Properties

 Label 1440.4.a.bb.1.2 Level $1440$ Weight $4$ Character 1440.1 Self dual yes Analytic conductor $84.963$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1440 = 2^{5} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1440.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$84.9627504083$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ Defining polynomial: $$x^{2} - x - 1$$ x^2 - x - 1 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 160) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.2 Root $$-0.618034$$ of defining polynomial Character $$\chi$$ $$=$$ 1440.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+5.00000 q^{5} +31.3050 q^{7} +O(q^{10})$$ $$q+5.00000 q^{5} +31.3050 q^{7} -8.94427 q^{11} -62.0000 q^{13} +46.0000 q^{17} -107.331 q^{19} +192.302 q^{23} +25.0000 q^{25} +90.0000 q^{29} +152.053 q^{31} +156.525 q^{35} -214.000 q^{37} +10.0000 q^{41} +67.0820 q^{43} +398.020 q^{47} +637.000 q^{49} +678.000 q^{53} -44.7214 q^{55} -411.437 q^{59} +250.000 q^{61} -310.000 q^{65} -49.1935 q^{67} -366.715 q^{71} +522.000 q^{73} -280.000 q^{77} -876.539 q^{79} +380.132 q^{83} +230.000 q^{85} -970.000 q^{89} -1940.91 q^{91} -536.656 q^{95} -934.000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 10 q^{5}+O(q^{10})$$ 2 * q + 10 * q^5 $$2 q + 10 q^{5} - 124 q^{13} + 92 q^{17} + 50 q^{25} + 180 q^{29} - 428 q^{37} + 20 q^{41} + 1274 q^{49} + 1356 q^{53} + 500 q^{61} - 620 q^{65} + 1044 q^{73} - 560 q^{77} + 460 q^{85} - 1940 q^{89} - 1868 q^{97}+O(q^{100})$$ 2 * q + 10 * q^5 - 124 * q^13 + 92 * q^17 + 50 * q^25 + 180 * q^29 - 428 * q^37 + 20 * q^41 + 1274 * q^49 + 1356 * q^53 + 500 * q^61 - 620 * q^65 + 1044 * q^73 - 560 * q^77 + 460 * q^85 - 1940 * q^89 - 1868 * q^97

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
$$5$$ 5.00000 0.447214
$$6$$ 0 0
$$7$$ 31.3050 1.69031 0.845154 0.534522i $$-0.179509\pi$$
0.845154 + 0.534522i $$0.179509\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −8.94427 −0.245164 −0.122582 0.992458i $$-0.539117\pi$$
−0.122582 + 0.992458i $$0.539117\pi$$
$$12$$ 0 0
$$13$$ −62.0000 −1.32275 −0.661373 0.750057i $$-0.730026\pi$$
−0.661373 + 0.750057i $$0.730026\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 46.0000 0.656273 0.328136 0.944630i $$-0.393579\pi$$
0.328136 + 0.944630i $$0.393579\pi$$
$$18$$ 0 0
$$19$$ −107.331 −1.29597 −0.647986 0.761652i $$-0.724389\pi$$
−0.647986 + 0.761652i $$0.724389\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 192.302 1.74338 0.871689 0.490059i $$-0.163025\pi$$
0.871689 + 0.490059i $$0.163025\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 90.0000 0.576296 0.288148 0.957586i $$-0.406961\pi$$
0.288148 + 0.957586i $$0.406961\pi$$
$$30$$ 0 0
$$31$$ 152.053 0.880950 0.440475 0.897765i $$-0.354810\pi$$
0.440475 + 0.897765i $$0.354810\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 156.525 0.755929
$$36$$ 0 0
$$37$$ −214.000 −0.950848 −0.475424 0.879757i $$-0.657705\pi$$
−0.475424 + 0.879757i $$0.657705\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.0000 0.0380912 0.0190456 0.999819i $$-0.493937\pi$$
0.0190456 + 0.999819i $$0.493937\pi$$
$$42$$ 0 0
$$43$$ 67.0820 0.237905 0.118953 0.992900i $$-0.462046\pi$$
0.118953 + 0.992900i $$0.462046\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 398.020 1.23526 0.617630 0.786469i $$-0.288093\pi$$
0.617630 + 0.786469i $$0.288093\pi$$
$$48$$ 0 0
$$49$$ 637.000 1.85714
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 678.000 1.75718 0.878589 0.477578i $$-0.158485\pi$$
0.878589 + 0.477578i $$0.158485\pi$$
$$54$$ 0 0
$$55$$ −44.7214 −0.109640
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −411.437 −0.907872 −0.453936 0.891034i $$-0.649981\pi$$
−0.453936 + 0.891034i $$0.649981\pi$$
$$60$$ 0 0
$$61$$ 250.000 0.524741 0.262371 0.964967i $$-0.415496\pi$$
0.262371 + 0.964967i $$0.415496\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −310.000 −0.591550
$$66$$ 0 0
$$67$$ −49.1935 −0.0897006 −0.0448503 0.998994i $$-0.514281\pi$$
−0.0448503 + 0.998994i $$0.514281\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −366.715 −0.612973 −0.306486 0.951875i $$-0.599153\pi$$
