# Properties

 Label 5850.2.a.k.1.1 Level $5850$ Weight $2$ Character 5850.1 Self dual yes Analytic conductor $46.712$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5850.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$46.7124851824$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1950) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 5850.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{11} -1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -5.00000 q^{17} -5.00000 q^{22} +1.00000 q^{26} -1.00000 q^{28} +7.00000 q^{29} -9.00000 q^{31} -1.00000 q^{32} +5.00000 q^{34} -8.00000 q^{37} +2.00000 q^{41} +8.00000 q^{43} +5.00000 q^{44} +9.00000 q^{47} -6.00000 q^{49} -1.00000 q^{52} -11.0000 q^{53} +1.00000 q^{56} -7.00000 q^{58} -1.00000 q^{59} -7.00000 q^{61} +9.00000 q^{62} +1.00000 q^{64} -15.0000 q^{67} -5.00000 q^{68} +8.00000 q^{71} +4.00000 q^{73} +8.00000 q^{74} -5.00000 q^{77} -4.00000 q^{79} -2.00000 q^{82} +9.00000 q^{83} -8.00000 q^{86} -5.00000 q^{88} -16.0000 q^{89} +1.00000 q^{91} -9.00000 q^{94} +2.00000 q^{97} +6.00000 q^{98} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −5.00000 −1.21268 −0.606339 0.795206i $$-0.707363\pi$$
−0.606339 + 0.795206i $$0.707363\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −5.00000 −1.06600
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 1.00000 0.196116
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ 7.00000 1.29987 0.649934 0.759991i $$-0.274797\pi$$
0.649934 + 0.759991i $$0.274797\pi$$
$$30$$ 0 0
$$31$$ −9.00000 −1.61645 −0.808224 0.588875i $$-0.799571\pi$$
−0.808224 + 0.588875i $$0.799571\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 5.00000 0.857493
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 5.00000 0.753778
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 9.00000 1.31278 0.656392 0.754420i $$-0.272082\pi$$
0.656392 + 0.754420i $$0.272082\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −1.00000 −0.138675
$$53$$ −11.0000 −1.51097 −0.755483 0.655168i $$-0.772598\pi$$
−0.755483 + 0.655168i $$0.772598\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ −7.00000 −0.919145
$$59$$ −1.00000 −0.130189 −0.0650945 0.997879i $$-0.520735\pi$$
−0.0650945 + 0.997879i $$0.520735\pi$$
$$60$$ 0 0
$$61$$ −7.00000 −0.896258 −0.448129 0.893969i $$-0.647910\pi$$
−0.448129 + 0.893969i $$0.647910\pi$$
$$62$$ 9.00000 1.14300
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −15.0000 −1.83254 −0.916271 0.400559i $$-0.868816\pi$$
−0.916271 + 0.400559i $$0.868816\pi$$
$$68$$ −5.00000 −0.606339
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ 0 0
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 8.00000 0.929981
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −5.00000 −0.569803
$$78$$ 0 0
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −2.00000 −0.220863
$$83$$ 9.00000 0.987878 0.493939 0.869496i $$-0.335557\pi$$
0.493939 + 0.869496i $$0.335557\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −8.00000 −0.862662
$$87$$ 0 0
$$88$$ −5.00000 −0.533002
$$89$$ −16.0000 −1.69600 −0.847998 0.529999i $$-0.822192\pi$$
−0.847998 + 0.529999i $$0.822192\pi$$
$$90$$ 0 0
$$91$$ 1.00000 0.104828
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −9.00000 −0.928279
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ 6.00000 0.606092
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 7.00000 0.696526 0.348263 0.937397i $$-0.386772\pi$$
0.348263 + 0.937397i $$0.386772\pi$$
$$102$$ 0 0
$$103$$ 6.00000 0.591198 0.295599 0.955312i $$-0.404481\pi$$
0.295599 + 0.955312i $$0.404481\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ 0 0
$$106$$ 11.0000 1.06841
$$107$$ −6.00000 −0.580042 −0.290021 0.957020i $$-0.593662\pi$$
−0.290021 + 0.957020i $$0.593662\pi$$
$$108$$ 0 0
$$109$$ 6.00000 0.574696 0.287348 0.957826i $$-0.407226\pi$$
0.287348 + 0.957826i $$0.407226\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −1.00000 −0.0944911
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 7.00000 0.649934
$$117$$ 0 0
