# Properties

 Label 6048.2.c.b.3025.1 Level 6048 Weight 2 Character 6048.3025 Analytic conductor 48.294 Analytic rank 0 Dimension 2 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ = $$6048 = 2^{5} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 6048.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$48.2935231425$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1512) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 3025.1 Root $$-1.00000i$$ Character $$\chi$$ = 6048.3025 Dual form 6048.2.c.b.3025.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000i q^{5} +1.00000 q^{7} +O(q^{10})$$ $$q-2.00000i q^{5} +1.00000 q^{7} -5.00000i q^{13} +1.00000 q^{17} +4.00000i q^{19} +5.00000 q^{23} +1.00000 q^{25} +9.00000i q^{29} +7.00000 q^{31} -2.00000i q^{35} -2.00000i q^{37} +2.00000 q^{41} +5.00000i q^{43} +1.00000 q^{49} +9.00000i q^{53} +1.00000i q^{59} -6.00000i q^{61} -10.0000 q^{65} -9.00000i q^{67} +15.0000 q^{71} +14.0000 q^{79} +4.00000i q^{83} -2.00000i q^{85} -13.0000 q^{89} -5.00000i q^{91} +8.00000 q^{95} -14.0000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{7} + O(q^{10})$$ $$2q + 2q^{7} + 2q^{17} + 10q^{23} + 2q^{25} + 14q^{31} + 4q^{41} + 2q^{49} - 20q^{65} + 30q^{71} + 28q^{79} - 26q^{89} + 16q^{95} - 28q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times$$.

 $$n$$ $$2593$$ $$3781$$ $$3809$$ $$4159$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ − 2.00000i − 0.894427i −0.894427 0.447214i $$-0.852416\pi$$
0.894427 0.447214i $$-0.147584\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ − 5.00000i − 1.38675i −0.720577 0.693375i $$-0.756123\pi$$
0.720577 0.693375i $$-0.243877\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.00000 0.242536 0.121268 0.992620i $$-0.461304\pi$$
0.121268 + 0.992620i $$0.461304\pi$$
$$18$$ 0 0
$$19$$ 4.00000i 0.917663i 0.888523 + 0.458831i $$0.151732\pi$$
−0.888523 + 0.458831i $$0.848268\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 5.00000 1.04257 0.521286 0.853382i $$-0.325452\pi$$
0.521286 + 0.853382i $$0.325452\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 9.00000i 1.67126i 0.549294 + 0.835629i $$0.314897\pi$$
−0.549294 + 0.835629i $$0.685103\pi$$
$$30$$ 0 0
$$31$$ 7.00000 1.25724 0.628619 0.777714i $$-0.283621\pi$$
0.628619 + 0.777714i $$0.283621\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ − 2.00000i − 0.338062i
$$36$$ 0 0
$$37$$ − 2.00000i − 0.328798i −0.986394 0.164399i $$-0.947432\pi$$
0.986394 0.164399i $$-0.0525685\pi$$
$$38$$ 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
$$43$$ 5.00000i 0.762493i 0.924473 + 0.381246i $$0.124505\pi$$
−0.924473 + 0.381246i $$0.875495\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 9.00000i 1.23625i 0.786082 + 0.618123i $$0.212106\pi$$
−0.786082 + 0.618123i $$0.787894\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 1.00000i 0.130189i 0.997879 + 0.0650945i $$0.0207349\pi$$
−0.997879 + 0.0650945i $$0.979265\pi$$
$$60$$ 0 0
$$61$$ − 6.00000i − 0.768221i −0.923287 0.384111i $$-0.874508\pi$$
0.923287 0.384111i $$-0.125492\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −10.0000 −1.24035
$$66$$ 0 0
$$67$$ − 9.00000i − 1.09952i −0.835321 0.549762i $$-0.814718\pi$$
0.835321 0.549762i $$-0.185282\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 15.0000 1.78017 0.890086 0.455792i $$-0.150644\pi$$
0.890086 + 0.455792i $$0.150644\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 14.0000 1.57512 0.787562 0.616236i $$-0.211343\pi$$
0.787562 + 0.616236i $$0.211343\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 4.00000i 0.439057i 0.975606 + 0.219529i $$0.0704519\pi$$
