LMFDB - Embedded newform 300.2.w.a.67.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.19
Character	$\chi$	$=$	300.67
Dual form			300.2.w.a.103.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.578573 + 1.29045i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-1.33051 + 1.49324i) q^{4} +(0.979302 + 2.01022i) q^{5} +(0.369579 + 1.36507i) q^{6} +(0.0808033 - 0.0808033i) q^{7} +(-2.69674 - 0.853002i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(0.578573 + 1.29045i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-1.33051 + 1.49324i) q^{4} +(0.979302 + 2.01022i) q^{5} +(0.369579 + 1.36507i) q^{6} +(0.0808033 - 0.0808033i) q^{7} +(-2.69674 - 0.853002i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-2.02748 + 2.42679i) q^{10} +(0.521065 - 0.169304i) q^{11} +(-1.54772 + 1.26671i) q^{12} +(-0.379036 - 0.743901i) q^{13} +(0.151023 + 0.0575218i) q^{14} +(0.652778 + 2.13866i) q^{15} +(-0.459504 - 3.97352i) q^{16} +(0.514721 + 3.24982i) q^{17} +(0.151486 + 1.40608i) q^{18} +(-2.87295 - 2.08732i) q^{19} +(-4.30469 - 1.21228i) q^{20} +(0.0924489 - 0.0671680i) q^{21} +(0.519953 + 0.574452i) q^{22} +(3.38282 - 6.63917i) q^{23} +(-2.53010 - 1.26436i) q^{24} +(-3.08194 + 3.93722i) q^{25} +(0.740664 - 0.919527i) q^{26} +(0.891007 + 0.453990i) q^{27} +(0.0131490 + 0.228168i) q^{28} +(4.57530 + 6.29737i) q^{29} +(-2.38215 + 2.07975i) q^{30} +(1.38542 - 1.90687i) q^{31} +(4.86176 - 2.89194i) q^{32} +(0.541135 - 0.0857074i) q^{33} +(-3.89592 + 2.54448i) q^{34} +(0.241563 + 0.0833013i) q^{35} +(-1.72682 + 1.00900i) q^{36} +(0.401778 - 0.204716i) q^{37} +(1.03136 - 4.91506i) q^{38} +(-0.257998 - 0.794036i) q^{39} +(-0.926199 - 6.25637i) q^{40} +(1.29216 - 3.97687i) q^{41} +(0.140165 + 0.0804388i) q^{42} +(-2.31395 - 2.31395i) q^{43} +(-0.440470 + 1.00333i) q^{44} +(0.310180 + 2.21445i) q^{45} +(10.5247 + 0.524113i) q^{46} +(0.528548 - 3.33712i) q^{47} +(0.167748 - 3.99648i) q^{48} +6.98694i q^{49} +(-6.86389 - 1.69911i) q^{50} +3.29033i q^{51} +(1.61513 + 0.423774i) q^{52} +(2.22344 - 14.0382i) q^{53} +(-0.0703383 + 1.41246i) q^{54} +(0.850619 + 0.881654i) q^{55} +(-0.286831 + 0.148980i) q^{56} +(-2.51105 - 2.51105i) q^{57} +(-5.47927 + 9.54767i) q^{58} +(1.80325 - 5.54984i) q^{59} +(-4.06205 - 1.87075i) q^{60} +(-2.07653 - 6.39089i) q^{61} +(3.26228 + 0.684550i) q^{62} +(0.101818 - 0.0518789i) q^{63} +(6.54477 + 4.60065i) q^{64} +(1.12421 - 1.49045i) q^{65} +(0.423687 + 0.648718i) q^{66} +(-12.2481 + 1.93991i) q^{67} +(-5.53758 - 3.55531i) q^{68} +(4.37977 - 6.02824i) q^{69} +(0.0322659 + 0.359920i) q^{70} +(9.28233 + 12.7760i) q^{71} +(-2.30116 - 1.64459i) q^{72} +(1.31572 + 0.670391i) q^{73} +(0.496633 + 0.400030i) q^{74} +(-3.65991 + 3.40662i) q^{75} +(6.93934 - 1.51280i) q^{76} +(0.0284234 - 0.0557842i) q^{77} +(0.875391 - 0.792341i) q^{78} +(4.21793 - 3.06451i) q^{79} +(7.53764 - 4.81498i) q^{80} +(0.809017 + 0.587785i) q^{81} +(5.87955 - 0.633441i) q^{82} +(0.973158 + 6.14428i) q^{83} +(-0.0227061 + 0.227415i) q^{84} +(-6.02877 + 4.21725i) q^{85} +(1.64724 - 4.32483i) q^{86} +(3.53385 + 6.93557i) q^{87} +(-1.54959 + 0.0120993i) q^{88} +(9.70119 - 3.15211i) q^{89} +(-2.67817 + 1.68149i) q^{90} +(-0.0907370 - 0.0294822i) q^{91} +(5.41297 + 13.8848i) q^{92} +(1.66666 - 1.66666i) q^{93} +(4.61218 - 1.24870i) q^{94} +(1.38248 - 7.81937i) q^{95} +(5.25430 - 2.09579i) q^{96} +(-1.70626 - 0.270245i) q^{97} +(-9.01628 + 4.04246i) q^{98} +0.547881 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	0.578573	+	1.29045i	0.409113	+	0.912484i
$2$	0.578573	+	1.29045i	0.409113	+	0.912484i
$3$	0.987688	+	0.156434i	0.570242	+	0.0903175i
$3$	0.987688	+	0.156434i	0.570242	+	0.0903175i
$4$	−1.33051	+	1.49324i	−0.665253	+	0.746618i
$5$	0.979302	+	2.01022i	0.437957	+	0.898996i
$5$	0.979302	+	2.01022i	0.437957	+	0.898996i
$6$	0.369579	+	1.36507i	0.150880	+	0.557287i
$7$	0.0808033	−	0.0808033i	0.0305408	−	0.0305408i	−0.691671	−	0.722212i	$-0.743125\pi$
$7$	0.0808033	−	0.0808033i	0.0305408	−	0.0305408i	0.722212	+	0.691671i	$0.243125\pi$
$8$	−2.69674	−	0.853002i	−0.953440	−	0.301582i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	−2.02748	+	2.42679i	−0.641145	+	0.767419i
$11$	0.521065	−	0.169304i	0.157107	−	0.0510472i	−0.229408	−	0.973330i	$-0.573679\pi$
$11$	0.521065	−	0.169304i	0.157107	−	0.0510472i	0.386515	+	0.922283i	$0.373679\pi$
$12$	−1.54772	+	1.26671i	−0.446788	+	0.365669i
$13$	−0.379036	−	0.743901i	−0.105126	−	0.206321i	0.832452	−	0.554098i	$-0.186937\pi$
$13$	−0.379036	−	0.743901i	−0.105126	−	0.206321i	−0.937577	+	0.347777i	$0.886937\pi$
$14$	0.151023	+	0.0575218i	0.0403626	+	0.0153733i
$15$	0.652778	+	2.13866i	0.168547	+	0.552201i
$16$	−0.459504	−	3.97352i	−0.114876	−	0.993380i
$17$	0.514721	+	3.24982i	0.124838	+	0.788197i	0.968076	+	0.250656i	$0.0806465\pi$
$17$	0.514721	+	3.24982i	0.124838	+	0.788197i	−0.843238	+	0.537540i	$0.819354\pi$
$18$	0.151486	+	1.40608i	0.0357055	+	0.331415i
$19$	−2.87295	−	2.08732i	−0.659100	−	0.478864i	0.207259	−	0.978286i	$-0.433546\pi$
$19$	−2.87295	−	2.08732i	−0.659100	−	0.478864i	−0.866359	+	0.499422i	$0.833546\pi$
$20$	−4.30469	−	1.21228i	−0.962559	−	0.271074i
$21$	0.0924489	−	0.0671680i	0.0201740	−	0.0146573i
$22$	0.519953	+	0.574452i	0.110854	+	0.122474i
$23$	3.38282	−	6.63917i	0.705367	−	1.38436i	−0.208367	−	0.978051i	$-0.566815\pi$
$23$	3.38282	−	6.63917i	0.705367	−	1.38436i	0.913735	−	0.406311i	$-0.133185\pi$
$24$	−2.53010	−	1.26436i	−0.516454	−	0.258087i
$25$	−3.08194	+	3.93722i	−0.616387	+	0.787443i
$26$	0.740664	−	0.919527i	0.145256	−	0.180334i
$27$	0.891007	+	0.453990i	0.171474	+	0.0873705i
$28$	0.0131490	+	0.228168i	0.00248493	+	0.0431196i
$29$	4.57530	+	6.29737i	0.849613	+	1.16939i	0.983948	+	0.178455i	$0.0571100\pi$
$29$	4.57530	+	6.29737i	0.849613	+	1.16939i	−0.134335	+	0.990936i	$0.542890\pi$
$30$	−2.38215	+	2.07975i	−0.434919	+	0.379708i
$31$	1.38542	−	1.90687i	0.248829	−	0.342484i	−0.666272	−	0.745709i	$-0.732111\pi$
$31$	1.38542	−	1.90687i	0.248829	−	0.342484i	0.915101	+	0.403225i	$0.132111\pi$
$32$	4.86176	−	2.89194i	0.859446	−	0.511227i
$33$	0.541135	−	0.0857074i	0.0941996	−	0.0149197i
$34$	−3.89592	+	2.54448i	−0.668144	+	0.436374i
$35$	0.241563	+	0.0833013i	0.0408316	+	0.0140805i
$36$	−1.72682	+	1.00900i	−0.287804	+	0.168167i
$37$	0.401778	−	0.204716i	0.0660518	−	0.0336551i	−0.420653	−	0.907222i	$-0.638199\pi$
$37$	0.401778	−	0.204716i	0.0660518	−	0.0336551i	0.486704	+	0.873567i	$0.338199\pi$
$38$	1.03136	−	4.91506i	0.167309	−	0.797327i
$39$	−0.257998	−	0.794036i	−0.0413128	−	0.127148i
$40$	−0.926199	−	6.25637i	−0.146445	−	0.989219i
$41$	1.29216	−	3.97687i	0.201802	−	0.621083i	−0.798028	−	0.602621i	$-0.794123\pi$
$41$	1.29216	−	3.97687i	0.201802	−	0.621083i	0.999830	−	0.0184617i	$-0.00587687\pi$
$42$	0.140165	+	0.0804388i	0.0216280	+	0.0124120i
$43$	−2.31395	−	2.31395i	−0.352875	−	0.352875i	0.508303	−	0.861178i	$-0.330273\pi$
$43$	−2.31395	−	2.31395i	−0.352875	−	0.352875i	−0.861178	+	0.508303i	$0.830273\pi$
$44$	−0.440470	+	1.00333i	−0.0664033	+	0.151258i
$45$	0.310180	+	2.21445i	0.0462390	+	0.330111i
$46$	10.5247	+	0.524113i	1.55178	+	0.0772762i
$47$	0.528548	−	3.33712i	0.0770966	−	0.486769i	−0.918683	−	0.394995i	$-0.870746\pi$
$47$	0.528548	−	3.33712i	0.0770966	−	0.486769i	0.995780	−	0.0917738i	$-0.0292537\pi$
$48$	0.167748	−	3.99648i	0.0242124	−	0.576842i
$49$			6.98694i			0.998135i
$50$	−6.86389	−	1.69911i	−0.970701	−	0.240290i
$51$			3.29033i			0.460738i
$52$	1.61513	+	0.423774i	0.223978	+	0.0587669i
$53$	2.22344	−	14.0382i	0.305413	−	1.92830i	−0.0616376	−	0.998099i	$-0.519632\pi$
$53$	2.22344	−	14.0382i	0.305413	−	1.92830i	0.367050	−	0.930201i	$-0.380368\pi$
$54$	−0.0703383	+	1.41246i	−0.00957184	+	0.192212i
$55$	0.850619	+	0.881654i	0.114697	+	0.118882i
$56$	−0.286831	+	0.148980i	−0.0383293	+	0.0199083i
$57$	−2.51105	−	2.51105i	−0.332597	−	0.332597i
$58$	−5.47927	+	9.54767i	−0.719463	+	1.25367i
$59$	1.80325	−	5.54984i	0.234763	−	0.722528i	−0.762389	−	0.647119i	$-0.775974\pi$
$59$	1.80325	−	5.54984i	0.234763	−	0.722528i	0.997153	−	0.0754088i	$-0.0240262\pi$
$60$	−4.06205	−	1.87075i	−0.524409	−	0.241513i
$61$	−2.07653	−	6.39089i	−0.265872	−	0.818269i	−0.991491	−	0.130173i	$-0.958447\pi$
$61$	−2.07653	−	6.39089i	−0.265872	−	0.818269i	0.725619	−	0.688096i	$-0.241553\pi$
$62$	3.26228	+	0.684550i	0.414310	+	0.0869379i
$63$	0.101818	−	0.0518789i	0.0128279	−	0.00653613i
$64$	6.54477	+	4.60065i	0.818097	+	0.575081i
$65$	1.12421	−	1.49045i	0.139441	−	0.184867i
$66$	0.423687	+	0.648718i	0.0521523	+	0.0798517i
$67$	−12.2481	+	1.93991i	−1.49634	+	0.236998i	−0.850298	−	0.526301i	$-0.823579\pi$
$67$	−12.2481	+	1.93991i	−1.49634	+	0.236998i	−0.646046	+	0.763298i	$0.723579\pi$
$68$	−5.53758	−	3.55531i	−0.671531	−	0.431144i
$69$	4.37977	−	6.02824i	0.527262	−	0.725714i
$70$	0.0322659	+	0.359920i	0.00385651	+	0.0430187i
$71$	9.28233	+	12.7760i	1.10161	+	1.51624i	0.833233	+	0.552923i	$0.186488\pi$
$71$	9.28233	+	12.7760i	1.10161	+	1.51624i	0.268378	+	0.963314i	$0.413512\pi$
$72$	−2.30116	−	1.64459i	−0.271194	−	0.193817i
$73$	1.31572	+	0.670391i	0.153993	+	0.0784633i	0.529289	−	0.848442i	$-0.322459\pi$
$73$	1.31572	+	0.670391i	0.153993	+	0.0784633i	−0.375296	+	0.926905i	$0.622459\pi$
$74$	0.496633	+	0.400030i	0.0577324	+	0.0465025i
$75$	−3.65991	+	3.40662i	−0.422610	+	0.393363i
$76$	6.93934	−	1.51280i	0.795997	−	0.173530i
$77$	0.0284234	−	0.0557842i	0.00323915	−	0.00635719i
