# Properties

 Label 3200.2.d.q.1601.1 Level $3200$ Weight $2$ Character 3200.1601 Analytic conductor $25.552$ Analytic rank $0$ Dimension $4$ CM discriminant -8 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3200,2,Mod(1601,3200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3200.1601");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3200 = 2^{7} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3200.d (of order $$2$$, degree $$1$$, minimal)

## 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: no Analytic conductor: $$25.5521286468$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - 2x^{2} + 4$$ x^4 - 2*x^2 + 4 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 1601.1 Root $$-1.22474 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 3200.1601 Dual form 3200.2.d.q.1601.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-3.14626i q^{3} -6.89898 q^{9} +O(q^{10})$$ $$q-3.14626i q^{3} -6.89898 q^{9} +6.61037i q^{11} +7.89898 q^{17} -2.51059i q^{19} +12.2672i q^{27} +20.7980 q^{33} +12.7980 q^{41} -8.48528i q^{43} -7.00000 q^{49} -24.8523i q^{51} -7.89898 q^{57} -14.1421i q^{59} -7.88171i q^{67} +13.6969 q^{73} +17.8990 q^{81} +14.1742i q^{83} +13.8990 q^{89} +10.0000 q^{97} -45.6048i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 8 q^{9}+O(q^{10})$$ 4 * q - 8 * q^9 $$4 q - 8 q^{9} + 12 q^{17} + 44 q^{33} + 12 q^{41} - 28 q^{49} - 12 q^{57} - 4 q^{73} + 52 q^{81} + 36 q^{89} + 40 q^{97}+O(q^{100})$$ 4 * q - 8 * q^9 + 12 * q^17 + 44 * q^33 + 12 * q^41 - 28 * q^49 - 12 * q^57 - 4 * q^73 + 52 * q^81 + 36 * q^89 + 40 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3200\mathbb{Z}\right)^\times$$.

 $$n$$ $$901$$ $$1151$$ $$2177$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$3$$ − 3.14626i − 1.81650i −0.418432 0.908248i $$-0.637420\pi$$
0.418432 0.908248i $$-0.362580\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ −6.89898 −2.29966
$$10$$ 0 0
$$11$$ 6.61037i 1.99310i 0.0829925 + 0.996550i $$0.473552\pi$$
−0.0829925 + 0.996550i $$0.526448\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 7.89898 1.91578 0.957892 0.287129i $$-0.0927008\pi$$
0.957892 + 0.287129i $$0.0927008\pi$$
$$18$$ 0 0
$$19$$ − 2.51059i − 0.575969i −0.957635 0.287984i $$-0.907015\pi$$
0.957635 0.287984i $$-0.0929851\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 12.2672i 2.36083i
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 20.7980 3.62046
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 12.7980 1.99871 0.999353 0.0359748i $$-0.0114536\pi$$
0.999353 + 0.0359748i $$0.0114536\pi$$
$$42$$ 0 0
$$43$$ − 8.48528i − 1.29399i −0.762493 0.646997i $$-0.776025\pi$$
0.762493 0.646997i $$-0.223975\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ − 24.8523i − 3.48001i
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −7.89898 −1.04625
$$58$$ 0 0
$$59$$ − 14.1421i − 1.84115i −0.390567 0.920575i $$-0.627721\pi$$
0.390567 0.920575i $$-0.372279\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ − 7.88171i − 0.962905i −0.876472 0.481452i $$-0.840109\pi$$
0.876472 0.481452i $$-0.159891\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 13.6969 1.60311 0.801553 0.597924i $$-0.204008\pi$$
0.801553 + 0.597924i $$0.204008\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 17.8990 1.98878
$$82$$ 0 0
$$83$$ 14.1742i 1.55583i 0.628372 + 0.777913i $$0.283721\pi$$
−0.628372 + 0.777913i $$0.716279\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 13.8990 1.47329 0.736644 0.676280i $$-0.236409\pi$$
0.736644 + 0.676280i $$0.236409\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 0 0
$$99$$ − 45.6048i − 4.58345i
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 4.70334i 0.454689i 0.973814 + 0.227345i $$0.0730044\pi$$
