# Properties

 Label 950.2.a.e.1.1 Level $950$ Weight $2$ Character 950.1 Self dual yes Analytic conductor $7.586$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 950.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{12} +3.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +7.00000 q^{17} -2.00000 q^{18} -1.00000 q^{19} +1.00000 q^{21} +5.00000 q^{23} +1.00000 q^{24} +3.00000 q^{26} -5.00000 q^{27} +1.00000 q^{28} -5.00000 q^{29} +10.0000 q^{31} +1.00000 q^{32} +7.00000 q^{34} -2.00000 q^{36} -2.00000 q^{37} -1.00000 q^{38} +3.00000 q^{39} +2.00000 q^{41} +1.00000 q^{42} -6.00000 q^{43} +5.00000 q^{46} +1.00000 q^{48} -6.00000 q^{49} +7.00000 q^{51} +3.00000 q^{52} -9.00000 q^{53} -5.00000 q^{54} +1.00000 q^{56} -1.00000 q^{57} -5.00000 q^{58} -7.00000 q^{59} -4.00000 q^{61} +10.0000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -7.00000 q^{67} +7.00000 q^{68} +5.00000 q^{69} -2.00000 q^{72} +9.00000 q^{73} -2.00000 q^{74} -1.00000 q^{76} +3.00000 q^{78} -10.0000 q^{79} +1.00000 q^{81} +2.00000 q^{82} +2.00000 q^{83} +1.00000 q^{84} -6.00000 q^{86} -5.00000 q^{87} -10.0000 q^{89} +3.00000 q^{91} +5.00000 q^{92} +10.0000 q^{93} +1.00000 q^{96} +18.0000 q^{97} -6.00000 q^{98} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 1.00000 0.577350 0.288675 0.957427i $$-0.406785\pi$$
0.288675 + 0.957427i $$0.406785\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 1.00000 0.408248
$$7$$ 1.00000 0.377964 0.188982 0.981981i $$-0.439481\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ 1.00000 0.353553
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 3.00000 0.832050 0.416025 0.909353i $$-0.363423\pi$$
0.416025 + 0.909353i $$0.363423\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 7.00000 1.69775 0.848875 0.528594i $$-0.177281\pi$$
0.848875 + 0.528594i $$0.177281\pi$$
$$18$$ −2.00000 −0.471405
$$19$$ −1.00000 −0.229416
$$20$$ 0 0
$$21$$ 1.00000 0.218218
$$22$$ 0 0
$$23$$ 5.00000 1.04257 0.521286 0.853382i $$-0.325452\pi$$
0.521286 + 0.853382i $$0.325452\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 0 0
$$26$$ 3.00000 0.588348
$$27$$ −5.00000 −0.962250
$$28$$ 1.00000 0.188982
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 0 0
$$31$$ 10.0000 1.79605 0.898027 0.439941i $$-0.145001\pi$$
0.898027 + 0.439941i $$0.145001\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 7.00000 1.20049
$$35$$ 0 0
$$36$$ −2.00000 −0.333333
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ 3.00000 0.480384
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 1.00000 0.154303
$$43$$ −6.00000 −0.914991 −0.457496 0.889212i $$-0.651253\pi$$
−0.457496 + 0.889212i $$0.651253\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 5.00000 0.737210
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ 7.00000 0.980196
$$52$$ 3.00000 0.416025
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ −5.00000 −0.680414
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ −1.00000 −0.132453
$$58$$ −5.00000 −0.656532
$$59$$ −7.00000 −0.911322 −0.455661 0.890153i $$-0.650597\pi$$
−0.455661 + 0.890153i $$0.650597\pi$$
$$60$$ 0 0
$$61$$ −4.00000 −0.512148 −0.256074 0.966657i $$-0.582429\pi$$
−0.256074 + 0.966657i $$0.582429\pi$$
$$62$$ 10.0000 1.27000
$$63$$ −2.00000 −0.251976
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −7.00000 −0.855186 −0.427593 0.903971i $$-0.640638\pi$$
−0.427593 + 0.903971i $$0.640638\pi$$
$$68$$ 7.00000 0.848875
$$69$$ 5.00000 0.601929
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ −2.00000 −0.235702
$$73$$ 9.00000 1.05337 0.526685 0.850060i $$-0.323435\pi$$
0.526685 + 0.850060i $$0.323435\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 0 0
$$76$$ −1.00000 −0.114708
$$77$$ 0 0
$$78$$ 3.00000 0.339683
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 2.00000 0.220863
$$83$$ 2.00000 0.219529 0.109764 0.993958i $$-0.464990\pi$$
0.109764 + 0.993958i $$0.464990\pi$$
$$84$$ 1.00000 0.109109
$$85$$ 0 0
$$86$$ −6.00000 −0.646997
$$87$$ −5.00000 −0.536056
$$88$$ 0 0
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 0 0
$$91$$ 3.00000 0.314485
$$92$$ 5.00000 0.521286
$$93$$ 10.0000 1.03695
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ 18.0000 1.82762 0.913812 0.406138i $$-0.133125\pi$$
0.913812 + 0.406138i $$0.133125\pi$$
$$98$$ −6.00000 −0.606092
