Properties

 Label 234.4.a.h.1.1 Level $234$ Weight $4$ Character 234.1 Self dual yes Analytic conductor $13.806$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,4,Mod(1,234)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("234.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$234 = 2 \cdot 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 234.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$13.8064469413$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 78) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 234.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.00000 q^{2} +4.00000 q^{4} -10.0000 q^{5} -8.00000 q^{7} +8.00000 q^{8} +O(q^{10})$$ $$q+2.00000 q^{2} +4.00000 q^{4} -10.0000 q^{5} -8.00000 q^{7} +8.00000 q^{8} -20.0000 q^{10} -40.0000 q^{11} +13.0000 q^{13} -16.0000 q^{14} +16.0000 q^{16} -130.000 q^{17} -20.0000 q^{19} -40.0000 q^{20} -80.0000 q^{22} -25.0000 q^{25} +26.0000 q^{26} -32.0000 q^{28} +18.0000 q^{29} -184.000 q^{31} +32.0000 q^{32} -260.000 q^{34} +80.0000 q^{35} -74.0000 q^{37} -40.0000 q^{38} -80.0000 q^{40} +362.000 q^{41} +76.0000 q^{43} -160.000 q^{44} +452.000 q^{47} -279.000 q^{49} -50.0000 q^{50} +52.0000 q^{52} -382.000 q^{53} +400.000 q^{55} -64.0000 q^{56} +36.0000 q^{58} -464.000 q^{59} +358.000 q^{61} -368.000 q^{62} +64.0000 q^{64} -130.000 q^{65} -700.000 q^{67} -520.000 q^{68} +160.000 q^{70} +748.000 q^{71} +1058.00 q^{73} -148.000 q^{74} -80.0000 q^{76} +320.000 q^{77} -976.000 q^{79} -160.000 q^{80} +724.000 q^{82} +1008.00 q^{83} +1300.00 q^{85} +152.000 q^{86} -320.000 q^{88} +386.000 q^{89} -104.000 q^{91} +904.000 q^{94} +200.000 q^{95} -614.000 q^{97} -558.000 q^{98} +O(q^{100})$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 0.707107
$$3$$ 0 0
$$4$$ 4.00000 0.500000
$$5$$ −10.0000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0 0
$$7$$ −8.00000 −0.431959 −0.215980 0.976398i $$-0.569295\pi$$
−0.215980 + 0.976398i $$0.569295\pi$$
$$8$$ 8.00000 0.353553
$$9$$ 0 0
$$10$$ −20.0000 −0.632456
$$11$$ −40.0000 −1.09640 −0.548202 0.836346i $$-0.684688\pi$$
−0.548202 + 0.836346i $$0.684688\pi$$
$$12$$ 0 0
$$13$$ 13.0000 0.277350
$$14$$ −16.0000 −0.305441
$$15$$ 0 0
$$16$$ 16.0000 0.250000
$$17$$ −130.000 −1.85468 −0.927342 0.374215i $$-0.877912\pi$$
−0.927342 + 0.374215i $$0.877912\pi$$
$$18$$ 0 0
$$19$$ −20.0000 −0.241490 −0.120745 0.992684i $$-0.538528\pi$$
−0.120745 + 0.992684i $$0.538528\pi$$
$$20$$ −40.0000 −0.447214
$$21$$ 0 0
$$22$$ −80.0000 −0.775275
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ −25.0000 −0.200000
$$26$$ 26.0000 0.196116
$$27$$ 0 0
$$28$$ −32.0000 −0.215980
$$29$$ 18.0000 0.115259 0.0576296 0.998338i $$-0.481646\pi$$
0.0576296 + 0.998338i $$0.481646\pi$$
$$30$$ 0 0
$$31$$ −184.000 −1.06604 −0.533022 0.846101i $$-0.678944\pi$$
−0.533022 + 0.846101i $$0.678944\pi$$
$$32$$ 32.0000 0.176777
$$33$$ 0 0
$$34$$ −260.000 −1.31146
$$35$$ 80.0000 0.386356
$$36$$ 0 0
$$37$$ −74.0000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ −40.0000 −0.170759
$$39$$ 0 0
$$40$$ −80.0000 −0.316228
$$41$$ 362.000 1.37890 0.689450 0.724333i $$-0.257852\pi$$
0.689450 + 0.724333i $$0.257852\pi$$
$$42$$ 0 0
$$43$$ 76.0000 0.269532 0.134766 0.990877i $$-0.456972\pi$$
0.134766 + 0.990877i $$0.456972\pi$$
$$44$$ −160.000 −0.548202
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 452.000 1.40279 0.701393 0.712774i $$-0.252562\pi$$
0.701393 + 0.712774i $$0.252562\pi$$
$$48$$ 0 0
$$49$$ −279.000 −0.813411
$$50$$ −50.0000 −0.141421
$$51$$ 0 0
$$52$$ 52.0000 0.138675
$$53$$ −382.000 −0.990033 −0.495016 0.868884i $$-0.664838\pi$$
−0.495016 + 0.868884i $$0.664838\pi$$
$$54$$ 0 0
$$55$$ 400.000 0.980654
$$56$$ −64.0000 −0.152721
$$57$$ 0 0
$$58$$ 36.0000 0.0815005
$$59$$ −464.000 −1.02386 −0.511929 0.859028i $$-0.671069\pi$$
−0.511929 + 0.859028i $$0.671069\pi$$
$$60$$ 0 0
$$61$$ 358.000 0.751430 0.375715 0.926735i $$-0.377397\pi$$
0.375715 + 0.926735i $$0.377397\pi$$
$$62$$ −368.000 −0.753807
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −130.000 −0.248069
$$66$$ 0 0
$$67$$ −700.000 −1.27640 −0.638199 0.769872i $$-0.720320\pi$$
−0.638199 + 0.769872i $$0.720320\pi$$
$$68$$ −520.000 −0.927342
$$69$$ 0 0
$$70$$ 160.000 0.273195
$$71$$ 748.000 1.25030 0.625150 0.780505i $$-0.285038\pi$$
0.625150 + 0.780505i $$0.285038\pi$$
$$72$$ 0 0
$$73$$ 1058.00 1.69629 0.848147 0.529760i $$-0.177718\pi$$
0.848147 + 0.529760i $$0.177718\pi$$
$$74$$ −148.000 −0.232495
$$75$$ 0 0
$$76$$ −80.0000 −0.120745
$$77$$ 320.000 0.473602
