# Properties

 Label 7350.2.a.br.1.1 Level 7350 Weight 2 Character 7350.1 Self dual yes Analytic conductor 58.690 Analytic rank 1 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: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 294) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7350.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} +1.00000 q^{16} +1.00000 q^{18} -4.00000 q^{19} -4.00000 q^{22} -1.00000 q^{24} +4.00000 q^{26} -1.00000 q^{27} +2.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +1.00000 q^{36} +6.00000 q^{37} -4.00000 q^{38} -4.00000 q^{39} -4.00000 q^{43} -4.00000 q^{44} -8.00000 q^{47} -1.00000 q^{48} +4.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} +4.00000 q^{57} +2.00000 q^{58} -4.00000 q^{59} +4.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +4.00000 q^{66} -4.00000 q^{67} +8.00000 q^{71} +1.00000 q^{72} -16.0000 q^{73} +6.00000 q^{74} -4.00000 q^{76} -4.00000 q^{78} -8.00000 q^{79} +1.00000 q^{81} -12.0000 q^{83} -4.00000 q^{86} -2.00000 q^{87} -4.00000 q^{88} -8.00000 q^{89} +8.00000 q^{93} -8.00000 q^{94} -1.00000 q^{96} +8.00000 q^{97} -4.00000 q^{99} +O(q^{100})$$

## 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
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −4.00000 −0.852803
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ 4.00000 0.784465
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 4.00000 0.696311
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ −4.00000 −0.640513
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 4.00000 0.554700
$$53$$ 10.0000 1.37361 0.686803 0.726844i $$-0.259014\pi$$
0.686803 + 0.726844i $$0.259014\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 4.00000 0.529813
$$58$$ 2.00000 0.262613
$$59$$ −4.00000 −0.520756 −0.260378 0.965507i $$-0.583847\pi$$
−0.260378 + 0.965507i $$0.583847\pi$$
$$60$$ 0 0
$$61$$ 4.00000 0.512148 0.256074 0.966657i $$-0.417571\pi$$
0.256074 + 0.966657i $$0.417571\pi$$
$$62$$ −8.00000 −1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 4.00000 0.492366
$$67$$ −4.00000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −16.0000 −1.87266 −0.936329 0.351123i $$-0.885800\pi$$
−0.936329 + 0.351123i $$0.885800\pi$$
$$74$$ 6.00000 0.697486
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 0 0
$$78$$ −4.00000 −0.452911
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −4.00000 −0.431331
$$87$$ −2.00000 −0.214423
$$88$$ −4.00000 −0.426401
$$89$$ −8.00000 −0.847998 −0.423999 0.905663i $$-0.639374\pi$$
−0.423999 + 0.905663i $$0.639374\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 8.00000 0.829561
$$94$$ −8.00000 −0.825137
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ 0 0
$$99$$ −4.00000 −0.402015
$$100$$ 0 0
$$101$$ −4.00000 −0.398015 −0.199007 0.979998i $$-0.563772\pi$$
−0.199007 + 0.979998i $$0.563772\pi$$
$$102$$ 0 0
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 0 0
$$106$$ 10.0000 0.971286
$$107$$ −4.00000 −0.386695 −0.193347 0.981130i $$-0.561934\pi$$
−0.193347 + 0.981130i $$0.561934\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ 0 0
$$111$$ −6.00000 −0.569495
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 4.00000 0.374634
$$115$$ 0 0
$$116$$ 2.00000 0.185695
$$117$$ 4.00000 0.369800
$$118$$ −4.00000 −0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 4.00000 0.362143
$$123$$ 0 0
$$124$$ −8.00000 −0.718421
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 4.00000 0.352180
$$130$$ 0 0
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 4.00000 0.348155
$$133$$ 0 0
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 10.0000 0.854358 0.427179 0.904167i $$-0.359507\pi$$
0.427179 + 0.904167i $$0.359507\pi$$
$$138$$ 0 0
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 0 0
$$141$$ 8.00000 0.673722
$$142$$ 8.00000 0.671345
