# Properties

 Label 320.6.a.e.1.1 Level 320 Weight 6 Character 320.1 Self dual yes Analytic conductor 51.323 Analytic rank 0 Dimension 1 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 320.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$51.3228223402$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 40) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 320.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-8.00000 q^{3} -25.0000 q^{5} +108.000 q^{7} -179.000 q^{9} +O(q^{10})$$ $$q-8.00000 q^{3} -25.0000 q^{5} +108.000 q^{7} -179.000 q^{9} -604.000 q^{11} +306.000 q^{13} +200.000 q^{15} +930.000 q^{17} -1324.00 q^{19} -864.000 q^{21} +852.000 q^{23} +625.000 q^{25} +3376.00 q^{27} -5902.00 q^{29} +3320.00 q^{31} +4832.00 q^{33} -2700.00 q^{35} -10774.0 q^{37} -2448.00 q^{39} -17958.0 q^{41} +9264.00 q^{43} +4475.00 q^{45} +9796.00 q^{47} -5143.00 q^{49} -7440.00 q^{51} +31434.0 q^{53} +15100.0 q^{55} +10592.0 q^{57} +33228.0 q^{59} +40210.0 q^{61} -19332.0 q^{63} -7650.00 q^{65} +58864.0 q^{67} -6816.00 q^{69} +55312.0 q^{71} +27258.0 q^{73} -5000.00 q^{75} -65232.0 q^{77} -31456.0 q^{79} +16489.0 q^{81} +24552.0 q^{83} -23250.0 q^{85} +47216.0 q^{87} -90854.0 q^{89} +33048.0 q^{91} -26560.0 q^{93} +33100.0 q^{95} +154706. q^{97} +108116. q^{99} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −8.00000 −0.513200 −0.256600 0.966518i $$-0.582602\pi$$
−0.256600 + 0.966518i $$0.582602\pi$$
$$4$$ 0 0
$$5$$ −25.0000 −0.447214
$$6$$ 0 0
$$7$$ 108.000 0.833065 0.416532 0.909121i $$-0.363245\pi$$
0.416532 + 0.909121i $$0.363245\pi$$
$$8$$ 0 0
$$9$$ −179.000 −0.736626
$$10$$ 0 0
$$11$$ −604.000 −1.50506 −0.752532 0.658555i $$-0.771168\pi$$
−0.752532 + 0.658555i $$0.771168\pi$$
$$12$$ 0 0
$$13$$ 306.000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$14$$ 0 0
$$15$$ 200.000 0.229510
$$16$$ 0 0
$$17$$ 930.000 0.780478 0.390239 0.920714i $$-0.372392\pi$$
0.390239 + 0.920714i $$0.372392\pi$$
$$18$$ 0 0
$$19$$ −1324.00 −0.841403 −0.420701 0.907199i $$-0.638216\pi$$
−0.420701 + 0.907199i $$0.638216\pi$$
$$20$$ 0 0
$$21$$ −864.000 −0.427529
$$22$$ 0 0
$$23$$ 852.000 0.335830 0.167915 0.985801i $$-0.446297\pi$$
0.167915 + 0.985801i $$0.446297\pi$$
$$24$$ 0 0
$$25$$ 625.000 0.200000
$$26$$ 0 0
$$27$$ 3376.00 0.891237
$$28$$ 0 0
$$29$$ −5902.00 −1.30318 −0.651590 0.758572i $$-0.725898\pi$$
−0.651590 + 0.758572i $$0.725898\pi$$
$$30$$ 0 0
$$31$$ 3320.00 0.620489 0.310244 0.950657i $$-0.399589\pi$$
0.310244 + 0.950657i $$0.399589\pi$$
$$32$$ 0 0
$$33$$ 4832.00 0.772400
$$34$$ 0 0
$$35$$ −2700.00 −0.372558
$$36$$ 0 0
$$37$$ −10774.0 −1.29382 −0.646908 0.762568i $$-0.723938\pi$$
−0.646908 + 0.762568i $$0.723938\pi$$
$$38$$ 0 0
$$39$$ −2448.00 −0.257721
$$40$$ 0 0
$$41$$ −17958.0 −1.66839 −0.834196 0.551467i $$-0.814068\pi$$
−0.834196 + 0.551467i $$0.814068\pi$$
$$42$$ 0 0
$$43$$ 9264.00 0.764060 0.382030 0.924150i $$-0.375225\pi$$
0.382030 + 0.924150i $$0.375225\pi$$
$$44$$ 0 0
$$45$$ 4475.00 0.329429
$$46$$ 0 0
$$47$$ 9796.00 0.646851 0.323425 0.946254i $$-0.395166\pi$$
0.323425 + 0.946254i $$0.395166\pi$$
$$48$$ 0 0
$$49$$ −5143.00 −0.306003
$$50$$ 0 0
$$51$$ −7440.00 −0.400541
$$52$$ 0 0
$$53$$ 31434.0 1.53713 0.768564 0.639773i $$-0.220972\pi$$
0.768564 + 0.639773i $$0.220972\pi$$
$$54$$ 0 0
$$55$$ 15100.0 0.673085
$$56$$ 0 0
$$57$$ 10592.0 0.431808
$$58$$ 0 0
$$59$$ 33228.0 1.24272 0.621361 0.783524i $$-0.286580\pi$$
0.621361 + 0.783524i $$0.286580\pi$$
$$60$$ 0 0
$$61$$ 40210.0 1.38360 0.691798 0.722091i $$-0.256819\pi$$
0.691798 + 0.722091i $$0.256819\pi$$
$$62$$ 0 0
$$63$$ −19332.0 −0.613657
$$64$$ 0 0
$$65$$ −7650.00 −0.224584
$$66$$ 0 0
$$67$$ 58864.0 1.60200 0.801000 0.598664i $$-0.204301\pi$$
0.801000 + 0.598664i $$0.204301\pi$$
$$68$$ 0 0
$$69$$ −6816.00 −0.172348
$$70$$ 0 0
$$71$$ 55312.0 1.30219 0.651094 0.758997i $$-0.274310\pi$$
0.651094 + 0.758997i $$0.274310\pi$$
$$72$$ 0 0
$$73$$ 27258.0 0.598669 0.299335 0.954148i $$-0.403235\pi$$
0.299335 + 0.954148i $$0.403235\pi$$
$$74$$ 0 0
$$75$$ −5000.00 −0.102640
$$76$$ 0 0
$$77$$ −65232.0 −1.25382
$$78$$ 0 0
$$79$$ −31456.0 −0.567069 −0.283534 0.958962i $$-0.591507\pi$$
−0.283534 + 0.958962i $$0.591507\pi$$
$$80$$ 0 0
$$81$$ 16489.0 0.279243
$$82$$ 0 0
