# Properties

 Label 7605.2.a.bx.1.1 Level $7605$ Weight $2$ Character 7605.1 Self dual yes Analytic conductor $60.726$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7605 = 3^{2} \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7605.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$60.7262307372$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.316.1 Defining polynomial: $$x^{3} - x^{2} - 4x + 2$$ x^3 - x^2 - 4*x + 2 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 195) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$2.34292$$ of defining polynomial Character $$\chi$$ $$=$$ 7605.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.48929 q^{2} +4.19656 q^{4} -1.00000 q^{5} +1.19656 q^{7} -5.46787 q^{8} +O(q^{10})$$ $$q-2.48929 q^{2} +4.19656 q^{4} -1.00000 q^{5} +1.19656 q^{7} -5.46787 q^{8} +2.48929 q^{10} -1.19656 q^{11} -2.97858 q^{14} +5.21798 q^{16} -6.17513 q^{17} -6.97858 q^{19} -4.19656 q^{20} +2.97858 q^{22} -4.17513 q^{23} +1.00000 q^{25} +5.02142 q^{28} -6.00000 q^{29} +2.97858 q^{31} -2.05333 q^{32} +15.3717 q^{34} -1.19656 q^{35} -7.78202 q^{37} +17.3717 q^{38} +5.46787 q^{40} -6.17513 q^{41} -9.95715 q^{43} -5.02142 q^{44} +10.3931 q^{46} -1.02142 q^{47} -5.56825 q^{49} -2.48929 q^{50} -10.1751 q^{53} +1.19656 q^{55} -6.54262 q^{56} +14.9357 q^{58} +5.37169 q^{59} +12.5682 q^{61} -7.41454 q^{62} -5.32464 q^{64} -9.37169 q^{67} -25.9143 q^{68} +2.97858 q^{70} -5.19656 q^{71} +11.9572 q^{73} +19.3717 q^{74} -29.2860 q^{76} -1.43175 q^{77} -1.78202 q^{79} -5.21798 q^{80} +15.3717 q^{82} -5.37169 q^{83} +6.17513 q^{85} +24.7862 q^{86} +6.54262 q^{88} +10.1751 q^{89} -17.5212 q^{92} +2.54262 q^{94} +6.97858 q^{95} +1.82487 q^{97} +13.8610 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 8 q^{4} - 3 q^{5} - q^{7} + 6 q^{8}+O(q^{10})$$ 3 * q + 8 * q^4 - 3 * q^5 - q^7 + 6 * q^8 $$3 q + 8 q^{4} - 3 q^{5} - q^{7} + 6 q^{8} + q^{11} + 6 q^{14} + 26 q^{16} + q^{17} - 6 q^{19} - 8 q^{20} - 6 q^{22} + 7 q^{23} + 3 q^{25} + 30 q^{28} - 18 q^{29} - 6 q^{31} + 22 q^{32} + 22 q^{34} + q^{35} - 13 q^{37} + 28 q^{38} - 6 q^{40} + q^{41} - 30 q^{44} + 22 q^{46} - 18 q^{47} + 12 q^{49} - 11 q^{53} - q^{55} + 16 q^{56} - 8 q^{59} + 9 q^{61} - 28 q^{62} + 30 q^{64} - 4 q^{67} - 18 q^{68} - 6 q^{70} - 11 q^{71} + 6 q^{73} + 34 q^{74} - 4 q^{76} - 33 q^{77} + 5 q^{79} - 26 q^{80} + 22 q^{82} + 8 q^{83} - q^{85} + 56 q^{86} - 16 q^{88} + 11 q^{89} - 2 q^{92} - 28 q^{94} + 6 q^{95} + 25 q^{97} + 10 q^{98}+O(q^{100})$$ 3 * q + 8 * q^4 - 3 * q^5 - q^7 + 6 * q^8 + q^11 + 6 * q^14 + 26 * q^16 + q^17 - 6 * q^19 - 8 * q^20 - 6 * q^22 + 7 * q^23 + 3 * q^25 + 30 * q^28 - 18 * q^29 - 6 * q^31 + 22 * q^32 + 22 * q^34 + q^35 - 13 * q^37 + 28 * q^38 - 6 * q^40 + q^41 - 30 * q^44 + 22 * q^46 - 18 * q^47 + 12 * q^49 - 11 * q^53 - q^55 + 16 * q^56 - 8 * q^59 + 9 * q^61 - 28 * q^62 + 30 * q^64 - 4 * q^67 - 18 * q^68 - 6 * q^70 - 11 * q^71 + 6 * q^73 + 34 * q^74 - 4 * q^76 - 33 * q^77 + 5 * q^79 - 26 * q^80 + 22 * q^82 + 8 * q^83 - q^85 + 56 * q^86 - 16 * q^88 + 11 * q^89 - 2 * q^92 - 28 * q^94 + 6 * q^95 + 25 * q^97 + 10 * q^98

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.48929 −1.76019 −0.880096 0.474795i $$-0.842522\pi$$
−0.880096 + 0.474795i $$0.842522\pi$$
$$3$$ 0 0
$$4$$ 4.19656 2.09828
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 1.19656 0.452256 0.226128 0.974098i $$-0.427393\pi$$
0.226128 + 0.974098i $$0.427393\pi$$
$$8$$ −5.46787 −1.93318
$$9$$ 0 0
$$10$$ 2.48929 0.787182
$$11$$ −1.19656 −0.360776 −0.180388 0.983596i $$-0.557735\pi$$
−0.180388 + 0.983596i $$0.557735\pi$$
$$12$$ 0 0
$$13$$ 0 0
$$14$$ −2.97858 −0.796058
$$15$$ 0 0
$$16$$ 5.21798 1.30450
$$17$$ −6.17513 −1.49769 −0.748845 0.662745i $$-0.769391\pi$$
−0.748845 + 0.662745i $$0.769391\pi$$
$$18$$ 0 0
$$19$$ −6.97858 −1.60100 −0.800498 0.599336i $$-0.795431\pi$$
−0.800498 + 0.599336i $$0.795431\pi$$
$$20$$ −4.19656 −0.938379
$$21$$ 0 0
$$22$$ 2.97858 0.635035
$$23$$ −4.17513 −0.870576 −0.435288 0.900291i $$-0.643353\pi$$
−0.435288 + 0.900291i $$0.643353\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 5.02142 0.948960
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 2.97858 0.534968 0.267484 0.963562i $$-0.413808\pi$$
0.267484 + 0.963562i $$0.413808\pi$$
$$32$$ −2.05333 −0.362980
$$33$$ 0 0
$$34$$ 15.3717 2.63622
$$35$$ −1.19656 −0.202255
$$36$$ 0 0
$$37$$ −7.78202 −1.27936 −0.639678 0.768643i $$-0.720932\pi$$
−0.639678 + 0.768643i $$0.720932\pi$$
$$38$$ 17.3717 2.81806
$$39$$ 0 0
$$40$$ 5.46787 0.864545
$$41$$ −6.17513 −0.964394 −0.482197 0.876063i $$-0.660161\pi$$
−0.482197 + 0.876063i $$0.660161\pi$$
$$42$$ 0 0
$$43$$ −9.95715 −1.51845 −0.759226 0.650827i $$-0.774422\pi$$
