# Properties

 Label 9200.2.a.bg.1.1 Level $9200$ Weight $2$ Character 9200.1 Self dual yes Analytic conductor $73.462$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9200 = 2^{4} \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9200.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$73.4623698596$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 115) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 9200.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} +1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} +1.00000 q^{7} +1.00000 q^{9} -2.00000 q^{13} +5.00000 q^{17} -8.00000 q^{19} +2.00000 q^{21} -1.00000 q^{23} -4.00000 q^{27} -5.00000 q^{29} +5.00000 q^{31} -7.00000 q^{37} -4.00000 q^{39} -7.00000 q^{41} +4.00000 q^{43} -2.00000 q^{47} -6.00000 q^{49} +10.0000 q^{51} +1.00000 q^{53} -16.0000 q^{57} -3.00000 q^{59} -6.00000 q^{61} +1.00000 q^{63} +13.0000 q^{67} -2.00000 q^{69} -13.0000 q^{71} -8.00000 q^{73} +14.0000 q^{79} -11.0000 q^{81} -3.00000 q^{83} -10.0000 q^{87} -14.0000 q^{89} -2.00000 q^{91} +10.0000 q^{93} -14.0000 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 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
$$7$$ 1.00000 0.377964 0.188982 0.981981i $$-0.439481\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 5.00000 1.21268 0.606339 0.795206i $$-0.292637\pi$$
0.606339 + 0.795206i $$0.292637\pi$$
$$18$$ 0 0
$$19$$ −8.00000 −1.83533 −0.917663 0.397360i $$-0.869927\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ 2.00000 0.436436
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 0 0
$$31$$ 5.00000 0.898027 0.449013 0.893525i $$-0.351776\pi$$
0.449013 + 0.893525i $$0.351776\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −7.00000 −1.15079 −0.575396 0.817875i $$-0.695152\pi$$
−0.575396 + 0.817875i $$0.695152\pi$$
$$38$$ 0 0
$$39$$ −4.00000 −0.640513
$$40$$ 0 0
$$41$$ −7.00000 −1.09322 −0.546608 0.837389i $$-0.684081\pi$$
−0.546608 + 0.837389i $$0.684081\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −2.00000 −0.291730 −0.145865 0.989305i $$-0.546597\pi$$
−0.145865 + 0.989305i $$0.546597\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ 10.0000 1.40028
$$52$$ 0 0
$$53$$ 1.00000 0.137361 0.0686803 0.997639i $$-0.478121\pi$$
0.0686803 + 0.997639i $$0.478121\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −16.0000 −2.11925
$$58$$ 0 0
$$59$$ −3.00000 −0.390567 −0.195283 0.980747i $$-0.562563\pi$$
−0.195283 + 0.980747i $$0.562563\pi$$
$$60$$ 0 0
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 0 0
$$63$$ 1.00000 0.125988
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 13.0000 1.58820 0.794101 0.607785i $$-0.207942\pi$$
0.794101 + 0.607785i $$0.207942\pi$$
$$68$$ 0 0
$$69$$ −2.00000 −0.240772
$$70$$ 0 0
$$71$$ −13.0000 −1.54282 −0.771408 0.636341i $$-0.780447\pi$$
−0.771408 + 0.636341i $$0.780447\pi$$
$$72$$ 0 0
$$73$$ −8.00000 −0.936329 −0.468165 0.883641i $$-0.655085\pi$$
−0.468165 + 0.883641i $$0.655085\pi$$
$$74$$ 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
$$83$$ −3.00000 −0.329293 −0.164646 0.986353i $$-0.552648\pi$$
−0.164646 + 0.986353i $$0.552648\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −10.0000 −1.07211
$$88$$ 0 0
$$89$$ −14.0000 −1.48400 −0.741999 0.670402i $$-0.766122\pi$$
−0.741999 + 0.670402i $$0.766122\pi$$
$$90$$ 0 0
$$91$$ −2.00000 −0.209657
$$92$$ 0 0
$$93$$ 10.0000 1.03695
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 15.0000 1.49256 0.746278 0.665635i $$-0.231839\pi$$
