# Properties

 Label 2070.4.a.bj.1.2 Level $2070$ Weight $4$ Character 2070.1 Self dual yes Analytic conductor $122.134$ Analytic rank $0$ Dimension $4$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 2070.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$122.133953712$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ Defining polynomial: $$x^{4} - 68x^{2} - 111x + 342$$ x^4 - 68*x^2 - 111*x + 342 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 230) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$1.58997$$ of defining polynomial Character $$\chi$$ $$=$$ 2070.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -18.5077 q^{7} +8.00000 q^{8} +O(q^{10})$$ $$q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -18.5077 q^{7} +8.00000 q^{8} +10.0000 q^{10} -47.9296 q^{11} +42.3717 q^{13} -37.0155 q^{14} +16.0000 q^{16} -1.70534 q^{17} +21.4208 q^{19} +20.0000 q^{20} -95.8592 q^{22} +23.0000 q^{23} +25.0000 q^{25} +84.7434 q^{26} -74.0310 q^{28} -57.6332 q^{29} +295.699 q^{31} +32.0000 q^{32} -3.41069 q^{34} -92.5387 q^{35} -7.85184 q^{37} +42.8416 q^{38} +40.0000 q^{40} -465.929 q^{41} +182.374 q^{43} -191.718 q^{44} +46.0000 q^{46} -449.193 q^{47} -0.463605 q^{49} +50.0000 q^{50} +169.487 q^{52} +368.316 q^{53} -239.648 q^{55} -148.062 q^{56} -115.266 q^{58} +377.032 q^{59} +849.042 q^{61} +591.398 q^{62} +64.0000 q^{64} +211.858 q^{65} +92.3424 q^{67} -6.82138 q^{68} -185.077 q^{70} +626.854 q^{71} +439.227 q^{73} -15.7037 q^{74} +85.6831 q^{76} +887.068 q^{77} +641.707 q^{79} +80.0000 q^{80} -931.859 q^{82} +609.932 q^{83} -8.52672 q^{85} +364.747 q^{86} -383.437 q^{88} -1122.87 q^{89} -784.204 q^{91} +92.0000 q^{92} -898.386 q^{94} +107.104 q^{95} -1428.80 q^{97} -0.927209 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 8 q^{2} + 16 q^{4} + 20 q^{5} - q^{7} + 32 q^{8}+O(q^{10})$$ 4 * q + 8 * q^2 + 16 * q^4 + 20 * q^5 - q^7 + 32 * q^8 $$4 q + 8 q^{2} + 16 q^{4} + 20 q^{5} - q^{7} + 32 q^{8} + 40 q^{10} + 39 q^{11} - 20 q^{13} - 2 q^{14} + 64 q^{16} + 23 q^{17} + 53 q^{19} + 80 q^{20} + 78 q^{22} + 92 q^{23} + 100 q^{25} - 40 q^{26} - 4 q^{28} - 161 q^{29} + 388 q^{31} + 128 q^{32} + 46 q^{34} - 5 q^{35} + 466 q^{37} + 106 q^{38} + 160 q^{40} - 484 q^{41} + 894 q^{43} + 156 q^{44} + 184 q^{46} + 265 q^{47} + 1643 q^{49} + 200 q^{50} - 80 q^{52} - 576 q^{53} + 195 q^{55} - 8 q^{56} - 322 q^{58} + 94 q^{59} + 1153 q^{61} + 776 q^{62} + 256 q^{64} - 100 q^{65} - 1472 q^{67} + 92 q^{68} - 10 q^{70} - 200 q^{71} + 1147 q^{73} + 932 q^{74} + 212 q^{76} + 2176 q^{77} - 908 q^{79} + 320 q^{80} - 968 q^{82} + 1048 q^{83} + 115 q^{85} + 1788 q^{86} + 312 q^{88} + 1784 q^{89} + 2329 q^{91} + 368 q^{92} + 530 q^{94} + 265 q^{95} - 2047 q^{97} + 3286 q^{98}+O(q^{100})$$ 4 * q + 8 * q^2 + 16 * q^4 + 20 * q^5 - q^7 + 32 * q^8 + 40 * q^10 + 39 * q^11 - 20 * q^13 - 2 * q^14 + 64 * q^16 + 23 * q^17 + 53 * q^19 + 80 * q^20 + 78 * q^22 + 92 * q^23 + 100 * q^25 - 40 * q^26 - 4 * q^28 - 161 * q^29 + 388 * q^31 + 128 * q^32 + 46 * q^34 - 5 * q^35 + 466 * q^37 + 106 * q^38 + 160 * q^40 - 484 * q^41 + 894 * q^43 + 156 * q^44 + 184 * q^46 + 265 * q^47 + 1643 * q^49 + 200 * q^50 - 80 * q^52 - 576 * q^53 + 195 * q^55 - 8 * q^56 - 322 * q^58 + 94 * q^59 + 1153 * q^61 + 776 * q^62 + 256 * q^64 - 100 * q^65 - 1472 * q^67 + 92 * q^68 - 10 * q^70 - 200 * q^71 + 1147 * q^73 + 932 * q^74 + 212 * q^76 + 2176 * q^77 - 908 * q^79 + 320 * q^80 - 968 * q^82 + 1048 * q^83 + 115 * q^85 + 1788 * q^86 + 312 * q^88 + 1784 * q^89 + 2329 * q^91 + 368 * q^92 + 530 * q^94 + 265 * q^95 - 2047 * q^97 + 3286 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 0.707107
$$3$$ 0 0
$$4$$ 4.00000 0.500000
$$5$$ 5.00000 0.447214
$$6$$ 0 0
$$7$$ −18.5077 −0.999324 −0.499662 0.866220i $$-0.666542\pi$$
−0.499662 + 0.866220i $$0.666542\pi$$
$$8$$ 8.00000 0.353553
$$9$$ 0 0
$$10$$ 10.0000 0.316228
$$11$$ −47.9296 −1.31376 −0.656878 0.753997i $$-0.728123\pi$$
−0.656878 + 0.753997i $$0.728123\pi$$
$$12$$ 0 0
$$13$$ 42.3717 0.903984 0.451992 0.892022i $$-0.350714\pi$$
0.451992 + 0.892022i $$0.350714\pi$$
$$14$$ −37.0155 −0.706629
$$15$$ 0 0
$$16$$ 16.0000 0.250000
$$17$$ −1.70534 −0.0243298 −0.0121649 0.999926i $$-0.503872\pi$$
−0.0121649 + 0.999926i $$0.503872\pi$$
$$18$$ 0 0
$$19$$ 21.4208 0.258645 0.129323 0.991603i $$-0.458720\pi$$
0.129323 + 0.991603i $$0.458720\pi$$
$$20$$ 20.0000 0.223607
$$21$$ 0 0
$$22$$ −95.8592 −0.928966
$$23$$ 23.0000 0.208514
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 84.7434 0.639213
$$27$$ 0 0
$$28$$ −74.0310 −0.499662
$$29$$ −57.6332 −0.369042 −0.184521 0.982829i $$-0.559073\pi$$
−0.184521 + 0.982829i $$0.559073\pi$$
$$30$$ 0 0
$$31$$ 295.699 1.71320 0.856599 0.515983i $$-0.172573\pi$$