$$78$$ 0 0
$$79$$ −976.000 −1.38998 −0.694991 0.719018i $$-0.744592\pi$$
−0.694991 + 0.719018i $$0.744592\pi$$
$$80$$ −160.000 −0.223607
$$81$$ 0 0
$$82$$ 724.000 0.975030
$$83$$ 1008.00 1.33304 0.666520 0.745487i $$-0.267783\pi$$
0.666520 + 0.745487i $$0.267783\pi$$
$$84$$ 0 0
$$85$$ 1300.00 1.65888
$$86$$ 152.000 0.190588
$$87$$ 0 0
$$88$$ −320.000 −0.387638
$$89$$ 386.000 0.459729 0.229865 0.973223i $$-0.426172\pi$$
0.229865 + 0.973223i $$0.426172\pi$$
$$90$$ 0 0
$$91$$ −104.000 −0.119804
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 904.000 0.991920
$$95$$ 200.000 0.215995
$$96$$ 0 0
$$97$$ −614.000 −0.642704 −0.321352 0.946960i $$-0.604137\pi$$
−0.321352 + 0.946960i $$0.604137\pi$$
$$98$$ −558.000 −0.575168
$$99$$ 0 0
$$100$$ −100.000 −0.100000
$$101$$ −518.000 −0.510326 −0.255163 0.966898i $$-0.582129\pi$$
−0.255163 + 0.966898i $$0.582129\pi$$
$$102$$ 0 0
$$103$$ 112.000 0.107143 0.0535713 0.998564i $$-0.482940\pi$$
0.0535713 + 0.998564i $$0.482940\pi$$
$$104$$ 104.000 0.0980581
$$105$$ 0 0
$$106$$ −764.000 −0.700059
$$107$$ 372.000 0.336099 0.168050 0.985779i $$-0.446253\pi$$
0.168050 + 0.985779i $$0.446253\pi$$
$$108$$ 0 0
$$109$$ 934.000 0.820743 0.410371 0.911918i $$-0.365399\pi$$
0.410371 + 0.911918i $$0.365399\pi$$
$$110$$ 800.000 0.693427
$$111$$ 0 0
$$112$$ −128.000 −0.107990
$$113$$ −1914.00 −1.59340 −0.796699 0.604376i $$-0.793422\pi$$
−0.796699 + 0.604376i $$0.793422\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 72.0000 0.0576296
$$117$$ 0 0
$$118$$ −928.000 −0.723977
$$119$$ 1040.00 0.801148
$$120$$ 0 0
$$121$$ 269.000 0.202104
$$122$$ 716.000 0.531341
$$123$$ 0 0
$$124$$ −736.000 −0.533022
$$125$$ 1500.00 1.07331
$$126$$ 0 0
$$127$$ 1296.00 0.905523 0.452761 0.891632i $$-0.350439\pi$$
0.452761 + 0.891632i $$0.350439\pi$$
$$128$$ 128.000 0.0883883
$$129$$ 0 0
$$130$$ −260.000 −0.175412
$$131$$ 892.000 0.594919 0.297460 0.954734i $$-0.403861\pi$$
0.297460 + 0.954734i $$0.403861\pi$$
$$132$$ 0 0
$$133$$ 160.000 0.104314
$$134$$ −1400.00 −0.902549
$$135$$ 0 0
$$136$$ −1040.00 −0.655730
$$137$$ −2326.00 −1.45054 −0.725269 0.688466i $$-0.758284\pi$$
−0.725269 + 0.688466i $$0.758284\pi$$
$$138$$ 0 0
$$139$$ 1932.00 1.17892 0.589461 0.807797i $$-0.299340\pi$$
0.589461 + 0.807797i $$0.299340\pi$$
$$140$$ 320.000 0.193178
$$141$$ 0 0
$$142$$ 1496.00 0.884095
$$143$$ −520.000 −0.304088
$$144$$ 0 0
$$145$$ −180.000 −0.103091
$$146$$ 2116.00 1.19946
$$147$$ 0 0
$$148$$ −296.000 −0.164399
$$149$$ −882.000 −0.484941 −0.242471 0.970159i $$-0.577958\pi$$
−0.242471 + 0.970159i $$0.577958\pi$$
$$150$$ 0 0
$$151$$ −1776.00 −0.957145 −0.478572 0.878048i $$-0.658846\pi$$
−0.478572 + 0.878048i $$0.658846\pi$$
$$152$$ −160.000 −0.0853797
$$153$$ 0 0
$$154$$ 640.000 0.334887
$$155$$ 1840.00 0.953499
$$156$$ 0 0
$$157$$ −2410.00 −1.22509 −0.612544 0.790436i $$-0.709854\pi$$
−0.612544 + 0.790436i $$0.709854\pi$$
$$158$$ −1952.00 −0.982866
$$159$$ 0 0
$$160$$ −320.000 −0.158114
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 3212.00 1.54346 0.771728 0.635953i $$-0.219393\pi$$
0.771728 + 0.635953i $$0.219393\pi$$
$$164$$ 1448.00 0.689450
$$165$$ 0 0
$$166$$ 2016.00 0.942602
$$167$$ −1668.00 −0.772896 −0.386448 0.922311i $$-0.626298\pi$$
−0.386448 + 0.922311i $$0.626298\pi$$
$$168$$ 0 0
$$169$$ 169.000 0.0769231
$$170$$ 2600.00 1.17301
$$171$$ 0 0
$$172$$ 304.000 0.134766
$$173$$ −3598.00 −1.58122 −0.790609 0.612321i $$-0.790236\pi$$
−0.790609 + 0.612321i $$0.790236\pi$$
$$174$$ 0 0
$$175$$ 200.000 0.0863919
$$176$$ −640.000 −0.274101
$$177$$ 0 0
$$178$$ 772.000 0.325078
$$179$$ −1068.00 −0.445956 −0.222978 0.974824i $$-0.571578\pi$$
−0.222978 + 0.974824i $$0.571578\pi$$
$$180$$ 0 0
$$181$$ −4786.00 −1.96542 −0.982709 0.185158i $$-0.940720\pi$$
−0.982709 + 0.185158i $$0.940720\pi$$
$$182$$ −208.000 −0.0847142
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 740.000 0.294086
$$186$$ 0 0
$$187$$ 5200.00 2.03348
$$188$$ 1808.00 0.701393
$$189$$ 0 0
$$190$$ 400.000 0.152732
$$191$$ 1312.00 0.497031 0.248516 0.968628i $$-0.420057\pi$$
0.248516 + 0.968628i $$0.420057\pi$$
$$192$$ 0 0
$$193$$ −350.000 −0.130537 −0.0652683 0.997868i $$-0.520790\pi$$
−0.0652683 + 0.997868i $$0.520790\pi$$
$$194$$ −1228.00 −0.454460
$$195$$ 0 0
$$196$$ −1116.00 −0.406706
$$197$$ 342.000 0.123688 0.0618439 0.998086i $$-0.480302\pi$$
0.0618439 + 0.998086i $$0.480302\pi$$
$$198$$ 0 0
$$199$$ −3368.00 −1.19975 −0.599877 0.800092i $$-0.704784\pi$$
−0.599877 + 0.800092i $$0.704784\pi$$
$$200$$ −200.000 −0.0707107