0.746278 + 0.665635i $$0.231839\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 9.00000 0.870063 0.435031 0.900415i $$-0.356737\pi$$
0.435031 + 0.900415i $$0.356737\pi$$
$$108$$ 0 0
$$109$$ 18.0000 1.72409 0.862044 0.506834i $$-0.169184\pi$$
0.862044 + 0.506834i $$0.169184\pi$$
$$110$$ 0 0
$$111$$ −14.0000 −1.32882
$$112$$ 0 0
$$113$$ 1.00000 0.0940721 0.0470360 0.998893i $$-0.485022\pi$$
0.0470360 + 0.998893i $$0.485022\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ 5.00000 0.458349
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ −14.0000 −1.26234
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −20.0000 −1.77471 −0.887357 0.461084i $$-0.847461\pi$$
−0.887357 + 0.461084i $$0.847461\pi$$
$$128$$ 0 0
$$129$$ 8.00000 0.704361
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ −8.00000 −0.693688
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 0 0
$$139$$ −9.00000 −0.763370 −0.381685 0.924292i $$-0.624656\pi$$
−0.381685 + 0.924292i $$0.624656\pi$$
$$140$$ 0 0
$$141$$ −4.00000 −0.336861
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −12.0000 −0.989743
$$148$$ 0 0
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 5.00000 0.404226
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 3.00000 0.239426 0.119713 0.992809i $$-0.461803\pi$$
0.119713 + 0.992809i $$0.461803\pi$$
$$158$$ 0 0
$$159$$ 2.00000 0.158610
$$160$$ 0 0
$$161$$ −1.00000 −0.0788110
$$162$$ 0 0
$$163$$ 24.0000 1.87983 0.939913 0.341415i $$-0.110906\pi$$
0.939913 + 0.341415i $$0.110906\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 16.0000 1.23812 0.619059 0.785345i $$-0.287514\pi$$
0.619059 + 0.785345i $$0.287514\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −8.00000 −0.611775
$$172$$ 0 0
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −6.00000 −0.450988
$$178$$ 0 0
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ −12.0000 −0.887066
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −4.00000 −0.290957
$$190$$ 0 0
$$191$$ 8.00000 0.578860 0.289430 0.957199i $$-0.406534\pi$$
0.289430 + 0.957199i $$0.406534\pi$$
$$192$$ 0 0
$$193$$ 12.0000 0.863779 0.431889 0.901927i $$-0.357847\pi$$
0.431889 + 0.901927i $$0.357847\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ −2.00000 −0.141776 −0.0708881 0.997484i $$-0.522583\pi$$
−0.0708881 + 0.997484i $$0.522583\pi$$
$$200$$ 0 0
$$201$$ 26.0000 1.83390
$$202$$ 0 0
$$203$$ −5.00000 −0.350931
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −1.00000 −0.0695048
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 9.00000 0.619586 0.309793 0.950804i $$-0.399740\pi$$
0.309793 + 0.950804i $$0.399740\pi$$
$$212$$ 0 0
$$213$$ −26.0000 −1.78149
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 5.00000 0.339422
$$218$$ 0 0
$$219$$ −16.0000 −1.08118
$$220$$ 0 0
$$221$$ −10.0000 −0.672673
$$222$$ 0 0
$$223$$ −14.0000 −0.937509 −0.468755 0.883328i $$-0.655297\pi$$
−0.468755 + 0.883328i $$0.655297\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 4.00000 0.264327 0.132164 0.991228i $$-0.457808\pi$$
0.132164 + 0.991228i $$0.457808\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 28.0000 1.81880
$$238$$ 0 0
$$239$$ 1.00000 0.0646846 0.0323423 0.999477i $$-0.489703\pi$$
0.0323423 + 0.999477i $$0.489703\pi$$
$$240$$ 0 0
$$241$$ 6.00000 0.386494 0.193247 0.981150i $$-0.438098\pi$$
0.193247 + 0.981150i $$0.438098\pi$$
$$242$$ 0 0
$$243$$ −10.0000 −0.641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 16.0000 1.01806
$$248$$ 0 0
$$249$$ −6.00000 −0.380235
$$250$$ 0 0