0.856599 + 0.515983i $$0.172573\pi$$
$$32$$ 32.0000 0.176777
$$33$$ 0 0
$$34$$ −3.41069 −0.0172038
$$35$$ −92.5387 −0.446911
$$36$$ 0 0
$$37$$ −7.85184 −0.0348874 −0.0174437 0.999848i $$-0.505553\pi$$
−0.0174437 + 0.999848i $$0.505553\pi$$
$$38$$ 42.8416 0.182890
$$39$$ 0 0
$$40$$ 40.0000 0.158114
$$41$$ −465.929 −1.77478 −0.887390 0.461020i $$-0.847484\pi$$
−0.887390 + 0.461020i $$0.847484\pi$$
$$42$$ 0 0
$$43$$ 182.374 0.646784 0.323392 0.946265i $$-0.395177\pi$$
0.323392 + 0.946265i $$0.395177\pi$$
$$44$$ −191.718 −0.656878
$$45$$ 0 0
$$46$$ 46.0000 0.147442
$$47$$ −449.193 −1.39408 −0.697038 0.717035i $$-0.745499\pi$$
−0.697038 + 0.717035i $$0.745499\pi$$
$$48$$ 0 0
$$49$$ −0.463605 −0.00135162
$$50$$ 50.0000 0.141421
$$51$$ 0 0
$$52$$ 169.487 0.451992
$$53$$ 368.316 0.954567 0.477283 0.878749i $$-0.341621\pi$$
0.477283 + 0.878749i $$0.341621\pi$$
$$54$$ 0 0
$$55$$ −239.648 −0.587529
$$56$$ −148.062 −0.353314
$$57$$ 0 0
$$58$$ −115.266 −0.260952
$$59$$ 377.032 0.831955 0.415977 0.909375i $$-0.363440\pi$$
0.415977 + 0.909375i $$0.363440\pi$$
$$60$$ 0 0
$$61$$ 849.042 1.78211 0.891055 0.453896i $$-0.149966\pi$$
0.891055 + 0.453896i $$0.149966\pi$$
$$62$$ 591.398 1.21141
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ 211.858 0.404274
$$66$$ 0 0
$$67$$ 92.3424 0.168379 0.0841897 0.996450i $$-0.473170\pi$$
0.0841897 + 0.996450i $$0.473170\pi$$
$$68$$ −6.82138 −0.0121649
$$69$$ 0 0
$$70$$ −185.077 −0.316014
$$71$$ 626.854 1.04780 0.523901 0.851779i $$-0.324476\pi$$
0.523901 + 0.851779i $$0.324476\pi$$
$$72$$ 0 0
$$73$$ 439.227 0.704214 0.352107 0.935960i $$-0.385465\pi$$
0.352107 + 0.935960i $$0.385465\pi$$
$$74$$ −15.7037 −0.0246691
$$75$$ 0 0
$$76$$ 85.6831 0.129323
$$77$$ 887.068 1.31287
$$78$$ 0 0
$$79$$ 641.707 0.913894 0.456947 0.889494i $$-0.348943\pi$$
0.456947 + 0.889494i $$0.348943\pi$$
$$80$$ 80.0000 0.111803
$$81$$ 0 0
$$82$$ −931.859 −1.25496
$$83$$ 609.932 0.806611 0.403306 0.915065i $$-0.367861\pi$$
0.403306 + 0.915065i $$0.367861\pi$$
$$84$$ 0 0
$$85$$ −8.52672 −0.0108806
$$86$$ 364.747 0.457346
$$87$$ 0 0
$$88$$ −383.437 −0.464483
$$89$$ −1122.87 −1.33735 −0.668673 0.743557i $$-0.733137\pi$$
−0.668673 + 0.743557i $$0.733137\pi$$
$$90$$ 0 0
$$91$$ −784.204 −0.903373
$$92$$ 92.0000 0.104257
$$93$$ 0 0
$$94$$ −898.386 −0.985760
$$95$$ 107.104 0.115670
$$96$$ 0 0
$$97$$ −1428.80 −1.49559 −0.747795 0.663930i $$-0.768887\pi$$
−0.747795 + 0.663930i $$0.768887\pi$$
$$98$$ −0.927209 −0.000955737 0
$$99$$ 0 0
$$100$$ 100.000 0.100000
$$101$$ 1512.15 1.48975 0.744875 0.667204i $$-0.232509\pi$$
0.744875 + 0.667204i $$0.232509\pi$$
$$102$$ 0 0
$$103$$ 957.279 0.915762 0.457881 0.889013i $$-0.348609\pi$$
0.457881 + 0.889013i $$0.348609\pi$$
$$104$$ 338.974 0.319607
$$105$$ 0 0
$$106$$ 736.631 0.674981
$$107$$ 1742.16 1.57403 0.787013 0.616936i $$-0.211626\pi$$
0.787013 + 0.616936i $$0.211626\pi$$
$$108$$ 0 0
$$109$$ 1166.77 1.02529 0.512644 0.858601i $$-0.328666\pi$$
0.512644 + 0.858601i $$0.328666\pi$$
$$110$$ −479.296 −0.415446
$$111$$ 0 0
$$112$$ −296.124 −0.249831
$$113$$ 393.287 0.327410 0.163705 0.986509i $$-0.447655\pi$$
0.163705 + 0.986509i $$0.447655\pi$$
$$114$$ 0 0
$$115$$ 115.000 0.0932505
$$116$$ −230.533 −0.184521
$$117$$ 0 0
$$118$$ 754.063 0.588281
$$119$$ 31.5621 0.0243134
$$120$$ 0 0
$$121$$ 966.245 0.725954
$$122$$ 1698.08 1.26014
$$123$$ 0 0
$$124$$ 1182.80 0.856599
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ −1067.87 −0.746127 −0.373063 0.927806i $$-0.621693\pi$$
−0.373063 + 0.927806i $$0.621693\pi$$
$$128$$ 128.000 0.0883883
$$129$$ 0 0
$$130$$ 423.717 0.285865
$$131$$ 175.497 0.117047 0.0585237 0.998286i $$-0.481361\pi$$
0.0585237 + 0.998286i $$0.481361\pi$$
$$132$$ 0 0
$$133$$ −396.450 −0.258471
$$134$$ 184.685 0.119062
$$135$$ 0 0
$$136$$ −13.6428 −0.00860189
$$137$$ −475.898 −0.296779 −0.148389 0.988929i $$-0.547409\pi$$
−0.148389 + 0.988929i $$0.547409\pi$$
$$138$$ 0 0
$$139$$ 153.167 0.0934638 0.0467319 0.998907i $$-0.485119\pi$$
0.0467319 + 0.998907i $$0.485119\pi$$
$$140$$ −370.155 −0.223456
$$141$$ 0 0
$$142$$ 1253.71 0.740907
$$143$$ −2030.86 −1.18761
$$144$$ 0 0
$$145$$ −288.166 −0.165041
$$146$$ 878.454 0.497954
$$147$$ 0 0
$$148$$ −31.4074 −0.0174437
$$149$$ −506.906 −0.278707 −0.139353 0.990243i $$-0.544502\pi$$
−0.139353 + 0.990243i $$0.544502\pi$$
$$150$$ 0 0
$$151$$ 2437.84 1.31383 0.656916 0.753964i $$-0.271861\pi$$
0.656916 + 0.753964i $$0.271861\pi$$
$$152$$ 171.366 0.0914450
$$153$$ 0 0
$$154$$ 1774.14 0.928338
$$155$$ 1478.50 0.766166
$$156$$ 0 0
$$157$$ 255.966 0.130117 0.0650584 0.997881i $$-0.479277\pi$$
0.0650584 + 0.997881i $$0.479277\pi$$
$$158$$ 1283.41 0.646221
$$159$$ 0 0
$$160$$ 160.000 0.0790569
$$161$$ −425.678 −0.208373
$$162$$ 0 0
