Properties

 Label 9025.2.a.bh.1.1 Level $9025$ Weight $2$ Character 9025.1 Self dual yes Analytic conductor $72.065$ Analytic rank $0$ Dimension $4$ CM no Inner twists $1$

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: $$0$$ Dimension: $$4$$ Coefficient field: 4.4.2225.1 Defining polynomial: $$x^{4} - x^{3} - 5x^{2} + 2x + 4$$ x^4 - x^3 - 5*x^2 + 2*x + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1805) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Root $$2.43828$$ of defining polynomial Character $$\chi$$ $$=$$ 9025.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q-2.43828 q^{2} +2.94523 q^{3} +3.94523 q^{4} -7.18129 q^{6} +3.82025 q^{7} -4.74301 q^{8} +5.67435 q^{9} +O(q^{10})$$ $$q-2.43828 q^{2} +2.94523 q^{3} +3.94523 q^{4} -7.18129 q^{6} +3.82025 q^{7} -4.74301 q^{8} +5.67435 q^{9} -2.12498 q^{11} +11.6196 q^{12} -3.65438 q^{13} -9.31485 q^{14} +3.67435 q^{16} +3.04243 q^{17} -13.8357 q^{18} +11.2515 q^{21} +5.18129 q^{22} +4.81167 q^{23} -13.9692 q^{24} +8.91042 q^{26} +7.87657 q^{27} +15.0717 q^{28} -6.03385 q^{29} -3.57184 q^{31} +0.526911 q^{32} -6.25853 q^{33} -7.41831 q^{34} +22.3866 q^{36} +3.93134 q^{37} -10.7630 q^{39} +7.60945 q^{41} -27.4343 q^{42} +5.60415 q^{43} -8.38351 q^{44} -11.7322 q^{46} +8.41831 q^{47} +10.8218 q^{48} +7.59430 q^{49} +8.96065 q^{51} -14.4174 q^{52} +4.80028 q^{53} -19.2053 q^{54} -18.1195 q^{56} +14.7122 q^{58} +5.13510 q^{59} -13.5100 q^{61} +8.70916 q^{62} +21.6774 q^{63} -8.63346 q^{64} +15.2601 q^{66} -5.38101 q^{67} +12.0031 q^{68} +14.1714 q^{69} +0.123434 q^{71} -26.9135 q^{72} +12.4860 q^{73} -9.58572 q^{74} -8.11794 q^{77} +26.2432 q^{78} +4.25699 q^{79} +6.17521 q^{81} -18.5540 q^{82} -4.39739 q^{83} +44.3897 q^{84} -13.6645 q^{86} -17.7711 q^{87} +10.0788 q^{88} +0.0772394 q^{89} -13.9607 q^{91} +18.9831 q^{92} -10.5199 q^{93} -20.5262 q^{94} +1.55187 q^{96} -18.0231 q^{97} -18.5171 q^{98} -12.0579 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - q^{2} - q^{3} + 3 q^{4} - 7 q^{6} + 11 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10})$$ 4 * q - q^2 - q^3 + 3 * q^4 - 7 * q^6 + 11 * q^7 - 6 * q^8 + 5 * q^9 $$4 q - q^{2} - q^{3} + 3 q^{4} - 7 q^{6} + 11 q^{7} - 6 q^{8} + 5 q^{9} + 16 q^{12} + 2 q^{13} - 11 q^{14} - 3 q^{16} + 7 q^{17} - 17 q^{18} + 2 q^{21} - q^{22} + 11 q^{23} - 13 q^{24} + 9 q^{26} + 14 q^{27} + 13 q^{28} - 15 q^{29} - q^{31} - 3 q^{32} - 12 q^{33} - 22 q^{34} + 16 q^{36} + 11 q^{37} - 29 q^{39} + 22 q^{41} - 19 q^{42} + 26 q^{43} - 12 q^{44} + 10 q^{46} + 26 q^{47} + 13 q^{48} + 13 q^{49} - 11 q^{51} - 27 q^{52} + 16 q^{53} - 25 q^{54} - 8 q^{56} + 3 q^{58} - 10 q^{59} + 2 q^{61} + 31 q^{62} + 17 q^{63} + 4 q^{64} + 22 q^{66} - 3 q^{67} - 4 q^{68} + 14 q^{69} + 18 q^{71} - 29 q^{72} + 24 q^{73} - 17 q^{74} + 6 q^{77} + 15 q^{78} + 30 q^{79} - 4 q^{81} + 13 q^{82} + 12 q^{83} + 52 q^{84} - 16 q^{86} + q^{87} + 23 q^{88} + 9 q^{89} - 9 q^{91} + 25 q^{92} - 7 q^{93} - 11 q^{94} - 6 q^{96} - 19 q^{97} - 48 q^{98} - 9 q^{99}+O(q^{100})$$ 4 * q - q^2 - q^3 + 3 * q^4 - 7 * q^6 + 11 * q^7 - 6 * q^8 + 5 * q^9 + 16 * q^12 + 2 * q^13 - 11 * q^14 - 3 * q^16 + 7 * q^17 - 17 * q^18 + 2 * q^21 - q^22 + 11 * q^23 - 13 * q^24 + 9 * q^26 + 14 * q^27 + 13 * q^28 - 15 * q^29 - q^31 - 3 * q^32 - 12 * q^33 - 22 * q^34 + 16 * q^36 + 11 * q^37 - 29 * q^39 + 22 * q^41 - 19 * q^42 + 26 * q^43 - 12 * q^44 + 10 * q^46 + 26 * q^47 + 13 * q^48 + 13 * q^49 - 11 * q^51 - 27 * q^52 + 16 * q^53 - 25 * q^54 - 8 * q^56 + 3 * q^58 - 10 * q^59 + 2 * q^61 + 31 * q^62 + 17 * q^63 + 4 * q^64 + 22 * q^66 - 3 * q^67 - 4 * q^68 + 14 * q^69 + 18 * q^71 - 29 * q^72 + 24 * q^73 - 17 * q^74 + 6 * q^77 + 15 * q^78 + 30 * q^79 - 4 * q^81 + 13 * q^82 + 12 * q^83 + 52 * q^84 - 16 * q^86 + q^87 + 23 * q^88 + 9 * q^89 - 9 * q^91 + 25 * q^92 - 7 * q^93 - 11 * q^94 - 6 * q^96 - 19 * q^97 - 48 * q^98 - 9 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.43828 −1.72413 −0.862063 0.506801i $$-0.830828\pi$$
−0.862063 + 0.506801i $$0.830828\pi$$
$$3$$ 2.94523 1.70043 0.850213 0.526438i $$-0.176473\pi$$
0.850213 + 0.526438i $$0.176473\pi$$
$$4$$ 3.94523 1.97261
$$5$$ 0 0
$$6$$ −7.18129 −2.93175
$$7$$ 3.82025 1.44392 0.721959 0.691936i $$-0.243242\pi$$
0.721959 + 0.691936i $$0.243242\pi$$
$$8$$ −4.74301 −1.67691
$$9$$ 5.67435 1.89145
$$10$$ 0 0
$$11$$ −2.12498 −0.640704 −0.320352 0.947299i $$-0.603801\pi$$
−0.320352 + 0.947299i $$0.603801\pi$$
$$12$$ 11.6196 3.35428
$$13$$ −3.65438 −1.01354 −0.506772 0.862080i $$-0.669161\pi$$
−0.506772 + 0.862080i $$0.669161\pi$$
$$14$$ −9.31485 −2.48950
$$15$$ 0 0
$$16$$ 3.67435 0.918588
$$17$$ 3.04243 0.737898 0.368949 0.929450i $$-0.379718\pi$$
0.368949 + 0.929450i $$0.379718\pi$$
$$18$$ −13.8357 −3.26110
$$19$$ 0 0
$$20$$ 0 0
$$21$$ 11.2515 2.45528
$$22$$ 5.18129 1.10466
$$23$$ 4.81167 1.00330 0.501651 0.865070i $$-0.332726\pi$$
0.501651 + 0.865070i $$0.332726\pi$$
$$24$$ −13.9692 −2.85146
$$25$$ 0 0