$$251$$ −18.0000 −1.13615 −0.568075 0.822977i $$-0.692312\pi$$
−0.568075 + 0.822977i $$0.692312\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −22.0000 −1.37232 −0.686161 0.727450i $$-0.740706\pi$$
−0.686161 + 0.727450i $$0.740706\pi$$
$$258$$ 0 0
$$259$$ −7.00000 −0.434959
$$260$$ 0 0
$$261$$ −5.00000 −0.309492
$$262$$ 0 0
$$263$$ −13.0000 −0.801614 −0.400807 0.916162i $$-0.631270\pi$$
−0.400807 + 0.916162i $$0.631270\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −28.0000 −1.71357
$$268$$ 0 0
$$269$$ −15.0000 −0.914566 −0.457283 0.889321i $$-0.651177\pi$$
−0.457283 + 0.889321i $$0.651177\pi$$
$$270$$ 0 0
$$271$$ 15.0000 0.911185 0.455593 0.890188i $$-0.349427\pi$$
0.455593 + 0.890188i $$0.349427\pi$$
$$272$$ 0 0
$$273$$ −4.00000 −0.242091
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 26.0000 1.56219 0.781094 0.624413i $$-0.214662\pi$$
0.781094 + 0.624413i $$0.214662\pi$$
$$278$$ 0 0
$$279$$ 5.00000 0.299342
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ 11.0000 0.653882 0.326941 0.945045i $$-0.393982\pi$$
0.326941 + 0.945045i $$0.393982\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −7.00000 −0.413197
$$288$$ 0 0
$$289$$ 8.00000 0.470588
$$290$$ 0 0
$$291$$ −28.0000 −1.64139
$$292$$ 0 0
$$293$$ −29.0000 −1.69420 −0.847099 0.531435i $$-0.821653\pi$$
−0.847099 + 0.531435i $$0.821653\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 2.00000 0.115663
$$300$$ 0 0
$$301$$ 4.00000 0.230556
$$302$$ 0 0
$$303$$ 30.0000 1.72345
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 14.0000 0.799022 0.399511 0.916728i $$-0.369180\pi$$
0.399511 + 0.916728i $$0.369180\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −4.00000 −0.226819 −0.113410 0.993548i $$-0.536177\pi$$
−0.113410 + 0.993548i $$0.536177\pi$$
$$312$$ 0 0
$$313$$ −21.0000 −1.18699 −0.593495 0.804838i $$-0.702252\pi$$
−0.593495 + 0.804838i $$0.702252\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 24.0000 1.34797 0.673987 0.738743i $$-0.264580\pi$$
0.673987 + 0.738743i $$0.264580\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 18.0000 1.00466
$$322$$ 0 0
$$323$$ −40.0000 −2.22566
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 36.0000 1.99080
$$328$$ 0 0
$$329$$ −2.00000 −0.110264
$$330$$ 0 0
$$331$$ 5.00000 0.274825 0.137412 0.990514i $$-0.456121\pi$$
0.137412 + 0.990514i $$0.456121\pi$$
$$332$$ 0 0
$$333$$ −7.00000 −0.383598
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −26.0000 −1.41631 −0.708155 0.706057i $$-0.750472\pi$$
−0.708155 + 0.706057i $$0.750472\pi$$
$$338$$ 0 0
$$339$$ 2.00000 0.108625
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −13.0000 −0.701934
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 8.00000 0.429463 0.214731 0.976673i $$-0.431112\pi$$
0.214731 + 0.976673i $$0.431112\pi$$
$$348$$ 0 0
$$349$$ 23.0000 1.23116 0.615581 0.788074i $$-0.288921\pi$$
0.615581 + 0.788074i $$0.288921\pi$$
$$350$$ 0 0
$$351$$ 8.00000 0.427008
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 10.0000 0.529256
$$358$$ 0 0
$$359$$ 6.00000 0.316668 0.158334 0.987386i $$-0.449388\pi$$
0.158334 + 0.987386i $$0.449388\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ 0 0
$$363$$ −22.0000 −1.15470
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −13.0000 −0.678594 −0.339297 0.940679i $$-0.610189\pi$$
−0.339297 + 0.940679i $$0.610189\pi$$
$$368$$ 0 0
$$369$$ −7.00000 −0.364405
$$370$$ 0 0
$$371$$ 1.00000 0.0519174
$$372$$ 0 0
$$373$$ 6.00000 0.310668 0.155334 0.987862i $$-0.450355\pi$$
