LMFDB - Embedded newform 300.2.j.d.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(7,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("300.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.j (of order $4$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-1.35818 - 0.394157i$ of defining polynomial
Character	$\chi$	$=$	300.7
Dual form			300.2.j.d.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35818 - 0.394157i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(2.47817 - 2.47817i) q^{7} +(-1.87233 - 2.12000i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.35818 - 0.394157i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(2.47817 - 2.47817i) q^{7} +(-1.87233 - 2.12000i) q^{8} +1.00000i q^{9} -3.02831i q^{11} +(0.437425 + 1.95158i) q^{12} +(-0.363328 + 0.363328i) q^{13} +(-4.34258 + 2.38900i) q^{14} +(1.70734 + 3.61732i) q^{16} +(2.36333 + 2.36333i) q^{17} +(0.394157 - 1.35818i) q^{18} +4.95634 q^{19} +3.50466 q^{21} +(-1.19363 + 4.11297i) q^{22} +(-0.900390 - 0.900390i) q^{23} +(0.175128 - 2.82300i) q^{24} +(0.636672 - 0.350255i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(6.83963 - 1.53303i) q^{28} +3.50466i q^{29} -3.85607i q^{31} +(-0.893077 - 5.58591i) q^{32} +(2.14134 - 2.14134i) q^{33} +(-2.27829 - 4.14134i) q^{34} +(-1.07067 + 1.68928i) q^{36} +(0.363328 + 0.363328i) q^{37} +(-6.73158 - 1.95358i) q^{38} -0.513824 q^{39} +2.72666 q^{41} +(-4.75995 - 1.38139i) q^{42} +(3.92870 + 3.92870i) q^{43} +(3.24231 - 5.11566i) q^{44} +(0.867993 + 1.57778i) q^{46} +(5.85673 - 5.85673i) q^{47} +(-1.35056 + 3.76510i) q^{48} -5.28267i q^{49} +3.34225i q^{51} +(-1.00277 + 0.224760i) q^{52} +(-3.14134 + 3.14134i) q^{53} +(1.23909 - 0.681664i) q^{54} +(-9.89367 - 0.613763i) q^{56} +(3.50466 + 3.50466i) q^{57} +(1.38139 - 4.75995i) q^{58} -8.68516 q^{59} -15.2920 q^{61} +(-1.51990 + 5.23723i) q^{62} +(2.47817 + 2.47817i) q^{63} +(-0.988770 + 7.93866i) q^{64} +(-3.75233 + 2.06429i) q^{66} +(-3.92870 + 3.92870i) q^{67} +(1.46199 + 6.52267i) q^{68} -1.27334i q^{69} +4.25583i q^{71} +(2.12000 - 1.87233i) q^{72} +(-9.28267 + 9.28267i) q^{73} +(-0.350255 - 0.636672i) q^{74} +(8.37266 + 5.30660i) q^{76} +(-7.50466 - 7.50466i) q^{77} +(0.697863 + 0.202527i) q^{78} -0.399759 q^{79} -1.00000 q^{81} +(-3.70328 - 1.07473i) q^{82} +(-0.199879 - 0.199879i) q^{83} +(5.92036 + 3.75233i) q^{84} +(-3.78734 - 6.88438i) q^{86} +(-2.47817 + 2.47817i) q^{87} +(-6.42000 + 5.66999i) q^{88} +4.28267i q^{89} +1.80078i q^{91} +(-0.556993 - 2.48503i) q^{92} +(2.72666 - 2.72666i) q^{93} +(-10.2629 + 5.64600i) q^{94} +(3.31834 - 4.58134i) q^{96} +(-6.73599 - 6.73599i) q^{97} +(-2.08220 + 7.17480i) q^{98} +3.02831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q - 4 * q^6 + 12 * q^8	$ 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48} + 8 q^{52} - 4 q^{53} - 64 q^{56} + 20 q^{58} - 32 q^{61} + 56 q^{62} - 24 q^{66} + 16 q^{68} + 12 q^{72} - 44 q^{73} + 8 q^{76} - 48 q^{77} + 24 q^{78} - 12 q^{81} - 16 q^{82} + 64 q^{86} - 60 q^{88} - 56 q^{92} + 16 q^{93} + 44 q^{96} + 20 q^{97} - 24 q^{98}+O(q^{100}) $ 12 * q - 4 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 + 12 * q^16 + 20 * q^17 - 12 * q^22 + 16 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^38 + 16 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 - 64 * q^56 + 20 * q^58 - 32 * q^61 + 56 * q^62 - 24 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 + 8 * q^76 - 48 * q^77 + 24 * q^78 - 12 * q^81 - 16 * q^82 + 64 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 44 * q^96 + 20 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.35818	−	0.394157i	−0.960375	−	0.278711i
$2$	−1.35818	−	0.394157i	−0.960375	−	0.278711i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.68928	+	1.07067i	0.844640	+	0.535334i
$5$		0			0
$5$		0			0
$6$	−0.681664	−	1.23909i	−0.278288	−	0.505855i
$7$	2.47817	−	2.47817i	0.936661	−	0.936661i	−0.0614493	−	0.998110i	$-0.519572\pi$
$7$	2.47817	−	2.47817i	0.936661	−	0.936661i	0.998110	+	0.0614493i	$0.0195722\pi$
$8$	−1.87233	−	2.12000i	−0.661968	−	0.749532i
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	3.02831i		−	0.913069i	−0.889706	−	0.456534i	$-0.849091\pi$
$11$		−	3.02831i		−	0.913069i	0.889706	−	0.456534i	$-0.150909\pi$
$12$	0.437425	+	1.95158i	0.126274	+	0.563372i
$13$	−0.363328	+	0.363328i	−0.100769	+	0.100769i	−0.755694	−	0.654925i	$-0.772700\pi$
$13$	−0.363328	+	0.363328i	−0.100769	+	0.100769i	0.654925	+	0.755694i	$0.272700\pi$
$14$	−4.34258	+	2.38900i	−1.16060	+	0.638488i
$15$		0			0
$16$	1.70734	+	3.61732i	0.426835	+	0.904330i
$17$	2.36333	+	2.36333i	0.573191	+	0.573191i	0.933019	−	0.359828i	$-0.117164\pi$
$17$	2.36333	+	2.36333i	0.573191	+	0.573191i	−0.359828	+	0.933019i	$0.617164\pi$
$18$	0.394157	−	1.35818i	0.0929036	−	0.320125i
$19$	4.95634			1.13706			0.568532	−	0.822661i	$-0.307512\pi$
$19$	4.95634			1.13706			0.568532	+	0.822661i	$0.307512\pi$
$20$		0			0
$21$	3.50466			0.764780
$22$	−1.19363	+	4.11297i	−0.254482	+	0.876888i
$23$	−0.900390	−	0.900390i	−0.187744	−	0.187744i	0.606976	−	0.794720i	$-0.292382\pi$
$23$	−0.900390	−	0.900390i	−0.187744	−	0.187744i	−0.794720	+	0.606976i	$0.792382\pi$
$24$	0.175128	−	2.82300i	0.0357478	−	0.576243i
$25$		0			0
$26$	0.636672	−	0.350255i	0.124862	−	0.0686907i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	6.83963	−	1.53303i	1.29257	−	0.289715i
$29$			3.50466i			0.650800i	0.945576	+	0.325400i	$0.105499\pi$
$29$			3.50466i			0.650800i	−0.945576	+	0.325400i	$0.894501\pi$
$30$		0			0
$31$		−	3.85607i		−	0.692571i	−0.938129	−	0.346286i	$-0.887443\pi$
$31$		−	3.85607i		−	0.692571i	0.938129	−	0.346286i	$-0.112557\pi$
$32$	−0.893077	−	5.58591i	−0.157875	−	0.987459i
$33$	2.14134	−	2.14134i	0.372759	−	0.372759i
$34$	−2.27829	−	4.14134i	−0.390724	−	0.710233i
$35$		0			0
$36$	−1.07067	+	1.68928i	−0.178445	+	0.281547i
$37$	0.363328	+	0.363328i	0.0597308	+	0.0597308i	0.736341	−	0.676610i	$-0.236552\pi$
$37$	0.363328	+	0.363328i	0.0597308	+	0.0597308i	−0.676610	+	0.736341i	$0.736552\pi$
$38$	−6.73158	−	1.95358i	−1.09201	−	0.316912i
$39$	−0.513824			−0.0822776
$40$		0			0
$41$	2.72666			0.425832			0.212916	−	0.977070i	$-0.431704\pi$
$41$	2.72666			0.425832			0.212916	+	0.977070i	$0.431704\pi$
$42$	−4.75995	−	1.38139i	−0.734476	−	0.213153i
$43$	3.92870	+	3.92870i	0.599121	+	0.599121i	0.940079	−	0.340958i	$-0.110751\pi$
$43$	3.92870	+	3.92870i	0.599121	+	0.599121i	−0.340958	+	0.940079i	$0.610751\pi$
$44$	3.24231	−	5.11566i	0.488797	−	0.771215i
$45$		0			0
$46$	0.867993	+	1.57778i	0.127979	+	0.232631i
$47$	5.85673	−	5.85673i	0.854292	−	0.854292i	−0.136366	−	0.990659i	$-0.543542\pi$
$47$	5.85673	−	5.85673i	0.854292	−	0.854292i	0.990659	+	0.136366i	$0.0435423\pi$
$48$	−1.35056	+	3.76510i	−0.194936	+	0.543446i
$49$		−	5.28267i		−	0.754667i
$50$		0			0
$51$			3.34225i			0.468009i
$52$	−1.00277	+	0.224760i	−0.139059	+	0.0311685i
$53$	−3.14134	+	3.14134i	−0.431496	+	0.431496i	−0.889137	−	0.457641i	$-0.848694\pi$
$53$	−3.14134	+	3.14134i	−0.431496	+	0.431496i	0.457641	+	0.889137i	$0.348694\pi$
$54$	1.23909	−	0.681664i	0.168618	−	0.0927627i
$55$		0			0
$56$	−9.89367	−	0.613763i	−1.32210	−	0.0820176i
$57$	3.50466	+	3.50466i	0.464204	+	0.464204i
$58$	1.38139	−	4.75995i	0.181385	−	0.625012i
$59$	−8.68516			−1.13071			−0.565356	−	0.824847i	$-0.691261\pi$
$59$	−8.68516			−1.13071			−0.565356	+	0.824847i	$0.691261\pi$
$60$		0			0
$61$	−15.2920			−1.95794			−0.978970	−	0.204004i	$-0.934604\pi$
$61$	−15.2920			−1.95794			−0.978970	+	0.204004i	$0.934604\pi$
$62$	−1.51990	+	5.23723i	−0.193027	+	0.665128i
$63$	2.47817	+	2.47817i	0.312220	+	0.312220i
$64$	−0.988770	+	7.93866i	−0.123596	+	0.992333i
$65$		0			0
$66$	−3.75233	+	2.06429i	−0.461880	+	0.254096i
$67$	−3.92870	+	3.92870i	−0.479967	+	0.479967i	−0.905121	−	0.425154i	$-0.860220\pi$
$67$	−3.92870	+	3.92870i	−0.479967	+	0.479967i	0.425154	+	0.905121i	$0.360220\pi$
$68$	1.46199	+	6.52267i	0.177292	+	0.790989i
$69$		−	1.27334i		−	0.153293i
$70$		0			0
