# Properties

 Label 1449.2.a.a.1.1 Level $1449$ Weight $2$ Character 1449.1 Self dual yes Analytic conductor $11.570$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1449 = 3^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1449.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$11.5703232529$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 483) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1449.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{2} +2.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +O(q^{10})$$ $$q-2.00000 q^{2} +2.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +8.00000 q^{10} +5.00000 q^{11} -2.00000 q^{13} +2.00000 q^{14} -4.00000 q^{16} -5.00000 q^{19} -8.00000 q^{20} -10.0000 q^{22} +1.00000 q^{23} +11.0000 q^{25} +4.00000 q^{26} -2.00000 q^{28} +2.00000 q^{29} +6.00000 q^{31} +8.00000 q^{32} +4.00000 q^{35} +6.00000 q^{37} +10.0000 q^{38} -5.00000 q^{41} +8.00000 q^{43} +10.0000 q^{44} -2.00000 q^{46} +9.00000 q^{47} +1.00000 q^{49} -22.0000 q^{50} -4.00000 q^{52} -9.00000 q^{53} -20.0000 q^{55} -4.00000 q^{58} -9.00000 q^{59} -5.00000 q^{61} -12.0000 q^{62} -8.00000 q^{64} +8.00000 q^{65} +4.00000 q^{67} -8.00000 q^{70} -12.0000 q^{71} -12.0000 q^{74} -10.0000 q^{76} -5.00000 q^{77} -10.0000 q^{79} +16.0000 q^{80} +10.0000 q^{82} +18.0000 q^{83} -16.0000 q^{86} -10.0000 q^{89} +2.00000 q^{91} +2.00000 q^{92} -18.0000 q^{94} +20.0000 q^{95} -18.0000 q^{97} -2.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.00000 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$3$$ 0 0
$$4$$ 2.00000 1.00000
$$5$$ −4.00000 −1.78885 −0.894427 0.447214i $$-0.852416\pi$$
−0.894427 + 0.447214i $$0.852416\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 8.00000 2.52982
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 2.00000 0.534522
$$15$$ 0 0
$$16$$ −4.00000 −1.00000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ −5.00000 −1.14708 −0.573539 0.819178i $$-0.694430\pi$$
−0.573539 + 0.819178i $$0.694430\pi$$
$$20$$ −8.00000 −1.78885
$$21$$ 0 0
$$22$$ −10.0000 −2.13201
$$23$$ 1.00000 0.208514
$$24$$ 0 0
$$25$$ 11.0000 2.20000
$$26$$ 4.00000 0.784465
$$27$$ 0 0
$$28$$ −2.00000 −0.377964
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 8.00000 1.41421
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 4.00000 0.676123
$$36$$ 0 0
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ 10.0000 1.62221
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −5.00000 −0.780869 −0.390434 0.920631i $$-0.627675\pi$$
−0.390434 + 0.920631i $$0.627675\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 10.0000 1.50756
$$45$$ 0 0
$$46$$ −2.00000 −0.294884
$$47$$ 9.00000 1.31278 0.656392 0.754420i $$-0.272082\pi$$
0.656392 + 0.754420i $$0.272082\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ −22.0000 −3.11127
$$51$$ 0 0
$$52$$ −4.00000 −0.554700
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ 0 0
$$55$$ −20.0000 −2.69680
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −4.00000 −0.525226
$$59$$ −9.00000 −1.17170 −0.585850 0.810419i $$-0.699239\pi$$
−0.585850 + 0.810419i $$0.699239\pi$$
$$60$$ 0 0
$$61$$ −5.00000 −0.640184 −0.320092 0.947386i $$-0.603714\pi$$
−0.320092 + 0.947386i $$0.603714\pi$$
$$62$$ −12.0000 −1.52400
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 8.00000 0.992278
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −8.00000 −0.956183
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ −12.0000 −1.39497
$$75$$ 0 0
$$76$$ −10.0000 −1.14708
$$77$$ −5.00000 −0.569803
$$78$$ 0 0
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 16.0000 1.78885
$$81$$ 0 0
$$82$$ 10.0000 1.10432
$$83$$ 18.0000 1.97576 0.987878 0.155230i $$-0.0496119\pi$$
0.987878 + 0.155230i $$0.0496119\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −16.0000 −1.72532
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 2.00000 0.208514
$$93$$ 0 0
$$94$$ −18.0000 −1.85656
$$95$$ 20.0000 2.05196
$$96$$ 0 0
$$97$$ −18.0000 −1.82762 −0.913812 0.406138i $$-0.866875\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ −2.00000 −0.202031
