# Properties

 Label 1764.4.a.k.1.1 Level $1764$ Weight $4$ Character 1764.1 Self dual yes Analytic conductor $104.079$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1764.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$104.079369250$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 28) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1764.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+6.00000 q^{5} +O(q^{10})$$ $$q+6.00000 q^{5} +12.0000 q^{11} +82.0000 q^{13} -30.0000 q^{17} -68.0000 q^{19} -216.000 q^{23} -89.0000 q^{25} -246.000 q^{29} +112.000 q^{31} +110.000 q^{37} -246.000 q^{41} -172.000 q^{43} +192.000 q^{47} -558.000 q^{53} +72.0000 q^{55} +540.000 q^{59} -110.000 q^{61} +492.000 q^{65} +140.000 q^{67} +840.000 q^{71} +550.000 q^{73} -208.000 q^{79} +516.000 q^{83} -180.000 q^{85} -1398.00 q^{89} -408.000 q^{95} -1586.00 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 6.00000 0.536656 0.268328 0.963328i $$-0.413529\pi$$
0.268328 + 0.963328i $$0.413529\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 12.0000 0.328921 0.164461 0.986384i $$-0.447412\pi$$
0.164461 + 0.986384i $$0.447412\pi$$
$$12$$ 0 0
$$13$$ 82.0000 1.74944 0.874720 0.484629i $$-0.161046\pi$$
0.874720 + 0.484629i $$0.161046\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −30.0000 −0.428004 −0.214002 0.976833i $$-0.568650\pi$$
−0.214002 + 0.976833i $$0.568650\pi$$
$$18$$ 0 0
$$19$$ −68.0000 −0.821067 −0.410533 0.911846i $$-0.634657\pi$$
−0.410533 + 0.911846i $$0.634657\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −216.000 −1.95822 −0.979111 0.203326i $$-0.934825\pi$$
−0.979111 + 0.203326i $$0.934825\pi$$
$$24$$ 0 0
$$25$$ −89.0000 −0.712000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −246.000 −1.57521 −0.787604 0.616181i $$-0.788679\pi$$
−0.787604 + 0.616181i $$0.788679\pi$$
$$30$$ 0 0
$$31$$ 112.000 0.648897 0.324448 0.945903i $$-0.394821\pi$$
0.324448 + 0.945903i $$0.394821\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 110.000 0.488754 0.244377 0.969680i $$-0.421417\pi$$
0.244377 + 0.969680i $$0.421417\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −246.000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ −172.000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 192.000 0.595874 0.297937 0.954586i $$-0.403701\pi$$
0.297937 + 0.954586i $$0.403701\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −558.000 −1.44617 −0.723087 0.690757i $$-0.757277\pi$$
−0.723087 + 0.690757i $$0.757277\pi$$
$$54$$ 0 0
$$55$$ 72.0000 0.176518
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 540.000 1.19156 0.595780 0.803148i $$-0.296843\pi$$
0.595780 + 0.803148i $$0.296843\pi$$
$$60$$ 0 0
$$61$$ −110.000 −0.230886 −0.115443 0.993314i $$-0.536829\pi$$
−0.115443 + 0.993314i $$0.536829\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 492.000 0.938848
$$66$$ 0 0
$$67$$ 140.000 0.255279 0.127640 0.991821i $$-0.459260\pi$$
0.127640 + 0.991821i $$0.459260\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 840.000 1.40408 0.702040 0.712138i $$-0.252273\pi$$
0.702040 + 0.712138i $$0.252273\pi$$
$$72$$ 0 0
$$73$$ 550.000 0.881817 0.440908 0.897552i $$-0.354656\pi$$
0.440908 + 0.897552i $$0.354656\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −208.000 −0.296226 −0.148113 0.988970i $$-0.547320\pi$$
−0.148113 + 0.988970i $$0.547320\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 516.000 0.682390 0.341195 0.939993i $$-0.389168\pi$$
0.341195 + 0.939993i $$0.389168\pi$$
$$84$$ 0 0
$$85$$ −180.000 −0.229691
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −1398.00 −1.66503 −0.832515 0.554002i $$-0.813100\pi$$
−0.832515 + 0.554002i $$0.813100\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −408.000 −0.440631
$$96$$ 0 0