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −4.00000 −0.398015 −0.199007 0.979998i $$-0.563772\pi$$
−0.199007 + 0.979998i $$0.563772\pi$$
$$102$$ 7.00000 0.693103
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 3.00000 0.294174
$$105$$ 0 0
$$106$$ −9.00000 −0.874157
$$107$$ −9.00000 −0.870063 −0.435031 0.900415i $$-0.643263\pi$$
−0.435031 + 0.900415i $$0.643263\pi$$
$$108$$ −5.00000 −0.481125
$$109$$ 13.0000 1.24517 0.622587 0.782551i $$-0.286082\pi$$
0.622587 + 0.782551i $$0.286082\pi$$
$$110$$ 0 0
$$111$$ −2.00000 −0.189832
$$112$$ 1.00000 0.0944911
$$113$$ −8.00000 −0.752577 −0.376288 0.926503i $$-0.622800\pi$$
−0.376288 + 0.926503i $$0.622800\pi$$
$$114$$ −1.00000 −0.0936586
$$115$$ 0 0
$$116$$ −5.00000 −0.464238
$$117$$ −6.00000 −0.554700
$$118$$ −7.00000 −0.644402
$$119$$ 7.00000 0.641689
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ −4.00000 −0.362143
$$123$$ 2.00000 0.180334
$$124$$ 10.0000 0.898027
$$125$$ 0 0
$$126$$ −2.00000 −0.178174
$$127$$ 6.00000 0.532414 0.266207 0.963916i $$-0.414230\pi$$
0.266207 + 0.963916i $$0.414230\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −6.00000 −0.528271
$$130$$ 0 0
$$131$$ −20.0000 −1.74741 −0.873704 0.486458i $$-0.838289\pi$$
−0.873704 + 0.486458i $$0.838289\pi$$
$$132$$ 0 0
$$133$$ −1.00000 −0.0867110
$$134$$ −7.00000 −0.604708
$$135$$ 0 0
$$136$$ 7.00000 0.600245
$$137$$ 3.00000 0.256307 0.128154 0.991754i $$-0.459095\pi$$
0.128154 + 0.991754i $$0.459095\pi$$
$$138$$ 5.00000 0.425628
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −2.00000 −0.166667
$$145$$ 0 0
$$146$$ 9.00000 0.744845
$$147$$ −6.00000 −0.494872
$$148$$ −2.00000 −0.164399
$$149$$ 4.00000 0.327693 0.163846 0.986486i $$-0.447610\pi$$
0.163846 + 0.986486i $$0.447610\pi$$
$$150$$ 0 0
$$151$$ −6.00000 −0.488273 −0.244137 0.969741i $$-0.578505\pi$$
−0.244137 + 0.969741i $$0.578505\pi$$
$$152$$ −1.00000 −0.0811107
$$153$$ −14.0000 −1.13183
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 3.00000 0.240192
$$157$$ −18.0000 −1.43656 −0.718278 0.695756i $$-0.755069\pi$$
−0.718278 + 0.695756i $$0.755069\pi$$
$$158$$ −10.0000 −0.795557
$$159$$ −9.00000 −0.713746
$$160$$ 0 0
$$161$$ 5.00000 0.394055
$$162$$ 1.00000 0.0785674
$$163$$ 18.0000 1.40987 0.704934 0.709273i $$-0.250976\pi$$
0.704934 + 0.709273i $$0.250976\pi$$
$$164$$ 2.00000 0.156174
$$165$$ 0 0
$$166$$ 2.00000 0.155230
$$167$$ −14.0000 −1.08335 −0.541676 0.840587i $$-0.682210\pi$$
−0.541676 + 0.840587i $$0.682210\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ 2.00000 0.152944
$$172$$ −6.00000 −0.457496
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ −5.00000 −0.379049
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −7.00000 −0.526152
$$178$$ −10.0000 −0.749532
$$179$$ 24.0000 1.79384 0.896922 0.442189i $$-0.145798\pi$$
0.896922 + 0.442189i $$0.145798\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 3.00000 0.222375
$$183$$ −4.00000 −0.295689
$$184$$ 5.00000 0.368605
$$185$$ 0 0
$$186$$ 10.0000 0.733236
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −5.00000 −0.363696
$$190$$ 0 0
$$191$$ −7.00000 −0.506502 −0.253251 0.967401i $$-0.581500\pi$$
−0.253251 + 0.967401i $$0.581500\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 2.00000 0.143963 0.0719816 0.997406i $$-0.477068\pi$$
0.0719816 + 0.997406i $$0.477068\pi$$
$$194$$ 18.0000 1.29232
$$195$$ 0 0
$$196$$ −6.00000 −0.428571
$$197$$ 10.0000 0.712470 0.356235 0.934396i $$-0.384060\pi$$
0.356235 + 0.934396i $$0.384060\pi$$
$$198$$ 0 0
$$199$$ 17.0000 1.20510 0.602549 0.798082i $$-0.294152\pi$$
0.602549 + 0.798082i $$0.294152\pi$$
$$200$$ 0 0
$$201$$ −7.00000 −0.493742
$$202$$ −4.00000 −0.281439
$$203$$ −5.00000 −0.350931
$$204$$ 7.00000 0.490098
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −10.0000 −0.695048
$$208$$ 3.00000 0.208013
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 5.00000 0.344214 0.172107 0.985078i $$-0.444942\pi$$
0.172107 + 0.985078i $$0.444942\pi$$
$$212$$ −9.00000 −0.618123
$$213$$ 0 0
$$214$$ −9.00000 −0.615227
$$215$$ 0 0
$$216$$ −5.00000 −0.340207
$$217$$ 10.0000 0.678844
$$218$$ 13.0000 0.880471
$$219$$ 9.00000 0.608164
$$220$$ 0 0
$$221$$ 21.0000 1.41261
$$222$$ −2.00000 −0.134231
$$223$$ 22.0000 1.47323 0.736614 0.676313i $$-0.236423\pi$$
0.736614 + 0.676313i $$0.236423\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −8.00000 −0.532152
