# Properties

 Label 9025.2.a.bx.1.6 Level $9025$ Weight $2$ Character 9025.1 Self dual yes Analytic conductor $72.065$ Analytic rank $1$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9025 = 5^{2} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9025.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$72.0649878242$$ Analytic rank: $$1$$ Dimension: $$6$$ Coefficient field: 6.6.66064384.1 Defining polynomial: $$x^{6} - 9x^{4} + 13x^{2} - 1$$ x^6 - 9*x^4 + 13*x^2 - 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 95) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.6 Root $$1.30397$$ of defining polynomial Character $$\chi$$ $$=$$ 9025.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.41987 q^{2} -0.537080 q^{3} +3.85577 q^{4} -1.29966 q^{6} -3.18676 q^{7} +4.49073 q^{8} -2.71155 q^{9} +O(q^{10})$$ $$q+2.41987 q^{2} -0.537080 q^{3} +3.85577 q^{4} -1.29966 q^{6} -3.18676 q^{7} +4.49073 q^{8} -2.71155 q^{9} +4.15544 q^{11} -2.07086 q^{12} -2.07086 q^{13} -7.71155 q^{14} +3.15544 q^{16} +5.79470 q^{17} -6.56159 q^{18} +1.71155 q^{21} +10.0556 q^{22} -2.60794 q^{23} -2.41188 q^{24} -5.01121 q^{26} +3.06756 q^{27} -12.2874 q^{28} -6.00000 q^{29} -2.59933 q^{31} -1.34571 q^{32} -2.23180 q^{33} +14.0224 q^{34} -10.4551 q^{36} -4.30266 q^{37} +1.11222 q^{39} +0.599328 q^{41} +4.14172 q^{42} +3.18676 q^{43} +16.0224 q^{44} -6.31087 q^{46} +11.7086 q^{47} -1.69472 q^{48} +3.15544 q^{49} -3.11222 q^{51} -7.98476 q^{52} -11.7503 q^{53} +7.42309 q^{54} -14.3109 q^{56} -14.5192 q^{58} +1.71155 q^{59} -8.75476 q^{61} -6.29004 q^{62} +8.64104 q^{63} -9.56732 q^{64} -5.40067 q^{66} -4.76228 q^{67} +22.3430 q^{68} +1.40067 q^{69} -13.7115 q^{71} -12.1768 q^{72} -2.72714 q^{73} -10.4119 q^{74} -13.2424 q^{77} +2.69142 q^{78} +1.40067 q^{79} +6.48711 q^{81} +1.45030 q^{82} -7.07154 q^{83} +6.59933 q^{84} +7.71155 q^{86} +3.22248 q^{87} +18.6609 q^{88} -16.5353 q^{89} +6.59933 q^{91} -10.0556 q^{92} +1.39605 q^{93} +28.3333 q^{94} +0.722754 q^{96} -2.07086 q^{97} +7.63575 q^{98} -11.2677 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 8 q^{4} + 14 q^{9}+O(q^{10})$$ 6 * q + 8 * q^4 + 14 * q^9 $$6 q + 8 q^{4} + 14 q^{9} + 2 q^{11} - 16 q^{14} - 4 q^{16} - 20 q^{21} + 8 q^{24} + 8 q^{26} - 36 q^{29} + 8 q^{34} - 32 q^{36} - 8 q^{39} - 12 q^{41} + 20 q^{44} + 8 q^{46} - 4 q^{49} - 4 q^{51} - 16 q^{54} - 40 q^{56} - 20 q^{59} - 14 q^{61} - 12 q^{64} - 48 q^{66} + 24 q^{69} - 52 q^{71} - 40 q^{74} + 24 q^{79} + 38 q^{81} + 24 q^{84} + 16 q^{86} - 24 q^{89} + 24 q^{91} + 48 q^{94} - 64 q^{96} - 30 q^{99}+O(q^{100})$$ 6 * q + 8 * q^4 + 14 * q^9 + 2 * q^11 - 16 * q^14 - 4 * q^16 - 20 * q^21 + 8 * q^24 + 8 * q^26 - 36 * q^29 + 8 * q^34 - 32 * q^36 - 8 * q^39 - 12 * q^41 + 20 * q^44 + 8 * q^46 - 4 * q^49 - 4 * q^51 - 16 * q^54 - 40 * q^56 - 20 * q^59 - 14 * q^61 - 12 * q^64 - 48 * q^66 + 24 * q^69 - 52 * q^71 - 40 * q^74 + 24 * q^79 + 38 * q^81 + 24 * q^84 + 16 * q^86 - 24 * q^89 + 24 * q^91 + 48 * q^94 - 64 * q^96 - 30 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.41987 1.71111 0.855553 0.517715i $$-0.173217\pi$$
0.855553 + 0.517715i $$0.173217\pi$$
$$3$$ −0.537080 −0.310083 −0.155042 0.987908i $$-0.549551\pi$$
−0.155042 + 0.987908i $$0.549551\pi$$
$$4$$ 3.85577 1.92789
$$5$$ 0 0
$$6$$ −1.29966 −0.530586
$$7$$ −3.18676 −1.20448 −0.602241 0.798314i $$-0.705725\pi$$
−0.602241 + 0.798314i $$0.705725\pi$$
$$8$$ 4.49073 1.58771
$$9$$ −2.71155 −0.903848
$$10$$ 0 0
$$11$$ 4.15544 1.25291 0.626456 0.779457i $$-0.284505\pi$$
0.626456 + 0.779457i $$0.284505\pi$$
$$12$$ −2.07086 −0.597805
$$13$$ −2.07086 −0.574353 −0.287176 0.957878i $$-0.592717\pi$$
−0.287176 + 0.957878i $$0.592717\pi$$
$$14$$ −7.71155 −2.06100
$$15$$ 0 0
$$16$$ 3.15544 0.788859
$$17$$ 5.79470 1.40542 0.702710 0.711476i $$-0.251973\pi$$
0.702710 + 0.711476i $$0.251973\pi$$
$$18$$ −6.56159 −1.54658
$$19$$ 0 0
$$20$$ 0 0
$$21$$ 1.71155 0.373490
$$22$$ 10.0556 2.14386
$$23$$ −2.60794 −0.543793 −0.271896 0.962327i $$-0.587651\pi$$
−0.271896 + 0.962327i $$0.587651\pi$$
$$24$$ −2.41188 −0.492323
$$25$$ 0 0
$$26$$ −5.01121 −0.982779
$$27$$ 3.06756 0.590352
$$28$$ −12.2874 −2.32210
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ −2.59933 −0.466853 −0.233427 0.972374i $$-0.574994\pi$$
−0.233427 + 0.972374i $$0.574994\pi$$
$$32$$ −1.34571 −0.237890
$$33$$ −2.23180 −0.388507
$$34$$ 14.0224 2.40482
$$35$$ 0 0
$$36$$ −10.4551 −1.74252
$$37$$ −4.30266 −0.707353 −0.353677 0.935368i $$-0.615069\pi$$
−0.353677 + 0.935368i $$0.615069\pi$$
$$38$$ 0 0
$$39$$ 1.11222 0.178097
$$40$$ 0 0
$$41$$ 0.599328 0.0935993 0.0467997 0.998904i $$-0.485098\pi$$
0.0467997 + 0.998904i $$0.485098\pi$$
$$42$$ 4.14172 0.639081
$$43$$ 3.18676 0.485976 0.242988 0.970029i $$-0.421872\pi$$
0.242988 + 0.970029i $$0.421872\pi$$
$$44$$ 16.0224 2.41547
$$45$$ 0 0
$$46$$ −6.31087 −0.930487
$$47$$ 11.7086 1.70787 0.853937 0.520376i $$-0.174208\pi$$
