# Properties

 Label 9200.2.a.cx.1.1 Level $9200$ Weight $2$ Character 9200.1 Self dual yes Analytic conductor $73.462$ Analytic rank $1$ Dimension $6$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9200 = 2^{4} \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9200.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$73.4623698596$$ Analytic rank: $$1$$ Dimension: $$6$$ Coefficient field: 6.6.143376304.1 Defining polynomial: $$x^{6} - 12x^{4} + 22x^{2} - 6x - 1$$ x^6 - 12*x^4 + 22*x^2 - 6*x - 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 460) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$3.16223$$ of defining polynomial Character $$\chi$$ $$=$$ 9200.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.21923 q^{3} +2.43185 q^{7} +7.36343 q^{9} +O(q^{10})$$ $$q-3.21923 q^{3} +2.43185 q^{7} +7.36343 q^{9} +0.884969 q^{11} +5.10522 q^{13} +0.366626 q^{17} +2.79847 q^{19} -7.82867 q^{21} -1.00000 q^{23} -14.0469 q^{27} +8.02431 q^{29} -7.24179 q^{31} -2.84892 q^{33} -3.10036 q^{37} -16.4349 q^{39} -3.47185 q^{41} -8.56841 q^{43} -5.25528 q^{47} -1.08612 q^{49} -1.18025 q^{51} -11.6413 q^{53} -9.00892 q^{57} +9.33209 q^{59} +5.46699 q^{61} +17.9067 q^{63} -1.49020 q^{67} +3.21923 q^{69} -8.29949 q^{71} -10.2409 q^{73} +2.15211 q^{77} -6.06522 q^{79} +23.1298 q^{81} -16.2520 q^{83} -25.8321 q^{87} -17.6033 q^{89} +12.4151 q^{91} +23.3130 q^{93} -6.55618 q^{97} +6.51641 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 4 q^{3} - 9 q^{7} + 10 q^{9}+O(q^{10})$$ 6 * q - 4 * q^3 - 9 * q^7 + 10 * q^9 $$6 q - 4 q^{3} - 9 q^{7} + 10 q^{9} - 2 q^{11} + 8 q^{13} + 5 q^{17} - 4 q^{19} - 6 q^{23} - 22 q^{27} + 5 q^{29} - 9 q^{31} - 10 q^{33} + 21 q^{37} + 8 q^{39} - q^{41} - 16 q^{43} - 16 q^{47} + 19 q^{49} + 12 q^{51} - q^{53} + 12 q^{57} + 11 q^{59} - 4 q^{61} - 19 q^{63} - 25 q^{67} + 4 q^{69} + 17 q^{71} - 14 q^{73} + 20 q^{77} - 10 q^{79} + 14 q^{81} - 21 q^{83} - 64 q^{87} - 24 q^{89} + 4 q^{91} + 4 q^{97} + 16 q^{99}+O(q^{100})$$ 6 * q - 4 * q^3 - 9 * q^7 + 10 * q^9 - 2 * q^11 + 8 * q^13 + 5 * q^17 - 4 * q^19 - 6 * q^23 - 22 * q^27 + 5 * q^29 - 9 * q^31 - 10 * q^33 + 21 * q^37 + 8 * q^39 - q^41 - 16 * q^43 - 16 * q^47 + 19 * q^49 + 12 * q^51 - q^53 + 12 * q^57 + 11 * q^59 - 4 * q^61 - 19 * q^63 - 25 * q^67 + 4 * q^69 + 17 * q^71 - 14 * q^73 + 20 * q^77 - 10 * q^79 + 14 * q^81 - 21 * q^83 - 64 * q^87 - 24 * q^89 + 4 * q^91 + 4 * q^97 + 16 * q^99

## 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
$$3$$ −3.21923 −1.85862 −0.929311 0.369298i $$-0.879598\pi$$
−0.929311 + 0.369298i $$0.879598\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.43185 0.919152 0.459576 0.888138i $$-0.348001\pi$$
0.459576 + 0.888138i $$0.348001\pi$$
$$8$$ 0 0
$$9$$ 7.36343 2.45448
$$10$$ 0 0
$$11$$ 0.884969 0.266828 0.133414 0.991060i $$-0.457406\pi$$
0.133414 + 0.991060i $$0.457406\pi$$
$$12$$ 0 0
$$13$$ 5.10522 1.41593 0.707967 0.706245i $$-0.249612\pi$$
0.707967 + 0.706245i $$0.249612\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0.366626 0.0889198 0.0444599 0.999011i $$-0.485843\pi$$
0.0444599 + 0.999011i $$0.485843\pi$$
$$18$$ 0 0
$$19$$ 2.79847 0.642014 0.321007 0.947077i $$-0.395979\pi$$
0.321007 + 0.947077i $$0.395979\pi$$
$$20$$ 0 0
$$21$$ −7.82867 −1.70836
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −14.0469 −2.70332
$$28$$ 0 0
$$29$$ 8.02431 1.49008 0.745038 0.667022i $$-0.232431\pi$$
0.745038 + 0.667022i $$0.232431\pi$$
$$30$$ 0 0
$$31$$ −7.24179 −1.30066 −0.650332 0.759650i $$-0.725370\pi$$
−0.650332 + 0.759650i $$0.725370\pi$$
$$32$$ 0 0
$$33$$ −2.84892 −0.495933
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −3.10036 −0.509697 −0.254848 0.966981i $$-0.582026\pi$$
−0.254848 + 0.966981i $$0.582026\pi$$
$$38$$ 0 0
$$39$$ −16.4349 −2.63169
$$40$$ 0 0
$$41$$ −3.47185 −0.542212 −0.271106 0.962550i $$-0.587389\pi$$
−0.271106 + 0.962550i $$0.587389\pi$$
$$42$$ 0 0
$$43$$ −8.56841 −1.30667 −0.653335 0.757069i $$-0.726631\pi$$
−0.653335 + 0.757069i $$0.726631\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −5.25528 −0.766561 −0.383281 0.923632i $$-0.625206\pi$$
−0.383281 + 0.923632i $$0.625206\pi$$
$$48$$ 0 0
$$49$$ −1.08612 −0.155160
$$50$$ 0 0
$$51$$ −1.18025 −0.165268
$$52$$ 0 0
