# Properties

 Label 6400.2.a.bq.1.2 Level $6400$ Weight $2$ Character 6400.1 Self dual yes Analytic conductor $51.104$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$6400 = 2^{8} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6400.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$51.1042572936$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ Defining polynomial: $$x^{2} - x - 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 3200) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-0.618034$$ of defining polynomial Character $$\chi$$ $$=$$ 6400.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.23607 q^{3} +2.00000 q^{9} +O(q^{10})$$ $$q+2.23607 q^{3} +2.00000 q^{9} +2.23607 q^{11} -4.00000 q^{13} -3.00000 q^{17} +2.23607 q^{19} -8.94427 q^{23} -2.23607 q^{27} +4.00000 q^{29} -8.94427 q^{31} +5.00000 q^{33} -8.00000 q^{37} -8.94427 q^{39} +5.00000 q^{41} -8.94427 q^{43} +8.94427 q^{47} -7.00000 q^{49} -6.70820 q^{51} -4.00000 q^{53} +5.00000 q^{57} -8.94427 q^{59} +8.00000 q^{61} +6.70820 q^{67} -20.0000 q^{69} -8.94427 q^{71} -9.00000 q^{73} -11.0000 q^{81} +6.70820 q^{83} +8.94427 q^{87} +15.0000 q^{89} -20.0000 q^{93} -2.00000 q^{97} +4.47214 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{9} + O(q^{10})$$ $$2 q + 4 q^{9} - 8 q^{13} - 6 q^{17} + 8 q^{29} + 10 q^{33} - 16 q^{37} + 10 q^{41} - 14 q^{49} - 8 q^{53} + 10 q^{57} + 16 q^{61} - 40 q^{69} - 18 q^{73} - 22 q^{81} + 30 q^{89} - 40 q^{93} - 4 q^{97} + O(q^{100})$$

## 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
$$3$$ 2.23607 1.29099 0.645497 0.763763i $$-0.276650\pi$$
0.645497 + 0.763763i $$0.276650\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ 2.00000 0.666667
$$10$$ 0 0
$$11$$ 2.23607 0.674200 0.337100 0.941469i $$-0.390554\pi$$
0.337100 + 0.941469i $$0.390554\pi$$
$$12$$ 0 0
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.00000 −0.727607 −0.363803 0.931476i $$-0.618522\pi$$
−0.363803 + 0.931476i $$0.618522\pi$$
$$18$$ 0 0
$$19$$ 2.23607 0.512989 0.256495 0.966546i $$-0.417432\pi$$
0.256495 + 0.966546i $$0.417432\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −8.94427 −1.86501 −0.932505 0.361158i $$-0.882382\pi$$
−0.932505 + 0.361158i $$0.882382\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −2.23607 −0.430331
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ −8.94427 −1.60644 −0.803219 0.595683i $$-0.796881\pi$$
−0.803219 + 0.595683i $$0.796881\pi$$
$$32$$ 0 0
$$33$$ 5.00000 0.870388
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ 0 0
$$39$$ −8.94427 −1.43223
$$40$$ 0 0
$$41$$ 5.00000 0.780869 0.390434 0.920631i $$-0.372325\pi$$
0.390434 + 0.920631i $$0.372325\pi$$
$$42$$ 0 0
$$43$$ −8.94427 −1.36399 −0.681994 0.731357i $$-0.738887\pi$$
−0.681994 + 0.731357i $$0.738887\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 8.94427 1.30466 0.652328 0.757937i $$-0.273792\pi$$
0.652328 + 0.757937i $$0.273792\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ −6.70820 −0.939336
$$52$$ 0 0
$$53$$ −4.00000 −0.549442 −0.274721 0.961524i $$-0.588586\pi$$
−0.274721 + 0.961524i $$0.588586\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 5.00000 0.662266
$$58$$ 0 0
$$59$$ −8.94427 −1.16445 −0.582223 0.813029i $$-0.697817\pi$$
−0.582223 + 0.813029i $$0.697817\pi$$
$$60$$ 0 0
$$61$$ 8.00000 1.02430 0.512148 0.858898i $$-0.328850\pi$$
0.512148 + 0.858898i $$0.328850\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 6.70820 0.819538 0.409769 0.912189i $$-0.365609\pi$$
0.409769 + 0.912189i $$0.365609\pi$$
$$68$$ 0 0
$$69$$ −20.0000 −2.40772
$$70$$ 0 0
$$71$$ −8.94427 −1.06149 −0.530745 0.847532i $$-0.678088\pi$$
−0.530745 + 0.847532i $$0.678088\pi$$
$$72$$ 0 0
$$73$$ −9.00000 −1.05337 −0.526685 0.850060i $$-0.676565\pi$$
−0.526685 + 0.850060i $$0.676565\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 0 0