0.853937 + 0.520376i $$0.174208\pi$$
$$48$$ −1.69472 −0.244612
$$49$$ 3.15544 0.450777
$$50$$ 0 0
$$51$$ −3.11222 −0.435798
$$52$$ −7.98476 −1.10729
$$53$$ −11.7503 −1.61403 −0.807017 0.590529i $$-0.798919\pi$$
−0.807017 + 0.590529i $$0.798919\pi$$
$$54$$ 7.42309 1.01015
$$55$$ 0 0
$$56$$ −14.3109 −1.91237
$$57$$ 0 0
$$58$$ −14.5192 −1.90647
$$59$$ 1.71155 0.222824 0.111412 0.993774i $$-0.464463\pi$$
0.111412 + 0.993774i $$0.464463\pi$$
$$60$$ 0 0
$$61$$ −8.75476 −1.12093 −0.560466 0.828177i $$-0.689378\pi$$
−0.560466 + 0.828177i $$0.689378\pi$$
$$62$$ −6.29004 −0.798836
$$63$$ 8.64104 1.08867
$$64$$ −9.56732 −1.19591
$$65$$ 0 0
$$66$$ −5.40067 −0.664777
$$67$$ −4.76228 −0.581805 −0.290902 0.956753i $$-0.593956\pi$$
−0.290902 + 0.956753i $$0.593956\pi$$
$$68$$ 22.3430 2.70949
$$69$$ 1.40067 0.168621
$$70$$ 0 0
$$71$$ −13.7115 −1.62726 −0.813631 0.581382i $$-0.802512\pi$$
−0.813631 + 0.581382i $$0.802512\pi$$
$$72$$ −12.1768 −1.43505
$$73$$ −2.72714 −0.319188 −0.159594 0.987183i $$-0.551018\pi$$
−0.159594 + 0.987183i $$0.551018\pi$$
$$74$$ −10.4119 −1.21036
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −13.2424 −1.50911
$$78$$ 2.69142 0.304743
$$79$$ 1.40067 0.157588 0.0787939 0.996891i $$-0.474893\pi$$
0.0787939 + 0.996891i $$0.474893\pi$$
$$80$$ 0 0
$$81$$ 6.48711 0.720790
$$82$$ 1.45030 0.160158
$$83$$ −7.07154 −0.776203 −0.388101 0.921617i $$-0.626869\pi$$
−0.388101 + 0.921617i $$0.626869\pi$$
$$84$$ 6.59933 0.720046
$$85$$ 0 0
$$86$$ 7.71155 0.831557
$$87$$ 3.22248 0.345486
$$88$$ 18.6609 1.98926
$$89$$ −16.5353 −1.75274 −0.876370 0.481639i $$-0.840042\pi$$
−0.876370 + 0.481639i $$0.840042\pi$$
$$90$$ 0 0
$$91$$ 6.59933 0.691798
$$92$$ −10.0556 −1.04837
$$93$$ 1.39605 0.144763
$$94$$ 28.3333 2.92236
$$95$$ 0 0
$$96$$ 0.722754 0.0737658
$$97$$ −2.07086 −0.210264 −0.105132 0.994458i $$-0.533526\pi$$
−0.105132 + 0.994458i $$0.533526\pi$$
$$98$$ 7.63575 0.771327
$$99$$ −11.2677 −1.13244
$$100$$ 0 0
$$101$$ −1.71155 −0.170305 −0.0851525 0.996368i $$-0.527138\pi$$
−0.0851525 + 0.996368i $$0.527138\pi$$
$$102$$ −7.53116 −0.745696
$$103$$ −5.75296 −0.566856 −0.283428 0.958994i $$-0.591472\pi$$
−0.283428 + 0.958994i $$0.591472\pi$$
$$104$$ −9.29966 −0.911907
$$105$$ 0 0
$$106$$ −28.4343 −2.76178
$$107$$ 15.4324 1.49191 0.745955 0.665996i $$-0.231993\pi$$
0.745955 + 0.665996i $$0.231993\pi$$
$$108$$ 11.8278 1.13813
$$109$$ −11.7115 −1.12176 −0.560881 0.827896i $$-0.689538\pi$$
−0.560881 + 0.827896i $$0.689538\pi$$
$$110$$ 0 0
$$111$$ 2.31087 0.219338
$$112$$ −10.0556 −0.950167
$$113$$ 10.5927 0.996477 0.498239 0.867040i $$-0.333980\pi$$
0.498239 + 0.867040i $$0.333980\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −23.1346 −2.14800
$$117$$ 5.61523 0.519128
$$118$$ 4.14172 0.381276
$$119$$ −18.4663 −1.69280
$$120$$ 0 0
$$121$$ 6.26765 0.569787
$$122$$ −21.1854 −1.91804
$$123$$ −0.321887 −0.0290236
$$124$$ −10.0224 −0.900040
$$125$$ 0 0
$$126$$ 20.9102 1.86283
$$127$$ 6.07484 0.539055 0.269528 0.962993i $$-0.413132\pi$$
0.269528 + 0.962993i $$0.413132\pi$$
$$128$$ −20.4602 −1.80845
$$129$$ −1.71155 −0.150693
$$130$$ 0 0
$$131$$ −13.5785 −1.18636 −0.593181 0.805069i $$-0.702128\pi$$
−0.593181 + 0.805069i $$0.702128\pi$$
$$132$$ −8.60532 −0.748997
$$133$$ 0 0
$$134$$ −11.5241 −0.995530
$$135$$ 0 0
$$136$$ 26.0224 2.23140
$$137$$ −7.94302 −0.678618 −0.339309 0.940675i $$-0.610193\pi$$
−0.339309 + 0.940675i $$0.610193\pi$$
$$138$$ 3.38944 0.288529
$$139$$ 3.26765 0.277159 0.138579 0.990351i $$-0.455746\pi$$
0.138579 + 0.990351i $$0.455746\pi$$
$$140$$ 0 0
$$141$$ −6.28845 −0.529583
$$142$$ −33.1802 −2.78442
$$143$$ −8.60532 −0.719613
$$144$$ −8.55611 −0.713009
$$145$$ 0 0
$$146$$ −6.59933 −0.546164
$$147$$ −1.69472 −0.139778
$$148$$ −16.5901 −1.36370
$$149$$ 8.44389 0.691751 0.345875 0.938280i $$-0.387582\pi$$
0.345875 + 0.938280i $$0.387582\pi$$
$$150$$ 0 0
$$151$$ −0.887783 −0.0722468 −0.0361234 0.999347i $$-0.511501\pi$$
−0.0361234 + 0.999347i $$0.511501\pi$$
$$152$$ 0 0
$$153$$ −15.7126 −1.27029
$$154$$ −32.0448 −2.58225
$$155$$ 0 0
$$156$$ 4.28845 0.343351
$$157$$ 4.14172 0.330545 0.165273 0.986248i $$-0.447150\pi$$
0.165273 + 0.986248i $$0.447150\pi$$
$$158$$ 3.38944 0.269650
$$159$$ 6.31087 0.500485
$$160$$ 0 0
$$161$$ 8.31087 0.654989
$$162$$ 15.6980 1.23335
$$163$$ −24.7126 −1.93564 −0.967819 0.251647i $$-0.919028\pi$$
−0.967819 + 0.251647i $$0.919028\pi$$
$$164$$ 2.31087 0.180449
$$165$$ 0 0
$$166$$ −17.1122 −1.32817
$$167$$ 3.60464 0.278935 0.139468 0.990227i $$-0.455461\pi$$
0.139468 + 0.990227i $$0.455461\pi$$
$$168$$ 7.68608 0.592994
$$169$$ −8.71155 −0.670119
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 12.2874 0.936907
$$173$$ 22.4205 1.70460 0.852300 0.523054i $$-0.175207\pi$$
0.852300 + 0.523054i $$0.175207\pi$$
$$174$$ 7.79798 0.591164
$$175$$ 0 0
$$176$$ 13.1122 0.988371
$$177$$ −0.919237 −0.0690941
$$178$$ −40.0133 −2.99912
$$179$$ 5.13464 0.383781 0.191890 0.981416i $$-0.438538\pi$$
