LMFDB - Embedded newform 720.2.z.g.667.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			667.5
Root			$0.235136 + 1.39453i$ of defining polynomial
Character	$\chi$	$=$	720.667
Dual form			720.2.z.g.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.430311 + 1.34716i) q^{2} +(-1.62967 - 1.15939i) q^{4} +(0.177336 + 2.22902i) q^{5} +(-0.115101 - 0.115101i) q^{7} +(2.26315 - 1.69652i) q^{8} +O(q^{10})$	\(q+(-0.430311 + 1.34716i) q^{2} +(-1.62967 - 1.15939i) q^{4} +(0.177336 + 2.22902i) q^{5} +(-0.115101 - 0.115101i) q^{7} +(2.26315 - 1.69652i) q^{8} +(-3.07916 - 0.720273i) q^{10} +(-2.95966 + 2.95966i) q^{11} -1.55822i q^{13} +(0.204588 - 0.105530i) q^{14} +(1.31162 + 3.77884i) q^{16} +(-0.299668 - 0.299668i) q^{17} +(-2.26261 + 2.26261i) q^{19} +(2.29532 - 3.83817i) q^{20} +(-2.71356 - 5.26071i) q^{22} +(-4.14573 + 4.14573i) q^{23} +(-4.93710 + 0.790575i) q^{25} +(2.09917 + 0.670518i) q^{26} +(0.0541288 + 0.321023i) q^{28} +(-0.289656 - 0.289656i) q^{29} -4.18508i q^{31} +(-5.65510 + 0.140879i) q^{32} +(0.532650 - 0.274749i) q^{34} +(0.236151 - 0.276974i) q^{35} +1.63643i q^{37} +(-2.07447 - 4.02172i) q^{38} +(4.18292 + 4.74376i) q^{40} -7.61648i q^{41} +6.72651i q^{43} +(8.25467 - 1.39185i) q^{44} +(-3.80100 - 7.36890i) q^{46} +(-4.38366 + 4.38366i) q^{47} -6.97350i q^{49} +(1.05946 - 6.99125i) q^{50} +(-1.80659 + 2.53938i) q^{52} -11.4324 q^{53} +(-7.12202 - 6.07231i) q^{55} +(-0.455760 - 0.0652196i) q^{56} +(0.514854 - 0.265570i) q^{58} +(-1.63497 - 1.63497i) q^{59} +(-1.23034 + 1.23034i) q^{61} +(5.63796 + 1.80089i) q^{62} +(2.24366 - 7.67893i) q^{64} +(3.47331 - 0.276329i) q^{65} +2.49337i q^{67} +(0.140926 + 0.835791i) q^{68} +(0.271509 + 0.437317i) q^{70} -8.00096 q^{71} +(-1.12102 - 1.12102i) q^{73} +(-2.20453 - 0.704173i) q^{74} +(6.31056 - 1.06405i) q^{76} +0.681319 q^{77} +3.62218 q^{79} +(-8.19054 + 3.59376i) q^{80} +(10.2606 + 3.27745i) q^{82} -1.62629 q^{83} +(0.614825 - 0.721109i) q^{85} +(-9.06167 - 2.89449i) q^{86} +(-1.67703 + 11.7193i) q^{88} +15.7149 q^{89} +(-0.179352 + 0.179352i) q^{91} +(11.5627 - 1.94962i) q^{92} +(-4.01915 - 7.79182i) q^{94} +(-5.44467 - 4.64218i) q^{95} +(9.69217 + 9.69217i) q^{97} +(9.39441 + 3.00077i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.430311	+	1.34716i	−0.304276	+	0.952584i
$2$	−0.430311	+	1.34716i	−0.304276	+	0.952584i
$3$		0			0
$3$		0			0
$4$	−1.62967	−	1.15939i	−0.814833	−	0.579696i
$5$	0.177336	+	2.22902i	0.0793073	+	0.996850i
$5$	0.177336	+	2.22902i	0.0793073	+	0.996850i
$6$		0			0
$7$	−0.115101	−	0.115101i	−0.0435040	−	0.0435040i	0.685020	−	0.728524i	$-0.259793\pi$
$7$	−0.115101	−	0.115101i	−0.0435040	−	0.0435040i	−0.728524	+	0.685020i	$0.759793\pi$
$8$	2.26315	−	1.69652i	0.800143	−	0.599809i
$9$		0			0
$10$	−3.07916	−	0.720273i	−0.973715	−	0.227770i
$11$	−2.95966	+	2.95966i	−0.892372	+	0.892372i	−0.994746	−	0.102374i	$-0.967356\pi$
$11$	−2.95966	+	2.95966i	−0.892372	+	0.892372i	0.102374	+	0.994746i	$0.467356\pi$
$12$		0			0
$13$		−	1.55822i		−	0.432172i	−0.976374	−	0.216086i	$-0.930671\pi$
$13$		−	1.55822i		−	0.432172i	0.976374	−	0.216086i	$-0.0693292\pi$
$14$	0.204588	−	0.105530i	0.0546784	−	0.0282040i
$15$		0			0
$16$	1.31162	+	3.77884i	0.327905	+	0.944711i
$17$	−0.299668	−	0.299668i	−0.0726801	−	0.0726801i	0.669832	−	0.742512i	$-0.266366\pi$
$17$	−0.299668	−	0.299668i	−0.0726801	−	0.0726801i	−0.742512	+	0.669832i	$0.766366\pi$
$18$		0			0
$19$	−2.26261	+	2.26261i	−0.519079	+	0.519079i	−0.917293	−	0.398214i	$-0.869630\pi$
$19$	−2.26261	+	2.26261i	−0.519079	+	0.519079i	0.398214	+	0.917293i	$0.369630\pi$
$20$	2.29532	−	3.83817i	0.513248	−	0.858240i
$21$		0			0
$22$	−2.71356	−	5.26071i	−0.578532	−	1.12159i
$23$	−4.14573	+	4.14573i	−0.864444	+	0.864444i	−0.991851	−	0.127406i	$-0.959335\pi$
$23$	−4.14573	+	4.14573i	−0.864444	+	0.864444i	0.127406	+	0.991851i	$0.459335\pi$
$24$		0			0
$25$	−4.93710	+	0.790575i	−0.987421	+	0.158115i
$26$	2.09917	+	0.670518i	0.411680	+	0.131499i
$27$		0			0
$28$	0.0541288	+	0.321023i	0.0102294	+	0.0606676i
$29$	−0.289656	−	0.289656i	−0.0537878	−	0.0537878i	0.679701	−	0.733489i	$-0.262109\pi$
$29$	−0.289656	−	0.289656i	−0.0537878	−	0.0537878i	−0.733489	+	0.679701i	$0.762109\pi$
$30$		0			0
$31$		−	4.18508i		−	0.751663i	−0.926688	−	0.375832i	$-0.877357\pi$
$31$		−	4.18508i		−	0.751663i	0.926688	−	0.375832i	$-0.122643\pi$
$32$	−5.65510	+	0.140879i	−0.999690	+	0.0249041i
$33$		0			0
$34$	0.532650	−	0.274749i	0.0913487	−	0.0471191i
$35$	0.236151	−	0.276974i	0.0399168	−	0.0468172i
$36$		0			0
$37$			1.63643i			0.269027i	0.990912	+	0.134514i	$0.0429472\pi$
$37$			1.63643i			0.269027i	−0.990912	+	0.134514i	$0.957053\pi$
$38$	−2.07447	−	4.02172i	−0.336523	−	0.652410i
$39$		0			0
$40$	4.18292	+	4.74376i	0.661377	+	0.750054i
$41$		−	7.61648i		−	1.18949i	−0.803913	−	0.594747i	$-0.797252\pi$
$41$		−	7.61648i		−	1.18949i	0.803913	−	0.594747i	$-0.202748\pi$
$42$		0			0
$43$			6.72651i			1.02578i	0.858453	+	0.512892i	$0.171426\pi$
$43$			6.72651i			1.02578i	−0.858453	+	0.512892i	$0.828574\pi$
$44$	8.25467	−	1.39185i	1.24444	−	0.209829i
$45$		0			0
$46$	−3.80100	−	7.36890i	−0.560427	−	1.08649i
$47$	−4.38366	+	4.38366i	−0.639423	+	0.639423i	−0.950413	−	0.310990i	$-0.899339\pi$
$47$	−4.38366	+	4.38366i	−0.639423	+	0.639423i	0.310990	+	0.950413i	$0.399339\pi$
$48$		0			0
$49$		−	6.97350i		−	0.996215i
$50$	1.05946	−	6.99125i	0.149830	−	0.988712i
$51$		0			0
$52$	−1.80659	+	2.53938i	−0.250529	+	0.352148i
$53$	−11.4324			−1.57036			−0.785182	−	0.619265i	$-0.787431\pi$
$53$	−11.4324			−1.57036			−0.785182	+	0.619265i	$0.787431\pi$
$54$		0			0
$55$	−7.12202	−	6.07231i	−0.960333	−	0.818790i
$56$	−0.455760	−	0.0652196i	−0.0609035	−	0.00871533i
$57$		0			0
$58$	0.514854	−	0.265570i	0.0676037	−	0.0348711i
$59$	−1.63497	−	1.63497i	−0.212855	−	0.212855i	0.592624	−	0.805479i	$-0.298092\pi$
$59$	−1.63497	−	1.63497i	−0.212855	−	0.212855i	−0.805479	+	0.592624i	$0.798092\pi$
$60$		0			0
$61$	−1.23034	+	1.23034i	−0.157528	+	0.157528i	−0.781471	−	0.623942i	$-0.785530\pi$
$61$	−1.23034	+	1.23034i	−0.157528	+	0.157528i	0.623942	+	0.781471i	$0.285530\pi$
$62$	5.63796	+	1.80089i	0.716022	+	0.228713i
$63$		0			0
$64$	2.24366	−	7.67893i	0.280458	−	0.959866i
$65$	3.47331	−	0.276329i	0.430811	−	0.0342744i
$66$		0			0
$67$			2.49337i			0.304614i	0.988333	+	0.152307i	$0.0486702\pi$
$67$			2.49337i			0.304614i	−0.988333	+	0.152307i	$0.951330\pi$
$68$	0.140926	+	0.835791i	0.0170897	+	0.101354i
$69$		0			0
$70$	0.271509	+	0.437317i	0.0324516	+	0.0522694i
$71$	−8.00096			−0.949540			−0.474770	−	0.880110i	$-0.657469\pi$
$71$	−8.00096			−0.949540			−0.474770	+	0.880110i	$0.657469\pi$
$72$		0			0
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	0.638454	−	0.769660i	$-0.279574\pi$
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	−0.769660	+	0.638454i	$0.779574\pi$
$74$	−2.20453	−	0.704173i	−0.256271	−	0.0818584i
$75$		0			0
$76$	6.31056	−	1.06405i	0.723871	−	0.122054i
$77$	0.681319			0.0776435
$78$		0			0
$79$	3.62218			0.407527			0.203763	−	0.979020i	$-0.434683\pi$
$79$	3.62218			0.407527			0.203763	+	0.979020i	$0.434683\pi$
$80$	−8.19054	+	3.59376i	−0.915730	+	0.401794i
$81$		0			0
$82$	10.2606	+	3.27745i	1.13309	+	0.361934i
$83$	−1.62629			−0.178509			−0.0892545	−	0.996009i	$-0.528448\pi$
$83$	−1.62629			−0.178509			−0.0892545	+	0.996009i	$0.528448\pi$
$84$		0			0
