# Properties

 Label 252.6.a.c.1.1 Level $252$ Weight $6$ Character 252.1 Self dual yes Analytic conductor $40.417$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,6,Mod(1,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("252.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 252.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: $$40.4167225929$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 84) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 252.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+34.0000 q^{5} -49.0000 q^{7} +O(q^{10})$$ $$q+34.0000 q^{5} -49.0000 q^{7} +332.000 q^{11} -1026.00 q^{13} -922.000 q^{17} +452.000 q^{19} +3776.00 q^{23} -1969.00 q^{25} -1166.00 q^{29} -9792.00 q^{31} -1666.00 q^{35} +2390.00 q^{37} +7230.00 q^{41} +4652.00 q^{43} -24672.0 q^{47} +2401.00 q^{49} -1110.00 q^{53} +11288.0 q^{55} -46892.0 q^{59} -9762.00 q^{61} -34884.0 q^{65} -26252.0 q^{67} -65440.0 q^{71} -5606.00 q^{73} -16268.0 q^{77} -9840.00 q^{79} -61108.0 q^{83} -31348.0 q^{85} +62958.0 q^{89} +50274.0 q^{91} +15368.0 q^{95} -37838.0 q^{97} +O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 34.0000 0.608210 0.304105 0.952638i $$-0.401643\pi$$
0.304105 + 0.952638i $$0.401643\pi$$
$$6$$ 0 0
$$7$$ −49.0000 −0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 332.000 0.827287 0.413644 0.910439i $$-0.364256\pi$$
0.413644 + 0.910439i $$0.364256\pi$$
$$12$$ 0 0
$$13$$ −1026.00 −1.68379 −0.841897 0.539638i $$-0.818561\pi$$
−0.841897 + 0.539638i $$0.818561\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −922.000 −0.773764 −0.386882 0.922129i $$-0.626448\pi$$
−0.386882 + 0.922129i $$0.626448\pi$$
$$18$$ 0 0
$$19$$ 452.000 0.287246 0.143623 0.989632i $$-0.454125\pi$$
0.143623 + 0.989632i $$0.454125\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 3776.00 1.48838 0.744188 0.667971i $$-0.232837\pi$$
0.744188 + 0.667971i $$0.232837\pi$$
$$24$$ 0 0
$$25$$ −1969.00 −0.630080
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −1166.00 −0.257456 −0.128728 0.991680i $$-0.541089\pi$$
−0.128728 + 0.991680i $$0.541089\pi$$
$$30$$ 0 0
$$31$$ −9792.00 −1.83007 −0.915034 0.403377i $$-0.867836\pi$$
−0.915034 + 0.403377i $$0.867836\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1666.00 −0.229882
$$36$$ 0 0
$$37$$ 2390.00 0.287008 0.143504 0.989650i $$-0.454163\pi$$
0.143504 + 0.989650i $$0.454163\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 7230.00 0.671705 0.335853 0.941915i $$-0.390976\pi$$
0.335853 + 0.941915i $$0.390976\pi$$
$$42$$ 0 0
$$43$$ 4652.00 0.383679 0.191840 0.981426i $$-0.438555\pi$$
0.191840 + 0.981426i $$0.438555\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −24672.0 −1.62914 −0.814572 0.580062i $$-0.803028\pi$$
−0.814572 + 0.580062i $$0.803028\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −1110.00 −0.0542792 −0.0271396 0.999632i $$-0.508640\pi$$
−0.0271396 + 0.999632i $$0.508640\pi$$
$$54$$ 0 0
$$55$$ 11288.0 0.503165
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −46892.0 −1.75375 −0.876877 0.480715i $$-0.840377\pi$$
−0.876877 + 0.480715i $$0.840377\pi$$
$$60$$ 0 0
$$61$$ −9762.00 −0.335903 −0.167952 0.985795i $$-0.553715\pi$$
−0.167952 + 0.985795i $$0.553715\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −34884.0 −1.02410
$$66$$ 0 0
$$67$$ −26252.0 −0.714456 −0.357228 0.934017i $$-0.616278\pi$$
−0.357228 + 0.934017i $$0.616278\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −65440.0 −1.54063 −0.770313 0.637666i $$-0.779900\pi$$
−0.770313 + 0.637666i $$0.779900\pi$$
$$72$$ 0 0
$$73$$ −5606.00 −0.123125 −0.0615625 0.998103i $$-0.519608\pi$$
−0.0615625 + 0.998103i $$0.519608\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −16268.0 −0.312685
$$78$$ 0 0
$$79$$ −9840.00 −0.177389 −0.0886946 0.996059i $$-0.528270\pi$$
−0.0886946 + 0.996059i $$0.528270\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −61108.0 −0.973650 −0.486825 0.873500i $$-0.661845\pi$$
−0.486825 + 0.873500i $$0.661845\pi$$
$$84$$ 0 0
$$85$$ −31348.0 −0.470611
