LMFDB - Embedded newform 336.2.bq.b.109.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.25
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18402 + 0.773373i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.803789 + 1.83137i) q^{4} +(-4.06164 - 1.08831i) q^{5} +(-1.34384 - 0.440575i) q^{6} +(-2.62820 + 0.304251i) q^{7} +(-0.464633 + 2.79000i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(1.18402 + 0.773373i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.803789 + 1.83137i) q^{4} +(-4.06164 - 1.08831i) q^{5} +(-1.34384 - 0.440575i) q^{6} +(-2.62820 + 0.304251i) q^{7} +(-0.464633 + 2.79000i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-3.96738 - 4.42974i) q^{10} +(-0.970020 - 3.62016i) q^{11} +(-1.25039 - 1.56093i) q^{12} +(0.0588814 + 0.0588814i) q^{13} +(-3.34713 - 1.67234i) q^{14} +4.20492 q^{15} +(-2.70785 + 2.94407i) q^{16} +(-2.36571 + 4.09753i) q^{17} +(1.41207 + 0.0777523i) q^{18} +(0.709823 - 2.64909i) q^{19} +(-1.27160 - 8.31315i) q^{20} +(2.45990 - 0.974112i) q^{21} +(1.65122 - 5.03652i) q^{22} +(-6.09208 + 3.51726i) q^{23} +(-0.273305 - 2.81519i) q^{24} +(10.9824 + 6.34068i) q^{25} +(0.0241793 + 0.115254i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.66971 - 4.56866i) q^{28} +(1.33075 + 1.33075i) q^{29} +(4.97869 + 3.25197i) q^{30} +(-4.34953 + 7.53361i) q^{31} +(-5.48300 + 1.39166i) q^{32} +(1.87394 + 3.24575i) q^{33} +(-5.96996 + 3.02197i) q^{34} +(11.0059 + 1.62455i) q^{35} +(1.61179 + 1.18412i) q^{36} +(3.23201 + 0.866013i) q^{37} +(2.88918 - 2.58761i) q^{38} +(-0.0721147 - 0.0416354i) q^{39} +(4.92357 - 10.8263i) q^{40} -6.05310i q^{41} +(3.66591 + 0.749055i) q^{42} +(-1.31081 + 1.31081i) q^{43} +(5.85018 - 4.68632i) q^{44} +(-4.06164 + 1.08831i) q^{45} +(-9.93328 - 0.546950i) q^{46} +(-1.56674 - 2.71367i) q^{47} +(1.85360 - 3.54460i) q^{48} +(6.81486 - 1.59926i) q^{49} +(8.09961 + 16.0009i) q^{50} +(1.22458 - 4.57020i) q^{51} +(-0.0605055 + 0.155162i) q^{52} +(-0.818053 - 3.05301i) q^{53} +(-1.38408 + 0.290369i) q^{54} +15.7595i q^{55} +(0.372288 - 7.47405i) q^{56} +2.74254i q^{57} +(0.546464 + 2.60479i) q^{58} +(-1.60481 - 5.98923i) q^{59} +(3.37987 + 7.70077i) q^{60} +(-0.0796808 + 0.297373i) q^{61} +(-10.9762 + 5.55611i) q^{62} +(-2.12396 + 1.57759i) q^{63} +(-7.56823 - 2.59266i) q^{64} +(-0.175074 - 0.303237i) q^{65} +(-0.291405 + 5.29227i) q^{66} +(-12.5143 + 3.35320i) q^{67} +(-9.40563 - 1.03894i) q^{68} +(4.97416 - 4.97416i) q^{69} +(11.7748 + 10.4352i) q^{70} -4.95669i q^{71} +(0.992617 + 2.64853i) q^{72} +(10.5223 + 6.07505i) q^{73} +(3.15700 + 3.52492i) q^{74} +(-12.2493 - 3.28218i) q^{75} +(5.42202 - 0.829364i) q^{76} +(3.65084 + 9.21938i) q^{77} +(-0.0531853 - 0.105069i) q^{78} +(-3.19808 - 5.53924i) q^{79} +(14.2024 - 9.01079i) q^{80} +(0.500000 - 0.866025i) q^{81} +(4.68130 - 7.16697i) q^{82} +(1.77457 + 1.77457i) q^{83} +(3.76120 + 3.72201i) q^{84} +(14.0681 - 14.0681i) q^{85} +(-2.56577 + 0.538277i) q^{86} +(-1.62983 - 0.940982i) q^{87} +(10.5510 - 1.02431i) q^{88} +(0.469248 - 0.270920i) q^{89} +(-5.65072 - 1.85258i) q^{90} +(-0.172667 - 0.136837i) q^{91} +(-11.3382 - 8.32972i) q^{92} +(2.25148 - 8.40265i) q^{93} +(0.243634 - 4.42469i) q^{94} +(-5.76609 + 9.98716i) q^{95} +(4.93598 - 2.76334i) q^{96} -6.14973 q^{97} +(9.30574 + 3.37687i) q^{98} +(-2.65014 - 2.65014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

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

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

$2$	1.18402	+	0.773373i	0.837226	+	0.546857i
$2$	1.18402	+	0.773373i	0.837226	+	0.546857i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	0.803789	+	1.83137i	0.401895	+	0.915686i
$5$	−4.06164	−	1.08831i	−1.81642	−	0.486709i	−0.820086	−	0.572241i	$-0.806074\pi$
$5$	−4.06164	−	1.08831i	−1.81642	−	0.486709i	−0.996335	+	0.0855320i	$0.972741\pi$
$6$	−1.34384	−	0.440575i	−0.548619	−	0.179864i
$7$	−2.62820	+	0.304251i	−0.993366	+	0.114996i
$7$	−2.62820	+	0.304251i	−0.993366	+	0.114996i
$8$	−0.464633	+	2.79000i	−0.164273	+	0.986415i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−3.96738	−	4.42974i	−1.25459	−	1.40081i
$11$	−0.970020	−	3.62016i	−0.292472	−	1.09152i	−0.943204	−	0.332213i	$-0.892205\pi$
$11$	−0.970020	−	3.62016i	−0.292472	−	1.09152i	0.650732	−	0.759307i	$-0.274462\pi$
$12$	−1.25039	−	1.56093i	−0.360958	−	0.450603i
$13$	0.0588814	+	0.0588814i	0.0163308	+	0.0163308i	0.715225	−	0.698894i	$-0.246324\pi$
$13$	0.0588814	+	0.0588814i	0.0163308	+	0.0163308i	−0.698894	+	0.715225i	$0.746324\pi$
$14$	−3.34713	−	1.67234i	−0.894558	−	0.446952i
$15$	4.20492			1.08571
$16$	−2.70785	+	2.94407i	−0.676961	+	0.736019i
$17$	−2.36571	+	4.09753i	−0.573769	+	0.993797i	0.422405	+	0.906407i	$0.361186\pi$
$17$	−2.36571	+	4.09753i	−0.573769	+	0.993797i	−0.996174	+	0.0873900i	$0.972147\pi$
$18$	1.41207	+	0.0777523i	0.332829	+	0.0183264i
$19$	0.709823	−	2.64909i	0.162844	−	0.607744i	−0.835461	−	0.549550i	$-0.814799\pi$
$19$	0.709823	−	2.64909i	0.162844	−	0.607744i	0.998305	−	0.0581939i	$-0.0185342\pi$
$20$	−1.27160	−	8.31315i	−0.284338	−	1.85888i
$21$	2.45990	−	0.974112i	0.536794	−	0.212569i
$22$	1.65122	−	5.03652i	0.352041	−	1.07379i
$23$	−6.09208	+	3.51726i	−1.27029	+	0.733400i	−0.975042	−	0.222021i	$-0.928735\pi$
$23$	−6.09208	+	3.51726i	−1.27029	+	0.733400i	−0.295245	+	0.955422i	$0.595401\pi$
$24$	−0.273305	−	2.81519i	−0.0557881	−	0.574649i
$25$	10.9824	+	6.34068i	2.19648	+	1.26814i
$26$	0.0241793	+	0.115254i	0.00474194	+	0.0226031i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.66971	−	4.56866i	−0.504529	−	0.863395i
$29$	1.33075	+	1.33075i	0.247114	+	0.247114i	0.819785	−	0.572671i	$-0.194093\pi$
$29$	1.33075	+	1.33075i	0.247114	+	0.247114i	−0.572671	+	0.819785i	$0.694093\pi$
$30$	4.97869	+	3.25197i	0.908981	+	0.593726i
$31$	−4.34953	+	7.53361i	−0.781199	+	1.35308i	0.150045	+	0.988679i	$0.452058\pi$
$31$	−4.34953	+	7.53361i	−0.781199	+	1.35308i	−0.931244	+	0.364397i	$0.881275\pi$
$32$	−5.48300	+	1.39166i	−0.969267	+	0.246013i
$33$	1.87394	+	3.24575i	0.326210	+	0.565013i
$34$	−5.96996	+	3.02197i	−1.02384	+	0.518263i
$35$	11.0059	+	1.62455i	1.86034	+	0.274599i
$36$	1.61179	+	1.18412i	0.268631	+	0.197353i
$37$	3.23201	+	0.866013i	0.531339	+	0.142372i	0.514506	−	0.857487i	$-0.327975\pi$
$37$	3.23201	+	0.866013i	0.531339	+	0.142372i	0.0168322	+	0.999858i	$0.494642\pi$
$38$	2.88918	−	2.58761i	0.468687	−	0.419766i
$39$	−0.0721147	−	0.0416354i	−0.0115476	−	0.00666700i
$40$	4.92357	−	10.8263i	0.778485	−	1.71179i
$41$		−	6.05310i		−	0.945336i	−0.881241	−	0.472668i	$-0.843291\pi$
$41$		−	6.05310i		−	0.945336i	0.881241	−	0.472668i	$-0.156709\pi$
$42$	3.66591	+	0.749055i	0.565663	+	0.115582i
$43$	−1.31081	+	1.31081i	−0.199897	+	0.199897i	−0.799956	−	0.600059i	$-0.795144\pi$
$43$	−1.31081	+	1.31081i	−0.199897	+	0.199897i	0.600059	+	0.799956i	$0.295144\pi$
$44$	5.85018	−	4.68632i	0.881947	−	0.706489i
$45$	−4.06164	+	1.08831i	−0.605474	+	0.162236i
$46$	−9.93328	−	0.546950i	−1.46458	−	0.0806434i
$47$	−1.56674	−	2.71367i	−0.228532	−	0.395829i	0.728841	−	0.684683i	$-0.240059\pi$
$47$	−1.56674	−	2.71367i	−0.228532	−	0.395829i	−0.957373	+	0.288854i	$0.906726\pi$
$48$	1.85360	−	3.54460i	0.267543	−	0.511619i
$49$	6.81486	−	1.59926i	0.973552	−	0.228466i
$50$	8.09961	+	16.0009i	1.14546	+	2.26287i
$51$	1.22458	−	4.57020i	0.171476	−	0.639956i
$52$	−0.0605055	+	0.155162i	−0.00839060	+	0.0215171i
$53$	−0.818053	−	3.05301i	−0.112368	−	0.419364i	0.886708	−	0.462329i	$-0.152986\pi$
$53$	−0.818053	−	3.05301i	−0.112368	−	0.419364i	−0.999077	+	0.0429654i	$0.986319\pi$
$54$	−1.38408	+	0.290369i	−0.188350	+	0.0395142i
$55$			15.7595i			2.12501i
$56$	0.372288	−	7.47405i	0.0497491	−	0.998762i
$57$			2.74254i			0.363259i
$58$	0.546464	+	2.60479i	0.0717542	+	0.342026i
$59$	−1.60481	−	5.98923i	−0.208929	−	0.779732i	−0.988216	−	0.153065i	$-0.951086\pi$
$59$	−1.60481	−	5.98923i	−0.208929	−	0.779732i	0.779288	−	0.626667i	$-0.215581\pi$
$60$	3.37987	+	7.70077i	0.436339	+	0.994166i
$61$	−0.0796808	+	0.297373i	−0.0102021	+	0.0380747i	−0.970839	−	0.239731i	$-0.922941\pi$
$61$	−0.0796808	+	0.297373i	−0.0102021	+	0.0380747i	0.960637	+	0.277806i	$0.0896073\pi$
$62$	−10.9762	+	5.55611i	−1.39398	+	0.705627i
$63$	−2.12396	+	1.57759i	−0.267594	+	0.198757i
$64$	−7.56823	−	2.59266i	−0.946029	−	0.324082i
$65$	−0.175074	−	0.303237i	−0.0217152	−	0.0376119i
$66$	−0.291405	+	5.29227i	−0.0358695	+	0.651434i
$67$	−12.5143	+	3.35320i	−1.52887	+	0.409659i	−0.922650	−	0.385639i	$-0.873981\pi$
$67$	−12.5143	+	3.35320i	−1.52887	+	0.409659i	−0.606219	+	0.795298i	$0.707314\pi$
$68$	−9.40563	−	1.03894i	−1.14060	−	0.125990i
$69$	4.97416	−	4.97416i	0.598819	−	0.598819i
$70$	11.7748	+	10.4352i	1.40736	+	1.24724i
$71$		−	4.95669i		−	0.588251i	−0.955767	−	0.294126i	$-0.904972\pi$
$71$		−	4.95669i		−	0.588251i	0.955767	−	0.294126i	$-0.0950284\pi$
$72$	0.992617	+	2.64853i	0.116981	+	0.312132i
$73$	10.5223	+	6.07505i	1.23154	+	0.711031i	0.967351	−	0.253440i	$-0.0815619\pi$
$73$	10.5223	+	6.07505i	1.23154	+	0.711031i	0.264190	+	0.964471i	$0.414895\pi$
$74$	3.15700	+	3.52492i	0.366993	+	0.409764i
$75$	−12.2493	−	3.28218i	−1.41442	−	0.378993i
$76$	5.42202	−	0.829364i	0.621949	−	0.0951346i