$$97$$ −1586.00 −1.66014 −0.830072 0.557657i $$-0.811701\pi$$
−0.830072 + 0.557657i $$0.811701\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1242.00 −1.22360 −0.611800 0.791012i $$-0.709554\pi$$
−0.611800 + 0.791012i $$0.709554\pi$$
$$102$$ 0 0
$$103$$ −680.000 −0.650509 −0.325254 0.945627i $$-0.605450\pi$$
−0.325254 + 0.945627i $$0.605450\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −996.000 −0.899878 −0.449939 0.893059i $$-0.648554\pi$$
−0.449939 + 0.893059i $$0.648554\pi$$
$$108$$ 0 0
$$109$$ 1382.00 1.21442 0.607209 0.794542i $$-0.292289\pi$$
0.607209 + 0.794542i $$0.292289\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 750.000 0.624372 0.312186 0.950021i $$-0.398939\pi$$
0.312186 + 0.950021i $$0.398939\pi$$
$$114$$ 0 0
$$115$$ −1296.00 −1.05089
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1187.00 −0.891811
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1284.00 −0.918756
$$126$$ 0 0
$$127$$ 176.000 0.122972 0.0614861 0.998108i $$-0.480416\pi$$
0.0614861 + 0.998108i $$0.480416\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1548.00 −1.03244 −0.516219 0.856457i $$-0.672661\pi$$
−0.516219 + 0.856457i $$0.672661\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −378.000 −0.235728 −0.117864 0.993030i $$-0.537605\pi$$
−0.117864 + 0.993030i $$0.537605\pi$$
$$138$$ 0 0
$$139$$ 2500.00 1.52552 0.762760 0.646682i $$-0.223844\pi$$
0.762760 + 0.646682i $$0.223844\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 984.000 0.575428
$$144$$ 0 0
$$145$$ −1476.00 −0.845346
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −846.000 −0.465148 −0.232574 0.972579i $$-0.574715\pi$$
−0.232574 + 0.972579i $$0.574715\pi$$
$$150$$ 0 0
$$151$$ −2536.00 −1.36673 −0.683367 0.730075i $$-0.739485\pi$$
−0.683367 + 0.730075i $$0.739485\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 672.000 0.348234
$$156$$ 0 0
$$157$$ 1186.00 0.602886 0.301443 0.953484i $$-0.402532\pi$$
0.301443 + 0.953484i $$0.402532\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 2108.00 1.01295 0.506476 0.862254i $$-0.330948\pi$$
0.506476 + 0.862254i $$0.330948\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1944.00 −0.900786 −0.450393 0.892830i $$-0.648716\pi$$
−0.450393 + 0.892830i $$0.648716\pi$$
$$168$$ 0 0
$$169$$ 4527.00 2.06054
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1362.00 −0.598560 −0.299280 0.954165i $$-0.596747\pi$$
−0.299280 + 0.954165i $$0.596747\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1596.00 −0.666428 −0.333214 0.942851i $$-0.608133\pi$$
−0.333214 + 0.942851i $$0.608133\pi$$
$$180$$ 0 0
$$181$$ 1690.00 0.694015 0.347007 0.937862i $$-0.387198\pi$$
0.347007 + 0.937862i $$0.387198\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 660.000 0.262293
$$186$$ 0 0
$$187$$ −360.000 −0.140780
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3552.00 −1.34562 −0.672811 0.739815i $$-0.734913\pi$$
−0.672811 + 0.739815i $$0.734913\pi$$
$$192$$ 0 0
$$193$$ −2686.00 −1.00177 −0.500887 0.865512i $$-0.666993\pi$$
−0.500887 + 0.865512i $$0.666993\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1410.00 0.509941 0.254970 0.966949i $$-0.417934\pi$$
0.254970 + 0.966949i $$0.417934\pi$$
$$198$$ 0 0
$$199$$ 2968.00 1.05727 0.528633 0.848850i $$-0.322705\pi$$
0.528633 + 0.848850i $$0.322705\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −1476.00 −0.502870
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −816.000 −0.270067
$$210$$ 0 0
$$211$$ −1348.00 −0.439811 −0.219906 0.975521i $$-0.570575\pi$$
−0.219906 + 0.975521i $$0.570575\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −1032.00 −0.327357
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −2460.00 −0.748767
$$222$$ 0 0
$$223$$ −3872.00 −1.16273 −0.581364 0.813644i $$-0.697481\pi$$