$$83$$ 6.70820 0.736321 0.368161 0.929762i $$-0.379988\pi$$
0.368161 + 0.929762i $$0.379988\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 8.94427 0.958927
$$88$$ 0 0
$$89$$ 15.0000 1.59000 0.794998 0.606612i $$-0.207472\pi$$
0.794998 + 0.606612i $$0.207472\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −20.0000 −2.07390
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −2.00000 −0.203069 −0.101535 0.994832i $$-0.532375\pi$$
−0.101535 + 0.994832i $$0.532375\pi$$
$$98$$ 0 0
$$99$$ 4.47214 0.449467
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −8.94427 −0.881305 −0.440653 0.897678i $$-0.645253\pi$$
−0.440653 + 0.897678i $$0.645253\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 2.23607 0.216169 0.108084 0.994142i $$-0.465528\pi$$
0.108084 + 0.994142i $$0.465528\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ 0 0
$$111$$ −17.8885 −1.69791
$$112$$ 0 0
$$113$$ −1.00000 −0.0940721 −0.0470360 0.998893i $$-0.514978\pi$$
−0.0470360 + 0.998893i $$0.514978\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −8.00000 −0.739600
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −6.00000 −0.545455
$$122$$ 0 0
$$123$$ 11.1803 1.00810
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 8.94427 0.793676 0.396838 0.917889i $$-0.370108\pi$$
0.396838 + 0.917889i $$0.370108\pi$$
$$128$$ 0 0
$$129$$ −20.0000 −1.76090
$$130$$ 0 0
$$131$$ 8.94427 0.781465 0.390732 0.920504i $$-0.372222\pi$$
0.390732 + 0.920504i $$0.372222\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 13.0000 1.11066 0.555332 0.831628i $$-0.312591\pi$$
0.555332 + 0.831628i $$0.312591\pi$$
$$138$$ 0 0
$$139$$ 20.1246 1.70695 0.853474 0.521136i $$-0.174492\pi$$
0.853474 + 0.521136i $$0.174492\pi$$
$$140$$ 0 0
$$141$$ 20.0000 1.68430
$$142$$ 0 0
$$143$$ −8.94427 −0.747958
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −15.6525 −1.29099
$$148$$ 0 0
$$149$$ −20.0000 −1.63846 −0.819232 0.573462i $$-0.805600\pi$$
−0.819232 + 0.573462i $$0.805600\pi$$
$$150$$ 0 0
$$151$$ −17.8885 −1.45575 −0.727875 0.685710i $$-0.759492\pi$$
−0.727875 + 0.685710i $$0.759492\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 12.0000 0.957704 0.478852 0.877896i $$-0.341053\pi$$
0.478852 + 0.877896i $$0.341053\pi$$
$$158$$ 0 0
$$159$$ −8.94427 −0.709327
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −11.1803 −0.875712 −0.437856 0.899045i $$-0.644262\pi$$
−0.437856 + 0.899045i $$0.644262\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 8.94427 0.692129 0.346064 0.938211i $$-0.387518\pi$$
0.346064 + 0.938211i $$0.387518\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 4.47214 0.341993
$$172$$ 0 0
$$173$$ −24.0000 −1.82469 −0.912343 0.409426i $$-0.865729\pi$$
−0.912343 + 0.409426i $$0.865729\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −20.0000 −1.50329
$$178$$ 0 0
$$179$$ −15.6525 −1.16992 −0.584960 0.811062i $$-0.698890\pi$$
−0.584960 + 0.811062i $$0.698890\pi$$
$$180$$ 0 0
$$181$$ 20.0000 1.48659 0.743294 0.668965i $$-0.233262\pi$$
0.743294 + 0.668965i $$0.233262\pi$$
$$182$$ 0 0
$$183$$ 17.8885 1.32236
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −6.70820 −0.490552
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 8.94427 0.647185 0.323592 0.946197i $$-0.395109\pi$$
0.323592 + 0.946197i $$0.395109\pi$$
$$192$$ 0 0
$$193$$ 21.0000 1.51161 0.755807 0.654795i $$-0.227245\pi$$
0.755807 + 0.654795i $$0.227245\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ 17.8885 1.26809 0.634043 0.773298i $$-0.281394\pi$$
0.634043 + 0.773298i $$0.281394\pi$$
$$200$$ 0 0
$$201$$ 15.0000 1.05802
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −17.8885 −1.24334
$$208$$ 0 0
$$209$$ 5.00000 0.345857
$$210$$ 0 0
$$211$$ 6.70820 0.461812 0.230906 0.972976i $$-0.425831\pi$$
0.230906 + 0.972976i $$0.425831\pi$$
