# Properties

 Label 9800.2.a.bi.1.1 Level $9800$ Weight $2$ Character 9800.1 Self dual yes Analytic conductor $78.253$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9800 = 2^{3} \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9800.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$78.2533939809$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 9800.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} +1.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} +1.00000 q^{9} -1.00000 q^{11} +3.00000 q^{13} +2.00000 q^{17} -5.00000 q^{19} -7.00000 q^{23} -4.00000 q^{27} -6.00000 q^{29} +4.00000 q^{31} -2.00000 q^{33} +5.00000 q^{37} +6.00000 q^{39} -5.00000 q^{41} -6.00000 q^{43} +9.00000 q^{47} +4.00000 q^{51} -11.0000 q^{53} -10.0000 q^{57} +8.00000 q^{59} -12.0000 q^{61} +4.00000 q^{67} -14.0000 q^{69} -4.00000 q^{71} -12.0000 q^{73} +14.0000 q^{79} -11.0000 q^{81} +4.00000 q^{83} -12.0000 q^{87} +6.00000 q^{89} +8.00000 q^{93} -6.00000 q^{97} -1.00000 q^{99} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 2.00000 1.15470 0.577350 0.816497i $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −1.00000 −0.301511 −0.150756 0.988571i $$-0.548171\pi$$
−0.150756 + 0.988571i $$0.548171\pi$$
$$12$$ 0 0
$$13$$ 3.00000 0.832050 0.416025 0.909353i $$-0.363423\pi$$
0.416025 + 0.909353i $$0.363423\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ −5.00000 −1.14708 −0.573539 0.819178i $$-0.694430\pi$$
−0.573539 + 0.819178i $$0.694430\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −7.00000 −1.45960 −0.729800 0.683660i $$-0.760387\pi$$
−0.729800 + 0.683660i $$0.760387\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ −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 $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ −2.00000 −0.348155
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 5.00000 0.821995 0.410997 0.911636i $$-0.365181\pi$$
0.410997 + 0.911636i $$0.365181\pi$$
$$38$$ 0 0
$$39$$ 6.00000 0.960769
$$40$$ 0 0
$$41$$ −5.00000 −0.780869 −0.390434 0.920631i $$-0.627675\pi$$
−0.390434 + 0.920631i $$0.627675\pi$$
$$42$$ 0 0
$$43$$ −6.00000 −0.914991 −0.457496 0.889212i $$-0.651253\pi$$
−0.457496 + 0.889212i $$0.651253\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 9.00000 1.31278 0.656392 0.754420i $$-0.272082\pi$$
0.656392 + 0.754420i $$0.272082\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ 0 0
$$53$$ −11.0000 −1.51097 −0.755483 0.655168i $$-0.772598\pi$$
−0.755483 + 0.655168i $$0.772598\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −10.0000 −1.32453
$$58$$ 0 0
$$59$$ 8.00000 1.04151 0.520756 0.853706i $$-0.325650\pi$$
0.520756 + 0.853706i $$0.325650\pi$$
$$60$$ 0 0
$$61$$ −12.0000 −1.53644 −0.768221 0.640184i $$-0.778858\pi$$
−0.768221 + 0.640184i $$0.778858\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 0 0
$$69$$ −14.0000 −1.68540
$$70$$ 0 0
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ 0 0
$$73$$ −12.0000 −1.40449 −0.702247 0.711934i $$-0.747820\pi$$
−0.702247 + 0.711934i $$0.747820\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 14.0000 1.57512 0.787562 0.616236i $$-0.211343\pi$$
0.787562 + 0.616236i $$0.211343\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 0 0
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −12.0000 −1.28654
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 8.00000 0.829561
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 0 0
$$99$$ −1.00000 −0.100504
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 0 0
