# Properties

 Label 7600.2.a.cd.1.3 Level $7600$ Weight $2$ Character 7600.1 Self dual yes Analytic conductor $60.686$ Analytic rank $1$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7600 = 2^{4} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7600.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$60.6863055362$$ Analytic rank: $$1$$ Dimension: $$3$$ Coefficient field: 3.3.568.1 Defining polynomial: $$x^{3} - x^{2} - 6 x - 2$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$-1.76156$$ of defining polynomial Character $$\chi$$ $$=$$ 7600.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.76156 q^{3} -0.761557 q^{7} +4.62620 q^{9} +O(q^{10})$$ $$q+2.76156 q^{3} -0.761557 q^{7} +4.62620 q^{9} +0.864641 q^{11} -5.62620 q^{13} +3.62620 q^{17} -1.00000 q^{19} -2.10308 q^{21} -8.01395 q^{23} +4.49084 q^{27} -7.35548 q^{29} -8.11704 q^{31} +2.38776 q^{33} -0.476886 q^{37} -15.5371 q^{39} -2.65847 q^{41} +6.86464 q^{43} +1.25240 q^{47} -6.42003 q^{49} +10.0140 q^{51} -2.37380 q^{53} -2.76156 q^{57} -4.49084 q^{59} -10.8646 q^{61} -3.52311 q^{63} +1.03228 q^{67} -22.1310 q^{69} +10.1816 q^{71} -16.4017 q^{73} -0.658473 q^{77} +12.5693 q^{79} -1.47689 q^{81} -0.270718 q^{83} -20.3126 q^{87} +0.387755 q^{89} +4.28467 q^{91} -22.4157 q^{93} +8.50479 q^{97} +4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3q + 2q^{3} + 4q^{7} + 5q^{9} + O(q^{10})$$ $$3q + 2q^{3} + 4q^{7} + 5q^{9} - 8q^{13} + 2q^{17} - 3q^{19} - 10q^{21} + 2q^{27} - 8q^{29} - 4q^{31} - 8q^{33} - 14q^{37} - 10q^{39} + 2q^{41} + 18q^{43} - 14q^{47} - 3q^{49} + 6q^{51} - 16q^{53} - 2q^{57} - 2q^{59} - 30q^{61} + 2q^{63} + 2q^{67} - 22q^{69} + 8q^{71} - 10q^{73} + 8q^{77} - 17q^{81} - 6q^{83} + 6q^{87} - 14q^{89} - 6q^{91} - 4q^{93} - 10q^{97} + 12q^{99} + O(q^{100})$$

## 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
$$3$$ 2.76156 1.59439 0.797193 0.603725i $$-0.206317\pi$$
0.797193 + 0.603725i $$0.206317\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −0.761557 −0.287842 −0.143921 0.989589i $$-0.545971\pi$$
−0.143921 + 0.989589i $$0.545971\pi$$
$$8$$ 0 0
$$9$$ 4.62620 1.54207
$$10$$ 0 0
$$11$$ 0.864641 0.260699 0.130350 0.991468i $$-0.458390\pi$$
0.130350 + 0.991468i $$0.458390\pi$$
$$12$$ 0 0
$$13$$ −5.62620 −1.56043 −0.780213 0.625514i $$-0.784889\pi$$
−0.780213 + 0.625514i $$0.784889\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 3.62620 0.879482 0.439741 0.898125i $$-0.355070\pi$$
0.439741 + 0.898125i $$0.355070\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −0.229416
$$20$$ 0 0
$$21$$ −2.10308 −0.458930
$$22$$ 0 0
$$23$$ −8.01395 −1.67102 −0.835512 0.549472i $$-0.814829\pi$$
−0.835512 + 0.549472i $$0.814829\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 4.49084 0.864262
$$28$$ 0 0
$$29$$ −7.35548 −1.36588 −0.682939 0.730475i $$-0.739299\pi$$
−0.682939 + 0.730475i $$0.739299\pi$$
$$30$$ 0 0
$$31$$ −8.11704 −1.45786 −0.728931 0.684587i $$-0.759983\pi$$
−0.728931 + 0.684587i $$0.759983\pi$$
$$32$$ 0 0
$$33$$ 2.38776 0.415655
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −0.476886 −0.0783995 −0.0391998 0.999231i $$-0.512481\pi$$
−0.0391998 + 0.999231i $$0.512481\pi$$
$$38$$ 0 0
$$39$$ −15.5371 −2.48792
$$40$$ 0 0
$$41$$ −2.65847 −0.415184 −0.207592 0.978216i $$-0.566563\pi$$
−0.207592 + 0.978216i $$0.566563\pi$$
$$42$$ 0 0
$$43$$ 6.86464 1.04685 0.523424 0.852072i $$-0.324654\pi$$
0.523424 + 0.852072i $$0.324654\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 1.25240 0.182681 0.0913404 0.995820i $$-0.470885\pi$$
0.0913404 + 0.995820i $$0.470885\pi$$
$$48$$ 0 0
$$49$$ −6.42003 −0.917147
$$50$$ 0 0
$$51$$ 10.0140 1.40223
$$52$$ 0 0
$$53$$ −2.37380 −0.326067 −0.163033 0.986621i $$-0.552128\pi$$
−0.163033 + 0.986621i $$0.552128\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −2.76156 −0.365777
$$58$$ 0 0
$$59$$ −4.49084 −0.584657 −0.292329 0.956318i $$-0.594430\pi$$
−0.292329 + 0.956318i $$0.594430\pi$$
$$60$$ 0 0
$$61$$ −10.8646 −1.39107 −0.695537 0.718490i $$-0.744834\pi$$
−0.695537 + 0.718490i $$0.744834\pi$$
$$62$$ 0 0
$$63$$ −3.52311 −0.443871
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.03228 0.126113 0.0630563 0.998010i $$-0.479915\pi$$
