LMFDB - Embedded newform 370.2.n.a.359.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(269,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("370.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.n (of order $6$, degree $2$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			359.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.359
Dual form			370.2.n.a.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.00000i) q^{5} +(-2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.00000i) q^{5} +(-2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-2.23205 + 0.133975i) q^{10} +1.26795 q^{11} +(-1.26795 - 0.732051i) q^{13} -2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 0.866025i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(0.633975 - 1.09808i) q^{19} +(-1.86603 + 1.23205i) q^{20} +(1.09808 - 0.633975i) q^{22} -1.46410i q^{23} +(3.00000 + 4.00000i) q^{25} -1.46410 q^{26} +(-2.36603 + 1.36603i) q^{28} +1.73205 q^{29} +7.66025 q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.866025 - 1.50000i) q^{34} +(3.36603 + 5.09808i) q^{35} -3.00000 q^{36} +(-2.59808 - 5.50000i) q^{37} -1.26795i q^{38} +(-1.00000 + 2.00000i) q^{40} +(-2.96410 + 5.13397i) q^{41} +8.73205i q^{43} +(0.633975 - 1.09808i) q^{44} +(0.401924 + 6.69615i) q^{45} +(-0.732051 - 1.26795i) q^{46} -6.73205i q^{47} +(0.232051 + 0.401924i) q^{49} +(4.59808 + 1.96410i) q^{50} +(-1.26795 + 0.732051i) q^{52} +(7.26795 - 4.19615i) q^{53} +(-2.53590 - 1.26795i) q^{55} +(-1.36603 + 2.36603i) q^{56} +(1.50000 - 0.866025i) q^{58} +(-4.73205 - 8.19615i) q^{59} +(-3.86603 + 6.69615i) q^{61} +(6.63397 - 3.83013i) q^{62} +8.19615i q^{63} -1.00000 q^{64} +(1.80385 + 2.73205i) q^{65} +(7.56218 + 4.36603i) q^{67} -1.73205i q^{68} +(5.46410 + 2.73205i) q^{70} +(4.56218 - 7.90192i) q^{71} +(-2.59808 + 1.50000i) q^{72} +11.8564i q^{73} +(-5.00000 - 3.46410i) q^{74} +(-0.633975 - 1.09808i) q^{76} +(-3.00000 - 1.73205i) q^{77} +(7.83013 - 13.5622i) q^{79} +(0.133975 + 2.23205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +5.92820i q^{82} +(2.19615 - 1.26795i) q^{83} +(-3.86603 + 0.232051i) q^{85} +(4.36603 + 7.56218i) q^{86} -1.26795i q^{88} +(-3.23205 - 5.59808i) q^{89} +(3.69615 + 5.59808i) q^{90} +(2.00000 + 3.46410i) q^{91} +(-1.26795 - 0.732051i) q^{92} +(-3.36603 - 5.83013i) q^{94} +(-2.36603 + 1.56218i) q^{95} +7.19615i q^{97} +(0.401924 + 0.232051i) q^{98} +(-1.90192 - 3.29423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 8 q^{5} - 6 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 8 * q^5 - 6 * q^7 - 6 * q^9	$ 4 q + 2 q^{4} - 8 q^{5} - 6 q^{7} - 6 q^{9} - 2 q^{10} + 12 q^{11} - 12 q^{13} - 4 q^{14} - 2 q^{16} + 6 q^{17} + 6 q^{19} - 4 q^{20} - 6 q^{22} + 12 q^{25} + 8 q^{26} - 6 q^{28} - 4 q^{31} + 10 q^{35} - 12 q^{36} - 4 q^{40} + 2 q^{41} + 6 q^{44} + 12 q^{45} + 4 q^{46} - 6 q^{49} + 8 q^{50} - 12 q^{52} + 36 q^{53} - 24 q^{55} - 2 q^{56} + 6 q^{58} - 12 q^{59} - 12 q^{61} + 30 q^{62} - 4 q^{64} + 28 q^{65} + 6 q^{67} + 8 q^{70} - 6 q^{71} - 20 q^{74} - 6 q^{76} - 12 q^{77} + 14 q^{79} + 4 q^{80} - 18 q^{81} - 12 q^{83} - 12 q^{85} + 14 q^{86} - 6 q^{89} - 6 q^{90} + 8 q^{91} - 12 q^{92} - 10 q^{94} - 6 q^{95} + 12 q^{98} - 18 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 8 * q^5 - 6 * q^7 - 6 * q^9 - 2 * q^10 + 12 * q^11 - 12 * q^13 - 4 * q^14 - 2 * q^16 + 6 * q^17 + 6 * q^19 - 4 * q^20 - 6 * q^22 + 12 * q^25 + 8 * q^26 - 6 * q^28 - 4 * q^31 + 10 * q^35 - 12 * q^36 - 4 * q^40 + 2 * q^41 + 6 * q^44 + 12 * q^45 + 4 * q^46 - 6 * q^49 + 8 * q^50 - 12 * q^52 + 36 * q^53 - 24 * q^55 - 2 * q^56 + 6 * q^58 - 12 * q^59 - 12 * q^61 + 30 * q^62 - 4 * q^64 + 28 * q^65 + 6 * q^67 + 8 * q^70 - 6 * q^71 - 20 * q^74 - 6 * q^76 - 12 * q^77 + 14 * q^79 + 4 * q^80 - 18 * q^81 - 12 * q^83 - 12 * q^85 + 14 * q^86 - 6 * q^89 - 6 * q^90 + 8 * q^91 - 12 * q^92 - 10 * q^94 - 6 * q^95 + 12 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$3$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	−2.36603	−	1.36603i	−0.894274	−	0.516309i	−0.0189356	−	0.999821i	$-0.506028\pi$
$7$	−2.36603	−	1.36603i	−0.894274	−	0.516309i	−0.875338	+	0.483512i	$0.839361\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−2.23205	+	0.133975i	−0.705836	+	0.0423665i
$11$	1.26795			0.382301			0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795			0.382301			0.191151	+	0.981561i	$0.438778\pi$
$12$		0			0
$13$	−1.26795	−	0.732051i	−0.351666	−	0.203034i	0.313753	−	0.949505i	$-0.398414\pi$
$13$	−1.26795	−	0.732051i	−0.351666	−	0.203034i	−0.665419	+	0.746470i	$0.731747\pi$
$14$	−2.73205			−0.730171
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	−0.306944	−	0.951727i	$-0.599307\pi$
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	0.670748	+	0.741685i	$0.265973\pi$
$18$	−2.59808	−	1.50000i	−0.612372	−	0.353553i
$19$	0.633975	−	1.09808i	0.145444	−	0.251916i	−0.784095	−	0.620641i	$-0.786872\pi$
$19$	0.633975	−	1.09808i	0.145444	−	0.251916i	0.929538	+	0.368725i	$0.120206\pi$
$20$	−1.86603	+	1.23205i	−0.417256	+	0.275495i
$21$		0			0
$22$	1.09808	−	0.633975i	0.234111	−	0.135164i
$23$		−	1.46410i		−	0.305286i	−0.988281	−	0.152643i	$-0.951221\pi$
$23$		−	1.46410i		−	0.305286i	0.988281	−	0.152643i	$-0.0487785\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	−1.46410			−0.287134
$27$		0			0
$28$	−2.36603	+	1.36603i	−0.447137	+	0.258155i
$29$	1.73205			0.321634			0.160817	−	0.986984i	$-0.448587\pi$
$29$	1.73205			0.321634			0.160817	+	0.986984i	$0.448587\pi$
$30$		0			0
$31$	7.66025			1.37582			0.687911	−	0.725795i	$-0.258528\pi$
$31$	7.66025			1.37582			0.687911	+	0.725795i	$0.258528\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	0.866025	−	1.50000i	0.148522	−	0.257248i
$35$	3.36603	+	5.09808i	0.568962	+	0.861732i
$36$	−3.00000			−0.500000
$37$	−2.59808	−	5.50000i	−0.427121	−	0.904194i
$37$	−2.59808	−	5.50000i	−0.427121	−	0.904194i
$38$		−	1.26795i		−	0.205689i
$39$		0			0
$40$	−1.00000	+	2.00000i	−0.158114	+	0.316228i
$41$	−2.96410	+	5.13397i	−0.462915	+	0.801792i	−0.999105	−	0.0423053i	$-0.986530\pi$
$41$	−2.96410	+	5.13397i	−0.462915	+	0.801792i	0.536190	+	0.844097i	$0.319863\pi$
$42$		0			0
$43$			8.73205i			1.33163i	0.746119	+	0.665813i	$0.231915\pi$
$43$			8.73205i			1.33163i	−0.746119	+	0.665813i	$0.768085\pi$
$44$	0.633975	−	1.09808i	0.0955753	−	0.165541i
$45$	0.401924	+	6.69615i	0.0599153	+	0.998203i
$46$	−0.732051	−	1.26795i	−0.107935	−	0.186949i
$47$		−	6.73205i		−	0.981971i	−0.871168	−	0.490985i	$-0.836637\pi$
$47$		−	6.73205i		−	0.981971i	0.871168	−	0.490985i	$-0.163363\pi$
$48$		0			0
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$	4.59808	+	1.96410i	0.650266	+	0.277766i
$51$		0			0
$52$	−1.26795	+	0.732051i	−0.175833	+	0.101517i
$53$	7.26795	−	4.19615i	0.998330	−	0.576386i	0.0905760	−	0.995890i	$-0.471129\pi$
$53$	7.26795	−	4.19615i	0.998330	−	0.576386i	0.907754	+	0.419504i	$0.137796\pi$
$54$		0			0
$55$	−2.53590	−	1.26795i	−0.341940	−	0.170970i
$56$	−1.36603	+	2.36603i	−0.182543	+	0.316173i
$57$		0			0
$58$	1.50000	−	0.866025i	0.196960	−	0.113715i
$59$	−4.73205	−	8.19615i	−0.616061	−	1.06705i	−0.990197	−	0.139675i	$-0.955394\pi$
$59$	−4.73205	−	8.19615i	−0.616061	−	1.06705i	0.374137	−	0.927373i	$-0.377939\pi$
$60$		0			0
$61$	−3.86603	+	6.69615i	−0.494994	+	0.857354i	−0.999983	−	0.00577101i	$-0.998163\pi$
$61$	−3.86603	+	6.69615i	−0.494994	+	0.857354i	0.504990	+	0.863125i	$0.331496\pi$
$62$	6.63397	−	3.83013i	0.842516	−	0.486427i
$63$			8.19615i			1.03262i
$64$	−1.00000			−0.125000
$65$	1.80385	+	2.73205i	0.223740	+	0.338869i
$66$		0			0
$67$	7.56218	+	4.36603i	0.923867	+	0.533395i	0.884867	−	0.465844i	$-0.154249\pi$
$67$	7.56218	+	4.36603i	0.923867	+	0.533395i	0.0390004	+	0.999239i	$0.487583\pi$