$$143$$ −16.0000 −1.33799
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −16.0000 −1.32417
$$147$$ 0 0
$$148$$ 6.00000 0.493197
$$149$$ −10.0000 −0.819232 −0.409616 0.912258i $$-0.634337\pi$$
−0.409616 + 0.912258i $$0.634337\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −4.00000 −0.320256
$$157$$ 4.00000 0.319235 0.159617 0.987179i $$-0.448974\pi$$
0.159617 + 0.987179i $$0.448974\pi$$
$$158$$ −8.00000 −0.636446
$$159$$ −10.0000 −0.793052
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000 0.0785674
$$163$$ −12.0000 −0.939913 −0.469956 0.882690i $$-0.655730\pi$$
−0.469956 + 0.882690i $$0.655730\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −12.0000 −0.931381
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ −4.00000 −0.305888
$$172$$ −4.00000 −0.304997
$$173$$ −4.00000 −0.304114 −0.152057 0.988372i $$-0.548590\pi$$
−0.152057 + 0.988372i $$0.548590\pi$$
$$174$$ −2.00000 −0.151620
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ 4.00000 0.300658
$$178$$ −8.00000 −0.599625
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −20.0000 −1.48659 −0.743294 0.668965i $$-0.766738\pi$$
−0.743294 + 0.668965i $$0.766738\pi$$
$$182$$ 0 0
$$183$$ −4.00000 −0.295689
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 8.00000 0.586588
$$187$$ 0 0
$$188$$ −8.00000 −0.583460
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ −2.00000 −0.143963 −0.0719816 0.997406i $$-0.522932\pi$$
−0.0719816 + 0.997406i $$0.522932\pi$$
$$194$$ 8.00000 0.574367
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ −4.00000 −0.284268
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ 4.00000 0.282138
$$202$$ −4.00000 −0.281439
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −8.00000 −0.557386
$$207$$ 0 0
$$208$$ 4.00000 0.277350
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ −28.0000 −1.92760 −0.963800 0.266627i $$-0.914091\pi$$
−0.963800 + 0.266627i $$0.914091\pi$$
$$212$$ 10.0000 0.686803
$$213$$ −8.00000 −0.548151
$$214$$ −4.00000 −0.273434
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ −14.0000 −0.948200
$$219$$ 16.0000 1.08118
$$220$$ 0 0
$$221$$ 0 0
$$222$$ −6.00000 −0.402694
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 14.0000 0.931266
$$227$$ 20.0000 1.32745 0.663723 0.747978i $$-0.268975\pi$$
0.663723 + 0.747978i $$0.268975\pi$$
$$228$$ 4.00000 0.264906
$$229$$ −4.00000 −0.264327 −0.132164 0.991228i $$-0.542192\pi$$
−0.132164 + 0.991228i $$0.542192\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 2.00000 0.131306
$$233$$ 10.0000 0.655122 0.327561 0.944830i $$-0.393773\pi$$
0.327561 + 0.944830i $$0.393773\pi$$
$$234$$ 4.00000 0.261488
$$235$$ 0 0
$$236$$ −4.00000 −0.260378
$$237$$ 8.00000 0.519656
$$238$$ 0 0
$$239$$ −24.0000 −1.55243 −0.776215 0.630468i $$-0.782863\pi$$
−0.776215 + 0.630468i $$0.782863\pi$$
$$240$$ 0 0
$$241$$ −8.00000 −0.515325 −0.257663 0.966235i $$-0.582952\pi$$
−0.257663 + 0.966235i $$0.582952\pi$$
$$242$$ 5.00000 0.321412
$$243$$ −1.00000 −0.0641500
$$244$$ 4.00000 0.256074
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −16.0000 −1.01806
$$248$$ −8.00000 −0.508001
$$249$$ 12.0000 0.760469
$$250$$ 0 0
$$251$$ 20.0000 1.26239 0.631194 0.775625i $$-0.282565\pi$$
0.631194 + 0.775625i $$0.282565\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 16.0000 1.00393
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 8.00000 0.499026 0.249513 0.968371i $$-0.419729\pi$$
0.249513 + 0.968371i $$0.419729\pi$$
$$258$$ 4.00000 0.249029
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 2.00000 0.123797
$$262$$ 12.0000 0.741362
$$263$$ −8.00000 −0.493301 −0.246651 0.969104i $$-0.579330\pi$$
−0.246651 + 0.969104i $$0.579330\pi$$
$$264$$ 4.00000 0.246183
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 8.00000 0.489592
$$268$$ −4.00000 −0.244339