$$201$$ 0 0
$$202$$ −1036.00 −0.360855
$$203$$ −144.000 −0.0497873
$$204$$ 0 0
$$205$$ −3620.00 −1.23333
$$206$$ 224.000 0.0757613
$$207$$ 0 0
$$208$$ 208.000 0.0693375
$$209$$ 800.000 0.264771
$$210$$ 0 0
$$211$$ −2004.00 −0.653844 −0.326922 0.945051i $$-0.606011\pi$$
−0.326922 + 0.945051i $$0.606011\pi$$
$$212$$ −1528.00 −0.495016
$$213$$ 0 0
$$214$$ 744.000 0.237658
$$215$$ −760.000 −0.241077
$$216$$ 0 0
$$217$$ 1472.00 0.460488
$$218$$ 1868.00 0.580353
$$219$$ 0 0
$$220$$ 1600.00 0.490327
$$221$$ −1690.00 −0.514397
$$222$$ 0 0
$$223$$ −5608.00 −1.68403 −0.842017 0.539451i $$-0.818632\pi$$
−0.842017 + 0.539451i $$0.818632\pi$$
$$224$$ −256.000 −0.0763604
$$225$$ 0 0
$$226$$ −3828.00 −1.12670
$$227$$ 1928.00 0.563726 0.281863 0.959455i $$-0.409048\pi$$
0.281863 + 0.959455i $$0.409048\pi$$
$$228$$ 0 0
$$229$$ −3938.00 −1.13638 −0.568189 0.822898i $$-0.692356\pi$$
−0.568189 + 0.822898i $$0.692356\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 144.000 0.0407503
$$233$$ −2562.00 −0.720353 −0.360176 0.932884i $$-0.617283\pi$$
−0.360176 + 0.932884i $$0.617283\pi$$
$$234$$ 0 0
$$235$$ −4520.00 −1.25469
$$236$$ −1856.00 −0.511929
$$237$$ 0 0
$$238$$ 2080.00 0.566497
$$239$$ −7164.00 −1.93891 −0.969457 0.245260i $$-0.921127\pi$$
−0.969457 + 0.245260i $$0.921127\pi$$
$$240$$ 0 0
$$241$$ −6182.00 −1.65236 −0.826178 0.563410i $$-0.809489\pi$$
−0.826178 + 0.563410i $$0.809489\pi$$
$$242$$ 538.000 0.142909
$$243$$ 0 0
$$244$$ 1432.00 0.375715
$$245$$ 2790.00 0.727537
$$246$$ 0 0
$$247$$ −260.000 −0.0669773
$$248$$ −1472.00 −0.376904
$$249$$ 0 0
$$250$$ 3000.00 0.758947
$$251$$ 1396.00 0.351055 0.175527 0.984475i $$-0.443837\pi$$
0.175527 + 0.984475i $$0.443837\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 2592.00 0.640301
$$255$$ 0 0
$$256$$ 256.000 0.0625000
$$257$$ −6906.00 −1.67620 −0.838102 0.545514i $$-0.816335\pi$$
−0.838102 + 0.545514i $$0.816335\pi$$
$$258$$ 0 0
$$259$$ 592.000 0.142027
$$260$$ −520.000 −0.124035
$$261$$ 0 0
$$262$$ 1784.00 0.420671
$$263$$ 6848.00 1.60557 0.802787 0.596266i $$-0.203350\pi$$
0.802787 + 0.596266i $$0.203350\pi$$
$$264$$ 0 0
$$265$$ 3820.00 0.885512
$$266$$ 320.000 0.0737611
$$267$$ 0 0
$$268$$ −2800.00 −0.638199
$$269$$ 6034.00 1.36766 0.683828 0.729643i $$-0.260314\pi$$
0.683828 + 0.729643i $$0.260314\pi$$
$$270$$ 0 0
$$271$$ 4832.00 1.08311 0.541556 0.840665i $$-0.317836\pi$$
0.541556 + 0.840665i $$0.317836\pi$$
$$272$$ −2080.00 −0.463671
$$273$$ 0 0
$$274$$ −4652.00 −1.02568
$$275$$ 1000.00 0.219281
$$276$$ 0 0
$$277$$ −4082.00 −0.885428 −0.442714 0.896663i $$-0.645984\pi$$
−0.442714 + 0.896663i $$0.645984\pi$$
$$278$$ 3864.00 0.833623
$$279$$ 0 0
$$280$$ 640.000 0.136598
$$281$$ −3350.00 −0.711189 −0.355595 0.934640i $$-0.615722\pi$$
−0.355595 + 0.934640i $$0.615722\pi$$
$$282$$ 0 0
$$283$$ 7796.00 1.63754 0.818770 0.574121i $$-0.194656\pi$$
0.818770 + 0.574121i $$0.194656\pi$$
$$284$$ 2992.00 0.625150
$$285$$ 0 0
$$286$$ −1040.00 −0.215023
$$287$$ −2896.00 −0.595629
$$288$$ 0 0
$$289$$ 11987.0 2.43985
$$290$$ −360.000 −0.0728963
$$291$$ 0 0
$$292$$ 4232.00 0.848147
$$293$$ −3922.00 −0.781999 −0.390999 0.920391i $$-0.627871\pi$$
−0.390999 + 0.920391i $$0.627871\pi$$
$$294$$ 0 0
$$295$$ 4640.00 0.915767
$$296$$ −592.000 −0.116248
$$297$$ 0 0
$$298$$ −1764.00 −0.342905
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −608.000 −0.116427
$$302$$ −3552.00 −0.676803
$$303$$ 0 0
$$304$$ −320.000 −0.0603726
$$305$$ −3580.00 −0.672099
$$306$$ 0 0
$$307$$ 5956.00 1.10725 0.553627 0.832765i $$-0.313243\pi$$
0.553627 + 0.832765i $$0.313243\pi$$
$$308$$ 1280.00 0.236801
$$309$$ 0 0
$$310$$ 3680.00 0.674226
$$311$$ −2352.00 −0.428841 −0.214421 0.976741i $$-0.568786\pi$$
−0.214421 + 0.976741i $$0.568786\pi$$
$$312$$ 0 0
$$313$$ 8442.00 1.52450 0.762252 0.647280i $$-0.224093\pi$$
0.762252 + 0.647280i $$0.224093\pi$$
$$314$$ −4820.00 −0.866269
$$315$$ 0 0
$$316$$ −3904.00 −0.694991
$$317$$ 5550.00 0.983341 0.491670 0.870781i $$-0.336386\pi$$
0.491670 + 0.870781i $$0.336386\pi$$
$$318$$ 0 0
$$319$$ −720.000 −0.126371
$$320$$ −640.000 −0.111803
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2600.00 0.447888
$$324$$ 0 0
$$325$$ −325.000 −0.0554700
$$326$$ 6424.00 1.09139
$$327$$ 0 0
$$328$$ 2896.00 0.487515
$$329$$ −3616.00 −0.605947
$$330$$ 0 0
$$331$$ 140.000 0.0232480 0.0116240 0.999932i $$-0.496300\pi$$
0.0116240 + 0.999932i $$0.496300\pi$$
$$332$$ 4032.00 0.666520
$$333$$ 0 0
$$334$$ −3336.00 −0.546520
$$335$$ 7000.00 1.14164
$$336$$ 0 0