$$103$$ −20.0000 −1.97066 −0.985329 0.170664i $$-0.945409\pi$$
−0.985329 + 0.170664i $$0.945409\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ −4.00000 −0.383131 −0.191565 0.981480i $$-0.561356\pi$$
−0.191565 + 0.981480i $$0.561356\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ −20.0000 −1.88144 −0.940721 0.339182i $$-0.889850\pi$$
−0.940721 + 0.339182i $$0.889850\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 3.00000 0.277350
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ 0 0
$$123$$ −10.0000 −0.901670
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −17.0000 −1.50851 −0.754253 0.656584i $$-0.772001\pi$$
−0.754253 + 0.656584i $$0.772001\pi$$
$$128$$ 0 0
$$129$$ −12.0000 −1.05654
$$130$$ 0 0
$$131$$ 7.00000 0.611593 0.305796 0.952097i $$-0.401077\pi$$
0.305796 + 0.952097i $$0.401077\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 12.0000 1.02523 0.512615 0.858619i $$-0.328677\pi$$
0.512615 + 0.858619i $$0.328677\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 18.0000 1.51587
$$142$$ 0 0
$$143$$ −3.00000 −0.250873
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 10.0000 0.819232 0.409616 0.912258i $$-0.365663\pi$$
0.409616 + 0.912258i $$0.365663\pi$$
$$150$$ 0 0
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ 0 0
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −5.00000 −0.399043 −0.199522 0.979893i $$-0.563939\pi$$
−0.199522 + 0.979893i $$0.563939\pi$$
$$158$$ 0 0
$$159$$ −22.0000 −1.74471
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −5.00000 −0.386912 −0.193456 0.981109i $$-0.561970\pi$$
−0.193456 + 0.981109i $$0.561970\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ −5.00000 −0.382360
$$172$$ 0 0
$$173$$ −19.0000 −1.44454 −0.722272 0.691609i $$-0.756902\pi$$
−0.722272 + 0.691609i $$0.756902\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 16.0000 1.20263
$$178$$ 0 0
$$179$$ 9.00000 0.672692 0.336346 0.941739i $$-0.390809\pi$$
0.336346 + 0.941739i $$0.390809\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ −24.0000 −1.77413
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −2.00000 −0.146254
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ 20.0000 1.43963 0.719816 0.694165i $$-0.244226\pi$$
0.719816 + 0.694165i $$0.244226\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 27.0000 1.92367 0.961835 0.273629i $$-0.0882242\pi$$
0.961835 + 0.273629i $$0.0882242\pi$$
$$198$$ 0 0
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 0 0
$$201$$ 8.00000 0.564276
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −7.00000 −0.486534
$$208$$ 0 0
$$209$$ 5.00000 0.345857
$$210$$ 0 0
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 0 0
$$213$$ −8.00000 −0.548151
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −24.0000 −1.62177
$$220$$ 0 0
$$221$$ 6.00000 0.403604
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 8.00000 0.530979 0.265489 0.964114i $$-0.414466\pi$$
0.265489 + 0.964114i $$0.414466\pi$$
$$228$$ 0 0
$$229$$ −28.0000 −1.85029 −0.925146 0.379611i $$-0.876058\pi$$
−0.925146 + 0.379611i $$0.876058\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −2.00000 −0.131024 −0.0655122 0.997852i $$-0.520868\pi$$
−0.0655122 + 0.997852i $$0.520868\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 28.0000 1.81880
$$238$$ 0 0
$$239$$ 6.00000 0.388108 0.194054 0.980991i $$-0.437836\pi$$
0.194054 + 0.980991i $$0.437836\pi$$
$$240$$ 0 0
$$241$$ 23.0000 1.48156 0.740780 0.671748i $$-0.234456\pi$$