$68$		−	1.73205i		−	0.210042i
$69$		0			0
$70$	5.46410	+	2.73205i	0.653085	+	0.326543i
$71$	4.56218	−	7.90192i	0.541431	−	0.937786i	−0.457391	−	0.889266i	$-0.651216\pi$
$71$	4.56218	−	7.90192i	0.541431	−	0.937786i	0.998822	−	0.0485203i	$-0.0154506\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$			11.8564i			1.38769i	0.720126	+	0.693844i	$0.244084\pi$
$73$			11.8564i			1.38769i	−0.720126	+	0.693844i	$0.755916\pi$
$74$	−5.00000	−	3.46410i	−0.581238	−	0.402694i
$75$		0			0
$76$	−0.633975	−	1.09808i	−0.0727219	−	0.125958i
$77$	−3.00000	−	1.73205i	−0.341882	−	0.197386i
$78$		0			0
$79$	7.83013	−	13.5622i	0.880958	−	1.52586i	0.0306808	−	0.999529i	$-0.490232\pi$
$79$	7.83013	−	13.5622i	0.880958	−	1.52586i	0.850277	−	0.526335i	$-0.176434\pi$
$80$	0.133975	+	2.23205i	0.0149788	+	0.249551i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$			5.92820i			0.654661i
$83$	2.19615	−	1.26795i	0.241059	−	0.139176i	−0.374604	−	0.927185i	$-0.622221\pi$
$83$	2.19615	−	1.26795i	0.241059	−	0.139176i	0.615663	+	0.788009i	$0.288888\pi$
$84$		0			0
$85$	−3.86603	+	0.232051i	−0.419329	+	0.0251694i
$86$	4.36603	+	7.56218i	0.470801	+	0.815451i
$87$		0			0
$88$		−	1.26795i		−	0.135164i
$89$	−3.23205	−	5.59808i	−0.342597	−	0.593395i	0.642317	−	0.766439i	$-0.277973\pi$
$89$	−3.23205	−	5.59808i	−0.342597	−	0.593395i	−0.984914	+	0.173044i	$0.944640\pi$
$90$	3.69615	+	5.59808i	0.389609	+	0.590089i
$91$	2.00000	+	3.46410i	0.209657	+	0.363137i
$92$	−1.26795	−	0.732051i	−0.132193	−	0.0763216i
$93$		0			0
$94$	−3.36603	−	5.83013i	−0.347179	−	0.601332i
$95$	−2.36603	+	1.56218i	−0.242749	+	0.160276i
$96$		0			0
$97$			7.19615i			0.730659i	0.930878	+	0.365329i	$0.119044\pi$
$97$			7.19615i			0.730659i	−0.930878	+	0.365329i	$0.880956\pi$
$98$	0.401924	+	0.232051i	0.0406004	+	0.0234407i
$99$	−1.90192	−	3.29423i	−0.191151	−	0.331082i
$100$	4.96410	−	0.598076i	0.496410	−	0.0598076i
$101$	0.267949			0.0266619			0.0133310	−	0.999911i	$-0.495756\pi$
$101$	0.267949			0.0266619			0.0133310	+	0.999911i	$0.495756\pi$
$102$		0			0
$103$			3.80385i			0.374804i	0.982283	+	0.187402i	$0.0600067\pi$
$103$			3.80385i			0.374804i	−0.982283	+	0.187402i	$0.939993\pi$
$104$	−0.732051	+	1.26795i	−0.0717835	+	0.124333i
$105$		0			0
$106$	4.19615	−	7.26795i	0.407566	−	0.705926i
$107$	5.36603	+	3.09808i	0.518753	+	0.299502i	0.736424	−	0.676520i	$-0.236513\pi$
$107$	5.36603	+	3.09808i	0.518753	+	0.299502i	−0.217671	+	0.976022i	$0.569846\pi$
$108$		0			0
$109$	−1.40192	−	2.42820i	−0.134280	−	0.232580i	0.791042	−	0.611762i	$-0.209539\pi$
$109$	−1.40192	−	2.42820i	−0.134280	−	0.232580i	−0.925322	+	0.379182i	$0.876205\pi$
$110$	−2.83013	+	0.169873i	−0.269842	+	0.0161968i
$111$		0			0
$112$			2.73205i			0.258155i
$113$	14.6603	−	8.46410i	1.37912	−	0.796236i	0.387067	−	0.922052i	$-0.373488\pi$
$113$	14.6603	−	8.46410i	1.37912	−	0.796236i	0.992054	+	0.125816i	$0.0401548\pi$
$114$		0			0
$115$	−1.46410	+	2.92820i	−0.136528	+	0.273056i
$116$	0.866025	−	1.50000i	0.0804084	−	0.139272i
$117$			4.39230i			0.406069i
$118$	−8.19615	−	4.73205i	−0.754517	−	0.435621i
$119$	−4.73205			−0.433786
$120$		0			0
$121$	−9.39230			−0.853846
$122$			7.73205i			0.700027i
$123$		0			0
$124$	3.83013	−	6.63397i	0.343956	−	0.595749i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	4.09808	+	7.09808i	0.365086	+	0.632347i
$127$	9.46410	−	5.46410i	0.839803	−	0.484861i	−0.0173941	−	0.999849i	$-0.505537\pi$
$127$	9.46410	−	5.46410i	0.839803	−	0.484861i	0.857197	+	0.514988i	$0.172204\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	2.92820	+	1.46410i	0.256820	+	0.128410i
$131$	−1.46410	−	2.53590i	−0.127919	−	0.221562i	0.794951	−	0.606674i	$-0.207496\pi$
$131$	−1.46410	−	2.53590i	−0.127919	−	0.221562i	−0.922870	+	0.385111i	$0.874163\pi$
$132$		0			0
$133$	−3.00000	+	1.73205i	−0.260133	+	0.150188i
$134$	8.73205			0.754334
$135$		0			0
$136$	−0.866025	−	1.50000i	−0.0742611	−	0.128624i
$137$		−	1.73205i		−	0.147979i	−0.997259	−	0.0739895i	$-0.976427\pi$
$137$		−	1.73205i		−	0.147979i	0.997259	−	0.0739895i	$-0.0235731\pi$
$138$		0			0
$139$	5.46410	+	9.46410i	0.463459	+	0.802735i	0.999131	−	0.0416919i	$-0.0132748\pi$
$139$	5.46410	+	9.46410i	0.463459	+	0.802735i	−0.535671	+	0.844426i	$0.679941\pi$
$140$	6.09808	−	0.366025i	0.515382	−	0.0309348i
$141$		0			0
$142$		−	9.12436i		−	0.765699i
$143$	−1.60770	−	0.928203i	−0.134442	−	0.0776203i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	−3.46410	−	1.73205i	−0.287678	−	0.143839i
$146$	5.92820	+	10.2679i	0.490622	+	0.849782i
$147$		0			0
$148$	−6.06218	−	0.500000i	−0.498308	−	0.0410997i
$149$	−11.5885			−0.949363			−0.474682	−	0.880158i	$-0.657437\pi$
$149$	−11.5885			−0.949363			−0.474682	+	0.880158i	$0.657437\pi$
$150$		0			0
$151$	5.26795	−	9.12436i	0.428700	−	0.742530i	−0.568058	−	0.822988i	$-0.692305\pi$
$151$	5.26795	−	9.12436i	0.428700	−	0.742530i	0.996758	+	0.0804588i	$0.0256385\pi$
$152$	−1.09808	−	0.633975i	−0.0890657	−	0.0514221i
$153$	−4.50000	−	2.59808i	−0.363803	−	0.210042i
$154$	−3.46410			−0.279145
$155$	−15.3205	−	7.66025i	−1.23057	−	0.615286i
$156$		0			0
$157$	−14.7224	+	8.50000i	−1.17498	+	0.678374i	−0.954847	−	0.297097i	$-0.903982\pi$
$157$	−14.7224	+	8.50000i	−1.17498	+	0.678374i	−0.220131	+	0.975470i	$0.570648\pi$
$158$		−	15.6603i		−	1.24586i
$159$		0			0
$160$	1.23205	+	1.86603i	0.0974022	+	0.147522i
$161$	−2.00000	+	3.46410i	−0.157622	+	0.273009i
$162$			9.00000i			0.707107i
$163$	7.90192	−	4.56218i	0.618926	−	0.357337i	−0.157524	−	0.987515i	$-0.550351\pi$
$163$	7.90192	−	4.56218i	0.618926	−	0.357337i	0.776451	+	0.630178i	$0.217018\pi$
$164$	2.96410	+	5.13397i	0.231457	+	0.400896i
$165$		0			0
$166$	1.26795	−	2.19615i	0.0984119	−	0.170454i
$167$	−15.4641	−	8.92820i	−1.19665	−	0.690885i	−0.236842	−	0.971548i	$-0.576112\pi$
$167$	−15.4641	−	8.92820i	−1.19665	−	0.690885i	−0.959806	+	0.280663i	$0.909446\pi$
$168$		0			0
$169$	−5.42820	−	9.40192i	−0.417554	−	0.723225i
$170$	−3.23205	+	2.13397i	−0.247887	+	0.163668i
$171$	−3.80385			−0.290887
$172$	7.56218	+	4.36603i	0.576611	+	0.332906i
$173$	0.0621778	−	0.0358984i	0.00472729	−	0.00272930i	−0.497634	−	0.867387i	$-0.665798\pi$
$173$	0.0621778	−	0.0358984i	0.00472729	−	0.00272930i	0.502362	+	0.864658i	$0.332465\pi$
$174$		0			0
$175$	−1.63397	−	13.5622i	−0.123517	−	1.02520i
$176$	−0.633975	−	1.09808i	−0.0477876	−	0.0827706i
$177$		0			0
$178$	−5.59808	−	3.23205i	−0.419594	−	0.242252i
$179$	14.9282			1.11579			0.557893	−	0.829913i	$-0.311610\pi$
$179$	14.9282			1.11579			0.557893	+	0.829913i	$0.311610\pi$
$180$	6.00000	+	3.00000i	0.447214	+	0.223607i
$181$	−5.79423	+	10.0359i	−0.430682	+	0.745962i	−0.996932	−	0.0782707i	$-0.975060\pi$
$181$	−5.79423	+	10.0359i	−0.430682	+	0.745962i	0.566251	+	0.824233i	$0.308393\pi$
$182$	3.46410	+	2.00000i	0.256776	+	0.148250i
$183$		0			0
$184$	−1.46410			−0.107935
$185$	−0.303848	+	13.5981i	−0.0223393	+	0.999750i
$186$		0			0
$187$	1.90192	−	1.09808i	0.139082	−	0.0802993i
$188$	−5.83013	−	3.36603i	−0.425206	−	0.245493i
$189$		0			0
$190$	−1.26795	+	2.53590i	−0.0919867	+	0.183973i
$191$	−19.3205			−1.39798			−0.698991	−	0.715130i	$-0.746367\pi$
$191$	−19.3205			−1.39798			−0.698991	+	0.715130i	$0.746367\pi$
$192$		0			0
$193$			16.6603i			1.19923i	0.800288	+	0.599616i	$0.204680\pi$
$193$			16.6603i			1.19923i	−0.800288	+	0.599616i	$0.795320\pi$
$194$	3.59808	+	6.23205i	0.258327	+	0.447435i
$195$		0			0
$196$	0.464102			0.0331501
$197$	−5.25833	+	3.03590i	−0.374641	+	0.216299i	−0.675484	−	0.737375i	$-0.736065\pi$
$197$	−5.25833	+	3.03590i	−0.374641	+	0.216299i	0.300843	+	0.953674i	$0.402732\pi$
$198$	−3.29423	−	1.90192i	−0.234111	−	0.135164i
$199$	−1.80385			−0.127871			−0.0639357	−	0.997954i	$-0.520365\pi$