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 62958.0 0.842512 0.421256 0.906942i $$-0.361589\pi$$
0.421256 + 0.906942i $$0.361589\pi$$
$$90$$ 0 0
$$91$$ 50274.0 0.636414
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 15368.0 0.174706
$$96$$ 0 0
$$97$$ −37838.0 −0.408318 −0.204159 0.978938i $$-0.565446\pi$$
−0.204159 + 0.978938i $$0.565446\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 56146.0 0.547666 0.273833 0.961777i $$-0.411709\pi$$
0.273833 + 0.961777i $$0.411709\pi$$
$$102$$ 0 0
$$103$$ −26392.0 −0.245120 −0.122560 0.992461i $$-0.539110\pi$$
−0.122560 + 0.992461i $$0.539110\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −47124.0 −0.397908 −0.198954 0.980009i $$-0.563754\pi$$
−0.198954 + 0.980009i $$0.563754\pi$$
$$108$$ 0 0
$$109$$ −221474. −1.78549 −0.892743 0.450566i $$-0.851222\pi$$
−0.892743 + 0.450566i $$0.851222\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −54194.0 −0.399259 −0.199630 0.979871i $$-0.563974\pi$$
−0.199630 + 0.979871i $$0.563974\pi$$
$$114$$ 0 0
$$115$$ 128384. 0.905245
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 45178.0 0.292455
$$120$$ 0 0
$$121$$ −50827.0 −0.315596
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −173196. −0.991432
$$126$$ 0 0
$$127$$ −245760. −1.35208 −0.676039 0.736866i $$-0.736305\pi$$
−0.676039 + 0.736866i $$0.736305\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 150268. 0.765047 0.382524 0.923946i $$-0.375055\pi$$
0.382524 + 0.923946i $$0.375055\pi$$
$$132$$ 0 0
$$133$$ −22148.0 −0.108569
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 401638. 1.82824 0.914120 0.405443i $$-0.132883\pi$$
0.914120 + 0.405443i $$0.132883\pi$$
$$138$$ 0 0
$$139$$ 374092. 1.64226 0.821129 0.570743i $$-0.193345\pi$$
0.821129 + 0.570743i $$0.193345\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −340632. −1.39298
$$144$$ 0 0
$$145$$ −39644.0 −0.156588
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 456042. 1.68283 0.841413 0.540393i $$-0.181724\pi$$
0.841413 + 0.540393i $$0.181724\pi$$
$$150$$ 0 0
$$151$$ −8024.00 −0.0286384 −0.0143192 0.999897i $$-0.504558\pi$$
−0.0143192 + 0.999897i $$0.504558\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −332928. −1.11307
$$156$$ 0 0
$$157$$ 110078. 0.356411 0.178206 0.983993i $$-0.442971\pi$$
0.178206 + 0.983993i $$0.442971\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −185024. −0.562553
$$162$$ 0 0
$$163$$ −3628.00 −0.0106954 −0.00534772 0.999986i $$-0.501702\pi$$
−0.00534772 + 0.999986i $$0.501702\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −192824. −0.535020 −0.267510 0.963555i $$-0.586201\pi$$
−0.267510 + 0.963555i $$0.586201\pi$$
$$168$$ 0 0
$$169$$ 681383. 1.83516
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −157142. −0.399188 −0.199594 0.979879i $$-0.563962\pi$$
−0.199594 + 0.979879i $$0.563962\pi$$
$$174$$ 0 0
$$175$$ 96481.0 0.238148
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 446868. 1.04243 0.521215 0.853426i $$-0.325479\pi$$
0.521215 + 0.853426i $$0.325479\pi$$
$$180$$ 0 0
$$181$$ 805638. 1.82786 0.913931 0.405869i $$-0.133031\pi$$
0.913931 + 0.405869i $$0.133031\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 81260.0 0.174561
$$186$$ 0 0
$$187$$ −306104. −0.640125
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 747912. 1.48343 0.741715 0.670715i $$-0.234013\pi$$
0.741715 + 0.670715i $$0.234013\pi$$
$$192$$ 0 0
$$193$$ −577534. −1.11605 −0.558026 0.829824i $$-0.688441\pi$$
−0.558026 + 0.829824i $$0.688441\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 771098. 1.41561 0.707806 0.706407i $$-0.249685\pi$$
0.707806 + 0.706407i $$0.249685\pi$$
$$198$$ 0 0
$$199$$ 557240. 0.997492 0.498746 0.866748i $$-0.333794\pi$$
0.498746 + 0.866748i $$0.333794\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 57134.0 0.0973093
$$204$$ 0 0
$$205$$ 245820. 0.408538
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 150064. 0.237635
$$210$$ 0 0
$$211$$ −19660.0 −0.0304003 −0.0152001 0.999884i $$-0.504839\pi$$