−0.759226 + 0.650827i $$0.774422\pi$$
$$44$$ −5.02142 −0.757008
$$45$$ 0 0
$$46$$ 10.3931 1.53238
$$47$$ −1.02142 −0.148990 −0.0744949 0.997221i $$-0.523734\pi$$
−0.0744949 + 0.997221i $$0.523734\pi$$
$$48$$ 0 0
$$49$$ −5.56825 −0.795464
$$50$$ −2.48929 −0.352039
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −10.1751 −1.39766 −0.698831 0.715287i $$-0.746296\pi$$
−0.698831 + 0.715287i $$0.746296\pi$$
$$54$$ 0 0
$$55$$ 1.19656 0.161344
$$56$$ −6.54262 −0.874294
$$57$$ 0 0
$$58$$ 14.9357 1.96116
$$59$$ 5.37169 0.699335 0.349667 0.936874i $$-0.386295\pi$$
0.349667 + 0.936874i $$0.386295\pi$$
$$60$$ 0 0
$$61$$ 12.5682 1.60920 0.804600 0.593818i $$-0.202380\pi$$
0.804600 + 0.593818i $$0.202380\pi$$
$$62$$ −7.41454 −0.941647
$$63$$ 0 0
$$64$$ −5.32464 −0.665579
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −9.37169 −1.14493 −0.572467 0.819928i $$-0.694014\pi$$
−0.572467 + 0.819928i $$0.694014\pi$$
$$68$$ −25.9143 −3.14257
$$69$$ 0 0
$$70$$ 2.97858 0.356008
$$71$$ −5.19656 −0.616718 −0.308359 0.951270i $$-0.599780\pi$$
−0.308359 + 0.951270i $$0.599780\pi$$
$$72$$ 0 0
$$73$$ 11.9572 1.39948 0.699740 0.714398i $$-0.253299\pi$$
0.699740 + 0.714398i $$0.253299\pi$$
$$74$$ 19.3717 2.25191
$$75$$ 0 0
$$76$$ −29.2860 −3.35933
$$77$$ −1.43175 −0.163163
$$78$$ 0 0
$$79$$ −1.78202 −0.200493 −0.100246 0.994963i $$-0.531963\pi$$
−0.100246 + 0.994963i $$0.531963\pi$$
$$80$$ −5.21798 −0.583388
$$81$$ 0 0
$$82$$ 15.3717 1.69752
$$83$$ −5.37169 −0.589620 −0.294810 0.955556i $$-0.595256\pi$$
−0.294810 + 0.955556i $$0.595256\pi$$
$$84$$ 0 0
$$85$$ 6.17513 0.669787
$$86$$ 24.7862 2.67277
$$87$$ 0 0
$$88$$ 6.54262 0.697445
$$89$$ 10.1751 1.07856 0.539281 0.842126i $$-0.318696\pi$$
0.539281 + 0.842126i $$0.318696\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −17.5212 −1.82671
$$93$$ 0 0
$$94$$ 2.54262 0.262251
$$95$$ 6.97858 0.715987
$$96$$ 0 0
$$97$$ 1.82487 0.185287 0.0926435 0.995699i $$-0.470468\pi$$
0.0926435 + 0.995699i $$0.470468\pi$$
$$98$$ 13.8610 1.40017
$$99$$ 0 0
$$100$$ 4.19656 0.419656
$$101$$ 10.3503 1.02989 0.514945 0.857223i $$-0.327812\pi$$
0.514945 + 0.857223i $$0.327812\pi$$
$$102$$ 0 0
$$103$$ 18.7434 1.84684 0.923420 0.383790i $$-0.125381\pi$$
0.923420 + 0.383790i $$0.125381\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 25.3288 2.46016
$$107$$ 18.5682 1.79506 0.897530 0.440953i $$-0.145359\pi$$
0.897530 + 0.440953i $$0.145359\pi$$
$$108$$ 0 0
$$109$$ −8.39312 −0.803915 −0.401957 0.915658i $$-0.631670\pi$$
−0.401957 + 0.915658i $$0.631670\pi$$
$$110$$ −2.97858 −0.283996
$$111$$ 0 0
$$112$$ 6.24361 0.589966
$$113$$ −7.95715 −0.748546 −0.374273 0.927319i $$-0.622108\pi$$
−0.374273 + 0.927319i $$0.622108\pi$$
$$114$$ 0 0
$$115$$ 4.17513 0.389333
$$116$$ −25.1793 −2.33784
$$117$$ 0 0
$$118$$ −13.3717 −1.23096
$$119$$ −7.38890 −0.677340
$$120$$ 0 0
$$121$$ −9.56825 −0.869841
$$122$$ −31.2860 −2.83250
$$123$$ 0 0
$$124$$ 12.4998 1.12251
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −10.3931 −0.922240 −0.461120 0.887338i $$-0.652552\pi$$
−0.461120 + 0.887338i $$0.652552\pi$$
$$128$$ 17.3612 1.53453
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 6.39312 0.558569 0.279285 0.960208i $$-0.409903\pi$$
0.279285 + 0.960208i $$0.409903\pi$$
$$132$$ 0 0
$$133$$ −8.35027 −0.724060
$$134$$ 23.3288 2.01531
$$135$$ 0 0
$$136$$ 33.7648 2.89531
$$137$$ 16.7434 1.43048 0.715242 0.698877i $$-0.246316\pi$$
0.715242 + 0.698877i $$0.246316\pi$$
$$138$$ 0 0
$$139$$ 5.78202 0.490424 0.245212 0.969469i $$-0.421142\pi$$
0.245212 + 0.969469i $$0.421142\pi$$
$$140$$ −5.02142 −0.424388
$$141$$ 0 0
$$142$$ 12.9357 1.08554
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 6.00000 0.498273
$$146$$ −29.7648 −2.46335
$$147$$ 0 0
$$148$$ −32.6577 −2.68445
$$149$$ 15.3461 1.25720 0.628599 0.777730i $$-0.283629\pi$$
0.628599 + 0.777730i $$0.283629\pi$$
$$150$$ 0 0
$$151$$ 8.58546 0.698675 0.349337 0.936997i $$-0.386407\pi$$
0.349337 + 0.936997i $$0.386407\pi$$
$$152$$ 38.1579 3.09502
$$153$$ 0 0
$$154$$ 3.56404 0.287198
$$155$$ −2.97858 −0.239245
$$156$$ 0 0
$$157$$ 2.78623 0.222365 0.111183 0.993800i $$-0.464536\pi$$
0.111183 + 0.993800i $$0.464536\pi$$
$$158$$ 4.43596 0.352906
$$159$$ 0 0
$$160$$ 2.05333 0.162330
$$161$$ −4.99579 −0.393723
$$162$$ 0 0
$$163$$ −8.76060 −0.686183 −0.343091 0.939302i $$-0.611474\pi$$
−0.343091 + 0.939302i $$0.611474\pi$$
$$164$$ −25.9143 −2.02357
$$165$$ 0 0
$$166$$ 13.3717 1.03784
$$167$$ −17.3717 −1.34426 −0.672131 0.740432i $$-0.734621\pi$$
−0.672131 + 0.740432i $$0.734621\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ −15.3717 −1.17895
$$171$$ 0 0
$$172$$ −41.7858 −3.18614
$$173$$ 7.95715 0.604971 0.302486 0.953154i $$-0.402184\pi$$
0.302486 + 0.953154i $$0.402184\pi$$