$$53$$ −11.6413 −1.59905 −0.799526 0.600632i $$-0.794916\pi$$
−0.799526 + 0.600632i $$0.794916\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −9.00892 −1.19326
$$58$$ 0 0
$$59$$ 9.33209 1.21493 0.607467 0.794345i $$-0.292186\pi$$
0.607467 + 0.794345i $$0.292186\pi$$
$$60$$ 0 0
$$61$$ 5.46699 0.699976 0.349988 0.936754i $$-0.386186\pi$$
0.349988 + 0.936754i $$0.386186\pi$$
$$62$$ 0 0
$$63$$ 17.9067 2.25604
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.49020 −0.182057 −0.0910285 0.995848i $$-0.529015\pi$$
−0.0910285 + 0.995848i $$0.529015\pi$$
$$68$$ 0 0
$$69$$ 3.21923 0.387549
$$70$$ 0 0
$$71$$ −8.29949 −0.984969 −0.492484 0.870321i $$-0.663911\pi$$
−0.492484 + 0.870321i $$0.663911\pi$$
$$72$$ 0 0
$$73$$ −10.2409 −1.19860 −0.599302 0.800523i $$-0.704555\pi$$
−0.599302 + 0.800523i $$0.704555\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 2.15211 0.245256
$$78$$ 0 0
$$79$$ −6.06522 −0.682391 −0.341195 0.939992i $$-0.610832\pi$$
−0.341195 + 0.939992i $$0.610832\pi$$
$$80$$ 0 0
$$81$$ 23.1298 2.56998
$$82$$ 0 0
$$83$$ −16.2520 −1.78389 −0.891943 0.452148i $$-0.850658\pi$$
−0.891943 + 0.452148i $$0.850658\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −25.8321 −2.76949
$$88$$ 0 0
$$89$$ −17.6033 −1.86594 −0.932972 0.359949i $$-0.882794\pi$$
−0.932972 + 0.359949i $$0.882794\pi$$
$$90$$ 0 0
$$91$$ 12.4151 1.30146
$$92$$ 0 0
$$93$$ 23.3130 2.41744
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −6.55618 −0.665679 −0.332839 0.942984i $$-0.608007\pi$$
−0.332839 + 0.942984i $$0.608007\pi$$
$$98$$ 0 0
$$99$$ 6.51641 0.654924
$$100$$ 0 0
$$101$$ 13.4912 1.34243 0.671213 0.741265i $$-0.265774\pi$$
0.671213 + 0.741265i $$0.265774\pi$$
$$102$$ 0 0
$$103$$ −12.5460 −1.23619 −0.618096 0.786103i $$-0.712096\pi$$
−0.618096 + 0.786103i $$0.712096\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.46269 −0.141404 −0.0707020 0.997497i $$-0.522524\pi$$
−0.0707020 + 0.997497i $$0.522524\pi$$
$$108$$ 0 0
$$109$$ −19.2173 −1.84069 −0.920343 0.391113i $$-0.872090\pi$$
−0.920343 + 0.391113i $$0.872090\pi$$
$$110$$ 0 0
$$111$$ 9.98078 0.947334
$$112$$ 0 0
$$113$$ −0.834901 −0.0785409 −0.0392705 0.999229i $$-0.512503\pi$$
−0.0392705 + 0.999229i $$0.512503\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 37.5920 3.47538
$$118$$ 0 0
$$119$$ 0.891578 0.0817308
$$120$$ 0 0
$$121$$ −10.2168 −0.928803
$$122$$ 0 0
$$123$$ 11.1767 1.00777
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −7.87453 −0.698751 −0.349376 0.936983i $$-0.613606\pi$$
−0.349376 + 0.936983i $$0.613606\pi$$
$$128$$ 0 0
$$129$$ 27.5837 2.42861
$$130$$ 0 0
$$131$$ 12.8740 1.12481 0.562403 0.826863i $$-0.309877\pi$$
0.562403 + 0.826863i $$0.309877\pi$$
$$132$$ 0 0
$$133$$ 6.80546 0.590108
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 3.26675 0.279097 0.139549 0.990215i $$-0.455435\pi$$
0.139549 + 0.990215i $$0.455435\pi$$
$$138$$ 0 0
$$139$$ 12.5578 1.06514 0.532570 0.846386i $$-0.321226\pi$$
0.532570 + 0.846386i $$0.321226\pi$$
$$140$$ 0 0
$$141$$ 16.9179 1.42475
$$142$$ 0 0
$$143$$ 4.51797 0.377811
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 3.49647 0.288384
$$148$$ 0 0
$$149$$ −0.188265 −0.0154233 −0.00771164 0.999970i $$-0.502455\pi$$
−0.00771164 + 0.999970i $$0.502455\pi$$
$$150$$ 0 0
$$151$$ 18.6708 1.51941 0.759704 0.650269i $$-0.225344\pi$$
0.759704 + 0.650269i $$0.225344\pi$$
$$152$$ 0 0
$$153$$ 2.69962 0.218252
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 20.0277 1.59839 0.799193 0.601074i $$-0.205260\pi$$
0.799193 + 0.601074i $$0.205260\pi$$
$$158$$ 0 0
$$159$$ 37.4759 2.97203
$$160$$ 0 0
$$161$$ −2.43185 −0.191656
$$162$$ 0 0
$$163$$ −3.35607 −0.262867 −0.131434 0.991325i $$-0.541958\pi$$
−0.131434 + 0.991325i $$0.541958\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.57745 0.199449 0.0997246 0.995015i $$-0.468204\pi$$
0.0997246 + 0.995015i $$0.468204\pi$$
$$168$$ 0 0
$$169$$ 13.0633 1.00487
$$170$$ 0 0
$$171$$ 20.6064 1.57581
$$172$$ 0 0
$$173$$ −19.4182 −1.47634 −0.738170 0.674615i $$-0.764310\pi$$
−0.738170 + 0.674615i $$0.764310\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −30.0421 −2.25810
$$178$$ 0 0
$$179$$ 20.3628 1.52199 0.760993 0.648760i $$-0.224712\pi$$
0.760993 + 0.648760i $$0.224712\pi$$