0.155334 + 0.987862i $$0.450355\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 10.0000 0.515026
$$378$$ 0 0
$$379$$ −6.00000 −0.308199 −0.154100 0.988055i $$-0.549248\pi$$
−0.154100 + 0.988055i $$0.549248\pi$$
$$380$$ 0 0
$$381$$ −40.0000 −2.04926
$$382$$ 0 0
$$383$$ 3.00000 0.153293 0.0766464 0.997058i $$-0.475579\pi$$
0.0766464 + 0.997058i $$0.475579\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 4.00000 0.203331
$$388$$ 0 0
$$389$$ 22.0000 1.11544 0.557722 0.830028i $$-0.311675\pi$$
0.557722 + 0.830028i $$0.311675\pi$$
$$390$$ 0 0
$$391$$ −5.00000 −0.252861
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −16.0000 −0.803017 −0.401508 0.915855i $$-0.631514\pi$$
−0.401508 + 0.915855i $$0.631514\pi$$
$$398$$ 0 0
$$399$$ −16.0000 −0.801002
$$400$$ 0 0
$$401$$ 2.00000 0.0998752 0.0499376 0.998752i $$-0.484098\pi$$
0.0499376 + 0.998752i $$0.484098\pi$$
$$402$$ 0 0
$$403$$ −10.0000 −0.498135
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −19.0000 −0.939490 −0.469745 0.882802i $$-0.655654\pi$$
−0.469745 + 0.882802i $$0.655654\pi$$
$$410$$ 0 0
$$411$$ −12.0000 −0.591916
$$412$$ 0 0
$$413$$ −3.00000 −0.147620
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −18.0000 −0.881464
$$418$$ 0 0
$$419$$ 2.00000 0.0977064 0.0488532 0.998806i $$-0.484443\pi$$
0.0488532 + 0.998806i $$0.484443\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ 0 0
$$423$$ −2.00000 −0.0972433
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −6.00000 −0.290360
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 0 0
$$433$$ −19.0000 −0.913082 −0.456541 0.889702i $$-0.650912\pi$$
−0.456541 + 0.889702i $$0.650912\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 8.00000 0.382692
$$438$$ 0 0
$$439$$ 28.0000 1.33637 0.668184 0.743996i $$-0.267072\pi$$
0.668184 + 0.743996i $$0.267072\pi$$
$$440$$ 0 0
$$441$$ −6.00000 −0.285714
$$442$$ 0 0
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 15.0000 0.707894 0.353947 0.935266i $$-0.384839\pi$$
0.353947 + 0.935266i $$0.384839\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −16.0000 −0.751746
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.00000 −0.0467780 −0.0233890 0.999726i $$-0.507446\pi$$
−0.0233890 + 0.999726i $$0.507446\pi$$
$$458$$ 0 0
$$459$$ −20.0000 −0.933520
$$460$$ 0 0
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −27.0000 −1.24941 −0.624705 0.780860i $$-0.714781\pi$$
−0.624705 + 0.780860i $$0.714781\pi$$
$$468$$ 0 0
$$469$$ 13.0000 0.600284
$$470$$ 0 0
$$471$$ 6.00000 0.276465
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 1.00000 0.0457869
$$478$$ 0 0
$$479$$ 28.0000 1.27935 0.639676 0.768644i $$-0.279068\pi$$
0.639676 + 0.768644i $$0.279068\pi$$
$$480$$ 0 0
$$481$$ 14.0000 0.638345
$$482$$ 0 0
$$483$$ −2.00000 −0.0910032
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −32.0000 −1.45006 −0.725029 0.688718i $$-0.758174\pi$$
−0.725029 + 0.688718i $$0.758174\pi$$
$$488$$ 0 0
$$489$$ 48.0000 2.17064
$$490$$ 0 0
$$491$$ 31.0000 1.39901 0.699505 0.714628i $$-0.253404\pi$$
0.699505 + 0.714628i $$0.253404\pi$$
$$492$$ 0 0
$$493$$ −25.0000 −1.12594
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −13.0000 −0.583130
$$498$$ 0 0
$$499$$ 11.0000 0.492428 0.246214 0.969216i $$-0.420813\pi$$
0.246214 + 0.969216i $$0.420813\pi$$
$$500$$ 0 0
$$501$$ 32.0000 1.42965
$$502$$ 0 0
$$503$$ −9.00000 −0.401290 −0.200645 0.979664i $$-0.564304\pi$$
−0.200645 + 0.979664i $$0.564304\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −18.0000 −0.799408
$$508$$ 0 0
