# Properties

 Label 2175.1.b.c.2174.3 Level $2175$ Weight $1$ Character 2175.2174 Analytic conductor $1.085$ Analytic rank $0$ Dimension $6$ Projective image $D_{9}$ CM discriminant -87 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,1,Mod(2174,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2175.2174");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2175 = 3 \cdot 5^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2175.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: $$1.08546640248$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.419904.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} + 6x^{4} + 9x^{2} + 1$$ x^6 + 6*x^4 + 9*x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{9}$$ Projective field: Galois closure of 9.1.895152515625.1

## Embedding invariants

 Embedding label 2174.3 Root $$1.87939i$$ of defining polynomial Character $$\chi$$ $$=$$ 2175.2174 Dual form 2175.1.b.c.2174.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-0.347296i q^{2} +1.00000i q^{3} +0.879385 q^{4} +0.347296 q^{6} -1.87939i q^{7} -0.652704i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-0.347296i q^{2} +1.00000i q^{3} +0.879385 q^{4} +0.347296 q^{6} -1.87939i q^{7} -0.652704i q^{8} -1.00000 q^{9} -1.53209 q^{11} +0.879385i q^{12} -0.347296i q^{13} -0.652704 q^{14} +0.652704 q^{16} -1.53209i q^{17} +0.347296i q^{18} +1.87939 q^{21} +0.532089i q^{22} +0.652704 q^{24} -0.120615 q^{26} -1.00000i q^{27} -1.65270i q^{28} +1.00000 q^{29} -0.879385i q^{32} -1.53209i q^{33} -0.532089 q^{34} -0.879385 q^{36} +0.347296 q^{39} +1.00000 q^{41} -0.652704i q^{42} -1.34730 q^{44} +1.87939i q^{47} +0.652704i q^{48} -2.53209 q^{49} +1.53209 q^{51} -0.305407i q^{52} -0.347296 q^{54} -1.22668 q^{56} -0.347296i q^{58} +1.87939i q^{63} +0.347296 q^{64} -0.532089 q^{66} +1.53209i q^{67} -1.34730i q^{68} +0.652704i q^{72} +2.87939i q^{77} -0.120615i q^{78} +1.00000 q^{81} -0.347296i q^{82} +1.65270 q^{84} +1.00000i q^{87} +1.00000i q^{88} +0.347296 q^{89} -0.652704 q^{91} +0.652704 q^{94} +0.879385 q^{96} +0.879385i q^{98} +1.53209 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 6 q^{4} - 6 q^{9}+O(q^{10})$$ 6 * q - 6 * q^4 - 6 * q^9 $$6 q - 6 q^{4} - 6 q^{9} - 6 q^{14} + 6 q^{16} + 6 q^{24} - 12 q^{26} + 6 q^{29} + 6 q^{34} + 6 q^{36} + 6 q^{41} - 6 q^{44} - 6 q^{49} + 6 q^{56} + 6 q^{66} + 6 q^{81} + 12 q^{84} - 6 q^{91} + 6 q^{94} - 6 q^{96}+O(q^{100})$$ 6 * q - 6 * q^4 - 6 * q^9 - 6 * q^14 + 6 * q^16 + 6 * q^24 - 12 * q^26 + 6 * q^29 + 6 * q^34 + 6 * q^36 + 6 * q^41 - 6 * q^44 - 6 * q^49 + 6 * q^56 + 6 * q^66 + 6 * q^81 + 12 * q^84 - 6 * q^91 + 6 * q^94 - 6 * q^96

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2175\mathbb{Z}\right)^\times$$.