$$174$$ 0 0
$$175$$ 1.19656 0.0904513
$$176$$ −6.24361 −0.470630
$$177$$ 0 0
$$178$$ −25.3288 −1.89848
$$179$$ 15.5640 1.16331 0.581655 0.813435i $$-0.302405\pi$$
0.581655 + 0.813435i $$0.302405\pi$$
$$180$$ 0 0
$$181$$ 15.7820 1.17307 0.586534 0.809925i $$-0.300492\pi$$
0.586534 + 0.809925i $$0.300492\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 22.8291 1.68298
$$185$$ 7.78202 0.572145
$$186$$ 0 0
$$187$$ 7.38890 0.540330
$$188$$ −4.28646 −0.312622
$$189$$ 0 0
$$190$$ −17.3717 −1.26028
$$191$$ −10.7434 −0.777364 −0.388682 0.921372i $$-0.627070\pi$$
−0.388682 + 0.921372i $$0.627070\pi$$
$$192$$ 0 0
$$193$$ −9.73917 −0.701041 −0.350521 0.936555i $$-0.613995\pi$$
−0.350521 + 0.936555i $$0.613995\pi$$
$$194$$ −4.54262 −0.326141
$$195$$ 0 0
$$196$$ −23.3675 −1.66911
$$197$$ −9.56404 −0.681410 −0.340705 0.940170i $$-0.610666\pi$$
−0.340705 + 0.940170i $$0.610666\pi$$
$$198$$ 0 0
$$199$$ 5.95715 0.422291 0.211146 0.977455i $$-0.432281\pi$$
0.211146 + 0.977455i $$0.432281\pi$$
$$200$$ −5.46787 −0.386636
$$201$$ 0 0
$$202$$ −25.7648 −1.81281
$$203$$ −7.17935 −0.503891
$$204$$ 0 0
$$205$$ 6.17513 0.431290
$$206$$ −46.6577 −3.25080
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 8.35027 0.577600
$$210$$ 0 0
$$211$$ 23.9143 1.64633 0.823164 0.567803i $$-0.192206\pi$$
0.823164 + 0.567803i $$0.192206\pi$$
$$212$$ −42.7005 −2.93269
$$213$$ 0 0
$$214$$ −46.2217 −3.15965
$$215$$ 9.95715 0.679072
$$216$$ 0 0
$$217$$ 3.56404 0.241943
$$218$$ 20.8929 1.41504
$$219$$ 0 0
$$220$$ 5.02142 0.338544
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −2.62831 −0.176004 −0.0880022 0.996120i $$-0.528048\pi$$
−0.0880022 + 0.996120i $$0.528048\pi$$
$$224$$ −2.45692 −0.164160
$$225$$ 0 0
$$226$$ 19.8077 1.31759
$$227$$ 15.7648 1.04635 0.523174 0.852226i $$-0.324748\pi$$
0.523174 + 0.852226i $$0.324748\pi$$
$$228$$ 0 0
$$229$$ −8.74338 −0.577779 −0.288890 0.957362i $$-0.593286\pi$$
−0.288890 + 0.957362i $$0.593286\pi$$
$$230$$ −10.3931 −0.685302
$$231$$ 0 0
$$232$$ 32.8072 2.15390
$$233$$ 2.17513 0.142498 0.0712489 0.997459i $$-0.477302\pi$$
0.0712489 + 0.997459i $$0.477302\pi$$
$$234$$ 0 0
$$235$$ 1.02142 0.0666303
$$236$$ 22.5426 1.46740
$$237$$ 0 0
$$238$$ 18.3931 1.19225
$$239$$ 2.80344 0.181340 0.0906698 0.995881i $$-0.471099\pi$$
0.0906698 + 0.995881i $$0.471099\pi$$
$$240$$ 0 0
$$241$$ 6.00000 0.386494 0.193247 0.981150i $$-0.438098\pi$$
0.193247 + 0.981150i $$0.438098\pi$$
$$242$$ 23.8181 1.53109
$$243$$ 0 0
$$244$$ 52.7434 3.37655
$$245$$ 5.56825 0.355742
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −16.2865 −1.03419
$$249$$ 0 0
$$250$$ 2.48929 0.157436
$$251$$ 23.9143 1.50946 0.754729 0.656037i $$-0.227768\pi$$
0.754729 + 0.656037i $$0.227768\pi$$
$$252$$ 0 0
$$253$$ 4.99579 0.314083
$$254$$ 25.8715 1.62332
$$255$$ 0 0
$$256$$ −32.5678 −2.03549
$$257$$ 19.9572 1.24489 0.622447 0.782662i $$-0.286139\pi$$
0.622447 + 0.782662i $$0.286139\pi$$
$$258$$ 0 0
$$259$$ −9.31163 −0.578597
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −15.9143 −0.983189
$$263$$ −8.00000 −0.493301 −0.246651 0.969104i $$-0.579330\pi$$
−0.246651 + 0.969104i $$0.579330\pi$$
$$264$$ 0 0
$$265$$ 10.1751 0.625054
$$266$$ 20.7862 1.27449
$$267$$ 0 0
$$268$$ −39.3288 −2.40239
$$269$$ 2.35027 0.143298 0.0716492 0.997430i $$-0.477174\pi$$
0.0716492 + 0.997430i $$0.477174\pi$$
$$270$$ 0 0
$$271$$ −10.9786 −0.666901 −0.333451 0.942768i $$-0.608213\pi$$
−0.333451 + 0.942768i $$0.608213\pi$$
$$272$$ −32.2217 −1.95373
$$273$$ 0 0
$$274$$ −41.6791 −2.51793
$$275$$ −1.19656 −0.0721551
$$276$$ 0 0
$$277$$ 1.21377 0.0729283 0.0364642 0.999335i $$-0.488391\pi$$
0.0364642 + 0.999335i $$0.488391\pi$$
$$278$$ −14.3931 −0.863242
$$279$$ 0 0
$$280$$ 6.54262 0.390996
$$281$$ 11.9572 0.713304 0.356652 0.934237i $$-0.383918\pi$$
0.356652 + 0.934237i $$0.383918\pi$$
$$282$$ 0 0
$$283$$ −29.8715 −1.77567 −0.887837 0.460158i $$-0.847793\pi$$
−0.887837 + 0.460158i $$0.847793\pi$$
$$284$$ −21.8077 −1.29405
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −7.38890 −0.436153
$$288$$ 0 0
$$289$$ 21.1323 1.24308
$$290$$ −14.9357 −0.877056
$$291$$ 0 0
$$292$$ 50.1789 2.93650
$$293$$ 0.777809 0.0454401 0.0227200 0.999742i $$-0.492767\pi$$
0.0227200 + 0.999742i $$0.492767\pi$$
$$294$$ 0 0
$$295$$ −5.37169 −0.312752
$$296$$ 42.5510 2.47323
$$297$$ 0 0
$$298$$ −38.2008 −2.21291
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −11.9143 −0.686729
$$302$$ −21.3717 −1.22980
$$303$$ 0 0
$$304$$ −36.4141 −2.08849
$$305$$ −12.5682 −0.719656
$$306$$ 0 0
$$307$$ −0.760597 −0.0434095 −0.0217048 0.999764i $$-0.506909\pi$$
−0.0217048 + 0.999764i $$0.506909\pi$$
$$308$$ −6.00842 −0.342362
$$309$$ 0 0
$$310$$ 7.41454 0.421117
$$311$$ 23.1281 1.31147 0.655736 0.754990i $$-0.272358\pi$$