$$212$$ 0 0
$$213$$ −20.0000 −1.37038
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −20.1246 −1.35990
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ −17.8885 −1.19791 −0.598953 0.800784i $$-0.704416\pi$$
−0.598953 + 0.800784i $$0.704416\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 8.94427 0.593652 0.296826 0.954932i $$-0.404072\pi$$
0.296826 + 0.954932i $$0.404072\pi$$
$$228$$ 0 0
$$229$$ −16.0000 −1.05731 −0.528655 0.848837i $$-0.677303\pi$$
−0.528655 + 0.848837i $$0.677303\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −8.94427 −0.578557 −0.289278 0.957245i $$-0.593415\pi$$
−0.289278 + 0.957245i $$0.593415\pi$$
$$240$$ 0 0
$$241$$ 5.00000 0.322078 0.161039 0.986948i $$-0.448515\pi$$
0.161039 + 0.986948i $$0.448515\pi$$
$$242$$ 0 0
$$243$$ −17.8885 −1.14755
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −8.94427 −0.569110
$$248$$ 0 0
$$249$$ 15.0000 0.950586
$$250$$ 0 0
$$251$$ −29.0689 −1.83481 −0.917406 0.397953i $$-0.869721\pi$$
−0.917406 + 0.397953i $$0.869721\pi$$
$$252$$ 0 0
$$253$$ −20.0000 −1.25739
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 8.00000 0.495188
$$262$$ 0 0
$$263$$ 8.94427 0.551527 0.275764 0.961225i $$-0.411069\pi$$
0.275764 + 0.961225i $$0.411069\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 33.5410 2.05268
$$268$$ 0 0
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 26.8328 1.62998 0.814989 0.579477i $$-0.196743\pi$$
0.814989 + 0.579477i $$0.196743\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −12.0000 −0.721010 −0.360505 0.932757i $$-0.617396\pi$$
−0.360505 + 0.932757i $$0.617396\pi$$
$$278$$ 0 0
$$279$$ −17.8885 −1.07096
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 0 0
$$283$$ 24.5967 1.46212 0.731062 0.682311i $$-0.239025\pi$$
0.731062 + 0.682311i $$0.239025\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ −4.47214 −0.262161
$$292$$ 0 0
$$293$$ −24.0000 −1.40209 −0.701047 0.713115i $$-0.747284\pi$$
−0.701047 + 0.713115i $$0.747284\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −5.00000 −0.290129
$$298$$ 0 0
$$299$$ 35.7771 2.06904
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 2.23607 0.127619 0.0638096 0.997962i $$-0.479675\pi$$
0.0638096 + 0.997962i $$0.479675\pi$$
$$308$$ 0 0
$$309$$ −20.0000 −1.13776
$$310$$ 0 0
$$311$$ 17.8885 1.01437 0.507183 0.861838i $$-0.330687\pi$$
0.507183 + 0.861838i $$0.330687\pi$$
$$312$$ 0 0
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −32.0000 −1.79730 −0.898650 0.438667i $$-0.855451\pi$$
−0.898650 + 0.438667i $$0.855451\pi$$
$$318$$ 0 0
$$319$$ 8.94427 0.500783
$$320$$ 0 0
$$321$$ 5.00000 0.279073
$$322$$ 0 0
$$323$$ −6.70820 −0.373254
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.23607 0.122905 0.0614527 0.998110i $$-0.480427\pi$$
0.0614527 + 0.998110i $$0.480427\pi$$
$$332$$ 0 0
$$333$$ −16.0000 −0.876795
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −33.0000 −1.79762 −0.898812 0.438334i $$-0.855569\pi$$
−0.898812 + 0.438334i $$0.855569\pi$$
$$338$$ 0 0
$$339$$ −2.23607 −0.121447
$$340$$ 0 0
$$341$$ −20.0000 −1.08306
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −33.5410 −1.80058 −0.900288 0.435294i $$-0.856644\pi$$
−0.900288 + 0.435294i $$0.856644\pi$$
$$348$$ 0 0
$$349$$ −24.0000 −1.28469 −0.642345 0.766415i $$-0.722038\pi$$
−0.642345 + 0.766415i $$0.722038\pi$$
$$350$$ 0 0
$$351$$ 8.94427 0.477410
$$352$$ 0 0
$$353$$ −14.0000 −0.745145 −0.372572 0.928003i $$-0.621524\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 17.8885 0.944121 0.472061 0.881566i $$-0.343510\pi$$
0.472061 + 0.881566i $$0.343510\pi$$
$$360$$ 0 0
$$361$$ −14.0000 −0.736842
$$362$$ 0 0
$$363$$ −13.4164 −0.704179
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ 10.0000 0.520579
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −16.0000 −0.824042
$$378$$ 0 0
