LMFDB - Embedded newform 450.2.l.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	450.19
Dual form			450.2.l.a.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.166977 - 2.22982i) q^{5} -2.07768i q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.166977 - 2.22982i) q^{5} -2.07768i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.530249 + 2.17229i) q^{10} +(-0.160734 - 0.494689i) q^{11} +(-2.07919 - 0.675571i) q^{13} +(0.642040 + 1.97599i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-1.58450 + 2.18088i) q^{17} +(-5.55899 - 4.03884i) q^{19} +(-1.17557 - 1.90211i) q^{20} +(0.305735 + 0.420808i) q^{22} +(-3.67171 + 1.19301i) q^{23} +(-4.94424 - 0.744661i) q^{25} +2.18619 q^{26} +(-1.22123 - 1.68088i) q^{28} +(7.30844 - 5.30989i) q^{29} +(5.99083 + 4.35259i) q^{31} +1.00000i q^{32} +(0.833023 - 2.56378i) q^{34} +(-4.63287 - 0.346926i) q^{35} +(-5.04743 - 1.64001i) q^{37} +(6.53498 + 2.12334i) q^{38} +(1.70582 + 1.44575i) q^{40} +(0.996141 - 3.06581i) q^{41} -9.53920i q^{43} +(-0.420808 - 0.305735i) q^{44} +(3.12334 - 2.26924i) q^{46} +(-5.44627 - 7.49614i) q^{47} +2.68323 q^{49} +(4.93236 - 0.819639i) q^{50} +(-2.07919 + 0.675571i) q^{52} +(1.43326 + 1.97271i) q^{53} +(-1.12991 + 0.275807i) q^{55} +(1.68088 + 1.22123i) q^{56} +(-5.30989 + 7.30844i) q^{58} +(2.67261 - 8.22545i) q^{59} +(3.88998 + 11.9721i) q^{61} +(-7.04264 - 2.28829i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(-1.85358 + 4.52343i) q^{65} +(3.93455 - 5.41544i) q^{67} +2.69572i q^{68} +(4.51333 - 1.10169i) q^{70} +(-6.60886 + 4.80162i) q^{71} +(3.65537 - 1.18770i) q^{73} +5.30719 q^{74} -6.87129 q^{76} +(-1.02781 + 0.333955i) q^{77} +(2.84162 - 2.06455i) q^{79} +(-2.06909 - 0.847859i) q^{80} +3.22358i q^{82} +(-7.71827 + 10.6233i) q^{83} +(4.59841 + 3.89732i) q^{85} +(2.94777 + 9.07232i) q^{86} +(0.494689 + 0.160734i) q^{88} +(-3.04654 - 9.37628i) q^{89} +(-1.40362 + 4.31990i) q^{91} +(-2.26924 + 3.12334i) q^{92} +(7.49614 + 5.44627i) q^{94} +(-9.93414 + 11.7212i) q^{95} +(6.32443 + 8.70483i) q^{97} +(-2.55190 + 0.829164i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4}+O(q^{10}) $ 8 * q + 2 * q^4	$ 8 q + 2 q^{4} - 10 q^{11} - 20 q^{13} + 2 q^{14} - 2 q^{16} - 10 q^{17} - 8 q^{19} + 10 q^{23} - 10 q^{25} - 4 q^{26} - 10 q^{28} + 22 q^{29} + 24 q^{31} + 8 q^{34} - 10 q^{35} - 20 q^{37} + 10 q^{38} - 22 q^{41} + 10 q^{46} - 10 q^{47} + 8 q^{49} + 20 q^{50} - 20 q^{52} + 30 q^{53} + 10 q^{55} - 2 q^{56} + 30 q^{58} + 20 q^{59} - 10 q^{62} + 2 q^{64} - 20 q^{65} + 10 q^{67} - 10 q^{70} - 20 q^{71} - 20 q^{73} + 4 q^{74} - 12 q^{76} + 20 q^{77} + 16 q^{79} - 70 q^{83} + 20 q^{85} + 18 q^{86} + 10 q^{88} + 34 q^{89} - 24 q^{91} - 30 q^{92} + 30 q^{94} - 30 q^{95} + 60 q^{97} - 20 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 - 10 * q^11 - 20 * q^13 + 2 * q^14 - 2 * q^16 - 10 * q^17 - 8 * q^19 + 10 * q^23 - 10 * q^25 - 4 * q^26 - 10 * q^28 + 22 * q^29 + 24 * q^31 + 8 * q^34 - 10 * q^35 - 20 * q^37 + 10 * q^38 - 22 * q^41 + 10 * q^46 - 10 * q^47 + 8 * q^49 + 20 * q^50 - 20 * q^52 + 30 * q^53 + 10 * q^55 - 2 * q^56 + 30 * q^58 + 20 * q^59 - 10 * q^62 + 2 * q^64 - 20 * q^65 + 10 * q^67 - 10 * q^70 - 20 * q^71 - 20 * q^73 + 4 * q^74 - 12 * q^76 + 20 * q^77 + 16 * q^79 - 70 * q^83 + 20 * q^85 + 18 * q^86 + 10 * q^88 + 34 * q^89 - 24 * q^91 - 30 * q^92 + 30 * q^94 - 30 * q^95 + 60 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.166977	−	2.22982i	0.0746746	−	0.997208i
$5$	0.166977	−	2.22982i	0.0746746	−	0.997208i
$6$		0			0
$7$		−	2.07768i		−	0.785291i	−0.919690	−	0.392645i	$-0.871560\pi$
$7$		−	2.07768i		−	0.785291i	0.919690	−	0.392645i	$-0.128440\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$		0			0
$10$	0.530249	+	2.17229i	0.167679	+	0.686938i
$11$	−0.160734	−	0.494689i	−0.0484632	−	0.149154i	0.923896	−	0.382643i	$-0.124986\pi$
$11$	−0.160734	−	0.494689i	−0.0484632	−	0.149154i	−0.972360	+	0.233488i	$0.924986\pi$
$12$		0			0
$13$	−2.07919	−	0.675571i	−0.576664	−	0.187370i	0.00614146	−	0.999981i	$-0.498045\pi$
$13$	−2.07919	−	0.675571i	−0.576664	−	0.187370i	−0.582806	+	0.812612i	$0.698045\pi$
$14$	0.642040	+	1.97599i	0.171592	+	0.528107i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.58450	+	2.18088i	−0.384298	+	0.528941i	−0.956717	−	0.291020i	$-0.906005\pi$
$17$	−1.58450	+	2.18088i	−0.384298	+	0.528941i	0.572418	+	0.819962i	$0.306005\pi$
$18$		0			0
$19$	−5.55899	−	4.03884i	−1.27532	−	0.926574i	−0.275919	−	0.961181i	$-0.588982\pi$
$19$	−5.55899	−	4.03884i	−1.27532	−	0.926574i	−0.999401	+	0.0346072i	$0.988982\pi$
$20$	−1.17557	−	1.90211i	−0.262866	−	0.425325i
$21$		0			0
$22$	0.305735	+	0.420808i	0.0651829	+	0.0897165i
$23$	−3.67171	+	1.19301i	−0.765605	+	0.248760i	−0.665682	−	0.746235i	$-0.731859\pi$
$23$	−3.67171	+	1.19301i	−0.765605	+	0.248760i	−0.0999224	+	0.994995i	$0.531859\pi$
$24$		0			0
$25$	−4.94424	−	0.744661i	−0.988847	−	0.148932i
$26$	2.18619			0.428748
$27$		0			0
$28$	−1.22123	−	1.68088i	−0.230791	−	0.317657i
$29$	7.30844	−	5.30989i	1.35714	−	0.986022i	0.358523	−	0.933521i	$-0.383281\pi$
$29$	7.30844	−	5.30989i	1.35714	−	0.986022i	0.998621	−	0.0525013i	$-0.0167194\pi$
$30$		0			0
$31$	5.99083	+	4.35259i	1.07598	+	0.781749i	0.976978	−	0.213338i	$-0.0684335\pi$
$31$	5.99083	+	4.35259i	1.07598	+	0.781749i	0.0990065	+	0.995087i	$0.468434\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.833023	−	2.56378i	0.142862	−	0.439685i
$35$	−4.63287	−	0.346926i	−0.783098	−	0.0586413i
$36$		0			0
$37$	−5.04743	−	1.64001i	−0.829793	−	0.269616i	−0.136835	−	0.990594i	$-0.543693\pi$
$37$	−5.04743	−	1.64001i	−0.829793	−	0.269616i	−0.692958	+	0.720978i	$0.743693\pi$
$38$	6.53498	+	2.12334i	1.06011	+	0.344452i
$39$		0			0
$40$	1.70582	+	1.44575i	0.269714	+	0.228592i
$41$	0.996141	−	3.06581i	0.155571	−	0.478799i	−0.842647	−	0.538466i	$-0.819004\pi$
$41$	0.996141	−	3.06581i	0.155571	−	0.478799i	0.998218	+	0.0596673i	$0.0190040\pi$
$42$		0			0
$43$		−	9.53920i		−	1.45471i	−0.686259	−	0.727357i	$-0.740748\pi$
$43$		−	9.53920i		−	1.45471i	0.686259	−	0.727357i	$-0.259252\pi$
$44$	−0.420808	−	0.305735i	−0.0634392	−	0.0460912i
$45$		0			0
$46$	3.12334	−	2.26924i	0.460512	−	0.334582i
$47$	−5.44627	−	7.49614i	−0.794419	−	1.09342i	−0.993544	−	0.113450i	$-0.963810\pi$
$47$	−5.44627	−	7.49614i	−0.794419	−	1.09342i	0.199124	−	0.979974i	$-0.436190\pi$
$48$		0			0
$49$	2.68323			0.383319
$50$	4.93236	−	0.819639i	0.697541	−	0.115914i
$51$		0			0
$52$	−2.07919	+	0.675571i	−0.288332	+	0.0936848i
$53$	1.43326	+	1.97271i	0.196873	+	0.270973i	0.896028	−	0.443998i	$-0.146440\pi$
$53$	1.43326	+	1.97271i	0.196873	+	0.270973i	−0.699155	+	0.714970i	$0.746440\pi$
$54$		0			0
$55$	−1.12991	+	0.275807i	−0.152357	+	0.0371898i
$56$	1.68088	+	1.22123i	0.224617	+	0.163194i
$57$		0			0
$58$	−5.30989	+	7.30844i	−0.697223	+	0.959645i
$59$	2.67261	−	8.22545i	0.347944	−	1.07086i	−0.612045	−	0.790823i	$-0.709653\pi$
$59$	2.67261	−	8.22545i	0.347944	−	1.07086i	0.959989	−	0.280039i	$-0.0903473\pi$
$60$		0			0
$61$	3.88998	+	11.9721i	0.498061	+	1.53287i	0.812131	+	0.583475i	$0.198307\pi$
$61$	3.88998	+	11.9721i	0.498061	+	1.53287i	−0.314070	+	0.949400i	$0.601693\pi$
$62$	−7.04264	−	2.28829i	−0.894417	−	0.290614i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−1.85358	+	4.52343i	−0.229909	+	0.561062i
$66$		0			0
$67$	3.93455	−	5.41544i	0.480682	−	0.661601i	−0.497954	−	0.867203i	$-0.665915\pi$
$67$	3.93455	−	5.41544i	0.480682	−	0.661601i	0.978636	+	0.205602i	$0.0659152\pi$
$68$			2.69572i			0.326904i
$69$		0			0
$70$	4.51333	−	1.10169i	0.539446	−	0.131677i
$71$	−6.60886	+	4.80162i	−0.784328	+	0.569848i	−0.906275	−	0.422689i	$-0.861086\pi$