$$118$$ 1.00000 0.0920575
$$119$$ 5.00000 0.458349
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ 7.00000 0.633750
$$123$$ 0 0
$$124$$ −9.00000 −0.808224
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2.00000 0.174741 0.0873704 0.996176i $$-0.472154\pi$$
0.0873704 + 0.996176i $$0.472154\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 15.0000 1.29580
$$135$$ 0 0
$$136$$ 5.00000 0.428746
$$137$$ −12.0000 −1.02523 −0.512615 0.858619i $$-0.671323\pi$$
−0.512615 + 0.858619i $$0.671323\pi$$
$$138$$ 0 0
$$139$$ −2.00000 −0.169638 −0.0848189 0.996396i $$-0.527031\pi$$
−0.0848189 + 0.996396i $$0.527031\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −8.00000 −0.671345
$$143$$ −5.00000 −0.418121
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ −8.00000 −0.657596
$$149$$ 22.0000 1.80231 0.901155 0.433497i $$-0.142720\pi$$
0.901155 + 0.433497i $$0.142720\pi$$
$$150$$ 0 0
$$151$$ −21.0000 −1.70896 −0.854478 0.519488i $$-0.826123\pi$$
−0.854478 + 0.519488i $$0.826123\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 5.00000 0.402911
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −5.00000 −0.399043 −0.199522 0.979893i $$-0.563939\pi$$
−0.199522 + 0.979893i $$0.563939\pi$$
$$158$$ 4.00000 0.318223
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 2.00000 0.156174
$$165$$ 0 0
$$166$$ −9.00000 −0.698535
$$167$$ 4.00000 0.309529 0.154765 0.987951i $$-0.450538\pi$$
0.154765 + 0.987951i $$0.450538\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ 11.0000 0.836315 0.418157 0.908375i $$-0.362676\pi$$
0.418157 + 0.908375i $$0.362676\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 5.00000 0.376889
$$177$$ 0 0
$$178$$ 16.0000 1.19925
$$179$$ −2.00000 −0.149487 −0.0747435 0.997203i $$-0.523814\pi$$
−0.0747435 + 0.997203i $$0.523814\pi$$
$$180$$ 0 0
$$181$$ −11.0000 −0.817624 −0.408812 0.912619i $$-0.634057\pi$$
−0.408812 + 0.912619i $$0.634057\pi$$
$$182$$ −1.00000 −0.0741249
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −25.0000 −1.82818
$$188$$ 9.00000 0.656392
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −18.0000 −1.30243 −0.651217 0.758891i $$-0.725741\pi$$
−0.651217 + 0.758891i $$0.725741\pi$$
$$192$$ 0 0
$$193$$ −10.0000 −0.719816 −0.359908 0.932988i $$-0.617192\pi$$
−0.359908 + 0.932988i $$0.617192\pi$$
$$194$$ −2.00000 −0.143592
$$195$$ 0 0
$$196$$ −6.00000 −0.428571
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ 18.0000 1.27599 0.637993 0.770042i $$-0.279765\pi$$
0.637993 + 0.770042i $$0.279765\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −7.00000 −0.492518
$$203$$ −7.00000 −0.491304
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −6.00000 −0.418040
$$207$$ 0 0
$$208$$ −1.00000 −0.0693375
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 16.0000 1.10149 0.550743 0.834675i $$-0.314345\pi$$
0.550743 + 0.834675i $$0.314345\pi$$
$$212$$ −11.0000 −0.755483
$$213$$ 0 0
$$214$$ 6.00000 0.410152
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 9.00000 0.610960
$$218$$ −6.00000 −0.406371
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 5.00000 0.336336
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ 2.00000 0.133038
$$227$$ −29.0000 −1.92480 −0.962399 0.271640i $$-0.912434\pi$$
−0.962399 + 0.271640i $$0.912434\pi$$
$$228$$ 0 0
$$229$$ −2.00000 −0.132164 −0.0660819 0.997814i $$-0.521050\pi$$
−0.0660819 + 0.997814i $$0.521050\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −7.00000 −0.459573
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −1.00000 −0.0650945
$$237$$ 0 0
$$238$$ −5.00000 −0.324102
$$239$$ −1.00000 −0.0646846 −0.0323423 0.999477i $$-0.510297\pi$$
−0.0323423 + 0.999477i $$0.510297\pi$$
$$240$$ 0 0
$$241$$ −22.0000 −1.41714 −0.708572 0.705638i $$-0.750660\pi$$
−0.708572 + 0.705638i $$0.750660\pi$$
$$242$$ −14.0000 −0.899954
$$243$$ 0 0
$$244$$ −7.00000 −0.448129
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 9.00000 0.571501
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 6.00000 0.378717 0.189358 0.981908i $$-0.439359\pi$$