$71$			4.25583i			0.505075i	0.967587	+	0.252537i	$0.0812650\pi$
$71$			4.25583i			0.505075i	−0.967587	+	0.252537i	$0.918735\pi$
$72$	2.12000	−	1.87233i	0.249844	−	0.220656i
$73$	−9.28267	+	9.28267i	−1.08645	+	1.08645i	−0.0905640	+	0.995891i	$0.528867\pi$
$73$	−9.28267	+	9.28267i	−1.08645	+	1.08645i	−0.995891	+	0.0905640i	$0.971133\pi$
$74$	−0.350255	−	0.636672i	−0.0407163	−	0.0740116i
$75$		0			0
$76$	8.37266	+	5.30660i	0.960410	+	0.608709i
$77$	−7.50466	−	7.50466i	−0.855236	−	0.855236i
$78$	0.697863	+	0.202527i	0.0790174	+	0.0229317i
$79$	−0.399759			−0.0449764			−0.0224882	−	0.999747i	$-0.507159\pi$
$79$	−0.399759			−0.0449764			−0.0224882	+	0.999747i	$0.507159\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−3.70328	−	1.07473i	−0.408959	−	0.118684i
$83$	−0.199879	−	0.199879i	−0.0219396	−	0.0219396i	0.696052	−	0.717991i	$-0.254938\pi$
$83$	−0.199879	−	0.199879i	−0.0219396	−	0.0219396i	−0.717991	+	0.696052i	$0.754938\pi$
$84$	5.92036	+	3.75233i	0.645965	+	0.409413i
$85$		0			0
$86$	−3.78734	−	6.88438i	−0.408399	−	0.742362i
$87$	−2.47817	+	2.47817i	−0.265688	+	0.265688i
$88$	−6.42000	+	5.66999i	−0.684374	+	0.604422i
$89$			4.28267i			0.453962i	0.973899	+	0.226981i	$0.0728856\pi$
$89$			4.28267i			0.453962i	−0.973899	+	0.226981i	$0.927114\pi$
$90$		0			0
$91$			1.80078i			0.188773i
$92$	−0.556993	−	2.48503i	−0.0580705	−	0.259082i
$93$	2.72666	−	2.72666i	0.282741	−	0.282741i
$94$	−10.2629	+	5.64600i	−1.05854	+	0.582340i
$95$		0			0
$96$	3.31834	−	4.58134i	0.338676	−	0.467581i
$97$	−6.73599	−	6.73599i	−0.683936	−	0.683936i	0.276949	−	0.960885i	$-0.410677\pi$
$97$	−6.73599	−	6.73599i	−0.683936	−	0.683936i	−0.960885	+	0.276949i	$0.910677\pi$
$98$	−2.08220	+	7.17480i	−0.210334	+	0.724764i
$99$	3.02831			0.304356
$100$		0			0
$101$	5.78734			0.575862			0.287931	−	0.957651i	$-0.407033\pi$
$101$	5.78734			0.575862			0.287931	+	0.957651i	$0.407033\pi$
$102$	1.31737	−	4.53936i	0.130439	−	0.449464i
$103$	−13.0914	−	13.0914i	−1.28993	−	1.28993i	−0.934827	−	0.355104i	$-0.884445\pi$
$103$	−13.0914	−	13.0914i	−1.28993	−	1.28993i	−0.355104	−	0.934827i	$-0.615555\pi$
$104$	1.45052	+	0.0899847i	0.142236	+	0.00882373i
$105$		0			0
$106$	5.50466	−	3.02831i	0.534660	−	0.294135i
$107$	−9.71281	+	9.71281i	−0.938973	+	0.938973i	−0.998242	−	0.0592694i	$-0.981123\pi$
$107$	−9.71281	+	9.71281i	−0.938973	+	0.938973i	0.0592694	+	0.998242i	$0.481123\pi$
$108$	−1.95158	+	0.437425i	−0.187791	+	0.0420913i
$109$		−	10.4626i		−	1.00214i	−0.865407	−	0.501070i	$-0.832940\pi$
$109$		−	10.4626i		−	1.00214i	0.865407	−	0.501070i	$-0.167060\pi$
$110$		0			0
$111$			0.513824i			0.0487700i
$112$	13.1954	+	4.73325i	1.24685	+	0.447251i
$113$	10.6460	−	10.6460i	1.00149	−	1.00149i	0.00149259	−	0.999999i	$-0.499525\pi$
$113$	10.6460	−	10.6460i	1.00149	−	1.00149i	0.999999	−	0.00149259i	$-0.000475108\pi$
$114$	−3.37856	−	6.14134i	−0.316431	−	0.575189i
$115$		0			0
$116$	−3.75233	+	5.92036i	−0.348395	+	0.549692i
$117$	−0.363328	−	0.363328i	−0.0335897	−	0.0335897i
$118$	11.7960	+	3.42331i	1.08591	+	0.315142i
$119$	11.7135			1.07377
$120$		0			0
$121$	1.82936			0.166305
$122$	20.7692	+	6.02745i	1.88036	+	0.545699i
$123$	1.92804	+	1.92804i	0.173845	+	0.173845i
$124$	4.12858	−	6.51399i	0.370757	−	0.584974i
$125$		0			0
$126$	−2.38900	−	4.34258i	−0.212829	−	0.386868i
$127$	−1.77766	+	1.77766i	−0.157742	+	0.157742i	−0.781565	−	0.623823i	$-0.785578\pi$
$127$	−1.77766	+	1.77766i	−0.157742	+	0.157742i	0.623823	+	0.781565i	$0.285578\pi$
$128$	4.47200	−	10.3924i	0.395273	−	0.918564i
$129$			5.55602i			0.489180i
$130$		0			0
$131$			18.1981i			1.58997i	0.606626	+	0.794987i	$0.292523\pi$
$131$			18.1981i			1.58997i	−0.606626	+	0.794987i	$0.707477\pi$
$132$	5.90998	−	1.32466i	0.514398	−	0.115297i
$133$	12.2827	−	12.2827i	1.06504	−	1.06504i
$134$	6.88438	−	3.78734i	0.594720	−	0.327176i
$135$		0			0
$136$	0.585320	−	9.43517i	0.0501908	−	0.809060i
$137$	5.91934	+	5.91934i	0.505724	+	0.505724i	0.913211	−	0.407487i	$-0.133595\pi$
$137$	5.91934	+	5.91934i	0.505724	+	0.505724i	−0.407487	+	0.913211i	$0.633595\pi$
$138$	−0.501897	+	1.72942i	−0.0427243	+	0.147218i
$139$	−12.4140			−1.05294			−0.526470	−	0.850194i	$-0.676485\pi$
$139$	−12.4140			−1.05294			−0.526470	+	0.850194i	$0.676485\pi$
$140$		0			0
$141$	8.28267			0.697527
$142$	1.67747	−	5.78017i	0.140770	−	0.485061i
$143$	1.10027	+	1.10027i	0.0920091	+	0.0920091i
$144$	−3.61732	+	1.70734i	−0.301443	+	0.142278i
$145$		0			0
$146$	16.2663	−	8.94867i	1.34621	−	0.740597i
$147$	3.73541	−	3.73541i	0.308092	−	0.308092i
$148$	0.224760	+	1.00277i	0.0184751	+	0.0824270i
$149$		−	5.78734i		−	0.474117i	−0.971495	−	0.237059i	$-0.923817\pi$
$149$		−	5.78734i		−	0.474117i	0.971495	−	0.237059i	$-0.0761833\pi$
$150$		0			0
$151$		−	18.0708i		−	1.47058i	−0.677751	−	0.735292i	$-0.737045\pi$
$151$		−	18.0708i		−	1.47058i	0.677751	−	0.735292i	$-0.262955\pi$
$152$	−9.27990	−	10.5074i	−0.752700	−	0.852265i
$153$	−2.36333	+	2.36333i	−0.191064	+	0.191064i
$154$	7.23464	+	13.1507i	0.582984	+	1.05971i
$155$		0			0
$156$	−0.867993	−	0.550135i	−0.0694950	−	0.0440460i
$157$	3.91934	+	3.91934i	0.312798	+	0.312798i	0.845992	−	0.533195i	$-0.179009\pi$
$157$	3.91934	+	3.91934i	0.312798	+	0.312798i	−0.533195	+	0.845992i	$0.679009\pi$
$158$	0.542943	+	0.157568i	0.0431942	+	0.0125354i
$159$	−4.44252			−0.352315
$160$		0			0
$161$	−4.46264			−0.351705
$162$	1.35818	+	0.394157i	0.106708	+	0.0309679i
$163$	−3.22819	−	3.22819i	−0.252851	−	0.252851i	0.569287	−	0.822139i	$-0.307219\pi$
$163$	−3.22819	−	3.22819i	−0.252851	−	0.252851i	−0.822139	+	0.569287i	$0.807219\pi$
$164$	4.60609	+	2.91934i	0.359675	+	0.227962i
$165$		0			0
$166$	0.192688	+	0.350255i	0.0149555	+	0.0271851i
$167$	−6.95700	+	6.95700i	−0.538349	+	0.538349i	−0.923044	−	0.384695i	$-0.874307\pi$
$167$	−6.95700	+	6.95700i	−0.538349	+	0.538349i	0.384695	+	0.923044i	$0.374307\pi$
$168$	−6.56188	−	7.42988i	−0.506260	−	0.573227i
$169$			12.7360i			0.979691i
$170$		0			0
$171$			4.95634i			0.379021i
$172$	2.43034	+	10.8430i	0.185312	+	0.826771i
$173$	−0.627343	+	0.627343i	−0.0476960	+	0.0476960i	−0.730553	−	0.682857i	$-0.760737\pi$
$173$	−0.627343	+	0.627343i	−0.0476960	+	0.0476960i	0.682857	+	0.730553i	$0.260737\pi$
$174$	4.34258	−	2.38900i	0.329210	−	0.181110i
$175$		0			0
$176$	10.9543	−	5.17035i	0.825715	−	0.389730i
$177$	−6.14134	−	6.14134i	−0.461611	−	0.461611i
$178$	1.68804	−	5.81662i	0.126524	−	0.435974i
$179$	−8.93968			−0.668183			−0.334091	−	0.942541i	$-0.608429\pi$
$179$	−8.93968			−0.668183			−0.334091	+	0.942541i	$0.608429\pi$
$180$		0			0
$181$	−1.00933			−0.0750228			−0.0375114	−	0.999296i	$-0.511943\pi$
$181$	−1.00933			−0.0750228			−0.0375114	+	0.999296i	$0.511943\pi$
$182$	0.709789	−	2.44577i	0.0526131	−	0.181293i
$183$	−10.8131	−	10.8131i	−0.799326	−	0.799326i
$184$	−0.222998	+	3.59465i	−0.0164396	+	0.265001i
$185$		0			0
$186$	−4.77801	+	2.62855i	−0.350341	+	0.192734i
$187$	7.15688	−	7.15688i	0.523363	−	0.523363i
$188$	16.1643	−	3.62305i	1.17890	−	0.264238i
$189$			3.50466i			0.254927i
$190$		0			0
$191$		−	21.6262i		−	1.56481i	−0.622768	−	0.782407i	$-0.713992\pi$
$191$		−	21.6262i		−	1.56481i	0.622768	−	0.782407i	$-0.286008\pi$
$192$	−6.31265	+	4.91431i	−0.455576	+	0.354660i
$193$	−11.5653	+	11.5653i	−0.832492	+	0.832492i	−0.987857	−	0.155365i	$-0.950345\pi$
$193$	−11.5653	+	11.5653i	−0.832492	+	0.832492i	0.155365	+	0.987857i	$0.450345\pi$
$194$	6.49362	+	11.8037i	0.466214	+	0.847455i
$195$		0			0
$196$	5.65599	−	8.92392i	0.403999	−	0.637423i
$197$	9.42401	+	9.42401i	0.671433	+	0.671433i	0.958046	−	0.286614i	$-0.0925296\pi$
$197$	9.42401	+	9.42401i	0.671433	+	0.671433i	−0.286614	+	0.958046i	$0.592530\pi$
$198$	−4.11297	−	1.19363i	−0.292296	−	0.0848274i
$199$	11.0130			0.780688			0.390344	−	0.920669i	$-0.372356\pi$
$199$	11.0130			0.780688			0.390344	+	0.920669i	$0.372356\pi$
$200$		0			0
$201$	−5.55602			−0.391891
$202$	−7.86022	−	2.28112i	−0.553043	−	0.160499i
$203$	8.68516	+	8.68516i	0.609579	+	0.609579i
$204$	−3.57844	+	5.64600i	−0.250541	+	0.395299i