$85$	0.614825	−	0.721109i	0.0666871	−	0.0782152i
$86$	−9.06167	−	2.89449i	−0.977145	−	0.312121i
$87$		0			0
$88$	−1.67703	+	11.7193i	−0.178772	+	1.24928i
$89$	15.7149			1.66577			0.832887	−	0.553443i	$-0.186686\pi$
$89$	15.7149			1.66577			0.832887	+	0.553443i	$0.186686\pi$
$90$		0			0
$91$	−0.179352	+	0.179352i	−0.0188012	+	0.0188012i
$92$	11.5627	−	1.94962i	1.20549	−	0.203262i
$93$		0			0
$94$	−4.01915	−	7.79182i	−0.414543	−	0.803665i
$95$	−5.44467	−	4.64218i	−0.558611	−	0.476277i
$96$		0			0
$97$	9.69217	+	9.69217i	0.984091	+	0.984091i	0.999875	−	0.0157848i	$-0.00502467\pi$
$97$	9.69217	+	9.69217i	0.984091	+	0.984091i	−0.0157848	+	0.999875i	$0.505025\pi$
$98$	9.39441	+	3.00077i	0.948978	+	0.303124i
$99$		0			0
$100$	8.96241	+	4.43567i	0.896241	+	0.443567i
$101$	12.8067	+	12.8067i	1.27432	+	1.27432i	0.943800	+	0.330516i	$0.107223\pi$
$101$	12.8067	+	12.8067i	1.27432	+	1.27432i	0.330516	+	0.943800i	$0.392777\pi$
$102$		0			0
$103$	−4.33738	+	4.33738i	−0.427375	+	0.427375i	−0.887733	−	0.460358i	$-0.847721\pi$
$103$	−4.33738	+	4.33738i	−0.427375	+	0.427375i	0.460358	+	0.887733i	$0.347721\pi$
$104$	−2.64354	−	3.52648i	−0.259221	−	0.345800i
$105$		0			0
$106$	4.91950	−	15.4013i	0.477824	−	1.49590i
$107$	11.9807			1.15822			0.579108	−	0.815251i	$-0.303401\pi$
$107$	11.9807			1.15822			0.579108	+	0.815251i	$0.303401\pi$
$108$		0			0
$109$	4.01503	+	4.01503i	0.384570	+	0.384570i	0.872746	−	0.488175i	$-0.162337\pi$
$109$	4.01503	+	4.01503i	0.384570	+	0.384570i	−0.488175	+	0.872746i	$0.662337\pi$
$110$	11.2450	−	6.98150i	1.07217	−	0.665660i
$111$		0			0
$112$	0.283980	−	0.585916i	0.0268336	−	0.0553639i
$113$	−6.47754	+	6.47754i	−0.609356	+	0.609356i	−0.942778	−	0.333422i	$-0.891797\pi$
$113$	−6.47754	+	6.47754i	−0.609356	+	0.609356i	0.333422	+	0.942778i	$0.391797\pi$
$114$		0			0
$115$	−9.97612	−	8.50575i	−0.930278	−	0.793165i
$116$	0.136217	+	0.807867i	0.0126475	+	0.0750086i
$117$		0			0
$118$	2.90611	−	1.49902i	0.267529	−	0.137996i
$119$			0.0689840i			0.00632375i
$120$		0			0
$121$		−	6.51921i		−	0.592655i
$122$	−1.12803	−	2.18688i	−0.102127	−	0.197991i
$123$		0			0
$124$	−4.85215	+	6.82028i	−0.435736	+	0.612480i
$125$	−2.63774	−	10.8647i	−0.235927	−	0.971771i
$126$		0			0
$127$	−12.2756	+	12.2756i	−1.08928	+	1.08928i	−0.0936781	+	0.995603i	$0.529862\pi$
$127$	−12.2756	+	12.2756i	−1.08928	+	1.08928i	−0.995603	+	0.0936781i	$0.970138\pi$
$128$	9.37925	+	6.32690i	0.829017	+	0.559224i
$129$		0			0
$130$	−1.12234	+	4.79800i	−0.0984360	+	0.420813i
$131$	−7.99562	−	7.99562i	−0.698581	−	0.698581i	0.265524	−	0.964104i	$-0.414455\pi$
$131$	−7.99562	−	7.99562i	−0.698581	−	0.698581i	−0.964104	+	0.265524i	$0.914455\pi$
$132$		0			0
$133$	0.520857			0.0451641
$134$	−3.35896	−	1.07292i	−0.290170	−	0.0926865i
$135$		0			0
$136$	−1.18658	−	0.169801i	−0.101749	−	0.0145603i
$137$	3.08551	−	3.08551i	0.263613	−	0.263613i	−0.562907	−	0.826520i	$-0.690317\pi$
$137$	3.08551	−	3.08551i	0.263613	−	0.263613i	0.826520	+	0.562907i	$0.190317\pi$
$138$		0			0
$139$	12.2206	+	12.2206i	1.03654	+	1.03654i	0.999307	+	0.0372284i	$0.0118529\pi$
$139$	12.2206	+	12.2206i	1.03654	+	1.03654i	0.0372284	+	0.999307i	$0.488147\pi$
$140$	−0.705969	+	0.177583i	−0.0596653	+	0.0150085i
$141$		0			0
$142$	3.44290	−	10.7786i	0.288922	−	0.904516i
$143$	4.61180	+	4.61180i	0.385658	+	0.385658i
$144$		0			0
$145$	0.594284	−	0.697017i	0.0493526	−	0.0578841i
$146$	1.99258	−	1.02780i	0.164907	−	0.0850616i
$147$		0			0
$148$	1.89726	−	2.66683i	0.155954	−	0.219212i
$149$	−2.59172	+	2.59172i	−0.212322	+	0.212322i	−0.805253	−	0.592931i	$-0.797971\pi$
$149$	−2.59172	+	2.59172i	−0.212322	+	0.212322i	0.592931	+	0.805253i	$0.297971\pi$
$150$		0			0
$151$	−16.9594			−1.38014			−0.690068	−	0.723745i	$-0.742419\pi$
$151$	−16.9594			−1.38014			−0.690068	+	0.723745i	$0.742419\pi$
$152$	−1.28207	+	8.95919i	−0.103989	+	0.726686i
$153$		0			0
$154$	−0.293179	+	0.917844i	−0.0236250	+	0.0739620i
$155$	9.32865	−	0.742168i	0.749296	−	0.0596124i
$156$		0			0
$157$	8.55235			0.682552			0.341276	−	0.939963i	$-0.389141\pi$
$157$	8.55235			0.682552			0.341276	+	0.939963i	$0.389141\pi$
$158$	−1.55866	+	4.87964i	−0.124000	+	0.388203i
$159$		0			0
$160$	−1.31688	−	12.5804i	−0.104108	−	0.994566i
$161$	0.954354			0.0752136
$162$		0			0
$163$	−3.57797			−0.280248			−0.140124	−	0.990134i	$-0.544750\pi$
$163$	−3.57797			−0.280248			−0.140124	+	0.990134i	$0.544750\pi$
$164$	−8.83049	+	12.4123i	−0.689545	+	0.969238i
$165$		0			0
$166$	0.699812	−	2.19087i	0.0543159	−	0.170045i
$167$	−0.482874	−	0.482874i	−0.0373659	−	0.0373659i	0.688177	−	0.725543i	$-0.258411\pi$
$167$	−0.482874	−	0.482874i	−0.0373659	−	0.0373659i	−0.725543	+	0.688177i	$0.758411\pi$
$168$		0			0
$169$	10.5720			0.813227
$170$	0.706881	+	1.13857i	0.0542153	+	0.0873241i
$171$		0			0
$172$	7.79867	−	10.9620i	0.594643	−	0.835842i
$173$			11.8189i			0.898576i	0.893387	+	0.449288i	$0.148322\pi$
$173$			11.8189i			0.898576i	−0.893387	+	0.449288i	$0.851678\pi$
$174$		0			0
$175$	0.659260	+	0.477269i	0.0498354	+	0.0360781i
$176$	−15.0661	−	7.30216i	−1.13565	−	0.550421i
$177$		0			0
$178$	−6.76228	+	21.1704i	−0.506855	+	1.58679i
$179$	4.71524	−	4.71524i	0.352433	−	0.352433i	−0.508581	−	0.861014i	$-0.669830\pi$
$179$	4.71524	−	4.71524i	0.352433	−	0.352433i	0.861014	+	0.508581i	$0.169830\pi$
$180$		0			0
$181$	13.1843	+	13.1843i	0.979983	+	0.979983i	0.999804	−	0.0198205i	$-0.00630948\pi$
$181$	13.1843	+	13.1843i	0.979983	+	0.979983i	−0.0198205	+	0.999804i	$0.506309\pi$
$182$	−0.164439	−	0.318793i	−0.0121890	−	0.0236305i
$183$		0			0
$184$	−2.34910	+	16.4157i	−0.173178	+	1.21018i
$185$	−3.64764	+	0.290199i	−0.268180	+	0.0213358i
$186$		0			0
$187$	1.77383			0.129715
$188$	12.2263	−	2.06152i	0.891694	−	0.150352i
$189$		0			0
$190$	8.59664	−	5.33724i	0.623666	−	0.387204i
$191$			13.9872i			1.01208i	0.862510	+	0.506040i	$0.168891\pi$
$191$			13.9872i			1.01208i	−0.862510	+	0.506040i	$0.831109\pi$
$192$		0			0
$193$	3.88875	−	3.88875i	0.279919	−	0.279919i	−0.553158	−	0.833076i	$-0.686577\pi$
$193$	3.88875	−	3.88875i	0.279919	−	0.279919i	0.833076	+	0.553158i	$0.186577\pi$
$194$	−17.2275	+	8.88623i	−1.23686	+	0.637994i
$195$		0			0
$196$	−8.08503	+	11.3645i	−0.577502	+	0.811748i
$197$			22.3277i			1.59078i	0.606097	+	0.795391i	$0.292734\pi$
$197$			22.3277i			1.59078i	−0.606097	+	0.795391i	$0.707266\pi$
$198$		0			0
$199$		−	9.83847i		−	0.697431i	−0.937229	−	0.348715i	$-0.886618\pi$
$199$		−	9.83847i		−	0.697431i	0.937229	−	0.348715i	$-0.113382\pi$
$200$	−9.83217	+	10.1651i	−0.695239	+	0.718779i
$201$		0			0
$202$	−22.7635	+	11.7418i	−1.60164	+	0.826150i
$203$			0.0666793i			0.00467997i
$204$		0			0
$205$	16.9773	−	1.35068i	1.18575	−	0.0943355i
$206$	−3.97671	−	7.70955i	−0.277071	−	0.537150i
$207$		0			0
$208$	5.88827	−	2.04379i	0.408278	−	0.141711i
$209$		−	13.3931i		−	0.926423i
$210$		0			0
$211$	11.0531	+	11.0531i	0.760925	+	0.760925i	0.976490	−	0.215565i	$-0.0691592\pi$
$211$	11.0531	+	11.0531i	0.760925	+	0.760925i	−0.215565	+	0.976490i	$0.569159\pi$
$212$	18.6310	+	13.2547i	1.27958	+	0.910334i
$213$		0			0
$214$	−5.15541	+	16.1398i	−0.352417	+	1.10330i
$215$	−14.9936	+	1.19286i	−1.02255	+	0.0813521i
$216$		0			0
$217$	−0.481706	+	0.481706i	−0.0327004	+	0.0327004i
$218$	−7.13659	+	3.68117i	−0.483351	+	0.249320i
$219$		0			0
$220$	4.56632	+	18.1530i	0.307861	+	1.22388i
