# Properties

 Label 950.2.a.j.1.3 Level $950$ Weight $2$ Character 950.1 Self dual yes Analytic conductor $7.586$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Learn more

## 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: $$3$$ Coefficient field: 3.3.993.1 Defining polynomial: $$x^{3} - x^{2} - 6 x + 3$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$2.77339$$ of defining polynomial Character $$\chi$$ $$=$$ 950.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.77339 q^{3} +1.00000 q^{4} -1.77339 q^{6} +2.69168 q^{7} -1.00000 q^{8} +0.144903 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.77339 q^{3} +1.00000 q^{4} -1.77339 q^{6} +2.69168 q^{7} -1.00000 q^{8} +0.144903 q^{9} +5.54677 q^{11} +1.77339 q^{12} +2.91829 q^{13} -2.69168 q^{14} +1.00000 q^{16} -4.91829 q^{17} -0.144903 q^{18} +1.00000 q^{19} +4.77339 q^{21} -5.54677 q^{22} -3.60997 q^{23} -1.77339 q^{24} -2.91829 q^{26} -5.06319 q^{27} +2.69168 q^{28} +1.08171 q^{29} +7.54677 q^{31} -1.00000 q^{32} +9.83658 q^{33} +4.91829 q^{34} +0.144903 q^{36} -4.54677 q^{37} -1.00000 q^{38} +5.17526 q^{39} -4.77339 q^{42} +9.54677 q^{43} +5.54677 q^{44} +3.60997 q^{46} +0.836581 q^{47} +1.77339 q^{48} +0.245129 q^{49} -8.72203 q^{51} +2.91829 q^{52} -9.78523 q^{53} +5.06319 q^{54} -2.69168 q^{56} +1.77339 q^{57} -1.08171 q^{58} +12.9933 q^{59} -7.38336 q^{61} -7.54677 q^{62} +0.390032 q^{63} +1.00000 q^{64} -9.83658 q^{66} -2.85510 q^{67} -4.91829 q^{68} -6.40187 q^{69} +14.4769 q^{71} -0.144903 q^{72} -5.15674 q^{73} +4.54677 q^{74} +1.00000 q^{76} +14.9301 q^{77} -5.17526 q^{78} -3.09355 q^{79} -9.41371 q^{81} -1.71019 q^{83} +4.77339 q^{84} -9.54677 q^{86} +1.91829 q^{87} -5.54677 q^{88} -5.09355 q^{89} +7.85510 q^{91} -3.60997 q^{92} +13.3834 q^{93} -0.836581 q^{94} -1.77339 q^{96} +17.2570 q^{97} -0.245129 q^{98} +0.803744 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3q - 3q^{2} - 2q^{3} + 3q^{4} + 2q^{6} - 2q^{7} - 3q^{8} + 5q^{9} + O(q^{10})$$ $$3q - 3q^{2} - 2q^{3} + 3q^{4} + 2q^{6} - 2q^{7} - 3q^{8} + 5q^{9} + 2q^{11} - 2q^{12} + 6q^{13} + 2q^{14} + 3q^{16} - 12q^{17} - 5q^{18} + 3q^{19} + 7q^{21} - 2q^{22} + 2q^{23} + 2q^{24} - 6q^{26} - 17q^{27} - 2q^{28} + 6q^{29} + 8q^{31} - 3q^{32} + 24q^{33} + 12q^{34} + 5q^{36} + q^{37} - 3q^{38} - 11q^{39} - 7q^{42} + 14q^{43} + 2q^{44} - 2q^{46} - 3q^{47} - 2q^{48} + 9q^{49} + 15q^{51} + 6q^{52} + 10q^{53} + 17q^{54} + 2q^{56} - 2q^{57} - 6q^{58} + 6q^{59} - 2q^{61} - 8q^{62} + 14q^{63} + 3q^{64} - 24q^{66} - 4q^{67} - 12q^{68} - 6q^{71} - 5q^{72} + 12q^{73} - q^{74} + 3q^{76} + 10q^{77} + 11q^{78} + 20q^{79} + 23q^{81} + 4q^{83} + 7q^{84} - 14q^{86} + 3q^{87} - 2q^{88} + 14q^{89} + 19q^{91} + 2q^{92} + 20q^{93} + 3q^{94} + 2q^{96} + 28q^{97} - 9q^{98} - 36q^{99} + O(q^{100})$$

## 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
$$3$$ 1.77339 1.02387 0.511933 0.859025i $$-0.328930\pi$$
0.511933 + 0.859025i $$0.328930\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −1.77339 −0.723982
$$7$$ 2.69168 1.01736 0.508679 0.860956i $$-0.330134\pi$$
0.508679 + 0.860956i $$0.330134\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0.144903 0.0483010
$$10$$ 0 0
$$11$$ 5.54677 1.67242 0.836208 0.548413i $$-0.184768\pi$$
0.836208 + 0.548413i $$0.184768\pi$$
$$12$$ 1.77339 0.511933
$$13$$ 2.91829 0.809388 0.404694 0.914452i $$-0.367378\pi$$
0.404694 + 0.914452i $$0.367378\pi$$
$$14$$ −2.69168 −0.719381
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −4.91829 −1.19286 −0.596430 0.802665i $$-0.703415\pi$$
−0.596430 + 0.802665i $$0.703415\pi$$
$$18$$ −0.144903 −0.0341539
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ 4.77339 1.04164
$$22$$ −5.54677 −1.18258
$$23$$ −3.60997 −0.752730 −0.376365 0.926471i $$-0.622826\pi$$
−0.376365 + 0.926471i $$0.622826\pi$$
$$24$$ −1.77339 −0.361991
$$25$$ 0 0
$$26$$ −2.91829 −0.572324
$$27$$ −5.06319 −0.974412
$$28$$ 2.69168 0.508679
$$29$$ 1.08171 0.200868 0.100434 0.994944i $$-0.467977\pi$$
0.100434 + 0.994944i $$0.467977\pi$$
$$30$$ 0 0
$$31$$ 7.54677 1.35544 0.677720 0.735320i $$-0.262968\pi$$
0.677720 + 0.735320i $$0.262968\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 9.83658 1.71233
$$34$$ 4.91829 0.843480
$$35$$ 0 0
$$36$$ 0.144903 0.0241505
$$37$$ −4.54677 −0.747485 −0.373743 0.927532i $$-0.621926\pi$$
−0.373743 + 0.927532i $$0.621926\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ 5.17526 0.828705
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ −4.77339 −0.736550
$$43$$ 9.54677 1.45587 0.727935 0.685646i $$-0.240480\pi$$
0.727935 + 0.685646i $$0.240480\pi$$
$$44$$ 5.54677 0.836208
$$45$$ 0 0
$$46$$ 3.60997 0.532261
$$47$$ 0.836581 0.122028 0.0610139 0.998137i $$-0.480567\pi$$
0.0610139 + 0.998137i $$0.480567\pi$$
$$48$$ 1.77339 0.255966
$$49$$ 0.245129 0.0350184
$$50$$ 0 0
$$51$$ −8.72203 −1.22133
$$52$$ 2.91829 0.404694