$$269$$ −28.0000 −1.70719 −0.853595 0.520937i $$-0.825583\pi$$
−0.853595 + 0.520937i $$0.825583\pi$$
$$270$$ 0 0
$$271$$ 32.0000 1.94386 0.971931 0.235267i $$-0.0755965\pi$$
0.971931 + 0.235267i $$0.0755965\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 10.0000 0.604122
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −22.0000 −1.32185 −0.660926 0.750451i $$-0.729836\pi$$
−0.660926 + 0.750451i $$0.729836\pi$$
$$278$$ −12.0000 −0.719712
$$279$$ −8.00000 −0.478947
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 8.00000 0.476393
$$283$$ −28.0000 −1.66443 −0.832214 0.554455i $$-0.812927\pi$$
−0.832214 + 0.554455i $$0.812927\pi$$
$$284$$ 8.00000 0.474713
$$285$$ 0 0
$$286$$ −16.0000 −0.946100
$$287$$ 0 0
$$288$$ 1.00000 0.0589256
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ −8.00000 −0.468968
$$292$$ −16.0000 −0.936329
$$293$$ −12.0000 −0.701047 −0.350524 0.936554i $$-0.613996\pi$$
−0.350524 + 0.936554i $$0.613996\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 6.00000 0.348743
$$297$$ 4.00000 0.232104
$$298$$ −10.0000 −0.579284
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −8.00000 −0.460348
$$303$$ 4.00000 0.229794
$$304$$ −4.00000 −0.229416
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 20.0000 1.14146 0.570730 0.821138i $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ 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 $$0.861843\pi$$
$$312$$ −4.00000 −0.226455
$$313$$ 24.0000 1.35656 0.678280 0.734803i $$-0.262726\pi$$
0.678280 + 0.734803i $$0.262726\pi$$
$$314$$ 4.00000 0.225733
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ −30.0000 −1.68497 −0.842484 0.538721i $$-0.818908\pi$$
−0.842484 + 0.538721i $$0.818908\pi$$
$$318$$ −10.0000 −0.560772
$$319$$ −8.00000 −0.447914
$$320$$ 0 0
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −12.0000 −0.664619
$$327$$ 14.0000 0.774202
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 6.00000 0.328798
$$334$$ 8.00000 0.437741
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ 3.00000 0.163178
$$339$$ −14.0000 −0.760376
$$340$$ 0 0
$$341$$ 32.0000 1.73290
$$342$$ −4.00000 −0.216295
$$343$$ 0 0
$$344$$ −4.00000 −0.215666
$$345$$ 0 0
$$346$$ −4.00000 −0.215041
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ −2.00000 −0.107211
$$349$$ 12.0000 0.642345 0.321173 0.947021i $$-0.395923\pi$$
0.321173 + 0.947021i $$0.395923\pi$$
$$350$$ 0 0
$$351$$ −4.00000 −0.213504
$$352$$ −4.00000 −0.213201
$$353$$ −24.0000 −1.27739 −0.638696 0.769460i $$-0.720526\pi$$
−0.638696 + 0.769460i $$0.720526\pi$$
$$354$$ 4.00000 0.212598
$$355$$ 0 0
$$356$$ −8.00000 −0.423999
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −20.0000 −1.05118
$$363$$ −5.00000 −0.262432
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −4.00000 −0.209083
$$367$$ −16.0000 −0.835193 −0.417597 0.908633i $$-0.637127\pi$$
−0.417597 + 0.908633i $$0.637127\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 8.00000 0.414781
$$373$$ −22.0000 −1.13912 −0.569558 0.821951i $$-0.692886\pi$$
−0.569558 + 0.821951i $$0.692886\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −8.00000 −0.412568
$$377$$ 8.00000 0.412021
$$378$$ 0 0
$$379$$ 36.0000 1.84920 0.924598 0.380945i $$-0.124401\pi$$
0.924598 + 0.380945i $$0.124401\pi$$
$$380$$ 0 0
$$381$$ −16.0000 −0.819705
$$382$$ 0 0
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −2.00000 −0.101797
$$387$$ −4.00000 −0.203331
$$388$$ 8.00000 0.406138
$$389$$ −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
$$393$$ −12.0000 −0.605320
$$394$$ −6.00000 −0.302276
$$395$$ 0 0
$$396$$ −4.00000 −0.201008
$$397$$ 4.00000 0.200754 0.100377 0.994949i $$-0.467995\pi$$
0.100377 + 0.994949i $$0.467995\pi$$
$$398$$ −8.00000 −0.401004
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ 4.00000 0.199502
$$403$$ −32.0000 −1.59403
$$404$$ −4.00000 −0.199007
