# Properties

 Label 300.3.b.b.149.1 Level $300$ Weight $3$ Character 300.149 Analytic conductor $8.174$ Analytic rank $0$ Dimension $2$ CM discriminant -3 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(149,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("300.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 300.b (of order $$2$$, degree $$1$$, not 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: $$8.17440793081$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 149.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 300.149 Dual form 300.3.b.b.149.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-3.00000i q^{3} +13.0000i q^{7} -9.00000 q^{9} +O(q^{10})$$ $$q-3.00000i q^{3} +13.0000i q^{7} -9.00000 q^{9} +23.0000i q^{13} -11.0000 q^{19} +39.0000 q^{21} +27.0000i q^{27} +59.0000 q^{31} -26.0000i q^{37} +69.0000 q^{39} +83.0000i q^{43} -120.000 q^{49} +33.0000i q^{57} -121.000 q^{61} -117.000i q^{63} +13.0000i q^{67} -46.0000i q^{73} +142.000 q^{79} +81.0000 q^{81} -299.000 q^{91} -177.000i q^{93} -167.000i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 18 q^{9}+O(q^{10})$$ 2 * q - 18 * q^9 $$2 q - 18 q^{9} - 22 q^{19} + 78 q^{21} + 118 q^{31} + 138 q^{39} - 240 q^{49} - 242 q^{61} + 284 q^{79} + 162 q^{81} - 598 q^{91}+O(q^{100})$$ 2 * q - 18 * q^9 - 22 * q^19 + 78 * q^21 + 118 * q^31 + 138 * q^39 - 240 * q^49 - 242 * q^61 + 284 * q^79 + 162 * q^81 - 598 * q^91

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$151$$ $$277$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$

## 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
$$3$$ − 3.00000i − 1.00000i
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 13.0000i 1.85714i 0.371154 + 0.928571i $$0.378962\pi$$
−0.371154 + 0.928571i $$0.621038\pi$$
$$8$$ 0 0
$$9$$ −9.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 23.0000i 1.76923i 0.466321 + 0.884615i $$0.345579\pi$$
−0.466321 + 0.884615i $$0.654421\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ −11.0000 −0.578947 −0.289474 0.957186i $$-0.593480\pi$$
−0.289474 + 0.957186i $$0.593480\pi$$
$$20$$ 0 0
$$21$$ 39.0000 1.85714
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 27.0000i 1.00000i
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 59.0000 1.90323 0.951613 0.307299i $$-0.0994253\pi$$
0.951613 + 0.307299i $$0.0994253\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ − 26.0000i − 0.702703i −0.936244 0.351351i $$-0.885722\pi$$
0.936244 0.351351i $$-0.114278\pi$$
$$38$$ 0 0
$$39$$ 69.0000 1.76923
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 83.0000i 1.93023i 0.261822 + 0.965116i $$0.415677\pi$$
−0.261822 + 0.965116i $$0.584323\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −120.000 −2.44898
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 33.0000i 0.578947i
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −121.000 −1.98361 −0.991803 0.127774i $$-0.959217\pi$$
−0.991803 + 0.127774i $$0.959217\pi$$
$$62$$ 0 0
$$63$$ − 117.000i − 1.85714i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 13.0000i 0.194030i 0.995283 + 0.0970149i $$0.0309295\pi$$
−0.995283 + 0.0970149i $$0.969071\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ − 46.0000i − 0.630137i −0.949069 0.315068i $$-0.897973\pi$$
0.949069 0.315068i $$-0.102027\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 142.000 1.79747 0.898734 0.438494i $$-0.144488\pi$$
0.898734 + 0.438494i $$0.144488\pi$$
$$80$$ 0 0
$$81$$ 81.0000 1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ −299.000 −3.28571
$$92$$ 0 0
$$93$$ − 177.000i − 1.90323i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ − 167.000i − 1.72165i −0.508902 0.860825i $$-0.669948\pi$$
0.508902 0.860825i $$-0.330052\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 194.000i 1.88350i 0.336321 + 0.941748i $$0.390817\pi$$
−0.336321 + 0.941748i $$0.609183\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −71.0000 −0.651376 −0.325688 0.945477i $$-0.605596\pi$$
−0.325688 + 0.945477i $$0.605596\pi$$
$$110$$ 0 0
$$111$$ −78.0000 −0.702703