$$180$$ 0 0
$$181$$ −22.5629 −1.67709 −0.838543 0.544835i $$-0.816592\pi$$
−0.838543 + 0.544835i $$0.816592\pi$$
$$182$$ 0 0
$$183$$ −17.5995 −1.30099
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0.324453 0.0237263
$$188$$ 0 0
$$189$$ −34.1598 −2.48476
$$190$$ 0 0
$$191$$ 16.6554 1.20514 0.602571 0.798065i $$-0.294143\pi$$
0.602571 + 0.798065i $$0.294143\pi$$
$$192$$ 0 0
$$193$$ 14.5214 1.04527 0.522636 0.852556i $$-0.324949\pi$$
0.522636 + 0.852556i $$0.324949\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −13.3479 −0.950995 −0.475498 0.879717i $$-0.657732\pi$$
−0.475498 + 0.879717i $$0.657732\pi$$
$$198$$ 0 0
$$199$$ −18.7856 −1.33168 −0.665838 0.746097i $$-0.731926\pi$$
−0.665838 + 0.746097i $$0.731926\pi$$
$$200$$ 0 0
$$201$$ 4.79730 0.338375
$$202$$ 0 0
$$203$$ 19.5139 1.36961
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −7.36343 −0.511794
$$208$$ 0 0
$$209$$ 2.47656 0.171307
$$210$$ 0 0
$$211$$ −17.1078 −1.17775 −0.588874 0.808225i $$-0.700429\pi$$
−0.588874 + 0.808225i $$0.700429\pi$$
$$212$$ 0 0
$$213$$ 26.7180 1.83068
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −17.6109 −1.19551
$$218$$ 0 0
$$219$$ 32.9677 2.22775
$$220$$ 0 0
$$221$$ 1.87171 0.125905
$$222$$ 0 0
$$223$$ 13.5184 0.905262 0.452631 0.891698i $$-0.350485\pi$$
0.452631 + 0.891698i $$0.350485\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −8.29581 −0.550612 −0.275306 0.961357i $$-0.588779\pi$$
−0.275306 + 0.961357i $$0.588779\pi$$
$$228$$ 0 0
$$229$$ −6.22318 −0.411239 −0.205620 0.978632i $$-0.565921\pi$$
−0.205620 + 0.978632i $$0.565921\pi$$
$$230$$ 0 0
$$231$$ −6.92813 −0.455838
$$232$$ 0 0
$$233$$ −13.6347 −0.893242 −0.446621 0.894723i $$-0.647373\pi$$
−0.446621 + 0.894723i $$0.647373\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 19.5253 1.26831
$$238$$ 0 0
$$239$$ −11.5281 −0.745693 −0.372847 0.927893i $$-0.621618\pi$$
−0.372847 + 0.927893i $$0.621618\pi$$
$$240$$ 0 0
$$241$$ −17.5952 −1.13341 −0.566704 0.823921i $$-0.691782\pi$$
−0.566704 + 0.823921i $$0.691782\pi$$
$$242$$ 0 0
$$243$$ −32.3195 −2.07329
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 14.2868 0.909049
$$248$$ 0 0
$$249$$ 52.3188 3.31557
$$250$$ 0 0
$$251$$ −12.5471 −0.791968 −0.395984 0.918257i $$-0.629596\pi$$
−0.395984 + 0.918257i $$0.629596\pi$$
$$252$$ 0 0
$$253$$ −0.884969 −0.0556375
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4.88072 0.304451 0.152225 0.988346i $$-0.451356\pi$$
0.152225 + 0.988346i $$0.451356\pi$$
$$258$$ 0 0
$$259$$ −7.53961 −0.468489
$$260$$ 0 0
$$261$$ 59.0864 3.65736
$$262$$ 0 0
$$263$$ 11.6045 0.715566 0.357783 0.933805i $$-0.383533\pi$$
0.357783 + 0.933805i $$0.383533\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 56.6690 3.46808
$$268$$ 0 0
$$269$$ −6.04327 −0.368465 −0.184232 0.982883i $$-0.558980\pi$$
−0.184232 + 0.982883i $$0.558980\pi$$
$$270$$ 0 0
$$271$$ −3.93401 −0.238974 −0.119487 0.992836i $$-0.538125\pi$$
−0.119487 + 0.992836i $$0.538125\pi$$
$$272$$ 0 0
$$273$$ −39.9671 −2.41892
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 7.92174 0.475971 0.237986 0.971269i $$-0.423513\pi$$
0.237986 + 0.971269i $$0.423513\pi$$
$$278$$ 0 0
$$279$$ −53.3244 −3.19245
$$280$$ 0 0
$$281$$ −6.00419 −0.358180 −0.179090 0.983833i $$-0.557315\pi$$
−0.179090 + 0.983833i $$0.557315\pi$$
$$282$$ 0 0
$$283$$ −7.65299 −0.454923 −0.227461 0.973787i $$-0.573043\pi$$
−0.227461 + 0.973787i $$0.573043\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −8.44301 −0.498375
$$288$$ 0 0
$$289$$ −16.8656 −0.992093
$$290$$ 0 0
$$291$$ 21.1058 1.23725
$$292$$ 0 0
$$293$$ −13.5480 −0.791485 −0.395743 0.918361i $$-0.629513\pi$$
−0.395743 + 0.918361i $$0.629513\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −12.4310 −0.721323
$$298$$ 0 0
$$299$$ −5.10522 −0.295243
$$300$$ 0 0
$$301$$ −20.8371 −1.20103
$$302$$ 0 0
$$303$$ −43.4313 −2.49506
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −10.0870 −0.575697 −0.287848 0.957676i $$-0.592940\pi$$
−0.287848 + 0.957676i $$0.592940\pi$$
$$308$$ 0 0
$$309$$ 40.3883 2.29761
$$310$$ 0 0
$$311$$ 28.2481 1.60180 0.800902 0.598795i $$-0.204354\pi$$
0.800902 + 0.598795i $$0.204354\pi$$
$$312$$ 0 0
$$313$$ −14.4504 −0.816786 −0.408393 0.912806i $$-0.633911\pi$$