 $$n$$ $$901$$ $$1451$$ $$2002$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ − 0.347296i − 0.347296i −0.984808 0.173648i $$-0.944444\pi$$
0.984808 0.173648i $$-0.0555556\pi$$
$$3$$ 1.00000i 1.00000i
$$4$$ 0.879385 0.879385
$$5$$ 0 0
$$6$$ 0.347296 0.347296
$$7$$ − 1.87939i − 1.87939i −0.342020 0.939693i $$-0.611111\pi$$
0.342020 0.939693i $$-0.388889\pi$$
$$8$$ − 0.652704i − 0.652704i
$$9$$ −1.00000 −1.00000
$$10$$ 0 0
$$11$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$12$$ 0.879385i 0.879385i
$$13$$ − 0.347296i − 0.347296i −0.984808 0.173648i $$-0.944444\pi$$
0.984808 0.173648i $$-0.0555556\pi$$
$$14$$ −0.652704 −0.652704
$$15$$ 0 0
$$16$$ 0.652704 0.652704
$$17$$ − 1.53209i − 1.53209i −0.642788 0.766044i $$-0.722222\pi$$
0.642788 0.766044i $$-0.277778\pi$$
$$18$$ 0.347296i 0.347296i
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 1.87939 1.87939
$$22$$ 0.532089i 0.532089i
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0.652704 0.652704
$$25$$ 0 0
$$26$$ −0.120615 −0.120615
$$27$$ − 1.00000i − 1.00000i
$$28$$ − 1.65270i − 1.65270i
$$29$$ 1.00000 1.00000
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ − 0.879385i − 0.879385i
$$33$$ − 1.53209i − 1.53209i
$$34$$ −0.532089 −0.532089
$$35$$ 0 0
$$36$$ −0.879385 −0.879385
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 0 0
$$39$$ 0.347296 0.347296
$$40$$ 0 0
$$41$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$42$$ − 0.652704i − 0.652704i
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ −1.34730 −1.34730
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 1.87939i 1.87939i 0.342020 + 0.939693i $$0.388889\pi$$
−0.342020 + 0.939693i $$0.611111\pi$$
$$48$$ 0.652704i 0.652704i
$$49$$ −2.53209 −2.53209
$$50$$ 0 0
$$51$$ 1.53209 1.53209
$$52$$ − 0.305407i − 0.305407i
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ −0.347296 −0.347296
$$55$$ 0 0
$$56$$ −1.22668 −1.22668
$$57$$ 0 0
$$58$$ − 0.347296i − 0.347296i
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 1.87939i 1.87939i
$$64$$ 0.347296 0.347296
$$65$$ 0 0
$$66$$ −0.532089 −0.532089
$$67$$ 1.53209i 1.53209i 0.642788 + 0.766044i $$0.277778\pi$$
−0.642788 + 0.766044i $$0.722222\pi$$
$$68$$ − 1.34730i − 1.34730i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0.652704i 0.652704i
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 2.87939i 2.87939i
$$78$$ − 0.120615i − 0.120615i
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 1.00000 1.00000
$$82$$ − 0.347296i − 0.347296i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 1.65270 1.65270
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 1.00000i 1.00000i
$$88$$ 1.00000i 1.00000i
$$89$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$90$$ 0 0
$$91$$ −0.652704 −0.652704
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0.652704 0.652704
$$95$$ 0 0
$$96$$ 0.879385 0.879385
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0.879385i 0.879385i
$$99$$ 1.53209 1.53209
$$100$$ 0 0
$$101$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$102$$ − 0.532089i − 0.532089i
$$103$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$104$$ −0.226682 −0.226682
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ − 0.879385i − 0.879385i
$$109$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ − 1.22668i − 1.22668i
$$113$$ − 1.87939i − 1.87939i −0.342020 0.939693i $$-0.611111\pi$$
0.342020 0.939693i $$-0.388889\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0.879385 0.879385
$$117$$ 0.347296i 0.347296i
$$118$$ 0 0
$$119$$ −2.87939 −2.87939
$$120$$ 0 0
$$121$$ 1.34730 1.34730
$$122$$ 0 0
$$123$$ 1.00000i 1.00000i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0.652704 0.652704
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ − 1.00000i − 1.00000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$132$$ − 1.34730i − 1.34730i
$$133$$ 0 0
$$134$$ 0.532089 0.532089