$221$	−0.466948	+	0.466948i	−0.0314103	+	0.0314103i
$222$		0			0
$223$	5.93975	+	5.93975i	0.397755	+	0.397755i	0.877440	−	0.479686i	$-0.159249\pi$
$223$	5.93975	+	5.93975i	0.397755	+	0.397755i	−0.479686	+	0.877440i	$0.659249\pi$
$224$	0.667122	+	0.634691i	0.0445740	+	0.0424071i
$225$		0			0
$226$	−5.93891	−	11.5136i	−0.395051	−	0.765875i
$227$			23.2105i			1.54054i	0.637720	+	0.770269i	$0.279878\pi$
$227$			23.2105i			1.54054i	−0.637720	+	0.770269i	$0.720122\pi$
$228$		0			0
$229$	5.59944	−	5.59944i	0.370021	−	0.370021i	−0.497464	−	0.867485i	$-0.665735\pi$
$229$	5.59944	−	5.59944i	0.370021	−	0.370021i	0.867485	+	0.497464i	$0.165735\pi$
$230$	15.7514	−	9.77929i	1.03862	−	0.644828i
$231$		0			0
$232$	−1.14694	−	0.164128i	−0.0753003	−	0.0107755i
$233$	−3.01998	−	3.01998i	−0.197845	−	0.197845i	0.601230	−	0.799076i	$-0.294677\pi$
$233$	−3.01998	−	3.01998i	−0.197845	−	0.197845i	−0.799076	+	0.601230i	$0.794677\pi$
$234$		0			0
$235$	−10.5487	−	8.99391i	−0.688120	−	0.586698i
$236$	0.768884	+	4.56004i	0.0500501	+	0.296833i
$237$		0			0
$238$	−0.0929323	−	0.0296846i	−0.00602391	−	0.00192416i
$239$	0.00138865			8.98241e−5			4.49120e−5	−	1.00000i	$-0.499986\pi$
$239$	0.00138865			8.98241e−5			4.49120e−5		1.00000i	$0.499986\pi$
$240$		0			0
$241$	−12.8578			−0.828245			−0.414123	−	0.910221i	$-0.635912\pi$
$241$	−12.8578			−0.828245			−0.414123	+	0.910221i	$0.635912\pi$
$242$	8.78240	+	2.80529i	0.564554	+	0.180331i
$243$		0			0
$244$	3.43148	−	0.578593i	0.219678	−	0.0370407i
$245$	15.5441	−	1.23666i	0.993077	−	0.0790071i
$246$		0			0
$247$	3.52565	+	3.52565i	0.224332	+	0.224332i
$248$	−7.10006	−	9.47146i	−0.450854	−	0.601438i
$249$		0			0
$250$	15.7715	+	1.12176i	0.997480	+	0.0709463i
$251$	9.14111	−	9.14111i	0.576982	−	0.576982i	−0.357089	−	0.934071i	$-0.616231\pi$
$251$	9.14111	−	9.14111i	0.576982	−	0.576982i	0.934071	+	0.357089i	$0.116231\pi$
$252$		0			0
$253$		−	24.5399i		−	1.54281i
$254$	−11.2548	−	21.8194i	−0.706190	−	1.36907i
$255$		0			0
$256$	−12.5593	+	9.91280i	−0.784957	+	0.619550i
$257$	−21.2733	−	21.2733i	−1.32699	−	1.32699i	−0.907980	−	0.419013i	$-0.862376\pi$
$257$	−21.2733	−	21.2733i	−1.32699	−	1.32699i	−0.419013	−	0.907980i	$-0.637624\pi$
$258$		0			0
$259$	0.188354	−	0.188354i	0.0117038	−	0.0117038i
$260$	−5.98071	−	3.57660i	−0.370908	−	0.221812i
$261$		0			0
$262$	14.2120	−	7.33076i	0.878018	−	0.452896i
$263$	16.7214	−	16.7214i	1.03108	−	1.03108i	0.0315818	−	0.999501i	$-0.489946\pi$
$263$	16.7214	−	16.7214i	1.03108	−	1.03108i	0.999501	−	0.0315818i	$-0.0100545\pi$
$264$		0			0
$265$	−2.02739	−	25.4832i	−0.124541	−	1.56542i
$266$	−0.224131	+	0.701677i	−0.0137423	+	0.0430226i
$267$		0			0
$268$	2.89079	−	4.06336i	0.176583	−	0.248209i
$269$	−15.9096	−	15.9096i	−0.970026	−	0.970026i	0.0295378	−	0.999564i	$-0.490596\pi$
$269$	−15.9096	−	15.9096i	−0.970026	−	0.970026i	−0.999564	+	0.0295378i	$0.990596\pi$
$270$		0			0
$271$			12.3601i			0.750824i	0.926858	+	0.375412i	$0.122499\pi$
$271$			12.3601i			0.750824i	−0.926858	+	0.375412i	$0.877501\pi$
$272$	0.739348	−	1.52545i	0.0448295	−	0.0924938i
$273$		0			0
$274$	2.82894	+	5.48440i	0.170902	+	0.331324i
$275$	12.2723	−	16.9520i	0.740049	−	1.02224i
$276$		0			0
$277$			21.0270i			1.26339i	0.775217	+	0.631695i	$0.217641\pi$
$277$			21.0270i			1.26339i	−0.775217	+	0.631695i	$0.782359\pi$
$278$	−21.7217	+	11.2044i	−1.30278	+	0.671994i
$279$		0			0
$280$	0.0645531	−	1.02747i	0.00385779	−	0.0614029i
$281$		−	10.6807i		−	0.637158i	−0.947896	−	0.318579i	$-0.896794\pi$
$281$		−	10.6807i		−	0.637158i	0.947896	−	0.318579i	$-0.103206\pi$
$282$		0			0
$283$		−	12.5946i		−	0.748673i	−0.927293	−	0.374336i	$-0.877871\pi$
$283$		−	12.5946i		−	0.748673i	0.927293	−	0.374336i	$-0.122129\pi$
$284$	13.0389	+	9.27626i	0.773716	+	0.550445i
$285$		0			0
$286$	−8.19733	+	4.22832i	−0.484718	+	0.250026i
$287$	−0.876663	+	0.876663i	−0.0517478	+	0.0517478i
$288$		0			0
$289$		−	16.8204i		−	0.989435i
$290$	0.683265	+	1.10053i	0.0401227	+	0.0646252i
$291$		0			0
$292$	0.527185	+	3.12659i	0.0308512	+	0.182970i
$293$	−3.43132			−0.200460			−0.100230	−	0.994964i	$-0.531958\pi$
$293$	−3.43132			−0.200460			−0.100230	+	0.994964i	$0.531958\pi$
$294$		0			0
$295$	3.35446	−	3.93434i	0.195304	−	0.229066i
$296$	2.77623	+	3.70348i	0.161365	+	0.215260i
$297$		0			0
$298$	−2.37621	−	4.60670i	−0.137650	−	0.266859i
$299$	6.45996	+	6.45996i	0.373589	+	0.373589i
$300$		0			0
$301$	0.774227	−	0.774227i	0.0446257	−	0.0446257i
$302$	7.29781	−	22.8470i	0.419942	−	1.31470i
$303$		0			0
$304$	−11.5177	−	5.58238i	−0.660588	−	0.320171i
$305$	−2.96063	−	2.52427i	−0.169525	−	0.144539i
$306$		0			0
$307$		−	11.8104i		−	0.674053i	−0.941495	−	0.337027i	$-0.890579\pi$
$307$		−	11.8104i		−	0.674053i	0.941495	−	0.337027i	$-0.109421\pi$
$308$	−1.11032	−	0.789916i	−0.0632665	−	0.0450097i
$309$		0			0
$310$	−3.01440	+	12.8865i	−0.171207	+	0.731906i
$311$	−22.6262			−1.28301			−0.641506	−	0.767118i	$-0.721690\pi$
$311$	−22.6262			−1.28301			−0.641506	+	0.767118i	$0.721690\pi$
$312$		0			0
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	0.878486	−	0.477767i	$-0.158554\pi$
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	−0.477767	+	0.878486i	$0.658554\pi$
$314$	−3.68017	+	11.5214i	−0.207684	+	0.650188i
$315$		0			0
$316$	−5.90294	−	4.19952i	−0.332066	−	0.236242i
$317$	25.1265			1.41124			0.705621	−	0.708589i	$-0.250668\pi$
$317$	25.1265			1.41124			0.705621	+	0.708589i	$0.250668\pi$
$318$		0			0
$319$	1.71457			0.0959974
$320$	17.5144	+	3.63943i	0.979085	+	0.203450i
$321$		0			0
$322$	−0.410669	+	1.28566i	−0.0228857	+	0.0716473i
$323$	1.35606			0.0754535
$324$		0			0
$325$	1.23189	+	7.69309i	0.0683329	+	0.426736i
$326$	1.53964	−	4.82008i	0.0852726	−	0.266960i
$327$		0			0
$328$	−12.9215	−	17.2372i	−0.713469	−	0.951765i
$329$	1.00913			0.0556349
$330$		0			0
$331$	5.80829	−	5.80829i	0.319253	−	0.319253i	−0.529227	−	0.848480i	$-0.677518\pi$
$331$	5.80829	−	5.80829i	0.319253	−	0.319253i	0.848480	+	0.529227i	$0.177518\pi$
$332$	2.65032	+	1.88551i	0.145455	+	0.103481i
$333$		0			0
$334$	0.858293	−	0.442721i	0.0469637	−	0.0242246i
$335$	−5.55778	+	0.442166i	−0.303654	+	0.0241581i
$336$		0			0
$337$	−7.41679	−	7.41679i	−0.404019	−	0.404019i	0.475628	−	0.879647i	$-0.342221\pi$
$337$	−7.41679	−	7.41679i	−0.404019	−	0.404019i	−0.879647	+	0.475628i	$0.842221\pi$
$338$	−4.54923	+	14.2421i	−0.247445	+	0.774667i
$339$		0			0
$340$	−1.83801	+	0.462343i	−0.0996799	+	0.0250741i
$341$	12.3864	+	12.3864i	0.670763	+	0.670763i
$342$		0			0
$343$	−1.60836	+	1.60836i	−0.0868434	+	0.0868434i
$344$	11.4116	+	15.2231i	0.615274	+	0.820774i
$345$		0			0
$346$	−15.9220	−	5.08581i	−0.855970	−	0.273415i
$347$	18.2493			0.979673			0.489837	−	0.871814i	$-0.337056\pi$
$347$	18.2493			0.979673			0.489837	+	0.871814i	$0.337056\pi$
$348$		0			0
$349$	−19.4413	−	19.4413i	−1.04067	−	1.04067i	−0.999137	−	0.0415330i	$-0.986776\pi$
$349$	−19.4413	−	19.4413i	−1.04067	−	1.04067i	−0.0415330	−	0.999137i	$-0.513224\pi$
$350$	−0.926643	+	0.682754i	−0.0495312	+	0.0364947i
$351$		0			0
$352$	16.3202	−	17.1541i	0.869871	−	0.914319i
$353$	1.13598	−	1.13598i	0.0604622	−	0.0604622i	−0.676229	−	0.736691i	$-0.736387\pi$
$353$	1.13598	−	1.13598i	0.0604622	−	0.0604622i	0.736691	+	0.676229i	$0.236387\pi$
$354$		0			0
$355$	−1.41886	−	17.8343i	−0.0753054	−	0.946549i
$356$	−25.6100	−	18.2197i	−1.35733	−	0.965643i