$199$	−1.80385			−0.127871			−0.0639357	+	0.997954i	$0.520365\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$		0			0
$202$	0.232051	−	0.133975i	0.0163270	−	0.00942642i
$203$	−4.09808	−	2.36603i	−0.287629	−	0.166062i
$204$		0			0
$205$	11.0622	−	7.30385i	0.772616	−	0.510123i
$206$	1.90192	+	3.29423i	0.132513	+	0.229520i
$207$	−3.80385	+	2.19615i	−0.264386	+	0.152643i
$208$			1.46410i			0.101517i
$209$	0.803848	−	1.39230i	0.0556033	−	0.0963077i
$210$		0			0
$211$	18.0526			1.24279			0.621395	−	0.783498i	$-0.286566\pi$
$211$	18.0526			1.24279			0.621395	+	0.783498i	$0.286566\pi$
$212$		−	8.39230i		−	0.576386i
$213$		0			0
$214$	6.19615			0.423560
$215$	8.73205	−	17.4641i	0.595521	−	1.19104i
$216$		0			0
$217$	−18.1244	−	10.4641i	−1.23036	−	0.710350i
$218$	−2.42820	−	1.40192i	−0.164459	−	0.0949503i
$219$		0			0
$220$	−2.36603	+	1.56218i	−0.159517	+	0.105322i
$221$	−2.53590			−0.170583
$222$		0			0
$223$		−	1.07180i		−	0.0717728i	−0.999356	−	0.0358864i	$-0.988575\pi$
$223$		−	1.07180i		−	0.0717728i	0.999356	−	0.0358864i	$-0.0114255\pi$
$224$	1.36603	+	2.36603i	0.0912714	+	0.158087i
$225$	5.89230	−	13.7942i	0.392820	−	0.919615i
$226$	8.46410	−	14.6603i	0.563024	−	0.975186i
$227$	3.75833	+	2.16987i	0.249449	+	0.144020i	0.619512	−	0.784987i	$-0.287331\pi$
$227$	3.75833	+	2.16987i	0.249449	+	0.144020i	−0.370063	+	0.929007i	$0.620664\pi$
$228$		0			0
$229$	−12.7942	+	22.1603i	−0.845466	+	1.46439i	0.0397491	+	0.999210i	$0.487344\pi$
$229$	−12.7942	+	22.1603i	−0.845466	+	1.46439i	−0.885216	+	0.465181i	$0.845989\pi$
$230$	0.196152	+	3.26795i	0.0129339	+	0.215482i
$231$		0			0
$232$		−	1.73205i		−	0.113715i
$233$		−	13.7321i		−	0.899617i	−0.893125	−	0.449808i	$-0.851492\pi$
$233$		−	13.7321i		−	0.899617i	0.893125	−	0.449808i	$-0.148508\pi$
$234$	2.19615	+	3.80385i	0.143567	+	0.248665i
$235$	−6.73205	+	13.4641i	−0.439151	+	0.878301i
$236$	−9.46410			−0.616061
$237$		0			0
$238$	−4.09808	+	2.36603i	−0.265639	+	0.153367i
$239$	−7.29423	−	12.6340i	−0.471824	−	0.817224i	0.527656	−	0.849458i	$-0.323071\pi$
$239$	−7.29423	−	12.6340i	−0.471824	−	0.817224i	−0.999480	+	0.0322343i	$0.989738\pi$
$240$		0			0
$241$	8.73205	−	15.1244i	0.562481	−	0.974245i	−0.434798	−	0.900528i	$-0.643180\pi$
$241$	8.73205	−	15.1244i	0.562481	−	0.974245i	0.997279	−	0.0737175i	$-0.0234863\pi$
$242$	−8.13397	+	4.69615i	−0.522872	+	0.301880i
$243$		0			0
$244$	3.86603	+	6.69615i	0.247497	+	0.428677i
$245$	−0.0621778	−	1.03590i	−0.00397240	−	0.0661811i
$246$		0			0
$247$	−1.60770	+	0.928203i	−0.102295	+	0.0590602i
$248$		−	7.66025i		−	0.486427i
$249$		0			0
$250$	−7.23205	−	8.52628i	−0.457395	−	0.539249i
$251$	11.8038			0.745052			0.372526	−	0.928022i	$-0.378492\pi$
$251$	11.8038			0.745052			0.372526	+	0.928022i	$0.378492\pi$
$252$	7.09808	+	4.09808i	0.447137	+	0.258155i
$253$		−	1.85641i		−	0.116711i
$254$	5.46410	−	9.46410i	0.342848	−	0.593831i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.0885	+	6.40192i	−0.691679	+	0.399341i	−0.804241	−	0.594304i	$-0.797428\pi$
$257$	−11.0885	+	6.40192i	−0.691679	+	0.399341i	0.112562	+	0.993645i	$0.464094\pi$
$258$		0			0
$259$	−1.36603	+	16.5622i	−0.0848807	+	1.02912i
$260$	3.26795	−	0.196152i	0.202670	−	0.0121649i
$261$	−2.59808	−	4.50000i	−0.160817	−	0.278543i
$262$	−2.53590	−	1.46410i	−0.156668	−	0.0904525i
$263$	7.85641	+	4.53590i	0.484447	+	0.279695i	0.722268	−	0.691614i	$-0.243100\pi$
$263$	7.85641	+	4.53590i	0.484447	+	0.279695i	−0.237821	+	0.971309i	$0.576433\pi$
$264$		0			0
$265$	−18.7321	+	1.12436i	−1.15070	+	0.0690686i
$266$	−1.73205	+	3.00000i	−0.106199	+	0.183942i
$267$		0			0
$268$	7.56218	−	4.36603i	0.461934	−	0.266697i
$269$	17.8564			1.08872			0.544362	−	0.838850i	$-0.316772\pi$
$269$	17.8564			1.08872			0.544362	+	0.838850i	$0.316772\pi$
$270$		0			0
$271$	−4.36603	−	7.56218i	−0.265217	−	0.459370i	0.702403	−	0.711779i	$-0.252110\pi$
$271$	−4.36603	−	7.56218i	−0.265217	−	0.459370i	−0.967620	+	0.252410i	$0.918777\pi$
$272$	−1.50000	−	0.866025i	−0.0909509	−	0.0525105i
$273$		0			0
$274$	−0.866025	−	1.50000i	−0.0523185	−	0.0906183i
$275$	3.80385	+	5.07180i	0.229381	+	0.305841i
$276$		0			0
$277$	1.20577	+	0.696152i	0.0724478	+	0.0418277i	0.535786	−	0.844354i	$-0.320015\pi$
$277$	1.20577	+	0.696152i	0.0724478	+	0.0418277i	−0.463339	+	0.886181i	$0.653349\pi$
$278$	9.46410	+	5.46410i	0.567619	+	0.327715i
$279$	−11.4904	−	19.9019i	−0.687911	−	1.19150i
$280$	5.09808	−	3.36603i	0.304668	−	0.201158i
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	0.907293	−	0.420500i	$-0.138145\pi$
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	−0.817810	+	0.575488i	$0.804812\pi$
$282$		0			0
$283$	−5.02628	−	2.90192i	−0.298781	−	0.172501i	0.343114	−	0.939294i	$-0.388518\pi$
$283$	−5.02628	−	2.90192i	−0.298781	−	0.172501i	−0.641895	+	0.766792i	$0.721852\pi$
$284$	−4.56218	−	7.90192i	−0.270715	−	0.468893i
$285$		0			0
$286$	−1.85641			−0.109772
$287$	14.0263	−	8.09808i	0.827945	−	0.478014i
$288$			3.00000i			0.176777i
$289$	−7.00000	+	12.1244i	−0.411765	+	0.713197i
$290$	−3.86603	+	0.232051i	−0.227021	+	0.0136265i
$291$		0			0
$292$	10.2679	+	5.92820i	0.600886	+	0.346922i
$293$	24.9904	+	14.4282i	1.45995	+	0.842905i	0.999008	−	0.0445239i	$-0.0141771\pi$
$293$	24.9904	+	14.4282i	1.45995	+	0.842905i	0.460945	+	0.887429i	$0.347510\pi$
$294$		0			0
$295$	1.26795	+	21.1244i	0.0738229	+	1.22991i
$296$	−5.50000	+	2.59808i	−0.319681	+	0.151010i
$297$		0			0
$298$	−10.0359	+	5.79423i	−0.581364	+	0.335651i
$299$	−1.07180	+	1.85641i	−0.0619836	+	0.107359i
$300$		0			0
$301$	11.9282	−	20.6603i	0.687530	−	1.19084i
$302$		−	10.5359i		−	0.606273i
$303$		0			0
$304$	−1.26795			−0.0727219
$305$	14.4282	−	9.52628i	0.826157	−	0.545473i
$306$	−5.19615			−0.297044
$307$			6.87564i			0.392414i	0.980563	+	0.196207i	$0.0628624\pi$
$307$			6.87564i			0.392414i	−0.980563	+	0.196207i	$0.937138\pi$
$308$	−3.00000	+	1.73205i	−0.170941	+	0.0986928i
$309$		0			0
$310$	−17.0981	+	1.02628i	−0.971105	+	0.0582888i
$311$	−2.36603	−	4.09808i	−0.134165	−	0.232381i	0.791113	−	0.611670i	$-0.209502\pi$
$311$	−2.36603	−	4.09808i	−0.134165	−	0.232381i	−0.925278	+	0.379289i	$0.876169\pi$
$312$		0			0
$313$	2.42820	−	1.40192i	0.137250	−	0.0792414i	−0.429803	−	0.902923i	$-0.641417\pi$
$313$	2.42820	−	1.40192i	0.137250	−	0.0792414i	0.567053	+	0.823681i	$0.308084\pi$
$314$	−8.50000	+	14.7224i	−0.479683	+	0.830835i
$315$	8.19615	−	16.3923i	0.461801	−	0.923602i
$316$	−7.83013	−	13.5622i	−0.440479	−	0.762932i
$317$	12.4019	−	7.16025i	0.696561	−	0.402160i	−0.109504	−	0.993986i	$-0.534926\pi$
$317$	12.4019	−	7.16025i	0.696561	−	0.402160i	0.806065	+	0.591826i	$0.201593\pi$
$318$		0			0
$319$	2.19615			0.122961
$320$	2.00000	+	1.00000i	0.111803	+	0.0559017i
$321$		0			0
$322$			4.00000i			0.222911i
$323$		−	2.19615i		−	0.122197i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	−0.875644	−	7.26795i	−0.0485720	−	0.403153i
$326$	4.56218	−	7.90192i	0.252676	−	0.437647i
$327$		0			0
$328$	5.13397	+	2.96410i	0.283476	+	0.163665i
$329$	−9.19615	+	15.9282i	−0.507000	+	0.878150i
$330$		0			0
$331$	10.1962	+	17.6603i	0.560431	+	0.970695i	0.997459	+	0.0712472i	$0.0226979\pi$
$331$	10.1962	+	17.6603i	0.560431	+	0.970695i	−0.437027	+	0.899448i	$0.643969\pi$
$332$		−	2.53590i		−	0.139176i
$333$	−10.3923	+	15.0000i	−0.569495	+	0.821995i
$334$	−17.8564			−0.977059
$335$	−10.7583	−	16.2942i	−0.587790	−	0.890249i
$336$		0			0
$337$	−1.03590	−	0.598076i	−0.0564290	−	0.0325793i	0.471520	−	0.881855i	$-0.343705\pi$
$337$	−1.03590	−	0.598076i	−0.0564290	−	0.0325793i	−0.527949	+	0.849276i	$0.677039\pi$
$338$	−9.40192	−	5.42820i	−0.511397	−	0.295255i
$339$		0			0
$340$	−1.73205	+	3.46410i	−0.0939336	+	0.187867i
$341$	9.71281			0.525978
$342$	−3.29423	+	1.90192i	−0.178131	+	0.102844i
$343$			17.8564i			0.964155i