$78$	0.875391	−	0.792341i	0.0991185	−	0.0897149i
$79$	4.21793	−	3.06451i	0.474554	−	0.344784i	−0.324659	−	0.945831i	$-0.605250\pi$
$79$	4.21793	−	3.06451i	0.474554	−	0.344784i	0.799214	+	0.601047i	$0.205250\pi$
$80$	7.53764	−	4.81498i	0.842734	−	0.538331i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	5.87955	−	0.633441i	0.649288	−	0.0699519i
$83$	0.973158	+	6.14428i	0.106818	+	0.674422i	0.981750	+	0.190176i	$0.0609059\pi$
$83$	0.973158	+	6.14428i	0.106818	+	0.674422i	−0.874932	+	0.484246i	$0.839094\pi$
$84$	−0.0227061	+	0.227415i	−0.00247744	+	0.0248131i
$85$	−6.02877	+	4.21725i	−0.653912	+	0.457425i
$86$	1.64724	−	4.32483i	0.177627	−	0.466358i
$87$	3.53385	+	6.93557i	0.378868	+	0.743571i
$88$	−1.54959	+	0.0120993i	−0.165187	+	0.00128979i
$89$	9.70119	−	3.15211i	1.02832	−	0.334123i	0.254197	−	0.967153i	$-0.418189\pi$
$89$	9.70119	−	3.15211i	1.02832	−	0.334123i	0.774127	+	0.633030i	$0.218189\pi$
$90$	−2.67817	+	1.68149i	−0.282304	+	0.177245i
$91$	−0.0907370	−	0.0294822i	−0.00951182	−	0.00309058i
$92$	5.41297	+	13.8848i	0.564341	+	1.44759i
$93$	1.66666	−	1.66666i	0.172825	−	0.172825i
$94$	4.61218	−	1.24870i	0.475710	−	0.128794i
$95$	1.38248	−	7.81937i	0.141839	−	0.802250i
$96$	5.25430	−	2.09579i	0.536265	−	0.213900i
$97$	−1.70626	−	0.270245i	−0.173244	−	0.0274392i	0.0692096	−	0.997602i	$-0.477952\pi$
$97$	−1.70626	−	0.270245i	−0.173244	−	0.0274392i	−0.242454	+	0.970163i	$0.577952\pi$
$98$	−9.01628	+	4.04246i	−0.910782	+	0.408350i
$99$	0.547881			0.0550641
$100$	−1.77865	−	9.84055i	−0.177865	−	0.984055i
$101$	−11.4729			−1.14160			−0.570798	−	0.821091i	$-0.693366\pi$
$101$	−11.4729			−1.14160			−0.570798	+	0.821091i	$0.693366\pi$
$102$	−4.24599	+	1.90370i	−0.420416	+	0.188494i
$103$	−11.2138	−	1.77608i	−1.10492	−	0.175003i	−0.422789	−	0.906228i	$-0.638949\pi$
$103$	−11.2138	−	1.77608i	−1.10492	−	0.175003i	−0.682136	+	0.731225i	$0.738949\pi$
$104$	0.387612	+	2.32942i	0.0380085	+	0.228419i
$105$	0.225558	+	0.120064i	0.0220122	+	0.0117171i
$106$	19.4020	−	5.25291i	1.88449	−	0.510208i
$107$	−2.58147	+	2.58147i	−0.249560	+	0.249560i	−0.820790	−	0.571230i	$-0.806466\pi$
$107$	−2.58147	+	2.58147i	−0.249560	+	0.249560i	0.571230	+	0.820790i	$0.306466\pi$
$108$	−1.86340	+	0.726445i	−0.179306	+	0.0699022i
$109$	4.86280	+	1.58002i	0.465772	+	0.151338i	0.532495	−	0.846433i	$-0.321255\pi$
$109$	4.86280	+	1.58002i	0.465772	+	0.151338i	−0.0667234	+	0.997772i	$0.521255\pi$
$110$	−0.645583	+	1.60778i	−0.0615539	+	0.153296i
$111$	0.428856	−	0.139344i	0.0407052	−	0.0132259i
$112$	−0.358203	−	0.283944i	−0.0338470	−	0.0268302i
$113$	−7.03160	−	13.8003i	−0.661477	−	1.29822i	−0.941105	−	0.338114i	$-0.890211\pi$
$113$	−7.03160	−	13.8003i	−0.661477	−	1.29822i	0.279628	−	0.960108i	$-0.409789\pi$
$114$	1.78755	−	4.69320i	0.167420	−	0.439559i
$115$	16.6590	+	0.298460i	1.55346	+	0.0278316i
$116$	−15.4909	−	1.54668i	−1.43830	−	0.143606i
$117$	−0.130607	−	0.824620i	−0.0120746	−	0.0762362i
$118$	8.20509	−	0.883986i	0.755339	−	0.0813775i
$119$	0.304187	+	0.221005i	0.0278848	+	0.0202595i
$120$	0.0639155	−	6.32423i	0.00583466	−	0.577321i
$121$	−8.65634	+	6.28920i	−0.786940	+	0.571745i
$122$	7.04568	−	6.37724i	0.637886	−	0.577368i
$123$	1.89837	−	3.72577i	0.171171	−	0.335941i
$124$	1.00409	+	4.60586i	0.0901701	+	0.413619i
$125$	−10.9328	−	2.33964i	−0.977859	−	0.209263i
$126$	0.125856	+	0.101375i	0.0112122	+	0.00903121i
$127$	−9.45960	−	4.81991i	−0.839404	−	0.427698i	−0.0192321	−	0.999815i	$-0.506122\pi$
$127$	−9.45960	−	4.81991i	−0.839404	−	0.427698i	−0.820172	+	0.572117i	$0.806122\pi$
$128$	−2.15026	+	11.1075i	−0.190058	+	0.981773i
$129$	−1.92348	−	2.64745i	−0.169353	−	0.233095i
$130$	2.57378	+	0.588401i	0.225736	+	0.0516061i
$131$	−13.0987	+	18.0288i	−1.14444	+	1.57518i	−0.387257	+	0.921972i	$0.626578\pi$
$131$	−13.0987	+	18.0288i	−1.14444	+	1.57518i	−0.757178	+	0.653209i	$0.773422\pi$
$132$	−0.592003	+	0.922077i	−0.0515272	+	0.0802565i
$133$	−0.400806	+	0.0634815i	−0.0347543	+	0.00550454i
$134$	−9.58977	−	14.6832i	−0.828430	−	1.26843i
$135$	−0.0400547	+	2.23571i	−0.00344736	+	0.192419i
$136$	1.38404	−	9.20296i	0.118680	−	0.789148i
$137$	−6.60920	+	3.36756i	−0.564662	+	0.287710i	−0.712927	−	0.701238i	$-0.752631\pi$
$137$	−6.60920	+	3.36756i	−0.564662	+	0.287710i	0.148265	+	0.988948i	$0.452631\pi$
$138$	10.3131	+	2.16409i	0.877912	+	0.184219i
$139$	2.89675	+	8.91529i	0.245699	+	0.756185i	0.995521	+	0.0945444i	$0.0301394\pi$
$139$	2.89675	+	8.91529i	0.245699	+	0.756185i	−0.749821	+	0.661640i	$0.769861\pi$
$140$	−0.445789	+	0.249877i	−0.0376761	+	0.0211185i
$141$	1.04408	−	3.21335i	0.0879275	−	0.270613i
$142$	−11.1163	+	19.3702i	−0.932858	+	1.62551i
$143$	−0.323448	−	0.323448i	−0.0270481	−	0.0270481i
$144$	0.790870	−	3.92104i	0.0659059	−	0.326753i
$145$	−8.17846	+	15.3644i	−0.679184	+	1.27594i
$146$	−0.103866	+	2.08573i	−0.00859601	+	0.172616i
$147$	−1.09300	+	6.90092i	−0.0901490	+	0.569178i
$148$	−0.228879	+	0.872324i	−0.0188137	+	0.0717046i
$149$			20.8441i			1.70762i	0.520587	+	0.853809i	$0.325713\pi$
$149$			20.8441i			1.70762i	−0.520587	+	0.853809i	$0.674287\pi$
$150$	−6.51359	−	2.75194i	−0.531832	−	0.224695i
$151$		−	19.3780i		−	1.57696i	−0.615062	−	0.788479i	$-0.710869\pi$
$151$		−	19.3780i		−	1.57696i	0.615062	−	0.788479i	$-0.289131\pi$
$152$	5.96710	+	8.07959i	0.483996	+	0.655341i
$153$	−0.514721	+	3.24982i	−0.0416127	+	0.262732i
$154$	0.0884315	+	0.00440374i	0.00712602	+	0.000354864i
$155$	5.18997	+	0.917596i	0.416868	+	0.0737031i
$156$	1.52895	+	0.671219i	0.122414	+	0.0537405i
$157$	−11.0581	−	11.0581i	−0.882529	−	0.882529i	0.111262	−	0.993791i	$-0.464511\pi$
$157$	−11.0581	−	11.0581i	−0.882529	−	0.882529i	−0.993791	+	0.111262i	$0.964511\pi$
$158$	6.39496	+	3.66998i	0.508756	+	0.291968i
$159$	4.39213	−	13.5176i	0.348318	−	1.07201i
$160$	10.5745	+	6.94111i	0.835991	+	0.548743i
$161$	−0.263123	−	0.809810i	−0.0207370	−	0.0638219i
$162$	−0.290430	+	1.38407i	−0.0228184	+	0.108743i
$163$	−18.5208	+	9.43684i	−1.45066	+	0.739150i	−0.989002	−	0.147905i	$-0.952747\pi$
$163$	−18.5208	+	9.43684i	−1.45066	+	0.739150i	−0.461663	+	0.887056i	$0.652747\pi$
$164$	4.21917	+	7.22075i	0.329462	+	0.563846i
$165$	0.702225	+	1.00387i	0.0546682	+	0.0781508i
$166$	−7.36582	+	4.81072i	−0.571698	+	0.373384i
$167$	−16.9741	+	2.68843i	−1.31349	+	0.208037i	−0.773587	−	0.633690i	$-0.781540\pi$
$167$	−16.9741	+	2.68843i	−1.31349	+	0.208037i	−0.539905	+	0.841726i	$0.681540\pi$
$168$	−0.306605	+	0.102275i	−0.0236551	+	0.00789072i
$169$	7.23149	−	9.95329i	0.556268	−	0.765638i
$170$	−8.93023	−	5.33982i	−0.684917	−	0.409546i
$171$	−2.08732	−	2.87295i	−0.159621	−	0.219700i
$172$	6.53401	−	0.376547i	0.498213	−	0.0287114i
$173$	11.8394	+	6.03246i	0.900130	+	0.458639i	0.841881	−	0.539663i	$-0.181448\pi$
$173$	11.8394	+	6.03246i	0.900130	+	0.458639i	0.0582491	+	0.998302i	$0.481448\pi$
$174$	−6.90539	+	8.57298i	−0.523497	+	0.649916i
$175$	0.0691094	+	0.567171i	0.00522418	+	0.0428741i
$176$	−0.912166	−	1.99267i	−0.0687571	−	0.150203i
$177$	2.64924	−	5.19942i	0.199129	−	0.390812i
$178$	9.68047	+	10.6951i	0.725582	+	0.801635i
$179$	−11.9838	+	8.70672i	−0.895709	+	0.650771i	−0.937360	−	0.348362i	$-0.886738\pi$
$179$	−11.9838	+	8.70672i	−0.895709	+	0.650771i	0.0416514	+	0.999132i	$0.486738\pi$
$180$	−3.71939	−	2.48317i	−0.277227	−	0.185084i
$181$	2.28163	+	1.65770i	0.169592	+	0.123216i	0.669344	−	0.742953i	$-0.266575\pi$
$181$	2.28163	+	1.65770i	0.169592	+	0.123216i	−0.499752	+	0.866169i	$0.666575\pi$
$182$	−0.0144527	−	0.134149i	−0.00107131	−	0.00994378i
$183$	−1.05120	−	6.63705i	−0.0777073	−	0.490625i
$184$	−14.7858	+	15.0185i	−1.09002	+	1.10718i
$185$	0.804985	+	0.607181i	0.0591836	+	0.0446408i
$186$	3.11503	+	1.18646i	0.228405	+	0.0869951i
$187$	0.818412	+	1.60622i	0.0598482	+	0.117459i
$188$	4.27987	+	5.22930i	0.312141	+	0.381386i
$189$	0.108680	−	0.0353123i	0.00790532	−	0.00256859i
$190$	10.8903	−	2.74006i	0.790068	−	0.198785i
$191$	−0.659670	−	0.214340i	−0.0477320	−	0.0155091i	0.285054	−	0.958512i	$-0.407989\pi$
$191$	−0.659670	−	0.214340i	−0.0477320	−	0.0155091i	−0.332786	+	0.943002i	$0.607989\pi$
$192$	5.74450	+	5.56783i	0.414573	+	0.401824i
$193$	0.643179	−	0.643179i	0.0462971	−	0.0462971i	−0.683579	−	0.729876i	$-0.739578\pi$
$193$	0.643179	−	0.643179i	0.0462971	−	0.0462971i	0.729876	+	0.683579i	$0.239578\pi$
$194$	−0.638458	−	2.35819i	−0.0458386	−	0.169308i
$195$	1.34353	−	1.29623i	0.0962119	−	0.0928252i
$196$	−10.4331	−	9.29617i	−0.745225	−	0.664012i
$197$	4.69155	+	0.743068i	0.334259	+	0.0529414i	0.321308	−	0.946975i	$-0.395877\pi$
$197$	4.69155	+	0.743068i	0.334259	+	0.0529414i	0.0129509	+	0.999916i	$0.495877\pi$
$198$	0.316989	+	0.707011i	0.0225274	+	0.0502451i
$199$	17.8531			1.26557			0.632786	−	0.774327i	$-0.281911\pi$
$199$	17.8531			1.26557			0.632786	+	0.774327i	$0.281911\pi$
$200$	11.6696	−	7.98873i	0.825167	−	0.564889i
$201$	−12.4008			−0.874684
$202$	−6.63790	−	14.8052i	−0.467041	−	1.04169i
$203$	0.878547	+	0.139148i	0.0616619	+	0.00976629i
$204$	−4.91324	−	4.37780i	−0.343995	−	0.306508i
$205$	9.25978	−	1.29703i	0.646731	−	0.0905883i
$206$	−4.19603	−	15.4984i	−0.292352	−	1.07982i
$207$	5.26887	−	5.26887i	0.366212	−	0.366212i
$208$	−2.78174	+	1.84793i	−0.192879	+	0.128131i
$209$	−1.85039	−	0.601227i	−0.127994	−	0.0415878i
$210$	−0.0244352	+	0.360536i	−0.00168619	+	0.0248794i
$211$	−3.94777	+	1.28271i	−0.271776	+	0.0883053i	−0.441734	−	0.897146i	$-0.645637\pi$