0.655736 + 0.754990i $$0.272358\pi$$
$$312$$ 0 0
$$313$$ −33.9143 −1.91695 −0.958475 0.285176i $$-0.907948\pi$$
−0.958475 + 0.285176i $$0.907948\pi$$
$$314$$ −6.93573 −0.391406
$$315$$ 0 0
$$316$$ −7.47835 −0.420690
$$317$$ 9.64973 0.541983 0.270991 0.962582i $$-0.412648\pi$$
0.270991 + 0.962582i $$0.412648\pi$$
$$318$$ 0 0
$$319$$ 7.17935 0.401966
$$320$$ 5.32464 0.297656
$$321$$ 0 0
$$322$$ 12.4360 0.693029
$$323$$ 43.0937 2.39780
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 21.8077 1.20781
$$327$$ 0 0
$$328$$ 33.7648 1.86435
$$329$$ −1.22219 −0.0673816
$$330$$ 0 0
$$331$$ −15.3288 −0.842550 −0.421275 0.906933i $$-0.638417\pi$$
−0.421275 + 0.906933i $$0.638417\pi$$
$$332$$ −22.5426 −1.23719
$$333$$ 0 0
$$334$$ 43.2432 2.36616
$$335$$ 9.37169 0.512030
$$336$$ 0 0
$$337$$ −22.3503 −1.21750 −0.608748 0.793363i $$-0.708328\pi$$
−0.608748 + 0.793363i $$0.708328\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 25.9143 1.40540
$$341$$ −3.56404 −0.193004
$$342$$ 0 0
$$343$$ −15.0386 −0.812010
$$344$$ 54.4444 2.93544
$$345$$ 0 0
$$346$$ −19.8077 −1.06487
$$347$$ 5.78202 0.310395 0.155198 0.987883i $$-0.450399\pi$$
0.155198 + 0.987883i $$0.450399\pi$$
$$348$$ 0 0
$$349$$ 27.5212 1.47318 0.736588 0.676342i $$-0.236436\pi$$
0.736588 + 0.676342i $$0.236436\pi$$
$$350$$ −2.97858 −0.159212
$$351$$ 0 0
$$352$$ 2.45692 0.130955
$$353$$ −28.7434 −1.52986 −0.764928 0.644116i $$-0.777225\pi$$
−0.764928 + 0.644116i $$0.777225\pi$$
$$354$$ 0 0
$$355$$ 5.19656 0.275805
$$356$$ 42.7005 2.26312
$$357$$ 0 0
$$358$$ −38.7434 −2.04765
$$359$$ −12.5855 −0.664235 −0.332118 0.943238i $$-0.607763\pi$$
−0.332118 + 0.943238i $$0.607763\pi$$
$$360$$ 0 0
$$361$$ 29.7005 1.56319
$$362$$ −39.2860 −2.06483
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −11.9572 −0.625866
$$366$$ 0 0
$$367$$ −27.9143 −1.45712 −0.728558 0.684985i $$-0.759809\pi$$
−0.728558 + 0.684985i $$0.759809\pi$$
$$368$$ −21.7858 −1.13566
$$369$$ 0 0
$$370$$ −19.3717 −1.00709
$$371$$ −12.1751 −0.632102
$$372$$ 0 0
$$373$$ −2.35027 −0.121692 −0.0608462 0.998147i $$-0.519380\pi$$
−0.0608462 + 0.998147i $$0.519380\pi$$
$$374$$ −18.3931 −0.951085
$$375$$ 0 0
$$376$$ 5.58500 0.288025
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −24.5510 −1.26110 −0.630551 0.776148i $$-0.717171\pi$$
−0.630551 + 0.776148i $$0.717171\pi$$
$$380$$ 29.2860 1.50234
$$381$$ 0 0
$$382$$ 26.7434 1.36831
$$383$$ 5.80765 0.296757 0.148379 0.988931i $$-0.452595\pi$$
0.148379 + 0.988931i $$0.452595\pi$$
$$384$$ 0 0
$$385$$ 1.43175 0.0729687
$$386$$ 24.2436 1.23397
$$387$$ 0 0
$$388$$ 7.65815 0.388784
$$389$$ −13.6497 −0.692069 −0.346034 0.938222i $$-0.612472\pi$$
−0.346034 + 0.938222i $$0.612472\pi$$
$$390$$ 0 0
$$391$$ 25.7820 1.30385
$$392$$ 30.4464 1.53778
$$393$$ 0 0
$$394$$ 23.8077 1.19941
$$395$$ 1.78202 0.0896631
$$396$$ 0 0
$$397$$ 12.1323 0.608902 0.304451 0.952528i $$-0.401527\pi$$
0.304451 + 0.952528i $$0.401527\pi$$
$$398$$ −14.8291 −0.743314
$$399$$ 0 0
$$400$$ 5.21798 0.260899
$$401$$ −37.4439 −1.86986 −0.934930 0.354832i $$-0.884538\pi$$
−0.934930 + 0.354832i $$0.884538\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 43.4355 2.16100
$$405$$ 0 0
$$406$$ 17.8715 0.886946
$$407$$ 9.31163 0.461561
$$408$$ 0 0
$$409$$ 14.0000 0.692255 0.346128 0.938187i $$-0.387496\pi$$
0.346128 + 0.938187i $$0.387496\pi$$
$$410$$ −15.3717 −0.759154
$$411$$ 0 0
$$412$$ 78.6577 3.87519
$$413$$ 6.42754 0.316279
$$414$$ 0 0
$$415$$ 5.37169 0.263686
$$416$$ 0 0
$$417$$ 0 0
$$418$$ −20.7862 −1.01669
$$419$$ −3.17935 −0.155321 −0.0776606 0.996980i $$-0.524745\pi$$
−0.0776606 + 0.996980i $$0.524745\pi$$
$$420$$ 0 0
$$421$$ 16.3074 0.794775 0.397388 0.917651i $$-0.369917\pi$$
0.397388 + 0.917651i $$0.369917\pi$$
$$422$$ −59.5296 −2.89786
$$423$$ 0 0
$$424$$ 55.6363 2.70194
$$425$$ −6.17513 −0.299538
$$426$$ 0 0
$$427$$ 15.0386 0.727771
$$428$$ 77.9227 3.76654
$$429$$ 0 0
$$430$$ −24.7862 −1.19530
$$431$$ 4.58546 0.220874 0.110437 0.993883i $$-0.464775\pi$$
0.110437 + 0.993883i $$0.464775\pi$$
$$432$$ 0 0
$$433$$ −38.3503 −1.84300 −0.921498 0.388383i $$-0.873034\pi$$
−0.921498 + 0.388383i $$0.873034\pi$$
$$434$$ −8.87192 −0.425866
$$435$$ 0 0
$$436$$ −35.2222 −1.68684
$$437$$ 29.1365 1.39379
$$438$$ 0 0
$$439$$ 7.73917 0.369371 0.184685 0.982798i $$-0.440873\pi$$
0.184685 + 0.982798i $$0.440873\pi$$
$$440$$ −6.54262 −0.311907
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −34.9185 −1.65903 −0.829514 0.558485i $$-0.811383\pi$$
−0.829514 + 0.558485i $$0.811383\pi$$
$$444$$ 0 0
$$445$$ −10.1751 −0.482348
$$446$$ 6.54262 0.309802
$$447$$ 0 0
$$448$$ −6.37123 −0.301012
$$449$$ −6.17513 −0.291423 −0.145711 0.989327i $$-0.546547\pi$$
−0.145711 + 0.989327i $$0.546547\pi$$