$$337$$ −6174.00 −0.997980 −0.498990 0.866608i $$-0.666296\pi$$
−0.498990 + 0.866608i $$0.666296\pi$$
$$338$$ 338.000 0.0543928
$$339$$ 0 0
$$340$$ 5200.00 0.829440
$$341$$ 7360.00 1.16882
$$342$$ 0 0
$$343$$ 4976.00 0.783320
$$344$$ 608.000 0.0952941
$$345$$ 0 0
$$346$$ −7196.00 −1.11809
$$347$$ 2988.00 0.462260 0.231130 0.972923i $$-0.425758\pi$$
0.231130 + 0.972923i $$0.425758\pi$$
$$348$$ 0 0
$$349$$ −162.000 −0.0248472 −0.0124236 0.999923i $$-0.503955\pi$$
−0.0124236 + 0.999923i $$0.503955\pi$$
$$350$$ 400.000 0.0610883
$$351$$ 0 0
$$352$$ −1280.00 −0.193819
$$353$$ 10754.0 1.62147 0.810733 0.585416i $$-0.199069\pi$$
0.810733 + 0.585416i $$0.199069\pi$$
$$354$$ 0 0
$$355$$ −7480.00 −1.11830
$$356$$ 1544.00 0.229865
$$357$$ 0 0
$$358$$ −2136.00 −0.315338
$$359$$ −3588.00 −0.527486 −0.263743 0.964593i $$-0.584957\pi$$
−0.263743 + 0.964593i $$0.584957\pi$$
$$360$$ 0 0
$$361$$ −6459.00 −0.941682
$$362$$ −9572.00 −1.38976
$$363$$ 0 0
$$364$$ −416.000 −0.0599020
$$365$$ −10580.0 −1.51721
$$366$$ 0 0
$$367$$ 11272.0 1.60325 0.801626 0.597826i $$-0.203968\pi$$
0.801626 + 0.597826i $$0.203968\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 1480.00 0.207950
$$371$$ 3056.00 0.427654
$$372$$ 0 0
$$373$$ −10914.0 −1.51503 −0.757514 0.652819i $$-0.773586\pi$$
−0.757514 + 0.652819i $$0.773586\pi$$
$$374$$ 10400.0 1.43789
$$375$$ 0 0
$$376$$ 3616.00 0.495960
$$377$$ 234.000 0.0319671
$$378$$ 0 0
$$379$$ 8100.00 1.09781 0.548904 0.835886i $$-0.315045\pi$$
0.548904 + 0.835886i $$0.315045\pi$$
$$380$$ 800.000 0.107998
$$381$$ 0 0
$$382$$ 2624.00 0.351454
$$383$$ −6180.00 −0.824499 −0.412250 0.911071i $$-0.635257\pi$$
−0.412250 + 0.911071i $$0.635257\pi$$
$$384$$ 0 0
$$385$$ −3200.00 −0.423603
$$386$$ −700.000 −0.0923033
$$387$$ 0 0
$$388$$ −2456.00 −0.321352
$$389$$ 7522.00 0.980413 0.490206 0.871606i $$-0.336921\pi$$
0.490206 + 0.871606i $$0.336921\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −2232.00 −0.287584
$$393$$ 0 0
$$394$$ 684.000 0.0874605
$$395$$ 9760.00 1.24324
$$396$$ 0 0
$$397$$ 6078.00 0.768378 0.384189 0.923254i $$-0.374481\pi$$
0.384189 + 0.923254i $$0.374481\pi$$
$$398$$ −6736.00 −0.848355
$$399$$ 0 0
$$400$$ −400.000 −0.0500000
$$401$$ −1830.00 −0.227895 −0.113947 0.993487i $$-0.536350\pi$$
−0.113947 + 0.993487i $$0.536350\pi$$
$$402$$ 0 0
$$403$$ −2392.00 −0.295668
$$404$$ −2072.00 −0.255163
$$405$$ 0 0
$$406$$ −288.000 −0.0352049
$$407$$ 2960.00 0.360496
$$408$$ 0 0
$$409$$ 12434.0 1.50323 0.751616 0.659601i $$-0.229275\pi$$
0.751616 + 0.659601i $$0.229275\pi$$
$$410$$ −7240.00 −0.872093
$$411$$ 0 0
$$412$$ 448.000 0.0535713
$$413$$ 3712.00 0.442265
$$414$$ 0 0
$$415$$ −10080.0 −1.19231
$$416$$ 416.000 0.0490290
$$417$$ 0 0
$$418$$ 1600.00 0.187221
$$419$$ 14188.0 1.65425 0.827123 0.562021i $$-0.189976\pi$$
0.827123 + 0.562021i $$0.189976\pi$$
$$420$$ 0 0
$$421$$ 8638.00 0.999977 0.499989 0.866032i $$-0.333338\pi$$
0.499989 + 0.866032i $$0.333338\pi$$
$$422$$ −4008.00 −0.462337
$$423$$ 0 0
$$424$$ −3056.00 −0.350029
$$425$$ 3250.00 0.370937
$$426$$ 0 0
$$427$$ −2864.00 −0.324587
$$428$$ 1488.00 0.168050
$$429$$ 0 0
$$430$$ −1520.00 −0.170467
$$431$$ −4292.00 −0.479671 −0.239836 0.970813i $$-0.577094\pi$$
−0.239836 + 0.970813i $$0.577094\pi$$
$$432$$ 0 0
$$433$$ −5982.00 −0.663918 −0.331959 0.943294i $$-0.607710\pi$$
−0.331959 + 0.943294i $$0.607710\pi$$
$$434$$ 2944.00 0.325614
$$435$$ 0 0
$$436$$ 3736.00 0.410371
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 256.000 0.0278319 0.0139160 0.999903i $$-0.495570\pi$$
0.0139160 + 0.999903i $$0.495570\pi$$
$$440$$ 3200.00 0.346714
$$441$$ 0 0
$$442$$ −3380.00 −0.363733
$$443$$ −12556.0 −1.34662 −0.673311 0.739359i $$-0.735128\pi$$
−0.673311 + 0.739359i $$0.735128\pi$$
$$444$$ 0 0
$$445$$ −3860.00 −0.411194
$$446$$ −11216.0 −1.19079
$$447$$ 0 0
$$448$$ −512.000 −0.0539949
$$449$$ −5574.00 −0.585865 −0.292932 0.956133i $$-0.594631\pi$$
−0.292932 + 0.956133i $$0.594631\pi$$
$$450$$ 0 0
$$451$$ −14480.0 −1.51183
$$452$$ −7656.00 −0.796699
$$453$$ 0 0
$$454$$ 3856.00 0.398615
$$455$$ 1040.00 0.107156
$$456$$ 0 0
$$457$$ 1266.00 0.129586 0.0647932 0.997899i $$-0.479361\pi$$
0.0647932 + 0.997899i $$0.479361\pi$$
$$458$$ −7876.00 −0.803540
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −7554.00 −0.763178 −0.381589 0.924332i $$-0.624623\pi$$
−0.381589 + 0.924332i $$0.624623\pi$$
$$462$$ 0 0
$$463$$ −6752.00 −0.677737 −0.338868 0.940834i $$-0.610044\pi$$
−0.338868 + 0.940834i $$0.610044\pi$$
$$464$$ 288.000 0.0288148
$$465$$ 0 0
$$466$$ −5124.00 −0.509366