$$99$$ 0 0
$$100$$ 22.0000 2.20000
$$101$$ −5.00000 −0.497519 −0.248759 0.968565i $$-0.580023\pi$$
−0.248759 + 0.968565i $$0.580023\pi$$
$$102$$ 0 0
$$103$$ −19.0000 −1.87213 −0.936063 0.351833i $$-0.885559\pi$$
−0.936063 + 0.351833i $$0.885559\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 18.0000 1.74831
$$107$$ −4.00000 −0.386695 −0.193347 0.981130i $$-0.561934\pi$$
−0.193347 + 0.981130i $$0.561934\pi$$
$$108$$ 0 0
$$109$$ −12.0000 −1.14939 −0.574696 0.818367i $$-0.694880\pi$$
−0.574696 + 0.818367i $$0.694880\pi$$
$$110$$ 40.0000 3.81385
$$111$$ 0 0
$$112$$ 4.00000 0.377964
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ −4.00000 −0.373002
$$116$$ 4.00000 0.371391
$$117$$ 0 0
$$118$$ 18.0000 1.65703
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ 10.0000 0.905357
$$123$$ 0 0
$$124$$ 12.0000 1.07763
$$125$$ −24.0000 −2.14663
$$126$$ 0 0
$$127$$ 9.00000 0.798621 0.399310 0.916816i $$-0.369250\pi$$
0.399310 + 0.916816i $$0.369250\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ −16.0000 −1.40329
$$131$$ 5.00000 0.436852 0.218426 0.975854i $$-0.429908\pi$$
0.218426 + 0.975854i $$0.429908\pi$$
$$132$$ 0 0
$$133$$ 5.00000 0.433555
$$134$$ −8.00000 −0.691095
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −9.00000 −0.768922 −0.384461 0.923141i $$-0.625613\pi$$
−0.384461 + 0.923141i $$0.625613\pi$$
$$138$$ 0 0
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 8.00000 0.676123
$$141$$ 0 0
$$142$$ 24.0000 2.01404
$$143$$ −10.0000 −0.836242
$$144$$ 0 0
$$145$$ −8.00000 −0.664364
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 12.0000 0.986394
$$149$$ −3.00000 −0.245770 −0.122885 0.992421i $$-0.539215\pi$$
−0.122885 + 0.992421i $$0.539215\pi$$
$$150$$ 0 0
$$151$$ −19.0000 −1.54620 −0.773099 0.634285i $$-0.781294\pi$$
−0.773099 + 0.634285i $$0.781294\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 10.0000 0.805823
$$155$$ −24.0000 −1.92773
$$156$$ 0 0
$$157$$ 7.00000 0.558661 0.279330 0.960195i $$-0.409888\pi$$
0.279330 + 0.960195i $$0.409888\pi$$
$$158$$ 20.0000 1.59111
$$159$$ 0 0
$$160$$ −32.0000 −2.52982
$$161$$ −1.00000 −0.0788110
$$162$$ 0 0
$$163$$ 13.0000 1.01824 0.509119 0.860696i $$-0.329971\pi$$
0.509119 + 0.860696i $$0.329971\pi$$
$$164$$ −10.0000 −0.780869
$$165$$ 0 0
$$166$$ −36.0000 −2.79414
$$167$$ −19.0000 −1.47026 −0.735132 0.677924i $$-0.762880\pi$$
−0.735132 + 0.677924i $$0.762880\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 16.0000 1.21999
$$173$$ −2.00000 −0.152057 −0.0760286 0.997106i $$-0.524224\pi$$
−0.0760286 + 0.997106i $$0.524224\pi$$
$$174$$ 0 0
$$175$$ −11.0000 −0.831522
$$176$$ −20.0000 −1.50756
$$177$$ 0 0
$$178$$ 20.0000 1.49906
$$179$$ −8.00000 −0.597948 −0.298974 0.954261i $$-0.596644\pi$$
−0.298974 + 0.954261i $$0.596644\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ −4.00000 −0.296500
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −24.0000 −1.76452
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 18.0000 1.31278
$$189$$ 0 0
$$190$$ −40.0000 −2.90191
$$191$$ 23.0000 1.66422 0.832111 0.554609i $$-0.187132\pi$$
0.832111 + 0.554609i $$0.187132\pi$$
$$192$$ 0 0
$$193$$ −19.0000 −1.36765 −0.683825 0.729646i $$-0.739685\pi$$
−0.683825 + 0.729646i $$0.739685\pi$$
$$194$$ 36.0000 2.58465
$$195$$ 0 0
$$196$$ 2.00000 0.142857
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ 0 0
$$199$$ 3.00000 0.212664 0.106332 0.994331i $$-0.466089\pi$$
0.106332 + 0.994331i $$0.466089\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 10.0000 0.703598
$$203$$ −2.00000 −0.140372
$$204$$ 0 0
$$205$$ 20.0000 1.39686
$$206$$ 38.0000 2.64759
$$207$$ 0 0
$$208$$ 8.00000 0.554700
$$209$$ −25.0000 −1.72929
$$210$$ 0 0
$$211$$ 13.0000 0.894957 0.447478 0.894295i $$-0.352322\pi$$
0.447478 + 0.894295i $$0.352322\pi$$
$$212$$ −18.0000 −1.23625
$$213$$ 0 0
$$214$$ 8.00000 0.546869
$$215$$ −32.0000 −2.18238
$$216$$ 0 0
$$217$$ −6.00000 −0.407307
$$218$$ 24.0000 1.62549
$$219$$ 0 0
$$220$$ −40.0000 −2.69680
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 10.0000 0.669650 0.334825 0.942280i $$-0.391323\pi$$
