# Properties

 Label 1280.4.d.v.641.4 Level $1280$ Weight $4$ Character 1280.641 Analytic conductor $75.522$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1280.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$75.5224448073$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 160) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 641.4 Root $$-1.61803i$$ of defining polynomial Character $$\chi$$ $$=$$ 1280.641 Dual form 1280.4.d.v.641.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+4.47214i q^{3} +5.00000i q^{5} +31.3050 q^{7} +7.00000 q^{9} +O(q^{10})$$ $$q+4.47214i q^{3} +5.00000i q^{5} +31.3050 q^{7} +7.00000 q^{9} +8.94427i q^{11} -62.0000i q^{13} -22.3607 q^{15} -46.0000 q^{17} +107.331i q^{19} +140.000i q^{21} -192.302 q^{23} -25.0000 q^{25} +152.053i q^{27} -90.0000i q^{29} -152.053 q^{31} -40.0000 q^{33} +156.525i q^{35} +214.000i q^{37} +277.272 q^{39} +10.0000 q^{41} +67.0820i q^{43} +35.0000i q^{45} +398.020 q^{47} +637.000 q^{49} -205.718i q^{51} +678.000i q^{53} -44.7214 q^{55} -480.000 q^{57} +411.437i q^{59} +250.000i q^{61} +219.135 q^{63} +310.000 q^{65} +49.1935i q^{67} -860.000i q^{69} +366.715 q^{71} -522.000 q^{73} -111.803i q^{75} +280.000i q^{77} +876.539 q^{79} -491.000 q^{81} +380.132i q^{83} -230.000i q^{85} +402.492 q^{87} -970.000 q^{89} -1940.91i q^{91} -680.000i q^{93} -536.656 q^{95} -934.000 q^{97} +62.6099i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 28 q^{9} + O(q^{10})$$ $$4 q + 28 q^{9} - 184 q^{17} - 100 q^{25} - 160 q^{33} + 40 q^{41} + 2548 q^{49} - 1920 q^{57} + 1240 q^{65} - 2088 q^{73} - 1964 q^{81} - 3880 q^{89} - 3736 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$261$$ $$511$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 4.47214i 0.860663i 0.902671 + 0.430331i $$0.141603\pi$$
−0.902671 + 0.430331i $$0.858397\pi$$
$$4$$ 0 0
$$5$$ 5.00000i 0.447214i
$$6$$ 0 0
$$7$$ 31.3050 1.69031 0.845154 0.534522i $$-0.179509\pi$$
0.845154 + 0.534522i $$0.179509\pi$$
$$8$$ 0 0
$$9$$ 7.00000 0.259259
$$10$$ 0 0
$$11$$ 8.94427i 0.245164i 0.992458 + 0.122582i $$0.0391174\pi$$
−0.992458 + 0.122582i $$0.960883\pi$$
$$12$$ 0 0
$$13$$ − 62.0000i − 1.32275i −0.750057 0.661373i $$-0.769974\pi$$
0.750057 0.661373i $$-0.230026\pi$$
$$14$$ 0 0
$$15$$ −22.3607 −0.384900
$$16$$ 0 0
$$17$$ −46.0000 −0.656273 −0.328136 0.944630i $$-0.606421\pi$$
−0.328136 + 0.944630i $$0.606421\pi$$
$$18$$ 0 0
$$19$$ 107.331i 1.29597i 0.761652 + 0.647986i $$0.224389\pi$$
−0.761652 + 0.647986i $$0.775611\pi$$
$$20$$ 0 0
$$21$$ 140.000i 1.45479i
$$22$$ 0 0
$$23$$ −192.302 −1.74338 −0.871689 0.490059i $$-0.836975\pi$$
−0.871689 + 0.490059i $$0.836975\pi$$
$$24$$ 0 0
$$25$$ −25.0000 −0.200000
$$26$$ 0 0
$$27$$ 152.053i 1.08380i
$$28$$ 0 0
$$29$$ − 90.0000i − 0.576296i −0.957586 0.288148i $$-0.906961\pi$$
0.957586 0.288148i $$-0.0930395\pi$$
$$30$$ 0 0
$$31$$ −152.053 −0.880950 −0.440475 0.897765i $$-0.645190\pi$$
−0.440475 + 0.897765i $$0.645190\pi$$
$$32$$ 0 0
$$33$$ −40.0000 −0.211003
$$34$$ 0 0
$$35$$ 156.525i 0.755929i
$$36$$ 0 0
$$37$$ 214.000i 0.950848i 0.879757 + 0.475424i $$0.157705\pi$$
−0.879757 + 0.475424i $$0.842295\pi$$
$$38$$ 0 0
$$39$$ 277.272 1.13844
$$40$$ 0 0
$$41$$ 10.0000 0.0380912 0.0190456 0.999819i $$-0.493937\pi$$
0.0190456 + 0.999819i $$0.493937\pi$$
$$42$$ 0 0
$$43$$ 67.0820i 0.237905i 0.992900 + 0.118953i $$0.0379536\pi$$
−0.992900 + 0.118953i $$0.962046\pi$$
$$44$$ 0 0
$$45$$ 35.0000i 0.115944i
$$46$$ 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
$$51$$ − 205.718i − 0.564830i
$$52$$ 0 0
$$53$$ 678.000i 1.75718i 0.477578 + 0.878589i $$0.341515\pi$$
−0.477578 + 0.878589i $$0.658485\pi$$
$$54$$ 0 0
$$55$$ −44.7214 −0.109640
$$56$$ 0 0
$$57$$ −480.000 −1.11540
$$58$$ 0 0
$$59$$ 411.437i 0.907872i 0.891034 + 0.453936i $$0.149981\pi$$
−0.891034 + 0.453936i $$0.850019\pi$$
$$60$$ 0 0
$$61$$ 250.000i 0.524741i 0.964967 + 0.262371i $$0.0845043\pi$$
−0.964967 + 0.262371i $$0.915496\pi$$
$$62$$ 0 0
$$63$$ 219.135 0.438228
$$64$$ 0 0
$$65$$ 310.000 0.591550
$$66$$ 0 0
$$67$$ 49.1935i 0.0897006i 0.998994 + 0.0448503i $$0.0142811\pi$$
−0.998994 + 0.0448503i $$0.985719\pi$$
$$68$$ 0 0
$$69$$ − 860.000i − 1.50046i
$$70$$ 0 0
