# Properties

 Label 7350.2.a.q.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 $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −8.00000 −1.83533 −0.917663 0.397360i $$-0.869927\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 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 $$-0.586828\pi$$
−0.269408 + 0.963026i $$0.586828\pi$$
$$32$$ −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 $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ −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 $$-0.245953\pi$$
0.716039 + 0.698060i $$0.245953\pi$$
$$60$$ 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
$$66$$ 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 $$-0.301014\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ −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 $$-0.625514\pi$$
−0.384175 + 0.923260i $$0.625514\pi$$
$$84$$ 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 $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 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 $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ 0 0
$$99$$ 5.00000 0.502519
$$100$$ 0 0
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ −4.00000 −0.396059
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ 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 $$-0.513910\pi$$
−0.0436852 + 0.999045i $$0.513910\pi$$
$$132$$ −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 $$-0.297654\pi$$
0.593732 + 0.804663i $$0.297654\pi$$
$$140$$ 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 $$-0.551026\pi$$
−0.159617 + 0.987179i $$0.551026\pi$$
$$158$$ −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 $$-0.682210\pi$$
−0.541676 + 0.840587i $$0.682210\pi$$
$$168$$ 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 $$-0.184706\pi$$
0.836315 + 0.548250i $$0.184706\pi$$
$$174$$ −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 $$-0.454719\pi$$
0.141776 + 0.989899i $$0.454719\pi$$
$$200$$ 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 $$-0.575305\pi$$
−0.234377 + 0.972146i $$0.575305\pi$$
$$224$$ 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 $$0.468257\pi$$
$$228$$ 8.00000 0.529813
$$229$$ 20.0000 1.32164 0.660819 0.750546i $$-0.270209\pi$$
0.660819 + 0.750546i $$0.270209\pi$$
$$230$$ 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 $$-0.202060\pi$$
0.805196 + 0.593009i $$0.202060\pi$$
$$242$$ −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 $$-0.730613\pi$$
−0.662754 + 0.748837i $$0.730613\pi$$
$$252$$ 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 $$0.559920\pi$$
$$258$$ −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 $$-0.893989\pi$$
−0.945052 + 0.326921i $$0.893989\pi$$
$$270$$ 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
$$275$$ 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 $$-0.403941\pi$$
0.297219 + 0.954809i $$0.403941\pi$$
$$284$$ 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 $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 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 $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ 32.0000 1.81455 0.907277 0.420534i $$-0.138157\pi$$
0.907277 + 0.420534i $$0.138157\pi$$
$$312$$ 0 0
$$313$$ 1.00000 0.0565233 0.0282617 0.999601i $$-0.491003\pi$$
0.0282617 + 0.999601i $$0.491003\pi$$
$$314$$ 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 $$-0.377745\pi$$
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 $$0.279474\pi$$
$$354$$ 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 $$-0.353667\pi$$
0.443696 + 0.896177i $$0.353667\pi$$
$$368$$ 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 $$-0.835018\pi$$
−0.868659 + 0.495410i $$0.835018\pi$$
$$384$$ 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 $$-0.141067\pi$$
0.903394 + 0.428811i $$0.141067\pi$$
$$398$$ −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 $$-0.287909\pi$$
0.618085 + 0.786111i $$0.287909\pi$$
