# Properties

 Label 7350.2.a.bl.1.1 Level $7350$ Weight $2$ Character 7350.1 Self dual yes Analytic conductor $58.690$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7350.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$58.6900454856$$ Analytic rank: $$0$$ 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 $$\chi$$ $$=$$ 7350.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +5.00000 q^{11} +1.00000 q^{12} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} +8.00000 q^{19} -5.00000 q^{22} +4.00000 q^{23} -1.00000 q^{24} +1.00000 q^{27} -5.00000 q^{29} +3.00000 q^{31} -1.00000 q^{32} +5.00000 q^{33} -4.00000 q^{34} +1.00000 q^{36} +4.00000 q^{37} -8.00000 q^{38} -2.00000 q^{43} +5.00000 q^{44} -4.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} +4.00000 q^{51} +9.00000 q^{53} -1.00000 q^{54} +8.00000 q^{57} +5.00000 q^{58} -11.0000 q^{59} -6.00000 q^{61} -3.00000 q^{62} +1.00000 q^{64} -5.00000 q^{66} +2.00000 q^{67} +4.00000 q^{68} +4.00000 q^{69} +2.00000 q^{71} -1.00000 q^{72} -10.0000 q^{73} -4.00000 q^{74} +8.00000 q^{76} +3.00000 q^{79} +1.00000 q^{81} +7.00000 q^{83} +2.00000 q^{86} -5.00000 q^{87} -5.00000 q^{88} -6.00000 q^{89} +4.00000 q^{92} +3.00000 q^{93} -6.00000 q^{94} -1.00000 q^{96} -7.00000 q^{97} +5.00000 q^{99} +O(q^{100})$$

## 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
$$3$$ 1.00000 0.577350
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 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 $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 8.00000 1.83533 0.917663 0.397360i $$-0.130073\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −5.00000 −1.06600
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 0 0
$$31$$ 3.00000 0.538816 0.269408 0.963026i $$-0.413172\pi$$
0.269408 + 0.963026i $$0.413172\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 5.00000 0.870388
$$34$$ −4.00000 −0.685994
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 4.00000 0.657596 0.328798 0.944400i $$-0.393356\pi$$
0.328798 + 0.944400i $$0.393356\pi$$
$$38$$ −8.00000 −1.29777
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 5.00000 0.753778
$$45$$ 0 0
$$46$$ −4.00000 −0.589768
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ 0 0
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 8.00000 1.05963
$$58$$ 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 $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ −3.00000 −0.381000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −5.00000 −0.615457
$$67$$ 2.00000 0.244339 0.122169 0.992509i $$-0.461015\pi$$
0.122169 + 0.992509i $$0.461015\pi$$
$$68$$ 4.00000 0.485071
$$69$$ 4.00000 0.481543
$$70$$ 0 0
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ −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 $$0.446023\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 7.00000 0.768350 0.384175 0.923260i $$-0.374486\pi$$
0.384175 + 0.923260i $$0.374486\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 2.00000 0.215666
$$87$$ −5.00000 −0.536056
$$88$$ −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
$$93$$ 3.00000 0.311086
$$94$$ −6.00000 −0.618853
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ −7.00000 −0.710742 −0.355371 0.934725i $$-0.615646\pi$$
−0.355371 + 0.934725i $$0.615646\pi$$
$$98$$ 0 0
$$99$$ 5.00000 0.502519
$$100$$ 0 0
$$101$$ 10.0000 0.995037 0.497519 0.867453i $$-0.334245\pi$$
0.497519 + 0.867453i $$0.334245\pi$$
$$102$$ −4.00000 −0.396059
$$103$$ −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 $$0.546322\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ 4.00000 0.379663
$$112$$ 0 0
$$113$$ −16.0000 −1.50515 −0.752577 0.658505i $$-0.771189\pi$$
−0.752577 + 0.658505i $$0.771189\pi$$