$$509$$ 26.0000 1.15243 0.576215 0.817298i $$-0.304529\pi$$
0.576215 + 0.817298i $$0.304529\pi$$
$$510$$ 0 0
$$511$$ −8.00000 −0.353899
$$512$$ 0 0
$$513$$ 32.0000 1.41283
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −12.0000 −0.526742
$$520$$ 0 0
$$521$$ −20.0000 −0.876216 −0.438108 0.898922i $$-0.644351\pi$$
−0.438108 + 0.898922i $$0.644351\pi$$
$$522$$ 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
$$527$$ 25.0000 1.08902
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ −3.00000 −0.130189
$$532$$ 0 0
$$533$$ 14.0000 0.606407
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 8.00000 0.345225
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 14.0000 0.601907 0.300954 0.953639i $$-0.402695\pi$$
0.300954 + 0.953639i $$0.402695\pi$$
$$542$$ 0 0
$$543$$ −28.0000 −1.20160
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −4.00000 −0.171028 −0.0855138 0.996337i $$-0.527253\pi$$
−0.0855138 + 0.996337i $$0.527253\pi$$
$$548$$ 0 0
$$549$$ −6.00000 −0.256074
$$550$$ 0 0
$$551$$ 40.0000 1.70406
$$552$$ 0 0
$$553$$ 14.0000 0.595341
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 33.0000 1.39825 0.699127 0.714997i $$-0.253572\pi$$
0.699127 + 0.714997i $$0.253572\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −25.0000 −1.05362 −0.526812 0.849982i $$-0.676613\pi$$
−0.526812 + 0.849982i $$0.676613\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −11.0000 −0.461957
$$568$$ 0 0
$$569$$ −12.0000 −0.503066 −0.251533 0.967849i $$-0.580935\pi$$
−0.251533 + 0.967849i $$0.580935\pi$$
$$570$$ 0 0
$$571$$ −18.0000 −0.753277 −0.376638 0.926360i $$-0.622920\pi$$
−0.376638 + 0.926360i $$0.622920\pi$$
$$572$$ 0 0
$$573$$ 16.0000 0.668410
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −22.0000 −0.915872 −0.457936 0.888985i $$-0.651411\pi$$
−0.457936 + 0.888985i $$0.651411\pi$$
$$578$$ 0 0
$$579$$ 24.0000 0.997406
$$580$$ 0 0
$$581$$ −3.00000 −0.124461
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 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
$$589$$ −40.0000 −1.64817
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −4.00000 −0.163709
$$598$$ 0 0
$$599$$ 48.0000 1.96123 0.980613 0.195952i $$-0.0627798\pi$$
0.980613 + 0.195952i $$0.0627798\pi$$
$$600$$ 0 0
$$601$$ −25.0000 −1.01977 −0.509886 0.860242i $$-0.670312\pi$$
−0.509886 + 0.860242i $$0.670312\pi$$
$$602$$ 0 0
$$603$$ 13.0000 0.529401
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −38.0000 −1.54237 −0.771186 0.636610i $$-0.780336\pi$$
−0.771186 + 0.636610i $$0.780336\pi$$
$$608$$ 0 0
$$609$$ −10.0000 −0.405220
$$610$$ 0 0
$$611$$ 4.00000 0.161823
$$612$$ 0 0
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 47.0000 1.89215 0.946074 0.323949i $$-0.105011\pi$$
0.946074 + 0.323949i $$0.105011\pi$$
$$618$$ 0 0
$$619$$ 10.0000 0.401934 0.200967 0.979598i $$-0.435592\pi$$
0.200967 + 0.979598i $$0.435592\pi$$
$$620$$ 0 0
$$621$$ 4.00000 0.160514
$$622$$ 0 0
$$623$$ −14.0000 −0.560898
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −35.0000 −1.39554
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ 0 0
$$633$$ 18.0000 0.715436
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 12.0000 0.475457
$$638$$ 0 0
$$639$$ −13.0000 −0.514272
$$640$$ 0 0
$$641$$ −24.0000 −0.947943 −0.473972 0.880540i $$-0.657180\pi$$
−0.473972 + 0.880540i $$0.657180\pi$$
$$642$$ 0 0
$$643$$ 37.0000 1.45914 0.729569 0.683907i $$-0.239721\pi$$
0.729569 + 0.683907i $$0.239721\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −18.0000 −0.707653 −0.353827 0.935311i $$-0.615120\pi$$