−0.306486 + 0.951875i $$0.599153\pi$$
$$72$$ 0 0
$$73$$ 522.000 0.836924 0.418462 0.908234i $$-0.362569\pi$$
0.418462 + 0.908234i $$0.362569\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −280.000 −0.414402
$$78$$ 0 0
$$79$$ −876.539 −1.24833 −0.624166 0.781291i $$-0.714561\pi$$
−0.624166 + 0.781291i $$0.714561\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 380.132 0.502709 0.251355 0.967895i $$-0.419124\pi$$
0.251355 + 0.967895i $$0.419124\pi$$
$$84$$ 0 0
$$85$$ 230.000 0.293494
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −970.000 −1.15528 −0.577639 0.816292i $$-0.696026\pi$$
−0.577639 + 0.816292i $$0.696026\pi$$
$$90$$ 0 0
$$91$$ −1940.91 −2.23585
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −536.656 −0.579577
$$96$$ 0 0
$$97$$ −934.000 −0.977663 −0.488832 0.872378i $$-0.662577\pi$$
−0.488832 + 0.872378i $$0.662577\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 602.000 0.593082 0.296541 0.955020i $$-0.404167\pi$$
0.296541 + 0.955020i $$0.404167\pi$$
$$102$$ 0 0
$$103$$ 1829.10 1.74978 0.874888 0.484325i $$-0.160935\pi$$
0.874888 + 0.484325i $$0.160935\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1525.00 −1.37782 −0.688912 0.724845i $$-0.741911\pi$$
−0.688912 + 0.724845i $$0.741911\pi$$
$$108$$ 0 0
$$109$$ 2154.00 1.89281 0.946403 0.322989i $$-0.104688\pi$$
0.946403 + 0.322989i $$0.104688\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2182.00 1.81651 0.908254 0.418420i $$-0.137416\pi$$
0.908254 + 0.418420i $$0.137416\pi$$
$$114$$ 0 0
$$115$$ 961.509 0.779663
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 1440.03 1.10930
$$120$$ 0 0
$$121$$ −1251.00 −0.939895
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ −1310.34 −0.915539 −0.457770 0.889071i $$-0.651352\pi$$
−0.457770 + 0.889071i $$0.651352\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −205.718 −0.137204 −0.0686019 0.997644i $$-0.521854\pi$$
−0.0686019 + 0.997644i $$0.521854\pi$$
$$132$$ 0 0
$$133$$ −3360.00 −2.19059
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2094.00 1.30586 0.652929 0.757419i $$-0.273540\pi$$
0.652929 + 0.757419i $$0.273540\pi$$
$$138$$ 0 0
$$139$$ 1377.42 0.840511 0.420256 0.907406i $$-0.361940\pi$$
0.420256 + 0.907406i $$0.361940\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 554.545 0.324289
$$144$$ 0 0
$$145$$ 450.000 0.257727
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 334.000 0.183640 0.0918200 0.995776i $$-0.470732\pi$$
0.0918200 + 0.995776i $$0.470732\pi$$
$$150$$ 0 0
$$151$$ −3139.44 −1.69195 −0.845973 0.533225i $$-0.820980\pi$$
−0.845973 + 0.533225i $$0.820980\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 760.263 0.393973
$$156$$ 0 0
$$157$$ 834.000 0.423952 0.211976 0.977275i $$-0.432010\pi$$
0.211976 + 0.977275i $$0.432010\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 6020.00 2.94685
$$162$$ 0 0
$$163$$ 3090.25 1.48495 0.742475 0.669874i $$-0.233652\pi$$
0.742475 + 0.669874i $$0.233652\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 4.47214 0.00207224 0.00103612 0.999999i $$-0.499670\pi$$
0.00103612 + 0.999999i $$0.499670\pi$$
$$168$$ 0 0
$$169$$ 1647.00 0.749659
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1838.00 0.807749 0.403874 0.914814i $$-0.367663\pi$$
0.403874 + 0.914814i $$0.367663\pi$$
$$174$$ 0 0
$$175$$ 782.624 0.338062
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 1842.52 0.769365 0.384683 0.923049i $$-0.374311\pi$$
0.384683 + 0.923049i $$0.374311\pi$$
$$180$$ 0 0
$$181$$ 1862.00 0.764648 0.382324 0.924028i $$-0.375124\pi$$
0.382324 + 0.924028i $$0.375124\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1070.00 −0.425232
$$186$$ 0 0
$$187$$ −411.437 −0.160894
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −2066.13 −0.782721 −0.391360 0.920237i $$-0.627995\pi$$
−0.391360 + 0.920237i $$0.627995\pi$$
$$192$$ 0 0
$$193$$ 3378.00 1.25986 0.629932 0.776650i $$-0.283083\pi$$
0.629932 + 0.776650i $$0.283083\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −66.0000 −0.0238696 −0.0119348 0.999929i $$-0.503799\pi$$
−0.0119348 + 0.999929i $$0.503799\pi$$