$$227$$ 25.0000 1.65931 0.829654 0.558278i $$-0.188538\pi$$
0.829654 + 0.558278i $$0.188538\pi$$
$$228$$ −1.00000 −0.0662266
$$229$$ −18.0000 −1.18947 −0.594737 0.803921i $$-0.702744\pi$$
−0.594737 + 0.803921i $$0.702744\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −5.00000 −0.328266
$$233$$ −26.0000 −1.70332 −0.851658 0.524097i $$-0.824403\pi$$
−0.851658 + 0.524097i $$0.824403\pi$$
$$234$$ −6.00000 −0.392232
$$235$$ 0 0
$$236$$ −7.00000 −0.455661
$$237$$ −10.0000 −0.649570
$$238$$ 7.00000 0.453743
$$239$$ −27.0000 −1.74648 −0.873242 0.487286i $$-0.837987\pi$$
−0.873242 + 0.487286i $$0.837987\pi$$
$$240$$ 0 0
$$241$$ −28.0000 −1.80364 −0.901819 0.432113i $$-0.857768\pi$$
−0.901819 + 0.432113i $$0.857768\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ 16.0000 1.02640
$$244$$ −4.00000 −0.256074
$$245$$ 0 0
$$246$$ 2.00000 0.127515
$$247$$ −3.00000 −0.190885
$$248$$ 10.0000 0.635001
$$249$$ 2.00000 0.126745
$$250$$ 0 0
$$251$$ 4.00000 0.252478 0.126239 0.992000i $$-0.459709\pi$$
0.126239 + 0.992000i $$0.459709\pi$$
$$252$$ −2.00000 −0.125988
$$253$$ 0 0
$$254$$ 6.00000 0.376473
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ −6.00000 −0.373544
$$259$$ −2.00000 −0.124274
$$260$$ 0 0
$$261$$ 10.0000 0.618984
$$262$$ −20.0000 −1.23560
$$263$$ 8.00000 0.493301 0.246651 0.969104i $$-0.420670\pi$$
0.246651 + 0.969104i $$0.420670\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −1.00000 −0.0613139
$$267$$ −10.0000 −0.611990
$$268$$ −7.00000 −0.427593
$$269$$ −10.0000 −0.609711 −0.304855 0.952399i $$-0.598608\pi$$
−0.304855 + 0.952399i $$0.598608\pi$$
$$270$$ 0 0
$$271$$ 5.00000 0.303728 0.151864 0.988401i $$-0.451472\pi$$
0.151864 + 0.988401i $$0.451472\pi$$
$$272$$ 7.00000 0.424437
$$273$$ 3.00000 0.181568
$$274$$ 3.00000 0.181237
$$275$$ 0 0
$$276$$ 5.00000 0.300965
$$277$$ −28.0000 −1.68236 −0.841178 0.540758i $$-0.818138\pi$$
−0.841178 + 0.540758i $$0.818138\pi$$
$$278$$ 12.0000 0.719712
$$279$$ −20.0000 −1.19737
$$280$$ 0 0
$$281$$ −26.0000 −1.55103 −0.775515 0.631329i $$-0.782510\pi$$
−0.775515 + 0.631329i $$0.782510\pi$$
$$282$$ 0 0
$$283$$ 26.0000 1.54554 0.772770 0.634686i $$-0.218871\pi$$
0.772770 + 0.634686i $$0.218871\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 2.00000 0.118056
$$288$$ −2.00000 −0.117851
$$289$$ 32.0000 1.88235
$$290$$ 0 0
$$291$$ 18.0000 1.05518
$$292$$ 9.00000 0.526685
$$293$$ −31.0000 −1.81104 −0.905520 0.424304i $$-0.860519\pi$$
−0.905520 + 0.424304i $$0.860519\pi$$
$$294$$ −6.00000 −0.349927
$$295$$ 0 0
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ 4.00000 0.231714
$$299$$ 15.0000 0.867472
$$300$$ 0 0
$$301$$ −6.00000 −0.345834
$$302$$ −6.00000 −0.345261
$$303$$ −4.00000 −0.229794
$$304$$ −1.00000 −0.0573539
$$305$$ 0 0
$$306$$ −14.0000 −0.800327
$$307$$ −4.00000 −0.228292 −0.114146 0.993464i $$-0.536413\pi$$
−0.114146 + 0.993464i $$0.536413\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 33.0000 1.87126 0.935629 0.352985i $$-0.114833\pi$$
0.935629 + 0.352985i $$0.114833\pi$$
$$312$$ 3.00000 0.169842
$$313$$ 29.0000 1.63918 0.819588 0.572953i $$-0.194202\pi$$
0.819588 + 0.572953i $$0.194202\pi$$
$$314$$ −18.0000 −1.01580
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ −3.00000 −0.168497 −0.0842484 0.996445i $$-0.526849\pi$$
−0.0842484 + 0.996445i $$0.526849\pi$$
$$318$$ −9.00000 −0.504695
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −9.00000 −0.502331
$$322$$ 5.00000 0.278639
$$323$$ −7.00000 −0.389490
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 18.0000 0.996928
$$327$$ 13.0000 0.718902
$$328$$ 2.00000 0.110432
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −17.0000 −0.934405 −0.467202 0.884150i $$-0.654738\pi$$
−0.467202 + 0.884150i $$0.654738\pi$$
$$332$$ 2.00000 0.109764
$$333$$ 4.00000 0.219199
$$334$$ −14.0000 −0.766046
$$335$$ 0 0
$$336$$ 1.00000 0.0545545
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ −4.00000 −0.217571
$$339$$ −8.00000 −0.434500
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 2.00000 0.108148
$$343$$ −13.0000 −0.701934
$$344$$ −6.00000 −0.323498
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ 18.0000 0.966291 0.483145 0.875540i $$-0.339494\pi$$
0.483145 + 0.875540i $$0.339494\pi$$
$$348$$ −5.00000 −0.268028
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ −15.0000 −0.800641
$$352$$ 0 0