$$379$$ −29.0689 −1.49317 −0.746584 0.665291i $$-0.768307\pi$$
−0.746584 + 0.665291i $$0.768307\pi$$
$$380$$ 0 0
$$381$$ 20.0000 1.02463
$$382$$ 0 0
$$383$$ 17.8885 0.914062 0.457031 0.889451i $$-0.348913\pi$$
0.457031 + 0.889451i $$0.348913\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −17.8885 −0.909326
$$388$$ 0 0
$$389$$ 20.0000 1.01404 0.507020 0.861934i $$-0.330747\pi$$
0.507020 + 0.861934i $$0.330747\pi$$
$$390$$ 0 0
$$391$$ 26.8328 1.35699
$$392$$ 0 0
$$393$$ 20.0000 1.00887
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −8.00000 −0.401508 −0.200754 0.979642i $$-0.564339\pi$$
−0.200754 + 0.979642i $$0.564339\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −27.0000 −1.34832 −0.674158 0.738587i $$-0.735493\pi$$
−0.674158 + 0.738587i $$0.735493\pi$$
$$402$$ 0 0
$$403$$ 35.7771 1.78218
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −17.8885 −0.886702
$$408$$ 0 0
$$409$$ −19.0000 −0.939490 −0.469745 0.882802i $$-0.655654\pi$$
−0.469745 + 0.882802i $$0.655654\pi$$
$$410$$ 0 0
$$411$$ 29.0689 1.43386
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 45.0000 2.20366
$$418$$ 0 0
$$419$$ 20.1246 0.983152 0.491576 0.870835i $$-0.336421\pi$$
0.491576 + 0.870835i $$0.336421\pi$$
$$420$$ 0 0
$$421$$ 32.0000 1.55958 0.779792 0.626038i $$-0.215325\pi$$
0.779792 + 0.626038i $$0.215325\pi$$
$$422$$ 0 0
$$423$$ 17.8885 0.869771
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −20.0000 −0.965609
$$430$$ 0 0
$$431$$ 17.8885 0.861661 0.430830 0.902433i $$-0.358221\pi$$
0.430830 + 0.902433i $$0.358221\pi$$
$$432$$ 0 0
$$433$$ −11.0000 −0.528626 −0.264313 0.964437i $$-0.585145\pi$$
−0.264313 + 0.964437i $$0.585145\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −20.0000 −0.956730
$$438$$ 0 0
$$439$$ 26.8328 1.28066 0.640330 0.768100i $$-0.278798\pi$$
0.640330 + 0.768100i $$0.278798\pi$$
$$440$$ 0 0
$$441$$ −14.0000 −0.666667
$$442$$ 0 0
$$443$$ −11.1803 −0.531194 −0.265597 0.964084i $$-0.585569\pi$$
−0.265597 + 0.964084i $$0.585569\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −44.7214 −2.11525
$$448$$ 0 0
$$449$$ −11.0000 −0.519122 −0.259561 0.965727i $$-0.583578\pi$$
−0.259561 + 0.965727i $$0.583578\pi$$
$$450$$ 0 0
$$451$$ 11.1803 0.526462
$$452$$ 0 0
$$453$$ −40.0000 −1.87936
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 37.0000 1.73079 0.865393 0.501093i $$-0.167069\pi$$
0.865393 + 0.501093i $$0.167069\pi$$
$$458$$ 0 0
$$459$$ 6.70820 0.313112
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 35.7771 1.66270 0.831351 0.555748i $$-0.187568\pi$$
0.831351 + 0.555748i $$0.187568\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 8.94427 0.413892 0.206946 0.978352i $$-0.433648\pi$$
0.206946 + 0.978352i $$0.433648\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 26.8328 1.23639
$$472$$ 0 0
$$473$$ −20.0000 −0.919601
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −8.00000 −0.366295
$$478$$ 0 0
$$479$$ 26.8328 1.22602 0.613011 0.790074i $$-0.289958\pi$$
0.613011 + 0.790074i $$0.289958\pi$$
$$480$$ 0 0
$$481$$ 32.0000 1.45907
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −26.8328 −1.21591 −0.607955 0.793971i $$-0.708010\pi$$
−0.607955 + 0.793971i $$0.708010\pi$$
$$488$$ 0 0
$$489$$ −25.0000 −1.13054
$$490$$ 0 0
$$491$$ 26.8328 1.21095 0.605474 0.795865i $$-0.292984\pi$$
0.605474 + 0.795865i $$0.292984\pi$$
$$492$$ 0 0
$$493$$ −12.0000 −0.540453
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −26.8328 −1.20120 −0.600601 0.799549i $$-0.705072\pi$$
−0.600601 + 0.799549i $$0.705072\pi$$
$$500$$ 0 0
$$501$$ 20.0000 0.893534
$$502$$ 0 0
$$503$$ −17.8885 −0.797611 −0.398805 0.917036i $$-0.630575\pi$$
−0.398805 + 0.917036i $$0.630575\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 6.70820 0.297922
$$508$$ 0 0
$$509$$ −4.00000 −0.177297 −0.0886484 0.996063i $$-0.528255\pi$$
