# Properties

 Label 280.3.c.c.69.1 Level $280$ Weight $3$ Character 280.69 Self dual yes Analytic conductor $7.629$ Analytic rank $0$ Dimension $1$ CM discriminant -280 Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 280.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: yes Analytic conductor: $$7.62944740209$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 69.1 Character $$\chi$$ $$=$$ 280.69

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +14.0000 q^{14} +16.0000 q^{16} -6.00000 q^{17} +18.0000 q^{18} +18.0000 q^{19} -20.0000 q^{20} +25.0000 q^{25} +28.0000 q^{28} +32.0000 q^{32} -12.0000 q^{34} -35.0000 q^{35} +36.0000 q^{36} -66.0000 q^{37} +36.0000 q^{38} -40.0000 q^{40} -54.0000 q^{43} -45.0000 q^{45} -66.0000 q^{47} +49.0000 q^{49} +50.0000 q^{50} -34.0000 q^{53} +56.0000 q^{56} -62.0000 q^{59} +102.000 q^{61} +63.0000 q^{63} +64.0000 q^{64} -6.00000 q^{67} -24.0000 q^{68} -70.0000 q^{70} -138.000 q^{71} +72.0000 q^{72} +106.000 q^{73} -132.000 q^{74} +72.0000 q^{76} -122.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +30.0000 q^{85} -108.000 q^{86} -90.0000 q^{90} -132.000 q^{94} -90.0000 q^{95} -166.000 q^{97} +98.0000 q^{98} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$$.

 $$n$$ $$57$$ $$71$$ $$141$$ $$241$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 1.00000
$$3$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 4.00000 1.00000
$$5$$ −5.00000 −1.00000
$$6$$ 0 0
$$7$$ 7.00000 1.00000
$$8$$ 8.00000 1.00000
$$9$$ 9.00000 1.00000
$$10$$ −10.0000 −1.00000
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 14.0000 1.00000
$$15$$ 0 0
$$16$$ 16.0000 1.00000
$$17$$ −6.00000 −0.352941 −0.176471 0.984306i $$-0.556468\pi$$
−0.176471 + 0.984306i $$0.556468\pi$$
$$18$$ 18.0000 1.00000
$$19$$ 18.0000 0.947368 0.473684 0.880695i $$-0.342924\pi$$
0.473684 + 0.880695i $$0.342924\pi$$
$$20$$ −20.0000 −1.00000
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 25.0000 1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 28.0000 1.00000
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 32.0000 1.00000
$$33$$ 0 0
$$34$$ −12.0000 −0.352941
$$35$$ −35.0000 −1.00000
$$36$$ 36.0000 1.00000
$$37$$ −66.0000 −1.78378 −0.891892 0.452249i $$-0.850622\pi$$
−0.891892 + 0.452249i $$0.850622\pi$$
$$38$$ 36.0000 0.947368
$$39$$ 0 0
$$40$$ −40.0000 −1.00000
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ −54.0000 −1.25581 −0.627907 0.778288i $$-0.716088\pi$$
−0.627907 + 0.778288i $$0.716088\pi$$
$$44$$ 0 0
$$45$$ −45.0000 −1.00000
$$46$$ 0 0
$$47$$ −66.0000 −1.40426 −0.702128 0.712051i $$-0.747766\pi$$
−0.702128 + 0.712051i $$0.747766\pi$$
$$48$$ 0 0
$$49$$ 49.0000 1.00000
$$50$$ 50.0000 1.00000
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −34.0000 −0.641509 −0.320755 0.947162i $$-0.603937\pi$$
−0.320755 + 0.947162i $$0.603937\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 56.0000 1.00000
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −62.0000 −1.05085 −0.525424 0.850841i $$-0.676093\pi$$
−0.525424 + 0.850841i $$0.676093\pi$$
$$60$$ 0 0
$$61$$ 102.000 1.67213 0.836066 0.548630i $$-0.184850\pi$$
0.836066 + 0.548630i $$0.184850\pi$$
$$62$$ 0 0
$$63$$ 63.0000 1.00000
$$64$$ 64.0000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.00000 −0.0895522 −0.0447761 0.998997i $$-0.514257\pi$$
−0.0447761 + 0.998997i $$0.514257\pi$$
$$68$$ −24.0000 −0.352941
$$69$$ 0 0
$$70$$ −70.0000 −1.00000
