# Properties

 Label 1850.2.a.c.1.1 Level $1850$ Weight $2$ Character 1850.1 Self dual yes Analytic conductor $14.772$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1850 = 2 \cdot 5^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1850.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$14.7723243739$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1850.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +3.00000 q^{11} -1.00000 q^{12} +6.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} +2.00000 q^{18} -3.00000 q^{19} -4.00000 q^{21} -3.00000 q^{22} +2.00000 q^{23} +1.00000 q^{24} -6.00000 q^{26} +5.00000 q^{27} +4.00000 q^{28} -1.00000 q^{32} -3.00000 q^{33} -3.00000 q^{34} -2.00000 q^{36} -1.00000 q^{37} +3.00000 q^{38} -6.00000 q^{39} -3.00000 q^{41} +4.00000 q^{42} -4.00000 q^{43} +3.00000 q^{44} -2.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} -3.00000 q^{51} +6.00000 q^{52} -2.00000 q^{53} -5.00000 q^{54} -4.00000 q^{56} +3.00000 q^{57} -12.0000 q^{59} +12.0000 q^{61} -8.00000 q^{63} +1.00000 q^{64} +3.00000 q^{66} +9.00000 q^{67} +3.00000 q^{68} -2.00000 q^{69} -2.00000 q^{71} +2.00000 q^{72} -9.00000 q^{73} +1.00000 q^{74} -3.00000 q^{76} +12.0000 q^{77} +6.00000 q^{78} -2.00000 q^{79} +1.00000 q^{81} +3.00000 q^{82} -7.00000 q^{83} -4.00000 q^{84} +4.00000 q^{86} -3.00000 q^{88} -3.00000 q^{89} +24.0000 q^{91} +2.00000 q^{92} -4.00000 q^{94} +1.00000 q^{96} +2.00000 q^{97} -9.00000 q^{98} -6.00000 q^{99} +O(q^{100})$$

## 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 −0.288675 0.957427i $$-0.593215\pi$$
−0.288675 + 0.957427i $$0.593215\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 1.00000 0.408248
$$7$$ 4.00000 1.51186 0.755929 0.654654i $$-0.227186\pi$$
0.755929 + 0.654654i $$0.227186\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ −4.00000 −1.06904
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 2.00000 0.471405
$$19$$ −3.00000 −0.688247 −0.344124 0.938924i $$-0.611824\pi$$
−0.344124 + 0.938924i $$0.611824\pi$$
$$20$$ 0 0
$$21$$ −4.00000 −0.872872
$$22$$ −3.00000 −0.639602
$$23$$ 2.00000 0.417029 0.208514 0.978019i $$-0.433137\pi$$
0.208514 + 0.978019i $$0.433137\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 0 0
$$26$$ −6.00000 −1.17670
$$27$$ 5.00000 0.962250
$$28$$ 4.00000 0.755929
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ −3.00000 −0.522233
$$34$$ −3.00000 −0.514496
$$35$$ 0 0
$$36$$ −2.00000 −0.333333
$$37$$ −1.00000 −0.164399
$$38$$ 3.00000 0.486664
$$39$$ −6.00000 −0.960769
$$40$$ 0 0
$$41$$ −3.00000 −0.468521 −0.234261 0.972174i $$-0.575267\pi$$
−0.234261 + 0.972174i $$0.575267\pi$$
$$42$$ 4.00000 0.617213
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 0 0
$$46$$ −2.00000 −0.294884
$$47$$ 4.00000 0.583460 0.291730 0.956501i $$-0.405769\pi$$
0.291730 + 0.956501i $$0.405769\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 9.00000 1.28571
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 6.00000 0.832050
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ −5.00000 −0.680414
$$55$$ 0 0
$$56$$ −4.00000 −0.534522
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ 12.0000 1.53644 0.768221 0.640184i $$-0.221142\pi$$
0.768221 + 0.640184i $$0.221142\pi$$
$$62$$ 0 0
$$63$$ −8.00000 −1.00791
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 3.00000 0.369274
$$67$$ 9.00000 1.09952 0.549762 0.835321i $$-0.314718\pi$$
0.549762 + 0.835321i $$0.314718\pi$$
$$68$$ 3.00000 0.363803
$$69$$ −2.00000 −0.240772
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ 2.00000 0.235702
$$73$$ −9.00000 −1.05337 −0.526685 0.850060i $$-0.676565\pi$$
−0.526685 + 0.850060i $$0.676565\pi$$
$$74$$ 1.00000 0.116248
$$75$$ 0 0
$$76$$ −3.00000 −0.344124
$$77$$ 12.0000 1.36753
$$78$$ 6.00000 0.679366
$$79$$ −2.00000 −0.225018 −0.112509 0.993651i $$-0.535889\pi$$
−0.112509 + 0.993651i $$0.535889\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 3.00000 0.331295
$$83$$ −7.00000 −0.768350 −0.384175 0.923260i $$-0.625514\pi$$
−0.384175 + 0.923260i $$0.625514\pi$$
$$84$$ −4.00000 −0.436436
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ −3.00000 −0.319801
$$89$$ −3.00000 −0.317999 −0.159000 0.987279i $$-0.550827\pi$$
−0.159000 + 0.987279i $$0.550827\pi$$
$$90$$ 0 0
$$91$$ 24.0000 2.51588
$$92$$ 2.00000 0.208514
$$93$$ 0 0
$$94$$ −4.00000 −0.412568