$$135$$ 0 0
$$136$$ −1.00000 −1.00000
$$137$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$138$$ 0 0
$$139$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$140$$ 0 0
$$141$$ −1.87939 −1.87939
$$142$$ 0 0
$$143$$ 0.532089i 0.532089i
$$144$$ −0.652704 −0.652704
$$145$$ 0 0
$$146$$ 0 0
$$147$$ − 2.53209i − 2.53209i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$152$$ 0 0
$$153$$ 1.53209i 1.53209i
$$154$$ 1.00000 1.00000
$$155$$ 0 0
$$156$$ 0.305407 0.305407
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ − 0.347296i − 0.347296i
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0.879385 0.879385
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ − 1.22668i − 1.22668i
$$169$$ 0.879385 0.879385
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0.347296 0.347296
$$175$$ 0 0
$$176$$ −1.00000 −1.00000
$$177$$ 0 0
$$178$$ − 0.120615i − 0.120615i
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$182$$ 0.226682i 0.226682i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 2.34730i 2.34730i
$$188$$ 1.65270i 1.65270i
$$189$$ −1.87939 −1.87939
$$190$$ 0 0
$$191$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$192$$ 0.347296i 0.347296i
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −2.22668 −2.22668
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ − 0.532089i − 0.532089i
$$199$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$200$$ 0 0
$$201$$ −1.53209 −1.53209
$$202$$ 0.120615i 0.120615i
$$203$$ − 1.87939i − 1.87939i
$$204$$ 1.34730 1.34730
$$205$$ 0 0
$$206$$ 0.347296 0.347296
$$207$$ 0 0
$$208$$ − 0.226682i − 0.226682i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ −0.652704 −0.652704
$$217$$ 0 0
$$218$$ 0.120615i 0.120615i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −0.532089 −0.532089
$$222$$ 0 0
$$223$$ − 1.53209i − 1.53209i −0.642788 0.766044i $$-0.722222\pi$$
0.642788 0.766044i $$-0.277778\pi$$
$$224$$ −1.65270 −1.65270
$$225$$ 0 0
$$226$$ −0.652704 −0.652704
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ −2.87939 −2.87939
$$232$$ − 0.652704i − 0.652704i
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0.120615 0.120615
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 1.00000i 1.00000i
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$242$$ − 0.467911i − 0.467911i
$$243$$ 1.00000i 1.00000i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0.347296 0.347296
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$252$$ 1.65270i 1.65270i
$$253$$ 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
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −1.00000 −1.00000
$$262$$ − 0.652704i − 0.652704i
$$263$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$264$$ −1.00000 −1.00000
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0.347296i 0.347296i
$$268$$ 1.34730i 1.34730i
$$269$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ − 1.00000i − 1.00000i
$$273$$ − 0.652704i − 0.652704i
$$274$$ 0.347296 0.347296
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 1.53209i 1.53209i 0.642788 + 0.766044i $$0.277778\pi$$
−0.642788 + 0.766044i $$0.722222\pi$$
$$278$$ − 0.652704i − 0.652704i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0.652704i 0.652704i
$$283$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0.184793 0.184793
$$287$$ − 1.87939i − 1.87939i
$$288$$ 0.879385i 0.879385i
$$289$$ −1.34730 −1.34730
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0.347296i 0.347296i 0.984808 + 0.173648i $$0.0555556\pi$$
−0.984808 + 0.173648i $$0.944444\pi$$
$$294$$ −0.879385 −0.879385
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 1.53209i 1.53209i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0.347296i 0.347296i
$$303$$ − 0.347296i − 0.347296i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0.532089 0.532089
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 2.53209i 2.53209i