0.189358 + 0.981908i $$0.439359\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 8.00000 0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −27.0000 −1.68421 −0.842107 0.539311i $$-0.818685\pi$$
−0.842107 + 0.539311i $$0.818685\pi$$
$$258$$ 0 0
$$259$$ 8.00000 0.497096
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −2.00000 −0.123560
$$263$$ −26.0000 −1.60323 −0.801614 0.597841i $$-0.796025\pi$$
−0.801614 + 0.597841i $$0.796025\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −15.0000 −0.916271
$$269$$ −9.00000 −0.548740 −0.274370 0.961624i $$-0.588469\pi$$
−0.274370 + 0.961624i $$0.588469\pi$$
$$270$$ 0 0
$$271$$ 7.00000 0.425220 0.212610 0.977137i $$-0.431804\pi$$
0.212610 + 0.977137i $$0.431804\pi$$
$$272$$ −5.00000 −0.303170
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 26.0000 1.56219 0.781094 0.624413i $$-0.214662\pi$$
0.781094 + 0.624413i $$0.214662\pi$$
$$278$$ 2.00000 0.119952
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −30.0000 −1.78965 −0.894825 0.446417i $$-0.852700\pi$$
−0.894825 + 0.446417i $$0.852700\pi$$
$$282$$ 0 0
$$283$$ −22.0000 −1.30776 −0.653882 0.756596i $$-0.726861\pi$$
−0.653882 + 0.756596i $$0.726861\pi$$
$$284$$ 8.00000 0.474713
$$285$$ 0 0
$$286$$ 5.00000 0.295656
$$287$$ −2.00000 −0.118056
$$288$$ 0 0
$$289$$ 8.00000 0.470588
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 4.00000 0.234082
$$293$$ 14.0000 0.817889 0.408944 0.912559i $$-0.365897\pi$$
0.408944 + 0.912559i $$0.365897\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 8.00000 0.464991
$$297$$ 0 0
$$298$$ −22.0000 −1.27443
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 21.0000 1.20841
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 12.0000 0.684876 0.342438 0.939540i $$-0.388747\pi$$
0.342438 + 0.939540i $$0.388747\pi$$
$$308$$ −5.00000 −0.284901
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 18.0000 1.02069 0.510343 0.859971i $$-0.329518\pi$$
0.510343 + 0.859971i $$0.329518\pi$$
$$312$$ 0 0
$$313$$ 21.0000 1.18699 0.593495 0.804838i $$-0.297748\pi$$
0.593495 + 0.804838i $$0.297748\pi$$
$$314$$ 5.00000 0.282166
$$315$$ 0 0
$$316$$ −4.00000 −0.225018
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 35.0000 1.95962
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 4.00000 0.221540
$$327$$ 0 0
$$328$$ −2.00000 −0.110432
$$329$$ −9.00000 −0.496186
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ 9.00000 0.493939
$$333$$ 0 0
$$334$$ −4.00000 −0.218870
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −13.0000 −0.708155 −0.354078 0.935216i $$-0.615205\pi$$
−0.354078 + 0.935216i $$0.615205\pi$$
$$338$$ −1.00000 −0.0543928
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −45.0000 −2.43689
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ −8.00000 −0.431331
$$345$$ 0 0
$$346$$ −11.0000 −0.591364
$$347$$ 6.00000 0.322097 0.161048 0.986947i $$-0.448512\pi$$
0.161048 + 0.986947i $$0.448512\pi$$
$$348$$ 0 0
$$349$$ 32.0000 1.71292 0.856460 0.516213i $$-0.172659\pi$$
0.856460 + 0.516213i $$0.172659\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −5.00000 −0.266501
$$353$$ 2.00000 0.106449 0.0532246 0.998583i $$-0.483050\pi$$
0.0532246 + 0.998583i $$0.483050\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −16.0000 −0.847998
$$357$$ 0 0
$$358$$ 2.00000 0.105703
$$359$$ −27.0000 −1.42501 −0.712503 0.701669i $$-0.752438\pi$$
−0.712503 + 0.701669i $$0.752438\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 11.0000 0.578147
$$363$$ 0 0
$$364$$ 1.00000 0.0524142
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −36.0000 −1.87918 −0.939592 0.342296i $$-0.888796\pi$$
−0.939592 + 0.342296i $$0.888796\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 11.0000 0.571092
$$372$$ 0 0
$$373$$ −17.0000 −0.880227 −0.440113 0.897942i $$-0.645062\pi$$
−0.440113 + 0.897942i $$0.645062\pi$$
$$374$$ 25.0000 1.29272
$$375$$ 0 0
$$376$$ −9.00000 −0.464140
$$377$$ −7.00000 −0.360518
$$378$$ 0 0
$$379$$ −15.0000 −0.770498 −0.385249 0.922813i $$-0.625884\pi$$
