Properties

 Label 7800.2.a.bu.1.3 Level $7800$ Weight $2$ Character 7800.1 Self dual yes Analytic conductor $62.283$ Analytic rank $0$ Dimension $4$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7800.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$62.2833135766$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: 4.4.461844.1 Defining polynomial: $$x^{4} - x^{3} - 14 x^{2} - 12 x + 6$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.3 Root $$0.352593$$ of defining polynomial Character $$\chi$$ $$=$$ 7800.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} -0.647407 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} -0.647407 q^{7} +1.00000 q^{9} +0.502467 q^{11} -1.00000 q^{13} +4.73074 q^{17} -6.58086 q^{19} +0.647407 q^{21} -2.85013 q^{23} -1.00000 q^{27} +0.294814 q^{29} +2.20272 q^{31} -0.502467 q^{33} -7.28605 q^{37} +1.00000 q^{39} +7.58580 q^{41} -0.444688 q^{43} -8.07840 q^{47} -6.58086 q^{49} -4.73074 q^{51} +12.7220 q^{53} +6.58086 q^{57} +10.8141 q^{59} +11.4359 q^{61} -0.647407 q^{63} +8.63864 q^{67} +2.85013 q^{69} -2.58086 q^{71} -10.6114 q^{73} -0.325301 q^{77} +5.28605 q^{79} +1.00000 q^{81} -5.35259 q^{83} -0.294814 q^{87} +4.99507 q^{89} +0.647407 q^{91} -2.20272 q^{93} +1.29481 q^{97} +0.502467 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{3} - 3q^{7} + 4q^{9} + O(q^{10})$$ $$4q - 4q^{3} - 3q^{7} + 4q^{9} + 5q^{11} - 4q^{13} - 7q^{17} + 3q^{19} + 3q^{21} - 8q^{23} - 4q^{27} + 2q^{29} + 5q^{31} - 5q^{33} + q^{37} + 4q^{39} + 7q^{41} - 6q^{43} + 3q^{49} + 7q^{51} - 6q^{53} - 3q^{57} - 9q^{59} + 19q^{61} - 3q^{63} + 4q^{67} + 8q^{69} + 19q^{71} + 6q^{73} + 17q^{77} - 9q^{79} + 4q^{81} - 21q^{83} - 2q^{87} + 14q^{89} + 3q^{91} - 5q^{93} + 6q^{97} + 5q^{99} + O(q^{100})$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.00000 −0.577350
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −0.647407 −0.244697 −0.122348 0.992487i $$-0.539043\pi$$
−0.122348 + 0.992487i $$0.539043\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0.502467 0.151500 0.0757498 0.997127i $$-0.475865\pi$$
0.0757498 + 0.997127i $$0.475865\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 4.73074 1.14737 0.573686 0.819075i $$-0.305513\pi$$
0.573686 + 0.819075i $$0.305513\pi$$
$$18$$ 0 0
$$19$$ −6.58086 −1.50975 −0.754877 0.655867i $$-0.772303\pi$$
−0.754877 + 0.655867i $$0.772303\pi$$
$$20$$ 0 0
$$21$$ 0.647407 0.141276
$$22$$ 0 0
$$23$$ −2.85013 −0.594292 −0.297146 0.954832i $$-0.596035\pi$$
−0.297146 + 0.954832i $$0.596035\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 0.294814 0.0547456 0.0273728 0.999625i $$-0.491286\pi$$
0.0273728 + 0.999625i $$0.491286\pi$$
$$30$$ 0 0
$$31$$ 2.20272 0.395620 0.197810 0.980240i $$-0.436617\pi$$
0.197810 + 0.980240i $$0.436617\pi$$
$$32$$ 0 0
$$33$$ −0.502467 −0.0874683
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −7.28605 −1.19782 −0.598910 0.800817i $$-0.704399\pi$$
−0.598910 + 0.800817i $$0.704399\pi$$
$$38$$ 0 0
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ 7.58580 1.18470 0.592351 0.805680i $$-0.298200\pi$$
0.592351 + 0.805680i $$0.298200\pi$$
$$42$$ 0 0
$$43$$ −0.444688 −0.0678143 −0.0339072 0.999425i $$-0.510795\pi$$
−0.0339072 + 0.999425i $$0.510795\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −8.07840 −1.17836 −0.589178 0.808004i $$-0.700548\pi$$
−0.589178 + 0.808004i $$0.700548\pi$$
$$48$$ 0 0
$$49$$ −6.58086 −0.940123
$$50$$ 0 0
$$51$$ −4.73074 −0.662436
$$52$$ 0 0
$$53$$ 12.7220 1.74750 0.873749 0.486377i $$-0.161682\pi$$
0.873749 + 0.486377i $$0.161682\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 6.58086 0.871657
$$58$$ 0 0
$$59$$ 10.8141 1.40787 0.703936 0.710263i $$-0.251424\pi$$
0.703936 + 0.710263i $$0.251424\pi$$
$$60$$ 0 0
$$61$$ 11.4359 1.46422 0.732110 0.681186i $$-0.238536\pi$$
0.732110 + 0.681186i $$0.238536\pi$$
$$62$$ 0 0
$$63$$ −0.647407 −0.0815656
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 8.63864 1.05538 0.527689 0.849438i $$-0.323059\pi$$
0.527689 + 0.849438i $$0.323059\pi$$
$$68$$ 0 0
$$69$$ 2.85013 0.343115
$$70$$ 0 0