$211$	−3.94777	+	1.28271i	−0.271776	+	0.0883053i	0.169958	+	0.985451i	$0.445637\pi$
$212$	18.0041	+	21.9981i	1.23653	+	1.51083i
$213$	7.16944	+	14.0708i	0.491242	+	0.964117i
$214$	−4.82482	−	1.83768i	−0.329818	−	0.125621i
$215$	2.38549	−	6.91761i	0.162689	−	0.471777i
$216$	−2.01555	−	1.98432i	−0.137141	−	0.135016i
$217$	−0.0421347	−	0.266028i	−0.00286029	−	0.0180592i
$218$	0.774553	+	7.18934i	0.0524594	+	0.486924i
$219$	1.19465	+	0.867961i	0.0807266	+	0.0586513i
$220$	−2.44827	+	0.0971277i	−0.165062	+	0.00654834i
$221$	2.22244	−	1.61470i	0.149498	−	0.108617i
$222$	0.427940	+	0.472795i	0.0287214	+	0.0317319i
$223$	5.03433	−	9.88043i	0.337124	−	0.661643i	−0.658753	−	0.752359i	$-0.728916\pi$
$223$	5.03433	−	9.88043i	0.337124	−	0.661643i	0.995877	+	0.0907167i	$0.0289158\pi$
$224$	0.159168	−	0.626524i	0.0106349	−	0.0418614i
$225$	−4.14776	+	2.79214i	−0.276517	+	0.186143i
$226$	13.7402	−	17.0584i	0.913988	−	1.13471i
$227$	7.98815	+	4.07017i	0.530192	+	0.270147i	0.698527	−	0.715583i	$-0.253839\pi$
$227$	7.98815	+	4.07017i	0.530192	+	0.270147i	−0.168335	+	0.985730i	$0.553839\pi$
$228$	7.09056	−	0.408620i	0.469584	−	0.0270615i
$229$	−11.2030	−	15.4196i	−0.740315	−	1.01896i	−0.998600	−	0.0528873i	$-0.983158\pi$
$229$	−11.2030	−	15.4196i	−0.740315	−	1.01896i	0.258286	−	0.966069i	$-0.416842\pi$
$230$	9.25328	+	21.6702i	0.610143	+	1.42889i
$231$	0.0368001	−	0.0506510i	0.00242127	−	0.00333259i
$232$	−6.96672	−	20.8851i	−0.457388	−	1.37117i
$233$	20.2185	−	3.20229i	1.32456	−	0.209789i	0.546222	−	0.837640i	$-0.316065\pi$
$233$	20.2185	−	3.20229i	1.32456	−	0.209789i	0.778333	+	0.627851i	$0.216065\pi$
$234$	0.988563	−	0.645644i	0.0646244	−	0.0422071i
$235$	7.22594	−	2.20555i	0.471368	−	0.143874i
$236$	5.88798	+	10.0768i	0.383275	+	0.655942i
$237$	4.64540	−	2.36695i	0.301751	−	0.153750i
$238$	−0.109201	+	0.520405i	−0.00707843	+	0.0337328i
$239$	1.41153	+	4.34425i	0.0913044	+	0.281006i	0.986273	−	0.165123i	$-0.0528022\pi$
$239$	1.41153	+	4.34425i	0.0913044	+	0.281006i	−0.894969	+	0.446129i	$0.852802\pi$
$240$	8.19807	−	3.57655i	0.529183	−	0.230865i
$241$	−5.60469	+	17.2495i	−0.361030	+	1.11113i	0.591401	+	0.806378i	$0.298575\pi$
$241$	−5.60469	+	17.2495i	−0.361030	+	1.11113i	−0.952430	+	0.304757i	$0.901425\pi$
$242$	−13.1242	−	7.53179i	−0.843656	−	0.484162i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	12.3059	+	5.40238i	0.787806	+	0.345852i
$245$	−14.0453	+	6.84232i	−0.897319	+	0.437140i
$246$	5.90625	+	0.294122i	0.376569	+	0.0187525i
$247$	−0.463807	+	2.92836i	−0.0295113	+	0.186327i
$248$	−5.36268	+	3.96056i	−0.340531	+	0.251496i
$249$			6.22086i			0.394231i
$250$	−3.30625	−	15.4618i	−0.209105	−	0.977893i
$251$			16.9015i			1.06681i	0.845859	+	0.533406i	$0.179088\pi$
$251$			16.9015i			1.06681i	−0.845859	+	0.533406i	$0.820912\pi$
$252$	−0.0580022	+	0.221064i	−0.00365380	+	0.0139257i
$253$	0.638632	−	4.03217i	0.0401505	−	0.253500i
$254$	0.746765	−	14.9958i	0.0468562	−	0.940919i
$255$	−6.61427	+	3.22222i	−0.414202	+	0.201784i
$256$	−15.5777	+	3.65170i	−0.973607	+	0.228231i
$257$	−13.4787	−	13.4787i	−0.840776	−	0.840776i	0.148184	−	0.988960i	$-0.452657\pi$
$257$	−13.4787	−	13.4787i	−0.840776	−	0.840776i	−0.988960	+	0.148184i	$0.952657\pi$
$258$	2.30351	−	4.01389i	0.143411	−	0.249894i
$259$	0.0159232	−	0.0490067i	0.000989421	−	0.00304513i
$260$	0.729821	+	3.66176i	0.0452616	+	0.227093i
$261$	2.40538	+	7.40300i	0.148889	+	0.458234i
$262$	−30.8437	−	6.47217i	−1.90553	−	0.399852i
$263$	12.5493	−	6.39419i	0.773823	−	0.394283i	−0.0220417	−	0.999757i	$-0.507017\pi$
$263$	12.5493	−	6.39419i	0.773823	−	0.394283i	0.795865	+	0.605475i	$0.207017\pi$
$264$	−1.53241	−	0.230459i	−0.0943132	−	0.0141838i
$265$	30.3973	−	9.27808i	1.86729	−	0.569948i
$266$	−0.313815	−	0.480490i	−0.0192412	−	0.0294608i
$267$	10.0749	−	1.59570i	0.616571	−	0.0976552i
$268$	13.3994	−	20.8704i	0.818501	−	1.27486i
$269$	5.30034	−	7.29529i	0.323167	−	0.444802i	−0.616264	−	0.787540i	$-0.711354\pi$
$269$	5.30034	−	7.29529i	0.323167	−	0.444802i	0.939431	+	0.342738i	$0.111354\pi$
$270$	−2.90824	+	1.24183i	−0.176990	+	0.0755755i
$271$	−6.50668	−	8.95567i	−0.395253	−	0.544018i	0.564292	−	0.825575i	$-0.309149\pi$
$271$	−6.50668	−	8.95567i	−0.395253	−	0.544018i	−0.959545	+	0.281557i	$0.909149\pi$
$272$	12.6767	−	3.53856i	0.768638	−	0.214557i
$273$	−0.0850078	−	0.0433137i	−0.00514491	−	0.00262146i
$274$	−8.16956	−	6.58045i	−0.493541	−	0.397540i
$275$	−0.939302	+	2.57333i	−0.0566421	+	0.155178i
$276$	3.17426	+	14.5606i	0.191068	+	0.876447i
$277$	12.5869	−	24.7032i	0.756274	−	1.48427i	−0.114943	−	0.993372i	$-0.536668\pi$
$277$	12.5869	−	24.7032i	0.756274	−	1.48427i	0.871217	−	0.490899i	$-0.163332\pi$
$278$	−9.82872	+	8.89625i	−0.589488	+	0.533562i
$279$	1.90687	−	1.38542i	0.114161	−	0.0829430i
$280$	−0.580375	−	0.430695i	−0.0346841	−	0.0257390i
$281$	7.95866	+	5.78231i	0.474774	+	0.344943i	0.799299	−	0.600934i	$-0.205204\pi$
$281$	7.95866	+	5.78231i	0.474774	+	0.344943i	−0.324525	+	0.945877i	$0.605204\pi$
$282$	4.75073	−	0.511827i	0.282902	−	0.0304788i
$283$	2.38077	+	15.0316i	0.141522	+	0.893535i	0.951628	+	0.307252i	$0.0994093\pi$
$283$	2.38077	+	15.0316i	0.141522	+	0.893535i	−0.810106	+	0.586283i	$0.800591\pi$
$284$	−31.4278	−	3.13789i	−1.86490	−	0.186200i
$285$	2.58868	−	7.50683i	0.153340	−	0.444666i
$286$	0.230254	−	0.604532i	0.0136152	−	0.0357467i
$287$	−0.216933	−	0.425755i	−0.0128052	−	0.0251315i
$288$	5.51747	−	1.24803i	0.325120	−	0.0735408i
$289$	5.87157	−	1.90779i	0.345387	−	0.112223i
$290$	−24.5587	−	1.66446i	−1.44214	−	0.0977406i
$291$	−1.64297	−	0.533835i	−0.0963129	−	0.0312940i
$292$	−2.75162	+	1.07271i	−0.161026	+	0.0627759i
$293$	−18.5529	+	18.5529i	−1.08387	+	1.08387i	−0.0877260	+	0.996145i	$0.527960\pi$
$293$	−18.5529	+	18.5529i	−1.08387	+	1.08387i	−0.996145	+	0.0877260i	$0.972040\pi$
$294$	−9.53765	+	2.58223i	−0.556247	+	0.150599i
$295$	12.9223	−	1.81004i	0.752366	−	0.105385i
$296$	−1.25811	+	0.209348i	−0.0731262	+	0.0121681i
$297$	0.541135	+	0.0857074i	0.0313999	+	0.00497325i
$298$	−26.8982	+	12.0598i	−1.55817	+	0.698608i
$299$	−6.22109			−0.359775
$300$	−0.217355	−	9.99764i	−0.0125490	−	0.577214i
$301$	−0.373950			−0.0215541
$302$	25.0063	−	11.2116i	1.43895	−	0.645154i
$303$	−11.3316	−	1.79476i	−0.650986	−	0.103106i
$304$	−6.97387	+	12.3749i	−0.399979	+	0.709747i
$305$	10.8135	−	10.4329i	0.619180	−	0.597384i
$306$	−4.49152	+	1.21604i	−0.256763	+	0.0695162i
$307$	7.59845	−	7.59845i	0.433667	−	0.433667i	−0.456207	−	0.889874i	$-0.650792\pi$
$307$	7.59845	−	7.59845i	0.433667	−	0.433667i	0.889874	+	0.456207i	$0.150792\pi$
$308$	0.0454813	+	0.116664i	0.00259154	+	0.00664755i
$309$	−10.7979	−	3.50844i	−0.614269	−	0.199588i
$310$	1.81866	+	7.22827i	0.103293	+	0.410538i
$311$	18.8976	−	6.14019i	1.07158	−	0.348178i	0.280479	−	0.959860i	$-0.409507\pi$
$311$	18.8976	−	6.14019i	1.07158	−	0.348178i	0.791104	+	0.611682i	$0.209507\pi$
$312$	0.0184377	+	2.36138i	0.00104383	+	0.133687i
$313$	−1.19984	−	2.35482i	−0.0678190	−	0.133102i	0.854608	−	0.519273i	$-0.173797\pi$
$313$	−1.19984	−	2.35482i	−0.0678190	−	0.133102i	−0.922427	+	0.386171i	$0.873797\pi$
$314$	7.87194	−	20.6677i	0.444239	−	1.16635i
$315$	0.203998	+	0.153871i	0.0114940	+	0.00866966i
$316$	−1.03596	+	10.3757i	−0.0582771	+	0.583679i
$317$	2.11922	+	13.3802i	0.119027	+	0.751508i	0.972934	+	0.231082i	$0.0742267\pi$
$317$	2.11922	+	13.3802i	0.119027	+	0.751508i	−0.853907	+	0.520426i	$0.825773\pi$
$318$	19.9849	−	2.15310i	1.12070	−	0.120740i
$319$	3.45020	+	2.50672i	0.193174	+	0.140349i
$320$	−2.83898	+	17.6618i	−0.158704	+	0.987326i
$321$	−2.95352	+	2.14586i	−0.164849	+	0.119770i
$322$	0.892780	−	0.808080i	0.0497527	−	0.0450326i
$323$	5.30465	−	10.4110i	0.295158	−	0.579281i
$324$	−1.95410	+	0.426001i	−0.108561	+	0.0236667i
$325$	4.09706	+	0.800307i	0.227264	+	0.0443930i
$326$	−22.8934	−	18.4403i	−1.26795	−	1.02131i
$327$	4.55576	+	2.32128i	0.251934	+	0.128367i
$328$	−6.87690	+	9.62235i	−0.379713	+	0.531305i
$329$	−0.226942	−	0.312359i	−0.0125117	−	0.0172209i
$330$	−0.889147	+	1.48699i	−0.0489459	+	0.0818563i
$331$	−1.74817	+	2.40616i	−0.0960883	+	0.132254i	−0.854354	−	0.519691i	$-0.826047\pi$
$331$	−1.74817	+	2.40616i	−0.0960883	+	0.132254i	0.758266	+	0.651946i	$0.226047\pi$
$332$	−10.4696	−	6.72185i	−0.574596	−	0.368909i
$333$	0.445374	−	0.0705403i	0.0244063	−	0.00386558i
$334$	−13.2900	−	20.3487i	−0.727197	−	1.11343i
$335$	−15.8942	−	22.7216i	−0.868395	−	1.24141i
$336$	−0.309374	−	0.336483i	−0.0168777	−	0.0183567i
$337$	7.68126	−	3.91380i	0.418425	−	0.213198i	−0.232086	−	0.972695i	$-0.574555\pi$
$337$	7.68126	−	3.91380i	0.418425	−	0.213198i	0.650511	+	0.759497i	$0.274555\pi$
$338$	17.0281	+	3.57315i	0.926209	+	0.194354i
$339$	−4.78619	−	14.7304i	−0.259950	−	0.800044i
$340$	1.72397	−	14.6135i	0.0934953	−	0.792526i
$341$	0.399054	−	1.22816i	0.0216100	−	0.0665087i
$342$	2.49972	−	4.35579i	0.135169	−	0.235534i
$343$	1.13019	+	1.13019i	0.0610246	+	0.0610246i
$344$	4.26631	+	8.21393i	0.230024	+	0.442866i
$345$	16.4072	+	2.90082i	0.883332	+	0.156175i
$346$	−0.934630	+	18.7683i	−0.0502460	+	1.00899i
$347$	4.55737	−	28.7741i	0.244653	−	1.54468i	−0.493321	−	0.869847i	$-0.664217\pi$
$347$	4.55737	−	28.7741i	0.244653	−	1.54468i	0.737974	−	0.674829i	$-0.235783\pi$
$348$	−15.0582	−	3.95095i	−0.807207	−	0.211793i
$349$			24.7013i			1.32223i	0.750284	+	0.661115i	$0.229917\pi$
$349$			24.7013i			1.32223i	−0.750284	+	0.661115i	$0.770083\pi$