$$114$$ −8.00000 −0.749269
$$115$$ 0 0
$$116$$ −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
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −9.00000 −0.798621 −0.399310 0.916816i $$-0.630750\pi$$
−0.399310 + 0.916816i $$0.630750\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −2.00000 −0.176090
$$130$$ 0 0
$$131$$ 1.00000 0.0873704 0.0436852 0.999045i $$-0.486090\pi$$
0.0436852 + 0.999045i $$0.486090\pi$$
$$132$$ 5.00000 0.435194
$$133$$ 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 $$0.472772\pi$$
$$138$$ −4.00000 −0.340503
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ −2.00000 −0.167836
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 10.0000 0.827606
$$147$$ 0 0
$$148$$ 4.00000 0.328798
$$149$$ −18.0000 −1.47462 −0.737309 0.675556i $$-0.763904\pi$$
−0.737309 + 0.675556i $$0.763904\pi$$
$$150$$ 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
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 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
$$159$$ 9.00000 0.713746
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −7.00000 −0.543305
$$167$$ 14.0000 1.08335 0.541676 0.840587i $$-0.317790\pi$$
0.541676 + 0.840587i $$0.317790\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 8.00000 0.611775
$$172$$ −2.00000 −0.152499
$$173$$ −22.0000 −1.67263 −0.836315 0.548250i $$-0.815294\pi$$
−0.836315 + 0.548250i $$0.815294\pi$$
$$174$$ 5.00000 0.379049
$$175$$ 0 0
$$176$$ 5.00000 0.376889
$$177$$ −11.0000 −0.826811
$$178$$ 6.00000 0.449719
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ −6.00000 −0.443533
$$184$$ −4.00000 −0.294884
$$185$$ 0 0
$$186$$ −3.00000 −0.219971
$$187$$ 20.0000 1.46254
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 24.0000 1.73658 0.868290 0.496058i $$-0.165220\pi$$
0.868290 + 0.496058i $$0.165220\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ −5.00000 −0.359908 −0.179954 0.983675i $$-0.557595\pi$$
−0.179954 + 0.983675i $$0.557595\pi$$
$$194$$ 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 $$0.522698\pi$$
$$198$$ −5.00000 −0.355335
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 0 0
$$201$$ 2.00000 0.141069
$$202$$ −10.0000 −0.703598
$$203$$ 0 0
$$204$$ 4.00000 0.280056
$$205$$ 0 0
$$206$$ 8.00000 0.557386
$$207$$ 4.00000 0.278019
$$208$$ 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
$$213$$ 2.00000 0.137038
$$214$$ 3.00000 0.205076
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 2.00000 0.135457
$$219$$ −10.0000 −0.675737
$$220$$ 0 0
$$221$$ 0 0
$$222$$ −4.00000 −0.268462
$$223$$ 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 $$-0.531743\pi$$
−0.0995585 + 0.995032i $$0.531743\pi$$
$$228$$ 8.00000 0.529813
$$229$$ −20.0000 −1.32164 −0.660819 0.750546i $$-0.729791\pi$$
−0.660819 + 0.750546i $$0.729791\pi$$
$$230$$ 0 0
$$231$$ 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
$$235$$ 0 0
$$236$$ −11.0000 −0.716039
$$237$$ 3.00000 0.194871
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ −25.0000 −1.61039 −0.805196 0.593009i $$-0.797940\pi$$
−0.805196 + 0.593009i $$0.797940\pi$$
$$242$$ −14.0000 −0.899954
$$243$$ 1.00000 0.0641500
$$244$$ −6.00000 −0.384111
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −3.00000 −0.190500
$$249$$ 7.00000 0.443607
$$250$$ 0 0
$$251$$ 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 $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 2.00000 0.124515
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −5.00000 −0.309492
$$262$$ −1.00000 −0.0617802
$$263$$ 30.0000 1.84988 0.924940 0.380114i $$-0.124115\pi$$
0.924940 + 0.380114i $$0.124115\pi$$
$$264$$ −5.00000 −0.307729
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ 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 $$-0.349427\pi$$