$$309$$ −1.00000 −1.00000
$$310$$ 0 0
$$311$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$312$$ − 0.226682i − 0.226682i
$$313$$ 1.87939i 1.87939i 0.342020 + 0.939693i $$0.388889\pi$$
−0.342020 + 0.939693i $$0.611111\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ − 0.347296i − 0.347296i −0.984808 0.173648i $$-0.944444\pi$$
0.984808 0.173648i $$-0.0555556\pi$$
$$318$$ 0 0
$$319$$ −1.53209 −1.53209
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0.879385 0.879385
$$325$$ 0 0
$$326$$ 0 0
$$327$$ − 0.347296i − 0.347296i
$$328$$ − 0.652704i − 0.652704i
$$329$$ 3.53209 3.53209
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 1.22668 1.22668
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ − 0.305407i − 0.305407i
$$339$$ 1.87939 1.87939
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 2.87939i 2.87939i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0.879385i 0.879385i
$$349$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$350$$ 0 0
$$351$$ −0.347296 −0.347296
$$352$$ 1.34730i 1.34730i
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0.305407 0.305407
$$357$$ − 2.87939i − 2.87939i
$$358$$ 0 0
$$359$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ − 0.532089i − 0.532089i
$$363$$ 1.34730i 1.34730i
$$364$$ −0.573978 −0.573978
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ −1.00000 −1.00000
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$374$$ 0.815207 0.815207
$$375$$ 0 0
$$376$$ 1.22668 1.22668
$$377$$ − 0.347296i − 0.347296i
$$378$$ 0.652704i 0.652704i
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0.694593i 0.694593i
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 1.00000 1.00000
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.65270i 1.65270i
$$393$$ 1.87939i 1.87939i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 1.34730 1.34730
$$397$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$398$$ 0.120615i 0.120615i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0.532089i 0.532089i
$$403$$ 0 0
$$404$$ −0.305407 −0.305407
$$405$$ 0 0
$$406$$ −0.652704 −0.652704
$$407$$ 0 0
$$408$$ − 1.00000i − 1.00000i
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ −1.00000 −1.00000
$$412$$ 0.879385i 0.879385i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −0.305407 −0.305407
$$417$$ 1.87939i 1.87939i
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ − 1.87939i − 1.87939i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −0.532089 −0.532089
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ − 0.652704i − 0.652704i
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −0.305407 −0.305407
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$440$$ 0 0
$$441$$ 2.53209 2.53209
$$442$$ 0.184793i 0.184793i
$$443$$ 0.347296i 0.347296i 0.984808 + 0.173648i $$0.0555556\pi$$
−0.984808 + 0.173648i $$0.944444\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −0.532089 −0.532089
$$447$$ 0 0
$$448$$ − 0.652704i − 0.652704i
$$449$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$450$$ 0 0
$$451$$ −1.53209 −1.53209
$$452$$ − 1.65270i − 1.65270i
$$453$$ − 1.00000i − 1.00000i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ − 1.87939i − 1.87939i −0.342020 0.939693i $$-0.611111\pi$$
0.342020 0.939693i $$-0.388889\pi$$
$$458$$ 0 0
$$459$$ −1.53209 −1.53209
$$460$$ 0 0
$$461$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$462$$ 1.00000i 1.00000i
$$463$$ − 0.347296i − 0.347296i −0.984808 0.173648i $$-0.944444\pi$$
0.984808 0.173648i $$-0.0555556\pi$$
$$464$$ 0.652704 0.652704
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$468$$ 0.305407i 0.305407i
$$469$$ 2.87939 2.87939
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −2.53209 −2.53209
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0.652704i 0.652704i
$$483$$ 0 0
$$484$$ 1.18479 1.18479
$$485$$ 0 0
$$486$$ 0.347296 0.347296