$$71$$ −138.000 −1.94366 −0.971831 0.235679i $$-0.924269\pi$$
−0.971831 + 0.235679i $$0.924269\pi$$
$$72$$ 72.0000 1.00000
$$73$$ 106.000 1.45205 0.726027 0.687666i $$-0.241365\pi$$
0.726027 + 0.687666i $$0.241365\pi$$
$$74$$ −132.000 −1.78378
$$75$$ 0 0
$$76$$ 72.0000 0.947368
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −122.000 −1.54430 −0.772152 0.635438i $$-0.780820\pi$$
−0.772152 + 0.635438i $$0.780820\pi$$
$$80$$ −80.0000 −1.00000
$$81$$ 81.0000 1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 30.0000 0.352941
$$86$$ −108.000 −1.25581
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ −90.0000 −1.00000
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −132.000 −1.40426
$$95$$ −90.0000 −0.947368
$$96$$ 0 0
$$97$$ −166.000 −1.71134 −0.855670 0.517522i $$-0.826855\pi$$
−0.855670 + 0.517522i $$0.826855\pi$$
$$98$$ 98.0000 1.00000
$$99$$ 0 0
$$100$$ 100.000 1.00000
$$101$$ 22.0000 0.217822 0.108911 0.994052i $$-0.465264\pi$$
0.108911 + 0.994052i $$0.465264\pi$$
$$102$$ 0 0
$$103$$ 46.0000 0.446602 0.223301 0.974750i $$-0.428317\pi$$
0.223301 + 0.974750i $$0.428317\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −68.0000 −0.641509
$$107$$ 74.0000 0.691589 0.345794 0.938310i $$-0.387609\pi$$
0.345794 + 0.938310i $$0.387609\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 112.000 1.00000
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −124.000 −1.05085
$$119$$ −42.0000 −0.352941
$$120$$ 0 0
$$121$$ 121.000 1.00000
$$122$$ 204.000 1.67213
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −125.000 −1.00000
$$126$$ 126.000 1.00000
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 128.000 1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 242.000 1.84733 0.923664 0.383203i $$-0.125179\pi$$
0.923664 + 0.383203i $$0.125179\pi$$
$$132$$ 0 0
$$133$$ 126.000 0.947368
$$134$$ −12.0000 −0.0895522
$$135$$ 0 0
$$136$$ −48.0000 −0.352941
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ −222.000 −1.59712 −0.798561 0.601914i $$-0.794405\pi$$
−0.798561 + 0.601914i $$0.794405\pi$$
$$140$$ −140.000 −1.00000
$$141$$ 0 0
$$142$$ −276.000 −1.94366
$$143$$ 0 0
$$144$$ 144.000 1.00000
$$145$$ 0 0
$$146$$ 212.000 1.45205
$$147$$ 0 0
$$148$$ −264.000 −1.78378
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 22.0000 0.145695 0.0728477 0.997343i $$-0.476791\pi$$
0.0728477 + 0.997343i $$0.476791\pi$$
$$152$$ 144.000 0.947368
$$153$$ −54.0000 −0.352941
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ −244.000 −1.54430
$$159$$ 0 0
$$160$$ −160.000 −1.00000
$$161$$ 0 0
$$162$$ 162.000 1.00000
$$163$$ 186.000 1.14110 0.570552 0.821261i $$-0.306729\pi$$
0.570552 + 0.821261i $$0.306729\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −306.000 −1.83234 −0.916168 0.400795i $$-0.868734\pi$$
−0.916168 + 0.400795i $$0.868734\pi$$
$$168$$ 0 0
$$169$$ 169.000 1.00000
$$170$$ 60.0000 0.352941
$$171$$ 162.000 0.947368
$$172$$ −216.000 −1.25581
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 175.000 1.00000
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ −180.000 −1.00000
$$181$$ −138.000 −0.762431 −0.381215 0.924486i $$-0.624494\pi$$
−0.381215 + 0.924486i $$0.624494\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 330.000 1.78378
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −264.000 −1.40426
$$189$$ 0 0
$$190$$ −180.000 −0.947368
$$191$$ 102.000 0.534031 0.267016 0.963692i $$-0.413962\pi$$