$$26$$ 8.91042 1.74748
$$27$$ 7.87657 1.51585
$$28$$ 15.0717 2.84829
$$29$$ −6.03385 −1.12046 −0.560229 0.828338i $$-0.689287\pi$$
−0.560229 + 0.828338i $$0.689287\pi$$
$$30$$ 0 0
$$31$$ −3.57184 −0.641521 −0.320761 0.947160i $$-0.603939\pi$$
−0.320761 + 0.947160i $$0.603939\pi$$
$$32$$ 0.526911 0.0931455
$$33$$ −6.25853 −1.08947
$$34$$ −7.41831 −1.27223
$$35$$ 0 0
$$36$$ 22.3866 3.73110
$$37$$ 3.93134 0.646309 0.323154 0.946346i $$-0.395257\pi$$
0.323154 + 0.946346i $$0.395257\pi$$
$$38$$ 0 0
$$39$$ −10.7630 −1.72346
$$40$$ 0 0
$$41$$ 7.60945 1.18840 0.594198 0.804318i $$-0.297469\pi$$
0.594198 + 0.804318i $$0.297469\pi$$
$$42$$ −27.4343 −4.23321
$$43$$ 5.60415 0.854625 0.427312 0.904104i $$-0.359460\pi$$
0.427312 + 0.904104i $$0.359460\pi$$
$$44$$ −8.38351 −1.26386
$$45$$ 0 0
$$46$$ −11.7322 −1.72982
$$47$$ 8.41831 1.22794 0.613969 0.789330i $$-0.289572\pi$$
0.613969 + 0.789330i $$0.289572\pi$$
$$48$$ 10.8218 1.56199
$$49$$ 7.59430 1.08490
$$50$$ 0 0
$$51$$ 8.96065 1.25474
$$52$$ −14.4174 −1.99933
$$53$$ 4.80028 0.659369 0.329685 0.944091i $$-0.393058\pi$$
0.329685 + 0.944091i $$0.393058\pi$$
$$54$$ −19.2053 −2.61351
$$55$$ 0 0
$$56$$ −18.1195 −2.42132
$$57$$ 0 0
$$58$$ 14.7122 1.93181
$$59$$ 5.13510 0.668533 0.334266 0.942479i $$-0.391511\pi$$
0.334266 + 0.942479i $$0.391511\pi$$
$$60$$ 0 0
$$61$$ −13.5100 −1.72978 −0.864891 0.501960i $$-0.832612\pi$$
−0.864891 + 0.501960i $$0.832612\pi$$
$$62$$ 8.70916 1.10606
$$63$$ 21.6774 2.73110
$$64$$ −8.63346 −1.07918
$$65$$ 0 0
$$66$$ 15.2601 1.87839
$$67$$ −5.38101 −0.657395 −0.328698 0.944435i $$-0.606610\pi$$
−0.328698 + 0.944435i $$0.606610\pi$$
$$68$$ 12.0031 1.45559
$$69$$ 14.1714 1.70604
$$70$$ 0 0
$$71$$ 0.123434 0.0146489 0.00732443 0.999973i $$-0.497669\pi$$
0.00732443 + 0.999973i $$0.497669\pi$$
$$72$$ −26.9135 −3.17179
$$73$$ 12.4860 1.46138 0.730689 0.682710i $$-0.239199\pi$$
0.730689 + 0.682710i $$0.239199\pi$$
$$74$$ −9.58572 −1.11432
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −8.11794 −0.925125
$$78$$ 26.2432 2.97146
$$79$$ 4.25699 0.478949 0.239474 0.970903i $$-0.423025\pi$$
0.239474 + 0.970903i $$0.423025\pi$$
$$80$$ 0 0
$$81$$ 6.17521 0.686134
$$82$$ −18.5540 −2.04895
$$83$$ −4.39739 −0.482677 −0.241338 0.970441i $$-0.577586\pi$$
−0.241338 + 0.970441i $$0.577586\pi$$
$$84$$ 44.3897 4.84331
$$85$$ 0 0
$$86$$ −13.6645 −1.47348
$$87$$ −17.7711 −1.90526
$$88$$ 10.0788 1.07440
$$89$$ 0.0772394 0.00818736 0.00409368 0.999992i $$-0.498697\pi$$
0.00409368 + 0.999992i $$0.498697\pi$$
$$90$$ 0 0
$$91$$ −13.9607 −1.46347
$$92$$ 18.9831 1.97913
$$93$$ −10.5199 −1.09086
$$94$$ −20.5262 −2.11712
$$95$$ 0 0
$$96$$ 1.55187 0.158387
$$97$$ −18.0231 −1.82996 −0.914982 0.403495i $$-0.867795\pi$$
−0.914982 + 0.403495i $$0.867795\pi$$
$$98$$ −18.5171 −1.87051
$$99$$ −12.0579 −1.21186
$$100$$ 0 0
$$101$$ 18.6498 1.85573 0.927864 0.372918i $$-0.121643\pi$$
0.927864 + 0.372918i $$0.121643\pi$$
$$102$$ −21.8486 −2.16333
$$103$$ 0.377423 0.0371886 0.0185943 0.999827i $$-0.494081\pi$$
0.0185943 + 0.999827i $$0.494081\pi$$
$$104$$ 17.3328 1.69962
$$105$$ 0 0
$$106$$ −11.7044 −1.13684
$$107$$ 2.76144 0.266958 0.133479 0.991052i $$-0.457385\pi$$
0.133479 + 0.991052i $$0.457385\pi$$
$$108$$ 31.0748 2.99018
$$109$$ 3.00308 0.287643 0.143822 0.989604i $$-0.454061\pi$$
0.143822 + 0.989604i $$0.454061\pi$$
$$110$$ 0 0
$$111$$ 11.5787 1.09900
$$112$$ 14.0369 1.32637
$$113$$ 3.61708 0.340266 0.170133 0.985421i $$-0.445580\pi$$
0.170133 + 0.985421i $$0.445580\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −23.8049 −2.21023
$$117$$ −20.7362 −1.91707
$$118$$ −12.5208 −1.15264
$$119$$ 11.6229 1.06547
$$120$$ 0 0
$$121$$ −6.48448 −0.589498
$$122$$ 32.9413 2.98236
$$123$$ 22.4116 2.02078
$$124$$ −14.0917 −1.26547
$$125$$ 0 0
$$126$$ −52.8557 −4.70876
$$127$$ 13.6188 1.20847 0.604236 0.796805i $$-0.293478\pi$$
0.604236 + 0.796805i $$0.293478\pi$$
$$128$$ 19.9970 1.76750
$$129$$ 16.5055 1.45323
$$130$$ 0 0
$$131$$ 5.67059 0.495442 0.247721 0.968831i $$-0.420318\pi$$
0.247721 + 0.968831i $$0.420318\pi$$
$$132$$ −24.6913 −2.14910
$$133$$ 0 0
$$134$$ 13.1204 1.13343
$$135$$ 0 0
$$136$$ −14.4303 −1.23739
$$137$$ 8.10501 0.692457 0.346229 0.938150i $$-0.387462\pi$$
0.346229 + 0.938150i $$0.387462\pi$$
$$138$$ −34.5540 −2.94143
$$139$$ −17.5325 −1.48709 −0.743543 0.668688i $$-0.766856\pi$$
−0.743543 + 0.668688i $$0.766856\pi$$
$$140$$ 0 0
$$141$$ 24.7938 2.08802
$$142$$ −0.300966 −0.0252565
$$143$$ 7.76547 0.649382
$$144$$ 20.8496 1.73746
$$145$$ 0 0
$$146$$ −30.4445 −2.51960
$$147$$ 22.3669 1.84479
$$148$$ 15.5100 1.27492
$$149$$ 19.1952 1.57253 0.786265 0.617889i $$-0.212012\pi$$
0.786265 + 0.617889i $$0.212012\pi$$
$$150$$ 0 0
$$151$$ 11.1473 0.907152 0.453576 0.891218i $$-0.350148\pi$$
0.453576 + 0.891218i $$0.350148\pi$$
$$152$$ 0 0
$$153$$ 17.2638 1.39570
$$154$$ 19.7938 1.59503
$$155$$ 0 0
$$156$$ −42.4624 −3.39971
$$157$$ −11.1452 −0.889486 −0.444743 0.895658i $$-0.646705\pi$$