$$83$$ 24552.0 0.391194 0.195597 0.980684i $$-0.437336\pi$$
0.195597 + 0.980684i $$0.437336\pi$$
$$84$$ 0 0
$$85$$ −23250.0 −0.349040
$$86$$ 0 0
$$87$$ 47216.0 0.668792
$$88$$ 0 0
$$89$$ −90854.0 −1.21582 −0.607910 0.794006i $$-0.707992\pi$$
−0.607910 + 0.794006i $$0.707992\pi$$
$$90$$ 0 0
$$91$$ 33048.0 0.418352
$$92$$ 0 0
$$93$$ −26560.0 −0.318435
$$94$$ 0 0
$$95$$ 33100.0 0.376287
$$96$$ 0 0
$$97$$ 154706. 1.66947 0.834733 0.550654i $$-0.185622\pi$$
0.834733 + 0.550654i $$0.185622\pi$$
$$98$$ 0 0
$$99$$ 108116. 1.10867
$$100$$ 0 0
$$101$$ 72714.0 0.709275 0.354637 0.935004i $$-0.384604\pi$$
0.354637 + 0.935004i $$0.384604\pi$$
$$102$$ 0 0
$$103$$ 129396. 1.20179 0.600894 0.799329i $$-0.294811\pi$$
0.600894 + 0.799329i $$0.294811\pi$$
$$104$$ 0 0
$$105$$ 21600.0 0.191197
$$106$$ 0 0
$$107$$ −206680. −1.74518 −0.872588 0.488458i $$-0.837560\pi$$
−0.872588 + 0.488458i $$0.837560\pi$$
$$108$$ 0 0
$$109$$ 70146.0 0.565505 0.282753 0.959193i $$-0.408752\pi$$
0.282753 + 0.959193i $$0.408752\pi$$
$$110$$ 0 0
$$111$$ 86192.0 0.663987
$$112$$ 0 0
$$113$$ −151854. −1.11874 −0.559371 0.828917i $$-0.688957\pi$$
−0.559371 + 0.828917i $$0.688957\pi$$
$$114$$ 0 0
$$115$$ −21300.0 −0.150188
$$116$$ 0 0
$$117$$ −54774.0 −0.369922
$$118$$ 0 0
$$119$$ 100440. 0.650189
$$120$$ 0 0
$$121$$ 203765. 1.26522
$$122$$ 0 0
$$123$$ 143664. 0.856220
$$124$$ 0 0
$$125$$ −15625.0 −0.0894427
$$126$$ 0 0
$$127$$ 336596. 1.85182 0.925912 0.377740i $$-0.123299\pi$$
0.925912 + 0.377740i $$0.123299\pi$$
$$128$$ 0 0
$$129$$ −74112.0 −0.392116
$$130$$ 0 0
$$131$$ 275308. 1.40165 0.700827 0.713332i $$-0.252815\pi$$
0.700827 + 0.713332i $$0.252815\pi$$
$$132$$ 0 0
$$133$$ −142992. −0.700943
$$134$$ 0 0
$$135$$ −84400.0 −0.398573
$$136$$ 0 0
$$137$$ −228502. −1.04013 −0.520066 0.854126i $$-0.674093\pi$$
−0.520066 + 0.854126i $$0.674093\pi$$
$$138$$ 0 0
$$139$$ 224284. 0.984603 0.492302 0.870425i $$-0.336156\pi$$
0.492302 + 0.870425i $$0.336156\pi$$
$$140$$ 0 0
$$141$$ −78368.0 −0.331964
$$142$$ 0 0
$$143$$ −184824. −0.755820
$$144$$ 0 0
$$145$$ 147550. 0.582800
$$146$$ 0 0
$$147$$ 41144.0 0.157041
$$148$$ 0 0
$$149$$ 183802. 0.678242 0.339121 0.940743i $$-0.389870\pi$$
0.339121 + 0.940743i $$0.389870\pi$$
$$150$$ 0 0
$$151$$ −296032. −1.05657 −0.528283 0.849069i $$-0.677164\pi$$
−0.528283 + 0.849069i $$0.677164\pi$$
$$152$$ 0 0
$$153$$ −166470. −0.574920
$$154$$ 0 0
$$155$$ −83000.0 −0.277491
$$156$$ 0 0
$$157$$ −134766. −0.436346 −0.218173 0.975910i $$-0.570010\pi$$
−0.218173 + 0.975910i $$0.570010\pi$$
$$158$$ 0 0
$$159$$ −251472. −0.788854
$$160$$ 0 0
$$161$$ 92016.0 0.279768
$$162$$ 0 0
$$163$$ −60248.0 −0.177613 −0.0888063 0.996049i $$-0.528305\pi$$
−0.0888063 + 0.996049i $$0.528305\pi$$
$$164$$ 0 0
$$165$$ −120800. −0.345428
$$166$$ 0 0
$$167$$ 62012.0 0.172062 0.0860309 0.996292i $$-0.472582\pi$$
0.0860309 + 0.996292i $$0.472582\pi$$
$$168$$ 0 0
$$169$$ −277657. −0.747811
$$170$$ 0 0
$$171$$ 236996. 0.619799
$$172$$ 0 0
$$173$$ 591682. 1.50305 0.751524 0.659705i $$-0.229319\pi$$
0.751524 + 0.659705i $$0.229319\pi$$
$$174$$ 0 0
$$175$$ 67500.0 0.166613
$$176$$ 0 0
$$177$$ −265824. −0.637766
$$178$$ 0 0
$$179$$ −241404. −0.563134 −0.281567 0.959542i $$-0.590854\pi$$
−0.281567 + 0.959542i $$0.590854\pi$$
$$180$$ 0 0
$$181$$ −187622. −0.425684 −0.212842 0.977087i $$-0.568272\pi$$
−0.212842 + 0.977087i $$0.568272\pi$$
$$182$$ 0 0
$$183$$ −321680. −0.710062
$$184$$ 0 0
$$185$$ 269350. 0.578612
$$186$$ 0 0
$$187$$ −561720. −1.17467
$$188$$ 0 0
$$189$$ 364608. 0.742458
$$190$$ 0 0
$$191$$ −37560.0 −0.0744976 −0.0372488 0.999306i $$-0.511859\pi$$
−0.0372488 + 0.999306i $$0.511859\pi$$
$$192$$ 0 0
$$193$$ 164434. 0.317759 0.158880 0.987298i $$-0.449212\pi$$
0.158880 + 0.987298i $$0.449212\pi$$
$$194$$ 0 0
$$195$$ 61200.0 0.115256
$$196$$ 0 0
$$197$$ −360518. −0.661853 −0.330926 0.943657i $$-0.607361\pi$$
−0.330926 + 0.943657i $$0.607361\pi$$
$$198$$ 0 0
$$199$$ 654168. 1.17100 0.585500 0.810673i $$-0.300898\pi$$
0.585500 + 0.810673i $$0.300898\pi$$
$$200$$ 0 0
$$201$$ −470912. −0.822147
$$202$$ 0 0
$$203$$ −637416. −1.08563
$$204$$ 0 0
$$205$$ 448950. 0.746128
$$206$$ 0 0
$$207$$ −152508. −0.247381
$$208$$ 0 0
$$209$$ 799696. 1.26637
$$210$$ 0 0
$$211$$ −693156. −1.07183 −0.535914 0.844273i $$-0.680033\pi$$