−0.975606 + 0.219529i $$0.929548\pi$$
$$84$$ 0 0
$$85$$ − 2.00000i − 0.216930i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −13.0000 −1.37800 −0.688999 0.724763i $$-0.741949\pi$$
−0.688999 + 0.724763i $$0.741949\pi$$
$$90$$ 0 0
$$91$$ − 5.00000i − 0.524142i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 8.00000 0.820783
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ − 8.00000i − 0.796030i −0.917379 0.398015i $$-0.869699\pi$$
0.917379 0.398015i $$-0.130301\pi$$
$$102$$ 0 0
$$103$$ 3.00000 0.295599 0.147799 0.989017i $$-0.452781\pi$$
0.147799 + 0.989017i $$0.452781\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ − 16.0000i − 1.53252i −0.642529 0.766261i $$-0.722115\pi$$
0.642529 0.766261i $$-0.277885\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ − 10.0000i − 0.932505i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 1.00000 0.0916698
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ − 12.0000i − 1.07331i
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 13.0000i 1.13582i 0.823092 + 0.567908i $$0.192247\pi$$
−0.823092 + 0.567908i $$0.807753\pi$$
$$132$$ 0 0
$$133$$ 4.00000i 0.346844i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −12.0000 −1.02523 −0.512615 0.858619i $$-0.671323\pi$$
−0.512615 + 0.858619i $$0.671323\pi$$
$$138$$ 0 0
$$139$$ − 20.0000i − 1.69638i −0.529694 0.848189i $$-0.677693\pi$$
0.529694 0.848189i $$-0.322307\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 18.0000 1.49482
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ − 9.00000i − 0.737309i −0.929567 0.368654i $$-0.879819\pi$$
0.929567 0.368654i $$-0.120181\pi$$
$$150$$ 0 0
$$151$$ −12.0000 −0.976546 −0.488273 0.872691i $$-0.662373\pi$$
−0.488273 + 0.872691i $$0.662373\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ − 14.0000i − 1.12451i
$$156$$ 0 0
$$157$$ 13.0000i 1.03751i 0.854922 + 0.518756i $$0.173605\pi$$
−0.854922 + 0.518756i $$0.826395\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 5.00000 0.394055
$$162$$ 0 0
$$163$$ 11.0000i 0.861586i 0.902451 + 0.430793i $$0.141766\pi$$
−0.902451 + 0.430793i $$0.858234\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 4.00000 0.309529 0.154765 0.987951i $$-0.450538\pi$$
0.154765 + 0.987951i $$0.450538\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ − 6.00000i − 0.456172i −0.973641 0.228086i $$-0.926753\pi$$
0.973641 0.228086i $$-0.0732467\pi$$
$$174$$ 0 0
$$175$$ 1.00000 0.0755929
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 10.0000i 0.747435i 0.927543 + 0.373718i $$0.121917\pi$$
−0.927543 + 0.373718i $$0.878083\pi$$
$$180$$ 0 0
$$181$$ − 19.0000i − 1.41226i −0.708083 0.706129i $$-0.750440\pi$$
0.708083 0.706129i $$-0.249560\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −4.00000 −0.294086
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4.00000 −0.289430 −0.144715 0.989473i $$-0.546227\pi$$
−0.144715 + 0.989473i $$0.546227\pi$$
$$192$$ 0 0
$$193$$ 9.00000 0.647834 0.323917 0.946085i $$-0.395000\pi$$
0.323917 + 0.946085i $$0.395000\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 14.0000i 0.997459i 0.866758 + 0.498729i $$0.166200\pi$$
−0.866758 + 0.498729i $$0.833800\pi$$
$$198$$ 0 0
$$199$$ −13.0000 −0.921546 −0.460773 0.887518i $$-0.652428\pi$$
−0.460773 + 0.887518i $$0.652428\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 9.00000i 0.631676i
$$204$$ 0 0
$$205$$ − 4.00000i − 0.279372i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ − 1.00000i − 0.0688428i −0.999407 0.0344214i $$-0.989041\pi$$