$$53$$ −9.78523 −1.34410 −0.672052 0.740504i $$-0.734587\pi$$
−0.672052 + 0.740504i $$0.734587\pi$$
$$54$$ 5.06319 0.689013
$$55$$ 0 0
$$56$$ −2.69168 −0.359691
$$57$$ 1.77339 0.234891
$$58$$ −1.08171 −0.142035
$$59$$ 12.9933 1.69159 0.845793 0.533511i $$-0.179128\pi$$
0.845793 + 0.533511i $$0.179128\pi$$
$$60$$ 0 0
$$61$$ −7.38336 −0.945342 −0.472671 0.881239i $$-0.656710\pi$$
−0.472671 + 0.881239i $$0.656710\pi$$
$$62$$ −7.54677 −0.958441
$$63$$ 0.390032 0.0491394
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −9.83658 −1.21080
$$67$$ −2.85510 −0.348806 −0.174403 0.984674i $$-0.555799\pi$$
−0.174403 + 0.984674i $$0.555799\pi$$
$$68$$ −4.91829 −0.596430
$$69$$ −6.40187 −0.770695
$$70$$ 0 0
$$71$$ 14.4769 1.71809 0.859046 0.511898i $$-0.171057\pi$$
0.859046 + 0.511898i $$0.171057\pi$$
$$72$$ −0.144903 −0.0170770
$$73$$ −5.15674 −0.603551 −0.301776 0.953379i $$-0.597579\pi$$
−0.301776 + 0.953379i $$0.597579\pi$$
$$74$$ 4.54677 0.528552
$$75$$ 0 0
$$76$$ 1.00000 0.114708
$$77$$ 14.9301 1.70145
$$78$$ −5.17526 −0.585983
$$79$$ −3.09355 −0.348052 −0.174026 0.984741i $$-0.555678\pi$$
−0.174026 + 0.984741i $$0.555678\pi$$
$$80$$ 0 0
$$81$$ −9.41371 −1.04597
$$82$$ 0 0
$$83$$ −1.71019 −0.187718 −0.0938591 0.995585i $$-0.529920\pi$$
−0.0938591 + 0.995585i $$0.529920\pi$$
$$84$$ 4.77339 0.520819
$$85$$ 0 0
$$86$$ −9.54677 −1.02946
$$87$$ 1.91829 0.205662
$$88$$ −5.54677 −0.591288
$$89$$ −5.09355 −0.539915 −0.269958 0.962872i $$-0.587010\pi$$
−0.269958 + 0.962872i $$0.587010\pi$$
$$90$$ 0 0
$$91$$ 7.85510 0.823438
$$92$$ −3.60997 −0.376365
$$93$$ 13.3834 1.38779
$$94$$ −0.836581 −0.0862867
$$95$$ 0 0
$$96$$ −1.77339 −0.180996
$$97$$ 17.2570 1.75218 0.876090 0.482148i $$-0.160143\pi$$
0.876090 + 0.482148i $$0.160143\pi$$
$$98$$ −0.245129 −0.0247618
$$99$$ 0.803744 0.0807793
$$100$$ 0 0
$$101$$ −9.38336 −0.933679 −0.466839 0.884342i $$-0.654607\pi$$
−0.466839 + 0.884342i $$0.654607\pi$$
$$102$$ 8.72203 0.863610
$$103$$ 12.9301 1.27404 0.637022 0.770846i $$-0.280166\pi$$
0.637022 + 0.770846i $$0.280166\pi$$
$$104$$ −2.91829 −0.286162
$$105$$ 0 0
$$106$$ 9.78523 0.950425
$$107$$ −18.9420 −1.83119 −0.915595 0.402102i $$-0.868280\pi$$
−0.915595 + 0.402102i $$0.868280\pi$$
$$108$$ −5.06319 −0.487206
$$109$$ −2.69168 −0.257816 −0.128908 0.991657i $$-0.541147\pi$$
−0.128908 + 0.991657i $$0.541147\pi$$
$$110$$ 0 0
$$111$$ −8.06319 −0.765324
$$112$$ 2.69168 0.254340
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ −1.77339 −0.166093
$$115$$ 0 0
$$116$$ 1.08171 0.100434
$$117$$ 0.422869 0.0390942
$$118$$ −12.9933 −1.19613
$$119$$ −13.2385 −1.21357
$$120$$ 0 0
$$121$$ 19.7667 1.79697
$$122$$ 7.38336 0.668458
$$123$$ 0 0
$$124$$ 7.54677 0.677720
$$125$$ 0 0
$$126$$ −0.390032 −0.0347468
$$127$$ 1.87361 0.166256 0.0831282 0.996539i $$-0.473509\pi$$
0.0831282 + 0.996539i $$0.473509\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 16.9301 1.49061
$$130$$ 0 0
$$131$$ −11.5468 −1.00885 −0.504423 0.863457i $$-0.668295\pi$$
−0.504423 + 0.863457i $$0.668295\pi$$
$$132$$ 9.83658 0.856164
$$133$$ 2.69168 0.233398
$$134$$ 2.85510 0.246643
$$135$$ 0 0
$$136$$ 4.91829 0.421740
$$137$$ −4.23845 −0.362115 −0.181058 0.983472i $$-0.557952\pi$$
−0.181058 + 0.983472i $$0.557952\pi$$
$$138$$ 6.40187 0.544964
$$139$$ 9.21994 0.782025 0.391012 0.920385i $$-0.372125\pi$$
0.391012 + 0.920385i $$0.372125\pi$$
$$140$$ 0 0
$$141$$ 1.48358 0.124940
$$142$$ −14.4769 −1.21487
$$143$$ 16.1871 1.35363
$$144$$ 0.144903 0.0120752
$$145$$ 0 0
$$146$$ 5.15674 0.426775
$$147$$ 0.434709 0.0358542
$$148$$ −4.54677 −0.373743
$$149$$ −7.25697 −0.594514 −0.297257 0.954797i $$-0.596072\pi$$
−0.297257 + 0.954797i $$0.596072\pi$$
$$150$$ 0 0
$$151$$ 20.0000 1.62758 0.813788 0.581161i $$-0.197401\pi$$
0.813788 + 0.581161i $$0.197401\pi$$
$$152$$ −1.00000 −0.0811107
$$153$$ −0.712675 −0.0576163
$$154$$ −14.9301 −1.20310
$$155$$ 0 0
$$156$$ 5.17526 0.414352
$$157$$ 9.54677 0.761916 0.380958 0.924592i $$-0.375594\pi$$
0.380958 + 0.924592i $$0.375594\pi$$
$$158$$ 3.09355 0.246110
$$159$$ −17.3530 −1.37618
$$160$$ 0 0
$$161$$ −9.71687 −0.765797
$$162$$ 9.41371 0.739611
$$163$$ −15.7102 −1.23052 −0.615259 0.788325i $$-0.710948\pi$$
−0.615259 + 0.788325i $$0.710948\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 1.71019 0.132737
$$167$$ −6.45323 −0.499366 −0.249683 0.968328i $$-0.580326\pi$$
−0.249683 + 0.968328i $$0.580326\pi$$
$$168$$ −4.77339 −0.368275
$$169$$ −4.48358 −0.344891
$$170$$ 0 0
$$171$$ 0.144903 0.0110810
$$172$$ 9.54677 0.727935
$$173$$ 0.873614 0.0664196 0.0332098 0.999448i $$-0.489427\pi$$
0.0332098 + 0.999448i $$0.489427\pi$$
$$174$$ −1.91829 −0.145425
$$175$$ 0 0
$$176$$ 5.54677 0.418104
$$177$$ 23.0422 1.73196
$$178$$ 5.09355 0.381778
$$179$$ −12.3834 −0.925575 −0.462788 0.886469i $$-0.653151\pi$$
−0.462788 + 0.886469i $$0.653151\pi$$
$$180$$ 0 0