−0.973814 + 0.227345i $$0.926996\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −0.797959 −0.0750657 −0.0375328 0.999295i $$-0.511950\pi$$
−0.0375328 + 0.999295i $$0.511950\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −32.6969 −2.97245
$$122$$ 0 0
$$123$$ − 40.2658i − 3.63064i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0 0
$$129$$ −26.6969 −2.35053
$$130$$ 0 0
$$131$$ − 14.1421i − 1.23560i −0.786334 0.617802i $$-0.788023\pi$$
0.786334 0.617802i $$-0.211977\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 16.5959 1.41788 0.708942 0.705266i $$-0.249173\pi$$
0.708942 + 0.705266i $$0.249173\pi$$
$$138$$ 0 0
$$139$$ 14.8099i 1.25616i 0.778148 + 0.628080i $$0.216159\pi$$
−0.778148 + 0.628080i $$0.783841\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 22.0239i 1.81650i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ −54.4949 −4.40565
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ − 10.9959i − 0.861263i −0.902528 0.430632i $$-0.858291\pi$$
0.902528 0.430632i $$-0.141709\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 17.3205i 1.32453i
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −44.4949 −3.34444
$$178$$ 0 0
$$179$$ 5.68896i 0.425213i 0.977138 + 0.212607i $$0.0681952\pi$$
−0.977138 + 0.212607i $$0.931805\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 52.2151i 3.81835i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ −3.69694 −0.266111 −0.133056 0.991109i $$-0.542479\pi$$
−0.133056 + 0.991109i $$0.542479\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −24.7980 −1.74911
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 16.5959 1.14796
$$210$$ 0 0
$$211$$ 24.8523i 1.71090i 0.517884 + 0.855451i $$0.326720\pi$$
−0.517884 + 0.855451i $$0.673280\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ − 43.0942i − 2.91204i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 2.82843i 0.187729i 0.995585 + 0.0938647i $$0.0299221\pi$$
−0.995585 + 0.0938647i $$0.970078\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −30.0000 −1.96537 −0.982683 0.185296i $$-0.940675\pi$$
−0.982683 + 0.185296i $$0.940675\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −1.69694 −0.109309 −0.0546547 0.998505i $$-0.517406\pi$$
−0.0546547 + 0.998505i $$0.517406\pi$$
$$242$$ 0 0
$$243$$ − 19.5133i − 1.25178i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 44.5959 2.82615
$$250$$ 0 0
$$251$$ − 20.7525i − 1.30989i −0.755678 0.654943i $$-0.772693\pi$$
0.755678 0.654943i $$-0.227307\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 30.0000 1.87135 0.935674 0.352865i $$-0.114792\pi$$
0.935674 + 0.352865i $$0.114792\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ − 43.7299i − 2.67622i
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 6.32464i 0.375961i 0.982173 + 0.187980i $$0.0601941\pi$$
−0.982173 + 0.187980i $$0.939806\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 45.3939 2.67023
$$290$$ 0 0
$$291$$ − 31.4626i − 1.84437i
$$292$$ 0 0
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −81.0908 −4.70537
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ − 25.2022i − 1.43837i −0.694820 0.719183i $$-0.744516\pi$$
0.694820 0.719183i $$-0.255484\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 14.7980 0.825942
$$322$$ 0 0
$$323$$ − 19.8311i − 1.10343i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ − 9.78874i − 0.538038i −0.963135 0.269019i $$-0.913301\pi$$
0.963135 0.269019i $$-0.0866994\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 22.3939 1.21987 0.609936 0.792451i $$-0.291195\pi$$
0.609936 + 0.792451i $$0.291195\pi$$
$$338$$ 0 0
$$339$$ 2.51059i 0.136357i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ − 23.5809i − 1.26589i −0.774197 0.632945i $$-0.781846\pi$$
0.774197 0.632945i $$-0.218154\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 30.0000 1.59674 0.798369 0.602168i $$-0.205696\pi$$
