LMFDB - Embedded newform 336.2.bq.b.109.29

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			109.29
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37705 - 0.322068i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.79254 - 0.887008i) q^{4} +(2.43839 + 0.653364i) q^{5} +(-1.24677 + 0.667501i) q^{6} +(-1.71258 - 2.01670i) q^{7} +(2.18275 - 1.79878i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(1.37705 - 0.322068i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.79254 - 0.887008i) q^{4} +(2.43839 + 0.653364i) q^{5} +(-1.24677 + 0.667501i) q^{6} +(-1.71258 - 2.01670i) q^{7} +(2.18275 - 1.79878i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.56822 + 0.114391i) q^{10} +(-0.0306943 - 0.114553i) q^{11} +(-1.50189 + 1.32073i) q^{12} +(2.21079 + 2.21079i) q^{13} +(-3.00783 - 2.22553i) q^{14} -2.52441 q^{15} +(2.42643 - 3.18000i) q^{16} +(-2.45970 + 4.26033i) q^{17} +(1.03153 - 0.967445i) q^{18} +(0.896147 - 3.34447i) q^{19} +(4.95046 - 0.991685i) q^{20} +(2.17619 + 1.50473i) q^{21} +(-0.0791615 - 0.147860i) q^{22} +(2.22830 - 1.28651i) q^{23} +(-1.64282 + 2.30242i) q^{24} +(1.18873 + 0.686313i) q^{25} +(3.75639 + 2.33235i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.85870 - 2.09595i) q^{28} +(0.376969 + 0.376969i) q^{29} +(-3.47624 + 0.813029i) q^{30} +(-4.09139 + 7.08650i) q^{31} +(2.31715 - 5.16051i) q^{32} +(0.0592969 + 0.102705i) q^{33} +(-2.01502 + 6.65888i) q^{34} +(-2.85830 - 6.03643i) q^{35} +(1.10889 - 1.66444i) q^{36} +(-8.27560 - 2.21744i) q^{37} +(0.156897 - 4.89412i) q^{38} +(-2.70765 - 1.56326i) q^{39} +(6.49765 - 2.95999i) q^{40} -0.368479i q^{41} +(3.48135 + 1.37121i) q^{42} +(-3.90599 + 3.90599i) q^{43} +(-0.156630 - 0.178115i) q^{44} +(2.43839 - 0.653364i) q^{45} +(2.65414 - 2.48925i) q^{46} +(0.566727 + 0.981599i) q^{47} +(-1.52071 + 3.69965i) q^{48} +(-1.13414 + 6.90751i) q^{49} +(1.85798 + 0.562237i) q^{50} +(1.27323 - 4.75178i) q^{51} +(5.92392 + 2.00195i) q^{52} +(-3.15583 - 11.7777i) q^{53} +(-0.745987 + 1.20146i) q^{54} -0.299379i q^{55} +(-7.36573 - 1.32140i) q^{56} +3.46245i q^{57} +(0.640515 + 0.397696i) q^{58} +(-0.157153 - 0.586505i) q^{59} +(-4.52511 + 2.23917i) q^{60} +(-3.57410 + 13.3387i) q^{61} +(-3.35173 + 11.0762i) q^{62} +(-2.49149 - 0.890221i) q^{63} +(1.52881 - 7.85256i) q^{64} +(3.94631 + 6.83521i) q^{65} +(0.114733 + 0.122333i) q^{66} +(-6.83072 + 1.83029i) q^{67} +(-0.630181 + 9.81860i) q^{68} +(-1.81940 + 1.81940i) q^{69} +(-5.88017 - 7.39191i) q^{70} +7.37232i q^{71} +(0.990930 - 2.64916i) q^{72} +(-4.59243 - 2.65144i) q^{73} +(-12.1101 - 0.388228i) q^{74} +(-1.32585 - 0.355262i) q^{75} +(-1.36018 - 6.78999i) q^{76} +(-0.178452 + 0.258082i) q^{77} +(-4.23205 - 1.28065i) q^{78} +(2.74794 + 4.75958i) q^{79} +(7.99429 - 6.16874i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.118675 - 0.507414i) q^{82} +(-2.86646 - 2.86646i) q^{83} +(5.23562 + 0.767005i) q^{84} +(-8.78125 + 8.78125i) q^{85} +(-4.12076 + 6.63675i) q^{86} +(-0.461691 - 0.266557i) q^{87} +(-0.273053 - 0.194828i) q^{88} +(3.57423 - 2.06358i) q^{89} +(3.14736 - 1.68504i) q^{90} +(0.672338 - 8.24464i) q^{91} +(2.85318 - 4.28264i) q^{92} +(2.11786 - 7.90397i) q^{93} +(1.09655 + 1.16919i) q^{94} +(4.37031 - 7.56960i) q^{95} +(-0.902559 + 5.58439i) q^{96} +14.6069 q^{97} +(0.662922 + 9.87727i) q^{98} +(-0.0838585 - 0.0838585i) 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 $

$2$	1.37705	−	0.322068i	0.973723	−	0.227736i
$2$	1.37705	−	0.322068i	0.973723	−	0.227736i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.79254	−	0.887008i	0.896272	−	0.443504i
$5$	2.43839	+	0.653364i	1.09048	+	0.292193i	0.758883	−	0.651227i	$-0.225746\pi$
$5$	2.43839	+	0.653364i	1.09048	+	0.292193i	0.331598	+	0.943421i	$0.392412\pi$
$6$	−1.24677	+	0.667501i	−0.508993	+	0.272506i
$7$	−1.71258	−	2.01670i	−0.647295	−	0.762240i
$7$	−1.71258	−	2.01670i	−0.647295	−	0.762240i
$8$	2.18275	−	1.79878i	0.771719	−	0.635964i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	3.56822	+	0.114391i	1.12837	+	0.0361735i
$11$	−0.0306943	−	0.114553i	−0.00925469	−	0.0345390i	0.961144	−	0.276047i	$-0.0890246\pi$
$11$	−0.0306943	−	0.114553i	−0.00925469	−	0.0345390i	−0.970399	+	0.241508i	$0.922358\pi$
$12$	−1.50189	+	1.32073i	−0.433559	+	0.381261i
$13$	2.21079	+	2.21079i	0.613162	+	0.613162i	0.943769	−	0.330606i	$-0.107253\pi$
$13$	2.21079	+	2.21079i	0.613162	+	0.613162i	−0.330606	+	0.943769i	$0.607253\pi$
$14$	−3.00783	−	2.22553i	−0.803875	−	0.594798i
$15$	−2.52441			−0.651799
$16$	2.42643	−	3.18000i	0.606609	−	0.795001i
$17$	−2.45970	+	4.26033i	−0.596565	+	1.03328i	0.396759	+	0.917923i	$0.370135\pi$
$17$	−2.45970	+	4.26033i	−0.596565	+	1.03328i	−0.993324	+	0.115358i	$0.963198\pi$
$18$	1.03153	−	0.967445i	0.243134	−	0.228029i
$19$	0.896147	−	3.34447i	0.205590	−	0.767273i	−0.783679	−	0.621166i	$-0.786659\pi$
$19$	0.896147	−	3.34447i	0.205590	−	0.767273i	0.989269	−	0.146107i	$-0.0466743\pi$
$20$	4.95046	−	0.991685i	1.10696	−	0.221748i
$21$	2.17619	+	1.50473i	0.474883	+	0.328359i
$22$	−0.0791615	−	0.147860i	−0.0168773	−	0.0315238i
$23$	2.22830	−	1.28651i	0.464632	−	0.268256i	−0.249358	−	0.968411i	$-0.580220\pi$
$23$	2.22830	−	1.28651i	0.464632	−	0.268256i	0.713990	+	0.700156i	$0.246886\pi$
$24$	−1.64282	+	2.30242i	−0.335339	+	0.469980i
$25$	1.18873	+	0.686313i	0.237746	+	0.137263i
$26$	3.75639	+	2.33235i	0.736689	+	0.457411i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−4.85870	−	2.09595i	−0.918209	−	0.396097i
$29$	0.376969	+	0.376969i	0.0700013	+	0.0700013i	0.741241	−	0.671239i	$-0.234238\pi$
$29$	0.376969	+	0.376969i	0.0700013	+	0.0700013i	−0.671239	+	0.741241i	$0.734238\pi$
$30$	−3.47624	+	0.813029i	−0.634671	+	0.148438i
$31$	−4.09139	+	7.08650i	−0.734836	+	1.27277i	0.219959	+	0.975509i	$0.429408\pi$
$31$	−4.09139	+	7.08650i	−0.734836	+	1.27277i	−0.954795	+	0.297264i	$0.903926\pi$
$32$	2.31715	−	5.16051i	0.409618	−	0.912257i
$33$	0.0592969	+	0.102705i	0.0103223	+	0.0178787i
$34$	−2.01502	+	6.65888i	−0.345574	+	1.14199i
$35$	−2.85830	−	6.03643i	−0.483141	−	1.02034i
$36$	1.10889	−	1.66444i	0.184814	−	0.277407i
$37$	−8.27560	−	2.21744i	−1.36050	−	0.364545i	−0.496500	−	0.868037i	$-0.665382\pi$
$37$	−8.27560	−	2.21744i	−1.36050	−	0.364545i	−0.864000	+	0.503492i	$0.832048\pi$
$38$	0.156897	−	4.89412i	0.0254520	−	0.793932i
$39$	−2.70765	−	1.56326i	−0.433571	−	0.250322i
$40$	6.49765	−	2.95999i	1.02737	−	0.468015i
$41$		−	0.368479i		−	0.0575467i	−0.999586	−	0.0287733i	$-0.990840\pi$
$41$		−	0.368479i		−	0.0575467i	0.999586	−	0.0287733i	$-0.00916010\pi$
$42$	3.48135	+	1.37121i	0.537183	+	0.211583i
$43$	−3.90599	+	3.90599i	−0.595658	+	0.595658i	−0.939154	−	0.343496i	$-0.888389\pi$
$43$	−3.90599	+	3.90599i	−0.595658	+	0.595658i	0.343496	+	0.939154i	$0.388389\pi$
$44$	−0.156630	−	0.178115i	−0.0236129	−	0.0268518i
$45$	2.43839	−	0.653364i	0.363494	−	0.0973978i
$46$	2.65414	−	2.48925i	0.391332	−	0.367020i
$47$	0.566727	+	0.981599i	0.0826656	+	0.143181i	0.904394	−	0.426698i	$-0.140323\pi$
$47$	0.566727	+	0.981599i	0.0826656	+	0.143181i	−0.821729	+	0.569879i	$0.806990\pi$
$48$	−1.52071	+	3.69965i	−0.219496	+	0.533999i
$49$	−1.13414	+	6.90751i	−0.162019	+	0.986788i
$50$	1.85798	+	0.562237i	0.262758	+	0.0795124i
$51$	1.27323	−	4.75178i	0.178289	−	0.665382i
$52$	5.92392	+	2.00195i	0.821500	+	0.277621i
$53$	−3.15583	−	11.7777i	−0.433487	−	1.61780i	−0.744661	−	0.667443i	$-0.767389\pi$
$53$	−3.15583	−	11.7777i	−0.433487	−	1.61780i	0.311173	−	0.950353i	$-0.399278\pi$
$54$	−0.745987	+	1.20146i	−0.101516	+	0.163498i
$55$		−	0.299379i		−	0.0403683i
$56$	−7.36573	−	1.32140i	−0.984286	−	0.176579i
$57$			3.46245i			0.458612i
$58$	0.640515	+	0.397696i	0.0841037	+	0.0522201i
$59$	−0.157153	−	0.586505i	−0.0204596	−	0.0763564i	0.954941	−	0.296795i	$-0.0959178\pi$
$59$	−0.157153	−	0.586505i	−0.0204596	−	0.0763564i	−0.975401	+	0.220439i	$0.929251\pi$
$60$	−4.52511	+	2.23917i	−0.584189	+	0.289075i
$61$	−3.57410	+	13.3387i	−0.457616	+	1.70785i	0.222665	+	0.974895i	$0.428524\pi$
$61$	−3.57410	+	13.3387i	−0.457616	+	1.70785i	−0.680281	+	0.732951i	$0.738142\pi$
$62$	−3.35173	+	11.0762i	−0.425670	+	1.40668i
$63$	−2.49149	−	0.890221i	−0.313898	−	0.112157i
$64$	1.52881	−	7.85256i	0.191101	−	0.981570i
$65$	3.94631	+	6.83521i	0.489480	+	0.847804i
$66$	0.114733	+	0.122333i	0.0141227	+	0.0150581i
$67$	−6.83072	+	1.83029i	−0.834506	+	0.223605i	−0.650678	−	0.759353i	$-0.725515\pi$
$67$	−6.83072	+	1.83029i	−0.834506	+	0.223605i	−0.183827	+	0.982959i	$0.558849\pi$
$68$	−0.630181	+	9.81860i	−0.0764207	+	1.19068i
$69$	−1.81940	+	1.81940i	−0.219030	+	0.219030i
$70$	−5.88017	−	7.39191i	−0.702814	−	0.883503i
$71$			7.37232i			0.874934i	0.899234	+	0.437467i	$0.144124\pi$
$71$			7.37232i			0.874934i	−0.899234	+	0.437467i	$0.855876\pi$
$72$	0.990930	−	2.64916i	0.116782	−	0.312207i
$73$	−4.59243	−	2.65144i	−0.537503	−	0.310327i	0.206563	−	0.978433i	$-0.433772\pi$
$73$	−4.59243	−	2.65144i	−0.537503	−	0.310327i	−0.744066	+	0.668106i	$0.767105\pi$
$74$	−12.1101	−	0.388228i	−1.40777	−	0.0451306i
$75$	−1.32585	−	0.355262i	−0.153096	−	0.0410221i
$76$	−1.36018	−	6.78999i	−0.156024	−	0.778866i
$77$	−0.178452	+	0.258082i	−0.0203365	+	0.0294112i
$78$	−4.23205	−	1.28065i	−0.479186	−	0.145005i