0.740780 + 0.671748i $$0.234456\pi$$
$$242$$ 0 0
$$243$$ −10.0000 −0.641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −15.0000 −0.954427
$$248$$ 0 0
$$249$$ 8.00000 0.506979
$$250$$ 0 0
$$251$$ 29.0000 1.83046 0.915232 0.402928i $$-0.132007\pi$$
0.915232 + 0.402928i $$0.132007\pi$$
$$252$$ 0 0
$$253$$ 7.00000 0.440086
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −12.0000 −0.748539 −0.374270 0.927320i $$-0.622107\pi$$
−0.374270 + 0.927320i $$0.622107\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ −8.00000 −0.493301 −0.246651 0.969104i $$-0.579330\pi$$
−0.246651 + 0.969104i $$0.579330\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ 0 0
$$269$$ −12.0000 −0.731653 −0.365826 0.930683i $$-0.619214\pi$$
−0.365826 + 0.930683i $$0.619214\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 0 0
$$279$$ 4.00000 0.239474
$$280$$ 0 0
$$281$$ −3.00000 −0.178965 −0.0894825 0.995988i $$-0.528521\pi$$
−0.0894825 + 0.995988i $$0.528521\pi$$
$$282$$ 0 0
$$283$$ 22.0000 1.30776 0.653882 0.756596i $$-0.273139\pi$$
0.653882 + 0.756596i $$0.273139\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ −12.0000 −0.703452
$$292$$ 0 0
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 4.00000 0.232104
$$298$$ 0 0
$$299$$ −21.0000 −1.21446
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 24.0000 1.37876
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 6.00000 0.342438 0.171219 0.985233i $$-0.445229\pi$$
0.171219 + 0.985233i $$0.445229\pi$$
$$308$$ 0 0
$$309$$ −40.0000 −2.27552
$$310$$ 0 0
$$311$$ −4.00000 −0.226819 −0.113410 0.993548i $$-0.536177\pi$$
−0.113410 + 0.993548i $$0.536177\pi$$
$$312$$ 0 0
$$313$$ −16.0000 −0.904373 −0.452187 0.891923i $$-0.649356\pi$$
−0.452187 + 0.891923i $$0.649356\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.00000 −0.112331 −0.0561656 0.998421i $$-0.517887\pi$$
−0.0561656 + 0.998421i $$0.517887\pi$$
$$318$$ 0 0
$$319$$ 6.00000 0.335936
$$320$$ 0 0
$$321$$ −24.0000 −1.33955
$$322$$ 0 0
$$323$$ −10.0000 −0.556415
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −8.00000 −0.442401
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −27.0000 −1.48405 −0.742027 0.670370i $$-0.766135\pi$$
−0.742027 + 0.670370i $$0.766135\pi$$
$$332$$ 0 0
$$333$$ 5.00000 0.273998
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 26.0000 1.41631 0.708155 0.706057i $$-0.249528\pi$$
0.708155 + 0.706057i $$0.249528\pi$$
$$338$$ 0 0
$$339$$ −40.0000 −2.17250
$$340$$ 0 0
$$341$$ −4.00000 −0.216612
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −8.00000 −0.429463 −0.214731 0.976673i $$-0.568888\pi$$
−0.214731 + 0.976673i $$0.568888\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ −12.0000 −0.640513
$$352$$ 0 0
$$353$$ −20.0000 −1.06449 −0.532246 0.846590i $$-0.678652\pi$$
−0.532246 + 0.846590i $$0.678652\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 30.0000 1.58334 0.791670 0.610949i $$-0.209212\pi$$
0.791670 + 0.610949i $$0.209212\pi$$
$$360$$ 0 0
$$361$$ 6.00000 0.315789
$$362$$ 0 0
$$363$$ −20.0000 −1.04973
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −19.0000 −0.991792 −0.495896 0.868382i $$-0.665160\pi$$
−0.495896 + 0.868382i $$0.665160\pi$$
$$368$$ 0 0
$$369$$ −5.00000 −0.260290
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −14.0000 −0.724893 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −18.0000 −0.927047
$$378$$ 0 0
$$379$$ −21.0000 −1.07870 −0.539349 0.842082i $$-0.681330\pi$$
−0.539349 + 0.842082i $$0.681330\pi$$
$$380$$ 0 0
$$381$$ −34.0000 −1.74187
$$382$$ 0 0