−0.535914 + 0.844273i $$0.680033\pi$$
$$212$$ 0 0
$$213$$ −442496. −0.668283
$$214$$ 0 0
$$215$$ −231600. −0.341698
$$216$$ 0 0
$$217$$ 358560. 0.516907
$$218$$ 0 0
$$219$$ −218064. −0.307237
$$220$$ 0 0
$$221$$ 284580. 0.391944
$$222$$ 0 0
$$223$$ −494756. −0.666237 −0.333119 0.942885i $$-0.608101\pi$$
−0.333119 + 0.942885i $$0.608101\pi$$
$$224$$ 0 0
$$225$$ −111875. −0.147325
$$226$$ 0 0
$$227$$ 907088. 1.16838 0.584191 0.811616i $$-0.301412\pi$$
0.584191 + 0.811616i $$0.301412\pi$$
$$228$$ 0 0
$$229$$ −1.08949e6 −1.37289 −0.686446 0.727181i $$-0.740830\pi$$
−0.686446 + 0.727181i $$0.740830\pi$$
$$230$$ 0 0
$$231$$ 521856. 0.643459
$$232$$ 0 0
$$233$$ 499706. 0.603010 0.301505 0.953465i $$-0.402511\pi$$
0.301505 + 0.953465i $$0.402511\pi$$
$$234$$ 0 0
$$235$$ −244900. −0.289280
$$236$$ 0 0
$$237$$ 251648. 0.291020
$$238$$ 0 0
$$239$$ −1.62038e6 −1.83495 −0.917473 0.397799i $$-0.869774\pi$$
−0.917473 + 0.397799i $$0.869774\pi$$
$$240$$ 0 0
$$241$$ 1.00122e6 1.11042 0.555208 0.831711i $$-0.312638\pi$$
0.555208 + 0.831711i $$0.312638\pi$$
$$242$$ 0 0
$$243$$ −952280. −1.03454
$$244$$ 0 0
$$245$$ 128575. 0.136849
$$246$$ 0 0
$$247$$ −405144. −0.422539
$$248$$ 0 0
$$249$$ −196416. −0.200761
$$250$$ 0 0
$$251$$ 368980. 0.369674 0.184837 0.982769i $$-0.440824\pi$$
0.184837 + 0.982769i $$0.440824\pi$$
$$252$$ 0 0
$$253$$ −514608. −0.505447
$$254$$ 0 0
$$255$$ 186000. 0.179128
$$256$$ 0 0
$$257$$ 279010. 0.263504 0.131752 0.991283i $$-0.457940\pi$$
0.131752 + 0.991283i $$0.457940\pi$$
$$258$$ 0 0
$$259$$ −1.16359e6 −1.07783
$$260$$ 0 0
$$261$$ 1.05646e6 0.959955
$$262$$ 0 0
$$263$$ −811740. −0.723648 −0.361824 0.932246i $$-0.617846\pi$$
−0.361824 + 0.932246i $$0.617846\pi$$
$$264$$ 0 0
$$265$$ −785850. −0.687424
$$266$$ 0 0
$$267$$ 726832. 0.623959
$$268$$ 0 0
$$269$$ −353214. −0.297617 −0.148808 0.988866i $$-0.547544\pi$$
−0.148808 + 0.988866i $$0.547544\pi$$
$$270$$ 0 0
$$271$$ 1.71622e6 1.41954 0.709772 0.704432i $$-0.248798\pi$$
0.709772 + 0.704432i $$0.248798\pi$$
$$272$$ 0 0
$$273$$ −264384. −0.214698
$$274$$ 0 0
$$275$$ −377500. −0.301013
$$276$$ 0 0
$$277$$ 245882. 0.192543 0.0962714 0.995355i $$-0.469308\pi$$
0.0962714 + 0.995355i $$0.469308\pi$$
$$278$$ 0 0
$$279$$ −594280. −0.457068
$$280$$ 0 0
$$281$$ −1.67618e6 −1.26635 −0.633177 0.774007i $$-0.718250\pi$$
−0.633177 + 0.774007i $$0.718250\pi$$
$$282$$ 0 0
$$283$$ −1.25882e6 −0.934321 −0.467161 0.884173i $$-0.654723\pi$$
−0.467161 + 0.884173i $$0.654723\pi$$
$$284$$ 0 0
$$285$$ −264800. −0.193110
$$286$$ 0 0
$$287$$ −1.93946e6 −1.38988
$$288$$ 0 0
$$289$$ −554957. −0.390854
$$290$$ 0 0
$$291$$ −1.23765e6 −0.856771
$$292$$ 0 0
$$293$$ −719158. −0.489390 −0.244695 0.969600i $$-0.578688\pi$$
−0.244695 + 0.969600i $$0.578688\pi$$
$$294$$ 0 0
$$295$$ −830700. −0.555762
$$296$$ 0 0
$$297$$ −2.03910e6 −1.34137
$$298$$ 0 0
$$299$$ 260712. 0.168649
$$300$$ 0 0
$$301$$ 1.00051e6 0.636511
$$302$$ 0 0
$$303$$ −581712. −0.364000
$$304$$ 0 0
$$305$$ −1.00525e6 −0.618763
$$306$$ 0 0
$$307$$ 1.86013e6 1.12641 0.563206 0.826317i $$-0.309568\pi$$
0.563206 + 0.826317i $$0.309568\pi$$
$$308$$ 0 0
$$309$$ −1.03517e6 −0.616758
$$310$$ 0 0
$$311$$ −278384. −0.163209 −0.0816043 0.996665i $$-0.526004\pi$$
−0.0816043 + 0.996665i $$0.526004\pi$$
$$312$$ 0 0
$$313$$ −474182. −0.273580 −0.136790 0.990600i $$-0.543679\pi$$
−0.136790 + 0.990600i $$0.543679\pi$$
$$314$$ 0 0
$$315$$ 483300. 0.274436
$$316$$ 0 0
$$317$$ 1.83738e6 1.02695 0.513476 0.858104i $$-0.328357\pi$$
0.513476 + 0.858104i $$0.328357\pi$$
$$318$$ 0 0
$$319$$ 3.56481e6 1.96137
$$320$$ 0 0
$$321$$ 1.65344e6 0.895624
$$322$$ 0 0
$$323$$ −1.23132e6 −0.656696
$$324$$ 0 0
$$325$$ 191250. 0.100437
$$326$$ 0 0
$$327$$ −561168. −0.290217
$$328$$ 0 0
$$329$$ 1.05797e6 0.538868
$$330$$ 0 0
$$331$$ 2.99743e6 1.50376 0.751880 0.659299i $$-0.229147\pi$$
0.751880 + 0.659299i $$0.229147\pi$$
$$332$$ 0 0
$$333$$ 1.92855e6 0.953058
$$334$$ 0 0
$$335$$ −1.47160e6 −0.716437
$$336$$ 0 0
$$337$$ 1.87531e6 0.899496 0.449748 0.893155i $$-0.351514\pi$$
0.449748 + 0.893155i $$0.351514\pi$$
$$338$$ 0 0
$$339$$ 1.21483e6 0.574139
$$340$$ 0 0
$$341$$ −2.00528e6 −0.933876
$$342$$ 0 0
$$343$$ −2.37060e6 −1.08799
$$344$$ 0 0
$$345$$ 170400. 0.0770765
$$346$$ 0 0
