LMFDB - Embedded newform 840.2.g.d.421.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(421,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.421"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 2 x^{13} + x^{12} - 8 x^{10} + 24 x^{9} - 32 x^{8} + 48 x^{7} + \cdots + 256 $ x^16 - 2x^15 + 2x^14 - 2x^13 + x^12 - 8x^10 + 24x^9 - 32x^8 + 48x^7 - 32x^6 + 16x^4 - 64x^3 + 128x^2 - 256x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			421.7
Root			$1.37218 - 0.342246i$ of defining polynomial
Character	$\chi$	$=$	840.421
Dual form			840.2.g.d.421.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.342246 - 1.37218i) q^{2} -1.00000i q^{3} +(-1.76574 + 0.939244i) q^{4} +1.00000i q^{5} +(-1.37218 + 0.342246i) q^{6} -1.00000 q^{7} +(1.89312 + 2.10145i) q^{8} -1.00000 q^{9} +(1.37218 - 0.342246i) q^{10} -4.47074i q^{11} +(0.939244 + 1.76574i) q^{12} -4.04157i q^{13} +(0.342246 + 1.37218i) q^{14} +1.00000 q^{15} +(2.23564 - 3.31691i) q^{16} +0.406877 q^{17} +(0.342246 + 1.37218i) q^{18} +1.45854i q^{19} +(-0.939244 - 1.76574i) q^{20} +1.00000i q^{21} +(-6.13464 + 1.53009i) q^{22} -7.46982 q^{23} +(2.10145 - 1.89312i) q^{24} -1.00000 q^{25} +(-5.54575 + 1.38321i) q^{26} +1.00000i q^{27} +(1.76574 - 0.939244i) q^{28} +10.3578i q^{29} +(-0.342246 - 1.37218i) q^{30} -8.18358 q^{31} +(-5.31653 - 1.93250i) q^{32} -4.47074 q^{33} +(-0.139252 - 0.558307i) q^{34} -1.00000i q^{35} +(1.76574 - 0.939244i) q^{36} -3.35010i q^{37} +(2.00138 - 0.499181i) q^{38} -4.04157 q^{39} +(-2.10145 + 1.89312i) q^{40} -8.85021 q^{41} +(1.37218 - 0.342246i) q^{42} +0.733692i q^{43} +(4.19911 + 7.89414i) q^{44} -1.00000i q^{45} +(2.55652 + 10.2499i) q^{46} -1.71284 q^{47} +(-3.31691 - 2.23564i) q^{48} +1.00000 q^{49} +(0.342246 + 1.37218i) q^{50} -0.406877i q^{51} +(3.79602 + 7.13634i) q^{52} -1.37002i q^{53} +(1.37218 - 0.342246i) q^{54} +4.47074 q^{55} +(-1.89312 - 2.10145i) q^{56} +1.45854 q^{57} +(14.2127 - 3.54492i) q^{58} -8.61466i q^{59} +(-1.76574 + 0.939244i) q^{60} +6.60083i q^{61} +(2.80080 + 11.2293i) q^{62} +1.00000 q^{63} +(-0.832167 + 7.95660i) q^{64} +4.04157 q^{65} +(1.53009 + 6.13464i) q^{66} -14.5631i q^{67} +(-0.718437 + 0.382156i) q^{68} +7.46982i q^{69} +(-1.37218 + 0.342246i) q^{70} -15.1696 q^{71} +(-1.89312 - 2.10145i) q^{72} +7.02763 q^{73} +(-4.59692 + 1.14656i) q^{74} +1.00000i q^{75} +(-1.36993 - 2.57540i) q^{76} +4.47074i q^{77} +(1.38321 + 5.54575i) q^{78} +11.0077 q^{79} +(3.31691 + 2.23564i) q^{80} +1.00000 q^{81} +(3.02895 + 12.1440i) q^{82} -5.72787i q^{83} +(-0.939244 - 1.76574i) q^{84} +0.406877i q^{85} +(1.00675 - 0.251103i) q^{86} +10.3578 q^{87} +(9.39503 - 8.46366i) q^{88} -12.6985 q^{89} +(-1.37218 + 0.342246i) q^{90} +4.04157i q^{91} +(13.1897 - 7.01598i) q^{92} +8.18358i q^{93} +(0.586214 + 2.35032i) q^{94} -1.45854 q^{95} +(-1.93250 + 5.31653i) q^{96} -3.29679 q^{97} +(-0.342246 - 1.37218i) q^{98} +4.47074i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{6} - 16 q^{7} - 2 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{14} + 16 q^{15} + 4 q^{16} + 2 q^{18} + 2 q^{24} - 16 q^{25} - 2 q^{30} - 2 q^{32} + 24 q^{34} - 28 q^{38} - 2 q^{40} + 2 q^{42}+ \cdots - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^6 - 16 * q^7 - 2 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^14 + 16 * q^15 + 4 * q^16 + 2 * q^18 + 2 * q^24 - 16 * q^25 - 2 * q^30 - 2 * q^32 + 24 * q^34 - 28 * q^38 - 2 * q^40 + 2 * q^42 + 8 * q^44 - 36 * q^46 + 32 * q^47 + 16 * q^49 + 2 * q^50 + 4 * q^52 + 2 * q^54 + 2 * q^56 + 32 * q^58 - 12 * q^62 + 16 * q^63 - 48 * q^64 + 28 * q^66 + 56 * q^68 - 2 * q^70 - 64 * q^71 + 2 * q^72 + 24 * q^74 + 8 * q^76 - 24 * q^78 + 48 * q^79 + 16 * q^81 + 4 * q^82 - 36 * q^86 - 16 * q^87 - 2 * q^90 + 80 * q^92 - 44 * q^94 - 2 * q^96 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$1$	$1$	$1$	$-1$	$1$

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 $

$2$	−0.342246	−	1.37218i	−0.242004	−	0.970275i
$2$	−0.342246	−	1.37218i	−0.242004	−	0.970275i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.76574	+	0.939244i	−0.882868	+	0.469622i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.37218	+	0.342246i	−0.560189	+	0.139721i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	1.89312	+	2.10145i	0.669320	+	0.742974i
$9$	−1.00000			−0.333333
$10$	1.37218	−	0.342246i	0.433920	−	0.108228i
$11$		−	4.47074i		−	1.34798i	−0.738741	−	0.673989i	$-0.764579\pi$
$11$		−	4.47074i		−	1.34798i	0.738741	−	0.673989i	$-0.235421\pi$
$12$	0.939244	+	1.76574i	0.271136	+	0.509724i
$13$		−	4.04157i		−	1.12093i	−0.828178	−	0.560465i	$-0.810622\pi$
$13$		−	4.04157i		−	1.12093i	0.828178	−	0.560465i	$-0.189378\pi$
$14$	0.342246	+	1.37218i	0.0914691	+	0.366730i
$15$	1.00000			0.258199
$16$	2.23564	−	3.31691i	0.558911	−	0.829228i
$17$	0.406877			0.0986821			0.0493411	−	0.998782i	$-0.484288\pi$
$17$	0.406877			0.0986821			0.0493411	+	0.998782i	$0.484288\pi$
$18$	0.342246	+	1.37218i	0.0806681	+	0.323425i
$19$			1.45854i			0.334613i	0.985905	+	0.167306i	$0.0535069\pi$
$19$			1.45854i			0.334613i	−0.985905	+	0.167306i	$0.946493\pi$
$20$	−0.939244	−	1.76574i	−0.210021	−	0.394830i
$21$			1.00000i			0.218218i
$22$	−6.13464	+	1.53009i	−1.30791	+	0.326217i
$23$	−7.46982			−1.55756			−0.778782	−	0.627294i	$-0.784162\pi$
$23$	−7.46982			−1.55756			−0.778782	+	0.627294i	$0.784162\pi$
$24$	2.10145	−	1.89312i	0.428956	−	0.386432i
$25$	−1.00000			−0.200000
$26$	−5.54575	+	1.38321i	−1.08761	+	0.271270i
$27$			1.00000i			0.192450i
$28$	1.76574	−	0.939244i	0.333693	−	0.177500i
$29$			10.3578i			1.92340i	0.274112	+	0.961698i	$0.411616\pi$
$29$			10.3578i			1.92340i	−0.274112	+	0.961698i	$0.588384\pi$
$30$	−0.342246	−	1.37218i	−0.0624853	−	0.250524i
$31$	−8.18358			−1.46981			−0.734907	−	0.678167i	$-0.762774\pi$
$31$	−8.18358			−1.46981			−0.734907	+	0.678167i	$0.762774\pi$
$32$	−5.31653	−	1.93250i	−0.939838	−	0.341620i
$33$	−4.47074			−0.778256
$34$	−0.139252	−	0.558307i	−0.0238815	−	0.0957488i
$35$		−	1.00000i		−	0.169031i
$36$	1.76574	−	0.939244i	0.294289	−	0.156541i
$37$		−	3.35010i		−	0.550753i	−0.961337	−	0.275376i	$-0.911198\pi$
$37$		−	3.35010i		−	0.550753i	0.961337	−	0.275376i	$-0.0888024\pi$
$38$	2.00138	−	0.499181i	0.324666	−	0.0809778i
$39$	−4.04157			−0.647169
$40$	−2.10145	+	1.89312i	−0.332268	+	0.299329i
$41$	−8.85021			−1.38217			−0.691085	−	0.722773i	$-0.742867\pi$
$41$	−8.85021			−1.38217			−0.691085	+	0.722773i	$0.742867\pi$
$42$	1.37218	−	0.342246i	0.211731	−	0.0528097i
$43$			0.733692i			0.111887i	0.998434	+	0.0559435i	$0.0178167\pi$
$43$			0.733692i			0.111887i	−0.998434	+	0.0559435i	$0.982183\pi$
$44$	4.19911	+	7.89414i	0.633040	+	1.19009i
$45$		−	1.00000i		−	0.149071i
$46$	2.55652	+	10.2499i	0.376938	+	1.51127i
$47$	−1.71284			−0.249844			−0.124922	−	0.992167i	$-0.539868\pi$
$47$	−1.71284			−0.249844			−0.124922	+	0.992167i	$0.539868\pi$
$48$	−3.31691	−	2.23564i	−0.478755	−	0.322687i
$49$	1.00000			0.142857
$50$	0.342246	+	1.37218i	0.0484009	+	0.194055i
$51$		−	0.406877i		−	0.0569742i
$52$	3.79602	+	7.13634i	0.526413	+	0.989633i
$53$		−	1.37002i		−	0.188187i	−0.995563	−	0.0940936i	$-0.970005\pi$
$53$		−	1.37002i		−	0.188187i	0.995563	−	0.0940936i	$-0.0299953\pi$
$54$	1.37218	−	0.342246i	0.186730	−	0.0465738i
$55$	4.47074			0.602834
$56$	−1.89312	−	2.10145i	−0.252979	−	0.280818i
$57$	1.45854			0.193189
$58$	14.2127	−	3.54492i	1.86622	−	0.465470i
$59$		−	8.61466i		−	1.12153i	−0.827974	−	0.560767i	$-0.810506\pi$
$59$		−	8.61466i		−	1.12153i	0.827974	−	0.560767i	$-0.189494\pi$
$60$	−1.76574	+	0.939244i	−0.227955	+	0.121256i
$61$			6.60083i			0.845149i	0.906328	+	0.422575i	$0.138874\pi$
$61$			6.60083i			0.845149i	−0.906328	+	0.422575i	$0.861126\pi$
$62$	2.80080	+	11.2293i	0.355702	+	1.42612i
$63$	1.00000			0.125988
$64$	−0.832167	+	7.95660i	−0.104021	+	0.994575i
$65$	4.04157			0.501295