$344$	8.73205			0.470801
$345$		0			0
$346$	0.0358984	−	0.0621778i	0.00192991	−	0.00334270i
$347$			27.7128i			1.48770i	0.668346	+	0.743851i	$0.267003\pi$
$347$			27.7128i			1.48770i	−0.668346	+	0.743851i	$0.732997\pi$
$348$		0			0
$349$	16.7942	+	29.0885i	0.898974	+	1.55707i	0.828807	+	0.559534i	$0.189020\pi$
$349$	16.7942	+	29.0885i	0.898974	+	1.55707i	0.0701672	+	0.997535i	$0.477647\pi$
$350$	−8.19615	−	10.9282i	−0.438103	−	0.584137i
$351$		0			0
$352$	−1.09808	−	0.633975i	−0.0585277	−	0.0337910i
$353$	11.8923	−	6.86603i	0.632964	−	0.365442i	−0.148935	−	0.988847i	$-0.547585\pi$
$353$	11.8923	−	6.86603i	0.632964	−	0.365442i	0.781899	+	0.623405i	$0.214251\pi$
$354$		0			0
$355$	−17.0263	+	11.2417i	−0.903661	+	0.596646i
$356$	−6.46410			−0.342597
$357$		0			0
$358$	12.9282	−	7.46410i	0.683277	−	0.394490i
$359$	17.4641			0.921720			0.460860	−	0.887473i	$-0.347541\pi$
$359$	17.4641			0.921720			0.460860	+	0.887473i	$0.347541\pi$
$360$	6.69615	−	0.401924i	0.352918	−	0.0211832i
$361$	8.69615	+	15.0622i	0.457692	+	0.792746i
$362$			11.5885i			0.609076i
$363$		0			0
$364$	4.00000			0.209657
$365$	11.8564	−	23.7128i	0.620593	−	1.24119i
$366$		0			0
$367$	29.3205	+	16.9282i	1.53052	+	0.883645i	0.999338	+	0.0363862i	$0.0115846\pi$
$367$	29.3205	+	16.9282i	1.53052	+	0.883645i	0.531180	+	0.847259i	$0.321749\pi$
$368$	−1.26795	+	0.732051i	−0.0660964	+	0.0381608i
$369$	17.7846			0.925830
$370$	6.53590	+	11.9282i	0.339785	+	0.620118i
$371$	−22.9282			−1.19037
$372$		0			0
$373$	−0.866025	−	0.500000i	−0.0448411	−	0.0258890i	0.477412	−	0.878680i	$-0.341575\pi$
$373$	−0.866025	−	0.500000i	−0.0448411	−	0.0258890i	−0.522253	+	0.852791i	$0.674908\pi$
$374$	1.09808	−	1.90192i	0.0567802	−	0.0983461i
$375$		0			0
$376$	−6.73205			−0.347179
$377$	−2.19615	−	1.26795i	−0.113108	−	0.0653027i
$378$		0			0
$379$	18.2942	+	31.6865i	0.939711	+	1.62763i	0.766009	+	0.642830i	$0.222240\pi$
$379$	18.2942	+	31.6865i	0.939711	+	1.62763i	0.173702	+	0.984798i	$0.444427\pi$
$380$	0.169873	+	2.83013i	0.00871430	+	0.145182i
$381$		0			0
$382$	−16.7321	+	9.66025i	−0.856086	+	0.494262i
$383$	13.4378	+	7.75833i	0.686641	+	0.396432i	0.802352	−	0.596851i	$-0.203582\pi$
$383$	13.4378	+	7.75833i	0.686641	+	0.396432i	−0.115712	+	0.993283i	$0.536915\pi$
$384$		0			0
$385$	4.26795	+	6.46410i	0.217515	+	0.329441i
$386$	8.33013	+	14.4282i	0.423992	+	0.734376i
$387$	22.6865	−	13.0981i	1.15322	−	0.665813i
$388$	6.23205	+	3.59808i	0.316384	+	0.182665i
$389$	−4.13397	+	7.16025i	−0.209601	+	0.363039i	−0.951589	−	0.307374i	$-0.900550\pi$
$389$	−4.13397	+	7.16025i	−0.209601	+	0.363039i	0.741988	+	0.670413i	$0.233883\pi$
$390$		0			0
$391$	−1.26795	−	2.19615i	−0.0641229	−	0.111064i
$392$	0.401924	−	0.232051i	0.0203002	−	0.0117203i
$393$		0			0
$394$	−3.03590	+	5.25833i	−0.152946	+	0.264911i
$395$	−29.2224	+	19.2942i	−1.47034	+	0.970798i
$396$	−3.80385			−0.191151
$397$		−	0.0717968i		−	0.00360338i	−0.999998	−	0.00180169i	$-0.999427\pi$
$397$		−	0.0717968i		−	0.00360338i	0.999998	−	0.00180169i	$-0.000573496\pi$
$398$	−1.56218	+	0.901924i	−0.0783049	+	0.0452094i
$399$		0			0
$400$	1.96410	−	4.59808i	0.0982051	−	0.229904i
$401$	15.3205			0.765070			0.382535	−	0.923941i	$-0.375051\pi$
$401$	15.3205			0.765070			0.382535	+	0.923941i	$0.375051\pi$
$402$		0			0
$403$	−9.71281	−	5.60770i	−0.483830	−	0.279339i
$404$	0.133975	−	0.232051i	0.00666549	−	0.0115450i
$405$	16.7942	−	11.0885i	0.834512	−	0.550990i
$406$	−4.73205			−0.234848
$407$	−3.29423	−	6.97372i	−0.163289	−	0.345674i
$408$		0			0
$409$	−1.89230	−	3.27757i	−0.0935685	−	0.162065i	0.815442	−	0.578839i	$-0.196494\pi$
$409$	−1.89230	−	3.27757i	−0.0935685	−	0.162065i	−0.909010	+	0.416774i	$0.863161\pi$
$410$	5.92820	−	11.8564i	0.292773	−	0.585546i
$411$		0			0
$412$	3.29423	+	1.90192i	0.162295	+	0.0937011i
$413$			25.8564i			1.27231i
$414$	−2.19615	+	3.80385i	−0.107935	+	0.186949i
$415$	−5.66025	+	0.339746i	−0.277851	+	0.0166775i
$416$	0.732051	+	1.26795i	0.0358917	+	0.0621663i
$417$		0			0
$418$		−	1.60770i		−	0.0786349i
$419$	14.0981	+	24.4186i	0.688736	+	1.19293i	0.972247	+	0.233957i	$0.0751675\pi$
$419$	14.0981	+	24.4186i	0.688736	+	1.19293i	−0.283511	+	0.958969i	$0.591499\pi$
$420$		0			0
$421$	−16.5167			−0.804973			−0.402486	−	0.915426i	$-0.631854\pi$
$421$	−16.5167			−0.804973			−0.402486	+	0.915426i	$0.631854\pi$
$422$	15.6340	−	9.02628i	0.761050	−	0.439392i
$423$	−17.4904	+	10.0981i	−0.850411	+	0.490985i
$424$	−4.19615	−	7.26795i	−0.203783	−	0.352963i
$425$	7.96410	+	3.40192i	0.386316	+	0.165018i
$426$		0			0
$427$	18.2942	−	10.5622i	0.885320	−	0.511140i
$428$	5.36603	−	3.09808i	0.259377	−	0.149751i
$429$		0			0
$430$	−1.16987	−	19.4904i	−0.0564163	−	0.939910i
$431$	−6.36603	+	11.0263i	−0.306641	+	0.531117i	−0.977625	−	0.210354i	$-0.932538\pi$
$431$	−6.36603	+	11.0263i	−0.306641	+	0.531117i	0.670985	+	0.741471i	$0.265872\pi$
$432$		0			0
$433$		−	32.3731i		−	1.55575i	−0.628419	−	0.777875i	$-0.716298\pi$
$433$		−	32.3731i		−	1.55575i	0.628419	−	0.777875i	$-0.283702\pi$
$434$	−20.9282			−1.00459
$435$		0			0
$436$	−2.80385			−0.134280
$437$	−1.60770	−	0.928203i	−0.0769065	−	0.0444020i
$438$		0			0
$439$	−16.9282	+	29.3205i	−0.807939	+	1.39939i	0.106350	+	0.994329i	$0.466084\pi$
$439$	−16.9282	+	29.3205i	−0.807939	+	1.39939i	−0.914289	+	0.405063i	$0.867250\pi$
$440$	−1.26795	+	2.53590i	−0.0604471	+	0.120894i
$441$	0.696152	−	1.20577i	0.0331501	−	0.0574177i
$442$	−2.19615	+	1.26795i	−0.104460	+	0.0603102i
$443$		−	24.7846i		−	1.17755i	−0.808296	−	0.588776i	$-0.799610\pi$
$443$		−	24.7846i		−	1.17755i	0.808296	−	0.588776i	$-0.200390\pi$
$444$		0			0
$445$	0.866025	+	14.4282i	0.0410535	+	0.683962i
$446$	−0.535898	−	0.928203i	−0.0253755	−	0.0439517i
$447$		0			0
$448$	2.36603	+	1.36603i	0.111784	+	0.0645386i
$449$	21.1244	−	36.5885i	0.996920	−	1.72672i	0.430542	−	0.902571i	$-0.358323\pi$
$449$	21.1244	−	36.5885i	0.996920	−	1.72672i	0.566378	−	0.824145i	$-0.308344\pi$
$450$	−1.79423	−	14.8923i	−0.0845807	−	0.702030i
$451$	−3.75833	+	6.50962i	−0.176973	+	0.306526i
$452$		−	16.9282i		−	0.796236i
$453$		0			0
$454$	4.33975			0.203674
$455$	−0.535898	−	8.92820i	−0.0251233	−	0.418561i
$456$		0			0
$457$	−7.62436	−	4.40192i	−0.356652	−	0.205913i	0.310959	−	0.950423i	$-0.399350\pi$
$457$	−7.62436	−	4.40192i	−0.356652	−	0.205913i	−0.667611	+	0.744510i	$0.732683\pi$
$458$			25.5885i			1.19567i
$459$		0			0
$460$	1.80385	+	2.73205i	0.0841048	+	0.127383i
$461$	−16.8564	−	29.1962i	−0.785081	−	1.35980i	−0.928951	−	0.370204i	$-0.879288\pi$
$461$	−16.8564	−	29.1962i	−0.785081	−	1.35980i	0.143869	−	0.989597i	$-0.454045\pi$
$462$		0			0
$463$	−18.1699	−	10.4904i	−0.844426	−	0.487529i	0.0143405	−	0.999897i	$-0.495435\pi$
$463$	−18.1699	−	10.4904i	−0.844426	−	0.487529i	−0.858766	+	0.512368i	$0.828768\pi$
$464$	−0.866025	−	1.50000i	−0.0402042	−	0.0696358i
$465$		0			0
$466$	−6.86603	−	11.8923i	−0.318062	−	0.550900i
$467$			14.5359i			0.672641i	0.941748	+	0.336321i	$0.109183\pi$
$467$			14.5359i			0.672641i	−0.941748	+	0.336321i	$0.890817\pi$
$468$	3.80385	+	2.19615i	0.175833	+	0.101517i
$469$	−11.9282	−	20.6603i	−0.550793	−	0.954002i
$470$	0.901924	+	15.0263i	0.0416026	+	0.693111i
$471$		0			0
$472$	−8.19615	+	4.73205i	−0.377258	+	0.217810i
$473$			11.0718i			0.509082i
$474$		0			0
$475$	6.29423	−	0.758330i	0.288799	−	0.0347946i
$476$	−2.36603	+	4.09808i	−0.108447	+	0.187835i
$477$	−21.8038	−	12.5885i	−0.998330	−	0.576386i
$478$	−12.6340	−	7.29423i	−0.577865	−	0.333630i
$479$	−1.26795	−	2.19615i	−0.0579341	−	0.100345i	0.835604	−	0.549333i	$-0.185118\pi$
$479$	−1.26795	−	2.19615i	−0.0579341	−	0.100345i	−0.893538	+	0.448988i	$0.851785\pi$
$480$		0			0
$481$	−0.732051	+	8.87564i	−0.0333786	+	0.404695i
$482$		−	17.4641i		−	0.795468i
$483$		0			0