0.455593 + 0.890188i $$0.349427\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 0 0
$$276$$ 4.00000 0.240772
$$277$$ 16.0000 0.961347 0.480673 0.876900i $$-0.340392\pi$$
0.480673 + 0.876900i $$0.340392\pi$$
$$278$$ 14.0000 0.839664
$$279$$ 3.00000 0.179605
$$280$$ 0 0
$$281$$ 2.00000 0.119310 0.0596550 0.998219i $$-0.481000\pi$$
0.0596550 + 0.998219i $$0.481000\pi$$
$$282$$ −6.00000 −0.357295
$$283$$ −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
$$288$$ −1.00000 −0.0589256
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ −7.00000 −0.410347
$$292$$ −10.0000 −0.585206
$$293$$ 21.0000 1.22683 0.613417 0.789760i $$-0.289795\pi$$
0.613417 + 0.789760i $$0.289795\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −4.00000 −0.232495
$$297$$ 5.00000 0.290129
$$298$$ 18.0000 1.04271
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −19.0000 −1.09333
$$303$$ 10.0000 0.574485
$$304$$ 8.00000 0.458831
$$305$$ 0 0
$$306$$ −4.00000 −0.228665
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ −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 $$0.526849\pi$$
$$318$$ −9.00000 −0.504695
$$319$$ −25.0000 −1.39973
$$320$$ 0 0
$$321$$ −3.00000 −0.167444
$$322$$ 0 0
$$323$$ 32.0000 1.78053
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −4.00000 −0.221540
$$327$$ −2.00000 −0.110600
$$328$$ 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
$$333$$ 4.00000 0.219199
$$334$$ −14.0000 −0.766046
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −9.00000 −0.490261 −0.245131 0.969490i $$-0.578831\pi$$
−0.245131 + 0.969490i $$0.578831\pi$$
$$338$$ 13.0000 0.707107
$$339$$ −16.0000 −0.869001
$$340$$ 0 0
$$341$$ 15.0000 0.812296
$$342$$ −8.00000 −0.432590
$$343$$ 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 $$0.604388\pi$$
$$348$$ −5.00000 −0.268028
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −5.00000 −0.266501
$$353$$ −24.0000 −1.27739 −0.638696 0.769460i $$-0.720526\pi$$
−0.638696 + 0.769460i $$0.720526\pi$$
$$354$$ 11.0000 0.584643
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ 10.0000 0.527780 0.263890 0.964553i $$-0.414994\pi$$
0.263890 + 0.964553i $$0.414994\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ 0 0
$$363$$ 14.0000 0.734809
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 6.00000 0.313625
$$367$$ −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
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 3.00000 0.155543
$$373$$ 32.0000 1.65690 0.828449 0.560065i $$-0.189224\pi$$
0.828449 + 0.560065i $$0.189224\pi$$
$$374$$ −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 $$0.365203\pi$$
$$380$$ 0 0
$$381$$ −9.00000 −0.461084
$$382$$ −24.0000 −1.22795
$$383$$ 34.0000 1.73732 0.868659 0.495410i $$-0.164982\pi$$
0.868659 + 0.495410i $$0.164982\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ 5.00000 0.254493
$$387$$ −2.00000 −0.101666
$$388$$ −7.00000 −0.355371
$$389$$ −2.00000 −0.101404 −0.0507020 0.998714i $$-0.516146\pi$$
−0.0507020 + 0.998714i $$0.516146\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ 0 0
$$393$$ 1.00000 0.0504433
$$394$$ 2.00000 0.100759
$$395$$ 0 0
$$396$$ 5.00000 0.251259
$$397$$ −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
$$400$$ 0 0
$$401$$ 24.0000 1.19850 0.599251 0.800561i $$-0.295465\pi$$
0.599251 + 0.800561i $$0.295465\pi$$
$$402$$ −2.00000 −0.0997509
$$403$$ 0 0
$$404$$ 10.0000 0.497519
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 20.0000 0.991363
$$408$$ −4.00000 −0.198030
$$409$$ −25.0000 −1.23617 −0.618085 0.786111i $$-0.712091\pi$$
−0.618085 + 0.786111i $$0.712091\pi$$
$$410$$ 0 0
$$411$$ 2.00000 0.0986527
$$412$$ −8.00000 −0.394132
$$413$$ 0 0
$$414$$ −4.00000 −0.196589