0.798369 + 0.602168i $$0.205696\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ 12.6969 0.668260
$$362$$ 0 0
$$363$$ 102.873i 5.39944i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ −88.2929 −4.59634
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ − 37.1516i − 1.90835i −0.299249 0.954175i $$-0.596736\pi$$
0.299249 0.954175i $$-0.403264\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 58.5398i 2.97574i
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −44.4949 −2.24447
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −37.2929 −1.86232 −0.931158 0.364615i $$-0.881200\pi$$
−0.931158 + 0.364615i $$0.881200\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −18.3939 −0.909519 −0.454759 0.890614i $$-0.650275\pi$$
−0.454759 + 0.890614i $$0.650275\pi$$
$$410$$ 0 0
$$411$$ − 52.2151i − 2.57558i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 46.5959 2.28181
$$418$$ 0 0
$$419$$ 33.9732i 1.65970i 0.557986 + 0.829851i $$0.311574\pi$$
−0.557986 + 0.829851i $$0.688426\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 33.6969 1.61937 0.809686 0.586864i $$-0.199638\pi$$
0.809686 + 0.586864i $$0.199638\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 48.2929 2.29966
$$442$$ 0 0
$$443$$ − 37.7873i − 1.79533i −0.440681 0.897664i $$-0.645263\pi$$
0.440681 0.897664i $$-0.354737\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 16.1010 0.759854 0.379927 0.925016i $$-0.375949\pi$$
0.379927 + 0.925016i $$0.375949\pi$$
$$450$$ 0 0
$$451$$ 84.5992i 3.98362i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 42.3939 1.98310 0.991551 0.129718i $$-0.0414071\pi$$
0.991551 + 0.129718i $$0.0414071\pi$$
$$458$$ 0 0
$$459$$ 96.8985i 4.52284i
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ − 31.1127i − 1.43972i −0.694117 0.719862i $$-0.744205\pi$$
0.694117 0.719862i $$-0.255795\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 56.0908 2.57906
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ −34.5959 −1.56448
$$490$$ 0 0
$$491$$ − 14.1421i − 0.638226i −0.947717 0.319113i $$-0.896615\pi$$
0.947717 0.319113i $$-0.103385\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 42.4264i 1.89927i 0.313363 + 0.949633i $$0.398544\pi$$
−0.313363 + 0.949633i $$0.601456\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ − 40.9014i − 1.81650i
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 30.7980 1.35976
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −36.1918 −1.58559 −0.792797 0.609486i $$-0.791376\pi$$
−0.792797 + 0.609486i $$0.791376\pi$$
$$522$$ 0 0
$$523$$ − 45.6369i − 1.99556i −0.0665832 0.997781i $$-0.521210\pi$$
0.0665832 0.997781i $$-0.478790\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ 97.5663i 4.23402i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 17.8990 0.772398
$$538$$ 0 0
$$539$$ − 46.2726i − 1.99310i
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 44.0798i 1.88472i 0.334606 + 0.942358i $$0.391397\pi$$
−0.334606 + 0.942358i $$0.608603\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 164.283 6.93602
$$562$$ 0 0
$$563$$ 36.7696i 1.54965i 0.632175 + 0.774826i $$0.282163\pi$$
−0.632175 + 0.774826i $$0.717837\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −40.5959 −1.70187 −0.850935 0.525271i $$-0.823964\pi$$
−0.850935 + 0.525271i $$0.823964\pi$$
$$570$$ 0 0
$$571$$ 42.4264i 1.77549i 0.460336 + 0.887745i $$0.347729\pi$$
−0.460336 + 0.887745i $$0.652271\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −12.3939 −0.515964 −0.257982 0.966150i $$-0.583058\pi$$
−0.257982 + 0.966150i $$0.583058\pi$$
$$578$$ 0 0
$$579$$ 11.6315i 0.483391i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ − 18.8455i − 0.777836i −0.921272 0.388918i $$-0.872849\pi$$