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −24.0000 −1.18964
$$408$$ 0 0
$$409$$ 24.0000 1.18672 0.593362 0.804936i $$-0.297800\pi$$
0.593362 + 0.804936i $$0.297800\pi$$
$$410$$ 0 0
$$411$$ −10.0000 −0.493264
$$412$$ −8.00000 −0.394132
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 4.00000 0.196116
$$417$$ 12.0000 0.587643
$$418$$ 16.0000 0.782586
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ 0 0
$$421$$ 6.00000 0.292422 0.146211 0.989253i $$-0.453292\pi$$
0.146211 + 0.989253i $$0.453292\pi$$
$$422$$ −28.0000 −1.36302
$$423$$ −8.00000 −0.388973
$$424$$ 10.0000 0.485643
$$425$$ 0 0
$$426$$ −8.00000 −0.387601
$$427$$ 0 0
$$428$$ −4.00000 −0.193347
$$429$$ 16.0000 0.772487
$$430$$ 0 0
$$431$$ 40.0000 1.92673 0.963366 0.268190i $$-0.0864254\pi$$
0.963366 + 0.268190i $$0.0864254\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ −8.00000 −0.384455 −0.192228 0.981350i $$-0.561571\pi$$
−0.192228 + 0.981350i $$0.561571\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −14.0000 −0.670478
$$437$$ 0 0
$$438$$ 16.0000 0.764510
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 12.0000 0.570137 0.285069 0.958507i $$-0.407984\pi$$
0.285069 + 0.958507i $$0.407984\pi$$
$$444$$ −6.00000 −0.284747
$$445$$ 0 0
$$446$$ −16.0000 −0.757622
$$447$$ 10.0000 0.472984
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 14.0000 0.658505
$$453$$ 8.00000 0.375873
$$454$$ 20.0000 0.938647
$$455$$ 0 0
$$456$$ 4.00000 0.187317
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ −4.00000 −0.186908
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ 2.00000 0.0928477
$$465$$ 0 0
$$466$$ 10.0000 0.463241
$$467$$ 20.0000 0.925490 0.462745 0.886492i $$-0.346865\pi$$
0.462745 + 0.886492i $$0.346865\pi$$
$$468$$ 4.00000 0.184900
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −4.00000 −0.184310
$$472$$ −4.00000 −0.184115
$$473$$ 16.0000 0.735681
$$474$$ 8.00000 0.367452
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 10.0000 0.457869
$$478$$ −24.0000 −1.09773
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 24.0000 1.09431
$$482$$ −8.00000 −0.364390
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 8.00000 0.362515 0.181257 0.983436i $$-0.441983\pi$$
0.181257 + 0.983436i $$0.441983\pi$$
$$488$$ 4.00000 0.181071
$$489$$ 12.0000 0.542659
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −16.0000 −0.719874
$$495$$ 0 0
$$496$$ −8.00000 −0.359211
$$497$$ 0 0
$$498$$ 12.0000 0.537733
$$499$$ −12.0000 −0.537194 −0.268597 0.963253i $$-0.586560\pi$$
−0.268597 + 0.963253i $$0.586560\pi$$
$$500$$ 0 0
$$501$$ −8.00000 −0.357414
$$502$$ 20.0000 0.892644
$$503$$ −16.0000 −0.713405 −0.356702 0.934218i $$-0.616099\pi$$
−0.356702 + 0.934218i $$0.616099\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −3.00000 −0.133235
$$508$$ 16.0000 0.709885
$$509$$ 4.00000 0.177297 0.0886484 0.996063i $$-0.471745\pi$$
0.0886484 + 0.996063i $$0.471745\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 4.00000 0.176604
$$514$$ 8.00000 0.352865
$$515$$ 0 0
$$516$$ 4.00000 0.176090
$$517$$ 32.0000 1.40736
$$518$$ 0 0
$$519$$ 4.00000 0.175581
$$520$$ 0 0
$$521$$ −32.0000 −1.40195 −0.700973 0.713188i $$-0.747251\pi$$
−0.700973 + 0.713188i $$0.747251\pi$$
$$522$$ 2.00000 0.0875376
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ −8.00000 −0.348817
$$527$$ 0 0
$$528$$ 4.00000 0.174078
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 8.00000 0.346194
$$535$$ 0 0
$$536$$ −4.00000 −0.172774
$$537$$ −12.0000 −0.517838
$$538$$ −28.0000 −1.20717
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 32.0000 1.37452
$$543$$ 20.0000 0.858282
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ 10.0000 0.427179
$$549$$ 4.00000 0.170716
$$550$$ 0 0
$$551$$ −8.00000 −0.340811
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −22.0000 −0.934690