$$198$$ 0 0
$$199$$ 1216.42 0.433316 0.216658 0.976248i $$-0.430484\pi$$
0.216658 + 0.976248i $$0.430484\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 2817.45 0.974118
$$204$$ 0 0
$$205$$ 50.0000 0.0170349
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 960.000 0.317725
$$210$$ 0 0
$$211$$ 5286.06 1.72468 0.862341 0.506329i $$-0.168998\pi$$
0.862341 + 0.506329i $$0.168998\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 335.410 0.106394
$$216$$ 0 0
$$217$$ 4760.00 1.48908
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −2852.00 −0.868083
$$222$$ 0 0
$$223$$ −2965.03 −0.890371 −0.445186 0.895438i $$-0.646862\pi$$
−0.445186 + 0.895438i $$0.646862\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −4369.28 −1.27753 −0.638765 0.769402i $$-0.720554\pi$$
−0.638765 + 0.769402i $$0.720554\pi$$
$$228$$ 0 0
$$229$$ −3250.00 −0.937843 −0.468921 0.883240i $$-0.655357\pi$$
−0.468921 + 0.883240i $$0.655357\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −3298.00 −0.927293 −0.463646 0.886020i $$-0.653459\pi$$
−0.463646 + 0.886020i $$0.653459\pi$$
$$234$$ 0 0
$$235$$ 1990.10 0.552425
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −554.545 −0.150086 −0.0750429 0.997180i $$-0.523909\pi$$
−0.0750429 + 0.997180i $$0.523909\pi$$
$$240$$ 0 0
$$241$$ 5150.00 1.37652 0.688259 0.725465i $$-0.258375\pi$$
0.688259 + 0.725465i $$0.258375\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 3185.00 0.830540
$$246$$ 0 0
$$247$$ 6654.54 1.71424
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 1386.36 0.348631 0.174316 0.984690i $$-0.444229\pi$$
0.174316 + 0.984690i $$0.444229\pi$$
$$252$$ 0 0
$$253$$ −1720.00 −0.427413
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4166.00 1.01116 0.505580 0.862780i $$-0.331279\pi$$
0.505580 + 0.862780i $$0.331279\pi$$
$$258$$ 0 0
$$259$$ −6699.26 −1.60723
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 961.509 0.225434 0.112717 0.993627i $$-0.464045\pi$$
0.112717 + 0.993627i $$0.464045\pi$$
$$264$$ 0 0
$$265$$ 3390.00 0.785834
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1494.00 0.338627 0.169314 0.985562i $$-0.445845\pi$$
0.169314 + 0.985562i $$0.445845\pi$$
$$270$$ 0 0
$$271$$ −5017.74 −1.12474 −0.562372 0.826884i $$-0.690111\pi$$
−0.562372 + 0.826884i $$0.690111\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −223.607 −0.0490327
$$276$$ 0 0
$$277$$ −1006.00 −0.218212 −0.109106 0.994030i $$-0.534799\pi$$
−0.109106 + 0.994030i $$0.534799\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 3210.00 0.681468 0.340734 0.940160i $$-0.389324\pi$$
0.340734 + 0.940160i $$0.389324\pi$$
$$282$$ 0 0
$$283$$ −3635.85 −0.763705 −0.381853 0.924223i $$-0.624714\pi$$
−0.381853 + 0.924223i $$0.624714\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 313.050 0.0643858
$$288$$ 0 0
$$289$$ −2797.00 −0.569306
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 3622.00 0.722183 0.361091 0.932530i $$-0.382404\pi$$
0.361091 + 0.932530i $$0.382404\pi$$
$$294$$ 0 0
$$295$$ −2057.18 −0.406013
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −11922.7 −2.30605
$$300$$ 0 0
$$301$$ 2100.00 0.402133
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 1250.00 0.234671
$$306$$ 0 0
$$307$$ −2088.49 −0.388261 −0.194131 0.980976i $$-0.562189\pi$$
−0.194131 + 0.980976i $$0.562189\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −8899.55 −1.62266 −0.811330 0.584589i $$-0.801256\pi$$
−0.811330 + 0.584589i $$0.801256\pi$$
$$312$$ 0 0
$$313$$ 8778.00 1.58518 0.792591 0.609754i $$-0.208732\pi$$
0.792591 + 0.609754i $$0.208732\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 5046.00 0.894043 0.447021 0.894523i $$-0.352485\pi$$
0.447021 + 0.894523i $$0.352485\pi$$
$$318$$ 0 0
$$319$$ −804.984 −0.141287
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −4937.24 −0.850512
$$324$$ 0 0
$$325$$ −1550.00 −0.264549
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 12460.0 2.08797
$$330$$ 0 0
$$331$$ 313.050 0.0519842 0.0259921 0.999662i $$-0.491726\pi$$
0.0259921 + 0.999662i $$0.491726\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −245.967 −0.0401153