−0.0152001 + 0.999884i $$0.504839\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 158168. 0.233358
$$216$$ 0 0
$$217$$ 479808. 0.691701
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 945972. 1.30286
$$222$$ 0 0
$$223$$ −896848. −1.20769 −0.603847 0.797100i $$-0.706366\pi$$
−0.603847 + 0.797100i $$0.706366\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −234228. −0.301699 −0.150850 0.988557i $$-0.548201\pi$$
−0.150850 + 0.988557i $$0.548201\pi$$
$$228$$ 0 0
$$229$$ −1.03563e6 −1.30501 −0.652506 0.757784i $$-0.726282\pi$$
−0.652506 + 0.757784i $$0.726282\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −457114. −0.551613 −0.275807 0.961213i $$-0.588945\pi$$
−0.275807 + 0.961213i $$0.588945\pi$$
$$234$$ 0 0
$$235$$ −838848. −0.990863
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −676344. −0.765901 −0.382951 0.923769i $$-0.625092\pi$$
−0.382951 + 0.923769i $$0.625092\pi$$
$$240$$ 0 0
$$241$$ −96670.0 −0.107213 −0.0536067 0.998562i $$-0.517072\pi$$
−0.0536067 + 0.998562i $$0.517072\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 81634.0 0.0868872
$$246$$ 0 0
$$247$$ −463752. −0.483664
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −288876. −0.289419 −0.144710 0.989474i $$-0.546225\pi$$
−0.144710 + 0.989474i $$0.546225\pi$$
$$252$$ 0 0
$$253$$ 1.25363e6 1.23131
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 711846. 0.672285 0.336142 0.941811i $$-0.390878\pi$$
0.336142 + 0.941811i $$0.390878\pi$$
$$258$$ 0 0
$$259$$ −117110. −0.108479
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.87368e6 1.67034 0.835172 0.549988i $$-0.185368\pi$$
0.835172 + 0.549988i $$0.185368\pi$$
$$264$$ 0 0
$$265$$ −37740.0 −0.0330132
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.37660e6 1.15992 0.579960 0.814645i $$-0.303068\pi$$
0.579960 + 0.814645i $$0.303068\pi$$
$$270$$ 0 0
$$271$$ −781776. −0.646635 −0.323317 0.946291i $$-0.604798\pi$$
−0.323317 + 0.946291i $$0.604798\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −653708. −0.521257
$$276$$ 0 0
$$277$$ 2.06932e6 1.62042 0.810210 0.586139i $$-0.199353\pi$$
0.810210 + 0.586139i $$0.199353\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.87911e6 −1.41967 −0.709835 0.704368i $$-0.751230\pi$$
−0.709835 + 0.704368i $$0.751230\pi$$
$$282$$ 0 0
$$283$$ 670156. 0.497405 0.248702 0.968580i $$-0.419996\pi$$
0.248702 + 0.968580i $$0.419996\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −354270. −0.253881
$$288$$ 0 0
$$289$$ −569773. −0.401289
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.69611e6 −1.15421 −0.577105 0.816670i $$-0.695818\pi$$
−0.577105 + 0.816670i $$0.695818\pi$$
$$294$$ 0 0
$$295$$ −1.59433e6 −1.06665
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −3.87418e6 −2.50612
$$300$$ 0 0
$$301$$ −227948. −0.145017
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −331908. −0.204300
$$306$$ 0 0
$$307$$ −1.09459e6 −0.662834 −0.331417 0.943484i $$-0.607527\pi$$
−0.331417 + 0.943484i $$0.607527\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.21249e6 −0.710848 −0.355424 0.934705i $$-0.615663\pi$$
−0.355424 + 0.934705i $$0.615663\pi$$
$$312$$ 0 0
$$313$$ 1.69436e6 0.977564 0.488782 0.872406i $$-0.337441\pi$$
0.488782 + 0.872406i $$0.337441\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −333342. −0.186312 −0.0931562 0.995652i $$-0.529696\pi$$
−0.0931562 + 0.995652i $$0.529696\pi$$
$$318$$ 0 0
$$319$$ −387112. −0.212990
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −416744. −0.222261
$$324$$ 0 0
$$325$$ 2.02019e6 1.06092
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 1.20893e6 0.615759
$$330$$ 0 0
$$331$$ 1.83614e6 0.921162 0.460581 0.887618i $$-0.347641\pi$$
0.460581 + 0.887618i $$0.347641\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −892568. −0.434540
$$336$$ 0 0
$$337$$ −973518. −0.466949 −0.233474 0.972363i $$-0.575009\pi$$
−0.233474 + 0.972363i $$0.575009\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −3.25094e6 −1.51399
$$342$$ 0 0
$$343$$ −117649. −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −3.39810e6 −1.51500 −0.757500 0.652835i $$-0.773579\pi$$