$$555$$ 0 0
$$556$$ −12.0000 −0.508913
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ −8.00000 −0.338667
$$559$$ −16.0000 −0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 6.00000 0.253095
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 8.00000 0.336861
$$565$$ 0 0
$$566$$ −28.0000 −1.17693
$$567$$ 0 0
$$568$$ 8.00000 0.335673
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 36.0000 1.50655 0.753277 0.657704i $$-0.228472\pi$$
0.753277 + 0.657704i $$0.228472\pi$$
$$572$$ −16.0000 −0.668994
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −16.0000 −0.666089 −0.333044 0.942911i $$-0.608076\pi$$
−0.333044 + 0.942911i $$0.608076\pi$$
$$578$$ −17.0000 −0.707107
$$579$$ 2.00000 0.0831172
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −8.00000 −0.331611
$$583$$ −40.0000 −1.65663
$$584$$ −16.0000 −0.662085
$$585$$ 0 0
$$586$$ −12.0000 −0.495715
$$587$$ 28.0000 1.15568 0.577842 0.816149i $$-0.303895\pi$$
0.577842 + 0.816149i $$0.303895\pi$$
$$588$$ 0 0
$$589$$ 32.0000 1.31854
$$590$$ 0 0
$$591$$ 6.00000 0.246807
$$592$$ 6.00000 0.246598
$$593$$ −24.0000 −0.985562 −0.492781 0.870153i $$-0.664020\pi$$
−0.492781 + 0.870153i $$0.664020\pi$$
$$594$$ 4.00000 0.164122
$$595$$ 0 0
$$596$$ −10.0000 −0.409616
$$597$$ 8.00000 0.327418
$$598$$ 0 0
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ 32.0000 1.30531 0.652654 0.757656i $$-0.273656\pi$$
0.652654 + 0.757656i $$0.273656\pi$$
$$602$$ 0 0
$$603$$ −4.00000 −0.162893
$$604$$ −8.00000 −0.325515
$$605$$ 0 0
$$606$$ 4.00000 0.162489
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −32.0000 −1.29458
$$612$$ 0 0
$$613$$ −26.0000 −1.05013 −0.525065 0.851062i $$-0.675959\pi$$
−0.525065 + 0.851062i $$0.675959\pi$$
$$614$$ 20.0000 0.807134
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −22.0000 −0.885687 −0.442843 0.896599i $$-0.646030\pi$$
−0.442843 + 0.896599i $$0.646030\pi$$
$$618$$ 8.00000 0.321807
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −32.0000 −1.28308
$$623$$ 0 0
$$624$$ −4.00000 −0.160128
$$625$$ 0 0
$$626$$ 24.0000 0.959233
$$627$$ −16.0000 −0.638978
$$628$$ 4.00000 0.159617
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ −8.00000 −0.318223
$$633$$ 28.0000 1.11290
$$634$$ −30.0000 −1.19145
$$635$$ 0 0
$$636$$ −10.0000 −0.396526
$$637$$ 0 0
$$638$$ −8.00000 −0.316723
$$639$$ 8.00000 0.316475
$$640$$ 0 0
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 4.00000 0.157867
$$643$$ −36.0000 −1.41970 −0.709851 0.704352i $$-0.751238\pi$$
−0.709851 + 0.704352i $$0.751238\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 16.0000 0.628055
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −12.0000 −0.469956
$$653$$ 46.0000 1.80012 0.900060 0.435767i $$-0.143523\pi$$
0.900060 + 0.435767i $$0.143523\pi$$
$$654$$ 14.0000 0.547443
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −16.0000 −0.624219
$$658$$ 0 0
$$659$$ 4.00000 0.155818 0.0779089 0.996960i $$-0.475176\pi$$
0.0779089 + 0.996960i $$0.475176\pi$$
$$660$$ 0 0
$$661$$ −28.0000 −1.08907 −0.544537 0.838737i $$-0.683295\pi$$
−0.544537 + 0.838737i $$0.683295\pi$$
$$662$$ 20.0000 0.777322
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ 0 0
$$668$$ 8.00000 0.309529
$$669$$ 16.0000 0.618596
$$670$$ 0 0
$$671$$ −16.0000 −0.617673
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ −14.0000 −0.539260
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ 12.0000 0.461197 0.230599 0.973049i $$-0.425932\pi$$
0.230599 + 0.973049i $$0.425932\pi$$
$$678$$ −14.0000 −0.537667
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −20.0000 −0.766402
$$682$$ 32.0000 1.22534
$$683$$ 44.0000 1.68361 0.841807 0.539779i $$-0.181492\pi$$
0.841807 + 0.539779i $$0.181492\pi$$
$$684$$ −4.00000 −0.152944
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 4.00000 0.152610