$$487$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$492$$ 0.879385i 0.879385i
$$493$$ − 1.53209i − 1.53209i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0.120615i 0.120615i
$$503$$ 0.347296i 0.347296i 0.984808 + 0.173648i $$0.0555556\pi$$
−0.984808 + 0.173648i $$0.944444\pi$$
$$504$$ 1.22668 1.22668
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.879385i 0.879385i
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ − 1.00000i − 1.00000i
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ − 2.87939i − 2.87939i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0.347296i 0.347296i
$$523$$ − 0.347296i − 0.347296i −0.984808 0.173648i $$-0.944444\pi$$
0.984808 0.173648i $$-0.0555556\pi$$
$$524$$ 1.65270 1.65270
$$525$$ 0 0
$$526$$ −0.347296 −0.347296
$$527$$ 0 0
$$528$$ − 1.00000i − 1.00000i
$$529$$ −1.00000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ − 0.347296i − 0.347296i
$$534$$ 0.120615 0.120615
$$535$$ 0 0
$$536$$ 1.00000 1.00000
$$537$$ 0 0
$$538$$ − 0.532089i − 0.532089i
$$539$$ 3.87939 3.87939
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 1.53209i 1.53209i
$$544$$ −1.34730 −1.34730
$$545$$ 0 0
$$546$$ −0.226682 −0.226682
$$547$$ 1.53209i 1.53209i 0.642788 + 0.766044i $$0.277778\pi$$
−0.642788 + 0.766044i $$0.722222\pi$$
$$548$$ 0.879385i 0.879385i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0.532089 0.532089
$$555$$ 0 0
$$556$$ 1.65270 1.65270
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −2.34730 −2.34730
$$562$$ 0 0
$$563$$ 1.53209i 1.53209i 0.642788 + 0.766044i $$0.277778\pi$$
−0.642788 + 0.766044i $$0.722222\pi$$
$$564$$ −1.65270 −1.65270
$$565$$ 0 0
$$566$$ 0.347296 0.347296
$$567$$ − 1.87939i − 1.87939i
$$568$$ 0 0
$$569$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$570$$ 0 0
$$571$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ 0.467911i 0.467911i
$$573$$ − 2.00000i − 2.00000i
$$574$$ −0.652704 −0.652704
$$575$$ 0 0
$$576$$ −0.347296 −0.347296
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 0.467911i 0.467911i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0.120615 0.120615
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ − 2.22668i − 2.22668i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0.532089 0.532089
$$595$$ 0 0
$$596$$ 0 0
$$597$$ − 0.347296i − 0.347296i
$$598$$ 0 0
$$599$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ − 1.53209i − 1.53209i
$$604$$ −0.879385 −0.879385
$$605$$ 0 0
$$606$$ −0.120615 −0.120615
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 1.87939 1.87939
$$610$$ 0 0
$$611$$ 0.652704 0.652704
$$612$$ 1.34730i 1.34730i
$$613$$ 1.87939i 1.87939i 0.342020 + 0.939693i $$0.388889\pi$$
−0.342020 + 0.939693i $$0.611111\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 1.87939 1.87939
$$617$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$618$$ 0.347296i 0.347296i
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ − 0.652704i − 0.652704i
$$623$$ − 0.652704i − 0.652704i
$$624$$ 0.226682 0.226682
$$625$$ 0 0
$$626$$ 0.652704 0.652704
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −0.120615 −0.120615
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0.879385i 0.879385i
$$638$$ 0.532089i 0.532089i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$642$$ 0 0
$$643$$ − 1.53209i − 1.53209i −0.642788 0.766044i $$-0.722222\pi$$
0.642788 0.766044i $$-0.277778\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ − 0.652704i − 0.652704i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.53209i 1.53209i 0.642788 + 0.766044i $$0.277778\pi$$
−0.642788 + 0.766044i $$0.722222\pi$$
$$654$$ −0.120615 −0.120615
$$655$$ 0 0
$$656$$ 0.652704 0.652704
$$657$$ 0 0
$$658$$ − 1.22668i − 1.22668i
$$659$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$660$$ 0 0
$$661$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$662$$ 0 0
$$663$$ − 0.532089i − 0.532089i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 1.53209 1.53209