$205$		0			0
$206$	12.6203	+	22.9404i	0.879300	+	1.59834i
$207$	0.900390	−	0.900390i	0.0625814	−	0.0625814i
$208$	−1.93460	−	0.693949i	−0.134140	−	0.0481167i
$209$		−	15.0093i		−	1.03822i
$210$		0			0
$211$			27.9835i			1.92646i	0.268669	+	0.963232i	$0.413416\pi$
$211$			27.9835i			1.92646i	−0.268669	+	0.963232i	$0.586584\pi$
$212$	−8.66993	+	1.94327i	−0.595453	+	0.133464i
$213$	−3.00933	+	3.00933i	−0.206196	+	0.206196i
$214$	17.0201	−	9.36333i	1.16347	−	0.640064i
$215$		0			0
$216$	2.82300	+	0.175128i	0.192081	+	0.0119159i
$217$	−9.55602	−	9.55602i	−0.648705	−	0.648705i
$218$	−4.12392	+	14.2101i	−0.279307	+	0.962430i
$219$	−13.1277			−0.887086
$220$		0			0
$221$	−1.71733			−0.115520
$222$	0.202527	−	0.697863i	0.0135927	−	0.0468375i
$223$	8.53479	+	8.53479i	0.571531	+	0.571531i	0.932556	−	0.361025i	$-0.117573\pi$
$223$	8.53479	+	8.53479i	0.571531	+	0.571531i	−0.361025	+	0.932556i	$0.617573\pi$
$224$	−16.0560	−	11.6297i	−1.07279	−	0.777039i
$225$		0			0
$226$	−18.6553	+	10.2629i	−1.24093	+	0.682681i
$227$	1.02765	−	1.02765i	0.0682074	−	0.0682074i	−0.672180	−	0.740388i	$-0.734642\pi$
$227$	1.02765	−	1.02765i	0.0682074	−	0.0682074i	0.740388	+	0.672180i	$0.234642\pi$
$228$	2.16803	+	9.67269i	0.143581	+	0.640590i
$229$			8.84802i			0.584693i	0.956312	+	0.292347i	$0.0944361\pi$
$229$			8.84802i			0.584693i	−0.956312	+	0.292347i	$0.905564\pi$
$230$		0			0
$231$		−	10.6132i		−	0.698297i
$232$	7.42988	−	6.56188i	0.487795	−	0.430809i
$233$	4.91002	−	4.91002i	0.321666	−	0.321666i	−0.527740	−	0.849406i	$-0.676960\pi$
$233$	4.91002	−	4.91002i	0.321666	−	0.321666i	0.849406	+	0.527740i	$0.176960\pi$
$234$	0.350255	+	0.636672i	0.0228969	+	0.0416205i
$235$		0			0
$236$	−14.6717	−	9.29892i	−0.955045	−	0.605308i
$237$	−0.282672	−	0.282672i	−0.0183615	−	0.0183615i
$238$	−15.9089	−	4.61694i	−1.03122	−	0.299272i
$239$	19.0259			1.23068			0.615340	−	0.788262i	$-0.289019\pi$
$239$	19.0259			1.23068			0.615340	+	0.788262i	$0.289019\pi$
$240$		0			0
$241$	2.90663			0.187232			0.0936161	−	0.995608i	$-0.470157\pi$
$241$	2.90663			0.187232			0.0936161	+	0.995608i	$0.470157\pi$
$242$	−2.48459	−	0.721054i	−0.159716	−	0.0463511i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−25.8325	−	16.3727i	−1.65376	−	1.04815i
$245$		0			0
$246$	−1.85866	−	3.37856i	−0.118504	−	0.215409i
$247$	−1.80078	+	1.80078i	−0.114581	+	0.114581i
$248$	−8.17486	+	7.21984i	−0.519104	+	0.458460i
$249$		−	0.282672i		−	0.0179136i
$250$		0			0
$251$			2.77379i			0.175080i	0.996161	+	0.0875401i	$0.0279006\pi$
$251$			2.77379i			0.175080i	−0.996161	+	0.0875401i	$0.972099\pi$
$252$	1.53303	+	6.83963i	0.0965717	+	0.430856i
$253$	−2.72666	+	2.72666i	−0.171423	+	0.171423i
$254$	3.11505	−	1.71370i	0.195456	−	0.107527i
$255$		0			0
$256$	−10.1700	+	12.3520i	−0.635624	+	0.771999i
$257$	2.08066	+	2.08066i	0.129788	+	0.129788i	0.769017	−	0.639229i	$-0.220746\pi$
$257$	2.08066	+	2.08066i	0.129788	+	0.129788i	−0.639229	+	0.769017i	$0.720746\pi$
$258$	2.18994	−	7.54604i	0.136340	−	0.469796i
$259$	1.80078			0.111895
$260$		0			0
$261$	−3.50466			−0.216933
$262$	7.17290	−	24.7162i	0.443143	−	1.52697i
$263$	−4.75646	−	4.75646i	−0.293296	−	0.293296i	0.545085	−	0.838381i	$-0.316497\pi$
$263$	−4.75646	−	4.75646i	−0.293296	−	0.293296i	−0.838381	+	0.545085i	$0.816497\pi$
$264$	−8.54891	−	0.530340i	−0.526149	−	0.0326402i
$265$		0			0
$266$	−21.5233	+	11.8407i	−1.31968	+	0.726001i
$267$	−3.02831	+	3.02831i	−0.185329	+	0.185329i
$268$	−10.8430	+	2.43034i	−0.662342	+	0.148457i
$269$			21.6846i			1.32214i	0.750326	+	0.661068i	$0.229896\pi$
$269$			21.6846i			1.32214i	−0.750326	+	0.661068i	$0.770104\pi$
$270$		0			0
$271$			3.15556i			0.191687i	0.995396	+	0.0958434i	$0.0305548\pi$
$271$			3.15556i			0.191687i	−0.995396	+	0.0958434i	$0.969445\pi$
$272$	−4.51391	+	12.5839i	−0.273696	+	0.763012i
$273$	−1.27334	+	1.27334i	−0.0770663	+	0.0770663i
$274$	−5.70636	−	10.3727i	−0.344734	−	0.626635i
$275$		0			0
$276$	1.36333	−	2.15103i	0.0820627	−	0.129477i
$277$	3.53397	+	3.53397i	0.212336	+	0.212336i	0.805259	−	0.592923i	$-0.202026\pi$
$277$	3.53397	+	3.53397i	0.212336	+	0.212336i	−0.592923	+	0.805259i	$0.702026\pi$
$278$	16.8604	+	4.89305i	1.01122	+	0.293466i
$279$	3.85607			0.230857
$280$		0			0
$281$	0.179969			0.0107361			0.00536804	−	0.999986i	$-0.498291\pi$
$281$	0.179969			0.0107361			0.00536804	+	0.999986i	$0.498291\pi$
$282$	−11.2493	−	3.26467i	−0.669887	−	0.194408i
$283$	9.84007	+	9.84007i	0.584931	+	0.584931i	0.936254	−	0.351323i	$-0.114268\pi$
$283$	9.84007	+	9.84007i	0.584931	+	0.584931i	−0.351323	+	0.936254i	$0.614268\pi$
$284$	−4.55658	+	7.18930i	−0.270384	+	0.426606i
$285$		0			0
$286$	−1.06068	−	1.92804i	−0.0627193	−	0.114007i
$287$	6.75712	−	6.75712i	0.398860	−	0.398860i
$288$	5.58591	−	0.893077i	0.329153	−	0.0526250i
$289$		−	5.82936i		−	0.342903i
$290$		0			0
$291$		−	9.52612i		−	0.558431i
$292$	−25.6197	+	5.74238i	−1.49928	+	0.336047i
$293$	−15.8680	+	15.8680i	−0.927018	+	0.927018i	−0.997512	−	0.0704942i	$-0.977542\pi$
$293$	−15.8680	+	15.8680i	−0.927018	+	0.927018i	0.0704942	+	0.997512i	$0.477542\pi$
$294$	−6.54569	+	3.60101i	−0.381752	+	0.210015i
$295$		0			0
$296$	0.0899847	−	1.45052i	0.00523026	−	0.0843100i
$297$	2.14134	+	2.14134i	0.124253	+	0.124253i
$298$	−2.28112	+	7.86022i	−0.132142	+	0.455330i
$299$	0.654274			0.0378376
$300$		0			0
$301$	19.4720			1.12235
$302$	−7.12274	+	24.5434i	−0.409868	+	1.41231i
$303$	4.09226	+	4.09226i	0.235094	+	0.235094i
$304$	8.46216	+	17.9287i	0.485338	+	1.02828i
$305$		0			0
$306$	4.14134	−	2.27829i	0.236744	−	0.130241i
$307$	7.78477	−	7.78477i	0.444300	−	0.444300i	−0.449154	−	0.893454i	$-0.648275\pi$
$307$	7.78477	−	7.78477i	0.444300	−	0.444300i	0.893454	+	0.449154i	$0.148275\pi$
$308$	−4.64248	−	20.7125i	−0.264530	−	1.18020i
$309$		−	18.5140i		−	1.05322i
$310$		0			0
$311$		−	7.05788i		−	0.400215i	−0.979774	−	0.200108i	$-0.935871\pi$
$311$		−	7.05788i		−	0.400215i	0.979774	−	0.200108i	$-0.0641292\pi$
$312$	0.962047	+	1.08930i	0.0544652	+	0.0616697i
$313$	11.3013	−	11.3013i	0.638789	−	0.638789i	−0.311468	−	0.950257i	$-0.600821\pi$
$313$	11.3013	−	11.3013i	0.638789	−	0.638789i	0.950257	+	0.311468i	$0.100821\pi$
$314$	−3.77832	−	6.86799i	−0.213223	−	0.387583i
$315$		0			0
$316$	−0.675305	−	0.428009i	−0.0379889	−	0.0240774i
$317$	−19.4754	−	19.4754i	−1.09385	−	1.09385i	−0.995114	−	0.0987310i	$-0.968522\pi$
$317$	−19.4754	−	19.4754i	−1.09385	−	1.09385i	−0.0987310	−	0.995114i	$-0.531478\pi$
$318$	6.03372	+	1.75105i	0.338354	+	0.0981940i
$319$	10.6132			0.594225
$320$		0			0
$321$	−13.7360			−0.766668
$322$	6.06105	+	1.75898i	0.337769	+	0.0980241i
$323$	11.7135	+	11.7135i	0.651755	+	0.651755i
$324$	−1.68928	−	1.07067i	−0.0938489	−	0.0594816i
$325$		0			0
$326$	3.11203	+	5.65685i	0.172359	+	0.313304i
$327$	7.39820	−	7.39820i	0.409122	−	0.409122i
$328$	−5.10520	−	5.78050i	−0.281887	−	0.319175i
$329$		−	29.0280i		−	1.60036i
$330$		0			0
$331$		−	15.0143i		−	0.825259i	−0.910899	−	0.412630i	$-0.864610\pi$
$331$		−	15.0143i		−	0.825259i	0.910899	−	0.412630i	$-0.135390\pi$
$332$	−0.123648	−	0.551657i	−0.00678607	−	0.0302761i
$333$	−0.363328	+	0.363328i	−0.0199103	+	0.0199103i
$334$	12.1910	−	6.70668i	0.667061	−	0.366973i
$335$		0			0
$336$	5.98365	+	12.6775i	0.326435	+	0.691614i
$337$	21.5840	+	21.5840i	1.17576	+	1.17576i	0.980815	+	0.194940i	$0.0624513\pi$
$337$	21.5840	+	21.5840i	1.17576	+	1.17576i	0.194940	+	0.980815i	$0.437549\pi$
$338$	5.01997	−	17.2977i	0.273051	−	0.940871i
$339$	15.0557			0.817714
$340$		0			0
$341$	−11.6774			−0.632365
$342$	1.95358	−	6.73158i	0.105637	−	0.364002i
$343$	4.25583	+	4.25583i	0.229793	+	0.229793i
$344$	0.973012	−	15.6846i	0.0524613	−	0.845659i
$345$		0			0
$346$	1.09931	−	0.604770i	0.0590995	−	0.0325127i
$347$	16.9969	−	16.9969i	0.912444	−	0.912444i	−0.0840201	−	0.996464i	$-0.526776\pi$
$347$	16.9969	−	16.9969i	0.912444	−	0.912444i	0.996464	+	0.0840201i	$0.0267760\pi$
$348$	−6.83963	+	1.53303i	−0.366643	+	0.0821790i