$79$	2.74794	+	4.75958i	0.309168	+	0.535494i	0.978181	−	0.207757i	$-0.0666162\pi$
$79$	2.74794	+	4.75958i	0.309168	+	0.535494i	−0.669013	+	0.743251i	$0.733283\pi$
$80$	7.99429	−	6.16874i	0.893789	−	0.689686i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−0.118675	−	0.507414i	−0.0131055	−	0.0560345i
$83$	−2.86646	−	2.86646i	−0.314634	−	0.314634i	0.532067	−	0.846702i	$-0.321415\pi$
$83$	−2.86646	−	2.86646i	−0.314634	−	0.314634i	−0.846702	+	0.532067i	$0.821415\pi$
$84$	5.23562	+	0.767005i	0.571253	+	0.0836871i
$85$	−8.78125	+	8.78125i	−0.952460	+	0.952460i
$86$	−4.12076	+	6.63675i	−0.444353	+	0.715659i
$87$	−0.461691	−	0.266557i	−0.0494984	−	0.0285779i
$88$	−0.273053	−	0.194828i	−0.0291076	−	0.0207687i
$89$	3.57423	−	2.06358i	0.378867	−	0.218739i	−0.298458	−	0.954423i	$-0.596472\pi$
$89$	3.57423	−	2.06358i	0.378867	−	0.218739i	0.677325	+	0.735684i	$0.263139\pi$
$90$	3.14736	−	1.68504i	0.331761	−	0.177619i
$91$	0.672338	−	8.24464i	0.0704801	−	0.864274i
$92$	2.85318	−	4.28264i	0.297465	−	0.446496i
$93$	2.11786	−	7.90397i	0.219612	−	0.819603i
$94$	1.09655	+	1.16919i	0.113101	+	0.120593i
$95$	4.37031	−	7.56960i	0.448384	−	0.776624i
$96$	−0.902559	+	5.58439i	−0.0921170	+	0.569954i
$97$	14.6069			1.48311			0.741555	−	0.670892i	$-0.234088\pi$
$97$	14.6069			1.48311			0.741555	+	0.670892i	$0.234088\pi$
$98$	0.662922	+	9.87727i	0.0669653	+	0.997755i
$99$	−0.0838585	−	0.0838585i	−0.00842810	−	0.00842810i
$100$	2.73961	+	0.175835i	0.273961	+	0.0175835i
$101$	−4.36981	−	16.3084i	−0.434812	−	1.62274i	−0.741515	−	0.670936i	$-0.765892\pi$
$101$	−4.36981	−	16.3084i	−0.434812	−	1.62274i	0.306703	−	0.951805i	$-0.400774\pi$
$102$	0.222917	−	6.95351i	0.0220721	−	0.688500i
$103$	−17.0791	+	9.86064i	−1.68286	+	0.971598i	−0.723109	+	0.690734i	$0.757288\pi$
$103$	−17.0791	+	9.86064i	−1.68286	+	0.971598i	−0.959748	+	0.280864i	$0.909379\pi$
$104$	8.80232	+	0.848887i	0.863138	+	0.0832402i
$105$	4.32325	+	5.09096i	0.421906	+	0.496827i
$106$	−8.13898	−	15.2022i	−0.790527	−	1.47656i
$107$	12.3994	+	3.32241i	1.19870	+	0.321190i	0.802318	−	0.596897i	$-0.203600\pi$
$107$	12.3994	+	3.32241i	1.19870	+	0.321190i	0.396379	+	0.918087i	$0.370267\pi$
$108$	−0.640311	+	1.89473i	−0.0616140	+	0.182320i
$109$	16.1426	−	4.32540i	1.54618	−	0.414298i	0.617925	−	0.786237i	$-0.287974\pi$
$109$	16.1426	−	4.32540i	1.54618	−	0.414298i	0.928257	+	0.371939i	$0.121307\pi$
$110$	−0.0964203	−	0.412260i	−0.00919331	−	0.0393075i
$111$	8.56753			0.813194
$112$	−10.5686	+	0.552627i	−0.998636	+	0.0522183i
$113$	11.0353			1.03811			0.519055	−	0.854741i	$-0.326284\pi$
$113$	11.0353			1.03811			0.519055	+	0.854741i	$0.326284\pi$
$114$	1.11514	+	4.76797i	0.104443	+	0.446561i
$115$	6.27402	−	1.68112i	0.585055	−	0.156765i
$116$	1.01011	+	0.341359i	0.0937861	+	0.0316944i
$117$	3.01999	+	0.809205i	0.279198	+	0.0748110i
$118$	−0.405303	−	0.757033i	−0.0373111	−	0.0696906i
$119$	12.8042	−	2.33568i	1.17376	−	0.214111i
$120$	−5.51015	+	4.54084i	−0.503006	+	0.414520i
$121$	9.51410	−	5.49297i	0.864918	−	0.499361i
$122$	−0.625750	+	19.5192i	−0.0566528	+	1.76718i
$123$	0.0953693	+	0.355923i	0.00859916	+	0.0320925i
$124$	−1.04822	+	16.3320i	−0.0941333	+	1.46665i
$125$	−6.47495	−	6.47495i	−0.579137	−	0.579137i
$126$	−3.71762	−	0.423453i	−0.331192	−	0.0377242i
$127$	−13.0710			−1.15986			−0.579930	−	0.814666i	$-0.696920\pi$
$127$	−13.0710			−1.15986			−0.579930	+	0.814666i	$0.696920\pi$
$128$	−0.423811	−	11.3058i	−0.0374600	−	0.999298i
$129$	2.76195	−	4.78384i	0.243176	−	0.421194i
$130$	7.63568	+	8.14146i	0.669693	+	0.714054i
$131$	4.05494	−	15.1332i	0.354282	−	1.32220i	−0.527104	−	0.849801i	$-0.676722\pi$
$131$	4.05494	−	15.1332i	0.354282	−	1.32220i	0.881386	−	0.472397i	$-0.156611\pi$
$132$	0.197393	+	0.131507i	0.0171808	+	0.0114462i
$133$	−8.27950	+	3.92041i	−0.717924	+	0.339943i
$134$	−8.81678	+	4.72035i	−0.761654	+	0.407777i
$135$	−2.18620	+	1.26220i	−0.188158	+	0.108633i
$136$	2.29446	+	13.7237i	0.196748	+	1.17680i
$137$	13.3092	+	7.68408i	1.13708	+	0.656496i	0.945707	−	0.325021i	$-0.105371\pi$
$137$	13.3092	+	7.68408i	1.13708	+	0.656496i	0.191377	+	0.981517i	$0.438705\pi$
$138$	−1.91944	+	3.09137i	−0.163393	+	0.263155i
$139$	13.6496	−	13.6496i	1.15774	−	1.15774i	0.172785	−	0.984960i	$-0.444723\pi$
$139$	13.6496	−	13.6496i	1.15774	−	1.15774i	0.984960	−	0.172785i	$-0.0552766\pi$
$140$	−10.4780	−	8.28524i	−0.885552	−	0.700231i
$141$	−0.801472	−	0.801472i	−0.0674962	−	0.0674962i
$142$	2.37439	+	10.1521i	0.199254	+	0.851943i
$143$	0.185393	−	0.321111i	0.0155034	−	0.0268526i
$144$	0.511353	−	3.96718i	0.0426127	−	0.330598i
$145$	0.672899	+	1.16549i	0.0558812	+	0.0967890i
$146$	−7.17795	−	2.17210i	−0.594052	−	0.179764i
$147$	−0.692305	−	6.96568i	−0.0571003	−	0.574520i
$148$	−16.8013	+	3.36566i	−1.38106	+	0.276655i
$149$	0.255016	+	0.0683313i	0.0208917	+	0.00559792i	0.269250	−	0.963070i	$-0.413224\pi$
$149$	0.255016	+	0.0683313i	0.0208917	+	0.00559792i	−0.248358	+	0.968668i	$0.579891\pi$
$150$	−1.94019	−	0.0621990i	−0.158416	−	0.00507853i
$151$	−15.0004	−	8.66051i	−1.22072	−	0.704782i	−0.255647	−	0.966770i	$-0.582289\pi$
$151$	−15.0004	−	8.66051i	−1.22072	−	0.704782i	−0.965071	+	0.261988i	$0.915622\pi$
$152$	−4.05988	−	8.91211i	−0.329300	−	0.722867i
$153$			4.91940i			0.397710i
$154$	−0.162618	+	0.412866i	−0.0131041	+	0.0332697i
$155$	−14.6065	+	14.6065i	−1.17322	+	1.17322i
$156$	−6.24021	−	0.400512i	−0.499617	−	0.0320666i
$157$	−3.46005	+	0.927118i	−0.276142	+	0.0739920i	−0.394232	−	0.919011i	$-0.628989\pi$
$157$	−3.46005	+	0.927118i	−0.276142	+	0.0739920i	0.118090	+	0.993003i	$0.462323\pi$
$158$	5.31697	+	5.66916i	0.422995	+	0.451014i
$159$	6.09660	+	10.5596i	0.483492	+	0.837433i
$160$	9.02180	−	11.0694i	0.713236	−	0.875111i
$161$	−6.41064	−	2.29055i	−0.505229	−	0.180521i
$162$	0.409607	−	1.35360i	0.0321818	−	0.106349i
$163$	1.53008	−	5.71033i	0.119845	−	0.447268i	−0.879759	−	0.475421i	$-0.842296\pi$
$163$	1.53008	−	5.71033i	0.119845	−	0.447268i	0.999604	+	0.0281530i	$0.00896257\pi$
$164$	−0.326843	−	0.660514i	−0.0255222	−	0.0515775i
$165$	0.0774850	+	0.289178i	0.00603220	+	0.0225125i
$166$	−4.87045	−	3.02407i	−0.378020	−	0.234713i
$167$			13.8084i			1.06853i	0.845317	+	0.534265i	$0.179411\pi$
$167$			13.8084i			1.06853i	−0.845317	+	0.534265i	$0.820589\pi$
$168$	7.45675	−	0.630017i	0.575301	−	0.0486069i
$169$		−	3.22483i		−	0.248064i
$170$	−9.26408	+	14.9204i	−0.710523	+	1.14434i
$171$	−0.896147	−	3.34447i	−0.0685301	−	0.255758i
$172$	−3.53702	+	10.4663i	−0.269695	+	0.798049i
$173$	1.49425	−	5.57663i	0.113606	−	0.423983i	−0.885573	−	0.464500i	$-0.846234\pi$
$173$	1.49425	−	5.57663i	0.113606	−	0.423983i	0.999179	+	0.0405173i	$0.0129006\pi$
$174$	−0.721621	−	0.218368i	−0.0547060	−	0.0165544i
$175$	−0.651708	−	3.57267i	−0.0492645	−	0.270069i
$176$	−0.438756	−	0.180347i	−0.0330725	−	0.0135942i
$177$	0.303597	+	0.525846i	0.0228198	+	0.0395250i
$178$	4.25728	−	3.99280i	0.319097	−	0.299273i
$179$	23.3221	−	6.24913i	1.74317	−	0.467082i	0.760026	−	0.649893i	$-0.225186\pi$
$179$	23.3221	−	6.24913i	1.74317	−	0.467082i	0.983148	+	0.182811i	$0.0585197\pi$
$180$	3.79138	−	3.33405i	0.282593	−	0.248506i
$181$	1.68267	−	1.68267i	0.125072	−	0.125072i	−0.641800	−	0.766872i	$-0.721812\pi$
$181$	1.68267	−	1.68267i	0.125072	−	0.125072i	0.766872	+	0.641800i	$0.221812\pi$
$182$	−1.72949	−	11.5698i	−0.128198	−	0.857614i
$183$		−	13.8092i		−	1.02081i
$184$	2.54968	−	6.81634i	0.187965	−	0.502507i
$185$	−18.7303	−	10.8140i	−1.37708	−	0.795058i
$186$	0.370794	−	11.5663i	0.0271879	−	0.848080i
$187$	0.563531	+	0.150998i	0.0412095	+	0.0110421i
$188$	1.88657	+	1.25687i	0.137592	+	0.0916667i
$189$	2.63700	+	0.215043i	0.191813	+	0.0156421i
$190$	3.58022	−	11.8313i	0.259737	−	0.858330i
$191$	9.07735	+	15.7224i	0.656814	+	1.13763i	0.981436	+	0.191791i	$0.0614296\pi$
$191$	9.07735	+	15.7224i	0.656814	+	1.13763i	−0.324622	+	0.945844i	$0.605237\pi$
$192$	0.555680	+	7.98068i	0.0401028	+	0.575956i
$193$	−0.231053	+	0.400196i	−0.0166316	+	0.0288067i	−0.874221	−	0.485527i	$-0.838628\pi$
$193$	−0.231053	+	0.400196i	−0.0166316	+	0.0288067i	0.857590	+	0.514334i	$0.171961\pi$
$194$	20.1145	−	4.70443i	1.44414	−	0.337758i
$195$	−5.58093	−	5.58093i	−0.399659	−	0.399659i
$196$	4.09403	+	13.3880i	0.292431	+	0.956287i
$197$	−13.2334	+	13.2334i	−0.942837	+	0.942837i	−0.998452	−	0.0556150i	$-0.982288\pi$
$197$	−13.2334	+	13.2334i	−0.942837	+	0.942837i	0.0556150	+	0.998452i	$0.482288\pi$
$198$	−0.142486	−	0.0884694i	−0.0101260	−	0.00628725i
$199$	1.31472	+	0.759055i	0.0931981	+	0.0538080i	0.545875	−	0.837867i	$-0.316197\pi$
$199$	1.31472	+	0.759055i	0.0931981	+	0.0538080i	−0.452677	+	0.891675i	$0.649531\pi$
$200$	3.82922	−	0.640207i	0.270767	−	0.0452695i
$201$	6.12426	−	3.53584i	0.431972	−	0.249399i
$202$	−11.2698	−	21.0501i	−0.792944	−	1.48108i
$203$	0.114643	−	1.40582i	0.00804633	−	0.0986693i
$204$	−1.93253	−	9.64714i	−0.135304	−	0.675435i
$205$	0.240751	−	0.898494i	0.0168148	−	0.0627536i
$206$	−20.3431	+	19.0793i	−1.41737	+	1.32931i
$207$	1.28651	−	2.22830i	0.0894185	−	0.154877i
$208$	12.3946	−	1.66598i	0.859414	−	0.115515i
$209$	−0.410625			−0.0284035
$210$	7.59297	+	5.61814i	0.523965	+	0.387689i
$211$	17.5331	+	17.5331i	1.20703	+	1.20703i	0.971985	+	0.235042i	$0.0755229\pi$