$66$	1.53009	+	6.13464i	0.188341	+	0.755122i
$67$		−	14.5631i		−	1.77916i	−0.456779	−	0.889580i	$-0.650997\pi$
$67$		−	14.5631i		−	1.77916i	0.456779	−	0.889580i	$-0.349003\pi$
$68$	−0.718437	+	0.382156i	−0.0871233	+	0.0463433i
$69$			7.46982i			0.899260i
$70$	−1.37218	+	0.342246i	−0.164006	+	0.0409062i
$71$	−15.1696			−1.80031			−0.900153	−	0.435574i	$-0.856545\pi$
$71$	−15.1696			−1.80031			−0.900153	+	0.435574i	$0.856545\pi$
$72$	−1.89312	−	2.10145i	−0.223107	−	0.247658i
$73$	7.02763			0.822522			0.411261	−	0.911518i	$-0.365088\pi$
$73$	7.02763			0.822522			0.411261	+	0.911518i	$0.365088\pi$
$74$	−4.59692	+	1.14656i	−0.534382	+	0.133285i
$75$			1.00000i			0.115470i
$76$	−1.36993	−	2.57540i	−0.157141	−	0.295419i
$77$			4.47074i			0.509488i
$78$	1.38321	+	5.54575i	0.156618	+	0.627932i
$79$	11.0077			1.23846			0.619232	−	0.785208i	$-0.287444\pi$
$79$	11.0077			1.23846			0.619232	+	0.785208i	$0.287444\pi$
$80$	3.31691	+	2.23564i	0.370842	+	0.249953i
$81$	1.00000			0.111111
$82$	3.02895	+	12.1440i	0.334491	+	1.34109i
$83$		−	5.72787i		−	0.628716i	−0.949305	−	0.314358i	$-0.898211\pi$
$83$		−	5.72787i		−	0.628716i	0.949305	−	0.314358i	$-0.101789\pi$
$84$	−0.939244	−	1.76574i	−0.102480	−	0.192658i
$85$			0.406877i			0.0441320i
$86$	1.00675	−	0.251103i	0.108561	−	0.0270771i
$87$	10.3578			1.11047
$88$	9.39503	−	8.46366i	1.00151	−	0.902229i
$89$	−12.6985			−1.34603			−0.673017	−	0.739627i	$-0.735002\pi$
$89$	−12.6985			−1.34603			−0.673017	+	0.739627i	$0.735002\pi$
$90$	−1.37218	+	0.342246i	−0.144640	+	0.0360759i
$91$			4.04157i			0.423672i
$92$	13.1897	−	7.01598i	1.37512	−	0.731466i
$93$			8.18358i			0.848598i
$94$	0.586214	+	2.35032i	0.0604634	+	0.242417i
$95$	−1.45854			−0.149643
$96$	−1.93250	+	5.31653i	−0.197235	+	0.542616i
$97$	−3.29679			−0.334739			−0.167369	−	0.985894i	$-0.553527\pi$
$97$	−3.29679			−0.334739			−0.167369	+	0.985894i	$0.553527\pi$
$98$	−0.342246	−	1.37218i	−0.0345721	−	0.138611i
$99$			4.47074i			0.449326i
$100$	1.76574	−	0.939244i	0.176574	−	0.0939244i
$101$		−	10.1105i		−	1.00603i	−0.864277	−	0.503016i	$-0.832224\pi$
$101$		−	10.1105i		−	1.00603i	0.864277	−	0.503016i	$-0.167776\pi$
$102$	−0.558307	+	0.139252i	−0.0552806	+	0.0137880i
$103$	6.82111			0.672104			0.336052	−	0.941843i	$-0.390908\pi$
$103$	6.82111			0.672104			0.336052	+	0.941843i	$0.390908\pi$
$104$	8.49315	−	7.65119i	0.832822	−	0.750261i
$105$	−1.00000			−0.0975900
$106$	−1.87991	+	0.468885i	−0.182593	+	0.0455422i
$107$			3.55654i			0.343824i	0.985112	+	0.171912i	$0.0549945\pi$
$107$			3.55654i			0.343824i	−0.985112	+	0.171912i	$0.945006\pi$
$108$	−0.939244	−	1.76574i	−0.0903788	−	0.169908i
$109$		−	5.86714i		−	0.561970i	−0.959712	−	0.280985i	$-0.909339\pi$
$109$		−	5.86714i		−	0.561970i	0.959712	−	0.280985i	$-0.0906611\pi$
$110$	−1.53009	−	6.13464i	−0.145889	−	0.584915i
$111$	−3.35010			−0.317977
$112$	−2.23564	+	3.31691i	−0.211248	+	0.313419i
$113$	−1.09580			−0.103084			−0.0515419	−	0.998671i	$-0.516414\pi$
$113$	−1.09580			−0.103084			−0.0515419	+	0.998671i	$0.516414\pi$
$114$	−0.499181	−	2.00138i	−0.0467525	−	0.187446i
$115$		−	7.46982i		−	0.696564i
$116$	−9.72850	−	18.2891i	−0.903268	−	1.69810i
$117$			4.04157i			0.373643i
$118$	−11.8208	+	2.94833i	−1.08820	+	0.271416i
$119$	−0.406877			−0.0372983
$120$	1.89312	+	2.10145i	0.172818	+	0.191835i
$121$	−8.98751			−0.817046
$122$	9.05750	−	2.25911i	0.820028	−	0.204530i
$123$			8.85021i			0.797997i
$124$	14.4500	−	7.68638i	1.29765	−	0.690257i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.342246	−	1.37218i	−0.0304897	−	0.122243i
$127$	19.5015			1.73047			0.865237	−	0.501363i	$-0.167168\pi$
$127$	19.5015			1.73047			0.865237	+	0.501363i	$0.167168\pi$
$128$	11.2027	−	1.58123i	0.990185	−	0.139763i
$129$	0.733692			0.0645979
$130$	−1.38321	−	5.54575i	−0.121316	−	0.486394i
$131$		−	3.87854i		−	0.338869i	−0.985541	−	0.169435i	$-0.945806\pi$
$131$		−	3.87854i		−	0.338869i	0.985541	−	0.169435i	$-0.0541942\pi$
$132$	7.89414	−	4.19911i	0.687097	−	0.365486i
$133$		−	1.45854i		−	0.126472i
$134$	−19.9831	+	4.98415i	−1.72628	+	0.430565i
$135$	−1.00000			−0.0860663
$136$	0.770268	+	0.855031i	0.0660500	+	0.0733183i
$137$	4.38222			0.374398			0.187199	−	0.982322i	$-0.440059\pi$
$137$	4.38222			0.374398			0.187199	+	0.982322i	$0.440059\pi$
$138$	10.2499	−	2.55652i	0.872530	−	0.217625i
$139$			6.01555i			0.510232i	0.966910	+	0.255116i	$0.0821137\pi$
$139$			6.01555i			0.510232i	−0.966910	+	0.255116i	$0.917886\pi$
$140$	0.939244	+	1.76574i	0.0793806	+	0.149232i
$141$			1.71284i			0.144248i
$142$	5.19175	+	20.8154i	0.435682	+	1.74679i
$143$	−18.0688			−1.51099
$144$	−2.23564	+	3.31691i	−0.186304	+	0.276409i
$145$	−10.3578			−0.860169
$146$	−2.40518	−	9.64315i	−0.199054	−	0.798073i
$147$		−	1.00000i		−	0.0824786i
$148$	3.14656	+	5.91539i	0.258645	+	0.486242i
$149$			22.8286i			1.87019i	0.354391	+	0.935097i	$0.384688\pi$
$149$			22.8286i			1.87019i	−0.354391	+	0.935097i	$0.615312\pi$
$150$	1.37218	−	0.342246i	0.112038	−	0.0279443i
$151$	−4.76642			−0.387886			−0.193943	−	0.981013i	$-0.562128\pi$
$151$	−4.76642			−0.387886			−0.193943	+	0.981013i	$0.562128\pi$
$152$	−3.06505	+	2.76120i	−0.248609	+	0.223963i
$153$	−0.406877			−0.0328940
$154$	6.13464	−	1.53009i	0.494344	−	0.123298i
$155$		−	8.18358i		−	0.657321i
$156$	7.13634	−	3.79602i	0.571365	−	0.303925i
$157$			6.28285i			0.501426i	0.968061	+	0.250713i	$0.0806651\pi$
$157$			6.28285i			0.501426i	−0.968061	+	0.250713i	$0.919335\pi$
$158$	−3.76734	−	15.1045i	−0.299714	−	1.20165i
$159$	−1.37002			−0.108650
$160$	1.93250	−	5.31653i	0.152777	−	0.420308i
$161$	7.46982			0.588704
$162$	−0.342246	−	1.37218i	−0.0268894	−	0.107808i
$163$		−	23.3643i		−	1.83003i	−0.403415	−	0.915017i	$-0.632177\pi$
$163$		−	23.3643i		−	1.83003i	0.403415	−	0.915017i	$-0.367823\pi$
$164$	15.6271	−	8.31250i	1.22027	−	0.649097i
$165$		−	4.47074i		−	0.348047i
$166$	−7.85965	+	1.96034i	−0.610027	+	0.152152i
$167$	−18.1409			−1.40379			−0.701893	−	0.712282i	$-0.747661\pi$
$167$	−18.1409			−1.40379			−0.701893	+	0.712282i	$0.747661\pi$
$168$	−2.10145	+	1.89312i	−0.162130	+	0.146058i
$169$	−3.33429			−0.256484
$170$	0.558307	−	0.139252i	0.0428202	−	0.0106801i
$171$		−	1.45854i		−	0.111538i
$172$	−0.689115	−	1.29551i	−0.0525445	−	0.0987813i
$173$			0.894269i			0.0679900i	0.999422	+	0.0339950i	$0.0108230\pi$
$173$			0.894269i			0.0679900i	−0.999422	+	0.0339950i	$0.989177\pi$
$174$	−3.54492	−	14.2127i	−0.268739	−	1.07746i
$175$	1.00000			0.0755929
$176$	−14.8290	−	9.99498i	−1.11778	−	0.753400i
$177$	−8.61466			−0.647518
$178$	4.34599	+	17.4245i	0.325746	+	1.30602i
$179$			8.25385i			0.616921i	0.951237	+	0.308461i	$0.0998138\pi$
$179$			8.25385i			0.616921i	−0.951237	+	0.308461i	$0.900186\pi$
$180$	0.939244	+	1.76574i	0.0700071	+	0.131610i
$181$		−	8.50431i		−	0.632120i	−0.948739	−	0.316060i	$-0.897640\pi$
$181$		−	8.50431i		−	0.632120i	0.948739	−	0.316060i	$-0.102360\pi$
$182$	5.54575	−	1.38321i	0.411078	−	0.102530i
$183$	6.60083			0.487947
$184$	−14.1413	−	15.6974i	−1.04251	−	1.15723i
$185$	3.35010			0.246304
$186$	11.2293	−	2.80080i	0.823374	−	0.205364i
$187$		−	1.81904i		−	0.133021i
$188$	3.02443	−	1.60878i	0.220579	−	0.117332i
$189$		−	1.00000i		−	0.0727393i
$190$	0.499181	+	2.00138i	0.0362144	+	0.145195i
$191$	20.3803			1.47467			0.737333	−	0.675530i	$-0.236085\pi$
$191$	20.3803			1.47467			0.737333	+	0.675530i	$0.236085\pi$
$192$	7.95660	+	0.832167i	0.574218	+	0.0600565i
$193$	17.1450			1.23412			0.617062	−	0.786915i	$-0.288323\pi$
$193$	17.1450			1.23412			0.617062	+	0.786915i	$0.288323\pi$
$194$	1.12831	+	4.52378i	0.0810082	+	0.324788i
$195$		−	4.04157i		−	0.289423i
$196$	−1.76574	+	0.939244i	−0.126124	+	0.0670888i
$197$		−	15.6168i		−	1.11265i	−0.830964	−	0.556326i	$-0.812210\pi$
$197$		−	15.6168i		−	1.11265i	0.830964	−	0.556326i	$-0.187790\pi$
$198$	6.13464	−	1.53009i	0.435970	−	0.108739i