0.267016 + 0.963692i $$0.413962\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ −332.000 −1.71134
$$195$$ 0 0
$$196$$ 196.000 1.00000
$$197$$ 254.000 1.28934 0.644670 0.764461i $$-0.276995\pi$$
0.644670 + 0.764461i $$0.276995\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 200.000 1.00000
$$201$$ 0 0
$$202$$ 44.0000 0.217822
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 92.0000 0.446602
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ −136.000 −0.641509
$$213$$ 0 0
$$214$$ 148.000 0.691589
$$215$$ 270.000 1.25581
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −194.000 −0.869955 −0.434978 0.900441i $$-0.643244\pi$$
−0.434978 + 0.900441i $$0.643244\pi$$
$$224$$ 224.000 1.00000
$$225$$ 225.000 1.00000
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 438.000 1.91266 0.956332 0.292283i $$-0.0944149\pi$$
0.956332 + 0.292283i $$0.0944149\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 330.000 1.40426
$$236$$ −248.000 −1.05085
$$237$$ 0 0
$$238$$ −84.0000 −0.352941
$$239$$ 198.000 0.828452 0.414226 0.910174i $$-0.364052\pi$$
0.414226 + 0.910174i $$0.364052\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 242.000 1.00000
$$243$$ 0 0
$$244$$ 408.000 1.67213
$$245$$ −245.000 −1.00000
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −250.000 −1.00000
$$251$$ 2.00000 0.00796813 0.00398406 0.999992i $$-0.498732\pi$$
0.00398406 + 0.999992i $$0.498732\pi$$
$$252$$ 252.000 1.00000
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 256.000 1.00000
$$257$$ −486.000 −1.89105 −0.945525 0.325549i $$-0.894451\pi$$
−0.945525 + 0.325549i $$0.894451\pi$$
$$258$$ 0 0
$$259$$ −462.000 −1.78378
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 484.000 1.84733
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 170.000 0.641509
$$266$$ 252.000 0.947368
$$267$$ 0 0
$$268$$ −24.0000 −0.0895522
$$269$$ 358.000 1.33086 0.665428 0.746462i $$-0.268249\pi$$
0.665428 + 0.746462i $$0.268249\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −96.0000 −0.352941
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 414.000 1.49458 0.747292 0.664495i $$-0.231353\pi$$
0.747292 + 0.664495i $$0.231353\pi$$
$$278$$ −444.000 −1.59712
$$279$$ 0 0
$$280$$ −280.000 −1.00000
$$281$$ −558.000 −1.98577 −0.992883 0.119098i $$-0.962000\pi$$
−0.992883 + 0.119098i $$0.962000\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ −552.000 −1.94366
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 288.000 1.00000
$$289$$ −253.000 −0.875433
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 424.000 1.45205
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 310.000 1.05085
$$296$$ −528.000 −1.78378
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −378.000 −1.25581
$$302$$ 44.0000 0.145695
$$303$$ 0 0
$$304$$ 288.000 0.947368
$$305$$ −510.000 −1.67213
$$306$$ −108.000 −0.352941
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ −374.000 −1.19489 −0.597444 0.801911i $$-0.703817\pi$$
−0.597444 + 0.801911i $$0.703817\pi$$
$$314$$ 0 0
$$315$$ −315.000 −1.00000
$$316$$ −488.000 −1.54430
$$317$$ −626.000 −1.97476 −0.987382 0.158358i $$-0.949380\pi$$
−0.987382 + 0.158358i $$0.949380\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −320.000 −1.00000
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −108.000 −0.334365
$$324$$ 324.000 1.00000
$$325$$ 0 0
$$326$$ 372.000 1.14110
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −462.000 −1.40426