0.334825 + 0.942280i $$0.391323\pi$$
$$224$$ −8.00000 −0.534522
$$225$$ 0 0
$$226$$ −4.00000 −0.266076
$$227$$ 18.0000 1.19470 0.597351 0.801980i $$-0.296220\pi$$
0.597351 + 0.801980i $$0.296220\pi$$
$$228$$ 0 0
$$229$$ −13.0000 −0.859064 −0.429532 0.903052i $$-0.641321\pi$$
−0.429532 + 0.903052i $$0.641321\pi$$
$$230$$ 8.00000 0.527504
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 12.0000 0.786146 0.393073 0.919507i $$-0.371412\pi$$
0.393073 + 0.919507i $$0.371412\pi$$
$$234$$ 0 0
$$235$$ −36.0000 −2.34838
$$236$$ −18.0000 −1.17170
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ 17.0000 1.09507 0.547533 0.836784i $$-0.315567\pi$$
0.547533 + 0.836784i $$0.315567\pi$$
$$242$$ −28.0000 −1.79991
$$243$$ 0 0
$$244$$ −10.0000 −0.640184
$$245$$ −4.00000 −0.255551
$$246$$ 0 0
$$247$$ 10.0000 0.636285
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 48.0000 3.03579
$$251$$ −10.0000 −0.631194 −0.315597 0.948893i $$-0.602205\pi$$
−0.315597 + 0.948893i $$0.602205\pi$$
$$252$$ 0 0
$$253$$ 5.00000 0.314347
$$254$$ −18.0000 −1.12942
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ −17.0000 −1.06043 −0.530215 0.847863i $$-0.677889\pi$$
−0.530215 + 0.847863i $$0.677889\pi$$
$$258$$ 0 0
$$259$$ −6.00000 −0.372822
$$260$$ 16.0000 0.992278
$$261$$ 0 0
$$262$$ −10.0000 −0.617802
$$263$$ −7.00000 −0.431638 −0.215819 0.976433i $$-0.569242\pi$$
−0.215819 + 0.976433i $$0.569242\pi$$
$$264$$ 0 0
$$265$$ 36.0000 2.21146
$$266$$ −10.0000 −0.613139
$$267$$ 0 0
$$268$$ 8.00000 0.488678
$$269$$ 18.0000 1.09748 0.548740 0.835993i $$-0.315108\pi$$
0.548740 + 0.835993i $$0.315108\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 18.0000 1.08742
$$275$$ 55.0000 3.31662
$$276$$ 0 0
$$277$$ 7.00000 0.420589 0.210295 0.977638i $$-0.432558\pi$$
0.210295 + 0.977638i $$0.432558\pi$$
$$278$$ −24.0000 −1.43942
$$279$$ 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
$$283$$ −20.0000 −1.18888 −0.594438 0.804141i $$-0.702626\pi$$
−0.594438 + 0.804141i $$0.702626\pi$$
$$284$$ −24.0000 −1.42414
$$285$$ 0 0
$$286$$ 20.0000 1.18262
$$287$$ 5.00000 0.295141
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 16.0000 0.939552
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 4.00000 0.233682 0.116841 0.993151i $$-0.462723\pi$$
0.116841 + 0.993151i $$0.462723\pi$$
$$294$$ 0 0
$$295$$ 36.0000 2.09600
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ −2.00000 −0.115663
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 38.0000 2.18665
$$303$$ 0 0
$$304$$ 20.0000 1.14708
$$305$$ 20.0000 1.14520
$$306$$ 0 0
$$307$$ −8.00000 −0.456584 −0.228292 0.973593i $$-0.573314\pi$$
−0.228292 + 0.973593i $$0.573314\pi$$
$$308$$ −10.0000 −0.569803
$$309$$ 0 0
$$310$$ 48.0000 2.72622
$$311$$ 15.0000 0.850572 0.425286 0.905059i $$-0.360174\pi$$
0.425286 + 0.905059i $$0.360174\pi$$
$$312$$ 0 0
$$313$$ −25.0000 −1.41308 −0.706542 0.707671i $$-0.749746\pi$$
−0.706542 + 0.707671i $$0.749746\pi$$
$$314$$ −14.0000 −0.790066
$$315$$ 0 0
$$316$$ −20.0000 −1.12509
$$317$$ −30.0000 −1.68497 −0.842484 0.538721i $$-0.818908\pi$$
−0.842484 + 0.538721i $$0.818908\pi$$
$$318$$ 0 0
$$319$$ 10.0000 0.559893
$$320$$ 32.0000 1.78885
$$321$$ 0 0
$$322$$ 2.00000 0.111456
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −22.0000 −1.22034
$$326$$ −26.0000 −1.44001
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −9.00000 −0.496186
$$330$$ 0 0
$$331$$ 29.0000 1.59398 0.796992 0.603990i $$-0.206423\pi$$
0.796992 + 0.603990i $$0.206423\pi$$
$$332$$ 36.0000 1.97576
$$333$$ 0 0
$$334$$ 38.0000 2.07927
$$335$$ −16.0000 −0.874173
$$336$$ 0 0
$$337$$ 22.0000 1.19842 0.599208 0.800593i $$-0.295482\pi$$
0.599208 + 0.800593i $$0.295482\pi$$
$$338$$ 18.0000 0.979071
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 30.0000 1.62459
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 4.00000 0.215041
$$347$$ −2.00000 −0.107366 −0.0536828 0.998558i $$-0.517096\pi$$
−0.0536828 + 0.998558i $$0.517096\pi$$
$$348$$ 0 0
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 22.0000 1.17595
$$351$$ 0 0
$$352$$ 40.0000 2.13201
$$353$$ 14.0000 0.745145 0.372572 0.928003i $$-0.378476\pi$$