$357$		0			0
$358$	4.32315	+	8.38118i	0.228485	+	0.442959i
$359$		−	28.4140i		−	1.49963i	−0.661645	−	0.749817i	$-0.730141\pi$
$359$		−	28.4140i		−	1.49963i	0.661645	−	0.749817i	$-0.269859\pi$
$360$		0			0
$361$			8.76116i			0.461114i
$362$	−23.4347	+	12.0880i	−1.23170	+	0.635331i
$363$		0			0
$364$	0.500224	−	0.0843445i	0.0262189	−	0.00442085i
$365$	2.29998	−	2.69758i	0.120387	−	0.141198i
$366$		0			0
$367$	−2.29692	+	2.29692i	−0.119898	+	0.119898i	−0.764510	−	0.644612i	$-0.777019\pi$
$367$	−2.29692	+	2.29692i	−0.119898	+	0.119898i	0.644612	+	0.764510i	$0.277019\pi$
$368$	−21.1037	−	10.2285i	−1.10011	−	0.533195i
$369$		0			0
$370$	1.17868	−	5.03882i	0.0612764	−	0.261956i
$371$	1.31588	+	1.31588i	0.0683172	+	0.0683172i
$372$		0			0
$373$	−18.0787			−0.936081			−0.468040	−	0.883707i	$-0.655040\pi$
$373$	−18.0787			−0.936081			−0.468040	+	0.883707i	$0.655040\pi$
$374$	−0.763298	+	2.38963i	−0.0394692	+	0.123565i
$375$		0			0
$376$	−2.48392	+	17.3578i	−0.128098	+	0.895162i
$377$	−0.451348	+	0.451348i	−0.0232456	+	0.0232456i
$378$		0			0
$379$	−2.79031	−	2.79031i	−0.143328	−	0.143328i	0.631802	−	0.775130i	$-0.282316\pi$
$379$	−2.79031	−	2.79031i	−0.143328	−	0.143328i	−0.775130	+	0.631802i	$0.782316\pi$
$380$	3.49088	+	13.8777i	0.179078	+	0.711911i
$381$		0			0
$382$	−18.8430	−	6.01885i	−0.964090	−	0.307951i
$383$	8.12206	+	8.12206i	0.415018	+	0.415018i	0.883482	−	0.468464i	$-0.155193\pi$
$383$	8.12206	+	8.12206i	0.415018	+	0.415018i	−0.468464	+	0.883482i	$0.655193\pi$
$384$		0			0
$385$	0.120823	+	1.51868i	0.00615770	+	0.0773990i
$386$	3.56539	+	6.91213i	0.181474	+	0.351818i
$387$		0			0
$388$	−4.55796	−	27.0320i	−0.231396	−	1.37234i
$389$	14.4341	−	14.4341i	0.731839	−	0.731839i	−0.239145	−	0.970984i	$-0.576867\pi$
$389$	14.4341	−	14.4341i	0.731839	−	0.731839i	0.970984	+	0.239145i	$0.0768670\pi$
$390$		0			0
$391$	2.48468			0.125656
$392$	−11.8307	−	15.7821i	−0.597539	−	0.797114i
$393$		0			0
$394$	−30.0789	−	9.60785i	−1.51535	−	0.484036i
$395$	0.642344	+	8.07392i	0.0323198	+	0.406243i
$396$		0			0
$397$	−35.1624			−1.76475			−0.882374	−	0.470549i	$-0.844056\pi$
$397$	−35.1624			−1.76475			−0.882374	+	0.470549i	$0.844056\pi$
$398$	13.2540	+	4.23360i	0.664362	+	0.212211i
$399$		0			0
$400$	−9.46305	−	17.6196i	−0.473153	−	0.880980i
$401$	23.5164			1.17435			0.587176	−	0.809459i	$-0.300240\pi$
$401$	23.5164			1.17435			0.587176	+	0.809459i	$0.300240\pi$
$402$		0			0
$403$	−6.52128			−0.324848
$404$	−6.02265	−	35.7187i	−0.299638	−	1.77707i
$405$		0			0
$406$	−0.0898275	−	0.0286928i	−0.00445806	−	0.00142400i
$407$	−4.84328	−	4.84328i	−0.240072	−	0.240072i
$408$		0			0
$409$	23.2595			1.15011			0.575054	−	0.818115i	$-0.304981\pi$
$409$	23.2595			1.15011			0.575054	+	0.818115i	$0.304981\pi$
$410$	−5.48594	+	23.4523i	−0.270931	+	1.15823i
$411$		0			0
$412$	12.0972	−	2.03975i	0.595986	−	0.100491i
$413$			0.376374i			0.0185201i
$414$		0			0
$415$	−0.288401	−	3.62505i	−0.0141571	−	0.177947i
$416$	0.219520	+	8.81188i	0.0107628	+	0.432038i
$417$		0			0
$418$	18.0427	+	5.76322i	0.882496	+	0.281888i
$419$	−6.63975	+	6.63975i	−0.324373	+	0.324373i	−0.850442	−	0.526069i	$-0.823665\pi$
$419$	−6.63975	+	6.63975i	−0.324373	+	0.324373i	0.526069	+	0.850442i	$0.323665\pi$
$420$		0			0
$421$	7.28216	+	7.28216i	0.354911	+	0.354911i	0.861933	−	0.507022i	$-0.169254\pi$
$421$	7.28216	+	7.28216i	0.354911	+	0.354911i	−0.507022	+	0.861933i	$0.669254\pi$
$422$	−19.6465	+	10.1340i	−0.956376	+	0.493314i
$423$		0			0
$424$	−25.8733	+	19.3953i	−1.25652	+	0.941919i
$425$	1.71640	+	1.24258i	0.0832576	+	0.0602740i
$426$		0			0
$427$	0.283225			0.0137062
$428$	−19.5245	−	13.8903i	−0.943751	−	0.671413i
$429$		0			0
$430$	4.84493	−	20.7120i	0.233643	−	0.998821i
$431$			11.7250i			0.564771i	0.959301	+	0.282386i	$0.0911258\pi$
$431$			11.7250i			0.564771i	−0.959301	+	0.282386i	$0.908874\pi$
$432$		0			0
$433$	−20.8827	+	20.8827i	−1.00356	+	1.00356i	−0.00356603	+	0.999994i	$0.501135\pi$
$433$	−20.8827	+	20.8827i	−1.00356	+	1.00356i	−0.999994	+	0.00356603i	$0.998865\pi$
$434$	−0.441651	−	0.856218i	−0.0211999	−	0.0410998i
$435$		0			0
$436$	−1.88816	−	11.1982i	−0.0904265	−	0.536294i
$437$		−	18.7604i		−	0.897430i
$438$		0			0
$439$		−	7.53661i		−	0.359703i	−0.983694	−	0.179851i	$-0.942438\pi$
$439$		−	7.53661i		−	0.359703i	0.983694	−	0.179851i	$-0.0575617\pi$
$440$	−26.4199	−	1.65990i	−1.25952	−	0.0791325i
$441$		0			0
$442$	−0.428120	−	0.829985i	−0.0203636	−	0.0394784i
$443$		−	25.7280i		−	1.22237i	−0.791486	−	0.611187i	$-0.790692\pi$
$443$		−	25.7280i		−	1.22237i	0.791486	−	0.611187i	$-0.209308\pi$
$444$		0			0
$445$	2.78682	+	35.0289i	0.132108	+	1.66053i
$446$	−10.5577	+	5.44584i	−0.499922	+	0.257868i
$447$		0			0
$448$	−1.14210	+	0.625604i	−0.0539591	+	0.0295570i
$449$		−	2.33824i		−	0.110348i	−0.998477	−	0.0551741i	$-0.982429\pi$
$449$		−	2.33824i		−	0.110348i	0.998477	−	0.0551741i	$-0.0175714\pi$
$450$		0			0
$451$	22.5422	+	22.5422i	1.06147	+	1.06147i
$452$	18.0662	−	3.04621i	0.849765	−	0.143282i
$453$		0			0
$454$	−31.2682	−	9.98774i	−1.46749	−	0.468748i
$455$	−0.431586	−	0.367975i	−0.0202331	−	0.0172509i
$456$		0			0
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	−0.418912	−	0.908027i	$-0.637588\pi$
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	0.908027	+	0.418912i	$0.137588\pi$
$458$	5.13383	+	9.95282i	0.239888	+	0.465065i
$459$		0			0
$460$	6.39625	+	25.4278i	0.298226	+	1.18558i
$461$	−15.6903	+	15.6903i	−0.730769	+	0.730769i	−0.970772	−	0.240003i	$-0.922852\pi$
$461$	−15.6903	+	15.6903i	−0.730769	+	0.730769i	0.240003	+	0.970772i	$0.422852\pi$
$462$		0			0
$463$	−19.6332	−	19.6332i	−0.912434	−	0.912434i	0.0840297	−	0.996463i	$-0.473221\pi$
$463$	−19.6332	−	19.6332i	−0.912434	−	0.912434i	−0.996463	+	0.0840297i	$0.973221\pi$
$464$	0.714647	−	1.47448i	0.0331766	−	0.0684511i
$465$		0			0
$466$	5.36791	−	2.76886i	0.248664	−	0.128265i
$467$			24.4862i			1.13309i	0.824032	+	0.566543i	$0.191719\pi$
$467$			24.4862i			1.13309i	−0.824032	+	0.566543i	$0.808281\pi$
$468$		0			0
$469$	0.286989	−	0.286989i	0.0132519	−	0.0132519i
$470$	16.6554	−	10.3406i	0.768257	−	0.476974i
$471$		0			0
$472$	−6.47395	−	0.926426i	−0.297987	−	0.0426422i
$473$	−19.9082	−	19.9082i	−0.915380	−	0.915380i
$474$		0			0
$475$	9.38199	−	12.9595i	0.430475	−	0.594624i
$476$	0.0799795	−	0.112421i	0.00366586	−	0.00515280i
$477$		0			0
$478$	−0.000597550		0.00187073i	−2.73313e−5		8.55650e-5i
$479$	−37.0609			−1.69335			−0.846677	−	0.532108i	$-0.821400\pi$
$479$	−37.0609			−1.69335			−0.846677	+	0.532108i	$0.821400\pi$
$480$		0			0
$481$	2.54991			0.116266
$482$	5.53286	−	17.3215i	0.252015	−	0.788973i
$483$		0			0
$484$	−7.55832	+	10.6241i	−0.343560	+	0.482915i
$485$	−19.8853	+	23.3229i	−0.902945	+	1.05904i
$486$		0			0
$487$	20.1912	+	20.1912i	0.914950	+	0.914950i	0.996656	−	0.0817061i	$-0.0260369\pi$
$487$	20.1912	+	20.1912i	0.914950	+	0.914950i	−0.0817061	+	0.996656i	$0.526037\pi$
$488$	−0.697145	+	4.87172i	−0.0315583	+	0.220532i
$489$		0			0
$490$	−5.02283	+	21.4725i	−0.226908	+	0.970029i
$491$	7.45822	−	7.45822i	0.336585	−	0.336585i	−0.518496	−	0.855080i	$-0.673508\pi$
$491$	7.45822	−	7.45822i	0.336585	−	0.336585i	0.855080	+	0.518496i	$0.173508\pi$
$492$		0			0
$493$			0.173601i			0.00781860i
$494$	−6.26673	+	3.23248i	−0.281953	+	0.145436i
$495$		0			0
$496$	15.8148	−	5.48923i	0.710104	−	0.246474i