$211$	17.5331	+	17.5331i	1.20703	+	1.20703i	0.235042	+	0.971985i	$0.424477\pi$
$212$	−16.1039	−	18.3129i	−1.10602	−	1.25773i
$213$	−1.90810	−	7.12112i	−0.130741	−	0.487931i
$214$	18.1447	+	0.581686i	1.24034	+	0.0397632i
$215$	−12.0764	+	6.97229i	−0.823601	+	0.475506i
$216$	−0.271511	+	2.81537i	−0.0184740	+	0.191561i
$217$	21.2982	−	3.88510i	1.44581	−	0.263738i
$218$	20.8361	−	11.1553i	1.41120	−	0.755533i
$219$	5.12219	+	1.37249i	0.346125	+	0.0927440i
$220$	−0.265551	−	0.536650i	−0.0179035	−	0.0361810i
$221$	−14.8566	+	3.98080i	−0.999360	+	0.267778i
$222$	11.7979	−	2.75932i	0.791825	−	0.185194i
$223$	−1.36397			−0.0913380			−0.0456690	−	0.998957i	$-0.514542\pi$
$223$	−1.36397			−0.0913380			−0.0456690	+	0.998957i	$0.514542\pi$
$224$	−14.3755	+	4.16479i	−0.960502	+	0.278272i
$225$	1.37263			0.0915084
$226$	15.1961	−	3.55410i	1.01083	−	0.236415i
$227$	5.28600	−	1.41638i	0.350844	−	0.0940084i	−0.0790930	−	0.996867i	$-0.525202\pi$
$227$	5.28600	−	1.41638i	0.350844	−	0.0940084i	0.429937	+	0.902859i	$0.358536\pi$
$228$	3.07122	+	6.20659i	0.203396	+	0.411041i
$229$	13.7852	+	3.69374i	0.910952	+	0.244089i	0.683714	−	0.729750i	$-0.260364\pi$
$229$	13.7852	+	3.69374i	0.910952	+	0.244089i	0.227238	+	0.973839i	$0.427030\pi$
$230$	8.09821	−	4.33564i	0.533980	−	0.285884i
$231$	0.105575	−	0.295475i	0.00694630	−	0.0194408i
$232$	1.50091	+	0.144746i	0.0985397	+	0.00950307i
$233$	−17.7776	+	10.2639i	−1.16465	+	0.672411i	−0.952414	−	0.304808i	$-0.901408\pi$
$233$	−17.7776	+	10.2639i	−1.16465	+	0.672411i	−0.212236	+	0.977219i	$0.568074\pi$
$234$	4.41931	+	0.141675i	0.288899	+	0.00926159i
$235$	0.740558	+	2.76380i	0.0483087	+	0.180290i
$236$	−0.801939	−	0.911939i	−0.0522018	−	0.0593622i
$237$	−3.88618	−	3.88618i	−0.252434	−	0.252434i
$238$	16.8798	−	7.34018i	1.09416	−	0.475793i
$239$	17.1974			1.11241			0.556203	−	0.831047i	$-0.312258\pi$
$239$	17.1974			1.11241			0.556203	+	0.831047i	$0.312258\pi$
$240$	−6.12531	+	8.02762i	−0.395387	+	0.518180i
$241$	−2.17570	+	3.76842i	−0.140149	+	0.242746i	−0.927553	−	0.373692i	$-0.878092\pi$
$241$	−2.17570	+	3.76842i	−0.140149	+	0.242746i	0.787403	+	0.616438i	$0.211425\pi$
$242$	11.3323	−	10.6283i	0.728468	−	0.683212i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	5.42481	+	27.0805i	0.347288	+	1.73365i
$245$	−7.27859	+	16.1022i	−0.465012	+	1.02873i
$246$	0.245960	+	0.459409i	0.0156818	+	0.0292909i
$247$	9.37510	−	5.41272i	0.596523	−	0.344403i
$248$	3.81654	+	22.8276i	0.242350	+	1.44955i
$249$	3.51068	+	2.02689i	0.222480	+	0.128449i
$250$	−11.0017	−	6.83097i	−0.695810	−	0.432029i
$251$	−16.8797	+	16.8797i	−1.06544	+	1.06544i	−0.0677355	+	0.997703i	$0.521577\pi$
$251$	−16.8797	+	16.8797i	−1.06544	+	1.06544i	−0.997703	+	0.0677355i	$0.978423\pi$
$252$	−5.25573	+	0.614208i	−0.331080	+	0.0386914i
$253$	−0.215769	−	0.215769i	−0.0135653	−	0.0135653i
$254$	−17.9994	+	4.20973i	−1.12938	+	0.264142i
$255$	6.20928	−	10.7548i	0.388840	−	0.673491i
$256$	−4.22483	−	15.4321i	−0.264052	−	0.964508i
$257$	−12.5112	−	21.6701i	−0.780428	−	1.35174i	−0.931693	−	0.363247i	$-0.881668\pi$
$257$	−12.5112	−	21.6701i	−0.780428	−	1.35174i	0.151265	−	0.988493i	$-0.451665\pi$
$258$	2.26263	−	7.47714i	0.140865	−	0.465506i
$259$	9.70072	+	20.4869i	0.602774	+	1.27300i
$260$	13.1368	+	8.75202i	0.814711	+	0.542777i
$261$	0.514949	+	0.137980i	0.0318745	+	0.00854076i
$262$	0.709936	−	22.1452i	0.0438600	−	1.36814i
$263$	0.331922	+	0.191635i	0.0204672	+	0.0118167i	0.510199	−	0.860057i	$-0.329572\pi$
$263$	0.331922	+	0.191635i	0.0204672	+	0.0118167i	−0.489732	+	0.871873i	$0.662905\pi$
$264$	0.314174	+	0.117518i	0.0193361	+	0.00723274i
$265$		−	30.7806i		−	1.89084i
$266$	−10.1387	+	8.06517i	−0.621641	+	0.494507i
$267$	−2.91834	+	2.91834i	−0.178600	+	0.178600i
$268$	−10.6209	+	9.33977i	−0.648775	+	0.570518i
$269$	−16.8434	+	4.51318i	−1.02696	+	0.275173i	−0.732700	−	0.680552i	$-0.761740\pi$
$269$	−16.8434	+	4.51318i	−1.02696	+	0.275173i	−0.294261	+	0.955725i	$0.595074\pi$
$270$	−2.60400	+	2.44222i	−0.158474	+	0.148629i
$271$	−10.4157	−	18.0406i	−0.632710	−	1.09589i	−0.986995	−	0.160749i	$-0.948609\pi$
$271$	−10.4157	−	18.0406i	−0.632710	−	1.09589i	0.354285	−	0.935137i	$-0.384724\pi$
$272$	7.57955	+	18.1593i	0.459577	+	1.10107i
$273$	1.48444	+	8.13773i	0.0898425	+	0.492518i
$274$	20.8023	+	6.29491i	1.25671	+	0.380290i
$275$	0.0421318	−	0.157238i	0.00254065	−	0.00948182i
$276$	−1.64753	+	4.87517i	−0.0991698	+	0.293451i
$277$	0.0492930	+	0.183964i	0.00296173	+	0.0110533i	0.967391	−	0.253288i	$-0.0815121\pi$
$277$	0.0492930	+	0.183964i	0.00296173	+	0.0110533i	−0.964429	+	0.264341i	$0.914845\pi$
$278$	14.4001	−	23.1923i	0.863662	−	1.39098i
$279$			8.18279i			0.489891i
$280$	−17.0971	−	8.03459i	−1.02175	−	0.480158i
$281$		−	10.1130i		−	0.603289i	−0.953420	−	0.301644i	$-0.902464\pi$
$281$		−	10.1130i		−	0.603289i	0.953420	−	0.301644i	$-0.0975356\pi$
$282$	−1.36180	−	0.845541i	−0.0810939	−	0.0503512i
$283$	−0.894021	−	3.33653i	−0.0531441	−	0.198336i	0.934250	−	0.356620i	$-0.116071\pi$
$283$	−0.894021	−	3.33653i	−0.0531441	−	0.198336i	−0.987394	+	0.158283i	$0.949404\pi$
$284$	6.53931	+	13.2152i	0.388037	+	0.784179i
$285$	−2.26224	+	8.44279i	−0.134003	+	0.500108i
$286$	0.151877	−	0.501895i	0.00898067	−	0.0296777i
$287$	−0.743110	+	0.631049i	−0.0438644	+	0.0372497i
$288$	−0.573541	−	5.62770i	−0.0337962	−	0.331616i
$289$	−3.60025	−	6.23582i	−0.211780	−	0.366813i
$290$	1.30198	+	1.38823i	0.0764552	+	0.0815195i
$291$	−14.1092	+	3.78056i	−0.827098	+	0.221620i
$292$	−10.5840	−	0.679305i	−0.619380	−	0.0397533i
$293$	23.0354	−	23.0354i	1.34574	−	1.34574i	0.455512	−	0.890230i	$-0.349456\pi$
$293$	23.0354	−	23.0354i	1.34574	−	1.34574i	0.890230	−	0.455512i	$-0.150544\pi$
$294$	−3.19676	−	9.36914i	−0.186439	−	0.546419i
$295$		−	1.53280i		−	0.0892433i
$296$	−22.0522	+	10.0458i	−1.28176	+	0.583902i
$297$	0.102705	+	0.0592969i	0.00595956	+	0.00344076i
$298$	0.373177	+	0.0119634i	0.0216176	+	0.000693021i
$299$	7.77049	+	2.08210i	0.449379	+	0.120411i
$300$	−2.69177	+	0.539221i	−0.155410	+	0.0311319i
$301$	14.5665	+	1.18788i	0.839601	+	0.0684681i
$302$	−23.4457	−	7.09481i	−1.34915	−	0.408261i
$303$	8.44182	+	14.6217i	0.484970	+	0.839993i
$304$	−8.46097	−	10.9649i	−0.485270	−	0.628879i
$305$	−17.4301	+	30.1898i	−0.998043	+	1.72866i
$306$	1.58438	+	6.77427i	0.0905730	+	0.387259i
$307$	−7.05671	−	7.05671i	−0.402748	−	0.402748i	0.476452	−	0.879200i	$-0.341922\pi$
$307$	−7.05671	−	7.05671i	−0.402748	−	0.402748i	−0.879200	+	0.476452i	$0.841922\pi$
$308$	−0.0909621	+	0.620912i	−0.00518305	+	0.0353797i
$309$	13.9451	−	13.9451i	0.793306	−	0.793306i
$310$	−15.4096	+	24.8182i	−0.875207	+	1.40958i
$311$	−8.49689	−	4.90568i	−0.481815	−	0.278176i	0.239358	−	0.970931i	$-0.423063\pi$
$311$	−8.49689	−	4.90568i	−0.481815	−	0.278176i	−0.721172	+	0.692756i	$0.756396\pi$
$312$	−8.72209	+	1.45825i	−0.493791	+	0.0825569i
$313$	−19.0137	+	10.9775i	−1.07472	+	0.620487i	−0.929466	−	0.368908i	$-0.879732\pi$
$313$	−19.0137	+	10.9775i	−1.07472	+	0.620487i	−0.145250	+	0.989395i	$0.546399\pi$
$314$	−4.46607	+	2.39106i	−0.252035	+	0.134935i
$315$	−5.49358	−	3.79855i	−0.309528	−	0.214024i
$316$	9.14760	+	6.09431i	0.514592	+	0.342832i
$317$	0.580137	−	2.16510i	0.0325837	−	0.121604i	−0.947718	−	0.319108i	$-0.896617\pi$
$317$	0.580137	−	2.16510i	0.0325837	−	0.121604i	0.980302	+	0.197504i	$0.0632834\pi$
$318$	11.7963	+	12.5776i	0.661501	+	0.705319i
$319$	0.0316120	−	0.0547536i	0.00176993	−	0.00306562i
$320$	8.85841	−	18.1487i	0.495200	−	1.01455i
$321$	−12.8368			−0.716481
$322$	−9.56550	−	1.08955i	−0.533064	−	0.0607184i
$323$	12.0443	+	12.0443i	0.670161	+	0.670161i
$324$	0.128101	−	1.99589i	0.00711673	−	0.110883i
$325$	1.11074	+	4.14532i	0.0616125	+	0.229941i
$326$	0.267885	−	8.35621i	0.0148368	−	0.462808i
$327$	−14.4731	+	8.35603i	−0.800363	+	0.462090i
$328$	−0.662811	−	0.804297i	−0.0365976	−	0.0444099i
$329$	1.00902	−	2.82398i	0.0556293	−	0.155691i
$330$	0.199836	+	0.373258i	0.0110006	+	0.0205472i
$331$	12.2365	+	3.27875i	0.672576	+	0.180216i	0.578915	−	0.815388i	$-0.303476\pi$
$331$	12.2365	+	3.27875i	0.672576	+	0.180216i	0.0936613	+	0.995604i	$0.470143\pi$
$332$	−7.68082	−	2.59568i	−0.421540	−	0.142457i
$333$	−8.27560	+	2.21744i	−0.453500	+	0.121515i
$334$	4.44725	+	19.0149i	0.243343	+	1.04045i
$335$	−17.8518			−0.975348
$336$	10.0654	−	3.26914i	0.549114	−	0.178346i
$337$	−20.1768			−1.09910			−0.549550	−	0.835461i	$-0.685201\pi$
$337$	−20.1768			−1.09910			−0.549550	+	0.835461i	$0.685201\pi$
$338$	−1.03861	−	4.44076i	−0.0564931	−	0.241545i
$339$	−10.6592	+	2.85614i	−0.578931	+	0.155124i
$340$	−7.95175	+	23.5298i	−0.431244	+	1.27608i
$341$	0.937361	+	0.251165i	0.0507610	+	0.0136014i
$342$	−2.31119	−	4.31688i	−0.124975	−	0.233430i
$343$	15.8727	−	9.54246i	0.857043	−	0.515245i
$344$	−1.49980	+	15.5518i	−0.0808639	+	0.838498i
$345$	−5.62513	+	3.24767i	−0.302847	+	0.174849i
$346$	0.261613	−	8.16056i	0.0140644	−	0.438714i
$347$	−6.57477	−	24.5374i	−0.352952	−	1.31723i	−0.883042	−	0.469294i	$-0.844509\pi$
$347$	−6.57477	−	24.5374i	−0.352952	−	1.31723i	0.530090	−	0.847941i	$-0.322158\pi$
$348$	−1.06404	−	0.0682926i	−0.0570385	−	0.00366087i
$349$	−9.20377	−	9.20377i	−0.492667	−	0.492667i	0.416479	−	0.909145i	$-0.363264\pi$