$349$		−	4.38538i		−	0.234744i	−0.993088	−	0.117372i	$-0.962553\pi$
$349$		−	4.38538i		−	0.234744i	0.993088	−	0.117372i	$-0.0374469\pi$
$350$		0			0
$351$		−	0.513824i		−	0.0274259i
$352$	−16.9159	+	2.70451i	−0.901618	+	0.144151i
$353$	2.62734	−	2.62734i	0.139839	−	0.139839i	−0.633722	−	0.773561i	$-0.718474\pi$
$353$	2.62734	−	2.62734i	0.139839	−	0.139839i	0.773561	+	0.633722i	$0.218474\pi$
$354$	5.92036	+	10.7617i	0.314664	+	0.571976i
$355$		0			0
$356$	−4.58532	+	7.23464i	−0.243021	+	0.383435i
$357$	8.28267	+	8.28267i	0.438366	+	0.438366i
$358$	12.1416	+	3.52363i	0.641706	+	0.186230i
$359$	−34.9952			−1.84697			−0.923487	−	0.383630i	$-0.874674\pi$
$359$	−34.9952			−1.84697			−0.923487	+	0.383630i	$0.874674\pi$
$360$		0			0
$361$	5.56534			0.292913
$362$	1.37085	+	0.397834i	0.0720500	+	0.0209097i
$363$	1.29355	+	1.29355i	0.0678939	+	0.0678939i
$364$	−1.92804	+	3.04202i	−0.101057	+	0.159445i
$365$		0			0
$366$	10.4240	+	18.9481i	0.544872	+	0.990433i
$367$	9.93581	−	9.93581i	0.518645	−	0.518645i	−0.398516	−	0.917161i	$-0.630475\pi$
$367$	9.93581	−	9.93581i	0.518645	−	0.518645i	0.917161	+	0.398516i	$0.130475\pi$
$368$	1.71973	−	4.79427i	0.0896469	−	0.249918i
$369$			2.72666i			0.141944i
$370$		0			0
$371$			15.5695i			0.808330i
$372$	7.52543	−	1.68674i	0.390176	−	0.0874536i
$373$	7.08998	−	7.08998i	0.367105	−	0.367105i	−0.499315	−	0.866421i	$-0.666415\pi$
$373$	7.08998	−	7.08998i	0.367105	−	0.367105i	0.866421	+	0.499315i	$0.166415\pi$
$374$	−12.5412	+	6.89937i	−0.648492	+	0.356758i
$375$		0			0
$376$	−23.3820	−	1.45052i	−1.20583	−	0.0748051i
$377$	−1.27334	−	1.27334i	−0.0655805	−	0.0655805i
$378$	1.38139	−	4.75995i	0.0710509	−	0.244825i
$379$	−30.0388			−1.54299			−0.771495	−	0.636235i	$-0.780491\pi$
$379$	−30.0388			−1.54299			−0.771495	+	0.636235i	$0.780491\pi$
$380$		0			0
$381$	−2.51399			−0.128796
$382$	−8.52410	+	29.3721i	−0.436131	+	1.50281i
$383$	−11.9133	−	11.9133i	−0.608744	−	0.608744i	0.333874	−	0.942618i	$-0.391644\pi$
$383$	−11.9133	−	11.9133i	−0.608744	−	0.608744i	−0.942618	+	0.333874i	$0.891644\pi$
$384$	10.5107	−	4.18633i	0.536372	−	0.213633i
$385$		0			0
$386$	20.2663	−	11.1492i	1.03153	−	0.567480i
$387$	−3.92870	+	3.92870i	−0.199707	+	0.199707i
$388$	−4.16697	−	18.5910i	−0.211546	−	0.943814i
$389$			16.3340i			0.828168i	0.910239	+	0.414084i	$0.135898\pi$
$389$			16.3340i			0.828168i	−0.910239	+	0.414084i	$0.864102\pi$
$390$		0			0
$391$		−	4.25583i		−	0.215227i
$392$	−11.1992	+	9.89090i	−0.565647	+	0.499566i
$393$	−12.8680	+	12.8680i	−0.649104	+	0.649104i
$394$	−9.08492	−	16.5140i	−0.457692	−	0.831963i
$395$		0			0
$396$	5.11566	+	3.24231i	0.257072	+	0.162932i
$397$	19.1927	+	19.1927i	0.963253	+	0.963253i	0.999348	−	0.0360950i	$-0.0114919\pi$
$397$	19.1927	+	19.1927i	0.963253	+	0.963253i	−0.0360950	+	0.999348i	$0.511492\pi$
$398$	−14.9575	−	4.34083i	−0.749753	−	0.217586i
$399$	17.3703			0.869604
$400$		0			0
$401$	26.5653			1.32661			0.663305	−	0.748349i	$-0.269153\pi$
$401$	26.5653			1.32661			0.663305	+	0.748349i	$0.269153\pi$
$402$	7.54604	+	2.18994i	0.376362	+	0.109224i
$403$	1.40102	+	1.40102i	0.0697898	+	0.0697898i
$404$	9.77644	+	6.19632i	0.486396	+	0.308278i
$405$		0			0
$406$	−8.37266	−	15.2193i	−0.415528	−	0.755321i
$407$	1.10027	−	1.10027i	0.0545383	−	0.0545383i
$408$	7.08556	−	6.25779i	0.350787	−	0.309807i
$409$			25.3947i			1.25569i	0.778339	+	0.627844i	$0.216062\pi$
$409$			25.3947i			1.25569i	−0.778339	+	0.627844i	$0.783938\pi$
$410$		0			0
$411$			8.37122i			0.412922i
$412$	−8.09849	−	36.1315i	−0.398984	−	1.78007i
$413$	−21.5233	+	21.5233i	−1.05909	+	1.05909i
$414$	−1.57778	+	0.867993i	−0.0775438	+	0.0426595i
$415$		0			0
$416$	2.35400	+	1.70504i	0.115414	+	0.0835964i
$417$	−8.77801	−	8.77801i	−0.429861	−	0.429861i
$418$	−5.91603	+	20.3853i	−0.289362	+	0.997078i
$419$	40.0788			1.95798			0.978988	−	0.203919i	$-0.0653679\pi$
$419$	40.0788			1.95798			0.978988	+	0.203919i	$0.0653679\pi$
$420$		0			0
$421$	19.3947			0.945240			0.472620	−	0.881266i	$-0.343308\pi$
$421$	19.3947			0.945240			0.472620	+	0.881266i	$0.343308\pi$
$422$	11.0299	−	38.0065i	0.536927	−	1.85013i
$423$	5.85673	+	5.85673i	0.284764	+	0.284764i
$424$	12.5412	+	0.778008i	0.609056	+	0.0377834i
$425$		0			0
$426$	5.27334	−	2.90105i	0.255494	−	0.140556i
$427$	−37.8962	+	37.8962i	−1.83393	+	1.83393i
$428$	−26.8069	+	6.00847i	−1.29576	+	0.290430i
$429$			1.55602i			0.0751251i
$430$		0			0
$431$		−	15.8241i		−	0.762218i	−0.924530	−	0.381109i	$-0.875542\pi$
$431$		−	15.8241i		−	0.762218i	0.924530	−	0.381109i	$-0.124458\pi$
$432$	−3.76510	−	1.35056i	−0.181149	−	0.0649788i
$433$	21.1214	−	21.1214i	1.01503	−	1.01503i	0.0151424	−	0.999885i	$-0.495180\pi$
$433$	21.1214	−	21.1214i	1.01503	−	1.01503i	0.999885	−	0.0151424i	$-0.00482018\pi$
$434$	9.21218	+	16.7453i	0.442199	+	0.803801i
$435$		0			0
$436$	11.2020	−	17.6743i	0.536479	−	0.846447i
$437$	−4.46264	−	4.46264i	−0.213477	−	0.213477i
$438$	17.8297	+	5.17436i	0.851936	+	0.247241i
$439$	−6.61188			−0.315568			−0.157784	−	0.987474i	$-0.550435\pi$
$439$	−6.61188			−0.315568			−0.157784	+	0.987474i	$0.550435\pi$
$440$		0			0
$441$	5.28267			0.251556
$442$	2.33243	+	0.676896i	0.110942	+	0.0321967i
$443$	−14.5419	−	14.5419i	−0.690906	−	0.690906i	0.271525	−	0.962431i	$-0.412472\pi$
$443$	−14.5419	−	14.5419i	−0.690906	−	0.690906i	−0.962431	+	0.271525i	$0.912472\pi$
$444$	−0.550135	+	0.867993i	−0.0261082	+	0.0411931i
$445$		0			0
$446$	−8.22769	−	14.9558i	−0.389593	−	0.708177i
$447$	4.09226	−	4.09226i	0.193557	−	0.193557i
$448$	17.2230	+	22.1237i	0.813711	+	1.04525i
$449$			33.6120i			1.58625i	0.609060	+	0.793124i	$0.291547\pi$
$449$			33.6120i			1.58625i	−0.609060	+	0.793124i	$0.708453\pi$
$450$		0			0
$451$		−	8.25715i		−	0.388814i
$452$	29.3824	−	6.58575i	1.38203	−	0.309768i
$453$	12.7780	−	12.7780i	0.600363	−	0.600363i
$454$	−1.80078	+	0.990671i	−0.0845148	+	0.0464945i
$455$		0			0
$456$	0.867993	−	13.9918i	0.0406475	−	0.655224i
$457$	−15.5653	−	15.5653i	−0.728116	−	0.728116i	0.242128	−	0.970244i	$-0.422155\pi$
$457$	−15.5653	−	15.5653i	−0.728116	−	0.728116i	−0.970244	+	0.242128i	$0.922155\pi$
$458$	3.48751	−	12.0172i	0.162960	−	0.561525i
$459$	−3.34225			−0.156003
$460$		0			0
$461$	−26.1473			−1.21780			−0.608900	−	0.793247i	$-0.708389\pi$
$461$	−26.1473			−1.21780			−0.608900	+	0.793247i	$0.708389\pi$
$462$	−4.18326	+	14.4146i	−0.194623	+	0.670627i
$463$	−5.77898	−	5.77898i	−0.268572	−	0.268572i	0.559953	−	0.828525i	$-0.310819\pi$
$463$	−5.77898	−	5.77898i	−0.268572	−	0.268572i	−0.828525	+	0.559953i	$0.810819\pi$
$464$	−12.6775	+	5.98365i	−0.588538	+	0.277784i
$465$		0			0
$466$	−8.60398	+	4.73335i	−0.398572	+	0.219268i
$467$	−2.25517	+	2.25517i	−0.104357	+	0.104357i	−0.757357	−	0.653000i	$-0.773510\pi$
$467$	−2.25517	+	2.25517i	−0.104357	+	0.104357i	0.653000	+	0.757357i	$0.273510\pi$
$468$	−0.224760	−	1.00277i	−0.0103895	−	0.0463529i
$469$			19.4720i			0.899132i
$470$		0			0
$471$			5.54279i			0.255398i
$472$	16.2615	+	18.4125i	0.748495	+	0.847505i
$473$	11.8973	−	11.8973i	0.547038	−	0.547038i
$474$	0.272501	+	0.495336i	0.0125164	+	0.0227515i
$475$		0			0
$476$	19.7873	+	12.5412i	0.906951	+	0.574827i
$477$	−3.14134	−	3.14134i	−0.143832	−	0.143832i
$478$	−25.8405	−	7.49917i	−1.18191	−	0.343004i
$479$	1.40102			0.0640143			0.0320071	−	0.999488i	$-0.489810\pi$
$479$	1.40102			0.0640143			0.0320071	+	0.999488i	$0.489810\pi$
$480$		0			0
$481$	−0.264015			−0.0120380
$482$	−3.94771	−	1.14567i	−0.179813	−	0.0521837i
$483$	−3.15556	−	3.15556i	−0.143583	−	0.143583i
$484$	3.09030	+	1.95864i	0.140468	+	0.0890289i
$485$		0			0
$486$	0.681664	+	1.23909i	0.0309209	+	0.0562061i
$487$	−0.978144	+	0.978144i	−0.0443239	+	0.0443239i	−0.728921	−	0.684597i	$-0.759978\pi$
$487$	−0.978144	+	0.978144i	−0.0443239	+	0.0443239i	0.684597	+	0.728921i	$0.259978\pi$
$488$	28.6317	+	32.4190i	1.29609	+	1.46754i
$489$		−	4.56534i		−	0.206452i
$490$		0			0
$491$		−	36.1134i		−	1.62978i	−0.579619	−	0.814888i	$-0.696799\pi$
$491$		−	36.1134i		−	1.62978i	0.579619	−	0.814888i	$-0.303201\pi$