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ −9.00000 −0.909137
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ 3.00000 0.297044
$$103$$ 14.0000 1.37946 0.689730 0.724066i $$-0.257729\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ −6.00000 −0.588348
$$105$$ 0 0
$$106$$ 2.00000 0.194257
$$107$$ −1.00000 −0.0966736 −0.0483368 0.998831i $$-0.515392\pi$$
−0.0483368 + 0.998831i $$0.515392\pi$$
$$108$$ 5.00000 0.481125
$$109$$ 18.0000 1.72409 0.862044 0.506834i $$-0.169184\pi$$
0.862044 + 0.506834i $$0.169184\pi$$
$$110$$ 0 0
$$111$$ 1.00000 0.0949158
$$112$$ 4.00000 0.377964
$$113$$ 5.00000 0.470360 0.235180 0.971952i $$-0.424432\pi$$
0.235180 + 0.971952i $$0.424432\pi$$
$$114$$ −3.00000 −0.280976
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −12.0000 −1.10940
$$118$$ 12.0000 1.10469
$$119$$ 12.0000 1.10004
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ −12.0000 −1.08643
$$123$$ 3.00000 0.270501
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 8.00000 0.712697
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ −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 $$0.324356\pi$$
$$132$$ −3.00000 −0.261116
$$133$$ −12.0000 −1.04053
$$134$$ −9.00000 −0.777482
$$135$$ 0 0
$$136$$ −3.00000 −0.257248
$$137$$ −7.00000 −0.598050 −0.299025 0.954245i $$-0.596661\pi$$
−0.299025 + 0.954245i $$0.596661\pi$$
$$138$$ 2.00000 0.170251
$$139$$ 3.00000 0.254457 0.127228 0.991873i $$-0.459392\pi$$
0.127228 + 0.991873i $$0.459392\pi$$
$$140$$ 0 0
$$141$$ −4.00000 −0.336861
$$142$$ 2.00000 0.167836
$$143$$ 18.0000 1.50524
$$144$$ −2.00000 −0.166667
$$145$$ 0 0
$$146$$ 9.00000 0.744845
$$147$$ −9.00000 −0.742307
$$148$$ −1.00000 −0.0821995
$$149$$ −18.0000 −1.47462 −0.737309 0.675556i $$-0.763904\pi$$
−0.737309 + 0.675556i $$0.763904\pi$$
$$150$$ 0 0
$$151$$ 22.0000 1.79033 0.895167 0.445730i $$-0.147056\pi$$
0.895167 + 0.445730i $$0.147056\pi$$
$$152$$ 3.00000 0.243332
$$153$$ −6.00000 −0.485071
$$154$$ −12.0000 −0.966988
$$155$$ 0 0
$$156$$ −6.00000 −0.480384
$$157$$ 24.0000 1.91541 0.957704 0.287754i $$-0.0929087\pi$$
0.957704 + 0.287754i $$0.0929087\pi$$
$$158$$ 2.00000 0.159111
$$159$$ 2.00000 0.158610
$$160$$ 0 0
$$161$$ 8.00000 0.630488
$$162$$ −1.00000 −0.0785674
$$163$$ −17.0000 −1.33154 −0.665771 0.746156i $$-0.731897\pi$$
−0.665771 + 0.746156i $$0.731897\pi$$
$$164$$ −3.00000 −0.234261
$$165$$ 0 0
$$166$$ 7.00000 0.543305
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 4.00000 0.308607
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 6.00000 0.458831
$$172$$ −4.00000 −0.304997
$$173$$ 24.0000 1.82469 0.912343 0.409426i $$-0.134271\pi$$
0.912343 + 0.409426i $$0.134271\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 3.00000 0.226134
$$177$$ 12.0000 0.901975
$$178$$ 3.00000 0.224860
$$179$$ 21.0000 1.56961 0.784807 0.619740i $$-0.212762\pi$$
0.784807 + 0.619740i $$0.212762\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ −24.0000 −1.77900
$$183$$ −12.0000 −0.887066
$$184$$ −2.00000 −0.147442
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 9.00000 0.658145
$$188$$ 4.00000 0.291730
$$189$$ 20.0000 1.45479
$$190$$ 0 0
$$191$$ 6.00000 0.434145 0.217072 0.976156i $$-0.430349\pi$$
0.217072 + 0.976156i $$0.430349\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 11.0000 0.791797 0.395899 0.918294i $$-0.370433\pi$$
0.395899 + 0.918294i $$0.370433\pi$$
$$194$$ −2.00000 −0.143592
$$195$$ 0 0
$$196$$ 9.00000 0.642857
$$197$$ 12.0000 0.854965 0.427482 0.904024i $$-0.359401\pi$$
0.427482 + 0.904024i $$0.359401\pi$$
$$198$$ 6.00000 0.426401
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ 0 0
$$201$$ −9.00000 −0.634811
$$202$$ 10.0000 0.703598
$$203$$ 0 0
$$204$$ −3.00000 −0.210042
$$205$$ 0 0
$$206$$ −14.0000 −0.975426
$$207$$ −4.00000 −0.278019
$$208$$ 6.00000 0.416025
$$209$$ −9.00000 −0.622543
$$210$$ 0 0
$$211$$ 9.00000 0.619586 0.309793 0.950804i $$-0.399740\pi$$
0.309793 + 0.950804i $$0.399740\pi$$
$$212$$ −2.00000 −0.137361
$$213$$ 2.00000 0.137038
$$214$$ 1.00000 0.0683586
$$215$$ 0 0
$$216$$ −5.00000 −0.340207
$$217$$ 0 0
$$218$$ −18.0000 −1.21911
$$219$$ 9.00000 0.608164
$$220$$ 0 0
$$221$$ 18.0000 1.21081
$$222$$ −1.00000 −0.0671156
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ −4.00000 −0.267261
$$225$$ 0 0
$$226$$ −5.00000 −0.332595
$$227$$ 28.0000 1.85843 0.929213 0.369546i $$-0.120487\pi$$
0.929213 + 0.369546i $$0.120487\pi$$