$484$	−4.69615	+	8.13397i	−0.213461	+	0.369726i
$485$	7.19615	−	14.3923i	0.326760	−	0.653521i
$486$		0			0
$487$		−	33.4641i		−	1.51640i	−0.652020	−	0.758202i	$-0.726078\pi$
$487$		−	33.4641i		−	1.51640i	0.652020	−	0.758202i	$-0.273922\pi$
$488$	6.69615	+	3.86603i	0.303121	+	0.175007i
$489$		0			0
$490$	−0.571797	−	0.866025i	−0.0258311	−	0.0391230i
$491$	−29.6603			−1.33855			−0.669274	−	0.743015i	$-0.733395\pi$
$491$	−29.6603			−1.33855			−0.669274	+	0.743015i	$0.733395\pi$
$492$		0			0
$493$	2.59808	−	1.50000i	0.117011	−	0.0675566i
$494$	−0.928203	+	1.60770i	−0.0417618	+	0.0723336i
$495$	0.509619	+	8.49038i	0.0229057	+	0.381614i
$496$	−3.83013	−	6.63397i	−0.171978	−	0.297874i
$497$	−21.5885	+	12.4641i	−0.968375	+	0.559091i
$498$		0			0
$499$	−3.75833	+	6.50962i	−0.168246	+	0.291411i	−0.937803	−	0.347167i	$-0.887144\pi$
$499$	−3.75833	+	6.50962i	−0.168246	+	0.291411i	0.769557	+	0.638578i	$0.220477\pi$
$500$	−10.5263	−	3.76795i	−0.470750	−	0.168508i
$501$		0			0
$502$	10.2224	−	5.90192i	0.456249	−	0.263416i
$503$	−12.1699	+	7.02628i	−0.542628	+	0.313286i	−0.746143	−	0.665785i	$-0.768097\pi$
$503$	−12.1699	+	7.02628i	−0.542628	+	0.313286i	0.203515	+	0.979072i	$0.434763\pi$
$504$	8.19615			0.365086
$505$	−0.535898	−	0.267949i	−0.0238472	−	0.0119236i
$506$	−0.928203	−	1.60770i	−0.0412637	−	0.0714708i
$507$		0			0
$508$		−	10.9282i		−	0.484861i
$509$	20.2583	+	35.0885i	0.897935	+	1.55527i	0.830130	+	0.557570i	$0.188266\pi$
$509$	20.2583	+	35.0885i	0.897935	+	1.55527i	0.0678047	+	0.997699i	$0.478401\pi$
$510$		0			0
$511$	16.1962	−	28.0526i	0.716476	−	1.24097i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−6.40192	+	11.0885i	−0.282377	+	0.489091i
$515$	3.80385	−	7.60770i	0.167618	−	0.335235i
$516$		0			0
$517$		−	8.53590i		−	0.375408i
$518$	7.09808	+	15.0263i	0.311872	+	0.660217i
$519$		0			0
$520$	2.73205	−	1.80385i	0.119808	−	0.0791039i
$521$	17.1244	−	29.6603i	0.750232	−	1.29944i	−0.197479	−	0.980307i	$-0.563275\pi$
$521$	17.1244	−	29.6603i	0.750232	−	1.29944i	0.947710	−	0.319132i	$-0.103391\pi$
$522$	−4.50000	−	2.59808i	−0.196960	−	0.113715i
$523$	−10.7321	−	6.19615i	−0.469280	−	0.270939i	0.246658	−	0.969102i	$-0.420667\pi$
$523$	−10.7321	−	6.19615i	−0.469280	−	0.270939i	−0.715938	+	0.698164i	$0.754001\pi$
$524$	−2.92820			−0.127919
$525$		0			0
$526$	9.07180			0.395549
$527$	11.4904	−	6.63397i	0.500529	−	0.288980i
$528$		0			0
$529$	20.8564			0.906800
$530$	−15.6603	+	10.3397i	−0.680238	+	0.449130i
$531$	−14.1962	+	24.5885i	−0.616061	+	1.06705i
$532$			3.46410i			0.150188i
$533$	7.51666	−	4.33975i	0.325583	−	0.187975i
$534$		0			0
$535$	−7.63397	−	11.5622i	−0.330046	−	0.499877i
$536$	4.36603	−	7.56218i	0.188584	−	0.326636i
$537$		0			0
$538$	15.4641	−	8.92820i	0.666705	−	0.384922i
$539$	0.294229	+	0.509619i	0.0126733	+	0.0219508i
$540$		0			0
$541$	24.2679			1.04336			0.521680	−	0.853141i	$-0.325305\pi$
$541$	24.2679			1.04336			0.521680	+	0.853141i	$0.325305\pi$
$542$	−7.56218	−	4.36603i	−0.324823	−	0.187537i
$543$		0			0
$544$	−1.73205			−0.0742611
$545$	0.375644	+	6.25833i	0.0160908	+	0.268077i
$546$		0			0
$547$		−	43.3731i		−	1.85450i	−0.374445	−	0.927249i	$-0.622167\pi$
$547$		−	43.3731i		−	1.85450i	0.374445	−	0.927249i	$-0.377833\pi$
$548$	−1.50000	−	0.866025i	−0.0640768	−	0.0369948i
$549$	23.1962			0.989988
$550$	5.83013	+	2.49038i	0.248597	+	0.106190i
$551$	1.09808	−	1.90192i	0.0467796	−	0.0810247i
$552$		0			0
$553$	−37.0526	+	21.3923i	−1.57564	+	0.909693i
$554$	1.39230			0.0591534
$555$		0			0
$556$	10.9282			0.463459
$557$	−13.7942	+	7.96410i	−0.584480	+	0.337450i	−0.762912	−	0.646502i	$-0.776231\pi$
$557$	−13.7942	+	7.96410i	−0.584480	+	0.337450i	0.178432	+	0.983952i	$0.442898\pi$
$558$	−19.9019	−	11.4904i	−0.842516	−	0.486427i
$559$	6.39230	−	11.0718i	0.270366	−	0.468287i
$560$	2.73205	−	5.46410i	0.115450	−	0.230900i
$561$		0			0
$562$	2.59808	+	1.50000i	0.109593	+	0.0632737i
$563$			5.85641i			0.246818i	0.992356	+	0.123409i	$0.0393827\pi$
$563$			5.85641i			0.246818i	−0.992356	+	0.123409i	$0.960617\pi$
$564$		0			0
$565$	−37.7846	+	2.26795i	−1.58961	+	0.0954133i
$566$	−5.80385			−0.243954
$567$	21.2942	−	12.2942i	0.894274	−	0.516309i
$568$	−7.90192	−	4.56218i	−0.331557	−	0.191425i
$569$	−43.1051			−1.80706			−0.903530	−	0.428524i	$-0.859034\pi$
$569$	−43.1051			−1.80706			−0.903530	+	0.428524i	$0.859034\pi$
$570$		0			0
$571$	13.1244	+	22.7321i	0.549237	+	0.951307i	0.998327	+	0.0578201i	$0.0184150\pi$
$571$	13.1244	+	22.7321i	0.549237	+	0.951307i	−0.449090	+	0.893487i	$0.648252\pi$
$572$	−1.60770	+	0.928203i	−0.0672211	+	0.0388101i
$573$		0			0
$574$	8.09808	−	14.0263i	0.338007	−	0.585446i
$575$	5.85641	−	4.39230i	0.244229	−	0.183172i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−1.73205	+	1.00000i	−0.0721062	+	0.0416305i	−0.535620	−	0.844459i	$-0.679922\pi$
$577$	−1.73205	+	1.00000i	−0.0721062	+	0.0416305i	0.463513	+	0.886090i	$0.346589\pi$
$578$			14.0000i			0.582323i
$579$		0			0
$580$	−3.23205	+	2.13397i	−0.134204	+	0.0886085i
$581$	−6.92820			−0.287430
$582$		0			0
$583$	9.21539	−	5.32051i	0.381662	−	0.220353i
$584$	11.8564			0.490622
$585$	4.39230	−	8.78461i	0.181599	−	0.363199i
$586$	28.8564			1.19205
$587$	−16.3923	−	9.46410i	−0.676583	−	0.390625i	0.121983	−	0.992532i	$-0.461075\pi$
$587$	−16.3923	−	9.46410i	−0.676583	−	0.390625i	−0.798566	+	0.601907i	$0.794408\pi$
$588$		0			0
$589$	4.85641	−	8.41154i	0.200105	−	0.346592i
$590$	11.6603	+	17.6603i	0.480045	+	0.727061i
$591$		0			0
$592$	−3.46410	+	5.00000i	−0.142374	+	0.205499i
$593$		−	19.7321i		−	0.810298i	−0.914251	−	0.405149i	$-0.867220\pi$
$593$		−	19.7321i		−	0.810298i	0.914251	−	0.405149i	$-0.132780\pi$
$594$		0			0
$595$	9.46410	+	4.73205i	0.387990	+	0.193995i
$596$	−5.79423	+	10.0359i	−0.237341	+	0.411086i
$597$		0			0
$598$			2.14359i			0.0876581i
$599$	−0.0262794	+	0.0455173i	−0.00107375	+	0.00185979i	−0.866562	−	0.499070i	$-0.833675\pi$
$599$	−0.0262794	+	0.0455173i	−0.00107375	+	0.00185979i	0.865488	+	0.500930i	$0.167008\pi$
$600$		0			0
$601$	−18.6244	−	32.2583i	−0.759703	−	1.31584i	−0.943002	−	0.332787i	$-0.892011\pi$
$601$	−18.6244	−	32.2583i	−0.759703	−	1.31584i	0.183299	−	0.983057i	$-0.441322\pi$
$602$		−	23.8564i		−	0.972315i
$603$		−	26.1962i		−	1.06679i
$604$	−5.26795	−	9.12436i	−0.214350	−	0.371265i
$605$	18.7846	+	9.39230i	0.763703	+	0.381851i
$606$		0			0
$607$	−22.9019	+	13.2224i	−0.929560	+	0.536682i	−0.886673	−	0.462398i	$-0.846989\pi$
$607$	−22.9019	+	13.2224i	−0.929560	+	0.536682i	−0.0428879	+	0.999080i	$0.513656\pi$
$608$	−1.09808	+	0.633975i	−0.0445329	+	0.0257111i
$609$		0			0
$610$	7.73205	−	15.4641i	0.313062	−	0.626123i
$611$	−4.92820	+	8.53590i	−0.199374	+	0.345325i
$612$	−4.50000	+	2.59808i	−0.181902	+	0.105021i
$613$	27.9904	−	16.1603i	1.13052	−	0.652707i	0.186455	−	0.982464i	$-0.440300\pi$
$613$	27.9904	−	16.1603i	1.13052	−	0.652707i	0.944066	+	0.329757i	$0.106967\pi$
$614$	3.43782	+	5.95448i	0.138739	+	0.240303i
$615$		0			0
$616$	−1.73205	+	3.00000i	−0.0697863	+	0.120873i
$617$	−28.3923	+	16.3923i	−1.14303	+	0.659929i	−0.947179	−	0.320704i	$-0.896080\pi$
$617$	−28.3923	+	16.3923i	−1.14303	+	0.659929i	−0.195852	+	0.980634i	$0.562747\pi$
$618$		0			0
$619$	−30.4449			−1.22368			−0.611841	−	0.790981i	$-0.709571\pi$
$619$	−30.4449			−1.22368			−0.611841	+	0.790981i	$0.709571\pi$
$620$	−14.2942	+	9.43782i	−0.574070	+	0.379032i
$621$		0			0
$622$	−4.09808	−	2.36603i	−0.164318	−	0.0948690i
$623$			17.6603i			0.707543i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	1.40192	−	2.42820i	0.0560321	−	0.0970505i
$627$		0			0
$628$			17.0000i			0.678374i
$629$	−8.66025	−	6.00000i	−0.345307	−	0.239236i
$630$	−1.09808	−	18.2942i	−0.0437484	−	0.728860i
$631$	−6.39230	−	11.0718i	−0.254474	−	0.440761i	0.710279	−	0.703920i	$-0.248569\pi$