$492$	1.19271	+	5.32128i	0.0537715	+	0.239902i
$493$	−8.28267	+	8.28267i	−0.373033	+	0.373033i
$494$	3.15556	−	1.73599i	0.141976	−	0.0781057i
$495$		0			0
$496$	13.9486	−	6.58363i	0.626313	−	0.295614i
$497$	10.5467	+	10.5467i	0.473084	+	0.473084i
$498$	−0.111417	+	0.383918i	−0.00499272	+	0.0172038i
$499$	6.35736			0.284595			0.142297	−	0.989824i	$-0.454551\pi$
$499$	6.35736			0.284595			0.142297	+	0.989824i	$0.454551\pi$
$500$		0			0
$501$	−9.83869			−0.439560
$502$	1.09331	−	3.76730i	0.0487968	−	0.168143i
$503$	−17.1704	−	17.1704i	−0.765592	−	0.765592i	0.211735	−	0.977327i	$-0.432089\pi$
$503$	−17.1704	−	17.1704i	−0.765592	−	0.765592i	−0.977327	+	0.211735i	$0.932089\pi$
$504$	0.613763	−	9.89367i	0.0273392	−	0.440699i
$505$		0			0
$506$	4.77801	−	2.62855i	0.212408	−	0.116853i
$507$	−9.00570	+	9.00570i	−0.399957	+	0.399957i
$508$	−4.90626	+	1.09968i	−0.217680	+	0.0487906i
$509$		−	18.8739i		−	0.836572i	−0.908315	−	0.418286i	$-0.862631\pi$
$509$		−	18.8739i		−	0.836572i	0.908315	−	0.418286i	$-0.137369\pi$
$510$		0			0
$511$			46.0081i			2.03528i
$512$	18.6812	−	12.7676i	0.825602	−	0.564253i
$513$	−3.50466	+	3.50466i	−0.154735	+	0.154735i
$514$	−2.00579	−	3.64600i	−0.0884717	−	0.160818i
$515$		0			0
$516$	−5.94865	+	9.38567i	−0.261875	+	0.413181i
$517$	−17.7360	−	17.7360i	−0.780028	−	0.780028i
$518$	−2.44577	−	0.709789i	−0.107461	−	0.0311864i
$519$	−0.887197			−0.0389436
$520$		0			0
$521$	−33.9346			−1.48670			−0.743351	−	0.668901i	$-0.766765\pi$
$521$	−33.9346			−1.48670			−0.743351	+	0.668901i	$0.766765\pi$
$522$	4.75995	+	1.38139i	0.208337	+	0.0604617i
$523$	−3.78345	−	3.78345i	−0.165439	−	0.165439i	0.619532	−	0.784971i	$-0.287322\pi$
$523$	−3.78345	−	3.78345i	−0.165439	−	0.165439i	−0.784971	+	0.619532i	$0.787322\pi$
$524$	−19.4841	+	30.7417i	−0.851167	+	1.34296i
$525$		0			0
$526$	4.58532	+	8.33491i	0.199929	+	0.363419i
$527$	9.11317	−	9.11317i	0.396976	−	0.396976i
$528$	11.4019	+	4.08991i	0.496203	+	0.177990i
$529$		−	21.3786i		−	0.929504i
$530$		0			0
$531$		−	8.68516i		−	0.376904i
$532$	33.8995	−	7.59822i	1.46973	−	0.329425i
$533$	−0.990671	+	0.990671i	−0.0429107	+	0.0429107i
$534$	5.30660	−	2.91934i	0.229639	−	0.126332i
$535$		0			0
$536$	15.6846	+	0.973012i	0.677473	+	0.0420277i
$537$	−6.32131	−	6.32131i	−0.272784	−	0.272784i
$538$	8.54715	−	29.4515i	0.368494	−	1.26975i
$539$	−15.9976			−0.689063
$540$		0			0
$541$	28.4813			1.22451			0.612253	−	0.790662i	$-0.290263\pi$
$541$	28.4813			1.22451			0.612253	+	0.790662i	$0.290263\pi$
$542$	1.24379	−	4.28581i	0.0534252	−	0.184091i
$543$	−0.713703	−	0.713703i	−0.0306279	−	0.0306279i
$544$	11.0907	−	15.3120i	0.475510	−	0.656496i
$545$		0			0
$546$	2.23132	−	1.22753i	0.0954917	−	0.0525333i
$547$	−0.726896	+	0.726896i	−0.0310798	+	0.0310798i	−0.722476	−	0.691396i	$-0.756996\pi$
$547$	−0.726896	+	0.726896i	−0.0310798	+	0.0310798i	0.691396	+	0.722476i	$0.256996\pi$
$548$	3.66178	+	16.3371i	0.156424	+	0.697886i
$549$		−	15.2920i		−	0.652647i
$550$		0			0
$551$			17.3703i			0.740001i
$552$	−2.69948	+	2.38412i	−0.114898	+	0.101475i
$553$	−0.990671	+	0.990671i	−0.0421276	+	0.0421276i
$554$	−3.40681	−	6.19269i	−0.144742	−	0.263102i
$555$		0			0
$556$	−20.9707	−	13.2912i	−0.889356	−	0.563675i
$557$	11.4427	+	11.4427i	0.484841	+	0.484841i	0.906674	−	0.421832i	$-0.138613\pi$
$557$	11.4427	+	11.4427i	0.484841	+	0.484841i	−0.421832	+	0.906674i	$0.638613\pi$
$558$	−5.23723	−	1.51990i	−0.221709	−	0.0643424i
$559$	−2.85481			−0.120746
$560$		0			0
$561$	10.1214			0.427324
$562$	−0.244430	−	0.0709362i	−0.0103107	−	0.00299226i
$563$	7.08426	+	7.08426i	0.298566	+	0.298566i	0.840452	−	0.541886i	$-0.182290\pi$
$563$	7.08426	+	7.08426i	0.298566	+	0.298566i	−0.541886	+	0.840452i	$0.682290\pi$
$564$	13.9918	+	8.86799i	0.589159	+	0.373410i
$565$		0			0
$566$	−9.48601	−	17.2431i	−0.398727	−	0.724780i
$567$	−2.47817	+	2.47817i	−0.104073	+	0.104073i
$568$	9.02235	−	7.96832i	0.378569	−	0.334343i
$569$		−	46.2427i		−	1.93860i	−0.245890	−	0.969298i	$-0.579080\pi$
$569$		−	46.2427i		−	1.93860i	0.245890	−	0.969298i	$-0.420920\pi$
$570$		0			0
$571$			31.2381i			1.30727i	0.756808	+	0.653637i	$0.226758\pi$
$571$			31.2381i			1.30727i	−0.756808	+	0.653637i	$0.773242\pi$
$572$	0.680641	+	3.03669i	0.0284590	+	0.126970i
$573$	15.2920	−	15.2920i	0.638833	−	0.638833i
$574$	−11.8407	+	6.51399i	−0.494222	+	0.271889i
$575$		0			0
$576$	−7.93866	−	0.988770i	−0.330778	−	0.0411988i
$577$	−1.16131	−	1.16131i	−0.0483461	−	0.0483461i	0.682520	−	0.730866i	$-0.260884\pi$
$577$	−1.16131	−	1.16131i	−0.0483461	−	0.0483461i	−0.730866	+	0.682520i	$0.760884\pi$
$578$	−2.29768	+	7.91729i	−0.0955709	+	0.329316i
$579$	−16.3559			−0.679727
$580$		0			0
$581$	−0.990671			−0.0411000
$582$	−3.75479	+	12.9381i	−0.155641	+	0.536303i
$583$	9.51293	+	9.51293i	0.393985	+	0.393985i
$584$	37.0594	+	2.29902i	1.53353	+	0.0951341i
$585$		0			0
$586$	27.8060	−	15.2970i	1.14866	−	0.631915i
$587$	−23.6268	+	23.6268i	−0.975183	+	0.975183i	−0.999699	−	0.0245164i	$-0.992195\pi$
$587$	−23.6268	+	23.6268i	−0.975183	+	0.975183i	0.0245164	+	0.999699i	$0.492195\pi$
$588$	10.3096	−	2.31077i	0.425159	−	0.0952947i
$589$		−	19.1120i		−	0.787498i
$590$		0			0
$591$			13.3276i			0.548223i
$592$	−0.693949	+	1.93460i	−0.0285211	+	0.0795115i
$593$	0.260625	−	0.260625i	0.0107026	−	0.0107026i	−0.701735	−	0.712438i	$-0.747591\pi$
$593$	0.260625	−	0.260625i	0.0107026	−	0.0107026i	0.712438	+	0.701735i	$0.247591\pi$
$594$	−2.06429	−	3.75233i	−0.0846988	−	0.153960i
$595$		0			0
$596$	6.19632	−	9.77644i	0.253811	−	0.400458i
$597$	7.78734	+	7.78734i	0.318714	+	0.318714i
$598$	−0.888619	−	0.257887i	−0.0363383	−	0.0105458i
$599$	−33.0851			−1.35182			−0.675910	−	0.736984i	$-0.736249\pi$
$599$	−33.0851			−1.35182			−0.675910	+	0.736984i	$0.736249\pi$
$600$		0			0
$601$	−24.3200			−0.992033			−0.496016	−	0.868313i	$-0.665204\pi$
$601$	−24.3200			−0.992033			−0.496016	+	0.868313i	$0.665204\pi$
$602$	−26.4464	−	7.67501i	−1.07787	−	0.312810i
$603$	−3.92870	−	3.92870i	−0.159989	−	0.159989i
$604$	19.3479	−	30.5267i	0.787253	−	1.24211i
$605$		0			0
$606$	−3.94502	−	7.17101i	−0.160255	−	0.291302i
$607$	4.53347	−	4.53347i	0.184008	−	0.184008i	−0.609092	−	0.793100i	$-0.708466\pi$
$607$	4.53347	−	4.53347i	0.184008	−	0.184008i	0.793100	+	0.609092i	$0.208466\pi$
$608$	−4.42639	−	27.6857i	−0.179514	−	1.12280i
$609$			12.2827i			0.497719i
$610$		0			0
$611$			4.25583i			0.172173i
$612$	−6.52267	+	1.46199i	−0.263663	+	0.0590972i
$613$	20.2793	−	20.2793i	0.819073	−	0.819073i	−0.166901	−	0.985974i	$-0.553376\pi$
$613$	20.2793	−	20.2793i	0.819073	−	0.819073i	0.985974	+	0.166901i	$0.0533761\pi$
$614$	−13.6415	+	7.50466i	−0.550526	+	0.302864i
$615$		0			0
$616$	−1.85866	+	29.9611i	−0.0748877	+	1.20717i
$617$	−17.1086	−	17.1086i	−0.688768	−	0.688768i	0.273192	−	0.961960i	$-0.411921\pi$
$617$	−17.1086	−	17.1086i	−0.688768	−	0.688768i	−0.961960	+	0.273192i	$0.911921\pi$
$618$	−7.29742	+	25.1453i	−0.293545	+	1.01149i
$619$	29.4373			1.18319			0.591593	−	0.806237i	$-0.298499\pi$
$619$	29.4373			1.18319			0.591593	+	0.806237i	$0.298499\pi$
$620$		0			0
$621$	1.27334			0.0510975
$622$	−2.78191	+	9.58583i	−0.111544	+	0.384357i
$623$	10.6132	+	10.6132i	0.425209	+	0.425209i
$624$	−0.877272	−	1.85866i	−0.0351190	−	0.0744061i
$625$		0			0
$626$	−19.8037	+	10.8947i	−0.791514	+	0.435439i
$627$	10.6132	−	10.6132i	0.423850	−	0.423850i
$628$	2.42456	+	10.8172i	0.0967503	+	0.431653i
$629$			1.71733i			0.0684743i
$630$		0			0
$631$		−	5.25710i		−	0.209282i	−0.994510	−	0.104641i	$-0.966631\pi$
$631$		−	5.25710i		−	0.209282i	0.994510	−	0.104641i	$-0.0333693\pi$
$632$	0.748480	+	0.847487i	0.0297729	+	0.0337112i
$633$	−19.7873	+	19.7873i	−0.786476	+	0.786476i
$634$	18.7746	+	34.1273i	0.745635	+	1.35537i
$635$		0			0
$636$	−7.50466	−	4.75646i	−0.297579	−	0.188606i
$637$	1.91934	+	1.91934i	0.0760472	+	0.0760472i
$638$	−14.4146	−	4.18326i	−0.570679	−	0.165617i
$639$	−4.25583			−0.168358
$640$		0			0
$641$	20.0773			0.793004			0.396502	−	0.918034i	$-0.370224\pi$