$199$	−3.08580			−0.218747			−0.109373	−	0.994001i	$-0.534884\pi$
$199$	−3.08580			−0.218747			−0.109373	+	0.994001i	$0.534884\pi$
$200$	−1.89312	−	2.10145i	−0.133864	−	0.148595i
$201$	−14.5631			−1.02720
$202$	−13.8734	+	3.46028i	−0.976128	+	0.243464i
$203$		−	10.3578i		−	0.726975i
$204$	0.382156	+	0.718437i	0.0267563	+	0.0503006i
$205$		−	8.85021i		−	0.618126i
$206$	−2.33450	−	9.35976i	−0.162652	−	0.652126i
$207$	7.46982			0.519188
$208$	−13.4055	−	9.03551i	−0.929506	−	0.626500i
$209$	6.52077			0.451051
$210$	0.342246	+	1.37218i	0.0236172	+	0.0946892i
$211$		−	19.1140i		−	1.31587i	−0.753077	−	0.657933i	$-0.771431\pi$
$211$		−	19.1140i		−	1.31587i	0.753077	−	0.657933i	$-0.228569\pi$
$212$	1.28679	+	2.41910i	0.0883768	+	0.166144i
$213$			15.1696i			1.03941i
$214$	4.88020	−	1.21721i	0.333604	−	0.0832069i
$215$	−0.733692			−0.0500374
$216$	−2.10145	+	1.89312i	−0.142985	+	0.128811i
$217$	8.18358			0.555538
$218$	−8.05075	+	2.00800i	−0.545265	+	0.135999i
$219$		−	7.02763i		−	0.474883i
$220$	−7.89414	+	4.19911i	−0.532223	+	0.283104i
$221$		−	1.64442i		−	0.110616i
$222$	1.14656	+	4.59692i	0.0769519	+	0.308525i
$223$	−0.120914			−0.00809701			−0.00404850	−	0.999992i	$-0.501289\pi$
$223$	−0.120914			−0.00809701			−0.00404850	+	0.999992i	$0.501289\pi$
$224$	5.31653	+	1.93250i	0.355225	+	0.129120i
$225$	1.00000			0.0666667
$226$	0.375032	+	1.50363i	0.0249467	+	0.100020i
$227$		−	20.5673i		−	1.36510i	−0.730838	−	0.682551i	$-0.760871\pi$
$227$		−	20.5673i		−	1.36510i	0.730838	−	0.682551i	$-0.239129\pi$
$228$	−2.57540	+	1.36993i	−0.170560	+	0.0907257i
$229$			10.7194i			0.708355i	0.935178	+	0.354178i	$0.115239\pi$
$229$			10.7194i			0.708355i	−0.935178	+	0.354178i	$0.884761\pi$
$230$	−10.2499	+	2.55652i	−0.675859	+	0.168572i
$231$	4.47074			0.294153
$232$	−21.7664	+	19.6086i	−1.42903	+	1.28737i
$233$	−8.18606			−0.536287			−0.268143	−	0.963379i	$-0.586410\pi$
$233$	−8.18606			−0.536287			−0.268143	+	0.963379i	$0.586410\pi$
$234$	5.54575	−	1.38321i	0.362537	−	0.0904233i
$235$		−	1.71284i		−	0.111734i
$236$	8.09127	+	15.2112i	0.526697	+	0.990166i
$237$		−	11.0077i		−	0.715027i
$238$	0.139252	+	0.558307i	0.00902636	+	0.0361897i
$239$	20.0186			1.29490			0.647449	−	0.762109i	$-0.275836\pi$
$239$	20.0186			1.29490			0.647449	+	0.762109i	$0.275836\pi$
$240$	2.23564	−	3.31691i	0.144310	−	0.214106i
$241$	−15.4729			−0.996697			−0.498348	−	0.866977i	$-0.666060\pi$
$241$	−15.4729			−0.996697			−0.498348	+	0.866977i	$0.666060\pi$
$242$	3.07594	+	12.3324i	0.197729	+	0.792759i
$243$		−	1.00000i		−	0.0641500i
$244$	−6.19979	−	11.6553i	−0.396901	−	0.746155i
$245$			1.00000i			0.0638877i
$246$	12.1440	−	3.02895i	0.774276	−	0.193119i
$247$	5.89481			0.375078
$248$	−15.4925	−	17.1974i	−0.983777	−	1.09203i
$249$	−5.72787			−0.362989
$250$	−1.37218	+	0.342246i	−0.0867840	+	0.0216455i
$251$			10.6904i			0.674775i	0.941366	+	0.337388i	$0.109543\pi$
$251$			10.6904i			0.674775i	−0.941366	+	0.337388i	$0.890457\pi$
$252$	−1.76574	+	0.939244i	−0.111231	+	0.0591668i
$253$			33.3956i			2.09956i
$254$	−6.67429	−	26.7594i	−0.418782	−	1.67904i
$255$	0.406877			0.0254796
$256$	−6.00380	−	14.8309i	−0.375237	−	0.926929i
$257$	12.1810			0.759830			0.379915	−	0.925021i	$-0.375953\pi$
$257$	12.1810			0.759830			0.379915	+	0.925021i	$0.375953\pi$
$258$	−0.251103	−	1.00675i	−0.0156330	−	0.0626778i
$259$			3.35010i			0.208165i
$260$	−7.13634	+	3.79602i	−0.442577	+	0.235419i
$261$		−	10.3578i		−	0.641132i
$262$	−5.32204	+	1.32741i	−0.328796	+	0.0820079i
$263$	13.2080			0.814441			0.407221	−	0.913330i	$-0.366498\pi$
$263$	13.2080			0.814441			0.407221	+	0.913330i	$0.366498\pi$
$264$	−8.46366	−	9.39503i	−0.520902	−	0.578224i
$265$	1.37002			0.0841599
$266$	−2.00138	+	0.499181i	−0.122712	+	0.0306067i
$267$			12.6985i			0.777133i
$268$	13.6783	+	25.7145i	0.835532	+	1.57076i
$269$		−	24.8107i		−	1.51273i	−0.654147	−	0.756367i	$-0.726972\pi$
$269$		−	24.8107i		−	1.51273i	0.654147	−	0.756367i	$-0.273028\pi$
$270$	0.342246	+	1.37218i	0.0208284	+	0.0835080i
$271$	−10.3871			−0.630971			−0.315485	−	0.948930i	$-0.602167\pi$
$271$	−10.3871			−0.630971			−0.315485	+	0.948930i	$0.602167\pi$
$272$	0.909631	−	1.34957i	0.0551545	−	0.0818300i
$273$	4.04157			0.244607
$274$	−1.49980	−	6.01318i	−0.0906060	−	0.363269i
$275$			4.47074i			0.269596i
$276$	−7.01598	−	13.1897i	−0.422312	−	0.793928i
$277$		−	7.26184i		−	0.436322i	−0.975913	−	0.218161i	$-0.929994\pi$
$277$		−	7.26184i		−	0.436322i	0.975913	−	0.218161i	$-0.0700057\pi$
$278$	8.25440	−	2.05880i	0.495066	−	0.123479i
$279$	8.18358			0.489938
$280$	2.10145	−	1.89312i	0.125586	−	0.113136i
$281$	23.4123			1.39666			0.698331	−	0.715775i	$-0.253927\pi$
$281$	23.4123			1.39666			0.698331	+	0.715775i	$0.253927\pi$
$282$	2.35032	−	0.586214i	0.139960	−	0.0349085i
$283$		−	21.6138i		−	1.28481i	−0.766367	−	0.642403i	$-0.777937\pi$
$283$		−	21.6138i		−	1.28481i	0.766367	−	0.642403i	$-0.222063\pi$
$284$	26.7856	−	14.2480i	1.58943	−	0.845463i
$285$			1.45854i			0.0863967i
$286$	6.18398	+	24.7936i	0.365666	+	1.46608i
$287$	8.85021			0.522411
$288$	5.31653	+	1.93250i	0.313279	+	0.113873i
$289$	−16.8345			−0.990262
$290$	3.54492	+	14.2127i	0.208165	+	0.834600i
$291$			3.29679i			0.193261i
$292$	−12.4089	+	6.60066i	−0.726178	+	0.386274i
$293$			31.3799i			1.83323i	0.399769	+	0.916616i	$0.369090\pi$
$293$			31.3799i			1.83323i	−0.399769	+	0.916616i	$0.630910\pi$
$294$	−1.37218	+	0.342246i	−0.0800269	+	0.0199602i
$295$	8.61466			0.501565
$296$	7.04006	−	6.34215i	0.409195	−	0.368630i
$297$	4.47074			0.259419
$298$	31.3249	−	7.81301i	1.81460	−	0.452595i
$299$			30.1898i			1.74592i
$300$	−0.939244	−	1.76574i	−0.0542273	−	0.101945i
$301$		−	0.733692i		−	0.0422893i
$302$	1.63129	+	6.54037i	0.0938701	+	0.376356i
$303$	−10.1105			−0.580833
$304$	4.83786	+	3.26078i	0.277470	+	0.187019i
$305$	−6.60083			−0.377962
$306$	0.139252	+	0.558307i	0.00796050	+	0.0319163i
$307$			28.3072i			1.61558i	0.589473	+	0.807788i	$0.299335\pi$
$307$			28.3072i			1.61558i	−0.589473	+	0.807788i	$0.700665\pi$
$308$	−4.19911	−	7.89414i	−0.239267	−	0.449810i
$309$		−	6.82111i		−	0.388039i
$310$	−11.2293	+	2.80080i	−0.637782	+	0.159075i
$311$	−21.4064			−1.21384			−0.606922	−	0.794762i	$-0.707596\pi$
$311$	−21.4064			−1.21384			−0.606922	+	0.794762i	$0.707596\pi$
$312$	−7.65119	−	8.49315i	−0.433163	−	0.480830i
$313$	16.2120			0.916359			0.458179	−	0.888860i	$-0.348502\pi$
$313$	16.2120			0.916359			0.458179	+	0.888860i	$0.348502\pi$
$314$	8.62118	−	2.15028i	0.486521	−	0.121347i
$315$			1.00000i			0.0563436i
$316$	−19.4367	+	10.3389i	−1.09340	+	0.581609i
$317$			12.4683i			0.700292i	0.936695	+	0.350146i	$0.113868\pi$
$317$			12.4683i			0.700292i	−0.936695	+	0.350146i	$0.886132\pi$
$318$	0.468885	+	1.87991i	0.0262938	+	0.105420i
$319$	46.3070			2.59270
$320$	−7.95660	−	0.832167i	−0.444788	−	0.0465195i
$321$	3.55654			0.198507
$322$	−2.55652	−	10.2499i	−0.142469	−	0.571205i
$323$			0.593448i			0.0330203i
$324$	−1.76574	+	0.939244i	−0.0980964	+	0.0521802i
$325$			4.04157i			0.224186i
$326$	−32.0600	+	7.99634i	−1.77564	+	0.442876i
$327$	−5.86714			−0.324453
$328$	−16.7545	−	18.5983i	−0.925115	−	1.02692i
$329$	1.71284			0.0944322
$330$	−6.13464	+	1.53009i	−0.337701	+	0.0842288i
$331$		−	15.1175i		−	0.830935i	−0.909608	−	0.415467i	$-0.863618\pi$
$331$		−	15.1175i		−	0.830935i	0.909608	−	0.415467i	$-0.136382\pi$
$332$	5.37987	+	10.1139i	0.295259	+	0.555073i
$333$			3.35010i			0.183584i
$334$	6.20865	+	24.8925i	0.339722	+	1.36206i
$335$	14.5631			0.795665
$336$	3.31691	+	2.23564i	0.180952	+	0.121964i
$337$	−5.22053			−0.284381			−0.142190	−	0.989839i	$-0.545414\pi$
$337$	−5.22053			−0.284381			−0.142190	+	0.989839i	$0.545414\pi$
$338$	1.14115	+	4.57524i	0.0620703	+	0.248860i
$339$			1.09580i			0.0595155i
$340$	−0.382156	−	0.718437i	−0.0207253	−	0.0389627i
$341$			36.5867i			1.98128i