$631$	−6.39230	−	11.0718i	−0.254474	−	0.440761i	−0.964752	+	0.263159i	$0.915236\pi$
$632$	−13.5622	−	7.83013i	−0.539474	−	0.311466i
$633$		0			0
$634$	7.16025	−	12.4019i	0.284370	−	0.492543i
$635$	−24.3923	+	1.46410i	−0.967979	+	0.0581011i
$636$		0			0
$637$		−	0.679492i		−	0.0269225i
$638$	1.90192	−	1.09808i	0.0752979	−	0.0434733i
$639$	−27.3731			−1.08286
$640$	2.23205	−	0.133975i	0.0882296	−	0.00529581i
$641$	14.3564	+	24.8660i	0.567044	+	0.982149i	0.996856	+	0.0792307i	$0.0252464\pi$
$641$	14.3564	+	24.8660i	0.567044	+	0.982149i	−0.429812	+	0.902918i	$0.641420\pi$
$642$		0			0
$643$		−	39.6603i		−	1.56405i	−0.623248	−	0.782024i	$-0.714187\pi$
$643$		−	39.6603i		−	1.56405i	0.623248	−	0.782024i	$-0.285813\pi$
$644$	2.00000	+	3.46410i	0.0788110	+	0.136505i
$645$		0			0
$646$	−1.09808	−	1.90192i	−0.0432032	−	0.0748302i
$647$	6.75833	+	3.90192i	0.265697	+	0.153400i	0.626931	−	0.779075i	$-0.284311\pi$
$647$	6.75833	+	3.90192i	0.265697	+	0.153400i	−0.361233	+	0.932475i	$0.617644\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$	−4.39230	−	5.85641i	−0.172280	−	0.229707i
$651$		0			0
$652$		−	9.12436i		−	0.357337i
$653$	−36.6506	−	21.1603i	−1.43425	−	0.828065i	−0.436809	−	0.899554i	$-0.643891\pi$
$653$	−36.6506	−	21.1603i	−1.43425	−	0.828065i	−0.997441	+	0.0714896i	$0.977225\pi$
$654$		0			0
$655$	0.392305	+	6.53590i	0.0153286	+	0.255379i
$656$	5.92820			0.231457
$657$	30.8038	−	17.7846i	1.20177	−	0.693844i
$658$			18.3923i			0.717007i
$659$	−7.26795	+	12.5885i	−0.283119	+	0.490377i	−0.972151	−	0.234354i	$-0.924703\pi$
$659$	−7.26795	+	12.5885i	−0.283119	+	0.490377i	0.689032	+	0.724731i	$0.258036\pi$
$660$		0			0
$661$	19.1340	−	33.1410i	0.744225	−	1.28904i	−0.206330	−	0.978482i	$-0.566152\pi$
$661$	19.1340	−	33.1410i	0.744225	−	1.28904i	0.950556	−	0.310554i	$-0.100514\pi$
$662$	17.6603	+	10.1962i	0.686385	+	0.396285i
$663$		0			0
$664$	−1.26795	−	2.19615i	−0.0492060	−	0.0852272i
$665$	7.73205	−	0.464102i	0.299836	−	0.0179971i
$666$	−1.50000	+	18.1865i	−0.0581238	+	0.704714i
$667$		−	2.53590i		−	0.0981904i
$668$	−15.4641	+	8.92820i	−0.598324	+	0.345443i
$669$		0			0
$670$	−17.4641	−	8.73205i	−0.674697	−	0.337349i
$671$	−4.90192	+	8.49038i	−0.189237	+	0.327768i
$672$		0			0
$673$	33.5885	+	19.3923i	1.29474	+	0.747518i	0.979490	−	0.201490i	$-0.0645785\pi$
$673$	33.5885	+	19.3923i	1.29474	+	0.747518i	0.315249	+	0.949009i	$0.397912\pi$
$674$	−1.19615			−0.0460741
$675$		0			0
$676$	−10.8564			−0.417554
$677$			39.0000i			1.49889i	0.662066	+	0.749446i	$0.269680\pi$
$677$			39.0000i			1.49889i	−0.662066	+	0.749446i	$0.730320\pi$
$678$		0			0
$679$	9.83013	−	17.0263i	0.377246	−	0.653409i
$680$	0.232051	+	3.86603i	0.00889874	+	0.148255i
$681$		0			0
$682$	8.41154	−	4.85641i	0.322095	−	0.185961i
$683$	−13.5622	+	7.83013i	−0.518942	+	0.299611i	−0.736502	−	0.676436i	$-0.763524\pi$
$683$	−13.5622	+	7.83013i	−0.518942	+	0.299611i	0.217559	+	0.976047i	$0.430190\pi$
$684$	−1.90192	+	3.29423i	−0.0727219	+	0.125958i
$685$	−1.73205	+	3.46410i	−0.0661783	+	0.132357i
$686$	8.92820	+	15.4641i	0.340880	+	0.590422i
$687$		0			0
$688$	7.56218	−	4.36603i	0.288305	−	0.166453i
$689$	−12.2872			−0.468105
$690$		0			0
$691$	5.90192	+	10.2224i	0.224520	+	0.388880i	0.956175	−	0.292795i	$-0.0945853\pi$
$691$	5.90192	+	10.2224i	0.224520	+	0.388880i	−0.731655	+	0.681675i	$0.761252\pi$
$692$		−	0.0717968i		−	0.00272930i
$693$			10.3923i			0.394771i
$694$	13.8564	+	24.0000i	0.525982	+	0.911028i
$695$	−1.46410	−	24.3923i	−0.0555365	−	0.925253i
$696$		0			0
$697$			10.2679i			0.388926i
$698$	29.0885	+	16.7942i	1.10101	+	0.635671i
$699$		0			0
$700$	−12.5622	−	5.36603i	−0.474806	−	0.202817i
$701$	15.3923	+	26.6603i	0.581359	+	1.00694i	0.995319	+	0.0966485i	$0.0308123\pi$
$701$	15.3923	+	26.6603i	0.581359	+	1.00694i	−0.413959	+	0.910295i	$0.635854\pi$
$702$		0			0
$703$	−7.68653	−	0.633975i	−0.289903	−	0.0239108i
$704$	−1.26795			−0.0477876
$705$		0			0
$706$	6.86603	−	11.8923i	0.258406	−	0.447573i
$707$	−0.633975	−	0.366025i	−0.0238431	−	0.0137658i
$708$		0			0
$709$	−1.07180			−0.0402522			−0.0201261	−	0.999797i	$-0.506407\pi$
$709$	−1.07180			−0.0402522			−0.0201261	+	0.999797i	$0.506407\pi$
$710$	−9.12436	+	18.2487i	−0.342431	+	0.684862i
$711$	−46.9808			−1.76192
$712$	−5.59808	+	3.23205i	−0.209797	+	0.121126i
$713$		−	11.2154i		−	0.420020i
$714$		0			0
$715$	2.28719	+	3.46410i	0.0855359	+	0.129550i
$716$	7.46410	−	12.9282i	0.278947	−	0.483150i
$717$		0			0
$718$	15.1244	−	8.73205i	0.564436	−	0.325877i
$719$	6.19615	+	10.7321i	0.231077	+	0.400238i	0.958125	−	0.286349i	$-0.0924416\pi$
$719$	6.19615	+	10.7321i	0.231077	+	0.400238i	−0.727048	+	0.686587i	$0.759108\pi$
$720$	5.59808	−	3.69615i	0.208628	−	0.137747i
$721$	5.19615	−	9.00000i	0.193515	−	0.335178i
$722$	15.0622	+	8.69615i	0.560556	+	0.323637i
$723$		0			0
$724$	5.79423	+	10.0359i	0.215341	+	0.372981i
$725$	5.19615	+	6.92820i	0.192980	+	0.257307i
$726$		0			0
$727$	33.1244	+	19.1244i	1.22851	+	0.709283i	0.966719	−	0.255840i	$-0.0823521\pi$
$727$	33.1244	+	19.1244i	1.22851	+	0.709283i	0.261795	+	0.965123i	$0.415685\pi$
$728$	3.46410	−	2.00000i	0.128388	−	0.0741249i
$729$	27.0000			1.00000
$730$	−1.58846	−	26.4641i	−0.0587914	−	0.979480i
$731$	7.56218	+	13.0981i	0.279697	+	0.484450i
$732$		0			0
$733$	−15.1244	−	8.73205i	−0.558631	−	0.322526i	0.193965	−	0.981008i	$-0.437865\pi$
$733$	−15.1244	−	8.73205i	−0.558631	−	0.322526i	−0.752596	+	0.658483i	$0.771199\pi$
$734$	33.8564			1.24966
$735$		0			0
$736$	−0.732051	+	1.26795i	−0.0269838	+	0.0467372i
$737$	9.58846	+	5.53590i	0.353195	+	0.203917i
$738$	15.4019	−	8.89230i	0.566953	−	0.327330i
$739$	−30.9282			−1.13771			−0.568856	−	0.822437i	$-0.692614\pi$
$739$	−30.9282			−1.13771			−0.568856	+	0.822437i	$0.692614\pi$
$740$	11.6244	+	7.06218i	0.427320	+	0.259611i
$741$		0			0
$742$	−19.8564	+	11.4641i	−0.728952	+	0.420860i
$743$	22.2224	+	12.8301i	0.815262	+	0.470692i	0.848780	−	0.528746i	$-0.177338\pi$
$743$	22.2224	+	12.8301i	0.815262	+	0.470692i	−0.0335179	+	0.999438i	$0.510671\pi$
$744$		0			0
$745$	23.1769	+	11.5885i	0.849136	+	0.424568i
$746$	−1.00000			−0.0366126
$747$	−6.58846	−	3.80385i	−0.241059	−	0.139176i
$748$		−	2.19615i		−	0.0802993i
$749$	−8.46410	−	14.6603i	−0.309272	−	0.535674i
$750$		0			0
$751$	30.1962			1.10187			0.550937	−	0.834547i	$-0.314271\pi$
$751$	30.1962			1.10187			0.550937	+	0.834547i	$0.314271\pi$
$752$	−5.83013	+	3.36603i	−0.212603	+	0.122746i
$753$		0			0
$754$	−2.53590			−0.0923520
$755$	−19.6603	+	12.9808i	−0.715510	+	0.472418i
$756$		0			0
$757$	1.33013	−	0.767949i	0.0483443	−	0.0279116i	−0.475633	−	0.879644i	$-0.657781\pi$
$757$	1.33013	−	0.767949i	0.0483443	−	0.0279116i	0.523977	+	0.851732i	$0.324448\pi$
$758$	31.6865	+	18.2942i	1.15091	+	0.664476i
$759$		0			0
$760$	1.56218	+	2.36603i	0.0566661	+	0.0858248i
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	0.856821	−	0.515615i	$-0.172436\pi$
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	−0.874946	+	0.484221i	$0.839103\pi$
$762$		0			0
$763$			7.66025i			0.277320i
$764$	−9.66025	+	16.7321i	−0.349496	+	0.605344i
$765$	6.40192	+	9.69615i	0.231462	+	0.350565i
$766$	15.5167			0.560640
$767$			13.8564i			0.500326i
$768$		0			0
$769$	3.60770			0.130097			0.0650484	−	0.997882i	$-0.479280\pi$
$769$	3.60770			0.130097			0.0650484	+	0.997882i	$0.479280\pi$
$770$	6.92820	+	3.46410i	0.249675	+	0.124838i
$771$		0			0
$772$	14.4282	+	8.33013i	0.519282	+	0.299808i
$773$	−35.3827	−	20.4282i	−1.27263	−	0.734751i	−0.297145	−	0.954832i	$-0.596035\pi$
$773$	−35.3827	−	20.4282i	−1.27263	−	0.734751i	−0.975482	+	0.220081i	$0.929368\pi$
$774$	13.0981	−	22.6865i	0.470801	−	0.815451i
$775$	22.9808	+	30.6410i	0.825493	+	1.10066i