$350$	−0.691919	+	0.417332i	−0.0369846	+	0.0223073i
$351$		−	0.834899i		−	0.0445636i
$352$	2.04368	−	2.33001i	0.108928	−	0.124190i
$353$	0.908260	−	5.73453i	0.0483418	−	0.305218i	−0.951656	−	0.307165i	$-0.900620\pi$
$353$	0.908260	−	5.73453i	0.0483418	−	0.305218i	0.999998	+	0.00194675i	$0.000619670\pi$
$354$	8.24235	+	0.410456i	0.438076	+	0.0218155i
$355$	−16.5924	+	31.1711i	−0.880632	+	1.65439i
$356$	−8.20066	+	18.6801i	−0.434634	+	0.990041i
$357$	0.265869	+	0.265869i	0.0140713	+	0.0140713i
$358$	−18.1690	−	10.4269i	−0.960264	−	0.551081i
$359$	4.60845	−	14.1833i	0.243225	−	0.748568i	−0.752699	−	0.658365i	$-0.771248\pi$
$359$	4.60845	−	14.1833i	0.243225	−	0.748568i	0.995923	−	0.0902033i	$-0.0287517\pi$
$360$	1.05246	−	6.23637i	0.0554693	−	0.328686i
$361$	−1.97439	−	6.07654i	−0.103915	−	0.319818i
$362$	−0.819085	+	3.90342i	−0.0430502	+	0.205159i
$363$	−9.53362	+	4.85762i	−0.500385	+	0.254959i
$364$	0.164750	−	0.0962654i	0.00863525	−	0.00504568i
$365$	−0.0591473	+	3.30139i	−0.00309591	+	0.172803i
$366$	7.95656	−	5.19654i	0.415896	−	0.271627i
$367$	19.7109	−	3.12190i	1.02890	−	0.162962i	0.380912	−	0.924611i	$-0.375610\pi$
$367$	19.7109	−	3.12190i	1.02890	−	0.162962i	0.647989	+	0.761649i	$0.275610\pi$
$368$	−27.9353	−	10.3910i	−1.45623	−	0.541668i
$369$	2.45784	−	3.38293i	0.127950	−	0.176108i
$370$	−0.317793	+	1.39009i	−0.0165212	+	0.0722673i
$371$	−0.954674	−	1.31400i	−0.0495642	−	0.0682193i
$372$	0.271214	+	4.70623i	0.0140618	+	0.244007i
$373$	30.1435	+	15.3589i	1.56077	+	0.795253i	0.999476	−	0.0323617i	$-0.0103029\pi$
$373$	30.1435	+	15.3589i	1.56077	+	0.795253i	0.561296	+	0.827615i	$0.310303\pi$
$374$	−1.59924	+	1.98543i	−0.0826945	+	0.102664i
$375$	−10.4322	−	4.02110i	−0.538716	−	0.207649i
$376$	−4.27192	+	8.54848i	−0.220308	+	0.440854i
$377$	2.95041	−	5.79050i	0.151954	−	0.298226i
$378$	0.108448	+	0.119815i	0.00557797	+	0.00616263i
$379$	11.0434	−	8.02353i	0.567264	−	0.412141i	−0.266846	−	0.963739i	$-0.585982\pi$
$379$	11.0434	−	8.02353i	0.567264	−	0.412141i	0.834110	+	0.551598i	$0.185982\pi$
$380$	9.83676	+	12.4681i	0.504615	+	0.639599i
$381$	−8.58914	−	6.24037i	−0.440035	−	0.319704i
$382$	−0.105073	−	0.975280i	−0.00537601	−	0.0498997i
$383$	−3.32987	−	21.0240i	−0.170148	−	1.07427i	−0.913936	−	0.405858i	$-0.866973\pi$
$383$	−3.32987	−	21.0240i	−0.170148	−	1.07427i	0.743788	−	0.668416i	$-0.233027\pi$
$384$	−3.86138	+	10.6344i	−0.197050	+	0.542683i
$385$	0.139973	+	0.00250775i	0.00713370	+	0.000127807i
$386$	1.20212	+	0.457863i	0.0611860	+	0.0233046i
$387$	−1.48565	−	2.91575i	−0.0755198	−	0.148216i
$388$	2.67373	−	2.18828i	0.135738	−	0.111093i
$389$	−5.57557	+	1.81161i	−0.282693	+	0.0918524i	−0.446932	−	0.894568i	$-0.647483\pi$
$389$	−5.57557	+	1.81161i	−0.282693	+	0.0918524i	0.164239	+	0.986421i	$0.447483\pi$
$390$	2.45005	+	0.983785i	0.124063	+	0.0498159i
$391$	23.3173	+	7.57625i	1.17921	+	0.383147i
$392$	5.95988	−	18.8419i	0.301019	−	0.951662i
$393$	−15.7577	+	15.7577i	−0.794872	+	0.794872i
$394$	1.75551	+	6.48411i	0.0884415	+	0.326665i
$395$	10.2909	+	5.47788i	0.517794	+	0.275622i
$396$	−0.728959	+	0.818115i	−0.0366316	+	0.0411118i
$397$	8.40000	+	1.33043i	0.421584	+	0.0667723i	0.363622	−	0.931547i	$-0.381540\pi$
$397$	8.40000	+	1.33043i	0.421584	+	0.0667723i	0.0579615	+	0.998319i	$0.481540\pi$
$398$	10.3293	+	23.0385i	0.517762	+	1.15481i
$399$	−0.405802			−0.0203155
$400$	17.0608	+	10.4370i	0.853038	+	0.521848i
$401$	20.6802			1.03272			0.516360	−	0.856372i	$-0.327287\pi$
$401$	20.6802			1.03272			0.516360	+	0.856372i	$0.327287\pi$
$402$	−7.17476	−	16.0026i	−0.357844	−	0.798135i
$403$	−1.94365	−	0.307843i	−0.0968199	−	0.0153348i
$404$	15.2648	−	17.1317i	0.759450	−	0.852335i
$405$	−0.389304	+	2.20192i	−0.0193446	+	0.109414i
$406$	0.328740	+	1.21423i	0.0163151	+	0.0602610i
$407$	0.174693	−	0.174693i	0.00865921	−	0.00865921i
$408$	2.80666	−	8.87315i	0.138950	−	0.439286i
$409$	−24.9795	−	8.11632i	−1.23515	−	0.401326i	−0.382575	−	0.923924i	$-0.624963\pi$
$409$	−24.9795	−	8.11632i	−1.23515	−	0.401326i	−0.852579	+	0.522598i	$0.824963\pi$
$410$	7.03121	+	11.1988i	0.347246	+	0.553071i
$411$	−7.05464	+	2.29219i	−0.347980	+	0.113065i
$412$	17.5721	−	14.3817i	0.865715	−	0.708535i
$413$	−0.302737	−	0.594154i	−0.0148967	−	0.0292364i
$414$	9.84763	+	3.75077i	0.483984	+	0.184340i
$415$	−11.3983	+	7.97336i	−0.559521	+	0.391397i
$416$	−3.99410	−	2.52052i	−0.195827	−	0.123579i
$417$	1.46643	+	9.25868i	0.0718114	+	0.453399i
$418$	−0.294732	−	2.73568i	−0.0144158	−	0.133807i
$419$	−27.5322	−	20.0033i	−1.34504	−	0.977227i	−0.999242	−	0.0389168i	$-0.987609\pi$
$419$	−27.5322	−	20.0033i	−1.34504	−	0.977227i	−0.345795	−	0.938310i	$-0.612391\pi$
$420$	−0.479390	+	0.177064i	−0.0233919	+	0.00863984i
$421$	−3.66642	+	2.66381i	−0.178690	+	0.129826i	−0.673535	−	0.739155i	$-0.735225\pi$
$421$	−3.66642	+	2.66381i	−0.178690	+	0.129826i	0.494845	+	0.868981i	$0.335225\pi$
$422$	−3.93934	−	4.35225i	−0.191764	−	0.211864i
$423$	1.53390	−	3.01046i	0.0745810	−	0.146373i
$424$	−17.9707	+	35.9608i	−0.872733	+	1.74641i
$425$	−14.3816	−	7.98917i	−0.697609	−	0.387532i
$426$	−14.0096	+	17.3928i	−0.678767	+	0.842683i
$427$	−0.684195	−	0.348615i	−0.0331105	−	0.0168706i
$428$	−0.420080	−	7.28940i	−0.0203053	−	0.352347i
$429$	−0.268868	−	0.370065i	−0.0129811	−	0.0178669i
$430$	10.3070	−	0.923994i	0.497047	−	0.0445590i
$431$	−6.87989	+	9.46936i	−0.331393	+	0.456123i	−0.941903	−	0.335885i	$-0.890964\pi$
$431$	−6.87989	+	9.46936i	−0.331393	+	0.456123i	0.610510	+	0.792009i	$0.290964\pi$
$432$	1.39452	−	3.74904i	0.0670938	−	0.180376i
$433$	−16.1360	+	2.55570i	−0.775448	+	0.122819i	−0.531601	−	0.846995i	$-0.678409\pi$
$433$	−16.1360	+	2.55570i	−0.775448	+	0.122819i	−0.243847	+	0.969814i	$0.578409\pi$
$434$	0.318917	−	0.208289i	0.0153085	−	0.00999820i
$435$	−10.4813	+	13.8958i	−0.502539	+	0.666253i
$436$	−8.82933	+	5.15908i	−0.422848	+	0.247075i
$437$	−23.5767	+	12.0130i	−1.12783	+	0.574657i
$438$	−0.428868	+	2.04380i	−0.0204921	+	0.0976568i
$439$	7.35130	+	22.6250i	0.350858	+	1.07983i	0.958372	+	0.285522i	$0.0921669\pi$
$439$	7.35130	+	22.6250i	0.350858	+	1.07983i	−0.607514	+	0.794309i	$0.707833\pi$
$440$	−1.54184	−	3.10317i	−0.0735044	−	0.147938i
$441$	−2.15908	+	6.64498i	−0.102814	+	0.316427i
$442$	3.36953	+	1.93372i	0.160272	+	0.0919779i
$443$	28.7205	+	28.7205i	1.36455	+	1.36455i	0.868016	+	0.496536i	$0.165395\pi$
$443$	28.7205	+	28.7205i	1.36455	+	1.36455i	0.496536	+	0.868016i	$0.334605\pi$
$444$	−0.362522	+	0.825780i	−0.0172046	+	0.0391898i
$445$	15.8368	+	16.4146i	0.750737	+	0.778128i
$446$	15.6629	+	0.779987i	0.741660	+	0.0369334i
$447$	−3.26074	+	20.5875i	−0.154228	+	0.973755i
$448$	0.900587	−	0.157092i	0.0425487	−	0.00742190i
$449$			16.4871i			0.778074i	0.921222	+	0.389037i	$0.127192\pi$
$449$			16.4871i			0.778074i	−0.921222	+	0.389037i	$0.872808\pi$
$450$	−6.00290	−	3.73701i	−0.282979	−	0.176164i
$451$		−	2.29098i		−	0.107878i
$452$	29.9627	+	7.86154i	1.40933	+	0.369776i
$453$	3.03139	−	19.1394i	0.142427	−	0.899248i
$454$	−0.630605	+	12.6632i	−0.0295958	+	0.594312i
$455$	−0.0295932	−	0.211273i	−0.00138735	−	0.00990463i
$456$	4.62971	+	8.91357i	0.216806	+	0.417416i
$457$	12.2230	+	12.2230i	0.571769	+	0.571769i	0.932623	−	0.360853i	$-0.117514\pi$
$457$	12.2230	+	12.2230i	0.571769	+	0.571769i	−0.360853	+	0.932623i	$0.617514\pi$
$458$	13.4164	−	23.3782i	0.626908	−	1.09239i
$459$	−1.01677	+	3.12929i	−0.0474586	+	0.146063i
$460$	−22.6105	+	24.4786i	−1.05422	+	1.14132i
$461$	7.32565	+	22.5460i	0.341189	+	1.05007i	0.963592	+	0.267376i	$0.0861566\pi$
$461$	7.32565	+	22.5460i	0.341189	+	1.05007i	−0.622403	+	0.782697i	$0.713843\pi$
$462$	0.0866539	+	0.0181833i	0.00403150	+	0.000845962i
$463$	−17.2393	+	8.78385i	−0.801178	+	0.408220i	−0.806109	−	0.591767i	$-0.798430\pi$
$463$	−17.2393	+	8.78385i	−0.801178	+	0.408220i	0.00493114	+	0.999988i	$0.498430\pi$
$464$	22.9203	−	21.0737i	1.06405	−	0.978323i
$465$	4.98252	+	1.71819i	0.231059	+	0.0796791i
$466$	15.8302	+	24.2381i	0.733322	+	1.12281i
$467$	−25.3795	+	4.01972i	−1.17442	+	0.186011i	−0.712997	−	0.701167i	$-0.752663\pi$
$467$	−25.3795	+	4.01972i	−1.17442	+	0.186011i	−0.461428	+	0.887178i	$0.652663\pi$
$468$	1.40513	+	0.902136i	0.0649520	+	0.0417012i
$469$	−0.832936	+	1.14644i	−0.0384614	+	0.0529376i
$470$	7.02688	+	8.04861i	0.324126	+	0.371255i
$471$	−9.19205	−	12.6518i	−0.423547	−	0.582963i
$472$	−9.59692	+	13.4283i	−0.441734	+	0.618086i
$473$	−1.59748	−	0.813959i	−0.0734524	−	0.0374259i
$474$	5.74212	+	4.62519i	0.263744	+	0.212442i
$475$	17.0725	−	4.87844i	0.783339	−	0.223838i
$476$	−0.734736	+	0.160175i	−0.0336765	+	0.00734159i
$477$	6.45267	−	12.6641i	0.295447	−	0.579848i
$478$	−4.78935	+	4.33497i	−0.219060	+	0.198277i
$479$	−27.4905	+	19.9730i	−1.25607	+	0.912590i	−0.998558	−	0.0536842i	$-0.982904\pi$
$479$	−27.4905	+	19.9730i	−1.25607	+	0.912590i	−0.257515	+	0.966274i	$0.582904\pi$
$480$	9.35853	+	8.50987i	0.427156	+	0.388421i
$481$	−0.304577	−	0.221288i	−0.0138875	−	0.0100899i
$482$	−25.5022	+	2.74752i	−1.16159	+	0.125146i
$483$	−0.133201	−	0.841001i	−0.00606088	−	0.0382669i
$484$	2.12606	−	21.2938i	0.0966392	−	0.967899i
$485$	−1.12769	−	3.69460i	−0.0512058	−	0.167763i
$486$	−0.503371	+	1.32160i	−0.0228334	+	0.0599488i
$487$	12.2987	+	24.1375i	0.557307	+	1.09378i	0.982078	+	0.188475i	$0.0603545\pi$
$487$	12.2987	+	24.1375i	0.557307	+	1.09378i	−0.424771	+	0.905301i	$0.639645\pi$
