LMFDB - Embedded newform 756.2.ci.a.95.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.20
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30138 + 0.553549i) q^{2} +(-1.64933 - 0.528879i) q^{3} +(1.38717 - 1.44075i) q^{4} +(0.746991 + 0.131715i) q^{5} +(2.43916 - 0.224713i) q^{6} +(-2.50378 + 0.855036i) q^{7} +(-1.00770 + 2.64283i) q^{8} +(2.44057 + 1.74459i) q^{9} +O(q^{10})$	\(q+(-1.30138 + 0.553549i) q^{2} +(-1.64933 - 0.528879i) q^{3} +(1.38717 - 1.44075i) q^{4} +(0.746991 + 0.131715i) q^{5} +(2.43916 - 0.224713i) q^{6} +(-2.50378 + 0.855036i) q^{7} +(-1.00770 + 2.64283i) q^{8} +(2.44057 + 1.74459i) q^{9} +(-1.04503 + 0.242086i) q^{10} +(-0.356610 - 2.02244i) q^{11} +(-3.04988 + 1.64263i) q^{12} +(-0.148152 + 0.840214i) q^{13} +(2.78506 - 2.49869i) q^{14} +(-1.16237 - 0.612309i) q^{15} +(-0.151538 - 3.99713i) q^{16} +(2.92448 - 1.68845i) q^{17} +(-4.14182 - 0.919395i) q^{18} +(-2.38475 - 1.37684i) q^{19} +(1.22597 - 0.893520i) q^{20} +(4.58177 - 0.0860394i) q^{21} +(1.58360 + 2.43455i) q^{22} +(6.64204 + 5.57333i) q^{23} +(3.05977 - 3.82594i) q^{24} +(-4.15782 - 1.51332i) q^{25} +(-0.272298 - 1.17544i) q^{26} +(-3.10263 - 4.16817i) q^{27} +(-2.24126 + 4.79341i) q^{28} +(2.38405 - 0.420373i) q^{29} +(1.85163 + 0.153414i) q^{30} +(-1.70079 - 0.299896i) q^{31} +(2.40982 + 5.11789i) q^{32} +(-0.481457 + 3.52427i) q^{33} +(-2.87121 + 3.81615i) q^{34} +(-1.98292 + 0.308920i) q^{35} +(5.89901 - 1.09622i) q^{36} -6.22459 q^{37} +(3.86561 + 0.471707i) q^{38} +(0.688724 - 1.30743i) q^{39} +(-1.10084 + 1.84144i) q^{40} +(-11.4470 - 2.01842i) q^{41} +(-5.91498 + 2.64820i) q^{42} +(-4.80537 - 5.72682i) q^{43} +(-3.40851 - 2.29167i) q^{44} +(1.59330 + 1.62465i) q^{45} +(-11.7289 - 3.57631i) q^{46} +(-0.253974 - 1.44036i) q^{47} +(-1.86406 + 6.67273i) q^{48} +(5.53783 - 4.28165i) q^{49} +(6.24859 - 0.332154i) q^{50} +(-5.71642 + 1.23811i) q^{51} +(1.00503 + 1.37897i) q^{52} +(-2.10872 - 1.21747i) q^{53} +(6.34498 + 3.70691i) q^{54} -1.55771i q^{55} +(0.263344 - 7.47868i) q^{56} +(3.20506 + 3.53210i) q^{57} +(-2.86986 + 1.86676i) q^{58} +(-0.205226 + 0.0746962i) q^{59} +(-2.49459 + 0.825318i) q^{60} +(-1.60629 - 9.10973i) q^{61} +(2.37938 - 0.551195i) q^{62} +(-7.60235 - 2.28129i) q^{63} +(-5.96908 - 5.32635i) q^{64} +(-0.221337 + 0.608119i) q^{65} +(-1.32430 - 4.85291i) q^{66} +(-6.09084 + 7.25878i) q^{67} +(1.62410 - 6.55562i) q^{68} +(-8.00729 - 12.7051i) q^{69} +(2.40953 - 1.49967i) q^{70} +(6.49112 - 11.2429i) q^{71} +(-7.07002 + 4.69199i) q^{72} +0.279307 q^{73} +(8.10054 - 3.44562i) q^{74} +(6.05724 + 4.69495i) q^{75} +(-5.29173 + 1.52594i) q^{76} +(2.62213 + 4.75882i) q^{77} +(-0.172560 + 2.08271i) q^{78} +(-5.76075 - 6.86539i) q^{79} +(0.413283 - 3.00578i) q^{80} +(2.91280 + 8.51561i) q^{81} +(16.0142 - 3.70977i) q^{82} +(-1.88526 - 10.6919i) q^{83} +(6.23171 - 6.72055i) q^{84} +(2.40696 - 0.876060i) q^{85} +(9.42368 + 4.79274i) q^{86} +(-4.15442 - 0.567543i) q^{87} +(5.70431 + 1.09555i) q^{88} +(-8.44063 - 4.87320i) q^{89} +(-2.97281 - 1.23232i) q^{90} +(-0.347472 - 2.23039i) q^{91} +(17.2434 - 1.83840i) q^{92} +(2.64656 + 1.39414i) q^{93} +(1.12783 + 1.73386i) q^{94} +(-1.60004 - 1.34259i) q^{95} +(-1.26783 - 9.71559i) q^{96} +(-12.5663 + 10.5444i) q^{97} +(-4.83670 + 8.63750i) q^{98} +(2.65799 - 5.55804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.30138	+	0.553549i	−0.920213	+	0.391418i
$2$	−1.30138	+	0.553549i	−0.920213	+	0.391418i
$3$	−1.64933	−	0.528879i	−0.952241	−	0.305349i
$3$	−1.64933	−	0.528879i	−0.952241	−	0.305349i
$4$	1.38717	−	1.44075i	0.693583	−	0.720376i
$5$	0.746991	+	0.131715i	0.334065	+	0.0589046i	0.338165	−	0.941087i	$-0.390194\pi$
$5$	0.746991	+	0.131715i	0.334065	+	0.0589046i	−0.00409992	+	0.999992i	$0.501305\pi$
$6$	2.43916	−	0.224713i	0.995783	−	0.0917389i
$7$	−2.50378	+	0.855036i	−0.946340	+	0.323173i
$7$	−2.50378	+	0.855036i	−0.946340	+	0.323173i
$8$	−1.00770	+	2.64283i	−0.356276	+	0.934381i
$9$	2.44057	+	1.74459i	0.813525	+	0.581531i
$10$	−1.04503	+	0.242086i	−0.330467	+	0.0765543i
$11$	−0.356610	−	2.02244i	−0.107522	−	0.609787i	−0.990183	−	0.139777i	$-0.955361\pi$
$11$	−0.356610	−	2.02244i	−0.107522	−	0.609787i	0.882661	−	0.470010i	$-0.155750\pi$
$12$	−3.04988	+	1.64263i	−0.880424	+	0.474187i
$13$	−0.148152	+	0.840214i	−0.0410901	+	0.233033i	−0.998436	−	0.0559118i	$-0.982193\pi$
$13$	−0.148152	+	0.840214i	−0.0410901	+	0.233033i	0.957346	+	0.288945i	$0.0933045\pi$
$14$	2.78506	−	2.49869i	0.744338	−	0.667803i
$15$	−1.16237	−	0.612309i	−0.300124	−	0.158098i
$16$	−0.151538	−	3.99713i	−0.0378845	−	0.999282i
$17$	2.92448	−	1.68845i	0.709291	−	0.409509i	−0.101508	−	0.994835i	$-0.532367\pi$
$17$	2.92448	−	1.68845i	0.709291	−	0.409509i	0.810798	+	0.585326i	$0.199033\pi$
$18$	−4.14182	−	0.919395i	−0.976237	−	0.216703i
$19$	−2.38475	−	1.37684i	−0.547100	−	0.315868i	0.200852	−	0.979622i	$-0.435629\pi$
$19$	−2.38475	−	1.37684i	−0.547100	−	0.315868i	−0.747951	+	0.663753i	$0.768962\pi$
$20$	1.22597	−	0.893520i	0.274135	−	0.199797i
$21$	4.58177	−	0.0860394i	0.999824	−	0.0187753i
$22$	1.58360	+	2.43455i	0.337625	+	0.519048i
$23$	6.64204	+	5.57333i	1.38496	+	1.16212i	0.967335	+	0.253500i	$0.0815819\pi$
$23$	6.64204	+	5.57333i	1.38496	+	1.16212i	0.417625	+	0.908619i	$0.362863\pi$
$24$	3.05977	−	3.82594i	0.624572	−	0.780967i
$25$	−4.15782	−	1.51332i	−0.831563	−	0.302664i
$26$	−0.272298	−	1.17544i	−0.0534019	−	0.230524i
$27$	−3.10263	−	4.16817i	−0.597102	−	0.802166i
$28$	−2.24126	+	4.79341i	−0.423559	+	0.905869i
$29$	2.38405	−	0.420373i	0.442708	−	0.0780613i	0.0521490	−	0.998639i	$-0.483393\pi$
$29$	2.38405	−	0.420373i	0.442708	−	0.0780613i	0.390559	+	0.920578i	$0.372282\pi$
$30$	1.85163	+	0.153414i	0.338060	+	0.0280095i
$31$	−1.70079	−	0.299896i	−0.305471	−	0.0538628i	0.0188114	−	0.999823i	$-0.494012\pi$
$31$	−1.70079	−	0.299896i	−0.305471	−	0.0538628i	−0.324283	+	0.945960i	$0.605123\pi$
$32$	2.40982	+	5.11789i	0.425999	+	0.904724i
$33$	−0.481457	+	3.52427i	−0.0838109	+	0.613496i
$34$	−2.87121	+	3.81615i	−0.492409	+	0.654465i
$35$	−1.98292	+	0.308920i	−0.335175	+	0.0522170i
$36$	5.89901	−	1.09622i	0.983168	−	0.182704i
$37$	−6.22459			−1.02332			−0.511658	−	0.859189i	$-0.670969\pi$
$37$	−6.22459			−1.02332			−0.511658	+	0.859189i	$0.670969\pi$
$38$	3.86561	+	0.471707i	0.627085	+	0.0765210i
$39$	0.688724	−	1.30743i	0.110284	−	0.209357i
$40$	−1.10084	+	1.84144i	−0.174058	+	0.291157i
$41$	−11.4470	−	2.01842i	−1.78773	−	0.315224i	−0.820979	−	0.570958i	$-0.806572\pi$
$41$	−11.4470	−	2.01842i	−1.78773	−	0.315224i	−0.966747	+	0.255734i	$0.917683\pi$
$42$	−5.91498	+	2.64820i	−0.912702	+	0.408627i
$43$	−4.80537	−	5.72682i	−0.732812	−	0.873331i	0.262996	−	0.964797i	$-0.415289\pi$
$43$	−4.80537	−	5.72682i	−0.732812	−	0.873331i	−0.995808	+	0.0914655i	$0.970845\pi$
$44$	−3.40851	−	2.29167i	−0.513852	−	0.345482i
$45$	1.59330	+	1.62465i	0.237515	+	0.242189i
$46$	−11.7289	−	3.57631i	−1.72933	−	0.527299i
$47$	−0.253974	−	1.44036i	−0.0370460	−	0.210098i	0.960666	−	0.277706i	$-0.0895743\pi$
$47$	−0.253974	−	1.44036i	−0.0370460	−	0.210098i	−0.997712	+	0.0676084i	$0.978463\pi$
$48$	−1.86406	+	6.67273i	−0.269054	+	0.963125i
$49$	5.53783	−	4.28165i	0.791118	−	0.611664i
$50$	6.24859	−	0.332154i	0.883683	−	0.0469736i
$51$	−5.71642	+	1.23811i	−0.800459	+	0.173370i
$52$	1.00503	+	1.37897i	0.139372	+	0.191228i
$53$	−2.10872	−	1.21747i	−0.289656	−	0.167233i	0.348131	−	0.937446i	$-0.386816\pi$
$53$	−2.10872	−	1.21747i	−0.289656	−	0.167233i	−0.637787	+	0.770213i	$0.720150\pi$
$54$	6.34498	+	3.70691i	0.863443	+	0.504447i
$55$		−	1.55771i		−	0.210042i
$56$	0.263344	−	7.47868i	0.0351908	−	0.999381i
$57$	3.20506	+	3.53210i	0.424521	+	0.467839i
$58$	−2.86986	+	1.86676i	−0.376831	+	0.245117i
$59$	−0.205226	+	0.0746962i	−0.0267182	+	0.00972461i	−0.355345	−	0.934735i	$-0.615636\pi$
$59$	−0.205226	+	0.0746962i	−0.0267182	+	0.00972461i	0.328627	+	0.944460i	$0.393414\pi$
$60$	−2.49459	+	0.825318i	−0.322050	+	0.106548i
$61$	−1.60629	−	9.10973i	−0.205664	−	1.16638i	−0.896391	−	0.443265i	$-0.853820\pi$
$61$	−1.60629	−	9.10973i	−0.205664	−	1.16638i	0.690726	−	0.723116i	$-0.257291\pi$
$62$	2.37938	−	0.551195i	0.302181	−	0.0700018i
$63$	−7.60235	−	2.28129i	−0.957806	−	0.287416i
$64$	−5.96908	−	5.32635i	−0.746135	−	0.665794i
$65$	−0.221337	+	0.608119i	−0.0274535	+	0.0754278i
$66$	−1.32430	−	4.85291i	−0.163010	−	0.597352i
$67$	−6.09084	+	7.25878i	−0.744115	+	0.886802i	−0.996733	−	0.0807644i	$-0.974264\pi$
$67$	−6.09084	+	7.25878i	−0.744115	+	0.886802i	0.252618	+	0.967566i	$0.418708\pi$
$68$	1.62410	−	6.55562i	0.196951	−	0.794985i
$69$	−8.00729	−	12.7051i	−0.963964	−	1.52951i
$70$	2.40953	−	1.49967i	0.287994	−	0.179244i
$71$	6.49112	−	11.2429i	0.770354	−	1.33429i	−0.167015	−	0.985954i	$-0.553413\pi$
$71$	6.49112	−	11.2429i	0.770354	−	1.33429i	0.937369	−	0.348338i	$-0.113254\pi$
$72$	−7.07002	+	4.69199i	−0.833210	+	0.552957i
$73$	0.279307			0.0326904			0.0163452	−	0.999866i	$-0.494797\pi$
$73$	0.279307			0.0326904			0.0163452	+	0.999866i	$0.494797\pi$
$74$	8.10054	−	3.44562i	0.941669	−	0.400545i
$75$	6.05724	+	4.69495i	0.699430	+	0.542126i
$76$	−5.29173	+	1.52594i	−0.607003	+	0.175037i
$77$	2.62213	+	4.75882i	0.298819	+	0.542318i
$78$	−0.172560	+	2.08271i	−0.0195386	+	0.235820i
$79$	−5.76075	−	6.86539i	−0.648135	−	0.772417i	0.337497	−	0.941327i	$-0.390420\pi$