$$347$$ 180312. 0.0803898 0.0401949 0.999192i $$-0.487202\pi$$
0.0401949 + 0.999192i $$0.487202\pi$$
$$348$$ 0 0
$$349$$ 87058.0 0.0382600 0.0191300 0.999817i $$-0.493910\pi$$
0.0191300 + 0.999817i $$0.493910\pi$$
$$350$$ 0 0
$$351$$ 1.03306e6 0.447565
$$352$$ 0 0
$$353$$ 2.65901e6 1.13575 0.567876 0.823114i $$-0.307765\pi$$
0.567876 + 0.823114i $$0.307765\pi$$
$$354$$ 0 0
$$355$$ −1.38280e6 −0.582356
$$356$$ 0 0
$$357$$ −803520. −0.333677
$$358$$ 0 0
$$359$$ 2.14937e6 0.880186 0.440093 0.897952i $$-0.354945\pi$$
0.440093 + 0.897952i $$0.354945\pi$$
$$360$$ 0 0
$$361$$ −723123. −0.292041
$$362$$ 0 0
$$363$$ −1.63012e6 −0.649311
$$364$$ 0 0
$$365$$ −681450. −0.267733
$$366$$ 0 0
$$367$$ 3.08258e6 1.19467 0.597337 0.801991i $$-0.296226\pi$$
0.597337 + 0.801991i $$0.296226\pi$$
$$368$$ 0 0
$$369$$ 3.21448e6 1.22898
$$370$$ 0 0
$$371$$ 3.39487e6 1.28053
$$372$$ 0 0
$$373$$ −2.28727e6 −0.851227 −0.425613 0.904905i $$-0.639942\pi$$
−0.425613 + 0.904905i $$0.639942\pi$$
$$374$$ 0 0
$$375$$ 125000. 0.0459020
$$376$$ 0 0
$$377$$ −1.80601e6 −0.654436
$$378$$ 0 0
$$379$$ −1.30154e6 −0.465435 −0.232718 0.972544i $$-0.574762\pi$$
−0.232718 + 0.972544i $$0.574762\pi$$
$$380$$ 0 0
$$381$$ −2.69277e6 −0.950356
$$382$$ 0 0
$$383$$ 2.03276e6 0.708093 0.354046 0.935228i $$-0.384806\pi$$
0.354046 + 0.935228i $$0.384806\pi$$
$$384$$ 0 0
$$385$$ 1.63080e6 0.560724
$$386$$ 0 0
$$387$$ −1.65826e6 −0.562826
$$388$$ 0 0
$$389$$ −94230.0 −0.0315730 −0.0157865 0.999875i $$-0.505025\pi$$
−0.0157865 + 0.999875i $$0.505025\pi$$
$$390$$ 0 0
$$391$$ 792360. 0.262108
$$392$$ 0 0
$$393$$ −2.20246e6 −0.719329
$$394$$ 0 0
$$395$$ 786400. 0.253601
$$396$$ 0 0
$$397$$ 5.55551e6 1.76908 0.884540 0.466465i $$-0.154473\pi$$
0.884540 + 0.466465i $$0.154473\pi$$
$$398$$ 0 0
$$399$$ 1.14394e6 0.359724
$$400$$ 0 0
$$401$$ −784814. −0.243728 −0.121864 0.992547i $$-0.538887\pi$$
−0.121864 + 0.992547i $$0.538887\pi$$
$$402$$ 0 0
$$403$$ 1.01592e6 0.311600
$$404$$ 0 0
$$405$$ −412225. −0.124881
$$406$$ 0 0
$$407$$ 6.50750e6 1.94728
$$408$$ 0 0
$$409$$ −4.59401e6 −1.35795 −0.678974 0.734162i $$-0.737575\pi$$
−0.678974 + 0.734162i $$0.737575\pi$$
$$410$$ 0 0
$$411$$ 1.82802e6 0.533796
$$412$$ 0 0
$$413$$ 3.58862e6 1.03527
$$414$$ 0 0
$$415$$ −613800. −0.174947
$$416$$ 0 0
$$417$$ −1.79427e6 −0.505299
$$418$$ 0 0
$$419$$ 1.41301e6 0.393198 0.196599 0.980484i $$-0.437010\pi$$
0.196599 + 0.980484i $$0.437010\pi$$
$$420$$ 0 0
$$421$$ −5.94556e6 −1.63489 −0.817443 0.576010i $$-0.804609\pi$$
−0.817443 + 0.576010i $$0.804609\pi$$
$$422$$ 0 0
$$423$$ −1.75348e6 −0.476487
$$424$$ 0 0
$$425$$ 581250. 0.156096
$$426$$ 0 0
$$427$$ 4.34268e6 1.15263
$$428$$ 0 0
$$429$$ 1.47859e6 0.387887
$$430$$ 0 0
$$431$$ 6.48114e6 1.68058 0.840289 0.542139i $$-0.182385\pi$$
0.840289 + 0.542139i $$0.182385\pi$$
$$432$$ 0 0
$$433$$ 4.05597e6 1.03962 0.519810 0.854282i $$-0.326003\pi$$
0.519810 + 0.854282i $$0.326003\pi$$
$$434$$ 0 0
$$435$$ −1.18040e6 −0.299093
$$436$$ 0 0
$$437$$ −1.12805e6 −0.282569
$$438$$ 0 0
$$439$$ 1.21450e6 0.300772 0.150386 0.988627i $$-0.451948\pi$$
0.150386 + 0.988627i $$0.451948\pi$$
$$440$$ 0 0
$$441$$ 920597. 0.225410
$$442$$ 0 0
$$443$$ −5.53154e6 −1.33917 −0.669586 0.742734i $$-0.733528\pi$$
−0.669586 + 0.742734i $$0.733528\pi$$
$$444$$ 0 0
$$445$$ 2.27135e6 0.543731
$$446$$ 0 0
$$447$$ −1.47042e6 −0.348074
$$448$$ 0 0
$$449$$ 2.20111e6 0.515258 0.257629 0.966244i $$-0.417059\pi$$
0.257629 + 0.966244i $$0.417059\pi$$
$$450$$ 0 0
$$451$$ 1.08466e7 2.51104
$$452$$ 0 0
$$453$$ 2.36826e6 0.542229
$$454$$ 0 0
$$455$$ −826200. −0.187093
$$456$$ 0 0
$$457$$ 3.29835e6 0.738764 0.369382 0.929278i $$-0.379569\pi$$
0.369382 + 0.929278i $$0.379569\pi$$
$$458$$ 0 0
$$459$$ 3.13968e6 0.695591
$$460$$ 0 0
$$461$$ 3.94266e6 0.864046 0.432023 0.901863i $$-0.357800\pi$$
0.432023 + 0.901863i $$0.357800\pi$$
$$462$$ 0 0
$$463$$ −8.82040e6 −1.91221 −0.956106 0.293021i $$-0.905339\pi$$
−0.956106 + 0.293021i $$0.905339\pi$$
$$464$$ 0 0
$$465$$ 664000. 0.142408
$$466$$ 0 0
$$467$$ −1.28709e6 −0.273096 −0.136548 0.990633i $$-0.543601\pi$$
−0.136548 + 0.990633i $$0.543601\pi$$
$$468$$ 0 0
$$469$$ 6.35731e6 1.33457
$$470$$ 0 0
$$471$$ 1.07813e6 0.223933
$$472$$ 0 0
$$473$$ −5.59546e6 −1.14996
$$474$$ 0 0
$$475$$ −827500. −0.168281