$488$	0.148398	+	19.0058i	0.00671767	+	0.860353i
$489$	−19.7691	+	6.42336i	−0.893988	+	0.290474i
$490$	−16.9559	−	14.1659i	−0.765988	−	0.639949i
$491$	−1.87731	−	0.609975i	−0.0847218	−	0.0275278i	0.266349	−	0.963877i	$-0.414182\pi$
$491$	−1.87731	−	0.609975i	−0.0847218	−	0.0275278i	−0.351071	+	0.936349i	$0.614182\pi$
$492$	3.03765	+	7.79188i	0.136948	+	0.351285i
$493$	−18.1103	+	18.1103i	−0.815647	+	0.815647i
$494$	−4.04724	+	1.09575i	−0.182094	+	0.0493002i
$495$	0.536540	+	1.10136i	0.0241157	+	0.0495024i
$496$	−8.21359	−	4.62879i	−0.368801	−	0.207839i
$497$	1.78239	+	0.282303i	0.0799511	+	0.0126630i
$498$	−8.02770	+	3.59922i	−0.359730	+	0.161285i
$499$	−15.8221			−0.708297			−0.354148	−	0.935189i	$-0.615229\pi$
$499$	−15.8221			−0.708297			−0.354148	+	0.935189i	$0.615229\pi$
$500$	18.0398	−	13.2123i	0.806764	−	0.590874i
$501$	−17.1856			−0.767798
$502$	−21.8105	+	9.77874i	−0.973449	+	0.436447i
$503$	16.5176	+	2.61613i	0.736482	+	0.116647i	0.513397	−	0.858151i	$-0.328387\pi$
$503$	16.5176	+	2.61613i	0.736482	+	0.116647i	0.223086	+	0.974799i	$0.428387\pi$
$504$	−0.318829	+	0.0530527i	−0.0142018	+	0.00236315i
$505$	−11.2354	−	23.0630i	−0.499970	−	1.02629i
$506$	5.57279	−	1.50878i	0.247741	−	0.0670735i
$507$	8.69949	−	8.69949i	0.386358	−	0.386358i
$508$	19.7833	−	7.71249i	0.877743	−	0.342187i
$509$	−18.6546	−	6.06124i	−0.826850	−	0.268660i	−0.135132	−	0.990828i	$-0.543146\pi$
$509$	−18.6546	−	6.06124i	−0.826850	−	0.268660i	−0.691718	+	0.722168i	$0.743146\pi$
$510$	−7.98495	−	6.67107i	−0.353579	−	0.295400i
$511$	0.160484	−	0.0521444i	0.00709939	−	0.00230673i
$512$	−13.7252	−	17.9894i	−0.606572	−	0.795028i
$513$	−1.61219	−	3.16411i	−0.0711801	−	0.139699i
$514$	9.59511	−	25.1919i	0.423222	−	1.11117i
$515$	−7.41134	−	24.2814i	−0.326583	−	1.06997i
$516$	6.51247	+	0.650233i	0.286695	+	0.0286249i
$517$	−0.289581	−	1.82834i	−0.0127358	−	0.0804104i
$518$	0.0724533	−	0.00780585i	0.00318341	−	0.000342969i
$519$	10.7499	+	7.81027i	0.471869	+	0.342833i
$520$	−4.30305	+	3.06039i	−0.188701	+	0.134207i
$521$	18.9520	−	13.7694i	0.830303	−	0.603250i	−0.0893421	−	0.996001i	$-0.528476\pi$
$521$	18.9520	−	13.7694i	0.830303	−	0.603250i	0.919645	+	0.392751i	$0.128476\pi$
$522$	−8.16149	+	7.38719i	−0.357219	+	0.323328i
$523$	−0.561777	+	1.10255i	−0.0245648	+	0.0482111i	−0.902963	−	0.429719i	$-0.858613\pi$
$523$	−0.561777	+	1.10255i	−0.0245648	+	0.0482111i	0.878398	+	0.477930i	$0.158613\pi$
$524$	−9.49333	−	43.5468i	−0.414718	−	1.90235i
$525$	−0.0204665	+	0.570999i	−0.000893231	+	0.0249204i
$526$	15.5120	+	12.4947i	0.676357	+	0.544795i
$527$	6.91009	+	3.52086i	0.301008	+	0.153371i
$528$	−0.589214	−	2.11083i	−0.0256423	−	0.0918620i
$529$	−19.1160	−	26.3109i	−0.831129	−	1.14395i
$530$	29.5599	+	33.8581i	1.28400	+	1.47070i
$531$	3.42999	−	4.72098i	0.148849	−	0.204873i
$532$	0.438482	−	0.682960i	0.0190106	−	0.0296101i
$533$	−3.44817	+	0.546137i	−0.149357	+	0.0236558i
$534$	7.88820	+	12.0778i	0.341356	+	0.522659i
$535$	−7.71735	−	2.66127i	−0.333650	−	0.115057i
$536$	34.6847	+	5.21624i	1.49815	+	0.225307i
$537$	−13.1983	+	6.72485i	−0.569547	+	0.290199i
$538$	12.4808	+	2.61895i	0.538086	+	0.112911i
$539$	1.18292	+	3.64065i	0.0509520	+	0.156814i
$540$	−3.28515	−	3.03444i	−0.141370	−	0.130581i
$541$	5.99846	−	18.4614i	0.257894	−	0.793716i	−0.735352	−	0.677686i	$-0.762983\pi$
$541$	5.99846	−	18.4614i	0.257894	−	0.793716i	0.993246	−	0.116030i	$-0.0370170\pi$
$542$	7.79223	−	13.5780i	0.334705	−	0.583226i
$543$	1.99422	+	1.99422i	0.0855800	+	0.0855800i
$544$	11.9007	+	14.3113i	0.510239	+	0.613592i
$545$	1.58597	+	11.3226i	0.0679354	+	0.485007i
$546$	0.00671074	−	0.134758i	0.000287193	−	0.00576712i
$547$	−0.958973	+	6.05472i	−0.0410027	+	0.258881i	−0.999671	−	0.0256447i	$-0.991836\pi$
$547$	−0.958973	+	6.05472i	−0.0410027	+	0.258881i	0.958668	+	0.284526i	$0.0918361\pi$
$548$	3.76503	−	14.3497i	0.160834	−	0.612987i
$549$		−	6.71978i		−	0.286793i
$550$	−3.86420	+	0.276741i	−0.164770	+	0.0118003i
$551$		−	27.6421i		−	1.17759i
$552$	−16.9532	+	12.5206i	−0.721575	+	0.532912i
$553$	0.0932005	−	0.588445i	0.00396329	−	0.0250232i
$554$	39.1606	+	1.95013i	1.66377	+	0.0828532i
$555$	0.700090	+	0.725633i	0.0297172	+	0.0308014i
$556$	−17.1668	−	7.53632i	−0.728033	−	0.319611i
$557$	−4.22564	−	4.22564i	−0.179046	−	0.179046i	0.611894	−	0.790940i	$-0.290408\pi$
$557$	−4.22564	−	4.22564i	−0.179046	−	0.179046i	−0.790940	+	0.611894i	$0.790408\pi$
$558$	2.89108	+	1.65915i	0.122389	+	0.0702373i
$559$	−0.844279	+	2.59842i	−0.0357092	+	0.109902i
$560$	0.220000	−	0.998132i	0.00929670	−	0.0421788i
$561$	0.557067	+	1.71448i	0.0235194	+	0.0723852i
$562$	−2.85709	+	13.6157i	−0.120519	+	0.574344i
$563$	7.19657	−	3.66683i	0.303299	−	0.154539i	−0.295717	−	0.955276i	$-0.595559\pi$
$563$	7.19657	−	3.66683i	0.303299	−	0.154539i	0.599016	+	0.800737i	$0.295559\pi$
$564$	3.40913	+	5.83444i	0.143550	+	0.245674i
$565$	20.8555	−	27.6497i	0.877398	−	1.16323i
$566$	−18.0200	+	11.7691i	−0.757437	+	0.494693i
$567$	0.112866	−	0.0178763i	0.00473994	−	0.000750732i
$568$	−14.1340	−	42.3715i	−0.593050	−	1.77787i
$569$	20.6135	−	28.3720i	0.864161	−	1.18942i	−0.116400	−	0.993202i	$-0.537135\pi$
$569$	20.6135	−	28.3720i	0.864161	−	1.18942i	0.980561	−	0.196214i	$-0.0628646\pi$
$570$	11.1849	−	1.00270i	0.468484	−	0.0419984i
$571$	−5.87123	−	8.08106i	−0.245703	−	0.338182i	0.668297	−	0.743894i	$-0.267023\pi$
$571$	−5.87123	−	8.08106i	−0.245703	−	0.338182i	−0.914001	+	0.405713i	$0.867023\pi$
$572$	0.913335	−	0.0526344i	0.0381885	−	0.00220075i
$573$	−0.618018	−	0.314896i	−0.0258181	−	0.0131550i
$574$	0.423903	−	0.526271i	0.0176934	−	0.0219661i
$575$	15.7142	+	33.7804i	0.655327	+	1.40874i
$576$	4.80277	+	6.39792i	0.200115	+	0.266580i
$577$	−12.4104	+	24.3568i	−0.516651	+	1.01399i	0.474376	+	0.880323i	$0.342674\pi$
$577$	−12.4104	+	24.3568i	−0.516651	+	1.01399i	−0.991027	+	0.133663i	$0.957326\pi$
$578$	5.85904	+	6.47316i	0.243704	+	0.269248i
$579$	0.735876	−	0.534645i	0.0305820	−	0.0222191i
$580$	−12.0611	−	32.6548i	−0.500811	−	1.35592i
$581$	0.575112	+	0.417843i	0.0238597	+	0.0173351i
$582$	−0.261695	−	2.42903i	−0.0108476	−	0.100687i
$583$	−1.21818	−	7.69128i	−0.0504518	−	0.318540i
$584$	−2.97629	−	2.93018i	−0.123160	−	0.121252i
$585$	1.52976	−	1.07010i	0.0632478	−	0.0442432i
$586$	−34.6757	−	13.2073i	−1.43244	−	0.545589i
$587$	−16.2223	−	31.8381i	−0.669566	−	1.31410i	−0.936597	−	0.350409i	$-0.886042\pi$
$587$	−16.2223	−	31.8381i	−0.669566	−	1.31410i	0.267030	−	0.963688i	$-0.413958\pi$
$588$	−8.85046	−	10.8138i	−0.364987	−	0.445955i
$589$	−7.96049	+	2.58652i	−0.328006	+	0.106576i
$590$	9.81226	+	15.6283i	0.403964	+	0.643407i
$591$	4.51755	+	1.46784i	0.185827	+	0.0603789i
$592$	−0.998061	−	1.50240i	−0.0410201	−	0.0617484i
$593$	−12.3866	+	12.3866i	−0.508656	+	0.508656i	−0.914114	−	0.405458i	$-0.867112\pi$
$593$	−12.3866	+	12.3866i	−0.508656	+	0.508656i	0.405458	+	0.914114i	$0.367112\pi$
$594$	0.202485	+	0.747894i	0.00830808	+	0.0306865i
$595$	−0.146377	+	0.827913i	−0.00600086	+	0.0339411i
$596$	−31.1252	−	27.7332i	−1.27494	−	1.13600i
$597$	17.6333	+	2.79284i	0.721683	+	0.114303i
$598$	−3.59936	−	8.02799i	−0.147189	−	0.328289i
$599$	−10.8175			−0.441989			−0.220995	−	0.975275i	$-0.570930\pi$
$599$	−10.8175			−0.441989			−0.220995	+	0.975275i	$0.570930\pi$
$600$	12.7757	−	6.06485i	0.521564	−	0.247596i
$601$	11.1241			0.453761			0.226881	−	0.973923i	$-0.427147\pi$
$601$	11.1241			0.453761			0.226881	+	0.973923i	$0.427147\pi$
$602$	−0.216357	−	0.482563i	−0.00881807	−	0.0196678i
$603$	−12.2481	−	1.93991i	−0.498782	−	0.0789992i
$604$	28.9359	+	25.7825i	1.17738	+	1.04908i
$605$	−21.1198	−	11.2421i	−0.858643	−	0.457056i
$606$	−4.24014	−	15.6613i	−0.172244	−	0.636196i
$607$	−23.0754	+	23.0754i	−0.936602	+	0.936602i	−0.998107	−	0.0615046i	$-0.980410\pi$
$607$	−23.0754	+	23.0754i	−0.936602	+	0.936602i	0.0615046	+	0.998107i	$0.480410\pi$
$608$	−20.0040	−	1.83966i	−0.811269	−	0.0746080i
$609$	0.845963	+	0.274870i	0.0342802	+	0.0111383i
$610$	19.7195	+	7.91810i	0.798418	+	0.320594i
$611$	−2.68282	+	0.871702i	−0.108535	+	0.0352653i
$612$	−4.16791	−	5.09251i	−0.168478	−	0.205852i
$613$	−14.3058	−	28.0768i	−0.577807	−	1.13401i	−0.976215	−	0.216802i	$-0.930437\pi$
$613$	−14.3058	−	28.0768i	−0.577807	−	1.13401i	0.398408	−	0.917208i	$-0.369563\pi$
$614$	14.2017	+	5.40914i	0.573132	+	0.218295i
$615$	9.34868	+	0.167490i	0.376975	+	0.00675385i
$616$	−0.124235	+	0.126190i	−0.00500555	+	0.00508434i
$617$	2.38218	+	15.0405i	0.0959030	+	0.605508i	0.988094	+	0.153850i	$0.0491672\pi$
$617$	2.38218	+	15.0405i	0.0959030	+	0.605508i	−0.892191	+	0.451658i	$0.850833\pi$
$618$	−1.71990	−	15.9639i	−0.0691844	−	0.642164i
$619$	−16.5938	−	12.0561i	−0.666962	−	0.484576i	0.202045	−	0.979376i	$-0.435241\pi$
$619$	−16.5938	−	12.0561i	−0.666962	−	0.484576i	−0.869007	+	0.494800i	$0.835241\pi$
$620$	−8.27547	+	6.52897i	−0.332351	+	0.262210i
$621$	6.02824	−	4.37977i	0.241905	−	0.175754i
$622$	18.8572	+	20.8338i	0.756105	+	0.835357i
$623$	0.529187	−	1.03859i	0.0212014	−	0.0416102i
$624$	−3.03657	+	1.39002i	−0.121560	+	0.0556455i
$625$	−6.00334	−	24.2685i	−0.240133	−	0.970740i
$626$	2.34457	−	2.91076i	0.0937080	−	0.116338i
$627$	−1.73355	−	0.883290i	−0.0692314	−	0.0352752i
$628$	31.2251	−	1.79946i	1.24602	−	0.0718064i
$629$	0.872093	+	1.20033i	0.0347726	+	0.0478604i
$630$	−0.0805347	+	0.352275i	−0.00320858	+	0.0140350i
$631$	15.9680	−	21.9780i	0.635675	−	0.874931i	−0.362701	−	0.931906i	$-0.618145\pi$