$$383$$ 21.0000 1.07305 0.536525 0.843884i $$-0.319737\pi$$
0.536525 + 0.843884i $$0.319737\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −6.00000 −0.304997
$$388$$ 0 0
$$389$$ −16.0000 −0.811232 −0.405616 0.914044i $$-0.632943\pi$$
−0.405616 + 0.914044i $$0.632943\pi$$
$$390$$ 0 0
$$391$$ −14.0000 −0.708010
$$392$$ 0 0
$$393$$ 14.0000 0.706207
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −18.0000 −0.903394 −0.451697 0.892171i $$-0.649181\pi$$
−0.451697 + 0.892171i $$0.649181\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 13.0000 0.649189 0.324595 0.945853i $$-0.394772\pi$$
0.324595 + 0.945853i $$0.394772\pi$$
$$402$$ 0 0
$$403$$ 12.0000 0.597763
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −5.00000 −0.247841
$$408$$ 0 0
$$409$$ −6.00000 −0.296681 −0.148340 0.988936i $$-0.547393\pi$$
−0.148340 + 0.988936i $$0.547393\pi$$
$$410$$ 0 0
$$411$$ 24.0000 1.18383
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 8.00000 0.391762
$$418$$ 0 0
$$419$$ −5.00000 −0.244266 −0.122133 0.992514i $$-0.538973\pi$$
−0.122133 + 0.992514i $$0.538973\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 0 0
$$423$$ 9.00000 0.437595
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ −16.0000 −0.770693 −0.385346 0.922772i $$-0.625918\pi$$
−0.385346 + 0.922772i $$0.625918\pi$$
$$432$$ 0 0
$$433$$ −24.0000 −1.15337 −0.576683 0.816968i $$-0.695653\pi$$
−0.576683 + 0.816968i $$0.695653\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 35.0000 1.67428
$$438$$ 0 0
$$439$$ −10.0000 −0.477274 −0.238637 0.971109i $$-0.576701\pi$$
−0.238637 + 0.971109i $$0.576701\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 32.0000 1.52037 0.760183 0.649709i $$-0.225109\pi$$
0.760183 + 0.649709i $$0.225109\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 20.0000 0.945968
$$448$$ 0 0
$$449$$ 13.0000 0.613508 0.306754 0.951789i $$-0.400757\pi$$
0.306754 + 0.951789i $$0.400757\pi$$
$$450$$ 0 0
$$451$$ 5.00000 0.235441
$$452$$ 0 0
$$453$$ −20.0000 −0.939682
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 0 0
$$459$$ −8.00000 −0.373408
$$460$$ 0 0
$$461$$ 14.0000 0.652045 0.326023 0.945362i $$-0.394291\pi$$
0.326023 + 0.945362i $$0.394291\pi$$
$$462$$ 0 0
$$463$$ −9.00000 −0.418265 −0.209133 0.977887i $$-0.567064\pi$$
−0.209133 + 0.977887i $$0.567064\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 10.0000 0.462745 0.231372 0.972865i $$-0.425678\pi$$
0.231372 + 0.972865i $$0.425678\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −10.0000 −0.460776
$$472$$ 0 0
$$473$$ 6.00000 0.275880
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −11.0000 −0.503655
$$478$$ 0 0
$$479$$ −16.0000 −0.731059 −0.365529 0.930800i $$-0.619112\pi$$
−0.365529 + 0.930800i $$0.619112\pi$$
$$480$$ 0 0
$$481$$ 15.0000 0.683941
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 8.00000 0.362515 0.181257 0.983436i $$-0.441983\pi$$
0.181257 + 0.983436i $$0.441983\pi$$
$$488$$ 0 0
$$489$$ −8.00000 −0.361773
$$490$$ 0 0
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ 0 0
$$493$$ −12.0000 −0.540453
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 28.0000 1.25345 0.626726 0.779240i $$-0.284395\pi$$
0.626726 + 0.779240i $$0.284395\pi$$
$$500$$ 0 0
$$501$$ −10.0000 −0.446767
$$502$$ 0 0
$$503$$ −16.0000 −0.713405 −0.356702 0.934218i $$-0.616099\pi$$
−0.356702 + 0.934218i $$0.616099\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −8.00000 −0.355292
$$508$$ 0 0
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 20.0000 0.883022