$$181$$ −17.6403 −1.31119 −0.655597 0.755111i $$-0.727583\pi$$
−0.655597 + 0.755111i $$0.727583\pi$$
$$182$$ −7.85510 −0.582259
$$183$$ −13.0935 −0.967903
$$184$$ 3.60997 0.266130
$$185$$ 0 0
$$186$$ −13.3834 −0.981315
$$187$$ −27.2806 −1.99496
$$188$$ 0.836581 0.0610139
$$189$$ −13.6285 −0.991326
$$190$$ 0 0
$$191$$ −15.1567 −1.09670 −0.548352 0.836248i $$-0.684744\pi$$
−0.548352 + 0.836248i $$0.684744\pi$$
$$192$$ 1.77339 0.127983
$$193$$ −23.3834 −1.68317 −0.841585 0.540124i $$-0.818377\pi$$
−0.841585 + 0.540124i $$0.818377\pi$$
$$194$$ −17.2570 −1.23898
$$195$$ 0 0
$$196$$ 0.245129 0.0175092
$$197$$ 23.0935 1.64535 0.822674 0.568514i $$-0.192481\pi$$
0.822674 + 0.568514i $$0.192481\pi$$
$$198$$ −0.803744 −0.0571196
$$199$$ −25.7852 −1.82787 −0.913933 0.405865i $$-0.866970\pi$$
−0.913933 + 0.405865i $$0.866970\pi$$
$$200$$ 0 0
$$201$$ −5.06319 −0.357130
$$202$$ 9.38336 0.660211
$$203$$ 2.91161 0.204355
$$204$$ −8.72203 −0.610665
$$205$$ 0 0
$$206$$ −12.9301 −0.900885
$$207$$ −0.523095 −0.0363576
$$208$$ 2.91829 0.202347
$$209$$ 5.54677 0.383678
$$210$$ 0 0
$$211$$ 14.2266 0.979400 0.489700 0.871891i $$-0.337106\pi$$
0.489700 + 0.871891i $$0.337106\pi$$
$$212$$ −9.78523 −0.672052
$$213$$ 25.6732 1.75910
$$214$$ 18.9420 1.29485
$$215$$ 0 0
$$216$$ 5.06319 0.344507
$$217$$ 20.3135 1.37897
$$218$$ 2.69168 0.182303
$$219$$ −9.14490 −0.617955
$$220$$ 0 0
$$221$$ −14.3530 −0.965487
$$222$$ 8.06319 0.541166
$$223$$ 4.45323 0.298210 0.149105 0.988821i $$-0.452361\pi$$
0.149105 + 0.988821i $$0.452361\pi$$
$$224$$ −2.69168 −0.179845
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −5.94865 −0.394826 −0.197413 0.980320i $$-0.563254\pi$$
−0.197413 + 0.980320i $$0.563254\pi$$
$$228$$ 1.77339 0.117445
$$229$$ 1.09355 0.0722638 0.0361319 0.999347i $$-0.488496\pi$$
0.0361319 + 0.999347i $$0.488496\pi$$
$$230$$ 0 0
$$231$$ 26.4769 1.74205
$$232$$ −1.08171 −0.0710177
$$233$$ −14.0935 −0.923299 −0.461650 0.887062i $$-0.652742\pi$$
−0.461650 + 0.887062i $$0.652742\pi$$
$$234$$ −0.422869 −0.0276438
$$235$$ 0 0
$$236$$ 12.9933 0.845793
$$237$$ −5.48606 −0.356358
$$238$$ 13.2385 0.858121
$$239$$ 15.6100 1.00972 0.504862 0.863200i $$-0.331543\pi$$
0.504862 + 0.863200i $$0.331543\pi$$
$$240$$ 0 0
$$241$$ −5.21994 −0.336246 −0.168123 0.985766i $$-0.553771\pi$$
−0.168123 + 0.985766i $$0.553771\pi$$
$$242$$ −19.7667 −1.27065
$$243$$ −1.50458 −0.0965188
$$244$$ −7.38336 −0.472671
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 2.91829 0.185686
$$248$$ −7.54677 −0.479221
$$249$$ −3.03284 −0.192198
$$250$$ 0 0
$$251$$ −28.6403 −1.80776 −0.903881 0.427785i $$-0.859294\pi$$
−0.903881 + 0.427785i $$0.859294\pi$$
$$252$$ 0.390032 0.0245697
$$253$$ −20.0237 −1.25888
$$254$$ −1.87361 −0.117561
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −6.45323 −0.402541 −0.201271 0.979536i $$-0.564507\pi$$
−0.201271 + 0.979536i $$0.564507\pi$$
$$258$$ −16.9301 −1.05402
$$259$$ −12.2385 −0.760460
$$260$$ 0 0
$$261$$ 0.156743 0.00970214
$$262$$ 11.5468 0.713362
$$263$$ −22.1871 −1.36812 −0.684058 0.729428i $$-0.739786\pi$$
−0.684058 + 0.729428i $$0.739786\pi$$
$$264$$ −9.83658 −0.605400
$$265$$ 0 0
$$266$$ −2.69168 −0.165037
$$267$$ −9.03284 −0.552801
$$268$$ −2.85510 −0.174403
$$269$$ −20.4070 −1.24424 −0.622119 0.782922i $$-0.713728\pi$$
−0.622119 + 0.782922i $$0.713728\pi$$
$$270$$ 0 0
$$271$$ 15.9368 0.968092 0.484046 0.875043i $$-0.339167\pi$$
0.484046 + 0.875043i $$0.339167\pi$$
$$272$$ −4.91829 −0.298215
$$273$$ 13.9301 0.843090
$$274$$ 4.23845 0.256054
$$275$$ 0 0
$$276$$ −6.40187 −0.385347
$$277$$ −4.02368 −0.241759 −0.120880 0.992667i $$-0.538572\pi$$
−0.120880 + 0.992667i $$0.538572\pi$$
$$278$$ −9.21994 −0.552975
$$279$$ 1.09355 0.0654691
$$280$$ 0 0
$$281$$ 1.67316 0.0998124 0.0499062 0.998754i $$-0.484108\pi$$
0.0499062 + 0.998754i $$0.484108\pi$$
$$282$$ −1.48358 −0.0883460
$$283$$ −16.8931 −1.00419 −0.502095 0.864812i $$-0.667437\pi$$
−0.502095 + 0.864812i $$0.667437\pi$$
$$284$$ 14.4769 0.859046
$$285$$ 0 0
$$286$$ −16.1871 −0.957163
$$287$$ 0 0
$$288$$ −0.144903 −0.00853849
$$289$$ 7.18958 0.422916
$$290$$ 0 0
$$291$$ 30.6033 1.79400
$$292$$ −5.15674 −0.301776
$$293$$ 1.08171 0.0631942 0.0315971 0.999501i $$-0.489941\pi$$
0.0315971 + 0.999501i $$0.489941\pi$$
$$294$$ −0.434709 −0.0253527
$$295$$ 0 0
$$296$$ 4.54677 0.264276
$$297$$ −28.0844 −1.62962
$$298$$ 7.25697 0.420385
$$299$$ −10.5349 −0.609251
$$300$$ 0 0
$$301$$ 25.6968 1.48114
$$302$$ −20.0000 −1.15087
$$303$$ −16.6403 −0.955962
$$304$$ 1.00000 0.0573539
$$305$$ 0 0
$$306$$ 0.712675 0.0407409
$$307$$ −2.38336 −0.136025 −0.0680126 0.997684i $$-0.521666\pi$$
−0.0680126 + 0.997684i $$0.521666\pi$$
$$308$$ 14.9301 0.850723
$$309$$ 22.9301 1.30445
$$310$$ 0 0
$$311$$ −29.4584 −1.67043 −0.835216 0.549922i $$-0.814657\pi$$
−0.835216 + 0.549922i $$0.814657\pi$$
$$312$$ −5.17526 −0.292991