$$353$$ −27.0000 −1.43706 −0.718532 0.695493i $$-0.755186\pi$$
−0.718532 + 0.695493i $$0.755186\pi$$
$$354$$ −7.00000 −0.372046
$$355$$ 0 0
$$356$$ −10.0000 −0.529999
$$357$$ 7.00000 0.370479
$$358$$ 24.0000 1.26844
$$359$$ 27.0000 1.42501 0.712503 0.701669i $$-0.247562\pi$$
0.712503 + 0.701669i $$0.247562\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ −10.0000 −0.525588
$$363$$ −11.0000 −0.577350
$$364$$ 3.00000 0.157243
$$365$$ 0 0
$$366$$ −4.00000 −0.209083
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 5.00000 0.260643
$$369$$ −4.00000 −0.208232
$$370$$ 0 0
$$371$$ −9.00000 −0.467257
$$372$$ 10.0000 0.518476
$$373$$ −3.00000 −0.155334 −0.0776671 0.996979i $$-0.524747\pi$$
−0.0776671 + 0.996979i $$0.524747\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −15.0000 −0.772539
$$378$$ −5.00000 −0.257172
$$379$$ −7.00000 −0.359566 −0.179783 0.983706i $$-0.557540\pi$$
−0.179783 + 0.983706i $$0.557540\pi$$
$$380$$ 0 0
$$381$$ 6.00000 0.307389
$$382$$ −7.00000 −0.358151
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ 2.00000 0.101797
$$387$$ 12.0000 0.609994
$$388$$ 18.0000 0.913812
$$389$$ 24.0000 1.21685 0.608424 0.793612i $$-0.291802\pi$$
0.608424 + 0.793612i $$0.291802\pi$$
$$390$$ 0 0
$$391$$ 35.0000 1.77003
$$392$$ −6.00000 −0.303046
$$393$$ −20.0000 −1.00887
$$394$$ 10.0000 0.503793
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 20.0000 1.00377 0.501886 0.864934i $$-0.332640\pi$$
0.501886 + 0.864934i $$0.332640\pi$$
$$398$$ 17.0000 0.852133
$$399$$ −1.00000 −0.0500626
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ −7.00000 −0.349128
$$403$$ 30.0000 1.49441
$$404$$ −4.00000 −0.199007
$$405$$ 0 0
$$406$$ −5.00000 −0.248146
$$407$$ 0 0
$$408$$ 7.00000 0.346552
$$409$$ 26.0000 1.28562 0.642809 0.766027i $$-0.277769\pi$$
0.642809 + 0.766027i $$0.277769\pi$$
$$410$$ 0 0
$$411$$ 3.00000 0.147979
$$412$$ 0 0
$$413$$ −7.00000 −0.344447
$$414$$ −10.0000 −0.491473
$$415$$ 0 0
$$416$$ 3.00000 0.147087
$$417$$ 12.0000 0.587643
$$418$$ 0 0
$$419$$ −26.0000 −1.27018 −0.635092 0.772437i $$-0.719038\pi$$
−0.635092 + 0.772437i $$0.719038\pi$$
$$420$$ 0 0
$$421$$ 31.0000 1.51085 0.755424 0.655237i $$-0.227431\pi$$
0.755424 + 0.655237i $$0.227431\pi$$
$$422$$ 5.00000 0.243396
$$423$$ 0 0
$$424$$ −9.00000 −0.437079
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −4.00000 −0.193574
$$428$$ −9.00000 −0.435031
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ −5.00000 −0.240563
$$433$$ −12.0000 −0.576683 −0.288342 0.957528i $$-0.593104\pi$$
−0.288342 + 0.957528i $$0.593104\pi$$
$$434$$ 10.0000 0.480015
$$435$$ 0 0
$$436$$ 13.0000 0.622587
$$437$$ −5.00000 −0.239182
$$438$$ 9.00000 0.430037
$$439$$ 10.0000 0.477274 0.238637 0.971109i $$-0.423299\pi$$
0.238637 + 0.971109i $$0.423299\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ 21.0000 0.998868
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ −2.00000 −0.0949158
$$445$$ 0 0
$$446$$ 22.0000 1.04173
$$447$$ 4.00000 0.189194
$$448$$ 1.00000 0.0472456
$$449$$ 14.0000 0.660701 0.330350 0.943858i $$-0.392833\pi$$
0.330350 + 0.943858i $$0.392833\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −8.00000 −0.376288
$$453$$ −6.00000 −0.281905
$$454$$ 25.0000 1.17331
$$455$$ 0 0
$$456$$ −1.00000 −0.0468293
$$457$$ 41.0000 1.91790 0.958950 0.283577i $$-0.0915211\pi$$
0.958950 + 0.283577i $$0.0915211\pi$$
$$458$$ −18.0000 −0.841085
$$459$$ −35.0000 −1.63366
$$460$$ 0 0
$$461$$ −10.0000 −0.465746 −0.232873 0.972507i $$-0.574813\pi$$
−0.232873 + 0.972507i $$0.574813\pi$$
$$462$$ 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
$$466$$ −26.0000 −1.20443
$$467$$ 8.00000 0.370196 0.185098 0.982720i $$-0.440740\pi$$
0.185098 + 0.982720i $$0.440740\pi$$
$$468$$ −6.00000 −0.277350
$$469$$ −7.00000 −0.323230
$$470$$ 0 0
$$471$$ −18.0000 −0.829396
$$472$$ −7.00000 −0.322201
$$473$$ 0 0
$$474$$ −10.0000 −0.459315
$$475$$ 0 0
$$476$$ 7.00000 0.320844
$$477$$ 18.0000 0.824163
$$478$$ −27.0000 −1.23495
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ −28.0000 −1.27537
$$483$$ 5.00000 0.227508
$$484$$ −11.0000 −0.500000
$$485$$ 0 0
$$486$$ 16.0000 0.725775
$$487$$ 2.00000 0.0906287 0.0453143 0.998973i $$-0.485571\pi$$
0.0453143 + 0.998973i $$0.485571\pi$$
$$488$$ −4.00000 −0.181071
$$489$$ 18.0000 0.813988
$$490$$ 0 0
$$491$$ 14.0000 0.631811 0.315906 0.948791i $$-0.397692\pi$$
0.315906 + 0.948791i $$0.397692\pi$$
