# Properties

 Label 882.2.a.d.1.1 Level $882$ Weight $2$ Character 882.1 Self dual yes Analytic conductor $7.043$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 882.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$7.04280545828$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 882.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{8} -1.00000 q^{10} -5.00000 q^{11} +1.00000 q^{16} -4.00000 q^{17} -8.00000 q^{19} +1.00000 q^{20} +5.00000 q^{22} +4.00000 q^{23} -4.00000 q^{25} +5.00000 q^{29} -3.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} -4.00000 q^{37} +8.00000 q^{38} -1.00000 q^{40} +2.00000 q^{43} -5.00000 q^{44} -4.00000 q^{46} -6.00000 q^{47} +4.00000 q^{50} +9.00000 q^{53} -5.00000 q^{55} -5.00000 q^{58} -11.0000 q^{59} +6.00000 q^{61} +3.00000 q^{62} +1.00000 q^{64} -2.00000 q^{67} -4.00000 q^{68} -2.00000 q^{71} -10.0000 q^{73} +4.00000 q^{74} -8.00000 q^{76} +3.00000 q^{79} +1.00000 q^{80} -7.00000 q^{83} -4.00000 q^{85} -2.00000 q^{86} +5.00000 q^{88} -6.00000 q^{89} +4.00000 q^{92} +6.00000 q^{94} -8.00000 q^{95} -7.00000 q^{97} +O(q^{100})$$

## 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
$$5$$ 1.00000 0.447214 0.223607 0.974679i $$-0.428217\pi$$
0.223607 + 0.974679i $$0.428217\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ −1.00000 −0.316228
$$11$$ −5.00000 −1.50756 −0.753778 0.657129i $$-0.771771\pi$$
−0.753778 + 0.657129i $$0.771771\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −4.00000 −0.970143 −0.485071 0.874475i $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ 0 0
$$19$$ −8.00000 −1.83533 −0.917663 0.397360i $$-0.869927\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ 5.00000 1.06600
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ −4.00000 −0.800000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 5.00000 0.928477 0.464238 0.885710i $$-0.346328\pi$$
0.464238 + 0.885710i $$0.346328\pi$$
$$30$$ 0 0
$$31$$ −3.00000 −0.538816 −0.269408 0.963026i $$-0.586828\pi$$
−0.269408 + 0.963026i $$0.586828\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 4.00000 0.685994
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −4.00000 −0.657596 −0.328798 0.944400i $$-0.606644\pi$$
−0.328798 + 0.944400i $$0.606644\pi$$
$$38$$ 8.00000 1.29777
$$39$$ 0 0
$$40$$ −1.00000 −0.158114
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ −5.00000 −0.753778
$$45$$ 0 0
$$46$$ −4.00000 −0.589768
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 4.00000 0.565685
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ 0 0
$$55$$ −5.00000 −0.674200
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −5.00000 −0.656532
$$59$$ −11.0000 −1.43208 −0.716039 0.698060i $$-0.754047\pi$$
−0.716039 + 0.698060i $$0.754047\pi$$
$$60$$ 0 0
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 3.00000 0.381000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ 0 0
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 4.00000 0.464991
$$75$$ 0 0
$$76$$ −8.00000 −0.917663
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 3.00000 0.337526 0.168763 0.985657i $$-0.446023\pi$$
0.168763 + 0.985657i $$0.446023\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −7.00000 −0.768350 −0.384175 0.923260i $$-0.625514\pi$$
−0.384175 + 0.923260i $$0.625514\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ −2.00000 −0.215666
$$87$$ 0 0
$$88$$ 5.00000 0.533002
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 0 0
$$94$$ 6.00000 0.618853
$$95$$ −8.00000 −0.820783
$$96$$ 0 0
$$97$$ −7.00000 −0.710742 −0.355371 0.934725i $$-0.615646\pi$$
−0.355371 + 0.934725i $$0.615646\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −4.00000 −0.400000
$$101$$ 10.0000 0.995037 0.497519 0.867453i $$-0.334245\pi$$
0.497519 + 0.867453i $$0.334245\pi$$
$$102$$ 0 0
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −9.00000 −0.874157
$$107$$ −3.00000 −0.290021 −0.145010 0.989430i $$-0.546322\pi$$
−0.145010 + 0.989430i $$0.546322\pi$$
$$108$$ 0 0
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 5.00000 0.476731
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −16.0000 −1.50515 −0.752577 0.658505i $$-0.771189\pi$$
−0.752577 + 0.658505i $$0.771189\pi$$
$$114$$ 0 0
$$115$$ 4.00000 0.373002
$$116$$ 5.00000 0.464238
$$117$$ 0 0