$497$	0.920917	+	0.920917i	0.0413088	+	0.0413088i
$498$		0			0
$499$	8.17420	−	8.17420i	0.365927	−	0.365927i	−0.500062	−	0.865990i	$-0.666689\pi$
$499$	8.17420	−	8.17420i	0.365927	−	0.365927i	0.865990	+	0.500062i	$0.166689\pi$
$500$	−8.29785	+	20.7640i	−0.371091	+	0.928596i
$501$		0			0
$502$	8.38100	+	16.2480i	0.374062	+	0.725185i
$503$	29.2327	−	29.2327i	1.30342	−	1.30342i	0.377348	−	0.926072i	$-0.376836\pi$
$503$	29.2327	−	29.2327i	1.30342	−	1.30342i	0.926072	−	0.377348i	$-0.123164\pi$
$504$		0			0
$505$	−26.2754	+	30.8176i	−1.16924	+	1.37136i
$506$	33.0591	+	10.5598i	1.46966	+	0.469440i
$507$		0			0
$508$	34.2373	−	5.77287i	1.51903	−	0.256130i
$509$	20.0340	+	20.0340i	0.887992	+	0.887992i	0.994330	−	0.106338i	$-0.0339125\pi$
$509$	20.0340	+	20.0340i	0.887992	+	0.887992i	−0.106338	+	0.994330i	$0.533912\pi$
$510$		0			0
$511$			0.258061i			0.0114159i
$512$	−7.94969	−	21.1850i	−0.351330	−	0.936252i
$513$		0			0
$514$	37.8126	−	19.5044i	1.66784	−	0.860301i
$515$	−10.4373	−	8.89895i	−0.459922	−	0.392135i
$516$		0			0
$517$		−	25.9483i		−	1.14121i
$518$	0.172692	+	0.334794i	0.00758765	+	0.0147100i
$519$		0			0
$520$	7.39181	−	6.51790i	0.324152	−	0.285829i
$521$			5.89264i			0.258161i	0.991634	+	0.129081i	$0.0412026\pi$
$521$			5.89264i			0.258161i	−0.991634	+	0.129081i	$0.958797\pi$
$522$		0			0
$523$			24.6537i			1.07803i	0.842296	+	0.539015i	$0.181203\pi$
$523$			24.6537i			1.07803i	−0.842296	+	0.539015i	$0.818797\pi$
$524$	3.76012	+	22.3003i	0.164262	+	0.974191i
$525$		0			0
$526$	15.3309	+	29.7217i	0.668460	+	1.29593i
$527$	−1.25413	+	1.25413i	−0.0546309	+	0.0546309i
$528$		0			0
$529$		−	11.3742i		−	0.494528i
$530$	35.2022	+	8.23447i	1.52909	+	0.357683i
$531$		0			0
$532$	−0.848823	−	0.603878i	−0.0368012	−	0.0261814i
$533$	−11.8681			−0.514066
$534$		0			0
$535$	2.12461	+	26.7052i	0.0918549	+	1.15457i
$536$	4.23004	+	5.64286i	0.182710	+	0.243735i
$537$		0			0
$538$	28.2788	−	14.5867i	1.21919	−	0.628876i
$539$	20.6392	+	20.6392i	0.888994	+	0.888994i
$540$		0			0
$541$	−27.1762	+	27.1762i	−1.16840	+	1.16840i	−0.185812	+	0.982585i	$0.559492\pi$
$541$	−27.1762	+	27.1762i	−1.16840	+	1.16840i	−0.982585	+	0.185812i	$0.940508\pi$
$542$	−16.6510	−	5.31869i	−0.715223	−	0.228457i
$543$		0			0
$544$	1.73687	+	1.65243i	0.0744676	+	0.0708475i
$545$	−8.23759	+	9.66162i	−0.352860	+	0.413858i
$546$		0			0
$547$			3.69225i			0.157869i	0.996880	+	0.0789347i	$0.0251519\pi$
$547$			3.69225i			0.157869i	−0.996880	+	0.0789347i	$0.974848\pi$
$548$	−8.60567	+	1.45103i	−0.367616	+	0.0619850i
$549$		0			0
$550$	17.5561	+	23.8274i	0.748594	+	1.01600i
$551$	1.31076			0.0558402
$552$		0			0
$553$	−0.416915	−	0.416915i	−0.0177290	−	0.0177290i
$554$	−28.3267	−	9.04815i	−1.20349	−	0.384419i
$555$		0			0
$556$	−5.74700	−	34.0839i	−0.243727	−	1.44548i
$557$	−12.2117			−0.517426			−0.258713	−	0.965954i	$-0.583298\pi$
$557$	−12.2117			−0.517426			−0.258713	+	0.965954i	$0.583298\pi$
$558$		0			0
$559$	10.4814			0.443315
$560$	1.35638	+	0.529093i	0.0573176	+	0.0223583i
$561$		0			0
$562$	14.3886	+	4.59603i	0.606947	+	0.193872i
$563$	12.2211			0.515057			0.257528	−	0.966271i	$-0.417092\pi$
$563$	12.2211			0.515057			0.257528	+	0.966271i	$0.417092\pi$
$564$		0			0
$565$	−15.5873	−	13.2899i	−0.655763	−	0.559110i
$566$	16.9669	+	5.41960i	0.713174	+	0.227803i
$567$		0			0
$568$	−18.1074	+	13.5738i	−0.759768	+	0.569543i
$569$	30.9592			1.29788			0.648938	−	0.760841i	$-0.275213\pi$
$569$	30.9592			1.29788			0.648938	+	0.760841i	$0.275213\pi$
$570$		0			0
$571$	30.1508	−	30.1508i	1.26177	−	1.26177i	0.311539	−	0.950233i	$-0.399156\pi$
$571$	30.1508	−	30.1508i	1.26177	−	1.26177i	0.950233	−	0.311539i	$-0.100844\pi$
$572$	−2.16881	−	12.8626i	−0.0906823	−	0.537812i
$573$		0			0
$574$	−0.803765	−	1.55824i	−0.0335485	−	0.0650397i
$575$	17.1904	−	23.7454i	0.716889	−	0.990252i
$576$		0			0
$577$	1.98215	+	1.98215i	0.0825181	+	0.0825181i	0.747161	−	0.664643i	$-0.231416\pi$
$577$	1.98215	+	1.98215i	0.0825181	+	0.0825181i	−0.664643	+	0.747161i	$0.731416\pi$
$578$	22.6597	+	7.23800i	0.942520	+	0.301061i
$579$		0			0
$580$	−1.77660	+	0.446896i	−0.0737693	+	0.0185564i
$581$	0.187188	+	0.187188i	0.00776586	+	0.00776586i
$582$		0			0
$583$	33.8361	−	33.8361i	1.40135	−	1.40135i
$584$	−4.43886	−	0.635204i	−0.183681	−	0.0262849i
$585$		0			0
$586$	1.47653	−	4.62253i	0.0609951	−	0.190955i
$587$	−26.9680			−1.11309			−0.556544	−	0.830818i	$-0.687873\pi$
$587$	−26.9680			−1.11309			−0.556544	+	0.830818i	$0.687873\pi$
$588$		0			0
$589$	9.46923	+	9.46923i	0.390173	+	0.390173i
$590$	3.85671	+	6.21197i	0.158778	+	0.255743i
$591$		0			0
$592$	−6.18381	+	2.14637i	−0.254153	+	0.0882152i
$593$	−16.6701	+	16.6701i	−0.684560	+	0.684560i	−0.961024	−	0.276464i	$-0.910837\pi$
$593$	−16.6701	+	16.6701i	−0.684560	+	0.684560i	0.276464	+	0.961024i	$0.410837\pi$
$594$		0			0
$595$	−0.153767	+	0.0122334i	−0.00630383	+	0.000501520i
$596$	7.22846	−	1.21882i	0.296089	−	0.0499247i
$597$		0			0
$598$	−11.4824	+	5.92279i	−0.469549	+	0.242201i
$599$			28.8376i			1.17827i	0.808033	+	0.589137i	$0.200532\pi$
$599$			28.8376i			1.17827i	−0.808033	+	0.589137i	$0.799468\pi$
$600$		0			0
$601$		−	1.91377i		−	0.0780642i	−0.999238	−	0.0390321i	$-0.987573\pi$
$601$		−	1.91377i		−	0.0780642i	0.999238	−	0.0390321i	$-0.0124275\pi$
$602$	0.709847	+	1.37616i	0.0289312	+	0.0560882i
$603$		0			0
$604$	27.6381	+	19.6626i	1.12458	+	0.800059i
$605$	14.5315	−	1.15609i	0.590789	−	0.0470019i
$606$		0			0
$607$	−7.89049	+	7.89049i	−0.320265	+	0.320265i	−0.848869	−	0.528604i	$-0.822716\pi$
$607$	−7.89049	+	7.89049i	−0.320265	+	0.320265i	0.528604	+	0.848869i	$0.322716\pi$
$608$	12.4766	−	13.1141i	0.505991	−	0.531845i
$609$		0			0
$610$	4.67457	−	2.90222i	0.189268	−	0.117507i
$611$	6.83071	+	6.83071i	0.276341	+	0.276341i
$612$		0			0
$613$	−40.1035			−1.61976			−0.809882	−	0.586592i	$-0.800469\pi$
$613$	−40.1035			−1.61976			−0.809882	+	0.586592i	$0.800469\pi$
$614$	15.9104	+	5.08213i	0.642092	+	0.205098i
$615$		0			0
$616$	1.54193	−	1.15587i	0.0621259	−	0.0465713i
$617$	−14.5821	+	14.5821i	−0.587052	+	0.587052i	−0.936832	−	0.349780i	$-0.886256\pi$
$617$	−14.5821	+	14.5821i	−0.587052	+	0.587052i	0.349780	+	0.936832i	$0.386256\pi$
$618$		0			0
$619$	−4.01752	−	4.01752i	−0.161478	−	0.161478i	0.621743	−	0.783221i	$-0.286425\pi$
$619$	−4.01752	−	4.01752i	−0.161478	−	0.161478i	−0.783221	+	0.621743i	$0.786425\pi$
$620$	−16.0630	−	9.60609i	−0.645108	−	0.385790i
$621$		0			0
$622$	9.73628	−	30.4810i	0.390389	−	1.22218i
$623$	−1.80880	−	1.80880i	−0.0724679	−	0.0724679i
$624$		0			0
$625$	23.7500	−	7.80630i	0.949999	−	0.312252i
$626$	−12.6013	+	6.49993i	−0.503648	+	0.259790i
$627$		0			0
$628$	−13.9375	−	9.91553i	−0.556166	−	0.395673i
$629$	0.490385	−	0.490385i	0.0195529	−	0.0195529i
$630$		0			0
$631$	−26.9309			−1.07210			−0.536052	−	0.844185i	$-0.680085\pi$
$631$	−26.9309			−1.07210			−0.536052	+	0.844185i	$0.680085\pi$
$632$	8.19752	−	6.14508i	0.326080	−	0.244438i
$633$		0			0
$634$	−10.8122	+	33.8493i	−0.429407	+	1.34433i
$635$	−29.5395	−	25.1856i	−1.17224	−	0.999462i
$636$		0			0
$637$	−10.8662			−0.430536
$638$	−0.737797	+	2.30979i	−0.0292097	+	0.0914456i
$639$		0			0
$640$	−12.4395	+	22.0286i	−0.491715	+	0.870756i
$641$	−18.6880			−0.738131			−0.369065	−	0.929403i	$-0.620322\pi$
$641$	−18.6880			−0.738131			−0.369065	+	0.929403i	$0.620322\pi$