−0.408393 + 0.912806i $$0.633911\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 14.7835 0.830324 0.415162 0.909748i $$-0.363725\pi$$
0.415162 + 0.909748i $$0.363725\pi$$
$$318$$ 0 0
$$319$$ 7.10127 0.397595
$$320$$ 0 0
$$321$$ 4.70875 0.262817
$$322$$ 0 0
$$323$$ 1.02599 0.0570877
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 61.8649 3.42114
$$328$$ 0 0
$$329$$ −12.7800 −0.704586
$$330$$ 0 0
$$331$$ 20.1494 1.10751 0.553757 0.832679i $$-0.313194\pi$$
0.553757 + 0.832679i $$0.313194\pi$$
$$332$$ 0 0
$$333$$ −22.8293 −1.25104
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 24.0660 1.31096 0.655479 0.755214i $$-0.272467\pi$$
0.655479 + 0.755214i $$0.272467\pi$$
$$338$$ 0 0
$$339$$ 2.68774 0.145978
$$340$$ 0 0
$$341$$ −6.40876 −0.347054
$$342$$ 0 0
$$343$$ −19.6642 −1.06177
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 26.3788 1.41609 0.708045 0.706168i $$-0.249578\pi$$
0.708045 + 0.706168i $$0.249578\pi$$
$$348$$ 0 0
$$349$$ 0.535518 0.0286656 0.0143328 0.999897i $$-0.495438\pi$$
0.0143328 + 0.999897i $$0.495438\pi$$
$$350$$ 0 0
$$351$$ −71.7124 −3.82773
$$352$$ 0 0
$$353$$ −5.27606 −0.280816 −0.140408 0.990094i $$-0.544841\pi$$
−0.140408 + 0.990094i $$0.544841\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −2.87019 −0.151907
$$358$$ 0 0
$$359$$ −20.4351 −1.07852 −0.539261 0.842139i $$-0.681296\pi$$
−0.539261 + 0.842139i $$0.681296\pi$$
$$360$$ 0 0
$$361$$ −11.1685 −0.587818
$$362$$ 0 0
$$363$$ 32.8903 1.72629
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −12.4382 −0.649268 −0.324634 0.945840i $$-0.605241\pi$$
−0.324634 + 0.945840i $$0.605241\pi$$
$$368$$ 0 0
$$369$$ −25.5647 −1.33085
$$370$$ 0 0
$$371$$ −28.3098 −1.46977
$$372$$ 0 0
$$373$$ 2.99999 0.155334 0.0776669 0.996979i $$-0.475253\pi$$
0.0776669 + 0.996979i $$0.475253\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 40.9659 2.10985
$$378$$ 0 0
$$379$$ 3.02165 0.155212 0.0776059 0.996984i $$-0.475272\pi$$
0.0776059 + 0.996984i $$0.475272\pi$$
$$380$$ 0 0
$$381$$ 25.3499 1.29871
$$382$$ 0 0
$$383$$ −8.15719 −0.416813 −0.208406 0.978042i $$-0.566828\pi$$
−0.208406 + 0.978042i $$0.566828\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −63.0929 −3.20719
$$388$$ 0 0
$$389$$ 11.7789 0.597214 0.298607 0.954376i $$-0.403478\pi$$
0.298607 + 0.954376i $$0.403478\pi$$
$$390$$ 0 0
$$391$$ −0.366626 −0.0185411
$$392$$ 0 0
$$393$$ −41.4443 −2.09059
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −16.7004 −0.838167 −0.419083 0.907948i $$-0.637649\pi$$
−0.419083 + 0.907948i $$0.637649\pi$$
$$398$$ 0 0
$$399$$ −21.9083 −1.09679
$$400$$ 0 0
$$401$$ 9.99936 0.499344 0.249672 0.968330i $$-0.419677\pi$$
0.249672 + 0.968330i $$0.419677\pi$$
$$402$$ 0 0
$$403$$ −36.9710 −1.84165
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −2.74373 −0.136002
$$408$$ 0 0
$$409$$ 2.20305 0.108934 0.0544668 0.998516i $$-0.482654\pi$$
0.0544668 + 0.998516i $$0.482654\pi$$
$$410$$ 0 0
$$411$$ −10.5164 −0.518736
$$412$$ 0 0
$$413$$ 22.6942 1.11671
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −40.4264 −1.97969
$$418$$ 0 0
$$419$$ −4.12814 −0.201673 −0.100836 0.994903i $$-0.532152\pi$$
−0.100836 + 0.994903i $$0.532152\pi$$
$$420$$ 0 0
$$421$$ −15.7354 −0.766899 −0.383449 0.923562i $$-0.625264\pi$$
−0.383449 + 0.923562i $$0.625264\pi$$
$$422$$ 0 0
$$423$$ −38.6969 −1.88151
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 13.2949 0.643385
$$428$$ 0 0
$$429$$ −14.5444 −0.702209
$$430$$ 0 0
$$431$$ 1.35158 0.0651034 0.0325517 0.999470i $$-0.489637\pi$$
0.0325517 + 0.999470i $$0.489637\pi$$
$$432$$ 0 0
$$433$$ 39.4114 1.89399 0.946996 0.321244i $$-0.104101\pi$$
0.946996 + 0.321244i $$0.104101\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.79847 −0.133869
$$438$$ 0 0
$$439$$ −10.1059 −0.482326 −0.241163 0.970485i $$-0.577529\pi$$
−0.241163 + 0.970485i $$0.577529\pi$$
$$440$$ 0 0
$$441$$ −7.99756 −0.380836
$$442$$ 0 0
$$443$$ −6.25526 −0.297197 −0.148598 0.988898i $$-0.547476\pi$$
−0.148598 + 0.988898i $$0.547476\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0.606068 0.0286660
$$448$$ 0 0
$$449$$ 2.28779 0.107968 0.0539839 0.998542i $$-0.482808\pi$$
0.0539839 + 0.998542i $$0.482808\pi$$
$$450$$ 0 0
$$451$$ −3.07248 −0.144677