$79$	−5.76075	−	6.86539i	−0.648135	−	0.772417i	−0.985632	+	0.168910i	$0.945975\pi$
$80$	0.413283	−	3.00578i	0.0462065	−	0.336056i
$81$	2.91280	+	8.51561i	0.323644	+	0.946179i
$82$	16.0142	−	3.70977i	1.76847	−	0.409675i
$83$	−1.88526	−	10.6919i	−0.206935	−	1.17358i	−0.894366	−	0.447336i	$-0.852373\pi$
$83$	−1.88526	−	10.6919i	−0.206935	−	1.17358i	0.687432	−	0.726249i	$-0.258738\pi$
$84$	6.23171	−	6.72055i	0.679936	−	0.733272i
$85$	2.40696	−	0.876060i	0.261071	−	0.0950221i
$86$	9.42368	+	4.79274i	1.01618	+	0.516815i
$87$	−4.15442	−	0.567543i	−0.445400	−	0.0608470i
$88$	5.70431	+	1.09555i	0.608081	+	0.116786i
$89$	−8.44063	−	4.87320i	−0.894705	−	0.516558i	−0.0192263	−	0.999815i	$-0.506120\pi$
$89$	−8.44063	−	4.87320i	−0.894705	−	0.516558i	−0.875478	+	0.483257i	$0.839454\pi$
$90$	−2.97281	−	1.23232i	−0.313362	−	0.129898i
$91$	−0.347472	−	2.23039i	−0.0364250	−	0.233808i
$92$	17.2434	−	1.83840i	1.79775	−	0.191666i
$93$	2.64656	+	1.39414i	0.274435	+	0.144566i
$94$	1.12783	+	1.73386i	0.116326	+	0.178835i
$95$	−1.60004	−	1.34259i	−0.164161	−	0.137747i
$96$	−1.26783	−	9.71559i	−0.129398	−	0.991593i
$97$	−12.5663	+	10.5444i	−1.27592	+	1.07062i	−0.282125	+	0.959378i	$0.591039\pi$
$97$	−12.5663	+	10.5444i	−1.27592	+	1.07062i	−0.993793	+	0.111245i	$0.964516\pi$
$98$	−4.83670	+	8.63750i	−0.488581	+	0.872519i
$99$	2.65799	−	5.55804i	0.267138	−	0.558604i
$100$	−7.94790	+	3.89116i	−0.794790	+	0.389116i
$101$	−8.76779	−	10.4490i	−0.872427	−	1.03972i	−0.998860	−	0.0477431i	$-0.984797\pi$
$101$	−8.76779	−	10.4490i	−0.872427	−	1.03972i	0.126432	−	0.991975i	$-0.459647\pi$
$102$	6.75386	−	4.77557i	0.668732	−	0.472852i
$103$	−5.38360	−	0.949273i	−0.530461	−	0.0935347i	−0.0979988	−	0.995187i	$-0.531244\pi$
$103$	−5.38360	−	0.949273i	−0.530461	−	0.0935347i	−0.432463	+	0.901652i	$0.642355\pi$
$104$	−2.07125	−	1.23822i	−0.203103	−	0.121418i
$105$	3.43387	+	0.539216i	0.335112	+	0.0526221i
$106$	3.41818	+	0.417109i	0.332003	+	0.0405132i
$107$	−3.21171	−	5.56284i	−0.310488	−	0.537780i	0.667980	−	0.744179i	$-0.267159\pi$
$107$	−3.21171	−	5.56284i	−0.310488	−	0.537780i	−0.978468	+	0.206399i	$0.933826\pi$
$108$	−10.3092	−	1.31183i	−0.992001	−	0.126231i
$109$	−1.81056	+	3.13598i	−0.173420	+	0.300372i	−0.939613	−	0.342238i	$-0.888815\pi$
$109$	−1.81056	+	3.13598i	−0.173420	+	0.300372i	0.766193	+	0.642610i	$0.222148\pi$
$110$	0.862271	+	2.02717i	0.0822143	+	0.193283i
$111$	10.2664	+	3.29206i	0.974443	+	0.312468i
$112$	3.79711	+	9.87836i	0.358793	+	0.933417i
$113$	−2.94116	+	3.50514i	−0.276681	+	0.329736i	−0.886433	−	0.462856i	$-0.846825\pi$
$113$	−2.94116	+	3.50514i	−0.276681	+	0.329736i	0.609752	+	0.792592i	$0.291269\pi$
$114$	−6.12619	−	2.82244i	−0.573770	−	0.264346i
$115$	4.22745	+	5.03808i	0.394212	+	0.469804i
$116$	2.70143	−	4.01796i	0.250821	−	0.373058i
$117$	−1.82741	+	1.79214i	−0.168944	+	0.165683i
$118$	0.225729	−	0.210811i	0.0207800	−	0.0194067i
$119$	−5.87857	+	6.72804i	−0.538888	+	0.616759i
$120$	2.78955	−	2.45493i	0.254650	−	0.224103i
$121$	6.37354	−	2.31978i	0.579413	−	0.210889i
$122$	7.13307	+	10.9660i	0.645798	+	0.992818i
$123$	17.8124	+	9.38314i	1.60609	+	0.846049i
$124$	−2.79136	+	2.03442i	−0.250671	+	0.182696i
$125$	−6.19099	−	3.57437i	−0.553739	−	0.319701i
$126$	11.1563	−	1.23945i	0.993885	−	0.110419i
$127$	−3.22999	+	1.86483i	−0.286615	+	0.165477i	−0.636414	−	0.771347i	$-0.719583\pi$
$127$	−3.22999	+	1.86483i	−0.286615	+	0.165477i	0.349799	+	0.936825i	$0.386250\pi$
$128$	10.7164	+	3.62742i	0.947207	+	0.320621i
$129$	4.89684	+	11.9869i	0.431143	+	1.05538i
$130$	−0.0485805	−	0.913913i	−0.00426079	−	0.0801554i
$131$	9.73635	+	8.16977i	0.850669	+	0.713796i	0.959937	−	0.280216i	$-0.0904061\pi$
$131$	9.73635	+	8.16977i	0.850669	+	0.713796i	−0.109268	+	0.994012i	$0.534851\pi$
$132$	4.40974	+	5.58240i	0.383818	+	0.485886i
$133$	7.14814	+	1.40825i	0.619822	+	0.122111i
$134$	3.90839	−	12.8180i	0.337634	−	1.10731i
$135$	−1.76863	−	3.52225i	−0.152219	−	0.303147i
$136$	1.51528	+	9.43035i	0.129935	+	0.808646i
$137$	−5.20178	+	14.2918i	−0.444418	+	1.22103i	0.492140	+	0.870516i	$0.336215\pi$
$137$	−5.20178	+	14.2918i	−0.444418	+	1.22103i	−0.936558	+	0.350512i	$0.886007\pi$
$138$	17.4534	+	12.1017i	1.48573	+	1.03016i
$139$	−6.66309	−	18.3067i	−0.565156	−	1.55275i	−0.811975	−	0.583692i	$-0.801608\pi$
$139$	−6.66309	−	18.3067i	−0.565156	−	1.55275i	0.246819	−	0.969062i	$-0.420615\pi$
$140$	−2.30557	+	3.28543i	−0.194856	+	0.277669i
$141$	−0.342889	+	2.50995i	−0.0288765	+	0.211376i
$142$	−2.22387	+	18.2245i	−0.186623	+	1.52936i
$143$	1.75211			0.146519
$144$	6.60352	−	10.0197i	0.550293	−	0.834972i
$145$	1.83624			0.152491
$146$	−0.363483	+	0.154610i	−0.0300821	+	0.0127956i
$147$	−11.3982	+	4.13300i	−0.940105	+	0.340884i
$148$	−8.63454	+	8.96810i	−0.709755	+	0.737173i
$149$	2.92992	+	8.04989i	0.240029	+	0.659473i	0.999955	+	0.00946424i	$0.00301261\pi$
$149$	2.92992	+	8.04989i	0.240029	+	0.659473i	−0.759927	+	0.650009i	$0.774765\pi$
$150$	−10.4816	−	2.75692i	−0.855823	−	0.225101i
$151$	12.0426	−	2.12343i	0.980009	−	0.172802i	0.339377	−	0.940650i	$-0.389784\pi$
$151$	12.0426	−	2.12343i	0.980009	−	0.172802i	0.640632	+	0.767848i	$0.278673\pi$
$152$	6.04186	−	4.91505i	0.490059	−	0.398663i
$153$	10.0831	+	0.981239i	0.815168	+	0.0793285i
$154$	−6.04662	−	4.74154i	−0.487251	−	0.382084i
$155$	−1.23098	−	0.448039i	−0.0988744	−	0.0359873i
$156$	−0.928316	−	2.80591i	−0.0743247	−	0.224653i
$157$	10.7546	−	3.91437i	0.858314	−	0.312401i	0.124888	−	0.992171i	$-0.460143\pi$
$157$	10.7546	−	3.91437i	0.858314	−	0.312401i	0.733425	+	0.679770i	$0.237920\pi$
$158$	11.2972	+	5.74561i	0.898760	+	0.457096i
$159$	2.83408	+	3.12327i	0.224758	+	0.247692i
$160$	1.12601	+	4.14043i	0.0890189	+	0.327329i
$161$	−21.3956	−	8.27521i	−1.68621	−	0.652178i
$162$	−8.50446	−	9.46964i	−0.668173	−	0.744006i
$163$	−7.44598	+	4.29894i	−0.583215	+	0.336719i	−0.762410	−	0.647094i	$-0.775984\pi$
$163$	−7.44598	+	4.29894i	−0.583215	+	0.336719i	0.179195	+	0.983814i	$0.442651\pi$
$164$	−18.7870	+	13.6925i	−1.46702	+	1.06920i
$165$	−0.823842	+	2.56918i	−0.0641360	+	0.200010i
$166$	8.37191	+	12.8706i	0.649787	+	0.998950i
$167$	7.61574	+	6.39037i	0.589324	+	0.494502i	0.887994	−	0.459855i	$-0.152099\pi$
$167$	7.61574	+	6.39037i	0.589324	+	0.494502i	−0.298670	+	0.954356i	$0.596543\pi$
$168$	−4.38966	+	12.1955i	−0.338669	+	0.940905i
$169$	11.5320	+	4.19730i	0.887076	+	0.322869i
$170$	−2.64742	+	2.47245i	−0.203047	+	0.189629i
$171$	−3.41814	−	7.52069i	−0.261392	−	0.575122i
$172$	−14.9168	−	1.02070i	−1.13739	−	0.0778275i
$173$	−2.65093	+	7.28336i	−0.201546	+	0.553744i	−0.998751	−	0.0499654i	$-0.984089\pi$
$173$	−2.65093	+	7.28336i	−0.201546	+	0.553744i	0.797205	+	0.603709i	$0.206311\pi$
$174$	5.72063	−	1.56109i	0.433680	−	0.118346i
$175$	11.7042	+	0.233939i	0.884754	+	0.0176842i
$176$	−8.02990	+	1.73189i	−0.605276	+	0.130546i
$177$	0.377991	−	0.0146588i	0.0284115	−	0.00110182i
$178$	13.6820	+	1.66957i	1.02551	+	0.125139i
$179$	12.4143	+	21.5022i	0.927887	+	1.60715i	0.786851	+	0.617144i	$0.211710\pi$
$179$	12.4143	+	21.5022i	0.927887	+	1.60715i	0.141037	+	0.990004i	$0.454956\pi$
$180$	4.55090	−	0.0418838i	0.339204	−	0.00312184i
$181$	−2.68468	−	4.65001i	−0.199551	−	0.345632i	0.748832	−	0.662760i	$-0.230615\pi$
$181$	−2.68468	−	4.65001i	−0.199551	−	0.345632i	−0.948383	+	0.317128i	$0.897282\pi$
$182$	1.68682	+	2.71023i	0.125035	+	0.200896i
$183$	−2.16864	+	15.8745i	−0.160311	+	1.17347i
$184$	−21.4225	+	11.9375i	−1.57929	+	0.880046i
$185$	−4.64971	−	0.819870i	−0.341854	−	0.0602781i
$186$	−4.21590	−	0.349302i	−0.309124	−	0.0256121i
$187$	−4.45768	−	5.31246i	−0.325978	−	0.388485i
$188$	−2.42751	−	1.63211i	−0.177044	−	0.119034i
$189$	11.3322	+	7.78333i	0.824300	+	0.566154i
$190$	2.82545	+	0.861519i	0.204979	+	0.0625012i
$191$	−10.3625	+	8.69514i	−0.749801	+	0.629158i	−0.935450	−	0.353458i	$-0.885006\pi$
$191$	−10.3625	+	8.69514i	−0.749801	+	0.629158i	0.185649	+	0.982616i	$0.440561\pi$
$192$	7.02799	+	11.9418i	0.507201	+	0.861828i
$193$	1.79357	−	10.1719i	0.129104	−	0.732187i	−0.849681	−	0.527297i	$-0.823205\pi$
$193$	1.79357	−	10.1719i	0.129104	−	0.732187i	0.978785	−	0.204889i	$-0.0656835\pi$
$194$	10.5167	−	20.6783i	0.755055	−	1.48462i
$195$	0.686679	−	0.885927i	0.0491741	−	0.0634426i
$196$	1.51309	−	13.9180i	0.108078	−	0.994142i
$197$	15.6277	−	9.02263i	1.11342	−	0.642836i	0.173710	−	0.984797i	$-0.444424\pi$
$197$	15.6277	−	9.02263i	1.11342	−	0.642836i	0.939714	+	0.341961i	$0.111091\pi$
$198$	−0.382401	+	8.70444i	−0.0271760	+	0.618598i
$199$	−1.94225	+	1.12136i	−0.137683	+	0.0794910i	−0.567259	−	0.823539i	$-0.691996\pi$
$199$	−1.94225	+	1.12136i	−0.137683	+	0.0794910i	0.429577	+	0.903030i	$0.358663\pi$
$200$	8.18928	−	9.46342i	0.579069	−	0.669165i
$201$	13.8848	−	8.75080i	0.979360	−	0.617234i
$202$	17.1943	+	8.74474i	1.20978	+	0.615278i
$203$	−5.60971	+	3.09097i	−0.393725	+	0.216944i
$204$	−6.14581	+	9.95341i	−0.430293	+	0.696878i
$205$	−8.28498	−	3.01549i	−0.578648	−	0.210611i
$206$	7.53156	−	1.74472i	0.524749	−	0.121561i
$207$	6.48719	+	25.1898i	0.450891	+	1.75081i
$208$	3.38089	+	0.464860i	0.234423	+	0.0322322i
$209$	−1.93414	+	5.31400i	−0.133787	+	0.367577i
$210$	−4.76725	+	1.19909i	−0.328971	+	0.0827454i
$211$	12.3882	−	14.7636i	0.852836	−	1.01637i	−0.146793	−	0.989167i	$-0.546895\pi$
