# Properties

 Label 7800.2.a.bz.1.5 Level $7800$ Weight $2$ Character 7800.1 Self dual yes Analytic conductor $62.283$ Analytic rank $1$ Dimension $5$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7800.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$62.2833135766$$ Analytic rank: $$1$$ Dimension: $$5$$ Coefficient field: 5.5.504568.1 Defining polynomial: $$x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 2$$ x^5 - x^4 - 6*x^3 + 3*x^2 + 7*x - 2 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 1560) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.5 Root $$1.28447$$ of defining polynomial Character $$\chi$$ $$=$$ 7800.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} +3.71215 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} +3.71215 q^{7} +1.00000 q^{9} +3.31842 q^{11} -1.00000 q^{13} -1.55706 q^{17} -5.33709 q^{19} -3.71215 q^{21} -0.442940 q^{23} -1.00000 q^{27} +2.56894 q^{29} +0.613062 q^{31} -3.31842 q^{33} +0.257322 q^{37} +1.00000 q^{39} -10.6114 q^{41} -12.6935 q^{43} -7.44442 q^{47} +6.78003 q^{49} +1.55706 q^{51} +5.39521 q^{53} +5.33709 q^{57} -13.1358 q^{59} -5.27452 q^{61} +3.71215 q^{63} -10.5384 q^{67} +0.442940 q^{69} +0.311845 q^{71} -9.46841 q^{73} +12.3184 q^{77} +16.1871 q^{79} +1.00000 q^{81} -11.7546 q^{83} -2.56894 q^{87} -4.58762 q^{89} -3.71215 q^{91} -0.613062 q^{93} -10.8500 q^{97} +3.31842 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$5 q - 5 q^{3} - q^{7} + 5 q^{9}+O(q^{10})$$ 5 * q - 5 * q^3 - q^7 + 5 * q^9 $$5 q - 5 q^{3} - q^{7} + 5 q^{9} + 5 q^{11} - 5 q^{13} - 7 q^{17} + 6 q^{19} + q^{21} - 3 q^{23} - 5 q^{27} + 2 q^{29} - 5 q^{33} - 9 q^{37} + 5 q^{39} - q^{41} - 4 q^{43} - 14 q^{47} + 2 q^{49} + 7 q^{51} - 5 q^{53} - 6 q^{57} + 20 q^{59} - 19 q^{61} - q^{63} - 12 q^{67} + 3 q^{69} + 13 q^{71} - 16 q^{73} - 11 q^{77} + 7 q^{79} + 5 q^{81} + 2 q^{83} - 2 q^{87} + 9 q^{89} + q^{91} - 13 q^{97} + 5 q^{99}+O(q^{100})$$ 5 * q - 5 * q^3 - q^7 + 5 * q^9 + 5 * q^11 - 5 * q^13 - 7 * q^17 + 6 * q^19 + q^21 - 3 * q^23 - 5 * q^27 + 2 * q^29 - 5 * q^33 - 9 * q^37 + 5 * q^39 - q^41 - 4 * q^43 - 14 * q^47 + 2 * q^49 + 7 * q^51 - 5 * q^53 - 6 * q^57 + 20 * q^59 - 19 * q^61 - q^63 - 12 * q^67 + 3 * q^69 + 13 * q^71 - 16 * q^73 - 11 * q^77 + 7 * q^79 + 5 * q^81 + 2 * q^83 - 2 * q^87 + 9 * q^89 + q^91 - 13 * q^97 + 5 * q^99

## 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
$$3$$ −1.00000 −0.577350
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 3.71215 1.40306 0.701530 0.712640i $$-0.252501\pi$$
0.701530 + 0.712640i $$0.252501\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 3.31842 1.00054 0.500270 0.865869i $$-0.333234\pi$$
0.500270 + 0.865869i $$0.333234\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1.55706 −0.377642 −0.188821 0.982011i $$-0.560467\pi$$
−0.188821 + 0.982011i $$0.560467\pi$$
$$18$$ 0 0
$$19$$ −5.33709 −1.22441 −0.612207 0.790698i $$-0.709718\pi$$
−0.612207 + 0.790698i $$0.709718\pi$$
$$20$$ 0 0
$$21$$ −3.71215 −0.810057
$$22$$ 0 0
$$23$$ −0.442940 −0.0923594 −0.0461797 0.998933i $$-0.514705\pi$$
−0.0461797 + 0.998933i $$0.514705\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 2.56894 0.477041 0.238521 0.971137i $$-0.423338\pi$$
0.238521 + 0.971137i $$0.423338\pi$$
$$30$$ 0 0
$$31$$ 0.613062 0.110109 0.0550546 0.998483i $$-0.482467\pi$$
0.0550546 + 0.998483i $$0.482467\pi$$
$$32$$ 0 0
$$33$$ −3.31842 −0.577662
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.257322 0.0423034 0.0211517 0.999776i $$-0.493267\pi$$
0.0211517 + 0.999776i $$0.493267\pi$$
$$38$$ 0 0
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ −10.6114 −1.65722 −0.828611 0.559826i $$-0.810868\pi$$
−0.828611 + 0.559826i $$0.810868\pi$$
$$42$$ 0 0
$$43$$ −12.6935 −1.93574 −0.967870 0.251450i $$-0.919093\pi$$
−0.967870 + 0.251450i $$0.919093\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −7.44442 −1.08588 −0.542940 0.839771i $$-0.682689\pi$$
−0.542940 + 0.839771i $$0.682689\pi$$
$$48$$ 0 0
$$49$$ 6.78003 0.968576
$$50$$ 0 0
$$51$$ 1.55706 0.218032
$$52$$ 0 0
$$53$$ 5.39521 0.741089 0.370545 0.928815i $$-0.379171\pi$$
0.370545 + 0.928815i $$0.379171\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 5.33709 0.706915