$$410$$ 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 $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 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 $$-0.616526\pi$$
−0.357955 + 0.933739i $$0.616526\pi$$
$$440$$ 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 $$-0.394291\pi$$
0.326023 + 0.945362i $$0.394291\pi$$
$$462$$ 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 $$-0.653135\pi$$
−0.462745 + 0.886492i $$0.653135\pi$$
$$468$$ 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 $$-0.834679\pi$$
−0.868132 + 0.496333i $$0.834679\pi$$
$$480$$ 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 $$-0.607869\pi$$
−0.332432 + 0.943127i $$0.607869\pi$$
$$510$$ 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 $$-0.370988\pi$$
0.394297 + 0.918983i $$0.370988\pi$$
$$522$$ 5.00000 0.218844
$$523$$ 8.00000 0.349816 0.174908 0.984585i $$-0.444037\pi$$
0.174908 + 0.984585i $$0.444037\pi$$
$$524$$ −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 $$-0.383380\pi$$
0.358232 + 0.933632i $$0.383380\pi$$
$$564$$ 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 $$-0.276743\pi$$
0.645273 + 0.763952i $$0.276743\pi$$
$$578$$ 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 $$-0.243084\pi$$
0.722302 + 0.691577i $$0.243084\pi$$
$$588$$ 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 $$-0.235217\pi$$
0.739171 + 0.673517i $$0.235217\pi$$
$$594$$ 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 $$-0.753046\pi$$
−0.713840 + 0.700309i $$0.753046\pi$$
$$602$$ 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 $$-0.684591\pi$$
−0.547948 + 0.836512i $$0.684591\pi$$
$$608$$ 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 $$-0.564408\pi$$
−0.200967 + 0.979598i $$0.564408\pi$$
$$620$$ 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 $$-0.410973\pi$$
0.276053 + 0.961142i $$0.410973\pi$$
$$644$$ 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 $$0.615120\pi$$
$$648$$ −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 $$-0.562301\pi$$
−0.194477 + 0.980907i $$0.562301\pi$$
$$662$$ 4.00000 0.155464
$$663$$ 0 0
$$664$$ 7.00000 0.271653
$$665$$ 0 0
$$666$$ −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 $$-0.673639\pi$$
−0.518847 + 0.854867i $$0.673639\pi$$
$$678$$ −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 $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ 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 $$-0.464312\pi$$
0.111881 + 0.993722i $$0.464312\pi$$
$$720$$ 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 $$-0.458564\pi$$
0.129808 + 0.991539i $$0.458564\pi$$
$$728$$ 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 $$-0.535344\pi$$
−0.110808 + 0.993842i $$0.535344\pi$$
$$734$$ −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 $$-0.546318\pi$$
−0.145000 + 0.989432i $$0.546318\pi$$
$$762$$ −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 $$-0.282618\pi$$
0.631066 + 0.775729i $$0.282618\pi$$
$$770$$ 0 0
$$771$$ 6.00000 0.216085
$$772$$ −5.00000 −0.179954
$$773$$ 10.0000 0.359675 0.179838 0.983696i $$-0.442443\pi$$
0.179838 + 0.983696i $$0.442443\pi$$
$$774$$ 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 $$-0.603957\pi$$
−0.320815 + 0.947142i $$0.603957\pi$$
$$788$$ −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 $$-0.378696\pi$$
0.371929 + 0.928261i $$0.378696\pi$$
$$798$$ 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 $$-0.420948\pi$$
0.245803 + 0.969320i $$0.420948\pi$$
$$812$$ 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 $$-0.312449\pi$$
0.555703 + 0.831381i $$0.312449\pi$$
$$830$$ 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 $$-0.339426\pi$$
0.483334 + 0.875436i $$0.339426\pi$$
$$840$$ 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 $$-0.422959\pi$$
0.239675 + 0.970853i $$0.422959\pi$$
$$854$$ 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 $$0.303040\pi$$