$$688$$ −4.00000 −0.152499
$$689$$ 40.0000 1.52388
$$690$$ 0 0
$$691$$ −20.0000 −0.760836 −0.380418 0.924815i $$-0.624220\pi$$
−0.380418 + 0.924815i $$0.624220\pi$$
$$692$$ −4.00000 −0.152057
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 0 0
$$696$$ −2.00000 −0.0758098
$$697$$ 0 0
$$698$$ 12.0000 0.454207
$$699$$ −10.0000 −0.378235
$$700$$ 0 0
$$701$$ 34.0000 1.28416 0.642081 0.766637i $$-0.278071\pi$$
0.642081 + 0.766637i $$0.278071\pi$$
$$702$$ −4.00000 −0.150970
$$703$$ −24.0000 −0.905177
$$704$$ −4.00000 −0.150756
$$705$$ 0 0
$$706$$ −24.0000 −0.903252
$$707$$ 0 0
$$708$$ 4.00000 0.150329
$$709$$ −38.0000 −1.42712 −0.713560 0.700594i $$-0.752918\pi$$
−0.713560 + 0.700594i $$0.752918\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ −8.00000 −0.299813
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 24.0000 0.896296
$$718$$ 16.0000 0.597115
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −3.00000 −0.111648
$$723$$ 8.00000 0.297523
$$724$$ −20.0000 −0.743294
$$725$$ 0 0
$$726$$ −5.00000 −0.185567
$$727$$ −8.00000 −0.296704 −0.148352 0.988935i $$-0.547397\pi$$
−0.148352 + 0.988935i $$0.547397\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −4.00000 −0.147844
$$733$$ −4.00000 −0.147743 −0.0738717 0.997268i $$-0.523536\pi$$
−0.0738717 + 0.997268i $$0.523536\pi$$
$$734$$ −16.0000 −0.590571
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 16.0000 0.589368
$$738$$ 0 0
$$739$$ −20.0000 −0.735712 −0.367856 0.929883i $$-0.619908\pi$$
−0.367856 + 0.929883i $$0.619908\pi$$
$$740$$ 0 0
$$741$$ 16.0000 0.587775
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 8.00000 0.293294
$$745$$ 0 0
$$746$$ −22.0000 −0.805477
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ −8.00000 −0.291730
$$753$$ −20.0000 −0.728841
$$754$$ 8.00000 0.291343
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −10.0000 −0.363456 −0.181728 0.983349i $$-0.558169\pi$$
−0.181728 + 0.983349i $$0.558169\pi$$
$$758$$ 36.0000 1.30758
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −16.0000 −0.580000 −0.290000 0.957027i $$-0.593655\pi$$
−0.290000 + 0.957027i $$0.593655\pi$$
$$762$$ −16.0000 −0.579619
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 24.0000 0.867155
$$767$$ −16.0000 −0.577727
$$768$$ −1.00000 −0.0360844
$$769$$ −40.0000 −1.44244 −0.721218 0.692708i $$-0.756418\pi$$
−0.721218 + 0.692708i $$0.756418\pi$$
$$770$$ 0 0
$$771$$ −8.00000 −0.288113
$$772$$ −2.00000 −0.0719816
$$773$$ 36.0000 1.29483 0.647415 0.762138i $$-0.275850\pi$$
0.647415 + 0.762138i $$0.275850\pi$$
$$774$$ −4.00000 −0.143777
$$775$$ 0 0
$$776$$ 8.00000 0.287183
$$777$$ 0 0
$$778$$ −6.00000 −0.215110
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −32.0000 −1.14505
$$782$$ 0 0
$$783$$ −2.00000 −0.0714742
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −12.0000 −0.428026
$$787$$ 20.0000 0.712923 0.356462 0.934310i $$-0.383983\pi$$
0.356462 + 0.934310i $$0.383983\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ 8.00000 0.284808
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −4.00000 −0.142134
$$793$$ 16.0000 0.568177
$$794$$ 4.00000 0.141955
$$795$$ 0 0
$$796$$ −8.00000 −0.283552
$$797$$ 12.0000 0.425062 0.212531 0.977154i $$-0.431829\pi$$
0.212531 + 0.977154i $$0.431829\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −8.00000 −0.282666
$$802$$ −18.0000 −0.635602
$$803$$ 64.0000 2.25851
$$804$$ 4.00000 0.141069
$$805$$ 0 0
$$806$$ −32.0000 −1.12715
$$807$$ 28.0000 0.985647
$$808$$ −4.00000 −0.140720
$$809$$ 42.0000 1.47664 0.738321 0.674450i $$-0.235619\pi$$
0.738321 + 0.674450i $$0.235619\pi$$
$$810$$ 0 0
$$811$$ 44.0000 1.54505 0.772524 0.634985i $$-0.218994\pi$$
0.772524 + 0.634985i $$0.218994\pi$$
$$812$$ 0 0
$$813$$ −32.0000 −1.12229
$$814$$ −24.0000 −0.841200
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 16.0000 0.559769