$$58$$ 0 0
$$59$$ −13.1358 −1.71014 −0.855068 0.518516i $$-0.826485\pi$$
−0.855068 + 0.518516i $$0.826485\pi$$
$$60$$ 0 0
$$61$$ −5.27452 −0.675333 −0.337667 0.941266i $$-0.609638\pi$$
−0.337667 + 0.941266i $$0.609638\pi$$
$$62$$ 0 0
$$63$$ 3.71215 0.467687
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −10.5384 −1.28747 −0.643736 0.765248i $$-0.722617\pi$$
−0.643736 + 0.765248i $$0.722617\pi$$
$$68$$ 0 0
$$69$$ 0.442940 0.0533237
$$70$$ 0 0
$$71$$ 0.311845 0.0370092 0.0185046 0.999829i $$-0.494109\pi$$
0.0185046 + 0.999829i $$0.494109\pi$$
$$72$$ 0 0
$$73$$ −9.46841 −1.10819 −0.554097 0.832452i $$-0.686936\pi$$
−0.554097 + 0.832452i $$0.686936\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 12.3184 1.40382
$$78$$ 0 0
$$79$$ 16.1871 1.82119 0.910597 0.413295i $$-0.135622\pi$$
0.910597 + 0.413295i $$0.135622\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −11.7546 −1.29023 −0.645117 0.764084i $$-0.723191\pi$$
−0.645117 + 0.764084i $$0.723191\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −2.56894 −0.275420
$$88$$ 0 0
$$89$$ −4.58762 −0.486287 −0.243144 0.969990i $$-0.578179\pi$$
−0.243144 + 0.969990i $$0.578179\pi$$
$$90$$ 0 0
$$91$$ −3.71215 −0.389139
$$92$$ 0 0
$$93$$ −0.613062 −0.0635716
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −10.8500 −1.10165 −0.550827 0.834619i $$-0.685688\pi$$
−0.550827 + 0.834619i $$0.685688\pi$$
$$98$$ 0 0
$$99$$ 3.31842 0.333513
$$100$$ 0 0
$$101$$ 1.68306 0.167471 0.0837356 0.996488i $$-0.473315\pi$$
0.0837356 + 0.996488i $$0.473315\pi$$
$$102$$ 0 0
$$103$$ −1.78535 −0.175916 −0.0879578 0.996124i $$-0.528034\pi$$
−0.0879578 + 0.996124i $$0.528034\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.11943 −0.108220 −0.0541098 0.998535i $$-0.517232\pi$$
−0.0541098 + 0.998535i $$0.517232\pi$$
$$108$$ 0 0
$$109$$ −0.914914 −0.0876329 −0.0438164 0.999040i $$-0.513952\pi$$
−0.0438164 + 0.999040i $$0.513952\pi$$
$$110$$ 0 0
$$111$$ −0.257322 −0.0244239
$$112$$ 0 0
$$113$$ −2.41386 −0.227077 −0.113538 0.993534i $$-0.536218\pi$$
−0.113538 + 0.993534i $$0.536218\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.00000 −0.0924500
$$118$$ 0 0
$$119$$ −5.78003 −0.529855
$$120$$ 0 0
$$121$$ 0.0118848 0.00108043
$$122$$ 0 0
$$123$$ 10.6114 0.956797
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 14.0418 1.24601 0.623005 0.782218i $$-0.285912\pi$$
0.623005 + 0.782218i $$0.285912\pi$$
$$128$$ 0 0
$$129$$ 12.6935 1.11760
$$130$$ 0 0
$$131$$ 13.7650 1.20265 0.601327 0.799003i $$-0.294639\pi$$
0.601327 + 0.799003i $$0.294639\pi$$
$$132$$ 0 0
$$133$$ −19.8121 −1.71792
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.50470 0.555734 0.277867 0.960620i $$-0.410373\pi$$
0.277867 + 0.960620i $$0.410373\pi$$
$$138$$ 0 0
$$139$$ 9.78003 0.829532 0.414766 0.909928i $$-0.363863\pi$$
0.414766 + 0.909928i $$0.363863\pi$$
$$140$$ 0 0
$$141$$ 7.44442 0.626933
$$142$$ 0 0
$$143$$ −3.31842 −0.277500
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −6.78003 −0.559208
$$148$$ 0 0
$$149$$ −5.93148 −0.485926 −0.242963 0.970036i $$-0.578119\pi$$
−0.242963 + 0.970036i $$0.578119\pi$$
$$150$$ 0 0
$$151$$ −0.272818 −0.0222016 −0.0111008 0.999938i $$-0.503534\pi$$
−0.0111008 + 0.999938i $$0.503534\pi$$
$$152$$ 0 0
$$153$$ −1.55706 −0.125881
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −14.6561 −1.16969 −0.584844 0.811146i $$-0.698844\pi$$
−0.584844 + 0.811146i $$0.698844\pi$$
$$158$$ 0 0
$$159$$ −5.39521 −0.427868
$$160$$ 0 0
$$161$$ −1.64426 −0.129586
$$162$$ 0 0
$$163$$ 3.48345 0.272845 0.136422 0.990651i $$-0.456440\pi$$
0.136422 + 0.990651i $$0.456440\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −4.69135 −0.363028 −0.181514 0.983388i $$-0.558100\pi$$
−0.181514 + 0.983388i $$0.558100\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ −5.33709 −0.408138
$$172$$ 0 0
$$173$$ −3.26475 −0.248214 −0.124107 0.992269i $$-0.539607\pi$$
−0.124107 + 0.992269i $$0.539607\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 13.1358 0.987348
$$178$$ 0 0
$$179$$ 19.7204 1.47397 0.736987 0.675907i $$-0.236248\pi$$
0.736987 + 0.675907i $$0.236248\pi$$
$$180$$ 0 0
$$181$$ −22.0558 −1.63940 −0.819698 0.572796i $$-0.805859\pi$$