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −9.00000 −0.395820
$$518$$ 0 0
$$519$$ −38.0000 −1.66801
$$520$$ 0 0
$$521$$ −15.0000 −0.657162 −0.328581 0.944476i $$-0.606570\pi$$
−0.328581 + 0.944476i $$0.606570\pi$$
$$522$$ 0 0
$$523$$ −28.0000 −1.22435 −0.612177 0.790721i $$-0.709706\pi$$
−0.612177 + 0.790721i $$0.709706\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 8.00000 0.348485
$$528$$ 0 0
$$529$$ 26.0000 1.13043
$$530$$ 0 0
$$531$$ 8.00000 0.347170
$$532$$ 0 0
$$533$$ −15.0000 −0.649722
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 18.0000 0.776757
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −40.0000 −1.71973 −0.859867 0.510518i $$-0.829454\pi$$
−0.859867 + 0.510518i $$0.829454\pi$$
$$542$$ 0 0
$$543$$ 4.00000 0.171656
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ 0 0
$$549$$ −12.0000 −0.512148
$$550$$ 0 0
$$551$$ 30.0000 1.27804
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −21.0000 −0.889799 −0.444899 0.895581i $$-0.646761\pi$$
−0.444899 + 0.895581i $$0.646761\pi$$
$$558$$ 0 0
$$559$$ −18.0000 −0.761319
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ 0 0
$$563$$ −6.00000 −0.252870 −0.126435 0.991975i $$-0.540353\pi$$
−0.126435 + 0.991975i $$0.540353\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −11.0000 −0.461144 −0.230572 0.973055i $$-0.574060\pi$$
−0.230572 + 0.973055i $$0.574060\pi$$
$$570$$ 0 0
$$571$$ 28.0000 1.17176 0.585882 0.810397i $$-0.300748\pi$$
0.585882 + 0.810397i $$0.300748\pi$$
$$572$$ 0 0
$$573$$ 24.0000 1.00261
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 4.00000 0.166522 0.0832611 0.996528i $$-0.473466\pi$$
0.0832611 + 0.996528i $$0.473466\pi$$
$$578$$ 0 0
$$579$$ 40.0000 1.66234
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 11.0000 0.455573
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ −20.0000 −0.824086
$$590$$ 0 0
$$591$$ 54.0000 2.22126
$$592$$ 0 0
$$593$$ 12.0000 0.492781 0.246390 0.969171i $$-0.420755\pi$$
0.246390 + 0.969171i $$0.420755\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −8.00000 −0.327418
$$598$$ 0 0
$$599$$ 34.0000 1.38920 0.694601 0.719395i $$-0.255581\pi$$
0.694601 + 0.719395i $$0.255581\pi$$
$$600$$ 0 0
$$601$$ −14.0000 −0.571072 −0.285536 0.958368i $$-0.592172\pi$$
−0.285536 + 0.958368i $$0.592172\pi$$
$$602$$ 0 0
$$603$$ 4.00000 0.162893
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −33.0000 −1.33943 −0.669714 0.742619i $$-0.733583\pi$$
−0.669714 + 0.742619i $$0.733583\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 27.0000 1.09230
$$612$$ 0 0
$$613$$ 41.0000 1.65597 0.827987 0.560747i $$-0.189486\pi$$
0.827987 + 0.560747i $$0.189486\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ 0 0
$$619$$ 35.0000 1.40677 0.703384 0.710810i $$-0.251671\pi$$
0.703384 + 0.710810i $$0.251671\pi$$
$$620$$ 0 0
$$621$$ 28.0000 1.12360
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 10.0000 0.399362
$$628$$ 0 0
$$629$$ 10.0000 0.398726
$$630$$ 0 0
$$631$$ 40.0000 1.59237 0.796187 0.605050i $$-0.206847\pi$$
0.796187 + 0.605050i $$0.206847\pi$$
$$632$$ 0 0
$$633$$ −26.0000 −1.03341
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −4.00000 −0.158238
$$640$$ 0 0
$$641$$ 35.0000 1.38242 0.691208 0.722655i $$-0.257079\pi$$
0.691208 + 0.722655i $$0.257079\pi$$
$$642$$ 0 0
$$643$$ 34.0000 1.34083 0.670415 0.741987i $$-0.266116\pi$$
0.670415 + 0.741987i $$0.266116\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −23.0000 −0.904223 −0.452112 0.891961i $$-0.649329\pi$$