$349$	−9.20377	−	9.20377i	−0.492667	−	0.492667i	−0.909145	+	0.416479i	$0.863264\pi$
$350$	−2.04808	−	4.70986i	−0.109474	−	0.251753i
$351$	−3.12653			−0.166882
$352$	−0.662274	−	0.107038i	−0.0352993	−	0.00570514i
$353$	−2.41763	+	4.18746i	−0.128678	+	0.222876i	−0.923164	−	0.384405i	$-0.874407\pi$
$353$	−2.41763	+	4.18746i	−0.128678	+	0.222876i	0.794487	+	0.607281i	$0.207740\pi$
$354$	0.587427	+	0.626338i	0.0312214	+	0.0332895i
$355$	−4.81681	+	17.9766i	−0.255650	+	0.954099i
$356$	4.57655	−	6.86943i	0.242557	−	0.364079i
$357$	−11.7634	+	5.57007i	−0.622586	+	0.294799i
$358$	30.1031	−	16.1167i	1.59100	−	0.851792i
$359$	5.96620	−	3.44459i	0.314884	−	0.181798i	−0.334226	−	0.942493i	$-0.608475\pi$
$359$	5.96620	−	3.44459i	0.314884	−	0.181798i	0.649110	+	0.760695i	$0.275142\pi$
$360$	4.14714	−	5.81225i	0.218573	−	0.306332i
$361$	6.07211	+	3.50573i	0.319585	+	0.184512i
$362$	1.77519	−	2.85906i	0.0933022	−	0.150269i
$363$	−7.76823	+	7.76823i	−0.407726	+	0.407726i
$364$	−6.10787	−	15.3753i	−0.320139	−	0.805883i
$365$	−9.46577	−	9.46577i	−0.495461	−	0.495461i
$366$	−4.44751	−	19.0160i	−0.232475	−	0.993985i
$367$	−4.76550	+	8.25409i	−0.248757	+	0.430860i	−0.963181	−	0.268853i	$-0.913355\pi$
$367$	−4.76550	+	8.25409i	−0.248757	+	0.430860i	0.714424	+	0.699713i	$0.246689\pi$
$368$	1.31572	−	10.2076i	0.0685866	−	0.532109i
$369$	−0.184239	−	0.319112i	−0.00959112	−	0.0166123i
$370$	−29.2755	−	8.85895i	−1.52196	−	0.460555i
$371$	−18.3475	+	26.5347i	−0.952555	+	1.37761i
$372$	−3.21452	−	16.0468i	−0.166665	−	0.831986i
$373$	−29.9553	−	8.02650i	−1.55103	−	0.415596i	−0.621218	−	0.783638i	$-0.713362\pi$
$373$	−29.9553	−	8.02650i	−1.55103	−	0.415596i	−0.929809	+	0.368042i	$0.880028\pi$
$374$	0.824643	+	0.0264366i	0.0426413	+	0.00136700i
$375$	7.93016	+	4.57848i	0.409512	+	0.236432i
$376$	3.00270	+	1.12317i	0.154852	+	0.0579232i
$377$			1.66680i			0.0858444i
$378$	3.70054	−	0.553166i	0.190335	−	0.0284518i
$379$	−6.80723	+	6.80723i	−0.349664	+	0.349664i	−0.859984	−	0.510321i	$-0.829527\pi$
$379$	−6.80723	+	6.80723i	−0.349664	+	0.349664i	0.510321	+	0.859984i	$0.329527\pi$
$380$	1.11968	−	17.4453i	0.0574386	−	0.894927i
$381$	12.6256	−	3.38301i	0.646828	−	0.173317i
$382$	17.5637	+	18.7271i	0.898635	+	0.958161i
$383$	17.1878	+	29.7702i	0.878257	+	1.52119i	0.853252	+	0.521499i	$0.174627\pi$
$383$	17.1878	+	29.7702i	0.878257	+	1.52119i	0.0250049	+	0.999687i	$0.492040\pi$
$384$	3.33552	+	10.8108i	0.170215	+	0.551688i
$385$	−0.603757	+	0.512711i	−0.0307703	+	0.0261302i
$386$	−0.189282	+	0.625505i	−0.00963420	+	0.0318374i
$387$	−1.42969	+	5.33568i	−0.0726753	+	0.271228i
$388$	26.1836	−	12.9565i	1.32927	−	0.657765i
$389$	4.15000	+	15.4880i	0.210413	+	0.785274i	0.987731	+	0.156165i	$0.0499132\pi$
$389$	4.15000	+	15.4880i	0.210413	+	0.785274i	−0.777318	+	0.629108i	$0.783420\pi$
$390$	−9.48266	−	5.88779i	−0.480173	−	0.298140i
$391$			12.6577i			0.640127i
$392$	9.94954	+	17.1174i	0.502527	+	0.864561i
$393$			15.6671i			0.790300i
$394$	−13.9610	+	22.4850i	−0.703344	+	1.13278i
$395$	3.59082	+	13.4011i	0.180674	+	0.674283i
$396$	−0.224703	−	0.0759370i	−0.0112918	−	0.00381598i
$397$	1.58378	−	5.91074i	0.0794875	−	0.296651i	−0.914726	−	0.404075i	$-0.867593\pi$
$397$	1.58378	−	5.91074i	0.0794875	−	0.296651i	0.994213	+	0.107424i	$0.0342601\pi$
$398$	2.05491	+	0.621829i	0.103003	+	0.0311695i
$399$	6.98271	−	5.92972i	0.349573	−	0.296857i
$400$	5.06685	−	2.11487i	0.253342	−	0.105743i
$401$	−10.2337	−	17.7252i	−0.511044	−	0.885155i	−0.999918	−	0.0128001i	$-0.995925\pi$
$401$	−10.2337	−	17.7252i	−0.511044	−	0.885155i	0.488874	−	0.872355i	$-0.337408\pi$
$402$	7.29464	−	6.84146i	0.363824	−	0.341221i
$403$	−24.7120	+	6.62155i	−1.23099	+	0.329843i
$404$	−22.2987	−	25.3574i	−1.10940	−	1.26158i
$405$	1.78502	−	1.78502i	0.0886986	−	0.0886986i
$406$	−0.294901	−	1.97281i	−0.0146357	−	0.0979090i
$407$			1.01606i			0.0503640i
$408$	−5.76823	−	12.6622i	−0.285570	−	0.626873i
$409$	4.58389	+	2.64651i	0.226659	+	0.130862i	0.609030	−	0.793147i	$-0.291559\pi$
$409$	4.58389	+	2.64651i	0.226659	+	0.130862i	−0.382371	+	0.924009i	$0.624892\pi$
$410$	0.0421505	−	1.31481i	0.00208166	−	0.0649339i
$411$	−14.8445	−	3.97757i	−0.732226	−	0.196199i
$412$	−21.8686	+	32.8250i	−1.07739	+	1.61717i
$413$	−0.913664	+	1.32137i	−0.0449585	+	0.0650202i
$414$	1.05393	−	3.48283i	0.0517977	−	0.171172i
$415$	−5.11669	−	8.86238i	−0.251169	−	0.435037i
$416$	16.5315	−	6.28605i	0.810524	−	0.308199i
$417$	−9.65173	+	16.7173i	−0.472647	+	0.818649i
$418$	−0.565452	+	0.132249i	−0.0276571	+	0.00646851i
$419$	−0.198751	−	0.198751i	−0.00970961	−	0.00970961i	0.702235	−	0.711945i	$-0.252185\pi$
$419$	−0.198751	−	0.198751i	−0.00970961	−	0.00970961i	−0.711945	+	0.702235i	$0.752185\pi$
$420$	12.2653	+	5.29102i	0.598487	+	0.258176i
$421$	−17.2124	+	17.2124i	−0.838882	+	0.838882i	−0.988712	−	0.149830i	$-0.952128\pi$
$421$	−17.2124	+	17.2124i	−0.838882	+	0.838882i	0.149830	+	0.988712i	$0.452128\pi$
$422$	29.7908	+	18.4971i	1.45019	+	0.900426i
$423$	0.981599	+	0.566727i	0.0477270	+	0.0275552i
$424$	−28.0739	−	20.0312i	−1.36339	−	0.972802i
$425$	−5.84783	+	3.37625i	−0.283662	+	0.163772i
$426$	−4.92103	−	9.19161i	−0.238425	−	0.445335i
$427$	33.0211	−	15.6357i	1.59800	−	0.756666i
$428$	25.1735	−	5.04280i	1.21681	−	0.243753i
$429$	−0.0959667	+	0.358153i	−0.00463332	+	0.0172918i
$430$	−14.3842	+	13.4906i	−0.693669	+	0.650575i
$431$	15.6349	−	27.0805i	0.753108	−	1.30442i	−0.193202	−	0.981159i	$-0.561887\pi$
$431$	15.6349	−	27.0805i	0.753108	−	1.30442i	0.946309	−	0.323262i	$-0.104780\pi$
$432$	0.532853	+	3.96435i	0.0256369	+	0.190735i
$433$	6.68280			0.321155			0.160577	−	0.987023i	$-0.448664\pi$
$433$	6.68280			0.321155			0.160577	+	0.987023i	$0.448664\pi$
$434$	28.0774	−	12.2094i	1.34776	−	0.586072i
$435$	−0.951622	−	0.951622i	−0.0456268	−	0.0456268i
$436$	25.0997	−	22.0721i	1.20206	−	1.05706i
$437$	−2.30580	−	8.60537i	−0.110301	−	0.411651i
$438$	7.49555	+	0.240294i	0.358151	+	0.0114817i
$439$	20.2758	−	11.7062i	0.967712	−	0.558709i	0.0691737	−	0.997605i	$-0.477964\pi$
$439$	20.2758	−	11.7062i	0.967712	−	0.558709i	0.898538	+	0.438896i	$0.144630\pi$
$440$	−0.538516	−	0.653470i	−0.0256727	−	0.0311530i
$441$	2.47157	+	6.54915i	0.117694	+	0.311864i
$442$	−19.1762	+	10.2666i	−0.912117	+	0.488332i
$443$	2.26224	+	0.606165i	0.107482	+	0.0287998i	0.312159	−	0.950030i	$-0.398948\pi$
$443$	2.26224	+	0.606165i	0.107482	+	0.0287998i	−0.204677	+	0.978830i	$0.565614\pi$
$444$	15.3577	−	7.59946i	0.728843	−	0.360655i
$445$	10.0636	−	2.69654i	0.477062	−	0.127828i
$446$	−1.87825	+	0.439290i	−0.0889379	+	0.0208010i
$447$	−0.264012			−0.0124873
$448$	−18.4544	+	10.3650i	−0.871891	+	0.489701i
$449$	22.1783			1.04666			0.523329	−	0.852131i	$-0.324690\pi$
$449$	22.1783			1.04666			0.523329	+	0.852131i	$0.324690\pi$
$450$	1.89018	−	0.442078i	0.0891038	−	0.0208398i
$451$	−0.0422103	+	0.0113102i	−0.00198760	+	0.000532577i
$452$	19.7812	−	9.78836i	0.930429	−	0.460406i
$453$	16.7308	+	4.48301i	0.786082	+	0.210630i
$454$	6.82292	−	3.65288i	0.320216	−	0.171438i
$455$	7.02618	−	19.6644i	0.329392	−	0.921880i
$456$	6.22817	+	7.55766i	0.291661	+	0.353920i
$457$	−4.46406	+	2.57733i	−0.208820	+	0.120562i	−0.600763	−	0.799427i	$-0.705136\pi$
$457$	−4.46406	+	2.57733i	−0.208820	+	0.120562i	0.391943	+	0.919990i	$0.371803\pi$
$458$	20.1726	+	0.646697i	0.942603	+	0.0302182i
$459$	−1.27323	−	4.75178i	−0.0594295	−	0.221794i
$460$	9.75529	−	8.57858i	0.454843	−	0.399978i
$461$	4.31952	+	4.31952i	0.201180	+	0.201180i	0.800506	−	0.599325i	$-0.204564\pi$
$461$	4.31952	+	4.31952i	0.201180	+	0.201180i	−0.599325	+	0.800506i	$0.704564\pi$
$462$	0.0502189	−	0.440887i	0.00233640	−	0.0205119i
$463$	−21.0266			−0.977189			−0.488594	−	0.872511i	$-0.662490\pi$
$463$	−21.0266			−0.977189			−0.488594	+	0.872511i	$0.662490\pi$
$464$	2.11345	−	0.284072i	0.0981145	−	0.0131877i
$465$	10.3283	−	17.8892i	0.478965	−	0.829592i
$466$	−21.1750	+	19.8595i	−0.980914	+	0.919975i
$467$	4.03823	−	15.0709i	0.186867	−	0.697396i	−0.807356	−	0.590064i	$-0.799102\pi$
$467$	4.03823	−	15.0709i	0.186867	−	0.697396i	0.994223	−	0.107332i	$-0.0342309\pi$
$468$	6.13124	−	1.22822i	0.283417	−	0.0567746i
$469$	15.3893	+	10.6410i	0.710612	+	0.491355i
$470$	1.90992	+	3.56739i	0.0880979	+	0.164551i
$471$	3.10220	−	1.79105i	0.142942	−	0.0825274i
$472$	−1.39802	−	0.997510i	−0.0643490	−	0.0459141i
$473$	0.567334	+	0.327551i	0.0260861	+	0.0150608i
$474$	−6.60308	−	4.09986i	−0.303290	−	0.188313i
$475$	3.36063	−	3.36063i	0.154196	−	0.154196i
$476$	20.8804	−	15.5443i	0.957051	−	0.712470i
$477$	−8.62190	−	8.62190i	−0.394770	−	0.394770i
$478$	23.6817	−	5.53872i	1.08317	−	0.253335i
$479$	−4.52288	+	7.83385i	−0.206656	+	0.357938i	−0.950659	−	0.310238i	$-0.899591\pi$
$479$	−4.52288	+	7.83385i	−0.206656	+	0.357938i	0.744003	+	0.668176i	$0.232925\pi$
$480$	−5.84943	+	13.0272i	−0.266989	+	0.594608i
$481$	−13.3933	−	23.1979i	−0.610682	−	1.05773i
$482$	−1.78237	+	5.89004i	−0.0811845	+	0.268284i
$483$	6.78504	+	0.553309i	0.308730	+	0.0251764i
$484$	12.1821	−	18.2855i	0.553734	−	0.831158i
$485$	35.6174	+	9.54366i	1.61730	+	0.433355i
$486$	−0.0453139	+	1.41349i	−0.00205548	+	0.0641171i