$$228$$ 3.00000 0.198680
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ −12.0000 −0.789542
$$232$$ 0 0
$$233$$ −26.0000 −1.70332 −0.851658 0.524097i $$-0.824403\pi$$
−0.851658 + 0.524097i $$0.824403\pi$$
$$234$$ 12.0000 0.784465
$$235$$ 0 0
$$236$$ −12.0000 −0.781133
$$237$$ 2.00000 0.129914
$$238$$ −12.0000 −0.777844
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ −21.0000 −1.35273 −0.676364 0.736567i $$-0.736446\pi$$
−0.676364 + 0.736567i $$0.736446\pi$$
$$242$$ 2.00000 0.128565
$$243$$ −16.0000 −1.02640
$$244$$ 12.0000 0.768221
$$245$$ 0 0
$$246$$ −3.00000 −0.191273
$$247$$ −18.0000 −1.14531
$$248$$ 0 0
$$249$$ 7.00000 0.443607
$$250$$ 0 0
$$251$$ −9.00000 −0.568075 −0.284037 0.958813i $$-0.591674\pi$$
−0.284037 + 0.958813i $$0.591674\pi$$
$$252$$ −8.00000 −0.503953
$$253$$ 6.00000 0.377217
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −22.0000 −1.37232 −0.686161 0.727450i $$-0.740706\pi$$
−0.686161 + 0.727450i $$0.740706\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ −4.00000 −0.248548
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −12.0000 −0.741362
$$263$$ 26.0000 1.60323 0.801614 0.597841i $$-0.203975\pi$$
0.801614 + 0.597841i $$0.203975\pi$$
$$264$$ 3.00000 0.184637
$$265$$ 0 0
$$266$$ 12.0000 0.735767
$$267$$ 3.00000 0.183597
$$268$$ 9.00000 0.549762
$$269$$ −28.0000 −1.70719 −0.853595 0.520937i $$-0.825583\pi$$
−0.853595 + 0.520937i $$0.825583\pi$$
$$270$$ 0 0
$$271$$ −28.0000 −1.70088 −0.850439 0.526073i $$-0.823664\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ 3.00000 0.181902
$$273$$ −24.0000 −1.45255
$$274$$ 7.00000 0.422885
$$275$$ 0 0
$$276$$ −2.00000 −0.120386
$$277$$ 28.0000 1.68236 0.841178 0.540758i $$-0.181862\pi$$
0.841178 + 0.540758i $$0.181862\pi$$
$$278$$ −3.00000 −0.179928
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −6.00000 −0.357930 −0.178965 0.983855i $$-0.557275\pi$$
−0.178965 + 0.983855i $$0.557275\pi$$
$$282$$ 4.00000 0.238197
$$283$$ 7.00000 0.416107 0.208053 0.978117i $$-0.433287\pi$$
0.208053 + 0.978117i $$0.433287\pi$$
$$284$$ −2.00000 −0.118678
$$285$$ 0 0
$$286$$ −18.0000 −1.06436
$$287$$ −12.0000 −0.708338
$$288$$ 2.00000 0.117851
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ −2.00000 −0.117242
$$292$$ −9.00000 −0.526685
$$293$$ 12.0000 0.701047 0.350524 0.936554i $$-0.386004\pi$$
0.350524 + 0.936554i $$0.386004\pi$$
$$294$$ 9.00000 0.524891
$$295$$ 0 0
$$296$$ 1.00000 0.0581238
$$297$$ 15.0000 0.870388
$$298$$ 18.0000 1.04271
$$299$$ 12.0000 0.693978
$$300$$ 0 0
$$301$$ −16.0000 −0.922225
$$302$$ −22.0000 −1.26596
$$303$$ 10.0000 0.574485
$$304$$ −3.00000 −0.172062
$$305$$ 0 0
$$306$$ 6.00000 0.342997
$$307$$ −29.0000 −1.65512 −0.827559 0.561379i $$-0.810271\pi$$
−0.827559 + 0.561379i $$0.810271\pi$$
$$308$$ 12.0000 0.683763
$$309$$ −14.0000 −0.796432
$$310$$ 0 0
$$311$$ 28.0000 1.58773 0.793867 0.608091i $$-0.208065\pi$$
0.793867 + 0.608091i $$0.208065\pi$$
$$312$$ 6.00000 0.339683
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ −24.0000 −1.35440
$$315$$ 0 0
$$316$$ −2.00000 −0.112509
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ −2.00000 −0.112154
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 1.00000 0.0558146
$$322$$ −8.00000 −0.445823
$$323$$ −9.00000 −0.500773
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 17.0000 0.941543
$$327$$ −18.0000 −0.995402
$$328$$ 3.00000 0.165647
$$329$$ 16.0000 0.882109
$$330$$ 0 0
$$331$$ −3.00000 −0.164895 −0.0824475 0.996595i $$-0.526274\pi$$
−0.0824475 + 0.996595i $$0.526274\pi$$
$$332$$ −7.00000 −0.384175
$$333$$ 2.00000 0.109599
$$334$$ 18.0000 0.984916
$$335$$ 0 0
$$336$$ −4.00000 −0.218218
$$337$$ −9.00000 −0.490261 −0.245131 0.969490i $$-0.578831\pi$$
−0.245131 + 0.969490i $$0.578831\pi$$
$$338$$ −23.0000 −1.25104
$$339$$ −5.00000 −0.271563
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −6.00000 −0.324443
$$343$$ 8.00000 0.431959
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ −24.0000 −1.29025
$$347$$ −31.0000 −1.66417 −0.832084 0.554650i $$-0.812852\pi$$
−0.832084 + 0.554650i $$0.812852\pi$$
$$348$$ 0 0
$$349$$ −16.0000 −0.856460 −0.428230 0.903670i $$-0.640863\pi$$
−0.428230 + 0.903670i $$0.640863\pi$$
$$350$$ 0 0
$$351$$ 30.0000 1.60128
$$352$$ −3.00000 −0.159901
$$353$$ −14.0000 −0.745145 −0.372572 0.928003i $$-0.621524\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ −12.0000 −0.637793