$342$	−2.00138	+	0.499181i	−0.108222	+	0.0269926i
$343$	−1.00000			−0.0539949
$344$	−1.54181	+	1.38897i	−0.0831291	+	0.0748882i
$345$	−7.46982			−0.402162
$346$	1.22709	−	0.306060i	0.0659690	−	0.0164539i
$347$		−	14.7015i		−	0.789220i	−0.918849	−	0.394610i	$-0.870880\pi$
$347$		−	14.7015i		−	0.789220i	0.918849	−	0.394610i	$-0.129120\pi$
$348$	−18.2891	+	9.72850i	−0.980401	+	0.521502i
$349$		−	30.0714i		−	1.60969i	−0.593487	−	0.804844i	$-0.702249\pi$
$349$		−	30.0714i		−	1.60969i	0.593487	−	0.804844i	$-0.297751\pi$
$350$	−0.342246	−	1.37218i	−0.0182938	−	0.0733459i
$351$	4.04157			0.215723
$352$	−8.63969	+	23.7688i	−0.460497	+	1.26688i
$353$	−12.4365			−0.661928			−0.330964	−	0.943643i	$-0.607374\pi$
$353$	−12.4365			−0.661928			−0.330964	+	0.943643i	$0.607374\pi$
$354$	2.94833	+	11.8208i	0.156702	+	0.628270i
$355$		−	15.1696i		−	0.805121i
$356$	22.4221	−	11.9269i	1.18837	−	0.632126i
$357$			0.406877i			0.0215342i
$358$	11.3257	−	2.82485i	0.598584	−	0.149298i
$359$	1.74003			0.0918355			0.0459178	−	0.998945i	$-0.485379\pi$
$359$	1.74003			0.0918355			0.0459178	+	0.998945i	$0.485379\pi$
$360$	2.10145	−	1.89312i	0.110756	−	0.0997764i
$361$	16.8727			0.888034
$362$	−11.6694	+	2.91056i	−0.613330	+	0.152976i
$363$			8.98751i			0.471722i
$364$	−3.79602	−	7.13634i	−0.198965	−	0.374046i
$365$			7.02763i			0.367843i
$366$	−2.25911	−	9.05750i	−0.118085	−	0.473443i
$367$	4.06059			0.211961			0.105981	−	0.994368i	$-0.466202\pi$
$367$	4.06059			0.211961			0.105981	+	0.994368i	$0.466202\pi$
$368$	−16.6998	+	24.7767i	−0.870540	+	1.29158i
$369$	8.85021			0.460724
$370$	−1.14656	−	4.59692i	−0.0596067	−	0.238983i
$371$			1.37002i			0.0711281i
$372$	−7.68638	−	14.4500i	−0.398520	−	0.749200i
$373$		−	17.2068i		−	0.890935i	−0.895298	−	0.445468i	$-0.853037\pi$
$373$		−	17.2068i		−	0.890935i	0.895298	−	0.445468i	$-0.146963\pi$
$374$	−2.49604	+	0.622559i	−0.129067	+	0.0321918i
$375$	−1.00000			−0.0516398
$376$	−3.24263	−	3.59945i	−0.167226	−	0.185628i
$377$	41.8618			2.15599
$378$	−1.37218	+	0.342246i	−0.0705771	+	0.0176032i
$379$		−	1.80158i		−	0.0925408i	−0.998929	−	0.0462704i	$-0.985266\pi$
$379$		−	1.80158i		−	0.0925408i	0.998929	−	0.0462704i	$-0.0147336\pi$
$380$	2.57540	−	1.36993i	0.132115	−	0.0702758i
$381$		−	19.5015i		−	0.999090i
$382$	−6.97507	−	27.9653i	−0.356876	−	1.43083i
$383$	−21.2791			−1.08731			−0.543655	−	0.839309i	$-0.682960\pi$
$383$	−21.2791			−1.08731			−0.543655	+	0.839309i	$0.682960\pi$
$384$	−1.58123	−	11.2027i	−0.0806920	−	0.571684i
$385$	−4.47074			−0.227850
$386$	−5.86780	−	23.5259i	−0.298663	−	1.19744i
$387$		−	0.733692i		−	0.0372956i
$388$	5.82126	−	3.09649i	0.295530	−	0.157200i
$389$			15.7874i			0.800454i	0.916416	+	0.400227i	$0.131069\pi$
$389$			15.7874i			0.800454i	−0.916416	+	0.400227i	$0.868931\pi$
$390$	−5.54575	+	1.38321i	−0.280820	+	0.0700416i
$391$	−3.03930			−0.153704
$392$	1.89312	+	2.10145i	0.0956172	+	0.106139i
$393$	−3.87854			−0.195646
$394$	−21.4290	+	5.34479i	−1.07958	+	0.269267i
$395$			11.0077i			0.553858i
$396$	−4.19911	−	7.89414i	−0.211013	−	0.396696i
$397$			0.380029i			0.0190731i	0.999955	+	0.00953655i	$0.00303562\pi$
$397$			0.380029i			0.0190731i	−0.999955	+	0.00953655i	$0.996964\pi$
$398$	1.05610	+	4.23427i	0.0529377	+	0.212245i
$399$	−1.45854			−0.0730185
$400$	−2.23564	+	3.31691i	−0.111782	+	0.165846i
$401$	23.2916			1.16313			0.581564	−	0.813501i	$-0.302441\pi$
$401$	23.2916			1.16313			0.581564	+	0.813501i	$0.302441\pi$
$402$	4.98415	+	19.9831i	0.248587	+	0.996665i
$403$			33.0745i			1.64756i
$404$	9.49622	+	17.8525i	0.472455	+	0.888194i
$405$			1.00000i			0.0496904i
$406$	−14.2127	+	3.54492i	−0.705366	+	0.175931i
$407$	−14.9774			−0.742403
$408$	0.855031	−	0.770268i	0.0423303	−	0.0381340i
$409$	−34.6481			−1.71324			−0.856620	−	0.515949i	$-0.827440\pi$
$409$	−34.6481			−1.71324			−0.856620	+	0.515949i	$0.827440\pi$
$410$	−12.1440	+	3.02895i	−0.599752	+	0.149589i
$411$		−	4.38222i		−	0.216159i
$412$	−12.0443	+	6.40668i	−0.593379	+	0.315635i
$413$			8.61466i			0.423900i
$414$	−2.55652	−	10.2499i	−0.125646	−	0.503755i
$415$	5.72787			0.281170
$416$	−7.81032	+	21.4871i	−0.382933	+	1.05349i
$417$	6.01555			0.294583
$418$	−2.23171	−	8.94764i	−0.109156	−	0.437643i
$419$			34.2871i			1.67504i	0.546409	+	0.837518i	$0.315994\pi$
$419$			34.2871i			1.67504i	−0.546409	+	0.837518i	$0.684006\pi$
$420$	1.76574	−	0.939244i	0.0861591	−	0.0458304i
$421$			13.9561i			0.680179i	0.940393	+	0.340090i	$0.110457\pi$
$421$			13.9561i			0.680179i	−0.940393	+	0.340090i	$0.889543\pi$
$422$	−26.2278	+	6.54170i	−1.27675	+	0.318445i
$423$	1.71284			0.0832813
$424$	2.87903	−	2.59362i	0.139818	−	0.125958i
$425$	−0.406877			−0.0197364
$426$	20.8154	−	5.19175i	1.00851	−	0.251541i
$427$		−	6.60083i		−	0.319436i
$428$	−3.34046	−	6.27991i	−0.161467	−	0.303551i
$429$			18.0688i			0.872370i
$430$	0.251103	+	1.00675i	0.0121093	+	0.0485500i
$431$	9.25573			0.445833			0.222916	−	0.974838i	$-0.428442\pi$
$431$	9.25573			0.445833			0.222916	+	0.974838i	$0.428442\pi$
$432$	3.31691	+	2.23564i	0.159585	+	0.107562i
$433$	−6.47062			−0.310958			−0.155479	−	0.987839i	$-0.549692\pi$
$433$	−6.47062			−0.310958			−0.155479	+	0.987839i	$0.549692\pi$
$434$	−2.80080	−	11.2293i	−0.134443	−	0.539025i
$435$			10.3578i			0.496619i
$436$	5.51067	+	10.3598i	0.263913	+	0.496145i
$437$		−	10.8951i		−	0.521181i
$438$	−9.64315	+	2.40518i	−0.460768	+	0.114924i
$439$	−28.3172			−1.35151			−0.675753	−	0.737128i	$-0.736182\pi$
$439$	−28.3172			−1.35151			−0.675753	+	0.737128i	$0.736182\pi$
$440$	8.46366	+	9.39503i	0.403489	+	0.447890i
$441$	−1.00000			−0.0476190
$442$	−2.25644	+	0.562797i	−0.107328	+	0.0267695i
$443$		−	16.8236i		−	0.799315i	−0.916664	−	0.399658i	$-0.869129\pi$
$443$		−	16.8236i		−	0.799315i	0.916664	−	0.399658i	$-0.130871\pi$
$444$	5.91539	−	3.14656i	0.280732	−	0.149329i
$445$		−	12.6985i		−	0.601964i
$446$	0.0413824	+	0.165915i	0.00195951	+	0.00785633i
$447$	22.8286			1.07976
$448$	0.832167	−	7.95660i	0.0393162	−	0.375914i
$449$	−9.97948			−0.470961			−0.235480	−	0.971879i	$-0.575666\pi$
$449$	−9.97948			−0.470961			−0.235480	+	0.971879i	$0.575666\pi$
$450$	−0.342246	−	1.37218i	−0.0161336	−	0.0646850i
$451$			39.5670i			1.86314i
$452$	1.93489	−	1.02922i	0.0910094	−	0.0484104i
$453$			4.76642i			0.223946i
$454$	−28.2220	+	7.03909i	−1.32452	+	0.330361i
$455$	−4.04157			−0.189472
$456$	2.76120	+	3.06505i	0.129305	+	0.143534i
$457$	12.5312			0.586185			0.293093	−	0.956084i	$-0.405316\pi$
$457$	12.5312			0.586185			0.293093	+	0.956084i	$0.405316\pi$
$458$	14.7088	−	3.66866i	0.687299	−	0.171425i
$459$			0.406877i			0.0189914i
$460$	7.01598	+	13.1897i	0.327122	+	0.614974i
$461$		−	25.4244i		−	1.18413i	−0.805889	−	0.592066i	$-0.798312\pi$
$461$		−	25.4244i		−	1.18413i	0.805889	−	0.592066i	$-0.201688\pi$
$462$	−1.53009	−	6.13464i	−0.0711863	−	0.285409i
$463$	−9.54185			−0.443448			−0.221724	−	0.975110i	$-0.571168\pi$
$463$	−9.54185			−0.443448			−0.221724	+	0.975110i	$0.571168\pi$
$464$	34.3559	+	23.1564i	1.59493	+	1.07501i
$465$	−8.18358			−0.379505
$466$	2.80165	+	11.2327i	0.129784	+	0.520346i
$467$		−	24.4349i		−	1.13071i	−0.824847	−	0.565356i	$-0.808739\pi$
$467$		−	24.4349i		−	1.13071i	0.824847	−	0.565356i	$-0.191261\pi$
$468$	−3.79602	−	7.13634i	−0.175471	−	0.329878i
$469$			14.5631i			0.672459i
$470$	−2.35032	+	0.586214i	−0.108412	+	0.0270400i
$471$	6.28285			0.289499
$472$	18.1033	−	16.3086i	0.833270	−	0.750665i
$473$	3.28014			0.150821
$474$	−15.1045	+	3.76734i	−0.693773	+	0.173040i
$475$		−	1.45854i		−	0.0669226i
$476$	0.718437	−	0.382156i	0.0329295	−	0.0175161i
$477$			1.37002i			0.0627291i
$478$	−6.85130	−	27.4691i	−0.313371	−	1.25641i
$479$	−29.9239			−1.36726			−0.683628	−	0.729831i	$-0.739599\pi$
$479$	−29.9239			−1.36726			−0.683628	+	0.729831i	$0.739599\pi$
$480$	−5.31653	−	1.93250i	−0.242665	−	0.0882060i