$631$	15.9680	−	21.9780i	0.635675	−	0.874931i	0.998376	+	0.0569743i	$0.0181453\pi$
$632$	−13.9887	+	4.66626i	−0.556440	+	0.185614i
$633$	−4.09983	+	0.649349i	−0.162954	+	0.0258093i
$634$	−16.0403	+	10.4762i	−0.637043	+	0.416062i
$635$	0.425251	−	23.7360i	0.0168756	−	0.941934i
$636$	14.3412	+	24.5437i	0.568664	+	0.973221i
$637$	5.19759	−	2.64830i	0.205936	−	0.104930i
$638$	−1.23859	+	5.90263i	−0.0490364	+	0.233687i
$639$	4.88001	+	15.0191i	0.193050	+	0.594148i
$640$	−24.4342	+	6.55510i	−0.965847	+	0.259113i
$641$	11.5391	−	35.5136i	0.455765	−	1.40270i	−0.414469	−	0.910063i	$-0.636033\pi$
$641$	11.5391	−	35.5136i	0.455765	−	1.40270i	0.870234	−	0.492638i	$-0.163967\pi$
$642$	−4.47794	−	2.56982i	−0.176730	−	0.101423i
$643$	32.3947	+	32.3947i	1.27752	+	1.27752i	0.942051	+	0.335471i	$0.108895\pi$
$643$	32.3947	+	32.3947i	1.27752	+	1.27752i	0.335471	+	0.942051i	$0.391105\pi$
$644$	1.55932	+	0.684552i	0.0614460	+	0.0269751i
$645$	3.43827	−	6.45927i	0.135382	−	0.254333i
$646$	16.5039	+	0.821867i	0.649338	+	0.0323359i
$647$	−1.56537	+	9.88334i	−0.0615410	+	0.388554i	0.937622	+	0.347656i	$0.113022\pi$
$647$	−1.56537	+	9.88334i	−0.0615410	+	0.388554i	−0.999163	+	0.0408988i	$0.986978\pi$
$648$	−1.68032	−	2.27520i	−0.0660093	−	0.0893781i
$649$		−	3.19713i		−	0.125498i
$650$	1.33770	+	5.75008i	0.0524688	+	0.225537i
$651$		−	0.269344i		−	0.0105564i
$652$	10.5507	−	40.2118i	0.413196	−	1.57481i
$653$	3.02216	−	19.0811i	0.118266	−	0.746703i	−0.855272	−	0.518179i	$-0.826610\pi$
$653$	3.02216	−	19.0811i	0.118266	−	0.746703i	0.973538	−	0.228524i	$-0.0733899\pi$
$654$	−0.359643	+	7.22199i	−0.0140632	+	0.282402i
$655$	−49.0692	−	8.67554i	−1.91729	−	0.338981i
$656$	−16.3959	−	3.30705i	−0.640153	−	0.129118i
$657$	1.04416	+	1.04416i	0.0407365	+	0.0407365i
$658$	0.271780	−	0.473579i	0.0105951	−	0.0184620i
$659$	−9.26020	+	28.5000i	−0.360726	+	1.11020i	0.591888	+	0.806020i	$0.298383\pi$
$659$	−9.26020	+	28.5000i	−0.360726	+	1.11020i	−0.952614	+	0.304181i	$0.901617\pi$
$660$	−2.43332	−	0.287062i	−0.0947170	−	0.0111739i
$661$	−11.0378	−	33.9707i	−0.429319	−	1.32131i	−0.898797	−	0.438365i	$-0.855558\pi$
$661$	−11.0378	−	33.9707i	−0.429319	−	1.32131i	0.469478	−	0.882944i	$-0.344442\pi$
$662$	−4.11646	−	0.863789i	−0.159991	−	0.0335721i
$663$	2.44768	−	1.24715i	0.0950599	−	0.0484355i
$664$	2.61673	−	17.3996i	0.101549	−	0.675235i
$665$	−0.520122	−	0.743539i	−0.0201694	−	0.0288332i
$666$	0.348710	+	0.533919i	0.0135122	+	0.0206889i
$667$	57.2867	−	9.07332i	2.21815	−	0.351320i
$668$	18.5696	−	28.9232i	0.718481	−	1.11907i
$669$	6.51799	−	8.97124i	0.252000	−	0.346848i
$670$	20.1250	−	33.6568i	0.777498	−	1.30027i
$671$	−2.16401	−	2.97851i	−0.0835407	−	0.114984i
$672$	0.255218	−	0.593911i	0.00984527	−	0.0229106i
$673$	14.5989	+	7.43852i	0.562747	+	0.286734i	0.712133	−	0.702045i	$-0.247729\pi$
$673$	14.5989	+	7.43852i	0.562747	+	0.286734i	−0.149385	+	0.988779i	$0.547729\pi$
$674$	9.49472	+	7.64784i	0.365723	+	0.294584i
$675$	−4.53348	+	2.10892i	−0.174494	+	0.0811722i
$676$	5.24106	+	24.0412i	0.201579	+	0.924663i
$677$	−19.3278	+	37.9329i	−0.742827	+	1.45788i	0.140973	+	0.990013i	$0.454977\pi$
$677$	−19.3278	+	37.9329i	−0.742827	+	1.45788i	−0.883800	+	0.467866i	$0.845023\pi$
$678$	16.2396	−	14.6989i	0.623678	−	0.564508i
$679$	−0.159708	+	0.116035i	−0.00612903	+	0.00445300i
$680$	19.8553	−	6.23026i	0.761417	−	0.238920i
$681$	7.25309	+	5.26968i	0.277939	+	0.201935i
$682$	1.81576	−	0.195623i	0.0695290	−	0.00749080i
$683$	4.71709	+	29.7825i	0.180494	+	1.13960i	0.897005	+	0.442020i	$0.145738\pi$
$683$	4.71709	+	29.7825i	0.180494	+	1.13960i	−0.716511	+	0.697576i	$0.754262\pi$
$684$	7.06718	+	0.705618i	0.270221	+	0.0269800i
$685$	−13.2419	−	9.98807i	−0.505948	−	0.381625i
$686$	−0.804553	+	2.11235i	−0.0307180	+	0.0806499i
$687$	−8.65291	−	16.9823i	−0.330129	−	0.647915i
$688$	−8.13127	+	10.2578i	−0.310002	+	0.391075i
$689$	−11.2858	+	3.66698i	−0.429955	+	0.139701i
$690$	5.74939	+	22.8509i	0.218876	+	0.869920i
$691$	−21.6237	−	7.02595i	−0.822603	−	0.267280i	−0.132676	−	0.991159i	$-0.542357\pi$
$691$	−21.6237	−	7.02595i	−0.822603	−	0.267280i	−0.689926	+	0.723880i	$0.742357\pi$
$692$	−24.7602	+	9.65274i	−0.941243	+	0.366942i
$693$	0.0442706	−	0.0442706i	0.00168170	−	0.00168170i
$694$	39.7683	−	10.7669i	1.50958	−	0.408705i
$695$	−15.0849	+	14.5539i	−0.572201	+	0.552059i
$696$	−3.61380	−	21.7178i	−0.136981	−	0.823210i
$697$	13.5892	+	2.15232i	0.514728	+	0.0815249i
$698$	−31.8757	+	14.2915i	−1.20651	+	0.540942i
$699$	20.4705			0.774265
$700$	−0.938870	−	0.651428i	−0.0354859	−	0.0246216i
$701$	24.5720			0.928072			0.464036	−	0.885816i	$-0.346401\pi$
$701$	24.5720			0.928072			0.464036	+	0.885816i	$0.346401\pi$
$702$	1.07739	−	0.483050i	0.0406636	−	0.0182316i
$703$	−1.58159	−	0.250500i	−0.0596510	−	0.00944778i
$704$	4.18916	+	1.28918i	0.157885	+	0.0485877i
$705$	7.48200	−	1.04801i	0.281788	−	0.0394704i
$706$	7.92560	−	2.14578i	0.298284	−	0.0807576i
$707$	−0.927047	+	0.927047i	−0.0348652	+	0.0348652i
$708$	4.23913	+	10.8738i	0.159316	+	0.408662i
$709$	23.7263	+	7.70913i	0.891059	+	0.289522i	0.718542	−	0.695484i	$-0.244810\pi$
$709$	23.7263	+	7.70913i	0.891059	+	0.289522i	0.172517	+	0.985007i	$0.444810\pi$
$710$	−49.8245	−	3.37684i	−1.86988	−	0.126731i
$711$	4.95848	−	1.61111i	0.185957	−	0.0604212i
$712$	−28.8503	+	0.225264i	−1.08121	+	0.00844213i
$713$	−7.97338	−	15.6486i	−0.298606	−	0.586046i
$714$	−0.189265	+	0.496915i	−0.00708308	+	0.0185966i
$715$	0.333448	−	0.966955i	0.0124702	−	0.0361621i
$716$	2.94330	−	29.4789i	0.109996	−	1.10168i
$717$	0.714563	+	4.51157i	0.0266859	+	0.168488i
$718$	20.9692	−	2.25914i	0.782563	−	0.0843104i
$719$	40.3089	+	29.2861i	1.50327	+	1.09219i	0.969057	+	0.246836i	$0.0793909\pi$
$719$	40.3089	+	29.2861i	1.50327	+	1.09219i	0.534210	+	0.845352i	$0.320609\pi$
$720$	8.65663	−	2.25006i	0.322614	−	0.0838547i
$721$	−1.04962	+	0.762595i	−0.0390900	+	0.0284005i
$722$	6.69913	−	6.06357i	0.249316	−	0.225663i
$723$	−8.23409	+	16.1603i	−0.306229	+	0.601009i
$724$	−5.51106	+	1.20143i	−0.204817	+	0.0446507i
$725$	−38.8949	−	1.39412i	−1.44452	−	0.0517763i
$726$	−11.7844	−	9.49214i	−0.437360	−	0.352286i
$727$	−12.3755	−	6.30561i	−0.458981	−	0.233862i	0.209183	−	0.977876i	$-0.432919\pi$
$727$	−12.3755	−	6.30561i	−0.458981	−	0.233862i	−0.668164	+	0.744014i	$0.732919\pi$
$728$	0.219545	+	0.156905i	0.00813689	+	0.00581528i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	−4.29449	+	1.83377i	−0.158946	+	0.0678708i
$731$	6.32889	−	8.71097i	0.234082	−	0.322187i
$732$	11.3093	+	7.26094i	0.418004	+	0.268372i
$733$	−20.2370	+	3.20522i	−0.747470	+	0.118388i	−0.518538	−	0.855055i	$-0.673523\pi$
$733$	−20.2370	+	3.20522i	−0.747470	+	0.118388i	−0.228932	+	0.973442i	$0.573523\pi$
$734$	15.4328	+	23.6296i	0.569637	+	0.872186i
$735$	−14.9427	+	4.56092i	−0.551170	+	0.168232i
$736$	−2.75357	−	42.0609i	−0.101498	−	1.55039i
$737$	−6.05363	+	3.08448i	−0.222988	+	0.113618i
$738$	5.78753	+	1.21444i	0.213042	+	0.0447042i
$739$	−0.864509	−	2.66068i	−0.0318015	−	0.0978749i	0.933896	−	0.357545i	$-0.116386\pi$
$739$	−0.864509	−	2.66068i	−0.0318015	−	0.0978749i	−0.965697	+	0.259670i	$0.916386\pi$
$740$	−1.97770	+	0.394173i	−0.0727018	+	0.0144901i
$741$	−0.916193	+	2.81975i	−0.0336572	+	0.103586i
$742$	1.14329	−	1.99220i	0.0419716	−	0.0731359i
$743$	12.0348	+	12.0348i	0.441514	+	0.441514i	0.892520	−	0.451007i	$-0.148935\pi$
$743$	12.0348	+	12.0348i	0.441514	+	0.441514i	−0.451007	+	0.892520i	$0.648935\pi$
$744$	−5.91623	+	3.07289i	−0.216899	+	0.112657i
$745$	−41.9012	+	20.4127i	−1.53514	+	0.747863i
$746$	−2.37961	+	47.7849i	−0.0871236	+	1.74953i
$747$	−0.973158	+	6.14428i	−0.0356060	+	0.224807i
$748$	−3.48737	−	0.915010i	−0.127511	−	0.0334561i
$749$			0.417182i			0.0152435i
$750$	−0.846776	−	15.7887i	−0.0309199	−	0.576522i
$751$			15.7846i			0.575988i	0.957632	+	0.287994i	$0.0929883\pi$
$751$			15.7846i			0.575988i	−0.957632	+	0.287994i	$0.907012\pi$
$752$	−13.5030	−	0.566774i	−0.492403	−	0.0206681i
$753$	−2.64398	+	16.6934i	−0.0963518	+	0.608341i
$754$	9.17936	+	0.457117i	0.334293	+	0.0166472i
$755$	38.9539	−	18.9769i	1.41768	−	0.690640i
$756$	−0.0918701	+	0.209268i	−0.00334128	+	0.00761102i
$757$	29.9500	+	29.9500i	1.08855	+	1.08855i	0.995678	+	0.0928725i	$0.0296049\pi$
$757$	29.9500	+	29.9500i	1.08855	+	1.08855i	0.0928725	+	0.995678i	$0.470395\pi$
$758$	16.7434	+	9.60878i	0.608147	+	0.349007i
$759$	1.26154	−	3.88262i	0.0457910	−	0.140930i
$760$	−10.3981	+	19.9075i	−0.377180	+	0.722121i
$761$	2.86616	+	8.82112i	0.103898	+	0.319765i	0.989470	−	0.144736i	$-0.0462334\pi$
$761$	2.86616	+	8.82112i	0.103898	+	0.319765i	−0.885572	+	0.464502i	$0.846233\pi$
$762$	3.08343	−	14.6943i	0.111701	−	0.532320i
$763$	0.520601	−	0.265259i	0.0188470	−	0.00960304i
$764$	1.19775	−	0.699862i	0.0433332	−	0.0253201i
$765$	−7.03691	+	2.14785i	−0.254420	+	0.0776558i
$766$	25.2037	−	16.4609i	0.910648	−	0.594757i
$767$	−4.81203	+	0.762150i	−0.173752	+	0.0275197i
$768$	−15.9572	+	1.16985i	−0.575805	+	0.0422133i
$769$	−4.01537	+	5.52668i	−0.144798	+	0.199297i	−0.875256	−	0.483661i	$-0.839307\pi$
$769$	−4.01537	+	5.52668i	−0.144798	+	0.199297i	0.730458	+	0.682958i	$0.239307\pi$
$770$	0.0777487	+	0.182079i	0.00280187	+	0.00656167i
$771$	−11.2042	−	15.4213i	−0.403509	−	0.555383i
$772$	0.104664	+	1.81617i	0.00376693	+	0.0653655i
$773$	9.38905	+	4.78396i	0.337701	+	0.172067i	0.614614	−	0.788828i	$-0.289312\pi$