−0.0886484 + 0.996063i $$0.528255\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −5.00000 −0.220755
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 20.0000 0.879599
$$518$$ 0 0
$$519$$ −53.6656 −2.35566
$$520$$ 0 0
$$521$$ −3.00000 −0.131432 −0.0657162 0.997838i $$-0.520933\pi$$
−0.0657162 + 0.997838i $$0.520933\pi$$
$$522$$ 0 0
$$523$$ −33.5410 −1.46665 −0.733323 0.679880i $$-0.762032\pi$$
−0.733323 + 0.679880i $$0.762032\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 26.8328 1.16886
$$528$$ 0 0
$$529$$ 57.0000 2.47826
$$530$$ 0 0
$$531$$ −17.8885 −0.776297
$$532$$ 0 0
$$533$$ −20.0000 −0.866296
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −35.0000 −1.51036
$$538$$ 0 0
$$539$$ −15.6525 −0.674200
$$540$$ 0 0
$$541$$ −40.0000 −1.71973 −0.859867 0.510518i $$-0.829454\pi$$
−0.859867 + 0.510518i $$0.829454\pi$$
$$542$$ 0 0
$$543$$ 44.7214 1.91918
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.1246 0.860466 0.430233 0.902718i $$-0.358431\pi$$
0.430233 + 0.902718i $$0.358431\pi$$
$$548$$ 0 0
$$549$$ 16.0000 0.682863
$$550$$ 0 0
$$551$$ 8.94427 0.381039
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −12.0000 −0.508456 −0.254228 0.967144i $$-0.581821\pi$$
−0.254228 + 0.967144i $$0.581821\pi$$
$$558$$ 0 0
$$559$$ 35.7771 1.51321
$$560$$ 0 0
$$561$$ −15.0000 −0.633300
$$562$$ 0 0
$$563$$ 8.94427 0.376956 0.188478 0.982077i $$-0.439645\pi$$
0.188478 + 0.982077i $$0.439645\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −11.0000 −0.461144 −0.230572 0.973055i $$-0.574060\pi$$
−0.230572 + 0.973055i $$0.574060\pi$$
$$570$$ 0 0
$$571$$ −44.7214 −1.87153 −0.935765 0.352623i $$-0.885290\pi$$
−0.935765 + 0.352623i $$0.885290\pi$$
$$572$$ 0 0
$$573$$ 20.0000 0.835512
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 23.0000 0.957503 0.478751 0.877951i $$-0.341090\pi$$
0.478751 + 0.877951i $$0.341090\pi$$
$$578$$ 0 0
$$579$$ 46.9574 1.95148
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −8.94427 −0.370434
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 6.70820 0.276877 0.138439 0.990371i $$-0.455792\pi$$
0.138439 + 0.990371i $$0.455792\pi$$
$$588$$ 0 0
$$589$$ −20.0000 −0.824086
$$590$$ 0 0
$$591$$ −26.8328 −1.10375
$$592$$ 0 0
$$593$$ −9.00000 −0.369586 −0.184793 0.982777i $$-0.559161\pi$$
−0.184793 + 0.982777i $$0.559161\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 40.0000 1.63709
$$598$$ 0 0
$$599$$ 35.7771 1.46181 0.730906 0.682478i $$-0.239098\pi$$
0.730906 + 0.682478i $$0.239098\pi$$
$$600$$ 0 0
$$601$$ −25.0000 −1.01977 −0.509886 0.860242i $$-0.670312\pi$$
−0.509886 + 0.860242i $$0.670312\pi$$
$$602$$ 0 0
$$603$$ 13.4164 0.546358
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 17.8885 0.726074 0.363037 0.931775i $$-0.381740\pi$$
0.363037 + 0.931775i $$0.381740\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −35.7771 −1.44739
$$612$$ 0 0
$$613$$ 4.00000 0.161558 0.0807792 0.996732i $$-0.474259\pi$$
0.0807792 + 0.996732i $$0.474259\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −22.0000 −0.885687 −0.442843 0.896599i $$-0.646030\pi$$
−0.442843 + 0.896599i $$0.646030\pi$$
$$618$$ 0 0
$$619$$ −8.94427 −0.359501 −0.179750 0.983712i $$-0.557529\pi$$
−0.179750 + 0.983712i $$0.557529\pi$$
$$620$$ 0 0
$$621$$ 20.0000 0.802572
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 11.1803 0.446500
$$628$$ 0 0
$$629$$ 24.0000 0.956943
$$630$$ 0 0
$$631$$ 8.94427 0.356066 0.178033 0.984025i $$-0.443027\pi$$
0.178033 + 0.984025i $$0.443027\pi$$
$$632$$ 0 0
$$633$$ 15.0000 0.596196
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 28.0000 1.10940
$$638$$ 0 0
$$639$$ −17.8885 −0.707660
$$640$$ 0 0
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 0 0
$$643$$ 8.94427 0.352728 0.176364 0.984325i $$-0.443566\pi$$