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ −594.000 −1.78378
$$334$$ −612.000 −1.83234
$$335$$ 30.0000 0.0895522
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 338.000 1.00000
$$339$$ 0 0
$$340$$ 120.000 0.352941
$$341$$ 0 0
$$342$$ 324.000 0.947368
$$343$$ 343.000 1.00000
$$344$$ −432.000 −1.25581
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −566.000 −1.63112 −0.815562 0.578670i $$-0.803572\pi$$
−0.815562 + 0.578670i $$0.803572\pi$$
$$348$$ 0 0
$$349$$ 198.000 0.567335 0.283668 0.958923i $$-0.408449\pi$$
0.283668 + 0.958923i $$0.408449\pi$$
$$350$$ 350.000 1.00000
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 666.000 1.88669 0.943343 0.331820i $$-0.107663\pi$$
0.943343 + 0.331820i $$0.107663\pi$$
$$354$$ 0 0
$$355$$ 690.000 1.94366
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 438.000 1.22006 0.610028 0.792380i $$-0.291158\pi$$
0.610028 + 0.792380i $$0.291158\pi$$
$$360$$ −360.000 −1.00000
$$361$$ −37.0000 −0.102493
$$362$$ −276.000 −0.762431
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −530.000 −1.45205
$$366$$ 0 0
$$367$$ −706.000 −1.92371 −0.961853 0.273567i $$-0.911796\pi$$
−0.961853 + 0.273567i $$0.911796\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 660.000 1.78378
$$371$$ −238.000 −0.641509
$$372$$ 0 0
$$373$$ 606.000 1.62466 0.812332 0.583195i $$-0.198198\pi$$
0.812332 + 0.583195i $$0.198198\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −528.000 −1.40426
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ −360.000 −0.947368
$$381$$ 0 0
$$382$$ 204.000 0.534031
$$383$$ 606.000 1.58225 0.791123 0.611657i $$-0.209497\pi$$
0.791123 + 0.611657i $$0.209497\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −486.000 −1.25581
$$388$$ −664.000 −1.71134
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 392.000 1.00000
$$393$$ 0 0
$$394$$ 508.000 1.28934
$$395$$ 610.000 1.54430
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 400.000 1.00000
$$401$$ −318.000 −0.793017 −0.396509 0.918031i $$-0.629778\pi$$
−0.396509 + 0.918031i $$0.629778\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 88.0000 0.217822
$$405$$ −405.000 −1.00000
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 184.000 0.446602
$$413$$ −434.000 −1.05085
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −782.000 −1.86635 −0.933174 0.359424i $$-0.882973\pi$$
−0.933174 + 0.359424i $$0.882973\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ −594.000 −1.40426
$$424$$ −272.000 −0.641509
$$425$$ −150.000 −0.352941
$$426$$ 0 0
$$427$$ 714.000 1.67213
$$428$$ 296.000 0.691589
$$429$$ 0 0
$$430$$ 540.000 1.25581
$$431$$ 582.000 1.35035 0.675174 0.737658i $$-0.264069\pi$$
0.675174 + 0.737658i $$0.264069\pi$$
$$432$$ 0 0
$$433$$ 506.000 1.16859 0.584296 0.811541i $$-0.301371\pi$$
0.584296 + 0.811541i $$0.301371\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 441.000 1.00000
$$442$$ 0 0
$$443$$ −374.000 −0.844244 −0.422122 0.906539i $$-0.638715\pi$$
−0.422122 + 0.906539i $$0.638715\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −388.000 −0.869955
$$447$$ 0 0
$$448$$ 448.000 1.00000
$$449$$ −222.000 −0.494432 −0.247216 0.968960i $$-0.579516\pi$$
−0.247216 + 0.968960i $$0.579516\pi$$
$$450$$ 450.000 1.00000
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 876.000 1.91266
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −698.000 −1.51410 −0.757050 0.653357i $$-0.773360\pi$$