$211$	12.3882	−	14.7636i	0.852836	−	1.01637i	0.999630	−	0.0272037i	$-0.00866029\pi$
$212$	−4.67923	+	1.34931i	−0.321371	+	0.0926712i
$213$	−16.6522	+	15.1103i	−1.14099	+	1.03534i
$214$	7.25895	+	5.46152i	0.496212	+	0.373342i
$215$	−2.83526	−	4.91082i	−0.193363	−	0.334915i
$216$	14.1423	−	3.99945i	0.962261	−	0.272128i
$217$	4.51483	−	0.703367i	0.306487	−	0.0477476i
$218$	0.620300	−	5.08332i	0.0420120	−	0.344286i
$219$	−0.460669	−	0.147720i	−0.0311291	−	0.00998196i
$220$	−2.24428	−	2.16081i	−0.151309	−	0.145682i
$221$	0.985390	+	2.70734i	0.0662845	+	0.182115i
$222$	−15.1828	+	1.39875i	−1.01900	+	0.0938779i
$223$	2.32331	−	6.38325i	0.155581	−	0.427454i	−0.837274	−	0.546783i	$-0.815852\pi$
$223$	2.32331	−	6.38325i	0.155581	−	0.427454i	0.992855	+	0.119329i	$0.0380744\pi$
$224$	−10.4096	−	10.7536i	−0.695523	−	0.718504i
$225$	−7.50733	−	10.9471i	−0.500489	−	0.729804i
$226$	1.88729	−	6.18959i	0.125541	−	0.411725i
$227$	−1.73273	−	9.82683i	−0.115006	−	0.652229i	−0.986747	−	0.162264i	$-0.948120\pi$
$227$	−1.73273	−	9.82683i	−0.115006	−	0.652229i	0.871742	−	0.489966i	$-0.162991\pi$
$228$	9.53484	+	0.281915i	0.631460	+	0.0186703i
$229$	−6.15247	+	2.23931i	−0.406566	+	0.147978i	−0.537204	−	0.843452i	$-0.680520\pi$
$229$	−6.15247	+	2.23931i	−0.406566	+	0.147978i	0.130638	+	0.991430i	$0.458297\pi$
$230$	−8.29034	−	4.21634i	−0.546649	−	0.278018i
$231$	−1.80791	−	9.23565i	−0.118952	−	0.607661i
$232$	−1.29144	+	6.72425i	−0.0847870	+	0.441469i
$233$		−	3.75011i		−	0.245678i	−0.992427	−	0.122839i	$-0.960800\pi$
$233$		−	3.75011i		−	0.245678i	0.992427	−	0.122839i	$-0.0391999\pi$
$234$	1.38611	−	3.34381i	0.0906128	−	0.218592i
$235$		−	1.10939i		−	0.0723685i
$236$	−0.177064	+	0.399296i	−0.0115259	+	0.0259920i
$237$	5.87041	+	14.3700i	0.381324	+	0.933434i
$238$	3.92594	−	12.0098i	0.254481	−	0.778480i
$239$	−7.20923	+	2.62395i	−0.466326	+	0.169729i	−0.564488	−	0.825442i	$-0.690926\pi$
$239$	−7.20923	+	2.62395i	−0.466326	+	0.169729i	0.0981611	+	0.995171i	$0.468704\pi$
$240$	−2.27133	+	4.73894i	−0.146614	+	0.305898i
$241$	15.2348	+	5.54500i	0.981357	+	0.357185i	0.782368	−	0.622817i	$-0.214012\pi$
$241$	15.2348	+	5.54500i	0.981357	+	0.357185i	0.198989	+	0.980002i	$0.436234\pi$
$242$	−7.01027	+	6.54698i	−0.450637	+	0.420856i
$243$	−0.300436	−	15.5856i	−0.0192730	−	0.999814i
$244$	−15.3531	−	10.3224i	−0.982879	−	0.660827i
$245$	4.70066	−	2.46894i	0.300314	−	0.157735i
$246$	−28.3747	−	2.35095i	−1.80911	−	0.149891i
$247$	1.51014	−	1.79972i	0.0960882	−	0.114513i
$248$	2.50646	−	4.19270i	0.159160	−	0.266237i
$249$	−2.54528	+	18.6315i	−0.161301	+	1.18072i
$250$	10.0354	+	1.22459i	0.634695	+	0.0774497i
$251$	−11.9570	−	20.7102i	−0.754722	−	1.30722i	−0.945513	−	0.325586i	$-0.894439\pi$
$251$	−11.9570	−	20.7102i	−0.754722	−	1.30722i	0.190791	−	0.981631i	$-0.438895\pi$
$252$	−13.8325	+	7.78857i	−0.871366	+	0.490634i
$253$	8.90309	−	15.4206i	0.559732	−	0.969485i
$254$	3.17116	−	4.21481i	0.198976	−	0.264461i
$255$	−4.43319	+	0.171923i	−0.277617	+	0.0107662i
$256$	−15.9541	+	1.21143i	−0.997130	+	0.0757146i
$257$	−1.98605	−	5.45663i	−0.123887	−	0.340375i	0.862210	−	0.506552i	$-0.169080\pi$
$257$	−1.98605	−	5.45663i	−0.123887	−	0.340375i	−0.986096	+	0.166176i	$0.946858\pi$
$258$	−13.0080	−	12.8888i	−0.809840	−	0.802421i
$259$	15.5850	−	5.32225i	0.968405	−	0.330709i
$260$	0.569117	+	1.16245i	0.0352952	+	0.0720923i
$261$	6.55184	+	3.13325i	0.405549	+	0.193943i
$262$	−17.1930	−	5.24240i	−1.06219	−	0.323877i
$263$	−0.710318	+	0.596028i	−0.0438001	+	0.0367527i	−0.664425	−	0.747355i	$-0.731323\pi$
$263$	−0.710318	+	0.596028i	−0.0438001	+	0.0367527i	0.620625	+	0.784108i	$0.286879\pi$
$264$	−8.82887	−	4.82381i	−0.543379	−	0.296885i
$265$	−1.41484	−	1.18719i	−0.0869129	−	0.0729286i
$266$	−10.0820	+	2.12419i	−0.618165	+	0.130242i
$267$	11.3440	+	12.5016i	0.694244	+	0.765084i
$268$	2.00910	+	18.8445i	0.122725	+	1.15111i
$269$	−15.9416	−	9.20391i	−0.971979	−	0.561172i	−0.0721399	−	0.997395i	$-0.522983\pi$
$269$	−15.9416	−	9.20391i	−0.971979	−	0.561172i	−0.899839	+	0.436222i	$0.856316\pi$
$270$	4.25139	+	3.60476i	0.258732	+	0.219379i
$271$	−21.9954	+	12.6990i	−1.33612	+	0.771411i	−0.986230	−	0.165379i	$-0.947115\pi$
$271$	−21.9954	+	12.6990i	−1.33612	+	0.771411i	−0.349893	+	0.936790i	$0.613782\pi$
$272$	−7.19212	−	11.4337i	−0.436086	−	0.693268i
$273$	−0.606508	+	3.86241i	−0.0367075	+	0.233764i
$274$	−1.14172	−	21.4784i	−0.0689738	−	1.29756i
$275$	−1.57788	+	8.94858i	−0.0951495	+	0.539620i
$276$	−29.4123	−	6.08756i	−1.77041	−	0.366428i
$277$	13.5031	−	11.3305i	0.811325	−	0.680782i	−0.139599	−	0.990208i	$-0.544581\pi$
$277$	13.5031	−	11.3305i	0.811325	−	0.680782i	0.950924	+	0.309426i	$0.100137\pi$
$278$	18.8049	+	20.1356i	1.12784	+	1.20765i
$279$	−3.62771	−	3.69910i	−0.217185	−	0.221460i
$280$	1.18177	−	5.55182i	0.0706241	−	0.331785i
$281$	16.6389	+	19.8295i	0.992596	+	1.18293i	0.983118	+	0.182975i	$0.0585727\pi$
$281$	16.6389	+	19.8295i	0.992596	+	1.18293i	0.00947851	+	0.999955i	$0.496983\pi$
$282$	−0.943153	−	3.45620i	−0.0561639	−	0.205814i
$283$	−3.85840	+	4.59826i	−0.229358	+	0.273338i	−0.868433	−	0.495806i	$-0.834873\pi$
$283$	−3.85840	+	4.59826i	−0.229358	+	0.273338i	0.639075	+	0.769144i	$0.279317\pi$
$284$	−7.19405	−	24.9479i	−0.426888	−	1.48039i
$285$	1.92892	+	3.06060i	0.114260	+	0.181295i
$286$	−2.28016	+	0.969880i	−0.134829	+	0.0573502i
$287$	30.3867	−	4.73395i	1.79367	−	0.279436i
$288$	−3.04729	+	16.6947i	−0.179564	+	0.983746i
$289$	−2.79827	+	4.84675i	−0.164604	+	0.285103i
$290$	−2.38964	+	1.01645i	−0.140324	+	0.0596879i
$291$	26.3027	−	10.7451i	1.54189	−	0.629890i
$292$	0.387445	−	0.402412i	0.0226735	−	0.0235494i
$293$	−6.05224	−	16.6284i	−0.353576	−	0.971441i	−0.981212	−	0.192934i	$-0.938200\pi$
$293$	−6.05224	−	16.6284i	−0.353576	−	0.971441i	0.627636	−	0.778507i	$-0.284023\pi$
$294$	12.5455	−	11.6880i	0.731669	−	0.681661i
$295$	−0.163141	+	0.0287661i	−0.00949842	+	0.00167483i
$296$	6.27252	−	16.4505i	0.364583	−	0.956167i
$297$	−7.32344	+	7.76128i	−0.424949	+	0.450355i
$298$	−8.26895	−	8.85410i	−0.479007	−	0.512904i
$299$	−5.66682	+	4.75503i	−0.327721	+	0.274990i
$300$	15.1667	−	2.21432i	0.875648	−	0.127844i
$301$	16.9282	+	10.2299i	0.975727	+	0.589643i
$302$	−14.4965	+	9.42953i	−0.834179	+	0.542608i
$303$	8.93468	+	21.8710i	0.513284	+	1.25646i
$304$	−5.14202	+	9.74081i	−0.294915	+	0.558674i
$305$		−	7.01646i		−	0.401761i
$306$	−13.6650	+	4.30451i	−0.781178	+	0.246073i
$307$	25.6680	+	14.8194i	1.46495	+	0.845789i	0.999234	−	0.0391450i	$-0.0124634\pi$
$307$	25.6680	+	14.8194i	1.46495	+	0.845789i	0.465716	+	0.884934i	$0.345797\pi$
$308$	10.4936	+	2.82343i	0.597929	+	0.160880i
$309$	8.37727	+	4.41294i	0.476566	+	0.251043i
$310$	1.84998	−	0.0983385i	0.105072	−	0.00558525i
$311$	20.7837	+	17.4396i	1.17853	+	0.988906i	0.999988	+	0.00497470i	$0.00158350\pi$
$311$	20.7837	+	17.4396i	1.17853	+	0.988906i	0.178545	+	0.983932i	$0.442861\pi$
$312$	2.76130	+	3.13768i	0.156328	+	0.177636i
$313$	−4.73490	−	1.72336i	−0.267632	−	0.0974102i	0.204718	−	0.978821i	$-0.434372\pi$
$313$	−4.73490	−	1.72336i	−0.267632	−	0.0974102i	−0.472351	+	0.881411i	$0.656594\pi$
$314$	−11.8290	+	11.0473i	−0.667552	+	0.623435i
$315$	−5.37841	−	2.70545i	−0.303039	−	0.152435i
$316$	−17.8824	−	1.22363i	−1.00597	−	0.0688344i
$317$	−0.246124	+	0.0433983i	−0.0138237	+	0.00243749i	−0.180556	−	0.983565i	$-0.557790\pi$
$317$	−0.246124	+	0.0433983i	−0.0138237	+	0.00243749i	0.166732	+	0.986002i	$0.446679\pi$
$318$	−5.41710	−	2.49575i	−0.303776	−	0.139955i
$319$	−1.70035	−	4.67169i	−0.0952016	−	0.261564i
$320$	−3.75729	−	4.76496i	−0.210039	−	0.266369i
$321$	2.35509	+	10.8736i	0.131448	+	0.606903i
$322$	32.4245	−	1.07435i	1.80695	−	0.0598709i
$323$	−9.29888			−0.517404
$324$	16.3094	+	7.61594i	0.906079	+	0.423108i
$325$	1.88750	−	3.26925i	0.104700	−	0.181345i
$326$	7.31036	−	9.71626i	0.404883	−	0.538134i
$327$	4.64476	−	4.21469i	0.256856	−	0.233073i
$328$	16.8695	−	28.2186i	0.931463	−	1.55811i
$329$	1.86746	+	3.38919i	0.102956	+	0.186852i
$330$	−0.350039	−	3.79951i	−0.0192690	−	0.209156i
$331$	−6.34196	+	1.11826i	−0.348586	+	0.0614650i	−0.345200	−	0.938529i	$-0.612189\pi$
$331$	−6.34196	+	1.11826i	−0.348586	+	0.0614650i	−0.00338577	+	0.999994i	$0.501078\pi$
$332$	−18.0195	−	12.1152i	−0.988949	−	0.664908i
$333$	−15.1916	−	10.8594i	−0.832493	−	0.595090i
$334$	−13.4483	−	4.10059i	−0.735861	−	0.224374i
$335$	−5.50590	+	4.62000i	−0.300819	+	0.252417i
$336$	−1.03822	−	18.3009i	−0.0566397	−	0.998395i
$337$	−2.97411	+	16.8670i	−0.162010	+	0.918805i	0.790084	+	0.612999i	$0.210037\pi$
$337$	−2.97411	+	16.8670i	−0.162010	+	0.918805i	−0.952094	+	0.305806i	$0.901074\pi$
$338$	−17.3309	+	0.921251i	−0.942676	+	0.0501095i
$339$	6.70474	−	4.22561i	0.364151	−	0.229504i
$340$	2.07666	−	4.68307i	0.112623	−	0.253975i
$341$			3.54669i			0.192064i
$342$	8.61137	+	7.89515i	0.465650	+	0.426921i
$343$	−10.2045	+	15.4553i	−0.550993	+	0.834510i
$344$	19.9774	−	6.92886i	1.07711	−	0.373579i
$345$	−4.30793	−	10.5453i	−0.231931	−	0.567738i
$346$	−0.581843	−	10.9458i	−0.0312800	−	0.588451i
$347$	1.72460	−	9.78068i	0.0925813	−	0.525054i	−0.902880	−	0.429892i	$-0.858552\pi$
$347$	1.72460	−	9.78068i	0.0925813	−	0.525054i	0.995462	−	0.0951627i	$-0.0303371\pi$
$348$	−6.58056	+	5.19821i	−0.352755	+	0.278653i
$349$	−1.89212	−	10.7307i	−0.101283	−	0.574403i	−0.992640	−	0.121102i	$-0.961357\pi$