$$163$$ 321.632 0.154553 0.0772767 0.997010i $$-0.475378\pi$$
0.0772767 + 0.997010i $$0.475378\pi$$
$$164$$ −1863.72 −0.887390
$$165$$ 0 0
$$166$$ 1219.86 0.570360
$$167$$ 2926.22 1.35591 0.677957 0.735102i $$-0.262866\pi$$
0.677957 + 0.735102i $$0.262866\pi$$
$$168$$ 0 0
$$169$$ −401.640 −0.182813
$$170$$ −17.0534 −0.00769376
$$171$$ 0 0
$$172$$ 729.495 0.323392
$$173$$ −1811.84 −0.796254 −0.398127 0.917330i $$-0.630340\pi$$
−0.398127 + 0.917330i $$0.630340\pi$$
$$174$$ 0 0
$$175$$ −462.693 −0.199865
$$176$$ −766.873 −0.328439
$$177$$ 0 0
$$178$$ −2245.74 −0.945646
$$179$$ −912.664 −0.381093 −0.190547 0.981678i $$-0.561026\pi$$
−0.190547 + 0.981678i $$0.561026\pi$$
$$180$$ 0 0
$$181$$ 3670.55 1.50735 0.753673 0.657249i $$-0.228280\pi$$
0.753673 + 0.657249i $$0.228280\pi$$
$$182$$ −1568.41 −0.638781
$$183$$ 0 0
$$184$$ 184.000 0.0737210
$$185$$ −39.2592 −0.0156021
$$186$$ 0 0
$$187$$ 81.7364 0.0319634
$$188$$ −1796.77 −0.697038
$$189$$ 0 0
$$190$$ 214.208 0.0817909
$$191$$ 1840.96 0.697419 0.348710 0.937231i $$-0.386620\pi$$
0.348710 + 0.937231i $$0.386620\pi$$
$$192$$ 0 0
$$193$$ −611.817 −0.228184 −0.114092 0.993470i $$-0.536396\pi$$
−0.114092 + 0.993470i $$0.536396\pi$$
$$194$$ −2857.59 −1.05754
$$195$$ 0 0
$$196$$ −1.85442 −0.000675808 0
$$197$$ −2830.26 −1.02359 −0.511796 0.859107i $$-0.671020\pi$$
−0.511796 + 0.859107i $$0.671020\pi$$
$$198$$ 0 0
$$199$$ −1162.74 −0.414195 −0.207097 0.978320i $$-0.566402\pi$$
−0.207097 + 0.978320i $$0.566402\pi$$
$$200$$ 200.000 0.0707107
$$201$$ 0 0
$$202$$ 3024.31 1.05341
$$203$$ 1066.66 0.368792
$$204$$ 0 0
$$205$$ −2329.65 −0.793705
$$206$$ 1914.56 0.647542
$$207$$ 0 0
$$208$$ 677.947 0.225996
$$209$$ −1026.69 −0.339797
$$210$$ 0 0
$$211$$ 1399.58 0.456641 0.228320 0.973586i $$-0.426677\pi$$
0.228320 + 0.973586i $$0.426677\pi$$
$$212$$ 1473.26 0.477283
$$213$$ 0 0
$$214$$ 3484.32 1.11300
$$215$$ 911.869 0.289251
$$216$$ 0 0
$$217$$ −5472.72 −1.71204
$$218$$ 2333.54 0.724988
$$219$$ 0 0
$$220$$ −958.592 −0.293765
$$221$$ −72.2583 −0.0219938
$$222$$ 0 0
$$223$$ 4257.98 1.27863 0.639317 0.768943i $$-0.279217\pi$$
0.639317 + 0.768943i $$0.279217\pi$$
$$224$$ −592.248 −0.176657
$$225$$ 0 0
$$226$$ 786.574 0.231514
$$227$$ 4025.03 1.17688 0.588438 0.808542i $$-0.299743\pi$$
0.588438 + 0.808542i $$0.299743\pi$$
$$228$$ 0 0
$$229$$ 3623.04 1.04549 0.522745 0.852489i $$-0.324908\pi$$
0.522745 + 0.852489i $$0.324908\pi$$
$$230$$ 230.000 0.0659380
$$231$$ 0 0
$$232$$ −461.066 −0.130476
$$233$$ −6502.81 −1.82838 −0.914192 0.405282i $$-0.867173\pi$$
−0.914192 + 0.405282i $$0.867173\pi$$
$$234$$ 0 0
$$235$$ −2245.96 −0.623449
$$236$$ 1508.13 0.415977
$$237$$ 0 0
$$238$$ 63.1241 0.0171921
$$239$$ 2690.07 0.728059 0.364030 0.931387i $$-0.381401\pi$$
0.364030 + 0.931387i $$0.381401\pi$$
$$240$$ 0 0
$$241$$ −44.6958 −0.0119465 −0.00597326 0.999982i $$-0.501901\pi$$
−0.00597326 + 0.999982i $$0.501901\pi$$
$$242$$ 1932.49 0.513327
$$243$$ 0 0
$$244$$ 3396.17 0.891055
$$245$$ −2.31802 −0.000604461 0
$$246$$ 0 0
$$247$$ 907.635 0.233811
$$248$$ 2365.59 0.605707
$$249$$ 0 0
$$250$$ 250.000 0.0632456
$$251$$ 6801.41 1.71036 0.855181 0.518329i $$-0.173446\pi$$
0.855181 + 0.518329i $$0.173446\pi$$
$$252$$ 0 0
$$253$$ −1102.38 −0.273937
$$254$$ −2135.74 −0.527591
$$255$$ 0 0
$$256$$ 256.000 0.0625000
$$257$$ −5576.00 −1.35339 −0.676695 0.736263i $$-0.736589\pi$$
−0.676695 + 0.736263i $$0.736589\pi$$
$$258$$ 0 0
$$259$$ 145.320 0.0348638
$$260$$ 847.434 0.202137
$$261$$ 0 0
$$262$$ 350.993 0.0827651
$$263$$ 5669.58 1.32928 0.664641 0.747163i $$-0.268585\pi$$
0.664641 + 0.747163i $$0.268585\pi$$
$$264$$ 0 0
$$265$$ 1841.58 0.426895
$$266$$ −792.900 −0.182766
$$267$$ 0 0
$$268$$ 369.370 0.0841897
$$269$$ −6040.21 −1.36906 −0.684532 0.728983i $$-0.739994\pi$$
−0.684532 + 0.728983i $$0.739994\pi$$
$$270$$ 0 0
$$271$$ −6899.26 −1.54650 −0.773248 0.634104i $$-0.781369\pi$$
−0.773248 + 0.634104i $$0.781369\pi$$
$$272$$ −27.2855 −0.00608245
$$273$$ 0 0
$$274$$ −951.795 −0.209854
$$275$$ −1198.24 −0.262751
$$276$$ 0 0
$$277$$ 5617.68 1.21853 0.609267 0.792965i $$-0.291464\pi$$
0.609267 + 0.792965i $$0.291464\pi$$
$$278$$ 306.334 0.0660889
$$279$$ 0 0
$$280$$ −740.310 −0.158007
$$281$$ −3069.89 −0.651723 −0.325861 0.945418i $$-0.605654\pi$$
−0.325861 + 0.945418i $$0.605654\pi$$
$$282$$ 0 0
$$283$$ 1404.86 0.295089 0.147544 0.989055i $$-0.452863\pi$$
0.147544 + 0.989055i $$0.452863\pi$$
$$284$$ 2507.42 0.523901
$$285$$ 0 0
$$286$$ −4061.72 −0.839770
$$287$$ 8623.30 1.77358
$$288$$ 0 0
$$289$$ −4910.09 −0.999408
$$290$$ −576.332 −0.116701
$$291$$ 0 0
$$292$$ 1756.91 0.352107
$$293$$ 2407.05 0.479936 0.239968 0.970781i $$-0.422863\pi$$
0.239968 + 0.970781i $$0.422863\pi$$
$$294$$ 0 0