$$860$$ 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 $$-0.249819\pi$$
0.707508 + 0.706705i $$0.249819\pi$$
$$882$$ 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 $$-0.293421\pi$$
0.604381 + 0.796696i $$0.293421\pi$$
$$888$$ 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 $$-0.468619\pi$$
0.0984268 + 0.995144i $$0.468619\pi$$
$$930$$ 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 $$-0.306284\pi$$
0.571700 + 0.820463i $$0.306284\pi$$
$$938$$ 0 0
$$939$$ −1.00000 −0.0326338
$$940$$ 0 0
$$941$$ 11.0000 0.358590 0.179295 0.983795i $$-0.442618\pi$$
0.179295 + 0.983795i $$0.442618\pi$$
$$942$$ −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 $$-0.577373\pi$$
−0.240686 + 0.970603i $$0.577373\pi$$
$$972$$ −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 $$-0.906153\pi$$
−0.956851 + 0.290578i $$0.906153\pi$$
$$984$$ 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 $$-0.294476\pi$$
0.601736 + 0.798695i $$0.294476\pi$$
$$998$$ −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.q.1.1 1
5.4 even 2 294.2.a.f.1.1 1
7.3 odd 6 1050.2.i.l.751.1 2
7.5 odd 6 1050.2.i.l.151.1 2
7.6 odd 2 7350.2.a.bl.1.1 1
15.14 odd 2 882.2.a.d.1.1 1
20.19 odd 2 2352.2.a.f.1.1 1
35.3 even 12 1050.2.o.a.499.1 4
35.4 even 6 294.2.e.b.79.1 2
35.9 even 6 294.2.e.b.67.1 2
35.12 even 12 1050.2.o.a.949.1 4
35.17 even 12 1050.2.o.a.499.2 4
35.19 odd 6 42.2.e.a.25.1 2
35.24 odd 6 42.2.e.a.37.1 yes 2
35.33 even 12 1050.2.o.a.949.2 4
35.34 odd 2 294.2.a.e.1.1 1
40.19 odd 2 9408.2.a.cr.1.1 1
40.29 even 2 9408.2.a.z.1.1 1
60.59 even 2 7056.2.a.bl.1.1 1
105.44 odd 6 882.2.g.i.361.1 2
105.59 even 6 126.2.g.c.37.1 2
105.74 odd 6 882.2.g.i.667.1 2
105.89 even 6 126.2.g.c.109.1 2
105.104 even 2 882.2.a.c.1.1 1
140.19 even 6 336.2.q.b.193.1 2
140.39 odd 6 2352.2.q.u.961.1 2
140.59 even 6 336.2.q.b.289.1 2
140.79 odd 6 2352.2.q.u.1537.1 2
140.139 even 2 2352.2.a.t.1.1 1
280.19 even 6 1344.2.q.s.193.1 2
280.59 even 6 1344.2.q.s.961.1 2
280.69 odd 2 9408.2.a.ce.1.1 1
280.139 even 2 9408.2.a.q.1.1 1
280.229 odd 6 1344.2.q.g.193.1 2
280.269 odd 6 1344.2.q.g.961.1 2
315.59 even 6 1134.2.h.l.541.1 2
315.94 odd 6 1134.2.h.e.541.1 2
315.124 odd 6 1134.2.h.e.109.1 2
315.164 even 6 1134.2.e.e.919.1 2
315.194 even 6 1134.2.e.e.865.1 2
315.229 odd 6 1134.2.e.l.865.1 2
315.299 even 6 1134.2.h.l.109.1 2
315.304 odd 6 1134.2.e.l.919.1 2
420.59 odd 6 1008.2.s.k.289.1 2
420.299 odd 6 1008.2.s.k.865.1 2
420.419 odd 2 7056.2.a.w.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.e.a.25.1 2 35.19 odd 6
42.2.e.a.37.1 yes 2 35.24 odd 6
126.2.g.c.37.1 2 105.59 even 6
126.2.g.c.109.1 2 105.89 even 6
294.2.a.e.1.1 1 35.34 odd 2
294.2.a.f.1.1 1 5.4 even 2
294.2.e.b.67.1 2 35.9 even 6
294.2.e.b.79.1 2 35.4 even 6
336.2.q.b.193.1 2 140.19 even 6
336.2.q.b.289.1 2 140.59 even 6
882.2.a.c.1.1 1 105.104 even 2
882.2.a.d.1.1 1 15.14 odd 2
882.2.g.i.361.1 2 105.44 odd 6
882.2.g.i.667.1 2 105.74 odd 6
1008.2.s.k.289.1 2 420.59 odd 6
1008.2.s.k.865.1 2 420.299 odd 6
1050.2.i.l.151.1 2 7.5 odd 6
1050.2.i.l.751.1 2 7.3 odd 6
1050.2.o.a.499.1 4 35.3 even 12
1050.2.o.a.499.2 4 35.17 even 12
1050.2.o.a.949.1 4 35.12 even 12
1050.2.o.a.949.2 4 35.33 even 12
1134.2.e.e.865.1 2 315.194 even 6
1134.2.e.e.919.1 2 315.164 even 6
1134.2.e.l.865.1 2 315.229 odd 6
1134.2.e.l.919.1 2 315.304 odd 6
1134.2.h.e.109.1 2 315.124 odd 6
1134.2.h.e.541.1 2 315.94 odd 6
1134.2.h.l.109.1 2 315.299 even 6
1134.2.h.l.541.1 2 315.59 even 6
1344.2.q.g.193.1 2 280.229 odd 6
1344.2.q.g.961.1 2 280.269 odd 6
1344.2.q.s.193.1 2 280.19 even 6
1344.2.q.s.961.1 2 280.59 even 6
2352.2.a.f.1.1 1 20.19 odd 2
2352.2.a.t.1.1 1 140.139 even 2
2352.2.q.u.961.1 2 140.39 odd 6
2352.2.q.u.1537.1 2 140.79 odd 6
7056.2.a.w.1.1 1 420.419 odd 2
7056.2.a.bl.1.1 1 60.59 even 2
7350.2.a.q.1.1 1 1.1 even 1 trivial
7350.2.a.bl.1.1 1 7.6 odd 2
9408.2.a.q.1.1 1 280.139 even 2
9408.2.a.z.1.1 1 40.29 even 2
9408.2.a.ce.1.1 1 280.69 odd 2
9408.2.a.cr.1.1 1 40.19 odd 2