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −14.0000 −0.685583
$$418$$ −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
$$423$$ 6.00000 0.291730
$$424$$ −9.00000 −0.437079
$$425$$ 0 0
$$426$$ −2.00000 −0.0969003
$$427$$ 0 0
$$428$$ −3.00000 −0.145010
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −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
$$438$$ 10.0000 0.477818
$$439$$ 15.0000 0.715911 0.357955 0.933739i $$-0.383474\pi$$
0.357955 + 0.933739i $$0.383474\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −17.0000 −0.807694 −0.403847 0.914826i $$-0.632327\pi$$
−0.403847 + 0.914826i $$0.632327\pi$$
$$444$$ 4.00000 0.189832
$$445$$ 0 0
$$446$$ −7.00000 −0.331460
$$447$$ −18.0000 −0.851371
$$448$$ 0 0
$$449$$ 16.0000 0.755087 0.377543 0.925992i $$-0.376769\pi$$
0.377543 + 0.925992i $$0.376769\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −16.0000 −0.752577
$$453$$ 19.0000 0.892698
$$454$$ 3.00000 0.140797
$$455$$ 0 0
$$456$$ −8.00000 −0.374634
$$457$$ −31.0000 −1.45012 −0.725059 0.688686i $$-0.758188\pi$$
−0.725059 + 0.688686i $$0.758188\pi$$
$$458$$ 20.0000 0.934539
$$459$$ 4.00000 0.186704
$$460$$ 0 0
$$461$$ −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 $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ −5.00000 −0.232119
$$465$$ 0 0
$$466$$ −4.00000 −0.185296
$$467$$ 20.0000 0.925490 0.462745 0.886492i $$-0.346865\pi$$
0.462745 + 0.886492i $$0.346865\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 4.00000 0.184310
$$472$$ 11.0000 0.506316
$$473$$ −10.0000 −0.459800
$$474$$ −3.00000 −0.137795
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 9.00000 0.412082
$$478$$ 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
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ −5.00000 −0.226572 −0.113286 0.993562i $$-0.536138\pi$$
−0.113286 + 0.993562i $$0.536138\pi$$
$$488$$ 6.00000 0.271607
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ 9.00000 0.406164 0.203082 0.979162i $$-0.434904\pi$$
0.203082 + 0.979162i $$0.434904\pi$$
$$492$$ 0 0
$$493$$ −20.0000 −0.900755
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 3.00000 0.134704
$$497$$ 0 0
$$498$$ −7.00000 −0.313678
$$499$$ 10.0000 0.447661 0.223831 0.974628i $$-0.428144\pi$$
0.223831 + 0.974628i $$0.428144\pi$$
$$500$$ 0 0
$$501$$ 14.0000 0.625474
$$502$$ −21.0000 −0.937276
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −20.0000 −0.889108
$$507$$ −13.0000 −0.577350
$$508$$ −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
$$513$$ 8.00000 0.353209
$$514$$ −6.00000 −0.264649
$$515$$ 0 0
$$516$$ −2.00000 −0.0880451
$$517$$ 30.0000 1.31940
$$518$$ 0 0
$$519$$ −22.0000 −0.965693
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 5.00000 0.218844
$$523$$ −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
$$528$$ 5.00000 0.217597
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ −11.0000 −0.477359
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ −2.00000 −0.0863868
$$537$$ 12.0000 0.517838
$$538$$ −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
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ 2.00000 0.0854358
$$549$$ −6.00000 −0.256074
$$550$$ 0 0
$$551$$ −40.0000 −1.70406
$$552$$ −4.00000 −0.170251
$$553$$ 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 $$0.337993\pi$$
$$558$$ −3.00000 −0.127000
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 20.0000 0.844401
$$562$$ −2.00000 −0.0843649
$$563$$ −17.0000 −0.716465 −0.358232 0.933632i $$-0.616620\pi$$
−0.358232 + 0.933632i $$0.616620\pi$$
$$564$$ 6.00000 0.252646
$$565$$ 0 0
$$566$$ 10.0000 0.420331
$$567$$ 0 0
$$568$$ −2.00000 −0.0839181
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ −30.0000 −1.25546 −0.627730 0.778431i $$-0.716016\pi$$