$$476$$ 0 0
$$477$$ −5.62669e6 −1.13229
$$478$$ 0 0
$$479$$ −6.51179e6 −1.29677 −0.648383 0.761314i $$-0.724555\pi$$
−0.648383 + 0.761314i $$0.724555\pi$$
$$480$$ 0 0
$$481$$ −3.29684e6 −0.649734
$$482$$ 0 0
$$483$$ −736128. −0.143577
$$484$$ 0 0
$$485$$ −3.86765e6 −0.746608
$$486$$ 0 0
$$487$$ 5.79523e6 1.10726 0.553628 0.832764i $$-0.313243\pi$$
0.553628 + 0.832764i $$0.313243\pi$$
$$488$$ 0 0
$$489$$ 481984. 0.0911508
$$490$$ 0 0
$$491$$ 990276. 0.185376 0.0926878 0.995695i $$-0.470454\pi$$
0.0926878 + 0.995695i $$0.470454\pi$$
$$492$$ 0 0
$$493$$ −5.48886e6 −1.01710
$$494$$ 0 0
$$495$$ −2.70290e6 −0.495812
$$496$$ 0 0
$$497$$ 5.97370e6 1.08481
$$498$$ 0 0
$$499$$ 2.91500e6 0.524067 0.262033 0.965059i $$-0.415607\pi$$
0.262033 + 0.965059i $$0.415607\pi$$
$$500$$ 0 0
$$501$$ −496096. −0.0883022
$$502$$ 0 0
$$503$$ −2.47872e6 −0.436824 −0.218412 0.975857i $$-0.570088\pi$$
−0.218412 + 0.975857i $$0.570088\pi$$
$$504$$ 0 0
$$505$$ −1.81785e6 −0.317197
$$506$$ 0 0
$$507$$ 2.22126e6 0.383777
$$508$$ 0 0
$$509$$ 6.75807e6 1.15619 0.578093 0.815971i $$-0.303797\pi$$
0.578093 + 0.815971i $$0.303797\pi$$
$$510$$ 0 0
$$511$$ 2.94386e6 0.498730
$$512$$ 0 0
$$513$$ −4.46982e6 −0.749889
$$514$$ 0 0
$$515$$ −3.23490e6 −0.537456
$$516$$ 0 0
$$517$$ −5.91678e6 −0.973552
$$518$$ 0 0
$$519$$ −4.73346e6 −0.771365
$$520$$ 0 0
$$521$$ −6.33903e6 −1.02312 −0.511562 0.859246i $$-0.670933\pi$$
−0.511562 + 0.859246i $$0.670933\pi$$
$$522$$ 0 0
$$523$$ 231920. 0.0370752 0.0185376 0.999828i $$-0.494099\pi$$
0.0185376 + 0.999828i $$0.494099\pi$$
$$524$$ 0 0
$$525$$ −540000. −0.0855058
$$526$$ 0 0
$$527$$ 3.08760e6 0.484278
$$528$$ 0 0
$$529$$ −5.71044e6 −0.887218
$$530$$ 0 0
$$531$$ −5.94781e6 −0.915421
$$532$$ 0 0
$$533$$ −5.49515e6 −0.837841
$$534$$ 0 0
$$535$$ 5.16700e6 0.780466
$$536$$ 0 0
$$537$$ 1.93123e6 0.289001
$$538$$ 0 0
$$539$$ 3.10637e6 0.460555
$$540$$ 0 0
$$541$$ 9.44440e6 1.38733 0.693667 0.720295i $$-0.255994\pi$$
0.693667 + 0.720295i $$0.255994\pi$$
$$542$$ 0 0
$$543$$ 1.50098e6 0.218461
$$544$$ 0 0
$$545$$ −1.75365e6 −0.252902
$$546$$ 0 0
$$547$$ 3.10162e6 0.443220 0.221610 0.975135i $$-0.428869\pi$$
0.221610 + 0.975135i $$0.428869\pi$$
$$548$$ 0 0
$$549$$ −7.19759e6 −1.01919
$$550$$ 0 0
$$551$$ 7.81425e6 1.09650
$$552$$ 0 0
$$553$$ −3.39725e6 −0.472405
$$554$$ 0 0
$$555$$ −2.15480e6 −0.296944
$$556$$ 0 0
$$557$$ 1.22330e6 0.167068 0.0835342 0.996505i $$-0.473379\pi$$
0.0835342 + 0.996505i $$0.473379\pi$$
$$558$$ 0 0
$$559$$ 2.83478e6 0.383699
$$560$$ 0 0
$$561$$ 4.49376e6 0.602841
$$562$$ 0 0
$$563$$ −1.40896e7 −1.87339 −0.936693 0.350151i $$-0.886130\pi$$
−0.936693 + 0.350151i $$0.886130\pi$$
$$564$$ 0 0
$$565$$ 3.79635e6 0.500317
$$566$$ 0 0
$$567$$ 1.78081e6 0.232627
$$568$$ 0 0
$$569$$ 1.48468e6 0.192244 0.0961220 0.995370i $$-0.469356\pi$$
0.0961220 + 0.995370i $$0.469356\pi$$
$$570$$ 0 0
$$571$$ −2.86470e6 −0.367696 −0.183848 0.982955i $$-0.558855\pi$$
−0.183848 + 0.982955i $$0.558855\pi$$
$$572$$ 0 0
$$573$$ 300480. 0.0382322
$$574$$ 0 0
$$575$$ 532500. 0.0671661
$$576$$ 0 0
$$577$$ 4.21728e6 0.527343 0.263671 0.964613i $$-0.415067\pi$$
0.263671 + 0.964613i $$0.415067\pi$$
$$578$$ 0 0
$$579$$ −1.31547e6 −0.163074
$$580$$ 0 0
$$581$$ 2.65162e6 0.325889
$$582$$ 0 0
$$583$$ −1.89861e7 −2.31348
$$584$$ 0 0
$$585$$ 1.36935e6 0.165434
$$586$$ 0 0
$$587$$ −2.01047e6 −0.240826 −0.120413 0.992724i $$-0.538422\pi$$
−0.120413 + 0.992724i $$0.538422\pi$$
$$588$$ 0 0
$$589$$ −4.39568e6 −0.522081
$$590$$ 0 0
$$591$$ 2.88414e6 0.339663
$$592$$ 0 0
$$593$$ 7.33691e6 0.856795 0.428397 0.903590i $$-0.359078\pi$$
0.428397 + 0.903590i $$0.359078\pi$$
$$594$$ 0 0
$$595$$ −2.51100e6 −0.290773
$$596$$ 0 0
$$597$$ −5.23334e6 −0.600957
$$598$$ 0 0
$$599$$ −1.14884e6 −0.130826 −0.0654128 0.997858i $$-0.520836\pi$$
−0.0654128 + 0.997858i $$0.520836\pi$$
$$600$$ 0 0
$$601$$ 1.16409e7 1.31462 0.657312 0.753618i $$-0.271693\pi$$
0.657312 + 0.753618i $$0.271693\pi$$
$$602$$ 0 0
$$603$$ −1.05367e7 −1.18007
$$604$$ 0 0
$$605$$ −5.09412e6 −0.565824
$$606$$ 0 0
$$607$$ 155540. 0.0171345 0.00856723 0.999963i $$-0.497273\pi$$
0.00856723 + 0.999963i $$0.497273\pi$$
$$608$$ 0 0
$$609$$ 5.09933e6 0.557147
$$610$$ 0 0
$$611$$ 2.99758e6 0.324838
$$612$$ 0 0