−0.452112 + 0.891961i $$0.649329\pi$$
$$648$$ 0 0
$$649$$ −8.00000 −0.314027
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −45.0000 −1.76099 −0.880493 0.474059i $$-0.842788\pi$$
−0.880493 + 0.474059i $$0.842788\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −12.0000 −0.468165
$$658$$ 0 0
$$659$$ −16.0000 −0.623272 −0.311636 0.950202i $$-0.600877\pi$$
−0.311636 + 0.950202i $$0.600877\pi$$
$$660$$ 0 0
$$661$$ −36.0000 −1.40024 −0.700119 0.714026i $$-0.746870\pi$$
−0.700119 + 0.714026i $$0.746870\pi$$
$$662$$ 0 0
$$663$$ 12.0000 0.466041
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 42.0000 1.62625
$$668$$ 0 0
$$669$$ 32.0000 1.23719
$$670$$ 0 0
$$671$$ 12.0000 0.463255
$$672$$ 0 0
$$673$$ 42.0000 1.61898 0.809491 0.587133i $$-0.199743\pi$$
0.809491 + 0.587133i $$0.199743\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −21.0000 −0.807096 −0.403548 0.914959i $$-0.632223\pi$$
−0.403548 + 0.914959i $$0.632223\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 16.0000 0.613121
$$682$$ 0 0
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −56.0000 −2.13653
$$688$$ 0 0
$$689$$ −33.0000 −1.25720
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −10.0000 −0.378777
$$698$$ 0 0
$$699$$ −4.00000 −0.151294
$$700$$ 0 0
$$701$$ 42.0000 1.58632 0.793159 0.609015i $$-0.208435\pi$$
0.793159 + 0.609015i $$0.208435\pi$$
$$702$$ 0 0
$$703$$ −25.0000 −0.942893
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −18.0000 −0.676004 −0.338002 0.941145i $$-0.609751\pi$$
−0.338002 + 0.941145i $$0.609751\pi$$
$$710$$ 0 0
$$711$$ 14.0000 0.525041
$$712$$ 0 0
$$713$$ −28.0000 −1.04861
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 12.0000 0.448148
$$718$$ 0 0
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 46.0000 1.71076
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −41.0000 −1.52061 −0.760303 0.649569i $$-0.774949\pi$$
−0.760303 + 0.649569i $$0.774949\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ −31.0000 −1.14501 −0.572506 0.819901i $$-0.694029\pi$$
−0.572506 + 0.819901i $$0.694029\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −4.00000 −0.147342
$$738$$ 0 0
$$739$$ −41.0000 −1.50821 −0.754105 0.656754i $$-0.771929\pi$$
−0.754105 + 0.656754i $$0.771929\pi$$
$$740$$ 0 0
$$741$$ −30.0000 −1.10208
$$742$$ 0 0
$$743$$ 3.00000 0.110059 0.0550297 0.998485i $$-0.482475\pi$$
0.0550297 + 0.998485i $$0.482475\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 4.00000 0.146352
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 18.0000 0.656829 0.328415 0.944534i $$-0.393486\pi$$
0.328415 + 0.944534i $$0.393486\pi$$
$$752$$ 0 0
$$753$$ 58.0000 2.11364
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 6.00000 0.218074 0.109037 0.994038i $$-0.465223\pi$$
0.109037 + 0.994038i $$0.465223\pi$$
$$758$$ 0 0
$$759$$ 14.0000 0.508168
$$760$$ 0 0
$$761$$ −3.00000 −0.108750 −0.0543750 0.998521i $$-0.517317\pi$$
−0.0543750 + 0.998521i $$0.517317\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 24.0000 0.866590
$$768$$ 0 0
$$769$$ −41.0000 −1.47850 −0.739249 0.673432i $$-0.764819\pi$$
−0.739249 + 0.673432i $$0.764819\pi$$
$$770$$ 0 0
$$771$$ −24.0000 −0.864339
$$772$$ 0 0
$$773$$ −15.0000 −0.539513 −0.269756 0.962929i $$-0.586943\pi$$
−0.269756 + 0.962929i $$0.586943\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 25.0000 0.895718
$$780$$ 0 0
$$781$$ 4.00000 0.143131
$$782$$ 0 0
$$783$$ 24.0000 0.857690
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 18.0000 0.641631 0.320815 0.947142i $$-0.396043\pi$$