$641$	20.0773			0.793004			0.396502	+	0.918034i	$0.370224\pi$
$642$	18.6559	+	5.41413i	0.736289	+	0.213679i
$643$	9.28480	+	9.28480i	0.366157	+	0.366157i	0.866073	−	0.499917i	$-0.166636\pi$
$643$	9.28480	+	9.28480i	0.366157	+	0.366157i	−0.499917	+	0.866073i	$0.666636\pi$
$644$	−7.53866	−	4.77801i	−0.297065	−	0.188280i
$645$		0			0
$646$	−11.2920	−	20.5259i	−0.444278	−	0.807580i
$647$	−28.7387	+	28.7387i	−1.12983	+	1.12983i	−0.139630	+	0.990204i	$0.544591\pi$
$647$	−28.7387	+	28.7387i	−1.12983	+	1.12983i	−0.990204	+	0.139630i	$0.955409\pi$
$648$	1.87233	+	2.12000i	0.0735520	+	0.0832813i
$649$			26.3013i			1.03242i
$650$		0			0
$651$		−	13.5142i		−	0.529665i
$652$	−1.99700	−	8.90963i	−0.0782084	−	0.348928i
$653$	11.9380	−	11.9380i	0.467170	−	0.467170i	−0.433826	−	0.900996i	$-0.642837\pi$
$653$	11.9380	−	11.9380i	0.467170	−	0.467170i	0.900996	+	0.433826i	$0.142837\pi$
$654$	−12.9641	+	7.13201i	−0.506937	+	0.278884i
$655$		0			0
$656$	4.65533	+	9.86318i	0.181760	+	0.385093i
$657$	−9.28267	−	9.28267i	−0.362152	−	0.362152i
$658$	−11.4416	+	39.4251i	−0.446039	+	1.53695i
$659$	−17.9963			−0.701038			−0.350519	−	0.936556i	$-0.613995\pi$
$659$	−17.9963			−0.701038			−0.350519	+	0.936556i	$0.613995\pi$
$660$		0			0
$661$	−9.06794			−0.352702			−0.176351	−	0.984327i	$-0.556429\pi$
$661$	−9.06794			−0.352702			−0.176351	+	0.984327i	$0.556429\pi$
$662$	−5.91798	+	20.3920i	−0.230009	+	0.792558i
$663$	−1.21433	−	1.21433i	−0.0471608	−	0.0471608i
$664$	−0.0495037	+	0.797984i	−0.00192112	+	0.0309678i
$665$		0			0
$666$	0.636672	−	0.350255i	0.0246705	−	0.0135721i
$667$	3.15556	−	3.15556i	0.122184	−	0.122184i
$668$	−19.2010	+	4.30369i	−0.742908	+	0.166515i
$669$			12.0700i			0.466654i
$670$		0			0
$671$			46.3089i			1.78773i
$672$	−3.12993	−	19.5767i	−0.120740	−	0.755189i
$673$	−35.7640	+	35.7640i	−1.37860	+	1.37860i	−0.531611	+	0.846988i	$0.678413\pi$
$673$	−35.7640	+	35.7640i	−1.37860	+	1.37860i	−0.846988	+	0.531611i	$0.821587\pi$
$674$	−20.8074	−	37.8223i	−0.801470	−	1.45686i
$675$		0			0
$676$	−13.6360	+	21.5147i	−0.524462	+	0.827487i
$677$	−16.2020	−	16.2020i	−0.622694	−	0.622694i	0.323525	−	0.946219i	$-0.395132\pi$
$677$	−16.2020	−	16.2020i	−0.622694	−	0.622694i	−0.946219	+	0.323525i	$0.895132\pi$
$678$	−20.4483	−	5.93431i	−0.785312	−	0.227906i
$679$	−33.3859			−1.28123
$680$		0			0
$681$	1.45331			0.0556911
$682$	15.8599	+	4.60272i	0.607308	+	0.176247i
$683$	−33.3943	−	33.3943i	−1.27780	−	1.27780i	−0.941899	−	0.335897i	$-0.890961\pi$
$683$	−33.3943	−	33.3943i	−1.27780	−	1.27780i	−0.335897	−	0.941899i	$-0.609039\pi$
$684$	−5.30660	+	8.37266i	−0.202903	+	0.320137i
$685$		0			0
$686$	−4.10270	−	7.45763i	−0.156642	−	0.284734i
$687$	−6.25649	+	6.25649i	−0.238700	+	0.238700i
$688$	−7.50373	+	20.9190i	−0.286077	+	0.797528i
$689$		−	2.28267i		−	0.0869629i
$690$		0			0
$691$		−	24.6365i		−	0.937216i	−0.883406	−	0.468608i	$-0.844756\pi$
$691$		−	24.6365i		−	0.937216i	0.883406	−	0.468608i	$-0.155244\pi$
$692$	−1.73143	+	0.388082i	−0.0658193	+	0.0147527i
$693$	7.50466	−	7.50466i	0.285079	−	0.285079i
$694$	−29.7843	+	16.3854i	−1.13060	+	0.621980i
$695$		0			0
$696$	9.89367	+	0.613763i	0.375019	+	0.0232646i
$697$	6.44398	+	6.44398i	0.244083	+	0.244083i
$698$	−1.72853	+	5.95611i	−0.0654256	+	0.225442i
$699$	6.94381			0.262639
$700$		0			0
$701$	−23.0420			−0.870285			−0.435143	−	0.900362i	$-0.643302\pi$
$701$	−23.0420			−0.870285			−0.435143	+	0.900362i	$0.643302\pi$
$702$	−0.202527	+	0.697863i	−0.00764389	+	0.0263391i
$703$	1.80078	+	1.80078i	0.0679177	+	0.0679177i
$704$	24.0407	+	2.99430i	0.906068	+	0.112852i
$705$		0			0
$706$	−4.60398	+	2.53281i	−0.173273	+	0.0953235i
$707$	14.3420	−	14.3420i	0.539387	−	0.539387i
$708$	−3.79911	−	16.9498i	−0.142779	−	0.637012i
$709$		−	37.7360i		−	1.41720i	−0.705608	−	0.708602i	$-0.749326\pi$
$709$		−	37.7360i		−	1.41720i	0.705608	−	0.708602i	$-0.250674\pi$
$710$		0			0
$711$		−	0.399759i		−	0.0149921i
$712$	9.07925	−	8.01857i	0.340259	−	0.300509i
$713$	−3.47197	+	3.47197i	−0.130026	+	0.130026i
$714$	−7.98465	−	14.5140i	−0.298818	−	0.543173i
$715$		0			0
$716$	−15.1016	−	9.57143i	−0.564374	−	0.357701i
$717$	13.4533	+	13.4533i	0.502423	+	0.502423i
$718$	47.5296	+	13.7936i	1.77379	+	0.514772i
$719$	41.3423			1.54181			0.770903	−	0.636953i	$-0.219805\pi$
$719$	41.3423			1.54181			0.770903	+	0.636953i	$0.219805\pi$
$720$		0			0
$721$	−64.8853			−2.41646
$722$	−7.55871	−	2.19362i	−0.281306	−	0.0816380i
$723$	2.05529	+	2.05529i	0.0764372	+	0.0764372i
$724$	−1.70504	−	1.08066i	−0.0633673	−	0.0401623i
$725$		0			0
$726$	−1.24701	−	2.26673i	−0.0462808	−	0.0841264i
$727$	−9.48981	+	9.48981i	−0.351958	+	0.351958i	−0.860838	−	0.508880i	$-0.830060\pi$
$727$	−9.48981	+	9.48981i	−0.351958	+	0.351958i	0.508880	+	0.860838i	$0.330060\pi$
$728$	3.81765	−	3.37165i	0.141491	−	0.124962i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			18.5696i			0.686821i
$732$	−6.68911	−	29.8435i	−0.247237	−	1.10305i
$733$	−3.21134	+	3.21134i	−0.118614	+	0.118614i	−0.763922	−	0.645308i	$-0.776729\pi$
$733$	−3.21134	+	3.21134i	−0.118614	+	0.118614i	0.645308	+	0.763922i	$0.276729\pi$
$734$	−17.4108	+	9.57830i	−0.642646	+	0.353542i
$735$		0			0
$736$	−4.22538	+	5.83362i	−0.155750	+	0.215030i
$737$	11.8973	+	11.8973i	0.438243	+	0.438243i
$738$	1.07473	−	3.70328i	0.0395614	−	0.136320i
$739$	25.3832			0.933737			0.466868	−	0.884327i	$-0.345382\pi$
$739$	25.3832			0.933737			0.466868	+	0.884327i	$0.345382\pi$
$740$		0			0
$741$	−2.54669			−0.0935549
$742$	6.13684	−	21.1462i	0.225290	−	0.776300i
$743$	32.7400	+	32.7400i	1.20111	+	1.20111i	0.973828	+	0.227285i	$0.0729850\pi$
$743$	32.7400	+	32.7400i	1.20111	+	1.20111i	0.227285	+	0.973828i	$0.427015\pi$
$744$	−10.8857	−	0.675305i	−0.399089	−	0.0247579i
$745$		0			0
$746$	−12.4240	+	6.83488i	−0.454875	+	0.250243i
$747$	0.199879	−	0.199879i	0.00731321	−	0.00731321i
$748$	19.7526	−	4.42734i	0.722228	−	0.161880i
$749$			48.1400i			1.75900i
$750$		0			0
$751$		−	24.4810i		−	0.893323i	−0.894703	−	0.446662i	$-0.852613\pi$
$751$		−	24.4810i		−	0.893323i	0.894703	−	0.446662i	$-0.147387\pi$
$752$	31.1851	+	11.1862i	1.13720	+	0.407920i
$753$	−1.96137	+	1.96137i	−0.0714762	+	0.0714762i
$754$	1.22753	+	2.23132i	0.0447039	+	0.0812599i
$755$		0			0
$756$	−3.75233	+	5.92036i	−0.136471	+	0.215322i
$757$	−22.9473	−	22.9473i	−0.834035	−	0.834035i	0.154031	−	0.988066i	$-0.450774\pi$
$757$	−22.9473	−	22.9473i	−0.834035	−	0.834035i	−0.988066	+	0.154031i	$0.950774\pi$
$758$	40.7980	+	11.8400i	1.48185	+	0.430048i
$759$	−3.85607			−0.139967
$760$		0			0
$761$	37.0466			1.34294			0.671470	−	0.741032i	$-0.265663\pi$
$761$	37.0466			1.34294			0.671470	+	0.741032i	$0.265663\pi$
$762$	3.41444	+	0.990907i	0.123692	+	0.0358968i
$763$	−25.9282	−	25.9282i	−0.938665	−	0.938665i
$764$	23.1544	−	36.5327i	0.837698	−	1.32170i
$765$		0			0
$766$	11.4847	+	20.8761i	0.414959	+	0.754286i
$767$	3.15556	−	3.15556i	0.113941	−	0.113941i
$768$	−15.9254	+	1.54291i	−0.574660	+	0.0556749i
$769$			6.62395i			0.238866i	0.992842	+	0.119433i	$0.0381077\pi$
$769$			6.62395i			0.238866i	−0.992842	+	0.119433i	$0.961892\pi$
$770$		0			0
$771$			2.94249i			0.105971i
$772$	−31.9198	+	7.15447i	−1.14882	+	0.257495i
$773$	−16.2606	+	16.2606i	−0.584854	+	0.584854i	−0.936233	−	0.351379i	$-0.885713\pi$
$773$	−16.2606	+	16.2606i	−0.584854	+	0.584854i	0.351379	+	0.936233i	$0.385713\pi$
$774$	6.88438	−	3.78734i	0.247454	−	0.136133i
$775$		0			0
$776$	−1.66829	+	26.8922i	−0.0598880	+	0.965375i
$777$	1.27334	+	1.27334i	0.0456809	+	0.0456809i
$778$	6.43817	−	22.1845i	0.230819	−	0.795352i
$779$	13.5142			0.484198
$780$		0			0
$781$	12.8880			0.461168
$782$	−1.67747	+	5.78017i	−0.0599860	+	0.206698i
$783$	−2.47817	−	2.47817i	−0.0885626	−	0.0885626i
$784$	19.1091	−	9.01932i	0.682468	−	0.322118i
$785$		0			0
$786$	22.5490	−	12.4050i	0.804296	−	0.442471i
$787$	31.2117	−	31.2117i	1.11258	−	1.11258i	0.119776	−	0.992801i	$-0.461782\pi$
$787$	31.2117	−	31.2117i	1.11258	−	1.11258i	0.992801	−	0.119776i	$-0.0382177\pi$