$$313$$ −32.0355 −1.81075 −0.905377 0.424608i $$-0.860412\pi$$
−0.905377 + 0.424608i $$0.860412\pi$$
$$314$$ −9.54677 −0.538756
$$315$$ 0 0
$$316$$ −3.09355 −0.174026
$$317$$ 26.6665 1.49774 0.748870 0.662717i $$-0.230597\pi$$
0.748870 + 0.662717i $$0.230597\pi$$
$$318$$ 17.3530 0.973108
$$319$$ 6.00000 0.335936
$$320$$ 0 0
$$321$$ −33.5915 −1.87489
$$322$$ 9.71687 0.541500
$$323$$ −4.91829 −0.273661
$$324$$ −9.41371 −0.522984
$$325$$ 0 0
$$326$$ 15.7102 0.870107
$$327$$ −4.77339 −0.263969
$$328$$ 0 0
$$329$$ 2.25181 0.124146
$$330$$ 0 0
$$331$$ −19.8721 −1.09227 −0.546135 0.837697i $$-0.683901\pi$$
−0.546135 + 0.837697i $$0.683901\pi$$
$$332$$ −1.71019 −0.0938591
$$333$$ −0.658841 −0.0361043
$$334$$ 6.45323 0.353105
$$335$$ 0 0
$$336$$ 4.77339 0.260410
$$337$$ −27.5705 −1.50186 −0.750929 0.660383i $$-0.770394\pi$$
−0.750929 + 0.660383i $$0.770394\pi$$
$$338$$ 4.48358 0.243875
$$339$$ 10.6403 0.577903
$$340$$ 0 0
$$341$$ 41.8603 2.26686
$$342$$ −0.144903 −0.00783545
$$343$$ −18.1819 −0.981732
$$344$$ −9.54677 −0.514728
$$345$$ 0 0
$$346$$ −0.873614 −0.0469658
$$347$$ 27.2806 1.46450 0.732251 0.681035i $$-0.238470\pi$$
0.732251 + 0.681035i $$0.238470\pi$$
$$348$$ 1.91829 0.102831
$$349$$ 30.9538 1.65692 0.828460 0.560049i $$-0.189218\pi$$
0.828460 + 0.560049i $$0.189218\pi$$
$$350$$ 0 0
$$351$$ −14.7759 −0.788677
$$352$$ −5.54677 −0.295644
$$353$$ −11.1819 −0.595154 −0.297577 0.954698i $$-0.596179\pi$$
−0.297577 + 0.954698i $$0.596179\pi$$
$$354$$ −23.0422 −1.22468
$$355$$ 0 0
$$356$$ −5.09355 −0.269958
$$357$$ −23.4769 −1.24253
$$358$$ 12.3834 0.654481
$$359$$ 20.3387 1.07343 0.536717 0.843762i $$-0.319664\pi$$
0.536717 + 0.843762i $$0.319664\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 17.6403 0.927155
$$363$$ 35.0540 1.83986
$$364$$ 7.85510 0.411719
$$365$$ 0 0
$$366$$ 13.0935 0.684411
$$367$$ 32.9538 1.72017 0.860087 0.510147i $$-0.170409\pi$$
0.860087 + 0.510147i $$0.170409\pi$$
$$368$$ −3.60997 −0.188183
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −26.3387 −1.36744
$$372$$ 13.3834 0.693895
$$373$$ 10.0869 0.522278 0.261139 0.965301i $$-0.415902\pi$$
0.261139 + 0.965301i $$0.415902\pi$$
$$374$$ 27.2806 1.41065
$$375$$ 0 0
$$376$$ −0.836581 −0.0431434
$$377$$ 3.15674 0.162581
$$378$$ 13.6285 0.700974
$$379$$ −18.4256 −0.946457 −0.473229 0.880940i $$-0.656912\pi$$
−0.473229 + 0.880940i $$0.656912\pi$$
$$380$$ 0 0
$$381$$ 3.32264 0.170224
$$382$$ 15.1567 0.775486
$$383$$ −28.1871 −1.44029 −0.720147 0.693822i $$-0.755926\pi$$
−0.720147 + 0.693822i $$0.755926\pi$$
$$384$$ −1.77339 −0.0904978
$$385$$ 0 0
$$386$$ 23.3834 1.19018
$$387$$ 1.38336 0.0703199
$$388$$ 17.2570 0.876090
$$389$$ 20.0237 1.01524 0.507620 0.861581i $$-0.330525\pi$$
0.507620 + 0.861581i $$0.330525\pi$$
$$390$$ 0 0
$$391$$ 17.7549 0.897902
$$392$$ −0.245129 −0.0123809
$$393$$ −20.4769 −1.03292
$$394$$ −23.0935 −1.16344
$$395$$ 0 0
$$396$$ 0.803744 0.0403896
$$397$$ 8.32684 0.417912 0.208956 0.977925i $$-0.432993\pi$$
0.208956 + 0.977925i $$0.432993\pi$$
$$398$$ 25.7852 1.29250
$$399$$ 4.77339 0.238968
$$400$$ 0 0
$$401$$ −22.1501 −1.10612 −0.553061 0.833141i $$-0.686540\pi$$
−0.553061 + 0.833141i $$0.686540\pi$$
$$402$$ 5.06319 0.252529
$$403$$ 22.0237 1.09708
$$404$$ −9.38336 −0.466839
$$405$$ 0 0
$$406$$ −2.91161 −0.144501
$$407$$ −25.2199 −1.25011
$$408$$ 8.72203 0.431805
$$409$$ 34.0237 1.68236 0.841181 0.540753i $$-0.181861\pi$$
0.841181 + 0.540753i $$0.181861\pi$$
$$410$$ 0 0
$$411$$ −7.51642 −0.370758
$$412$$ 12.9301 0.637022
$$413$$ 34.9738 1.72095
$$414$$ 0.523095 0.0257087
$$415$$ 0 0
$$416$$ −2.91829 −0.143081
$$417$$ 16.3505 0.800688
$$418$$ −5.54677 −0.271302
$$419$$ 37.5334 1.83363 0.916814 0.399315i $$-0.130752\pi$$
0.916814 + 0.399315i $$0.130752\pi$$
$$420$$ 0 0
$$421$$ 33.8341 1.64897 0.824487 0.565882i $$-0.191464\pi$$
0.824487 + 0.565882i $$0.191464\pi$$
$$422$$ −14.2266 −0.692541
$$423$$ 0.121223 0.00589406
$$424$$ 9.78523 0.475213
$$425$$ 0 0
$$426$$ −25.6732 −1.24387
$$427$$ −19.8736 −0.961752
$$428$$ −18.9420 −0.915595
$$429$$ 28.7060 1.38594
$$430$$ 0 0
$$431$$ 24.8037 1.19475 0.597377 0.801960i $$-0.296210\pi$$
0.597377 + 0.801960i $$0.296210\pi$$
$$432$$ −5.06319 −0.243603
$$433$$ −1.68651 −0.0810487 −0.0405244 0.999179i $$-0.512903\pi$$
−0.0405244 + 0.999179i $$0.512903\pi$$
$$434$$ −20.3135 −0.975079
$$435$$ 0 0
$$436$$ −2.69168 −0.128908
$$437$$ −3.60997 −0.172688
$$438$$ 9.14490 0.436960
$$439$$ 0.326839 0.0155992 0.00779958 0.999970i $$-0.497517\pi$$
0.00779958 + 0.999970i $$0.497517\pi$$
$$440$$ 0 0
$$441$$ 0.0355199 0.00169142
$$442$$ 14.3530 0.682703
$$443$$ −0.490258 −0.0232929 −0.0116464 0.999932i $$-0.503707\pi$$
−0.0116464 + 0.999932i $$0.503707\pi$$
$$444$$ −8.06319 −0.382662
$$445$$ 0 0
$$446$$ −4.45323 −0.210866
$$447$$ −12.8694 −0.608703
$$448$$ 2.69168 0.127170
$$449$$ 23.5468 1.11124 0.555621 0.831436i $$-0.312481\pi$$