$642$		0			0
$643$	29.6249			1.16829			0.584146	−	0.811648i	$-0.301429\pi$
$643$	29.6249			1.16829			0.584146	+	0.811648i	$0.301429\pi$
$644$	−1.55528	−	1.10647i	−0.0612865	−	0.0436011i
$645$		0			0
$646$	−0.583529	+	1.82683i	−0.0229586	+	0.0718758i
$647$	5.04426	+	5.04426i	0.198310	+	0.198310i	0.799275	−	0.600965i	$-0.205217\pi$
$647$	5.04426	+	5.04426i	0.198310	+	0.198310i	−0.600965	+	0.799275i	$0.705217\pi$
$648$		0			0
$649$	9.67794			0.379893
$650$	−10.8939	−	1.65087i	−0.427294	−	0.0647525i
$651$		0			0
$652$	5.83089	+	4.14827i	0.228355	+	0.162459i
$653$			3.04934i			0.119330i	0.998218	+	0.0596649i	$0.0190032\pi$
$653$			3.04934i			0.119330i	−0.998218	+	0.0596649i	$0.980997\pi$
$654$		0			0
$655$	16.4045	−	19.2404i	0.640978	−	0.751783i
$656$	28.7815	−	9.98991i	1.12373	−	0.390040i
$657$		0			0
$658$	−0.434238	+	1.35945i	−0.0169284	+	0.0529970i
$659$	−22.0441	+	22.0441i	−0.858718	+	0.858718i	−0.991187	−	0.132469i	$-0.957709\pi$
$659$	−22.0441	+	22.0441i	−0.858718	+	0.858718i	0.132469	+	0.991187i	$0.457709\pi$
$660$		0			0
$661$	8.09788	+	8.09788i	0.314971	+	0.314971i	0.846832	−	0.531861i	$-0.178507\pi$
$661$	8.09788	+	8.09788i	0.314971	+	0.314971i	−0.531861	+	0.846832i	$0.678507\pi$
$662$	5.32531	+	10.3241i	0.206974	+	0.401256i
$663$		0			0
$664$	−3.68054	+	2.75904i	−0.142833	+	0.107071i
$665$	0.0923670	+	1.16100i	0.00358184	+	0.0450218i
$666$		0			0
$667$	2.40167			0.0929931
$668$	0.227083	+	1.34676i	0.00878609	+	0.0521078i
$669$		0			0
$670$	1.79591	−	7.67748i	0.0693820	−	0.296607i
$671$		−	7.28276i		−	0.281148i
$672$		0			0
$673$	−27.1768	+	27.1768i	−1.04759	+	1.04759i	−0.0487786	+	0.998810i	$0.515533\pi$
$673$	−27.1768	+	27.1768i	−1.04759	+	1.04759i	−0.998810	+	0.0487786i	$0.984467\pi$
$674$	13.1831	−	6.80006i	0.507795	−	0.261929i
$675$		0			0
$676$	−17.2287	−	12.2570i	−0.662644	−	0.471425i
$677$		−	28.6501i		−	1.10111i	−0.834798	−	0.550557i	$-0.814415\pi$
$677$		−	28.6501i		−	1.10111i	0.834798	−	0.550557i	$-0.185585\pi$
$678$		0			0
$679$		−	2.23115i		−	0.0856238i
$680$	0.168066	−	2.67504i	0.00644502	−	0.102583i
$681$		0			0
$682$	−22.0165	+	11.3565i	−0.843055	+	0.434861i
$683$			30.8472i			1.18034i	0.807281	+	0.590168i	$0.200938\pi$
$683$			30.8472i			1.18034i	−0.807281	+	0.590168i	$0.799062\pi$
$684$		0			0
$685$	7.42485	+	6.33051i	0.283689	+	0.241876i
$686$	−1.47462	−	2.85881i	−0.0563013	−	0.109150i
$687$		0			0
$688$	−25.4184	+	8.82261i	−0.969069	+	0.336359i
$689$			17.8142i			0.678668i
$690$		0			0
$691$	0.253186	+	0.253186i	0.00963164	+	0.00963164i	0.711906	−	0.702275i	$-0.247832\pi$
$691$	0.253186	+	0.253186i	0.00963164	+	0.00963164i	−0.702275	+	0.711906i	$0.747832\pi$
$692$	13.7028	−	19.2609i	0.520901	−	0.732189i
$693$		0			0
$694$	−7.85286	+	24.5847i	−0.298091	+	0.933221i
$695$	−25.0728	+	29.4071i	−0.951066	+	1.11548i
$696$		0			0
$697$	−2.28241	+	2.28241i	−0.0864525	+	0.0864525i
$698$	34.5563	−	17.8247i	1.30798	−	0.674675i
$699$		0			0
$700$	−0.521032	−	1.54213i	−0.0196932	−	0.0582870i
$701$	−10.5238	+	10.5238i	−0.397479	+	0.397479i	−0.877343	−	0.479864i	$-0.840686\pi$
$701$	−10.5238	+	10.5238i	−0.397479	+	0.397479i	0.479864	+	0.877343i	$0.340686\pi$
$702$		0			0
$703$	−3.70261	−	3.70261i	−0.139646	−	0.139646i
$704$	16.0866	+	29.3675i	0.606285	+	1.10683i
$705$		0			0
$706$	1.04152	+	2.01917i	0.0391982	+	0.0759925i
$707$		−	2.94813i		−	0.110876i
$708$		0			0
$709$	1.58968	−	1.58968i	0.0597015	−	0.0597015i	−0.676626	−	0.736327i	$-0.736558\pi$
$709$	1.58968	−	1.58968i	0.0597015	−	0.0597015i	0.736327	+	0.676626i	$0.236558\pi$
$710$	24.6362	+	5.76288i	0.924581	+	0.216277i
$711$		0			0
$712$	35.5651	−	26.6606i	1.33286	−	0.999147i
$713$	17.3502	+	17.3502i	0.649771	+	0.649771i
$714$		0			0
$715$	−9.46198	+	11.0977i	−0.353858	+	0.415029i
$716$	−13.1511	+	2.21745i	−0.491478	+	0.0828699i
$717$		0			0
$718$	38.2781	+	12.2269i	1.42853	+	0.456302i
$719$	22.8919			0.853722			0.426861	−	0.904317i	$-0.359619\pi$
$719$	22.8919			0.853722			0.426861	+	0.904317i	$0.359619\pi$
$720$		0			0
$721$	0.998472			0.0371850
$722$	−11.8027	−	3.77002i	−0.439249	−	0.140306i
$723$		0			0
$724$	−6.20023	−	36.7718i	−0.230430	−	1.36661i
$725$	1.65906	+	1.20107i	0.0616158	+	0.0446065i
$726$		0			0
$727$	20.1893	+	20.1893i	0.748780	+	0.748780i	0.974250	−	0.225470i	$-0.0723919\pi$
$727$	20.1893	+	20.1893i	0.748780	+	0.748780i	−0.225470	+	0.974250i	$0.572392\pi$
$728$	−0.101626	+	0.710175i	−0.00376653	+	0.0263208i
$729$		0			0
$730$	2.64436	+	4.25924i	0.0978720	+	0.157641i
$731$	2.01572	−	2.01572i	0.0745540	−	0.0745540i
$732$		0			0
$733$			14.3253i			0.529118i	0.964370	+	0.264559i	$0.0852263\pi$
$733$			14.3253i			0.529118i	−0.964370	+	0.264559i	$0.914774\pi$
$734$	−2.10592	−	4.08270i	−0.0777311	−	0.150695i
$735$		0			0
$736$	22.8605	−	24.0286i	0.842648	−	0.885705i
$737$	−7.37954	−	7.37954i	−0.271829	−	0.271829i
$738$		0			0
$739$	−32.3401	+	32.3401i	−1.18965	+	1.18965i	−0.212487	+	0.977164i	$0.568156\pi$
$739$	−32.3401	+	32.3401i	−1.18965	+	1.18965i	−0.977164	+	0.212487i	$0.931844\pi$
$740$	6.28089	+	3.75612i	0.230890	+	0.138078i
$741$		0			0
$742$	−2.33894	+	1.20646i	−0.0858651	+	0.0442906i
$743$	6.06842	−	6.06842i	0.222629	−	0.222629i	−0.586976	−	0.809605i	$-0.699682\pi$
$743$	6.06842	−	6.06842i	0.222629	−	0.222629i	0.809605	+	0.586976i	$0.199682\pi$
$744$		0			0
$745$	−6.23662	−	5.31741i	−0.228492	−	0.194815i
$746$	7.77947	−	24.3549i	0.284827	−	0.891696i
$747$		0			0
$748$	−2.89075	−	2.05657i	−0.105696	−	0.0751955i
$749$	−1.37898	−	1.37898i	−0.0503870	−	0.0503870i
$750$		0			0
$751$		−	49.6431i		−	1.81150i	−0.423810	−	0.905751i	$-0.639308\pi$
$751$		−	49.6431i		−	1.81150i	0.423810	−	0.905751i	$-0.360692\pi$
$752$	−22.3149	−	10.8155i	−0.813740	−	0.394400i
$753$		0			0
$754$	−0.413816	−	0.802256i	−0.0150703	−	0.0292164i
$755$	−3.00752	−	37.8029i	−0.109455	−	1.37579i
$756$		0			0
$757$		−	9.18443i		−	0.333814i	−0.985973	−	0.166907i	$-0.946622\pi$
$757$		−	9.18443i		−	0.333814i	0.985973	−	0.166907i	$-0.0533779\pi$
$758$	4.95968	−	2.55828i	0.180144	−	0.0929211i
$759$		0			0
$760$	−20.1976	−	1.26896i	−0.732644	−	0.0460302i
$761$		−	4.75310i		−	0.172300i	−0.996282	−	0.0861499i	$-0.972544\pi$
$761$		−	4.75310i		−	0.172300i	0.996282	−	0.0861499i	$-0.0274564\pi$
$762$		0			0
$763$		−	0.924267i		−	0.0334607i
$764$	16.2167	−	22.7945i	0.586698	−	0.824675i
$765$		0			0
$766$	−14.4367	+	7.44668i	−0.521619	+	0.269060i
$767$	−2.54765	+	2.54765i	−0.0919902	+	0.0919902i
$768$		0			0
$769$			19.4153i			0.700135i	0.936724	+	0.350067i	$0.113841\pi$
$769$			19.4153i			0.700135i	−0.936724	+	0.350067i	$0.886159\pi$
$770$	−2.09789	−	0.490736i	−0.0756027	−	0.0176849i
$771$		0			0
$772$	−10.8460	+	1.82877i	−0.390355	+	0.0658190i
$773$	−26.0890			−0.938356			−0.469178	−	0.883104i	$-0.655450\pi$
$773$	−26.0890			−0.938356			−0.469178	+	0.883104i	$0.655450\pi$
$774$		0			0
$775$	3.30862	+	20.6622i	0.118849	+	0.742208i
$776$	38.3777	+	5.49187i	1.37768	+	0.197147i
$777$		0			0
$778$	13.2339	+	25.6562i	0.474458	+	0.919819i
$779$	17.2331	+	17.2331i	0.617442	+	0.617442i
$780$		0			0
$781$	23.6802	−	23.6802i	0.847343	−	0.847343i
$782$	−1.06919	+	3.34726i	−0.0382340	+	0.119698i
$783$		0			0
$784$	26.3518	−	9.14657i	0.941135	−	0.326663i
$785$	1.51664	+	19.0634i	0.0541313	+	0.680402i
$786$		0			0
$787$		−	14.2339i		−	0.507384i	−0.967285	−	0.253692i	$-0.918355\pi$