$$336$$ 0 0
$$337$$ −2574.00 −0.416067 −0.208034 0.978122i $$-0.566706\pi$$
−0.208034 + 0.978122i $$0.566706\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1360.00 −0.215977
$$342$$ 0 0
$$343$$ 9203.66 1.44884
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 2643.03 0.408892 0.204446 0.978878i $$-0.434461\pi$$
0.204446 + 0.978878i $$0.434461\pi$$
$$348$$ 0 0
$$349$$ −10170.0 −1.55985 −0.779925 0.625873i $$-0.784743\pi$$
−0.779925 + 0.625873i $$0.784743\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 318.000 0.0479474 0.0239737 0.999713i $$-0.492368\pi$$
0.0239737 + 0.999713i $$0.492368\pi$$
$$354$$ 0 0
$$355$$ −1833.58 −0.274130
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 12378.9 1.81987 0.909933 0.414755i $$-0.136133\pi$$
0.909933 + 0.414755i $$0.136133\pi$$
$$360$$ 0 0
$$361$$ 4661.00 0.679545
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2610.00 0.374284
$$366$$ 0 0
$$367$$ 3072.36 0.436991 0.218496 0.975838i $$-0.429885\pi$$
0.218496 + 0.975838i $$0.429885\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 21224.8 2.97017
$$372$$ 0 0
$$373$$ −3278.00 −0.455036 −0.227518 0.973774i $$-0.573061\pi$$
−0.227518 + 0.973774i $$0.573061\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −5580.00 −0.762293
$$378$$ 0 0
$$379$$ −5116.12 −0.693397 −0.346699 0.937977i $$-0.612697\pi$$
−0.346699 + 0.937977i $$0.612697\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −1149.34 −0.153338 −0.0766690 0.997057i $$-0.524428\pi$$
−0.0766690 + 0.997057i $$0.524428\pi$$
$$384$$ 0 0
$$385$$ −1400.00 −0.185326
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −834.000 −0.108703 −0.0543515 0.998522i $$-0.517309\pi$$
−0.0543515 + 0.998522i $$0.517309\pi$$
$$390$$ 0 0
$$391$$ 8845.88 1.14413
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −4382.69 −0.558271
$$396$$ 0 0
$$397$$ −8734.00 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −242.000 −0.0301369 −0.0150685 0.999886i $$-0.504797\pi$$
−0.0150685 + 0.999886i $$0.504797\pi$$
$$402$$ 0 0
$$403$$ −9427.26 −1.16527
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1914.07 0.233113
$$408$$ 0 0
$$409$$ −6514.00 −0.787522 −0.393761 0.919213i $$-0.628826\pi$$
−0.393761 + 0.919213i $$0.628826\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −12880.0 −1.53458
$$414$$ 0 0
$$415$$ 1900.66 0.224818
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 16081.8 1.87505 0.937527 0.347913i $$-0.113110\pi$$
0.937527 + 0.347913i $$0.113110\pi$$
$$420$$ 0 0
$$421$$ 7250.00 0.839295 0.419648 0.907687i $$-0.362154\pi$$
0.419648 + 0.907687i $$0.362154\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1150.00 0.131255
$$426$$ 0 0
$$427$$ 7826.24 0.886975
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 4981.96 0.556781 0.278390 0.960468i $$-0.410199\pi$$
0.278390 + 0.960468i $$0.410199\pi$$
$$432$$ 0 0
$$433$$ 11482.0 1.27434 0.637171 0.770723i $$-0.280105\pi$$
0.637171 + 0.770723i $$0.280105\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −20640.0 −2.25937
$$438$$ 0 0
$$439$$ −3792.37 −0.412301 −0.206150 0.978520i $$-0.566094\pi$$
−0.206150 + 0.978520i $$0.566094\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −746.847 −0.0800988 −0.0400494 0.999198i $$-0.512752\pi$$
−0.0400494 + 0.999198i $$0.512752\pi$$
$$444$$ 0 0
$$445$$ −4850.00 −0.516656
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 1306.00 0.137269 0.0686347 0.997642i $$-0.478136\pi$$
0.0686347 + 0.997642i $$0.478136\pi$$
$$450$$ 0 0
$$451$$ −89.4427 −0.00933857
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −9704.54 −0.999902
$$456$$ 0 0
$$457$$ −9526.00 −0.975071 −0.487536 0.873103i $$-0.662104\pi$$
−0.487536 + 0.873103i $$0.662104\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −1518.00 −0.153363 −0.0766815 0.997056i $$-0.524432\pi$$
−0.0766815 + 0.997056i $$0.524432\pi$$
$$462$$ 0 0
$$463$$ −17293.7 −1.73587 −0.867936 0.496676i $$-0.834554\pi$$
−0.867936 + 0.496676i $$0.834554\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −16980.7 −1.68260 −0.841299 0.540570i $$-0.818208\pi$$
−0.841299 + 0.540570i $$0.818208\pi$$