$$71$$ 366.715 0.612973 0.306486 0.951875i $$-0.400847\pi$$
0.306486 + 0.951875i $$0.400847\pi$$
$$72$$ 0 0
$$73$$ −522.000 −0.836924 −0.418462 0.908234i $$-0.637431\pi$$
−0.418462 + 0.908234i $$0.637431\pi$$
$$74$$ 0 0
$$75$$ − 111.803i − 0.172133i
$$76$$ 0 0
$$77$$ 280.000i 0.414402i
$$78$$ 0 0
$$79$$ 876.539 1.24833 0.624166 0.781291i $$-0.285439\pi$$
0.624166 + 0.781291i $$0.285439\pi$$
$$80$$ 0 0
$$81$$ −491.000 −0.673525
$$82$$ 0 0
$$83$$ 380.132i 0.502709i 0.967895 + 0.251355i $$0.0808760\pi$$
−0.967895 + 0.251355i $$0.919124\pi$$
$$84$$ 0 0
$$85$$ − 230.000i − 0.293494i
$$86$$ 0 0
$$87$$ 402.492 0.495997
$$88$$ 0 0
$$89$$ −970.000 −1.15528 −0.577639 0.816292i $$-0.696026\pi$$
−0.577639 + 0.816292i $$0.696026\pi$$
$$90$$ 0 0
$$91$$ − 1940.91i − 2.23585i
$$92$$ 0 0
$$93$$ − 680.000i − 0.758201i
$$94$$ 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
$$99$$ 62.6099i 0.0635609i
$$100$$ 0 0
$$101$$ 602.000i 0.593082i 0.955020 + 0.296541i $$0.0958331\pi$$
−0.955020 + 0.296541i $$0.904167\pi$$
$$102$$ 0 0
$$103$$ 1829.10 1.74978 0.874888 0.484325i $$-0.160935\pi$$
0.874888 + 0.484325i $$0.160935\pi$$
$$104$$ 0 0
$$105$$ −700.000 −0.650600
$$106$$ 0 0
$$107$$ 1525.00i 1.37782i 0.724845 + 0.688912i $$0.241911\pi$$
−0.724845 + 0.688912i $$0.758089\pi$$
$$108$$ 0 0
$$109$$ 2154.00i 1.89281i 0.322989 + 0.946403i $$0.395312\pi$$
−0.322989 + 0.946403i $$0.604688\pi$$
$$110$$ 0 0
$$111$$ −957.037 −0.818360
$$112$$ 0 0
$$113$$ −2182.00 −1.81651 −0.908254 0.418420i $$-0.862584\pi$$
−0.908254 + 0.418420i $$0.862584\pi$$
$$114$$ 0 0
$$115$$ − 961.509i − 0.779663i
$$116$$ 0 0
$$117$$ − 434.000i − 0.342934i
$$118$$ 0 0
$$119$$ −1440.03 −1.10930
$$120$$ 0 0
$$121$$ 1251.00 0.939895
$$122$$ 0 0
$$123$$ 44.7214i 0.0327837i
$$124$$ 0 0
$$125$$ − 125.000i − 0.0894427i
$$126$$ 0 0
$$127$$ 1310.34 0.915539 0.457770 0.889071i $$-0.348648\pi$$
0.457770 + 0.889071i $$0.348648\pi$$
$$128$$ 0 0
$$129$$ −300.000 −0.204756
$$130$$ 0 0
$$131$$ − 205.718i − 0.137204i −0.997644 0.0686019i $$-0.978146\pi$$
0.997644 0.0686019i $$-0.0218538\pi$$
$$132$$ 0 0
$$133$$ 3360.00i 2.19059i
$$134$$ 0 0
$$135$$ −760.263 −0.484689
$$136$$ 0 0
$$137$$ 2094.00 1.30586 0.652929 0.757419i $$-0.273540\pi$$
0.652929 + 0.757419i $$0.273540\pi$$
$$138$$ 0 0
$$139$$ 1377.42i 0.840511i 0.907406 + 0.420256i $$0.138060\pi$$
−0.907406 + 0.420256i $$0.861940\pi$$
$$140$$ 0 0
$$141$$ 1780.00i 1.06314i
$$142$$ 0 0
$$143$$ 554.545 0.324289
$$144$$ 0 0
$$145$$ 450.000 0.257727
$$146$$ 0 0
$$147$$ 2848.75i 1.59837i
$$148$$ 0 0
$$149$$ 334.000i 0.183640i 0.995776 + 0.0918200i $$0.0292684\pi$$
−0.995776 + 0.0918200i $$0.970732\pi$$
$$150$$ 0 0
$$151$$ −3139.44 −1.69195 −0.845973 0.533225i $$-0.820980\pi$$
−0.845973 + 0.533225i $$0.820980\pi$$
$$152$$ 0 0
$$153$$ −322.000 −0.170145
$$154$$ 0 0
$$155$$ − 760.263i − 0.393973i
$$156$$ 0 0
$$157$$ 834.000i 0.423952i 0.977275 + 0.211976i $$0.0679898\pi$$
−0.977275 + 0.211976i $$0.932010\pi$$
$$158$$ 0 0
$$159$$ −3032.11 −1.51234
$$160$$ 0 0
$$161$$ −6020.00 −2.94685
$$162$$ 0 0
$$163$$ − 3090.25i − 1.48495i −0.669874 0.742475i $$-0.733652\pi$$
0.669874 0.742475i $$-0.266348\pi$$
$$164$$ 0 0
$$165$$ − 200.000i − 0.0943635i
$$166$$ 0 0
$$167$$ −4.47214 −0.00207224 −0.00103612 0.999999i $$-0.500330\pi$$
−0.00103612 + 0.999999i $$0.500330\pi$$
$$168$$ 0 0
$$169$$ −1647.00 −0.749659
$$170$$ 0 0
$$171$$ 751.319i 0.335993i
$$172$$ 0 0
$$173$$ − 1838.00i − 0.807749i −0.914814 0.403874i $$-0.867663\pi$$
0.914814 0.403874i $$-0.132337\pi$$
$$174$$ 0 0
$$175$$ −782.624 −0.338062
$$176$$ 0 0
$$177$$ −1840.00 −0.781372
$$178$$ 0 0
$$179$$ 1842.52i 0.769365i 0.923049 + 0.384683i $$0.125689\pi$$
−0.923049 + 0.384683i $$0.874311\pi$$
$$180$$ 0 0
$$181$$ − 1862.00i − 0.764648i −0.924028 0.382324i $$-0.875124\pi$$
0.924028 0.382324i $$-0.124876\pi$$
$$182$$ 0 0
$$183$$ −1118.03 −0.451625
$$184$$ 0 0
$$185$$ −1070.00 −0.425232
$$186$$ 0 0
$$187$$ − 411.437i − 0.160894i
$$188$$ 0 0
$$189$$ 4760.00i 1.83195i
$$190$$ 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
$$195$$ 1386.36i 0.509125i
$$196$$ 0 0
$$197$$ − 66.0000i − 0.0238696i −0.999929 0.0119348i $$-0.996201\pi$$
0.999929 0.0119348i $$-0.00379905\pi$$
