Properties

 Label 1575.4.a.k.1.1 Level $1575$ Weight $4$ Character 1575.1 Self dual yes Analytic conductor $92.928$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1575.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$92.9280082590$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1575.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+4.00000 q^{2} +8.00000 q^{4} +7.00000 q^{7} +O(q^{10})$$ $$q+4.00000 q^{2} +8.00000 q^{4} +7.00000 q^{7} -62.0000 q^{11} +62.0000 q^{13} +28.0000 q^{14} -64.0000 q^{16} +84.0000 q^{17} +100.000 q^{19} -248.000 q^{22} -42.0000 q^{23} +248.000 q^{26} +56.0000 q^{28} +10.0000 q^{29} -48.0000 q^{31} -256.000 q^{32} +336.000 q^{34} +246.000 q^{37} +400.000 q^{38} +248.000 q^{41} -68.0000 q^{43} -496.000 q^{44} -168.000 q^{46} +324.000 q^{47} +49.0000 q^{49} +496.000 q^{52} +258.000 q^{53} +40.0000 q^{58} -120.000 q^{59} +622.000 q^{61} -192.000 q^{62} -512.000 q^{64} -904.000 q^{67} +672.000 q^{68} +678.000 q^{71} +642.000 q^{73} +984.000 q^{74} +800.000 q^{76} -434.000 q^{77} +740.000 q^{79} +992.000 q^{82} +468.000 q^{83} -272.000 q^{86} -200.000 q^{89} +434.000 q^{91} -336.000 q^{92} +1296.00 q^{94} +1266.00 q^{97} +196.000 q^{98} +O(q^{100})$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.00000 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$3$$ 0 0
$$4$$ 8.00000 1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 7.00000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −62.0000 −1.69943 −0.849714 0.527244i $$-0.823225\pi$$
−0.849714 + 0.527244i $$0.823225\pi$$
$$12$$ 0 0
$$13$$ 62.0000 1.32275 0.661373 0.750057i $$-0.269974\pi$$
0.661373 + 0.750057i $$0.269974\pi$$
$$14$$ 28.0000 0.534522
$$15$$ 0 0
$$16$$ −64.0000 −1.00000
$$17$$ 84.0000 1.19841 0.599206 0.800595i $$-0.295483\pi$$
0.599206 + 0.800595i $$0.295483\pi$$
$$18$$ 0 0
$$19$$ 100.000 1.20745 0.603726 0.797192i $$-0.293682\pi$$
0.603726 + 0.797192i $$0.293682\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −248.000 −2.40335
$$23$$ −42.0000 −0.380765 −0.190383 0.981710i $$-0.560973\pi$$
−0.190383 + 0.981710i $$0.560973\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 248.000 1.87065
$$27$$ 0 0
$$28$$ 56.0000 0.377964
$$29$$ 10.0000 0.0640329 0.0320164 0.999487i $$-0.489807\pi$$
0.0320164 + 0.999487i $$0.489807\pi$$
$$30$$ 0 0
$$31$$ −48.0000 −0.278099 −0.139049 0.990285i $$-0.544405\pi$$
−0.139049 + 0.990285i $$0.544405\pi$$
$$32$$ −256.000 −1.41421
$$33$$ 0 0
$$34$$ 336.000 1.69481
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 246.000 1.09303 0.546516 0.837449i $$-0.315954\pi$$
0.546516 + 0.837449i $$0.315954\pi$$
$$38$$ 400.000 1.70759
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 248.000 0.944661 0.472330 0.881422i $$-0.343413\pi$$
0.472330 + 0.881422i $$0.343413\pi$$
$$42$$ 0 0
$$43$$ −68.0000 −0.241161 −0.120580 0.992704i $$-0.538476\pi$$
−0.120580 + 0.992704i $$0.538476\pi$$
$$44$$ −496.000 −1.69943
$$45$$ 0 0
$$46$$ −168.000 −0.538484
$$47$$ 324.000 1.00554 0.502769 0.864421i $$-0.332315\pi$$
0.502769 + 0.864421i $$0.332315\pi$$
$$48$$ 0 0
$$49$$ 49.0000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 496.000 1.32275
$$53$$ 258.000 0.668661 0.334330 0.942456i $$-0.391490\pi$$
0.334330 + 0.942456i $$0.391490\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 40.0000 0.0905562
$$59$$ −120.000 −0.264791 −0.132396 0.991197i $$-0.542267\pi$$
−0.132396 + 0.991197i $$0.542267\pi$$
$$60$$ 0 0
$$61$$ 622.000 1.30556 0.652778 0.757549i $$-0.273603\pi$$
0.652778 + 0.757549i $$0.273603\pi$$
$$62$$ −192.000 −0.393291
$$63$$ 0 0
$$64$$ −512.000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −904.000 −1.64838 −0.824188 0.566316i $$-0.808368\pi$$
−0.824188 + 0.566316i $$0.808368\pi$$
$$68$$ 672.000 1.19841
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 678.000 1.13329 0.566646 0.823961i $$-0.308241\pi$$
0.566646 + 0.823961i $$0.308241\pi$$
$$72$$ 0 0
$$73$$ 642.000 1.02932 0.514660 0.857394i $$-0.327918\pi$$
0.514660 + 0.857394i $$0.327918\pi$$
$$74$$ 984.000 1.54578
$$75$$ 0 0
$$76$$ 800.000 1.20745
$$77$$ −434.000 −0.642323
$$78$$ 0 0
$$79$$ 740.000 1.05388 0.526940 0.849903i $$-0.323339\pi$$
0.526940 + 0.849903i $$0.323339\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 992.000 1.33595
$$83$$ 468.000 0.618912 0.309456 0.950914i $$-0.399853\pi$$
0.309456 + 0.950914i $$0.399853\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −272.000 −0.341052
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −200.000 −0.238202 −0.119101 0.992882i $$-0.538001\pi$$