$$450$$ 0 0
$$451$$ 7.38890 0.347930
$$452$$ −33.3927 −1.57066
$$453$$ 0 0
$$454$$ −39.2432 −1.84177
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.38890 −0.0649702 −0.0324851 0.999472i $$-0.510342\pi$$
−0.0324851 + 0.999472i $$0.510342\pi$$
$$458$$ 21.7648 1.01700
$$459$$ 0 0
$$460$$ 17.5212 0.816930
$$461$$ 28.4826 1.32657 0.663283 0.748369i $$-0.269163\pi$$
0.663283 + 0.748369i $$0.269163\pi$$
$$462$$ 0 0
$$463$$ −16.3759 −0.761053 −0.380526 0.924770i $$-0.624257\pi$$
−0.380526 + 0.924770i $$0.624257\pi$$
$$464$$ −31.3079 −1.45343
$$465$$ 0 0
$$466$$ −5.41454 −0.250824
$$467$$ −25.7476 −1.19146 −0.595728 0.803186i $$-0.703136\pi$$
−0.595728 + 0.803186i $$0.703136\pi$$
$$468$$ 0 0
$$469$$ −11.2138 −0.517804
$$470$$ −2.54262 −0.117282
$$471$$ 0 0
$$472$$ −29.3717 −1.35194
$$473$$ 11.9143 0.547820
$$474$$ 0 0
$$475$$ −6.97858 −0.320199
$$476$$ −31.0080 −1.42125
$$477$$ 0 0
$$478$$ −6.97858 −0.319193
$$479$$ −7.58967 −0.346781 −0.173391 0.984853i $$-0.555472\pi$$
−0.173391 + 0.984853i $$0.555472\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −14.9357 −0.680304
$$483$$ 0 0
$$484$$ −40.1537 −1.82517
$$485$$ −1.82487 −0.0828629
$$486$$ 0 0
$$487$$ −4.41033 −0.199851 −0.0999255 0.994995i $$-0.531860\pi$$
−0.0999255 + 0.994995i $$0.531860\pi$$
$$488$$ −68.7215 −3.11088
$$489$$ 0 0
$$490$$ −13.8610 −0.626175
$$491$$ 0.0856914 0.00386720 0.00193360 0.999998i $$-0.499385\pi$$
0.00193360 + 0.999998i $$0.499385\pi$$
$$492$$ 0 0
$$493$$ 37.0508 1.66868
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 15.5422 0.697863
$$497$$ −6.21798 −0.278915
$$498$$ 0 0
$$499$$ 17.7220 0.793344 0.396672 0.917960i $$-0.370165\pi$$
0.396672 + 0.917960i $$0.370165\pi$$
$$500$$ −4.19656 −0.187676
$$501$$ 0 0
$$502$$ −59.5296 −2.65694
$$503$$ 8.70054 0.387938 0.193969 0.981008i $$-0.437864\pi$$
0.193969 + 0.981008i $$0.437864\pi$$
$$504$$ 0 0
$$505$$ −10.3503 −0.460581
$$506$$ −12.4360 −0.552846
$$507$$ 0 0
$$508$$ −43.6153 −1.93512
$$509$$ −33.3545 −1.47841 −0.739206 0.673480i $$-0.764799\pi$$
−0.739206 + 0.673480i $$0.764799\pi$$
$$510$$ 0 0
$$511$$ 14.3074 0.632923
$$512$$ 46.3482 2.04832
$$513$$ 0 0
$$514$$ −49.6791 −2.19125
$$515$$ −18.7434 −0.825932
$$516$$ 0 0
$$517$$ 1.22219 0.0537519
$$518$$ 23.1793 1.01844
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −18.7005 −0.819285 −0.409643 0.912246i $$-0.634347\pi$$
−0.409643 + 0.912246i $$0.634347\pi$$
$$522$$ 0 0
$$523$$ −4.00000 −0.174908 −0.0874539 0.996169i $$-0.527873\pi$$
−0.0874539 + 0.996169i $$0.527873\pi$$
$$524$$ 26.8291 1.17203
$$525$$ 0 0
$$526$$ 19.9143 0.868305
$$527$$ −18.3931 −0.801217
$$528$$ 0 0
$$529$$ −5.56825 −0.242098
$$530$$ −25.3288 −1.10021
$$531$$ 0 0
$$532$$ −35.0424 −1.51928
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −18.5682 −0.802775
$$536$$ 51.2432 2.21337
$$537$$ 0 0
$$538$$ −5.85050 −0.252233
$$539$$ 6.66273 0.286984
$$540$$ 0 0
$$541$$ 41.5296 1.78550 0.892749 0.450555i $$-0.148774\pi$$
0.892749 + 0.450555i $$0.148774\pi$$
$$542$$ 27.3288 1.17387
$$543$$ 0 0
$$544$$ 12.6796 0.543632
$$545$$ 8.39312 0.359522
$$546$$ 0 0
$$547$$ −7.91431 −0.338391 −0.169196 0.985582i $$-0.554117\pi$$
−0.169196 + 0.985582i $$0.554117\pi$$
$$548$$ 70.2646 3.00155
$$549$$ 0 0
$$550$$ 2.97858 0.127007
$$551$$ 41.8715 1.78378
$$552$$ 0 0
$$553$$ −2.13229 −0.0906742
$$554$$ −3.02142 −0.128368
$$555$$ 0 0
$$556$$ 24.2646 1.02905
$$557$$ 42.7005 1.80928 0.904640 0.426177i $$-0.140140\pi$$
0.904640 + 0.426177i $$0.140140\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −6.24361 −0.263841
$$561$$ 0 0
$$562$$ −29.7648 −1.25555
$$563$$ −1.04706 −0.0441282 −0.0220641 0.999757i $$-0.507024\pi$$
−0.0220641 + 0.999757i $$0.507024\pi$$
$$564$$ 0 0
$$565$$ 7.95715 0.334760
$$566$$ 74.3587 3.12553
$$567$$ 0 0
$$568$$ 28.4141 1.19223
$$569$$ −16.7778 −0.703362 −0.351681 0.936120i $$-0.614390\pi$$
−0.351681 + 0.936120i $$0.614390\pi$$
$$570$$ 0 0
$$571$$ −20.6111 −0.862548 −0.431274 0.902221i $$-0.641936\pi$$
−0.431274 + 0.902221i $$0.641936\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 18.3931 0.767714
$$575$$ −4.17513 −0.174115
$$576$$ 0 0
$$577$$ −1.38890 −0.0578208 −0.0289104 0.999582i $$-0.509204\pi$$
−0.0289104 + 0.999582i $$0.509204\pi$$
$$578$$ −52.6044 −2.18805
$$579$$ 0 0
$$580$$ 25.1793 1.04552
$$581$$ −6.42754 −0.266659
$$582$$ 0 0
$$583$$ 12.1751 0.504243
$$584$$ −65.3801 −2.70545
$$585$$ 0 0
$$586$$ −1.93619 −0.0799833
$$587$$ −0.935731 −0.0386218 −0.0193109 0.999814i $$-0.506147\pi$$
−0.0193109 + 0.999814i $$0.506147\pi$$
$$588$$ 0 0
$$589$$ −20.7862 −0.856482
$$590$$ 13.3717 0.550504
$$591$$ 0 0
$$592$$ −40.6064 −1.66891
$$593$$ −0.478807 −0.0196622 −0.00983112 0.999952i $$-0.503129\pi$$