−0.581364 + 0.813644i $$0.697481\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 5364.00 1.56838 0.784188 0.620524i $$-0.213080\pi$$
0.784188 + 0.620524i $$0.213080\pi$$
$$228$$ 0 0
$$229$$ 874.000 0.252208 0.126104 0.992017i $$-0.459753\pi$$
0.126104 + 0.992017i $$0.459753\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −378.000 −0.106282 −0.0531408 0.998587i $$-0.516923\pi$$
−0.0531408 + 0.998587i $$0.516923\pi$$
$$234$$ 0 0
$$235$$ 1152.00 0.319780
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −1920.00 −0.519642 −0.259821 0.965657i $$-0.583664\pi$$
−0.259821 + 0.965657i $$0.583664\pi$$
$$240$$ 0 0
$$241$$ −4322.00 −1.15521 −0.577603 0.816318i $$-0.696012\pi$$
−0.577603 + 0.816318i $$0.696012\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −5576.00 −1.43641
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 5292.00 1.33079 0.665395 0.746492i $$-0.268263\pi$$
0.665395 + 0.746492i $$0.268263\pi$$
$$252$$ 0 0
$$253$$ −2592.00 −0.644101
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −5118.00 −1.24223 −0.621113 0.783721i $$-0.713319\pi$$
−0.621113 + 0.783721i $$0.713319\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −3768.00 −0.883440 −0.441720 0.897153i $$-0.645632\pi$$
−0.441720 + 0.897153i $$0.645632\pi$$
$$264$$ 0 0
$$265$$ −3348.00 −0.776098
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 3918.00 0.888047 0.444024 0.896015i $$-0.353551\pi$$
0.444024 + 0.896015i $$0.353551\pi$$
$$270$$ 0 0
$$271$$ −4880.00 −1.09387 −0.546935 0.837175i $$-0.684206\pi$$
−0.546935 + 0.837175i $$0.684206\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1068.00 −0.234192
$$276$$ 0 0
$$277$$ −3538.00 −0.767429 −0.383714 0.923452i $$-0.625355\pi$$
−0.383714 + 0.923452i $$0.625355\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 5430.00 1.15276 0.576382 0.817180i $$-0.304464\pi$$
0.576382 + 0.817180i $$0.304464\pi$$
$$282$$ 0 0
$$283$$ 6436.00 1.35187 0.675937 0.736959i $$-0.263739\pi$$
0.675937 + 0.736959i $$0.263739\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4013.00 −0.816813
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1350.00 0.269174 0.134587 0.990902i $$-0.457029\pi$$
0.134587 + 0.990902i $$0.457029\pi$$
$$294$$ 0 0
$$295$$ 3240.00 0.639458
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −17712.0 −3.42579
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −660.000 −0.123907
$$306$$ 0 0
$$307$$ −3332.00 −0.619437 −0.309719 0.950828i $$-0.600235\pi$$
−0.309719 + 0.950828i $$0.600235\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −4728.00 −0.862059 −0.431029 0.902338i $$-0.641849\pi$$
−0.431029 + 0.902338i $$0.641849\pi$$
$$312$$ 0 0
$$313$$ −5114.00 −0.923516 −0.461758 0.887006i $$-0.652781\pi$$
−0.461758 + 0.887006i $$0.652781\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −7206.00 −1.27675 −0.638374 0.769726i $$-0.720393\pi$$
−0.638374 + 0.769726i $$0.720393\pi$$
$$318$$ 0 0
$$319$$ −2952.00 −0.518120
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2040.00 0.351420
$$324$$ 0 0
$$325$$ −7298.00 −1.24560
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 6260.00 1.03952 0.519759 0.854313i $$-0.326022\pi$$
0.519759 + 0.854313i $$0.326022\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 840.000 0.136997
$$336$$ 0 0
$$337$$ −5326.00 −0.860907 −0.430454 0.902613i $$-0.641646\pi$$
−0.430454 + 0.902613i $$0.641646\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1344.00 0.213436
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −36.0000 −0.00556940 −0.00278470 0.999996i $$-0.500886\pi$$
−0.00278470 + 0.999996i $$0.500886\pi$$
$$348$$ 0 0
$$349$$ −3134.00 −0.480685 −0.240343 0.970688i $$-0.577260\pi$$
−0.240343 + 0.970688i $$0.577260\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1218.00 0.183648 0.0918238 0.995775i $$-0.470730\pi$$