−0.119101 + 0.992882i $$0.538001\pi$$
$$90$$ 0 0
$$91$$ 434.000 0.499951
$$92$$ −336.000 −0.380765
$$93$$ 0 0
$$94$$ 1296.00 1.42204
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1266.00 1.32518 0.662592 0.748981i $$-0.269456\pi$$
0.662592 + 0.748981i $$0.269456\pi$$
$$98$$ 196.000 0.202031
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −232.000 −0.228563 −0.114281 0.993448i $$-0.536457\pi$$
−0.114281 + 0.993448i $$0.536457\pi$$
$$102$$ 0 0
$$103$$ 1792.00 1.71428 0.857141 0.515082i $$-0.172239\pi$$
0.857141 + 0.515082i $$0.172239\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 1032.00 0.945629
$$107$$ −1906.00 −1.72206 −0.861028 0.508558i $$-0.830179\pi$$
−0.861028 + 0.508558i $$0.830179\pi$$
$$108$$ 0 0
$$109$$ −90.0000 −0.0790866 −0.0395433 0.999218i $$-0.512590\pi$$
−0.0395433 + 0.999218i $$0.512590\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −448.000 −0.377964
$$113$$ 458.000 0.381283 0.190642 0.981660i $$-0.438943\pi$$
0.190642 + 0.981660i $$0.438943\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 80.0000 0.0640329
$$117$$ 0 0
$$118$$ −480.000 −0.374471
$$119$$ 588.000 0.452957
$$120$$ 0 0
$$121$$ 2513.00 1.88805
$$122$$ 2488.00 1.84634
$$123$$ 0 0
$$124$$ −384.000 −0.278099
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −804.000 −0.561760 −0.280880 0.959743i $$-0.590626\pi$$
−0.280880 + 0.959743i $$0.590626\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −812.000 −0.541563 −0.270782 0.962641i $$-0.587282\pi$$
−0.270782 + 0.962641i $$0.587282\pi$$
$$132$$ 0 0
$$133$$ 700.000 0.456374
$$134$$ −3616.00 −2.33116
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 414.000 0.258178 0.129089 0.991633i $$-0.458795\pi$$
0.129089 + 0.991633i $$0.458795\pi$$
$$138$$ 0 0
$$139$$ −1620.00 −0.988537 −0.494268 0.869309i $$-0.664564\pi$$
−0.494268 + 0.869309i $$0.664564\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 2712.00 1.60272
$$143$$ −3844.00 −2.24791
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 2568.00 1.45568
$$147$$ 0 0
$$148$$ 1968.00 1.09303
$$149$$ −2370.00 −1.30307 −0.651537 0.758617i $$-0.725875\pi$$
−0.651537 + 0.758617i $$0.725875\pi$$
$$150$$ 0 0
$$151$$ −568.000 −0.306114 −0.153057 0.988217i $$-0.548912\pi$$
−0.153057 + 0.988217i $$0.548912\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ −1736.00 −0.908382
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 266.000 0.135217 0.0676086 0.997712i $$-0.478463\pi$$
0.0676086 + 0.997712i $$0.478463\pi$$
$$158$$ 2960.00 1.49041
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −294.000 −0.143916
$$162$$ 0 0
$$163$$ 272.000 0.130704 0.0653518 0.997862i $$-0.479183\pi$$
0.0653518 + 0.997862i $$0.479183\pi$$
$$164$$ 1984.00 0.944661
$$165$$ 0 0
$$166$$ 1872.00 0.875273
$$167$$ −1876.00 −0.869277 −0.434638 0.900605i $$-0.643124\pi$$
−0.434638 + 0.900605i $$0.643124\pi$$
$$168$$ 0 0
$$169$$ 1647.00 0.749659
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −544.000 −0.241161
$$173$$ −152.000 −0.0667997 −0.0333998 0.999442i $$-0.510633\pi$$
−0.0333998 + 0.999442i $$0.510633\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 3968.00 1.69943
$$177$$ 0 0
$$178$$ −800.000 −0.336868
$$179$$ −610.000 −0.254713 −0.127356 0.991857i $$-0.540649\pi$$
−0.127356 + 0.991857i $$0.540649\pi$$
$$180$$ 0 0
$$181$$ 1042.00 0.427907 0.213954 0.976844i $$-0.431366\pi$$
0.213954 + 0.976844i $$0.431366\pi$$
$$182$$ 1736.00 0.707038
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −5208.00 −2.03661
$$188$$ 2592.00 1.00554
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 2038.00 0.772065 0.386033 0.922485i $$-0.373845\pi$$
0.386033 + 0.922485i $$0.373845\pi$$
$$192$$ 0 0
$$193$$ 2602.00 0.970446 0.485223 0.874390i $$-0.338738\pi$$
0.485223 + 0.874390i $$0.338738\pi$$
$$194$$ 5064.00 1.87409
$$195$$ 0 0
$$196$$ 392.000 0.142857
$$197$$ 2354.00 0.851348 0.425674 0.904877i $$-0.360037\pi$$
0.425674 + 0.904877i $$0.360037\pi$$
$$198$$ 0 0
$$199$$ 1680.00 0.598452 0.299226 0.954182i $$-0.403271\pi$$
0.299226 + 0.954182i $$0.403271\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −928.000 −0.323237
$$203$$ 70.0000 0.0242022
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 7168.00 2.42436
$$207$$ 0 0
$$208$$ −3968.00 −1.32275
$$209$$ −6200.00 −2.05198
$$210$$ 0 0
$$211$$ −668.000 −0.217948 −0.108974 0.994045i $$-0.534757\pi$$
−0.108974 + 0.994045i $$0.534757\pi$$
$$212$$ 2064.00 0.668661
$$213$$ 0 0
$$214$$ −7624.00 −2.43535
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −336.000 −0.105111