−0.819698 + 0.572796i $$0.805859\pi$$
$$182$$ 0 0
$$183$$ 5.27452 0.389904
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −5.16697 −0.377846
$$188$$ 0 0
$$189$$ −3.71215 −0.270019
$$190$$ 0 0
$$191$$ 22.2729 1.61161 0.805805 0.592182i $$-0.201733\pi$$
0.805805 + 0.592182i $$0.201733\pi$$
$$192$$ 0 0
$$193$$ 15.7733 1.13539 0.567693 0.823241i $$-0.307836\pi$$
0.567693 + 0.823241i $$0.307836\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.72871 0.194413 0.0972063 0.995264i $$-0.469009\pi$$
0.0972063 + 0.995264i $$0.469009\pi$$
$$198$$ 0 0
$$199$$ −22.1029 −1.56684 −0.783418 0.621495i $$-0.786526\pi$$
−0.783418 + 0.621495i $$0.786526\pi$$
$$200$$ 0 0
$$201$$ 10.5384 0.743322
$$202$$ 0 0
$$203$$ 9.53630 0.669317
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −0.442940 −0.0307865
$$208$$ 0 0
$$209$$ −17.7107 −1.22507
$$210$$ 0 0
$$211$$ 1.01720 0.0700268 0.0350134 0.999387i $$-0.488853\pi$$
0.0350134 + 0.999387i $$0.488853\pi$$
$$212$$ 0 0
$$213$$ −0.311845 −0.0213672
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 2.27578 0.154490
$$218$$ 0 0
$$219$$ 9.46841 0.639816
$$220$$ 0 0
$$221$$ 1.55706 0.104739
$$222$$ 0 0
$$223$$ 6.85535 0.459068 0.229534 0.973301i $$-0.426280\pi$$
0.229534 + 0.973301i $$0.426280\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −2.88224 −0.191301 −0.0956504 0.995415i $$-0.530493\pi$$
−0.0956504 + 0.995415i $$0.530493\pi$$
$$228$$ 0 0
$$229$$ 14.1857 0.937416 0.468708 0.883353i $$-0.344720\pi$$
0.468708 + 0.883353i $$0.344720\pi$$
$$230$$ 0 0
$$231$$ −12.3184 −0.810494
$$232$$ 0 0
$$233$$ −0.429354 −0.0281279 −0.0140639 0.999901i $$-0.504477\pi$$
−0.0140639 + 0.999901i $$0.504477\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −16.1871 −1.05147
$$238$$ 0 0
$$239$$ 19.7255 1.27594 0.637969 0.770062i $$-0.279775\pi$$
0.637969 + 0.770062i $$0.279775\pi$$
$$240$$ 0 0
$$241$$ 19.6598 1.26640 0.633200 0.773988i $$-0.281741\pi$$
0.633200 + 0.773988i $$0.281741\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 5.33709 0.339591
$$248$$ 0 0
$$249$$ 11.7546 0.744917
$$250$$ 0 0
$$251$$ 23.4175 1.47810 0.739051 0.673650i $$-0.235274\pi$$
0.739051 + 0.673650i $$0.235274\pi$$
$$252$$ 0 0
$$253$$ −1.46986 −0.0924093
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −30.7987 −1.92117 −0.960586 0.277981i $$-0.910335\pi$$
−0.960586 + 0.277981i $$0.910335\pi$$
$$258$$ 0 0
$$259$$ 0.955216 0.0593543
$$260$$ 0 0
$$261$$ 2.56894 0.159014
$$262$$ 0 0
$$263$$ 24.1471 1.48897 0.744486 0.667638i $$-0.232695\pi$$
0.744486 + 0.667638i $$0.232695\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 4.58762 0.280758
$$268$$ 0 0
$$269$$ 12.7557 0.777726 0.388863 0.921295i $$-0.372868\pi$$
0.388863 + 0.921295i $$0.372868\pi$$
$$270$$ 0 0
$$271$$ −10.4222 −0.633102 −0.316551 0.948575i $$-0.602525\pi$$
−0.316551 + 0.948575i $$0.602525\pi$$
$$272$$ 0 0
$$273$$ 3.71215 0.224669
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −19.9404 −1.19810 −0.599052 0.800710i $$-0.704456\pi$$
−0.599052 + 0.800710i $$0.704456\pi$$
$$278$$ 0 0
$$279$$ 0.613062 0.0367031
$$280$$ 0 0
$$281$$ 28.5272 1.70179 0.850895 0.525336i $$-0.176060\pi$$
0.850895 + 0.525336i $$0.176060\pi$$
$$282$$ 0 0
$$283$$ −19.1888 −1.14066 −0.570329 0.821416i $$-0.693184\pi$$
−0.570329 + 0.821416i $$0.693184\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −39.3910 −2.32518
$$288$$ 0 0
$$289$$ −14.5756 −0.857386
$$290$$ 0 0
$$291$$ 10.8500 0.636040
$$292$$ 0 0
$$293$$ 11.9828 0.700045 0.350022 0.936741i $$-0.386174\pi$$
0.350022 + 0.936741i $$0.386174\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −3.31842 −0.192554
$$298$$ 0 0
$$299$$ 0.442940 0.0256159
$$300$$ 0 0
$$301$$ −47.1201 −2.71596
$$302$$ 0 0
$$303$$ −1.68306 −0.0966895
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −25.0299 −1.42853 −0.714267 0.699874i $$-0.753240\pi$$
−0.714267 + 0.699874i $$0.753240\pi$$
$$308$$ 0 0
$$309$$ 1.78535 0.101565
$$310$$ 0 0
$$311$$ 27.6360 1.56710 0.783548 0.621331i $$-0.213408\pi$$
0.783548 + 0.621331i $$0.213408\pi$$
$$312$$ 0 0
$$313$$ −14.5441 −0.822083 −0.411042 0.911617i $$-0.634835\pi$$
−0.411042 + 0.911617i $$0.634835\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −8.00364 −0.449529 −0.224765 0.974413i $$-0.572161\pi$$