−0.444743 + 0.895658i $$0.646705\pi$$
$$158$$ −10.3797 −0.825768
$$159$$ 14.1379 1.12121
$$160$$ 0 0
$$161$$ 18.3818 1.44869
$$162$$ −15.0569 −1.18298
$$163$$ 6.68669 0.523742 0.261871 0.965103i $$-0.415660\pi$$
0.261871 + 0.965103i $$0.415660\pi$$
$$164$$ 30.0210 2.34425
$$165$$ 0 0
$$166$$ 10.7221 0.832195
$$167$$ −18.6569 −1.44371 −0.721856 0.692043i $$-0.756711\pi$$
−0.721856 + 0.692043i $$0.756711\pi$$
$$168$$ −53.3659 −4.11727
$$169$$ 0.354510 0.0272700
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 22.1096 1.68584
$$173$$ 14.7385 1.12054 0.560272 0.828308i $$-0.310696\pi$$
0.560272 + 0.828308i $$0.310696\pi$$
$$174$$ 43.3309 3.28490
$$175$$ 0 0
$$176$$ −7.80791 −0.588543
$$177$$ 15.1240 1.13679
$$178$$ −0.188331 −0.0141160
$$179$$ −12.1961 −0.911582 −0.455791 0.890087i $$-0.650643\pi$$
−0.455791 + 0.890087i $$0.650643\pi$$
$$180$$ 0 0
$$181$$ −13.1841 −0.979966 −0.489983 0.871732i $$-0.662997\pi$$
−0.489983 + 0.871732i $$0.662997\pi$$
$$182$$ 34.0400 2.52321
$$183$$ −39.7901 −2.94137
$$184$$ −22.8218 −1.68244
$$185$$ 0 0
$$186$$ 25.6504 1.88078
$$187$$ −6.46510 −0.472775
$$188$$ 33.2121 2.42224
$$189$$ 30.0904 2.18876
$$190$$ 0 0
$$191$$ 4.61708 0.334080 0.167040 0.985950i $$-0.446579\pi$$
0.167040 + 0.985950i $$0.446579\pi$$
$$192$$ −25.4275 −1.83507
$$193$$ 5.22468 0.376081 0.188040 0.982161i $$-0.439786\pi$$
0.188040 + 0.982161i $$0.439786\pi$$
$$194$$ 43.9453 3.15509
$$195$$ 0 0
$$196$$ 29.9612 2.14009
$$197$$ −21.1783 −1.50889 −0.754445 0.656363i $$-0.772094\pi$$
−0.754445 + 0.656363i $$0.772094\pi$$
$$198$$ 29.4005 2.08940
$$199$$ 15.3752 1.08992 0.544960 0.838462i $$-0.316545\pi$$
0.544960 + 0.838462i $$0.316545\pi$$
$$200$$ 0 0
$$201$$ −15.8483 −1.11785
$$202$$ −45.4736 −3.19951
$$203$$ −23.0508 −1.61785
$$204$$ 35.3518 2.47512
$$205$$ 0 0
$$206$$ −0.920265 −0.0641179
$$207$$ 27.3031 1.89770
$$208$$ −13.4275 −0.931029
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 20.8659 1.43647 0.718235 0.695800i $$-0.244950\pi$$
0.718235 + 0.695800i $$0.244950\pi$$
$$212$$ 18.9382 1.30068
$$213$$ 0.363540 0.0249093
$$214$$ −6.73316 −0.460270
$$215$$ 0 0
$$216$$ −37.3586 −2.54193
$$217$$ −13.6453 −0.926305
$$218$$ −7.32237 −0.495934
$$219$$ 36.7741 2.48497
$$220$$ 0 0
$$221$$ −11.1182 −0.747892
$$222$$ −28.2321 −1.89482
$$223$$ −13.6759 −0.915806 −0.457903 0.889002i $$-0.651399\pi$$
−0.457903 + 0.889002i $$0.651399\pi$$
$$224$$ 2.01293 0.134495
$$225$$ 0 0
$$226$$ −8.81947 −0.586662
$$227$$ −3.71196 −0.246372 −0.123186 0.992384i $$-0.539311\pi$$
−0.123186 + 0.992384i $$0.539311\pi$$
$$228$$ 0 0
$$229$$ 11.3086 0.747293 0.373646 0.927571i $$-0.378107\pi$$
0.373646 + 0.927571i $$0.378107\pi$$
$$230$$ 0 0
$$231$$ −23.9092 −1.57311
$$232$$ 28.6186 1.87890
$$233$$ 10.6753 0.699362 0.349681 0.936869i $$-0.386290\pi$$
0.349681 + 0.936869i $$0.386290\pi$$
$$234$$ 50.5608 3.30527
$$235$$ 0 0
$$236$$ 20.2591 1.31876
$$237$$ 12.5378 0.814417
$$238$$ −28.3398 −1.83700
$$239$$ −17.2813 −1.11783 −0.558916 0.829224i $$-0.688783\pi$$
−0.558916 + 0.829224i $$0.688783\pi$$
$$240$$ 0 0
$$241$$ 17.4986 1.12719 0.563593 0.826052i $$-0.309419\pi$$
0.563593 + 0.826052i $$0.309419\pi$$
$$242$$ 15.8110 1.01637
$$243$$ −5.44232 −0.349125
$$244$$ −53.3001 −3.41219
$$245$$ 0 0
$$246$$ −54.6457 −3.48408
$$247$$ 0 0
$$248$$ 16.9413 1.07577
$$249$$ −12.9513 −0.820756
$$250$$ 0 0
$$251$$ 17.9012 1.12991 0.564956 0.825121i $$-0.308893\pi$$
0.564956 + 0.825121i $$0.308893\pi$$
$$252$$ 85.5224 5.38740
$$253$$ −10.2247 −0.642820
$$254$$ −33.2065 −2.08356
$$255$$ 0 0
$$256$$ −31.4914 −1.96821
$$257$$ 26.7208 1.66680 0.833400 0.552671i $$-0.186391\pi$$
0.833400 + 0.552671i $$0.186391\pi$$
$$258$$ −40.2450 −2.50555
$$259$$ 15.0187 0.933217
$$260$$ 0 0
$$261$$ −34.2382 −2.11929
$$262$$ −13.8265 −0.854204
$$263$$ 19.7817 1.21979 0.609895 0.792482i $$-0.291211\pi$$
0.609895 + 0.792482i $$0.291211\pi$$
$$264$$ 29.6843 1.82694
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0.227487 0.0139220
$$268$$ −21.2293 −1.29679
$$269$$ 7.04833 0.429744 0.214872 0.976642i $$-0.431067\pi$$
0.214872 + 0.976642i $$0.431067\pi$$
$$270$$ 0 0
$$271$$ 26.1672 1.58955 0.794773 0.606907i $$-0.207590\pi$$
0.794773 + 0.606907i $$0.207590\pi$$
$$272$$ 11.1790 0.677825
$$273$$ −41.1173 −2.48853
$$274$$ −19.7623 −1.19388
$$275$$ 0 0
$$276$$ 55.9096 3.36536
$$277$$ −2.86953 −0.172413 −0.0862066 0.996277i $$-0.527475\pi$$
−0.0862066 + 0.996277i $$0.527475\pi$$
$$278$$ 42.7492 2.56393
$$279$$ −20.2679 −1.21341
$$280$$ 0 0
$$281$$ −22.4401 −1.33866 −0.669332 0.742963i $$-0.733420\pi$$
−0.669332 + 0.742963i $$0.733420\pi$$
$$282$$ −60.4544 −3.60001
$$283$$ 4.68139 0.278280 0.139140 0.990273i $$-0.455566\pi$$
0.139140 + 0.990273i $$0.455566\pi$$
$$284$$ 0.486973 0.0288965
$$285$$ 0 0
$$286$$ −18.9344 −1.11962
$$287$$ 29.0700 1.71595
$$288$$ 2.98988 0.176180
$$289$$ −7.74360 −0.455506
$$290$$ 0 0
$$291$$ −53.0820 −3.11172