0.320815 + 0.947142i $$0.396043\pi$$
$$788$$ 0 0
$$789$$ −16.0000 −0.569615
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −36.0000 −1.27840
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −2.00000 −0.0708436 −0.0354218 0.999372i $$-0.511277\pi$$
−0.0354218 + 0.999372i $$0.511277\pi$$
$$798$$ 0 0
$$799$$ 18.0000 0.636794
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ 0 0
$$803$$ 12.0000 0.423471
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −24.0000 −0.844840
$$808$$ 0 0
$$809$$ 55.0000 1.93370 0.966849 0.255351i $$-0.0821909\pi$$
0.966849 + 0.255351i $$0.0821909\pi$$
$$810$$ 0 0
$$811$$ −5.00000 −0.175574 −0.0877869 0.996139i $$-0.527979\pi$$
−0.0877869 + 0.996139i $$0.527979\pi$$
$$812$$ 0 0
$$813$$ −16.0000 −0.561144
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 30.0000 1.04957
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 30.0000 1.04701 0.523504 0.852023i $$-0.324625\pi$$
0.523504 + 0.852023i $$0.324625\pi$$
$$822$$ 0 0
$$823$$ −4.00000 −0.139431 −0.0697156 0.997567i $$-0.522209\pi$$
−0.0697156 + 0.997567i $$0.522209\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 14.0000 0.486828 0.243414 0.969923i $$-0.421733\pi$$
0.243414 + 0.969923i $$0.421733\pi$$
$$828$$ 0 0
$$829$$ 38.0000 1.31979 0.659897 0.751356i $$-0.270600\pi$$
0.659897 + 0.751356i $$0.270600\pi$$
$$830$$ 0 0
$$831$$ −4.00000 −0.138758
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −16.0000 −0.553041
$$838$$ 0 0
$$839$$ −14.0000 −0.483334 −0.241667 0.970359i $$-0.577694\pi$$
−0.241667 + 0.970359i $$0.577694\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ −6.00000 −0.206651
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 44.0000 1.51008
$$850$$ 0 0
$$851$$ −35.0000 −1.19978
$$852$$ 0 0
$$853$$ −23.0000 −0.787505 −0.393753 0.919216i $$-0.628823\pi$$
−0.393753 + 0.919216i $$0.628823\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ 40.0000 1.36478 0.682391 0.730987i $$-0.260940\pi$$
0.682391 + 0.730987i $$0.260940\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 13.0000 0.442525 0.221263 0.975214i $$-0.428982\pi$$
0.221263 + 0.975214i $$0.428982\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −26.0000 −0.883006
$$868$$ 0 0
$$869$$ −14.0000 −0.474917
$$870$$ 0 0
$$871$$ 12.0000 0.406604
$$872$$ 0 0
$$873$$ −6.00000 −0.203069
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −9.00000 −0.303908 −0.151954 0.988388i $$-0.548557\pi$$
−0.151954 + 0.988388i $$0.548557\pi$$
$$878$$ 0 0
$$879$$ −42.0000 −1.41662
$$880$$ 0 0
$$881$$ −7.00000 −0.235836 −0.117918 0.993023i $$-0.537622\pi$$
−0.117918 + 0.993023i $$0.537622\pi$$
$$882$$ 0 0
$$883$$ −8.00000 −0.269221 −0.134611 0.990899i $$-0.542978\pi$$
−0.134611 + 0.990899i $$0.542978\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 11.0000 0.368514
$$892$$ 0 0
$$893$$ −45.0000 −1.50587
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −42.0000 −1.40234
$$898$$ 0 0
$$899$$ −24.0000 −0.800445
$$900$$ 0 0
$$901$$ −22.0000 −0.732926
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −22.0000 −0.730498 −0.365249 0.930910i $$-0.619016\pi$$
−0.365249 + 0.930910i $$0.619016\pi$$
$$908$$ 0 0
$$909$$ 12.0000 0.398015
$$910$$ 0 0
$$911$$ 42.0000 1.39152 0.695761 0.718273i $$-0.255067\pi$$
0.695761 + 0.718273i $$0.255067\pi$$
$$912$$ 0 0
$$913$$ −4.00000 −0.132381
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −18.0000 −0.593765 −0.296883 0.954914i $$-0.595947\pi$$
−0.296883 + 0.954914i $$0.595947\pi$$
$$920$$ 0 0