$77$	3.65084	+	9.21938i	0.416052	+	1.05065i
$78$	−0.0531853	−	0.105069i	−0.00602204	−	0.0118967i
$79$	−3.19808	−	5.53924i	−0.359812	−	0.623213i	0.628117	−	0.778119i	$-0.283826\pi$
$79$	−3.19808	−	5.53924i	−0.359812	−	0.623213i	−0.987929	+	0.154906i	$0.950493\pi$
$80$	14.2024	−	9.01079i	1.58787	−	1.00744i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	4.68130	−	7.16697i	0.516964	−	0.791460i
$83$	1.77457	+	1.77457i	0.194785	+	0.194785i	0.797760	−	0.602975i	$-0.206018\pi$
$83$	1.77457	+	1.77457i	0.194785	+	0.194785i	−0.602975	+	0.797760i	$0.706018\pi$
$84$	3.76120	+	3.72201i	0.410381	+	0.406105i
$85$	14.0681	−	14.0681i	1.52590	−	1.52590i
$86$	−2.56577	+	0.538277i	−0.276674	+	0.0580439i
$87$	−1.62983	−	0.940982i	−0.174736	−	0.100884i
$88$	10.5510	−	1.02431i	1.12474	−	0.109192i
$89$	0.469248	−	0.270920i	0.0497402	−	0.0287175i	−0.474924	−	0.880027i	$-0.657524\pi$
$89$	0.469248	−	0.270920i	0.0497402	−	0.0287175i	0.524664	+	0.851309i	$0.324191\pi$
$90$	−5.65072	−	1.85258i	−0.595638	−	0.195279i
$91$	−0.172667	−	0.136837i	−0.0181004	−	0.0143444i
$92$	−11.3382	−	8.32972i	−1.18209	−	0.868434i
$93$	2.25148	−	8.40265i	0.233468	−	0.871314i
$94$	0.243634	−	4.42469i	0.0251290	−	0.456372i
$95$	−5.76609	+	9.98716i	−0.591588	+	1.02466i
$96$	4.93598	−	2.76334i	0.503777	−	0.282033i
$97$	−6.14973			−0.624411			−0.312205	−	0.950015i	$-0.601068\pi$
$97$	−6.14973			−0.624411			−0.312205	+	0.950015i	$0.601068\pi$
$98$	9.30574	+	3.37687i	0.940021	+	0.341116i
$99$	−2.65014	−	2.65014i	−0.266350	−	0.266350i
$100$	−2.78462	+	25.2094i	−0.278462	+	2.52094i
$101$	3.86219	+	14.4139i	0.384302	+	1.43424i	0.839264	+	0.543725i	$0.182986\pi$
$101$	3.86219	+	14.4139i	0.384302	+	1.43424i	−0.454961	+	0.890511i	$0.650347\pi$
$102$	4.98439	−	4.46413i	0.493529	−	0.442015i
$103$	11.2813	−	6.51327i	1.11158	−	0.641771i	0.172342	−	0.985037i	$-0.444866\pi$
$103$	11.2813	−	6.51327i	1.11158	−	0.641771i	0.939238	+	0.343266i	$0.111533\pi$
$104$	−0.191638	+	0.136921i	−0.0187916	+	0.0134262i
$105$	−11.0514	+	1.27935i	−1.07850	+	0.124852i
$106$	1.39253	−	4.24748i	0.135254	−	0.412552i
$107$	−9.10100	−	2.43860i	−0.879827	−	0.235749i	−0.209494	−	0.977810i	$-0.567182\pi$
$107$	−9.10100	−	2.43860i	−0.879827	−	0.235749i	−0.670332	+	0.742061i	$0.733848\pi$
$108$	−1.86334	−	0.726611i	−0.179300	−	0.0699181i
$109$	−5.26273	+	1.41015i	−0.504079	+	0.135067i	−0.501892	−	0.864930i	$-0.667363\pi$
$109$	−5.26273	+	1.41015i	−0.504079	+	0.135067i	−0.00218631	+	0.999998i	$0.500696\pi$
$110$	−12.1880	+	18.6595i	−1.16208	+	1.77911i
$111$	−3.34602			−0.317590
$112$	6.22102	−	8.56148i	0.587831	−	0.808984i
$113$	−15.1776			−1.42779			−0.713895	−	0.700253i	$-0.753071\pi$
$113$	−15.1776			−1.42779			−0.713895	+	0.700253i	$0.753071\pi$
$114$	−2.12101	+	3.24722i	−0.198651	+	0.304130i
$115$	28.5717	−	7.65577i	2.66433	−	0.713904i
$116$	−1.36745	+	3.50674i	−0.126965	+	0.325593i
$117$	0.0804335	+	0.0215521i	0.00743608	+	0.00199249i
$118$	2.73179	−	8.33247i	0.251482	−	0.767066i
$119$	4.97088	−	11.4889i	0.455680	−	1.05319i
$120$	−1.95375	+	11.7317i	−0.178352	+	1.07096i
$121$	−2.63837	+	1.52327i	−0.239852	+	0.138479i
$122$	−0.324323	+	0.290471i	−0.0293629	+	0.0262980i
$123$	1.56666	+	5.84685i	0.141261	+	0.527193i
$124$	−17.2930	−	1.91018i	−1.55295	−	0.171539i
$125$	−22.8392	−	22.8392i	−2.04280	−	2.04280i
$126$	−3.73487	+	0.225276i	−0.332729	+	0.0200692i
$127$	7.17780			0.636927			0.318463	−	0.947935i	$-0.396833\pi$
$127$	7.17780			0.636927			0.318463	+	0.947935i	$0.396833\pi$
$128$	−6.95582	−	8.92281i	−0.614813	−	0.788673i
$129$	0.926884	−	1.60541i	0.0816076	−	0.141348i
$130$	0.0272247	−	0.494434i	0.00238777	−	0.0433647i
$131$	−4.21341	+	15.7246i	−0.368127	+	1.37387i	0.495005	+	0.868890i	$0.335166\pi$
$131$	−4.21341	+	15.7246i	−0.368127	+	1.37387i	−0.863132	+	0.504978i	$0.831500\pi$
$132$	−4.43793	+	6.04077i	−0.386272	+	0.525782i
$133$	−1.05957	+	7.17831i	−0.0918760	+	0.622439i
$134$	−17.4104	−	5.70799i	−1.50403	−	0.493095i
$135$	3.64157	−	2.10246i	0.313416	−	0.180951i
$136$	−10.3329	−	8.50419i	−0.886042	−	0.729228i
$137$	16.8530	+	9.73006i	1.43985	+	0.831295i	0.997838	−	0.0657164i	$-0.0209333\pi$
$137$	16.8530	+	9.73006i	1.43985	+	0.831295i	0.442007	+	0.897012i	$0.354267\pi$
$138$	9.73637	−	2.04261i	0.828815	−	0.173878i
$139$	−1.41908	+	1.41908i	−0.120365	+	0.120365i	−0.764723	−	0.644359i	$-0.777124\pi$
$139$	−1.41908	+	1.41908i	−0.120365	+	0.120365i	0.644359	+	0.764723i	$0.277124\pi$
$140$	5.87129	+	21.4617i	0.496215	+	1.81385i
$141$	2.21570	+	2.21570i	0.186595	+	0.186595i
$142$	3.83337	−	5.86881i	0.321689	−	0.492499i
$143$	0.156044	−	0.270276i	0.0130491	−	0.0226017i
$144$	−0.873026	+	3.90357i	−0.0727522	+	0.325297i
$145$	−3.95675	−	6.85330i	−0.328591	−	0.569135i
$146$	7.76029	+	15.3306i	0.642246	+	1.26877i
$147$	−6.16873	+	3.30859i	−0.508788	+	0.272888i
$148$	1.01186	+	6.61510i	0.0831743	+	0.543758i
$149$	−12.7950	−	3.42841i	−1.04821	−	0.280866i	−0.306697	−	0.951807i	$-0.599224\pi$
$149$	−12.7950	−	3.42841i	−1.04821	−	0.280866i	−0.741511	+	0.670941i	$0.765890\pi$
$150$	−11.9650	−	13.3594i	−0.976935	−	1.09079i
$151$	−11.7105	−	6.76103i	−0.952983	−	0.550205i	−0.0589768	−	0.998259i	$-0.518784\pi$
$151$	−11.7105	−	6.76103i	−0.952983	−	0.550205i	−0.894006	+	0.448054i	$0.852117\pi$
$152$	7.06117	+	3.21126i	0.572737	+	0.260468i
$153$			4.73142i			0.382513i
$154$	−2.80736	+	13.7394i	−0.226224	+	1.10715i
$155$	25.8652	−	25.8652i	2.07754	−	2.07754i
$156$	0.0182849	−	0.165535i	0.00146397	−	0.0132534i
$157$	−15.6175	+	4.18470i	−1.24641	+	0.333975i	−0.820949	−	0.571001i	$-0.806555\pi$
$157$	−15.6175	+	4.18470i	−1.24641	+	0.333975i	−0.425462	+	0.904976i	$0.639889\pi$
$158$	0.497316	−	9.03186i	0.0395643	−	0.718536i
$159$	1.58036	+	2.73726i	0.125330	+	0.217079i
$160$	23.7845	+	0.314807i	1.88033	+	0.0248877i
$161$	14.9411	−	11.0976i	1.17752	−	0.874613i
$162$	1.26177	−	0.638702i	0.0991339	−	0.0501812i
$163$	0.987804	−	3.68653i	0.0773707	−	0.288752i	−0.916390	−	0.400287i	$-0.868910\pi$
$163$	0.987804	−	3.68653i	0.0773707	−	0.288752i	0.993760	+	0.111536i	$0.0355770\pi$
$164$	11.0855	−	4.86542i	0.865631	−	0.379925i
$165$	−4.07886	−	15.2225i	−0.317539	−	1.18507i
$166$	0.728718	+	3.47353i	0.0565595	+	0.269598i
$167$			1.08479i			0.0839433i	0.999119	+	0.0419716i	$0.0133639\pi$
$167$			1.08479i			0.0839433i	−0.999119	+	0.0419716i	$0.986636\pi$
$168$	1.57482	+	7.31573i	0.121500	+	0.564421i
$169$		−	12.9931i		−	0.999467i
$170$	27.5367	−	5.77696i	2.11197	−	0.443073i
$171$	−0.709823	−	2.64909i	−0.0542815	−	0.202581i
$172$	−3.45420	−	1.34697i	−0.263380	−	0.102705i
$173$	0.909327	−	3.39365i	0.0691348	−	0.258015i	−0.922705	−	0.385508i	$-0.874026\pi$
$173$	0.909327	−	3.39365i	0.0691348	−	0.258015i	0.991839	+	0.127493i	$0.0406930\pi$
$174$	−1.20201	−	2.37460i	−0.0911244	−	0.180018i
$175$	−30.7930	−	13.3232i	−2.32773	−	1.00714i
$176$	13.2847	+	6.94704i	1.00137	+	0.523652i
$177$	3.10026	+	5.36980i	0.233029	+	0.403619i
$178$	0.765120	+	0.0421293i	0.0573481	+	0.00315773i
$179$	−5.23352	+	1.40232i	−0.391171	+	0.104814i	−0.449043	−	0.893510i	$-0.648235\pi$
$179$	−5.23352	+	1.40232i	−0.391171	+	0.104814i	0.0578720	+	0.998324i	$0.481568\pi$
$180$	−5.25781	−	6.56360i	−0.391894	−	0.489222i
$181$	−6.01594	+	6.01594i	−0.447162	+	0.447162i	−0.894410	−	0.447248i	$-0.852404\pi$
$181$	−6.01594	+	6.01594i	−0.447162	+	0.447162i	0.447248	+	0.894410i	$0.352404\pi$
$182$	−0.0986140	−	0.295553i	−0.00730976	−	0.0219079i
$183$		−	0.307863i		−	0.0227579i
$184$	−6.98259	−	18.6312i	−0.514764	−	1.37351i
$185$	−12.1848	−	7.03487i	−0.895841	−	0.517214i
$186$	9.16417	−	8.20764i	0.671950	−	0.601813i
$187$	17.1285	+	4.58957i	1.25256	+	0.335623i
$188$	3.71041	−	5.05049i	0.270609	−	0.368345i
$189$	1.64328	−	2.07356i	0.119531	−	0.150829i
$190$	−14.5509	+	7.36562i	−1.05564	+	0.534359i
$191$	9.43701	+	16.3454i	0.682838	+	1.18271i	0.974111	+	0.226070i	$0.0725879\pi$
$191$	9.43701	+	16.3454i	0.682838	+	1.18271i	−0.291273	+	0.956640i	$0.594079\pi$
$192$	7.98138	+	0.545511i	0.576006	+	0.0393689i
$193$	−8.77358	+	15.1963i	−0.631536	+	1.09385i	0.355702	+	0.934600i	$0.384242\pi$
$193$	−8.77358	+	15.1963i	−0.631536	+	1.09385i	−0.987238	+	0.159253i	$0.949091\pi$
$194$	−7.28139	−	4.75604i	−0.522773	−	0.341464i
$195$	0.247592	+	0.247592i	0.0177304	+	0.0177304i
$196$	8.40656	+	11.1951i	0.600469	+	0.799648i
$197$	9.23316	−	9.23316i	0.657836	−	0.657836i	−0.297032	−	0.954868i	$-0.595997\pi$
$197$	9.23316	−	9.23316i	0.657836	−	0.657836i	0.954868	+	0.297032i	$0.0959968\pi$
$198$	−1.08826	−	5.18736i	−0.0773396	−	0.368650i
$199$	−8.45777	−	4.88309i	−0.599555	−	0.346153i	0.169311	−	0.985563i	$-0.445846\pi$
$199$	−8.45777	−	4.88309i	−0.599555	−	0.346153i	−0.768867	+	0.639409i	$0.779179\pi$
$200$	−22.7933	+	27.6948i	−1.61173	+	1.95832i
$201$	11.2200	−	6.47789i	0.791401	−	0.456915i
$202$	−6.57441	+	20.0532i	−0.462574	+	1.41094i
$203$	−3.90236	−	3.09259i	−0.273892	−	0.217057i
$204$	9.35404	−	1.43081i	0.654914	−	0.100177i
$205$	−6.58767	+	24.5855i	−0.460103	+	1.71713i
$206$	18.3944	+	1.01284i	1.28160	+	0.0705681i
$207$	−3.51726	+	6.09208i	−0.244467	+	0.423429i
$208$	−0.332793	+	0.0139095i	−0.0230750	+	0.000964448i
$209$	−10.2787			−0.710993