$$292$$ 49.2602 2.88273
$$293$$ −3.26229 −0.190585 −0.0952926 0.995449i $$-0.530379\pi$$
−0.0952926 + 0.995449i $$0.530379\pi$$
$$294$$ −54.5369 −3.18066
$$295$$ 0 0
$$296$$ −18.6464 −1.08380
$$297$$ −16.7375 −0.971209
$$298$$ −46.8033 −2.71124
$$299$$ −17.5837 −1.01689
$$300$$ 0 0
$$301$$ 21.4093 1.23401
$$302$$ −27.1802 −1.56404
$$303$$ 54.9280 3.15553
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −42.0941 −2.40636
$$307$$ 1.71746 0.0980207 0.0490103 0.998798i $$-0.484393\pi$$
0.0490103 + 0.998798i $$0.484393\pi$$
$$308$$ −32.0271 −1.82491
$$309$$ 1.11160 0.0632365
$$310$$ 0 0
$$311$$ −0.892946 −0.0506343 −0.0253172 0.999679i $$-0.508060\pi$$
−0.0253172 + 0.999679i $$0.508060\pi$$
$$312$$ 51.0489 2.89008
$$313$$ −11.5358 −0.652040 −0.326020 0.945363i $$-0.605708\pi$$
−0.326020 + 0.945363i $$0.605708\pi$$
$$314$$ 27.1752 1.53359
$$315$$ 0 0
$$316$$ 16.7948 0.944780
$$317$$ −18.8246 −1.05729 −0.528647 0.848842i $$-0.677301\pi$$
−0.528647 + 0.848842i $$0.677301\pi$$
$$318$$ −34.4722 −1.93311
$$319$$ 12.8218 0.717883
$$320$$ 0 0
$$321$$ 8.13305 0.453943
$$322$$ −44.8200 −2.49772
$$323$$ 0 0
$$324$$ 24.3626 1.35348
$$325$$ 0 0
$$326$$ −16.3041 −0.902998
$$327$$ 8.84476 0.489116
$$328$$ −36.0917 −1.99283
$$329$$ 32.1601 1.77304
$$330$$ 0 0
$$331$$ −15.5779 −0.856240 −0.428120 0.903722i $$-0.640824\pi$$
−0.428120 + 0.903722i $$0.640824\pi$$
$$332$$ −17.3487 −0.952134
$$333$$ 22.3078 1.22246
$$334$$ 45.4908 2.48914
$$335$$ 0 0
$$336$$ 41.3419 2.25539
$$337$$ 6.43425 0.350496 0.175248 0.984524i $$-0.443927\pi$$
0.175248 + 0.984524i $$0.443927\pi$$
$$338$$ −0.864396 −0.0470170
$$339$$ 10.6531 0.578598
$$340$$ 0 0
$$341$$ 7.59007 0.411026
$$342$$ 0 0
$$343$$ 2.27039 0.122590
$$344$$ −26.5805 −1.43313
$$345$$ 0 0
$$346$$ −35.9366 −1.93196
$$347$$ 19.3367 1.03805 0.519023 0.854760i $$-0.326296\pi$$
0.519023 + 0.854760i $$0.326296\pi$$
$$348$$ −70.1108 −3.75833
$$349$$ 7.78870 0.416920 0.208460 0.978031i $$-0.433155\pi$$
0.208460 + 0.978031i $$0.433155\pi$$
$$350$$ 0 0
$$351$$ −28.7840 −1.53638
$$352$$ −1.11967 −0.0596788
$$353$$ 24.7007 1.31468 0.657342 0.753593i $$-0.271681\pi$$
0.657342 + 0.753593i $$0.271681\pi$$
$$354$$ −36.8767 −1.95997
$$355$$ 0 0
$$356$$ 0.304727 0.0161505
$$357$$ 34.2319 1.81175
$$358$$ 29.7376 1.57168
$$359$$ 24.8224 1.31008 0.655038 0.755596i $$-0.272653\pi$$
0.655038 + 0.755596i $$0.272653\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 32.1466 1.68959
$$363$$ −19.0982 −1.00240
$$364$$ −55.0779 −2.88687
$$365$$ 0 0
$$366$$ 97.0195 5.07129
$$367$$ 7.01716 0.366293 0.183146 0.983086i $$-0.441372\pi$$
0.183146 + 0.983086i $$0.441372\pi$$
$$368$$ 17.6798 0.921621
$$369$$ 43.1787 2.24779
$$370$$ 0 0
$$371$$ 18.3383 0.952075
$$372$$ −41.5033 −2.15184
$$373$$ 36.2105 1.87491 0.937455 0.348107i $$-0.113175\pi$$
0.937455 + 0.348107i $$0.113175\pi$$
$$374$$ 15.7637 0.815124
$$375$$ 0 0
$$376$$ −39.9281 −2.05914
$$377$$ 22.0500 1.13563
$$378$$ −73.3690 −3.77370
$$379$$ −28.2455 −1.45087 −0.725437 0.688288i $$-0.758362\pi$$
−0.725437 + 0.688288i $$0.758362\pi$$
$$380$$ 0 0
$$381$$ 40.1104 2.05492
$$382$$ −11.2578 −0.575997
$$383$$ −26.4312 −1.35057 −0.675287 0.737555i $$-0.735980\pi$$
−0.675287 + 0.737555i $$0.735980\pi$$
$$384$$ 58.8957 3.00551
$$385$$ 0 0
$$386$$ −12.7392 −0.648411
$$387$$ 31.7999 1.61648
$$388$$ −71.1050 −3.60981
$$389$$ −5.61736 −0.284811 −0.142406 0.989808i $$-0.545484\pi$$
−0.142406 + 0.989808i $$0.545484\pi$$
$$390$$ 0 0
$$391$$ 14.6392 0.740335
$$392$$ −36.0199 −1.81928
$$393$$ 16.7012 0.842462
$$394$$ 51.6387 2.60152
$$395$$ 0 0
$$396$$ −47.5710 −2.39053
$$397$$ 29.0391 1.45743 0.728715 0.684818i $$-0.240118\pi$$
0.728715 + 0.684818i $$0.240118\pi$$
$$398$$ −37.4891 −1.87916
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 25.4613 1.27148 0.635739 0.771904i $$-0.280695\pi$$
0.635739 + 0.771904i $$0.280695\pi$$
$$402$$ 38.6426 1.92732
$$403$$ 13.0529 0.650210
$$404$$ 73.5778 3.66063
$$405$$ 0 0
$$406$$ 56.2044 2.78938
$$407$$ −8.35401 −0.414093
$$408$$ −42.5005 −2.10409
$$409$$ −19.8024 −0.979166 −0.489583 0.871957i $$-0.662851\pi$$
−0.489583 + 0.871957i $$0.662851\pi$$
$$410$$ 0 0
$$411$$ 23.8711 1.17747
$$412$$ 1.48902 0.0733588
$$413$$ 19.6174 0.965307
$$414$$ −66.5727 −3.27187
$$415$$ 0 0
$$416$$ −1.92553 −0.0944070
$$417$$ −51.6371 −2.52868
$$418$$ 0 0
$$419$$ 0.172123 0.00840877 0.00420439 0.999991i $$-0.498662\pi$$
0.00420439 + 0.999991i $$0.498662\pi$$
$$420$$ 0 0
$$421$$ 17.4056 0.848297 0.424149 0.905593i $$-0.360573\pi$$
0.424149 + 0.905593i $$0.360573\pi$$
$$422$$ −50.8771 −2.47666
$$423$$ 47.7685 2.32258
$$424$$ −22.7678 −1.10570
$$425$$ 0 0
$$426$$ −0.886412 −0.0429468
$$427$$ −51.6117 −2.49766
$$428$$ 10.8945 0.526605
$$429$$ 22.8711 1.10423
$$430$$ 0 0
$$431$$ −5.06518 −0.243981 −0.121990 0.992531i $$-0.538928\pi$$
−0.121990 + 0.992531i $$0.538928\pi$$
$$432$$ 28.9413 1.39244
$$433$$ −12.5169 −0.601524 −0.300762 0.953699i $$-0.597241\pi$$