$$355$$ 0 0
$$356$$ −3.00000 −0.159000
$$357$$ −12.0000 −0.635107
$$358$$ −21.0000 −1.10988
$$359$$ 34.0000 1.79445 0.897226 0.441572i $$-0.145579\pi$$
0.897226 + 0.441572i $$0.145579\pi$$
$$360$$ 0 0
$$361$$ −10.0000 −0.526316
$$362$$ 10.0000 0.525588
$$363$$ 2.00000 0.104973
$$364$$ 24.0000 1.25794
$$365$$ 0 0
$$366$$ 12.0000 0.627250
$$367$$ −2.00000 −0.104399 −0.0521996 0.998637i $$-0.516623\pi$$
−0.0521996 + 0.998637i $$0.516623\pi$$
$$368$$ 2.00000 0.104257
$$369$$ 6.00000 0.312348
$$370$$ 0 0
$$371$$ −8.00000 −0.415339
$$372$$ 0 0
$$373$$ 28.0000 1.44979 0.724893 0.688862i $$-0.241889\pi$$
0.724893 + 0.688862i $$0.241889\pi$$
$$374$$ −9.00000 −0.465379
$$375$$ 0 0
$$376$$ −4.00000 −0.206284
$$377$$ 0 0
$$378$$ −20.0000 −1.02869
$$379$$ 1.00000 0.0513665 0.0256833 0.999670i $$-0.491824\pi$$
0.0256833 + 0.999670i $$0.491824\pi$$
$$380$$ 0 0
$$381$$ −8.00000 −0.409852
$$382$$ −6.00000 −0.306987
$$383$$ 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
$$386$$ −11.0000 −0.559885
$$387$$ 8.00000 0.406663
$$388$$ 2.00000 0.101535
$$389$$ −12.0000 −0.608424 −0.304212 0.952604i $$-0.598393\pi$$
−0.304212 + 0.952604i $$0.598393\pi$$
$$390$$ 0 0
$$391$$ 6.00000 0.303433
$$392$$ −9.00000 −0.454569
$$393$$ −12.0000 −0.605320
$$394$$ −12.0000 −0.604551
$$395$$ 0 0
$$396$$ −6.00000 −0.301511
$$397$$ −30.0000 −1.50566 −0.752828 0.658217i $$-0.771311\pi$$
−0.752828 + 0.658217i $$0.771311\pi$$
$$398$$ −8.00000 −0.401004
$$399$$ 12.0000 0.600751
$$400$$ 0 0
$$401$$ −5.00000 −0.249688 −0.124844 0.992176i $$-0.539843\pi$$
−0.124844 + 0.992176i $$0.539843\pi$$
$$402$$ 9.00000 0.448879
$$403$$ 0 0
$$404$$ −10.0000 −0.497519
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −3.00000 −0.148704
$$408$$ 3.00000 0.148522
$$409$$ 15.0000 0.741702 0.370851 0.928692i $$-0.379066\pi$$
0.370851 + 0.928692i $$0.379066\pi$$
$$410$$ 0 0
$$411$$ 7.00000 0.345285
$$412$$ 14.0000 0.689730
$$413$$ −48.0000 −2.36193
$$414$$ 4.00000 0.196589
$$415$$ 0 0
$$416$$ −6.00000 −0.294174
$$417$$ −3.00000 −0.146911
$$418$$ 9.00000 0.440204
$$419$$ 27.0000 1.31904 0.659518 0.751689i $$-0.270760\pi$$
0.659518 + 0.751689i $$0.270760\pi$$
$$420$$ 0 0
$$421$$ −32.0000 −1.55958 −0.779792 0.626038i $$-0.784675\pi$$
−0.779792 + 0.626038i $$0.784675\pi$$
$$422$$ −9.00000 −0.438113
$$423$$ −8.00000 −0.388973
$$424$$ 2.00000 0.0971286
$$425$$ 0 0
$$426$$ −2.00000 −0.0969003
$$427$$ 48.0000 2.32288
$$428$$ −1.00000 −0.0483368
$$429$$ −18.0000 −0.869048
$$430$$ 0 0
$$431$$ 2.00000 0.0963366 0.0481683 0.998839i $$-0.484662\pi$$
0.0481683 + 0.998839i $$0.484662\pi$$
$$432$$ 5.00000 0.240563
$$433$$ 5.00000 0.240285 0.120142 0.992757i $$-0.461665\pi$$
0.120142 + 0.992757i $$0.461665\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 18.0000 0.862044
$$437$$ −6.00000 −0.287019
$$438$$ −9.00000 −0.430037
$$439$$ 16.0000 0.763638 0.381819 0.924237i $$-0.375298\pi$$
0.381819 + 0.924237i $$0.375298\pi$$
$$440$$ 0 0
$$441$$ −18.0000 −0.857143
$$442$$ −18.0000 −0.856173
$$443$$ 5.00000 0.237557 0.118779 0.992921i $$-0.462102\pi$$
0.118779 + 0.992921i $$0.462102\pi$$
$$444$$ 1.00000 0.0474579
$$445$$ 0 0
$$446$$ −8.00000 −0.378811
$$447$$ 18.0000 0.851371
$$448$$ 4.00000 0.188982
$$449$$ −37.0000 −1.74614 −0.873069 0.487597i $$-0.837874\pi$$
−0.873069 + 0.487597i $$0.837874\pi$$
$$450$$ 0 0
$$451$$ −9.00000 −0.423793
$$452$$ 5.00000 0.235180
$$453$$ −22.0000 −1.03365
$$454$$ −28.0000 −1.31411
$$455$$ 0 0
$$456$$ −3.00000 −0.140488
$$457$$ −33.0000 −1.54367 −0.771837 0.635820i $$-0.780662\pi$$
−0.771837 + 0.635820i $$0.780662\pi$$
$$458$$ 0 0
$$459$$ 15.0000 0.700140
$$460$$ 0 0
$$461$$ 20.0000 0.931493 0.465746 0.884918i $$-0.345786\pi$$
0.465746 + 0.884918i $$0.345786\pi$$
$$462$$ 12.0000 0.558291
$$463$$ 6.00000 0.278844 0.139422 0.990233i $$-0.455476\pi$$
0.139422 + 0.990233i $$0.455476\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 26.0000 1.20443
$$467$$ −28.0000 −1.29569 −0.647843 0.761774i $$-0.724329\pi$$
−0.647843 + 0.761774i $$0.724329\pi$$
$$468$$ −12.0000 −0.554700
$$469$$ 36.0000 1.66233
$$470$$ 0 0
$$471$$ −24.0000 −1.10586
$$472$$ 12.0000 0.552345
$$473$$ −12.0000 −0.551761
$$474$$ −2.00000 −0.0918630
$$475$$ 0 0
$$476$$ 12.0000 0.550019
$$477$$ 4.00000 0.183147
$$478$$ 12.0000 0.548867
$$479$$ 16.0000 0.731059 0.365529 0.930800i $$-0.380888\pi$$