−0.224765 + 0.974413i $$0.572161\pi$$
$$318$$ 0 0
$$319$$ 8.52483 0.477299
$$320$$ 0 0
$$321$$ 1.11943 0.0624806
$$322$$ 0 0
$$323$$ 8.31017 0.462390
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0.914914 0.0505949
$$328$$ 0 0
$$329$$ −27.6348 −1.52355
$$330$$ 0 0
$$331$$ 5.59929 0.307765 0.153882 0.988089i $$-0.450822\pi$$
0.153882 + 0.988089i $$0.450822\pi$$
$$332$$ 0 0
$$333$$ 0.257322 0.0141011
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −34.5802 −1.88370 −0.941852 0.336027i $$-0.890917\pi$$
−0.941852 + 0.336027i $$0.890917\pi$$
$$338$$ 0 0
$$339$$ 2.41386 0.131103
$$340$$ 0 0
$$341$$ 2.03440 0.110169
$$342$$ 0 0
$$343$$ −0.816545 −0.0440893
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −31.0537 −1.66705 −0.833525 0.552482i $$-0.813681\pi$$
−0.833525 + 0.552482i $$0.813681\pi$$
$$348$$ 0 0
$$349$$ 2.94804 0.157805 0.0789026 0.996882i $$-0.474858\pi$$
0.0789026 + 0.996882i $$0.474858\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ 0 0
$$353$$ −1.80547 −0.0960957 −0.0480478 0.998845i $$-0.515300\pi$$
−0.0480478 + 0.998845i $$0.515300\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 5.78003 0.305912
$$358$$ 0 0
$$359$$ −9.29216 −0.490422 −0.245211 0.969470i $$-0.578857\pi$$
−0.245211 + 0.969470i $$0.578857\pi$$
$$360$$ 0 0
$$361$$ 9.48457 0.499188
$$362$$ 0 0
$$363$$ −0.0118848 −0.000623788 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 18.0955 0.944579 0.472289 0.881444i $$-0.343428\pi$$
0.472289 + 0.881444i $$0.343428\pi$$
$$368$$ 0 0
$$369$$ −10.6114 −0.552407
$$370$$ 0 0
$$371$$ 20.0278 1.03979
$$372$$ 0 0
$$373$$ 29.4689 1.52584 0.762922 0.646491i $$-0.223764\pi$$
0.762922 + 0.646491i $$0.223764\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −2.56894 −0.132307
$$378$$ 0 0
$$379$$ −21.2489 −1.09148 −0.545740 0.837954i $$-0.683751\pi$$
−0.545740 + 0.837954i $$0.683751\pi$$
$$380$$ 0 0
$$381$$ −14.0418 −0.719384
$$382$$ 0 0
$$383$$ 8.19163 0.418573 0.209286 0.977854i $$-0.432886\pi$$
0.209286 + 0.977854i $$0.432886\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −12.6935 −0.645247
$$388$$ 0 0
$$389$$ −24.4557 −1.23995 −0.619976 0.784621i $$-0.712858\pi$$
−0.619976 + 0.784621i $$0.712858\pi$$
$$390$$ 0 0
$$391$$ 0.689684 0.0348788
$$392$$ 0 0
$$393$$ −13.7650 −0.694352
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −34.4916 −1.73108 −0.865541 0.500837i $$-0.833025\pi$$
−0.865541 + 0.500837i $$0.833025\pi$$
$$398$$ 0 0
$$399$$ 19.8121 0.991844
$$400$$ 0 0
$$401$$ −16.9434 −0.846114 −0.423057 0.906103i $$-0.639043\pi$$
−0.423057 + 0.906103i $$0.639043\pi$$
$$402$$ 0 0
$$403$$ −0.613062 −0.0305388
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0.853901 0.0423263
$$408$$ 0 0
$$409$$ −3.05299 −0.150961 −0.0754804 0.997147i $$-0.524049\pi$$
−0.0754804 + 0.997147i $$0.524049\pi$$
$$410$$ 0 0
$$411$$ −6.50470 −0.320853
$$412$$ 0 0
$$413$$ −48.7620 −2.39942
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −9.78003 −0.478930
$$418$$ 0 0
$$419$$ 20.9567 1.02380 0.511902 0.859044i $$-0.328941\pi$$
0.511902 + 0.859044i $$0.328941\pi$$
$$420$$ 0 0
$$421$$ −37.4462 −1.82502 −0.912508 0.409059i $$-0.865857\pi$$
−0.912508 + 0.409059i $$0.865857\pi$$
$$422$$ 0 0
$$423$$ −7.44442 −0.361960
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −19.5798 −0.947533
$$428$$ 0 0
$$429$$ 3.31842 0.160215
$$430$$ 0 0
$$431$$ −27.2671 −1.31341 −0.656706 0.754147i $$-0.728051\pi$$
−0.656706 + 0.754147i $$0.728051\pi$$
$$432$$ 0 0
$$433$$ −12.5679 −0.603975 −0.301988 0.953312i $$-0.597650\pi$$
−0.301988 + 0.953312i $$0.597650\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 2.36401 0.113086
$$438$$ 0 0
$$439$$ 14.7241 0.702742 0.351371 0.936236i $$-0.385716\pi$$
0.351371 + 0.936236i $$0.385716\pi$$
$$440$$ 0 0
$$441$$ 6.78003 0.322859
$$442$$ 0 0
$$443$$ −8.65996 −0.411447 −0.205724 0.978610i $$-0.565955\pi$$
−0.205724 + 0.978610i $$0.565955\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 5.93148 0.280549
$$448$$ 0 0
$$449$$ −21.5690 −1.01791 −0.508953 0.860795i $$-0.669967\pi$$
−0.508953 + 0.860795i $$0.669967\pi$$
$$450$$ 0 0
$$451$$ −35.2130 −1.65812
$$452$$ 0 0
$$453$$ 0.272818 0.0128181