−0.300762 + 0.953699i $$0.597241\pi$$
$$434$$ 33.2712 1.59707
$$435$$ 0 0
$$436$$ 11.8478 0.567409
$$437$$ 0 0
$$438$$ −89.6658 −4.28440
$$439$$ −14.7581 −0.704367 −0.352183 0.935931i $$-0.614561\pi$$
−0.352183 + 0.935931i $$0.614561\pi$$
$$440$$ 0 0
$$441$$ 43.0928 2.05204
$$442$$ 27.1094 1.28946
$$443$$ −5.35950 −0.254638 −0.127319 0.991862i $$-0.540637\pi$$
−0.127319 + 0.991862i $$0.540637\pi$$
$$444$$ 45.6805 2.16790
$$445$$ 0 0
$$446$$ 33.3457 1.57896
$$447$$ 56.5341 2.67397
$$448$$ −32.9820 −1.55825
$$449$$ −7.16065 −0.337932 −0.168966 0.985622i $$-0.554043\pi$$
−0.168966 + 0.985622i $$0.554043\pi$$
$$450$$ 0 0
$$451$$ −16.1699 −0.761411
$$452$$ 14.2702 0.671214
$$453$$ 32.8312 1.54255
$$454$$ 9.05082 0.424776
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −32.3884 −1.51507 −0.757534 0.652796i $$-0.773596\pi$$
−0.757534 + 0.652796i $$0.773596\pi$$
$$458$$ −27.5736 −1.28843
$$459$$ 23.9639 1.11854
$$460$$ 0 0
$$461$$ −25.2124 −1.17426 −0.587130 0.809493i $$-0.699742\pi$$
−0.587130 + 0.809493i $$0.699742\pi$$
$$462$$ 58.2973 2.71224
$$463$$ 40.8494 1.89843 0.949216 0.314627i $$-0.101879\pi$$
0.949216 + 0.314627i $$0.101879\pi$$
$$464$$ −22.1705 −1.02924
$$465$$ 0 0
$$466$$ −26.0294 −1.20579
$$467$$ −14.6209 −0.676577 −0.338288 0.941042i $$-0.609848\pi$$
−0.338288 + 0.941042i $$0.609848\pi$$
$$468$$ −81.8092 −3.78163
$$469$$ −20.5568 −0.949225
$$470$$ 0 0
$$471$$ −32.8252 −1.51250
$$472$$ −24.3558 −1.12107
$$473$$ −11.9087 −0.547562
$$474$$ −30.5707 −1.40416
$$475$$ 0 0
$$476$$ 45.8548 2.10175
$$477$$ 27.2385 1.24716
$$478$$ 42.1366 1.92729
$$479$$ 1.06944 0.0488640 0.0244320 0.999701i $$-0.492222\pi$$
0.0244320 + 0.999701i $$0.492222\pi$$
$$480$$ 0 0
$$481$$ −14.3666 −0.655062
$$482$$ −42.6666 −1.94341
$$483$$ 54.1385 2.46339
$$484$$ −25.5827 −1.16285
$$485$$ 0 0
$$486$$ 13.2699 0.601936
$$487$$ 6.25304 0.283352 0.141676 0.989913i $$-0.454751\pi$$
0.141676 + 0.989913i $$0.454751\pi$$
$$488$$ 64.0782 2.90068
$$489$$ 19.6938 0.890585
$$490$$ 0 0
$$491$$ −0.813681 −0.0367209 −0.0183605 0.999831i $$-0.505845\pi$$
−0.0183605 + 0.999831i $$0.505845\pi$$
$$492$$ 88.4186 3.98622
$$493$$ −18.3576 −0.826784
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −13.1242 −0.589294
$$497$$ 0.471547 0.0211518
$$498$$ 31.5790 1.41509
$$499$$ 1.57636 0.0705676 0.0352838 0.999377i $$-0.488766\pi$$
0.0352838 + 0.999377i $$0.488766\pi$$
$$500$$ 0 0
$$501$$ −54.9487 −2.45493
$$502$$ −43.6481 −1.94811
$$503$$ −3.00182 −0.133845 −0.0669223 0.997758i $$-0.521318\pi$$
−0.0669223 + 0.997758i $$0.521318\pi$$
$$504$$ −102.816 −4.57980
$$505$$ 0 0
$$506$$ 24.9307 1.10830
$$507$$ 1.04411 0.0463707
$$508$$ 53.7292 2.38385
$$509$$ −32.7217 −1.45036 −0.725182 0.688557i $$-0.758245\pi$$
−0.725182 + 0.688557i $$0.758245\pi$$
$$510$$ 0 0
$$511$$ 47.6997 2.11011
$$512$$ 36.7910 1.62595
$$513$$ 0 0
$$514$$ −65.1529 −2.87377
$$515$$ 0 0
$$516$$ 65.1179 2.86665
$$517$$ −17.8887 −0.786745
$$518$$ −36.6199 −1.60898
$$519$$ 43.4081 1.90540
$$520$$ 0 0
$$521$$ −16.4073 −0.718819 −0.359409 0.933180i $$-0.617022\pi$$
−0.359409 + 0.933180i $$0.617022\pi$$
$$522$$ 83.4824 3.65393
$$523$$ 20.4437 0.893940 0.446970 0.894549i $$-0.352503\pi$$
0.446970 + 0.894549i $$0.352503\pi$$
$$524$$ 22.3718 0.977315
$$525$$ 0 0
$$526$$ −48.2333 −2.10307
$$527$$ −10.8671 −0.473378
$$528$$ −22.9960 −1.00077
$$529$$ 0.152154 0.00661541
$$530$$ 0 0
$$531$$ 29.1384 1.26450
$$532$$ 0 0
$$533$$ −27.8079 −1.20449
$$534$$ −0.554678 −0.0240033
$$535$$ 0 0
$$536$$ 25.5222 1.10239
$$537$$ −35.9203 −1.55008
$$538$$ −17.1858 −0.740933
$$539$$ −16.1377 −0.695101
$$540$$ 0 0
$$541$$ −28.8016 −1.23828 −0.619139 0.785281i $$-0.712518\pi$$
−0.619139 + 0.785281i $$0.712518\pi$$
$$542$$ −63.8031 −2.74058
$$543$$ −38.8301 −1.66636
$$544$$ 1.60309 0.0687320
$$545$$ 0 0
$$546$$ 100.256 4.29054
$$547$$ −26.9553 −1.15253 −0.576264 0.817264i $$-0.695490\pi$$
−0.576264 + 0.817264i $$0.695490\pi$$
$$548$$ 31.9761 1.36595
$$549$$ −76.6606 −3.27180
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −67.2153 −2.86087
$$553$$ 16.2628 0.691563
$$554$$ 6.99672 0.297262
$$555$$ 0 0
$$556$$ −69.1696 −2.93345
$$557$$ −7.95439 −0.337039 −0.168519 0.985698i $$-0.553899\pi$$
−0.168519 + 0.985698i $$0.553899\pi$$
$$558$$ 49.4188 2.09207
$$559$$ −20.4797 −0.866199
$$560$$ 0 0
$$561$$ −19.0412 −0.803919
$$562$$ 54.7153 2.30803
$$563$$ 34.0931 1.43685 0.718426 0.695603i $$-0.244863\pi$$
0.718426 + 0.695603i $$0.244863\pi$$
$$564$$ 97.8172 4.11885
$$565$$ 0 0
$$566$$ −11.4146 −0.479789
$$567$$ 23.5908 0.990722
$$568$$ −0.585446 −0.0245648
$$569$$ 25.7236 1.07839 0.539195 0.842181i $$-0.318729\pi$$
0.539195 + 0.842181i $$0.318729\pi$$
$$570$$ 0 0
$$571$$ −31.6325 −1.32378 −0.661890 0.749601i $$-0.730245\pi$$
−0.661890 + 0.749601i $$0.730245\pi$$
$$572$$ 30.6365 1.28098
$$573$$ 13.5983 0.568079
$$574$$ −70.8809 −2.95851
$$575$$ 0 0
$$576$$ −48.9893 −2.04122