0.191890 + 0.981416i $$0.438538\pi$$
$$180$$ 0 0
$$181$$ −20.8462 −1.54948 −0.774742 0.632277i $$-0.782120\pi$$
−0.774742 + 0.632277i $$0.782120\pi$$
$$182$$ 15.9695 1.18374
$$183$$ 4.70201 0.347583
$$184$$ −11.7115 −0.863387
$$185$$ 0 0
$$186$$ 3.37825 0.247706
$$187$$ 24.0795 1.76087
$$188$$ 45.1457 3.29259
$$189$$ −9.77557 −0.711068
$$190$$ 0 0
$$191$$ −5.26765 −0.381154 −0.190577 0.981672i $$-0.561036\pi$$
−0.190577 + 0.981672i $$0.561036\pi$$
$$192$$ 5.13842 0.370833
$$193$$ −2.07086 −0.149064 −0.0745318 0.997219i $$-0.523746\pi$$
−0.0745318 + 0.997219i $$0.523746\pi$$
$$194$$ −5.01121 −0.359784
$$195$$ 0 0
$$196$$ 12.1666 0.869046
$$197$$ 10.4318 0.743232 0.371616 0.928387i $$-0.378804\pi$$
0.371616 + 0.928387i $$0.378804\pi$$
$$198$$ −27.2663 −1.93773
$$199$$ −2.73235 −0.193691 −0.0968455 0.995299i $$-0.530875\pi$$
−0.0968455 + 0.995299i $$0.530875\pi$$
$$200$$ 0 0
$$201$$ 2.55773 0.180408
$$202$$ −4.14172 −0.291410
$$203$$ 19.1206 1.34200
$$204$$ −12.0000 −0.840168
$$205$$ 0 0
$$206$$ −13.9214 −0.969951
$$207$$ 7.07154 0.491506
$$208$$ −6.53446 −0.453083
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 15.7340 1.08317 0.541585 0.840646i $$-0.317824\pi$$
0.541585 + 0.840646i $$0.317824\pi$$
$$212$$ −45.3066 −3.11167
$$213$$ 7.36420 0.504586
$$214$$ 37.3445 2.55282
$$215$$ 0 0
$$216$$ 13.7756 0.937309
$$217$$ 8.28343 0.562316
$$218$$ −28.3404 −1.91946
$$219$$ 1.46469 0.0989748
$$220$$ 0 0
$$221$$ −12.0000 −0.807207
$$222$$ 5.59201 0.375311
$$223$$ −18.8219 −1.26041 −0.630203 0.776430i $$-0.717028\pi$$
−0.630203 + 0.776430i $$0.717028\pi$$
$$224$$ 4.28845 0.286534
$$225$$ 0 0
$$226$$ 25.6330 1.70508
$$227$$ 14.4418 0.958533 0.479267 0.877669i $$-0.340903\pi$$
0.479267 + 0.877669i $$0.340903\pi$$
$$228$$ 0 0
$$229$$ −4.17785 −0.276080 −0.138040 0.990427i $$-0.544080\pi$$
−0.138040 + 0.990427i $$0.544080\pi$$
$$230$$ 0 0
$$231$$ 7.11222 0.467950
$$232$$ −26.9444 −1.76898
$$233$$ 12.0847 0.791697 0.395849 0.918316i $$-0.370450\pi$$
0.395849 + 0.918316i $$0.370450\pi$$
$$234$$ 13.5881 0.888283
$$235$$ 0 0
$$236$$ 6.59933 0.429580
$$237$$ −0.752273 −0.0488654
$$238$$ −44.6861 −2.89657
$$239$$ −11.3541 −0.734435 −0.367218 0.930135i $$-0.619690\pi$$
−0.367218 + 0.930135i $$0.619690\pi$$
$$240$$ 0 0
$$241$$ 3.40067 0.219057 0.109528 0.993984i $$-0.465066\pi$$
0.109528 + 0.993984i $$0.465066\pi$$
$$242$$ 15.1669 0.974966
$$243$$ −12.6868 −0.813857
$$244$$ −33.7564 −2.16103
$$245$$ 0 0
$$246$$ −0.778925 −0.0496625
$$247$$ 0 0
$$248$$ −11.6729 −0.741229
$$249$$ 3.79798 0.240687
$$250$$ 0 0
$$251$$ 3.04322 0.192086 0.0960432 0.995377i $$-0.469381\pi$$
0.0960432 + 0.995377i $$0.469381\pi$$
$$252$$ 33.3179 2.09883
$$253$$ −10.8371 −0.681324
$$254$$ 14.7003 0.922381
$$255$$ 0 0
$$256$$ −30.3765 −1.89853
$$257$$ −17.2881 −1.07840 −0.539201 0.842177i $$-0.681274\pi$$
−0.539201 + 0.842177i $$0.681274\pi$$
$$258$$ −4.14172 −0.257852
$$259$$ 13.7115 0.851994
$$260$$ 0 0
$$261$$ 16.2693 1.00704
$$262$$ −32.8583 −2.02999
$$263$$ −1.19336 −0.0735859 −0.0367930 0.999323i $$-0.511714\pi$$
−0.0367930 + 0.999323i $$0.511714\pi$$
$$264$$ −10.0224 −0.616837
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 8.88078 0.543495
$$268$$ −18.3623 −1.12165
$$269$$ −22.1089 −1.34800 −0.674000 0.738731i $$-0.735425\pi$$
−0.674000 + 0.738731i $$0.735425\pi$$
$$270$$ 0 0
$$271$$ −4.08644 −0.248234 −0.124117 0.992268i $$-0.539610\pi$$
−0.124117 + 0.992268i $$0.539610\pi$$
$$272$$ 18.2848 1.10868
$$273$$ −3.54437 −0.214515
$$274$$ −19.2211 −1.16119
$$275$$ 0 0
$$276$$ 5.40067 0.325082
$$277$$ −10.0199 −0.602037 −0.301019 0.953618i $$-0.597327\pi$$
−0.301019 + 0.953618i $$0.597327\pi$$
$$278$$ 7.90730 0.474248
$$279$$ 7.04820 0.421964
$$280$$ 0 0
$$281$$ −0.599328 −0.0357529 −0.0178765 0.999840i $$-0.505691\pi$$
−0.0178765 + 0.999840i $$0.505691\pi$$
$$282$$ −15.2172 −0.906174
$$283$$ 5.41856 0.322100 0.161050 0.986946i $$-0.448512\pi$$
0.161050 + 0.986946i $$0.448512\pi$$
$$284$$ −52.8686 −3.13717
$$285$$ 0 0
$$286$$ −20.8238 −1.23133
$$287$$ −1.90991 −0.112739
$$288$$ 3.64895 0.215017
$$289$$ 16.5785 0.975207
$$290$$ 0 0
$$291$$ 1.11222 0.0651993
$$292$$ −10.5152 −0.615358
$$293$$ −3.46691 −0.202539 −0.101269 0.994859i $$-0.532290\pi$$
−0.101269 + 0.994859i $$0.532290\pi$$
$$294$$ −4.10101 −0.239176
$$295$$ 0 0
$$296$$ −19.3221 −1.12307
$$297$$ 12.7470 0.739658
$$298$$ 20.4331 1.18366
$$299$$ 5.40067 0.312329
$$300$$ 0 0
$$301$$ −10.1554 −0.585350
$$302$$ −2.14832 −0.123622
$$303$$ 0.919237 0.0528088
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −38.0224 −2.17360
$$307$$ 16.5901 0.946846 0.473423 0.880835i $$-0.343018\pi$$
0.473423 + 0.880835i $$0.343018\pi$$
$$308$$ −51.0596 −2.90939
$$309$$ 3.08980 0.175772
$$310$$ 0 0
$$311$$ −4.15544 −0.235633 −0.117817 0.993035i $$-0.537589\pi$$
−0.117817 + 0.993035i $$0.537589\pi$$
$$312$$ 4.99466 0.282767