−0.757050 + 0.653357i $$0.773360\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ −42.0000 −0.0895522
$$470$$ 660.000 1.40426
$$471$$ 0 0
$$472$$ −496.000 −1.05085
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 450.000 0.947368
$$476$$ −168.000 −0.352941
$$477$$ −306.000 −0.641509
$$478$$ 396.000 0.828452
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 484.000 1.00000
$$485$$ 830.000 1.71134
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 816.000 1.67213
$$489$$ 0 0
$$490$$ −490.000 −1.00000
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −966.000 −1.94366
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ −500.000 −1.00000
$$501$$ 0 0
$$502$$ 4.00000 0.00796813
$$503$$ 366.000 0.727634 0.363817 0.931470i $$-0.381473\pi$$
0.363817 + 0.931470i $$0.381473\pi$$
$$504$$ 504.000 1.00000
$$505$$ −110.000 −0.217822
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 998.000 1.96071 0.980354 0.197248i $$-0.0632004\pi$$
0.980354 + 0.197248i $$0.0632004\pi$$
$$510$$ 0 0
$$511$$ 742.000 1.45205
$$512$$ 512.000 1.00000
$$513$$ 0 0
$$514$$ −972.000 −1.89105
$$515$$ −230.000 −0.446602
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −924.000 −1.78378
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 968.000 1.84733
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 529.000 1.00000
$$530$$ 340.000 0.641509
$$531$$ −558.000 −1.05085
$$532$$ 504.000 0.947368
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −370.000 −0.691589
$$536$$ −48.0000 −0.0895522
$$537$$ 0 0
$$538$$ 716.000 1.33086
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −192.000 −0.352941
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 954.000 1.74406 0.872029 0.489454i $$-0.162804\pi$$
0.872029 + 0.489454i $$0.162804\pi$$
$$548$$ 0 0
$$549$$ 918.000 1.67213
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −854.000 −1.54430
$$554$$ 828.000 1.49458
$$555$$ 0 0
$$556$$ −888.000 −1.59712
$$557$$ −146.000 −0.262118 −0.131059 0.991375i $$-0.541838\pi$$
−0.131059 + 0.991375i $$0.541838\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −560.000 −1.00000
$$561$$ 0 0
$$562$$ −1116.00 −1.98577
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 567.000 1.00000
$$568$$ −1104.00 −1.94366
$$569$$ 18.0000 0.0316344 0.0158172 0.999875i $$-0.494965\pi$$
0.0158172 + 0.999875i $$0.494965\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 576.000 1.00000
$$577$$ 1114.00 1.93068 0.965338 0.261003i $$-0.0840533\pi$$
0.965338 + 0.261003i $$0.0840533\pi$$
$$578$$ −506.000 −0.875433
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 848.000 1.45205
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 620.000 1.05085
$$591$$ 0 0
$$592$$ −1056.00 −1.78378
$$593$$ 186.000 0.313659 0.156830 0.987626i $$-0.449873\pi$$
0.156830 + 0.987626i $$0.449873\pi$$
$$594$$ 0 0
$$595$$ 210.000 0.352941
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 918.000 1.53255 0.766277 0.642510i $$-0.222107\pi$$
0.766277 + 0.642510i $$0.222107\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ −756.000 −1.25581
$$603$$ −54.0000 −0.0895522
$$604$$ 88.0000 0.145695
$$605$$ −605.000 −1.00000
$$606$$ 0 0
$$607$$ 1054.00 1.73641 0.868204 0.496207i $$-0.165274\pi$$
0.868204 + 0.496207i $$0.165274\pi$$
$$608$$ 576.000 0.947368
$$609$$ 0 0
$$610$$ −1020.00 −1.67213
$$611$$ 0 0
$$612$$ −216.000 −0.352941
$$613$$ 1086.00 1.77162 0.885808 0.464053i $$-0.153605\pi$$