0.0630563 + 0.998010i $$0.479915\pi$$
$$68$$ 0 0
$$69$$ −22.1310 −2.66426
$$70$$ 0 0
$$71$$ 10.1816 1.20833 0.604166 0.796858i $$-0.293506\pi$$
0.604166 + 0.796858i $$0.293506\pi$$
$$72$$ 0 0
$$73$$ −16.4017 −1.91967 −0.959837 0.280557i $$-0.909481\pi$$
−0.959837 + 0.280557i $$0.909481\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −0.658473 −0.0750400
$$78$$ 0 0
$$79$$ 12.5693 1.41416 0.707081 0.707133i $$-0.250012\pi$$
0.707081 + 0.707133i $$0.250012\pi$$
$$80$$ 0 0
$$81$$ −1.47689 −0.164098
$$82$$ 0 0
$$83$$ −0.270718 −0.0297152 −0.0148576 0.999890i $$-0.504729\pi$$
−0.0148576 + 0.999890i $$0.504729\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −20.3126 −2.17774
$$88$$ 0 0
$$89$$ 0.387755 0.0411020 0.0205510 0.999789i $$-0.493458\pi$$
0.0205510 + 0.999789i $$0.493458\pi$$
$$90$$ 0 0
$$91$$ 4.28467 0.449156
$$92$$ 0 0
$$93$$ −22.4157 −2.32440
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 8.50479 0.863531 0.431765 0.901986i $$-0.357891\pi$$
0.431765 + 0.901986i $$0.357891\pi$$
$$98$$ 0 0
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ 16.4157 1.63342 0.816710 0.577049i $$-0.195796\pi$$
0.816710 + 0.577049i $$0.195796\pi$$
$$102$$ 0 0
$$103$$ −9.64015 −0.949872 −0.474936 0.880020i $$-0.657529\pi$$
−0.474936 + 0.880020i $$0.657529\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 4.28467 0.414215 0.207107 0.978318i $$-0.433595\pi$$
0.207107 + 0.978318i $$0.433595\pi$$
$$108$$ 0 0
$$109$$ −13.4200 −1.28541 −0.642703 0.766116i $$-0.722187\pi$$
−0.642703 + 0.766116i $$0.722187\pi$$
$$110$$ 0 0
$$111$$ −1.31695 −0.124999
$$112$$ 0 0
$$113$$ 10.3232 0.971125 0.485563 0.874202i $$-0.338615\pi$$
0.485563 + 0.874202i $$0.338615\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −26.0279 −2.40628
$$118$$ 0 0
$$119$$ −2.76156 −0.253152
$$120$$ 0 0
$$121$$ −10.2524 −0.932036
$$122$$ 0 0
$$123$$ −7.34153 −0.661963
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 16.9817 1.50688 0.753440 0.657517i $$-0.228393\pi$$
0.753440 + 0.657517i $$0.228393\pi$$
$$128$$ 0 0
$$129$$ 18.9571 1.66908
$$130$$ 0 0
$$131$$ −0.541436 −0.0473055 −0.0236528 0.999720i $$-0.507530\pi$$
−0.0236528 + 0.999720i $$0.507530\pi$$
$$132$$ 0 0
$$133$$ 0.761557 0.0660354
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2.87859 −0.245935 −0.122967 0.992411i $$-0.539241\pi$$
−0.122967 + 0.992411i $$0.539241\pi$$
$$138$$ 0 0
$$139$$ −3.58767 −0.304302 −0.152151 0.988357i $$-0.548620\pi$$
−0.152151 + 0.988357i $$0.548620\pi$$
$$140$$ 0 0
$$141$$ 3.45856 0.291264
$$142$$ 0 0
$$143$$ −4.86464 −0.406802
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −17.7293 −1.46229
$$148$$ 0 0
$$149$$ −16.8401 −1.37959 −0.689796 0.724004i $$-0.742300\pi$$
−0.689796 + 0.724004i $$0.742300\pi$$
$$150$$ 0 0
$$151$$ 16.9817 1.38195 0.690975 0.722879i $$-0.257182\pi$$
0.690975 + 0.722879i $$0.257182\pi$$
$$152$$ 0 0
$$153$$ 16.7755 1.35622
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −14.8401 −1.18437 −0.592183 0.805804i $$-0.701734\pi$$
−0.592183 + 0.805804i $$0.701734\pi$$
$$158$$ 0 0
$$159$$ −6.55539 −0.519876
$$160$$ 0 0
$$161$$ 6.10308 0.480990
$$162$$ 0 0
$$163$$ 13.3694 1.04717 0.523587 0.851972i $$-0.324593\pi$$
0.523587 + 0.851972i $$0.324593\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 9.84632 0.761931 0.380966 0.924589i $$-0.375592\pi$$
0.380966 + 0.924589i $$0.375592\pi$$
$$168$$ 0 0
$$169$$ 18.6541 1.43493
$$170$$ 0 0
$$171$$ −4.62620 −0.353774
$$172$$ 0 0
$$173$$ −2.98168 −0.226693 −0.113346 0.993556i $$-0.536157\pi$$
−0.113346 + 0.993556i $$0.536157\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −12.4017 −0.932169
$$178$$ 0 0
$$179$$ −11.7938 −0.881512 −0.440756 0.897627i $$-0.645290\pi$$
−0.440756 + 0.897627i $$0.645290\pi$$
$$180$$ 0 0
$$181$$ 14.5693 1.08293 0.541465 0.840723i $$-0.317870\pi$$
0.541465 + 0.840723i $$0.317870\pi$$
$$182$$ 0 0
$$183$$ −30.0033 −2.21791
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 3.13536 0.229280
$$188$$ 0 0
$$189$$ −3.42003 −0.248771
$$190$$ 0 0
$$191$$ −13.2384 −0.957900 −0.478950 0.877842i $$-0.658983\pi$$
−0.478950 + 0.877842i $$0.658983\pi$$
$$192$$ 0 0
$$193$$ −2.54144 −0.182937 −0.0914683 0.995808i $$-0.529156\pi$$