$$198$$ 0 0
$$199$$ 1216.42 0.433316 0.216658 0.976248i $$-0.430484\pi$$
0.216658 + 0.976248i $$0.430484\pi$$
$$200$$ 0 0
$$201$$ −220.000 −0.0772020
$$202$$ 0 0
$$203$$ − 2817.45i − 0.974118i
$$204$$ 0 0
$$205$$ 50.0000i 0.0170349i
$$206$$ 0 0
$$207$$ −1346.11 −0.451987
$$208$$ 0 0
$$209$$ −960.000 −0.317725
$$210$$ 0 0
$$211$$ − 5286.06i − 1.72468i −0.506329 0.862341i $$-0.668998\pi$$
0.506329 0.862341i $$-0.331002\pi$$
$$212$$ 0 0
$$213$$ 1640.00i 0.527563i
$$214$$ 0 0
$$215$$ −335.410 −0.106394
$$216$$ 0 0
$$217$$ −4760.00 −1.48908
$$218$$ 0 0
$$219$$ − 2334.45i − 0.720310i
$$220$$ 0 0
$$221$$ 2852.00i 0.868083i
$$222$$ 0 0
$$223$$ 2965.03 0.890371 0.445186 0.895438i $$-0.353138\pi$$
0.445186 + 0.895438i $$0.353138\pi$$
$$224$$ 0 0
$$225$$ −175.000 −0.0518519
$$226$$ 0 0
$$227$$ − 4369.28i − 1.27753i −0.769402 0.638765i $$-0.779446\pi$$
0.769402 0.638765i $$-0.220554\pi$$
$$228$$ 0 0
$$229$$ 3250.00i 0.937843i 0.883240 + 0.468921i $$0.155357\pi$$
−0.883240 + 0.468921i $$0.844643\pi$$
$$230$$ 0 0
$$231$$ −1252.20 −0.356661
$$232$$ 0 0
$$233$$ −3298.00 −0.927293 −0.463646 0.886020i $$-0.653459\pi$$
−0.463646 + 0.886020i $$0.653459\pi$$
$$234$$ 0 0
$$235$$ 1990.10i 0.552425i
$$236$$ 0 0
$$237$$ 3920.00i 1.07439i
$$238$$ 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
$$243$$ 1909.60i 0.504119i
$$244$$ 0 0
$$245$$ 3185.00i 0.830540i
$$246$$ 0 0
$$247$$ 6654.54 1.71424
$$248$$ 0 0
$$249$$ −1700.00 −0.432663
$$250$$ 0 0
$$251$$ − 1386.36i − 0.348631i −0.984690 0.174316i $$-0.944229\pi$$
0.984690 0.174316i $$-0.0557713\pi$$
$$252$$ 0 0
$$253$$ − 1720.00i − 0.427413i
$$254$$ 0 0
$$255$$ 1028.59 0.252600
$$256$$ 0 0
$$257$$ −4166.00 −1.01116 −0.505580 0.862780i $$-0.668721\pi$$
−0.505580 + 0.862780i $$0.668721\pi$$
$$258$$ 0 0
$$259$$ 6699.26i 1.60723i
$$260$$ 0 0
$$261$$ − 630.000i − 0.149410i
$$262$$ 0 0
$$263$$ −961.509 −0.225434 −0.112717 0.993627i $$-0.535955\pi$$
−0.112717 + 0.993627i $$0.535955\pi$$
$$264$$ 0 0
$$265$$ −3390.00 −0.785834
$$266$$ 0 0
$$267$$ − 4337.97i − 0.994305i
$$268$$ 0 0
$$269$$ − 1494.00i − 0.338627i −0.985562 0.169314i $$-0.945845\pi$$
0.985562 0.169314i $$-0.0541551\pi$$
$$270$$ 0 0
$$271$$ 5017.74 1.12474 0.562372 0.826884i $$-0.309889\pi$$
0.562372 + 0.826884i $$0.309889\pi$$
$$272$$ 0 0
$$273$$ 8680.00 1.92431
$$274$$ 0 0
$$275$$ − 223.607i − 0.0490327i
$$276$$ 0 0
$$277$$ 1006.00i 0.218212i 0.994030 + 0.109106i $$0.0347988\pi$$
−0.994030 + 0.109106i $$0.965201\pi$$
$$278$$ 0 0
$$279$$ −1064.37 −0.228395
$$280$$ 0 0
$$281$$ 3210.00 0.681468 0.340734 0.940160i $$-0.389324\pi$$
0.340734 + 0.940160i $$0.389324\pi$$
$$282$$ 0 0
$$283$$ − 3635.85i − 0.763705i −0.924223 0.381853i $$-0.875286\pi$$
0.924223 0.381853i $$-0.124714\pi$$
$$284$$ 0 0
$$285$$ − 2400.00i − 0.498820i
$$286$$ 0 0
$$287$$ 313.050 0.0643858
$$288$$ 0 0
$$289$$ −2797.00 −0.569306
$$290$$ 0 0
$$291$$ − 4176.97i − 0.841439i
$$292$$ 0 0
$$293$$ 3622.00i 0.722183i 0.932530 + 0.361091i $$0.117596\pi$$
−0.932530 + 0.361091i $$0.882404\pi$$
$$294$$ 0 0
$$295$$ −2057.18 −0.406013
$$296$$ 0 0
$$297$$ −1360.00 −0.265708
$$298$$ 0 0
$$299$$ 11922.7i 2.30605i
$$300$$ 0 0
$$301$$ 2100.00i 0.402133i
$$302$$ 0 0
$$303$$ −2692.23 −0.510443
$$304$$ 0 0
$$305$$ −1250.00 −0.234671
$$306$$ 0 0
$$307$$ 2088.49i 0.388261i 0.980976 + 0.194131i $$0.0621886\pi$$
−0.980976 + 0.194131i $$0.937811\pi$$
$$308$$ 0 0
$$309$$ 8180.00i 1.50597i
$$310$$ 0 0
$$311$$ 8899.55 1.62266 0.811330 0.584589i $$-0.198744\pi$$
0.811330 + 0.584589i $$0.198744\pi$$
$$312$$ 0 0
$$313$$ −8778.00 −1.58518 −0.792591 0.609754i $$-0.791268\pi$$
−0.792591 + 0.609754i $$0.791268\pi$$
$$314$$ 0 0
$$315$$ 1095.67i 0.195982i
$$316$$ 0 0
$$317$$ − 5046.00i − 0.894043i −0.894523 0.447021i $$-0.852485\pi$$
0.894523 0.447021i $$-0.147515\pi$$
$$318$$ 0 0
$$319$$ 804.984 0.141287
$$320$$ 0 0
$$321$$ −6820.00 −1.18584
$$322$$ 0 0
$$323$$ − 4937.24i − 0.850512i
$$324$$ 0 0
$$325$$ 1550.00i 0.264549i
$$326$$ 0 0
$$327$$ −9632.98 −1.62907
$$328$$ 0 0
$$329$$ 12460.0 2.08797
$$330$$ 0 0
$$331$$ 313.050i 0.0519842i 0.999662 + 0.0259921i $$0.00827447\pi$$
−0.999662 + 0.0259921i $$0.991726\pi$$
$$332$$ 0 0
$$333$$ 1498.00i 0.246516i