$487$	13.4985	+	7.79333i	0.611673	+	0.353150i	0.773620	−	0.633650i	$-0.218444\pi$
$487$	13.4985	+	7.79333i	0.611673	+	0.353150i	−0.161947	+	0.986799i	$0.551777\pi$
$488$	16.1920	+	35.5441i	0.732977	+	1.60900i
$489$			5.91177i			0.267339i
$490$	−4.83700	+	24.5178i	−0.218513	+	1.10760i
$491$	21.9535	−	21.9535i	0.990749	−	0.990749i	−0.00920852	−	0.999958i	$-0.502931\pi$
$491$	21.9535	−	21.9535i	0.990749	−	0.990749i	0.999958	+	0.00920852i	$0.00293120\pi$
$492$	0.486660	+	0.553415i	0.0219403	+	0.0249499i
$493$	−2.53324	+	0.678780i	−0.114091	+	0.0305707i
$494$	11.1667	−	10.4730i	0.502415	−	0.471203i
$495$	−0.149689	−	0.259270i	−0.00672804	−	0.0116533i
$496$	12.6076	+	30.2056i	0.566098	+	1.35627i
$497$	14.8677	−	12.6257i	0.666910	−	0.566340i
$498$	5.48718	+	1.66046i	0.245886	+	0.0744069i
$499$	7.06950	−	26.3837i	0.316474	−	1.18110i	−0.606135	−	0.795362i	$-0.707281\pi$
$499$	7.06950	−	26.3837i	0.316474	−	1.18110i	0.922609	−	0.385736i	$-0.126053\pi$
$500$	−17.3500	−	5.86331i	−0.775915	−	0.262215i
$501$	−3.57389	−	13.3379i	−0.159670	−	0.595895i
$502$	−17.8078	+	28.6807i	−0.794803	+	1.28008i
$503$			20.0732i			0.895019i	0.894279	+	0.447509i	$0.147689\pi$
$503$			20.0732i			0.895019i	−0.894279	+	0.447509i	$0.852311\pi$
$504$	−7.03960	+	2.53850i	−0.313569	+	0.113074i
$505$		−	42.6212i		−	1.89662i
$506$	−0.366618	−	0.227633i	−0.0162982	−	0.0101195i
$507$	0.834647	+	3.11495i	0.0370680	+	0.138340i
$508$	−23.4303	+	11.5940i	−1.03955	+	0.514402i
$509$	1.35833	−	5.06936i	0.0602070	−	0.224695i	−0.929266	−	0.369410i	$-0.879560\pi$
$509$	1.35833	−	5.06936i	0.0602070	−	0.224695i	0.989473	+	0.144715i	$0.0462264\pi$
$510$	5.08673	−	16.8097i	0.225244	−	0.744347i
$511$	2.51775	+	13.8023i	0.111379	+	0.610579i
$512$	−10.7880	−	19.8902i	−0.476767	−	0.879030i
$513$	1.73122	+	2.99857i	0.0764354	+	0.132390i
$514$	−24.2078	−	25.8113i	−1.06776	−	1.13849i
$515$	−48.0882	+	12.8852i	−2.11902	+	0.567789i
$516$	0.707619	−	11.0251i	0.0311512	−	0.485354i
$517$	0.0950497	−	0.0950497i	0.00418028	−	0.00418028i
$518$	19.9566	+	25.0873i	0.876841	+	1.10227i
$519$			5.77335i			0.253422i
$520$	20.9088	+	7.82103i	0.916913	+	0.342975i
$521$	1.62833	+	0.940115i	0.0713383	+	0.0411872i	0.535245	−	0.844697i	$-0.320219\pi$
$521$	1.62833	+	0.940115i	0.0713383	+	0.0411872i	−0.463907	+	0.885884i	$0.653553\pi$
$522$	0.753550	+	0.0241575i	0.0329820	+	0.00105734i
$523$	−13.7576	−	3.68633i	−0.601577	−	0.161192i	−0.0548380	−	0.998495i	$-0.517464\pi$
$523$	−13.7576	−	3.68633i	−0.601577	−	0.161192i	−0.546739	+	0.837303i	$0.684131\pi$
$524$	−6.15464	−	30.7238i	−0.268867	−	1.34217i
$525$	1.55418	+	3.28226i	0.0678299	+	0.143250i
$526$	0.518793	+	0.156990i	0.0226204	+	0.00684510i
$527$	−20.1272	−	34.8613i	−0.876755	−	1.51858i
$528$	0.470483	+	0.0606433i	0.0204751	+	0.00263916i
$529$	−8.18979	+	14.1851i	−0.356078	+	0.616745i
$530$	−9.91344	−	42.3865i	−0.430612	−	1.84115i
$531$	−0.429351	−	0.429351i	−0.0186323	−	0.0186323i
$532$	−11.3639	+	14.3715i	−0.492689	+	0.623083i
$533$	0.814628	−	0.814628i	0.0352855	−	0.0352855i
$534$	−3.07881	+	4.95862i	−0.133233	+	0.214580i
$535$	28.0638	+	16.2027i	1.21331	+	0.700502i
$536$	−11.6175	+	16.2820i	−0.501799	+	0.703275i
$537$	−20.9100	+	12.0724i	−0.902333	+	0.520962i
$538$	−21.7407	+	11.6396i	−0.937309	+	0.501819i
$539$	0.826087	−	0.0821031i	0.0355821	−	0.00353643i
$540$	−2.79928	+	4.20173i	−0.120462	+	0.180814i
$541$	−1.40913	+	5.25895i	−0.0605833	+	0.226100i	−0.989579	−	0.143990i	$-0.954007\pi$
$541$	−1.40913	+	5.25895i	−0.0605833	+	0.226100i	0.928996	+	0.370090i	$0.120673\pi$
$542$	−20.1533	−	21.4882i	−0.865657	−	0.922999i
$543$	−1.18983	+	2.06085i	−0.0510605	+	0.0884394i
$544$	16.2859	+	22.5651i	0.698254	+	0.967471i
$545$	42.1880			1.80714
$546$	4.66505	+	10.7280i	0.199646	+	0.459115i
$547$	3.73692	+	3.73692i	0.159779	+	0.159779i	0.782469	−	0.622690i	$-0.213960\pi$
$547$	3.73692	+	3.73692i	0.159779	+	0.159779i	−0.622690	+	0.782469i	$0.713960\pi$
$548$	30.6732	+	1.96868i	1.31030	+	0.0840979i
$549$	3.57410	+	13.3387i	0.152539	+	0.569282i
$550$	0.00737642	−	0.230094i	0.000314531	−	0.00981126i
$551$	1.59858	−	0.922940i	0.0681017	−	0.0393186i
$552$	−0.698603	+	7.24398i	−0.0297345	+	0.308324i
$553$	4.89255	−	13.6929i	0.208053	−	0.582283i
$554$	0.127128	+	0.237452i	0.00540115	+	0.0100884i
$555$	20.8910	+	5.59772i	0.886772	+	0.237610i
$556$	12.3602	−	36.5748i	0.524190	−	1.55112i
$557$	11.8390	−	3.17225i	0.501635	−	0.134413i	0.000876416	−	1.00000i	$-0.499721\pi$
$557$	11.8390	−	3.17225i	0.501635	−	0.134413i	0.500759	+	0.865587i	$0.333054\pi$
$558$	2.63541	+	11.2681i	0.111566	+	0.477018i
$559$	−17.2706			−0.730470
$560$	−26.1313	−	5.55761i	−1.10425	−	0.234852i
$561$	−0.583411			−0.0246316
$562$	−3.25706	−	13.9261i	−0.137391	−	0.587436i
$563$	17.2348	−	4.61805i	0.726360	−	0.194628i	0.123352	−	0.992363i	$-0.460636\pi$
$563$	17.2348	−	4.61805i	0.726360	−	0.194628i	0.603008	+	0.797735i	$0.293969\pi$
$564$	−2.14759	−	0.725763i	−0.0904298	−	0.0305601i
$565$	26.9083	+	7.21005i	1.13204	+	0.303329i
$566$	−2.30570	−	4.30665i	−0.0969160	−	0.181022i
$567$	−2.60280	+	0.474790i	−0.109307	+	0.0199393i
$568$	13.2612	+	16.0919i	0.556426	+	0.675203i
$569$	−15.0833	+	8.70837i	−0.632327	+	0.365074i	−0.781653	−	0.623714i	$-0.785623\pi$
$569$	−15.0833	+	8.70837i	−0.632327	+	0.365074i	0.149326	+	0.988788i	$0.452290\pi$
$570$	−0.396071	+	12.3548i	−0.0165896	+	0.517484i
$571$	−3.94626	−	14.7277i	−0.165146	−	0.616333i	−0.998022	−	0.0628729i	$-0.979974\pi$
$571$	−3.94626	−	14.7277i	−0.165146	−	0.616333i	0.832876	−	0.553460i	$-0.186693\pi$
$572$	0.0474982	−	0.740051i	0.00198600	−	0.0309431i
$573$	−12.8373	−	12.8373i	−0.536286	−	0.536286i
$574$	−0.820060	+	1.10832i	−0.0342287	+	0.0462604i
$575$	3.53179			0.147286
$576$	−2.60230	−	7.56492i	−0.108429	−	0.315205i
$577$	8.25136	−	14.2918i	0.343509	−	0.594974i	−0.641573	−	0.767062i	$-0.721718\pi$
$577$	8.25136	−	14.2918i	0.343509	−	0.594974i	0.985082	+	0.172088i	$0.0550512\pi$
$578$	−6.96609	−	7.42752i	−0.289751	−	0.308944i
$579$	0.119602	−	0.446360i	0.00497048	−	0.0185501i
$580$	2.24000	+	1.49233i	0.0930111	+	0.0619658i
$581$	−0.871737	+	10.6898i	−0.0361658	+	0.443488i
$582$	−18.2115	+	9.75015i	−0.754893	+	0.404157i
$583$	−1.25231	+	0.723020i	−0.0518652	+	0.0299444i
$584$	−14.7935	+	2.47332i	−0.612158	+	0.102347i
$585$	6.83521	+	3.94631i	0.282601	+	0.163160i
$586$	24.3020	−	39.1399i	1.00391	−	1.61685i
$587$	−14.3768	+	14.3768i	−0.593393	+	0.593393i	−0.938546	−	0.345153i	$-0.887827\pi$
$587$	−14.3768	+	14.3768i	−0.593393	+	0.593393i	0.345153	+	0.938546i	$0.387827\pi$
$588$	−7.41960	−	11.8722i	−0.305979	−	0.489602i
$589$	20.0341	+	20.0341i	0.825490	+	0.825490i
$590$	−0.493667	−	2.11075i	−0.0203239	−	0.0868983i
$591$	9.35739	−	16.2075i	0.384912	−	0.666687i
$592$	−27.1317	+	20.9359i	−1.11510	+	0.860462i
$593$	−14.5944	−	25.2783i	−0.599321	−	1.03805i	−0.992922	−	0.118772i	$-0.962104\pi$
$593$	−14.5944	−	25.2783i	−0.599321	−	1.03805i	0.393601	−	0.919281i	$-0.371229\pi$
$594$	0.160528	+	0.0485769i	0.00658655	+	0.00199313i
$595$	32.7477	+	2.67053i	1.34253	+	0.109481i
$596$	0.517738	−	0.103714i	0.0212074	−	0.00424830i
$597$	−1.46638	−	0.392916i	−0.0600150	−	0.0160810i
$598$	11.3709	+	0.364532i	0.464993	+	0.0149068i
$599$	12.4175	+	7.16926i	0.507366	+	0.292928i	0.731750	−	0.681573i	$-0.238704\pi$
$599$	12.4175	+	7.16926i	0.507366	+	0.292928i	−0.224384	+	0.974501i	$0.572037\pi$
$600$	−3.53305	+	1.60947i	−0.144236	+	0.0657063i
$601$			7.82864i			0.319337i	0.987171	+	0.159668i	$0.0510425\pi$
$601$			7.82864i			0.319337i	−0.987171	+	0.159668i	$0.948957\pi$
$602$	20.4414	−	3.05564i	0.833131	−	0.124539i
$603$	−5.00044	+	5.00044i	−0.203633	+	0.203633i
$604$	−34.5709	−	2.21884i	−1.40667	−	0.0902834i
$605$	26.7880	−	7.17782i	1.08909	−	0.291820i
$606$	16.3340	+	17.4160i	0.663523	+	0.707475i
$607$	−16.4144	−	28.4305i	−0.666239	−	1.15396i	−0.978948	−	0.204111i	$-0.934570\pi$
$607$	−16.4144	−	28.4305i	−0.666239	−	1.15396i	0.312709	−	0.949849i	$-0.398764\pi$
$608$	−15.1826	−	12.3742i	−0.615737	−	0.501840i
$609$	0.253117	+	1.38759i	0.0102568	+	0.0562280i
$610$	−14.2790	+	47.1865i	−0.578139	+	1.91053i
$611$	−0.917196	+	3.42302i	−0.0371058	+	0.138481i
$612$	4.36355	+	8.81825i	0.176386	+	0.356456i
$613$	−6.57147	−	24.5251i	−0.265419	−	0.990558i	−0.961993	−	0.273073i	$-0.911960\pi$
$613$	−6.57147	−	24.5251i	−0.265419	−	0.990558i	0.696574	−	0.717485i	$-0.254707\pi$
$614$	−11.9902	−	7.44472i	−0.483885	−	0.300444i
$615$			0.930190i			0.0375089i
$616$	0.0747161	+	0.884324i	0.00301040	+	0.0356304i
$617$			44.9357i			1.80904i	0.426429	+	0.904521i	$0.359771\pi$
$617$			44.9357i			1.80904i	−0.426429	+	0.904521i	$0.640229\pi$
$618$	14.7118	−	23.6943i	0.591796	−	0.953125i
$619$	4.88269	+	18.2224i	0.196252	+	0.732422i	0.991939	+	0.126714i	$0.0404431\pi$
$619$	4.88269	+	18.2224i	0.196252	+	0.732422i	−0.795687	+	0.605707i	$0.792890\pi$
$620$	−13.2267	+	39.1388i	−0.531197	+	1.57185i
$621$	−0.665946	+	2.48534i	−0.0267235	+	0.0997334i
$622$	−13.2806	−	4.01881i	−0.532505	−	0.161139i
$623$	−10.2828	−	3.67409i	−0.411971	−	0.147199i
$624$	−11.5411	+	4.81718i	−0.462015	+	0.192842i
$625$	−14.9895	−	25.9626i	−0.599581	−	1.03850i
$626$	−22.6473	+	21.2403i	−0.905168	+	0.848935i
$627$	0.396633	−	0.106277i	0.0158400	−	0.00424431i