$$118$$ 11.0000 1.01263
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ −6.00000 −0.543214
$$123$$ 0 0
$$124$$ −3.00000 −0.269408
$$125$$ −9.00000 −0.804984
$$126$$ 0 0
$$127$$ 9.00000 0.798621 0.399310 0.916816i $$-0.369250\pi$$
0.399310 + 0.916816i $$0.369250\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1.00000 0.0873704 0.0436852 0.999045i $$-0.486090\pi$$
0.0436852 + 0.999045i $$0.486090\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2.00000 0.172774
$$135$$ 0 0
$$136$$ 4.00000 0.342997
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 0 0
$$139$$ 14.0000 1.18746 0.593732 0.804663i $$-0.297654\pi$$
0.593732 + 0.804663i $$0.297654\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 2.00000 0.167836
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 5.00000 0.415227
$$146$$ 10.0000 0.827606
$$147$$ 0 0
$$148$$ −4.00000 −0.328798
$$149$$ 18.0000 1.47462 0.737309 0.675556i $$-0.236096\pi$$
0.737309 + 0.675556i $$0.236096\pi$$
$$150$$ 0 0
$$151$$ 19.0000 1.54620 0.773099 0.634285i $$-0.218706\pi$$
0.773099 + 0.634285i $$0.218706\pi$$
$$152$$ 8.00000 0.648886
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.00000 −0.240966
$$156$$ 0 0
$$157$$ 4.00000 0.319235 0.159617 0.987179i $$-0.448974\pi$$
0.159617 + 0.987179i $$0.448974\pi$$
$$158$$ −3.00000 −0.238667
$$159$$ 0 0
$$160$$ −1.00000 −0.0790569
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 7.00000 0.543305
$$167$$ −14.0000 −1.08335 −0.541676 0.840587i $$-0.682210\pi$$
−0.541676 + 0.840587i $$0.682210\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 4.00000 0.306786
$$171$$ 0 0
$$172$$ 2.00000 0.152499
$$173$$ 22.0000 1.67263 0.836315 0.548250i $$-0.184706\pi$$
0.836315 + 0.548250i $$0.184706\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −5.00000 −0.376889
$$177$$ 0 0
$$178$$ 6.00000 0.449719
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −4.00000 −0.294884
$$185$$ −4.00000 −0.294086
$$186$$ 0 0
$$187$$ 20.0000 1.46254
$$188$$ −6.00000 −0.437595
$$189$$ 0 0
$$190$$ 8.00000 0.580381
$$191$$ −24.0000 −1.73658 −0.868290 0.496058i $$-0.834780\pi$$
−0.868290 + 0.496058i $$0.834780\pi$$
$$192$$ 0 0
$$193$$ 5.00000 0.359908 0.179954 0.983675i $$-0.442405\pi$$
0.179954 + 0.983675i $$0.442405\pi$$
$$194$$ 7.00000 0.502571
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ 4.00000 0.283552 0.141776 0.989899i $$-0.454719\pi$$
0.141776 + 0.989899i $$0.454719\pi$$
$$200$$ 4.00000 0.282843
$$201$$ 0 0
$$202$$ −10.0000 −0.703598
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 8.00000 0.557386
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 40.0000 2.76686
$$210$$ 0 0
$$211$$ 2.00000 0.137686 0.0688428 0.997628i $$-0.478069\pi$$
0.0688428 + 0.997628i $$0.478069\pi$$
$$212$$ 9.00000 0.618123
$$213$$ 0 0
$$214$$ 3.00000 0.205076
$$215$$ 2.00000 0.136399
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 2.00000 0.135457
$$219$$ 0 0
$$220$$ −5.00000 −0.337100
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 7.00000 0.468755 0.234377 0.972146i $$-0.424695\pi$$
0.234377 + 0.972146i $$0.424695\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 16.0000 1.06430
$$227$$ 3.00000 0.199117 0.0995585 0.995032i $$-0.468257\pi$$
0.0995585 + 0.995032i $$0.468257\pi$$
$$228$$ 0 0
$$229$$ 20.0000 1.32164 0.660819 0.750546i $$-0.270209\pi$$
0.660819 + 0.750546i $$0.270209\pi$$
$$230$$ −4.00000 −0.263752
$$231$$ 0 0
$$232$$ −5.00000 −0.328266
$$233$$ 4.00000 0.262049 0.131024 0.991379i $$-0.458173\pi$$
0.131024 + 0.991379i $$0.458173\pi$$
$$234$$ 0 0
$$235$$ −6.00000 −0.391397
$$236$$ −11.0000 −0.716039
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ 25.0000 1.61039 0.805196 0.593009i $$-0.202060\pi$$
0.805196 + 0.593009i $$0.202060\pi$$
$$242$$ −14.0000 −0.899954
$$243$$ 0 0
$$244$$ 6.00000 0.384111
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 3.00000 0.190500
$$249$$ 0 0
$$250$$ 9.00000 0.569210
$$251$$ 21.0000 1.32551 0.662754 0.748837i $$-0.269387\pi$$
0.662754 + 0.748837i $$0.269387\pi$$
$$252$$ 0 0
$$253$$ −20.0000 −1.25739
$$254$$ −9.00000 −0.564710
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −1.00000 −0.0617802
$$263$$ 30.0000 1.84988 0.924940 0.380114i $$-0.124115\pi$$
0.924940 + 0.380114i $$0.124115\pi$$
$$264$$ 0 0
$$265$$ 9.00000 0.552866