$$670$$ 0 0
$$671$$ 0 0
$$672$$ − 1.65270i − 1.65270i
$$673$$ − 0.347296i − 0.347296i −0.984808 0.173648i $$-0.944444\pi$$
0.984808 0.173648i $$-0.0555556\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0.773318 0.773318
$$677$$ − 1.53209i − 1.53209i −0.642788 0.766044i $$-0.722222\pi$$
0.642788 0.766044i $$-0.277778\pi$$
$$678$$ − 0.652704i − 0.652704i
$$679$$ 0 0
$$680$$ 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
$$686$$ 1.00000 1.00000
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$692$$ 0 0
$$693$$ − 2.87939i − 2.87939i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0.652704 0.652704
$$697$$ − 1.53209i − 1.53209i
$$698$$ − 0.347296i − 0.347296i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0.120615i 0.120615i
$$703$$ 0 0
$$704$$ −0.532089 −0.532089
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0.652704i 0.652704i
$$708$$ 0 0
$$709$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ − 0.226682i − 0.226682i
$$713$$ 0 0
$$714$$ −1.00000 −1.00000
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0.347296i 0.347296i
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 1.87939 1.87939
$$722$$ − 0.347296i − 0.347296i
$$723$$ − 1.87939i − 1.87939i
$$724$$ 1.34730 1.34730
$$725$$ 0 0
$$726$$ 0.467911 0.467911
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0.426022i 0.426022i
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ − 2.34730i − 2.34730i
$$738$$ 0.347296i 0.347296i
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ − 1.87939i − 1.87939i −0.342020 0.939693i $$-0.611111\pi$$
0.342020 0.939693i $$-0.388889\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −0.694593 −0.694593
$$747$$ 0 0
$$748$$ 2.06418i 2.06418i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 1.22668i 1.22668i
$$753$$ − 0.347296i − 0.347296i
$$754$$ −0.120615 −0.120615
$$755$$ 0 0
$$756$$ −1.65270 −1.65270
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0.652704i 0.652704i
$$764$$ −1.75877 −1.75877
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ − 0.120615i − 0.120615i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ − 1.00000i − 1.00000i
$$784$$ −1.65270 −1.65270
$$785$$ 0 0
$$786$$ 0.652704 0.652704
$$787$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$788$$ 0 0
$$789$$ 1.00000 1.00000
$$790$$ 0 0
$$791$$ −3.53209 −3.53209
$$792$$ − 1.00000i − 1.00000i
$$793$$ 0 0
$$794$$ −0.347296 −0.347296
$$795$$ 0 0
$$796$$ −0.305407 −0.305407
$$797$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$798$$ 0 0
$$799$$ 2.87939 2.87939
$$800$$ 0 0
$$801$$ −0.347296 −0.347296
$$802$$ 0 0
$$803$$ 0 0
$$804$$ −1.34730 −1.34730
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 1.53209i 1.53209i
$$808$$ 0.226682i 0.226682i
$$809$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$810$$ 0 0
$$811$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$812$$ − 1.65270i − 1.65270i
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 1.00000 1.00000
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0.652704 0.652704
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0.347296i 0.347296i
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0.652704 0.652704
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ −1.53209 −1.53209
$$832$$ − 0.120615i − 0.120615i
$$833$$ 3.87939i 3.87939i
$$834$$ 0.652704 0.652704
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ −0.652704 −0.652704
$$847$$ − 2.53209i − 2.53209i
$$848$$ 0 0
$$849$$ −1.00000 −1.00000
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0.184793i 0.184793i
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 1.87939 1.87939
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ −0.879385 −0.879385
$$865$$ 0 0
$$866$$ 0 0
$$867$$ − 1.34730i − 1.34730i
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0.532089 0.532089
$$872$$ 0.226682i 0.226682i