$$334$$ 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
$$339$$ − 9758.20i − 1.56340i
$$340$$ 0 0
$$341$$ − 1360.00i − 0.215977i
$$342$$ 0 0
$$343$$ 9203.66 1.44884
$$344$$ 0 0
$$345$$ 4300.00 0.671027
$$346$$ 0 0
$$347$$ − 2643.03i − 0.408892i −0.978878 0.204446i $$-0.934461\pi$$
0.978878 0.204446i $$-0.0655392\pi$$
$$348$$ 0 0
$$349$$ − 10170.0i − 1.55985i −0.625873 0.779925i $$-0.715257\pi$$
0.625873 0.779925i $$-0.284743\pi$$
$$350$$ 0 0
$$351$$ 9427.26 1.43359
$$352$$ 0 0
$$353$$ −318.000 −0.0479474 −0.0239737 0.999713i $$-0.507632\pi$$
−0.0239737 + 0.999713i $$0.507632\pi$$
$$354$$ 0 0
$$355$$ 1833.58i 0.274130i
$$356$$ 0 0
$$357$$ − 6440.00i − 0.954737i
$$358$$ 0 0
$$359$$ −12378.9 −1.81987 −0.909933 0.414755i $$-0.863867\pi$$
−0.909933 + 0.414755i $$0.863867\pi$$
$$360$$ 0 0
$$361$$ −4661.00 −0.679545
$$362$$ 0 0
$$363$$ 5594.64i 0.808933i
$$364$$ 0 0
$$365$$ − 2610.00i − 0.374284i
$$366$$ 0 0
$$367$$ −3072.36 −0.436991 −0.218496 0.975838i $$-0.570115\pi$$
−0.218496 + 0.975838i $$0.570115\pi$$
$$368$$ 0 0
$$369$$ 70.0000 0.00987549
$$370$$ 0 0
$$371$$ 21224.8i 2.97017i
$$372$$ 0 0
$$373$$ 3278.00i 0.455036i 0.973774 + 0.227518i $$0.0730610\pi$$
−0.973774 + 0.227518i $$0.926939\pi$$
$$374$$ 0 0
$$375$$ 559.017 0.0769800
$$376$$ 0 0
$$377$$ −5580.00 −0.762293
$$378$$ 0 0
$$379$$ − 5116.12i − 0.693397i −0.937977 0.346699i $$-0.887303\pi$$
0.937977 0.346699i $$-0.112697\pi$$
$$380$$ 0 0
$$381$$ 5860.00i 0.787971i
$$382$$ 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
$$387$$ 469.574i 0.0616791i
$$388$$ 0 0
$$389$$ − 834.000i − 0.108703i −0.998522 0.0543515i $$-0.982691\pi$$
0.998522 0.0543515i $$-0.0173092\pi$$
$$390$$ 0 0
$$391$$ 8845.88 1.14413
$$392$$ 0 0
$$393$$ 920.000 0.118086
$$394$$ 0 0
$$395$$ 4382.69i 0.558271i
$$396$$ 0 0
$$397$$ − 8734.00i − 1.10415i −0.833795 0.552074i $$-0.813837\pi$$
0.833795 0.552074i $$-0.186163\pi$$
$$398$$ 0 0
$$399$$ −15026.4 −1.88536
$$400$$ 0 0
$$401$$ 242.000 0.0301369 0.0150685 0.999886i $$-0.495203\pi$$
0.0150685 + 0.999886i $$0.495203\pi$$
$$402$$ 0 0
$$403$$ 9427.26i 1.16527i
$$404$$ 0 0
$$405$$ − 2455.00i − 0.301210i
$$406$$ 0 0
$$407$$ −1914.07 −0.233113
$$408$$ 0 0
$$409$$ 6514.00 0.787522 0.393761 0.919213i $$-0.371174\pi$$
0.393761 + 0.919213i $$0.371174\pi$$
$$410$$ 0 0
$$411$$ 9364.65i 1.12390i
$$412$$ 0 0
$$413$$ 12880.0i 1.53458i
$$414$$ 0 0
$$415$$ −1900.66 −0.224818
$$416$$ 0 0
$$417$$ −6160.00 −0.723397
$$418$$ 0 0
$$419$$ 16081.8i 1.87505i 0.347913 + 0.937527i $$0.386890\pi$$
−0.347913 + 0.937527i $$0.613110\pi$$
$$420$$ 0 0
$$421$$ − 7250.00i − 0.839295i −0.907687 0.419648i $$-0.862154\pi$$
0.907687 0.419648i $$-0.137846\pi$$
$$422$$ 0 0
$$423$$ 2786.14 0.320252
$$424$$ 0 0
$$425$$ 1150.00 0.131255
$$426$$ 0 0
$$427$$ 7826.24i 0.886975i
$$428$$ 0 0
$$429$$ 2480.00i 0.279104i
$$430$$ 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
$$435$$ 2012.46i 0.221816i
$$436$$ 0 0
$$437$$ − 20640.0i − 2.25937i
$$438$$ 0 0
$$439$$ −3792.37 −0.412301 −0.206150 0.978520i $$-0.566094\pi$$
−0.206150 + 0.978520i $$0.566094\pi$$
$$440$$ 0 0
$$441$$ 4459.00 0.481481
$$442$$ 0 0
$$443$$ 746.847i 0.0800988i 0.999198 + 0.0400494i $$0.0127515\pi$$
−0.999198 + 0.0400494i $$0.987248\pi$$
$$444$$ 0 0
$$445$$ − 4850.00i − 0.516656i
$$446$$ 0 0
$$447$$ −1493.69 −0.158052
$$448$$ 0 0
$$449$$ −1306.00 −0.137269 −0.0686347 0.997642i $$-0.521864\pi$$
−0.0686347 + 0.997642i $$0.521864\pi$$
$$450$$ 0 0
$$451$$ 89.4427i 0.00933857i
$$452$$ 0 0
$$453$$ − 14040.0i − 1.45620i
$$454$$ 0 0
$$455$$ 9704.54 0.999902
$$456$$ 0 0
$$457$$ 9526.00 0.975071 0.487536 0.873103i $$-0.337896\pi$$
0.487536 + 0.873103i $$0.337896\pi$$
$$458$$ 0 0
$$459$$ − 6994.42i − 0.711267i
$$460$$ 0 0
$$461$$ 1518.00i 0.153363i 0.997056 + 0.0766815i $$0.0244325\pi$$
−0.997056 + 0.0766815i $$0.975568\pi$$
$$462$$ 0 0
$$463$$ 17293.7 1.73587 0.867936 0.496676i $$-0.165446\pi$$
0.867936 + 0.496676i $$0.165446\pi$$
$$464$$ 0 0
$$465$$ 3400.00 0.339078
$$466$$ 0 0
$$467$$ − 16980.7i − 1.68260i −0.540570 0.841299i $$-0.681792\pi$$
0.540570 0.841299i $$-0.318208\pi$$
$$468$$ 0 0
$$469$$ 1540.00i 0.151622i
$$470$$ 0 0
$$471$$ −3729.76 −0.364880
$$472$$ 0 0
$$473$$ −600.000 −0.0583256