$71$	−6.60886	+	4.80162i	−0.784328	+	0.569848i	0.121947	+	0.992537i	$0.461086\pi$
$72$		0			0
$73$	3.65537	−	1.18770i	0.427828	−	0.139010i	−0.0871848	−	0.996192i	$-0.527787\pi$
$73$	3.65537	−	1.18770i	0.427828	−	0.139010i	0.515013	+	0.857182i	$0.327787\pi$
$74$	5.30719			0.616948
$75$		0			0
$76$	−6.87129			−0.788191
$77$	−1.02781	+	0.333955i	−0.117130	+	0.0380577i
$78$		0			0
$79$	2.84162	−	2.06455i	0.319707	−	0.232281i	−0.416344	−	0.909207i	$-0.636689\pi$
$79$	2.84162	−	2.06455i	0.319707	−	0.232281i	0.736050	+	0.676927i	$0.236689\pi$
$80$	−2.06909	−	0.847859i	−0.231331	−	0.0947935i
$81$		0			0
$82$			3.22358i			0.355985i
$83$	−7.71827	+	10.6233i	−0.847190	+	1.16606i	0.137285	+	0.990532i	$0.456163\pi$
$83$	−7.71827	+	10.6233i	−0.847190	+	1.16606i	−0.984475	+	0.175526i	$0.943837\pi$
$84$		0			0
$85$	4.59841	+	3.89732i	0.498767	+	0.422724i
$86$	2.94777	+	9.07232i	0.317867	+	0.978293i
$87$		0			0
$88$	0.494689	+	0.160734i	0.0527340	+	0.0171343i
$89$	−3.04654	−	9.37628i	−0.322932	−	0.993883i	−0.972365	−	0.233465i	$-0.924994\pi$
$89$	−3.04654	−	9.37628i	−0.322932	−	0.993883i	0.649433	−	0.760419i	$-0.275006\pi$
$90$		0			0
$91$	−1.40362	+	4.31990i	−0.147140	+	0.452849i
$92$	−2.26924	+	3.12334i	−0.236585	+	0.325631i
$93$		0			0
$94$	7.49614	+	5.44627i	0.773168	+	0.561739i
$95$	−9.93414	+	11.7212i	−1.01922	+	1.20257i
$96$		0			0
$97$	6.32443	+	8.70483i	0.642149	+	0.883842i	0.998728	−	0.0504234i	$-0.0160571\pi$
$97$	6.32443	+	8.70483i	0.642149	+	0.883842i	−0.356579	+	0.934265i	$0.616057\pi$
$98$	−2.55190	+	0.829164i	−0.257781	+	0.0837582i
$99$		0			0
$100$	−4.43767	+	2.30371i	−0.443767	+	0.230371i
$101$	17.6400			1.75524			0.877622	−	0.479353i	$-0.159129\pi$
$101$	17.6400			1.75524			0.877622	+	0.479353i	$0.159129\pi$
$102$		0			0
$103$	5.11231	+	7.03649i	0.503731	+	0.693326i	0.982846	−	0.184426i	$-0.0590425\pi$
$103$	5.11231	+	7.03649i	0.503731	+	0.693326i	−0.479116	+	0.877752i	$0.659043\pi$
$104$	1.76867	−	1.28501i	0.173432	−	0.126006i
$105$		0			0
$106$	−1.97271	−	1.43326i	−0.191607	−	0.139210i
$107$		−	5.40977i		−	0.522983i	−0.965206	−	0.261491i	$-0.915786\pi$
$107$		−	5.40977i		−	0.522983i	0.965206	−	0.261491i	$-0.0842143\pi$
$108$		0			0
$109$	−0.891135	+	2.74263i	−0.0853553	+	0.262697i	−0.984620	−	0.174707i	$-0.944102\pi$
$109$	−0.891135	+	2.74263i	−0.0853553	+	0.262697i	0.899265	+	0.437404i	$0.144102\pi$
$110$	0.989378	−	0.611469i	0.0943335	−	0.0583013i
$111$		0			0
$112$	−1.97599	−	0.642040i	−0.186714	−	0.0606670i
$113$	6.05780	+	1.96830i	0.569870	+	0.185162i	0.579757	−	0.814789i	$-0.303147\pi$
$113$	6.05780	+	1.96830i	0.569870	+	0.185162i	−0.00988741	+	0.999951i	$0.503147\pi$
$114$		0			0
$115$	2.04711	+	8.38648i	0.190894	+	0.782043i
$116$	2.79158	−	8.59159i	0.259191	−	0.797709i
$117$		0			0
$118$			8.64875i			0.796182i
$119$	4.53118	+	3.29210i	0.415373	+	0.301786i
$120$		0			0
$121$	8.68031	−	6.30661i	0.789119	−	0.573328i
$122$	−7.39919	−	10.1841i	−0.669891	−	0.922026i
$123$		0			0
$124$	7.40507			0.664995
$125$	−2.48604	+	10.9004i	−0.222358	+	0.974965i
$126$		0			0
$127$	−14.2348	+	4.62515i	−1.26313	+	0.410416i	−0.862609	−	0.505871i	$-0.831171\pi$
$127$	−14.2348	+	4.62515i	−1.26313	+	0.410416i	−0.400522	+	0.916287i	$0.631171\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$		0			0
$130$	0.365045	−	4.87483i	0.0320165	−	0.427550i
$131$	11.2090	+	8.14385i	0.979339	+	0.711531i	0.957561	−	0.288232i	$-0.0930673\pi$
$131$	11.2090	+	8.14385i	0.979339	+	0.711531i	0.0217781	+	0.999763i	$0.493067\pi$
$132$		0			0
$133$	−8.39144	+	11.5498i	−0.727630	+	1.00150i
$134$	−2.06851	+	6.36623i	−0.178692	+	0.549959i
$135$		0			0
$136$	−0.833023	−	2.56378i	−0.0714311	−	0.219842i
$137$	18.9202	+	6.14755i	1.61646	+	0.525221i	0.971103	−	0.238659i	$-0.0767077\pi$
$137$	18.9202	+	6.14755i	1.61646	+	0.525221i	0.645359	+	0.763879i	$0.276708\pi$
$138$		0			0
$139$	−1.74398	−	5.36743i	−0.147923	−	0.455259i	0.849453	−	0.527665i	$-0.176932\pi$
$139$	−1.74398	−	5.36743i	−0.147923	−	0.455259i	−0.997375	+	0.0724056i	$0.976932\pi$
$140$	−3.95199	+	2.44246i	−0.334004	+	0.206426i
$141$		0			0
$142$	4.80162	−	6.60886i	0.402943	−	0.554604i
$143$			1.13714i			0.0950925i
$144$		0			0
$145$	−10.6198	−	17.1832i	−0.881925	−	1.42698i
$146$	−3.10944	+	2.25914i	−0.257339	+	0.186968i
$147$		0			0
$148$	−5.04743	+	1.64001i	−0.414897	+	0.134808i
$149$	−15.0956			−1.23668			−0.618339	−	0.785911i	$-0.712194\pi$
$149$	−15.0956			−1.23668			−0.618339	+	0.785911i	$0.712194\pi$
$150$		0			0
$151$	−20.9353			−1.70369			−0.851847	−	0.523791i	$-0.824517\pi$
$151$	−20.9353			−1.70369			−0.851847	+	0.523791i	$0.824517\pi$
$152$	6.53498	−	2.12334i	0.530057	−	0.172226i
$153$		0			0
$154$	0.874305	−	0.635220i	0.0704535	−	0.0511875i
$155$	10.7059	−	12.6317i	0.859915	−	1.01460i
$156$		0			0
$157$		−	5.71998i		−	0.456504i	−0.973602	−	0.228252i	$-0.926699\pi$
$157$		−	5.71998i		−	0.456504i	0.973602	−	0.228252i	$-0.0733010\pi$
$158$	−2.06455	+	2.84162i	−0.164247	+	0.226067i
$159$		0			0
$160$	2.22982	+	0.166977i	0.176283	+	0.0132007i
$161$	2.47870	+	7.62866i	0.195349	+	0.601222i
$162$		0			0
$163$	11.3129	+	3.67577i	0.886091	+	0.287908i	0.716484	−	0.697603i	$-0.245750\pi$
$163$	11.3129	+	3.67577i	0.886091	+	0.287908i	0.169607	+	0.985512i	$0.445750\pi$
$164$	−0.996141	−	3.06581i	−0.0777856	−	0.239399i
$165$		0			0
$166$	4.05774	−	12.4884i	0.314941	−	0.969290i
$167$	5.25731	−	7.23607i	0.406823	−	0.559944i	−0.555617	−	0.831438i	$-0.687518\pi$
$167$	5.25731	−	7.23607i	0.406823	−	0.559944i	0.962440	+	0.271495i	$0.0875179\pi$
$168$		0			0
$169$	−6.65058	−	4.83193i	−0.511583	−	0.371687i
$170$	−5.57768	−	2.28559i	−0.427789	−	0.175297i
$171$		0			0
$172$	−5.60700	−	7.71737i	−0.427530	−	0.588444i
$173$	15.5394	−	5.04904i	1.18144	−	0.383872i	0.348536	−	0.937295i	$-0.386679\pi$
$173$	15.5394	−	5.04904i	1.18144	−	0.383872i	0.832900	+	0.553424i	$0.186679\pi$
$174$		0			0
$175$	−1.54717	+	10.2726i	−0.116955	+	0.776533i
$176$	−0.520147			−0.0392076
$177$		0			0
$178$	5.79486	+	7.97594i	0.434343	+	0.597822i
$179$	−2.97599	+	2.16219i	−0.222436	+	0.161609i	−0.693423	−	0.720531i	$-0.743898\pi$
$179$	−2.97599	+	2.16219i	−0.222436	+	0.161609i	0.470986	+	0.882140i	$0.343898\pi$
$180$		0			0
$181$	18.6472	+	13.5480i	1.38604	+	1.00702i	0.996287	+	0.0860956i	$0.0274391\pi$
$181$	18.6472	+	13.5480i	1.38604	+	1.00702i	0.389751	+	0.920920i	$0.372561\pi$
$182$		−	4.54222i		−	0.336691i
$183$		0			0
$184$	1.19301	−	3.67171i	0.0879500	−	0.270682i
$185$	−4.49975	+	10.9811i	−0.330828	+	0.807343i
$186$		0			0
$187$	1.33354	+	0.433294i	0.0975183	+	0.0316856i
$188$	−8.81224	−	2.86327i	−0.642699	−	0.208826i
$189$		0			0
$190$	5.82588	−	14.2173i	0.422654	−	1.03143i
$191$	0.552424	−	1.70019i	0.0399720	−	0.123021i	−0.929079	−	0.369881i	$-0.879399\pi$
$191$	0.552424	−	1.70019i	0.0399720	−	0.123021i	0.969051	+	0.246859i	$0.0793986\pi$
$192$		0			0
$193$		−	6.60138i		−	0.475178i	−0.971366	−	0.237589i	$-0.923643\pi$
$193$		−	6.60138i		−	0.475178i	0.971366	−	0.237589i	$-0.0763571\pi$
$194$	−8.70483	−	6.32443i	−0.624970	−	0.454068i
$195$		0			0
$196$	2.17078	−	1.57716i	0.155056	−	0.112655i
$197$	−7.43989	−	10.2401i	−0.530070	−	0.729579i	0.457071	−	0.889430i	$-0.348899\pi$
$197$	−7.43989	−	10.2401i	−0.530070	−	0.729579i	−0.987141	+	0.159851i	$0.948899\pi$
$198$		0			0
$199$	−6.24148			−0.442447			−0.221223	−	0.975223i	$-0.571005\pi$
$199$	−6.24148			−0.442447			−0.221223	+	0.975223i	$0.571005\pi$
$200$	3.50859	−	3.56227i	0.248095	−	0.251891i
$201$		0			0
$202$	−16.7766	+	5.45106i	−1.18040	+	0.383535i
$203$	−11.0323	−	15.1846i	−0.774314	−	1.06575i
$204$		0			0
$205$	−6.66988	−	2.73314i	−0.465845	−	0.190891i