0.885808 + 0.464053i $$0.153605\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ −1182.00 −1.90953 −0.954766 0.297359i $$-0.903894\pi$$
−0.954766 + 0.297359i $$0.903894\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 625.000 1.00000
$$626$$ −748.000 −1.19489
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 396.000 0.629571
$$630$$ −630.000 −1.00000
$$631$$ −1258.00 −1.99366 −0.996830 0.0795556i $$-0.974650\pi$$
−0.996830 + 0.0795556i $$0.974650\pi$$
$$632$$ −976.000 −1.54430
$$633$$ 0 0
$$634$$ −1252.00 −1.97476
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −1242.00 −1.94366
$$640$$ −640.000 −1.00000
$$641$$ 162.000 0.252730 0.126365 0.991984i $$-0.459669\pi$$
0.126365 + 0.991984i $$0.459669\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −216.000 −0.334365
$$647$$ −1266.00 −1.95672 −0.978362 0.206902i $$-0.933662\pi$$
−0.978362 + 0.206902i $$0.933662\pi$$
$$648$$ 648.000 1.00000
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 744.000 1.14110
$$653$$ 46.0000 0.0704441 0.0352221 0.999380i $$-0.488786\pi$$
0.0352221 + 0.999380i $$0.488786\pi$$
$$654$$ 0 0
$$655$$ −1210.00 −1.84733
$$656$$ 0 0
$$657$$ 954.000 1.45205
$$658$$ −924.000 −1.40426
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ −1098.00 −1.66112 −0.830560 0.556930i $$-0.811979\pi$$
−0.830560 + 0.556930i $$0.811979\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −630.000 −0.947368
$$666$$ −1188.00 −1.78378
$$667$$ 0 0
$$668$$ −1224.00 −1.83234
$$669$$ 0 0
$$670$$ 60.0000 0.0895522
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 676.000 1.00000
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ −1162.00 −1.71134
$$680$$ 240.000 0.352941
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1226.00 1.79502 0.897511 0.440992i $$-0.145373\pi$$
0.897511 + 0.440992i $$0.145373\pi$$
$$684$$ 648.000 0.947368
$$685$$ 0 0
$$686$$ 686.000 1.00000
$$687$$ 0 0
$$688$$ −864.000 −1.25581
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 1362.00 1.97106 0.985528 0.169511i $$-0.0542190\pi$$
0.985528 + 0.169511i $$0.0542190\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −1132.00 −1.63112
$$695$$ 1110.00 1.59712
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 396.000 0.567335
$$699$$ 0 0
$$700$$ 700.000 1.00000
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ −1188.00 −1.68990
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 1332.00 1.88669
$$707$$ 154.000 0.217822
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 1380.00 1.94366
$$711$$ −1098.00 −1.54430
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 876.000 1.22006
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ −720.000 −1.00000
$$721$$ 322.000 0.446602
$$722$$ −74.0000 −0.102493
$$723$$ 0 0
$$724$$ −552.000 −0.762431
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 814.000 1.11967 0.559835 0.828604i $$-0.310865\pi$$
0.559835 + 0.828604i $$0.310865\pi$$
$$728$$ 0 0
$$729$$ 729.000 1.00000
$$730$$ −1060.00 −1.45205
$$731$$ 324.000 0.443228
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ −1412.00 −1.92371
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 1320.00 1.78378
$$741$$ 0 0
$$742$$ −476.000 −0.641509
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 1212.00 1.62466
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 518.000 0.691589
$$750$$ 0 0
$$751$$ −1018.00 −1.35553 −0.677763 0.735280i $$-0.737050\pi$$
−0.677763 + 0.735280i $$0.737050\pi$$