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ − 207.000i − 1.76923i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 121.000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ − 146.000i − 1.14961i −0.818292 0.574803i $$-0.805079\pi$$
0.818292 0.574803i $$-0.194921\pi$$
$$128$$ 0 0
$$129$$ 249.000 1.93023
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ − 143.000i − 1.07519i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 0 0
$$139$$ 22.0000 0.158273 0.0791367 0.996864i $$-0.474784\pi$$
0.0791367 + 0.996864i $$0.474784\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 360.000i 2.44898i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 59.0000 0.390728 0.195364 0.980731i $$-0.437411\pi$$
0.195364 + 0.980731i $$0.437411\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 193.000i 1.22930i 0.788800 + 0.614650i $$0.210703\pi$$
−0.788800 + 0.614650i $$0.789297\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ − 37.0000i − 0.226994i −0.993538 0.113497i $$-0.963795\pi$$
0.993538 0.113497i $$-0.0362052\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −360.000 −2.13018
$$170$$ 0 0
$$171$$ 99.0000 0.578947
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ −1.00000 −0.00552486 −0.00276243 0.999996i $$-0.500879\pi$$
−0.00276243 + 0.999996i $$0.500879\pi$$
$$182$$ 0 0
$$183$$ 363.000i 1.98361i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −351.000 −1.85714
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 143.000i 0.740933i 0.928846 + 0.370466i $$0.120802\pi$$
−0.928846 + 0.370466i $$0.879198\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 109.000 0.547739 0.273869 0.961767i $$-0.411696\pi$$
0.273869 + 0.961767i $$0.411696\pi$$
$$200$$ 0 0
$$201$$ 39.0000 0.194030
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 419.000 1.98578 0.992891 0.119027i $$-0.0379776\pi$$
0.992891 + 0.119027i $$0.0379776\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 767.000i 3.53456i
$$218$$ 0 0
$$219$$ −138.000 −0.630137
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 83.0000i 0.372197i 0.982531 + 0.186099i $$0.0595844\pi$$
−0.982531 + 0.186099i $$0.940416\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 409.000 1.78603 0.893013 0.450031i $$-0.148587\pi$$
0.893013 + 0.450031i $$0.148587\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ − 426.000i − 1.79747i
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 479.000 1.98755 0.993776 0.111397i $$-0.0355327\pi$$
0.993776 + 0.111397i $$0.0355327\pi$$
$$242$$ 0 0
$$243$$ − 243.000i − 1.00000i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ − 253.000i − 1.02429i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 338.000 1.30502
$$260$$ 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
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 242.000 0.892989 0.446494 0.894786i $$-0.352672\pi$$
0.446494 + 0.894786i $$0.352672\pi$$
$$272$$ 0 0
$$273$$ 897.000i 3.28571i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ − 407.000i − 1.46931i −0.678439 0.734657i $$-0.737343\pi$$
0.678439 0.734657i $$-0.262657\pi$$
$$278$$ 0 0
$$279$$ −531.000 −1.90323
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ − 517.000i − 1.82686i −0.407001 0.913428i $$-0.633426\pi$$
0.407001 0.913428i $$-0.366574\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −289.000 −1.00000
$$290$$ 0 0
$$291$$ −501.000 −1.72165
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −1079.00 −3.58472
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 253.000i 0.824104i 0.911160 + 0.412052i $$0.135188\pi$$
−0.911160 + 0.412052i $$0.864812\pi$$
$$308$$ 0 0
$$309$$ 582.000 1.88350
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ − 457.000i − 1.46006i −0.683413 0.730032i $$-0.739505\pi$$
0.683413 0.730032i $$-0.260495\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 213.000i 0.651376i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 362.000 1.09366 0.546828 0.837245i $$-0.315835\pi$$
0.546828 + 0.837245i $$0.315835\pi$$
$$332$$ 0 0
$$333$$ 234.000i 0.702703i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ − 167.000i − 0.495549i −0.968818 0.247774i $$-0.920301\pi$$