$$452$$ 0 0
$$453$$ −60.1055 −2.82400
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −14.3062 −0.669217 −0.334609 0.942357i $$-0.608604\pi$$
−0.334609 + 0.942357i $$0.608604\pi$$
$$458$$ 0 0
$$459$$ −5.14995 −0.240379
$$460$$ 0 0
$$461$$ −2.38995 −0.111311 −0.0556556 0.998450i $$-0.517725\pi$$
−0.0556556 + 0.998450i $$0.517725\pi$$
$$462$$ 0 0
$$463$$ 9.52232 0.442540 0.221270 0.975213i $$-0.428980\pi$$
0.221270 + 0.975213i $$0.428980\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 6.14501 0.284357 0.142178 0.989841i $$-0.454589\pi$$
0.142178 + 0.989841i $$0.454589\pi$$
$$468$$ 0 0
$$469$$ −3.62394 −0.167338
$$470$$ 0 0
$$471$$ −64.4738 −2.97080
$$472$$ 0 0
$$473$$ −7.58278 −0.348657
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −85.7197 −3.92483
$$478$$ 0 0
$$479$$ 1.40986 0.0644180 0.0322090 0.999481i $$-0.489746\pi$$
0.0322090 + 0.999481i $$0.489746\pi$$
$$480$$ 0 0
$$481$$ −15.8281 −0.721697
$$482$$ 0 0
$$483$$ 7.82867 0.356217
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −31.2993 −1.41831 −0.709154 0.705054i $$-0.750923\pi$$
−0.709154 + 0.705054i $$0.750923\pi$$
$$488$$ 0 0
$$489$$ 10.8039 0.488571
$$490$$ 0 0
$$491$$ 25.9254 1.17000 0.584999 0.811034i $$-0.301095\pi$$
0.584999 + 0.811034i $$0.301095\pi$$
$$492$$ 0 0
$$493$$ 2.94192 0.132497
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −20.1831 −0.905336
$$498$$ 0 0
$$499$$ 8.04562 0.360172 0.180086 0.983651i $$-0.442362\pi$$
0.180086 + 0.983651i $$0.442362\pi$$
$$500$$ 0 0
$$501$$ −8.29740 −0.370701
$$502$$ 0 0
$$503$$ 5.50490 0.245451 0.122726 0.992441i $$-0.460836\pi$$
0.122726 + 0.992441i $$0.460836\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −42.0538 −1.86767
$$508$$ 0 0
$$509$$ −8.26586 −0.366378 −0.183189 0.983078i $$-0.558642\pi$$
−0.183189 + 0.983078i $$0.558642\pi$$
$$510$$ 0 0
$$511$$ −24.9043 −1.10170
$$512$$ 0 0
$$513$$ −39.3098 −1.73557
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −4.65076 −0.204540
$$518$$ 0 0
$$519$$ 62.5116 2.74396
$$520$$ 0 0
$$521$$ 11.9776 0.524747 0.262374 0.964966i $$-0.415495\pi$$
0.262374 + 0.964966i $$0.415495\pi$$
$$522$$ 0 0
$$523$$ 0.711546 0.0311137 0.0155569 0.999879i $$-0.495048\pi$$
0.0155569 + 0.999879i $$0.495048\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.65503 −0.115655
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 68.7162 2.98203
$$532$$ 0 0
$$533$$ −17.7246 −0.767737
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −65.5524 −2.82880
$$538$$ 0 0
$$539$$ −0.961182 −0.0414011
$$540$$ 0 0
$$541$$ 34.9533 1.50276 0.751381 0.659869i $$-0.229388\pi$$
0.751381 + 0.659869i $$0.229388\pi$$
$$542$$ 0 0
$$543$$ 72.6351 3.11707
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −17.8478 −0.763118 −0.381559 0.924345i $$-0.624613\pi$$
−0.381559 + 0.924345i $$0.624613\pi$$
$$548$$ 0 0
$$549$$ 40.2558 1.71808
$$550$$ 0 0
$$551$$ 22.4558 0.956650
$$552$$ 0 0
$$553$$ −14.7497 −0.627221
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 3.29661 0.139682 0.0698410 0.997558i $$-0.477751\pi$$
0.0698410 + 0.997558i $$0.477751\pi$$
$$558$$ 0 0
$$559$$ −43.7437 −1.85016
$$560$$ 0 0
$$561$$ −1.04449 −0.0440983
$$562$$ 0 0
$$563$$ −4.44153 −0.187188 −0.0935941 0.995610i $$-0.529836\pi$$
−0.0935941 + 0.995610i $$0.529836\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 56.2481 2.36220
$$568$$ 0 0
$$569$$ −6.00088 −0.251570 −0.125785 0.992058i $$-0.540145\pi$$
−0.125785 + 0.992058i $$0.540145\pi$$
$$570$$ 0 0
$$571$$ −18.1609 −0.760008 −0.380004 0.924985i $$-0.624077\pi$$
−0.380004 + 0.924985i $$0.624077\pi$$
$$572$$ 0 0
$$573$$ −53.6175 −2.23990
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −10.0474 −0.418279 −0.209140 0.977886i $$-0.567066\pi$$
−0.209140 + 0.977886i $$0.567066\pi$$
$$578$$ 0 0
$$579$$ −46.7476 −1.94277
$$580$$ 0 0
$$581$$ −39.5223 −1.63966
$$582$$ 0 0
$$583$$ −10.3022 −0.426672
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 42.3593 1.74836 0.874178 0.485605i $$-0.161401\pi$$
0.874178 + 0.485605i $$0.161401\pi$$
$$588$$ 0 0
$$589$$ −20.2660 −0.835044
$$590$$ 0 0
$$591$$ 42.9698 1.76754
$$592$$ 0 0
$$593$$ 19.6741 0.807917 0.403958 0.914777i $$-0.367634\pi$$
0.403958 + 0.914777i $$0.367634\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 60.4751 2.47508