0.999407 0.0344214i $$-0.0109588\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 10.0000 0.681994
$$216$$ 0 0
$$217$$ 7.00000 0.475191
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ − 5.00000i − 0.336336i
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ − 25.0000i − 1.65931i −0.558278 0.829654i $$-0.688538\pi$$
0.558278 0.829654i $$-0.311462\pi$$
$$228$$ 0 0
$$229$$ − 10.0000i − 0.660819i −0.943838 0.330409i $$-0.892813\pi$$
0.943838 0.330409i $$-0.107187\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −10.0000 −0.655122 −0.327561 0.944830i $$-0.606227\pi$$
−0.327561 + 0.944830i $$0.606227\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −24.0000 −1.55243 −0.776215 0.630468i $$-0.782863\pi$$
−0.776215 + 0.630468i $$0.782863\pi$$
$$240$$ 0 0
$$241$$ 26.0000 1.67481 0.837404 0.546585i $$-0.184072\pi$$
0.837404 + 0.546585i $$0.184072\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ − 2.00000i − 0.127775i
$$246$$ 0 0
$$247$$ 20.0000 1.27257
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 12.0000i 0.757433i 0.925513 + 0.378717i $$0.123635\pi$$
−0.925513 + 0.378717i $$0.876365\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 0 0
$$259$$ − 2.00000i − 0.124274i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 31.0000 1.91154 0.955771 0.294112i $$-0.0950239\pi$$
0.955771 + 0.294112i $$0.0950239\pi$$
$$264$$ 0 0
$$265$$ 18.0000 1.10573
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 15.0000 0.911185 0.455593 0.890188i $$-0.349427\pi$$
0.455593 + 0.890188i $$0.349427\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 26.0000i 1.56219i 0.624413 + 0.781094i $$0.285338\pi$$
−0.624413 + 0.781094i $$0.714662\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ − 16.0000i − 0.951101i −0.879688 0.475551i $$-0.842249\pi$$
0.879688 0.475551i $$-0.157751\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 2.00000 0.118056
$$288$$ 0 0
$$289$$ −16.0000 −0.941176
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 12.0000i 0.701047i 0.936554 + 0.350524i $$0.113996\pi$$
−0.936554 + 0.350524i $$0.886004\pi$$
$$294$$ 0 0
$$295$$ 2.00000 0.116445
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ − 25.0000i − 1.44579i
$$300$$ 0 0
$$301$$ 5.00000i 0.288195i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −12.0000 −0.687118
$$306$$ 0 0
$$307$$ 6.00000i 0.342438i 0.985233 + 0.171219i $$0.0547706\pi$$
−0.985233 + 0.171219i $$0.945229\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −34.0000 −1.92796 −0.963982 0.265969i $$-0.914308\pi$$
−0.963982 + 0.265969i $$0.914308\pi$$
$$312$$ 0 0
$$313$$ 32.0000 1.80875 0.904373 0.426742i $$-0.140339\pi$$
0.904373 + 0.426742i $$0.140339\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ − 14.0000i − 0.786318i −0.919470 0.393159i $$-0.871382\pi$$
0.919470 0.393159i $$-0.128618\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 4.00000i 0.222566i
$$324$$ 0 0
$$325$$ − 5.00000i − 0.277350i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ − 13.0000i − 0.714545i −0.934000 0.357272i $$-0.883707\pi$$
0.934000 0.357272i $$-0.116293\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −18.0000 −0.983445
$$336$$ 0 0
$$337$$ 19.0000 1.03500 0.517498 0.855684i $$-0.326864\pi$$
0.517498 + 0.855684i $$0.326864\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ − 16.0000i − 0.858925i −0.903085 0.429463i $$-0.858703\pi$$
0.903085 0.429463i $$-0.141297\pi$$
$$348$$ 0 0
$$349$$ − 23.0000i − 1.23116i −0.788074 0.615581i $$-0.788921\pi$$