−0.385249 + 0.922813i $$0.625884\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 18.0000 0.920960
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 10.0000 0.508987
$$387$$ 0 0
$$388$$ 2.00000 0.101535
$$389$$ −2.00000 −0.101404 −0.0507020 0.998714i $$-0.516146\pi$$
−0.0507020 + 0.998714i $$0.516146\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 6.00000 0.303046
$$393$$ 0 0
$$394$$ 6.00000 0.302276
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −34.0000 −1.70641 −0.853206 0.521575i $$-0.825345\pi$$
−0.853206 + 0.521575i $$0.825345\pi$$
$$398$$ −18.0000 −0.902258
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 9.00000 0.448322
$$404$$ 7.00000 0.348263
$$405$$ 0 0
$$406$$ 7.00000 0.347404
$$407$$ −40.0000 −1.98273
$$408$$ 0 0
$$409$$ −14.0000 −0.692255 −0.346128 0.938187i $$-0.612504\pi$$
−0.346128 + 0.938187i $$0.612504\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 6.00000 0.295599
$$413$$ 1.00000 0.0492068
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.00000 0.0490290
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 2.00000 0.0977064 0.0488532 0.998806i $$-0.484443\pi$$
0.0488532 + 0.998806i $$0.484443\pi$$
$$420$$ 0 0
$$421$$ 28.0000 1.36464 0.682318 0.731055i $$-0.260972\pi$$
0.682318 + 0.731055i $$0.260972\pi$$
$$422$$ −16.0000 −0.778868
$$423$$ 0 0
$$424$$ 11.0000 0.534207
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 7.00000 0.338754
$$428$$ −6.00000 −0.290021
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ 34.0000 1.63394 0.816968 0.576683i $$-0.195653\pi$$
0.816968 + 0.576683i $$0.195653\pi$$
$$434$$ −9.00000 −0.432014
$$435$$ 0 0
$$436$$ 6.00000 0.287348
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 4.00000 0.190910 0.0954548 0.995434i $$-0.469569\pi$$
0.0954548 + 0.995434i $$0.469569\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −5.00000 −0.237826
$$443$$ 32.0000 1.52037 0.760183 0.649709i $$-0.225109\pi$$
0.760183 + 0.649709i $$0.225109\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −16.0000 −0.757622
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ −36.0000 −1.69895 −0.849473 0.527633i $$-0.823080\pi$$
−0.849473 + 0.527633i $$0.823080\pi$$
$$450$$ 0 0
$$451$$ 10.0000 0.470882
$$452$$ −2.00000 −0.0940721
$$453$$ 0 0
$$454$$ 29.0000 1.36104
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2.00000 0.0935561 0.0467780 0.998905i $$-0.485105\pi$$
0.0467780 + 0.998905i $$0.485105\pi$$
$$458$$ 2.00000 0.0934539
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ −11.0000 −0.511213 −0.255607 0.966781i $$-0.582275\pi$$
−0.255607 + 0.966781i $$0.582275\pi$$
$$464$$ 7.00000 0.324967
$$465$$ 0 0
$$466$$ 6.00000 0.277945
$$467$$ 32.0000 1.48078 0.740392 0.672176i $$-0.234640\pi$$
0.740392 + 0.672176i $$0.234640\pi$$
$$468$$ 0 0
$$469$$ 15.0000 0.692636
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.00000 0.0460287
$$473$$ 40.0000 1.83920
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 5.00000 0.229175
$$477$$ 0 0
$$478$$ 1.00000 0.0457389
$$479$$ −29.0000 −1.32504 −0.662522 0.749043i $$-0.730514\pi$$
−0.662522 + 0.749043i $$0.730514\pi$$
$$480$$ 0 0
$$481$$ 8.00000 0.364769
$$482$$ 22.0000 1.00207
$$483$$ 0 0
$$484$$ 14.0000 0.636364
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −1.00000 −0.0453143 −0.0226572 0.999743i $$-0.507213\pi$$
−0.0226572 + 0.999743i $$0.507213\pi$$
$$488$$ 7.00000 0.316875
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −30.0000 −1.35388 −0.676941 0.736038i $$-0.736695\pi$$
−0.676941 + 0.736038i $$0.736695\pi$$
$$492$$ 0 0
$$493$$ −35.0000 −1.57632
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −9.00000 −0.404112
$$497$$ −8.00000 −0.358849
$$498$$ 0 0
$$499$$ 11.0000 0.492428 0.246214 0.969216i $$-0.420813\pi$$
0.246214 + 0.969216i $$0.420813\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −6.00000 −0.267793
$$503$$ 2.00000 0.0891756 0.0445878 0.999005i $$-0.485803\pi$$
0.0445878 + 0.999005i $$0.485803\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −8.00000 −0.354943