$$613$$ 1.18137e7 1.26980 0.634899 0.772595i $$-0.281042\pi$$
0.634899 + 0.772595i $$0.281042\pi$$
$$614$$ 0 0
$$615$$ −3.59160e6 −0.382913
$$616$$ 0 0
$$617$$ 6.42252e6 0.679192 0.339596 0.940571i $$-0.389710\pi$$
0.339596 + 0.940571i $$0.389710\pi$$
$$618$$ 0 0
$$619$$ 3.85252e6 0.404128 0.202064 0.979372i $$-0.435235\pi$$
0.202064 + 0.979372i $$0.435235\pi$$
$$620$$ 0 0
$$621$$ 2.87635e6 0.299304
$$622$$ 0 0
$$623$$ −9.81223e6 −1.01286
$$624$$ 0 0
$$625$$ 390625. 0.0400000
$$626$$ 0 0
$$627$$ −6.39757e6 −0.649899
$$628$$ 0 0
$$629$$ −1.00198e7 −1.00980
$$630$$ 0 0
$$631$$ 6.75136e6 0.675022 0.337511 0.941322i $$-0.390415\pi$$
0.337511 + 0.941322i $$0.390415\pi$$
$$632$$ 0 0
$$633$$ 5.54525e6 0.550062
$$634$$ 0 0
$$635$$ −8.41490e6 −0.828161
$$636$$ 0 0
$$637$$ −1.57376e6 −0.153670
$$638$$ 0 0
$$639$$ −9.90085e6 −0.959224
$$640$$ 0 0
$$641$$ −7.35493e6 −0.707022 −0.353511 0.935430i $$-0.615012\pi$$
−0.353511 + 0.935430i $$0.615012\pi$$
$$642$$ 0 0
$$643$$ 1.59694e7 1.52322 0.761610 0.648036i $$-0.224409\pi$$
0.761610 + 0.648036i $$0.224409\pi$$
$$644$$ 0 0
$$645$$ 1.85280e6 0.175359
$$646$$ 0 0
$$647$$ −1.72667e7 −1.62162 −0.810809 0.585311i $$-0.800972\pi$$
−0.810809 + 0.585311i $$0.800972\pi$$
$$648$$ 0 0
$$649$$ −2.00697e7 −1.87038
$$650$$ 0 0
$$651$$ −2.86848e6 −0.265277
$$652$$ 0 0
$$653$$ 1.36251e6 0.125043 0.0625213 0.998044i $$-0.480086\pi$$
0.0625213 + 0.998044i $$0.480086\pi$$
$$654$$ 0 0
$$655$$ −6.88270e6 −0.626838
$$656$$ 0 0
$$657$$ −4.87918e6 −0.440995
$$658$$ 0 0
$$659$$ −8.81808e6 −0.790971 −0.395485 0.918472i $$-0.629424\pi$$
−0.395485 + 0.918472i $$0.629424\pi$$
$$660$$ 0 0
$$661$$ 1.52035e6 0.135344 0.0676720 0.997708i $$-0.478443\pi$$
0.0676720 + 0.997708i $$0.478443\pi$$
$$662$$ 0 0
$$663$$ −2.27664e6 −0.201146
$$664$$ 0 0
$$665$$ 3.57480e6 0.313471
$$666$$ 0 0
$$667$$ −5.02850e6 −0.437647
$$668$$ 0 0
$$669$$ 3.95805e6 0.341913
$$670$$ 0 0
$$671$$ −2.42868e7 −2.08240
$$672$$ 0 0
$$673$$ −315086. −0.0268158 −0.0134079 0.999910i $$-0.504268\pi$$
−0.0134079 + 0.999910i $$0.504268\pi$$
$$674$$ 0 0
$$675$$ 2.11000e6 0.178247
$$676$$ 0 0
$$677$$ 1.74092e6 0.145985 0.0729924 0.997332i $$-0.476745\pi$$
0.0729924 + 0.997332i $$0.476745\pi$$
$$678$$ 0 0
$$679$$ 1.67082e7 1.39077
$$680$$ 0 0
$$681$$ −7.25670e6 −0.599614
$$682$$ 0 0
$$683$$ −1.98935e7 −1.63177 −0.815885 0.578214i $$-0.803750\pi$$
−0.815885 + 0.578214i $$0.803750\pi$$
$$684$$ 0 0
$$685$$ 5.71255e6 0.465161
$$686$$ 0 0
$$687$$ 8.71595e6 0.704568
$$688$$ 0 0
$$689$$ 9.61880e6 0.771921
$$690$$ 0 0
$$691$$ 2.01519e7 1.60554 0.802770 0.596289i $$-0.203359\pi$$
0.802770 + 0.596289i $$0.203359\pi$$
$$692$$ 0 0
$$693$$ 1.16765e7 0.923593
$$694$$ 0 0
$$695$$ −5.60710e6 −0.440328
$$696$$ 0 0
$$697$$ −1.67009e7 −1.30214
$$698$$ 0 0
$$699$$ −3.99765e6 −0.309465
$$700$$ 0 0
$$701$$ −8.10766e6 −0.623161 −0.311581 0.950220i $$-0.600858\pi$$
−0.311581 + 0.950220i $$0.600858\pi$$
$$702$$ 0 0
$$703$$ 1.42648e7 1.08862
$$704$$ 0 0
$$705$$ 1.95920e6 0.148459
$$706$$ 0 0
$$707$$ 7.85311e6 0.590872
$$708$$ 0 0
$$709$$ 1.35613e7 1.01317 0.506587 0.862189i $$-0.330907\pi$$
0.506587 + 0.862189i $$0.330907\pi$$
$$710$$ 0 0
$$711$$ 5.63062e6 0.417717
$$712$$ 0 0
$$713$$ 2.82864e6 0.208379
$$714$$ 0 0
$$715$$ 4.62060e6 0.338013
$$716$$ 0 0
$$717$$ 1.29631e7 0.941695
$$718$$ 0 0
$$719$$ −4.28314e6 −0.308987 −0.154493 0.987994i $$-0.549375\pi$$
−0.154493 + 0.987994i $$0.549375\pi$$
$$720$$ 0 0
$$721$$ 1.39748e7 1.00117
$$722$$ 0 0
$$723$$ −8.00974e6 −0.569866
$$724$$ 0 0
$$725$$ −3.68875e6 −0.260636
$$726$$ 0 0
$$727$$ −1.12084e7 −0.786515 −0.393258 0.919428i $$-0.628652\pi$$
−0.393258 + 0.919428i $$0.628652\pi$$
$$728$$ 0 0
$$729$$ 3.61141e6 0.251686
$$730$$ 0 0
$$731$$ 8.61552e6 0.596332
$$732$$ 0 0
$$733$$ −4.70549e6 −0.323478 −0.161739 0.986834i $$-0.551710\pi$$
−0.161739 + 0.986834i $$0.551710\pi$$
$$734$$ 0 0
$$735$$ −1.02860e6 −0.0702309
$$736$$ 0 0
$$737$$ −3.55539e7 −2.41112
$$738$$ 0 0
$$739$$ −2.31099e7 −1.55663 −0.778317 0.627872i $$-0.783926\pi$$
−0.778317 + 0.627872i $$0.783926\pi$$
$$740$$ 0 0
$$741$$ 3.24115e6 0.216847
$$742$$ 0 0
$$743$$ −5.75294e6 −0.382312 −0.191156 0.981560i $$-0.561224\pi$$
−0.191156 + 0.981560i $$0.561224\pi$$
$$744$$ 0 0
$$745$$ −4.59505e6 −0.303319
$$746$$ 0 0
$$747$$ −4.39481e6 −0.288163