$$467$$ −7924.00 −0.785180 −0.392590 0.919714i $$-0.628421\pi$$
−0.392590 + 0.919714i $$0.628421\pi$$
$$468$$ 0 0
$$469$$ 5600.00 0.551352
$$470$$ −9040.00 −0.887200
$$471$$ 0 0
$$472$$ −3712.00 −0.361989
$$473$$ −3040.00 −0.295517
$$474$$ 0 0
$$475$$ 500.000 0.0482980
$$476$$ 4160.00 0.400574
$$477$$ 0 0
$$478$$ −14328.0 −1.37102
$$479$$ 11084.0 1.05729 0.528644 0.848844i $$-0.322701\pi$$
0.528644 + 0.848844i $$0.322701\pi$$
$$480$$ 0 0
$$481$$ −962.000 −0.0911922
$$482$$ −12364.0 −1.16839
$$483$$ 0 0
$$484$$ 1076.00 0.101052
$$485$$ 6140.00 0.574852
$$486$$ 0 0
$$487$$ 4432.00 0.412388 0.206194 0.978511i $$-0.433892\pi$$
0.206194 + 0.978511i $$0.433892\pi$$
$$488$$ 2864.00 0.265670
$$489$$ 0 0
$$490$$ 5580.00 0.514446
$$491$$ 1140.00 0.104781 0.0523905 0.998627i $$-0.483316\pi$$
0.0523905 + 0.998627i $$0.483316\pi$$
$$492$$ 0 0
$$493$$ −2340.00 −0.213769
$$494$$ −520.000 −0.0473601
$$495$$ 0 0
$$496$$ −2944.00 −0.266511
$$497$$ −5984.00 −0.540079
$$498$$ 0 0
$$499$$ 1764.00 0.158251 0.0791257 0.996865i $$-0.474787\pi$$
0.0791257 + 0.996865i $$0.474787\pi$$
$$500$$ 6000.00 0.536656
$$501$$ 0 0
$$502$$ 2792.00 0.248233
$$503$$ −16976.0 −1.50482 −0.752408 0.658697i $$-0.771108\pi$$
−0.752408 + 0.658697i $$0.771108\pi$$
$$504$$ 0 0
$$505$$ 5180.00 0.456449
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 5184.00 0.452761
$$509$$ −9474.00 −0.825005 −0.412503 0.910956i $$-0.635345\pi$$
−0.412503 + 0.910956i $$0.635345\pi$$
$$510$$ 0 0
$$511$$ −8464.00 −0.732731
$$512$$ 512.000 0.0441942
$$513$$ 0 0
$$514$$ −13812.0 −1.18526
$$515$$ −1120.00 −0.0958313
$$516$$ 0 0
$$517$$ −18080.0 −1.53802
$$518$$ 1184.00 0.100429
$$519$$ 0 0
$$520$$ −1040.00 −0.0877058
$$521$$ −14114.0 −1.18684 −0.593422 0.804892i $$-0.702223\pi$$
−0.593422 + 0.804892i $$0.702223\pi$$
$$522$$ 0 0
$$523$$ 20284.0 1.69590 0.847952 0.530074i $$-0.177836\pi$$
0.847952 + 0.530074i $$0.177836\pi$$
$$524$$ 3568.00 0.297460
$$525$$ 0 0
$$526$$ 13696.0 1.13531
$$527$$ 23920.0 1.97718
$$528$$ 0 0
$$529$$ −12167.0 −1.00000
$$530$$ 7640.00 0.626152
$$531$$ 0 0
$$532$$ 640.000 0.0521570
$$533$$ 4706.00 0.382438
$$534$$ 0 0
$$535$$ −3720.00 −0.300616
$$536$$ −5600.00 −0.451275
$$537$$ 0 0
$$538$$ 12068.0 0.967079
$$539$$ 11160.0 0.891828
$$540$$ 0 0
$$541$$ −14362.0 −1.14135 −0.570675 0.821176i $$-0.693318\pi$$
−0.570675 + 0.821176i $$0.693318\pi$$
$$542$$ 9664.00 0.765875
$$543$$ 0 0
$$544$$ −4160.00 −0.327865
$$545$$ −9340.00 −0.734095
$$546$$ 0 0
$$547$$ −20956.0 −1.63805 −0.819025 0.573757i $$-0.805485\pi$$
−0.819025 + 0.573757i $$0.805485\pi$$
$$548$$ −9304.00 −0.725269
$$549$$ 0 0
$$550$$ 2000.00 0.155055
$$551$$ −360.000 −0.0278340
$$552$$ 0 0
$$553$$ 7808.00 0.600416
$$554$$ −8164.00 −0.626092
$$555$$ 0 0
$$556$$ 7728.00 0.589461
$$557$$ 4134.00 0.314476 0.157238 0.987561i $$-0.449741\pi$$
0.157238 + 0.987561i $$0.449741\pi$$
$$558$$ 0 0
$$559$$ 988.000 0.0747548
$$560$$ 1280.00 0.0965891
$$561$$ 0 0
$$562$$ −6700.00 −0.502887
$$563$$ 16228.0 1.21479 0.607397 0.794399i $$-0.292214\pi$$
0.607397 + 0.794399i $$0.292214\pi$$
$$564$$ 0 0
$$565$$ 19140.0 1.42518
$$566$$ 15592.0 1.15792
$$567$$ 0 0
$$568$$ 5984.00 0.442048
$$569$$ −2514.00 −0.185224 −0.0926119 0.995702i $$-0.529522\pi$$
−0.0926119 + 0.995702i $$0.529522\pi$$
$$570$$ 0 0
$$571$$ −11612.0 −0.851046 −0.425523 0.904948i $$-0.639910\pi$$
−0.425523 + 0.904948i $$0.639910\pi$$
$$572$$ −2080.00 −0.152044
$$573$$ 0 0
$$574$$ −5792.00 −0.421173
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 6354.00 0.458441 0.229221 0.973375i $$-0.426382\pi$$
0.229221 + 0.973375i $$0.426382\pi$$
$$578$$ 23974.0 1.72524
$$579$$ 0 0
$$580$$ −720.000 −0.0515455
$$581$$ −8064.00 −0.575819
$$582$$ 0 0
$$583$$ 15280.0 1.08548
$$584$$ 8464.00 0.599731
$$585$$ 0 0
$$586$$ −7844.00 −0.552957
$$587$$ 13240.0 0.930960 0.465480 0.885059i $$-0.345882\pi$$
0.465480 + 0.885059i $$0.345882\pi$$
$$588$$ 0 0
$$589$$ 3680.00 0.257439
$$590$$ 9280.00 0.647545
$$591$$ 0 0
$$592$$ −1184.00 −0.0821995
$$593$$ 1146.00 0.0793602 0.0396801 0.999212i $$-0.487366\pi$$
0.0396801 + 0.999212i $$0.487366\pi$$
$$594$$ 0 0
$$595$$ −10400.0 −0.716569
$$596$$ −3528.00 −0.242471
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −10464.0 −0.713769 −0.356884 0.934149i $$-0.616161\pi$$
−0.356884 + 0.934149i $$0.616161\pi$$
$$600$$ 0 0
$$601$$ 6650.00 0.451346 0.225673 0.974203i $$-0.427542\pi$$
0.225673 + 0.974203i $$0.427542\pi$$
$$602$$ −1216.00 −0.0823263
$$603$$ 0 0
$$604$$ −7104.00 −0.478572
$$605$$ −2690.00 −0.180767