$$818$$ 24.0000 0.839140
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −10.0000 −0.349002 −0.174501 0.984657i $$-0.555831\pi$$
−0.174501 + 0.984657i $$0.555831\pi$$
$$822$$ −10.0000 −0.348790
$$823$$ −16.0000 −0.557725 −0.278862 0.960331i $$-0.589957\pi$$
−0.278862 + 0.960331i $$0.589957\pi$$
$$824$$ −8.00000 −0.278693
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −36.0000 −1.25184 −0.625921 0.779886i $$-0.715277\pi$$
−0.625921 + 0.779886i $$0.715277\pi$$
$$828$$ 0 0
$$829$$ 52.0000 1.80603 0.903017 0.429604i $$-0.141347\pi$$
0.903017 + 0.429604i $$0.141347\pi$$
$$830$$ 0 0
$$831$$ 22.0000 0.763172
$$832$$ 4.00000 0.138675
$$833$$ 0 0
$$834$$ 12.0000 0.415526
$$835$$ 0 0
$$836$$ 16.0000 0.553372
$$837$$ 8.00000 0.276520
$$838$$ −28.0000 −0.967244
$$839$$ −24.0000 −0.828572 −0.414286 0.910147i $$-0.635969\pi$$
−0.414286 + 0.910147i $$0.635969\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 6.00000 0.206774
$$843$$ −6.00000 −0.206651
$$844$$ −28.0000 −0.963800
$$845$$ 0 0
$$846$$ −8.00000 −0.275046
$$847$$ 0 0
$$848$$ 10.0000 0.343401
$$849$$ 28.0000 0.960958
$$850$$ 0 0
$$851$$ 0 0
$$852$$ −8.00000 −0.274075
$$853$$ 52.0000 1.78045 0.890223 0.455525i $$-0.150548\pi$$
0.890223 + 0.455525i $$0.150548\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −4.00000 −0.136717
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 16.0000 0.546231
$$859$$ 36.0000 1.22830 0.614152 0.789188i $$-0.289498\pi$$
0.614152 + 0.789188i $$0.289498\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 40.0000 1.36241
$$863$$ −48.0000 −1.63394 −0.816970 0.576681i $$-0.804348\pi$$
−0.816970 + 0.576681i $$0.804348\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ −8.00000 −0.271851
$$867$$ 17.0000 0.577350
$$868$$ 0 0
$$869$$ 32.0000 1.08553
$$870$$ 0 0
$$871$$ −16.0000 −0.542139
$$872$$ −14.0000 −0.474100
$$873$$ 8.00000 0.270759
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 16.0000 0.540590
$$877$$ −18.0000 −0.607817 −0.303908 0.952701i $$-0.598292\pi$$
−0.303908 + 0.952701i $$0.598292\pi$$
$$878$$ 0 0
$$879$$ 12.0000 0.404750
$$880$$ 0 0
$$881$$ 8.00000 0.269527 0.134763 0.990878i $$-0.456973\pi$$
0.134763 + 0.990878i $$0.456973\pi$$
$$882$$ 0 0
$$883$$ −4.00000 −0.134611 −0.0673054 0.997732i $$-0.521440\pi$$
−0.0673054 + 0.997732i $$0.521440\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 12.0000 0.403148
$$887$$ 24.0000 0.805841 0.402921 0.915235i $$-0.367995\pi$$
0.402921 + 0.915235i $$0.367995\pi$$
$$888$$ −6.00000 −0.201347
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −4.00000 −0.134005
$$892$$ −16.0000 −0.535720
$$893$$ 32.0000 1.07084
$$894$$ 10.0000 0.334450
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −30.0000 −1.00111
$$899$$ −16.0000 −0.533630
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 14.0000 0.465633
$$905$$ 0 0
$$906$$ 8.00000 0.265782
$$907$$ 20.0000 0.664089 0.332045 0.943264i $$-0.392262\pi$$
0.332045 + 0.943264i $$0.392262\pi$$
$$908$$ 20.0000 0.663723
$$909$$ −4.00000 −0.132672
$$910$$ 0 0
$$911$$ −8.00000 −0.265052 −0.132526 0.991180i $$-0.542309\pi$$
−0.132526 + 0.991180i $$0.542309\pi$$
$$912$$ 4.00000 0.132453
$$913$$ 48.0000 1.58857
$$914$$ 22.0000 0.727695
$$915$$ 0 0
$$916$$ −4.00000 −0.132164
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −48.0000 −1.58337 −0.791687 0.610927i $$-0.790797\pi$$
−0.791687 + 0.610927i $$0.790797\pi$$
$$920$$ 0 0
$$921$$ −20.0000 −0.659022
$$922$$ −12.0000 −0.395199
$$923$$ 32.0000 1.05329
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −8.00000 −0.262896
$$927$$ −8.00000 −0.262754
$$928$$ 2.00000 0.0656532
$$929$$ −48.0000 −1.57483 −0.787414 0.616424i $$-0.788581\pi$$
−0.787414 + 0.616424i $$0.788581\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 10.0000 0.327561
$$933$$ 32.0000 1.04763
$$934$$ 20.0000 0.654420