$481$	−13.5397			−0.617355
$482$	5.29554	+	21.2315i	0.241205	+	0.967070i
$483$		−	7.46982i		−	0.339889i
$484$	15.8696	−	8.44146i	0.721344	−	0.383703i
$485$		−	3.29679i		−	0.149700i
$486$	−1.37218	+	0.342246i	−0.0622432	+	0.0155246i
$487$	15.6113			0.707414			0.353707	−	0.935356i	$-0.384921\pi$
$487$	15.6113			0.707414			0.353707	+	0.935356i	$0.384921\pi$
$488$	−13.8713	+	12.4962i	−0.627924	+	0.565676i
$489$	−23.3643			−1.05657
$490$	1.37218	−	0.342246i	0.0619886	−	0.0154611i
$491$		−	2.60503i		−	0.117564i	−0.998271	−	0.0587818i	$-0.981278\pi$
$491$		−	2.60503i		−	0.117564i	0.998271	−	0.0587818i	$-0.0187216\pi$
$492$	−8.31250	−	15.6271i	−0.374757	−	0.704525i
$493$			4.21435i			0.189805i
$494$	−2.01747	−	8.08871i	−0.0907704	−	0.363928i
$495$	−4.47074			−0.200945
$496$	−18.2956	+	27.1442i	−0.821495	+	1.21881i
$497$	15.1696			0.680452
$498$	1.96034	+	7.85965i	0.0878450	+	0.352199i
$499$			32.5674i			1.45792i	0.684557	+	0.728959i	$0.259996\pi$
$499$			32.5674i			1.45792i	−0.684557	+	0.728959i	$0.740004\pi$
$500$	0.939244	+	1.76574i	0.0420042	+	0.0789661i
$501$			18.1409i			0.810476i
$502$	14.6692	−	3.65876i	0.654718	−	0.163299i
$503$	−31.1728			−1.38993			−0.694963	−	0.719045i	$-0.744579\pi$
$503$	−31.1728			−1.38993			−0.694963	+	0.719045i	$0.744579\pi$
$504$	1.89312	+	2.10145i	0.0843264	+	0.0936059i
$505$	10.1105			0.449911
$506$	45.8247	−	11.4295i	2.03715	−	0.508104i
$507$			3.33429i			0.148081i
$508$	−34.4344	+	18.3166i	−1.52778	+	0.812668i
$509$			19.4226i			0.860893i	0.902616	+	0.430446i	$0.141644\pi$
$509$			19.4226i			0.860893i	−0.902616	+	0.430446i	$0.858356\pi$
$510$	−0.139252	−	0.558307i	−0.00616618	−	0.0247222i
$511$	−7.02763			−0.310884
$512$	−18.2958	+	13.3141i	−0.808567	+	0.588404i
$513$	−1.45854			−0.0643963
$514$	−4.16890	−	16.7145i	−0.183882	−	0.737244i
$515$			6.82111i			0.300574i
$516$	−1.29551	+	0.689115i	−0.0570314	+	0.0303366i
$517$			7.65768i			0.336784i
$518$	4.59692	−	1.14656i	0.201977	−	0.0503768i
$519$	0.894269			0.0392541
$520$	7.65119	+	8.49315i	0.335527	+	0.372449i
$521$	33.5808			1.47120			0.735600	−	0.677416i	$-0.236900\pi$
$521$	33.5808			1.47120			0.735600	+	0.677416i	$0.236900\pi$
$522$	−14.2127	+	3.54492i	−0.622074	+	0.155157i
$523$			20.4177i			0.892802i	0.894833	+	0.446401i	$0.147294\pi$
$523$			20.4177i			0.892802i	−0.894833	+	0.446401i	$0.852706\pi$
$524$	3.64289	+	6.84847i	0.159140	+	0.299177i
$525$		−	1.00000i		−	0.0436436i
$526$	−4.52039	−	18.1237i	−0.197098	−	0.790232i
$527$	−3.32971			−0.145044
$528$	−9.99498	+	14.8290i	−0.434976	+	0.645351i
$529$	32.7982			1.42601
$530$	−0.468885	−	1.87991i	−0.0203671	−	0.0816583i
$531$			8.61466i			0.373845i
$532$	1.36993	+	2.57540i	0.0593939	+	0.111658i
$533$			35.7688i			1.54932i
$534$	17.4245	−	4.34599i	0.754032	−	0.188070i
$535$	−3.55654			−0.153763
$536$	30.6035	−	27.5697i	1.32187	−	1.19083i
$537$	8.25385			0.356180
$538$	−34.0446	+	8.49136i	−1.46777	+	0.366089i
$539$		−	4.47074i		−	0.192568i
$540$	1.76574	−	0.939244i	0.0759852	−	0.0404186i
$541$		−	28.7679i		−	1.23683i	−0.785853	−	0.618414i	$-0.787776\pi$
$541$		−	28.7679i		−	1.23683i	0.785853	−	0.618414i	$-0.212224\pi$
$542$	3.55494	+	14.2529i	0.152698	+	0.612215i
$543$	−8.50431			−0.364955
$544$	−2.16317	−	0.786288i	−0.0927452	−	0.0337118i
$545$	5.86714			0.251321
$546$	−1.38321	−	5.54575i	−0.0591960	−	0.237336i
$547$		−	4.86263i		−	0.207911i	−0.994582	−	0.103956i	$-0.966850\pi$
$547$		−	4.86263i		−	0.207911i	0.994582	−	0.103956i	$-0.0331500\pi$
$548$	−7.73784	+	4.11597i	−0.330544	+	0.175826i
$549$		−	6.60083i		−	0.281716i
$550$	6.13464	−	1.53009i	0.261582	−	0.0652434i
$551$	−15.1073			−0.643593
$552$	−15.6974	+	14.1413i	−0.668127	+	0.601893i
$553$	−11.0077			−0.468095
$554$	−9.96452	+	2.48533i	−0.423352	+	0.105592i
$555$		−	3.35010i		−	0.142204i
$556$	−5.65007	−	10.6219i	−0.239616	−	0.450468i
$557$		−	26.1813i		−	1.10934i	−0.832071	−	0.554669i	$-0.812845\pi$
$557$		−	26.1813i		−	1.10934i	0.832071	−	0.554669i	$-0.187155\pi$
$558$	−2.80080	−	11.2293i	−0.118567	−	0.475375i
$559$	2.96527			0.125417
$560$	−3.31691	−	2.23564i	−0.140165	−	0.0944732i
$561$	−1.81904			−0.0767999
$562$	−8.01277	−	32.1258i	−0.337998	−	1.35515i
$563$			30.1734i			1.27166i	0.771830	+	0.635829i	$0.219342\pi$
$563$			30.1734i			1.27166i	−0.771830	+	0.635829i	$0.780658\pi$
$564$	−1.60878	−	3.02443i	−0.0677418	−	0.127351i
$565$		−	1.09580i		−	0.0461005i
$566$	−29.6579	+	7.39723i	−1.24662	+	0.310929i
$567$	−1.00000			−0.0419961
$568$	−28.7180	−	31.8782i	−1.20498	−	1.33758i
$569$	−31.7447			−1.33081			−0.665404	−	0.746483i	$-0.731741\pi$
$569$	−31.7447			−1.33081			−0.665404	+	0.746483i	$0.731741\pi$
$570$	2.00138	−	0.499181i	0.0838285	−	0.0209084i
$571$			18.7801i			0.785923i	0.919555	+	0.392961i	$0.128549\pi$
$571$			18.7801i			0.785923i	−0.919555	+	0.392961i	$0.871451\pi$
$572$	31.9047	−	16.9710i	1.33400	−	0.709594i
$573$		−	20.3803i		−	0.851399i
$574$	−3.02895	−	12.1440i	−0.126426	−	0.506883i
$575$	7.46982			0.311513
$576$	0.832167	−	7.95660i	0.0346736	−	0.331525i
$577$	5.94472			0.247482			0.123741	−	0.992315i	$-0.460511\pi$
$577$	5.94472			0.247482			0.123741	+	0.992315i	$0.460511\pi$
$578$	5.76152	+	23.0998i	0.239648	+	0.960826i
$579$		−	17.1450i		−	0.712521i
$580$	18.2891	−	9.72850i	0.759415	−	0.403954i
$581$			5.72787i			0.237632i
$582$	4.52378	−	1.12831i	0.187517	−	0.0467701i
$583$	−6.12502			−0.253672
$584$	13.3042	+	14.7682i	0.550531	+	0.611113i
$585$	−4.04157			−0.167098
$586$	43.0587	−	10.7396i	1.77874	−	0.443650i
$587$			15.8477i			0.654103i	0.945006	+	0.327052i	$0.106055\pi$
$587$			15.8477i			0.654103i	−0.945006	+	0.327052i	$0.893945\pi$
$588$	0.939244	+	1.76574i	0.0387338	+	0.0728177i
$589$		−	11.9361i		−	0.491819i
$590$	−2.94833	−	11.8208i	−0.121381	−	0.486656i
$591$	−15.6168			−0.642390
$592$	−11.1120	−	7.48962i	−0.456699	−	0.307822i
$593$	31.5774			1.29673			0.648363	−	0.761331i	$-0.275454\pi$
$593$	31.5774			1.29673			0.648363	+	0.761331i	$0.275454\pi$
$594$	−1.53009	−	6.13464i	−0.0627804	−	0.251707i
$595$		−	0.406877i		−	0.0166803i
$596$	−21.4416	−	40.3093i	−0.878284	−	1.65113i
$597$			3.08580i			0.126294i
$598$	41.4257	−	10.3323i	1.69402	−	0.422521i
$599$	−7.81904			−0.319477			−0.159739	−	0.987159i	$-0.551065\pi$
$599$	−7.81904			−0.319477			−0.159739	+	0.987159i	$0.551065\pi$
$600$	−2.10145	+	1.89312i	−0.0857913	+	0.0772864i
$601$	18.7020			0.762872			0.381436	−	0.924395i	$-0.375430\pi$
$601$	18.7020			0.762872			0.381436	+	0.924395i	$0.375430\pi$
$602$	−1.00675	+	0.251103i	−0.0410322	+	0.0102342i
$603$			14.5631i			0.593053i
$604$	8.41624	−	4.47683i	0.342452	−	0.182160i
$605$		−	8.98751i		−	0.365394i
$606$	3.46028	+	13.8734i	0.140564	+	0.563568i
$607$	−25.0133			−1.01526			−0.507628	−	0.861576i	$-0.669478\pi$
$607$	−25.0133			−1.01526			−0.507628	+	0.861576i	$0.669478\pi$
$608$	2.81863	−	7.75438i	0.114311	−	0.314482i
$609$	−10.3578			−0.419719
$610$	2.25911	+	9.05750i	0.0914686	+	0.366727i
$611$			6.92258i			0.280058i
$612$	0.718437	−	0.382156i	0.0290411	−	0.0154478i
$613$		−	29.3209i		−	1.18426i	−0.805842	−	0.592131i	$-0.798287\pi$
$613$		−	29.3209i		−	1.18426i	0.805842	−	0.592131i	$-0.201713\pi$
$614$	38.8424	−	9.68802i	1.56755	−	0.390977i
$615$	−8.85021			−0.356875
$616$	−9.39503	+	8.46366i	−0.378536	+	0.341011i
$617$	−15.5422			−0.625707			−0.312853	−	0.949801i	$-0.601285\pi$
$617$	−15.5422			−0.625707			−0.312853	+	0.949801i	$0.601285\pi$
$618$	−9.35976	+	2.33450i	−0.376505	+	0.0939072i
$619$			13.8407i			0.556303i	0.960537	+	0.278152i	$0.0897218\pi$
$619$			13.8407i			0.556303i	−0.960537	+	0.278152i	$0.910278\pi$
$620$	7.68638	+	14.4500i	0.308692	+	0.580328i
$621$		−	7.46982i		−	0.299753i
$622$	7.32624	+	29.3733i	0.293756	+	1.17776i
$623$	12.6985			0.508753
$624$	−9.03551	+	13.4055i	−0.361710	+	0.536651i
$625$	1.00000			0.0400000
$626$	−5.54850	−	22.2458i	−0.221763	−	0.889120i