$206$	−7.03649	−	5.11231i	−0.490256	−	0.356192i
$207$		0			0
$208$	−1.28501	+	1.76867i	−0.0890995	+	0.122635i
$209$	−1.10445	+	3.39915i	−0.0763965	+	0.235124i
$210$		0			0
$211$	−6.94607	−	21.3778i	−0.478187	−	1.47171i	−0.841611	−	0.540084i	$-0.818392\pi$
$211$	−6.94607	−	21.3778i	−0.478187	−	1.47171i	0.363424	−	0.931624i	$-0.381608\pi$
$212$	2.31906	+	0.753509i	0.159274	+	0.0517512i
$213$		0			0
$214$	1.67171	+	5.14500i	0.114276	+	0.351705i
$215$	−21.2707	−	1.59283i	−1.45065	−	0.108630i
$216$		0			0
$217$	9.04331	−	12.4471i	0.613900	−	0.844961i
$218$		−	2.88377i		−	0.195314i
$219$		0			0
$220$	−0.752000	+	0.887277i	−0.0506999	+	0.0598202i
$221$	4.76783	−	3.46403i	0.320719	−	0.233016i
$222$		0			0
$223$	17.0524	−	5.54065i	1.14191	−	0.371029i	0.323820	−	0.946119i	$-0.395033\pi$
$223$	17.0524	−	5.54065i	1.14191	−	0.371029i	0.818091	+	0.575089i	$0.195033\pi$
$224$	2.07768			0.138821
$225$		0			0
$226$	−6.36955			−0.423696
$227$	8.42412	−	2.73716i	0.559129	−	0.181672i	−0.0158003	−	0.999875i	$-0.505030\pi$
$227$	8.42412	−	2.73716i	0.559129	−	0.181672i	0.574929	+	0.818203i	$0.305030\pi$
$228$		0			0
$229$	17.8490	−	12.9681i	1.17950	−	0.856953i	0.187380	−	0.982287i	$-0.440000\pi$
$229$	17.8490	−	12.9681i	1.17950	−	0.856953i	0.992115	+	0.125334i	$0.0400003\pi$
$230$	−4.53849	−	7.34342i	−0.299259	−	0.484211i
$231$		0			0
$232$			9.03373i			0.593093i
$233$	−6.78466	+	9.33828i	−0.444478	+	0.611771i	−0.971200	−	0.238267i	$-0.923421\pi$
$233$	−6.78466	+	9.33828i	−0.444478	+	0.611771i	0.526722	+	0.850037i	$0.323421\pi$
$234$		0			0
$235$	−17.6245	+	10.8925i	−1.14969	+	0.710550i
$236$	−2.67261	−	8.22545i	−0.173972	−	0.535431i
$237$		0			0
$238$	−5.32672	−	1.73076i	−0.345280	−	0.112188i
$239$	−0.273457	−	0.841616i	−0.0176885	−	0.0544396i	0.941823	−	0.336110i	$-0.109111\pi$
$239$	−0.273457	−	0.841616i	−0.0176885	−	0.0544396i	−0.959511	+	0.281671i	$0.909111\pi$
$240$		0			0
$241$	3.91637	−	12.0534i	0.252276	−	0.776425i	−0.742078	−	0.670313i	$-0.766160\pi$
$241$	3.91637	−	12.0534i	0.252276	−	0.776425i	0.994354	−	0.106112i	$-0.0338402\pi$
$242$	−6.30661	+	8.68031i	−0.405404	+	0.557991i
$243$		0			0
$244$	10.1841	+	7.39919i	0.651971	+	0.473684i
$245$	0.448039	−	5.98314i	0.0286242	−	0.382248i
$246$		0			0
$247$	8.82968	+	12.1530i	0.561819	+	0.773278i
$248$	−7.04264	+	2.28829i	−0.447208	+	0.145307i
$249$		0			0
$250$	−1.00406	−	11.1352i	−0.0635021	−	0.704250i
$251$	−18.0966			−1.14225			−0.571124	−	0.820864i	$-0.693493\pi$
$251$	−18.0966			−1.14225			−0.571124	+	0.820864i	$0.693493\pi$
$252$		0			0
$253$	1.18034	+	1.62460i	0.0742073	+	0.102138i
$254$	12.1088	−	8.79756i	0.759774	−	0.552008i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			1.28053i			0.0798774i	0.999202	+	0.0399387i	$0.0127163\pi$
$257$			1.28053i			0.0798774i	−0.999202	+	0.0399387i	$0.987284\pi$
$258$		0			0
$259$	−3.40742	+	10.4870i	−0.211727	+	0.651629i
$260$	1.15923	+	4.74904i	0.0718921	+	0.294523i
$261$		0			0
$262$	−13.1770	−	4.28147i	−0.814079	−	0.264510i
$263$	6.76605	+	2.19842i	0.417213	+	0.135561i	0.510098	−	0.860116i	$-0.329609\pi$
$263$	6.76605	+	2.19842i	0.417213	+	0.135561i	−0.0928855	+	0.995677i	$0.529609\pi$
$264$		0			0
$265$	4.63812	−	2.86652i	0.284918	−	0.176089i
$266$	4.41164	−	13.5776i	0.270495	−	0.832498i
$267$		0			0
$268$		−	6.69385i		−	0.408892i
$269$	7.62892	+	5.54274i	0.465143	+	0.337947i	0.795546	−	0.605894i	$-0.207184\pi$
$269$	7.62892	+	5.54274i	0.465143	+	0.337947i	−0.330402	+	0.943840i	$0.607184\pi$
$270$		0			0
$271$	−1.11231	+	0.808141i	−0.0675681	+	0.0490911i	−0.621057	−	0.783766i	$-0.713296\pi$
$271$	−1.11231	+	0.808141i	−0.0675681	+	0.0490911i	0.553488	+	0.832857i	$0.313296\pi$
$272$	1.58450	+	2.18088i	0.0960746	+	0.132235i
$273$		0			0
$274$	−19.8939			−1.20183
$275$	0.426333	+	2.56555i	0.0257088	+	0.154709i
$276$		0			0
$277$	18.6375	−	6.05571i	1.11982	−	0.363852i	0.310122	−	0.950697i	$-0.399630\pi$
$277$	18.6375	−	6.05571i	1.11982	−	0.363852i	0.809700	+	0.586845i	$0.199630\pi$
$278$	3.31725	+	4.56581i	0.198956	+	0.273839i
$279$		0			0
$280$	3.00380	−	3.54415i	0.179512	−	0.211804i
$281$	−2.29605	−	1.66817i	−0.136971	−	0.0995150i	0.517190	−	0.855871i	$-0.326978\pi$
$281$	−2.29605	−	1.66817i	−0.136971	−	0.0995150i	−0.654161	+	0.756356i	$0.726978\pi$
$282$		0			0
$283$	−1.31285	+	1.80699i	−0.0780411	+	0.107414i	−0.846253	−	0.532781i	$-0.821147\pi$
$283$	−1.31285	+	1.80699i	−0.0780411	+	0.107414i	0.768212	+	0.640196i	$0.221147\pi$
$284$	−2.52436	+	7.76919i	−0.149793	+	0.461016i
$285$		0			0
$286$	−0.351396	−	1.08149i	−0.0207785	−	0.0639496i
$287$	−6.36978	−	2.06967i	−0.375996	−	0.122169i
$288$		0			0
$289$	3.00770	+	9.25673i	0.176923	+	0.544514i
$290$	15.4099	+	13.0605i	0.904901	+	0.766938i
$291$		0			0
$292$	2.25914	−	3.10944i	0.132206	−	0.181966i
$293$		−	24.0260i		−	1.40361i	−0.712367	−	0.701807i	$-0.752377\pi$
$293$		−	24.0260i		−	1.40361i	0.712367	−	0.701807i	$-0.247623\pi$
$294$		0			0
$295$	−17.8950	−	7.33292i	−1.04189	−	0.426939i
$296$	4.29360	−	3.11949i	0.249561	−	0.181316i
$297$		0			0
$298$	14.3568	−	4.66479i	0.831664	−	0.270224i
$299$	8.44016			0.488107
$300$		0			0
$301$	−19.8194			−1.14237
$302$	19.9107	−	6.46937i	1.14573	−	0.372271i
$303$		0			0
$304$	−5.55899	+	4.03884i	−0.318830	+	0.231643i
$305$	27.3453	−	6.67490i	1.56579	−	0.382204i
$306$		0			0
$307$		−	17.1204i		−	0.977111i	−0.872533	−	0.488556i	$-0.837524\pi$
$307$		−	17.1204i		−	0.977111i	0.872533	−	0.488556i	$-0.162476\pi$
$308$	−0.635220	+	0.874305i	−0.0361950	+	0.0498182i
$309$		0			0
$310$	−6.27846	+	15.3218i	−0.356592	+	0.870218i
$311$	6.22754	+	19.1664i	0.353131	+	1.08683i	0.957085	+	0.289807i	$0.0935912\pi$
$311$	6.22754	+	19.1664i	0.353131	+	1.08683i	−0.603954	+	0.797020i	$0.706409\pi$
$312$		0			0
$313$	−24.2560	−	7.88127i	−1.37103	−	0.445476i	−0.471322	−	0.881961i	$-0.656223\pi$
$313$	−24.2560	−	7.88127i	−1.37103	−	0.445476i	−0.899711	+	0.436486i	$0.856223\pi$
$314$	1.76757	+	5.44002i	0.0997498	+	0.306998i
$315$		0			0
$316$	1.08540	−	3.34052i	0.0610586	−	0.187919i
$317$	−18.5260	+	25.4988i	−1.04052	+	1.43215i	−0.143775	+	0.989610i	$0.545924\pi$
$317$	−18.5260	+	25.4988i	−1.04052	+	1.43215i	−0.896747	+	0.442544i	$0.854076\pi$
$318$		0			0
$319$	−3.80146	−	2.76193i	−0.212841	−	0.154638i
$320$	−2.17229	+	0.530249i	−0.121435	+	0.0296418i
$321$		0			0
$322$	−4.71477	−	6.48932i	−0.262744	−	0.361636i
$323$	17.6165	−	5.72394i	0.980207	−	0.318488i
$324$		0			0
$325$	9.77695	+	4.88847i	0.542328	+	0.271164i
$326$	−11.8950			−0.658805
$327$		0			0
$328$	1.89477	+	2.60793i	0.104621	+	0.143999i
$329$	−15.5746	+	11.3156i	−0.858656	+	0.623850i
$330$		0			0
$331$	5.90633	+	4.29120i	0.324641	+	0.235866i	0.738153	−	0.674633i	$-0.235698\pi$
$331$	5.90633	+	4.29120i	0.324641	+	0.235866i	−0.413512	+	0.910499i	$0.635698\pi$
$332$			13.1311i			0.720663i
$333$		0			0
$334$	−2.76393	+	8.50651i	−0.151236	+	0.465455i
$335$	−11.4185	−	9.67761i	−0.623859	−	0.528744i
$336$		0			0
$337$	25.4358	+	8.26459i	1.38558	+	0.450201i	0.904498	−	0.426477i	$-0.140246\pi$
$337$	25.4358	+	8.26459i	1.38558	+	0.450201i	0.481077	+	0.876678i	$0.340246\pi$
$338$	7.81822	+	2.54029i	0.425255	+	0.138174i
$339$		0			0
$340$	6.01098	+	0.450124i	0.325991	+	0.0244114i
$341$	1.19025	−	3.66321i	0.0644556	−	0.198374i
$342$		0			0
$343$		−	20.1187i		−	1.08631i
$344$	7.71737	+	5.60700i	0.416093	+	0.302309i
$345$		0			0
$346$	−13.2186	+	9.60385i	−0.710635	+	0.516306i
$347$	2.86327	+	3.94095i	0.153708	+	0.211562i	0.878926	−	0.476958i	$-0.158261\pi$
$347$	2.86327	+	3.94095i	0.153708	+	0.211562i	−0.725217	+	0.688520i	$0.758261\pi$
$348$		0			0
$349$	−16.7173			−0.894855			−0.447428	−	0.894320i	$-0.647660\pi$