0.365529 + 0.930800i $$0.380888\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 21.0000 0.956524
$$483$$ −8.00000 −0.364013
$$484$$ −2.00000 −0.0909091
$$485$$ 0 0
$$486$$ 16.0000 0.725775
$$487$$ 28.0000 1.26880 0.634401 0.773004i $$-0.281247\pi$$
0.634401 + 0.773004i $$0.281247\pi$$
$$488$$ −12.0000 −0.543214
$$489$$ 17.0000 0.768767
$$490$$ 0 0
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ 3.00000 0.135250
$$493$$ 0 0
$$494$$ 18.0000 0.809858
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −8.00000 −0.358849
$$498$$ −7.00000 −0.313678
$$499$$ −16.0000 −0.716258 −0.358129 0.933672i $$-0.616585\pi$$
−0.358129 + 0.933672i $$0.616585\pi$$
$$500$$ 0 0
$$501$$ 18.0000 0.804181
$$502$$ 9.00000 0.401690
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 8.00000 0.356348
$$505$$ 0 0
$$506$$ −6.00000 −0.266733
$$507$$ −23.0000 −1.02147
$$508$$ 8.00000 0.354943
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ −36.0000 −1.59255
$$512$$ −1.00000 −0.0441942
$$513$$ −15.0000 −0.662266
$$514$$ 22.0000 0.970378
$$515$$ 0 0
$$516$$ 4.00000 0.176090
$$517$$ 12.0000 0.527759
$$518$$ 4.00000 0.175750
$$519$$ −24.0000 −1.05348
$$520$$ 0 0
$$521$$ −11.0000 −0.481919 −0.240959 0.970535i $$-0.577462\pi$$
−0.240959 + 0.970535i $$0.577462\pi$$
$$522$$ 0 0
$$523$$ 37.0000 1.61790 0.808949 0.587879i $$-0.200037\pi$$
0.808949 + 0.587879i $$0.200037\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ −26.0000 −1.13365
$$527$$ 0 0
$$528$$ −3.00000 −0.130558
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 24.0000 1.04151
$$532$$ −12.0000 −0.520266
$$533$$ −18.0000 −0.779667
$$534$$ −3.00000 −0.129823
$$535$$ 0 0
$$536$$ −9.00000 −0.388741
$$537$$ −21.0000 −0.906217
$$538$$ 28.0000 1.20717
$$539$$ 27.0000 1.16297
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 28.0000 1.20270
$$543$$ 10.0000 0.429141
$$544$$ −3.00000 −0.128624
$$545$$ 0 0
$$546$$ 24.0000 1.02711
$$547$$ 5.00000 0.213785 0.106892 0.994271i $$-0.465910\pi$$
0.106892 + 0.994271i $$0.465910\pi$$
$$548$$ −7.00000 −0.299025
$$549$$ −24.0000 −1.02430
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 2.00000 0.0851257
$$553$$ −8.00000 −0.340195
$$554$$ −28.0000 −1.18961
$$555$$ 0 0
$$556$$ 3.00000 0.127228
$$557$$ 32.0000 1.35588 0.677942 0.735116i $$-0.262872\pi$$
0.677942 + 0.735116i $$0.262872\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 0 0
$$561$$ −9.00000 −0.379980
$$562$$ 6.00000 0.253095
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ −4.00000 −0.168430
$$565$$ 0 0
$$566$$ −7.00000 −0.294232
$$567$$ 4.00000 0.167984
$$568$$ 2.00000 0.0839181
$$569$$ 19.0000 0.796521 0.398261 0.917272i $$-0.369614\pi$$
0.398261 + 0.917272i $$0.369614\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ 18.0000 0.752618
$$573$$ −6.00000 −0.250654
$$574$$ 12.0000 0.500870
$$575$$ 0 0
$$576$$ −2.00000 −0.0833333
$$577$$ −15.0000 −0.624458 −0.312229 0.950007i $$-0.601076\pi$$
−0.312229 + 0.950007i $$0.601076\pi$$
$$578$$ 8.00000 0.332756
$$579$$ −11.0000 −0.457144
$$580$$ 0 0
$$581$$ −28.0000 −1.16164
$$582$$ 2.00000 0.0829027
$$583$$ −6.00000 −0.248495
$$584$$ 9.00000 0.372423
$$585$$ 0 0
$$586$$ −12.0000 −0.495715
$$587$$ −13.0000 −0.536567 −0.268284 0.963340i $$-0.586456\pi$$
−0.268284 + 0.963340i $$0.586456\pi$$
$$588$$ −9.00000 −0.371154
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −12.0000 −0.493614
$$592$$ −1.00000 −0.0410997
$$593$$ −9.00000 −0.369586 −0.184793 0.982777i $$-0.559161\pi$$
−0.184793 + 0.982777i $$0.559161\pi$$
$$594$$ −15.0000 −0.615457
$$595$$ 0 0
$$596$$ −18.0000 −0.737309
$$597$$ −8.00000 −0.327418
$$598$$ −12.0000 −0.490716
$$599$$ −36.0000 −1.47092 −0.735460 0.677568i $$-0.763034\pi$$
−0.735460 + 0.677568i $$0.763034\pi$$
$$600$$ 0 0
$$601$$ −33.0000 −1.34610 −0.673049 0.739598i $$-0.735016\pi$$
−0.673049 + 0.739598i $$0.735016\pi$$
$$602$$ 16.0000 0.652111
$$603$$ −18.0000 −0.733017
$$604$$ 22.0000 0.895167
$$605$$ 0 0
$$606$$ −10.0000 −0.406222
$$607$$ −26.0000 −1.05531 −0.527654 0.849460i $$-0.676928\pi$$
−0.527654 + 0.849460i $$0.676928\pi$$
$$608$$ 3.00000 0.121666
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 24.0000 0.970936
$$612$$ −6.00000 −0.242536
$$613$$ −46.0000 −1.85792 −0.928961 0.370177i $$-0.879297\pi$$
−0.928961 + 0.370177i $$0.879297\pi$$
$$614$$ 29.0000 1.17034
$$615$$ 0 0
$$616$$ −12.0000 −0.483494
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ 14.0000 0.563163