0.372572 + 0.928003i $$0.378476\pi$$
$$354$$ 0 0
$$355$$ 48.0000 2.54758
$$356$$ −20.0000 −1.06000
$$357$$ 0 0
$$358$$ 16.0000 0.845626
$$359$$ −32.0000 −1.68890 −0.844448 0.535638i $$-0.820071\pi$$
−0.844448 + 0.535638i $$0.820071\pi$$
$$360$$ 0 0
$$361$$ 6.00000 0.315789
$$362$$ 28.0000 1.47165
$$363$$ 0 0
$$364$$ 4.00000 0.209657
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 27.0000 1.40939 0.704694 0.709511i $$-0.251084\pi$$
0.704694 + 0.709511i $$0.251084\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 0 0
$$370$$ 48.0000 2.49540
$$371$$ 9.00000 0.467257
$$372$$ 0 0
$$373$$ −34.0000 −1.76045 −0.880227 0.474554i $$-0.842610\pi$$
−0.880227 + 0.474554i $$0.842610\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ −30.0000 −1.54100 −0.770498 0.637442i $$-0.779993\pi$$
−0.770498 + 0.637442i $$0.779993\pi$$
$$380$$ 40.0000 2.05196
$$381$$ 0 0
$$382$$ −46.0000 −2.35356
$$383$$ −6.00000 −0.306586 −0.153293 0.988181i $$-0.548988\pi$$
−0.153293 + 0.988181i $$0.548988\pi$$
$$384$$ 0 0
$$385$$ 20.0000 1.01929
$$386$$ 38.0000 1.93415
$$387$$ 0 0
$$388$$ −36.0000 −1.82762
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −4.00000 −0.201517
$$395$$ 40.0000 2.01262
$$396$$ 0 0
$$397$$ 30.0000 1.50566 0.752828 0.658217i $$-0.228689\pi$$
0.752828 + 0.658217i $$0.228689\pi$$
$$398$$ −6.00000 −0.300753
$$399$$ 0 0
$$400$$ −44.0000 −2.20000
$$401$$ −3.00000 −0.149813 −0.0749064 0.997191i $$-0.523866\pi$$
−0.0749064 + 0.997191i $$0.523866\pi$$
$$402$$ 0 0
$$403$$ −12.0000 −0.597763
$$404$$ −10.0000 −0.497519
$$405$$ 0 0
$$406$$ 4.00000 0.198517
$$407$$ 30.0000 1.48704
$$408$$ 0 0
$$409$$ 14.0000 0.692255 0.346128 0.938187i $$-0.387496\pi$$
0.346128 + 0.938187i $$0.387496\pi$$
$$410$$ −40.0000 −1.97546
$$411$$ 0 0
$$412$$ −38.0000 −1.87213
$$413$$ 9.00000 0.442861
$$414$$ 0 0
$$415$$ −72.0000 −3.53434
$$416$$ −16.0000 −0.784465
$$417$$ 0 0
$$418$$ 50.0000 2.44558
$$419$$ 18.0000 0.879358 0.439679 0.898155i $$-0.355092\pi$$
0.439679 + 0.898155i $$0.355092\pi$$
$$420$$ 0 0
$$421$$ 8.00000 0.389896 0.194948 0.980814i $$-0.437546\pi$$
0.194948 + 0.980814i $$0.437546\pi$$
$$422$$ −26.0000 −1.26566
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 5.00000 0.241967
$$428$$ −8.00000 −0.386695
$$429$$ 0 0
$$430$$ 64.0000 3.08635
$$431$$ −27.0000 −1.30054 −0.650272 0.759701i $$-0.725345\pi$$
−0.650272 + 0.759701i $$0.725345\pi$$
$$432$$ 0 0
$$433$$ −11.0000 −0.528626 −0.264313 0.964437i $$-0.585145\pi$$
−0.264313 + 0.964437i $$0.585145\pi$$
$$434$$ 12.0000 0.576018
$$435$$ 0 0
$$436$$ −24.0000 −1.14939
$$437$$ −5.00000 −0.239182
$$438$$ 0 0
$$439$$ −36.0000 −1.71819 −0.859093 0.511819i $$-0.828972\pi$$
−0.859093 + 0.511819i $$0.828972\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ 0 0
$$445$$ 40.0000 1.89618
$$446$$ −20.0000 −0.947027
$$447$$ 0 0
$$448$$ 8.00000 0.377964
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ 0 0
$$451$$ −25.0000 −1.17720
$$452$$ 4.00000 0.188144
$$453$$ 0 0
$$454$$ −36.0000 −1.68956
$$455$$ −8.00000 −0.375046
$$456$$ 0 0
$$457$$ 10.0000 0.467780 0.233890 0.972263i $$-0.424854\pi$$
0.233890 + 0.972263i $$0.424854\pi$$
$$458$$ 26.0000 1.21490
$$459$$ 0 0
$$460$$ −8.00000 −0.373002
$$461$$ −2.00000 −0.0931493 −0.0465746 0.998915i $$-0.514831\pi$$
−0.0465746 + 0.998915i $$0.514831\pi$$
$$462$$ 0 0
$$463$$ −35.0000 −1.62659 −0.813294 0.581853i $$-0.802328\pi$$
−0.813294 + 0.581853i $$0.802328\pi$$
$$464$$ −8.00000 −0.371391
$$465$$ 0 0
$$466$$ −24.0000 −1.11178
$$467$$ 6.00000 0.277647 0.138823 0.990317i $$-0.455668\pi$$
0.138823 + 0.990317i $$0.455668\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ 72.0000 3.32111
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 40.0000 1.83920
$$474$$ 0 0
$$475$$ −55.0000 −2.52357
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 24.0000 1.09773
$$479$$ −32.0000 −1.46212 −0.731059 0.682315i $$-0.760973\pi$$
−0.731059 + 0.682315i $$0.760973\pi$$
$$480$$ 0 0
$$481$$ −12.0000 −0.547153
$$482$$ −34.0000 −1.54866
$$483$$ 0 0
$$484$$ 28.0000 1.27273
$$485$$ 72.0000 3.26935
$$486$$ 0 0