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$878$$ 0.532089i 0.532089i
$$879$$ −0.347296 −0.347296
$$880$$ 0 0
$$881$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$882$$ − 0.879385i − 0.879385i
$$883$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$884$$ −0.467911 −0.467911
$$885$$ 0 0
$$886$$ 0.120615 0.120615
$$887$$ 1.87939i 1.87939i 0.342020 + 0.939693i $$0.388889\pi$$
−0.342020 + 0.939693i $$0.611111\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −1.53209 −1.53209
$$892$$ − 1.34730i − 1.34730i
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ −1.87939 −1.87939
$$897$$ 0 0
$$898$$ 0.652704i 0.652704i
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0.532089i 0.532089i
$$903$$ 0 0
$$904$$ −1.22668 −1.22668
$$905$$ 0 0
$$906$$ −0.347296 −0.347296
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 0.347296 0.347296
$$910$$ 0 0
$$911$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ −0.652704 −0.652704
$$915$$ 0 0
$$916$$ 0 0
$$917$$ − 3.53209i − 3.53209i
$$918$$ 0.532089i 0.532089i
$$919$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ − 0.347296i − 0.347296i
$$923$$ 0 0
$$924$$ −2.53209 −2.53209
$$925$$ 0 0
$$926$$ −0.120615 −0.120615
$$927$$ − 1.00000i − 1.00000i
$$928$$ − 0.879385i − 0.879385i
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 1.87939i 1.87939i
$$934$$ 0.347296 0.347296
$$935$$ 0 0
$$936$$ 0.226682 0.226682
$$937$$ 0.347296i 0.347296i 0.984808 + 0.173648i $$0.0555556\pi$$
−0.984808 + 0.173648i $$0.944444\pi$$
$$938$$ − 1.00000i − 1.00000i
$$939$$ −1.87939 −1.87939
$$940$$ 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
$$947$$ − 1.53209i − 1.53209i −0.642788 0.766044i $$-0.722222\pi$$
0.642788 0.766044i $$-0.277778\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0.347296 0.347296
$$952$$ 1.87939i 1.87939i
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ − 1.53209i − 1.53209i
$$958$$ 0.347296i 0.347296i
$$959$$ 1.87939 1.87939
$$960$$ 0 0
$$961$$ 1.00000 1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −1.65270 −1.65270
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ − 0.879385i − 0.879385i
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$972$$ 0.879385i 0.879385i
$$973$$ − 3.53209i − 3.53209i
$$974$$ 0.694593 0.694593
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ −0.532089 −0.532089
$$980$$ 0 0
$$981$$ 0.347296 0.347296
$$982$$ − 0.347296i − 0.347296i
$$983$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$984$$ 0.652704 0.652704
$$985$$ 0 0
$$986$$ −0.532089 −0.532089
$$987$$ 3.53209i 3.53209i
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 0.120615i 0.120615i
$$999$$ 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 2175.1.b.c.2174.3 6
3.2 odd 2 2175.1.b.d.2174.4 6
5.2 odd 4 2175.1.h.f.1826.2 yes 3
5.3 odd 4 2175.1.h.d.1826.2 yes 3
5.4 even 2 inner 2175.1.b.c.2174.4 6
15.2 even 4 2175.1.h.c.1826.2 3
15.8 even 4 2175.1.h.e.1826.2 yes 3
15.14 odd 2 2175.1.b.d.2174.3 6
29.28 even 2 2175.1.b.d.2174.4 6
87.86 odd 2 CM 2175.1.b.c.2174.3 6
145.28 odd 4 2175.1.h.e.1826.2 yes 3
145.57 odd 4 2175.1.h.c.1826.2 3
145.144 even 2 2175.1.b.d.2174.3 6
435.173 even 4 2175.1.h.d.1826.2 yes 3
435.347 even 4 2175.1.h.f.1826.2 yes 3
435.434 odd 2 inner 2175.1.b.c.2174.4 6

By twisted newform
Twist Min Dim Char Parity Ord Type
2175.1.b.c.2174.3 6 1.1 even 1 trivial
2175.1.b.c.2174.3 6 87.86 odd 2 CM
2175.1.b.c.2174.4 6 5.4 even 2 inner
2175.1.b.c.2174.4 6 435.434 odd 2 inner
2175.1.b.d.2174.3 6 15.14 odd 2
2175.1.b.d.2174.3 6 145.144 even 2
2175.1.b.d.2174.4 6 3.2 odd 2
2175.1.b.d.2174.4 6 29.28 even 2
2175.1.h.c.1826.2 3 15.2 even 4
2175.1.h.c.1826.2 3 145.57 odd 4
2175.1.h.d.1826.2 yes 3 5.3 odd 4
2175.1.h.d.1826.2 yes 3 435.173 even 4
2175.1.h.e.1826.2 yes 3 15.8 even 4
2175.1.h.e.1826.2 yes 3 145.28 odd 4
2175.1.h.f.1826.2 yes 3 5.2 odd 4
2175.1.h.f.1826.2 yes 3 435.347 even 4