−0.0914683 + 0.995808i $$0.529156\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 19.9109 1.41859 0.709295 0.704911i $$-0.249013\pi$$
0.709295 + 0.704911i $$0.249013\pi$$
$$198$$ 0 0
$$199$$ 20.3126 1.43992 0.719960 0.694015i $$-0.244160\pi$$
0.719960 + 0.694015i $$0.244160\pi$$
$$200$$ 0 0
$$201$$ 2.85069 0.201072
$$202$$ 0 0
$$203$$ 5.60162 0.393157
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −37.0741 −2.57683
$$208$$ 0 0
$$209$$ −0.864641 −0.0598085
$$210$$ 0 0
$$211$$ −18.0419 −1.24205 −0.621026 0.783790i $$-0.713284\pi$$
−0.621026 + 0.783790i $$0.713284\pi$$
$$212$$ 0 0
$$213$$ 28.1170 1.92655
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 6.18159 0.419634
$$218$$ 0 0
$$219$$ −45.2943 −3.06070
$$220$$ 0 0
$$221$$ −20.4017 −1.37237
$$222$$ 0 0
$$223$$ −13.5231 −0.905575 −0.452787 0.891619i $$-0.649570\pi$$
−0.452787 + 0.891619i $$0.649570\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 13.6016 0.902771 0.451386 0.892329i $$-0.350930\pi$$
0.451386 + 0.892329i $$0.350930\pi$$
$$228$$ 0 0
$$229$$ 13.5877 0.897898 0.448949 0.893557i $$-0.351798\pi$$
0.448949 + 0.893557i $$0.351798\pi$$
$$230$$ 0 0
$$231$$ −1.81841 −0.119643
$$232$$ 0 0
$$233$$ −25.5510 −1.67390 −0.836952 0.547277i $$-0.815664\pi$$
−0.836952 + 0.547277i $$0.815664\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 34.7110 2.25472
$$238$$ 0 0
$$239$$ 11.3309 0.732935 0.366468 0.930431i $$-0.380567\pi$$
0.366468 + 0.930431i $$0.380567\pi$$
$$240$$ 0 0
$$241$$ −1.25240 −0.0806739 −0.0403370 0.999186i $$-0.512843\pi$$
−0.0403370 + 0.999186i $$0.512843\pi$$
$$242$$ 0 0
$$243$$ −17.5510 −1.12590
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 5.62620 0.357986
$$248$$ 0 0
$$249$$ −0.747604 −0.0473775
$$250$$ 0 0
$$251$$ −10.5939 −0.668682 −0.334341 0.942452i $$-0.608514\pi$$
−0.334341 + 0.942452i $$0.608514\pi$$
$$252$$ 0 0
$$253$$ −6.92919 −0.435635
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0.153681 0.00958637 0.00479319 0.999989i $$-0.498474\pi$$
0.00479319 + 0.999989i $$0.498474\pi$$
$$258$$ 0 0
$$259$$ 0.363176 0.0225666
$$260$$ 0 0
$$261$$ −34.0279 −2.10627
$$262$$ 0 0
$$263$$ 0.504792 0.0311268 0.0155634 0.999879i $$-0.495046\pi$$
0.0155634 + 0.999879i $$0.495046\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 1.07081 0.0655324
$$268$$ 0 0
$$269$$ −3.49521 −0.213107 −0.106553 0.994307i $$-0.533981\pi$$
−0.106553 + 0.994307i $$0.533981\pi$$
$$270$$ 0 0
$$271$$ −5.47252 −0.332432 −0.166216 0.986089i $$-0.553155\pi$$
−0.166216 + 0.986089i $$0.553155\pi$$
$$272$$ 0 0
$$273$$ 11.8324 0.716127
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −12.9538 −0.778317 −0.389158 0.921171i $$-0.627234\pi$$
−0.389158 + 0.921171i $$0.627234\pi$$
$$278$$ 0 0
$$279$$ −37.5510 −2.24812
$$280$$ 0 0
$$281$$ 0.153681 0.00916785 0.00458393 0.999989i $$-0.498541\pi$$
0.00458393 + 0.999989i $$0.498541\pi$$
$$282$$ 0 0
$$283$$ −18.2341 −1.08390 −0.541952 0.840410i $$-0.682314\pi$$
−0.541952 + 0.840410i $$0.682314\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 2.02458 0.119507
$$288$$ 0 0
$$289$$ −3.85069 −0.226511
$$290$$ 0 0
$$291$$ 23.4865 1.37680
$$292$$ 0 0
$$293$$ −2.03853 −0.119092 −0.0595462 0.998226i $$-0.518965\pi$$
−0.0595462 + 0.998226i $$0.518965\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 3.88296 0.225312
$$298$$ 0 0
$$299$$ 45.0881 2.60751
$$300$$ 0 0
$$301$$ −5.22782 −0.301326
$$302$$ 0 0
$$303$$ 45.3328 2.60430
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 16.5414 0.944070 0.472035 0.881580i $$-0.343520\pi$$
0.472035 + 0.881580i $$0.343520\pi$$
$$308$$ 0 0
$$309$$ −26.6218 −1.51446
$$310$$ 0 0
$$311$$ 21.4725 1.21759 0.608797 0.793326i $$-0.291652\pi$$
0.608797 + 0.793326i $$0.291652\pi$$
$$312$$ 0 0
$$313$$ 1.12141 0.0633856 0.0316928 0.999498i $$-0.489910\pi$$
0.0316928 + 0.999498i $$0.489910\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 29.8882 1.67869 0.839344 0.543601i $$-0.182940\pi$$
0.839344 + 0.543601i $$0.182940\pi$$
$$318$$ 0 0
$$319$$ −6.35985 −0.356083
$$320$$ 0 0
$$321$$ 11.8324 0.660418
$$322$$ 0 0
$$323$$ −3.62620 −0.201767
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −37.0602 −2.04943