$$487$$ −20.0000 −0.906287 −0.453143 0.891438i $$-0.649697\pi$$
−0.453143 + 0.891438i $$0.649697\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 8.00000 0.361403
$$491$$ −14.0000 −0.631811 −0.315906 0.948791i $$-0.602308\pi$$
−0.315906 + 0.948791i $$0.602308\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −20.0000 −0.899843
$$495$$ 0 0
$$496$$ −24.0000 −1.07763
$$497$$ 12.0000 0.538274
$$498$$ 0 0
$$499$$ −20.0000 −0.895323 −0.447661 0.894203i $$-0.647743\pi$$
−0.447661 + 0.894203i $$0.647743\pi$$
$$500$$ −48.0000 −2.14663
$$501$$ 0 0
$$502$$ 20.0000 0.892644
$$503$$ 36.0000 1.60516 0.802580 0.596544i $$-0.203460\pi$$
0.802580 + 0.596544i $$0.203460\pi$$
$$504$$ 0 0
$$505$$ 20.0000 0.889988
$$506$$ −10.0000 −0.444554
$$507$$ 0 0
$$508$$ 18.0000 0.798621
$$509$$ 19.0000 0.842160 0.421080 0.907023i $$-0.361651\pi$$
0.421080 + 0.907023i $$0.361651\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −32.0000 −1.41421
$$513$$ 0 0
$$514$$ 34.0000 1.49968
$$515$$ 76.0000 3.34896
$$516$$ 0 0
$$517$$ 45.0000 1.97910
$$518$$ 12.0000 0.527250
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 30.0000 1.31432 0.657162 0.753749i $$-0.271757\pi$$
0.657162 + 0.753749i $$0.271757\pi$$
$$522$$ 0 0
$$523$$ 19.0000 0.830812 0.415406 0.909636i $$-0.363640\pi$$
0.415406 + 0.909636i $$0.363640\pi$$
$$524$$ 10.0000 0.436852
$$525$$ 0 0
$$526$$ 14.0000 0.610429
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ −72.0000 −3.12748
$$531$$ 0 0
$$532$$ 10.0000 0.433555
$$533$$ 10.0000 0.433148
$$534$$ 0 0
$$535$$ 16.0000 0.691740
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −36.0000 −1.55207
$$539$$ 5.00000 0.215365
$$540$$ 0 0
$$541$$ 11.0000 0.472927 0.236463 0.971640i $$-0.424012\pi$$
0.236463 + 0.971640i $$0.424012\pi$$
$$542$$ 16.0000 0.687259
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 48.0000 2.05609
$$546$$ 0 0
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ −18.0000 −0.768922
$$549$$ 0 0
$$550$$ −110.000 −4.69042
$$551$$ −10.0000 −0.426014
$$552$$ 0 0
$$553$$ 10.0000 0.425243
$$554$$ −14.0000 −0.594803
$$555$$ 0 0
$$556$$ 24.0000 1.01783
$$557$$ −46.0000 −1.94908 −0.974541 0.224208i $$-0.928020\pi$$
−0.974541 + 0.224208i $$0.928020\pi$$
$$558$$ 0 0
$$559$$ −16.0000 −0.676728
$$560$$ −16.0000 −0.676123
$$561$$ 0 0
$$562$$ 4.00000 0.168730
$$563$$ −40.0000 −1.68580 −0.842900 0.538071i $$-0.819153\pi$$
−0.842900 + 0.538071i $$0.819153\pi$$
$$564$$ 0 0
$$565$$ −8.00000 −0.336563
$$566$$ 40.0000 1.68133
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 17.0000 0.712677 0.356339 0.934357i $$-0.384025\pi$$
0.356339 + 0.934357i $$0.384025\pi$$
$$570$$ 0 0
$$571$$ 8.00000 0.334790 0.167395 0.985890i $$-0.446465\pi$$
0.167395 + 0.985890i $$0.446465\pi$$
$$572$$ −20.0000 −0.836242
$$573$$ 0 0
$$574$$ −10.0000 −0.417392
$$575$$ 11.0000 0.458732
$$576$$ 0 0
$$577$$ −2.00000 −0.0832611 −0.0416305 0.999133i $$-0.513255\pi$$
−0.0416305 + 0.999133i $$0.513255\pi$$
$$578$$ 34.0000 1.41421
$$579$$ 0 0
$$580$$ −16.0000 −0.664364
$$581$$ −18.0000 −0.746766
$$582$$ 0 0
$$583$$ −45.0000 −1.86371
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −8.00000 −0.330477
$$587$$ 17.0000 0.701665 0.350833 0.936438i $$-0.385899\pi$$
0.350833 + 0.936438i $$0.385899\pi$$
$$588$$ 0 0
$$589$$ −30.0000 −1.23613
$$590$$ −72.0000 −2.96419
$$591$$ 0 0
$$592$$ −24.0000 −0.986394
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ 0 0
$$598$$ 4.00000 0.163572
$$599$$ −42.0000 −1.71607 −0.858037 0.513588i $$-0.828316\pi$$
−0.858037 + 0.513588i $$0.828316\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 16.0000 0.652111
$$603$$ 0 0
$$604$$ −38.0000 −1.54620
$$605$$ −56.0000 −2.27672
$$606$$ 0 0
$$607$$ 8.00000 0.324710 0.162355 0.986732i $$-0.448091\pi$$
0.162355 + 0.986732i $$0.448091\pi$$
$$608$$ −40.0000 −1.62221
$$609$$ 0 0
$$610$$ −40.0000 −1.61955
$$611$$ −18.0000 −0.728202
$$612$$ 0 0
$$613$$ 34.0000 1.37325 0.686624 0.727013i $$-0.259092\pi$$
0.686624 + 0.727013i $$0.259092\pi$$
$$614$$ 16.0000 0.645707
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ 0 0