0.968818 0.247774i $$-0.0796992\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ − 923.000i − 2.69096i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 502.000 1.43840 0.719198 0.694805i $$-0.244510\pi$$
0.719198 + 0.694805i $$0.244510\pi$$
$$350$$ 0 0
$$351$$ −621.000 −1.76923
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ −240.000 −0.664820
$$362$$ 0 0
$$363$$ − 363.000i − 1.00000i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ − 227.000i − 0.618529i −0.950976 0.309264i $$-0.899917\pi$$
0.950976 0.309264i $$-0.100083\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ − 577.000i − 1.54692i −0.633847 0.773458i $$-0.718525\pi$$
0.633847 0.773458i $$-0.281475\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −611.000 −1.61214 −0.806069 0.591822i $$-0.798409\pi$$
−0.806069 + 0.591822i $$0.798409\pi$$
$$380$$ 0 0
$$381$$ −438.000 −1.14961
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ − 747.000i − 1.93023i
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 793.000i 1.99748i 0.0501728 + 0.998741i $$0.484023\pi$$
−0.0501728 + 0.998741i $$0.515977\pi$$
$$398$$ 0 0
$$399$$ −429.000 −1.07519
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 1357.00i 3.36725i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 769.000 1.88020 0.940098 0.340905i $$-0.110733\pi$$
0.940098 + 0.340905i $$0.110733\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ − 66.0000i − 0.158273i
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −358.000 −0.850356 −0.425178 0.905110i $$-0.639789\pi$$
−0.425178 + 0.905110i $$0.639789\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ − 1573.00i − 3.68384i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 503.000i 1.16166i 0.814024 + 0.580831i $$0.197272\pi$$
−0.814024 + 0.580831i $$0.802728\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 709.000 1.61503 0.807517 0.589844i $$-0.200811\pi$$
0.807517 + 0.589844i $$0.200811\pi$$
$$440$$ 0 0
$$441$$ 1080.00 2.44898
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ − 177.000i − 0.390728i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 814.000i 1.78118i 0.454805 + 0.890591i $$0.349709\pi$$
−0.454805 + 0.890591i $$0.650291\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ − 526.000i − 1.13607i −0.823005 0.568035i $$-0.807704\pi$$
0.823005 0.568035i $$-0.192296\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ −169.000 −0.360341
$$470$$ 0 0
$$471$$ 579.000 1.22930
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 598.000 1.24324
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 613.000i 1.25873i 0.777111 + 0.629363i $$0.216684\pi$$
−0.777111 + 0.629363i $$0.783316\pi$$
$$488$$ 0 0
$$489$$ −111.000 −0.226994
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −851.000 −1.70541 −0.852705 0.522392i $$-0.825040\pi$$
−0.852705 + 0.522392i $$0.825040\pi$$
$$500$$ 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
$$507$$ 1080.00i 2.13018i
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 598.000 1.17025
$$512$$ 0 0
$$513$$ − 297.000i − 0.578947i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 803.000i 1.53537i 0.640826 + 0.767686i $$0.278592\pi$$
−0.640826 + 0.767686i $$0.721408\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −529.000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −241.000 −0.445471 −0.222736 0.974879i $$-0.571499\pi$$
−0.222736 + 0.974879i $$0.571499\pi$$
$$542$$ 0 0
$$543$$ 3.00000i 0.00552486i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ − 506.000i − 0.925046i −0.886607 0.462523i $$-0.846944\pi$$
0.886607 0.462523i $$-0.153056\pi$$
$$548$$ 0 0
$$549$$ 1089.00 1.98361
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 1846.00i 3.33816i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ −1909.00 −3.41503
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1053.00i 1.85714i
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −181.000 −0.316988 −0.158494 0.987360i $$-0.550664\pi$$
−0.158494 + 0.987360i $$0.550664\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 1033.00i 1.79029i 0.445770 + 0.895147i $$0.352930\pi$$