$627$		−	6.52077i		−	0.260414i
$628$	−5.90113	−	11.0939i	−0.235481	−	0.442693i
$629$		−	1.36308i		−	0.0543494i
$630$	1.37218	−	0.342246i	0.0546688	−	0.0136354i
$631$	34.7681			1.38410			0.692049	−	0.721851i	$-0.256708\pi$
$631$	34.7681			1.38410			0.692049	+	0.721851i	$0.256708\pi$
$632$	20.8389	+	23.1321i	0.828929	+	0.920146i
$633$	−19.1140			−0.759715
$634$	17.1088	−	4.26724i	0.679476	−	0.169474i
$635$			19.5015i			0.773892i
$636$	2.41910	−	1.28679i	0.0959236	−	0.0510244i
$637$		−	4.04157i		−	0.160133i
$638$	−15.8484	−	63.5414i	−0.627444	−	2.51563i
$639$	15.1696			0.600102
$640$	1.58123	+	11.2027i	0.0625038	+	0.442824i
$641$	−1.92133			−0.0758878			−0.0379439	−	0.999280i	$-0.512081\pi$
$641$	−1.92133			−0.0758878			−0.0379439	+	0.999280i	$0.512081\pi$
$642$	−1.21721	−	4.88020i	−0.0480395	−	0.192606i
$643$		−	16.2575i		−	0.641134i	−0.947226	−	0.320567i	$-0.896127\pi$
$643$		−	16.2575i		−	0.641134i	0.947226	−	0.320567i	$-0.103873\pi$
$644$	−13.1897	+	7.01598i	−0.519748	+	0.276468i
$645$			0.733692i			0.0288891i
$646$	0.814315	−	0.203105i	0.0320388	−	0.00799106i
$647$	−18.1864			−0.714981			−0.357491	−	0.933917i	$-0.616368\pi$
$647$	−18.1864			−0.714981			−0.357491	+	0.933917i	$0.616368\pi$
$648$	1.89312	+	2.10145i	0.0743689	+	0.0825527i
$649$	−38.5139			−1.51180
$650$	5.54575	−	1.38321i	0.217522	−	0.0542540i
$651$		−	8.18358i		−	0.320740i
$652$	21.9448	+	41.2552i	0.859424	+	1.61568i
$653$		−	21.7325i		−	0.850457i	−0.905086	−	0.425228i	$-0.860194\pi$
$653$		−	21.7325i		−	0.850457i	0.905086	−	0.425228i	$-0.139806\pi$
$654$	2.00800	+	8.05075i	0.0785192	+	0.314809i
$655$	3.87854			0.151547
$656$	−19.7859	+	29.3554i	−0.772510	+	1.14613i
$657$	−7.02763			−0.274174
$658$	−0.586214	−	2.35032i	−0.0228530	−	0.0916252i
$659$		−	23.6212i		−	0.920153i	−0.887879	−	0.460076i	$-0.847822\pi$
$659$		−	23.6212i		−	0.920153i	0.887879	−	0.460076i	$-0.152178\pi$
$660$	4.19911	+	7.89414i	0.163450	+	0.307279i
$661$		−	25.2301i		−	0.981339i	−0.871346	−	0.490669i	$-0.836752\pi$
$661$		−	25.2301i		−	0.981339i	0.871346	−	0.490669i	$-0.163248\pi$
$662$	−20.7439	+	5.17391i	−0.806235	+	0.201090i
$663$	−1.64442			−0.0638640
$664$	12.0368	−	10.8436i	0.467119	−	0.420812i
$665$	1.45854			0.0565599
$666$	4.59692	−	1.14656i	0.178127	−	0.0444282i
$667$		−	77.3709i		−	2.99581i
$668$	32.0320	−	17.0387i	1.23936	−	0.659248i
$669$			0.120914i			0.00467481i
$670$	−4.98415	−	19.9831i	−0.192554	−	0.772014i
$671$	29.5106			1.13924
$672$	1.93250	−	5.31653i	0.0745477	−	0.205089i
$673$	39.8528			1.53621			0.768107	−	0.640321i	$-0.221199\pi$
$673$	39.8528			1.53621			0.768107	+	0.640321i	$0.221199\pi$
$674$	1.78671	+	7.16349i	0.0688214	+	0.275927i
$675$		−	1.00000i		−	0.0384900i
$676$	5.88748	−	3.13171i	0.226441	−	0.120450i
$677$		−	45.7966i		−	1.76011i	−0.474876	−	0.880053i	$-0.657507\pi$
$677$		−	45.7966i		−	1.76011i	0.474876	−	0.880053i	$-0.342493\pi$
$678$	1.50363	−	0.375032i	0.0577464	−	0.0144030i
$679$	3.29679			0.126519
$680$	−0.855031	+	0.770268i	−0.0327889	+	0.0295384i
$681$	−20.5673			−0.788142
$682$	50.2034	−	12.5216i	1.92239	−	0.479478i
$683$			21.5512i			0.824634i	0.911040	+	0.412317i	$0.135280\pi$
$683$			21.5512i			0.824634i	−0.911040	+	0.412317i	$0.864720\pi$
$684$	1.36993	+	2.57540i	0.0523805	+	0.0984729i
$685$			4.38222i			0.167436i
$686$	0.342246	+	1.37218i	0.0130670	+	0.0523899i
$687$	10.7194			0.408969
$688$	2.43359	+	1.64027i	0.0927797	+	0.0625348i
$689$	−5.53705			−0.210945
$690$	2.55652	+	10.2499i	0.0973249	+	0.390207i
$691$		−	24.5483i		−	0.933860i	−0.884294	−	0.466930i	$-0.845360\pi$
$691$		−	24.5483i		−	0.933860i	0.884294	−	0.466930i	$-0.154640\pi$
$692$	−0.839936	−	1.57904i	−0.0319296	−	0.0600262i
$693$		−	4.47074i		−	0.169829i
$694$	−20.1731	+	5.03154i	−0.765760	+	0.190995i
$695$	−6.01555			−0.228183
$696$	19.6086	+	21.7664i	0.743262	+	0.825053i
$697$	−3.60095			−0.136396
$698$	−41.2633	+	10.2918i	−1.56184	+	0.389551i
$699$			8.18606i			0.309625i
$700$	−1.76574	+	0.939244i	−0.0667385	+	0.0355001i
$701$			1.97333i			0.0745318i	0.999305	+	0.0372659i	$0.0118648\pi$
$701$			1.97333i			0.0745318i	−0.999305	+	0.0372659i	$0.988135\pi$
$702$	−1.38321	−	5.54575i	−0.0522059	−	0.209311i
$703$	4.88626			0.184289
$704$	35.5719	+	3.72040i	1.34067	+	0.140218i
$705$	−1.71284			−0.0645095
$706$	4.25634	+	17.0651i	0.160190	+	0.642253i
$707$			10.1105i			0.380245i
$708$	15.2112	−	8.09127i	0.571672	−	0.304088i
$709$		−	10.8862i		−	0.408840i	−0.978883	−	0.204420i	$-0.934469\pi$
$709$		−	10.8862i		−	0.408840i	0.978883	−	0.204420i	$-0.0655309\pi$
$710$	−20.8154	+	5.19175i	−0.781189	+	0.194843i
$711$	−11.0077			−0.412821
$712$	−24.0397	−	26.6851i	−0.900927	−	1.00007i
$713$	61.1299			2.28933
$714$	0.558307	−	0.139252i	0.0208941	−	0.00521137i
$715$		−	18.0688i		−	0.675735i
$716$	−7.75237	−	14.5741i	−0.289720	−	0.544660i
$717$		−	20.0186i		−	0.747609i
$718$	−0.595520	−	2.38763i	−0.0222246	−	0.0891057i
$719$	52.7520			1.96732			0.983658	−	0.180045i	$-0.0576244\pi$
$719$	52.7520			1.96732			0.983658	+	0.180045i	$0.0576244\pi$
$720$	−3.31691	−	2.23564i	−0.123614	−	0.0833175i
$721$	−6.82111			−0.254031
$722$	−5.77460	−	23.1523i	−0.214908	−	0.861638i
$723$			15.4729i			0.575443i
$724$	7.98761	+	15.0164i	0.296857	+	0.558078i
$725$		−	10.3578i		−	0.384679i
$726$	12.3324	−	3.07594i	0.457700	−	0.114159i
$727$	15.3463			0.569162			0.284581	−	0.958652i	$-0.408146\pi$
$727$	15.3463			0.569162			0.284581	+	0.958652i	$0.408146\pi$
$728$	−8.49315	+	7.65119i	−0.314777	+	0.283572i
$729$	−1.00000			−0.0370370
$730$	9.64315	−	2.40518i	0.356909	−	0.0890197i
$731$			0.298522i			0.0110412i
$732$	−11.6553	+	6.19979i	−0.430793	+	0.229151i
$733$		−	25.6724i		−	0.948233i	−0.880462	−	0.474116i	$-0.842768\pi$
$733$		−	25.6724i		−	0.948233i	0.880462	−	0.474116i	$-0.157232\pi$
$734$	−1.38972	−	5.57185i	−0.0512955	−	0.205661i
$735$	1.00000			0.0368856
$736$	39.7135	+	14.4354i	1.46386	+	0.532096i
$737$	−65.1076			−2.39827
$738$	−3.02895	−	12.1440i	−0.111497	−	0.447029i
$739$			26.3301i			0.968569i	0.874911	+	0.484284i	$0.160920\pi$
$739$			26.3301i			0.968569i	−0.874911	+	0.484284i	$0.839080\pi$
$740$	−5.91539	+	3.14656i	−0.217454	+	0.115670i
$741$		−	5.89481i		−	0.216551i
$742$	1.87991	−	0.468885i	0.0690138	−	0.0172133i
$743$	−43.2626			−1.58715			−0.793576	−	0.608471i	$-0.791783\pi$
$743$	−43.2626			−1.58715			−0.793576	+	0.608471i	$0.791783\pi$
$744$	−17.1974	+	15.4925i	−0.630486	+	0.567984i
$745$	−22.8286			−0.836376
$746$	−23.6108	+	5.88896i	−0.864452	+	0.215610i
$747$			5.72787i			0.209572i
$748$	1.70852	+	3.21194i	0.0624697	+	0.117440i
$749$		−	3.55654i		−	0.129953i
$750$	0.342246	+	1.37218i	0.0124971	+	0.0501048i
$751$	16.9442			0.618304			0.309152	−	0.951013i	$-0.399955\pi$
$751$	16.9442			0.618304			0.309152	+	0.951013i	$0.399955\pi$
$752$	−3.82931	+	5.68135i	−0.139641	+	0.207178i
$753$	10.6904			0.389582
$754$	−14.3270	−	57.4418i	−0.521760	−	2.09191i
$755$		−	4.76642i		−	0.173468i
$756$	0.939244	+	1.76574i	0.0341600	+	0.0642192i
$757$			24.7705i			0.900298i	0.892954	+	0.450149i	$0.148629\pi$
$757$			24.7705i			0.900298i	−0.892954	+	0.450149i	$0.851371\pi$
$758$	−2.47208	+	0.616583i	−0.0897901	+	0.0223953i
$759$	33.3956			1.21218
$760$	−2.76120	−	3.06505i	−0.100159	−	0.111181i
$761$	27.1182			0.983034			0.491517	−	0.870868i	$-0.336442\pi$
$761$	27.1182			0.983034			0.491517	+	0.870868i	$0.336442\pi$
$762$	−26.7594	+	6.67429i	−0.969392	+	0.241784i
$763$			5.86714i			0.212405i
$764$	−35.9862	+	19.1420i	−1.30193	+	0.692535i
$765$		−	0.406877i		−	0.0147107i
$766$	7.28268	+	29.1987i	0.263134	+	1.05499i
$767$	−34.8168			−1.25716
$768$	−14.8309	+	6.00380i	−0.535163	+	0.216643i
$769$	−25.0784			−0.904350			−0.452175	−	0.891929i	$-0.649352\pi$
$769$	−25.0784			−0.904350			−0.452175	+	0.891929i	$0.649352\pi$
$770$	1.53009	+	6.13464i	0.0551407	+	0.221077i
$771$		−	12.1810i		−	0.438688i