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.192394 0.00899982 0.00449991 0.999990i $$-0.498568\pi$$
0.00449991 + 0.999990i $$0.498568\pi$$
$$458$$ 0 0
$$459$$ 1.55706 0.0726773
$$460$$ 0 0
$$461$$ −12.0821 −0.562720 −0.281360 0.959602i $$-0.590785\pi$$
−0.281360 + 0.959602i $$0.590785\pi$$
$$462$$ 0 0
$$463$$ −25.7245 −1.19552 −0.597759 0.801676i $$-0.703942\pi$$
−0.597759 + 0.801676i $$0.703942\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −18.4317 −0.852918 −0.426459 0.904507i $$-0.640239\pi$$
−0.426459 + 0.904507i $$0.640239\pi$$
$$468$$ 0 0
$$469$$ −39.1201 −1.80640
$$470$$ 0 0
$$471$$ 14.6561 0.675319
$$472$$ 0 0
$$473$$ −42.1223 −1.93679
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 5.39521 0.247030
$$478$$ 0 0
$$479$$ 25.5826 1.16890 0.584450 0.811430i $$-0.301310\pi$$
0.584450 + 0.811430i $$0.301310\pi$$
$$480$$ 0 0
$$481$$ −0.257322 −0.0117329
$$482$$ 0 0
$$483$$ 1.64426 0.0748164
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 30.1997 1.36848 0.684239 0.729258i $$-0.260134\pi$$
0.684239 + 0.729258i $$0.260134\pi$$
$$488$$ 0 0
$$489$$ −3.48345 −0.157527
$$490$$ 0 0
$$491$$ −10.7256 −0.484039 −0.242020 0.970271i $$-0.577810\pi$$
−0.242020 + 0.970271i $$0.577810\pi$$
$$492$$ 0 0
$$493$$ −4.00000 −0.180151
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 1.15761 0.0519260
$$498$$ 0 0
$$499$$ 7.01044 0.313830 0.156915 0.987612i $$-0.449845\pi$$
0.156915 + 0.987612i $$0.449845\pi$$
$$500$$ 0 0
$$501$$ 4.69135 0.209594
$$502$$ 0 0
$$503$$ 32.2604 1.43842 0.719210 0.694793i $$-0.244504\pi$$
0.719210 + 0.694793i $$0.244504\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −1.00000 −0.0444116
$$508$$ 0 0
$$509$$ 17.3631 0.769604 0.384802 0.922999i $$-0.374270\pi$$
0.384802 + 0.922999i $$0.374270\pi$$
$$510$$ 0 0
$$511$$ −35.1481 −1.55486
$$512$$ 0 0
$$513$$ 5.33709 0.235638
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −24.7037 −1.08647
$$518$$ 0 0
$$519$$ 3.26475 0.143307
$$520$$ 0 0
$$521$$ 27.6513 1.21142 0.605712 0.795684i $$-0.292888\pi$$
0.605712 + 0.795684i $$0.292888\pi$$
$$522$$ 0 0
$$523$$ 7.49745 0.327840 0.163920 0.986474i $$-0.447586\pi$$
0.163920 + 0.986474i $$0.447586\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −0.954575 −0.0415819
$$528$$ 0 0
$$529$$ −22.8038 −0.991470
$$530$$ 0 0
$$531$$ −13.1358 −0.570045
$$532$$ 0 0
$$533$$ 10.6114 0.459630
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −19.7204 −0.850999
$$538$$ 0 0
$$539$$ 22.4990 0.969099
$$540$$ 0 0
$$541$$ 18.8836 0.811871 0.405936 0.913902i $$-0.366946\pi$$
0.405936 + 0.913902i $$0.366946\pi$$
$$542$$ 0 0
$$543$$ 22.0558 0.946506
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 21.3808 0.914178 0.457089 0.889421i $$-0.348892\pi$$
0.457089 + 0.889421i $$0.348892\pi$$
$$548$$ 0 0
$$549$$ −5.27452 −0.225111
$$550$$ 0 0
$$551$$ −13.7107 −0.584095
$$552$$ 0 0
$$553$$ 60.0890 2.55524
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −3.80681 −0.161300 −0.0806498 0.996743i $$-0.525700\pi$$
−0.0806498 + 0.996743i $$0.525700\pi$$
$$558$$ 0 0
$$559$$ 12.6935 0.536878
$$560$$ 0 0
$$561$$ 5.16697 0.218150
$$562$$ 0 0
$$563$$ −29.3983 −1.23899 −0.619495 0.785001i $$-0.712662\pi$$
−0.619495 + 0.785001i $$0.712662\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 3.71215 0.155896
$$568$$ 0 0
$$569$$ 12.4014 0.519892 0.259946 0.965623i $$-0.416295\pi$$
0.259946 + 0.965623i $$0.416295\pi$$
$$570$$ 0 0
$$571$$ −4.56899 −0.191206 −0.0956032 0.995420i $$-0.530478\pi$$
−0.0956032 + 0.995420i $$0.530478\pi$$
$$572$$ 0 0
$$573$$ −22.2729 −0.930463
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −27.4496 −1.14274 −0.571370 0.820692i $$-0.693588\pi$$
−0.571370 + 0.820692i $$0.693588\pi$$
$$578$$ 0 0
$$579$$ −15.7733 −0.655515
$$580$$ 0 0
$$581$$ −43.6348 −1.81028
$$582$$ 0 0
$$583$$ 17.9036 0.741489
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 19.5191 0.805641 0.402820 0.915279i $$-0.368030\pi$$
0.402820 + 0.915279i $$0.368030\pi$$
$$588$$ 0 0
$$589$$ −3.27197 −0.134819
$$590$$ 0 0
$$591$$ −2.72871 −0.112244
$$592$$ 0 0
$$593$$ 14.8539 0.609975 0.304987 0.952356i $$-0.401348\pi$$
0.304987 + 0.952356i $$0.401348\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 22.1029 0.904613
