1.71978
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 22.0000 0.785214
$$786$$ 0 0
$$787$$ −4.00000 −0.142585 −0.0712923 0.997455i $$-0.522712\pi$$
−0.0712923 + 0.997455i $$0.522712\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ 0 0
$$790$$ −8.00000 −0.284627
$$791$$ −6.00000 −0.213335
$$792$$ 0 0
$$793$$ −20.0000 −0.710221
$$794$$ 2.00000 0.0709773
$$795$$ 0 0
$$796$$ 20.0000 0.708881
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.00000 0.0353553
$$801$$ 0 0
$$802$$ 30.0000 1.05934
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −8.00000 −0.281788
$$807$$ 0 0
$$808$$ −6.00000 −0.211079
$$809$$ 30.0000 1.05474 0.527372 0.849635i $$-0.323177\pi$$
0.527372 + 0.849635i $$0.323177\pi$$
$$810$$ 0 0
$$811$$ −16.0000 −0.561836 −0.280918 0.959732i $$-0.590639\pi$$
−0.280918 + 0.959732i $$0.590639\pi$$
$$812$$ −6.00000 −0.210559
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −20.0000 −0.700569
$$816$$ 0 0
$$817$$ −32.0000 −1.11954
$$818$$ 26.0000 0.909069
$$819$$ 0 0
$$820$$ −6.00000 −0.209529
$$821$$ 18.0000 0.628204 0.314102 0.949389i $$-0.398297\pi$$
0.314102 + 0.949389i $$0.398297\pi$$
$$822$$ 0 0
$$823$$ 32.0000 1.11545 0.557725 0.830026i $$-0.311674\pi$$
0.557725 + 0.830026i $$0.311674\pi$$
$$824$$ 8.00000 0.278693
$$825$$ 0 0
$$826$$ 12.0000 0.417533
$$827$$ 36.0000 1.25184 0.625921 0.779886i $$-0.284723\pi$$
0.625921 + 0.779886i $$0.284723\pi$$
$$828$$ 0 0
$$829$$ −34.0000 −1.18087 −0.590434 0.807086i $$-0.701044\pi$$
−0.590434 + 0.807086i $$0.701044\pi$$
$$830$$ 12.0000 0.416526
$$831$$ 0 0
$$832$$ 2.00000 0.0693375
$$833$$ 6.00000 0.207888
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 12.0000 0.414533
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 38.0000 1.30957
$$843$$ 0 0
$$844$$ −4.00000 −0.137686
$$845$$ 9.00000 0.309609
$$846$$ 0 0
$$847$$ −11.0000 −0.377964
$$848$$ 6.00000 0.206041
$$849$$ 0 0
$$850$$ 6.00000 0.205798
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 26.0000 0.890223 0.445112 0.895475i $$-0.353164\pi$$
0.445112 + 0.895475i $$0.353164\pi$$
$$854$$ −10.0000 −0.342193
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ 6.00000 0.204956 0.102478 0.994735i $$-0.467323\pi$$
0.102478 + 0.994735i $$0.467323\pi$$
$$858$$ 0 0
$$859$$ −40.0000 −1.36478 −0.682391 0.730987i $$-0.739060\pi$$
−0.682391 + 0.730987i $$0.739060\pi$$
$$860$$ 4.00000 0.136399
$$861$$ 0 0
$$862$$ 12.0000 0.408722
$$863$$ 24.0000 0.816970 0.408485 0.912765i $$-0.366057\pi$$
0.408485 + 0.912765i $$0.366057\pi$$
$$864$$ 0 0
$$865$$ 6.00000 0.204006
$$866$$ −10.0000 −0.339814
$$867$$ 0 0
$$868$$ −4.00000 −0.135769
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −8.00000 −0.271070