0.0918238 + 0.995775i $$0.470730\pi$$
$$354$$ 0 0
$$355$$ 5040.00 0.753508
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 10008.0 1.47131 0.735657 0.677354i $$-0.236873\pi$$
0.735657 + 0.677354i $$0.236873\pi$$
$$360$$ 0 0
$$361$$ −2235.00 −0.325849
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3300.00 0.473233
$$366$$ 0 0
$$367$$ 1072.00 0.152474 0.0762370 0.997090i $$-0.475709\pi$$
0.0762370 + 0.997090i $$0.475709\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −274.000 −0.0380353 −0.0190177 0.999819i $$-0.506054\pi$$
−0.0190177 + 0.999819i $$0.506054\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −20172.0 −2.75573
$$378$$ 0 0
$$379$$ 7652.00 1.03709 0.518545 0.855051i $$-0.326474\pi$$
0.518545 + 0.855051i $$0.326474\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 2160.00 0.288175 0.144087 0.989565i $$-0.453975\pi$$
0.144087 + 0.989565i $$0.453975\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 1074.00 0.139984 0.0699922 0.997548i $$-0.477703\pi$$
0.0699922 + 0.997548i $$0.477703\pi$$
$$390$$ 0 0
$$391$$ 6480.00 0.838127
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −1248.00 −0.158971
$$396$$ 0 0
$$397$$ −6926.00 −0.875582 −0.437791 0.899077i $$-0.644239\pi$$
−0.437791 + 0.899077i $$0.644239\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1938.00 −0.241344 −0.120672 0.992692i $$-0.538505\pi$$
−0.120672 + 0.992692i $$0.538505\pi$$
$$402$$ 0 0
$$403$$ 9184.00 1.13521
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1320.00 0.160762
$$408$$ 0 0
$$409$$ 9574.00 1.15747 0.578733 0.815517i $$-0.303547\pi$$
0.578733 + 0.815517i $$0.303547\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 3096.00 0.366209
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −5052.00 −0.589037 −0.294518 0.955646i $$-0.595159\pi$$
−0.294518 + 0.955646i $$0.595159\pi$$
$$420$$ 0 0
$$421$$ 3422.00 0.396147 0.198074 0.980187i $$-0.436531\pi$$
0.198074 + 0.980187i $$0.436531\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2670.00 0.304739
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −2208.00 −0.246765 −0.123382 0.992359i $$-0.539374\pi$$
−0.123382 + 0.992359i $$0.539374\pi$$
$$432$$ 0 0
$$433$$ 6814.00 0.756259 0.378129 0.925753i $$-0.376567\pi$$
0.378129 + 0.925753i $$0.376567\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 14688.0 1.60783
$$438$$ 0 0
$$439$$ −12584.0 −1.36811 −0.684056 0.729429i $$-0.739786\pi$$
−0.684056 + 0.729429i $$0.739786\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6996.00 −0.750316 −0.375158 0.926961i $$-0.622412\pi$$
−0.375158 + 0.926961i $$0.622412\pi$$
$$444$$ 0 0
$$445$$ −8388.00 −0.893549
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −9474.00 −0.995781 −0.497891 0.867240i $$-0.665892\pi$$
−0.497891 + 0.867240i $$0.665892\pi$$
$$450$$ 0 0
$$451$$ −2952.00 −0.308213
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5786.00 0.592249 0.296124 0.955149i $$-0.404306\pi$$
0.296124 + 0.955149i $$0.404306\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 3438.00 0.347340 0.173670 0.984804i $$-0.444437\pi$$
0.173670 + 0.984804i $$0.444437\pi$$
$$462$$ 0 0
$$463$$ 9392.00 0.942728 0.471364 0.881939i $$-0.343762\pi$$
0.471364 + 0.881939i $$0.343762\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −4956.00 −0.491084 −0.245542 0.969386i $$-0.578966\pi$$
−0.245542 + 0.969386i $$0.578966\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −2064.00 −0.200640
$$474$$ 0 0
$$475$$ 6052.00 0.584600
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −20592.0 −1.96424 −0.982122 0.188248i $$-0.939719\pi$$
−0.982122 + 0.188248i $$0.939719\pi$$
$$480$$ 0 0
$$481$$ 9020.00 0.855045
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −9516.00 −0.890926
$$486$$ 0 0
$$487$$ −13432.0 −1.24982 −0.624910 0.780697i $$-0.714864\pi$$