$$509$$ −6.00000 −0.265945 −0.132973 0.991120i $$-0.542452\pi$$
−0.132973 + 0.991120i $$0.542452\pi$$
$$510$$ 0 0
$$511$$ −4.00000 −0.176950
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 27.0000 1.19092
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 45.0000 1.97910
$$518$$ −8.00000 −0.351500
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 26.0000 1.13908 0.569540 0.821963i $$-0.307121\pi$$
0.569540 + 0.821963i $$0.307121\pi$$
$$522$$ 0 0
$$523$$ −18.0000 −0.787085 −0.393543 0.919306i $$-0.628751\pi$$
−0.393543 + 0.919306i $$0.628751\pi$$
$$524$$ 2.00000 0.0873704
$$525$$ 0 0
$$526$$ 26.0000 1.13365
$$527$$ 45.0000 1.96023
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −2.00000 −0.0866296
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 15.0000 0.647901
$$537$$ 0 0
$$538$$ 9.00000 0.388018
$$539$$ −30.0000 −1.29219
$$540$$ 0 0
$$541$$ 28.0000 1.20381 0.601907 0.798566i $$-0.294408\pi$$
0.601907 + 0.798566i $$0.294408\pi$$
$$542$$ −7.00000 −0.300676
$$543$$ 0 0
$$544$$ 5.00000 0.214373
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.00000 −0.0855138 −0.0427569 0.999086i $$-0.513614\pi$$
−0.0427569 + 0.999086i $$0.513614\pi$$
$$548$$ −12.0000 −0.512615
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 4.00000 0.170097
$$554$$ −26.0000 −1.10463
$$555$$ 0 0
$$556$$ −2.00000 −0.0848189
$$557$$ −2.00000 −0.0847427 −0.0423714 0.999102i $$-0.513491\pi$$
−0.0423714 + 0.999102i $$0.513491\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 30.0000 1.26547
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 22.0000 0.924729
$$567$$ 0 0
$$568$$ −8.00000 −0.335673
$$569$$ 9.00000 0.377300 0.188650 0.982044i $$-0.439589\pi$$
0.188650 + 0.982044i $$0.439589\pi$$
$$570$$ 0 0
$$571$$ −32.0000 −1.33916 −0.669579 0.742741i $$-0.733526\pi$$
−0.669579 + 0.742741i $$0.733526\pi$$
$$572$$ −5.00000 −0.209061
$$573$$ 0 0
$$574$$ 2.00000 0.0834784
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −42.0000 −1.74848 −0.874241 0.485491i $$-0.838641\pi$$
−0.874241 + 0.485491i $$0.838641\pi$$
$$578$$ −8.00000 −0.332756
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −9.00000 −0.373383
$$582$$ 0 0
$$583$$ −55.0000 −2.27787
$$584$$ −4.00000 −0.165521
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ 15.0000 0.619116 0.309558 0.950881i $$-0.399819\pi$$
0.309558 + 0.950881i $$0.399819\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −8.00000 −0.328798
$$593$$ −22.0000 −0.903432 −0.451716 0.892162i $$-0.649188\pi$$
−0.451716 + 0.892162i $$0.649188\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 22.0000 0.901155
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −6.00000 −0.245153 −0.122577 0.992459i $$-0.539116\pi$$
−0.122577 + 0.992459i $$0.539116\pi$$
$$600$$ 0 0
$$601$$ −35.0000 −1.42768 −0.713840 0.700309i $$-0.753046\pi$$
−0.713840 + 0.700309i $$0.753046\pi$$
$$602$$ 8.00000 0.326056
$$603$$ 0 0
$$604$$ −21.0000 −0.854478
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 2.00000 0.0811775 0.0405887 0.999176i $$-0.487077\pi$$
0.0405887 + 0.999176i $$0.487077\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −9.00000 −0.364101
$$612$$ 0 0
$$613$$ 2.00000 0.0807792 0.0403896 0.999184i $$-0.487140\pi$$
0.0403896 + 0.999184i $$0.487140\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ 0 0
$$616$$ 5.00000 0.201456
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ 0 0
$$619$$ −28.0000 −1.12542 −0.562708 0.826656i $$-0.690240\pi$$
−0.562708 + 0.826656i $$0.690240\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −18.0000 −0.721734
$$623$$ 16.0000 0.641026
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −21.0000 −0.839329
$$627$$ 0 0
$$628$$ −5.00000 −0.199522
$$629$$ 40.0000 1.59490
$$630$$ 0 0
$$631$$ −36.0000 −1.43314 −0.716569 0.697517i $$-0.754288\pi$$
−0.716569 + 0.697517i $$0.754288\pi$$
$$632$$ 4.00000 0.159111
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.00000 0.237729
$$638$$ −35.0000 −1.38566
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −33.0000 −1.30342 −0.651711 0.758468i $$-0.725948\pi$$