−0.353827 + 0.935311i $$0.615120\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 10.0000 0.391931
$$652$$ 0 0
$$653$$ −2.00000 −0.0782660 −0.0391330 0.999234i $$-0.512460\pi$$
−0.0391330 + 0.999234i $$0.512460\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −8.00000 −0.312110
$$658$$ 0 0
$$659$$ −22.0000 −0.856998 −0.428499 0.903542i $$-0.640958\pi$$
−0.428499 + 0.903542i $$0.640958\pi$$
$$660$$ 0 0
$$661$$ −16.0000 −0.622328 −0.311164 0.950356i $$-0.600719\pi$$
−0.311164 + 0.950356i $$0.600719\pi$$
$$662$$ 0 0
$$663$$ −20.0000 −0.776736
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 5.00000 0.193601
$$668$$ 0 0
$$669$$ −28.0000 −1.08254
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −24.0000 −0.925132 −0.462566 0.886585i $$-0.653071\pi$$
−0.462566 + 0.886585i $$0.653071\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 3.00000 0.115299 0.0576497 0.998337i $$-0.481639\pi$$
0.0576497 + 0.998337i $$0.481639\pi$$
$$678$$ 0 0
$$679$$ −14.0000 −0.537271
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 46.0000 1.76014 0.880071 0.474843i $$-0.157495\pi$$
0.880071 + 0.474843i $$0.157495\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 8.00000 0.305219
$$688$$ 0 0
$$689$$ −2.00000 −0.0761939
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −35.0000 −1.32572
$$698$$ 0 0
$$699$$ −12.0000 −0.453882
$$700$$ 0 0
$$701$$ −28.0000 −1.05755 −0.528773 0.848763i $$-0.677348\pi$$
−0.528773 + 0.848763i $$0.677348\pi$$
$$702$$ 0 0
$$703$$ 56.0000 2.11208
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 15.0000 0.564133
$$708$$ 0 0
$$709$$ 4.00000 0.150223 0.0751116 0.997175i $$-0.476069\pi$$
0.0751116 + 0.997175i $$0.476069\pi$$
$$710$$ 0 0
$$711$$ 14.0000 0.525041
$$712$$ 0 0
$$713$$ −5.00000 −0.187251
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 2.00000 0.0746914
$$718$$ 0 0
$$719$$ 45.0000 1.67822 0.839108 0.543964i $$-0.183077\pi$$
0.839108 + 0.543964i $$0.183077\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 12.0000 0.446285
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 27.0000 1.00137 0.500687 0.865628i $$-0.333081\pi$$
0.500687 + 0.865628i $$0.333081\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 20.0000 0.739727
$$732$$ 0 0
$$733$$ −7.00000 −0.258551 −0.129275 0.991609i $$-0.541265\pi$$
−0.129275 + 0.991609i $$0.541265\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −7.00000 −0.257499 −0.128750 0.991677i $$-0.541096\pi$$
−0.128750 + 0.991677i $$0.541096\pi$$
$$740$$ 0 0
$$741$$ 32.0000 1.17555
$$742$$ 0 0
$$743$$ −32.0000 −1.17397 −0.586983 0.809599i $$-0.699684\pi$$
−0.586983 + 0.809599i $$0.699684\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −3.00000 −0.109764
$$748$$ 0 0
$$749$$ 9.00000 0.328853
$$750$$ 0 0
$$751$$ −14.0000 −0.510867 −0.255434 0.966827i $$-0.582218\pi$$
−0.255434 + 0.966827i $$0.582218\pi$$
$$752$$ 0 0
$$753$$ −36.0000 −1.31191
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 35.0000 1.27210 0.636048 0.771649i $$-0.280568\pi$$
0.636048 + 0.771649i $$0.280568\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 25.0000 0.906249 0.453125 0.891447i $$-0.350309\pi$$
0.453125 + 0.891447i $$0.350309\pi$$
$$762$$ 0 0
$$763$$ 18.0000 0.651644
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 6.00000 0.216647
$$768$$ 0 0
$$769$$ 10.0000 0.360609 0.180305 0.983611i $$-0.442292\pi$$
0.180305 + 0.983611i $$0.442292\pi$$
$$770$$ 0 0
$$771$$ −44.0000 −1.58462
$$772$$ 0 0
$$773$$ 42.0000 1.51064 0.755318 0.655359i $$-0.227483\pi$$