$$577$$ −26.8689 −1.11856 −0.559282 0.828977i $$-0.688923\pi$$
−0.559282 + 0.828977i $$0.688923\pi$$
$$578$$ 18.8811 0.785350
$$579$$ 15.3879 0.639498
$$580$$ 0 0
$$581$$ −16.7991 −0.696946
$$582$$ 129.429 5.36500
$$583$$ −10.2005 −0.422461
$$584$$ −59.2213 −2.45060
$$585$$ 0 0
$$586$$ 7.95439 0.328593
$$587$$ −42.5145 −1.75476 −0.877380 0.479796i $$-0.840711\pi$$
−0.877380 + 0.479796i $$0.840711\pi$$
$$588$$ 88.2426 3.63906
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −62.3748 −2.56576
$$592$$ 14.4451 0.593691
$$593$$ 23.2139 0.953280 0.476640 0.879099i $$-0.341855\pi$$
0.476640 + 0.879099i $$0.341855\pi$$
$$594$$ 40.8108 1.67449
$$595$$ 0 0
$$596$$ 75.7293 3.10199
$$597$$ 45.2834 1.85333
$$598$$ 42.8740 1.75325
$$599$$ −0.313115 −0.0127935 −0.00639676 0.999980i $$-0.502036\pi$$
−0.00639676 + 0.999980i $$0.502036\pi$$
$$600$$ 0 0
$$601$$ −20.9580 −0.854893 −0.427447 0.904041i $$-0.640587\pi$$
−0.427447 + 0.904041i $$0.640587\pi$$
$$602$$ −52.2018 −2.12759
$$603$$ −30.5338 −1.24343
$$604$$ 43.9785 1.78946
$$605$$ 0 0
$$606$$ −133.930 −5.44053
$$607$$ 10.1085 0.410290 0.205145 0.978732i $$-0.434233\pi$$
0.205145 + 0.978732i $$0.434233\pi$$
$$608$$ 0 0
$$609$$ −67.8899 −2.75104
$$610$$ 0 0
$$611$$ −30.7637 −1.24457
$$612$$ 68.1097 2.75317
$$613$$ 36.3560 1.46840 0.734202 0.678931i $$-0.237556\pi$$
0.734202 + 0.678931i $$0.237556\pi$$
$$614$$ −4.18766 −0.169000
$$615$$ 0 0
$$616$$ 38.5035 1.55135
$$617$$ −35.3399 −1.42273 −0.711365 0.702822i $$-0.751923\pi$$
−0.711365 + 0.702822i $$0.751923\pi$$
$$618$$ −2.71039 −0.109028
$$619$$ −32.5878 −1.30982 −0.654908 0.755709i $$-0.727292\pi$$
−0.654908 + 0.755709i $$0.727292\pi$$
$$620$$ 0 0
$$621$$ 37.8994 1.52085
$$622$$ 2.17726 0.0873000
$$623$$ 0.295074 0.0118219
$$624$$ −39.5470 −1.58315
$$625$$ 0 0
$$626$$ 28.1275 1.12420
$$627$$ 0 0
$$628$$ −43.9704 −1.75461
$$629$$ 11.9608 0.476910
$$630$$ 0 0
$$631$$ 1.66950 0.0664616 0.0332308 0.999448i $$-0.489420\pi$$
0.0332308 + 0.999448i $$0.489420\pi$$
$$632$$ −20.1909 −0.803153
$$633$$ 61.4549 2.44261
$$634$$ 45.8997 1.82291
$$635$$ 0 0
$$636$$ 55.7772 2.21171
$$637$$ −27.7525 −1.09959
$$638$$ −31.2632 −1.23772
$$639$$ 0.700405 0.0277076
$$640$$ 0 0
$$641$$ 21.3997 0.845238 0.422619 0.906307i $$-0.361111\pi$$
0.422619 + 0.906307i $$0.361111\pi$$
$$642$$ −19.8307 −0.782655
$$643$$ 8.43473 0.332633 0.166317 0.986072i $$-0.446813\pi$$
0.166317 + 0.986072i $$0.446813\pi$$
$$644$$ 72.5202 2.85770
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 29.2025 1.14807 0.574034 0.818831i $$-0.305378\pi$$
0.574034 + 0.818831i $$0.305378\pi$$
$$648$$ −29.2891 −1.15058
$$649$$ −10.9120 −0.428332
$$650$$ 0 0
$$651$$ −40.1885 −1.57511
$$652$$ 26.3805 1.03314
$$653$$ 7.61427 0.297970 0.148985 0.988839i $$-0.452399\pi$$
0.148985 + 0.988839i $$0.452399\pi$$
$$654$$ −21.5660 −0.843299
$$655$$ 0 0
$$656$$ 27.9598 1.09165
$$657$$ 70.8501 2.76412
$$658$$ −78.4153 −3.05695
$$659$$ −18.2941 −0.712637 −0.356318 0.934365i $$-0.615968\pi$$
−0.356318 + 0.934365i $$0.615968\pi$$
$$660$$ 0 0
$$661$$ −20.3586 −0.791859 −0.395930 0.918281i $$-0.629578\pi$$
−0.395930 + 0.918281i $$0.629578\pi$$
$$662$$ 37.9834 1.47627
$$663$$ −32.7456 −1.27174
$$664$$ 20.8569 0.809404
$$665$$ 0 0
$$666$$ −54.3928 −2.10768
$$667$$ −29.0329 −1.12416
$$668$$ −73.6056 −2.84789
$$669$$ −40.2786 −1.55726
$$670$$ 0 0
$$671$$ 28.7085 1.10828
$$672$$ 5.92853 0.228698
$$673$$ −29.6829 −1.14419 −0.572096 0.820186i $$-0.693870\pi$$
−0.572096 + 0.820186i $$0.693870\pi$$
$$674$$ −15.6885 −0.604299
$$675$$ 0 0
$$676$$ 1.39862 0.0537932
$$677$$ −9.17128 −0.352481 −0.176240 0.984347i $$-0.556394\pi$$
−0.176240 + 0.984347i $$0.556394\pi$$
$$678$$ −25.9753 −0.997576
$$679$$ −68.8526 −2.64232
$$680$$ 0 0
$$681$$ −10.9326 −0.418937
$$682$$ −18.5067 −0.708660
$$683$$ 15.6556 0.599043 0.299522 0.954089i $$-0.403173\pi$$
0.299522 + 0.954089i $$0.403173\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −5.53586 −0.211360
$$687$$ 33.3064 1.27072
$$688$$ 20.5916 0.785048
$$689$$ −17.5421 −0.668299
$$690$$ 0 0
$$691$$ −13.7912 −0.524643 −0.262321 0.964981i $$-0.584488\pi$$
−0.262321 + 0.964981i $$0.584488\pi$$
$$692$$ 58.1466 2.21040
$$693$$ −46.0640 −1.74983
$$694$$ −47.1483 −1.78972
$$695$$ 0 0
$$696$$ 84.2883 3.19494
$$697$$ 23.1513 0.876916
$$698$$ −18.9911 −0.718822
$$699$$ 31.4412 1.18921
$$700$$ 0 0
$$701$$ −13.7313 −0.518622 −0.259311 0.965794i $$-0.583496\pi$$
−0.259311 + 0.965794i $$0.583496\pi$$
$$702$$ 70.1835 2.64891
$$703$$ 0 0
$$704$$ 18.3459 0.691437
$$705$$ 0 0
$$706$$ −60.2272 −2.26668
$$707$$ 71.2470 2.67952
$$708$$ 59.6677 2.24245
$$709$$ −12.3146 −0.462483 −0.231242 0.972896i $$-0.574279\pi$$
−0.231242 + 0.972896i $$0.574279\pi$$
$$710$$ 0 0
$$711$$ 24.1557 0.905908
$$712$$ −0.366347 −0.0137294
$$713$$ −17.1865 −0.643640
$$714$$ −83.4671 −3.12368
$$715$$ 0 0
$$716$$ −48.1165 −1.79820
$$717$$ −50.8972 −1.90079
$$718$$ −60.5240 −2.25874