$$492$$ 2.00000 0.0901670
$$493$$ −35.0000 −1.57632
$$494$$ −3.00000 −0.134976
$$495$$ 0 0
$$496$$ 10.0000 0.449013
$$497$$ 0 0
$$498$$ 2.00000 0.0896221
$$499$$ 42.0000 1.88018 0.940089 0.340929i $$-0.110742\pi$$
0.940089 + 0.340929i $$0.110742\pi$$
$$500$$ 0 0
$$501$$ −14.0000 −0.625474
$$502$$ 4.00000 0.178529
$$503$$ 17.0000 0.757993 0.378996 0.925398i $$-0.376269\pi$$
0.378996 + 0.925398i $$0.376269\pi$$
$$504$$ −2.00000 −0.0890871
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −4.00000 −0.177646
$$508$$ 6.00000 0.266207
$$509$$ −42.0000 −1.86162 −0.930809 0.365507i $$-0.880896\pi$$
−0.930809 + 0.365507i $$0.880896\pi$$
$$510$$ 0 0
$$511$$ 9.00000 0.398137
$$512$$ 1.00000 0.0441942
$$513$$ 5.00000 0.220755
$$514$$ 6.00000 0.264649
$$515$$ 0 0
$$516$$ −6.00000 −0.264135
$$517$$ 0 0
$$518$$ −2.00000 −0.0878750
$$519$$ −6.00000 −0.263371
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 10.0000 0.437688
$$523$$ 19.0000 0.830812 0.415406 0.909636i $$-0.363640\pi$$
0.415406 + 0.909636i $$0.363640\pi$$
$$524$$ −20.0000 −0.873704
$$525$$ 0 0
$$526$$ 8.00000 0.348817
$$527$$ 70.0000 3.04925
$$528$$ 0 0
$$529$$ 2.00000 0.0869565
$$530$$ 0 0
$$531$$ 14.0000 0.607548
$$532$$ −1.00000 −0.0433555
$$533$$ 6.00000 0.259889
$$534$$ −10.0000 −0.432742
$$535$$ 0 0
$$536$$ −7.00000 −0.302354
$$537$$ 24.0000 1.03568
$$538$$ −10.0000 −0.431131
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −28.0000 −1.20381 −0.601907 0.798566i $$-0.705592\pi$$
−0.601907 + 0.798566i $$0.705592\pi$$
$$542$$ 5.00000 0.214768
$$543$$ −10.0000 −0.429141
$$544$$ 7.00000 0.300123
$$545$$ 0 0
$$546$$ 3.00000 0.128388
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ 3.00000 0.128154
$$549$$ 8.00000 0.341432
$$550$$ 0 0
$$551$$ 5.00000 0.213007
$$552$$ 5.00000 0.212814
$$553$$ −10.0000 −0.425243
$$554$$ −28.0000 −1.18961
$$555$$ 0 0
$$556$$ 12.0000 0.508913
$$557$$ −8.00000 −0.338971 −0.169485 0.985533i $$-0.554211\pi$$
−0.169485 + 0.985533i $$0.554211\pi$$
$$558$$ −20.0000 −0.846668
$$559$$ −18.0000 −0.761319
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −26.0000 −1.09674
$$563$$ 44.0000 1.85438 0.927189 0.374593i $$-0.122217\pi$$
0.927189 + 0.374593i $$0.122217\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 26.0000 1.09286
$$567$$ 1.00000 0.0419961
$$568$$ 0 0
$$569$$ −8.00000 −0.335377 −0.167689 0.985840i $$-0.553630\pi$$
−0.167689 + 0.985840i $$0.553630\pi$$
$$570$$ 0 0
$$571$$ 10.0000 0.418487 0.209243 0.977864i $$-0.432900\pi$$
0.209243 + 0.977864i $$0.432900\pi$$
$$572$$ 0 0
$$573$$ −7.00000 −0.292429
$$574$$ 2.00000 0.0834784
$$575$$ 0 0
$$576$$ −2.00000 −0.0833333
$$577$$ 11.0000 0.457936 0.228968 0.973434i $$-0.426465\pi$$
0.228968 + 0.973434i $$0.426465\pi$$
$$578$$ 32.0000 1.33102
$$579$$ 2.00000 0.0831172
$$580$$ 0 0
$$581$$ 2.00000 0.0829740
$$582$$ 18.0000 0.746124
$$583$$ 0 0
$$584$$ 9.00000 0.372423
$$585$$ 0 0
$$586$$ −31.0000 −1.28060
$$587$$ −30.0000 −1.23823 −0.619116 0.785299i $$-0.712509\pi$$
−0.619116 + 0.785299i $$0.712509\pi$$
$$588$$ −6.00000 −0.247436
$$589$$ −10.0000 −0.412043
$$590$$ 0 0
$$591$$ 10.0000 0.411345
$$592$$ −2.00000 −0.0821995
$$593$$ 34.0000 1.39621 0.698106 0.715994i $$-0.254026\pi$$
0.698106 + 0.715994i $$0.254026\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 4.00000 0.163846
$$597$$ 17.0000 0.695764
$$598$$ 15.0000 0.613396
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ −6.00000 −0.244542
$$603$$ 14.0000 0.570124
$$604$$ −6.00000 −0.244137
$$605$$ 0 0
$$606$$ −4.00000 −0.162489
$$607$$ −22.0000 −0.892952 −0.446476 0.894795i $$-0.647321\pi$$
−0.446476 + 0.894795i $$0.647321\pi$$
$$608$$ −1.00000 −0.0405554
$$609$$ −5.00000 −0.202610
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −14.0000 −0.565916
$$613$$ 16.0000 0.646234 0.323117 0.946359i $$-0.395269\pi$$
0.323117 + 0.946359i $$0.395269\pi$$
$$614$$ −4.00000 −0.161427
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 2.00000 0.0805170 0.0402585 0.999189i $$-0.487182\pi$$
0.0402585 + 0.999189i $$0.487182\pi$$
$$618$$ 0 0
$$619$$ −8.00000 −0.321547 −0.160774 0.986991i $$-0.551399\pi$$
−0.160774 + 0.986991i $$0.551399\pi$$
$$620$$ 0 0
$$621$$ −25.0000 −1.00322
$$622$$ 33.0000 1.32318
$$623$$ −10.0000 −0.400642
$$624$$ 3.00000 0.120096
$$625$$ 0 0
$$626$$ 29.0000 1.15907
$$627$$ 0 0
$$628$$ −18.0000 −0.718278