$$71$$ −2.58086 −0.306292 −0.153146 0.988204i $$-0.548941\pi$$
−0.153146 + 0.988204i $$0.548941\pi$$
$$72$$ 0 0
$$73$$ −10.6114 −1.24196 −0.620982 0.783825i $$-0.713266\pi$$
−0.620982 + 0.783825i $$0.713266\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −0.325301 −0.0370715
$$78$$ 0 0
$$79$$ 5.28605 0.594727 0.297364 0.954764i $$-0.403893\pi$$
0.297364 + 0.954764i $$0.403893\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −5.35259 −0.587523 −0.293762 0.955879i $$-0.594907\pi$$
−0.293762 + 0.955879i $$0.594907\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −0.294814 −0.0316074
$$88$$ 0 0
$$89$$ 4.99507 0.529476 0.264738 0.964320i $$-0.414715\pi$$
0.264738 + 0.964320i $$0.414715\pi$$
$$90$$ 0 0
$$91$$ 0.647407 0.0678667
$$92$$ 0 0
$$93$$ −2.20272 −0.228411
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1.29481 0.131468 0.0657342 0.997837i $$-0.479061\pi$$
0.0657342 + 0.997837i $$0.479061\pi$$
$$98$$ 0 0
$$99$$ 0.502467 0.0504999
$$100$$ 0 0
$$101$$ −4.28605 −0.426478 −0.213239 0.977000i $$-0.568401\pi$$
−0.213239 + 0.977000i $$0.568401\pi$$
$$102$$ 0 0
$$103$$ −7.25556 −0.714912 −0.357456 0.933930i $$-0.616356\pi$$
−0.357456 + 0.933930i $$0.616356\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −10.1362 −0.979901 −0.489951 0.871750i $$-0.662985\pi$$
−0.489951 + 0.871750i $$0.662985\pi$$
$$108$$ 0 0
$$109$$ 17.4527 1.67167 0.835833 0.548983i $$-0.184985\pi$$
0.835833 + 0.548983i $$0.184985\pi$$
$$110$$ 0 0
$$111$$ 7.28605 0.691561
$$112$$ 0 0
$$113$$ −15.8669 −1.49263 −0.746317 0.665591i $$-0.768180\pi$$
−0.746317 + 0.665591i $$0.768180\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.00000 −0.0924500
$$118$$ 0 0
$$119$$ −3.06271 −0.280758
$$120$$ 0 0
$$121$$ −10.7475 −0.977048
$$122$$ 0 0
$$123$$ −7.58580 −0.683988
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −9.99124 −0.886579 −0.443289 0.896379i $$-0.646189\pi$$
−0.443289 + 0.896379i $$0.646189\pi$$
$$128$$ 0 0
$$129$$ 0.444688 0.0391526
$$130$$ 0 0
$$131$$ 16.2811 1.42249 0.711244 0.702945i $$-0.248132\pi$$
0.711244 + 0.702945i $$0.248132\pi$$
$$132$$ 0 0
$$133$$ 4.26050 0.369432
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −4.73567 −0.404596 −0.202298 0.979324i $$-0.564841\pi$$
−0.202298 + 0.979324i $$0.564841\pi$$
$$138$$ 0 0
$$139$$ −17.4615 −1.48106 −0.740532 0.672022i $$-0.765426\pi$$
−0.740532 + 0.672022i $$0.765426\pi$$
$$140$$ 0 0
$$141$$ 8.07840 0.680324
$$142$$ 0 0
$$143$$ −0.502467 −0.0420184
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 6.58086 0.542781
$$148$$ 0 0
$$149$$ 5.29481 0.433768 0.216884 0.976197i $$-0.430411\pi$$
0.216884 + 0.976197i $$0.430411\pi$$
$$150$$ 0 0
$$151$$ 18.5143 1.50667 0.753337 0.657635i $$-0.228443\pi$$
0.753337 + 0.657635i $$0.228443\pi$$
$$152$$ 0 0
$$153$$ 4.73074 0.382458
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 17.5809 1.40311 0.701553 0.712617i $$-0.252490\pi$$
0.701553 + 0.712617i $$0.252490\pi$$
$$158$$ 0 0
$$159$$ −12.7220 −1.00892
$$160$$ 0 0
$$161$$ 1.84519 0.145421
$$162$$ 0 0
$$163$$ 10.0119 0.784189 0.392094 0.919925i $$-0.371751\pi$$
0.392094 + 0.919925i $$0.371751\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 8.69642 0.672949 0.336475 0.941693i $$-0.390765\pi$$
0.336475 + 0.941693i $$0.390765\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ −6.58086 −0.503251
$$172$$ 0 0
$$173$$ −18.0069 −1.36904 −0.684520 0.728994i $$-0.739988\pi$$
−0.684520 + 0.728994i $$0.739988\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −10.8141 −0.812835
$$178$$ 0 0
$$179$$ −2.73457 −0.204391 −0.102196 0.994764i $$-0.532587\pi$$
−0.102196 + 0.994764i $$0.532587\pi$$
$$180$$ 0 0
$$181$$ 16.8757 1.25436 0.627180 0.778875i $$-0.284209\pi$$
0.627180 + 0.778875i $$0.284209\pi$$
$$182$$ 0 0
$$183$$ −11.4359 −0.845368
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 2.37704 0.173826
$$188$$ 0 0
$$189$$ 0.647407 0.0470919
$$190$$ 0 0
$$191$$ 12.5896 0.910954 0.455477 0.890248i $$-0.349469\pi$$
0.455477 + 0.890248i $$0.349469\pi$$
$$192$$ 0 0
$$193$$ 20.0728 1.44487 0.722437 0.691437i $$-0.243022\pi$$