$$872$$ 14.0000 0.474100
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −1.00000 −0.0338062
$$876$$ 0 0
$$877$$ 14.0000 0.472746 0.236373 0.971662i $$-0.424041\pi$$
0.236373 + 0.971662i $$0.424041\pi$$
$$878$$ −28.0000 −0.944954
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 30.0000 1.01073 0.505363 0.862907i $$-0.331359\pi$$
0.505363 + 0.862907i $$0.331359\pi$$
$$882$$ 0 0
$$883$$ 44.0000 1.48072 0.740359 0.672212i $$-0.234656\pi$$
0.740359 + 0.672212i $$0.234656\pi$$
$$884$$ 12.0000 0.403604
$$885$$ 0 0
$$886$$ 12.0000 0.403148
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ 0 0
$$889$$ 8.00000 0.268311
$$890$$ −6.00000 −0.201120
$$891$$ 0 0
$$892$$ 8.00000 0.267860
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −24.0000 −0.802232
$$896$$ 1.00000 0.0334077
$$897$$ 0 0
$$898$$ −18.0000 −0.600668
$$899$$ 24.0000 0.800445
$$900$$ 0 0
$$901$$ 36.0000 1.19933
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −6.00000 −0.199557
$$905$$ 10.0000 0.332411
$$906$$ 0 0
$$907$$ −28.0000 −0.929725 −0.464862 0.885383i $$-0.653896\pi$$
−0.464862 + 0.885383i $$0.653896\pi$$
$$908$$ −12.0000 −0.398234
$$909$$ 0 0
$$910$$ −2.00000 −0.0662994
$$911$$ −12.0000 −0.397578 −0.198789 0.980042i $$-0.563701\pi$$
−0.198789 + 0.980042i $$0.563701\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 2.00000 0.0661541
$$915$$ 0 0
$$916$$ 14.0000 0.462573
$$917$$ 12.0000 0.396275
$$918$$ 0 0
$$919$$ 32.0000 1.05558 0.527791 0.849374i $$-0.323020\pi$$
0.527791 + 0.849374i $$0.323020\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 18.0000 0.592798
$$923$$ −24.0000 −0.789970
$$924$$ 0 0
$$925$$ −10.0000 −0.328798
$$926$$ −40.0000 −1.31448
$$927$$ 0 0
$$928$$ −6.00000 −0.196960
$$929$$ 30.0000 0.984268 0.492134 0.870519i $$-0.336217\pi$$
0.492134 + 0.870519i $$0.336217\pi$$
$$930$$ 0 0
$$931$$ 8.00000 0.262189
$$932$$ −30.0000 −0.982683
$$933$$ 0 0
$$934$$ 36.0000 1.17796
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 38.0000 1.24141 0.620703 0.784046i $$-0.286847\pi$$
0.620703 + 0.784046i $$0.286847\pi$$
$$938$$ −4.00000 −0.130605
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 18.0000 0.586783 0.293392 0.955992i $$-0.405216\pi$$
0.293392 + 0.955992i $$0.405216\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 12.0000 0.390567
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 36.0000 1.16984 0.584921 0.811090i $$-0.301125\pi$$
0.584921 + 0.811090i $$0.301125\pi$$
$$948$$ 0 0
$$949$$ −20.0000 −0.649227
$$950$$ 8.00000 0.259554
$$951$$ 0 0
$$952$$ 6.00000 0.194461
$$953$$ −30.0000 −0.971795 −0.485898 0.874016i $$-0.661507\pi$$
−0.485898 + 0.874016i $$0.661507\pi$$
$$954$$ 0 0
$$955$$ 12.0000 0.388311
$$956$$ 12.0000 0.388108