$$598$$ 0 0
$$599$$ 18.2740 0.746655 0.373328 0.927700i $$-0.378217\pi$$
0.373328 + 0.927700i $$0.378217\pi$$
$$600$$ 0 0
$$601$$ −8.17793 −0.333585 −0.166792 0.985992i $$-0.553341\pi$$
−0.166792 + 0.985992i $$0.553341\pi$$
$$602$$ 0 0
$$603$$ −10.9730 −0.446855
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −21.7927 −0.884538 −0.442269 0.896883i $$-0.645826\pi$$
−0.442269 + 0.896883i $$0.645826\pi$$
$$608$$ 0 0
$$609$$ −62.8197 −2.54558
$$610$$ 0 0
$$611$$ −26.8294 −1.08540
$$612$$ 0 0
$$613$$ −15.2379 −0.615455 −0.307727 0.951475i $$-0.599568\pi$$
−0.307727 + 0.951475i $$0.599568\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 20.2945 0.817024 0.408512 0.912753i $$-0.366048\pi$$
0.408512 + 0.912753i $$0.366048\pi$$
$$618$$ 0 0
$$619$$ −2.08510 −0.0838073 −0.0419037 0.999122i $$-0.513342\pi$$
−0.0419037 + 0.999122i $$0.513342\pi$$
$$620$$ 0 0
$$621$$ 14.0469 0.563681
$$622$$ 0 0
$$623$$ −42.8085 −1.71509
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −7.97262 −0.318396
$$628$$ 0 0
$$629$$ −1.13667 −0.0453221
$$630$$ 0 0
$$631$$ −39.0512 −1.55461 −0.777303 0.629127i $$-0.783413\pi$$
−0.777303 + 0.629127i $$0.783413\pi$$
$$632$$ 0 0
$$633$$ 55.0738 2.18899
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −5.54488 −0.219696
$$638$$ 0 0
$$639$$ −61.1127 −2.41758
$$640$$ 0 0
$$641$$ −21.8361 −0.862475 −0.431238 0.902238i $$-0.641923\pi$$
−0.431238 + 0.902238i $$0.641923\pi$$
$$642$$ 0 0
$$643$$ 16.3727 0.645676 0.322838 0.946454i $$-0.395363\pi$$
0.322838 + 0.946454i $$0.395363\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 20.9991 0.825560 0.412780 0.910831i $$-0.364558\pi$$
0.412780 + 0.910831i $$0.364558\pi$$
$$648$$ 0 0
$$649$$ 8.25861 0.324179
$$650$$ 0 0
$$651$$ 56.6936 2.22200
$$652$$ 0 0
$$653$$ −23.2756 −0.910846 −0.455423 0.890275i $$-0.650512\pi$$
−0.455423 + 0.890275i $$0.650512\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −75.4080 −2.94195
$$658$$ 0 0
$$659$$ 2.09639 0.0816637 0.0408318 0.999166i $$-0.486999\pi$$
0.0408318 + 0.999166i $$0.486999\pi$$
$$660$$ 0 0
$$661$$ −31.3184 −1.21814 −0.609072 0.793115i $$-0.708458\pi$$
−0.609072 + 0.793115i $$0.708458\pi$$
$$662$$ 0 0
$$663$$ −6.02545 −0.234009
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −8.02431 −0.310703
$$668$$ 0 0
$$669$$ −43.5190 −1.68254
$$670$$ 0 0
$$671$$ 4.83812 0.186773
$$672$$ 0 0
$$673$$ 44.3377 1.70909 0.854545 0.519377i $$-0.173836\pi$$
0.854545 + 0.519377i $$0.173836\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 3.03772 0.116749 0.0583746 0.998295i $$-0.481408\pi$$
0.0583746 + 0.998295i $$0.481408\pi$$
$$678$$ 0 0
$$679$$ −15.9436 −0.611860
$$680$$ 0 0
$$681$$ 26.7061 1.02338
$$682$$ 0 0
$$683$$ 22.6750 0.867635 0.433817 0.901001i $$-0.357166\pi$$
0.433817 + 0.901001i $$0.357166\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 20.0338 0.764338
$$688$$ 0 0
$$689$$ −59.4313 −2.26415
$$690$$ 0 0
$$691$$ 18.2394 0.693860 0.346930 0.937891i $$-0.387224\pi$$
0.346930 + 0.937891i $$0.387224\pi$$
$$692$$ 0 0
$$693$$ 15.8469 0.601974
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −1.27287 −0.0482134
$$698$$ 0 0
$$699$$ 43.8934 1.66020
$$700$$ 0 0
$$701$$ 17.4315 0.658378 0.329189 0.944264i $$-0.393225\pi$$
0.329189 + 0.944264i $$0.393225\pi$$
$$702$$ 0 0
$$703$$ −8.67629 −0.327232
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 32.8086 1.23389
$$708$$ 0 0
$$709$$ −32.4207 −1.21758 −0.608792 0.793330i $$-0.708346\pi$$
−0.608792 + 0.793330i $$0.708346\pi$$
$$710$$ 0 0
$$711$$ −44.6608 −1.67491
$$712$$ 0 0
$$713$$ 7.24179 0.271207
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 37.1117 1.38596
$$718$$ 0 0
$$719$$ −0.494269 −0.0184331 −0.00921656 0.999958i $$-0.502934\pi$$
−0.00921656 + 0.999958i $$0.502934\pi$$
$$720$$ 0 0
$$721$$ −30.5099 −1.13625
$$722$$ 0 0
$$723$$ 56.6430 2.10658
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 4.25774 0.157911 0.0789555 0.996878i $$-0.474842\pi$$
0.0789555 + 0.996878i $$0.474842\pi$$
$$728$$ 0 0
$$729$$ 34.6543 1.28349
$$730$$ 0 0
$$731$$ −3.14140 −0.116189
$$732$$ 0 0
$$733$$ 14.8525 0.548589 0.274295 0.961646i $$-0.411556\pi$$
0.274295 + 0.961646i $$0.411556\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −1.31878 −0.0485780