$$328$$ 0 0
$$329$$ −0.953771 −0.0525831
$$330$$ 0 0
$$331$$ −32.3126 −1.77606 −0.888030 0.459786i $$-0.847926\pi$$
−0.888030 + 0.459786i $$0.847926\pi$$
$$332$$ 0 0
$$333$$ −2.20617 −0.120897
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −26.3511 −1.43544 −0.717718 0.696334i $$-0.754813\pi$$
−0.717718 + 0.696334i $$0.754813\pi$$
$$338$$ 0 0
$$339$$ 28.5081 1.54835
$$340$$ 0 0
$$341$$ −7.01832 −0.380063
$$342$$ 0 0
$$343$$ 10.2201 0.551835
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −2.77551 −0.148997 −0.0744986 0.997221i $$-0.523736\pi$$
−0.0744986 + 0.997221i $$0.523736\pi$$
$$348$$ 0 0
$$349$$ 11.5510 0.618312 0.309156 0.951011i $$-0.399953\pi$$
0.309156 + 0.951011i $$0.399953\pi$$
$$350$$ 0 0
$$351$$ −25.2663 −1.34862
$$352$$ 0 0
$$353$$ 8.40171 0.447178 0.223589 0.974684i $$-0.428223\pi$$
0.223589 + 0.974684i $$0.428223\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −7.62620 −0.403621
$$358$$ 0 0
$$359$$ −22.7895 −1.20278 −0.601391 0.798955i $$-0.705387\pi$$
−0.601391 + 0.798955i $$0.705387\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ −28.3126 −1.48602
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4.06455 0.212168 0.106084 0.994357i $$-0.466169\pi$$
0.106084 + 0.994357i $$0.466169\pi$$
$$368$$ 0 0
$$369$$ −12.2986 −0.640241
$$370$$ 0 0
$$371$$ 1.80779 0.0938556
$$372$$ 0 0
$$373$$ 18.4017 0.952804 0.476402 0.879227i $$-0.341941\pi$$
0.476402 + 0.879227i $$0.341941\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 41.3834 2.13135
$$378$$ 0 0
$$379$$ −1.23844 −0.0636145 −0.0318073 0.999494i $$-0.510126\pi$$
−0.0318073 + 0.999494i $$0.510126\pi$$
$$380$$ 0 0
$$381$$ 46.8959 2.40255
$$382$$ 0 0
$$383$$ 16.8646 0.861743 0.430871 0.902413i $$-0.358206\pi$$
0.430871 + 0.902413i $$0.358206\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 31.7572 1.61431
$$388$$ 0 0
$$389$$ 8.59392 0.435729 0.217865 0.975979i $$-0.430091\pi$$
0.217865 + 0.975979i $$0.430091\pi$$
$$390$$ 0 0
$$391$$ −29.0602 −1.46964
$$392$$ 0 0
$$393$$ −1.49521 −0.0754233
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −16.0558 −0.805818 −0.402909 0.915240i $$-0.632001\pi$$
−0.402909 + 0.915240i $$0.632001\pi$$
$$398$$ 0 0
$$399$$ 2.10308 0.105286
$$400$$ 0 0
$$401$$ −14.8925 −0.743698 −0.371849 0.928293i $$-0.621276\pi$$
−0.371849 + 0.928293i $$0.621276\pi$$
$$402$$ 0 0
$$403$$ 45.6681 2.27489
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −0.412335 −0.0204387
$$408$$ 0 0
$$409$$ −18.3511 −0.907404 −0.453702 0.891153i $$-0.649897\pi$$
−0.453702 + 0.891153i $$0.649897\pi$$
$$410$$ 0 0
$$411$$ −7.94940 −0.392115
$$412$$ 0 0
$$413$$ 3.42003 0.168289
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −9.90754 −0.485174
$$418$$ 0 0
$$419$$ −34.7509 −1.69769 −0.848847 0.528639i $$-0.822703\pi$$
−0.848847 + 0.528639i $$0.822703\pi$$
$$420$$ 0 0
$$421$$ −40.1589 −1.95722 −0.978612 0.205713i $$-0.934049\pi$$
−0.978612 + 0.205713i $$0.934049\pi$$
$$422$$ 0 0
$$423$$ 5.79383 0.281706
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 8.27405 0.400409
$$428$$ 0 0
$$429$$ −13.4340 −0.648599
$$430$$ 0 0
$$431$$ −34.9571 −1.68382 −0.841912 0.539615i $$-0.818570\pi$$
−0.841912 + 0.539615i $$0.818570\pi$$
$$432$$ 0 0
$$433$$ −1.13536 −0.0545619 −0.0272809 0.999628i $$-0.508685\pi$$
−0.0272809 + 0.999628i $$0.508685\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 8.01395 0.383359
$$438$$ 0 0
$$439$$ 6.80009 0.324551 0.162275 0.986746i $$-0.448117\pi$$
0.162275 + 0.986746i $$0.448117\pi$$
$$440$$ 0 0
$$441$$ −29.7003 −1.41430
$$442$$ 0 0
$$443$$ 38.0679 1.80866 0.904330 0.426835i $$-0.140371\pi$$
0.904330 + 0.426835i $$0.140371\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −46.5048 −2.19960
$$448$$ 0 0
$$449$$ −18.5414 −0.875024 −0.437512 0.899212i $$-0.644140\pi$$
−0.437512 + 0.899212i $$0.644140\pi$$
$$450$$ 0 0
$$451$$ −2.29862 −0.108238
$$452$$ 0 0
$$453$$ 46.8959 2.20336
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −16.3738 −0.765934 −0.382967 0.923762i $$-0.625098\pi$$
−0.382967 + 0.923762i $$0.625098\pi$$
$$458$$ 0 0
$$459$$ 16.2847 0.760103
$$460$$ 0 0
$$461$$ 1.70470 0.0793959 0.0396979 0.999212i $$-0.487360\pi$$