$$295$$ 1885.16 0.372062
$$296$$ −62.8147 −0.0123346
$$297$$ 0 0
$$298$$ −1013.81 −0.197076
$$299$$ 974.549 0.188494
$$300$$ 0 0
$$301$$ −3375.33 −0.646347
$$302$$ 4875.68 0.929020
$$303$$ 0 0
$$304$$ 342.732 0.0646614
$$305$$ 4245.21 0.796984
$$306$$ 0 0
$$307$$ −459.743 −0.0854689 −0.0427344 0.999086i $$-0.513607\pi$$
−0.0427344 + 0.999086i $$0.513607\pi$$
$$308$$ 3548.27 0.656434
$$309$$ 0 0
$$310$$ 2956.99 0.541761
$$311$$ −4119.48 −0.751107 −0.375553 0.926801i $$-0.622547\pi$$
−0.375553 + 0.926801i $$0.622547\pi$$
$$312$$ 0 0
$$313$$ 1684.15 0.304133 0.152066 0.988370i $$-0.451407\pi$$
0.152066 + 0.988370i $$0.451407\pi$$
$$314$$ 511.933 0.0920065
$$315$$ 0 0
$$316$$ 2566.83 0.456947
$$317$$ −8686.47 −1.53906 −0.769528 0.638613i $$-0.779508\pi$$
−0.769528 + 0.638613i $$0.779508\pi$$
$$318$$ 0 0
$$319$$ 2762.34 0.484831
$$320$$ 320.000 0.0559017
$$321$$ 0 0
$$322$$ −851.356 −0.147342
$$323$$ −36.5298 −0.00629279
$$324$$ 0 0
$$325$$ 1059.29 0.180797
$$326$$ 643.265 0.109286
$$327$$ 0 0
$$328$$ −3727.44 −0.627479
$$329$$ 8313.55 1.39313
$$330$$ 0 0
$$331$$ 4307.91 0.715359 0.357680 0.933844i $$-0.383568\pi$$
0.357680 + 0.933844i $$0.383568\pi$$
$$332$$ 2439.73 0.403306
$$333$$ 0 0
$$334$$ 5852.44 0.958776
$$335$$ 461.712 0.0753015
$$336$$ 0 0
$$337$$ −290.156 −0.0469015 −0.0234507 0.999725i $$-0.507465\pi$$
−0.0234507 + 0.999725i $$0.507465\pi$$
$$338$$ −803.280 −0.129268
$$339$$ 0 0
$$340$$ −34.1069 −0.00544031
$$341$$ −14172.7 −2.25072
$$342$$ 0 0
$$343$$ 6356.73 1.00067
$$344$$ 1458.99 0.228673
$$345$$ 0 0
$$346$$ −3623.69 −0.563037
$$347$$ −1042.94 −0.161349 −0.0806743 0.996741i $$-0.525707\pi$$
−0.0806743 + 0.996741i $$0.525707\pi$$
$$348$$ 0 0
$$349$$ −1819.56 −0.279080 −0.139540 0.990216i $$-0.544562\pi$$
−0.139540 + 0.990216i $$0.544562\pi$$
$$350$$ −925.387 −0.141326
$$351$$ 0 0
$$352$$ −1533.75 −0.232241
$$353$$ 4514.29 0.680656 0.340328 0.940307i $$-0.389462\pi$$
0.340328 + 0.940307i $$0.389462\pi$$
$$354$$ 0 0
$$355$$ 3134.27 0.468591
$$356$$ −4491.47 −0.668673
$$357$$ 0 0
$$358$$ −1825.33 −0.269474
$$359$$ −11527.9 −1.69476 −0.847379 0.530988i $$-0.821821\pi$$
−0.847379 + 0.530988i $$0.821821\pi$$
$$360$$ 0 0
$$361$$ −6400.15 −0.933103
$$362$$ 7341.10 1.06585
$$363$$ 0 0
$$364$$ −3136.82 −0.451686
$$365$$ 2196.13 0.314934
$$366$$ 0 0
$$367$$ 6894.09 0.980568 0.490284 0.871563i $$-0.336893\pi$$
0.490284 + 0.871563i $$0.336893\pi$$
$$368$$ 368.000 0.0521286
$$369$$ 0 0
$$370$$ −78.5184 −0.0110324
$$371$$ −6816.69 −0.953922
$$372$$ 0 0
$$373$$ 7733.25 1.07349 0.536746 0.843744i $$-0.319653\pi$$
0.536746 + 0.843744i $$0.319653\pi$$
$$374$$ 163.473 0.0226016
$$375$$ 0 0
$$376$$ −3593.54 −0.492880
$$377$$ −2442.02 −0.333608
$$378$$ 0 0
$$379$$ −9495.72 −1.28697 −0.643486 0.765458i $$-0.722512\pi$$
−0.643486 + 0.765458i $$0.722512\pi$$
$$380$$ 428.416 0.0578349
$$381$$ 0 0
$$382$$ 3681.92 0.493150
$$383$$ 12877.0 1.71797 0.858987 0.511998i $$-0.171094\pi$$
0.858987 + 0.511998i $$0.171094\pi$$
$$384$$ 0 0
$$385$$ 4435.34 0.587132
$$386$$ −1223.63 −0.161351
$$387$$ 0 0
$$388$$ −5715.18 −0.747795
$$389$$ 8200.40 1.06884 0.534418 0.845221i $$-0.320531\pi$$
0.534418 + 0.845221i $$0.320531\pi$$
$$390$$ 0 0
$$391$$ −39.2229 −0.00507312
$$392$$ −3.70884 −0.000477869 0
$$393$$ 0 0
$$394$$ −5660.52 −0.723789
$$395$$ 3208.53 0.408706
$$396$$ 0 0
$$397$$ 7842.68 0.991468 0.495734 0.868475i $$-0.334899\pi$$
0.495734 + 0.868475i $$0.334899\pi$$
$$398$$ −2325.49 −0.292880
$$399$$ 0 0
$$400$$ 400.000 0.0500000
$$401$$ 14534.2 1.80999 0.904993 0.425427i $$-0.139876\pi$$
0.904993 + 0.425427i $$0.139876\pi$$
$$402$$ 0 0
$$403$$ 12529.3 1.54870
$$404$$ 6048.61 0.744875
$$405$$ 0 0
$$406$$ 2133.32 0.260776
$$407$$ 376.335 0.0458335
$$408$$ 0 0
$$409$$ 13388.0 1.61857 0.809283 0.587419i $$-0.199856\pi$$
0.809283 + 0.587419i $$0.199856\pi$$
$$410$$ −4659.29 −0.561234
$$411$$ 0 0
$$412$$ 3829.12 0.457881
$$413$$ −6978.00 −0.831393
$$414$$ 0 0
$$415$$ 3049.66 0.360727
$$416$$ 1355.89 0.159803
$$417$$ 0 0
$$418$$ −2053.38 −0.240273
$$419$$ 3103.10 0.361805 0.180903 0.983501i $$-0.442098\pi$$
0.180903 + 0.983501i $$0.442098\pi$$
$$420$$ 0 0
$$421$$ −6075.82 −0.703367 −0.351684 0.936119i $$-0.614391\pi$$
−0.351684 + 0.936119i $$0.614391\pi$$
$$422$$ 2799.16 0.322894
$$423$$ 0 0
$$424$$ 2946.53 0.337490
$$425$$ −42.6336 −0.00486596
$$426$$ 0 0
$$427$$ −15713.8 −1.78090
$$428$$ 6968.63 0.787013
$$429$$ 0 0
$$430$$ 1823.74 0.204531
$$431$$ −14120.3 −1.57808 −0.789040 0.614341i $$-0.789422\pi$$
−0.789040 + 0.614341i $$0.789422\pi$$
$$432$$ 0 0
$$433$$ 8555.96 0.949592 0.474796 0.880096i $$-0.342522\pi$$
0.474796 + 0.880096i $$0.342522\pi$$
$$434$$ −10945.4 −1.21060
$$435$$ 0 0
$$436$$ 4667.09 0.512644
$$437$$ 492.678 0.0539313