−0.651711 + 0.758468i $$0.725948\pi$$
$$642$$ 0 0
$$643$$ −28.0000 −1.10421 −0.552106 0.833774i $$-0.686176\pi$$
−0.552106 + 0.833774i $$0.686176\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 48.0000 1.88707 0.943537 0.331266i $$-0.107476\pi$$
0.943537 + 0.331266i $$0.107476\pi$$
$$648$$ 0 0
$$649$$ −5.00000 −0.196267
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ 27.0000 1.05659 0.528296 0.849060i $$-0.322831\pi$$
0.528296 + 0.849060i $$0.322831\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 2.00000 0.0780869
$$657$$ 0 0
$$658$$ 9.00000 0.350857
$$659$$ −44.0000 −1.71400 −0.856998 0.515319i $$-0.827673\pi$$
−0.856998 + 0.515319i $$0.827673\pi$$
$$660$$ 0 0
$$661$$ 30.0000 1.16686 0.583432 0.812162i $$-0.301709\pi$$
0.583432 + 0.812162i $$0.301709\pi$$
$$662$$ 20.0000 0.777322
$$663$$ 0 0
$$664$$ −9.00000 −0.349268
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 4.00000 0.154765
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −35.0000 −1.35116
$$672$$ 0 0
$$673$$ 11.0000 0.424019 0.212009 0.977268i $$-0.431999\pi$$
0.212009 + 0.977268i $$0.431999\pi$$
$$674$$ 13.0000 0.500741
$$675$$ 0 0
$$676$$ 1.00000 0.0384615
$$677$$ −18.0000 −0.691796 −0.345898 0.938272i $$-0.612426\pi$$
−0.345898 + 0.938272i $$0.612426\pi$$
$$678$$ 0 0
$$679$$ −2.00000 −0.0767530
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 45.0000 1.72314
$$683$$ −19.0000 −0.727015 −0.363507 0.931591i $$-0.618421\pi$$
−0.363507 + 0.931591i $$0.618421\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −13.0000 −0.496342
$$687$$ 0 0
$$688$$ 8.00000 0.304997
$$689$$ 11.0000 0.419067
$$690$$ 0 0
$$691$$ 7.00000 0.266293 0.133146 0.991096i $$-0.457492\pi$$
0.133146 + 0.991096i $$0.457492\pi$$
$$692$$ 11.0000 0.418157
$$693$$ 0 0
$$694$$ −6.00000 −0.227757
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −10.0000 −0.378777
$$698$$ −32.0000 −1.21122
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 25.0000 0.944237 0.472118 0.881535i $$-0.343489\pi$$
0.472118 + 0.881535i $$0.343489\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 5.00000 0.188445
$$705$$ 0 0
$$706$$ −2.00000 −0.0752710
$$707$$ −7.00000 −0.263262
$$708$$ 0 0
$$709$$ −46.0000 −1.72757 −0.863783 0.503864i $$-0.831911\pi$$
−0.863783 + 0.503864i $$0.831911\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 16.0000 0.599625
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −2.00000 −0.0747435
$$717$$ 0 0
$$718$$ 27.0000 1.00763
$$719$$ 18.0000 0.671287 0.335643 0.941989i $$-0.391046\pi$$
0.335643 + 0.941989i $$0.391046\pi$$
$$720$$ 0 0
$$721$$ −6.00000 −0.223452
$$722$$ 19.0000 0.707107
$$723$$ 0 0
$$724$$ −11.0000 −0.408812
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −38.0000 −1.40934 −0.704671 0.709534i $$-0.748905\pi$$
−0.704671 + 0.709534i $$0.748905\pi$$
$$728$$ −1.00000 −0.0370625
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −40.0000 −1.47945
$$732$$ 0 0
$$733$$ 20.0000 0.738717 0.369358 0.929287i $$-0.379577\pi$$
0.369358 + 0.929287i $$0.379577\pi$$
$$734$$ 36.0000 1.32878
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −75.0000 −2.76266
$$738$$ 0 0
$$739$$ 3.00000 0.110357 0.0551784 0.998477i $$-0.482427\pi$$
0.0551784 + 0.998477i $$0.482427\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −11.0000 −0.403823
$$743$$ −39.0000 −1.43077 −0.715386 0.698730i $$-0.753749\pi$$
−0.715386 + 0.698730i $$0.753749\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 17.0000 0.622414
$$747$$ 0 0
$$748$$ −25.0000 −0.914091
$$749$$ 6.00000 0.219235
$$750$$ 0 0
$$751$$ −40.0000 −1.45962 −0.729810 0.683650i $$-0.760392\pi$$
−0.729810 + 0.683650i $$0.760392\pi$$
$$752$$ 9.00000 0.328196
$$753$$ 0 0
$$754$$ 7.00000 0.254925
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 33.0000 1.19941 0.599703 0.800223i $$-0.295286\pi$$
0.599703 + 0.800223i $$0.295286\pi$$
$$758$$ 15.0000 0.544825
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 8.00000 0.290000 0.145000 0.989432i $$-0.453682\pi$$
0.145000 + 0.989432i $$0.453682\pi$$