$210$	−14.0744	−	7.03206i	−0.971227	−	0.485258i
$211$	6.45197	+	6.45197i	0.444172	+	0.444172i	0.893411	−	0.449239i	$-0.148305\pi$
$211$	6.45197	+	6.45197i	0.444172	+	0.444172i	−0.449239	+	0.893411i	$0.648305\pi$
$212$	4.93366	−	3.95214i	0.338845	−	0.271434i
$213$	1.28289	+	4.78780i	0.0879019	+	0.328054i
$214$	−8.88978	−	9.92581i	−0.607693	−	0.678514i
$215$	6.75062	−	3.89747i	0.460389	−	0.265805i
$216$	−1.64428	−	2.30138i	−0.111879	−	0.156589i
$217$	9.13933	−	21.1232i	0.620418	−	1.43393i
$218$	−7.32173	−	2.40042i	−0.495890	−	0.162577i
$219$	−11.7361	−	3.14468i	−0.793052	−	0.212498i
$220$	−28.8615	+	12.6673i	−1.94584	+	0.854030i
$221$	−0.380565	+	0.101972i	−0.0255995	+	0.00685938i
$222$	−3.96174	−	2.58772i	−0.265895	−	0.173676i
$223$	0.783532			0.0524692			0.0262346	−	0.999656i	$-0.491648\pi$
$223$	0.783532			0.0524692			0.0262346	+	0.999656i	$0.491648\pi$
$224$	13.9870	−	5.32576i	0.934546	−	0.355842i
$225$	12.6814			0.845424
$226$	−17.9705	−	11.7380i	−1.19538	−	0.780797i
$227$	2.57450	−	0.689836i	0.170876	−	0.0457861i	−0.172367	−	0.985033i	$-0.555141\pi$
$227$	2.57450	−	0.689836i	0.170876	−	0.0457861i	0.343243	+	0.939247i	$0.388475\pi$
$228$	−5.02262	+	2.20443i	−0.332631	+	0.145992i
$229$	−22.3600	−	5.99136i	−1.47759	−	0.395920i	−0.572066	−	0.820208i	$-0.693858\pi$
$229$	−22.3600	−	5.99136i	−1.47759	−	0.395920i	−0.905528	+	0.424288i	$0.860525\pi$
$230$	39.7502	+	13.0320i	2.62105	+	0.859307i
$231$	−5.91260	−	7.96033i	−0.389020	−	0.523752i
$232$	−4.33110	+	3.09448i	−0.284351	+	0.203163i
$233$	−5.86786	+	3.38781i	−0.384416	+	0.221943i	−0.679738	−	0.733455i	$-0.737907\pi$
$233$	−5.86786	+	3.38781i	−0.384416	+	0.221943i	0.295322	+	0.955398i	$0.404573\pi$
$234$	0.0785668	+	0.0877231i	0.00513607	+	0.00573464i
$235$	3.41020	+	12.7270i	0.222457	+	0.830220i
$236$	9.67858	−	7.75309i	0.630022	−	0.504683i
$237$	4.52277	+	4.52277i	0.293785	+	0.293785i
$238$	14.7708	−	9.75870i	0.957449	−	0.632562i
$239$	−0.885613			−0.0572855			−0.0286428	−	0.999590i	$-0.509119\pi$
$239$	−0.885613			−0.0572855			−0.0286428	+	0.999590i	$0.509119\pi$
$240$	−11.3863	+	12.3796i	−0.734981	+	0.799100i
$241$	7.13173	−	12.3525i	0.459395	−	0.795696i	−0.539534	−	0.841964i	$-0.681399\pi$
$241$	7.13173	−	12.3525i	0.459395	−	0.795696i	0.998929	+	0.0462680i	$0.0147328\pi$
$242$	−4.30193	−	0.236875i	−0.276538	−	0.0152269i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−0.608647	+	0.0930999i	−0.0389646	+	0.00596011i
$245$	−29.4200	−	0.921072i	−1.87958	−	0.0588451i
$246$	−2.66684	+	8.13437i	−0.170032	+	0.518629i
$247$	0.197778	−	0.114187i	0.0125843	−	0.00726555i
$248$	−18.9979	−	15.6356i	−1.20637	−	0.992860i
$249$	−2.17340	−	1.25481i	−0.137734	−	0.0795206i
$250$	−9.37877	−	44.7052i	−0.593165	−	2.82740i
$251$	−9.48444	+	9.48444i	−0.598653	+	0.598653i	−0.939954	−	0.341301i	$-0.889132\pi$
$251$	−9.48444	+	9.48444i	−0.598653	+	0.598653i	0.341301	+	0.939954i	$0.389132\pi$
$252$	−4.59637	−	2.62172i	−0.289544	−	0.165153i
$253$	18.6425	+	18.6425i	1.17204	+	1.17204i
$254$	8.49863	+	5.55111i	0.533252	+	0.348308i
$255$	−9.94762	+	17.2298i	−0.622944	+	1.07897i
$256$	−1.33515	−	15.9442i	−0.0834466	−	0.996512i
$257$	9.35031	+	16.1952i	0.583257	+	1.01023i	0.995090	+	0.0989711i	$0.0315551\pi$
$257$	9.35031	+	16.1952i	0.583257	+	1.01023i	−0.411834	+	0.911259i	$0.635112\pi$
$258$	2.33903	−	1.18401i	0.145621	−	0.0737129i
$259$	−8.75784	−	1.29272i	−0.544186	−	0.0803254i
$260$	0.414616	−	0.564363i	0.0257134	−	0.0350003i
$261$	1.81784	+	0.487088i	0.112521	+	0.0301500i
$262$	−17.1498	+	15.3597i	−1.05952	+	0.948926i
$263$	4.73987	+	2.73656i	0.292273	+	0.168744i	0.638966	−	0.769235i	$-0.279362\pi$
$263$	4.73987	+	2.73656i	0.292273	+	0.168744i	−0.346694	+	0.937978i	$0.612696\pi$
$264$	−9.92635	+	3.72020i	−0.610924	+	0.228963i
$265$			13.2905i			0.816432i
$266$	−6.80605	+	7.67980i	−0.417306	+	0.470879i
$267$	−0.383139	+	0.383139i	−0.0234477	+	0.0234477i
$268$	−16.1998	−	20.2231i	−0.989563	−	1.23532i
$269$	20.7342	−	5.55571i	1.26419	−	0.338738i	0.436385	−	0.899760i	$-0.356258\pi$
$269$	20.7342	−	5.55571i	1.26419	−	0.338738i	0.827801	+	0.561022i	$0.189592\pi$
$270$	5.93766	+	0.326942i	0.361355	+	0.0198971i
$271$	2.61671	+	4.53228i	0.158954	+	0.275316i	0.934492	−	0.355985i	$-0.115855\pi$
$271$	2.61671	+	4.53228i	0.158954	+	0.275316i	−0.775538	+	0.631301i	$0.782521\pi$
$272$	−5.65746	−	18.0603i	−0.343034	−	1.09507i
$273$	0.202199	+	0.0874853i	0.0122377	+	0.00529485i
$274$	12.4292	+	24.5542i	0.750876	+	1.48337i
$275$	12.3012	−	45.9086i	0.741789	−	2.76839i
$276$	13.1077	+	5.11136i	0.788992	+	0.307668i
$277$	−4.30221	−	16.0561i	−0.258495	−	0.964716i	−0.966113	−	0.258121i	$-0.916897\pi$
$277$	−4.30221	−	16.0561i	−0.258495	−	0.964716i	0.707618	−	0.706595i	$-0.249770\pi$
$278$	−2.77769	+	0.582735i	−0.166595	+	0.0349502i
$279$			8.69906i			0.520799i
$280$	−9.64621	+	29.9517i	−0.576471	+	1.78996i
$281$			30.9319i			1.84524i	0.385708	+	0.922621i	$0.373957\pi$
$281$			30.9319i			1.84524i	−0.385708	+	0.922621i	$0.626043\pi$
$282$	0.909862	+	4.33698i	0.0541815	+	0.258264i
$283$	−1.02320	−	3.81862i	−0.0608227	−	0.226993i	0.928823	−	0.370523i	$-0.120821\pi$
$283$	−1.02320	−	3.81862i	−0.0608227	−	0.226993i	−0.989646	+	0.143529i	$0.954155\pi$
$284$	9.07755	−	3.98414i	0.538653	−	0.236415i
$285$	2.98475	−	11.1392i	0.176801	−	0.659831i
$286$	0.393783	−	0.199331i	0.0232849	−	0.0117867i
$287$	1.84166	+	15.9088i	0.108710	+	0.939064i
$288$	−4.05259	+	3.94671i	−0.238801	+	0.232562i
$289$	−2.69317	−	4.66471i	−0.158422	−	0.274395i
$290$	0.615293	−	11.1745i	0.0361313	−	0.656187i
$291$	5.94019	−	1.59167i	0.348220	−	0.0933052i
$292$	−2.66797	+	24.1533i	−0.156131	+	1.41346i
$293$	−2.67782	+	2.67782i	−0.156440	+	0.156440i	−0.780987	−	0.624547i	$-0.785284\pi$
$293$	−2.67782	+	2.67782i	−0.156440	+	0.156440i	0.624547	+	0.780987i	$0.285284\pi$
$294$	−9.86265	−	0.853309i	−0.575201	−	0.0497660i
$295$			26.0727i			1.51801i
$296$	−3.91788	+	8.61493i	−0.227722	+	0.500732i
$297$	3.24575	+	1.87394i	0.188338	+	0.108737i
$298$	−12.4981	−	13.9546i	−0.723993	−	0.808368i
$299$	−0.565812	−	0.151609i	−0.0327217	−	0.00876776i
$300$	−3.83493	−	25.0711i	−0.221410	−	1.44748i
$301$	3.04626	−	3.84389i	0.175583	−	0.221558i
$302$	−8.63657	−	17.0617i	−0.496979	−	0.981792i
$303$	−7.46118	−	12.9231i	−0.428634	−	0.742415i
$304$	5.87704	+	9.26311i	0.337071	+	0.531276i
$305$	0.647270	−	1.12110i	0.0370626	−	0.0641942i
$306$	−3.65915	+	5.60208i	−0.209180	+	0.320250i
$307$	−9.63760	−	9.63760i	−0.550047	−	0.550047i	0.376408	−	0.926454i	$-0.377159\pi$
$307$	−9.63760	−	9.63760i	−0.550047	−	0.550047i	−0.926454	+	0.376408i	$0.877159\pi$
$308$	−13.9496	+	14.0965i	−0.794853	+	0.803222i
$309$	−9.21115	+	9.21115i	−0.524004	+	0.524004i
$310$	50.6282	−	10.6214i	2.87549	−	0.603253i
$311$	12.4679	+	7.19832i	0.706987	+	0.408179i	0.809944	−	0.586507i	$-0.199497\pi$
$311$	12.4679	+	7.19832i	0.706987	+	0.408179i	−0.102957	+	0.994686i	$0.532831\pi$
$312$	0.149670	−	0.181855i	0.00847339	−	0.0102955i
$313$	8.61090	−	4.97150i	0.486717	−	0.281006i	−0.236495	−	0.971633i	$-0.575999\pi$
$313$	8.61090	−	4.97150i	0.486717	−	0.281006i	0.723211	+	0.690627i	$0.242665\pi$
$314$	−21.7277	−	7.12340i	−1.22616	−	0.401997i
$315$	10.3437	−	4.09606i	0.582800	−	0.230787i
$316$	7.57382	−	10.3093i	0.426061	−	0.579941i
$317$	−1.17954	+	4.40209i	−0.0662493	+	0.247246i	−0.991107	−	0.133068i	$-0.957517\pi$
$317$	−1.17954	+	4.40209i	−0.0662493	+	0.247246i	0.924858	+	0.380314i	$0.124184\pi$
$318$	−0.245753	+	4.46316i	−0.0137811	+	0.250282i
$319$	3.52668	−	6.10839i	0.197456	−	0.342004i
$320$	27.9178	+	18.7671i	1.56065	+	1.04911i
$321$	9.42205			0.525887
$322$	26.2730	−	1.58471i	1.46414	−	0.0883126i
$323$	9.17551	+	9.17551i	0.510539	+	0.510539i
$324$	1.98791	+	0.219584i	0.110439	+	0.0121991i
$325$	0.273310	+	1.02001i	0.0151605	+	0.0565797i
$326$	4.02064	−	3.60098i	0.222683	−	0.199440i
$327$	4.71844	−	2.72419i	0.260930	−	0.150648i
$328$	16.8882	+	2.81247i	0.932493	+	0.155293i
$329$	4.94333	+	6.65537i	0.272535	+	0.366923i
$330$	6.94324	−	21.1782i	0.382213	−	1.16582i
$331$	21.4754	+	5.75433i	1.18040	+	0.316286i	0.795084	−	0.606500i	$-0.207427\pi$
$331$	21.4754	+	5.75433i	1.18040	+	0.316286i	0.385313	+	0.922786i	$0.374093\pi$
$332$	−1.82352	+	4.67629i	−0.100079	+	0.256645i
$333$	3.23201	−	0.866013i	0.177113	−	0.0474572i
$334$	−0.838944	+	1.28440i	−0.0459050	+	0.0702795i
$335$	54.4781			2.97645
$336$	−3.79317	+	9.87987i	−0.206934	+	0.538991i
$337$	16.2445			0.884893			0.442447	−	0.896795i	$-0.354111\pi$
$337$	16.2445			0.884893			0.442447	+	0.896795i	$0.354111\pi$
$338$	10.0485	−	15.3840i	0.546565	−	0.836779i
$339$	14.6604	−	3.92826i	0.796246	−	0.213354i
$340$	37.0716	+	14.4561i	2.01049	+	0.783992i
$341$	31.4920	+	8.43827i	1.70539	+	0.456958i
$342$	1.20830	−	3.68553i	0.0653371	−	0.199291i
$343$	−17.4242	+	6.27661i	−0.940821	+	0.338905i
$344$	−3.04812	−	4.26622i	−0.164344	−	0.230019i
$345$	−25.6167	+	14.7898i	−1.37916	+	0.796257i
$346$	3.70122	−	3.31489i	0.198979	−	0.178210i
$347$	6.48273	+	24.1939i	0.348011	+	1.29880i	0.889054	+	0.457801i	$0.151363\pi$
$347$	6.48273	+	24.1939i	0.348011	+	1.29880i	−0.541043	+	0.840995i	$0.681970\pi$
$348$	0.413249	−	3.74117i	0.0221525	−	0.200548i