0.788074 0.615581i $$-0.211079\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −33.0000 −1.75641 −0.878206 0.478282i $$-0.841260\pi$$
−0.878206 + 0.478282i $$0.841260\pi$$
$$354$$ 0 0
$$355$$ − 30.0000i − 1.59223i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1.00000 −0.0527780 −0.0263890 0.999652i $$-0.508401\pi$$
−0.0263890 + 0.999652i $$0.508401\pi$$
$$360$$ 0 0
$$361$$ 3.00000 0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −21.0000 −1.09619 −0.548096 0.836416i $$-0.684647\pi$$
−0.548096 + 0.836416i $$0.684647\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 9.00000i 0.467257i
$$372$$ 0 0
$$373$$ − 22.0000i − 1.13912i −0.821951 0.569558i $$-0.807114\pi$$
0.821951 0.569558i $$-0.192886\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 45.0000 2.31762
$$378$$ 0 0
$$379$$ 16.0000i 0.821865i 0.911666 + 0.410932i $$0.134797\pi$$
−0.911666 + 0.410932i $$0.865203\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ − 10.0000i − 0.507020i −0.967333 0.253510i $$-0.918415\pi$$
0.967333 0.253510i $$-0.0815851\pi$$
$$390$$ 0 0
$$391$$ 5.00000 0.252861
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ − 28.0000i − 1.40883i
$$396$$ 0 0
$$397$$ − 10.0000i − 0.501886i −0.968002 0.250943i $$-0.919259\pi$$
0.968002 0.250943i $$-0.0807406\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 24.0000 1.19850 0.599251 0.800561i $$-0.295465\pi$$
0.599251 + 0.800561i $$0.295465\pi$$
$$402$$ 0 0
$$403$$ − 35.0000i − 1.74347i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −32.0000 −1.58230 −0.791149 0.611623i $$-0.790517\pi$$
−0.791149 + 0.611623i $$0.790517\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 1.00000i 0.0492068i
$$414$$ 0 0
$$415$$ 8.00000 0.392705
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 15.0000i 0.732798i 0.930458 + 0.366399i $$0.119409\pi$$
−0.930458 + 0.366399i $$0.880591\pi$$
$$420$$ 0 0
$$421$$ − 4.00000i − 0.194948i −0.995238 0.0974740i $$-0.968924\pi$$
0.995238 0.0974740i $$-0.0310763\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.00000 0.0485071
$$426$$ 0 0
$$427$$ − 6.00000i − 0.290360i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 0 0
$$433$$ 8.00000 0.384455 0.192228 0.981350i $$-0.438429\pi$$
0.192228 + 0.981350i $$0.438429\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 20.0000i 0.956730i
$$438$$ 0 0
$$439$$ −9.00000 −0.429547 −0.214773 0.976664i $$-0.568901\pi$$
−0.214773 + 0.976664i $$0.568901\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ − 6.00000i − 0.285069i −0.989790 0.142534i $$-0.954475\pi$$
0.989790 0.142534i $$-0.0455251\pi$$
$$444$$ 0 0
$$445$$ 26.0000i 1.23252i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −10.0000 −0.468807
$$456$$ 0 0
$$457$$ 5.00000 0.233890 0.116945 0.993138i $$-0.462690\pi$$
0.116945 + 0.993138i $$0.462690\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 12.0000i 0.558896i 0.960161 + 0.279448i $$0.0901514\pi$$
−0.960161 + 0.279448i $$0.909849\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 32.0000i 1.48078i 0.672176 + 0.740392i $$0.265360\pi$$
−0.672176 + 0.740392i $$0.734640\pi$$
$$468$$ 0 0
$$469$$ − 9.00000i − 0.415581i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 4.00000i 0.183533i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −26.0000 −1.18797 −0.593985 0.804476i $$-0.702446\pi$$
−0.593985 + 0.804476i $$0.702446\pi$$
$$480$$ 0 0
$$481$$ −10.0000 −0.455961
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 28.0000i 1.27141i
$$486$$ 0 0
$$487$$ 16.0000 0.725029 0.362515 0.931978i $$-0.381918\pi$$
0.362515 + 0.931978i $$0.381918\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 4.00000i 0.180517i 0.995918 + 0.0902587i $$0.0287694\pi$$