$787$		−	14.2339i		−	0.507384i	0.967285	−	0.253692i	$-0.0816449\pi$
$788$	25.8866	−	36.3867i	0.922170	−	1.29622i
$789$		0			0
$790$	−11.1532	−	2.60896i	−0.396815	−	0.0928225i
$791$	1.49114			0.0530189
$792$		0			0
$793$	1.91713	+	1.91713i	0.0680794	+	0.0680794i
$794$	15.1307	−	47.3692i	0.536970	−	1.68107i
$795$		0			0
$796$	−11.4067	+	16.0334i	−0.404298	+	0.568289i
$797$	−19.8283			−0.702353			−0.351176	−	0.936309i	$-0.614218\pi$
$797$	−19.8283			−0.702353			−0.351176	+	0.936309i	$0.614218\pi$
$798$		0			0
$799$	2.62729			0.0929467
$800$	27.8084	−	5.16631i	0.983177	−	0.182657i
$801$		0			0
$802$	−10.1194	+	31.6803i	−0.357327	+	1.11867i
$803$	6.63568			0.234168
$804$		0			0
$805$	0.169242	+	2.12728i	0.00596499	+	0.0749767i
$806$	2.80618	−	8.78518i	0.0988433	−	0.309445i
$807$		0			0
$808$	50.7103	+	7.25667i	1.78398	+	0.255289i
$809$	−21.3864			−0.751907			−0.375954	−	0.926639i	$-0.622685\pi$
$809$	−21.3864			−0.751907			−0.375954	+	0.926639i	$0.622685\pi$
$810$		0			0
$811$	−9.90624	+	9.90624i	−0.347855	+	0.347855i	−0.859310	−	0.511455i	$-0.829107\pi$
$811$	−9.90624	+	9.90624i	−0.347855	+	0.347855i	0.511455	+	0.859310i	$0.329107\pi$
$812$	0.0773075	−	0.108665i	0.00271296	−	0.00381339i
$813$		0			0
$814$	8.60877	−	4.44054i	0.301737	−	0.155641i
$815$	−0.634504	−	7.97538i	−0.0222257	−	0.279365i
$816$		0			0
$817$	−15.2195	−	15.2195i	−0.532463	−	0.532463i
$818$	−10.0088	+	31.3342i	−0.349950	+	1.09557i
$819$		0			0
$820$	−29.2333	−	17.4822i	−1.02087	−	0.610506i
$821$	−22.6209	−	22.6209i	−0.789474	−	0.789474i	0.191934	−	0.981408i	$-0.438524\pi$
$821$	−22.6209	−	22.6209i	−0.789474	−	0.789474i	−0.981408	+	0.191934i	$0.938524\pi$
$822$		0			0
$823$	4.89892	−	4.89892i	0.170766	−	0.170766i	−0.616550	−	0.787316i	$-0.711470\pi$
$823$	4.89892	−	4.89892i	0.170766	−	0.170766i	0.787316	+	0.616550i	$0.211470\pi$
$824$	−2.45769	+	17.1746i	−0.0856177	+	0.598304i
$825$		0			0
$826$	−0.507034	−	0.161958i	−0.0176420	−	0.00563523i
$827$	−1.05434			−0.0366630			−0.0183315	−	0.999832i	$-0.505835\pi$
$827$	−1.05434			−0.0366630			−0.0183315	+	0.999832i	$0.505835\pi$
$828$		0			0
$829$	11.7754	+	11.7754i	0.408978	+	0.408978i	0.881382	−	0.472404i	$-0.156614\pi$
$829$	11.7754	+	11.7754i	0.408978	+	0.408978i	−0.472404	+	0.881382i	$0.656614\pi$
$830$	5.00762	+	1.17138i	0.173817	+	0.0406591i
$831$		0			0
$832$	−11.9655	−	3.49612i	−0.414828	−	0.121206i
$833$	−2.08973	+	2.08973i	−0.0724050	+	0.0724050i
$834$		0			0
$835$	0.990707	−	1.16197i	0.0342848	−	0.0402116i
$836$	−15.5279	+	21.8263i	−0.537044	+	0.754880i
$837$		0			0
$838$	−6.08763	−	11.8019i	−0.210294	−	0.407691i
$839$			41.1678i			1.42127i	0.703560	+	0.710636i	$0.251593\pi$
$839$			41.1678i			1.42127i	−0.703560	+	0.710636i	$0.748407\pi$
$840$		0			0
$841$		−	28.8322i		−	0.994214i
$842$	−12.9438	+	6.67662i	−0.446073	+	0.230092i
$843$		0			0
$844$	−5.19796	−	30.8277i	−0.178921	−	1.06113i
$845$	1.87479	+	23.5651i	0.0644948	+	0.810666i
$846$		0			0
$847$	−0.750366	+	0.750366i	−0.0257829	+	0.0257829i
$848$	−14.9950	−	43.2013i	−0.514930	−	1.48354i
$849$		0			0
$850$	−2.41254	+	1.77757i	−0.0827493	+	0.0609700i
$851$	−6.78419	−	6.78419i	−0.232559	−	0.232559i
$852$		0			0
$853$	11.7179			0.401212			0.200606	−	0.979672i	$-0.435709\pi$
$853$	11.7179			0.401212			0.200606	+	0.979672i	$0.435709\pi$
$854$	−0.121875	+	0.381549i	−0.00417047	+	0.0130563i
$855$		0			0
$856$	27.1140	−	20.3254i	0.926738	−	0.694708i
$857$	12.2154	−	12.2154i	0.417270	−	0.417270i	−0.466992	−	0.884262i	$-0.654662\pi$
$857$	12.2154	−	12.2154i	0.417270	−	0.417270i	0.884262	+	0.466992i	$0.154662\pi$
$858$		0			0
$859$	17.2170	+	17.2170i	0.587436	+	0.587436i	0.936936	−	0.349500i	$-0.113649\pi$
$859$	17.2170	+	17.2170i	0.587436	+	0.587436i	−0.349500	+	0.936936i	$0.613649\pi$
$860$	25.8175	+	15.4395i	0.880369	+	0.526482i
$861$		0			0
$862$	−15.7954	−	5.04537i	−0.537992	−	0.171846i
$863$	11.1929	+	11.1929i	0.381011	+	0.381011i	0.871466	−	0.490455i	$-0.163169\pi$
$863$	11.1929	+	11.1929i	0.381011	+	0.381011i	−0.490455	+	0.871466i	$0.663169\pi$
$864$		0			0
$865$	−26.3447	+	2.09593i	−0.895746	+	0.0712637i
$866$	−19.1463	−	37.1184i	−0.650616	−	1.26133i
$867$		0			0
$868$	1.34351	−	0.226533i	0.0456016	−	0.00768905i
$869$	−10.7204	+	10.7204i	−0.363665	+	0.363665i
$870$		0			0
$871$	3.88522			0.131646
$872$	15.8982	+	2.27504i	0.538380	+	0.0770425i
$873$		0			0
$874$	25.2732	+	8.07279i	0.854878	+	0.273066i
$875$	−0.946933	+	1.55415i	−0.0320122	+	0.0525397i
$876$		0			0
$877$	43.1739			1.45788			0.728940	−	0.684578i	$-0.240013\pi$
$877$	43.1739			1.45788			0.728940	+	0.684578i	$0.240013\pi$
$878$	10.1530	+	3.24308i	0.342647	+	0.109449i
$879$		0			0
$880$	13.6049	−	34.8775i	0.458622	−	1.17572i
$881$	33.4204			1.12596			0.562981	−	0.826470i	$-0.309654\pi$
$881$	33.4204			1.12596			0.562981	+	0.826470i	$0.309654\pi$
$882$		0			0
$883$	2.00362			0.0674270			0.0337135	−	0.999432i	$-0.489267\pi$
$883$	2.00362			0.0674270			0.0337135	+	0.999432i	$0.489267\pi$
$884$	1.30234	−	0.219593i	0.0438026	−	0.00738571i
$885$		0			0
$886$	34.6597	+	11.0710i	1.16441	+	0.371939i
$887$	16.1765	+	16.1765i	0.543154	+	0.543154i	0.924452	−	0.381298i	$-0.124523\pi$
$887$	16.1765	+	16.1765i	0.543154	+	0.543154i	−0.381298	+	0.924452i	$0.624523\pi$
$888$		0			0
$889$	2.82586			0.0947762
$890$	−48.3886	−	11.3190i	−1.62199	−	0.379414i
$891$		0			0
$892$	−2.79330	−	16.5663i	−0.0935266	−	0.554681i
$893$		−	19.8371i		−	0.663822i
$894$		0			0
$895$	11.3466	+	9.67419i	0.379274	+	0.323373i
$896$	−0.351329	−	1.80779i	−0.0117371	−	0.0603940i
$897$		0			0
$898$	3.14997	+	1.00617i	0.105116	+	0.0335763i
$899$	−1.21223	+	1.21223i	−0.0404303	+	0.0404303i
$900$		0			0
$901$	3.42593	+	3.42593i	0.114134	+	0.114134i
$902$	−40.0680	+	20.6677i	−1.33412	+	0.688161i
$903$		0			0
$904$	−3.67037	+	25.6489i	−0.122075	+	0.853070i
$905$	−27.0501	+	31.7262i	−0.899176	+	1.05462i
$906$		0			0
$907$	−29.7116			−0.986559			−0.493279	−	0.869871i	$-0.664202\pi$
$907$	−29.7116			−0.986559			−0.493279	+	0.869871i	$0.664202\pi$
$908$	26.9101	−	37.8254i	0.893044	−	1.25528i
$909$		0			0
$910$	0.681436	−	0.423071i	0.0225894	−	0.0140247i
$911$		−	44.6931i		−	1.48075i	−0.672195	−	0.740374i	$-0.734648\pi$
$911$		−	44.6931i		−	1.48075i	0.672195	−	0.740374i	$-0.265352\pi$
$912$		0			0
$913$	4.81328	−	4.81328i	0.159296	−	0.159296i
$914$	9.58663	+	18.5854i	0.317097	+	0.614749i
$915$		0			0
$916$	−15.6172	+	2.63326i	−0.516005	+	0.0870055i
$917$			1.84061i			0.0607821i
$918$		0			0
$919$		−	40.1278i		−	1.32369i	−0.749639	−	0.661847i	$-0.769773\pi$
$919$		−	40.1278i		−	1.32369i	0.749639	−	0.661847i	$-0.230227\pi$
$920$	−37.0076	−	2.32509i	−1.22010	−	0.0766560i
$921$		0			0
$922$	−14.3856	−	27.8890i	−0.473764	−	0.918474i
$923$			12.4673i			0.410365i
$924$		0			0
$925$	−1.29372	−	8.07922i	−0.0425372	−	0.265643i
$926$	34.8974	−	18.0007i	1.14680	−	0.591538i
$927$		0			0
$928$	1.67884	+	1.59723i	0.0551106	+	0.0524316i
$929$		−	27.7519i		−	0.910512i	−0.890361	−	0.455256i	$-0.849548\pi$
$929$		−	27.7519i		−	0.910512i	0.890361	−	0.455256i	$-0.150452\pi$
$930$		0			0
$931$	15.7783	+	15.7783i	0.517114	+	0.517114i
$932$	1.42021	+	8.42289i	0.0465206	+	0.275901i
$933$		0			0
$934$	−32.9867	−	10.5367i	−1.07936	−	0.344770i
$935$	0.314565	+	3.95391i	0.0102874	+	0.129307i
$936$		0			0
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	−0.930591	−	0.366060i	$-0.880706\pi$