$$474$$ 0 0
$$475$$ − 2683.28i − 0.259195i
$$476$$ 0 0
$$477$$ 4746.00i 0.455565i
$$478$$ 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
$$483$$ − 26922.3i − 2.53624i
$$484$$ 0 0
$$485$$ − 4670.00i − 0.437224i
$$486$$ 0 0
$$487$$ −1310.34 −0.121924 −0.0609620 0.998140i $$-0.519417\pi$$
−0.0609620 + 0.998140i $$0.519417\pi$$
$$488$$ 0 0
$$489$$ 13820.0 1.27804
$$490$$ 0 0
$$491$$ − 2960.55i − 0.272114i −0.990701 0.136057i $$-0.956557\pi$$
0.990701 0.136057i $$-0.0434430\pi$$
$$492$$ 0 0
$$493$$ 4140.00i 0.378207i
$$494$$ 0 0
$$495$$ −313.050 −0.0284253
$$496$$ 0 0
$$497$$ 11480.0 1.03611
$$498$$ 0 0
$$499$$ − 19319.6i − 1.73320i −0.499006 0.866598i $$-0.666301\pi$$
0.499006 0.866598i $$-0.333699\pi$$
$$500$$ 0 0
$$501$$ − 20.0000i − 0.00178350i
$$502$$ 0 0
$$503$$ −3072.36 −0.272345 −0.136173 0.990685i $$-0.543480\pi$$
−0.136173 + 0.990685i $$0.543480\pi$$
$$504$$ 0 0
$$505$$ −3010.00 −0.265234
$$506$$ 0 0
$$507$$ − 7365.61i − 0.645203i
$$508$$ 0 0
$$509$$ 18550.0i 1.61535i 0.589626 + 0.807676i $$0.299275\pi$$
−0.589626 + 0.807676i $$0.700725\pi$$
$$510$$ 0 0
$$511$$ −16341.2 −1.41466
$$512$$ 0 0
$$513$$ −16320.0 −1.40457
$$514$$ 0 0
$$515$$ 9145.52i 0.782524i
$$516$$ 0 0
$$517$$ 3560.00i 0.302841i
$$518$$ 0 0
$$519$$ 8219.79 0.695200
$$520$$ 0 0
$$521$$ 2102.00 0.176757 0.0883784 0.996087i $$-0.471832\pi$$
0.0883784 + 0.996087i $$0.471832\pi$$
$$522$$ 0 0
$$523$$ − 17696.2i − 1.47955i −0.672856 0.739773i $$-0.734933\pi$$
0.672856 0.739773i $$-0.265067\pi$$
$$524$$ 0 0
$$525$$ − 3500.00i − 0.290957i
$$526$$ 0 0
$$527$$ 6994.42 0.578144
$$528$$ 0 0
$$529$$ 24813.0 2.03937
$$530$$ 0 0
$$531$$ 2880.06i 0.235374i
$$532$$ 0 0
$$533$$ − 620.000i − 0.0503850i
$$534$$ 0 0
$$535$$ −7624.99 −0.616182
$$536$$ 0 0
$$537$$ −8240.00 −0.662164
$$538$$ 0 0
$$539$$ 5697.50i 0.455304i
$$540$$ 0 0
$$541$$ − 9922.00i − 0.788503i −0.919003 0.394251i $$-0.871004\pi$$
0.919003 0.394251i $$-0.128996\pi$$
$$542$$ 0 0
$$543$$ 8327.12 0.658105
$$544$$ 0 0
$$545$$ −10770.0 −0.846488
$$546$$ 0 0
$$547$$ 3716.34i 0.290493i 0.989396 + 0.145246i $$0.0463975\pi$$
−0.989396 + 0.145246i $$0.953603\pi$$
$$548$$ 0 0
$$549$$ 1750.00i 0.136044i
$$550$$ 0 0
$$551$$ 9659.81 0.746864
$$552$$ 0 0
$$553$$ 27440.0 2.11007
$$554$$ 0 0
$$555$$ − 4785.19i − 0.365982i
$$556$$ 0 0
$$557$$ − 15094.0i − 1.14821i −0.818781 0.574105i $$-0.805350\pi$$
0.818781 0.574105i $$-0.194650\pi$$
$$558$$ 0 0
$$559$$ 4159.09 0.314688
$$560$$ 0 0
$$561$$ 1840.00 0.138476
$$562$$ 0 0
$$563$$ 5657.25i 0.423490i 0.977325 + 0.211745i $$0.0679146\pi$$
−0.977325 + 0.211745i $$0.932085\pi$$
$$564$$ 0 0
$$565$$ − 10910.0i − 0.812367i
$$566$$ 0 0
$$567$$ −15370.7 −1.13847
$$568$$ 0 0
$$569$$ 5906.00 0.435136 0.217568 0.976045i $$-0.430188\pi$$
0.217568 + 0.976045i $$0.430188\pi$$
$$570$$ 0 0
$$571$$ 4892.52i 0.358573i 0.983797 + 0.179287i $$0.0573790\pi$$
−0.983797 + 0.179287i $$0.942621\pi$$
$$572$$ 0 0
$$573$$ − 9240.00i − 0.673659i
$$574$$ 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
$$579$$ 15106.9i 1.08432i
$$580$$ 0 0
$$581$$ 11900.0i 0.849734i
$$582$$ 0 0
$$583$$ −6064.22 −0.430796
$$584$$ 0 0
$$585$$ 2170.00 0.153365
$$586$$ 0 0
$$587$$ − 9029.24i − 0.634884i −0.948278 0.317442i $$-0.897176\pi$$
0.948278 0.317442i $$-0.102824\pi$$
$$588$$ 0 0
$$589$$ − 16320.0i − 1.14169i
$$590$$ 0 0
$$591$$ 295.161 0.0205437
$$592$$ 0 0
$$593$$ 11442.0 0.792355 0.396178 0.918174i $$-0.370336\pi$$
0.396178 + 0.918174i $$0.370336\pi$$
$$594$$ 0 0
$$595$$ − 7200.14i − 0.496096i
$$596$$ 0 0
$$597$$ 5440.00i 0.372939i
$$598$$ 0 0
$$599$$ 14149.8 0.965187 0.482593 0.875845i $$-0.339695\pi$$
0.482593 + 0.875845i $$0.339695\pi$$
$$600$$ 0 0
$$601$$ −3110.00 −0.211081 −0.105540 0.994415i $$-0.533657\pi$$
−0.105540 + 0.994415i $$0.533657\pi$$
$$602$$ 0 0
$$603$$ 344.354i 0.0232557i
$$604$$ 0 0
$$605$$ 6255.00i 0.420334i
$$606$$ 0 0
$$607$$ −11193.8 −0.748502 −0.374251 0.927327i $$-0.622100\pi$$
−0.374251 + 0.927327i $$0.622100\pi$$
$$608$$ 0 0
$$609$$ 12600.0 0.838387
$$610$$ 0 0
$$611$$ − 24677.2i − 1.63394i
$$612$$ 0 0
$$613$$ 5342.00i 0.351976i 0.984392 + 0.175988i $$0.0563120\pi$$
−0.984392 + 0.175988i $$0.943688\pi$$
$$614$$ 0 0