$349$	−1.89212	−	10.7307i	−0.101283	−	0.574403i	0.891357	−	0.453302i	$-0.149754\pi$
$350$	−15.3611	+	6.17441i	−0.821084	+	0.330036i
$351$	3.96182	−	1.98935i	0.211466	−	0.106184i
$352$	9.49124	−	6.69879i	0.505885	−	0.357047i
$353$	5.91913	−	16.2627i	0.315044	−	0.865575i	−0.676575	−	0.736374i	$-0.736537\pi$
$353$	5.91913	−	16.2627i	0.315044	−	0.865575i	0.991618	−	0.129201i	$-0.0412413\pi$
$354$	−0.483794	+	0.228313i	−0.0257134	+	0.0121347i
$355$	6.32967	−	7.54341i	0.335944	−	0.400363i
$356$	−18.7296	+	5.40092i	−0.992669	+	0.286248i
$357$	13.2540	−	7.98771i	0.701477	−	0.422754i
$358$	−28.0582	−	21.1105i	−1.48292	−	1.11573i
$359$	−0.431384	+	0.747179i	−0.0227676	+	0.0394346i	−0.877185	−	0.480153i	$-0.840581\pi$
$359$	−0.431384	+	0.747179i	−0.0227676	+	0.0394346i	0.854417	+	0.519588i	$0.173914\pi$
$360$	−5.89925	+	2.57365i	−0.310918	+	0.135643i
$361$	−5.70864	−	9.88765i	−0.300455	−	0.520403i
$362$	6.06779	+	4.56531i	0.318916	+	0.239947i
$363$	−11.7390	+	0.455247i	−0.616135	+	0.0238942i
$364$	−3.69544	−	2.59329i	−0.193694	−	0.135926i
$365$	0.208640	+	0.0367888i	0.0109207	+	0.00192561i
$366$	−5.96508	−	21.8591i	−0.311800	−	1.14260i
$367$	−8.08112	+	1.42492i	−0.421831	+	0.0743802i	−0.380535	−	0.924767i	$-0.624260\pi$
$367$	−8.08112	+	1.42492i	−0.421831	+	0.0743802i	−0.0412966	+	0.999147i	$0.513149\pi$
$368$	21.2708	−	27.3936i	1.10882	−	1.42799i
$369$	−24.4160	−	24.8965i	−1.27105	−	1.29606i
$370$	6.50487	−	1.50689i	0.338172	−	0.0783392i
$371$	6.32076	+	1.24525i	0.328158	+	0.0646500i
$372$	5.67983	−	1.87913i	0.294485	−	0.0974284i
$373$	5.36729	−	30.4394i	0.277908	−	1.57609i	−0.451663	−	0.892189i	$-0.649169\pi$
$373$	5.36729	−	30.4394i	0.277908	−	1.57609i	0.729571	−	0.683905i	$-0.239720\pi$
$374$	8.74183	+	4.44597i	0.452029	+	0.229895i
$375$	8.32057	+	9.16960i	0.429673	+	0.473516i
$376$	4.06255	+	0.780240i	0.209510	+	0.0402378i
$377$			2.06539i			0.106373i
$378$	−19.0560	−	3.85609i	−0.980134	−	0.198336i
$379$			26.3070i			1.35130i	0.737223	+	0.675650i	$0.236137\pi$
$379$			26.3070i			1.35130i	−0.737223	+	0.675650i	$0.763863\pi$
$380$	−4.15387	+	0.442862i	−0.213089	+	0.0227184i
$381$	6.31358	−	1.36745i	0.323455	−	0.0700567i
$382$	8.67229	−	17.0518i	0.443713	−	0.872445i
$383$	−5.58692	+	31.6850i	−0.285478	+	1.61903i	0.418093	+	0.908404i	$0.362699\pi$
$383$	−5.58692	+	31.6850i	−0.285478	+	1.61903i	−0.703571	+	0.710625i	$0.748412\pi$
$384$	−15.7565	−	11.6505i	−0.804068	−	0.594537i
$385$	1.33190	+	3.90017i	0.0678800	+	0.198771i
$386$	3.29651	+	14.2303i	0.167788	+	0.724301i
$387$	−1.73690	−	22.3601i	−0.0882917	−	1.13663i
$388$	−2.23971	+	32.7318i	−0.113704	+	1.66171i
$389$	20.5382	−	3.62145i	1.04133	−	0.183615i	0.373271	−	0.927722i	$-0.378236\pi$
$389$	20.5382	−	3.62145i	1.04133	−	0.183615i	0.668060	+	0.744108i	$0.267125\pi$
$390$	−0.403224	+	1.53304i	−0.0204180	+	0.0776283i
$391$	28.8348	+	5.08435i	1.45824	+	0.257127i
$392$	5.73519	+	18.9501i	0.289671	+	0.957126i
$393$	−11.7376	−	18.6240i	−0.592085	−	0.939456i
$394$	−15.3430	+	20.3925i	−0.772970	+	1.02736i
$395$	−3.39895	−	5.88716i	−0.171020	−	0.296215i
$396$	−4.32069	−	11.5394i	−0.217123	−	0.579879i
$397$	11.8721	−	20.5631i	0.595844	−	1.03203i	−0.397583	−	0.917566i	$-0.630151\pi$
$397$	11.8721	−	20.5631i	0.595844	−	1.03203i	0.993427	−	0.114467i	$-0.0365159\pi$
$398$	1.90687	−	2.53444i	0.0955830	−	0.127040i
$399$	−11.0448	−	6.10317i	−0.552934	−	0.305541i
$400$	−5.41887	+	16.8486i	−0.270944	+	0.842432i
$401$	6.60013	−	7.86573i	0.329595	−	0.392796i	−0.575643	−	0.817701i	$-0.695248\pi$
$401$	6.60013	−	7.86573i	0.329595	−	0.392796i	0.905238	+	0.424905i	$0.139693\pi$
$402$	−13.2254	+	19.0740i	−0.659623	+	0.951326i
$403$	0.503953	−	1.38460i	0.0251037	−	0.0689718i
$404$	−27.2169	−	1.86235i	−1.35409	−	0.0926552i
$405$	1.05420	+	6.74474i	0.0523838	+	0.335149i
$406$	5.58935	−	7.12778i	0.277395	−	0.353746i
$407$	2.21975	+	12.5888i	0.110029	+	0.624005i
$408$	2.48831	−	16.3552i	0.123190	−	0.809701i
$409$	4.42766	−	25.1105i	0.218934	−	1.24164i	−0.655014	−	0.755616i	$-0.727337\pi$
$409$	4.42766	−	25.1105i	0.218934	−	1.24164i	0.873948	−	0.486019i	$-0.161551\pi$
$410$	12.4511	−	0.661858i	0.614916	−	0.0326869i
$411$	16.1381	−	20.8207i	0.796032	−	1.02701i
$412$	−8.83561	+	6.43963i	−0.435299	+	0.317258i
$413$	0.449973	−	0.362498i	0.0221417	−	0.0178374i
$414$	−22.3861	−	29.1904i	−1.10021	−	1.43463i
$415$		−	8.23505i		−	0.404243i
$416$	−4.65714	+	1.26653i	−0.228335	+	0.0620969i
$417$	1.30760	+	33.7177i	0.0640335	+	1.65116i
$418$	−0.424517	−	7.98616i	−0.0207638	−	0.390616i
$419$	−2.88619	+	16.3684i	−0.141000	+	0.799650i	0.829493	+	0.558518i	$0.188630\pi$
$419$	−2.88619	+	16.3684i	−0.141000	+	0.799650i	−0.970492	+	0.241132i	$0.922481\pi$
$420$	5.54023	−	4.19938i	0.270336	−	0.204909i
$421$	−3.06082	+	2.56833i	−0.149175	+	0.125173i	−0.714321	−	0.699818i	$-0.753264\pi$
$421$	−3.06082	+	2.56833i	−0.149175	+	0.125173i	0.565146	+	0.824991i	$0.308820\pi$
$422$	−7.94928	+	26.0705i	−0.386965	+	1.26909i
$423$	1.89300	−	3.95839i	0.0920407	−	0.192463i
$424$	5.34253	−	4.34615i	0.259456	−	0.211068i
$425$	−14.7146	+	2.59458i	−0.713764	+	0.125856i
$426$	13.3064	−	28.8820i	0.644699	−	1.39934i
$427$	11.8109	+	21.4353i	0.571572	+	1.03733i
$428$	−12.4699	−	3.08931i	−0.602753	−	0.149327i
$429$	−2.88981	−	0.926655i	−0.139521	−	0.0447393i
$430$	6.40813	+	4.82137i	0.309027	+	0.232507i
$431$	0.615495	−	1.06607i	0.0296474	−	0.0513508i	−0.850821	−	0.525456i	$-0.823895\pi$
$431$	0.615495	−	1.06607i	0.0296474	−	0.0513508i	0.880468	+	0.474105i	$0.157228\pi$
$432$	−16.1906	+	13.0333i	−0.778969	+	0.627063i
$433$	−24.5789			−1.18119			−0.590594	−	0.806969i	$-0.701107\pi$
$433$	−24.5789			−1.18119			−0.590594	+	0.806969i	$0.701107\pi$
$434$	−5.48615	+	3.41453i	−0.263344	+	0.163902i
$435$	−3.02856	−	0.971147i	−0.145208	−	0.0465630i
$436$	2.00662	+	6.95869i	0.0960998	+	0.333261i
$437$	−8.16604	−	22.4360i	−0.390635	−	1.07326i
$438$	0.681274	−	0.0627640i	0.0325525	−	0.00299898i
$439$	−24.0344	+	4.23792i	−1.14710	+	0.202265i	−0.714709	−	0.699422i	$-0.753441\pi$
$439$	−24.0344	+	4.23792i	−1.14710	+	0.202265i	−0.432391	+	0.901686i	$0.642330\pi$
$440$	4.11677	+	1.56971i	0.196259	+	0.0748328i
$441$	20.9852	−	0.788425i	0.999295	−	0.0375440i
$442$	−2.78101	−	2.97781i	−0.132279	−	0.141640i
$443$	−24.9431	−	9.07856i	−1.18508	−	0.431336i	−0.327090	−	0.944993i	$-0.606068\pi$
$443$	−24.9431	−	9.07856i	−1.18508	−	0.431336i	−0.857995	+	0.513658i	$0.828290\pi$
$444$	18.9842	−	10.2247i	0.900952	−	0.485243i
$445$	−5.66320	−	4.75199i	−0.268462	−	0.225266i
$446$	0.509936	+	9.59309i	0.0241462	+	0.454246i
$447$	−0.574984	−	14.8265i	−0.0271958	−	0.701269i
$448$	19.4995	+	8.23223i	0.921265	+	0.388936i
$449$	−16.5254	−	9.54097i	−0.779884	−	0.450266i	0.0565054	−	0.998402i	$-0.482004\pi$
$449$	−16.5254	−	9.54097i	−0.779884	−	0.450266i	−0.836389	+	0.548136i	$0.815338\pi$
$450$	15.8296	+	10.0906i	0.746215	+	0.475675i
$451$			23.8707i			1.12403i
$452$	0.970159	+	9.09970i	0.0456325	+	0.428014i
$453$	−20.9852	−	2.86683i	−0.985969	−	0.134695i
$454$	7.69457	+	11.8293i	0.361124	+	0.555175i
$455$	0.0342158	−	1.71185i	0.00160406	−	0.0802526i
$456$	−12.5645	+	4.91113i	−0.588386	+	0.229985i
$457$	−26.0725	+	21.8775i	−1.21962	+	1.02338i	−0.220778	+	0.975324i	$0.570860\pi$
$457$	−26.0725	+	21.8775i	−1.21962	+	1.02338i	−0.998844	+	0.0480603i	$0.984696\pi$
$458$	6.76711	−	6.31989i	0.316206	−	0.295309i
$459$	−16.1113	−	6.95111i	−0.752013	−	0.324450i
$460$	13.1228	+	0.897944i	0.611854	+	0.0418669i
$461$	−8.65407	+	1.52595i	−0.403060	+	0.0710704i	−0.371503	−	0.928432i	$-0.621158\pi$
$461$	−8.65407	+	1.52595i	−0.403060	+	0.0710704i	−0.0315567	+	0.999502i	$0.510046\pi$
$462$	7.46516	+	11.0183i	0.347311	+	0.512618i
$463$	−8.41807	−	23.1285i	−0.391221	−	1.07487i	−0.966445	−	0.256875i	$-0.917307\pi$
$463$	−8.41807	−	23.1285i	−0.391221	−	1.07487i	0.575224	−	0.817996i	$-0.304915\pi$
$464$	−2.04156	−	9.46567i	−0.0947770	−	0.439433i
$465$	1.79333	+	1.39000i	0.0831635	+	0.0644598i
$466$	2.07587	+	4.88031i	0.0961629	+	0.226076i
$467$	−9.18248	+	15.9045i	−0.424914	+	0.735973i	−0.996412	−	0.0846302i	$-0.973029\pi$
$467$	−9.18248	+	15.9045i	−0.424914	+	0.735973i	0.571498	+	0.820603i	$0.306362\pi$
$468$	0.0471108	+	5.11884i	0.00217770	+	0.236618i
$469$	9.04361	−	23.3823i	0.417595	−	1.07969i
$470$	0.614101	+	1.44373i	0.0283264	+	0.0665945i
$471$	−19.8082	+	0.768177i	−0.912712	+	0.0353957i
$472$	0.00939704	−	0.617648i	0.000432534	−	0.0284296i
$473$	−9.86848	+	11.7608i	−0.453753	+	0.540762i
$474$	−15.5941	−	15.4513i	−0.716262	−	0.709700i
$475$	7.83176	+	9.33353i	0.359346	+	0.428252i
$476$	1.53889	+	17.8025i	0.0705351	+	0.815976i
$477$	−3.02250	−	6.65019i	−0.138391	−	0.304491i
$478$	7.92945	−	7.40541i	0.362685	−	0.338716i
$479$	17.4793	−	14.6669i	0.798652	−	0.670148i	−0.149219	−	0.988804i	$-0.547676\pi$
$479$	17.4793	−	14.6669i	0.798652	−	0.670148i	0.947870	+	0.318656i	$0.103231\pi$
$480$	0.332625	−	7.42445i	0.0151822	−	0.338878i
$481$	0.922188	−	5.22999i	0.0420481	−	0.238467i
$482$	−22.8956	+	1.21705i	−1.04287	+	0.0554352i
$483$	30.9118	+	24.9642i	1.40654	+	1.13591i
$484$	5.49894	−	12.4006i	0.249952	−	0.563665i
$485$	−10.7758	+	6.22141i	−0.489304	+	0.282500i
$486$	9.01836	+	20.1164i	0.409081	+	0.912498i
$487$	−24.5809	−	14.1918i	−1.11387	−	0.643091i	−0.174038	−	0.984739i	$-0.555681\pi$