$773$	9.38905	+	4.78396i	0.337701	+	0.172067i	−0.276914	+	0.960895i	$0.589312\pi$
$774$	2.90307	−	3.60413i	0.104349	−	0.129548i
$775$	3.23797	+	11.3316i	0.116311	+	0.407041i
$776$	4.37081	+	2.18422i	0.156903	+	0.0784089i
$777$	0.0233935	−	0.0459124i	0.000839238	−	0.00164710i
$778$	−5.56367	−	6.14683i	−0.199467	−	0.220375i
$779$	−12.0133	+	8.72819i	−0.430422	+	0.312720i
$780$	0.148010	+	3.73085i	0.00529961	+	0.133586i
$781$	6.99974	+	5.08561i	0.250470	+	0.181977i
$782$	3.71401	+	34.4731i	0.132813	+	1.23276i
$783$	1.21768	+	7.68814i	0.0435164	+	0.274752i
$784$	27.7627	−	3.21053i	0.991527	−	0.114662i
$785$	11.3999	−	33.0582i	0.406880	−	1.17990i
$786$	−29.4515	−	11.2175i	−1.05050	−	0.400115i
$787$	−14.4754	−	28.4096i	−0.515993	−	1.01269i	−0.991144	−	0.132789i	$-0.957607\pi$
$787$	−14.4754	−	28.4096i	−0.515993	−	1.01269i	0.475152	−	0.879904i	$-0.342393\pi$
$788$	−7.35171	+	6.01693i	−0.261894	+	0.214344i
$789$	13.3951	−	4.35232i	0.476877	−	0.154947i
$790$	−1.11484	+	16.4493i	−0.0396644	+	0.585239i
$791$	−1.68328	−	0.546932i	−0.0598507	−	0.0194467i
$792$	−1.47749	−	0.467344i	−0.0525003	−	0.0166063i
$793$	−3.96711	+	3.96711i	−0.140876	+	0.140876i
$794$	3.14316	+	11.6095i	0.111547	+	0.412006i
$795$	31.4745	−	4.40866i	1.11628	−	0.156359i
$796$	−23.7537	+	26.6589i	−0.841926	+	0.944899i
$797$	23.1153	+	3.66111i	0.818787	+	0.129683i	0.551757	−	0.834005i	$-0.313958\pi$
$797$	23.1153	+	3.66111i	0.818787	+	0.129683i	0.267030	+	0.963688i	$0.413958\pi$
$798$	−0.234786	−	0.523666i	−0.00831134	−	0.0185376i
$799$	11.1171			0.393294
$800$	−3.59745	+	28.0546i	−0.127189	+	0.991878i
$801$	10.2004			0.360415
$802$	11.9650	+	26.6867i	0.422499	+	0.942341i
$803$	0.799074	+	0.126561i	0.0281987	+	0.00446624i
$804$	16.4993	−	18.5173i	0.581886	−	0.653054i
$805$	1.37022	−	1.32198i	0.0482937	−	0.0465938i
$806$	−0.727286	−	2.68628i	−0.0256176	−	0.0946203i
$807$	6.37632	−	6.37632i	0.224457	−	0.224457i
$808$	30.9394	+	9.78640i	1.08844	+	0.344284i
$809$	37.9775	+	12.3396i	1.33522	+	0.433839i	0.887694	−	0.460433i	$-0.152306\pi$
$809$	37.9775	+	12.3396i	1.33522	+	0.433839i	0.447524	+	0.894272i	$0.352306\pi$
$810$	−3.06670	+	0.771595i	−0.107753	+	0.0271111i
$811$	−43.4885	+	14.1303i	−1.52709	+	0.496181i	−0.947779	−	0.318928i	$-0.896677\pi$
$811$	−43.4885	+	14.1303i	−1.52709	+	0.496181i	−0.579308	+	0.815109i	$0.696677\pi$
$812$	−1.37669	+	1.12674i	−0.0483125	+	0.0395408i
$813$	−5.02559	−	9.86328i	−0.176255	−	0.345920i
$814$	0.326505	+	0.124359i	0.0114440	+	0.00435880i
$815$	−37.1076	−	27.9894i	−1.29982	−	0.980425i
$816$	13.0742	−	1.51192i	0.457688	−	0.0529278i
$817$	1.81791	+	11.4778i	0.0636006	+	0.401559i
$818$	−3.97876	−	36.9305i	−0.139114	−	1.29125i
$819$	−0.0771855	−	0.0560786i	−0.00269708	−	0.00195954i
$820$	−10.3834	+	15.5527i	−0.362605	+	0.543125i
$821$	9.30020	−	6.75699i	0.324579	−	0.235821i	−0.413548	−	0.910482i	$-0.635711\pi$
$821$	9.30020	−	6.75699i	0.324579	−	0.235821i	0.738127	+	0.674662i	$0.235711\pi$
$822$	−7.03957	−	7.77744i	−0.245533	−	0.271269i
$823$	20.5479	−	40.3274i	0.716253	−	1.40573i	−0.189483	−	0.981884i	$-0.560681\pi$
$823$	20.5479	−	40.3274i	0.716253	−	1.40573i	0.905736	−	0.423842i	$-0.139319\pi$
$824$	28.7255	+	14.3550i	1.00070	+	0.500080i
$825$	−1.33030	+	2.39471i	−0.0463150	+	0.0833731i
$826$	0.591569	−	0.734427i	0.0205833	−	0.0255540i
$827$	26.3787	+	13.4406i	0.917278	+	0.467377i	0.847865	−	0.530211i	$-0.177887\pi$
$827$	26.3787	+	13.4406i	0.917278	+	0.467377i	0.0694128	+	0.997588i	$0.477887\pi$
$828$	0.857397	+	14.8779i	0.0297966	+	0.517044i
$829$	−1.32329	−	1.82135i	−0.0459597	−	0.0632581i	0.785419	−	0.618965i	$-0.212448\pi$
$829$	−1.32329	−	1.82135i	−0.0459597	−	0.0632581i	−0.831378	+	0.555707i	$0.812448\pi$
$830$	−16.8839	−	10.0957i	−0.586050	−	0.350428i
$831$	16.2964	−	22.4300i	0.565315	−	0.778089i
$832$	0.941716	−	6.61247i	0.0326481	−	0.229246i
$833$	−22.7063	+	3.59632i	−0.786727	+	0.124605i
$834$	−11.0994	+	7.24917i	−0.384341	+	0.251018i
$835$	−22.0270	−	31.4887i	−0.762277	−	1.08971i
$836$	3.35973	−	1.96313i	0.116199	−	0.0678962i
$837$	2.10012	−	1.07006i	0.0725908	−	0.0369868i
$838$	9.88384	−	47.1023i	0.341432	−	1.62712i
$839$	10.6542	+	32.7902i	0.367823	+	1.13204i	0.948194	+	0.317691i	$0.102907\pi$
$839$	10.6542	+	32.7902i	0.367823	+	1.13204i	−0.580371	+	0.814352i	$0.697093\pi$
$840$	−0.505854	−	0.516183i	−0.0174536	−	0.0178100i
$841$	−9.76191	+	30.0441i	−0.336618	+	1.03600i
$842$	−5.55880	−	3.19011i	−0.191569	−	0.109939i
$843$	6.95613	+	6.95613i	0.239582	+	0.239582i
$844$	3.33715	−	7.60161i	0.114869	−	0.261658i
$845$	27.0901	+	4.78958i	0.931927	+	0.164767i
$846$	4.77231	+	0.237653i	0.164075	+	0.00817069i
$847$	−0.191273	+	1.20765i	−0.00657221	+	0.0414953i
$848$	−56.8029	−	2.38424i	−1.95062	−	0.0818753i
$849$			15.2189i			0.522313i
$850$	1.98881	−	23.1810i	0.0682155	−	0.795101i
$851$		−	3.35999i		−	0.115179i
$852$	−30.5500	−	8.01565i	−1.04663	−	0.274612i
$853$	−5.21245	+	32.9101i	−0.178471	+	1.12682i	0.721997	+	0.691897i	$0.243225\pi$
$853$	−5.21245	+	32.9101i	−0.178471	+	1.12682i	−0.900467	+	0.434924i	$0.856775\pi$
$854$	0.0540121	−	1.08462i	0.00184826	−	0.0371148i
$855$	3.73113	−	7.00945i	0.127602	−	0.239718i
$856$	9.16354	−	4.75954i	0.313203	−	0.162678i
$857$	17.1757	+	17.1757i	0.586710	+	0.586710i	0.936739	−	0.350029i	$-0.113828\pi$
$857$	17.1757	+	17.1757i	0.586710	+	0.586710i	−0.350029	+	0.936739i	$0.613828\pi$
$858$	0.321989	−	0.561069i	0.0109925	−	0.0191546i
$859$	9.50209	−	29.2444i	0.324207	−	0.997807i	−0.647590	−	0.761989i	$-0.724223\pi$
$859$	9.50209	−	29.2444i	0.324207	−	0.997807i	0.971797	−	0.235818i	$-0.0757770\pi$
$860$	7.15571	+	12.7660i	0.244008	+	0.435318i
$861$	−0.147659	−	0.454449i	−0.00503222	−	0.0154876i
$862$	−16.2002	−	3.39942i	−0.551782	−	0.115785i
$863$	−33.7650	+	17.2041i	−1.14937	+	0.585635i	−0.921624	−	0.388085i	$-0.873137\pi$
$863$	−33.7650	+	17.2041i	−1.14937	+	0.585635i	−0.227749	+	0.973720i	$0.573137\pi$
$864$	5.64477	−	0.369542i	0.192039	−	0.0125721i
$865$	−0.532233	+	29.7073i	−0.0180965	+	1.01008i
$866$	−12.6339	−	19.3440i	−0.429316	−	0.657337i
$867$	6.09773	−	0.965785i	0.207090	−	0.0327998i
$868$	0.453303	+	0.291035i	0.0153861	+	0.00987837i
$869$	1.67898	−	2.31092i	0.0569556	−	0.0783927i
$870$	−23.9960	−	5.48580i	−0.813541	−	0.185986i
$871$	6.08558	+	8.37608i	0.206202	+	0.283813i
$872$	−11.7659	−	8.40887i	−0.398445	−	0.284760i
$873$	−1.53924	−	0.784280i	−0.0520953	−	0.0265439i
$874$	−29.1429	−	23.4742i	−0.985775	−	0.794026i
$875$	−1.07246	+	0.694356i	−0.0362556	+	0.0234735i
$876$	−2.88555	+	0.629059i	−0.0974938	+	0.0212539i
$877$	−9.77765	+	19.1897i	−0.330168	+	0.647991i	−0.995096	−	0.0989168i	$-0.968462\pi$
$877$	−9.77765	+	19.1897i	−0.330168	+	0.647991i	0.664928	+	0.746908i	$0.268462\pi$
$878$	−24.9431	+	22.5767i	−0.841788	+	0.761925i
$879$	−21.2268	+	15.4222i	−0.715961	+	0.520176i
$880$	3.11241	−	3.78507i	0.104919	−	0.127595i
$881$	−4.08907	−	2.97088i	−0.137764	−	0.100092i	0.516769	−	0.856125i	$-0.327135\pi$
$881$	−4.08907	−	2.97088i	−0.137764	−	0.100092i	−0.654533	+	0.756034i	$0.727135\pi$
$882$	−9.82418	+	1.05842i	−0.330797	+	0.0356389i
$883$	−2.70778	−	17.0963i	−0.0911241	−	0.575335i	−0.990430	−	0.138015i	$-0.955928\pi$
$883$	−2.70778	−	17.0963i	−0.0911241	−	0.575335i	0.899306	−	0.437320i	$-0.144072\pi$
$884$	−0.545849	+	5.46700i	−0.0183589	+	0.183875i
$885$	13.0464	+	0.233737i	0.438549	+	0.00785699i
$886$	−20.4454	+	53.6792i	−0.686876	+	1.80339i
$887$	−6.24858	−	12.2635i	−0.209807	−	0.411769i	0.761990	−	0.647589i	$-0.224223\pi$
$887$	−6.24858	−	12.2635i	−0.209807	−	0.411769i	−0.971797	+	0.235820i	$0.924223\pi$
$888$	−1.27537	+	0.00995814i	−0.0427986	+	0.000334173i
$889$	−1.15383	+	0.374902i	−0.0386983	+	0.0125738i
$890$	−12.0195	+	29.9336i	−0.402893	+	1.00338i
$891$	0.521065	+	0.169304i	0.0174563	+	0.00567191i
$892$	8.05560	+	20.6634i	0.269721	+	0.691862i
$893$	−8.48413	+	8.48413i	−0.283910	+	0.283910i
$894$	−28.4537	+	7.70356i	−0.951633	+	0.257646i
$895$	−29.2381	−	15.5635i	−0.977322	−	0.520229i
$896$	0.723774	+	1.07127i	0.0241796	+	0.0357886i
$897$	−6.14450	−	0.973193i	−0.205159	−	0.0324940i
$898$	−21.2757	+	9.53899i	−0.709980	+	0.318320i
$899$	18.3470			0.611906
$900$	1.34930	−	9.90855i	0.0449766	−	0.330285i
$901$	46.7662			1.55801
$902$	2.95639	−	1.32550i	0.0984369	−	0.0441343i
$903$	−0.369346	−	0.0584987i	−0.0122911	−	0.00194671i
$904$	7.19069	+	43.2137i	0.239159	+	1.43727i
$905$	−1.09793	+	6.20995i	−0.0364965	+	0.206426i
$906$	26.4523	−	7.16171i	0.878818	−	0.237932i
$907$	27.9127	−	27.9127i	0.926827	−	0.926827i	−0.0706721	−	0.997500i	$-0.522514\pi$
$907$	27.9127	−	27.9127i	0.926827	−	0.926827i	0.997500	+	0.0706721i	$0.0225144\pi$
$908$	−16.7060	+	6.51281i	−0.554408	+	0.216135i
$909$	−10.9114	−	3.54532i	−0.361907	−	0.117591i
$910$	0.255515	−	0.160425i	0.00847023	−	0.00531805i
$911$	15.2643	−	4.95966i	0.505727	−	0.164321i	−0.0450309	−	0.998986i	$-0.514339\pi$
$911$	15.2643	−	4.95966i	0.505727	−	0.164321i	0.550758	+	0.834665i	$0.314339\pi$
$912$	−8.82387	+	11.1315i	−0.292187	+	0.368602i
$913$	1.54733	+	3.03681i	0.0512092	+	0.100504i
$914$	−8.70126	+	22.8451i	−0.287812	+	0.755648i
$915$	12.3124	−	8.61282i	0.407037	−	0.284731i
$916$	37.9308	+	3.78717i	1.25327	+	0.125132i
$917$	0.398368	+	2.51520i	0.0131553	+	0.0830592i
$918$	−4.62645	+	0.498437i	−0.152696	+	0.0164509i
$919$	−36.9460	−	26.8429i	−1.21874	−	0.885465i	−0.222743	−	0.974877i	$-0.571501\pi$