$349$	−16.7173			−0.894855			−0.447428	+	0.894320i	$0.647660\pi$
$350$	−1.70295	−	10.2479i	−0.0910265	−	0.547773i
$351$		0			0
$352$	0.494689	−	0.160734i	0.0263670	−	0.00856717i
$353$	15.9175	+	21.9086i	0.847203	+	1.16608i	0.984472	+	0.175541i	$0.0561676\pi$
$353$	15.9175	+	21.9086i	0.847203	+	1.16608i	−0.137269	+	0.990534i	$0.543832\pi$
$354$		0			0
$355$	9.60324	+	15.5384i	0.509687	+	0.824691i
$356$	−7.97594	−	5.79486i	−0.422724	−	0.307127i
$357$		0			0
$358$	2.16219	−	2.97599i	0.114275	−	0.157286i
$359$	−2.62299	+	8.07273i	−0.138436	+	0.426062i	−0.996109	−	0.0881339i	$-0.971910\pi$
$359$	−2.62299	+	8.07273i	−0.138436	+	0.426062i	0.857673	+	0.514196i	$0.171910\pi$
$360$		0			0
$361$	8.71879	+	26.8337i	0.458884	+	1.41230i
$362$	−21.9211	−	7.12261i	−1.15215	−	0.374356i
$363$		0			0
$364$	1.40362	+	4.31990i	0.0735698	+	0.226424i
$365$	−2.03800	−	8.34915i	−0.106674	−	0.437014i
$366$		0			0
$367$	−7.49289	+	10.3131i	−0.391126	+	0.538339i	−0.958489	−	0.285129i	$-0.907964\pi$
$367$	−7.49289	+	10.3131i	−0.391126	+	0.538339i	0.567363	+	0.823468i	$0.307964\pi$
$368$			3.86067i			0.201251i
$369$		0			0
$370$	0.886181	−	11.8341i	0.0460703	−	0.615225i
$371$	4.09867	−	2.97786i	0.212792	−	0.154603i
$372$		0			0
$373$	−10.4051	+	3.38081i	−0.538754	+	0.175052i	−0.565740	−	0.824584i	$-0.691409\pi$
$373$	−10.4051	+	3.38081i	−0.538754	+	0.175052i	0.0269853	+	0.999636i	$0.491409\pi$
$374$	−1.40217			−0.0725045
$375$		0			0
$376$	9.26574			0.477844
$377$	−18.7829	+	6.10292i	−0.967367	+	0.314316i
$378$		0			0
$379$	−11.5124	+	8.36427i	−0.591354	+	0.429644i	−0.842799	−	0.538228i	$-0.819094\pi$
$379$	−11.5124	+	8.36427i	−0.591354	+	0.429644i	0.251446	+	0.967871i	$0.419094\pi$
$380$	−1.14735	+	15.3218i	−0.0588578	+	0.785990i
$381$		0			0
$382$			1.78768i			0.0914658i
$383$	4.21101	−	5.79595i	0.215172	−	0.296159i	−0.687763	−	0.725935i	$-0.741407\pi$
$383$	4.21101	−	5.79595i	0.215172	−	0.296159i	0.902936	+	0.429776i	$0.141407\pi$
$384$		0			0
$385$	0.573040	+	2.34759i	0.0292048	+	0.119644i
$386$	2.03994	+	6.27828i	0.103830	+	0.319556i
$387$		0			0
$388$	10.2331	+	3.32495i	0.519509	+	0.168799i
$389$	−0.283978	−	0.873994i	−0.0143982	−	0.0443133i	0.943599	−	0.331090i	$-0.107416\pi$
$389$	−0.283978	−	0.873994i	−0.0143982	−	0.0443133i	−0.957998	+	0.286776i	$0.907416\pi$
$390$		0			0
$391$	3.21602	−	9.89790i	0.162641	−	0.500558i
$392$	−1.57716	+	2.17078i	−0.0796588	+	0.109641i
$393$		0			0
$394$	10.2401	+	7.43989i	0.515891	+	0.374816i
$395$	−4.12911	−	6.68104i	−0.207758	−	0.336160i
$396$		0			0
$397$	12.8148	+	17.6381i	0.643159	+	0.885232i	0.998779	−	0.0493984i	$-0.0157304\pi$
$397$	12.8148	+	17.6381i	0.643159	+	0.885232i	−0.355620	+	0.934630i	$0.615730\pi$
$398$	5.93600	−	1.92872i	0.297545	−	0.0966782i
$399$		0			0
$400$	−2.23607	+	4.47214i	−0.111803	+	0.223607i
$401$	−22.8035			−1.13875			−0.569375	−	0.822078i	$-0.692815\pi$
$401$	−22.8035			−1.13875			−0.569375	+	0.822078i	$0.692815\pi$
$402$		0			0
$403$	−9.51560	−	13.0971i	−0.474006	−	0.652413i
$404$	14.2711	−	10.3685i	0.710011	−	0.515853i
$405$		0			0
$406$	15.1846	+	11.0323i	0.753600	+	0.547523i
$407$			2.76052i			0.136834i
$408$		0			0
$409$	−1.54554	+	4.75668i	−0.0764220	+	0.235203i	−0.981969	−	0.189044i	$-0.939461\pi$
$409$	−1.54554	+	4.75668i	−0.0764220	+	0.235203i	0.905547	+	0.424247i	$0.139461\pi$
$410$	7.18802	+	0.538266i	0.354991	+	0.0265830i
$411$		0			0
$412$	8.27189	+	2.68770i	0.407527	+	0.132414i
$413$	−17.0899	−	5.55284i	−0.840938	−	0.273237i
$414$		0			0
$415$	22.3993	+	18.9842i	1.09954	+	0.931900i
$416$	0.675571	−	2.07919i	0.0331226	−	0.101941i
$417$		0			0
$418$		−	3.57408i		−	0.174814i
$419$	18.4661	+	13.4164i	0.902128	+	0.655434i	0.939012	−	0.343885i	$-0.111743\pi$
$419$	18.4661	+	13.4164i	0.902128	+	0.655434i	−0.0368836	+	0.999320i	$0.511743\pi$
$420$		0			0
$421$	−12.7124	+	9.23612i	−0.619566	+	0.450141i	−0.852770	−	0.522287i	$-0.825079\pi$
$421$	−12.7124	+	9.23612i	−0.619566	+	0.450141i	0.233204	+	0.972428i	$0.425079\pi$
$422$	13.2122	+	18.1850i	0.643160	+	0.885234i
$423$		0			0
$424$	−2.43841			−0.118419
$425$	9.45818	−	9.60288i	0.458789	−	0.465808i
$426$		0			0
$427$	24.8743	−	8.08215i	1.20375	−	0.391123i
$428$	−3.17979	−	4.37660i	−0.153701	−	0.211551i
$429$		0			0
$430$	20.7219	−	5.05815i	0.999298	−	0.243926i
$431$	−7.73154	−	5.61729i	−0.372415	−	0.270576i	0.385796	−	0.922584i	$-0.373927\pi$
$431$	−7.73154	−	5.61729i	−0.372415	−	0.270576i	−0.758212	+	0.652008i	$0.773927\pi$
$432$		0			0
$433$	4.77408	−	6.57096i	0.229428	−	0.315780i	−0.678747	−	0.734373i	$-0.737476\pi$
$433$	4.77408	−	6.57096i	0.229428	−	0.315780i	0.908174	+	0.418593i	$0.137476\pi$
$434$	−4.75435	+	14.6324i	−0.228216	+	0.702377i
$435$		0			0
$436$	0.891135	+	2.74263i	0.0426776	+	0.131348i
$437$	25.2294	+	8.19753i	1.20689	+	0.392141i
$438$		0			0
$439$	−2.84899	−	8.76829i	−0.135975	−	0.418488i	0.859766	−	0.510689i	$-0.170610\pi$
$439$	−2.84899	−	8.76829i	−0.135975	−	0.418488i	−0.995740	+	0.0922014i	$0.970610\pi$
$440$	0.441011	−	1.07623i	0.0210244	−	0.0513073i
$441$		0			0
$442$	−3.46403	+	4.76783i	−0.164767	+	0.226782i
$443$		−	9.63232i		−	0.457645i	−0.973468	−	0.228823i	$-0.926512\pi$
$443$		−	9.63232i		−	0.457645i	0.973468	−	0.228823i	$-0.0734876\pi$
$444$		0			0
$445$	−21.4162	+	5.22762i	−1.01522	+	0.247813i
$446$	−14.5056	+	10.5389i	−0.686861	+	0.499033i
$447$		0			0
$448$	−1.97599	+	0.642040i	−0.0933570	+	0.0303335i
$449$	−21.3096			−1.00566			−0.502831	−	0.864385i	$-0.667708\pi$
$449$	−21.3096			−1.00566			−0.502831	+	0.864385i	$0.667708\pi$
$450$		0			0
$451$	−1.67674			−0.0789544
$452$	6.05780	−	1.96830i	0.284935	−	0.0925810i
$453$		0			0
$454$	−7.16599	+	5.20640i	−0.336317	+	0.244348i
$455$	9.39825	+	3.85116i	0.440597	+	0.180545i
$456$		0			0
$457$			13.4662i			0.629923i	0.949104	+	0.314961i	$0.101992\pi$
$457$			13.4662i			0.629923i	−0.949104	+	0.314961i	$0.898008\pi$
$458$	−12.9681	+	17.8490i	−0.605958	+	0.834029i
$459$		0			0
$460$	6.58560	+	5.58154i	0.307055	+	0.260241i
$461$	−10.1468	−	31.2286i	−0.472582	−	1.45446i	−0.849191	−	0.528086i	$-0.822910\pi$
$461$	−10.1468	−	31.2286i	−0.472582	−	1.45446i	0.376608	−	0.926373i	$-0.377090\pi$
$462$		0			0
$463$	−21.8083	−	7.08596i	−1.01352	−	0.329312i	−0.245264	−	0.969456i	$-0.578875\pi$
$463$	−21.8083	−	7.08596i	−1.01352	−	0.329312i	−0.768255	+	0.640144i	$0.778875\pi$
$464$	−2.79158	−	8.59159i	−0.129596	−	0.398854i
$465$		0			0
$466$	3.56690	−	10.9778i	0.165234	−	0.508537i
$467$	12.2459	−	16.8551i	0.566674	−	0.779960i	−0.425482	−	0.904967i	$-0.639895\pi$
$467$	12.2459	−	16.8551i	0.566674	−	0.779960i	0.992156	+	0.125007i	$0.0398954\pi$
$468$		0			0
$469$	−11.2516	−	8.17475i	−0.519549	−	0.377475i
$470$	13.3959	−	15.8057i	0.617907	−	0.729062i
$471$		0			0
$472$	5.08361	+	6.99698i	0.233992	+	0.322062i
$473$	−4.71894	+	1.53328i	−0.216977	+	0.0705001i
$474$		0			0
$475$	24.4774	+	24.1086i	1.12310	+	1.10618i
$476$	5.60085			0.256714
$477$		0			0
$478$	0.520147	+	0.715921i	0.0237910	+	0.0327455i
$479$	−10.9401	+	7.94842i	−0.499864	+	0.363172i	−0.808965	−	0.587857i	$-0.799972\pi$
$479$	−10.9401	+	7.94842i	−0.499864	+	0.363172i	0.309101	+	0.951029i	$0.399972\pi$
$480$		0			0
$481$	9.38664	+	6.81980i	0.427994	+	0.310956i
$482$			12.6736i			0.577269i
$483$		0			0
$484$	3.31558	−	10.2043i	0.150708	−	0.463832i
$485$	20.4663	−	12.6489i	0.929326	−	0.574355i
$486$		0			0
$487$	−25.3198	−	8.22690i	−1.14735	−	0.372796i	−0.327205	−	0.944953i	$-0.606107\pi$
$487$	−25.3198	−	8.22690i	−1.14735	−	0.372796i	−0.820144	+	0.572157i	$0.806107\pi$
$488$	−11.9721	−	3.88998i	−0.541953	−	0.176091i
$489$		0			0
$490$	1.42278	+	5.82875i	0.0642746	+	0.263316i