$$629$$ −14.0000 −0.558217
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ −10.0000 −0.397779
$$633$$ 5.00000 0.198732
$$634$$ −3.00000 −0.119145
$$635$$ 0 0
$$636$$ −9.00000 −0.356873
$$637$$ −18.0000 −0.713186
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −12.0000 −0.473972 −0.236986 0.971513i $$-0.576159\pi$$
−0.236986 + 0.971513i $$0.576159\pi$$
$$642$$ −9.00000 −0.355202
$$643$$ 2.00000 0.0788723 0.0394362 0.999222i $$-0.487444\pi$$
0.0394362 + 0.999222i $$0.487444\pi$$
$$644$$ 5.00000 0.197028
$$645$$ 0 0
$$646$$ −7.00000 −0.275411
$$647$$ 9.00000 0.353827 0.176913 0.984226i $$-0.443389\pi$$
0.176913 + 0.984226i $$0.443389\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 10.0000 0.391931
$$652$$ 18.0000 0.704934
$$653$$ 12.0000 0.469596 0.234798 0.972044i $$-0.424557\pi$$
0.234798 + 0.972044i $$0.424557\pi$$
$$654$$ 13.0000 0.508340
$$655$$ 0 0
$$656$$ 2.00000 0.0780869
$$657$$ −18.0000 −0.702247
$$658$$ 0 0
$$659$$ 15.0000 0.584317 0.292159 0.956370i $$-0.405627\pi$$
0.292159 + 0.956370i $$0.405627\pi$$
$$660$$ 0 0
$$661$$ 17.0000 0.661223 0.330612 0.943767i $$-0.392745\pi$$
0.330612 + 0.943767i $$0.392745\pi$$
$$662$$ −17.0000 −0.660724
$$663$$ 21.0000 0.815572
$$664$$ 2.00000 0.0776151
$$665$$ 0 0
$$666$$ 4.00000 0.154997
$$667$$ −25.0000 −0.968004
$$668$$ −14.0000 −0.541676
$$669$$ 22.0000 0.850569
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 1.00000 0.0385758
$$673$$ 28.0000 1.07932 0.539660 0.841883i $$-0.318553\pi$$
0.539660 + 0.841883i $$0.318553\pi$$
$$674$$ 14.0000 0.539260
$$675$$ 0 0
$$676$$ −4.00000 −0.153846
$$677$$ −19.0000 −0.730229 −0.365115 0.930963i $$-0.618970\pi$$
−0.365115 + 0.930963i $$0.618970\pi$$
$$678$$ −8.00000 −0.307238
$$679$$ 18.0000 0.690777
$$680$$ 0 0
$$681$$ 25.0000 0.958002
$$682$$ 0 0
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 2.00000 0.0764719
$$685$$ 0 0
$$686$$ −13.0000 −0.496342
$$687$$ −18.0000 −0.686743
$$688$$ −6.00000 −0.228748
$$689$$ −27.0000 −1.02862
$$690$$ 0 0
$$691$$ 10.0000 0.380418 0.190209 0.981744i $$-0.439083\pi$$
0.190209 + 0.981744i $$0.439083\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ 18.0000 0.683271
$$695$$ 0 0
$$696$$ −5.00000 −0.189525
$$697$$ 14.0000 0.530288
$$698$$ 10.0000 0.378506
$$699$$ −26.0000 −0.983410
$$700$$ 0 0
$$701$$ 24.0000 0.906467 0.453234 0.891392i $$-0.350270\pi$$
0.453234 + 0.891392i $$0.350270\pi$$
$$702$$ −15.0000 −0.566139
$$703$$ 2.00000 0.0754314
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −27.0000 −1.01616
$$707$$ −4.00000 −0.150435
$$708$$ −7.00000 −0.263076
$$709$$ −34.0000 −1.27690 −0.638448 0.769665i $$-0.720423\pi$$
−0.638448 + 0.769665i $$0.720423\pi$$
$$710$$ 0 0
$$711$$ 20.0000 0.750059
$$712$$ −10.0000 −0.374766
$$713$$ 50.0000 1.87251
$$714$$ 7.00000 0.261968
$$715$$ 0 0
$$716$$ 24.0000 0.896922
$$717$$ −27.0000 −1.00833
$$718$$ 27.0000 1.00763
$$719$$ 29.0000 1.08152 0.540759 0.841178i $$-0.318137\pi$$
0.540759 + 0.841178i $$0.318137\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000 0.0372161
$$723$$ −28.0000 −1.04133
$$724$$ −10.0000 −0.371647
$$725$$ 0 0
$$726$$ −11.0000 −0.408248
$$727$$ −11.0000 −0.407967 −0.203984 0.978974i $$-0.565389\pi$$
−0.203984 + 0.978974i $$0.565389\pi$$
$$728$$ 3.00000 0.111187
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −42.0000 −1.55343
$$732$$ −4.00000 −0.147844
$$733$$ −24.0000 −0.886460 −0.443230 0.896408i $$-0.646168\pi$$
−0.443230 + 0.896408i $$0.646168\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ 5.00000 0.184302
$$737$$ 0 0
$$738$$ −4.00000 −0.147242
$$739$$ 50.0000 1.83928 0.919640 0.392763i $$-0.128481\pi$$
0.919640 + 0.392763i $$0.128481\pi$$
$$740$$ 0 0
$$741$$ −3.00000 −0.110208
$$742$$ −9.00000 −0.330400
$$743$$ −34.0000 −1.24734 −0.623670 0.781688i $$-0.714359\pi$$
−0.623670 + 0.781688i $$0.714359\pi$$
$$744$$ 10.0000 0.366618
$$745$$ 0 0
$$746$$ −3.00000 −0.109838
$$747$$ −4.00000 −0.146352
$$748$$ 0 0
$$749$$ −9.00000 −0.328853
$$750$$ 0 0
$$751$$ 46.0000 1.67856 0.839282 0.543696i $$-0.182976\pi$$
0.839282 + 0.543696i $$0.182976\pi$$
$$752$$ 0 0
$$753$$ 4.00000 0.145768
$$754$$ −15.0000 −0.546268
$$755$$ 0 0
$$756$$ −5.00000 −0.181848
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ −7.00000 −0.254251
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −45.0000 −1.63125 −0.815624 0.578582i $$-0.803606\pi$$