−0.624910 + 0.780697i $$0.714864\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 14172.0 1.30259 0.651297 0.758823i $$-0.274225\pi$$
0.651297 + 0.758823i $$0.274225\pi$$
$$492$$ 0 0
$$493$$ 7380.00 0.674196
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −5956.00 −0.534323 −0.267162 0.963652i $$-0.586086\pi$$
−0.267162 + 0.963652i $$0.586086\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 16968.0 1.50411 0.752053 0.659102i $$-0.229064\pi$$
0.752053 + 0.659102i $$0.229064\pi$$
$$504$$ 0 0
$$505$$ −7452.00 −0.656653
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 5214.00 0.454040 0.227020 0.973890i $$-0.427102\pi$$
0.227020 + 0.973890i $$0.427102\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −4080.00 −0.349100
$$516$$ 0 0
$$517$$ 2304.00 0.195996
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1398.00 −0.117558 −0.0587788 0.998271i $$-0.518721\pi$$
−0.0587788 + 0.998271i $$0.518721\pi$$
$$522$$ 0 0
$$523$$ 18580.0 1.55344 0.776718 0.629849i $$-0.216883\pi$$
0.776718 + 0.629849i $$0.216883\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −3360.00 −0.277730
$$528$$ 0 0
$$529$$ 34489.0 2.83463
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −20172.0 −1.63930
$$534$$ 0 0
$$535$$ −5976.00 −0.482925
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −18970.0 −1.50755 −0.753774 0.657133i $$-0.771769\pi$$
−0.753774 + 0.657133i $$0.771769\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 8292.00 0.651725
$$546$$ 0 0
$$547$$ −16036.0 −1.25347 −0.626737 0.779231i $$-0.715610\pi$$
−0.626737 + 0.779231i $$0.715610\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 16728.0 1.29335
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −8310.00 −0.632147 −0.316074 0.948735i $$-0.602365\pi$$
−0.316074 + 0.948735i $$0.602365\pi$$
$$558$$ 0 0
$$559$$ −14104.0 −1.06715
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 7092.00 0.530892 0.265446 0.964126i $$-0.414481\pi$$
0.265446 + 0.964126i $$0.414481\pi$$
$$564$$ 0 0
$$565$$ 4500.00 0.335073
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 7158.00 0.527380 0.263690 0.964608i $$-0.415060\pi$$
0.263690 + 0.964608i $$0.415060\pi$$
$$570$$ 0 0
$$571$$ 6500.00 0.476386 0.238193 0.971218i $$-0.423445\pi$$
0.238193 + 0.971218i $$0.423445\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 19224.0 1.39425
$$576$$ 0 0
$$577$$ −21794.0 −1.57244 −0.786218 0.617949i $$-0.787964\pi$$
−0.786218 + 0.617949i $$0.787964\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −6696.00 −0.475678
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 9756.00 0.685985 0.342993 0.939338i $$-0.388559\pi$$
0.342993 + 0.939338i $$0.388559\pi$$
$$588$$ 0 0
$$589$$ −7616.00 −0.532787
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 5586.00 0.386829 0.193414 0.981117i $$-0.438044\pi$$
0.193414 + 0.981117i $$0.438044\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 24.0000 0.00163708 0.000818542 1.00000i $$-0.499739\pi$$
0.000818542 1.00000i $$0.499739\pi$$
$$600$$ 0 0
$$601$$ −4298.00 −0.291712 −0.145856 0.989306i $$-0.546594\pi$$
−0.145856 + 0.989306i $$0.546594\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −7122.00 −0.478596
$$606$$ 0 0
$$607$$ −8480.00 −0.567039 −0.283519 0.958966i $$-0.591502\pi$$
−0.283519 + 0.958966i $$0.591502\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 15744.0 1.04245
$$612$$ 0 0
$$613$$ −1906.00 −0.125583 −0.0627917 0.998027i $$-0.520000\pi$$
−0.0627917 + 0.998027i $$0.520000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −7482.00 −0.488191 −0.244096 0.969751i $$-0.578491\pi$$
−0.244096 + 0.969751i $$0.578491\pi$$
$$618$$ 0 0
$$619$$ 7348.00 0.477126 0.238563 0.971127i $$-0.423324\pi$$
0.238563 + 0.971127i $$0.423324\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 3421.00 0.218944