$491$	3.71521	−	11.4342i	0.167665	−	0.516020i	−0.831558	−	0.555438i	$-0.812551\pi$
$491$	3.71521	−	11.4342i	0.167665	−	0.516020i	0.999223	+	0.0394184i	$0.0125505\pi$
$492$		0			0
$493$			24.3524i			1.09678i
$494$	−12.1530	−	8.82968i	−0.546790	−	0.397266i
$495$		0			0
$496$	5.99083	−	4.35259i	0.268996	−	0.195437i
$497$	9.97625	+	13.7311i	0.447496	+	0.615925i
$498$		0			0
$499$	27.3600			1.22480			0.612400	−	0.790548i	$-0.290204\pi$
$499$	27.3600			1.22480			0.612400	+	0.790548i	$0.290204\pi$
$500$	4.39587	+	10.2799i	0.196589	+	0.459731i
$501$		0			0
$502$	17.2109	−	5.59216i	0.768161	−	0.249590i
$503$	−5.38563	−	7.41268i	−0.240133	−	0.330515i	0.671892	−	0.740649i	$-0.265482\pi$
$503$	−5.38563	−	7.41268i	−0.240133	−	0.330515i	−0.912025	+	0.410134i	$0.865482\pi$
$504$		0			0
$505$	2.94548	−	39.3341i	0.131072	−	1.75034i
$506$	−1.62460	−	1.18034i	−0.0722222	−	0.0524725i
$507$		0			0
$508$	−8.79756	+	12.1088i	−0.390329	+	0.537241i
$509$	−0.725667	+	2.23337i	−0.0321646	+	0.0989925i	−0.965850	−	0.259102i	$-0.916573\pi$
$509$	−0.725667	+	2.23337i	−0.0321646	+	0.0989925i	0.933685	+	0.358094i	$0.116573\pi$
$510$		0			0
$511$	−2.46767	−	7.59470i	−0.109163	−	0.335970i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$		0			0
$514$	−0.395706	−	1.21786i	−0.0174538	−	0.0537174i
$515$	16.5438	−	10.2246i	0.729006	−	0.450551i
$516$		0			0
$517$	−2.83286	+	3.89910i	−0.124589	+	0.171482i
$518$		−	11.0267i		−	0.484483i
$519$		0			0
$520$	−2.57002	−	4.15838i	−0.112703	−	0.182357i
$521$	−1.24129	+	0.901848i	−0.0543818	+	0.0395107i	−0.614644	−	0.788805i	$-0.710700\pi$
$521$	−1.24129	+	0.901848i	−0.0543818	+	0.0395107i	0.560262	+	0.828315i	$0.310700\pi$
$522$		0			0
$523$	39.5506	−	12.8508i	1.72943	−	0.561926i	0.736062	−	0.676914i	$-0.236683\pi$
$523$	39.5506	−	12.8508i	1.72943	−	0.561926i	0.993367	+	0.114988i	$0.0366830\pi$
$524$	13.8551			0.605265
$525$		0			0
$526$	−7.11425			−0.310196
$527$	−18.9850	+	6.16859i	−0.826999	+	0.268708i
$528$		0			0
$529$	−6.54920	+	4.75827i	−0.284748	+	0.206881i
$530$	−3.52532	+	4.15948i	−0.153130	+	0.180676i
$531$		0			0
$532$			14.2764i			0.618959i
$533$	−4.14234	+	5.70144i	−0.179425	+	0.246957i
$534$		0			0
$535$	−12.0628	−	0.903310i	−0.521522	−	0.0390535i
$536$	2.06851	+	6.36623i	0.0893462	+	0.274979i
$537$		0			0
$538$	−8.96833	−	2.91399i	−0.386652	−	0.125631i
$539$	−0.431287	−	1.32737i	−0.0185769	−	0.0571737i
$540$		0			0
$541$	5.88428	−	18.1100i	0.252985	−	0.778608i	−0.741235	−	0.671246i	$-0.765760\pi$
$541$	5.88428	−	18.1100i	0.252985	−	0.778608i	0.994220	−	0.107362i	$-0.0342404\pi$
$542$	0.808141	−	1.11231i	0.0347126	−	0.0477778i
$543$		0			0
$544$	−2.18088	−	1.58450i	−0.0935045	−	0.0679350i
$545$	5.96679	+	2.44503i	0.255589	+	0.104734i
$546$		0			0
$547$	−16.0588	−	22.1030i	−0.686624	−	0.945057i	0.313365	−	0.949633i	$-0.398544\pi$
$547$	−16.0588	−	22.1030i	−0.686624	−	0.945057i	−0.999990	+	0.00457542i	$0.998544\pi$
$548$	18.9202	−	6.14755i	0.808231	−	0.262610i
$549$		0			0
$550$	−1.19827	−	2.30824i	−0.0510942	−	0.0984238i
$551$	−62.0734			−2.64441
$552$		0			0
$553$	−4.28949	−	5.90398i	−0.182408	−	0.251063i
$554$	−15.8540	+	11.5186i	−0.673574	+	0.489380i
$555$		0			0
$556$	−4.56581	−	3.31725i	−0.193633	−	0.140683i
$557$			9.89921i			0.419443i	0.977761	+	0.209721i	$0.0672557\pi$
$557$			9.89921i			0.419443i	−0.977761	+	0.209721i	$0.932744\pi$
$558$		0			0
$559$	−6.44440	+	19.8338i	−0.272569	+	0.838881i
$560$	−1.76158	+	4.29892i	−0.0744404	+	0.181662i
$561$		0			0
$562$	2.69916	+	0.877011i	0.113857	+	0.0369945i
$563$	1.91338	+	0.621694i	0.0806392	+	0.0262013i	0.349059	−	0.937101i	$-0.386501\pi$
$563$	1.91338	+	0.621694i	0.0806392	+	0.0262013i	−0.268420	+	0.963302i	$0.586501\pi$
$564$		0			0
$565$	5.40048	−	13.1792i	0.227200	−	0.554452i
$566$	0.690208	−	2.12424i	0.0290116	−	0.0892886i
$567$		0			0
$568$		−	8.16901i		−	0.342764i
$569$	−19.0969	−	13.8747i	−0.800585	−	0.581659i	0.110501	−	0.993876i	$-0.464755\pi$
$569$	−19.0969	−	13.8747i	−0.800585	−	0.581659i	−0.911086	+	0.412217i	$0.864755\pi$
$570$		0			0
$571$	−17.1782	+	12.4807i	−0.718886	+	0.522301i	−0.886028	−	0.463631i	$-0.846546\pi$
$571$	−17.1782	+	12.4807i	−0.718886	+	0.522301i	0.167142	+	0.985933i	$0.446546\pi$
$572$	0.668395	+	0.919967i	0.0279470	+	0.0384657i
$573$		0			0
$574$	6.69758			0.279552
$575$	19.0422	−	3.16435i	0.794115	−	0.131963i
$576$		0			0
$577$	−43.1167	+	14.0095i	−1.79497	+	0.583222i	−0.999734	−	0.0230749i	$-0.992654\pi$
$577$	−43.1167	+	14.0095i	−1.79497	+	0.583222i	−0.795238	+	0.606297i	$0.792654\pi$
$578$	−5.72098	−	7.87425i	−0.237961	−	0.327526i
$579$		0			0
$580$	−18.6916	−	7.65933i	−0.776127	−	0.318036i
$581$	22.0718	+	16.0361i	0.915694	+	0.665291i
$582$		0			0
$583$	0.745506	−	1.02610i	0.0308757	−	0.0424967i
$584$	−1.18770	+	3.65537i	−0.0491474	+	0.151260i
$585$		0			0
$586$	7.42445	+	22.8501i	0.306701	+	0.943929i
$587$	15.5245	+	5.04421i	0.640764	+	0.208197i	0.611337	−	0.791370i	$-0.290632\pi$
$587$	15.5245	+	5.04421i	0.640764	+	0.208197i	0.0294265	+	0.999567i	$0.490632\pi$
$588$		0			0
$589$	−15.7235	−	48.3920i	−0.647877	−	1.99396i
$590$	19.2852	+	1.44415i	0.793959	+	0.0594545i
$591$		0			0
$592$	−3.11949	+	4.29360i	−0.128210	+	0.176466i
$593$		−	32.8357i		−	1.34840i	−0.738549	−	0.674199i	$-0.764489\pi$
$593$		−	32.8357i		−	1.34840i	0.738549	−	0.674199i	$-0.235511\pi$
$594$		0			0
$595$	8.09740	−	9.55403i	0.331961	−	0.391677i
$596$	−12.2126	+	8.87296i	−0.500247	+	0.363451i
$597$		0			0
$598$	−8.02707	+	2.60815i	−0.328251	+	0.106655i
$599$	−13.1905			−0.538947			−0.269474	−	0.963008i	$-0.586850\pi$
$599$	−13.1905			−0.538947			−0.269474	+	0.963008i	$0.586850\pi$
$600$		0			0
$601$	−19.1992			−0.783152			−0.391576	−	0.920146i	$-0.628070\pi$
$601$	−19.1992			−0.783152			−0.391576	+	0.920146i	$0.628070\pi$
$602$	18.8494	−	6.12454i	0.768244	−	0.249618i
$603$		0			0
$604$	−16.9370	+	12.3055i	−0.689158	+	0.500703i
$605$	−12.6132	−	20.4086i	−0.512800	−	0.829728i
$606$		0			0
$607$			6.54268i			0.265559i	0.991146	+	0.132779i	$0.0423902\pi$
$607$			6.54268i			0.265559i	−0.991146	+	0.132779i	$0.957610\pi$
$608$	4.03884	−	5.55899i	0.163797	−	0.225447i
$609$		0			0
$610$	−23.9443	+	14.7984i	−0.969475	+	0.599169i
$611$	6.25966	+	19.2653i	0.253239	+	0.779389i
$612$		0			0
$613$	8.87528	+	2.88375i	0.358469	+	0.116474i	0.482714	−	0.875778i	$-0.339651\pi$
$613$	8.87528	+	2.88375i	0.358469	+	0.116474i	−0.124245	+	0.992252i	$0.539651\pi$
$614$	5.29049	+	16.2824i	0.213507	+	0.657106i
$615$		0			0
$616$	0.333955	−	1.02781i	0.0134554	−	0.0414115i
$617$	19.3979	−	26.6989i	0.780929	−	1.07486i	−0.214250	−	0.976779i	$-0.568731\pi$
$617$	19.3979	−	26.6989i	0.780929	−	1.07486i	0.995179	−	0.0980778i	$-0.0312694\pi$
$618$		0			0
$619$	22.7569	+	16.5339i	0.914678	+	0.664553i	0.942194	−	0.335069i	$-0.108760\pi$
$619$	22.7569	+	16.5339i	0.914678	+	0.664553i	−0.0275155	+	0.999621i	$0.508760\pi$
$620$	1.23648	−	16.5120i	0.0496583	−	0.663139i
$621$		0			0
$622$	−11.8455	−	16.3039i	−0.474961	−	0.653727i
$623$	−19.4809	+	6.32974i	−0.780487	+	0.253596i
$624$		0			0
$625$	23.8910	+	7.36356i	0.955638	+	0.294542i
$626$	25.5043			1.01936
$627$		0			0
$628$	−3.36212	−	4.62756i	−0.134163	−	0.184660i
$629$	11.5743	−	8.40925i	0.461499	−	0.335299i
$630$		0			0
$631$	1.93909	+	1.40883i	0.0771940	+	0.0560847i	0.625713	−	0.780053i	$-0.284808\pi$
$631$	1.93909	+	1.40883i	0.0771940	+	0.0560847i	−0.548519	+	0.836138i	$0.684808\pi$
$632$			3.51243i			0.139717i
$633$		0			0
$634$	9.73967	−	29.9756i	0.386812	−	1.19048i
$635$	7.93640	+	32.5133i	0.314946	+	1.29025i
$636$		0			0
$637$	−5.57895	−	1.81271i	−0.221046	−	0.0718223i
$638$	4.46889	+	1.45203i	0.176925	+	0.0574864i
$639$		0			0