−0.815624 + 0.578582i $$0.803606\pi$$
$$762$$ 6.00000 0.217357
$$763$$ 13.0000 0.470632
$$764$$ −7.00000 −0.253251
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −21.0000 −0.758266
$$768$$ 1.00000 0.0360844
$$769$$ 49.0000 1.76699 0.883493 0.468445i $$-0.155186\pi$$
0.883493 + 0.468445i $$0.155186\pi$$
$$770$$ 0 0
$$771$$ 6.00000 0.216085
$$772$$ 2.00000 0.0719816
$$773$$ −15.0000 −0.539513 −0.269756 0.962929i $$-0.586943\pi$$
−0.269756 + 0.962929i $$0.586943\pi$$
$$774$$ 12.0000 0.431331
$$775$$ 0 0
$$776$$ 18.0000 0.646162
$$777$$ −2.00000 −0.0717496
$$778$$ 24.0000 0.860442
$$779$$ −2.00000 −0.0716574
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 35.0000 1.25160
$$783$$ 25.0000 0.893427
$$784$$ −6.00000 −0.214286
$$785$$ 0 0
$$786$$ −20.0000 −0.713376
$$787$$ −11.0000 −0.392108 −0.196054 0.980593i $$-0.562813\pi$$
−0.196054 + 0.980593i $$0.562813\pi$$
$$788$$ 10.0000 0.356235
$$789$$ 8.00000 0.284808
$$790$$ 0 0
$$791$$ −8.00000 −0.284447
$$792$$ 0 0
$$793$$ −12.0000 −0.426132
$$794$$ 20.0000 0.709773
$$795$$ 0 0
$$796$$ 17.0000 0.602549
$$797$$ −5.00000 −0.177109 −0.0885545 0.996071i $$-0.528225\pi$$
−0.0885545 + 0.996071i $$0.528225\pi$$
$$798$$ −1.00000 −0.0353996
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 20.0000 0.706665
$$802$$ 18.0000 0.635602
$$803$$ 0 0
$$804$$ −7.00000 −0.246871
$$805$$ 0 0
$$806$$ 30.0000 1.05670
$$807$$ −10.0000 −0.352017
$$808$$ −4.00000 −0.140720
$$809$$ −39.0000 −1.37117 −0.685583 0.727994i $$-0.740453\pi$$
−0.685583 + 0.727994i $$0.740453\pi$$
$$810$$ 0 0
$$811$$ 11.0000 0.386262 0.193131 0.981173i $$-0.438136\pi$$
0.193131 + 0.981173i $$0.438136\pi$$
$$812$$ −5.00000 −0.175466
$$813$$ 5.00000 0.175358
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 7.00000 0.245049
$$817$$ 6.00000 0.209913
$$818$$ 26.0000 0.909069
$$819$$ −6.00000 −0.209657
$$820$$ 0 0
$$821$$ −56.0000 −1.95441 −0.977207 0.212290i $$-0.931908\pi$$
−0.977207 + 0.212290i $$0.931908\pi$$
$$822$$ 3.00000 0.104637
$$823$$ 31.0000 1.08059 0.540296 0.841475i $$-0.318312\pi$$
0.540296 + 0.841475i $$0.318312\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ −7.00000 −0.243561
$$827$$ 9.00000 0.312961 0.156480 0.987681i $$-0.449985\pi$$
0.156480 + 0.987681i $$0.449985\pi$$
$$828$$ −10.0000 −0.347524
$$829$$ −51.0000 −1.77130 −0.885652 0.464350i $$-0.846288\pi$$
−0.885652 + 0.464350i $$0.846288\pi$$
$$830$$ 0 0
$$831$$ −28.0000 −0.971309
$$832$$ 3.00000 0.104006
$$833$$ −42.0000 −1.45521
$$834$$ 12.0000 0.415526
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −50.0000 −1.72825
$$838$$ −26.0000 −0.898155
$$839$$ −48.0000 −1.65714 −0.828572 0.559883i $$-0.810846\pi$$
−0.828572 + 0.559883i $$0.810846\pi$$
$$840$$ 0 0
$$841$$ −4.00000 −0.137931
$$842$$ 31.0000 1.06833
$$843$$ −26.0000 −0.895488
$$844$$ 5.00000 0.172107
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −11.0000 −0.377964
$$848$$ −9.00000 −0.309061
$$849$$ 26.0000 0.892318
$$850$$ 0 0
$$851$$ −10.0000 −0.342796
$$852$$ 0 0
$$853$$ 46.0000 1.57501 0.787505 0.616308i $$-0.211372\pi$$
0.787505 + 0.616308i $$0.211372\pi$$
$$854$$ −4.00000 −0.136877
$$855$$ 0 0
$$856$$ −9.00000 −0.307614
$$857$$ −24.0000 −0.819824 −0.409912 0.912125i $$-0.634441\pi$$
−0.409912 + 0.912125i $$0.634441\pi$$
$$858$$ 0 0
$$859$$ 56.0000 1.91070 0.955348 0.295484i $$-0.0954809\pi$$
0.955348 + 0.295484i $$0.0954809\pi$$
$$860$$ 0 0
$$861$$ 2.00000 0.0681598
$$862$$ 12.0000 0.408722
$$863$$ −24.0000 −0.816970 −0.408485 0.912765i $$-0.633943\pi$$
−0.408485 + 0.912765i $$0.633943\pi$$
$$864$$ −5.00000 −0.170103
$$865$$ 0 0
$$866$$ −12.0000 −0.407777
$$867$$ 32.0000 1.08678
$$868$$ 10.0000 0.339422
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −21.0000 −0.711558
$$872$$ 13.0000 0.440236
$$873$$ −36.0000 −1.21842
$$874$$ −5.00000 −0.169128
$$875$$ 0 0
$$876$$ 9.00000 0.304082
$$877$$ 5.00000 0.168838 0.0844190 0.996430i $$-0.473097\pi$$
0.0844190 + 0.996430i $$0.473097\pi$$
$$878$$ 10.0000 0.337484
$$879$$ −31.0000 −1.04560
$$880$$ 0 0
$$881$$ 2.00000 0.0673817 0.0336909 0.999432i $$-0.489274\pi$$
0.0336909 + 0.999432i $$0.489274\pi$$
$$882$$ 12.0000 0.404061
$$883$$ −26.0000 −0.874970 −0.437485 0.899226i $$-0.644131\pi$$
−0.437485 + 0.899226i $$0.644131\pi$$
$$884$$ 21.0000 0.706306
$$885$$ 0 0
$$886$$ −24.0000 −0.806296
$$887$$ −52.0000 −1.74599 −0.872995 0.487730i $$-0.837825\pi$$