$$218$$ −360.000 −0.111845
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 5208.00 1.58519
$$222$$ 0 0
$$223$$ 1832.00 0.550134 0.275067 0.961425i $$-0.411300\pi$$
0.275067 + 0.961425i $$0.411300\pi$$
$$224$$ −1792.00 −0.534522
$$225$$ 0 0
$$226$$ 1832.00 0.539216
$$227$$ 4944.00 1.44557 0.722786 0.691072i $$-0.242861\pi$$
0.722786 + 0.691072i $$0.242861\pi$$
$$228$$ 0 0
$$229$$ −5470.00 −1.57846 −0.789231 0.614096i $$-0.789521\pi$$
−0.789231 + 0.614096i $$0.789521\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −2802.00 −0.787833 −0.393917 0.919146i $$-0.628880\pi$$
−0.393917 + 0.919146i $$0.628880\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −960.000 −0.264791
$$237$$ 0 0
$$238$$ 2352.00 0.640578
$$239$$ 1170.00 0.316657 0.158328 0.987386i $$-0.449390\pi$$
0.158328 + 0.987386i $$0.449390\pi$$
$$240$$ 0 0
$$241$$ −2338.00 −0.624912 −0.312456 0.949932i $$-0.601152\pi$$
−0.312456 + 0.949932i $$0.601152\pi$$
$$242$$ 10052.0 2.67011
$$243$$ 0 0
$$244$$ 4976.00 1.30556
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 6200.00 1.59715
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −2792.00 −0.702109 −0.351055 0.936355i $$-0.614177\pi$$
−0.351055 + 0.936355i $$0.614177\pi$$
$$252$$ 0 0
$$253$$ 2604.00 0.647083
$$254$$ −3216.00 −0.794448
$$255$$ 0 0
$$256$$ 4096.00 1.00000
$$257$$ 7024.00 1.70484 0.852422 0.522854i $$-0.175133\pi$$
0.852422 + 0.522854i $$0.175133\pi$$
$$258$$ 0 0
$$259$$ 1722.00 0.413127
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3248.00 −0.765886
$$263$$ 2438.00 0.571610 0.285805 0.958288i $$-0.407739\pi$$
0.285805 + 0.958288i $$0.407739\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 2800.00 0.645410
$$267$$ 0 0
$$268$$ −7232.00 −1.64838
$$269$$ 6780.00 1.53674 0.768372 0.640004i $$-0.221067\pi$$
0.768372 + 0.640004i $$0.221067\pi$$
$$270$$ 0 0
$$271$$ −1928.00 −0.432168 −0.216084 0.976375i $$-0.569329\pi$$
−0.216084 + 0.976375i $$0.569329\pi$$
$$272$$ −5376.00 −1.19841
$$273$$ 0 0
$$274$$ 1656.00 0.365119
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −5554.00 −1.20472 −0.602360 0.798224i $$-0.705773\pi$$
−0.602360 + 0.798224i $$0.705773\pi$$
$$278$$ −6480.00 −1.39800
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1942.00 −0.412278 −0.206139 0.978523i $$-0.566090\pi$$
−0.206139 + 0.978523i $$0.566090\pi$$
$$282$$ 0 0
$$283$$ −4828.00 −1.01412 −0.507058 0.861912i $$-0.669267\pi$$
−0.507058 + 0.861912i $$0.669267\pi$$
$$284$$ 5424.00 1.13329
$$285$$ 0 0
$$286$$ −15376.0 −3.17903
$$287$$ 1736.00 0.357048
$$288$$ 0 0
$$289$$ 2143.00 0.436190
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 5136.00 1.02932
$$293$$ −6152.00 −1.22663 −0.613317 0.789837i $$-0.710165\pi$$
−0.613317 + 0.789837i $$0.710165\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −9480.00 −1.84282
$$299$$ −2604.00 −0.503656
$$300$$ 0 0
$$301$$ −476.000 −0.0911501
$$302$$ −2272.00 −0.432910
$$303$$ 0 0
$$304$$ −6400.00 −1.20745
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −5884.00 −1.09387 −0.546934 0.837176i $$-0.684205\pi$$
−0.546934 + 0.837176i $$0.684205\pi$$
$$308$$ −3472.00 −0.642323
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −9132.00 −1.66504 −0.832521 0.553993i $$-0.813103\pi$$
−0.832521 + 0.553993i $$0.813103\pi$$
$$312$$ 0 0
$$313$$ 9382.00 1.69426 0.847128 0.531389i $$-0.178330\pi$$
0.847128 + 0.531389i $$0.178330\pi$$
$$314$$ 1064.00 0.191226
$$315$$ 0 0
$$316$$ 5920.00 1.05388
$$317$$ 3114.00 0.551734 0.275867 0.961196i $$-0.411035\pi$$
0.275867 + 0.961196i $$0.411035\pi$$
$$318$$ 0 0
$$319$$ −620.000 −0.108819
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −1176.00 −0.203528
$$323$$ 8400.00 1.44702
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 1088.00 0.184843
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 2268.00 0.380057
$$330$$ 0 0
$$331$$ 1532.00 0.254400 0.127200 0.991877i $$-0.459401\pi$$
0.127200 + 0.991877i $$0.459401\pi$$
$$332$$ 3744.00 0.618912
$$333$$ 0 0
$$334$$ −7504.00 −1.22934
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 4166.00 0.673402 0.336701 0.941612i $$-0.390689\pi$$
0.336701 + 0.941612i $$0.390689\pi$$
$$338$$ 6588.00 1.06018
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 2976.00 0.472608
$$342$$ 0 0
$$343$$ 343.000 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −608.000 −0.0944690
$$347$$ −11366.0 −1.75838 −0.879191 0.476469i $$-0.841917\pi$$
−0.879191 + 0.476469i $$0.841917\pi$$
$$348$$ 0 0
$$349$$ 9310.00 1.42795 0.713973 0.700174i $$-0.246894\pi$$