$640$	1.90211	−	1.17557i	0.0751876	−	0.0464685i
$641$	−3.76246	+	11.5797i	−0.148608	+	0.457370i	−0.997457	−	0.0712658i	$-0.977296\pi$
$641$	−3.76246	+	11.5797i	−0.148608	+	0.457370i	0.848849	+	0.528635i	$0.177296\pi$
$642$		0			0
$643$		−	27.0249i		−	1.06576i	−0.846192	−	0.532878i	$-0.821110\pi$
$643$		−	27.0249i		−	1.06576i	0.846192	−	0.532878i	$-0.178890\pi$
$644$	6.48932	+	4.71477i	0.255715	+	0.185788i
$645$		0			0
$646$	−14.9855	+	10.8876i	−0.589595	+	0.428366i
$647$	19.9375	+	27.4417i	0.783826	+	1.07884i	0.994850	+	0.101363i	$0.0323203\pi$
$647$	19.9375	+	27.4417i	0.783826	+	1.07884i	−0.211024	+	0.977481i	$0.567680\pi$
$648$		0			0
$649$	−4.49862			−0.176586
$650$	−10.8091	−	1.62797i	−0.423966	−	0.0638543i
$651$		0			0
$652$	11.3129	−	3.67577i	0.443046	−	0.143954i
$653$	−8.73039	−	12.0163i	−0.341646	−	0.470236i	0.603275	−	0.797533i	$-0.293862\pi$
$653$	−8.73039	−	12.0163i	−0.341646	−	0.470236i	−0.944921	+	0.327297i	$0.893862\pi$
$654$		0			0
$655$	20.0310	−	23.6344i	0.782676	−	0.923471i
$656$	−2.60793	−	1.89477i	−0.101823	−	0.0739785i
$657$		0			0
$658$	11.3156	−	15.5746i	0.441129	−	0.607162i
$659$	1.45835	−	4.48835i	0.0568094	−	0.174841i	−0.918625	−	0.395129i	$-0.870700\pi$
$659$	1.45835	−	4.48835i	0.0568094	−	0.174841i	0.975435	+	0.220288i	$0.0706997\pi$
$660$		0			0
$661$	1.08059	+	3.32571i	0.0420300	+	0.129355i	0.969870	−	0.243624i	$-0.0783363\pi$
$661$	1.08059	+	3.32571i	0.0420300	+	0.129355i	−0.927840	+	0.372979i	$0.878336\pi$
$662$	−6.94330	−	2.25602i	−0.269859	−	0.0876826i
$663$		0			0
$664$	−4.05774	−	12.4884i	−0.157471	−	0.484645i
$665$	24.3529	+	20.6400i	0.944365	+	0.800384i
$666$		0			0
$667$	−20.4997	+	28.2155i	−0.793753	+	1.09251i
$668$		−	8.94427i		−	0.346064i
$669$		0			0
$670$	13.8502	+	5.67544i	0.535079	+	0.219261i
$671$	5.29723	−	3.84867i	0.204497	−	0.148576i
$672$		0			0
$673$	−23.4287	+	7.61244i	−0.903110	+	0.293438i	−0.723520	−	0.690303i	$-0.757477\pi$
$673$	−23.4287	+	7.61244i	−0.903110	+	0.293438i	−0.179590	+	0.983742i	$0.557477\pi$
$674$	−26.7448			−1.03017
$675$		0			0
$676$	−8.22056			−0.316176
$677$	−28.3655	+	9.21651i	−1.09017	+	0.354219i	−0.798314	−	0.602242i	$-0.794274\pi$
$677$	−28.3655	+	9.21651i	−1.09017	+	0.354219i	−0.291861	+	0.956461i	$0.594274\pi$
$678$		0			0
$679$	18.0859	−	13.1402i	0.694072	−	0.504273i
$680$	−5.85588	+	1.42940i	−0.224563	+	0.0548150i
$681$		0			0
$682$			3.85173i			0.147490i
$683$	15.3138	−	21.0776i	0.585964	−	0.806511i	−0.408369	−	0.912817i	$-0.633902\pi$
$683$	15.3138	−	21.0776i	0.585964	−	0.806511i	0.994333	+	0.106306i	$0.0339023\pi$
$684$		0			0
$685$	16.8672	−	41.1623i	0.644463	−	1.57273i
$686$	6.21702	+	19.1340i	0.237367	+	0.730540i
$687$		0			0
$688$	−9.07232	−	2.94777i	−0.345879	−	0.112383i
$689$	−1.64732	−	5.06992i	−0.0627577	−	0.193148i
$690$		0			0
$691$	10.6313	−	32.7197i	0.404432	−	1.24471i	−0.516936	−	0.856024i	$-0.672928\pi$
$691$	10.6313	−	32.7197i	0.404432	−	1.24471i	0.921368	−	0.388690i	$-0.127072\pi$
$692$	9.60385	−	13.2186i	0.365084	−	0.502495i
$693$		0			0
$694$	−3.94095	−	2.86327i	−0.149597	−	0.108688i
$695$	−12.2596	+	2.99254i	−0.465034	+	0.113513i
$696$		0			0
$697$	5.10777	+	7.03025i	0.193471	+	0.266290i
$698$	15.8991	−	5.16592i	0.601789	−	0.195533i
$699$		0			0
$700$	4.78637	+	9.22008i	0.180908	+	0.348486i
$701$	−13.2937			−0.502095			−0.251047	−	0.967975i	$-0.580775\pi$
$701$	−13.2937			−0.502095			−0.251047	+	0.967975i	$0.580775\pi$
$702$		0			0
$703$	21.4349	+	29.5026i	0.808432	+	1.11271i
$704$	−0.420808	+	0.305735i	−0.0158598	+	0.0115228i
$705$		0			0
$706$	−21.9086	−	15.9175i	−0.824540	−	0.599063i
$707$		−	36.6503i		−	1.37838i
$708$		0			0
$709$	2.24820	−	6.91924i	0.0844329	−	0.259858i	−0.899923	−	0.436049i	$-0.856378\pi$
$709$	2.24820	−	6.91924i	0.0844329	−	0.259858i	0.984356	+	0.176191i	$0.0563776\pi$
$710$	−13.9348	−	11.8103i	−0.522966	−	0.443233i
$711$		0			0
$712$	9.37628	+	3.04654i	0.351391	+	0.114174i
$713$	−27.1893	−	8.83434i	−1.01825	−	0.330849i
$714$		0			0
$715$	2.53563	+	0.189877i	0.0948270	+	0.00710100i
$716$	−1.13673	+	3.49849i	−0.0424815	+	0.130745i
$717$		0			0
$718$		−	8.48817i		−	0.316776i
$719$	26.0071	+	18.8953i	0.969902	+	0.704675i	0.955429	−	0.295220i	$-0.0953930\pi$
$719$	26.0071	+	18.8953i	0.969902	+	0.704675i	0.0144727	+	0.999895i	$0.495393\pi$
$720$		0			0
$721$	14.6196	−	10.6218i	0.544462	−	0.395575i
$722$	−16.5841	−	22.8261i	−0.617197	−	0.849499i
$723$		0			0
$724$	23.0493			0.856619
$725$	−40.0887	+	20.8111i	−1.48886	+	0.772903i
$726$		0			0
$727$	2.97260	−	0.965858i	0.110248	−	0.0358217i	−0.253374	−	0.967369i	$-0.581540\pi$
$727$	2.97260	−	0.965858i	0.110248	−	0.0358217i	0.363621	+	0.931547i	$0.381540\pi$
$728$	−2.66985	−	3.67473i	−0.0989511	−	0.136195i
$729$		0			0
$730$	4.51828	+	7.31073i	0.167229	+	0.270582i
$731$	20.8039	+	15.1149i	0.769458	+	0.559044i
$732$		0			0
$733$	−27.2488	+	37.5047i	−1.00646	+	1.38527i	−0.0851773	+	0.996366i	$0.527146\pi$
$733$	−27.2488	+	37.5047i	−1.00646	+	1.38527i	−0.921279	+	0.388902i	$0.872854\pi$
$734$	3.93925	−	12.1238i	0.145400	−	0.447496i
$735$		0			0
$736$	−1.19301	−	3.67171i	−0.0439750	−	0.135341i
$737$	−3.31138	−	1.07593i	−0.121976	−	0.0396324i
$738$		0			0
$739$	14.8417	+	45.6779i	0.545959	+	1.68029i	0.718698	+	0.695322i	$0.244738\pi$
$739$	14.8417	+	45.6779i	0.545959	+	1.68029i	−0.172739	+	0.984968i	$0.555262\pi$
$740$	2.81413	+	11.5287i	0.103449	+	0.423805i
$741$		0			0
$742$	−2.97786	+	4.09867i	−0.109321	+	0.150467i
$743$			2.88963i			0.106010i	0.998594	+	0.0530051i	$0.0168799\pi$
$743$			2.88963i			0.106010i	−0.998594	+	0.0530051i	$0.983120\pi$
$744$		0			0
$745$	−2.52062	+	33.6605i	−0.0923484	+	1.23323i
$746$	8.85108	−	6.43069i	0.324061	−	0.235444i
$747$		0			0
$748$	1.33354	−	0.433294i	0.0487591	−	0.0158428i
$749$	−11.2398			−0.410693
$750$		0			0
$751$	−39.4965			−1.44125			−0.720624	−	0.693326i	$-0.756144\pi$
$751$	−39.4965			−1.44125			−0.720624	+	0.693326i	$0.756144\pi$
$752$	−8.81224	+	2.86327i	−0.321349	+	0.104413i
$753$		0			0
$754$	15.9777	−	11.6084i	0.581872	−	0.422755i
$755$	−3.49573	+	46.6821i	−0.127223	+	1.69894i
$756$		0			0
$757$		−	25.4654i		−	0.925555i	−0.886475	−	0.462777i	$-0.846853\pi$
$757$		−	25.4654i		−	0.925555i	0.886475	−	0.462777i	$-0.153147\pi$
$758$	8.36427	−	11.5124i	0.303804	−	0.418150i
$759$		0			0
$760$	−3.64349	−	14.9264i	−0.132163	−	0.541438i
$761$	−12.8769	−	39.6310i	−0.466787	−	1.43662i	−0.856721	−	0.515780i	$-0.827502\pi$
$761$	−12.8769	−	39.6310i	−0.466787	−	1.43662i	0.389934	−	0.920843i	$-0.372498\pi$
$762$		0			0
$763$	5.69832	+	1.85150i	0.206293	+	0.0670287i
$764$	−0.552424	−	1.70019i	−0.0199860	−	0.0615106i
$765$		0			0
$766$	−2.21386	+	6.81355i	−0.0799899	+	0.246184i
$767$	−11.1137	+	15.2967i	−0.401294	+	0.552334i
$768$		0			0
$769$	1.67667	+	1.21817i	0.0604621	+	0.0439283i	0.617606	−	0.786488i	$-0.288103\pi$
$769$	1.67667	+	1.21817i	0.0604621	+	0.0439283i	−0.557144	+	0.830416i	$0.688103\pi$
$770$	−1.27044	−	2.05562i	−0.0457835	−	0.0740792i
$771$		0			0
$772$	−3.88019	−	5.34063i	−0.139651	−	0.192213i
$773$	−7.59855	+	2.46892i	−0.273301	+	0.0888009i	−0.442461	−	0.896788i	$-0.645895\pi$
$773$	−7.59855	+	2.46892i	−0.273301	+	0.0888009i	0.169160	+	0.985589i	$0.445895\pi$
$774$		0			0
$775$	−26.3789	−	25.9814i	−0.947557	−	0.933279i
$776$	−10.7598			−0.386253
$777$		0			0
$778$	0.540158	+	0.743464i	0.0193656	+	0.0266545i
$779$	−17.9199	+	13.0195i	−0.642045	+	0.466473i
$780$		0			0
$781$	3.43758	+	2.49755i	0.123006	+	0.0893693i
$782$			10.4073i			0.372163i
$783$		0			0
$784$	0.829164	−	2.55190i	0.0296130	−	0.0911394i
$785$	−12.7545	−	0.955107i	−0.455229	−	0.0340892i
$786$		0			0