−0.995918 + 0.0902587i $$0.971231\pi$$
$$492$$ 0 0
$$493$$ 9.00000i 0.405340i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 15.0000 0.672842
$$498$$ 0 0
$$499$$ − 24.0000i − 1.07439i −0.843459 0.537194i $$-0.819484\pi$$
0.843459 0.537194i $$-0.180516\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −6.00000 −0.267527 −0.133763 0.991013i $$-0.542706\pi$$
−0.133763 + 0.991013i $$0.542706\pi$$
$$504$$ 0 0
$$505$$ −16.0000 −0.711991
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ − 18.0000i − 0.797836i −0.916987 0.398918i $$-0.869386\pi$$
0.916987 0.398918i $$-0.130614\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ − 6.00000i − 0.264392i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 39.0000 1.70862 0.854311 0.519763i $$-0.173980\pi$$
0.854311 + 0.519763i $$0.173980\pi$$
$$522$$ 0 0
$$523$$ − 36.0000i − 1.57417i −0.616844 0.787085i $$-0.711589\pi$$
0.616844 0.787085i $$-0.288411\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 7.00000 0.304925
$$528$$ 0 0
$$529$$ 2.00000 0.0869565
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ − 10.0000i − 0.433148i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ − 38.0000i − 1.63375i −0.576816 0.816874i $$-0.695705\pi$$
0.576816 0.816874i $$-0.304295\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −32.0000 −1.37073
$$546$$ 0 0
$$547$$ 28.0000i 1.19719i 0.801050 + 0.598597i $$0.204275\pi$$
−0.801050 + 0.598597i $$0.795725\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −36.0000 −1.53365
$$552$$ 0 0
$$553$$ 14.0000 0.595341
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 33.0000i 1.39825i 0.714997 + 0.699127i $$0.246428\pi$$
−0.714997 + 0.699127i $$0.753572\pi$$
$$558$$ 0 0
$$559$$ 25.0000 1.05739
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 15.0000i 0.632175i 0.948730 + 0.316087i $$0.102369\pi$$
−0.948730 + 0.316087i $$0.897631\pi$$
$$564$$ 0 0
$$565$$ − 12.0000i − 0.504844i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ 0 0
$$571$$ 19.0000i 0.795125i 0.917575 + 0.397563i $$0.130144\pi$$
−0.917575 + 0.397563i $$0.869856\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 5.00000 0.208514
$$576$$ 0 0
$$577$$ 30.0000 1.24892 0.624458 0.781058i $$-0.285320\pi$$
0.624458 + 0.781058i $$0.285320\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 4.00000i 0.165948i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ − 23.0000i − 0.949312i −0.880172 0.474656i $$-0.842573\pi$$
0.880172 0.474656i $$-0.157427\pi$$
$$588$$ 0 0
$$589$$ 28.0000i 1.15372i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ − 2.00000i − 0.0819920i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 35.0000 1.43006 0.715031 0.699093i $$-0.246413\pi$$
0.715031 + 0.699093i $$0.246413\pi$$
$$600$$ 0 0
$$601$$ 38.0000 1.55005 0.775026 0.631929i $$-0.217737\pi$$
0.775026 + 0.631929i $$0.217737\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ − 22.0000i − 0.894427i
$$606$$ 0 0
$$607$$ −1.00000 −0.0405887 −0.0202944 0.999794i $$-0.506460\pi$$
−0.0202944 + 0.999794i $$0.506460\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ − 16.0000i − 0.646234i −0.946359 0.323117i $$-0.895269\pi$$
0.946359 0.323117i $$-0.104731\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 46.0000 1.85189 0.925945 0.377658i $$-0.123271\pi$$
0.925945 + 0.377658i $$0.123271\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −13.0000 −0.520834
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ − 2.00000i − 0.0797452i
$$630$$ 0 0
$$631$$ −34.0000 −1.35352 −0.676759 0.736204i $$-0.736616\pi$$