0.713973 + 0.700174i $$0.246894\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 15872.0 2.40335
$$353$$ −8572.00 −1.29247 −0.646234 0.763139i $$-0.723657\pi$$
−0.646234 + 0.763139i $$0.723657\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −1600.00 −0.238202
$$357$$ 0 0
$$358$$ −2440.00 −0.360218
$$359$$ 4790.00 0.704196 0.352098 0.935963i $$-0.385468\pi$$
0.352098 + 0.935963i $$0.385468\pi$$
$$360$$ 0 0
$$361$$ 3141.00 0.457938
$$362$$ 4168.00 0.605153
$$363$$ 0 0
$$364$$ 3472.00 0.499951
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −5424.00 −0.771473 −0.385736 0.922609i $$-0.626053\pi$$
−0.385736 + 0.922609i $$0.626053\pi$$
$$368$$ 2688.00 0.380765
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1806.00 0.252730
$$372$$ 0 0
$$373$$ −1838.00 −0.255142 −0.127571 0.991829i $$-0.540718\pi$$
−0.127571 + 0.991829i $$0.540718\pi$$
$$374$$ −20832.0 −2.88021
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 620.000 0.0846993
$$378$$ 0 0
$$379$$ −4260.00 −0.577365 −0.288683 0.957425i $$-0.593217\pi$$
−0.288683 + 0.957425i $$0.593217\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 8152.00 1.09187
$$383$$ 9048.00 1.20713 0.603566 0.797313i $$-0.293746\pi$$
0.603566 + 0.797313i $$0.293746\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 10408.0 1.37242
$$387$$ 0 0
$$388$$ 10128.0 1.32518
$$389$$ 11490.0 1.49760 0.748800 0.662796i $$-0.230631\pi$$
0.748800 + 0.662796i $$0.230631\pi$$
$$390$$ 0 0
$$391$$ −3528.00 −0.456314
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 9416.00 1.20399
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1866.00 0.235899 0.117949 0.993020i $$-0.462368\pi$$
0.117949 + 0.993020i $$0.462368\pi$$
$$398$$ 6720.00 0.846340
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −13662.0 −1.70137 −0.850683 0.525679i $$-0.823811\pi$$
−0.850683 + 0.525679i $$0.823811\pi$$
$$402$$ 0 0
$$403$$ −2976.00 −0.367854
$$404$$ −1856.00 −0.228563
$$405$$ 0 0
$$406$$ 280.000 0.0342270
$$407$$ −15252.0 −1.85753
$$408$$ 0 0
$$409$$ −13210.0 −1.59705 −0.798524 0.601963i $$-0.794385\pi$$
−0.798524 + 0.601963i $$0.794385\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 14336.0 1.71428
$$413$$ −840.000 −0.100082
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −15872.0 −1.87065
$$417$$ 0 0
$$418$$ −24800.0 −2.90193
$$419$$ −6960.00 −0.811499 −0.405750 0.913984i $$-0.632990\pi$$
−0.405750 + 0.913984i $$0.632990\pi$$
$$420$$ 0 0
$$421$$ 8162.00 0.944873 0.472437 0.881365i $$-0.343375\pi$$
0.472437 + 0.881365i $$0.343375\pi$$
$$422$$ −2672.00 −0.308225
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 4354.00 0.493454
$$428$$ −15248.0 −1.72206
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −16602.0 −1.85543 −0.927715 0.373290i $$-0.878230\pi$$
−0.927715 + 0.373290i $$0.878230\pi$$
$$432$$ 0 0
$$433$$ −7738.00 −0.858810 −0.429405 0.903112i $$-0.641277\pi$$
−0.429405 + 0.903112i $$0.641277\pi$$
$$434$$ −1344.00 −0.148650
$$435$$ 0 0
$$436$$ −720.000 −0.0790866
$$437$$ −4200.00 −0.459756
$$438$$ 0 0
$$439$$ −840.000 −0.0913235 −0.0456617 0.998957i $$-0.514540\pi$$
−0.0456617 + 0.998957i $$0.514540\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 20832.0 2.24180
$$443$$ 6618.00 0.709776 0.354888 0.934909i $$-0.384519\pi$$
0.354888 + 0.934909i $$0.384519\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 7328.00 0.778006
$$447$$ 0 0
$$448$$ −3584.00 −0.377964
$$449$$ −3090.00 −0.324780 −0.162390 0.986727i $$-0.551920\pi$$
−0.162390 + 0.986727i $$0.551920\pi$$
$$450$$ 0 0
$$451$$ −15376.0 −1.60538
$$452$$ 3664.00 0.381283
$$453$$ 0 0
$$454$$ 19776.0 2.04435
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5914.00 −0.605351 −0.302675 0.953094i $$-0.597880\pi$$
−0.302675 + 0.953094i $$0.597880\pi$$
$$458$$ −21880.0 −2.23228
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 15968.0 1.61324 0.806620 0.591070i $$-0.201294\pi$$
0.806620 + 0.591070i $$0.201294\pi$$
$$462$$ 0 0
$$463$$ 1172.00 0.117640 0.0588202 0.998269i $$-0.481266\pi$$
0.0588202 + 0.998269i $$0.481266\pi$$
$$464$$ −640.000 −0.0640329
$$465$$ 0 0
$$466$$ −11208.0 −1.11416
$$467$$ 5304.00 0.525567 0.262784 0.964855i $$-0.415359\pi$$
0.262784 + 0.964855i $$0.415359\pi$$
$$468$$ 0 0
$$469$$ −6328.00 −0.623027
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 4216.00 0.409835
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 4704.00 0.452957
$$477$$ 0 0
$$478$$ 4680.00 0.447821
$$479$$ −5740.00 −0.547531 −0.273765 0.961796i $$-0.588269\pi$$
−0.273765 + 0.961796i $$0.588269\pi$$
$$480$$ 0 0
$$481$$ 15252.0 1.44580
$$482$$ −9352.00 −0.883759