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −2.00000 −0.122169
$$269$$ 31.0000 1.89010 0.945052 0.326921i $$-0.106011\pi$$
0.945052 + 0.326921i $$0.106011\pi$$
$$270$$ 0 0
$$271$$ −15.0000 −0.911185 −0.455593 0.890188i $$-0.650573\pi$$
−0.455593 + 0.890188i $$0.650573\pi$$
$$272$$ −4.00000 −0.242536
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 20.0000 1.20605
$$276$$ 0 0
$$277$$ −16.0000 −0.961347 −0.480673 0.876900i $$-0.659608\pi$$
−0.480673 + 0.876900i $$0.659608\pi$$
$$278$$ −14.0000 −0.839664
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −2.00000 −0.119310 −0.0596550 0.998219i $$-0.519000\pi$$
−0.0596550 + 0.998219i $$0.519000\pi$$
$$282$$ 0 0
$$283$$ −10.0000 −0.594438 −0.297219 0.954809i $$-0.596059\pi$$
−0.297219 + 0.954809i $$0.596059\pi$$
$$284$$ −2.00000 −0.118678
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ −5.00000 −0.293610
$$291$$ 0 0
$$292$$ −10.0000 −0.585206
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 0 0
$$295$$ −11.0000 −0.640445
$$296$$ 4.00000 0.232495
$$297$$ 0 0
$$298$$ −18.0000 −1.04271
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −19.0000 −1.09333
$$303$$ 0 0
$$304$$ −8.00000 −0.458831
$$305$$ 6.00000 0.343559
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 3.00000 0.170389
$$311$$ −32.0000 −1.81455 −0.907277 0.420534i $$-0.861843\pi$$
−0.907277 + 0.420534i $$0.861843\pi$$
$$312$$ 0 0
$$313$$ −1.00000 −0.0565233 −0.0282617 0.999601i $$-0.508997\pi$$
−0.0282617 + 0.999601i $$0.508997\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ 0 0
$$316$$ 3.00000 0.168763
$$317$$ −3.00000 −0.168497 −0.0842484 0.996445i $$-0.526849\pi$$
−0.0842484 + 0.996445i $$0.526849\pi$$
$$318$$ 0 0
$$319$$ −25.0000 −1.39973
$$320$$ 1.00000 0.0559017
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 32.0000 1.78053
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 4.00000 0.221540
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ −7.00000 −0.384175
$$333$$ 0 0
$$334$$ 14.0000 0.766046
$$335$$ −2.00000 −0.109272
$$336$$ 0 0
$$337$$ 9.00000 0.490261 0.245131 0.969490i $$-0.421169\pi$$
0.245131 + 0.969490i $$0.421169\pi$$
$$338$$ 13.0000 0.707107
$$339$$ 0 0
$$340$$ −4.00000 −0.216930
$$341$$ 15.0000 0.812296
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −2.00000 −0.107833
$$345$$ 0 0
$$346$$ −22.0000 −1.18273
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 5.00000 0.266501
$$353$$ 24.0000 1.27739 0.638696 0.769460i $$-0.279474\pi$$
0.638696 + 0.769460i $$0.279474\pi$$
$$354$$ 0 0
$$355$$ −2.00000 −0.106149
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ −10.0000 −0.527780 −0.263890 0.964553i $$-0.585006\pi$$
−0.263890 + 0.964553i $$0.585006\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −10.0000 −0.523424
$$366$$ 0 0
$$367$$ −17.0000 −0.887393 −0.443696 0.896177i $$-0.646333\pi$$
−0.443696 + 0.896177i $$0.646333\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 0 0
$$370$$ 4.00000 0.207950
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −32.0000 −1.65690 −0.828449 0.560065i $$-0.810776\pi$$
−0.828449 + 0.560065i $$0.810776\pi$$
$$374$$ −20.0000 −1.03418
$$375$$ 0 0
$$376$$ 6.00000 0.309426
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 16.0000 0.821865 0.410932 0.911666i $$-0.365203\pi$$
0.410932 + 0.911666i $$0.365203\pi$$
$$380$$ −8.00000 −0.410391
$$381$$ 0 0
$$382$$ 24.0000 1.22795
$$383$$ −34.0000 −1.73732 −0.868659 0.495410i $$-0.835018\pi$$
−0.868659 + 0.495410i $$0.835018\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −5.00000 −0.254493
$$387$$ 0 0
$$388$$ −7.00000 −0.355371
$$389$$ 2.00000 0.101404 0.0507020 0.998714i $$-0.483854\pi$$
0.0507020 + 0.998714i $$0.483854\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 2.00000 0.100759
$$395$$ 3.00000 0.150946
$$396$$ 0 0
$$397$$ −36.0000 −1.80679 −0.903394 0.428811i $$-0.858933\pi$$
−0.903394 + 0.428811i $$0.858933\pi$$
$$398$$ −4.00000 −0.200502
$$399$$ 0 0
$$400$$ −4.00000 −0.200000
$$401$$ −24.0000 −1.19850 −0.599251 0.800561i $$-0.704535\pi$$
−0.599251 + 0.800561i $$0.704535\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 10.0000 0.497519
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 20.0000 0.991363
$$408$$ 0 0
$$409$$ 25.0000 1.23617 0.618085 0.786111i $$-0.287909\pi$$