−0.445770 + 0.895147i $$0.647070\pi$$
$$578$$ 0 0
$$579$$ 429.000 0.740933
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ −649.000 −1.10187
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ − 327.000i − 0.547739i
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 1199.00 1.99501 0.997504 0.0706077i $$-0.0224939\pi$$
0.997504 + 0.0706077i $$0.0224939\pi$$
$$602$$ 0 0
$$603$$ − 117.000i − 0.194030i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 814.000i 1.34102i 0.741900 + 0.670511i $$0.233925\pi$$
−0.741900 + 0.670511i $$0.766075\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ − 1126.00i − 1.83687i −0.395574 0.918434i $$-0.629454\pi$$
0.395574 0.918434i $$-0.370546\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 949.000 1.53312 0.766559 0.642174i $$-0.221967\pi$$
0.766559 + 0.642174i $$0.221967\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1261.00 −1.99842 −0.999208 0.0398015i $$-0.987327\pi$$
−0.999208 + 0.0398015i $$0.987327\pi$$
$$632$$ 0 0
$$633$$ − 1257.00i − 1.98578i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ − 2760.00i − 4.33281i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 314.000i 0.488336i 0.969733 + 0.244168i $$0.0785148\pi$$
−0.969733 + 0.244168i $$0.921485\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 2301.00 3.53456
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 414.000i 0.630137i
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 122.000 0.184569 0.0922844 0.995733i $$-0.470583\pi$$
0.0922844 + 0.995733i $$0.470583\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 249.000 0.372197
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1154.00i 1.71471i 0.514725 + 0.857355i $$0.327894\pi$$
−0.514725 + 0.857355i $$0.672106\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 2171.00 3.19735
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ − 1227.00i − 1.78603i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −1318.00 −1.90738 −0.953690 0.300790i $$-0.902750\pi$$
−0.953690 + 0.300790i $$0.902750\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 286.000i 0.406828i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −1391.00 −1.96192 −0.980959 0.194214i $$-0.937784\pi$$
−0.980959 + 0.194214i $$0.937784\pi$$
$$710$$ 0 0
$$711$$ −1278.00 −1.79747
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ −2522.00 −3.49792
$$722$$ 0 0
$$723$$ − 1437.00i − 1.98755i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ − 947.000i − 1.30261i −0.758815 0.651307i $$-0.774221\pi$$
0.758815 0.651307i $$-0.225779\pi$$
$$728$$ 0 0
$$729$$ −729.000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 1034.00i 1.41064i 0.708888 + 0.705321i $$0.249197\pi$$
−0.708888 + 0.705321i $$0.750803\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 1222.00 1.65359 0.826793 0.562506i $$-0.190163\pi$$
0.826793 + 0.562506i $$0.190163\pi$$
$$740$$ 0 0
$$741$$ −759.000 −1.02429
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 1202.00 1.60053 0.800266 0.599645i $$-0.204691\pi$$
0.800266 + 0.599645i $$0.204691\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 673.000i 0.889036i 0.895770 + 0.444518i $$0.146625\pi$$
−0.895770 + 0.444518i $$0.853375\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ − 923.000i − 1.20970i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −671.000 −0.872562 −0.436281 0.899811i $$-0.643705\pi$$
−0.436281 + 0.899811i $$0.643705\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ − 1014.00i − 1.30502i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 613.000i 0.778907i 0.921046 + 0.389454i $$0.127336\pi$$
−0.921046 + 0.389454i $$0.872664\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ − 2783.00i − 3.50946i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ −1261.00 −1.55487 −0.777435 0.628963i $$-0.783480\pi$$
−0.777435 + 0.628963i $$0.783480\pi$$
$$812$$ 0 0
$$813$$ − 726.000i − 0.892989i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ − 913.000i − 1.11750i
$$818$$ 0 0
$$819$$ 2691.00 3.28571
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 563.000i 0.684083i 0.939685 + 0.342041i $$0.111118\pi$$