$$483$$ 0 0
$$484$$ 20104.0 1.88805
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −8944.00 −0.832220 −0.416110 0.909314i $$-0.636607\pi$$
−0.416110 + 0.909314i $$0.636607\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 5558.00 0.510853 0.255427 0.966828i $$-0.417784\pi$$
0.255427 + 0.966828i $$0.417784\pi$$
$$492$$ 0 0
$$493$$ 840.000 0.0767377
$$494$$ 24800.0 2.25871
$$495$$ 0 0
$$496$$ 3072.00 0.278099
$$497$$ 4746.00 0.428344
$$498$$ 0 0
$$499$$ −19820.0 −1.77809 −0.889043 0.457823i $$-0.848629\pi$$
−0.889043 + 0.457823i $$0.848629\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −11168.0 −0.992933
$$503$$ 1848.00 0.163814 0.0819068 0.996640i $$-0.473899\pi$$
0.0819068 + 0.996640i $$0.473899\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 10416.0 0.915114
$$507$$ 0 0
$$508$$ −6432.00 −0.561760
$$509$$ −340.000 −0.0296075 −0.0148038 0.999890i $$-0.504712\pi$$
−0.0148038 + 0.999890i $$0.504712\pi$$
$$510$$ 0 0
$$511$$ 4494.00 0.389047
$$512$$ 16384.0 1.41421
$$513$$ 0 0
$$514$$ 28096.0 2.41101
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −20088.0 −1.70884
$$518$$ 6888.00 0.584250
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −10212.0 −0.858725 −0.429363 0.903132i $$-0.641262\pi$$
−0.429363 + 0.903132i $$0.641262\pi$$
$$522$$ 0 0
$$523$$ 9332.00 0.780229 0.390115 0.920766i $$-0.372435\pi$$
0.390115 + 0.920766i $$0.372435\pi$$
$$524$$ −6496.00 −0.541563
$$525$$ 0 0
$$526$$ 9752.00 0.808379
$$527$$ −4032.00 −0.333276
$$528$$ 0 0
$$529$$ −10403.0 −0.855018
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 5600.00 0.456374
$$533$$ 15376.0 1.24955
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 27120.0 2.17328
$$539$$ −3038.00 −0.242775
$$540$$ 0 0
$$541$$ −8998.00 −0.715073 −0.357536 0.933899i $$-0.616383\pi$$
−0.357536 + 0.933899i $$0.616383\pi$$
$$542$$ −7712.00 −0.611179
$$543$$ 0 0
$$544$$ −21504.0 −1.69481
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 3416.00 0.267016 0.133508 0.991048i $$-0.457376\pi$$
0.133508 + 0.991048i $$0.457376\pi$$
$$548$$ 3312.00 0.258178
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1000.00 0.0773166
$$552$$ 0 0
$$553$$ 5180.00 0.398329
$$554$$ −22216.0 −1.70373
$$555$$ 0 0
$$556$$ −12960.0 −0.988537
$$557$$ −526.000 −0.0400132 −0.0200066 0.999800i $$-0.506369\pi$$
−0.0200066 + 0.999800i $$0.506369\pi$$
$$558$$ 0 0
$$559$$ −4216.00 −0.318994
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −7768.00 −0.583049
$$563$$ −6712.00 −0.502446 −0.251223 0.967929i $$-0.580833\pi$$
−0.251223 + 0.967929i $$0.580833\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −19312.0 −1.43418
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −4190.00 −0.308706 −0.154353 0.988016i $$-0.549329\pi$$
−0.154353 + 0.988016i $$0.549329\pi$$
$$570$$ 0 0
$$571$$ 3032.00 0.222216 0.111108 0.993808i $$-0.464560\pi$$
0.111108 + 0.993808i $$0.464560\pi$$
$$572$$ −30752.0 −2.24791
$$573$$ 0 0
$$574$$ 6944.00 0.504942
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −5434.00 −0.392063 −0.196032 0.980598i $$-0.562805\pi$$
−0.196032 + 0.980598i $$0.562805\pi$$
$$578$$ 8572.00 0.616865
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 3276.00 0.233927
$$582$$ 0 0
$$583$$ −15996.0 −1.13634
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −24608.0 −1.73472
$$587$$ 464.000 0.0326258 0.0163129 0.999867i $$-0.494807\pi$$
0.0163129 + 0.999867i $$0.494807\pi$$
$$588$$ 0 0
$$589$$ −4800.00 −0.335790
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −15744.0 −1.09303
$$593$$ 11748.0 0.813546 0.406773 0.913529i $$-0.366654\pi$$
0.406773 + 0.913529i $$0.366654\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −18960.0 −1.30307
$$597$$ 0 0
$$598$$ −10416.0 −0.712277
$$599$$ −7650.00 −0.521821 −0.260910 0.965363i $$-0.584023\pi$$
−0.260910 + 0.965363i $$0.584023\pi$$
$$600$$ 0 0
$$601$$ −22878.0 −1.55277 −0.776384 0.630261i $$-0.782948\pi$$
−0.776384 + 0.630261i $$0.782948\pi$$
$$602$$ −1904.00 −0.128906
$$603$$ 0 0
$$604$$ −4544.00 −0.306114
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −704.000 −0.0470749 −0.0235375 0.999723i $$-0.507493\pi$$
−0.0235375 + 0.999723i $$0.507493\pi$$
$$608$$ −25600.0 −1.70759
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 20088.0 1.33007
$$612$$ 0 0
$$613$$ −24958.0 −1.64444 −0.822222 0.569167i $$-0.807266\pi$$
−0.822222 + 0.569167i $$0.807266\pi$$
$$614$$ −23536.0 −1.54696
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −8826.00 −0.575886 −0.287943 0.957648i $$-0.592971\pi$$
−0.287943 + 0.957648i $$0.592971\pi$$