−0.757500 + 0.652835i $$0.773579\pi$$
$$348$$ 0 0
$$349$$ −34370.0 −0.0151048 −0.00755242 0.999971i $$-0.502404\pi$$
−0.00755242 + 0.999971i $$0.502404\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2.50239e6 1.06885 0.534427 0.845215i $$-0.320528\pi$$
0.534427 + 0.845215i $$0.320528\pi$$
$$354$$ 0 0
$$355$$ −2.22496e6 −0.937025
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 3.02800e6 1.23999 0.619997 0.784604i $$-0.287134\pi$$
0.619997 + 0.784604i $$0.287134\pi$$
$$360$$ 0 0
$$361$$ −2.27180e6 −0.917490
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −190604. −0.0748859
$$366$$ 0 0
$$367$$ −3.20944e6 −1.24384 −0.621919 0.783081i $$-0.713647\pi$$
−0.621919 + 0.783081i $$0.713647\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 54390.0 0.0205156
$$372$$ 0 0
$$373$$ 1.51505e6 0.563837 0.281919 0.959438i $$-0.409029\pi$$
0.281919 + 0.959438i $$0.409029\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 1.19632e6 0.433503
$$378$$ 0 0
$$379$$ 643516. 0.230124 0.115062 0.993358i $$-0.463293\pi$$
0.115062 + 0.993358i $$0.463293\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −4.75082e6 −1.65490 −0.827449 0.561541i $$-0.810209\pi$$
−0.827449 + 0.561541i $$0.810209\pi$$
$$384$$ 0 0
$$385$$ −553112. −0.190178
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −379574. −0.127181 −0.0635905 0.997976i $$-0.520255\pi$$
−0.0635905 + 0.997976i $$0.520255\pi$$
$$390$$ 0 0
$$391$$ −3.48147e6 −1.15165
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −334560. −0.107890
$$396$$ 0 0
$$397$$ −5.42133e6 −1.72635 −0.863176 0.504902i $$-0.831528\pi$$
−0.863176 + 0.504902i $$0.831528\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 6.20643e6 1.92744 0.963720 0.266915i $$-0.0860042\pi$$
0.963720 + 0.266915i $$0.0860042\pi$$
$$402$$ 0 0
$$403$$ 1.00466e7 3.08146
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 793480. 0.237438
$$408$$ 0 0
$$409$$ −4.25397e6 −1.25744 −0.628719 0.777633i $$-0.716420\pi$$
−0.628719 + 0.777633i $$0.716420\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 2.29771e6 0.662857
$$414$$ 0 0
$$415$$ −2.07767e6 −0.592184
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 725484. 0.201880 0.100940 0.994893i $$-0.467815\pi$$
0.100940 + 0.994893i $$0.467815\pi$$
$$420$$ 0 0
$$421$$ −6.49867e6 −1.78698 −0.893489 0.449086i $$-0.851750\pi$$
−0.893489 + 0.449086i $$0.851750\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.81542e6 0.487533
$$426$$ 0 0
$$427$$ 478338. 0.126959
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 1.96524e6 0.509592 0.254796 0.966995i $$-0.417992\pi$$
0.254796 + 0.966995i $$0.417992\pi$$
$$432$$ 0 0
$$433$$ 4.33531e6 1.11122 0.555611 0.831442i $$-0.312484\pi$$
0.555611 + 0.831442i $$0.312484\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 1.70675e6 0.427530
$$438$$ 0 0
$$439$$ 6.47748e6 1.60415 0.802075 0.597224i $$-0.203730\pi$$
0.802075 + 0.597224i $$0.203730\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −4.32696e6 −1.04755 −0.523774 0.851857i $$-0.675476\pi$$
−0.523774 + 0.851857i $$0.675476\pi$$
$$444$$ 0 0
$$445$$ 2.14057e6 0.512424
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −482210. −0.112881 −0.0564404 0.998406i $$-0.517975\pi$$
−0.0564404 + 0.998406i $$0.517975\pi$$
$$450$$ 0 0
$$451$$ 2.40036e6 0.555693
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 1.70932e6 0.387074
$$456$$ 0 0
$$457$$ 8.52164e6 1.90868 0.954339 0.298725i $$-0.0965613\pi$$
0.954339 + 0.298725i $$0.0965613\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 5.99857e6 1.31461 0.657303 0.753627i $$-0.271697\pi$$
0.657303 + 0.753627i $$0.271697\pi$$
$$462$$ 0 0
$$463$$ −4.59483e6 −0.996133 −0.498066 0.867139i $$-0.665956\pi$$
−0.498066 + 0.867139i $$0.665956\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −8.84330e6 −1.87639 −0.938193 0.346113i $$-0.887501\pi$$
−0.938193 + 0.346113i $$0.887501\pi$$
$$468$$ 0 0
$$469$$ 1.28635e6 0.270039
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 1.54446e6 0.317413