$$762$$ 0 0
$$763$$ −6.00000 −0.217215
$$764$$ −18.0000 −0.651217
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1.00000 0.0361079
$$768$$ 0 0
$$769$$ −8.00000 −0.288487 −0.144244 0.989542i $$-0.546075\pi$$
−0.144244 + 0.989542i $$0.546075\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −10.0000 −0.359908
$$773$$ −14.0000 −0.503545 −0.251773 0.967786i $$-0.581013\pi$$
−0.251773 + 0.967786i $$0.581013\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −2.00000 −0.0717958
$$777$$ 0 0
$$778$$ 2.00000 0.0717035
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 40.0000 1.43131
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −6.00000 −0.214286
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −5.00000 −0.178231 −0.0891154 0.996021i $$-0.528404\pi$$
−0.0891154 + 0.996021i $$0.528404\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2.00000 0.0711118
$$792$$ 0 0
$$793$$ 7.00000 0.248577
$$794$$ 34.0000 1.20661
$$795$$ 0 0
$$796$$ 18.0000 0.637993
$$797$$ 13.0000 0.460484 0.230242 0.973133i $$-0.426048\pi$$
0.230242 + 0.973133i $$0.426048\pi$$
$$798$$ 0 0
$$799$$ −45.0000 −1.59199
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 20.0000 0.705785
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −9.00000 −0.317011
$$807$$ 0 0
$$808$$ −7.00000 −0.246259
$$809$$ 34.0000 1.19538 0.597688 0.801729i $$-0.296086\pi$$
0.597688 + 0.801729i $$0.296086\pi$$
$$810$$ 0 0
$$811$$ −29.0000 −1.01833 −0.509164 0.860670i $$-0.670045\pi$$
−0.509164 + 0.860670i $$0.670045\pi$$
$$812$$ −7.00000 −0.245652
$$813$$ 0 0
$$814$$ 40.0000 1.40200
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 14.0000 0.489499
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 16.0000 0.558404 0.279202 0.960232i $$-0.409930\pi$$
0.279202 + 0.960232i $$0.409930\pi$$
$$822$$ 0 0
$$823$$ −28.0000 −0.976019 −0.488009 0.872838i $$-0.662277\pi$$
−0.488009 + 0.872838i $$0.662277\pi$$
$$824$$ −6.00000 −0.209020
$$825$$ 0 0
$$826$$ −1.00000 −0.0347945
$$827$$ 21.0000 0.730242 0.365121 0.930960i $$-0.381028\pi$$
0.365121 + 0.930960i $$0.381028\pi$$
$$828$$ 0 0
$$829$$ −37.0000 −1.28506 −0.642532 0.766259i $$-0.722116\pi$$
−0.642532 + 0.766259i $$0.722116\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −1.00000 −0.0346688
$$833$$ 30.0000 1.03944
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ −2.00000 −0.0690889
$$839$$ 16.0000 0.552381 0.276191 0.961103i $$-0.410928\pi$$
0.276191 + 0.961103i $$0.410928\pi$$
$$840$$ 0 0
$$841$$ 20.0000 0.689655
$$842$$ −28.0000 −0.964944
$$843$$ 0 0
$$844$$ 16.0000 0.550743
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −14.0000 −0.481046
$$848$$ −11.0000 −0.377742
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −8.00000 −0.273915 −0.136957 0.990577i $$-0.543732\pi$$
−0.136957 + 0.990577i $$0.543732\pi$$
$$854$$ −7.00000 −0.239535
$$855$$ 0 0
$$856$$ 6.00000 0.205076
$$857$$ 26.0000 0.888143 0.444072 0.895991i $$-0.353534\pi$$
0.444072 + 0.895991i $$0.353534\pi$$
$$858$$ 0 0
$$859$$ 36.0000 1.22830 0.614152 0.789188i $$-0.289498\pi$$
0.614152 + 0.789188i $$0.289498\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 12.0000 0.408722
$$863$$ −27.0000 −0.919091 −0.459545 0.888154i $$-0.651988\pi$$
−0.459545 + 0.888154i $$0.651988\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ −34.0000 −1.15537
$$867$$ 0 0
$$868$$ 9.00000 0.305480
$$869$$ −20.0000 −0.678454
$$870$$ 0 0
$$871$$ 15.0000 0.508256
$$872$$ −6.00000 −0.203186
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 40.0000 1.35070 0.675352 0.737496i $$-0.263992\pi$$
0.675352 + 0.737496i $$0.263992\pi$$
$$878$$ −4.00000 −0.134993
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 33.0000 1.11180 0.555899 0.831250i $$-0.312374\pi$$
0.555899 + 0.831250i $$0.312374\pi$$
$$882$$ 0 0
$$883$$ 32.0000 1.07689 0.538443 0.842662i $$-0.319013\pi$$
0.538443 + 0.842662i $$0.319013\pi$$
$$884$$ 5.00000 0.168168
$$885$$ 0 0
$$886$$ −32.0000 −1.07506
$$887$$ −4.00000 −0.134307 −0.0671534 0.997743i $$-0.521392\pi$$
−0.0671534 + 0.997743i $$0.521392\pi$$