0.755318 + 0.655359i $$0.227483\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −14.0000 −0.502247
$$778$$ 0 0
$$779$$ 56.0000 2.00641
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 20.0000 0.714742
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 17.0000 0.605985 0.302992 0.952993i $$-0.402014\pi$$
0.302992 + 0.952993i $$0.402014\pi$$
$$788$$ 0 0
$$789$$ −26.0000 −0.925625
$$790$$ 0 0
$$791$$ 1.00000 0.0355559
$$792$$ 0 0
$$793$$ 12.0000 0.426132
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 15.0000 0.531327 0.265664 0.964066i $$-0.414409\pi$$
0.265664 + 0.964066i $$0.414409\pi$$
$$798$$ 0 0
$$799$$ −10.0000 −0.353775
$$800$$ 0 0
$$801$$ −14.0000 −0.494666
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −30.0000 −1.05605
$$808$$ 0 0
$$809$$ −25.0000 −0.878953 −0.439477 0.898254i $$-0.644836\pi$$
−0.439477 + 0.898254i $$0.644836\pi$$
$$810$$ 0 0
$$811$$ −31.0000 −1.08856 −0.544279 0.838905i $$-0.683197\pi$$
−0.544279 + 0.838905i $$0.683197\pi$$
$$812$$ 0 0
$$813$$ 30.0000 1.05215
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −32.0000 −1.11954
$$818$$ 0 0
$$819$$ −2.00000 −0.0698857
$$820$$ 0 0
$$821$$ 30.0000 1.04701 0.523504 0.852023i $$-0.324625\pi$$
0.523504 + 0.852023i $$0.324625\pi$$
$$822$$ 0 0
$$823$$ −34.0000 −1.18517 −0.592583 0.805510i $$-0.701892\pi$$
−0.592583 + 0.805510i $$0.701892\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −9.00000 −0.312961 −0.156480 0.987681i $$-0.550015\pi$$
−0.156480 + 0.987681i $$0.550015\pi$$
$$828$$ 0 0
$$829$$ 37.0000 1.28506 0.642532 0.766259i $$-0.277884\pi$$
0.642532 + 0.766259i $$0.277884\pi$$
$$830$$ 0 0
$$831$$ 52.0000 1.80386
$$832$$ 0 0
$$833$$ −30.0000 −1.03944
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −20.0000 −0.691301
$$838$$ 0 0
$$839$$ −14.0000 −0.483334 −0.241667 0.970359i $$-0.577694\pi$$
−0.241667 + 0.970359i $$0.577694\pi$$
$$840$$ 0 0
$$841$$ −4.00000 −0.137931
$$842$$ 0 0
$$843$$ −24.0000 −0.826604
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −11.0000 −0.377964
$$848$$ 0 0
$$849$$ 22.0000 0.755038
$$850$$ 0 0
$$851$$ 7.00000 0.239957
$$852$$ 0 0
$$853$$ −8.00000 −0.273915 −0.136957 0.990577i $$-0.543732\pi$$
−0.136957 + 0.990577i $$0.543732\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −24.0000 −0.819824 −0.409912 0.912125i $$-0.634441\pi$$
−0.409912 + 0.912125i $$0.634441\pi$$
$$858$$ 0 0
$$859$$ −43.0000 −1.46714 −0.733571 0.679613i $$-0.762148\pi$$
−0.733571 + 0.679613i $$0.762148\pi$$
$$860$$ 0 0
$$861$$ −14.0000 −0.477119
$$862$$ 0 0
$$863$$ −18.0000 −0.612727 −0.306364 0.951915i $$-0.599112\pi$$
−0.306364 + 0.951915i $$0.599112\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 16.0000 0.543388
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −26.0000 −0.880976
$$872$$ 0 0
$$873$$ −14.0000 −0.473828
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −8.00000 −0.270141 −0.135070 0.990836i $$-0.543126\pi$$
−0.135070 + 0.990836i $$0.543126\pi$$
$$878$$ 0 0
$$879$$ −58.0000 −1.95629
$$880$$ 0 0
$$881$$ 54.0000 1.81931 0.909653 0.415369i $$-0.136347\pi$$
0.909653 + 0.415369i $$0.136347\pi$$
$$882$$ 0 0
$$883$$ −20.0000 −0.673054 −0.336527 0.941674i $$-0.609252\pi$$
−0.336527 + 0.941674i $$0.609252\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 42.0000 1.41022 0.705111 0.709097i $$-0.250897\pi$$
0.705111 + 0.709097i $$0.250897\pi$$
$$888$$ 0 0
$$889$$ −20.0000 −0.670778
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 16.0000 0.535420