$$474$$ 0 0
$$475$$ −889988. −0.180988
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 6.56062e6 1.30649 0.653245 0.757146i $$-0.273407\pi$$
0.653245 + 0.757146i $$0.273407\pi$$
$$480$$ 0 0
$$481$$ −2.45214e6 −0.483262
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.28649e6 −0.248343
$$486$$ 0 0
$$487$$ 7.87772e6 1.50514 0.752572 0.658510i $$-0.228813\pi$$
0.752572 + 0.658510i $$0.228813\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −637860. −0.119405 −0.0597024 0.998216i $$-0.519015\pi$$
−0.0597024 + 0.998216i $$0.519015\pi$$
$$492$$ 0 0
$$493$$ 1.07505e6 0.199210
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 3.20656e6 0.582302
$$498$$ 0 0
$$499$$ −4.93646e6 −0.887492 −0.443746 0.896153i $$-0.646351\pi$$
−0.443746 + 0.896153i $$0.646351\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −226872. −0.0399817 −0.0199908 0.999800i $$-0.506364\pi$$
−0.0199908 + 0.999800i $$0.506364\pi$$
$$504$$ 0 0
$$505$$ 1.90896e6 0.333096
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −5.37404e6 −0.919404 −0.459702 0.888073i $$-0.652044\pi$$
−0.459702 + 0.888073i $$0.652044\pi$$
$$510$$ 0 0
$$511$$ 274694. 0.0465368
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −897328. −0.149085
$$516$$ 0 0
$$517$$ −8.19110e6 −1.34777
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 9.61419e6 1.55174 0.775869 0.630894i $$-0.217312\pi$$
0.775869 + 0.630894i $$0.217312\pi$$
$$522$$ 0 0
$$523$$ 4.96430e6 0.793604 0.396802 0.917904i $$-0.370120\pi$$
0.396802 + 0.917904i $$0.370120\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 9.02822e6 1.41604
$$528$$ 0 0
$$529$$ 7.82183e6 1.21526
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −7.41798e6 −1.13101
$$534$$ 0 0
$$535$$ −1.60222e6 −0.242012
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 797132. 0.118184
$$540$$ 0 0
$$541$$ 1.20449e7 1.76934 0.884668 0.466221i $$-0.154385\pi$$
0.884668 + 0.466221i $$0.154385\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −7.53012e6 −1.08595
$$546$$ 0 0
$$547$$ 4.23695e6 0.605459 0.302730 0.953077i $$-0.402102\pi$$
0.302730 + 0.953077i $$0.402102\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −527032. −0.0739534
$$552$$ 0 0
$$553$$ 482160. 0.0670468
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 1.02575e7 1.40089 0.700444 0.713708i $$-0.252986\pi$$
0.700444 + 0.713708i $$0.252986\pi$$
$$558$$ 0 0
$$559$$ −4.77295e6 −0.646037
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 5.40777e6 0.719031 0.359515 0.933139i $$-0.382942\pi$$
0.359515 + 0.933139i $$0.382942\pi$$
$$564$$ 0 0
$$565$$ −1.84260e6 −0.242834
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −5.38967e6 −0.697882 −0.348941 0.937145i $$-0.613459\pi$$
−0.348941 + 0.937145i $$0.613459\pi$$
$$570$$ 0 0
$$571$$ −8.24552e6 −1.05835 −0.529173 0.848514i $$-0.677498\pi$$
−0.529173 + 0.848514i $$0.677498\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −7.43494e6 −0.937795
$$576$$ 0 0
$$577$$ −1.15408e6 −0.144310 −0.0721549 0.997393i $$-0.522988\pi$$
−0.0721549 + 0.997393i $$0.522988\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 2.99429e6 0.368005
$$582$$ 0 0
$$583$$ −368520. −0.0449045
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7.16464e6 0.858221 0.429111 0.903252i $$-0.358827\pi$$
0.429111 + 0.903252i $$0.358827\pi$$
$$588$$ 0 0
$$589$$ −4.42598e6 −0.525680
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.45534e7 −1.69953 −0.849763 0.527165i $$-0.823255\pi$$
−0.849763 + 0.527165i $$0.823255\pi$$
$$594$$ 0 0
$$595$$ 1.53605e6 0.177874
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 1.04320e7 1.18795 0.593977 0.804482i $$-0.297557\pi$$
0.593977 + 0.804482i $$0.297557\pi$$
$$600$$ 0 0
$$601$$ 416858. 0.0470763 0.0235381 0.999723i $$-0.492507\pi$$
0.0235381 + 0.999723i $$0.492507\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1.72812e6 −0.191949
$$606$$ 0 0
$$607$$ −7.90834e6 −0.871191 −0.435596 0.900143i $$-0.643462\pi$$
−0.435596 + 0.900143i $$0.643462\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 2.53135e7 2.74314