0.555621 + 0.831436i $$0.312481\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 6.00000 0.282216
$$453$$ 35.4677 1.66642
$$454$$ 5.94865 0.279184
$$455$$ 0 0
$$456$$ −1.77339 −0.0830465
$$457$$ 8.01184 0.374778 0.187389 0.982286i $$-0.439997\pi$$
0.187389 + 0.982286i $$0.439997\pi$$
$$458$$ −1.09355 −0.0510982
$$459$$ 24.9023 1.16234
$$460$$ 0 0
$$461$$ 3.83658 0.178687 0.0893437 0.996001i $$-0.471523\pi$$
0.0893437 + 0.996001i $$0.471523\pi$$
$$462$$ −26.4769 −1.23182
$$463$$ 6.58381 0.305975 0.152988 0.988228i $$-0.451110\pi$$
0.152988 + 0.988228i $$0.451110\pi$$
$$464$$ 1.08171 0.0502171
$$465$$ 0 0
$$466$$ 14.0935 0.652871
$$467$$ −22.6033 −1.04596 −0.522978 0.852346i $$-0.675179\pi$$
−0.522978 + 0.852346i $$0.675179\pi$$
$$468$$ 0.422869 0.0195471
$$469$$ −7.68500 −0.354860
$$470$$ 0 0
$$471$$ 16.9301 0.780099
$$472$$ −12.9933 −0.598066
$$473$$ 52.9538 2.43482
$$474$$ 5.48606 0.251983
$$475$$ 0 0
$$476$$ −13.2385 −0.606783
$$477$$ −1.41791 −0.0649215
$$478$$ −15.6100 −0.713983
$$479$$ −35.7904 −1.63530 −0.817652 0.575712i $$-0.804725\pi$$
−0.817652 + 0.575712i $$0.804725\pi$$
$$480$$ 0 0
$$481$$ −13.2688 −0.605006
$$482$$ 5.21994 0.237762
$$483$$ −17.2318 −0.784073
$$484$$ 19.7667 0.898487
$$485$$ 0 0
$$486$$ 1.50458 0.0682491
$$487$$ 21.4070 0.970045 0.485023 0.874502i $$-0.338811\pi$$
0.485023 + 0.874502i $$0.338811\pi$$
$$488$$ 7.38336 0.334229
$$489$$ −27.8603 −1.25988
$$490$$ 0 0
$$491$$ −4.32684 −0.195267 −0.0976337 0.995222i $$-0.531127\pi$$
−0.0976337 + 0.995222i $$0.531127\pi$$
$$492$$ 0 0
$$493$$ −5.32016 −0.239608
$$494$$ −2.91829 −0.131300
$$495$$ 0 0
$$496$$ 7.54677 0.338860
$$497$$ 38.9672 1.74792
$$498$$ 3.03284 0.135905
$$499$$ −37.6968 −1.68754 −0.843771 0.536703i $$-0.819670\pi$$
−0.843771 + 0.536703i $$0.819670\pi$$
$$500$$ 0 0
$$501$$ −11.4441 −0.511283
$$502$$ 28.6403 1.27828
$$503$$ 16.9183 0.754349 0.377175 0.926142i $$-0.376896\pi$$
0.377175 + 0.926142i $$0.376896\pi$$
$$504$$ −0.390032 −0.0173734
$$505$$ 0 0
$$506$$ 20.0237 0.890161
$$507$$ −7.95113 −0.353122
$$508$$ 1.87361 0.0831282
$$509$$ −6.79955 −0.301385 −0.150692 0.988581i $$-0.548150\pi$$
−0.150692 + 0.988581i $$0.548150\pi$$
$$510$$ 0 0
$$511$$ −13.8803 −0.614028
$$512$$ −1.00000 −0.0441942
$$513$$ −5.06319 −0.223545
$$514$$ 6.45323 0.284640
$$515$$ 0 0
$$516$$ 16.9301 0.745307
$$517$$ 4.64032 0.204081
$$518$$ 12.2385 0.537727
$$519$$ 1.54926 0.0680048
$$520$$ 0 0
$$521$$ −1.35968 −0.0595685 −0.0297842 0.999556i $$-0.509482\pi$$
−0.0297842 + 0.999556i $$0.509482\pi$$
$$522$$ −0.156743 −0.00686045
$$523$$ 21.9486 0.959747 0.479874 0.877338i $$-0.340682\pi$$
0.479874 + 0.877338i $$0.340682\pi$$
$$524$$ −11.5468 −0.504423
$$525$$ 0 0
$$526$$ 22.1871 0.967404
$$527$$ −37.1172 −1.61685
$$528$$ 9.83658 0.428082
$$529$$ −9.96813 −0.433397
$$530$$ 0 0
$$531$$ 1.88277 0.0817053
$$532$$ 2.69168 0.116699
$$533$$ 0 0
$$534$$ 9.03284 0.390889
$$535$$ 0 0
$$536$$ 2.85510 0.123321
$$537$$ −21.9605 −0.947665
$$538$$ 20.4070 0.879810
$$539$$ 1.35968 0.0585654
$$540$$ 0 0
$$541$$ −39.8973 −1.71532 −0.857659 0.514218i $$-0.828082\pi$$
−0.857659 + 0.514218i $$0.828082\pi$$
$$542$$ −15.9368 −0.684544
$$543$$ −31.2831 −1.34249
$$544$$ 4.91829 0.210870
$$545$$ 0 0
$$546$$ −13.9301 −0.596155
$$547$$ 7.34632 0.314106 0.157053 0.987590i $$-0.449801\pi$$
0.157053 + 0.987590i $$0.449801\pi$$
$$548$$ −4.23845 −0.181058
$$549$$ −1.06987 −0.0456609
$$550$$ 0 0
$$551$$ 1.08171 0.0460824
$$552$$ 6.40187 0.272482
$$553$$ −8.32684 −0.354093
$$554$$ 4.02368 0.170950
$$555$$ 0 0
$$556$$ 9.21994 0.391012
$$557$$ 26.9672 1.14264 0.571318 0.820729i $$-0.306432\pi$$
0.571318 + 0.820729i $$0.306432\pi$$
$$558$$ −1.09355 −0.0462936
$$559$$ 27.8603 1.17836
$$560$$ 0 0
$$561$$ −48.3792 −2.04257
$$562$$ −1.67316 −0.0705780
$$563$$ 44.8973 1.89220 0.946098 0.323881i $$-0.104988\pi$$
0.946098 + 0.323881i $$0.104988\pi$$
$$564$$ 1.48358 0.0624701
$$565$$ 0 0
$$566$$ 16.8931 0.710070
$$567$$ −25.3387 −1.06412
$$568$$ −14.4769 −0.607437
$$569$$ 31.1172 1.30450 0.652251 0.758003i $$-0.273825\pi$$
0.652251 + 0.758003i $$0.273825\pi$$
$$570$$ 0 0
$$571$$ 33.2570 1.39176 0.695880 0.718158i $$-0.255014\pi$$
0.695880 + 0.718158i $$0.255014\pi$$
$$572$$ 16.1871 0.676817
$$573$$ −26.8788 −1.12288
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0.144903 0.00603762
$$577$$ −23.4702 −0.977078 −0.488539 0.872542i $$-0.662470\pi$$
−0.488539 + 0.872542i $$0.662470\pi$$
$$578$$ −7.18958 −0.299047
$$579$$ −41.4677 −1.72334
$$580$$ 0 0
$$581$$ −4.60329 −0.190977
$$582$$ −30.6033 −1.26855
$$583$$ −54.2765 −2.24790
$$584$$ 5.15674 0.213388
$$585$$ 0 0
$$586$$ −1.08171 −0.0446850
$$587$$ 10.1501 0.418938 0.209469 0.977815i $$-0.432826\pi$$
0.209469 + 0.977815i $$0.432826\pi$$
$$588$$ 0.434709 0.0179271
$$589$$ 7.54677 0.310959
$$590$$ 0 0
$$591$$ 40.9538 1.68461
$$592$$ −4.54677 −0.186871