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −3300.00 −0.209189
$$630$$ 0 0
$$631$$ 4520.00 0.285164 0.142582 0.989783i $$-0.454460\pi$$
0.142582 + 0.989783i $$0.454460\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 1056.00 0.0659938
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 19806.0 1.22042 0.610211 0.792239i $$-0.291085\pi$$
0.610211 + 0.792239i $$0.291085\pi$$
$$642$$ 0 0
$$643$$ 5020.00 0.307884 0.153942 0.988080i $$-0.450803\pi$$
0.153942 + 0.988080i $$0.450803\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 28392.0 1.72520 0.862600 0.505886i $$-0.168834\pi$$
0.862600 + 0.505886i $$0.168834\pi$$
$$648$$ 0 0
$$649$$ 6480.00 0.391930
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 17562.0 1.05246 0.526228 0.850343i $$-0.323606\pi$$
0.526228 + 0.850343i $$0.323606\pi$$
$$654$$ 0 0
$$655$$ −9288.00 −0.554064
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −4716.00 −0.278770 −0.139385 0.990238i $$-0.544513\pi$$
−0.139385 + 0.990238i $$0.544513\pi$$
$$660$$ 0 0
$$661$$ 22762.0 1.33939 0.669697 0.742635i $$-0.266424\pi$$
0.669697 + 0.742635i $$0.266424\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 53136.0 3.08461
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −1320.00 −0.0759434
$$672$$ 0 0
$$673$$ 4802.00 0.275042 0.137521 0.990499i $$-0.456086\pi$$
0.137521 + 0.990499i $$0.456086\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 21558.0 1.22384 0.611921 0.790919i $$-0.290397\pi$$
0.611921 + 0.790919i $$0.290397\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −3780.00 −0.211768 −0.105884 0.994378i $$-0.533767\pi$$
−0.105884 + 0.994378i $$0.533767\pi$$
$$684$$ 0 0
$$685$$ −2268.00 −0.126505
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −45756.0 −2.52999
$$690$$ 0 0
$$691$$ 5500.00 0.302793 0.151396 0.988473i $$-0.451623\pi$$
0.151396 + 0.988473i $$0.451623\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 15000.0 0.818680
$$696$$ 0 0
$$697$$ 7380.00 0.401058
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −10230.0 −0.551187 −0.275593 0.961274i $$-0.588874\pi$$
−0.275593 + 0.961274i $$0.588874\pi$$
$$702$$ 0 0
$$703$$ −7480.00 −0.401299
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 10190.0 0.539765 0.269883 0.962893i $$-0.413015\pi$$
0.269883 + 0.962893i $$0.413015\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −24192.0 −1.27068
$$714$$ 0 0
$$715$$ 5904.00 0.308807
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 9408.00 0.487982 0.243991 0.969777i $$-0.421543\pi$$
0.243991 + 0.969777i $$0.421543\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 21894.0 1.12155
$$726$$ 0 0
$$727$$ 33064.0 1.68676 0.843381 0.537316i $$-0.180562\pi$$
0.843381 + 0.537316i $$0.180562\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 5160.00 0.261080
$$732$$ 0 0
$$733$$ 6322.00 0.318565 0.159283 0.987233i $$-0.449082\pi$$
0.159283 + 0.987233i $$0.449082\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 1680.00 0.0839669
$$738$$ 0 0
$$739$$ −20740.0 −1.03239 −0.516193 0.856472i $$-0.672651\pi$$
−0.516193 + 0.856472i $$0.672651\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −32040.0 −1.58201 −0.791005 0.611810i $$-0.790442\pi$$
−0.791005 + 0.611810i $$0.790442\pi$$
$$744$$ 0 0
$$745$$ −5076.00 −0.249624
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −12832.0 −0.623497 −0.311749 0.950165i $$-0.600915\pi$$
−0.311749 + 0.950165i $$0.600915\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −15216.0 −0.733466
$$756$$ 0 0
$$757$$ −19906.0 −0.955741 −0.477870 0.878430i $$-0.658591\pi$$
−0.477870 + 0.878430i $$0.658591\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 10842.0 0.516455 0.258227 0.966084i $$-0.416862\pi$$