$628$	−5.37993	+	4.73099i	−0.214683	+	0.188787i
$629$	29.8025	−	29.8025i	1.18830	−	1.18830i
$630$	−8.78833	−	3.46150i	−0.350135	−	0.137910i
$631$		−	18.7641i		−	0.746988i	−0.927633	−	0.373494i	$-0.878160\pi$
$631$		−	18.7641i		−	0.746988i	0.927633	−	0.373494i	$-0.121840\pi$
$632$	14.5595	+	5.44604i	0.579146	+	0.216632i
$633$	−21.4736	−	12.3978i	−0.853497	−	0.492767i
$634$	0.101570	−	3.16830i	0.00403386	−	0.125829i
$635$	−31.8721	−	8.54009i	−1.26480	−	0.338903i
$636$	20.2949	+	13.5209i	0.804746	+	0.536138i
$637$	−17.7784	+	12.7637i	−0.704405	+	0.505717i
$638$	0.0258970	−	0.0855798i	0.00102527	−	0.00338814i
$639$	3.68616	+	6.38462i	0.145822	+	0.252572i
$640$	6.35337	−	27.8448i	0.251139	−	1.10066i
$641$	−20.7976	+	36.0224i	−0.821454	+	1.42280i	0.0831446	+	0.996537i	$0.473504\pi$
$641$	−20.7976	+	36.0224i	−0.821454	+	1.42280i	−0.904599	+	0.426263i	$0.859830\pi$
$642$	−17.6770	+	4.13432i	−0.697654	+	0.163169i
$643$	16.2384	+	16.2384i	0.640381	+	0.640381i	0.950649	−	0.310268i	$-0.100419\pi$
$643$	16.2384	+	16.2384i	0.640381	+	0.640381i	−0.310268	+	0.950649i	$0.600419\pi$
$644$	−13.5231	+	1.58037i	−0.532885	+	0.0622752i
$645$	9.86031	−	9.86031i	0.388249	−	0.388249i
$646$	20.4646	+	12.7065i	0.805171	+	0.499931i
$647$	−36.3089	−	20.9629i	−1.42745	−	0.824138i	−0.430530	−	0.902576i	$-0.641673\pi$
$647$	−36.3089	−	20.9629i	−1.42745	−	0.824138i	−0.996919	+	0.0784387i	$0.975006\pi$
$648$	−0.466411	−	2.78971i	−0.0183223	−	0.109590i
$649$	−0.0623620	+	0.0360047i	−0.00244792	+	0.00141331i
$650$	2.86461	+	5.35059i	0.112359	+	0.209867i
$651$	−19.5669	+	9.26509i	−0.766888	+	0.363128i
$652$	−2.32237	−	11.5932i	−0.0909511	−	0.454025i
$653$	−4.70500	+	17.5593i	−0.184121	+	0.687149i	0.810696	+	0.585467i	$0.199089\pi$
$653$	−4.70500	+	17.5593i	−0.184121	+	0.687149i	−0.994817	+	0.101681i	$0.967578\pi$
$654$	−17.2390	+	16.1680i	−0.674097	+	0.632219i
$655$	19.7750	−	34.2514i	0.772675	−	1.33831i
$656$	−1.17176	−	0.894089i	−0.0457497	−	0.0349083i
$657$	−5.30288			−0.206885
$658$	0.479964	−	4.21375i	0.0187110	−	0.164269i
$659$	−6.21601	−	6.21601i	−0.242141	−	0.242141i	0.575594	−	0.817735i	$-0.304771\pi$
$659$	−6.21601	−	6.21601i	−0.242141	−	0.242141i	−0.817735	+	0.575594i	$0.804771\pi$
$660$	0.395398	+	0.449635i	0.0153909	+	0.0175020i
$661$	11.6242	+	43.3821i	0.452129	+	1.68737i	0.696394	+	0.717660i	$0.254787\pi$
$661$	11.6242	+	43.3821i	0.452129	+	1.68737i	−0.244265	+	0.969709i	$0.578547\pi$
$662$	17.9062	+	0.574041i	0.695945	+	0.0223107i
$663$	13.3200	−	7.69032i	0.517307	−	0.298667i
$664$	−11.4129	−	1.10065i	−0.442905	−	0.0427134i
$665$	−22.7501	+	4.14996i	−0.882211	+	0.160928i
$666$	−10.6818	+	5.71883i	−0.413910	+	0.221600i
$667$	1.32497	+	0.355025i	0.0513031	+	0.0137466i
$668$	12.2482	+	24.7523i	0.473897	+	0.957694i
$669$	1.31749	−	0.353021i	0.0509371	−	0.0136486i
$670$	−24.5829	+	5.74949i	−0.949719	+	0.222122i
$671$	1.63769			0.0632224
$672$	12.8077	−	7.74353i	0.494069	−	0.298713i
$673$	32.1555			1.23950			0.619752	−	0.784798i	$-0.287233\pi$
$673$	32.1555			1.23950			0.619752	+	0.784798i	$0.287233\pi$
$674$	−27.7845	+	6.49830i	−1.07022	+	0.250305i
$675$	−1.32585	+	0.355262i	−0.0510322	+	0.0136740i
$676$	−2.86045	−	5.78065i	−0.110017	−	0.222333i
$677$	10.2500	+	2.74648i	0.393939	+	0.105556i	0.450350	−	0.892852i	$-0.351299\pi$
$677$	10.2500	+	2.74648i	0.393939	+	0.105556i	−0.0564110	+	0.998408i	$0.517966\pi$
$678$	−13.7585	+	7.36605i	−0.528391	+	0.282891i
$679$	−25.0156	−	29.4578i	−0.960010	−	1.13049i
$680$	−3.37178	+	34.9628i	−0.129302	+	1.34076i
$681$	−4.73930	+	2.73623i	−0.181610	+	0.104853i
$682$	1.37169	+	0.0439739i	0.0525246	+	0.00168385i
$683$	3.57905	+	13.3572i	0.136949	+	0.511100i	0.999982	+	0.00595301i	$0.00189491\pi$
$683$	3.57905	+	13.3572i	0.136949	+	0.511100i	−0.863034	+	0.505147i	$0.831438\pi$
$684$	−4.57295	−	5.20022i	−0.174851	−	0.198835i
$685$	27.4326	+	27.4326i	1.04814	+	1.04814i
$686$	18.7842	−	18.2525i	0.717183	−	0.696885i
$687$	−14.2715			−0.544492
$688$	2.94343	+	21.8987i	0.112217	+	0.834880i
$689$	19.0612	−	33.0150i	0.726174	−	1.25777i
$690$	−6.70013	+	6.28388i	−0.255069	+	0.239223i
$691$	4.45273	−	16.6178i	0.169390	−	0.632171i	−0.828050	−	0.560655i	$-0.810550\pi$
$691$	4.45273	−	16.6178i	0.169390	−	0.632171i	0.997439	−	0.0715162i	$-0.0227838\pi$
$692$	−2.26800	−	11.3218i	−0.0862163	−	0.430389i
$693$	−0.0255028	+	0.312732i	−0.000968770	+	0.0118797i
$694$	−16.9565	−	31.6717i	−0.643660	−	1.20224i
$695$	42.2012	−	24.3649i	1.60078	−	0.924213i
$696$	−1.48723	+	0.248650i	−0.0563734	+	0.00942506i
$697$	1.56984	+	0.906347i	0.0594619	+	0.0343303i
$698$	−15.6383	−	9.70984i	−0.591919	−	0.367523i
$699$	14.5154	−	14.5154i	0.549021	−	0.549021i
$700$	−4.33720	−	5.82610i	−0.163931	−	0.220206i
$701$	29.5927	+	29.5927i	1.11770	+	1.11770i	0.992078	+	0.125621i	$0.0400923\pi$
$701$	29.5927	+	29.5927i	1.11770	+	1.11770i	0.125621	+	0.992078i	$0.459908\pi$
$702$	−4.30539	+	1.00695i	−0.162496	+	0.0380050i
$703$	−14.8323	+	25.6903i	−0.559411	+	0.968928i
$704$	−0.946459	+	0.0659002i	−0.0356710	+	0.00248371i
$705$	−1.43065	−	2.47796i	−0.0538813	−	0.0933252i
$706$	−1.98056	+	6.54499i	−0.0745393	+	0.246324i
$707$	−25.4054	+	36.7419i	−0.955467	+	1.38182i
$708$	1.01064	+	0.673309i	0.0379822	+	0.0253045i
$709$	−19.6868	−	5.27506i	−0.739353	−	0.198109i	−0.130562	−	0.991440i	$-0.541678\pi$
$709$	−19.6868	−	5.27506i	−0.739353	−	0.198109i	−0.608790	+	0.793331i	$0.708345\pi$
$710$	−0.843325	+	26.3060i	−0.0316494	+	0.987248i
$711$	4.75958	+	2.74794i	0.178498	+	0.103056i
$712$	4.08973	−	10.9335i	0.153269	−	0.409751i
$713$			21.0544i			0.788495i
$714$	−14.4049	+	11.4589i	−0.539089	+	0.428838i
$715$	0.661864	−	0.661864i	0.0247523	−	0.0247523i
$716$	36.2628	−	31.8887i	1.35521	−	1.19174i
$717$	−16.6114	+	4.45101i	−0.620363	+	0.166226i
$718$	7.10637	−	6.66489i	0.265208	−	0.248732i
$719$	2.29650	+	3.97766i	0.0856451	+	0.148342i	0.905666	−	0.423992i	$-0.139372\pi$
$719$	2.29650	+	3.97766i	0.0856451	+	0.148342i	−0.820021	+	0.572334i	$0.806038\pi$
$720$	3.83889	−	9.33943i	0.143067	−	0.348060i
$721$	49.1353	+	17.5563i	1.82989	+	0.653831i
$722$	9.49069	+	2.87195i	0.353207	+	0.106883i
$723$	1.12623	−	4.20313i	0.0418848	−	0.156316i
$724$	1.52372	−	4.50881i	0.0566287	−	0.167569i
$725$	0.189395	+	0.706832i	0.00703396	+	0.0262511i
$726$	−8.19536	+	13.1992i	−0.304158	+	0.489866i
$727$			4.09205i			0.151766i	0.997117	+	0.0758830i	$0.0241775\pi$
$727$			4.09205i			0.151766i	−0.997117	+	0.0758830i	$0.975822\pi$
$728$	−13.3627	−	19.2054i	−0.495256	−	0.711799i
$729$		−	1.00000i		−	0.0370370i
$730$	−16.0835	−	9.98624i	−0.595276	−	0.369607i
$731$	−7.03323	−	26.2484i	−0.260133	−	0.970831i
$732$	−12.2489	−	24.7537i	−0.452733	−	0.914923i
$733$	1.11551	−	4.16314i	0.0412023	−	0.153769i	−0.942260	−	0.334882i	$-0.891303\pi$
$733$	1.11551	−	4.16314i	0.0412023	−	0.153769i	0.983462	+	0.181113i	$0.0579701\pi$
$734$	−3.90397	+	12.9011i	−0.144098	+	0.476189i
$735$	2.86302	−	17.4374i	0.105604	−	0.643187i
$736$	−1.47573	−	14.4802i	−0.0543962	−	0.533746i
$737$	0.419329	+	0.726299i	0.0154462	+	0.0267536i
$738$	−0.356483	−	0.380096i	−0.0131223	−	0.0139915i
$739$	−28.3131	+	7.58649i	−1.04152	+	0.279073i	−0.738742	−	0.673989i	$-0.764580\pi$
$739$	−28.3131	+	7.58649i	−1.04152	+	0.279073i	−0.302775	+	0.953062i	$0.597913\pi$
$740$	−43.1670	−	2.77056i	−1.58685	−	0.101848i
$741$	−7.65474	+	7.65474i	−0.281204	+	0.281204i
$742$	−16.7195	+	42.4488i	−0.613793	+	1.55834i
$743$		−	8.96540i		−	0.328909i	−0.986385	−	0.164454i	$-0.947414\pi$
$743$		−	8.96540i		−	0.328909i	0.986385	−	0.164454i	$-0.0525863\pi$
$744$	−9.59470	−	21.0619i	−0.351759	−	0.772168i
$745$	0.577183	+	0.333237i	0.0211463	+	0.0122088i
$746$	−43.8351	−	1.40527i	−1.60492	−	0.0514508i
$747$	−3.91565	−	1.04920i	−0.143266	−	0.0383881i
$748$	1.14409	−	0.229186i	0.0418321	−	0.00837988i
$749$	−14.5347	−	30.6958i	−0.531086	−	1.12160i
$750$	12.3948	+	3.75076i	0.452595	+	0.136958i
$751$	−4.73488	−	8.20105i	−0.172778	−	0.299260i	0.766612	−	0.642111i	$-0.221941\pi$
$751$	−4.73488	−	8.20105i	−0.172778	−	0.299260i	−0.939390	+	0.342850i	$0.888608\pi$
$752$	4.49661	+	0.579594i	0.163975	+	0.0211356i
$753$	11.9358	−	20.6734i	0.434964	−	0.753379i
$754$	0.536821	+	2.29527i	0.0195499	+	0.0835886i
$755$	−30.9184	−	30.9184i	−1.12524	−	1.12524i
$756$	4.91768	−	1.95356i	0.178854	−	0.0710504i
$757$	9.41101	−	9.41101i	0.342049	−	0.342049i	−0.515088	−	0.857137i	$-0.672241\pi$
$757$	9.41101	−	9.41101i	0.342049	−	0.342049i	0.857137	+	0.515088i	$0.172241\pi$
$758$	−7.18152	+	11.5663i	−0.260845	+	0.420107i
$759$	0.264262	+	0.152572i	0.00959212	+	0.00553801i
$760$	−4.07672	−	24.3838i	−0.147878	−	0.884492i
$761$	11.3344	−	6.54391i	0.410871	−	0.237217i	−0.280293	−	0.959915i	$-0.590432\pi$
$761$	11.3344	−	6.54391i	0.410871	−	0.237217i	0.691164	+	0.722698i	$0.257098\pi$
$762$	16.2965	−	8.72487i	0.590360	−	0.316069i
$763$	−36.3685	−	25.1472i	−1.31663	−	0.910388i
$764$	30.2175	+	20.1315i	1.09323	+	0.728331i
$765$	−3.21416	+	11.9954i	−0.116208	+	0.433695i
$766$	33.2566	+	35.4595i	1.20161	+	1.28120i
$767$	0.949204	−	1.64407i	0.0342738	−	0.0593639i
$768$	8.07500	+	13.8128i	0.291382	+	0.498428i
$769$	−37.7750			−1.36220			−0.681100	−	0.732190i	$-0.738498\pi$
$769$	−37.7750			−1.36220			−0.681100	+	0.732190i	$0.738498\pi$