$349$	11.8027	+	11.8027i	0.631785	+	0.631785i	0.948516	−	0.316731i	$-0.102585\pi$
$349$	11.8027	+	11.8027i	0.631785	+	0.631785i	−0.316731	+	0.948516i	$0.602585\pi$
$350$	−26.1557	−	39.5893i	−1.39808	−	2.11614i
$351$	−0.0832709			−0.00444467
$352$	10.3567	+	18.4994i	0.552011	+	0.986023i
$353$	−13.6008	+	23.5572i	−0.723897	+	1.25383i	0.235530	+	0.971867i	$0.424317\pi$
$353$	−13.6008	+	23.5572i	−0.723897	+	1.25383i	−0.959427	+	0.281959i	$0.909016\pi$
$354$	−0.482104	+	8.75558i	−0.0256235	+	0.465354i
$355$	−5.39444	+	20.1323i	−0.286307	+	1.06851i
$356$	0.873332	+	0.641604i	0.0462865	+	0.0340050i
$357$	−1.82796	+	12.3840i	−0.0967458	+	0.655430i
$358$	−7.28108	−	2.38709i	−0.384817	−	0.126162i
$359$	8.25692	−	4.76714i	0.435784	−	0.251600i	−0.266024	−	0.963966i	$-0.585710\pi$
$359$	8.25692	−	4.76714i	0.435784	−	0.251600i	0.701807	+	0.712367i	$0.252377\pi$
$360$	−1.14922	−	11.8377i	−0.0605694	−	0.623899i
$361$	9.94063	+	5.73923i	0.523191	+	0.302065i
$362$	−11.7755	+	2.47041i	−0.618909	+	0.129842i
$363$	2.15422	−	2.15422i	0.113067	−	0.113067i
$364$	0.111812	−	0.426205i	0.00586056	−	0.0223392i
$365$	−36.1262	−	36.1262i	−1.89093	−	1.89093i
$366$	0.238093	−	0.364515i	0.0124453	−	0.0190535i
$367$	2.61975	−	4.53755i	0.136750	−	0.236858i	−0.789515	−	0.613732i	$-0.789668\pi$
$367$	2.61975	−	4.53755i	0.136750	−	0.236858i	0.926265	+	0.376874i	$0.123001\pi$
$368$	6.14133	−	27.4597i	0.320139	−	1.43144i
$369$	−3.02655	−	5.24214i	−0.157556	−	0.272895i
$370$	−8.98637	−	17.7528i	−0.467179	−	0.922922i
$371$	3.07889	+	7.77504i	0.159848	+	0.403660i
$372$	17.1981	−	2.63066i	0.891680	−	0.136393i
$373$	−8.88646	−	2.38112i	−0.460124	−	0.123290i	0.0213088	−	0.999773i	$-0.493217\pi$
$373$	−8.88646	−	2.38112i	−0.460124	−	0.123290i	−0.481432	+	0.876483i	$0.659883\pi$
$374$	16.7310	+	18.6809i	0.865139	+	0.965964i
$375$	27.9722	+	16.1497i	1.44448	+	0.833969i
$376$	8.29909	−	3.11034i	0.427993	−	0.160403i
$377$			0.156713i			0.00807112i
$378$	3.54930	−	1.18426i	0.182556	−	0.0609115i
$379$	−0.217763	+	0.217763i	−0.0111857	+	0.0111857i	−0.712678	−	0.701492i	$-0.752518\pi$
$379$	−0.217763	+	0.217763i	−0.0111857	+	0.0111857i	0.701492	+	0.712678i	$0.252518\pi$
$380$	−22.9249	−	2.53228i	−1.17602	−	0.129903i
$381$	−6.93322	+	1.85775i	−0.355200	+	0.0951755i
$382$	−1.46750	+	26.6515i	−0.0750837	+	1.36361i
$383$	14.4548	+	25.0365i	0.738607	+	1.27931i	0.953122	+	0.302585i	$0.0978496\pi$
$383$	14.4548	+	25.0365i	0.738607	+	1.27931i	−0.214515	+	0.976721i	$0.568817\pi$
$384$	9.02820	+	6.81848i	0.460718	+	0.347954i
$385$	−4.79484	−	41.4191i	−0.244368	−	2.11091i
$386$	−22.1405	+	11.2074i	−1.12692	+	0.570442i
$387$	−0.479790	+	1.79060i	−0.0243891	+	0.0910214i
$388$	−4.94309	−	11.2624i	−0.250947	−	0.571764i
$389$	−6.74468	−	25.1715i	−0.341969	−	1.27624i	−0.896114	−	0.443824i	$-0.853621\pi$
$389$	−6.74468	−	25.1715i	−0.341969	−	1.27624i	0.554145	−	0.832420i	$-0.313045\pi$
$390$	0.101672	+	0.484633i	0.00514836	+	0.0245403i
$391$		−	33.2833i		−	1.68321i
$392$	1.29554	+	19.7566i	0.0654345	+	0.997857i
$393$		−	16.2794i		−	0.821185i
$394$	18.0729	−	3.79154i	0.910499	−	0.191015i
$395$	6.96103	+	25.9789i	0.350247	+	1.30714i
$396$	2.72324	−	6.98356i	0.136848	−	0.350937i
$397$	1.65072	−	6.16056i	0.0828471	−	0.309189i	−0.912051	−	0.410077i	$-0.865502\pi$
$397$	1.65072	−	6.16056i	0.0828471	−	0.309189i	0.994898	+	0.100888i	$0.0321684\pi$
$398$	−6.23768	−	12.3227i	−0.312667	−	0.617680i
$399$	−0.834421	−	7.20795i	−0.0417733	−	0.360849i
$400$	−48.4060	+	15.1634i	−2.42030	+	0.758168i
$401$	−6.99319	−	12.1126i	−0.349223	−	0.604872i	0.636888	−	0.770956i	$-0.280221\pi$
$401$	−6.99319	−	12.1126i	−0.349223	−	0.604872i	−0.986112	+	0.166084i	$0.946888\pi$
$402$	18.2945	+	1.00734i	0.912449	+	0.0502416i
$403$	−0.699696	+	0.187483i	−0.0348543	+	0.00933919i
$404$	−23.2928	+	18.6588i	−1.15886	+	0.928312i
$405$	−2.97333	+	2.97333i	−0.147746	+	0.147746i
$406$	−2.22873	−	6.67966i	−0.110610	−	0.331506i
$407$		−	12.5404i		−	0.621607i
$408$	12.1819	+	5.54005i	0.603094	+	0.274274i
$409$	−29.1010	−	16.8015i	−1.43895	−	0.830779i	−0.441174	−	0.897422i	$-0.645438\pi$
$409$	−29.1010	−	16.8015i	−1.43895	−	0.830779i	−0.997777	+	0.0666432i	$0.978771\pi$
$410$	−26.8137	+	24.0149i	−1.32423	+	1.18601i
$411$	−18.7970	−	5.03665i	−0.927189	−	0.248440i
$412$	20.9960	+	15.4250i	1.03440	+	0.759934i
$413$	6.03999	+	15.2526i	0.297209	+	0.750533i
$414$	−8.87595	+	4.49297i	−0.436229	+	0.220817i
$415$	−5.27639	−	9.13898i	−0.259008	−	0.448615i
$416$	−0.404789	−	0.240904i	−0.0198464	−	0.0118113i
$417$	1.00344	−	1.73801i	0.0491387	−	0.0851107i
$418$	−12.1701	−	7.94927i	−0.595261	−	0.388811i
$419$	−4.24949	−	4.24949i	−0.207601	−	0.207601i	0.595646	−	0.803247i	$-0.296896\pi$
$419$	−4.24949	−	4.24949i	−0.207601	−	0.207601i	−0.803247	+	0.595646i	$0.796896\pi$
$420$	−11.2259	−	19.2108i	−0.547770	−	0.937393i
$421$	−18.6993	+	18.6993i	−0.911346	+	0.911346i	−0.996378	−	0.0850323i	$-0.972901\pi$
$421$	−18.6993	+	18.6993i	−0.911346	+	0.911346i	0.0850323	+	0.996378i	$0.472901\pi$
$422$	2.64946	+	12.6290i	0.128974	+	0.614771i
$423$	−2.71367	−	1.56674i	−0.131943	−	0.0761773i
$424$	8.89801	−	0.863837i	0.432126	−	0.0419516i
$425$	−51.9622	+	30.0004i	−2.52054	+	1.45523i
$426$	−2.18379	+	6.66098i	−0.105805	+	0.322726i
$427$	0.118941	−	0.805798i	0.00575596	−	0.0389953i
$428$	−2.84929	−	18.6274i	−0.137726	−	0.900391i
$429$	−0.0807744	+	0.301454i	−0.00389983	+	0.0145543i
$430$	11.0070	+	0.606075i	0.530807	+	0.0292275i
$431$	17.5113	−	30.3305i	0.843490	−	1.46097i	−0.0434363	−	0.999056i	$-0.513831\pi$
$431$	17.5113	−	30.3305i	0.843490	−	1.46097i	0.886926	−	0.461911i	$-0.152836\pi$
$432$	−0.167039	−	3.99651i	−0.00803666	−	0.192282i
$433$	−22.8747			−1.09929			−0.549643	−	0.835399i	$-0.685236\pi$
$433$	−22.8747			−1.09929			−0.549643	+	0.835399i	$0.685236\pi$
$434$	27.1572	−	17.9421i	1.30359	−	0.861247i
$435$	5.59570	+	5.59570i	0.268293	+	0.268293i
$436$	−6.81263	−	8.50456i	−0.326266	−	0.407295i
$437$	4.99327	+	18.6351i	0.238860	+	0.891439i
$438$	−11.4637	−	12.7997i	−0.547758	−	0.611595i
$439$	−16.3052	+	9.41380i	−0.778204	+	0.449296i	−0.835793	−	0.549044i	$-0.814992\pi$
$439$	−16.3052	+	9.41380i	−0.778204	+	0.449296i	0.0575897	+	0.998340i	$0.481658\pi$
$440$	−43.9690	−	7.32239i	−2.09614	−	0.349081i
$441$	5.10221	−	4.79243i	0.242963	−	0.228211i
$442$	−0.529457	−	0.173582i	−0.0251837	−	0.00825644i
$443$	−20.2047	−	5.41383i	−0.959955	−	0.257219i	−0.255373	−	0.966842i	$-0.582198\pi$
$443$	−20.2047	−	5.41383i	−0.959955	−	0.257219i	−0.704581	+	0.709623i	$0.748865\pi$
$444$	−2.68949	−	6.12780i	−0.127638	−	0.290813i
$445$	−2.20076	+	0.589693i	−0.104326	+	0.0279541i
$446$	0.927714	+	0.605962i	0.0439285	+	0.0286931i
$447$	13.2464			0.626531
$448$	20.6796	+	4.51138i	0.977021	+	0.213143i
$449$	−8.88699			−0.419403			−0.209702	−	0.977765i	$-0.567249\pi$
$449$	−8.88699			−0.419403			−0.209702	+	0.977765i	$0.567249\pi$
$450$	15.0149	+	9.80742i	0.707811	+	0.462326i
$451$	−21.9132	+	5.87163i	−1.03185	+	0.276484i
$452$	−12.1996	−	27.7959i	−0.573821	−	1.30741i
$453$	13.0613	+	3.49977i	0.613674	+	0.164433i
$454$	3.58176	+	1.17427i	0.168100	+	0.0551114i
$455$	0.552388	+	0.743700i	0.0258964	+	0.0348652i
$456$	−7.65171	−	1.27428i	−0.358324	−	0.0596735i
$457$	−18.8711	+	10.8952i	−0.882754	+	0.509658i	−0.871565	−	0.490279i	$-0.836895\pi$
$457$	−18.8711	+	10.8952i	−0.882754	+	0.509658i	−0.0111886	+	0.999937i	$0.503562\pi$
$458$	−21.8411	−	24.3865i	−1.02057	−	1.13951i
$459$	−1.22458	−	4.57020i	−0.0571586	−	0.213319i
$460$	36.9862	+	46.1718i	1.72449	+	2.15277i
$461$	16.1161	+	16.1161i	0.750603	+	0.750603i	0.974592	−	0.223989i	$-0.0719080\pi$
$461$	16.1161	+	16.1161i	0.750603	+	0.750603i	−0.223989	+	0.974592i	$0.571908\pi$
$462$	−0.844307	−	13.9978i	−0.0392807	−	0.651237i
$463$	9.93834			0.461874			0.230937	−	0.972969i	$-0.425821\pi$
$463$	9.93834			0.461874			0.230937	+	0.972969i	$0.425821\pi$
$464$	−7.52129	+	0.314361i	−0.349167	+	0.0145939i
$465$	−18.2894	+	31.6782i	−0.848152	+	1.46904i
$466$	−9.56768	−	0.526820i	−0.443214	−	0.0244045i
$467$	0.284928	−	1.06336i	0.0131849	−	0.0492066i	−0.959020	−	0.283338i	$-0.908558\pi$
$467$	0.284928	−	1.06336i	0.0131849	−	0.0492066i	0.972205	+	0.234132i	$0.0752247\pi$
$468$	0.0251817	+	0.164627i	0.00116402	+	0.00760988i
$469$	31.8699	−	12.6204i	1.47162	−	0.582755i
$470$	−5.80501	+	17.7064i	−0.267765	+	0.816734i
$471$	14.0023	−	8.08421i	0.645190	−	0.372501i
$472$	17.4556	−	1.69463i	0.803460	−	0.0780016i
$473$	6.01687	+	3.47384i	0.276656	+	0.159727i
$474$	1.85725	+	8.85282i	0.0853061	+	0.406623i
$475$	24.5926	−	24.5926i	1.12839	−	1.12839i
$476$	25.0360	−	0.131120i	1.14752	−	0.00600988i
$477$	−2.23496	−	2.23496i	−0.102332	−	0.102332i
$478$	−1.04858	−	0.684909i	−0.0479609	−	0.0313270i
$479$	16.5510	−	28.6672i	0.756235	−	1.30984i	−0.188523	−	0.982069i	$-0.560370\pi$
$479$	16.5510	−	28.6672i	0.756235	−	1.30984i	0.944758	−	0.327769i	$-0.106297\pi$
$480$	−23.0556	+	5.85181i	−1.05234	+	0.267097i
$481$	0.139313	+	0.241297i	0.00635212	+	0.0110022i
$482$	17.9972	−	9.11010i	0.819750	−	0.414954i
$483$	−11.5597	+	14.5865i	−0.525984	+	0.663708i
$484$	−4.91036	−	3.60746i	−0.223198	−	0.163975i
$485$	24.9780	+	6.69284i	1.13419	+	0.303906i