$$752$$ −1056.00 −1.40426
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −110.000 −0.145695
$$756$$ 0 0
$$757$$ 1374.00 1.81506 0.907530 0.419988i $$-0.137966\pi$$
0.907530 + 0.419988i $$0.137966\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ −720.000 −0.947368
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 408.000 0.534031
$$765$$ 270.000 0.352941
$$766$$ 1212.00 1.58225
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ −972.000 −1.25581
$$775$$ 0 0
$$776$$ −1328.00 −1.71134
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 784.000 1.00000
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ 1016.00 1.28934
$$789$$ 0 0
$$790$$ 1220.00 1.54430
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 396.000 0.495620
$$800$$ 800.000 1.00000
$$801$$ 0 0
$$802$$ −636.000 −0.793017
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 176.000 0.217822
$$809$$ 498.000 0.615575 0.307787 0.951455i $$-0.400411\pi$$
0.307787 + 0.951455i $$0.400411\pi$$
$$810$$ −810.000 −1.00000
$$811$$ 1122.00 1.38348 0.691739 0.722148i $$-0.256845\pi$$
0.691739 + 0.722148i $$0.256845\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −930.000 −1.14110
$$816$$ 0 0
$$817$$ −972.000 −1.18972
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 368.000 0.446602
$$825$$ 0 0
$$826$$ −868.000 −1.05085
$$827$$ 394.000 0.476421 0.238210 0.971214i $$-0.423439\pi$$
0.238210 + 0.971214i $$0.423439\pi$$
$$828$$ 0 0
$$829$$ −762.000 −0.919180 −0.459590 0.888131i $$-0.652004\pi$$
−0.459590 + 0.888131i $$0.652004\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −294.000 −0.352941
$$834$$ 0 0
$$835$$ 1530.00 1.83234
$$836$$ 0 0
$$837$$ 0 0
$$838$$ −1564.00 −1.86635
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 841.000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −845.000 −1.00000
$$846$$ −1188.00 −1.40426
$$847$$ 847.000 1.00000
$$848$$ −544.000 −0.641509
$$849$$ 0 0
$$850$$ −300.000 −0.352941
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 1428.00 1.67213
$$855$$ −810.000 −0.947368
$$856$$ 592.000 0.691589
$$857$$ 1674.00 1.95333 0.976663 0.214779i $$-0.0689030\pi$$
0.976663 + 0.214779i $$0.0689030\pi$$
$$858$$ 0 0
$$859$$ −1662.00 −1.93481 −0.967404 0.253238i $$-0.918504\pi$$
−0.967404 + 0.253238i $$0.918504\pi$$
$$860$$ 1080.00 1.25581
$$861$$ 0 0
$$862$$ 1164.00 1.35035
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 1012.00 1.16859
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ −1494.00 −1.71134
$$874$$ 0 0
$$875$$ −875.000 −1.00000
$$876$$ 0 0
$$877$$ −1746.00 −1.99088 −0.995439 0.0954002i $$-0.969587\pi$$
−0.995439 + 0.0954002i $$0.969587\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 882.000 1.00000
$$883$$ −1734.00 −1.96376 −0.981880 0.189504i $$-0.939312\pi$$
−0.981880 + 0.189504i $$0.939312\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ −748.000 −0.844244
$$887$$ 1614.00 1.81962 0.909808 0.415029i $$-0.136228\pi$$
0.909808 + 0.415029i $$0.136228\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −776.000 −0.869955
$$893$$ −1188.00 −1.33035
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 896.000 1.00000
$$897$$ 0 0
$$898$$ −444.000 −0.494432
$$899$$ 0 0
$$900$$ 900.000 1.00000
$$901$$ 204.000 0.226415
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 690.000 0.762431
$$906$$ 0 0
$$907$$ −1686.00 −1.85888 −0.929438 0.368979i $$-0.879707\pi$$
−0.929438 + 0.368979i $$0.879707\pi$$
$$908$$ 0 0