$487$	−24.5809	−	14.1918i	−1.11387	−	0.643091i	−0.939828	+	0.341648i	$0.889015\pi$
$488$	25.6941	+	4.93472i	1.16312	+	0.223384i
$489$	14.5545	−	3.15234i	0.658177	−	0.142554i
$490$	−4.75066	+	5.81507i	−0.214613	+	0.262698i
$491$	5.59312	+	4.69318i	0.252414	+	0.211800i	0.760211	−	0.649676i	$-0.225096\pi$
$491$	5.59312	+	4.69318i	0.252414	+	0.211800i	−0.507797	+	0.861477i	$0.669540\pi$
$492$	38.2276	−	12.6473i	1.72343	−	0.570186i
$493$	6.26234	−	5.25473i	0.282042	−	0.236661i
$494$	−0.969034	+	3.17805i	−0.0435989	+	0.142987i
$495$	2.71757	−	3.80171i	0.122146	−	0.170874i
$496$	−0.940986	+	6.84373i	−0.0422515	+	0.307293i
$497$	−6.63920	+	33.7000i	−0.297809	+	1.51165i
$498$	−7.00107	−	25.6555i	−0.313725	−	1.14965i
$499$	9.66179	+	26.5456i	0.432521	+	1.18834i	0.944260	+	0.329201i	$0.106779\pi$
$499$	9.66179	+	26.5456i	0.432521	+	1.18834i	−0.511739	+	0.859141i	$0.670998\pi$
$500$	−13.7377	+	3.96144i	−0.614370	+	0.177161i
$501$	−9.18114	−	14.5676i	−0.410183	−	0.650834i
$502$	27.0247	+	20.3330i	1.20617	+	0.907505i
$503$	−11.1818	+	19.3674i	−0.498571	+	0.863551i	−0.999999	−	0.00164874i	$-0.999475\pi$
$503$	−11.1818	+	19.3674i	−0.498571	+	0.863551i	0.501427	+	0.865200i	$0.332809\pi$
$504$	13.6900	−	17.7928i	0.609799	−	0.792556i
$505$	−5.17317	−	8.96019i	−0.230203	−	0.398723i
$506$	−3.05022	+	24.9963i	−0.135599	+	1.11122i
$507$	−16.8002	−	13.0218i	−0.746123	−	0.578317i
$508$	−1.79377	+	7.24045i	−0.0795855	+	0.321243i
$509$	0.407759	−	0.485948i	0.0180736	−	0.0215393i	−0.756932	−	0.653494i	$-0.773303\pi$
$509$	0.407759	−	0.485948i	0.0180736	−	0.0215393i	0.775006	+	0.631954i	$0.217747\pi$
$510$	5.67409	−	2.67773i	0.251253	−	0.118572i
$511$	−0.699322	+	0.238817i	−0.0309362	+	0.0105647i
$512$	20.0917	−	10.4079i	0.887935	−	0.459968i
$513$	1.66011	+	14.2119i	0.0732955	+	0.627470i
$514$	5.60512	+	6.00176i	0.247231	+	0.264726i
$515$	−3.89647	−	1.41820i	−0.171699	−	0.0624933i
$516$	24.0628	+	9.57264i	1.05931	+	0.421412i
$517$	−2.82247	+	1.02729i	−0.124132	+	0.0451803i
$518$	−17.3358	+	15.5533i	−0.761693	+	0.683374i
$519$	8.22427	−	10.6106i	0.361005	−	0.465755i
$520$	−1.38411	−	1.19776i	−0.0606973	−	0.0525251i
$521$			36.8329i			1.61368i	0.590770	+	0.806840i	$0.298824\pi$
$521$			36.8329i			1.61368i	−0.590770	+	0.806840i	$0.701176\pi$
$522$	−10.2608	−	0.450775i	−0.449104	−	0.0197299i
$523$		−	0.688353i		−	0.0300996i	−0.999887	−	0.0150498i	$-0.995209\pi$
$523$		−	0.688353i		−	0.0300996i	0.999887	−	0.0150498i	$-0.00479067\pi$
$524$	25.2766	−	2.69485i	1.10421	−	0.117725i
$525$	−19.1804	−	6.57595i	−0.837099	−	0.286998i
$526$	0.594462	−	1.16885i	0.0259198	−	0.0509644i
$527$	−5.48029	+	1.99466i	−0.238725	+	0.0868889i
$528$	14.1599	+	1.39038i	0.616231	+	0.0605087i
$529$	9.06073	+	51.3860i	0.393945	+	2.23417i
$530$	2.49841	+	0.761801i	0.108524	+	0.0330905i
$531$	−0.631184	−	0.175734i	−0.0273910	−	0.00762621i
$532$	11.9446	−	8.34523i	0.517864	−	0.361812i
$533$	3.39181	−	9.31892i	0.146916	−	0.403647i
$534$	−21.6831	−	9.98979i	−0.938320	−	0.432301i
$535$	−1.66641	−	4.57842i	−0.0720452	−	0.197943i
$536$	−13.0460	−	23.4117i	−0.563501	−	1.01123i
$537$	−9.10319	−	42.0298i	−0.392832	−	1.81372i
$538$	25.8409	+	3.15328i	1.11408	+	0.135947i
$539$	−10.6342	−	9.67302i	−0.458047	−	0.416646i
$540$	−7.52808	−	2.33779i	−0.323957	−	0.100603i
$541$	3.17078	+	5.49194i	0.136322	+	0.236117i	0.926102	−	0.377274i	$-0.123138\pi$
$541$	3.17078	+	5.49194i	0.136322	+	0.236117i	−0.789780	+	0.613391i	$0.789805\pi$
$542$	21.5947	−	28.7017i	0.927573	−	1.23285i
$543$	1.96863	+	9.08926i	0.0844822	+	0.390058i
$544$	15.6888	+	10.8983i	0.672650	+	0.467261i
$545$	−1.76552	+	2.10407i	−0.0756267	+	0.0901284i
$546$	−1.34874	−	5.36219i	−0.0577207	−	0.229480i
$547$	5.53907	−	15.2185i	0.236833	−	0.650694i	−0.763157	−	0.646214i	$-0.776351\pi$
$547$	5.53907	−	15.2185i	0.236833	−	0.650694i	0.999990	−	0.00448083i	$-0.00142630\pi$
$548$	13.3752	+	27.3195i	0.571359	+	1.16703i
$549$	11.9725	−	25.0353i	0.510973	−	1.06848i
$550$	−2.90007	−	12.5189i	−0.123659	−	0.533808i
$551$	−6.26416	−	2.27997i	−0.266862	−	0.0971300i
$552$	41.6463	−	8.35897i	1.77258	−	0.355781i
$553$	20.2938	+	12.2638i	0.862980	+	0.521509i
$554$	−11.3007	+	22.2199i	−0.480121	+	0.944032i
$555$	7.23530	+	3.81137i	0.307121	+	0.161784i
$556$	−35.6182	−	15.7946i	−1.51055	−	0.669839i
$557$	9.55173	−	5.51470i	0.404720	−	0.233665i	−0.283799	−	0.958884i	$-0.591595\pi$
$557$	9.55173	−	5.51470i	0.404720	−	0.233665i	0.688519	+	0.725219i	$0.258261\pi$
$558$	6.76866	+	2.80581i	0.286540	+	0.118780i
$559$	5.52368	−	3.18910i	0.233627	−	0.134884i
$560$	1.53528	+	7.87918i	0.0648775	+	0.332956i
$561$	4.54253	+	11.1196i	0.191786	+	0.469468i
$562$	−32.6302	−	16.5952i	−1.37642	−	0.700027i
$563$	6.26545	−	35.5331i	0.264057	−	1.49754i	−0.507650	−	0.861563i	$-0.669486\pi$
$563$	6.26545	−	35.5331i	0.264057	−	1.49754i	0.771707	−	0.635978i	$-0.219403\pi$
$564$	3.14057	+	3.97574i	0.132242	+	0.167409i
$565$	−2.65870	+	2.23091i	−0.111852	+	0.0938553i
$566$	2.47587	−	8.11989i	0.104069	−	0.341305i
$567$	−14.5742	−	18.8307i	−0.612057	−	0.790813i
$568$	23.1721	+	28.4844i	0.972279	+	1.19518i
$569$	−6.91908	−	8.24584i	−0.290063	−	0.345684i	0.601259	−	0.799054i	$-0.294666\pi$
$569$	−6.91908	−	8.24584i	−0.290063	−	0.345684i	−0.891322	+	0.453370i	$0.850221\pi$
$570$	−4.20445	−	2.91525i	−0.176105	−	0.122106i
$571$	15.8842	+	2.80082i	0.664735	+	0.117211i	0.495827	−	0.868421i	$-0.334865\pi$
$571$	15.8842	+	2.80082i	0.664735	+	0.117211i	0.168908	+	0.985632i	$0.445976\pi$
$572$	2.43047	−	2.52436i	0.101623	−	0.105549i
$573$	21.6898	−	8.86065i	0.906104	−	0.370159i
$574$	−36.9241	+	22.9812i	−1.54118	+	0.959216i
$575$	−19.1821	−	33.2244i	−0.799950	−	1.38555i
$576$	−5.27567	−	23.4130i	−0.219820	−	0.975541i
$577$	16.0234	+	27.7533i	0.667061	+	1.15538i	0.978722	+	0.205190i	$0.0657814\pi$
$577$	16.0234	+	27.7533i	0.667061	+	1.15538i	−0.311661	+	0.950193i	$0.600885\pi$
$578$	0.958695	−	7.85644i	0.0398764	−	0.326785i
$579$	−8.33788	+	15.8282i	−0.346511	+	0.657796i
$580$	2.54717	−	2.64556i	0.105765	−	0.109851i
$581$	13.8622	+	25.1581i	0.575102	+	1.04373i
$582$	−28.2818	+	28.5433i	−1.17232	+	1.18316i
$583$	−1.71027	+	4.69892i	−0.0708321	+	0.194609i
$584$	−0.281457	+	0.738160i	−0.0116468	+	0.0305453i
$585$	−1.60111	+	1.09802i	−0.0661977	+	0.0453973i
$586$	17.0809	+	18.2896i	0.705605	+	0.755537i
$587$	−23.6895	−	8.62226i	−0.977769	−	0.355879i	−0.196796	−	0.980444i	$-0.563054\pi$
$587$	−23.6895	−	8.62226i	−0.977769	−	0.355879i	−0.780972	+	0.624566i	$0.785276\pi$
$588$	−9.85653	+	22.1551i	−0.406476	+	0.913661i
$589$	3.64306	+	3.05689i	0.150110	+	0.125957i
$590$	0.196384	−	0.127742i	0.00808501	−	0.00525905i
$591$	−30.5470	+	6.61615i	−1.25654	+	0.272152i
$592$	0.943262	+	24.8805i	0.0387678	+	1.02258i
$593$	22.1444	−	12.7851i	0.909360	−	0.525019i	0.0291351	−	0.999575i	$-0.490725\pi$
$593$	22.1444	−	12.7851i	0.909360	−	0.525019i	0.880225	+	0.474556i	$0.157391\pi$
$594$	5.23430	−	14.1542i	0.214766	−	0.580756i
$595$	−5.27742	+	4.25150i	−0.216353	+	0.174294i
$596$	15.6622	+	6.94525i	0.641549	+	0.284489i
$597$	3.79648	−	0.822274i	0.155379	−	0.0336534i
$598$	4.74253	−	9.32495i	0.193937	−	0.381326i
$599$	4.19482	−	1.52679i	0.171396	−	0.0623829i	−0.254897	−	0.966968i	$-0.582042\pi$
$599$	4.19482	−	1.52679i	0.171396	−	0.0623829i	0.426293	+	0.904585i	$0.359819\pi$
$600$	−18.5118	+	11.2772i	−0.755742	+	0.460388i
$601$	6.26923	+	2.28181i	0.255727	+	0.0930771i	0.466703	−	0.884414i	$-0.345442\pi$
$601$	6.26923	+	2.28181i	0.255727	+	0.0930771i	−0.210975	+	0.977491i	$0.567664\pi$
$602$	−27.6928	−	3.94238i	−1.12867	−	0.160680i
$603$	−27.5288	+	7.08956i	−1.12106	+	0.288709i
$604$	13.6457	−	20.2959i	0.555235	−	0.825828i
$605$	5.06653	−	0.893366i	0.205984	−	0.0363205i
$606$	−23.7341	−	23.5166i	−0.964131	−	0.955298i
$607$	1.92422	+	5.28676i	0.0781018	+	0.214583i	0.972598	−	0.232492i	$-0.0746879\pi$
$607$	1.92422	+	5.28676i	0.0781018	+	0.214583i	−0.894496	+	0.447075i	$0.852466\pi$
$608$	1.29969	−	15.5228i	0.0527093	−	0.629534i
$609$	10.8870	−	2.13117i	0.441164	−	0.0863595i
$610$	3.88396	+	9.13106i	0.157257	+	0.369706i
$611$	1.24784			0.0504821
$612$	15.4006	−	13.1661i	0.622533	−	0.532207i
$613$	−47.5439			−1.92028			−0.960140	−	0.279518i	$-0.909825\pi$
$613$	−47.5439			−1.92028			−0.960140	+	0.279518i	$0.909825\pi$
$614$	−41.6070	−	5.07717i	−1.67912	−	0.204898i
$615$	12.0698	+	9.35528i	0.486702	+	0.377241i
$616$	−15.2191	+	2.13438i	−0.613193	+	0.0859965i
$617$	12.2816	+	33.7434i	0.494439	+	1.35846i	0.896580	+	0.442881i	$0.146044\pi$
$617$	12.2816	+	33.7434i	0.494439	+	1.35846i	−0.402142	+	0.915577i	$0.631734\pi$
$618$	−13.3448	−	1.10566i	−0.536805	−	0.0444763i
$619$	−6.23930	+	17.1423i	−0.250779	+	0.689008i	0.748876	+	0.662711i	$0.230594\pi$
$619$	−6.23930	+	17.1423i	−0.250779	+	0.689008i	−0.999654	+	0.0262978i	$0.991628\pi$
$620$	−2.35308	+	1.15203i	−0.0945020	+	0.0462666i
$621$	2.62283	−	44.9772i	0.105250	−	1.80487i
$622$	−36.7010	−	11.1907i	−1.47158	−	0.448705i
$623$	25.3002	+	4.98437i	1.01363	+	0.199695i
$624$	−5.33035	−	2.55479i	−0.213385	−	0.102273i
$625$	12.7936	+	10.7351i	0.511744	+	0.429404i
$626$	7.11586	−	0.378255i	0.284407	−	0.0151181i
$627$	6.00050	−	7.74161i	0.239637	−	0.309170i
$628$	9.27884	−	20.9247i	0.370266	−	0.834985i
$629$	−18.2037	+	10.5099i	−0.725829	+	0.419057i
$630$	8.49694	+	0.543596i	0.338526	+	0.0216574i