$$935$$ 0 0
$$936$$ 4.00000 0.130744
$$937$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$938$$ 0 0
$$939$$ −24.0000 −0.783210
$$940$$ 0 0
$$941$$ 12.0000 0.391189 0.195594 0.980685i $$-0.437336\pi$$
0.195594 + 0.980685i $$0.437336\pi$$
$$942$$ −4.00000 −0.130327
$$943$$ 0 0
$$944$$ −4.00000 −0.130189
$$945$$ 0 0
$$946$$ 16.0000 0.520205
$$947$$ 28.0000 0.909878 0.454939 0.890523i $$-0.349661\pi$$
0.454939 + 0.890523i $$0.349661\pi$$
$$948$$ 8.00000 0.259828
$$949$$ −64.0000 −2.07753
$$950$$ 0 0
$$951$$ 30.0000 0.972817
$$952$$ 0 0
$$953$$ 6.00000 0.194359 0.0971795 0.995267i $$-0.469018\pi$$
0.0971795 + 0.995267i $$0.469018\pi$$
$$954$$ 10.0000 0.323762
$$955$$ 0 0
$$956$$ −24.0000 −0.776215
$$957$$ 8.00000 0.258603
$$958$$ 24.0000 0.775405
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 24.0000 0.773791
$$963$$ −4.00000 −0.128898
$$964$$ −8.00000 −0.257663
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 8.00000 0.257263 0.128631 0.991692i $$-0.458942\pi$$
0.128631 + 0.991692i $$0.458942\pi$$
$$968$$ 5.00000 0.160706
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −4.00000 −0.128366 −0.0641831 0.997938i $$-0.520444\pi$$
−0.0641831 + 0.997938i $$0.520444\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ 8.00000 0.256337
$$975$$ 0 0
$$976$$ 4.00000 0.128037
$$977$$ −14.0000 −0.447900 −0.223950 0.974601i $$-0.571895\pi$$
−0.223950 + 0.974601i $$0.571895\pi$$
$$978$$ 12.0000 0.383718
$$979$$ 32.0000 1.02272
$$980$$ 0 0
$$981$$ −14.0000 −0.446986
$$982$$ −12.0000 −0.382935
$$983$$ −8.00000 −0.255160 −0.127580 0.991828i $$-0.540721\pi$$
−0.127580 + 0.991828i $$0.540721\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −16.0000 −0.509028
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 8.00000 0.254128 0.127064 0.991894i $$-0.459445\pi$$
0.127064 + 0.991894i $$0.459445\pi$$
$$992$$ −8.00000 −0.254000
$$993$$ −20.0000 −0.634681
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 12.0000 0.380235
$$997$$ 28.0000 0.886769 0.443384 0.896332i $$-0.353778\pi$$
0.443384 + 0.896332i $$0.353778\pi$$
$$998$$ −12.0000 −0.379853
$$999$$ −6.00000 −0.189832
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.br.1.1 1
5.4 even 2 294.2.a.c.1.1 yes 1
7.6 odd 2 7350.2.a.cj.1.1 1
15.14 odd 2 882.2.a.l.1.1 1
20.19 odd 2 2352.2.a.b.1.1 1
35.4 even 6 294.2.e.d.79.1 2
35.9 even 6 294.2.e.d.67.1 2
35.19 odd 6 294.2.e.e.67.1 2
35.24 odd 6 294.2.e.e.79.1 2
35.34 odd 2 294.2.a.b.1.1 1
40.19 odd 2 9408.2.a.de.1.1 1
40.29 even 2 9408.2.a.bo.1.1 1
60.59 even 2 7056.2.a.ca.1.1 1
105.44 odd 6 882.2.g.a.361.1 2
105.59 even 6 882.2.g.f.667.1 2
105.74 odd 6 882.2.g.a.667.1 2
105.89 even 6 882.2.g.f.361.1 2
105.104 even 2 882.2.a.f.1.1 1
140.19 even 6 2352.2.q.a.1537.1 2
140.39 odd 6 2352.2.q.y.961.1 2
140.59 even 6 2352.2.q.a.961.1 2
140.79 odd 6 2352.2.q.y.1537.1 2
140.139 even 2 2352.2.a.y.1.1 1
280.69 odd 2 9408.2.a.br.1.1 1
280.139 even 2 9408.2.a.b.1.1 1
420.419 odd 2 7056.2.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
294.2.a.b.1.1 1 35.34 odd 2
294.2.a.c.1.1 yes 1 5.4 even 2
294.2.e.d.67.1 2 35.9 even 6
294.2.e.d.79.1 2 35.4 even 6
294.2.e.e.67.1 2 35.19 odd 6
294.2.e.e.79.1 2 35.24 odd 6
882.2.a.f.1.1 1 105.104 even 2
882.2.a.l.1.1 1 15.14 odd 2
882.2.g.a.361.1 2 105.44 odd 6
882.2.g.a.667.1 2 105.74 odd 6
882.2.g.f.361.1 2 105.89 even 6
882.2.g.f.667.1 2 105.59 even 6
2352.2.a.b.1.1 1 20.19 odd 2
2352.2.a.y.1.1 1 140.139 even 2
2352.2.q.a.961.1 2 140.59 even 6
2352.2.q.a.1537.1 2 140.19 even 6
2352.2.q.y.961.1 2 140.39 odd 6
2352.2.q.y.1537.1 2 140.79 odd 6
7056.2.a.a.1.1 1 420.419 odd 2
7056.2.a.ca.1.1 1 60.59 even 2
7350.2.a.br.1.1 1 1.1 even 1 trivial
7350.2.a.cj.1.1 1 7.6 odd 2
9408.2.a.b.1.1 1 280.139 even 2
9408.2.a.bo.1.1 1 40.29 even 2
9408.2.a.br.1.1 1 280.69 odd 2
9408.2.a.de.1.1 1 40.19 odd 2