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ −48.0000 −1.92773
$$621$$ 0 0
$$622$$ −30.0000 −1.20289
$$623$$ 10.0000 0.400642
$$624$$ 0 0
$$625$$ 41.0000 1.64000
$$626$$ 50.0000 1.99840
$$627$$ 0 0
$$628$$ 14.0000 0.558661
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −10.0000 −0.398094 −0.199047 0.979990i $$-0.563785\pi$$
−0.199047 + 0.979990i $$0.563785\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 60.0000 2.38290
$$635$$ −36.0000 −1.42862
$$636$$ 0 0
$$637$$ −2.00000 −0.0792429
$$638$$ −20.0000 −0.791808
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 9.00000 0.355479 0.177739 0.984078i $$-0.443122\pi$$
0.177739 + 0.984078i $$0.443122\pi$$
$$642$$ 0 0
$$643$$ −31.0000 −1.22252 −0.611260 0.791430i $$-0.709337\pi$$
−0.611260 + 0.791430i $$0.709337\pi$$
$$644$$ −2.00000 −0.0788110
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 28.0000 1.10079 0.550397 0.834903i $$-0.314476\pi$$
0.550397 + 0.834903i $$0.314476\pi$$
$$648$$ 0 0
$$649$$ −45.0000 −1.76640
$$650$$ 44.0000 1.72582
$$651$$ 0 0
$$652$$ 26.0000 1.01824
$$653$$ −24.0000 −0.939193 −0.469596 0.882881i $$-0.655601\pi$$
−0.469596 + 0.882881i $$0.655601\pi$$
$$654$$ 0 0
$$655$$ −20.0000 −0.781465
$$656$$ 20.0000 0.780869
$$657$$ 0 0
$$658$$ 18.0000 0.701713
$$659$$ −24.0000 −0.934907 −0.467454 0.884018i $$-0.654829\pi$$
−0.467454 + 0.884018i $$0.654829\pi$$
$$660$$ 0 0
$$661$$ −5.00000 −0.194477 −0.0972387 0.995261i $$-0.531001\pi$$
−0.0972387 + 0.995261i $$0.531001\pi$$
$$662$$ −58.0000 −2.25423
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −20.0000 −0.775567
$$666$$ 0 0
$$667$$ 2.00000 0.0774403
$$668$$ −38.0000 −1.47026
$$669$$ 0 0
$$670$$ 32.0000 1.23627
$$671$$ −25.0000 −0.965114
$$672$$ 0 0
$$673$$ 49.0000 1.88881 0.944406 0.328783i $$-0.106638\pi$$
0.944406 + 0.328783i $$0.106638\pi$$
$$674$$ −44.0000 −1.69482
$$675$$ 0 0
$$676$$ −18.0000 −0.692308
$$677$$ −36.0000 −1.38359 −0.691796 0.722093i $$-0.743180\pi$$
−0.691796 + 0.722093i $$0.743180\pi$$
$$678$$ 0 0
$$679$$ 18.0000 0.690777
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −60.0000 −2.29752
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 36.0000 1.37549
$$686$$ 2.00000 0.0763604
$$687$$ 0 0
$$688$$ −32.0000 −1.21999
$$689$$ 18.0000 0.685745
$$690$$ 0 0
$$691$$ −4.00000 −0.152167 −0.0760836 0.997101i $$-0.524242\pi$$
−0.0760836 + 0.997101i $$0.524242\pi$$
$$692$$ −4.00000 −0.152057
$$693$$ 0 0
$$694$$ 4.00000 0.151838
$$695$$ −48.0000 −1.82074
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 4.00000 0.151402
$$699$$ 0 0
$$700$$ −22.0000 −0.831522
$$701$$ 15.0000 0.566542 0.283271 0.959040i $$-0.408580\pi$$
0.283271 + 0.959040i $$0.408580\pi$$
$$702$$ 0 0
$$703$$ −30.0000 −1.13147
$$704$$ −40.0000 −1.50756
$$705$$ 0 0
$$706$$ −28.0000 −1.05379
$$707$$ 5.00000 0.188044
$$708$$ 0 0
$$709$$ −6.00000 −0.225335 −0.112667 0.993633i $$-0.535939\pi$$
−0.112667 + 0.993633i $$0.535939\pi$$
$$710$$ −96.0000 −3.60282
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 6.00000 0.224702
$$714$$ 0 0
$$715$$ 40.0000 1.49592
$$716$$ −16.0000 −0.597948
$$717$$ 0 0
$$718$$ 64.0000 2.38846
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ 19.0000 0.707597
$$722$$ −12.0000 −0.446594
$$723$$ 0 0
$$724$$ −28.0000 −1.04061
$$725$$ 22.0000 0.817059
$$726$$ 0 0
$$727$$ 41.0000 1.52061 0.760303 0.649569i $$-0.225051\pi$$
0.760303 + 0.649569i $$0.225051\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −6.00000 −0.221615 −0.110808 0.993842i $$-0.535344\pi$$
−0.110808 + 0.993842i $$0.535344\pi$$
$$734$$ −54.0000 −1.99318
$$735$$ 0 0
$$736$$ 8.00000 0.294884
$$737$$ 20.0000 0.736709
$$738$$ 0 0
$$739$$ 12.0000 0.441427 0.220714 0.975339i $$-0.429161\pi$$
0.220714 + 0.975339i $$0.429161\pi$$
$$740$$ −48.0000 −1.76452
$$741$$ 0 0
$$742$$ −18.0000 −0.660801
$$743$$ −15.0000 −0.550297 −0.275148 0.961402i $$-0.588727\pi$$
−0.275148 + 0.961402i $$0.588727\pi$$
$$744$$ 0 0
$$745$$ 12.0000 0.439646
$$746$$ 68.0000 2.48966
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 4.00000 0.146157
$$750$$ 0 0
$$751$$ −32.0000 −1.16770 −0.583848 0.811863i $$-0.698454\pi$$