$$606$$ 0 0
$$607$$ −6664.00 −0.445607 −0.222803 0.974863i $$-0.571521\pi$$
−0.222803 + 0.974863i $$0.571521\pi$$
$$608$$ −640.000 −0.0426898
$$609$$ 0 0
$$610$$ −7160.00 −0.475246
$$611$$ 5876.00 0.389063
$$612$$ 0 0
$$613$$ 2134.00 0.140606 0.0703030 0.997526i $$-0.477603\pi$$
0.0703030 + 0.997526i $$0.477603\pi$$
$$614$$ 11912.0 0.782947
$$615$$ 0 0
$$616$$ 2560.00 0.167444
$$617$$ 714.000 0.0465876 0.0232938 0.999729i $$-0.492585\pi$$
0.0232938 + 0.999729i $$0.492585\pi$$
$$618$$ 0 0
$$619$$ 29228.0 1.89786 0.948928 0.315494i $$-0.102170\pi$$
0.948928 + 0.315494i $$0.102170\pi$$
$$620$$ 7360.00 0.476750
$$621$$ 0 0
$$622$$ −4704.00 −0.303237
$$623$$ −3088.00 −0.198584
$$624$$ 0 0
$$625$$ −11875.0 −0.760000
$$626$$ 16884.0 1.07799
$$627$$ 0 0
$$628$$ −9640.00 −0.612544
$$629$$ 9620.00 0.609816
$$630$$ 0 0
$$631$$ −13536.0 −0.853977 −0.426989 0.904257i $$-0.640426\pi$$
−0.426989 + 0.904257i $$0.640426\pi$$
$$632$$ −7808.00 −0.491433
$$633$$ 0 0
$$634$$ 11100.0 0.695327
$$635$$ −12960.0 −0.809924
$$636$$ 0 0
$$637$$ −3627.00 −0.225600
$$638$$ −1440.00 −0.0893576
$$639$$ 0 0
$$640$$ −1280.00 −0.0790569
$$641$$ −17218.0 −1.06095 −0.530476 0.847700i $$-0.677987\pi$$
−0.530476 + 0.847700i $$0.677987\pi$$
$$642$$ 0 0
$$643$$ 15044.0 0.922671 0.461335 0.887226i $$-0.347370\pi$$
0.461335 + 0.887226i $$0.347370\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 5200.00 0.316705
$$647$$ −25176.0 −1.52978 −0.764892 0.644158i $$-0.777208\pi$$
−0.764892 + 0.644158i $$0.777208\pi$$
$$648$$ 0 0
$$649$$ 18560.0 1.12256
$$650$$ −650.000 −0.0392232
$$651$$ 0 0
$$652$$ 12848.0 0.771728
$$653$$ 16034.0 0.960887 0.480443 0.877026i $$-0.340476\pi$$
0.480443 + 0.877026i $$0.340476\pi$$
$$654$$ 0 0
$$655$$ −8920.00 −0.532112
$$656$$ 5792.00 0.344725
$$657$$ 0 0
$$658$$ −7232.00 −0.428469
$$659$$ −25356.0 −1.49883 −0.749415 0.662100i $$-0.769665\pi$$
−0.749415 + 0.662100i $$0.769665\pi$$
$$660$$ 0 0
$$661$$ 18310.0 1.07742 0.538711 0.842490i $$-0.318911\pi$$
0.538711 + 0.842490i $$0.318911\pi$$
$$662$$ 280.000 0.0164388
$$663$$ 0 0
$$664$$ 8064.00 0.471301
$$665$$ −1600.00 −0.0933013
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −6672.00 −0.386448
$$669$$ 0 0
$$670$$ 14000.0 0.807264
$$671$$ −14320.0 −0.823871
$$672$$ 0 0
$$673$$ 24802.0 1.42057 0.710287 0.703912i $$-0.248565\pi$$
0.710287 + 0.703912i $$0.248565\pi$$
$$674$$ −12348.0 −0.705678
$$675$$ 0 0
$$676$$ 676.000 0.0384615
$$677$$ 22706.0 1.28901 0.644507 0.764598i $$-0.277063\pi$$
0.644507 + 0.764598i $$0.277063\pi$$
$$678$$ 0 0
$$679$$ 4912.00 0.277622
$$680$$ 10400.0 0.586503
$$681$$ 0 0
$$682$$ 14720.0 0.826478
$$683$$ 14792.0 0.828697 0.414349 0.910118i $$-0.364009\pi$$
0.414349 + 0.910118i $$0.364009\pi$$
$$684$$ 0 0
$$685$$ 23260.0 1.29740
$$686$$ 9952.00 0.553891
$$687$$ 0 0
$$688$$ 1216.00 0.0673831
$$689$$ −4966.00 −0.274586
$$690$$ 0 0
$$691$$ −1148.00 −0.0632011 −0.0316006 0.999501i $$-0.510060\pi$$
−0.0316006 + 0.999501i $$0.510060\pi$$
$$692$$ −14392.0 −0.790609
$$693$$ 0 0
$$694$$ 5976.00 0.326867
$$695$$ −19320.0 −1.05446
$$696$$ 0 0
$$697$$ −47060.0 −2.55742
$$698$$ −324.000 −0.0175696
$$699$$ 0 0
$$700$$ 800.000 0.0431959
$$701$$ −14870.0 −0.801187 −0.400594 0.916256i $$-0.631196\pi$$
−0.400594 + 0.916256i $$0.631196\pi$$
$$702$$ 0 0
$$703$$ 1480.00 0.0794015
$$704$$ −2560.00 −0.137051
$$705$$ 0 0
$$706$$ 21508.0 1.14655
$$707$$ 4144.00 0.220440
$$708$$ 0 0
$$709$$ −6354.00 −0.336572 −0.168286 0.985738i $$-0.553823\pi$$
−0.168286 + 0.985738i $$0.553823\pi$$
$$710$$ −14960.0 −0.790759
$$711$$ 0 0
$$712$$ 3088.00 0.162539
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 5200.00 0.271985
$$716$$ −4272.00 −0.222978
$$717$$ 0 0
$$718$$ −7176.00 −0.372989
$$719$$ −9288.00 −0.481758 −0.240879 0.970555i $$-0.577436\pi$$
−0.240879 + 0.970555i $$0.577436\pi$$
$$720$$ 0 0
$$721$$ −896.000 −0.0462813
$$722$$ −12918.0 −0.665870
$$723$$ 0 0
$$724$$ −19144.0 −0.982709
$$725$$ −450.000 −0.0230518
$$726$$ 0 0
$$727$$ −21544.0 −1.09907 −0.549534 0.835471i $$-0.685195\pi$$
−0.549534 + 0.835471i $$0.685195\pi$$
$$728$$ −832.000 −0.0423571
$$729$$ 0 0
$$730$$ −21160.0 −1.07283
$$731$$ −9880.00 −0.499897
$$732$$ 0 0
$$733$$ 19990.0 1.00730 0.503648 0.863909i $$-0.331991\pi$$
0.503648 + 0.863909i $$0.331991\pi$$
$$734$$ 22544.0 1.13367
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 28000.0 1.39945
$$738$$ 0 0
$$739$$ 532.000 0.0264816 0.0132408 0.999912i $$-0.495785\pi$$
0.0132408 + 0.999912i $$0.495785\pi$$
$$740$$ 2960.00 0.147043
$$741$$ 0 0