−0.627730 + 0.778431i $$0.716016\pi$$
$$572$$ 0 0
$$573$$ 24.0000 1.00261
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −31.0000 −1.29055 −0.645273 0.763952i $$-0.723257\pi$$
−0.645273 + 0.763952i $$0.723257\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ −5.00000 −0.207793
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 7.00000 0.290159
$$583$$ 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 $$-0.756916\pi$$
−0.722302 + 0.691577i $$0.756916\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ 0 0
$$591$$ −2.00000 −0.0822690
$$592$$ 4.00000 0.164399
$$593$$ −36.0000 −1.47834 −0.739171 0.673517i $$-0.764783\pi$$
−0.739171 + 0.673517i $$0.764783\pi$$
$$594$$ −5.00000 −0.205152
$$595$$ 0 0
$$596$$ −18.0000 −0.737309
$$597$$ −4.00000 −0.163709
$$598$$ 0 0
$$599$$ −30.0000 −1.22577 −0.612883 0.790173i $$-0.709990\pi$$
−0.612883 + 0.790173i $$0.709990\pi$$
$$600$$ 0 0
$$601$$ 35.0000 1.42768 0.713840 0.700309i $$-0.246954\pi$$
0.713840 + 0.700309i $$0.246954\pi$$
$$602$$ 0 0
$$603$$ 2.00000 0.0814463
$$604$$ 19.0000 0.773099
$$605$$ 0 0
$$606$$ −10.0000 −0.406222
$$607$$ 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
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 4.00000 0.161690
$$613$$ −12.0000 −0.484675 −0.242338 0.970192i $$-0.577914\pi$$
−0.242338 + 0.970192i $$0.577914\pi$$
$$614$$ 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 $$0.512818\pi$$
$$618$$ 8.00000 0.321807
$$619$$ 10.0000 0.401934 0.200967 0.979598i $$-0.435592\pi$$
0.200967 + 0.979598i $$0.435592\pi$$
$$620$$ 0 0
$$621$$ 4.00000 0.160514
$$622$$ 32.0000 1.28308
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 1.00000 0.0399680
$$627$$ 40.0000 1.59745
$$628$$ 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
$$633$$ 2.00000 0.0794929
$$634$$ 3.00000 0.119145
$$635$$ 0 0
$$636$$ 9.00000 0.356873
$$637$$ 0 0
$$638$$ 25.0000 0.989759
$$639$$ 2.00000 0.0791188
$$640$$ 0 0
$$641$$ 26.0000 1.02694 0.513469 0.858108i $$-0.328360\pi$$
0.513469 + 0.858108i $$0.328360\pi$$
$$642$$ 3.00000 0.118401
$$643$$ −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 $$-0.384880\pi$$
0.353827 + 0.935311i $$0.384880\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ −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 $$0.223679\pi$$
$$654$$ 2.00000 0.0782062
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −10.0000 −0.390137
$$658$$ 0 0
$$659$$ −40.0000 −1.55818 −0.779089 0.626913i $$-0.784318\pi$$
−0.779089 + 0.626913i $$0.784318\pi$$
$$660$$ 0 0
$$661$$ 10.0000 0.388955 0.194477 0.980907i $$-0.437699\pi$$
0.194477 + 0.980907i $$0.437699\pi$$
$$662$$ 4.00000 0.155464
$$663$$ 0 0
$$664$$ −7.00000 −0.271653
$$665$$ 0 0
$$666$$ −4.00000 −0.154997
$$667$$ −20.0000 −0.774403
$$668$$ 14.0000 0.541676
$$669$$ 7.00000 0.270636
$$670$$ 0 0
$$671$$ −30.0000 −1.15814
$$672$$ 0 0
$$673$$ 19.0000 0.732396 0.366198 0.930537i $$-0.380659\pi$$
0.366198 + 0.930537i $$0.380659\pi$$
$$674$$ 9.00000 0.346667
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ 27.0000 1.03769 0.518847 0.854867i $$-0.326361\pi$$
0.518847 + 0.854867i $$0.326361\pi$$
$$678$$ 16.0000 0.614476
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −3.00000 −0.114960
$$682$$ −15.0000 −0.574380
$$683$$ 9.00000 0.344375 0.172188 0.985064i $$-0.444916\pi$$
0.172188 + 0.985064i $$0.444916\pi$$
$$684$$ 8.00000 0.305888
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −20.0000 −0.763048
$$688$$ −2.00000 −0.0762493
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ −22.0000 −0.836315
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 0 0
$$696$$ 5.00000 0.189525
$$697$$ 0 0
$$698$$ 14.0000 0.529908
$$699$$ 4.00000 0.151294
$$700$$ 0 0