$770$	−0.666277	+	0.900480i	−0.0240110	+	0.0324510i
$771$	17.6935	+	17.6935i	0.637217	+	0.637217i
$772$	−0.0591963	+	0.922315i	−0.00213052	+	0.0331948i
$773$	3.59696	+	13.4240i	0.129374	+	0.482829i	0.999958	−	0.00919065i	$-0.00292552\pi$
$773$	3.59696	+	13.4240i	0.129374	+	0.482829i	−0.870584	+	0.492020i	$0.836259\pi$
$774$	−0.250310	+	7.80797i	−0.00899719	+	0.280652i
$775$	−9.72711	+	5.61595i	−0.349408	+	0.201731i
$776$	31.8833	−	26.2746i	1.14455	−	0.943205i
$777$	−14.6726	−	17.2781i	−0.526376	−	0.619849i
$778$	10.7030	+	19.9912i	0.383720	+	0.716720i
$779$	−1.23236	−	0.330211i	−0.0441540	−	0.0118310i
$780$	−14.9544	−	5.05374i	−0.535453	−	0.180953i
$781$	0.844521	−	0.226289i	0.0302193	−	0.00809724i
$782$	4.07664	+	17.4303i	0.145780	+	0.623307i
$783$	−0.533114			−0.0190520
$784$	19.2140	+	20.3672i	0.686214	+	0.727399i
$785$	−9.04269			−0.322748
$786$	5.04586	+	21.5744i	0.179980	+	0.769533i
$787$	9.15431	−	2.45289i	0.326316	−	0.0874361i	−0.0919420	−	0.995764i	$-0.529307\pi$
$787$	9.15431	−	2.45289i	0.326316	−	0.0874361i	0.418258	+	0.908328i	$0.362641\pi$
$788$	−11.9833	+	35.4595i	−0.426887	+	1.26319i
$789$	−0.370210	−	0.0991976i	−0.0131798	−	0.00353153i
$790$	9.26081	+	17.2975i	0.329485	+	0.615419i
$791$	−18.8988	−	22.2548i	−0.671963	−	0.791289i
$792$	−0.333885	−	0.0321995i	−0.0118641	−	0.00114416i
$793$	−37.3906	+	21.5875i	−1.32778	+	0.766594i
$794$	0.277287	−	8.64948i	0.00984054	−	0.306958i
$795$	7.96661	+	29.7318i	0.282546	+	1.05448i
$796$	3.02998	+	0.194472i	0.107395	+	0.00689286i
$797$	17.3722	+	17.3722i	0.615353	+	0.615353i	0.944336	−	0.328983i	$-0.106706\pi$
$797$	17.3722	+	17.3722i	0.615353	+	0.615353i	−0.328983	+	0.944336i	$0.606706\pi$
$798$	7.70578	−	10.4144i	0.272782	−	0.368667i
$799$	−5.57591			−0.197262
$800$	6.29618	−	4.54415i	0.222604	−	0.160660i
$801$	2.06358	−	3.57423i	0.0729131	−	0.126289i
$802$	−19.8010	−	21.1126i	−0.699197	−	0.745512i
$803$	−0.162768	+	0.607460i	−0.00574397	+	0.0214368i
$804$	7.84169	−	11.7704i	0.276555	−	0.415111i
$805$	−14.1351	−	9.77374i	−0.498195	−	0.344479i
$806$	−31.8971	+	17.0771i	−1.12353	+	0.601517i
$807$	15.1014	−	8.71880i	0.531594	−	0.306916i
$808$	−38.8733	−	27.7368i	−1.36756	−	0.975776i
$809$	45.3999	+	26.2117i	1.59618	+	0.921553i	0.992215	+	0.124540i	$0.0397454\pi$
$809$	45.3999	+	26.2117i	1.59618	+	0.921553i	0.603962	+	0.797013i	$0.293588\pi$
$810$	1.88317	−	3.03297i	0.0661680	−	0.106568i
$811$	−30.8256	+	30.8256i	−1.08243	+	1.08243i	−0.0861525	+	0.996282i	$0.527457\pi$
$811$	−30.8256	+	30.8256i	−1.08243	+	1.08243i	−0.996282	+	0.0861525i	$0.972543\pi$
$812$	−1.04147	−	2.62169i	−0.0365485	−	0.0920032i
$813$	14.7301	+	14.7301i	0.516606	+	0.516606i
$814$	0.327239	+	1.39916i	0.0114697	+	0.0490406i
$815$	7.46185	−	12.9243i	0.261377	−	0.452719i
$816$	−12.0212	−	15.5788i	−0.420828	−	0.545366i
$817$	9.56311	+	16.5638i	0.334571	+	0.579494i
$818$	7.16462	+	2.16806i	0.250505	+	0.0758045i
$819$	−3.54006	−	7.47624i	−0.123700	−	0.261241i
$820$	−0.365415	−	1.82414i	−0.0127608	−	0.0637017i
$821$	−6.50371	−	1.74267i	−0.226981	−	0.0608194i	0.143536	−	0.989645i	$-0.454153\pi$
$821$	−6.50371	−	1.74267i	−0.226981	−	0.0608194i	−0.370517	+	0.928826i	$0.620819\pi$
$822$	−21.7227	−	0.696391i	−0.757667	−	0.0242894i
$823$	28.9754	+	16.7289i	1.01002	+	0.583134i	0.911197	−	0.411972i	$-0.135160\pi$
$823$	28.9754	+	16.7289i	1.01002	+	0.583134i	0.0988205	+	0.995105i	$0.468493\pi$
$824$	−19.5424	+	52.2449i	−0.680792	+	1.82004i
$825$			0.162785i			0.00566744i
$826$	−0.832594	+	2.11385i	−0.0289696	+	0.0735504i
$827$	27.3081	−	27.3081i	0.949596	−	0.949596i	−0.0491935	−	0.998789i	$-0.515665\pi$
$827$	27.3081	−	27.3081i	0.949596	−	0.949596i	0.998789	+	0.0491935i	$0.0156651\pi$
$828$	0.329606	−	5.13547i	0.0114546	−	0.178470i
$829$	−1.72085	+	0.461101i	−0.0597677	+	0.0160147i	−0.288579	−	0.957456i	$-0.593183\pi$
$829$	−1.72085	+	0.461101i	−0.0597677	+	0.0160147i	0.228811	+	0.973471i	$0.426516\pi$
$830$	−9.90024	−	10.5560i	−0.343642	−	0.366405i
$831$	−0.0952268	−	0.164938i	−0.00330338	−	0.00572162i
$832$	20.7402	−	13.9805i	0.719038	−	0.484686i
$833$	−26.6386	−	21.8222i	−0.922974	−	0.756094i
$834$	−7.90684	+	26.1291i	−0.273791	+	0.904776i
$835$	−9.02194	+	33.6704i	−0.312217	+	1.16521i
$836$	−0.736063	+	0.364227i	−0.0254573	+	0.0125971i
$837$	−2.11786	−	7.90397i	−0.0732040	−	0.273201i
$838$	−0.337701	−	0.209679i	−0.0116657	−	0.00724324i
$839$		−	2.31053i		−	0.0797685i	−0.999204	−	0.0398843i	$-0.987301\pi$
$839$		−	2.31053i		−	0.0797685i	0.999204	−	0.0398843i	$-0.0126989\pi$
$840$	18.5941	+	3.33575i	0.641557	+	0.115094i
$841$		−	28.7158i		−	0.990200i
$842$	−18.1588	+	29.2460i	−0.625795	+	1.00788i
$843$	2.61743	+	9.76837i	0.0901490	+	0.336441i
$844$	46.9808	+	15.8769i	1.61715	+	0.546504i
$845$	2.10699	−	7.86339i	0.0724826	−	0.270509i
$846$	1.53424	+	0.464271i	0.0527482	+	0.0159620i
$847$	−27.3713	−	9.77991i	−0.940489	−	0.336042i
$848$	−45.1107	−	18.5423i	−1.54911	−	0.636747i
$849$	1.72712	+	2.99145i	0.0592745	+	0.102666i
$850$	−6.96539	+	6.53267i	−0.238911	+	0.224069i
$851$	−21.2933	+	5.70551i	−0.729923	+	0.195582i
$852$	−9.73684	−	11.0724i	−0.333579	−	0.379335i
$853$	11.9779	−	11.9779i	0.410115	−	0.410115i	−0.471663	−	0.881779i	$-0.656346\pi$
$853$	11.9779	−	11.9779i	0.410115	−	0.410115i	0.881779	+	0.471663i	$0.156346\pi$
$854$	40.4360	−	32.1662i	1.38369	−	1.10071i
$855$		−	8.74062i		−	0.298923i
$856$	33.0411	−	15.0518i	1.12932	−	0.514459i
$857$	32.2595	+	18.6250i	1.10196	+	0.636219i	0.936736	−	0.350037i	$-0.113831\pi$
$857$	32.2595	+	18.6250i	1.10196	+	0.636219i	0.165227	+	0.986256i	$0.447164\pi$
$858$	−0.0168018	+	0.524102i	−0.000573603	+	0.0178926i
$859$	24.1496	+	6.47087i	0.823974	+	0.220783i	0.646083	−	0.763267i	$-0.276406\pi$
$859$	24.1496	+	6.47087i	0.823974	+	0.220783i	0.177891	+	0.984050i	$0.443073\pi$
$860$	−15.4629	+	23.2100i	−0.527282	+	0.791453i
$861$	0.554461	−	0.801878i	0.0188960	−	0.0273279i
$862$	12.8084	−	42.3267i	0.436254	−	1.44165i
$863$	12.5030	+	21.6558i	0.425606	+	0.737171i	0.996477	−	0.0838687i	$-0.0267276\pi$
$863$	12.5030	+	21.6558i	0.425606	+	0.737171i	−0.570871	+	0.821040i	$0.693394\pi$
$864$	2.01056	+	5.28750i	0.0684005	+	0.179884i
$865$	7.28714	−	12.6217i	0.247770	−	0.429151i
$866$	9.20256	−	2.15231i	0.312716	−	0.0731386i
$867$	5.09153	+	5.09153i	0.172917	+	0.172917i
$868$	34.7318	−	25.8559i	1.17887	−	0.877605i
$869$	0.460877	−	0.460877i	0.0156342	−	0.0156342i
$870$	−1.61692	−	1.00395i	−0.0548187	−	0.0340370i
$871$	−19.1477	−	11.0549i	−0.648794	−	0.374581i
$872$	27.4549	−	38.4782i	0.929739	−	1.30304i
$873$	12.6500	−	7.30347i	0.428137	−	0.247185i
$874$	−5.94672	−	11.1074i	−0.201151	−	0.375714i
$875$	−1.96914	+	24.1469i	−0.0665691	+	0.816314i
$876$	10.3992	−	2.08318i	0.351355	−	0.0703840i
$877$	−6.62611	+	24.7290i	−0.223748	+	0.835038i	0.759155	+	0.650910i	$0.225613\pi$
$877$	−6.62611	+	24.7290i	−0.223748	+	0.835038i	−0.982902	+	0.184128i	$0.941054\pi$
$878$	24.1506	−	22.6503i	0.815045	−	0.764410i
$879$	−16.2885	+	28.2125i	−0.549397	+	0.951583i
$880$	−0.952026	−	0.726423i	−0.0320928	−	0.0244877i
$881$	−46.0691			−1.55211			−0.776053	−	0.630667i	$-0.782781\pi$
$881$	−46.0691			−1.55211			−0.776053	+	0.630667i	$0.782781\pi$
$882$	5.51274	+	8.22251i	0.185624	+	0.276866i
$883$	−13.4822	−	13.4822i	−0.453711	−	0.453711i	0.442873	−	0.896584i	$-0.353959\pi$
$883$	−13.4822	−	13.4822i	−0.453711	−	0.453711i	−0.896584	+	0.442873i	$0.853959\pi$
$884$	−23.1000	+	20.3136i	−0.776938	+	0.683222i
$885$	0.396719	+	1.48058i	0.0133356	+	0.0497690i
$886$	3.31045	+	0.106127i	0.111217	+	0.00356541i
$887$	5.04511	−	2.91279i	0.169398	−	0.0978021i	−0.412904	−	0.910775i	$-0.635485\pi$
$887$	5.04511	−	2.91279i	0.169398	−	0.0978021i	0.582302	+	0.812973i	$0.302152\pi$
$888$	18.7008	−	15.4111i	0.627557	−	0.517162i
$889$	22.3851	+	26.3602i	0.750771	+	0.884091i
$890$	12.9897	−	6.95445i	0.435415	−	0.233114i
$891$	−0.114553	−	0.0306943i	−0.00383766	−	0.00102830i
$892$	−2.44497	+	1.20985i	−0.0818637	+	0.0405087i
$893$	3.79080	−	1.01574i	0.126854	−	0.0339905i
$894$	−0.363558	+	0.0850297i	−0.0121592	+	0.00284382i
$895$	60.9512			2.03738
$896$	−22.0745	+	20.2167i	−0.737457	+	0.675394i
$897$	−8.04461			−0.268602
$898$	30.5407	−	7.14291i	1.01916	−	0.238362i
$899$	−4.21372	+	1.12906i	−0.140535	+	0.0376563i
$900$	2.46049	−	1.21753i	0.0820164	−	0.0405843i
$901$	57.9394	+	15.5248i	1.93024	+	0.517207i
$902$	−0.0544831	+	0.0291693i	−0.00181409	+	0.000971232i
$903$	−14.3776	+	2.62269i	−0.478458	+	0.0872778i
$904$	24.0872	−	19.8500i	0.801129	−	0.660200i
$905$	5.20241	−	3.00361i	0.172934	−	0.0998435i
$906$	24.4830	+	0.784882i	0.813394	+	0.0260760i
$907$	−2.53767	−	9.47072i	−0.0842620	−	0.314470i	0.910911	−	0.412602i	$-0.135380\pi$
$907$	−2.53767	−	9.47072i	−0.0842620	−	0.314470i	−0.995173	+	0.0981320i	$0.968713\pi$
$908$	8.21905	−	7.22764i	0.272759	−	0.239858i
$909$	−11.9385	−	11.9385i	−0.395976	−	0.395976i
$910$	3.34216	−	29.3418i	0.110791	−	0.972670i
$911$	−24.6547			−0.816846			−0.408423	−	0.912793i	$-0.633921\pi$
$911$	−24.6547			−0.816846			−0.408423	+	0.912793i	$0.633921\pi$
$912$	11.0106	+	8.40140i	0.364597	+	0.278198i
$913$	−0.240377	+	0.416345i	−0.00795531	+	0.0137790i
$914$	−5.31717	+	4.98684i	−0.175876	+	0.164950i