$$598$$ 0 0
$$599$$ −42.6098 −1.74099 −0.870494 0.492178i $$-0.836201\pi$$
−0.870494 + 0.492178i $$0.836201\pi$$
$$600$$ 0 0
$$601$$ 34.4960 1.40712 0.703561 0.710635i $$-0.251592\pi$$
0.703561 + 0.710635i $$0.251592\pi$$
$$602$$ 0 0
$$603$$ −10.5384 −0.429157
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 44.0061 1.78615 0.893076 0.449906i $$-0.148543\pi$$
0.893076 + 0.449906i $$0.148543\pi$$
$$608$$ 0 0
$$609$$ −9.53630 −0.386430
$$610$$ 0 0
$$611$$ 7.44442 0.301169
$$612$$ 0 0
$$613$$ −11.4907 −0.464104 −0.232052 0.972703i $$-0.574544\pi$$
−0.232052 + 0.972703i $$0.574544\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 47.2506 1.90224 0.951120 0.308823i $$-0.0999350\pi$$
0.951120 + 0.308823i $$0.0999350\pi$$
$$618$$ 0 0
$$619$$ 25.5964 1.02881 0.514403 0.857549i $$-0.328014\pi$$
0.514403 + 0.857549i $$0.328014\pi$$
$$620$$ 0 0
$$621$$ 0.442940 0.0177746
$$622$$ 0 0
$$623$$ −17.0299 −0.682290
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 17.7107 0.707297
$$628$$ 0 0
$$629$$ −0.400665 −0.0159756
$$630$$ 0 0
$$631$$ 6.54777 0.260663 0.130331 0.991470i $$-0.458396\pi$$
0.130331 + 0.991470i $$0.458396\pi$$
$$632$$ 0 0
$$633$$ −1.01720 −0.0404300
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −6.78003 −0.268635
$$638$$ 0 0
$$639$$ 0.311845 0.0123364
$$640$$ 0 0
$$641$$ −0.899023 −0.0355093 −0.0177546 0.999842i $$-0.505652\pi$$
−0.0177546 + 0.999842i $$0.505652\pi$$
$$642$$ 0 0
$$643$$ 2.48862 0.0981416 0.0490708 0.998795i $$-0.484374\pi$$
0.0490708 + 0.998795i $$0.484374\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0.773002 0.0303898 0.0151949 0.999885i $$-0.495163\pi$$
0.0151949 + 0.999885i $$0.495163\pi$$
$$648$$ 0 0
$$649$$ −43.5901 −1.71106
$$650$$ 0 0
$$651$$ −2.27578 −0.0891948
$$652$$ 0 0
$$653$$ 43.1740 1.68953 0.844764 0.535139i $$-0.179741\pi$$
0.844764 + 0.535139i $$0.179741\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −9.46841 −0.369398
$$658$$ 0 0
$$659$$ −39.3552 −1.53306 −0.766530 0.642208i $$-0.778019\pi$$
−0.766530 + 0.642208i $$0.778019\pi$$
$$660$$ 0 0
$$661$$ −20.7673 −0.807756 −0.403878 0.914813i $$-0.632338\pi$$
−0.403878 + 0.914813i $$0.632338\pi$$
$$662$$ 0 0
$$663$$ −1.55706 −0.0604712
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −1.13789 −0.0440592
$$668$$ 0 0
$$669$$ −6.85535 −0.265043
$$670$$ 0 0
$$671$$ −17.5031 −0.675698
$$672$$ 0 0
$$673$$ 49.6479 1.91379 0.956893 0.290439i $$-0.0938014\pi$$
0.956893 + 0.290439i $$0.0938014\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 30.5884 1.17561 0.587803 0.809004i $$-0.299993\pi$$
0.587803 + 0.809004i $$0.299993\pi$$
$$678$$ 0 0
$$679$$ −40.2769 −1.54569
$$680$$ 0 0
$$681$$ 2.88224 0.110448
$$682$$ 0 0
$$683$$ −28.9405 −1.10738 −0.553688 0.832724i $$-0.686780\pi$$
−0.553688 + 0.832724i $$0.686780\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −14.1857 −0.541218
$$688$$ 0 0
$$689$$ −5.39521 −0.205541
$$690$$ 0 0
$$691$$ −31.9739 −1.21635 −0.608173 0.793805i $$-0.708097\pi$$
−0.608173 + 0.793805i $$0.708097\pi$$
$$692$$ 0 0
$$693$$ 12.3184 0.467939
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 16.5226 0.625837
$$698$$ 0 0
$$699$$ 0.429354 0.0162396
$$700$$ 0 0
$$701$$ 4.51673 0.170595 0.0852973 0.996356i $$-0.472816\pi$$
0.0852973 + 0.996356i $$0.472816\pi$$
$$702$$ 0 0
$$703$$ −1.37335 −0.0517969
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 6.24778 0.234972
$$708$$ 0 0
$$709$$ −29.7979 −1.11908 −0.559542 0.828802i $$-0.689023\pi$$
−0.559542 + 0.828802i $$0.689023\pi$$
$$710$$ 0 0
$$711$$ 16.1871 0.607065
$$712$$ 0 0
$$713$$ −0.271550 −0.0101696
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −19.7255 −0.736663
$$718$$ 0 0
$$719$$ 41.8431 1.56049 0.780243 0.625477i $$-0.215096\pi$$
0.780243 + 0.625477i $$0.215096\pi$$
$$720$$ 0 0
$$721$$ −6.62747 −0.246820
$$722$$ 0 0
$$723$$ −19.6598 −0.731157
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −15.4317 −0.572330 −0.286165 0.958180i $$-0.592381\pi$$
−0.286165 + 0.958180i $$0.592381\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 19.7645 0.731018
$$732$$ 0 0
$$733$$ −39.1794 −1.44712 −0.723561 0.690260i $$-0.757496\pi$$