−0.872995 + 0.487730i $$0.837825\pi$$
$$888$$ −2.00000 −0.0671156
$$889$$ 6.00000 0.201234
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 22.0000 0.736614
$$893$$ 0 0
$$894$$ 4.00000 0.133780
$$895$$ 0 0
$$896$$ 1.00000 0.0334077
$$897$$ 15.0000 0.500835
$$898$$ 14.0000 0.467186
$$899$$ −50.0000 −1.66759
$$900$$ 0 0
$$901$$ −63.0000 −2.09883
$$902$$ 0 0
$$903$$ −6.00000 −0.199667
$$904$$ −8.00000 −0.266076
$$905$$ 0 0
$$906$$ −6.00000 −0.199337
$$907$$ −5.00000 −0.166022 −0.0830111 0.996549i $$-0.526454\pi$$
−0.0830111 + 0.996549i $$0.526454\pi$$
$$908$$ 25.0000 0.829654
$$909$$ 8.00000 0.265343
$$910$$ 0 0
$$911$$ −32.0000 −1.06021 −0.530104 0.847933i $$-0.677847\pi$$
−0.530104 + 0.847933i $$0.677847\pi$$
$$912$$ −1.00000 −0.0331133
$$913$$ 0 0
$$914$$ 41.0000 1.35616
$$915$$ 0 0
$$916$$ −18.0000 −0.594737
$$917$$ −20.0000 −0.660458
$$918$$ −35.0000 −1.15517
$$919$$ 11.0000 0.362857 0.181428 0.983404i $$-0.441928\pi$$
0.181428 + 0.983404i $$0.441928\pi$$
$$920$$ 0 0
$$921$$ −4.00000 −0.131804
$$922$$ −10.0000 −0.329332
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −16.0000 −0.525793
$$927$$ 0 0
$$928$$ −5.00000 −0.164133
$$929$$ 21.0000 0.688988 0.344494 0.938789i $$-0.388051\pi$$
0.344494 + 0.938789i $$0.388051\pi$$
$$930$$ 0 0
$$931$$ 6.00000 0.196642
$$932$$ −26.0000 −0.851658
$$933$$ 33.0000 1.08037
$$934$$ 8.00000 0.261768
$$935$$ 0 0
$$936$$ −6.00000 −0.196116
$$937$$ 13.0000 0.424691 0.212346 0.977195i $$-0.431890\pi$$
0.212346 + 0.977195i $$0.431890\pi$$
$$938$$ −7.00000 −0.228558
$$939$$ 29.0000 0.946379
$$940$$ 0 0
$$941$$ −37.0000 −1.20617 −0.603083 0.797679i $$-0.706061\pi$$
−0.603083 + 0.797679i $$0.706061\pi$$
$$942$$ −18.0000 −0.586472
$$943$$ 10.0000 0.325645
$$944$$ −7.00000 −0.227831
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 28.0000 0.909878 0.454939 0.890523i $$-0.349661\pi$$
0.454939 + 0.890523i $$0.349661\pi$$
$$948$$ −10.0000 −0.324785
$$949$$ 27.0000 0.876457
$$950$$ 0 0
$$951$$ −3.00000 −0.0972817
$$952$$ 7.00000 0.226871
$$953$$ −44.0000 −1.42530 −0.712650 0.701520i $$-0.752505\pi$$
−0.712650 + 0.701520i $$0.752505\pi$$
$$954$$ 18.0000 0.582772
$$955$$ 0 0
$$956$$ −27.0000 −0.873242
$$957$$ 0 0
$$958$$ −24.0000 −0.775405
$$959$$ 3.00000 0.0968751
$$960$$ 0 0
$$961$$ 69.0000 2.22581
$$962$$ −6.00000 −0.193448
$$963$$ 18.0000 0.580042
$$964$$ −28.0000 −0.901819
$$965$$ 0 0
$$966$$ 5.00000 0.160872
$$967$$ −12.0000 −0.385894 −0.192947 0.981209i $$-0.561805\pi$$
−0.192947 + 0.981209i $$0.561805\pi$$
$$968$$ −11.0000 −0.353553
$$969$$ −7.00000 −0.224872
$$970$$ 0 0
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ 16.0000 0.513200
$$973$$ 12.0000 0.384702
$$974$$ 2.00000 0.0640841
$$975$$ 0 0
$$976$$ −4.00000 −0.128037
$$977$$ 18.0000 0.575871 0.287936 0.957650i $$-0.407031\pi$$
0.287936 + 0.957650i $$0.407031\pi$$
$$978$$ 18.0000 0.575577
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −26.0000 −0.830116
$$982$$ 14.0000 0.446758
$$983$$ 18.0000 0.574111 0.287055 0.957914i $$-0.407324\pi$$
0.287055 + 0.957914i $$0.407324\pi$$
$$984$$ 2.00000 0.0637577
$$985$$ 0 0
$$986$$ −35.0000 −1.11463
$$987$$ 0 0
$$988$$ −3.00000 −0.0954427
$$989$$ −30.0000 −0.953945
$$990$$ 0 0
$$991$$ −46.0000 −1.46124 −0.730619 0.682785i $$-0.760768\pi$$
−0.730619 + 0.682785i $$0.760768\pi$$
$$992$$ 10.0000 0.317500
$$993$$ −17.0000 −0.539479
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 2.00000 0.0633724
$$997$$ −14.0000 −0.443384 −0.221692 0.975117i $$-0.571158\pi$$
−0.221692 + 0.975117i $$0.571158\pi$$
$$998$$ 42.0000 1.32949
$$999$$ 10.0000 0.316386
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 950.2.a.e.1.1 1
3.2 odd 2 8550.2.a.l.1.1 1
4.3 odd 2 7600.2.a.g.1.1 1
5.2 odd 4 950.2.b.d.799.2 2
5.3 odd 4 950.2.b.d.799.1 2
5.4 even 2 190.2.a.a.1.1 1
15.14 odd 2 1710.2.a.r.1.1 1
20.19 odd 2 1520.2.a.g.1.1 1
35.34 odd 2 9310.2.a.i.1.1 1
40.19 odd 2 6080.2.a.i.1.1 1
40.29 even 2 6080.2.a.r.1.1 1
95.94 odd 2 3610.2.a.h.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.a.1.1 1 5.4 even 2
950.2.a.e.1.1 1 1.1 even 1 trivial
950.2.b.d.799.1 2 5.3 odd 4
950.2.b.d.799.2 2 5.2 odd 4
1520.2.a.g.1.1 1 20.19 odd 2
1710.2.a.r.1.1 1 15.14 odd 2
3610.2.a.h.1.1 1 95.94 odd 2
6080.2.a.i.1.1 1 40.19 odd 2
6080.2.a.r.1.1 1 40.29 even 2
7600.2.a.g.1.1 1 4.3 odd 2
8550.2.a.l.1.1 1 3.2 odd 2
9310.2.a.i.1.1 1 35.34 odd 2