$$909$$ 198.000 0.217822
$$910$$ 0 0
$$911$$ 1542.00 1.69265 0.846323 0.532670i $$-0.178811\pi$$
0.846323 + 0.532670i $$0.178811\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 1752.00 1.91266
$$917$$ 1694.00 1.84733
$$918$$ 0 0
$$919$$ −682.000 −0.742111 −0.371055 0.928611i $$-0.621004\pi$$
−0.371055 + 0.928611i $$0.621004\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −1396.00 −1.51410
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −1650.00 −1.78378
$$926$$ 0 0
$$927$$ 414.000 0.446602
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 882.000 0.947368
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 1514.00 1.61580 0.807898 0.589323i $$-0.200605\pi$$
0.807898 + 0.589323i $$0.200605\pi$$
$$938$$ −84.0000 −0.0895522
$$939$$ 0 0
$$940$$ 1320.00 1.40426
$$941$$ 1702.00 1.80871 0.904357 0.426777i $$-0.140351\pi$$
0.904357 + 0.426777i $$0.140351\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −992.000 −1.05085
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −1606.00 −1.69588 −0.847941 0.530091i $$-0.822158\pi$$
−0.847941 + 0.530091i $$0.822158\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 900.000 0.947368
$$951$$ 0 0
$$952$$ −336.000 −0.352941
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ −612.000 −0.641509
$$955$$ −510.000 −0.534031
$$956$$ 792.000 0.828452
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 961.000 1.00000
$$962$$ 0 0
$$963$$ 666.000 0.691589
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 968.000 1.00000
$$969$$ 0 0
$$970$$ 1660.00 1.71134
$$971$$ −1438.00 −1.48095 −0.740474 0.672085i $$-0.765399\pi$$
−0.740474 + 0.672085i $$0.765399\pi$$
$$972$$ 0 0
$$973$$ −1554.00 −1.59712
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 1632.00 1.67213
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ −980.000 −1.00000
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −594.000 −0.604273 −0.302136 0.953265i $$-0.597700\pi$$
−0.302136 + 0.953265i $$0.597700\pi$$
$$984$$ 0 0
$$985$$ −1270.00 −1.28934
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −538.000 −0.542886 −0.271443 0.962455i $$-0.587501\pi$$
−0.271443 + 0.962455i $$0.587501\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ −1932.00 −1.94366
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 0 0
$$999$$ 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 280.3.c.c.69.1 yes 1
4.3 odd 2 1120.3.c.a.209.1 1
5.4 even 2 280.3.c.a.69.1 1
7.6 odd 2 280.3.c.d.69.1 yes 1
8.3 odd 2 1120.3.c.c.209.1 1
8.5 even 2 280.3.c.b.69.1 yes 1
20.19 odd 2 1120.3.c.b.209.1 1
28.27 even 2 1120.3.c.d.209.1 1
35.34 odd 2 280.3.c.b.69.1 yes 1
40.19 odd 2 1120.3.c.d.209.1 1
40.29 even 2 280.3.c.d.69.1 yes 1
56.13 odd 2 280.3.c.a.69.1 1
56.27 even 2 1120.3.c.b.209.1 1
140.139 even 2 1120.3.c.c.209.1 1
280.69 odd 2 CM 280.3.c.c.69.1 yes 1
280.139 even 2 1120.3.c.a.209.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
280.3.c.a.69.1 1 5.4 even 2
280.3.c.a.69.1 1 56.13 odd 2
280.3.c.b.69.1 yes 1 8.5 even 2
280.3.c.b.69.1 yes 1 35.34 odd 2
280.3.c.c.69.1 yes 1 1.1 even 1 trivial
280.3.c.c.69.1 yes 1 280.69 odd 2 CM
280.3.c.d.69.1 yes 1 7.6 odd 2
280.3.c.d.69.1 yes 1 40.29 even 2
1120.3.c.a.209.1 1 4.3 odd 2
1120.3.c.a.209.1 1 280.139 even 2
1120.3.c.b.209.1 1 20.19 odd 2
1120.3.c.b.209.1 1 56.27 even 2
1120.3.c.c.209.1 1 8.3 odd 2
1120.3.c.c.209.1 1 140.139 even 2
1120.3.c.d.209.1 1 28.27 even 2
1120.3.c.d.209.1 1 40.19 odd 2