$$615$$ −223.607 −0.0146613
$$616$$ 0 0
$$617$$ −19714.0 −1.28631 −0.643157 0.765734i $$-0.722376\pi$$
−0.643157 + 0.765734i $$0.722376\pi$$
$$618$$ 0 0
$$619$$ 13166.0i 0.854903i 0.904038 + 0.427451i $$0.140589\pi$$
−0.904038 + 0.427451i $$0.859411\pi$$
$$620$$ 0 0
$$621$$ − 29240.0i − 1.88947i
$$622$$ 0 0
$$623$$ −30365.8 −1.95278
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ − 4293.25i − 0.273454i
$$628$$ 0 0
$$629$$ − 9844.00i − 0.624016i
$$630$$ 0 0
$$631$$ −12262.6 −0.773639 −0.386820 0.922155i $$-0.626426\pi$$
−0.386820 + 0.922155i $$0.626426\pi$$
$$632$$ 0 0
$$633$$ 23640.0 1.48437
$$634$$ 0 0
$$635$$ 6551.68i 0.409442i
$$636$$ 0 0
$$637$$ − 39494.0i − 2.45653i
$$638$$ 0 0
$$639$$ 2567.01 0.158919
$$640$$ 0 0
$$641$$ −2690.00 −0.165754 −0.0828772 0.996560i $$-0.526411\pi$$
−0.0828772 + 0.996560i $$0.526411\pi$$
$$642$$ 0 0
$$643$$ 12240.2i 0.750712i 0.926881 + 0.375356i $$0.122480\pi$$
−0.926881 + 0.375356i $$0.877520\pi$$
$$644$$ 0 0
$$645$$ − 1500.00i − 0.0915697i
$$646$$ 0 0
$$647$$ 17973.5 1.09214 0.546068 0.837741i $$-0.316124\pi$$
0.546068 + 0.837741i $$0.316124\pi$$
$$648$$ 0 0
$$649$$ −3680.00 −0.222577
$$650$$ 0 0
$$651$$ − 21287.4i − 1.28159i
$$652$$ 0 0
$$653$$ − 3478.00i − 0.208430i −0.994555 0.104215i $$-0.966767\pi$$
0.994555 0.104215i $$-0.0332330\pi$$
$$654$$ 0 0
$$655$$ 1028.59 0.0613594
$$656$$ 0 0
$$657$$ −3654.00 −0.216980
$$658$$ 0 0
$$659$$ − 10572.1i − 0.624934i −0.949929 0.312467i $$-0.898845\pi$$
0.949929 0.312467i $$-0.101155\pi$$
$$660$$ 0 0
$$661$$ 110.000i 0.00647277i 0.999995 + 0.00323639i $$0.00103018\pi$$
−0.999995 + 0.00323639i $$0.998970\pi$$
$$662$$ 0 0
$$663$$ −12754.5 −0.747127
$$664$$ 0 0
$$665$$ −16800.0 −0.979663
$$666$$ 0 0
$$667$$ 17307.2i 1.00470i
$$668$$ 0 0
$$669$$ 13260.0i 0.766310i
$$670$$ 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
$$675$$ − 3801.32i − 0.216760i
$$676$$ 0 0
$$677$$ − 18386.0i − 1.04377i −0.853016 0.521884i $$-0.825229\pi$$
0.853016 0.521884i $$-0.174771\pi$$
$$678$$ 0 0
$$679$$ −29238.8 −1.65255
$$680$$ 0 0
$$681$$ 19540.0 1.09952
$$682$$ 0 0
$$683$$ − 15317.1i − 0.858113i −0.903278 0.429057i $$-0.858846\pi$$
0.903278 0.429057i $$-0.141154\pi$$
$$684$$ 0 0
$$685$$ 10470.0i 0.583997i
$$686$$ 0 0
$$687$$ −14534.4 −0.807167
$$688$$ 0 0
$$689$$ 42036.0 2.32430
$$690$$ 0 0
$$691$$ 9507.76i 0.523433i 0.965145 + 0.261717i $$0.0842886\pi$$
−0.965145 + 0.261717i $$0.915711\pi$$
$$692$$ 0 0
$$693$$ 1960.00i 0.107438i
$$694$$ 0 0
$$695$$ −6887.09 −0.375888
$$696$$ 0 0
$$697$$ −460.000 −0.0249982
$$698$$ 0 0
$$699$$ − 14749.1i − 0.798086i
$$700$$ 0 0
$$701$$ − 15830.0i − 0.852911i −0.904508 0.426456i $$-0.859762\pi$$
0.904508 0.426456i $$-0.140238\pi$$
$$702$$ 0 0
$$703$$ −22968.9 −1.23227
$$704$$ 0 0
$$705$$ −8900.00 −0.475452
$$706$$ 0 0
$$707$$ 18845.6i 1.00249i
$$708$$ 0 0
$$709$$ 20050.0i 1.06205i 0.847356 + 0.531025i $$0.178193\pi$$
−0.847356 + 0.531025i $$0.821807\pi$$
$$710$$ 0 0
$$711$$ 6135.77 0.323642
$$712$$ 0 0
$$713$$ 29240.0 1.53583
$$714$$ 0 0
$$715$$ 2772.72i 0.145027i
$$716$$ 0 0
$$717$$ − 2480.00i − 0.129173i
$$718$$ 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
$$723$$ 23031.5i 1.18472i
$$724$$ 0 0
$$725$$ 2250.00i 0.115259i
$$726$$ 0 0
$$727$$ 11336.9 0.578351 0.289175 0.957276i $$-0.406619\pi$$
0.289175 + 0.957276i $$0.406619\pi$$
$$728$$ 0 0
$$729$$ −21797.0 −1.10740
$$730$$ 0 0
$$731$$ − 3085.77i − 0.156131i
$$732$$ 0 0
$$733$$ − 17198.0i − 0.866607i −0.901248 0.433303i $$-0.857348\pi$$
0.901248 0.433303i $$-0.142652\pi$$
$$734$$ 0 0
$$735$$ −14243.8 −0.714815
$$736$$ 0 0
$$737$$ −440.000 −0.0219913
$$738$$ 0 0
$$739$$ 4597.36i 0.228845i 0.993432 + 0.114423i $$0.0365018\pi$$
−0.993432 + 0.114423i $$0.963498\pi$$
$$740$$ 0 0
$$741$$ 29760.0i 1.47539i
$$742$$ 0 0
$$743$$ 2419.43 0.119462 0.0597309 0.998215i $$-0.480976\pi$$
0.0597309 + 0.998215i $$0.480976\pi$$
$$744$$ 0 0
$$745$$ −1670.00 −0.0821263
$$746$$ 0 0
$$747$$ 2660.92i 0.130332i
$$748$$ 0 0
$$749$$ 47740.0i 2.32895i
$$750$$ 0 0
$$751$$ 7432.69 0.361149 0.180574 0.983561i $$-0.442204\pi$$
0.180574 + 0.983561i $$0.442204\pi$$
$$752$$ 0 0
$$753$$ 6200.00 0.300054
$$754$$ 0 0
$$755$$ − 15697.2i − 0.756662i
$$756$$ 0 0