$$618$$ 0 0
$$619$$ 21220.0 1.37787 0.688937 0.724821i $$-0.258078\pi$$
0.688937 + 0.724821i $$0.258078\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −36528.0 −2.35473
$$623$$ −1400.00 −0.0900318
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 37528.0 2.39604
$$627$$ 0 0
$$628$$ 2128.00 0.135217
$$629$$ 20664.0 1.30990
$$630$$ 0 0
$$631$$ −3268.00 −0.206176 −0.103088 0.994672i $$-0.532872\pi$$
−0.103088 + 0.994672i $$0.532872\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 12456.0 0.780270
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 3038.00 0.188964
$$638$$ −2480.00 −0.153894
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −13062.0 −0.804864 −0.402432 0.915450i $$-0.631835\pi$$
−0.402432 + 0.915450i $$0.631835\pi$$
$$642$$ 0 0
$$643$$ 28012.0 1.71802 0.859009 0.511961i $$-0.171081\pi$$
0.859009 + 0.511961i $$0.171081\pi$$
$$644$$ −2352.00 −0.143916
$$645$$ 0 0
$$646$$ 33600.0 2.04640
$$647$$ 3844.00 0.233575 0.116788 0.993157i $$-0.462740\pi$$
0.116788 + 0.993157i $$0.462740\pi$$
$$648$$ 0 0
$$649$$ 7440.00 0.449993
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 2176.00 0.130704
$$653$$ −28482.0 −1.70687 −0.853436 0.521198i $$-0.825485\pi$$
−0.853436 + 0.521198i $$0.825485\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −15872.0 −0.944661
$$657$$ 0 0
$$658$$ 9072.00 0.537482
$$659$$ 9330.00 0.551510 0.275755 0.961228i $$-0.411072\pi$$
0.275755 + 0.961228i $$0.411072\pi$$
$$660$$ 0 0
$$661$$ 8782.00 0.516763 0.258381 0.966043i $$-0.416811\pi$$
0.258381 + 0.966043i $$0.416811\pi$$
$$662$$ 6128.00 0.359776
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −420.000 −0.0243815
$$668$$ −15008.0 −0.869277
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −38564.0 −2.21870
$$672$$ 0 0
$$673$$ 10562.0 0.604956 0.302478 0.953156i $$-0.402186\pi$$
0.302478 + 0.953156i $$0.402186\pi$$
$$674$$ 16664.0 0.952334
$$675$$ 0 0
$$676$$ 13176.0 0.749659
$$677$$ −26016.0 −1.47692 −0.738461 0.674296i $$-0.764447\pi$$
−0.738461 + 0.674296i $$0.764447\pi$$
$$678$$ 0 0
$$679$$ 8862.00 0.500872
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 11904.0 0.668369
$$683$$ 8898.00 0.498496 0.249248 0.968440i $$-0.419817\pi$$
0.249248 + 0.968440i $$0.419817\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1372.00 0.0763604
$$687$$ 0 0
$$688$$ 4352.00 0.241161
$$689$$ 15996.0 0.884469
$$690$$ 0 0
$$691$$ 30572.0 1.68309 0.841544 0.540189i $$-0.181647\pi$$
0.841544 + 0.540189i $$0.181647\pi$$
$$692$$ −1216.00 −0.0667997
$$693$$ 0 0
$$694$$ −45464.0 −2.48673
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 20832.0 1.13209
$$698$$ 37240.0 2.01942
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 30618.0 1.64968 0.824840 0.565366i $$-0.191265\pi$$
0.824840 + 0.565366i $$0.191265\pi$$
$$702$$ 0 0
$$703$$ 24600.0 1.31978
$$704$$ 31744.0 1.69943
$$705$$ 0 0
$$706$$ −34288.0 −1.82783
$$707$$ −1624.00 −0.0863887
$$708$$ 0 0
$$709$$ −8130.00 −0.430647 −0.215323 0.976543i $$-0.569081\pi$$
−0.215323 + 0.976543i $$0.569081\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 2016.00 0.105890
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −4880.00 −0.254713
$$717$$ 0 0
$$718$$ 19160.0 0.995884
$$719$$ 27840.0 1.44403 0.722014 0.691878i $$-0.243216\pi$$
0.722014 + 0.691878i $$0.243216\pi$$
$$720$$ 0 0
$$721$$ 12544.0 0.647938
$$722$$ 12564.0 0.647623
$$723$$ 0 0
$$724$$ 8336.00 0.427907
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −14624.0 −0.746044 −0.373022 0.927822i $$-0.621678\pi$$
−0.373022 + 0.927822i $$0.621678\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −5712.00 −0.289010
$$732$$ 0 0
$$733$$ 20862.0 1.05124 0.525618 0.850721i $$-0.323834\pi$$
0.525618 + 0.850721i $$0.323834\pi$$
$$734$$ −21696.0 −1.09103
$$735$$ 0 0
$$736$$ 10752.0 0.538484
$$737$$ 56048.0 2.80130
$$738$$ 0 0
$$739$$ −13920.0 −0.692903 −0.346452 0.938068i $$-0.612614\pi$$
−0.346452 + 0.938068i $$0.612614\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 7224.00 0.357414
$$743$$ 25578.0 1.26294 0.631471 0.775400i $$-0.282452\pi$$
0.631471 + 0.775400i $$0.282452\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −7352.00 −0.360826
$$747$$ 0 0
$$748$$ −41664.0 −2.03661
$$749$$ −13342.0 −0.650876
$$750$$ 0 0
$$751$$ 33472.0 1.62638 0.813189 0.581999i $$-0.197729\pi$$
0.813189 + 0.581999i $$0.197729\pi$$
$$752$$ −20736.0 −1.00554
$$753$$ 0 0
$$754$$ 2480.00 0.119783
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −25934.0 −1.24516 −0.622581 0.782556i $$-0.713916\pi$$