−0.583848 + 0.811863i $$0.698454\pi$$
$$752$$ −36.0000 −1.31278
$$753$$ 0 0
$$754$$ 8.00000 0.291343
$$755$$ 76.0000 2.76592
$$756$$ 0 0
$$757$$ 8.00000 0.290765 0.145382 0.989376i $$-0.453559\pi$$
0.145382 + 0.989376i $$0.453559\pi$$
$$758$$ 60.0000 2.17930
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 21.0000 0.761249 0.380625 0.924730i $$-0.375709\pi$$
0.380625 + 0.924730i $$0.375709\pi$$
$$762$$ 0 0
$$763$$ 12.0000 0.434429
$$764$$ 46.0000 1.66422
$$765$$ 0 0
$$766$$ 12.0000 0.433578
$$767$$ 18.0000 0.649942
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ −40.0000 −1.44150
$$771$$ 0 0
$$772$$ −38.0000 −1.36765
$$773$$ −20.0000 −0.719350 −0.359675 0.933078i $$-0.617112\pi$$
−0.359675 + 0.933078i $$0.617112\pi$$
$$774$$ 0 0
$$775$$ 66.0000 2.37079
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 12.0000 0.430221
$$779$$ 25.0000 0.895718
$$780$$ 0 0
$$781$$ −60.0000 −2.14697
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −4.00000 −0.142857
$$785$$ −28.0000 −0.999363
$$786$$ 0 0
$$787$$ −23.0000 −0.819861 −0.409931 0.912117i $$-0.634447\pi$$
−0.409931 + 0.912117i $$0.634447\pi$$
$$788$$ 4.00000 0.142494
$$789$$ 0 0
$$790$$ −80.0000 −2.84627
$$791$$ −2.00000 −0.0711118
$$792$$ 0 0
$$793$$ 10.0000 0.355110
$$794$$ −60.0000 −2.12932
$$795$$ 0 0
$$796$$ 6.00000 0.212664
$$797$$ −46.0000 −1.62940 −0.814702 0.579880i $$-0.803099\pi$$
−0.814702 + 0.579880i $$0.803099\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 88.0000 3.11127
$$801$$ 0 0
$$802$$ 6.00000 0.211867
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 4.00000 0.140981
$$806$$ 24.0000 0.845364
$$807$$ 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
$$811$$ 2.00000 0.0702295 0.0351147 0.999383i $$-0.488820\pi$$
0.0351147 + 0.999383i $$0.488820\pi$$
$$812$$ −4.00000 −0.140372
$$813$$ 0 0
$$814$$ −60.0000 −2.10300
$$815$$ −52.0000 −1.82148
$$816$$ 0 0
$$817$$ −40.0000 −1.39942
$$818$$ −28.0000 −0.978997
$$819$$ 0 0
$$820$$ 40.0000 1.39686
$$821$$ 4.00000 0.139601 0.0698005 0.997561i $$-0.477764\pi$$
0.0698005 + 0.997561i $$0.477764\pi$$
$$822$$ 0 0
$$823$$ 27.0000 0.941161 0.470580 0.882357i $$-0.344045\pi$$
0.470580 + 0.882357i $$0.344045\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ −18.0000 −0.626300
$$827$$ 21.0000 0.730242 0.365121 0.930960i $$-0.381028\pi$$
0.365121 + 0.930960i $$0.381028\pi$$
$$828$$ 0 0
$$829$$ 26.0000 0.903017 0.451509 0.892267i $$-0.350886\pi$$
0.451509 + 0.892267i $$0.350886\pi$$
$$830$$ 144.000 4.99831
$$831$$ 0 0
$$832$$ 16.0000 0.554700
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 76.0000 2.63009
$$836$$ −50.0000 −1.72929
$$837$$ 0 0
$$838$$ −36.0000 −1.24360
$$839$$ −46.0000 −1.58810 −0.794048 0.607855i $$-0.792030\pi$$
−0.794048 + 0.607855i $$0.792030\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ −16.0000 −0.551396
$$843$$ 0 0
$$844$$ 26.0000 0.894957
$$845$$ 36.0000 1.23844
$$846$$ 0 0
$$847$$ −14.0000 −0.481046
$$848$$ 36.0000 1.23625
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 6.00000 0.205677
$$852$$ 0 0
$$853$$ 8.00000 0.273915 0.136957 0.990577i $$-0.456268\pi$$
0.136957 + 0.990577i $$0.456268\pi$$
$$854$$ −10.0000 −0.342193
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −1.00000 −0.0341593 −0.0170797 0.999854i $$-0.505437\pi$$
−0.0170797 + 0.999854i $$0.505437\pi$$
$$858$$ 0 0
$$859$$ −40.0000 −1.36478 −0.682391 0.730987i $$-0.739060\pi$$
−0.682391 + 0.730987i $$0.739060\pi$$
$$860$$ −64.0000 −2.18238
$$861$$ 0 0
$$862$$ 54.0000 1.83925
$$863$$ 30.0000 1.02121 0.510606 0.859815i $$-0.329421\pi$$
0.510606 + 0.859815i $$0.329421\pi$$
$$864$$ 0 0
$$865$$ 8.00000 0.272008
$$866$$ 22.0000 0.747590
$$867$$ 0 0
$$868$$ −12.0000 −0.407307
$$869$$ −50.0000 −1.69613
$$870$$ 0 0
$$871$$ −8.00000 −0.271070
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 10.0000 0.338255
$$875$$ 24.0000 0.811348
$$876$$ 0 0
$$877$$ −17.0000 −0.574049 −0.287025 0.957923i $$-0.592666\pi$$
−0.287025 + 0.957923i $$0.592666\pi$$
$$878$$ 72.0000 2.42988
$$879$$ 0 0
$$880$$ 80.0000 2.69680
$$881$$ −6.00000 −0.202145 −0.101073 0.994879i $$-0.532227\pi$$