0.0396979 + 0.999212i $$0.487360\pi$$
$$462$$ 0 0
$$463$$ −10.0279 −0.466036 −0.233018 0.972472i $$-0.574860\pi$$
−0.233018 + 0.972472i $$0.574860\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 32.7509 1.51553 0.757766 0.652526i $$-0.226291\pi$$
0.757766 + 0.652526i $$0.226291\pi$$
$$468$$ 0 0
$$469$$ −0.786137 −0.0363004
$$470$$ 0 0
$$471$$ −40.9817 −1.88834
$$472$$ 0 0
$$473$$ 5.93545 0.272912
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −10.9817 −0.502816
$$478$$ 0 0
$$479$$ −27.2803 −1.24647 −0.623234 0.782035i $$-0.714182\pi$$
−0.623234 + 0.782035i $$0.714182\pi$$
$$480$$ 0 0
$$481$$ 2.68305 0.122337
$$482$$ 0 0
$$483$$ 16.8540 0.766884
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −11.0741 −0.501817 −0.250908 0.968011i $$-0.580729\pi$$
−0.250908 + 0.968011i $$0.580729\pi$$
$$488$$ 0 0
$$489$$ 36.9205 1.66960
$$490$$ 0 0
$$491$$ −8.11704 −0.366317 −0.183158 0.983083i $$-0.558632\pi$$
−0.183158 + 0.983083i $$0.558632\pi$$
$$492$$ 0 0
$$493$$ −26.6724 −1.20127
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −7.75386 −0.347808
$$498$$ 0 0
$$499$$ −0.295298 −0.0132193 −0.00660967 0.999978i $$-0.502104\pi$$
−0.00660967 + 0.999978i $$0.502104\pi$$
$$500$$ 0 0
$$501$$ 27.1912 1.21481
$$502$$ 0 0
$$503$$ 19.6016 0.873993 0.436996 0.899463i $$-0.356042\pi$$
0.436996 + 0.899463i $$0.356042\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 51.5144 2.28783
$$508$$ 0 0
$$509$$ −1.79383 −0.0795102 −0.0397551 0.999209i $$-0.512658\pi$$
−0.0397551 + 0.999209i $$0.512658\pi$$
$$510$$ 0 0
$$511$$ 12.4908 0.552562
$$512$$ 0 0
$$513$$ −4.49084 −0.198275
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 1.08287 0.0476247
$$518$$ 0 0
$$519$$ −8.23407 −0.361436
$$520$$ 0 0
$$521$$ −2.61850 −0.114719 −0.0573593 0.998354i $$-0.518268\pi$$
−0.0573593 + 0.998354i $$0.518268\pi$$
$$522$$ 0 0
$$523$$ 14.9956 0.655713 0.327857 0.944728i $$-0.393674\pi$$
0.327857 + 0.944728i $$0.393674\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −29.4340 −1.28216
$$528$$ 0 0
$$529$$ 41.2234 1.79232
$$530$$ 0 0
$$531$$ −20.7755 −0.901580
$$532$$ 0 0
$$533$$ 14.9571 0.647864
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −32.5693 −1.40547
$$538$$ 0 0
$$539$$ −5.55102 −0.239099
$$540$$ 0 0
$$541$$ 3.40608 0.146439 0.0732194 0.997316i $$-0.476673\pi$$
0.0732194 + 0.997316i $$0.476673\pi$$
$$542$$ 0 0
$$543$$ 40.2341 1.72661
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 4.74760 0.202993 0.101496 0.994836i $$-0.467637\pi$$
0.101496 + 0.994836i $$0.467637\pi$$
$$548$$ 0 0
$$549$$ −50.2620 −2.14513
$$550$$ 0 0
$$551$$ 7.35548 0.313354
$$552$$ 0 0
$$553$$ −9.57227 −0.407054
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −43.0462 −1.82393 −0.911964 0.410271i $$-0.865434\pi$$
−0.911964 + 0.410271i $$0.865434\pi$$
$$558$$ 0 0
$$559$$ −38.6218 −1.63353
$$560$$ 0 0
$$561$$ 8.65847 0.365561
$$562$$ 0 0
$$563$$ 17.0096 0.716869 0.358434 0.933555i $$-0.383311\pi$$
0.358434 + 0.933555i $$0.383311\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1.12473 0.0472343
$$568$$ 0 0
$$569$$ −19.7572 −0.828264 −0.414132 0.910217i $$-0.635915\pi$$
−0.414132 + 0.910217i $$0.635915\pi$$
$$570$$ 0 0
$$571$$ 11.3973 0.476964 0.238482 0.971147i $$-0.423350\pi$$
0.238482 + 0.971147i $$0.423350\pi$$
$$572$$ 0 0
$$573$$ −36.5587 −1.52726
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 18.3372 0.763386 0.381693 0.924289i $$-0.375341\pi$$
0.381693 + 0.924289i $$0.375341\pi$$
$$578$$ 0 0
$$579$$ −7.01832 −0.291672
$$580$$ 0 0
$$581$$ 0.206167 0.00855327
$$582$$ 0 0
$$583$$ −2.05249 −0.0850053
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −11.9475 −0.493127 −0.246563 0.969127i $$-0.579301\pi$$
−0.246563 + 0.969127i $$0.579301\pi$$
$$588$$ 0 0
$$589$$ 8.11704 0.334457
$$590$$ 0 0
$$591$$ 54.9850 2.26178
$$592$$ 0 0
$$593$$ 24.3911 1.00162 0.500811 0.865557i $$-0.333035\pi$$
0.500811 + 0.865557i $$0.333035\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 56.0943 2.29579
$$598$$ 0 0
$$599$$ 21.0708 0.860930 0.430465 0.902607i $$-0.358350\pi$$
0.430465 + 0.902607i $$0.358350\pi$$
$$600$$ 0 0
$$601$$ 32.3878 1.32112 0.660562 0.750771i $$-0.270318\pi$$
0.660562 + 0.750771i $$0.270318\pi$$