$$748$$ 0 0
$$749$$ −2.23214e7 −1.45384
$$750$$ 0 0
$$751$$ 1.92424e7 1.24497 0.622485 0.782632i $$-0.286123\pi$$
0.622485 + 0.782632i $$0.286123\pi$$
$$752$$ 0 0
$$753$$ −2.95184e6 −0.189717
$$754$$ 0 0
$$755$$ 7.40080e6 0.472510
$$756$$ 0 0
$$757$$ −4.49210e6 −0.284911 −0.142456 0.989801i $$-0.545500\pi$$
−0.142456 + 0.989801i $$0.545500\pi$$
$$758$$ 0 0
$$759$$ 4.11686e6 0.259395
$$760$$ 0 0
$$761$$ 7.33500e6 0.459133 0.229567 0.973293i $$-0.426269\pi$$
0.229567 + 0.973293i $$0.426269\pi$$
$$762$$ 0 0
$$763$$ 7.57577e6 0.471102
$$764$$ 0 0
$$765$$ 4.16175e6 0.257112
$$766$$ 0 0
$$767$$ 1.01678e7 0.624076
$$768$$ 0 0
$$769$$ −5.85526e6 −0.357051 −0.178526 0.983935i $$-0.557133\pi$$
−0.178526 + 0.983935i $$0.557133\pi$$
$$770$$ 0 0
$$771$$ −2.23208e6 −0.135230
$$772$$ 0 0
$$773$$ −1.34557e7 −0.809952 −0.404976 0.914327i $$-0.632720\pi$$
−0.404976 + 0.914327i $$0.632720\pi$$
$$774$$ 0 0
$$775$$ 2.07500e6 0.124098
$$776$$ 0 0
$$777$$ 9.30874e6 0.553144
$$778$$ 0 0
$$779$$ 2.37764e7 1.40379
$$780$$ 0 0
$$781$$ −3.34084e7 −1.95988
$$782$$ 0 0
$$783$$ −1.99252e7 −1.16144
$$784$$ 0 0
$$785$$ 3.36915e6 0.195140
$$786$$ 0 0
$$787$$ 1.00706e7 0.579587 0.289794 0.957089i $$-0.406413\pi$$
0.289794 + 0.957089i $$0.406413\pi$$
$$788$$ 0 0
$$789$$ 6.49392e6 0.371377
$$790$$ 0 0
$$791$$ −1.64002e7 −0.931985
$$792$$ 0 0
$$793$$ 1.23043e7 0.694820
$$794$$ 0 0
$$795$$ 6.28680e6 0.352786
$$796$$ 0 0
$$797$$ 1.18844e7 0.662723 0.331362 0.943504i $$-0.392492\pi$$
0.331362 + 0.943504i $$0.392492\pi$$
$$798$$ 0 0
$$799$$ 9.11028e6 0.504853
$$800$$ 0 0
$$801$$ 1.62629e7 0.895604
$$802$$ 0 0
$$803$$ −1.64638e7 −0.901036
$$804$$ 0 0
$$805$$ −2.30040e6 −0.125116
$$806$$ 0 0
$$807$$ 2.82571e6 0.152737
$$808$$ 0 0
$$809$$ 1.06053e7 0.569705 0.284852 0.958571i $$-0.408055\pi$$
0.284852 + 0.958571i $$0.408055\pi$$
$$810$$ 0 0
$$811$$ −1.38944e6 −0.0741799 −0.0370900 0.999312i $$-0.511809\pi$$
−0.0370900 + 0.999312i $$0.511809\pi$$
$$812$$ 0 0
$$813$$ −1.37297e7 −0.728510
$$814$$ 0 0
$$815$$ 1.50620e6 0.0794307
$$816$$ 0 0
$$817$$ −1.22655e7 −0.642882
$$818$$ 0 0
$$819$$ −5.91559e6 −0.308169
$$820$$ 0 0
$$821$$ 1.12661e7 0.583334 0.291667 0.956520i $$-0.405790\pi$$
0.291667 + 0.956520i $$0.405790\pi$$
$$822$$ 0 0
$$823$$ 2.77093e7 1.42602 0.713011 0.701152i $$-0.247331\pi$$
0.713011 + 0.701152i $$0.247331\pi$$
$$824$$ 0 0
$$825$$ 3.02000e6 0.154480
$$826$$ 0 0
$$827$$ 1.23662e7 0.628740 0.314370 0.949300i $$-0.398207\pi$$
0.314370 + 0.949300i $$0.398207\pi$$
$$828$$ 0 0
$$829$$ −1.23182e7 −0.622530 −0.311265 0.950323i $$-0.600753\pi$$
−0.311265 + 0.950323i $$0.600753\pi$$
$$830$$ 0 0
$$831$$ −1.96706e6 −0.0988130
$$832$$ 0 0
$$833$$ −4.78299e6 −0.238829
$$834$$ 0 0
$$835$$ −1.55030e6 −0.0769484
$$836$$ 0 0
$$837$$ 1.12083e7 0.553002
$$838$$ 0 0
$$839$$ 1.17277e7 0.575183 0.287592 0.957753i $$-0.407145\pi$$
0.287592 + 0.957753i $$0.407145\pi$$
$$840$$ 0 0
$$841$$ 1.43225e7 0.698277
$$842$$ 0 0
$$843$$ 1.34095e7 0.649894
$$844$$ 0 0
$$845$$ 6.94142e6 0.334431
$$846$$ 0 0
$$847$$ 2.20066e7 1.05401
$$848$$ 0 0
$$849$$ 1.00705e7 0.479494
$$850$$ 0 0
$$851$$ −9.17945e6 −0.434503
$$852$$ 0 0
$$853$$ −1.57059e7 −0.739077 −0.369538 0.929215i $$-0.620484\pi$$
−0.369538 + 0.929215i $$0.620484\pi$$
$$854$$ 0 0
$$855$$ −5.92490e6 −0.277182
$$856$$ 0 0
$$857$$ 2.52390e7 1.17387 0.586935 0.809634i $$-0.300334\pi$$
0.586935 + 0.809634i $$0.300334\pi$$
$$858$$ 0 0
$$859$$ 3.66248e6 0.169353 0.0846763 0.996409i $$-0.473014\pi$$
0.0846763 + 0.996409i $$0.473014\pi$$
$$860$$ 0 0
$$861$$ 1.55157e7 0.713286
$$862$$ 0 0
$$863$$ 4.17938e7 1.91023 0.955113 0.296243i $$-0.0957338\pi$$
0.955113 + 0.296243i $$0.0957338\pi$$
$$864$$ 0 0
$$865$$ −1.47921e7 −0.672184
$$866$$ 0 0
$$867$$ 4.43966e6 0.200586
$$868$$ 0 0
$$869$$ 1.89994e7 0.853475
$$870$$ 0 0
$$871$$ 1.80124e7 0.804500
$$872$$ 0 0
$$873$$ −2.76924e7 −1.22977
$$874$$ 0 0
$$875$$ −1.68750e6 −0.0745116
$$876$$ 0 0
$$877$$ −1.08990e7 −0.478505 −0.239253 0.970957i $$-0.576902\pi$$
−0.239253 + 0.970957i $$0.576902\pi$$
$$878$$ 0 0
$$879$$ 5.75326e6 0.251155
$$880$$ 0 0
$$881$$ −3.04336e7 −1.32103 −0.660517 0.750811i $$-0.729663\pi$$
−0.660517 + 0.750811i $$0.729663\pi$$
$$882$$ 0 0
$$883$$ 6.09028e6 0.262867 0.131433 0.991325i $$-0.458042\pi$$