0.618085 + 0.786111i $$0.287909\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −8.00000 −0.394132
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −7.00000 −0.343616
$$416$$ 0 0
$$417$$ 0 0
$$418$$ −40.0000 −1.95646
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ −2.00000 −0.0973585
$$423$$ 0 0
$$424$$ −9.00000 −0.437079
$$425$$ 16.0000 0.776114
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −3.00000 −0.145010
$$429$$ 0 0
$$430$$ −2.00000 −0.0964486
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −2.00000 −0.0957826
$$437$$ −32.0000 −1.53077
$$438$$ 0 0
$$439$$ −15.0000 −0.715911 −0.357955 0.933739i $$-0.616526\pi$$
−0.357955 + 0.933739i $$0.616526\pi$$
$$440$$ 5.00000 0.238366
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −17.0000 −0.807694 −0.403847 0.914826i $$-0.632327\pi$$
−0.403847 + 0.914826i $$0.632327\pi$$
$$444$$ 0 0
$$445$$ −6.00000 −0.284427
$$446$$ −7.00000 −0.331460
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −16.0000 −0.755087 −0.377543 0.925992i $$-0.623231\pi$$
−0.377543 + 0.925992i $$0.623231\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −16.0000 −0.752577
$$453$$ 0 0
$$454$$ −3.00000 −0.140797
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 31.0000 1.45012 0.725059 0.688686i $$-0.241812\pi$$
0.725059 + 0.688686i $$0.241812\pi$$
$$458$$ −20.0000 −0.934539
$$459$$ 0 0
$$460$$ 4.00000 0.186501
$$461$$ −14.0000 −0.652045 −0.326023 0.945362i $$-0.605709\pi$$
−0.326023 + 0.945362i $$0.605709\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ 5.00000 0.232119
$$465$$ 0 0
$$466$$ −4.00000 −0.185296
$$467$$ −20.0000 −0.925490 −0.462745 0.886492i $$-0.653135\pi$$
−0.462745 + 0.886492i $$0.653135\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 6.00000 0.276759
$$471$$ 0 0
$$472$$ 11.0000 0.506316
$$473$$ −10.0000 −0.459800
$$474$$ 0 0
$$475$$ 32.0000 1.46826
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −12.0000 −0.548867
$$479$$ 38.0000 1.73626 0.868132 0.496333i $$-0.165321\pi$$
0.868132 + 0.496333i $$0.165321\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −25.0000 −1.13872
$$483$$ 0 0
$$484$$ 14.0000 0.636364
$$485$$ −7.00000 −0.317854
$$486$$ 0 0
$$487$$ 5.00000 0.226572 0.113286 0.993562i $$-0.463862\pi$$
0.113286 + 0.993562i $$0.463862\pi$$
$$488$$ −6.00000 −0.271607
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −9.00000 −0.406164 −0.203082 0.979162i $$-0.565096\pi$$
−0.203082 + 0.979162i $$0.565096\pi$$
$$492$$ 0 0
$$493$$ −20.0000 −0.900755
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −3.00000 −0.134704
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 10.0000 0.447661 0.223831 0.974628i $$-0.428144\pi$$
0.223831 + 0.974628i $$0.428144\pi$$
$$500$$ −9.00000 −0.402492
$$501$$ 0 0
$$502$$ −21.0000 −0.937276
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 10.0000 0.444994
$$506$$ 20.0000 0.889108
$$507$$ 0 0
$$508$$ 9.00000 0.399310
$$509$$ 15.0000 0.664863 0.332432 0.943127i $$-0.392131\pi$$
0.332432 + 0.943127i $$0.392131\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 6.00000 0.264649
$$515$$ −8.00000 −0.352522
$$516$$ 0 0
$$517$$ 30.0000 1.31940
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 0 0
$$523$$ −8.00000 −0.349816 −0.174908 0.984585i $$-0.555963\pi$$
−0.174908 + 0.984585i $$0.555963\pi$$
$$524$$ 1.00000 0.0436852
$$525$$ 0 0
$$526$$ −30.0000 −1.30806
$$527$$ 12.0000 0.522728
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ −9.00000 −0.390935
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −3.00000 −0.129701
$$536$$ 2.00000 0.0863868
$$537$$ 0 0
$$538$$ −31.0000 −1.33650
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −18.0000 −0.773880 −0.386940 0.922105i $$-0.626468\pi$$
−0.386940 + 0.922105i $$0.626468\pi$$
$$542$$ 15.0000 0.644305
$$543$$ 0 0
$$544$$ 4.00000 0.171499
$$545$$ −2.00000 −0.0856706
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 2.00000 0.0854358
$$549$$ 0 0
$$550$$ −20.0000 −0.852803
$$551$$ −40.0000 −1.70406
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 16.0000 0.679775
$$555$$ 0 0
$$556$$ 14.0000 0.593732
$$557$$ 23.0000 0.974541 0.487271 0.873251i $$-0.337993\pi$$
0.487271 + 0.873251i $$0.337993\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 2.00000 0.0843649
$$563$$ 17.0000 0.716465 0.358232 0.933632i $$-0.383380\pi$$