$$438$$ 0 0
$$439$$ −10894.1 −1.18439 −0.592194 0.805796i $$-0.701738\pi$$
−0.592194 + 0.805796i $$0.701738\pi$$
$$440$$ −1917.18 −0.207723
$$441$$ 0 0
$$442$$ −144.517 −0.0155519
$$443$$ −16120.5 −1.72891 −0.864456 0.502708i $$-0.832337\pi$$
−0.864456 + 0.502708i $$0.832337\pi$$
$$444$$ 0 0
$$445$$ −5614.34 −0.598079
$$446$$ 8515.96 0.904130
$$447$$ 0 0
$$448$$ −1184.50 −0.124915
$$449$$ −4811.29 −0.505699 −0.252849 0.967506i $$-0.581368\pi$$
−0.252849 + 0.967506i $$0.581368\pi$$
$$450$$ 0 0
$$451$$ 22331.8 2.33163
$$452$$ 1573.15 0.163705
$$453$$ 0 0
$$454$$ 8050.06 0.832177
$$455$$ −3921.02 −0.404001
$$456$$ 0 0
$$457$$ −226.329 −0.0231667 −0.0115834 0.999933i $$-0.503687\pi$$
−0.0115834 + 0.999933i $$0.503687\pi$$
$$458$$ 7246.08 0.739273
$$459$$ 0 0
$$460$$ 460.000 0.0466252
$$461$$ 4349.17 0.439395 0.219697 0.975568i $$-0.429493\pi$$
0.219697 + 0.975568i $$0.429493\pi$$
$$462$$ 0 0
$$463$$ −989.313 −0.0993030 −0.0496515 0.998767i $$-0.515811\pi$$
−0.0496515 + 0.998767i $$0.515811\pi$$
$$464$$ −922.131 −0.0922605
$$465$$ 0 0
$$466$$ −13005.6 −1.29286
$$467$$ −8512.91 −0.843535 −0.421767 0.906704i $$-0.638590\pi$$
−0.421767 + 0.906704i $$0.638590\pi$$
$$468$$ 0 0
$$469$$ −1709.05 −0.168266
$$470$$ −4491.93 −0.440845
$$471$$ 0 0
$$472$$ 3016.25 0.294140
$$473$$ −8741.10 −0.849717
$$474$$ 0 0
$$475$$ 535.519 0.0517291
$$476$$ 126.248 0.0121567
$$477$$ 0 0
$$478$$ 5380.14 0.514816
$$479$$ 12058.6 1.15025 0.575125 0.818065i $$-0.304953\pi$$
0.575125 + 0.818065i $$0.304953\pi$$
$$480$$ 0 0
$$481$$ −332.696 −0.0315377
$$482$$ −89.3916 −0.00844746
$$483$$ 0 0
$$484$$ 3864.98 0.362977
$$485$$ −7143.98 −0.668848
$$486$$ 0 0
$$487$$ 11605.3 1.07985 0.539924 0.841714i $$-0.318453\pi$$
0.539924 + 0.841714i $$0.318453\pi$$
$$488$$ 6792.34 0.630071
$$489$$ 0 0
$$490$$ −4.63605 −0.000427419 0
$$491$$ 4651.88 0.427569 0.213785 0.976881i $$-0.431421\pi$$
0.213785 + 0.976881i $$0.431421\pi$$
$$492$$ 0 0
$$493$$ 98.2845 0.00897872
$$494$$ 1815.27 0.165330
$$495$$ 0 0
$$496$$ 4731.19 0.428300
$$497$$ −11601.6 −1.04709
$$498$$ 0 0
$$499$$ −7953.03 −0.713480 −0.356740 0.934204i $$-0.616112\pi$$
−0.356740 + 0.934204i $$0.616112\pi$$
$$500$$ 500.000 0.0447214
$$501$$ 0 0
$$502$$ 13602.8 1.20941
$$503$$ 11805.6 1.04649 0.523245 0.852182i $$-0.324721\pi$$
0.523245 + 0.852182i $$0.324721\pi$$
$$504$$ 0 0
$$505$$ 7560.76 0.666237
$$506$$ −2204.76 −0.193703
$$507$$ 0 0
$$508$$ −4271.48 −0.373063
$$509$$ 2732.89 0.237983 0.118991 0.992895i $$-0.462034\pi$$
0.118991 + 0.992895i $$0.462034\pi$$
$$510$$ 0 0
$$511$$ −8129.09 −0.703738
$$512$$ 512.000 0.0441942
$$513$$ 0 0
$$514$$ −11152.0 −0.956992
$$515$$ 4786.40 0.409541
$$516$$ 0 0
$$517$$ 21529.6 1.83147
$$518$$ 290.640 0.0246525
$$519$$ 0 0
$$520$$ 1694.87 0.142932
$$521$$ −14710.9 −1.23704 −0.618518 0.785771i $$-0.712267\pi$$
−0.618518 + 0.785771i $$0.712267\pi$$
$$522$$ 0 0
$$523$$ −7034.35 −0.588127 −0.294064 0.955786i $$-0.595008\pi$$
−0.294064 + 0.955786i $$0.595008\pi$$
$$524$$ 701.987 0.0585237
$$525$$ 0 0
$$526$$ 11339.2 0.939944
$$527$$ −504.269 −0.0416818
$$528$$ 0 0
$$529$$ 529.000 0.0434783
$$530$$ 3683.16 0.301861
$$531$$ 0 0
$$532$$ −1585.80 −0.129235
$$533$$ −19742.2 −1.60437
$$534$$ 0 0
$$535$$ 8710.79 0.703926
$$536$$ 738.739 0.0595311
$$537$$ 0 0
$$538$$ −12080.4 −0.968075
$$539$$ 22.2204 0.00177569
$$540$$ 0 0
$$541$$ 1552.90 0.123409 0.0617045 0.998094i $$-0.480346\pi$$
0.0617045 + 0.998094i $$0.480346\pi$$
$$542$$ −13798.5 −1.09354
$$543$$ 0 0
$$544$$ −54.5710 −0.00430094
$$545$$ 5833.86 0.458523
$$546$$ 0 0
$$547$$ 174.657 0.0136523 0.00682614 0.999977i $$-0.497827\pi$$
0.00682614 + 0.999977i $$0.497827\pi$$
$$548$$ −1903.59 −0.148389
$$549$$ 0 0
$$550$$ −2396.48 −0.185793
$$551$$ −1234.55 −0.0954510
$$552$$ 0 0
$$553$$ −11876.5 −0.913276
$$554$$ 11235.4 0.861633
$$555$$ 0 0
$$556$$ 612.669 0.0467319
$$557$$ 1990.63 0.151429 0.0757143 0.997130i $$-0.475876\pi$$
0.0757143 + 0.997130i $$0.475876\pi$$
$$558$$ 0 0
$$559$$ 7727.48 0.584683
$$560$$ −1480.62 −0.111728
$$561$$ 0 0
$$562$$ −6139.78 −0.460838
$$563$$ −208.006 −0.0155709 −0.00778543 0.999970i $$-0.502478\pi$$
−0.00778543 + 0.999970i $$0.502478\pi$$
$$564$$ 0 0
$$565$$ 1966.44 0.146422
$$566$$ 2809.71 0.208659
$$567$$ 0 0
$$568$$ 5014.83 0.370454
$$569$$ 3003.05 0.221256 0.110628 0.993862i $$-0.464714\pi$$
0.110628 + 0.993862i $$0.464714\pi$$
$$570$$ 0 0
$$571$$ −10796.1 −0.791249 −0.395624 0.918412i $$-0.629472\pi$$
−0.395624 + 0.918412i $$0.629472\pi$$
$$572$$ −8123.43 −0.593807
$$573$$ 0 0
$$574$$ 17246.6 1.25411
$$575$$ 575.000 0.0417029
$$576$$ 0 0
$$577$$ −26011.3 −1.87671 −0.938357 0.345667i $$-0.887653\pi$$
−0.938357 + 0.345667i $$0.887653\pi$$
$$578$$ −9820.18 −0.706688
$$579$$ 0 0