0.722437 + 0.691437i $$0.243022\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 15.6163 1.11261 0.556307 0.830977i $$-0.312218\pi$$
0.556307 + 0.830977i $$0.312218\pi$$
$$198$$ 0 0
$$199$$ −15.7307 −1.11512 −0.557561 0.830136i $$-0.688263\pi$$
−0.557561 + 0.830136i $$0.688263\pi$$
$$200$$ 0 0
$$201$$ −8.63864 −0.609323
$$202$$ 0 0
$$203$$ −0.190865 −0.0133961
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −2.85013 −0.198097
$$208$$ 0 0
$$209$$ −3.30667 −0.228727
$$210$$ 0 0
$$211$$ 6.85013 0.471582 0.235791 0.971804i $$-0.424232\pi$$
0.235791 + 0.971804i $$0.424232\pi$$
$$212$$ 0 0
$$213$$ 2.58086 0.176838
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −1.42606 −0.0968070
$$218$$ 0 0
$$219$$ 10.6114 0.717049
$$220$$ 0 0
$$221$$ −4.73074 −0.318224
$$222$$ 0 0
$$223$$ 1.15974 0.0776621 0.0388311 0.999246i $$-0.487637\pi$$
0.0388311 + 0.999246i $$0.487637\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 26.1207 1.73369 0.866847 0.498574i $$-0.166143\pi$$
0.866847 + 0.498574i $$0.166143\pi$$
$$228$$ 0 0
$$229$$ −4.02062 −0.265690 −0.132845 0.991137i $$-0.542411\pi$$
−0.132845 + 0.991137i $$0.542411\pi$$
$$230$$ 0 0
$$231$$ 0.325301 0.0214032
$$232$$ 0 0
$$233$$ −6.99507 −0.458262 −0.229131 0.973396i $$-0.573588\pi$$
−0.229131 + 0.973396i $$0.573588\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −5.28605 −0.343366
$$238$$ 0 0
$$239$$ −15.4037 −0.996382 −0.498191 0.867067i $$-0.666002\pi$$
−0.498191 + 0.867067i $$0.666002\pi$$
$$240$$ 0 0
$$241$$ 5.14987 0.331733 0.165866 0.986148i $$-0.446958\pi$$
0.165866 + 0.986148i $$0.446958\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 6.58086 0.418730
$$248$$ 0 0
$$249$$ 5.35259 0.339207
$$250$$ 0 0
$$251$$ 17.5858 1.11001 0.555003 0.831848i $$-0.312717\pi$$
0.555003 + 0.831848i $$0.312717\pi$$
$$252$$ 0 0
$$253$$ −1.43209 −0.0900350
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 15.3421 0.957013 0.478507 0.878084i $$-0.341178\pi$$
0.478507 + 0.878084i $$0.341178\pi$$
$$258$$ 0 0
$$259$$ 4.71704 0.293103
$$260$$ 0 0
$$261$$ 0.294814 0.0182485
$$262$$ 0 0
$$263$$ −21.0168 −1.29595 −0.647975 0.761661i $$-0.724384\pi$$
−0.647975 + 0.761661i $$0.724384\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −4.99507 −0.305693
$$268$$ 0 0
$$269$$ −5.57210 −0.339737 −0.169868 0.985467i $$-0.554334\pi$$
−0.169868 + 0.985467i $$0.554334\pi$$
$$270$$ 0 0
$$271$$ −5.50939 −0.334671 −0.167336 0.985900i $$-0.553516\pi$$
−0.167336 + 0.985900i $$0.553516\pi$$
$$272$$ 0 0
$$273$$ −0.647407 −0.0391829
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 29.5672 1.77652 0.888259 0.459342i $$-0.151915\pi$$
0.888259 + 0.459342i $$0.151915\pi$$
$$278$$ 0 0
$$279$$ 2.20272 0.131873
$$280$$ 0 0
$$281$$ −5.14111 −0.306693 −0.153346 0.988172i $$-0.549005\pi$$
−0.153346 + 0.988172i $$0.549005\pi$$
$$282$$ 0 0
$$283$$ −14.3509 −0.853070 −0.426535 0.904471i $$-0.640266\pi$$
−0.426535 + 0.904471i $$0.640266\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −4.91110 −0.289893
$$288$$ 0 0
$$289$$ 5.37989 0.316464
$$290$$ 0 0
$$291$$ −1.29481 −0.0759033
$$292$$ 0 0
$$293$$ 15.4516 0.902693 0.451346 0.892349i $$-0.350944\pi$$
0.451346 + 0.892349i $$0.350944\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −0.502467 −0.0291561
$$298$$ 0 0
$$299$$ 2.85013 0.164827
$$300$$ 0 0
$$301$$ 0.287894 0.0165940
$$302$$ 0 0
$$303$$ 4.28605 0.246227
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 2.12432 0.121241 0.0606207 0.998161i $$-0.480692\pi$$
0.0606207 + 0.998161i $$0.480692\pi$$
$$308$$ 0 0
$$309$$ 7.25556 0.412755
$$310$$ 0 0
$$311$$ 32.6331 1.85045 0.925226 0.379417i $$-0.123875\pi$$
0.925226 + 0.379417i $$0.123875\pi$$
$$312$$ 0 0
$$313$$ −18.7318 −1.05879 −0.529393 0.848377i $$-0.677580\pi$$
−0.529393 + 0.848377i $$0.677580\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −26.3452 −1.47969 −0.739846 0.672776i $$-0.765102\pi$$
−0.739846 + 0.672776i $$0.765102\pi$$
$$318$$ 0 0
$$319$$ 0.148134 0.00829393
$$320$$ 0 0
$$321$$ 10.1362 0.565746
$$322$$ 0 0
$$323$$ −31.1323 −1.73225