0.258227 + 0.966084i $$0.416862\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 44280.0 2.08456
$$768$$ 0 0
$$769$$ −28274.0 −1.32586 −0.662930 0.748681i $$-0.730687\pi$$
−0.662930 + 0.748681i $$0.730687\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −32346.0 −1.50505 −0.752526 0.658563i $$-0.771165\pi$$
−0.752526 + 0.658563i $$0.771165\pi$$
$$774$$ 0 0
$$775$$ −9968.00 −0.462014
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 16728.0 0.769375
$$780$$ 0 0
$$781$$ 10080.0 0.461832
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 7116.00 0.323543
$$786$$ 0 0
$$787$$ −30116.0 −1.36407 −0.682033 0.731322i $$-0.738904\pi$$
−0.682033 + 0.731322i $$0.738904\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −9020.00 −0.403921
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −6594.00 −0.293063 −0.146532 0.989206i $$-0.546811\pi$$
−0.146532 + 0.989206i $$0.546811\pi$$
$$798$$ 0 0
$$799$$ −5760.00 −0.255036
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 6600.00 0.290048
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 43014.0 1.86933 0.934667 0.355524i $$-0.115697\pi$$
0.934667 + 0.355524i $$0.115697\pi$$
$$810$$ 0 0
$$811$$ 14164.0 0.613274 0.306637 0.951827i $$-0.400796\pi$$
0.306637 + 0.951827i $$0.400796\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 12648.0 0.543608
$$816$$ 0 0
$$817$$ 11696.0 0.500846
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −34830.0 −1.48060 −0.740302 0.672275i $$-0.765317\pi$$
−0.740302 + 0.672275i $$0.765317\pi$$
$$822$$ 0 0
$$823$$ 31016.0 1.31367 0.656835 0.754035i $$-0.271895\pi$$
0.656835 + 0.754035i $$0.271895\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −9876.00 −0.415263 −0.207631 0.978207i $$-0.566575\pi$$
−0.207631 + 0.978207i $$0.566575\pi$$
$$828$$ 0 0
$$829$$ 3154.00 0.132139 0.0660693 0.997815i $$-0.478954\pi$$
0.0660693 + 0.997815i $$0.478954\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −11664.0 −0.483412
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 36936.0 1.51987 0.759936 0.649998i $$-0.225230\pi$$
0.759936 + 0.649998i $$0.225230\pi$$
$$840$$ 0 0
$$841$$ 36127.0 1.48128
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 27162.0 1.10580
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −23760.0 −0.957088
$$852$$ 0 0
$$853$$ −9638.00 −0.386869 −0.193434 0.981113i $$-0.561963\pi$$
−0.193434 + 0.981113i $$0.561963\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 10266.0 0.409195 0.204597 0.978846i $$-0.434411\pi$$
0.204597 + 0.978846i $$0.434411\pi$$
$$858$$ 0 0
$$859$$ 4084.00 0.162217 0.0811084 0.996705i $$-0.474154\pi$$
0.0811084 + 0.996705i $$0.474154\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 192.000 0.00757330 0.00378665 0.999993i $$-0.498795\pi$$
0.00378665 + 0.999993i $$0.498795\pi$$
$$864$$ 0 0
$$865$$ −8172.00 −0.321221
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −2496.00 −0.0974350
$$870$$ 0 0
$$871$$ 11480.0 0.446596
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 19910.0 0.766605 0.383303 0.923623i $$-0.374787\pi$$
0.383303 + 0.923623i $$0.374787\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 14802.0 0.566052 0.283026 0.959112i $$-0.408662\pi$$
0.283026 + 0.959112i $$0.408662\pi$$
$$882$$ 0 0
$$883$$ −32548.0 −1.24046 −0.620231 0.784419i $$-0.712961\pi$$
−0.620231 + 0.784419i $$0.712961\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1464.00 0.0554186 0.0277093 0.999616i $$-0.491179\pi$$
0.0277093 + 0.999616i $$0.491179\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −13056.0 −0.489252
$$894$$ 0 0
$$895$$ −9576.00 −0.357643
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −27552.0 −1.02215
$$900$$ 0 0
$$901$$ 16740.0 0.618968
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 10140.0 0.372448
$$906$$ 0 0