$$701$$ −5.00000 −0.188847 −0.0944237 0.995532i $$-0.530101\pi$$
−0.0944237 + 0.995532i $$0.530101\pi$$
$$702$$ 0 0
$$703$$ 32.0000 1.20690
$$704$$ 5.00000 0.188445
$$705$$ 0 0
$$706$$ 24.0000 0.903252
$$707$$ 0 0
$$708$$ −11.0000 −0.413405
$$709$$ 38.0000 1.42712 0.713560 0.700594i $$-0.247082\pi$$
0.713560 + 0.700594i $$0.247082\pi$$
$$710$$ 0 0
$$711$$ 3.00000 0.112509
$$712$$ 6.00000 0.224860
$$713$$ 12.0000 0.449404
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ −12.0000 −0.448148
$$718$$ −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
$$723$$ −25.0000 −0.929760
$$724$$ 0 0
$$725$$ 0 0
$$726$$ −14.0000 −0.519589
$$727$$ −7.00000 −0.259616 −0.129808 0.991539i $$-0.541436\pi$$
−0.129808 + 0.991539i $$0.541436\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −8.00000 −0.295891
$$732$$ −6.00000 −0.221766
$$733$$ 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 $$0.686053\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −30.0000 −1.10059 −0.550297 0.834969i $$-0.685485\pi$$
−0.550297 + 0.834969i $$0.685485\pi$$
$$744$$ −3.00000 −0.109985
$$745$$ 0 0
$$746$$ −32.0000 −1.17160
$$747$$ 7.00000 0.256117
$$748$$ 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
$$753$$ 21.0000 0.765283
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 54.0000 1.96266 0.981332 0.192323i $$-0.0616021\pi$$
0.981332 + 0.192323i $$0.0616021\pi$$
$$758$$ −16.0000 −0.581146
$$759$$ 20.0000 0.725954
$$760$$ 0 0
$$761$$ 8.00000 0.290000 0.145000 0.989432i $$-0.453682\pi$$
0.145000 + 0.989432i $$0.453682\pi$$
$$762$$ 9.00000 0.326036
$$763$$ 0 0
$$764$$ 24.0000 0.868290
$$765$$ 0 0
$$766$$ −34.0000 −1.22847
$$767$$ 0 0
$$768$$ 1.00000 0.0360844
$$769$$ −35.0000 −1.26213 −0.631066 0.775729i $$-0.717382\pi$$
−0.631066 + 0.775729i $$0.717382\pi$$
$$770$$ 0 0
$$771$$ 6.00000 0.216085
$$772$$ −5.00000 −0.179954
$$773$$ −10.0000 −0.359675 −0.179838 0.983696i $$-0.557557\pi$$
−0.179838 + 0.983696i $$0.557557\pi$$
$$774$$ 2.00000 0.0718885
$$775$$ 0 0
$$776$$ 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
$$783$$ −5.00000 −0.178685
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −1.00000 −0.0356688
$$787$$ 18.0000 0.641631 0.320815 0.947142i $$-0.396043\pi$$
0.320815 + 0.947142i $$0.396043\pi$$
$$788$$ −2.00000 −0.0712470
$$789$$ 30.0000 1.06803
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −5.00000 −0.177667
$$793$$ 0 0
$$794$$ 36.0000 1.27759
$$795$$ 0 0
$$796$$ −4.00000 −0.141776
$$797$$ −21.0000 −0.743858 −0.371929 0.928261i $$-0.621304\pi$$
−0.371929 + 0.928261i $$0.621304\pi$$
$$798$$ 0 0
$$799$$ 24.0000 0.849059
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ −24.0000 −0.847469
$$803$$ −50.0000 −1.76446
$$804$$ 2.00000 0.0705346
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 31.0000 1.09125
$$808$$ −10.0000 −0.351799
$$809$$ 40.0000 1.40633 0.703163 0.711029i $$-0.251771\pi$$
0.703163 + 0.711029i $$0.251771\pi$$
$$810$$ 0 0
$$811$$ −14.0000 −0.491606 −0.245803 0.969320i $$-0.579052\pi$$
−0.245803 + 0.969320i $$0.579052\pi$$
$$812$$ 0 0
$$813$$ 15.0000 0.526073
$$814$$ −20.0000 −0.701000
$$815$$ 0 0
$$816$$ 4.00000 0.140028
$$817$$ −16.0000 −0.559769
$$818$$ 25.0000 0.874105
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −25.0000 −0.872506 −0.436253 0.899824i $$-0.643695\pi$$
−0.436253 + 0.899824i $$0.643695\pi$$
$$822$$ −2.00000 −0.0697580
$$823$$ −40.0000 −1.39431 −0.697156 0.716919i $$-0.745552\pi$$
−0.697156 + 0.716919i $$0.745552\pi$$
$$824$$ 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 $$0.550015\pi$$
$$828$$ 4.00000 0.139010
$$829$$ −32.0000 −1.11141 −0.555703 0.831381i $$-0.687551\pi$$
−0.555703 + 0.831381i $$0.687551\pi$$
$$830$$ 0 0
$$831$$ 16.0000 0.555034
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 14.0000 0.484780