0.176364 + 0.984325i $$0.443566\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −17.8885 −0.703271 −0.351636 0.936137i $$-0.614374\pi$$
−0.351636 + 0.936137i $$0.614374\pi$$
$$648$$ 0 0
$$649$$ −20.0000 −0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 24.0000 0.939193 0.469596 0.882881i $$-0.344399\pi$$
0.469596 + 0.882881i $$0.344399\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −18.0000 −0.702247
$$658$$ 0 0
$$659$$ 6.70820 0.261315 0.130657 0.991428i $$-0.458291\pi$$
0.130657 + 0.991428i $$0.458291\pi$$
$$660$$ 0 0
$$661$$ 28.0000 1.08907 0.544537 0.838737i $$-0.316705\pi$$
0.544537 + 0.838737i $$0.316705\pi$$
$$662$$ 0 0
$$663$$ 26.8328 1.04210
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −35.7771 −1.38529
$$668$$ 0 0
$$669$$ −40.0000 −1.54649
$$670$$ 0 0
$$671$$ 17.8885 0.690580
$$672$$ 0 0
$$673$$ 14.0000 0.539660 0.269830 0.962908i $$-0.413032\pi$$
0.269830 + 0.962908i $$0.413032\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 8.00000 0.307465 0.153732 0.988113i $$-0.450871\pi$$
0.153732 + 0.988113i $$0.450871\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 20.0000 0.766402
$$682$$ 0 0
$$683$$ −15.6525 −0.598925 −0.299463 0.954108i $$-0.596807\pi$$
−0.299463 + 0.954108i $$0.596807\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −35.7771 −1.36498
$$688$$ 0 0
$$689$$ 16.0000 0.609551
$$690$$ 0 0
$$691$$ −15.6525 −0.595448 −0.297724 0.954652i $$-0.596228\pi$$
−0.297724 + 0.954652i $$0.596228\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −15.0000 −0.568166
$$698$$ 0 0
$$699$$ −13.4164 −0.507455
$$700$$ 0 0
$$701$$ 12.0000 0.453234 0.226617 0.973984i $$-0.427233\pi$$
0.226617 + 0.973984i $$0.427233\pi$$
$$702$$ 0 0
$$703$$ −17.8885 −0.674679
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 16.0000 0.600893 0.300446 0.953799i $$-0.402864\pi$$
0.300446 + 0.953799i $$0.402864\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 80.0000 2.99602
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −20.0000 −0.746914
$$718$$ 0 0
$$719$$ 17.8885 0.667130 0.333565 0.942727i $$-0.391748\pi$$
0.333565 + 0.942727i $$0.391748\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 11.1803 0.415801
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 26.8328 0.995174 0.497587 0.867414i $$-0.334220\pi$$
0.497587 + 0.867414i $$0.334220\pi$$
$$728$$ 0 0
$$729$$ −7.00000 −0.259259
$$730$$ 0 0
$$731$$ 26.8328 0.992448
$$732$$ 0 0
$$733$$ −4.00000 −0.147743 −0.0738717 0.997268i $$-0.523536\pi$$
−0.0738717 + 0.997268i $$0.523536\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 15.0000 0.552532
$$738$$ 0 0
$$739$$ −26.8328 −0.987061 −0.493531 0.869728i $$-0.664294\pi$$
−0.493531 + 0.869728i $$0.664294\pi$$
$$740$$ 0 0
$$741$$ −20.0000 −0.734718
$$742$$ 0 0
$$743$$ −8.94427 −0.328134 −0.164067 0.986449i $$-0.552461\pi$$
−0.164067 + 0.986449i $$0.552461\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 13.4164 0.490881
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 26.8328 0.979143 0.489572 0.871963i $$-0.337153\pi$$
0.489572 + 0.871963i $$0.337153\pi$$
$$752$$ 0 0
$$753$$ −65.0000 −2.36873
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 8.00000 0.290765 0.145382 0.989376i $$-0.453559\pi$$
0.145382 + 0.989376i $$0.453559\pi$$
$$758$$ 0 0
$$759$$ −44.7214 −1.62328
$$760$$ 0 0
$$761$$ 13.0000 0.471250 0.235625 0.971844i $$-0.424286\pi$$
0.235625 + 0.971844i $$0.424286\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 35.7771 1.29184
$$768$$ 0 0
$$769$$ 5.00000 0.180305 0.0901523 0.995928i $$-0.471265\pi$$
0.0901523 + 0.995928i $$0.471265\pi$$
$$770$$ 0 0
$$771$$ 40.2492 1.44954
$$772$$ 0 0
$$773$$ 4.00000 0.143870 0.0719350 0.997409i $$-0.477083\pi$$
0.0719350 + 0.997409i $$0.477083\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 11.1803 0.400577
$$780$$ 0 0
$$781$$ −20.0000 −0.715656
$$782$$ 0 0