$486$	−1.05347	+	0.943508i	−0.0477862	+	0.0427984i
$487$	−17.3223	−	10.0010i	−0.784949	−	0.453190i	0.0532324	−	0.998582i	$-0.483048\pi$
$487$	−17.3223	−	10.0010i	−0.784949	−	0.453190i	−0.838181	+	0.545392i	$0.816381\pi$
$488$	−0.792649	−	0.360479i	−0.0358815	−	0.0163181i
$489$			3.81658i			0.172592i
$490$	−34.1215	−	23.8432i	−1.54145	−	1.07713i
$491$	−10.2023	+	10.2023i	−0.460426	+	0.460426i	−0.898795	−	0.438369i	$-0.855556\pi$
$491$	−10.2023	+	10.2023i	−0.460426	+	0.460426i	0.438369	+	0.898795i	$0.355556\pi$
$492$	−9.44849	+	7.56877i	−0.425971	+	0.341226i
$493$	−8.60095	+	2.30462i	−0.387367	+	0.103795i
$494$	0.322481	+	0.0177566i	0.0145091	+	0.000798907i
$495$	7.87975	+	13.6481i	0.354168	+	0.613438i
$496$	−10.4016	−	33.2052i	−0.467048	−	1.49096i
$497$	1.50808	+	13.0272i	0.0676465	+	0.584349i
$498$	−1.60290	−	3.16657i	−0.0718278	−	0.141897i
$499$	0.385619	−	1.43915i	0.0172627	−	0.0644252i	−0.956757	−	0.290888i	$-0.906049\pi$
$499$	0.385619	−	1.43915i	0.0172627	−	0.0644252i	0.974020	+	0.226462i	$0.0727161\pi$
$500$	23.4692	−	60.1850i	1.04957	−	2.69155i
$501$	−0.280763	−	1.04782i	−0.0125436	−	0.0468133i
$502$	−18.5647	+	3.89473i	−0.828585	+	0.173830i
$503$			42.4879i			1.89444i	0.320580	+	0.947221i	$0.396122\pi$
$503$			42.4879i			1.89444i	−0.320580	+	0.947221i	$0.603878\pi$
$504$	−3.41461	−	6.65886i	−0.152099	−	0.296609i
$505$		−	62.7473i		−	2.79222i
$506$	7.65543	+	36.4907i	0.340325	+	1.62221i
$507$	3.36285	+	12.5503i	0.149350	+	0.557380i
$508$	5.76944	+	13.1452i	0.255977	+	0.583225i
$509$	7.21770	−	26.9368i	0.319919	−	1.19395i	−0.599403	−	0.800448i	$-0.704595\pi$
$509$	7.21770	−	26.9368i	0.319919	−	1.19395i	0.919322	−	0.393507i	$-0.128738\pi$
$510$	−25.1032	+	12.7071i	−1.11159	+	0.562681i
$511$	−29.5030	−	12.7650i	−1.30514	−	0.564692i
$512$	10.7500	−	19.9108i	0.475086	−	0.879939i
$513$	1.37127	+	2.37511i	0.0605431	+	0.104864i
$514$	−1.45402	+	26.4067i	−0.0641339	+	1.16475i
$515$	−52.9091	+	14.1770i	−2.33145	+	0.624711i
$516$	3.68512	+	0.407058i	0.162228	+	0.0179197i
$517$	−8.30415	+	8.30415i	−0.365216	+	0.365216i
$518$	−9.36968	−	8.30367i	−0.411680	−	0.364842i
$519$			3.51337i			0.154220i
$520$	0.927376	−	0.347562i	0.0406681	−	0.0152416i
$521$	−25.2674	−	14.5881i	−1.10699	−	0.639118i	−0.168938	−	0.985627i	$-0.554034\pi$
$521$	−25.2674	−	14.5881i	−1.10699	−	0.639118i	−0.938047	+	0.346509i	$0.887367\pi$
$522$	1.77565	+	1.98259i	0.0777180	+	0.0867754i
$523$	19.8651	+	5.32285i	0.868642	+	0.232752i	0.665501	−	0.746397i	$-0.268218\pi$
$523$	19.8651	+	5.32285i	0.868642	+	0.232752i	0.203142	+	0.979149i	$0.434885\pi$
$524$	−32.1844	+	4.92299i	−1.40598	+	0.215062i
$525$	33.1921	+	4.89937i	1.44862	+	0.213826i
$526$	3.49570	+	6.90582i	0.152420	+	0.301108i
$527$	−20.5795	−	35.6447i	−0.896456	−	1.55271i
$528$	−14.6301	−	3.27199i	−0.636692	−	0.142395i
$529$	13.2423	−	22.9363i	0.575752	−	0.997231i
$530$	−10.2785	+	15.7362i	−0.446472	+	0.683538i
$531$	−4.38442	−	4.38442i	−0.190268	−	0.190268i
$532$	−13.9978	+	3.82939i	−0.606883	+	0.166025i
$533$	0.356415	−	0.356415i	0.0154381	−	0.0154381i
$534$	−0.749953	+	0.157334i	−0.0324536	+	0.00680850i
$535$	34.3110	+	19.8095i	1.48339	+	0.856438i
$536$	−3.54088	−	36.4730i	−0.152943	−	1.57539i
$537$	4.69224	−	2.70907i	0.202485	−	0.116905i
$538$	28.8463	+	9.45721i	1.24365	+	0.407729i
$539$	−12.4002	−	23.1196i	−0.534112	−	0.995832i
$540$	6.77744	+	4.97913i	0.291655	+	0.214268i
$541$	−9.54783	+	35.6330i	−0.410493	+	1.53198i	0.383201	+	0.923665i	$0.374822\pi$
$541$	−9.54783	+	35.6330i	−0.410493	+	1.53198i	−0.793694	+	0.608317i	$0.791845\pi$
$542$	−0.406911	+	7.38999i	−0.0174783	+	0.317427i
$543$	4.25391	−	7.36800i	0.182553	−	0.316191i
$544$	7.26883	−	25.7590i	0.311648	−	1.10441i
$545$	22.9100			0.981357
$546$	0.171749	+	0.259959i	0.00735016	+	0.0111252i
$547$	−1.06110	−	1.06110i	−0.0453695	−	0.0453695i	0.684058	−	0.729428i	$-0.260213\pi$
$547$	−1.06110	−	1.06110i	−0.0453695	−	0.0453695i	−0.729428	+	0.684058i	$0.760213\pi$
$548$	−4.27313	+	38.6850i	−0.182539	+	1.65254i
$549$	0.0796808	+	0.297373i	0.00340069	+	0.0126916i
$550$	50.0692	−	44.8431i	2.13496	−	1.91212i
$551$	4.46988	−	2.58068i	0.190423	−	0.109941i
$552$	11.5668	+	16.1891i	0.492314	+	0.689053i
$553$	10.0905	+	13.5852i	0.429092	+	0.577702i
$554$	7.32344	−	22.3379i	0.311143	−	0.949045i
$555$	13.5903	+	3.64152i	0.576877	+	0.154574i
$556$	−3.73950	−	1.45822i	−0.158590	−	0.0618423i
$557$	17.4451	−	4.67439i	0.739172	−	0.198060i	0.130462	−	0.991453i	$-0.458354\pi$
$557$	17.4451	−	4.67439i	0.739172	−	0.198060i	0.608710	+	0.793393i	$0.291687\pi$
$558$	−6.72762	+	10.2998i	−0.284803	+	0.436027i
$559$	−0.154365			−0.00652894
$560$	−34.5851	+	28.0032i	−1.46149	+	1.18335i
$561$	−17.7328			−0.748677
$562$	−23.9219	+	36.6239i	−1.00908	+	1.54488i
$563$	−24.1354	+	6.46707i	−1.01719	+	0.272555i	−0.728630	−	0.684908i	$-0.759842\pi$
$563$	−24.1354	+	6.46707i	−1.01719	+	0.272555i	−0.288558	+	0.957462i	$0.593176\pi$
$564$	−2.27681	+	5.83872i	−0.0958711	+	0.245855i
$565$	61.6460	+	16.5180i	2.59347	+	0.694918i
$566$	1.74174	−	5.31262i	0.0732106	−	0.223306i
$567$	−1.05061	+	2.42821i	−0.0441215	+	0.101975i
$568$	13.8292	+	2.30304i	0.580260	+	0.0966336i
$569$	28.9666	−	16.7239i	1.21434	−	0.701102i	0.250641	−	0.968080i	$-0.419359\pi$
$569$	28.9666	−	16.7239i	1.21434	−	0.701102i	0.963703	+	0.266978i	$0.0860253\pi$
$570$	12.1488	−	10.8807i	0.508856	−	0.455743i
$571$	2.11053	+	7.87662i	0.0883231	+	0.329626i	0.995923	−	0.0902106i	$-0.0287540\pi$
$571$	2.11053	+	7.87662i	0.0883231	+	0.329626i	−0.907600	+	0.419837i	$0.862087\pi$
$572$	0.620403	+	0.0685296i	0.0259404	+	0.00286537i
$573$	−13.3459	−	13.3459i	−0.557535	−	0.557535i
$574$	−10.1228	+	20.2605i	−0.422519	+	0.845658i
$575$	−89.2074			−3.72020
$576$	−7.85061	+	1.53881i	−0.327109	+	0.0641171i
$577$	10.9702	−	19.0009i	0.456694	−	0.791017i	−0.542090	−	0.840320i	$-0.682367\pi$
$577$	10.9702	−	19.0009i	0.456694	−	0.791017i	0.998784	+	0.0493034i	$0.0157001\pi$
$578$	0.418800	−	7.60591i	0.0174198	−	0.316364i
$579$	4.54154	−	16.9493i	0.188740	−	0.704387i
$580$	9.37054	−	12.7549i	0.389091	−	0.529618i
$581$	−5.20385	−	4.12402i	−0.215892	−	0.171093i
$582$	8.26423	+	2.70942i	0.342563	+	0.112309i
$583$	−10.2589	+	5.92297i	−0.424880	+	0.245304i
$584$	−21.8384	+	26.5346i	−0.903680	+	1.09801i
$585$	−0.303237	−	0.175074i	−0.0125373	−	0.00723841i
$586$	−5.24153	+	1.09963i	−0.216526	+	0.0454253i
$587$	−15.4781	+	15.4781i	−0.638849	+	0.638849i	−0.950271	−	0.311423i	$-0.899194\pi$
$587$	−15.4781	+	15.4781i	−0.638849	+	0.638849i	0.311423	+	0.950271i	$0.399194\pi$
$588$	−11.0176	−	8.63784i	−0.454359	−	0.356218i
$589$	16.8698	+	16.8698i	0.695110	+	0.695110i
$590$	−20.1639	+	30.8705i	−0.830134	+	1.27092i
$591$	−6.52883	+	11.3083i	−0.268560	+	0.465160i
$592$	−11.3014	+	7.17023i	−0.464484	+	0.294695i
$593$	−20.4642	−	35.4451i	−0.840366	−	1.45556i	−0.889586	−	0.456768i	$-0.849007\pi$
$593$	−20.4642	−	35.4451i	−0.840366	−	1.45556i	0.0492204	−	0.998788i	$-0.484326\pi$
$594$	2.39377	+	4.72894i	0.0982176	+	0.194031i
$595$	−32.6935	+	41.2539i	−1.34030	+	1.69124i
$596$	−4.00579	−	26.1881i	−0.164084	−	1.07271i
$597$	9.43341	+	2.52768i	0.386084	+	0.103451i
$598$	−0.552680	−	0.617090i	−0.0226008	−	0.0252347i
$599$	−22.2951	−	12.8721i	−0.910953	−	0.525939i	−0.0302151	−	0.999543i	$-0.509619\pi$
$599$	−22.2951	−	12.8721i	−0.910953	−	0.525939i	−0.880738	+	0.473605i	$0.842953\pi$
$600$	14.8487	−	32.6504i	0.606195	−	1.33295i
$601$		−	10.3842i		−	0.423580i	−0.977315	−	0.211790i	$-0.932071\pi$
$601$		−	10.3842i		−	0.423580i	0.977315	−	0.211790i	$-0.0679292\pi$
$602$	6.57958	−	2.19534i	0.268164	−	0.0894752i
$603$	−9.16112	+	9.16112i	−0.373070	+	0.373070i
$604$	2.96923	−	26.8806i	0.120816	−	1.09376i
$605$	12.3739	−	3.31558i	0.503071	−	0.134798i
$606$	1.16025	−	21.0715i	0.0471318	−	0.855971i
$607$	−5.28619	−	9.15595i	−0.214560	−	0.371629i	0.738576	−	0.674170i	$-0.235498\pi$
$607$	−5.28619	−	9.15595i	−0.214560	−	0.371629i	−0.953136	+	0.302541i	$0.902165\pi$
$608$	−0.205324	+	15.5128i	−0.00832699	+	0.629128i
$609$	4.56981	+	1.97721i	0.185178	+	0.0801206i
$610$	1.63341	−	0.826825i	0.0661348	−	0.0334772i
$611$	0.0675328	−	0.252036i	0.00273209	−	0.0101963i
$612$	−8.66499	+	3.80307i	−0.350261	+	0.153730i
$613$	0.574966	+	2.14580i	0.0232226	+	0.0866681i	0.976565	−	0.215224i	$-0.0690483\pi$
$613$	0.574966	+	2.14580i	0.0232226	+	0.0866681i	−0.953342	+	0.301893i	$0.902382\pi$
$614$	−3.95762	−	18.8645i	−0.159716	−	0.761310i
$615$		−	25.4528i		−	1.02636i
$616$	−27.4184	+	5.90223i	−1.10472	+	0.237808i
$617$		−	6.67667i		−	0.268793i	−0.990928	−	0.134396i	$-0.957091\pi$
$617$		−	6.67667i		−	0.268793i	0.990928	−	0.134396i	$-0.0429095\pi$
$618$	−18.0298	+	3.78250i	−0.725265	+	0.152154i
$619$	1.05482	+	3.93663i	0.0423967	+	0.158226i	0.983879	−	0.178836i	$-0.0572332\pi$
$619$	1.05482	+	3.93663i	0.0423967	+	0.158226i	−0.941482	+	0.337063i	$0.890567\pi$
$620$	68.1589	+	26.5786i	2.73733	+	1.06742i
$621$	1.82067	−	6.79483i	0.0730610	−	0.272667i
$622$	9.19516	+	18.1652i	0.368692	+	0.728359i
$623$	−1.15085	+	0.854802i	−0.0461078	+	0.0342469i
$624$	0.317853	−	0.0995687i	0.0127243	−	0.00398594i
$625$	36.2050	+	62.7089i	1.44820	+	2.50836i
$626$	14.0403	+	0.773091i	0.561162	+	0.0308989i