$$835$$ 0 0
$$836$$ 40.0000 1.38343
$$837$$ 3.00000 0.103695
$$838$$ 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
$$843$$ 2.00000 0.0688837
$$844$$ 2.00000 0.0688428
$$845$$ 0 0
$$846$$ −6.00000 −0.206284
$$847$$ 0 0
$$848$$ 9.00000 0.309061
$$849$$ −10.0000 −0.343199
$$850$$ 0 0
$$851$$ 16.0000 0.548473
$$852$$ 2.00000 0.0685189
$$853$$ −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 $$-0.400530\pi$$
0.307434 + 0.951569i $$0.400530\pi$$
$$858$$ 0 0
$$859$$ −34.0000 −1.16007 −0.580033 0.814593i $$-0.696960\pi$$
−0.580033 + 0.814593i $$0.696960\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −12.0000 −0.408722
$$863$$ −10.0000 −0.340404 −0.170202 0.985409i $$-0.554442\pi$$
−0.170202 + 0.985409i $$0.554442\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ 14.0000 0.475739
$$867$$ −1.00000 −0.0339618
$$868$$ 0 0
$$869$$ 15.0000 0.508840
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 2.00000 0.0677285
$$873$$ −7.00000 −0.236914
$$874$$ −32.0000 −1.08242
$$875$$ 0 0
$$876$$ −10.0000 −0.337869
$$877$$ 32.0000 1.08056 0.540282 0.841484i $$-0.318318\pi$$
0.540282 + 0.841484i $$0.318318\pi$$
$$878$$ −15.0000 −0.506225
$$879$$ 21.0000 0.708312
$$880$$ 0 0
$$881$$ −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 $$-0.264982\pi$$
0.673054 + 0.739594i $$0.264982\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 17.0000 0.571126
$$887$$ −36.0000 −1.20876 −0.604381 0.796696i $$-0.706579\pi$$
−0.604381 + 0.796696i $$0.706579\pi$$
$$888$$ −4.00000 −0.134231
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 5.00000 0.167506
$$892$$ 7.00000 0.234377
$$893$$ 48.0000 1.60626
$$894$$ 18.0000 0.602010
$$895$$ 0 0
$$896$$ 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
$$906$$ −19.0000 −0.631233
$$907$$ −12.0000 −0.398453 −0.199227 0.979953i $$-0.563843\pi$$
−0.199227 + 0.979953i $$0.563843\pi$$
$$908$$ −3.00000 −0.0995585
$$909$$ 10.0000 0.331679
$$910$$ 0 0
$$911$$ 30.0000 0.993944 0.496972 0.867766i $$-0.334445\pi$$
0.496972 + 0.867766i $$0.334445\pi$$
$$912$$ 8.00000 0.264906
$$913$$ 35.0000 1.15833
$$914$$ 31.0000 1.02539
$$915$$ 0 0
$$916$$ −20.0000 −0.660819
$$917$$ 0 0
$$918$$ −4.00000 −0.132020
$$919$$ −32.0000 −1.05558 −0.527791 0.849374i $$-0.676980\pi$$
−0.527791 + 0.849374i $$0.676980\pi$$
$$920$$ 0 0
$$921$$ −28.0000 −0.922631
$$922$$ 14.0000 0.461065
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 16.0000 0.525793
$$927$$ −8.00000 −0.262754
$$928$$ 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
$$933$$ −32.0000 −1.04763
$$934$$ −20.0000 −0.654420
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −35.0000 −1.14340 −0.571700 0.820463i $$-0.693716\pi$$
−0.571700 + 0.820463i $$0.693716\pi$$
$$938$$ 0 0
$$939$$ −1.00000 −0.0326338
$$940$$ 0 0
$$941$$ −11.0000 −0.358590 −0.179295 0.983795i $$-0.557382\pi$$
−0.179295 + 0.983795i $$0.557382\pi$$
$$942$$ −4.00000 −0.130327
$$943$$ 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 $$0.325958\pi$$
$$948$$ 3.00000 0.0974355
$$949$$ 0 0
$$950$$ 0 0
$$951$$ −3.00000 −0.0972817
$$952$$ 0 0
$$953$$ −2.00000 −0.0647864 −0.0323932 0.999475i $$-0.510313\pi$$
−0.0323932 + 0.999475i $$0.510313\pi$$
$$954$$ −9.00000 −0.291386
$$955$$ 0 0
$$956$$ −12.0000 −0.388108
$$957$$ −25.0000 −0.808135
$$958$$ −38.0000 −1.22772
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −22.0000 −0.709677
$$962$$ 0 0
$$963$$ −3.00000 −0.0966736
$$964$$ −25.0000 −0.805196
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 61.0000 1.96163 0.980814 0.194946i $$-0.0624533\pi$$
0.980814 + 0.194946i $$0.0624533\pi$$
$$968$$ −14.0000 −0.449977
$$969$$ 32.0000 1.02799
$$970$$ 0 0
$$971$$ 15.0000 0.481373 0.240686 0.970603i $$-0.422627\pi$$