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −17.4527 −0.965137
$$328$$ 0 0
$$329$$ 5.23001 0.288340
$$330$$ 0 0
$$331$$ 24.3116 1.33629 0.668143 0.744033i $$-0.267089\pi$$
0.668143 + 0.744033i $$0.267089\pi$$
$$332$$ 0 0
$$333$$ −7.28605 −0.399273
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 1.72382 0.0939024 0.0469512 0.998897i $$-0.485049\pi$$
0.0469512 + 0.998897i $$0.485049\pi$$
$$338$$ 0 0
$$339$$ 15.8669 0.861772
$$340$$ 0 0
$$341$$ 1.10679 0.0599362
$$342$$ 0 0
$$343$$ 8.79235 0.474742
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −3.44086 −0.184715 −0.0923575 0.995726i $$-0.529440\pi$$
−0.0923575 + 0.995726i $$0.529440\pi$$
$$348$$ 0 0
$$349$$ 12.2059 0.653368 0.326684 0.945134i $$-0.394069\pi$$
0.326684 + 0.945134i $$0.394069\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ 0 0
$$353$$ 16.3967 0.872707 0.436353 0.899775i $$-0.356270\pi$$
0.436353 + 0.899775i $$0.356270\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 3.06271 0.162096
$$358$$ 0 0
$$359$$ 0.511231 0.0269817 0.0134909 0.999909i $$-0.495706\pi$$
0.0134909 + 0.999909i $$0.495706\pi$$
$$360$$ 0 0
$$361$$ 24.3078 1.27936
$$362$$ 0 0
$$363$$ 10.7475 0.564099
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 16.3028 0.851001 0.425501 0.904958i $$-0.360098\pi$$
0.425501 + 0.904958i $$0.360098\pi$$
$$368$$ 0 0
$$369$$ 7.58580 0.394901
$$370$$ 0 0
$$371$$ −8.23630 −0.427607
$$372$$ 0 0
$$373$$ 32.3372 1.67435 0.837177 0.546932i $$-0.184204\pi$$
0.837177 + 0.546932i $$0.184204\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −0.294814 −0.0151837
$$378$$ 0 0
$$379$$ 9.36445 0.481019 0.240510 0.970647i $$-0.422685\pi$$
0.240510 + 0.970647i $$0.422685\pi$$
$$380$$ 0 0
$$381$$ 9.99124 0.511867
$$382$$ 0 0
$$383$$ 10.0423 0.513140 0.256570 0.966526i $$-0.417408\pi$$
0.256570 + 0.966526i $$0.417408\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −0.444688 −0.0226048
$$388$$ 0 0
$$389$$ 35.8974 1.82007 0.910035 0.414531i $$-0.136054\pi$$
0.910035 + 0.414531i $$0.136054\pi$$
$$390$$ 0 0
$$391$$ −13.4832 −0.681875
$$392$$ 0 0
$$393$$ −16.2811 −0.821274
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 39.2979 1.97231 0.986153 0.165840i $$-0.0530336\pi$$
0.986153 + 0.165840i $$0.0530336\pi$$
$$398$$ 0 0
$$399$$ −4.26050 −0.213292
$$400$$ 0 0
$$401$$ −2.69333 −0.134499 −0.0672493 0.997736i $$-0.521422\pi$$
−0.0672493 + 0.997736i $$0.521422\pi$$
$$402$$ 0 0
$$403$$ −2.20272 −0.109725
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −3.66100 −0.181469
$$408$$ 0 0
$$409$$ 25.8963 1.28049 0.640245 0.768171i $$-0.278833\pi$$
0.640245 + 0.768171i $$0.278833\pi$$
$$410$$ 0 0
$$411$$ 4.73567 0.233594
$$412$$ 0 0
$$413$$ −7.00110 −0.344502
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 17.4615 0.855092
$$418$$ 0 0
$$419$$ −19.0374 −0.930038 −0.465019 0.885301i $$-0.653953\pi$$
−0.465019 + 0.885301i $$0.653953\pi$$
$$420$$ 0 0
$$421$$ 22.5721 1.10010 0.550048 0.835133i $$-0.314609\pi$$
0.550048 + 0.835133i $$0.314609\pi$$
$$422$$ 0 0
$$423$$ −8.07840 −0.392785
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −7.40370 −0.358290
$$428$$ 0 0
$$429$$ 0.502467 0.0242593
$$430$$ 0 0
$$431$$ −9.75246 −0.469760 −0.234880 0.972024i $$-0.575470\pi$$
−0.234880 + 0.972024i $$0.575470\pi$$
$$432$$ 0 0
$$433$$ 8.14604 0.391474 0.195737 0.980656i $$-0.437290\pi$$
0.195737 + 0.980656i $$0.437290\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 18.7563 0.897235
$$438$$ 0 0
$$439$$ 0.870744 0.0415583 0.0207792 0.999784i $$-0.493385\pi$$
0.0207792 + 0.999784i $$0.493385\pi$$
$$440$$ 0 0
$$441$$ −6.58086 −0.313374
$$442$$ 0 0
$$443$$ −33.3470 −1.58436 −0.792182 0.610284i $$-0.791055\pi$$
−0.792182 + 0.610284i $$0.791055\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −5.29481 −0.250436
$$448$$ 0 0
$$449$$ 38.0641 1.79635 0.898177 0.439634i $$-0.144892\pi$$
0.898177 + 0.439634i $$0.144892\pi$$
$$450$$ 0 0
$$451$$ 3.81161 0.179482
$$452$$ 0 0
$$453$$ −18.5143 −0.869879
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.0938351 0.00438942 0.00219471 0.999998i $$-0.499301\pi$$