$$580$$ −1152.66 −0.0825203
$$581$$ −11288.5 −0.806066
$$582$$ 0 0
$$583$$ −17653.2 −1.25407
$$584$$ 3513.81 0.248977
$$585$$ 0 0
$$586$$ 4814.09 0.339366
$$587$$ 2774.97 0.195120 0.0975598 0.995230i $$-0.468896\pi$$
0.0975598 + 0.995230i $$0.468896\pi$$
$$588$$ 0 0
$$589$$ 6334.11 0.443111
$$590$$ 3770.32 0.263087
$$591$$ 0 0
$$592$$ −125.629 −0.00872185
$$593$$ 2384.07 0.165096 0.0825481 0.996587i $$-0.473694\pi$$
0.0825481 + 0.996587i $$0.473694\pi$$
$$594$$ 0 0
$$595$$ 157.810 0.0108733
$$596$$ −2027.62 −0.139353
$$597$$ 0 0
$$598$$ 1949.10 0.133285
$$599$$ 1090.87 0.0744102 0.0372051 0.999308i $$-0.488155\pi$$
0.0372051 + 0.999308i $$0.488155\pi$$
$$600$$ 0 0
$$601$$ −5192.37 −0.352414 −0.176207 0.984353i $$-0.556383\pi$$
−0.176207 + 0.984353i $$0.556383\pi$$
$$602$$ −6750.65 −0.457036
$$603$$ 0 0
$$604$$ 9751.36 0.656916
$$605$$ 4831.22 0.324657
$$606$$ 0 0
$$607$$ 1205.44 0.0806054 0.0403027 0.999188i $$-0.487168\pi$$
0.0403027 + 0.999188i $$0.487168\pi$$
$$608$$ 685.465 0.0457225
$$609$$ 0 0
$$610$$ 8490.42 0.563553
$$611$$ −19033.1 −1.26022
$$612$$ 0 0
$$613$$ −14243.2 −0.938466 −0.469233 0.883075i $$-0.655469\pi$$
−0.469233 + 0.883075i $$0.655469\pi$$
$$614$$ −919.487 −0.0604356
$$615$$ 0 0
$$616$$ 7096.55 0.464169
$$617$$ 422.492 0.0275671 0.0137835 0.999905i $$-0.495612\pi$$
0.0137835 + 0.999905i $$0.495612\pi$$
$$618$$ 0 0
$$619$$ −8826.35 −0.573119 −0.286560 0.958062i $$-0.592512\pi$$
−0.286560 + 0.958062i $$0.592512\pi$$
$$620$$ 5913.98 0.383083
$$621$$ 0 0
$$622$$ −8238.96 −0.531113
$$623$$ 20781.7 1.33644
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 3368.29 0.215054
$$627$$ 0 0
$$628$$ 1023.87 0.0650584
$$629$$ 13.3901 0.000848804 0
$$630$$ 0 0
$$631$$ −19684.1 −1.24186 −0.620929 0.783867i $$-0.713244\pi$$
−0.620929 + 0.783867i $$0.713244\pi$$
$$632$$ 5133.65 0.323110
$$633$$ 0 0
$$634$$ −17372.9 −1.08828
$$635$$ −5339.35 −0.333678
$$636$$ 0 0
$$637$$ −19.6437 −0.00122184
$$638$$ 5524.67 0.342827
$$639$$ 0 0
$$640$$ 640.000 0.0395285
$$641$$ −15113.1 −0.931253 −0.465626 0.884981i $$-0.654171\pi$$
−0.465626 + 0.884981i $$0.654171\pi$$
$$642$$ 0 0
$$643$$ −16917.8 −1.03760 −0.518798 0.854897i $$-0.673620\pi$$
−0.518798 + 0.854897i $$0.673620\pi$$
$$644$$ −1702.71 −0.104187
$$645$$ 0 0
$$646$$ −73.0596 −0.00444968
$$647$$ −19564.5 −1.18881 −0.594405 0.804166i $$-0.702612\pi$$
−0.594405 + 0.804166i $$0.702612\pi$$
$$648$$ 0 0
$$649$$ −18071.0 −1.09299
$$650$$ 2118.58 0.127843
$$651$$ 0 0
$$652$$ 1286.53 0.0772767
$$653$$ 22735.0 1.36247 0.681233 0.732067i $$-0.261444\pi$$
0.681233 + 0.732067i $$0.261444\pi$$
$$654$$ 0 0
$$655$$ 877.483 0.0523452
$$656$$ −7454.87 −0.443695
$$657$$ 0 0
$$658$$ 16627.1 0.985094
$$659$$ 30730.7 1.81654 0.908269 0.418388i $$-0.137405\pi$$
0.908269 + 0.418388i $$0.137405\pi$$
$$660$$ 0 0
$$661$$ −29204.3 −1.71848 −0.859240 0.511573i $$-0.829063\pi$$
−0.859240 + 0.511573i $$0.829063\pi$$
$$662$$ 8615.81 0.505835
$$663$$ 0 0
$$664$$ 4879.45 0.285180
$$665$$ −1982.25 −0.115592
$$666$$ 0 0
$$667$$ −1325.56 −0.0769506
$$668$$ 11704.9 0.677957
$$669$$ 0 0
$$670$$ 923.424 0.0532462
$$671$$ −40694.2 −2.34126
$$672$$ 0 0
$$673$$ −17530.1 −1.00406 −0.502032 0.864849i $$-0.667414\pi$$
−0.502032 + 0.864849i $$0.667414\pi$$
$$674$$ −580.312 −0.0331644
$$675$$ 0 0
$$676$$ −1606.56 −0.0914064
$$677$$ 20553.4 1.16681 0.583407 0.812180i $$-0.301719\pi$$
0.583407 + 0.812180i $$0.301719\pi$$
$$678$$ 0 0
$$679$$ 26443.8 1.49458
$$680$$ −68.2138 −0.00384688
$$681$$ 0 0
$$682$$ −28345.5 −1.59150
$$683$$ −13174.8 −0.738098 −0.369049 0.929410i $$-0.620316\pi$$
−0.369049 + 0.929410i $$0.620316\pi$$
$$684$$ 0 0
$$685$$ −2379.49 −0.132723
$$686$$ 12713.5 0.707584
$$687$$ 0 0
$$688$$ 2917.98 0.161696
$$689$$ 15606.2 0.862913
$$690$$ 0 0
$$691$$ −14800.8 −0.814831 −0.407415 0.913243i $$-0.633570\pi$$
−0.407415 + 0.913243i $$0.633570\pi$$
$$692$$ −7247.38 −0.398127
$$693$$ 0 0
$$694$$ −2085.88 −0.114091
$$695$$ 765.836 0.0417983
$$696$$ 0 0
$$697$$ 794.570 0.0431800
$$698$$ −3639.13 −0.197339
$$699$$ 0 0
$$700$$ −1850.77 −0.0999324
$$701$$ 12311.5 0.663336 0.331668 0.943396i $$-0.392389\pi$$
0.331668 + 0.943396i $$0.392389\pi$$
$$702$$ 0 0
$$703$$ −168.192 −0.00902347
$$704$$ −3067.49 −0.164219
$$705$$ 0 0
$$706$$ 9028.59 0.481297
$$707$$ −27986.5 −1.48874
$$708$$ 0 0
$$709$$ 3893.89 0.206260 0.103130 0.994668i $$-0.467114\pi$$
0.103130 + 0.994668i $$0.467114\pi$$
$$710$$ 6268.54 0.331344
$$711$$ 0 0
$$712$$ −8982.94 −0.472823
$$713$$ 6801.08 0.357227
$$714$$ 0 0
$$715$$ −10154.3 −0.531117
$$716$$ −3650.65 −0.190547
$$717$$ 0 0
$$718$$ −23055.8 −1.19838
$$719$$ 19942.5 1.03440 0.517198 0.855866i $$-0.326975\pi$$
0.517198 + 0.855866i $$0.326975\pi$$
$$720$$ 0 0
$$721$$ −17717.1 −0.915143