$776$	7.19615			0.258327
$777$		0			0
$778$			8.26795i			0.296420i
$779$	3.75833	+	6.50962i	0.134656	+	0.233231i
$780$		0			0
$781$	5.78461	−	10.0192i	0.206990	−	0.358517i
$782$	−2.19615	−	1.26795i	−0.0785343	−	0.0453418i
$783$		0			0
$784$	0.232051	−	0.401924i	0.00828753	−	0.0143544i
$785$	37.9449	−	2.27757i	1.35431	−	0.0812899i
$786$		0			0
$787$			45.5692i			1.62437i	0.583402	+	0.812184i	$0.301721\pi$
$787$			45.5692i			1.62437i	−0.583402	+	0.812184i	$0.698279\pi$
$788$			6.07180i			0.216299i
$789$		0			0
$790$	−15.6603	+	31.3205i	−0.557167	+	1.11433i
$791$	−46.2487			−1.64441
$792$	−3.29423	+	1.90192i	−0.117055	+	0.0675819i
$793$	9.80385	−	5.66025i	0.348145	−	0.201002i
$794$	−0.0358984	−	0.0621778i	−0.00127399	−	0.00220661i
$795$		0			0
$796$	−0.901924	+	1.56218i	−0.0319678	+	0.0553699i
$797$	−22.9808	+	13.2679i	−0.814020	+	0.469975i	−0.848350	−	0.529436i	$-0.822404\pi$
$797$	−22.9808	+	13.2679i	−0.814020	+	0.469975i	0.0343297	+	0.999411i	$0.489070\pi$
$798$		0			0
$799$	−5.83013	−	10.0981i	−0.206255	−	0.357244i
$800$	−0.598076	−	4.96410i	−0.0211452	−	0.175507i
$801$	−9.69615	+	16.7942i	−0.342597	+	0.593395i
$802$	13.2679	−	7.66025i	0.468508	−	0.270493i
$803$			15.0333i			0.530514i
$804$		0			0
$805$	7.46410	−	4.92820i	0.263075	−	0.173696i
$806$	−11.2154			−0.395045
$807$		0			0
$808$		−	0.267949i		−	0.00942642i
$809$	5.66025	−	9.80385i	0.199004	−	0.344685i	−0.749202	−	0.662342i	$-0.769563\pi$
$809$	5.66025	−	9.80385i	0.199004	−	0.344685i	0.948206	+	0.317657i	$0.102896\pi$
$810$	9.00000	−	18.0000i	0.316228	−	0.632456i
$811$	20.1962	−	34.9808i	0.709183	−	1.22834i	−0.255978	−	0.966683i	$-0.582397\pi$
$811$	20.1962	−	34.9808i	0.709183	−	1.22834i	0.965161	−	0.261658i	$-0.0842693\pi$
$812$	−4.09808	+	2.36603i	−0.143814	+	0.0830312i
$813$		0			0
$814$	−6.33975	−	4.39230i	−0.222208	−	0.153950i
$815$	−20.3660	+	1.22243i	−0.713391	+	0.0428199i
$816$		0			0
$817$	9.58846	+	5.53590i	0.335458	+	0.193677i
$818$	−3.27757	−	1.89230i	−0.114597	−	0.0661629i
$819$	6.00000	−	10.3923i	0.209657	−	0.363137i
$820$	−0.794229	−	13.2321i	−0.0277357	−	0.462083i
$821$	−14.0000	+	24.2487i	−0.488603	+	0.846286i	−0.999914	−	0.0131101i	$-0.995827\pi$
$821$	−14.0000	+	24.2487i	−0.488603	+	0.846286i	0.511311	+	0.859396i	$0.329160\pi$
$822$		0			0
$823$	−44.4449	+	25.6603i	−1.54925	+	0.894460i	−0.551052	+	0.834471i	$0.685773\pi$
$823$	−44.4449	+	25.6603i	−1.54925	+	0.894460i	−0.998199	+	0.0599890i	$0.980893\pi$
$824$	3.80385			0.132513
$825$		0			0
$826$	12.9282	+	22.3923i	0.449830	+	0.779128i
$827$	44.7846	+	25.8564i	1.55731	+	0.899115i	0.997513	+	0.0704882i	$0.0224557\pi$
$827$	44.7846	+	25.8564i	1.55731	+	0.899115i	0.559801	+	0.828627i	$0.310878\pi$
$828$			4.39230i			0.152643i
$829$	−22.4641	−	38.9090i	−0.780210	−	1.35136i	−0.931819	−	0.362924i	$-0.881779\pi$
$829$	−22.4641	−	38.9090i	−0.780210	−	1.35136i	0.151608	−	0.988441i	$-0.451555\pi$
$830$	−4.73205	+	3.12436i	−0.164252	+	0.108448i
$831$		0			0
$832$	1.26795	+	0.732051i	0.0439582	+	0.0253793i
$833$	0.696152	+	0.401924i	0.0241203	+	0.0139258i
$834$		0			0
$835$	22.0000	+	33.3205i	0.761341	+	1.15310i
$836$	−0.803848	−	1.39230i	−0.0278016	−	0.0481539i
$837$		0			0
$838$	24.4186	+	14.0981i	0.843526	+	0.487010i
$839$	−26.1962	−	45.3731i	−0.904392	−	1.56645i	−0.821732	−	0.569874i	$-0.806992\pi$
$839$	−26.1962	−	45.3731i	−0.904392	−	1.56645i	−0.0826598	−	0.996578i	$-0.526341\pi$
$840$		0			0
$841$	−26.0000			−0.896552
$842$	−14.3038	+	8.25833i	−0.492943	+	0.284601i
$843$		0			0
$844$	9.02628	−	15.6340i	0.310697	−	0.538144i
$845$	1.45448	+	24.2321i	0.0500357	+	0.833608i
$846$	−10.0981	+	17.4904i	−0.347179	+	0.601332i
$847$	22.2224	+	12.8301i	0.763572	+	0.440848i
$848$	−7.26795	−	4.19615i	−0.249582	−	0.144096i
$849$		0			0
$850$	8.59808	−	1.03590i	0.294912	−	0.0355310i
$851$	−8.05256	+	3.80385i	−0.276038	+	0.130394i
$852$		0			0
$853$	45.7750	−	26.4282i	1.56731	−	0.904884i	0.570824	−	0.821072i	$-0.306624\pi$
$853$	45.7750	−	26.4282i	1.56731	−	0.904884i	0.996482	−	0.0838122i	$-0.0267096\pi$
$854$	10.5622	−	18.2942i	0.361430	−	0.626016i
$855$	7.60770	+	3.80385i	0.260178	+	0.130089i
$856$	3.09808	−	5.36603i	0.105890	−	0.183407i
$857$			32.5167i			1.11075i	0.831601	+	0.555374i	$0.187425\pi$
$857$			32.5167i			1.11075i	−0.831601	+	0.555374i	$0.812575\pi$
$858$		0			0
$859$	−38.0526			−1.29834			−0.649168	−	0.760645i	$-0.724883\pi$
$859$	−38.0526			−1.29834			−0.649168	+	0.760645i	$0.724883\pi$
$860$	−10.7583	−	16.2942i	−0.366856	−	0.555629i
$861$		0			0
$862$			12.7321i			0.433655i
$863$	15.8038	−	9.12436i	0.537969	−	0.310597i	−0.206286	−	0.978492i	$-0.566138\pi$
$863$	15.8038	−	9.12436i	0.537969	−	0.310597i	0.744256	+	0.667895i	$0.232804\pi$
$864$		0			0
$865$	−0.160254	+	0.00961894i	−0.00544880	+	0.000327054i
$866$	−16.1865	−	28.0359i	−0.550041	−	0.952699i
$867$		0			0
$868$	−18.1244	+	10.4641i	−0.615181	+	0.355175i
$869$	9.92820	−	17.1962i	0.336791	−	0.583340i
$870$		0			0
$871$	−6.39230	−	11.0718i	−0.216595	−	0.375154i
$872$	−2.42820	+	1.40192i	−0.0822293	+	0.0474751i
$873$	18.6962	−	10.7942i	0.632769	−	0.365329i
$874$	−1.85641			−0.0627939
$875$	−10.2942	+	28.7583i	−0.348008	+	0.972209i
$876$		0			0
$877$		−	27.1051i		−	0.915275i	−0.889139	−	0.457637i	$-0.848696\pi$
$877$		−	27.1051i		−	0.915275i	0.889139	−	0.457637i	$-0.151304\pi$
$878$			33.8564i			1.14260i
$879$		0			0
$880$	0.169873	+	2.83013i	0.00572642	+	0.0954036i
$881$	−8.76795	+	15.1865i	−0.295400	+	0.511647i	−0.975078	−	0.221863i	$-0.928786\pi$
$881$	−8.76795	+	15.1865i	−0.295400	+	0.511647i	0.679678	+	0.733511i	$0.262119\pi$
$882$		−	1.39230i		−	0.0468813i
$883$	−17.6603	−	10.1962i	−0.594315	−	0.343128i	0.172487	−	0.985012i	$-0.444820\pi$
$883$	−17.6603	−	10.1962i	−0.594315	−	0.343128i	−0.766802	+	0.641884i	$0.778153\pi$
$884$	−1.26795	+	2.19615i	−0.0426457	+	0.0738646i
$885$		0			0
$886$	−12.3923	−	21.4641i	−0.416328	−	0.721101i
$887$		−	5.46410i		−	0.183467i	−0.995784	−	0.0917333i	$-0.970759\pi$
$887$		−	5.46410i		−	0.183467i	0.995784	−	0.0917333i	$-0.0292407\pi$
$888$		0			0
$889$	−29.8564			−1.00135
$890$	7.96410	+	12.0622i	0.266957	+	0.404325i
$891$	−5.70577	+	9.88269i	−0.191151	+	0.331082i
$892$	−0.928203	−	0.535898i	−0.0310785	−	0.0179432i
$893$	−7.39230	−	4.26795i	−0.247374	−	0.142821i
$894$		0			0
$895$	−29.8564	−	14.9282i	−0.997990	−	0.498995i
$896$	2.73205			0.0912714
$897$		0			0
$898$		−	42.2487i		−	1.40986i
$899$	13.2679			0.442511
$900$	−9.00000	−	12.0000i	−0.300000	−	0.400000i
$901$	7.26795	−	12.5885i	0.242130	−	0.419382i
$902$			7.51666i			0.250277i
$903$		0			0
$904$	−8.46410	−	14.6603i	−0.281512	−	0.487593i
$905$	21.6244	−	14.2776i	0.718818	−	0.474602i
$906$		0			0
$907$	2.83013	+	1.63397i	0.0939728	+	0.0542552i	0.546250	−	0.837622i	$-0.316055\pi$
$907$	2.83013	+	1.63397i	0.0939728	+	0.0542552i	−0.452277	+	0.891877i	$0.649388\pi$
$908$	3.75833	−	2.16987i	0.124725	−	0.0720098i
$909$	−0.401924	−	0.696152i	−0.0133310	−	0.0230899i
$910$	−4.92820	−	7.46410i	−0.163368	−	0.247433i
$911$	18.9282			0.627119			0.313560	−	0.949568i	$-0.398478\pi$
$911$	18.9282			0.627119			0.313560	+	0.949568i	$0.398478\pi$
$912$		0			0
$913$	2.78461	−	1.60770i	0.0921571	−	0.0532069i
$914$	−8.80385			−0.291205
$915$		0			0
$916$	12.7942	+	22.1603i	0.422733	+	0.732195i
$917$			8.00000i			0.264183i
$918$		0			0
$919$	55.0333			1.81538			0.907691	−	0.419639i	$-0.137843\pi$
$919$	55.0333			1.81538			0.907691	+	0.419639i	$0.137843\pi$
$920$	2.92820	+	1.46410i	0.0965400	+	0.0482700i
$921$		0			0
$922$	−29.1962	−	16.8564i	−0.961524	−	0.555136i
$923$	−11.5692	+	6.67949i	−0.380805	+	0.219858i
$924$		0			0
$925$	14.2058	−	26.8923i	0.467083	−	0.884214i
$926$	−20.9808			−0.689471
$927$	9.88269	−	5.70577i	0.324590	−	0.187402i
$928$	−1.50000	−	0.866025i	−0.0492399	−	0.0284287i