0.358232 + 0.933632i $$0.383380\pi$$
$$564$$ 0 0
$$565$$ −16.0000 −0.673125
$$566$$ 10.0000 0.420331
$$567$$ 0 0
$$568$$ 2.00000 0.0839181
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ 0 0
$$571$$ −30.0000 −1.25546 −0.627730 0.778431i $$-0.716016\pi$$
−0.627730 + 0.778431i $$0.716016\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −16.0000 −0.667246
$$576$$ 0 0
$$577$$ −31.0000 −1.29055 −0.645273 0.763952i $$-0.723257\pi$$
−0.645273 + 0.763952i $$0.723257\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ 0 0
$$580$$ 5.00000 0.207614
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −45.0000 −1.86371
$$584$$ 10.0000 0.413803
$$585$$ 0 0
$$586$$ 21.0000 0.867502
$$587$$ 35.0000 1.44460 0.722302 0.691577i $$-0.243084\pi$$
0.722302 + 0.691577i $$0.243084\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ 11.0000 0.452863
$$591$$ 0 0
$$592$$ −4.00000 −0.164399
$$593$$ 36.0000 1.47834 0.739171 0.673517i $$-0.235217\pi$$
0.739171 + 0.673517i $$0.235217\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 18.0000 0.737309
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 0 0
$$601$$ −35.0000 −1.42768 −0.713840 0.700309i $$-0.753046\pi$$
−0.713840 + 0.700309i $$0.753046\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 19.0000 0.773099
$$605$$ 14.0000 0.569181
$$606$$ 0 0
$$607$$ 27.0000 1.09590 0.547948 0.836512i $$-0.315409\pi$$
0.547948 + 0.836512i $$0.315409\pi$$
$$608$$ 8.00000 0.324443
$$609$$ 0 0
$$610$$ −6.00000 −0.242933
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 12.0000 0.484675 0.242338 0.970192i $$-0.422086\pi$$
0.242338 + 0.970192i $$0.422086\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −2.00000 −0.0805170 −0.0402585 0.999189i $$-0.512818\pi$$
−0.0402585 + 0.999189i $$0.512818\pi$$
$$618$$ 0 0
$$619$$ −10.0000 −0.401934 −0.200967 0.979598i $$-0.564408\pi$$
−0.200967 + 0.979598i $$0.564408\pi$$
$$620$$ −3.00000 −0.120483
$$621$$ 0 0
$$622$$ 32.0000 1.28308
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ 1.00000 0.0399680
$$627$$ 0 0
$$628$$ 4.00000 0.159617
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ −19.0000 −0.756378 −0.378189 0.925728i $$-0.623453\pi$$
−0.378189 + 0.925728i $$0.623453\pi$$
$$632$$ −3.00000 −0.119334
$$633$$ 0 0
$$634$$ 3.00000 0.119145
$$635$$ 9.00000 0.357154
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 25.0000 0.989759
$$639$$ 0 0
$$640$$ −1.00000 −0.0395285
$$641$$ −26.0000 −1.02694 −0.513469 0.858108i $$-0.671640\pi$$
−0.513469 + 0.858108i $$0.671640\pi$$
$$642$$ 0 0
$$643$$ −14.0000 −0.552106 −0.276053 0.961142i $$-0.589027\pi$$
−0.276053 + 0.961142i $$0.589027\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −32.0000 −1.25902
$$647$$ −18.0000 −0.707653 −0.353827 0.935311i $$-0.615120\pi$$
−0.353827 + 0.935311i $$0.615120\pi$$
$$648$$ 0 0
$$649$$ 55.0000 2.15894
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ 39.0000 1.52619 0.763094 0.646288i $$-0.223679\pi$$
0.763094 + 0.646288i $$0.223679\pi$$
$$654$$ 0 0
$$655$$ 1.00000 0.0390732
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 40.0000 1.55818 0.779089 0.626913i $$-0.215682\pi$$
0.779089 + 0.626913i $$0.215682\pi$$
$$660$$ 0 0
$$661$$ −10.0000 −0.388955 −0.194477 0.980907i $$-0.562301\pi$$
−0.194477 + 0.980907i $$0.562301\pi$$
$$662$$ 4.00000 0.155464
$$663$$ 0 0
$$664$$ 7.00000 0.271653
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 20.0000 0.774403
$$668$$ −14.0000 −0.541676
$$669$$ 0 0
$$670$$ 2.00000 0.0772667
$$671$$ −30.0000 −1.15814
$$672$$ 0 0
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ −9.00000 −0.346667
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ −27.0000 −1.03769 −0.518847 0.854867i $$-0.673639\pi$$
−0.518847 + 0.854867i $$0.673639\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 4.00000 0.153393
$$681$$ 0 0
$$682$$ −15.0000 −0.574380
$$683$$ 9.00000 0.344375 0.172188 0.985064i $$-0.444916\pi$$
0.172188 + 0.985064i $$0.444916\pi$$
$$684$$ 0 0
$$685$$ 2.00000 0.0764161
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 2.00000 0.0762493
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −8.00000 −0.304334 −0.152167 0.988355i $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ 22.0000 0.836315
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 14.0000 0.531050