−0.676759 + 0.736204i $$0.736616\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ − 16.0000i − 0.634941i
$$636$$ 0 0
$$637$$ − 5.00000i − 0.198107i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −26.0000 −1.02694 −0.513469 0.858108i $$-0.671640\pi$$
−0.513469 + 0.858108i $$0.671640\pi$$
$$642$$ 0 0
$$643$$ 14.0000i 0.552106i 0.961142 + 0.276053i $$0.0890266\pi$$
−0.961142 + 0.276053i $$0.910973\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −18.0000 −0.707653 −0.353827 0.935311i $$-0.615120\pi$$
−0.353827 + 0.935311i $$0.615120\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ − 21.0000i − 0.821794i −0.911682 0.410897i $$-0.865216\pi$$
0.911682 0.410897i $$-0.134784\pi$$
$$654$$ 0 0
$$655$$ 26.0000 1.01590
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 36.0000i 1.40236i 0.712984 + 0.701180i $$0.247343\pi$$
−0.712984 + 0.701180i $$0.752657\pi$$
$$660$$ 0 0
$$661$$ 22.0000i 0.855701i 0.903850 + 0.427850i $$0.140729\pi$$
−0.903850 + 0.427850i $$0.859271\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 8.00000 0.310227
$$666$$ 0 0
$$667$$ 45.0000i 1.74241i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −37.0000 −1.42625 −0.713123 0.701039i $$-0.752720\pi$$
−0.713123 + 0.701039i $$0.752720\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ − 12.0000i − 0.461197i −0.973049 0.230599i $$-0.925932\pi$$
0.973049 0.230599i $$-0.0740685\pi$$
$$678$$ 0 0
$$679$$ −14.0000 −0.537271
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 46.0000i 1.76014i 0.474843 + 0.880071i $$0.342505\pi$$
−0.474843 + 0.880071i $$0.657495\pi$$
$$684$$ 0 0
$$685$$ 24.0000i 0.916993i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 45.0000 1.71436
$$690$$ 0 0
$$691$$ − 8.00000i − 0.304334i −0.988355 0.152167i $$-0.951375\pi$$
0.988355 0.152167i $$-0.0486252\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −40.0000 −1.51729
$$696$$ 0 0
$$697$$ 2.00000 0.0757554
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 22.0000i 0.830929i 0.909610 + 0.415464i $$0.136381\pi$$
−0.909610 + 0.415464i $$0.863619\pi$$
$$702$$ 0 0
$$703$$ 8.00000 0.301726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ − 8.00000i − 0.300871i
$$708$$ 0 0
$$709$$ − 16.0000i − 0.600893i −0.953799 0.300446i $$-0.902864\pi$$
0.953799 0.300446i $$-0.0971356\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 35.0000 1.31076
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 14.0000 0.522112 0.261056 0.965324i $$-0.415929\pi$$
0.261056 + 0.965324i $$0.415929\pi$$
$$720$$ 0 0
$$721$$ 3.00000 0.111726
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 9.00000i 0.334252i
$$726$$ 0 0
$$727$$ 33.0000 1.22390 0.611951 0.790896i $$-0.290385\pi$$
0.611951 + 0.790896i $$0.290385\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 5.00000i 0.184932i
$$732$$ 0 0
$$733$$ 49.0000i 1.80986i 0.425564 + 0.904928i $$0.360076\pi$$
−0.425564 + 0.904928i $$0.639924\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 32.0000i 1.17714i 0.808447 + 0.588570i $$0.200309\pi$$
−0.808447 + 0.588570i $$0.799691\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −23.0000 −0.843788 −0.421894 0.906645i $$-0.638635\pi$$
−0.421894 + 0.906645i $$0.638635\pi$$
$$744$$ 0 0
$$745$$ −18.0000 −0.659469
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 46.0000 1.67856 0.839282 0.543696i $$-0.182976\pi$$
0.839282 + 0.543696i $$0.182976\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 24.0000i 0.873449i
$$756$$ 0 0
$$757$$ 24.0000i 0.872295i 0.899875 + 0.436147i $$0.143657\pi$$