−0.939685 + 0.342041i $$0.888882\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ −458.000 −0.552473 −0.276236 0.961090i $$-0.589087\pi$$
−0.276236 + 0.961090i $$0.589087\pi$$
$$830$$ 0 0
$$831$$ −1221.00 −1.46931
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 1593.00i 1.90323i
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 841.000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 1573.00i 1.85714i
$$848$$ 0 0
$$849$$ −1551.00 −1.82686
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ − 1177.00i − 1.37984i −0.723888 0.689918i $$-0.757647\pi$$
0.723888 0.689918i $$-0.242353\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ −1418.00 −1.65076 −0.825378 0.564580i $$-0.809038\pi$$
−0.825378 + 0.564580i $$0.809038\pi$$
$$860$$ 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
$$867$$ 867.000i 1.00000i
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −299.000 −0.343284
$$872$$ 0 0
$$873$$ 1503.00i 1.72165i
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ − 1727.00i − 1.96921i −0.174785 0.984607i $$-0.555923\pi$$
0.174785 0.984607i $$-0.444077\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 443.000i 0.501699i 0.968026 + 0.250849i $$0.0807099\pi$$
−0.968026 + 0.250849i $$0.919290\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 1898.00 2.13498
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 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
$$903$$ 3237.00i 3.58472i
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 214.000i 0.235943i 0.993017 + 0.117971i $$0.0376391\pi$$
−0.993017 + 0.117971i $$0.962361\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −971.000 −1.05658 −0.528292 0.849063i $$-0.677167\pi$$
−0.528292 + 0.849063i $$0.677167\pi$$
$$920$$ 0 0
$$921$$ 759.000 0.824104
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ − 1746.00i − 1.88350i
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 1320.00 1.41783
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ − 1847.00i − 1.97118i −0.169138 0.985592i $$-0.554098\pi$$
0.169138 0.985592i $$-0.445902\pi$$
$$938$$ 0 0
$$939$$ −1371.00 −1.46006
$$940$$ 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
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 1058.00 1.11486
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 2520.00 2.62227
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 1534.00i 1.58635i 0.608994 + 0.793175i $$0.291573\pi$$
−0.608994 + 0.793175i $$0.708427\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 286.000i 0.293936i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 639.000 0.651376
$$982$$ 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
$$991$$ 1739.00 1.75479 0.877397 0.479766i $$-0.159278\pi$$
0.877397 + 0.479766i $$0.159278\pi$$
$$992$$ 0 0
$$993$$ − 1086.00i − 1.09366i
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 1894.00i 1.89970i 0.312707 + 0.949850i $$0.398764\pi$$
−0.312707 + 0.949850i $$0.601236\pi$$
$$998$$ 0 0
$$999$$ 702.000 0.702703
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 300.3.b.b.149.1 2
3.2 odd 2 CM 300.3.b.b.149.1 2
4.3 odd 2 1200.3.c.b.449.2 2
5.2 odd 4 300.3.g.a.101.1 1
5.3 odd 4 300.3.g.c.101.1 yes 1
5.4 even 2 inner 300.3.b.b.149.2 2
12.11 even 2 1200.3.c.b.449.2 2
15.2 even 4 300.3.g.a.101.1 1
15.8 even 4 300.3.g.c.101.1 yes 1
15.14 odd 2 inner 300.3.b.b.149.2 2
20.3 even 4 1200.3.l.a.401.1 1
20.7 even 4 1200.3.l.e.401.1 1
20.19 odd 2 1200.3.c.b.449.1 2
60.23 odd 4 1200.3.l.a.401.1 1
60.47 odd 4 1200.3.l.e.401.1 1
60.59 even 2 1200.3.c.b.449.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
300.3.b.b.149.1 2 1.1 even 1 trivial
300.3.b.b.149.1 2 3.2 odd 2 CM
300.3.b.b.149.2 2 5.4 even 2 inner
300.3.b.b.149.2 2 15.14 odd 2 inner
300.3.g.a.101.1 1 5.2 odd 4
300.3.g.a.101.1 1 15.2 even 4
300.3.g.c.101.1 yes 1 5.3 odd 4
300.3.g.c.101.1 yes 1 15.8 even 4
1200.3.c.b.449.1 2 20.19 odd 2
1200.3.c.b.449.1 2 60.59 even 2
1200.3.c.b.449.2 2 4.3 odd 2
1200.3.c.b.449.2 2 12.11 even 2
1200.3.l.a.401.1 1 20.3 even 4
1200.3.l.a.401.1 1 60.23 odd 4
1200.3.l.e.401.1 1 20.7 even 4
1200.3.l.e.401.1 1 60.47 odd 4