0.00219471 + 0.999998i $$0.499301\pi$$
$$458$$ 0 0
$$459$$ −4.73074 −0.220812
$$460$$ 0 0
$$461$$ −31.1617 −1.45135 −0.725673 0.688040i $$-0.758472\pi$$
−0.725673 + 0.688040i $$0.758472\pi$$
$$462$$ 0 0
$$463$$ 16.7748 0.779592 0.389796 0.920901i $$-0.372546\pi$$
0.389796 + 0.920901i $$0.372546\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −24.7594 −1.14573 −0.572864 0.819651i $$-0.694168\pi$$
−0.572864 + 0.819651i $$0.694168\pi$$
$$468$$ 0 0
$$469$$ −5.59272 −0.258248
$$470$$ 0 0
$$471$$ −17.5809 −0.810083
$$472$$ 0 0
$$473$$ −0.223441 −0.0102738
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 12.7220 0.582499
$$478$$ 0 0
$$479$$ 16.8130 0.768204 0.384102 0.923291i $$-0.374511\pi$$
0.384102 + 0.923291i $$0.374511\pi$$
$$480$$ 0 0
$$481$$ 7.28605 0.332215
$$482$$ 0 0
$$483$$ −1.84519 −0.0839591
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −5.78741 −0.262253 −0.131126 0.991366i $$-0.541859\pi$$
−0.131126 + 0.991366i $$0.541859\pi$$
$$488$$ 0 0
$$489$$ −10.0119 −0.452752
$$490$$ 0 0
$$491$$ −0.650602 −0.0293612 −0.0146806 0.999892i $$-0.504673\pi$$
−0.0146806 + 0.999892i $$0.504673\pi$$
$$492$$ 0 0
$$493$$ 1.39469 0.0628136
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 1.67087 0.0749487
$$498$$ 0 0
$$499$$ −31.5300 −1.41148 −0.705738 0.708472i $$-0.749385\pi$$
−0.705738 + 0.708472i $$0.749385\pi$$
$$500$$ 0 0
$$501$$ −8.69642 −0.388527
$$502$$ 0 0
$$503$$ −2.61135 −0.116434 −0.0582172 0.998304i $$-0.518542\pi$$
−0.0582172 + 0.998304i $$0.518542\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −1.00000 −0.0444116
$$508$$ 0 0
$$509$$ −2.27037 −0.100632 −0.0503161 0.998733i $$-0.516023\pi$$
−0.0503161 + 0.998733i $$0.516023\pi$$
$$510$$ 0 0
$$511$$ 6.86986 0.303905
$$512$$ 0 0
$$513$$ 6.58086 0.290552
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −4.05913 −0.178520
$$518$$ 0 0
$$519$$ 18.0069 0.790416
$$520$$ 0 0
$$521$$ 2.87185 0.125818 0.0629090 0.998019i $$-0.479962\pi$$
0.0629090 + 0.998019i $$0.479962\pi$$
$$522$$ 0 0
$$523$$ −14.1469 −0.618602 −0.309301 0.950964i $$-0.600095\pi$$
−0.309301 + 0.950964i $$0.600095\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 10.4205 0.453924
$$528$$ 0 0
$$529$$ −14.8768 −0.646817
$$530$$ 0 0
$$531$$ 10.8141 0.469291
$$532$$ 0 0
$$533$$ −7.58580 −0.328577
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 2.73457 0.118005
$$538$$ 0 0
$$539$$ −3.30667 −0.142428
$$540$$ 0 0
$$541$$ 14.5504 0.625570 0.312785 0.949824i $$-0.398738\pi$$
0.312785 + 0.949824i $$0.398738\pi$$
$$542$$ 0 0
$$543$$ −16.8757 −0.724205
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −13.5378 −0.578834 −0.289417 0.957203i $$-0.593461\pi$$
−0.289417 + 0.957203i $$0.593461\pi$$
$$548$$ 0 0
$$549$$ 11.4359 0.488073
$$550$$ 0 0
$$551$$ −1.94013 −0.0826524
$$552$$ 0 0
$$553$$ −3.42223 −0.145528
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 3.20098 0.135630 0.0678149 0.997698i $$-0.478397\pi$$
0.0678149 + 0.997698i $$0.478397\pi$$
$$558$$ 0 0
$$559$$ 0.444688 0.0188083
$$560$$ 0 0
$$561$$ −2.37704 −0.100359
$$562$$ 0 0
$$563$$ −14.0088 −0.590399 −0.295200 0.955436i $$-0.595386\pi$$
−0.295200 + 0.955436i $$0.595386\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −0.647407 −0.0271885
$$568$$ 0 0
$$569$$ 28.0571 1.17622 0.588108 0.808782i $$-0.299873\pi$$
0.588108 + 0.808782i $$0.299873\pi$$
$$570$$ 0 0
$$571$$ 43.4733 1.81930 0.909651 0.415373i $$-0.136349\pi$$
0.909651 + 0.415373i $$0.136349\pi$$
$$572$$ 0 0
$$573$$ −12.5896 −0.525939
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 41.6281 1.73300 0.866501 0.499175i $$-0.166364\pi$$
0.866501 + 0.499175i $$0.166364\pi$$
$$578$$ 0 0
$$579$$ −20.0728 −0.834198
$$580$$ 0 0
$$581$$ 3.46531 0.143765
$$582$$ 0 0
$$583$$ 6.39237 0.264745
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 41.2489 1.70252 0.851262 0.524741i $$-0.175838\pi$$
0.851262 + 0.524741i $$0.175838\pi$$
$$588$$ 0 0
$$589$$ −14.4958 −0.597289
$$590$$ 0 0
$$591$$ −15.6163 −0.642368
$$592$$ 0 0
$$593$$ −20.5416 −0.843543 −0.421771 0.906702i $$-0.638592\pi$$