0.131433 + 0.991325i $$0.458042\pi$$
$$884$$ 0 0
$$885$$ 6.64560e6 0.285217
$$886$$ 0 0
$$887$$ −2.77908e7 −1.18602 −0.593010 0.805195i $$-0.702060\pi$$
−0.593010 + 0.805195i $$0.702060\pi$$
$$888$$ 0 0
$$889$$ 3.63524e7 1.54269
$$890$$ 0 0
$$891$$ −9.95936e6 −0.420278
$$892$$ 0 0
$$893$$ −1.29699e7 −0.544262
$$894$$ 0 0
$$895$$ 6.03510e6 0.251841
$$896$$ 0 0
$$897$$ −2.08570e6 −0.0865506
$$898$$ 0 0
$$899$$ −1.95946e7 −0.808608
$$900$$ 0 0
$$901$$ 2.92336e7 1.19969
$$902$$ 0 0
$$903$$ −8.00410e6 −0.326658
$$904$$ 0 0
$$905$$ 4.69055e6 0.190372
$$906$$ 0 0
$$907$$ 3.71510e7 1.49952 0.749761 0.661709i $$-0.230169\pi$$
0.749761 + 0.661709i $$0.230169\pi$$
$$908$$ 0 0
$$909$$ −1.30158e7 −0.522470
$$910$$ 0 0
$$911$$ 7.85959e6 0.313765 0.156882 0.987617i $$-0.449856\pi$$
0.156882 + 0.987617i $$0.449856\pi$$
$$912$$ 0 0
$$913$$ −1.48294e7 −0.588772
$$914$$ 0 0
$$915$$ 8.04200e6 0.317549
$$916$$ 0 0
$$917$$ 2.97333e7 1.16767
$$918$$ 0 0
$$919$$ 1.62693e7 0.635448 0.317724 0.948183i $$-0.397081\pi$$
0.317724 + 0.948183i $$0.397081\pi$$
$$920$$ 0 0
$$921$$ −1.48810e7 −0.578074
$$922$$ 0 0
$$923$$ 1.69255e7 0.653938
$$924$$ 0 0
$$925$$ −6.73375e6 −0.258763
$$926$$ 0 0
$$927$$ −2.31619e7 −0.885268
$$928$$ 0 0
$$929$$ −3.69365e7 −1.40416 −0.702079 0.712099i $$-0.747745\pi$$
−0.702079 + 0.712099i $$0.747745\pi$$
$$930$$ 0 0
$$931$$ 6.80933e6 0.257472
$$932$$ 0 0
$$933$$ 2.22707e6 0.0837587
$$934$$ 0 0
$$935$$ 1.40430e7 0.525328
$$936$$ 0 0
$$937$$ 4.89705e6 0.182216 0.0911078 0.995841i $$-0.470959\pi$$
0.0911078 + 0.995841i $$0.470959\pi$$
$$938$$ 0 0
$$939$$ 3.79346e6 0.140401
$$940$$ 0 0
$$941$$ 6.83943e6 0.251794 0.125897 0.992043i $$-0.459819\pi$$
0.125897 + 0.992043i $$0.459819\pi$$
$$942$$ 0 0
$$943$$ −1.53002e7 −0.560297
$$944$$ 0 0
$$945$$ −9.11520e6 −0.332037
$$946$$ 0 0
$$947$$ 1.03790e7 0.376082 0.188041 0.982161i $$-0.439786\pi$$
0.188041 + 0.982161i $$0.439786\pi$$
$$948$$ 0 0
$$949$$ 8.34095e6 0.300642
$$950$$ 0 0
$$951$$ −1.46990e7 −0.527032
$$952$$ 0 0
$$953$$ 2.59587e7 0.925873 0.462937 0.886391i $$-0.346796\pi$$
0.462937 + 0.886391i $$0.346796\pi$$
$$954$$ 0 0
$$955$$ 939000. 0.0333163
$$956$$ 0 0
$$957$$ −2.85185e7 −1.00658
$$958$$ 0 0
$$959$$ −2.46782e7 −0.866497
$$960$$ 0 0
$$961$$ −1.76068e7 −0.614994
$$962$$ 0 0
$$963$$ 3.69957e7 1.28554
$$964$$ 0 0
$$965$$ −4.11085e6 −0.142106
$$966$$ 0 0
$$967$$ 3.92120e7 1.34851 0.674253 0.738501i $$-0.264466\pi$$
0.674253 + 0.738501i $$0.264466\pi$$
$$968$$ 0 0
$$969$$ 9.85056e6 0.337017
$$970$$ 0 0
$$971$$ −1.06876e7 −0.363774 −0.181887 0.983319i $$-0.558221\pi$$
−0.181887 + 0.983319i $$0.558221\pi$$
$$972$$ 0 0
$$973$$ 2.42227e7 0.820238
$$974$$ 0 0
$$975$$ −1.53000e6 −0.0515442
$$976$$ 0 0
$$977$$ 2.77266e7 0.929308 0.464654 0.885492i $$-0.346179\pi$$
0.464654 + 0.885492i $$0.346179\pi$$
$$978$$ 0 0
$$979$$ 5.48758e7 1.82989
$$980$$ 0 0
$$981$$ −1.25561e7 −0.416566
$$982$$ 0 0
$$983$$ 9.49272e6 0.313334 0.156667 0.987652i $$-0.449925\pi$$
0.156667 + 0.987652i $$0.449925\pi$$
$$984$$ 0 0
$$985$$ 9.01295e6 0.295990
$$986$$ 0 0
$$987$$ −8.46374e6 −0.276547
$$988$$ 0 0
$$989$$ 7.89293e6 0.256595
$$990$$ 0 0
$$991$$ 2.03243e7 0.657403 0.328702 0.944434i $$-0.393389\pi$$
0.328702 + 0.944434i $$0.393389\pi$$
$$992$$ 0 0
$$993$$ −2.39794e7 −0.771730
$$994$$ 0 0
$$995$$ −1.63542e7 −0.523687
$$996$$ 0 0
$$997$$ −4.70508e7 −1.49909 −0.749547 0.661951i $$-0.769729\pi$$
−0.749547 + 0.661951i $$0.769729\pi$$
$$998$$ 0 0
$$999$$ −3.63730e7 −1.15310
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 320.6.a.e.1.1 1
4.3 odd 2 320.6.a.l.1.1 1
8.3 odd 2 40.6.a.b.1.1 1
8.5 even 2 80.6.a.f.1.1 1
24.5 odd 2 720.6.a.h.1.1 1
24.11 even 2 360.6.a.b.1.1 1
40.3 even 4 200.6.c.c.49.1 2
40.13 odd 4 400.6.c.h.49.2 2
40.19 odd 2 200.6.a.c.1.1 1
40.27 even 4 200.6.c.c.49.2 2
40.29 even 2 400.6.a.f.1.1 1
40.37 odd 4 400.6.c.h.49.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.b.1.1 1 8.3 odd 2
80.6.a.f.1.1 1 8.5 even 2
200.6.a.c.1.1 1 40.19 odd 2
200.6.c.c.49.1 2 40.3 even 4
200.6.c.c.49.2 2 40.27 even 4
320.6.a.e.1.1 1 1.1 even 1 trivial
320.6.a.l.1.1 1 4.3 odd 2
360.6.a.b.1.1 1 24.11 even 2
400.6.a.f.1.1 1 40.29 even 2
400.6.c.h.49.1 2 40.37 odd 4
400.6.c.h.49.2 2 40.13 odd 4
720.6.a.h.1.1 1 24.5 odd 2