−0.101073 + 0.994879i $$0.532227\pi$$
$$882$$ 0 0
$$883$$ 32.0000 1.07689 0.538443 0.842662i $$-0.319013\pi$$
0.538443 + 0.842662i $$0.319013\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ −72.0000 −2.41889
$$887$$ 16.0000 0.537227 0.268614 0.963248i $$-0.413434\pi$$
0.268614 + 0.963248i $$0.413434\pi$$
$$888$$ 0 0
$$889$$ −9.00000 −0.301850
$$890$$ −80.0000 −2.68161
$$891$$ 0 0
$$892$$ 20.0000 0.669650
$$893$$ −45.0000 −1.50587
$$894$$ 0 0
$$895$$ 32.0000 1.06964
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 12.0000 0.400445
$$899$$ 12.0000 0.400222
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 50.0000 1.66482
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 56.0000 1.86150
$$906$$ 0 0
$$907$$ 44.0000 1.46100 0.730498 0.682915i $$-0.239288\pi$$
0.730498 + 0.682915i $$0.239288\pi$$
$$908$$ 36.0000 1.19470
$$909$$ 0 0
$$910$$ 16.0000 0.530395
$$911$$ −24.0000 −0.795155 −0.397578 0.917568i $$-0.630149\pi$$
−0.397578 + 0.917568i $$0.630149\pi$$
$$912$$ 0 0
$$913$$ 90.0000 2.97857
$$914$$ −20.0000 −0.661541
$$915$$ 0 0
$$916$$ −26.0000 −0.859064
$$917$$ −5.00000 −0.165115
$$918$$ 0 0
$$919$$ 2.00000 0.0659739 0.0329870 0.999456i $$-0.489498\pi$$
0.0329870 + 0.999456i $$0.489498\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 4.00000 0.131733
$$923$$ 24.0000 0.789970
$$924$$ 0 0
$$925$$ 66.0000 2.17007
$$926$$ 70.0000 2.30034
$$927$$ 0 0
$$928$$ 16.0000 0.525226
$$929$$ −26.0000 −0.853032 −0.426516 0.904480i $$-0.640259\pi$$
−0.426516 + 0.904480i $$0.640259\pi$$
$$930$$ 0 0
$$931$$ −5.00000 −0.163868
$$932$$ 24.0000 0.786146
$$933$$ 0 0
$$934$$ −12.0000 −0.392652
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −27.0000 −0.882052 −0.441026 0.897494i $$-0.645385\pi$$
−0.441026 + 0.897494i $$0.645385\pi$$
$$938$$ 8.00000 0.261209
$$939$$ 0 0
$$940$$ −72.0000 −2.34838
$$941$$ −20.0000 −0.651981 −0.325991 0.945373i $$-0.605698\pi$$
−0.325991 + 0.945373i $$0.605698\pi$$
$$942$$ 0 0
$$943$$ −5.00000 −0.162822
$$944$$ 36.0000 1.17170
$$945$$ 0 0
$$946$$ −80.0000 −2.60102
$$947$$ −32.0000 −1.03986 −0.519930 0.854209i $$-0.674042\pi$$
−0.519930 + 0.854209i $$0.674042\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 110.000 3.56887
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 55.0000 1.78162 0.890812 0.454371i $$-0.150136\pi$$
0.890812 + 0.454371i $$0.150136\pi$$
$$954$$ 0 0
$$955$$ −92.0000 −2.97705
$$956$$ −24.0000 −0.776215
$$957$$ 0 0
$$958$$ 64.0000 2.06775
$$959$$ 9.00000 0.290625
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ 24.0000 0.773791
$$963$$ 0 0
$$964$$ 34.0000 1.09507
$$965$$ 76.0000 2.44653
$$966$$ 0 0
$$967$$ 28.0000 0.900419 0.450210 0.892923i $$-0.351349\pi$$
0.450210 + 0.892923i $$0.351349\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ −144.000 −4.62356
$$971$$ 18.0000 0.577647 0.288824 0.957382i $$-0.406736\pi$$
0.288824 + 0.957382i $$0.406736\pi$$
$$972$$ 0 0
$$973$$ −12.0000 −0.384702
$$974$$ 40.0000 1.28168
$$975$$ 0 0
$$976$$ 20.0000 0.640184
$$977$$ 3.00000 0.0959785 0.0479893 0.998848i $$-0.484719\pi$$
0.0479893 + 0.998848i $$0.484719\pi$$
$$978$$ 0 0
$$979$$ −50.0000 −1.59801
$$980$$ −8.00000 −0.255551
$$981$$ 0 0
$$982$$ 28.0000 0.893516
$$983$$ −42.0000 −1.33959 −0.669796 0.742545i $$-0.733618\pi$$
−0.669796 + 0.742545i $$0.733618\pi$$
$$984$$ 0 0
$$985$$ −8.00000 −0.254901
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 20.0000 0.636285
$$989$$ 8.00000 0.254385
$$990$$ 0 0
$$991$$ 5.00000 0.158830 0.0794151 0.996842i $$-0.474695\pi$$
0.0794151 + 0.996842i $$0.474695\pi$$
$$992$$ 48.0000 1.52400
$$993$$ 0 0
$$994$$ −24.0000 −0.761234
$$995$$ −12.0000 −0.380426
$$996$$ 0 0
$$997$$ −56.0000 −1.77354 −0.886769 0.462213i $$-0.847056\pi$$
−0.886769 + 0.462213i $$0.847056\pi$$
$$998$$ 40.0000 1.26618
$$999$$ 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 1449.2.a.a.1.1 1
3.2 odd 2 483.2.a.b.1.1 1
12.11 even 2 7728.2.a.l.1.1 1
21.20 even 2 3381.2.a.l.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.a.b.1.1 1 3.2 odd 2
1449.2.a.a.1.1 1 1.1 even 1 trivial
3381.2.a.l.1.1 1 21.20 even 2
7728.2.a.l.1.1 1 12.11 even 2