0.921272 0.388918i $$-0.127151\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 48.1918 1.97900 0.989501 0.144528i $$-0.0461663\pi$$
0.989501 + 0.144528i $$0.0461663\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −8.30306 −0.338689 −0.169344 0.985557i $$-0.554165\pi$$
−0.169344 + 0.985557i $$0.554165\pi$$
$$602$$ 0 0
$$603$$ 54.3758i 2.21435i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −30.0000 −1.20775 −0.603877 0.797077i $$-0.706378\pi$$
−0.603877 + 0.797077i $$0.706378\pi$$
$$618$$ 0 0
$$619$$ 42.4264i 1.70526i 0.522514 + 0.852631i $$0.324994\pi$$
−0.522514 + 0.852631i $$0.675006\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ − 52.2151i − 2.08527i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 78.1918 3.10785
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −42.0000 −1.65890 −0.829450 0.558581i $$-0.811346\pi$$
−0.829450 + 0.558581i $$0.811346\pi$$
$$642$$ 0 0
$$643$$ − 8.48528i − 0.334627i −0.985904 0.167313i $$-0.946491\pi$$
0.985904 0.167313i $$-0.0535092\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 93.4847 3.66960
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −94.4949 −3.68660
$$658$$ 0 0
$$659$$ 8.45317i 0.329289i 0.986353 + 0.164644i $$0.0526477\pi$$
−0.986353 + 0.164644i $$0.947352\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 10.0000 0.385472 0.192736 0.981251i $$-0.438264\pi$$
0.192736 + 0.981251i $$0.438264\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 8.89898 0.341010
$$682$$ 0 0
$$683$$ 51.9294i 1.98702i 0.113728 + 0.993512i $$0.463721\pi$$
−0.113728 + 0.993512i $$0.536279\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ − 27.1092i − 1.03128i −0.856804 0.515642i $$-0.827553\pi$$
0.856804 0.515642i $$-0.172447\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 101.091 3.82909
$$698$$ 0 0
$$699$$ 94.3879i 3.57008i
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 5.33902i 0.198560i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ −7.69694 −0.285072
$$730$$ 0 0
$$731$$ − 67.0251i − 2.47901i
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 52.1010 1.91917
$$738$$ 0 0
$$739$$ 42.4264i 1.56068i 0.625355 + 0.780340i $$0.284954\pi$$
−0.625355 + 0.780340i $$0.715046\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ − 97.7878i − 3.57787i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ −65.2929 −2.37940
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 17.2020 0.623574 0.311787 0.950152i $$-0.399073\pi$$
0.311787 + 0.950152i $$0.399073\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −55.0908 −1.98663 −0.993313 0.115454i $$-0.963168\pi$$
−0.993313 + 0.115454i $$0.963168\pi$$
$$770$$ 0 0
$$771$$ − 94.3879i − 3.39930i
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ − 32.1304i − 1.15119i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 25.4558i 0.907403i 0.891154 + 0.453701i $$0.149897\pi$$
−0.891154 + 0.453701i $$0.850103\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −95.8888 −3.38806
$$802$$ 0 0
$$803$$ 90.5418i 3.19515i
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −6.00000 −0.210949 −0.105474 0.994422i $$-0.533636\pi$$
−0.105474 + 0.994422i $$0.533636\pi$$
$$810$$ 0 0
$$811$$ 42.4264i 1.48979i 0.667180 + 0.744896i $$0.267501\pi$$
−0.667180 + 0.744896i $$0.732499\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −21.3031 −0.745300
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 56.6649i 1.97043i 0.171321 + 0.985215i $$0.445196\pi$$
−0.171321 + 0.985215i $$0.554804\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −55.2929 −1.91578
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 29.0000 1.00000
$$842$$ 0 0
$$843$$ 56.6328i 1.95054i
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 19.8990 0.682931