$$612$$ 0 0
$$613$$ −1.13761e7 −1.22277 −0.611383 0.791335i $$-0.709387\pi$$
−0.611383 + 0.791335i $$0.709387\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 8.77271e6 0.927728 0.463864 0.885906i $$-0.346463\pi$$
0.463864 + 0.885906i $$0.346463\pi$$
$$618$$ 0 0
$$619$$ 1.44110e7 1.51171 0.755854 0.654740i $$-0.227222\pi$$
0.755854 + 0.654740i $$0.227222\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −3.08494e6 −0.318439
$$624$$ 0 0
$$625$$ 264461. 0.0270808
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −2.20358e6 −0.222076
$$630$$ 0 0
$$631$$ −1.29466e7 −1.29444 −0.647221 0.762303i $$-0.724069\pi$$
−0.647221 + 0.762303i $$0.724069\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −8.35584e6 −0.822348
$$636$$ 0 0
$$637$$ −2.46343e6 −0.240542
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 4.89035e6 0.470105 0.235052 0.971983i $$-0.424474\pi$$
0.235052 + 0.971983i $$0.424474\pi$$
$$642$$ 0 0
$$643$$ 1.22604e6 0.116943 0.0584717 0.998289i $$-0.481377\pi$$
0.0584717 + 0.998289i $$0.481377\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −1.21098e7 −1.13731 −0.568654 0.822577i $$-0.692536\pi$$
−0.568654 + 0.822577i $$0.692536\pi$$
$$648$$ 0 0
$$649$$ −1.55681e7 −1.45086
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −9.28697e6 −0.852298 −0.426149 0.904653i $$-0.640130\pi$$
−0.426149 + 0.904653i $$0.640130\pi$$
$$654$$ 0 0
$$655$$ 5.10911e6 0.465310
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −451612. −0.0405090 −0.0202545 0.999795i $$-0.506448\pi$$
−0.0202545 + 0.999795i $$0.506448\pi$$
$$660$$ 0 0
$$661$$ −1.85508e6 −0.165143 −0.0825714 0.996585i $$-0.526313\pi$$
−0.0825714 + 0.996585i $$0.526313\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −753032. −0.0660327
$$666$$ 0 0
$$667$$ −4.40282e6 −0.383192
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −3.24098e6 −0.277889
$$672$$ 0 0
$$673$$ 2.14534e7 1.82582 0.912911 0.408158i $$-0.133829\pi$$
0.912911 + 0.408158i $$0.133829\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1.56987e7 −1.31641 −0.658205 0.752839i $$-0.728684\pi$$
−0.658205 + 0.752839i $$0.728684\pi$$
$$678$$ 0 0
$$679$$ 1.85406e6 0.154330
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −1.40250e7 −1.15040 −0.575201 0.818012i $$-0.695076\pi$$
−0.575201 + 0.818012i $$0.695076\pi$$
$$684$$ 0 0
$$685$$ 1.36557e7 1.11196
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 1.13886e6 0.0913950
$$690$$ 0 0
$$691$$ −1.89819e7 −1.51232 −0.756160 0.654387i $$-0.772927\pi$$
−0.756160 + 0.654387i $$0.772927\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 1.27191e7 0.998839
$$696$$ 0 0
$$697$$ −6.66606e6 −0.519741
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −2.22806e7 −1.71250 −0.856251 0.516560i $$-0.827212\pi$$
−0.856251 + 0.516560i $$0.827212\pi$$
$$702$$ 0 0
$$703$$ 1.08028e6 0.0824419
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −2.75115e6 −0.206998
$$708$$ 0 0
$$709$$ −476266. −0.0355823 −0.0177911 0.999842i $$-0.505663\pi$$
−0.0177911 + 0.999842i $$0.505663\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −3.69746e7 −2.72383
$$714$$ 0 0
$$715$$ −1.15815e7 −0.847226
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 263568. 0.0190139 0.00950693 0.999955i $$-0.496974\pi$$
0.00950693 + 0.999955i $$0.496974\pi$$
$$720$$ 0 0
$$721$$ 1.29321e6 0.0926468
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.29585e6 0.162218
$$726$$ 0 0
$$727$$ 9.28319e6 0.651420 0.325710 0.945470i $$-0.394397\pi$$
0.325710 + 0.945470i $$0.394397\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −4.28914e6 −0.296877
$$732$$ 0 0
$$733$$ −1.89547e7 −1.30304 −0.651520 0.758631i $$-0.725868\pi$$
−0.651520 + 0.758631i $$0.725868\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −8.71566e6 −0.591060
$$738$$ 0 0
$$739$$ 1.95454e7 1.31654 0.658269 0.752783i $$-0.271289\pi$$
0.658269 + 0.752783i $$0.271289\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1.54683e7 −1.02795 −0.513973 0.857806i $$-0.671827\pi$$
−0.513973 + 0.857806i $$0.671827\pi$$