$788$	5.82981	+	26.0098i	0.207678	+	0.926560i
$789$		−	6.72666i		−	0.239475i
$790$		0			0
$791$		−	52.7652i		−	1.87612i
$792$	−5.66999	−	6.42000i	−0.201474	−	0.228125i
$793$	5.55602	−	5.55602i	0.197300	−	0.197300i
$794$	−18.5021	−	33.6320i	−0.656615	−	1.19355i
$795$		0			0
$796$	18.6040	+	11.7912i	0.659401	+	0.417929i
$797$	−17.3540	−	17.3540i	−0.614710	−	0.614710i	0.329460	−	0.944170i	$-0.393133\pi$
$797$	−17.3540	−	17.3540i	−0.614710	−	0.614710i	−0.944170	+	0.329460i	$0.893133\pi$
$798$	−23.5919	−	6.84663i	−0.835146	−	0.242368i
$799$	27.6828			0.979346
$800$		0			0
$801$	−4.28267			−0.151321
$802$	−36.0804	−	10.4709i	−1.27404	−	0.369741i
$803$	28.1108	+	28.1108i	0.992008	+	0.992008i
$804$	−9.38567	−	5.94865i	−0.331007	−	0.209793i
$805$		0			0
$806$	−1.35061	−	2.45505i	−0.0475732	−	0.0864756i
$807$	−15.3334	+	15.3334i	−0.539760	+	0.539760i
$808$	−10.8358	−	12.2691i	−0.381202	−	0.431627i
$809$			27.4320i			0.964458i	0.876045	+	0.482229i	$0.160173\pi$
$809$			27.4320i			0.964458i	−0.876045	+	0.482229i	$0.839827\pi$
$810$		0			0
$811$		−	27.1840i		−	0.954559i	−0.878751	−	0.477280i	$-0.841623\pi$
$811$		−	27.1840i		−	0.954559i	0.878751	−	0.477280i	$-0.158377\pi$
$812$	5.37275	+	23.9706i	0.188547	+	0.841203i
$813$	−2.23132	+	2.23132i	−0.0782558	+	0.0782558i
$814$	−1.92804	+	1.06068i	−0.0675777	+	0.0371768i
$815$		0			0
$816$	−12.0900	+	5.70636i	−0.423234	+	0.199762i
$817$	19.4720	+	19.4720i	0.681238	+	0.681238i
$818$	10.0095	−	34.4905i	0.349974	−	1.20593i
$819$	−1.80078			−0.0629243
$820$		0			0
$821$	23.6074			0.823903			0.411951	−	0.911206i	$-0.364847\pi$
$821$	23.6074			0.823903			0.411951	+	0.911206i	$0.364847\pi$
$822$	3.29957	−	11.3696i	0.115086	−	0.396560i
$823$	−24.6596	−	24.6596i	−0.859579	−	0.859579i	0.131709	−	0.991288i	$-0.457954\pi$
$823$	−24.6596	−	24.6596i	−0.859579	−	0.859579i	−0.991288	+	0.131709i	$0.957954\pi$
$824$	−3.24231	+	52.2650i	−0.112951	+	1.82074i
$825$		0			0
$826$	37.7160	−	20.7489i	1.31231	−	0.721946i
$827$	13.5406	−	13.5406i	0.470854	−	0.470854i	−0.431337	−	0.902191i	$-0.641958\pi$
$827$	13.5406	−	13.5406i	0.470854	−	0.470854i	0.902191	+	0.431337i	$0.141958\pi$
$828$	2.48503	−	0.556993i	0.0863608	−	0.0193568i
$829$		−	9.00933i		−	0.312907i	−0.987685	−	0.156453i	$-0.949994\pi$
$829$		−	9.00933i		−	0.312907i	0.987685	−	0.156453i	$-0.0500061\pi$
$830$		0			0
$831$			4.99779i			0.173371i
$832$	−2.52509	−	3.24359i	−0.0875418	−	0.112451i
$833$	12.4847	−	12.4847i	0.432569	−	0.432569i
$834$	8.46216	+	15.3820i	0.293021	+	0.532635i
$835$		0			0
$836$	16.0700	−	25.3550i	0.555793	−	0.876920i
$837$	2.72666	+	2.72666i	0.0942470	+	0.0942470i
$838$	−54.4340	−	15.7973i	−1.88039	−	0.545709i
$839$	−10.2597			−0.354203			−0.177102	−	0.984193i	$-0.556672\pi$
$839$	−10.2597			−0.354203			−0.177102	+	0.984193i	$0.556672\pi$
$840$		0			0
$841$	16.7173			0.576460
$842$	−26.3414	−	7.64455i	−0.907785	−	0.263449i
$843$	0.127258	+	0.127258i	0.00438298	+	0.00438298i
$844$	−29.9611	+	47.2720i	−1.03130	+	1.62717i
$845$		0			0
$846$	−5.64600	−	10.2629i	−0.194113	−	0.352847i
$847$	4.53347	−	4.53347i	0.155772	−	0.155772i
$848$	−16.7265	−	5.99988i	−0.574392	−	0.206037i
$849$			13.9160i			0.477594i
$850$		0			0
$851$		−	0.654274i		−	0.0224282i
$852$	−8.30559	+	1.86161i	−0.284545	+	0.0637777i
$853$	−17.1086	+	17.1086i	−0.585789	+	0.585789i	−0.936488	−	0.350699i	$-0.885944\pi$
$853$	−17.1086	+	17.1086i	−0.585789	+	0.585789i	0.350699	+	0.936488i	$0.385944\pi$
$854$	66.4067	−	36.5327i	2.27239	−	1.25012i
$855$		0			0
$856$	38.7767	+	2.40555i	1.32536	+	0.0822200i
$857$	26.7674	+	26.7674i	0.914356	+	0.914356i	0.996611	−	0.0822556i	$-0.0262124\pi$
$857$	26.7674	+	26.7674i	0.914356	+	0.914356i	−0.0822556	+	0.996611i	$0.526212\pi$
$858$	0.613314	−	2.11334i	0.0209382	−	0.0721483i
$859$	−28.6378			−0.977109			−0.488554	−	0.872533i	$-0.662476\pi$
$859$	−28.6378			−0.977109			−0.488554	+	0.872533i	$0.662476\pi$
$860$		0			0
$861$	9.55602			0.325668
$862$	−6.23716	+	21.4918i	−0.212438	+	0.732015i
$863$	15.8157	+	15.8157i	0.538371	+	0.538371i	0.923050	−	0.384679i	$-0.125688\pi$
$863$	15.8157	+	15.8157i	0.538371	+	0.538371i	−0.384679	+	0.923050i	$0.625688\pi$
$864$	4.58134	+	3.31834i	0.155860	+	0.112892i
$865$		0			0
$866$	−37.0116	+	20.3614i	−1.25771	+	0.691908i
$867$	4.12198	−	4.12198i	0.139990	−	0.139990i
$868$	−5.91147	−	26.3741i	−0.200648	−	0.895196i
$869$			1.21059i			0.0410665i
$870$		0			0
$871$		−	2.85481i		−	0.0967316i
$872$	−22.1808	+	19.5895i	−0.751135	+	0.663384i
$873$	6.73599	−	6.73599i	0.227979	−	0.227979i
$874$	4.30207	+	7.82003i	0.145520	+	0.264516i
$875$		0			0
$876$	−22.1763	−	14.0554i	−0.749269	−	0.474888i
$877$	17.3727	+	17.3727i	0.586633	+	0.586633i	0.936718	−	0.350085i	$-0.113847\pi$
$877$	17.3727	+	17.3727i	0.586633	+	0.586633i	−0.350085	+	0.936718i	$0.613847\pi$
$878$	8.98009	+	2.60612i	0.303063	+	0.0879522i
$879$	−22.4407			−0.756907
$880$		0			0
$881$	56.5254			1.90439			0.952194	−	0.305493i	$-0.0988211\pi$
$881$	56.5254			1.90439			0.952194	+	0.305493i	$0.0988211\pi$
$882$	−7.17480	−	2.08220i	−0.241588	−	0.0701114i
$883$	15.1962	+	15.1962i	0.511392	+	0.511392i	0.914953	−	0.403561i	$-0.132228\pi$
$883$	15.1962	+	15.1962i	0.511392	+	0.511392i	−0.403561	+	0.914953i	$0.632228\pi$
$884$	−2.90105	−	1.83869i	−0.0975728	−	0.0618418i
$885$		0			0
$886$	14.0187	+	25.4822i	0.470966	+	0.856092i
$887$	11.0676	−	11.0676i	0.371613	−	0.371613i	−0.496451	−	0.868065i	$-0.665364\pi$
$887$	11.0676	−	11.0676i	0.371613	−	0.371613i	0.868065	+	0.496451i	$0.165364\pi$
$888$	1.08930	−	0.962047i	0.0365547	−	0.0322842i
$889$			8.81070i			0.295501i
$890$		0			0
$891$			3.02831i			0.101452i
$892$	5.27973	+	23.5556i	0.176778	+	0.788699i
$893$	29.0280	−	29.0280i	0.971385	−	0.971385i
$894$	−7.17101	+	3.94502i	−0.239834	+	0.131941i
$895$		0			0
$896$	−14.6717	−	36.8364i	−0.490146	−	1.23062i
$897$	0.462642	+	0.462642i	0.0154472	+	0.0154472i
$898$	13.2484	−	45.6510i	0.442105	−	1.52339i
$899$	13.5142			0.450725
$900$		0			0
$901$	−14.8480			−0.494659
$902$	−3.25461	+	11.2147i	−0.108367	+	0.373407i
$903$	13.7688	+	13.7688i	0.458196	+	0.458196i
$904$	−42.5023	−	2.63667i	−1.41361	−	0.0876944i
$905$		0			0
$906$	−22.3913	+	12.3182i	−0.743902	+	0.409246i
$907$	28.1654	−	28.1654i	0.935217	−	0.935217i	−0.0628084	−	0.998026i	$-0.520006\pi$
$907$	28.1654	−	28.1654i	0.935217	−	0.935217i	0.998026	+	0.0628084i	$0.0200057\pi$
$908$	2.83625	−	0.635716i	0.0941244	−	0.0210970i
$909$			5.78734i			0.191954i
$910$		0			0
$911$			34.8499i			1.15463i	0.816522	+	0.577315i	$0.195899\pi$
$911$			34.8499i			1.15463i	−0.816522	+	0.577315i	$0.804101\pi$
$912$	−6.69383	+	18.6611i	−0.221655	+	0.617932i
$913$	−0.605296	+	0.605296i	−0.0200324	+	0.0200324i
$914$	15.0053	+	27.2757i	0.496331	+	0.902198i
$915$		0			0
$916$	−9.47329	+	14.9468i	−0.313006	+	0.493856i
$917$	45.0980	+	45.0980i	1.48927	+	1.48927i
$918$	4.53936	+	1.31737i	0.149821	+	0.0434797i
$919$	−21.1171			−0.696590			−0.348295	−	0.937385i	$-0.613239\pi$
$919$	−21.1171			−0.696590			−0.348295	+	0.937385i	$0.613239\pi$
$920$		0			0
$921$	11.0093			0.362770
$922$	35.5126	+	10.3061i	1.16954	+	0.339414i
$923$	−1.54626	−	1.54626i	−0.0508959	−	0.0508959i
$924$	11.3632	−	17.9287i	0.373822	−	0.589810i
$925$		0			0
$926$	5.57104	+	10.1267i	0.183076	+	0.332784i
$927$	13.0914	−	13.0914i	0.429977	−	0.429977i
$928$	19.5767	−	3.12993i	0.642638	−	0.102745i
$929$		−	39.0653i		−	1.28169i	−0.767670	−	0.640845i	$-0.778584\pi$
$929$		−	39.0653i		−	1.28169i	0.767670	−	0.640845i	$-0.221416\pi$
$930$		0			0
$931$		−	26.1827i		−	0.858105i
$932$	13.5514	−	3.03740i	0.443891	−	0.0994933i
$933$	4.99067	−	4.99067i	0.163387	−	0.163387i
$934$	3.95181	−	2.17403i	0.129307	−	0.0711364i
$935$		0			0
$936$	−0.0899847	+	1.45052i	−0.00294124	+	0.0474119i
$937$	−1.82936	−	1.82936i	−0.0597626	−	0.0597626i	0.676594	−	0.736356i	$-0.263455\pi$
$937$	−1.82936	−	1.82936i	−0.0597626	−	0.0597626i	−0.736356	+	0.676594i	$0.763455\pi$
$938$	7.67501	−	26.4464i	0.250598	−	0.863504i