$$722$$ −12800.3 −0.659803
$$723$$ 0 0
$$724$$ 14682.2 0.753673
$$725$$ −1440.83 −0.0738084
$$726$$ 0 0
$$727$$ 36167.0 1.84506 0.922530 0.385926i $$-0.126118\pi$$
0.922530 + 0.385926i $$0.126118\pi$$
$$728$$ −6273.63 −0.319391
$$729$$ 0 0
$$730$$ 4392.27 0.222692
$$731$$ −311.010 −0.0157361
$$732$$ 0 0
$$733$$ −11669.5 −0.588025 −0.294013 0.955802i $$-0.594991\pi$$
−0.294013 + 0.955802i $$0.594991\pi$$
$$734$$ 13788.2 0.693366
$$735$$ 0 0
$$736$$ 736.000 0.0368605
$$737$$ −4425.93 −0.221209
$$738$$ 0 0
$$739$$ 75.0536 0.00373598 0.00186799 0.999998i $$-0.499405\pi$$
0.00186799 + 0.999998i $$0.499405\pi$$
$$740$$ −157.037 −0.00780106
$$741$$ 0 0
$$742$$ −13633.4 −0.674524
$$743$$ −28279.8 −1.39635 −0.698173 0.715929i $$-0.746003\pi$$
−0.698173 + 0.715929i $$0.746003\pi$$
$$744$$ 0 0
$$745$$ −2534.53 −0.124641
$$746$$ 15466.5 0.759074
$$747$$ 0 0
$$748$$ 326.946 0.0159817
$$749$$ −32243.4 −1.57296
$$750$$ 0 0
$$751$$ −17268.1 −0.839044 −0.419522 0.907745i $$-0.637802\pi$$
−0.419522 + 0.907745i $$0.637802\pi$$
$$752$$ −7187.09 −0.348519
$$753$$ 0 0
$$754$$ −4884.03 −0.235897
$$755$$ 12189.2 0.587564
$$756$$ 0 0
$$757$$ −12525.8 −0.601400 −0.300700 0.953719i $$-0.597220\pi$$
−0.300700 + 0.953719i $$0.597220\pi$$
$$758$$ −18991.4 −0.910026
$$759$$ 0 0
$$760$$ 856.831 0.0408954
$$761$$ 18670.1 0.889343 0.444672 0.895694i $$-0.353320\pi$$
0.444672 + 0.895694i $$0.353320\pi$$
$$762$$ 0 0
$$763$$ −21594.3 −1.02460
$$764$$ 7363.83 0.348710
$$765$$ 0 0
$$766$$ 25754.0 1.21479
$$767$$ 15975.5 0.752074
$$768$$ 0 0
$$769$$ −32969.6 −1.54605 −0.773027 0.634373i $$-0.781258\pi$$
−0.773027 + 0.634373i $$0.781258\pi$$
$$770$$ 8870.68 0.415165
$$771$$ 0 0
$$772$$ −2447.27 −0.114092
$$773$$ 23251.3 1.08188 0.540938 0.841062i $$-0.318069\pi$$
0.540938 + 0.841062i $$0.318069\pi$$
$$774$$ 0 0
$$775$$ 7392.48 0.342640
$$776$$ −11430.4 −0.528771
$$777$$ 0 0
$$778$$ 16400.8 0.755781
$$779$$ −9980.57 −0.459039
$$780$$ 0 0
$$781$$ −30044.8 −1.37655
$$782$$ −78.4458 −0.00358723
$$783$$ 0 0
$$784$$ −7.41767 −0.000337904 0
$$785$$ 1279.83 0.0581900
$$786$$ 0 0
$$787$$ −29782.8 −1.34897 −0.674486 0.738288i $$-0.735635\pi$$
−0.674486 + 0.738288i $$0.735635\pi$$
$$788$$ −11321.0 −0.511796
$$789$$ 0 0
$$790$$ 6417.07 0.288999
$$791$$ −7278.86 −0.327189
$$792$$ 0 0
$$793$$ 35975.3 1.61100
$$794$$ 15685.4 0.701073
$$795$$ 0 0
$$796$$ −4650.98 −0.207097
$$797$$ −35307.2 −1.56919 −0.784596 0.620008i $$-0.787129\pi$$
−0.784596 + 0.620008i $$0.787129\pi$$
$$798$$ 0 0
$$799$$ 766.029 0.0339176
$$800$$ 800.000 0.0353553
$$801$$ 0 0
$$802$$ 29068.4 1.27985
$$803$$ −21052.0 −0.925165
$$804$$ 0 0
$$805$$ −2128.39 −0.0931874
$$806$$ 25058.5 1.09510
$$807$$ 0 0
$$808$$ 12097.2 0.526706
$$809$$ −7752.46 −0.336912 −0.168456 0.985709i $$-0.553878\pi$$
−0.168456 + 0.985709i $$0.553878\pi$$
$$810$$ 0 0
$$811$$ 23471.6 1.01627 0.508137 0.861276i $$-0.330334\pi$$
0.508137 + 0.861276i $$0.330334\pi$$
$$812$$ 4266.64 0.184396
$$813$$ 0 0
$$814$$ 752.671 0.0324092
$$815$$ 1608.16 0.0691184
$$816$$ 0 0
$$817$$ 3906.59 0.167288
$$818$$ 26776.0 1.14450
$$819$$ 0 0
$$820$$ −9318.59 −0.396853
$$821$$ −2467.55 −0.104894 −0.0524470 0.998624i $$-0.516702\pi$$
−0.0524470 + 0.998624i $$0.516702\pi$$
$$822$$ 0 0
$$823$$ 21984.5 0.931144 0.465572 0.885010i $$-0.345849\pi$$
0.465572 + 0.885010i $$0.345849\pi$$
$$824$$ 7658.23 0.323771
$$825$$ 0 0
$$826$$ −13956.0 −0.587883
$$827$$ 587.293 0.0246943 0.0123472 0.999924i $$-0.496070\pi$$
0.0123472 + 0.999924i $$0.496070\pi$$
$$828$$ 0 0
$$829$$ 41822.8 1.75219 0.876096 0.482137i $$-0.160139\pi$$
0.876096 + 0.482137i $$0.160139\pi$$
$$830$$ 6099.32 0.255073
$$831$$ 0 0
$$832$$ 2711.79 0.112998
$$833$$ 0.790605 3.28846e−5 0
$$834$$ 0 0
$$835$$ 14631.1 0.606383
$$836$$ −4106.76 −0.169898
$$837$$ 0 0
$$838$$ 6206.20 0.255835
$$839$$ 10126.5 0.416693 0.208346 0.978055i $$-0.433192\pi$$
0.208346 + 0.978055i $$0.433192\pi$$
$$840$$ 0 0
$$841$$ −21067.4 −0.863808
$$842$$ −12151.6 −0.497356
$$843$$ 0 0
$$844$$ 5598.33 0.228320
$$845$$ −2008.20 −0.0817564
$$846$$ 0 0
$$847$$ −17883.0 −0.725463
$$848$$ 5893.05 0.238642
$$849$$ 0 0
$$850$$ −85.2672 −0.00344075
$$851$$ −180.592 −0.00727453
$$852$$ 0 0
$$853$$ 11584.4 0.464995 0.232498 0.972597i $$-0.425310\pi$$
0.232498 + 0.972597i $$0.425310\pi$$
$$854$$ −31427.7 −1.25929
$$855$$ 0 0
$$856$$ 13937.3 0.556502
$$857$$ 9221.47 0.367561 0.183780 0.982967i $$-0.441166\pi$$
0.183780 + 0.982967i $$0.441166\pi$$
$$858$$ 0 0
$$859$$ 34654.2 1.37647 0.688235 0.725488i $$-0.258386\pi$$
0.688235 + 0.725488i $$0.258386\pi$$
$$860$$ 3647.47 0.144625
$$861$$ 0 0
$$862$$ −28240.7 −1.11587
$$863$$ −42887.7 −1.69167 −0.845837 0.533441i $$-0.820899\pi$$
−0.845837 + 0.533441i $$0.820899\pi$$
$$864$$ 0 0