$$783$$ −8.94427 −0.319642
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −26.8328 −0.956487 −0.478243 0.878227i $$-0.658726\pi$$
−0.478243 + 0.878227i $$0.658726\pi$$
$$788$$ 0 0
$$789$$ 20.0000 0.712019
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −32.0000 −1.13635
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −52.0000 −1.84193 −0.920967 0.389640i $$-0.872599\pi$$
−0.920967 + 0.389640i $$0.872599\pi$$
$$798$$ 0 0
$$799$$ −26.8328 −0.949277
$$800$$ 0 0
$$801$$ 30.0000 1.06000
$$802$$ 0 0
$$803$$ −20.1246 −0.710182
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −10.0000 −0.351581 −0.175791 0.984428i $$-0.556248\pi$$
−0.175791 + 0.984428i $$0.556248\pi$$
$$810$$ 0 0
$$811$$ 26.8328 0.942228 0.471114 0.882072i $$-0.343852\pi$$
0.471114 + 0.882072i $$0.343852\pi$$
$$812$$ 0 0
$$813$$ 60.0000 2.10429
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −20.0000 −0.699711
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −28.0000 −0.977207 −0.488603 0.872506i $$-0.662493\pi$$
−0.488603 + 0.872506i $$0.662493\pi$$
$$822$$ 0 0
$$823$$ −35.7771 −1.24711 −0.623555 0.781779i $$-0.714312\pi$$
−0.623555 + 0.781779i $$0.714312\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 24.5967 0.855313 0.427656 0.903941i $$-0.359339\pi$$
0.427656 + 0.903941i $$0.359339\pi$$
$$828$$ 0 0
$$829$$ −20.0000 −0.694629 −0.347314 0.937749i $$-0.612906\pi$$
−0.347314 + 0.937749i $$0.612906\pi$$
$$830$$ 0 0
$$831$$ −26.8328 −0.930820
$$832$$ 0 0
$$833$$ 21.0000 0.727607
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 20.0000 0.691301
$$838$$ 0 0
$$839$$ 35.7771 1.23516 0.617581 0.786507i $$-0.288113\pi$$
0.617581 + 0.786507i $$0.288113\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ 0 0
$$843$$ 22.3607 0.770143
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 55.0000 1.88760
$$850$$ 0 0
$$851$$ 71.5542 2.45285
$$852$$ 0 0
$$853$$ 4.00000 0.136957 0.0684787 0.997653i $$-0.478185\pi$$
0.0684787 + 0.997653i $$0.478185\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −27.0000 −0.922302 −0.461151 0.887322i $$-0.652563\pi$$
−0.461151 + 0.887322i $$0.652563\pi$$
$$858$$ 0 0
$$859$$ 38.0132 1.29699 0.648496 0.761218i $$-0.275398\pi$$
0.648496 + 0.761218i $$0.275398\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −26.8328 −0.913400 −0.456700 0.889621i $$-0.650969\pi$$
−0.456700 + 0.889621i $$0.650969\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −17.8885 −0.607527
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −26.8328 −0.909195
$$872$$ 0 0
$$873$$ −4.00000 −0.135379
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 32.0000 1.08056 0.540282 0.841484i $$-0.318318\pi$$
0.540282 + 0.841484i $$0.318318\pi$$
$$878$$ 0 0
$$879$$ −53.6656 −1.81010
$$880$$ 0 0
$$881$$ −30.0000 −1.01073 −0.505363 0.862907i $$-0.668641\pi$$
−0.505363 + 0.862907i $$0.668641\pi$$
$$882$$ 0 0
$$883$$ −33.5410 −1.12875 −0.564373 0.825520i $$-0.690882\pi$$
−0.564373 + 0.825520i $$0.690882\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 17.8885 0.600639 0.300319 0.953839i $$-0.402907\pi$$
0.300319 + 0.953839i $$0.402907\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −24.5967 −0.824022
$$892$$ 0 0
$$893$$ 20.0000 0.669274
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 80.0000 2.67112
$$898$$ 0 0
$$899$$ −35.7771 −1.19323
$$900$$ 0 0
$$901$$ 12.0000 0.399778
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −8.94427 −0.296990 −0.148495 0.988913i $$-0.547443\pi$$
−0.148495 + 0.988913i $$0.547443\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −35.7771 −1.18535 −0.592674 0.805443i $$-0.701928\pi$$
−0.592674 + 0.805443i $$0.701928\pi$$
$$912$$ 0 0
$$913$$ 15.0000 0.496428
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −8.94427 −0.295044 −0.147522 0.989059i $$-0.547130\pi$$
−0.147522 + 0.989059i $$0.547130\pi$$