$$468$$ 0 0
$$469$$ −1540.00 −0.151622
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −600.000 −0.0583256
$$474$$ 0 0
$$475$$ −2683.28 −0.259195
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 3810.26 0.363456 0.181728 0.983349i $$-0.441831\pi$$
0.181728 + 0.983349i $$0.441831\pi$$
$$480$$ 0 0
$$481$$ 13268.0 1.25773
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −4670.00 −0.437224
$$486$$ 0 0
$$487$$ −1310.34 −0.121924 −0.0609620 0.998140i $$-0.519417\pi$$
−0.0609620 + 0.998140i $$0.519417\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2960.55 0.272114 0.136057 0.990701i $$-0.456557\pi$$
0.136057 + 0.990701i $$0.456557\pi$$
$$492$$ 0 0
$$493$$ 4140.00 0.378207
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −11480.0 −1.03611
$$498$$ 0 0
$$499$$ 19319.6 1.73320 0.866598 0.499006i $$-0.166301\pi$$
0.866598 + 0.499006i $$0.166301\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 3072.36 0.272345 0.136173 0.990685i $$-0.456520\pi$$
0.136173 + 0.990685i $$0.456520\pi$$
$$504$$ 0 0
$$505$$ 3010.00 0.265234
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −18550.0 −1.61535 −0.807676 0.589626i $$-0.799275\pi$$
−0.807676 + 0.589626i $$0.799275\pi$$
$$510$$ 0 0
$$511$$ 16341.2 1.41466
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 9145.52 0.782524
$$516$$ 0 0
$$517$$ −3560.00 −0.302841
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 2102.00 0.176757 0.0883784 0.996087i $$-0.471832\pi$$
0.0883784 + 0.996087i $$0.471832\pi$$
$$522$$ 0 0
$$523$$ −17696.2 −1.47955 −0.739773 0.672856i $$-0.765067\pi$$
−0.739773 + 0.672856i $$0.765067\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 6994.42 0.578144
$$528$$ 0 0
$$529$$ 24813.0 2.03937
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −620.000 −0.0503850
$$534$$ 0 0
$$535$$ −7624.99 −0.616182
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −5697.50 −0.455304
$$540$$ 0 0
$$541$$ −9922.00 −0.788503 −0.394251 0.919003i $$-0.628996\pi$$
−0.394251 + 0.919003i $$0.628996\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 10770.0 0.846488
$$546$$ 0 0
$$547$$ −3716.34 −0.290493 −0.145246 0.989396i $$-0.546397\pi$$
−0.145246 + 0.989396i $$0.546397\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −9659.81 −0.746864
$$552$$ 0 0
$$553$$ −27440.0 −2.11007
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 15094.0 1.14821 0.574105 0.818781i $$-0.305350\pi$$
0.574105 + 0.818781i $$0.305350\pi$$
$$558$$ 0 0
$$559$$ −4159.09 −0.314688
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 5657.25 0.423490 0.211745 0.977325i $$-0.432085\pi$$
0.211745 + 0.977325i $$0.432085\pi$$
$$564$$ 0 0
$$565$$ 10910.0 0.812367
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 5906.00 0.435136 0.217568 0.976045i $$-0.430188\pi$$
0.217568 + 0.976045i $$0.430188\pi$$
$$570$$ 0 0
$$571$$ 4892.52 0.358573 0.179287 0.983797i $$-0.442621\pi$$
0.179287 + 0.983797i $$0.442621\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 4807.55 0.348676
$$576$$ 0 0
$$577$$ −13286.0 −0.958585 −0.479292 0.877655i $$-0.659107\pi$$
−0.479292 + 0.877655i $$0.659107\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 11900.0 0.849734
$$582$$ 0 0
$$583$$ −6064.22 −0.430796
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 9029.24 0.634884 0.317442 0.948278i $$-0.397176\pi$$
0.317442 + 0.948278i $$0.397176\pi$$
$$588$$ 0 0
$$589$$ −16320.0 −1.14169
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −11442.0 −0.792355 −0.396178 0.918174i $$-0.629664\pi$$
−0.396178 + 0.918174i $$0.629664\pi$$
$$594$$ 0 0
$$595$$ 7200.14 0.496096
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −14149.8 −0.965187 −0.482593 0.875845i $$-0.660305\pi$$
−0.482593 + 0.875845i $$0.660305\pi$$
$$600$$ 0 0
$$601$$ 3110.00 0.211081 0.105540 0.994415i $$-0.466343\pi$$
0.105540 + 0.994415i $$0.466343\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −6255.00 −0.420334
$$606$$ 0 0
$$607$$ 11193.8 0.748502 0.374251 0.927327i $$-0.377900\pi$$
0.374251 + 0.927327i $$0.377900\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −24677.2 −1.63394
$$612$$ 0 0