$$619$$ −16.0000 −0.643094 −0.321547 0.946894i $$-0.604203\pi$$
−0.321547 + 0.946894i $$0.604203\pi$$
$$620$$ 0 0
$$621$$ 10.0000 0.401286
$$622$$ −28.0000 −1.12270
$$623$$ −12.0000 −0.480770
$$624$$ −6.00000 −0.240192
$$625$$ 0 0
$$626$$ 10.0000 0.399680
$$627$$ 9.00000 0.359425
$$628$$ 24.0000 0.957704
$$629$$ −3.00000 −0.119618
$$630$$ 0 0
$$631$$ 22.0000 0.875806 0.437903 0.899022i $$-0.355721\pi$$
0.437903 + 0.899022i $$0.355721\pi$$
$$632$$ 2.00000 0.0795557
$$633$$ −9.00000 −0.357718
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ 2.00000 0.0793052
$$637$$ 54.0000 2.13956
$$638$$ 0 0
$$639$$ 4.00000 0.158238
$$640$$ 0 0
$$641$$ −6.00000 −0.236986 −0.118493 0.992955i $$-0.537806\pi$$
−0.118493 + 0.992955i $$0.537806\pi$$
$$642$$ −1.00000 −0.0394669
$$643$$ 20.0000 0.788723 0.394362 0.918955i $$-0.370966\pi$$
0.394362 + 0.918955i $$0.370966\pi$$
$$644$$ 8.00000 0.315244
$$645$$ 0 0
$$646$$ 9.00000 0.354100
$$647$$ 42.0000 1.65119 0.825595 0.564263i $$-0.190840\pi$$
0.825595 + 0.564263i $$0.190840\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ −36.0000 −1.41312
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −17.0000 −0.665771
$$653$$ 36.0000 1.40879 0.704394 0.709809i $$-0.251219\pi$$
0.704394 + 0.709809i $$0.251219\pi$$
$$654$$ 18.0000 0.703856
$$655$$ 0 0
$$656$$ −3.00000 −0.117130
$$657$$ 18.0000 0.702247
$$658$$ −16.0000 −0.623745
$$659$$ 9.00000 0.350590 0.175295 0.984516i $$-0.443912\pi$$
0.175295 + 0.984516i $$0.443912\pi$$
$$660$$ 0 0
$$661$$ −16.0000 −0.622328 −0.311164 0.950356i $$-0.600719\pi$$
−0.311164 + 0.950356i $$0.600719\pi$$
$$662$$ 3.00000 0.116598
$$663$$ −18.0000 −0.699062
$$664$$ 7.00000 0.271653
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ 0 0
$$668$$ −18.0000 −0.696441
$$669$$ −8.00000 −0.309298
$$670$$ 0 0
$$671$$ 36.0000 1.38976
$$672$$ 4.00000 0.154303
$$673$$ −34.0000 −1.31060 −0.655302 0.755367i $$-0.727459\pi$$
−0.655302 + 0.755367i $$0.727459\pi$$
$$674$$ 9.00000 0.346667
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ −8.00000 −0.307465 −0.153732 0.988113i $$-0.549129\pi$$
−0.153732 + 0.988113i $$0.549129\pi$$
$$678$$ 5.00000 0.192024
$$679$$ 8.00000 0.307012
$$680$$ 0 0
$$681$$ −28.0000 −1.07296
$$682$$ 0 0
$$683$$ 17.0000 0.650487 0.325243 0.945630i $$-0.394554\pi$$
0.325243 + 0.945630i $$0.394554\pi$$
$$684$$ 6.00000 0.229416
$$685$$ 0 0
$$686$$ −8.00000 −0.305441
$$687$$ 0 0
$$688$$ −4.00000 −0.152499
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ −1.00000 −0.0380418 −0.0190209 0.999819i $$-0.506055\pi$$
−0.0190209 + 0.999819i $$0.506055\pi$$
$$692$$ 24.0000 0.912343
$$693$$ −24.0000 −0.911685
$$694$$ 31.0000 1.17674
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −9.00000 −0.340899
$$698$$ 16.0000 0.605609
$$699$$ 26.0000 0.983410
$$700$$ 0 0
$$701$$ −10.0000 −0.377695 −0.188847 0.982006i $$-0.560475\pi$$
−0.188847 + 0.982006i $$0.560475\pi$$
$$702$$ −30.0000 −1.13228
$$703$$ 3.00000 0.113147
$$704$$ 3.00000 0.113067
$$705$$ 0 0
$$706$$ 14.0000 0.526897
$$707$$ −40.0000 −1.50435
$$708$$ 12.0000 0.450988
$$709$$ 32.0000 1.20179 0.600893 0.799330i $$-0.294812\pi$$
0.600893 + 0.799330i $$0.294812\pi$$
$$710$$ 0 0
$$711$$ 4.00000 0.150012
$$712$$ 3.00000 0.112430
$$713$$ 0 0
$$714$$ 12.0000 0.449089
$$715$$ 0 0
$$716$$ 21.0000 0.784807
$$717$$ 12.0000 0.448148
$$718$$ −34.0000 −1.26887
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ 0 0
$$721$$ 56.0000 2.08555
$$722$$ 10.0000 0.372161
$$723$$ 21.0000 0.780998
$$724$$ −10.0000 −0.371647
$$725$$ 0 0
$$726$$ −2.00000 −0.0742270
$$727$$ −44.0000 −1.63187 −0.815935 0.578144i $$-0.803777\pi$$
−0.815935 + 0.578144i $$0.803777\pi$$
$$728$$ −24.0000 −0.889499
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −12.0000 −0.443836
$$732$$ −12.0000 −0.443533
$$733$$ 40.0000 1.47743 0.738717 0.674016i $$-0.235432\pi$$
0.738717 + 0.674016i $$0.235432\pi$$
$$734$$ 2.00000 0.0738213
$$735$$ 0 0
$$736$$ −2.00000 −0.0737210
$$737$$ 27.0000 0.994558
$$738$$ −6.00000 −0.220863
$$739$$ −12.0000 −0.441427 −0.220714 0.975339i $$-0.570839\pi$$
−0.220714 + 0.975339i $$0.570839\pi$$
$$740$$ 0 0
$$741$$ 18.0000 0.661247
$$742$$ 8.00000 0.293689
$$743$$ 6.00000 0.220119 0.110059 0.993925i $$-0.464896\pi$$
0.110059 + 0.993925i $$0.464896\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −28.0000 −1.02515
$$747$$ 14.0000 0.512233
$$748$$ 9.00000 0.329073