−0.421771 + 0.906702i $$0.638592\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 15.7307 0.643816
$$598$$ 0 0
$$599$$ 14.0316 0.573315 0.286658 0.958033i $$-0.407456\pi$$
0.286658 + 0.958033i $$0.407456\pi$$
$$600$$ 0 0
$$601$$ −14.6610 −0.598035 −0.299017 0.954248i $$-0.596659\pi$$
−0.299017 + 0.954248i $$0.596659\pi$$
$$602$$ 0 0
$$603$$ 8.63864 0.351793
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −21.8875 −0.888388 −0.444194 0.895931i $$-0.646510\pi$$
−0.444194 + 0.895931i $$0.646510\pi$$
$$608$$ 0 0
$$609$$ 0.190865 0.00773423
$$610$$ 0 0
$$611$$ 8.07840 0.326817
$$612$$ 0 0
$$613$$ 24.0099 0.969749 0.484875 0.874584i $$-0.338865\pi$$
0.484875 + 0.874584i $$0.338865\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −2.21468 −0.0891595 −0.0445798 0.999006i $$-0.514195\pi$$
−0.0445798 + 0.999006i $$0.514195\pi$$
$$618$$ 0 0
$$619$$ 12.4348 0.499798 0.249899 0.968272i $$-0.419603\pi$$
0.249899 + 0.968272i $$0.419603\pi$$
$$620$$ 0 0
$$621$$ 2.85013 0.114372
$$622$$ 0 0
$$623$$ −3.23384 −0.129561
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 3.30667 0.132056
$$628$$ 0 0
$$629$$ −34.4684 −1.37434
$$630$$ 0 0
$$631$$ 26.4684 1.05369 0.526845 0.849961i $$-0.323375\pi$$
0.526845 + 0.849961i $$0.323375\pi$$
$$632$$ 0 0
$$633$$ −6.85013 −0.272268
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.58086 0.260743
$$638$$ 0 0
$$639$$ −2.58086 −0.102097
$$640$$ 0 0
$$641$$ −6.44852 −0.254701 −0.127351 0.991858i $$-0.540647\pi$$
−0.127351 + 0.991858i $$0.540647\pi$$
$$642$$ 0 0
$$643$$ 2.01863 0.0796071 0.0398035 0.999208i $$-0.487327\pi$$
0.0398035 + 0.999208i $$0.487327\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −0.142954 −0.00562012 −0.00281006 0.999996i $$-0.500894\pi$$
−0.00281006 + 0.999996i $$0.500894\pi$$
$$648$$ 0 0
$$649$$ 5.43371 0.213292
$$650$$ 0 0
$$651$$ 1.42606 0.0558915
$$652$$ 0 0
$$653$$ 22.1823 0.868062 0.434031 0.900898i $$-0.357091\pi$$
0.434031 + 0.900898i $$0.357091\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −10.6114 −0.413988
$$658$$ 0 0
$$659$$ 28.4989 1.11016 0.555079 0.831797i $$-0.312688\pi$$
0.555079 + 0.831797i $$0.312688\pi$$
$$660$$ 0 0
$$661$$ −21.8680 −0.850567 −0.425284 0.905060i $$-0.639826\pi$$
−0.425284 + 0.905060i $$0.639826\pi$$
$$662$$ 0 0
$$663$$ 4.73074 0.183727
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −0.840257 −0.0325349
$$668$$ 0 0
$$669$$ −1.15974 −0.0448382
$$670$$ 0 0
$$671$$ 5.74618 0.221829
$$672$$ 0 0
$$673$$ 10.0679 0.388089 0.194044 0.980993i $$-0.437839\pi$$
0.194044 + 0.980993i $$0.437839\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 27.7003 1.06461 0.532304 0.846554i $$-0.321326\pi$$
0.532304 + 0.846554i $$0.321326\pi$$
$$678$$ 0 0
$$679$$ −0.838272 −0.0321699
$$680$$ 0 0
$$681$$ −26.1207 −1.00095
$$682$$ 0 0
$$683$$ −7.73631 −0.296022 −0.148011 0.988986i $$-0.547287\pi$$
−0.148011 + 0.988986i $$0.547287\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 4.02062 0.153396
$$688$$ 0 0
$$689$$ −12.7220 −0.484669
$$690$$ 0 0
$$691$$ 46.7115 1.77699 0.888494 0.458888i $$-0.151752\pi$$
0.888494 + 0.458888i $$0.151752\pi$$
$$692$$ 0 0
$$693$$ −0.325301 −0.0123572
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 35.8864 1.35930
$$698$$ 0 0
$$699$$ 6.99507 0.264578
$$700$$ 0 0
$$701$$ −39.7670 −1.50198 −0.750990 0.660313i $$-0.770423\pi$$
−0.750990 + 0.660313i $$0.770423\pi$$
$$702$$ 0 0
$$703$$ 47.9485 1.80841
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 2.77482 0.104358
$$708$$ 0 0
$$709$$ −35.5988 −1.33694 −0.668470 0.743739i $$-0.733050\pi$$
−0.668470 + 0.743739i $$0.733050\pi$$
$$710$$ 0 0
$$711$$ 5.28605 0.198242
$$712$$ 0 0
$$713$$ −6.27803 −0.235114
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 15.4037 0.575262
$$718$$ 0 0
$$719$$ 38.6995 1.44325 0.721624 0.692285i $$-0.243396\pi$$
0.721624 + 0.692285i $$0.243396\pi$$
$$720$$ 0 0
$$721$$ 4.69730 0.174937
$$722$$ 0 0
$$723$$ −5.14987 −0.191526
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 19.8788 0.737263 0.368631 0.929576i $$-0.379826\pi$$
0.368631 + 0.929576i $$0.379826\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −2.10370 −0.0778083