$787$	17.0337	+	5.53459i	0.607186	+	0.197287i	0.596443	−	0.802656i	$-0.296580\pi$
$787$	17.0337	+	5.53459i	0.607186	+	0.197287i	0.0107432	+	0.999942i	$0.496580\pi$
$788$	−12.0380	−	3.91138i	−0.428836	−	0.139337i
$789$		0			0
$790$	5.99157	+	5.07808i	0.213171	+	0.180670i
$791$	4.08950	−	12.5862i	0.145406	−	0.447514i
$792$		0			0
$793$		−	27.5203i		−	0.977276i
$794$	−17.6381	−	12.8148i	−0.625954	−	0.454782i
$795$		0			0
$796$	−5.04946	+	3.66865i	−0.178973	+	0.130032i
$797$	15.4319	+	21.2401i	0.546625	+	0.752364i	0.989549	−	0.144195i	$-0.0460591\pi$
$797$	15.4319	+	21.2401i	0.546625	+	0.752364i	−0.442925	+	0.896559i	$0.646059\pi$
$798$		0			0
$799$	24.9778			0.883652
$800$	0.744661	−	4.94424i	0.0263277	−	0.174805i
$801$		0			0
$802$	21.6874	−	7.04666i	0.765808	−	0.248826i
$803$	−1.17509	−	1.61737i	−0.0414679	−	0.0570756i
$804$		0			0
$805$	17.4245	−	4.25325i	0.614131	−	0.149908i
$806$	13.0971	+	9.51560i	0.461326	+	0.335173i
$807$		0			0
$808$	−10.3685	+	14.2711i	−0.364763	+	0.502054i
$809$	9.12577	−	28.0862i	0.320845	−	0.987459i	−0.652436	−	0.757844i	$-0.726253\pi$
$809$	9.12577	−	28.0862i	0.320845	−	0.987459i	0.973281	−	0.229616i	$-0.0737470\pi$
$810$		0			0
$811$	9.10810	+	28.0318i	0.319829	+	0.984331i	0.973721	+	0.227744i	$0.0731348\pi$
$811$	9.10810	+	28.0318i	0.319829	+	0.984331i	−0.653893	+	0.756587i	$0.726865\pi$
$812$	−17.8506	−	5.80001i	−0.626433	−	0.203540i
$813$		0			0
$814$	−0.853047	−	2.62541i	−0.0298993	−	0.0920205i
$815$	10.0853	−	24.6119i	0.353273	−	0.862118i
$816$		0			0
$817$	−38.5273	+	53.0283i	−1.34790	+	1.85523i
$818$		−	5.00147i		−	0.174872i
$819$		0			0
$820$	−7.00255	+	1.70930i	−0.244540	+	0.0596913i
$821$	36.2580	−	26.3430i	1.26541	−	0.919377i	0.266404	−	0.963862i	$-0.414165\pi$
$821$	36.2580	−	26.3430i	1.26541	−	0.919377i	0.999010	+	0.0444846i	$0.0141646\pi$
$822$		0			0
$823$	20.6983	−	6.72529i	0.721498	−	0.234429i	0.0748255	−	0.997197i	$-0.476160\pi$
$823$	20.6983	−	6.72529i	0.721498	−	0.234429i	0.646673	+	0.762768i	$0.276160\pi$
$824$	−8.69758			−0.302995
$825$		0			0
$826$	17.9694			0.625234
$827$	−18.1721	+	5.90446i	−0.631905	+	0.205318i	−0.607419	−	0.794382i	$-0.707795\pi$
$827$	−18.1721	+	5.90446i	−0.631905	+	0.205318i	−0.0244861	+	0.999700i	$0.507795\pi$
$828$		0			0
$829$	−29.3862	+	21.3503i	−1.02063	+	0.741528i	−0.966411	−	0.257001i	$-0.917265\pi$
$829$	−29.3862	+	21.3503i	−1.02063	+	0.741528i	−0.0542146	+	0.998529i	$0.517265\pi$
$830$	−27.1694	−	11.1333i	−0.943065	−	0.386443i
$831$		0			0
$832$			2.18619i			0.0757926i
$833$	−4.25159	+	5.85181i	−0.147309	+	0.202753i
$834$		0			0
$835$	−15.2573	−	12.9311i	−0.528001	−	0.447501i
$836$	1.10445	+	3.39915i	0.0381983	+	0.117562i
$837$		0			0
$838$	−21.7082	−	7.05342i	−0.749897	−	0.243656i
$839$	6.13673	+	18.8869i	0.211863	+	0.652049i	0.999361	+	0.0357313i	$0.0113761\pi$
$839$	6.13673	+	18.8869i	0.211863	+	0.652049i	−0.787498	+	0.616317i	$0.788624\pi$
$840$		0			0
$841$	16.2568	−	50.0334i	0.560581	−	1.72529i
$842$	9.23612	−	12.7124i	0.318298	−	0.438099i
$843$		0			0
$844$	−18.1850	−	13.2122i	−0.625955	−	0.454783i
$845$	−11.8848	+	14.0228i	−0.408851	+	0.482399i
$846$		0			0
$847$	−13.1031	−	18.0349i	−0.450229	−	0.619687i
$848$	2.31906	−	0.753509i	0.0796369	−	0.0258756i
$849$		0			0
$850$	−6.02781	+	12.0556i	−0.206752	+	0.413504i
$851$	20.4893			0.702363
$852$		0			0
$853$	15.3025	+	21.0621i	0.523948	+	0.721153i	0.986193	−	0.165600i	$-0.0529559\pi$
$853$	15.3025	+	21.0621i	0.523948	+	0.721153i	−0.462245	+	0.886752i	$0.652956\pi$
$854$	−21.1594	+	15.3732i	−0.724058	+	0.526059i
$855$		0			0
$856$	4.37660	+	3.17979i	0.149589	+	0.108683i
$857$		−	34.8614i		−	1.19084i	−0.803414	−	0.595421i	$-0.796985\pi$
$857$		−	34.8614i		−	1.19084i	0.803414	−	0.595421i	$-0.203015\pi$
$858$		0			0
$859$	4.67229	−	14.3798i	0.159417	−	0.490634i	−0.839165	−	0.543877i	$-0.816956\pi$
$859$	4.67229	−	14.3798i	0.159417	−	0.490634i	0.998582	+	0.0532431i	$0.0169558\pi$
$860$	−18.1446	+	11.2140i	−0.618727	+	0.382394i
$861$		0			0
$862$	9.08897	+	2.95319i	0.309572	+	0.100586i
$863$	21.7819	+	7.07738i	0.741466	+	0.240917i	0.655305	−	0.755364i	$-0.272540\pi$
$863$	21.7819	+	7.07738i	0.741466	+	0.240917i	0.0861610	+	0.996281i	$0.472540\pi$
$864$		0			0
$865$	−8.66376	−	35.4931i	−0.294577	−	1.20680i
$866$	−2.50988	+	7.72462i	−0.0852892	+	0.262493i
$867$		0			0
$868$		−	15.3854i		−	0.522215i
$869$	−1.47806	−	1.07387i	−0.0501397	−	0.0364286i
$870$		0			0
$871$	−11.8392	+	8.60168i	−0.401156	+	0.291457i
$872$	−1.69504	−	2.33302i	−0.0574013	−	0.0790061i
$873$		0			0
$874$	−26.5278			−0.897315
$875$	22.6477	+	5.16520i	0.765631	+	0.174616i
$876$		0			0
$877$	15.6806	−	5.09493i	0.529495	−	0.172043i	−0.0320550	−	0.999486i	$-0.510205\pi$
$877$	15.6806	−	5.09493i	0.529495	−	0.172043i	0.561550	+	0.827443i	$0.310205\pi$
$878$	5.41910	+	7.45875i	0.182886	+	0.251721i
$879$		0			0
$880$	−0.0868528	+	1.15984i	−0.00292781	+	0.0390981i
$881$	18.7621	+	13.6315i	0.632112	+	0.459257i	0.857131	−	0.515098i	$-0.172244\pi$
$881$	18.7621	+	13.6315i	0.632112	+	0.459257i	−0.225019	+	0.974354i	$0.572244\pi$
$882$		0			0
$883$	−14.3841	+	19.7980i	−0.484062	+	0.666254i	−0.979279	−	0.202515i	$-0.935089\pi$
$883$	−14.3841	+	19.7980i	−0.484062	+	0.666254i	0.495217	+	0.868769i	$0.335089\pi$
$884$	1.82115	−	5.60491i	0.0612518	−	0.188514i
$885$		0			0
$886$	2.97655	+	9.16088i	0.0999991	+	0.307766i
$887$	−3.75624	−	1.22048i	−0.126122	−	0.0409796i	0.245276	−	0.969453i	$-0.421121\pi$
$887$	−3.75624	−	1.22048i	−0.126122	−	0.0409796i	−0.371398	+	0.928474i	$0.621121\pi$
$888$		0			0
$889$	9.60960	+	29.5753i	0.322296	+	0.991924i
$890$	18.7526	−	11.5897i	0.628587	−	0.388488i
$891$		0			0
$892$	10.5389	−	14.5056i	0.352870	−	0.485684i
$893$			63.6676i			2.13055i
$894$		0			0
$895$	4.32437	+	6.99698i	0.144548	+	0.233883i
$896$	1.68088	−	1.22123i	0.0561543	−	0.0407985i
$897$		0			0
$898$	20.2666	−	6.58502i	0.676306	−	0.219745i
$899$	66.8954			2.23109
$900$		0			0
$901$	−6.57325			−0.218987
$902$	1.59467	−	0.518140i	0.0530967	−	0.0172522i
$903$		0			0
$904$	−5.15307	+	3.74393i	−0.171389	+	0.124521i
$905$	33.3234	−	39.3179i	1.10771	−	1.30697i
$906$		0			0
$907$		−	52.8637i		−	1.75531i	−0.479291	−	0.877656i	$-0.659106\pi$
$907$		−	52.8637i		−	1.75531i	0.479291	−	0.877656i	$-0.340894\pi$
$908$	5.20640	−	7.16599i	0.172780	−	0.237812i
$909$		0			0
$910$	−10.1283	−	0.758448i	−0.335751	−	0.0251423i
$911$	−3.55654	−	10.9459i	−0.117833	−	0.362654i	0.874694	−	0.484676i	$-0.161062\pi$
$911$	−3.55654	−	10.9459i	−0.117833	−	0.362654i	−0.992527	+	0.122021i	$0.961062\pi$
$912$		0			0
$913$	6.49582	+	2.11062i	0.214980	+	0.0698513i
$914$	−4.16129	−	12.8071i	−0.137643	−	0.423622i
$915$		0			0
$916$	6.81771	−	20.9828i	0.225264	−	0.693290i
$917$	16.9203	−	23.2888i	0.558759	−	0.769066i
$918$		0			0
$919$	25.1008	+	18.2368i	0.828000	+	0.601577i	0.918993	−	0.394274i	$-0.129004\pi$
$919$	25.1008	+	18.2368i	0.828000	+	0.601577i	−0.0909927	+	0.995852i	$0.529004\pi$
$920$	−7.98807	−	3.27330i	−0.263359	−	0.107918i
$921$		0			0
$922$	19.3003	+	26.5646i	0.635622	+	0.874858i
$923$	16.9849	−	5.51874i	0.559066	−	0.181652i
$924$		0			0
$925$	23.7345	+	11.8672i	0.780384	+	0.390192i
$926$	22.9306			0.753547
$927$		0			0
$928$	5.30989	+	7.30844i	0.174306	+	0.239911i
$929$	9.67177	−	7.02695i	0.317320	−	0.230547i	−0.417711	−	0.908580i	$-0.637167\pi$
$929$	9.67177	−	7.02695i	0.317320	−	0.230547i	0.735031	+	0.678033i	$0.237167\pi$
$930$		0			0
$931$	−14.9161	−	10.8371i	−0.488854	−	0.355173i
$932$			11.5427i			0.378095i
$933$		0			0
$934$	−6.43806	+	19.8143i	−0.210660	+	0.648344i
$935$	1.18884	−	2.90122i	0.0388793	−	0.0948799i
$936$		0			0
$937$	−13.9740	−	4.54042i	−0.456510	−	0.148329i	0.0717304	−	0.997424i	$-0.477148\pi$