$$749$$ −4.00000 −0.146157
$$750$$ 0 0
$$751$$ 20.0000 0.729810 0.364905 0.931045i $$-0.381101\pi$$
0.364905 + 0.931045i $$0.381101\pi$$
$$752$$ 4.00000 0.145865
$$753$$ 9.00000 0.327978
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 20.0000 0.727393
$$757$$ 16.0000 0.581530 0.290765 0.956795i $$-0.406090\pi$$
0.290765 + 0.956795i $$0.406090\pi$$
$$758$$ −1.00000 −0.0363216
$$759$$ −6.00000 −0.217786
$$760$$ 0 0
$$761$$ 45.0000 1.63125 0.815624 0.578582i $$-0.196394\pi$$
0.815624 + 0.578582i $$0.196394\pi$$
$$762$$ 8.00000 0.289809
$$763$$ 72.0000 2.60658
$$764$$ 6.00000 0.217072
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ −72.0000 −2.59977
$$768$$ −1.00000 −0.0360844
$$769$$ 23.0000 0.829401 0.414701 0.909958i $$-0.363886\pi$$
0.414701 + 0.909958i $$0.363886\pi$$
$$770$$ 0 0
$$771$$ 22.0000 0.792311
$$772$$ 11.0000 0.395899
$$773$$ 46.0000 1.65451 0.827253 0.561830i $$-0.189903\pi$$
0.827253 + 0.561830i $$0.189903\pi$$
$$774$$ −8.00000 −0.287554
$$775$$ 0 0
$$776$$ −2.00000 −0.0717958
$$777$$ 4.00000 0.143499
$$778$$ 12.0000 0.430221
$$779$$ 9.00000 0.322458
$$780$$ 0 0
$$781$$ −6.00000 −0.214697
$$782$$ −6.00000 −0.214560
$$783$$ 0 0
$$784$$ 9.00000 0.321429
$$785$$ 0 0
$$786$$ 12.0000 0.428026
$$787$$ 32.0000 1.14068 0.570338 0.821410i $$-0.306812\pi$$
0.570338 + 0.821410i $$0.306812\pi$$
$$788$$ 12.0000 0.427482
$$789$$ −26.0000 −0.925625
$$790$$ 0 0
$$791$$ 20.0000 0.711118
$$792$$ 6.00000 0.213201
$$793$$ 72.0000 2.55679
$$794$$ 30.0000 1.06466
$$795$$ 0 0
$$796$$ 8.00000 0.283552
$$797$$ 16.0000 0.566749 0.283375 0.959009i $$-0.408546\pi$$
0.283375 + 0.959009i $$0.408546\pi$$
$$798$$ −12.0000 −0.424795
$$799$$ 12.0000 0.424529
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ 5.00000 0.176556
$$803$$ −27.0000 −0.952809
$$804$$ −9.00000 −0.317406
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 28.0000 0.985647
$$808$$ 10.0000 0.351799
$$809$$ −38.0000 −1.33601 −0.668004 0.744157i $$-0.732851\pi$$
−0.668004 + 0.744157i $$0.732851\pi$$
$$810$$ 0 0
$$811$$ 20.0000 0.702295 0.351147 0.936320i $$-0.385792\pi$$
0.351147 + 0.936320i $$0.385792\pi$$
$$812$$ 0 0
$$813$$ 28.0000 0.982003
$$814$$ 3.00000 0.105150
$$815$$ 0 0
$$816$$ −3.00000 −0.105021
$$817$$ 12.0000 0.419827
$$818$$ −15.0000 −0.524463
$$819$$ −48.0000 −1.67726
$$820$$ 0 0
$$821$$ −4.00000 −0.139601 −0.0698005 0.997561i $$-0.522236\pi$$
−0.0698005 + 0.997561i $$0.522236\pi$$
$$822$$ −7.00000 −0.244153
$$823$$ 42.0000 1.46403 0.732014 0.681290i $$-0.238581\pi$$
0.732014 + 0.681290i $$0.238581\pi$$
$$824$$ −14.0000 −0.487713
$$825$$ 0 0
$$826$$ 48.0000 1.67013
$$827$$ 7.00000 0.243414 0.121707 0.992566i $$-0.461163\pi$$
0.121707 + 0.992566i $$0.461163\pi$$
$$828$$ −4.00000 −0.139010
$$829$$ 6.00000 0.208389 0.104194 0.994557i $$-0.466774\pi$$
0.104194 + 0.994557i $$0.466774\pi$$
$$830$$ 0 0
$$831$$ −28.0000 −0.971309
$$832$$ 6.00000 0.208013
$$833$$ 27.0000 0.935495
$$834$$ 3.00000 0.103882
$$835$$ 0 0
$$836$$ −9.00000 −0.311272
$$837$$ 0 0
$$838$$ −27.0000 −0.932700
$$839$$ −42.0000 −1.45000 −0.725001 0.688748i $$-0.758161\pi$$
−0.725001 + 0.688748i $$0.758161\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ 32.0000 1.10279
$$843$$ 6.00000 0.206651
$$844$$ 9.00000 0.309793
$$845$$ 0 0
$$846$$ 8.00000 0.275046
$$847$$ −8.00000 −0.274883
$$848$$ −2.00000 −0.0686803
$$849$$ −7.00000 −0.240239
$$850$$ 0 0
$$851$$ −2.00000 −0.0685591
$$852$$ 2.00000 0.0685189
$$853$$ 40.0000 1.36957 0.684787 0.728743i $$-0.259895\pi$$
0.684787 + 0.728743i $$0.259895\pi$$
$$854$$ −48.0000 −1.64253
$$855$$ 0 0
$$856$$ 1.00000 0.0341793
$$857$$ 3.00000 0.102478 0.0512390 0.998686i $$-0.483683\pi$$
0.0512390 + 0.998686i $$0.483683\pi$$
$$858$$ 18.0000 0.614510
$$859$$ 9.00000 0.307076 0.153538 0.988143i $$-0.450933\pi$$
0.153538 + 0.988143i $$0.450933\pi$$
$$860$$ 0 0
$$861$$ 12.0000 0.408959
$$862$$ −2.00000 −0.0681203
$$863$$ 6.00000 0.204242 0.102121 0.994772i $$-0.467437\pi$$
0.102121 + 0.994772i $$0.467437\pi$$
$$864$$ −5.00000 −0.170103
$$865$$ 0 0
$$866$$ −5.00000 −0.169907
$$867$$ 8.00000 0.271694
$$868$$ 0 0
$$869$$ −6.00000 −0.203536
$$870$$ 0 0
$$871$$ 54.0000 1.82972
$$872$$ −18.0000 −0.609557
$$873$$ −4.00000 −0.135379
$$874$$ 6.00000 0.202953
$$875$$ 0 0
$$876$$ 9.00000 0.304082
$$877$$ 26.0000 0.877958 0.438979 0.898497i $$-0.355340\pi$$
0.438979 + 0.898497i $$0.355340\pi$$