−0.723561 + 0.690260i $$0.757496\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −34.9708 −1.28817
$$738$$ 0 0
$$739$$ 32.5361 1.19686 0.598430 0.801175i $$-0.295791\pi$$
0.598430 + 0.801175i $$0.295791\pi$$
$$740$$ 0 0
$$741$$ −5.33709 −0.196063
$$742$$ 0 0
$$743$$ −8.13346 −0.298388 −0.149194 0.988808i $$-0.547668\pi$$
−0.149194 + 0.988808i $$0.547668\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −11.7546 −0.430078
$$748$$ 0 0
$$749$$ −4.15550 −0.151839
$$750$$ 0 0
$$751$$ −48.9359 −1.78570 −0.892848 0.450358i $$-0.851296\pi$$
−0.892848 + 0.450358i $$0.851296\pi$$
$$752$$ 0 0
$$753$$ −23.4175 −0.853382
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 3.54775 0.128945 0.0644726 0.997919i $$-0.479463\pi$$
0.0644726 + 0.997919i $$0.479463\pi$$
$$758$$ 0 0
$$759$$ 1.46986 0.0533525
$$760$$ 0 0
$$761$$ 40.8645 1.48134 0.740669 0.671870i $$-0.234509\pi$$
0.740669 + 0.671870i $$0.234509\pi$$
$$762$$ 0 0
$$763$$ −3.39630 −0.122954
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 13.1358 0.474306
$$768$$ 0 0
$$769$$ −42.6263 −1.53714 −0.768571 0.639764i $$-0.779032\pi$$
−0.768571 + 0.639764i $$0.779032\pi$$
$$770$$ 0 0
$$771$$ 30.7987 1.10919
$$772$$ 0 0
$$773$$ −36.3873 −1.30876 −0.654379 0.756166i $$-0.727070\pi$$
−0.654379 + 0.756166i $$0.727070\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −0.955216 −0.0342682
$$778$$ 0 0
$$779$$ 56.6340 2.02912
$$780$$ 0 0
$$781$$ 1.03483 0.0370291
$$782$$ 0 0
$$783$$ −2.56894 −0.0918066
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −12.7280 −0.453705 −0.226853 0.973929i $$-0.572844\pi$$
−0.226853 + 0.973929i $$0.572844\pi$$
$$788$$ 0 0
$$789$$ −24.1471 −0.859658
$$790$$ 0 0
$$791$$ −8.96059 −0.318602
$$792$$ 0 0
$$793$$ 5.27452 0.187304
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −20.3707 −0.721566 −0.360783 0.932650i $$-0.617490\pi$$
−0.360783 + 0.932650i $$0.617490\pi$$
$$798$$ 0 0
$$799$$ 11.5914 0.410074
$$800$$ 0 0
$$801$$ −4.58762 −0.162096
$$802$$ 0 0
$$803$$ −31.4201 −1.10879
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −12.7557 −0.449021
$$808$$ 0 0
$$809$$ −36.4656 −1.28206 −0.641030 0.767516i $$-0.721493\pi$$
−0.641030 + 0.767516i $$0.721493\pi$$
$$810$$ 0 0
$$811$$ 32.4823 1.14061 0.570304 0.821433i $$-0.306825\pi$$
0.570304 + 0.821433i $$0.306825\pi$$
$$812$$ 0 0
$$813$$ 10.4222 0.365522
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 67.7464 2.37015
$$818$$ 0 0
$$819$$ −3.71215 −0.129713
$$820$$ 0 0
$$821$$ 15.7750 0.550550 0.275275 0.961366i $$-0.411231\pi$$
0.275275 + 0.961366i $$0.411231\pi$$
$$822$$ 0 0
$$823$$ −33.4570 −1.16624 −0.583120 0.812386i $$-0.698168\pi$$
−0.583120 + 0.812386i $$0.698168\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −30.0516 −1.04500 −0.522499 0.852640i $$-0.675000\pi$$
−0.522499 + 0.852640i $$0.675000\pi$$
$$828$$ 0 0
$$829$$ 3.52850 0.122550 0.0612750 0.998121i $$-0.480483\pi$$
0.0612750 + 0.998121i $$0.480483\pi$$
$$830$$ 0 0
$$831$$ 19.9404 0.691726
$$832$$ 0 0
$$833$$ −10.5569 −0.365776
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −0.613062 −0.0211905
$$838$$ 0 0
$$839$$ 7.19133 0.248272 0.124136 0.992265i $$-0.460384\pi$$
0.124136 + 0.992265i $$0.460384\pi$$
$$840$$ 0 0
$$841$$ −22.4005 −0.772432
$$842$$ 0 0
$$843$$ −28.5272 −0.982529
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0.0441180 0.00151591
$$848$$ 0 0
$$849$$ 19.1888 0.658559
$$850$$ 0 0
$$851$$ −0.113978 −0.00390712
$$852$$ 0 0
$$853$$ −16.1780 −0.553924 −0.276962 0.960881i $$-0.589328\pi$$
−0.276962 + 0.960881i $$0.589328\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −1.79125 −0.0611881 −0.0305940 0.999532i $$-0.509740\pi$$
−0.0305940 + 0.999532i $$0.509740\pi$$
$$858$$ 0 0
$$859$$ 17.7341 0.605078 0.302539 0.953137i $$-0.402166\pi$$
0.302539 + 0.953137i $$0.402166\pi$$
$$860$$ 0 0
$$861$$ 39.3910 1.34244
$$862$$ 0 0
$$863$$ 2.45249 0.0834837 0.0417419 0.999128i $$-0.486709\pi$$
0.0417419 + 0.999128i $$0.486709\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 14.5756 0.495012
$$868$$ 0 0
$$869$$ 53.7156 1.82218
$$870$$ 0 0
$$871$$ 10.5384 0.357081
$$872$$ 0 0
$$873$$ −10.8500 −0.367218
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 48.8367 1.64910 0.824549 0.565791i $$-0.191429\pi$$