$$613$$ −5342.00 −0.351976 −0.175988 0.984392i $$-0.556312\pi$$
−0.175988 + 0.984392i $$0.556312\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −19714.0 −1.28631 −0.643157 0.765734i $$-0.722376\pi$$
−0.643157 + 0.765734i $$0.722376\pi$$
$$618$$ 0 0
$$619$$ 13166.0 0.854903 0.427451 0.904038i $$-0.359411\pi$$
0.427451 + 0.904038i $$0.359411\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −30365.8 −1.95278
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −9844.00 −0.624016
$$630$$ 0 0
$$631$$ −12262.6 −0.773639 −0.386820 0.922155i $$-0.626426\pi$$
−0.386820 + 0.922155i $$0.626426\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −6551.68 −0.409442
$$636$$ 0 0
$$637$$ −39494.0 −2.45653
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2690.00 0.165754 0.0828772 0.996560i $$-0.473589\pi$$
0.0828772 + 0.996560i $$0.473589\pi$$
$$642$$ 0 0
$$643$$ −12240.2 −0.750712 −0.375356 0.926881i $$-0.622480\pi$$
−0.375356 + 0.926881i $$0.622480\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −17973.5 −1.09214 −0.546068 0.837741i $$-0.683876\pi$$
−0.546068 + 0.837741i $$0.683876\pi$$
$$648$$ 0 0
$$649$$ 3680.00 0.222577
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 3478.00 0.208430 0.104215 0.994555i $$-0.466767\pi$$
0.104215 + 0.994555i $$0.466767\pi$$
$$654$$ 0 0
$$655$$ −1028.59 −0.0613594
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −10572.1 −0.624934 −0.312467 0.949929i $$-0.601155\pi$$
−0.312467 + 0.949929i $$0.601155\pi$$
$$660$$ 0 0
$$661$$ −110.000 −0.00647277 −0.00323639 0.999995i $$-0.501030\pi$$
−0.00323639 + 0.999995i $$0.501030\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −16800.0 −0.979663
$$666$$ 0 0
$$667$$ 17307.2 1.00470
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −2236.07 −0.128647
$$672$$ 0 0
$$673$$ −14278.0 −0.817796 −0.408898 0.912580i $$-0.634087\pi$$
−0.408898 + 0.912580i $$0.634087\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −18386.0 −1.04377 −0.521884 0.853016i $$-0.674771\pi$$
−0.521884 + 0.853016i $$0.674771\pi$$
$$678$$ 0 0
$$679$$ −29238.8 −1.65255
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 15317.1 0.858113 0.429057 0.903278i $$-0.358846\pi$$
0.429057 + 0.903278i $$0.358846\pi$$
$$684$$ 0 0
$$685$$ 10470.0 0.583997
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −42036.0 −2.32430
$$690$$ 0 0
$$691$$ −9507.76 −0.523433 −0.261717 0.965145i $$-0.584289\pi$$
−0.261717 + 0.965145i $$0.584289\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6887.09 0.375888
$$696$$ 0 0
$$697$$ 460.000 0.0249982
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 15830.0 0.852911 0.426456 0.904508i $$-0.359762\pi$$
0.426456 + 0.904508i $$0.359762\pi$$
$$702$$ 0 0
$$703$$ 22968.9 1.23227
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 18845.6 1.00249
$$708$$ 0 0
$$709$$ −20050.0 −1.06205 −0.531025 0.847356i $$-0.678193\pi$$
−0.531025 + 0.847356i $$0.678193\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 29240.0 1.53583
$$714$$ 0 0
$$715$$ 2772.72 0.145027
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 21126.4 1.09580 0.547900 0.836544i $$-0.315427\pi$$
0.547900 + 0.836544i $$0.315427\pi$$
$$720$$ 0 0
$$721$$ 57260.0 2.95766
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2250.00 0.115259
$$726$$ 0 0
$$727$$ 11336.9 0.578351 0.289175 0.957276i $$-0.406619\pi$$
0.289175 + 0.957276i $$0.406619\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 3085.77 0.156131
$$732$$ 0 0
$$733$$ −17198.0 −0.866607 −0.433303 0.901248i $$-0.642652\pi$$
−0.433303 + 0.901248i $$0.642652\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 440.000 0.0219913
$$738$$ 0 0
$$739$$ −4597.36 −0.228845 −0.114423 0.993432i $$-0.536502\pi$$
−0.114423 + 0.993432i $$0.536502\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −2419.43 −0.119462 −0.0597309 0.998215i $$-0.519024\pi$$
−0.0597309 + 0.998215i $$0.519024\pi$$
$$744$$ 0 0
$$745$$ 1670.00 0.0821263
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −47740.0 −2.32895
$$750$$ 0 0
$$751$$ −7432.69 −0.361149 −0.180574 0.983561i $$-0.557796\pi$$
−0.180574 + 0.983561i $$0.557796\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −15697.2 −0.756662