$$878$$ −16.0000 −0.539974
$$879$$ −12.0000 −0.404750
$$880$$ 0 0
$$881$$ 6.00000 0.202145 0.101073 0.994879i $$-0.467773\pi$$
0.101073 + 0.994879i $$0.467773\pi$$
$$882$$ 18.0000 0.606092
$$883$$ −7.00000 −0.235569 −0.117784 0.993039i $$-0.537579\pi$$
−0.117784 + 0.993039i $$0.537579\pi$$
$$884$$ 18.0000 0.605406
$$885$$ 0 0
$$886$$ −5.00000 −0.167978
$$887$$ −36.0000 −1.20876 −0.604381 0.796696i $$-0.706579\pi$$
−0.604381 + 0.796696i $$0.706579\pi$$
$$888$$ −1.00000 −0.0335578
$$889$$ 32.0000 1.07325
$$890$$ 0 0
$$891$$ 3.00000 0.100504
$$892$$ 8.00000 0.267860
$$893$$ −12.0000 −0.401565
$$894$$ −18.0000 −0.602010
$$895$$ 0 0
$$896$$ −4.00000 −0.133631
$$897$$ −12.0000 −0.400668
$$898$$ 37.0000 1.23471
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −6.00000 −0.199889
$$902$$ 9.00000 0.299667
$$903$$ 16.0000 0.532447
$$904$$ −5.00000 −0.166298
$$905$$ 0 0
$$906$$ 22.0000 0.730901
$$907$$ 36.0000 1.19536 0.597680 0.801735i $$-0.296089\pi$$
0.597680 + 0.801735i $$0.296089\pi$$
$$908$$ 28.0000 0.929213
$$909$$ 20.0000 0.663358
$$910$$ 0 0
$$911$$ 18.0000 0.596367 0.298183 0.954509i $$-0.403619\pi$$
0.298183 + 0.954509i $$0.403619\pi$$
$$912$$ 3.00000 0.0993399
$$913$$ −21.0000 −0.694999
$$914$$ 33.0000 1.09154
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 48.0000 1.58510
$$918$$ −15.0000 −0.495074
$$919$$ −34.0000 −1.12156 −0.560778 0.827966i $$-0.689498\pi$$
−0.560778 + 0.827966i $$0.689498\pi$$
$$920$$ 0 0
$$921$$ 29.0000 0.955582
$$922$$ −20.0000 −0.658665
$$923$$ −12.0000 −0.394985
$$924$$ −12.0000 −0.394771
$$925$$ 0 0
$$926$$ −6.00000 −0.197172
$$927$$ −28.0000 −0.919641
$$928$$ 0 0
$$929$$ −54.0000 −1.77168 −0.885841 0.463988i $$-0.846418\pi$$
−0.885841 + 0.463988i $$0.846418\pi$$
$$930$$ 0 0
$$931$$ −27.0000 −0.884889
$$932$$ −26.0000 −0.851658
$$933$$ −28.0000 −0.916679
$$934$$ 28.0000 0.916188
$$935$$ 0 0
$$936$$ 12.0000 0.392232
$$937$$ 7.00000 0.228680 0.114340 0.993442i $$-0.463525\pi$$
0.114340 + 0.993442i $$0.463525\pi$$
$$938$$ −36.0000 −1.17544
$$939$$ 10.0000 0.326338
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 24.0000 0.781962
$$943$$ −6.00000 −0.195387
$$944$$ −12.0000 −0.390567
$$945$$ 0 0
$$946$$ 12.0000 0.390154
$$947$$ −24.0000 −0.779895 −0.389948 0.920837i $$-0.627507\pi$$
−0.389948 + 0.920837i $$0.627507\pi$$
$$948$$ 2.00000 0.0649570
$$949$$ −54.0000 −1.75291
$$950$$ 0 0
$$951$$ 18.0000 0.583690
$$952$$ −12.0000 −0.388922
$$953$$ 33.0000 1.06897 0.534487 0.845176i $$-0.320505\pi$$
0.534487 + 0.845176i $$0.320505\pi$$
$$954$$ −4.00000 −0.129505
$$955$$ 0 0
$$956$$ −12.0000 −0.388108
$$957$$ 0 0
$$958$$ −16.0000 −0.516937
$$959$$ −28.0000 −0.904167
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 6.00000 0.193448
$$963$$ 2.00000 0.0644491
$$964$$ −21.0000 −0.676364
$$965$$ 0 0
$$966$$ 8.00000 0.257396
$$967$$ −48.0000 −1.54358 −0.771788 0.635880i $$-0.780637\pi$$
−0.771788 + 0.635880i $$0.780637\pi$$
$$968$$ 2.00000 0.0642824
$$969$$ 9.00000 0.289122
$$970$$ 0 0
$$971$$ 3.00000 0.0962746 0.0481373 0.998841i $$-0.484672\pi$$
0.0481373 + 0.998841i $$0.484672\pi$$
$$972$$ −16.0000 −0.513200
$$973$$ 12.0000 0.384702
$$974$$ −28.0000 −0.897178
$$975$$ 0 0
$$976$$ 12.0000 0.384111
$$977$$ 23.0000 0.735835 0.367918 0.929858i $$-0.380071\pi$$
0.367918 + 0.929858i $$0.380071\pi$$
$$978$$ −17.0000 −0.543600
$$979$$ −9.00000 −0.287641
$$980$$ 0 0
$$981$$ −36.0000 −1.14939
$$982$$ 20.0000 0.638226
$$983$$ 18.0000 0.574111 0.287055 0.957914i $$-0.407324\pi$$
0.287055 + 0.957914i $$0.407324\pi$$
$$984$$ −3.00000 −0.0956365
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −16.0000 −0.509286
$$988$$ −18.0000 −0.572656
$$989$$ −8.00000 −0.254385
$$990$$ 0 0
$$991$$ −12.0000 −0.381193 −0.190596 0.981669i $$-0.561042\pi$$
−0.190596 + 0.981669i $$0.561042\pi$$
$$992$$ 0 0
$$993$$ 3.00000 0.0952021
$$994$$ 8.00000 0.253745
$$995$$ 0 0
$$996$$ 7.00000 0.221803
$$997$$ −18.0000 −0.570066 −0.285033 0.958518i $$-0.592005\pi$$
−0.285033 + 0.958518i $$0.592005\pi$$
$$998$$ 16.0000 0.506471
$$999$$ −5.00000 −0.158193
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 1850.2.a.c.1.1 1
5.2 odd 4 1850.2.b.e.149.1 2
5.3 odd 4 1850.2.b.e.149.2 2
5.4 even 2 1850.2.a.m.1.1 yes 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1850.2.a.c.1.1 1 1.1 even 1 trivial
1850.2.a.m.1.1 yes 1 5.4 even 2
1850.2.b.e.149.1 2 5.2 odd 4
1850.2.b.e.149.2 2 5.3 odd 4