−0.00983112 + 0.999952i $$0.503129\pi$$
$$594$$ 0 0
$$595$$ 7.38890 0.302916
$$596$$ 64.4006 2.63795
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −29.0852 −1.18839 −0.594195 0.804321i $$-0.702529\pi$$
−0.594195 + 0.804321i $$0.702529\pi$$
$$600$$ 0 0
$$601$$ 11.4318 0.466311 0.233155 0.972439i $$-0.425095\pi$$
0.233155 + 0.972439i $$0.425095\pi$$
$$602$$ 29.6582 1.20878
$$603$$ 0 0
$$604$$ 36.0294 1.46601
$$605$$ 9.56825 0.389005
$$606$$ 0 0
$$607$$ 27.9143 1.13301 0.566503 0.824059i $$-0.308296\pi$$
0.566503 + 0.824059i $$0.308296\pi$$
$$608$$ 14.3293 0.581130
$$609$$ 0 0
$$610$$ 31.2860 1.26673
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 4.65394 0.187971 0.0939855 0.995574i $$-0.470039\pi$$
0.0939855 + 0.995574i $$0.470039\pi$$
$$614$$ 1.89334 0.0764092
$$615$$ 0 0
$$616$$ 7.82862 0.315424
$$617$$ −15.9572 −0.642411 −0.321205 0.947010i $$-0.604088\pi$$
−0.321205 + 0.947010i $$0.604088\pi$$
$$618$$ 0 0
$$619$$ −1.02142 −0.0410545 −0.0205272 0.999789i $$-0.506534\pi$$
−0.0205272 + 0.999789i $$0.506534\pi$$
$$620$$ −12.4998 −0.502003
$$621$$ 0 0
$$622$$ −57.5725 −2.30845
$$623$$ 12.1751 0.487786
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 84.4225 3.37420
$$627$$ 0 0
$$628$$ 11.6926 0.466585
$$629$$ 48.0550 1.91608
$$630$$ 0 0
$$631$$ 20.4998 0.816083 0.408041 0.912963i $$-0.366212\pi$$
0.408041 + 0.912963i $$0.366212\pi$$
$$632$$ 9.74384 0.387589
$$633$$ 0 0
$$634$$ −24.0210 −0.953994
$$635$$ 10.3931 0.412438
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −17.8715 −0.707538
$$639$$ 0 0
$$640$$ −17.3612 −0.686262
$$641$$ −38.2646 −1.51136 −0.755680 0.654941i $$-0.772693\pi$$
−0.755680 + 0.654941i $$0.772693\pi$$
$$642$$ 0 0
$$643$$ 33.1109 1.30577 0.652883 0.757459i $$-0.273560\pi$$
0.652883 + 0.757459i $$0.273560\pi$$
$$644$$ −20.9651 −0.826141
$$645$$ 0 0
$$646$$ −107.273 −4.22058
$$647$$ 16.9614 0.666820 0.333410 0.942782i $$-0.391801\pi$$
0.333410 + 0.942782i $$0.391801\pi$$
$$648$$ 0 0
$$649$$ −6.42754 −0.252303
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −36.7643 −1.43980
$$653$$ 19.1709 0.750216 0.375108 0.926981i $$-0.377606\pi$$
0.375108 + 0.926981i $$0.377606\pi$$
$$654$$ 0 0
$$655$$ −6.39312 −0.249800
$$656$$ −32.2217 −1.25805
$$657$$ 0 0
$$658$$ 3.04239 0.118605
$$659$$ −37.8715 −1.47526 −0.737631 0.675204i $$-0.764056\pi$$
−0.737631 + 0.675204i $$0.764056\pi$$
$$660$$ 0 0
$$661$$ −24.3931 −0.948782 −0.474391 0.880314i $$-0.657332\pi$$
−0.474391 + 0.880314i $$0.657332\pi$$
$$662$$ 38.1579 1.48305
$$663$$ 0 0
$$664$$ 29.3717 1.13984
$$665$$ 8.35027 0.323810
$$666$$ 0 0
$$667$$ 25.0508 0.969971
$$668$$ −72.9013 −2.82064
$$669$$ 0 0
$$670$$ −23.3288 −0.901272
$$671$$ −15.0386 −0.580560
$$672$$ 0 0
$$673$$ −21.1281 −0.814428 −0.407214 0.913333i $$-0.633500\pi$$
−0.407214 + 0.913333i $$0.633500\pi$$
$$674$$ 55.6363 2.14303
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 15.3973 0.591767 0.295884 0.955224i $$-0.404386\pi$$
0.295884 + 0.955224i $$0.404386\pi$$
$$678$$ 0 0
$$679$$ 2.18356 0.0837972
$$680$$ −33.7648 −1.29482
$$681$$ 0 0
$$682$$ 8.87192 0.339723
$$683$$ 30.0722 1.15068 0.575341 0.817914i $$-0.304869\pi$$
0.575341 + 0.817914i $$0.304869\pi$$
$$684$$ 0 0
$$685$$ −16.7434 −0.639732
$$686$$ 37.4355 1.42929
$$687$$ 0 0
$$688$$ −51.9562 −1.98081
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 8.14950 0.310022 0.155011 0.987913i $$-0.450459\pi$$
0.155011 + 0.987913i $$0.450459\pi$$
$$692$$ 33.3927 1.26940
$$693$$ 0 0
$$694$$ −14.3931 −0.546355
$$695$$ −5.78202 −0.219325
$$696$$ 0 0
$$697$$ 38.1323 1.44436
$$698$$ −68.5082 −2.59307
$$699$$ 0 0
$$700$$ 5.02142 0.189792
$$701$$ 28.6921 1.08369 0.541843 0.840480i $$-0.317727\pi$$
0.541843 + 0.840480i $$0.317727\pi$$
$$702$$ 0 0
$$703$$ 54.3074 2.04824
$$704$$ 6.37123 0.240125
$$705$$ 0 0
$$706$$ 71.5506 2.69284
$$707$$ 12.3847 0.465774
$$708$$ 0 0
$$709$$ −12.3074 −0.462215 −0.231108 0.972928i $$-0.574235\pi$$
−0.231108 + 0.972928i $$0.574235\pi$$
$$710$$ −12.9357 −0.485469
$$711$$ 0 0
$$712$$ −55.6363 −2.08506
$$713$$ −12.4360 −0.465730
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 65.3154 2.44095
$$717$$ 0 0
$$718$$ 31.3288 1.16918
$$719$$ 28.7862 1.07355 0.536773 0.843727i $$-0.319643\pi$$
0.536773 + 0.843727i $$0.319643\pi$$
$$720$$ 0 0
$$721$$ 22.4275 0.835245
$$722$$ −73.9332 −2.75151
$$723$$ 0 0
$$724$$ 66.2302 2.46142
$$725$$ −6.00000 −0.222834
$$726$$ 0 0
$$727$$ 34.3931 1.27557 0.637785 0.770214i $$-0.279851\pi$$
0.637785 + 0.770214i $$0.279851\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 29.7648 1.10164
$$731$$ 61.4868 2.27417
$$732$$ 0 0
$$733$$ 29.0042 1.07129 0.535647 0.844442i $$-0.320068\pi$$
0.535647 + 0.844442i $$0.320068\pi$$
$$734$$ 69.4868 2.56480
$$735$$ 0 0