$$921$$ 12.0000 0.395413
$$922$$ 0 0
$$923$$ −12.0000 −0.394985
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −20.0000 −0.656886
$$928$$ 0 0
$$929$$ −31.0000 −1.01708 −0.508539 0.861039i $$-0.669814\pi$$
−0.508539 + 0.861039i $$0.669814\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ −8.00000 −0.261908
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 38.0000 1.24141 0.620703 0.784046i $$-0.286847\pi$$
0.620703 + 0.784046i $$0.286847\pi$$
$$938$$ 0 0
$$939$$ −32.0000 −1.04428
$$940$$ 0 0
$$941$$ 24.0000 0.782378 0.391189 0.920310i $$-0.372064\pi$$
0.391189 + 0.920310i $$0.372064\pi$$
$$942$$ 0 0
$$943$$ 35.0000 1.13976
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −14.0000 −0.454939 −0.227469 0.973785i $$-0.573045\pi$$
−0.227469 + 0.973785i $$0.573045\pi$$
$$948$$ 0 0
$$949$$ −36.0000 −1.16861
$$950$$ 0 0
$$951$$ −4.00000 −0.129709
$$952$$ 0 0
$$953$$ 20.0000 0.647864 0.323932 0.946080i $$-0.394995\pi$$
0.323932 + 0.946080i $$0.394995\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 12.0000 0.387905
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 0 0
$$963$$ −12.0000 −0.386695
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 8.00000 0.257263 0.128631 0.991692i $$-0.458942\pi$$
0.128631 + 0.991692i $$0.458942\pi$$
$$968$$ 0 0
$$969$$ −20.0000 −0.642493
$$970$$ 0 0
$$971$$ 7.00000 0.224641 0.112320 0.993672i $$-0.464172\pi$$
0.112320 + 0.993672i $$0.464172\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −18.0000 −0.575871 −0.287936 0.957650i $$-0.592969\pi$$
−0.287936 + 0.957650i $$0.592969\pi$$
$$978$$ 0 0
$$979$$ −6.00000 −0.191761
$$980$$ 0 0
$$981$$ −4.00000 −0.127710
$$982$$ 0 0
$$983$$ 3.00000 0.0956851 0.0478426 0.998855i $$-0.484765\pi$$
0.0478426 + 0.998855i $$0.484765\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 42.0000 1.33552
$$990$$ 0 0
$$991$$ 44.0000 1.39771 0.698853 0.715265i $$-0.253694\pi$$
0.698853 + 0.715265i $$0.253694\pi$$
$$992$$ 0 0
$$993$$ −54.0000 −1.71364
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −46.0000 −1.45683 −0.728417 0.685134i $$-0.759744\pi$$
−0.728417 + 0.685134i $$0.759744\pi$$
$$998$$ 0 0
$$999$$ −20.0000 −0.632772
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 9800.2.a.bi.1.1 1
5.4 even 2 1960.2.a.a.1.1 1
7.2 even 3 1400.2.q.a.1201.1 2
7.4 even 3 1400.2.q.a.401.1 2
7.6 odd 2 9800.2.a.g.1.1 1
20.19 odd 2 3920.2.a.bf.1.1 1
35.2 odd 12 1400.2.bh.e.249.2 4
35.4 even 6 280.2.q.c.121.1 yes 2
35.9 even 6 280.2.q.c.81.1 2
35.18 odd 12 1400.2.bh.e.849.2 4
35.19 odd 6 1960.2.q.c.361.1 2
35.23 odd 12 1400.2.bh.e.249.1 4
35.24 odd 6 1960.2.q.c.961.1 2
35.32 odd 12 1400.2.bh.e.849.1 4
35.34 odd 2 1960.2.a.m.1.1 1
105.44 odd 6 2520.2.bi.e.361.1 2
105.74 odd 6 2520.2.bi.e.1801.1 2
140.39 odd 6 560.2.q.c.401.1 2
140.79 odd 6 560.2.q.c.81.1 2
140.139 even 2 3920.2.a.i.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.q.c.81.1 2 35.9 even 6
280.2.q.c.121.1 yes 2 35.4 even 6
560.2.q.c.81.1 2 140.79 odd 6
560.2.q.c.401.1 2 140.39 odd 6
1400.2.q.a.401.1 2 7.4 even 3
1400.2.q.a.1201.1 2 7.2 even 3
1400.2.bh.e.249.1 4 35.23 odd 12
1400.2.bh.e.249.2 4 35.2 odd 12
1400.2.bh.e.849.1 4 35.32 odd 12
1400.2.bh.e.849.2 4 35.18 odd 12
1960.2.a.a.1.1 1 5.4 even 2
1960.2.a.m.1.1 1 35.34 odd 2
1960.2.q.c.361.1 2 35.19 odd 6
1960.2.q.c.961.1 2 35.24 odd 6
2520.2.bi.e.361.1 2 105.44 odd 6
2520.2.bi.e.1801.1 2 105.74 odd 6
3920.2.a.i.1.1 1 140.139 even 2
3920.2.a.bf.1.1 1 20.19 odd 2
9800.2.a.g.1.1 1 7.6 odd 2
9800.2.a.bi.1.1 1 1.1 even 1 trivial