$$744$$ 0 0
$$745$$ 1.55054e7 1.02351
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 2.30908e6 0.150395
$$750$$ 0 0
$$751$$ −1.45188e7 −0.939354 −0.469677 0.882838i $$-0.655630\pi$$
−0.469677 + 0.882838i $$0.655630\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −272816. −0.0174182
$$756$$ 0 0
$$757$$ 8.54477e6 0.541952 0.270976 0.962586i $$-0.412654\pi$$
0.270976 + 0.962586i $$0.412654\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 8.50398e6 0.532305 0.266153 0.963931i $$-0.414247\pi$$
0.266153 + 0.963931i $$0.414247\pi$$
$$762$$ 0 0
$$763$$ 1.08522e7 0.674850
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 4.81112e7 2.95296
$$768$$ 0 0
$$769$$ −1.66581e7 −1.01580 −0.507901 0.861415i $$-0.669578\pi$$
−0.507901 + 0.861415i $$0.669578\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.17326e7 −1.30817 −0.654083 0.756423i $$-0.726945\pi$$
−0.654083 + 0.756423i $$0.726945\pi$$
$$774$$ 0 0
$$775$$ 1.92804e7 1.15309
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 3.26796e6 0.192945
$$780$$ 0 0
$$781$$ −2.17261e7 −1.27454
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 3.74265e6 0.216773
$$786$$ 0 0
$$787$$ 2.05602e6 0.118329 0.0591644 0.998248i $$-0.481156\pi$$
0.0591644 + 0.998248i $$0.481156\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2.65551e6 0.150906
$$792$$ 0 0
$$793$$ 1.00158e7 0.565592
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −3.17641e7 −1.77129 −0.885647 0.464359i $$-0.846285\pi$$
−0.885647 + 0.464359i $$0.846285\pi$$
$$798$$ 0 0
$$799$$ 2.27476e7 1.26057
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −1.86119e6 −0.101860
$$804$$ 0 0
$$805$$ −6.29082e6 −0.342151
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 2.14050e7 1.14986 0.574930 0.818203i $$-0.305029\pi$$
0.574930 + 0.818203i $$0.305029\pi$$
$$810$$ 0 0
$$811$$ −6.61432e6 −0.353129 −0.176564 0.984289i $$-0.556498\pi$$
−0.176564 + 0.984289i $$0.556498\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −123352. −0.00650507
$$816$$ 0 0
$$817$$ 2.10270e6 0.110211
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −1.78006e7 −0.921674 −0.460837 0.887485i $$-0.652451\pi$$
−0.460837 + 0.887485i $$0.652451\pi$$
$$822$$ 0 0
$$823$$ −1.23818e7 −0.637212 −0.318606 0.947887i $$-0.603215\pi$$
−0.318606 + 0.947887i $$0.603215\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 2.17279e7 1.10473 0.552363 0.833604i $$-0.313726\pi$$
0.552363 + 0.833604i $$0.313726\pi$$
$$828$$ 0 0
$$829$$ −1.35893e7 −0.686771 −0.343385 0.939195i $$-0.611574\pi$$
−0.343385 + 0.939195i $$0.611574\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −2.21372e6 −0.110538
$$834$$ 0 0
$$835$$ −6.55602e6 −0.325405
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 171272. 0.00840004 0.00420002 0.999991i $$-0.498663\pi$$
0.00420002 + 0.999991i $$0.498663\pi$$
$$840$$ 0 0
$$841$$ −1.91516e7 −0.933716
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 2.31670e7 1.11617
$$846$$ 0 0
$$847$$ 2.49052e6 0.119284
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 9.02464e6 0.427175
$$852$$ 0 0
$$853$$ 2.90172e7 1.36547 0.682737 0.730664i $$-0.260789\pi$$
0.682737 + 0.730664i $$0.260789\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 3.84967e7 1.79049 0.895243 0.445578i $$-0.147002\pi$$
0.895243 + 0.445578i $$0.147002\pi$$
$$858$$ 0 0
$$859$$ −1.98458e7 −0.917670 −0.458835 0.888521i $$-0.651733\pi$$
−0.458835 + 0.888521i $$0.651733\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 1.70833e7 0.780808 0.390404 0.920644i $$-0.372335\pi$$
0.390404 + 0.920644i $$0.372335\pi$$
$$864$$ 0 0
$$865$$ −5.34283e6 −0.242790
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −3.26688e6 −0.146752
$$870$$ 0 0
$$871$$ 2.69346e7 1.20300
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 8.48660e6 0.374726
$$876$$ 0 0
$$877$$ −2.53810e7 −1.11432 −0.557159 0.830406i $$-0.688109\pi$$
−0.557159 + 0.830406i $$0.688109\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 2.59580e7 1.12676 0.563381 0.826198i $$-0.309501\pi$$