$$742$$ 6112.00 0.302397
$$743$$ 25452.0 1.25672 0.628360 0.777922i $$-0.283726\pi$$
0.628360 + 0.777922i $$0.283726\pi$$
$$744$$ 0 0
$$745$$ 8820.00 0.433745
$$746$$ −21828.0 −1.07129
$$747$$ 0 0
$$748$$ 20800.0 1.01674
$$749$$ −2976.00 −0.145181
$$750$$ 0 0
$$751$$ 6440.00 0.312915 0.156457 0.987685i $$-0.449993\pi$$
0.156457 + 0.987685i $$0.449993\pi$$
$$752$$ 7232.00 0.350697
$$753$$ 0 0
$$754$$ 468.000 0.0226042
$$755$$ 17760.0 0.856096
$$756$$ 0 0
$$757$$ −786.000 −0.0377380 −0.0188690 0.999822i $$-0.506007\pi$$
−0.0188690 + 0.999822i $$0.506007\pi$$
$$758$$ 16200.0 0.776267
$$759$$ 0 0
$$760$$ 1600.00 0.0763659
$$761$$ 1498.00 0.0713567 0.0356784 0.999363i $$-0.488641\pi$$
0.0356784 + 0.999363i $$0.488641\pi$$
$$762$$ 0 0
$$763$$ −7472.00 −0.354528
$$764$$ 5248.00 0.248516
$$765$$ 0 0
$$766$$ −12360.0 −0.583009
$$767$$ −6032.00 −0.283967
$$768$$ 0 0
$$769$$ 14738.0 0.691113 0.345556 0.938398i $$-0.387690\pi$$
0.345556 + 0.938398i $$0.387690\pi$$
$$770$$ −6400.00 −0.299532
$$771$$ 0 0
$$772$$ −1400.00 −0.0652683
$$773$$ 3822.00 0.177837 0.0889184 0.996039i $$-0.471659\pi$$
0.0889184 + 0.996039i $$0.471659\pi$$
$$774$$ 0 0
$$775$$ 4600.00 0.213209
$$776$$ −4912.00 −0.227230
$$777$$ 0 0
$$778$$ 15044.0 0.693256
$$779$$ −7240.00 −0.332991
$$780$$ 0 0
$$781$$ −29920.0 −1.37083
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −4464.00 −0.203353
$$785$$ 24100.0 1.09575
$$786$$ 0 0
$$787$$ −11900.0 −0.538995 −0.269498 0.963001i $$-0.586858\pi$$
−0.269498 + 0.963001i $$0.586858\pi$$
$$788$$ 1368.00 0.0618439
$$789$$ 0 0
$$790$$ 19520.0 0.879102
$$791$$ 15312.0 0.688283
$$792$$ 0 0
$$793$$ 4654.00 0.208409
$$794$$ 12156.0 0.543325
$$795$$ 0 0
$$796$$ −13472.0 −0.599877
$$797$$ 21274.0 0.945500 0.472750 0.881197i $$-0.343261\pi$$
0.472750 + 0.881197i $$0.343261\pi$$
$$798$$ 0 0
$$799$$ −58760.0 −2.60173
$$800$$ −800.000 −0.0353553
$$801$$ 0 0
$$802$$ −3660.00 −0.161146
$$803$$ −42320.0 −1.85983
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −4784.00 −0.209069
$$807$$ 0 0
$$808$$ −4144.00 −0.180427
$$809$$ 27566.0 1.19798 0.598992 0.800755i $$-0.295568\pi$$
0.598992 + 0.800755i $$0.295568\pi$$
$$810$$ 0 0
$$811$$ −11244.0 −0.486844 −0.243422 0.969921i $$-0.578270\pi$$
−0.243422 + 0.969921i $$0.578270\pi$$
$$812$$ −576.000 −0.0248936
$$813$$ 0 0
$$814$$ 5920.00 0.254909
$$815$$ −32120.0 −1.38051
$$816$$ 0 0
$$817$$ −1520.00 −0.0650894
$$818$$ 24868.0 1.06295
$$819$$ 0 0
$$820$$ −14480.0 −0.616663
$$821$$ −13554.0 −0.576173 −0.288086 0.957604i $$-0.593019\pi$$
−0.288086 + 0.957604i $$0.593019\pi$$
$$822$$ 0 0
$$823$$ 14384.0 0.609228 0.304614 0.952476i $$-0.401473\pi$$
0.304614 + 0.952476i $$0.401473\pi$$
$$824$$ 896.000 0.0378806
$$825$$ 0 0
$$826$$ 7424.00 0.312729
$$827$$ 2488.00 0.104615 0.0523073 0.998631i $$-0.483342\pi$$
0.0523073 + 0.998631i $$0.483342\pi$$
$$828$$ 0 0
$$829$$ −20858.0 −0.873858 −0.436929 0.899496i $$-0.643934\pi$$
−0.436929 + 0.899496i $$0.643934\pi$$
$$830$$ −20160.0 −0.843089
$$831$$ 0 0
$$832$$ 832.000 0.0346688
$$833$$ 36270.0 1.50862
$$834$$ 0 0
$$835$$ 16680.0 0.691300
$$836$$ 3200.00 0.132386
$$837$$ 0 0
$$838$$ 28376.0 1.16973
$$839$$ −23116.0 −0.951195 −0.475598 0.879663i $$-0.657768\pi$$
−0.475598 + 0.879663i $$0.657768\pi$$
$$840$$ 0 0
$$841$$ −24065.0 −0.986715
$$842$$ 17276.0 0.707091
$$843$$ 0 0
$$844$$ −8016.00 −0.326922
$$845$$ −1690.00 −0.0688021
$$846$$ 0 0
$$847$$ −2152.00 −0.0873006
$$848$$ −6112.00 −0.247508
$$849$$ 0 0
$$850$$ 6500.00 0.262292
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 934.000 0.0374907 0.0187453 0.999824i $$-0.494033\pi$$
0.0187453 + 0.999824i $$0.494033\pi$$
$$854$$ −5728.00 −0.229518
$$855$$ 0 0
$$856$$ 2976.00 0.118829
$$857$$ −12642.0 −0.503900 −0.251950 0.967740i $$-0.581072\pi$$
−0.251950 + 0.967740i $$0.581072\pi$$
$$858$$ 0 0
$$859$$ −22796.0 −0.905459 −0.452730 0.891648i $$-0.649550\pi$$
−0.452730 + 0.891648i $$0.649550\pi$$
$$860$$ −3040.00 −0.120539
$$861$$ 0 0
$$862$$ −8584.00 −0.339179
$$863$$ 76.0000 0.00299776 0.00149888 0.999999i $$-0.499523\pi$$
0.00149888 + 0.999999i $$0.499523\pi$$
$$864$$ 0 0
$$865$$ 35980.0 1.41429
$$866$$ −11964.0 −0.469461
$$867$$ 0 0
$$868$$ 5888.00 0.230244
$$869$$ 39040.0 1.52398
$$870$$ 0 0
$$871$$ −9100.00 −0.354009
$$872$$ 7472.00 0.290176
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −12000.0 −0.463627
$$876$$ 0 0
$$877$$ −46130.0 −1.77617 −0.888084 0.459681i $$-0.847964\pi$$
−0.888084 + 0.459681i $$0.847964\pi$$
$$878$$ 512.000 0.0196801
$$879$$ 0 0
$$880$$ 6400.00 0.245164