$631$	19.9563	+	11.5218i	0.794448	+	0.458675i	0.841526	−	0.540216i	$-0.181658\pi$
$631$	19.9563	+	11.5218i	0.794448	+	0.458675i	−0.0470779	+	0.998891i	$0.514991\pi$
$632$	23.9492	−	8.30641i	0.952646	−	0.330411i
$633$	−28.2403	+	17.7983i	−1.12245	+	0.707417i
$634$	0.296277	−	0.192719i	0.0117667	−	0.00765387i
$635$	−2.65840	+	0.967578i	−0.105495	+	0.0383972i
$636$	8.43121	+	0.249285i	0.334319	+	0.00988477i
$637$	2.77706	+	5.28729i	0.110031	+	0.209490i
$638$	4.79881	+	5.13840i	0.189987	+	0.203431i
$639$	35.4564	−	16.1149i	1.40263	−	0.637495i
$640$	7.52730	+	4.12116i	0.297542	+	0.162903i
$641$	20.1490	+	24.0126i	0.795837	+	0.948441i	0.999532	−	0.0305929i	$-0.00973954\pi$
$641$	20.1490	+	24.0126i	0.795837	+	0.948441i	−0.203695	+	0.979034i	$0.565295\pi$
$642$	−9.08392	−	12.8470i	−0.358514	−	0.507029i
$643$	13.8340	−	16.4867i	0.545559	−	0.650172i	−0.420865	−	0.907123i	$-0.638273\pi$
$643$	13.8340	−	16.4867i	0.545559	−	0.650172i	0.966424	+	0.256951i	$0.0827179\pi$
$644$	−41.6018	+	19.3467i	−1.63934	+	0.762366i
$645$	2.07905	+	9.59907i	0.0818626	+	0.377963i
$646$	12.1014	−	5.14739i	0.476122	−	0.202521i
$647$	14.0181	−	24.2800i	0.551107	−	0.954545i	−0.447088	−	0.894490i	$-0.647539\pi$
$647$	14.0181	−	24.2800i	0.551107	−	0.954545i	0.998195	−	0.0600549i	$-0.0191276\pi$
$648$	−25.4405	−	0.883148i	−0.999398	−	0.0346933i
$649$	0.224254	+	0.388419i	0.00880273	+	0.0152468i
$650$	−0.646663	+	5.29936i	−0.0253642	+	0.207858i
$651$	−7.81844	−	1.22772i	−0.306429	−	0.0481180i
$652$	−4.13511	+	16.6912i	−0.161943	+	0.653677i
$653$	22.7201	+	4.00617i	0.889108	+	0.156774i	0.599503	−	0.800373i	$-0.295365\pi$
$653$	22.7201	+	4.00617i	0.889108	+	0.156774i	0.289605	+	0.957146i	$0.406476\pi$
$654$	−3.71154	+	8.05600i	−0.145133	+	0.315015i
$655$	6.19689	+	7.38517i	0.242133	+	0.288562i
$656$	−6.33323	+	46.0611i	−0.247271	+	1.79838i
$657$	0.681669	+	0.487276i	0.0265944	+	0.0190105i
$658$	−4.30635	−	3.37688i	−0.167879	−	0.131645i
$659$	−11.4794	+	9.63233i	−0.447173	+	0.375222i	−0.838385	−	0.545078i	$-0.816500\pi$
$659$	−11.4794	+	9.63233i	−0.447173	+	0.375222i	0.391213	+	0.920300i	$0.372056\pi$
$660$	2.55875	+	4.75083i	0.0995992	+	0.184926i
$661$	−18.9263	−	15.8811i	−0.736149	−	0.617703i	0.195651	−	0.980674i	$-0.437318\pi$
$661$	−18.9263	−	15.8811i	−0.736149	−	0.617703i	−0.931800	+	0.362971i	$0.881762\pi$
$662$	7.63427	−	4.96586i	0.296714	−	0.193004i
$663$	−0.193378	−	4.98644i	−0.00751020	−	0.193657i
$664$	30.1565	+	5.79176i	1.17030	+	0.224764i
$665$	5.15411	+	1.99346i	0.199868	+	0.0773032i
$666$	25.7812	+	5.72286i	0.999000	+	0.221756i
$667$	18.1779	+	10.4950i	0.703849	+	0.406368i
$668$	19.7712	−	2.10790i	0.764973	−	0.0815571i
$669$	−7.20788	+	9.29933i	−0.278673	+	0.359533i
$670$	4.60785	−	9.06014i	0.178017	−	0.350024i
$671$	−17.8510	+	6.49724i	−0.689131	+	0.250823i
$672$	11.4816	+	23.2416i	0.442911	+	0.896566i
$673$	−8.44562	−	47.8975i	−0.325555	−	1.84631i	−0.505749	−	0.862681i	$-0.668784\pi$
$673$	−8.44562	−	47.8975i	−0.325555	−	1.84631i	0.180194	−	0.983631i	$-0.442327\pi$
$674$	−5.46628	−	23.5967i	−0.210553	−	0.908910i
$675$	6.59238	+	22.0258i	0.253741	+	0.847773i
$676$	22.0441	−	10.7924i	0.847849	−	0.415092i
$677$	8.35024	+	9.95143i	0.320926	+	0.382464i	0.902254	−	0.431205i	$-0.141911\pi$
$677$	8.35024	+	9.95143i	0.320926	+	0.382464i	−0.581328	+	0.813669i	$0.697467\pi$
$678$	−6.38631	+	9.21052i	−0.245265	+	0.353728i
$679$	22.4475	−	37.1455i	0.861455	−	1.42552i
$680$	−0.110211	+	7.24398i	−0.00422642	+	0.277794i
$681$	−2.33935	+	17.1241i	−0.0896443	+	0.656196i
$682$	−1.96327	−	4.61558i	−0.0751774	−	0.176740i
$683$	−28.0551			−1.07350			−0.536750	−	0.843741i	$-0.680348\pi$
$683$	−28.0551			−1.07350			−0.536750	+	0.843741i	$0.680348\pi$
$684$	−15.5770	−	5.50775i	−0.595601	−	0.210594i
$685$	−5.76812	+	9.99068i	−0.220389	+	0.381724i
$686$	4.72466	−	25.7619i	0.180388	−	0.983595i
$687$	11.3318	−	0.439456i	0.432334	−	0.0167663i
$688$	−22.1626	+	20.0755i	−0.844942	+	0.765372i
$689$	1.33535	−	1.59141i	0.0508728	−	0.0606278i
$690$	11.4436	+	11.3387i	0.435649	+	0.431658i
$691$	13.6551	−	37.5172i	0.519465	−	1.42722i	−0.351645	−	0.936133i	$-0.614378\pi$
$691$	13.6551	−	37.5172i	0.519465	−	1.42722i	0.871111	−	0.491086i	$-0.163400\pi$
$692$	6.81625	+	13.9226i	0.259115	+	0.529256i
$693$	−1.90270	+	16.1888i	−0.0722775	+	0.614961i
$694$	3.16973	+	13.6830i	0.120321	+	0.519400i
$695$	−2.56601	−	14.5526i	−0.0973343	−	0.552010i
$696$	5.68632	−	10.4075i	0.215539	−	0.394495i
$697$	−36.8846	+	13.4249i	−1.39710	+	0.508505i
$698$	8.40236	+	12.9174i	0.318034	+	0.488929i
$699$	−1.98336	+	6.18517i	−0.0750174	+	0.233945i
$700$	16.5727	−	16.5383i	0.626390	−	0.625091i
$701$		−	0.291218i		−	0.0109991i	−0.999985	−	0.00549957i	$-0.998249\pi$
$701$		−	0.291218i		−	0.0109991i	0.999985	−	0.00549957i	$-0.00175058\pi$
$702$	−4.05462	+	4.78196i	−0.153032	+	0.180483i
$703$	14.8441	+	8.57025i	0.559856	+	0.323233i
$704$	−8.64357	+	13.9715i	−0.325767	+	0.526571i
$705$	−0.586733	+	1.82975i	−0.0220976	+	0.0689123i
$706$	1.29917	+	24.4404i	0.0488949	+	0.919827i
$707$	30.8869	+	18.6653i	1.16162	+	0.701982i
$708$	0.503216	−	0.564925i	0.0189120	−	0.0212312i
$709$	4.87136	+	27.6268i	0.182948	+	1.03755i	0.928564	+	0.371172i	$0.121044\pi$
$709$	4.87136	+	27.6268i	0.182948	+	1.03755i	−0.745617	+	0.666375i	$0.767845\pi$
$710$	−4.06164	+	13.3206i	−0.152431	+	0.499913i
$711$	−2.08222	−	26.8056i	−0.0780894	−	1.00529i
$712$	21.3846	−	17.3964i	0.801423	−	0.651958i
$713$	−9.62531	−	11.4710i	−0.360471	−	0.429592i
$714$	−12.8269	+	17.7318i	−0.480034	+	0.663595i
$715$	1.30881	+	0.230779i	0.0489468	+	0.00863064i
$716$	48.2000	+	11.9412i	1.80132	+	0.446263i
$717$	13.2781	−	0.514938i	0.495881	−	0.0192307i
$718$	0.147793	−	1.21115i	0.00551559	−	0.0451999i
$719$	53.1314			1.98147			0.990733	−	0.135822i	$-0.0433676\pi$
$719$	53.1314			1.98147			0.990733	+	0.135822i	$0.0433676\pi$
$720$	6.25251	−	6.61482i	0.233017	−	0.246520i
$721$	14.2910	−	2.22640i	0.532225	−	0.0829154i
$722$	12.9024	+	9.70755i	0.480177	+	0.361278i
$723$	−22.1945	−	17.2029i	−0.825422	−	0.639782i
$724$	−10.4236	−	2.58237i	−0.387391	−	0.0959730i
$725$	−10.5486	−	1.86001i	−0.391766	−	0.0690789i
$726$	15.0248	−	7.09054i	0.557623	−	0.263154i
$727$	−50.5739	+	8.91755i	−1.87568	+	0.330734i	−0.990828	−	0.135132i	$-0.956854\pi$
$727$	−50.5739	+	8.91755i	−1.87568	+	0.330734i	−0.884855	+	0.465866i	$0.845743\pi$
$728$	6.24467	+	1.32925i	0.231443	+	0.0492652i
$729$	−7.74736	+	25.8646i	−0.286939	+	0.957949i
$730$	−0.291883	+	0.0676162i	−0.0108031	+	0.00250259i
$731$	−23.7227	−	8.63434i	−0.877414	−	0.319353i
$732$	19.8629	+	25.1450i	0.734155	+	0.929387i
$733$	6.24860	+	5.24320i	0.230797	+	0.193662i	0.750851	−	0.660472i	$-0.229644\pi$
$733$	6.24860	+	5.24320i	0.230797	+	0.193662i	−0.520054	+	0.854134i	$0.674088\pi$
$734$	9.72783	−	6.32766i	0.359061	−	0.233558i
$735$	−9.05871	+	1.58601i	−0.334136	+	0.0585008i
$736$	−12.5176	+	47.4239i	−0.461405	+	1.74807i
$737$	16.8525	+	9.72978i	0.620769	+	0.358401i
$738$	45.5559	+	18.8843i	1.67694	+	0.695140i
$739$	−35.8416	+	20.6932i	−1.31846	+	0.761210i	−0.983480	−	0.181017i	$-0.942061\pi$
$739$	−35.8416	+	20.6932i	−1.31846	+	0.761210i	−0.334975	+	0.942227i	$0.608728\pi$
$740$	−7.63116	+	5.56179i	−0.280527	+	0.204456i
$741$	−3.44256	+	2.16965i	−0.126466	+	0.0797040i
$742$	−8.91501	+	1.87832i	−0.327280	+	0.0689552i
$743$	0.00104784	−	0.00594258i	3.84414e−5	−	0.000218012i	−0.984789	−	0.173757i	$-0.944409\pi$
$743$	0.00104784	−	0.00594258i	3.84414e−5	−	0.000218012i	0.984827	+	0.173539i	$0.0555203\pi$
$744$	−6.35141	+	5.58952i	−0.232854	+	0.204922i
$745$	1.12834	+	6.39912i	0.0413391	+	0.234445i
$746$	9.86485	+	42.5843i	0.361178	+	1.55912i
$747$	14.0518	−	29.3833i	0.514129	−	1.07508i
$748$	−13.8375	−	0.946846i	−0.505948	−	0.0346201i
$749$	12.7978	+	11.1820i	0.467623	+	0.408582i
$750$	−15.9040	−	7.32726i	−0.580733	−	0.267554i
$751$	−0.118336	−	0.0208658i	−0.00431813	−	0.000761402i	0.171489	−	0.985186i	$-0.445142\pi$
$751$	−0.118336	−	0.0208658i	−0.00431813	−	0.000761402i	−0.175807	+	0.984425i	$0.556253\pi$
$752$	−5.71882	+	1.23344i	−0.208544	+	0.0449788i
$753$	8.76790	+	40.4818i	0.319520	+	1.47524i
$754$	−1.14330	−	2.68786i	−0.0416364	−	0.0978860i
$755$	9.27537			0.337565
$756$	26.9336	−	5.53019i	0.979564	−	0.201131i
$757$	33.0329			1.20060			0.600301	−	0.799774i	$-0.295047\pi$
$757$	33.0329			1.20060			0.600301	+	0.799774i	$0.295047\pi$
$758$	−14.5622	−	34.2353i	−0.528923	−	1.24348i
$759$	−22.8398	+	20.7250i	−0.829031	+	0.752269i
$760$	5.16060	−	2.87570i	0.187195	−	0.104313i
$761$	−12.8932	−	2.27342i	−0.467378	−	0.0824113i	−0.0650006	−	0.997885i	$-0.520705\pi$
$761$	−12.8932	−	2.27342i	−0.467378	−	0.0824113i	−0.402377	+	0.915474i	$0.631816\pi$
$762$	−7.45940	+	5.27445i	−0.270226	+	0.191073i
$763$	1.85186	−	9.39988i	0.0670419	−	0.340299i
$764$	−1.84691	+	26.9914i	−0.0668190	+	0.976513i
$765$	7.40272	+	2.06107i	0.267646	+	0.0745180i
$766$	−10.2685	−	44.3268i	−0.371017	−	1.60159i
$767$	−0.0323560	−	0.183500i	−0.00116831	−	0.00662581i
$768$	26.9542	+	6.43972i	0.972627	+	0.232373i
$769$	2.93135	−	16.6245i	0.105707	−	0.599496i	−0.885228	−	0.465157i	$-0.845998\pi$
$769$	2.93135	−	16.6245i	0.105707	−	0.599496i	0.990935	−	0.134339i	$-0.0428910\pi$
$770$	−3.89224	−	4.33832i	−0.140267	−	0.156342i
$771$	0.389754	+	10.0502i	0.0140366	+	0.361948i