0.563381 + 0.826198i $$0.309501\pi$$
$$882$$ 0 0
$$883$$ 4.37666e6 0.188904 0.0944520 0.995529i $$-0.469890\pi$$
0.0944520 + 0.995529i $$0.469890\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −3.23310e7 −1.37978 −0.689889 0.723915i $$-0.742341\pi$$
−0.689889 + 0.723915i $$0.742341\pi$$
$$888$$ 0 0
$$889$$ 1.20422e7 0.511038
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −1.11517e7 −0.467966
$$894$$ 0 0
$$895$$ 1.51935e7 0.634017
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 1.14175e7 0.471163
$$900$$ 0 0
$$901$$ 1.02342e6 0.0419993
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 2.73917e7 1.11173
$$906$$ 0 0
$$907$$ −3.67108e7 −1.48175 −0.740876 0.671642i $$-0.765589\pi$$
−0.740876 + 0.671642i $$0.765589\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −3.52261e7 −1.40627 −0.703135 0.711056i $$-0.748217\pi$$
−0.703135 + 0.711056i $$0.748217\pi$$
$$912$$ 0 0
$$913$$ −2.02879e7 −0.805488
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −7.36313e6 −0.289161
$$918$$ 0 0
$$919$$ −3.16978e6 −0.123806 −0.0619029 0.998082i $$-0.519717\pi$$
−0.0619029 + 0.998082i $$0.519717\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 6.71414e7 2.59410
$$924$$ 0 0
$$925$$ −4.70591e6 −0.180838
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 2.98030e7 1.13298 0.566488 0.824070i $$-0.308302\pi$$
0.566488 + 0.824070i $$0.308302\pi$$
$$930$$ 0 0
$$931$$ 1.08525e6 0.0410352
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −1.04075e7 −0.389331
$$936$$ 0 0
$$937$$ −1.62312e7 −0.603952 −0.301976 0.953316i $$-0.597646\pi$$
−0.301976 + 0.953316i $$0.597646\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −1.09759e7 −0.404079 −0.202040 0.979377i $$-0.564757\pi$$
−0.202040 + 0.979377i $$0.564757\pi$$
$$942$$ 0 0
$$943$$ 2.73005e7 0.999749
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −3.50304e6 −0.126932 −0.0634658 0.997984i $$-0.520215\pi$$
−0.0634658 + 0.997984i $$0.520215\pi$$
$$948$$ 0 0
$$949$$ 5.75176e6 0.207317
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 1.00120e7 0.357098 0.178549 0.983931i $$-0.442860\pi$$
0.178549 + 0.983931i $$0.442860\pi$$
$$954$$ 0 0
$$955$$ 2.54290e7 0.902238
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −1.96803e7 −0.691010
$$960$$ 0 0
$$961$$ 6.72541e7 2.34915
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −1.96362e7 −0.678794
$$966$$ 0 0
$$967$$ −652984. −0.0224562 −0.0112281 0.999937i $$-0.503574\pi$$
−0.0112281 + 0.999937i $$0.503574\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 1.24897e7 0.425112 0.212556 0.977149i $$-0.431821\pi$$
0.212556 + 0.977149i $$0.431821\pi$$
$$972$$ 0 0
$$973$$ −1.83305e7 −0.620715
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 7.43408e6 0.249167 0.124584 0.992209i $$-0.460241\pi$$
0.124584 + 0.992209i $$0.460241\pi$$
$$978$$ 0 0
$$979$$ 2.09021e7 0.696999
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −2.44904e7 −0.808373 −0.404187 0.914677i $$-0.632445\pi$$
−0.404187 + 0.914677i $$0.632445\pi$$
$$984$$ 0 0
$$985$$ 2.62173e7 0.860990
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 1.75660e7 0.571059
$$990$$ 0 0
$$991$$ 4.87464e7 1.57673 0.788367 0.615206i $$-0.210927\pi$$
0.788367 + 0.615206i $$0.210927\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 1.89462e7 0.606685
$$996$$ 0 0
$$997$$ 2.35242e6 0.0749510 0.0374755 0.999298i $$-0.488068\pi$$
0.0374755 + 0.999298i $$0.488068\pi$$
$$998$$ 0 0
$$999$$ 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 252.6.a.c.1.1 1
3.2 odd 2 84.6.a.b.1.1 1
4.3 odd 2 1008.6.a.u.1.1 1
12.11 even 2 336.6.a.e.1.1 1
21.2 odd 6 588.6.i.c.361.1 2
21.5 even 6 588.6.i.e.361.1 2
21.11 odd 6 588.6.i.c.373.1 2
21.17 even 6 588.6.i.e.373.1 2
21.20 even 2 588.6.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.a.b.1.1 1 3.2 odd 2
252.6.a.c.1.1 1 1.1 even 1 trivial
336.6.a.e.1.1 1 12.11 even 2
588.6.a.b.1.1 1 21.20 even 2
588.6.i.c.361.1 2 21.2 odd 6
588.6.i.c.373.1 2 21.11 odd 6
588.6.i.e.361.1 2 21.5 even 6
588.6.i.e.373.1 2 21.17 even 6
1008.6.a.u.1.1 1 4.3 odd 2