$$756$$ 0 0
$$757$$ 11474.0 0.550898 0.275449 0.961316i $$-0.411174\pi$$
0.275449 + 0.961316i $$0.411174\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −31802.0 −1.51488 −0.757439 0.652906i $$-0.773550\pi$$
−0.757439 + 0.652906i $$0.773550\pi$$
$$762$$ 0 0
$$763$$ 67430.9 3.19942
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 25509.1 1.20089
$$768$$ 0 0
$$769$$ −5310.00 −0.249003 −0.124502 0.992219i $$-0.539733\pi$$
−0.124502 + 0.992219i $$0.539733\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −37938.0 −1.76525 −0.882623 0.470082i $$-0.844224\pi$$
−0.882623 + 0.470082i $$0.844224\pi$$
$$774$$ 0 0
$$775$$ 3801.32 0.176190
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1073.31 −0.0493651
$$780$$ 0 0
$$781$$ 3280.00 0.150279
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 4170.00 0.189597
$$786$$ 0 0
$$787$$ −37633.0 −1.70454 −0.852270 0.523103i $$-0.824774\pi$$
−0.852270 + 0.523103i $$0.824774\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 68307.4 3.07046
$$792$$ 0 0
$$793$$ −15500.0 −0.694100
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 17526.0 0.778924 0.389462 0.921042i $$-0.372661\pi$$
0.389462 + 0.921042i $$0.372661\pi$$
$$798$$ 0 0
$$799$$ 18308.9 0.810667
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −4668.91 −0.205183
$$804$$ 0 0
$$805$$ 30100.0 1.31787
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −8970.00 −0.389825 −0.194912 0.980821i $$-0.562442\pi$$
−0.194912 + 0.980821i $$0.562442\pi$$
$$810$$ 0 0
$$811$$ 3550.88 0.153746 0.0768731 0.997041i $$-0.475506\pi$$
0.0768731 + 0.997041i $$0.475506\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 15451.2 0.664090
$$816$$ 0 0
$$817$$ −7200.00 −0.308318
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 15550.0 0.661022 0.330511 0.943802i $$-0.392779\pi$$
0.330511 + 0.943802i $$0.392779\pi$$
$$822$$ 0 0
$$823$$ 26712.1 1.13138 0.565689 0.824619i $$-0.308610\pi$$
0.565689 + 0.824619i $$0.308610\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −863.122 −0.0362923 −0.0181461 0.999835i $$-0.505776\pi$$
−0.0181461 + 0.999835i $$0.505776\pi$$
$$828$$ 0 0
$$829$$ 19066.0 0.798781 0.399391 0.916781i $$-0.369222\pi$$
0.399391 + 0.916781i $$0.369222\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 29302.0 1.21879
$$834$$ 0 0
$$835$$ 22.3607 0.000926734 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −47744.5 −1.96463 −0.982315 0.187238i $$-0.940047\pi$$
−0.982315 + 0.187238i $$0.940047\pi$$
$$840$$ 0 0
$$841$$ −16289.0 −0.667883
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 8235.00 0.335258
$$846$$ 0 0
$$847$$ −39162.5 −1.58871
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −41152.6 −1.65769
$$852$$ 0 0
$$853$$ −14462.0 −0.580503 −0.290252 0.956950i $$-0.593739\pi$$
−0.290252 + 0.956950i $$0.593739\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −29346.0 −1.16971 −0.584854 0.811138i $$-0.698848\pi$$
−0.584854 + 0.811138i $$0.698848\pi$$
$$858$$ 0 0
$$859$$ −22807.9 −0.905932 −0.452966 0.891528i $$-0.649634\pi$$
−0.452966 + 0.891528i $$0.649634\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 24753.3 0.976375 0.488187 0.872739i $$-0.337658\pi$$
0.488187 + 0.872739i $$0.337658\pi$$
$$864$$ 0 0
$$865$$ 9190.00 0.361236
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 7840.00 0.306046
$$870$$ 0 0
$$871$$ 3050.00 0.118651
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 3913.12 0.151186
$$876$$ 0 0
$$877$$ −32126.0 −1.23696 −0.618482 0.785799i $$-0.712252\pi$$
−0.618482 + 0.785799i $$0.712252\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 33570.0 1.28377 0.641885 0.766801i $$-0.278152\pi$$
0.641885 + 0.766801i $$0.278152\pi$$
$$882$$ 0 0
$$883$$ 6435.40 0.245265 0.122632 0.992452i $$-0.460866\pi$$
0.122632 + 0.992452i $$0.460866\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −46827.7 −1.77263 −0.886314 0.463084i $$-0.846743\pi$$
−0.886314 + 0.463084i $$0.846743\pi$$
$$888$$ 0 0
$$889$$ −41020.0 −1.54754
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −42720.0 −1.60086
$$894$$ 0 0