$$602$$ 0 0
$$603$$ 4.77551 0.194474
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 19.0183 0.771930 0.385965 0.922513i $$-0.373869\pi$$
0.385965 + 0.922513i $$0.373869\pi$$
$$608$$ 0 0
$$609$$ 15.4692 0.626843
$$610$$ 0 0
$$611$$ −7.04623 −0.285060
$$612$$ 0 0
$$613$$ 23.5756 0.952210 0.476105 0.879389i $$-0.342048\pi$$
0.476105 + 0.879389i $$0.342048\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 26.2707 1.05762 0.528810 0.848740i $$-0.322639\pi$$
0.528810 + 0.848740i $$0.322639\pi$$
$$618$$ 0 0
$$619$$ −11.4985 −0.462165 −0.231083 0.972934i $$-0.574227\pi$$
−0.231083 + 0.972934i $$0.574227\pi$$
$$620$$ 0 0
$$621$$ −35.9894 −1.44420
$$622$$ 0 0
$$623$$ −0.295298 −0.0118309
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −2.38776 −0.0953578
$$628$$ 0 0
$$629$$ −1.72928 −0.0689510
$$630$$ 0 0
$$631$$ 45.8130 1.82379 0.911893 0.410427i $$-0.134620\pi$$
0.911893 + 0.410427i $$0.134620\pi$$
$$632$$ 0 0
$$633$$ −49.8236 −1.98031
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 36.1204 1.43114
$$638$$ 0 0
$$639$$ 47.1020 1.86333
$$640$$ 0 0
$$641$$ 1.36943 0.0540894 0.0270447 0.999634i $$-0.491390\pi$$
0.0270447 + 0.999634i $$0.491390\pi$$
$$642$$ 0 0
$$643$$ −24.7389 −0.975606 −0.487803 0.872954i $$-0.662201\pi$$
−0.487803 + 0.872954i $$0.662201\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −6.82611 −0.268362 −0.134181 0.990957i $$-0.542840\pi$$
−0.134181 + 0.990957i $$0.542840\pi$$
$$648$$ 0 0
$$649$$ −3.88296 −0.152420
$$650$$ 0 0
$$651$$ 17.0708 0.669058
$$652$$ 0 0
$$653$$ −6.91713 −0.270688 −0.135344 0.990799i $$-0.543214\pi$$
−0.135344 + 0.990799i $$0.543214\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −75.8776 −2.96027
$$658$$ 0 0
$$659$$ −9.44461 −0.367910 −0.183955 0.982935i $$-0.558890\pi$$
−0.183955 + 0.982935i $$0.558890\pi$$
$$660$$ 0 0
$$661$$ −22.1955 −0.863306 −0.431653 0.902040i $$-0.642070\pi$$
−0.431653 + 0.902040i $$0.642070\pi$$
$$662$$ 0 0
$$663$$ −56.3405 −2.18808
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 58.9465 2.28242
$$668$$ 0 0
$$669$$ −37.3449 −1.44384
$$670$$ 0 0
$$671$$ −9.39401 −0.362652
$$672$$ 0 0
$$673$$ −12.2986 −0.474077 −0.237039 0.971500i $$-0.576177\pi$$
−0.237039 + 0.971500i $$0.576177\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 35.9527 1.38178 0.690888 0.722962i $$-0.257220\pi$$
0.690888 + 0.722962i $$0.257220\pi$$
$$678$$ 0 0
$$679$$ −6.47689 −0.248560
$$680$$ 0 0
$$681$$ 37.5616 1.43937
$$682$$ 0 0
$$683$$ −9.00958 −0.344742 −0.172371 0.985032i $$-0.555143\pi$$
−0.172371 + 0.985032i $$0.555143\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 37.5231 1.43160
$$688$$ 0 0
$$689$$ 13.3555 0.508803
$$690$$ 0 0
$$691$$ 9.11078 0.346590 0.173295 0.984870i $$-0.444559\pi$$
0.173295 + 0.984870i $$0.444559\pi$$
$$692$$ 0 0
$$693$$ −3.04623 −0.115717
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −9.64015 −0.365147
$$698$$ 0 0
$$699$$ −70.5606 −2.66885
$$700$$ 0 0
$$701$$ −14.7476 −0.557009 −0.278505 0.960435i $$-0.589839\pi$$
−0.278505 + 0.960435i $$0.589839\pi$$
$$702$$ 0 0
$$703$$ 0.476886 0.0179861
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −12.5015 −0.470166
$$708$$ 0 0
$$709$$ −8.63389 −0.324253 −0.162126 0.986770i $$-0.551835\pi$$
−0.162126 + 0.986770i $$0.551835\pi$$
$$710$$ 0 0
$$711$$ 58.1483 2.18073
$$712$$ 0 0
$$713$$ 65.0496 2.43613
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 31.2909 1.16858
$$718$$ 0 0
$$719$$ 38.2759 1.42745 0.713726 0.700425i $$-0.247006\pi$$
0.713726 + 0.700425i $$0.247006\pi$$
$$720$$ 0 0
$$721$$ 7.34153 0.273413
$$722$$ 0 0
$$723$$ −3.45856 −0.128625
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −31.1893 −1.15675 −0.578373 0.815772i $$-0.696312\pi$$
−0.578373 + 0.815772i $$0.696312\pi$$
$$728$$ 0 0
$$729$$ −44.0375 −1.63102
$$730$$ 0 0
$$731$$ 24.8925 0.920684
$$732$$ 0 0
$$733$$ 13.9634 0.515748 0.257874 0.966179i $$-0.416978\pi$$
0.257874 + 0.966179i $$0.416978\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0.892548 0.0328774
$$738$$ 0 0
$$739$$ −9.02165 −0.331867 −0.165933 0.986137i $$-0.553064\pi$$
−0.165933 + 0.986137i $$0.553064\pi$$
$$740$$ 0 0
$$741$$ 15.5371 0.570768
$$742$$ 0 0