$$313$$ −0.919237 −0.0519583 −0.0259792 0.999662i $$-0.508270\pi$$
−0.0259792 + 0.999662i $$0.508270\pi$$
$$314$$ 10.0224 0.565598
$$315$$ 0 0
$$316$$ 5.40067 0.303812
$$317$$ 26.7292 1.50126 0.750630 0.660723i $$-0.229750\pi$$
0.750630 + 0.660723i $$0.229750\pi$$
$$318$$ 15.2715 0.856383
$$319$$ −24.9326 −1.39596
$$320$$ 0 0
$$321$$ −8.28845 −0.462616
$$322$$ 20.1112 1.12076
$$323$$ 0 0
$$324$$ 25.0128 1.38960
$$325$$ 0 0
$$326$$ −59.8012 −3.31208
$$327$$ 6.29004 0.347840
$$328$$ 2.69142 0.148609
$$329$$ −37.3125 −2.05710
$$330$$ 0 0
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ −27.2663 −1.49643
$$333$$ 11.6669 0.639340
$$334$$ 8.72275 0.477288
$$335$$ 0 0
$$336$$ 5.40067 0.294631
$$337$$ −22.5040 −1.22587 −0.612935 0.790133i $$-0.710011\pi$$
−0.612935 + 0.790133i $$0.710011\pi$$
$$338$$ −21.0808 −1.14664
$$339$$ −5.68913 −0.308991
$$340$$ 0 0
$$341$$ −10.8013 −0.584926
$$342$$ 0 0
$$343$$ 12.2517 0.661530
$$344$$ 14.3109 0.771591
$$345$$ 0 0
$$346$$ 54.2547 2.91675
$$347$$ −14.4543 −0.775946 −0.387973 0.921671i $$-0.626825\pi$$
−0.387973 + 0.921671i $$0.626825\pi$$
$$348$$ 12.4252 0.666058
$$349$$ −13.3541 −0.714828 −0.357414 0.933946i $$-0.616342\pi$$
−0.357414 + 0.933946i $$0.616342\pi$$
$$350$$ 0 0
$$351$$ −6.35248 −0.339070
$$352$$ −5.59201 −0.298055
$$353$$ 17.6410 0.938937 0.469469 0.882949i $$-0.344446\pi$$
0.469469 + 0.882949i $$0.344446\pi$$
$$354$$ −2.22443 −0.118227
$$355$$ 0 0
$$356$$ −63.7564 −3.37908
$$357$$ 9.91789 0.524910
$$358$$ 12.4252 0.656690
$$359$$ 12.4663 0.657947 0.328973 0.944339i $$-0.393297\pi$$
0.328973 + 0.944339i $$0.393297\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ −50.4451 −2.65133
$$363$$ −3.36623 −0.176681
$$364$$ 25.4455 1.33371
$$365$$ 0 0
$$366$$ 11.3783 0.594751
$$367$$ −16.4291 −0.857594 −0.428797 0.903401i $$-0.641062\pi$$
−0.428797 + 0.903401i $$0.641062\pi$$
$$368$$ −8.22918 −0.428976
$$369$$ −1.62511 −0.0845996
$$370$$ 0 0
$$371$$ 37.4455 1.94407
$$372$$ 5.38284 0.279087
$$373$$ 5.29334 0.274079 0.137039 0.990566i $$-0.456241\pi$$
0.137039 + 0.990566i $$0.456241\pi$$
$$374$$ 58.2693 3.01303
$$375$$ 0 0
$$376$$ 52.5801 2.71161
$$377$$ 12.4252 0.639928
$$378$$ −23.6556 −1.21671
$$379$$ −14.5353 −0.746629 −0.373314 0.927705i $$-0.621779\pi$$
−0.373314 + 0.927705i $$0.621779\pi$$
$$380$$ 0 0
$$381$$ −3.26268 −0.167152
$$382$$ −12.7470 −0.652195
$$383$$ −0.453598 −0.0231778 −0.0115889 0.999933i $$-0.503689\pi$$
−0.0115889 + 0.999933i $$0.503689\pi$$
$$384$$ 10.9888 0.560769
$$385$$ 0 0
$$386$$ −5.01121 −0.255064
$$387$$ −8.64104 −0.439249
$$388$$ −7.98476 −0.405365
$$389$$ 16.1554 0.819113 0.409557 0.912285i $$-0.365683\pi$$
0.409557 + 0.912285i $$0.365683\pi$$
$$390$$ 0 0
$$391$$ −15.1122 −0.764258
$$392$$ 14.1702 0.715704
$$393$$ 7.29276 0.367871
$$394$$ 25.2435 1.27175
$$395$$ 0 0
$$396$$ −43.4455 −2.18322
$$397$$ 32.7563 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$398$$ −6.61192 −0.331426
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −12.0864 −0.603568 −0.301784 0.953376i $$-0.597582\pi$$
−0.301784 + 0.953376i $$0.597582\pi$$
$$402$$ 6.18936 0.308697
$$403$$ 5.38284 0.268138
$$404$$ −6.59933 −0.328329
$$405$$ 0 0
$$406$$ 46.2693 2.29631
$$407$$ −17.8794 −0.886251
$$408$$ −13.9761 −0.691921
$$409$$ 19.1346 0.946147 0.473073 0.881023i $$-0.343145\pi$$
0.473073 + 0.881023i $$0.343145\pi$$
$$410$$ 0 0
$$411$$ 4.26604 0.210428
$$412$$ −22.1821 −1.09283
$$413$$ −5.45428 −0.268388
$$414$$ 17.1122 0.841020
$$415$$ 0 0
$$416$$ 2.78678 0.136633
$$417$$ −1.75499 −0.0859423
$$418$$ 0 0
$$419$$ 8.04484 0.393016 0.196508 0.980502i $$-0.437040\pi$$
0.196508 + 0.980502i $$0.437040\pi$$
$$420$$ 0 0
$$421$$ 29.3591 1.43087 0.715437 0.698678i $$-0.246228\pi$$
0.715437 + 0.698678i $$0.246228\pi$$
$$422$$ 38.0742 1.85342
$$423$$ −31.7484 −1.54366
$$424$$ −52.7676 −2.56262
$$425$$ 0 0
$$426$$ 17.8204 0.863401
$$427$$ 27.8993 1.35014
$$428$$ 59.5040 2.87623
$$429$$ 4.62175 0.223140
$$430$$ 0 0
$$431$$ 32.0448 1.54355 0.771773 0.635898i $$-0.219370\pi$$
0.771773 + 0.635898i $$0.219370\pi$$
$$432$$ 9.67948 0.465704
$$433$$ −0.482831 −0.0232034 −0.0116017 0.999933i $$-0.503693\pi$$
−0.0116017 + 0.999933i $$0.503693\pi$$
$$434$$ 20.0448 0.962183
$$435$$ 0 0
$$436$$ −45.1571 −2.16263
$$437$$ 0 0
$$438$$ 3.54437 0.169356
$$439$$ 27.3591 1.30578 0.652889 0.757454i $$-0.273557\pi$$
0.652889 + 0.757454i $$0.273557\pi$$
$$440$$ 0 0
$$441$$ −8.55611 −0.407434
$$442$$ −29.0384 −1.38122
$$443$$ 23.3815 1.11089 0.555444 0.831554i $$-0.312548\pi$$
0.555444 + 0.831554i $$0.312548\pi$$
$$444$$ 8.91020 0.422859
$$445$$ 0 0
$$446$$ −45.5465 −2.15669
$$447$$ −4.53505 −0.214500
$$448$$ 30.4887 1.44046
$$449$$ −23.1346 −1.09179 −0.545895 0.837853i $$-0.683810\pi$$
−0.545895 + 0.837853i $$0.683810\pi$$
$$450$$ 0 0
$$451$$ 2.49047 0.117272
$$452$$ 40.8430 1.92109
$$453$$ 0.476811 0.0224025
$$454$$ 34.9472 1.64015
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 21.2503 0.994049 0.497025 0.867736i $$-0.334426\pi$$