$$738$$ 0 0
$$739$$ 42.1389 1.55010 0.775052 0.631898i $$-0.217724\pi$$
0.775052 + 0.631898i $$0.217724\pi$$
$$740$$ 0 0
$$741$$ −45.9926 −1.68958
$$742$$ 0 0
$$743$$ −3.97014 −0.145650 −0.0728252 0.997345i $$-0.523202\pi$$
−0.0728252 + 0.997345i $$0.523202\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −119.670 −4.37851
$$748$$ 0 0
$$749$$ −3.55705 −0.129972
$$750$$ 0 0
$$751$$ −51.5382 −1.88066 −0.940328 0.340269i $$-0.889482\pi$$
−0.940328 + 0.340269i $$0.889482\pi$$
$$752$$ 0 0
$$753$$ 40.3921 1.47197
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −39.9808 −1.45313 −0.726564 0.687099i $$-0.758884\pi$$
−0.726564 + 0.687099i $$0.758884\pi$$
$$758$$ 0 0
$$759$$ 2.84892 0.103409
$$760$$ 0 0
$$761$$ −20.6683 −0.749226 −0.374613 0.927181i $$-0.622224\pi$$
−0.374613 + 0.927181i $$0.622224\pi$$
$$762$$ 0 0
$$763$$ −46.7336 −1.69187
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 47.6424 1.72027
$$768$$ 0 0
$$769$$ −0.0670558 −0.00241809 −0.00120905 0.999999i $$-0.500385\pi$$
−0.00120905 + 0.999999i $$0.500385\pi$$
$$770$$ 0 0
$$771$$ −15.7121 −0.565859
$$772$$ 0 0
$$773$$ 21.2074 0.762778 0.381389 0.924415i $$-0.375446\pi$$
0.381389 + 0.924415i $$0.375446\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 24.2717 0.870744
$$778$$ 0 0
$$779$$ −9.71588 −0.348108
$$780$$ 0 0
$$781$$ −7.34480 −0.262817
$$782$$ 0 0
$$783$$ −112.716 −4.02816
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −19.1047 −0.681010 −0.340505 0.940243i $$-0.610598\pi$$
−0.340505 + 0.940243i $$0.610598\pi$$
$$788$$ 0 0
$$789$$ −37.3577 −1.32997
$$790$$ 0 0
$$791$$ −2.03035 −0.0721910
$$792$$ 0 0
$$793$$ 27.9102 0.991121
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −51.0751 −1.80917 −0.904587 0.426290i $$-0.859820\pi$$
−0.904587 + 0.426290i $$0.859820\pi$$
$$798$$ 0 0
$$799$$ −1.92672 −0.0681625
$$800$$ 0 0
$$801$$ −129.621 −4.57992
$$802$$ 0 0
$$803$$ −9.06286 −0.319822
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 19.4547 0.684837
$$808$$ 0 0
$$809$$ −5.02800 −0.176775 −0.0883876 0.996086i $$-0.528171\pi$$
−0.0883876 + 0.996086i $$0.528171\pi$$
$$810$$ 0 0
$$811$$ −51.3571 −1.80339 −0.901696 0.432371i $$-0.857677\pi$$
−0.901696 + 0.432371i $$0.857677\pi$$
$$812$$ 0 0
$$813$$ 12.6645 0.444162
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −23.9785 −0.838900
$$818$$ 0 0
$$819$$ 91.4179 3.19440
$$820$$ 0 0
$$821$$ 13.7483 0.479818 0.239909 0.970795i $$-0.422882\pi$$
0.239909 + 0.970795i $$0.422882\pi$$
$$822$$ 0 0
$$823$$ 9.07220 0.316237 0.158119 0.987420i $$-0.449457\pi$$
0.158119 + 0.987420i $$0.449457\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 48.2010 1.67611 0.838057 0.545583i $$-0.183692\pi$$
0.838057 + 0.545583i $$0.183692\pi$$
$$828$$ 0 0
$$829$$ 41.0601 1.42608 0.713038 0.701125i $$-0.247319\pi$$
0.713038 + 0.701125i $$0.247319\pi$$
$$830$$ 0 0
$$831$$ −25.5019 −0.884651
$$832$$ 0 0
$$833$$ −0.398199 −0.0137968
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 101.724 3.51611
$$838$$ 0 0
$$839$$ −29.3970 −1.01490 −0.507449 0.861682i $$-0.669412\pi$$
−0.507449 + 0.861682i $$0.669412\pi$$
$$840$$ 0 0
$$841$$ 35.3895 1.22033
$$842$$ 0 0
$$843$$ 19.3288 0.665721
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −24.8458 −0.853711
$$848$$ 0 0
$$849$$ 24.6367 0.845530
$$850$$ 0 0
$$851$$ 3.10036 0.106279
$$852$$ 0 0
$$853$$ −1.39913 −0.0479053 −0.0239527 0.999713i $$-0.507625\pi$$
−0.0239527 + 0.999713i $$0.507625\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −3.68808 −0.125982 −0.0629912 0.998014i $$-0.520064\pi$$
−0.0629912 + 0.998014i $$0.520064\pi$$
$$858$$ 0 0
$$859$$ −16.0281 −0.546871 −0.273435 0.961890i $$-0.588160\pi$$
−0.273435 + 0.961890i $$0.588160\pi$$
$$860$$ 0 0
$$861$$ 27.1800 0.926291
$$862$$ 0 0
$$863$$ 35.0979 1.19475 0.597374 0.801963i $$-0.296211\pi$$
0.597374 + 0.801963i $$0.296211\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 54.2942 1.84393
$$868$$ 0 0
$$869$$ −5.36753 −0.182081
$$870$$ 0 0
$$871$$ −7.60781 −0.257781
$$872$$ 0 0
$$873$$ −48.2759 −1.63389
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 53.2491 1.79809 0.899046 0.437853i $$-0.144261\pi$$
0.899046 + 0.437853i $$0.144261\pi$$
$$878$$ 0 0