$$881$$ −6682.00 −0.255530 −0.127765 0.991804i $$-0.540780\pi$$
−0.127765 + 0.991804i $$0.540780\pi$$
$$882$$ 0 0
$$883$$ 47404.0 1.80665 0.903325 0.428957i $$-0.141119\pi$$
0.903325 + 0.428957i $$0.141119\pi$$
$$884$$ −6760.00 −0.257198
$$885$$ 0 0
$$886$$ −25112.0 −0.952206
$$887$$ −33672.0 −1.27463 −0.637314 0.770604i $$-0.719955\pi$$
−0.637314 + 0.770604i $$0.719955\pi$$
$$888$$ 0 0
$$889$$ −10368.0 −0.391149
$$890$$ −7720.00 −0.290758
$$891$$ 0 0
$$892$$ −22432.0 −0.842017
$$893$$ −9040.00 −0.338759
$$894$$ 0 0
$$895$$ 10680.0 0.398875
$$896$$ −1024.00 −0.0381802
$$897$$ 0 0
$$898$$ −11148.0 −0.414269
$$899$$ −3312.00 −0.122871
$$900$$ 0 0
$$901$$ 49660.0 1.83620
$$902$$ −28960.0 −1.06903
$$903$$ 0 0
$$904$$ −15312.0 −0.563351
$$905$$ 47860.0 1.75792
$$906$$ 0 0
$$907$$ −14540.0 −0.532296 −0.266148 0.963932i $$-0.585751\pi$$
−0.266148 + 0.963932i $$0.585751\pi$$
$$908$$ 7712.00 0.281863
$$909$$ 0 0
$$910$$ 2080.00 0.0757707
$$911$$ 7840.00 0.285127 0.142564 0.989786i $$-0.454465\pi$$
0.142564 + 0.989786i $$0.454465\pi$$
$$912$$ 0 0
$$913$$ −40320.0 −1.46155
$$914$$ 2532.00 0.0916314
$$915$$ 0 0
$$916$$ −15752.0 −0.568189
$$917$$ −7136.00 −0.256981
$$918$$ 0 0
$$919$$ 47720.0 1.71288 0.856440 0.516246i $$-0.172671\pi$$
0.856440 + 0.516246i $$0.172671\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −15108.0 −0.539648
$$923$$ 9724.00 0.346771
$$924$$ 0 0
$$925$$ 1850.00 0.0657596
$$926$$ −13504.0 −0.479232
$$927$$ 0 0
$$928$$ 576.000 0.0203751
$$929$$ −7502.00 −0.264944 −0.132472 0.991187i $$-0.542291\pi$$
−0.132472 + 0.991187i $$0.542291\pi$$
$$930$$ 0 0
$$931$$ 5580.00 0.196431
$$932$$ −10248.0 −0.360176
$$933$$ 0 0
$$934$$ −15848.0 −0.555206
$$935$$ −52000.0 −1.81880
$$936$$ 0 0
$$937$$ 22058.0 0.769054 0.384527 0.923114i $$-0.374365\pi$$
0.384527 + 0.923114i $$0.374365\pi$$
$$938$$ 11200.0 0.389865
$$939$$ 0 0
$$940$$ −18080.0 −0.627345
$$941$$ −23338.0 −0.808498 −0.404249 0.914649i $$-0.632467\pi$$
−0.404249 + 0.914649i $$0.632467\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −7424.00 −0.255965
$$945$$ 0 0
$$946$$ −6080.00 −0.208962
$$947$$ 30488.0 1.04617 0.523087 0.852279i $$-0.324780\pi$$
0.523087 + 0.852279i $$0.324780\pi$$
$$948$$ 0 0
$$949$$ 13754.0 0.470468
$$950$$ 1000.00 0.0341519
$$951$$ 0 0
$$952$$ 8320.00 0.283249
$$953$$ −9522.00 −0.323660 −0.161830 0.986819i $$-0.551740\pi$$
−0.161830 + 0.986819i $$0.551740\pi$$
$$954$$ 0 0
$$955$$ −13120.0 −0.444558
$$956$$ −28656.0 −0.969457
$$957$$ 0 0
$$958$$ 22168.0 0.747615
$$959$$ 18608.0 0.626573
$$960$$ 0 0
$$961$$ 4065.00 0.136451
$$962$$ −1924.00 −0.0644826
$$963$$ 0 0
$$964$$ −24728.0 −0.826178
$$965$$ 3500.00 0.116755
$$966$$ 0 0
$$967$$ −7616.00 −0.253272 −0.126636 0.991949i $$-0.540418\pi$$
−0.126636 + 0.991949i $$0.540418\pi$$
$$968$$ 2152.00 0.0714544
$$969$$ 0 0
$$970$$ 12280.0 0.406481
$$971$$ −51316.0 −1.69599 −0.847996 0.530002i $$-0.822191\pi$$
−0.847996 + 0.530002i $$0.822191\pi$$
$$972$$ 0 0
$$973$$ −15456.0 −0.509246
$$974$$ 8864.00 0.291603
$$975$$ 0 0
$$976$$ 5728.00 0.187857
$$977$$ 48666.0 1.59362 0.796808 0.604232i $$-0.206520\pi$$
0.796808 + 0.604232i $$0.206520\pi$$
$$978$$ 0 0
$$979$$ −15440.0 −0.504050
$$980$$ 11160.0 0.363768
$$981$$ 0 0
$$982$$ 2280.00 0.0740914
$$983$$ −17388.0 −0.564182 −0.282091 0.959388i $$-0.591028\pi$$
−0.282091 + 0.959388i $$0.591028\pi$$
$$984$$ 0 0
$$985$$ −3420.00 −0.110630
$$986$$ −4680.00 −0.151158
$$987$$ 0 0
$$988$$ −1040.00 −0.0334887
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 11496.0 0.368499 0.184249 0.982880i $$-0.441015\pi$$
0.184249 + 0.982880i $$0.441015\pi$$
$$992$$ −5888.00 −0.188452
$$993$$ 0 0
$$994$$ −11968.0 −0.381893
$$995$$ 33680.0 1.07309
$$996$$ 0 0
$$997$$ 48862.0 1.55213 0.776066 0.630652i $$-0.217212\pi$$
0.776066 + 0.630652i $$0.217212\pi$$
$$998$$ 3528.00 0.111901
$$999$$ 0 0
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 234.4.a.h.1.1 1
3.2 odd 2 78.4.a.c.1.1 1
4.3 odd 2 1872.4.a.d.1.1 1
12.11 even 2 624.4.a.d.1.1 1
15.14 odd 2 1950.4.a.l.1.1 1
24.5 odd 2 2496.4.a.a.1.1 1
24.11 even 2 2496.4.a.j.1.1 1
39.5 even 4 1014.4.b.h.337.2 2
39.8 even 4 1014.4.b.h.337.1 2
39.38 odd 2 1014.4.a.j.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
78.4.a.c.1.1 1 3.2 odd 2
234.4.a.h.1.1 1 1.1 even 1 trivial
624.4.a.d.1.1 1 12.11 even 2
1014.4.a.j.1.1 1 39.38 odd 2
1014.4.b.h.337.1 2 39.8 even 4
1014.4.b.h.337.2 2 39.5 even 4
1872.4.a.d.1.1 1 4.3 odd 2
1950.4.a.l.1.1 1 15.14 odd 2
2496.4.a.a.1.1 1 24.5 odd 2
2496.4.a.j.1.1 1 24.11 even 2