$772$	−12.1672	−	16.6942i	−0.437906	−	0.600836i
$773$	31.1755	−	17.9992i	1.12130	−	0.647385i	0.179570	−	0.983745i	$-0.442529\pi$
$773$	31.1755	−	17.9992i	1.12130	−	0.647385i	0.941733	+	0.336360i	$0.109196\pi$
$774$	14.6378	+	28.1375i	0.526145	+	1.01138i
$775$	6.61774	+	3.82075i	0.237716	+	0.137246i
$776$	−15.2040	−	43.8363i	−0.545791	−	1.57363i
$777$	−28.5196	+	0.535560i	−1.02314	+	0.0192131i
$778$	−24.7234	+	16.0818i	−0.886376	+	0.576561i
$779$	24.5193	+	20.5741i	0.878495	+	0.737145i
$780$	−0.323864	−	2.21826i	−0.0115962	−	0.0794266i
$781$	−25.0529	−	9.11852i	−0.896464	−	0.326286i
$782$	−40.3394	+	9.34482i	−1.44253	+	0.334170i
$783$	−9.14903	−	8.63289i	−0.326960	−	0.308514i
$784$	−17.9535	−	21.4866i	−0.641196	−	0.767377i
$785$	8.54920	−	1.50745i	0.305134	−	0.0538034i
$786$	25.5844	+	17.7395i	0.912565	+	0.632747i
$787$	−9.33661	−	1.64630i	−0.332814	−	0.0586841i	0.00474408	−	0.999989i	$-0.498490\pi$
$787$	−9.33661	−	1.64630i	−0.332814	−	0.0586841i	−0.337558	+	0.941305i	$0.609601\pi$
$788$	8.67878	−	35.0315i	0.309169	−	1.24795i
$789$	1.48678	−	0.607374i	0.0529306	−	0.0216231i
$790$	7.68216	+	5.77993i	0.273319	+	0.205641i
$791$	4.36700	−	11.2909i	0.155273	−	0.401458i
$792$	12.0105	+	12.6255i	0.426774	+	0.448626i
$793$	7.89209			0.280256
$794$	−4.06741	+	33.3322i	−0.144347	+	1.18291i
$795$	1.70566	+	2.70635i	0.0604934	+	0.0959843i
$796$	−1.07862	+	4.35382i	−0.0382308	+	0.154317i
$797$	−3.17837	−	0.560432i	−0.112584	−	0.0198515i	0.117072	−	0.993123i	$-0.462649\pi$
$797$	−3.17837	−	0.560432i	−0.112584	−	0.0198515i	−0.229656	+	0.973272i	$0.573760\pi$
$798$	17.7519	+	1.82866i	0.628411	+	0.0647338i
$799$	−3.17472	−	3.78348i	−0.112313	−	0.133850i
$800$	−2.27456	−	24.9261i	−0.0804178	−	0.881269i
$801$	−12.0982	−	26.6189i	−0.427470	−	0.940531i
$802$	−4.23519	+	13.8898i	−0.149550	+	0.490465i
$803$	−0.0996036	−	0.564880i	−0.00351493	−	0.0199342i
$804$	6.65282	−	32.1434i	0.234627	−	1.13361i
$805$	−14.8924	−	8.99962i	−0.524887	−	0.317195i
$806$	0.110611	+	2.08085i	0.00389610	+	0.0732947i
$807$	21.4253	+	23.6115i	0.754205	+	0.831163i
$808$	36.4503	−	12.6423i	1.28232	−	0.444753i
$809$	15.9271	+	9.19552i	0.559967	+	0.323297i	0.753132	−	0.657869i	$-0.228542\pi$
$809$	15.9271	+	9.19552i	0.559967	+	0.323297i	−0.193165	+	0.981166i	$0.561875\pi$
$810$	−5.10547	−	8.19390i	−0.179388	−	0.287904i
$811$			14.1600i			0.497226i	0.968603	+	0.248613i	$0.0799748\pi$
$811$			14.1600i			0.497226i	−0.968603	+	0.248613i	$0.920025\pi$
$812$	−3.32827	+	12.3699i	−0.116800	+	0.434099i
$813$	42.9938	−	9.31199i	1.50786	−	0.326586i
$814$	−9.85727	−	15.1541i	−0.345497	−	0.531150i
$815$	−6.12832	+	2.23053i	−0.214666	+	0.0781319i
$816$	5.81515	+	22.6616i	0.203571	+	0.793316i
$817$	3.57472	+	20.2733i	0.125064	+	0.709271i
$818$	8.13785	+	35.1292i	0.284533	+	1.22826i
$819$	3.04308	−	6.04962i	0.106334	−	0.211391i
$820$	−15.8372	+	7.75363i	−0.553059	+	0.270768i
$821$	5.89147	−	16.1867i	0.205614	−	0.564919i	−0.793429	−	0.608663i	$-0.791706\pi$
$821$	5.89147	−	16.1867i	0.205614	−	0.564919i	0.999043	+	0.0437438i	$0.0139285\pi$
$822$	−9.47642	+	36.0288i	−0.330528	+	1.25665i
$823$	35.1508	−	41.8911i	1.22528	−	1.46023i	0.380791	−	0.924661i	$-0.375652\pi$
$823$	35.1508	−	41.8911i	1.22528	−	1.46023i	0.844490	−	0.535572i	$-0.179904\pi$
$824$	7.93381	−	13.2713i	0.276387	−	0.462329i
$825$	7.33516	−	13.9246i	0.255377	−	0.484794i
$826$	−0.384924	+	0.720829i	−0.0133932	+	0.0250809i
$827$	0.0466528	−	0.0808050i	0.00162228	−	0.00280986i	−0.865213	−	0.501404i	$-0.832817\pi$
$827$	0.0466528	−	0.0808050i	0.00162228	−	0.00280986i	0.866835	+	0.498594i	$0.166150\pi$
$828$	45.2910	+	25.5960i	1.57397	+	0.889521i
$829$	28.1248			0.976816			0.488408	−	0.872615i	$-0.337578\pi$
$829$	28.1248			0.976816			0.488408	+	0.872615i	$0.337578\pi$
$830$	4.55850	+	10.7169i	0.158228	+	0.371989i
$831$	−28.2636	+	11.5462i	−0.980453	+	0.400532i
$832$	5.35961	−	4.22619i	0.185811	−	0.146517i
$833$	8.96592	−	21.8719i	0.310651	−	0.757817i
$834$	−20.3661	−	43.1557i	−0.705221	−	1.49436i
$835$	4.84719	+	5.77666i	0.167744	+	0.199909i
$836$	4.97319	+	10.1580i	0.172001	+	0.351323i
$837$	4.02691	+	8.01966i	0.139190	+	0.277200i
$838$	−5.30470	−	22.8991i	−0.183248	−	0.791038i
$839$	1.01962	+	5.78254i	0.0352011	+	0.199636i	0.997337	−	0.0729361i	$-0.0232369\pi$
$839$	1.01962	+	5.78254i	0.0352011	+	0.199636i	−0.962135	+	0.272572i	$0.912126\pi$
$840$	−4.88537	+	8.53177i	−0.168561	+	0.294374i
$841$	−21.7441	+	7.91420i	−0.749796	+	0.272903i
$842$	2.56158	−	5.03668i	0.0882779	−	0.173575i
$843$	−16.9557	−	41.5054i	−0.583984	−	1.42952i
$844$	−4.08631	−	38.3279i	−0.140657	−	1.31930i
$845$	8.06145	+	4.65428i	0.277322	+	0.160112i
$846$	−0.272342	+	6.19922i	−0.00936332	+	0.213134i
$847$	−13.9745	+	11.2578i	−0.480168	+	0.386824i
$848$	−4.54684	+	8.61334i	−0.156139	+	0.295783i
$849$	8.79570	−	5.54342i	0.301868	−	0.190250i
$850$	17.7130	−	11.5218i	0.607552	−	0.395194i
$851$	−41.3440	−	34.6917i	−1.41725	−	1.18922i
$852$	−1.32909	+	44.9521i	−0.0455340	+	1.54004i
$853$	−41.6046	+	34.9104i	−1.42451	+	1.19531i	−0.475647	+	0.879636i	$0.657786\pi$
$853$	−41.6046	+	34.9104i	−1.42451	+	1.19531i	−0.948868	+	0.315673i	$0.897770\pi$
$854$	−27.2360	−	21.3575i	−0.931997	−	0.730838i
$855$	−1.56274	−	6.06811i	−0.0534445	−	0.207525i
$856$	17.9381	−	2.88232i	0.613111	−	0.0985157i
$857$	6.03027	+	7.18660i	0.205990	+	0.245489i	0.859142	−	0.511738i	$-0.170998\pi$
$857$	6.03027	+	7.18660i	0.205990	+	0.245489i	−0.653152	+	0.757227i	$0.726554\pi$
$858$	4.27368	−	0.393723i	0.145901	−	0.0134415i
$859$	−8.18637	−	1.44348i	−0.279315	−	0.0492508i	0.0322355	−	0.999480i	$-0.489737\pi$
$859$	−8.18637	−	1.44348i	−0.279315	−	0.0492508i	−0.311551	+	0.950229i	$0.600848\pi$
$860$	−11.0083	−	2.72721i	−0.375379	−	0.0929971i
$861$	−52.6213	−	8.26304i	−1.79333	−	0.281604i
$862$	−0.210870	+	1.72807i	−0.00718226	+	0.0588582i
$863$	−20.9898	−	36.3554i	−0.714501	−	1.23755i	−0.963152	−	0.268959i	$-0.913320\pi$
$863$	−20.9898	−	36.3554i	−0.714501	−	1.23755i	0.248650	−	0.968593i	$-0.420013\pi$
$864$	13.8555	−	25.9235i	0.471373	−	0.881934i
$865$	−2.93954	+	5.09144i	−0.0999475	+	0.173114i
$866$	31.9865	−	13.6056i	1.08694	−	0.462339i
$867$	7.17862	−	6.51394i	0.243799	−	0.221225i
$868$	5.24944	−	7.48044i	0.178178	−	0.253903i
$869$	−11.8305	+	14.0990i	−0.401321	+	0.478276i
$870$	4.47888	−	0.412627i	0.151848	−	0.0139894i
$871$	−5.19656	−	6.19302i	−0.176079	−	0.209842i
$872$	−6.46335	−	7.94511i	−0.218877	−	0.269055i
$873$	−49.0648	+	3.81128i	−1.66059	+	0.128992i
$874$	23.0465	+	24.6774i	0.779561	+	0.834726i
$875$	18.5571	+	3.65591i	0.627344	+	0.123592i
$876$	−0.851852	+	0.458798i	−0.0287814	+	0.0155014i
$877$	−42.7011	+	15.5419i	−1.44191	+	0.524814i	−0.940321	−	0.340290i	$-0.889475\pi$
$877$	−42.7011	+	15.5419i	−1.44191	+	0.524814i	−0.501593	+	0.865104i	$0.667253\pi$
$878$	28.9320	−	18.8194i	0.976406	−	0.635123i
$879$	1.18773	+	30.6266i	0.0400610	+	1.03301i
$880$	−6.22638	+	0.236053i	−0.209891	+	0.00795734i
$881$	7.44332	+	4.29740i	0.250772	+	0.144783i	0.620118	−	0.784509i	$-0.287085\pi$
$881$	7.44332	+	4.29740i	0.250772	+	0.144783i	−0.369346	+	0.929292i	$0.620418\pi$
$882$	−26.8732	+	12.6424i	−0.904869	+	0.425691i
$883$	6.34850	−	3.66531i	0.213644	−	0.123347i	−0.389360	−	0.921086i	$-0.627304\pi$
$883$	6.34850	−	3.66531i	0.213644	−	0.123347i	0.603004	+	0.797738i	$0.293970\pi$
$884$	5.26750	+	2.33582i	0.177165	+	0.0785622i
$885$	0.284286	+	0.0388369i	0.00955618	+	0.00130549i
$886$	37.4859	−	1.99262i	1.25936	−	0.0669435i
$887$	35.7895	+	30.0310i	1.20169	+	1.00834i	0.999580	+	0.0289791i	$0.00922562\pi$
$887$	35.7895	+	30.0310i	1.20169	+	1.00834i	0.202114	+	0.979362i	$0.435219\pi$
$888$	−19.0458	+	23.8149i	−0.639135	+	0.799177i
$889$	6.49268	−	7.43089i	0.217757	−	0.249224i
$890$	10.0004	+	3.04927i	0.335215	+	0.102212i
$891$	16.1835	−	8.92770i	0.542169	−	0.299089i
$892$	−5.97387	−	12.2020i	−0.200020	−	0.408552i
$893$	−1.37748	+	3.78458i	−0.0460955	+	0.126646i
$894$	8.95547	+	18.9766i	0.299516	+	0.634672i
$895$	6.44121	+	17.6971i	0.215306	+	0.591548i
$896$	−29.9332	+	0.0806868i	−0.999996	+	0.00269556i
$897$	11.8613	−	4.84554i	0.396037	−	0.161788i
$898$	26.7872	+	3.26876i	0.893901	+	0.109080i
$899$	−4.18085			−0.139439
$900$	−26.1859	−	4.36919i	−0.872864	−	0.145640i
$901$	−8.22257			−0.273933
$902$	−13.2136	−	31.0648i	−0.439965	−	1.03434i
$903$	−22.5098	−	25.8255i	−0.749080	−	0.859419i
$904$	−6.29967	−	11.3051i	−0.209524	−	0.376002i
$905$	−1.39296	−	3.82713i	−0.0463036	−	0.127218i
$906$	28.8966	−	7.88550i	0.960024	−	0.261978i
$907$	−53.2147	+	9.38319i	−1.76696	+	0.311564i	−0.960201	−	0.279310i	$-0.909894\pi$
$907$	−53.2147	+	9.38319i	−1.76696	+	0.311564i	−0.806764	+	0.590874i	$0.798783\pi$
$908$	−16.5616	−	11.1350i	−0.549617	−	0.369528i
$909$	−3.16912	−	40.7979i	−0.105113	−	1.35318i
$910$	0.903063	+	2.24670i	0.0299363	+	0.0744773i
$911$	−51.9580	−	18.9112i	−1.72145	−	0.626555i	−0.723483	−	0.690342i	$-0.757460\pi$
$911$	−51.9580	−	18.9112i	−1.72145	−	0.626555i	−0.997964	+	0.0637867i	$0.979682\pi$
$912$	13.6326	−	13.3463i	0.451420	−	0.441940i
$913$	−20.9513	+	7.62565i	−0.693387	+	0.252372i
$914$	21.8200	−	42.9033i	0.721740	−	1.41911i
$915$	−3.71086	+	11.5725i	−0.122677	+	0.382573i
$916$	−5.30820	+	11.9705i	−0.175388	+	0.395516i
$917$	−31.3631	−	12.1304i	−1.03570	−	0.400580i
$918$	24.8147	+	0.127599i	0.819008	+	0.00421141i