0.497025 + 0.867736i $$0.334426\pi$$
$$458$$ −10.1099 −0.472403
$$459$$ 17.7756 0.829692
$$460$$ 0 0
$$461$$ 31.5785 1.47076 0.735379 0.677656i $$-0.237004\pi$$
0.735379 + 0.677656i $$0.237004\pi$$
$$462$$ 17.2106 0.800712
$$463$$ −15.6119 −0.725547 −0.362774 0.931877i $$-0.618170\pi$$
−0.362774 + 0.931877i $$0.618170\pi$$
$$464$$ −18.9326 −0.878925
$$465$$ 0 0
$$466$$ 29.2435 1.35468
$$467$$ −29.8264 −1.38020 −0.690101 0.723713i $$-0.742434\pi$$
−0.690101 + 0.723713i $$0.742434\pi$$
$$468$$ 21.6510 1.00082
$$469$$ 15.1762 0.700774
$$470$$ 0 0
$$471$$ −2.22443 −0.102496
$$472$$ 7.68608 0.353781
$$473$$ 13.2424 0.608885
$$474$$ −1.82040 −0.0836139
$$475$$ 0 0
$$476$$ −71.2019 −3.26353
$$477$$ 31.8616 1.45884
$$478$$ −27.4754 −1.25670
$$479$$ 4.53531 0.207223 0.103612 0.994618i $$-0.466960\pi$$
0.103612 + 0.994618i $$0.466960\pi$$
$$480$$ 0 0
$$481$$ 8.91020 0.406270
$$482$$ 8.22918 0.374829
$$483$$ −4.46360 −0.203101
$$484$$ 24.1666 1.09848
$$485$$ 0 0
$$486$$ −30.7003 −1.39260
$$487$$ −39.2550 −1.77881 −0.889407 0.457116i $$-0.848882\pi$$
−0.889407 + 0.457116i $$0.848882\pi$$
$$488$$ −39.3153 −1.77972
$$489$$ 13.2726 0.600209
$$490$$ 0 0
$$491$$ 38.8910 1.75513 0.877564 0.479460i $$-0.159168\pi$$
0.877564 + 0.479460i $$0.159168\pi$$
$$492$$ −1.24112 −0.0559542
$$493$$ −34.7682 −1.56588
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −8.20202 −0.368281
$$497$$ 43.6954 1.96001
$$498$$ 9.19063 0.411842
$$499$$ 4.73235 0.211849 0.105924 0.994374i $$-0.466220\pi$$
0.105924 + 0.994374i $$0.466220\pi$$
$$500$$ 0 0
$$501$$ −1.93598 −0.0864931
$$502$$ 7.36420 0.328680
$$503$$ 1.85567 0.0827400 0.0413700 0.999144i $$-0.486828\pi$$
0.0413700 + 0.999144i $$0.486828\pi$$
$$504$$ 38.8046 1.72849
$$505$$ 0 0
$$506$$ −26.2244 −1.16582
$$507$$ 4.67880 0.207793
$$508$$ 23.4232 1.03924
$$509$$ −22.8878 −1.01448 −0.507242 0.861804i $$-0.669335\pi$$
−0.507242 + 0.861804i $$0.669335\pi$$
$$510$$ 0 0
$$511$$ 8.69074 0.384456
$$512$$ −32.5867 −1.44014
$$513$$ 0 0
$$514$$ −41.8350 −1.84526
$$515$$ 0 0
$$516$$ −6.59933 −0.290519
$$517$$ 48.6543 2.13982
$$518$$ 33.1802 1.45785
$$519$$ −12.0416 −0.528568
$$520$$ 0 0
$$521$$ 29.7340 1.30267 0.651334 0.758791i $$-0.274210\pi$$
0.651334 + 0.758791i $$0.274210\pi$$
$$522$$ 39.3695 1.72316
$$523$$ −30.6497 −1.34022 −0.670109 0.742263i $$-0.733752\pi$$
−0.670109 + 0.742263i $$0.733752\pi$$
$$524$$ −52.3557 −2.28717
$$525$$ 0 0
$$526$$ −2.88778 −0.125913
$$527$$ −15.0623 −0.656125
$$528$$ −7.04231 −0.306477
$$529$$ −16.1987 −0.704289
$$530$$ 0 0
$$531$$ −4.64093 −0.201399
$$532$$ 0 0
$$533$$ −1.24112 −0.0537590
$$534$$ 21.4903 0.929978
$$535$$ 0 0
$$536$$ −21.3861 −0.923739
$$537$$ −2.75771 −0.119004
$$538$$ −53.5006 −2.30657
$$539$$ 13.1122 0.564783
$$540$$ 0 0
$$541$$ 2.21946 0.0954220 0.0477110 0.998861i $$-0.484807\pi$$
0.0477110 + 0.998861i $$0.484807\pi$$
$$542$$ −9.88865 −0.424754
$$543$$ 11.1961 0.480469
$$544$$ −7.79798 −0.334336
$$545$$ 0 0
$$546$$ −8.57691 −0.367058
$$547$$ 14.4297 0.616970 0.308485 0.951229i $$-0.400178\pi$$
0.308485 + 0.951229i $$0.400178\pi$$
$$548$$ −30.6265 −1.30830
$$549$$ 23.7389 1.01315
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 6.29004 0.267722
$$553$$ −4.46360 −0.189812
$$554$$ −24.2469 −1.03015
$$555$$ 0 0
$$556$$ 12.5993 0.534331
$$557$$ 19.4610 0.824588 0.412294 0.911051i $$-0.364728\pi$$
0.412294 + 0.911051i $$0.364728\pi$$
$$558$$ 17.0557 0.722026
$$559$$ −6.59933 −0.279122
$$560$$ 0 0
$$561$$ −12.9326 −0.546016
$$562$$ −1.45030 −0.0611771
$$563$$ 12.3649 0.521118 0.260559 0.965458i $$-0.416093\pi$$
0.260559 + 0.965458i $$0.416093\pi$$
$$564$$ −24.2469 −1.02098
$$565$$ 0 0
$$566$$ 13.1122 0.551148
$$567$$ −20.6729 −0.868179
$$568$$ −61.5748 −2.58362
$$569$$ −15.0898 −0.632597 −0.316299 0.948660i $$-0.602440\pi$$
−0.316299 + 0.948660i $$0.602440\pi$$
$$570$$ 0 0
$$571$$ 17.1571 0.718000 0.359000 0.933337i $$-0.383118\pi$$
0.359000 + 0.933337i $$0.383118\pi$$
$$572$$ −33.1802 −1.38733
$$573$$ 2.82915 0.118190
$$574$$ −4.62175 −0.192908
$$575$$ 0 0
$$576$$ 25.9422 1.08093
$$577$$ −22.5165 −0.937374 −0.468687 0.883364i $$-0.655273\pi$$
−0.468687 + 0.883364i $$0.655273\pi$$
$$578$$ 40.1179 1.66868
$$579$$ 1.11222 0.0462222
$$580$$ 0 0
$$581$$ 22.5353 0.934922
$$582$$ 2.69142 0.111563
$$583$$ −48.8278 −2.02224
$$584$$ −12.2469 −0.506778
$$585$$ 0 0
$$586$$ −8.38946 −0.346566
$$587$$ 7.49544 0.309370 0.154685 0.987964i $$-0.450564\pi$$
0.154685 + 0.987964i $$0.450564\pi$$
$$588$$ −6.53446 −0.269477
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −5.60269 −0.230464
$$592$$ −13.5768 −0.558002
$$593$$ 27.8094 1.14199 0.570997 0.820952i $$-0.306557\pi$$
0.570997 + 0.820952i $$0.306557\pi$$
$$594$$ 30.8462 1.26563
$$595$$ 0 0
$$596$$ 32.5577 1.33362
$$597$$ 1.46749 0.0600603
$$598$$ 13.0689 0.534428
$$599$$ 45.4903 1.85869 0.929343 0.369219i $$-0.120375\pi$$