0.240686 + 0.970603i $$0.422627\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 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 $$0.340676\pi$$
$$978$$ −4.00000 −0.127906
$$979$$ −30.0000 −0.958804
$$980$$ 0 0
$$981$$ −2.00000 −0.0638551
$$982$$ −9.00000 −0.287202
$$983$$ 60.0000 1.91370 0.956851 0.290578i $$-0.0938475\pi$$
0.956851 + 0.290578i $$0.0938475\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 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
$$993$$ −4.00000 −0.126936
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 7.00000 0.221803
$$997$$ −38.0000 −1.20347 −0.601736 0.798695i $$-0.705524\pi$$
−0.601736 + 0.798695i $$0.705524\pi$$
$$998$$ −10.0000 −0.316544
$$999$$ 4.00000 0.126554
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 7350.2.a.bl.1.1 1
5.4 even 2 294.2.a.e.1.1 1
7.2 even 3 1050.2.i.l.151.1 2
7.4 even 3 1050.2.i.l.751.1 2
7.6 odd 2 7350.2.a.q.1.1 1
15.14 odd 2 882.2.a.c.1.1 1
20.19 odd 2 2352.2.a.t.1.1 1
35.2 odd 12 1050.2.o.a.949.1 4
35.4 even 6 42.2.e.a.37.1 yes 2
35.9 even 6 42.2.e.a.25.1 2
35.18 odd 12 1050.2.o.a.499.1 4
35.19 odd 6 294.2.e.b.67.1 2
35.23 odd 12 1050.2.o.a.949.2 4
35.24 odd 6 294.2.e.b.79.1 2
35.32 odd 12 1050.2.o.a.499.2 4
35.34 odd 2 294.2.a.f.1.1 1
40.19 odd 2 9408.2.a.q.1.1 1
40.29 even 2 9408.2.a.ce.1.1 1
60.59 even 2 7056.2.a.w.1.1 1
105.44 odd 6 126.2.g.c.109.1 2
105.59 even 6 882.2.g.i.667.1 2
105.74 odd 6 126.2.g.c.37.1 2
105.89 even 6 882.2.g.i.361.1 2
105.104 even 2 882.2.a.d.1.1 1
140.19 even 6 2352.2.q.u.1537.1 2
140.39 odd 6 336.2.q.b.289.1 2
140.59 even 6 2352.2.q.u.961.1 2
140.79 odd 6 336.2.q.b.193.1 2
140.139 even 2 2352.2.a.f.1.1 1
280.69 odd 2 9408.2.a.z.1.1 1
280.109 even 6 1344.2.q.g.961.1 2
280.139 even 2 9408.2.a.cr.1.1 1
280.149 even 6 1344.2.q.g.193.1 2
280.179 odd 6 1344.2.q.s.961.1 2
280.219 odd 6 1344.2.q.s.193.1 2
315.4 even 6 1134.2.h.e.541.1 2
315.74 odd 6 1134.2.e.e.919.1 2
315.79 even 6 1134.2.h.e.109.1 2
315.149 odd 6 1134.2.e.e.865.1 2
315.184 even 6 1134.2.e.l.865.1 2
315.214 even 6 1134.2.e.l.919.1 2
315.254 odd 6 1134.2.h.l.109.1 2
315.284 odd 6 1134.2.h.l.541.1 2
420.179 even 6 1008.2.s.k.289.1 2
420.359 even 6 1008.2.s.k.865.1 2
420.419 odd 2 7056.2.a.bl.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.e.a.25.1 2 35.9 even 6
42.2.e.a.37.1 yes 2 35.4 even 6
126.2.g.c.37.1 2 105.74 odd 6
126.2.g.c.109.1 2 105.44 odd 6
294.2.a.e.1.1 1 5.4 even 2
294.2.a.f.1.1 1 35.34 odd 2
294.2.e.b.67.1 2 35.19 odd 6
294.2.e.b.79.1 2 35.24 odd 6
336.2.q.b.193.1 2 140.79 odd 6
336.2.q.b.289.1 2 140.39 odd 6
882.2.a.c.1.1 1 15.14 odd 2
882.2.a.d.1.1 1 105.104 even 2
882.2.g.i.361.1 2 105.89 even 6
882.2.g.i.667.1 2 105.59 even 6
1008.2.s.k.289.1 2 420.179 even 6
1008.2.s.k.865.1 2 420.359 even 6
1050.2.i.l.151.1 2 7.2 even 3
1050.2.i.l.751.1 2 7.4 even 3
1050.2.o.a.499.1 4 35.18 odd 12
1050.2.o.a.499.2 4 35.32 odd 12
1050.2.o.a.949.1 4 35.2 odd 12
1050.2.o.a.949.2 4 35.23 odd 12
1134.2.e.e.865.1 2 315.149 odd 6
1134.2.e.e.919.1 2 315.74 odd 6
1134.2.e.l.865.1 2 315.184 even 6
1134.2.e.l.919.1 2 315.214 even 6
1134.2.h.e.109.1 2 315.79 even 6
1134.2.h.e.541.1 2 315.4 even 6
1134.2.h.l.109.1 2 315.254 odd 6
1134.2.h.l.541.1 2 315.284 odd 6
1344.2.q.g.193.1 2 280.149 even 6
1344.2.q.g.961.1 2 280.109 even 6
1344.2.q.s.193.1 2 280.219 odd 6
1344.2.q.s.961.1 2 280.179 odd 6
2352.2.a.f.1.1 1 140.139 even 2
2352.2.a.t.1.1 1 20.19 odd 2
2352.2.q.u.961.1 2 140.59 even 6
2352.2.q.u.1537.1 2 140.19 even 6
7056.2.a.w.1.1 1 60.59 even 2
7056.2.a.bl.1.1 1 420.419 odd 2
7350.2.a.q.1.1 1 7.6 odd 2
7350.2.a.bl.1.1 1 1.1 even 1 trivial
9408.2.a.q.1.1 1 40.19 odd 2
9408.2.a.z.1.1 1 280.69 odd 2
9408.2.a.ce.1.1 1 40.29 even 2
9408.2.a.cr.1.1 1 280.139 even 2