−0.899875 + 0.436147i $$0.856343\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −11.0000 −0.398750 −0.199375 0.979923i $$-0.563891\pi$$
−0.199375 + 0.979923i $$0.563891\pi$$
$$762$$ 0 0
$$763$$ − 16.0000i − 0.579239i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 5.00000 0.180540
$$768$$ 0 0
$$769$$ −2.00000 −0.0721218 −0.0360609 0.999350i $$-0.511481\pi$$
−0.0360609 + 0.999350i $$0.511481\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ − 32.0000i − 1.15096i −0.817816 0.575480i $$-0.804815\pi$$
0.817816 0.575480i $$-0.195185\pi$$
$$774$$ 0 0
$$775$$ 7.00000 0.251447
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 8.00000i 0.286630i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 26.0000 0.927980
$$786$$ 0 0
$$787$$ 48.0000i 1.71102i 0.517790 + 0.855508i $$0.326755\pi$$
−0.517790 + 0.855508i $$0.673245\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 6.00000 0.213335
$$792$$ 0 0
$$793$$ −30.0000 −1.06533
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 2.00000i 0.0708436i 0.999372 + 0.0354218i $$0.0112775\pi$$
−0.999372 + 0.0354218i $$0.988723\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ − 10.0000i − 0.352454i
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 6.00000 0.210949 0.105474 0.994422i $$-0.466364\pi$$
0.105474 + 0.994422i $$0.466364\pi$$
$$810$$ 0 0
$$811$$ 14.0000i 0.491606i 0.969320 + 0.245803i $$0.0790517\pi$$
−0.969320 + 0.245803i $$0.920948\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 22.0000 0.770626
$$816$$ 0 0
$$817$$ −20.0000 −0.699711
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ − 35.0000i − 1.22151i −0.791820 0.610754i $$-0.790866\pi$$
0.791820 0.610754i $$-0.209134\pi$$
$$822$$ 0 0
$$823$$ −44.0000 −1.53374 −0.766872 0.641800i $$-0.778188\pi$$
−0.766872 + 0.641800i $$0.778188\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ − 12.0000i − 0.417281i −0.977992 0.208640i $$-0.933096\pi$$
0.977992 0.208640i $$-0.0669038\pi$$
$$828$$ 0 0
$$829$$ − 34.0000i − 1.18087i −0.807086 0.590434i $$-0.798956\pi$$
0.807086 0.590434i $$-0.201044\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 1.00000 0.0346479
$$834$$ 0 0
$$835$$ − 8.00000i − 0.276851i
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −44.0000 −1.51905 −0.759524 0.650479i $$-0.774568\pi$$
−0.759524 + 0.650479i $$0.774568\pi$$
$$840$$ 0 0
$$841$$ −52.0000 −1.79310
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 24.0000i 0.825625i
$$846$$ 0 0
$$847$$ 11.0000 0.377964
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ − 10.0000i − 0.342796i
$$852$$ 0 0
$$853$$ − 9.00000i − 0.308154i −0.988059 0.154077i $$-0.950760\pi$$
0.988059 0.154077i $$-0.0492404\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 9.00000 0.307434 0.153717 0.988115i $$-0.450876\pi$$
0.153717 + 0.988115i $$0.450876\pi$$
$$858$$ 0 0
$$859$$ 2.00000i 0.0682391i 0.999418 + 0.0341196i $$0.0108627\pi$$
−0.999418 + 0.0341196i $$0.989137\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 45.0000 1.53182 0.765909 0.642949i $$-0.222289\pi$$
0.765909 + 0.642949i $$0.222289\pi$$
$$864$$ 0 0
$$865$$ −12.0000 −0.408012
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −45.0000 −1.52477
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ − 12.0000i − 0.405674i
$$876$$ 0 0
$$877$$ − 34.0000i − 1.14810i −0.818821 0.574049i $$-0.805372\pi$$
0.818821 0.574049i $$-0.194628\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 47.0000 1.58347 0.791735 0.610865i $$-0.209178\pi$$
0.791735 + 0.610865i $$0.209178\pi$$
$$882$$ 0 0
$$883$$ 29.0000i 0.975928i 0.872864 + 0.487964i $$0.162260\pi$$