$$757$$ − 11474.0i − 0.550898i −0.961316 0.275449i $$-0.911174\pi$$
0.961316 0.275449i $$-0.0888265\pi$$
$$758$$ 0 0
$$759$$ 7692.07 0.367858
$$760$$ 0 0
$$761$$ −31802.0 −1.51488 −0.757439 0.652906i $$-0.773550\pi$$
−0.757439 + 0.652906i $$0.773550\pi$$
$$762$$ 0 0
$$763$$ 67430.9i 3.19942i
$$764$$ 0 0
$$765$$ − 1610.00i − 0.0760911i
$$766$$ 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
$$771$$ − 18630.9i − 0.870267i
$$772$$ 0 0
$$773$$ − 37938.0i − 1.76525i −0.470082 0.882623i $$-0.655776\pi$$
0.470082 0.882623i $$-0.344224\pi$$
$$774$$ 0 0
$$775$$ 3801.32 0.176190
$$776$$ 0 0
$$777$$ −29960.0 −1.38328
$$778$$ 0 0
$$779$$ 1073.31i 0.0493651i
$$780$$ 0 0
$$781$$ 3280.00i 0.150279i
$$782$$ 0 0
$$783$$ 13684.7 0.624588
$$784$$ 0 0
$$785$$ −4170.00 −0.189597
$$786$$ 0 0
$$787$$ 37633.0i 1.70454i 0.523103 + 0.852270i $$0.324774\pi$$
−0.523103 + 0.852270i $$0.675226\pi$$
$$788$$ 0 0
$$789$$ − 4300.00i − 0.194023i
$$790$$ 0 0
$$791$$ −68307.4 −3.07046
$$792$$ 0 0
$$793$$ 15500.0 0.694100
$$794$$ 0 0
$$795$$ − 15160.5i − 0.676338i
$$796$$ 0 0
$$797$$ − 17526.0i − 0.778924i −0.921042 0.389462i $$-0.872661\pi$$
0.921042 0.389462i $$-0.127339\pi$$
$$798$$ 0 0
$$799$$ −18308.9 −0.810667
$$800$$ 0 0
$$801$$ −6790.00 −0.299517
$$802$$ 0 0
$$803$$ − 4668.91i − 0.205183i
$$804$$ 0 0
$$805$$ − 30100.0i − 1.31787i
$$806$$ 0 0
$$807$$ 6681.37 0.291444
$$808$$ 0 0
$$809$$ −8970.00 −0.389825 −0.194912 0.980821i $$-0.562442\pi$$
−0.194912 + 0.980821i $$0.562442\pi$$
$$810$$ 0 0
$$811$$ 3550.88i 0.153746i 0.997041 + 0.0768731i $$0.0244936\pi$$
−0.997041 + 0.0768731i $$0.975506\pi$$
$$812$$ 0 0
$$813$$ 22440.0i 0.968026i
$$814$$ 0 0
$$815$$ 15451.2 0.664090
$$816$$ 0 0
$$817$$ −7200.00 −0.308318
$$818$$ 0 0
$$819$$ − 13586.3i − 0.579665i
$$820$$ 0 0
$$821$$ 15550.0i 0.661022i 0.943802 + 0.330511i $$0.107221\pi$$
−0.943802 + 0.330511i $$0.892779\pi$$
$$822$$ 0 0
$$823$$ 26712.1 1.13138 0.565689 0.824619i $$-0.308610\pi$$
0.565689 + 0.824619i $$0.308610\pi$$
$$824$$ 0 0
$$825$$ 1000.00 0.0422006
$$826$$ 0 0
$$827$$ 863.122i 0.0362923i 0.999835 + 0.0181461i $$0.00577641\pi$$
−0.999835 + 0.0181461i $$0.994224\pi$$
$$828$$ 0 0
$$829$$ 19066.0i 0.798781i 0.916781 + 0.399391i $$0.130778\pi$$
−0.916781 + 0.399391i $$0.869222\pi$$
$$830$$ 0 0
$$831$$ −4498.97 −0.187807
$$832$$ 0 0
$$833$$ −29302.0 −1.21879
$$834$$ 0 0
$$835$$ − 22.3607i 0 0.000926734i
$$836$$ 0 0
$$837$$ − 23120.0i − 0.954772i
$$838$$ 0 0
$$839$$ 47744.5 1.96463 0.982315 0.187238i $$-0.0599534\pi$$
0.982315 + 0.187238i $$0.0599534\pi$$
$$840$$ 0 0
$$841$$ 16289.0 0.667883
$$842$$ 0 0
$$843$$ 14355.6i 0.586514i
$$844$$ 0 0
$$845$$ − 8235.00i − 0.335258i
$$846$$ 0 0
$$847$$ 39162.5 1.58871
$$848$$ 0 0
$$849$$ 16260.0 0.657293
$$850$$ 0 0
$$851$$ − 41152.6i − 1.65769i
$$852$$ 0 0
$$853$$ 14462.0i 0.580503i 0.956950 + 0.290252i $$0.0937390\pi$$
−0.956950 + 0.290252i $$0.906261\pi$$
$$854$$ 0 0
$$855$$ −3756.59 −0.150261
$$856$$ 0 0
$$857$$ −29346.0 −1.16971 −0.584854 0.811138i $$-0.698848\pi$$
−0.584854 + 0.811138i $$0.698848\pi$$
$$858$$ 0 0
$$859$$ − 22807.9i − 0.905932i −0.891528 0.452966i $$-0.850366\pi$$
0.891528 0.452966i $$-0.149634\pi$$
$$860$$ 0 0
$$861$$ 1400.00i 0.0554145i
$$862$$ 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
$$867$$ − 12508.6i − 0.489981i
$$868$$ 0 0
$$869$$ 7840.00i 0.306046i
$$870$$ 0 0
$$871$$ 3050.00 0.118651
$$872$$ 0 0
$$873$$ −6538.00 −0.253468
$$874$$ 0 0
$$875$$ − 3913.12i − 0.151186i
$$876$$ 0 0
$$877$$ − 32126.0i − 1.23696i −0.785799 0.618482i $$-0.787748\pi$$
0.785799 0.618482i $$-0.212252\pi$$
$$878$$ 0 0
$$879$$ −16198.1 −0.621556
$$880$$ 0 0
$$881$$ −33570.0 −1.28377 −0.641885 0.766801i $$-0.721848\pi$$
−0.641885 + 0.766801i $$0.721848\pi$$
$$882$$ 0 0
$$883$$ − 6435.40i − 0.245265i −0.992452 0.122632i $$-0.960866\pi$$
0.992452 0.122632i $$-0.0391336\pi$$
$$884$$ 0 0
$$885$$ − 9200.00i − 0.349440i
$$886$$ 0 0
$$887$$ 46827.7 1.77263 0.886314 0.463084i $$-0.153257\pi$$
0.886314 + 0.463084i $$0.153257\pi$$
$$888$$ 0 0
$$889$$ 41020.0 1.54754
$$890$$ 0 0
$$891$$ − 4391.64i − 0.165124i
$$892$$ 0 0
$$893$$ 42720.0i 1.60086i
$$894$$ 0 0
$$895$$ −9212.60 −0.344071
$$896$$ 0 0
$$897$$ −53320.0 −1.98473