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −14.0000 −0.529908
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 5.00000 0.188847 0.0944237 0.995532i $$-0.469899\pi$$
0.0944237 + 0.995532i $$0.469899\pi$$
$$702$$ 0 0
$$703$$ 32.0000 1.20690
$$704$$ −5.00000 −0.188445
$$705$$ 0 0
$$706$$ −24.0000 −0.903252
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 38.0000 1.42712 0.713560 0.700594i $$-0.247082\pi$$
0.713560 + 0.700594i $$0.247082\pi$$
$$710$$ 2.00000 0.0750587
$$711$$ 0 0
$$712$$ 6.00000 0.224860
$$713$$ −12.0000 −0.449404
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −12.0000 −0.448461
$$717$$ 0 0
$$718$$ 10.0000 0.373197
$$719$$ −6.00000 −0.223762 −0.111881 0.993722i $$-0.535688\pi$$
−0.111881 + 0.993722i $$0.535688\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −45.0000 −1.67473
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −20.0000 −0.742781
$$726$$ 0 0
$$727$$ −7.00000 −0.259616 −0.129808 0.991539i $$-0.541436\pi$$
−0.129808 + 0.991539i $$0.541436\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 10.0000 0.370117
$$731$$ −8.00000 −0.295891
$$732$$ 0 0
$$733$$ 6.00000 0.221615 0.110808 0.993842i $$-0.464656\pi$$
0.110808 + 0.993842i $$0.464656\pi$$
$$734$$ 17.0000 0.627481
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ 10.0000 0.368355
$$738$$ 0 0
$$739$$ −30.0000 −1.10357 −0.551784 0.833987i $$-0.686053\pi$$
−0.551784 + 0.833987i $$0.686053\pi$$
$$740$$ −4.00000 −0.147043
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −30.0000 −1.10059 −0.550297 0.834969i $$-0.685485\pi$$
−0.550297 + 0.834969i $$0.685485\pi$$
$$744$$ 0 0
$$745$$ 18.0000 0.659469
$$746$$ 32.0000 1.17160
$$747$$ 0 0
$$748$$ 20.0000 0.731272
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 45.0000 1.64207 0.821037 0.570875i $$-0.193396\pi$$
0.821037 + 0.570875i $$0.193396\pi$$
$$752$$ −6.00000 −0.218797
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 19.0000 0.691481
$$756$$ 0 0
$$757$$ −54.0000 −1.96266 −0.981332 0.192323i $$-0.938398\pi$$
−0.981332 + 0.192323i $$0.938398\pi$$
$$758$$ −16.0000 −0.581146
$$759$$ 0 0
$$760$$ 8.00000 0.290191
$$761$$ 8.00000 0.290000 0.145000 0.989432i $$-0.453682\pi$$
0.145000 + 0.989432i $$0.453682\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −24.0000 −0.868290
$$765$$ 0 0
$$766$$ 34.0000 1.22847
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 35.0000 1.26213 0.631066 0.775729i $$-0.282618\pi$$
0.631066 + 0.775729i $$0.282618\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 5.00000 0.179954
$$773$$ 10.0000 0.359675 0.179838 0.983696i $$-0.442443\pi$$
0.179838 + 0.983696i $$0.442443\pi$$
$$774$$ 0 0
$$775$$ 12.0000 0.431053
$$776$$ 7.00000 0.251285
$$777$$ 0 0
$$778$$ −2.00000 −0.0717035
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 10.0000 0.357828
$$782$$ 16.0000 0.572159
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 4.00000 0.142766
$$786$$ 0 0
$$787$$ 18.0000 0.641631 0.320815 0.947142i $$-0.396043\pi$$
0.320815 + 0.947142i $$0.396043\pi$$
$$788$$ −2.00000 −0.0712470
$$789$$ 0 0
$$790$$ −3.00000 −0.106735
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 36.0000 1.27759
$$795$$ 0 0
$$796$$ 4.00000 0.141776
$$797$$ 21.0000 0.743858 0.371929 0.928261i $$-0.378696\pi$$
0.371929 + 0.928261i $$0.378696\pi$$
$$798$$ 0 0
$$799$$ 24.0000 0.849059
$$800$$ 4.00000 0.141421
$$801$$ 0 0
$$802$$ 24.0000 0.847469
$$803$$ 50.0000 1.76446
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −10.0000 −0.351799
$$809$$ −40.0000 −1.40633 −0.703163 0.711029i $$-0.748229\pi$$
−0.703163 + 0.711029i $$0.748229\pi$$
$$810$$ 0 0
$$811$$ 14.0000 0.491606 0.245803 0.969320i $$-0.420948\pi$$
0.245803 + 0.969320i $$0.420948\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ −20.0000 −0.701000
$$815$$ −4.00000 −0.140114
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ −25.0000 −0.874105
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 25.0000 0.872506 0.436253 0.899824i $$-0.356305\pi$$
0.436253 + 0.899824i $$0.356305\pi$$
$$822$$ 0 0
$$823$$ 40.0000 1.39431 0.697156 0.716919i $$-0.254448\pi$$
0.697156 + 0.716919i $$0.254448\pi$$
$$824$$ 8.00000 0.278693
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −9.00000 −0.312961 −0.156480 0.987681i $$-0.550015\pi$$