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −6.00000 −0.193750
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ −20.0000 −0.644826
$$963$$ 0 0
$$964$$ 26.0000 0.837404
$$965$$ −2.00000 −0.0643823
$$966$$ 0 0
$$967$$ 8.00000 0.257263 0.128631 0.991692i $$-0.458942\pi$$
0.128631 + 0.991692i $$0.458942\pi$$
$$968$$ −11.0000 −0.353553
$$969$$ 0 0
$$970$$ 10.0000 0.321081
$$971$$ −36.0000 −1.15529 −0.577647 0.816286i $$-0.696029\pi$$
−0.577647 + 0.816286i $$0.696029\pi$$
$$972$$ 0 0
$$973$$ −16.0000 −0.512936
$$974$$ 32.0000 1.02535
$$975$$ 0 0
$$976$$ −10.0000 −0.320092
$$977$$ −6.00000 −0.191957 −0.0959785 0.995383i $$-0.530598\pi$$
−0.0959785 + 0.995383i $$0.530598\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ −1.00000 −0.0319438
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −24.0000 −0.765481 −0.382741 0.923856i $$-0.625020\pi$$
−0.382741 + 0.923856i $$0.625020\pi$$
$$984$$ 0 0
$$985$$ 18.0000 0.573528
$$986$$ −36.0000 −1.14647
$$987$$ 0 0
$$988$$ 16.0000 0.509028
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 8.00000 0.254128 0.127064 0.991894i $$-0.459445\pi$$
0.127064 + 0.991894i $$0.459445\pi$$
$$992$$ −4.00000 −0.127000
$$993$$ 0 0
$$994$$ −12.0000 −0.380617
$$995$$ −20.0000 −0.634043
$$996$$ 0 0
$$997$$ 26.0000 0.823428 0.411714 0.911313i $$-0.364930\pi$$
0.411714 + 0.911313i $$0.364930\pi$$
$$998$$ 20.0000 0.633089
$$999$$ 0 0
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 630.2.a.h.1.1 1
3.2 odd 2 210.2.a.b.1.1 1
4.3 odd 2 5040.2.a.g.1.1 1
5.2 odd 4 3150.2.g.i.2899.2 2
5.3 odd 4 3150.2.g.i.2899.1 2
5.4 even 2 3150.2.a.f.1.1 1
7.6 odd 2 4410.2.a.bi.1.1 1
12.11 even 2 1680.2.a.g.1.1 1
15.2 even 4 1050.2.g.c.799.1 2
15.8 even 4 1050.2.g.c.799.2 2
15.14 odd 2 1050.2.a.k.1.1 1
21.2 odd 6 1470.2.i.l.361.1 2
21.5 even 6 1470.2.i.s.361.1 2
21.11 odd 6 1470.2.i.l.961.1 2
21.17 even 6 1470.2.i.s.961.1 2
21.20 even 2 1470.2.a.b.1.1 1
24.5 odd 2 6720.2.a.n.1.1 1
24.11 even 2 6720.2.a.bi.1.1 1
60.59 even 2 8400.2.a.cm.1.1 1
105.104 even 2 7350.2.a.cs.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.a.b.1.1 1 3.2 odd 2
630.2.a.h.1.1 1 1.1 even 1 trivial
1050.2.a.k.1.1 1 15.14 odd 2
1050.2.g.c.799.1 2 15.2 even 4
1050.2.g.c.799.2 2 15.8 even 4
1470.2.a.b.1.1 1 21.20 even 2
1470.2.i.l.361.1 2 21.2 odd 6
1470.2.i.l.961.1 2 21.11 odd 6
1470.2.i.s.361.1 2 21.5 even 6
1470.2.i.s.961.1 2 21.17 even 6
1680.2.a.g.1.1 1 12.11 even 2
3150.2.a.f.1.1 1 5.4 even 2
3150.2.g.i.2899.1 2 5.3 odd 4
3150.2.g.i.2899.2 2 5.2 odd 4
4410.2.a.bi.1.1 1 7.6 odd 2
5040.2.a.g.1.1 1 4.3 odd 2
6720.2.a.n.1.1 1 24.5 odd 2
6720.2.a.bi.1.1 1 24.11 even 2
7350.2.a.cs.1.1 1 105.104 even 2
8400.2.a.cm.1.1 1 60.59 even 2