$919$	−36.9460	−	26.8429i	−1.21874	−	0.885465i	−0.995995	+	0.0894125i	$0.971501\pi$
$920$	−44.6702	−	15.0150i	−1.47273	−	0.495030i
$921$	8.69356	−	6.31624i	0.286463	−	0.208127i
$922$	−24.8560	+	22.4979i	−0.818590	+	0.740928i
$923$	5.98576	−	11.7477i	0.197024	−	0.386681i
$924$	0.0266711	+	0.122343i	0.000877413	+	0.00402478i
$925$	−0.432242	+	2.21281i	−0.0142120	+	0.0727566i
$926$	−21.3093	−	17.1643i	−0.700267	−	0.564053i
$927$	−10.1161	−	5.15440i	−0.332256	−	0.169293i
$928$	40.4556	+	17.3848i	1.32802	+	0.570683i
$929$	−7.41525	−	10.2062i	−0.243286	−	0.334855i	0.669860	−	0.742488i	$-0.266354\pi$
$929$	−7.41525	−	10.2062i	−0.243286	−	0.334855i	−0.913146	+	0.407633i	$0.866354\pi$
$930$	0.665523	+	7.42378i	0.0218233	+	0.243435i
$931$	14.5840	−	20.0731i	0.477971	−	0.657870i
$932$	−22.1190	+	34.4516i	−0.724533	+	1.12850i
$933$	19.6254	−	3.10836i	0.642508	−	0.101763i
$934$	−19.8711	−	30.4252i	−0.650204	−	0.995544i
$935$	−2.42738	+	3.21816i	−0.0793840	+	0.105245i
$936$	−0.351190	+	2.33519i	−0.0114790	+	0.0763281i
$937$	−22.9827	+	11.7103i	−0.750812	+	0.382558i	−0.787134	−	0.616782i	$-0.788436\pi$
$937$	−22.9827	+	11.7103i	−0.750812	+	0.382558i	0.0363216	+	0.999340i	$0.488436\pi$
$938$	−1.96133	−	0.411562i	−0.0640398	−	0.0134380i
$939$	−0.816693	−	2.51352i	−0.0266518	−	0.0820257i
$940$	−6.32075	+	13.7245i	−0.206160	+	0.447645i
$941$	−1.17001	+	3.60092i	−0.0381412	+	0.117387i	−0.968314	−	0.249735i	$-0.919657\pi$
$941$	−1.17001	+	3.60092i	−0.0381412	+	0.117387i	0.930173	+	0.367121i	$0.119657\pi$
$942$	11.0082	−	19.1818i	0.358665	−	0.624978i
$943$	−22.0319	−	22.0319i	−0.717458	−	0.717458i
$944$	−22.8810	−	4.61508i	−0.744713	−	0.150208i
$945$	0.177416	+	0.183889i	0.00577135	+	0.00598192i
$946$	0.126109	−	2.53240i	0.00410017	−	0.0823355i
$947$	4.94264	−	31.2066i	0.160614	−	1.01408i	−0.767301	−	0.641287i	$-0.778401\pi$
$947$	4.94264	−	31.2066i	0.160614	−	1.01408i	0.927915	−	0.372791i	$-0.121599\pi$
$948$	−2.64632	+	10.0859i	−0.0859485	+	0.327575i
$949$		−	1.23286i		−	0.0400205i
$950$	16.1730	+	19.2086i	0.524723	+	0.623209i
$951$			13.5470i			0.439292i
$952$	−0.631795	−	0.855465i	−0.0204766	−	0.0277258i
$953$	3.41362	−	21.5528i	0.110578	−	0.698162i	−0.868654	−	0.495419i	$-0.835014\pi$
$953$	3.41362	−	21.5528i	0.110578	−	0.698162i	0.979232	−	0.202743i	$-0.0649856\pi$
$954$	20.0757	+	0.999735i	0.649973	+	0.0323676i
$955$	−0.215147	−	1.53598i	−0.00696198	−	0.0497032i
$956$	−8.36504	−	3.67230i	−0.270545	−	0.118771i
$957$	3.01559	+	3.01559i	0.0974802	+	0.0974802i
$958$	−41.6794	−	23.9192i	−1.34660	−	0.772793i
$959$	−0.261936	+	0.806155i	−0.00845835	+	0.0260321i
$960$	−5.56695	+	17.0003i	−0.179673	+	0.548681i
$961$	7.86277	+	24.1991i	0.253638	+	0.780617i
$962$	0.109340	−	0.521071i	0.00352528	−	0.0168000i
$963$	−3.25284	+	1.65741i	−0.104821	+	0.0534091i
$964$	−18.3004	−	31.3196i	−0.589417	−	1.00874i
$965$	1.92280	+	0.663063i	0.0618970	+	0.0213447i
$966$	1.00820	−	0.658470i	0.0324383	−	0.0211859i
$967$	25.3994	−	4.02287i	0.816791	−	0.129367i	0.265960	−	0.963984i	$-0.414311\pi$
$967$	25.3994	−	4.02287i	0.816791	−	0.129367i	0.550830	+	0.834617i	$0.314311\pi$
$968$	28.7086	−	9.57643i	0.922729	−	0.307798i
$969$	6.86797	−	9.45295i	0.220631	−	0.303672i
$970$	4.11523	−	3.59282i	0.132132	−	0.115358i
$971$	33.1950	+	45.6890i	1.06528	+	1.46623i	0.874765	+	0.484547i	$0.161016\pi$
$971$	33.1950	+	45.6890i	1.06528	+	1.46623i	0.190514	+	0.981684i	$0.438984\pi$
$972$	−1.99669	+	0.115067i	−0.0640438	+	0.00369077i
$973$	0.954452	+	0.486317i	0.0305983	+	0.0155906i
$974$	−24.0325	+	29.8361i	−0.770051	+	0.956011i
$975$	3.92143	+	1.43138i	0.125586	+	0.0458407i
$976$	−24.4401	+	11.1878i	−0.782310	+	0.358111i
$977$	10.2310	−	20.0795i	0.327320	−	0.642401i	−0.667437	−	0.744666i	$-0.732609\pi$
$977$	10.2310	−	20.0795i	0.327320	−	0.642401i	0.994757	+	0.102265i	$0.0326088\pi$
$978$	−19.7269	−	21.7945i	−0.630795	−	0.696913i
$979$	4.52129	−	3.28491i	0.144501	−	0.104986i
$980$	8.47011	−	30.0766i	0.270568	−	0.960763i
$981$	4.13654	+	3.00537i	0.132070	+	0.0959542i
$982$	−0.299020	−	2.77548i	−0.00954212	−	0.0885692i
$983$	0.276219	+	1.74398i	0.00881001	+	0.0556242i	0.991702	−	0.128560i	$-0.0410356\pi$
$983$	0.276219	+	1.74398i	0.00881001	+	0.0556242i	−0.982892	+	0.184185i	$0.941036\pi$
$984$	−8.29750	+	8.42810i	−0.264515	+	0.268678i
$985$	3.10071	+	10.1587i	0.0987970	+	0.323684i
$986$	−33.8485	−	12.8922i	−1.07796	−	0.410573i
$987$	−0.175284	−	0.344014i	−0.00557935	−	0.0109501i
$988$	−3.75563	−	4.58877i	−0.119483	−	0.145988i
$989$	−23.1904	+	7.53502i	−0.737412	+	0.239600i
$990$	−1.11082	+	1.32959i	−0.0353041	+	0.0422572i
$991$	−1.11091	−	0.360956i	−0.0352891	−	0.0114661i	0.291319	−	0.956626i	$-0.405906\pi$
$991$	−1.11091	−	0.360956i	−0.0352891	−	0.0114661i	−0.326608	+	0.945160i	$0.605906\pi$
$992$	1.22104	−	13.2773i	0.0387681	−	0.421554i
$993$	−2.10306	+	2.10306i	−0.0667385	+	0.0667385i
$994$	0.666945	+	2.46341i	0.0211542	+	0.0781346i
$995$	17.4836	+	35.8886i	0.554266	+	1.13774i
$996$	−9.28922	−	8.27690i	−0.294340	−	0.262264i
$997$	−54.1659	−	8.57903i	−1.71545	−	0.271701i	−0.780159	−	0.625581i	$-0.784862\pi$
$997$	−54.1659	−	8.57903i	−1.71545	−	0.271701i	−0.935291	+	0.353881i	$0.884862\pi$
$998$	−9.15427	−	20.4176i	−0.289773	−	0.646309i
$999$	0.450925			0.0142667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.67.19	yes	240
3.2	odd	2		900.2.bj.f.667.12		240
4.3	odd	2	inner	300.2.w.a.67.1	✓	240
12.11	even	2		900.2.bj.f.667.30		240
25.3	odd	20	inner	300.2.w.a.103.1	yes	240
75.53	even	20		900.2.bj.f.703.30		240
100.3	even	20	inner	300.2.w.a.103.19	yes	240
300.203	odd	20		900.2.bj.f.703.12		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.1	✓	240	4.3	odd	2	inner
300.2.w.a.67.19	yes	240	1.1	even	1	trivial
300.2.w.a.103.1	yes	240	25.3	odd	20	inner
300.2.w.a.103.19	yes	240	100.3	even	20	inner
900.2.bj.f.667.12		240	3.2	odd	2
900.2.bj.f.667.30		240	12.11	even	2
900.2.bj.f.703.12		240	300.203	odd	20
900.2.bj.f.703.30		240	75.53	even	20

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.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.578573 + 1.29045i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-1.33051 + 1.49324i) q^{4} +(0.979302 + 2.01022i) q^{5} +(0.369579 + 1.36507i) q^{6} +(0.0808033 - 0.0808033i) q^{7} +(-2.69674 - 0.853002i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(0.578573 + 1.29045i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-1.33051 + 1.49324i) q^{4} +(0.979302 + 2.01022i) q^{5} +(0.369579 + 1.36507i) q^{6} +(0.0808033 - 0.0808033i) q^{7} +(-2.69674 - 0.853002i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-2.02748 + 2.42679i) q^{10} +(0.521065 - 0.169304i) q^{11} +(-1.54772 + 1.26671i) q^{12} +(-0.379036 - 0.743901i) q^{13} +(0.151023 + 0.0575218i) q^{14} +(0.652778 + 2.13866i) q^{15} +(-0.459504 - 3.97352i) q^{16} +(0.514721 + 3.24982i) q^{17} +(0.151486 + 1.40608i) q^{18} +(-2.87295 - 2.08732i) q^{19} +(-4.30469 - 1.21228i) q^{20} +(0.0924489 - 0.0671680i) q^{21} +(0.519953 + 0.574452i) q^{22} +(3.38282 - 6.63917i) q^{23} +(-2.53010 - 1.26436i) q^{24} +(-3.08194 + 3.93722i) q^{25} +(0.740664 - 0.919527i) q^{26} +(0.891007 + 0.453990i) q^{27} +(0.0131490 + 0.228168i) q^{28} +(4.57530 + 6.29737i) q^{29} +(-2.38215 + 2.07975i) q^{30} +(1.38542 - 1.90687i) q^{31} +(4.86176 - 2.89194i) q^{32} +(0.541135 - 0.0857074i) q^{33} +(-3.89592 + 2.54448i) q^{34} +(0.241563 + 0.0833013i) q^{35} +(-1.72682 + 1.00900i) q^{36} +(0.401778 - 0.204716i) q^{37} +(1.03136 - 4.91506i) q^{38} +(-0.257998 - 0.794036i) q^{39} +(-0.926199 - 6.25637i) q^{40} +(1.29216 - 3.97687i) q^{41} +(0.140165 + 0.0804388i) q^{42} +(-2.31395 - 2.31395i) q^{43} +(-0.440470 + 1.00333i) q^{44} +(0.310180 + 2.21445i) q^{45} +(10.5247 + 0.524113i) q^{46} +(0.528548 - 3.33712i) q^{47} +(0.167748 - 3.99648i) q^{48} +6.98694i q^{49} +(-6.86389 - 1.69911i) q^{50} +3.29033i q^{51} +(1.61513 + 0.423774i) q^{52} +(2.22344 - 14.0382i) q^{53} +(-0.0703383 + 1.41246i) q^{54} +(0.850619 + 0.881654i) q^{55} +(-0.286831 + 0.148980i) q^{56} +(-2.51105 - 2.51105i) q^{57} +(-5.47927 + 9.54767i) q^{58} +(1.80325 - 5.54984i) q^{59} +(-4.06205 - 1.87075i) q^{60} +(-2.07653 - 6.39089i) q^{61} +(3.26228 + 0.684550i) q^{62} +(0.101818 - 0.0518789i) q^{63} +(6.54477 + 4.60065i) q^{64} +(1.12421 - 1.49045i) q^{65} +(0.423687 + 0.648718i) q^{66} +(-12.2481 + 1.93991i) q^{67} +(-5.53758 - 3.55531i) q^{68} +(4.37977 - 6.02824i) q^{69} +(0.0322659 + 0.359920i) q^{70} +(9.28233 + 12.7760i) q^{71} +(-2.30116 - 1.64459i) q^{72} +(1.31572 + 0.670391i) q^{73} +(0.496633 + 0.400030i) q^{74} +(-3.65991 + 3.40662i) q^{75} +(6.93934 - 1.51280i) q^{76} +(0.0284234 - 0.0557842i) q^{77} +(0.875391 - 0.792341i) q^{78} +(4.21793 - 3.06451i) q^{79} +(7.53764 - 4.81498i) q^{80} +(0.809017 + 0.587785i) q^{81} +(5.87955 - 0.633441i) q^{82} +(0.973158 + 6.14428i) q^{83} +(-0.0227061 + 0.227415i) q^{84} +(-6.02877 + 4.21725i) q^{85} +(1.64724 - 4.32483i) q^{86} +(3.53385 + 6.93557i) q^{87} +(-1.54959 + 0.0120993i) q^{88} +(9.70119 - 3.15211i) q^{89} +(-2.67817 + 1.68149i) q^{90} +(-0.0907370 - 0.0294822i) q^{91} +(5.41297 + 13.8848i) q^{92} +(1.66666 - 1.66666i) q^{93} +(4.61218 - 1.24870i) q^{94} +(1.38248 - 7.81937i) q^{95} +(5.25430 - 2.09579i) q^{96} +(-1.70626 - 0.270245i) q^{97} +(-9.01628 + 4.04246i) q^{98} +0.547881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

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