$937$	−13.9740	−	4.54042i	−0.456510	−	0.148329i	−0.528240	+	0.849095i	$0.677148\pi$
$938$	13.2270	+	4.29772i	0.431877	+	0.140325i
$939$		0			0
$940$	−7.85604	+	19.1717i	−0.256236	+	0.625310i
$941$	−15.6185	+	48.0688i	−0.509149	+	1.56700i	0.284533	+	0.958666i	$0.408162\pi$
$941$	−15.6185	+	48.0688i	−0.509149	+	1.56700i	−0.793682	+	0.608333i	$0.791838\pi$
$942$		0			0
$943$			12.4452i			0.405271i
$944$	−6.99698	−	5.08361i	−0.227732	−	0.165457i
$945$		0			0
$946$	4.01417	−	2.91646i	0.130512	−	0.0948224i
$947$	23.3247	+	32.1037i	0.757952	+	1.04323i	0.997382	+	0.0723177i	$0.0230395\pi$
$947$	23.3247	+	32.1037i	0.757952	+	1.04323i	−0.239430	+	0.970914i	$0.576960\pi$
$948$		0			0
$949$	−8.40259			−0.272759
$950$	−30.7293	−	15.3647i	−0.996991	−	0.498496i
$951$		0			0
$952$	−5.32672	+	1.73076i	−0.172640	+	0.0560942i
$953$	29.7563	+	40.9560i	0.963901	+	1.32670i	0.945068	+	0.326873i	$0.105995\pi$
$953$	29.7563	+	40.9560i	0.963901	+	1.32670i	0.0188330	+	0.999823i	$0.494005\pi$
$954$		0			0
$955$	−3.69888	−	1.51570i	−0.119693	−	0.0490470i
$956$	−0.715921	−	0.520147i	−0.0231545	−	0.0168228i
$957$		0			0
$958$	7.94842	−	10.9401i	0.256802	−	0.353457i
$959$	12.7727	−	39.3102i	0.412451	−	1.26939i
$960$		0			0
$961$	7.36546	+	22.6685i	0.237595	+	0.731243i
$962$	−11.0347	−	3.58538i	−0.355772	−	0.115597i
$963$		0			0
$964$	−3.91637	−	12.0534i	−0.126138	−	0.388212i
$965$	−14.7199	−	1.10228i	−0.473851	−	0.0354837i
$966$		0			0
$967$	6.49628	−	8.94137i	0.208906	−	0.287535i	−0.691687	−	0.722197i	$-0.743132\pi$
$967$	6.49628	−	8.94137i	0.208906	−	0.287535i	0.900594	+	0.434662i	$0.143132\pi$
$968$			10.7294i			0.344857i
$969$		0			0
$970$	−15.5559	+	18.3542i	−0.499469	+	0.589318i
$971$	19.9495	−	14.4942i	0.640211	−	0.465140i	−0.219712	−	0.975565i	$-0.570512\pi$
$971$	19.9495	−	14.4942i	0.640211	−	0.465140i	0.859923	+	0.510424i	$0.170512\pi$
$972$		0			0
$973$	−11.1518	+	3.62345i	−0.357511	+	0.116162i
$974$	26.6228			0.853050
$975$		0			0
$976$	12.5882			0.402940
$977$	−7.71967	+	2.50827i	−0.246974	+	0.0802467i	−0.429888	−	0.902882i	$-0.641447\pi$
$977$	−7.71967	+	2.50827i	−0.246974	+	0.0802467i	0.182914	+	0.983129i	$0.441447\pi$
$978$		0			0
$979$	−4.14866	+	3.01418i	−0.132592	+	0.0963336i
$980$	−3.15433	−	5.10381i	−0.100761	−	0.163035i
$981$		0			0
$982$			12.0227i			0.383659i
$983$	−15.6954	+	21.6028i	−0.500605	+	0.689023i	−0.982300	−	0.187316i	$-0.940021\pi$
$983$	−15.6954	+	21.6028i	−0.500605	+	0.689023i	0.481695	+	0.876339i	$0.340021\pi$
$984$		0			0
$985$	−24.0760	+	14.8798i	−0.767125	+	0.474109i
$986$	−7.52530	−	23.1605i	−0.239654	−	0.737580i
$987$		0			0
$988$	14.2867	+	4.64204i	0.454521	+	0.147683i
$989$	11.3804	+	35.0252i	0.361875	+	1.11374i
$990$		0			0
$991$	−16.3515	+	50.3248i	−0.519423	+	1.59862i	0.255665	+	0.966765i	$0.417706\pi$
$991$	−16.3515	+	50.3248i	−0.519423	+	1.59862i	−0.775088	+	0.631854i	$0.782294\pi$
$992$	−4.35259	+	5.99083i	−0.138195	+	0.190209i
$993$		0			0
$994$	−13.7311	−	9.97625i	−0.435525	−	0.316427i
$995$	−1.04219	+	13.9174i	−0.0330395	+	0.441211i
$996$		0			0
$997$	−16.6169	−	22.8712i	−0.526262	−	0.724337i	0.460293	−	0.887767i	$-0.347744\pi$
$997$	−16.6169	−	22.8712i	−0.526262	−	0.724337i	−0.986555	+	0.163430i	$0.947744\pi$
$998$	−26.0209	+	8.45469i	−0.823676	+	0.267629i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.a.19.1		8
3.2	odd	2		150.2.h.a.19.2	✓	8
15.2	even	4		750.2.g.c.151.2		8
15.8	even	4		750.2.g.e.151.1		8
15.14	odd	2		750.2.h.c.349.1		8
25.4	even	10	inner	450.2.l.a.379.1		8
75.2	even	20		3750.2.a.o.1.4		4
75.11	odd	10		3750.2.c.e.1249.1		8
75.14	odd	10		3750.2.c.e.1249.8		8
75.23	even	20		3750.2.a.m.1.1		4
75.29	odd	10		150.2.h.a.79.2	yes	8
75.47	even	20		750.2.g.c.601.2		8
75.53	even	20		750.2.g.e.601.1		8
75.71	odd	10		750.2.h.c.649.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.19.2	✓	8	3.2	odd	2
150.2.h.a.79.2	yes	8	75.29	odd	10
450.2.l.a.19.1		8	1.1	even	1	trivial
450.2.l.a.379.1		8	25.4	even	10	inner
750.2.g.c.151.2		8	15.2	even	4
750.2.g.c.601.2		8	75.47	even	20
750.2.g.e.151.1		8	15.8	even	4
750.2.g.e.601.1		8	75.53	even	20
750.2.h.c.349.1		8	15.14	odd	2
750.2.h.c.649.1		8	75.71	odd	10
3750.2.a.m.1.1		4	75.23	even	20
3750.2.a.o.1.4		4	75.2	even	20
3750.2.c.e.1249.1		8	75.11	odd	10
3750.2.c.e.1249.8		8	75.14	odd	10

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.166977 - 2.22982i) q^{5} -2.07768i q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.166977 - 2.22982i) q^{5} -2.07768i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.530249 + 2.17229i) q^{10} +(-0.160734 - 0.494689i) q^{11} +(-2.07919 - 0.675571i) q^{13} +(0.642040 + 1.97599i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-1.58450 + 2.18088i) q^{17} +(-5.55899 - 4.03884i) q^{19} +(-1.17557 - 1.90211i) q^{20} +(0.305735 + 0.420808i) q^{22} +(-3.67171 + 1.19301i) q^{23} +(-4.94424 - 0.744661i) q^{25} +2.18619 q^{26} +(-1.22123 - 1.68088i) q^{28} +(7.30844 - 5.30989i) q^{29} +(5.99083 + 4.35259i) q^{31} +1.00000i q^{32} +(0.833023 - 2.56378i) q^{34} +(-4.63287 - 0.346926i) q^{35} +(-5.04743 - 1.64001i) q^{37} +(6.53498 + 2.12334i) q^{38} +(1.70582 + 1.44575i) q^{40} +(0.996141 - 3.06581i) q^{41} -9.53920i q^{43} +(-0.420808 - 0.305735i) q^{44} +(3.12334 - 2.26924i) q^{46} +(-5.44627 - 7.49614i) q^{47} +2.68323 q^{49} +(4.93236 - 0.819639i) q^{50} +(-2.07919 + 0.675571i) q^{52} +(1.43326 + 1.97271i) q^{53} +(-1.12991 + 0.275807i) q^{55} +(1.68088 + 1.22123i) q^{56} +(-5.30989 + 7.30844i) q^{58} +(2.67261 - 8.22545i) q^{59} +(3.88998 + 11.9721i) q^{61} +(-7.04264 - 2.28829i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(-1.85358 + 4.52343i) q^{65} +(3.93455 - 5.41544i) q^{67} +2.69572i q^{68} +(4.51333 - 1.10169i) q^{70} +(-6.60886 + 4.80162i) q^{71} +(3.65537 - 1.18770i) q^{73} +5.30719 q^{74} -6.87129 q^{76} +(-1.02781 + 0.333955i) q^{77} +(2.84162 - 2.06455i) q^{79} +(-2.06909 - 0.847859i) q^{80} +3.22358i q^{82} +(-7.71827 + 10.6233i) q^{83} +(4.59841 + 3.89732i) q^{85} +(2.94777 + 9.07232i) q^{86} +(0.494689 + 0.160734i) q^{88} +(-3.04654 - 9.37628i) q^{89} +(-1.40362 + 4.31990i) q^{91} +(-2.26924 + 3.12334i) q^{92} +(7.49614 + 5.44627i) q^{94} +(-9.93414 + 11.7212i) q^{95} +(6.32443 + 8.70483i) q^{97} +(-2.55190 + 0.829164i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4}+O(q^{10}) \) 8 * q + 2 * q^4	\( 8 q + 2 q^{4} - 10 q^{11} - 20 q^{13} + 2 q^{14} - 2 q^{16} - 10 q^{17} - 8 q^{19} + 10 q^{23} - 10 q^{25} - 4 q^{26} - 10 q^{28} + 22 q^{29} + 24 q^{31} + 8 q^{34} - 10 q^{35} - 20 q^{37} + 10 q^{38} - 22 q^{41} + 10 q^{46} - 10 q^{47} + 8 q^{49} + 20 q^{50} - 20 q^{52} + 30 q^{53} + 10 q^{55} - 2 q^{56} + 30 q^{58} + 20 q^{59} - 10 q^{62} + 2 q^{64} - 20 q^{65} + 10 q^{67} - 10 q^{70} - 20 q^{71} - 20 q^{73} + 4 q^{74} - 12 q^{76} + 20 q^{77} + 16 q^{79} - 70 q^{83} + 20 q^{85} + 18 q^{86} + 10 q^{88} + 34 q^{89} - 24 q^{91} - 30 q^{92} + 30 q^{94} - 30 q^{95} + 60 q^{97} - 20 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 - 10 * q^11 - 20 * q^13 + 2 * q^14 - 2 * q^16 - 10 * q^17 - 8 * q^19 + 10 * q^23 - 10 * q^25 - 4 * q^26 - 10 * q^28 + 22 * q^29 + 24 * q^31 + 8 * q^34 - 10 * q^35 - 20 * q^37 + 10 * q^38 - 22 * q^41 + 10 * q^46 - 10 * q^47 + 8 * q^49 + 20 * q^50 - 20 * q^52 + 30 * q^53 + 10 * q^55 - 2 * q^56 + 30 * q^58 + 20 * q^59 - 10 * q^62 + 2 * q^64 - 20 * q^65 + 10 * q^67 - 10 * q^70 - 20 * q^71 - 20 * q^73 + 4 * q^74 - 12 * q^76 + 20 * q^77 + 16 * q^79 - 70 * q^83 + 20 * q^85 + 18 * q^86 + 10 * q^88 + 34 * q^89 - 24 * q^91 - 30 * q^92 + 30 * q^94 - 30 * q^95 + 60 * q^97 - 20 * q^98

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