$$898$$ 0 0
$$899$$ 13684.7i 0.507688i
$$900$$ 0 0
$$901$$ − 31188.0i − 1.15319i
$$902$$ 0 0
$$903$$ −9391.49 −0.346101
$$904$$ 0 0
$$905$$ 9310.00 0.341961
$$906$$ 0 0
$$907$$ − 11980.9i − 0.438608i −0.975657 0.219304i $$-0.929621\pi$$
0.975657 0.219304i $$-0.0703787\pi$$
$$908$$ 0 0
$$909$$ 4214.00i 0.153762i
$$910$$ 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
$$915$$ − 5590.17i − 0.201973i
$$916$$ 0 0
$$917$$ − 6440.00i − 0.231917i
$$918$$ 0 0
$$919$$ 37512.3 1.34648 0.673240 0.739424i $$-0.264902\pi$$
0.673240 + 0.739424i $$0.264902\pi$$
$$920$$ 0 0
$$921$$ −9340.00 −0.334162
$$922$$ 0 0
$$923$$ − 22736.3i − 0.810808i
$$924$$ 0 0
$$925$$ − 5350.00i − 0.190170i
$$926$$ 0 0
$$927$$ 12803.7 0.453646
$$928$$ 0 0
$$929$$ −21994.0 −0.776749 −0.388374 0.921502i $$-0.626963\pi$$
−0.388374 + 0.921502i $$0.626963\pi$$
$$930$$ 0 0
$$931$$ 68370.0i 2.40681i
$$932$$ 0 0
$$933$$ 39800.0i 1.39656i
$$934$$ 0 0
$$935$$ 2057.18 0.0719541
$$936$$ 0 0
$$937$$ 16286.0 0.567813 0.283906 0.958852i $$-0.408370\pi$$
0.283906 + 0.958852i $$0.408370\pi$$
$$938$$ 0 0
$$939$$ − 39256.4i − 1.36431i
$$940$$ 0 0
$$941$$ 24302.0i 0.841894i 0.907085 + 0.420947i $$0.138302\pi$$
−0.907085 + 0.420947i $$0.861698\pi$$
$$942$$ 0 0
$$943$$ −1923.02 −0.0664073
$$944$$ 0 0
$$945$$ −23800.0 −0.819274
$$946$$ 0 0
$$947$$ 19869.7i 0.681815i 0.940097 + 0.340907i $$0.110734\pi$$
−0.940097 + 0.340907i $$0.889266\pi$$
$$948$$ 0 0
$$949$$ 32364.0i 1.10704i
$$950$$ 0 0
$$951$$ 22566.4 0.769470
$$952$$ 0 0
$$953$$ 22422.0 0.762140 0.381070 0.924546i $$-0.375556\pi$$
0.381070 + 0.924546i $$0.375556\pi$$
$$954$$ 0 0
$$955$$ − 10330.6i − 0.350043i
$$956$$ 0 0
$$957$$ 3600.00i 0.121600i
$$958$$ 0 0
$$959$$ 65552.6 2.20730
$$960$$ 0 0
$$961$$ −6671.00 −0.223927
$$962$$ 0 0
$$963$$ 10675.0i 0.357214i
$$964$$ 0 0
$$965$$ 16890.0i 0.563428i
$$966$$ 0 0
$$967$$ −43777.7 −1.45584 −0.727920 0.685662i $$-0.759513\pi$$
−0.727920 + 0.685662i $$0.759513\pi$$
$$968$$ 0 0
$$969$$ 22080.0 0.732004
$$970$$ 0 0
$$971$$ 25714.8i 0.849873i 0.905223 + 0.424936i $$0.139704\pi$$
−0.905223 + 0.424936i $$0.860296\pi$$
$$972$$ 0 0
$$973$$ 43120.0i 1.42072i
$$974$$ 0 0
$$975$$ −6931.81 −0.227688
$$976$$ 0 0
$$977$$ 28986.0 0.949175 0.474588 0.880208i $$-0.342597\pi$$
0.474588 + 0.880208i $$0.342597\pi$$
$$978$$ 0 0
$$979$$ − 8675.94i − 0.283232i
$$980$$ 0 0
$$981$$ 15078.0i 0.490727i
$$982$$ 0 0
$$983$$ −32123.4 −1.04229 −0.521147 0.853467i $$-0.674496\pi$$
−0.521147 + 0.853467i $$0.674496\pi$$
$$984$$ 0 0
$$985$$ 330.000 0.0106748
$$986$$ 0 0
$$987$$ 55722.8i 1.79704i
$$988$$ 0 0
$$989$$ − 12900.0i − 0.414758i
$$990$$ 0 0
$$991$$ −11994.3 −0.384471 −0.192235 0.981349i $$-0.561574\pi$$
−0.192235 + 0.981349i $$0.561574\pi$$
$$992$$ 0 0
$$993$$ −1400.00 −0.0447408
$$994$$ 0 0
$$995$$ 6082.10i 0.193785i
$$996$$ 0 0
$$997$$ 406.000i 0.0128968i 0.999979 + 0.00644842i $$0.00205261\pi$$
−0.999979 + 0.00644842i $$0.997947\pi$$
$$998$$ 0 0
$$999$$ −32539.3 −1.03053
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 1280.4.d.v.641.4 4
4.3 odd 2 inner 1280.4.d.v.641.2 4
8.3 odd 2 inner 1280.4.d.v.641.3 4
8.5 even 2 inner 1280.4.d.v.641.1 4
16.3 odd 4 320.4.a.q.1.2 2
16.5 even 4 160.4.a.d.1.2 yes 2
16.11 odd 4 160.4.a.d.1.1 2
16.13 even 4 320.4.a.q.1.1 2
48.5 odd 4 1440.4.a.bb.1.1 2
48.11 even 4 1440.4.a.bb.1.2 2
80.19 odd 4 1600.4.a.cg.1.1 2
80.27 even 4 800.4.c.l.449.4 4
80.29 even 4 1600.4.a.cg.1.2 2
80.37 odd 4 800.4.c.l.449.1 4
80.43 even 4 800.4.c.l.449.2 4
80.53 odd 4 800.4.c.l.449.3 4
80.59 odd 4 800.4.a.o.1.2 2
80.69 even 4 800.4.a.o.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
160.4.a.d.1.1 2 16.11 odd 4
160.4.a.d.1.2 yes 2 16.5 even 4
320.4.a.q.1.1 2 16.13 even 4
320.4.a.q.1.2 2 16.3 odd 4
800.4.a.o.1.1 2 80.69 even 4
800.4.a.o.1.2 2 80.59 odd 4
800.4.c.l.449.1 4 80.37 odd 4
800.4.c.l.449.2 4 80.43 even 4
800.4.c.l.449.3 4 80.53 odd 4
800.4.c.l.449.4 4 80.27 even 4
1280.4.d.v.641.1 4 8.5 even 2 inner
1280.4.d.v.641.2 4 4.3 odd 2 inner
1280.4.d.v.641.3 4 8.3 odd 2 inner
1280.4.d.v.641.4 4 1.1 even 1 trivial
1440.4.a.bb.1.1 2 48.5 odd 4
1440.4.a.bb.1.2 2 48.11 even 4
1600.4.a.cg.1.1 2 80.19 odd 4
1600.4.a.cg.1.2 2 80.29 even 4