$$719$$ −6.92307 −0.258187 −0.129094 0.991632i $$-0.541207\pi$$
−0.129094 + 0.991632i $$0.541207\pi$$
$$720$$ 0 0
$$721$$ 1.44185 0.0536973
$$722$$ 0 0
$$723$$ 51.5374 1.91670
$$724$$ −52.0142 −1.93309
$$725$$ 0 0
$$726$$ 46.5669 1.72826
$$727$$ −34.2263 −1.26938 −0.634692 0.772765i $$-0.718873\pi$$
−0.634692 + 0.772765i $$0.718873\pi$$
$$728$$ 66.2155 2.45411
$$729$$ −34.5545 −1.27980
$$730$$ 0 0
$$731$$ 17.0503 0.630626
$$732$$ −156.981 −5.80218
$$733$$ −37.5214 −1.38589 −0.692943 0.720993i $$-0.743686\pi$$
−0.692943 + 0.720993i $$0.743686\pi$$
$$734$$ −17.1098 −0.631535
$$735$$ 0 0
$$736$$ 2.53532 0.0934531
$$737$$ 11.4345 0.421196
$$738$$ −105.282 −3.87548
$$739$$ −38.6683 −1.42244 −0.711218 0.702972i $$-0.751856\pi$$
−0.711218 + 0.702972i $$0.751856\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −44.7139 −1.64150
$$743$$ −34.5415 −1.26720 −0.633602 0.773659i $$-0.718424\pi$$
−0.633602 + 0.773659i $$0.718424\pi$$
$$744$$ 49.8959 1.82927
$$745$$ 0 0
$$746$$ −88.2915 −3.23258
$$747$$ −24.9523 −0.912959
$$748$$ −25.5063 −0.932601
$$749$$ 10.5494 0.385466
$$750$$ 0 0
$$751$$ 33.3178 1.21578 0.607892 0.794020i $$-0.292015\pi$$
0.607892 + 0.794020i $$0.292015\pi$$
$$752$$ 30.9318 1.12797
$$753$$ 52.7230 1.92133
$$754$$ −53.7642 −1.95798
$$755$$ 0 0
$$756$$ 118.714 4.31757
$$757$$ −27.2310 −0.989728 −0.494864 0.868970i $$-0.664782\pi$$
−0.494864 + 0.868970i $$0.664782\pi$$
$$758$$ 68.8706 2.50149
$$759$$ −30.1140 −1.09307
$$760$$ 0 0
$$761$$ 20.1113 0.729033 0.364516 0.931197i $$-0.381234\pi$$
0.364516 + 0.931197i $$0.381234\pi$$
$$762$$ −97.8006 −3.54294
$$763$$ 11.4725 0.415334
$$764$$ 18.2154 0.659011
$$765$$ 0 0
$$766$$ 64.4469 2.32856
$$767$$ −18.7656 −0.677587
$$768$$ −92.7493 −3.34680
$$769$$ −3.25931 −0.117534 −0.0587669 0.998272i $$-0.518717\pi$$
−0.0587669 + 0.998272i $$0.518717\pi$$
$$770$$ 0 0
$$771$$ 78.6988 2.83427
$$772$$ 20.6125 0.741861
$$773$$ 49.6874 1.78713 0.893565 0.448933i $$-0.148196\pi$$
0.893565 + 0.448933i $$0.148196\pi$$
$$774$$ −77.5372 −2.78702
$$775$$ 0 0
$$776$$ 85.4835 3.06868
$$777$$ 44.2335 1.58687
$$778$$ 13.6967 0.491051
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −0.262293 −0.00938559
$$782$$ −35.6945 −1.27643
$$783$$ −47.5260 −1.69844
$$784$$ 27.9041 0.996576
$$785$$ 0 0
$$786$$ −40.7222 −1.45251
$$787$$ 27.1159 0.966578 0.483289 0.875461i $$-0.339442\pi$$
0.483289 + 0.875461i $$0.339442\pi$$
$$788$$ −83.5531 −2.97646
$$789$$ 58.2615 2.07416
$$790$$ 0 0
$$791$$ 13.8181 0.491317
$$792$$ 57.1905 2.03218
$$793$$ 49.3708 1.75321
$$794$$ −70.8055 −2.51279
$$795$$ 0 0
$$796$$ 60.6586 2.14999
$$797$$ 27.3573 0.969044 0.484522 0.874779i $$-0.338994\pi$$
0.484522 + 0.874779i $$0.338994\pi$$
$$798$$ 0 0
$$799$$ 25.6122 0.906093
$$800$$ 0 0
$$801$$ 0.438283 0.0154860
$$802$$ −62.0820 −2.19219
$$803$$ −26.5325 −0.936311
$$804$$ −62.5251 −2.20509
$$805$$ 0 0
$$806$$ −31.8266 −1.12104
$$807$$ 20.7589 0.730748
$$808$$ −88.4564 −3.11188
$$809$$ −12.3922 −0.435686 −0.217843 0.975984i $$-0.569902\pi$$
−0.217843 + 0.975984i $$0.569902\pi$$
$$810$$ 0 0
$$811$$ 14.5389 0.510528 0.255264 0.966871i $$-0.417838\pi$$
0.255264 + 0.966871i $$0.417838\pi$$
$$812$$ −90.9407 −3.19139
$$813$$ 77.0683 2.70290
$$814$$ 20.3694 0.713948
$$815$$ 0 0
$$816$$ 32.9246 1.15259
$$817$$ 0 0
$$818$$ 48.2839 1.68821
$$819$$ −79.2176 −2.76809
$$820$$ 0 0
$$821$$ 6.47357 0.225929 0.112965 0.993599i $$-0.463965\pi$$
0.112965 + 0.993599i $$0.463965\pi$$
$$822$$ −58.2044 −2.03011
$$823$$ −0.210155 −0.00732553 −0.00366276 0.999993i $$-0.501166\pi$$
−0.00366276 + 0.999993i $$0.501166\pi$$
$$824$$ −1.79012 −0.0623619
$$825$$ 0 0
$$826$$ −47.8327 −1.66431
$$827$$ −23.1396 −0.804643 −0.402322 0.915498i $$-0.631797\pi$$
−0.402322 + 0.915498i $$0.631797\pi$$
$$828$$ 107.717 3.74342
$$829$$ 24.6843 0.857321 0.428660 0.903466i $$-0.358986\pi$$
0.428660 + 0.903466i $$0.358986\pi$$
$$830$$ 0 0
$$831$$ −8.45141 −0.293176
$$832$$ 31.5500 1.09380
$$833$$ 23.1052 0.800547
$$834$$ 125.906 4.35977
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −28.1338 −0.972448
$$838$$ −0.419685 −0.0144978
$$839$$ 31.2238 1.07797 0.538983 0.842317i $$-0.318809\pi$$
0.538983 + 0.842317i $$0.318809\pi$$
$$840$$ 0 0
$$841$$ 7.40738 0.255427
$$842$$ −42.4398 −1.46257
$$843$$ −66.0912 −2.27630
$$844$$ 82.3208 2.83360
$$845$$ 0 0
$$846$$ −116.473 −4.00443
$$847$$ −24.7723 −0.851187
$$848$$ 17.6379 0.605689
$$849$$ 13.7877 0.473194
$$850$$ 0 0
$$851$$ 18.9163 0.648443
$$852$$ 1.43425 0.0491364
$$853$$ −27.1366 −0.929140 −0.464570 0.885536i $$-0.653791\pi$$
−0.464570 + 0.885536i $$0.653791\pi$$
$$854$$ 125.844 4.30629
$$855$$ 0 0
$$856$$ −13.0975 −0.447664
$$857$$ 47.6457 1.62755 0.813773 0.581183i $$-0.197410\pi$$
0.813773 + 0.581183i $$0.197410\pi$$
$$858$$ −55.7661 −1.90382
$$859$$ −19.6361 −0.669974 −0.334987 0.942223i $$-0.608732\pi$$
−0.334987 + 0.942223i $$0.608732\pi$$
$$860$$ 0 0
$$861$$ 85.6177 2.91784