$$743$$ −15.0342 −0.551550 −0.275775 0.961222i $$-0.588934\pi$$
−0.275775 + 0.961222i $$0.588934\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −1.25240 −0.0458228
$$748$$ 0 0
$$749$$ −3.26302 −0.119228
$$750$$ 0 0
$$751$$ −29.6681 −1.08260 −0.541301 0.840829i $$-0.682068\pi$$
−0.541301 + 0.840829i $$0.682068\pi$$
$$752$$ 0 0
$$753$$ −29.2557 −1.06614
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −10.5819 −0.384604 −0.192302 0.981336i $$-0.561595\pi$$
−0.192302 + 0.981336i $$0.561595\pi$$
$$758$$ 0 0
$$759$$ −19.1354 −0.694570
$$760$$ 0 0
$$761$$ −0.979789 −0.0355173 −0.0177587 0.999842i $$-0.505653\pi$$
−0.0177587 + 0.999842i $$0.505653\pi$$
$$762$$ 0 0
$$763$$ 10.2201 0.369993
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 25.2663 0.912315
$$768$$ 0 0
$$769$$ 43.1772 1.55701 0.778505 0.627638i $$-0.215978\pi$$
0.778505 + 0.627638i $$0.215978\pi$$
$$770$$ 0 0
$$771$$ 0.424399 0.0152844
$$772$$ 0 0
$$773$$ −37.5250 −1.34968 −0.674840 0.737964i $$-0.735787\pi$$
−0.674840 + 0.737964i $$0.735787\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 1.00293 0.0359799
$$778$$ 0 0
$$779$$ 2.65847 0.0952497
$$780$$ 0 0
$$781$$ 8.80342 0.315011
$$782$$ 0 0
$$783$$ −33.0323 −1.18048
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 22.5833 0.805008 0.402504 0.915418i $$-0.368140\pi$$
0.402504 + 0.915418i $$0.368140\pi$$
$$788$$ 0 0
$$789$$ 1.39401 0.0496282
$$790$$ 0 0
$$791$$ −7.86171 −0.279530
$$792$$ 0 0
$$793$$ 61.1266 2.17067
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −35.9806 −1.27450 −0.637250 0.770657i $$-0.719928\pi$$
−0.637250 + 0.770657i $$0.719928\pi$$
$$798$$ 0 0
$$799$$ 4.54144 0.160664
$$800$$ 0 0
$$801$$ 1.79383 0.0633820
$$802$$ 0 0
$$803$$ −14.1816 −0.500457
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −9.65222 −0.339774
$$808$$ 0 0
$$809$$ −0.955660 −0.0335992 −0.0167996 0.999859i $$-0.505348\pi$$
−0.0167996 + 0.999859i $$0.505348\pi$$
$$810$$ 0 0
$$811$$ 7.53707 0.264662 0.132331 0.991206i $$-0.457754\pi$$
0.132331 + 0.991206i $$0.457754\pi$$
$$812$$ 0 0
$$813$$ −15.1127 −0.530024
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −6.86464 −0.240163
$$818$$ 0 0
$$819$$ 19.8217 0.692628
$$820$$ 0 0
$$821$$ 13.3082 0.464460 0.232230 0.972661i $$-0.425398\pi$$
0.232230 + 0.972661i $$0.425398\pi$$
$$822$$ 0 0
$$823$$ 24.4050 0.850706 0.425353 0.905028i $$-0.360150\pi$$
0.425353 + 0.905028i $$0.360150\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −11.6874 −0.406411 −0.203206 0.979136i $$-0.565136\pi$$
−0.203206 + 0.979136i $$0.565136\pi$$
$$828$$ 0 0
$$829$$ 25.6541 0.891004 0.445502 0.895281i $$-0.353025\pi$$
0.445502 + 0.895281i $$0.353025\pi$$
$$830$$ 0 0
$$831$$ −35.7726 −1.24094
$$832$$ 0 0
$$833$$ −23.2803 −0.806615
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −36.4523 −1.25998
$$838$$ 0 0
$$839$$ 2.91713 0.100710 0.0503552 0.998731i $$-0.483965\pi$$
0.0503552 + 0.998731i $$0.483965\pi$$
$$840$$ 0 0
$$841$$ 25.1031 0.865624
$$842$$ 0 0
$$843$$ 0.424399 0.0146171
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 7.80779 0.268279
$$848$$ 0 0
$$849$$ −50.3544 −1.72816
$$850$$ 0 0
$$851$$ 3.82174 0.131008
$$852$$ 0 0
$$853$$ 6.24281 0.213750 0.106875 0.994272i $$-0.465916\pi$$
0.106875 + 0.994272i $$0.465916\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 23.2158 0.793035 0.396517 0.918027i $$-0.370219\pi$$
0.396517 + 0.918027i $$0.370219\pi$$
$$858$$ 0 0
$$859$$ 7.13536 0.243455 0.121728 0.992564i $$-0.461157\pi$$
0.121728 + 0.992564i $$0.461157\pi$$
$$860$$ 0 0
$$861$$ 5.59099 0.190541
$$862$$ 0 0
$$863$$ −7.31362 −0.248959 −0.124479 0.992222i $$-0.539726\pi$$
−0.124479 + 0.992222i $$0.539726\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −10.6339 −0.361146
$$868$$ 0 0
$$869$$ 10.8680 0.368671
$$870$$ 0 0
$$871$$ −5.80779 −0.196789
$$872$$ 0 0
$$873$$ 39.3449 1.33162
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 22.0173 0.743471 0.371735 0.928339i $$-0.378763\pi$$
0.371735 + 0.928339i $$0.378763\pi$$
$$878$$ 0 0
$$879$$ −5.62953 −0.189879
$$880$$ 0 0
$$881$$ 11.7572 0.396110 0.198055 0.980191i $$-0.436538\pi$$
0.198055 + 0.980191i $$0.436538\pi$$
$$882$$ 0 0