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 4.00000 0.133556
$$898$$ 0 0
$$899$$ −25.0000 −0.833797
$$900$$ 0 0
$$901$$ 5.00000 0.166574
$$902$$ 0 0
$$903$$ 8.00000 0.266223
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 9.00000 0.298840 0.149420 0.988774i $$-0.452259\pi$$
0.149420 + 0.988774i $$0.452259\pi$$
$$908$$ 0 0
$$909$$ 15.0000 0.497519
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −4.00000 −0.131948 −0.0659739 0.997821i $$-0.521015\pi$$
−0.0659739 + 0.997821i $$0.521015\pi$$
$$920$$ 0 0
$$921$$ 28.0000 0.922631
$$922$$ 0 0
$$923$$ 26.0000 0.855800
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 35.0000 1.14831 0.574156 0.818746i $$-0.305330\pi$$
0.574156 + 0.818746i $$0.305330\pi$$
$$930$$ 0 0
$$931$$ 48.0000 1.57314
$$932$$ 0 0
$$933$$ −8.00000 −0.261908
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −54.0000 −1.76410 −0.882052 0.471153i $$-0.843838\pi$$
−0.882052 + 0.471153i $$0.843838\pi$$
$$938$$ 0 0
$$939$$ −42.0000 −1.37062
$$940$$ 0 0
$$941$$ 2.00000 0.0651981 0.0325991 0.999469i $$-0.489622\pi$$
0.0325991 + 0.999469i $$0.489622\pi$$
$$942$$ 0 0
$$943$$ 7.00000 0.227951
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 14.0000 0.454939 0.227469 0.973785i $$-0.426955\pi$$
0.227469 + 0.973785i $$0.426955\pi$$
$$948$$ 0 0
$$949$$ 16.0000 0.519382
$$950$$ 0 0
$$951$$ 48.0000 1.55651
$$952$$ 0 0
$$953$$ −54.0000 −1.74923 −0.874616 0.484817i $$-0.838886\pi$$
−0.874616 + 0.484817i $$0.838886\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −6.00000 −0.193750
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ 0 0
$$963$$ 9.00000 0.290021
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −18.0000 −0.578841 −0.289420 0.957202i $$-0.593463\pi$$
−0.289420 + 0.957202i $$0.593463\pi$$
$$968$$ 0 0
$$969$$ −80.0000 −2.56997
$$970$$ 0 0
$$971$$ 6.00000 0.192549 0.0962746 0.995355i $$-0.469307\pi$$
0.0962746 + 0.995355i $$0.469307\pi$$
$$972$$ 0 0
$$973$$ −9.00000 −0.288527
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 39.0000 1.24772 0.623860 0.781536i $$-0.285563\pi$$
0.623860 + 0.781536i $$0.285563\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 18.0000 0.574696
$$982$$ 0 0
$$983$$ 21.0000 0.669796 0.334898 0.942254i $$-0.391298\pi$$
0.334898 + 0.942254i $$0.391298\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −4.00000 −0.127321
$$988$$ 0 0
$$989$$ −4.00000 −0.127193
$$990$$ 0 0
$$991$$ −19.0000 −0.603555 −0.301777 0.953378i $$-0.597580\pi$$
−0.301777 + 0.953378i $$0.597580\pi$$
$$992$$ 0 0
$$993$$ 10.0000 0.317340
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −20.0000 −0.633406 −0.316703 0.948525i $$-0.602576\pi$$
−0.316703 + 0.948525i $$0.602576\pi$$
$$998$$ 0 0
$$999$$ 28.0000 0.885881
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 9200.2.a.bg.1.1 1
4.3 odd 2 575.2.a.a.1.1 1
5.2 odd 4 1840.2.e.b.369.1 2
5.3 odd 4 1840.2.e.b.369.2 2
5.4 even 2 9200.2.a.g.1.1 1
12.11 even 2 5175.2.a.z.1.1 1
20.3 even 4 115.2.b.a.24.2 yes 2
20.7 even 4 115.2.b.a.24.1 2
20.19 odd 2 575.2.a.e.1.1 1
60.23 odd 4 1035.2.b.a.829.1 2
60.47 odd 4 1035.2.b.a.829.2 2
60.59 even 2 5175.2.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
115.2.b.a.24.1 2 20.7 even 4
115.2.b.a.24.2 yes 2 20.3 even 4
575.2.a.a.1.1 1 4.3 odd 2
575.2.a.e.1.1 1 20.19 odd 2
1035.2.b.a.829.1 2 60.23 odd 4
1035.2.b.a.829.2 2 60.47 odd 4
1840.2.e.b.369.1 2 5.2 odd 4
1840.2.e.b.369.2 2 5.3 odd 4
5175.2.a.a.1.1 1 60.59 even 2
5175.2.a.z.1.1 1 12.11 even 2
9200.2.a.g.1.1 1 5.4 even 2
9200.2.a.bg.1.1 1 1.1 even 1 trivial