$627$	9.92846	−	2.66032i	0.396505	−	0.106243i
$628$	−20.2169	−	25.2378i	−0.806742	−	1.00710i
$629$	−11.1945	+	11.1945i	−0.446354	+	0.446354i
$630$	15.4149	+	3.14972i	0.614143	+	0.125488i
$631$		−	26.3401i		−	1.04858i	−0.851539	−	0.524291i	$-0.824331\pi$
$631$		−	26.3401i		−	1.04858i	0.851539	−	0.524291i	$-0.175669\pi$
$632$	16.9404	−	6.34894i	0.673854	−	0.252547i
$633$	−7.90202	−	4.56223i	−0.314077	−	0.181333i
$634$	−4.80104	+	4.29992i	−0.190674	+	0.170772i
$635$	−29.1536	−	7.81170i	−1.15693	−	0.309998i
$636$	−3.74266	+	5.09440i	−0.148406	+	0.202006i
$637$	0.495435	+	0.307102i	0.0196299	+	0.0121678i
$638$	8.89970	−	4.50499i	0.352343	−	0.178354i
$639$	−2.47835	−	4.29262i	−0.0980419	−	0.169814i
$640$	18.5412	+	43.8114i	0.732906	+	1.73180i
$641$	14.6929	−	25.4488i	0.580333	−	1.00517i	−0.415107	−	0.909773i	$-0.636256\pi$
$641$	14.6929	−	25.4488i	0.580333	−	1.00517i	0.995440	−	0.0953932i	$-0.0304109\pi$
$642$	11.1559	+	7.28675i	0.440287	+	0.287585i
$643$	−6.59289	−	6.59289i	−0.259998	−	0.259998i	0.565055	−	0.825053i	$-0.308855\pi$
$643$	−6.59289	−	6.59289i	−0.259998	−	0.259998i	−0.825053	+	0.565055i	$0.808855\pi$
$644$	32.3333	+	18.4425i	1.27411	+	0.726737i
$645$	−5.51186	+	5.51186i	−0.217029	+	0.217029i
$646$	3.76786	+	17.9600i	0.148245	+	0.706628i
$647$	−25.7308	−	14.8557i	−1.01158	−	0.584038i	−0.0999288	−	0.994995i	$-0.531861\pi$
$647$	−25.7308	−	14.8557i	−1.01158	−	0.584038i	−0.911655	+	0.410956i	$0.865195\pi$
$648$	2.18390	+	1.79739i	0.0857916	+	0.0706080i
$649$	−20.1253	+	11.6194i	−0.789988	+	0.456100i
$650$	−0.465241	+	1.41907i	−0.0182483	+	0.0556606i
$651$	−3.36083	+	22.7689i	−0.131721	+	0.892382i
$652$	7.54540	−	1.15416i	0.295501	−	0.0452004i
$653$	2.48778	−	9.28452i	0.0973543	−	0.363331i	−0.900012	−	0.435866i	$-0.856442\pi$
$653$	2.48778	−	9.28452i	0.0973543	−	0.363331i	0.997366	+	0.0725347i	$0.0231088\pi$
$654$	7.69352	+	0.423624i	0.300841	+	0.0165650i
$655$	34.2267	−	59.2824i	1.33735	−	2.31635i
$656$	17.8208	+	16.3909i	0.695785	+	0.639956i
$657$	12.1501			0.474021
$658$	0.705897	+	11.7031i	0.0275187	+	0.456235i
$659$	9.87502	+	9.87502i	0.384676	+	0.384676i	0.872784	−	0.488107i	$-0.162313\pi$
$659$	9.87502	+	9.87502i	0.384676	+	0.384676i	−0.488107	+	0.872784i	$0.662313\pi$
$660$	24.5995	−	19.7056i	0.957535	−	0.767039i
$661$	−7.96734	−	29.7345i	−0.309893	−	1.15654i	−0.928651	−	0.370956i	$-0.879030\pi$
$661$	−7.96734	−	29.7345i	−0.309893	−	1.15654i	0.618757	−	0.785582i	$-0.287636\pi$
$662$	20.9770	+	23.4217i	0.815295	+	0.910312i
$663$	0.341205	−	0.196995i	0.0132513	−	0.00765064i
$664$	−5.77559	+	4.12654i	−0.224137	+	0.160141i
$665$	12.1158	−	28.0026i	0.469832	−	1.08589i
$666$	4.49650	+	1.47417i	0.174236	+	0.0571230i
$667$	−12.7876	−	3.42643i	−0.495139	−	0.132672i
$668$	−1.98665	+	0.871939i	−0.0768657	+	0.0337363i
$669$	−0.756833	+	0.202793i	−0.0292609	+	0.00784043i
$670$	64.5029	+	42.1318i	2.49196	+	1.62769i
$671$	1.15383			0.0445431
$672$	−12.1320	+	8.76439i	−0.468002	+	0.338094i
$673$	−46.2788			−1.78392			−0.891958	−	0.452118i	$-0.850669\pi$
$673$	−46.2788			−1.78392			−0.891958	+	0.452118i	$0.850669\pi$
$674$	19.2337	+	12.5630i	0.740856	+	0.483910i
$675$	−12.2493	+	3.28218i	−0.471474	+	0.126331i
$676$	23.7951	−	10.4437i	0.915197	−	0.401680i
$677$	17.0688	+	4.57356i	0.656005	+	0.175776i	0.571443	−	0.820642i	$-0.306384\pi$
$677$	17.0688	+	4.57356i	0.656005	+	0.175776i	0.0845628	+	0.996418i	$0.473051\pi$
$678$	20.3962	+	6.68687i	0.783312	+	0.256808i
$679$	16.1627	−	1.87106i	0.620269	−	0.0718048i
$680$	32.7134	+	45.7864i	1.25450	+	1.75583i
$681$	−2.30824	+	1.33266i	−0.0884519	+	0.0510677i
$682$	30.7612	+	34.3461i	1.17791	+	1.31518i
$683$	1.29746	+	4.84220i	0.0496461	+	0.185282i	0.986296	−	0.164985i	$-0.0527576\pi$
$683$	1.29746	+	4.84220i	0.0496461	+	0.185282i	−0.936650	+	0.350267i	$0.886091\pi$
$684$	4.28093	−	3.42926i	0.163685	−	0.131121i
$685$	−57.8613	−	57.8613i	−2.21077	−	2.21077i
$686$	−25.4847	−	6.04382i	−0.973012	−	0.230754i
$687$	23.1488			0.883183
$688$	−0.309651	−	7.40860i	−0.0118053	−	0.282450i
$689$	0.131598	−	0.227934i	0.00501347	−	0.00868359i
$690$	−41.7686	−	2.29988i	−1.59011	−	0.0875550i
$691$	11.8408	−	44.1905i	0.450446	−	1.68109i	−0.250697	−	0.968066i	$-0.580660\pi$
$691$	11.8408	−	44.1905i	0.450446	−	1.68109i	0.701143	−	0.713021i	$-0.252674\pi$
$692$	6.94595	−	1.06247i	0.264045	−	0.0403889i
$693$	7.77142	+	6.15880i	0.295212	+	0.233953i
$694$	−11.0352	+	33.6595i	−0.418892	+	1.27770i
$695$	7.30819	−	4.21939i	0.277215	−	0.160050i
$696$	3.38261	−	4.11001i	0.128218	−	0.155790i
$697$	24.8028	+	14.3199i	0.939472	+	0.542404i
$698$	4.84671	+	23.1025i	0.183451	+	0.874443i
$699$	4.79109	−	4.79109i	0.181216	−	0.181216i
$700$	−0.351434	−	67.1025i	−0.0132829	−	2.53624i
$701$	25.6987	+	25.6987i	0.970626	+	0.970626i	0.999581	−	0.0289551i	$-0.00921798\pi$
$701$	25.6987	+	25.6987i	0.970626	+	0.970626i	−0.0289551	+	0.999581i	$0.509218\pi$
$702$	−0.0985941	−	0.0643994i	−0.00372119	−	0.00243060i
$703$	4.58830	−	7.94717i	0.173051	−	0.299733i
$704$	−2.04451	+	29.9132i	−0.0770552	+	1.12740i
$705$	−6.58800	−	11.4107i	−0.248118	−	0.429754i
$706$	−34.3221	+	17.3737i	−1.29173	+	0.653867i
$707$	−14.5360	−	36.7075i	−0.546684	−	1.38053i
$708$	−7.34215	+	9.99391i	−0.275935	+	0.375594i
$709$	26.3879	+	7.07062i	0.991019	+	0.265543i	0.717679	−	0.696375i	$-0.245205\pi$
$709$	26.3879	+	7.07062i	0.991019	+	0.265543i	0.273341	+	0.961917i	$0.411871\pi$
$710$	−21.9569	+	19.6651i	−0.824027	+	0.738017i
$711$	−5.53924	−	3.19808i	−0.207738	−	0.119937i
$712$	0.537840	+	1.43508i	0.0201564	+	0.0537820i
$713$		−	61.1938i		−	2.29173i
$714$	−11.7418	+	13.2491i	−0.439424	+	0.495837i
$715$	−0.927941	+	0.927941i	−0.0347030	+	0.0347030i
$716$	−6.77481	−	8.45735i	−0.253186	−	0.316066i
$717$	0.855436	−	0.229213i	0.0319469	−	0.00856013i
$718$	13.4631	+	0.741311i	0.502439	+	0.0276655i
$719$	14.7906	+	25.6182i	0.551598	+	0.955396i	0.998160	+	0.0606430i	$0.0193151\pi$
$719$	14.7906	+	25.6182i	0.551598	+	0.955396i	−0.446561	+	0.894753i	$0.647352\pi$
$720$	7.79422	−	14.9048i	0.290473	−	0.555468i
$721$	−27.6679	+	20.5505i	−1.03041	+	0.765341i
$722$	7.33131	+	14.4831i	0.272843	+	0.539007i
$723$	−3.69166	+	13.7775i	−0.137294	+	0.512389i
$724$	−15.8530	−	6.18188i	−0.589171	−	0.229748i
$725$	6.17694	+	23.0526i	0.229406	+	0.856154i
$726$	4.21665	−	0.884618i	0.156495	−	0.0328312i
$727$		−	6.34772i		−	0.235424i	−0.993048	−	0.117712i	$-0.962444\pi$
$727$		−	6.34772i		−	0.235424i	0.993048	−	0.117712i	$-0.0375559\pi$
$728$	0.462003	−	0.418162i	0.0171230	−	0.0154981i
$729$		−	1.00000i		−	0.0370370i
$730$	−14.8350	−	70.7131i	−0.549068	−	2.61721i
$731$	−2.27009	−	8.47209i	−0.0839623	−	0.313352i
$732$	0.563812	−	0.247457i	0.0208391	−	0.00914627i
$733$	12.4939	−	46.6280i	0.461474	−	1.72224i	−0.206849	−	0.978373i	$-0.566321\pi$
$733$	12.4939	−	46.6280i	0.461474	−	1.72224i	0.668323	−	0.743872i	$-0.267013\pi$
$734$	6.61105	−	3.34648i	0.244018	−	0.123521i
$735$	28.6560	−	6.72478i	1.05699	−	0.248047i
$736$	28.5080	−	27.7633i	1.05082	−	1.02337i
$737$	24.2783	+	42.0513i	0.894303	+	1.54898i
$738$	0.470642	−	8.54743i	0.0173246	−	0.314635i
$739$	−3.11776	+	0.835401i	−0.114689	+	0.0307307i	−0.315707	−	0.948857i	$-0.602242\pi$
$739$	−3.11776	+	0.835401i	−0.114689	+	0.0307307i	0.201018	+	0.979588i	$0.435575\pi$
$740$	3.08949	−	27.9694i	0.113572	−	1.02817i
$741$	−0.161485	+	0.161485i	−0.00593229	+	0.00593229i
$742$	−2.36755	+	11.5869i	−0.0869154	+	0.425368i
$743$			1.24432i			0.0456498i	0.999739	+	0.0228249i	$0.00726602\pi$
$743$			1.24432i			0.0456498i	−0.999739	+	0.0228249i	$0.992734\pi$
$744$	22.3973	+	10.1858i	0.821125	+	0.373429i
$745$	48.2375	+	27.8500i	1.76729	+	1.02034i
$746$	−8.68022	−	9.69183i	−0.317806	−	0.354843i
$747$	2.42411	+	0.649539i	0.0886937	+	0.0237654i
$748$	5.36251	+	35.0577i	0.196073	+	1.28184i
$749$	24.6612	+	3.64015i	0.901100	+	0.133008i
$750$	20.6297	+	40.7545i	0.753292	+	1.48814i
$751$	11.4034	+	19.7513i	0.416116	+	0.720734i	0.995545	−	0.0942890i	$-0.0300578\pi$
$751$	11.4034	+	19.7513i	0.416116	+	0.720734i	−0.579429	+	0.815023i	$0.696724\pi$
$752$	12.2317	+	2.73560i	0.446045	+	0.0997571i
$753$	6.70651	−	11.6160i	0.244399	−	0.423311i
$754$	−0.121197	+	0.185550i	−0.00441375	+	0.00675735i
$755$	40.2055	+	40.2055i	1.46323	+	1.46323i
$756$	5.11830	+	1.34275i	0.186151	+	0.0488355i
$757$	−37.1031	+	37.1031i	−1.34854	+	1.34854i	−0.461283	+	0.887253i	$0.652611\pi$
$757$	−37.1031	+	37.1031i	−1.34854	+	1.34854i	−0.887253	+	0.461283i	$0.847389\pi$
$758$	−0.426246	+	0.0894229i	−0.0154820	+	0.00324798i
$759$	−22.8323	−	13.1822i	−0.828761	−	0.478485i
$760$	−25.1851	−	20.7278i	−0.913559	−	0.751875i
$761$	−5.89072	+	3.40101i	−0.213538	+	0.123286i	−0.602955	−	0.797775i	$-0.706010\pi$
$761$	−5.89072	+	3.40101i	−0.213538	+	0.123286i	0.389416	+	0.921062i	$0.372677\pi$
$762$	−9.64578	−	3.16236i	−0.349430	−	0.114560i
$763$	13.4025	−	5.30733i	0.485202	−	0.192138i
$764$	−22.3491	+	30.4209i	−0.808562	+	1.10059i
$765$	5.14927	−	19.2173i	0.186172	−	0.694804i
$766$	−2.24779	+	40.8226i	−0.0812160	+	1.47498i
$767$	0.258161	−	0.447148i	0.00932165	−	0.0161456i
$768$	5.41631	+	15.0553i	0.195444	+	0.543263i
$769$	−19.3093			−0.696311			−0.348155	−	0.937437i	$-0.613192\pi$