−0.872864 + 0.487964i $$0.837740\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 12.0000 0.402921 0.201460 0.979497i $$-0.435431\pi$$
0.201460 + 0.979497i $$0.435431\pi$$
$$888$$ 0 0
$$889$$ 8.00000 0.268311
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 20.0000 0.668526
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 63.0000i 2.10117i
$$900$$ 0 0
$$901$$ 9.00000i 0.299833i
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −38.0000 −1.26316
$$906$$ 0 0
$$907$$ 28.0000i 0.929725i 0.885383 + 0.464862i $$0.153896\pi$$
−0.885383 + 0.464862i $$0.846104\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 13.0000i 0.429298i
$$918$$ 0 0
$$919$$ −18.0000 −0.593765 −0.296883 0.954914i $$-0.595947\pi$$
−0.296883 + 0.954914i $$0.595947\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ − 75.0000i − 2.46866i
$$924$$ 0 0
$$925$$ − 2.00000i − 0.0657596i
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −14.0000 −0.459325 −0.229663 0.973270i $$-0.573762\pi$$
−0.229663 + 0.973270i $$0.573762\pi$$
$$930$$ 0 0
$$931$$ 4.00000i 0.131095i
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −22.0000 −0.718709 −0.359354 0.933201i $$-0.617003\pi$$
−0.359354 + 0.933201i $$0.617003\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 24.0000i 0.782378i 0.920310 + 0.391189i $$0.127936\pi$$
−0.920310 + 0.391189i $$0.872064\pi$$
$$942$$ 0 0
$$943$$ 10.0000 0.325645
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ − 12.0000i − 0.389948i −0.980808 0.194974i $$-0.937538\pi$$
0.980808 0.194974i $$-0.0624622\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −36.0000 −1.16615 −0.583077 0.812417i $$-0.698151\pi$$
−0.583077 + 0.812417i $$0.698151\pi$$
$$954$$ 0 0
$$955$$ 8.00000i 0.258874i
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −12.0000 −0.387500
$$960$$ 0 0
$$961$$ 18.0000 0.580645
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ − 18.0000i − 0.579441i
$$966$$ 0 0
$$967$$ −50.0000 −1.60789 −0.803946 0.594703i $$-0.797270\pi$$
−0.803946 + 0.594703i $$0.797270\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ − 33.0000i − 1.05902i −0.848304 0.529510i $$-0.822376\pi$$
0.848304 0.529510i $$-0.177624\pi$$
$$972$$ 0 0
$$973$$ − 20.0000i − 0.641171i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −56.0000 −1.79160 −0.895799 0.444459i $$-0.853396\pi$$
−0.895799 + 0.444459i $$0.853396\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −62.0000 −1.97749 −0.988746 0.149601i $$-0.952201\pi$$
−0.988746 + 0.149601i $$0.952201\pi$$
$$984$$ 0 0
$$985$$ 28.0000 0.892154
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 25.0000i 0.794954i
$$990$$ 0 0
$$991$$ −20.0000 −0.635321 −0.317660 0.948205i $$-0.602897\pi$$
−0.317660 + 0.948205i $$0.602897\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 26.0000i 0.824255i
$$996$$ 0 0
$$997$$ 57.0000i 1.80521i 0.430472 + 0.902604i $$0.358347\pi$$
−0.430472 + 0.902604i $$0.641653\pi$$
$$998$$ 0 0
$$999$$ 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 6048.2.c.b.3025.1 2
3.2 odd 2 6048.2.c.a.3025.2 2
4.3 odd 2 1512.2.c.a.757.2 yes 2
8.3 odd 2 1512.2.c.a.757.1 2
8.5 even 2 inner 6048.2.c.b.3025.2 2
12.11 even 2 1512.2.c.b.757.1 yes 2
24.5 odd 2 6048.2.c.a.3025.1 2
24.11 even 2 1512.2.c.b.757.2 yes 2

By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.c.a.757.1 2 8.3 odd 2
1512.2.c.a.757.2 yes 2 4.3 odd 2
1512.2.c.b.757.1 yes 2 12.11 even 2
1512.2.c.b.757.2 yes 2 24.11 even 2
6048.2.c.a.3025.1 2 24.5 odd 2
6048.2.c.a.3025.2 2 3.2 odd 2
6048.2.c.b.3025.1 2 1.1 even 1 trivial
6048.2.c.b.3025.2 2 8.5 even 2 inner