$$865$$ −9059.22 −0.356096
$$866$$ 17111.9 0.671463
$$867$$ 0 0
$$868$$ −21890.9 −0.856020
$$869$$ −30756.7 −1.20063
$$870$$ 0 0
$$871$$ 3912.70 0.152212
$$872$$ 9334.17 0.362494
$$873$$ 0 0
$$874$$ 985.356 0.0381352
$$875$$ −2313.47 −0.0893823
$$876$$ 0 0
$$877$$ 45935.5 1.76868 0.884339 0.466846i $$-0.154610\pi$$
0.884339 + 0.466846i $$0.154610\pi$$
$$878$$ −21788.2 −0.837488
$$879$$ 0 0
$$880$$ −3834.37 −0.146882
$$881$$ 71.9309 0.00275075 0.00137538 0.999999i $$-0.499562\pi$$
0.00137538 + 0.999999i $$0.499562\pi$$
$$882$$ 0 0
$$883$$ 20003.8 0.762379 0.381189 0.924497i $$-0.375515\pi$$
0.381189 + 0.924497i $$0.375515\pi$$
$$884$$ −289.033 −0.0109969
$$885$$ 0 0
$$886$$ −32241.0 −1.22253
$$887$$ −26357.3 −0.997737 −0.498869 0.866678i $$-0.666251\pi$$
−0.498869 + 0.866678i $$0.666251\pi$$
$$888$$ 0 0
$$889$$ 19763.9 0.745623
$$890$$ −11228.7 −0.422906
$$891$$ 0 0
$$892$$ 17031.9 0.639317
$$893$$ −9622.06 −0.360571
$$894$$ 0 0
$$895$$ −4563.32 −0.170430
$$896$$ −2368.99 −0.0883286
$$897$$ 0 0
$$898$$ −9622.57 −0.357583
$$899$$ −17042.1 −0.632242
$$900$$ 0 0
$$901$$ −628.105 −0.0232244
$$902$$ 44663.6 1.64871
$$903$$ 0 0
$$904$$ 3146.30 0.115757
$$905$$ 18352.7 0.674106
$$906$$ 0 0
$$907$$ −39300.4 −1.43875 −0.719377 0.694620i $$-0.755572\pi$$
−0.719377 + 0.694620i $$0.755572\pi$$
$$908$$ 16100.1 0.588438
$$909$$ 0 0
$$910$$ −7842.04 −0.285672
$$911$$ −31099.2 −1.13103 −0.565513 0.824740i $$-0.691322\pi$$
−0.565513 + 0.824740i $$0.691322\pi$$
$$912$$ 0 0
$$913$$ −29233.8 −1.05969
$$914$$ −452.657 −0.0163814
$$915$$ 0 0
$$916$$ 14492.2 0.522745
$$917$$ −3248.05 −0.116968
$$918$$ 0 0
$$919$$ 18935.8 0.679690 0.339845 0.940481i $$-0.389625\pi$$
0.339845 + 0.940481i $$0.389625\pi$$
$$920$$ 920.000 0.0329690
$$921$$ 0 0
$$922$$ 8698.33 0.310699
$$923$$ 26560.9 0.947195
$$924$$ 0 0
$$925$$ −196.296 −0.00697748
$$926$$ −1978.63 −0.0702178
$$927$$ 0 0
$$928$$ −1844.26 −0.0652380
$$929$$ −40156.1 −1.41817 −0.709085 0.705123i $$-0.750892\pi$$
−0.709085 + 0.705123i $$0.750892\pi$$
$$930$$ 0 0
$$931$$ −9.93077 −0.000349590 0
$$932$$ −26011.2 −0.914192
$$933$$ 0 0
$$934$$ −17025.8 −0.596469
$$935$$ 408.682 0.0142945
$$936$$ 0 0
$$937$$ 126.898 0.00442432 0.00221216 0.999998i $$-0.499296\pi$$
0.00221216 + 0.999998i $$0.499296\pi$$
$$938$$ −3418.10 −0.118982
$$939$$ 0 0
$$940$$ −8983.86 −0.311725
$$941$$ 19266.6 0.667452 0.333726 0.942670i $$-0.391694\pi$$
0.333726 + 0.942670i $$0.391694\pi$$
$$942$$ 0 0
$$943$$ −10716.4 −0.370067
$$944$$ 6032.51 0.207989
$$945$$ 0 0
$$946$$ −17482.2 −0.600840
$$947$$ 54560.4 1.87220 0.936101 0.351732i $$-0.114407\pi$$
0.936101 + 0.351732i $$0.114407\pi$$
$$948$$ 0 0
$$949$$ 18610.8 0.636598
$$950$$ 1071.04 0.0365780
$$951$$ 0 0
$$952$$ 252.497 0.00859607
$$953$$ 44976.2 1.52877 0.764387 0.644758i $$-0.223042\pi$$
0.764387 + 0.644758i $$0.223042\pi$$
$$954$$ 0 0
$$955$$ 9204.79 0.311895
$$956$$ 10760.3 0.364030
$$957$$ 0 0
$$958$$ 24117.1 0.813350
$$959$$ 8807.79 0.296578
$$960$$ 0 0
$$961$$ 57647.0 1.93505
$$962$$ −665.391 −0.0223005
$$963$$ 0 0
$$964$$ −178.783 −0.00597326
$$965$$ −3059.08 −0.102047
$$966$$ 0 0
$$967$$ −39431.7 −1.31131 −0.655656 0.755059i $$-0.727608\pi$$
−0.655656 + 0.755059i $$0.727608\pi$$
$$968$$ 7729.96 0.256664
$$969$$ 0 0
$$970$$ −14288.0 −0.472947
$$971$$ −20249.9 −0.669258 −0.334629 0.942350i $$-0.608611\pi$$
−0.334629 + 0.942350i $$0.608611\pi$$
$$972$$ 0 0
$$973$$ −2834.78 −0.0934006
$$974$$ 23210.6 0.763567
$$975$$ 0 0
$$976$$ 13584.7 0.445527
$$977$$ 9673.55 0.316770 0.158385 0.987377i $$-0.449371\pi$$
0.158385 + 0.987377i $$0.449371\pi$$
$$978$$ 0 0
$$979$$ 53818.6 1.75695
$$980$$ −9.27209 −0.000302231 0
$$981$$ 0 0
$$982$$ 9303.77 0.302337
$$983$$ 17264.3 0.560168 0.280084 0.959975i $$-0.409638\pi$$
0.280084 + 0.959975i $$0.409638\pi$$
$$984$$ 0 0
$$985$$ −14151.3 −0.457764
$$986$$ 196.569 0.00634891
$$987$$ 0 0
$$988$$ 3630.54 0.116906
$$989$$ 4194.60 0.134864
$$990$$ 0 0
$$991$$ 23892.9 0.765876 0.382938 0.923774i $$-0.374912\pi$$
0.382938 + 0.923774i $$0.374912\pi$$
$$992$$ 9462.37 0.302854
$$993$$ 0 0
$$994$$ −23203.3 −0.740406
$$995$$ −5813.72 −0.185234
$$996$$ 0 0
$$997$$ −35830.2 −1.13817 −0.569083 0.822280i $$-0.692702\pi$$
−0.569083 + 0.822280i $$0.692702\pi$$
$$998$$ −15906.1 −0.504507
$$999$$ 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 2070.4.a.bj.1.2 4
3.2 odd 2 230.4.a.h.1.3 4
12.11 even 2 1840.4.a.m.1.2 4
15.2 even 4 1150.4.b.n.599.2 8
15.8 even 4 1150.4.b.n.599.7 8
15.14 odd 2 1150.4.a.p.1.2 4

By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.a.h.1.3 4 3.2 odd 2
1150.4.a.p.1.2 4 15.14 odd 2
1150.4.b.n.599.2 8 15.2 even 4
1150.4.b.n.599.7 8 15.8 even 4
1840.4.a.m.1.2 4 12.11 even 2
2070.4.a.bj.1.2 4 1.1 even 1 trivial