$769$	−19.3093			−0.696311			−0.348155	+	0.937437i	$0.613192\pi$
$770$	26.3552	−	52.7491i	0.949777	−	1.90095i
$771$	−13.2233	−	13.2233i	−0.476227	−	0.476227i
$772$	−34.8822	−	3.85307i	−1.25544	−	0.138675i
$773$	7.31666	+	27.3062i	0.263162	+	0.982134i	0.963366	+	0.268191i	$0.0864259\pi$
$773$	7.31666	+	27.3062i	0.263162	+	0.982134i	−0.700204	+	0.713943i	$0.746907\pi$
$774$	−1.95288	+	1.74905i	−0.0701949	+	0.0628681i
$775$	−95.5364	+	55.1580i	−3.43177	+	1.98133i
$776$	2.85737	−	17.1578i	0.102574	−	0.615928i
$777$	8.79400	−	1.01803i	0.315483	−	0.0365216i
$778$	11.4811	−	35.0196i	0.411618	−	1.25551i
$779$	−16.0352	−	4.29663i	−0.574522	−	0.153943i
$780$	−0.254421	+	0.652444i	−0.00910973	+	0.0233612i
$781$	−17.9440	+	4.80809i	−0.642088	+	0.172047i
$782$	25.7404	−	39.4080i	0.920475	−	1.40923i
$783$	−1.88196			−0.0672559
$784$	−13.7452	+	24.3940i	−0.490902	+	0.871215i
$785$	67.9869			2.42656
$786$	12.5900	−	19.2750i	0.449071	−	0.687517i
$787$	44.0954	−	11.8153i	1.57183	−	0.421171i	0.635447	−	0.772144i	$-0.280816\pi$
$787$	44.0954	−	11.8153i	1.57183	−	0.421171i	0.936386	+	0.350973i	$0.114149\pi$
$788$	24.3309	+	9.48784i	0.866751	+	0.337990i
$789$	−5.28664	−	1.41655i	−0.188209	−	0.0504305i
$790$	−11.8494	+	36.1429i	−0.421583	+	1.28591i
$791$	39.8898	−	4.61780i	1.41832	−	0.164190i
$792$	8.62526	−	6.16257i	0.306485	−	0.218977i
$793$	−0.0222014	+	0.0128180i	−0.000788396	+	0.000455181i
$794$	6.71888	−	6.01758i	0.238444	−	0.213556i
$795$	−3.43985	−	12.8377i	−0.121999	−	0.455306i
$796$	2.14450	−	19.4143i	0.0760097	−	0.688121i
$797$	−5.68280	−	5.68280i	−0.201295	−	0.201295i	0.599260	−	0.800555i	$-0.295462\pi$
$797$	−5.68280	−	5.68280i	−0.201295	−	0.201295i	−0.800555	+	0.599260i	$0.795462\pi$
$798$	4.58647	−	9.17965i	0.162359	−	0.324956i
$799$	14.8258			0.524498
$800$	−69.0404	−	19.4822i	−2.44095	−	0.688801i
$801$	0.270920	−	0.469248i	0.00957250	−	0.0165801i
$802$	1.08747	−	19.7498i	0.0384000	−	0.697390i
$803$	11.7858	−	43.9854i	0.415913	−	1.55221i
$804$	20.8820	+	15.3412i	0.736451	+	0.541043i
$805$	−72.7629	+	28.8139i	−2.56456	+	1.01556i
$806$	−0.973446	−	0.319143i	−0.0342882	−	0.0112413i
$807$	−18.5898	+	10.7328i	−0.654391	+	0.377813i
$808$	−42.0093	+	4.07835i	−1.47788	+	0.143476i
$809$	−12.1529	−	7.01651i	−0.427275	−	0.246687i	0.270910	−	0.962605i	$-0.412675\pi$
$809$	−12.1529	−	7.01651i	−0.427275	−	0.246687i	−0.698185	+	0.715917i	$0.746009\pi$
$810$	−5.81996	+	1.22098i	−0.204493	+	0.0429008i
$811$	−30.3969	+	30.3969i	−1.06738	+	1.06738i	−0.0698213	+	0.997560i	$0.522243\pi$
$811$	−30.3969	+	30.3969i	−1.06738	+	1.06738i	−0.997560	+	0.0698213i	$0.977757\pi$
$812$	2.52702	−	9.63246i	0.0886809	−	0.338033i
$813$	−3.70059	−	3.70059i	−0.129785	−	0.129785i
$814$	9.69844	−	14.8481i	0.339930	−	0.520425i
$815$	−8.02421	+	13.8983i	−0.281076	+	0.486837i
$816$	10.1390	+	15.9807i	0.354937	+	0.559435i
$817$	2.54202	+	4.40291i	0.0889340	+	0.154038i
$818$	−21.4622	−	42.3991i	−0.750410	−	1.48245i
$819$	−0.217952	−	0.0321712i	−0.00761587	−	0.00112415i
$820$	−50.3204	+	7.69711i	−1.75726	+	0.268795i
$821$	−16.7308	−	4.48299i	−0.583907	−	0.156457i	−0.0452401	−	0.998976i	$-0.514405\pi$
$821$	−16.7308	−	4.48299i	−0.583907	−	0.156457i	−0.538667	+	0.842519i	$0.681072\pi$
$822$	−18.3608	−	20.5006i	−0.640406	−	0.715040i
$823$	42.7429	+	24.6776i	1.48992	+	0.860208i	0.999934	−	0.0115198i	$-0.00366695\pi$
$823$	42.7429	+	24.6776i	1.48992	+	0.860208i	0.489990	+	0.871728i	$0.337000\pi$
$824$	12.9304	+	34.5012i	0.450451	+	1.20191i
$825$			47.5281i			1.65472i
$826$	−4.64452	+	22.7305i	−0.161604	+	0.790896i
$827$	17.4044	−	17.4044i	0.605210	−	0.605210i	−0.336480	−	0.941690i	$-0.609237\pi$
$827$	17.4044	−	17.4044i	0.605210	−	0.605210i	0.941690	+	0.336480i	$0.109237\pi$
$828$	−13.9840	−	1.54467i	−0.485978	−	0.0536810i
$829$	7.19664	−	1.92833i	0.249950	−	0.0669738i	−0.131669	−	0.991294i	$-0.542034\pi$
$829$	7.19664	−	1.92833i	0.249950	−	0.0669738i	0.381618	+	0.924320i	$0.375367\pi$
$830$	0.820503	−	14.9013i	0.0284801	−	0.517232i
$831$	8.31124	+	14.3955i	0.288314	+	0.499374i
$832$	−0.292969	−	0.598287i	−0.0101569	−	0.0207419i
$833$	−9.56896	+	31.7075i	−0.331545	+	1.09860i
$834$	2.53222	−	1.28180i	0.0876835	−	0.0443850i
$835$	1.18059	−	4.40601i	0.0408559	−	0.152476i
$836$	−8.26191	−	18.8241i	−0.285744	−	0.651046i
$837$	−2.25148	−	8.40265i	−0.0778227	−	0.290438i
$838$	−1.74503	−	8.31791i	−0.0602810	−	0.287338i
$839$			38.1371i			1.31664i	0.752739	+	0.658319i	$0.228732\pi$
$839$			38.1371i			1.31664i	−0.752739	+	0.658319i	$0.771268\pi$
$840$	1.56544	−	31.4278i	0.0540129	−	1.08436i
$841$		−	25.4582i		−	0.877869i
$842$	−36.6017	+	7.67873i	−1.26138	+	0.264626i
$843$	−8.00576	−	29.8779i	−0.275733	−	1.02905i
$844$	−6.62993	+	17.0020i	−0.228212	+	0.585233i
$845$	−14.1405	+	52.7732i	−0.486449	+	1.81545i
$846$	−2.00135	−	3.95372i	−0.0688080	−	0.135932i
$847$	6.47072	−	4.80617i	0.222336	−	0.165142i
$848$	11.2035	+	5.85868i	0.384728	+	0.201188i
$849$	1.97666	+	3.42368i	0.0678389	+	0.117500i
$850$	−84.7256	−	4.66520i	−2.90607	−	0.160015i
$851$	−22.7356	+	6.09200i	−0.779368	+	0.208831i
$852$	−7.73707	+	6.19782i	−0.265068	+	0.212334i
$853$	13.9491	−	13.9491i	0.477608	−	0.477608i	−0.426758	−	0.904366i	$-0.640344\pi$
$853$	13.9491	−	13.9491i	0.477608	−	0.477608i	0.904366	+	0.426758i	$0.140344\pi$
$854$	0.764010	−	0.862092i	0.0261439	−	0.0295002i
$855$			11.5322i			0.394392i
$856$	11.0323	−	24.2588i	0.377078	−	0.829147i
$857$	−5.47702	−	3.16216i	−0.187092	−	0.108017i	0.403529	−	0.914967i	$-0.367784\pi$
$857$	−5.47702	−	3.16216i	−0.187092	−	0.108017i	−0.590620	+	0.806950i	$0.701117\pi$
$858$	−0.328775	+	0.294458i	−0.0112242	+	0.0100526i
$859$	−29.9632	−	8.02863i	−1.02233	−	0.273933i	−0.291559	−	0.956553i	$-0.594174\pi$
$859$	−29.9632	−	8.02863i	−1.02233	−	0.273933i	−0.730774	+	0.682620i	$0.760841\pi$
$860$	12.5638	+	9.23015i	0.428422	+	0.314746i
$861$	−5.89640	−	14.8900i	−0.200949	−	0.507451i
$862$	44.1904	−	22.3690i	1.50513	−	0.761891i
$863$	7.76741	+	13.4536i	0.264406	+	0.457964i	0.967408	−	0.253224i	$-0.0814909\pi$
$863$	7.76741	+	13.4536i	0.264406	+	0.457964i	−0.703002	+	0.711188i	$0.748158\pi$
$864$	2.89302	−	4.86112i	0.0984224	−	0.165379i
$865$	−7.38672	+	12.7942i	−0.251156	+	0.435015i
$866$	−27.0840	−	17.6907i	−0.920351	−	0.601153i
$867$	3.80872	+	3.80872i	0.129351	+	0.129351i
$868$	46.0305	−	0.241074i	1.56238	−	0.00818258i
$869$	−16.9507	+	16.9507i	−0.575015	+	0.575015i
$870$	2.29784	+	10.9530i	0.0779040	+	0.371340i
$871$	−0.934302	−	0.539420i	−0.0316576	−	0.0182775i
$872$	−1.48907	−	15.3382i	−0.0504262	−	0.519418i
$873$	−5.32583	+	3.07487i	−0.180252	+	0.104068i
$874$	−8.49979	+	25.9260i	−0.287510	+	0.876958i
$875$	66.9748	+	53.0771i	2.26416	+	1.79433i
$876$	−3.67428	−	24.0208i	−0.124142	−	0.811588i
$877$	1.15679	−	4.31718i	0.0390619	−	0.145781i	−0.943641	−	0.330972i	$-0.892624\pi$
$877$	1.15679	−	4.31718i	0.0390619	−	0.145781i	0.982703	+	0.185191i	$0.0592903\pi$
$878$	−26.5860	−	1.46389i	−0.897233	−	0.0494038i
$879$	1.89350	−	3.27964i	0.0638663	−	0.110620i
$880$	−46.3971	−	42.6743i	−1.56405	−	1.43855i
$881$	−6.23054			−0.209912			−0.104956	−	0.994477i	$-0.533470\pi$
$881$	−6.23054			−0.209912			−0.104956	+	0.994477i	$0.533470\pi$
$882$	9.74744	−	1.72841i	0.328213	−	0.0581985i
$883$	28.9879	+	28.9879i	0.975522	+	0.975522i	0.999707	−	0.0241858i	$-0.00769934\pi$
$883$	28.9879	+	28.9879i	0.975522	+	0.975522i	−0.0241858	+	0.999707i	$0.507699\pi$
$884$	−0.492642	−	0.614991i	−0.0165694	−	0.0206844i
$885$	−6.74810	−	25.1843i	−0.226835	−	0.846559i
$886$	−19.7358	−	22.0358i	−0.663037	−	0.740308i
$887$	5.16604	−	2.98261i	0.173459	−	0.100146i	−0.410757	−	0.911745i	$-0.634736\pi$
$887$	5.16604	−	2.98261i	0.173459	−	0.100146i	0.584216	+	0.811598i	$0.301402\pi$
$888$	1.55467	−	9.33540i	0.0521714	−	0.313276i
$889$	−18.8647	+	2.18385i	−0.632701	+	0.0732440i
$890$	−3.06179	−	1.00380i	−0.102631	−	0.0336476i
$891$	−3.62016	−	0.970020i	−0.121280	−	0.0324969i
$892$	0.629794	+	1.43494i	0.0210871	+	0.0480453i
$893$	−8.30086	+	2.22421i	−0.277778	+	0.0744303i
$894$	15.6839	+	10.2444i	0.524548	+	0.342623i
$895$	22.7828			0.761546
$896$	20.9961	+	21.3346i	0.701429	+	0.712739i
$897$	0.585771			0.0195583
$898$	−10.5223	−	6.87296i	−0.351135	−	0.229354i
$899$	−15.8135	+	4.23721i	−0.527409	+	0.141319i
$900$	10.1931	+	23.2243i	0.339771	+	0.774143i
$901$	14.4451	+	3.87055i	0.481236	+	0.128947i
$902$	−30.4866	−	9.99498i	−1.01509	−	0.332797i
$903$	−1.94759	+	4.50134i	−0.0648117	+	0.149795i
$904$	7.05202	−	42.3456i	0.234547	−	1.40839i
$905$	30.9818	−	17.8874i	1.02987	−	0.594596i
$906$	12.7582	+	14.2450i	0.423862	+	0.473260i
$907$	12.2611	+	45.7591i	0.407124	+	1.51941i	0.800105	+	0.599860i	$0.204777\pi$
$907$	12.2611	+	45.7591i	0.407124	+	1.51941i	−0.392982	+	0.919546i	$0.628556\pi$
$908$	3.33271	+	4.16039i	0.110600	+	0.138067i
$909$	10.5517	+	10.5517i	0.349978	+	0.349978i
$910$	0.0788800	+	1.30775i	0.00261485	+	0.0433516i
$911$	−43.7180			−1.44844			−0.724222	−	0.689567i	$-0.757801\pi$
$911$	−43.7180			−1.44844			−0.724222	+	0.689567i	$0.757801\pi$
$912$	−8.07425	−	7.42639i	−0.267365	−	0.245912i
$913$	4.70288	−	8.14562i	0.155643	−	0.269581i
$914$	−30.7698	−	1.69426i	−1.01777	−	0.0560412i