$$736$$ 8.57292 0.316002
$$737$$ 11.2138 0.413065
$$738$$ 0 0
$$739$$ 6.27804 0.230941 0.115471 0.993311i $$-0.463162\pi$$
0.115471 + 0.993311i $$0.463162\pi$$
$$740$$ 32.6577 1.20052
$$741$$ 0 0
$$742$$ 30.3074 1.11262
$$743$$ 12.2352 0.448866 0.224433 0.974490i $$-0.427947\pi$$
0.224433 + 0.974490i $$0.427947\pi$$
$$744$$ 0 0
$$745$$ −15.3461 −0.562236
$$746$$ 5.85050 0.214202
$$747$$ 0 0
$$748$$ 31.0080 1.13376
$$749$$ 22.2180 0.811827
$$750$$ 0 0
$$751$$ −28.8757 −1.05369 −0.526844 0.849962i $$-0.676625\pi$$
−0.526844 + 0.849962i $$0.676625\pi$$
$$752$$ −5.32976 −0.194357
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −8.58546 −0.312457
$$756$$ 0 0
$$757$$ 30.3503 1.10310 0.551550 0.834142i $$-0.314037\pi$$
0.551550 + 0.834142i $$0.314037\pi$$
$$758$$ 61.1146 2.21978
$$759$$ 0 0
$$760$$ −38.1579 −1.38413
$$761$$ −27.1709 −0.984945 −0.492473 0.870328i $$-0.663907\pi$$
−0.492473 + 0.870328i $$0.663907\pi$$
$$762$$ 0 0
$$763$$ −10.0428 −0.363575
$$764$$ −45.0852 −1.63113
$$765$$ 0 0
$$766$$ −14.4569 −0.522350
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 38.3503 1.38295 0.691473 0.722402i $$-0.256962\pi$$
0.691473 + 0.722402i $$0.256962\pi$$
$$770$$ −3.56404 −0.128439
$$771$$ 0 0
$$772$$ −40.8710 −1.47098
$$773$$ −50.2646 −1.80789 −0.903946 0.427647i $$-0.859342\pi$$
−0.903946 + 0.427647i $$0.859342\pi$$
$$774$$ 0 0
$$775$$ 2.97858 0.106994
$$776$$ −9.97812 −0.358194
$$777$$ 0 0
$$778$$ 33.9781 1.21817
$$779$$ 43.0937 1.54399
$$780$$ 0 0
$$781$$ 6.21798 0.222497
$$782$$ −64.1789 −2.29503
$$783$$ 0 0
$$784$$ −29.0550 −1.03768
$$785$$ −2.78623 −0.0994448
$$786$$ 0 0
$$787$$ 13.2860 0.473595 0.236797 0.971559i $$-0.423902\pi$$
0.236797 + 0.971559i $$0.423902\pi$$
$$788$$ −40.1360 −1.42979
$$789$$ 0 0
$$790$$ −4.43596 −0.157824
$$791$$ −9.52119 −0.338535
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −30.2008 −1.07179
$$795$$ 0 0
$$796$$ 24.9995 0.886085
$$797$$ −9.82487 −0.348015 −0.174007 0.984744i $$-0.555672\pi$$
−0.174007 + 0.984744i $$0.555672\pi$$
$$798$$ 0 0
$$799$$ 6.30742 0.223141
$$800$$ −2.05333 −0.0725961
$$801$$ 0 0
$$802$$ 93.2087 3.29131
$$803$$ −14.3074 −0.504898
$$804$$ 0 0
$$805$$ 4.99579 0.176078
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −56.5939 −1.99097
$$809$$ 9.91431 0.348569 0.174284 0.984695i $$-0.444239\pi$$
0.174284 + 0.984695i $$0.444239\pi$$
$$810$$ 0 0
$$811$$ 36.5855 1.28469 0.642345 0.766416i $$-0.277962\pi$$
0.642345 + 0.766416i $$0.277962\pi$$
$$812$$ −30.1285 −1.05730
$$813$$ 0 0
$$814$$ −23.1793 −0.812436
$$815$$ 8.76060 0.306870
$$816$$ 0 0
$$817$$ 69.4868 2.43103
$$818$$ −34.8500 −1.21850
$$819$$ 0 0
$$820$$ 25.9143 0.904967
$$821$$ −34.4741 −1.20316 −0.601578 0.798814i $$-0.705461\pi$$
−0.601578 + 0.798814i $$0.705461\pi$$
$$822$$ 0 0
$$823$$ 13.2566 0.462097 0.231048 0.972942i $$-0.425784\pi$$
0.231048 + 0.972942i $$0.425784\pi$$
$$824$$ −102.486 −3.57028
$$825$$ 0 0
$$826$$ −16.0000 −0.556711
$$827$$ 28.1495 0.978854 0.489427 0.872044i $$-0.337206\pi$$
0.489427 + 0.872044i $$0.337206\pi$$
$$828$$ 0 0
$$829$$ 16.3418 0.567576 0.283788 0.958887i $$-0.408409\pi$$
0.283788 + 0.958887i $$0.408409\pi$$
$$830$$ −13.3717 −0.464138
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 34.3847 1.19136
$$834$$ 0 0
$$835$$ 17.3717 0.601172
$$836$$ 35.0424 1.21197
$$837$$ 0 0
$$838$$ 7.91431 0.273395
$$839$$ −30.3675 −1.04840 −0.524201 0.851595i $$-0.675636\pi$$
−0.524201 + 0.851595i $$0.675636\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ −40.5939 −1.39896
$$843$$ 0 0
$$844$$ 100.358 3.45446
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −11.4490 −0.393391
$$848$$ −53.0937 −1.82324
$$849$$ 0 0
$$850$$ 15.3717 0.527245
$$851$$ 32.4910 1.11378
$$852$$ 0 0
$$853$$ 42.1407 1.44287 0.721435 0.692482i $$-0.243483\pi$$
0.721435 + 0.692482i $$0.243483\pi$$
$$854$$ −37.4355 −1.28102
$$855$$ 0 0
$$856$$ −101.529 −3.47018
$$857$$ 2.17513 0.0743012 0.0371506 0.999310i $$-0.488172\pi$$
0.0371506 + 0.999310i $$0.488172\pi$$
$$858$$ 0 0
$$859$$ 18.5682 0.633541 0.316770 0.948502i $$-0.397402\pi$$
0.316770 + 0.948502i $$0.397402\pi$$
$$860$$ 41.7858 1.42488
$$861$$ 0 0
$$862$$ −11.4145 −0.388781
$$863$$ 33.7220 1.14791 0.573954 0.818887i $$-0.305409\pi$$
0.573954 + 0.818887i $$0.305409\pi$$
$$864$$ 0 0
$$865$$ −7.95715 −0.270551
$$866$$ 95.4649 3.24403
$$867$$ 0 0
$$868$$ 14.9567 0.507663
$$869$$ 2.13229 0.0723330
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 45.8924 1.55411
$$873$$ 0 0
$$874$$ −72.5292 −2.45334
$$875$$ −1.19656 −0.0404510
$$876$$ 0 0
$$877$$ −43.4868 −1.46844 −0.734222 0.678910i $$-0.762453\pi$$
−0.734222 + 0.678910i $$0.762453\pi$$
$$878$$ −19.2650 −0.650164
$$879$$ 0 0
$$880$$ 6.24361 0.210472