$772$	−30.2735	+	16.1033i	−1.08957	+	0.579571i
$773$		−	12.8187i		−	0.461057i	−0.973066	−	0.230529i	$-0.925954\pi$
$773$		−	12.8187i		−	0.461057i	0.973066	−	0.230529i	$-0.0740456\pi$
$774$	−1.00675	+	0.251103i	−0.0361870	+	0.00902571i
$775$	8.18358			0.293963
$776$	−6.24123	−	6.92804i	−0.224047	−	0.248702i
$777$	3.35010			0.120184
$778$	21.6631	−	5.40318i	0.776660	−	0.193713i
$779$		−	12.9084i		−	0.462492i
$780$	3.79602	+	7.13634i	0.135919	+	0.255522i
$781$			67.8195i			2.42677i
$782$	1.04019	+	4.17045i	0.0371970	+	0.149135i
$783$	−10.3578			−0.370158
$784$	2.23564	−	3.31691i	0.0798444	−	0.118461i
$785$	−6.28285			−0.224245
$786$	1.32741	+	5.32204i	0.0473473	+	0.189831i
$787$		−	0.149492i		−	0.00532880i	−0.999996	−	0.00266440i	$-0.999152\pi$
$787$		−	0.149492i		−	0.00532880i	0.999996	−	0.00266440i	$-0.000848106\pi$
$788$	14.6680	+	27.5752i	0.522526	+	0.982325i
$789$		−	13.2080i		−	0.470218i
$790$	15.1045	−	3.76734i	0.537394	−	0.134036i
$791$	1.09580			0.0389620
$792$	−9.39503	+	8.46366i	−0.333838	+	0.300743i
$793$	26.6777			0.947353
$794$	0.521467	−	0.130063i	0.0185062	−	0.00461577i
$795$		−	1.37002i		−	0.0485897i
$796$	5.44871	−	2.89832i	0.193125	−	0.102728i
$797$		−	48.6497i		−	1.72326i	−0.507537	−	0.861630i	$-0.669444\pi$
$797$		−	48.6497i		−	1.72326i	0.507537	−	0.861630i	$-0.330556\pi$
$798$	0.499181	+	2.00138i	0.0176708	+	0.0708480i
$799$	−0.696917			−0.0246551
$800$	5.31653	+	1.93250i	0.187968	+	0.0683241i
$801$	12.6985			0.448678
$802$	−7.97146	−	31.9602i	−0.281482	−	1.12855i
$803$		−	31.4187i		−	1.10874i
$804$	25.7145	−	13.6783i	0.906881	−	0.482395i
$805$			7.46982i			0.263277i
$806$	45.3841	−	11.3196i	1.59859	−	0.398717i
$807$	−24.8107			−0.873378
$808$	21.2467	−	19.1404i	0.747456	−	0.673358i
$809$	10.2614			0.360770			0.180385	−	0.983596i	$-0.442266\pi$
$809$	10.2614			0.360770			0.180385	+	0.983596i	$0.442266\pi$
$810$	1.37218	−	0.342246i	0.0482134	−	0.0120253i
$811$			12.9277i			0.453953i	0.973900	+	0.226977i	$0.0728841\pi$
$811$			12.9277i			0.453953i	−0.973900	+	0.226977i	$0.927116\pi$
$812$	9.72850	+	18.2891i	0.341403	+	0.641823i
$813$			10.3871i			0.364291i
$814$	5.12596	+	20.5516i	0.179665	+	0.720335i
$815$	23.3643			0.818416
$816$	−1.34957	−	0.909631i	−0.0472446	−	0.0318435i
$817$	−1.07012			−0.0374388
$818$	11.8582	+	47.5433i	0.414611	+	1.66231i
$819$		−	4.04157i		−	0.141224i
$820$	8.31250	+	15.6271i	0.290285	+	0.545723i
$821$			27.8648i			0.972487i	0.873823	+	0.486244i	$0.161633\pi$
$821$			27.8648i			0.972487i	−0.873823	+	0.486244i	$0.838367\pi$
$822$	−6.01318	+	1.49980i	−0.209734	+	0.0523114i
$823$	−54.7780			−1.90944			−0.954720	−	0.297505i	$-0.903846\pi$
$823$	−54.7780			−1.90944			−0.954720	+	0.297505i	$0.903846\pi$
$824$	12.9132	+	14.3342i	0.449853	+	0.499356i
$825$	4.47074			0.155651
$826$	11.8208	−	2.94833i	0.411299	−	0.102586i
$827$			21.2613i			0.739327i	0.929166	+	0.369664i	$0.120527\pi$
$827$			21.2613i			0.739327i	−0.929166	+	0.369664i	$0.879473\pi$
$828$	−13.1897	+	7.01598i	−0.458375	+	0.243822i
$829$		−	4.19360i		−	0.145650i	−0.997345	−	0.0728249i	$-0.976799\pi$
$829$		−	4.19360i		−	0.145650i	0.997345	−	0.0728249i	$-0.0232014\pi$
$830$	−1.96034	−	7.85965i	−0.0680444	−	0.272812i
$831$	−7.26184			−0.251910
$832$	32.1572	+	3.36326i	1.11485	+	0.116600i
$833$	0.406877			0.0140974
$834$	−2.05880	−	8.25440i	−0.0712903	−	0.285826i
$835$		−	18.1409i		−	0.627792i
$836$	−11.5139	+	6.12459i	−0.398218	+	0.211823i
$837$		−	8.18358i		−	0.282866i
$838$	47.0480	−	11.7346i	1.62525	−	0.405366i
$839$	−8.00382			−0.276323			−0.138161	−	0.990410i	$-0.544119\pi$
$839$	−8.00382			−0.276323			−0.138161	+	0.990410i	$0.544119\pi$
$840$	−1.89312	−	2.10145i	−0.0653190	−	0.0725068i
$841$	−78.2841			−2.69945
$842$	19.1503	−	4.77642i	0.659961	−	0.164606i
$843$		−	23.4123i		−	0.806363i
$844$	17.9527	+	33.7503i	0.617959	+	1.16173i
$845$		−	3.33429i		−	0.114703i
$846$	−0.586214	−	2.35032i	−0.0201545	−	0.0808058i
$847$	8.98751			0.308814
$848$	−4.54425	−	3.06289i	−0.156050	−	0.105180i
$849$	−21.6138			−0.741784
$850$	0.139252	+	0.558307i	0.00477630	+	0.0191498i
$851$			25.0246i			0.857833i
$852$	−14.2480	−	26.7856i	−0.488128	−	0.917659i
$853$		−	49.3821i		−	1.69081i	−0.534124	−	0.845406i	$-0.679359\pi$
$853$		−	49.3821i		−	1.69081i	0.534124	−	0.845406i	$-0.320641\pi$
$854$	−9.05750	+	2.25911i	−0.309941	+	0.0773050i
$855$	1.45854			0.0498811
$856$	−7.47389	+	6.73297i	−0.255452	+	0.230128i
$857$	27.8065			0.949853			0.474926	−	0.880025i	$-0.342475\pi$
$857$	27.8065			0.949853			0.474926	+	0.880025i	$0.342475\pi$
$858$	24.7936	−	6.18398i	0.846439	−	0.211117i
$859$			10.8688i			0.370838i	0.982660	+	0.185419i	$0.0593642\pi$
$859$			10.8688i			0.370838i	−0.982660	+	0.185419i	$0.940636\pi$
$860$	1.29551	−	0.689115i	0.0441764	−	0.0234986i
$861$		−	8.85021i		−	0.301614i
$862$	−3.16773	−	12.7005i	−0.107893	−	0.432580i
$863$	−31.8489			−1.08415			−0.542075	−	0.840330i	$-0.682361\pi$
$863$	−31.8489			−1.08415			−0.542075	+	0.840330i	$0.682361\pi$
$864$	1.93250	−	5.31653i	0.0657449	−	0.180872i
$865$	−0.894269			−0.0304061
$866$	2.21455	+	8.87884i	0.0752533	+	0.301715i
$867$			16.8345i			0.571728i
$868$	−14.4500	+	7.68638i	−0.490466	+	0.260893i
$869$		−	49.2126i		−	1.66942i
$870$	14.2127	−	3.54492i	0.481857	−	0.120184i
$871$	−58.8576			−1.99431
$872$	12.3295	−	11.1072i	0.417529	−	0.376138i
$873$	3.29679			0.111580
$874$	−14.9499	+	3.72879i	−0.505689	+	0.126128i
$875$			1.00000i			0.0338062i
$876$	6.60066	+	12.4089i	0.223016	+	0.419259i
$877$			4.13771i			0.139720i	0.997557	+	0.0698602i	$0.0222553\pi$
$877$			4.13771i			0.139720i	−0.997557	+	0.0698602i	$0.977745\pi$
$878$	9.69145	+	38.8562i	0.327071	+	1.31133i
$879$	31.3799			1.05842
$880$	9.99498	−	14.8290i	0.336931	−	0.499887i
$881$	42.0704			1.41739			0.708693	−	0.705517i	$-0.249285\pi$
$881$	42.0704			1.41739			0.708693	+	0.705517i	$0.249285\pi$
$882$	0.342246	+	1.37218i	0.0115240	+	0.0462036i
$883$			19.2369i			0.647375i	0.946164	+	0.323687i	$0.104923\pi$
$883$			19.2369i			0.647375i	−0.946164	+	0.323687i	$0.895077\pi$
$884$	1.54451	+	2.90361i	0.0519476	+	0.0976591i
$885$		−	8.61466i		−	0.289579i
$886$	−23.0850	+	5.75782i	−0.775556	+	0.193438i
$887$	−1.36403			−0.0457996			−0.0228998	−	0.999738i	$-0.507290\pi$
$887$	−1.36403			−0.0457996			−0.0228998	+	0.999738i	$0.507290\pi$
$888$	−6.34215	−	7.04006i	−0.212829	−	0.236249i
$889$	−19.5015			−0.654058
$890$	−17.4245	+	4.34599i	−0.584071	+	0.145678i
$891$		−	4.47074i		−	0.149775i
$892$	0.213502	−	0.113568i	0.00714859	−	0.00380253i
$893$		−	2.49826i		−	0.0836010i
$894$	−7.81301	−	31.3249i	−0.261306	−	1.04766i
$895$	−8.25385			−0.275896
$896$	−11.2027	+	1.58123i	−0.374255	+	0.0528253i
$897$	30.1898			1.00801
$898$	3.41544	+	13.6936i	0.113975	+	0.456961i
$899$		−	84.7639i		−	2.82704i
$900$	−1.76574	+	0.939244i	−0.0588578	+	0.0313081i
$901$		−	0.557431i		−	0.0185707i
$902$	54.2929	−	13.5416i	1.80776	−	0.450887i
$903$	−0.733692			−0.0244157
$904$	−2.07448	−	2.30276i	−0.0689961	−	0.0765886i
$905$	8.50431			0.282693
$906$	6.54037	−	1.63129i	0.217289	−	0.0541959i
$907$			28.2721i			0.938759i	0.882997	+	0.469379i	$0.155522\pi$
$907$			28.2721i			0.938759i	−0.882997	+	0.469379i	$0.844478\pi$
$908$	19.3177	+	36.3165i	0.641081	+	1.20520i
$909$			10.1105i			0.335344i
$910$	1.38321	+	5.54575i	0.0458530	+	0.183840i
$911$	−3.67647			−0.121807			−0.0609034	−	0.998144i	$-0.519398\pi$
$911$	−3.67647			−0.121807			−0.0609034	+	0.998144i	$0.519398\pi$
$912$	3.26078	−	4.83786i	0.107975	−	0.160198i
$913$	−25.6078			−0.847495
$914$	−4.28876	−	17.1950i	−0.141859	−	0.568761i
$915$			6.60083i			0.218217i
$916$	−10.0681	−	18.9275i	−0.332659	−	0.625384i
$917$			3.87854i			0.128081i
$918$	0.558307	−	0.139252i	0.0184269	−	0.00459600i
$919$	−29.3172			−0.967084			−0.483542	−	0.875321i	$-0.660650\pi$
$919$	−29.3172			−0.967084			−0.483542	+	0.875321i	$0.660650\pi$