0.929343 + 0.369219i $$0.120375\pi$$
$$600$$ 0 0
$$601$$ 16.5993 0.677101 0.338550 0.940948i $$-0.390063\pi$$
0.338550 + 0.940948i $$0.390063\pi$$
$$602$$ −24.5748 −1.00160
$$603$$ 12.9131 0.525863
$$604$$ −3.42309 −0.139284
$$605$$ 0 0
$$606$$ 2.22443 0.0903614
$$607$$ 5.08417 0.206360 0.103180 0.994663i $$-0.467098\pi$$
0.103180 + 0.994663i $$0.467098\pi$$
$$608$$ 0 0
$$609$$ −10.2693 −0.416132
$$610$$ 0 0
$$611$$ −24.2469 −0.980923
$$612$$ −60.5842 −2.44897
$$613$$ 4.63706 0.187289 0.0936445 0.995606i $$-0.470148\pi$$
0.0936445 + 0.995606i $$0.470148\pi$$
$$614$$ 40.1458 1.62015
$$615$$ 0 0
$$616$$ −59.4679 −2.39603
$$617$$ 40.2874 1.62191 0.810955 0.585108i $$-0.198948\pi$$
0.810955 + 0.585108i $$0.198948\pi$$
$$618$$ 7.47691 0.300766
$$619$$ −43.3815 −1.74365 −0.871825 0.489818i $$-0.837063\pi$$
−0.871825 + 0.489818i $$0.837063\pi$$
$$620$$ 0 0
$$621$$ −8.00000 −0.321029
$$622$$ −10.0556 −0.403194
$$623$$ 52.6940 2.11114
$$624$$ 3.50953 0.140494
$$625$$ 0 0
$$626$$ −2.22443 −0.0889062
$$627$$ 0 0
$$628$$ 15.9695 0.637253
$$629$$ −24.9326 −0.994129
$$630$$ 0 0
$$631$$ 7.53369 0.299911 0.149956 0.988693i $$-0.452087\pi$$
0.149956 + 0.988693i $$0.452087\pi$$
$$632$$ 6.29004 0.250204
$$633$$ −8.45040 −0.335873
$$634$$ 64.6812 2.56882
$$635$$ 0 0
$$636$$ 24.3333 0.964878
$$637$$ −6.53446 −0.258905
$$638$$ −60.3337 −2.38863
$$639$$ 37.1795 1.47080
$$640$$ 0 0
$$641$$ 23.3075 0.920591 0.460296 0.887766i $$-0.347743\pi$$
0.460296 + 0.887766i $$0.347743\pi$$
$$642$$ −20.0570 −0.791586
$$643$$ 1.87419 0.0739110 0.0369555 0.999317i $$-0.488234\pi$$
0.0369555 + 0.999317i $$0.488234\pi$$
$$644$$ 32.0448 1.26274
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −47.0371 −1.84922 −0.924609 0.380917i $$-0.875608\pi$$
−0.924609 + 0.380917i $$0.875608\pi$$
$$648$$ 29.1319 1.14441
$$649$$ 7.11222 0.279179
$$650$$ 0 0
$$651$$ −4.44887 −0.174365
$$652$$ −95.2861 −3.73169
$$653$$ 24.1630 0.945571 0.472785 0.881178i $$-0.343249\pi$$
0.472785 + 0.881178i $$0.343249\pi$$
$$654$$ 15.2211 0.595191
$$655$$ 0 0
$$656$$ 1.89114 0.0738367
$$657$$ 7.39477 0.288497
$$658$$ −90.2914 −3.51992
$$659$$ −10.2885 −0.400781 −0.200391 0.979716i $$-0.564221\pi$$
−0.200391 + 0.979716i $$0.564221\pi$$
$$660$$ 0 0
$$661$$ −5.93598 −0.230883 −0.115441 0.993314i $$-0.536828\pi$$
−0.115441 + 0.993314i $$0.536828\pi$$
$$662$$ −19.3590 −0.752407
$$663$$ 6.44496 0.250302
$$664$$ −31.7564 −1.23239
$$665$$ 0 0
$$666$$ 28.2323 1.09398
$$667$$ 15.6476 0.605879
$$668$$ 13.8987 0.537755
$$669$$ 10.1089 0.390831
$$670$$ 0 0
$$671$$ −36.3799 −1.40443
$$672$$ −2.30324 −0.0888496
$$673$$ 40.7053 1.56907 0.784537 0.620082i $$-0.212901\pi$$
0.784537 + 0.620082i $$0.212901\pi$$
$$674$$ −54.4567 −2.09759
$$675$$ 0 0
$$676$$ −33.5897 −1.29191
$$677$$ −18.8761 −0.725469 −0.362734 0.931893i $$-0.618157\pi$$
−0.362734 + 0.931893i $$0.618157\pi$$
$$678$$ −13.7669 −0.528716
$$679$$ 6.59933 0.253259
$$680$$ 0 0
$$681$$ −7.75638 −0.297225
$$682$$ −26.1379 −1.00087
$$683$$ 19.6576 0.752179 0.376089 0.926583i $$-0.377269\pi$$
0.376089 + 0.926583i $$0.377269\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 29.6475 1.13195
$$687$$ 2.24384 0.0856079
$$688$$ 10.0556 0.383367
$$689$$ 24.3333 0.927025
$$690$$ 0 0
$$691$$ −48.2451 −1.83533 −0.917665 0.397354i $$-0.869928\pi$$
−0.917665 + 0.397354i $$0.869928\pi$$
$$692$$ 86.4483 3.28627
$$693$$ 35.9073 1.36401
$$694$$ −34.9775 −1.32773
$$695$$ 0 0
$$696$$ 14.4713 0.548533
$$697$$ 3.47293 0.131546
$$698$$ −32.3152 −1.22315
$$699$$ −6.49047 −0.245492
$$700$$ 0 0
$$701$$ 0.512889 0.0193715 0.00968577 0.999953i $$-0.496917\pi$$
0.00968577 + 0.999953i $$0.496917\pi$$
$$702$$ −15.3722 −0.580185
$$703$$ 0 0
$$704$$ −39.7564 −1.49838
$$705$$ 0 0
$$706$$ 42.6890 1.60662
$$707$$ 5.45428 0.205129
$$708$$ −3.54437 −0.133205
$$709$$ −8.84618 −0.332225 −0.166113 0.986107i $$-0.553122\pi$$
−0.166113 + 0.986107i $$0.553122\pi$$
$$710$$ 0 0
$$711$$ −3.79798 −0.142436
$$712$$ −74.2556 −2.78285
$$713$$ 6.77889 0.253871
$$714$$ 24.0000 0.898177
$$715$$ 0 0
$$716$$ 19.7980 0.739885
$$717$$ 6.09806 0.227736
$$718$$ 30.1669 1.12582
$$719$$ 7.84456 0.292553 0.146276 0.989244i $$-0.453271\pi$$
0.146276 + 0.989244i $$0.453271\pi$$
$$720$$ 0 0
$$721$$ 18.3333 0.682767
$$722$$ 0 0
$$723$$ −1.82643 −0.0679258
$$724$$ −80.3781 −2.98723
$$725$$ 0 0
$$726$$ −8.14584 −0.302321
$$727$$ −2.91130 −0.107974 −0.0539870 0.998542i $$-0.517193\pi$$
−0.0539870 + 0.998542i $$0.517193\pi$$
$$728$$ 29.6358 1.09838
$$729$$ −12.6475 −0.468427
$$730$$ 0 0
$$731$$ 18.4663 0.683001
$$732$$ 18.1299 0.670100
$$733$$ −33.7775 −1.24760 −0.623800 0.781584i $$-0.714412\pi$$
−0.623800 + 0.781584i $$0.714412\pi$$
$$734$$ −39.7564 −1.46743
$$735$$ 0 0
$$736$$ 3.50953 0.129363
$$737$$ −19.7893 −0.728950
$$738$$ −3.93254 −0.144759
$$739$$ −35.8030 −1.31703 −0.658517 0.752566i $$-0.728816\pi$$
−0.658517 + 0.752566i $$0.728816\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 90.6133 3.32652