$$881$$ −26.7005 −0.899564 −0.449782 0.893138i $$-0.648498\pi$$
−0.449782 + 0.893138i $$0.648498\pi$$
$$882$$ 0 0
$$883$$ 20.2990 0.683116 0.341558 0.939861i $$-0.389045\pi$$
0.341558 + 0.939861i $$0.389045\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 86.9223 2.92021
$$887$$ −36.0550 −1.21061 −0.605305 0.795994i $$-0.706949\pi$$
−0.605305 + 0.795994i $$0.706949\pi$$
$$888$$ 0 0
$$889$$ −12.4360 −0.417089
$$890$$ 25.3288 0.849025
$$891$$ 0 0
$$892$$ −11.0298 −0.369307
$$893$$ 7.12808 0.238532
$$894$$ 0 0
$$895$$ −15.5640 −0.520248
$$896$$ 20.7737 0.694000
$$897$$ 0 0
$$898$$ 15.3717 0.512960
$$899$$ −17.8715 −0.596047
$$900$$ 0 0
$$901$$ 62.8328 2.09326
$$902$$ −18.3931 −0.612424
$$903$$ 0 0
$$904$$ 43.5087 1.44708
$$905$$ −15.7820 −0.524612
$$906$$ 0 0
$$907$$ −7.26504 −0.241232 −0.120616 0.992699i $$-0.538487\pi$$
−0.120616 + 0.992699i $$0.538487\pi$$
$$908$$ 66.1579 2.19553
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 6.65769 0.220579 0.110290 0.993899i $$-0.464822\pi$$
0.110290 + 0.993899i $$0.464822\pi$$
$$912$$ 0 0
$$913$$ 6.42754 0.212721
$$914$$ 3.45738 0.114360
$$915$$ 0 0
$$916$$ −36.6921 −1.21234
$$917$$ 7.64973 0.252616
$$918$$ 0 0
$$919$$ −27.1831 −0.896688 −0.448344 0.893861i $$-0.647986\pi$$
−0.448344 + 0.893861i $$0.647986\pi$$
$$920$$ −22.8291 −0.752652
$$921$$ 0 0
$$922$$ −70.9013 −2.33501
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −7.78202 −0.255871
$$926$$ 40.7643 1.33960
$$927$$ 0 0
$$928$$ 12.3200 0.404423
$$929$$ −15.3973 −0.505170 −0.252585 0.967575i $$-0.581281\pi$$
−0.252585 + 0.967575i $$0.581281\pi$$
$$930$$ 0 0
$$931$$ 38.8585 1.27353
$$932$$ 9.12808 0.299000
$$933$$ 0 0
$$934$$ 64.0932 2.09719
$$935$$ −7.38890 −0.241643
$$936$$ 0 0
$$937$$ 1.12808 0.0368527 0.0184264 0.999830i $$-0.494134\pi$$
0.0184264 + 0.999830i $$0.494134\pi$$
$$938$$ 27.9143 0.911434
$$939$$ 0 0
$$940$$ 4.28646 0.139809
$$941$$ −30.1407 −0.982559 −0.491280 0.871002i $$-0.663471\pi$$
−0.491280 + 0.871002i $$0.663471\pi$$
$$942$$ 0 0
$$943$$ 25.7820 0.839578
$$944$$ 28.0294 0.912279
$$945$$ 0 0
$$946$$ −29.6582 −0.964270
$$947$$ −20.0294 −0.650868 −0.325434 0.945565i $$-0.605510\pi$$
−0.325434 + 0.945565i $$0.605510\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 17.3717 0.563612
$$951$$ 0 0
$$952$$ 40.4015 1.30942
$$953$$ 43.2259 1.40023 0.700113 0.714032i $$-0.253133\pi$$
0.700113 + 0.714032i $$0.253133\pi$$
$$954$$ 0 0
$$955$$ 10.7434 0.347648
$$956$$ 11.7648 0.380501
$$957$$ 0 0
$$958$$ 18.8929 0.610401
$$959$$ 20.0344 0.646945
$$960$$ 0 0
$$961$$ −22.1281 −0.713809
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 25.1793 0.810972
$$965$$ 9.73917 0.313515
$$966$$ 0 0
$$967$$ −57.6875 −1.85511 −0.927553 0.373691i $$-0.878092\pi$$
−0.927553 + 0.373691i $$0.878092\pi$$
$$968$$ 52.3179 1.68156
$$969$$ 0 0
$$970$$ 4.54262 0.145855
$$971$$ 19.5296 0.626735 0.313368 0.949632i $$-0.398543\pi$$
0.313368 + 0.949632i $$0.398543\pi$$
$$972$$ 0 0
$$973$$ 6.91852 0.221798
$$974$$ 10.9786 0.351776
$$975$$ 0 0
$$976$$ 65.5809 2.09919
$$977$$ −40.3074 −1.28955 −0.644774 0.764373i $$-0.723049\pi$$
−0.644774 + 0.764373i $$0.723049\pi$$
$$978$$ 0 0
$$979$$ −12.1751 −0.389119
$$980$$ 23.3675 0.746447
$$981$$ 0 0
$$982$$ −0.213311 −0.00680702
$$983$$ 32.2008 1.02705 0.513523 0.858076i $$-0.328340\pi$$
0.513523 + 0.858076i $$0.328340\pi$$
$$984$$ 0 0
$$985$$ 9.56404 0.304736
$$986$$ −92.2302 −2.93721
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 41.5725 1.32193
$$990$$ 0 0
$$991$$ 26.4826 0.841246 0.420623 0.907235i $$-0.361811\pi$$
0.420623 + 0.907235i $$0.361811\pi$$
$$992$$ −6.11599 −0.194183
$$993$$ 0 0
$$994$$ 15.4783 0.490943
$$995$$ −5.95715 −0.188854
$$996$$ 0 0
$$997$$ 35.1365 1.11278 0.556392 0.830920i $$-0.312185\pi$$
0.556392 + 0.830920i $$0.312185\pi$$
$$998$$ −44.1151 −1.39644
$$999$$ 0 0
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 7605.2.a.bx.1.1 3
3.2 odd 2 2535.2.a.bc.1.3 3
13.12 even 2 585.2.a.n.1.3 3
39.38 odd 2 195.2.a.e.1.1 3
52.51 odd 2 9360.2.a.dd.1.2 3
65.12 odd 4 2925.2.c.w.2224.5 6
65.38 odd 4 2925.2.c.w.2224.2 6
65.64 even 2 2925.2.a.bh.1.1 3
156.155 even 2 3120.2.a.bj.1.2 3
195.38 even 4 975.2.c.i.274.5 6
195.77 even 4 975.2.c.i.274.2 6
195.194 odd 2 975.2.a.o.1.3 3
273.272 even 2 9555.2.a.bq.1.1 3

By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.e.1.1 3 39.38 odd 2
585.2.a.n.1.3 3 13.12 even 2
975.2.a.o.1.3 3 195.194 odd 2
975.2.c.i.274.2 6 195.77 even 4
975.2.c.i.274.5 6 195.38 even 4
2535.2.a.bc.1.3 3 3.2 odd 2
2925.2.a.bh.1.1 3 65.64 even 2
2925.2.c.w.2224.2 6 65.38 odd 4
2925.2.c.w.2224.5 6 65.12 odd 4
3120.2.a.bj.1.2 3 156.155 even 2
7605.2.a.bx.1.1 3 1.1 even 1 trivial
9360.2.a.dd.1.2 3 52.51 odd 2
9555.2.a.bq.1.1 3 273.272 even 2