$939$	15.9825			0.521569
$940$		0			0
$941$	1.58193			0.0515695			0.0257847	−	0.999668i	$-0.491792\pi$
$941$	1.58193			0.0515695			0.0257847	+	0.999668i	$0.491792\pi$
$942$	2.18473	−	7.52808i	0.0711823	−	0.245278i
$943$	−2.45505	−	2.45505i	−0.0799476	−	0.0799476i
$944$	−14.8285	−	31.4170i	−0.482627	−	1.02254i
$945$		0			0
$946$	−20.8480	+	11.4692i	−0.677827	+	0.372896i
$947$	15.9429	−	15.9429i	0.518075	−	0.518075i	−0.398913	−	0.916989i	$-0.630613\pi$
$947$	15.9429	−	15.9429i	0.518075	−	0.518075i	0.916989	+	0.398913i	$0.130613\pi$
$948$	−0.174865	−	0.780161i	−0.00567934	−	0.0253384i
$949$		−	6.74531i		−	0.218962i
$950$		0			0
$951$		−	27.5423i		−	0.893121i
$952$	−21.9315	−	24.8325i	−0.710803	−	0.804826i
$953$	27.2113	−	27.2113i	0.881462	−	0.881462i	−0.112221	−	0.993683i	$-0.535797\pi$
$953$	27.2113	−	27.2113i	0.881462	−	0.881462i	0.993683	+	0.112221i	$0.0357966\pi$
$954$	3.02831	+	5.50466i	0.0980450	+	0.178220i
$955$		0			0
$956$	32.1400	+	20.3704i	1.03948	+	0.658825i
$957$	7.50466	+	7.50466i	0.242591	+	0.242591i
$958$	−1.90283	−	0.552222i	−0.0614777	−	0.0178415i
$959$	29.3383			0.947383
$960$		0			0
$961$	16.1307			0.520345
$962$	0.358578	+	0.104063i	0.0115610	+	0.00335513i
$963$	−9.71281	−	9.71281i	−0.312991	−	0.312991i
$964$	4.91011	+	3.11203i	0.158144	+	0.100232i
$965$		0			0
$966$	3.04202	+	5.52960i	0.0978755	+	0.177912i
$967$	−14.8921	+	14.8921i	−0.478899	+	0.478899i	−0.904780	−	0.425880i	$-0.859964\pi$
$967$	−14.8921	+	14.8921i	−0.478899	+	0.478899i	0.425880	+	0.904780i	$0.359964\pi$
$968$	−3.42516	−	3.87824i	−0.110089	−	0.124651i
$969$			16.5653i			0.532156i
$970$		0			0
$971$		−	41.6250i		−	1.33581i	−0.744246	−	0.667905i	$-0.767191\pi$
$971$		−	41.6250i		−	1.33581i	0.744246	−	0.667905i	$-0.232809\pi$
$972$	−0.437425	−	1.95158i	−0.0140304	−	0.0625969i
$973$	−30.7640	+	30.7640i	−0.986248	+	0.986248i
$974$	1.71403	−	0.942949i	0.0549212	−	0.0302140i
$975$		0			0
$976$	−26.1086	−	55.3160i	−0.835717	−	1.77062i
$977$	12.0807	+	12.0807i	0.386494	+	0.386494i	0.873435	−	0.486941i	$-0.161887\pi$
$977$	12.0807	+	12.0807i	0.386494	+	0.386494i	−0.486941	+	0.873435i	$0.661887\pi$
$978$	−1.79946	+	6.20054i	−0.0575404	+	0.198271i
$979$	12.9692			0.414499
$980$		0			0
$981$	10.4626			0.334046
$982$	−14.2343	+	49.0484i	−0.454236	+	1.56520i
$983$	22.2258	+	22.2258i	0.708893	+	0.708893i	0.966302	−	0.257410i	$-0.0828690\pi$
$983$	22.2258	+	22.2258i	0.708893	+	0.708893i	−0.257410	+	0.966302i	$0.582869\pi$
$984$	0.477513	−	7.69735i	0.0152226	−	0.245383i
$985$		0			0
$986$	14.5140	−	7.98465i	0.462220	−	0.254283i
$987$	20.5259	−	20.5259i	0.653346	−	0.653346i
$988$	−4.97006	+	1.11399i	−0.158119	+	0.0354406i
$989$		−	7.07472i		−	0.224963i
$990$		0			0
$991$		−	0.353523i		−	0.0112300i	−0.999984	−	0.00561501i	$-0.998213\pi$
$991$		−	0.353523i		−	0.0112300i	0.999984	−	0.00561501i	$-0.00178732\pi$
$992$	−21.5397	+	3.44377i	−0.683886	+	0.109340i
$993$	10.6167	−	10.6167i	0.336911	−	0.336911i
$994$	−10.1672	−	18.4813i	−0.322484	−	0.586191i
$995$		0			0
$996$	0.302648	−	0.477513i	0.00958977	−	0.0151306i
$997$	−27.9380	−	27.9380i	−0.884805	−	0.884805i	0.109213	−	0.994018i	$-0.465167\pi$
$997$	−27.9380	−	27.9380i	−0.884805	−	0.884805i	−0.994018	+	0.109213i	$0.965167\pi$
$998$	−8.63442	−	2.50580i	−0.273318	−	0.0793197i
$999$	−0.513824			−0.0162567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.j.d.7.1		12
3.2	odd	2		900.2.k.n.307.6		12
4.3	odd	2	inner	300.2.j.d.7.3		12
5.2	odd	4		60.2.j.a.43.4	yes	12
5.3	odd	4	inner	300.2.j.d.43.3		12
5.4	even	2		60.2.j.a.7.6	yes	12
12.11	even	2		900.2.k.n.307.4		12
15.2	even	4		180.2.k.e.163.3		12
15.8	even	4		900.2.k.n.343.4		12
15.14	odd	2		180.2.k.e.127.1		12
20.3	even	4	inner	300.2.j.d.43.1		12
20.7	even	4		60.2.j.a.43.6	yes	12
20.19	odd	2		60.2.j.a.7.4	✓	12
40.19	odd	2		960.2.w.g.127.3		12
40.27	even	4		960.2.w.g.703.6		12
40.29	even	2		960.2.w.g.127.6		12
40.37	odd	4		960.2.w.g.703.3		12
60.23	odd	4		900.2.k.n.343.6		12
60.47	odd	4		180.2.k.e.163.1		12
60.59	even	2		180.2.k.e.127.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.4	✓	12	20.19	odd	2
60.2.j.a.7.6	yes	12	5.4	even	2
60.2.j.a.43.4	yes	12	5.2	odd	4
60.2.j.a.43.6	yes	12	20.7	even	4
180.2.k.e.127.1		12	15.14	odd	2
180.2.k.e.127.3		12	60.59	even	2
180.2.k.e.163.1		12	60.47	odd	4
180.2.k.e.163.3		12	15.2	even	4
300.2.j.d.7.1		12	1.1	even	1	trivial
300.2.j.d.7.3		12	4.3	odd	2	inner
300.2.j.d.43.1		12	20.3	even	4	inner
300.2.j.d.43.3		12	5.3	odd	4	inner
900.2.k.n.307.4		12	12.11	even	2
900.2.k.n.307.6		12	3.2	odd	2
900.2.k.n.343.4		12	15.8	even	4
900.2.k.n.343.6		12	60.23	odd	4
960.2.w.g.127.3		12	40.19	odd	2
960.2.w.g.127.6		12	40.29	even	2
960.2.w.g.703.3		12	40.37	odd	4
960.2.w.g.703.6		12	40.27	even	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35818 - 0.394157i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(2.47817 - 2.47817i) q^{7} +(-1.87233 - 2.12000i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.35818 - 0.394157i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(2.47817 - 2.47817i) q^{7} +(-1.87233 - 2.12000i) q^{8} +1.00000i q^{9} -3.02831i q^{11} +(0.437425 + 1.95158i) q^{12} +(-0.363328 + 0.363328i) q^{13} +(-4.34258 + 2.38900i) q^{14} +(1.70734 + 3.61732i) q^{16} +(2.36333 + 2.36333i) q^{17} +(0.394157 - 1.35818i) q^{18} +4.95634 q^{19} +3.50466 q^{21} +(-1.19363 + 4.11297i) q^{22} +(-0.900390 - 0.900390i) q^{23} +(0.175128 - 2.82300i) q^{24} +(0.636672 - 0.350255i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(6.83963 - 1.53303i) q^{28} +3.50466i q^{29} -3.85607i q^{31} +(-0.893077 - 5.58591i) q^{32} +(2.14134 - 2.14134i) q^{33} +(-2.27829 - 4.14134i) q^{34} +(-1.07067 + 1.68928i) q^{36} +(0.363328 + 0.363328i) q^{37} +(-6.73158 - 1.95358i) q^{38} -0.513824 q^{39} +2.72666 q^{41} +(-4.75995 - 1.38139i) q^{42} +(3.92870 + 3.92870i) q^{43} +(3.24231 - 5.11566i) q^{44} +(0.867993 + 1.57778i) q^{46} +(5.85673 - 5.85673i) q^{47} +(-1.35056 + 3.76510i) q^{48} -5.28267i q^{49} +3.34225i q^{51} +(-1.00277 + 0.224760i) q^{52} +(-3.14134 + 3.14134i) q^{53} +(1.23909 - 0.681664i) q^{54} +(-9.89367 - 0.613763i) q^{56} +(3.50466 + 3.50466i) q^{57} +(1.38139 - 4.75995i) q^{58} -8.68516 q^{59} -15.2920 q^{61} +(-1.51990 + 5.23723i) q^{62} +(2.47817 + 2.47817i) q^{63} +(-0.988770 + 7.93866i) q^{64} +(-3.75233 + 2.06429i) q^{66} +(-3.92870 + 3.92870i) q^{67} +(1.46199 + 6.52267i) q^{68} -1.27334i q^{69} +4.25583i q^{71} +(2.12000 - 1.87233i) q^{72} +(-9.28267 + 9.28267i) q^{73} +(-0.350255 - 0.636672i) q^{74} +(8.37266 + 5.30660i) q^{76} +(-7.50466 - 7.50466i) q^{77} +(0.697863 + 0.202527i) q^{78} -0.399759 q^{79} -1.00000 q^{81} +(-3.70328 - 1.07473i) q^{82} +(-0.199879 - 0.199879i) q^{83} +(5.92036 + 3.75233i) q^{84} +(-3.78734 - 6.88438i) q^{86} +(-2.47817 + 2.47817i) q^{87} +(-6.42000 + 5.66999i) q^{88} +4.28267i q^{89} +1.80078i q^{91} +(-0.556993 - 2.48503i) q^{92} +(2.72666 - 2.72666i) q^{93} +(-10.2629 + 5.64600i) q^{94} +(3.31834 - 4.58134i) q^{96} +(-6.73599 - 6.73599i) q^{97} +(-2.08220 + 7.17480i) q^{98} +3.02831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q - 4 * q^6 + 12 * q^8	\( 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48} + 8 q^{52} - 4 q^{53} - 64 q^{56} + 20 q^{58} - 32 q^{61} + 56 q^{62} - 24 q^{66} + 16 q^{68} + 12 q^{72} - 44 q^{73} + 8 q^{76} - 48 q^{77} + 24 q^{78} - 12 q^{81} - 16 q^{82} + 64 q^{86} - 60 q^{88} - 56 q^{92} + 16 q^{93} + 44 q^{96} + 20 q^{97} - 24 q^{98}+O(q^{100}) \) 12 * q - 4 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 + 12 * q^16 + 20 * q^17 - 12 * q^22 + 16 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^38 + 16 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 - 64 * q^56 + 20 * q^58 - 32 * q^61 + 56 * q^62 - 24 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 + 8 * q^76 - 48 * q^77 + 24 * q^78 - 12 * q^81 - 16 * q^82 + 64 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 44 * q^96 + 20 * q^97 - 24 * q^98

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