$929$	14.7679	−	25.5788i	0.484521	−	0.839214i	−0.515321	−	0.856997i	$-0.672327\pi$
$929$	14.7679	−	25.5788i	0.484521	−	0.839214i	0.999842	+	0.0177827i	$0.00566070\pi$
$930$		0			0
$931$	0.588457			0.0192859
$932$	−11.8923	−	6.86603i	−0.389545	−	0.224904i
$933$		0			0
$934$	7.26795	+	12.5885i	0.237815	+	0.411907i
$935$	−4.90192	+	0.294229i	−0.160310	+	0.00962231i
$936$	4.39230			0.143567
$937$	31.7487	−	18.3301i	1.03719	−	0.598819i	0.118150	−	0.992996i	$-0.462303\pi$
$937$	31.7487	−	18.3301i	1.03719	−	0.598819i	0.919035	+	0.394177i	$0.128970\pi$
$938$	−20.6603	−	11.9282i	−0.674581	−	0.389470i
$939$		0			0
$940$	8.29423	+	12.5622i	0.270528	+	0.409733i
$941$	9.33013	+	16.1603i	0.304153	+	0.526809i	0.977072	−	0.212907i	$-0.0682931\pi$
$941$	9.33013	+	16.1603i	0.304153	+	0.526809i	−0.672919	+	0.739716i	$0.734960\pi$
$942$		0			0
$943$	7.51666	+	4.33975i	0.244776	+	0.141322i
$944$	−4.73205	+	8.19615i	−0.154015	+	0.266762i
$945$		0			0
$946$	5.53590	+	9.58846i	0.179988	+	0.311748i
$947$	11.0718	−	6.39230i	0.359785	−	0.207722i	−0.309201	−	0.950997i	$-0.600062\pi$
$947$	11.0718	−	6.39230i	0.359785	−	0.207722i	0.668986	+	0.743275i	$0.266728\pi$
$948$		0			0
$949$	8.67949	−	15.0333i	0.281748	−	0.488002i
$950$	5.07180	−	3.80385i	0.164551	−	0.123413i
$951$		0			0
$952$			4.73205i			0.153367i
$953$	−11.1962	+	6.46410i	−0.362679	+	0.209393i	−0.670255	−	0.742131i	$-0.733815\pi$
$953$	−11.1962	+	6.46410i	−0.362679	+	0.209393i	0.307576	+	0.951523i	$0.400482\pi$
$954$	−25.1769			−0.815133
$955$	38.6410	+	19.3205i	1.25039	+	0.625197i
$956$	−14.5885			−0.471824
$957$		0			0
$958$	−2.19615	−	1.26795i	−0.0709545	−	0.0409656i
$959$	−2.36603	+	4.09808i	−0.0764029	+	0.132334i
$960$		0			0
$961$	27.6795			0.892887
$962$	3.80385	+	8.05256i	0.122641	+	0.259625i
$963$		−	18.5885i		−	0.599005i
$964$	−8.73205	−	15.1244i	−0.281240	−	0.487123i
$965$	16.6603	−	33.3205i	0.536313	−	1.07263i
$966$		0			0
$967$	−10.1436	−	5.85641i	−0.326196	−	0.188329i	0.327955	−	0.944693i	$-0.393641\pi$
$967$	−10.1436	−	5.85641i	−0.326196	−	0.188329i	−0.654151	+	0.756364i	$0.726974\pi$
$968$			9.39230i			0.301880i
$969$		0			0
$970$	−0.964102	−	16.0622i	−0.0309554	−	0.515725i
$971$	13.3205	+	23.0718i	0.427475	+	0.740409i	0.996648	−	0.0818089i	$-0.0260697\pi$
$971$	13.3205	+	23.0718i	0.427475	+	0.740409i	−0.569173	+	0.822218i	$0.692736\pi$
$972$		0			0
$973$		−	29.8564i		−	0.957152i
$974$	−16.7321	−	28.9808i	−0.536129	−	0.928604i
$975$		0			0
$976$	7.73205			0.247497
$977$	−24.3731	+	14.0718i	−0.779763	+	0.450197i	−0.836346	−	0.548201i	$-0.815313\pi$
$977$	−24.3731	+	14.0718i	−0.779763	+	0.450197i	0.0565830	+	0.998398i	$0.481979\pi$
$978$		0			0
$979$	−4.09808	−	7.09808i	−0.130975	−	0.226855i
$980$	−0.928203	−	0.464102i	−0.0296504	−	0.0148252i
$981$	−4.20577	+	7.28461i	−0.134280	+	0.232580i
$982$	−25.6865	+	14.8301i	−0.819690	+	0.473248i
$983$	−32.3660	+	18.6865i	−1.03232	+	0.596008i	−0.917647	−	0.397396i	$-0.869914\pi$
$983$	−32.3660	+	18.6865i	−1.03232	+	0.596008i	−0.114669	+	0.993404i	$0.536581\pi$
$984$		0			0
$985$	13.5526	−	0.813467i	0.431820	−	0.0259192i
$986$	1.50000	−	2.59808i	0.0477697	−	0.0827396i
$987$		0			0
$988$			1.85641i			0.0590602i
$989$	12.7846			0.406527
$990$	4.68653	+	7.09808i	0.148948	+	0.225592i
$991$	19.2679			0.612067			0.306033	−	0.952021i	$-0.400998\pi$
$991$	19.2679			0.612067			0.306033	+	0.952021i	$0.400998\pi$
$992$	−6.63397	−	3.83013i	−0.210629	−	0.121607i
$993$		0			0
$994$	−12.4641	+	21.5885i	−0.395337	+	0.684744i
$995$	3.60770	+	1.80385i	0.114372	+	0.0571858i
$996$		0			0
$997$	−10.7321	+	6.19615i	−0.339887	+	0.196234i	−0.660222	−	0.751070i	$-0.729538\pi$
$997$	−10.7321	+	6.19615i	−0.339887	+	0.196234i	0.320335	+	0.947304i	$0.396205\pi$
$998$			7.51666i			0.237936i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.n.a.359.2	yes	4
5.4	even	2		370.2.n.c.359.1	yes	4
37.10	even	3		370.2.n.c.269.1	yes	4
185.84	even	6	inner	370.2.n.a.269.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.a.269.2	✓	4	185.84	even	6	inner
370.2.n.a.359.2	yes	4	1.1	even	1	trivial
370.2.n.c.269.1	yes	4	37.10	even	3
370.2.n.c.359.1	yes	4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.00000i) q^{5} +(-2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.00000i) q^{5} +(-2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-2.23205 + 0.133975i) q^{10} +1.26795 q^{11} +(-1.26795 - 0.732051i) q^{13} -2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 0.866025i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(0.633975 - 1.09808i) q^{19} +(-1.86603 + 1.23205i) q^{20} +(1.09808 - 0.633975i) q^{22} -1.46410i q^{23} +(3.00000 + 4.00000i) q^{25} -1.46410 q^{26} +(-2.36603 + 1.36603i) q^{28} +1.73205 q^{29} +7.66025 q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.866025 - 1.50000i) q^{34} +(3.36603 + 5.09808i) q^{35} -3.00000 q^{36} +(-2.59808 - 5.50000i) q^{37} -1.26795i q^{38} +(-1.00000 + 2.00000i) q^{40} +(-2.96410 + 5.13397i) q^{41} +8.73205i q^{43} +(0.633975 - 1.09808i) q^{44} +(0.401924 + 6.69615i) q^{45} +(-0.732051 - 1.26795i) q^{46} -6.73205i q^{47} +(0.232051 + 0.401924i) q^{49} +(4.59808 + 1.96410i) q^{50} +(-1.26795 + 0.732051i) q^{52} +(7.26795 - 4.19615i) q^{53} +(-2.53590 - 1.26795i) q^{55} +(-1.36603 + 2.36603i) q^{56} +(1.50000 - 0.866025i) q^{58} +(-4.73205 - 8.19615i) q^{59} +(-3.86603 + 6.69615i) q^{61} +(6.63397 - 3.83013i) q^{62} +8.19615i q^{63} -1.00000 q^{64} +(1.80385 + 2.73205i) q^{65} +(7.56218 + 4.36603i) q^{67} -1.73205i q^{68} +(5.46410 + 2.73205i) q^{70} +(4.56218 - 7.90192i) q^{71} +(-2.59808 + 1.50000i) q^{72} +11.8564i q^{73} +(-5.00000 - 3.46410i) q^{74} +(-0.633975 - 1.09808i) q^{76} +(-3.00000 - 1.73205i) q^{77} +(7.83013 - 13.5622i) q^{79} +(0.133975 + 2.23205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +5.92820i q^{82} +(2.19615 - 1.26795i) q^{83} +(-3.86603 + 0.232051i) q^{85} +(4.36603 + 7.56218i) q^{86} -1.26795i q^{88} +(-3.23205 - 5.59808i) q^{89} +(3.69615 + 5.59808i) q^{90} +(2.00000 + 3.46410i) q^{91} +(-1.26795 - 0.732051i) q^{92} +(-3.36603 - 5.83013i) q^{94} +(-2.36603 + 1.56218i) q^{95} +7.19615i q^{97} +(0.401924 + 0.232051i) q^{98} +(-1.90192 - 3.29423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 8 q^{5} - 6 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 8 * q^5 - 6 * q^7 - 6 * q^9	\( 4 q + 2 q^{4} - 8 q^{5} - 6 q^{7} - 6 q^{9} - 2 q^{10} + 12 q^{11} - 12 q^{13} - 4 q^{14} - 2 q^{16} + 6 q^{17} + 6 q^{19} - 4 q^{20} - 6 q^{22} + 12 q^{25} + 8 q^{26} - 6 q^{28} - 4 q^{31} + 10 q^{35} - 12 q^{36} - 4 q^{40} + 2 q^{41} + 6 q^{44} + 12 q^{45} + 4 q^{46} - 6 q^{49} + 8 q^{50} - 12 q^{52} + 36 q^{53} - 24 q^{55} - 2 q^{56} + 6 q^{58} - 12 q^{59} - 12 q^{61} + 30 q^{62} - 4 q^{64} + 28 q^{65} + 6 q^{67} + 8 q^{70} - 6 q^{71} - 20 q^{74} - 6 q^{76} - 12 q^{77} + 14 q^{79} + 4 q^{80} - 18 q^{81} - 12 q^{83} - 12 q^{85} + 14 q^{86} - 6 q^{89} - 6 q^{90} + 8 q^{91} - 12 q^{92} - 10 q^{94} - 6 q^{95} + 12 q^{98} - 18 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 8 * q^5 - 6 * q^7 - 6 * q^9 - 2 * q^10 + 12 * q^11 - 12 * q^13 - 4 * q^14 - 2 * q^16 + 6 * q^17 + 6 * q^19 - 4 * q^20 - 6 * q^22 + 12 * q^25 + 8 * q^26 - 6 * q^28 - 4 * q^31 + 10 * q^35 - 12 * q^36 - 4 * q^40 + 2 * q^41 + 6 * q^44 + 12 * q^45 + 4 * q^46 - 6 * q^49 + 8 * q^50 - 12 * q^52 + 36 * q^53 - 24 * q^55 - 2 * q^56 + 6 * q^58 - 12 * q^59 - 12 * q^61 + 30 * q^62 - 4 * q^64 + 28 * q^65 + 6 * q^67 + 8 * q^70 - 6 * q^71 - 20 * q^74 - 6 * q^76 - 12 * q^77 + 14 * q^79 + 4 * q^80 - 18 * q^81 - 12 * q^83 - 12 * q^85 + 14 * q^86 - 6 * q^89 - 6 * q^90 + 8 * q^91 - 12 * q^92 - 10 * q^94 - 6 * q^95 + 12 * q^98 - 18 * q^99

Introduction

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