$919$	27.1302	−	15.6636i	0.894942	−	0.516695i	0.0193865	−	0.999812i	$-0.493829\pi$
$919$	27.1302	−	15.6636i	0.894942	−	0.516695i	0.875556	+	0.483117i	$0.160495\pi$
$920$	−17.5748	+	6.09556i	−0.579424	+	0.200965i
$921$	−34.4973	−	38.0174i	−1.13672	−	1.25272i
$922$	10.4175	−	6.77628i	0.343083	−	0.223165i
$923$	8.48480	+	7.11960i	0.279281	+	0.234344i
$924$	−15.8142	−	10.2066i	−0.520248	−	0.335773i
$925$	25.8807	+	9.41980i	0.850952	+	0.309721i
$926$	23.7578	+	25.4390i	0.780731	+	0.835979i
$927$	−11.4830	−	11.7089i	−0.377150	−	0.384572i
$928$	7.89655	+	11.1883i	0.259217	+	0.367274i
$929$	10.4071	−	28.5931i	0.341444	−	0.938110i	−0.643532	−	0.765419i	$-0.722532\pi$
$929$	10.4071	−	28.5931i	0.341444	−	0.938110i	0.984976	−	0.172691i	$-0.0552462\pi$
$930$	−3.10323	−	0.816221i	−0.101759	−	0.0267650i
$931$	−19.1015	+	2.58598i	−0.626026	+	0.0847520i
$932$	−5.40299	−	5.20203i	−0.176981	−	0.170398i
$933$	−25.0557	−	39.7556i	−0.820286	−	1.30154i
$934$	3.14594	−	25.7807i	0.102938	−	0.843571i
$935$	−2.63012	−	4.55550i	−0.0860141	−	0.148981i
$936$	−2.89484	−	6.63546i	−0.0946207	−	0.216887i
$937$	24.3831	+	42.2327i	0.796560	+	1.37968i	0.921844	+	0.387562i	$0.126683\pi$
$937$	24.3831	+	42.2327i	0.796560	+	1.37968i	−0.125284	+	0.992121i	$0.539984\pi$
$938$	1.17410	+	35.4353i	0.0383358	+	1.15700i
$939$	6.89796	+	5.34658i	0.225106	+	0.174479i
$940$	−1.59836	−	1.53891i	−0.0521326	−	0.0501936i
$941$	13.6363	+	2.40446i	0.444532	+	0.0783830i	0.391434	−	0.920206i	$-0.371979\pi$
$941$	13.6363	+	2.40446i	0.444532	+	0.0783830i	0.0530983	+	0.998589i	$0.483090\pi$
$942$	25.3527	−	11.9645i	0.826035	−	0.389824i
$943$	−64.7823	−	77.2045i	−2.10960	−	2.51413i
$944$	0.329670	+	0.808996i	0.0107298	+	0.0263306i
$945$	7.43991	+	7.30670i	0.242020	+	0.237687i
$946$	6.33244	−	20.7679i	0.205885	−	0.675223i
$947$	3.66774	−	3.07760i	0.119185	−	0.100008i	−0.581247	−	0.813727i	$-0.697435\pi$
$947$	3.66774	−	3.07760i	0.119185	−	0.100008i	0.700432	+	0.713719i	$0.252991\pi$
$948$	28.8469	+	11.4758i	0.936903	+	0.372717i
$949$	−0.0413799	+	0.234677i	−0.00134325	+	0.00761795i
$950$	−15.3587	−	7.81118i	−0.498300	−	0.253428i
$951$	0.428892	+	0.0585918i	0.0139078	+	0.00189997i
$952$	−11.8572	−	22.3159i	−0.384295	−	0.723262i
$953$	5.40218	−	3.11895i	0.174994	−	0.101033i	−0.409945	−	0.912110i	$-0.634452\pi$
$953$	5.40218	−	3.11895i	0.174994	−	0.101033i	0.584938	+	0.811078i	$0.301119\pi$
$954$	7.61463	+	6.98131i	0.246533	+	0.226028i
$955$	−8.88595	+	5.13030i	−0.287542	+	0.166013i
$956$	−6.21995	+	14.0266i	−0.201167	+	0.453652i
$957$	0.333687	+	8.60443i	0.0107866	+	0.278142i
$958$	−14.6284	+	28.7629i	−0.472621	+	0.929286i
$959$	0.804126	−	40.2312i	0.0259666	−	1.29913i
$960$	3.67693	+	9.84614i	0.118672	+	0.317783i
$961$	−26.3277	−	9.58250i	−0.849281	−	0.309113i
$962$	1.69494	+	7.31666i	0.0546471	+	0.235899i
$963$	1.86648	−	19.1796i	0.0601464	−	0.618056i
$964$	29.1221	−	14.2577i	0.937960	−	0.459209i
$965$	2.67957	−	7.36205i	0.0862584	−	0.236993i
$966$	−54.0468	−	15.3767i	−1.73893	−	0.494737i
$967$	23.4926	−	27.9974i	0.755471	−	0.900335i	−0.242081	−	0.970256i	$-0.577830\pi$
$967$	23.4926	−	27.9974i	0.755471	−	0.900335i	0.997553	+	0.0699205i	$0.0222746\pi$
$968$	−0.291836	+	19.1818i	−0.00937998	+	0.616527i
$969$	15.3369	+	4.91799i	0.492693	+	0.157988i
$970$	10.5795	−	14.0613i	0.339688	−	0.451482i
$971$	21.7498	+	37.6717i	0.697984	+	1.20894i	0.969164	+	0.246415i	$0.0792527\pi$
$971$	21.7498	+	37.6717i	0.697984	+	1.20894i	−0.271180	+	0.962529i	$0.587414\pi$
$972$	−22.8717	−	21.1869i	−0.733610	−	0.679571i
$973$	32.3358	+	40.1387i	1.03664	+	1.28679i
$974$	39.8448	+	4.86213i	1.27671	+	0.155793i
$975$	−4.84215	+	4.39381i	−0.155073	+	0.140715i
$976$	−36.1693	+	7.80102i	−1.15775	+	0.249705i
$977$	7.07012	+	19.4250i	0.226193	+	0.621461i	0.999927	−	0.0120495i	$-0.00383558\pi$
$977$	7.07012	+	19.4250i	0.226193	+	0.621461i	−0.773734	+	0.633510i	$0.781613\pi$
$978$	−17.1959	+	12.1590i	−0.549865	+	0.388803i
$979$	−6.84572	+	18.8085i	−0.218790	+	0.601121i
$980$	2.96347	−	10.1973i	0.0946647	−	0.325742i
$981$	−9.88979	+	4.49490i	−0.315757	+	0.143511i
$982$	−9.87666	−	3.01154i	−0.315177	−	0.0961020i
$983$	−2.56232	−	14.5316i	−0.0817252	−	0.463487i	−0.998015	−	0.0629715i	$-0.979942\pi$
$983$	−2.56232	−	14.5316i	−0.0817252	−	0.463487i	0.916290	−	0.400515i	$-0.131169\pi$
$984$	−42.7476	+	37.6198i	−1.36274	+	1.19928i
$985$	12.8621	−	4.68144i	0.409822	−	0.149163i
$986$	−5.24092	+	10.3049i	−0.166905	+	0.328175i
$987$	−1.28758	−	6.57754i	−0.0409841	−	0.209366i
$988$	−0.498130	−	4.67226i	−0.0158476	−	0.148644i
$989$		−	64.8196i		−	2.06114i
$990$	−1.43215	+	6.45177i	−0.0455168	+	0.205051i
$991$		−	56.8105i		−	1.80464i	−0.431062	−	0.902322i	$-0.641861\pi$
$991$		−	56.8105i		−	1.80464i	0.431062	−	0.902322i	$-0.358139\pi$
$992$	−2.56376	−	9.42716i	−0.0813996	−	0.299313i
$993$	11.0514	+	1.50975i	0.350706	+	0.0479106i
$994$	−10.0145	−	47.5315i	−0.317641	−	1.50761i
$995$	−1.59854	+	0.581823i	−0.0506773	+	0.0184450i
$996$	23.3126	+	29.5121i	0.738689	+	0.935127i
$997$	−51.2023	−	18.6361i	−1.62159	−	0.590212i	−0.637908	−	0.770112i	$-0.720200\pi$
$997$	−51.2023	−	18.6361i	−1.62159	−	0.590212i	−0.983685	+	0.179901i	$0.942422\pi$
$998$	−27.2679	−	29.1975i	−0.863150	−	0.924231i
$999$	19.3126	+	25.9452i	0.611024	+	0.820869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.20	yes	840
4.3	odd	2	inner	756.2.ci.a.95.95	yes	840
7.2	even	3		756.2.bs.a.527.113	yes	840
27.2	odd	18		756.2.bs.a.515.2	✓	840
28.23	odd	6		756.2.bs.a.527.2	yes	840
108.83	even	18		756.2.bs.a.515.113	yes	840
189.2	odd	18	inner	756.2.ci.a.191.95	yes	840
756.191	even	18	inner	756.2.ci.a.191.20	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.2	✓	840	27.2	odd	18
756.2.bs.a.515.113	yes	840	108.83	even	18
756.2.bs.a.527.2	yes	840	28.23	odd	6
756.2.bs.a.527.113	yes	840	7.2	even	3
756.2.ci.a.95.20	yes	840	1.1	even	1	trivial
756.2.ci.a.95.95	yes	840	4.3	odd	2	inner
756.2.ci.a.191.20	yes	840	756.191	even	18	inner
756.2.ci.a.191.95	yes	840	189.2	odd	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30138 + 0.553549i) q^{2} +(-1.64933 - 0.528879i) q^{3} +(1.38717 - 1.44075i) q^{4} +(0.746991 + 0.131715i) q^{5} +(2.43916 - 0.224713i) q^{6} +(-2.50378 + 0.855036i) q^{7} +(-1.00770 + 2.64283i) q^{8} +(2.44057 + 1.74459i) q^{9} +O(q^{10})\)	\(q+(-1.30138 + 0.553549i) q^{2} +(-1.64933 - 0.528879i) q^{3} +(1.38717 - 1.44075i) q^{4} +(0.746991 + 0.131715i) q^{5} +(2.43916 - 0.224713i) q^{6} +(-2.50378 + 0.855036i) q^{7} +(-1.00770 + 2.64283i) q^{8} +(2.44057 + 1.74459i) q^{9} +(-1.04503 + 0.242086i) q^{10} +(-0.356610 - 2.02244i) q^{11} +(-3.04988 + 1.64263i) q^{12} +(-0.148152 + 0.840214i) q^{13} +(2.78506 - 2.49869i) q^{14} +(-1.16237 - 0.612309i) q^{15} +(-0.151538 - 3.99713i) q^{16} +(2.92448 - 1.68845i) q^{17} +(-4.14182 - 0.919395i) q^{18} +(-2.38475 - 1.37684i) q^{19} +(1.22597 - 0.893520i) q^{20} +(4.58177 - 0.0860394i) q^{21} +(1.58360 + 2.43455i) q^{22} +(6.64204 + 5.57333i) q^{23} +(3.05977 - 3.82594i) q^{24} +(-4.15782 - 1.51332i) q^{25} +(-0.272298 - 1.17544i) q^{26} +(-3.10263 - 4.16817i) q^{27} +(-2.24126 + 4.79341i) q^{28} +(2.38405 - 0.420373i) q^{29} +(1.85163 + 0.153414i) q^{30} +(-1.70079 - 0.299896i) q^{31} +(2.40982 + 5.11789i) q^{32} +(-0.481457 + 3.52427i) q^{33} +(-2.87121 + 3.81615i) q^{34} +(-1.98292 + 0.308920i) q^{35} +(5.89901 - 1.09622i) q^{36} -6.22459 q^{37} +(3.86561 + 0.471707i) q^{38} +(0.688724 - 1.30743i) q^{39} +(-1.10084 + 1.84144i) q^{40} +(-11.4470 - 2.01842i) q^{41} +(-5.91498 + 2.64820i) q^{42} +(-4.80537 - 5.72682i) q^{43} +(-3.40851 - 2.29167i) q^{44} +(1.59330 + 1.62465i) q^{45} +(-11.7289 - 3.57631i) q^{46} +(-0.253974 - 1.44036i) q^{47} +(-1.86406 + 6.67273i) q^{48} +(5.53783 - 4.28165i) q^{49} +(6.24859 - 0.332154i) q^{50} +(-5.71642 + 1.23811i) q^{51} +(1.00503 + 1.37897i) q^{52} +(-2.10872 - 1.21747i) q^{53} +(6.34498 + 3.70691i) q^{54} -1.55771i q^{55} +(0.263344 - 7.47868i) q^{56} +(3.20506 + 3.53210i) q^{57} +(-2.86986 + 1.86676i) q^{58} +(-0.205226 + 0.0746962i) q^{59} +(-2.49459 + 0.825318i) q^{60} +(-1.60629 - 9.10973i) q^{61} +(2.37938 - 0.551195i) q^{62} +(-7.60235 - 2.28129i) q^{63} +(-5.96908 - 5.32635i) q^{64} +(-0.221337 + 0.608119i) q^{65} +(-1.32430 - 4.85291i) q^{66} +(-6.09084 + 7.25878i) q^{67} +(1.62410 - 6.55562i) q^{68} +(-8.00729 - 12.7051i) q^{69} +(2.40953 - 1.49967i) q^{70} +(6.49112 - 11.2429i) q^{71} +(-7.07002 + 4.69199i) q^{72} +0.279307 q^{73} +(8.10054 - 3.44562i) q^{74} +(6.05724 + 4.69495i) q^{75} +(-5.29173 + 1.52594i) q^{76} +(2.62213 + 4.75882i) q^{77} +(-0.172560 + 2.08271i) q^{78} +(-5.76075 - 6.86539i) q^{79} +(0.413283 - 3.00578i) q^{80} +(2.91280 + 8.51561i) q^{81} +(16.0142 - 3.70977i) q^{82} +(-1.88526 - 10.6919i) q^{83} +(6.23171 - 6.72055i) q^{84} +(2.40696 - 0.876060i) q^{85} +(9.42368 + 4.79274i) q^{86} +(-4.15442 - 0.567543i) q^{87} +(5.70431 + 1.09555i) q^{88} +(-8.44063 - 4.87320i) q^{89} +(-2.97281 - 1.23232i) q^{90} +(-0.347472 - 2.23039i) q^{91} +(17.2434 - 1.83840i) q^{92} +(2.64656 + 1.39414i) q^{93} +(1.12783 + 1.73386i) q^{94} +(-1.60004 - 1.34259i) q^{95} +(-1.26783 - 9.71559i) q^{96} +(-12.5663 + 10.5444i) q^{97} +(-4.83670 + 8.63750i) q^{98} +(2.65799 - 5.55804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

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