−0.622581 + 0.782556i $$0.713916\pi$$
$$758$$ −17040.0 −0.816518
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −26952.0 −1.28385 −0.641925 0.766768i $$-0.721864\pi$$
−0.641925 + 0.766768i $$0.721864\pi$$
$$762$$ 0 0
$$763$$ −630.000 −0.0298919
$$764$$ 16304.0 0.772065
$$765$$ 0 0
$$766$$ 36192.0 1.70714
$$767$$ −7440.00 −0.350251
$$768$$ 0 0
$$769$$ 23450.0 1.09965 0.549824 0.835281i $$-0.314695\pi$$
0.549824 + 0.835281i $$0.314695\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 20816.0 0.970446
$$773$$ 39568.0 1.84109 0.920545 0.390637i $$-0.127745\pi$$
0.920545 + 0.390637i $$0.127745\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 45960.0 2.11793
$$779$$ 24800.0 1.14063
$$780$$ 0 0
$$781$$ −42036.0 −1.92595
$$782$$ −14112.0 −0.645325
$$783$$ 0 0
$$784$$ −3136.00 −0.142857
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 12356.0 0.559649 0.279825 0.960051i $$-0.409724\pi$$
0.279825 + 0.960051i $$0.409724\pi$$
$$788$$ 18832.0 0.851348
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 3206.00 0.144112
$$792$$ 0 0
$$793$$ 38564.0 1.72692
$$794$$ 7464.00 0.333611
$$795$$ 0 0
$$796$$ 13440.0 0.598452
$$797$$ −21736.0 −0.966033 −0.483017 0.875611i $$-0.660459\pi$$
−0.483017 + 0.875611i $$0.660459\pi$$
$$798$$ 0 0
$$799$$ 27216.0 1.20505
$$800$$ 0 0
$$801$$ 0 0
$$802$$ −54648.0 −2.40609
$$803$$ −39804.0 −1.74926
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −11904.0 −0.520224
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 38310.0 1.66490 0.832452 0.554097i $$-0.186936\pi$$
0.832452 + 0.554097i $$0.186936\pi$$
$$810$$ 0 0
$$811$$ 2132.00 0.0923115 0.0461558 0.998934i $$-0.485303\pi$$
0.0461558 + 0.998934i $$0.485303\pi$$
$$812$$ 560.000 0.0242022
$$813$$ 0 0
$$814$$ −61008.0 −2.62694
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −6800.00 −0.291190
$$818$$ −52840.0 −2.25857
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −5002.00 −0.212632 −0.106316 0.994332i $$-0.533906\pi$$
−0.106316 + 0.994332i $$0.533906\pi$$
$$822$$ 0 0
$$823$$ 3612.00 0.152985 0.0764923 0.997070i $$-0.475628\pi$$
0.0764923 + 0.997070i $$0.475628\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ −3360.00 −0.141537
$$827$$ −27666.0 −1.16329 −0.581645 0.813443i $$-0.697591\pi$$
−0.581645 + 0.813443i $$0.697591\pi$$
$$828$$ 0 0
$$829$$ 12890.0 0.540034 0.270017 0.962856i $$-0.412971\pi$$
0.270017 + 0.962856i $$0.412971\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −31744.0 −1.32275
$$833$$ 4116.00 0.171202
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −49600.0 −2.05198
$$837$$ 0 0
$$838$$ −27840.0 −1.14763
$$839$$ 9340.00 0.384330 0.192165 0.981363i $$-0.438449\pi$$
0.192165 + 0.981363i $$0.438449\pi$$
$$840$$ 0 0
$$841$$ −24289.0 −0.995900
$$842$$ 32648.0 1.33625
$$843$$ 0 0
$$844$$ −5344.00 −0.217948
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 17591.0 0.713617
$$848$$ −16512.0 −0.668661
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −10332.0 −0.416188
$$852$$ 0 0
$$853$$ 33082.0 1.32791 0.663954 0.747773i $$-0.268877\pi$$
0.663954 + 0.747773i $$0.268877\pi$$
$$854$$ 17416.0 0.697849
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 7544.00 0.300698 0.150349 0.988633i $$-0.451960\pi$$
0.150349 + 0.988633i $$0.451960\pi$$
$$858$$ 0 0
$$859$$ 8180.00 0.324910 0.162455 0.986716i $$-0.448059\pi$$
0.162455 + 0.986716i $$0.448059\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −66408.0 −2.62397
$$863$$ 10518.0 0.414875 0.207437 0.978248i $$-0.433488\pi$$
0.207437 + 0.978248i $$0.433488\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ −30952.0 −1.21454
$$867$$ 0 0
$$868$$ −2688.00 −0.105111
$$869$$ −45880.0 −1.79099
$$870$$ 0 0
$$871$$ −56048.0 −2.18038
$$872$$ 0 0
$$873$$ 0 0
$$874$$ −16800.0 −0.650193
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −14134.0 −0.544209 −0.272104 0.962268i $$-0.587720\pi$$
−0.272104 + 0.962268i $$0.587720\pi$$
$$878$$ −3360.00 −0.129151
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −6492.00 −0.248265 −0.124132 0.992266i $$-0.539615\pi$$
−0.124132 + 0.992266i $$0.539615\pi$$
$$882$$ 0 0
$$883$$ −38228.0 −1.45694 −0.728468 0.685080i $$-0.759767\pi$$
−0.728468 + 0.685080i $$0.759767\pi$$
$$884$$ 41664.0 1.58519
$$885$$ 0 0
$$886$$ 26472.0 1.00377
$$887$$ −43076.0 −1.63061 −0.815305 0.579032i $$-0.803431\pi$$
−0.815305 + 0.579032i $$0.803431\pi$$
$$888$$ 0 0
$$889$$ −5628.00 −0.212325
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 14656.0 0.550134
$$893$$ 32400.0 1.21414
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −12360.0 −0.459308