$$593$$ 16.6732 0.684685 0.342342 0.939575i $$-0.388780\pi$$
0.342342 + 0.939575i $$0.388780\pi$$
$$594$$ 28.0844 1.15232
$$595$$ 0 0
$$596$$ −7.25697 −0.297257
$$597$$ −45.7272 −1.87149
$$598$$ 10.5349 0.430806
$$599$$ 18.2765 0.746756 0.373378 0.927679i $$-0.378200\pi$$
0.373378 + 0.927679i $$0.378200\pi$$
$$600$$ 0 0
$$601$$ 7.96297 0.324816 0.162408 0.986724i $$-0.448074\pi$$
0.162408 + 0.986724i $$0.448074\pi$$
$$602$$ −25.6968 −1.04733
$$603$$ −0.413712 −0.0168477
$$604$$ 20.0000 0.813788
$$605$$ 0 0
$$606$$ 16.6403 0.675967
$$607$$ 6.93013 0.281285 0.140643 0.990060i $$-0.455083\pi$$
0.140643 + 0.990060i $$0.455083\pi$$
$$608$$ −1.00000 −0.0405554
$$609$$ 5.16342 0.209232
$$610$$ 0 0
$$611$$ 2.44139 0.0987679
$$612$$ −0.712675 −0.0288082
$$613$$ 34.2765 1.38441 0.692206 0.721700i $$-0.256639\pi$$
0.692206 + 0.721700i $$0.256639\pi$$
$$614$$ 2.38336 0.0961844
$$615$$ 0 0
$$616$$ −14.9301 −0.601552
$$617$$ −35.5139 −1.42974 −0.714869 0.699259i $$-0.753514\pi$$
−0.714869 + 0.699259i $$0.753514\pi$$
$$618$$ −22.9301 −0.922385
$$619$$ −29.5334 −1.18705 −0.593524 0.804816i $$-0.702264\pi$$
−0.593524 + 0.804816i $$0.702264\pi$$
$$620$$ 0 0
$$621$$ 18.2780 0.733470
$$622$$ 29.4584 1.18117
$$623$$ −13.7102 −0.549287
$$624$$ 5.17526 0.207176
$$625$$ 0 0
$$626$$ 32.0355 1.28040
$$627$$ 9.83658 0.392835
$$628$$ 9.54677 0.380958
$$629$$ 22.3624 0.891646
$$630$$ 0 0
$$631$$ −15.1634 −0.603646 −0.301823 0.953364i $$-0.597595\pi$$
−0.301823 + 0.953364i $$0.597595\pi$$
$$632$$ 3.09355 0.123055
$$633$$ 25.2293 1.00277
$$634$$ −26.6665 −1.05906
$$635$$ 0 0
$$636$$ −17.3530 −0.688091
$$637$$ 0.715358 0.0283435
$$638$$ −6.00000 −0.237542
$$639$$ 2.09775 0.0829855
$$640$$ 0 0
$$641$$ −25.0802 −0.990608 −0.495304 0.868720i $$-0.664943\pi$$
−0.495304 + 0.868720i $$0.664943\pi$$
$$642$$ 33.5915 1.32575
$$643$$ −19.1306 −0.754437 −0.377218 0.926124i $$-0.623119\pi$$
−0.377218 + 0.926124i $$0.623119\pi$$
$$644$$ −9.71687 −0.382898
$$645$$ 0 0
$$646$$ 4.91829 0.193508
$$647$$ −12.4019 −0.487568 −0.243784 0.969830i $$-0.578389\pi$$
−0.243784 + 0.969830i $$0.578389\pi$$
$$648$$ 9.41371 0.369806
$$649$$ 72.0710 2.82904
$$650$$ 0 0
$$651$$ 36.0237 1.41188
$$652$$ −15.7102 −0.615259
$$653$$ 10.7801 0.421856 0.210928 0.977502i $$-0.432351\pi$$
0.210928 + 0.977502i $$0.432351\pi$$
$$654$$ 4.77339 0.186654
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −0.747227 −0.0291521
$$658$$ −2.25181 −0.0877845
$$659$$ 8.56529 0.333656 0.166828 0.985986i $$-0.446647\pi$$
0.166828 + 0.985986i $$0.446647\pi$$
$$660$$ 0 0
$$661$$ −26.2883 −1.02250 −0.511248 0.859433i $$-0.670817\pi$$
−0.511248 + 0.859433i $$0.670817\pi$$
$$662$$ 19.8721 0.772351
$$663$$ −25.4534 −0.988529
$$664$$ 1.71019 0.0663684
$$665$$ 0 0
$$666$$ 0.658841 0.0255296
$$667$$ −3.90494 −0.151200
$$668$$ −6.45323 −0.249683
$$669$$ 7.89729 0.305327
$$670$$ 0 0
$$671$$ −40.9538 −1.58100
$$672$$ −4.77339 −0.184137
$$673$$ 12.9301 0.498420 0.249210 0.968449i $$-0.419829\pi$$
0.249210 + 0.968449i $$0.419829\pi$$
$$674$$ 27.5705 1.06197
$$675$$ 0 0
$$676$$ −4.48358 −0.172445
$$677$$ 15.9250 0.612046 0.306023 0.952024i $$-0.401002\pi$$
0.306023 + 0.952024i $$0.401002\pi$$
$$678$$ −10.6403 −0.408639
$$679$$ 46.4502 1.78260
$$680$$ 0 0
$$681$$ −10.5493 −0.404248
$$682$$ −41.8603 −1.60291
$$683$$ −13.2898 −0.508520 −0.254260 0.967136i $$-0.581832\pi$$
−0.254260 + 0.967136i $$0.581832\pi$$
$$684$$ 0.144903 0.00554050
$$685$$ 0 0
$$686$$ 18.1819 0.694190
$$687$$ 1.93929 0.0739884
$$688$$ 9.54677 0.363967
$$689$$ −28.5561 −1.08790
$$690$$ 0 0
$$691$$ 27.2570 1.03690 0.518452 0.855107i $$-0.326508\pi$$
0.518452 + 0.855107i $$0.326508\pi$$
$$692$$ 0.873614 0.0332098
$$693$$ 2.16342 0.0821815
$$694$$ −27.2806 −1.03556
$$695$$ 0 0
$$696$$ −1.91829 −0.0727126
$$697$$ 0 0
$$698$$ −30.9538 −1.17162
$$699$$ −24.9933 −0.945334
$$700$$ 0 0
$$701$$ −41.4441 −1.56532 −0.782660 0.622449i $$-0.786138\pi$$
−0.782660 + 0.622449i $$0.786138\pi$$
$$702$$ 14.7759 0.557679
$$703$$ −4.54677 −0.171485
$$704$$ 5.54677 0.209052
$$705$$ 0 0
$$706$$ 11.1819 0.420838
$$707$$ −25.2570 −0.949886
$$708$$ 23.0422 0.865979
$$709$$ −36.7904 −1.38169 −0.690846 0.723002i $$-0.742762\pi$$
−0.690846 + 0.723002i $$0.742762\pi$$
$$710$$ 0 0
$$711$$ −0.448264 −0.0168112
$$712$$ 5.09355 0.190889
$$713$$ −27.2436 −1.02028
$$714$$ 23.4769 0.878601
$$715$$ 0 0
$$716$$ −12.3834 −0.462788
$$717$$ 27.6825 1.03382
$$718$$ −20.3387 −0.759033
$$719$$ −4.13726 −0.154294 −0.0771469 0.997020i $$-0.524581\pi$$
−0.0771469 + 0.997020i $$0.524581\pi$$
$$720$$ 0 0
$$721$$ 34.8037 1.29616
$$722$$ −1.00000 −0.0372161
$$723$$ −9.25697 −0.344270
$$724$$ −17.6403 −0.655597
$$725$$ 0 0
$$726$$ −35.0540 −1.30098
$$727$$ 40.4374 1.49974 0.749870 0.661585i $$-0.230116\pi$$
0.749870 + 0.661585i $$0.230116\pi$$
$$728$$ −7.85510 −0.291129
$$729$$ 25.5729 0.947146
$$730$$ 0 0
$$731$$ −46.9538 −1.73665