$$862$$ 12.3503 0.420654
$$863$$ −49.3684 −1.68052 −0.840260 0.542183i $$-0.817598\pi$$
−0.840260 + 0.542183i $$0.817598\pi$$
$$864$$ 4.15025 0.141194
$$865$$ 0 0
$$866$$ 30.5197 1.03710
$$867$$ −22.8066 −0.774554
$$868$$ −53.8339 −1.82724
$$869$$ −9.04600 −0.306865
$$870$$ 0 0
$$871$$ 19.6643 0.666299
$$872$$ −14.2437 −0.482351
$$873$$ −102.269 −3.46129
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 145.082 4.90188
$$877$$ 41.1968 1.39112 0.695559 0.718469i $$-0.255157\pi$$
0.695559 + 0.718469i $$0.255157\pi$$
$$878$$ 35.9845 1.21442
$$879$$ −9.60819 −0.324076
$$880$$ 0 0
$$881$$ −10.4510 −0.352103 −0.176052 0.984381i $$-0.556333\pi$$
−0.176052 + 0.984381i $$0.556333\pi$$
$$882$$ −105.072 −3.53797
$$883$$ 50.2957 1.69259 0.846293 0.532717i $$-0.178829\pi$$
0.846293 + 0.532717i $$0.178829\pi$$
$$884$$ −43.8639 −1.47530
$$885$$ 0 0
$$886$$ 13.0680 0.439027
$$887$$ −0.201711 −0.00677278 −0.00338639 0.999994i $$-0.501078\pi$$
−0.00338639 + 0.999994i $$0.501078\pi$$
$$888$$ −54.9178 −1.84292
$$889$$ 52.0272 1.74494
$$890$$ 0 0
$$891$$ −13.1222 −0.439609
$$892$$ −53.9545 −1.80653
$$893$$ 0 0
$$894$$ −137.846 −4.61027
$$895$$ 0 0
$$896$$ 76.3935 2.55213
$$897$$ −51.7879 −1.72915
$$898$$ 17.4597 0.582637
$$899$$ 21.5520 0.718798
$$900$$ 0 0
$$901$$ 14.6045 0.486548
$$902$$ 39.4268 1.31277
$$903$$ 63.0551 2.09834
$$904$$ −17.1558 −0.570595
$$905$$ 0 0
$$906$$ −80.0518 −2.65954
$$907$$ 6.11841 0.203158 0.101579 0.994827i $$-0.467610\pi$$
0.101579 + 0.994827i $$0.467610\pi$$
$$908$$ −14.6445 −0.485996
$$909$$ 105.826 3.51002
$$910$$ 0 0
$$911$$ 0.960234 0.0318140 0.0159070 0.999873i $$-0.494936\pi$$
0.0159070 + 0.999873i $$0.494936\pi$$
$$912$$ 0 0
$$913$$ 9.34435 0.309253
$$914$$ 78.9722 2.61217
$$915$$ 0 0
$$916$$ 44.6149 1.47412
$$917$$ 21.6631 0.715378
$$918$$ −58.4308 −1.92851
$$919$$ −51.3264 −1.69310 −0.846551 0.532307i $$-0.821325\pi$$
−0.846551 + 0.532307i $$0.821325\pi$$
$$920$$ 0 0
$$921$$ 5.05831 0.166677
$$922$$ 61.4750 2.02457
$$923$$ −0.451073 −0.0148473
$$924$$ −94.3270 −3.10313
$$925$$ 0 0
$$926$$ −99.6023 −3.27314
$$927$$ 2.14163 0.0703404
$$928$$ −3.17930 −0.104366
$$929$$ −46.0177 −1.50979 −0.754896 0.655844i $$-0.772313\pi$$
−0.754896 + 0.655844i $$0.772313\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 42.1165 1.37957
$$933$$ −2.62993 −0.0860999
$$934$$ 35.6500 1.16650
$$935$$ 0 0
$$936$$ 98.3522 3.21474
$$937$$ 3.79467 0.123966 0.0619832 0.998077i $$-0.480257\pi$$
0.0619832 + 0.998077i $$0.480257\pi$$
$$938$$ 50.1233 1.63658
$$939$$ −33.9754 −1.10875
$$940$$ 0 0
$$941$$ −23.1763 −0.755526 −0.377763 0.925902i $$-0.623307\pi$$
−0.377763 + 0.925902i $$0.623307\pi$$
$$942$$ 80.0371 2.60775
$$943$$ 36.6142 1.19232
$$944$$ 18.8682 0.614106
$$945$$ 0 0
$$946$$ 29.0367 0.944066
$$947$$ −18.3891 −0.597565 −0.298783 0.954321i $$-0.596581\pi$$
−0.298783 + 0.954321i $$0.596581\pi$$
$$948$$ 49.4644 1.60653
$$949$$ −45.6287 −1.48117
$$950$$ 0 0
$$951$$ −55.4427 −1.79785
$$952$$ −55.1273 −1.78669
$$953$$ 14.6072 0.473174 0.236587 0.971610i $$-0.423971\pi$$
0.236587 + 0.971610i $$0.423971\pi$$
$$954$$ −66.4151 −2.15027
$$955$$ 0 0
$$956$$ −68.1785 −2.20505
$$957$$ 37.7631 1.22071
$$958$$ −2.60760 −0.0842477
$$959$$ 30.9631 0.999852
$$960$$ 0 0
$$961$$ −18.2420 −0.588450
$$962$$ 35.0299 1.12941
$$963$$ 15.6694 0.504938
$$964$$ 69.0361 2.22350
$$965$$ 0 0
$$966$$ −132.005 −4.24719
$$967$$ −59.4737 −1.91254 −0.956272 0.292478i $$-0.905520\pi$$
−0.956272 + 0.292478i $$0.905520\pi$$
$$968$$ 30.7559 0.988533
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −22.3008 −0.715667 −0.357833 0.933785i $$-0.616484\pi$$
−0.357833 + 0.933785i $$0.616484\pi$$
$$972$$ −21.4712 −0.688689
$$973$$ −66.9785 −2.14723
$$974$$ −15.2467 −0.488535
$$975$$ 0 0
$$976$$ −49.6406 −1.58896
$$977$$ −15.2734 −0.488638 −0.244319 0.969695i $$-0.578564\pi$$
−0.244319 + 0.969695i $$0.578564\pi$$
$$978$$ −48.0191 −1.53548
$$979$$ −0.164132 −0.00524567
$$980$$ 0 0
$$981$$ 17.0406 0.544063
$$982$$ 1.98398 0.0633115
$$983$$ −41.4127 −1.32086 −0.660431 0.750887i $$-0.729626\pi$$
−0.660431 + 0.750887i $$0.729626\pi$$
$$984$$ −106.298 −3.38866
$$985$$ 0 0
$$986$$ 44.7610 1.42548
$$987$$ 94.7186 3.01493
$$988$$ 0 0
$$989$$ 26.9653 0.857447
$$990$$ 0 0
$$991$$ 18.9609 0.602314 0.301157 0.953575i $$-0.402627\pi$$
0.301157 + 0.953575i $$0.402627\pi$$
$$992$$ −1.88204 −0.0597549
$$993$$ −45.8805 −1.45597
$$994$$ −1.14976 −0.0364683
$$995$$ 0 0
$$996$$ −51.0958 −1.61903
$$997$$ 22.5133 0.713002 0.356501 0.934295i $$-0.383970\pi$$
0.356501 + 0.934295i $$0.383970\pi$$
$$998$$ −3.84361 −0.121668
$$999$$ 30.9655 0.979704
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.bh.1.1 4
5.4 even 2 1805.2.a.n.1.4 yes 4
19.18 odd 2 9025.2.a.bo.1.4 4
95.94 odd 2 1805.2.a.j.1.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.j.1.1 4 95.94 odd 2
1805.2.a.n.1.4 yes 4 5.4 even 2
9025.2.a.bh.1.1 4 1.1 even 1 trivial
9025.2.a.bo.1.4 4 19.18 odd 2