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −46.5959 −1.59169 −0.795843 0.605503i $$-0.792972\pi$$
−0.795843 + 0.605503i $$0.792972\pi$$
$$858$$ 0 0
$$859$$ − 54.4721i − 1.85856i −0.369370 0.929282i $$-0.620427\pi$$
0.369370 0.929282i $$-0.379573\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ − 142.821i − 4.85046i
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ −68.9898 −2.33495
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ − 31.4305i − 1.05772i −0.848709 0.528861i $$-0.822619\pi$$
0.848709 0.528861i $$-0.177381\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 118.319i 3.96383i
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 59.3970i 1.97224i 0.166022 + 0.986122i $$0.446908\pi$$
−0.166022 + 0.986122i $$0.553092\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ −93.6969 −3.10092
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ −79.2929 −2.61279
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 54.0000 1.77168 0.885841 0.463988i $$-0.153582\pi$$
0.885841 + 0.463988i $$0.153582\pi$$
$$930$$ 0 0
$$931$$ 17.5741i 0.575969i
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −61.0908 −1.99575 −0.997875 0.0651578i $$-0.979245\pi$$
−0.997875 + 0.0651578i $$0.979245\pi$$
$$938$$ 0 0
$$939$$ 31.4626i 1.02674i
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ − 53.7401i − 1.74632i −0.487435 0.873160i $$-0.662067\pi$$
0.487435 0.873160i $$-0.337933\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −18.1918 −0.589291 −0.294646 0.955607i $$-0.595202\pi$$
−0.294646 + 0.955607i $$0.595202\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ − 32.4483i − 1.04563i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ 0 0
$$969$$ −62.3939 −2.00438
$$970$$ 0 0
$$971$$ 31.2090i 1.00155i 0.865579 + 0.500773i $$0.166951\pi$$
−0.865579 + 0.500773i $$0.833049\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 56.8888 1.82003 0.910017 0.414572i $$-0.136069\pi$$
0.910017 + 0.414572i $$0.136069\pi$$
$$978$$ 0 0
$$979$$ 91.8773i 2.93641i
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 0 0
$$993$$ −30.7980 −0.977344
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 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 3200.2.d.q.1601.1 yes 4
4.3 odd 2 inner 3200.2.d.q.1601.4 yes 4
5.2 odd 4 3200.2.f.s.449.2 8
5.3 odd 4 3200.2.f.s.449.8 8
5.4 even 2 3200.2.d.n.1601.4 yes 4
8.3 odd 2 CM 3200.2.d.q.1601.1 yes 4
8.5 even 2 inner 3200.2.d.q.1601.4 yes 4
16.3 odd 4 6400.2.a.cr.1.1 4
16.5 even 4 6400.2.a.cr.1.1 4
16.11 odd 4 6400.2.a.cr.1.4 4
16.13 even 4 6400.2.a.cr.1.4 4
20.3 even 4 3200.2.f.s.449.1 8
20.7 even 4 3200.2.f.s.449.7 8
20.19 odd 2 3200.2.d.n.1601.1 4
40.3 even 4 3200.2.f.s.449.8 8
40.13 odd 4 3200.2.f.s.449.1 8
40.19 odd 2 3200.2.d.n.1601.4 yes 4
40.27 even 4 3200.2.f.s.449.2 8
40.29 even 2 3200.2.d.n.1601.1 4
40.37 odd 4 3200.2.f.s.449.7 8
80.19 odd 4 6400.2.a.cq.1.4 4
80.29 even 4 6400.2.a.cq.1.1 4
80.59 odd 4 6400.2.a.cq.1.1 4
80.69 even 4 6400.2.a.cq.1.4 4

By twisted newform
Twist Min Dim Char Parity Ord Type
3200.2.d.n.1601.1 4 20.19 odd 2
3200.2.d.n.1601.1 4 40.29 even 2
3200.2.d.n.1601.4 yes 4 5.4 even 2
3200.2.d.n.1601.4 yes 4 40.19 odd 2
3200.2.d.q.1601.1 yes 4 1.1 even 1 trivial
3200.2.d.q.1601.1 yes 4 8.3 odd 2 CM
3200.2.d.q.1601.4 yes 4 4.3 odd 2 inner
3200.2.d.q.1601.4 yes 4 8.5 even 2 inner
3200.2.f.s.449.1 8 20.3 even 4
3200.2.f.s.449.1 8 40.13 odd 4
3200.2.f.s.449.2 8 5.2 odd 4
3200.2.f.s.449.2 8 40.27 even 4
3200.2.f.s.449.7 8 20.7 even 4
3200.2.f.s.449.7 8 40.37 odd 4
3200.2.f.s.449.8 8 5.3 odd 4
3200.2.f.s.449.8 8 40.3 even 4
6400.2.a.cq.1.1 4 80.29 even 4
6400.2.a.cq.1.1 4 80.59 odd 4
6400.2.a.cq.1.4 4 80.19 odd 4
6400.2.a.cq.1.4 4 80.69 even 4
6400.2.a.cr.1.1 4 16.3 odd 4
6400.2.a.cr.1.1 4 16.5 even 4
6400.2.a.cr.1.4 4 16.11 odd 4
6400.2.a.cr.1.4 4 16.13 even 4