$$732$$ 0 0
$$733$$ 14.2693 0.527047 0.263524 0.964653i $$-0.415115\pi$$
0.263524 + 0.964653i $$0.415115\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 4.34063 0.159889
$$738$$ 0 0
$$739$$ −12.3801 −0.455410 −0.227705 0.973730i $$-0.573122\pi$$
−0.227705 + 0.973730i $$0.573122\pi$$
$$740$$ 0 0
$$741$$ −6.58086 −0.241754
$$742$$ 0 0
$$743$$ 4.23321 0.155301 0.0776506 0.996981i $$-0.475258\pi$$
0.0776506 + 0.996981i $$0.475258\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −5.35259 −0.195841
$$748$$ 0 0
$$749$$ 6.56223 0.239779
$$750$$ 0 0
$$751$$ −20.6418 −0.753231 −0.376616 0.926370i $$-0.622912\pi$$
−0.376616 + 0.926370i $$0.622912\pi$$
$$752$$ 0 0
$$753$$ −17.5858 −0.640862
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −28.7033 −1.04324 −0.521620 0.853178i $$-0.674672\pi$$
−0.521620 + 0.853178i $$0.674672\pi$$
$$758$$ 0 0
$$759$$ 1.43209 0.0519817
$$760$$ 0 0
$$761$$ −6.53963 −0.237061 −0.118531 0.992950i $$-0.537818\pi$$
−0.118531 + 0.992950i $$0.537818\pi$$
$$762$$ 0 0
$$763$$ −11.2990 −0.409052
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −10.8141 −0.390473
$$768$$ 0 0
$$769$$ 7.58690 0.273591 0.136795 0.990599i $$-0.456320\pi$$
0.136795 + 0.990599i $$0.456320\pi$$
$$770$$ 0 0
$$771$$ −15.3421 −0.552532
$$772$$ 0 0
$$773$$ 20.7151 0.745069 0.372534 0.928018i $$-0.378489\pi$$
0.372534 + 0.928018i $$0.378489\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −4.71704 −0.169223
$$778$$ 0 0
$$779$$ −49.9211 −1.78861
$$780$$ 0 0
$$781$$ −1.29680 −0.0464031
$$782$$ 0 0
$$783$$ −0.294814 −0.0105358
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −52.0486 −1.85533 −0.927667 0.373410i $$-0.878189\pi$$
−0.927667 + 0.373410i $$0.878189\pi$$
$$788$$ 0 0
$$789$$ 21.0168 0.748217
$$790$$ 0 0
$$791$$ 10.2724 0.365243
$$792$$ 0 0
$$793$$ −11.4359 −0.406102
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −19.1796 −0.679377 −0.339689 0.940538i $$-0.610322\pi$$
−0.339689 + 0.940538i $$0.610322\pi$$
$$798$$ 0 0
$$799$$ −38.2168 −1.35201
$$800$$ 0 0
$$801$$ 4.99507 0.176492
$$802$$ 0 0
$$803$$ −5.33186 −0.188157
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 5.57210 0.196147
$$808$$ 0 0
$$809$$ 42.4803 1.49353 0.746763 0.665090i $$-0.231607\pi$$
0.746763 + 0.665090i $$0.231607\pi$$
$$810$$ 0 0
$$811$$ −21.5094 −0.755297 −0.377648 0.925949i $$-0.623267\pi$$
−0.377648 + 0.925949i $$0.623267\pi$$
$$812$$ 0 0
$$813$$ 5.50939 0.193223
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 2.92643 0.102383
$$818$$ 0 0
$$819$$ 0.647407 0.0226222
$$820$$ 0 0
$$821$$ 21.3067 0.743608 0.371804 0.928311i $$-0.378739\pi$$
0.371804 + 0.928311i $$0.378739\pi$$
$$822$$ 0 0
$$823$$ −7.24680 −0.252608 −0.126304 0.991992i $$-0.540311\pi$$
−0.126304 + 0.991992i $$0.540311\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 43.7076 1.51986 0.759932 0.650003i $$-0.225232\pi$$
0.759932 + 0.650003i $$0.225232\pi$$
$$828$$ 0 0
$$829$$ −24.3665 −0.846285 −0.423142 0.906063i $$-0.639073\pi$$
−0.423142 + 0.906063i $$0.639073\pi$$
$$830$$ 0 0
$$831$$ −29.5672 −1.02567
$$832$$ 0 0
$$833$$ −31.1323 −1.07867
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −2.20272 −0.0761371
$$838$$ 0 0
$$839$$ −18.0553 −0.623338 −0.311669 0.950191i $$-0.600888\pi$$
−0.311669 + 0.950191i $$0.600888\pi$$
$$840$$ 0 0
$$841$$ −28.9131 −0.997003
$$842$$ 0 0
$$843$$ 5.14111 0.177069
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 6.95802 0.239081
$$848$$ 0 0
$$849$$ 14.3509 0.492520
$$850$$ 0 0
$$851$$ 20.7662 0.711855
$$852$$ 0 0
$$853$$ 6.28679 0.215256 0.107628 0.994191i $$-0.465675\pi$$
0.107628 + 0.994191i $$0.465675\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −4.82074 −0.164673 −0.0823367 0.996605i $$-0.526238\pi$$
−0.0823367 + 0.996605i $$0.526238\pi$$
$$858$$ 0 0
$$859$$ 7.32420 0.249898 0.124949 0.992163i $$-0.460123\pi$$
0.124949 + 0.992163i $$0.460123\pi$$
$$860$$ 0 0
$$861$$ 4.91110 0.167370
$$862$$ 0 0
$$863$$ 14.0567 0.478495 0.239247 0.970959i $$-0.423099\pi$$
0.239247 + 0.970959i $$0.423099\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −5.37989 −0.182710