$$899$$ −480.000 −0.0178074
$$900$$ 0 0
$$901$$ 21672.0 0.801331
$$902$$ −61504.0 −2.27035
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 32236.0 1.18013 0.590065 0.807355i $$-0.299102\pi$$
0.590065 + 0.807355i $$0.299102\pi$$
$$908$$ 39552.0 1.44557
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 46518.0 1.69178 0.845889 0.533359i $$-0.179070\pi$$
0.845889 + 0.533359i $$0.179070\pi$$
$$912$$ 0 0
$$913$$ −29016.0 −1.05180
$$914$$ −23656.0 −0.856095
$$915$$ 0 0
$$916$$ −43760.0 −1.57846
$$917$$ −5684.00 −0.204692
$$918$$ 0 0
$$919$$ 17840.0 0.640356 0.320178 0.947357i $$-0.396257\pi$$
0.320178 + 0.947357i $$0.396257\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 63872.0 2.28147
$$923$$ 42036.0 1.49906
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 4688.00 0.166369
$$927$$ 0 0
$$928$$ −2560.00 −0.0905562
$$929$$ −7000.00 −0.247215 −0.123607 0.992331i $$-0.539446\pi$$
−0.123607 + 0.992331i $$0.539446\pi$$
$$930$$ 0 0
$$931$$ 4900.00 0.172493
$$932$$ −22416.0 −0.787833
$$933$$ 0 0
$$934$$ 21216.0 0.743264
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −36114.0 −1.25912 −0.629559 0.776953i $$-0.716764\pi$$
−0.629559 + 0.776953i $$0.716764\pi$$
$$938$$ −25312.0 −0.881094
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 4748.00 0.164485 0.0822425 0.996612i $$-0.473792\pi$$
0.0822425 + 0.996612i $$0.473792\pi$$
$$942$$ 0 0
$$943$$ −10416.0 −0.359694
$$944$$ 7680.00 0.264791
$$945$$ 0 0
$$946$$ 16864.0 0.579594
$$947$$ 42694.0 1.46501 0.732507 0.680759i $$-0.238350\pi$$
0.732507 + 0.680759i $$0.238350\pi$$
$$948$$ 0 0
$$949$$ 39804.0 1.36153
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −16742.0 −0.569073 −0.284537 0.958665i $$-0.591840\pi$$
−0.284537 + 0.958665i $$0.591840\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 9360.00 0.316657
$$957$$ 0 0
$$958$$ −22960.0 −0.774326
$$959$$ 2898.00 0.0975822
$$960$$ 0 0
$$961$$ −27487.0 −0.922661
$$962$$ 61008.0 2.04467
$$963$$ 0 0
$$964$$ −18704.0 −0.624912
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 9956.00 0.331089 0.165545 0.986202i $$-0.447062\pi$$
0.165545 + 0.986202i $$0.447062\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 26388.0 0.872123 0.436061 0.899917i $$-0.356373\pi$$
0.436061 + 0.899917i $$0.356373\pi$$
$$972$$ 0 0
$$973$$ −11340.0 −0.373632
$$974$$ −35776.0 −1.17694
$$975$$ 0 0
$$976$$ −39808.0 −1.30556
$$977$$ −786.000 −0.0257383 −0.0128692 0.999917i $$-0.504096\pi$$
−0.0128692 + 0.999917i $$0.504096\pi$$
$$978$$ 0 0
$$979$$ 12400.0 0.404807
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 22232.0 0.722456
$$983$$ 51888.0 1.68359 0.841796 0.539796i $$-0.181499\pi$$
0.841796 + 0.539796i $$0.181499\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 3360.00 0.108524
$$987$$ 0 0
$$988$$ 49600.0 1.59715
$$989$$ 2856.00 0.0918256
$$990$$ 0 0
$$991$$ −51928.0 −1.66453 −0.832264 0.554379i $$-0.812956\pi$$
−0.832264 + 0.554379i $$0.812956\pi$$
$$992$$ 12288.0 0.393291
$$993$$ 0 0
$$994$$ 18984.0 0.605771
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 386.000 0.0122615 0.00613076 0.999981i $$-0.498049\pi$$
0.00613076 + 0.999981i $$0.498049\pi$$
$$998$$ −79280.0 −2.51459
$$999$$ 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 1575.4.a.k.1.1 1
3.2 odd 2 525.4.a.b.1.1 1
5.4 even 2 63.4.a.a.1.1 1
15.2 even 4 525.4.d.b.274.1 2
15.8 even 4 525.4.d.b.274.2 2
15.14 odd 2 21.4.a.b.1.1 1
20.19 odd 2 1008.4.a.m.1.1 1
35.4 even 6 441.4.e.m.226.1 2
35.9 even 6 441.4.e.m.361.1 2
35.19 odd 6 441.4.e.n.361.1 2
35.24 odd 6 441.4.e.n.226.1 2
35.34 odd 2 441.4.a.b.1.1 1
60.59 even 2 336.4.a.h.1.1 1
105.44 odd 6 147.4.e.c.67.1 2
105.59 even 6 147.4.e.b.79.1 2
105.74 odd 6 147.4.e.c.79.1 2
105.89 even 6 147.4.e.b.67.1 2
105.104 even 2 147.4.a.g.1.1 1
120.29 odd 2 1344.4.a.w.1.1 1
120.59 even 2 1344.4.a.i.1.1 1
420.419 odd 2 2352.4.a.l.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.a.b.1.1 1 15.14 odd 2
63.4.a.a.1.1 1 5.4 even 2
147.4.a.g.1.1 1 105.104 even 2
147.4.e.b.67.1 2 105.89 even 6
147.4.e.b.79.1 2 105.59 even 6
147.4.e.c.67.1 2 105.44 odd 6
147.4.e.c.79.1 2 105.74 odd 6
336.4.a.h.1.1 1 60.59 even 2
441.4.a.b.1.1 1 35.34 odd 2
441.4.e.m.226.1 2 35.4 even 6
441.4.e.m.361.1 2 35.9 even 6
441.4.e.n.226.1 2 35.24 odd 6
441.4.e.n.361.1 2 35.19 odd 6
525.4.a.b.1.1 1 3.2 odd 2
525.4.d.b.274.1 2 15.2 even 4
525.4.d.b.274.2 2 15.8 even 4
1008.4.a.m.1.1 1 20.19 odd 2
1344.4.a.i.1.1 1 120.59 even 2
1344.4.a.w.1.1 1 120.29 odd 2
1575.4.a.k.1.1 1 1.1 even 1 trivial
2352.4.a.l.1.1 1 420.419 odd 2