$$732$$ −13.0935 −0.483952
$$733$$ −28.1264 −1.03887 −0.519436 0.854509i $$-0.673858\pi$$
−0.519436 + 0.854509i $$0.673858\pi$$
$$734$$ −32.9538 −1.21635
$$735$$ 0 0
$$736$$ 3.60997 0.133065
$$737$$ −15.8366 −0.583348
$$738$$ 0 0
$$739$$ −38.1501 −1.40337 −0.701686 0.712486i $$-0.747569\pi$$
−0.701686 + 0.712486i $$0.747569\pi$$
$$740$$ 0 0
$$741$$ 5.17526 0.190118
$$742$$ 26.3387 0.966923
$$743$$ 17.8232 0.653871 0.326935 0.945047i $$-0.393984\pi$$
0.326935 + 0.945047i $$0.393984\pi$$
$$744$$ −13.3834 −0.490658
$$745$$ 0 0
$$746$$ −10.0869 −0.369307
$$747$$ −0.247812 −0.00906697
$$748$$ −27.2806 −0.997479
$$749$$ −50.9857 −1.86298
$$750$$ 0 0
$$751$$ 23.6968 0.864710 0.432355 0.901703i $$-0.357683\pi$$
0.432355 + 0.901703i $$0.357683\pi$$
$$752$$ 0.836581 0.0305070
$$753$$ −50.7904 −1.85090
$$754$$ −3.15674 −0.114962
$$755$$ 0 0
$$756$$ −13.6285 −0.495663
$$757$$ 6.51394 0.236753 0.118377 0.992969i $$-0.462231\pi$$
0.118377 + 0.992969i $$0.462231\pi$$
$$758$$ 18.4256 0.669246
$$759$$ −35.5097 −1.28892
$$760$$ 0 0
$$761$$ 34.7786 1.26072 0.630361 0.776302i $$-0.282907\pi$$
0.630361 + 0.776302i $$0.282907\pi$$
$$762$$ −3.32264 −0.120367
$$763$$ −7.24513 −0.262291
$$764$$ −15.1567 −0.548352
$$765$$ 0 0
$$766$$ 28.1871 1.01844
$$767$$ 37.9183 1.36915
$$768$$ 1.77339 0.0639916
$$769$$ −27.6850 −0.998347 −0.499173 0.866502i $$-0.666363\pi$$
−0.499173 + 0.866502i $$0.666363\pi$$
$$770$$ 0 0
$$771$$ −11.4441 −0.412148
$$772$$ −23.3834 −0.841585
$$773$$ 19.9738 0.718409 0.359205 0.933259i $$-0.383048\pi$$
0.359205 + 0.933259i $$0.383048\pi$$
$$774$$ −1.38336 −0.0497237
$$775$$ 0 0
$$776$$ −17.2570 −0.619489
$$777$$ −21.7035 −0.778609
$$778$$ −20.0237 −0.717884
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 80.3001 2.87336
$$782$$ −17.7549 −0.634913
$$783$$ −5.47691 −0.195729
$$784$$ 0.245129 0.00875461
$$785$$ 0 0
$$786$$ 20.4769 0.730387
$$787$$ −42.0118 −1.49756 −0.748780 0.662818i $$-0.769360\pi$$
−0.748780 + 0.662818i $$0.769360\pi$$
$$788$$ 23.0935 0.822674
$$789$$ −39.3463 −1.40077
$$790$$ 0 0
$$791$$ 16.1501 0.574230
$$792$$ −0.803744 −0.0285598
$$793$$ −21.5468 −0.765148
$$794$$ −8.32684 −0.295508
$$795$$ 0 0
$$796$$ −25.7852 −0.913933
$$797$$ 45.1054 1.59771 0.798857 0.601520i $$-0.205438\pi$$
0.798857 + 0.601520i $$0.205438\pi$$
$$798$$ −4.77339 −0.168976
$$799$$ −4.11455 −0.145562
$$800$$ 0 0
$$801$$ −0.738070 −0.0260784
$$802$$ 22.1501 0.782146
$$803$$ −28.6033 −1.00939
$$804$$ −5.06319 −0.178565
$$805$$ 0 0
$$806$$ −22.0237 −0.775751
$$807$$ −36.1896 −1.27393
$$808$$ 9.38336 0.330105
$$809$$ 6.85510 0.241012 0.120506 0.992713i $$-0.461548\pi$$
0.120506 + 0.992713i $$0.461548\pi$$
$$810$$ 0 0
$$811$$ −15.1819 −0.533110 −0.266555 0.963820i $$-0.585885\pi$$
−0.266555 + 0.963820i $$0.585885\pi$$
$$812$$ 2.91161 0.102178
$$813$$ 28.2621 0.991196
$$814$$ 25.2199 0.883958
$$815$$ 0 0
$$816$$ −8.72203 −0.305332
$$817$$ 9.54677 0.333999
$$818$$ −34.0237 −1.18961
$$819$$ 1.13823 0.0397729
$$820$$ 0 0
$$821$$ 22.5006 0.785276 0.392638 0.919693i $$-0.371563\pi$$
0.392638 + 0.919693i $$0.371563\pi$$
$$822$$ 7.51642 0.262165
$$823$$ 16.1896 0.564333 0.282167 0.959365i $$-0.408947\pi$$
0.282167 + 0.959365i $$0.408947\pi$$
$$824$$ −12.9301 −0.450442
$$825$$ 0 0
$$826$$ −34.9738 −1.21690
$$827$$ 25.0817 0.872177 0.436088 0.899904i $$-0.356364\pi$$
0.436088 + 0.899904i $$0.356364\pi$$
$$828$$ −0.523095 −0.0181788
$$829$$ 21.3068 0.740016 0.370008 0.929029i $$-0.379355\pi$$
0.370008 + 0.929029i $$0.379355\pi$$
$$830$$ 0 0
$$831$$ −7.13554 −0.247529
$$832$$ 2.91829 0.101174
$$833$$ −1.20562 −0.0417721
$$834$$ −16.3505 −0.566172
$$835$$ 0 0
$$836$$ 5.54677 0.191839
$$837$$ −38.2108 −1.32076
$$838$$ −37.5334 −1.29657
$$839$$ −11.4727 −0.396082 −0.198041 0.980194i $$-0.563458\pi$$
−0.198041 + 0.980194i $$0.563458\pi$$
$$840$$ 0 0
$$841$$ −27.8299 −0.959652
$$842$$ −33.8341 −1.16600
$$843$$ 2.96716 0.102195
$$844$$ 14.2266 0.489700
$$845$$ 0 0
$$846$$ −0.121223 −0.00416773
$$847$$ 53.2056 1.82817
$$848$$ −9.78523 −0.336026
$$849$$ −29.9580 −1.02816
$$850$$ 0 0
$$851$$ 16.4137 0.562655
$$852$$ 25.6732 0.879548
$$853$$ 38.9908 1.33502 0.667511 0.744600i $$-0.267360\pi$$
0.667511 + 0.744600i $$0.267360\pi$$
$$854$$ 19.8736 0.680061
$$855$$ 0 0
$$856$$ 18.9420 0.647423
$$857$$ 29.8973 1.02127 0.510636 0.859797i $$-0.329410\pi$$
0.510636 + 0.859797i $$0.329410\pi$$
$$858$$ −28.7060 −0.980007
$$859$$ −6.47691 −0.220989 −0.110495 0.993877i $$-0.535243\pi$$
−0.110495 + 0.993877i $$0.535243\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −24.8037 −0.844819
$$863$$ 5.09355 0.173386 0.0866932 0.996235i $$-0.472370\pi$$
0.0866932 + 0.996235i $$0.472370\pi$$
$$864$$ 5.06319 0.172253
$$865$$ 0 0
$$866$$ 1.68651 0.0573101
$$867$$ 12.7499 0.433010
$$868$$ 20.3135 0.689485
$$869$$ −17.1592 −0.582087
$$870$$ 0 0
$$871$$ −8.33200 −0.282319
$$872$$ 2.69168 0.0911517