$915$	−0.335051	+	1.25043i	−0.0110765	+	0.0413379i
$916$	−7.00037	−	45.7654i	−0.231299	−	1.51213i
$917$	6.28943	−	42.6094i	0.207695	−	1.40709i
$918$	2.08454	−	6.35825i	0.0688002	−	0.209854i
$919$	22.4763	−	12.9767i	0.741425	−	0.428062i	−0.0811620	−	0.996701i	$-0.525863\pi$
$919$	22.4763	−	12.9767i	0.741425	−	0.428062i	0.822587	+	0.568639i	$0.192530\pi$
$920$	8.08425	+	83.2723i	0.266530	+	2.74541i
$921$	11.8036	+	6.81481i	0.388942	+	0.224556i
$922$	6.61798	+	31.5455i	0.217952	+	1.03890i
$923$	0.291857	−	0.291857i	0.00960659	−	0.00960659i
$924$	9.82585	−	17.2266i	0.323247	−	0.566713i
$925$	30.0040	+	30.0040i	0.986525	+	0.986525i
$926$	11.7672	+	7.68604i	0.386693	+	0.252579i
$927$	6.51327	−	11.2813i	0.213924	−	0.370527i
$928$	−9.14845	−	5.44455i	−0.300312	−	0.178726i
$929$	17.7467	+	30.7382i	0.582251	+	1.00849i	0.995212	+	0.0977402i	$0.0311614\pi$
$929$	17.7467	+	30.7382i	0.582251	+	1.00849i	−0.412960	+	0.910749i	$0.635505\pi$
$930$	−46.1541	+	23.3630i	−1.51345	+	0.766103i
$931$	0.600744	−	19.1884i	0.0196886	−	0.628875i
$932$	−10.9209	−	8.02315i	−0.357725	−	0.262807i
$933$	−13.9061	−	3.72612i	−0.455265	−	0.121988i
$934$	1.15974	−	1.03869i	0.0379477	−	0.0339868i
$935$	−64.5750	−	37.2824i	−2.11183	−	1.21926i
$936$	−0.0975025	+	0.214396i	−0.00318697	+	0.00700775i
$937$			5.04936i			0.164956i	0.996593	+	0.0824778i	$0.0262833\pi$
$937$			5.04936i			0.164956i	−0.996593	+	0.0824778i	$0.973717\pi$
$938$	47.4948	+	9.70460i	1.55076	+	0.316866i
$939$	−7.03077	+	7.03077i	−0.229440	+	0.229440i
$940$	−20.5669	+	16.4752i	−0.670817	+	0.537362i
$941$	35.4657	−	9.50301i	1.15615	−	0.309789i	0.370723	−	0.928744i	$-0.379110\pi$
$941$	35.4657	−	9.50301i	1.15615	−	0.309789i	0.785427	+	0.618954i	$0.212443\pi$
$942$	22.8310	+	1.25713i	0.743875	+	0.0409595i
$943$	21.2904	+	36.8760i	0.693310	+	1.20085i
$944$	21.9783	+	11.4932i	0.715334	+	0.374073i
$945$	−8.93109	+	6.63363i	−0.290528	+	0.215792i
$946$	4.43750	+	8.76637i	0.144275	+	0.285019i
$947$	−7.61667	+	28.4258i	−0.247509	+	0.923715i	0.724597	+	0.689173i	$0.242026\pi$
$947$	−7.61667	+	28.4258i	−0.247509	+	0.923715i	−0.972106	+	0.234542i	$0.924641\pi$
$948$	−4.64752	+	11.9182i	−0.150944	+	0.387086i
$949$	0.261860	+	0.977275i	0.00850034	+	0.0317237i
$950$	48.1373	−	10.0988i	1.56178	−	0.327648i
$951$		−	4.55738i		−	0.147783i
$952$	29.7444	+	19.2069i	0.964022	+	0.622499i
$953$		−	9.34305i		−	0.302651i	−0.988484	−	0.151326i	$-0.951646\pi$
$953$		−	9.34305i		−	0.302651i	0.988484	−	0.151326i	$-0.0483542\pi$
$954$	−0.917773	−	4.37469i	−0.0297140	−	0.141636i
$955$	−20.5409	−	76.6595i	−0.664686	−	2.48064i
$956$	−0.711846	−	1.62189i	−0.0230227	−	0.0524556i
$957$	−1.82554	+	6.81302i	−0.0590114	+	0.220234i
$958$	41.7671	−	21.1423i	1.34943	−	0.683078i
$959$	−47.2533	−	20.4450i	−1.52589	−	0.660204i
$960$	−31.8238	−	10.9019i	−1.02711	−	0.351858i
$961$	−22.3369	−	38.6886i	−0.720544	−	1.24802i
$962$	−0.0216638	+	0.393441i	−0.000698469	+	0.0126850i
$963$	−9.10100	+	2.43860i	−0.293276	+	0.0785829i
$964$	28.3545	+	3.13203i	0.913236	+	0.100876i
$965$	52.1735	−	52.1735i	1.67952	−	1.67952i
$966$	−24.9677	+	8.33068i	−0.803321	+	0.268035i
$967$		−	49.3562i		−	1.58719i	−0.608447	−	0.793595i	$-0.708207\pi$
$967$		−	49.3562i		−	1.58719i	0.608447	−	0.793595i	$-0.291793\pi$
$968$	−3.02404	−	8.06883i	−0.0971963	−	0.259342i
$969$	−11.2377	−	6.48806i	−0.361006	−	0.208427i
$970$	24.3983	+	27.2417i	0.783383	+	0.874680i
$971$	−1.82127	−	0.488009i	−0.0584474	−	0.0156609i	0.229477	−	0.973314i	$-0.426298\pi$
$971$	−1.82127	−	0.488009i	−0.0584474	−	0.0156609i	−0.287924	+	0.957653i	$0.592965\pi$
$972$	−1.97701	+	0.302407i	−0.0634125	+	0.00969971i
$973$	3.29787	−	4.16138i	0.105725	−	0.133408i
$974$	−12.7754	−	25.2380i	−0.409349	−	0.808678i
$975$	−0.527994	−	0.914512i	−0.0169093	−	0.0292878i
$976$	−0.659724	−	1.03983i	−0.0211173	−	0.0332840i
$977$	−5.69094	+	9.85699i	−0.182069	+	0.315353i	−0.942585	−	0.333966i	$-0.891613\pi$
$977$	−5.69094	+	9.85699i	−0.182069	+	0.315353i	0.760516	+	0.649319i	$0.224946\pi$
$978$	−2.95164	+	4.51889i	−0.0943830	+	0.144498i
$979$	−1.43596	−	1.43596i	−0.0458934	−	0.0458934i
$980$	−21.9607	−	54.6194i	−0.701508	−	1.74475i
$981$	−3.85259	+	3.85259i	−0.123004	+	0.123004i
$982$	−19.9700	+	4.18953i	−0.637267	+	0.133693i
$983$	37.1467	+	21.4467i	1.18480	+	0.684042i	0.957119	−	0.289694i	$-0.0935536\pi$
$983$	37.1467	+	21.4467i	1.18480	+	0.684042i	0.227677	+	0.973737i	$0.426887\pi$
$984$	−17.0406	+	1.65434i	−0.543236	+	0.0527384i
$985$	−47.5504	+	27.4532i	−1.51508	+	0.874732i
$986$	−11.9660	−	3.92304i	−0.381075	−	0.124935i
$987$	−6.49743	−	5.14917i	−0.206815	−	0.163900i
$988$	0.368090	+	0.270422i	0.0117105	+	0.00860328i
$989$	3.37510	−	12.5960i	0.107322	−	0.400531i
$990$	−1.22534	+	22.2536i	−0.0389437	+	0.707265i
$991$	−29.8204	+	51.6504i	−0.947275	+	1.64073i	−0.196144	+	0.980575i	$0.562842\pi$
$991$	−29.8204	+	51.6504i	−0.947275	+	1.64073i	−0.751131	+	0.660153i	$0.770491\pi$
$992$	13.3643	−	47.3599i	0.424316	−	1.50368i
$993$	−22.2330			−0.705543
$994$	−8.28927	+	16.5907i	−0.262920	+	0.526225i
$995$	29.0381	+	29.0381i	0.920569	+	0.920569i
$996$	0.551074	−	4.98891i	0.0174614	−	0.158080i
$997$	−2.30540	−	8.60387i	−0.0730128	−	0.272487i	0.919763	−	0.392475i	$-0.128381\pi$
$997$	−2.30540	−	8.60387i	−0.0730128	−	0.272487i	−0.992775	+	0.119988i	$0.961714\pi$
$998$	1.56958	−	1.40575i	0.0496841	−	0.0444982i
$999$	−2.89774	+	1.67301i	−0.0916804	+	0.0529317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.25	yes	120
7.2	even	3	inner	336.2.bq.b.205.15	yes	120
16.5	even	4	inner	336.2.bq.b.277.15	yes	120
112.37	even	12	inner	336.2.bq.b.37.25	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.25	✓	120	112.37	even	12	inner
336.2.bq.b.109.25	yes	120	1.1	even	1	trivial
336.2.bq.b.205.15	yes	120	7.2	even	3	inner
336.2.bq.b.277.15	yes	120	16.5	even	4	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18402 + 0.773373i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.803789 + 1.83137i) q^{4} +(-4.06164 - 1.08831i) q^{5} +(-1.34384 - 0.440575i) q^{6} +(-2.62820 + 0.304251i) q^{7} +(-0.464633 + 2.79000i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.18402 + 0.773373i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.803789 + 1.83137i) q^{4} +(-4.06164 - 1.08831i) q^{5} +(-1.34384 - 0.440575i) q^{6} +(-2.62820 + 0.304251i) q^{7} +(-0.464633 + 2.79000i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-3.96738 - 4.42974i) q^{10} +(-0.970020 - 3.62016i) q^{11} +(-1.25039 - 1.56093i) q^{12} +(0.0588814 + 0.0588814i) q^{13} +(-3.34713 - 1.67234i) q^{14} +4.20492 q^{15} +(-2.70785 + 2.94407i) q^{16} +(-2.36571 + 4.09753i) q^{17} +(1.41207 + 0.0777523i) q^{18} +(0.709823 - 2.64909i) q^{19} +(-1.27160 - 8.31315i) q^{20} +(2.45990 - 0.974112i) q^{21} +(1.65122 - 5.03652i) q^{22} +(-6.09208 + 3.51726i) q^{23} +(-0.273305 - 2.81519i) q^{24} +(10.9824 + 6.34068i) q^{25} +(0.0241793 + 0.115254i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.66971 - 4.56866i) q^{28} +(1.33075 + 1.33075i) q^{29} +(4.97869 + 3.25197i) q^{30} +(-4.34953 + 7.53361i) q^{31} +(-5.48300 + 1.39166i) q^{32} +(1.87394 + 3.24575i) q^{33} +(-5.96996 + 3.02197i) q^{34} +(11.0059 + 1.62455i) q^{35} +(1.61179 + 1.18412i) q^{36} +(3.23201 + 0.866013i) q^{37} +(2.88918 - 2.58761i) q^{38} +(-0.0721147 - 0.0416354i) q^{39} +(4.92357 - 10.8263i) q^{40} -6.05310i q^{41} +(3.66591 + 0.749055i) q^{42} +(-1.31081 + 1.31081i) q^{43} +(5.85018 - 4.68632i) q^{44} +(-4.06164 + 1.08831i) q^{45} +(-9.93328 - 0.546950i) q^{46} +(-1.56674 - 2.71367i) q^{47} +(1.85360 - 3.54460i) q^{48} +(6.81486 - 1.59926i) q^{49} +(8.09961 + 16.0009i) q^{50} +(1.22458 - 4.57020i) q^{51} +(-0.0605055 + 0.155162i) q^{52} +(-0.818053 - 3.05301i) q^{53} +(-1.38408 + 0.290369i) q^{54} +15.7595i q^{55} +(0.372288 - 7.47405i) q^{56} +2.74254i q^{57} +(0.546464 + 2.60479i) q^{58} +(-1.60481 - 5.98923i) q^{59} +(3.37987 + 7.70077i) q^{60} +(-0.0796808 + 0.297373i) q^{61} +(-10.9762 + 5.55611i) q^{62} +(-2.12396 + 1.57759i) q^{63} +(-7.56823 - 2.59266i) q^{64} +(-0.175074 - 0.303237i) q^{65} +(-0.291405 + 5.29227i) q^{66} +(-12.5143 + 3.35320i) q^{67} +(-9.40563 - 1.03894i) q^{68} +(4.97416 - 4.97416i) q^{69} +(11.7748 + 10.4352i) q^{70} -4.95669i q^{71} +(0.992617 + 2.64853i) q^{72} +(10.5223 + 6.07505i) q^{73} +(3.15700 + 3.52492i) q^{74} +(-12.2493 - 3.28218i) q^{75} +(5.42202 - 0.829364i) q^{76} +(3.65084 + 9.21938i) q^{77} +(-0.0531853 - 0.105069i) q^{78} +(-3.19808 - 5.53924i) q^{79} +(14.2024 - 9.01079i) q^{80} +(0.500000 - 0.866025i) q^{81} +(4.68130 - 7.16697i) q^{82} +(1.77457 + 1.77457i) q^{83} +(3.76120 + 3.72201i) q^{84} +(14.0681 - 14.0681i) q^{85} +(-2.56577 + 0.538277i) q^{86} +(-1.62983 - 0.940982i) q^{87} +(10.5510 - 1.02431i) q^{88} +(0.469248 - 0.270920i) q^{89} +(-5.65072 - 1.85258i) q^{90} +(-0.172667 - 0.136837i) q^{91} +(-11.3382 - 8.32972i) q^{92} +(2.25148 - 8.40265i) q^{93} +(0.243634 - 4.42469i) q^{94} +(-5.76609 + 9.98716i) q^{95} +(4.93598 - 2.76334i) q^{96} -6.14973 q^{97} +(9.30574 + 3.37687i) q^{98} +(-2.65014 - 2.65014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Introduction

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