$$883$$ 55.6560 1.87297 0.936487 0.350703i $$-0.114057\pi$$
0.936487 + 0.350703i $$0.114057\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −6.41566 −0.215417 −0.107708 0.994183i $$-0.534351\pi$$
−0.107708 + 0.994183i $$0.534351\pi$$
$$888$$ 0 0
$$889$$ −12.9325 −0.433743
$$890$$ 0 0
$$891$$ −1.27698 −0.0427803
$$892$$ 0 0
$$893$$ −1.25240 −0.0419098
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 124.513 4.15738
$$898$$ 0 0
$$899$$ 59.7047 1.99126
$$900$$ 0 0
$$901$$ −8.60788 −0.286770
$$902$$ 0 0
$$903$$ −14.4369 −0.480430
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −57.1160 −1.89651 −0.948253 0.317516i $$-0.897151\pi$$
−0.948253 + 0.317516i $$0.897151\pi$$
$$908$$ 0 0
$$909$$ 75.9421 2.51884
$$910$$ 0 0
$$911$$ 26.6339 0.882420 0.441210 0.897404i $$-0.354549\pi$$
0.441210 + 0.897404i $$0.354549\pi$$
$$912$$ 0 0
$$913$$ −0.234074 −0.00774672
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0.412335 0.0136165
$$918$$ 0 0
$$919$$ −6.63246 −0.218785 −0.109392 0.993999i $$-0.534890\pi$$
−0.109392 + 0.993999i $$0.534890\pi$$
$$920$$ 0 0
$$921$$ 45.6801 1.50521
$$922$$ 0 0
$$923$$ −57.2836 −1.88551
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −44.5972 −1.46477
$$928$$ 0 0
$$929$$ −50.0173 −1.64101 −0.820507 0.571637i $$-0.806309\pi$$
−0.820507 + 0.571637i $$0.806309\pi$$
$$930$$ 0 0
$$931$$ 6.42003 0.210408
$$932$$ 0 0
$$933$$ 59.2976 1.94132
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 39.8882 1.30309 0.651545 0.758610i $$-0.274121\pi$$
0.651545 + 0.758610i $$0.274121\pi$$
$$938$$ 0 0
$$939$$ 3.09683 0.101061
$$940$$ 0 0
$$941$$ −5.59829 −0.182499 −0.0912495 0.995828i $$-0.529086\pi$$
−0.0912495 + 0.995828i $$0.529086\pi$$
$$942$$ 0 0
$$943$$ 21.3049 0.693782
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 12.7110 0.413051 0.206525 0.978441i $$-0.433784\pi$$
0.206525 + 0.978441i $$0.433784\pi$$
$$948$$ 0 0
$$949$$ 92.2793 2.99551
$$950$$ 0 0
$$951$$ 82.5379 2.67648
$$952$$ 0 0
$$953$$ 57.0129 1.84683 0.923415 0.383804i $$-0.125386\pi$$
0.923415 + 0.383804i $$0.125386\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −17.5631 −0.567734
$$958$$ 0 0
$$959$$ 2.19221 0.0707903
$$960$$ 0 0
$$961$$ 34.8863 1.12536
$$962$$ 0 0
$$963$$ 19.8217 0.638747
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −33.0183 −1.06180 −0.530899 0.847435i $$-0.678146\pi$$
−0.530899 + 0.847435i $$0.678146\pi$$
$$968$$ 0 0
$$969$$ −10.0140 −0.321695
$$970$$ 0 0
$$971$$ 3.04623 0.0977581 0.0488791 0.998805i $$-0.484435\pi$$
0.0488791 + 0.998805i $$0.484435\pi$$
$$972$$ 0 0
$$973$$ 2.73221 0.0875907
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −13.4465 −0.430192 −0.215096 0.976593i $$-0.569006\pi$$
−0.215096 + 0.976593i $$0.569006\pi$$
$$978$$ 0 0
$$979$$ 0.335269 0.0107152
$$980$$ 0 0
$$981$$ −62.0837 −1.98218
$$982$$ 0 0
$$983$$ −22.0646 −0.703750 −0.351875 0.936047i $$-0.614456\pi$$
−0.351875 + 0.936047i $$0.614456\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −2.63389 −0.0838378
$$988$$ 0 0
$$989$$ −55.0129 −1.74931
$$990$$ 0 0
$$991$$ −51.9946 −1.65166 −0.825831 0.563917i $$-0.809294\pi$$
−0.825831 + 0.563917i $$0.809294\pi$$
$$992$$ 0 0
$$993$$ −89.2330 −2.83172
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 37.7693 1.19616 0.598082 0.801435i $$-0.295930\pi$$
0.598082 + 0.801435i $$0.295930\pi$$
$$998$$ 0 0
$$999$$ −2.14162 −0.0677578
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 7600.2.a.cd.1.3 3
4.3 odd 2 950.2.a.i.1.1 3
5.2 odd 4 1520.2.d.j.609.1 6
5.3 odd 4 1520.2.d.j.609.6 6
5.4 even 2 7600.2.a.bi.1.1 3
12.11 even 2 8550.2.a.cl.1.3 3
20.3 even 4 190.2.b.b.39.4 yes 6
20.7 even 4 190.2.b.b.39.3 6
20.19 odd 2 950.2.a.n.1.3 3
60.23 odd 4 1710.2.d.d.1369.3 6
60.47 odd 4 1710.2.d.d.1369.6 6
60.59 even 2 8550.2.a.ck.1.1 3

By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.b.b.39.3 6 20.7 even 4
190.2.b.b.39.4 yes 6 20.3 even 4
950.2.a.i.1.1 3 4.3 odd 2
950.2.a.n.1.3 3 20.19 odd 2
1520.2.d.j.609.1 6 5.2 odd 4
1520.2.d.j.609.6 6 5.3 odd 4
1710.2.d.d.1369.3 6 60.23 odd 4
1710.2.d.d.1369.6 6 60.47 odd 4
7600.2.a.bi.1.1 3 5.4 even 2
7600.2.a.cd.1.3 3 1.1 even 1 trivial
8550.2.a.ck.1.1 3 60.59 even 2
8550.2.a.cl.1.3 3 12.11 even 2