0.824549 + 0.565791i $$0.191429\pi$$
$$878$$ 0 0
$$879$$ −11.9828 −0.404171
$$880$$ 0 0
$$881$$ 6.25328 0.210678 0.105339 0.994436i $$-0.466407\pi$$
0.105339 + 0.994436i $$0.466407\pi$$
$$882$$ 0 0
$$883$$ 25.0964 0.844560 0.422280 0.906465i $$-0.361230\pi$$
0.422280 + 0.906465i $$0.361230\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.57354 0.0528344 0.0264172 0.999651i $$-0.491590\pi$$
0.0264172 + 0.999651i $$0.491590\pi$$
$$888$$ 0 0
$$889$$ 52.1253 1.74823
$$890$$ 0 0
$$891$$ 3.31842 0.111171
$$892$$ 0 0
$$893$$ 39.7316 1.32957
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −0.442940 −0.0147893
$$898$$ 0 0
$$899$$ 1.57492 0.0525266
$$900$$ 0 0
$$901$$ −8.40067 −0.279867
$$902$$ 0 0
$$903$$ 47.1201 1.56806
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 20.6504 0.685686 0.342843 0.939393i $$-0.388610\pi$$
0.342843 + 0.939393i $$0.388610\pi$$
$$908$$ 0 0
$$909$$ 1.68306 0.0558237
$$910$$ 0 0
$$911$$ 39.4108 1.30574 0.652869 0.757471i $$-0.273565\pi$$
0.652869 + 0.757471i $$0.273565\pi$$
$$912$$ 0 0
$$913$$ −39.0066 −1.29093
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 51.0977 1.68739
$$918$$ 0 0
$$919$$ −7.84896 −0.258913 −0.129457 0.991585i $$-0.541323\pi$$
−0.129457 + 0.991585i $$0.541323\pi$$
$$920$$ 0 0
$$921$$ 25.0299 0.824764
$$922$$ 0 0
$$923$$ −0.311845 −0.0102645
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −1.78535 −0.0586385
$$928$$ 0 0
$$929$$ −29.2279 −0.958935 −0.479467 0.877560i $$-0.659170\pi$$
−0.479467 + 0.877560i $$0.659170\pi$$
$$930$$ 0 0
$$931$$ −36.1857 −1.18594
$$932$$ 0 0
$$933$$ −27.6360 −0.904764
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 8.62318 0.281707 0.140853 0.990030i $$-0.455015\pi$$
0.140853 + 0.990030i $$0.455015\pi$$
$$938$$ 0 0
$$939$$ 14.5441 0.474630
$$940$$ 0 0
$$941$$ −31.5064 −1.02708 −0.513540 0.858066i $$-0.671666\pi$$
−0.513540 + 0.858066i $$0.671666\pi$$
$$942$$ 0 0
$$943$$ 4.70021 0.153060
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 31.8565 1.03520 0.517598 0.855624i $$-0.326826\pi$$
0.517598 + 0.855624i $$0.326826\pi$$
$$948$$ 0 0
$$949$$ 9.46841 0.307358
$$950$$ 0 0
$$951$$ 8.00364 0.259536
$$952$$ 0 0
$$953$$ −32.9471 −1.06726 −0.533631 0.845717i $$-0.679173\pi$$
−0.533631 + 0.845717i $$0.679173\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −8.52483 −0.275569
$$958$$ 0 0
$$959$$ 24.1464 0.779728
$$960$$ 0 0
$$961$$ −30.6242 −0.987876
$$962$$ 0 0
$$963$$ −1.11943 −0.0360732
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 17.3801 0.558907 0.279453 0.960159i $$-0.409847\pi$$
0.279453 + 0.960159i $$0.409847\pi$$
$$968$$ 0 0
$$969$$ −8.31017 −0.266961
$$970$$ 0 0
$$971$$ −29.4311 −0.944490 −0.472245 0.881467i $$-0.656556\pi$$
−0.472245 + 0.881467i $$0.656556\pi$$
$$972$$ 0 0
$$973$$ 36.3049 1.16388
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −3.49492 −0.111812 −0.0559062 0.998436i $$-0.517805\pi$$
−0.0559062 + 0.998436i $$0.517805\pi$$
$$978$$ 0 0
$$979$$ −15.2236 −0.486550
$$980$$ 0 0
$$981$$ −0.914914 −0.0292110
$$982$$ 0 0
$$983$$ 12.1407 0.387230 0.193615 0.981078i $$-0.437979\pi$$
0.193615 + 0.981078i $$0.437979\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 27.6348 0.879625
$$988$$ 0 0
$$989$$ 5.62246 0.178784
$$990$$ 0 0
$$991$$ 46.5633 1.47913 0.739566 0.673084i $$-0.235031\pi$$
0.739566 + 0.673084i $$0.235031\pi$$
$$992$$ 0 0
$$993$$ −5.59929 −0.177688
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 10.8908 0.344915 0.172457 0.985017i $$-0.444829\pi$$
0.172457 + 0.985017i $$0.444829\pi$$
$$998$$ 0 0
$$999$$ −0.257322 −0.00814130
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 7800.2.a.bz.1.5 5
5.2 odd 4 1560.2.l.f.1249.10 yes 10
5.3 odd 4 1560.2.l.f.1249.5 10
5.4 even 2 7800.2.a.ca.1.1 5
15.2 even 4 4680.2.l.h.2809.1 10
15.8 even 4 4680.2.l.h.2809.2 10
20.3 even 4 3120.2.l.q.1249.10 10
20.7 even 4 3120.2.l.q.1249.5 10

By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.l.f.1249.5 10 5.3 odd 4
1560.2.l.f.1249.10 yes 10 5.2 odd 4
3120.2.l.q.1249.5 10 20.7 even 4
3120.2.l.q.1249.10 10 20.3 even 4
4680.2.l.h.2809.1 10 15.2 even 4
4680.2.l.h.2809.2 10 15.8 even 4
7800.2.a.bz.1.5 5 1.1 even 1 trivial
7800.2.a.ca.1.1 5 5.4 even 2