$920$	15.6974	−	14.1413i	0.517529	−	0.466224i
$921$	28.3072			0.932753
$922$	−34.8867	+	8.70140i	−1.14893	+	0.286565i
$923$			61.3092i			2.01802i
$924$	−7.89414	+	4.19911i	−0.259698	+	0.138141i
$925$			3.35010i			0.110151i
$926$	3.26566	+	13.0931i	0.107316	+	0.430266i
$927$	−6.82111			−0.224035
$928$	20.0164	−	55.0675i	0.657071	−	1.80768i
$929$	−19.8228			−0.650365			−0.325183	−	0.945651i	$-0.605426\pi$
$929$	−19.8228			−0.650365			−0.325183	+	0.945651i	$0.605426\pi$
$930$	2.80080	+	11.2293i	0.0918418	+	0.368224i
$931$			1.45854i			0.0478018i
$932$	14.4544	−	7.68871i	0.473470	−	0.251852i
$933$			21.4064i			0.700813i
$934$	−33.5290	+	8.36274i	−1.09710	+	0.273637i
$935$	1.81904			0.0594890
$936$	−8.49315	+	7.65119i	−0.277607	+	0.250087i
$937$	−6.16351			−0.201353			−0.100677	−	0.994919i	$-0.532101\pi$
$937$	−6.16351			−0.201353			−0.100677	+	0.994919i	$0.532101\pi$
$938$	19.9831	−	4.98415i	0.652471	−	0.162738i
$939$		−	16.2120i		−	0.529060i
$940$	1.60878	+	3.02443i	0.0524726	+	0.0986460i
$941$			31.3628i			1.02240i	0.859462	+	0.511200i	$0.170799\pi$
$941$			31.3628i			1.02240i	−0.859462	+	0.511200i	$0.829201\pi$
$942$	−2.15028	−	8.62118i	−0.0700599	−	0.280893i
$943$	66.1095			2.15282
$944$	−28.5741	−	19.2593i	−0.930007	−	0.626837i
$945$	1.00000			0.0325300
$946$	−1.12262	−	4.50094i	−0.0364994	−	0.146338i
$947$		−	9.19892i		−	0.298925i	−0.988767	−	0.149462i	$-0.952246\pi$
$947$		−	9.19892i		−	0.298925i	0.988767	−	0.149462i	$-0.0477543\pi$
$948$	10.3389	+	19.4367i	0.335792	+	0.631275i
$949$		−	28.4027i		−	0.921990i
$950$	−2.00138	+	0.499181i	−0.0649333	+	0.0161956i
$951$	12.4683			0.404314
$952$	−0.770268	−	0.855031i	−0.0249645	−	0.0277117i
$953$	31.9514			1.03501			0.517503	−	0.855681i	$-0.326862\pi$
$953$	31.9514			1.03501			0.517503	+	0.855681i	$0.326862\pi$
$954$	1.87991	−	0.468885i	0.0608645	−	0.0151807i
$955$			20.3803i			0.659490i
$956$	−35.3476	+	18.8024i	−1.14322	+	0.608112i
$957$		−	46.3070i		−	1.49689i
$958$	10.2413	+	41.0608i	0.330882	+	1.32661i
$959$	−4.38222			−0.141509
$960$	−0.832167	+	7.95660i	−0.0268581	+	0.256798i
$961$	35.9710			1.16036
$962$	4.63389	+	18.5788i	0.149403	+	0.599004i
$963$		−	3.55654i		−	0.114608i
$964$	27.3210	−	14.5328i	0.879952	−	0.468071i
$965$			17.1450i			0.551917i
$966$	−10.2499	+	2.55652i	−0.329785	+	0.0822545i
$967$	1.32028			0.0424572			0.0212286	−	0.999775i	$-0.493242\pi$
$967$	1.32028			0.0424572			0.0212286	+	0.999775i	$0.493242\pi$
$968$	−17.0145	−	18.8868i	−0.546865	−	0.607044i
$969$	0.593448			0.0190643
$970$	−4.52378	+	1.12831i	−0.145250	+	0.0362280i
$971$		−	24.6556i		−	0.791235i	−0.918415	−	0.395617i	$-0.870531\pi$
$971$		−	24.6556i		−	0.791235i	0.918415	−	0.395617i	$-0.129469\pi$
$972$	0.939244	+	1.76574i	0.0301263	+	0.0566360i
$973$		−	6.01555i		−	0.192850i
$974$	−5.34290	−	21.4214i	−0.171197	−	0.686387i
$975$	4.04157			0.129434
$976$	21.8944	+	14.7571i	0.700821	+	0.472363i
$977$	−36.4689			−1.16674			−0.583371	−	0.812206i	$-0.698267\pi$
$977$	−36.4689			−1.16674			−0.583371	+	0.812206i	$0.698267\pi$
$978$	7.99634	+	32.0600i	0.255695	+	1.02516i
$979$			56.7715i			1.81442i
$980$	−0.939244	−	1.76574i	−0.0300030	−	0.0564043i
$981$			5.86714i			0.187323i
$982$	−3.57457	+	0.891563i	−0.114069	+	0.0284509i
$983$	−31.3938			−1.00131			−0.500653	−	0.865648i	$-0.666907\pi$
$983$	−31.3938			−1.00131			−0.500653	+	0.865648i	$0.666907\pi$
$984$	−18.5983	+	16.7545i	−0.592891	+	0.534115i
$985$	15.6168			0.497593
$986$	5.78283	−	1.44234i	0.184163	−	0.0459336i
$987$		−	1.71284i		−	0.0545204i
$988$	−10.4087	+	5.53666i	−0.331144	+	0.176145i
$989$		−	5.48054i		−	0.174271i
$990$	1.53009	+	6.13464i	0.0486295	+	0.194972i
$991$	−50.5347			−1.60529			−0.802644	−	0.596459i	$-0.796574\pi$
$991$	−50.5347			−1.60529			−0.802644	+	0.596459i	$0.796574\pi$
$992$	43.5082	+	15.8148i	1.38139	+	0.502119i
$993$	−15.1175			−0.479740
$994$	−5.19175	−	20.8154i	−0.164672	−	0.660225i
$995$		−	3.08580i		−	0.0978266i
$996$	10.1139	−	5.37987i	0.320471	−	0.170468i
$997$			12.1767i			0.385641i	0.981234	+	0.192821i	$0.0617636\pi$
$997$			12.1767i			0.385641i	−0.981234	+	0.192821i	$0.938236\pi$
$998$	44.6883	−	11.1461i	1.41458	−	0.352823i
$999$	3.35010			0.105992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.g.d.421.7	✓	16
4.3	odd	2		3360.2.g.d.1681.15		16
8.3	odd	2		3360.2.g.d.1681.2		16
8.5	even	2	inner	840.2.g.d.421.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.g.d.421.7	✓	16	1.1	even	1	trivial
840.2.g.d.421.8	yes	16	8.5	even	2	inner
3360.2.g.d.1681.2		16	8.3	odd	2
3360.2.g.d.1681.15		16	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.342246 - 1.37218i) q^{2} -1.00000i q^{3} +(-1.76574 + 0.939244i) q^{4} +1.00000i q^{5} +(-1.37218 + 0.342246i) q^{6} -1.00000 q^{7} +(1.89312 + 2.10145i) q^{8} -1.00000 q^{9} +(1.37218 - 0.342246i) q^{10} -4.47074i q^{11} +(0.939244 + 1.76574i) q^{12} -4.04157i q^{13} +(0.342246 + 1.37218i) q^{14} +1.00000 q^{15} +(2.23564 - 3.31691i) q^{16} +0.406877 q^{17} +(0.342246 + 1.37218i) q^{18} +1.45854i q^{19} +(-0.939244 - 1.76574i) q^{20} +1.00000i q^{21} +(-6.13464 + 1.53009i) q^{22} -7.46982 q^{23} +(2.10145 - 1.89312i) q^{24} -1.00000 q^{25} +(-5.54575 + 1.38321i) q^{26} +1.00000i q^{27} +(1.76574 - 0.939244i) q^{28} +10.3578i q^{29} +(-0.342246 - 1.37218i) q^{30} -8.18358 q^{31} +(-5.31653 - 1.93250i) q^{32} -4.47074 q^{33} +(-0.139252 - 0.558307i) q^{34} -1.00000i q^{35} +(1.76574 - 0.939244i) q^{36} -3.35010i q^{37} +(2.00138 - 0.499181i) q^{38} -4.04157 q^{39} +(-2.10145 + 1.89312i) q^{40} -8.85021 q^{41} +(1.37218 - 0.342246i) q^{42} +0.733692i q^{43} +(4.19911 + 7.89414i) q^{44} -1.00000i q^{45} +(2.55652 + 10.2499i) q^{46} -1.71284 q^{47} +(-3.31691 - 2.23564i) q^{48} +1.00000 q^{49} +(0.342246 + 1.37218i) q^{50} -0.406877i q^{51} +(3.79602 + 7.13634i) q^{52} -1.37002i q^{53} +(1.37218 - 0.342246i) q^{54} +4.47074 q^{55} +(-1.89312 - 2.10145i) q^{56} +1.45854 q^{57} +(14.2127 - 3.54492i) q^{58} -8.61466i q^{59} +(-1.76574 + 0.939244i) q^{60} +6.60083i q^{61} +(2.80080 + 11.2293i) q^{62} +1.00000 q^{63} +(-0.832167 + 7.95660i) q^{64} +4.04157 q^{65} +(1.53009 + 6.13464i) q^{66} -14.5631i q^{67} +(-0.718437 + 0.382156i) q^{68} +7.46982i q^{69} +(-1.37218 + 0.342246i) q^{70} -15.1696 q^{71} +(-1.89312 - 2.10145i) q^{72} +7.02763 q^{73} +(-4.59692 + 1.14656i) q^{74} +1.00000i q^{75} +(-1.36993 - 2.57540i) q^{76} +4.47074i q^{77} +(1.38321 + 5.54575i) q^{78} +11.0077 q^{79} +(3.31691 + 2.23564i) q^{80} +1.00000 q^{81} +(3.02895 + 12.1440i) q^{82} -5.72787i q^{83} +(-0.939244 - 1.76574i) q^{84} +0.406877i q^{85} +(1.00675 - 0.251103i) q^{86} +10.3578 q^{87} +(9.39503 - 8.46366i) q^{88} -12.6985 q^{89} +(-1.37218 + 0.342246i) q^{90} +4.04157i q^{91} +(13.1897 - 7.01598i) q^{92} +8.18358i q^{93} +(0.586214 + 2.35032i) q^{94} -1.45854 q^{95} +(-1.93250 + 5.31653i) q^{96} -3.29679 q^{97} +(-0.342246 - 1.37218i) q^{98} +4.47074i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{6} - 16 q^{7} - 2 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{14} + 16 q^{15} + 4 q^{16} + 2 q^{18} + 2 q^{24} - 16 q^{25} - 2 q^{30} - 2 q^{32} + 24 q^{34} - 28 q^{38} - 2 q^{40} + 2 q^{42}+ \cdots - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^6 - 16 * q^7 - 2 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^14 + 16 * q^15 + 4 * q^16 + 2 * q^18 + 2 * q^24 - 16 * q^25 - 2 * q^30 - 2 * q^32 + 24 * q^34 - 28 * q^38 - 2 * q^40 + 2 * q^42 + 8 * q^44 - 36 * q^46 + 32 * q^47 + 16 * q^49 + 2 * q^50 + 4 * q^52 + 2 * q^54 + 2 * q^56 + 32 * q^58 - 12 * q^62 + 16 * q^63 - 48 * q^64 + 28 * q^66 + 56 * q^68 - 2 * q^70 - 64 * q^71 + 2 * q^72 + 24 * q^74 + 8 * q^76 - 24 * q^78 + 48 * q^79 + 16 * q^81 + 4 * q^82 - 36 * q^86 - 16 * q^87 - 2 * q^90 + 80 * q^92 - 44 * q^94 - 2 * q^96 - 2 * q^98

Introduction

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