$$920$$ 0 0
$$921$$ 5.00000 0.164756
$$922$$ 0 0
$$923$$ 35.7771 1.17762
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −17.8885 −0.587537
$$928$$ 0 0
$$929$$ −34.0000 −1.11550 −0.557752 0.830008i $$-0.688336\pi$$
−0.557752 + 0.830008i $$0.688336\pi$$
$$930$$ 0 0
$$931$$ −15.6525 −0.512989
$$932$$ 0 0
$$933$$ 40.0000 1.30954
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 23.0000 0.751377 0.375689 0.926746i $$-0.377406\pi$$
0.375689 + 0.926746i $$0.377406\pi$$
$$938$$ 0 0
$$939$$ 13.4164 0.437828
$$940$$ 0 0
$$941$$ −60.0000 −1.95594 −0.977972 0.208736i $$-0.933065\pi$$
−0.977972 + 0.208736i $$0.933065\pi$$
$$942$$ 0 0
$$943$$ −44.7214 −1.45633
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 8.94427 0.290650 0.145325 0.989384i $$-0.453577\pi$$
0.145325 + 0.989384i $$0.453577\pi$$
$$948$$ 0 0
$$949$$ 36.0000 1.16861
$$950$$ 0 0
$$951$$ −71.5542 −2.32030
$$952$$ 0 0
$$953$$ 21.0000 0.680257 0.340128 0.940379i $$-0.389529\pi$$
0.340128 + 0.940379i $$0.389529\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 20.0000 0.646508
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 49.0000 1.58065
$$962$$ 0 0
$$963$$ 4.47214 0.144113
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 53.6656 1.72577 0.862885 0.505400i $$-0.168655\pi$$
0.862885 + 0.505400i $$0.168655\pi$$
$$968$$ 0 0
$$969$$ −15.0000 −0.481869
$$970$$ 0 0
$$971$$ −51.4296 −1.65045 −0.825227 0.564802i $$-0.808953\pi$$
−0.825227 + 0.564802i $$0.808953\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −27.0000 −0.863807 −0.431903 0.901920i $$-0.642158\pi$$
−0.431903 + 0.901920i $$0.642158\pi$$
$$978$$ 0 0
$$979$$ 33.5410 1.07198
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 17.8885 0.570556 0.285278 0.958445i $$-0.407914\pi$$
0.285278 + 0.958445i $$0.407914\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 80.0000 2.54385
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 0 0
$$993$$ 5.00000 0.158670
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −8.00000 −0.253363 −0.126681 0.991943i $$-0.540433\pi$$
−0.126681 + 0.991943i $$0.540433\pi$$
$$998$$ 0 0
$$999$$ 17.8885 0.565968
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 6400.2.a.bq.1.2 2
4.3 odd 2 inner 6400.2.a.bq.1.1 2
5.4 even 2 6400.2.a.bt.1.1 2
8.3 odd 2 6400.2.a.bs.1.2 2
8.5 even 2 6400.2.a.bs.1.1 2
16.3 odd 4 3200.2.d.o.1601.1 4
16.5 even 4 3200.2.d.o.1601.2 yes 4
16.11 odd 4 3200.2.d.o.1601.4 yes 4
16.13 even 4 3200.2.d.o.1601.3 yes 4
20.19 odd 2 6400.2.a.bt.1.2 2
40.19 odd 2 6400.2.a.br.1.1 2
40.29 even 2 6400.2.a.br.1.2 2
80.3 even 4 3200.2.f.n.449.4 4
80.13 odd 4 3200.2.f.n.449.1 4
80.19 odd 4 3200.2.d.p.1601.4 yes 4
80.27 even 4 3200.2.f.n.449.3 4
80.29 even 4 3200.2.d.p.1601.2 yes 4
80.37 odd 4 3200.2.f.n.449.2 4
80.43 even 4 3200.2.f.m.449.1 4
80.53 odd 4 3200.2.f.m.449.4 4
80.59 odd 4 3200.2.d.p.1601.1 yes 4
80.67 even 4 3200.2.f.m.449.2 4
80.69 even 4 3200.2.d.p.1601.3 yes 4
80.77 odd 4 3200.2.f.m.449.3 4

By twisted newform
Twist Min Dim Char Parity Ord Type
3200.2.d.o.1601.1 4 16.3 odd 4
3200.2.d.o.1601.2 yes 4 16.5 even 4
3200.2.d.o.1601.3 yes 4 16.13 even 4
3200.2.d.o.1601.4 yes 4 16.11 odd 4
3200.2.d.p.1601.1 yes 4 80.59 odd 4
3200.2.d.p.1601.2 yes 4 80.29 even 4
3200.2.d.p.1601.3 yes 4 80.69 even 4
3200.2.d.p.1601.4 yes 4 80.19 odd 4
3200.2.f.m.449.1 4 80.43 even 4
3200.2.f.m.449.2 4 80.67 even 4
3200.2.f.m.449.3 4 80.77 odd 4
3200.2.f.m.449.4 4 80.53 odd 4
3200.2.f.n.449.1 4 80.13 odd 4
3200.2.f.n.449.2 4 80.37 odd 4
3200.2.f.n.449.3 4 80.27 even 4
3200.2.f.n.449.4 4 80.3 even 4
6400.2.a.bq.1.1 2 4.3 odd 2 inner
6400.2.a.bq.1.2 2 1.1 even 1 trivial
6400.2.a.br.1.1 2 40.19 odd 2
6400.2.a.br.1.2 2 40.29 even 2
6400.2.a.bs.1.1 2 8.5 even 2
6400.2.a.bs.1.2 2 8.3 odd 2
6400.2.a.bt.1.1 2 5.4 even 2
6400.2.a.bt.1.2 2 20.19 odd 2