$$888$$ 0 0
$$889$$ 8.00000 0.268311
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 16.0000 0.535720
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 1.00000 0.0334077
$$897$$ 0 0
$$898$$ 36.0000 1.20134
$$899$$ −63.0000 −2.10117
$$900$$ 0 0
$$901$$ 55.0000 1.83232
$$902$$ −10.0000 −0.332964
$$903$$ 0 0
$$904$$ 2.00000 0.0665190
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 40.0000 1.32818 0.664089 0.747653i $$-0.268820\pi$$
0.664089 + 0.747653i $$0.268820\pi$$
$$908$$ −29.0000 −0.962399
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −40.0000 −1.32526 −0.662630 0.748947i $$-0.730560\pi$$
−0.662630 + 0.748947i $$0.730560\pi$$
$$912$$ 0 0
$$913$$ 45.0000 1.48928
$$914$$ −2.00000 −0.0661541
$$915$$ 0 0
$$916$$ −2.00000 −0.0660819
$$917$$ −2.00000 −0.0660458
$$918$$ 0 0
$$919$$ −50.0000 −1.64935 −0.824674 0.565608i $$-0.808641\pi$$
−0.824674 + 0.565608i $$0.808641\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −6.00000 −0.197599
$$923$$ −8.00000 −0.263323
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 11.0000 0.361482
$$927$$ 0 0
$$928$$ −7.00000 −0.229786
$$929$$ 42.0000 1.37798 0.688988 0.724773i $$-0.258055\pi$$
0.688988 + 0.724773i $$0.258055\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −6.00000 −0.196537
$$933$$ 0 0
$$934$$ −32.0000 −1.04707
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 51.0000 1.66610 0.833049 0.553200i $$-0.186593\pi$$
0.833049 + 0.553200i $$0.186593\pi$$
$$938$$ −15.0000 −0.489767
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −8.00000 −0.260793 −0.130396 0.991462i $$-0.541625\pi$$
−0.130396 + 0.991462i $$0.541625\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −1.00000 −0.0325472
$$945$$ 0 0
$$946$$ −40.0000 −1.30051
$$947$$ 41.0000 1.33232 0.666160 0.745808i $$-0.267937\pi$$
0.666160 + 0.745808i $$0.267937\pi$$
$$948$$ 0 0
$$949$$ −4.00000 −0.129845
$$950$$ 0 0
$$951$$ 0 0
$$952$$ −5.00000 −0.162051
$$953$$ −51.0000 −1.65205 −0.826026 0.563632i $$-0.809404\pi$$
−0.826026 + 0.563632i $$0.809404\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −1.00000 −0.0323423
$$957$$ 0 0
$$958$$ 29.0000 0.936947
$$959$$ 12.0000 0.387500
$$960$$ 0 0
$$961$$ 50.0000 1.61290
$$962$$ −8.00000 −0.257930
$$963$$ 0 0
$$964$$ −22.0000 −0.708572
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −17.0000 −0.546683 −0.273342 0.961917i $$-0.588129\pi$$
−0.273342 + 0.961917i $$0.588129\pi$$
$$968$$ −14.0000 −0.449977
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 34.0000 1.09111 0.545556 0.838074i $$-0.316319\pi$$
0.545556 + 0.838074i $$0.316319\pi$$
$$972$$ 0 0
$$973$$ 2.00000 0.0641171
$$974$$ 1.00000 0.0320421
$$975$$ 0 0
$$976$$ −7.00000 −0.224065
$$977$$ 12.0000 0.383914 0.191957 0.981403i $$-0.438517\pi$$
0.191957 + 0.981403i $$0.438517\pi$$
$$978$$ 0 0
$$979$$ −80.0000 −2.55681
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 30.0000 0.957338
$$983$$ 31.0000 0.988746 0.494373 0.869250i $$-0.335398\pi$$
0.494373 + 0.869250i $$0.335398\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 35.0000 1.11463
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 36.0000 1.14358 0.571789 0.820401i $$-0.306250\pi$$
0.571789 + 0.820401i $$0.306250\pi$$
$$992$$ 9.00000 0.285750
$$993$$ 0 0
$$994$$ 8.00000 0.253745
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −11.0000 −0.348373 −0.174187 0.984713i $$-0.555730\pi$$
−0.174187 + 0.984713i $$0.555730\pi$$
$$998$$ −11.0000 −0.348199
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 5850.2.a.k.1.1 1
3.2 odd 2 1950.2.a.p.1.1 yes 1
5.2 odd 4 5850.2.e.be.5149.1 2
5.3 odd 4 5850.2.e.be.5149.2 2
5.4 even 2 5850.2.a.bu.1.1 1
15.2 even 4 1950.2.e.a.1249.2 2
15.8 even 4 1950.2.e.a.1249.1 2
15.14 odd 2 1950.2.a.l.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1950.2.a.l.1.1 1 15.14 odd 2
1950.2.a.p.1.1 yes 1 3.2 odd 2
1950.2.e.a.1249.1 2 15.8 even 4
1950.2.e.a.1249.2 2 15.2 even 4
5850.2.a.k.1.1 1 1.1 even 1 trivial
5850.2.a.bu.1.1 1 5.4 even 2
5850.2.e.be.5149.1 2 5.2 odd 4
5850.2.e.be.5149.2 2 5.3 odd 4