$$907$$ −49564.0 −1.81449 −0.907247 0.420599i $$-0.861820\pi$$
−0.907247 + 0.420599i $$0.861820\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −8448.00 −0.307239 −0.153619 0.988130i $$-0.549093\pi$$
−0.153619 + 0.988130i $$0.549093\pi$$
$$912$$ 0 0
$$913$$ 6192.00 0.224453
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 14600.0 0.524058 0.262029 0.965060i $$-0.415608\pi$$
0.262029 + 0.965060i $$0.415608\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 68880.0 2.45635
$$924$$ 0 0
$$925$$ −9790.00 −0.347993
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −21102.0 −0.745247 −0.372623 0.927983i $$-0.621542\pi$$
−0.372623 + 0.927983i $$0.621542\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −2160.00 −0.0755503
$$936$$ 0 0
$$937$$ 20806.0 0.725403 0.362701 0.931905i $$-0.381854\pi$$
0.362701 + 0.931905i $$0.381854\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 24510.0 0.849100 0.424550 0.905404i $$-0.360432\pi$$
0.424550 + 0.905404i $$0.360432\pi$$
$$942$$ 0 0
$$943$$ 53136.0 1.83494
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 44148.0 1.51491 0.757454 0.652889i $$-0.226443\pi$$
0.757454 + 0.652889i $$0.226443\pi$$
$$948$$ 0 0
$$949$$ 45100.0 1.54268
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −27114.0 −0.921625 −0.460812 0.887498i $$-0.652442\pi$$
−0.460812 + 0.887498i $$0.652442\pi$$
$$954$$ 0 0
$$955$$ −21312.0 −0.722136
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −17247.0 −0.578933
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −16116.0 −0.537609
$$966$$ 0 0
$$967$$ −10264.0 −0.341332 −0.170666 0.985329i $$-0.554592\pi$$
−0.170666 + 0.985329i $$0.554592\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 51468.0 1.70102 0.850508 0.525962i $$-0.176295\pi$$
0.850508 + 0.525962i $$0.176295\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 23790.0 0.779027 0.389514 0.921021i $$-0.372643\pi$$
0.389514 + 0.921021i $$0.372643\pi$$
$$978$$ 0 0
$$979$$ −16776.0 −0.547664
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 26424.0 0.857370 0.428685 0.903454i $$-0.358977\pi$$
0.428685 + 0.903454i $$0.358977\pi$$
$$984$$ 0 0
$$985$$ 8460.00 0.273663
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 37152.0 1.19450
$$990$$ 0 0
$$991$$ 39488.0 1.26577 0.632885 0.774246i $$-0.281871\pi$$
0.632885 + 0.774246i $$0.281871\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 17808.0 0.567388
$$996$$ 0 0
$$997$$ −30854.0 −0.980096 −0.490048 0.871695i $$-0.663021\pi$$
−0.490048 + 0.871695i $$0.663021\pi$$
$$998$$ 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 1764.4.a.k.1.1 1
3.2 odd 2 196.4.a.b.1.1 1
7.2 even 3 1764.4.k.e.361.1 2
7.3 odd 6 1764.4.k.k.1549.1 2
7.4 even 3 1764.4.k.e.1549.1 2
7.5 odd 6 1764.4.k.k.361.1 2
7.6 odd 2 252.4.a.c.1.1 1
12.11 even 2 784.4.a.n.1.1 1
21.2 odd 6 196.4.e.d.165.1 2
21.5 even 6 196.4.e.c.165.1 2
21.11 odd 6 196.4.e.d.177.1 2
21.17 even 6 196.4.e.c.177.1 2
21.20 even 2 28.4.a.b.1.1 1
28.27 even 2 1008.4.a.f.1.1 1
84.83 odd 2 112.4.a.c.1.1 1
105.62 odd 4 700.4.e.f.449.1 2
105.83 odd 4 700.4.e.f.449.2 2
105.104 even 2 700.4.a.e.1.1 1
168.83 odd 2 448.4.a.m.1.1 1
168.125 even 2 448.4.a.d.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.a.b.1.1 1 21.20 even 2
112.4.a.c.1.1 1 84.83 odd 2
196.4.a.b.1.1 1 3.2 odd 2
196.4.e.c.165.1 2 21.5 even 6
196.4.e.c.177.1 2 21.17 even 6
196.4.e.d.165.1 2 21.2 odd 6
196.4.e.d.177.1 2 21.11 odd 6
252.4.a.c.1.1 1 7.6 odd 2
448.4.a.d.1.1 1 168.125 even 2
448.4.a.m.1.1 1 168.83 odd 2
700.4.a.e.1.1 1 105.104 even 2
700.4.e.f.449.1 2 105.62 odd 4
700.4.e.f.449.2 2 105.83 odd 4
784.4.a.n.1.1 1 12.11 even 2
1008.4.a.f.1.1 1 28.27 even 2
1764.4.a.k.1.1 1 1.1 even 1 trivial
1764.4.k.e.361.1 2 7.2 even 3
1764.4.k.e.1549.1 2 7.4 even 3
1764.4.k.k.361.1 2 7.5 odd 6
1764.4.k.k.1549.1 2 7.3 odd 6