−0.156480 + 0.987681i $$0.550015\pi$$
$$828$$ 0 0
$$829$$ 32.0000 1.11141 0.555703 0.831381i $$-0.312449\pi$$
0.555703 + 0.831381i $$0.312449\pi$$
$$830$$ 7.00000 0.242974
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −14.0000 −0.484490
$$836$$ 40.0000 1.38343
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −28.0000 −0.966667 −0.483334 0.875436i $$-0.660574\pi$$
−0.483334 + 0.875436i $$0.660574\pi$$
$$840$$ 0 0
$$841$$ −4.00000 −0.137931
$$842$$ −30.0000 −1.03387
$$843$$ 0 0
$$844$$ 2.00000 0.0688428
$$845$$ −13.0000 −0.447214
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 9.00000 0.309061
$$849$$ 0 0
$$850$$ −16.0000 −0.548795
$$851$$ −16.0000 −0.548473
$$852$$ 0 0
$$853$$ −14.0000 −0.479351 −0.239675 0.970853i $$-0.577041\pi$$
−0.239675 + 0.970853i $$0.577041\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 3.00000 0.102538
$$857$$ −18.0000 −0.614868 −0.307434 0.951569i $$-0.599470\pi$$
−0.307434 + 0.951569i $$0.599470\pi$$
$$858$$ 0 0
$$859$$ 34.0000 1.16007 0.580033 0.814593i $$-0.303040\pi$$
0.580033 + 0.814593i $$0.303040\pi$$
$$860$$ 2.00000 0.0681994
$$861$$ 0 0
$$862$$ 12.0000 0.408722
$$863$$ −10.0000 −0.340404 −0.170202 0.985409i $$-0.554442\pi$$
−0.170202 + 0.985409i $$0.554442\pi$$
$$864$$ 0 0
$$865$$ 22.0000 0.748022
$$866$$ 14.0000 0.475739
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −15.0000 −0.508840
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 2.00000 0.0677285
$$873$$ 0 0
$$874$$ 32.0000 1.08242
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −32.0000 −1.08056 −0.540282 0.841484i $$-0.681682\pi$$
−0.540282 + 0.841484i $$0.681682\pi$$
$$878$$ 15.0000 0.506225
$$879$$ 0 0
$$880$$ −5.00000 −0.168550
$$881$$ −42.0000 −1.41502 −0.707508 0.706705i $$-0.750181\pi$$
−0.707508 + 0.706705i $$0.750181\pi$$
$$882$$ 0 0
$$883$$ −40.0000 −1.34611 −0.673054 0.739594i $$-0.735018\pi$$
−0.673054 + 0.739594i $$0.735018\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 17.0000 0.571126
$$887$$ 36.0000 1.20876 0.604381 0.796696i $$-0.293421\pi$$
0.604381 + 0.796696i $$0.293421\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 6.00000 0.201120
$$891$$ 0 0
$$892$$ 7.00000 0.234377
$$893$$ 48.0000 1.60626
$$894$$ 0 0
$$895$$ −12.0000 −0.401116
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 16.0000 0.533927
$$899$$ −15.0000 −0.500278
$$900$$ 0 0
$$901$$ −36.0000 −1.19933
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 16.0000 0.532152
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 12.0000 0.398453 0.199227 0.979953i $$-0.436157\pi$$
0.199227 + 0.979953i $$0.436157\pi$$
$$908$$ 3.00000 0.0995585
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −30.0000 −0.993944 −0.496972 0.867766i $$-0.665555\pi$$
−0.496972 + 0.867766i $$0.665555\pi$$
$$912$$ 0 0
$$913$$ 35.0000 1.15833
$$914$$ −31.0000 −1.02539
$$915$$ 0 0
$$916$$ 20.0000 0.660819
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −32.0000 −1.05558 −0.527791 0.849374i $$-0.676980\pi$$
−0.527791 + 0.849374i $$0.676980\pi$$
$$920$$ −4.00000 −0.131876
$$921$$ 0 0
$$922$$ 14.0000 0.461065
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 16.0000 0.526077
$$926$$ −16.0000 −0.525793
$$927$$ 0 0
$$928$$ −5.00000 −0.164133
$$929$$ −6.00000 −0.196854 −0.0984268 0.995144i $$-0.531381\pi$$
−0.0984268 + 0.995144i $$0.531381\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 4.00000 0.131024
$$933$$ 0 0
$$934$$ 20.0000 0.654420
$$935$$ 20.0000 0.654070
$$936$$ 0 0
$$937$$ −35.0000 −1.14340 −0.571700 0.820463i $$-0.693716\pi$$
−0.571700 + 0.820463i $$0.693716\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ −6.00000 −0.195698
$$941$$ −11.0000 −0.358590 −0.179295 0.983795i $$-0.557382\pi$$
−0.179295 + 0.983795i $$0.557382\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −11.0000 −0.358020
$$945$$ 0 0
$$946$$ 10.0000 0.325128
$$947$$ 32.0000 1.03986 0.519930 0.854209i $$-0.325958\pi$$
0.519930 + 0.854209i $$0.325958\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ −32.0000 −1.03822
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −2.00000 −0.0647864 −0.0323932 0.999475i $$-0.510313\pi$$
−0.0323932 + 0.999475i $$0.510313\pi$$
$$954$$ 0 0
$$955$$ −24.0000 −0.776622
$$956$$ 12.0000 0.388108
$$957$$ 0 0
$$958$$ −38.0000 −1.22772