$$879$$ 43.6142 1.47107
$$880$$ 0 0
$$881$$ 40.8449 1.37610 0.688050 0.725663i $$-0.258467\pi$$
0.688050 + 0.725663i $$0.258467\pi$$
$$882$$ 0 0
$$883$$ 14.9288 0.502393 0.251196 0.967936i $$-0.419176\pi$$
0.251196 + 0.967936i $$0.419176\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −34.9975 −1.17510 −0.587550 0.809188i $$-0.699908\pi$$
−0.587550 + 0.809188i $$0.699908\pi$$
$$888$$ 0 0
$$889$$ −19.1496 −0.642259
$$890$$ 0 0
$$891$$ 20.4692 0.685742
$$892$$ 0 0
$$893$$ −14.7068 −0.492143
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 16.4349 0.548745
$$898$$ 0 0
$$899$$ −58.1104 −1.93809
$$900$$ 0 0
$$901$$ −4.26799 −0.142187
$$902$$ 0 0
$$903$$ 67.0793 2.23226
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 16.3920 0.544288 0.272144 0.962257i $$-0.412267\pi$$
0.272144 + 0.962257i $$0.412267\pi$$
$$908$$ 0 0
$$909$$ 99.3416 3.29495
$$910$$ 0 0
$$911$$ 44.1111 1.46147 0.730733 0.682663i $$-0.239178\pi$$
0.730733 + 0.682663i $$0.239178\pi$$
$$912$$ 0 0
$$913$$ −14.3825 −0.475991
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 31.3076 1.03387
$$918$$ 0 0
$$919$$ −28.5629 −0.942203 −0.471101 0.882079i $$-0.656143\pi$$
−0.471101 + 0.882079i $$0.656143\pi$$
$$920$$ 0 0
$$921$$ 32.4724 1.07000
$$922$$ 0 0
$$923$$ −42.3708 −1.39465
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −92.3813 −3.03420
$$928$$ 0 0
$$929$$ 16.2273 0.532400 0.266200 0.963918i $$-0.414232\pi$$
0.266200 + 0.963918i $$0.414232\pi$$
$$930$$ 0 0
$$931$$ −3.03948 −0.0996148
$$932$$ 0 0
$$933$$ −90.9372 −2.97715
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −5.65418 −0.184714 −0.0923571 0.995726i $$-0.529440\pi$$
−0.0923571 + 0.995726i $$0.529440\pi$$
$$938$$ 0 0
$$939$$ 46.5192 1.51810
$$940$$ 0 0
$$941$$ −25.6246 −0.835338 −0.417669 0.908599i $$-0.637153\pi$$
−0.417669 + 0.908599i $$0.637153\pi$$
$$942$$ 0 0
$$943$$ 3.47185 0.113059
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −0.248718 −0.00808223 −0.00404112 0.999992i $$-0.501286\pi$$
−0.00404112 + 0.999992i $$0.501286\pi$$
$$948$$ 0 0
$$949$$ −52.2820 −1.69715
$$950$$ 0 0
$$951$$ −47.5914 −1.54326
$$952$$ 0 0
$$953$$ −39.1737 −1.26896 −0.634481 0.772939i $$-0.718786\pi$$
−0.634481 + 0.772939i $$0.718786\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −22.8606 −0.738978
$$958$$ 0 0
$$959$$ 7.94423 0.256533
$$960$$ 0 0
$$961$$ 21.4435 0.691726
$$962$$ 0 0
$$963$$ −10.7704 −0.347073
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −2.04114 −0.0656386 −0.0328193 0.999461i $$-0.510449\pi$$
−0.0328193 + 0.999461i $$0.510449\pi$$
$$968$$ 0 0
$$969$$ −3.30290 −0.106105
$$970$$ 0 0
$$971$$ 13.6713 0.438734 0.219367 0.975642i $$-0.429601\pi$$
0.219367 + 0.975642i $$0.429601\pi$$
$$972$$ 0 0
$$973$$ 30.5387 0.979025
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 45.8777 1.46776 0.733878 0.679281i $$-0.237708\pi$$
0.733878 + 0.679281i $$0.237708\pi$$
$$978$$ 0 0
$$979$$ −15.5784 −0.497887
$$980$$ 0 0
$$981$$ −141.505 −4.51792
$$982$$ 0 0
$$983$$ 59.6356 1.90208 0.951039 0.309070i $$-0.100018\pi$$
0.951039 + 0.309070i $$0.100018\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 41.1418 1.30956
$$988$$ 0 0
$$989$$ 8.56841 0.272460
$$990$$ 0 0
$$991$$ 42.3396 1.34496 0.672480 0.740115i $$-0.265229\pi$$
0.672480 + 0.740115i $$0.265229\pi$$
$$992$$ 0 0
$$993$$ −64.8656 −2.05845
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −7.02379 −0.222446 −0.111223 0.993795i $$-0.535477\pi$$
−0.111223 + 0.993795i $$0.535477\pi$$
$$998$$ 0 0
$$999$$ 43.5504 1.37787
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 9200.2.a.cx.1.1 6
4.3 odd 2 2300.2.a.o.1.6 6
5.2 odd 4 1840.2.e.f.369.12 12
5.3 odd 4 1840.2.e.f.369.1 12
5.4 even 2 9200.2.a.cy.1.6 6
20.3 even 4 460.2.c.a.369.12 yes 12
20.7 even 4 460.2.c.a.369.1 12
20.19 odd 2 2300.2.a.n.1.1 6
60.23 odd 4 4140.2.f.b.829.4 12
60.47 odd 4 4140.2.f.b.829.3 12

By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.c.a.369.1 12 20.7 even 4
460.2.c.a.369.12 yes 12 20.3 even 4
1840.2.e.f.369.1 12 5.3 odd 4
1840.2.e.f.369.12 12 5.2 odd 4
2300.2.a.n.1.1 6 20.19 odd 2
2300.2.a.o.1.6 6 4.3 odd 2
4140.2.f.b.829.3 12 60.47 odd 4
4140.2.f.b.829.4 12 60.23 odd 4
9200.2.a.cx.1.1 6 1.1 even 1 trivial
9200.2.a.cy.1.6 6 5.4 even 2