$$743$$ 5.66948 0.207993 0.103996 0.994578i $$-0.466837\pi$$
0.103996 + 0.994578i $$0.466837\pi$$
$$744$$ 6.26927 0.229843
$$745$$ 0 0
$$746$$ 12.8092 0.468978
$$747$$ 19.1748 0.701569
$$748$$ 92.8451 3.39475
$$749$$ −49.1795 −1.79698
$$750$$ 0 0
$$751$$ 27.4679 1.00232 0.501159 0.865355i $$-0.332907\pi$$
0.501159 + 0.865355i $$0.332907\pi$$
$$752$$ 36.9457 1.34727
$$753$$ −1.63445 −0.0595628
$$754$$ 30.0673 1.09498
$$755$$ 0 0
$$756$$ −37.6924 −1.37086
$$757$$ −41.6370 −1.51332 −0.756662 0.653806i $$-0.773171\pi$$
−0.756662 + 0.653806i $$0.773171\pi$$
$$758$$ −35.1736 −1.27756
$$759$$ 5.82040 0.211267
$$760$$ 0 0
$$761$$ −9.46967 −0.343275 −0.171638 0.985160i $$-0.554906\pi$$
−0.171638 + 0.985160i $$0.554906\pi$$
$$762$$ −7.89526 −0.286015
$$763$$ 37.3219 1.35114
$$764$$ −20.3109 −0.734822
$$765$$ 0 0
$$766$$ −1.09765 −0.0396597
$$767$$ −3.54437 −0.127980
$$768$$ 16.3146 0.588703
$$769$$ 1.90858 0.0688253 0.0344127 0.999408i $$-0.489044\pi$$
0.0344127 + 0.999408i $$0.489044\pi$$
$$770$$ 0 0
$$771$$ 9.28510 0.334395
$$772$$ −7.98476 −0.287378
$$773$$ 28.4007 1.02150 0.510751 0.859729i $$-0.329367\pi$$
0.510751 + 0.859729i $$0.329367\pi$$
$$774$$ −20.9102 −0.751602
$$775$$ 0 0
$$776$$ −9.29966 −0.333838
$$777$$ −7.36420 −0.264189
$$778$$ 39.0941 1.40159
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −56.9775 −2.03881
$$782$$ −36.5696 −1.30773
$$783$$ −18.4053 −0.657753
$$784$$ 9.95678 0.355599
$$785$$ 0 0
$$786$$ 17.6475 0.629466
$$787$$ −15.6708 −0.558605 −0.279303 0.960203i $$-0.590103\pi$$
−0.279303 + 0.960203i $$0.590103\pi$$
$$788$$ 40.2225 1.43287
$$789$$ 0.640931 0.0228178
$$790$$ 0 0
$$791$$ −33.7564 −1.20024
$$792$$ −50.6000 −1.79799
$$793$$ 18.1299 0.643811
$$794$$ 79.2659 2.81304
$$795$$ 0 0
$$796$$ −10.5353 −0.373414
$$797$$ 36.9225 1.30786 0.653932 0.756554i $$-0.273118\pi$$
0.653932 + 0.756554i $$0.273118\pi$$
$$798$$ 0 0
$$799$$ 67.8478 2.40028
$$800$$ 0 0
$$801$$ 44.8362 1.58421
$$802$$ −29.2476 −1.03277
$$803$$ −11.3325 −0.399914
$$804$$ 9.86201 0.347806
$$805$$ 0 0
$$806$$ 13.0258 0.458813
$$807$$ 11.8742 0.417993
$$808$$ −7.68608 −0.270396
$$809$$ 43.0465 1.51343 0.756716 0.653743i $$-0.226802\pi$$
0.756716 + 0.653743i $$0.226802\pi$$
$$810$$ 0 0
$$811$$ −32.2469 −1.13234 −0.566170 0.824288i $$-0.691575\pi$$
−0.566170 + 0.824288i $$0.691575\pi$$
$$812$$ 73.7245 2.58722
$$813$$ 2.19475 0.0769731
$$814$$ −43.2659 −1.51647
$$815$$ 0 0
$$816$$ −9.82040 −0.343783
$$817$$ 0 0
$$818$$ 46.3033 1.61896
$$819$$ −17.8944 −0.625280
$$820$$ 0 0
$$821$$ 5.18121 0.180826 0.0904128 0.995904i $$-0.471181\pi$$
0.0904128 + 0.995904i $$0.471181\pi$$
$$822$$ 10.3233 0.360065
$$823$$ −25.8517 −0.901133 −0.450567 0.892743i $$-0.648778\pi$$
−0.450567 + 0.892743i $$0.648778\pi$$
$$824$$ −25.8350 −0.900004
$$825$$ 0 0
$$826$$ −13.1987 −0.459240
$$827$$ 9.97816 0.346974 0.173487 0.984836i $$-0.444496\pi$$
0.173487 + 0.984836i $$0.444496\pi$$
$$828$$ 27.2663 0.947568
$$829$$ −21.9808 −0.763425 −0.381713 0.924281i $$-0.624666\pi$$
−0.381713 + 0.924281i $$0.624666\pi$$
$$830$$ 0 0
$$831$$ 5.38149 0.186682
$$832$$ 19.8126 0.686877
$$833$$ 18.2848 0.633531
$$834$$ −4.24685 −0.147056
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −7.97359 −0.275607
$$838$$ 19.4675 0.672492
$$839$$ 16.1089 0.556140 0.278070 0.960561i $$-0.410305\pi$$
0.278070 + 0.960561i $$0.410305\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 71.0451 2.44838
$$843$$ 0.321887 0.0110864
$$844$$ 60.6666 2.08823
$$845$$ 0 0
$$846$$ −76.8270 −2.64137
$$847$$ −19.9735 −0.686298
$$848$$ −37.0775 −1.27324
$$849$$ −2.91020 −0.0998779
$$850$$ 0 0
$$851$$ 11.2211 0.384653
$$852$$ 28.3947 0.972785
$$853$$ 44.9615 1.53945 0.769727 0.638373i $$-0.220392\pi$$
0.769727 + 0.638373i $$0.220392\pi$$
$$854$$ 67.5128 2.31024
$$855$$ 0 0
$$856$$ 69.3029 2.36872
$$857$$ 46.2431 1.57963 0.789817 0.613343i $$-0.210176\pi$$
0.789817 + 0.613343i $$0.210176\pi$$
$$858$$ 11.1840 0.381816
$$859$$ −10.7772 −0.367713 −0.183856 0.982953i $$-0.558858\pi$$
−0.183856 + 0.982953i $$0.558858\pi$$
$$860$$ 0 0
$$861$$ 1.02578 0.0349584
$$862$$ 77.5443 2.64117
$$863$$ −22.7966 −0.776007 −0.388003 0.921658i $$-0.626835\pi$$
−0.388003 + 0.921658i $$0.626835\pi$$
$$864$$ −4.12804 −0.140439
$$865$$ 0 0
$$866$$ −1.16839 −0.0397034
$$867$$ −8.90400 −0.302396
$$868$$ 31.9390 1.08408
$$869$$ 5.82040 0.197444
$$870$$ 0 0
$$871$$ 9.86201 0.334161
$$872$$ −52.5934 −1.78104
$$873$$ 5.61523 0.190047
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 5.64752 0.190812
$$877$$ 4.94644 0.167029 0.0835146 0.996507i $$-0.473385\pi$$
0.0835146 + 0.996507i $$0.473385\pi$$
$$878$$ 66.2054 2.23432
$$879$$ 1.86201 0.0628039
$$880$$ 0 0
$$881$$ 2.53033 0.0852490 0.0426245 0.999091i $$-0.486428\pi$$
0.0426245 + 0.999091i $$0.486428\pi$$
$$882$$ −20.7047 −0.697163
$$883$$ 29.7430 1.00093 0.500465 0.865757i $$-0.333162\pi$$