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	0.366060	+	0.930591i	$0.380706\pi$
$938$	0.263125	+	0.510114i	0.00859133	+	0.0166558i
$939$		0			0
$940$	6.76334	+	26.8871i	0.220596	+	0.876961i
$941$	4.81532	−	4.81532i	0.156975	−	0.156975i	−0.624250	−	0.781225i	$-0.714595\pi$
$941$	4.81532	−	4.81532i	0.156975	−	0.156975i	0.781225	+	0.624250i	$0.214595\pi$
$942$		0			0
$943$	31.5759	+	31.5759i	1.02825	+	1.02825i
$944$	4.03385	−	8.32277i	0.131291	−	0.270883i
$945$		0			0
$946$	35.3862	−	18.2528i	1.15050	−	0.593449i
$947$		−	3.37347i		−	0.109623i	−0.998497	−	0.0548115i	$-0.982544\pi$
$947$		−	3.37347i		−	0.109623i	0.998497	−	0.0548115i	$-0.0174558\pi$
$948$		0			0
$949$	−1.74680	+	1.74680i	−0.0567034	+	0.0567034i
$950$	13.4213	+	18.2156i	0.435446	+	0.590993i
$951$		0			0
$952$	0.117032	+	0.156121i	0.00379304	+	0.00505991i
$953$	−14.3663	−	14.3663i	−0.465369	−	0.465369i	0.435041	−	0.900410i	$-0.356734\pi$
$953$	−14.3663	−	14.3663i	−0.465369	−	0.465369i	−0.900410	+	0.435041i	$0.856734\pi$
$954$		0			0
$955$	−31.1778	+	2.48044i	−1.00889	+	0.0802652i
$956$	−0.00226303	−	0.00160999i	−7.31916e−5	−	5.20707e-5i
$957$		0			0
$958$	15.9477	−	49.9268i	0.515246	−	1.61306i
$959$	−0.710289			−0.0229364
$960$		0			0
$961$	13.4851			0.435003
$962$	−1.09726	+	3.43514i	−0.0353769	+	0.110753i
$963$		0			0
$964$	20.9539	+	14.9073i	0.674881	+	0.480131i
$965$	9.35775	+	7.97851i	0.301236	+	0.256837i
$966$		0			0
$967$	−11.8576	−	11.8576i	−0.381315	−	0.381315i	0.490260	−	0.871576i	$-0.336902\pi$
$967$	−11.8576	−	11.8576i	−0.381315	−	0.381315i	−0.871576	+	0.490260i	$0.836902\pi$
$968$	−11.0599	−	14.7539i	−0.355480	−	0.474209i
$969$		0			0
$970$	−22.8627	−	36.8247i	−0.734077	−	1.18237i
$971$	14.6082	−	14.6082i	0.468799	−	0.468799i	−0.432726	−	0.901525i	$-0.642448\pi$
$971$	14.6082	−	14.6082i	0.468799	−	0.468799i	0.901525	+	0.432726i	$0.142448\pi$
$972$		0			0
$973$		−	2.81319i		−	0.0901869i
$974$	−35.8892	+	18.5122i	−1.14996	+	0.593170i
$975$		0			0
$976$	−6.26298	−	3.03552i	−0.200473	−	0.0971645i
$977$	−12.9249	−	12.9249i	−0.413504	−	0.413504i	0.469454	−	0.882957i	$-0.344451\pi$
$977$	−12.9249	−	12.9249i	−0.413504	−	0.413504i	−0.882957	+	0.469454i	$0.844451\pi$
$978$		0			0
$979$	−46.5108	+	46.5108i	−1.48649	+	1.48649i
$980$	−26.7655	−	16.0064i	−0.854992	−	0.511305i
$981$		0			0
$982$	6.83804	+	13.2567i	0.218211	+	0.423040i
$983$	0.133323	−	0.133323i	0.00425235	−	0.00425235i	−0.704977	−	0.709230i	$-0.749043\pi$
$983$	0.133323	−	0.133323i	0.00425235	−	0.00425235i	0.709230	+	0.704977i	$0.249043\pi$
$984$		0			0
$985$	−49.7690	+	3.95951i	−1.58577	+	0.126161i
$986$	−0.233868	−	0.0747024i	−0.00744787	−	0.00237901i
$987$		0			0
$988$	−1.65802	−	9.83324i	−0.0527485	−	0.312837i
$989$	−27.8863	−	27.8863i	−0.886733	−	0.886733i
$990$		0			0
$991$			47.9032i			1.52170i	0.648930	+	0.760848i	$0.275217\pi$
$991$			47.9032i			1.52170i	−0.648930	+	0.760848i	$0.724783\pi$
$992$	0.589589	+	23.6671i	0.0187195	+	0.751430i
$993$		0			0
$994$	−1.63690	+	0.844340i	−0.0519194	+	0.0267808i
$995$	21.9302	−	1.74472i	0.695234	−	0.0553114i
$996$		0			0
$997$		−	54.9379i		−	1.73990i	−0.493138	−	0.869951i	$-0.664150\pi$
$997$		−	54.9379i		−	1.73990i	0.493138	−	0.869951i	$-0.335850\pi$
$998$	7.49449	+	14.5294i	0.237234	+	0.459919i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.g.667.5		18
3.2	odd	2		80.2.s.b.27.5	yes	18
5.3	odd	4		720.2.bd.g.523.9		18
12.11	even	2		320.2.s.b.207.9		18
15.2	even	4		400.2.j.d.43.9		18
15.8	even	4		80.2.j.b.43.1	✓	18
15.14	odd	2		400.2.s.d.107.5		18
16.3	odd	4		720.2.bd.g.307.9		18
24.5	odd	2		640.2.s.d.287.9		18
24.11	even	2		640.2.s.c.287.1		18
48.5	odd	4		640.2.j.c.607.9		18
48.11	even	4		640.2.j.d.607.1		18
48.29	odd	4		320.2.j.b.47.1		18
48.35	even	4		80.2.j.b.67.1	yes	18
60.23	odd	4		320.2.j.b.143.9		18
60.47	odd	4		1600.2.j.d.143.1		18
60.59	even	2		1600.2.s.d.207.1		18
80.3	even	4	inner	720.2.z.g.163.5		18
120.53	even	4		640.2.j.d.543.9		18
120.83	odd	4		640.2.j.c.543.1		18
240.29	odd	4		1600.2.j.d.1007.9		18
240.53	even	4		640.2.s.c.223.1		18
240.77	even	4		1600.2.s.d.943.1		18
240.83	odd	4		80.2.s.b.3.5	yes	18
240.173	even	4		320.2.s.b.303.9		18
240.179	even	4		400.2.j.d.307.9		18
240.203	odd	4		640.2.s.d.223.9		18
240.227	odd	4		400.2.s.d.243.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.1	✓	18	15.8	even	4
80.2.j.b.67.1	yes	18	48.35	even	4
80.2.s.b.3.5	yes	18	240.83	odd	4
80.2.s.b.27.5	yes	18	3.2	odd	2
320.2.j.b.47.1		18	48.29	odd	4
320.2.j.b.143.9		18	60.23	odd	4
320.2.s.b.207.9		18	12.11	even	2
320.2.s.b.303.9		18	240.173	even	4
400.2.j.d.43.9		18	15.2	even	4
400.2.j.d.307.9		18	240.179	even	4
400.2.s.d.107.5		18	15.14	odd	2
400.2.s.d.243.5		18	240.227	odd	4
640.2.j.c.543.1		18	120.83	odd	4
640.2.j.c.607.9		18	48.5	odd	4
640.2.j.d.543.9		18	120.53	even	4
640.2.j.d.607.1		18	48.11	even	4
640.2.s.c.223.1		18	240.53	even	4
640.2.s.c.287.1		18	24.11	even	2
640.2.s.d.223.9		18	240.203	odd	4
640.2.s.d.287.9		18	24.5	odd	2
720.2.z.g.163.5		18	80.3	even	4	inner
720.2.z.g.667.5		18	1.1	even	1	trivial
720.2.bd.g.307.9		18	16.3	odd	4
720.2.bd.g.523.9		18	5.3	odd	4
1600.2.j.d.143.1		18	60.47	odd	4
1600.2.j.d.1007.9		18	240.29	odd	4
1600.2.s.d.207.1		18	60.59	even	2
1600.2.s.d.943.1		18	240.77	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.430311 + 1.34716i) q^{2} +(-1.62967 - 1.15939i) q^{4} +(0.177336 + 2.22902i) q^{5} +(-0.115101 - 0.115101i) q^{7} +(2.26315 - 1.69652i) q^{8} +O(q^{10})\)	\(q+(-0.430311 + 1.34716i) q^{2} +(-1.62967 - 1.15939i) q^{4} +(0.177336 + 2.22902i) q^{5} +(-0.115101 - 0.115101i) q^{7} +(2.26315 - 1.69652i) q^{8} +(-3.07916 - 0.720273i) q^{10} +(-2.95966 + 2.95966i) q^{11} -1.55822i q^{13} +(0.204588 - 0.105530i) q^{14} +(1.31162 + 3.77884i) q^{16} +(-0.299668 - 0.299668i) q^{17} +(-2.26261 + 2.26261i) q^{19} +(2.29532 - 3.83817i) q^{20} +(-2.71356 - 5.26071i) q^{22} +(-4.14573 + 4.14573i) q^{23} +(-4.93710 + 0.790575i) q^{25} +(2.09917 + 0.670518i) q^{26} +(0.0541288 + 0.321023i) q^{28} +(-0.289656 - 0.289656i) q^{29} -4.18508i q^{31} +(-5.65510 + 0.140879i) q^{32} +(0.532650 - 0.274749i) q^{34} +(0.236151 - 0.276974i) q^{35} +1.63643i q^{37} +(-2.07447 - 4.02172i) q^{38} +(4.18292 + 4.74376i) q^{40} -7.61648i q^{41} +6.72651i q^{43} +(8.25467 - 1.39185i) q^{44} +(-3.80100 - 7.36890i) q^{46} +(-4.38366 + 4.38366i) q^{47} -6.97350i q^{49} +(1.05946 - 6.99125i) q^{50} +(-1.80659 + 2.53938i) q^{52} -11.4324 q^{53} +(-7.12202 - 6.07231i) q^{55} +(-0.455760 - 0.0652196i) q^{56} +(0.514854 - 0.265570i) q^{58} +(-1.63497 - 1.63497i) q^{59} +(-1.23034 + 1.23034i) q^{61} +(5.63796 + 1.80089i) q^{62} +(2.24366 - 7.67893i) q^{64} +(3.47331 - 0.276329i) q^{65} +2.49337i q^{67} +(0.140926 + 0.835791i) q^{68} +(0.271509 + 0.437317i) q^{70} -8.00096 q^{71} +(-1.12102 - 1.12102i) q^{73} +(-2.20453 - 0.704173i) q^{74} +(6.31056 - 1.06405i) q^{76} +0.681319 q^{77} +3.62218 q^{79} +(-8.19054 + 3.59376i) q^{80} +(10.2606 + 3.27745i) q^{82} -1.62629 q^{83} +(0.614825 - 0.721109i) q^{85} +(-9.06167 - 2.89449i) q^{86} +(-1.67703 + 11.7193i) q^{88} +15.7149 q^{89} +(-0.179352 + 0.179352i) q^{91} +(11.5627 - 1.94962i) q^{92} +(-4.01915 - 7.79182i) q^{94} +(-5.44467 - 4.64218i) q^{95} +(9.69217 + 9.69217i) q^{97} +(9.39441 + 3.00077i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

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