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −22.0000 −0.709677
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 25.0000 0.805196
$$965$$ 5.00000 0.160956
$$966$$ 0 0
$$967$$ −61.0000 −1.96163 −0.980814 0.194946i $$-0.937547\pi$$
−0.980814 + 0.194946i $$0.937547\pi$$
$$968$$ −14.0000 −0.449977
$$969$$ 0 0
$$970$$ 7.00000 0.224756
$$971$$ 15.0000 0.481373 0.240686 0.970603i $$-0.422627\pi$$
0.240686 + 0.970603i $$0.422627\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ −5.00000 −0.160210
$$975$$ 0 0
$$976$$ 6.00000 0.192055
$$977$$ 30.0000 0.959785 0.479893 0.877327i $$-0.340676\pi$$
0.479893 + 0.877327i $$0.340676\pi$$
$$978$$ 0 0
$$979$$ 30.0000 0.958804
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 9.00000 0.287202
$$983$$ −60.0000 −1.91370 −0.956851 0.290578i $$-0.906153\pi$$
−0.956851 + 0.290578i $$0.906153\pi$$
$$984$$ 0 0
$$985$$ −2.00000 −0.0637253
$$986$$ 20.0000 0.636930
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 8.00000 0.254385
$$990$$ 0 0
$$991$$ 47.0000 1.49300 0.746502 0.665383i $$-0.231732\pi$$
0.746502 + 0.665383i $$0.231732\pi$$
$$992$$ 3.00000 0.0952501
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 4.00000 0.126809
$$996$$ 0 0
$$997$$ −38.0000 −1.20347 −0.601736 0.798695i $$-0.705524\pi$$
−0.601736 + 0.798695i $$0.705524\pi$$
$$998$$ −10.0000 −0.316544
$$999$$ 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 882.2.a.d.1.1 1
3.2 odd 2 294.2.a.f.1.1 1
4.3 odd 2 7056.2.a.bl.1.1 1
7.2 even 3 882.2.g.i.361.1 2
7.3 odd 6 126.2.g.c.37.1 2
7.4 even 3 882.2.g.i.667.1 2
7.5 odd 6 126.2.g.c.109.1 2
7.6 odd 2 882.2.a.c.1.1 1
12.11 even 2 2352.2.a.f.1.1 1
15.14 odd 2 7350.2.a.q.1.1 1
21.2 odd 6 294.2.e.b.67.1 2
21.5 even 6 42.2.e.a.25.1 2
21.11 odd 6 294.2.e.b.79.1 2
21.17 even 6 42.2.e.a.37.1 yes 2
21.20 even 2 294.2.a.e.1.1 1
24.5 odd 2 9408.2.a.z.1.1 1
24.11 even 2 9408.2.a.cr.1.1 1
28.3 even 6 1008.2.s.k.289.1 2
28.19 even 6 1008.2.s.k.865.1 2
28.27 even 2 7056.2.a.w.1.1 1
63.5 even 6 1134.2.e.l.865.1 2
63.31 odd 6 1134.2.h.l.541.1 2
63.38 even 6 1134.2.e.l.919.1 2
63.40 odd 6 1134.2.e.e.865.1 2
63.47 even 6 1134.2.h.e.109.1 2
63.52 odd 6 1134.2.e.e.919.1 2
63.59 even 6 1134.2.h.e.541.1 2
63.61 odd 6 1134.2.h.l.109.1 2
84.11 even 6 2352.2.q.u.961.1 2
84.23 even 6 2352.2.q.u.1537.1 2
84.47 odd 6 336.2.q.b.193.1 2
84.59 odd 6 336.2.q.b.289.1 2
84.83 odd 2 2352.2.a.t.1.1 1
105.17 odd 12 1050.2.o.a.499.1 4
105.38 odd 12 1050.2.o.a.499.2 4
105.47 odd 12 1050.2.o.a.949.2 4
105.59 even 6 1050.2.i.l.751.1 2
105.68 odd 12 1050.2.o.a.949.1 4
105.89 even 6 1050.2.i.l.151.1 2
105.104 even 2 7350.2.a.bl.1.1 1
168.5 even 6 1344.2.q.g.193.1 2
168.59 odd 6 1344.2.q.s.961.1 2
168.83 odd 2 9408.2.a.q.1.1 1
168.101 even 6 1344.2.q.g.961.1 2
168.125 even 2 9408.2.a.ce.1.1 1
168.131 odd 6 1344.2.q.s.193.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.e.a.25.1 2 21.5 even 6
42.2.e.a.37.1 yes 2 21.17 even 6
126.2.g.c.37.1 2 7.3 odd 6
126.2.g.c.109.1 2 7.5 odd 6
294.2.a.e.1.1 1 21.20 even 2
294.2.a.f.1.1 1 3.2 odd 2
294.2.e.b.67.1 2 21.2 odd 6
294.2.e.b.79.1 2 21.11 odd 6
336.2.q.b.193.1 2 84.47 odd 6
336.2.q.b.289.1 2 84.59 odd 6
882.2.a.c.1.1 1 7.6 odd 2
882.2.a.d.1.1 1 1.1 even 1 trivial
882.2.g.i.361.1 2 7.2 even 3
882.2.g.i.667.1 2 7.4 even 3
1008.2.s.k.289.1 2 28.3 even 6
1008.2.s.k.865.1 2 28.19 even 6
1050.2.i.l.151.1 2 105.89 even 6
1050.2.i.l.751.1 2 105.59 even 6
1050.2.o.a.499.1 4 105.17 odd 12
1050.2.o.a.499.2 4 105.38 odd 12
1050.2.o.a.949.1 4 105.68 odd 12
1050.2.o.a.949.2 4 105.47 odd 12
1134.2.e.e.865.1 2 63.40 odd 6
1134.2.e.e.919.1 2 63.52 odd 6
1134.2.e.l.865.1 2 63.5 even 6
1134.2.e.l.919.1 2 63.38 even 6
1134.2.h.e.109.1 2 63.47 even 6
1134.2.h.e.541.1 2 63.59 even 6
1134.2.h.l.109.1 2 63.61 odd 6
1134.2.h.l.541.1 2 63.31 odd 6
1344.2.q.g.193.1 2 168.5 even 6
1344.2.q.g.961.1 2 168.101 even 6
1344.2.q.s.193.1 2 168.131 odd 6
1344.2.q.s.961.1 2 168.59 odd 6
2352.2.a.f.1.1 1 12.11 even 2
2352.2.a.t.1.1 1 84.83 odd 2
2352.2.q.u.961.1 2 84.11 even 6
2352.2.q.u.1537.1 2 84.23 even 6
7056.2.a.w.1.1 1 28.27 even 2
7056.2.a.bl.1.1 1 4.3 odd 2
7350.2.a.q.1.1 1 15.14 odd 2
7350.2.a.bl.1.1 1 105.104 even 2
9408.2.a.q.1.1 1 168.83 odd 2
9408.2.a.z.1.1 1 24.5 odd 2
9408.2.a.ce.1.1 1 168.125 even 2
9408.2.a.cr.1.1 1 24.11 even 2