$$868$$ 0 0
$$869$$ 2.65607 0.0901009
$$870$$ 0 0
$$871$$ −8.63864 −0.292709
$$872$$ 0 0
$$873$$ 1.29481 0.0438228
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 12.6747 0.427994 0.213997 0.976834i $$-0.431352\pi$$
0.213997 + 0.976834i $$0.431352\pi$$
$$878$$ 0 0
$$879$$ −15.4516 −0.521170
$$880$$ 0 0
$$881$$ −27.0325 −0.910747 −0.455374 0.890300i $$-0.650494\pi$$
−0.455374 + 0.890300i $$0.650494\pi$$
$$882$$ 0 0
$$883$$ 8.14693 0.274166 0.137083 0.990560i $$-0.456227\pi$$
0.137083 + 0.990560i $$0.456227\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −26.4173 −0.887006 −0.443503 0.896273i $$-0.646264\pi$$
−0.443503 + 0.896273i $$0.646264\pi$$
$$888$$ 0 0
$$889$$ 6.46840 0.216943
$$890$$ 0 0
$$891$$ 0.502467 0.0168333
$$892$$ 0 0
$$893$$ 53.1628 1.77903
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −2.85013 −0.0951629
$$898$$ 0 0
$$899$$ 0.649392 0.0216585
$$900$$ 0 0
$$901$$ 60.1843 2.00503
$$902$$ 0 0
$$903$$ −0.287894 −0.00958052
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −7.12815 −0.236686 −0.118343 0.992973i $$-0.537758\pi$$
−0.118343 + 0.992973i $$0.537758\pi$$
$$908$$ 0 0
$$909$$ −4.28605 −0.142159
$$910$$ 0 0
$$911$$ 17.1911 0.569567 0.284783 0.958592i $$-0.408078\pi$$
0.284783 + 0.958592i $$0.408078\pi$$
$$912$$ 0 0
$$913$$ −2.68950 −0.0890095
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −10.5405 −0.348078
$$918$$ 0 0
$$919$$ 3.35888 0.110799 0.0553996 0.998464i $$-0.482357\pi$$
0.0553996 + 0.998464i $$0.482357\pi$$
$$920$$ 0 0
$$921$$ −2.12432 −0.0699988
$$922$$ 0 0
$$923$$ 2.58086 0.0849502
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −7.25556 −0.238304
$$928$$ 0 0
$$929$$ 7.75048 0.254285 0.127142 0.991884i $$-0.459419\pi$$
0.127142 + 0.991884i $$0.459419\pi$$
$$930$$ 0 0
$$931$$ 43.3078 1.41935
$$932$$ 0 0
$$933$$ −32.6331 −1.06836
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 5.75320 0.187949 0.0939744 0.995575i $$-0.470043\pi$$
0.0939744 + 0.995575i $$0.470043\pi$$
$$938$$ 0 0
$$939$$ 18.7318 0.611291
$$940$$ 0 0
$$941$$ 1.43209 0.0466850 0.0233425 0.999728i $$-0.492569\pi$$
0.0233425 + 0.999728i $$0.492569\pi$$
$$942$$ 0 0
$$943$$ −21.6205 −0.704060
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −46.6830 −1.51699 −0.758496 0.651677i $$-0.774066\pi$$
−0.758496 + 0.651677i $$0.774066\pi$$
$$948$$ 0 0
$$949$$ 10.6114 0.344459
$$950$$ 0 0
$$951$$ 26.3452 0.854301
$$952$$ 0 0
$$953$$ −13.1145 −0.424819 −0.212409 0.977181i $$-0.568131\pi$$
−0.212409 + 0.977181i $$0.568131\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −0.148134 −0.00478850
$$958$$ 0 0
$$959$$ 3.06591 0.0990033
$$960$$ 0 0
$$961$$ −26.1480 −0.843485
$$962$$ 0 0
$$963$$ −10.1362 −0.326634
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 23.4765 0.754954 0.377477 0.926019i $$-0.376792\pi$$
0.377477 + 0.926019i $$0.376792\pi$$
$$968$$ 0 0
$$969$$ 31.1323 1.00012
$$970$$ 0 0
$$971$$ 57.3687 1.84105 0.920525 0.390683i $$-0.127761\pi$$
0.920525 + 0.390683i $$0.127761\pi$$
$$972$$ 0 0
$$973$$ 11.3047 0.362411
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −52.2961 −1.67310 −0.836550 0.547891i $$-0.815431\pi$$
−0.836550 + 0.547891i $$0.815431\pi$$
$$978$$ 0 0
$$979$$ 2.50986 0.0802154
$$980$$ 0 0
$$981$$ 17.4527 0.557222
$$982$$ 0 0
$$983$$ −17.5074 −0.558399 −0.279200 0.960233i $$-0.590069\pi$$
−0.279200 + 0.960233i $$0.590069\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −5.23001 −0.166473
$$988$$ 0 0
$$989$$ 1.26742 0.0403015
$$990$$ 0 0
$$991$$ −49.4527 −1.57092 −0.785459 0.618914i $$-0.787573\pi$$
−0.785459 + 0.618914i $$0.787573\pi$$
$$992$$ 0 0
$$993$$ −24.3116 −0.771505
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 40.0493 1.26837 0.634186 0.773180i $$-0.281335\pi$$
0.634186 + 0.773180i $$0.281335\pi$$
$$998$$ 0 0
$$999$$ 7.28605 0.230520
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 7800.2.a.bu.1.3 4
5.4 even 2 7800.2.a.bx.1.2 yes 4

By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bu.1.3 4 1.1 even 1 trivial
7800.2.a.bx.1.2 yes 4 5.4 even 2