$$895$$ 9212.60 0.344071
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 13684.7 0.507688
$$900$$ 0 0
$$901$$ 31188.0 1.15319
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 9310.00 0.341961
$$906$$ 0 0
$$907$$ −11980.9 −0.438608 −0.219304 0.975657i $$-0.570379\pi$$
−0.219304 + 0.975657i $$0.570379\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −24194.3 −0.879903 −0.439951 0.898022i $$-0.645004\pi$$
−0.439951 + 0.898022i $$0.645004\pi$$
$$912$$ 0 0
$$913$$ −3400.00 −0.123246
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −6440.00 −0.231917
$$918$$ 0 0
$$919$$ 37512.3 1.34648 0.673240 0.739424i $$-0.264902\pi$$
0.673240 + 0.739424i $$0.264902\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 22736.3 0.810808
$$924$$ 0 0
$$925$$ −5350.00 −0.190170
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 21994.0 0.776749 0.388374 0.921502i $$-0.373037\pi$$
0.388374 + 0.921502i $$0.373037\pi$$
$$930$$ 0 0
$$931$$ −68370.0 −2.40681
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −2057.18 −0.0719541
$$936$$ 0 0
$$937$$ −16286.0 −0.567813 −0.283906 0.958852i $$-0.591630\pi$$
−0.283906 + 0.958852i $$0.591630\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −24302.0 −0.841894 −0.420947 0.907085i $$-0.638302\pi$$
−0.420947 + 0.907085i $$0.638302\pi$$
$$942$$ 0 0
$$943$$ 1923.02 0.0664073
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 19869.7 0.681815 0.340907 0.940097i $$-0.389266\pi$$
0.340907 + 0.940097i $$0.389266\pi$$
$$948$$ 0 0
$$949$$ −32364.0 −1.10704
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 22422.0 0.762140 0.381070 0.924546i $$-0.375556\pi$$
0.381070 + 0.924546i $$0.375556\pi$$
$$954$$ 0 0
$$955$$ −10330.6 −0.350043
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 65552.6 2.20730
$$960$$ 0 0
$$961$$ −6671.00 −0.223927
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 16890.0 0.563428
$$966$$ 0 0
$$967$$ −43777.7 −1.45584 −0.727920 0.685662i $$-0.759513\pi$$
−0.727920 + 0.685662i $$0.759513\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −25714.8 −0.849873 −0.424936 0.905223i $$-0.639704\pi$$
−0.424936 + 0.905223i $$0.639704\pi$$
$$972$$ 0 0
$$973$$ 43120.0 1.42072
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −28986.0 −0.949175 −0.474588 0.880208i $$-0.657403\pi$$
−0.474588 + 0.880208i $$0.657403\pi$$
$$978$$ 0 0
$$979$$ 8675.94 0.283232
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 32123.4 1.04229 0.521147 0.853467i $$-0.325504\pi$$
0.521147 + 0.853467i $$0.325504\pi$$
$$984$$ 0 0
$$985$$ −330.000 −0.0106748
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 12900.0 0.414758
$$990$$ 0 0
$$991$$ 11994.3 0.384471 0.192235 0.981349i $$-0.438426\pi$$
0.192235 + 0.981349i $$0.438426\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 6082.10 0.193785
$$996$$ 0 0
$$997$$ −406.000 −0.0128968 −0.00644842 0.999979i $$-0.502053\pi$$
−0.00644842 + 0.999979i $$0.502053\pi$$
$$998$$ 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 1440.4.a.bb.1.2 2
3.2 odd 2 160.4.a.d.1.1 2
4.3 odd 2 inner 1440.4.a.bb.1.1 2
12.11 even 2 160.4.a.d.1.2 yes 2
15.2 even 4 800.4.c.l.449.4 4
15.8 even 4 800.4.c.l.449.2 4
15.14 odd 2 800.4.a.o.1.2 2
24.5 odd 2 320.4.a.q.1.2 2
24.11 even 2 320.4.a.q.1.1 2
48.5 odd 4 1280.4.d.v.641.3 4
48.11 even 4 1280.4.d.v.641.1 4
48.29 odd 4 1280.4.d.v.641.2 4
48.35 even 4 1280.4.d.v.641.4 4
60.23 odd 4 800.4.c.l.449.3 4
60.47 odd 4 800.4.c.l.449.1 4
60.59 even 2 800.4.a.o.1.1 2
120.29 odd 2 1600.4.a.cg.1.1 2
120.59 even 2 1600.4.a.cg.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
160.4.a.d.1.1 2 3.2 odd 2
160.4.a.d.1.2 yes 2 12.11 even 2
320.4.a.q.1.1 2 24.11 even 2
320.4.a.q.1.2 2 24.5 odd 2
800.4.a.o.1.1 2 60.59 even 2
800.4.a.o.1.2 2 15.14 odd 2
800.4.c.l.449.1 4 60.47 odd 4
800.4.c.l.449.2 4 15.8 even 4
800.4.c.l.449.3 4 60.23 odd 4
800.4.c.l.449.4 4 15.2 even 4
1280.4.d.v.641.1 4 48.11 even 4
1280.4.d.v.641.2 4 48.29 odd 4
1280.4.d.v.641.3 4 48.5 odd 4
1280.4.d.v.641.4 4 48.35 even 4
1440.4.a.bb.1.1 2 4.3 odd 2 inner
1440.4.a.bb.1.2 2 1.1 even 1 trivial
1600.4.a.cg.1.1 2 120.29 odd 2
1600.4.a.cg.1.2 2 120.59 even 2