0.500465 + 0.865757i $$0.333162\pi$$
$$884$$ −46.2693 −1.55620
$$885$$ 0 0
$$886$$ 56.5801 1.90085
$$887$$ −45.5450 −1.52925 −0.764626 0.644474i $$-0.777076\pi$$
−0.764626 + 0.644474i $$0.777076\pi$$
$$888$$ 10.3775 0.348246
$$889$$ −19.3591 −0.649282
$$890$$ 0 0
$$891$$ 26.9568 0.903086
$$892$$ −72.5729 −2.42992
$$893$$ 0 0
$$894$$ −10.9742 −0.367033
$$895$$ 0 0
$$896$$ 65.2019 2.17824
$$897$$ −2.90059 −0.0968480
$$898$$ −55.9828 −1.86817
$$899$$ 15.5960 0.520155
$$900$$ 0 0
$$901$$ −68.0897 −2.26840
$$902$$ 6.02662 0.200664
$$903$$ 5.45428 0.181507
$$904$$ 47.5689 1.58212
$$905$$ 0 0
$$906$$ 1.15382 0.0383331
$$907$$ −33.2034 −1.10250 −0.551250 0.834340i $$-0.685849\pi$$
−0.551250 + 0.834340i $$0.685849\pi$$
$$908$$ 55.6841 1.84794
$$909$$ 4.64093 0.153930
$$910$$ 0 0
$$911$$ −55.7788 −1.84803 −0.924017 0.382351i $$-0.875114\pi$$
−0.924017 + 0.382351i $$0.875114\pi$$
$$912$$ 0 0
$$913$$ −29.3853 −0.972513
$$914$$ 51.4231 1.70092
$$915$$ 0 0
$$916$$ −16.1089 −0.532252
$$917$$ 43.2715 1.42895
$$918$$ 43.0146 1.41969
$$919$$ −28.5769 −0.942665 −0.471333 0.881956i $$-0.656227\pi$$
−0.471333 + 0.881956i $$0.656227\pi$$
$$920$$ 0 0
$$921$$ −8.91020 −0.293601
$$922$$ 76.4159 2.51662
$$923$$ 28.3947 0.934622
$$924$$ 27.4231 0.902153
$$925$$ 0 0
$$926$$ −37.7788 −1.24149
$$927$$ 15.5994 0.512352
$$928$$ 8.07426 0.265051
$$929$$ −54.4937 −1.78788 −0.893940 0.448186i $$-0.852070\pi$$
−0.893940 + 0.448186i $$0.852070\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 46.5960 1.52630
$$933$$ 2.23180 0.0730659
$$934$$ −72.1761 −2.36167
$$935$$ 0 0
$$936$$ 25.2165 0.824226
$$937$$ −37.1484 −1.21359 −0.606793 0.794860i $$-0.707544\pi$$
−0.606793 + 0.794860i $$0.707544\pi$$
$$938$$ 36.7245 1.19910
$$939$$ 0.493704 0.0161114
$$940$$ 0 0
$$941$$ −32.3973 −1.05612 −0.528061 0.849206i $$-0.677081\pi$$
−0.528061 + 0.849206i $$0.677081\pi$$
$$942$$ −5.38284 −0.175382
$$943$$ −1.56301 −0.0508986
$$944$$ 5.40067 0.175777
$$945$$ 0 0
$$946$$ 32.0448 1.04187
$$947$$ 35.4662 1.15250 0.576249 0.817275i $$-0.304516\pi$$
0.576249 + 0.817275i $$0.304516\pi$$
$$948$$ −2.90059 −0.0942069
$$949$$ 5.64752 0.183326
$$950$$ 0 0
$$951$$ −14.3557 −0.465516
$$952$$ −82.9272 −2.68769
$$953$$ 14.3411 0.464553 0.232277 0.972650i $$-0.425383\pi$$
0.232277 + 0.972650i $$0.425383\pi$$
$$954$$ 77.1009 2.49623
$$955$$ 0 0
$$956$$ −43.7788 −1.41591
$$957$$ 13.3908 0.432864
$$958$$ 10.9749 0.354581
$$959$$ 25.3125 0.817383
$$960$$ 0 0
$$961$$ −24.2435 −0.782048
$$962$$ 21.5615 0.695172
$$963$$ −41.8458 −1.34846
$$964$$ 13.1122 0.422316
$$965$$ 0 0
$$966$$ −10.8013 −0.347528
$$967$$ −27.9351 −0.898331 −0.449165 0.893449i $$-0.648279\pi$$
−0.449165 + 0.893449i $$0.648279\pi$$
$$968$$ 28.1463 0.904657
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 42.5993 1.36708 0.683539 0.729914i $$-0.260440\pi$$
0.683539 + 0.729914i $$0.260440\pi$$
$$972$$ −48.9173 −1.56902
$$973$$ −10.4132 −0.333833
$$974$$ −94.9920 −3.04374
$$975$$ 0 0
$$976$$ −27.6251 −0.884258
$$977$$ −39.5597 −1.26563 −0.632813 0.774304i $$-0.718100\pi$$
−0.632813 + 0.774304i $$0.718100\pi$$
$$978$$ 32.1180 1.02702
$$979$$ −68.7114 −2.19603
$$980$$ 0 0
$$981$$ 31.7564 1.01390
$$982$$ 94.1112 3.00321
$$983$$ 39.7689 1.26843 0.634215 0.773157i $$-0.281323\pi$$
0.634215 + 0.773157i $$0.281323\pi$$
$$984$$ −1.44551 −0.0460811
$$985$$ 0 0
$$986$$ −84.1345 −2.67939
$$987$$ 20.0398 0.637874
$$988$$ 0 0
$$989$$ −8.31087 −0.264270
$$990$$ 0 0
$$991$$ −55.2019 −1.75355 −0.876773 0.480905i $$-0.840308\pi$$
−0.876773 + 0.480905i $$0.840308\pi$$
$$992$$ 3.49794 0.111060
$$993$$ 4.29664 0.136350
$$994$$ 105.737 3.35378
$$995$$ 0 0
$$996$$ 14.6442 0.464018
$$997$$ −11.6543 −0.369097 −0.184548 0.982823i $$-0.559082\pi$$
−0.184548 + 0.982823i $$0.559082\pi$$
$$998$$ 11.4517 0.362496
$$999$$ −13.1987 −0.417587
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 9025.2.a.bx.1.6 6
5.2 odd 4 1805.2.b.e.1084.6 6
5.3 odd 4 1805.2.b.e.1084.1 6
5.4 even 2 inner 9025.2.a.bx.1.1 6
19.18 odd 2 475.2.a.j.1.1 6
57.56 even 2 4275.2.a.br.1.6 6
76.75 even 2 7600.2.a.ck.1.3 6
95.18 even 4 95.2.b.b.39.6 yes 6
95.37 even 4 95.2.b.b.39.1 6
95.94 odd 2 475.2.a.j.1.6 6
285.113 odd 4 855.2.c.d.514.1 6
285.227 odd 4 855.2.c.d.514.6 6
285.284 even 2 4275.2.a.br.1.1 6
380.227 odd 4 1520.2.d.h.609.4 6
380.303 odd 4 1520.2.d.h.609.3 6
380.379 even 2 7600.2.a.ck.1.4 6

By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.b.b.39.1 6 95.37 even 4
95.2.b.b.39.6 yes 6 95.18 even 4
475.2.a.j.1.1 6 19.18 odd 2
475.2.a.j.1.6 6 95.94 odd 2
855.2.c.d.514.1 6 285.113 odd 4
855.2.c.d.514.6 6 285.227 odd 4
1520.2.d.h.609.3 6 380.303 odd 4
1520.2.d.h.609.4 6 380.227 odd 4
1805.2.b.e.1084.1 6 5.3 odd 4
1805.2.b.e.1084.6 6 5.2 odd 4
4275.2.a.br.1.1 6 285.284 even 2
4275.2.a.br.1.6 6 57.56 even 2
7600.2.a.ck.1.3 6 76.75 even 2
7600.2.a.ck.1.4 6 380.379 even 2
9025.2.a.bx.1.1 6 5.4 even 2 inner
9025.2.a.bx.1.6 6 1.1 even 1 trivial