$915$	9.02247	−	33.6723i	0.298274	−	1.11317i
$916$	27.9870	−	5.60640i	0.924716	−	0.185241i
$917$	−37.4636	+	17.7393i	−1.23716	+	0.585804i
$918$	−3.28370	−	6.13338i	−0.108378	−	0.202432i
$919$	−24.4083	+	14.0921i	−0.805155	+	0.464857i	−0.845271	−	0.534339i	$-0.820561\pi$
$919$	−24.4083	+	14.0921i	−0.805155	+	0.464857i	0.0401155	+	0.999195i	$0.487227\pi$
$920$	10.6707	−	14.9550i	0.351801	−	0.493052i
$921$	8.64267	+	4.98985i	0.284786	+	0.164421i
$922$	7.33938	+	4.55703i	0.241710	+	0.150078i
$923$	−16.2986	+	16.2986i	−0.536477	+	0.536477i
$924$	−0.0728412	−	0.623298i	−0.00239630	−	0.0205050i
$925$	−8.31558	−	8.31558i	−0.273415	−	0.273415i
$926$	−28.9547	+	6.77199i	−0.951511	+	0.222541i
$927$	−9.86064	+	17.0791i	−0.323866	+	0.560952i
$928$	2.81884	−	1.07186i	0.0925330	−	0.0351854i
$929$	26.8629	+	46.5280i	0.881344	+	1.52653i	0.849847	+	0.527029i	$0.176694\pi$
$929$	26.8629	+	46.5280i	0.881344	+	1.52653i	0.0314973	+	0.999504i	$0.489972\pi$
$930$	8.46113	−	27.9608i	0.277451	−	0.916870i
$931$	22.0856	+	9.98323i	0.723826	+	0.327187i
$932$	−22.7630	+	34.1674i	−0.745626	+	1.11919i
$933$	9.47705	+	2.53937i	0.310265	+	0.0831352i
$934$	0.707010	−	22.0539i	0.0231341	−	0.721627i
$935$	1.27545	+	0.736383i	0.0417117	+	0.0240823i
$936$	8.04747	−	3.66600i	0.263040	−	0.119827i
$937$		−	6.44549i		−	0.210565i	−0.994442	−	0.105282i	$-0.966425\pi$
$937$		−	6.44549i		−	0.210565i	0.994442	−	0.105282i	$-0.0335747\pi$
$938$	24.6190	+	9.69680i	0.803838	+	0.316612i
$939$	15.5246	−	15.5246i	0.506626	−	0.506626i
$940$	3.77900	+	4.29735i	0.123257	+	0.140164i
$941$	0.221064	−	0.0592338i	0.00720647	−	0.00193097i	−0.255214	−	0.966885i	$-0.582146\pi$
$941$	0.221064	−	0.0592338i	0.00720647	−	0.00193097i	0.262420	+	0.964954i	$0.415479\pi$
$942$	3.69504	−	3.46549i	0.120391	−	0.112912i
$943$	−0.474051	−	0.821080i	−0.0154372	−	0.0267380i
$944$	−2.24641	−	0.923367i	−0.0731144	−	0.0300530i
$945$	6.28952	+	2.24728i	0.204598	+	0.0731040i
$946$	0.886742	+	0.268334i	0.0288305	+	0.00872430i
$947$	−0.0815594	+	0.304384i	−0.00265032	+	0.00989114i	−0.967238	−	0.253870i	$-0.918296\pi$
$947$	−0.0815594	+	0.304384i	−0.00265032	+	0.00989114i	0.964588	+	0.263761i	$0.0849631\pi$
$948$	−10.4132	−	3.51908i	−0.338206	−	0.114294i
$949$	−4.29111	−	16.0147i	−0.139295	−	0.519858i
$950$	3.54541	−	5.71010i	0.115028	−	0.185260i
$951$			2.24148i			0.0726849i
$952$	23.7471	−	28.1301i	0.769647	−	0.911703i
$953$		−	50.0849i		−	1.62241i	−0.584763	−	0.811204i	$-0.698813\pi$
$953$		−	50.0849i		−	1.62241i	0.584763	−	0.811204i	$-0.301187\pi$
$954$	−14.6496	−	9.09597i	−0.474300	−	0.294493i
$955$	11.8616	+	44.2682i	0.383833	+	1.43249i
$956$	30.8271	−	15.2542i	0.997018	−	0.493356i
$957$	−0.0163636	+	0.0610698i	−0.000528960	+	0.00197411i
$958$	−3.70521	+	12.2443i	−0.119710	+	0.395595i
$959$	−7.29665	−	40.0003i	−0.235621	−	1.29168i
$960$	−3.85933	+	19.8231i	−0.124559	+	0.639786i
$961$	−17.9790	−	31.1405i	−0.579968	−	1.00453i
$962$	−25.9146	−	27.6311i	−0.835519	−	0.890864i
$963$	12.3994	−	3.32241i	0.399565	−	0.107063i
$964$	−0.557420	+	8.68493i	−0.0179533	+	0.279723i
$965$	−0.824871	+	0.824871i	−0.0265535	+	0.0265535i
$966$	9.52156	−	1.42331i	0.306351	−	0.0457941i
$967$		−	32.5149i		−	1.04561i	−0.852452	−	0.522805i	$-0.824886\pi$
$967$		−	32.5149i		−	1.04561i	0.852452	−	0.522805i	$-0.175114\pi$
$968$	10.8863	−	29.1035i	0.349899	−	0.935423i
$969$	−14.7511	−	8.51658i	−0.473875	−	0.273592i
$970$	52.1208	+	1.67090i	1.67350	+	0.0536493i
$971$	29.1114	+	7.80038i	0.934229	+	0.250326i	0.693657	−	0.720305i	$-0.255998\pi$
$971$	29.1114	+	7.80038i	0.934229	+	0.250326i	0.240572	+	0.970631i	$0.422665\pi$
$972$	0.392839	+	1.96104i	0.0126003	+	0.0629004i
$973$	−50.9032	−	4.15107i	−1.63188	−	0.133077i
$974$	21.0981	+	6.38441i	0.676025	+	0.204570i
$975$	−2.14578	−	3.71659i	−0.0687198	−	0.119026i
$976$	33.7448	+	43.7311i	1.08015	+	1.39980i
$977$	−11.4239	+	19.7869i	−0.365484	+	0.633037i	−0.988854	−	0.148890i	$-0.952430\pi$
$977$	−11.4239	+	19.7869i	−0.365484	+	0.633037i	0.623369	+	0.781927i	$0.285763\pi$
$978$	1.90399	+	8.14081i	0.0608829	+	0.260314i
$979$	−0.346098	−	0.346098i	−0.0110613	−	0.0110613i
$980$	1.23558	+	35.3201i	0.0394692	+	1.12826i
$981$	11.8172	−	11.8172i	0.377295	−	0.377295i
$982$	23.1606	−	37.3017i	0.739086	−	1.19034i
$983$	18.7339	+	10.8160i	0.597519	+	0.344978i	0.768065	−	0.640372i	$-0.221220\pi$
$983$	18.7339	+	10.8160i	0.597519	+	0.344978i	−0.170546	+	0.985350i	$0.554553\pi$
$984$	0.848393	+	0.605343i	0.0270458	+	0.0192976i
$985$	−40.9143	+	23.6219i	−1.30364	+	0.752655i
$986$	−3.26979	+	1.75059i	−0.104131	+	0.0557501i
$987$	−0.243741	+	2.98891i	−0.00775837	+	0.0951382i
$988$	12.0042	−	18.0183i	0.381903	−	0.573239i
$989$	−3.67862	+	13.7288i	−0.116973	+	0.436551i
$990$	−0.289633	−	0.308818i	−0.00920513	−	0.00981488i
$991$	−2.70518	+	4.68551i	−0.0859329	+	0.148840i	−0.905788	−	0.423730i	$-0.860720\pi$
$991$	−2.70518	+	4.68551i	−0.0859329	+	0.148840i	0.819855	+	0.572571i	$0.194054\pi$
$992$	27.0896	+	37.5341i	0.860094	+	1.19171i
$993$	−12.6681			−0.402010
$994$	16.4073	−	22.1747i	0.520409	−	0.703338i
$995$	2.70986	+	2.70986i	0.0859084	+	0.0859084i
$996$	8.09091	+	0.519294i	0.256370	+	0.0164545i
$997$	−1.59411	−	5.94931i	−0.0504860	−	0.188416i	0.936078	−	0.351793i	$-0.114428\pi$
$997$	−1.59411	−	5.94931i	−0.0504860	−	0.188416i	−0.986564	+	0.163377i	$0.947761\pi$
$998$	1.23772	−	38.6086i	0.0391795	−	1.22214i
$999$	7.41970	−	4.28376i	0.234749	−	0.135532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.29	yes	120
7.2	even	3	inner	336.2.bq.b.205.7	yes	120
16.5	even	4	inner	336.2.bq.b.277.7	yes	120
112.37	even	12	inner	336.2.bq.b.37.29	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.29	✓	120	112.37	even	12	inner
336.2.bq.b.109.29	yes	120	1.1	even	1	trivial
336.2.bq.b.205.7	yes	120	7.2	even	3	inner
336.2.bq.b.277.7	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)

\(f(q)\)	\(=\)	\(q+(1.37705 - 0.322068i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.79254 - 0.887008i) q^{4} +(2.43839 + 0.653364i) q^{5} +(-1.24677 + 0.667501i) q^{6} +(-1.71258 - 2.01670i) q^{7} +(2.18275 - 1.79878i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.37705 - 0.322068i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.79254 - 0.887008i) q^{4} +(2.43839 + 0.653364i) q^{5} +(-1.24677 + 0.667501i) q^{6} +(-1.71258 - 2.01670i) q^{7} +(2.18275 - 1.79878i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.56822 + 0.114391i) q^{10} +(-0.0306943 - 0.114553i) q^{11} +(-1.50189 + 1.32073i) q^{12} +(2.21079 + 2.21079i) q^{13} +(-3.00783 - 2.22553i) q^{14} -2.52441 q^{15} +(2.42643 - 3.18000i) q^{16} +(-2.45970 + 4.26033i) q^{17} +(1.03153 - 0.967445i) q^{18} +(0.896147 - 3.34447i) q^{19} +(4.95046 - 0.991685i) q^{20} +(2.17619 + 1.50473i) q^{21} +(-0.0791615 - 0.147860i) q^{22} +(2.22830 - 1.28651i) q^{23} +(-1.64282 + 2.30242i) q^{24} +(1.18873 + 0.686313i) q^{25} +(3.75639 + 2.33235i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.85870 - 2.09595i) q^{28} +(0.376969 + 0.376969i) q^{29} +(-3.47624 + 0.813029i) q^{30} +(-4.09139 + 7.08650i) q^{31} +(2.31715 - 5.16051i) q^{32} +(0.0592969 + 0.102705i) q^{33} +(-2.01502 + 6.65888i) q^{34} +(-2.85830 - 6.03643i) q^{35} +(1.10889 - 1.66444i) q^{36} +(-8.27560 - 2.21744i) q^{37} +(0.156897 - 4.89412i) q^{38} +(-2.70765 - 1.56326i) q^{39} +(6.49765 - 2.95999i) q^{40} -0.368479i q^{41} +(3.48135 + 1.37121i) q^{42} +(-3.90599 + 3.90599i) q^{43} +(-0.156630 - 0.178115i) q^{44} +(2.43839 - 0.653364i) q^{45} +(2.65414 - 2.48925i) q^{46} +(0.566727 + 0.981599i) q^{47} +(-1.52071 + 3.69965i) q^{48} +(-1.13414 + 6.90751i) q^{49} +(1.85798 + 0.562237i) q^{50} +(1.27323 - 4.75178i) q^{51} +(5.92392 + 2.00195i) q^{52} +(-3.15583 - 11.7777i) q^{53} +(-0.745987 + 1.20146i) q^{54} -0.299379i q^{55} +(-7.36573 - 1.32140i) q^{56} +3.46245i q^{57} +(0.640515 + 0.397696i) q^{58} +(-0.157153 - 0.586505i) q^{59} +(-4.52511 + 2.23917i) q^{60} +(-3.57410 + 13.3387i) q^{61} +(-3.35173 + 11.0762i) q^{62} +(-2.49149 - 0.890221i) q^{63} +(1.52881 - 7.85256i) q^{64} +(3.94631 + 6.83521i) q^{65} +(0.114733 + 0.122333i) q^{66} +(-6.83072 + 1.83029i) q^{67} +(-0.630181 + 9.81860i) q^{68} +(-1.81940 + 1.81940i) q^{69} +(-5.88017 - 7.39191i) q^{70} +7.37232i q^{71} +(0.990930 - 2.64916i) q^{72} +(-4.59243 - 2.65144i) q^{73} +(-12.1101 - 0.388228i) q^{74} +(-1.32585 - 0.355262i) q^{75} +(-1.36018 - 6.78999i) q^{76} +(-0.178452 + 0.258082i) q^{77} +(-4.23205 - 1.28065i) q^{78} +(2.74794 + 4.75958i) q^{79} +(7.99429 - 6.16874i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.118675 - 0.507414i) q^{82} +(-2.86646 - 2.86646i) q^{83} +(5.23562 + 0.767005i) q^{84} +(-8.78125 + 8.78125i) q^{85} +(-4.12076 + 6.63675i) q^{86} +(-0.461691 - 0.266557i) q^{87} +(-0.273053 - 0.194828i) q^{88} +(3.57423 - 2.06358i) q^{89} +(3.14736 - 1.68504i) q^{90} +(0.672338 - 8.24464i) q^{91} +(2.85318 - 4.28264i) q^{92} +(2.11786 - 7.90397i) q^{93} +(1.09655 + 1.16919i) q^{94} +(4.37031 - 7.56960i) q^{95} +(-0.902559 + 5.58439i) q^{96} +14.6069 q^{97} +(0.662922 + 9.87727i) q^{98} +(-0.0838585 - 0.0838585i) 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

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