$$873$$ 2.50059 0.0846320
$$874$$ 3.60997 0.122109
$$875$$ 0 0
$$876$$ −9.14490 −0.308978
$$877$$ 29.8341 1.00743 0.503713 0.863871i $$-0.331967\pi$$
0.503713 + 0.863871i $$0.331967\pi$$
$$878$$ −0.326839 −0.0110303
$$879$$ 1.91829 0.0647023
$$880$$ 0 0
$$881$$ −11.5796 −0.390127 −0.195064 0.980791i $$-0.562491\pi$$
−0.195064 + 0.980791i $$0.562491\pi$$
$$882$$ −0.0355199 −0.00119602
$$883$$ 48.0237 1.61613 0.808063 0.589096i $$-0.200516\pi$$
0.808063 + 0.589096i $$0.200516\pi$$
$$884$$ −14.3530 −0.482744
$$885$$ 0 0
$$886$$ 0.490258 0.0164705
$$887$$ −9.38336 −0.315062 −0.157531 0.987514i $$-0.550353\pi$$
−0.157531 + 0.987514i $$0.550353\pi$$
$$888$$ 8.06319 0.270583
$$889$$ 5.04316 0.169142
$$890$$ 0 0
$$891$$ −52.2157 −1.74929
$$892$$ 4.45323 0.149105
$$893$$ 0.836581 0.0279951
$$894$$ 12.8694 0.430418
$$895$$ 0 0
$$896$$ −2.69168 −0.0899226
$$897$$ −18.6825 −0.623791
$$898$$ −23.5468 −0.785766
$$899$$ 8.16342 0.272265
$$900$$ 0 0
$$901$$ 48.1266 1.60333
$$902$$ 0 0
$$903$$ 45.5705 1.51649
$$904$$ −6.00000 −0.199557
$$905$$ 0 0
$$906$$ −35.4677 −1.17834
$$907$$ 19.4347 0.645319 0.322659 0.946515i $$-0.395423\pi$$
0.322659 + 0.946515i $$0.395423\pi$$
$$908$$ −5.94865 −0.197413
$$909$$ −1.35968 −0.0450976
$$910$$ 0 0
$$911$$ −19.9866 −0.662187 −0.331094 0.943598i $$-0.607418\pi$$
−0.331094 + 0.943598i $$0.607418\pi$$
$$912$$ 1.77339 0.0587227
$$913$$ −9.48606 −0.313943
$$914$$ −8.01184 −0.265008
$$915$$ 0 0
$$916$$ 1.09355 0.0361319
$$917$$ −31.0802 −1.02636
$$918$$ −24.9023 −0.821897
$$919$$ 6.15158 0.202922 0.101461 0.994840i $$-0.467648\pi$$
0.101461 + 0.994840i $$0.467648\pi$$
$$920$$ 0 0
$$921$$ −4.22661 −0.139272
$$922$$ −3.83658 −0.126351
$$923$$ 42.2478 1.39060
$$924$$ 26.4769 0.871026
$$925$$ 0 0
$$926$$ −6.58381 −0.216357
$$927$$ 1.87361 0.0615375
$$928$$ −1.08171 −0.0355089
$$929$$ −7.17010 −0.235243 −0.117622 0.993058i $$-0.537527\pi$$
−0.117622 + 0.993058i $$0.537527\pi$$
$$930$$ 0 0
$$931$$ 0.245129 0.00803378
$$932$$ −14.0935 −0.461650
$$933$$ −52.2411 −1.71030
$$934$$ 22.6033 0.739602
$$935$$ 0 0
$$936$$ −0.422869 −0.0138219
$$937$$ 24.2646 0.792690 0.396345 0.918102i $$-0.370278\pi$$
0.396345 + 0.918102i $$0.370278\pi$$
$$938$$ 7.68500 0.250924
$$939$$ −56.8114 −1.85397
$$940$$ 0 0
$$941$$ −7.44806 −0.242800 −0.121400 0.992604i $$-0.538738\pi$$
−0.121400 + 0.992604i $$0.538738\pi$$
$$942$$ −16.9301 −0.551613
$$943$$ 0 0
$$944$$ 12.9933 0.422897
$$945$$ 0 0
$$946$$ −52.9538 −1.72168
$$947$$ 52.9538 1.72077 0.860384 0.509647i $$-0.170224\pi$$
0.860384 + 0.509647i $$0.170224\pi$$
$$948$$ −5.48606 −0.178179
$$949$$ −15.0489 −0.488507
$$950$$ 0 0
$$951$$ 47.2900 1.53348
$$952$$ 13.2385 0.429061
$$953$$ 12.8694 0.416881 0.208441 0.978035i $$-0.433161\pi$$
0.208441 + 0.978035i $$0.433161\pi$$
$$954$$ 1.41791 0.0459065
$$955$$ 0 0
$$956$$ 15.6100 0.504862
$$957$$ 10.6403 0.343953
$$958$$ 35.7904 1.15634
$$959$$ −11.4085 −0.368401
$$960$$ 0 0
$$961$$ 25.9538 0.837220
$$962$$ 13.2688 0.427804
$$963$$ −2.74475 −0.0884482
$$964$$ −5.21994 −0.168123
$$965$$ 0 0
$$966$$ 17.2318 0.554423
$$967$$ −25.8603 −0.831610 −0.415805 0.909454i $$-0.636500\pi$$
−0.415805 + 0.909454i $$0.636500\pi$$
$$968$$ −19.7667 −0.635326
$$969$$ −8.72203 −0.280192
$$970$$ 0 0
$$971$$ 35.0935 1.12621 0.563103 0.826387i $$-0.309608\pi$$
0.563103 + 0.826387i $$0.309608\pi$$
$$972$$ −1.50458 −0.0482594
$$973$$ 24.8171 0.795600
$$974$$ −21.4070 −0.685926
$$975$$ 0 0
$$976$$ −7.38336 −0.236335
$$977$$ 42.1737 1.34926 0.674629 0.738157i $$-0.264304\pi$$
0.674629 + 0.738157i $$0.264304\pi$$
$$978$$ 27.8603 0.890873
$$979$$ −28.2528 −0.902963
$$980$$ 0 0
$$981$$ −0.390032 −0.0124528
$$982$$ 4.32684 0.138075
$$983$$ 42.6270 1.35959 0.679795 0.733403i $$-0.262069\pi$$
0.679795 + 0.733403i $$0.262069\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 5.32016 0.169428
$$987$$ 3.99332 0.127109
$$988$$ 2.91829 0.0928432
$$989$$ −34.4636 −1.09588
$$990$$ 0 0
$$991$$ −34.1737 −1.08556 −0.542782 0.839873i $$-0.682629\pi$$
−0.542782 + 0.839873i $$0.682629\pi$$
$$992$$ −7.54677 −0.239610
$$993$$ −35.2409 −1.11834
$$994$$ −38.9672 −1.23596
$$995$$ 0 0
$$996$$ −3.03284 −0.0960991
$$997$$ −29.3834 −0.930580 −0.465290 0.885158i $$-0.654050\pi$$
−0.465290 + 0.885158i $$0.654050\pi$$
$$998$$ 37.6968 1.19327
$$999$$ 23.0212 0.728359
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.j.1.3 3
3.2 odd 2 8550.2.a.cp.1.3 3
4.3 odd 2 7600.2.a.bz.1.1 3
5.2 odd 4 950.2.b.h.799.1 6
5.3 odd 4 950.2.b.h.799.6 6
5.4 even 2 950.2.a.l.1.1 yes 3
15.14 odd 2 8550.2.a.ci.1.1 3
20.19 odd 2 7600.2.a.bk.1.3 3

By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.3 3 1.1 even 1 trivial
950.2.a.l.1.1 yes 3 5.4 even 2
950.2.b.h.799.1 6 5.2 odd 4
950.2.b.h.799.6 6 5.3 odd 4
7600.2.a.bk.1.3 3 20.19 odd 2
7600.2.a.bz.1.1 3 4.3 odd 2
8550.2.a.ci.1.1 3 15.14 odd 2
8550.2.a.cp.1.3 3 3.2 odd 2